LMFDB - Embedded newform 403.2.h.a.118.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.6
Character	$\chi$	$=$	403.118
Dual form			403.2.h.a.222.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.11604 q^{2} +(0.521580 + 0.903404i) q^{3} -0.754455 q^{4} +(-0.0866186 + 0.150028i) q^{5} +(-0.582104 - 1.00823i) q^{6} +(-0.0906774 - 0.157058i) q^{7} +3.07408 q^{8} +(0.955908 - 1.65568i) q^{9} +O(q^{10})$	\(q-1.11604 q^{2} +(0.521580 + 0.903404i) q^{3} -0.754455 q^{4} +(-0.0866186 + 0.150028i) q^{5} +(-0.582104 - 1.00823i) q^{6} +(-0.0906774 - 0.157058i) q^{7} +3.07408 q^{8} +(0.955908 - 1.65568i) q^{9} +(0.0966698 - 0.167437i) q^{10} +(0.292661 - 0.506904i) q^{11} +(-0.393509 - 0.681577i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.101200 + 0.175283i) q^{14} -0.180714 q^{15} -1.92189 q^{16} +(1.60387 + 2.77798i) q^{17} +(-1.06683 + 1.84781i) q^{18} +(2.80875 + 4.86490i) q^{19} +(0.0653498 - 0.113189i) q^{20} +(0.0945911 - 0.163837i) q^{21} +(-0.326622 + 0.565725i) q^{22} +0.834506 q^{23} +(1.60338 + 2.77714i) q^{24} +(2.48499 + 4.30414i) q^{25} +(-0.558020 + 0.966519i) q^{26} +5.12381 q^{27} +(0.0684120 + 0.118493i) q^{28} +1.05124 q^{29} +0.201684 q^{30} +(1.87930 - 5.24101i) q^{31} -4.00326 q^{32} +0.610586 q^{33} +(-1.78998 - 3.10033i) q^{34} +0.0314174 q^{35} +(-0.721189 + 1.24914i) q^{36} +(4.25093 + 7.36283i) q^{37} +(-3.13468 - 5.42942i) q^{38} +1.04316 q^{39} +(-0.266273 + 0.461198i) q^{40} +(-5.77036 + 9.99456i) q^{41} +(-0.105567 + 0.182848i) q^{42} +(-3.47496 - 6.01880i) q^{43} +(-0.220800 + 0.382436i) q^{44} +(0.165599 + 0.286826i) q^{45} -0.931342 q^{46} +11.9633 q^{47} +(-1.00242 - 1.73624i) q^{48} +(3.48356 - 6.03369i) q^{49} +(-2.77335 - 4.80359i) q^{50} +(-1.67309 + 2.89788i) q^{51} +(-0.377227 + 0.653377i) q^{52} +(-0.437237 + 0.757318i) q^{53} -5.71838 q^{54} +(0.0506998 + 0.0878147i) q^{55} +(-0.278750 - 0.482809i) q^{56} +(-2.92998 + 5.07487i) q^{57} -1.17323 q^{58} +(-6.01275 - 10.4144i) q^{59} +0.136341 q^{60} +12.2530 q^{61} +(-2.09737 + 5.84918i) q^{62} -0.346717 q^{63} +8.31157 q^{64} +(0.0866186 + 0.150028i) q^{65} -0.681438 q^{66} +(-1.13126 + 1.95940i) q^{67} +(-1.21004 - 2.09586i) q^{68} +(0.435262 + 0.753895i) q^{69} -0.0350631 q^{70} +(-3.93264 + 6.81152i) q^{71} +(2.93854 - 5.08970i) q^{72} +(6.46537 - 11.1983i) q^{73} +(-4.74421 - 8.21722i) q^{74} +(-2.59225 + 4.48991i) q^{75} +(-2.11907 - 3.67034i) q^{76} -0.106151 q^{77} -1.16421 q^{78} +(-0.979955 - 1.69733i) q^{79} +(0.166471 - 0.288337i) q^{80} +(-0.195244 - 0.338173i) q^{81} +(6.43996 - 11.1543i) q^{82} +(-6.25397 + 10.8322i) q^{83} +(-0.0713647 + 0.123607i) q^{84} -0.555698 q^{85} +(3.87819 + 6.71722i) q^{86} +(0.548308 + 0.949697i) q^{87} +(0.899665 - 1.55827i) q^{88} -15.0812 q^{89} +(-0.184815 - 0.320109i) q^{90} -0.181355 q^{91} -0.629597 q^{92} +(5.71496 - 1.03584i) q^{93} -13.3515 q^{94} -0.973160 q^{95} +(-2.08802 - 3.61656i) q^{96} -15.5006 q^{97} +(-3.88779 + 6.73384i) q^{98} +(-0.559515 - 0.969108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.11604			−0.789159			−0.394580	−	0.918862i	$-0.629110\pi$
$2$	−1.11604			−0.789159			−0.394580	+	0.918862i	$0.629110\pi$
$3$	0.521580	+	0.903404i	0.301135	+	0.521580i	0.976393	−	0.216001i	$-0.0693013\pi$
$3$	0.521580	+	0.903404i	0.301135	+	0.521580i	−0.675259	+	0.737581i	$0.735968\pi$
$4$	−0.754455			−0.377227
$5$	−0.0866186	+	0.150028i	−0.0387370	+	0.0670945i	−0.884744	−	0.466077i	$-0.845667\pi$
$5$	−0.0866186	+	0.150028i	−0.0387370	+	0.0670945i	0.846007	+	0.533172i	$0.179000\pi$
$6$	−0.582104	−	1.00823i	−0.237643	−	0.411610i
$7$	−0.0906774	−	0.157058i	−0.0342728	−	0.0593623i	0.848380	−	0.529387i	$-0.177578\pi$
$7$	−0.0906774	−	0.157058i	−0.0342728	−	0.0593623i	−0.882653	+	0.470025i	$0.844245\pi$
$8$	3.07408			1.08685
$9$	0.955908	−	1.65568i	0.318636	−	0.551894i
$10$	0.0966698	−	0.167437i	0.0305697	−	0.0529482i
$11$	0.292661	−	0.506904i	0.0882407	−	0.152837i	−0.818527	−	0.574468i	$-0.805209\pi$
$11$	0.292661	−	0.506904i	0.0882407	−	0.152837i	0.906768	+	0.421631i	$0.138542\pi$
$12$	−0.393509	−	0.681577i	−0.113596	−	0.196754i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	0.101200	+	0.175283i	0.0270467	+	0.0468463i
$15$	−0.180714			−0.0466602
$16$	−1.92189			−0.480472
$17$	1.60387	+	2.77798i	0.388994	+	0.673758i	0.992315	−	0.123741i	$-0.0394892\pi$
$17$	1.60387	+	2.77798i	0.388994	+	0.673758i	−0.603320	+	0.797499i	$0.706156\pi$
$18$	−1.06683	+	1.84781i	−0.251455	+	0.435532i
$19$	2.80875	+	4.86490i	0.644371	+	1.11608i	0.984446	+	0.175686i	$0.0562142\pi$
$19$	2.80875	+	4.86490i	0.644371	+	1.11608i	−0.340075	+	0.940398i	$0.610452\pi$
$20$	0.0653498	−	0.113189i	0.0146127	−	0.0253099i
$21$	0.0945911	−	0.163837i	0.0206415	−	0.0357521i
$22$	−0.326622	+	0.565725i	−0.0696360	+	0.120613i
$23$	0.834506			0.174006			0.0870032	−	0.996208i	$-0.472271\pi$
$23$	0.834506			0.174006			0.0870032	+	0.996208i	$0.472271\pi$
$24$	1.60338	+	2.77714i	0.327289	+	0.566881i
$25$	2.48499	+	4.30414i	0.496999	+	0.860827i
$26$	−0.558020	+	0.966519i	−0.109437	+	0.189550i
$27$	5.12381			0.986078
$28$	0.0684120	+	0.118493i	0.0129287	+	0.0223931i
$29$	1.05124			0.195211			0.0976055	−	0.995225i	$-0.468882\pi$
$29$	1.05124			0.195211			0.0976055	+	0.995225i	$0.468882\pi$
$30$	0.201684			0.0368223
$31$	1.87930	−	5.24101i	0.337532	−	0.941314i
$31$	1.87930	−	5.24101i	0.337532	−	0.941314i
$32$	−4.00326			−0.707683
$33$	0.610586			0.106289
$34$	−1.78998	−	3.10033i	−0.306979	−	0.531703i
$35$	0.0314174			0.00531051
$36$	−0.721189	+	1.24914i	−0.120198	+	0.208189i
$37$	4.25093	+	7.36283i	0.698849	+	1.21044i	0.968866	+	0.247587i	$0.0796376\pi$
$37$	4.25093	+	7.36283i	0.698849	+	1.21044i	−0.270016	+	0.962856i	$0.587029\pi$
$38$	−3.13468	−	5.42942i	−0.508512	−	0.880768i
$39$	1.04316			0.167039
$40$	−0.266273	+	0.461198i	−0.0421014	+	0.0729218i
$41$	−5.77036	+	9.99456i	−0.901179	+	1.56089i	−0.0752143	+	0.997167i	$0.523964\pi$
$41$	−5.77036	+	9.99456i	−0.901179	+	1.56089i	−0.825965	+	0.563721i	$0.809369\pi$
$42$	−0.105567	+	0.182848i	−0.0162894	+	0.0282141i
$43$	−3.47496	−	6.01880i	−0.529926	−	0.917859i	−0.999391	−	0.0349074i	$-0.988886\pi$
$43$	−3.47496	−	6.01880i	−0.529926	−	0.917859i	0.469465	−	0.882951i	$-0.344447\pi$
$44$	−0.220800	+	0.382436i	−0.0332868	+	0.0576544i
$45$	0.165599	+	0.286826i	0.0246860	+	0.0427574i
$46$	−0.931342			−0.137319
$47$	11.9633			1.74503			0.872514	−	0.488589i	$-0.162488\pi$
$47$	11.9633			1.74503			0.872514	+	0.488589i	$0.162488\pi$
$48$	−1.00242	−	1.73624i	−0.144687	−	0.250605i
$49$	3.48356	−	6.03369i	0.497651	−	0.861956i
$50$	−2.77335	−	4.80359i	−0.392211	−	0.679330i
$51$	−1.67309	+	2.89788i	−0.234279	+	0.405784i
$52$	−0.377227	+	0.653377i	−0.0523120	+	0.0906071i
$53$	−0.437237	+	0.757318i	−0.0600592	+	0.104026i	−0.894492	−	0.447085i	$-0.852462\pi$
$53$	−0.437237	+	0.757318i	−0.0600592	+	0.104026i	0.834432	+	0.551110i	$0.185796\pi$
$54$	−5.71838			−0.778173
$55$	0.0506998	+	0.0878147i	0.00683636	+	0.0118409i
$56$	−0.278750	−	0.482809i	−0.0372495	−	0.0645180i
$57$	−2.92998	+	5.07487i	−0.388085	+	0.672183i
$58$	−1.17323			−0.154053
$59$	−6.01275	−	10.4144i	−0.782794	−	1.35584i	−0.930308	−	0.366779i	$-0.880461\pi$
$59$	−6.01275	−	10.4144i	−0.782794	−	1.35584i	0.147514	−	0.989060i	$-0.452873\pi$
$60$	0.136341			0.0176015
$61$	12.2530			1.56884			0.784418	−	0.620232i	$-0.212962\pi$
$61$	12.2530			1.56884			0.784418	+	0.620232i	$0.212962\pi$
$62$	−2.09737	+	5.84918i	−0.266367	+	0.742847i
$63$	−0.346717			−0.0436822
$64$	8.31157			1.03895
$65$	0.0866186	+	0.150028i	0.0107437	+	0.0186087i
$66$	−0.681438			−0.0838792
$67$	−1.13126	+	1.95940i	−0.138205	+	0.239379i	−0.926817	−	0.375512i	$-0.877467\pi$
$67$	−1.13126	+	1.95940i	−0.138205	+	0.239379i	0.788612	+	0.614891i	$0.210800\pi$
$68$	−1.21004	−	2.09586i	−0.146739	−	0.254160i
$69$	0.435262	+	0.753895i	0.0523993	+	0.0907583i
$70$	−0.0350631			−0.00419084
$71$	−3.93264	+	6.81152i	−0.466718	+	0.808379i	−0.999277	−	0.0380135i	$-0.987897\pi$
$71$	−3.93264	+	6.81152i	−0.466718	+	0.808379i	0.532559	+	0.846393i	$0.321230\pi$
$72$	2.93854	−	5.08970i	0.346310	−	0.599827i
$73$	6.46537	−	11.1983i	0.756714	−	1.31067i	−0.187804	−	0.982207i	$-0.560137\pi$
$73$	6.46537	−	11.1983i	0.756714	−	1.31067i	0.944518	−	0.328460i	$-0.106530\pi$
$74$	−4.74421	−	8.21722i	−0.551504	−	0.955232i
$75$	−2.59225	+	4.48991i	−0.299327	+	0.518450i
$76$	−2.11907	−	3.67034i	−0.243074	−	0.421017i
$77$	−0.106151			−0.0120970
$78$	−1.16421			−0.131821
$79$	−0.979955	−	1.69733i	−0.110254	−	0.190965i	0.805619	−	0.592434i	$-0.201833\pi$
$79$	−0.979955	−	1.69733i	−0.110254	−	0.190965i	−0.915872	+	0.401469i	$0.868500\pi$
$80$	0.166471	−	0.288337i	0.0186121	−	0.0322370i
$81$	−0.195244	−	0.338173i	−0.0216938	−	0.0375748i
$82$	6.43996	−	11.1543i	0.711174	−	1.23179i
$83$	−6.25397	+	10.8322i	−0.686463	+	1.18899i	0.286512	+	0.958077i	$0.407504\pi$
$83$	−6.25397	+	10.8322i	−0.686463	+	1.18899i	−0.972975	+	0.230912i	$0.925829\pi$
$84$	−0.0713647	+	0.123607i	−0.00778653	+	0.0134867i
$85$	−0.555698			−0.0602739
$86$	3.87819	+	6.71722i	0.418196	+	0.724337i
$87$	0.548308	+	0.949697i	0.0587847	+	0.101818i
$88$	0.899665	−	1.55827i	0.0959046	−	0.166112i
$89$	−15.0812			−1.59860			−0.799300	−	0.600932i	$-0.794796\pi$
$89$	−15.0812			−1.59860			−0.799300	+	0.600932i	$0.794796\pi$
$90$	−0.184815	−	0.320109i	−0.0194812	−	0.0337424i
$91$	−0.181355			−0.0190112
$92$	−0.629597			−0.0656400
$93$	5.71496	−	1.03584i	0.592613	−	0.107412i
$94$	−13.3515			−1.37711
$95$	−0.973160			−0.0998441
$96$	−2.08802	−	3.61656i	−0.213108	−	0.369113i
$97$	−15.5006			−1.57385			−0.786924	−	0.617049i	$-0.788328\pi$
$97$	−15.5006			−1.57385			−0.786924	+	0.617049i	$0.788328\pi$
$98$	−3.88779	+	6.73384i	−0.392726	+	0.680221i
$99$	−0.559515	−	0.969108i	−0.0562333	−	0.0973990i
$100$	−1.87482	−	3.24728i	−0.187482	−	0.324728i
$101$	−8.82376			−0.877997			−0.438999	−	0.898488i	$-0.644667\pi$
$101$	−8.82376			−0.877997			−0.438999	+	0.898488i	$0.644667\pi$
$102$	1.86723	−	3.23414i	0.184884	−	0.320228i
$103$	7.56520	−	13.1033i	0.745422	−	1.29111i	−0.204576	−	0.978851i	$-0.565581\pi$
$103$	7.56520	−	13.1033i	0.745422	−	1.29111i	0.949997	−	0.312258i	$-0.101085\pi$
$104$	1.53704	−	2.66223i	0.150719	−	0.261053i
$105$	0.0163867	+	0.0283826i	0.00159918	+	0.00276986i
$106$	0.487975	−	0.845197i	0.0473963	−	0.0820928i
$107$	−1.11413	−	1.92973i	−0.107707	−	0.186554i	0.807134	−	0.590368i	$-0.201017\pi$
$107$	−1.11413	−	1.92973i	−0.107707	−	0.186554i	−0.914841	+	0.403815i	$0.867684\pi$
$108$	−3.86568			−0.371976
$109$	−2.45473			−0.235121			−0.117560	−	0.993066i	$-0.537507\pi$
$109$	−2.45473			−0.235121			−0.117560	+	0.993066i	$0.537507\pi$
$110$	−0.0565830	−	0.0980047i	−0.00539498	−	0.00934438i
$111$	−4.43441	+	7.68062i	−0.420895	+	0.729012i
$112$	0.174272	+	0.301848i	0.0164671	+	0.0285219i
$113$	7.88469	−	13.6567i	0.741729	−	1.28471i	−0.209978	−	0.977706i	$-0.567339\pi$
$113$	7.88469	−	13.6567i	0.741729	−	1.28471i	0.951707	−	0.307007i	$-0.0993275\pi$
$114$	3.26997	−	5.66376i	0.306261	−	0.530459i
$115$	−0.0722837	+	0.125199i	−0.00674049	+	0.0116749i
$116$	−0.793115			−0.0736389
$117$	−0.955908	−	1.65568i	−0.0883737	−	0.153068i
$118$	6.71047	+	11.6229i	0.617749	+	1.06997i
$119$	0.290869	−	0.503799i	0.0266639	−	0.0461832i
$120$	−0.555530			−0.0507127
$121$	5.32870	+	9.22958i	0.484427	+	0.839052i
$122$	−13.6748			−1.23806
$123$	−12.0388			−1.08550
$124$	−1.41785	+	3.95411i	−0.127326	+	0.355089i
$125$	−1.72717			−0.154483
$126$	0.386950			0.0344723
$127$	−2.93709	−	5.08720i	−0.260625	−	0.451416i	0.705783	−	0.708428i	$-0.250595\pi$
$127$	−2.93709	−	5.08720i	−0.260625	−	0.451416i	−0.966408	+	0.257012i	$0.917262\pi$
$128$	−1.26953			−0.112212
$129$	3.62494	−	6.27858i	0.319158	−	0.552798i
$130$	−0.0966698	−	0.167437i	−0.00847850	−	0.0146852i
$131$	−8.70679	−	15.0806i	−0.760715	−	1.31760i	−0.942482	−	0.334256i	$-0.891515\pi$
$131$	−8.70679	−	15.0806i	−0.760715	−	1.31760i	0.181767	−	0.983342i	$-0.441818\pi$
$132$	−0.460659			−0.0400952
$133$	0.509380	−	0.882273i	0.0441689	−	0.0765027i
$134$	1.26253	−	2.18677i	0.109066	−	0.188908i
$135$	−0.443817	+	0.768714i	−0.0381977	+	0.0661604i
$136$	4.93041	+	8.53973i	0.422779	+	0.732275i
$137$	−8.54955	+	14.8083i	−0.730437	+	1.26515i	0.226259	+	0.974067i	$0.427350\pi$
$137$	−8.54955	+	14.8083i	−0.730437	+	1.26515i	−0.956696	+	0.291087i	$0.905983\pi$
$138$	−0.485769	−	0.841377i	−0.0413514	−	0.0716228i
$139$	−0.583761			−0.0495140			−0.0247570	−	0.999693i	$-0.507881\pi$
$139$	−0.583761			−0.0495140			−0.0247570	+	0.999693i	$0.507881\pi$
$140$	−0.0237030			−0.00200327
$141$	6.23983	+	10.8077i	0.525488	+	0.910172i
$142$	4.38898	−	7.60193i	0.368315	−	0.637940i
$143$	−0.292661	−	0.506904i	−0.0244736	−	0.0423895i
$144$	−1.83715	+	3.18204i	−0.153096	+	0.265170i
$145$	−0.0910572	+	0.157716i	−0.00756189	+	0.0130976i
$146$	−7.21561	+	12.4978i	−0.597168	+	1.03433i
$147$	7.26781			0.599439
$148$	−3.20714	−	5.55493i	−0.263625	−	0.456612i
$149$	3.23289	+	5.59953i	0.264849	+	0.458731i	0.967524	−	0.252779i	$-0.0813447\pi$
$149$	3.23289	+	5.59953i	0.264849	+	0.458731i	−0.702675	+	0.711511i	$0.748011\pi$
$150$	2.89305	−	5.01091i	0.236217	−	0.409139i
$151$	13.7657			1.12024			0.560119	−	0.828412i	$-0.310756\pi$
$151$	13.7657			1.12024			0.560119	+	0.828412i	$0.310756\pi$
$152$	8.63433	+	14.9551i	0.700336	+	1.21302i
$153$	6.13259			0.495791
$154$	0.118469			0.00954649
$155$	0.623516	+	0.735916i	0.0500820	+	0.0591102i
$156$	−0.787017			−0.0630118
$157$	20.6701			1.64966			0.824828	−	0.565384i	$-0.191272\pi$
$157$	20.6701			1.64966			0.824828	+	0.565384i	$0.191272\pi$
$158$	1.09367	+	1.89429i	0.0870077	+	0.150702i
$159$	−0.912218			−0.0723436
$160$	0.346757	−	0.600600i	0.0274135	−	0.0474816i
$161$	−0.0756708	−	0.131066i	−0.00596370	−	0.0103294i
$162$	0.217900	+	0.377415i	0.0171199	+	0.0296525i
$163$	−11.7034			−0.916678			−0.458339	−	0.888777i	$-0.651555\pi$
$163$	−11.7034			−0.916678			−0.458339	+	0.888777i	$0.651555\pi$
$164$	4.35348	−	7.54044i	0.339950	−	0.588810i
$165$	−0.0528881	+	0.0916048i	−0.00411733	+	0.00713142i
$166$	6.97968	−	12.0892i	0.541729	−	0.938301i
$167$	−5.27973	−	9.14476i	−0.408558	−	0.707643i	0.586171	−	0.810188i	$-0.300635\pi$
$167$	−5.27973	−	9.14476i	−0.408558	−	0.707643i	−0.994728	+	0.102545i	$0.967302\pi$
$168$	0.290781	−	0.503647i	0.0224342	−	0.0388572i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.620181			0.0475657
$171$	10.7396			0.821280
$172$	2.62170	+	4.54091i	0.199903	+	0.346241i
$173$	−5.16983	+	8.95441i	−0.393055	+	0.680791i	−0.992851	−	0.119362i	$-0.961915\pi$
$173$	−5.16983	+	8.95441i	−0.393055	+	0.680791i	0.599796	+	0.800153i	$0.295248\pi$
$174$	−0.611933	−	1.05990i	−0.0463905	−	0.0803508i
$175$	0.450666	−	0.780576i	0.0340671	−	0.0590060i
$176$	−0.562463	+	0.974214i	−0.0423972	+	0.0734341i
$177$	6.27227	−	10.8639i	0.471453	−	0.816580i
$178$	16.8312			1.26155
$179$	−0.0178504	−	0.0309177i	−0.00133420	−	0.00231090i	0.865358	−	0.501155i	$-0.167091\pi$
$179$	−0.0178504	−	0.0309177i	−0.00133420	−	0.00231090i	−0.866692	+	0.498844i	$0.833758\pi$
$180$	−0.124937	−	0.216397i	−0.00931224	−	0.0161293i
$181$	−11.0336	+	19.1108i	−0.820121	+	1.42049i	0.0854710	+	0.996341i	$0.472761\pi$
$181$	−11.0336	+	19.1108i	−0.820121	+	1.42049i	−0.905592	+	0.424150i	$0.860573\pi$
$182$	0.202399			0.0150028
$183$	6.39093	+	11.0694i	0.472431	+	0.818274i
$184$	2.56534			0.189119
$185$	−1.47284			−0.108285
$186$	−6.37812	+	1.15604i	−0.467666	+	0.0847653i
$187$	1.87756			0.137301
$188$	−9.02578			−0.658272
$189$	−0.464614	−	0.804735i	−0.0337957	−	0.0585359i
$190$	1.08609			0.0787929
$191$	−4.06270	+	7.03679i	−0.293966	+	0.509165i	−0.974744	−	0.223326i	$-0.928309\pi$
$191$	−4.06270	+	7.03679i	−0.293966	+	0.509165i	0.680778	+	0.732490i	$0.261642\pi$
$192$	4.33515	+	7.50871i	0.312863	+	0.541894i
$193$	−2.60312	−	4.50873i	−0.187377	−	0.324546i	0.756998	−	0.653417i	$-0.226665\pi$
$193$	−2.60312	−	4.50873i	−0.187377	−	0.324546i	−0.944375	+	0.328871i	$0.893332\pi$
$194$	17.2993			1.24202
$195$	−0.0903571	+	0.156503i	−0.00647061	+	0.0112074i
$196$	−2.62818	+	4.55215i	−0.187727	+	0.325153i
$197$	7.63895	−	13.2311i	0.544253	−	0.942674i	−0.454401	−	0.890797i	$-0.650147\pi$
$197$	7.63895	−	13.2311i	0.544253	−	0.942674i	0.998654	−	0.0518763i	$-0.0165202\pi$
$198$	0.624441	+	1.08156i	0.0443771	+	0.0768633i
$199$	3.11810	−	5.40070i	0.221036	−	0.382846i	−0.734087	−	0.679056i	$-0.762390\pi$
$199$	3.11810	−	5.40070i	0.221036	−	0.382846i	0.955123	+	0.296210i	$0.0957228\pi$
$200$	7.63908	+	13.2313i	0.540164	+	0.935592i
$201$	−2.36017			−0.166474
$202$	9.84767			0.692880
$203$	−0.0953240	−	0.165106i	−0.00669043	−	0.0115882i
$204$	1.26227	−	2.18632i	0.0883766	−	0.153073i
$205$	−0.999641	−	1.73143i	−0.0698180	−	0.120928i
$206$	−8.44307	+	14.6238i	−0.588257	+	1.01889i
$207$	0.797711	−	1.38168i	0.0554447	−	0.0960331i
$208$	−0.960944	+	1.66440i	−0.0666295	+	0.115406i
$209$	3.28805			0.227439
$210$	−0.0182882	−	0.0316761i	−0.00126201	−	0.00218586i
$211$	4.93394	+	8.54583i	0.339666	+	0.588319i	0.984370	−	0.176113i	$-0.0563526\pi$
$211$	4.93394	+	8.54583i	0.339666	+	0.588319i	−0.644704	+	0.764433i	$0.723019\pi$
$212$	0.329876	−	0.571362i	0.0226560	−	0.0392413i
$213$	−8.20474			−0.562180
$214$	1.24341	+	2.15365i	0.0849978	+	0.147221i
$215$	1.20398			0.0821110
$216$	15.7510			1.07172
$217$	−0.993553	+	0.180083i	−0.0674467	+	0.0122248i
$218$	2.73958			0.185548
$219$	13.4888			0.911491
$220$	−0.0382507	−	0.0662522i	−0.00257886	−	0.00446672i
$221$	3.20773			0.215775
$222$	4.94898	−	8.57188i	0.332154	−	0.575307i
$223$	−9.99256	−	17.3076i	−0.669151	−	1.15900i	−0.978142	−	0.207939i	$-0.933324\pi$
$223$	−9.99256	−	17.3076i	−0.669151	−	1.15900i	0.308991	−	0.951065i	$-0.400009\pi$
$224$	0.363005	+	0.628743i	0.0242543	+	0.0420097i
$225$	9.50170			0.633447
$226$	−8.79963	+	15.2414i	−0.585343	+	1.01384i
$227$	−2.61968	+	4.53742i	−0.173874	+	0.301159i	−0.939771	−	0.341804i	$-0.888962\pi$
$227$	−2.61968	+	4.53742i	−0.173874	+	0.301159i	0.765897	+	0.642964i	$0.222295\pi$
$228$	2.21053	−	3.82876i	0.146396	−	0.253566i
$229$	7.76635	+	13.4517i	0.513215	+	0.888914i	0.999883	+	0.0153270i	$0.00487892\pi$
$229$	7.76635	+	13.4517i	0.513215	+	0.888914i	−0.486668	+	0.873587i	$0.661788\pi$
$230$	0.0806715	−	0.139727i	0.00531932	−	0.00921333i
$231$	−0.0553663	−	0.0958973i	−0.00364284	−	0.00630958i
$232$	3.23161			0.212165
$233$	24.0592			1.57617			0.788084	−	0.615568i	$-0.211073\pi$
$233$	24.0592			1.57617			0.788084	+	0.615568i	$0.211073\pi$
$234$	1.06683	+	1.84781i	0.0697410	+	0.120795i
$235$	−1.03625	+	1.79483i	−0.0675972	+	0.117082i
$236$	4.53635	+	7.85719i	0.295291	+	0.511459i
$237$	1.02225	−	1.77059i	0.0664023	−	0.115012i
$238$	−0.324621	+	0.562260i	−0.0210421	+	0.0364459i
$239$	−8.99259	+	15.5756i	−0.581682	+	1.00750i	0.413598	+	0.910460i	$0.364272\pi$
$239$	−8.99259	+	15.5756i	−0.581682	+	1.00750i	−0.995280	+	0.0970435i	$0.969061\pi$
$240$	0.347313			0.0224189
$241$	4.93020	+	8.53936i	0.317582	+	0.550068i	0.979983	−	0.199081i	$-0.0637957\pi$
$241$	4.93020	+	8.53936i	0.317582	+	0.550068i	−0.662401	+	0.749150i	$0.730462\pi$
$242$	−5.94704	−	10.3006i	−0.382290	−	0.662146i
$243$	7.88939	−	13.6648i	0.506105	−	0.876599i
$244$	−9.24434			−0.591808
$245$	0.603481	+	1.04526i	0.0385550	+	0.0667792i
$246$	13.4358			0.856637
$247$	5.61750			0.357433
$248$	5.77712	−	16.1113i	0.366847	−	1.02307i
$249$	−13.0478			−0.826870
$250$	1.92759			0.121912
$251$	−0.405837	−	0.702930i	−0.0256162	−	0.0443686i	0.852933	−	0.522020i	$-0.174821\pi$
$251$	−0.405837	−	0.702930i	−0.0256162	−	0.0443686i	−0.878549	+	0.477652i	$0.841488\pi$
$252$	0.261582			0.0164781
$253$	0.244228	−	0.423014i	0.0153545	−	0.0265947i
$254$	3.27792	+	5.67752i	0.205675	+	0.356239i
$255$	−0.289841	−	0.502020i	−0.0181506	−	0.0314377i
$256$	−15.2063			−0.950394
$257$	0.435810	−	0.754845i	0.0271851	−	0.0470859i	−0.852113	−	0.523358i	$-0.824679\pi$
$257$	0.435810	−	0.754845i	0.0271851	−	0.0470859i	0.879298	+	0.476272i	$0.158012\pi$
$258$	−4.04558	+	7.00714i	−0.251867	+	0.436246i
$259$	0.770927	−	1.33529i	0.0479031	−	0.0829706i
$260$	−0.0653498	−	0.113189i	−0.00405282	−	0.00701969i
$261$	1.00489	−	1.74052i	0.0622012	−	0.107736i
$262$	9.71712	+	16.8305i	0.600326	+	1.03979i
$263$	−22.9409			−1.41460			−0.707299	−	0.706914i	$-0.750087\pi$
$263$	−22.9409			−1.41460			−0.707299	+	0.706914i	$0.750087\pi$
$264$	1.87699			0.115521
$265$	−0.0757458	−	0.131196i	−0.00465303	−	0.00805928i
$266$	−0.568489	+	0.984651i	−0.0348563	+	0.0603729i
$267$	−7.86604	−	13.6244i	−0.481394	−	0.833799i
$268$	0.853484	−	1.47828i	0.0521348	−	0.0903002i
$269$	−8.97906	+	15.5522i	−0.547463	+	0.948234i	0.450985	+	0.892532i	$0.351073\pi$
$269$	−8.97906	+	15.5522i	−0.547463	+	0.948234i	−0.998447	+	0.0557018i	$0.982260\pi$
$270$	0.495318	−	0.857916i	0.0301441	−	0.0522111i
$271$	−26.4841			−1.60880			−0.804398	−	0.594090i	$-0.797512\pi$
$271$	−26.4841			−1.60880			−0.804398	+	0.594090i	$0.797512\pi$
$272$	−3.08245	−	5.33896i	−0.186901	−	0.323722i
$273$	−0.0945911	−	0.163837i	−0.00572491	−	0.00991584i
$274$	9.54164	−	16.5266i	0.576431	−	0.998409i
$275$	2.90905			0.175422
$276$	−0.328385	−	0.568780i	−0.0197665	−	0.0342365i
$277$	7.54712			0.453462			0.226731	−	0.973957i	$-0.427196\pi$
$277$	7.54712			0.453462			0.226731	+	0.973957i	$0.427196\pi$
$278$	0.651501			0.0390744
$279$	−6.88101	−	8.12145i	−0.411955	−	0.486218i
$280$	0.0965796			0.00577174
$281$	5.61930			0.335220			0.167610	−	0.985853i	$-0.446395\pi$
$281$	5.61930			0.335220			0.167610	+	0.985853i	$0.446395\pi$
$282$	−6.96390	−	12.0618i	−0.414694	−	0.718271i
$283$	−8.04598			−0.478284			−0.239142	−	0.970985i	$-0.576866\pi$
$283$	−8.04598			−0.478284			−0.239142	+	0.970985i	$0.576866\pi$
$284$	2.96699	−	5.13899i	0.176059	−	0.304943i
$285$	−0.507581	−	0.879156i	−0.0300665	−	0.0520767i
$286$	0.326622	+	0.565725i	0.0193135	+	0.0334520i
$287$	2.09297			0.123544
$288$	−3.82675	+	6.62812i	−0.225493	+	0.390566i
$289$	3.35523	−	5.81143i	0.197367	−	0.341849i
$290$	0.101623	−	0.176017i	0.00596753	−	0.0103361i
$291$	−8.08481	−	14.0033i	−0.473940	−	0.820888i
$292$	−4.87783	+	8.44864i	−0.285453	+	0.494419i
$293$	4.65478	+	8.06231i	0.271935	+	0.471005i	0.969357	−	0.245655i	$-0.0790031\pi$
$293$	4.65478	+	8.06231i	0.271935	+	0.471005i	−0.697422	+	0.716660i	$0.745670\pi$
$294$	−8.11117			−0.473053
$295$	2.08327			0.121292
$296$	13.0677	+	22.6340i	0.759546	+	1.31557i
$297$	1.49954	−	2.59728i	0.0870122	−	0.150710i
$298$	−3.60803	−	6.24930i	−0.209008	−	0.362012i
$299$	0.417253	−	0.722703i	0.0241304	−	0.0417950i
$300$	1.95573	−	3.38743i	0.112914	−	0.195573i
$301$	−0.630200	+	1.09154i	−0.0363241	+	0.0629152i
$302$	−15.3631			−0.884046
$303$	−4.60230	−	7.97142i	−0.264395	−	0.457946i
$304$	−5.39810	−	9.34979i	−0.309603	−	0.536247i
$305$	−1.06134	+	1.83829i	−0.0607720	+	0.105260i
$306$	−6.84422			−0.391258
$307$	−5.32156	−	9.21721i	−0.303717	−	0.526054i	0.673258	−	0.739408i	$-0.264894\pi$
$307$	−5.32156	−	9.21721i	−0.303717	−	0.526054i	−0.976975	+	0.213354i	$0.931561\pi$
$308$	0.0800862			0.00456333
$309$	15.7834			0.897889
$310$	−0.695868	−	0.821312i	−0.0395227	−	0.0466474i
$311$	−26.1614			−1.48348			−0.741739	−	0.670688i	$-0.765999\pi$
$311$	−26.1614			−1.48348			−0.741739	+	0.670688i	$0.765999\pi$
$312$	3.20676			0.181547
$313$	−13.1652	−	22.8028i	−0.744141	−	1.28889i	−0.950595	−	0.310433i	$-0.899526\pi$
$313$	−13.1652	−	22.8028i	−0.744141	−	1.28889i	0.206455	−	0.978456i	$-0.433807\pi$
$314$	−23.0687			−1.30184
$315$	0.0300321	−	0.0520172i	0.00169212	−	0.00293084i
$316$	0.739332	+	1.28056i	0.0415907	+	0.0720371i
$317$	−12.9093	−	22.3596i	−0.725059	−	1.25584i	−0.958950	−	0.283576i	$-0.908479\pi$
$317$	−12.9093	−	22.3596i	−0.725059	−	1.25584i	0.233891	−	0.972263i	$-0.424854\pi$
$318$	1.01807			0.0570906
$319$	0.307658	−	0.532880i	0.0172256	−	0.0298355i
$320$	−0.719937	+	1.24697i	−0.0402457	+	0.0697076i
$321$	1.16221	−	2.01301i	0.0648685	−	0.112355i
$322$	0.0844517	+	0.146275i	0.00470631	+	0.00815156i
$323$	−9.00971	+	15.6053i	−0.501314	+	0.868301i
$324$	0.147303	+	0.255136i	0.00818350	+	0.0141742i
$325$	4.96999			0.275685
$326$	13.0614			0.723405
$327$	−1.28034	−	2.21761i	−0.0708030	−	0.122634i
$328$	−17.7386	+	30.7241i	−0.979449	+	1.69645i
$329$	−1.08480	−	1.87893i	−0.0598071	−	0.103589i
$330$	0.0590252	−	0.102235i	0.00324923	−	0.00562783i
$331$	−8.62211	+	14.9339i	−0.473914	+	0.820843i	−0.999554	−	0.0298641i	$-0.990493\pi$
$331$	−8.62211	+	14.9339i	−0.473914	+	0.820843i	0.525640	+	0.850707i	$0.323826\pi$
$332$	4.71834	−	8.17240i	0.258952	−	0.448519i
$333$	16.2540			0.890714
$334$	5.89239	+	10.2059i	0.322417	+	0.558443i
$335$	−0.195976	−	0.339441i	−0.0107073	−	0.0185456i
$336$	−0.181794	+	0.314876i	−0.00991765	+	0.0171779i
$337$	−29.1132			−1.58590			−0.792950	−	0.609287i	$-0.791456\pi$
$337$	−29.1132			−1.58590			−0.792950	+	0.609287i	$0.791456\pi$
$338$	0.558020	+	0.966519i	0.0303523	+	0.0525717i
$339$	16.4500			0.893441
$340$	0.419249			0.0227370
$341$	−2.10669	−	2.48647i	−0.114084	−	0.134650i
$342$	−11.9859			−0.648121
$343$	−2.53300			−0.136769
$344$	−10.6823	−	18.5023i	−0.575951	−	0.997577i
$345$	−0.150807			−0.00811918
$346$	5.76974	−	9.99348i	0.310183	−	0.537253i
$347$	−4.83210	−	8.36944i	−0.259401	−	0.449295i	0.706681	−	0.707533i	$-0.250192\pi$
$347$	−4.83210	−	8.36944i	−0.259401	−	0.449295i	−0.966082	+	0.258237i	$0.916858\pi$
$348$	−0.413673	−	0.716503i	−0.0221752	−	0.0384086i
$349$	−11.3746			−0.608868			−0.304434	−	0.952533i	$-0.598467\pi$
$349$	−11.3746			−0.608868			−0.304434	+	0.952533i	$0.598467\pi$
$350$	−0.502961	+	0.871154i	−0.0268844	+	0.0465651i
$351$	2.56191	−	4.43735i	0.136744	−	0.236848i
$352$	−1.17160	+	2.02927i	−0.0624464	+	0.108160i
$353$	−1.31464	−	2.27702i	−0.0699710	−	0.121193i	0.828917	−	0.559371i	$-0.188957\pi$
$353$	−1.31464	−	2.27702i	−0.0699710	−	0.121193i	−0.898888	+	0.438178i	$0.855624\pi$
$354$	−7.00010	+	12.1245i	−0.372051	+	0.644412i
$355$	−0.681279	−	1.18001i	−0.0361585	−	0.0626284i
$356$	11.3781			0.603036
$357$	0.606845			0.0321177
$358$	0.0199217	+	0.0345054i	0.00105290	+	0.00182367i
$359$	1.75089	−	3.03263i	0.0924083	−	0.160056i	−0.816116	−	0.577889i	$-0.803877\pi$
$359$	1.75089	−	3.03263i	0.0924083	−	0.160056i	0.908524	+	0.417833i	$0.137210\pi$
$360$	0.509064	+	0.881725i	0.0268300	+	0.0464710i
$361$	−6.27815	+	10.8741i	−0.330429	+	0.572320i
$362$	12.3139	−	21.3284i	0.647206	−	1.12099i
$363$	−5.55869	+	9.62793i	−0.291755	+	0.505335i
$364$	0.136824			0.00717153
$365$	1.12004	+	1.93997i	0.0586257	+	0.101543i
$366$	−7.13253	−	12.3539i	−0.372823	−	0.645749i
$367$	−3.22881	+	5.59246i	−0.168543	+	0.291924i	−0.937908	−	0.346885i	$-0.887239\pi$
$367$	−3.22881	+	5.59246i	−0.168543	+	0.291924i	0.769365	+	0.638809i	$0.220573\pi$
$368$	−1.60383			−0.0836053
$369$	11.0319	+	19.1078i	0.574296	+	0.994711i
$370$	1.64375			0.0854544
$371$	0.158590			0.00823360
$372$	−4.31168	+	0.781498i	−0.223550	+	0.0405188i
$373$	−1.69183			−0.0875995			−0.0437997	−	0.999040i	$-0.513946\pi$
$373$	−1.69183			−0.0875995			−0.0437997	+	0.999040i	$0.513946\pi$
$374$	−2.09543			−0.108352
$375$	−0.900859	−	1.56033i	−0.0465202	−	0.0805753i
$376$	36.7762			1.89659
$377$	0.525621	−	0.910403i	0.0270709	−	0.0468881i
$378$	0.518528	+	0.898117i	0.0266702	+	0.0461941i
$379$	−3.30883	−	5.73106i	−0.169963	−	0.294385i	0.768444	−	0.639918i	$-0.221032\pi$
$379$	−3.30883	−	5.73106i	−0.169963	−	0.294385i	−0.938407	+	0.345533i	$0.887698\pi$
$380$	0.734205			0.0376639
$381$	3.06386	−	5.30676i	0.156966	−	0.271874i
$382$	4.53413	−	7.85334i	0.231986	−	0.401812i
$383$	18.2570	−	31.6220i	0.932889	−	1.61581i	0.154533	−	0.987988i	$-0.450613\pi$
$383$	18.2570	−	31.6220i	0.932889	−	1.61581i	0.778356	−	0.627823i	$-0.216054\pi$
$384$	−0.662163	−	1.14690i	−0.0337909	−	0.0585275i
$385$	0.00919466	−	0.0159256i	0.000468603	−	0.000811644i
$386$	2.90518	+	5.03193i	0.147870	+	0.256118i
$387$	−13.2870			−0.675414
$388$	11.6945			0.593699
$389$	2.57956	+	4.46794i	0.130789	+	0.226533i	0.923981	−	0.382438i	$-0.124916\pi$
$389$	2.57956	+	4.46794i	0.130789	+	0.226533i	−0.793192	+	0.608972i	$0.791582\pi$
$390$	0.100842	−	0.174664i	0.00510634	−	0.00884444i
$391$	1.33843	+	2.31824i	0.0676875	+	0.117238i
$392$	10.7087	−	18.5481i	0.540873	−	0.936819i
$393$	9.08257	−	15.7315i	0.458155	−	0.793548i
$394$	−8.52538	+	14.7664i	−0.429502	+	0.743920i
$395$	0.339529			0.0170836
$396$	0.422128	+	0.731148i	0.0212128	+	0.0367416i
$397$	5.94650	+	10.2996i	0.298446	+	0.516924i	0.975781	−	0.218751i	$-0.0701983\pi$
$397$	5.94650	+	10.2996i	0.298446	+	0.516924i	−0.677334	+	0.735675i	$0.736865\pi$
$398$	−3.47992	+	6.02740i	−0.174433	+	0.302126i
$399$	1.06273			0.0532031
$400$	−4.77588	−	8.27207i	−0.238794	−	0.413604i
$401$	10.1445			0.506590			0.253295	−	0.967389i	$-0.418486\pi$
$401$	10.1445			0.506590			0.253295	+	0.967389i	$0.418486\pi$
$402$	2.63404			0.131374
$403$	−3.59920	−	4.24803i	−0.179289	−	0.211609i
$404$	6.65713			0.331205
$405$	0.0676471			0.00336141
$406$	0.106385	+	0.184265i	0.00527982	+	0.00914491i
$407$	4.97634			0.246668
$408$	−5.14321	+	8.90830i	−0.254627	+	0.441027i
$409$	−5.07112	−	8.78343i	−0.250751	−	0.434313i	0.712982	−	0.701182i	$-0.247344\pi$
$409$	−5.07112	−	8.78343i	−0.250751	−	0.434313i	−0.963733	+	0.266869i	$0.914011\pi$
$410$	1.11564	+	1.93235i	0.0550975	+	0.0954317i
$411$	−17.8371			−0.879839
$412$	−5.70760	+	9.88586i	−0.281193	+	0.487041i
$413$	−1.09044	+	1.88870i	−0.0536571	+	0.0929369i
$414$	−0.890277	+	1.54200i	−0.0437547	+	0.0757854i
$415$	−1.08342	−	1.87654i	−0.0531830	−	0.0921157i
$416$	−2.00163	+	3.46692i	−0.0981379	+	0.169980i
$417$	−0.304478	−	0.527372i	−0.0149104	−	0.0258255i
$418$	−3.66959			−0.179486
$419$	−0.798510			−0.0390098			−0.0195049	−	0.999810i	$-0.506209\pi$
$419$	−0.798510			−0.0390098			−0.0195049	+	0.999810i	$0.506209\pi$
$420$	−0.0123630	−	0.0214134i	−0.000603253	−	0.00104487i
$421$	−8.13019	+	14.0819i	−0.396241	+	0.686310i	−0.993259	−	0.115918i	$-0.963019\pi$
$421$	−8.13019	+	14.0819i	−0.396241	+	0.686310i	0.597017	+	0.802228i	$0.296352\pi$
$422$	−5.50647	−	9.53749i	−0.268051	−	0.464278i
$423$	11.4358	−	19.8074i	0.556029	−	0.963070i
$424$	−1.34410	+	2.32806i	−0.0652754	+	0.113060i
$425$	−7.97119	+	13.8065i	−0.386660	+	0.669714i
$426$	9.15682			0.443649
$427$	−1.11107	−	1.92443i	−0.0537685	−	0.0931297i
$428$	0.840559	+	1.45589i	0.0406299	+	0.0703731i
$429$	0.305293	−	0.528783i	0.0147397	−	0.0255299i
$430$	−1.34369			−0.0647987
$431$	6.75158	+	11.6941i	0.325212	+	0.563284i	0.981555	−	0.191179i	$-0.0612310\pi$
$431$	6.75158	+	11.6941i	0.325212	+	0.563284i	−0.656343	+	0.754462i	$0.727898\pi$
$432$	−9.84740			−0.473783
$433$	20.6346			0.991636			0.495818	−	0.868426i	$-0.334868\pi$
$433$	20.6346			0.991636			0.495818	+	0.868426i	$0.334868\pi$
$434$	1.10884	−	0.200980i	0.0532262	−	0.00964734i
$435$	−0.189975			−0.00910858
$436$	1.85198			0.0886940
$437$	2.34392	+	4.05978i	0.112125	+	0.194206i
$438$	−15.0541			−0.719311
$439$	19.2874	−	33.4068i	0.920539	−	1.59442i	0.121957	−	0.992535i	$-0.461083\pi$
$439$	19.2874	−	33.4068i	0.920539	−	1.59442i	0.798582	−	0.601886i	$-0.205584\pi$
$440$	0.155855	+	0.269949i	0.00743011	+	0.0128693i
$441$	−6.65992	−	11.5353i	−0.317139	−	0.549301i
$442$	−3.57996			−0.170281
$443$	15.3210	−	26.5368i	0.727925	−	1.26080i	−0.229834	−	0.973230i	$-0.573818\pi$
$443$	15.3210	−	26.5368i	0.727925	−	1.26080i	0.957759	−	0.287573i	$-0.0928483\pi$
$444$	3.34556	−	5.79468i	0.158773	−	0.275003i
$445$	1.30631	−	2.26259i	0.0619250	−	0.107257i
$446$	11.1521	+	19.3160i	0.528067	+	0.914639i
$447$	−3.37242	+	5.84121i	−0.159510	+	0.276280i
$448$	−0.753672	−	1.30540i	−0.0356077	−	0.0616743i
$449$	−22.5532			−1.06435			−0.532175	−	0.846634i	$-0.678625\pi$
$449$	−22.5532			−1.06435			−0.532175	+	0.846634i	$0.678625\pi$
$450$	−10.6043			−0.499891
$451$	3.37752	+	5.85004i	0.159041	+	0.275468i
$452$	−5.94864	+	10.3034i	−0.279801	+	0.484629i
$453$	7.17992	+	12.4360i	0.337342	+	0.584294i
$454$	2.92367	−	5.06395i	0.137215	−	0.237663i
$455$	0.0157087	−	0.0272083i	0.000736435	−	0.00127554i
$456$	−9.00699	+	15.6006i	−0.421791	+	0.730563i
$457$	28.3411			1.32574			0.662870	−	0.748735i	$-0.269338\pi$
$457$	28.3411			1.32574			0.662870	+	0.748735i	$0.269338\pi$
$458$	−8.66756	−	15.0126i	−0.405008	−	0.701495i
$459$	8.21791	+	14.2338i	0.383579	+	0.664378i
$460$	0.0545348	−	0.0944570i	0.00254270	−	0.00440408i
$461$	1.08011			0.0503059			0.0251529	−	0.999684i	$-0.491993\pi$
$461$	1.08011			0.0503059			0.0251529	+	0.999684i	$0.491993\pi$
$462$	0.0617910	+	0.107025i	0.00287478	+	0.00497926i
$463$	−9.51130			−0.442028			−0.221014	−	0.975271i	$-0.570937\pi$
$463$	−9.51130			−0.442028			−0.221014	+	0.975271i	$0.570937\pi$
$464$	−2.02037			−0.0937934
$465$	−0.339616	+	0.947126i	−0.0157493	+	0.0439219i
$466$	−26.8510			−1.24385
$467$	−15.4249			−0.713779			−0.356889	−	0.934147i	$-0.616163\pi$
$467$	−15.4249			−0.713779			−0.356889	+	0.934147i	$0.616163\pi$
$468$	0.721189	+	1.24914i	0.0333370	+	0.0577414i
$469$	0.410319			0.0189468
$470$	1.15649	−	2.00310i	0.0533450	−	0.0923962i
$471$	10.7811	+	18.6735i	0.496768	+	0.860428i
$472$	−18.4837	−	32.0147i	−0.850781	−	1.47360i
$473$	−4.06794			−0.187044
$474$	−1.14087	+	1.97605i	−0.0524020	+	0.0907630i
$475$	−13.9595	+	24.1785i	−0.640504	+	1.10938i
$476$	−0.219447	+	0.380094i	−0.0100583	+	0.0174216i
$477$	0.835918	+	1.44785i	0.0382740	+	0.0662926i
$478$	10.0361	−	17.3830i	0.459040	−	0.795081i
$479$	12.8957	+	22.3360i	0.589219	+	1.02056i	0.994335	+	0.106292i	$0.0338979\pi$
$479$	12.8957	+	22.3360i	0.589219	+	1.02056i	−0.405116	+	0.914265i	$0.632769\pi$
$480$	0.723446			0.0330206
$481$	8.50187			0.387652
$482$	−5.50230	−	9.53027i	−0.250623	−	0.434092i
$483$	0.0789368	−	0.136723i	0.00359175	−	0.00622109i
$484$	−4.02026	−	6.96330i	−0.182739	−	0.316514i
$485$	1.34264	−	2.32552i	0.0609662	−	0.105597i
$486$	−8.80488	+	15.2505i	−0.399397	+	0.691776i
$487$	−7.99534	+	13.8483i	−0.362303	+	0.627528i	−0.988339	−	0.152266i	$-0.951343\pi$
$487$	−7.99534	+	13.8483i	−0.362303	+	0.627528i	0.626036	+	0.779794i	$0.284676\pi$
$488$	37.6667			1.70509
$489$	−6.10424	−	10.5729i	−0.276043	−	0.478121i
$490$	−0.673509	−	1.16655i	−0.0304260	−	0.0526995i
$491$	−19.3962	+	33.5952i	−0.875338	+	1.51613i	−0.0189368	+	0.999821i	$0.506028\pi$
$491$	−19.3962	+	33.5952i	−0.875338	+	1.51613i	−0.856402	+	0.516310i	$0.827305\pi$
$492$	9.08275			0.409482
$493$	1.68605	+	2.92033i	0.0759360	+	0.131525i
$494$	−6.26935			−0.282072
$495$	0.193857			0.00871324
$496$	−3.61180	+	10.0726i	−0.162175	+	0.452275i
$497$	1.42640			0.0639830
$498$	14.5619			0.652533
$499$	−9.00060	−	15.5895i	−0.402922	−	0.697882i	0.591155	−	0.806558i	$-0.298672\pi$
$499$	−9.00060	−	15.5895i	−0.402922	−	0.697882i	−0.994077	+	0.108676i	$0.965339\pi$
$500$	1.30307			0.0582752
$501$	5.50761	−	9.53946i	0.246062	−	0.426191i
$502$	0.452930	+	0.784498i	0.0202153	+	0.0350139i
$503$	−0.321240	−	0.556403i	−0.0143234	−	0.0248088i	0.858775	−	0.512353i	$-0.171226\pi$
$503$	−0.321240	−	0.556403i	−0.0143234	−	0.0248088i	−0.873098	+	0.487544i	$0.837893\pi$
$504$	−1.06584			−0.0474761
$505$	0.764302	−	1.32381i	0.0340110	−	0.0589088i
$506$	−0.272568	+	0.472101i	−0.0121171	+	0.0209875i
$507$	0.521580	−	0.903404i	0.0231642	−	0.0401216i
$508$	2.21590	+	3.83806i	0.0983149	+	0.170286i
$509$	10.8621	−	18.8138i	0.481456	−	0.833906i	−0.518318	−	0.855188i	$-0.673442\pi$
$509$	10.8621	−	18.8138i	0.481456	−	0.833906i	0.999774	+	0.0212823i	$0.00677489\pi$
$510$	0.323474	+	0.560274i	0.0143237	+	0.0248094i
$511$	−2.34505			−0.103739
$512$	19.5099			0.862224
$513$	14.3915	+	24.9268i	0.635401	+	1.10055i
$514$	−0.486381	+	0.842437i	−0.0214534	+	0.0371583i
$515$	1.31057	+	2.26998i	0.0577508	+	0.100027i
$516$	−2.73485	+	4.73690i	−0.120395	+	0.208530i
$517$	3.50120	−	6.06425i	0.153983	−	0.266706i
$518$	−0.860386	+	1.49023i	−0.0378032	+	0.0654770i
$519$	−10.7859			−0.473450
$520$	0.266273	+	0.461198i	0.0116768	+	0.0202249i
$521$	−12.2483	−	21.2147i	−0.536609	−	0.929435i	−0.999084	−	0.0428020i	$-0.986372\pi$
$521$	−12.2483	−	21.2147i	−0.536609	−	0.929435i	0.462474	−	0.886633i	$-0.346962\pi$
$522$	−1.12150	+	1.94249i	−0.0490867	+	0.0850206i
$523$	−36.8039			−1.60932			−0.804662	−	0.593734i	$-0.797653\pi$
$523$	−36.8039			−1.60932			−0.804662	+	0.593734i	$0.797653\pi$
$524$	6.56887	+	11.3776i	0.286963	+	0.497034i
$525$	0.940233			0.0410352
$526$	25.6030			1.11634
$527$	17.5736	−	3.18523i	0.765516	−	0.138751i
$528$	−1.17348			−0.0510691
$529$	−22.3036			−0.969722
$530$	0.0845353	+	0.146419i	0.00367198	+	0.00636006i
$531$	−22.9906			−0.997705
$532$	−0.384304	+	0.665635i	−0.0166617	+	0.0288589i
$533$	5.77036	+	9.99456i	0.249942	+	0.432913i
$534$	8.77882	+	15.2054i	0.379897	+	0.658000i
$535$	0.386017			0.0166890
$536$	−3.47758	+	6.02335i	−0.150209	+	0.260169i
$537$	0.0186208	−	0.0322522i	0.000803547	−	0.00139178i
$538$	10.0210	−	17.3569i	0.432036	−	0.748307i
$539$	−2.03900	−	3.53166i	−0.0878261	−	0.152119i
$540$	0.334840	−	0.579960i	0.0144092	−	0.0249575i
$541$	20.2107	+	35.0060i	0.868927	+	1.50503i	0.863094	+	0.505043i	$0.168523\pi$
$541$	20.2107	+	35.0060i	0.868927	+	1.50503i	0.00583244	+	0.999983i	$0.498143\pi$
$542$	29.5574			1.26960
$543$	−23.0196			−0.987867
$544$	−6.42069	−	11.1210i	−0.275285	−	0.476807i
$545$	0.212625	−	0.368278i	0.00910787	−	0.0157753i
$546$	0.105567	+	0.182848i	0.00451787	+	0.00782518i
$547$	0.131145	−	0.227150i	0.00560735	−	0.00971222i	−0.863208	−	0.504848i	$-0.831548\pi$
$547$	0.131145	−	0.227150i	0.00560735	−	0.00971222i	0.868815	+	0.495136i	$0.164882\pi$
$548$	6.45025	−	11.1722i	0.275541	−	0.477251i
$549$	11.7127	−	20.2871i	0.499888	−	0.865831i
$550$	−3.24661			−0.138436
$551$	2.95268	+	5.11419i	0.125788	+	0.217872i
$552$	1.33803	+	2.31754i	0.0569503	+	0.0986409i
$553$	−0.177720	+	0.307819i	−0.00755741	+	0.0130898i
$554$	−8.42289			−0.357854
$555$	−0.768204	−	1.33057i	−0.0326085	−	0.0564795i
$556$	0.440421			0.0186780
$557$	0.108532			0.00459863			0.00229932	−	0.999997i	$-0.499268\pi$
$557$	0.108532			0.00459863			0.00229932	+	0.999997i	$0.499268\pi$
$558$	7.67949	+	9.06386i	0.325099	+	0.383704i
$559$	−6.94991			−0.293950
$560$	−0.0603807			−0.00255155
$561$	0.979297	+	1.69619i	0.0413459	+	0.0716133i
$562$	−6.27137			−0.264542
$563$	15.5592	−	26.9492i	0.655740	−	1.13578i	−0.325968	−	0.945381i	$-0.605690\pi$
$563$	15.5592	−	26.9492i	0.655740	−	1.13578i	0.981708	−	0.190394i	$-0.0609766\pi$
$564$	−4.70767	−	8.15392i	−0.198229	−	0.343342i
$565$	1.36592	+	2.36585i	0.0574648	+	0.0995319i
$566$	8.97963			0.377442
$567$	−0.0354085	+	0.0613293i	−0.00148702	+	0.00257559i
$568$	−12.0892	+	20.9392i	−0.507253	+	0.878588i
$569$	−17.2321	+	29.8469i	−0.722409	+	1.25125i	0.237623	+	0.971358i	$0.423632\pi$
$569$	−17.2321	+	29.8469i	−0.722409	+	1.25125i	−0.960032	+	0.279892i	$0.909702\pi$
$570$	0.566481	+	0.981173i	0.0237273	+	0.0410968i
$571$	−13.1202	+	22.7248i	−0.549061	+	0.951002i	0.449278	+	0.893392i	$0.351681\pi$
$571$	−13.1202	+	22.7248i	−0.549061	+	0.951002i	−0.998339	+	0.0576101i	$0.981652\pi$
$572$	0.220800	+	0.382436i	0.00923210	+	0.0159905i
$573$	−8.47609			−0.354094
$574$	−2.33583			−0.0974958
$575$	2.07374	+	3.59183i	0.0864810	+	0.149790i
$576$	7.94510	−	13.7613i	0.331046	−	0.573388i
$577$	5.38685	+	9.33030i	0.224257	+	0.388425i	0.956096	−	0.293052i	$-0.0946710\pi$
$577$	5.38685	+	9.33030i	0.224257	+	0.388425i	−0.731839	+	0.681478i	$0.761338\pi$
$578$	−3.74457	+	6.48579i	−0.155754	+	0.269773i
$579$	2.71547	−	4.70333i	0.112851	−	0.195464i
$580$	0.0686985	−	0.118989i	0.00285255	−	0.00494076i
$581$	2.26838			0.0941081
$582$	9.02298	+	15.6283i	0.374014	+	0.647812i
$583$	0.255925	+	0.443275i	0.0105993	+	0.0183586i
$584$	19.8751	−	34.4246i	0.822436	−	1.42450i
$585$	0.331198			0.0136933
$586$	−5.19492	−	8.99786i	−0.214600	−	0.371698i
$587$	7.97657			0.329228			0.164614	−	0.986358i	$-0.447362\pi$
$587$	7.97657			0.329228			0.164614	+	0.986358i	$0.447362\pi$
$588$	−5.48324			−0.226125
$589$	30.7755	−	5.57810i	1.26808	−	0.229842i
$590$	−2.32501			−0.0957190
$591$	15.9373			0.655573
$592$	−8.16982	−	14.1506i	−0.335778	−	0.581584i
$593$	−14.6375			−0.601091			−0.300545	−	0.953768i	$-0.597169\pi$
$593$	−14.6375			−0.601091			−0.300545	+	0.953768i	$0.597169\pi$
$594$	−1.67355	+	2.89867i	−0.0686665	+	0.118934i
$595$	0.0503893	+	0.0872768i	0.00206576	+	0.00357800i
$596$	−2.43907	−	4.22459i	−0.0999081	−	0.173046i
$597$	6.50535			0.266246
$598$	−0.465671	+	0.806566i	−0.0190427	+	0.0329829i
$599$	19.5932	−	33.9365i	0.800557	−	1.38661i	−0.118692	−	0.992931i	$-0.537870\pi$
$599$	19.5932	−	33.9365i	0.800557	−	1.38661i	0.919250	−	0.393675i	$-0.128796\pi$
$600$	−7.96878	+	13.8023i	−0.325324	+	0.563478i
$601$	0.786399	+	1.36208i	0.0320779	+	0.0555605i	0.881619	−	0.471962i	$-0.156454\pi$
$601$	0.786399	+	1.36208i	0.0320779	+	0.0555605i	−0.849541	+	0.527523i	$0.823121\pi$
$602$	0.703329	−	1.21820i	0.0286655	−	0.0496502i
$603$	2.16276	+	3.74601i	0.0880744	+	0.152549i
$604$	−10.3856			−0.422584
$605$	−1.84626			−0.0750610
$606$	5.13635	+	8.89642i	0.208650	+	0.361392i
$607$	−2.31788	+	4.01469i	−0.0940800	+	0.162951i	−0.909224	−	0.416307i	$-0.863324\pi$
$607$	−2.31788	+	4.01469i	−0.0940800	+	0.162951i	0.815144	+	0.579258i	$0.196658\pi$
$608$	−11.2442	−	19.4754i	−0.456011	−	0.789833i
$609$	0.0994382	−	0.172232i	0.00402944	−	0.00697920i
$610$	1.18450	−	2.05161i	0.0479588	−	0.0830671i
$611$	5.98166	−	10.3605i	0.241992	−	0.419142i
$612$	−4.62676			−0.187026
$613$	9.14022	+	15.8313i	0.369170	+	0.639421i	0.989436	−	0.144970i	$-0.0463087\pi$
$613$	9.14022	+	15.8313i	0.369170	+	0.639421i	−0.620266	+	0.784391i	$0.712975\pi$
$614$	5.93907	+	10.2868i	0.239681	+	0.415140i
$615$	1.04279	−	1.80616i	0.0420492	−	0.0728314i
$616$	−0.326317			−0.0131477
$617$	−18.9165	−	32.7644i	−0.761550	−	1.31904i	−0.942051	−	0.335468i	$-0.891105\pi$
$617$	−18.9165	−	32.7644i	−0.761550	−	1.31904i	0.180502	−	0.983575i	$-0.442228\pi$
$618$	−17.6150			−0.708578
$619$	−16.3751			−0.658170			−0.329085	−	0.944300i	$-0.606740\pi$
$619$	−16.3751			−0.658170			−0.329085	+	0.944300i	$0.606740\pi$
$620$	−0.470414	−	0.555215i	−0.0188923	−	0.0222980i
$621$	4.27585			0.171584
$622$	29.1972			1.17070
$623$	1.36752	+	2.36862i	0.0547886	+	0.0948966i
$624$	−2.00484			−0.0802578
$625$	−12.2754	+	21.2616i	−0.491015	+	0.850462i
$626$	14.6929	+	25.4488i	0.587246	+	1.01714i
$627$	1.71498	+	2.97044i	0.0684898	+	0.118628i
$628$	−15.5947			−0.622295
$629$	−13.6359	+	23.6180i	−0.543697	+	0.941711i
$630$	−0.0335171	+	0.0580533i	−0.00133535	+	0.00231290i
$631$	−3.55895	+	6.16428i	−0.141680	+	0.245396i	−0.928129	−	0.372258i	$-0.878584\pi$
$631$	−3.55895	+	6.16428i	−0.141680	+	0.245396i	0.786450	+	0.617654i	$0.211917\pi$
$632$	−3.01246	−	5.21774i	−0.119829	−	0.207550i
$633$	−5.14689	+	8.91467i	−0.204570	+	0.354326i
$634$	14.4073	+	24.9542i	0.572187	+	0.991057i
$635$	1.01763			0.0403833
$636$	0.688227			0.0272900
$637$	−3.48356	−	6.03369i	−0.138023	−	0.239064i
$638$	−0.343359	+	0.594715i	−0.0135937	+	0.0235450i
$639$	7.51847	+	13.0224i	0.297426	+	0.515157i
$640$	0.109965	−	0.190465i	0.00434675	−	0.00752880i
$641$	8.71262	−	15.0907i	0.344128	−	0.596047i	−0.641067	−	0.767485i	$-0.721508\pi$
$641$	8.71262	−	15.0907i	0.344128	−	0.596047i	0.985195	+	0.171438i	$0.0548413\pi$
$642$	−1.29708	+	2.24660i	−0.0511916	+	0.0886664i
$643$	10.9671			0.432500			0.216250	−	0.976338i	$-0.430617\pi$
$643$	10.9671			0.432500			0.216250	+	0.976338i	$0.430617\pi$
$644$	0.0570902	+	0.0988831i	0.00224967	+	0.00389654i
$645$	0.627974	+	1.08768i	0.0247265	+	0.0428275i
$646$	10.0552	−	17.4161i	0.395616	−	0.685228i
$647$	23.9731			0.942481			0.471241	−	0.882005i	$-0.343806\pi$
$647$	23.9731			0.942481			0.471241	+	0.882005i	$0.343806\pi$
$648$	−0.600197	−	1.03957i	−0.0235780	−	0.0408382i
$649$	−7.03880			−0.276297
$650$	−5.54671			−0.217560
$651$	−0.680905	−	0.803651i	−0.0266868	−	0.0314976i
$652$	8.82965			0.345796
$653$	35.6392			1.39467			0.697335	−	0.716745i	$-0.254369\pi$
$653$	35.6392			1.39467			0.697335	+	0.716745i	$0.254369\pi$
$654$	1.42891	+	2.47495i	0.0558748	+	0.0967781i
$655$	3.01668			0.117871
$656$	11.0900	−	19.2084i	0.432992	−	0.749964i
$657$	−12.3606	−	21.4092i	−0.482233	−	0.835251i
$658$	1.21068	+	2.09696i	0.0471973	+	0.0817482i
$659$	7.95764			0.309986			0.154993	−	0.987916i	$-0.450465\pi$
$659$	7.95764			0.309986			0.154993	+	0.987916i	$0.450465\pi$
$660$	0.0399016	−	0.0691117i	0.00155317	−	0.00269017i
$661$	19.0817	−	33.0505i	0.742192	−	1.28551i	−0.209304	−	0.977851i	$-0.567120\pi$
$661$	19.0817	−	33.0505i	0.742192	−	1.28551i	0.951495	−	0.307663i	$-0.0995470\pi$
$662$	9.62262	−	16.6669i	0.373994	−	0.647776i
$663$	1.67309	+	2.89788i	0.0649774	+	0.112544i
$664$	−19.2252	+	33.2991i	−0.746083	+	1.29225i
$665$	0.0882436	+	0.152842i	0.00342194	+	0.00592697i
$666$	−18.1401			−0.702916
$667$	0.877268			0.0339680
$668$	3.98332	+	6.89931i	0.154119	+	0.266942i
$669$	10.4238	−	18.0546i	0.403009	−	0.698032i
$670$	0.218717	+	0.378829i	0.00844979	+	0.0146355i
$671$	3.58598	−	6.21110i	0.138435	−	0.239777i
$672$	−0.378673	+	0.655880i	−0.0146076	+	0.0253011i
$673$	10.7212	−	18.5696i	0.413270	−	0.715805i	−0.581975	−	0.813207i	$-0.697720\pi$
$673$	10.7212	−	18.5696i	0.413270	−	0.715805i	0.995245	+	0.0974019i	$0.0310532\pi$
$674$	32.4915			1.25153
$675$	12.7326	+	22.0536i	0.490080	+	0.848843i
$676$	0.377227	+	0.653377i	0.0145087	+	0.0251299i
$677$	−24.9484	+	43.2119i	−0.958845	+	1.66077i	−0.233533	+	0.972349i	$0.575029\pi$
$677$	−24.9484	+	43.2119i	−0.958845	+	1.66077i	−0.725313	+	0.688420i	$0.758305\pi$
$678$	−18.3589			−0.705068
$679$	1.40556	+	2.43449i	0.0539403	+	0.0934273i
$680$	−1.70826			−0.0655088
$681$	−5.46550			−0.209438
$682$	2.35116	+	2.77500i	0.0900304	+	0.106260i
$683$	−0.0275671			−0.00105483			−0.000527414	−	1.00000i	$-0.500168\pi$
$683$	−0.0275671			−0.00105483			−0.000527414		1.00000i	$0.500168\pi$
$684$	−8.10256			−0.309809
$685$	−1.48110	−	2.56534i	−0.0565899	−	0.0980166i
$686$	2.82693			0.107933
$687$	−8.10155	+	14.0323i	−0.309093	+	0.535365i
$688$	6.67848	+	11.5675i	0.254615	+	0.441006i
$689$	0.437237	+	0.757318i	0.0166574	+	0.0288515i
$690$	0.168307			0.00640732
$691$	24.9840	−	43.2736i	0.950437	−	1.64621i	0.205957	−	0.978561i	$-0.433969\pi$
$691$	24.9840	−	43.2736i	0.950437	−	1.64621i	0.744480	−	0.667645i	$-0.232697\pi$
$692$	3.90040	−	6.75569i	0.148271	−	0.256813i
$693$	−0.101471	+	0.175752i	−0.00385455	+	0.00667628i
$694$	5.39282	+	9.34063i	0.204709	+	0.354566i
$695$	0.0505646	−	0.0875804i	0.00191802	−	0.00332211i
$696$	1.68554	+	2.91944i	0.0638903	+	0.110661i
$697$	−37.0195			−1.40222
$698$	12.6945			0.480494
$699$	12.5488	+	21.7351i	0.474638	+	0.822098i
$700$	−0.340007	+	0.588909i	−0.0128511	+	0.0222587i
$701$	4.38904	+	7.60205i	0.165772	+	0.287125i	0.936929	−	0.349519i	$-0.113655\pi$
$701$	4.38904	+	7.60205i	0.165772	+	0.287125i	−0.771157	+	0.636645i	$0.780322\pi$
$702$	−2.85919	+	4.95226i	−0.107913	+	0.186911i
$703$	−23.8796	+	41.3607i	−0.900637	+	1.55995i
$704$	2.43248	−	4.21317i	0.0916774	−	0.158790i
$705$	−2.16194			−0.0814234
$706$	1.46719	+	2.54124i	0.0552183	+	0.0956408i
$707$	0.800116	+	1.38584i	0.0300915	+	0.0521199i
$708$	−4.73214	+	8.19631i	−0.177845	+	0.308036i
$709$	33.9270			1.27416			0.637078	−	0.770800i	$-0.280143\pi$
$709$	33.9270			1.27416			0.637078	+	0.770800i	$0.280143\pi$
$710$	0.760334	+	1.31694i	0.0285348	+	0.0494238i
$711$	−3.74699			−0.140523
$712$	−46.3608			−1.73744
$713$	1.56829	−	4.37366i	0.0587328	−	0.163795i
$714$	−0.677264			−0.0253460
$715$	0.101400			0.00379213
$716$	0.0134673	+	0.0233260i	0.000503296	+	0.000871735i
$717$	−18.7614			−0.700658
$718$	−1.95406	+	3.38453i	−0.0729249	+	0.126310i
$719$	7.01534	+	12.1509i	0.261628	+	0.453153i	0.966675	−	0.256008i	$-0.0824073\pi$
$719$	7.01534	+	12.1509i	0.261628	+	0.453153i	−0.705047	+	0.709161i	$0.749074\pi$
$720$	−0.318262	−	0.551247i	−0.0118609	−	0.0205438i
$721$	−2.74397			−0.102191
$722$	7.00667	−	12.1359i	0.260761	−	0.451651i
$723$	−5.14299	+	8.90792i	−0.191270	+	0.331289i
$724$	8.32435	−	14.4182i	0.309372	−	0.535848i
$725$	2.61233	+	4.52469i	0.0970196	+	0.168043i
$726$	6.20372	−	10.7452i	0.230242	−	0.398790i
$727$	−17.0289	−	29.4949i	−0.631566	−	1.09390i	−0.987232	−	0.159291i	$-0.949079\pi$
$727$	−17.0289	−	29.4949i	−0.631566	−	1.09390i	0.355665	−	0.934613i	$-0.384254\pi$
$728$	−0.557500			−0.0206623
$729$	15.2883			0.566235
$730$	−1.25001	−	2.16508i	−0.0462650	−	0.0801333i
$731$	11.1467	−	19.3067i	0.412277	−	0.714084i
$732$	−4.82166	−	8.35137i	−0.178214	−	0.308675i
$733$	20.4615	−	35.4403i	0.755762	−	1.30902i	−0.189233	−	0.981932i	$-0.560600\pi$
$733$	20.4615	−	35.4403i	0.755762	−	1.30902i	0.944995	−	0.327086i	$-0.106067\pi$
$734$	3.60348	−	6.24141i	0.133007	−	0.230375i
$735$	−0.629528	+	1.09037i	−0.0232205	+	0.0402191i
$736$	−3.34074			−0.123141
$737$	0.662152	+	1.14688i	0.0243907	+	0.0422459i
$738$	−12.3120	−	21.3250i	−0.453211	−	0.784985i
$739$	−6.09919	+	10.5641i	−0.224362	+	0.388607i	−0.956128	−	0.292950i	$-0.905363\pi$
$739$	−6.09919	+	10.5641i	−0.224362	+	0.388607i	0.731766	+	0.681556i	$0.238697\pi$
$740$	1.11119			0.0408482
$741$	2.92998	+	5.07487i	0.107635	+	0.186430i
$742$	−0.176993			−0.00649762
$743$	23.8548			0.875147			0.437573	−	0.899183i	$-0.355838\pi$
$743$	23.8548			0.875147			0.437573	+	0.899183i	$0.355838\pi$
$744$	17.5682	−	3.18427i	0.644083	−	0.116741i
$745$	−1.12011			−0.0410378
$746$	1.88815			0.0691300
$747$	11.9564	+	20.7092i	0.437463	+	0.757709i
$748$	−1.41653			−0.0517935
$749$	−0.202052	+	0.349965i	−0.00738283	+	0.0127874i
$750$	1.00539	+	1.74140i	0.0367118	+	0.0635868i
$751$	−17.6782	−	30.6195i	−0.645086	−	1.11732i	−0.984282	−	0.176605i	$-0.943488\pi$
$751$	−17.6782	−	30.6195i	−0.645086	−	1.11732i	0.339196	−	0.940716i	$-0.389845\pi$
$752$	−22.9922			−0.838438
$753$	0.423353	−	0.733269i	0.0154278	−	0.0267218i
$754$	−0.586615	+	1.01605i	−0.0213632	+	0.0370022i
$755$	−1.19237	+	2.06524i	−0.0433946	+	0.0751617i
$756$	0.350530	+	0.607136i	0.0127487	+	0.0220813i
$757$	−3.63714	+	6.29971i	−0.132194	+	0.228967i	−0.924522	−	0.381128i	$-0.875536\pi$
$757$	−3.63714	+	6.29971i	−0.132194	+	0.228967i	0.792328	+	0.610095i	$0.208869\pi$
$758$	3.69279	+	6.39609i	0.134128	+	0.232317i
$759$	0.509537			0.0184950
$760$	−2.99157			−0.108516
$761$	9.88488	+	17.1211i	0.358327	+	0.620640i	0.987681	−	0.156478i	$-0.0500141\pi$
$761$	9.88488	+	17.1211i	0.358327	+	0.620640i	−0.629355	+	0.777118i	$0.716681\pi$
$762$	−3.41939	+	5.92256i	−0.123871	+	0.214552i
$763$	0.222589	+	0.385535i	0.00805826	+	0.0139573i
$764$	3.06512	−	5.30894i	0.110892	−	0.192071i
$765$	−0.531196	+	0.920059i	−0.0192054	+	0.0332648i
$766$	−20.3755	+	35.2915i	−0.736198	+	1.27513i
$767$	−12.0255			−0.434216
$768$	−7.93131	−	13.7374i	−0.286196	−	0.495707i
$769$	−10.1807	−	17.6335i	−0.367125	−	0.635879i	0.621990	−	0.783025i	$-0.286325\pi$
$769$	−10.1807	−	17.6335i	−0.367125	−	0.635879i	−0.989115	+	0.147146i	$0.952991\pi$
$770$	−0.0102616	+	0.0177736i	−0.000369803	+	0.000640517i
$771$	0.909240			0.0327455
$772$	1.96393	+	3.40163i	0.0706835	+	0.122427i
$773$	36.9006			1.32722			0.663612	−	0.748077i	$-0.269023\pi$
$773$	36.9006			1.32722			0.663612	+	0.748077i	$0.269023\pi$
$774$	14.8288			0.533009
$775$	27.2281	−	4.93513i	0.978062	−	0.177275i
$776$	−47.6501			−1.71054
$777$	1.60840			0.0577011
$778$	−2.87890	−	4.98639i	−0.103213	−	0.178771i
$779$	−64.8300			−2.32278
$780$	0.0681703	−	0.118074i	0.00244089	−	0.00422774i
$781$	2.30186	+	3.98694i	0.0823670	+	0.142664i
$782$	−1.49375	−	2.58724i	−0.0534163	−	0.0925197i
$783$	5.38637			0.192493
$784$	−6.69501	+	11.5961i	−0.239107	+	0.414146i
$785$	−1.79042	+	3.10109i	−0.0639027	+	0.110683i
$786$	−10.1365	+	17.5570i	−0.361558	+	0.626236i
$787$	25.9800	+	44.9988i	0.926088	+	1.60403i	0.789801	+	0.613363i	$0.210184\pi$
$787$	25.9800	+	44.9988i	0.926088	+	1.60403i	0.136287	+	0.990669i	$0.456483\pi$
$788$	−5.76324	+	9.98223i	−0.205307	+	0.355602i
$789$	−11.9655	−	20.7249i	−0.425985	−	0.737827i
$790$	−0.378928			−0.0134817
$791$	−2.85985			−0.101685
$792$	−1.71999	−	2.97912i	−0.0611173	−	0.105858i
$793$	6.12650	−	10.6114i	0.217558	−	0.376822i
$794$	−6.63653	−	11.4948i	−0.235522	−	0.407936i
$795$	0.0790150	−	0.136858i	0.00280237	−	0.00485385i
$796$	−2.35246	+	4.07458i	−0.0833808	+	0.144420i
$797$	−0.770555	+	1.33464i	−0.0272945	+	0.0472754i	−0.879350	−	0.476176i	$-0.842023\pi$
$797$	−0.770555	+	1.33464i	−0.0272945	+	0.0472754i	0.852056	+	0.523451i	$0.175356\pi$
$798$	−1.18605			−0.0419857
$799$	19.1875	+	33.2338i	0.678806	+	1.17573i
$800$	−9.94807	−	17.2306i	−0.351718	−	0.609193i
$801$	−14.4162	+	24.9696i	−0.509372	+	0.882258i
$802$	−11.3216			−0.399780
$803$	−3.78433	−	6.55464i	−0.133546	−	0.231308i
$804$	1.78064			0.0627984
$805$	0.0262180			0.000924063
$806$	4.01685	+	4.74097i	0.141488	+	0.166994i
$807$	−18.7332			−0.659440
$808$	−27.1250			−0.954253
$809$	7.71492	+	13.3626i	0.271242	+	0.469805i	0.969180	−	0.246353i	$-0.0792322\pi$
$809$	7.71492	+	13.3626i	0.271242	+	0.469805i	−0.697938	+	0.716158i	$0.745899\pi$
$810$	−0.0754969			−0.00265269
$811$	0.974150	−	1.68728i	0.0342070	−	0.0592483i	−0.848415	−	0.529332i	$-0.822443\pi$
$811$	0.974150	−	1.68728i	0.0342070	−	0.0592483i	0.882622	+	0.470083i	$0.155776\pi$
$812$	0.0719176	+	0.124565i	0.00252381	+	0.00437137i
$813$	−13.8136	−	23.9259i	−0.484464	−	0.839117i
$814$	−5.55379			−0.194660
$815$	1.01373	−	1.75583i	0.0355094	−	0.0615040i
$816$	3.21549	−	5.56939i	0.112565	−	0.194968i
$817$	19.5206	−	33.8106i	0.682938	−	1.18288i
$818$	5.65957	+	9.80266i	0.197882	+	0.342742i
$819$	−0.173359	+	0.300266i	−0.00605764	+	0.0104921i
$820$	0.754184	+	1.30629i	0.0263373	+	0.0456175i
$821$	−24.8626			−0.867711			−0.433856	−	0.900982i	$-0.642847\pi$
$821$	−24.8626			−0.867711			−0.433856	+	0.900982i	$0.642847\pi$
$822$	19.9069			0.694334
$823$	2.92080	+	5.05897i	0.101813	+	0.176345i	0.912432	−	0.409229i	$-0.134202\pi$
$823$	2.92080	+	5.05897i	0.101813	+	0.176345i	−0.810619	+	0.585574i	$0.800869\pi$
$824$	23.2561	−	40.2807i	0.810163	−	1.40324i
$825$	1.51730	+	2.62804i	0.0528257	+	0.0914967i
$826$	1.21698	−	2.10787i	0.0423440	−	0.0733420i
$827$	16.1247	−	27.9289i	0.560712	−	0.971181i	−0.436723	−	0.899596i	$-0.643861\pi$
$827$	16.1247	−	27.9289i	0.560712	−	0.971181i	0.997434	−	0.0715851i	$-0.0228058\pi$
$828$	−0.601836	+	1.04241i	−0.0209153	+	0.0362263i
$829$	17.0299			0.591473			0.295736	−	0.955270i	$-0.404435\pi$
$829$	17.0299			0.591473			0.295736	+	0.955270i	$0.404435\pi$
$830$	1.20914	+	2.09429i	0.0419699	+	0.0726940i
$831$	3.93643	+	6.81809i	0.136553	+	0.236517i
$832$	4.15579	−	7.19803i	0.144076	−	0.249547i
$833$	22.3486			0.774334
$834$	0.339810	+	0.588568i	0.0117667	+	0.0203804i
$835$	1.82929			0.0633052
$836$	−2.48068			−0.0857963
$837$	9.62918	−	26.8540i	0.332833	−	0.928209i
$838$	0.891169			0.0307849
$839$	−35.4523			−1.22395			−0.611975	−	0.790877i	$-0.709625\pi$
$839$	−35.4523			−1.22395			−0.611975	+	0.790877i	$0.709625\pi$
$840$	0.0503740	+	0.0872504i	0.00173807	+	0.00301042i
$841$	−27.8949			−0.961893
$842$	9.07362	−	15.7160i	0.312698	−	0.541608i
$843$	2.93092	+	5.07650i	0.100946	+	0.174844i
$844$	−3.72243	−	6.44744i	−0.128131	−	0.221930i
$845$	0.173237			0.00595954
$846$	−12.7628	+	22.1059i	−0.438795	+	0.760016i
$847$	0.966385	−	1.67383i	0.0332054	−	0.0575134i
$848$	0.840322	−	1.45548i	0.0288568	−	0.0499814i
$849$	−4.19662	−	7.26876i	−0.144028	−	0.249463i
$850$	8.89617	−	15.4086i	0.305136	−	0.528511i
$851$	3.54743	+	6.14433i	0.121604	+	0.210625i
$852$	6.19010			0.212069
$853$	−52.4730			−1.79664			−0.898320	−	0.439341i	$-0.855212\pi$
$853$	−52.4730			−1.79664			−0.898320	+	0.439341i	$0.855212\pi$
$854$	1.24000	+	2.14774i	0.0424319	+	0.0734942i
$855$	−0.930251	+	1.61124i	−0.0318139	+	0.0551033i
$856$	−3.42492	−	5.93213i	−0.117061	−	0.202756i
$857$	−5.40490	+	9.36155i	−0.184628	+	0.319785i	−0.943451	−	0.331512i	$-0.892441\pi$
$857$	−5.40490	+	9.36155i	−0.184628	+	0.319785i	0.758823	+	0.651297i	$0.225775\pi$
$858$	−0.340719	+	0.590143i	−0.0116320	+	0.0201471i
$859$	−19.1594	+	33.1851i	−0.653710	+	1.13226i	0.328505	+	0.944502i	$0.393455\pi$
$859$	−19.1594	+	33.1851i	−0.653710	+	1.13226i	−0.982215	+	0.187757i	$0.939878\pi$
$860$	−0.908351			−0.0309745
$861$	1.09165	+	1.89079i	0.0372033	+	0.0644381i
$862$	−7.53503	−	13.0511i	−0.256644	−	0.444521i
$863$	20.8540	−	36.1203i	0.709880	−	1.22955i	−0.255021	−	0.966935i	$-0.582083\pi$
$863$	20.8540	−	36.1203i	0.709880	−	1.22955i	0.964901	−	0.262613i	$-0.0845841\pi$
$864$	−20.5119			−0.697831
$865$	−0.895607	−	1.55124i	−0.0304515	−	0.0527436i
$866$	−23.0291			−0.782559
$867$	7.00009			0.237736
$868$	0.749590	−	0.135864i	0.0254428	−	0.00461154i
$869$	−1.14718			−0.0389154
$870$	0.212019			0.00718812
$871$	1.13126	+	1.95940i	0.0383313	+	0.0663917i
$872$	−7.54605			−0.255541
$873$	−14.8172	+	25.6641i	−0.501485	+	0.868597i
$874$	−2.61591	−	4.53088i	−0.0884843	−	0.153259i
$875$	0.156616	+	0.271266i	0.00529457	+	0.00917047i
$876$	−10.1767			−0.343839
$877$	23.8015	−	41.2254i	0.803720	−	1.39208i	−0.113432	−	0.993546i	$-0.536184\pi$
$877$	23.8015	−	41.2254i	0.803720	−	1.39208i	0.917152	−	0.398538i	$-0.130482\pi$
$878$	−21.5256	+	37.2834i	−0.726452	+	1.25825i
$879$	−4.85568	+	8.41029i	−0.163778	+	0.283672i
$880$	−0.0974394	−	0.168770i	−0.00328468	−	0.00568924i
$881$	5.32324	−	9.22013i	0.179345	−	0.310634i	−0.762312	−	0.647210i	$-0.775936\pi$
$881$	5.32324	−	9.22013i	0.179345	−	0.310634i	0.941656	+	0.336576i	$0.109269\pi$
$882$	7.43273	+	12.8739i	0.250273	+	0.433486i
$883$	34.4079			1.15792			0.578958	−	0.815357i	$-0.303459\pi$
$883$	34.4079			1.15792			0.578958	+	0.815357i	$0.303459\pi$
$884$	−2.42009			−0.0813963
$885$	1.08659	+	1.88203i	0.0365253	+	0.0632637i
$886$	−17.0989	+	29.6162i	−0.574449	+	0.994974i
$887$	−1.29883	−	2.24965i	−0.0436106	−	0.0755357i	0.843396	−	0.537292i	$-0.180553\pi$
$887$	−1.29883	−	2.24965i	−0.0436106	−	0.0755357i	−0.887007	+	0.461756i	$0.847219\pi$
$888$	−13.6317	+	23.6109i	−0.457451	+	0.792328i
$889$	−0.532656	+	0.922588i	−0.0178647	+	0.0309426i
$890$	−1.45789	+	2.52515i	−0.0488687	+	0.0846431i
$891$	−0.228562			−0.00765711
$892$	7.53893	+	13.0578i	0.252422	+	0.437208i
$893$	33.6019	+	58.2003i	1.12445	+	1.94760i
$894$	3.76376	−	6.51902i	0.125879	−	0.218029i
$895$	0.00618470			0.000206732
$896$	0.115118	+	0.199390i	0.00384582	+	0.00666116i
$897$	0.870523			0.0290659
$898$	25.1703			0.839943
$899$	1.97560	−	5.50958i	0.0658899	−	0.183755i
$900$	−7.16860			−0.238953
$901$	−2.80508			−0.0934508
$902$	−3.76945	−	6.52888i	−0.125509	−	0.217388i
$903$	−1.31480			−0.0437538
$904$	24.2382	−	41.9818i	0.806150	−	1.39629i
$905$	−1.91143	−	3.31069i	−0.0635381	−	0.110051i
$906$	−8.01308	−	13.8791i	−0.266217	−	0.461101i
$907$	−14.2060			−0.471704			−0.235852	−	0.971789i	$-0.575788\pi$
$907$	−14.2060			−0.471704			−0.235852	+	0.971789i	$0.575788\pi$
$908$	1.97643	−	3.42328i	0.0655902	−	0.113606i
$909$	−8.43471	+	14.6093i	−0.279762	+	0.484561i
$910$	−0.0175315	+	0.0303655i	−0.000581165	+	0.00100661i
$911$	−21.4642	−	37.1770i	−0.711140	−	1.23173i	−0.964430	−	0.264340i	$-0.914846\pi$
$911$	−21.4642	−	37.1770i	−0.711140	−	1.23173i	0.253290	−	0.967390i	$-0.418487\pi$
$912$	5.63109	−	9.75333i	0.186464	−	0.322965i
$913$	3.66059	+	6.34033i	0.121148	+	0.209834i
$914$	−31.6298			−1.04622
$915$	−2.21429			−0.0732022
$916$	−5.85936	−	10.1487i	−0.193599	−	0.335323i
$917$	−1.57902	+	2.73494i	−0.0521437	+	0.0903156i
$918$	−9.17151	−	15.8855i	−0.302705	−	0.524300i
$919$	21.6720	−	37.5370i	0.714893	−	1.23823i	−0.248107	−	0.968733i	$-0.579809\pi$
$919$	21.6720	−	37.5370i	0.714893	−	1.23823i	0.963001	−	0.269499i	$-0.0868581\pi$
$920$	−0.222206	+	0.384872i	−0.00732591	+	0.0126889i
$921$	5.55124	−	9.61503i	0.182920	−	0.316826i
$922$	−1.20545			−0.0396993
$923$	3.93264	+	6.81152i	0.129444	+	0.224204i
$924$	0.0417714	+	0.0723501i	0.00137418	+	0.00238014i
$925$	−21.1271	+	36.5932i	−0.694655	+	1.20318i
$926$	10.6150			0.348830
$927$	−14.4633	−	25.0511i	−0.475036	−	0.822787i
$928$	−4.20840			−0.138147
$929$	−21.7790			−0.714545			−0.357273	−	0.934000i	$-0.616293\pi$
$929$	−21.7790			−0.714545			−0.357273	+	0.934000i	$0.616293\pi$
$930$	0.379025	−	1.05703i	0.0124287	−	0.0346614i
$931$	39.1377			1.28269
$932$	−18.1515			−0.594573
$933$	−13.6453	−	23.6343i	−0.446727	−	0.773753i
$934$	17.2148			0.563285
$935$	−0.162631	+	0.281686i	−0.00531861	+	0.00921211i
$936$	−2.93854	−	5.08970i	−0.0960492	−	0.166362i
$937$	24.2561	+	42.0128i	0.792413	+	1.37250i	0.924469	+	0.381257i	$0.124509\pi$
$937$	24.2561	+	42.0128i	0.792413	+	1.37250i	−0.132057	+	0.991242i	$0.542158\pi$
$938$	−0.457932			−0.0149520
$939$	13.7334	−	23.7870i	0.448173	−	0.776258i
$940$	0.781800	−	1.35412i	0.0254995	−	0.0441664i
$941$	−6.20894	+	10.7542i	−0.202406	+	0.350577i	−0.949303	−	0.314363i	$-0.898209\pi$
$941$	−6.20894	+	10.7542i	−0.202406	+	0.350577i	0.746897	+	0.664939i	$0.231543\pi$
$942$	−12.0322	−	20.8403i	−0.392029	−	0.679015i
$943$	−4.81540	+	8.34052i	−0.156811	+	0.271605i
$944$	11.5558	+	20.0153i	0.376111	+	0.651443i
$945$	0.160977			0.00523658
$946$	4.53999			0.147608
$947$	5.21952	+	9.04047i	0.169612	+	0.293776i	0.938283	−	0.345868i	$-0.112415\pi$
$947$	5.21952	+	9.04047i	0.169612	+	0.293776i	−0.768672	+	0.639643i	$0.779082\pi$
$948$	−0.771242	+	1.33583i	−0.0250488	+	0.0433857i
$949$	−6.46537	−	11.1983i	−0.209875	−	0.363514i
$950$	15.5793	−	26.9842i	0.505460	−	0.875482i
$951$	13.4665	−	23.3246i	0.436680	−	0.756353i
$952$	0.894154	−	1.54872i	0.0289797	−	0.0501943i
$953$	−41.2362			−1.33577			−0.667885	−	0.744264i	$-0.732800\pi$
$953$	−41.2362			−1.33577			−0.667885	+	0.744264i	$0.732800\pi$
$954$	−0.932918	−	1.61586i	−0.0302043	−	0.0523154i
$955$	−0.703810	−	1.21903i	−0.0227748	−	0.0394470i
$956$	6.78450	−	11.7511i	0.219426	−	0.380058i
$957$	0.641874			0.0207488
$958$	−14.3921	−	24.9279i	−0.464988	−	0.805383i
$959$	3.10100			0.100137
$960$	−1.50202			−0.0484775
$961$	−23.9365	−	19.6989i	−0.772144	−	0.635447i
$962$	−9.48843			−0.305919
$963$	−4.26001			−0.137277
$964$	−3.71961	−	6.44256i	−0.119801	−	0.207501i
$965$	0.901913			0.0290336
$966$	−0.0880966	+	0.152588i	−0.00283446	+	0.00490943i
$967$	14.6346	+	25.3478i	0.470615	+	0.815130i	0.999435	−	0.0336043i	$-0.0106986\pi$
$967$	14.6346	+	25.3478i	0.470615	+	0.815130i	−0.528820	+	0.848734i	$0.677365\pi$
$968$	16.3809	+	28.3725i	0.526501	+	0.911926i
$969$	−18.7972			−0.603852
$970$	−1.49844	+	2.59538i	−0.0481120	+	0.0833325i
$971$	12.0626	−	20.8931i	0.387109	−	0.670492i	−0.604951	−	0.796263i	$-0.706807\pi$
$971$	12.0626	−	20.8931i	0.387109	−	0.670492i	0.992059	+	0.125771i	$0.0401405\pi$
$972$	−5.95219	+	10.3095i	−0.190916	+	0.330677i
$973$	0.0529339	+	0.0916843i	0.00169698	+	0.00293926i
$974$	8.92311	−	15.4553i	0.285915	−	0.495219i
$975$	2.59225	+	4.48991i	0.0830184	+	0.143792i
$976$	−23.5489			−0.753782
$977$	−36.9272			−1.18141			−0.590703	−	0.806889i	$-0.701149\pi$
$977$	−36.9272			−1.18141			−0.590703	+	0.806889i	$0.701149\pi$
$978$	6.81258	+	11.7997i	0.217842	+	0.377314i
$979$	−4.41368	+	7.64471i	−0.141062	+	0.244326i
$980$	−0.455299	−	0.788601i	−0.0145440	−	0.0251909i
$981$	−2.34650	+	4.06425i	−0.0749179	+	0.129762i
$982$	21.6469	−	37.4936i	0.690782	−	1.19647i
$983$	−10.4024	+	18.0174i	−0.331784	+	0.574667i	−0.982862	−	0.184344i	$-0.940984\pi$
$983$	−10.4024	+	18.0174i	−0.331784	+	0.574667i	0.651078	+	0.759011i	$0.274317\pi$
$984$	−37.0084			−1.17978
$985$	1.32335	+	2.29211i	0.0421655	+	0.0730327i
$986$	−1.88170	−	3.25920i	−0.0599256	−	0.103794i
$987$	1.13162	−	1.96003i	0.0360200	−	0.0623884i
$988$	−4.23815			−0.134833
$989$	−2.89987	−	5.02272i	−0.0922105	−	0.159713i
$990$	−0.216353			−0.00687614
$991$	37.4801			1.19059			0.595297	−	0.803506i	$-0.297034\pi$
$991$	37.4801			1.19059			0.595297	+	0.803506i	$0.297034\pi$
$992$	−7.52332	+	20.9811i	−0.238866	+	0.666152i
$993$	−17.9885			−0.570847
$994$	−1.59192			−0.0504928
$995$	0.540170	+	0.935602i	0.0171245	+	0.0296606i
$996$	9.84397			0.311918
$997$	5.18585	−	8.98215i	0.164237	−	0.284468i	−0.772147	−	0.635444i	$-0.780817\pi$
$997$	5.18585	−	8.98215i	0.164237	−	0.284468i	0.936384	+	0.350977i	$0.114150\pi$
$998$	10.0450	+	17.3985i	0.317970	+	0.550740i
$999$	21.7810	+	37.7258i	0.689120	+	1.19359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.118.6	✓	30
31.5	even	3	inner	403.2.h.a.222.6	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.6	✓	30	1.1	even	1	trivial
403.2.h.a.222.6	yes	30	31.5	even	3	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.11604 q^{2} +(0.521580 + 0.903404i) q^{3} -0.754455 q^{4} +(-0.0866186 + 0.150028i) q^{5} +(-0.582104 - 1.00823i) q^{6} +(-0.0906774 - 0.157058i) q^{7} +3.07408 q^{8} +(0.955908 - 1.65568i) q^{9} +O(q^{10})\)	\(q-1.11604 q^{2} +(0.521580 + 0.903404i) q^{3} -0.754455 q^{4} +(-0.0866186 + 0.150028i) q^{5} +(-0.582104 - 1.00823i) q^{6} +(-0.0906774 - 0.157058i) q^{7} +3.07408 q^{8} +(0.955908 - 1.65568i) q^{9} +(0.0966698 - 0.167437i) q^{10} +(0.292661 - 0.506904i) q^{11} +(-0.393509 - 0.681577i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.101200 + 0.175283i) q^{14} -0.180714 q^{15} -1.92189 q^{16} +(1.60387 + 2.77798i) q^{17} +(-1.06683 + 1.84781i) q^{18} +(2.80875 + 4.86490i) q^{19} +(0.0653498 - 0.113189i) q^{20} +(0.0945911 - 0.163837i) q^{21} +(-0.326622 + 0.565725i) q^{22} +0.834506 q^{23} +(1.60338 + 2.77714i) q^{24} +(2.48499 + 4.30414i) q^{25} +(-0.558020 + 0.966519i) q^{26} +5.12381 q^{27} +(0.0684120 + 0.118493i) q^{28} +1.05124 q^{29} +0.201684 q^{30} +(1.87930 - 5.24101i) q^{31} -4.00326 q^{32} +0.610586 q^{33} +(-1.78998 - 3.10033i) q^{34} +0.0314174 q^{35} +(-0.721189 + 1.24914i) q^{36} +(4.25093 + 7.36283i) q^{37} +(-3.13468 - 5.42942i) q^{38} +1.04316 q^{39} +(-0.266273 + 0.461198i) q^{40} +(-5.77036 + 9.99456i) q^{41} +(-0.105567 + 0.182848i) q^{42} +(-3.47496 - 6.01880i) q^{43} +(-0.220800 + 0.382436i) q^{44} +(0.165599 + 0.286826i) q^{45} -0.931342 q^{46} +11.9633 q^{47} +(-1.00242 - 1.73624i) q^{48} +(3.48356 - 6.03369i) q^{49} +(-2.77335 - 4.80359i) q^{50} +(-1.67309 + 2.89788i) q^{51} +(-0.377227 + 0.653377i) q^{52} +(-0.437237 + 0.757318i) q^{53} -5.71838 q^{54} +(0.0506998 + 0.0878147i) q^{55} +(-0.278750 - 0.482809i) q^{56} +(-2.92998 + 5.07487i) q^{57} -1.17323 q^{58} +(-6.01275 - 10.4144i) q^{59} +0.136341 q^{60} +12.2530 q^{61} +(-2.09737 + 5.84918i) q^{62} -0.346717 q^{63} +8.31157 q^{64} +(0.0866186 + 0.150028i) q^{65} -0.681438 q^{66} +(-1.13126 + 1.95940i) q^{67} +(-1.21004 - 2.09586i) q^{68} +(0.435262 + 0.753895i) q^{69} -0.0350631 q^{70} +(-3.93264 + 6.81152i) q^{71} +(2.93854 - 5.08970i) q^{72} +(6.46537 - 11.1983i) q^{73} +(-4.74421 - 8.21722i) q^{74} +(-2.59225 + 4.48991i) q^{75} +(-2.11907 - 3.67034i) q^{76} -0.106151 q^{77} -1.16421 q^{78} +(-0.979955 - 1.69733i) q^{79} +(0.166471 - 0.288337i) q^{80} +(-0.195244 - 0.338173i) q^{81} +(6.43996 - 11.1543i) q^{82} +(-6.25397 + 10.8322i) q^{83} +(-0.0713647 + 0.123607i) q^{84} -0.555698 q^{85} +(3.87819 + 6.71722i) q^{86} +(0.548308 + 0.949697i) q^{87} +(0.899665 - 1.55827i) q^{88} -15.0812 q^{89} +(-0.184815 - 0.320109i) q^{90} -0.181355 q^{91} -0.629597 q^{92} +(5.71496 - 1.03584i) q^{93} -13.3515 q^{94} -0.973160 q^{95} +(-2.08802 - 3.61656i) q^{96} -15.5006 q^{97} +(-3.88779 + 6.73384i) q^{98} +(-0.559515 - 0.969108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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