LMFDB - Embedded newform 9.8.c.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,8,Mod(4,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("9.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	9.c (of order $3$, degree $2$, 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:	$2.81146522936$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 $ x^12 - 6x^11 + 375x^10 - 1820x^9 + 50808x^8 - 192378x^7 + 3002887x^6 - 8342916x^5 + 72369348x^4 - 131054670x^3 + 513267363x^2 - 449098992*x + 754412211
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.1
Root			$0.500000 - 11.4952i$ of defining polynomial
Character	$\chi$	$=$	9.4
Dual form			9.8.c.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.7051 - 18.5418i) q^{2} +(21.6493 - 41.4525i) q^{3} +(-165.199 + 286.133i) q^{4} +(32.6274 - 56.5123i) q^{5} +(-1000.36 + 42.3372i) q^{6} +(-118.194 - 204.717i) q^{7} +4333.37 q^{8} +(-1249.62 - 1794.83i) q^{9} +O(q^{10})$	\(q+(-10.7051 - 18.5418i) q^{2} +(21.6493 - 41.4525i) q^{3} +(-165.199 + 286.133i) q^{4} +(32.6274 - 56.5123i) q^{5} +(-1000.36 + 42.3372i) q^{6} +(-118.194 - 204.717i) q^{7} +4333.37 q^{8} +(-1249.62 - 1794.83i) q^{9} -1397.12 q^{10} +(-2305.59 - 3993.39i) q^{11} +(8284.48 + 13042.5i) q^{12} +(68.1364 - 118.016i) q^{13} +(-2530.55 + 4383.04i) q^{14} +(-1636.22 - 2575.94i) q^{15} +(-25243.8 - 43723.5i) q^{16} +5319.46 q^{17} +(-19902.1 + 42384.0i) q^{18} +38228.5 q^{19} +(10780.0 + 18671.5i) q^{20} +(-11044.8 + 467.439i) q^{21} +(-49363.1 + 85499.4i) q^{22} +(36480.5 - 63186.1i) q^{23} +(93814.3 - 179629. i) q^{24} +(36933.4 + 63970.5i) q^{25} -2917.63 q^{26} +(-101454. + 12943.0i) q^{27} +78101.7 q^{28} +(-35682.4 - 61803.7i) q^{29} +(-30246.6 + 57914.1i) q^{30} +(28810.3 - 49900.8i) q^{31} +(-263139. + 455770. i) q^{32} +(-215450. + 9118.28i) q^{33} +(-56945.4 - 98632.4i) q^{34} -15425.4 q^{35} +(719995. - 61052.5i) q^{36} +88485.6 q^{37} +(-409240. - 708824. i) q^{38} +(-3416.94 - 5379.38i) q^{39} +(141387. - 244889. i) q^{40} +(-127791. + 221341. i) q^{41} +(126903. + 199787. i) q^{42} +(324806. + 562580. i) q^{43} +1.52352e6 q^{44} +(-142202. + 12058.1i) q^{45} -1.56211e6 q^{46} +(522539. + 905063. i) q^{47} +(-2.35896e6 + 99835.7i) q^{48} +(383832. - 664817. i) q^{49} +(790752. - 1.36962e6i) q^{50} +(115162. - 220505. i) q^{51} +(22512.1 + 38992.1i) q^{52} -777845. q^{53} +(1.32606e6 + 1.74258e6i) q^{54} -300901. q^{55} +(-512177. - 887116. i) q^{56} +(827618. - 1.58467e6i) q^{57} +(-763967. + 1.32323e6i) q^{58} +(-1.01959e6 + 1.76598e6i) q^{59} +(1.00736e6 - 42633.5i) q^{60} +(-927927. - 1.60722e6i) q^{61} -1.23367e6 q^{62} +(-219736. + 467956. i) q^{63} +4.80532e6 q^{64} +(-4446.23 - 7701.10i) q^{65} +(2.47549e6 + 3.89722e6i) q^{66} +(1.81717e6 - 3.14743e6i) q^{67} +(-878768. + 1.52207e6i) q^{68} +(-1.82945e6 - 2.88014e6i) q^{69} +(165131. + 286015. i) q^{70} +1.93117e6 q^{71} +(-5.41506e6 - 7.77768e6i) q^{72} -2.06016e6 q^{73} +(-947248. - 1.64068e6i) q^{74} +(3.45132e6 - 146067. i) q^{75} +(-6.31529e6 + 1.09384e7i) q^{76} +(-545011. + 943987. i) q^{77} +(-63164.6 + 120943. i) q^{78} +(3.13421e6 + 5.42860e6i) q^{79} -3.29456e6 q^{80} +(-1.65988e6 + 4.48571e6i) q^{81} +5.47209e6 q^{82} +(568792. + 985177. i) q^{83} +(1.69085e6 - 3.23751e6i) q^{84} +(173560. - 300615. i) q^{85} +(6.95416e6 - 1.20450e7i) q^{86} +(-3.33441e6 + 141119. i) q^{87} +(-9.99096e6 - 1.73049e7i) q^{88} -428904. q^{89} +(1.74587e6 + 2.50760e6i) q^{90} -32213.2 q^{91} +(1.20531e7 + 2.08765e7i) q^{92} +(-1.44479e6 - 2.27457e6i) q^{93} +(1.11877e7 - 1.93776e7i) q^{94} +(1.24730e6 - 2.16038e6i) q^{95} +(1.31960e7 + 2.07749e7i) q^{96} +(5.85362e6 + 1.01388e7i) q^{97} -1.64359e7 q^{98} +(-4.28637e6 + 9.12836e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 9 q^{2} + 24 q^{3} - 321 q^{4} - 180 q^{5} - 1233 q^{6} - 84 q^{7} + 5922 q^{8} + 990 q^{9}+O(q^{10}) $ 12 * q - 9 * q^2 + 24 * q^3 - 321 * q^4 - 180 * q^5 - 1233 * q^6 - 84 * q^7 + 5922 * q^8 + 990 * q^9	\( 12 q - 9 q^{2} + 24 q^{3} - 321 q^{4} - 180 q^{5} - 1233 q^{6} - 84 q^{7} + 5922 q^{8} + 990 q^{9} + 252 q^{10} - 8460 q^{11} + 8052 q^{12} - 1848 q^{13} - 16272 q^{14} - 1188 q^{15} - 12417 q^{16} + 30564 q^{17} + 42876 q^{18} + 24432 q^{19} - 40788 q^{20} - 187224 q^{21} - 35001 q^{22} - 51588 q^{23} + 215469 q^{24} + 4746 q^{25} + 536472 q^{26} + 322272 q^{27} + 75516 q^{28} - 414648 q^{29} - 1112112 q^{30} + 8196 q^{31} - 1048977 q^{32} - 148518 q^{33} - 106623 q^{34} + 2210616 q^{35} + 2501811 q^{36} + 139344 q^{37} - 1952685 q^{38} - 2057316 q^{39} + 305496 q^{40} - 1731582 q^{41} + 538866 q^{42} + 408372 q^{43} + 5169114 q^{44} + 2687580 q^{45} - 1684008 q^{46} - 1631484 q^{47} - 7434525 q^{48} - 179010 q^{49} - 1654461 q^{50} + 2525688 q^{51} + 681594 q^{52} + 2835648 q^{53} + 5816529 q^{54} - 16056 q^{55} - 1784466 q^{56} - 3071850 q^{57} - 948384 q^{58} - 2055636 q^{59} + 371484 q^{60} - 2723196 q^{61} - 1026828 q^{62} - 2238804 q^{63} + 7178178 q^{64} - 1387620 q^{65} + 5754762 q^{66} + 3806556 q^{67} + 2142639 q^{68} - 3002292 q^{69} + 953442 q^{70} + 2408400 q^{71} - 9638325 q^{72} - 10670052 q^{73} + 9846504 q^{74} + 19174632 q^{75} - 6727827 q^{76} + 3478824 q^{77} - 13339962 q^{78} + 6020916 q^{79} - 38072448 q^{80} - 28538730 q^{81} + 9403002 q^{82} + 9605052 q^{83} + 30090090 q^{84} - 1698624 q^{85} + 34278561 q^{86} + 10290708 q^{87} - 16459029 q^{88} - 24630264 q^{89} - 13660596 q^{90} + 13570104 q^{91} + 39143394 q^{92} + 27331212 q^{93} + 12602808 q^{94} + 10422072 q^{95} - 3404376 q^{96} + 9977226 q^{97} - 95833314 q^{98} - 49382676 q^{99}+O(q^{100}) \) 12 * q - 9 * q^2 + 24 * q^3 - 321 * q^4 - 180 * q^5 - 1233 * q^6 - 84 * q^7 + 5922 * q^8 + 990 * q^9 + 252 * q^10 - 8460 * q^11 + 8052 * q^12 - 1848 * q^13 - 16272 * q^14 - 1188 * q^15 - 12417 * q^16 + 30564 * q^17 + 42876 * q^18 + 24432 * q^19 - 40788 * q^20 - 187224 * q^21 - 35001 * q^22 - 51588 * q^23 + 215469 * q^24 + 4746 * q^25 + 536472 * q^26 + 322272 * q^27 + 75516 * q^28 - 414648 * q^29 - 1112112 * q^30 + 8196 * q^31 - 1048977 * q^32 - 148518 * q^33 - 106623 * q^34 + 2210616 * q^35 + 2501811 * q^36 + 139344 * q^37 - 1952685 * q^38 - 2057316 * q^39 + 305496 * q^40 - 1731582 * q^41 + 538866 * q^42 + 408372 * q^43 + 5169114 * q^44 + 2687580 * q^45 - 1684008 * q^46 - 1631484 * q^47 - 7434525 * q^48 - 179010 * q^49 - 1654461 * q^50 + 2525688 * q^51 + 681594 * q^52 + 2835648 * q^53 + 5816529 * q^54 - 16056 * q^55 - 1784466 * q^56 - 3071850 * q^57 - 948384 * q^58 - 2055636 * q^59 + 371484 * q^60 - 2723196 * q^61 - 1026828 * q^62 - 2238804 * q^63 + 7178178 * q^64 - 1387620 * q^65 + 5754762 * q^66 + 3806556 * q^67 + 2142639 * q^68 - 3002292 * q^69 + 953442 * q^70 + 2408400 * q^71 - 9638325 * q^72 - 10670052 * q^73 + 9846504 * q^74 + 19174632 * q^75 - 6727827 * q^76 + 3478824 * q^77 - 13339962 * q^78 + 6020916 * q^79 - 38072448 * q^80 - 28538730 * q^81 + 9403002 * q^82 + 9605052 * q^83 + 30090090 * q^84 - 1698624 * q^85 + 34278561 * q^86 + 10290708 * q^87 - 16459029 * q^88 - 24630264 * q^89 - 13660596 * q^90 + 13570104 * q^91 + 39143394 * q^92 + 27331212 * q^93 + 12602808 * q^94 + 10422072 * q^95 - 3404376 * q^96 + 9977226 * q^97 - 95833314 * q^98 - 49382676 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−10.7051	−	18.5418i	−0.946207	−	1.63888i	−0.753317	−	0.657658i	$-0.771547\pi$
$2$	−10.7051	−	18.5418i	−0.946207	−	1.63888i	−0.192890	−	0.981220i	$-0.561786\pi$
$3$	21.6493	−	41.4525i	0.462934	−	0.886393i
$3$	21.6493	−	41.4525i	0.462934	−	0.886393i
$4$	−165.199	+	286.133i	−1.29061	+	2.23541i
$5$	32.6274	−	56.5123i	0.116731	−	0.202185i	−0.801739	−	0.597674i	$-0.796092\pi$
$5$	32.6274	−	56.5123i	0.116731	−	0.202185i	0.918471	+	0.395489i	$0.129425\pi$
$6$	−1000.36	+	42.3372i	−1.89072	+	0.0800190i
$7$	−118.194	−	204.717i	−0.130242	−	0.225586i	0.793528	−	0.608534i	$-0.208242\pi$
$7$	−118.194	−	204.717i	−0.130242	−	0.225586i	−0.923770	+	0.382948i	$0.874909\pi$
$8$	4333.37			2.99234
$9$	−1249.62	−	1794.83i	−0.571385	−	0.820682i
$10$	−1397.12			−0.441808
$11$	−2305.59	−	3993.39i	−0.522284	−	0.904623i	−0.999664	−	0.0259259i	$-0.991747\pi$
$11$	−2305.59	−	3993.39i	−0.522284	−	0.904623i	0.477379	−	0.878697i	$-0.341587\pi$
$12$	8284.48	+	13042.5i	1.38398	+	2.17884i
$13$	68.1364	−	118.016i	0.00860157	−	0.0148984i	−0.861693	−	0.507431i	$-0.830595\pi$
$13$	68.1364	−	118.016i	0.00860157	−	0.0148984i	0.870294	+	0.492532i	$0.163929\pi$
$14$	−2530.55	+	4383.04i	−0.246472	+	0.426901i
$15$	−1636.22	−	2575.94i	−0.125176	−	0.197068i
$16$	−25243.8	−	43723.5i	−1.54076	−	2.66867i
$17$	5319.46			0.262601			0.131301	−	0.991343i	$-0.458085\pi$
$17$	5319.46			0.262601			0.131301	+	0.991343i	$0.458085\pi$
$18$	−19902.1	+	42384.0i	−0.804350	+	1.71297i
$19$	38228.5			1.27864			0.639321	−	0.768940i	$-0.279215\pi$
$19$	38228.5			1.27864			0.639321	+	0.768940i	$0.279215\pi$
$20$	10780.0	+	18671.5i	0.301310	+	0.521885i
$21$	−11044.8	+	467.439i	−0.260251	+	0.0110143i
$22$	−49363.1	+	85499.4i	−0.988378	+	1.71192i
$23$	36480.5	−	63186.1i	0.625192	−	1.08286i	−0.363311	−	0.931668i	$-0.618354\pi$
$23$	36480.5	−	63186.1i	0.625192	−	1.08286i	0.988504	−	0.151197i	$-0.0483128\pi$
$24$	93814.3	−	179629.i	1.38526	−	2.65239i
$25$	36933.4	+	63970.5i	0.472748	+	0.818823i
$26$	−2917.63			−0.0325554
$27$	−101454.	+	12943.0i	−0.991960	+	0.126550i
$28$	78101.7			0.672369
$29$	−35682.4	−	61803.7i	−0.271682	−	0.470567i	0.697611	−	0.716477i	$-0.254246\pi$
$29$	−35682.4	−	61803.7i	−0.271682	−	0.470567i	−0.969293	+	0.245910i	$0.920913\pi$
$30$	−30246.6	+	57914.1i	−0.204528	+	0.391616i
$31$	28810.3	−	49900.8i	0.173693	−	0.300844i	−0.766015	−	0.642822i	$-0.777763\pi$
$31$	28810.3	−	49900.8i	0.173693	−	0.300844i	0.939708	+	0.341978i	$0.111097\pi$
$32$	−263139.	+	455770.i	−1.41958	+	2.45879i
$33$	−215450.	+	9118.28i	−1.04363	+	0.0441686i
$34$	−56945.4	−	98632.4i	−0.248475	−	0.430371i
$35$	−15425.4			−0.0608133
$36$	719995.	−	61052.5i	2.57200	−	0.218095i
$37$	88485.6			0.287188			0.143594	−	0.989637i	$-0.454134\pi$
$37$	88485.6			0.287188			0.143594	+	0.989637i	$0.454134\pi$
$38$	−409240.	−	708824.i	−1.20986	−	2.09554i
$39$	−3416.94	−	5379.38i	−0.00922384	−	0.0145213i
$40$	141387.	−	244889.i	0.349300	−	0.605005i
$41$	−127791.	+	221341.i	−0.289573	+	0.501555i	−0.973708	−	0.227800i	$-0.926847\pi$
$41$	−127791.	+	221341.i	−0.289573	+	0.501555i	0.684135	+	0.729356i	$0.260180\pi$
$42$	126903.	+	199787.i	0.264302	+	0.416098i
$43$	324806.	+	562580.i	0.622994	+	1.07906i	0.988925	+	0.148415i	$0.0474172\pi$
$43$	324806.	+	562580.i	0.622994	+	1.07906i	−0.365931	+	0.930642i	$0.619249\pi$
$44$	1.52352e6			2.69627
$45$	−142202.	+	12058.1i	−0.232628	+	0.0197259i
$46$	−1.56211e6			−2.36624
$47$	522539.	+	905063.i	0.734135	+	1.27156i	0.955102	+	0.296277i	$0.0957453\pi$
$47$	522539.	+	905063.i	0.734135	+	1.27156i	−0.220967	+	0.975281i	$0.570921\pi$
$48$	−2.35896e6	+	99835.7i	−3.07876	+	0.130299i
$49$	383832.	−	664817.i	0.466074	−	0.807264i
$50$	790752.	−	1.36962e6i	0.894634	−	1.54955i
$51$	115162.	−	220505.i	0.121567	−	0.232768i
$52$	22512.1	+	38992.1i	0.0222026	+	0.0384561i
$53$	−777845.			−0.717675			−0.358837	−	0.933400i	$-0.616827\pi$
$53$	−777845.			−0.717675			−0.358837	+	0.933400i	$0.616827\pi$
$54$	1.32606e6	+	1.74258e6i	1.14600	+	1.50596i
$55$	−300901.			−0.243868
$56$	−512177.	−	887116.i	−0.389728	−	0.675029i
$57$	827618.	−	1.58467e6i	0.591927	−	1.13338i
$58$	−763967.	+	1.32323e6i	−0.514134	+	0.890507i
$59$	−1.01959e6	+	1.76598e6i	−0.646314	+	1.11945i	0.337682	+	0.941260i	$0.390357\pi$
$59$	−1.01959e6	+	1.76598e6i	−0.646314	+	1.11945i	−0.983996	+	0.178189i	$0.942976\pi$
$60$	1.00736e6	−	42633.5i	0.602082	−	0.0254813i
$61$	−927927.	−	1.60722e6i	−0.523431	−	0.906609i	−0.999628	−	0.0272705i	$-0.991318\pi$
$61$	−927927.	−	1.60722e6i	−0.523431	−	0.906609i	0.476197	−	0.879339i	$-0.342015\pi$
$62$	−1.23367e6			−0.657396
$63$	−219736.	+	467956.i	−0.110716	+	0.235783i
$64$	4.80532e6			2.29135
$65$	−4446.23	−	7701.10i	−0.00200815	−	0.00347821i
$66$	2.47549e6	+	3.89722e6i	1.05988	+	1.66860i
$67$	1.81717e6	−	3.14743e6i	0.738131	−	1.27848i	−0.215205	−	0.976569i	$-0.569042\pi$
$67$	1.81717e6	−	3.14743e6i	0.738131	−	1.27848i	0.953336	−	0.301911i	$-0.0976247\pi$
$68$	−878768.	+	1.52207e6i	−0.338917	+	0.587021i
$69$	−1.82945e6	−	2.88014e6i	−0.670421	−	1.05546i
$70$	165131.	+	286015.i	0.0575419	+	0.0996656i
$71$	1.93117e6			0.640348			0.320174	−	0.947359i	$-0.396259\pi$
$71$	1.93117e6			0.640348			0.320174	+	0.947359i	$0.396259\pi$
$72$	−5.41506e6	−	7.77768e6i	−1.70978	−	2.45576i
$73$	−2.06016e6			−0.619826			−0.309913	−	0.950765i	$-0.600300\pi$
$73$	−2.06016e6			−0.619826			−0.309913	+	0.950765i	$0.600300\pi$
$74$	−947248.	−	1.64068e6i	−0.271740	−	0.470667i
$75$	3.45132e6	−	146067.i	0.944650	−	0.0399794i
$76$	−6.31529e6	+	1.09384e7i	−1.65024	+	2.85829i
$77$	−545011.	+	943987.i	−0.136047	+	0.235640i
$78$	−63164.6	+	120943.i	−0.0150710	+	0.0288569i
$79$	3.13421e6	+	5.42860e6i	0.715208	+	1.23878i	0.962879	+	0.269933i	$0.0870016\pi$
$79$	3.13421e6	+	5.42860e6i	0.715208	+	1.23878i	−0.247671	+	0.968844i	$0.579665\pi$
$80$	−3.29456e6			−0.719419
$81$	−1.65988e6	+	4.48571e6i	−0.347039	+	0.937851i
$82$	5.47209e6			1.09598
$83$	568792.	+	985177.i	0.109189	+	0.189122i	0.915442	−	0.402450i	$-0.131841\pi$
$83$	568792.	+	985177.i	0.109189	+	0.189122i	−0.806253	+	0.591571i	$0.798508\pi$
$84$	1.69085e6	−	3.23751e6i	0.311262	−	0.595983i
$85$	173560.	−	300615.i	0.0306538	−	0.0530939i
$86$	6.95416e6	−	1.20450e7i	1.17896	−	2.04202i
$87$	−3.33441e6	+	141119.i	−0.542878	+	0.0229756i
$88$	−9.99096e6	−	1.73049e7i	−1.56285	−	2.70694i
$89$	−428904.			−0.0644904			−0.0322452	−	0.999480i	$-0.510266\pi$
$89$	−428904.			−0.0644904			−0.0322452	+	0.999480i	$0.510266\pi$
$90$	1.74587e6	+	2.50760e6i	0.252442	+	0.362584i
$91$	−32213.2			−0.00448114
$92$	1.20531e7	+	2.08765e7i	1.61376	+	2.79512i
$93$	−1.44479e6	−	2.27457e6i	−0.186258	−	0.293231i
$94$	1.11877e7	−	1.93776e7i	1.38929	−	2.40632i
$95$	1.24730e6	−	2.16038e6i	0.149258	−	0.258522i
$96$	1.31960e7	+	2.07749e7i	1.52228	+	2.39656i
$97$	5.85362e6	+	1.01388e7i	0.651214	+	1.12793i	0.982829	+	0.184520i	$0.0590731\pi$
$97$	5.85362e6	+	1.01388e7i	0.651214	+	1.12793i	−0.331615	+	0.943415i	$0.607594\pi$
$98$	−1.64359e7			−1.76401
$99$	−4.28637e6	+	9.12836e6i	−0.443983	+	0.945517i
$100$	−2.44054e7			−2.44054
$101$	−9.34885e6	−	1.61927e7i	−0.902887	−	1.56385i	−0.823728	−	0.566985i	$-0.808110\pi$
$101$	−9.34885e6	−	1.61927e7i	−0.902887	−	1.56385i	−0.0791589	−	0.996862i	$-0.525223\pi$
$102$	−5.32138e6	+	225211.i	−0.496505	+	0.0210131i
$103$	414577.	−	718068.i	0.0373830	−	0.0647493i	−0.846729	−	0.532025i	$-0.821431\pi$
$103$	414577.	−	718068.i	0.0373830	−	0.0647493i	0.884112	+	0.467276i	$0.154764\pi$
$104$	295260.	−	511406.i	0.0257388	−	0.0445809i
$105$	−333949.	+	639422.i	−0.0281525	+	0.0539045i
$106$	8.32692e6	+	1.44226e7i	0.679069	+	1.17618i
$107$	9.20798e6			0.726643			0.363322	−	0.931664i	$-0.381643\pi$
$107$	9.20798e6			0.726643			0.363322	+	0.931664i	$0.381643\pi$
$108$	1.30566e7	−	3.11673e7i	0.997348	−	2.38077i
$109$	−1.08593e7			−0.803174			−0.401587	−	0.915821i	$-0.631541\pi$
$109$	−1.08593e7			−0.803174			−0.401587	+	0.915821i	$0.631541\pi$
$110$	3.22118e6	+	5.57925e6i	0.230749	+	0.399670i
$111$	1.91565e6	−	3.66795e6i	0.132949	−	0.254562i
$112$	−5.96731e6	+	1.03357e7i	−0.401343	+	0.695146i
$113$	3.17666e6	−	5.50213e6i	0.207107	−	0.358720i	−0.743695	−	0.668519i	$-0.766928\pi$
$113$	3.17666e6	−	5.50213e6i	0.207107	−	0.358720i	0.950802	+	0.309799i	$0.100262\pi$
$114$	−3.82423e7	+	1.61849e6i	−2.41756	+	0.102316i
$115$	−2.38053e6	−	4.12320e6i	−0.145959	−	0.252809i
$116$	2.35787e7			1.40255
$117$	−296963.	+	25181.2i	−0.0171416	+	0.00145354i
$118$	4.36593e7			2.44619
$119$	−628726.	−	1.08899e6i	−0.0342017	−	0.0592390i
$120$	−7.09034e6	−	1.11625e7i	−0.374570	−	0.589694i
$121$	−887875.	+	1.53784e6i	−0.0455620	+	0.0789157i
$122$	−1.98671e7	+	3.44109e7i	−0.990548	+	1.71568i
$123$	6.40856e6	+	1.00892e7i	0.310522	+	0.488863i
$124$	9.51884e6	+	1.64871e7i	0.448340	+	0.776548i
$125$	9.91820e6			0.454201
$126$	1.10290e7	−	935217.i	0.491181	−	0.0416500i
$127$	−1.79848e7			−0.779100			−0.389550	−	0.921005i	$-0.627369\pi$
$127$	−1.79848e7			−0.779100			−0.389550	+	0.921005i	$0.627369\pi$
$128$	−1.77597e7	−	3.07606e7i	−0.748514	−	1.29646i
$129$	3.03521e7	−	1.28456e6i	1.24487	−	0.0526855i
$130$	−95194.7	+	164882.i	−0.00380024	+	0.00658221i
$131$	−1.88048e6	+	3.25708e6i	−0.0730834	+	0.126584i	−0.900251	−	0.435371i	$-0.856617\pi$
$131$	−1.88048e6	+	3.25708e6i	−0.0730834	+	0.126584i	0.827168	+	0.561955i	$0.189951\pi$
$132$	3.29831e7	−	6.31537e7i	1.24820	−	2.38996i
$133$	−4.51836e6	−	7.82603e6i	−0.166533	−	0.288443i
$134$	−7.78119e7			−2.79370
$135$	−2.57873e6	+	6.15568e6i	−0.0902064	+	0.215331i
$136$	2.30512e7			0.785792
$137$	−652403.	−	1.13000e6i	−0.0216767	−	0.0375452i	0.854984	−	0.518655i	$-0.173567\pi$
$137$	−652403.	−	1.13000e6i	−0.0216767	−	0.0375452i	−0.876660	+	0.481110i	$0.840234\pi$
$138$	−3.38186e7	+	6.47534e7i	−1.09541	+	2.09742i
$139$	5.83704e6	−	1.01101e7i	0.184349	−	0.319302i	−0.759008	−	0.651081i	$-0.774316\pi$
$139$	5.83704e6	−	1.01101e7i	0.184349	−	0.319302i	0.943357	+	0.331779i	$0.107649\pi$
$140$	2.54826e6	−	4.41371e6i	0.0784865	−	0.135943i
$141$	4.88297e7	−	2.06657e6i	1.46696	−	0.0620844i
$142$	−2.06734e7	−	3.58073e7i	−0.605902	−	1.04945i
$143$	−628378.			−0.0179699
$144$	−4.69313e7	+	9.99461e7i	−1.30977	+	2.78931i
$145$	−4.65689e6			−0.126855
$146$	2.20542e7	+	3.81990e7i	0.586484	+	1.01582i
$147$	−1.92486e7	−	3.03036e7i	−0.499792	−	0.786834i
$148$	−1.46177e7	+	2.53186e7i	−0.370649	+	0.641984i
$149$	−1.59389e7	+	2.76070e7i	−0.394736	+	0.683703i	−0.993067	−	0.117546i	$-0.962497\pi$
$149$	−1.59389e7	+	2.76070e7i	−0.394736	+	0.683703i	0.598331	+	0.801249i	$0.295831\pi$
$150$	−3.96551e7	−	6.24300e7i	−0.959355	−	1.51034i
$151$	−3.55648e7	−	6.16000e7i	−0.840622	−	1.45600i	−0.889370	−	0.457188i	$-0.848857\pi$
$151$	−3.55648e7	−	6.16000e7i	−0.840622	−	1.45600i	0.0487485	−	0.998811i	$-0.484477\pi$
$152$	1.65658e8			3.82613
$153$	−6.64730e6	−	9.54754e6i	−0.150046	−	0.215512i
$154$	2.33376e7			0.514913
$155$	−1.88001e6	−	3.25627e6i	−0.0405507	−	0.0702360i
$156$	2.10369e6	−	89032.2i	0.0443655	−	0.00187763i
$157$	−3.52217e7	+	6.10057e7i	−0.726375	+	1.25812i	0.232030	+	0.972709i	$0.425463\pi$
$157$	−3.52217e7	+	6.10057e7i	−0.726375	+	1.25812i	−0.958405	+	0.285411i	$0.907870\pi$
$158$	6.71040e7	−	1.16228e8i	1.35347	−	2.34428i
$159$	−1.68398e7	+	3.22436e7i	−0.332236	+	0.636142i
$160$	1.71711e7	+	2.97412e7i	0.331419	+	0.574035i
$161$	−1.72471e7			−0.325705
$162$	1.00942e8	−	1.72429e7i	1.86539	−	0.318646i
$163$	3.98423e7			0.720590			0.360295	−	0.932838i	$-0.382676\pi$
$163$	3.98423e7			0.720590			0.360295	+	0.932838i	$0.382676\pi$
$164$	−4.22220e7	−	7.31306e7i	−0.747455	−	1.29463i
$165$	−6.51429e6	+	1.24731e7i	−0.112895	+	0.216163i
$166$	1.21780e7	−	2.10929e7i	0.206631	−	0.357896i
$167$	−2.58421e7	+	4.47599e7i	−0.429359	+	0.743672i	−0.996816	−	0.0797308i	$-0.974594\pi$
$167$	−2.58421e7	+	4.47599e7i	−0.429359	+	0.743672i	0.567457	+	0.823403i	$0.307927\pi$
$168$	−4.78614e7	+	2.02559e6i	−0.778759	+	0.0329586i
$169$	3.13650e7	+	5.43257e7i	0.499852	+	0.865769i
$170$	−7.43193e6			−0.116019
$171$	−4.77710e7	−	6.86137e7i	−0.730597	−	1.04936i
$172$	−2.14630e8			−3.21618
$173$	−9.10891e6	−	1.57771e7i	−0.133753	−	0.231668i	0.791367	−	0.611341i	$-0.209370\pi$
$173$	−9.10891e6	−	1.57771e7i	−0.133753	−	0.231668i	−0.925121	+	0.379673i	$0.876036\pi$
$174$	3.83118e7	+	6.03153e7i	0.551329	+	0.867971i
$175$	8.73059e6	−	1.51218e7i	0.123143	−	0.213290i
$176$	−1.16403e8	+	2.01617e8i	−1.60943	+	2.78761i
$177$	5.11310e7	+	8.04968e7i	0.693071	+	1.09112i
$178$	4.59147e6	+	7.95265e6i	0.0610213	+	0.105692i
$179$	1.05708e8			1.37759			0.688797	−	0.724955i	$-0.258139\pi$
$179$	1.05708e8			1.37759			0.688797	+	0.724955i	$0.258139\pi$
$180$	2.00414e7	−	4.26806e7i	0.256138	−	0.545477i
$181$	1.29009e8			1.61713			0.808566	−	0.588406i	$-0.200244\pi$
$181$	1.29009e8			1.61713			0.808566	+	0.588406i	$0.200244\pi$
$182$	344845.	+	597290.i	0.00424008	+	0.00734404i
$183$	−8.67121e7	+	3.66982e6i	−1.04593	+	0.0442656i
$184$	1.58084e8	−	2.73809e8i	1.87079	−	3.24030i
$185$	2.88706e6	−	5.00053e6i	0.0335239	−	0.0580651i
$186$	−2.67080e7	+	5.11386e7i	−0.304331	+	0.582712i
$187$	−1.22645e7	−	2.12427e7i	−0.137152	−	0.237555i
$188$	−3.45291e8			−3.78994
$189$	1.46408e7	+	1.92395e7i	0.157743	+	0.207290i
$190$	−5.34097e7			−0.564915
$191$	−8.43634e6	−	1.46122e7i	−0.0876067	−	0.151739i	0.818892	−	0.573947i	$-0.194589\pi$
$191$	−8.43634e6	−	1.46122e7i	−0.0876067	−	0.151739i	−0.906499	+	0.422208i	$0.861255\pi$
$192$	1.04032e8	−	1.99192e8i	1.06075	−	2.03104i
$193$	−3.10280e7	+	5.37420e7i	−0.310672	+	0.538100i	−0.978508	−	0.206208i	$-0.933888\pi$
$193$	−3.10280e7	+	5.37420e7i	−0.310672	+	0.538100i	0.667836	+	0.744309i	$0.267221\pi$
$194$	1.25327e8	−	2.17073e8i	1.23237	−	2.13452i
$195$	−415487.	+	17584.2i	−0.00401270	+	0.000169825i
$196$	1.26817e8	+	2.19654e8i	1.20304	+	2.08373i
$197$	−7.26554e6			−0.0677074			−0.0338537	−	0.999427i	$-0.510778\pi$
$197$	−7.26554e6			−0.0677074			−0.0338537	+	0.999427i	$0.510778\pi$
$198$	2.15142e8	−	1.82431e7i	1.96969	−	0.167021i
$199$	6.21194e7			0.558780			0.279390	−	0.960178i	$-0.409868\pi$
$199$	6.21194e7			0.558780			0.279390	+	0.960178i	$0.409868\pi$
$200$	1.60046e8	+	2.77208e8i	1.41462	+	2.45020i
$201$	−9.11284e7	−	1.43466e8i	−0.791530	−	1.24613i
$202$	−2.00161e8	+	3.46689e8i	−1.70864	+	2.95944i
$203$	−8.43485e6	+	1.46096e7i	−0.0707687	+	0.122575i
$204$	4.40690e7	+	6.93789e7i	0.363435	+	0.572165i
$205$	8.33901e6	+	1.44436e7i	0.0676045	+	0.117095i
$206$	−1.77524e7			−0.141488
$207$	−1.58995e8	+	1.34821e7i	−1.24591	+	0.105648i
$208$	−6.88008e6			−0.0530117
$209$	−8.81390e7	−	1.52661e8i	−0.667815	−	1.15669i
$210$	1.54310e7	−	653069.i	0.114981	−	0.00486622i
$211$	8.98867e7	−	1.55688e8i	0.658729	−	1.14095i	−0.322216	−	0.946666i	$-0.604428\pi$
$211$	8.98867e7	−	1.55688e8i	0.658729	−	1.14095i	0.980945	−	0.194286i	$-0.0622390\pi$
$212$	1.28499e8	−	2.22567e8i	0.926241	−	1.60430i
$213$	4.18084e7	−	8.00518e7i	0.296439	−	0.567600i
$214$	−9.85725e7	−	1.70733e8i	−0.687555	−	1.19088i
$215$	4.23903e7			0.290892
$216$	−4.39636e8	+	5.60868e7i	−2.96828	+	0.378680i
$217$	−1.36208e7			−0.0904882
$218$	1.16250e8	+	2.01351e8i	0.759969	+	1.31630i
$219$	−4.46009e7	+	8.53986e7i	−0.286938	+	0.549410i
$220$	4.97085e7	−	8.60976e7i	0.314740	−	0.545145i
$221$	362449.	−	627780.i	0.00225878	−	0.00391232i
$222$	−8.85176e7	+	3.74624e6i	−0.542993	+	0.0229805i
$223$	−3.72429e7	−	6.45066e7i	−0.224893	−	0.389527i	0.731394	−	0.681955i	$-0.238870\pi$
$223$	−3.72429e7	−	6.45066e7i	−0.224893	−	0.389527i	−0.956287	+	0.292428i	$0.905537\pi$
$224$	1.24405e8			0.739556
$225$	6.86637e7	−	1.46228e8i	0.401873	−	0.855838i
$226$	−1.36026e8			−0.783866
$227$	1.06638e8	+	1.84702e8i	0.605090	+	1.04805i	0.992037	+	0.125944i	$0.0401961\pi$
$227$	1.06638e8	+	1.84702e8i	0.605090	+	1.04805i	−0.386948	+	0.922102i	$0.626471\pi$
$228$	3.16703e8	+	4.98593e8i	1.76962	+	2.78596i
$229$	−7.52916e7	+	1.30409e8i	−0.414307	+	0.717601i	−0.995355	−	0.0962682i	$-0.969309\pi$
$229$	−7.52916e7	+	1.30409e8i	−0.414307	+	0.717601i	0.581048	+	0.813869i	$0.302643\pi$
$230$	−5.09677e7	+	8.82786e7i	−0.276215	+	0.478418i
$231$	2.73315e7	+	4.30287e7i	0.145889	+	0.229676i
$232$	−1.54625e8	−	2.67818e8i	−0.812964	−	1.40810i
$233$	−1.27302e8			−0.659309			−0.329654	−	0.944102i	$-0.606932\pi$
$233$	−1.27302e8			−0.659309			−0.329654	+	0.944102i	$0.606932\pi$
$234$	3.64593e6	+	5.23666e6i	0.0186017	+	0.0267177i
$235$	6.81963e7			0.342786
$236$	−3.36870e8	−	5.83476e8i	−1.66828	−	2.88955i
$237$	2.92882e8	−	1.23953e7i	1.42914	−	0.0604839i
$238$	−1.34612e7	+	2.33154e7i	−0.0647237	+	0.112105i
$239$	−1.55897e8	+	2.70021e8i	−0.738659	+	1.27940i	0.214440	+	0.976737i	$0.431207\pi$
$239$	−1.55897e8	+	2.70021e8i	−0.738659	+	1.27940i	−0.953099	+	0.302658i	$0.902126\pi$
$240$	−7.13247e7	+	1.36568e8i	−0.333043	+	0.637688i
$241$	−2.32957e7	−	4.03494e7i	−0.107205	−	0.185685i	0.807432	−	0.589961i	$-0.200857\pi$
$241$	−2.32957e7	−	4.03494e7i	−0.107205	−	0.185685i	−0.914637	+	0.404276i	$0.867524\pi$
$242$	3.80192e7			0.172444
$243$	1.50009e8	+	1.65918e8i	0.670648	+	0.741776i
$244$	6.13169e8			2.70219
$245$	−2.50469e7	−	4.33825e7i	−0.108811	−	0.188466i
$246$	1.18467e8	−	2.26832e8i	0.507368	−	0.971473i
$247$	2.60475e6	−	4.51156e6i	0.0109983	−	0.0190497i
$248$	1.24846e8	−	2.16239e8i	0.519747	−	0.900229i
$249$	5.31520e7	−	2.24950e6i	0.218183	−	0.00923395i
$250$	−1.06175e8	−	1.83901e8i	−0.429768	−	0.744380i
$251$	2.93904e8			1.17313			0.586567	−	0.809901i	$-0.300479\pi$
$251$	2.93904e8			1.17313			0.586567	+	0.809901i	$0.300479\pi$
$252$	−9.75973e7	−	1.40179e8i	−0.384181	−	0.551801i
$253$	−3.36436e8			−1.30611
$254$	1.92529e8	+	3.33471e8i	0.737190	+	1.27685i
$255$	−8.70380e6	−	1.37026e7i	−0.0328714	−	0.0517503i
$256$	−7.26979e7	+	1.25916e8i	−0.270821	+	0.469075i
$257$	−1.43637e7	+	2.48786e7i	−0.0527837	+	0.0914240i	−0.891210	−	0.453591i	$-0.850143\pi$
$257$	−1.43637e7	+	2.48786e7i	−0.0527837	+	0.0914240i	0.838426	+	0.545015i	$0.183476\pi$
$258$	−3.48741e8	−	5.49032e8i	−1.26425	−	1.99034i
$259$	−1.04584e7	−	1.81145e7i	−0.0374040	−	0.0647856i
$260$	2.93805e6			0.0103670
$261$	−6.63379e7	+	1.41275e8i	−0.230951	+	0.491839i
$262$	8.05229e7			0.276608
$263$	1.05540e8	+	1.82800e8i	0.357743	+	0.619630i	0.987583	−	0.157095i	$-0.0502129\pi$
$263$	1.05540e8	+	1.82800e8i	0.357743	+	0.619630i	−0.629840	+	0.776725i	$0.716880\pi$
$264$	−9.33627e8	+	3.95129e7i	−3.12291	+	0.132168i
$265$	−2.53791e7	+	4.39578e7i	−0.0837751	+	0.145103i
$266$	−9.67391e7	+	1.67557e8i	−0.315149	+	0.545854i
$267$	−9.28546e6	+	1.77792e7i	−0.0298548	+	0.0571639i
$268$	6.00388e8	+	1.03990e9i	1.90529	+	3.30005i
$269$	−3.22090e8			−1.00889			−0.504446	−	0.863444i	$-0.668303\pi$
$269$	−3.22090e8			−1.00889			−0.504446	+	0.863444i	$0.668303\pi$
$270$	1.41743e8	−	1.80829e7i	0.438256	−	0.0559107i
$271$	−3.74530e8			−1.14313			−0.571563	−	0.820558i	$-0.693663\pi$
$271$	−3.74530e8			−1.14313			−0.571563	+	0.820558i	$0.693663\pi$
$272$	−1.34283e8	−	2.32586e8i	−0.404605	−	0.700796i
$273$	−697391.	+	1.33532e6i	−0.00207447	+	0.00397205i
$274$	−1.39681e7	+	2.41934e7i	−0.0410214	+	0.0710511i
$275$	1.70306e8	−	2.94979e8i	0.493817	−	0.855317i
$276$	1.12632e9	−	4.76682e7i	3.22464	−	0.136473i
$277$	8.96175e7	+	1.55222e8i	0.253346	+	0.438808i	0.964445	−	0.264284i	$-0.0851357\pi$
$277$	8.96175e7	+	1.55222e8i	0.253346	+	0.438808i	−0.711099	+	0.703092i	$0.751802\pi$
$278$	−2.49945e8			−0.697730
$279$	−1.25565e8	+	1.06474e7i	−0.346143	+	0.0293515i
$280$	−6.68440e7			−0.181974
$281$	−1.99247e8	−	3.45106e8i	−0.535697	−	0.927854i	−0.999129	−	0.0417220i	$-0.986716\pi$
$281$	−1.99247e8	−	3.45106e8i	−0.535697	−	0.927854i	0.463432	−	0.886132i	$-0.346618\pi$
$282$	−5.61045e8	−	8.83267e8i	−1.48979	−	2.34542i
$283$	1.71350e8	−	2.96786e8i	0.449397	−	0.778379i	−0.548949	−	0.835856i	$-0.684972\pi$
$283$	1.71350e8	−	2.96786e8i	0.449397	−	0.778379i	0.998347	+	0.0574763i	$0.0183054\pi$
$284$	−3.19027e8	+	5.52570e8i	−0.826443	+	1.43144i
$285$	−6.25501e7	−	9.84742e7i	−0.160056	−	0.251980i
$286$	6.72685e6	+	1.16512e7i	0.0170032	+	0.0294504i
$287$	6.04165e7			0.150858
$288$	1.14685e9	−	9.72484e7i	2.82901	−	0.239888i
$289$	−3.82042e8			−0.931041
$290$	4.98525e7	+	8.63471e7i	0.120031	+	0.207900i
$291$	5.47004e8	−	2.31503e7i	1.30126	−	0.0550719i
$292$	3.40335e8	−	5.89477e8i	0.799957	−	1.38557i
$293$	3.04388e8	−	5.27216e8i	0.706954	−	1.22448i	−0.259028	−	0.965870i	$-0.583402\pi$
$293$	3.04388e8	−	5.27216e8i	0.706954	−	1.22448i	0.965982	−	0.258610i	$-0.0832645\pi$
$294$	−3.55824e8	+	6.81307e8i	−0.816620	+	1.56361i
$295$	6.65332e7	+	1.15239e8i	0.150890	+	0.261350i
$296$	3.83441e8			0.859365
$297$	2.85597e8	+	3.75303e8i	0.632565	+	0.831255i
$298$	6.82511e8			1.49401
$299$	−4.97130e6	−	8.61055e6i	−0.0107553	−	0.0186287i
$300$	−5.28359e8	+	1.01166e9i	−1.12981	+	2.16328i
$301$	7.67799e7	−	1.32987e8i	0.162280	−	0.281077i
$302$	−7.61449e8	+	1.31887e9i	−1.59080	+	2.75535i
$303$	−8.73623e8	+	3.69734e7i	−1.80416	+	0.0763555i
$304$	−9.65031e8	−	1.67148e9i	−1.97008	−	3.41228i
$305$	−1.21103e8			−0.244403
$306$	−1.05868e8	+	2.25460e8i	−0.211223	+	0.449827i
$307$	5.84300e8			1.15253			0.576265	−	0.817263i	$-0.304510\pi$
$307$	5.84300e8			1.15253			0.576265	+	0.817263i	$0.304510\pi$
$308$	−1.80070e8	−	3.11891e8i	−0.351168	−	0.608240i
$309$	−2.07904e7	−	3.27309e7i	−0.0400875	−	0.0631107i
$310$	−4.02514e7	+	6.97175e7i	−0.0767388	+	0.132915i
$311$	1.46239e8	−	2.53294e8i	0.275678	−	0.477489i	−0.694628	−	0.719369i	$-0.744431\pi$
$311$	1.46239e8	−	2.53294e8i	0.275678	−	0.477489i	0.970306	+	0.241881i	$0.0777642\pi$
$312$	−1.48069e7	−	2.33108e7i	−0.0276009	−	0.0434527i
$313$	4.13742e8	+	7.16621e8i	0.762648	+	1.32094i	0.941481	+	0.337065i	$0.109434\pi$
$313$	4.13742e8	+	7.16621e8i	0.762648	+	1.32094i	−0.178834	+	0.983879i	$0.557232\pi$
$314$	1.50821e9			2.74921
$315$	1.92759e7	+	2.76860e7i	0.0347478	+	0.0499084i
$316$	−2.07107e9			−3.69223
$317$	−1.21830e7	−	2.11016e7i	−0.0214807	−	0.0372057i	0.855085	−	0.518487i	$-0.173505\pi$
$317$	−1.21830e7	−	2.11016e7i	−0.0214807	−	0.0372057i	−0.876566	+	0.481282i	$0.840171\pi$
$318$	7.78126e8	−	3.29318e7i	1.35692	−	0.0574276i
$319$	−1.64538e8	+	2.84987e8i	−0.283790	+	0.491539i
$320$	1.56785e8	−	2.71560e8i	0.267473	−	0.463277i
$321$	1.99346e8	−	3.81694e8i	0.336388	−	0.644092i
$322$	1.84632e8	+	3.19791e8i	0.308184	+	0.533791i
$323$	2.03355e8			0.335773
$324$	−1.00930e9	−	1.21598e9i	−1.64859	−	1.98618i
$325$	1.00660e7			0.0162655
$326$	−4.26516e8	−	7.38748e8i	−0.681827	−	1.18096i
$327$	−2.35096e8	+	4.50146e8i	−0.371816	+	0.711928i
$328$	−5.53768e8	+	9.59154e8i	−0.866501	+	1.50082i
$329$	1.23521e8	−	2.13945e8i	0.191230	−	0.331221i
$330$	3.01010e8	−	1.27393e7i	0.461086	−	0.0195141i
$331$	8.03016e6	+	1.39086e7i	0.0121710	+	0.0210808i	0.872047	−	0.489423i	$-0.162792\pi$
$331$	8.03016e6	+	1.39086e7i	0.0121710	+	0.0210808i	−0.859876	+	0.510503i	$0.829459\pi$
$332$	−3.75855e8			−0.563686
$333$	−1.10573e8	−	1.58817e8i	−0.164095	−	0.235690i
$334$	1.10657e9			1.62505
$335$	−1.18579e8	−	2.05385e8i	−0.172326	−	0.298478i
$336$	2.99252e8	+	4.71120e8i	0.430377	+	0.677554i
$337$	1.21283e8	−	2.10068e8i	0.172621	−	0.298989i	−0.766714	−	0.641988i	$-0.778110\pi$
$337$	1.21283e8	−	2.10068e8i	0.172621	−	0.298989i	0.939335	+	0.343000i	$0.111443\pi$
$338$	6.71531e8	−	1.16313e9i	0.945927	−	1.63839i
$339$	−1.59305e8	−	2.50797e8i	−0.222090	−	0.349642i
$340$	5.73439e7	+	9.93225e7i	0.0791245	+	0.137048i
$341$	−2.65698e8			−0.362868
$342$	−7.60827e8	+	1.62028e9i	−1.02848	+	2.19027i
$343$	−3.76141e8			−0.503293
$344$	1.40750e9	+	2.43787e9i	1.86421	+	3.22891i
$345$	−2.22454e8	+	9.41467e6i	−0.291657	+	0.0123435i
$346$	−1.95024e8	+	3.37791e8i	−0.253117	+	0.438411i
$347$	−2.06422e8	+	3.57534e8i	−0.265218	+	0.459372i	−0.967621	−	0.252408i	$-0.918777\pi$
$347$	−2.06422e8	+	3.57534e8i	−0.265218	+	0.459372i	0.702402	+	0.711780i	$0.252111\pi$
$348$	5.10462e8	−	9.77397e8i	0.649286	−	1.24321i
$349$	−2.60275e8	−	4.50809e8i	−0.327750	−	0.567680i	0.654315	−	0.756222i	$-0.272957\pi$
$349$	−2.60275e8	−	4.50809e8i	−0.327750	−	0.567680i	−0.982065	+	0.188542i	$0.939624\pi$
$350$	−3.73847e8			−0.466075
$351$	−5.38521e6	+	1.28550e7i	−0.00664703	+	0.0158671i
$352$	2.42676e9			2.96570
$353$	7.22672e8	+	1.25170e9i	0.874439	+	1.51457i	0.857359	+	0.514719i	$0.172104\pi$
$353$	7.22672e8	+	1.25170e9i	0.874439	+	1.51457i	0.0170799	+	0.999854i	$0.494563\pi$
$354$	9.45192e8	−	1.80979e9i	1.13242	−	2.16828i
$355$	6.30090e7	−	1.09135e8i	0.0747487	−	0.129469i
$356$	7.08544e7	−	1.22723e8i	0.0832323	−	0.144163i
$357$	−5.87527e7	+	2.48653e6i	−0.0683422	+	0.00289237i
$358$	−1.13161e9	−	1.96001e9i	−1.30349	−	2.25771i
$359$	−1.00008e9			−1.14079			−0.570395	−	0.821371i	$-0.693210\pi$
$359$	−1.00008e9			−1.14079			−0.570395	+	0.821371i	$0.693210\pi$
$360$	−6.16214e8	+	5.22523e7i	−0.696102	+	0.0590265i
$361$	5.67544e8			0.634927
$362$	−1.38106e9	−	2.39206e9i	−1.53014	−	2.65028i
$363$	4.45257e7	+	7.00978e7i	0.0488582	+	0.0769186i
$364$	5.32157e6	−	9.21723e6i	0.00578342	−	0.0100172i
$365$	−6.72175e7	+	1.16424e8i	−0.0723532	+	0.125319i
$366$	9.96307e8	+	1.56851e9i	1.06221	+	1.67226i
$367$	−3.98743e8	−	6.90644e8i	−0.421078	−	0.729328i	0.574967	−	0.818176i	$-0.305015\pi$
$367$	−3.98743e8	−	6.90644e8i	−0.421078	−	0.729328i	−0.996045	+	0.0888481i	$0.971681\pi$
$368$	−3.68362e9			−3.85308
$369$	5.56961e8	−	4.72279e7i	0.577075	−	0.0489335i
$370$	−1.23625e8			−0.126882
$371$	9.19363e7	+	1.59238e8i	0.0934713	+	0.161897i
$372$	8.89507e8	−	3.76457e7i	0.895879	−	0.0379153i
$373$	−1.30751e8	+	2.26468e8i	−0.130456	+	0.225957i	−0.923853	−	0.382749i	$-0.874978\pi$
$373$	−1.30751e8	+	2.26468e8i	−0.130456	+	0.225957i	0.793396	+	0.608705i	$0.208311\pi$
$374$	−2.62585e8	+	4.54811e8i	−0.259549	+	0.449552i
$375$	2.14722e8	−	4.11134e8i	0.210265	−	0.402600i
$376$	2.26435e9	+	3.92198e9i	2.19678	+	3.80494i
$377$	−9.72507e6			−0.00934756
$378$	2.00004e8	−	4.77428e8i	0.190466	−	0.454660i
$379$	−3.42925e8			−0.323565			−0.161782	−	0.986826i	$-0.551724\pi$
$379$	−3.42925e8			−0.323565			−0.161782	+	0.986826i	$0.551724\pi$
$380$	4.12103e8	+	7.13784e8i	0.385268	+	0.667305i
$381$	−3.89358e8	+	7.45516e8i	−0.360672	+	0.690588i
$382$	−1.80624e8	+	3.12850e8i	−0.165788	+	0.287153i
$383$	−5.05976e8	+	8.76376e8i	−0.460187	+	0.797067i	−0.998970	−	0.0453777i	$-0.985551\pi$
$383$	−5.05976e8	+	8.76376e8i	−0.460187	+	0.797067i	0.538783	+	0.842444i	$0.318884\pi$
$384$	−1.65959e9	+	7.02370e7i	−1.49569	+	0.0633005i
$385$	3.55646e7	+	6.15997e7i	0.0317618	+	0.0550131i
$386$	1.32863e9			1.17584
$387$	6.03853e8	−	1.28598e9i	0.529594	−	1.12784i
$388$	−3.86804e9			−3.36186
$389$	6.08222e8	+	1.05347e9i	0.523888	+	0.907400i	0.999613	+	0.0278066i	$0.00885225\pi$
$389$	6.08222e8	+	1.05347e9i	0.523888	+	0.907400i	−0.475725	+	0.879594i	$0.657814\pi$
$390$	4.77388e6	+	7.51564e6i	0.00407517	+	0.00641563i
$391$	1.94057e8	−	3.36116e8i	0.164176	−	0.284361i
$392$	1.66329e9	−	2.88090e9i	1.39465	−	2.41561i
$393$	9.43033e7	+	1.48464e8i	0.0783706	+	0.123381i
$394$	7.77784e7	+	1.34716e8i	0.0640652	+	0.110964i
$395$	4.09044e8			0.333949
$396$	−1.90382e9	−	2.73446e9i	−1.54061	−	2.21278i
$397$	1.05353e9			0.845043			0.422522	−	0.906353i	$-0.361145\pi$
$397$	1.05353e9			0.845043			0.422522	+	0.906353i	$0.361145\pi$
$398$	−6.64994e8	−	1.15180e9i	−0.528722	−	0.915773i
$399$	−4.22228e8	+	1.78695e7i	−0.332768	+	0.0140834i
$400$	1.86468e9	−	3.22972e9i	1.45678	−	2.52322i
$401$	−8.32350e8	+	1.44167e9i	−0.644616	+	1.11651i	0.339774	+	0.940507i	$0.389649\pi$
$401$	−8.32350e8	+	1.44167e9i	−0.644616	+	1.11651i	−0.984390	+	0.176000i	$0.943684\pi$
$402$	−1.68457e9	+	3.22550e9i	−1.29330	+	2.47631i
$403$	−3.92606e6	−	6.80013e6i	−0.00298806	−	0.00517547i
$404$	6.17767e9			4.66112
$405$	1.99341e8	+	2.40161e8i	0.149109	+	0.179643i
$406$	3.61184e8			0.267847
$407$	−2.04011e8	−	3.53358e8i	−0.149994	−	0.259797i
$408$	4.99042e8	−	9.55530e8i	0.363770	−	0.696520i
$409$	9.26033e6	−	1.60394e7i	0.00669260	−	0.0115919i	−0.862660	−	0.505785i	$-0.831203\pi$
$409$	9.26033e6	−	1.60394e7i	0.00669260	−	0.0115919i	0.869352	+	0.494193i	$0.164536\pi$
$410$	1.78540e8	−	3.09240e8i	0.127936	−	0.221591i
$411$	−6.09652e7	+	2.58016e6i	−0.0433147	+	0.00183316i
$412$	1.36975e8	+	2.37248e8i	0.0964942	+	0.167133i
$413$	4.82036e8			0.336709
$414$	1.95204e9	+	2.80373e9i	1.35204	+	1.94194i
$415$	7.42329e7			0.0509833
$416$	3.58587e7	+	6.21091e7i	0.0244213	+	0.0422988i
$417$	−2.92719e8	−	4.60835e8i	−0.197686	−	0.311221i
$418$	−1.88708e9	+	3.26851e9i	−1.26378	+	2.18894i
$419$	7.91691e8	−	1.37125e9i	0.525783	−	0.910683i	−0.473766	−	0.880651i	$-0.657106\pi$
$419$	7.91691e8	−	1.37125e9i	0.525783	−	0.910683i	0.999549	−	0.0300324i	$-0.00956106\pi$
$420$	−1.27791e8	−	2.01185e8i	−0.0841645	−	0.132502i
$421$	−7.10933e8	−	1.23137e9i	−0.464345	−	0.804270i	0.534826	−	0.844962i	$-0.320377\pi$
$421$	−7.10933e8	−	1.23137e9i	−0.464345	−	0.804270i	−0.999172	+	0.0406923i	$0.987044\pi$
$422$	−3.84899e9			−2.49318
$423$	9.71463e8	−	2.06885e9i	0.624072	−	1.32904i
$424$	−3.37069e9			−2.14753
$425$	1.96466e8	+	3.40289e8i	0.124144	+	0.215024i
$426$	−1.93187e9	+	8.17603e7i	−1.21072	+	0.0512400i
$427$	−2.19350e8	+	3.79926e8i	−0.136345	+	0.236157i
$428$	−1.52115e9	+	2.63470e9i	−0.937817	+	1.62435i
$429$	−1.36039e7	+	2.60478e7i	−0.00831885	+	0.0159284i
$430$	−4.53792e8	−	7.85991e8i	−0.275244	−	0.476736i
$431$	−1.76729e9			−1.06326			−0.531628	−	0.846978i	$-0.678420\pi$
$431$	−1.76729e9			−1.06326			−0.531628	+	0.846978i	$0.678420\pi$
$432$	3.12699e9	+	4.10918e9i	1.86609	+	2.45223i
$433$	1.43174e9			0.847535			0.423767	−	0.905771i	$-0.360707\pi$
$433$	1.43174e9			0.847535			0.423767	+	0.905771i	$0.360707\pi$
$434$	1.45812e8	+	2.52553e8i	0.0856206	+	0.148299i
$435$	−1.00818e8	+	1.93040e8i	−0.0587255	+	0.112444i
$436$	1.79394e9	−	3.10720e9i	1.03659	−	1.79542i
$437$	1.39459e9	−	2.41551e9i	0.799398	−	1.38460i
$438$	2.06090e9	−	8.72213e7i	1.17192	−	0.0495979i
$439$	3.70176e8	+	6.41164e8i	0.208825	+	0.361696i	0.951345	−	0.308129i	$-0.0997027\pi$
$439$	3.70176e8	+	6.41164e8i	0.208825	+	0.361696i	−0.742520	+	0.669824i	$0.766369\pi$
$440$	−1.30392e9			−0.729736
$441$	−1.67288e9	+	1.41853e8i	−0.928815	+	0.0787596i
$442$	−1.55202e7			−0.00854910
$443$	−1.16814e9	−	2.02328e9i	−0.638386	−	1.10572i	−0.985787	−	0.168000i	$-0.946269\pi$
$443$	−1.16814e9	−	2.02328e9i	−0.638386	−	1.10572i	0.347401	−	0.937717i	$-0.387064\pi$
$444$	7.33057e8	+	1.15407e9i	0.397464	+	0.625737i
$445$	−1.39940e7	+	2.42384e7i	−0.00752806	+	0.0130390i
$446$	−7.97379e8	+	1.38110e9i	−0.425591	+	0.737146i
$447$	7.99314e8	+	1.25838e9i	0.423293	+	0.666400i
$448$	−5.67958e8	−	9.83732e8i	−0.298430	−	0.516897i
$449$	−5.43412e8			−0.283313			−0.141657	−	0.989916i	$-0.545243\pi$
$449$	−5.43412e8			−0.283313			−0.141657	+	0.989916i	$0.545243\pi$
$450$	−3.44638e9	+	2.92239e8i	−1.78287	+	0.151180i
$451$	1.17854e9			0.604958
$452$	1.04956e9	+	1.81789e9i	0.534592	+	0.925940i
$453$	−3.32342e9	+	1.40654e8i	−1.67974	+	0.0710898i
$454$	2.28313e9	−	3.95450e9i	1.14508	−	1.98334i
$455$	−1.05103e6	+	1.82044e6i	−0.000523090	+	0.000906018i
$456$	3.58638e9	−	6.86694e9i	1.77125	−	3.39146i
$457$	−8.93333e8	−	1.54730e9i	−0.437831	−	0.758345i	0.559691	−	0.828701i	$-0.310920\pi$
$457$	−8.93333e8	−	1.54730e9i	−0.437831	−	0.758345i	−0.997522	+	0.0703559i	$0.977586\pi$
$458$	3.22402e9			1.56808
$459$	−5.39679e8	+	6.88498e7i	−0.260490	+	0.0332321i
$460$	1.57304e9			0.753508
$461$	1.17001e9	+	2.02652e9i	0.556209	+	0.963382i	0.997808	+	0.0661700i	$0.0210780\pi$
$461$	1.17001e9	+	2.02652e9i	0.556209	+	0.963382i	−0.441599	+	0.897212i	$0.645589\pi$
$462$	5.05242e8	−	9.67402e8i	0.238371	−	0.456415i
$463$	−1.84161e9	+	3.18976e9i	−0.862312	+	1.49357i	0.00738049	+	0.999973i	$0.497651\pi$
$463$	−1.84161e9	+	3.18976e9i	−0.862312	+	1.49357i	−0.869692	+	0.493595i	$0.835683\pi$
$464$	−1.80152e9	+	3.12032e9i	−0.837192	+	1.45006i
$465$	−1.75681e8	+	7.43517e6i	−0.0810290	+	0.00342930i
$466$	1.36278e9	+	2.36040e9i	0.623843	+	1.08053i
$467$	8.38332e8			0.380897			0.190448	−	0.981697i	$-0.439006\pi$
$467$	8.38332e8			0.380897			0.190448	+	0.981697i	$0.439006\pi$
$468$	4.18527e7	−	8.91307e7i	0.0188740	−	0.0401945i
$469$	−8.59111e8			−0.384542
$470$	−7.30049e8	−	1.26448e9i	−0.324347	−	0.561785i
$471$	1.76632e9	+	2.78076e9i	0.778924	+	1.22628i
$472$	−4.41826e9	+	7.65266e9i	−1.93399	+	3.34977i
$473$	1.49773e9	−	2.59415e9i	0.650760	−	1.12715i
$474$	−3.36517e9	−	5.29787e9i	−1.45139	−	2.28495i
$475$	1.41191e9	+	2.44550e9i	0.604475	+	1.04698i
$476$	4.15459e8			0.176565
$477$	9.72010e8	+	1.39610e9i	0.410068	+	0.588983i
$478$	6.67556e9			2.79570
$479$	−1.38683e9	−	2.40207e9i	−0.576567	−	0.998644i	−0.995869	−	0.0907972i	$-0.971058\pi$
$479$	−1.38683e9	−	2.40207e9i	−0.576567	−	0.998644i	0.419302	−	0.907847i	$-0.362275\pi$
$480$	1.60459e9	−	6.79093e7i	0.662246	−	0.0280275i
$481$	6.02909e6	−	1.04427e7i	0.00247027	−	0.00427863i
$482$	−4.98767e8	+	8.63890e8i	−0.202877	+	0.351394i
$483$	−3.73386e8	+	7.14933e8i	−0.150780	+	0.288703i
$484$	−2.93352e8	−	5.08100e8i	−0.117606	−	0.203700i
$485$	7.63954e8			0.304068
$486$	1.47056e9	−	4.55761e9i	0.581108	−	1.80098i
$487$	6.08195e8			0.238612			0.119306	−	0.992858i	$-0.461933\pi$
$487$	6.08195e8			0.238612			0.119306	+	0.992858i	$0.461933\pi$
$488$	−4.02105e9	−	6.96467e9i	−1.56628	−	2.71288i
$489$	8.62557e8	−	1.65156e9i	0.333585	−	0.638726i
$490$	−5.36259e8	+	9.28828e8i	−0.205915	+	0.356656i
$491$	−1.37347e9	+	2.37892e9i	−0.523641	+	0.906973i	0.475980	+	0.879456i	$0.342093\pi$
$491$	−1.37347e9	+	2.37892e9i	−0.523641	+	0.906973i	−0.999621	+	0.0275169i	$0.991240\pi$
$492$	−3.94552e9	+	1.66982e8i	−1.49357	+	0.0632109i
$493$	−1.89811e8	−	3.28762e8i	−0.0713439	−	0.123571i
$494$	−1.11537e8			−0.0416268
$495$	3.76012e8	+	5.40067e8i	0.139342	+	0.200138i
$496$	−2.90912e9			−1.07047
$497$	−2.28252e8	−	3.95344e8i	−0.0834002	−	0.144453i
$498$	−6.10707e8	−	9.61452e8i	−0.221580	−	0.348839i
$499$	−1.14164e9	+	1.97737e9i	−0.411316	+	0.712421i	−0.995034	−	0.0995360i	$-0.968264\pi$
$499$	−1.14164e9	+	1.97737e9i	−0.411316	+	0.712421i	0.583718	+	0.811957i	$0.301597\pi$
$500$	−1.63847e9	+	2.83792e9i	−0.586198	+	1.01532i
$501$	1.29595e9	+	2.04024e9i	0.460421	+	0.724852i
$502$	−3.14627e9	−	5.44951e9i	−1.11003	−	1.92262i
$503$	5.24355e9			1.83712			0.918559	−	0.395283i	$-0.129353\pi$
$503$	5.24355e9			1.83712			0.918559	+	0.395283i	$0.129353\pi$
$504$	−9.52199e8	+	2.02783e9i	−0.331300	+	0.705544i
$505$	−1.22012e9			−0.421581
$506$	3.60158e9	+	6.23813e9i	1.23585	+	2.14056i
$507$	2.93097e9	−	1.24044e8i	0.998810	−	0.0422716i
$508$	2.97107e9	−	5.14604e9i	1.00552	−	1.74161i
$509$	−7.15597e8	+	1.23945e9i	−0.240523	+	0.416598i	−0.960863	−	0.277023i	$-0.910652\pi$
$509$	−7.15597e8	+	1.23945e9i	−0.240523	+	0.416598i	0.720341	+	0.693621i	$0.243986\pi$
$510$	−1.60896e8	+	3.08072e8i	−0.0537092	+	0.102839i
$511$	2.43497e8	+	4.21750e8i	0.0807274	+	0.139824i
$512$	−1.43352e9			−0.472018
$513$	−3.87842e9	+	4.94791e8i	−1.26836	+	0.161812i
$514$	6.15059e8			0.199777
$515$	−2.70531e7	−	4.68574e7i	−0.00872755	−	0.0151166i
$516$	−4.64658e9	+	8.89694e9i	−1.48888	+	2.85080i
$517$	2.40952e9	−	4.17340e9i	0.766854	−	1.32823i
$518$	−2.23917e8	+	3.87836e8i	−0.0707838	+	0.122601i
$519$	−8.51201e8	+	3.60245e7i	−0.267268	+	0.0113113i
$520$	−1.92672e7	−	3.33717e7i	−0.00600905	−	0.0104080i
$521$	−5.00475e9			−1.55042			−0.775211	−	0.631702i	$-0.782357\pi$
$521$	−5.00475e9			−1.55042			−0.775211	+	0.631702i	$0.782357\pi$
$522$	3.32964e9	−	2.82340e8i	1.02459	−	0.0868810i
$523$	−4.38432e9			−1.34013			−0.670064	−	0.742304i	$-0.733733\pi$
$523$	−4.38432e9			−1.34013			−0.670064	+	0.742304i	$0.733733\pi$
$524$	−6.21305e8	−	1.07613e9i	−0.188645	−	0.326743i
$525$	−4.37826e8	−	6.89281e8i	−0.132052	−	0.207892i
$526$	2.25963e9	−	3.91380e9i	0.676998	−	1.17260i
$527$	1.53255e8	−	2.65446e8i	0.0456119	−	0.0790021i
$528$	5.83747e9	+	9.19007e9i	1.72586	+	2.71706i
$529$	−9.59243e8	−	1.66146e9i	−0.281731	−	0.487972i
$530$	1.08674e9			0.317074
$531$	4.44374e9	−	3.76810e8i	1.28801	−	0.109217i
$532$	2.98571e9			0.859719
$533$	1.74145e7	+	3.01628e7i	0.00498157	+	0.00862833i
$534$	4.29059e8	−	1.81586e7i	0.121933	−	0.00516046i
$535$	3.00433e8	−	5.20365e8i	0.0848221	−	0.146916i
$536$	7.87447e9	−	1.36390e10i	2.20874	−	3.82565i
$537$	2.28849e9	−	4.38185e9i	0.637734	−	1.22109i
$538$	3.44801e9	+	5.97213e9i	0.954620	+	1.65345i
$539$	−3.53983e9			−0.973693
$540$	−1.33534e9	−	1.75477e9i	−0.364932	−	0.479558i
$541$	−5.37230e9			−1.45871			−0.729357	−	0.684133i	$-0.760181\pi$
$541$	−5.37230e9			−1.45871			−0.729357	+	0.684133i	$0.760181\pi$
$542$	4.00938e9	+	6.94446e9i	1.08163	+	1.87344i
$543$	2.79295e9	−	5.34775e9i	0.748625	−	1.43341i
$544$	−1.39976e9	+	2.42445e9i	−0.372784	+	0.645680i
$545$	−3.54311e8	+	6.13685e8i	−0.0937556	+	0.162389i
$546$	3.22248e7	−	1.36382e6i	0.00847258	−	0.000358576i
$547$	−1.22120e8	−	2.11518e8i	−0.0319029	−	0.0552575i	0.849633	−	0.527374i	$-0.176823\pi$
$547$	−1.22120e8	−	2.11518e8i	−0.0319029	−	0.0552575i	−0.881536	+	0.472117i	$0.843490\pi$
$548$	4.31105e8			0.111905
$549$	−1.72513e9	+	3.67388e9i	−0.444958	+	0.947593i
$550$	−7.29259e9			−1.86901
$551$	−1.36408e9	−	2.36266e9i	−0.347384	−	0.601687i
$552$	−7.92767e9	−	1.24807e10i	−2.00613	−	3.15830i
$553$	7.40886e8	−	1.28325e9i	0.186300	−	0.322682i
$554$	1.91873e9	−	3.32334e9i	0.479435	−	0.830405i
$555$	−1.44782e8	−	2.27934e8i	−0.0359491	−	0.0565956i
$556$	1.92854e9	+	3.34034e9i	0.475847	+	0.824192i
$557$	5.52077e9			1.35365			0.676825	−	0.736144i	$-0.263355\pi$
$557$	5.52077e9			1.35365			0.676825	+	0.736144i	$0.263355\pi$
$558$	1.54161e9	+	2.21423e9i	0.375626	+	0.539514i
$559$	8.85243e7			0.0214349
$560$	3.89396e8	+	6.74453e8i	0.0936986	+	0.162291i
$561$	−1.14608e9	+	4.85043e7i	−0.274060	+	0.0115987i
$562$	−4.26592e9	+	7.38878e9i	−1.01376	+	1.75588i
$563$	−2.31199e9	+	4.00448e9i	−0.546017	+	0.945728i	0.452526	+	0.891751i	$0.350523\pi$
$563$	−2.31199e9	+	4.00448e9i	−0.546017	+	0.945728i	−0.998542	+	0.0539770i	$0.982810\pi$
$564$	−7.47529e9	+	1.43132e10i	−1.75449	+	3.35938i
$565$	−2.07292e8	−	3.59040e8i	−0.0483519	−	0.0837479i
$566$	−7.33726e9			−1.70089
$567$	1.11449e9	−	1.90377e8i	0.256765	−	0.0438605i
$568$	8.36847e9			1.91614
$569$	2.27221e9	+	3.93559e9i	0.517078	+	0.895605i	0.999803	+	0.0198332i	$0.00631350\pi$
$569$	2.27221e9	+	3.93559e9i	0.517078	+	0.895605i	−0.482726	+	0.875772i	$0.660353\pi$
$570$	−1.15628e9	+	2.21397e9i	−0.261518	+	0.500736i
$571$	1.39633e9	−	2.41851e9i	0.313878	−	0.543653i	−0.665320	−	0.746558i	$-0.731705\pi$
$571$	1.39633e9	−	2.41851e9i	0.313878	−	0.543653i	0.979198	+	0.202905i	$0.0650383\pi$
$572$	1.03807e8	−	1.79799e8i	0.0231922	−	0.0401700i
$573$	−7.88351e8	+	3.33646e7i	−0.175057	+	0.00740874i
$574$	−6.46766e8	−	1.12023e9i	−0.142743	−	0.247238i
$575$	5.38940e9			1.18223
$576$	−6.00482e9	−	8.62474e9i	−1.30925	−	1.88047i
$577$	4.63375e9			1.00419			0.502096	−	0.864812i	$-0.332562\pi$
$577$	4.63375e9			1.00419			0.502096	+	0.864812i	$0.332562\pi$
$578$	4.08980e9	+	7.08374e9i	0.880957	+	1.52586i
$579$	1.55601e9	+	2.44966e9i	0.333148	+	0.524483i
$580$	7.69312e8	−	1.33249e9i	0.163721	−	0.283573i
$581$	1.34455e8	−	2.32883e8i	0.0284421	−	0.0492631i
$582$	−6.28498e9	−	9.89460e9i	−1.32152	−	2.08050i
$583$	1.79339e9	+	3.10624e9i	0.374830	+	0.649225i
$584$	−8.92742e9			−1.85473
$585$	−8.26608e6	+	1.76037e7i	−0.00170708	+	0.00363545i
$586$	−1.30340e10			−2.67570
$587$	−2.49329e9	−	4.31850e9i	−0.508791	−	0.881251i	−0.999948	−	0.0101804i	$-0.996759\pi$
$587$	−2.49329e9	−	4.31850e9i	−0.508791	−	0.881251i	0.491158	−	0.871071i	$-0.336574\pi$
$588$	1.18507e10	−	5.01544e8i	2.40394	−	0.101739i
$589$	1.10137e9	−	1.90763e9i	0.222091	−	0.384673i
$590$	1.42449e9	−	2.46729e9i	0.285547	−	0.494581i
$591$	−1.57294e8	+	3.01175e8i	−0.0313440	+	0.0600153i
$592$	−2.23371e9	−	3.86890e9i	−0.442488	−	0.766411i
$593$	−1.08733e9			−0.214126			−0.107063	−	0.994252i	$-0.534145\pi$
$593$	−1.08733e9			−0.214126			−0.107063	+	0.994252i	$0.534145\pi$
$594$	3.90145e9	−	9.31313e9i	0.763788	−	1.82324i
$595$	−8.20549e7			−0.0159696
$596$	−5.26618e9	−	9.12128e9i	−1.01890	−	1.76479i
$597$	1.34484e9	−	2.57500e9i	0.258678	−	0.495299i
$598$	−1.06437e8	+	1.84354e8i	−0.0203534	+	0.0352531i
$599$	−7.88181e8	+	1.36517e9i	−0.149841	+	0.259533i	−0.931169	−	0.364589i	$-0.881210\pi$
$599$	−7.88181e8	+	1.36517e9i	−0.149841	+	0.259533i	0.781327	+	0.624122i	$0.214543\pi$
$600$	1.49558e10	−	6.32961e8i	2.82671	−	0.119632i
$601$	2.98739e9	+	5.17431e9i	0.561347	+	0.972282i	0.997379	+	0.0723505i	$0.0230500\pi$
$601$	2.98739e9	+	5.17431e9i	0.561347	+	0.972282i	−0.436032	+	0.899931i	$0.643617\pi$
$602$	−3.28775e9			−0.614201
$603$	−7.91987e9	+	6.71572e8i	−1.47098	+	0.124733i
$604$	2.35010e10			4.33967
$605$	5.79381e7	+	1.00352e8i	0.0106370	+	0.0184239i
$606$	1.00378e10	+	1.58027e10i	1.83225	+	2.88455i
$607$	2.07004e9	−	3.58541e9i	0.375680	−	0.650696i	−0.614749	−	0.788723i	$-0.710743\pi$
$607$	2.07004e9	−	3.58541e9i	0.375680	−	0.650696i	0.990429	+	0.138027i	$0.0440759\pi$
$608$	−1.00594e10	+	1.74234e10i	−1.81514	+	3.14391i
$609$	4.22996e8	+	6.65933e8i	0.0758884	+	0.119473i
$610$	1.29643e9	+	2.24547e9i	0.231256	+	0.400547i
$611$	1.42416e8			0.0252588
$612$	3.82999e9	−	3.24767e8i	0.675410	−	0.0572719i
$613$	−3.24640e9			−0.569234			−0.284617	−	0.958641i	$-0.591866\pi$
$613$	−3.24640e9			−0.569234			−0.284617	+	0.958641i	$0.591866\pi$
$614$	−6.25500e9	−	1.08340e10i	−1.09053	−	1.88886i
$615$	7.79256e8	−	3.29796e7i	0.135088	−	0.00571719i
$616$	−2.36174e9	+	4.09065e9i	−0.407098	+	0.705114i
$617$	−2.56649e9	+	4.44529e9i	−0.439887	+	0.761907i	−0.997680	−	0.0680728i	$-0.978315\pi$
$617$	−2.56649e9	+	4.44529e9i	−0.439887	+	0.761907i	0.557793	+	0.829980i	$0.311648\pi$
$618$	−3.84326e8	+	7.35879e8i	−0.0654997	+	0.125414i
$619$	−4.08023e7	−	7.06717e7i	−0.00691461	−	0.0119765i	0.862547	−	0.505976i	$-0.168868\pi$
$619$	−4.08023e7	−	7.06717e7i	−0.00691461	−	0.0119765i	−0.869462	+	0.494000i	$0.835534\pi$
$620$	1.24230e9			0.209342
$621$	−2.88326e9	+	6.88262e9i	−0.483129	+	1.15328i
$622$	−6.26203e9			−1.04339
$623$	5.06937e7	+	8.78041e7i	0.00839936	+	0.0145481i
$624$	−1.48949e8	+	2.85197e8i	−0.0245409	+	0.0469892i
$625$	−2.56182e9	+	4.43720e9i	−0.419728	+	0.726990i
$626$	8.85830e9	−	1.53430e10i	1.44325	−	2.49977i
$627$	−8.23634e9	+	3.48578e8i	−1.33444	+	0.0564759i
$628$	−1.16371e10	−	2.01561e10i	−1.87494	−	3.24749i
$629$	4.70696e8			0.0754160
$630$	3.06998e8	−	6.53791e8i	0.0489152	−	0.104171i
$631$	5.87381e9			0.930716			0.465358	−	0.885123i	$-0.345926\pi$
$631$	5.87381e9			0.930716			0.465358	+	0.885123i	$0.345926\pi$
$632$	1.35817e10	+	2.35242e10i	2.14015	+	3.70684i
$633$	−4.50769e9	−	7.09657e9i	−0.706384	−	1.11208i
$634$	−2.60842e8	+	4.51791e8i	−0.0406504	+	0.0704085i
$635$	−5.86798e8	+	1.01636e9i	−0.0909454	+	0.157522i
$636$	−6.44404e9	−	1.01450e10i	−0.993249	−	1.56370i
$637$	−5.23059e7	−	9.05964e7i	−0.00801793	−	0.0138875i
$638$	7.04557e9			1.07410
$639$	−2.41322e9	−	3.46612e9i	−0.365885	−	0.525522i
$640$	−2.31781e9			−0.349500
$641$	−8.24069e8	−	1.42733e9i	−0.123583	−	0.214053i	0.797595	−	0.603193i	$-0.206105\pi$
$641$	−8.24069e8	−	1.42733e9i	−0.123583	−	0.214053i	−0.921178	+	0.389141i	$0.872772\pi$
$642$	−9.21131e9	+	3.89841e8i	−1.37388	+	0.0581453i
$643$	−2.07980e9	+	3.60232e9i	−0.308520	+	0.534373i	−0.978039	−	0.208422i	$-0.933167\pi$
$643$	−2.07980e9	+	3.60232e9i	−0.308520	+	0.534373i	0.669519	+	0.742795i	$0.266500\pi$
$644$	2.84919e9	−	4.93494e9i	0.420360	−	0.728084i
$645$	9.17718e8	−	1.75718e9i	0.134664	−	0.257844i
$646$	−2.17694e9	−	3.77056e9i	−0.317711	−	0.550291i
$647$	−3.14826e9			−0.456988			−0.228494	−	0.973545i	$-0.573380\pi$
$647$	−3.14826e9			−0.456988			−0.228494	+	0.973545i	$0.573380\pi$
$648$	−7.19286e9	+	1.94383e10i	−1.03846	+	2.80637i
$649$	9.40301e9			1.35024
$650$	−1.07758e8	−	1.86642e8i	−0.0153905	−	0.0266571i
$651$	−2.94879e8	+	5.64614e8i	−0.0418901	+	0.0802081i
$652$	−6.58190e9	+	1.14002e10i	−0.930004	+	1.61081i
$653$	6.14384e9	−	1.06414e10i	0.863463	−	1.49556i	−0.00510246	−	0.999987i	$-0.501624\pi$
$653$	6.14384e9	−	1.06414e10i	0.863463	−	1.49556i	0.868565	−	0.495575i	$-0.165042\pi$
$654$	1.08632e10	−	4.59753e8i	1.51858	−	0.0642692i
$655$	1.22710e8	+	2.12540e8i	0.0170623	+	0.0295527i
$656$	1.29038e10			1.78465
$657$	2.57441e9	+	3.69763e9i	0.354159	+	0.508680i
$658$	−5.28924e9			−0.723774
$659$	−2.76278e9	−	4.78528e9i	−0.376052	−	0.651341i	0.614432	−	0.788970i	$-0.289385\pi$
$659$	−2.76278e9	−	4.78528e9i	−0.376052	−	0.651341i	−0.990484	+	0.137629i	$0.956052\pi$
$660$	−2.49281e9	−	3.92449e9i	−0.337509	−	0.531349i
$661$	1.98631e9	−	3.44039e9i	0.267511	−	0.463342i	−0.700708	−	0.713449i	$-0.747132\pi$
$661$	1.98631e9	−	3.44039e9i	0.267511	−	0.463342i	0.968218	+	0.250106i	$0.0804656\pi$
$662$	1.71927e8	−	2.97787e8i	0.0230326	−	0.0398936i
$663$	−1.81763e7	−	2.86154e7i	−0.00242219	−	0.00381331i
$664$	2.46479e9	+	4.26914e9i	0.326732	+	0.565916i
$665$	−5.89690e8			−0.0777585
$666$	−1.76105e9	+	3.75038e9i	−0.231000	+	0.491944i
$667$	−5.20684e9			−0.679413
$668$	−8.53818e9	−	1.47886e10i	−1.10828	−	1.91959i
$669$	−3.48024e9	+	1.47291e8i	−0.449384	+	0.0190188i
$670$	−2.53880e9	+	4.39733e9i	−0.326112	+	0.564843i
$671$	−4.27883e9	+	7.41116e9i	−0.546760	+	0.947016i
$672$	2.69329e9	−	5.15691e9i	0.342366	−	0.655537i
$673$	6.56024e9	+	1.13627e10i	0.829597	+	1.43690i	0.898355	+	0.439270i	$0.144763\pi$
$673$	6.56024e9	+	1.13627e10i	0.829597	+	1.43690i	−0.0687581	+	0.997633i	$0.521904\pi$
$674$	−5.19338e9			−0.653341
$675$	−4.57500e9	−	6.01201e9i	−0.572569	−	0.752414i
$676$	−2.07258e10			−2.58047
$677$	5.73199e9	+	9.92810e9i	0.709978	+	1.22972i	0.964865	+	0.262748i	$0.0846286\pi$
$677$	5.73199e9	+	9.92810e9i	0.709978	+	1.22972i	−0.254886	+	0.966971i	$0.582038\pi$
$678$	−2.94486e9	+	5.63861e9i	−0.362878	+	0.694813i
$679$	1.38372e9	−	2.39667e9i	0.169631	−	0.293809i
$680$	7.52101e8	−	1.30268e9i	0.0917266	−	0.158875i
$681$	9.96497e9	−	4.21737e8i	1.20910	−	0.0511713i
$682$	2.84433e9	+	4.92652e9i	0.343348	+	0.594696i
$683$	7.63032e9			0.916368			0.458184	−	0.888857i	$-0.348500\pi$
$683$	7.63032e9			0.916368			0.458184	+	0.888857i	$0.348500\pi$
$684$	2.75243e10	−	2.33394e9i	3.28867	−	0.278865i
$685$	−8.51449e7			−0.0101214
$686$	4.02663e9	+	6.97433e9i	0.476220	+	0.824837i
$687$	3.77576e9	+	5.94428e9i	0.444280	+	0.699440i
$688$	1.63986e10	−	2.84033e10i	1.91977	−	3.32513i
$689$	−5.29996e7	+	9.17980e7i	−0.00617313	+	0.0106922i
$690$	2.55595e9	+	4.02390e9i	0.296197	+	0.466311i
$691$	−4.78482e9	−	8.28755e9i	−0.551686	−	0.955549i	−0.998153	−	0.0607485i	$-0.980651\pi$
$691$	−4.78482e9	−	8.28755e9i	−0.551686	−	0.955549i	0.446467	−	0.894800i	$-0.352682\pi$
$692$	6.01912e9			0.690497
$693$	2.37535e9	−	2.01420e8i	0.271120	−	0.0229899i
$694$	8.83910e9			1.00381
$695$	−3.80895e8	−	6.59730e8i	−0.0430387	−	0.0745451i
$696$	−1.44492e10	+	6.11520e8i	−1.62447	+	0.0687509i
$697$	−6.79782e8	+	1.17742e9i	−0.0760422	+	0.131709i
$698$	−5.57254e9	+	9.65192e9i	−0.620239	+	1.07429i
$699$	−2.75599e9	+	5.27698e9i	−0.305216	+	0.584407i
$700$	2.88456e9	+	4.99621e9i	0.317861	+	0.550551i
$701$	−1.24509e10			−1.36517			−0.682586	−	0.730805i	$-0.739145\pi$
$701$	−1.24509e10			−1.36517			−0.682586	+	0.730805i	$0.739145\pi$
$702$	2.96004e8	−	3.77629e7i	0.0322937	−	0.00411989i
$703$	3.38267e9			0.367211
$704$	−1.10791e10	−	1.91895e10i	−1.19674	−	2.07281i
$705$	1.47640e9	−	2.82691e9i	0.158687	−	0.303843i
$706$	1.54726e10	−	2.67993e10i	1.65480	−	2.86620i
$707$	−2.20995e9	+	3.82774e9i	−0.235188	+	0.407357i
$708$	−3.14795e10	+	1.33227e9i	−3.33359	+	0.141084i
$709$	−7.92899e9	−	1.37334e10i	−0.835518	−	1.44716i	−0.893608	−	0.448849i	$-0.851834\pi$
$709$	−7.92899e9	−	1.37334e10i	−0.835518	−	1.44716i	0.0580897	−	0.998311i	$-0.481499\pi$
$710$	−2.69807e9			−0.282911
$711$	5.82687e9	−	1.24091e10i	0.607983	−	1.29478i
$712$	−1.85860e9			−0.192977
$713$	−2.10203e9	−	3.64082e9i	−0.217183	−	0.376171i
$714$	6.75058e8	+	1.06276e9i	0.0694061	+	0.109268i
$715$	−2.05023e7	+	3.55111e7i	−0.00209765	+	0.00363323i
$716$	−1.74628e10	+	3.02464e10i	−1.77794	+	3.07949i
$717$	7.81799e9	+	1.23081e10i	0.792097	+	1.24702i
$718$	1.07060e10	+	1.85433e10i	1.07942	+	1.86962i
$719$	1.79885e10			1.80486			0.902432	−	0.430833i	$-0.141780\pi$
$719$	1.79885e10			1.80486			0.902432	+	0.430833i	$0.141780\pi$
$720$	4.11694e9	+	5.91318e9i	0.411065	+	0.590415i
$721$	−1.96001e8			−0.0194754
$722$	−6.07562e9	−	1.05233e10i	−0.600773	−	1.04057i
$723$	−2.17692e9	+	9.21315e7i	−0.214219	+	0.00906617i
$724$	−2.13121e10	+	3.69137e10i	−2.08709	+	3.61495i
$725$	2.63574e9	−	4.56524e9i	0.256874	−	0.444919i
$726$	8.23088e8	−	1.57599e9i	0.0798303	−	0.152853i
$727$	−8.60459e9	−	1.49036e10i	−0.830538	−	1.43853i	−0.897612	−	0.440786i	$-0.854700\pi$
$727$	−8.60459e9	−	1.49036e10i	−0.830538	−	1.43853i	0.0670741	−	0.997748i	$-0.478634\pi$
$728$	−1.39592e8			−0.0134091
$729$	1.01253e10	−	2.62623e9i	0.967970	−	0.251065i
$730$	2.87828e9			0.273844
$731$	1.72779e9	+	2.99262e9i	0.163599	+	0.283362i
$732$	1.32747e10	−	2.54174e10i	1.25094	−	2.39520i
$733$	−1.01647e10	+	1.76058e10i	−0.953304	+	1.65117i	−0.215102	+	0.976592i	$0.569009\pi$
$733$	−1.01647e10	+	1.76058e10i	−0.953304	+	1.65117i	−0.738202	+	0.674580i	$0.764325\pi$
$734$	−8.53718e9	+	1.47868e10i	−0.796853	+	1.38019i
$735$	−2.34056e9	+	9.90570e7i	−0.217427	+	0.00920194i
$736$	1.91989e10	+	3.32535e10i	1.77502	+	3.07443i
$737$	−1.67586e10			−1.54206
$738$	−6.83802e9	−	9.82148e9i	−0.626229	−	0.899455i
$739$	−8.40068e9			−0.765700			−0.382850	−	0.923810i	$-0.625057\pi$
$739$	−8.40068e9			−0.765700			−0.382850	+	0.923810i	$0.625057\pi$
$740$	9.53876e8	+	1.65216e9i	0.0865328	+	0.149879i
$741$	−1.30624e8	−	2.05645e8i	−0.0117940	−	0.0185676i
$742$	1.96838e9	−	3.40933e9i	0.176886	−	0.306376i
$743$	5.00275e9	−	8.66502e9i	0.447454	−	0.775013i	−0.550766	−	0.834660i	$-0.685664\pi$
$743$	5.00275e9	−	8.66502e9i	0.447454	−	0.775013i	0.998220	+	0.0596473i	$0.0189976\pi$
$744$	−6.26083e9	−	9.85657e9i	−0.557348	−	0.877447i
$745$	1.04009e9	+	1.80149e9i	0.0921562	+	0.159619i
$746$	5.59882e9			0.493754
$747$	1.05745e9	−	2.25198e9i	0.0928196	−	0.197671i
$748$	8.10431e9			0.708044
$749$	−1.08832e9	−	1.88503e9i	−0.0946395	−	0.163920i
$750$	−9.92178e9	+	4.19909e8i	−0.858767	+	0.0363447i
$751$	6.51619e9	−	1.12864e10i	0.561376	−	0.972332i	−0.436000	−	0.899946i	$-0.643605\pi$
$751$	6.51619e9	−	1.12864e10i	0.561376	−	0.972332i	0.997377	−	0.0723858i	$-0.0230613\pi$
$752$	2.63817e10	−	4.56944e10i	2.26225	−	3.91833i
$753$	6.36281e9	−	1.21831e10i	0.543083	−	1.03986i
$754$	1.04108e8	+	1.80320e8i	0.00884472	+	0.0153195i
$755$	−4.64154e9			−0.392508
$756$	−7.92370e9	+	1.01087e9i	−0.666963	+	0.0850882i
$757$	−8.11633e9			−0.680024			−0.340012	−	0.940421i	$-0.610431\pi$
$757$	−8.11633e9			−0.680024			−0.340012	+	0.940421i	$0.610431\pi$
$758$	3.67104e9	+	6.35843e9i	0.306159	+	0.530283i
$759$	−7.28359e9	+	1.39461e10i	−0.604644	+	1.15773i
$760$	5.40500e9	−	9.36173e9i	0.446630	−	0.773586i
$761$	−1.10813e9	+	1.91934e9i	−0.0911476	+	0.157872i	−0.907994	−	0.418983i	$-0.862387\pi$
$761$	−1.10813e9	+	1.91934e9i	−0.0911476	+	0.157872i	0.816847	+	0.576855i	$0.195720\pi$
$762$	1.79913e10	−	7.61427e8i	1.47306	−	0.0623428i
$763$	1.28350e9	+	2.22309e9i	0.104607	+	0.181185i
$764$	5.57469e9			0.452266
$765$	−7.56438e8	+	6.41427e7i	−0.0610883	+	0.00518003i
$766$	2.16661e10			1.74173
$767$	1.38942e8	+	2.40655e8i	0.0111186	+	0.0192580i
$768$	3.64569e9	+	5.73951e9i	0.290413	+	0.457204i
$769$	−6.59962e9	+	1.14309e10i	−0.523332	+	0.906437i	0.476300	+	0.879283i	$0.341978\pi$
$769$	−6.59962e9	+	1.14309e10i	−0.523332	+	0.906437i	−0.999631	+	0.0271540i	$0.991356\pi$
$770$	7.61446e8	−	1.31886e9i	0.0601065	−	0.104108i
$771$	7.20318e8	+	1.13401e9i	0.0566023	+	0.0891104i
$772$	−1.02516e10	−	1.77562e10i	−0.801917	−	1.38896i
$773$	1.25254e10			0.975355			0.487677	−	0.873024i	$-0.337844\pi$
$773$	1.25254e10			0.975355			0.487677	+	0.873024i	$0.337844\pi$
$774$	−3.03087e10	+	2.57005e9i	−2.34949	+	0.199227i
$775$	4.25624e9			0.328451
$776$	2.53659e10	+	4.39350e10i	1.94865	+	3.37517i
$777$	−9.77311e8	+	4.13617e7i	−0.0747410	+	0.00316318i
$778$	1.30222e10	−	2.25550e10i	0.991413	−	1.71718i
$779$	−4.88527e9	+	8.46154e9i	−0.370261	+	0.641310i
$780$	6.36065e7	−	1.21789e8i	0.00479922	−	0.00918921i
$781$	−4.45248e9	−	7.71192e9i	−0.334444	−	0.579274i
$782$	−8.30959e9			−0.621378
$783$	4.42003e9	+	5.80837e9i	0.329048	+	0.432402i
$784$	−3.87575e10			−2.87243
$785$	2.29838e9	+	3.98092e9i	0.169582	+	0.293724i
$786$	1.74326e9	−	3.33788e9i	0.128051	−	0.245183i
$787$	−3.66640e9	+	6.35038e9i	−0.268119	+	0.464396i	−0.968376	−	0.249495i	$-0.919735\pi$
$787$	−3.66640e9	+	6.35038e9i	−0.268119	+	0.464396i	0.700257	+	0.713891i	$0.253069\pi$
$788$	1.20026e9	−	2.07891e9i	0.0873841	−	0.151354i
$789$	9.86240e9	−	4.17396e8i	0.714847	−	0.0302537i
$790$	−4.37886e9	−	7.58441e9i	−0.315985	−	0.547302i
$791$	−1.50184e9			−0.107896
$792$	−1.85744e10	+	3.95566e10i	−1.32855	+	2.82931i
$793$	−2.52903e8			−0.0180093
$794$	−1.12781e10	−	1.95343e10i	−0.799586	−	1.38492i
$795$	1.27272e9	+	2.00368e9i	0.0898357	+	0.141431i
$796$	−1.02620e10	+	1.77744e10i	−0.721170	+	1.24910i
$797$	9.72182e9	−	1.68387e10i	0.680211	−	1.17816i	−0.294706	−	0.955588i	$-0.595222\pi$
$797$	9.72182e9	−	1.68387e10i	0.680211	−	1.17816i	0.974916	−	0.222571i	$-0.0714450\pi$
$798$	4.85132e9	+	7.63756e9i	0.337948	+	0.532040i
$799$	2.77962e9	+	4.81445e9i	0.192785	+	0.333913i
$800$	−3.88745e10			−2.68441
$801$	5.35967e8	+	7.69811e8i	0.0368489	+	0.0529262i
$802$	3.56416e10			2.43976
$803$	4.74987e9	+	8.22701e9i	0.323726	+	0.560709i
$804$	5.61045e10	−	2.37445e9i	3.80716	−	0.161127i
$805$	−5.62727e8	+	9.74671e8i	−0.0380200	+	0.0658526i
$806$	−8.40577e7	+	1.45592e8i	−0.00565464	+	0.00979412i
$807$	−6.97301e9	+	1.33514e10i	−0.467050	+	0.894274i
$808$	−4.05121e10	−	7.01689e10i	−2.70175	−	4.67956i
$809$	−2.66596e10			−1.77025			−0.885123	−	0.465356i	$-0.845926\pi$
$809$	−2.66596e10			−1.77025			−0.885123	+	0.465356i	$0.845926\pi$
$810$	2.31905e9	−	6.26708e9i	0.153325	−	0.414350i
$811$	2.23929e10			1.47413			0.737066	−	0.675820i	$-0.236210\pi$
$811$	2.23929e10			1.47413			0.737066	+	0.675820i	$0.236210\pi$
$812$	−2.78685e9	−	4.82697e9i	−0.182670	−	0.316394i
$813$	−8.10830e9	+	1.55252e10i	−0.529192	+	1.01326i
$814$	−4.36793e9	+	7.56547e9i	−0.283851	+	0.491644i
$815$	1.29995e9	−	2.25158e9i	0.0841154	−	0.145692i
$816$	−1.25484e10	+	5.31072e8i	−0.808486	+	0.0342167i
$817$	1.24168e10	+	2.15066e10i	0.796587	+	1.37973i
$818$	−3.96531e8			−0.0253303
$819$	4.02542e7	+	5.78172e7i	0.00256045	+	0.00367759i
$820$	−5.51037e9			−0.349006
$821$	−9.93766e9	−	1.72125e10i	−0.626734	−	1.08553i	−0.988203	−	0.153151i	$-0.951058\pi$
$821$	−9.93766e9	−	1.72125e10i	−0.626734	−	1.08553i	0.361469	−	0.932384i	$-0.382275\pi$
$822$	7.00480e8	+	1.10278e9i	0.0439890	+	0.0692530i
$823$	−8.48625e9	+	1.46986e10i	−0.530660	+	0.919130i	0.468700	+	0.883357i	$0.344723\pi$
$823$	−8.48625e9	+	1.46986e10i	−0.530660	+	0.919130i	−0.999360	+	0.0357725i	$0.988611\pi$
$824$	1.79652e9	−	3.11166e9i	0.111863	−	0.193752i
$825$	−8.54062e9	−	1.34457e10i	−0.529542	−	0.833671i
$826$	−5.16025e9	−	8.93781e9i	−0.318596	−	0.551825i
$827$	1.89569e10			1.16546			0.582730	−	0.812666i	$-0.301985\pi$
$827$	1.89569e10			1.16546			0.582730	+	0.812666i	$0.301985\pi$
$828$	2.24081e10	−	4.77209e10i	1.37183	−	2.92148i
$829$	−3.77995e9			−0.230433			−0.115217	−	0.993340i	$-0.536756\pi$
$829$	−3.77995e9			−0.230433			−0.115217	+	0.993340i	$0.536756\pi$
$830$	−7.94671e8	−	1.37641e9i	−0.0482407	−	0.0835554i
$831$	8.37449e9	−	3.54425e8i	0.506238	−	0.0214250i
$832$	3.27417e8	−	5.67103e8i	0.0197092	−	0.0341374i
$833$	2.04178e9	−	3.53647e9i	0.122392	−	0.211988i
$834$	−5.41112e9	+	1.03608e10i	−0.323003	+	0.618463i
$835$	1.68632e9	+	2.92080e9i	0.100239	+	0.173620i
$836$	5.82418e10			3.44757
$837$	−2.27704e9	+	5.43551e9i	−0.134224	+	0.320406i
$838$	−3.39006e10			−1.99000
$839$	6.28559e9	+	1.08870e10i	0.367434	+	0.636414i	0.989164	−	0.146818i	$-0.0469030\pi$
$839$	6.28559e9	+	1.08870e10i	0.367434	+	0.636414i	−0.621730	+	0.783232i	$0.713570\pi$
$840$	−1.44712e9	+	2.77085e9i	−0.0842419	+	0.161300i
$841$	6.07848e9	−	1.05282e10i	0.352378	−	0.610337i
$842$	−1.52212e10	+	2.63639e10i	−0.878733	+	1.52201i
$843$	−1.86190e10	+	7.87994e8i	−1.07044	+	0.0453029i
$844$	2.96983e10	+	5.14390e10i	1.70033	+	2.94506i
$845$	4.09343e9			0.233394
$846$	−4.87599e10	+	4.13463e9i	−2.76864	+	0.234769i
$847$	4.19765e8			0.0237363
$848$	1.96357e10	+	3.40101e10i	1.10576	+	1.91524i
$849$	−8.59294e9	−	1.35281e10i	−0.481909	−	0.758681i
$850$	4.20638e9	−	7.28566e9i	0.234932	−	0.406914i
$851$	3.22800e9	−	5.59106e9i	0.179548	−	0.310986i
$852$	1.59987e10	+	2.51872e10i	0.886231	+	1.39522i
$853$	−3.38980e9	−	5.87130e9i	−0.187004	−	0.323901i	0.757246	−	0.653130i	$-0.226545\pi$
$853$	−3.38980e9	−	5.87130e9i	−0.187004	−	0.323901i	−0.944250	+	0.329229i	$0.893211\pi$
$854$	9.39267e9			0.516044
$855$	−5.43616e9	+	4.60964e8i	−0.297448	+	0.0252223i
$856$	3.99016e10			2.17436
$857$	−1.10047e10	−	1.90608e10i	−0.597237	−	1.03445i	−0.993227	−	0.116191i	$-0.962932\pi$
$857$	−1.10047e10	−	1.90608e10i	−0.597237	−	1.03445i	0.395989	−	0.918255i	$-0.370402\pi$
$858$	6.28605e8	−	2.66038e7i	0.0339760	−	0.00143793i
$859$	1.05339e10	−	1.82452e10i	0.567039	−	0.982140i	−0.429818	−	0.902915i	$-0.641422\pi$
$859$	1.05339e10	−	1.82452e10i	0.567039	−	0.982140i	0.996857	−	0.0792243i	$-0.0252443\pi$
$860$	−7.00281e9	+	1.21292e10i	−0.375429	+	0.650262i
$861$	1.30797e9	−	2.50442e9i	0.0698374	−	0.133720i
$862$	1.89191e10	+	3.27688e10i	1.00606	+	1.74255i
$863$	1.10986e10			0.587800			0.293900	−	0.955836i	$-0.405047\pi$
$863$	1.10986e10			0.587800			0.293900	+	0.955836i	$0.405047\pi$
$864$	2.07974e10	−	4.96453e10i	1.09701	−	2.61867i
$865$	−1.18880e9			−0.0624529
$866$	−1.53270e10	−	2.65471e10i	−0.801943	−	1.38901i
$867$	−8.27093e9	+	1.58366e10i	−0.431010	+	0.825268i
$868$	2.25013e9	−	3.89734e9i	0.116785	−	0.202278i
$869$	1.44524e10	−	2.50322e10i	0.747084	−	1.29399i
$870$	4.65857e9	−	1.97160e8i	0.239848	−	0.0101508i
$871$	−2.47631e8	−	4.28909e8i	−0.0126982	−	0.0219939i
$872$	−4.70574e10			−2.40337
$873$	1.08826e10	−	2.31759e10i	0.553583	−	1.17892i
$874$	−5.97171e10			−3.02558
$875$	−1.17227e9	−	2.03043e9i	−0.0591560	−	0.102461i
$876$	−1.70673e10	−	2.68695e10i	−0.857829	−	1.35050i
$877$	3.74513e9	−	6.48675e9i	0.187486	−	0.324735i	−0.756926	−	0.653501i	$-0.773300\pi$
$877$	3.74513e9	−	6.48675e9i	0.187486	−	0.324735i	0.944411	+	0.328766i	$0.106633\pi$
$878$	7.92555e9	−	1.37275e10i	0.395184	−	0.684478i
$879$	−1.52646e10	−	2.40315e10i	−0.758098	−	1.19349i
$880$	7.59589e9	+	1.31565e10i	0.375741	+	0.650803i
$881$	−3.40216e10			−1.67625			−0.838124	−	0.545479i	$-0.816348\pi$
$881$	−3.40216e10			−1.67625			−0.838124	+	0.545479i	$0.816348\pi$
$882$	2.05385e10	+	2.94996e10i	1.00793	+	1.44769i
$883$	−1.52483e8			−0.00745350			−0.00372675	−	0.999993i	$-0.501186\pi$
$883$	−1.52483e8			−0.00745350			−0.00372675	+	0.999993i	$0.501186\pi$
$884$	1.19752e8	+	2.07417e8i	0.00583043	+	0.0100986i
$885$	6.21733e9	−	2.63129e8i	0.301511	−	0.0127605i
$886$	−2.50102e10	+	4.33190e10i	−1.20809	+	2.09247i
$887$	−1.61805e10	+	2.80255e10i	−0.778502	+	1.34840i	0.154303	+	0.988024i	$0.450687\pi$
$887$	−1.61805e10	+	2.80255e10i	−0.778502	+	1.34840i	−0.932805	+	0.360381i	$0.882647\pi$
$888$	8.30122e9	−	1.58946e10i	0.397829	−	0.761735i
$889$	2.12569e9	+	3.68180e9i	0.101471	+	0.175754i
$890$	5.99231e8			0.0284924
$891$	2.17402e10	−	3.71366e9i	1.02965	−	0.175885i
$892$	2.46099e10			1.16100
$893$	1.99758e10	+	3.45992e10i	0.938696	+	1.62587i
$894$	1.47759e10	−	2.82918e10i	0.691627	−	1.32428i
$895$	3.44897e9	−	5.97379e9i	0.160808	−	0.278528i
$896$	−4.19816e9	+	7.27142e9i	−0.194976	+	0.337708i
$897$	−4.64554e8	+	1.96608e7i	−0.0214913	+	0.000909553i
$898$	5.81728e9	+	1.00758e10i	0.268073	+	0.464316i
$899$	−4.11207e9			−0.188756
$900$	3.04974e10	+	4.38036e10i	1.39449	+	2.00291i
$901$	−4.13772e9			−0.188462
$902$	−1.26164e10	−	2.18522e10i	−0.572416	−	0.991453i
$903$	−3.85040e9	−	6.06178e9i	−0.174020	−	0.273964i
$904$	1.37656e10	−	2.38428e10i	0.619736	−	1.07341i
$905$	4.20923e9	−	7.29060e9i	0.188770	−	0.326959i
$906$	3.81856e10	+	6.01165e10i	1.70589	+	2.68562i
$907$	−5.07730e9	−	8.79415e9i	−0.225948	−	0.391353i	0.730656	−	0.682746i	$-0.239214\pi$
$907$	−5.07730e9	−	8.79415e9i	−0.225948	−	0.391353i	−0.956603	+	0.291393i	$0.905881\pi$
$908$	−7.04656e10			−3.12375
$909$	−1.73807e10	+	3.70143e10i	−0.767525	+	1.63454i
$910$	4.50056e7			0.00197980
$911$	−2.06340e9	−	3.57392e9i	−0.0904210	−	0.156614i	0.817267	−	0.576259i	$-0.195488\pi$
$911$	−2.06340e9	−	3.57392e9i	−0.0904210	−	0.156614i	−0.907688	+	0.419645i	$0.862155\pi$
$912$	−9.01793e10	+	3.81656e9i	−3.93663	+	0.166606i
$913$	2.62280e9	−	4.54282e9i	0.114056	−	0.197550i
$914$	−1.91264e10	+	3.31280e10i	−0.828557	+	1.43510i
$915$	−2.62180e9	+	5.02004e9i	−0.113143	+	0.216637i
$916$	−2.48761e10	−	4.30867e10i	−1.06942	−	1.85229i
$917$	8.89042e8			0.0380741
$918$	7.05392e9	+	9.26956e9i	0.300941	+	0.395467i
$919$	−8.67341e9			−0.368625			−0.184313	−	0.982868i	$-0.559006\pi$
$919$	−8.67341e9			−0.368625			−0.184313	+	0.982868i	$0.559006\pi$
$920$	−1.03157e10	−	1.78673e10i	−0.436759	−	0.756489i
$921$	1.26497e10	−	2.42207e10i	0.533545	−	1.02159i
$922$	2.50503e10	−	4.33883e10i	1.05258	−	1.82312i
$923$	1.31583e8	−	2.27908e8i	0.00550800	−	0.00954013i
$924$	−1.68270e10	+	7.12153e8i	−0.701707	+	0.0296976i
$925$	3.26808e9	+	5.66047e9i	0.135768	+	0.235156i
$926$	7.88585e10			3.26370
$927$	−1.80687e9	+	1.53215e8i	−0.0744987	+	0.00631718i
$928$	3.75577e10			1.54270
$929$	1.95971e10	+	3.39432e10i	0.801930	+	1.38898i	0.918344	+	0.395783i	$0.129527\pi$
$929$	1.95971e10	+	3.39432e10i	0.801930	+	1.38898i	−0.116414	+	0.993201i	$0.537140\pi$
$930$	2.01855e9	+	3.17785e9i	0.0822904	+	0.129552i
$931$	1.46733e10	−	2.54149e10i	0.595942	−	1.03220i
$932$	2.10301e10	−	3.64252e10i	0.850914	−	1.47383i
$933$	−7.33369e9	−	1.15456e10i	−0.295622	−	0.465405i
$934$	−8.97444e9	−	1.55442e10i	−0.360407	−	0.624243i
$935$	−1.60063e9			−0.0640400
$936$	−1.28685e9	+	1.09119e8i	−0.0512936	+	0.00434948i
$937$	−8.74627e9			−0.347324			−0.173662	−	0.984805i	$-0.555560\pi$
$937$	−8.74627e9			−0.347324			−0.173662	+	0.984805i	$0.555560\pi$
$938$	9.19688e9	+	1.59295e10i	0.363857	+	0.630218i
$939$	3.86629e10	−	1.63629e9i	1.52393	−	0.0644957i
$940$	−1.12659e10	+	1.95132e10i	−0.442405	+	0.766268i
$941$	−2.00195e10	+	3.46747e10i	−0.783229	+	1.35659i	0.146823	+	0.989163i	$0.453095\pi$
$941$	−2.00195e10	+	3.46747e10i	−0.783229	+	1.35659i	−0.930051	+	0.367429i	$0.880238\pi$
$942$	3.26516e10	−	6.25189e10i	1.27270	−	2.43688i
$943$	9.32380e9	+	1.61493e10i	0.362078	+	0.627137i
$944$	1.02953e11			3.98325
$945$	1.56496e9	−	1.99651e8i	0.0603244	−	0.00769591i
$946$	−6.41336e10			−2.46301
$947$	9.20351e9	+	1.59409e10i	0.352151	+	0.609943i	0.986626	−	0.163000i	$-0.0521171\pi$
$947$	9.20351e9	+	1.59409e10i	0.352151	+	0.609943i	−0.634475	+	0.772943i	$0.718784\pi$
$948$	−4.48371e10	+	8.58509e10i	−1.70926	+	3.27277i
$949$	−1.40372e8	+	2.43131e8i	−0.00533148	+	0.00923439i
$950$	3.02292e10	−	5.23586e10i	1.14392	−	1.98132i
$951$	−1.13847e9	+	4.81823e7i	−0.0429230	+	0.00181658i
$952$	−2.72451e9	−	4.71898e9i	−0.102343	−	0.177263i
$953$	−1.36320e10			−0.510194			−0.255097	−	0.966915i	$-0.582107\pi$
$953$	−1.36320e10			−0.510194			−0.255097	+	0.966915i	$0.582107\pi$
$954$	1.54808e10	−	3.29682e10i	0.577262	−	1.22935i
$955$	−1.10102e9			−0.0409058
$956$	−5.15078e10	−	8.92142e10i	−1.90665	−	3.30241i
$957$	8.25132e9	+	1.29903e10i	0.304321	+	0.479100i
$958$	−2.96924e10	+	5.14288e10i	−1.09110	+	1.88985i
$959$	−1.54220e8	+	2.67116e8i	−0.00564644	+	0.00977992i
$960$	−7.86255e9	−	1.23782e10i	−0.286823	−	0.451553i
$961$	1.20962e10	+	2.09513e10i	0.439662	+	0.761517i
$962$	−2.58168e8			−0.00934954
$963$	−1.15065e10	−	1.65268e10i	−0.415193	−	0.596343i
$964$	1.53937e10			0.553444
$965$	2.02472e9	+	3.50693e9i	0.0725304	+	0.125626i
$966$	1.72533e10	−	7.30193e8i	0.615817	−	0.0260626i
$967$	2.82952e9	−	4.90087e9i	0.100628	−	0.174293i	−0.811315	−	0.584609i	$-0.801248\pi$
$967$	2.82952e9	−	4.90087e9i	0.100628	−	0.174293i	0.911944	+	0.410315i	$0.134581\pi$
$968$	−3.84749e9	+	6.66405e9i	−0.136337	+	0.236143i
$969$	4.40248e9	−	8.42957e9i	0.155441	−	0.297627i
$970$	−8.17821e9	−	1.41651e10i	−0.287711	−	0.498331i
$971$	−9.65547e9			−0.338459			−0.169230	−	0.985577i	$-0.554128\pi$
$971$	−9.65547e9			−0.338459			−0.169230	+	0.985577i	$0.554128\pi$
$972$	−7.22559e10	+	1.55129e10i	−2.52372	+	0.541827i
$973$	−2.75961e9			−0.0960400
$974$	−6.51079e9	−	1.12770e10i	−0.225776	−	0.391055i
$975$	2.17922e8	−	4.17262e8i	0.00752984	−	0.0144176i
$976$	−4.68488e10	+	8.11445e10i	−1.61296	+	2.79373i
$977$	−2.13798e10	+	3.70308e10i	−0.733453	+	1.27038i	0.221946	+	0.975059i	$0.428759\pi$
$977$	−2.13798e10	+	3.70308e10i	−0.733453	+	1.27038i	−0.955399	+	0.295318i	$0.904574\pi$
$978$	−3.98567e10	+	1.68681e9i	−1.36243	+	0.0576609i
$979$	9.88876e8	+	1.71278e9i	0.0336824	+	0.0583395i
$980$	1.65509e10			0.561732
$981$	1.35700e10	+	1.94906e10i	0.458921	+	0.659151i
$982$	5.88125e10			1.98189
$983$	−1.84845e10	−	3.20161e10i	−0.620684	−	1.07506i	−0.989359	−	0.145497i	$-0.953522\pi$
$983$	−1.84845e10	−	3.20161e10i	−0.620684	−	1.07506i	0.368675	−	0.929558i	$-0.379812\pi$
$984$	2.77707e10	+	4.37200e10i	0.929187	+	1.46284i
$985$	−2.37056e8	+	4.10592e8i	−0.00790357	+	0.0136894i
$986$	−4.06389e9	+	7.03887e9i	−0.135012	+	0.233848i
$987$	−6.19442e9	−	9.75203e9i	−0.205065	−	0.322838i
$988$	8.60603e8	+	1.49061e9i	0.0283892	+	0.0491716i
$989$	4.73963e10			1.55796
$990$	5.98857e9	−	1.27534e10i	0.196155	−	0.417737i
$991$	−5.13146e10			−1.67488			−0.837440	−	0.546530i	$-0.815948\pi$
$991$	−5.13146e10			−1.67488			−0.837440	+	0.546530i	$0.815948\pi$
$992$	1.51622e10	+	2.62617e10i	0.493142	+	0.854146i
$993$	7.50395e8	−	3.17582e7i	0.0243202	−	0.00102928i
$994$	−4.88692e9	+	8.46440e9i	−0.157828	+	0.273365i
$995$	2.02679e9	−	3.51051e9i	0.0652272	−	0.112977i
$996$	−8.13698e9	+	1.55801e10i	−0.260949	+	0.499647i
$997$	−2.28440e10	−	3.95670e10i	−0.730028	−	1.26445i	−0.956871	−	0.290514i	$-0.906174\pi$
$997$	−2.28440e10	−	3.95670e10i	−0.730028	−	1.26445i	0.226843	−	0.973931i	$-0.427160\pi$
$998$	4.88854e10			1.55676
$999$	−8.97719e9	+	1.14527e9i	−0.284879	+	0.0363436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.8.c.a.4.1	✓	12
3.2	odd	2		27.8.c.a.10.6		12
4.3	odd	2		144.8.i.c.49.3		12
9.2	odd	6		27.8.c.a.19.6		12
9.4	even	3		81.8.a.e.1.6		6
9.5	odd	6		81.8.a.c.1.1		6
9.7	even	3	inner	9.8.c.a.7.1	yes	12
12.11	even	2		432.8.i.c.145.4		12
36.7	odd	6		144.8.i.c.97.3		12
36.11	even	6		432.8.i.c.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.8.c.a.4.1	✓	12	1.1	even	1	trivial
9.8.c.a.7.1	yes	12	9.7	even	3	inner
27.8.c.a.10.6		12	3.2	odd	2
27.8.c.a.19.6		12	9.2	odd	6
81.8.a.c.1.1		6	9.5	odd	6
81.8.a.e.1.6		6	9.4	even	3
144.8.i.c.49.3		12	4.3	odd	2
144.8.i.c.97.3		12	36.7	odd	6
432.8.i.c.145.4		12	12.11	even	2
432.8.i.c.289.4		12	36.11	even	6

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.7051 - 18.5418i) q^{2} +(21.6493 - 41.4525i) q^{3} +(-165.199 + 286.133i) q^{4} +(32.6274 - 56.5123i) q^{5} +(-1000.36 + 42.3372i) q^{6} +(-118.194 - 204.717i) q^{7} +4333.37 q^{8} +(-1249.62 - 1794.83i) q^{9} +O(q^{10})\)	\(q+(-10.7051 - 18.5418i) q^{2} +(21.6493 - 41.4525i) q^{3} +(-165.199 + 286.133i) q^{4} +(32.6274 - 56.5123i) q^{5} +(-1000.36 + 42.3372i) q^{6} +(-118.194 - 204.717i) q^{7} +4333.37 q^{8} +(-1249.62 - 1794.83i) q^{9} -1397.12 q^{10} +(-2305.59 - 3993.39i) q^{11} +(8284.48 + 13042.5i) q^{12} +(68.1364 - 118.016i) q^{13} +(-2530.55 + 4383.04i) q^{14} +(-1636.22 - 2575.94i) q^{15} +(-25243.8 - 43723.5i) q^{16} +5319.46 q^{17} +(-19902.1 + 42384.0i) q^{18} +38228.5 q^{19} +(10780.0 + 18671.5i) q^{20} +(-11044.8 + 467.439i) q^{21} +(-49363.1 + 85499.4i) q^{22} +(36480.5 - 63186.1i) q^{23} +(93814.3 - 179629. i) q^{24} +(36933.4 + 63970.5i) q^{25} -2917.63 q^{26} +(-101454. + 12943.0i) q^{27} +78101.7 q^{28} +(-35682.4 - 61803.7i) q^{29} +(-30246.6 + 57914.1i) q^{30} +(28810.3 - 49900.8i) q^{31} +(-263139. + 455770. i) q^{32} +(-215450. + 9118.28i) q^{33} +(-56945.4 - 98632.4i) q^{34} -15425.4 q^{35} +(719995. - 61052.5i) q^{36} +88485.6 q^{37} +(-409240. - 708824. i) q^{38} +(-3416.94 - 5379.38i) q^{39} +(141387. - 244889. i) q^{40} +(-127791. + 221341. i) q^{41} +(126903. + 199787. i) q^{42} +(324806. + 562580. i) q^{43} +1.52352e6 q^{44} +(-142202. + 12058.1i) q^{45} -1.56211e6 q^{46} +(522539. + 905063. i) q^{47} +(-2.35896e6 + 99835.7i) q^{48} +(383832. - 664817. i) q^{49} +(790752. - 1.36962e6i) q^{50} +(115162. - 220505. i) q^{51} +(22512.1 + 38992.1i) q^{52} -777845. q^{53} +(1.32606e6 + 1.74258e6i) q^{54} -300901. q^{55} +(-512177. - 887116. i) q^{56} +(827618. - 1.58467e6i) q^{57} +(-763967. + 1.32323e6i) q^{58} +(-1.01959e6 + 1.76598e6i) q^{59} +(1.00736e6 - 42633.5i) q^{60} +(-927927. - 1.60722e6i) q^{61} -1.23367e6 q^{62} +(-219736. + 467956. i) q^{63} +4.80532e6 q^{64} +(-4446.23 - 7701.10i) q^{65} +(2.47549e6 + 3.89722e6i) q^{66} +(1.81717e6 - 3.14743e6i) q^{67} +(-878768. + 1.52207e6i) q^{68} +(-1.82945e6 - 2.88014e6i) q^{69} +(165131. + 286015. i) q^{70} +1.93117e6 q^{71} +(-5.41506e6 - 7.77768e6i) q^{72} -2.06016e6 q^{73} +(-947248. - 1.64068e6i) q^{74} +(3.45132e6 - 146067. i) q^{75} +(-6.31529e6 + 1.09384e7i) q^{76} +(-545011. + 943987. i) q^{77} +(-63164.6 + 120943. i) q^{78} +(3.13421e6 + 5.42860e6i) q^{79} -3.29456e6 q^{80} +(-1.65988e6 + 4.48571e6i) q^{81} +5.47209e6 q^{82} +(568792. + 985177. i) q^{83} +(1.69085e6 - 3.23751e6i) q^{84} +(173560. - 300615. i) q^{85} +(6.95416e6 - 1.20450e7i) q^{86} +(-3.33441e6 + 141119. i) q^{87} +(-9.99096e6 - 1.73049e7i) q^{88} -428904. q^{89} +(1.74587e6 + 2.50760e6i) q^{90} -32213.2 q^{91} +(1.20531e7 + 2.08765e7i) q^{92} +(-1.44479e6 - 2.27457e6i) q^{93} +(1.11877e7 - 1.93776e7i) q^{94} +(1.24730e6 - 2.16038e6i) q^{95} +(1.31960e7 + 2.07749e7i) q^{96} +(5.85362e6 + 1.01388e7i) q^{97} -1.64359e7 q^{98} +(-4.28637e6 + 9.12836e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 9 q^{2} + 24 q^{3} - 321 q^{4} - 180 q^{5} - 1233 q^{6} - 84 q^{7} + 5922 q^{8} + 990 q^{9}+O(q^{10}) \) 12 * q - 9 * q^2 + 24 * q^3 - 321 * q^4 - 180 * q^5 - 1233 * q^6 - 84 * q^7 + 5922 * q^8 + 990 * q^9	\( 12 q - 9 q^{2} + 24 q^{3} - 321 q^{4} - 180 q^{5} - 1233 q^{6} - 84 q^{7} + 5922 q^{8} + 990 q^{9} + 252 q^{10} - 8460 q^{11} + 8052 q^{12} - 1848 q^{13} - 16272 q^{14} - 1188 q^{15} - 12417 q^{16} + 30564 q^{17} + 42876 q^{18} + 24432 q^{19} - 40788 q^{20} - 187224 q^{21} - 35001 q^{22} - 51588 q^{23} + 215469 q^{24} + 4746 q^{25} + 536472 q^{26} + 322272 q^{27} + 75516 q^{28} - 414648 q^{29} - 1112112 q^{30} + 8196 q^{31} - 1048977 q^{32} - 148518 q^{33} - 106623 q^{34} + 2210616 q^{35} + 2501811 q^{36} + 139344 q^{37} - 1952685 q^{38} - 2057316 q^{39} + 305496 q^{40} - 1731582 q^{41} + 538866 q^{42} + 408372 q^{43} + 5169114 q^{44} + 2687580 q^{45} - 1684008 q^{46} - 1631484 q^{47} - 7434525 q^{48} - 179010 q^{49} - 1654461 q^{50} + 2525688 q^{51} + 681594 q^{52} + 2835648 q^{53} + 5816529 q^{54} - 16056 q^{55} - 1784466 q^{56} - 3071850 q^{57} - 948384 q^{58} - 2055636 q^{59} + 371484 q^{60} - 2723196 q^{61} - 1026828 q^{62} - 2238804 q^{63} + 7178178 q^{64} - 1387620 q^{65} + 5754762 q^{66} + 3806556 q^{67} + 2142639 q^{68} - 3002292 q^{69} + 953442 q^{70} + 2408400 q^{71} - 9638325 q^{72} - 10670052 q^{73} + 9846504 q^{74} + 19174632 q^{75} - 6727827 q^{76} + 3478824 q^{77} - 13339962 q^{78} + 6020916 q^{79} - 38072448 q^{80} - 28538730 q^{81} + 9403002 q^{82} + 9605052 q^{83} + 30090090 q^{84} - 1698624 q^{85} + 34278561 q^{86} + 10290708 q^{87} - 16459029 q^{88} - 24630264 q^{89} - 13660596 q^{90} + 13570104 q^{91} + 39143394 q^{92} + 27331212 q^{93} + 12602808 q^{94} + 10422072 q^{95} - 3404376 q^{96} + 9977226 q^{97} - 95833314 q^{98} - 49382676 q^{99}+O(q^{100}) \) 12 * q - 9 * q^2 + 24 * q^3 - 321 * q^4 - 180 * q^5 - 1233 * q^6 - 84 * q^7 + 5922 * q^8 + 990 * q^9 + 252 * q^10 - 8460 * q^11 + 8052 * q^12 - 1848 * q^13 - 16272 * q^14 - 1188 * q^15 - 12417 * q^16 + 30564 * q^17 + 42876 * q^18 + 24432 * q^19 - 40788 * q^20 - 187224 * q^21 - 35001 * q^22 - 51588 * q^23 + 215469 * q^24 + 4746 * q^25 + 536472 * q^26 + 322272 * q^27 + 75516 * q^28 - 414648 * q^29 - 1112112 * q^30 + 8196 * q^31 - 1048977 * q^32 - 148518 * q^33 - 106623 * q^34 + 2210616 * q^35 + 2501811 * q^36 + 139344 * q^37 - 1952685 * q^38 - 2057316 * q^39 + 305496 * q^40 - 1731582 * q^41 + 538866 * q^42 + 408372 * q^43 + 5169114 * q^44 + 2687580 * q^45 - 1684008 * q^46 - 1631484 * q^47 - 7434525 * q^48 - 179010 * q^49 - 1654461 * q^50 + 2525688 * q^51 + 681594 * q^52 + 2835648 * q^53 + 5816529 * q^54 - 16056 * q^55 - 1784466 * q^56 - 3071850 * q^57 - 948384 * q^58 - 2055636 * q^59 + 371484 * q^60 - 2723196 * q^61 - 1026828 * q^62 - 2238804 * q^63 + 7178178 * q^64 - 1387620 * q^65 + 5754762 * q^66 + 3806556 * q^67 + 2142639 * q^68 - 3002292 * q^69 + 953442 * q^70 + 2408400 * q^71 - 9638325 * q^72 - 10670052 * q^73 + 9846504 * q^74 + 19174632 * q^75 - 6727827 * q^76 + 3478824 * q^77 - 13339962 * q^78 + 6020916 * q^79 - 38072448 * q^80 - 28538730 * q^81 + 9403002 * q^82 + 9605052 * q^83 + 30090090 * q^84 - 1698624 * q^85 + 34278561 * q^86 + 10290708 * q^87 - 16459029 * q^88 - 24630264 * q^89 - 13660596 * q^90 + 13570104 * q^91 + 39143394 * q^92 + 27331212 * q^93 + 12602808 * q^94 + 10422072 * q^95 - 3404376 * q^96 + 9977226 * q^97 - 95833314 * q^98 - 49382676 * q^99

Introduction

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