LMFDB - Embedded newform 33.8.e.b.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(4,33)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	33.4
Dual form			33.8.e.b.25.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.9629 + 12.3242i) q^{2} +(8.34346 - 25.6785i) q^{3} +(96.2976 + 296.374i) q^{4} +(-380.493 + 276.444i) q^{5} +(457.997 - 332.754i) q^{6} +(39.7826 + 122.438i) q^{7} +(-1189.75 + 3661.68i) q^{8} +(-589.773 - 428.495i) q^{9} +O(q^{10})$	\(q+(16.9629 + 12.3242i) q^{2} +(8.34346 - 25.6785i) q^{3} +(96.2976 + 296.374i) q^{4} +(-380.493 + 276.444i) q^{5} +(457.997 - 332.754i) q^{6} +(39.7826 + 122.438i) q^{7} +(-1189.75 + 3661.68i) q^{8} +(-589.773 - 428.495i) q^{9} -9861.22 q^{10} +(4281.98 + 1073.24i) q^{11} +8413.89 q^{12} +(7497.45 + 5447.22i) q^{13} +(-834.131 + 2567.19i) q^{14} +(3924.06 + 12077.0i) q^{15} +(-33039.0 + 24004.2i) q^{16} +(6110.28 - 4439.37i) q^{17} +(-4723.36 - 14537.0i) q^{18} +(13008.2 - 40035.0i) q^{19} +(-118571. - 86147.2i) q^{20} +3475.96 q^{21} +(59407.7 + 70977.3i) q^{22} -58373.4 q^{23} +(84100.0 + 61102.2i) q^{24} +(44211.5 - 136069. i) q^{25} +(60045.4 + 184801. i) q^{26} +(-15923.9 + 11569.4i) q^{27} +(-32456.5 + 23581.0i) q^{28} +(-16114.1 - 49594.1i) q^{29} +(-82276.7 + 253222. i) q^{30} +(252442. + 183410. i) q^{31} -363454. q^{32} +(63285.7 - 101000. i) q^{33} +158360. q^{34} +(-48984.3 - 35589.2i) q^{35} +(70200.9 - 216056. i) q^{36} +(41608.2 + 128057. i) q^{37} +(714057. - 518793. i) q^{38} +(202431. - 147075. i) q^{39} +(-559559. - 1.72215e6i) q^{40} +(42716.9 - 131469. i) q^{41} +(58962.2 + 42838.5i) q^{42} -543911. q^{43} +(94264.8 + 1.37242e6i) q^{44} +342860. q^{45} +(-990180. - 719408. i) q^{46} +(-257065. + 791164. i) q^{47} +(340734. + 1.04867e6i) q^{48} +(652852. - 474325. i) q^{49} +(2.42690e6 - 1.76325e6i) q^{50} +(-63015.8 - 193943. i) q^{51} +(-892425. + 2.74660e6i) q^{52} +(444660. + 323064. i) q^{53} -412698. q^{54} +(-1.92595e6 + 775369. i) q^{55} -495661. q^{56} +(-919507. - 668061. i) q^{57} +(337868. - 1.03985e6i) q^{58} +(-120241. - 370065. i) q^{59} +(-3.20143e6 + 2.32597e6i) q^{60} +(2.10717e6 - 1.53095e6i) q^{61} +(2.02175e6 + 6.22230e6i) q^{62} +(29001.5 - 89257.4i) q^{63} +(-1.93623e6 - 1.40675e6i) q^{64} -4.35858e6 q^{65} +(2.31826e6 - 933307. i) q^{66} -779463. q^{67} +(1.90412e6 + 1.38342e6i) q^{68} +(-487036. + 1.49894e6i) q^{69} +(-392305. - 1.20739e6i) q^{70} +(-1.68842e6 + 1.22671e6i) q^{71} +(2.27070e6 - 1.64976e6i) q^{72} +(-1.00541e6 - 3.09433e6i) q^{73} +(-872410. + 2.68500e6i) q^{74} +(-3.12518e6 - 2.27057e6i) q^{75} +1.31180e7 q^{76} +(38942.8 + 566974. i) q^{77} +5.24640e6 q^{78} +(-5.55799e6 - 4.03812e6i) q^{79} +(5.93527e6 - 1.82669e7i) q^{80} +(164224. + 505430. i) q^{81} +(2.34486e6 - 1.70364e6i) q^{82} +(-637291. + 463019. i) q^{83} +(334726. + 1.03018e6i) q^{84} +(-1.09768e6 + 3.37830e6i) q^{85} +(-9.22628e6 - 6.70328e6i) q^{86} -1.40795e6 q^{87} +(-9.02436e6 + 1.44024e7i) q^{88} +339461. q^{89} +(5.81589e6 + 4.22549e6i) q^{90} +(-368680. + 1.13468e6i) q^{91} +(-5.62122e6 - 1.73003e7i) q^{92} +(6.81593e6 - 4.95206e6i) q^{93} +(-1.41111e7 + 1.02523e7i) q^{94} +(6.11794e6 + 1.88291e7i) q^{95} +(-3.03246e6 + 9.33296e6i) q^{96} +(5.64733e6 + 4.10302e6i) q^{97} +1.69199e7 q^{98} +(-2.06552e6 - 2.46778e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9	\( 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9} - 10640 q^{10} + 13209 q^{11} + 45630 q^{12} + 13499 q^{13} - 3318 q^{14} - 22734 q^{15} - 113196 q^{16} + 30296 q^{17} + 21141 q^{18} - 6858 q^{19} + 76725 q^{20} - 177012 q^{21} - 48859 q^{22} - 166984 q^{23} + 44442 q^{24} + 99832 q^{25} + 340424 q^{26} - 137781 q^{27} + 657387 q^{28} + 192014 q^{29} - 184410 q^{30} + 396068 q^{31} - 303498 q^{32} + 168453 q^{33} - 1229124 q^{34} - 725859 q^{35} + 116640 q^{36} + 811053 q^{37} + 1548798 q^{38} + 364473 q^{39} - 1427263 q^{40} + 1041497 q^{41} + 300024 q^{42} - 5265288 q^{43} - 5341085 q^{44} + 100602 q^{45} + 1198651 q^{46} + 1667505 q^{47} + 730593 q^{48} + 2968140 q^{49} + 11247432 q^{50} + 340767 q^{51} + 2325763 q^{52} - 1625736 q^{53} - 905418 q^{54} - 8338690 q^{55} - 18201906 q^{56} + 1546479 q^{57} + 14965553 q^{58} - 2587454 q^{59} + 2071575 q^{60} + 5801619 q^{61} + 15631121 q^{62} + 939681 q^{63} - 3732846 q^{64} - 15368174 q^{65} - 235683 q^{66} - 7141262 q^{67} + 17394545 q^{68} - 5063553 q^{69} - 4329200 q^{70} + 3569199 q^{71} + 1199934 q^{72} + 125008 q^{73} - 13691530 q^{74} - 11794221 q^{75} - 19690428 q^{76} - 6038739 q^{77} + 12684438 q^{78} + 17075485 q^{79} + 26606436 q^{80} - 3720087 q^{81} + 19886007 q^{82} - 4645575 q^{83} + 1074519 q^{84} + 12002715 q^{85} - 12296287 q^{86} - 12259512 q^{87} - 50905990 q^{88} + 9601664 q^{89} + 8857350 q^{90} - 14129477 q^{91} - 90776021 q^{92} + 10693836 q^{93} + 1047679 q^{94} + 58935661 q^{95} + 26156304 q^{96} - 22170261 q^{97} + 140532178 q^{98} - 6579954 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9 - 10640 * q^10 + 13209 * q^11 + 45630 * q^12 + 13499 * q^13 - 3318 * q^14 - 22734 * q^15 - 113196 * q^16 + 30296 * q^17 + 21141 * q^18 - 6858 * q^19 + 76725 * q^20 - 177012 * q^21 - 48859 * q^22 - 166984 * q^23 + 44442 * q^24 + 99832 * q^25 + 340424 * q^26 - 137781 * q^27 + 657387 * q^28 + 192014 * q^29 - 184410 * q^30 + 396068 * q^31 - 303498 * q^32 + 168453 * q^33 - 1229124 * q^34 - 725859 * q^35 + 116640 * q^36 + 811053 * q^37 + 1548798 * q^38 + 364473 * q^39 - 1427263 * q^40 + 1041497 * q^41 + 300024 * q^42 - 5265288 * q^43 - 5341085 * q^44 + 100602 * q^45 + 1198651 * q^46 + 1667505 * q^47 + 730593 * q^48 + 2968140 * q^49 + 11247432 * q^50 + 340767 * q^51 + 2325763 * q^52 - 1625736 * q^53 - 905418 * q^54 - 8338690 * q^55 - 18201906 * q^56 + 1546479 * q^57 + 14965553 * q^58 - 2587454 * q^59 + 2071575 * q^60 + 5801619 * q^61 + 15631121 * q^62 + 939681 * q^63 - 3732846 * q^64 - 15368174 * q^65 - 235683 * q^66 - 7141262 * q^67 + 17394545 * q^68 - 5063553 * q^69 - 4329200 * q^70 + 3569199 * q^71 + 1199934 * q^72 + 125008 * q^73 - 13691530 * q^74 - 11794221 * q^75 - 19690428 * q^76 - 6038739 * q^77 + 12684438 * q^78 + 17075485 * q^79 + 26606436 * q^80 - 3720087 * q^81 + 19886007 * q^82 - 4645575 * q^83 + 1074519 * q^84 + 12002715 * q^85 - 12296287 * q^86 - 12259512 * q^87 - 50905990 * q^88 + 9601664 * q^89 + 8857350 * q^90 - 14129477 * q^91 - 90776021 * q^92 + 10693836 * q^93 + 1047679 * q^94 + 58935661 * q^95 + 26156304 * q^96 - 22170261 * q^97 + 140532178 * q^98 - 6579954 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	16.9629	+	12.3242i	1.49932	+	1.08932i	0.970652	+	0.240490i	$0.0773083\pi$
$2$	16.9629	+	12.3242i	1.49932	+	1.08932i	0.528668	+	0.848829i	$0.322692\pi$
$3$	8.34346	−	25.6785i	0.178411	−	0.549093i
$3$	8.34346	−	25.6785i	0.178411	−	0.549093i
$4$	96.2976	+	296.374i	0.752325	+	2.31542i
$5$	−380.493	+	276.444i	−1.36129	+	0.989038i	−0.362932	+	0.931816i	$0.618224\pi$
$5$	−380.493	+	276.444i	−1.36129	+	0.989038i	−0.998361	+	0.0572222i	$0.981776\pi$
$6$	457.997	−	332.754i	0.865632	−	0.628919i
$7$	39.7826	+	122.438i	0.0438379	+	0.134919i	0.970580	−	0.240779i	$-0.0774029\pi$
$7$	39.7826	+	122.438i	0.0438379	+	0.134919i	−0.926742	+	0.375698i	$0.877403\pi$
$8$	−1189.75	+	3661.68i	−0.821565	+	2.52852i
$9$	−589.773	−	428.495i	−0.269672	−	0.195928i
$10$	−9861.22			−3.11839
$11$	4281.98	+	1073.24i	0.969996	+	0.243121i
$11$	4281.98	+	1073.24i	0.969996	+	0.243121i
$12$	8413.89			1.40560
$13$	7497.45	+	5447.22i	0.946481	+	0.687659i	0.949972	−	0.312335i	$-0.101111\pi$
$13$	7497.45	+	5447.22i	0.946481	+	0.687659i	−0.00349070	+	0.999994i	$0.501111\pi$
$14$	−834.131	+	2567.19i	−0.0812431	+	0.250040i
$15$	3924.06	+	12077.0i	0.300204	+	0.923932i
$16$	−33039.0	+	24004.2i	−2.01654	+	1.46510i
$17$	6110.28	−	4439.37i	0.301640	−	0.219155i	−0.426661	−	0.904412i	$-0.640310\pi$
$17$	6110.28	−	4439.37i	0.301640	−	0.219155i	0.728301	+	0.685257i	$0.240310\pi$
$18$	−4723.36	−	14537.0i	−0.190896	−	0.587519i
$19$	13008.2	−	40035.0i	0.435089	−	1.33907i	−0.457906	−	0.889001i	$-0.651400\pi$
$19$	13008.2	−	40035.0i	0.435089	−	1.33907i	0.892995	−	0.450066i	$-0.148600\pi$
$20$	−118571.	−	86147.2i	−3.31417	−	2.40789i
$21$	3475.96			0.0819043
$22$	59407.7	+	70977.3i	1.18950	+	1.42115i
$23$	−58373.4			−1.00039			−0.500193	−	0.865914i	$-0.666738\pi$
$23$	−58373.4			−1.00039			−0.500193	+	0.865914i	$0.666738\pi$
$24$	84100.0	+	61102.2i	1.24181	+	0.902231i
$25$	44211.5	−	136069.i	0.565908	−	1.74169i
$26$	60045.4	+	184801.i	0.669998	+	2.06204i
$27$	−15923.9	+	11569.4i	−0.155695	+	0.113119i
$28$	−32456.5	+	23581.0i	−0.279414	+	0.203006i
$29$	−16114.1	−	49594.1i	−0.122691	−	0.377604i	0.870782	−	0.491669i	$-0.163613\pi$
$29$	−16114.1	−	49594.1i	−0.122691	−	0.377604i	−0.993473	+	0.114065i	$0.963613\pi$
$30$	−82276.7	+	253222.i	−0.556356	+	1.71229i
$31$	252442.	+	183410.i	1.52193	+	1.10575i	0.960520	+	0.278211i	$0.0897416\pi$
$31$	252442.	+	183410.i	1.52193	+	1.10575i	0.561412	+	0.827537i	$0.310258\pi$
$32$	−363454.			−1.96076
$33$	63285.7	−	101000.i	0.306554	−	0.489242i
$34$	158360.			0.690985
$35$	−48984.3	−	35589.2i	−0.193116	−	0.140307i
$36$	70200.9	−	216056.i	0.250775	−	0.771806i
$37$	41608.2	+	128057.i	0.135043	+	0.415621i	0.995597	−	0.0937396i	$-0.0298821\pi$
$37$	41608.2	+	128057.i	0.135043	+	0.415621i	−0.860553	+	0.509360i	$0.829882\pi$
$38$	714057.	−	518793.i	2.11101	−	1.53374i
$39$	202431.	−	147075.i	0.546451	−	0.397020i
$40$	−559559.	−	1.72215e6i	−1.38241	−	4.25461i
$41$	42716.9	−	131469.i	0.0967958	−	0.297907i	−0.890922	−	0.454157i	$-0.849941\pi$
$41$	42716.9	−	131469.i	0.0967958	−	0.297907i	0.987718	+	0.156250i	$0.0499405\pi$
$42$	58962.2	+	42838.5i	0.122801	+	0.0892199i
$43$	−543911.			−1.04325			−0.521624	−	0.853175i	$-0.674674\pi$
$43$	−543911.			−1.04325			−0.521624	+	0.853175i	$0.674674\pi$
$44$	94264.8	+	1.37242e6i	0.166827	+	2.42885i
$45$	342860.			0.560884
$46$	−990180.	−	719408.i	−1.49990	−	1.08974i
$47$	−257065.	+	791164.i	−0.361160	+	1.11154i	0.591190	+	0.806532i	$0.298658\pi$
$47$	−257065.	+	791164.i	−0.361160	+	1.11154i	−0.952351	+	0.305005i	$0.901342\pi$
$48$	340734.	+	1.04867e6i	0.444704	+	1.36866i
$49$	652852.	−	474325.i	0.792736	−	0.575956i
$50$	2.42690e6	−	1.76325e6i	2.74573	−	1.99489i
$51$	−63015.8	−	193943.i	−0.0665202	−	0.204728i
$52$	−892425.	+	2.74660e6i	−0.880156	+	2.70884i
$53$	444660.	+	323064.i	0.410263	+	0.298074i	0.773708	−	0.633542i	$-0.218400\pi$
$53$	444660.	+	323064.i	0.410263	+	0.298074i	−0.363445	+	0.931616i	$0.618400\pi$
$54$	−412698.			−0.356660
$55$	−1.92595e6	+	775369.i	−1.56090	+	0.628404i
$56$	−495661.			−0.377161
$57$	−919507.	−	668061.i	−0.657647	−	0.477809i
$58$	337868.	−	1.03985e6i	0.227378	−	0.699799i
$59$	−120241.	−	370065.i	−0.0762205	−	0.234583i	0.905686	−	0.423949i	$-0.139357\pi$
$59$	−120241.	−	370065.i	−0.0762205	−	0.234583i	−0.981906	+	0.189367i	$0.939357\pi$
$60$	−3.20143e6	+	2.32597e6i	−1.91344	+	1.39019i
$61$	2.10717e6	−	1.53095e6i	1.18863	−	0.863587i	0.195507	−	0.980702i	$-0.437365\pi$
$61$	2.10717e6	−	1.53095e6i	1.18863	−	0.863587i	0.993118	+	0.117116i	$0.0373648\pi$
$62$	2.02175e6	+	6.22230e6i	1.07735	+	3.31574i
$63$	29001.5	−	89257.4i	0.0146126	−	0.0449731i
$64$	−1.93623e6	−	1.40675e6i	−0.923264	−	0.670791i
$65$	−4.35858e6			−1.96856
$66$	2.31826e6	−	933307.i	0.992563	−	0.399596i
$67$	−779463.			−0.316617			−0.158308	−	0.987390i	$-0.550604\pi$
$67$	−779463.			−0.316617			−0.158308	+	0.987390i	$0.550604\pi$
$68$	1.90412e6	+	1.38342e6i	0.734366	+	0.533548i
$69$	−487036.	+	1.49894e6i	−0.178480	+	0.549304i
$70$	−392305.	−	1.20739e6i	−0.136704	−	0.420731i
$71$	−1.68842e6	+	1.22671e6i	−0.559857	+	0.406760i	−0.831407	−	0.555665i	$-0.812464\pi$
$71$	−1.68842e6	+	1.22671e6i	−0.559857	+	0.406760i	0.271550	+	0.962424i	$0.412464\pi$
$72$	2.27070e6	−	1.64976e6i	0.716962	−	0.520903i
$73$	−1.00541e6	−	3.09433e6i	−0.302492	−	0.930973i	−0.980601	−	0.196013i	$-0.937201\pi$
$73$	−1.00541e6	−	3.09433e6i	−0.302492	−	0.930973i	0.678110	−	0.734961i	$-0.262799\pi$
$74$	−872410.	+	2.68500e6i	−0.250270	+	0.770253i
$75$	−3.12518e6	−	2.27057e6i	−0.855382	−	0.621472i
$76$	1.31180e7			3.42783
$77$	38942.8	+	566974.i	0.00972097	+	0.141529i
$78$	5.24640e6			1.25179
$79$	−5.55799e6	−	4.03812e6i	−1.26830	−	0.921477i	−0.269170	−	0.963093i	$-0.586749\pi$
$79$	−5.55799e6	−	4.03812e6i	−1.26830	−	0.921477i	−0.999134	+	0.0416160i	$0.986749\pi$
$80$	5.93527e6	−	1.82669e7i	1.29606	−	3.98887i
$81$	164224.	+	505430.i	0.0343352	+	0.105673i
$82$	2.34486e6	−	1.70364e6i	0.469644	−	0.341216i
$83$	−637291.	+	463019.i	−0.122339	+	0.0888845i	−0.647272	−	0.762259i	$-0.724090\pi$
$83$	−637291.	+	463019.i	−0.122339	+	0.0888845i	0.524933	+	0.851143i	$0.324090\pi$
$84$	334726.	+	1.03018e6i	0.0616187	+	0.189643i
$85$	−1.09768e6	+	3.37830e6i	−0.193869	+	0.596668i
$86$	−9.22628e6	−	6.70328e6i	−1.56416	−	1.13643i
$87$	−1.40795e6			−0.229229
$88$	−9.02436e6	+	1.44024e7i	−1.41165	+	2.25291i
$89$	339461.			0.0510417			0.0255209	−	0.999674i	$-0.491876\pi$
$89$	339461.			0.0510417			0.0255209	+	0.999674i	$0.491876\pi$
$90$	5.81589e6	+	4.22549e6i	0.840944	+	0.610982i
$91$	−368680.	+	1.13468e6i	−0.0512866	+	0.157844i
$92$	−5.62122e6	−	1.73003e7i	−0.752615	−	2.31631i
$93$	6.81593e6	−	4.95206e6i	0.878688	−	0.638404i
$94$	−1.41111e7	+	1.02523e7i	−1.75231	+	1.27313i
$95$	6.11794e6	+	1.88291e7i	0.732103	+	2.25318i
$96$	−3.03246e6	+	9.33296e6i	−0.349821	+	1.07664i
$97$	5.64733e6	+	4.10302e6i	0.628264	+	0.456460i	0.855798	−	0.517310i	$-0.173066\pi$
$97$	5.64733e6	+	4.10302e6i	0.628264	+	0.456460i	−0.227535	+	0.973770i	$0.573066\pi$
$98$	1.69199e7			1.81596
$99$	−2.06552e6	−	2.46778e6i	−0.213947	−	0.255613i
$100$	4.45848e7			4.45848
$101$	−2.24704e6	−	1.63257e6i	−0.217013	−	0.157669i	0.473968	−	0.880542i	$-0.342821\pi$
$101$	−2.24704e6	−	1.63257e6i	−0.217013	−	0.157669i	−0.690981	+	0.722873i	$0.742821\pi$
$102$	1.32127e6	−	4.06644e6i	0.123279	−	0.379415i
$103$	−4.63436e6	−	1.42631e7i	−0.417888	−	1.28613i	−0.909643	−	0.415392i	$-0.863644\pi$
$103$	−4.63436e6	−	1.42631e7i	−0.417888	−	1.28613i	0.491755	−	0.870734i	$-0.336356\pi$
$104$	−2.88661e7	+	2.09725e7i	−2.51635	+	1.82824i
$105$	−1.32258e6	+	960909.i	−0.111496	+	0.0810065i
$106$	3.56118e6	+	1.09602e7i	0.290418	+	0.893815i
$107$	353135.	−	1.08684e6i	0.0278675	−	0.0857672i	−0.936155	−	0.351586i	$-0.885642\pi$
$107$	353135.	−	1.08684e6i	0.0278675	−	0.0857672i	0.964023	+	0.265819i	$0.0856424\pi$
$108$	−4.96229e6	−	3.60531e6i	−0.379052	−	0.275397i
$109$	−1.51794e7			−1.12269			−0.561347	−	0.827580i	$-0.689717\pi$
$109$	−1.51794e7			−1.12269			−0.561347	+	0.827580i	$0.689717\pi$
$110$	−4.22255e7	−	1.05834e7i	−3.02483	−	0.758145i
$111$	3.63547e6			0.252307
$112$	−4.25341e6	−	3.09028e6i	−0.286071	−	0.207843i
$113$	1.37059e6	−	4.21824e6i	0.0893579	−	0.275015i	−0.896384	−	0.443278i	$-0.853816\pi$
$113$	1.37059e6	−	4.21824e6i	0.0893579	−	0.275015i	0.985742	+	0.168262i	$0.0538156\pi$
$114$	−7.36412e6	−	2.26644e7i	−0.465537	−	1.43278i
$115$	2.22107e7	−	1.61370e7i	1.36182	−	0.989419i
$116$	1.31466e7	−	9.55158e6i	0.782008	−	0.568162i
$117$	−2.08769e6	−	6.42525e6i	−0.120508	−	0.370885i
$118$	2.52113e6	−	7.75924e6i	0.141256	−	0.434743i
$119$	786631.	+	571521.i	0.0427914	+	0.0310898i
$120$	−4.88909e7			−2.58281
$121$	1.71835e7	+	9.19116e6i	0.881785	+	0.471652i
$122$	5.46114e7			2.72285
$123$	−3.01953e6	−	2.19382e6i	−0.146309	−	0.106300i
$124$	−3.00482e7	+	9.24789e7i	−1.41528	+	4.35579i
$125$	9.43904e6	+	2.90504e7i	0.432258	+	1.33035i
$126$	1.59198e6	−	1.15664e6i	0.0708990	−	0.0515112i
$127$	2.87860e7	−	2.09142e7i	1.24700	−	0.906001i	0.248960	−	0.968514i	$-0.419911\pi$
$127$	2.87860e7	−	2.09142e7i	1.24700	−	0.906001i	0.998044	+	0.0625127i	$0.0199114\pi$
$128$	−1.13068e6	−	3.47989e6i	−0.0476548	−	0.146666i
$129$	−4.53810e6	+	1.39668e7i	−0.186127	+	0.572840i
$130$	−7.39340e7	−	5.37162e7i	−2.95150	−	2.14439i
$131$	3.05718e7			1.18815			0.594076	−	0.804409i	$-0.297518\pi$
$131$	3.05718e7			1.18815			0.594076	+	0.804409i	$0.297518\pi$
$132$	3.60281e7	+	9.03011e6i	1.36343	+	0.341731i
$133$	5.41931e6			0.199739
$134$	−1.32219e7	−	9.60629e6i	−0.474709	−	0.344897i
$135$	2.86064e6	−	8.80414e6i	0.100068	−	0.307977i
$136$	8.98587e6	+	2.76557e7i	0.306319	+	0.942753i
$137$	−3.31823e7	+	2.41083e7i	−1.10251	+	0.801023i	−0.981469	−	0.191623i	$-0.938625\pi$
$137$	−3.31823e7	+	2.41083e7i	−1.10251	+	0.801023i	−0.121046	+	0.992647i	$0.538625\pi$
$138$	−2.67348e7	+	1.94240e7i	−0.865966	+	0.629161i
$139$	−6.14553e6	−	1.89140e7i	−0.194092	−	0.597354i	−0.999986	−	0.00529403i	$-0.998315\pi$
$139$	−6.14553e6	−	1.89140e7i	−0.194092	−	0.597354i	0.805894	−	0.592060i	$-0.201685\pi$
$140$	5.83063e6	−	1.79448e7i	0.179584	−	0.552702i
$141$	1.81711e7	+	1.32021e7i	0.545902	+	0.396621i
$142$	−4.37588e7			−1.28250
$143$	2.62578e7	+	3.13714e7i	0.750899	+	0.897136i
$144$	2.97712e7			0.830860
$145$	1.98413e7	+	1.44156e7i	0.540483	+	0.392684i
$146$	2.10807e7	−	6.48797e7i	0.560596	−	1.72534i
$147$	−6.73291e6	−	2.07218e7i	−0.174821	−	0.538042i
$148$	−3.39459e7	+	2.46631e7i	−0.860739	+	0.625363i
$149$	1.52845e7	−	1.11048e7i	0.378528	−	0.275017i	−0.382210	−	0.924075i	$-0.624837\pi$
$149$	1.52845e7	−	1.11048e7i	0.378528	−	0.275017i	0.760738	+	0.649059i	$0.224837\pi$
$150$	−2.50289e7	−	7.70309e7i	−0.605510	−	1.86357i
$151$	−2.87284e6	+	8.84171e6i	−0.0679036	+	0.208986i	−0.979251	−	0.202653i	$-0.935044\pi$
$151$	−2.87284e6	+	8.84171e6i	−0.0679036	+	0.208986i	0.911347	+	0.411639i	$0.135044\pi$
$152$	1.31119e8	+	9.52636e7i	3.02840	+	2.20026i
$153$	−5.50593e6			−0.124283
$154$	−6.32694e6	+	1.00974e7i	−0.139595	+	0.222786i
$155$	−1.46755e8			−3.16542
$156$	6.30828e7	+	4.58323e7i	1.33038	+	0.966575i
$157$	1.49758e7	−	4.60909e7i	0.308846	−	0.950531i	−0.669368	−	0.742931i	$-0.733435\pi$
$157$	1.49758e7	−	4.60909e7i	0.308846	−	0.950531i	0.978214	−	0.207599i	$-0.0665651\pi$
$158$	−4.45127e7	−	1.36996e8i	−0.897810	−	2.76318i
$159$	1.20058e7	−	8.72274e6i	0.236866	−	0.172093i
$160$	1.38292e8	−	1.00475e8i	2.66917	−	1.93926i
$161$	−2.32224e6	−	7.14713e6i	−0.0438548	−	0.134971i
$162$	−3.44333e6	+	1.05975e7i	−0.0636321	+	0.195840i
$163$	1.05959e7	+	7.69837e6i	0.191638	+	0.139233i	0.679467	−	0.733706i	$-0.262211\pi$
$163$	1.05959e7	+	7.69837e6i	0.191638	+	0.139233i	−0.487829	+	0.872939i	$0.662211\pi$
$164$	4.30775e7			0.762601
$165$	3.84122e6	+	5.59249e7i	0.0665696	+	0.969196i
$166$	−1.65166e7			−0.280249
$167$	5.77992e7	+	4.19936e7i	0.960316	+	0.697710i	0.953224	−	0.302264i	$-0.0977426\pi$
$167$	5.77992e7	+	4.19936e7i	0.960316	+	0.697710i	0.00709193	+	0.999975i	$0.497743\pi$
$168$	−4.13553e6	+	1.27279e7i	−0.0672897	+	0.207097i
$169$	7.14926e6	+	2.20032e7i	0.113935	+	0.350656i
$170$	−6.02548e7	+	4.37777e7i	−0.940633	+	0.683410i
$171$	−2.48267e7	+	1.80376e7i	−0.379693	+	0.275863i
$172$	−5.23773e7	−	1.61201e8i	−0.784862	−	2.41556i
$173$	7.89590e6	−	2.43011e7i	0.115942	−	0.356832i	−0.876200	−	0.481947i	$-0.839930\pi$
$173$	7.89590e6	−	2.43011e7i	0.115942	−	0.356832i	0.992142	+	0.125114i	$0.0399298\pi$
$174$	−2.38829e7	−	1.73519e7i	−0.343688	−	0.249704i
$175$	1.84189e7			0.259795
$176$	−1.67234e8	+	6.73269e7i	−2.31223	+	0.930881i
$177$	−1.05059e7			−0.142406
$178$	5.75824e6	+	4.18360e6i	0.0765278	+	0.0556007i
$179$	2.03735e7	−	6.27033e7i	0.265510	−	0.817156i	−0.726065	−	0.687626i	$-0.758653\pi$
$179$	2.03735e7	−	6.27033e7i	0.265510	−	0.817156i	0.991575	−	0.129530i	$-0.0413470\pi$
$180$	3.30166e7	+	1.01615e8i	0.421967	+	1.29868i
$181$	−3.73768e7	+	2.71558e7i	−0.468519	+	0.340399i	−0.796864	−	0.604159i	$-0.793509\pi$
$181$	−3.73768e7	+	2.71558e7i	−0.468519	+	0.340399i	0.328345	+	0.944558i	$0.393509\pi$
$182$	−2.02379e7	+	1.47037e7i	−0.248838	+	0.180791i
$183$	−2.17314e7	−	6.68824e7i	−0.262125	−	0.806739i
$184$	6.94499e7	−	2.13745e8i	0.821882	−	2.52949i
$185$	−5.12323e7	−	3.72224e7i	−0.594898	−	0.432219i
$186$	1.76648e8			2.01286
$187$	3.09286e7	−	1.24515e7i	0.345871	−	0.139244i
$188$	−2.59235e8			−2.84538
$189$	−2.05003e6	−	1.48943e6i	−0.0220873	−	0.0160474i
$190$	−1.28276e8	+	3.94794e8i	−1.35678	+	4.17573i
$191$	1.79044e7	+	5.51042e7i	0.185928	+	0.572227i	0.999963	−	0.00858862i	$-0.00273388\pi$
$191$	1.79044e7	+	5.51042e7i	0.185928	+	0.572227i	−0.814035	+	0.580815i	$0.802734\pi$
$192$	−5.22781e7	+	3.79823e7i	−0.533047	+	0.387281i
$193$	−2.06581e7	+	1.50090e7i	−0.206843	+	0.150280i	−0.686384	−	0.727239i	$-0.740803\pi$
$193$	−2.06581e7	+	1.50090e7i	−0.206843	+	0.150280i	0.479541	+	0.877519i	$0.340803\pi$
$194$	4.52282e7	+	1.39198e8i	0.444737	+	1.36876i
$195$	−3.63657e7	+	1.11922e8i	−0.351213	+	1.08092i
$196$	2.03445e8	+	1.47812e8i	1.92997	+	1.40221i
$197$	−1.39360e8			−1.29869			−0.649344	−	0.760495i	$-0.724956\pi$
$197$	−1.39360e8			−1.29869			−0.649344	+	0.760495i	$0.724956\pi$
$198$	−4.62366e6	−	6.73165e7i	−0.0423309	−	0.616301i
$199$	−2.06776e7			−0.186000			−0.0930001	−	0.995666i	$-0.529646\pi$
$199$	−2.06776e7			−0.186000			−0.0930001	+	0.995666i	$0.529646\pi$
$200$	4.45641e8	+	3.23777e8i	3.93895	+	2.86182i
$201$	−6.50342e6	+	2.00155e7i	−0.0564879	+	0.173852i
$202$	−1.79960e7	−	5.53860e7i	−0.153619	−	0.472792i
$203$	5.43115e6	−	3.94596e6i	0.0455675	−	0.0331068i
$204$	5.14112e7	−	3.73524e7i	0.423987	−	0.308044i
$205$	2.00904e7	+	6.18320e7i	0.162874	+	0.501274i
$206$	9.71698e7	−	2.99058e8i	0.774455	−	2.38353i
$207$	3.44271e7	+	2.50127e7i	0.269776	+	0.196004i
$208$	−3.78464e8			−2.91611
$209$	9.86677e7	−	1.57468e8i	0.747589	−	1.19311i
$210$	−3.42772e7			−0.255410
$211$	−1.52315e8	−	1.10663e8i	−1.11623	−	0.810987i	−0.132595	−	0.991170i	$-0.542331\pi$
$211$	−1.52315e8	−	1.10663e8i	−1.11623	−	0.810987i	−0.983633	+	0.180183i	$0.942331\pi$
$212$	−5.29280e7	+	1.62896e8i	−0.381514	+	1.17418i
$213$	1.74128e7	+	5.35912e7i	0.123464	+	0.379984i
$214$	1.93846e7	−	1.40838e7i	0.135210	−	0.0982359i
$215$	2.06954e8	−	1.50361e8i	1.42017	−	1.03181i
$216$	−2.34179e7	−	7.20729e7i	−0.158110	−	0.486613i
$217$	−1.24136e7	+	3.82050e7i	−0.0824683	+	0.253811i
$218$	−2.57486e8	−	1.87074e8i	−1.68328	−	1.22297i
$219$	−8.78465e7			−0.565159
$220$	−4.15264e8	−	4.96136e8i	−2.62933	−	3.14138i
$221$	6.99938e7			0.436201
$222$	6.16680e7	+	4.48044e7i	0.378289	+	0.274843i
$223$	8.72090e6	−	2.68402e7i	0.0526616	−	0.162076i	−0.921267	−	0.388931i	$-0.872844\pi$
$223$	8.72090e6	−	2.68402e7i	0.0526616	−	0.162076i	0.973928	+	0.226855i	$0.0728444\pi$
$224$	−1.44591e7	−	4.45006e7i	−0.0859555	−	0.264544i
$225$	−8.43798e7	+	6.13055e7i	−0.493855	+	0.358807i
$226$	7.52357e7	−	5.46620e7i	0.433555	−	0.314996i
$227$	2.58610e7	+	7.95920e7i	0.146742	+	0.451626i	0.997231	−	0.0743673i	$-0.0236937\pi$
$227$	2.58610e7	+	7.95920e7i	0.146742	+	0.451626i	−0.850489	+	0.525993i	$0.823694\pi$
$228$	1.09449e8	−	3.36850e8i	0.611562	−	1.88220i
$229$	2.83211e8	+	2.05765e8i	1.55843	+	1.13226i	0.937284	+	0.348568i	$0.113332\pi$
$229$	2.83211e8	+	2.05765e8i	1.55843	+	1.13226i	0.621144	+	0.783696i	$0.286668\pi$
$230$	5.75633e8			3.11959
$231$	1.48840e7	+	3.73053e6i	0.0794469	+	0.0199126i
$232$	2.00770e8			1.05558
$233$	−5.88802e7	−	4.27790e7i	−0.304946	−	0.221556i	0.424779	−	0.905297i	$-0.360352\pi$
$233$	−5.88802e7	−	4.27790e7i	−0.304946	−	0.221556i	−0.729725	+	0.683741i	$0.760352\pi$
$234$	4.37731e7	−	1.34720e8i	0.223333	−	0.687347i
$235$	−1.20902e8	−	3.72097e8i	−0.607707	−	1.87033i
$236$	9.80985e7	−	7.12727e7i	0.485814	−	0.352965i
$237$	−1.50066e8	+	1.09029e8i	−0.732256	+	0.532015i
$238$	6.29996e6	+	1.93893e7i	0.0302913	+	0.0932271i
$239$	2.55057e7	−	7.84984e7i	0.120849	−	0.371936i	−0.872273	−	0.489020i	$-0.837355\pi$
$239$	2.55057e7	−	7.84984e7i	0.120849	−	0.371936i	0.993122	+	0.117084i	$0.0373546\pi$
$240$	−4.19546e8	−	3.04818e8i	−1.95903	−	1.42332i
$241$	3.40280e8			1.56595			0.782973	−	0.622055i	$-0.213702\pi$
$241$	3.40280e8			1.56595			0.782973	+	0.622055i	$0.213702\pi$
$242$	1.78207e8	+	3.67682e8i	0.808297	+	1.66770i
$243$	1.43489e7			0.0641500
$244$	6.56648e8	+	4.77083e8i	2.89380	+	2.10247i
$245$	−1.17281e8	+	3.60955e8i	−0.509504	+	1.56809i
$246$	−2.41827e7	−	7.44268e7i	−0.103570	−	0.318755i
$247$	3.15608e8	−	2.29302e8i	1.33263	−	0.968209i
$248$	−9.71932e8	+	7.06150e8i	−4.04627	+	2.93979i
$249$	6.57244e6	+	2.02279e7i	0.0269792	+	0.0830334i
$250$	−1.97911e8	+	6.09106e8i	−0.801086	+	2.46549i
$251$	−2.87959e8	−	2.09215e8i	−1.14940	−	0.835091i	−0.161003	−	0.986954i	$-0.551473\pi$
$251$	−2.87959e8	−	2.09215e8i	−1.14940	−	0.835091i	−0.988402	+	0.151863i	$0.951473\pi$
$252$	2.92463e7			0.115125
$253$	−2.49953e8	−	6.26485e7i	−0.970370	−	0.243214i
$254$	7.46044e8			2.85658
$255$	7.75914e7	+	5.63735e7i	0.293037	+	0.212904i
$256$	−7.09579e7	+	2.18386e8i	−0.264339	+	0.813551i
$257$	−5.89853e7	−	1.81538e8i	−0.216759	−	0.667117i	−0.999024	−	0.0441707i	$-0.985935\pi$
$257$	−5.89853e7	−	1.81538e8i	−0.216759	−	0.667117i	0.782265	−	0.622946i	$-0.214065\pi$
$258$	−2.49110e8	+	1.80989e8i	−0.903070	+	0.656119i
$259$	−1.40238e7	+	1.01889e7i	−0.0501552	+	0.0364399i
$260$	−4.19721e8	−	1.29177e9i	−1.48100	−	4.55804i
$261$	−1.17472e7	+	3.61541e7i	−0.0408970	+	0.125868i
$262$	5.18586e8	+	3.76774e8i	1.78142	+	1.29428i
$263$	−3.79230e6			−0.0128546			−0.00642729	−	0.999979i	$-0.502046\pi$
$263$	−3.79230e6			−0.0128546			−0.00642729	+	0.999979i	$0.502046\pi$
$264$	2.94537e8	+	3.51898e8i	0.985204	+	1.17707i
$265$	−2.58499e8			−0.853295
$266$	9.19270e7	+	6.67889e7i	0.299473	+	0.217580i
$267$	2.83228e6	−	8.71687e6i	0.00910641	−	0.0280266i
$268$	−7.50604e7	−	2.31012e8i	−0.238199	−	0.733100i
$269$	−4.57834e8	+	3.32636e8i	−1.43409	+	1.04192i	−0.444848	+	0.895606i	$0.646742\pi$
$269$	−4.57834e8	+	3.32636e8i	−1.43409	+	1.04192i	−0.989238	+	0.146318i	$0.953258\pi$
$270$	1.57029e8	−	1.14088e8i	0.485519	−	0.352750i
$271$	−3.13502e6	−	9.64860e6i	−0.00956859	−	0.0294491i	0.946158	−	0.323705i	$-0.104928\pi$
$271$	−3.13502e6	−	9.64860e6i	−0.00956859	−	0.0294491i	−0.955727	+	0.294255i	$0.904928\pi$
$272$	−9.53135e7	+	2.93345e8i	−0.287186	+	0.883868i
$273$	2.60608e7	+	1.89343e7i	0.0775209	+	0.0563222i
$274$	−8.59983e8			−2.52559
$275$	3.35347e8	−	5.35196e8i	0.972368	−	1.55184i
$276$	−4.91147e8			−1.40614
$277$	−1.67558e8	−	1.21738e8i	−0.473681	−	0.344150i	0.325193	−	0.945648i	$-0.394571\pi$
$277$	−1.67558e8	−	1.21738e8i	−0.473681	−	0.344150i	−0.798874	+	0.601498i	$0.794571\pi$
$278$	1.28855e8	−	3.96575e8i	0.359703	−	1.10705i
$279$	−7.02932e7	−	2.16340e8i	−0.193775	−	0.596379i
$280$	1.88596e8	−	1.37023e8i	0.513427	−	0.373027i
$281$	1.65758e8	−	1.20430e8i	0.445658	−	0.323789i	−0.342221	−	0.939619i	$-0.611179\pi$
$281$	1.65758e8	−	1.20430e8i	0.445658	−	0.323789i	0.787879	+	0.615830i	$0.211179\pi$
$282$	1.45528e8	+	4.47890e8i	0.386435	+	1.18932i
$283$	−7.19043e7	+	2.21299e8i	−0.188583	+	0.580399i	−0.999992	−	0.00408043i	$-0.998701\pi$
$283$	−7.19043e7	+	2.21299e8i	−0.188583	+	0.580399i	0.811409	+	0.584479i	$0.198701\pi$
$284$	−5.26156e8	−	3.82275e8i	−1.36301	−	0.990287i
$285$	5.34548e8			1.36782
$286$	5.87779e7	+	8.55756e8i	0.148571	+	2.16306i
$287$	1.77962e7			0.0444367
$288$	2.14355e8	+	1.55738e8i	0.528762	+	0.384168i
$289$	−1.09174e8	+	3.36004e8i	−0.266059	+	0.818845i
$290$	1.58905e8	+	4.89058e8i	0.382599	+	1.17752i
$291$	1.52478e8	−	1.10782e8i	0.362728	−	0.263537i
$292$	8.20260e8	−	5.95954e8i	1.92802	−	1.40079i
$293$	−344891.	−	1.06146e6i	−0.000801022	−	0.00246529i	0.950655	−	0.310249i	$-0.100413\pi$
$293$	−344891.	−	1.06146e6i	−0.000801022	−	0.00246529i	−0.951456	+	0.307784i	$0.900413\pi$
$294$	1.41171e8	−	4.34479e8i	0.323988	−	0.997133i
$295$	1.48053e8	+	1.07567e8i	0.335770	+	0.243951i
$296$	−5.18408e8			−1.16185
$297$	−8.06024e7	+	3.24497e7i	−0.178526	+	0.0718726i
$298$	3.96127e8			0.867116
$299$	−4.37652e8	−	3.17973e8i	−0.946846	−	0.687924i
$300$	3.71991e8	−	1.14487e9i	0.795441	−	2.44812i
$301$	−2.16382e7	−	6.65954e7i	−0.0457338	−	0.140754i
$302$	−1.57699e8	+	1.14575e8i	−0.329461	+	0.239368i
$303$	−6.06700e7	+	4.40793e7i	−0.125292	+	0.0910302i
$304$	5.31233e8	+	1.63497e9i	1.08449	+	3.33773i
$305$	−3.78541e8	+	1.16503e9i	−0.763948	+	2.35119i
$306$	−9.33963e7	−	6.78564e7i	−0.186339	−	0.135384i
$307$	−2.65182e7			−0.0523071			−0.0261535	−	0.999658i	$-0.508326\pi$
$307$	−2.65182e7			−0.0523071			−0.0261535	+	0.999658i	$0.508326\pi$
$308$	−1.64286e8	+	6.61398e7i	−0.320385	+	0.128984i
$309$	−4.04922e8			−0.780758
$310$	−2.48938e9	−	1.80864e9i	−4.74598	−	3.44816i
$311$	−1.65691e8	+	5.09946e8i	−0.312348	+	0.961308i	0.664484	+	0.747302i	$0.268651\pi$
$311$	−1.65691e8	+	5.09946e8i	−0.312348	+	0.961308i	−0.976832	+	0.214006i	$0.931349\pi$
$312$	2.97699e8	+	9.16222e8i	0.554927	+	1.70789i
$313$	−3.96920e8	+	2.88379e8i	−0.731640	+	0.531568i	−0.890082	−	0.455801i	$-0.849353\pi$
$313$	−3.96920e8	+	2.88379e8i	−0.731640	+	0.531568i	0.158442	+	0.987368i	$0.449353\pi$
$314$	8.22068e8	−	5.97267e8i	1.49849	−	1.08872i
$315$	1.36398e7	+	4.19791e7i	0.0245880	+	0.0756740i
$316$	6.61570e8	−	2.03610e9i	1.17943	−	3.62990i
$317$	1.98287e8	+	1.44064e8i	0.349612	+	0.254008i	0.748706	−	0.662902i	$-0.230675\pi$
$317$	1.98287e8	+	1.44064e8i	0.349612	+	0.254008i	−0.399094	+	0.916910i	$0.630675\pi$
$318$	3.11154e8			0.542601
$319$	−1.57739e7	−	2.29655e8i	−0.0272065	−	0.396103i
$320$	1.12561e9			1.92027
$321$	−2.49620e7	−	1.81360e7i	−0.0421223	−	0.0306036i
$322$	4.86911e7	−	1.49856e8i	0.0812744	−	0.250137i
$323$	−9.82469e7	−	3.02373e8i	−0.162222	−	0.499269i
$324$	−1.33982e8	+	9.73435e7i	−0.218846	+	0.159001i
$325$	1.07267e9	−	7.79342e8i	1.73331	−	1.25932i
$326$	8.48602e7	+	2.61173e8i	0.135657	+	0.417510i
$327$	−1.26649e8	+	3.89784e8i	−0.200301	+	0.616463i
$328$	4.30576e8	+	3.12832e8i	0.673739	+	0.489500i
$329$	−1.07095e8			−0.165800
$330$	−6.24074e8	+	9.95987e8i	−0.955955	+	1.52565i
$331$	1.17757e8			0.178479			0.0892395	−	0.996010i	$-0.471556\pi$
$331$	1.17757e8			0.178479			0.0892395	+	0.996010i	$0.471556\pi$
$332$	−1.98596e8	−	1.44289e8i	−0.297843	−	0.216396i
$333$	3.03324e7	−	9.33535e7i	0.0450144	−	0.138540i
$334$	4.62901e8	+	1.42466e9i	0.679791	+	2.09218i
$335$	2.96580e8	−	2.15478e8i	0.431008	−	0.313146i
$336$	−1.14842e8	+	8.34376e7i	−0.165163	+	0.119998i
$337$	1.96582e8	+	6.05016e8i	0.279794	+	0.861117i	0.987911	+	0.155022i	$0.0495448\pi$
$337$	1.96582e8	+	6.05016e8i	0.279794	+	0.861117i	−0.708117	+	0.706095i	$0.750455\pi$
$338$	−1.49900e8	+	4.61346e8i	−0.211151	+	0.649857i
$339$	−9.68827e7	−	7.03894e7i	−0.135066	−	0.0981315i
$340$	−1.10694e9			−1.52739
$341$	8.84107e8	+	1.05629e9i	1.20744	+	1.44258i
$342$	−6.43432e8			−0.869784
$343$	1.69821e8	+	1.23382e8i	0.227228	+	0.165091i
$344$	6.47120e8	−	1.99163e9i	0.857097	−	2.63787i
$345$	−2.29060e8	−	7.04976e8i	−0.300319	−	0.924288i
$346$	4.33429e8	−	3.14905e8i	0.562538	−	0.408708i
$347$	−6.22625e8	+	4.52364e8i	−0.799969	+	0.581212i	−0.910905	−	0.412616i	$-0.864615\pi$
$347$	−6.22625e8	+	4.52364e8i	−0.799969	+	0.581212i	0.110936	+	0.993828i	$0.464615\pi$
$348$	−1.35582e8	−	4.17279e8i	−0.172455	−	0.530761i
$349$	−1.83453e8	+	5.64611e8i	−0.231013	+	0.710985i	0.766612	+	0.642110i	$0.221941\pi$
$349$	−1.83453e8	+	5.64611e8i	−0.231013	+	0.710985i	−0.997625	+	0.0688747i	$0.978059\pi$
$350$	3.12437e8	+	2.26999e8i	0.389516	+	0.283000i
$351$	−1.82409e8			−0.225150
$352$	−1.55630e9	−	3.90072e8i	−1.90193	−	0.476701i
$353$	1.15650e9			1.39937			0.699687	−	0.714449i	$-0.253323\pi$
$353$	1.15650e9			1.39937			0.699687	+	0.714449i	$0.253323\pi$
$354$	−1.78211e8	−	1.29478e8i	−0.213512	−	0.155126i
$355$	3.03316e8	−	9.33510e8i	0.359829	−	1.10744i
$356$	3.26893e7	+	1.00607e8i	0.0384000	+	0.118183i
$357$	2.12390e7	−	1.54311e7i	0.0247057	−	0.0179497i
$358$	1.11836e9	−	8.12539e8i	1.28823	−	0.935953i
$359$	−8.68799e7	−	2.67389e8i	−0.0991034	−	0.305009i	0.889198	−	0.457523i	$-0.151263\pi$
$359$	−8.68799e7	−	2.67389e8i	−0.0991034	−	0.305009i	−0.988301	+	0.152514i	$0.951263\pi$
$360$	−4.07919e8	+	1.25544e9i	−0.460803	+	1.41820i
$361$	−7.10432e8	−	5.16159e8i	−0.794780	−	0.577442i
$362$	−9.68693e8			−1.07326
$363$	3.79385e8	−	3.64561e8i	0.416301	−	0.400034i
$364$	−3.71792e8			−0.404059
$365$	1.23796e9	+	8.99433e8i	1.33255	+	0.968153i
$366$	4.55648e8	−	1.40234e9i	0.485787	−	1.49510i
$367$	−4.17326e8	−	1.28440e9i	−0.440701	−	1.35634i	−0.887130	−	0.461520i	$-0.847304\pi$
$367$	−4.17326e8	−	1.28440e9i	−0.440701	−	1.35634i	0.446429	−	0.894819i	$-0.352696\pi$
$368$	1.92860e9	−	1.40121e9i	2.01732	−	1.46567i
$369$	−8.15273e7	+	5.92330e7i	−0.0844716	+	0.0613722i
$370$	−4.10308e8	−	1.26280e9i	−0.421118	−	1.29607i
$371$	−2.18657e7	+	6.72957e7i	−0.0222308	+	0.0684193i
$372$	2.12402e9	+	1.54319e9i	2.13923	+	1.55424i
$373$	1.82953e9			1.82541			0.912703	−	0.408624i	$-0.133991\pi$
$373$	1.82953e9			1.82541			0.912703	+	0.408624i	$0.133991\pi$
$374$	6.78093e8	+	1.69958e8i	0.670252	+	0.167993i
$375$	8.24725e8			0.807606
$376$	−2.59115e9	−	1.88258e9i	−2.51383	−	1.82640i
$377$	1.49335e8	−	4.59606e8i	0.143538	−	0.441765i
$378$	−1.64182e7	−	5.05300e7i	−0.0156352	−	0.0481203i
$379$	−9.86655e8	+	7.16847e8i	−0.930954	+	0.676378i	−0.946226	−	0.323506i	$-0.895138\pi$
$379$	−9.86655e8	+	7.16847e8i	−0.930954	+	0.676378i	0.0152724	+	0.999883i	$0.495138\pi$
$380$	−4.99130e9	+	3.62639e9i	−4.66628	+	3.39025i
$381$	−2.96872e8	−	9.13678e8i	−0.274999	−	0.846361i
$382$	−3.75407e8	+	1.15538e9i	−0.344572	+	1.06049i
$383$	−6.21439e8	−	4.51502e8i	−0.565201	−	0.410643i	0.268158	−	0.963375i	$-0.413585\pi$
$383$	−6.21439e8	−	4.51502e8i	−0.565201	−	0.410643i	−0.833359	+	0.552732i	$0.813585\pi$
$384$	−9.87923e7			−0.0890356
$385$	−1.71554e8	−	2.04964e8i	−0.153211	−	0.183048i
$386$	−5.35396e8			−0.473827
$387$	3.20784e8	+	2.33063e8i	0.281335	+	0.204402i
$388$	−6.72204e8	+	2.06883e9i	−0.584238	+	1.79810i
$389$	−3.00568e8	−	9.25054e8i	−0.258893	−	0.796790i	−0.993038	−	0.117797i	$-0.962417\pi$
$389$	−3.00568e8	−	9.25054e8i	−0.258893	−	0.796790i	0.734145	−	0.678993i	$-0.237583\pi$
$390$	−1.99622e9	+	1.45034e9i	−1.70405	+	1.23806i
$391$	−3.56677e8	+	2.59141e8i	−0.301757	+	0.219239i
$392$	9.60095e8	+	2.95487e9i	0.805031	+	2.47763i
$393$	2.55075e8	−	7.85039e8i	0.211979	−	0.652405i
$394$	−2.36394e9	−	1.71750e9i	−1.94715	−	1.41469i
$395$	3.23109e9			2.63791
$396$	5.32479e8	−	8.49806e8i	0.430893	−	0.687680i
$397$	−1.92509e9			−1.54413			−0.772064	−	0.635545i	$-0.780776\pi$
$397$	−1.92509e9			−1.54413			−0.772064	+	0.635545i	$0.780776\pi$
$398$	−3.50751e8	−	2.54835e8i	−0.278874	−	0.202614i
$399$	4.52158e7	−	1.39160e8i	0.0356357	−	0.109675i
$400$	1.80553e9	+	5.55685e9i	1.41057	+	4.34129i
$401$	2.86739e8	−	2.08328e8i	0.222065	−	0.161340i	−0.471190	−	0.882031i	$-0.656176\pi$
$401$	2.86739e8	−	2.08328e8i	0.222065	−	0.161340i	0.693256	+	0.720691i	$0.256176\pi$
$402$	−3.56992e8	+	2.59370e8i	−0.274074	+	0.199126i
$403$	8.93597e8	+	2.75021e9i	0.680102	+	2.09314i
$404$	2.67465e8	−	8.23174e8i	0.201805	−	0.621093i
$405$	−2.02210e8	−	1.46914e8i	−0.151255	−	0.109893i
$406$	1.40759e8			0.104384
$407$	4.07299e7	+	5.92992e8i	0.0299456	+	0.435982i
$408$	7.85130e8			0.572310
$409$	1.28687e9	+	9.34967e8i	0.930044	+	0.675717i	0.946004	−	0.324156i	$-0.105080\pi$
$409$	1.28687e9	+	9.34967e8i	0.930044	+	0.675717i	−0.0159595	+	0.999873i	$0.505080\pi$
$410$	−4.21241e8	+	1.29645e9i	−0.301847	+	0.928991i
$411$	3.42212e8	+	1.05322e9i	0.243135	+	0.748294i
$412$	3.78093e9	−	2.74700e9i	2.66353	−	1.93517i
$413$	4.05266e7	−	2.94443e7i	0.0283083	−	0.0205672i
$414$	2.75719e8	+	8.48575e8i	0.190970	+	0.587745i
$415$	1.14486e8	−	3.52351e8i	0.0786292	−	0.241996i
$416$	−2.72498e9	−	1.97981e9i	−1.85582	−	1.34833i
$417$	−5.36959e8			−0.362631
$418$	3.61436e9	−	1.45511e9i	2.42055	−	0.974490i
$419$	−2.80673e9			−1.86403			−0.932014	−	0.362423i	$-0.881950\pi$
$419$	−2.80673e9			−1.86403			−0.932014	+	0.362423i	$0.881950\pi$
$420$	−4.12149e8	−	2.99444e8i	−0.271445	−	0.197216i
$421$	−5.14426e8	+	1.58324e9i	−0.335997	+	1.03409i	0.630232	+	0.776407i	$0.282960\pi$
$421$	−5.14426e8	+	1.58324e9i	−0.335997	+	1.03409i	−0.966229	+	0.257685i	$0.917040\pi$
$422$	−1.21985e9	−	3.75432e9i	−0.790158	−	2.43186i
$423$	4.90620e8	−	3.56456e8i	0.315177	−	0.228989i
$424$	−1.71200e9	+	1.24384e9i	−1.09074	+	0.792471i
$425$	−3.33917e8	−	1.02769e9i	−0.210998	−	0.649384i
$426$	−3.65100e8	+	1.12366e9i	−0.228811	+	0.704209i
$427$	2.71275e8	+	1.97093e8i	0.168621	+	0.122511i
$428$	3.56116e8			0.219552
$429$	1.02465e9	−	4.12515e8i	0.626579	−	0.252254i
$430$	5.36362e9			3.25326
$431$	−6.84579e8	−	4.97375e8i	−0.411863	−	0.299236i	0.362493	−	0.931987i	$-0.381926\pi$
$431$	−6.84579e8	−	4.97375e8i	−0.411863	−	0.299236i	−0.774356	+	0.632751i	$0.781926\pi$
$432$	2.48395e8	−	7.64481e8i	0.148235	−	0.456219i
$433$	−7.15196e8	−	2.20115e9i	−0.423367	−	1.30299i	−0.904549	−	0.426370i	$-0.859792\pi$
$433$	−7.15196e8	−	2.20115e9i	−0.423367	−	1.30299i	0.481181	−	0.876621i	$-0.340208\pi$
$434$	−6.81417e8	+	4.95079e8i	−0.400128	+	0.290710i
$435$	5.35715e8	−	3.89220e8i	0.312048	−	0.226716i
$436$	−1.46174e9	−	4.49877e9i	−0.844631	−	2.59951i
$437$	−7.59330e8	+	2.33698e9i	−0.435257	+	1.33958i
$438$	−1.49013e9	−	1.08264e9i	−0.847353	−	0.615638i
$439$	−3.41411e8			−0.192598			−0.0962990	−	0.995352i	$-0.530700\pi$
$439$	−3.41411e8			−0.192598			−0.0962990	+	0.995352i	$0.530700\pi$
$440$	−5.47747e8	−	7.97473e9i	−0.306546	−	4.46305i
$441$	−5.88281e8			−0.326625
$442$	1.18729e9	+	8.62620e8i	0.654004	+	0.475162i
$443$	−1.65378e8	+	5.08983e8i	−0.0903787	+	0.278157i	−0.986022	−	0.166617i	$-0.946716\pi$
$443$	−1.65378e8	+	5.08983e8i	−0.0903787	+	0.278157i	0.895643	+	0.444773i	$0.146716\pi$
$444$	3.50087e8	+	1.07746e9i	0.189817	+	0.584197i
$445$	−1.29163e8	+	9.38422e7i	−0.0694828	+	0.0504822i
$446$	4.78716e8	−	3.47808e8i	0.255509	−	0.185638i
$447$	−1.57630e8	−	4.85135e8i	−0.0834761	−	0.256913i
$448$	9.52119e7	−	2.93032e8i	0.0500286	−	0.153972i
$449$	−3.73644e8	−	2.71468e8i	−0.194803	−	0.141533i	0.486108	−	0.873899i	$-0.338416\pi$
$449$	−3.73644e8	−	2.71468e8i	−0.194803	−	0.141533i	−0.680911	+	0.732366i	$0.738416\pi$
$450$	−2.18687e9			−1.13130
$451$	3.24011e8	−	5.17103e8i	0.166319	−	0.265436i
$452$	1.38216e9			0.704001
$453$	2.03073e8	+	1.47541e8i	0.102638	+	0.0745707i
$454$	−5.42234e8	+	1.66883e9i	−0.271951	+	0.836981i
$455$	−1.73396e8	−	5.33657e8i	−0.0862975	−	0.265596i
$456$	3.54021e9	−	2.57212e9i	1.74845	−	1.27032i
$457$	8.66057e7	−	6.29227e7i	0.0424463	−	0.0308390i	−0.566360	−	0.824158i	$-0.691649\pi$
$457$	8.66057e7	−	6.29227e7i	0.0424463	−	0.0308390i	0.608806	+	0.793319i	$0.291649\pi$
$458$	2.26818e9	+	6.98073e9i	1.10318	+	3.39525i
$459$	−4.59385e7	+	1.41384e8i	−0.0221734	+	0.0682427i
$460$	6.92141e9	+	5.02870e9i	3.31545	+	2.40881i
$461$	−2.85349e9			−1.35651			−0.678256	−	0.734826i	$-0.737264\pi$
$461$	−2.85349e9			−1.35651			−0.678256	+	0.734826i	$0.737264\pi$
$462$	2.06499e8	+	2.46714e8i	0.0974250	+	0.116398i
$463$	−2.45201e9			−1.14812			−0.574061	−	0.818812i	$-0.694633\pi$
$463$	−2.45201e9			−1.14812			−0.574061	+	0.818812i	$0.694633\pi$
$464$	1.72286e9	+	1.25173e9i	0.800640	+	0.581699i
$465$	−1.22444e9	+	3.76845e9i	−0.564746	+	1.73811i
$466$	−4.71558e8	−	1.45131e9i	−0.215866	−	0.664368i
$467$	1.61909e9	−	1.17634e9i	0.735635	−	0.534470i	−0.155706	−	0.987803i	$-0.549765\pi$
$467$	1.61909e9	−	1.17634e9i	0.735635	−	0.534470i	0.891341	+	0.453333i	$0.149765\pi$
$468$	1.70323e9	−	1.23747e9i	0.768093	−	0.558052i
$469$	−3.10091e7	−	9.54360e7i	−0.0138798	−	0.0427177i
$470$	2.53497e9	−	7.80184e9i	1.12624	−	3.46621i
$471$	−1.05860e9	−	7.69115e8i	−0.466828	−	0.339170i
$472$	1.49812e9			0.655766
$473$	−2.32901e9	−	5.83745e8i	−1.01195	−	0.253635i
$474$	−3.88925e9			−1.67742
$475$	−4.87242e9	−	3.54002e9i	−2.08601	−	1.51558i
$476$	−9.36330e7	+	2.88173e8i	−0.0397928	+	0.122470i
$477$	−1.23817e8	−	3.81070e8i	−0.0522355	−	0.160764i
$478$	1.40008e9	−	1.01722e9i	0.586349	−	0.426007i
$479$	2.20363e9	−	1.60103e9i	0.916147	−	0.665620i	−0.0264152	−	0.999651i	$-0.508409\pi$
$479$	2.20363e9	−	1.60103e9i	0.916147	−	0.665620i	0.942562	+	0.334031i	$0.108409\pi$
$480$	−1.42621e9	−	4.38943e9i	−0.588627	−	1.81161i
$481$	−3.85598e8	+	1.18675e9i	−0.157989	+	0.486241i
$482$	5.77212e9	+	4.19369e9i	2.34785	+	1.70582i
$483$	−2.02903e8			−0.0819359
$484$	−1.06929e9	+	5.97782e9i	−0.428683	+	2.39654i
$485$	−3.28303e9			−1.30671
$486$	2.43399e8	+	1.76839e8i	0.0961814	+	0.0698799i
$487$	−4.20270e8	+	1.29346e9i	−0.164883	+	0.507459i	−0.999028	−	0.0440875i	$-0.985962\pi$
$487$	−4.20270e8	+	1.29346e9i	−0.164883	+	0.507459i	0.834144	+	0.551546i	$0.185962\pi$
$488$	3.09884e9	+	9.53724e9i	1.20706	+	3.71495i
$489$	2.86089e8	−	2.07856e8i	0.110642	−	0.0803862i
$490$	−6.43792e9	+	4.67742e9i	−2.47206	+	1.79606i
$491$	−8.77987e8	−	2.70216e9i	−0.334736	−	1.03021i	−0.966852	−	0.255338i	$-0.917813\pi$
$491$	−8.77987e8	−	2.70216e9i	−0.334736	−	1.03021i	0.632116	−	0.774874i	$-0.282187\pi$
$492$	3.59416e8	−	1.10617e9i	0.136056	−	0.418739i
$493$	−3.18628e8	−	2.31497e8i	−0.119762	−	0.0870124i
$494$	8.17958e9			3.05272
$495$	1.46812e9	+	3.67970e8i	0.544055	+	0.136362i
$496$	−1.27430e10			−4.68907
$497$	−2.17366e8	−	1.57926e8i	−0.0794227	−	0.0577039i
$498$	−1.37806e8	+	4.24123e8i	−0.0499995	+	0.153883i
$499$	1.09374e9	+	3.36619e9i	0.394061	+	1.21279i	0.929691	+	0.368341i	$0.120074\pi$
$499$	1.09374e9	+	3.36619e9i	0.394061	+	1.21279i	−0.535630	+	0.844453i	$0.679926\pi$
$500$	−7.70080e9	+	5.59496e9i	−2.75512	+	2.00171i
$501$	1.56058e9	−	1.13383e9i	0.554439	−	0.402823i
$502$	−2.30620e9	−	7.09776e9i	−0.813643	−	2.50414i
$503$	−6.83133e8	+	2.10247e9i	−0.239341	+	0.736616i	0.757175	+	0.653212i	$0.226579\pi$
$503$	−6.83133e8	+	2.10247e9i	−0.239341	+	0.736616i	−0.996516	+	0.0834038i	$0.973421\pi$
$504$	2.92328e8	+	2.12389e8i	0.101710	+	0.0738966i
$505$	1.30630e9			0.451358
$506$	−3.46783e9	−	4.14319e9i	−1.18996	−	1.42170i
$507$	6.24658e8			0.212870
$508$	8.97044e9	+	6.51741e9i	3.03592	+	2.20573i
$509$	9.10384e8	−	2.80187e9i	0.305994	−	0.941751i	−0.673311	−	0.739359i	$-0.735128\pi$
$509$	9.10384e8	−	2.80187e9i	0.305994	−	0.941751i	0.979305	−	0.202392i	$-0.0648715\pi$
$510$	6.21412e8	+	1.91251e9i	0.207436	+	0.638423i
$511$	3.38867e8	−	2.46201e8i	0.112346	−	0.0816238i
$512$	−4.27399e9	+	3.10524e9i	−1.40731	+	1.02247i
$513$	2.56040e8	+	7.88009e8i	0.0837330	+	0.257704i
$514$	1.23676e9	−	3.80636e9i	0.401712	−	1.23634i
$515$	5.70629e9	+	4.14587e9i	1.84089	+	1.33749i
$516$	−4.57640e9			−1.46639
$517$	−1.94985e9	+	3.11186e9i	−0.620562	+	0.990381i
$518$	−3.63453e8			−0.114893
$519$	−5.58137e8	−	4.05510e8i	−0.175249	−	0.127326i
$520$	5.18564e9	−	1.59598e10i	1.61730	−	4.97754i
$521$	−1.22846e9	−	3.78081e9i	−0.380565	−	1.17126i	−0.939646	−	0.342147i	$-0.888846\pi$
$521$	−1.22846e9	−	3.78081e9i	−0.380565	−	1.17126i	0.559081	−	0.829113i	$-0.311154\pi$
$522$	−6.44837e8	+	4.68502e8i	−0.198428	+	0.144167i
$523$	1.51216e9	−	1.09865e9i	0.462211	−	0.335816i	−0.332187	−	0.943214i	$-0.607786\pi$
$523$	1.51216e9	−	1.09865e9i	0.462211	−	0.335816i	0.794398	+	0.607398i	$0.207786\pi$
$524$	2.94399e9	+	9.06068e9i	0.893876	+	2.75107i
$525$	1.53677e8	−	4.72970e8i	0.0463503	−	0.142652i
$526$	−6.43283e7	−	4.67372e7i	−0.0192731	−	0.0140027i
$527$	2.35671e9			0.701406
$528$	3.33541e8	+	4.85607e9i	0.0986122	+	1.43571i
$529$	2.62591e6			0.000771233
$530$	−4.38489e9	−	3.18581e9i	−1.27936	−	0.929510i
$531$	−8.76560e7	+	2.69777e8i	−0.0254068	+	0.0781942i
$532$	5.21867e8	+	1.60614e9i	0.150269	+	0.462480i
$533$	1.03641e9	−	7.52996e8i	0.296474	−	0.215401i
$534$	1.55472e8	−	1.12957e8i	0.0441834	−	0.0321011i
$535$	1.66085e8	+	5.11156e8i	0.0468912	+	0.144316i
$536$	9.27369e8	−	2.85415e9i	0.260121	−	0.800571i
$537$	−1.44014e9	−	1.04633e9i	−0.401325	−	0.291579i
$538$	−1.18657e10			−3.28514
$539$	3.30456e9	−	1.33038e9i	0.908977	−	0.365945i
$540$	2.88479e9			0.788380
$541$	3.96991e9	+	2.88431e9i	1.07793	+	0.783162i	0.977321	−	0.211764i	$-0.0679208\pi$
$541$	3.96991e9	+	2.88431e9i	1.07793	+	0.783162i	0.100609	+	0.994926i	$0.467921\pi$
$542$	6.57328e7	−	2.02305e8i	0.0177331	−	0.0545768i
$543$	3.85470e8	+	1.18636e9i	0.103322	+	0.317991i
$544$	−2.22080e9	+	1.61351e9i	−0.591444	+	0.429709i
$545$	5.77565e9	−	4.19626e9i	1.52832	−	1.11039i
$546$	2.08715e8	+	6.42360e8i	0.0548757	+	0.168890i
$547$	−1.88947e9	+	5.81521e9i	−0.493612	+	1.51918i	0.325497	+	0.945543i	$0.394468\pi$
$547$	−1.88947e9	+	5.81521e9i	−0.493612	+	1.51918i	−0.819109	+	0.573638i	$0.805532\pi$
$548$	−1.03404e10	−	7.51277e9i	−2.68415	−	1.95015i
$549$	−1.89876e9			−0.489741
$550$	1.22843e10	−	4.94555e9i	3.14834	−	1.26749i
$551$	−2.19511e9			−0.559019
$552$	−4.90920e9	−	3.56674e9i	−1.24229	−	0.902579i
$553$	2.73309e8	−	8.41157e8i	0.0687251	−	0.211514i
$554$	−1.34194e9	−	4.13005e9i	−0.335311	−	1.03198i
$555$	−1.38327e9	+	1.00501e9i	−0.343465	+	0.249542i
$556$	5.01381e9	−	3.64275e9i	1.23710	−	0.898809i
$557$	−1.36155e9	−	4.19041e9i	−0.333841	−	1.02746i	−0.967290	−	0.253673i	$-0.918361\pi$
$557$	−1.36155e9	−	4.19041e9i	−0.333841	−	1.02746i	0.633449	−	0.773784i	$-0.281639\pi$
$558$	1.47386e9	−	4.53606e9i	0.359116	−	1.10525i
$559$	−4.07794e9	−	2.96280e9i	−0.987416	−	0.717399i
$560$	2.47268e9			0.594991
$561$	−6.16856e7	−	8.98089e8i	−0.0147507	−	0.214758i
$562$	4.29593e9			1.02089
$563$	−1.41316e9	−	1.02672e9i	−0.333744	−	0.242479i	0.408274	−	0.912860i	$-0.366131\pi$
$563$	−1.41316e9	−	1.02672e9i	−0.333744	−	0.242479i	−0.742018	+	0.670380i	$0.766131\pi$
$564$	−2.16292e9	+	6.65677e9i	−0.507648	+	1.56238i
$565$	6.44609e8	+	1.98390e9i	0.150358	+	0.462755i
$566$	−3.94704e9	+	2.86769e9i	−0.914986	+	0.664776i
$567$	−5.53507e7	+	4.02146e7i	−0.0127521	+	0.00926496i
$568$	−2.48302e9	−	7.64196e9i	−0.568541	−	1.74979i
$569$	2.67178e9	−	8.22289e9i	0.608005	−	1.87125i	0.133369	−	0.991067i	$-0.457421\pi$
$569$	2.67178e9	−	8.22289e9i	0.608005	−	1.87125i	0.474637	−	0.880182i	$-0.342579\pi$
$570$	9.06746e9	+	6.58789e9i	2.05080	+	1.48999i
$571$	4.08755e8			0.0918834			0.0459417	−	0.998944i	$-0.485371\pi$
$571$	4.08755e8			0.0918834			0.0459417	+	0.998944i	$0.485371\pi$
$572$	−6.76910e9	+	1.08031e10i	−1.51232	+	2.41358i
$573$	1.56438e9			0.347377
$574$	3.01875e8	+	2.19325e8i	0.0666248	+	0.0484057i
$575$	−2.58078e9	+	7.94282e9i	−0.566126	+	1.74236i
$576$	5.39148e8	+	1.65933e9i	0.117552	+	0.361787i
$577$	−1.35025e9	+	9.81013e8i	−0.292616	+	0.212598i	−0.724401	−	0.689378i	$-0.757884\pi$
$577$	−1.35025e9	+	9.81013e8i	−0.292616	+	0.212598i	0.431785	+	0.901976i	$0.357884\pi$
$578$	−5.99290e9	+	4.35409e9i	−1.29089	+	0.937887i
$579$	2.13049e8	+	6.55698e8i	0.0456147	+	0.140388i
$580$	−2.36172e9	+	7.26862e9i	−0.502609	+	1.54687i
$581$	−8.20443e7	−	5.96087e7i	−0.0173553	−	0.0126094i
$582$	3.95176e9			0.830922
$583$	1.55730e9	+	1.86058e9i	0.325486	+	0.388874i
$584$	1.25267e10			2.60250
$585$	2.57058e9	+	1.86763e9i	0.530866	+	0.385697i
$586$	7.23141e6	−	2.22560e7i	0.00148450	−	0.00456883i
$587$	2.60244e9	+	8.00948e9i	0.531064	+	1.63445i	0.752003	+	0.659159i	$0.229088\pi$
$587$	2.60244e9	+	8.00948e9i	0.531064	+	1.63445i	−0.220939	+	0.975288i	$0.570912\pi$
$588$	5.49302e9	−	3.99092e9i	1.11427	−	0.809565i
$589$	1.06266e10	−	7.72068e9i	2.14285	−	1.55687i
$590$	1.18573e9	+	3.64929e9i	0.237685	+	0.731520i
$591$	−1.16274e9	+	3.57855e9i	−0.231700	+	0.713100i
$592$	−4.44860e9	−	3.23210e9i	−0.881247	−	0.640263i
$593$	4.72995e9			0.931461			0.465731	−	0.884927i	$-0.345792\pi$
$593$	4.72995e9			0.931461			0.465731	+	0.884927i	$0.345792\pi$
$594$	−1.76717e9	−	4.42924e8i	−0.345959	−	0.0867114i
$595$	−4.57302e8			−0.0890007
$596$	4.76303e9	+	3.46054e9i	0.921555	+	0.669549i
$597$	−1.72522e8	+	5.30969e8i	−0.0331845	+	0.102131i
$598$	−3.50505e9	−	1.07874e10i	−0.670256	−	2.06284i
$599$	6.93341e9	−	5.03741e9i	1.31811	−	0.957665i	0.318160	−	0.948037i	$-0.396935\pi$
$599$	6.93341e9	−	5.03741e9i	1.31811	−	0.957665i	0.999954	−	0.00962819i	$-0.00306480\pi$
$600$	1.20323e10	−	8.74199e9i	2.27415	−	1.65227i
$601$	1.17606e9	+	3.61955e9i	0.220989	+	0.680133i	0.998674	+	0.0514796i	$0.0163937\pi$
$601$	1.17606e9	+	3.61955e9i	0.220989	+	0.680133i	−0.777685	+	0.628654i	$0.783606\pi$
$602$	4.53693e8	−	1.39632e9i	0.0847567	−	0.260854i
$603$	4.59707e8	+	3.33996e8i	0.0853828	+	0.0620342i
$604$	−2.89710e9			−0.534975
$605$	−9.07905e9	+	1.25311e9i	−1.66685	+	0.230062i
$606$	−1.57238e9			−0.287014
$607$	−1.26220e9	−	9.17044e8i	−0.229070	−	0.166429i	0.467330	−	0.884083i	$-0.345216\pi$
$607$	−1.26220e9	−	9.17044e8i	−0.229070	−	0.166429i	−0.696400	+	0.717654i	$0.745216\pi$
$608$	−4.72786e9	+	1.45509e10i	−0.853105	+	2.62559i
$609$	−5.60119e7	−	1.72387e8i	−0.0100489	−	0.0309274i
$610$	−2.07793e10	+	1.50970e10i	−3.70660	+	2.69300i
$611$	−6.23698e9	+	4.53143e9i	−1.10619	+	0.803694i
$612$	−5.30208e8	−	1.63181e9i	−0.0935010	−	0.287766i
$613$	9.84845e8	−	3.03104e9i	0.172686	−	0.531472i	−0.826835	−	0.562445i	$-0.809861\pi$
$613$	9.84845e8	−	3.03104e9i	0.172686	−	0.531472i	0.999520	+	0.0309735i	$0.00986075\pi$
$614$	−4.49825e8	−	3.26817e8i	−0.0784250	−	0.0569791i
$615$	1.75538e9			0.304304
$616$	−2.12241e9	−	5.31963e8i	−0.365845	−	0.0916956i
$617$	3.12063e9			0.534864			0.267432	−	0.963577i	$-0.413825\pi$
$617$	3.12063e9			0.534864			0.267432	+	0.963577i	$0.413825\pi$
$618$	−6.86863e9	−	4.99035e9i	−1.17061	−	0.850495i
$619$	3.03064e9	−	9.32735e9i	0.513591	−	1.58067i	−0.272241	−	0.962229i	$-0.587765\pi$
$619$	3.03064e9	−	9.32735e9i	0.513591	−	1.58067i	0.785832	−	0.618441i	$-0.212235\pi$
$620$	−1.41321e10	−	4.34943e10i	−2.38143	−	7.32928i
$621$	9.29531e8	−	6.75344e8i	0.155755	−	0.113163i
$622$	−9.09529e9	+	6.60812e9i	−1.51548	+	1.10106i
$623$	1.35046e7	+	4.15630e7i	0.00223756	+	0.00688651i
$624$	−3.15770e9	+	9.71841e9i	−0.520266	+	1.60121i
$625$	−2.57954e9	−	1.87415e9i	−0.422632	−	0.307060i
$626$	−1.02869e10			−1.67601
$627$	−3.22032e9	−	3.84747e9i	−0.521750	−	0.623360i
$628$	1.51023e10			2.43323
$629$	8.22730e8	+	5.97749e8i	0.131820	+	0.0957726i
$630$	−2.85990e8	+	8.80187e8i	−0.0455679	+	0.140244i
$631$	7.27857e8	+	2.24011e9i	0.115330	+	0.354950i	0.992016	−	0.126114i	$-0.0402505\pi$
$631$	7.27857e8	+	2.24011e9i	0.115330	+	0.354950i	−0.876686	+	0.481064i	$0.840250\pi$
$632$	2.13990e10	−	1.55473e10i	3.37196	−	2.44988i
$633$	−4.11249e9	+	2.98790e9i	−0.644454	+	0.468224i
$634$	1.58803e9	+	4.88747e9i	0.247484	+	0.761678i
$635$	−5.17124e9	+	1.59154e10i	−0.801469	+	2.46667i
$636$	3.74132e9	+	2.71823e9i	0.576667	+	0.418973i
$637$	7.47848e9			1.14637
$638$	2.56275e9	−	4.09001e9i	0.390692	−	0.623522i
$639$	1.52143e9			0.230674
$640$	1.39221e9	+	1.01150e9i	0.209931	+	0.152524i
$641$	6.44180e8	−	1.98258e9i	0.0966059	−	0.297322i	−0.891063	−	0.453880i	$-0.850040\pi$
$641$	6.44180e8	−	1.98258e9i	0.0966059	−	0.297322i	0.987669	+	0.156557i	$0.0500396\pi$
$642$	−1.99915e8	−	6.15276e8i	−0.0298176	−	0.0917693i
$643$	−1.37548e9	+	9.99344e8i	−0.204040	+	0.148244i	−0.685113	−	0.728437i	$-0.740247\pi$
$643$	−1.37548e9	+	9.99344e8i	−0.204040	+	0.148244i	0.481073	+	0.876681i	$0.340247\pi$
$644$	1.89459e9	−	1.37650e9i	0.279522	−	0.203084i
$645$	−2.13434e9	−	6.56881e9i	−0.313187	−	0.963891i
$646$	2.05997e9	−	6.33993e9i	0.300640	−	0.925275i
$647$	−1.74868e9	−	1.27049e9i	−0.253832	−	0.184419i	0.453592	−	0.891210i	$-0.350142\pi$
$647$	−1.74868e9	−	1.27049e9i	−0.253832	−	0.184419i	−0.707423	+	0.706790i	$0.750142\pi$
$648$	−2.04611e9			−0.295405
$649$	−1.17703e8	−	1.71366e9i	−0.0169017	−	0.246075i
$650$	2.78004e10			3.97058
$651$	8.77476e8	+	6.37524e8i	0.124653	+	0.0905655i
$652$	−1.26123e9	+	3.88168e9i	−0.178209	+	0.548470i
$653$	1.25297e9	+	3.85623e9i	0.176093	+	0.541960i	0.999682	−	0.0252283i	$-0.00803126\pi$
$653$	1.25297e9	+	3.85623e9i	0.176093	+	0.541960i	−0.823588	+	0.567188i	$0.808031\pi$
$654$	−6.95212e9	+	5.05101e9i	−0.971841	+	0.706084i
$655$	−1.16324e10	+	8.45141e9i	−1.61742	+	1.17513i
$656$	1.74449e9	+	5.36900e9i	0.241271	+	0.742557i
$657$	−7.32944e8	+	2.25577e9i	−0.100831	+	0.310324i
$658$	−1.81664e9	−	1.31987e9i	−0.248587	−	0.180609i
$659$	−9.68087e9			−1.31770			−0.658849	−	0.752276i	$-0.728956\pi$
$659$	−9.68087e9			−1.31770			−0.658849	+	0.752276i	$0.728956\pi$
$660$	−1.62048e10	+	6.52387e9i	−2.19401	+	0.883287i
$661$	6.92152e9			0.932172			0.466086	−	0.884739i	$-0.345664\pi$
$661$	6.92152e9			0.932172			0.466086	+	0.884739i	$0.345664\pi$
$662$	1.99749e9	+	1.45126e9i	0.267597	+	0.194421i
$663$	5.83990e8	−	1.79734e9i	0.0778230	−	0.239515i
$664$	−9.37211e8	−	2.88444e9i	−0.124236	−	0.382361i
$665$	−2.06201e9	+	1.49814e9i	−0.271904	+	0.197550i
$666$	1.66504e9	−	1.20972e9i	0.218406	−	0.158681i
$667$	9.40634e8	+	2.89497e9i	0.122738	+	0.377750i
$668$	−6.87986e9	+	2.11740e10i	−0.893022	+	2.74844i
$669$	−6.16454e8	−	4.47880e8i	−0.0795993	−	0.0578322i
$670$	7.68646e9			0.987335
$671$	1.06659e10	−	4.29399e9i	1.36292	−	0.548697i
$672$	−1.26335e9			−0.160595
$673$	3.82877e9	+	2.78176e9i	0.484179	+	0.351777i	0.802941	−	0.596058i	$-0.203267\pi$
$673$	3.82877e9	+	2.78176e9i	0.484179	+	0.351777i	−0.318762	+	0.947835i	$0.603267\pi$
$674$	−4.12177e9	+	1.26855e10i	−0.518531	+	1.59587i
$675$	8.70216e8	+	2.67825e9i	0.108909	+	0.335187i
$676$	−5.83270e9	+	4.23770e9i	−0.726200	+	0.527615i
$677$	−1.14409e10	+	8.31230e9i	−1.41710	+	1.02958i	−0.424855	+	0.905261i	$0.639675\pi$
$677$	−1.14409e10	+	8.31230e9i	−1.41710	+	1.02958i	−0.992242	+	0.124320i	$0.960325\pi$
$678$	−7.75912e8	−	2.38801e9i	−0.0956112	−	0.294261i
$679$	−2.77701e8	+	8.54677e8i	−0.0340435	+	0.104775i
$680$	−1.10643e10	−	8.03870e9i	−1.34941	−	0.980403i
$681$	2.25958e9			0.274165
$682$	1.97907e9	+	2.88136e10i	0.238900	+	3.47818i
$683$	−2.81618e9			−0.338211			−0.169105	−	0.985598i	$-0.554088\pi$
$683$	−2.81618e9			−0.338211			−0.169105	+	0.985598i	$0.554088\pi$
$684$	−7.73663e9	−	5.62099e9i	−0.924390	−	0.671609i
$685$	5.96101e9	−	1.83461e10i	0.708603	−	2.18086i
$686$	1.36006e9	+	4.18584e9i	0.160851	+	0.495049i
$687$	7.64671e9	−	5.55566e9i	0.899759	−	0.653713i
$688$	1.79703e10	−	1.30562e10i	2.10375	−	1.52847i
$689$	1.57402e9	+	4.84432e9i	0.183333	+	0.564242i
$690$	4.80277e9	−	1.47814e10i	0.556570	−	1.71295i
$691$	−1.33492e10	−	9.69873e9i	−1.53915	−	1.11826i	−0.950866	−	0.309602i	$-0.899804\pi$
$691$	−1.33492e10	−	9.69873e9i	−1.53915	−	1.11826i	−0.588283	−	0.808655i	$-0.700196\pi$
$692$	7.96255e9			0.913442
$693$	2.19978e8	−	3.51073e8i	0.0251081	−	0.0400711i
$694$	−1.61365e10			−1.83253
$695$	7.56701e9	+	5.49775e9i	0.855022	+	0.621210i
$696$	1.67511e9	−	5.15547e9i	0.188327	−	0.579610i
$697$	−3.22629e8	−	9.92950e8i	−0.0360901	−	0.111074i
$698$	−1.00703e10	+	7.31650e9i	−1.12085	+	0.814347i
$699$	−1.58977e9	+	1.15503e9i	−0.176061	+	0.127916i
$700$	1.77370e9	+	5.45888e9i	0.195450	+	0.601534i
$701$	1.72298e9	−	5.30280e9i	0.188916	−	0.581423i	−0.811078	−	0.584938i	$-0.801119\pi$
$701$	1.72298e9	−	5.30280e9i	0.188916	−	0.581423i	0.999994	+	0.00351484i	$0.00111881\pi$
$702$	−3.09419e9	−	2.24806e9i	−0.337572	−	0.245261i
$703$	5.66801e9			0.615300
$704$	−6.78110e9	−	8.10170e9i	−0.732480	−	0.875129i
$705$	−1.05636e10			−1.13541
$706$	1.96175e10	+	1.42530e10i	2.09811	+	1.52437i
$707$	1.10496e8	−	3.40071e8i	0.0117592	−	0.0361910i
$708$	−1.01170e9	−	3.11369e9i	−0.107136	−	0.329730i
$709$	−4.83164e9	+	3.51039e9i	−0.509135	+	0.369908i	−0.812495	−	0.582968i	$-0.801891\pi$
$709$	−4.83164e9	+	3.51039e9i	−0.509135	+	0.369908i	0.303360	+	0.952876i	$0.401891\pi$
$710$	1.66499e10	−	1.20969e10i	1.74585	−	1.26844i
$711$	1.54764e9	+	4.76315e9i	0.161483	+	0.496993i
$712$	−4.03875e8	+	1.24300e9i	−0.0419341	+	0.129060i
$713$	−1.47359e10	−	1.07062e10i	−1.52252	−	1.10617i
$714$	5.50451e8			0.0565946
$715$	−1.86634e10	−	4.67780e9i	−1.90950	−	0.478597i
$716$	2.05455e10			2.09181
$717$	−1.80292e9	−	1.30990e9i	−0.182667	−	0.132715i
$718$	1.82163e9	−	5.60641e9i	0.183664	−	0.565261i
$719$	4.10871e9	+	1.26453e10i	0.412244	+	1.26876i	0.914693	+	0.404149i	$0.132432\pi$
$719$	4.10871e9	+	1.26453e10i	0.412244	+	1.26876i	−0.502450	+	0.864606i	$0.667568\pi$
$720$	−1.13277e10	+	8.23009e9i	−1.13104	+	0.821752i
$721$	1.56198e9	−	1.13484e9i	0.155204	−	0.112762i
$722$	−5.68969e9	−	1.75111e10i	−0.562611	−	1.73154i
$723$	2.83911e9	−	8.73789e9i	0.279382	−	0.859850i
$724$	−1.16476e10	−	8.46246e9i	−1.14064	−	0.828727i
$725$	−7.46065e9			−0.727099
$726$	1.09284e10	−	1.50836e9i	1.05993	−	0.146294i
$727$	8.63415e9			0.833392			0.416696	−	0.909046i	$-0.363188\pi$
$727$	8.63415e9			0.833392			0.416696	+	0.909046i	$0.363188\pi$
$728$	−3.71620e9	−	2.69998e9i	−0.356976	−	0.259358i
$729$	1.19720e8	−	3.68459e8i	0.0114451	−	0.0352243i
$730$	9.91457e9	+	3.05139e10i	0.943287	+	2.90314i
$731$	−3.32344e9	+	2.41462e9i	−0.314686	+	0.228633i
$732$	1.77295e10	−	1.28812e10i	1.67073	−	1.21386i
$733$	−3.61875e9	−	1.11374e10i	−0.339386	−	1.04452i	−0.964521	−	0.264007i	$-0.914956\pi$
$733$	−3.61875e9	−	1.11374e10i	−0.339386	−	1.04452i	0.625135	−	0.780517i	$-0.285044\pi$
$734$	8.75018e9	−	2.69303e10i	0.816734	−	2.51365i
$735$	8.29025e9	+	6.02322e9i	0.770126	+	0.559529i
$736$	2.12160e10			1.96151
$737$	−3.33764e9	−	8.36549e8i	−0.307117	−	0.0769760i
$738$	−2.11294e9			−0.193504
$739$	−1.23455e9	−	8.96950e8i	−0.112526	−	0.0817547i	0.530099	−	0.847936i	$-0.322155\pi$
$739$	−1.23455e9	−	8.96950e8i	−0.112526	−	0.0817547i	−0.642625	+	0.766181i	$0.722155\pi$
$740$	6.09820e9	−	1.87683e10i	0.553210	−	1.70261i
$741$	−3.25489e9	−	1.00175e10i	−0.293881	−	0.904474i
$742$	−1.20027e9	+	8.72049e8i	−0.107861	+	0.0783659i
$743$	8.11364e9	−	5.89490e9i	0.725696	−	0.527249i	−0.162503	−	0.986708i	$-0.551957\pi$
$743$	8.11364e9	−	5.89490e9i	0.725696	−	0.527249i	0.888199	+	0.459459i	$0.151957\pi$
$744$	1.00236e10	+	3.08495e10i	0.892316	+	2.74627i
$745$	−2.74577e9	+	8.45061e9i	−0.243286	+	0.748757i
$746$	3.10341e10	+	2.25476e10i	2.73687	+	1.98845i
$747$	5.74259e8			0.0504064
$748$	6.66865e9	+	7.96736e9i	0.582616	+	0.696079i
$749$	1.47119e8			0.0127933
$750$	1.39897e10	+	1.01641e10i	1.21086	+	0.879741i
$751$	3.67670e9	−	1.13157e10i	0.316751	−	0.974860i	−0.658277	−	0.752776i	$-0.728714\pi$
$751$	3.67670e9	−	1.13157e10i	0.316751	−	0.974860i	0.975028	−	0.222084i	$-0.0712858\pi$
$752$	−1.04981e10	−	3.23099e10i	−0.900221	−	2.77060i
$753$	−7.77490e9	+	5.64879e9i	−0.663609	+	0.482140i
$754$	8.19745e9	−	5.95580e9i	0.696433	−	0.505988i
$755$	−1.35114e9	−	4.15839e9i	−0.114258	−	0.351650i
$756$	2.44015e8	−	7.51002e8i	0.0205396	−	0.0632142i
$757$	1.45892e10	+	1.05997e10i	1.22235	+	0.888089i	0.996293	−	0.0860253i	$-0.0274166\pi$
$757$	1.45892e10	+	1.05997e10i	1.22235	+	0.888089i	0.226057	+	0.974114i	$0.427417\pi$
$758$	−2.55711e10			−2.13259
$759$	−3.69420e9	+	5.89573e9i	−0.306672	+	0.489431i
$760$	−7.62250e10			−6.29868
$761$	8.78728e9	+	6.38433e9i	0.722783	+	0.525133i	0.887272	−	0.461246i	$-0.152598\pi$
$761$	8.78728e9	+	6.38433e9i	0.722783	+	0.525133i	−0.164489	+	0.986379i	$0.552598\pi$
$762$	6.22459e9	−	1.91573e10i	0.509646	−	1.56853i
$763$	−6.03875e8	−	1.85854e9i	−0.0492166	−	0.151473i
$764$	−1.46073e10	+	1.06128e10i	−1.18507	+	0.861001i
$765$	2.09497e9	−	1.52208e9i	0.169185	−	0.122920i
$766$	−4.97697e9	−	1.53175e10i	−0.400096	−	1.23137i
$767$	1.11432e9	−	3.42953e9i	0.0891715	−	0.274442i
$768$	5.01579e9	+	3.64419e9i	0.399554	+	0.290293i
$769$	−5.19102e9			−0.411633			−0.205817	−	0.978591i	$-0.565985\pi$
$769$	−5.19102e9			−0.411633			−0.205817	+	0.978591i	$0.565985\pi$
$770$	−3.84023e8	−	5.59105e9i	−0.0303138	−	0.441343i
$771$	−5.15378e9			−0.404981
$772$	−6.43760e9	−	4.67719e9i	−0.503575	−	0.365868i
$773$	−7.03651e9	+	2.16561e10i	−0.547935	+	1.68637i	0.165974	+	0.986130i	$0.446923\pi$
$773$	−7.03651e9	+	2.16561e10i	−0.547935	+	1.68637i	−0.713908	+	0.700239i	$0.753077\pi$
$774$	2.56909e9	+	7.90684e9i	0.199152	+	0.612928i
$775$	3.61172e10	−	2.62407e10i	2.78714	−	2.02497i
$776$	−2.17429e10	+	1.57971e10i	−1.67033	+	1.21356i
$777$	1.44628e8	+	4.45120e8i	0.0110606	+	0.0340411i
$778$	6.30209e9	−	1.93958e10i	0.479795	−	1.47666i
$779$	−4.70770e9	−	3.42035e9i	−0.356802	−	0.259232i
$780$	−3.66726e10			−2.76701
$781$	−8.54634e9	+	3.44067e9i	−0.641951	+	0.258443i
$782$	−9.24399e9			−0.691251
$783$	8.30372e8	+	6.03300e8i	0.0618168	+	0.0449125i
$784$	−1.01838e10	+	3.13424e10i	−0.754748	+	2.32288i
$785$	7.04336e9	+	2.16772e10i	0.519680	+	1.59941i
$786$	1.40018e10	−	1.01729e10i	1.02850	−	0.747251i
$787$	−1.58497e9	+	1.15155e9i	−0.115907	+	0.0842114i	−0.644229	−	0.764833i	$-0.722822\pi$
$787$	−1.58497e9	+	1.15155e9i	−0.115907	+	0.0842114i	0.528322	+	0.849044i	$0.322822\pi$
$788$	−1.34200e10	−	4.13025e10i	−0.977035	−	3.00701i
$789$	−3.16409e7	+	9.73807e7i	−0.00229340	+	0.00705835i
$790$	5.48086e10	+	3.98208e10i	3.95507	+	2.87353i
$791$	5.70999e8			0.0410221
$792$	1.14937e10	−	4.62723e9i	0.822093	−	0.330966i
$793$	2.41378e10			1.71886
$794$	−3.26550e10	−	2.37252e10i	−2.31514	−	1.68205i
$795$	−2.15678e9	+	6.63788e9i	−0.152237	+	0.468538i
$796$	−1.99120e9	−	6.12828e9i	−0.139933	−	0.430668i
$797$	−3.03286e9	+	2.20350e9i	−0.212202	+	0.154173i	−0.688809	−	0.724943i	$-0.741866\pi$
$797$	−3.03286e9	+	2.20350e9i	−0.212202	+	0.154173i	0.476608	+	0.879116i	$0.341866\pi$
$798$	2.48203e9	−	1.80330e9i	0.172901	−	0.125620i
$799$	1.94154e9	+	5.97544e9i	0.134658	+	0.414435i
$800$	−1.60688e10	+	4.94548e10i	−1.10961	+	3.41502i
$801$	−2.00205e8	−	1.45458e8i	−0.0137645	−	0.0100005i
$802$	7.43139e9			0.508698
$803$	−9.84187e8	−	1.43289e10i	−0.0670769	−	0.976582i
$804$	−6.55832e9			−0.445037
$805$	2.85938e9	+	2.07746e9i	0.193191	+	0.140361i
$806$	−1.87363e10	+	5.76643e10i	−1.26041	+	3.87913i
$807$	4.72168e9	+	1.45318e10i	0.316256	+	0.973337i
$808$	8.65136e9	−	6.28558e9i	0.576959	−	0.419185i
$809$	1.94352e10	−	1.41205e10i	1.29053	−	0.937628i	0.290719	−	0.956809i	$-0.406106\pi$
$809$	1.94352e10	−	1.41205e10i	1.29053	−	0.937628i	0.999816	+	0.0191804i	$0.00610568\pi$
$810$	−1.61945e9	−	4.98416e9i	−0.107071	−	0.329530i
$811$	−2.03051e9	+	6.24926e9i	−0.133669	+	0.411392i	−0.995381	−	0.0960069i	$-0.969393\pi$
$811$	−2.03051e9	+	6.24926e9i	−0.133669	+	0.411392i	0.861711	+	0.507399i	$0.169393\pi$
$812$	1.69248e9	+	1.22966e9i	0.110938	+	0.0806009i
$813$	−2.73919e8			−0.0178774
$814$	−6.61729e9	+	1.05608e10i	−0.430026	+	0.686297i
$815$	−6.15984e9			−0.398582
$816$	6.73742e9	+	4.89502e9i	0.434088	+	0.315384i
$817$	−7.07528e9	+	2.17755e10i	−0.453906	+	1.39698i
$818$	1.03063e10	+	3.17194e10i	0.658362	+	2.02623i
$819$	7.03642e8	−	5.11226e8i	0.0447567	−	0.0325177i
$820$	−1.63907e10	+	1.19085e10i	−1.03812	+	0.754241i
$821$	2.99459e9	+	9.21639e9i	0.188858	+	0.581246i	0.999993	−	0.00361267i	$-0.00114995\pi$
$821$	2.99459e9	+	9.21639e9i	0.188858	+	0.581246i	−0.811135	+	0.584859i	$0.801150\pi$
$822$	−7.17524e9	+	2.20831e10i	−0.450593	+	1.38678i
$823$	−1.37164e10	−	9.96555e9i	−0.857710	−	0.623163i	0.0695508	−	0.997578i	$-0.477843\pi$
$823$	−1.37164e10	−	9.96555e9i	−0.857710	−	0.623163i	−0.927261	+	0.374415i	$0.877843\pi$
$824$	5.77407e10			3.59531
$825$	−1.09451e10	−	1.30766e10i	−0.678625	−	0.810786i
$826$	1.05032e9			0.0648475
$827$	7.05859e8	+	5.12837e8i	0.0433959	+	0.0315290i	0.609272	−	0.792961i	$-0.291462\pi$
$827$	7.05859e8	+	5.12837e8i	0.0433959	+	0.0315290i	−0.565876	+	0.824490i	$0.691462\pi$
$828$	−4.09787e9	+	1.26119e10i	−0.250872	+	0.772104i
$829$	−8.46059e9	−	2.60390e10i	−0.515774	−	1.58739i	−0.781869	−	0.623443i	$-0.785733\pi$
$829$	−8.46059e9	−	2.60390e10i	−0.515774	−	1.58739i	0.266095	−	0.963947i	$-0.414267\pi$
$830$	6.28447e9	−	4.56594e9i	0.381501	−	0.277177i
$831$	−4.52407e9	+	3.28693e9i	−0.273480	+	0.198695i
$832$	−6.85388e9	−	2.10941e10i	−0.412577	−	1.26978i
$833$	1.88340e9	−	5.79651e9i	0.112898	−	0.347463i
$834$	−9.10836e9	−	6.61761e9i	−0.543700	−	0.395021i
$835$	−3.36011e10			−1.99733
$836$	5.61709e10	+	1.40787e10i	3.32498	+	0.833375i
$837$	−6.14179e9			−0.362039
$838$	−4.76103e10	−	3.45909e10i	−2.79477	−	2.03052i
$839$	9.76124e9	−	3.00420e10i	0.570608	−	1.75615i	−0.0800609	−	0.996790i	$-0.525511\pi$
$839$	9.76124e9	−	3.00420e10i	0.570608	−	1.75615i	0.650669	−	0.759361i	$-0.274489\pi$
$840$	−1.94500e9	−	5.98611e9i	−0.113225	−	0.348471i
$841$	1.17555e10	−	8.54090e9i	0.681485	−	0.495128i
$842$	−2.82384e10	+	2.05164e10i	−1.63022	+	1.18443i
$843$	−1.70947e9	−	5.26122e9i	−0.0982801	−	0.302475i
$844$	1.81301e10	−	5.57986e10i	1.03801	−	3.19466i
$845$	−8.80289e9	−	6.39568e9i	−0.501911	−	0.364660i
$846$	1.27154e10			0.721993
$847$	−4.41746e8	+	2.46956e9i	−0.0249793	+	0.139646i
$848$	−2.24460e10			−1.26402
$849$	5.08270e9	+	3.69279e9i	0.285047	+	0.207099i
$850$	7.00133e9	−	2.15479e10i	0.391034	−	1.20348i
$851$	−2.42881e9	−	7.47512e9i	−0.135095	−	0.415781i
$852$	−1.42062e10	+	1.03214e10i	−0.786936	+	0.571743i
$853$	−1.17972e10	+	8.57118e9i	−0.650816	+	0.472845i	−0.863549	−	0.504265i	$-0.831764\pi$
$853$	−1.17972e10	+	8.57118e9i	−0.650816	+	0.472845i	0.212733	+	0.977110i	$0.431764\pi$
$854$	2.17258e9	+	6.68652e9i	0.119364	+	0.367365i
$855$	4.45998e9	−	1.37264e10i	0.244034	−	0.751061i
$856$	3.55951e9	+	2.58614e9i	0.193969	+	0.140927i
$857$	−1.08310e10			−0.587807			−0.293904	−	0.955835i	$-0.594954\pi$
$857$	−1.08310e10			−0.587807			−0.293904	+	0.955835i	$0.594954\pi$
$858$	2.24650e10	+	5.63064e9i	1.21423	+	0.304335i
$859$	1.75418e9			0.0944276			0.0472138	−	0.998885i	$-0.484966\pi$
$859$	1.75418e9			0.0944276			0.0472138	+	0.998885i	$0.484966\pi$
$860$	6.44922e10	+	4.68564e10i	3.45751	+	2.51202i
$861$	1.48482e8	−	4.56981e8i	0.00792800	−	0.0243999i
$862$	−5.48264e9	−	1.68738e10i	−0.291551	−	0.897301i
$863$	1.76943e10	−	1.28557e10i	0.937122	−	0.680859i	−0.0106041	−	0.999944i	$-0.503375\pi$
$863$	1.76943e10	−	1.28557e10i	0.937122	−	0.680859i	0.947726	+	0.319085i	$0.103375\pi$
$864$	5.78759e9	−	4.20493e9i	0.305281	−	0.221800i
$865$	3.71356e9	+	1.14292e10i	0.195090	+	0.600425i
$866$	1.49957e10	−	4.61520e10i	0.784610	−	2.41478i
$867$	7.71719e9	+	5.60687e9i	0.402154	+	0.292182i
$868$	−1.25183e10			−0.649723
$869$	−1.94653e10	−	2.32562e10i	−1.00622	−	1.20218i
$870$	1.38841e10			0.714826
$871$	−5.84399e9	−	4.24591e9i	−0.299672	−	0.217724i
$872$	1.80597e10	−	5.55821e10i	0.922367	−	2.83875i
$873$	−1.57252e9	−	4.83971e9i	−0.0799918	−	0.246189i
$874$	−4.16819e10	+	3.02837e10i	−2.11182	+	1.53433i
$875$	−3.18137e9	+	2.31140e9i	−0.160541	+	0.116640i
$876$	−8.45941e9	−	2.60354e10i	−0.425183	−	1.30858i
$877$	−9.16055e9	+	2.81933e10i	−0.458588	+	1.41139i	0.408282	+	0.912856i	$0.366128\pi$
$877$	−9.16055e9	+	2.81933e10i	−0.458588	+	1.41139i	−0.866870	+	0.498534i	$0.833872\pi$
$878$	−5.79131e9	−	4.20763e9i	−0.288766	−	0.209801i
$879$	−3.01344e7			−0.00149659
$880$	4.50194e10	−	7.18484e10i	2.22695	−	3.55409i
$881$	−1.75050e10			−0.862474			−0.431237	−	0.902239i	$-0.641923\pi$
$881$	−1.75050e10			−0.862474			−0.431237	+	0.902239i	$0.641923\pi$
$882$	−9.97892e9	−	7.25011e9i	−0.489715	−	0.355799i
$883$	−5.82121e9	+	1.79158e10i	−0.284545	+	0.875739i	0.701990	+	0.712187i	$0.252295\pi$
$883$	−5.82121e9	+	1.79158e10i	−0.284545	+	0.875739i	−0.986535	+	0.163552i	$0.947705\pi$
$884$	6.74023e9	+	2.07443e10i	0.328165	+	1.00999i
$885$	3.99744e9	−	2.90431e9i	0.193857	−	0.140845i
$886$	−9.07812e9	+	6.59564e9i	−0.438508	+	0.318595i
$887$	8.83806e9	+	2.72008e10i	0.425230	+	1.30872i	0.902773	+	0.430116i	$0.141527\pi$
$887$	8.83806e9	+	2.72008e10i	0.425230	+	1.30872i	−0.477543	+	0.878608i	$0.658473\pi$
$888$	−4.32531e9	+	1.33119e10i	−0.207287	+	0.637964i
$889$	3.70588e9	+	2.69248e9i	0.176903	+	0.128528i
$890$	−3.34750e9			−0.159168
$891$	1.60758e8	+	2.34049e9i	0.00761377	+	0.110850i
$892$	8.79452e9			0.414892
$893$	2.83303e10	+	2.05832e10i	1.33129	+	0.967236i
$894$	3.30507e9	−	1.01719e10i	0.154703	−	0.476127i
$895$	9.58199e9	+	2.94903e10i	0.446761	+	1.37499i
$896$	3.81090e8	−	2.76878e8i	0.0176990	−	0.0128591i
$897$	−1.18166e10	+	8.58526e9i	−0.546662	+	0.397173i
$898$	−2.99243e9	−	9.20975e9i	−0.137898	−	0.424405i
$899$	5.02816e9	−	1.54751e10i	0.230808	−	0.710353i
$900$	−2.62949e10	−	1.91044e10i	−1.20233	−	0.873542i
$901$	4.15120e9			0.189076
$902$	1.18690e10	−	4.77836e9i	0.538509	−	0.216798i
$903$	−1.89061e9			−0.0854466
$904$	1.38152e10	+	1.00373e10i	0.621968	+	0.451886i
$905$	6.71454e9	−	2.06652e10i	0.301125	−	0.926766i
$906$	1.62636e9	+	5.00543e9i	0.0726555	+	0.223611i
$907$	−1.49936e10	+	1.08935e10i	−0.667237	+	0.484776i	−0.869099	−	0.494638i	$-0.835301\pi$
$907$	−1.49936e10	+	1.08935e10i	−0.667237	+	0.484776i	0.201862	+	0.979414i	$0.435301\pi$
$908$	−2.10986e10	+	1.53290e10i	−0.935305	+	0.679539i
$909$	6.25694e8	+	1.92569e9i	0.0276305	+	0.0850379i
$910$	3.63563e9	−	1.11893e10i	0.159932	−	0.492219i
$911$	−1.74521e9	−	1.26797e9i	−0.0764774	−	0.0555641i	0.548890	−	0.835895i	$-0.315051\pi$
$911$	−1.74521e9	−	1.26797e9i	−0.0764774	−	0.0555641i	−0.625367	+	0.780331i	$0.715051\pi$
$912$	4.64158e10			2.02621
$913$	−3.22580e9	+	1.29867e9i	−0.140278	+	0.0564745i
$914$	2.24456e9			0.0972341
$915$	2.67579e10	+	1.94408e10i	1.15472	+	0.838957i
$916$	−3.37108e10	+	1.03751e11i	−1.44922	+	4.46024i
$917$	1.21623e9	+	3.74316e9i	0.0520861	+	0.160304i
$918$	−2.52170e9	+	1.83212e9i	−0.107583	+	0.0781637i
$919$	1.41602e10	−	1.02880e10i	0.601819	−	0.437247i	−0.244705	−	0.969598i	$-0.578691\pi$
$919$	1.41602e10	−	1.02880e10i	0.601819	−	0.437247i	0.846524	+	0.532350i	$0.178691\pi$
$920$	3.26634e10	+	1.00528e11i	1.38294	+	4.25625i
$921$	−2.21254e8	+	6.80949e8i	−0.00933216	+	0.0287214i
$922$	−4.84034e10	−	3.51671e10i	−2.03385	−	1.47767i
$923$	−1.93410e10			−0.809606
$924$	3.27660e8	+	4.77045e9i	0.0136638	+	0.198933i
$925$	1.92642e10			0.800302
$926$	−4.15931e10	−	3.02191e10i	−1.72140	−	1.25067i
$927$	−3.37845e9	+	1.03978e10i	−0.139296	+	0.428709i
$928$	5.85673e9	+	1.80252e10i	0.240568	+	0.740391i
$929$	2.73266e9	−	1.98539e9i	0.111823	−	0.0812440i	−0.530468	−	0.847705i	$-0.677984\pi$
$929$	2.73266e9	−	1.98539e9i	0.111823	−	0.0812440i	0.642291	+	0.766461i	$0.277984\pi$
$930$	−6.72133e10	+	4.88333e10i	−2.74009	+	1.99079i
$931$	−1.04972e10	−	3.23070e10i	−0.426333	−	1.31212i
$932$	7.00853e9	−	2.15700e10i	0.283577	−	0.872761i
$933$	1.17122e10	+	8.50942e9i	0.472121	+	0.343016i
$934$	4.19619e10			1.68516
$935$	−8.32595e9	+	1.32878e10i	−0.333114	+	0.531632i
$936$	2.60111e10			1.03679
$937$	1.24803e10	+	9.06745e9i	0.495605	+	0.360078i	0.807336	−	0.590092i	$-0.200909\pi$
$937$	1.24803e10	+	9.06745e9i	0.495605	+	0.360078i	−0.311731	+	0.950170i	$0.600909\pi$
$938$	6.50175e8	−	2.00103e9i	0.0257229	−	0.0791670i
$939$	4.09347e9	+	1.25984e10i	0.161347	+	0.496576i
$940$	9.86371e10	−	7.16640e10i	3.87340	−	2.81419i
$941$	−2.94129e10	+	2.13697e10i	−1.15073	+	0.836054i	−0.988578	−	0.150711i	$-0.951844\pi$
$941$	−2.94129e10	+	2.13697e10i	−1.15073	+	0.836054i	−0.162152	+	0.986766i	$0.551844\pi$
$942$	−8.47805e9	−	2.60928e10i	−0.330459	−	1.01705i
$943$	−2.49353e9	+	7.67430e9i	−0.0968331	+	0.298022i
$944$	1.28558e10	+	9.34027e9i	0.497389	+	0.361374i
$945$	1.19177e9			0.0459388
$946$	−3.23125e10	−	3.86053e10i	−1.24094	−	1.48261i
$947$	1.66204e9			0.0635942			0.0317971	−	0.999494i	$-0.489877\pi$
$947$	1.66204e9			0.0635942			0.0317971	+	0.999494i	$0.489877\pi$
$948$	−4.67644e10	−	3.39763e10i	−1.78273	−	1.29523i
$949$	9.31750e9	−	2.86763e10i	0.353890	−	1.08916i
$950$	−3.90221e10	−	1.20098e11i	−1.47665	−	4.54467i
$951$	5.35374e9	−	3.88972e9i	0.201849	−	0.146652i
$952$	−3.02863e9	+	2.20043e9i	−0.113767	+	0.0826566i
$953$	−3.85915e9	−	1.18772e10i	−0.144433	−	0.444519i	0.852505	−	0.522720i	$-0.175083\pi$
$953$	−3.85915e9	−	1.18772e10i	−0.144433	−	0.444519i	−0.996938	+	0.0782005i	$0.975083\pi$
$954$	2.59610e9	−	7.98998e9i	0.0968060	−	0.297938i
$955$	−2.20458e10	−	1.60172e10i	−0.819056	−	0.595079i
$956$	2.57210e10			0.952106
$957$	−6.02881e9	−	1.51107e9i	−0.222351	−	0.0557303i
$958$	5.71114e10			2.09867
$959$	−4.27186e9	−	3.10369e9i	−0.156405	−	0.113635i
$960$	9.39147e9	−	2.89040e10i	0.342598	−	1.05441i
$961$	2.15858e10	+	6.64344e10i	0.784580	+	2.41469i
$962$	−2.11666e10	+	1.53785e10i	−0.766548	+	0.556930i
$963$	−6.73975e8	+	4.89671e8i	−0.0243193	+	0.0176690i
$964$	3.27682e10	+	1.00850e11i	1.17810	+	3.62582i
$965$	3.71112e9	−	1.14217e10i	0.132941	−	0.409151i
$966$	−3.44182e9	−	2.50063e9i	−0.122848	−	0.0892543i
$967$	−2.47524e10			−0.880290			−0.440145	−	0.897927i	$-0.645073\pi$
$967$	−2.47524e10			−0.880290			−0.440145	+	0.897927i	$0.645073\pi$
$968$	−5.40993e10	+	5.19853e10i	−1.91702	+	1.84212i
$969$	−8.58421e9			−0.303087
$970$	−5.56895e10	−	4.04608e10i	−1.95917	−	1.42342i
$971$	4.30590e9	−	1.32522e10i	0.150937	−	0.464537i	−0.846789	−	0.531928i	$-0.821468\pi$
$971$	4.30590e9	−	1.32522e10i	0.150937	−	0.464537i	0.997727	+	0.0673914i	$0.0214676\pi$
$972$	1.38177e9	+	4.25264e9i	0.0482617	+	0.148534i
$973$	2.07131e9	−	1.50490e9i	0.0720859	−	0.0523735i
$974$	−2.30699e10	+	1.67612e10i	−0.799997	+	0.581232i
$975$	−1.10626e10	−	3.40471e10i	−0.382243	−	1.17642i
$976$	−3.28695e10	+	1.01162e11i	−1.13167	+	3.48291i
$977$	2.21555e10	+	1.60969e10i	0.760066	+	0.552221i	0.898931	−	0.438091i	$-0.144345\pi$
$977$	2.21555e10	+	1.60969e10i	0.760066	+	0.552221i	−0.138864	+	0.990311i	$0.544345\pi$
$978$	7.41456e9			0.253454
$979$	1.45357e9	+	3.64323e8i	0.0495103	+	0.0124093i
$980$	−1.18271e11			−4.01410
$981$	8.95240e9	+	6.50430e9i	0.302760	+	0.219968i
$982$	1.84090e10	−	5.66570e10i	0.620353	−	1.90925i
$983$	−2.35146e9	−	7.23705e9i	−0.0789588	−	0.243010i	0.903784	−	0.427990i	$-0.140778\pi$
$983$	−2.35146e9	−	7.23705e9i	−0.0789588	−	0.243010i	−0.982742	+	0.184980i	$0.940778\pi$
$984$	1.16256e10	−	8.44646e9i	0.388983	−	0.282613i
$985$	5.30253e10	−	3.85252e10i	1.76790	−	1.28445i
$986$	−2.55182e9	−	7.85370e9i	−0.0847776	−	0.260919i
$987$	−8.93546e8	+	2.75005e9i	−0.0295806	+	0.0910397i
$988$	9.83514e10	+	7.14565e10i	3.24438	+	2.35718i
$989$	3.17499e10			1.04365
$990$	2.03685e10	+	2.43353e10i	0.667170	+	0.797100i
$991$	4.64844e10			1.51722			0.758612	−	0.651542i	$-0.225878\pi$
$991$	4.64844e10			1.51722			0.758612	+	0.651542i	$0.225878\pi$
$992$	−9.17509e10	−	6.66609e10i	−2.98414	−	2.16811i
$993$	9.82497e8	−	3.02381e9i	0.0318426	−	0.0980015i
$994$	−1.74084e9	−	5.35774e9i	−0.0562219	−	0.173033i
$995$	7.86767e9	−	5.71620e9i	0.253201	−	0.183961i
$996$	−5.36210e9	+	3.89579e9i	−0.171960	+	0.124936i
$997$	1.23161e10	+	3.79051e10i	0.393586	+	1.21133i	0.930057	+	0.367415i	$0.119757\pi$
$997$	1.23161e10	+	3.79051e10i	0.393586	+	1.21133i	−0.536470	+	0.843919i	$0.680243\pi$
$998$	−2.29328e10	+	7.05798e10i	−0.730297	+	2.24762i
$999$	−2.14410e9	−	1.55778e9i	−0.0680403	−	0.0494342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.e.b.4.7	✓	28
3.2	odd	2		99.8.f.b.37.1		28
11.3	even	5	inner	33.8.e.b.25.7	yes	28
11.5	even	5		363.8.a.o.1.1		14
11.6	odd	10		363.8.a.r.1.14		14
33.14	odd	10		99.8.f.b.91.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.b.4.7	✓	28	1.1	even	1	trivial
33.8.e.b.25.7	yes	28	11.3	even	5	inner
99.8.f.b.37.1		28	3.2	odd	2
99.8.f.b.91.1		28	33.14	odd	10
363.8.a.o.1.1		14	11.5	even	5
363.8.a.r.1.14		14	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(16.9629 + 12.3242i) q^{2} +(8.34346 - 25.6785i) q^{3} +(96.2976 + 296.374i) q^{4} +(-380.493 + 276.444i) q^{5} +(457.997 - 332.754i) q^{6} +(39.7826 + 122.438i) q^{7} +(-1189.75 + 3661.68i) q^{8} +(-589.773 - 428.495i) q^{9} +O(q^{10})\)	\(q+(16.9629 + 12.3242i) q^{2} +(8.34346 - 25.6785i) q^{3} +(96.2976 + 296.374i) q^{4} +(-380.493 + 276.444i) q^{5} +(457.997 - 332.754i) q^{6} +(39.7826 + 122.438i) q^{7} +(-1189.75 + 3661.68i) q^{8} +(-589.773 - 428.495i) q^{9} -9861.22 q^{10} +(4281.98 + 1073.24i) q^{11} +8413.89 q^{12} +(7497.45 + 5447.22i) q^{13} +(-834.131 + 2567.19i) q^{14} +(3924.06 + 12077.0i) q^{15} +(-33039.0 + 24004.2i) q^{16} +(6110.28 - 4439.37i) q^{17} +(-4723.36 - 14537.0i) q^{18} +(13008.2 - 40035.0i) q^{19} +(-118571. - 86147.2i) q^{20} +3475.96 q^{21} +(59407.7 + 70977.3i) q^{22} -58373.4 q^{23} +(84100.0 + 61102.2i) q^{24} +(44211.5 - 136069. i) q^{25} +(60045.4 + 184801. i) q^{26} +(-15923.9 + 11569.4i) q^{27} +(-32456.5 + 23581.0i) q^{28} +(-16114.1 - 49594.1i) q^{29} +(-82276.7 + 253222. i) q^{30} +(252442. + 183410. i) q^{31} -363454. q^{32} +(63285.7 - 101000. i) q^{33} +158360. q^{34} +(-48984.3 - 35589.2i) q^{35} +(70200.9 - 216056. i) q^{36} +(41608.2 + 128057. i) q^{37} +(714057. - 518793. i) q^{38} +(202431. - 147075. i) q^{39} +(-559559. - 1.72215e6i) q^{40} +(42716.9 - 131469. i) q^{41} +(58962.2 + 42838.5i) q^{42} -543911. q^{43} +(94264.8 + 1.37242e6i) q^{44} +342860. q^{45} +(-990180. - 719408. i) q^{46} +(-257065. + 791164. i) q^{47} +(340734. + 1.04867e6i) q^{48} +(652852. - 474325. i) q^{49} +(2.42690e6 - 1.76325e6i) q^{50} +(-63015.8 - 193943. i) q^{51} +(-892425. + 2.74660e6i) q^{52} +(444660. + 323064. i) q^{53} -412698. q^{54} +(-1.92595e6 + 775369. i) q^{55} -495661. q^{56} +(-919507. - 668061. i) q^{57} +(337868. - 1.03985e6i) q^{58} +(-120241. - 370065. i) q^{59} +(-3.20143e6 + 2.32597e6i) q^{60} +(2.10717e6 - 1.53095e6i) q^{61} +(2.02175e6 + 6.22230e6i) q^{62} +(29001.5 - 89257.4i) q^{63} +(-1.93623e6 - 1.40675e6i) q^{64} -4.35858e6 q^{65} +(2.31826e6 - 933307. i) q^{66} -779463. q^{67} +(1.90412e6 + 1.38342e6i) q^{68} +(-487036. + 1.49894e6i) q^{69} +(-392305. - 1.20739e6i) q^{70} +(-1.68842e6 + 1.22671e6i) q^{71} +(2.27070e6 - 1.64976e6i) q^{72} +(-1.00541e6 - 3.09433e6i) q^{73} +(-872410. + 2.68500e6i) q^{74} +(-3.12518e6 - 2.27057e6i) q^{75} +1.31180e7 q^{76} +(38942.8 + 566974. i) q^{77} +5.24640e6 q^{78} +(-5.55799e6 - 4.03812e6i) q^{79} +(5.93527e6 - 1.82669e7i) q^{80} +(164224. + 505430. i) q^{81} +(2.34486e6 - 1.70364e6i) q^{82} +(-637291. + 463019. i) q^{83} +(334726. + 1.03018e6i) q^{84} +(-1.09768e6 + 3.37830e6i) q^{85} +(-9.22628e6 - 6.70328e6i) q^{86} -1.40795e6 q^{87} +(-9.02436e6 + 1.44024e7i) q^{88} +339461. q^{89} +(5.81589e6 + 4.22549e6i) q^{90} +(-368680. + 1.13468e6i) q^{91} +(-5.62122e6 - 1.73003e7i) q^{92} +(6.81593e6 - 4.95206e6i) q^{93} +(-1.41111e7 + 1.02523e7i) q^{94} +(6.11794e6 + 1.88291e7i) q^{95} +(-3.03246e6 + 9.33296e6i) q^{96} +(5.64733e6 + 4.10302e6i) q^{97} +1.69199e7 q^{98} +(-2.06552e6 - 2.46778e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9	\( 28 q - 6 q^{2} - 189 q^{3} + 160 q^{4} + 773 q^{5} - 162 q^{6} + 1289 q^{7} + 2956 q^{8} - 5103 q^{9} - 10640 q^{10} + 13209 q^{11} + 45630 q^{12} + 13499 q^{13} - 3318 q^{14} - 22734 q^{15} - 113196 q^{16} + 30296 q^{17} + 21141 q^{18} - 6858 q^{19} + 76725 q^{20} - 177012 q^{21} - 48859 q^{22} - 166984 q^{23} + 44442 q^{24} + 99832 q^{25} + 340424 q^{26} - 137781 q^{27} + 657387 q^{28} + 192014 q^{29} - 184410 q^{30} + 396068 q^{31} - 303498 q^{32} + 168453 q^{33} - 1229124 q^{34} - 725859 q^{35} + 116640 q^{36} + 811053 q^{37} + 1548798 q^{38} + 364473 q^{39} - 1427263 q^{40} + 1041497 q^{41} + 300024 q^{42} - 5265288 q^{43} - 5341085 q^{44} + 100602 q^{45} + 1198651 q^{46} + 1667505 q^{47} + 730593 q^{48} + 2968140 q^{49} + 11247432 q^{50} + 340767 q^{51} + 2325763 q^{52} - 1625736 q^{53} - 905418 q^{54} - 8338690 q^{55} - 18201906 q^{56} + 1546479 q^{57} + 14965553 q^{58} - 2587454 q^{59} + 2071575 q^{60} + 5801619 q^{61} + 15631121 q^{62} + 939681 q^{63} - 3732846 q^{64} - 15368174 q^{65} - 235683 q^{66} - 7141262 q^{67} + 17394545 q^{68} - 5063553 q^{69} - 4329200 q^{70} + 3569199 q^{71} + 1199934 q^{72} + 125008 q^{73} - 13691530 q^{74} - 11794221 q^{75} - 19690428 q^{76} - 6038739 q^{77} + 12684438 q^{78} + 17075485 q^{79} + 26606436 q^{80} - 3720087 q^{81} + 19886007 q^{82} - 4645575 q^{83} + 1074519 q^{84} + 12002715 q^{85} - 12296287 q^{86} - 12259512 q^{87} - 50905990 q^{88} + 9601664 q^{89} + 8857350 q^{90} - 14129477 q^{91} - 90776021 q^{92} + 10693836 q^{93} + 1047679 q^{94} + 58935661 q^{95} + 26156304 q^{96} - 22170261 q^{97} + 140532178 q^{98} - 6579954 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 189 * q^3 + 160 * q^4 + 773 * q^5 - 162 * q^6 + 1289 * q^7 + 2956 * q^8 - 5103 * q^9 - 10640 * q^10 + 13209 * q^11 + 45630 * q^12 + 13499 * q^13 - 3318 * q^14 - 22734 * q^15 - 113196 * q^16 + 30296 * q^17 + 21141 * q^18 - 6858 * q^19 + 76725 * q^20 - 177012 * q^21 - 48859 * q^22 - 166984 * q^23 + 44442 * q^24 + 99832 * q^25 + 340424 * q^26 - 137781 * q^27 + 657387 * q^28 + 192014 * q^29 - 184410 * q^30 + 396068 * q^31 - 303498 * q^32 + 168453 * q^33 - 1229124 * q^34 - 725859 * q^35 + 116640 * q^36 + 811053 * q^37 + 1548798 * q^38 + 364473 * q^39 - 1427263 * q^40 + 1041497 * q^41 + 300024 * q^42 - 5265288 * q^43 - 5341085 * q^44 + 100602 * q^45 + 1198651 * q^46 + 1667505 * q^47 + 730593 * q^48 + 2968140 * q^49 + 11247432 * q^50 + 340767 * q^51 + 2325763 * q^52 - 1625736 * q^53 - 905418 * q^54 - 8338690 * q^55 - 18201906 * q^56 + 1546479 * q^57 + 14965553 * q^58 - 2587454 * q^59 + 2071575 * q^60 + 5801619 * q^61 + 15631121 * q^62 + 939681 * q^63 - 3732846 * q^64 - 15368174 * q^65 - 235683 * q^66 - 7141262 * q^67 + 17394545 * q^68 - 5063553 * q^69 - 4329200 * q^70 + 3569199 * q^71 + 1199934 * q^72 + 125008 * q^73 - 13691530 * q^74 - 11794221 * q^75 - 19690428 * q^76 - 6038739 * q^77 + 12684438 * q^78 + 17075485 * q^79 + 26606436 * q^80 - 3720087 * q^81 + 19886007 * q^82 - 4645575 * q^83 + 1074519 * q^84 + 12002715 * q^85 - 12296287 * q^86 - 12259512 * q^87 - 50905990 * q^88 + 9601664 * q^89 + 8857350 * q^90 - 14129477 * q^91 - 90776021 * q^92 + 10693836 * q^93 + 1047679 * q^94 + 58935661 * q^95 + 26156304 * q^96 - 22170261 * q^97 + 140532178 * q^98 - 6579954 * q^99

Introduction

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