LMFDB - Embedded newform 418.2.n.e.125.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			125.4
Character	$\chi$	$=$	418.125
Dual form			418.2.n.e.311.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 - 0.406737i) q^{2} +(-0.470759 - 0.522831i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.330325 + 3.14283i) q^{5} +(-0.642715 - 0.286155i) q^{6} +(0.775272 + 2.38604i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.261847 - 2.49131i) q^{9} +O(q^{10})$	\(q+(0.913545 - 0.406737i) q^{2} +(-0.470759 - 0.522831i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.330325 + 3.14283i) q^{5} +(-0.642715 - 0.286155i) q^{6} +(0.775272 + 2.38604i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.261847 - 2.49131i) q^{9} +(1.58007 + 2.73676i) q^{10} +(0.465255 + 3.28383i) q^{11} -0.703539 q^{12} +(0.0102574 - 0.0975922i) q^{13} +(1.67874 + 1.86443i) q^{14} +(1.48767 - 1.65222i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(0.498351 + 4.74149i) q^{17} +(-0.774098 - 2.38243i) q^{18} +(4.15195 + 1.32714i) q^{19} +(2.55661 + 1.85749i) q^{20} +(0.882531 - 1.52859i) q^{21} +(1.76069 + 2.81069i) q^{22} +(-3.53011 - 6.11433i) q^{23} +(-0.642715 + 0.286155i) q^{24} +(-4.87753 + 1.03675i) q^{25} +(-0.0303238 - 0.0933270i) q^{26} +(-3.13333 + 2.27649i) q^{27} +(2.29193 + 1.02043i) q^{28} +(5.10772 - 5.67269i) q^{29} +(0.687032 - 2.11447i) q^{30} +(6.22121 + 4.51998i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.49787 - 1.78914i) q^{33} +(2.38381 + 4.12887i) q^{34} +(-7.24284 + 3.22472i) q^{35} +(-1.67619 - 1.86160i) q^{36} +(-2.59173 - 7.97652i) q^{37} +(4.33279 - 0.476353i) q^{38} +(-0.0558530 + 0.0405796i) q^{39} +(3.09109 + 0.657031i) q^{40} +(-3.15465 - 3.50360i) q^{41} +(0.184499 - 1.75539i) q^{42} +(3.59679 - 6.22983i) q^{43} +(2.75168 + 1.85156i) q^{44} +7.91626 q^{45} +(-5.71184 - 4.14989i) q^{46} +(-12.3998 + 2.63566i) q^{47} +(-0.470759 + 0.522831i) q^{48} +(0.570969 - 0.414833i) q^{49} +(-4.03416 + 2.93099i) q^{50} +(2.24440 - 2.49266i) q^{51} +(-0.0656616 - 0.0729246i) q^{52} +(-0.155277 + 1.47736i) q^{53} +(-1.93650 + 3.35412i) q^{54} +(-10.1668 + 2.54695i) q^{55} +2.50883 q^{56} +(-1.26070 - 2.79553i) q^{57} +(2.35884 - 7.25976i) q^{58} +(-4.15571 - 0.883322i) q^{59} +(-0.232396 - 2.21110i) q^{60} +(-7.38618 - 3.28854i) q^{61} +(7.52180 + 1.59881i) q^{62} +(6.14737 - 1.30666i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.310104 q^{65} +(0.640658 - 2.24370i) q^{66} +(3.84717 + 6.66350i) q^{67} +(3.85708 + 2.80233i) q^{68} +(-1.53493 + 4.72403i) q^{69} +(-5.30505 + 5.89185i) q^{70} +(1.54871 + 14.7350i) q^{71} +(-2.28846 - 1.01889i) q^{72} +(-5.02687 - 1.06850i) q^{73} +(-5.61200 - 6.23276i) q^{74} +(2.83819 + 2.06207i) q^{75} +(3.76445 - 2.19748i) q^{76} +(-7.47466 + 3.65598i) q^{77} +(-0.0345190 + 0.0597887i) q^{78} +(-7.51110 + 3.34416i) q^{79} +(3.09109 - 0.657031i) q^{80} +(-4.68561 - 0.995958i) q^{81} +(-4.30696 - 1.91758i) q^{82} +(-1.82109 + 1.32310i) q^{83} +(-0.545434 - 1.67867i) q^{84} +(-14.7371 + 3.13247i) q^{85} +(0.751935 - 7.15418i) q^{86} -5.37037 q^{87} +(3.26688 + 0.572275i) q^{88} +(-1.40487 - 2.43331i) q^{89} +(7.23187 - 3.21983i) q^{90} +(0.240811 - 0.0511860i) q^{91} +(-6.90594 - 1.46790i) q^{92} +(-0.565510 - 5.38046i) q^{93} +(-10.2558 + 7.45126i) q^{94} +(-2.79947 + 13.4873i) q^{95} +(-0.217405 + 0.669105i) q^{96} +(17.7076 - 7.88394i) q^{97} +(0.352878 - 0.611203i) q^{98} +(8.30287 - 0.299233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$3$	−0.470759	−	0.522831i	−0.271793	−	0.301857i	0.591761	−	0.806114i	$-0.298433\pi$
$3$	−0.470759	−	0.522831i	−0.271793	−	0.301857i	−0.863554	+	0.504257i	$0.831766\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	0.330325	+	3.14283i	0.147726	+	1.40552i	0.777571	+	0.628796i	$0.216452\pi$
$5$	0.330325	+	3.14283i	0.147726	+	1.40552i	−0.629845	+	0.776721i	$0.716882\pi$
$6$	−0.642715	−	0.286155i	−0.262387	−	0.116822i
$7$	0.775272	+	2.38604i	0.293025	+	0.901839i	0.983878	+	0.178843i	$0.0572355\pi$
$7$	0.775272	+	2.38604i	0.293025	+	0.901839i	−0.690852	+	0.722996i	$0.742765\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.261847	−	2.49131i	0.0872824	−	0.830437i
$10$	1.58007	+	2.73676i	0.499662	+	0.865441i
$11$	0.465255	+	3.28383i	0.140280	+	0.990112i
$11$	0.465255	+	3.28383i	0.140280	+	0.990112i
$12$	−0.703539			−0.203094
$13$	0.0102574	−	0.0975922i	0.00284488	−	0.0270672i	−0.993007	−	0.118052i	$-0.962335\pi$
$13$	0.0102574	−	0.0975922i	0.00284488	−	0.0270672i	0.995852	+	0.0909852i	$0.0290016\pi$
$14$	1.67874	+	1.86443i	0.448661	+	0.498289i
$15$	1.48767	−	1.65222i	0.384114	−	0.426602i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	0.498351	+	4.74149i	0.120868	+	1.14998i	0.871889	+	0.489703i	$0.162895\pi$
$17$	0.498351	+	4.74149i	0.120868	+	1.14998i	−0.751021	+	0.660278i	$0.770439\pi$
$18$	−0.774098	−	2.38243i	−0.182457	−	0.561544i
$19$	4.15195	+	1.32714i	0.952523	+	0.304466i
$19$	4.15195	+	1.32714i	0.952523	+	0.304466i
$20$	2.55661	+	1.85749i	0.571675	+	0.415346i
$21$	0.882531	−	1.52859i	0.192584	−	0.333565i
$22$	1.76069	+	2.81069i	0.375379	+	0.599241i
$23$	−3.53011	−	6.11433i	−0.736079	−	1.27493i	−0.954248	−	0.299015i	$-0.903342\pi$
$23$	−3.53011	−	6.11433i	−0.736079	−	1.27493i	0.218169	−	0.975911i	$-0.429992\pi$
$24$	−0.642715	+	0.286155i	−0.131194	+	0.0584111i
$25$	−4.87753	+	1.03675i	−0.975507	+	0.207350i
$26$	−0.0303238	−	0.0933270i	−0.00594698	−	0.0183029i
$27$	−3.13333	+	2.27649i	−0.603009	+	0.438112i
$28$	2.29193	+	1.02043i	0.433135	+	0.192844i
$29$	5.10772	−	5.67269i	0.948479	−	1.05339i	−0.0500266	−	0.998748i	$-0.515931\pi$
$29$	5.10772	−	5.67269i	0.948479	−	1.05339i	0.998506	−	0.0546451i	$-0.0174027\pi$
$30$	0.687032	−	2.11447i	0.125434	−	0.386047i
$31$	6.22121	+	4.51998i	1.11736	+	0.811812i	0.983807	−	0.179230i	$-0.0573605\pi$
$31$	6.22121	+	4.51998i	1.11736	+	0.811812i	0.133556	+	0.991041i	$0.457361\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.49787	−	1.78914i	0.260745	−	0.311450i
$34$	2.38381	+	4.12887i	0.408819	+	0.708096i
$35$	−7.24284	+	3.22472i	−1.22426	+	0.545077i
$36$	−1.67619	−	1.86160i	−0.279366	−	0.310267i
$37$	−2.59173	−	7.97652i	−0.426078	−	1.31133i	−0.901959	−	0.431822i	$-0.857871\pi$
$37$	−2.59173	−	7.97652i	−0.426078	−	1.31133i	0.475881	−	0.879510i	$-0.342129\pi$
$38$	4.33279	−	0.476353i	0.702872	−	0.0772746i
$39$	−0.0558530	+	0.0405796i	−0.00894364	+	0.00649793i
$40$	3.09109	+	0.657031i	0.488744	+	0.103886i
$41$	−3.15465	−	3.50360i	−0.492674	−	0.547170i	0.444616	−	0.895722i	$-0.353340\pi$
$41$	−3.15465	−	3.50360i	−0.492674	−	0.547170i	−0.937290	+	0.348551i	$0.886674\pi$
$42$	0.184499	−	1.75539i	0.0284688	−	0.270863i
$43$	3.59679	−	6.22983i	0.548506	−	0.950040i	−0.449871	−	0.893093i	$-0.648530\pi$
$43$	3.59679	−	6.22983i	0.548506	−	0.950040i	0.998377	−	0.0569469i	$-0.0181366\pi$
$44$	2.75168	+	1.85156i	0.414831	+	0.279133i
$45$	7.91626			1.18009
$46$	−5.71184	−	4.14989i	−0.842165	−	0.611869i
$47$	−12.3998	+	2.63566i	−1.80870	+	0.384451i	−0.983575	−	0.180499i	$-0.942229\pi$
$47$	−12.3998	+	2.63566i	−1.80870	+	0.384451i	−0.825125	+	0.564950i	$0.808895\pi$
$48$	−0.470759	+	0.522831i	−0.0679482	+	0.0754642i
$49$	0.570969	−	0.414833i	0.0815669	−	0.0592618i
$50$	−4.03416	+	2.93099i	−0.570517	+	0.414505i
$51$	2.24440	−	2.49266i	0.314278	−	0.349042i
$52$	−0.0656616	−	0.0729246i	−0.00910563	−	0.0101128i
$53$	−0.155277	+	1.47736i	−0.0213290	+	0.202931i	−0.999997	−	0.00251728i	$-0.999199\pi$
$53$	−0.155277	+	1.47736i	−0.0213290	+	0.202931i	0.978668	+	0.205449i	$0.0658654\pi$
$54$	−1.93650	+	3.35412i	−0.263525	+	0.456438i
$55$	−10.1668	+	2.54695i	−1.37090	+	0.343430i
$56$	2.50883			0.335257
$57$	−1.26070	−	2.79553i	−0.166984	−	0.370277i
$58$	2.35884	−	7.25976i	0.309731	−	0.953253i
$59$	−4.15571	−	0.883322i	−0.541027	−	0.114999i	−0.0707107	−	0.997497i	$-0.522527\pi$
$59$	−4.15571	−	0.883322i	−0.541027	−	0.114999i	−0.470316	+	0.882498i	$0.655860\pi$
$60$	−0.232396	−	2.21110i	−0.0300022	−	0.285452i
$61$	−7.38618	−	3.28854i	−0.945703	−	0.421054i	−0.124839	−	0.992177i	$-0.539841\pi$
$61$	−7.38618	−	3.28854i	−0.945703	−	0.421054i	−0.820865	+	0.571123i	$0.806508\pi$
$62$	7.52180	+	1.59881i	0.955270	+	0.203049i
$63$	6.14737	−	1.30666i	0.774496	−	0.164624i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.310104			0.0384637
$66$	0.640658	−	2.24370i	0.0788596	−	0.276180i
$67$	3.84717	+	6.66350i	0.470007	+	0.814076i	0.999412	−	0.0342935i	$-0.0109181\pi$
$67$	3.84717	+	6.66350i	0.470007	+	0.814076i	−0.529405	+	0.848369i	$0.677585\pi$
$68$	3.85708	+	2.80233i	0.467739	+	0.339833i
$69$	−1.53493	+	4.72403i	−0.184784	+	0.568706i
$70$	−5.30505	+	5.89185i	−0.634075	+	0.704211i
$71$	1.54871	+	14.7350i	0.183798	+	1.74873i	0.565780	+	0.824556i	$0.308575\pi$
$71$	1.54871	+	14.7350i	0.183798	+	1.74873i	−0.381982	+	0.924170i	$0.624758\pi$
$72$	−2.28846	−	1.01889i	−0.269698	−	0.120077i
$73$	−5.02687	−	1.06850i	−0.588351	−	0.125058i	−0.0958894	−	0.995392i	$-0.530570\pi$
$73$	−5.02687	−	1.06850i	−0.588351	−	0.125058i	−0.492462	+	0.870334i	$0.663903\pi$
$74$	−5.61200	−	6.23276i	−0.652382	−	0.724544i
$75$	2.83819	+	2.06207i	0.327726	+	0.238107i
$76$	3.76445	−	2.19748i	0.431812	−	0.252068i
$77$	−7.47466	+	3.65598i	−0.851816	+	0.416638i
$78$	−0.0345190	+	0.0597887i	−0.00390851	+	0.00676974i
$79$	−7.51110	+	3.34416i	−0.845064	+	0.376247i	−0.783149	−	0.621834i	$-0.786388\pi$
$79$	−7.51110	+	3.34416i	−0.845064	+	0.376247i	−0.0619157	+	0.998081i	$0.519721\pi$
$80$	3.09109	−	0.657031i	0.345594	−	0.0734583i
$81$	−4.68561	−	0.995958i	−0.520624	−	0.110662i
$82$	−4.30696	−	1.91758i	−0.475624	−	0.211762i
$83$	−1.82109	+	1.32310i	−0.199890	+	0.145229i	−0.683228	−	0.730205i	$-0.739424\pi$
$83$	−1.82109	+	1.32310i	−0.199890	+	0.145229i	0.483337	+	0.875434i	$0.339424\pi$
$84$	−0.545434	−	1.67867i	−0.0595117	−	0.183158i
$85$	−14.7371	+	3.13247i	−1.59846	+	0.339764i
$86$	0.751935	−	7.15418i	0.0810832	−	0.771455i
$87$	−5.37037			−0.575764
$88$	3.26688	+	0.572275i	0.348251	+	0.0610048i
$89$	−1.40487	−	2.43331i	−0.148916	−	0.257930i	0.781911	−	0.623390i	$-0.214245\pi$
$89$	−1.40487	−	2.43331i	−0.148916	−	0.257930i	−0.930827	+	0.365460i	$0.880912\pi$
$90$	7.23187	−	3.21983i	0.762306	−	0.339400i
$91$	0.240811	−	0.0511860i	0.0252439	−	0.00536575i
$92$	−6.90594	−	1.46790i	−0.719994	−	0.153039i
$93$	−0.565510	−	5.38046i	−0.0586406	−	0.557928i
$94$	−10.2558	+	7.45126i	−1.05780	+	0.768539i
$95$	−2.79947	+	13.4873i	−0.287220	+	1.38376i
$96$	−0.217405	+	0.669105i	−0.0221888	+	0.0682902i
$97$	17.7076	−	7.88394i	1.79794	−	0.800493i	0.826599	−	0.562792i	$-0.190273\pi$
$97$	17.7076	−	7.88394i	1.79794	−	0.800493i	0.971338	−	0.237701i	$-0.0763939\pi$
$98$	0.352878	−	0.611203i	0.0356461	−	0.0617408i
$99$	8.30287	−	0.299233i	0.834469	−	0.0300740i
$100$	−2.49325	+	4.31844i	−0.249325	+	0.431844i
$101$	0.958960	−	9.12390i	0.0954201	−	0.907862i	−0.837174	−	0.546936i	$-0.815794\pi$
$101$	0.958960	−	9.12390i	0.0954201	−	0.907862i	0.932595	−	0.360926i	$-0.117539\pi$
$102$	1.03650	−	3.19003i	0.102629	−	0.315860i
$103$	1.25466	+	3.86145i	0.123626	+	0.380480i	0.993648	−	0.112532i	$-0.0358960\pi$
$103$	1.25466	+	3.86145i	0.123626	+	0.380480i	−0.870023	+	0.493012i	$0.835896\pi$
$104$	−0.0896460	−	0.0399130i	−0.00879051	−	0.00391379i
$105$	5.09562	+	2.26871i	0.497281	+	0.221404i
$106$	0.459045	+	1.41280i	0.0445864	+	0.137223i
$107$	3.34651	−	10.2995i	0.323519	−	0.995689i	−0.648586	−	0.761142i	$-0.724639\pi$
$107$	3.34651	−	10.2995i	0.323519	−	0.995689i	0.972105	−	0.234547i	$-0.0753608\pi$
$108$	−0.404839	+	3.85179i	−0.0389557	+	0.370638i
$109$	9.08355	−	15.7332i	0.870046	−	1.50696i	0.00809762	−	0.999967i	$-0.497422\pi$
$109$	9.08355	−	15.7332i	0.870046	−	1.50696i	0.861948	−	0.506996i	$-0.169244\pi$
$110$	−8.25193	+	6.46198i	−0.786791	+	0.616125i
$111$	−2.95029	+	5.11006i	−0.280029	+	0.485025i
$112$	2.29193	−	1.02043i	0.216567	−	0.0964220i
$113$	2.66384	−	8.19844i	0.250593	−	0.771245i	−0.744074	−	0.668098i	$-0.767109\pi$
$113$	2.66384	−	8.19844i	0.250593	−	0.771245i	0.994666	−	0.103147i	$-0.0328912\pi$
$114$	−2.28875	−	2.04107i	−0.214361	−	0.191164i
$115$	18.0502	−	13.1143i	1.68319	−	1.22291i
$116$	−0.797904	−	7.59155i	−0.0740835	−	0.704857i
$117$	−0.240447	−	0.0511085i	−0.0222293	−	0.00472498i
$118$	−4.15571	+	0.883322i	−0.382564	+	0.0813164i
$119$	−10.9270	+	4.86503i	−1.00168	+	0.445977i
$120$	−1.11164	−	1.92542i	−0.101479	−	0.175766i
$121$	−10.5671	+	3.05564i	−0.960643	+	0.277785i
$122$	−8.08518			−0.731998
$123$	−0.346708	+	3.29870i	−0.0312616	+	0.297434i
$124$	7.52180	−	1.59881i	0.675478	−	0.143577i
$125$	0.0131818	+	0.0405695i	0.00117902	+	0.00362865i
$126$	5.08444	−	3.69406i	0.452958	−	0.329093i
$127$	−9.47974	−	4.22065i	−0.841191	−	0.374522i	−0.0595304	−	0.998226i	$-0.518960\pi$
$127$	−9.47974	−	4.22065i	−0.841191	−	0.374522i	−0.781660	+	0.623704i	$0.785627\pi$
$128$	−0.978148	−	0.207912i	−0.0864569	−	0.0183770i
$129$	−4.95037	+	1.05223i	−0.435856	+	0.0926441i
$130$	0.283294	−	0.126131i	0.0248465	−	0.0110624i
$131$	3.56890	−	6.18152i	0.311817	−	0.540082i	−0.666939	−	0.745112i	$-0.732396\pi$
$131$	3.56890	−	6.18152i	0.311817	−	0.540082i	0.978756	+	0.205030i	$0.0657292\pi$
$132$	−0.327325	−	2.31030i	−0.0284900	−	0.201086i
$133$	0.0522918	+	10.9356i	0.00453428	+	0.948239i
$134$	6.22485	+	4.52262i	0.537746	+	0.390695i
$135$	−8.18965	−	9.09553i	−0.704853	−	0.782819i
$136$	4.66343	+	0.991242i	0.399886	+	0.0849983i
$137$	11.3540	+	5.05513i	0.970038	+	0.431889i	0.829697	−	0.558215i	$-0.188513\pi$
$137$	11.3540	+	5.05513i	0.970038	+	0.431889i	0.140341	+	0.990103i	$0.455180\pi$
$138$	0.519208	+	4.93993i	0.0441979	+	0.420515i
$139$	5.73731	−	6.37193i	0.486632	−	0.540460i	−0.448955	−	0.893554i	$-0.648204\pi$
$139$	5.73731	−	6.37193i	0.486632	−	0.540460i	0.935588	+	0.353094i	$0.114870\pi$
$140$	−2.44997	+	7.54023i	−0.207060	+	0.637266i
$141$	7.21534	+	5.24225i	0.607641	+	0.441477i
$142$	7.40810	+	12.8312i	0.621674	+	1.07677i
$143$	0.325248	−	0.0117219i	0.0271986	−	0.000980231i
$144$	−2.50503			−0.208753
$145$	19.5155	+	14.1789i	1.62068	+	1.17749i
$146$	−5.02687	+	1.06850i	−0.416027	+	0.0884293i
$147$	−0.485676	−	0.103234i	−0.0400579	−	0.00851457i
$148$	−7.66191	−	3.41130i	−0.629805	−	0.280407i
$149$	0.679155	+	6.46173i	0.0556386	+	0.529366i	0.986473	+	0.163924i	$0.0524153\pi$
$149$	0.679155	+	6.46173i	0.0556386	+	0.529366i	−0.930834	+	0.365441i	$0.880918\pi$
$150$	3.43153	+	0.729395i	0.280184	+	0.0595549i
$151$	−0.0101002	+	0.0310853i	−0.000821944	+	0.00252968i	−0.951467	−	0.307752i	$-0.900423\pi$
$151$	−0.0101002	+	0.0310853i	−0.000821944	+	0.00252968i	0.950645	+	0.310282i	$0.100423\pi$
$152$	2.54520	−	3.53863i	0.206443	−	0.287021i
$153$	11.9430			0.965536
$154$	−5.34142	+	6.38012i	−0.430424	+	0.514125i
$155$	−12.1505	+	21.0453i	−0.975952	+	1.69040i
$156$	−0.00721645	+	0.0686599i	−0.000577778	+	0.00549719i
$157$	−6.22510	−	6.91367i	−0.496817	−	0.551771i	0.441629	−	0.897198i	$-0.354401\pi$
$157$	−6.22510	−	6.91367i	−0.496817	−	0.551771i	−0.938446	+	0.345427i	$0.887734\pi$
$158$	−5.50154	+	6.11008i	−0.437679	+	0.486092i
$159$	0.845510	−	0.614299i	0.0670533	−	0.0487171i
$160$	2.55661	−	1.85749i	0.202118	−	0.146847i
$161$	11.8523	−	13.1633i	0.934089	−	1.03741i
$162$	−4.68561	+	0.995958i	−0.368136	+	0.0782498i
$163$	−14.3655	−	10.4372i	−1.12519	−	0.817502i	−0.140206	−	0.990122i	$-0.544777\pi$
$163$	−14.3655	−	10.4372i	−1.12519	−	0.817502i	−0.984988	+	0.172621i	$0.944777\pi$
$164$	−4.71456			−0.368145
$165$	6.11776	+	4.11654i	0.476267	+	0.320472i
$166$	−1.12549	+	1.94941i	−0.0873553	+	0.151304i
$167$	1.73348	−	16.4929i	0.134141	−	1.27626i	−0.695729	−	0.718305i	$-0.744918\pi$
$167$	1.73348	−	16.4929i	0.134141	−	1.27626i	0.829869	−	0.557958i	$-0.188415\pi$
$168$	−1.18106	−	1.31170i	−0.0911205	−	0.101200i
$169$	12.7065	+	2.70085i	0.977423	+	0.207758i
$170$	−12.1889	+	8.85577i	−0.934847	+	0.679206i
$171$	4.39348	−	9.99630i	0.335978	−	0.764436i
$172$	−2.22294	−	6.84151i	−0.169498	−	0.521660i
$173$	10.3138	+	11.4546i	0.784143	+	0.870880i	0.994281	−	0.106792i	$-0.0340580\pi$
$173$	10.3138	+	11.4546i	0.784143	+	0.870880i	−0.210138	+	0.977672i	$0.567391\pi$
$174$	−4.90607	+	2.18432i	−0.371929	+	0.165593i
$175$	−6.25515	−	10.8342i	−0.472845	−	0.818991i
$176$	3.21721	−	0.805960i	0.242506	−	0.0607515i
$177$	1.49451	+	2.58856i	0.112334	+	0.194568i
$178$	−2.27313	−	1.65152i	−0.170378	−	0.123787i
$179$	−0.682468	+	2.10042i	−0.0510101	+	0.156993i	−0.973317	−	0.229466i	$-0.926302\pi$
$179$	−0.682468	+	2.10042i	−0.0510101	+	0.156993i	0.922307	+	0.386459i	$0.126302\pi$
$180$	5.29701	−	5.88293i	0.394816	−	0.438488i
$181$	−2.01728	−	0.898151i	−0.149943	−	0.0667590i	0.330393	−	0.943843i	$-0.392819\pi$
$181$	−2.01728	−	0.898151i	−0.149943	−	0.0667590i	−0.480336	+	0.877084i	$0.659485\pi$
$182$	0.199173	−	0.144708i	0.0147637	−	0.0107264i
$183$	1.75776	+	5.40983i	0.129937	+	0.399906i
$184$	−6.90594	+	1.46790i	−0.509113	+	0.108215i
$185$	24.2127	−	10.7802i	1.78016	−	0.792577i
$186$	−2.70505	−	4.68529i	−0.198344	−	0.343542i
$187$	−15.3384	+	3.84250i	−1.12165	+	0.280992i
$188$	−6.33842	+	10.9785i	−0.462277	+	0.800687i
$189$	−7.86099	−	5.71135i	−0.571803	−	0.415439i
$190$	2.92833	+	13.4599i	0.212443	+	0.976483i
$191$	7.53986	+	23.2053i	0.545565	+	1.67908i	0.719642	+	0.694346i	$0.244306\pi$
$191$	7.53986	+	23.2053i	0.545565	+	1.67908i	−0.174076	+	0.984732i	$0.555694\pi$
$192$	0.0735398	+	0.699685i	0.00530728	+	0.0504954i
$193$	−0.320480	−	3.04916i	−0.0230687	−	0.219484i	−0.999983	−	0.00585170i	$-0.998137\pi$
$193$	−0.320480	−	3.04916i	−0.0230687	−	0.219484i	0.976914	−	0.213632i	$-0.0685293\pi$
$194$	12.9700	−	14.4047i	0.931194	−	1.03420i
$195$	−0.145984	−	0.162132i	−0.0104542	−	0.0116105i
$196$	0.0737716	−	0.701890i	0.00526940	−	0.0501350i
$197$	−19.6880			−1.40271			−0.701357	−	0.712810i	$-0.747422\pi$
$197$	−19.6880			−1.40271			−0.701357	+	0.712810i	$0.747422\pi$
$198$	7.46334	−	3.65044i	0.530396	−	0.259426i
$199$	−5.42596	−	9.39804i	−0.384636	−	0.666210i	0.607082	−	0.794639i	$-0.292340\pi$
$199$	−5.42596	−	9.39804i	−0.384636	−	0.666210i	−0.991719	+	0.128429i	$0.959006\pi$
$200$	−0.521231	+	4.95918i	−0.0368566	+	0.350667i
$201$	1.67279	−	5.14832i	0.117990	−	0.363135i
$202$	−2.83497	−	8.72514i	−0.199468	−	0.613899i
$203$	17.4952	+	7.78935i	1.22792	+	0.546705i
$204$	−0.350609	−	3.33582i	−0.0245476	−	0.233554i
$205$	9.96916	−	11.0719i	0.696276	−	0.773293i
$206$	2.71678	+	3.01730i	0.189287	+	0.210225i
$207$	−16.1570	+	7.19358i	−1.12299	+	0.499989i
$208$	−0.0981298			−0.00680408
$209$	−2.42637	+	14.2518i	−0.167836	+	0.985815i
$210$	5.57785			0.384908
$211$	−0.337330	+	0.150189i	−0.0232228	+	0.0103394i	−0.418315	−	0.908302i	$-0.637379\pi$
$211$	−0.337330	+	0.150189i	−0.0232228	+	0.0103394i	0.395092	+	0.918641i	$0.370713\pi$
$212$	0.993994	+	1.10394i	0.0682678	+	0.0758191i
$213$	6.97486	−	7.74637i	0.477909	−	0.530772i
$214$	−1.13199	−	10.7702i	−0.0773815	−	0.736235i
$215$	20.7674	+	9.24625i	1.41633	+	0.630589i
$216$	1.19682	+	3.68345i	0.0814336	+	0.250627i
$217$	−5.96172	+	18.3483i	−0.404708	+	1.24556i
$218$	1.89898	−	18.0676i	0.128615	−	1.22369i
$219$	1.80781	+	3.13121i	0.122160	+	0.211588i
$220$	−4.91019	+	9.25967i	−0.331045	+	0.624287i
$221$	0.467844			0.0314706
$222$	−0.616779	+	5.86826i	−0.0413955	+	0.393852i
$223$	−4.21966	−	4.68640i	−0.282569	−	0.313825i	0.585106	−	0.810957i	$-0.301053\pi$
$223$	−4.21966	−	4.68640i	−0.282569	−	0.313825i	−0.867675	+	0.497132i	$0.834386\pi$
$224$	1.67874	−	1.86443i	0.112165	−	0.124572i
$225$	1.30570	+	12.4229i	0.0870468	+	0.828195i
$226$	−0.901072	−	8.57313i	−0.0599384	−	0.570276i
$227$	−1.06154	−	3.26709i	−0.0704569	−	0.216844i	0.909628	−	0.415424i	$-0.136367\pi$
$227$	−1.06154	−	3.26709i	−0.0704569	−	0.216844i	−0.980085	+	0.198580i	$0.936367\pi$
$228$	−2.92106	−	0.933691i	−0.193452	−	0.0618352i
$229$	4.18899	+	3.04348i	0.276816	+	0.201119i	0.717528	−	0.696530i	$-0.245274\pi$
$229$	4.18899	+	3.04348i	0.276816	+	0.201119i	−0.440711	+	0.897649i	$0.645274\pi$
$230$	11.1557	−	19.3222i	0.735582	−	1.27407i
$231$	5.43022	+	2.18690i	0.357283	+	0.143887i
$232$	−3.81668	−	6.61069i	−0.250577	−	0.434013i
$233$	−0.0762886	+	0.0339659i	−0.00499783	+	0.00222518i	−0.409234	−	0.912429i	$-0.634204\pi$
$233$	−0.0762886	+	0.0339659i	−0.00499783	+	0.00222518i	0.404236	+	0.914655i	$0.367537\pi$
$234$	−0.240447	+	0.0511085i	−0.0157185	+	0.00334107i
$235$	−12.3794	−	38.0999i	−0.807544	−	2.48537i
$236$	−3.43715	+	2.49723i	−0.223739	+	0.162556i
$237$	5.28435	+	2.35274i	0.343255	+	0.152827i
$238$	−8.00356	+	8.88886i	−0.518794	+	0.576179i
$239$	−6.78749	+	20.8897i	−0.439046	+	1.35124i	0.449837	+	0.893111i	$0.351482\pi$
$239$	−6.78749	+	20.8897i	−0.439046	+	1.35124i	−0.888883	+	0.458134i	$0.848518\pi$
$240$	−1.79867	−	1.30681i	−0.116104	−	0.0843544i
$241$	5.10957	+	8.85003i	0.329136	+	0.570081i	0.982341	−	0.187101i	$-0.0599091\pi$
$241$	5.10957	+	8.85003i	0.329136	+	0.570081i	−0.653204	+	0.757182i	$0.726576\pi$
$242$	−8.41066	+	7.08948i	−0.540658	+	0.455729i
$243$	7.49458	+	12.9810i	0.480778	+	0.832732i
$244$	−7.38618	+	3.28854i	−0.472852	+	0.210527i
$245$	1.49235	+	1.65743i	0.0953431	+	0.105889i
$246$	1.02497	+	3.15453i	0.0653497	+	0.201126i
$247$	0.172106	−	0.391585i	0.0109509	−	0.0249160i
$248$	6.22121	−	4.51998i	0.395047	−	0.287019i
$249$	1.54905	+	0.329261i	0.0981671	+	0.0208661i
$250$	0.0285433	+	0.0317006i	0.00180524	+	0.00200492i
$251$	−2.02441	+	19.2610i	−0.127780	+	1.21574i	0.723235	+	0.690602i	$0.242654\pi$
$251$	−2.02441	+	19.2610i	−0.127780	+	1.21574i	−0.851015	+	0.525141i	$0.824012\pi$
$252$	3.14236	−	5.44272i	0.197950	−	0.342859i
$253$	18.4360	−	14.4370i	1.15906	−	0.907647i
$254$	−10.3769			−0.651103
$255$	8.57537	+	6.23037i	0.537011	+	0.390161i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−12.0201	+	13.3497i	−0.749793	+	0.832729i	−0.990449	−	0.137881i	$-0.955971\pi$
$257$	−12.0201	+	13.3497i	−0.749793	+	0.832729i	0.240656	+	0.970610i	$0.422637\pi$
$258$	−4.09441	+	2.97476i	−0.254907	+	0.185201i
$259$	17.0230	−	12.3679i	1.05776	−	0.768507i
$260$	0.207500	−	0.230452i	0.0128686	−	0.0142920i
$261$	−12.7950	−	14.2103i	−0.791991	−	0.879595i
$262$	0.746104	−	7.09871i	0.0460945	−	0.438560i
$263$	−1.15157	+	1.99457i	−0.0710086	+	0.122991i	−0.899344	−	0.437243i	$-0.855955\pi$
$263$	−1.15157	+	1.99457i	−0.0710086	+	0.122991i	0.828335	+	0.560233i	$0.189288\pi$
$264$	−1.23871	−	1.97743i	−0.0762374	−	0.121702i
$265$	−4.69440			−0.288374
$266$	4.49569	+	9.96892i	0.275648	+	0.611234i
$267$	−0.610853	+	1.88001i	−0.0373836	+	0.115055i
$268$	7.52620	+	1.59974i	0.459736	+	0.0977199i
$269$	−0.832446	−	7.92020i	−0.0507551	−	0.482903i	−0.990144	−	0.140050i	$-0.955274\pi$
$269$	−0.832446	−	7.92020i	−0.0507551	−	0.482903i	0.939389	−	0.342853i	$-0.111393\pi$
$270$	−11.1811	−	4.97815i	−0.680460	−	0.302961i
$271$	22.3013	+	4.74028i	1.35471	+	0.287952i	0.827347	−	0.561691i	$-0.189849\pi$
$271$	22.3013	+	4.74028i	1.35471	+	0.287952i	0.527359	+	0.849643i	$0.323182\pi$
$272$	4.66343	−	0.991242i	0.282762	−	0.0601029i
$273$	−0.140126	−	0.101807i	−0.00848080	−	0.00616166i
$274$	12.4285			0.750833
$275$	−5.67381	−	15.5346i	−0.342144	−	0.936774i
$276$	2.48357	+	4.30167i	0.149493	+	0.258930i
$277$	−9.96951	−	7.24327i	−0.599010	−	0.435206i	0.246518	−	0.969138i	$-0.420714\pi$
$277$	−9.96951	−	7.24327i	−0.599010	−	0.435206i	−0.845527	+	0.533932i	$0.820714\pi$
$278$	2.64960	−	8.15462i	0.158912	−	0.489082i
$279$	12.8897	−	14.3154i	0.771684	−	0.857042i
$280$	0.828730	+	7.88484i	0.0495261	+	0.471209i
$281$	−0.602201	−	0.268117i	−0.0359243	−	0.0159945i	0.388696	−	0.921366i	$-0.372926\pi$
$281$	−0.602201	−	0.268117i	−0.0359243	−	0.0159945i	−0.424620	+	0.905372i	$0.639592\pi$
$282$	8.72376	+	1.85429i	0.519492	+	0.110421i
$283$	1.68192	+	1.86796i	0.0999799	+	0.111039i	0.791058	−	0.611741i	$-0.209531\pi$
$283$	1.68192	+	1.86796i	0.0999799	+	0.111039i	−0.691078	+	0.722780i	$0.742864\pi$
$284$	11.9866	+	8.70874i	0.711271	+	0.516769i
$285$	8.36944	−	4.88561i	0.495763	−	0.289398i
$286$	0.292362	−	0.142999i	0.0172877	−	0.00845570i
$287$	5.91402	−	10.2434i	0.349093	−	0.604647i
$288$	−2.28846	+	1.01889i	−0.134849	+	0.0600386i
$289$	−5.60489	+	1.19136i	−0.329699	+	0.0700798i
$290$	23.5954	+	5.01535i	1.38557	+	0.294512i
$291$	−12.4580	−	5.54666i	−0.730301	−	0.325151i
$292$	−4.15768	+	3.02073i	−0.243310	+	0.176775i
$293$	5.56308	+	17.1214i	0.324998	+	1.00024i	0.971441	+	0.237280i	$0.0762559\pi$
$293$	5.56308	+	17.1214i	0.324998	+	1.00024i	−0.646443	+	0.762962i	$0.723744\pi$
$294$	−0.485676	+	0.103234i	−0.0283252	+	0.00602071i
$295$	1.40340	−	13.3525i	0.0817091	−	0.777410i
$296$	−8.38701			−0.487485
$297$	−8.93342	−	9.23016i	−0.518369	−	0.535588i
$298$	3.24866	+	5.62685i	0.188190	+	0.325954i
$299$	−0.632921	+	0.281794i	−0.0366028	+	0.0162966i
$300$	3.43153	−	0.729395i	0.198120	−	0.0421116i
$301$	17.6531	+	3.75229i	1.01751	+	0.216278i
$302$	0.00341651	+	0.0325060i	0.000196598	+	0.00187051i
$303$	−5.22170	+	3.79378i	−0.299979	+	0.217947i
$304$	0.885868	−	4.26793i	0.0508080	−	0.244783i
$305$	7.89548	−	24.2998i	0.452094	−	1.39140i
$306$	10.9105	−	4.85766i	0.623711	−	0.277694i
$307$	−3.42227	+	5.92754i	−0.195319	+	0.338303i	−0.947005	−	0.321219i	$-0.895908\pi$
$307$	−3.42227	+	5.92754i	−0.195319	+	0.338303i	0.751686	+	0.659521i	$0.229241\pi$
$308$	−2.28460	+	8.00108i	−0.130177	+	0.455904i
$309$	1.42824	−	2.47379i	0.0812499	−	0.140729i
$310$	−2.54015	+	24.1679i	−0.144271	+	1.37264i
$311$	−1.40618	+	4.32777i	−0.0797370	+	0.245405i	−0.982976	−	0.183732i	$-0.941182\pi$
$311$	−1.40618	+	4.32777i	−0.0797370	+	0.245405i	0.903239	+	0.429137i	$0.141182\pi$
$312$	0.0213339	+	0.0656591i	0.00120780	+	0.00371722i
$313$	6.74411	+	3.00267i	0.381199	+	0.169721i	0.588385	−	0.808581i	$-0.299764\pi$
$313$	6.74411	+	3.00267i	0.381199	+	0.169721i	−0.207186	+	0.978302i	$0.566431\pi$
$314$	−8.49895	−	3.78398i	−0.479624	−	0.213542i
$315$	6.13726	+	18.8885i	0.345795	+	1.06425i
$316$	−2.54071	+	7.81951i	−0.142926	+	0.439882i
$317$	−2.78469	+	26.4945i	−0.156404	+	1.48808i	0.581705	+	0.813400i	$0.302386\pi$
$317$	−2.78469	+	26.4945i	−0.156404	+	1.48808i	−0.738109	+	0.674682i	$0.764281\pi$
$318$	0.522554	−	0.905090i	0.0293034	−	0.0507549i
$319$	21.0046	+	14.1336i	1.17603	+	0.791331i
$320$	1.58007	−	2.73676i	0.0883287	−	0.152990i
$321$	−6.96029	+	3.09892i	−0.388486	+	0.172965i
$322$	5.47359	−	16.8460i	0.305031	−	0.938790i
$323$	−4.22347	+	20.3478i	−0.235000	+	1.13218i
$324$	−3.87543	+	2.81566i	−0.215302	+	0.156426i
$325$	0.0511483	+	0.486644i	0.00283720	+	0.0269941i
$326$	−17.3687	−	3.69184i	−0.961965	−	0.204472i
$327$	−12.5019	+	2.65737i	−0.691359	+	0.146953i
$328$	−4.30696	+	1.91758i	−0.237812	+	0.105881i
$329$	−15.9020	−	27.5431i	−0.876708	−	1.51850i
$330$	7.26320	+	1.27233i	0.399826	+	0.0700395i
$331$	11.8043			0.648823			0.324412	−	0.945916i	$-0.394834\pi$
$331$	11.8043			0.648823			0.324412	+	0.945916i	$0.394834\pi$
$332$	−0.235292	+	2.23866i	−0.0129133	+	0.122862i
$333$	−20.5506	+	4.36817i	−1.12617	+	0.239374i
$334$	−5.12467	−	15.7721i	−0.280410	−	0.863012i
$335$	−19.6714	+	14.2921i	−1.07477	+	0.780862i
$336$	−1.61246	−	0.717915i	−0.0879671	−	0.0391655i
$337$	−11.2971	−	2.40128i	−0.615395	−	0.130806i	−0.110341	−	0.993894i	$-0.535194\pi$
$337$	−11.2971	−	2.40128i	−0.615395	−	0.130806i	−0.505054	+	0.863088i	$0.668528\pi$
$338$	12.7065	−	2.70085i	0.691142	−	0.146907i
$339$	−5.54043	+	2.46676i	−0.300915	+	0.133976i
$340$	−7.53316	+	13.0478i	−0.408543	+	0.707618i
$341$	−11.9484	+	22.5323i	−0.647041	+	1.22019i
$342$	−0.0522126	−	10.9191i	−0.00282334	−	0.590435i
$343$	15.6403	+	11.3633i	0.844496	+	0.613562i
$344$	−4.81345	−	5.34588i	−0.259524	−	0.288230i
$345$	−15.3539	−	3.26356i	−0.826624	−	0.175704i
$346$	14.0811	+	6.26933i	0.757007	+	0.337041i
$347$	−1.99922	−	19.0213i	−0.107324	−	1.02112i	−0.907128	−	0.420855i	$-0.861730\pi$
$347$	−1.99922	−	19.0213i	−0.107324	−	1.02112i	0.799804	−	0.600261i	$-0.204937\pi$
$348$	−3.59348	+	3.99096i	−0.192631	+	0.213938i
$349$	7.40961	−	22.8044i	0.396627	−	1.22069i	−0.531060	−	0.847334i	$-0.678206\pi$
$349$	7.40961	−	22.8044i	0.396627	−	1.22069i	0.927687	−	0.373359i	$-0.121794\pi$
$350$	−10.1210	−	7.35337i	−0.540993	−	0.393054i
$351$	0.190028	+	0.329139i	0.0101430	+	0.0175681i
$352$	2.61125	−	2.04484i	0.139180	−	0.108990i
$353$	−15.8233			−0.842187			−0.421094	−	0.907017i	$-0.638354\pi$
$353$	−15.8233			−0.842187			−0.421094	+	0.907017i	$0.638354\pi$
$354$	2.41817	+	1.75690i	0.128524	+	0.0933782i
$355$	−45.7981	+	9.73469i	−2.43071	+	0.516664i
$356$	−2.74834	−	0.584178i	−0.145662	−	0.0309614i
$357$	7.68760	+	3.42274i	0.406871	+	0.181151i
$358$	0.230852	+	2.19641i	0.0122009	+	0.116084i
$359$	20.9905	+	4.46168i	1.10784	+	0.235478i	0.725281	−	0.688453i	$-0.241710\pi$
$359$	20.9905	+	4.46168i	1.10784	+	0.235478i	0.382558	+	0.923932i	$0.375043\pi$
$360$	2.44626	−	7.52881i	0.128929	−	0.396803i
$361$	15.4774	+	11.0204i	0.814601	+	0.580021i
$362$	−2.20819			−0.116060
$363$	6.57213	+	4.08633i	0.344947	+	0.214477i
$364$	0.123096	−	0.213208i	0.00645196	−	0.0111751i
$365$	1.69760	−	16.1516i	0.0888564	−	0.845412i
$366$	3.80617	+	4.22718i	0.198952	+	0.220958i
$367$	−14.1031	+	15.6630i	−0.736174	+	0.817604i	−0.988688	−	0.149989i	$-0.952076\pi$
$367$	−14.1031	+	15.6630i	−0.736174	+	0.817604i	0.252514	+	0.967593i	$0.418743\pi$
$368$	−5.71184	+	4.14989i	−0.297750	+	0.216328i
$369$	−9.55459	+	6.94181i	−0.497392	+	0.361376i
$370$	17.7347	−	19.6964i	0.921985	−	1.02397i
$371$	−3.64543	+	0.774861i	−0.189261	+	0.0402288i
$372$	−4.37686	−	3.17998i	−0.226930	−	0.164874i
$373$	−21.7548			−1.12642			−0.563211	−	0.826313i	$-0.690434\pi$
$373$	−21.7548			−1.12642			−0.563211	+	0.826313i	$0.690434\pi$
$374$	−12.4494	+	9.74899i	−0.643745	+	0.504108i
$375$	0.0150055	−	0.0259904i	0.000774883	−	0.00134214i
$376$	−1.32509	+	12.6074i	−0.0683364	+	0.650177i
$377$	−0.501219	−	0.556660i	−0.0258141	−	0.0286695i
$378$	−9.50439	−	2.02022i	−0.488853	−	0.103909i
$379$	5.61814	−	4.08182i	0.288584	−	0.209669i	−0.434069	−	0.900880i	$-0.642922\pi$
$379$	5.61814	−	4.08182i	0.288584	−	0.209669i	0.722653	+	0.691211i	$0.242922\pi$
$380$	8.14979	+	11.1052i	0.418075	+	0.569683i
$381$	2.25599	+	6.94321i	0.115578	+	0.355712i
$382$	16.3265	+	18.1324i	0.835334	+	0.927733i
$383$	−18.2448	+	8.12312i	−0.932267	+	0.415072i	−0.815939	−	0.578139i	$-0.803779\pi$
$383$	−18.2448	+	8.12312i	−0.932267	+	0.415072i	−0.116329	+	0.993211i	$0.537113\pi$
$384$	0.351769	+	0.609282i	0.0179512	+	0.0310923i
$385$	−13.9592	−	22.2839i	−0.711426	−	1.13569i
$386$	−1.53298	−	2.65520i	−0.0780266	−	0.135146i
$387$	−14.5786	−	10.5920i	−0.741074	−	0.538421i
$388$	5.98980	−	18.4347i	0.304086	−	0.935881i
$389$	−21.1106	+	23.4457i	−1.07035	+	1.18875i	−0.0890992	+	0.996023i	$0.528399\pi$
$389$	−21.1106	+	23.4457i	−1.07035	+	1.18875i	−0.981253	+	0.192724i	$0.938268\pi$
$390$	−0.199308	−	0.0887378i	−0.0100924	−	0.00449341i
$391$	27.2318	−	19.7851i	1.37717	−	1.00057i
$392$	−0.218091	−	0.671214i	−0.0110152	−	0.0339014i
$393$	−4.91199	+	1.04408i	−0.247777	+	0.0526666i
$394$	−17.9859	+	8.00784i	−0.906117	+	0.403429i
$395$	−12.9912	−	22.5015i	−0.653659	−	1.13217i
$396$	5.33333	−	6.37046i	0.268010	−	0.320128i
$397$	−8.67314	+	15.0223i	−0.435292	+	0.753948i	−0.997319	−	0.0731705i	$-0.976688\pi$
$397$	−8.67314	+	15.0223i	−0.435292	+	0.753948i	0.562027	+	0.827119i	$0.310022\pi$
$398$	−8.77939	−	6.37860i	−0.440071	−	0.319730i
$399$	5.69287	−	5.17539i	0.285000	−	0.259093i
$400$	1.54091	+	4.74244i	0.0770457	+	0.237122i
$401$	−3.59728	−	34.2258i	−0.179640	−	1.70916i	−0.598514	−	0.801112i	$-0.704242\pi$
$401$	−3.59728	−	34.2258i	−0.179640	−	1.70916i	0.418875	−	0.908044i	$-0.362425\pi$
$402$	−0.565841	−	5.38361i	−0.0282216	−	0.268510i
$403$	0.504928	−	0.560779i	0.0251522	−	0.0279344i
$404$	−6.13871	−	6.81772i	−0.305412	−	0.339194i
$405$	1.58235	−	15.0551i	0.0786277	−	0.748093i
$406$	19.1508			0.950440
$407$	24.9877	−	12.2219i	1.23860	−	0.605818i
$408$	−1.67710	−	2.90482i	−0.0830288	−	0.143810i
$409$	2.63853	−	25.1040i	0.130467	−	1.24131i	−0.711851	−	0.702330i	$-0.752143\pi$
$409$	2.63853	−	25.1040i	0.130467	−	1.24131i	0.842318	−	0.538981i	$-0.181190\pi$
$410$	4.60394	−	14.1695i	0.227372	−	0.699781i
$411$	−2.70202	−	8.31597i	−0.133281	−	0.410197i
$412$	3.70915	+	1.65142i	0.182737	+	0.0813596i
$413$	−1.11416	−	10.6005i	−0.0548241	−	0.521617i
$414$	−11.8343	+	13.1433i	−0.581624	+	0.645959i
$415$	−4.75982	−	5.28632i	−0.233650	−	0.259495i
$416$	−0.0896460	+	0.0399130i	−0.00439526	+	0.00195689i
$417$	−6.03234			−0.295405
$418$	3.58011	+	14.0065i	0.175109	+	0.685082i
$419$	4.11568			0.201064			0.100532	−	0.994934i	$-0.467946\pi$
$419$	4.11568			0.201064			0.100532	+	0.994934i	$0.467946\pi$
$420$	5.09562	−	2.26871i	0.248641	−	0.110702i
$421$	2.99520	+	3.32651i	0.145977	+	0.162124i	0.811699	−	0.584076i	$-0.198543\pi$
$421$	2.99520	+	3.32651i	0.145977	+	0.162124i	−0.665722	+	0.746200i	$0.731876\pi$
$422$	−0.247079	+	0.274409i	−0.0120276	+	0.0133580i
$423$	3.31940	+	31.5820i	0.161395	+	1.53557i
$424$	1.35707	+	0.604208i	0.0659053	+	0.0293429i
$425$	−7.34648	−	22.6101i	−0.356356	−	1.09675i
$426$	3.22112	−	9.91359i	0.156064	−	0.480315i
$427$	2.12029	−	20.1732i	0.102608	−	0.976252i
$428$	−5.41476	−	9.37864i	−0.261732	−	0.453334i
$429$	−0.159242	−	0.164532i	−0.00768829	−	0.00794367i
$430$	22.7328			1.09627
$431$	1.51247	−	14.3902i	0.0728533	−	0.693152i	−0.895753	−	0.444552i	$-0.853363\pi$
$431$	1.51247	−	14.3902i	0.0728533	−	0.693152i	0.968606	−	0.248600i	$-0.0799705\pi$
$432$	2.59155	+	2.87820i	0.124686	+	0.138478i
$433$	−6.70290	+	7.44432i	−0.322121	+	0.357751i	−0.882356	−	0.470582i	$-0.844044\pi$
$433$	−6.70290	+	7.44432i	−0.322121	+	0.357751i	0.560236	+	0.828333i	$0.310711\pi$
$434$	2.01662	+	19.1868i	0.0968008	+	0.920998i
$435$	−1.77397	−	16.8782i	−0.0850551	−	0.809246i
$436$	−5.61394	−	17.2779i	−0.268859	−	0.827463i
$437$	−6.54231	−	30.0714i	−0.312961	−	1.43851i
$438$	2.92509	+	2.12520i	0.139766	+	0.101546i
$439$	−7.30953	+	12.6605i	−0.348865	+	0.604252i	−0.986048	−	0.166461i	$-0.946766\pi$
$439$	−7.30953	+	12.6605i	−0.348865	+	0.604252i	0.637183	+	0.770712i	$0.280099\pi$
$440$	−0.719434	+	10.4563i	−0.0342976	+	0.498484i
$441$	−0.883971	−	1.53108i	−0.0420939	−	0.0729087i
$442$	0.427397	−	0.190289i	0.0203292	−	0.00905115i
$443$	−0.771948	+	0.164083i	−0.0366763	+	0.00779580i	−0.226213	−	0.974078i	$-0.572635\pi$
$443$	−0.771948	+	0.164083i	−0.0366763	+	0.00779580i	0.189537	+	0.981874i	$0.439301\pi$
$444$	1.82338	+	5.61179i	0.0865338	+	0.266324i
$445$	7.18341	−	5.21905i	0.340526	−	0.247407i
$446$	−5.76098	−	2.56495i	−0.272790	−	0.121454i
$447$	3.05868	−	3.39700i	0.144670	−	0.160673i
$448$	0.775272	−	2.38604i	0.0366282	−	0.112730i
$449$	−15.9516	−	11.5895i	−0.752801	−	0.546942i	0.143893	−	0.989593i	$-0.454038\pi$
$449$	−15.9516	−	11.5895i	−0.752801	−	0.546942i	−0.896694	+	0.442651i	$0.854038\pi$
$450$	6.24568	+	10.8178i	0.294424	+	0.509957i
$451$	10.0375	−	11.9894i	0.472647	−	0.564559i
$452$	−4.31018	−	7.46545i	−0.202734	−	0.351145i
$453$	0.0210071	−	0.00935298i	0.000987001	−	0.000439441i
$454$	−2.29861	−	2.55287i	−0.107879	−	0.119812i
$455$	0.240415	+	0.739921i	0.0112708	+	0.0346880i
$456$	−3.04829	+	0.335133i	−0.142749	+	0.0156940i
$457$	−28.7683	+	20.9014i	−1.34572	+	0.977726i	−0.346512	+	0.938045i	$0.612634\pi$
$457$	−28.7683	+	20.9014i	−1.34572	+	0.977726i	−0.999212	+	0.0396807i	$0.987366\pi$
$458$	5.06473	+	1.07654i	0.236659	+	0.0503034i
$459$	−12.3555	−	13.7221i	−0.576704	−	0.640495i
$460$	2.33217	−	22.1891i	0.108738	−	1.03457i
$461$	4.51646	−	7.82274i	0.210353	−	0.364341i	−0.741472	−	0.670983i	$-0.765872\pi$
$461$	4.51646	−	7.82274i	0.210353	−	0.364341i	0.951825	+	0.306642i	$0.0992055\pi$
$462$	5.85025	−	0.210841i	0.272178	−	0.00980922i
$463$	−18.2099			−0.846286			−0.423143	−	0.906063i	$-0.639073\pi$
$463$	−18.2099			−0.846286			−0.423143	+	0.906063i	$0.639073\pi$
$464$	−6.17552	−	4.48678i	−0.286691	−	0.208293i
$465$	16.7231	−	3.55460i	0.775515	−	0.164841i
$466$	−0.0558779	+	0.0620587i	−0.00258850	+	0.00287482i
$467$	−11.3863	+	8.27262i	−0.526895	+	0.382811i	−0.819195	−	0.573515i	$-0.805579\pi$
$467$	−11.3863	+	8.27262i	−0.526895	+	0.382811i	0.292300	+	0.956327i	$0.405579\pi$
$468$	−0.198871	+	0.144488i	−0.00919283	+	0.00667898i
$469$	−12.9168	+	14.3455i	−0.596442	+	0.662415i
$470$	−26.8058	−	29.7709i	−1.23646	−	1.37323i
$471$	−0.684160	+	6.50935i	−0.0315244	+	0.299935i
$472$	−2.12427	+	3.67935i	−0.0977776	+	0.169356i
$473$	22.1311	+	8.91280i	1.01759	+	0.409811i
$474$	5.78444			0.265688
$475$	−21.6272	−	2.16860i	−0.992324	−	0.0995024i
$476$	−3.69620	+	11.3757i	−0.169415	+	0.521405i
$477$	3.63991	+	0.773687i	0.166660	+	0.0354247i
$478$	2.29594	+	21.8444i	0.105014	+	0.999142i
$479$	−14.1408	−	6.29587i	−0.646108	−	0.287666i	0.0574022	−	0.998351i	$-0.481718\pi$
$479$	−14.1408	−	6.29587i	−0.646108	−	0.287666i	−0.703510	+	0.710685i	$0.748385\pi$
$480$	−2.17470	−	0.462246i	−0.0992610	−	0.0210986i
$481$	−0.805030	+	0.171115i	−0.0367062	+	0.00780215i
$482$	8.26746	+	6.00666i	0.376572	+	0.273596i
$483$	−12.4617			−0.567028
$484$	−4.79997	+	9.89749i	−0.218181	+	0.449886i
$485$	30.6272	+	53.0478i	1.39071	+	2.40878i
$486$	12.1265	+	8.81041i	0.550069	+	0.399648i
$487$	−4.16707	+	12.8249i	−0.188828	+	0.581152i	−0.999993	−	0.00366456i	$-0.998834\pi$
$487$	−4.16707	+	12.8249i	−0.188828	+	0.581152i	0.811166	+	0.584817i	$0.198834\pi$
$488$	−5.41004	+	6.00846i	−0.244901	+	0.271990i
$489$	1.30583	+	12.4241i	0.0590516	+	0.561839i
$490$	2.03747	+	0.907140i	0.0920435	+	0.0409804i
$491$	−9.34122	−	1.98554i	−0.421563	−	0.0896061i	−0.00775467	−	0.999970i	$-0.502468\pi$
$491$	−9.34122	−	1.98554i	−0.421563	−	0.0896061i	−0.413809	+	0.910364i	$0.635802\pi$
$492$	2.21942	+	2.46492i	0.100059	+	0.111127i
$493$	29.4425	+	21.3912i	1.32602	+	0.963412i
$494$	−0.00204533	−	0.427733i	−9.20236e−5	−	0.0192446i
$495$	3.68308	+	25.9957i	0.165542	+	1.16842i
$496$	3.84492	−	6.65960i	0.172642	−	0.299025i
$497$	−33.9577	+	15.1190i	−1.52321	+	0.678178i
$498$	1.54905	−	0.329261i	0.0694146	−	0.0147545i
$499$	8.53347	+	1.81385i	0.382011	+	0.0811989i	0.394915	−	0.918718i	$-0.370774\pi$
$499$	8.53347	+	1.81385i	0.382011	+	0.0811989i	−0.0129038	+	0.999917i	$0.504108\pi$
$500$	0.0389694	+	0.0173503i	0.00174277	+	0.000775929i
$501$	−9.43908	+	6.85789i	−0.421707	+	0.306388i
$502$	5.98476	+	18.4192i	0.267113	+	0.822089i
$503$	10.8269	−	2.30132i	0.482746	−	0.102611i	0.0398909	−	0.999204i	$-0.487299\pi$
$503$	10.8269	−	2.30132i	0.482746	−	0.102611i	0.442855	+	0.896593i	$0.353966\pi$
$504$	0.656931	−	6.25028i	0.0292620	−	0.278410i
$505$	28.9916			1.29011
$506$	10.9701	−	20.6875i	0.487680	−	0.919670i
$507$	−4.56961	−	7.91480i	−0.202944	−	0.351509i
$508$	−9.47974	+	4.22065i	−0.420595	+	0.187261i
$509$	−14.0492	+	2.98626i	−0.622721	+	0.132364i	−0.508458	−	0.861087i	$-0.669784\pi$
$509$	−14.0492	+	2.98626i	−0.622721	+	0.132364i	−0.114264	+	0.993450i	$0.536451\pi$
$510$	10.3681	+	2.20381i	0.459108	+	0.0975864i
$511$	−1.34772	−	12.8227i	−0.0596197	−	0.567243i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−16.0306	+	5.29355i	−0.707770	+	0.233716i
$514$	−5.55110	+	17.0845i	−0.244849	+	0.753567i
$515$	−11.7214	+	5.21872i	−0.516509	+	0.229964i
$516$	−2.53048	+	4.38293i	−0.111398	+	0.192948i
$517$	−14.4242	−	39.4927i	−0.634374	−	1.73689i
$518$	10.5208	−	18.2226i	0.462258	−	0.800654i
$519$	1.13352	−	10.7847i	0.0497561	−	0.473398i
$520$	0.0958274	−	0.294926i	0.00420231	−	0.0129334i
$521$	−0.923732	−	2.84296i	−0.0404694	−	0.124552i	0.928781	−	0.370630i	$-0.120858\pi$
$521$	−0.923732	−	2.84296i	−0.0404694	−	0.124552i	−0.969250	+	0.246078i	$0.920858\pi$
$522$	−17.4687	−	7.77755i	−0.764583	−	0.340414i
$523$	−8.06483	−	3.59070i	−0.352651	−	0.157010i	0.222763	−	0.974873i	$-0.428492\pi$
$523$	−8.06483	−	3.59070i	−0.352651	−	0.157010i	−0.575414	+	0.817862i	$0.695159\pi$
$524$	−2.20570	−	6.78846i	−0.0963566	−	0.296555i
$525$	−2.71981	+	8.37071i	−0.118702	+	0.365328i
$526$	−0.240743	+	2.29052i	−0.0104969	+	0.0998713i
$527$	−18.3311	+	31.7504i	−0.798515	+	1.38307i
$528$	−1.93591	−	1.30264i	−0.0842497	−	0.0566903i
$529$	−13.4234	+	23.2500i	−0.583625	+	1.01087i
$530$	−4.28854	+	1.90938i	−0.186282	+	0.0829383i
$531$	−3.28879	+	10.1219i	−0.142721	+	0.439251i
$532$	8.16174	+	7.27850i	0.353856	+	0.315563i
$533$	−0.374282	+	0.271932i	−0.0162120	+	0.0117787i
$534$	0.206628	+	1.96593i	0.00894166	+	0.0850742i
$535$	33.4750	+	7.11533i	1.44725	+	0.307622i
$536$	7.52620	−	1.59974i	0.325082	−	0.0690984i
$537$	1.41944	−	0.631977i	0.0612535	−	0.0272718i
$538$	−3.98191	−	6.89687i	−0.171672	−	0.297345i
$539$	1.62789	+	1.68196i	0.0701180	+	0.0724472i
$540$	−12.2392			−0.526693
$541$	2.28224	−	21.7140i	0.0981211	−	0.933560i	−0.829114	−	0.559080i	$-0.811155\pi$
$541$	2.28224	−	21.7140i	0.0981211	−	0.933560i	0.927235	−	0.374480i	$-0.122179\pi$
$542$	22.3013	−	4.74028i	0.957922	−	0.203613i
$543$	0.480072	+	1.47751i	0.0206019	+	0.0634060i
$544$	3.85708	−	2.80233i	0.165371	−	0.120149i
$545$	52.4472	+	23.3510i	2.24659	+	1.00025i
$546$	−0.169420	−	0.0360114i	−0.00725051	−	0.00154114i
$547$	33.4870	−	7.11789i	1.43180	−	0.304339i	0.574227	−	0.818696i	$-0.305303\pi$
$547$	33.4870	−	7.11789i	1.43180	−	0.304339i	0.857576	+	0.514357i	$0.171970\pi$
$548$	11.3540	−	5.05513i	0.485019	−	0.215944i
$549$	−10.1268	+	17.5402i	−0.432202	+	0.748596i
$550$	−11.5018	−	11.8839i	−0.490438	−	0.506729i
$551$	28.7354	−	16.7741i	1.22417	−	0.714602i
$552$	4.01850	+	2.91961i	0.171039	+	0.124267i
$553$	−13.8024	−	15.3292i	−0.586939	−	0.651862i
$554$	−12.0537	−	2.56209i	−0.512113	−	0.108853i
$555$	−17.0346	−	7.58429i	−0.723079	−	0.321935i
$556$	−0.896256	−	8.52731i	−0.0380097	−	0.361638i
$557$	−5.81056	+	6.45328i	−0.246201	+	0.273434i	−0.853561	−	0.520993i	$-0.825562\pi$
$557$	−5.81056	+	6.45328i	−0.246201	+	0.273434i	0.607360	+	0.794427i	$0.292229\pi$
$558$	5.95269	−	18.3205i	0.251997	−	0.775568i
$559$	−0.571089	−	0.414921i	−0.0241545	−	0.0175493i
$560$	3.96414	+	6.86608i	0.167515	+	0.290145i
$561$	9.22967	+	6.21050i	0.389677	+	0.262207i
$562$	−0.659191			−0.0278063
$563$	0.174706	+	0.126932i	0.00736300	+	0.00534953i	0.591461	−	0.806334i	$-0.298551\pi$
$563$	0.174706	+	0.126932i	0.00736300	+	0.00534953i	−0.584098	+	0.811683i	$0.698551\pi$
$564$	8.72376	−	1.85429i	0.367336	−	0.0780798i
$565$	26.6463	+	5.66384i	1.12102	+	0.238279i
$566$	2.29628	+	1.02237i	0.0965199	+	0.0429734i
$567$	−1.25623	−	11.9522i	−0.0527566	−	0.501946i
$568$	14.4924	+	3.08046i	0.608088	+	0.129253i
$569$	−8.25878	+	25.4179i	−0.346226	+	1.06557i	0.614698	+	0.788762i	$0.289278\pi$
$569$	−8.25878	+	25.4179i	−0.346226	+	1.06557i	−0.960924	+	0.276811i	$0.910722\pi$
$570$	5.65871	−	7.86738i	0.237017	−	0.329528i
$571$	34.7015			1.45221			0.726107	−	0.687582i	$-0.241328\pi$
$571$	34.7015			1.45221			0.726107	+	0.687582i	$0.241328\pi$
$572$	0.208923	−	0.249550i	0.00873550	−	0.0104342i
$573$	8.58300	−	14.8662i	0.358560	−	0.621044i
$574$	1.23637	−	11.7632i	0.0516049	−	0.490988i
$575$	23.5573	+	26.1630i	0.982407	+	1.09107i
$576$	−1.67619	+	1.86160i	−0.0698414	+	0.0775668i
$577$	−0.00435313	+	0.00316273i	−0.000181223	+	0.000131666i	−0.587876	−	0.808951i	$-0.700036\pi$
$577$	−0.00435313	+	0.00316273i	−0.000181223	+	0.000131666i	0.587695	+	0.809083i	$0.300036\pi$
$578$	−4.63575	+	3.36807i	−0.192822	+	0.140093i
$579$	−1.44333	+	1.60298i	−0.0599827	+	0.0666176i
$580$	23.5954	−	5.01535i	0.979745	−	0.208251i
$581$	−4.56880	−	3.31943i	−0.189546	−	0.137713i
$582$	−13.6370			−0.565271
$583$	−4.92365	+	0.177447i	−0.203917	+	0.00734910i
$584$	−2.56959	+	4.45066i	−0.106330	+	0.184170i
$585$	0.0811999	−	0.772566i	0.00335720	−	0.0319417i
$586$	12.0460	+	13.3785i	0.497617	+	0.552659i
$587$	4.24151	+	0.901560i	0.175066	+	0.0372114i	0.294610	−	0.955617i	$-0.404810\pi$
$587$	4.24151	+	0.901560i	0.175066	+	0.0372114i	−0.119545	+	0.992829i	$0.538143\pi$
$588$	−0.401698	+	0.291851i	−0.0165658	+	0.0120357i
$589$	19.8316	+	27.0231i	0.817145	+	1.11347i
$590$	−4.14887	−	12.7689i	−0.170806	−	0.525687i
$591$	9.26832	+	10.2935i	0.381248	+	0.423418i
$592$	−7.66191	+	3.41130i	−0.314903	+	0.140204i
$593$	19.1423	+	33.1554i	0.786079	+	1.36153i	0.928352	+	0.371702i	$0.121226\pi$
$593$	19.1423	+	33.1554i	0.786079	+	1.36153i	−0.142273	+	0.989827i	$0.545441\pi$
$594$	−11.9153	−	4.79862i	−0.488892	−	0.196890i
$595$	−18.8995	−	32.7348i	−0.774802	−	1.34200i
$596$	5.25644	+	3.81903i	0.215312	+	0.156434i
$597$	−2.35927	+	7.26108i	−0.0965584	+	0.297176i
$598$	−0.463586	+	0.514864i	−0.0189574	+	0.0210544i
$599$	−20.9742	−	9.33832i	−0.856983	−	0.381553i	−0.0692714	−	0.997598i	$-0.522067\pi$
$599$	−20.9742	−	9.33832i	−0.856983	−	0.381553i	−0.787711	+	0.616045i	$0.788734\pi$
$600$	2.83819	−	2.06207i	0.115869	−	0.0841835i
$601$	14.1762	+	43.6298i	0.578259	+	1.77970i	0.624805	+	0.780781i	$0.285179\pi$
$601$	14.1762	+	43.6298i	0.578259	+	1.77970i	−0.0465460	+	0.998916i	$0.514821\pi$
$602$	17.6531	−	3.75229i	0.719488	−	0.152932i
$603$	17.6082	−	7.83968i	0.717062	−	0.319256i
$604$	0.0163425	+	0.0283060i	0.000664967	+	0.00115176i
$605$	−13.0939	−	32.2012i	−0.532343	−	1.30916i
$606$	−3.22719	+	5.58965i	−0.131095	+	0.227064i
$607$	−12.8785	−	9.35677i	−0.522722	−	0.379779i	0.294907	−	0.955526i	$-0.404711\pi$
$607$	−12.8785	−	9.35677i	−0.522722	−	0.379779i	−0.817628	+	0.575747i	$0.804711\pi$
$608$	−0.926643	−	4.25926i	−0.0375803	−	0.172736i
$609$	−4.16350	−	12.8139i	−0.168713	−	0.519246i
$610$	−2.67073	−	25.4103i	−0.108135	−	1.02883i
$611$	0.130031	+	1.23716i	0.00526049	+	0.0500502i
$612$	7.99144	−	8.87540i	0.323035	−	0.358767i
$613$	−22.9611	−	25.5009i	−0.927389	−	1.02997i	−0.999469	−	0.0325710i	$-0.989630\pi$
$613$	−22.9611	−	25.5009i	−0.927389	−	1.02997i	0.0720804	−	0.997399i	$-0.477036\pi$
$614$	−0.715449	+	6.80704i	−0.0288732	+	0.274710i
$615$	−10.4818			−0.422667
$616$	1.16725	+	8.23858i	0.0470297	+	0.331942i
$617$	−3.78738	−	6.55994i	−0.152474	−	0.264093i	0.779662	−	0.626200i	$-0.215391\pi$
$617$	−3.78738	−	6.55994i	−0.152474	−	0.264093i	−0.932137	+	0.362107i	$0.882057\pi$
$618$	0.298584	−	2.84084i	0.0120108	−	0.114275i
$619$	−0.0919808	+	0.283088i	−0.00369702	+	0.0113783i	−0.952888	−	0.303322i	$-0.901904\pi$
$619$	−0.0919808	+	0.283088i	−0.00369702	+	0.0113783i	0.949191	+	0.314701i	$0.101904\pi$
$620$	7.50942	+	23.1116i	0.301586	+	0.928185i
$621$	24.9802	+	11.1219i	1.00242	+	0.446307i
$622$	0.475655	+	4.52555i	0.0190720	+	0.181458i
$623$	4.71682	−	5.23856i	0.188975	−	0.209878i
$624$	0.0461955	+	0.0513053i	0.00184930	+	0.00205386i
$625$	−22.9001	+	10.1958i	−0.916005	+	0.407832i
$626$	7.38234			0.295058
$627$	8.59350	−	5.44057i	0.343191	−	0.217275i
$628$	−9.30326			−0.371240
$629$	36.5290	−	16.2638i	1.45651	−	0.648479i
$630$	13.2893	+	14.7593i	0.529459	+	0.588024i
$631$	10.0397	−	11.1502i	0.399674	−	0.443883i	−0.509392	−	0.860534i	$-0.670130\pi$
$631$	10.0397	−	11.1502i	0.399674	−	0.443883i	0.909066	+	0.416651i	$0.136796\pi$
$632$	0.859425	+	8.17688i	0.0341861	+	0.325259i
$633$	0.237325	+	0.105664i	0.00943282	+	0.00419976i
$634$	8.23236	+	25.3366i	0.326949	+	1.00625i
$635$	10.1334	−	31.1874i	0.402132	−	1.23763i
$636$	0.109243	−	1.03938i	0.00433179	−	0.0412142i
$637$	−0.0346278	−	0.0599772i	−0.00137200	−	0.00237638i
$638$	24.9373	+	4.36839i	0.987276	+	0.172946i
$639$	37.1151			1.46825
$640$	0.330325	−	3.14283i	0.0130572	−	0.124231i
$641$	28.1560	+	31.2704i	1.11209	+	1.23511i	0.969439	+	0.245333i	$0.0788974\pi$
$641$	28.1560	+	31.2704i	1.11209	+	1.23511i	0.142655	+	0.989772i	$0.454436\pi$
$642$	−5.09810	+	5.66201i	−0.201206	+	0.223462i
$643$	1.98026	+	18.8409i	0.0780938	+	0.743013i	0.961574	+	0.274545i	$0.0885273\pi$
$643$	1.98026	+	18.8409i	0.0780938	+	0.743013i	−0.883480	+	0.468468i	$0.844806\pi$
$644$	−1.85150	−	17.6159i	−0.0729595	−	0.694163i
$645$	−4.94223	−	15.2106i	−0.194600	−	0.598917i
$646$	4.41787	+	20.3065i	0.173819	+	0.798949i
$647$	28.6849	+	20.8408i	1.12772	+	0.819337i	0.985361	−	0.170478i	$-0.0545313\pi$
$647$	28.6849	+	20.8408i	1.12772	+	0.819337i	0.142359	+	0.989815i	$0.454531\pi$
$648$	−2.39515	+	4.14851i	−0.0940902	+	0.162969i
$649$	0.967218	−	14.0576i	0.0379666	−	0.551809i
$650$	0.244662	+	0.423767i	0.00959644	+	0.0166215i
$651$	12.3996	−	5.52065i	0.485978	−	0.216371i
$652$	−17.3687	+	3.69184i	−0.680212	+	0.144584i
$653$	−10.1214	−	31.1505i	−0.396081	−	1.21901i	−0.928116	−	0.372290i	$-0.878573\pi$
$653$	−10.1214	−	31.1505i	−0.396081	−	1.21901i	0.532035	−	0.846722i	$-0.321427\pi$
$654$	−10.3402	+	7.51263i	−0.404336	+	0.293767i
$655$	20.6064	+	9.17455i	0.805158	+	0.358479i
$656$	−3.15465	+	3.50360i	−0.123169	+	0.136793i
$657$	−3.97823	+	12.2437i	−0.155205	+	0.477673i
$658$	−25.7300	−	18.6940i	−1.00306	−	0.728767i
$659$	−8.49059	−	14.7061i	−0.330747	−	0.572870i	0.651912	−	0.758295i	$-0.273967\pi$
$659$	−8.49059	−	14.7061i	−0.330747	−	0.572870i	−0.982658	+	0.185425i	$0.940634\pi$
$660$	7.15276	−	1.79188i	0.278421	−	0.0697487i
$661$	−13.0107	−	22.5351i	−0.506056	−	0.876515i	−0.999975	−	0.00700699i	$-0.997770\pi$
$661$	−13.0107	−	22.5351i	−0.506056	−	0.876515i	0.493919	−	0.869508i	$-0.335564\pi$
$662$	10.7838	−	4.80124i	0.419123	−	0.186606i
$663$	−0.220242	−	0.244604i	−0.00855350	−	0.00949962i
$664$	0.695593	+	2.14082i	0.0269943	+	0.0830798i
$665$	−34.3515	+	3.77665i	−1.33210	+	0.146452i
$666$	−16.9972	+	12.3492i	−0.658629	+	0.478522i
$667$	−52.7156	−	11.2050i	−2.04115	−	0.433861i
$668$	−11.0967	−	12.3242i	−0.429345	−	0.476836i
$669$	−0.463755	+	4.41234i	−0.0179298	+	0.170591i
$670$	−12.1576	+	21.0576i	−0.469690	+	0.813526i
$671$	7.36254	−	25.7850i	0.284228	−	0.995417i
$672$	−1.76506			−0.0680887
$673$	30.9444	+	22.4824i	1.19282	+	0.866634i	0.993559	−	0.113313i	$-0.0361462\pi$
$673$	30.9444	+	22.4824i	1.19282	+	0.866634i	0.199260	+	0.979947i	$0.436146\pi$
$674$	−11.2971	+	2.40128i	−0.435150	+	0.0924940i
$675$	12.9227	−	14.3522i	0.497397	−	0.552415i
$676$	10.5094	−	7.63555i	0.404209	−	0.293675i
$677$	23.7995	−	17.2913i	0.914688	−	0.664560i	−0.0275081	−	0.999622i	$-0.508757\pi$
$677$	23.7995	−	17.2913i	0.914688	−	0.664560i	0.942196	+	0.335062i	$0.108757\pi$
$678$	−4.05811	+	4.50699i	−0.155851	+	0.173090i
$679$	32.5396	+	36.1389i	1.24876	+	1.38689i
$680$	−1.57486	+	14.9838i	−0.0603931	+	0.574602i
$681$	−1.20840	+	2.09302i	−0.0463062	+	0.0802046i
$682$	−1.75066	+	25.4442i	−0.0670362	+	0.974307i
$683$	−4.91588			−0.188101			−0.0940504	−	0.995567i	$-0.529981\pi$
$683$	−4.91588			−0.188101			−0.0940504	+	0.995567i	$0.529981\pi$
$684$	−4.48888	−	9.95382i	−0.171637	−	0.380594i
$685$	−12.1369	+	37.3535i	−0.463727	+	1.42721i
$686$	18.9100	+	4.01944i	0.721987	+	0.153463i
$687$	−0.380780	−	3.62288i	−0.0145277	−	0.138221i
$688$	−6.57167	−	2.92590i	−0.250543	−	0.111549i
$689$	0.142586	+	0.0303077i	0.00543211	+	0.00115463i
$690$	−15.3539	+	3.26356i	−0.584511	+	0.124242i
$691$	−22.9214	−	16.6534i	−0.871973	−	0.633525i	0.0591429	−	0.998250i	$-0.481163\pi$
$691$	−22.9214	−	16.6534i	−0.871973	−	0.633525i	−0.931116	+	0.364724i	$0.881163\pi$
$692$	15.4137			0.585942
$693$	7.15096	+	19.5790i	0.271643	+	0.743745i
$694$	−9.56303	−	16.5637i	−0.363008	−	0.628748i
$695$	21.9211	+	15.9266i	0.831514	+	0.604130i
$696$	−1.65953	+	5.10752i	−0.0629045	+	0.193600i
$697$	15.0402	−	16.7038i	0.569687	−	0.632701i
$698$	−2.50638	−	23.8466i	−0.0948680	−	0.902609i
$699$	0.0536720	+	0.0238963i	0.00203006	+	0.000903841i
$700$	−12.2369	−	2.60104i	−0.462512	−	0.0983100i
$701$	0.0289111	+	0.0321090i	0.00109196	+	0.00121274i	0.743691	−	0.668524i	$-0.233074\pi$
$701$	0.0289111	+	0.0321090i	0.00109196	+	0.00121274i	−0.742599	+	0.669737i	$0.766407\pi$
$702$	0.307473	+	0.223392i	0.0116048	+	0.00843138i
$703$	−0.174811	−	36.5577i	−0.00659313	−	1.37880i
$704$	1.55379	−	2.93014i	0.0585606	−	0.110434i
$705$	−14.0921	+	24.4082i	−0.530739	+	0.919268i
$706$	−14.4553	+	6.43590i	−0.544031	+	0.242218i
$707$	22.5135	−	4.78538i	0.846706	−	0.179973i
$708$	2.92370	+	0.621452i	0.109879	+	0.0233556i
$709$	12.1137	+	5.39335i	0.454938	+	0.202552i	0.621395	−	0.783497i	$-0.286566\pi$
$709$	12.1137	+	5.39335i	0.454938	+	0.202552i	−0.166457	+	0.986049i	$0.553233\pi$
$710$	−37.8792	+	27.5209i	−1.42158	+	1.03284i
$711$	6.36457	+	19.5881i	0.238690	+	0.734612i
$712$	−2.74834	+	0.584178i	−0.102998	+	0.0218930i
$713$	5.67506	−	53.9946i	0.212533	−	2.02211i
$714$	8.41512			0.314928
$715$	0.144277	+	1.01833i	0.00539567	+	0.0380833i
$716$	1.10426	+	1.91263i	0.0412680	+	0.0714783i
$717$	14.1171	−	6.28533i	0.527212	−	0.234730i
$718$	20.9905	−	4.46168i	0.783360	−	0.166508i
$719$	−44.8150	−	9.52571i	−1.67132	−	0.355249i	−0.727599	−	0.686003i	$-0.759364\pi$
$719$	−44.8150	−	9.52571i	−1.67132	−	0.355249i	−0.943717	+	0.330754i	$0.892697\pi$
$720$	−0.827475	−	7.87290i	−0.0308382	−	0.293406i
$721$	−8.24088	+	5.98735i	−0.306907	+	0.222981i
$722$	18.6217	+	3.77241i	0.693029	+	0.140395i
$723$	2.22170	−	6.83768i	0.0826258	−	0.254296i
$724$	−2.01728	+	0.898151i	−0.0749716	+	0.0333795i
$725$	−19.0319	+	32.9642i	−0.706827	+	1.22426i
$726$	7.66600	+	1.05992i	0.284512	+	0.0393373i
$727$	−23.8279	+	41.2712i	−0.883729	+	1.53066i	−0.0365646	+	0.999331i	$0.511641\pi$
$727$	−23.8279	+	41.2712i	−0.883729	+	1.53066i	−0.847164	+	0.531332i	$0.821692\pi$
$728$	0.0257340	−	0.244843i	0.000953765	−	0.00907447i
$729$	−1.18212	+	3.63819i	−0.0437822	+	0.134748i
$730$	−5.01860	−	15.4457i	−0.185747	−	0.571670i
$731$	31.3312	+	13.9495i	1.15882	+	0.515942i
$732$	5.19646	+	2.31361i	0.192067	+	0.0855136i
$733$	−4.91676	−	15.1322i	−0.181605	−	0.558922i	0.818269	−	0.574836i	$-0.194934\pi$
$733$	−4.91676	−	15.1322i	−0.181605	−	0.558922i	−0.999873	+	0.0159139i	$0.994934\pi$
$734$	−6.51306	+	20.0451i	−0.240401	+	0.739879i
$735$	0.164015	−	1.56050i	0.00604979	−	0.0575599i
$736$	−3.53011	+	6.11433i	−0.130122	+	0.225377i
$737$	−20.0919	+	15.7337i	−0.740094	+	0.579558i
$738$	−5.90506	+	10.2279i	−0.217368	+	0.376493i
$739$	0.612885	−	0.272874i	0.0225454	−	0.0100378i	−0.395433	−	0.918495i	$-0.629405\pi$
$739$	0.612885	−	0.272874i	0.0225454	−	0.0100378i	0.417978	+	0.908457i	$0.362739\pi$
$740$	8.19023	−	25.2069i	0.301079	−	0.926626i
$741$	−0.285754	+	0.0943600i	−0.0104974	+	0.00346640i
$742$	−3.01510	+	2.19060i	−0.110688	+	0.0804195i
$743$	1.65543	+	15.7503i	0.0607317	+	0.577824i	0.981998	+	0.188891i	$0.0604893\pi$
$743$	1.65543	+	15.7503i	0.0607317	+	0.577824i	−0.921266	+	0.388932i	$0.872844\pi$
$744$	−5.29188	−	1.12482i	−0.194010	−	0.0412380i
$745$	−20.0838	+	4.26894i	−0.735813	+	0.156402i
$746$	−19.8740	+	8.84848i	−0.727639	+	0.323966i
$747$	2.81940	+	4.88334i	0.103156	+	0.178672i
$748$	−7.40785	+	13.9698i	−0.270858	+	0.510786i
$749$	27.1695			0.992750
$750$	0.00313701	−	0.0298467i	0.000114548	−	0.00108985i
$751$	−20.0886	+	4.26995i	−0.733042	+	0.155813i	−0.559285	−	0.828976i	$-0.688924\pi$
$751$	−20.0886	+	4.26995i	−0.733042	+	0.155813i	−0.173757	+	0.984789i	$0.555591\pi$
$752$	3.91736	+	12.0564i	0.142851	+	0.439652i
$753$	11.0233	−	8.00886i	0.401710	−	0.291859i
$754$	−0.684301	−	0.304670i	−0.0249208	−	0.0110954i
$755$	−0.101032	−	0.0214750i	−0.00367694	−	0.000781557i
$756$	−9.50439	+	2.02022i	−0.345671	+	0.0734747i
$757$	−45.0029	+	20.0366i	−1.63566	+	0.728242i	−0.999077	−	0.0429663i	$-0.986319\pi$
$757$	−45.0029	+	20.0366i	−1.63566	+	0.728242i	−0.636582	+	0.771209i	$0.719653\pi$
$758$	3.47220	−	6.01403i	0.126116	−	0.218439i
$759$	−16.2270	−	2.84257i	−0.589004	−	0.103179i
$760$	11.9621	+	6.83025i	0.433910	+	0.247759i
$761$	−15.3503	−	11.1527i	−0.556449	−	0.404284i	0.273709	−	0.961813i	$-0.411750\pi$
$761$	−15.3503	−	11.1527i	−0.556449	−	0.404284i	−0.830157	+	0.557529i	$0.811750\pi$
$762$	4.88501	+	5.42535i	0.176965	+	0.196540i
$763$	44.5822	+	9.47624i	1.61398	+	0.343063i
$764$	22.2901	+	9.92418i	0.806426	+	0.359044i
$765$	3.94508	+	37.5349i	0.142635	+	1.35708i
$766$	−13.3635	+	14.8417i	−0.482843	+	0.536252i
$767$	−0.128832	+	0.396504i	−0.00465185	+	0.0143169i
$768$	0.569175	+	0.413530i	0.0205383	+	0.0149220i
$769$	0.0970451	+	0.168087i	0.00349954	+	0.00606138i	0.867770	−	0.496966i	$-0.165553\pi$
$769$	0.0970451	+	0.168087i	0.00349954	+	0.00606138i	−0.864270	+	0.503028i	$0.832219\pi$
$770$	−21.8160	−	14.6797i	−0.786196	−	0.529018i
$771$	12.6382			0.455153
$772$	−2.48041	−	1.80213i	−0.0892720	−	0.0648599i
$773$	25.9606	−	5.51810i	0.933738	−	0.198472i	0.284168	−	0.958774i	$-0.408283\pi$
$773$	25.9606	−	5.51810i	0.933738	−	0.198472i	0.649569	+	0.760302i	$0.274949\pi$
$774$	−17.6264	−	3.74661i	−0.633568	−	0.134669i
$775$	−35.0303	−	15.5965i	−1.25832	−	0.560242i
$776$	−2.02612	−	19.2772i	−0.0727334	−	0.692012i
$777$	−14.4801	−	3.07784i	−0.519470	−	0.110417i
$778$	−9.74929	+	30.0052i	−0.349529	+	1.07574i
$779$	−8.44822	−	18.7334i	−0.302689	−	0.671195i
$780$	−0.218170			−0.00781175
$781$	−47.6668	+	11.9413i	−1.70565	+	0.427292i
$782$	16.8302	−	29.1508i	0.601847	−	1.04243i
$783$	−3.09028	+	29.4021i	−0.110438	+	1.05075i
$784$	−0.472243	−	0.524479i	−0.0168658	−	0.0187314i
$785$	19.6722	−	21.8482i	0.702131	−	0.779795i
$786$	−4.06266	+	2.95170i	−0.144910	+	0.105283i
$787$	10.3238	−	7.50070i	0.368004	−	0.267371i	−0.388378	−	0.921500i	$-0.626965\pi$
$787$	10.3238	−	7.50070i	0.368004	−	0.267371i	0.756383	+	0.654129i	$0.226965\pi$
$788$	−13.1739	+	14.6311i	−0.469299	+	0.521210i
$789$	1.58493	−	0.336888i	0.0564252	−	0.0119935i
$790$	−21.0202	−	15.2721i	−0.747866	−	0.543357i
$791$	21.6270			0.768969
$792$	2.28114	−	7.98896i	0.0810568	−	0.283875i
$793$	−0.396698	+	0.687102i	−0.0140872	+	0.0243997i
$794$	−1.81318	+	17.2512i	−0.0643473	+	0.612224i
$795$	2.20993	+	2.45438i	0.0783782	+	0.0870478i
$796$	−10.6148	−	2.25624i	−0.376231	−	0.0799704i
$797$	19.8874	−	14.4491i	0.704449	−	0.511812i	−0.176929	−	0.984224i	$-0.556616\pi$
$797$	19.8874	−	14.4491i	0.704449	−	0.511812i	0.881378	+	0.472412i	$0.156616\pi$
$798$	3.09567	−	7.04345i	0.109586	−	0.249335i
$799$	−18.6764	−	57.4802i	−0.660725	−	2.03350i
$800$	3.33662	+	3.70569i	0.117967	+	0.131016i
$801$	−6.42998	+	2.86281i	−0.227192	+	0.101153i
$802$	−17.2072	−	29.8037i	−0.607606	−	1.05241i
$803$	1.16998	−	17.0045i	0.0412876	−	0.600077i
$804$	−2.70663	−	4.68803i	−0.0954556	−	0.165334i
$805$	45.2850	+	32.9015i	1.59609	+	1.15963i
$806$	0.233185	−	0.717670i	0.00821359	−	0.0252788i
$807$	−3.74904	+	4.16374i	−0.131973	+	0.146570i
$808$	−8.38101	−	3.73146i	−0.294843	−	0.131272i
$809$	22.4481	−	16.3095i	0.789232	−	0.573411i	−0.118503	−	0.992954i	$-0.537810\pi$
$809$	22.4481	−	16.3095i	0.789232	−	0.573411i	0.907736	+	0.419543i	$0.137810\pi$
$810$	−4.67790	−	14.3971i	−0.164365	−	0.505862i
$811$	−27.9595	+	5.94298i	−0.981791	+	0.208686i	−0.670728	−	0.741703i	$-0.734018\pi$
$811$	−27.9595	+	5.94298i	−0.981791	+	0.208686i	−0.311063	+	0.950389i	$0.600685\pi$
$812$	17.4952	−	7.78935i	0.613960	−	0.273352i
$813$	−8.02017	−	13.8913i	−0.281279	−	0.487190i
$814$	17.8563	−	21.3287i	0.625864	−	0.747570i
$815$	28.0570	−	48.5961i	0.982792	−	1.70225i
$816$	−2.71360	−	1.97155i	−0.0949951	−	0.0690180i
$817$	23.2016	−	21.0925i	0.811720	−	0.737934i
$818$	−7.80028	−	24.0068i	−0.272730	−	0.839378i
$819$	−0.0644645	−	0.613339i	−0.00225257	−	0.0214318i
$820$	−1.55733	−	14.8171i	−0.0543845	−	0.517434i
$821$	5.86073	−	6.50900i	0.204541	−	0.227166i	−0.632143	−	0.774852i	$-0.717824\pi$
$821$	5.86073	−	6.50900i	0.204541	−	0.227166i	0.836684	+	0.547686i	$0.184491\pi$
$822$	−5.85083	−	6.49801i	−0.204071	−	0.226644i
$823$	0.662234	−	6.30073i	0.0230840	−	0.219630i	−0.976898	−	0.213704i	$-0.931447\pi$
$823$	0.662234	−	6.30073i	0.0230840	−	0.219630i	0.999982	−	0.00592560i	$-0.00188619\pi$
$824$	4.06017			0.141443
$825$	−5.45099	+	10.2795i	−0.189779	+	0.357887i
$826$	−5.32945	−	9.23087i	−0.185435	−	0.321183i
$827$	−0.922290	+	8.77500i	−0.0320711	+	0.305137i	0.966714	+	0.255859i	$0.0823584\pi$
$827$	−0.922290	+	8.77500i	−0.0320711	+	0.305137i	−0.998785	+	0.0492772i	$0.984308\pi$
$828$	−5.46530	+	16.8205i	−0.189932	+	0.584552i
$829$	14.6862	+	45.1996i	0.510074	+	1.56985i	0.792070	+	0.610431i	$0.209004\pi$
$829$	14.6862	+	45.1996i	0.510074	+	1.56985i	−0.281996	+	0.959416i	$0.590996\pi$
$830$	−6.49845	−	2.89330i	−0.225565	−	0.100428i
$831$	0.906230	+	8.62221i	0.0314368	+	0.299101i
$832$	−0.0656616	+	0.0729246i	−0.00227641	+	0.00252821i
$833$	2.25147	+	2.50051i	0.0780088	+	0.0866376i
$834$	−5.51081	+	2.45357i	−0.190824	+	0.0849602i
$835$	52.4071			1.81362
$836$	8.96756	+	11.3394i	0.310150	+	0.392183i
$837$	−29.7828			−1.02944
$838$	3.75986	−	1.67400i	0.129882	−	0.0578273i
$839$	−28.3588	−	31.4957i	−0.979056	−	1.08735i	−0.996165	−	0.0874984i	$-0.972113\pi$
$839$	−28.3588	−	31.4957i	−0.979056	−	1.08735i	0.0171085	−	0.999854i	$-0.494554\pi$
$840$	3.73231	−	4.14515i	0.128777	−	0.143021i
$841$	−3.05936	−	29.1079i	−0.105495	−	1.00372i
$842$	4.08927	+	1.82066i	0.140925	+	0.0627440i
$843$	0.143312	+	0.441068i	0.00493591	+	0.0151912i
$844$	−0.114106	+	0.351181i	−0.00392768	+	0.0120882i
$845$	−4.29104	+	40.8265i	−0.147616	+	1.40448i
$846$	15.8780	+	27.5014i	0.545895	+	0.945519i
$847$	−15.4832	−	22.8445i	−0.532010	−	0.784948i
$848$	1.48550			0.0510123
$849$	0.184849	−	1.75872i	0.00634401	−	0.0603592i
$850$	−15.9077	−	17.6673i	−0.545630	−	0.605983i
$851$	−39.6220	+	44.0047i	−1.35822	+	1.50846i
$852$	−1.08958	−	10.3667i	−0.0373284	−	0.355156i
$853$	−0.460942	−	4.38557i	−0.0157824	−	0.150159i	0.983793	−	0.179310i	$-0.0573864\pi$
$853$	−0.460942	−	4.38557i	−0.0157824	−	0.150159i	−0.999575	+	0.0291506i	$0.990720\pi$
$854$	−6.26821	−	19.2916i	−0.214494	−	0.660144i
$855$	32.8679	+	10.5060i	1.12406	+	0.359296i
$856$	−8.76127	−	6.36543i	−0.299454	−	0.217566i
$857$	−10.2812	+	17.8075i	−0.351198	+	0.608292i	−0.986460	−	0.164005i	$-0.947559\pi$
$857$	−10.2812	+	17.8075i	−0.351198	+	0.608292i	0.635262	+	0.772297i	$0.280892\pi$
$858$	−0.212396	−	0.0855377i	−0.00725109	−	0.00292021i
$859$	−16.1149	−	27.9118i	−0.549832	−	0.952337i	−0.998286	−	0.0585311i	$-0.981358\pi$
$859$	−16.1149	−	27.9118i	−0.549832	−	0.952337i	0.448453	−	0.893806i	$-0.351975\pi$
$860$	20.7674	−	9.24625i	0.708163	−	0.315294i
$861$	−8.13964	+	1.73013i	−0.277398	+	0.0589628i
$862$	−4.47132	−	13.7613i	−0.152294	−	0.468712i
$863$	15.8988	−	11.5512i	0.541202	−	0.393206i	−0.283329	−	0.959023i	$-0.591439\pi$
$863$	15.8988	−	11.5512i	0.541202	−	0.393206i	0.824531	+	0.565816i	$0.191439\pi$
$864$	3.53817	+	1.57529i	0.120371	+	0.0535925i
$865$	−32.5931	+	36.1983i	−1.10820	+	1.23078i
$866$	−3.09552	+	9.52704i	−0.105190	+	0.323742i
$867$	3.26143	+	2.36957i	0.110764	+	0.0804748i
$868$	9.64627	+	16.7078i	0.327416	+	0.567100i
$869$	−14.4762	−	23.1093i	−0.491072	−	0.783929i
$870$	−8.48556	−	14.6974i	−0.287688	−	0.498289i
$871$	0.689767	−	0.307104i	0.0233719	−	0.0104058i
$872$	−12.1562	−	13.5008i	−0.411659	−	0.457194i
$873$	−15.0047	−	46.1796i	−0.507831	−	1.56294i
$874$	−18.2078	−	24.8106i	−0.615889	−	0.839229i
$875$	−0.0865811	+	0.0629049i	−0.00292698	+	0.00212657i
$876$	3.53660	+	0.751728i	0.119491	+	0.0253985i
$877$	26.3623	+	29.2783i	0.890192	+	0.988658i	0.999986	−	0.00529628i	$-0.00168587\pi$
$877$	26.3623	+	29.2783i	0.890192	+	0.988658i	−0.109794	+	0.993954i	$0.535019\pi$
$878$	−1.52811	+	14.5390i	−0.0515711	+	0.490667i
$879$	6.33273	−	10.9686i	0.213598	−	0.369962i
$880$	3.59572	+	9.84491i	0.121212	+	0.331872i
$881$	19.6706			0.662721			0.331360	−	0.943504i	$-0.392492\pi$
$881$	19.6706			0.662721			0.331360	+	0.943504i	$0.392492\pi$
$882$	−1.43030	−	1.03917i	−0.0481605	−	0.0349907i
$883$	13.0355	−	2.77078i	0.438679	−	0.0932441i	0.0167226	−	0.999860i	$-0.494677\pi$
$883$	13.0355	−	2.77078i	0.438679	−	0.0932441i	0.421957	+	0.906616i	$0.361343\pi$
$884$	0.313049	−	0.347676i	0.0105290	−	0.0116936i
$885$	−7.64175	+	5.55205i	−0.256875	+	0.186630i
$886$	−0.638471	+	0.463876i	−0.0214499	+	0.0155842i
$887$	−2.43084	+	2.69972i	−0.0816195	+	0.0906476i	−0.782571	−	0.622561i	$-0.786092\pi$
$887$	−2.43084	+	2.69972i	−0.0816195	+	0.0906476i	0.700952	+	0.713209i	$0.252759\pi$
$888$	3.94826	+	4.38499i	0.132495	+	0.147151i
$889$	2.72128	−	25.8912i	0.0912687	−	0.868363i
$890$	4.43959	−	7.68960i	0.148815	−	0.257756i
$891$	1.09055	−	15.8501i	0.0365348	−	0.530999i
$892$	−6.30618			−0.211146
$893$	−54.9814	−	5.51310i	−1.83988	−	0.184489i
$894$	1.41255	−	4.34739i	0.0472428	−	0.145399i
$895$	−6.82670	−	1.45106i	−0.228192	−	0.0485036i
$896$	−0.262244	−	2.49509i	−0.00876097	−	0.0833551i
$897$	0.445284	+	0.198253i	0.0148676	+	0.00661949i
$898$	−19.2864	−	4.09944i	−0.643594	−	0.136800i
$899$	57.4166	−	12.2043i	1.91495	−	0.407036i
$900$	10.1057	+	7.34223i	0.336857	+	0.244741i
$901$	−7.08229			−0.235945
$902$	4.29318	−	15.0355i	0.142947	−	0.500627i
$903$	−6.34856	−	10.9960i	−0.211267	−	0.365925i
$904$	−6.97401	−	5.06692i	−0.231952	−	0.168523i
$905$	2.15638	−	6.63665i	0.0716804	−	0.220610i
$906$	0.0153868	−	0.0170887i	0.000511191	−	0.000567735i
$907$	−1.47429	−	14.0269i	−0.0489530	−	0.465756i	−0.991349	−	0.131256i	$-0.958099\pi$
$907$	−1.47429	−	14.0269i	−0.0489530	−	0.465756i	0.942396	−	0.334501i	$-0.108568\pi$
$908$	−3.13823	−	1.39723i	−0.104146	−	0.0463687i
$909$	−22.4794	−	4.77814i	−0.745593	−	0.158481i
$910$	0.520583	+	0.578166i	0.0172572	+	0.0191660i
$911$	23.8840	+	17.3527i	0.791312	+	0.574922i	0.908352	−	0.418205i	$-0.137341\pi$
$911$	23.8840	+	17.3527i	0.791312	+	0.574922i	−0.117041	+	0.993127i	$0.537341\pi$
$912$	−2.64844	+	1.54601i	−0.0876985	+	0.0511935i
$913$	−5.19210	−	5.36456i	−0.171833	−	0.177541i
$914$	−17.7798	+	30.7955i	−0.588103	+	1.01862i
$915$	−16.4216	+	7.31135i	−0.542880	+	0.241706i
$916$	5.06473	−	1.07654i	0.167343	−	0.0355699i
$917$	17.5162	+	3.72319i	0.578437	+	0.122951i
$918$	−16.8686	−	7.51038i	−0.556747	−	0.247880i
$919$	−31.6982	+	23.0301i	−1.04563	+	0.759693i	−0.971376	−	0.237547i	$-0.923657\pi$
$919$	−31.6982	+	23.0301i	−1.04563	+	0.759693i	−0.0742511	+	0.997240i	$0.523657\pi$
$920$	−6.89457	−	21.2193i	−0.227307	−	0.699580i
$921$	4.71017	−	1.00118i	0.155205	−	0.0329899i
$922$	0.944197	−	8.98344i	0.0310955	−	0.295854i
$923$	1.45391			0.0478560
$924$	5.25871	−	2.57212i	0.172999	−	0.0846166i
$925$	20.9109	+	36.2188i	0.687547	+	1.19087i
$926$	−16.6356	+	7.40663i	−0.546679	+	0.243397i
$927$	9.94861	−	2.11464i	0.326755	−	0.0694539i
$928$	−7.46656	−	1.58707i	−0.245102	−	0.0520980i
$929$	−0.702089	−	6.67993i	−0.0230348	−	0.219161i	−0.999984	−	0.00568863i	$-0.998189\pi$
$929$	−0.702089	−	6.67993i	−0.0230348	−	0.219161i	0.976949	−	0.213473i	$-0.0684774\pi$
$930$	13.8315	−	10.0492i	0.453553	−	0.329526i
$931$	2.92117	−	0.964614i	0.0957376	−	0.0316139i
$932$	−0.0258055	+	0.0794211i	−0.000845286	+	0.00260152i
$933$	2.92466	−	1.30214i	0.0957491	−	0.0426303i
$934$	−7.03711	+	12.1886i	−0.230261	+	0.398824i
$935$	−17.1430	−	46.9367i	−0.560636	−	1.53499i
$936$	−0.122909	+	0.212885i	−0.00401741	+	0.00695836i
$937$	−1.93949	+	18.4530i	−0.0633604	+	0.602834i	0.916065	+	0.401029i	$0.131347\pi$
$937$	−1.93949	+	18.4530i	−0.0633604	+	0.602834i	−0.979426	+	0.201805i	$0.935319\pi$
$938$	−5.96521	+	18.3590i	−0.194771	+	0.599444i
$939$	−1.60496	−	4.93956i	−0.0523759	−	0.161197i
$940$	−36.5972	−	16.2941i	−1.19367	−	0.531456i
$941$	−4.12292	−	1.83564i	−0.134403	−	0.0598402i	0.338433	−	0.940990i	$-0.390103\pi$
$941$	−4.12292	−	1.83564i	−0.134403	−	0.0598402i	−0.472836	+	0.881150i	$0.656770\pi$
$942$	2.02258	+	6.22486i	0.0658992	+	0.202817i
$943$	−10.2859	+	31.6567i	−0.334954	+	1.03088i
$944$	−0.444094	+	4.22527i	−0.0144540	+	0.137521i
$945$	15.3531	−	26.5924i	0.499437	−	0.865050i
$946$	23.8430	−	0.859293i	0.775201	−	0.0279380i
$947$	27.7790	−	48.1146i	0.902696	−	1.56352i	0.0787163	−	0.996897i	$-0.474918\pi$
$947$	27.7790	−	48.1146i	0.902696	−	1.56352i	0.823980	−	0.566619i	$-0.191749\pi$
$948$	5.28435	−	2.35274i	0.171628	−	0.0764135i
$949$	−0.155839	+	0.479624i	−0.00505876	+	0.0155692i
$950$	−20.6395	+	6.81546i	−0.669633	+	0.221123i
$951$	15.1631	−	11.0166i	0.491697	−	0.357239i
$952$	1.25028	+	11.8956i	0.0405218	+	0.385539i
$953$	−48.6180	−	10.3341i	−1.57489	−	0.334753i	−0.664107	−	0.747637i	$-0.731188\pi$
$953$	−48.6180	−	10.3341i	−1.57489	−	0.334753i	−0.910784	+	0.412884i	$0.864521\pi$
$954$	3.63991	−	0.773687i	0.117847	−	0.0250490i
$955$	−70.4398	+	31.3618i	−2.27938	+	1.01484i
$956$	10.9824	+	19.0220i	0.355196	+	0.615217i
$957$	−2.49859	−	17.6354i	−0.0807679	−	0.570071i
$958$	−15.4790			−0.500103
$959$	−3.25931	+	31.0102i	−0.105248	+	1.00137i
$960$	−2.17470	+	0.462246i	−0.0701881	+	0.0149189i
$961$	8.69378	+	26.7567i	0.280445	+	0.863120i
$962$	−0.665833	+	0.483756i	−0.0214673	+	0.0155969i
$963$	−24.7829	−	11.0341i	−0.798619	−	0.355568i
$964$	9.99583	+	2.12468i	0.321944	+	0.0684313i
$965$	9.47715	−	2.01443i	0.305080	−	0.0648468i
$966$	−11.3844	+	5.06864i	−0.366286	+	0.163081i
$967$	−19.4484	+	33.6857i	−0.625420	+	1.08326i	0.363040	+	0.931774i	$0.381739\pi$
$967$	−19.4484	+	33.6857i	−0.625420	+	1.08326i	−0.988459	+	0.151485i	$0.951594\pi$
$968$	−0.359323	+	10.9941i	−0.0115491	+	0.353365i
$969$	12.6267	−	7.37077i	0.405629	−	0.236783i
$970$	49.5558	+	36.0044i	1.59114	+	1.15603i
$971$	−6.41689	−	7.12668i	−0.205928	−	0.228706i	0.631330	−	0.775514i	$-0.282509\pi$
$971$	−6.41689	−	7.12668i	−0.205928	−	0.228706i	−0.837258	+	0.546808i	$0.815843\pi$
$972$	14.6616	+	3.11642i	0.470272	+	0.0999593i
$973$	19.6517	+	8.74949i	0.630004	+	0.280496i
$974$	1.40956	+	13.4110i	0.0451651	+	0.429717i
$975$	0.230354	−	0.255834i	0.00737723	−	0.00819324i
$976$	−2.49846	+	7.68946i	−0.0799737	+	0.246134i
$977$	−22.7503	−	16.5290i	−0.727845	−	0.528811i	0.161036	−	0.986949i	$-0.448517\pi$
$977$	−22.7503	−	16.5290i	−0.727845	−	0.528811i	−0.888881	+	0.458138i	$0.848517\pi$
$978$	6.24629	+	10.8189i	0.199734	+	0.345950i
$979$	7.33694	−	5.74546i	0.234490	−	0.183626i
$980$	2.23029			0.0712440
$981$	−36.8177	−	26.7496i	−1.17550	−	0.854050i
$982$	−9.34122	+	1.98554i	−0.298090	+	0.0633610i
$983$	19.9646	+	4.24361i	0.636773	+	0.135350i	0.514976	−	0.857205i	$-0.327801\pi$
$983$	19.9646	+	4.24361i	0.636773	+	0.135350i	0.121797	+	0.992555i	$0.461134\pi$
$984$	3.03011	+	1.34909i	0.0965965	+	0.0430075i
$985$	−6.50344	−	61.8761i	−0.207217	−	1.97154i
$986$	35.5976	+	7.56651i	1.13366	+	0.240967i
$987$	−6.91438	+	21.2803i	−0.220087	+	0.677359i
$988$	−0.175843	−	0.389921i	−0.00559432	−	0.0124051i
$989$	−50.7883			−1.61498
$990$	13.9380	+	22.2502i	0.442980	+	0.707157i
$991$	6.68303	−	11.5754i	0.212294	−	0.367703i	−0.740138	−	0.672455i	$-0.765240\pi$
$991$	6.68303	−	11.5754i	0.212294	−	0.367703i	0.952432	+	0.304751i	$0.0985734\pi$
$992$	0.803807	−	7.64772i	0.0255209	−	0.242815i
$993$	−5.55699	−	6.17166i	−0.176346	−	0.195852i
$994$	−24.8725	+	27.6237i	−0.788907	+	0.876170i
$995$	27.7441	−	20.1573i	0.879548	−	0.639029i
$996$	1.28121	−	0.930850i	0.0405965	−	0.0294951i
$997$	−22.1800	+	24.6334i	−0.702448	+	0.780148i	−0.983764	−	0.179467i	$-0.942563\pi$
$997$	−22.1800	+	24.6334i	−0.702448	+	0.780148i	0.281316	+	0.959615i	$0.409229\pi$
$998$	8.53347	−	1.81385i	0.270122	−	0.0574163i
$999$	26.2792	+	19.0930i	0.831438	+	0.604075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.e.125.4	✓	72
11.3	even	5	inner	418.2.n.e.201.6	yes	72
19.7	even	3	inner	418.2.n.e.235.6	yes	72
209.102	even	15	inner	418.2.n.e.311.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.e.125.4	✓	72	1.1	even	1	trivial
418.2.n.e.201.6	yes	72	11.3	even	5	inner
418.2.n.e.235.6	yes	72	19.7	even	3	inner
418.2.n.e.311.4	yes	72	209.102	even	15	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 - 0.406737i) q^{2} +(-0.470759 - 0.522831i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.330325 + 3.14283i) q^{5} +(-0.642715 - 0.286155i) q^{6} +(0.775272 + 2.38604i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.261847 - 2.49131i) q^{9} +O(q^{10})\)	\(q+(0.913545 - 0.406737i) q^{2} +(-0.470759 - 0.522831i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.330325 + 3.14283i) q^{5} +(-0.642715 - 0.286155i) q^{6} +(0.775272 + 2.38604i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.261847 - 2.49131i) q^{9} +(1.58007 + 2.73676i) q^{10} +(0.465255 + 3.28383i) q^{11} -0.703539 q^{12} +(0.0102574 - 0.0975922i) q^{13} +(1.67874 + 1.86443i) q^{14} +(1.48767 - 1.65222i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(0.498351 + 4.74149i) q^{17} +(-0.774098 - 2.38243i) q^{18} +(4.15195 + 1.32714i) q^{19} +(2.55661 + 1.85749i) q^{20} +(0.882531 - 1.52859i) q^{21} +(1.76069 + 2.81069i) q^{22} +(-3.53011 - 6.11433i) q^{23} +(-0.642715 + 0.286155i) q^{24} +(-4.87753 + 1.03675i) q^{25} +(-0.0303238 - 0.0933270i) q^{26} +(-3.13333 + 2.27649i) q^{27} +(2.29193 + 1.02043i) q^{28} +(5.10772 - 5.67269i) q^{29} +(0.687032 - 2.11447i) q^{30} +(6.22121 + 4.51998i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.49787 - 1.78914i) q^{33} +(2.38381 + 4.12887i) q^{34} +(-7.24284 + 3.22472i) q^{35} +(-1.67619 - 1.86160i) q^{36} +(-2.59173 - 7.97652i) q^{37} +(4.33279 - 0.476353i) q^{38} +(-0.0558530 + 0.0405796i) q^{39} +(3.09109 + 0.657031i) q^{40} +(-3.15465 - 3.50360i) q^{41} +(0.184499 - 1.75539i) q^{42} +(3.59679 - 6.22983i) q^{43} +(2.75168 + 1.85156i) q^{44} +7.91626 q^{45} +(-5.71184 - 4.14989i) q^{46} +(-12.3998 + 2.63566i) q^{47} +(-0.470759 + 0.522831i) q^{48} +(0.570969 - 0.414833i) q^{49} +(-4.03416 + 2.93099i) q^{50} +(2.24440 - 2.49266i) q^{51} +(-0.0656616 - 0.0729246i) q^{52} +(-0.155277 + 1.47736i) q^{53} +(-1.93650 + 3.35412i) q^{54} +(-10.1668 + 2.54695i) q^{55} +2.50883 q^{56} +(-1.26070 - 2.79553i) q^{57} +(2.35884 - 7.25976i) q^{58} +(-4.15571 - 0.883322i) q^{59} +(-0.232396 - 2.21110i) q^{60} +(-7.38618 - 3.28854i) q^{61} +(7.52180 + 1.59881i) q^{62} +(6.14737 - 1.30666i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.310104 q^{65} +(0.640658 - 2.24370i) q^{66} +(3.84717 + 6.66350i) q^{67} +(3.85708 + 2.80233i) q^{68} +(-1.53493 + 4.72403i) q^{69} +(-5.30505 + 5.89185i) q^{70} +(1.54871 + 14.7350i) q^{71} +(-2.28846 - 1.01889i) q^{72} +(-5.02687 - 1.06850i) q^{73} +(-5.61200 - 6.23276i) q^{74} +(2.83819 + 2.06207i) q^{75} +(3.76445 - 2.19748i) q^{76} +(-7.47466 + 3.65598i) q^{77} +(-0.0345190 + 0.0597887i) q^{78} +(-7.51110 + 3.34416i) q^{79} +(3.09109 - 0.657031i) q^{80} +(-4.68561 - 0.995958i) q^{81} +(-4.30696 - 1.91758i) q^{82} +(-1.82109 + 1.32310i) q^{83} +(-0.545434 - 1.67867i) q^{84} +(-14.7371 + 3.13247i) q^{85} +(0.751935 - 7.15418i) q^{86} -5.37037 q^{87} +(3.26688 + 0.572275i) q^{88} +(-1.40487 - 2.43331i) q^{89} +(7.23187 - 3.21983i) q^{90} +(0.240811 - 0.0511860i) q^{91} +(-6.90594 - 1.46790i) q^{92} +(-0.565510 - 5.38046i) q^{93} +(-10.2558 + 7.45126i) q^{94} +(-2.79947 + 13.4873i) q^{95} +(-0.217405 + 0.669105i) q^{96} +(17.7076 - 7.88394i) q^{97} +(0.352878 - 0.611203i) q^{98} +(8.30287 - 0.299233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

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