LMFDB - Embedded newform 354.2.e.a.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			133.2
Character	$\chi$	$=$	354.133
Dual form			354.2.e.a.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.994138 + 0.108119i) q^{2} +(0.647386 + 0.762162i) q^{3} +(0.976621 - 0.214970i) q^{4} +(1.51851 - 1.15434i) q^{5} +(-0.725995 - 0.687699i) q^{6} +(0.899258 + 2.25697i) q^{7} +(-0.947653 + 0.319302i) q^{8} +(-0.161782 + 0.986827i) q^{9} +O(q^{10})$	\(q+(-0.994138 + 0.108119i) q^{2} +(0.647386 + 0.762162i) q^{3} +(0.976621 - 0.214970i) q^{4} +(1.51851 - 1.15434i) q^{5} +(-0.725995 - 0.687699i) q^{6} +(0.899258 + 2.25697i) q^{7} +(-0.947653 + 0.319302i) q^{8} +(-0.161782 + 0.986827i) q^{9} +(-1.38480 + 1.31175i) q^{10} +(0.972610 + 0.449977i) q^{11} +(0.796093 + 0.605174i) q^{12} +(0.210182 + 1.28205i) q^{13} +(-1.13801 - 2.14651i) q^{14} +(1.86286 + 0.410046i) q^{15} +(0.907575 - 0.419889i) q^{16} +(2.06051 - 5.17149i) q^{17} +(0.0541389 - 0.998533i) q^{18} +(-0.284191 + 0.419150i) q^{19} +(1.23486 - 1.45379i) q^{20} +(-1.13801 + 2.14651i) q^{21} +(-1.01556 - 0.342182i) q^{22} +(0.0435503 + 0.803238i) q^{23} +(-0.856857 - 0.515554i) q^{24} +(-0.364273 + 1.31199i) q^{25} +(-0.347564 - 1.25181i) q^{26} +(-0.856857 + 0.515554i) q^{27} +(1.36342 + 2.01089i) q^{28} +(2.20172 + 0.239451i) q^{29} +(-1.89627 - 0.206232i) q^{30} +(4.35309 + 6.42033i) q^{31} +(-0.856857 + 0.515554i) q^{32} +(0.286699 + 1.03260i) q^{33} +(-1.48929 + 5.36396i) q^{34} +(3.97084 + 2.38918i) q^{35} +(0.0541389 + 0.998533i) q^{36} +(0.0255399 + 0.00860541i) q^{37} +(0.237207 - 0.447419i) q^{38} +(-0.841062 + 0.990175i) q^{39} +(-1.07044 + 1.57878i) q^{40} +(0.0462812 - 0.853607i) q^{41} +(0.899258 - 2.25697i) q^{42} +(-1.31406 + 0.607949i) q^{43} +(1.04660 + 0.230375i) q^{44} +(0.893467 + 1.68526i) q^{45} +(-0.130140 - 0.793821i) q^{46} +(-1.35834 - 1.03258i) q^{47} +(0.907575 + 0.419889i) q^{48} +(0.796731 - 0.754703i) q^{49} +(0.220286 - 1.34369i) q^{50} +(5.27546 - 1.77751i) q^{51} +(0.480871 + 1.20689i) q^{52} +(-7.73242 - 7.32454i) q^{53} +(0.796093 - 0.605174i) q^{54} +(1.99635 - 0.439429i) q^{55} +(-1.57284 - 1.85169i) q^{56} +(-0.503441 + 0.0547525i) q^{57} -2.21470 q^{58} +(7.38772 + 2.10274i) q^{59} +1.90745 q^{60} +(-3.78077 + 0.411184i) q^{61} +(-5.02174 - 5.91205i) q^{62} +(-2.37272 + 0.522275i) q^{63} +(0.796093 - 0.605174i) q^{64} +(1.79909 + 1.70419i) q^{65} +(-0.396661 - 0.995545i) q^{66} +(-4.96225 + 1.67198i) q^{67} +(0.900619 - 5.49353i) q^{68} +(-0.584004 + 0.553198i) q^{69} +(-4.20588 - 1.94585i) q^{70} +(-6.31413 - 4.79988i) q^{71} +(-0.161782 - 0.986827i) q^{72} +(-4.54729 - 8.57710i) q^{73} +(-0.0263206 - 0.00579361i) q^{74} +(-1.23578 + 0.571731i) q^{75} +(-0.187442 + 0.470443i) q^{76} +(-0.140957 + 2.59980i) q^{77} +(0.729075 - 1.07531i) q^{78} +(9.21635 - 10.8503i) q^{79} +(0.893467 - 1.68526i) q^{80} +(-0.947653 - 0.319302i) q^{81} +(0.0462812 + 0.853607i) q^{82} +(-5.13114 - 3.08730i) q^{83} +(-0.649965 + 2.34096i) q^{84} +(-2.84076 - 10.2315i) q^{85} +(1.24063 - 0.746460i) q^{86} +(1.24286 + 1.83308i) q^{87} +(-1.06538 - 0.115867i) q^{88} +(-15.7542 - 1.71337i) q^{89} +(-1.07044 - 1.57878i) q^{90} +(-2.70454 + 1.62727i) q^{91} +(0.215205 + 0.775097i) q^{92} +(-2.07520 + 7.47420i) q^{93} +(1.46202 + 0.879668i) q^{94} +(0.0522956 + 0.964536i) q^{95} +(-0.947653 - 0.319302i) q^{96} +(-2.35658 + 4.44499i) q^{97} +(-0.710462 + 0.836421i) q^{98} +(-0.601400 + 0.886999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{28}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.994138	+	0.108119i	−0.702962	+	0.0764517i
$2$	−0.994138	+	0.108119i	−0.702962	+	0.0764517i
$3$	0.647386	+	0.762162i	0.373769	+	0.440034i
$3$	0.647386	+	0.762162i	0.373769	+	0.440034i
$4$	0.976621	−	0.214970i	0.488310	−	0.107485i
$5$	1.51851	−	1.15434i	0.679098	−	0.516237i	−0.207818	−	0.978168i	$-0.566636\pi$
$5$	1.51851	−	1.15434i	0.679098	−	0.516237i	0.886916	+	0.461930i	$0.152843\pi$
$6$	−0.725995	−	0.687699i	−0.296386	−	0.280752i
$7$	0.899258	+	2.25697i	0.339888	+	0.853054i	0.995215	+	0.0977087i	$0.0311513\pi$
$7$	0.899258	+	2.25697i	0.339888	+	0.853054i	−0.655327	+	0.755345i	$0.727469\pi$
$8$	−0.947653	+	0.319302i	−0.335046	+	0.112890i
$9$	−0.161782	+	0.986827i	−0.0539273	+	0.328942i
$10$	−1.38480	+	1.31175i	−0.437913	+	0.414813i
$11$	0.972610	+	0.449977i	0.293253	+	0.135673i	0.561000	−	0.827816i	$-0.310417\pi$
$11$	0.972610	+	0.449977i	0.293253	+	0.135673i	−0.267747	+	0.963489i	$0.586279\pi$
$12$	0.796093	+	0.605174i	0.229812	+	0.174699i
$13$	0.210182	+	1.28205i	0.0582939	+	0.355577i	0.999826	+	0.0186538i	$0.00593803\pi$
$13$	0.210182	+	1.28205i	0.0582939	+	0.355577i	−0.941532	+	0.336923i	$0.890614\pi$
$14$	−1.13801	−	2.14651i	−0.304145	−	0.573679i
$15$	1.86286	+	0.410046i	0.480988	+	0.105873i
$16$	0.907575	−	0.419889i	0.226894	−	0.104972i
$17$	2.06051	−	5.17149i	0.499747	−	1.25427i	−0.435472	−	0.900202i	$-0.643419\pi$
$17$	2.06051	−	5.17149i	0.499747	−	1.25427i	0.935219	−	0.354069i	$-0.115202\pi$
$18$	0.0541389	−	0.998533i	0.0127607	−	0.235357i
$19$	−0.284191	+	0.419150i	−0.0651978	+	0.0961596i	−0.858890	−	0.512160i	$-0.828846\pi$
$19$	−0.284191	+	0.419150i	−0.0651978	+	0.0961596i	0.793692	+	0.608319i	$0.208156\pi$
$20$	1.23486	−	1.45379i	0.276123	−	0.325077i
$21$	−1.13801	+	2.14651i	−0.248334	+	0.468407i
$22$	−1.01556	−	0.342182i	−0.216518	−	0.0729534i
$23$	0.0435503	+	0.803238i	0.00908087	+	0.167487i	0.999556	+	0.0297952i	$0.00948552\pi$
$23$	0.0435503	+	0.803238i	0.00908087	+	0.167487i	−0.990475	+	0.137692i	$0.956032\pi$
$24$	−0.856857	−	0.515554i	−0.174905	−	0.105237i
$25$	−0.364273	+	1.31199i	−0.0728546	+	0.262399i
$26$	−0.347564	−	1.25181i	−0.0681628	−	0.245500i
$27$	−0.856857	+	0.515554i	−0.164902	+	0.0992184i
$28$	1.36342	+	2.01089i	0.257661	+	0.380022i
$29$	2.20172	+	0.239451i	0.408848	+	0.0444649i	0.310233	−	0.950661i	$-0.399593\pi$
$29$	2.20172	+	0.239451i	0.408848	+	0.0444649i	0.0986157	+	0.995126i	$0.468559\pi$
$30$	−1.89627	−	0.206232i	−0.346210	−	0.0376526i
$31$	4.35309	+	6.42033i	0.781839	+	1.15313i	0.984758	+	0.173930i	$0.0556468\pi$
$31$	4.35309	+	6.42033i	0.781839	+	1.15313i	−0.202919	+	0.979195i	$0.565043\pi$
$32$	−0.856857	+	0.515554i	−0.151472	+	0.0911379i
$33$	0.286699	+	1.03260i	0.0499078	+	0.179752i
$34$	−1.48929	+	5.36396i	−0.255412	+	0.919911i
$35$	3.97084	+	2.38918i	0.671195	+	0.403845i
$36$	0.0541389	+	0.998533i	0.00902315	+	0.166422i
$37$	0.0255399	+	0.00860541i	0.00419874	+	0.00141472i	0.321400	−	0.946943i	$-0.395847\pi$
$37$	0.0255399	+	0.00860541i	0.00419874	+	0.00141472i	−0.317201	+	0.948358i	$0.602743\pi$
$38$	0.237207	−	0.447419i	0.0384800	−	0.0725810i
$39$	−0.841062	+	0.990175i	−0.134678	+	0.158555i
$40$	−1.07044	+	1.57878i	−0.169251	+	0.249627i
$41$	0.0462812	−	0.853607i	0.00722791	−	0.133311i	−0.992692	−	0.120674i	$-0.961495\pi$
$41$	0.0462812	−	0.853607i	0.00722791	−	0.133311i	0.999920	−	0.0126373i	$-0.00402269\pi$
$42$	0.899258	−	2.25697i	0.138759	−	0.348258i
$43$	−1.31406	+	0.607949i	−0.200392	+	0.0927114i	−0.517519	−	0.855672i	$-0.673144\pi$
$43$	−1.31406	+	0.607949i	−0.200392	+	0.0927114i	0.317126	+	0.948383i	$0.397282\pi$
$44$	1.04660	+	0.230375i	0.157781	+	0.0347303i
$45$	0.893467	+	1.68526i	0.133190	+	0.251223i
$46$	−0.130140	−	0.793821i	−0.0191882	−	0.117043i
$47$	−1.35834	−	1.03258i	−0.198134	−	0.150618i	0.501403	−	0.865214i	$-0.332817\pi$
$47$	−1.35834	−	1.03258i	−0.198134	−	0.150618i	−0.699537	+	0.714596i	$0.746611\pi$
$48$	0.907575	+	0.419889i	0.130997	+	0.0606058i
$49$	0.796731	−	0.754703i	0.113819	−	0.107815i
$50$	0.220286	−	1.34369i	0.0311532	−	0.190026i
$51$	5.27546	−	1.77751i	0.738712	−	0.248901i
$52$	0.480871	+	1.20689i	0.0666848	+	0.167366i
$53$	−7.73242	−	7.32454i	−1.06213	−	1.00610i	−0.999968	−	0.00803715i	$-0.997442\pi$
$53$	−7.73242	−	7.32454i	−1.06213	−	1.00610i	−0.0621625	−	0.998066i	$-0.519800\pi$
$54$	0.796093	−	0.605174i	0.108335	−	0.0823538i
$55$	1.99635	−	0.439429i	0.269187	−	0.0592526i
$56$	−1.57284	−	1.85169i	−0.210179	−	0.247442i
$57$	−0.503441	+	0.0547525i	−0.0666824	+	0.00725215i
$58$	−2.21470			−0.290804
$59$	7.38772	+	2.10274i	0.961800	+	0.273754i
$59$	7.38772	+	2.10274i	0.961800	+	0.273754i
$60$	1.90745			0.246251
$61$	−3.78077	+	0.411184i	−0.484078	+	0.0526467i	−0.346905	−	0.937900i	$-0.612767\pi$
$61$	−3.78077	+	0.411184i	−0.484078	+	0.0526467i	−0.137173	+	0.990547i	$0.543802\pi$
$62$	−5.02174	−	5.91205i	−0.637761	−	0.750830i
$63$	−2.37272	+	0.522275i	−0.298935	+	0.0658005i
$64$	0.796093	−	0.605174i	0.0995116	−	0.0756468i
$65$	1.79909	+	1.70419i	0.223149	+	0.211378i
$66$	−0.396661	−	0.995545i	−0.0488256	−	0.122543i
$67$	−4.96225	+	1.67198i	−0.606235	+	0.204264i	−0.605644	−	0.795735i	$-0.707085\pi$
$67$	−4.96225	+	1.67198i	−0.606235	+	0.204264i	−0.000590744		1.00000i	$0.500188\pi$
$68$	0.900619	−	5.49353i	0.109216	−	0.666189i
$69$	−0.584004	+	0.553198i	−0.0703058	+	0.0665972i
$70$	−4.20588	−	1.94585i	−0.502699	−	0.232573i
$71$	−6.31413	−	4.79988i	−0.749349	−	0.569641i	0.159285	−	0.987233i	$-0.449081\pi$
$71$	−6.31413	−	4.79988i	−0.749349	−	0.569641i	−0.908635	+	0.417592i	$0.862874\pi$
$72$	−0.161782	−	0.986827i	−0.0190662	−	0.116299i
$73$	−4.54729	−	8.57710i	−0.532220	−	1.00387i	−0.993195	−	0.116460i	$-0.962845\pi$
$73$	−4.54729	−	8.57710i	−0.532220	−	1.00387i	0.460975	−	0.887413i	$-0.347500\pi$
$74$	−0.0263206	−	0.00579361i	−0.00305971	−	0.000673494i
$75$	−1.23578	+	0.571731i	−0.142695	+	0.0660179i
$76$	−0.187442	+	0.470443i	−0.0215010	+	0.0539635i
$77$	−0.140957	+	2.59980i	−0.0160635	+	0.296274i
$78$	0.729075	−	1.07531i	0.0825515	−	0.121754i
$79$	9.21635	−	10.8503i	1.03692	−	1.22076i	0.0620294	−	0.998074i	$-0.480243\pi$
$79$	9.21635	−	10.8503i	1.03692	−	1.22076i	0.974891	−	0.222683i	$-0.0714814\pi$
$80$	0.893467	−	1.68526i	0.0998926	−	0.188417i
$81$	−0.947653	−	0.319302i	−0.105295	−	0.0354779i
$82$	0.0462812	+	0.853607i	0.00511090	+	0.0942651i
$83$	−5.13114	−	3.08730i	−0.563216	−	0.338876i	0.205308	−	0.978697i	$-0.434181\pi$
$83$	−5.13114	−	3.08730i	−0.563216	−	0.338876i	−0.768523	+	0.639822i	$0.779008\pi$
$84$	−0.649965	+	2.34096i	−0.0709170	+	0.255420i
$85$	−2.84076	−	10.2315i	−0.308124	−	1.10976i
$86$	1.24063	−	0.746460i	0.133780	−	0.0804929i
$87$	1.24286	+	1.83308i	0.133249	+	0.196527i
$88$	−1.06538	−	0.115867i	−0.113569	−	0.0123514i
$89$	−15.7542	−	1.71337i	−1.66994	−	0.181617i	−0.776290	−	0.630375i	$-0.782901\pi$
$89$	−15.7542	−	1.71337i	−1.66994	−	0.181617i	−0.893653	+	0.448758i	$0.851866\pi$
$90$	−1.07044	−	1.57878i	−0.112834	−	0.166418i
$91$	−2.70454	+	1.62727i	−0.283513	+	0.170584i
$92$	0.215205	+	0.775097i	0.0224366	+	0.0808095i
$93$	−2.07520	+	7.47420i	−0.215188	+	0.775038i
$94$	1.46202	+	0.879668i	0.150796	+	0.0907309i
$95$	0.0522956	+	0.964536i	0.00536542	+	0.0989593i
$96$	−0.947653	−	0.319302i	−0.0967194	−	0.0325886i
$97$	−2.35658	+	4.44499i	−0.239275	+	0.451320i	−0.973845	−	0.227212i	$-0.927039\pi$
$97$	−2.35658	+	4.44499i	−0.239275	+	0.451320i	0.734571	+	0.678532i	$0.237384\pi$
$98$	−0.710462	+	0.836421i	−0.0717675	+	0.0844913i
$99$	−0.601400	+	0.886999i	−0.0604430	+	0.0891468i
$100$	−0.0737169	+	1.35963i	−0.00737169	+	0.135963i
$101$	1.37965	−	3.46265i	0.137280	−	0.344547i	−0.844223	−	0.535991i	$-0.819938\pi$
$101$	1.37965	−	3.46265i	0.137280	−	0.344547i	0.981503	+	0.191445i	$0.0613173\pi$
$102$	−5.05235	+	2.33747i	−0.500257	+	0.231444i
$103$	−4.12505	−	0.907991i	−0.406453	−	0.0894670i	0.00703818	−	0.999975i	$-0.497760\pi$
$103$	−4.12505	−	0.907991i	−0.406453	−	0.0894670i	−0.413491	+	0.910508i	$0.635691\pi$
$104$	−0.608540	−	1.14783i	−0.0596723	−	0.112554i
$105$	0.749729	+	4.57315i	0.0731661	+	0.446293i
$106$	8.47902	+	6.44558i	0.823555	+	0.626050i
$107$	−7.85165	−	3.63256i	−0.759048	−	0.351173i	0.00188967	−	0.999998i	$-0.499398\pi$
$107$	−7.85165	−	3.63256i	−0.759048	−	0.351173i	−0.760937	+	0.648825i	$0.775261\pi$
$108$	−0.725995	+	0.687699i	−0.0698589	+	0.0661739i
$109$	1.81597	−	11.0769i	0.173939	−	1.06098i	−0.745141	−	0.666907i	$-0.767618\pi$
$109$	1.81597	−	11.0769i	0.173939	−	1.06098i	0.919080	−	0.394072i	$-0.128934\pi$
$110$	−1.93713	+	0.652696i	−0.184698	+	0.0622321i
$111$	0.00997549	+	0.0250366i	0.000946832	+	0.00237637i
$112$	1.76382	+	1.67078i	0.166665	+	0.157874i
$113$	−12.4836	+	9.48979i	−1.17436	+	0.892725i	−0.995832	−	0.0912103i	$-0.970926\pi$
$113$	−12.4836	+	9.48979i	−1.17436	+	0.892725i	−0.178527	+	0.983935i	$0.557133\pi$
$114$	0.494570	−	0.108863i	0.0463208	−	0.0101960i
$115$	0.993343	+	1.16945i	0.0926297	+	0.109052i
$116$	2.20172	−	0.239451i	0.204424	−	0.0222325i
$117$	−1.29917			−0.120108
$118$	−7.57176	−	1.29166i	−0.697037	−	0.118907i
$119$	13.5248			1.23982
$120$	−1.89627	+	0.206232i	−0.173105	+	0.0188263i
$121$	−6.37776	−	7.50848i	−0.579796	−	0.682589i
$122$	3.71415	−	0.817547i	0.336264	−	0.0740172i
$123$	0.680548	−	0.517339i	0.0613630	−	0.0466469i
$124$	5.63150	+	5.33444i	0.505724	+	0.479047i
$125$	4.49144	+	11.2727i	0.401727	+	1.00826i
$126$	2.30234	−	0.775750i	0.205109	−	0.0691093i
$127$	1.77475	−	10.8255i	0.157484	−	0.960607i	−0.783311	−	0.621630i	$-0.786471\pi$
$127$	1.77475	−	10.8255i	0.157484	−	0.960607i	0.940795	−	0.338977i	$-0.110081\pi$
$128$	−0.725995	+	0.687699i	−0.0641695	+	0.0607846i
$129$	−1.31406	−	0.607949i	−0.115697	−	0.0535269i
$130$	−1.97280	−	1.49968i	−0.173026	−	0.131531i
$131$	1.18782	+	7.24539i	0.103780	+	0.633033i	0.986579	+	0.163282i	$0.0522080\pi$
$131$	1.18782	+	7.24539i	0.103780	+	0.633033i	−0.882799	+	0.469751i	$0.844344\pi$
$132$	0.501973	+	0.946822i	0.0436912	+	0.0824103i
$133$	−1.20157	−	0.264485i	−0.104189	−	0.0229338i
$134$	4.75239	−	2.19869i	0.410544	−	0.189938i
$135$	−0.706021	+	1.77198i	−0.0607646	+	0.152508i
$136$	−0.301384	+	5.55870i	−0.0258435	+	0.476655i
$137$	4.79971	−	7.07904i	0.410067	−	0.604803i	−0.565436	−	0.824792i	$-0.691292\pi$
$137$	4.79971	−	7.07904i	0.410067	−	0.604803i	0.975502	+	0.219989i	$0.0706023\pi$
$138$	0.520769	−	0.613097i	0.0443308	−	0.0521903i
$139$	1.04399	−	1.96917i	0.0885498	−	0.167023i	−0.835281	−	0.549823i	$-0.814695\pi$
$139$	1.04399	−	1.96917i	0.0885498	−	0.167023i	0.923831	+	0.382800i	$0.125040\pi$
$140$	4.39161	+	1.47971i	0.371159	+	0.125058i
$141$	−0.0923750	−	1.70376i	−0.00777938	−	0.143482i
$142$	6.79607	+	4.08906i	0.570314	+	0.343146i
$143$	−0.372469	+	1.34151i	−0.0311474	+	0.112183i
$144$	0.267528	+	0.963550i	0.0222940	+	0.0802958i
$145$	3.61973	−	2.17792i	0.300603	−	0.180867i
$146$	5.44798	+	8.03517i	0.450878	+	0.664995i
$147$	1.09100	+	0.118653i	0.0899840	+	0.00978636i
$148$	0.0267927	+	0.00291389i	0.00220235	+	0.000239520i
$149$	6.47282	+	9.54670i	0.530274	+	0.782096i	0.994624	−	0.103556i	$-0.0330221\pi$
$149$	6.47282	+	9.54670i	0.530274	+	0.782096i	−0.464349	+	0.885652i	$0.653712\pi$
$150$	1.16672	−	0.701991i	0.0952621	−	0.0573173i
$151$	−2.54113	−	9.15232i	−0.206794	−	0.744805i	−0.992073	−	0.125663i	$-0.959894\pi$
$151$	−2.54113	−	9.15232i	−0.206794	−	0.744805i	0.785279	−	0.619142i	$-0.212520\pi$
$152$	0.135479	−	0.487951i	0.0109888	−	0.0395781i
$153$	4.77001	+	2.87002i	0.385632	+	0.232027i
$154$	−0.140957	−	2.59980i	−0.0113586	−	0.209497i
$155$	14.0215	+	4.72438i	1.12623	+	0.379472i
$156$	−0.608540	+	1.14783i	−0.0487222	+	0.0918998i
$157$	0.883810	−	1.04050i	0.0705357	−	0.0830411i	−0.725762	−	0.687945i	$-0.758513\pi$
$157$	0.883810	−	1.04050i	0.0705357	−	0.0830411i	0.796298	+	0.604904i	$0.206789\pi$
$158$	−7.98920	+	11.7832i	−0.635586	+	0.937420i
$159$	0.576622	−	10.6352i	0.0457291	−	0.843424i
$160$	−0.706021	+	1.77198i	−0.0558159	+	0.140087i
$161$	−1.77372	+	0.820610i	−0.139789	+	0.0646732i
$162$	0.976621	+	0.214970i	0.0767306	+	0.0168897i
$163$	5.71649	+	10.7824i	0.447750	+	0.844546i	0.999941	+	0.0108283i	$0.00344683\pi$
$163$	5.71649	+	10.7824i	0.447750	+	0.844546i	−0.552192	+	0.833717i	$0.686208\pi$
$164$	−0.138301	−	0.843599i	−0.0107995	−	0.0658740i
$165$	1.62732	+	1.23706i	0.126687	+	0.0963049i
$166$	5.43485	+	2.51443i	0.421827	+	0.195158i
$167$	8.81614	−	8.35109i	0.682213	−	0.646227i	−0.265959	−	0.963984i	$-0.585688\pi$
$167$	8.81614	−	8.35109i	0.682213	−	0.646227i	0.948172	+	0.317758i	$0.102930\pi$
$168$	0.393053	−	2.39751i	0.0303247	−	0.184972i
$169$	10.7200	−	3.61199i	0.824616	−	0.277846i
$170$	3.93033	+	9.86437i	0.301442	+	0.756563i
$171$	−0.367651	−	0.348258i	−0.0281150	−	0.0266319i
$172$	−1.15265	+	0.876220i	−0.0878886	+	0.0668111i
$173$	−0.568946	+	0.125235i	−0.0432562	+	0.00952141i	−0.236546	−	0.971620i	$-0.576015\pi$
$173$	−0.568946	+	0.125235i	−0.0432562	+	0.00952141i	0.193290	+	0.981142i	$0.438084\pi$
$174$	−1.43377	−	1.68796i	−0.108693	−	0.127964i
$175$	−3.28870	+	0.357668i	−0.248603	+	0.0270372i
$176$	1.07166			0.0807792
$177$	3.18008	+	6.99193i	0.239029	+	0.525546i
$178$	15.8471			1.18779
$179$	−3.85493	+	0.419249i	−0.288131	+	0.0313361i	−0.251043	−	0.967976i	$-0.580774\pi$
$179$	−3.85493	+	0.419249i	−0.288131	+	0.0313361i	−0.0370877	+	0.999312i	$0.511808\pi$
$180$	1.23486	+	1.45379i	0.0920409	+	0.108359i
$181$	−14.9083	+	3.28155i	−1.10812	+	0.243916i	−0.731088	−	0.682283i	$-0.760987\pi$
$181$	−14.9083	+	3.28155i	−1.10812	+	0.243916i	−0.377034	+	0.926199i	$0.623056\pi$
$182$	2.51275	−	1.91014i	0.186257	−	0.141589i
$183$	−2.76101	−	2.61537i	−0.204100	−	0.193333i
$184$	−0.297746	−	0.747286i	−0.0219501	−	0.0550906i
$185$	0.0487162	−	0.0164144i	0.00358169	−	0.00120681i
$186$	1.25493	−	7.65475i	0.0920162	−	0.561274i
$187$	4.33113	−	4.10266i	0.316723	−	0.300016i
$188$	−1.54856	−	0.716439i	−0.112940	−	0.0522517i
$189$	−1.93412	−	1.47028i	−0.140687	−	0.106947i
$190$	−0.156274	−	0.953228i	−0.0113373	−	0.0691544i
$191$	8.00834	+	15.1053i	0.579463	+	1.09298i	0.983951	+	0.178440i	$0.0571049\pi$
$191$	8.00834	+	15.1053i	0.579463	+	1.09298i	−0.404488	+	0.914543i	$0.632550\pi$
$192$	0.976621	+	0.214970i	0.0704815	+	0.0155142i
$193$	−15.5138	+	7.17746i	−1.11671	+	0.516645i	−0.889378	−	0.457173i	$-0.848862\pi$
$193$	−15.5138	+	7.17746i	−1.11671	+	0.516645i	−0.227331	+	0.973818i	$0.573000\pi$
$194$	1.86218	−	4.67372i	0.133697	−	0.335554i
$195$	−0.134161	+	2.47446i	−0.00960750	+	0.177200i
$196$	0.615865	−	0.908332i	0.0439903	−	0.0648809i
$197$	−6.89988	+	8.12317i	−0.491596	+	0.578752i	−0.950889	−	0.309533i	$-0.899827\pi$
$197$	−6.89988	+	8.12317i	−0.491596	+	0.578752i	0.459292	+	0.888285i	$0.348103\pi$
$198$	0.501973	−	0.946822i	0.0356737	−	0.0672877i
$199$	20.1186	+	6.77874i	1.42617	+	0.480532i	0.923384	−	0.383878i	$-0.125412\pi$
$199$	20.1186	+	6.77874i	1.42617	+	0.480532i	0.502786	+	0.864411i	$0.332308\pi$
$200$	−0.0737169	−	1.35963i	−0.00521257	−	0.0961402i
$201$	−4.48681	−	2.69962i	−0.316475	−	0.190417i
$202$	−0.997180	+	3.59152i	−0.0701613	+	0.252698i
$203$	1.43948	+	5.18453i	0.101032	+	0.363883i
$204$	4.77001	−	2.87002i	0.333968	−	0.200942i
$205$	−0.915075	−	1.34963i	−0.0639116	−	0.0942625i
$206$	4.19904	+	0.456673i	0.292561	+	0.0318179i
$207$	−0.799703	−	0.0869729i	−0.0555832	−	0.00604503i
$208$	0.729075	+	1.07531i	0.0505523	+	0.0745590i
$209$	−0.465015	+	0.279790i	−0.0321657	+	0.0193535i
$210$	−1.23978	−	4.46528i	−0.0855528	−	0.308133i
$211$	−2.79234	+	10.0571i	−0.192233	+	0.692360i	0.803099	+	0.595846i	$0.203183\pi$
$211$	−2.79234	+	10.0571i	−0.192233	+	0.692360i	−0.995332	+	0.0965141i	$0.969231\pi$
$212$	−9.12620	−	5.49106i	−0.626790	−	0.377127i
$213$	−0.429397	−	7.91976i	−0.0294218	−	0.542653i
$214$	8.19837	+	2.76235i	0.560429	+	0.188831i
$215$	−1.29363	+	2.44005i	−0.0882251	+	0.166410i
$216$	0.647386	−	0.762162i	0.0440491	−	0.0518586i
$217$	−10.5759	+	15.5983i	−0.717941	+	1.05888i
$218$	−0.607699	+	11.2084i	−0.0411586	+	0.759126i
$219$	3.59329	−	9.01847i	0.242812	−	0.609411i
$220$	1.85521	−	0.858310i	0.125078	−	0.0578673i
$221$	7.06320	+	1.55473i	0.475122	+	0.104582i
$222$	−0.0126239	−	0.0238113i	−0.000847264	−	0.00159811i
$223$	4.77536	+	29.1284i	0.319782	+	1.95058i	0.310336	+	0.950627i	$0.399558\pi$
$223$	4.77536	+	29.1284i	0.319782	+	1.95058i	0.00944569	+	0.999955i	$0.496993\pi$
$224$	−1.93412	−	1.47028i	−0.129229	−	0.0982374i
$225$	−1.23578	−	0.571731i	−0.0823851	−	0.0381154i
$226$	11.3844	−	10.7839i	0.757279	−	0.717333i
$227$	−0.0841801	+	0.513476i	−0.00558723	+	0.0340806i	−0.989473	−	0.144718i	$-0.953773\pi$
$227$	−0.0841801	+	0.513476i	−0.00558723	+	0.0340806i	0.983886	+	0.178798i	$0.0572209\pi$
$228$	−0.479901	+	0.161697i	−0.0317822	+	0.0107087i
$229$	−8.86979	−	22.2615i	−0.586132	−	1.47108i	−0.860497	−	0.509455i	$-0.829847\pi$
$229$	−8.86979	−	22.2615i	−0.586132	−	1.47108i	0.274365	−	0.961626i	$-0.411532\pi$
$230$	−1.11396	−	1.05520i	−0.0734523	−	0.0695777i
$231$	−2.07272	+	1.57564i	−0.136375	+	0.103669i
$232$	−2.16292	+	0.476095i	−0.142003	+	0.0312571i
$233$	6.64752	+	7.82606i	0.435493	+	0.512702i	0.935504	−	0.353317i	$-0.114946\pi$
$233$	6.64752	+	7.82606i	0.435493	+	0.512702i	−0.500010	+	0.866019i	$0.666670\pi$
$234$	1.29155	−	0.140465i	0.0844313	−	0.00918245i
$235$	−3.25461			−0.212307
$236$	7.66703	+	0.465441i	0.499081	+	0.0302976i
$237$	14.2362			0.924744
$238$	−13.4455	+	1.46229i	−0.871545	+	0.0947862i
$239$	−4.73890	−	5.57906i	−0.306534	−	0.360879i	0.587228	−	0.809422i	$-0.300219\pi$
$239$	−4.73890	−	5.57906i	−0.306534	−	0.360879i	−0.893762	+	0.448542i	$0.851943\pi$
$240$	1.86286	−	0.410046i	0.120247	−	0.0264684i
$241$	13.5202	−	10.2778i	0.870911	−	0.662049i	−0.0711592	−	0.997465i	$-0.522670\pi$
$241$	13.5202	−	10.2778i	0.870911	−	0.662049i	0.942070	+	0.335416i	$0.108877\pi$
$242$	7.15218	+	6.77491i	0.459760	+	0.435507i
$243$	−0.370138	−	0.928977i	−0.0237444	−	0.0595939i
$244$	−3.60399	+	1.21432i	−0.230722	+	0.0777392i
$245$	0.338658	−	2.06572i	0.0216361	−	0.131974i
$246$	−0.620625	+	0.587887i	−0.0395696	+	0.0374823i
$247$	−0.597103	−	0.276249i	−0.0379928	−	0.0175773i
$248$	−6.17525	−	4.69430i	−0.392129	−	0.298088i
$249$	−0.968803	−	5.90944i	−0.0613954	−	0.374495i
$250$	−5.68390	−	10.7210i	−0.359481	−	0.678054i
$251$	−28.2872	−	6.22648i	−1.78547	−	0.393012i	−0.805572	−	0.592499i	$-0.798142\pi$
$251$	−28.2872	−	6.22648i	−1.78547	−	0.393012i	−0.979901	+	0.199486i	$0.936073\pi$
$252$	−2.20497	+	1.02013i	−0.138900	+	0.0642621i
$253$	−0.319082	+	0.800834i	−0.0200605	+	0.0503480i
$254$	−0.593904	+	10.9539i	−0.0372649	+	0.687310i
$255$	5.95899	−	8.78885i	0.373166	−	0.550379i
$256$	0.647386	−	0.762162i	0.0404616	−	0.0476351i
$257$	5.79035	−	10.9217i	0.361192	−	0.681280i	−0.634608	−	0.772834i	$-0.718839\pi$
$257$	5.79035	−	10.9217i	0.361192	−	0.681280i	0.995800	+	0.0915539i	$0.0291834\pi$
$258$	1.37209	+	0.462310i	0.0854225	+	0.0287822i
$259$	0.00354487	+	0.0653813i	0.000220268	+	0.00406260i
$260$	2.12338	+	1.27759i	0.131686	+	0.0792329i
$261$	−0.592495	+	2.13397i	−0.0366745	+	0.132090i
$262$	−1.96422	−	7.07449i	−0.121350	−	0.437063i
$263$	−11.2739	+	6.78330i	−0.695180	+	0.418276i	−0.818819	−	0.574051i	$-0.805371\pi$
$263$	−11.2739	+	6.78330i	−0.695180	+	0.418276i	0.123639	+	0.992327i	$0.460543\pi$
$264$	−0.601400	−	0.886999i	−0.0370136	−	0.0545910i
$265$	−20.1968	−	2.19653i	−1.24068	−	0.134932i
$266$	1.22312	+	0.133022i	0.0749944	+	0.00815613i
$267$	−8.89319	−	13.1165i	−0.544255	−	0.802716i
$268$	−4.48681	+	2.69962i	−0.274075	+	0.164906i
$269$	0.160774	+	0.579056i	0.00980257	+	0.0353057i	0.968290	−	0.249831i	$-0.0803749\pi$
$269$	0.160774	+	0.579056i	0.00980257	+	0.0353057i	−0.958487	+	0.285136i	$0.907961\pi$
$270$	0.510298	−	1.83793i	0.0310557	−	0.111853i
$271$	22.7440	+	13.6846i	1.38160	+	0.831280i	0.995822	−	0.0913117i	$-0.0291060\pi$
$271$	22.7440	+	13.6846i	1.38160	+	0.831280i	0.385777	+	0.922592i	$0.373934\pi$
$272$	−0.301384	−	5.55870i	−0.0182741	−	0.337046i
$273$	−2.99112	−	1.00783i	−0.181031	−	0.0609965i
$274$	−4.00619	+	7.55648i	−0.242023	+	0.456504i
$275$	−0.944663	+	1.11214i	−0.0569653	+	0.0670648i
$276$	−0.451429	+	0.665808i	−0.0271728	+	0.0400769i
$277$	1.68027	−	30.9908i	0.100958	−	1.86206i	−0.310427	−	0.950597i	$-0.600472\pi$
$277$	1.68027	−	30.9908i	0.100958	−	1.86206i	0.411385	−	0.911462i	$-0.365045\pi$
$278$	−0.824962	+	2.07050i	−0.0494779	+	0.124180i
$279$	−7.04001	+	3.25705i	−0.421474	+	0.194995i
$280$	−4.52585	−	0.996215i	−0.270471	−	0.0595352i
$281$	0.916763	+	1.72920i	0.0546895	+	0.103155i	0.909350	−	0.416032i	$-0.136580\pi$
$281$	0.916763	+	1.72920i	0.0546895	+	0.103155i	−0.854661	+	0.519187i	$0.826235\pi$
$282$	0.276042	+	1.68378i	0.0164381	+	0.100268i
$283$	−0.486710	−	0.369987i	−0.0289319	−	0.0219935i	0.590608	−	0.806958i	$-0.298888\pi$
$283$	−0.486710	−	0.369987i	−0.0289319	−	0.0219935i	−0.619540	+	0.784965i	$0.712681\pi$
$284$	−7.19834	−	3.33031i	−0.427143	−	0.197617i
$285$	−0.701278	+	0.664285i	−0.0415401	+	0.0393489i
$286$	0.225243	−	1.37392i	0.0133189	−	0.0812416i
$287$	1.96818	−	0.663157i	0.116178	−	0.0391449i
$288$	−0.370138	−	0.928977i	−0.0218106	−	0.0547405i
$289$	−10.1567	−	9.62093i	−0.597452	−	0.565937i
$290$	−3.36304	+	2.55652i	−0.197485	+	0.150124i
$291$	−4.91342	+	1.08153i	−0.288030	+	0.0634001i
$292$	−6.28480	−	7.39904i	−0.367790	−	0.432996i
$293$	−29.0336	+	3.15759i	−1.69616	+	0.184468i	−0.904494	−	0.426487i	$-0.859751\pi$
$293$	−29.0336	+	3.15759i	−1.69616	+	0.184468i	−0.791665	+	0.610955i	$0.790785\pi$
$294$	−1.09743			−0.0640035
$295$	13.6456	−	5.33492i	0.794478	−	0.310611i
$296$	−0.0269507			−0.00156648
$297$	−1.06538	+	0.115867i	−0.0618194	+	0.00672326i
$298$	−7.46706	−	8.79090i	−0.432555	−	0.509243i
$299$	−1.02064	+	0.224660i	−0.0590251	+	0.0129924i
$300$	−1.08398	+	0.824020i	−0.0625836	+	0.0475748i
$301$	−2.55380	−	2.41909i	−0.147199	−	0.139434i
$302$	3.51577	+	8.82392i	0.202310	+	0.507760i
$303$	3.53226	−	1.19016i	0.202923	−	0.0683728i
$304$	−0.0819280	+	0.499739i	−0.00469889	+	0.0286620i
$305$	−5.26649	+	4.98869i	−0.301558	+	0.285651i
$306$	−5.05235	−	2.33747i	−0.288824	−	0.133624i
$307$	−4.76813	−	3.62464i	−0.272132	−	0.206869i	0.460204	−	0.887813i	$-0.347776\pi$
$307$	−4.76813	−	3.62464i	−0.272132	−	0.206869i	−0.732335	+	0.680944i	$0.761570\pi$
$308$	0.421218	+	2.56931i	0.0240011	+	0.146400i
$309$	−1.97846	−	3.73177i	−0.112551	−	0.212293i
$310$	−14.4501	−	3.18070i	−0.820709	−	0.180652i
$311$	14.1264	−	6.53558i	0.801036	−	0.370599i	0.0237277	−	0.999718i	$-0.492447\pi$
$311$	14.1264	−	6.53558i	0.801036	−	0.370599i	0.777308	+	0.629120i	$0.216584\pi$
$312$	0.480871	−	1.20689i	0.0272240	−	0.0683270i
$313$	−0.925187	+	17.0641i	−0.0522947	+	0.964518i	0.848207	+	0.529665i	$0.177682\pi$
$313$	−0.925187	+	17.0641i	−0.0522947	+	0.964518i	−0.900501	+	0.434853i	$0.856800\pi$
$314$	−0.766131	+	1.12996i	−0.0432353	+	0.0637673i
$315$	−3.00011	+	3.53201i	−0.169037	+	0.199006i
$316$	6.66838	−	12.5779i	0.375126	−	0.707562i
$317$	27.0365	+	9.10966i	1.51852	+	0.511649i	0.950329	−	0.311247i	$-0.100747\pi$
$317$	27.0365	+	9.10966i	1.51852	+	0.511649i	0.568192	+	0.822896i	$0.307643\pi$
$318$	0.576622	+	10.6352i	0.0323354	+	0.596391i
$319$	2.03366	+	1.22361i	0.113863	+	0.0685093i
$320$	0.510298	−	1.83793i	0.0285265	−	0.102743i
$321$	−2.31445	−	8.33590i	−0.129180	−	0.465265i
$322$	1.67460	−	1.00757i	0.0933217	−	0.0561498i
$323$	1.58205	+	2.33335i	0.0880277	+	0.129831i
$324$	−0.994138	−	0.108119i	−0.0552299	−	0.00600661i
$325$	−1.75861	−	0.191260i	−0.0975499	−	0.0106092i
$326$	−6.84876	−	10.1012i	−0.379318	−	0.559452i
$327$	9.61807	−	5.78700i	0.531880	−	0.320022i
$328$	0.228699	+	0.823701i	0.0126278	+	0.0454813i
$329$	1.10901	−	3.99429i	0.0611417	−	0.220212i
$330$	−1.75153	−	1.05386i	−0.0964187	−	0.0580132i
$331$	−0.716076	−	13.2072i	−0.0393591	−	0.725936i	−0.949907	−	0.312532i	$-0.898823\pi$
$331$	−0.716076	−	13.2072i	−0.0393591	−	0.725936i	0.910548	−	0.413403i	$-0.135660\pi$
$332$	−5.67485	−	1.91208i	−0.311448	−	0.104939i
$333$	−0.0126239	+	0.0238113i	−0.000691788	+	0.00130485i
$334$	−7.86155	+	9.25533i	−0.430165	+	0.506429i
$335$	−5.60519	+	8.26704i	−0.306244	+	0.451677i
$336$	−0.131532	+	2.42596i	−0.00717564	+	0.132347i
$337$	−2.18785	+	5.49109i	−0.119180	+	0.299119i	−0.976449	−	0.215750i	$-0.930780\pi$
$337$	−2.18785	+	5.49109i	−0.119180	+	0.299119i	0.857269	+	0.514869i	$0.172160\pi$
$338$	−10.2666	+	4.74986i	−0.558432	+	0.258358i
$339$	−15.3145	−	3.37097i	−0.831768	−	0.183086i
$340$	−4.97381	−	9.38160i	−0.269743	−	0.508789i
$341$	1.34486	+	8.20327i	0.0728282	+	0.444232i
$342$	0.403149	+	0.306466i	0.0217998	+	0.0165718i
$343$	17.8546	+	8.26043i	0.964059	+	0.446021i
$344$	1.05115	−	0.995707i	0.0566745	−	0.0536849i
$345$	−0.248237	+	1.51418i	−0.0133646	+	0.0815205i
$346$	0.552071	−	0.186014i	0.0296795	−	0.0100002i
$347$	−3.80780	−	9.55685i	−0.204413	−	0.513039i	0.790651	−	0.612267i	$-0.209742\pi$
$347$	−3.80780	−	9.55685i	−0.204413	−	0.513039i	−0.995065	+	0.0992278i	$0.968363\pi$
$348$	1.60786	+	1.52305i	0.0861904	+	0.0816439i
$349$	14.2451	−	10.8288i	0.762521	−	0.579653i	−0.149999	−	0.988686i	$-0.547927\pi$
$349$	14.2451	−	10.8288i	0.762521	−	0.579653i	0.912520	+	0.409033i	$0.134134\pi$
$350$	3.23075	−	0.711143i	0.172691	−	0.0380122i
$351$	−0.841062	−	0.990175i	−0.0448926	−	0.0528516i
$352$	−1.06538	+	0.115867i	−0.0567847	+	0.00617571i
$353$	1.30686			0.0695570			0.0347785	−	0.999395i	$-0.488927\pi$
$353$	1.30686			0.0695570			0.0347785	+	0.999395i	$0.488927\pi$
$354$	−3.91740	−	6.60712i	−0.208207	−	0.351164i
$355$	−15.1288			−0.802951
$356$	−15.7542	+	1.71337i	−0.834972	+	0.0908087i
$357$	8.75578	+	10.3081i	0.463405	+	0.545563i
$358$	3.78700	−	0.833582i	0.200149	−	0.0440562i
$359$	20.6332	−	15.6850i	1.08898	−	0.827821i	0.102999	−	0.994681i	$-0.467156\pi$
$359$	20.6332	−	15.6850i	1.08898	−	0.827821i	0.985981	+	0.166860i	$0.0533629\pi$
$360$	−1.38480	−	1.31175i	−0.0729855	−	0.0691355i
$361$	6.93770	+	17.4123i	0.365142	+	0.916438i
$362$	14.4661	−	4.87418i	0.760319	−	0.256181i
$363$	1.59380	−	9.72177i	0.0836530	−	0.510261i
$364$	−2.29150	+	2.17062i	−0.120107	+	0.113771i
$365$	−16.8060	−	7.77528i	−0.879666	−	0.406977i
$366$	3.02759	+	2.30152i	0.158255	+	0.120302i
$367$	1.77040	+	10.7990i	0.0924142	+	0.563702i	0.991927	+	0.126808i	$0.0404732\pi$
$367$	1.77040	+	10.7990i	0.0924142	+	0.563702i	−0.899513	+	0.436894i	$0.856079\pi$
$368$	0.376796	+	0.710713i	0.0196419	+	0.0370485i
$369$	0.834874	+	0.183770i	0.0434618	+	0.00956667i
$370$	−0.0466559	+	0.0215853i	−0.00242553	+	0.00112217i
$371$	9.57781	−	24.0385i	0.497255	−	1.24802i
$372$	−0.419952	+	7.74556i	−0.0217735	+	0.401589i
$373$	−0.0711024	+	0.104868i	−0.00368154	+	0.00542987i	−0.829525	−	0.558469i	$-0.811389\pi$
$373$	−0.0711024	+	0.104868i	−0.00368154	+	0.00542987i	0.825844	+	0.563899i	$0.190699\pi$
$374$	−3.86216	+	4.54689i	−0.199708	+	0.235114i
$375$	−5.68390	+	10.7210i	−0.293515	+	0.553629i
$376$	1.61694	+	0.544811i	0.0833874	+	0.0280965i
$377$	0.155772	+	2.87304i	0.00802265	+	0.147969i
$378$	2.08175	+	1.25255i	0.107074	+	0.0644241i
$379$	−7.68906	+	27.6935i	−0.394960	+	1.42252i	0.452550	+	0.891739i	$0.350515\pi$
$379$	−7.68906	+	27.6935i	−0.394960	+	1.42252i	−0.847510	+	0.530779i	$0.821899\pi$
$380$	0.258420	+	0.930744i	0.0132567	+	0.0477462i
$381$	9.39973	−	5.65563i	0.481563	−	0.289747i
$382$	−9.59456	−	14.1509i	−0.490901	−	0.724024i
$383$	−2.06468	−	0.224547i	−0.105500	−	0.0114738i	0.0552167	−	0.998474i	$-0.482415\pi$
$383$	−2.06468	−	0.224547i	−0.105500	−	0.0114738i	−0.160717	+	0.987001i	$0.551381\pi$
$384$	−0.994138	−	0.108119i	−0.0507319	−	0.00551743i
$385$	2.78701	+	4.11053i	0.142039	+	0.209492i
$386$	14.6469	−	8.81272i	0.745505	−	0.448556i
$387$	−0.387349	−	1.39511i	−0.0196901	−	0.0709172i
$388$	−1.34595	+	4.84766i	−0.0683301	+	0.246103i
$389$	14.9492	+	8.99463i	0.757954	+	0.456046i	0.841364	−	0.540469i	$-0.181753\pi$
$389$	14.9492	+	8.99463i	0.757954	+	0.456046i	−0.0834093	+	0.996515i	$0.526581\pi$
$390$	−0.134161	−	2.47446i	−0.00679353	−	0.125299i
$391$	4.24368	+	1.42986i	0.214612	+	0.0723112i
$392$	−0.514046	+	0.969594i	−0.0259633	+	0.0489719i
$393$	−4.75318	+	5.59588i	−0.239766	+	0.282275i
$394$	5.98117	−	8.82156i	0.301327	−	0.444424i
$395$	1.47014	−	27.1151i	0.0739708	−	1.36431i
$396$	−0.396661	+	0.995545i	−0.0199330	+	0.0500280i
$397$	23.2076	−	10.7370i	1.16475	−	0.538873i	0.260335	−	0.965518i	$-0.416167\pi$
$397$	23.2076	−	10.7370i	1.16475	−	0.538873i	0.904419	+	0.426646i	$0.140305\pi$
$398$	−20.7336	−	4.56380i	−1.03928	−	0.228763i
$399$	−0.576298	−	1.08701i	−0.0288510	−	0.0544188i
$400$	0.220286	+	1.34369i	0.0110143	+	0.0671844i
$401$	18.7250	+	14.2344i	0.935082	+	0.710831i	0.957353	−	0.288921i	$-0.0932965\pi$
$401$	18.7250	+	14.2344i	0.935082	+	0.710831i	−0.0222707	+	0.999752i	$0.507090\pi$
$402$	4.75239	+	2.19869i	0.237028	+	0.109661i
$403$	−7.31626	+	6.93033i	−0.364449	+	0.345224i
$404$	0.603023	−	3.67828i	0.0300015	−	0.183001i
$405$	−1.80760	+	0.609053i	−0.0898205	+	0.0302641i
$406$	−1.99159	−	4.99850i	−0.0988407	−	0.248072i
$407$	0.0209682	+	0.0198621i	0.00103935	+	0.000984528i
$408$	−4.43174	+	3.36892i	−0.219404	+	0.166787i
$409$	11.8770	−	2.61432i	0.587278	−	0.129270i	0.0886158	−	0.996066i	$-0.471756\pi$
$409$	11.8770	−	2.61432i	0.587278	−	0.129270i	0.498663	+	0.866796i	$0.333825\pi$
$410$	1.05563	+	1.24279i	0.0521339	+	0.0613768i
$411$	8.50264	−	0.924718i	0.419404	−	0.0456130i
$412$	−4.22380			−0.208091
$413$	1.89764	+	18.5648i	0.0933770	+	0.913512i
$414$	0.804418			0.0395350
$415$	−11.3555	+	1.23498i	−0.557419	+	0.0606229i
$416$	−0.841062	−	0.990175i	−0.0412365	−	0.0485473i
$417$	2.17669	−	0.479125i	0.106593	−	0.0234629i
$418$	0.432038	−	0.328427i	0.0211317	−	0.0160639i
$419$	−8.13914	−	7.70980i	−0.397623	−	0.376648i	0.462600	−	0.886567i	$-0.346917\pi$
$419$	−8.13914	−	7.70980i	−0.397623	−	0.376648i	−0.860222	+	0.509919i	$0.829675\pi$
$420$	1.71529	+	4.30506i	0.0836977	+	0.210065i
$421$	−3.99134	+	1.34484i	−0.194526	+	0.0655434i	−0.414878	−	0.909877i	$-0.636176\pi$
$421$	−3.99134	+	1.34484i	−0.194526	+	0.0655434i	0.220352	+	0.975420i	$0.429279\pi$
$422$	1.68861	−	10.3001i	0.0822002	−	0.501399i
$423$	1.23874	−	1.17339i	0.0602294	−	0.0570523i
$424$	9.66639	+	4.47215i	0.469442	+	0.217187i
$425$	6.03437	+	4.58721i	0.292710	+	0.222512i
$426$	1.28316	+	7.82691i	0.0621692	+	0.379215i
$427$	−4.32792	−	8.16332i	−0.209443	−	0.395051i
$428$	−8.44898	−	1.85976i	−0.408397	−	0.0898949i
$429$	−1.26358	+	0.584595i	−0.0610063	+	0.0282245i
$430$	1.02223	−	2.56561i	0.0492965	−	0.123725i
$431$	−0.607949	+	11.2130i	−0.0292839	+	0.540109i	0.946680	+	0.322176i	$0.104414\pi$
$431$	−0.607949	+	11.2130i	−0.0292839	+	0.540109i	−0.975964	+	0.217933i	$0.930068\pi$
$432$	−0.561187	+	0.827689i	−0.0270001	+	0.0398222i
$433$	−11.1351	+	13.1093i	−0.535121	+	0.629993i	−0.961584	−	0.274512i	$-0.911484\pi$
$433$	−11.1351	+	13.1093i	−0.535121	+	0.629993i	0.426463	+	0.904505i	$0.359760\pi$
$434$	8.82746	−	16.6504i	0.423732	−	0.799242i
$435$	4.00330	+	1.34887i	0.191943	+	0.0646732i
$436$	−0.607699	−	11.2084i	−0.0291035	−	0.536783i
$437$	−0.349054	−	0.210019i	−0.0166975	−	0.0100466i
$438$	−2.59715	+	9.35410i	−0.124097	+	0.446956i
$439$	10.3206	+	37.1713i	0.492574	+	1.77409i	0.622558	+	0.782574i	$0.286093\pi$
$439$	10.3206	+	37.1713i	0.492574	+	1.77409i	−0.129984	+	0.991516i	$0.541493\pi$
$440$	−1.75153	+	1.05386i	−0.0835010	+	0.0502409i
$441$	0.615865	+	0.908332i	0.0293269	+	0.0432539i
$442$	−7.18989	−	0.781947i	−0.341988	−	0.0371934i
$443$	−38.6947	−	4.20831i	−1.83844	−	0.199943i	−0.878045	−	0.478577i	$-0.841153\pi$
$443$	−38.6947	−	4.20831i	−1.83844	−	0.199943i	−0.960397	+	0.278635i	$0.910118\pi$
$444$	0.0151244	+	0.0223068i	0.000717772	+	0.00105863i
$445$	−25.9007	+	15.5840i	−1.22781	+	0.738751i
$446$	−7.89670	−	28.4413i	−0.373920	−	1.34674i
$447$	−3.08572	+	11.1137i	−0.145949	+	0.525662i
$448$	2.08175	+	1.25255i	0.0983535	+	0.0591774i
$449$	−1.31620	−	24.2759i	−0.0621155	−	1.14565i	−0.848945	−	0.528482i	$-0.822762\pi$
$449$	−1.31620	−	24.2759i	−0.0621155	−	1.14565i	0.786829	−	0.617171i	$-0.211721\pi$
$450$	1.29035	+	0.434769i	0.0608276	+	0.0204952i
$451$	0.429117	−	0.809401i	0.0202063	−	0.0381132i
$452$	−10.1517	+	11.9515i	−0.477497	+	0.562153i
$453$	5.33046	−	7.86183i	0.250447	−	0.369381i
$454$	0.0281701	−	0.519567i	0.00132209	−	0.0243845i
$455$	−2.22845	+	5.59299i	−0.104471	+	0.262203i
$456$	0.459605	−	0.212636i	0.0215230	−	0.00995759i
$457$	32.3595	+	7.12286i	1.51371	+	0.333193i	0.892716	−	0.450620i	$-0.148797\pi$
$457$	32.3595	+	7.12286i	1.51371	+	0.333193i	0.620997	+	0.783813i	$0.286728\pi$
$458$	11.2247	+	21.1720i	0.524495	+	0.989303i
$459$	0.900619	+	5.49353i	0.0420373	+	0.256416i
$460$	1.22152	+	0.928573i	0.0569535	+	0.0432949i
$461$	−10.1368	−	4.68978i	−0.472117	−	0.218425i	0.169379	−	0.985551i	$-0.445824\pi$
$461$	−10.1368	−	4.68978i	−0.472117	−	0.218425i	−0.641496	+	0.767126i	$0.721686\pi$
$462$	1.89021	−	1.79050i	0.0879406	−	0.0833018i
$463$	0.423967	−	2.58608i	0.0197034	−	0.120186i	−0.975143	−	0.221575i	$-0.928880\pi$
$463$	0.423967	−	2.58608i	0.0197034	−	0.120186i	0.994847	+	0.101389i	$0.0323287\pi$
$464$	2.09877	−	0.707157i	0.0974328	−	0.0328289i
$465$	5.47656	+	13.7451i	0.253969	+	0.637415i
$466$	−7.45469	−	7.06146i	−0.345332	−	0.327116i
$467$	−7.07058	+	5.37491i	−0.327187	+	0.248721i	−0.755852	−	0.654742i	$-0.772777\pi$
$467$	−7.07058	+	5.37491i	−0.327187	+	0.248721i	0.428665	+	0.903464i	$0.358984\pi$
$468$	−1.26879	+	0.279282i	−0.0586499	+	0.0129098i
$469$	−8.23594	−	9.69610i	−0.380300	−	0.447724i
$470$	3.23553	−	0.351885i	0.149244	−	0.0162312i
$471$	1.36520			0.0629050
$472$	−7.67241	+	0.366239i	−0.353151	+	0.0168575i
$473$	−1.55163			−0.0713441
$474$	−14.1528	+	1.53921i	−0.650059	+	0.0706982i
$475$	−0.446399	−	0.525541i	−0.0204822	−	0.0241135i
$476$	13.2086	−	2.90744i	0.605416	−	0.133262i
$477$	8.47902	−	6.44558i	0.388228	−	0.295123i
$478$	5.31432	+	5.03399i	0.243071	+	0.230249i
$479$	3.32738	+	8.35109i	0.152032	+	0.381571i	0.985191	−	0.171463i	$-0.0548493\pi$
$479$	3.32738	+	8.35109i	0.152032	+	0.381571i	−0.833159	+	0.553034i	$0.813470\pi$
$480$	−1.80760	+	0.609053i	−0.0825054	+	0.0277993i
$481$	−0.00566455	+	0.0345522i	−0.000258281	+	0.00157545i
$482$	−12.3297	+	11.6793i	−0.561602	+	0.531978i
$483$	−1.77372	−	0.820610i	−0.0807071	−	0.0373391i
$484$	−7.84275	−	5.96190i	−0.356489	−	0.270996i
$485$	1.55254	+	9.47006i	0.0704971	+	0.430013i
$486$	0.468408	+	0.883512i	0.0212474	+	0.0400769i
$487$	1.65071	+	0.363348i	0.0748007	+	0.0164649i	0.252213	−	0.967672i	$-0.418842\pi$
$487$	1.65071	+	0.363348i	0.0748007	+	0.0164649i	−0.177412	+	0.984137i	$0.556773\pi$
$488$	3.45157	−	1.59687i	0.156245	−	0.0722867i
$489$	−4.51719	+	11.3373i	−0.204274	+	0.512690i
$490$	−0.113329	+	2.09023i	−0.00511968	+	0.0944269i
$491$	16.2555	−	23.9750i	0.733599	−	1.08198i	−0.259619	−	0.965711i	$-0.583597\pi$
$491$	16.2555	−	23.9750i	0.733599	−	1.08198i	0.993218	−	0.116266i	$-0.0370926\pi$
$492$	0.553425	−	0.651542i	0.0249503	−	0.0293738i
$493$	5.77498	−	10.8928i	0.260092	−	0.490585i
$494$	0.623471	+	0.210072i	0.0280513	+	0.00945158i
$495$	0.110667	+	2.04114i	0.00497412	+	0.0917423i
$496$	6.64659	+	3.99912i	0.298441	+	0.179566i
$497$	5.15513	−	18.5671i	0.231239	−	0.832849i
$498$	1.60205	+	5.77005i	0.0717894	+	0.258562i
$499$	−31.9684	+	19.2347i	−1.43110	+	0.861065i	−0.999166	−	0.0408389i	$-0.986997\pi$
$499$	−31.9684	+	19.2347i	−1.43110	+	0.861065i	−0.431936	+	0.901904i	$0.642169\pi$
$500$	6.80972	+	10.0436i	0.304540	+	0.449163i
$501$	12.0723	+	1.31295i	0.539352	+	0.0586581i
$502$	28.7946	+	3.13160i	1.28516	+	0.139770i
$503$	−21.2782	−	31.3830i	−0.948748	−	1.39930i	−0.916596	−	0.399815i	$-0.869074\pi$
$503$	−21.2782	−	31.3830i	−0.948748	−	1.39930i	−0.0321517	−	0.999483i	$-0.510236\pi$
$504$	2.08175	−	1.25255i	0.0927286	−	0.0557929i
$505$	−1.90207	−	6.85065i	−0.0846412	−	0.304850i
$506$	0.230626	−	0.830639i	0.0102526	−	0.0369264i
$507$	9.69291	+	5.83203i	0.430477	+	0.259010i
$508$	−0.593904	−	10.9539i	−0.0263502	−	0.486001i
$509$	41.8795	+	14.1109i	1.85628	+	0.625453i	0.992603	+	0.121404i	$0.0387397\pi$
$509$	41.8795	+	14.1109i	1.85628	+	0.625453i	0.863675	+	0.504049i	$0.168157\pi$
$510$	−4.97381	+	9.38160i	−0.220244	+	0.415424i
$511$	15.2690	−	17.9761i	0.675463	−	0.795216i
$512$	−0.561187	+	0.827689i	−0.0248012	+	0.0365790i
$513$	0.0274165	−	0.505667i	0.00121047	−	0.0223258i
$514$	−4.57555	+	11.4838i	−0.201819	+	0.506527i
$515$	−7.31205	+	3.38292i	−0.322208	+	0.149069i
$516$	−1.41403	−	0.311251i	−0.0622492	−	0.0137021i
$517$	−0.856497	−	1.61552i	−0.0376687	−	0.0710507i
$518$	−0.0105931	−	0.0646148i	−0.000465432	−	0.00283901i
$519$	−0.463777	−	0.352554i	−0.0203576	−	0.0154754i
$520$	−2.24906	−	1.04053i	−0.0986278	−	0.0456301i
$521$	−19.5256	+	18.4957i	−0.855433	+	0.810310i	−0.983397	−	0.181469i	$-0.941915\pi$
$521$	−19.5256	+	18.4957i	−0.855433	+	0.810310i	0.127963	+	0.991779i	$0.459156\pi$
$522$	0.358298	−	2.18552i	0.0156823	−	0.0956577i
$523$	5.85346	−	1.97226i	0.255954	−	0.0862409i	−0.188400	−	0.982092i	$-0.560330\pi$
$523$	5.85346	−	1.97226i	0.255954	−	0.0862409i	0.444354	+	0.895852i	$0.353433\pi$
$524$	2.71759	+	6.82065i	0.118719	+	0.297961i
$525$	−2.40166	−	2.27497i	−0.104817	−	0.0992880i
$526$	10.4744	−	7.96246i	0.456707	−	0.347180i
$527$	42.1723	−	9.28282i	1.83705	−	0.404366i
$528$	0.693776	+	0.816777i	0.0301927	+	0.0355456i
$529$	22.2219	−	2.41677i	0.966169	−	0.105077i
$530$	20.3159			0.882465
$531$	−3.27024	+	6.95022i	−0.141917	+	0.301614i
$532$	−1.23033			−0.0533417
$533$	1.10409	−	0.120078i	0.0478237	−	0.00520114i
$534$	10.2592	+	12.0781i	0.443959	+	0.522669i
$535$	−16.1160	+	3.54740i	−0.696756	+	0.153368i
$536$	4.16863	−	3.16891i	0.180057	−	0.136876i
$537$	−2.81516	−	2.66666i	−0.121483	−	0.115075i
$538$	−0.222439	−	0.558279i	−0.00959001	−	0.0240691i
$539$	1.11451	−	0.375521i	0.0480052	−	0.0161748i
$540$	−0.308591	+	1.88232i	−0.0132797	+	0.0810024i
$541$	27.2485	−	25.8112i	1.17151	−	1.10971i	0.179468	−	0.983764i	$-0.442562\pi$
$541$	27.2485	−	25.8112i	1.17151	−	1.10971i	0.992037	−	0.125945i	$-0.0401963\pi$
$542$	−24.0902	−	11.1453i	−1.03476	−	0.478733i
$543$	−12.1525	−	9.23807i	−0.521513	−	0.396444i
$544$	0.900619	+	5.49353i	0.0386137	+	0.235533i
$545$	−10.0290	−	18.9167i	−0.429595	−	0.810303i
$546$	3.08256	+	0.678522i	0.131921	+	0.0290381i
$547$	−35.3611	+	16.3598i	−1.51193	+	0.699493i	−0.988310	−	0.152459i	$-0.951281\pi$
$547$	−35.3611	+	16.3598i	−1.51193	+	0.699493i	−0.523620	+	0.851952i	$0.675419\pi$
$548$	3.16571	−	7.94533i	0.135232	−	0.339408i
$549$	0.205894	−	3.79749i	0.00878733	−	0.162073i
$550$	0.818882	−	1.20776i	0.0349172	−	0.0514991i
$551$	−0.726073	+	0.854799i	−0.0309318	+	0.0364157i
$552$	0.376796	−	0.710713i	0.0160375	−	0.0302500i
$553$	32.7767	+	11.0438i	1.39381	+	0.469628i
$554$	1.68027	+	30.9908i	0.0713880	+	1.31667i
$555$	0.0440487	+	0.0265032i	0.00186976	+	0.00112500i
$556$	0.596266	−	2.14756i	0.0252873	−	0.0910767i
$557$	8.09495	+	29.1554i	0.342994	+	1.23535i	0.911027	+	0.412347i	$0.135291\pi$
$557$	8.09495	+	29.1554i	0.342994	+	1.23535i	−0.568033	+	0.823006i	$0.692295\pi$
$558$	6.64659	−	3.99912i	0.281373	−	0.169296i
$559$	−1.05561	−	1.55691i	−0.0446477	−	0.0658504i
$560$	4.60703	+	0.501045i	0.194682	+	0.0211730i
$561$	5.93080	+	0.645014i	0.250399	+	0.0272325i
$562$	−1.09835	−	1.61994i	−0.0463310	−	0.0683332i
$563$	−26.9076	+	16.1898i	−1.13402	+	0.682318i	−0.953542	−	0.301261i	$-0.902592\pi$
$563$	−26.9076	+	16.1898i	−1.13402	+	0.682318i	−0.180479	+	0.983579i	$0.557765\pi$
$564$	−0.456473	−	1.64407i	−0.0192210	−	0.0692276i
$565$	−8.00202	+	28.8207i	−0.336648	+	1.21250i
$566$	0.523859	+	0.315196i	0.0220195	+	0.0132487i
$567$	−0.131532	−	2.42596i	−0.00552381	−	0.101881i
$568$	7.51621	+	2.53251i	0.315373	+	0.106262i
$569$	12.9477	−	24.4219i	0.542795	−	1.02382i	−0.448701	−	0.893682i	$-0.648113\pi$
$569$	12.9477	−	24.4219i	0.542795	−	1.02382i	0.991496	−	0.130137i	$-0.0415419\pi$
$570$	0.625345	−	0.736213i	0.0261928	−	0.0308366i
$571$	−15.2398	+	22.4770i	−0.637766	+	0.940635i	0.362197	+	0.932101i	$0.382027\pi$
$571$	−15.2398	+	22.4770i	−0.637766	+	0.940635i	−0.999964	+	0.00853331i	$0.997284\pi$
$572$	−0.0753755	+	1.39022i	−0.00315161	+	0.0581280i
$573$	−6.32822	+	15.8826i	−0.264365	+	0.663506i
$574$	−1.88494	+	0.872068i	−0.0786760	+	0.0363994i
$575$	−1.06971	−	0.235460i	−0.0446099	−	0.00981938i
$576$	0.468408	+	0.883512i	0.0195170	+	0.0368130i
$577$	−1.17472	−	7.16549i	−0.0489044	−	0.298303i	0.951038	−	0.309075i	$-0.100019\pi$
$577$	−1.17472	−	7.16549i	−0.0489044	−	0.298303i	−0.999942	+	0.0107718i	$0.996571\pi$
$578$	11.1374	+	8.46640i	0.463253	+	0.352156i
$579$	−15.5138	−	7.17746i	−0.644732	−	0.298285i
$580$	3.06692	−	2.90514i	0.127347	−	0.120629i
$581$	2.35373	−	14.3571i	0.0976490	−	0.595633i
$582$	4.76768	−	1.60642i	0.197627	−	0.0665882i
$583$	−4.22476	−	10.6033i	−0.174972	−	0.439145i
$584$	7.04793	+	6.67616i	0.291646	+	0.276261i
$585$	−1.97280	+	1.49968i	−0.0815651	+	0.0620042i
$586$	28.5220	−	6.27816i	1.17823	−	0.259348i
$587$	−8.79603	−	10.3555i	−0.363051	−	0.427416i	0.550062	−	0.835124i	$-0.314604\pi$
$587$	−8.79603	−	10.3555i	−0.363051	−	0.427416i	−0.913113	+	0.407708i	$0.866328\pi$
$588$	1.09100	−	0.118653i	0.0449920	−	0.00489318i
$589$	−3.92819			−0.161858
$590$	−12.9888	+	6.77899i	−0.534741	+	0.279087i
$591$	−10.6581			−0.438414
$592$	0.0267927	−	0.00291389i	0.00110117	−	0.000119760i
$593$	−9.72673	−	11.4512i	−0.399429	−	0.470244i	0.525274	−	0.850933i	$-0.323963\pi$
$593$	−9.72673	−	11.4512i	−0.399429	−	0.470244i	−0.924703	+	0.380689i	$0.875687\pi$
$594$	1.04660	−	0.230375i	0.0429426	−	0.00945239i
$595$	20.5376	−	15.6123i	0.841958	−	0.640040i
$596$	8.37375	+	7.93204i	0.343002	+	0.324909i
$597$	7.85800	+	19.7221i	0.321607	+	0.807172i
$598$	0.990366	−	0.333693i	0.0404991	−	0.0136457i
$599$	−0.476158	+	2.90444i	−0.0194553	+	0.118672i	−0.994769	−	0.102153i	$-0.967427\pi$
$599$	−0.476158	+	2.90444i	−0.0194553	+	0.118672i	0.975313	+	0.220825i	$0.0708751\pi$
$600$	0.988533	−	0.936389i	0.0403567	−	0.0382279i
$601$	−14.0650	−	6.50717i	−0.573724	−	0.265433i	0.111501	−	0.993764i	$-0.464434\pi$
$601$	−14.0650	−	6.50717i	−0.573724	−	0.265433i	−0.685225	+	0.728331i	$0.740296\pi$
$602$	2.80038	+	2.12879i	0.114135	+	0.0867632i
$603$	−0.847148	−	5.16737i	−0.0344985	−	0.210432i
$604$	−4.44920	−	8.39207i	−0.181035	−	0.341469i
$605$	−18.3520	−	4.03959i	−0.746116	−	0.164233i
$606$	−3.38288	+	1.56509i	−0.137420	+	0.0635773i
$607$	−0.368286	+	0.924327i	−0.0149483	+	0.0375173i	−0.936261	−	0.351304i	$-0.885738\pi$
$607$	−0.368286	+	0.924327i	−0.0149483	+	0.0375173i	0.921313	+	0.388821i	$0.127118\pi$
$608$	0.0274165	−	0.505667i	0.00111189	−	0.0205075i
$609$	−3.01955	+	4.45351i	−0.122358	+	0.180465i
$610$	4.69625	−	5.52885i	0.190146	−	0.223857i
$611$	1.03833	−	1.95849i	0.0420062	−	0.0792321i
$612$	5.27546	+	1.77751i	0.213248	+	0.0718516i
$613$	0.387933	+	7.15500i	0.0156685	+	0.288988i	0.995858	+	0.0909248i	$0.0289823\pi$
$613$	0.387933	+	7.15500i	0.0156685	+	0.288988i	−0.980189	+	0.198063i	$0.936535\pi$
$614$	5.13207	+	3.08787i	0.207114	+	0.124616i
$615$	0.436233	−	1.57117i	0.0175906	−	0.0633557i
$616$	−0.696540	−	2.50871i	−0.0280644	−	0.101079i
$617$	9.96106	−	5.99337i	0.401017	−	0.241284i	−0.300731	−	0.953709i	$-0.597231\pi$
$617$	9.96106	−	5.99337i	0.401017	−	0.241284i	0.701748	+	0.712425i	$0.252403\pi$
$618$	2.37034	+	3.49599i	0.0953490	+	0.140629i
$619$	18.2664	+	1.98659i	0.734190	+	0.0798480i	0.467573	−	0.883955i	$-0.345129\pi$
$619$	18.2664	+	1.98659i	0.734190	+	0.0798480i	0.266617	+	0.963803i	$0.414094\pi$
$620$	14.7093	+	1.59973i	0.590738	+	0.0642466i
$621$	−0.451429	−	0.665808i	−0.0181152	−	0.0267180i
$622$	−13.3370	+	8.02460i	−0.534765	+	0.321757i
$623$	−10.3001	−	37.0975i	−0.412664	−	1.48628i
$624$	−0.347564	+	1.25181i	−0.0139137	+	0.0501126i
$625$	13.9992	+	8.42304i	0.559968	+	0.336922i
$626$	−0.925187	−	17.0641i	−0.0369779	−	0.682017i
$627$	−0.514290	−	0.173284i	−0.0205387	−	0.00692031i
$628$	0.639470	−	1.20617i	0.0255176	−	0.0481314i
$629$	0.0971281	−	0.114348i	0.00387275	−	0.00455936i
$630$	2.60065	−	3.83567i	0.103612	−	0.152817i
$631$	−0.728918	+	13.4441i	−0.0290178	+	0.535201i	0.947499	+	0.319759i	$0.103602\pi$
$631$	−0.728918	+	13.4441i	−0.0290178	+	0.535201i	−0.976517	+	0.215442i	$0.930881\pi$
$632$	−5.26938	+	13.2251i	−0.209605	+	0.526068i
$633$	−9.47287	+	4.38262i	−0.376513	+	0.174193i
$634$	−27.8629	−	6.13310i	−1.10658	−	0.243576i
$635$	−9.80134	−	18.4873i	−0.388954	−	0.733645i
$636$	−1.72311	−	10.5105i	−0.0683256	−	0.416768i
$637$	1.13503	+	0.862825i	0.0449714	+	0.0341864i
$638$	−2.15404	−	0.996564i	−0.0852792	−	0.0394543i
$639$	5.75816	−	5.45442i	0.227789	−	0.215773i
$640$	−0.308591	+	1.88232i	−0.0121981	+	0.0744054i
$641$	11.6934	−	3.93995i	0.461860	−	0.155619i	−0.0787458	−	0.996895i	$-0.525092\pi$
$641$	11.6934	−	3.93995i	0.461860	−	0.155619i	0.540606	+	0.841276i	$0.318195\pi$
$642$	3.20215	+	8.03680i	0.126379	+	0.317187i
$643$	−29.3306	−	27.7834i	−1.15669	−	1.09567i	−0.994043	−	0.108986i	$-0.965240\pi$
$643$	−29.3306	−	27.7834i	−1.15669	−	1.09567i	−0.162643	−	0.986685i	$-0.552002\pi$
$644$	−1.55584	+	1.18272i	−0.0613089	+	0.0466058i
$645$	−2.69719	+	0.593697i	−0.106202	+	0.0233768i
$646$	−1.82506	−	2.14862i	−0.0718059	−	0.0845365i
$647$	9.14882	−	0.994994i	0.359677	−	0.0391173i	0.0735034	−	0.997295i	$-0.476582\pi$
$647$	9.14882	−	0.994994i	0.359677	−	0.0391173i	0.286174	+	0.958178i	$0.407617\pi$
$648$	1.00000			0.0392837
$649$	6.23919	+	5.36946i	0.244910	+	0.210770i
$650$	1.76898			0.0693850
$651$	−18.7352	+	2.03757i	−0.734289	+	0.0798588i
$652$	7.90074	+	9.30147i	0.309417	+	0.364274i
$653$	25.1009	−	5.52513i	0.982275	−	0.216215i	0.305329	−	0.952247i	$-0.401234\pi$
$653$	25.1009	−	5.52513i	0.982275	−	0.216215i	0.676947	+	0.736032i	$0.263303\pi$
$654$	−8.93600	+	6.79297i	−0.349425	+	0.265626i
$655$	10.1674	+	9.63104i	0.397272	+	0.376316i
$656$	−0.316416	−	0.794145i	−0.0123540	−	0.0310062i
$657$	9.19978	−	3.09977i	0.358917	−	0.120933i
$658$	−0.670649	+	4.09078i	−0.0261446	+	0.159475i
$659$	−21.3537	+	20.2273i	−0.831820	+	0.787942i	−0.979574	−	0.201082i	$-0.935554\pi$
$659$	−21.3537	+	20.2273i	−0.831820	+	0.787942i	0.147754	+	0.989024i	$0.452796\pi$
$660$	1.85521	+	0.858310i	0.0722139	+	0.0334097i
$661$	−2.51468	−	1.91161i	−0.0978095	−	0.0743529i	0.555126	−	0.831766i	$-0.312670\pi$
$661$	−2.51468	−	1.91161i	−0.0978095	−	0.0743529i	−0.652936	+	0.757413i	$0.726463\pi$
$662$	2.13983	+	13.0524i	0.0831670	+	0.507296i
$663$	3.38766	+	6.38981i	0.131566	+	0.248160i
$664$	5.84832	+	1.28731i	0.226959	+	0.0499574i
$665$	−2.12990	+	0.985397i	−0.0825940	+	0.0382120i
$666$	0.00997549	−	0.0250366i	0.000386543	−	0.000970149i
$667$	−0.0964508	+	1.77893i	−0.00373459	+	0.0688805i
$668$	6.81478	−	10.0511i	0.263672	−	0.388887i
$669$	−19.1091	+	22.4969i	−0.738799	+	0.869781i
$670$	4.67851	−	8.82461i	0.180747	−	0.340924i
$671$	−3.86224	−	1.30134i	−0.149100	−	0.0502377i
$672$	−0.131532	−	2.42596i	−0.00507394	−	0.0935833i
$673$	31.0007	+	18.6525i	1.19499	+	0.719000i	0.967028	−	0.254670i	$-0.0819669\pi$
$673$	31.0007	+	18.6525i	1.19499	+	0.719000i	0.227960	+	0.973671i	$0.426795\pi$
$674$	1.58133	−	5.69545i	0.0609107	−	0.219381i
$675$	−0.364273	−	1.31199i	−0.0140209	−	0.0504987i
$676$	9.69291	−	5.83203i	0.372804	−	0.224309i
$677$	12.8940	+	19.0173i	0.495557	+	0.730892i	0.990421	−	0.138078i	$-0.0440925\pi$
$677$	12.8940	+	19.0173i	0.495557	+	0.730892i	−0.494864	+	0.868970i	$0.664782\pi$
$678$	15.5892	+	1.69542i	0.598698	+	0.0651124i
$679$	−12.1514	−	1.32154i	−0.466327	−	0.0507161i
$680$	5.95899	+	8.78885i	0.228517	+	0.337037i
$681$	−0.445849	+	0.268258i	−0.0170850	+	0.0102797i
$682$	−2.22390	−	8.00978i	−0.0851577	−	0.306710i
$683$	−2.74428	+	9.88401i	−0.105007	+	0.378201i	−0.997315	−	0.0732251i	$-0.976671\pi$
$683$	−2.74428	+	9.88401i	−0.105007	+	0.378201i	0.892308	+	0.451426i	$0.149085\pi$
$684$	−0.433921	−	0.261082i	−0.0165914	−	0.00998271i
$685$	−0.883223	−	16.2901i	−0.0337462	−	0.622412i
$686$	−18.6431	−	6.28158i	−0.711795	−	0.239832i
$687$	11.2247	−	21.1720i	0.428248	−	0.807762i
$688$	−0.937338	+	1.10352i	−0.0357357	+	0.0420713i
$689$	7.76522	−	11.4528i	0.295831	−	0.436319i
$690$	0.0830702	−	1.53214i	0.00316243	−	0.0583275i
$691$	−10.0252	+	25.1613i	−0.381375	+	0.957180i	0.605522	+	0.795829i	$0.292965\pi$
$691$	−10.0252	+	25.1613i	−0.381375	+	0.957180i	−0.986897	+	0.161351i	$0.948415\pi$
$692$	−0.528723	+	0.244613i	−0.0200990	+	0.00929880i
$693$	−2.54274	−	0.559700i	−0.0965908	−	0.0212612i
$694$	4.81875	+	9.08913i	0.182917	+	0.345019i
$695$	−0.687787	−	4.19532i	−0.0260893	−	0.159137i
$696$	−1.76311	−	1.34028i	−0.0668304	−	0.0508031i
$697$	−4.31906	−	1.99821i	−0.163596	−	0.0756875i
$698$	−12.9908	+	12.3055i	−0.491707	+	0.465770i
$699$	−1.66122	+	10.1330i	−0.0628330	+	0.383264i
$700$	−3.13493	+	1.05628i	−0.118489	+	0.0399236i
$701$	−1.63413	−	4.10137i	−0.0617204	−	0.154906i	0.894882	−	0.446303i	$-0.147260\pi$
$701$	−1.63413	−	4.10137i	−0.0617204	−	0.154906i	−0.956602	+	0.291396i	$0.905880\pi$
$702$	0.943189	+	0.893436i	0.0355984	+	0.0337206i
$703$	−0.0108652	+	0.00825949i	−0.000409788	+	0.000311513i
$704$	1.04660	−	0.230375i	0.0394453	−	0.00868257i
$705$	−2.10699	−	2.48054i	−0.0793538	−	0.0934225i
$706$	−1.29920	+	0.141296i	−0.0488959	+	0.00531775i
$707$	9.05575			0.340576
$708$	4.60879	+	6.14484i	0.173209	+	0.230937i
$709$	−29.1374			−1.09428			−0.547139	−	0.837042i	$-0.684283\pi$
$709$	−29.1374			−1.09428			−0.547139	+	0.837042i	$0.684283\pi$
$710$	15.0401	−	1.63571i	0.564444	−	0.0613870i
$711$	9.21635	+	10.8503i	0.345640	+	0.406919i
$712$	15.4766	−	3.40666i	0.580011	−	0.127670i
$713$	−4.96748	+	3.77618i	−0.186034	+	0.141419i
$714$	−9.81896	−	9.30101i	−0.367465	−	0.348082i
$715$	0.982965	+	2.46706i	0.0367608	+	0.0922627i
$716$	−3.67468	+	1.23814i	−0.137329	+	0.0462716i
$717$	1.18425	−	7.22361i	0.0442267	−	0.269771i
$718$	−18.8164	+	17.8239i	−0.702223	+	0.665181i
$719$	−16.8392	−	7.79066i	−0.627997	−	0.290542i	0.0799597	−	0.996798i	$-0.474521\pi$
$719$	−16.8392	−	7.79066i	−0.627997	−	0.290542i	−0.707957	+	0.706256i	$0.750383\pi$
$720$	1.51851	+	1.15434i	0.0565915	+	0.0430198i
$721$	−1.66017	−	10.1266i	−0.0618281	−	0.377135i
$722$	−8.77964	−	16.5602i	−0.326744	−	0.616305i
$723$	16.5861	+	3.65088i	0.616844	+	0.135778i
$724$	−13.8543	+	6.40967i	−0.514890	+	0.238213i
$725$	−1.11618	+	2.80141i	−0.0414540	+	0.104042i
$726$	−0.533352	+	9.83710i	−0.0197946	+	0.365089i
$727$	−7.57456	+	11.1716i	−0.280925	+	0.414333i	−0.941806	−	0.336158i	$-0.890872\pi$
$727$	−7.57456	+	11.1716i	−0.280925	+	0.414333i	0.660881	+	0.750491i	$0.270183\pi$
$728$	2.04338	−	2.40565i	0.0757326	−	0.0891593i
$729$	0.468408	−	0.883512i	0.0173485	−	0.0327227i
$730$	17.5481	+	5.91266i	0.649486	+	0.218837i
$731$	0.436368	+	8.04834i	0.0161397	+	0.297679i
$732$	−3.25868	−	1.96069i	−0.120444	−	0.0724690i
$733$	0.0355341	−	0.127982i	0.00131248	−	0.00472713i	−0.962891	−	0.269891i	$-0.913012\pi$
$733$	0.0355341	−	0.127982i	0.00131248	−	0.00472713i	0.964203	+	0.265164i	$0.0854261\pi$
$734$	−2.92760	−	10.5443i	−0.108060	−	0.389195i
$735$	1.79366	−	1.07921i	0.0661601	−	0.0398072i
$736$	−0.451429	−	0.665808i	−0.0166399	−	0.0245420i
$737$	−5.57868	−	0.606718i	−0.205493	−	0.0223488i
$738$	−0.849849	−	0.0924267i	−0.0312834	−	0.00340227i
$739$	−11.1450	−	16.4376i	−0.409975	−	0.604668i	0.565508	−	0.824743i	$-0.308680\pi$
$739$	−11.1450	−	16.4376i	−0.409975	−	0.604668i	−0.975483	+	0.220075i	$0.929370\pi$
$740$	0.0440487	−	0.0265032i	0.00161926	−	0.000974277i
$741$	−0.176010	−	0.633930i	−0.00646588	−	0.0232880i
$742$	−6.92265	+	24.9331i	−0.254138	+	0.915323i
$743$	−3.11157	−	1.87217i	−0.114152	−	0.0686831i	0.457333	−	0.889296i	$-0.348805\pi$
$743$	−3.11157	−	1.87217i	−0.114152	−	0.0686831i	−0.571485	+	0.820613i	$0.693632\pi$
$744$	−0.419952	−	7.74556i	−0.0153962	−	0.283966i
$745$	20.8492	+	7.02491i	0.763855	+	0.257373i
$746$	0.0593473	−	0.111941i	0.00217286	−	0.00409845i
$747$	3.87676	−	4.56407i	0.141843	−	0.166991i
$748$	3.34792	−	4.93781i	0.122412	−	0.180544i
$749$	1.13791	−	20.9875i	0.0415784	−	0.766868i
$750$	4.49144	−	11.2727i	0.164004	−	0.411620i
$751$	18.5837	−	8.59775i	0.678130	−	0.313736i	−0.0504208	−	0.998728i	$-0.516056\pi$
$751$	18.5837	−	8.59775i	0.678130	−	0.313736i	0.728551	+	0.684992i	$0.240194\pi$
$752$	−1.66637	−	0.366795i	−0.0607662	−	0.0133756i
$753$	−13.5672	−	25.5904i	−0.494415	−	0.932565i
$754$	−0.465489	−	2.83936i	−0.0169521	−	0.103403i
$755$	−14.4236	−	10.9646i	−0.524929	−	0.399041i
$756$	−2.20497	−	1.02013i	−0.0801941	−	0.0371017i
$757$	−9.24321	+	8.75564i	−0.335950	+	0.318229i	−0.837014	−	0.547181i	$-0.815701\pi$
$757$	−9.24321	+	8.75564i	−0.335950	+	0.318229i	0.501064	+	0.865410i	$0.332942\pi$
$758$	4.64979	−	28.3625i	0.168888	−	1.03017i
$759$	−0.816935	+	0.275257i	−0.0296528	+	0.00999121i
$760$	−0.357536	−	0.897348i	−0.0129692	−	0.0325502i
$761$	−9.99780	−	9.47042i	−0.362420	−	0.343302i	0.484723	−	0.874668i	$-0.338921\pi$
$761$	−9.99780	−	9.47042i	−0.362420	−	0.343302i	−0.847143	+	0.531365i	$0.821679\pi$
$762$	−8.73314	+	6.63876i	−0.316368	+	0.240497i
$763$	26.6333	−	5.86244i	0.964192	−	0.212235i
$764$	11.0683	+	13.0306i	0.400437	+	0.471431i
$765$	10.5563	−	1.14807i	0.381663	−	0.0415084i
$766$	2.07685			0.0750397
$767$	−1.14306	+	9.91340i	−0.0412736	+	0.357952i
$768$	1.00000			0.0360844
$769$	−28.0341	+	3.04890i	−1.01094	+	0.109946i	−0.598569	−	0.801071i	$-0.704264\pi$
$769$	−28.0341	+	3.04890i	−1.01094	+	0.109946i	−0.412368	+	0.911017i	$0.635298\pi$
$770$	−3.21509	−	3.78510i	−0.115864	−	0.136406i
$771$	12.0727	−	2.65741i	0.434789	−	0.0957043i
$772$	−13.6082	+	10.3447i	−0.489769	+	0.372313i
$773$	−17.2797	−	16.3682i	−0.621509	−	0.588725i	0.310761	−	0.950488i	$-0.399416\pi$
$773$	−17.2797	−	16.3682i	−0.621509	−	0.588725i	−0.932270	+	0.361763i	$0.882175\pi$
$774$	0.535916	+	1.34505i	0.0192631	+	0.0483467i
$775$	−10.0092	+	3.37248i	−0.359539	+	0.121143i
$776$	0.813932	−	4.96477i	0.0292185	−	0.178225i
$777$	−0.0475363	+	0.0450287i	−0.00170535	+	0.00161540i
$778$	−15.8341	−	7.32561i	−0.567678	−	0.262636i
$779$	0.344636	+	0.261986i	0.0123479	+	0.00938662i
$780$	0.400912	+	2.44545i	0.0143549	+	0.0875612i
$781$	−3.98135	−	7.50962i	−0.142464	−	0.268715i
$782$	−4.37339	−	0.962657i	−0.156392	−	0.0344245i
$783$	−2.01001	+	0.929928i	−0.0718317	+	0.0332329i
$784$	0.406201	−	1.01949i	0.0145072	−	0.0364103i
$785$	0.140980	−	2.60023i	0.00503181	−	0.0928062i
$786$	4.12030	−	6.07698i	0.146966	−	0.216759i
$787$	−13.2143	+	15.5571i	−0.471038	+	0.554549i	−0.945456	−	0.325751i	$-0.894383\pi$
$787$	−13.2143	+	15.5571i	−0.471038	+	0.554549i	0.474417	+	0.880300i	$0.342659\pi$
$788$	−4.99233	+	9.41652i	−0.177844	+	0.335450i
$789$	−12.4686	−	4.20115i	−0.443892	−	0.149565i
$790$	1.47014	+	27.1151i	0.0523052	+	0.964713i
$791$	−32.6441	−	19.6413i	−1.16069	−	0.698365i
$792$	0.286699	−	1.03260i	0.0101874	−	0.0366917i
$793$	−1.32181	−	4.76072i	−0.0469388	−	0.169058i
$794$	−21.9106	+	13.1832i	−0.777580	+	0.467854i
$795$	−11.4010	−	16.8152i	−0.404352	−	0.596375i
$796$	21.1055	+	2.29536i	0.748063	+	0.0813568i
$797$	−29.9921	−	3.26184i	−1.06238	−	0.115540i	−0.439797	−	0.898097i	$-0.644950\pi$
$797$	−29.9921	−	3.26184i	−1.06238	−	0.115540i	−0.622579	+	0.782557i	$0.713915\pi$
$798$	0.690447	+	1.01833i	0.0244416	+	0.0360486i
$799$	−8.13887	+	4.89700i	−0.287933	+	0.173243i
$800$	−0.364273	−	1.31199i	−0.0128790	−	0.0463860i
$801$	4.23955	−	15.2695i	0.149797	−	0.539521i
$802$	−20.1542	−	12.1264i	−0.711671	−	0.428198i
$803$	−0.563240	−	10.3883i	−0.0198763	−	0.366597i
$804$	−4.96225	−	1.67198i	−0.175005	−	0.0589661i
$805$	−1.74615	+	3.29358i	−0.0615436	+	0.116084i
$806$	6.52407	−	7.68073i	0.229801	−	0.270542i
$807$	−0.337252	+	0.497409i	−0.0118718	+	0.0175096i
$808$	−0.201796	+	3.72191i	−0.00709917	+	0.130937i
$809$	−6.28043	+	15.7627i	−0.220808	+	0.554187i	−0.997093	−	0.0761957i	$-0.975723\pi$
$809$	−6.28043	+	15.7627i	−0.220808	+	0.554187i	0.776285	+	0.630382i	$0.217102\pi$
$810$	1.73116	−	0.800919i	0.0608267	−	0.0281414i
$811$	−35.1782	−	7.74330i	−1.23527	−	0.271904i	−0.451115	−	0.892466i	$-0.648974\pi$
$811$	−35.1782	−	7.74330i	−1.23527	−	0.271904i	−0.784158	+	0.620562i	$0.786905\pi$
$812$	2.52034	+	4.75387i	0.0884467	+	0.166828i
$813$	4.29426	+	26.1938i	0.150606	+	0.918658i
$814$	−0.0229927	−	0.0174786i	−0.000805894	−	0.000612625i
$815$	21.1271	+	9.77446i	0.740052	+	0.342384i
$816$	4.04152	−	3.82833i	0.141482	−	0.134018i
$817$	0.118622	−	0.723562i	0.00415006	−	0.0253142i
$818$	−11.5247	+	3.88312i	−0.402951	+	0.135770i
$819$	−1.16829	−	2.93218i	−0.0408232	−	0.102458i
$820$	−1.18381	−	1.12137i	−0.0413405	−	0.0391598i
$821$	−12.7251	+	9.67338i	−0.444110	+	0.337603i	−0.803210	−	0.595695i	$-0.796877\pi$
$821$	−12.7251	+	9.67338i	−0.444110	+	0.337603i	0.359101	+	0.933299i	$0.383083\pi$
$822$	−8.35282	+	1.83859i	−0.291338	+	0.0641283i
$823$	−16.4663	−	19.3856i	−0.573980	−	0.675741i	0.396190	−	0.918169i	$-0.370332\pi$
$823$	−16.4663	−	19.3856i	−0.573980	−	0.675741i	−0.970170	+	0.242428i	$0.922056\pi$
$824$	4.19904	−	0.456673i	0.146280	−	0.0159089i
$825$	−1.45920			−0.0508027
$826$	−3.89372	−	18.2508i	−0.135480	−	0.635025i
$827$	−19.8700			−0.690946			−0.345473	−	0.938429i	$-0.612282\pi$
$827$	−19.8700			−0.690946			−0.345473	+	0.938429i	$0.612282\pi$
$828$	−0.799703	+	0.0869729i	−0.0277916	+	0.00302252i
$829$	−0.507278	−	0.597214i	−0.0176185	−	0.0207421i	0.753282	−	0.657697i	$-0.228469\pi$
$829$	−0.507278	−	0.597214i	−0.0176185	−	0.0207421i	−0.770901	+	0.636955i	$0.780194\pi$
$830$	11.1554	−	2.45549i	0.387209	−	0.0852312i
$831$	24.7078	−	18.7824i	0.857105	−	0.651554i
$832$	0.943189	+	0.893436i	0.0326992	+	0.0309743i
$833$	−2.26127	−	5.67536i	−0.0783483	−	0.196640i
$834$	−2.11213	+	0.711658i	−0.0731369	+	0.0246427i
$835$	3.74739	−	22.8580i	0.129684	−	0.791035i
$836$	−0.393996	+	0.373213i	−0.0136266	+	0.0129078i
$837$	−7.04001	−	3.25705i	−0.243338	−	0.112580i
$838$	8.92500	+	6.78461i	0.308309	+	0.234370i
$839$	7.78026	+	47.4575i	0.268604	+	1.63841i	0.684508	+	0.729006i	$0.260017\pi$
$839$	7.78026	+	47.4575i	0.268604	+	1.63841i	−0.415903	+	0.909409i	$0.636534\pi$
$840$	−2.17070	−	4.09437i	−0.0748961	−	0.141269i
$841$	−23.5318	−	5.17974i	−0.811441	−	0.178612i
$842$	3.82254	−	1.76849i	0.131733	−	0.0609463i
$843$	−0.724430	+	1.81818i	−0.0249507	+	0.0626215i
$844$	−0.565078	+	10.4223i	−0.0194508	+	0.358749i
$845$	12.1090	−	17.8594i	0.416561	−	0.614382i
$846$	−1.10461	+	1.30045i	−0.0379772	+	0.0447102i
$847$	11.2111	−	21.1465i	0.385219	−	0.726601i
$848$	−10.0933	−	3.40081i	−0.346604	−	0.116784i
$849$	−0.0330991	−	0.610476i	−0.00113596	−	0.0209515i
$850$	−6.49496	−	3.90789i	−0.222775	−	0.134040i
$851$	−0.00579992	+	0.0208894i	−0.000198819	+	0.000716081i
$852$	−2.12187	−	7.64230i	−0.0726942	−	0.261821i
$853$	−16.0485	+	9.65605i	−0.549489	+	0.330617i	−0.763077	−	0.646307i	$-0.776313\pi$
$853$	−16.0485	+	9.65605i	−0.549489	+	0.330617i	0.213588	+	0.976924i	$0.431485\pi$
$854$	5.18516	+	7.64754i	0.177432	+	0.261693i
$855$	−0.960291	−	0.104438i	−0.0328412	−	0.00357170i
$856$	8.60052	+	0.935363i	0.293960	+	0.0319701i
$857$	−30.9260	−	45.6124i	−1.05641	−	1.55809i	−0.807771	−	0.589496i	$-0.799326\pi$
$857$	−30.9260	−	45.6124i	−1.05641	−	1.55809i	−0.248641	−	0.968596i	$-0.579984\pi$
$858$	1.19297	−	0.717785i	0.0407273	−	0.0245048i
$859$	−7.38894	−	26.6126i	−0.252107	−	0.908009i	−0.975941	−	0.218034i	$-0.930036\pi$
$859$	−7.38894	−	26.6126i	−0.252107	−	0.908009i	0.723834	−	0.689974i	$-0.242378\pi$
$860$	−0.738850	+	2.66110i	−0.0251946	+	0.0907427i
$861$	1.77961	+	1.07075i	0.0606488	+	0.0364912i
$862$	−0.607949	−	11.2130i	−0.0207068	−	0.381915i
$863$	33.8001	+	11.3886i	1.15057	+	0.387672i	0.829019	−	0.559220i	$-0.188899\pi$
$863$	33.8001	+	11.3886i	1.15057	+	0.387672i	0.321551	+	0.946892i	$0.395796\pi$
$864$	0.468408	−	0.883512i	0.0159356	−	0.0300577i
$865$	−0.719387	+	0.846928i	−0.0244599	+	0.0287964i
$866$	9.65251	−	14.2364i	0.328006	−	0.483772i
$867$	0.757404	−	13.9695i	0.0257228	−	0.474429i
$868$	−6.97549	+	17.5072i	−0.236764	+	0.594232i
$869$	13.8463	−	6.40599i	0.469704	−	0.217308i
$870$	−4.12567	−	0.908128i	−0.139873	−	0.0307884i
$871$	−3.18653	−	6.01044i	−0.107972	−	0.203656i
$872$	1.81597	+	11.0769i	0.0614966	+	0.375113i
$873$	−4.00518	−	3.04466i	−0.135555	−	0.103046i
$874$	0.369715	+	0.171048i	0.0125058	+	0.00578579i
$875$	−21.4031	+	20.2741i	−0.723556	+	0.685389i
$876$	1.57057	−	9.58007i	0.0530647	−	0.323681i
$877$	35.8597	−	12.0825i	1.21090	−	0.407998i	0.359810	−	0.933025i	$-0.382841\pi$
$877$	35.8597	−	12.0825i	1.21090	−	0.407998i	0.851085	+	0.525027i	$0.175945\pi$
$878$	−14.2790	−	35.8376i	−0.481893	−	1.20946i
$879$	−21.2025	−	20.0841i	−0.715143	−	0.677420i
$880$	1.62732	−	1.23706i	0.0548570	−	0.0417012i
$881$	36.2538	−	7.98006i	1.22142	−	0.268855i	0.442956	−	0.896543i	$-0.353930\pi$
$881$	36.2538	−	7.98006i	1.22142	−	0.268855i	0.778465	+	0.627688i	$0.215999\pi$
$882$	−0.710462	−	0.836421i	−0.0239225	−	0.0281638i
$883$	37.6612	−	4.09590i	1.26740	−	0.137838i	0.550393	−	0.834905i	$-0.314478\pi$
$883$	37.6612	−	4.09590i	1.26740	−	0.137838i	0.717006	+	0.697067i	$0.245512\pi$
$884$	7.23228			0.243248
$885$	12.9001	+	6.94642i	0.433631	+	0.233501i
$886$	38.9229			1.30764
$887$	35.3853	−	3.84839i	1.18812	−	0.129216i	0.507369	−	0.861729i	$-0.330618\pi$
$887$	35.3853	−	3.84839i	1.18812	−	0.129216i	0.680753	+	0.732513i	$0.261653\pi$
$888$	−0.0174475	−	0.0205408i	−0.000585501	−	0.000689305i
$889$	26.0287	−	5.72936i	0.872976	−	0.192157i
$890$	24.0640	−	18.2930i	0.806627	−	0.613182i
$891$	−0.778019	−	0.736978i	−0.0260646	−	0.0246897i
$892$	10.9255	+	27.4208i	0.365811	+	0.918118i
$893$	0.818835	−	0.275898i	0.0274013	−	0.00923257i
$894$	1.86602	−	11.3822i	0.0624090	−	0.380678i
$895$	−5.36979	+	5.08654i	−0.179492	+	0.170024i
$896$	−2.20497	−	1.02013i	−0.0736630	−	0.0340801i
$897$	−0.831975	−	0.632451i	−0.0277788	−	0.0211169i
$898$	3.93318	+	23.9913i	0.131252	+	0.800601i
$899$	8.04692	+	15.1781i	0.268380	+	0.506218i
$900$	−1.32979	−	0.292709i	−0.0443264	−	0.00975697i
$901$	−53.8115	+	24.8959i	−1.79272	+	0.829402i
$902$	−0.339090	+	0.851052i	−0.0112905	+	0.0283369i
$903$	0.190442	−	3.51250i	0.00633751	−	0.116889i
$904$	8.80003	−	12.9791i	0.292685	−	0.431677i
$905$	−18.8503	+	22.1923i	−0.626605	+	0.737696i
$906$	−4.44920	+	8.39207i	−0.147815	+	0.278808i
$907$	6.00437	+	2.02311i	0.199372	+	0.0671762i	0.417216	−	0.908807i	$-0.363006\pi$
$907$	6.00437	+	2.02311i	0.199372	+	0.0671762i	−0.217844	+	0.975984i	$0.569902\pi$
$908$	0.0281701	+	0.519567i	0.000934858	+	0.0172424i
$909$	3.19383	+	1.92167i	0.105933	+	0.0637376i
$910$	1.61068	−	5.80114i	0.0533934	−	0.192306i
$911$	7.69215	+	27.7046i	0.254852	+	0.917895i	0.974654	+	0.223716i	$0.0718188\pi$
$911$	7.69215	+	27.7046i	0.254852	+	0.917895i	−0.719802	+	0.694179i	$0.755767\pi$
$912$	−0.433921	+	0.261082i	−0.0143686	+	0.00864528i
$913$	−3.60138	−	5.31164i	−0.119188	−	0.175790i
$914$	−32.9399	−	3.58243i	−1.08956	−	0.118496i
$915$	−7.21164	−	0.784313i	−0.238410	−	0.0259286i
$916$	−13.4480	−	19.8343i	−0.444334	−	0.655343i
$917$	−15.2844	+	9.19635i	−0.504737	+	0.303690i
$918$	−1.48929	−	5.36396i	−0.0491541	−	0.177037i
$919$	−8.26127	+	29.7544i	−0.272514	+	0.981507i	0.692953	+	0.720983i	$0.256309\pi$
$919$	−8.26127	+	29.7544i	−0.272514	+	0.981507i	−0.965467	+	0.260525i	$0.916104\pi$
$920$	−1.31475	−	0.791060i	−0.0433461	−	0.0260805i
$921$	−0.324260	−	5.98063i	−0.0106847	−	0.197068i
$922$	10.5844	+	3.56631i	0.348579	+	0.117450i
$923$	4.82657	−	9.10388i	0.158869	−	0.299658i
$924$	−1.68554	+	1.98438i	−0.0554503	+	0.0652812i
$925$	−0.0205938	+	0.0303735i	−0.000677119	+	0.000998675i
$926$	−0.141877	+	2.61676i	−0.00466236	+	0.0859922i
$927$	1.56339	−	3.92381i	0.0513484	−	0.128875i
$928$	−2.01001	+	0.929928i	−0.0659817	+	0.0305264i
$929$	53.1077	+	11.6899i	1.74241	+	0.383533i	0.968352	−	0.249587i	$-0.0802949\pi$
$929$	53.1077	+	11.6899i	1.74241	+	0.383533i	0.774054	+	0.633120i	$0.218226\pi$
$930$	−6.93057	−	13.0724i	−0.227262	−	0.428662i
$931$	0.0899104	+	0.548429i	0.00294669	+	0.0179740i
$932$	8.17447	+	6.21407i	0.267764	+	0.203549i
$933$	14.1264	+	6.53558i	0.462478	+	0.213965i
$934$	6.44800	−	6.10787i	0.210985	−	0.199856i
$935$	1.84099	−	11.2295i	0.0602067	−	0.367245i
$936$	1.23116	−	0.414826i	0.0402417	−	0.0135590i
$937$	−14.6550	−	36.7814i	−0.478759	−	1.20160i	−0.947927	−	0.318486i	$-0.896825\pi$
$937$	−14.6550	−	36.7814i	−0.478759	−	1.20160i	0.469168	−	0.883109i	$-0.344554\pi$
$938$	9.23599	+	8.74880i	0.301566	+	0.285658i
$939$	−13.6045	+	10.3419i	−0.443967	+	0.337495i
$940$	−3.17852	+	0.699644i	−0.103672	+	0.0228199i
$941$	22.8770	+	26.9329i	0.745769	+	0.877987i	0.995922	−	0.0902192i	$-0.0287568\pi$
$941$	22.8770	+	26.9329i	0.745769	+	0.877987i	−0.250153	+	0.968206i	$0.580481\pi$
$942$	−1.35719	+	0.147604i	−0.0442198	+	0.00480919i
$943$	0.687665			0.0223935
$944$	7.58784	−	1.19363i	0.246963	−	0.0388492i
$945$	−4.63419			−0.150750
$946$	1.54254	−	0.167761i	0.0501522	−	0.00545438i
$947$	18.6933	+	22.0075i	0.607451	+	0.715147i	0.976802	−	0.214143i	$-0.0686958\pi$
$947$	18.6933	+	22.0075i	0.607451	+	0.715147i	−0.369351	+	0.929290i	$0.620420\pi$
$948$	13.9034	−	3.06037i	0.451562	−	0.0993963i
$949$	10.0405	−	7.63261i	0.325929	−	0.247765i
$950$	0.500603	+	0.474197i	0.0162417	+	0.0153850i
$951$	10.5600	+	26.5037i	0.342432	+	0.859440i
$952$	−12.8168	+	4.31849i	−0.415396	+	0.139963i
$953$	−3.89321	+	23.7475i	−0.126113	+	0.769257i	0.845727	+	0.533616i	$0.179167\pi$
$953$	−3.89321	+	23.7475i	−0.126113	+	0.769257i	−0.971840	+	0.235641i	$0.924281\pi$
$954$	−7.73242	+	7.32454i	−0.250346	+	0.237141i
$955$	29.5974	+	13.6932i	0.957751	+	0.443103i
$956$	−5.82744	−	4.42990i	−0.188473	−	0.143273i
$957$	0.383973	+	2.34213i	0.0124121	+	0.0757104i
$958$	−4.21079	−	7.94239i	−0.136044	−	0.256607i
$959$	20.2933	+	4.46690i	0.655306	+	0.144244i
$960$	1.73116	−	0.800919i	0.0558729	−	0.0258495i
$961$	−10.7970	+	27.0984i	−0.348289	+	0.874141i
$962$	0.00189559	−	0.0349621i	6.11163e−5	−	0.00112722i
$963$	4.85496	−	7.16053i	0.156449	−	0.230745i
$964$	10.9947	−	12.9439i	0.354114	−	0.416896i
$965$	−15.2726	+	28.8073i	−0.491644	+	0.927339i
$966$	1.85205	+	0.624027i	0.0595886	+	0.0200777i
$967$	−1.85143	−	34.1477i	−0.0595381	−	1.09811i	−0.863798	−	0.503838i	$-0.831921\pi$
$967$	−1.85143	−	34.1477i	−0.0595381	−	1.09811i	0.804260	−	0.594277i	$-0.202562\pi$
$968$	8.44137	+	5.07900i	0.271316	+	0.163245i
$969$	−0.754194	+	2.71636i	−0.0242282	+	0.0872621i
$970$	−2.56733	−	9.24668i	−0.0824320	−	0.296893i
$971$	−19.0337	+	11.4522i	−0.610821	+	0.367519i	−0.787103	−	0.616821i	$-0.788420\pi$
$971$	−19.0337	+	11.4522i	−0.610821	+	0.367519i	0.176283	+	0.984340i	$0.443593\pi$
$972$	−0.561187	−	0.827689i	−0.0180001	−	0.0265481i
$973$	5.38316	+	0.585454i	0.172576	+	0.0187688i
$974$	−1.68032	−	0.182745i	−0.0538408	−	0.00585554i
$975$	−0.992727	−	1.46416i	−0.0317927	−	0.0468907i
$976$	−3.25868	+	1.96069i	−0.104308	+	0.0627600i
$977$	11.5304	+	41.5288i	0.368891	+	1.32863i	0.882383	+	0.470531i	$0.155938\pi$
$977$	11.5304	+	41.5288i	0.368891	+	1.32863i	−0.513492	+	0.858094i	$0.671649\pi$
$978$	3.26493	−	11.7592i	0.104401	−	0.376018i
$979$	−14.5517	−	8.75548i	−0.465075	−	0.279827i
$980$	−0.113329	−	2.09023i	−0.00362016	−	0.0667699i
$981$	10.6372	+	3.58410i	0.339621	+	0.114432i
$982$	−13.5680	+	25.5920i	−0.432973	+	0.816674i
$983$	−13.1496	+	15.4809i	−0.419408	+	0.493765i	−0.930773	−	0.365599i	$-0.880864\pi$
$983$	−13.1496	+	15.4809i	−0.419408	+	0.493765i	0.511365	+	0.859364i	$0.329140\pi$
$984$	−0.479737	+	0.707558i	−0.0152934	+	0.0225561i
$985$	−1.10063	+	20.2999i	−0.0350690	+	0.646810i
$986$	−4.56341	+	11.4533i	−0.145329	+	0.364747i
$987$	3.76225	−	1.74060i	0.119754	−	0.0554040i
$988$	−0.642529	−	0.141431i	−0.0204416	−	0.00449953i
$989$	−0.545556	−	1.02903i	−0.0173477	−	0.0327212i
$990$	−0.330704	−	2.01721i	−0.0105105	−	0.0641111i
$991$	−28.9269	−	21.9896i	−0.918893	−	0.698524i	0.0347720	−	0.999395i	$-0.488929\pi$
$991$	−28.9269	−	21.9896i	−0.918893	−	0.698524i	−0.953665	+	0.300871i	$0.902723\pi$
$992$	−7.04001	−	3.25705i	−0.223520	−	0.103412i
$993$	9.60248	−	9.09595i	0.304726	−	0.288651i
$994$	−3.11746	+	19.0156i	−0.0988797	+	0.603140i
$995$	38.3753	−	12.9301i	1.21658	−	0.409913i
$996$	−2.21651	−	5.56301i	−0.0702327	−	0.176271i
$997$	−41.1175	−	38.9486i	−1.30220	−	1.23351i	−0.955309	−	0.295609i	$-0.904477\pi$
$997$	−41.1175	−	38.9486i	−1.30220	−	1.23351i	−0.346895	−	0.937904i	$-0.612764\pi$
$998$	29.7013	−	22.5784i	0.940180	−	0.714706i
$999$	−0.0263206	+	0.00579361i	−0.000832748	+	0.000183302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.133.2	✓	56
59.4	even	29	inner	354.2.e.a.181.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.133.2	✓	56	1.1	even	1	trivial
354.2.e.a.181.2	yes	56	59.4	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994138 + 0.108119i) q^{2} +(0.647386 + 0.762162i) q^{3} +(0.976621 - 0.214970i) q^{4} +(1.51851 - 1.15434i) q^{5} +(-0.725995 - 0.687699i) q^{6} +(0.899258 + 2.25697i) q^{7} +(-0.947653 + 0.319302i) q^{8} +(-0.161782 + 0.986827i) q^{9} +O(q^{10})\)	\(q+(-0.994138 + 0.108119i) q^{2} +(0.647386 + 0.762162i) q^{3} +(0.976621 - 0.214970i) q^{4} +(1.51851 - 1.15434i) q^{5} +(-0.725995 - 0.687699i) q^{6} +(0.899258 + 2.25697i) q^{7} +(-0.947653 + 0.319302i) q^{8} +(-0.161782 + 0.986827i) q^{9} +(-1.38480 + 1.31175i) q^{10} +(0.972610 + 0.449977i) q^{11} +(0.796093 + 0.605174i) q^{12} +(0.210182 + 1.28205i) q^{13} +(-1.13801 - 2.14651i) q^{14} +(1.86286 + 0.410046i) q^{15} +(0.907575 - 0.419889i) q^{16} +(2.06051 - 5.17149i) q^{17} +(0.0541389 - 0.998533i) q^{18} +(-0.284191 + 0.419150i) q^{19} +(1.23486 - 1.45379i) q^{20} +(-1.13801 + 2.14651i) q^{21} +(-1.01556 - 0.342182i) q^{22} +(0.0435503 + 0.803238i) q^{23} +(-0.856857 - 0.515554i) q^{24} +(-0.364273 + 1.31199i) q^{25} +(-0.347564 - 1.25181i) q^{26} +(-0.856857 + 0.515554i) q^{27} +(1.36342 + 2.01089i) q^{28} +(2.20172 + 0.239451i) q^{29} +(-1.89627 - 0.206232i) q^{30} +(4.35309 + 6.42033i) q^{31} +(-0.856857 + 0.515554i) q^{32} +(0.286699 + 1.03260i) q^{33} +(-1.48929 + 5.36396i) q^{34} +(3.97084 + 2.38918i) q^{35} +(0.0541389 + 0.998533i) q^{36} +(0.0255399 + 0.00860541i) q^{37} +(0.237207 - 0.447419i) q^{38} +(-0.841062 + 0.990175i) q^{39} +(-1.07044 + 1.57878i) q^{40} +(0.0462812 - 0.853607i) q^{41} +(0.899258 - 2.25697i) q^{42} +(-1.31406 + 0.607949i) q^{43} +(1.04660 + 0.230375i) q^{44} +(0.893467 + 1.68526i) q^{45} +(-0.130140 - 0.793821i) q^{46} +(-1.35834 - 1.03258i) q^{47} +(0.907575 + 0.419889i) q^{48} +(0.796731 - 0.754703i) q^{49} +(0.220286 - 1.34369i) q^{50} +(5.27546 - 1.77751i) q^{51} +(0.480871 + 1.20689i) q^{52} +(-7.73242 - 7.32454i) q^{53} +(0.796093 - 0.605174i) q^{54} +(1.99635 - 0.439429i) q^{55} +(-1.57284 - 1.85169i) q^{56} +(-0.503441 + 0.0547525i) q^{57} -2.21470 q^{58} +(7.38772 + 2.10274i) q^{59} +1.90745 q^{60} +(-3.78077 + 0.411184i) q^{61} +(-5.02174 - 5.91205i) q^{62} +(-2.37272 + 0.522275i) q^{63} +(0.796093 - 0.605174i) q^{64} +(1.79909 + 1.70419i) q^{65} +(-0.396661 - 0.995545i) q^{66} +(-4.96225 + 1.67198i) q^{67} +(0.900619 - 5.49353i) q^{68} +(-0.584004 + 0.553198i) q^{69} +(-4.20588 - 1.94585i) q^{70} +(-6.31413 - 4.79988i) q^{71} +(-0.161782 - 0.986827i) q^{72} +(-4.54729 - 8.57710i) q^{73} +(-0.0263206 - 0.00579361i) q^{74} +(-1.23578 + 0.571731i) q^{75} +(-0.187442 + 0.470443i) q^{76} +(-0.140957 + 2.59980i) q^{77} +(0.729075 - 1.07531i) q^{78} +(9.21635 - 10.8503i) q^{79} +(0.893467 - 1.68526i) q^{80} +(-0.947653 - 0.319302i) q^{81} +(0.0462812 + 0.853607i) q^{82} +(-5.13114 - 3.08730i) q^{83} +(-0.649965 + 2.34096i) q^{84} +(-2.84076 - 10.2315i) q^{85} +(1.24063 - 0.746460i) q^{86} +(1.24286 + 1.83308i) q^{87} +(-1.06538 - 0.115867i) q^{88} +(-15.7542 - 1.71337i) q^{89} +(-1.07044 - 1.57878i) q^{90} +(-2.70454 + 1.62727i) q^{91} +(0.215205 + 0.775097i) q^{92} +(-2.07520 + 7.47420i) q^{93} +(1.46202 + 0.879668i) q^{94} +(0.0522956 + 0.964536i) q^{95} +(-0.947653 - 0.319302i) q^{96} +(-2.35658 + 4.44499i) q^{97} +(-0.710462 + 0.836421i) q^{98} +(-0.601400 + 0.886999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

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Database

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