LMFDB - Embedded newform 49.4.e.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			15.1
Character	$\chi$	$=$	49.15
Dual form			49.4.e.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16701 + 5.11301i) q^{2} +(-1.24065 + 1.55573i) q^{3} +(-17.5732 - 8.46282i) q^{4} +(0.849213 - 1.06488i) q^{5} +(-6.50660 - 8.15902i) q^{6} +(-18.2375 + 3.22369i) q^{7} +(37.6195 - 47.1733i) q^{8} +(5.12699 + 22.4628i) q^{9} +O(q^{10})$	\(q+(-1.16701 + 5.11301i) q^{2} +(-1.24065 + 1.55573i) q^{3} +(-17.5732 - 8.46282i) q^{4} +(0.849213 - 1.06488i) q^{5} +(-6.50660 - 8.15902i) q^{6} +(-18.2375 + 3.22369i) q^{7} +(37.6195 - 47.1733i) q^{8} +(5.12699 + 22.4628i) q^{9} +(4.45370 + 5.58476i) q^{10} +(4.10883 - 18.0020i) q^{11} +(34.9681 - 16.8397i) q^{12} +(-4.72905 + 20.7193i) q^{13} +(4.80067 - 97.0108i) q^{14} +(0.603085 + 2.64229i) q^{15} +(100.007 + 125.405i) q^{16} +(-113.591 + 54.7028i) q^{17} -120.836 q^{18} -50.2875 q^{19} +(-23.9353 + 11.5266i) q^{20} +(17.6112 - 32.3721i) q^{21} +(87.2491 + 42.0170i) q^{22} +(74.0563 + 35.6637i) q^{23} +(26.7162 + 117.051i) q^{24} +(27.4023 + 120.057i) q^{25} +(-100.419 - 48.3593i) q^{26} +(-89.7123 - 43.2031i) q^{27} +(347.774 + 97.6904i) q^{28} +(-52.6355 + 25.3479i) q^{29} -14.2139 q^{30} +319.654 q^{31} +(-323.012 + 155.554i) q^{32} +(22.9085 + 28.7264i) q^{33} +(-147.133 - 644.633i) q^{34} +(-12.0547 + 22.1584i) q^{35} +(100.001 - 438.133i) q^{36} +(-240.081 + 115.617i) q^{37} +(58.6861 - 257.121i) q^{38} +(-26.3665 - 33.0625i) q^{39} +(-18.2870 - 80.1204i) q^{40} +(153.419 - 192.382i) q^{41} +(144.966 + 127.825i) q^{42} +(225.042 + 282.193i) q^{43} +(-224.553 + 281.580i) q^{44} +(28.2741 + 13.6161i) q^{45} +(-268.773 + 337.031i) q^{46} +(-31.0669 + 136.113i) q^{47} -319.170 q^{48} +(322.216 - 117.584i) q^{49} -645.833 q^{50} +(55.8248 - 244.584i) q^{51} +(258.448 - 324.084i) q^{52} +(276.076 + 132.951i) q^{53} +(325.593 - 408.281i) q^{54} +(-15.6806 - 19.6629i) q^{55} +(-534.014 + 981.599i) q^{56} +(62.3892 - 78.2336i) q^{57} +(-68.1779 - 298.707i) q^{58} +(-350.804 - 439.895i) q^{59} +(11.7631 - 51.5373i) q^{60} +(-561.994 + 270.642i) q^{61} +(-373.040 + 1634.39i) q^{62} +(-165.917 - 393.139i) q^{63} +(-132.856 - 582.079i) q^{64} +(18.0476 + 22.6310i) q^{65} +(-173.613 + 83.6075i) q^{66} +923.511 q^{67} +2459.11 q^{68} +(-147.361 + 70.9653i) q^{69} +(-99.2280 - 87.4950i) q^{70} +(-176.608 - 85.0501i) q^{71} +(1252.52 + 603.182i) q^{72} +(-13.8656 - 60.7491i) q^{73} +(-310.974 - 1362.47i) q^{74} +(-220.773 - 106.319i) q^{75} +(883.713 + 425.574i) q^{76} +(-16.9023 + 341.557i) q^{77} +(199.819 - 96.2278i) q^{78} -432.393 q^{79} +218.468 q^{80} +(-381.973 + 183.948i) q^{81} +(804.608 + 1008.95i) q^{82} +(-166.433 - 729.192i) q^{83} +(-583.445 + 419.841i) q^{84} +(-38.2115 + 167.415i) q^{85} +(-1705.48 + 821.317i) q^{86} +(25.8678 - 113.334i) q^{87} +(-694.640 - 871.051i) q^{88} +(72.8537 + 319.193i) q^{89} +(-102.615 + 128.676i) q^{90} +(19.4536 - 393.114i) q^{91} +(-999.593 - 1253.45i) q^{92} +(-396.579 + 497.295i) q^{93} +(-659.691 - 317.691i) q^{94} +(-42.7048 + 53.5501i) q^{95} +(158.745 - 695.507i) q^{96} -1538.64 q^{97} +(225.180 + 1784.71i) q^{98} +425.441 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

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 $

$2$	−1.16701	+	5.11301i	−0.412601	+	1.80772i	0.159103	+	0.987262i	$0.449140\pi$
$2$	−1.16701	+	5.11301i	−0.412601	+	1.80772i	−0.571703	+	0.820460i	$0.693717\pi$
$3$	−1.24065	+	1.55573i	−0.238763	+	0.299400i	−0.886748	−	0.462254i	$-0.847041\pi$
$3$	−1.24065	+	1.55573i	−0.238763	+	0.299400i	0.647984	+	0.761654i	$0.275612\pi$
$4$	−17.5732	−	8.46282i	−2.19665	−	1.05785i
$5$	0.849213	−	1.06488i	0.0759559	−	0.0952457i	−0.742402	−	0.669955i	$-0.766313\pi$
$5$	0.849213	−	1.06488i	0.0759559	−	0.0952457i	0.818358	+	0.574709i	$0.194885\pi$
$6$	−6.50660	−	8.15902i	−0.442718	−	0.555151i
$7$	−18.2375	+	3.22369i	−0.984735	+	0.174063i
$7$	−18.2375	+	3.22369i	−0.984735	+	0.174063i
$8$	37.6195	−	47.1733i	1.66256	−	2.08479i
$9$	5.12699	+	22.4628i	0.189889	+	0.831956i
$10$	4.45370	+	5.58476i	0.140838	+	0.176606i
$11$	4.10883	−	18.0020i	0.112623	−	0.493436i	−0.886882	−	0.461996i	$-0.847134\pi$
$11$	4.10883	−	18.0020i	0.112623	−	0.493436i	0.999506	−	0.0314400i	$-0.0100093\pi$
$12$	34.9681	−	16.8397i	0.841201	−	0.405101i
$13$	−4.72905	+	20.7193i	−0.100892	+	0.442039i	0.899098	+	0.437747i	$0.144223\pi$
$13$	−4.72905	+	20.7193i	−0.100892	+	0.442039i	−0.999991	+	0.00429192i	$0.998634\pi$
$14$	4.80067	−	97.0108i	0.0916452	−	1.85195i
$15$	0.603085	+	2.64229i	0.0103811	+	0.0454824i
$16$	100.007	+	125.405i	1.56261	+	1.95945i
$17$	−113.591	+	54.7028i	−1.62059	+	0.780433i	−0.999993	−	0.00369931i	$-0.998822\pi$
$17$	−113.591	+	54.7028i	−1.62059	+	0.780433i	−0.620593	+	0.784133i	$0.713108\pi$
$18$	−120.836			−1.58229
$19$	−50.2875			−0.607197			−0.303598	−	0.952800i	$-0.598188\pi$
$19$	−50.2875			−0.607197			−0.303598	+	0.952800i	$0.598188\pi$
$20$	−23.9353	+	11.5266i	−0.267605	+	0.128872i
$21$	17.6112	−	32.3721i	0.183004	−	0.336389i
$22$	87.2491	+	42.0170i	0.845526	+	0.407184i
$23$	74.0563	+	35.6637i	0.671383	+	0.323321i	0.738334	−	0.674435i	$-0.235613\pi$
$23$	74.0563	+	35.6637i	0.671383	+	0.323321i	−0.0669509	+	0.997756i	$0.521327\pi$
$24$	26.7162	+	117.051i	0.227226	+	0.995541i
$25$	27.4023	+	120.057i	0.219218	+	0.960459i
$26$	−100.419	−	48.3593i	−0.757455	−	0.364771i
$27$	−89.7123	−	43.2031i	−0.639449	−	0.307943i
$28$	347.774	+	97.6904i	2.34725	+	0.659348i
$29$	−52.6355	+	25.3479i	−0.337040	+	0.162310i	−0.594746	−	0.803913i	$-0.702748\pi$
$29$	−52.6355	+	25.3479i	−0.337040	+	0.162310i	0.257706	+	0.966223i	$0.417033\pi$
$30$	−14.2139			−0.0865028
$31$	319.654			1.85199			0.925993	−	0.377541i	$-0.123230\pi$
$31$	319.654			1.85199			0.925993	+	0.377541i	$0.123230\pi$
$32$	−323.012	+	155.554i	−1.78441	+	0.859325i
$33$	22.9085	+	28.7264i	0.120844	+	0.151534i
$34$	−147.133	−	644.633i	−0.742151	−	3.25158i
$35$	−12.0547	+	22.1584i	−0.0582177	+	0.107013i
$36$	100.001	−	438.133i	0.462967	−	2.02839i
$37$	−240.081	+	115.617i	−1.06673	+	0.513712i	−0.883052	−	0.469274i	$-0.844516\pi$
$37$	−240.081	+	115.617i	−1.06673	+	0.513712i	−0.183681	+	0.982986i	$0.558801\pi$
$38$	58.6861	−	257.121i	0.250530	−	1.09764i
$39$	−26.3665	−	33.0625i	−0.108257	−	0.135750i
$40$	−18.2870	−	80.1204i	−0.0722855	−	0.316704i
$41$	153.419	−	192.382i	0.584392	−	0.732805i	−0.398463	−	0.917184i	$-0.630456\pi$
$41$	153.419	−	192.382i	0.584392	−	0.732805i	0.982855	+	0.184380i	$0.0590277\pi$
$42$	144.966	+	127.825i	0.532591	+	0.469615i
$43$	225.042	+	282.193i	0.798105	+	1.00079i	0.999772	+	0.0213378i	$0.00679255\pi$
$43$	225.042	+	282.193i	0.798105	+	1.00079i	−0.201667	+	0.979454i	$0.564636\pi$
$44$	−224.553	+	281.580i	−0.769377	+	0.964768i
$45$	28.2741	+	13.6161i	0.0936634	+	0.0451059i
$46$	−268.773	+	337.031i	−0.861488	+	1.08027i
$47$	−31.0669	+	136.113i	−0.0964164	+	0.422428i	−0.999982	−	0.00602220i	$-0.998083\pi$
$47$	−31.0669	+	136.113i	−0.0964164	+	0.422428i	0.903565	+	0.428450i	$0.140940\pi$
$48$	−319.170			−0.959753
$49$	322.216	−	117.584i	0.939404	−	0.342811i
$50$	−645.833			−1.82669
$51$	55.8248	−	244.584i	0.153275	−	0.671542i
$52$	258.448	−	324.084i	0.689237	−	0.864276i
$53$	276.076	+	132.951i	0.715509	+	0.344571i	0.755966	−	0.654610i	$-0.227167\pi$
$53$	276.076	+	132.951i	0.715509	+	0.344571i	−0.0404576	+	0.999181i	$0.512882\pi$
$54$	325.593	−	408.281i	0.820512	−	1.02889i
$55$	−15.6806	−	19.6629i	−0.0384432	−	0.0482063i
$56$	−534.014	+	981.599i	−1.27430	+	2.34235i
$57$	62.3892	−	78.2336i	0.144976	−	0.181795i
$58$	−68.1779	−	298.707i	−0.154348	−	0.676244i
$59$	−350.804	−	439.895i	−0.774082	−	0.970668i	0.225912	−	0.974148i	$-0.427464\pi$
$59$	−350.804	−	439.895i	−0.774082	−	0.970668i	−0.999994	+	0.00348006i	$0.998892\pi$
$60$	11.7631	−	51.5373i	0.0253101	−	0.110891i
$61$	−561.994	+	270.642i	−1.17961	+	0.568068i	−0.917796	−	0.397052i	$-0.870033\pi$
$61$	−561.994	+	270.642i	−1.17961	+	0.568068i	−0.261809	+	0.965120i	$0.584319\pi$
$62$	−373.040	+	1634.39i	−0.764131	+	3.34788i
$63$	−165.917	−	393.139i	−0.331803	−	0.786204i
$64$	−132.856	−	582.079i	−0.259484	−	1.13687i
$65$	18.0476	+	22.6310i	0.0344389	+	0.0431850i
$66$	−173.613	+	83.6075i	−0.323792	+	0.155930i
$67$	923.511			1.68395			0.841976	−	0.539515i	$-0.181392\pi$
$67$	923.511			1.68395			0.841976	+	0.539515i	$0.181392\pi$
$68$	2459.11			4.38545
$69$	−147.361	+	70.9653i	−0.257104	+	0.123815i
$70$	−99.2280	−	87.4950i	−0.169429	−	0.149395i
$71$	−176.608	−	85.0501i	−0.295205	−	0.142163i	0.280419	−	0.959878i	$-0.409527\pi$
$71$	−176.608	−	85.0501i	−0.295205	−	0.142163i	−0.575624	+	0.817714i	$0.695241\pi$
$72$	1252.52	+	603.182i	2.05015	+	0.987301i
$73$	−13.8656	−	60.7491i	−0.0222308	−	0.0973993i	0.962595	−	0.270943i	$-0.0873354\pi$
$73$	−13.8656	−	60.7491i	−0.0222308	−	0.0973993i	−0.984826	+	0.173543i	$0.944478\pi$
$74$	−310.974	−	1362.47i	−0.488513	−	2.14032i
$75$	−220.773	−	106.319i	−0.339903	−	0.163689i
$76$	883.713	+	425.574i	1.33380	+	0.642324i
$77$	−16.9023	+	341.557i	−0.0250155	+	0.505507i
$78$	199.819	−	96.2278i	0.290065	−	0.139688i
$79$	−432.393			−0.615798			−0.307899	−	0.951419i	$-0.599626\pi$
$79$	−432.393			−0.615798			−0.307899	+	0.951419i	$0.599626\pi$
$80$	218.468			0.305319
$81$	−381.973	+	183.948i	−0.523968	+	0.252330i
$82$	804.608	+	1008.95i	1.08359	+	1.35877i
$83$	−166.433	−	729.192i	−0.220102	−	0.964329i	−0.957401	−	0.288762i	$-0.906756\pi$
$83$	−166.433	−	729.192i	−0.220102	−	0.964329i	0.737299	−	0.675566i	$-0.236101\pi$
$84$	−583.445	+	419.841i	−0.757847	+	0.545339i
$85$	−38.2115	+	167.415i	−0.0487602	+	0.213632i
$86$	−1705.48	+	821.317i	−2.13845	+	1.02982i
$87$	25.8678	−	113.334i	0.0318773	−	0.139663i
$88$	−694.640	−	871.051i	−0.841464	−	1.05516i
$89$	72.8537	+	319.193i	0.0867694	+	0.380162i	0.999603	−	0.0281697i	$-0.00896789\pi$
$89$	72.8537	+	319.193i	0.0867694	+	0.380162i	−0.912834	+	0.408331i	$0.866111\pi$
$90$	−102.615	+	128.676i	−0.120185	+	0.150707i
$91$	19.4536	−	393.114i	0.0224098	−	0.452852i
$92$	−999.593	−	1253.45i	−1.13277	−	1.42045i
$93$	−396.579	+	497.295i	−0.442187	+	0.554484i
$94$	−659.691	−	317.691i	−0.723851	−	0.348588i
$95$	−42.7048	+	53.5501i	−0.0461202	+	0.0578329i
$96$	158.745	−	695.507i	0.168769	−	0.739426i
$97$	−1538.64			−1.61057			−0.805285	−	0.592889i	$-0.797987\pi$
$97$	−1538.64			−1.61057			−0.805285	+	0.592889i	$0.797987\pi$
$98$	225.180	+	1784.71i	0.232109	+	1.83963i
$99$	425.441			0.431903
$100$	534.477	−	2341.69i	0.534477	−	2.34169i
$101$	933.270	−	1170.28i	0.919444	−	1.15295i	−0.0684252	−	0.997656i	$-0.521797\pi$
$101$	933.270	−	1170.28i	0.919444	−	1.15295i	0.987869	−	0.155290i	$-0.0496311\pi$
$102$	1185.41	+	570.865i	1.15072	+	0.554158i
$103$	−765.314	+	959.673i	−0.732122	+	0.918052i	−0.998956	−	0.0456902i	$-0.985451\pi$
$103$	−765.314	+	959.673i	−0.732122	+	0.918052i	0.266833	+	0.963743i	$0.414023\pi$
$104$	799.494	+	1002.53i	0.753816	+	0.945255i
$105$	−19.5167	−	46.2447i	−0.0181394	−	0.0429811i
$106$	−1001.97	+	1256.42i	−0.918108	+	1.15127i
$107$	−324.218	−	1420.49i	−0.292928	−	1.28340i	−0.880429	−	0.474179i	$-0.842745\pi$
$107$	−324.218	−	1420.49i	−0.292928	−	1.28340i	0.587500	−	0.809224i	$-0.300112\pi$
$108$	1210.91	+	1518.44i	1.07889	+	1.35289i
$109$	−135.454	+	593.463i	−0.119029	+	0.521500i	0.879897	+	0.475164i	$0.157611\pi$
$109$	−135.454	+	593.463i	−0.119029	+	0.521500i	−0.998926	+	0.0463353i	$0.985246\pi$
$110$	118.836	−	57.2285i	0.103005	−	0.0496047i
$111$	117.989	−	516.942i	0.100892	−	0.442035i
$112$	−2228.15	−	1964.68i	−1.87982	−	1.65755i
$113$	173.007	+	757.993i	0.144028	+	0.631026i	0.994476	+	0.104967i	$0.0334738\pi$
$113$	173.007	+	757.993i	0.144028	+	0.631026i	−0.850448	+	0.526059i	$0.823669\pi$
$114$	327.200	+	410.296i	0.268817	+	0.337086i
$115$	100.867	−	48.5750i	0.0817905	−	0.0393882i
$116$	1139.49			0.912060
$117$	−489.660			−0.386915
$118$	2658.58	−	1280.30i	2.07408	−	0.998826i
$119$	1895.28	−	1363.83i	1.46000	−	1.05060i
$120$	147.333	+	70.9519i	0.112080	+	0.0539750i
$121$	892.002	+	429.565i	0.670174	+	0.322739i
$122$	−727.942	−	3189.32i	−0.540203	−	2.36678i
$123$	108.954	+	477.357i	0.0798701	+	0.349934i
$124$	−5617.35	−	2705.17i	−4.06817	−	1.95913i
$125$	304.511	+	146.645i	0.217890	+	0.104930i
$126$	2203.75	−	389.537i	1.55814	−	0.275419i
$127$	952.900	−	458.893i	0.665797	−	0.320631i	−0.0702813	−	0.997527i	$-0.522390\pi$
$127$	952.900	−	458.893i	0.665797	−	0.320631i	0.736078	+	0.676896i	$0.236675\pi$
$128$	263.093			0.181675
$129$	−718.214			−0.490195
$130$	−136.774	+	65.8669i	−0.0922760	+	0.0444378i
$131$	76.1010	+	95.4276i	0.0507555	+	0.0636454i	0.806561	−	0.591150i	$-0.201326\pi$
$131$	76.1010	+	95.4276i	0.0507555	+	0.0636454i	−0.755806	+	0.654796i	$0.772755\pi$
$132$	−159.470	−	698.685i	−0.105152	−	0.460703i
$133$	917.120	−	162.111i	0.597928	−	0.105690i
$134$	−1077.75	+	4721.92i	−0.694800	+	3.04412i
$135$	−122.191	+	58.8441i	−0.0779002	+	0.0375147i
$136$	−1692.74	+	7416.37i	−1.06729	+	4.67609i
$137$	862.337	+	1081.34i	0.537770	+	0.674342i	0.974276	−	0.225359i	$-0.0723556\pi$
$137$	862.337	+	1081.34i	0.537770	+	0.674342i	−0.436506	+	0.899701i	$0.643784\pi$
$138$	−190.875	−	836.276i	−0.117741	−	0.515859i
$139$	363.821	−	456.218i	0.222007	−	0.278388i	−0.658338	−	0.752723i	$-0.728740\pi$
$139$	363.821	−	456.218i	0.222007	−	0.278388i	0.880344	+	0.474335i	$0.157311\pi$
$140$	399.362	−	287.377i	0.241088	−	0.173484i
$141$	−173.211	−	217.200i	−0.103454	−	0.129727i
$142$	640.966	−	803.746i	0.378793	−	0.474992i
$143$	353.557	+	170.264i	0.206755	+	0.0995679i
$144$	−2304.21	+	2889.39i	−1.33346	+	1.67210i
$145$	−17.7063	+	77.5762i	−0.0101409	+	0.0444300i
$146$	326.792			0.185243
$147$	−216.828	+	647.161i	−0.121658	+	0.363108i
$148$	5197.45			2.88667
$149$	−102.284	+	448.134i	−0.0562377	+	0.246393i	−0.995232	−	0.0975405i	$-0.968902\pi$
$149$	−102.284	+	448.134i	−0.0562377	+	0.246393i	0.938994	+	0.343934i	$0.111760\pi$
$150$	801.254	−	1004.74i	0.436148	−	0.546912i
$151$	132.423	+	63.7713i	0.0713668	+	0.0343685i	0.469227	−	0.883078i	$-0.344533\pi$
$151$	132.423	+	63.7713i	0.0713668	+	0.0343685i	−0.397860	+	0.917446i	$0.630247\pi$
$152$	−1891.79	+	2372.23i	−1.00950	+	1.26588i
$153$	−1811.16	−	2271.12i	−0.957017	−	1.20006i
$154$	−1726.66	−	485.022i	−0.903495	−	0.253794i
$155$	271.454	−	340.393i	0.140669	−	0.176394i
$156$	183.542	+	804.150i	0.0941995	+	0.412715i
$157$	2070.11	+	2595.84i	1.05231	+	1.31956i	0.945624	+	0.325263i	$0.105453\pi$
$157$	2070.11	+	2595.84i	1.05231	+	1.31956i	0.106687	+	0.994293i	$0.465976\pi$
$158$	504.608	−	2210.83i	0.254079	−	1.11319i
$159$	−549.350	+	264.553i	−0.274002	+	0.131952i
$160$	−108.659	+	476.068i	−0.0536892	+	0.235228i
$161$	−1465.57	−	411.683i	−0.717412	−	0.201523i
$162$	−494.764	−	2167.70i	−0.239953	−	1.05130i
$163$	1029.09	+	1290.43i	0.494505	+	0.620090i	0.964980	−	0.262324i	$-0.0844888\pi$
$163$	1029.09	+	1290.43i	0.494505	+	0.620090i	−0.470475	+	0.882413i	$0.655917\pi$
$164$	−4324.16	+	2082.41i	−2.05891	+	0.991516i
$165$	50.0443			0.0236118
$166$	3922.60			1.83405
$167$	−1543.27	+	743.199i	−0.715100	+	0.344374i	−0.755805	−	0.654797i	$-0.772754\pi$
$167$	−1543.27	+	743.199i	−0.715100	+	0.344374i	0.0407048	+	0.999171i	$0.487040\pi$
$168$	−864.574	−	2048.60i	−0.397044	−	0.940792i
$169$	1572.50	+	757.277i	0.715750	+	0.344687i
$170$	−811.404	−	390.751i	−0.366070	−	0.176290i
$171$	−257.824	−	1129.60i	−0.115300	−	0.505161i
$172$	−1566.55	−	6863.53i	−0.694469	−	3.04267i
$173$	−708.633	−	341.260i	−0.311424	−	0.149974i	0.271643	−	0.962398i	$-0.412433\pi$
$173$	−708.633	−	341.260i	−0.311424	−	0.149974i	−0.583067	+	0.812424i	$0.698147\pi$
$174$	549.292	+	264.525i	0.239320	+	0.115251i
$175$	−886.778	−	2101.21i	−0.383052	−	0.907639i
$176$	2668.44	−	1285.05i	1.14285	−	0.550367i
$177$	1119.58			0.475440
$178$	−1717.06			−0.723028
$179$	−451.445	+	217.405i	−0.188506	+	0.0907798i	−0.525756	−	0.850635i	$-0.676218\pi$
$179$	−451.445	+	217.405i	−0.188506	+	0.0907798i	0.337250	+	0.941415i	$0.390503\pi$
$180$	−381.636	−	478.557i	−0.158031	−	0.198164i
$181$	291.942	+	1279.08i	0.119889	+	0.525267i	0.998831	+	0.0483390i	$0.0153928\pi$
$181$	291.942	+	1279.08i	0.119889	+	0.525267i	−0.878942	+	0.476928i	$0.841750\pi$
$182$	1987.29	+	558.235i	0.809385	+	0.227358i
$183$	276.193	−	1210.08i	0.111567	−	0.488808i
$184$	4468.33	−	2151.84i	1.79027	−	0.862149i
$185$	−80.7619	+	353.841i	−0.0320959	+	0.140621i
$186$	−2079.86	−	2608.06i	−0.819907	−	1.02813i
$187$	518.029	+	2269.63i	0.202578	+	0.887550i
$188$	1697.84	−	2129.03i	0.658659	−	0.825933i
$189$	1775.40	+	498.715i	0.683289	+	0.191937i
$190$	−223.965	−	280.844i	−0.0855166	−	0.107234i
$191$	−419.302	+	525.788i	−0.158846	+	0.199187i	−0.854885	−	0.518817i	$-0.826373\pi$
$191$	−419.302	+	525.788i	−0.158846	+	0.199187i	0.696039	+	0.718004i	$0.254944\pi$
$192$	1070.38	+	515.470i	0.402335	+	0.193754i
$193$	−1405.40	+	1762.31i	−0.524159	+	0.657275i	−0.971486	−	0.237096i	$-0.923805\pi$
$193$	−1405.40	+	1762.31i	−0.524159	+	0.657275i	0.447327	+	0.894370i	$0.352376\pi$
$194$	1795.61	−	7867.08i	0.664522	−	2.91146i
$195$	−57.5984			−0.0211523
$196$	−6657.46	−	660.518i	−2.42619	−	0.240714i
$197$	−979.957			−0.354411			−0.177206	−	0.984174i	$-0.556706\pi$
$197$	−979.957			−0.354411			−0.177206	+	0.984174i	$0.556706\pi$
$198$	−496.494	+	2175.28i	−0.178204	+	0.780761i
$199$	−2106.20	+	2641.09i	−0.750273	+	0.940812i	−0.999619	−	0.0276022i	$-0.991213\pi$
$199$	−2106.20	+	2641.09i	−0.750273	+	0.940812i	0.249346	+	0.968414i	$0.419784\pi$
$200$	6694.36	+	3223.84i	2.36682	+	1.13980i
$201$	−1145.75	+	1436.73i	−0.402066	+	0.504175i
$202$	4894.54	+	6137.55i	1.70484	+	2.13781i
$203$	878.228	−	631.964i	0.303643	−	0.218498i
$204$	−3050.89	+	3825.70i	−1.04708	+	1.31300i
$205$	−74.5777	−	326.746i	−0.0254084	−	0.111322i
$206$	−4013.69	−	5033.01i	−1.35751	−	1.70226i
$207$	−421.420	+	1846.36i	−0.141501	+	0.619957i
$208$	−3071.24	+	1479.03i	−1.02381	+	0.493040i
$209$	−206.623	+	905.273i	−0.0683846	+	0.299613i
$210$	259.226	−	45.8210i	0.0851823	−	0.0150569i
$211$	−287.927	−	1261.49i	−0.0939418	−	0.411586i	0.905990	−	0.423300i	$-0.139128\pi$
$211$	−287.927	−	1261.49i	−0.0939418	−	0.411586i	−0.999931	+	0.0117141i	$0.996271\pi$
$212$	−3726.40	−	4672.76i	−1.20722	−	1.51380i
$213$	351.424	−	169.237i	0.113048	−	0.0544409i
$214$	7641.35			2.44090
$215$	491.610			0.155942
$216$	−5412.96	+	2606.75i	−1.70512	+	0.821142i
$217$	−5829.70	+	1030.46i	−1.82371	+	0.322362i
$218$	−2876.31	−	1385.16i	−0.893615	−	0.430342i
$219$	111.711	+	53.7974i	0.0344692	+	0.0165995i
$220$	109.156	+	478.243i	0.0334513	+	0.146560i
$221$	−596.224	−	2612.23i	−0.181477	−	0.795101i
$222$	2505.43	+	1206.55i	0.757449	+	0.364768i
$223$	−1685.95	−	811.912i	−0.506277	−	0.243810i	0.163268	−	0.986582i	$-0.447796\pi$
$223$	−1685.95	−	811.912i	−0.506277	−	0.243810i	−0.669545	+	0.742772i	$0.733511\pi$
$224$	5389.48	−	3878.22i	1.60759	−	1.15681i
$225$	−2556.34	+	1231.07i	−0.757433	+	0.364760i
$226$	−4077.53			−1.20015
$227$	5085.76			1.48702			0.743510	−	0.668724i	$-0.233159\pi$
$227$	5085.76			1.48702			0.743510	+	0.668724i	$0.233159\pi$
$228$	−1758.46	+	846.828i	−0.510775	+	0.245976i
$229$	−1753.14	−	2198.36i	−0.505897	−	0.634375i	0.461651	−	0.887062i	$-0.347257\pi$
$229$	−1753.14	−	2198.36i	−0.505897	−	0.634375i	−0.967548	+	0.252687i	$0.918686\pi$
$230$	130.652	+	572.422i	0.0374561	+	0.164106i
$231$	−510.400	−	450.048i	−0.145376	−	0.128186i
$232$	−784.373	+	3436.56i	−0.221968	+	0.972507i
$233$	1056.79	−	508.922i	0.297135	−	0.143093i	−0.279377	−	0.960182i	$-0.590128\pi$
$233$	1056.79	−	508.922i	0.297135	−	0.143093i	0.576512	+	0.817089i	$0.304414\pi$
$234$	571.439	−	2503.64i	0.159642	−	0.699435i
$235$	118.561	+	148.671i	0.0329110	+	0.0412691i
$236$	2442.01	+	10699.2i	0.673565	+	2.95108i
$237$	536.449	−	672.686i	0.147030	−	0.184370i
$238$	4761.44	+	11282.2i	1.29680	+	3.07276i
$239$	480.300	+	602.277i	0.129992	+	0.163004i	0.842568	−	0.538591i	$-0.181043\pi$
$239$	480.300	+	602.277i	0.129992	+	0.163004i	−0.712576	+	0.701595i	$0.752472\pi$
$240$	−271.043	+	339.877i	−0.0728989	+	0.0914124i
$241$	1162.97	+	560.058i	0.310845	+	0.149695i	0.582802	−	0.812614i	$-0.301956\pi$
$241$	1162.97	+	560.058i	0.310845	+	0.149695i	−0.271957	+	0.962310i	$0.587671\pi$
$242$	−3237.35	+	4059.51i	−0.859937	+	1.07833i
$243$	785.963	−	3443.53i	0.207488	−	0.909064i
$244$	12166.4			3.19211
$245$	148.417	−	442.975i	0.0387020	−	0.115513i
$246$	−2567.88			−0.665538
$247$	237.812	−	1041.92i	0.0612616	−	0.268404i
$248$	12025.2	−	15079.1i	3.07904	−	3.86099i
$249$	1340.91	+	645.749i	0.341272	+	0.164348i
$250$	−1105.16	+	1385.83i	−0.279586	+	0.350590i
$251$	−2167.45	−	2717.89i	−0.545052	−	0.683473i	0.430664	−	0.902512i	$-0.358279\pi$
$251$	−2167.45	−	2717.89i	−0.545052	−	0.683473i	−0.975716	+	0.219039i	$0.929708\pi$
$252$	−411.368	+	8312.84i	−0.102832	+	2.07801i
$253$	946.300	−	1186.62i	0.235152	−	0.294871i
$254$	1234.28	+	5407.72i	0.304903	+	1.33587i
$255$	−213.046	−	267.151i	−0.0523194	−	0.0656064i
$256$	755.814	−	3311.44i	0.184525	−	0.808456i
$257$	2948.11	−	1419.73i	0.715556	−	0.344594i	−0.0404289	−	0.999182i	$-0.512872\pi$
$257$	2948.11	−	1419.73i	0.715556	−	0.344594i	0.755985	+	0.654589i	$0.227158\pi$
$258$	838.164	−	3672.23i	0.202255	−	0.886137i
$259$	4005.78	−	2882.52i	0.961031	−	0.691548i
$260$	−125.633	−	550.432i	−0.0299669	−	0.131294i
$261$	−839.247	−	1052.38i	−0.199035	−	0.249582i
$262$	−576.733	+	277.740i	−0.135995	+	0.0654918i
$263$	−3494.16			−0.819236			−0.409618	−	0.912257i	$-0.634338\pi$
$263$	−3494.16			−0.819236			−0.409618	+	0.912257i	$0.634338\pi$
$264$	2216.92			0.516827
$265$	376.024	−	181.084i	0.0871660	−	0.0419769i
$266$	−241.414	+	4878.43i	−0.0556467	+	1.12450i
$267$	−586.963	−	282.667i	−0.134538	−	0.0647900i
$268$	−16229.1	−	7815.50i	−3.69906	−	1.78137i
$269$	596.227	+	2612.24i	0.135140	+	0.592086i	0.996463	+	0.0840289i	$0.0267788\pi$
$269$	596.227	+	2612.24i	0.135140	+	0.592086i	−0.861324	+	0.508057i	$0.830364\pi$
$270$	−158.272	−	693.435i	−0.0356746	−	0.156300i
$271$	1273.96	+	613.505i	0.285562	+	0.137519i	0.571182	−	0.820824i	$-0.306485\pi$
$271$	1273.96	+	613.505i	0.285562	+	0.137519i	−0.285620	+	0.958343i	$0.592199\pi$
$272$	−18219.9	−	8774.26i	−4.06156	−	1.95595i
$273$	587.443	+	517.982i	0.130233	+	0.114834i
$274$	−6535.25	+	3147.21i	−1.44091	+	0.693904i
$275$	2273.86			0.498614
$276$	3190.17			0.695746
$277$	−657.088	+	316.437i	−0.142529	+	0.0686384i	−0.503789	−	0.863827i	$-0.668061\pi$
$277$	−657.088	+	316.437i	−0.142529	+	0.0686384i	0.361260	+	0.932465i	$0.382347\pi$
$278$	1908.06	+	2392.63i	0.411647	+	0.516190i
$279$	1638.86	+	7180.33i	0.351671	+	1.54077i
$280$	591.792	+	1402.25i	0.126308	+	0.299287i
$281$	1792.44	−	7853.19i	0.380527	−	1.66720i	−0.315304	−	0.948991i	$-0.602107\pi$
$281$	1792.44	−	7853.19i	0.380527	−	1.66720i	0.695831	−	0.718206i	$-0.255036\pi$
$282$	1312.69	−	632.157i	0.277196	−	0.133491i
$283$	−14.8037	+	64.8591i	−0.00310949	+	0.0136236i	−0.976459	−	0.215704i	$-0.930795\pi$
$283$	−14.8037	+	64.8591i	−0.00310949	+	0.0136236i	0.973349	+	0.229327i	$0.0736526\pi$
$284$	2383.81	+	2989.21i	0.498075	+	0.624566i
$285$	−30.3276	−	132.874i	−0.00630335	−	0.0276168i
$286$	−1283.17	+	1609.04i	−0.265298	+	0.332673i
$287$	−2177.81	+	4003.15i	−0.447917	+	0.823339i
$288$	−5150.27	−	6458.23i	−1.05376	−	1.32137i
$289$	6847.42	−	8586.39i	1.39373	−	1.74769i
$290$	−375.985	−	181.065i	−0.0761330	−	0.0366637i
$291$	1908.92	−	2393.70i	0.384545	−	0.482204i
$292$	−270.446	+	1184.90i	−0.0542008	+	0.237469i
$293$	5784.42			1.15334			0.576672	−	0.816976i	$-0.304351\pi$
$293$	5784.42			1.15334			0.576672	+	0.816976i	$0.304351\pi$
$294$	−3055.90	−	1863.89i	−0.606203	−	0.369742i
$295$	−766.342			−0.151248
$296$	−3577.69	+	15674.9i	−0.702531	+	3.07799i
$297$	−1146.35	+	1437.48i	−0.223967	+	0.280846i
$298$	−2171.95	−	1045.96i	−0.422207	−	0.203324i
$299$	−1089.14	+	1365.74i	−0.210658	+	0.264157i
$300$	2979.94	+	3736.73i	0.573490	+	0.719133i
$301$	−5013.91	−	4421.04i	−0.960122	−	0.846594i
$302$	−480.602	+	602.656i	−0.0915747	+	0.114831i
$303$	662.780	+	2903.83i	0.125662	+	0.550563i
$304$	−5029.10	−	6306.29i	−0.948812	−	1.18977i
$305$	−189.051	+	828.288i	−0.0354920	+	0.155500i
$306$	13725.9	−	6610.06i	2.56424	−	1.23488i
$307$	−459.809	+	2014.56i	−0.0854811	+	0.374517i	−0.999516	−	0.0311191i	$-0.990093\pi$
$307$	−459.809	+	2014.56i	−0.0854811	+	0.374517i	0.914035	+	0.405636i	$0.132950\pi$
$308$	3187.56	−	5859.21i	0.589702	−	1.08396i
$309$	−543.502	−	2381.24i	−0.100061	−	0.438395i
$310$	1423.64	+	1785.19i	0.260831	+	0.327071i
$311$	−7766.08	+	3739.95i	−1.41599	+	0.681907i	−0.976336	−	0.216258i	$-0.930615\pi$
$311$	−7766.08	+	3739.95i	−1.41599	+	0.681907i	−0.439658	+	0.898165i	$0.644900\pi$
$312$	−2551.56			−0.462993
$313$	−4123.53			−0.744651			−0.372326	−	0.928102i	$-0.621440\pi$
$313$	−4123.53			−0.744651			−0.372326	+	0.928102i	$0.621440\pi$
$314$	−15688.4	+	7555.12i	−2.81957	+	1.35784i
$315$	−559.544	−	157.177i	−0.100085	−	0.0281141i
$316$	7598.54	+	3659.26i	1.35269	+	0.651423i
$317$	8374.27	+	4032.84i	1.48374	+	0.714532i	0.988074	−	0.153980i	$-0.0492091\pi$
$317$	8374.27	+	4032.84i	1.48374	+	0.714532i	0.495668	+	0.868512i	$0.334923\pi$
$318$	−711.565	−	3117.57i	−0.125480	−	0.549763i
$319$	240.042	+	1051.69i	0.0421309	+	0.184588i
$320$	−732.667	−	352.834i	−0.127992	−	0.0616376i
$321$	2612.14	+	1257.94i	0.454191	+	0.218727i
$322$	3815.28	−	7013.06i	0.660302	−	1.21373i
$323$	5712.23	−	2750.86i	0.984015	−	0.473877i
$324$	8269.21			1.41790
$325$	−2617.09			−0.446677
$326$	−7798.96	+	3755.78i	−1.32498	+	0.638078i
$327$	−755.216	−	947.011i	−0.127717	−	0.160152i
$328$	−3303.73	−	14474.6i	−0.556153	−	2.43667i
$329$	127.798	−	2582.51i	0.0214156	−	0.432762i
$330$	−58.4023	+	255.877i	−0.00974224	+	0.0426836i
$331$	866.688	−	417.375i	0.143920	−	0.0693081i	−0.360538	−	0.932745i	$-0.617407\pi$
$331$	866.688	−	417.375i	0.143920	−	0.0693081i	0.504458	+	0.863437i	$0.331693\pi$
$332$	−3246.25	+	14222.8i	−0.536630	+	2.35113i
$333$	−3827.98	−	4800.14i	−0.629946	−	0.789928i
$334$	−1998.97	−	8758.07i	−0.327482	−	1.43479i
$335$	784.257	−	983.427i	0.127906	−	0.160389i
$336$	5820.87	−	1028.90i	0.945102	−	0.167057i
$337$	−2652.29	−	3325.87i	−0.428723	−	0.537601i	0.519809	−	0.854282i	$-0.326003\pi$
$337$	−2652.29	−	3325.87i	−0.428723	−	0.537601i	−0.948532	+	0.316681i	$0.897432\pi$
$338$	−5707.10	+	7156.47i	−0.918418	+	1.15166i
$339$	−1393.87	−	671.253i	−0.223318	−	0.107544i
$340$	2088.30	−	2618.65i	0.333101	−	0.417695i
$341$	1313.40	−	5754.40i	0.208577	−	0.913836i
$342$	6076.54			0.960764
$343$	−5497.37	+	3183.17i	−0.865393	+	0.501093i
$344$	21777.9			3.41333
$345$	−49.5714	+	217.186i	−0.00773575	+	0.0338925i
$346$	2571.85	−	3224.99i	0.399605	−	0.501089i
$347$	−5280.24	−	2542.83i	−0.816882	−	0.393390i	−0.0217032	−	0.999764i	$-0.506909\pi$
$347$	−5280.24	−	2542.83i	−0.816882	−	0.393390i	−0.795179	+	0.606375i	$0.792623\pi$
$348$	−1413.71	+	1772.73i	−0.217767	+	0.273071i
$349$	507.422	+	636.288i	0.0778272	+	0.0975922i	0.819221	−	0.573478i	$-0.194406\pi$
$349$	507.422	+	636.288i	0.0778272	+	0.0975922i	−0.741394	+	0.671070i	$0.765835\pi$
$350$	11778.4	−	2081.97i	1.79881	−	0.317959i
$351$	1319.39	−	1654.47i	0.200638	−	0.251592i
$352$	1473.08	+	6453.99i	0.223055	+	0.977270i
$353$	6102.06	+	7651.74i	0.920057	+	1.15371i	0.987756	+	0.156009i	$0.0498628\pi$
$353$	6102.06	+	7651.74i	0.920057	+	1.15371i	−0.0676991	+	0.997706i	$0.521566\pi$
$354$	−1306.56	+	5724.43i	−0.196167	+	0.859464i
$355$	−240.546	+	115.841i	−0.0359630	+	0.0173189i
$356$	1421.00	−	6225.80i	0.211553	−	0.926872i
$357$	−229.643	+	4640.58i	−0.0340448	+	0.687970i
$358$	−584.750	−	2561.96i	−0.0863268	−	0.378223i
$359$	4359.74	+	5466.94i	0.640942	+	0.803716i	0.991120	−	0.132967i	$-0.0424505\pi$
$359$	4359.74	+	5466.94i	0.640942	+	0.803716i	−0.350178	+	0.936683i	$0.613879\pi$
$360$	1705.97	−	821.553i	0.249757	−	0.120277i
$361$	−4330.17			−0.631312
$362$	−6880.66			−0.999004
$363$	−1774.95	+	854.771i	−0.256641	+	0.123592i
$364$	−3668.71	+	6743.65i	−0.528277	+	0.971053i
$365$	−76.4653	−	36.8238i	−0.0109654	−	0.00528067i
$366$	5864.84	+	2824.36i	0.837596	+	0.403365i
$367$	−206.082	−	902.904i	−0.0293117	−	0.128423i	0.958155	−	0.286249i	$-0.0924085\pi$
$367$	−206.082	−	902.904i	−0.0293117	−	0.128423i	−0.987467	+	0.157826i	$0.949551\pi$
$368$	2933.76	+	12853.6i	0.415578	+	1.82077i
$369$	5108.02	+	2459.89i	0.720631	+	0.347038i
$370$	−1714.94	−	825.873i	−0.240961	−	0.116041i
$371$	−5463.54	−	1534.72i	−0.764563	−	0.214767i
$372$	11177.7	−	5382.89i	1.55789	−	0.750241i
$373$	−8784.82			−1.21947			−0.609733	−	0.792607i	$-0.708723\pi$
$373$	−8784.82			−1.21947			−0.609733	+	0.792607i	$0.708723\pi$
$374$	−12209.2			−1.68803
$375$	−605.930	+	291.801i	−0.0834403	+	0.0401827i
$376$	5252.18	+	6586.02i	0.720373	+	0.903320i
$377$	−276.275	−	1210.44i	−0.0377425	−	0.165361i
$378$	−4621.85	+	8495.66i	−0.628895	+	1.15600i
$379$	−922.786	+	4042.99i	−0.125067	+	0.547954i	0.873106	+	0.487530i	$0.162102\pi$
$379$	−922.786	+	4042.99i	−0.125067	+	0.547954i	−0.998173	+	0.0604232i	$0.980755\pi$
$380$	1203.65	−	579.645i	0.162489	−	0.0782504i
$381$	−468.305	+	2051.78i	−0.0629711	+	0.275895i
$382$	−2199.03	−	2757.50i	−0.294534	−	0.369335i
$383$	1402.26	+	6143.72i	0.187082	+	0.819659i	0.978145	+	0.207924i	$0.0666708\pi$
$383$	1402.26	+	6143.72i	0.187082	+	0.819659i	−0.791063	+	0.611734i	$0.790472\pi$
$384$	−326.407	+	409.301i	−0.0433773	+	0.0543934i
$385$	349.363	+	308.053i	0.0462473	+	0.0407788i
$386$	−7370.61	−	9242.45i	−0.971902	−	1.21873i
$387$	−5185.07	+	6501.87i	−0.681064	+	0.854027i
$388$	27038.9	+	13021.2i	3.53786	+	1.70374i
$389$	−766.441	+	961.087i	−0.0998975	+	0.125267i	−0.829267	−	0.558852i	$-0.811242\pi$
$389$	−766.441	+	961.087i	−0.0998975	+	0.125267i	0.729370	+	0.684120i	$0.239813\pi$
$390$	67.2180	−	294.501i	0.00872747	−	0.0382376i
$391$	−10363.1			−1.34037
$392$	6574.74	−	19623.4i	0.847129	−	2.52840i
$393$	−242.874			−0.0311740
$394$	1143.62	−	5010.53i	0.146230	−	0.640677i
$395$	−367.194	+	460.447i	−0.0467735	+	0.0586521i
$396$	−7476.36	−	3600.43i	−0.948741	−	0.456889i
$397$	3543.64	−	4443.58i	0.447985	−	0.561755i	−0.505643	−	0.862743i	$-0.668745\pi$
$397$	3543.64	−	4443.58i	0.447985	−	0.561755i	0.953628	+	0.300987i	$0.0973162\pi$
$398$	−11045.9	−	13851.2i	−1.39116	−	1.74446i
$399$	−885.625	+	1627.91i	−0.111120	+	0.204255i
$400$	−12315.4	+	15443.0i	−1.53942	+	1.93037i
$401$	−1700.14	−	7448.79i	−0.211723	−	0.927619i	−0.963396	−	0.268083i	$-0.913610\pi$
$401$	−1700.14	−	7448.79i	−0.211723	−	0.927619i	0.751673	−	0.659536i	$-0.229247\pi$
$402$	−6008.91	−	7534.94i	−0.745516	−	0.934847i
$403$	−1511.66	+	6623.01i	−0.186851	+	0.818649i
$404$	−26304.4	+	12667.6i	−3.23934	+	1.55999i
$405$	−128.493	+	562.966i	−0.0157652	+	0.0690717i
$406$	2206.34	+	5227.90i	0.269701	+	0.639055i
$407$	1094.88	+	4796.98i	0.133344	+	0.584220i
$408$	−9437.76	−	11834.6i	−1.14519	−	1.43603i
$409$	7942.12	−	3824.72i	0.960178	−	0.462397i	0.112934	−	0.993602i	$-0.463975\pi$
$409$	7942.12	−	3824.72i	0.960178	−	0.462397i	0.847243	+	0.531205i	$0.178261\pi$
$410$	1757.69			0.211722
$411$	−2752.13			−0.330298
$412$	21570.6	−	10387.8i	2.57938	−	1.24216i
$413$	7815.89	+	6891.71i	0.931222	+	0.821111i
$414$	−8948.67	−	4309.45i	−1.06233	−	0.511589i
$415$	−917.839	−	442.008i	−0.108566	−	0.0522827i
$416$	−1695.44	−	7428.21i	−0.199822	−	0.875476i
$417$	258.375	+	1132.01i	0.0303421	+	0.132938i
$418$	−4387.54	−	2112.93i	−0.513401	−	0.247241i
$419$	12427.6	+	5984.81i	1.44899	+	0.697797i	0.982420	−	0.186686i	$-0.0597748\pi$
$419$	12427.6	+	5984.81i	1.44899	+	0.697797i	0.466571	+	0.884484i	$0.345489\pi$
$420$	−48.3890	+	977.834i	−0.00562176	+	0.113603i
$421$	672.092	−	323.663i	0.0778047	−	0.0374688i	−0.394577	−	0.918863i	$-0.629109\pi$
$421$	672.092	−	323.663i	0.0778047	−	0.0374688i	0.472381	+	0.881394i	$0.343394\pi$
$422$	6786.03			0.782793
$423$	−3216.76			−0.369750
$424$	16657.6	−	8021.87i	1.90793	−	0.918813i
$425$	−9680.14	−	12138.5i	−1.10484	−	1.38542i
$426$	455.194	+	1994.34i	0.0517705	+	0.226821i
$427$	9376.92	−	6747.53i	1.06272	−	0.764722i
$428$	−6323.80	+	27706.4i	−0.714188	+	3.12906i
$429$	−703.526	+	338.800i	−0.0791761	+	0.0381292i
$430$	−573.714	+	2513.61i	−0.0643418	+	0.281900i
$431$	4889.32	+	6131.01i	0.546427	+	0.685198i	0.975984	−	0.217842i	$-0.0699016\pi$
$431$	4889.32	+	6131.01i	0.546427	+	0.685198i	−0.429557	+	0.903040i	$0.641330\pi$
$432$	−3553.97	−	15571.0i	−0.395811	−	1.73416i
$433$	5178.32	−	6493.41i	0.574721	−	0.720677i	−0.406481	−	0.913659i	$-0.633244\pi$
$433$	5178.32	−	6493.41i	0.574721	−	0.720677i	0.981202	+	0.192982i	$0.0618158\pi$
$434$	1534.55	−	31009.9i	0.169726	−	3.42978i
$435$	−98.7201	−	123.791i	−0.0108811	−	0.0136444i
$436$	7402.73	−	9282.73i	0.813135	−	1.01964i
$437$	−3724.11	−	1793.44i	−0.407662	−	0.196320i
$438$	−405.435	+	508.400i	−0.0442293	+	0.0554618i
$439$	−2244.50	+	9833.81i	−0.244019	+	1.06912i	0.693301	+	0.720648i	$0.256156\pi$
$439$	−2244.50	+	9833.81i	−0.244019	+	1.06912i	−0.937320	+	0.348469i	$0.886702\pi$
$440$	−1517.46			−0.164414
$441$	4293.27	+	6635.02i	0.463586	+	0.716447i
$442$	14052.1			1.51220
$443$	2818.18	−	12347.3i	0.302248	−	1.32424i	−0.564477	−	0.825449i	$-0.690922\pi$
$443$	2818.18	−	12347.3i	0.302248	−	1.32424i	0.866725	−	0.498787i	$-0.166221\pi$
$444$	−6448.22	+	8085.81i	−0.689232	+	0.864270i
$445$	401.770	+	193.482i	0.0427994	+	0.0206111i
$446$	6118.84	−	7672.78i	0.649631	−	0.814611i
$447$	−570.277	−	715.104i	−0.0603426	−	0.0756673i
$448$	4299.41	+	10187.4i	0.453410	+	1.07435i
$449$	−5748.77	+	7208.72i	−0.604234	+	0.757685i	−0.986031	−	0.166561i	$-0.946734\pi$
$449$	−5748.77	+	7208.72i	−0.604234	+	0.757685i	0.381797	+	0.924246i	$0.375305\pi$
$450$	−3311.18	−	14507.2i	−0.346868	−	1.51973i
$451$	−2832.87	−	3552.31i	−0.295776	−	0.370891i
$452$	3374.47	−	14784.5i	0.351154	−	1.53851i
$453$	−263.501	+	126.895i	−0.0273297	+	0.0131613i
$454$	−5935.14	+	26003.5i	−0.613546	+	2.68812i
$455$	−402.099	−	354.553i	−0.0414301	−	0.0365312i
$456$	−1343.49	−	5886.22i	−0.137971	−	0.604490i
$457$	9386.38	+	11770.1i	0.960780	+	1.20478i	0.978774	+	0.204942i	$0.0657005\pi$
$457$	9386.38	+	11770.1i	0.960780	+	1.20478i	−0.0179944	+	0.999838i	$0.505728\pi$
$458$	13286.2	−	6398.29i	1.35551	−	0.652778i
$459$	12553.9			1.27661
$460$	−2183.64			−0.221332
$461$	−1886.08	+	908.289i	−0.190550	+	0.0917641i	−0.526726	−	0.850035i	$-0.676581\pi$
$461$	−1886.08	+	908.289i	−0.190550	+	0.0917641i	0.336176	+	0.941799i	$0.390866\pi$
$462$	2896.74	−	2084.47i	0.291707	−	0.209910i
$463$	−6677.67	−	3215.79i	−0.670275	−	0.322788i	0.0676119	−	0.997712i	$-0.478462\pi$
$463$	−6677.67	−	3215.79i	−0.670275	−	0.322788i	−0.737887	+	0.674924i	$0.764176\pi$
$464$	−8442.67	−	4065.77i	−0.844700	−	0.406786i
$465$	192.779	+	844.618i	0.0192256	+	0.0842327i
$466$	1368.84	+	5997.28i	0.136074	+	0.596178i
$467$	8334.47	+	4013.67i	0.825853	+	0.397710i	0.798558	−	0.601918i	$-0.205596\pi$
$467$	8334.47	+	4013.67i	0.825853	+	0.397710i	0.0272948	+	0.999627i	$0.491311\pi$
$468$	8604.90	+	4143.90i	0.849918	+	0.409299i
$469$	−16842.6	+	2977.11i	−1.65825	+	0.293113i
$470$	−898.521	+	432.705i	−0.0881823	+	0.0424663i
$471$	−6606.70			−0.646328
$472$	−33948.3			−3.31059
$473$	6004.69	−	2891.70i	0.583712	−	0.281101i
$474$	2813.41	+	3527.90i	0.272625	+	0.341861i
$475$	−1377.99	−	6037.38i	−0.133109	−	0.583188i
$476$	−44848.0	+	7927.39i	−4.31850	+	0.763343i
$477$	−1571.02	+	6883.09i	−0.150801	+	0.660702i
$478$	−3639.96	+	1752.91i	−0.348301	+	0.167733i
$479$	1814.61	−	7950.32i	0.173093	−	0.758370i	−0.811620	−	0.584186i	$-0.801414\pi$
$479$	1814.61	−	7950.32i	0.173093	−	0.758370i	0.984713	−	0.174184i	$-0.0557289\pi$
$480$	−605.823	−	759.678i	−0.0576081	−	0.0722383i
$481$	−1260.15	−	5521.08i	−0.119455	−	0.523367i
$482$	−4220.79	+	5292.70i	−0.398862	+	0.500157i
$483$	2458.73	−	1769.28i	0.231628	−	0.166677i
$484$	−12040.0	−	15097.7i	−1.13073	−	1.41789i
$485$	−1306.63	+	1638.47i	−0.122332	+	0.153400i
$486$	16689.6	+	8037.28i	1.55773	+	0.750161i
$487$	8074.11	−	10124.6i	0.751279	−	0.942075i	−0.248367	−	0.968666i	$-0.579894\pi$
$487$	8074.11	−	10124.6i	0.751279	−	0.942075i	0.999646	+	0.0265915i	$0.00846532\pi$
$488$	−8374.83	+	36692.5i	−0.776866	+	3.40367i
$489$	−3284.30			−0.303725
$490$	2091.73	+	1275.81i	0.192847	+	0.117623i
$491$	1928.10			0.177218			0.0886091	−	0.996066i	$-0.471758\pi$
$491$	1928.10			0.177218			0.0886091	+	0.996066i	$0.471758\pi$
$492$	2125.12	−	9310.76i	0.194731	−	0.853174i
$493$	4592.34	−	5758.61i	0.419530	−	0.526075i
$494$	5049.83	+	2431.87i	0.459924	+	0.221488i
$495$	361.290	−	453.043i	0.0328056	−	0.0411369i
$496$	31967.6	+	40086.2i	2.89393	+	3.62887i
$497$	3495.08	+	981.774i	0.315444	+	0.0886088i
$498$	−4866.58	+	6102.50i	−0.437905	+	0.549115i
$499$	460.288	+	2016.65i	0.0412932	+	0.180917i	0.991369	−	0.131102i	$-0.0418516\pi$
$499$	460.288	+	2016.65i	0.0412932	+	0.180917i	−0.950076	+	0.312020i	$0.898995\pi$
$500$	−4110.20	−	5154.03i	−0.367628	−	0.460991i
$501$	758.443	−	3322.95i	0.0676342	−	0.296325i
$502$	16426.0	−	7910.37i	1.46042	−	0.703301i
$503$	−923.902	+	4047.88i	−0.0818981	+	0.358819i	−0.999227	−	0.0393111i	$-0.987484\pi$
$503$	−923.902	+	4047.88i	−0.0818981	+	0.358819i	0.917329	+	0.398130i	$0.130341\pi$
$504$	−24787.4	−	6962.82i	−2.19071	−	0.615375i
$505$	−453.666	−	1987.64i	−0.0399760	−	0.175146i
$506$	4962.87	+	6223.25i	0.436021	+	0.546753i
$507$	−3129.05	+	1506.87i	−0.274094	+	0.131997i
$508$	−20629.1			−1.80170
$509$	9669.43			0.842024			0.421012	−	0.907055i	$-0.361675\pi$
$509$	9669.43			0.842024			0.421012	+	0.907055i	$0.361675\pi$
$510$	1614.57	−	777.537i	0.140185	−	0.0675096i
$511$	448.711	+	1063.22i	0.0388450	+	0.0920429i
$512$	17945.7	+	8642.19i	1.54901	+	0.745965i
$513$	4511.40	+	2172.58i	0.388272	+	0.186982i
$514$	3818.64	+	16730.6i	0.327691	+	1.43571i
$515$	372.022	+	1629.93i	0.0318315	+	0.139463i
$516$	12621.3	+	6078.11i	1.07679	+	0.518554i
$517$	2322.65	+	1118.53i	0.197582	+	0.0951506i
$518$	10063.6	+	23845.5i	0.853605	+	2.02261i
$519$	1410.07	−	679.055i	0.119259	−	0.0574320i
$520$	1746.52			0.147288
$521$	3992.34			0.335715			0.167857	−	0.985811i	$-0.446315\pi$
$521$	3992.34			0.335715			0.167857	+	0.985811i	$0.446315\pi$
$522$	6360.26	−	3062.94i	0.533297	−	0.256822i
$523$	9190.93	+	11525.1i	0.768434	+	0.963586i	0.999957	−	0.00924324i	$-0.00294226\pi$
$523$	9190.93	+	11525.1i	0.768434	+	0.963586i	−0.231523	+	0.972829i	$0.574371\pi$
$524$	−529.753	−	2321.00i	−0.0441648	−	0.193499i
$525$	4369.10	+	1227.29i	0.363206	+	0.102025i
$526$	4077.72	−	17865.7i	0.338018	−	1.48095i
$527$	−36310.0	+	17486.0i	−3.00130	+	1.44535i
$528$	−1311.41	+	5745.68i	−0.108091	+	0.473577i
$529$	−3373.56	−	4230.30i	−0.277271	−	0.347687i
$530$	487.059	+	2133.94i	0.0399179	+	0.174892i
$531$	8082.70	−	10135.4i	0.660564	−	0.828321i
$532$	−17488.7	−	4912.60i	−1.42524	−	0.400354i
$533$	3260.49	+	4088.52i	0.264967	+	0.332258i
$534$	2130.27	−	2671.28i	0.172633	−	0.216475i
$535$	−1787.98	−	861.047i	−0.144488	−	0.0695819i
$536$	34742.0	−	43565.1i	2.79967	−	3.51068i
$537$	221.864	−	972.049i	0.0178289	−	0.0781136i
$538$	−14052.2			−1.12609
$539$	−792.817	−	6283.65i	−0.0633563	−	0.502144i
$540$	2645.27			0.210805
$541$	3950.01	−	17306.1i	0.313908	−	1.37532i	−0.534137	−	0.845398i	$-0.679363\pi$
$541$	3950.01	−	17306.1i	0.313908	−	1.37532i	0.848045	−	0.529924i	$-0.177780\pi$
$542$	−4623.58	+	5797.78i	−0.366420	+	0.459476i
$543$	−2352.10	−	1132.71i	−0.185890	−	0.0895200i
$544$	28182.1	−	35339.3i	2.22114	−	2.78522i
$545$	516.937	+	648.219i	0.0406297	+	0.0509480i
$546$	−3334.00	+	2399.11i	−0.261322	+	0.188045i
$547$	7490.29	−	9392.53i	0.585488	−	0.734178i	−0.397550	−	0.917580i	$-0.630140\pi$
$547$	7490.29	−	9392.53i	0.585488	−	0.734178i	0.983038	+	0.183402i	$0.0587110\pi$
$548$	−6002.89	−	26300.4i	−0.467939	−	2.05018i
$549$	−8960.72	−	11236.4i	−0.696601	−	0.873511i
$550$	−2653.62	+	11626.3i	−0.205729	+	0.901356i
$551$	2646.91	−	1274.68i	0.204650	−	0.0985541i
$552$	−2195.97	+	9621.19i	−0.169324	+	0.741857i
$553$	7885.79	−	1393.90i	0.606398	−	0.107188i
$554$	−851.116	−	3728.98i	−0.0652716	−	0.285973i
$555$	−450.283	−	564.637i	−0.0344387	−	0.0431847i
$556$	−10254.4	+	4938.26i	−0.782164	+	0.376671i
$557$	−18320.4			−1.39365			−0.696824	−	0.717242i	$-0.745404\pi$
$557$	−18320.4			−1.39365			−0.696824	+	0.717242i	$0.745404\pi$
$558$	−38625.7			−2.93039
$559$	−6911.08	+	3328.20i	−0.522911	+	0.251821i
$560$	−3984.32	+	704.273i	−0.300658	+	0.0531446i
$561$	−4173.62	−	2009.91i	−0.314101	−	0.151263i
$562$	38061.7	+	18329.5i	2.85682	+	1.37577i
$563$	−3666.36	−	16063.4i	−0.274456	−	1.20247i	−0.904692	−	0.426067i	$-0.859899\pi$
$563$	−3666.36	−	16063.4i	−0.274456	−	1.20247i	0.630236	−	0.776404i	$-0.282958\pi$
$564$	1205.76	+	5282.76i	0.0900204	+	0.394405i
$565$	954.091	+	459.466i	0.0710423	+	0.0342122i
$566$	−314.349	−	151.383i	−0.0233447	−	0.0112422i
$567$	6373.25	−	4586.13i	0.472048	−	0.339681i
$568$	−10656.0	+	5131.66i	−0.787176	+	0.379084i
$569$	−9794.41			−0.721622			−0.360811	−	0.932639i	$-0.617500\pi$
$569$	−9794.41			−0.721622			−0.360811	+	0.932639i	$0.617500\pi$
$570$	714.779			0.0525242
$571$	12305.9	−	5926.21i	0.901903	−	0.434333i	0.0753269	−	0.997159i	$-0.476000\pi$
$571$	12305.9	−	5926.21i	0.901903	−	0.434333i	0.826576	+	0.562825i	$0.190286\pi$
$572$	−4772.22	−	5984.18i	−0.348840	−	0.437432i
$573$	−297.775	−	1304.64i	−0.0217099	−	0.0951171i
$574$	−17926.6	−	15806.9i	−1.30356	−	1.14942i
$575$	−2252.37	+	9868.28i	−0.163357	+	0.715714i
$576$	12394.0	−	5968.63i	0.896557	−	0.431759i
$577$	−377.359	+	1653.32i	−0.0272264	+	0.119287i	−0.986715	−	0.162461i	$-0.948057\pi$
$577$	−377.359	+	1653.32i	−0.0272264	+	0.119287i	0.959489	+	0.281748i	$0.0909141\pi$
$578$	35911.3	+	45031.3i	2.58428	+	3.24058i
$579$	−998.070	−	4372.83i	−0.0716380	−	0.313866i
$580$	967.669	−	1213.42i	0.0692763	−	0.0868698i
$581$	5386.02	+	12762.1i	0.384595	+	0.911296i
$582$	10011.3	+	12553.8i	0.713028	+	0.894109i
$583$	3527.73	−	4423.64i	0.250607	−	0.314251i
$584$	−3387.35	−	1631.26i	−0.240017	−	0.115586i
$585$	−415.825	+	521.429i	−0.0293885	+	0.0368520i
$586$	−6750.49	+	29575.8i	−0.475870	+	2.08492i
$587$	−11850.5			−0.833260			−0.416630	−	0.909076i	$-0.636789\pi$
$587$	−11850.5			−0.833260			−0.416630	+	0.909076i	$0.636789\pi$
$588$	9287.17	−	9537.72i	0.651355	−	0.668927i
$589$	−16074.6			−1.12452
$590$	894.330	−	3918.31i	0.0624050	−	0.273414i
$591$	1215.78	−	1524.55i	0.0846205	−	0.106111i
$592$	−38508.8	−	18544.8i	−2.67348	−	1.28748i
$593$	−1687.20	+	2115.68i	−0.116838	+	0.146510i	−0.836811	−	0.547492i	$-0.815583\pi$
$593$	−1687.20	+	2115.68i	−0.116838	+	0.146510i	0.719973	+	0.694002i	$0.244154\pi$
$594$	−6012.05	−	7538.88i	−0.415282	−	0.520747i
$595$	157.188	−	3176.43i	0.0108304	−	0.218859i
$596$	5589.93	−	7009.55i	0.384182	−	0.481749i
$597$	−1495.76	−	6553.33i	−0.102541	−	0.449263i
$598$	−5712.01	−	7162.63i	−0.390604	−	0.489802i
$599$	4331.12	−	18975.9i	0.295434	−	1.29438i	−0.581413	−	0.813609i	$-0.697500\pi$
$599$	4331.12	−	18975.9i	0.295434	−	1.29438i	0.876846	−	0.480771i	$-0.159643\pi$
$600$	−13320.8	+	6414.95i	−0.906364	+	0.436482i
$601$	−4307.26	+	18871.4i	−0.292341	+	1.28083i	0.588917	+	0.808194i	$0.299555\pi$
$601$	−4307.26	+	18871.4i	−0.292341	+	1.28083i	−0.881258	+	0.472636i	$0.843303\pi$
$602$	28456.1	−	20476.7i	1.92655	−	1.38633i
$603$	4734.83	+	20744.7i	0.319763	+	1.40097i
$604$	−1787.41	−	2241.34i	−0.120411	−	0.150991i
$605$	1214.93	−	585.082i	0.0816432	−	0.0393173i
$606$	−15620.8			−1.04711
$607$	−16016.8			−1.07101			−0.535504	−	0.844532i	$-0.679878\pi$
$607$	−16016.8			−1.07101			−0.535504	+	0.844532i	$0.679878\pi$
$608$	16243.5	−	7822.44i	1.08349	−	0.521779i
$609$	−106.411	+	2150.33i	−0.00708045	+	0.143080i
$610$	−4014.42	−	1933.24i	−0.266458	−	0.128319i
$611$	−2673.25	−	1287.37i	−0.177002	−	0.0852395i
$612$	12607.8	+	55238.5i	0.832747	+	3.64850i
$613$	6264.79	+	27447.9i	0.412778	+	1.80850i	0.570833	+	0.821066i	$0.306620\pi$
$613$	6264.79	+	27447.9i	0.412778	+	1.80850i	−0.158055	+	0.987430i	$0.550522\pi$
$614$	−9763.84	−	4702.02i	−0.641753	−	0.309052i
$615$	600.853	+	289.356i	0.0393963	+	0.0189723i
$616$	15476.5	+	13646.5i	1.01228	+	0.892588i
$617$	−20587.5	+	9914.43i	−1.34331	+	0.646904i	−0.960850	−	0.277067i	$-0.910637\pi$
$617$	−20587.5	+	9914.43i	−1.34331	+	0.646904i	−0.382460	+	0.923972i	$0.624923\pi$
$618$	12809.6			0.833781
$619$	5432.81			0.352768			0.176384	−	0.984321i	$-0.443560\pi$
$619$	5432.81			0.352768			0.176384	+	0.984321i	$0.443560\pi$
$620$	−7651.01	+	3684.53i	−0.495600	+	0.238668i
$621$	−5102.98	−	6398.93i	−0.329751	−	0.413495i
$622$	−10059.3	−	44072.6i	−0.648458	−	2.84108i
$623$	−2357.65	−	5586.44i	−0.151617	−	0.359255i
$624$	1509.37	−	6612.97i	0.0968318	−	0.424248i
$625$	−13454.0	+	6479.09i	−0.861053	+	0.414661i
$626$	4812.21	−	21083.7i	0.307244	−	1.34612i
$627$	−1152.01	−	1444.58i	−0.0733763	−	0.0920109i
$628$	−14410.4	−	63136.1i	−0.915666	−	4.01179i
$629$	20946.6	−	26266.2i	1.32782	−	1.66503i
$630$	1456.64	−	2677.53i	0.0921175	−	0.169326i
$631$	13130.0	+	16464.5i	0.828364	+	1.03874i	0.998577	+	0.0533278i	$0.0169828\pi$
$631$	13130.0	+	16464.5i	0.828364	+	1.03874i	−0.170214	+	0.985407i	$0.554446\pi$
$632$	−16266.4	+	20397.4i	−1.02380	+	1.28381i
$633$	2319.75	+	1117.13i	0.145659	+	0.0701455i
$634$	−30392.8	+	38111.4i	−1.90387	+	2.38738i
$635$	320.550	−	1404.42i	0.0200325	−	0.0877681i
$636$	11892.7			0.741473
$637$	912.491	+	7232.15i	0.0567570	+	0.449840i
$638$	−5657.44			−0.351066
$639$	1005.00	−	4403.17i	0.0622175	−	0.272593i
$640$	223.422	−	280.163i	0.0137993	−	0.0173037i
$641$	−2238.36	−	1077.94i	−0.137925	−	0.0664210i	0.363649	−	0.931536i	$-0.381531\pi$
$641$	−2238.36	−	1077.94i	−0.137925	−	0.0664210i	−0.501573	+	0.865115i	$0.667245\pi$
$642$	−9480.26	+	11887.9i	−0.582797	+	0.730805i
$643$	−17344.2	−	21749.0i	−1.06375	−	1.33390i	−0.939844	−	0.341603i	$-0.889030\pi$
$643$	−17344.2	−	21749.0i	−1.06375	−	1.33390i	−0.123903	−	0.992294i	$-0.539541\pi$
$644$	22270.9	+	19637.5i	1.36272	+	1.20159i
$645$	−609.916	+	764.811i	−0.0372332	+	0.0466890i
$646$	7398.96	+	32417.0i	0.450632	+	1.97435i
$647$	−4547.40	−	5702.26i	−0.276316	−	0.346490i	0.624237	−	0.781235i	$-0.285410\pi$
$647$	−4547.40	−	5702.26i	−0.276316	−	0.346490i	−0.900554	+	0.434745i	$0.856838\pi$
$648$	−5692.16	+	24939.0i	−0.345076	+	1.51188i
$649$	−9360.36	+	4507.71i	−0.566142	+	0.272640i
$650$	3054.18	−	13381.2i	0.184299	−	0.807469i
$651$	5629.51	−	10347.9i	0.338921	−	0.622988i
$652$	−7163.66	−	31386.1i	−0.430292	−	1.88523i
$653$	−8407.89	−	10543.2i	−0.503868	−	0.631831i	0.463229	−	0.886239i	$-0.346691\pi$
$653$	−8407.89	−	10543.2i	−0.503868	−	0.631831i	−0.967097	+	0.254408i	$0.918119\pi$
$654$	5723.42	−	2756.25i	0.342207	−	0.164798i
$655$	166.245			0.00991714
$656$	39468.6			2.34907
$657$	1293.51	−	622.921i	0.0768106	−	0.0369900i
$658$	13055.3	+	3667.26i	0.773477	+	0.217271i
$659$	22337.9	+	10757.4i	1.32043	+	0.635884i	0.955456	−	0.295135i	$-0.0953645\pi$
$659$	22337.9	+	10757.4i	1.32043	+	0.635884i	0.364971	+	0.931019i	$0.381079\pi$
$660$	−879.440	−	423.516i	−0.0518669	−	0.0249778i
$661$	1844.56	+	8081.52i	0.108540	+	0.475544i	0.999759	+	0.0219706i	$0.00699401\pi$
$661$	1844.56	+	8081.52i	0.108540	+	0.475544i	−0.891219	+	0.453574i	$0.850149\pi$
$662$	1122.61	+	4918.47i	0.0659084	+	0.288764i
$663$	4803.62	+	2313.30i	0.281383	+	0.135507i
$664$	−40659.6	−	19580.6i	−2.37635	−	1.14439i
$665$	606.201	−	1114.29i	0.0353496	−	0.0649779i
$666$	29010.5	−	13970.7i	1.68789	−	0.812843i
$667$	−4801.99			−0.278761
$668$	33409.7			1.93512
$669$	3354.79	−	1615.58i	0.193877	−	0.0933663i
$670$	4113.04	+	5157.59i	0.237165	+	0.297395i
$671$	2562.95	+	11229.0i	0.147454	+	0.646037i
$672$	−653.020	+	13196.1i	−0.0374863	+	0.757515i
$673$	3498.82	−	15329.3i	0.200400	−	0.878011i	−0.770293	−	0.637690i	$-0.779890\pi$
$673$	3498.82	−	15329.3i	0.200400	−	0.878011i	0.970693	−	0.240321i	$-0.0772528\pi$
$674$	20100.5	−	9679.87i	1.14873	−	0.553197i
$675$	2728.53	−	11954.5i	0.155587	−	0.681672i
$676$	−21225.2	−	26615.6i	−1.20763	−	1.51432i
$677$	7467.19	+	32715.9i	0.423911	+	1.85727i	0.508802	+	0.860883i	$0.330088\pi$
$677$	7467.19	+	32715.9i	0.423911	+	1.85727i	−0.0848916	+	0.996390i	$0.527054\pi$
$678$	5058.79	−	6343.52i	0.286551	−	0.359324i
$679$	28061.0	−	4960.09i	1.58598	−	0.280340i
$680$	6460.05	+	8100.64i	0.364311	+	0.456832i
$681$	−6309.65	+	7912.06i	−0.355046	+	0.445214i
$682$	27889.5	+	13430.9i	1.56590	+	0.754099i
$683$	18504.6	−	23204.0i	1.03669	−	1.29996i	0.0838514	−	0.996478i	$-0.473278\pi$
$683$	18504.6	−	23204.0i	1.03669	−	1.29996i	0.952836	−	0.303486i	$-0.0981507\pi$
$684$	−5028.80	+	22032.6i	−0.281112	+	1.23163i
$685$	1883.80			0.105075
$686$	−9860.09	−	31822.9i	−0.548776	−	1.77114i
$687$	5595.08			0.310722
$688$	−12882.7	+	56442.6i	−0.713876	+	3.12769i
$689$	−4060.23	+	5091.37i	−0.224503	+	0.281518i
$690$	−1052.63	−	506.918i	−0.0580765	−	0.0279682i
$691$	1440.43	−	1806.25i	0.0793005	−	0.0994397i	−0.740599	−	0.671948i	$-0.765458\pi$
$691$	1440.43	−	1806.25i	0.0793005	−	0.0994397i	0.819899	+	0.572508i	$0.194029\pi$
$692$	9564.94	+	11994.1i	0.525440	+	0.658881i
$693$	−7758.99	+	1371.49i	−0.425310	+	0.0751782i
$694$	19163.6	−	24030.4i	1.04819	−	1.31438i
$695$	−176.855	−	774.852i	−0.00965250	−	0.0422904i
$696$	−4373.22	−	5483.85i	−0.238170	−	0.298656i
$697$	−6903.31	+	30245.4i	−0.375153	+	1.64365i
$698$	−3845.51	+	1851.90i	−0.208531	+	0.100423i
$699$	−519.361	+	2275.47i	−0.0281030	+	0.123127i
$700$	−2198.65	+	44429.7i	−0.118716	+	2.39898i
$701$	−164.619	−	721.242i	−0.00886956	−	0.0388601i	0.970299	−	0.241907i	$-0.0777728\pi$
$701$	−164.619	−	721.242i	−0.00886956	−	0.0388601i	−0.979169	+	0.203047i	$0.934916\pi$
$702$	6919.56	+	8676.85i	0.372025	+	0.466505i
$703$	12073.1	−	5814.09i	0.647717	−	0.311924i
$704$	−11024.5			−0.590198
$705$	−378.385			−0.0202139
$706$	−46244.6	+	22270.2i	−2.46521	+	1.18718i
$707$	−13247.9	+	24351.7i	−0.704723	+	1.29539i
$708$	−19674.7	−	9474.81i	−1.04438	−	0.502945i
$709$	3828.42	+	1843.67i	0.202791	+	0.0976592i	0.532523	−	0.846415i	$-0.321244\pi$
$709$	3828.42	+	1843.67i	0.202791	+	0.0976592i	−0.329732	+	0.944075i	$0.606958\pi$
$710$	−311.576	−	1365.10i	−0.0164693	−	0.0721569i
$711$	−2216.88	−	9712.77i	−0.116933	−	0.512317i
$712$	17798.1	+	8571.12i	0.936815	+	0.451147i
$713$	23672.4	+	11400.0i	1.24339	+	0.598786i
$714$	−23459.3	−	6589.78i	−1.22961	−	0.345401i
$715$	481.556	−	231.905i	0.0251877	−	0.0121297i
$716$	9773.20			0.510114
$717$	−1532.86			−0.0798407
$718$	−33040.4	+	15911.4i	−1.71735	+	0.827031i
$719$	−19293.8	−	24193.7i	−1.00075	−	1.25490i	−0.966815	−	0.255477i	$-0.917768\pi$
$719$	−19293.8	−	24193.7i	−1.00075	−	1.25490i	−0.0339346	−	0.999424i	$-0.510804\pi$
$720$	1120.09	+	4907.41i	0.0579765	+	0.254012i
$721$	10863.8	−	19969.2i	0.561148	−	1.03147i
$722$	5053.36	−	22140.2i	0.260480	−	1.14124i
$723$	−2314.14	+	1114.43i	−0.119037	+	0.0573253i
$724$	5694.27	−	24948.2i	0.292301	−	1.28065i
$725$	−4485.54	−	5624.69i	−0.229777	−	0.288132i
$726$	−2299.07	−	10072.9i	−0.117529	−	0.514930i
$727$	−6264.69	+	7855.68i	−0.319594	+	0.400758i	−0.915514	−	0.402286i	$-0.868216\pi$
$727$	−6264.69	+	7855.68i	−0.319594	+	0.400758i	0.595921	+	0.803043i	$0.296787\pi$
$728$	−17812.7	−	15706.4i	−0.906842	−	0.799614i
$729$	−2754.91	−	3454.55i	−0.139964	−	0.175510i
$730$	277.516	−	347.994i	0.0140703	−	0.0176436i
$731$	−40999.5	−	19744.3i	−2.07445	−	0.999002i
$732$	−15094.3	+	18927.7i	−0.762160	+	0.955719i
$733$	3657.03	−	16022.5i	0.184278	−	0.807374i	−0.795285	−	0.606236i	$-0.792679\pi$
$733$	3657.03	−	16022.5i	0.184278	−	0.807374i	0.979563	−	0.201138i	$-0.0644640\pi$
$734$	4857.06			0.244247
$735$	505.015	+	780.473i	0.0253439	+	0.0391676i
$736$	−29468.7			−1.47586
$737$	3794.55	−	16625.0i	0.189653	−	0.830922i
$738$	−18538.6	+	23246.6i	−0.924681	+	1.15951i
$739$	7184.07	+	3459.67i	0.357605	+	0.172214i	0.604056	−	0.796942i	$-0.293550\pi$
$739$	7184.07	+	3459.67i	0.357605	+	0.172214i	−0.246451	+	0.969155i	$0.579264\pi$
$740$	4413.74	−	5534.65i	0.219260	−	0.274943i
$741$	1325.90	+	1662.63i	0.0657332	+	0.0824269i
$742$	14223.1	−	26144.1i	0.703699	−	1.29351i
$743$	−18397.7	+	23070.0i	−0.908407	+	1.13911i	0.0813982	+	0.996682i	$0.474061\pi$
$743$	−18397.7	+	23070.0i	−0.908407	+	1.13911i	−0.989806	+	0.142425i	$0.954510\pi$
$744$	8539.94	+	37415.9i	0.420819	+	1.84373i
$745$	390.348	+	489.481i	0.0191963	+	0.0240714i
$746$	10252.0	−	44916.9i	0.503152	−	2.20445i
$747$	15526.4	−	7477.13i	0.760485	−	0.366230i
$748$	10104.0	−	44268.7i	0.493904	−	2.16394i
$749$	10492.2	+	24861.1i	0.511849	+	1.21282i
$750$	−784.852	−	3438.66i	−0.0382117	−	0.167416i
$751$	21583.7	+	27065.1i	1.04874	+	1.31507i	0.947340	+	0.320229i	$0.103760\pi$
$751$	21583.7	+	27065.1i	1.04874	+	1.31507i	0.101397	+	0.994846i	$0.467669\pi$
$752$	−20176.1	+	9716.31i	−0.978388	+	0.471167i
$753$	6917.35			0.334770
$754$	6511.42			0.314499
$755$	180.364	−	86.8586i	0.00869418	−	0.00418690i
$756$	−26979.0	−	23788.9i	−1.29791	−	1.14444i
$757$	7570.79	+	3645.90i	0.363494	+	0.175050i	0.606711	−	0.794922i	$-0.292488\pi$
$757$	7570.79	+	3645.90i	0.363494	+	0.175050i	−0.243217	+	0.969972i	$0.578203\pi$
$758$	−19594.9	−	9436.43i	−0.938945	−	0.452172i
$759$	672.033	+	2944.37i	0.0321387	+	0.140809i
$760$	919.605	+	4029.05i	0.0438916	+	0.192301i
$761$	18733.2	+	9021.41i	0.892348	+	0.429732i	0.823119	−	0.567869i	$-0.192232\pi$
$761$	18733.2	+	9021.41i	0.892348	+	0.429732i	0.0692285	+	0.997601i	$0.477946\pi$
$762$	−9944.25	−	4788.90i	−0.472759	−	0.227669i
$763$	557.210	−	11260.0i	0.0264382	−	0.534257i
$764$	11818.1	−	5691.31i	0.559640	−	0.269508i
$765$	−3956.53			−0.186992
$766$	−33049.4			−1.55891
$767$	10773.3	−	5188.14i	0.507171	−	0.244241i

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16701 + 5.11301i) q^{2} +(-1.24065 + 1.55573i) q^{3} +(-17.5732 - 8.46282i) q^{4} +(0.849213 - 1.06488i) q^{5} +(-6.50660 - 8.15902i) q^{6} +(-18.2375 + 3.22369i) q^{7} +(37.6195 - 47.1733i) q^{8} +(5.12699 + 22.4628i) q^{9} +O(q^{10})\)	\(q+(-1.16701 + 5.11301i) q^{2} +(-1.24065 + 1.55573i) q^{3} +(-17.5732 - 8.46282i) q^{4} +(0.849213 - 1.06488i) q^{5} +(-6.50660 - 8.15902i) q^{6} +(-18.2375 + 3.22369i) q^{7} +(37.6195 - 47.1733i) q^{8} +(5.12699 + 22.4628i) q^{9} +(4.45370 + 5.58476i) q^{10} +(4.10883 - 18.0020i) q^{11} +(34.9681 - 16.8397i) q^{12} +(-4.72905 + 20.7193i) q^{13} +(4.80067 - 97.0108i) q^{14} +(0.603085 + 2.64229i) q^{15} +(100.007 + 125.405i) q^{16} +(-113.591 + 54.7028i) q^{17} -120.836 q^{18} -50.2875 q^{19} +(-23.9353 + 11.5266i) q^{20} +(17.6112 - 32.3721i) q^{21} +(87.2491 + 42.0170i) q^{22} +(74.0563 + 35.6637i) q^{23} +(26.7162 + 117.051i) q^{24} +(27.4023 + 120.057i) q^{25} +(-100.419 - 48.3593i) q^{26} +(-89.7123 - 43.2031i) q^{27} +(347.774 + 97.6904i) q^{28} +(-52.6355 + 25.3479i) q^{29} -14.2139 q^{30} +319.654 q^{31} +(-323.012 + 155.554i) q^{32} +(22.9085 + 28.7264i) q^{33} +(-147.133 - 644.633i) q^{34} +(-12.0547 + 22.1584i) q^{35} +(100.001 - 438.133i) q^{36} +(-240.081 + 115.617i) q^{37} +(58.6861 - 257.121i) q^{38} +(-26.3665 - 33.0625i) q^{39} +(-18.2870 - 80.1204i) q^{40} +(153.419 - 192.382i) q^{41} +(144.966 + 127.825i) q^{42} +(225.042 + 282.193i) q^{43} +(-224.553 + 281.580i) q^{44} +(28.2741 + 13.6161i) q^{45} +(-268.773 + 337.031i) q^{46} +(-31.0669 + 136.113i) q^{47} -319.170 q^{48} +(322.216 - 117.584i) q^{49} -645.833 q^{50} +(55.8248 - 244.584i) q^{51} +(258.448 - 324.084i) q^{52} +(276.076 + 132.951i) q^{53} +(325.593 - 408.281i) q^{54} +(-15.6806 - 19.6629i) q^{55} +(-534.014 + 981.599i) q^{56} +(62.3892 - 78.2336i) q^{57} +(-68.1779 - 298.707i) q^{58} +(-350.804 - 439.895i) q^{59} +(11.7631 - 51.5373i) q^{60} +(-561.994 + 270.642i) q^{61} +(-373.040 + 1634.39i) q^{62} +(-165.917 - 393.139i) q^{63} +(-132.856 - 582.079i) q^{64} +(18.0476 + 22.6310i) q^{65} +(-173.613 + 83.6075i) q^{66} +923.511 q^{67} +2459.11 q^{68} +(-147.361 + 70.9653i) q^{69} +(-99.2280 - 87.4950i) q^{70} +(-176.608 - 85.0501i) q^{71} +(1252.52 + 603.182i) q^{72} +(-13.8656 - 60.7491i) q^{73} +(-310.974 - 1362.47i) q^{74} +(-220.773 - 106.319i) q^{75} +(883.713 + 425.574i) q^{76} +(-16.9023 + 341.557i) q^{77} +(199.819 - 96.2278i) q^{78} -432.393 q^{79} +218.468 q^{80} +(-381.973 + 183.948i) q^{81} +(804.608 + 1008.95i) q^{82} +(-166.433 - 729.192i) q^{83} +(-583.445 + 419.841i) q^{84} +(-38.2115 + 167.415i) q^{85} +(-1705.48 + 821.317i) q^{86} +(25.8678 - 113.334i) q^{87} +(-694.640 - 871.051i) q^{88} +(72.8537 + 319.193i) q^{89} +(-102.615 + 128.676i) q^{90} +(19.4536 - 393.114i) q^{91} +(-999.593 - 1253.45i) q^{92} +(-396.579 + 497.295i) q^{93} +(-659.691 - 317.691i) q^{94} +(-42.7048 + 53.5501i) q^{95} +(158.745 - 695.507i) q^{96} -1538.64 q^{97} +(225.180 + 1784.71i) q^{98} +425.441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

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