LMFDB - Embedded newform 105.2.q.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(4,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("105.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.q (of order $6$, 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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.3
Root			$-1.96595 - 0.526774i$ of defining polynomial
Character	$\chi$	$=$	105.4
Dual form			105.2.q.a.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34443 + 0.776205i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.204988 - 0.355049i) q^{4} +(-1.98074 + 1.03763i) q^{5} -1.55241 q^{6} +(0.478401 + 2.60214i) q^{7} -2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.34443 + 0.776205i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.204988 - 0.355049i) q^{4} +(-1.98074 + 1.03763i) q^{5} -1.55241 q^{6} +(0.478401 + 2.60214i) q^{7} -2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.85754 - 2.93248i) q^{10} +(-2.21538 + 3.83715i) q^{11} +(0.355049 - 0.204988i) q^{12} -1.73246i q^{13} +(-2.66297 - 3.12705i) q^{14} +(-2.23418 - 0.0917505i) q^{15} +(2.32594 + 4.02864i) q^{16} +(2.36638 + 1.36623i) q^{17} +(-1.34443 - 0.776205i) q^{18} +(-0.152578 - 0.264273i) q^{19} +(-0.0376154 + 0.915960i) q^{20} +(-0.886763 + 2.49272i) q^{21} -6.87834i q^{22} +(6.08316 - 3.51212i) q^{23} +(1.23418 - 2.13767i) q^{24} +(2.84663 - 4.11056i) q^{25} +(1.34474 + 2.32916i) q^{26} +1.00000i q^{27} +(1.02195 + 0.363551i) q^{28} +7.79430 q^{29} +(3.07491 - 1.61083i) q^{30} +(2.64243 - 4.57683i) q^{31} +(-1.97875 - 1.14243i) q^{32} +(-3.83715 + 2.21538i) q^{33} -4.24190 q^{34} +(-3.64765 - 4.65775i) q^{35} +0.409975 q^{36} +(-3.18183 + 1.83703i) q^{37} +(0.410260 + 0.236864i) q^{38} +(0.866230 - 1.50035i) q^{39} +(2.56126 + 4.88919i) q^{40} -6.71562 q^{41} +(-0.742674 - 4.03959i) q^{42} +9.71562i q^{43} +(0.908250 + 1.57313i) q^{44} +(-1.88899 - 1.19655i) q^{45} +(-5.45224 + 9.44356i) q^{46} +(1.57313 - 0.908250i) q^{47} +4.65187i q^{48} +(-6.54227 + 2.48973i) q^{49} +(-0.636449 + 7.73591i) q^{50} +(1.36623 + 2.36638i) q^{51} +(-0.615108 - 0.355133i) q^{52} +(-1.48535 - 0.857566i) q^{53} +(-0.776205 - 1.34443i) q^{54} +(0.406524 - 9.89912i) q^{55} +(6.42304 - 1.18087i) q^{56} -0.305156i q^{57} +(-10.4789 + 6.04998i) q^{58} +(-0.571217 + 0.989377i) q^{59} +(-0.490556 + 0.774437i) q^{60} +(-4.77818 - 8.27604i) q^{61} +8.20428i q^{62} +(-2.01432 + 1.71538i) q^{63} -5.75669 q^{64} +(1.79766 + 3.43154i) q^{65} +(3.43917 - 5.95682i) q^{66} +(7.26104 + 4.19216i) q^{67} +(0.970157 - 0.560120i) q^{68} +7.02423 q^{69} +(8.51937 + 3.43067i) q^{70} +10.2888 q^{71} +(2.13767 - 1.23418i) q^{72} +(-11.1028 - 6.41022i) q^{73} +(2.85183 - 4.93951i) q^{74} +(4.52053 - 2.13653i) q^{75} -0.125106 q^{76} +(-11.0446 - 3.92903i) q^{77} +2.68949i q^{78} +(3.35686 + 5.81425i) q^{79} +(-8.78732 - 5.56620i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.02866 - 5.21270i) q^{82} -5.09946i q^{83} +(0.703262 + 0.825821i) q^{84} +(-6.10482 - 0.250704i) q^{85} +(-7.54131 - 13.0619i) q^{86} +(6.75007 + 3.89715i) q^{87} +(9.47149 + 5.46837i) q^{88} +(2.03533 + 3.52529i) q^{89} +(3.46837 + 0.142434i) q^{90} +(4.50810 - 0.828810i) q^{91} -2.87976i q^{92} +(4.57683 - 2.64243i) q^{93} +(-1.40998 + 2.44215i) q^{94} +(0.576436 + 0.365135i) q^{95} +(-1.14243 - 1.97875i) q^{96} -2.87834i q^{97} +(6.86305 - 8.42540i) q^{98} -4.43075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9	$ 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9} - 4 q^{10} - 24 q^{14} - 4 q^{15} - 24 q^{19} - 8 q^{20} - 4 q^{21} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 24 q^{29} - 12 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35} + 16 q^{36} - 4 q^{39} + 32 q^{40} + 16 q^{41} + 20 q^{44} - 2 q^{45} - 32 q^{46} - 40 q^{49} - 40 q^{50} + 4 q^{51} - 4 q^{54} + 8 q^{55} + 84 q^{56} + 4 q^{59} + 16 q^{60} + 16 q^{61} + 16 q^{64} + 30 q^{65} + 28 q^{66} + 40 q^{69} + 16 q^{70} - 56 q^{71} + 40 q^{74} + 8 q^{75} - 64 q^{76} - 16 q^{79} + 52 q^{80} - 8 q^{81} + 12 q^{84} - 64 q^{85} - 48 q^{86} + 16 q^{89} - 8 q^{90} + 8 q^{91} - 32 q^{94} - 22 q^{95} + 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9 - 4 * q^10 - 24 * q^14 - 4 * q^15 - 24 * q^19 - 8 * q^20 - 4 * q^21 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 24 * q^29 - 12 * q^30 + 16 * q^31 + 16 * q^34 - 10 * q^35 + 16 * q^36 - 4 * q^39 + 32 * q^40 + 16 * q^41 + 20 * q^44 - 2 * q^45 - 32 * q^46 - 40 * q^49 - 40 * q^50 + 4 * q^51 - 4 * q^54 + 8 * q^55 + 84 * q^56 + 4 * q^59 + 16 * q^60 + 16 * q^61 + 16 * q^64 + 30 * q^65 + 28 * q^66 + 40 * q^69 + 16 * q^70 - 56 * q^71 + 40 * q^74 + 8 * q^75 - 64 * q^76 - 16 * q^79 + 52 * q^80 - 8 * q^81 + 12 * q^84 - 64 * q^85 - 48 * q^86 + 16 * q^89 - 8 * q^90 + 8 * q^91 - 32 * q^94 - 22 * q^95 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.34443	+	0.776205i	−0.950653	+	0.548860i	−0.893284	−	0.449493i	$-0.851605\pi$
$2$	−1.34443	+	0.776205i	−0.950653	+	0.548860i	−0.0573691	+	0.998353i	$0.518271\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.204988	−	0.355049i	0.102494	−	0.177524i
$5$	−1.98074	+	1.03763i	−0.885812	+	0.464044i
$5$	−1.98074	+	1.03763i	−0.885812	+	0.464044i
$6$	−1.55241			−0.633769
$7$	0.478401	+	2.60214i	0.180818	+	0.983516i
$7$	0.478401	+	2.60214i	0.180818	+	0.983516i
$8$		−	2.46837i		−	0.872700i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.85754	−	2.93248i	0.587405	−	0.927331i
$11$	−2.21538	+	3.83715i	−0.667961	+	1.15694i	0.310512	+	0.950569i	$0.399500\pi$
$11$	−2.21538	+	3.83715i	−0.667961	+	1.15694i	−0.978473	+	0.206373i	$0.933834\pi$
$12$	0.355049	−	0.204988i	0.102494	−	0.0591748i
$13$		−	1.73246i		−	0.480498i	−0.970711	−	0.240249i	$-0.922771\pi$
$13$		−	1.73246i		−	0.480498i	0.970711	−	0.240249i	$-0.0772291\pi$
$14$	−2.66297	−	3.12705i	−0.711708	−	0.835739i
$15$	−2.23418	−	0.0917505i	−0.576864	−	0.0236899i
$16$	2.32594	+	4.02864i	0.581484	+	1.00716i
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	0.758718	−	0.651419i	$-0.225826\pi$
$17$	2.36638	+	1.36623i	0.573931	+	0.331359i	−0.184787	+	0.982779i	$0.559159\pi$
$18$	−1.34443	−	0.776205i	−0.316884	−	0.182953i
$19$	−0.152578	−	0.264273i	−0.0350038	−	0.0606284i	0.847993	−	0.530008i	$-0.177811\pi$
$19$	−0.152578	−	0.264273i	−0.0350038	−	0.0606284i	−0.882997	+	0.469379i	$0.844478\pi$
$20$	−0.0376154	+	0.915960i	−0.00841106	+	0.204815i
$21$	−0.886763	+	2.49272i	−0.193508	+	0.543956i
$22$		−	6.87834i		−	1.46647i
$23$	6.08316	−	3.51212i	1.26843	−	0.732327i	0.293737	−	0.955886i	$-0.405101\pi$
$23$	6.08316	−	3.51212i	1.26843	−	0.732327i	0.974690	+	0.223560i	$0.0717678\pi$
$24$	1.23418	−	2.13767i	0.251927	−	0.436350i
$25$	2.84663	−	4.11056i	0.569326	−	0.822112i
$26$	1.34474	+	2.32916i	0.263726	+	0.456786i
$27$			1.00000i			0.192450i
$28$	1.02195	+	0.363551i	0.193131	+	0.0687046i
$29$	7.79430			1.44737			0.723683	−	0.690132i	$-0.242448\pi$
$29$	7.79430			1.44737			0.723683	+	0.690132i	$0.242448\pi$
$30$	3.07491	−	1.61083i	0.561400	−	0.294097i
$31$	2.64243	−	4.57683i	0.474595	−	0.822023i	−0.524982	−	0.851114i	$-0.675928\pi$
$31$	2.64243	−	4.57683i	0.474595	−	0.822023i	0.999577	+	0.0290906i	$0.00926112\pi$
$32$	−1.97875	−	1.14243i	−0.349798	−	0.201956i
$33$	−3.83715	+	2.21538i	−0.667961	+	0.385648i
$34$	−4.24190			−0.727479
$35$	−3.64765	−	4.65775i	−0.616566	−	0.787303i
$36$	0.409975			0.0683292
$37$	−3.18183	+	1.83703i	−0.523090	+	0.302006i	−0.738198	−	0.674584i	$-0.764323\pi$
$37$	−3.18183	+	1.83703i	−0.523090	+	0.302006i	0.215108	+	0.976590i	$0.430990\pi$
$38$	0.410260	+	0.236864i	0.0665530	+	0.0384244i
$39$	0.866230	−	1.50035i	0.138708	−	0.240249i
$40$	2.56126	+	4.88919i	0.404972	+	0.773049i
$41$	−6.71562			−1.04880			−0.524402	−	0.851471i	$-0.675711\pi$
$41$	−6.71562			−1.04880			−0.524402	+	0.851471i	$0.675711\pi$
$42$	−0.742674	−	4.03959i	−0.114597	−	0.623322i
$43$			9.71562i			1.48162i	0.671715	+	0.740809i	$0.265558\pi$
$43$			9.71562i			1.48162i	−0.671715	+	0.740809i	$0.734442\pi$
$44$	0.908250	+	1.57313i	0.136924	+	0.237159i
$45$	−1.88899	−	1.19655i	−0.281593	−	0.178371i
$46$	−5.45224	+	9.44356i	−0.803889	+	1.39238i
$47$	1.57313	−	0.908250i	0.229465	−	0.132482i	−0.380860	−	0.924633i	$-0.624372\pi$
$47$	1.57313	−	0.908250i	0.229465	−	0.132482i	0.610325	+	0.792151i	$0.291039\pi$
$48$			4.65187i			0.671440i
$49$	−6.54227	+	2.48973i	−0.934609	+	0.355676i
$50$	−0.636449	+	7.73591i	−0.0900075	+	1.09402i
$51$	1.36623	+	2.36638i	0.191310	+	0.331359i
$52$	−0.615108	−	0.355133i	−0.0853001	−	0.0492480i
$53$	−1.48535	−	0.857566i	−0.204028	−	0.117796i	0.394505	−	0.918894i	$-0.370916\pi$
$53$	−1.48535	−	0.857566i	−0.204028	−	0.117796i	−0.598533	+	0.801098i	$0.704249\pi$
$54$	−0.776205	−	1.34443i	−0.105628	−	0.182953i
$55$	0.406524	−	9.89912i	0.0548157	−	1.33480i
$56$	6.42304	−	1.18087i	0.858315	−	0.157800i
$57$		−	0.305156i		−	0.0404189i
$58$	−10.4789	+	6.04998i	−1.37594	+	0.794401i
$59$	−0.571217	+	0.989377i	−0.0743661	+	0.128806i	−0.900810	−	0.434213i	$-0.857027\pi$
$59$	−0.571217	+	0.989377i	−0.0743661	+	0.128806i	0.826444	+	0.563018i	$0.190360\pi$
$60$	−0.490556	+	0.774437i	−0.0633305	+	0.0999794i
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	−0.990940	−	0.134307i	$-0.957119\pi$
$61$	−4.77818	−	8.27604i	−0.611783	−	1.05964i	0.379157	−	0.925332i	$-0.376214\pi$
$62$			8.20428i			1.04194i
$63$	−2.01432	+	1.71538i	−0.253780	+	0.216117i
$64$	−5.75669			−0.719586
$65$	1.79766	+	3.43154i	0.222972	+	0.425631i
$66$	3.43917	−	5.95682i	0.423333	−	0.733234i
$67$	7.26104	+	4.19216i	0.887078	+	0.512154i	0.872985	−	0.487746i	$-0.162181\pi$
$67$	7.26104	+	4.19216i	0.887078	+	0.512154i	0.0140921	+	0.999901i	$0.495514\pi$
$68$	0.970157	−	0.560120i	0.117649	−	0.0679245i
$69$	7.02423			0.845618
$70$	8.51937	+	3.43067i	1.01826	+	0.410044i
$71$	10.2888			1.22106			0.610529	−	0.791994i	$-0.290957\pi$
$71$	10.2888			1.22106			0.610529	+	0.791994i	$0.290957\pi$
$72$	2.13767	−	1.23418i	0.251927	−	0.145450i
$73$	−11.1028	−	6.41022i	−1.29949	−	0.750260i	−0.319172	−	0.947697i	$-0.603405\pi$
$73$	−11.1028	−	6.41022i	−1.29949	−	0.750260i	−0.980316	+	0.197437i	$0.936738\pi$
$74$	2.85183	−	4.93951i	0.331518	−	0.574206i
$75$	4.52053	−	2.13653i	0.521986	−	0.246706i
$76$	−0.125106			−0.0143507
$77$	−11.0446	−	3.92903i	−1.25865	−	0.447754i
$78$			2.68949i			0.304524i
$79$	3.35686	+	5.81425i	0.377676	+	0.654154i	0.990724	−	0.135892i	$-0.0433900\pi$
$79$	3.35686	+	5.81425i	0.377676	+	0.654154i	−0.613048	+	0.790046i	$0.710057\pi$
$80$	−8.78732	−	5.56620i	−0.982452	−	0.622320i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	9.02866	−	5.21270i	0.997049	−	0.575646i
$83$		−	5.09946i		−	0.559739i	−0.960038	−	0.279869i	$-0.909709\pi$
$83$		−	5.09946i		−	0.559739i	0.960038	−	0.279869i	$-0.0902911\pi$
$84$	0.703262	+	0.825821i	0.0767322	+	0.0901044i
$85$	−6.10482	−	0.250704i	−0.662161	−	0.0271927i
$86$	−7.54131	−	13.0619i	−0.813201	−	1.40850i
$87$	6.75007	+	3.89715i	0.723683	+	0.417819i
$88$	9.47149	+	5.46837i	1.00966	+	0.582930i
$89$	2.03533	+	3.52529i	0.215744	+	0.373680i	0.953503	−	0.301385i	$-0.0974489\pi$
$89$	2.03533	+	3.52529i	0.215744	+	0.373680i	−0.737758	+	0.675065i	$0.764116\pi$
$90$	3.46837	+	0.142434i	0.365598	+	0.0150139i
$91$	4.50810	−	0.828810i	0.472577	−	0.0868829i
$92$		−	2.87976i		−	0.300236i
$93$	4.57683	−	2.64243i	0.474595	−	0.274008i
$94$	−1.40998	+	2.44215i	−0.145428	+	0.251888i
$95$	0.576436	+	0.365135i	0.0591411	+	0.0374620i
$96$	−1.14243	−	1.97875i	−0.116599	−	0.201956i
$97$		−	2.87834i		−	0.292252i	−0.989266	−	0.146126i	$-0.953320\pi$
$97$		−	2.87834i		−	0.292252i	0.989266	−	0.146126i	$-0.0466804\pi$
$98$	6.86305	−	8.42540i	0.693273	−	0.851094i
$99$	−4.43075			−0.445308
$100$	−0.875925	−	1.85331i	−0.0875925	−	0.185331i
$101$	−3.60883	+	6.25068i	−0.359092	+	0.621966i	−0.987809	−	0.155668i	$-0.950247\pi$
$101$	−3.60883	+	6.25068i	−0.359092	+	0.621966i	0.628717	+	0.777634i	$0.283580\pi$
$102$	−3.67359	−	2.12095i	−0.363740	−	0.210005i
$103$	9.76304	−	5.63670i	0.961981	−	0.555400i	0.0651989	−	0.997872i	$-0.479232\pi$
$103$	9.76304	−	5.63670i	0.961981	−	0.555400i	0.896782	+	0.442472i	$0.145898\pi$
$104$	−4.27635			−0.419331
$105$	−0.830088	−	5.85756i	−0.0810083	−	0.571639i
$106$	2.66259			0.258613
$107$	−5.98940	+	3.45798i	−0.579017	+	0.334296i	−0.760743	−	0.649054i	$-0.775165\pi$
$107$	−5.98940	+	3.45798i	−0.579017	+	0.334296i	0.181726	+	0.983349i	$0.441832\pi$
$108$	0.355049	+	0.204988i	0.0341646	+	0.0197249i
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	−0.740497	−	0.672060i	$-0.765410\pi$
$109$	2.21097	−	3.82952i	0.211773	−	0.366801i	0.952269	+	0.305259i	$0.0987430\pi$
$110$	7.13721	+	13.6242i	0.680506	+	1.29902i
$111$	−3.67406			−0.348727
$112$	−9.37035	+	7.97971i	−0.885415	+	0.754012i
$113$		−	2.86151i		−	0.269188i	−0.990901	−	0.134594i	$-0.957027\pi$
$113$		−	2.86151i		−	0.269188i	0.990901	−	0.134594i	$-0.0429730\pi$
$114$	0.236864	+	0.410260i	0.0221843	+	0.0384244i
$115$	−8.40485	+	13.2687i	−0.783756	+	1.23731i
$116$	1.59774	−	2.76736i	0.148346	−	0.256943i
$117$	1.50035	−	0.866230i	0.138708	−	0.0800830i
$118$		−	1.77353i		−	0.163266i
$119$	−2.42304	+	6.81125i	−0.222120	+	0.624387i
$120$	−0.226474	+	5.51479i	−0.0206742	+	0.503430i
$121$	−4.31579	−	7.47517i	−0.392345	−	0.679561i
$122$	12.8478	+	7.41769i	1.16319	+	0.671566i
$123$	−5.81590	−	3.35781i	−0.524402	−	0.302764i
$124$	−1.08333	−	1.87639i	−0.0972861	−	0.168504i
$125$	−1.37317	+	11.0957i	−0.122820	+	0.992429i
$126$	1.37662	−	3.86972i	0.122639	−	0.344742i
$127$		−	13.7325i		−	1.21856i	−0.792956	−	0.609279i	$-0.791459\pi$
$127$		−	13.7325i		−	1.21856i	0.792956	−	0.609279i	$-0.208541\pi$
$128$	11.6970	−	6.75324i	1.03387	−	0.596908i
$129$	−4.85781	+	8.41398i	−0.427706	+	0.740809i
$130$	−5.08040	−	3.21811i	−0.445581	−	0.282247i
$131$	−10.9909	−	19.0368i	−0.960277	−	1.66325i	−0.721801	−	0.692100i	$-0.756686\pi$
$131$	−10.9909	−	19.0368i	−0.960277	−	1.66325i	−0.238476	−	0.971148i	$-0.576648\pi$
$132$			1.81650i			0.158106i
$133$	0.614682	−	0.523458i	0.0532997	−	0.0453896i
$134$	−13.0159			−1.12440
$135$	−1.03763	−	1.98074i	−0.0893053	−	0.170475i
$136$	3.37236	−	5.84110i	0.289177	−	0.500870i
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	0.606927	−	0.794758i	$-0.292402\pi$
$137$	2.59973	+	1.50095i	0.222110	+	0.128235i	−0.384817	+	0.922993i	$0.625735\pi$
$138$	−9.44356	+	5.45224i	−0.803889	+	0.464126i
$139$	21.7364			1.84366			0.921829	−	0.387597i	$-0.126695\pi$
$139$	21.7364			1.84366			0.921829	+	0.387597i	$0.126695\pi$
$140$	−2.40145	+	0.340315i	−0.202960	+	0.0287619i
$141$	1.81650			0.152977
$142$	−13.8325	+	7.98622i	−1.16080	+	0.670189i
$143$	6.64770	+	3.83805i	0.555908	+	0.320954i
$144$	−2.32594	+	4.02864i	−0.193828	+	0.335720i
$145$	−15.4385	+	8.08764i	−1.28209	+	0.671642i
$146$	19.9026			1.64715
$147$	−6.91063	−	1.11496i	−0.569979	−	0.0919606i
$148$			1.50628i			0.123815i
$149$	−2.60654	−	4.51467i	−0.213536	−	0.369856i	0.739282	−	0.673396i	$-0.235165\pi$
$149$	−2.60654	−	4.51467i	−0.213536	−	0.369856i	−0.952819	+	0.303540i	$0.901832\pi$
$150$	−4.41914	+	6.38127i	−0.360821	+	0.521029i
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	−0.597887	−	0.801580i	$-0.703993\pi$
$151$	4.85686	−	8.41233i	0.395246	−	0.684585i	0.993132	+	0.116995i	$0.0373262\pi$
$152$	−0.652324	+	0.376619i	−0.0529104	+	0.0305478i
$153$			2.73246i			0.220906i
$154$	17.8984	−	3.29060i	1.44230	−	0.265164i
$155$	−0.484889	+	11.8074i	−0.0389472	+	0.948391i
$156$	−0.355133	−	0.615108i	−0.0284334	−	0.0492480i
$157$	8.20284	+	4.73591i	0.654658	+	0.377967i	0.790238	−	0.612800i	$-0.209957\pi$
$157$	8.20284	+	4.73591i	0.654658	+	0.377967i	−0.135581	+	0.990766i	$0.543290\pi$
$158$	−9.02610	−	5.21122i	−0.718078	−	0.414582i
$159$	−0.857566	−	1.48535i	−0.0680094	−	0.117796i
$160$	5.10482	+	0.209638i	0.403571	+	0.0165733i
$161$	12.0492	+	14.1490i	0.949610	+	1.11510i
$162$		−	1.55241i		−	0.121969i
$163$	−4.67358	+	2.69830i	−0.366063	+	0.211347i	−0.671737	−	0.740789i	$-0.734452\pi$
$163$	−4.67358	+	2.69830i	−0.366063	+	0.211347i	0.305674	+	0.952136i	$0.401118\pi$
$164$	−1.37662	+	2.38437i	−0.107496	+	0.186188i
$165$	5.30162	−	8.36963i	0.412731	−	0.651575i
$166$	3.95823	+	6.85585i	0.307218	+	0.532117i
$167$		−	0.312550i		−	0.0241859i	−0.999927	−	0.0120929i	$-0.996151\pi$
$167$		−	0.312550i		−	0.0241859i	0.999927	−	0.0120929i	$-0.00384939\pi$
$168$	6.15295	+	2.18886i	0.474711	+	0.168874i
$169$	9.99859			0.769122
$170$	8.40208	−	4.40154i	0.644410	−	0.337582i
$171$	0.152578	−	0.264273i	0.0116679	−	0.0202095i
$172$	3.44952	+	1.99158i	0.263024	+	0.151857i
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	−0.781937	−	0.623358i	$-0.785768\pi$
$173$	−8.32661	+	4.80737i	−0.633061	+	0.365498i	0.148876	+	0.988856i	$0.452435\pi$
$174$	−12.1000			−0.917295
$175$	12.0581	+	5.44084i	0.911505	+	0.411289i
$176$	−20.6113			−1.55363
$177$	−0.989377	+	0.571217i	−0.0743661	+	0.0429353i
$178$	−5.47269	−	3.15966i	−0.410196	−	0.236827i
$179$	−4.42730	+	7.66831i	−0.330912	+	0.573157i	−0.982691	−	0.185252i	$-0.940690\pi$
$179$	−4.42730	+	7.66831i	−0.330912	+	0.573157i	0.651779	+	0.758409i	$0.274023\pi$
$180$	−0.812053	+	0.425404i	−0.0605268	+	0.0317078i
$181$	−16.9234			−1.25790			−0.628952	−	0.777445i	$-0.716516\pi$
$181$	−16.9234			−1.25790			−0.628952	+	0.777445i	$0.716516\pi$
$182$	−5.41748	+	4.61348i	−0.401571	+	0.341974i
$183$		−	9.55635i		−	0.706426i
$184$	−8.66920	−	15.0155i	−0.639102	−	1.10696i
$185$	4.39620	−	6.94026i	0.323215	−	0.510258i
$186$	−4.10214	+	7.10511i	−0.300784	+	0.520972i
$187$	−10.4848	+	6.05343i	−0.766728	+	0.442670i
$188$		−	0.744719i		−	0.0543142i
$189$	−2.60214	+	0.478401i	−0.189278	+	0.0347985i
$190$	−1.05839	−	0.0434647i	−0.0767840	−	0.00315326i
$191$	−0.159271	−	0.275865i	−0.0115244	−	0.0199609i	0.860206	−	0.509947i	$-0.170335\pi$
$191$	−0.159271	−	0.275865i	−0.0115244	−	0.0199609i	−0.871730	+	0.489986i	$0.837002\pi$
$192$	−4.98544	−	2.87834i	−0.359793	−	0.207727i
$193$	1.81289	+	1.04667i	0.130494	+	0.0753410i	0.563826	−	0.825894i	$-0.309329\pi$
$193$	1.81289	+	1.04667i	0.130494	+	0.0753410i	−0.433332	+	0.901234i	$0.642662\pi$
$194$	2.23418	+	3.86972i	0.160405	+	0.277830i
$195$	−0.158954	+	3.87063i	−0.0113829	+	0.277182i
$196$	−0.457107	+	2.83319i	−0.0326505	+	0.202371i
$197$		−	22.5798i		−	1.60874i	−0.594126	−	0.804372i	$-0.702502\pi$
$197$		−	22.5798i		−	1.60874i	0.594126	−	0.804372i	$-0.297498\pi$
$198$	5.95682	−	3.43917i	0.423333	−	0.244411i
$199$	−3.75204	+	6.49872i	−0.265975	+	0.460682i	−0.967819	−	0.251649i	$-0.919027\pi$
$199$	−3.75204	+	6.49872i	−0.265975	+	0.460682i	0.701844	+	0.712331i	$0.252361\pi$
$200$	−10.1464	−	7.02654i	−0.717457	−	0.496851i
$201$	4.19216	+	7.26104i	0.295693	+	0.512154i
$202$		−	11.2048i		−	0.788365i
$203$	3.72880	+	20.2819i	0.261710	+	1.42351i
$204$	1.12024			0.0784325
$205$	13.3019	−	6.96836i	0.929043	−	0.486691i
$206$	−8.75046	+	15.1562i	−0.609673	+	1.05599i
$207$	6.08316	+	3.51212i	0.422809	+	0.244109i
$208$	6.97945	−	4.02959i	0.483938	−	0.279402i
$209$	1.35207			0.0935248
$210$	5.66265	+	7.23073i	0.390760	+	0.498968i
$211$	7.67216			0.528173			0.264087	−	0.964499i	$-0.414930\pi$
$211$	7.67216			0.528173			0.264087	+	0.964499i	$0.414930\pi$
$212$	−0.608955	+	0.351581i	−0.0418232	+	0.0241467i
$213$	8.91037	+	5.14441i	0.610529	+	0.352489i
$214$	5.36820	−	9.29800i	0.366963	−	0.635598i
$215$	−10.0813	−	19.2441i	−0.687536	−	1.31244i
$216$	2.46837			0.167951
$217$	13.1737	+	4.68643i	0.894289	+	0.318135i
$218$			6.86467i			0.464934i
$219$	−6.41022	−	11.1028i	−0.433163	−	0.750260i
$220$	−3.43134	−	2.17353i	−0.231341	−	0.146540i
$221$	2.36694	−	4.09966i	0.159217	−	0.275773i
$222$	4.93951	−	2.85183i	0.331518	−	0.191402i
$223$		−	6.90208i		−	0.462198i	−0.972930	−	0.231099i	$-0.925768\pi$
$223$		−	6.90208i		−	0.462198i	0.972930	−	0.231099i	$-0.0742321\pi$
$224$	2.02614	−	5.69554i	0.135377	−	0.380549i
$225$	4.98316	+	0.409975i	0.332211	+	0.0273317i
$226$	2.22112	+	3.84709i	0.147746	+	0.255904i
$227$	−5.49684	−	3.17360i	−0.364838	−	0.210639i	0.306363	−	0.951915i	$-0.400888\pi$
$227$	−5.49684	−	3.17360i	−0.364838	−	0.210639i	−0.671201	+	0.741275i	$0.734221\pi$
$228$	−0.108345	−	0.0625532i	−0.00717535	−	0.00414269i
$229$	3.37834	+	5.85146i	0.223247	+	0.386676i	0.955792	−	0.294043i	$-0.0950009\pi$
$229$	3.37834	+	5.85146i	0.223247	+	0.386676i	−0.732545	+	0.680719i	$0.761668\pi$
$230$	1.00049	−	24.3626i	0.0659705	−	1.60642i
$231$	−7.60041	−	8.92495i	−0.500071	−	0.587219i
$232$		−	19.2392i		−	1.26312i
$233$	−6.41899	+	3.70601i	−0.420522	+	0.242789i	−0.695301	−	0.718719i	$-0.744729\pi$
$233$	−6.41899	+	3.70601i	−0.420522	+	0.242789i	0.274779	+	0.961508i	$0.411395\pi$
$234$	−1.34474	+	2.32916i	−0.0879086	+	0.152262i
$235$	−2.17353	+	3.43134i	−0.141786	+	0.223836i
$236$	0.234185	+	0.405620i	0.0152441	+	0.0264036i
$237$			6.71372i			0.436103i
$238$	−2.02933	−	11.0380i	−0.131542	−	0.715488i
$239$	−7.36355			−0.476309			−0.238154	−	0.971227i	$-0.576542\pi$
$239$	−7.36355			−0.476309			−0.238154	+	0.971227i	$0.576542\pi$
$240$	−4.82694	−	9.21413i	−0.311578	−	0.594769i
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	−0.997734	−	0.0672759i	$-0.978569\pi$
$241$	−6.84002	+	11.8473i	−0.440605	+	0.763149i	0.557130	+	0.830425i	$0.311903\pi$
$242$	11.6045	+	6.69988i	0.745967	+	0.430684i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−3.91787			−0.250816
$245$	10.3751	−	11.7200i	0.662839	−	0.748762i
$246$	10.4254			0.664699
$247$	−0.457842	+	0.264335i	−0.0291318	+	0.0168193i
$248$	−11.2973	−	6.52250i	−0.717380	−	0.414179i
$249$	2.54973	−	4.41626i	0.161583	−	0.279869i
$250$	−6.76641	−	15.9832i	−0.427945	−	1.01087i
$251$	23.4843			1.48231			0.741157	−	0.671331i	$-0.234277\pi$
$251$	23.4843			1.48231			0.741157	+	0.671331i	$0.234277\pi$
$252$	0.196132	+	1.06681i	0.0123552	+	0.0672029i
$253$			31.1226i			1.95666i
$254$	10.6592	+	18.4623i	0.668818	+	1.15843i
$255$	−5.16158	−	3.26953i	−0.323230	−	0.204746i
$256$	−4.72710	+	8.18758i	−0.295444	+	0.511724i
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	−0.0508890	−	0.998704i	$-0.516205\pi$
$257$	12.6417	−	7.29871i	0.788570	−	0.455281i	0.839459	+	0.543423i	$0.182872\pi$
$258$		−	15.0826i		−	0.939003i
$259$	−6.30241	−	7.40074i	−0.391612	−	0.459860i
$260$	1.58686	+	0.0651672i	0.0984131	+	0.00404150i
$261$	3.89715	+	6.75007i	0.241228	+	0.417819i
$262$	29.5528	+	17.0623i	1.82578	+	1.05411i
$263$	−4.40755	−	2.54470i	−0.271781	−	0.156913i	0.357916	−	0.933754i	$-0.383488\pi$
$263$	−4.40755	−	2.54470i	−0.271781	−	0.156913i	−0.629697	+	0.776841i	$0.716821\pi$
$264$	5.46837	+	9.47149i	0.336555	+	0.582930i
$265$	3.83192	+	0.157364i	0.235393	+	0.00966680i
$266$	−0.420084	+	1.18087i	−0.0257570	+	0.0724038i
$267$			4.07065i			0.249120i
$268$	2.97685	−	1.71868i	0.181840	−	0.104985i
$269$	15.2550	−	26.4224i	0.930112	−	1.61100i	0.146984	−	0.989139i	$-0.453043\pi$
$269$	15.2550	−	26.4224i	0.930112	−	1.61100i	0.783127	−	0.621862i	$-0.213623\pi$
$270$	2.93248	+	1.85754i	0.178465	+	0.113046i
$271$	9.74401	+	16.8771i	0.591907	+	1.02521i	0.993975	+	0.109603i	$0.0349579\pi$
$271$	9.74401	+	16.8771i	0.591907	+	1.02521i	−0.402069	+	0.915609i	$0.631709\pi$
$272$			12.7110i			0.770720i
$273$	4.31854	+	1.53628i	0.261370	+	0.0929799i
$274$	−4.66019			−0.281532
$275$	9.46645	+	20.0294i	0.570849	+	1.20782i
$276$	1.43988	−	2.49395i	0.0866706	−	0.150118i
$277$	−22.0665	−	12.7401i	−1.32585	−	0.765478i	−0.341193	−	0.939993i	$-0.610831\pi$
$277$	−22.0665	−	12.7401i	−1.32585	−	0.765478i	−0.984655	+	0.174515i	$0.944164\pi$
$278$	−29.2230	+	16.8719i	−1.75268	+	1.01191i
$279$	5.28487			0.316397
$280$	−11.4970	+	9.00376i	−0.687080	+	0.538078i
$281$	−22.1914			−1.32383			−0.661914	−	0.749580i	$-0.730255\pi$
$281$	−22.1914			−1.32383			−0.661914	+	0.749580i	$0.730255\pi$
$282$	−2.44215	+	1.40998i	−0.145428	+	0.0839628i
$283$	−15.6960	−	9.06209i	−0.933031	−	0.538685i	−0.0452618	−	0.998975i	$-0.514412\pi$
$283$	−15.6960	−	9.06209i	−0.933031	−	0.538685i	−0.887769	+	0.460290i	$0.847746\pi$
$284$	2.10908	−	3.65303i	0.125151	−	0.216768i
$285$	0.316641	+	0.604434i	0.0187562	+	0.0358036i
$286$	−11.9165			−0.704635
$287$	−3.21276	−	17.4750i	−0.189643	−	1.03152i
$288$		−	2.28487i		−	0.134637i
$289$	−4.76683	−	8.25640i	−0.280402	−	0.485670i
$290$	14.4782	−	22.8566i	0.850190	−	1.34219i
$291$	1.43917	−	2.49272i	0.0843658	−	0.146126i
$292$	−4.55188	+	2.62803i	−0.266379	+	0.153794i
$293$			13.8958i			0.811801i	0.913917	+	0.405901i	$0.133042\pi$
$293$			13.8958i			0.811801i	−0.913917	+	0.405901i	$0.866958\pi$
$294$	10.1563	−	3.86508i	0.592326	−	0.225416i
$295$	0.104819	−	2.55241i	0.00610279	−	0.148607i
$296$	4.53447	+	7.85394i	0.263561	+	0.456501i
$297$	−3.83715	−	2.21538i	−0.222654	−	0.128549i
$298$	7.00861	+	4.04642i	0.405998	+	0.234403i
$299$	−6.08460	−	10.5388i	−0.351881	−	0.609476i
$300$	0.168080	−	2.04297i	0.00970408	−	0.117951i
$301$	−25.2814	+	4.64796i	−1.45720	+	0.267904i
$302$			15.0797i			0.867737i
$303$	−6.25068	+	3.60883i	−0.359092	+	0.207322i
$304$	0.709774	−	1.22936i	0.0407083	−	0.0705089i
$305$	18.0518	+	11.4347i	1.03364	+	0.654747i
$306$	−2.12095	−	3.67359i	−0.121247	−	0.210005i
$307$			29.8332i			1.70267i	0.524622	+	0.851335i	$0.324207\pi$
$307$			29.8332i			1.70267i	−0.524622	+	0.851335i	$0.675793\pi$
$308$	−3.65901	+	3.11598i	−0.208491	+	0.177549i
$309$	11.2734			0.641321
$310$	−8.51304	−	16.2505i	−0.483508	−	0.922967i
$311$	−6.75662	+	11.7028i	−0.383133	+	0.663606i	−0.991508	−	0.130044i	$-0.958488\pi$
$311$	−6.75662	+	11.7028i	−0.383133	+	0.663606i	0.608375	+	0.793650i	$0.291822\pi$
$312$	−3.70343	−	2.13817i	−0.209665	−	0.121050i
$313$	25.1023	−	14.4928i	1.41887	−	0.819184i	0.422669	−	0.906284i	$-0.361093\pi$
$313$	25.1023	−	14.4928i	1.41887	−	0.819184i	0.996200	+	0.0871001i	$0.0277600\pi$
$314$	−14.7041			−0.829803
$315$	2.20990	−	5.48784i	0.124514	−	0.309205i
$316$	2.75246			0.154838
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	−0.471557	−	0.881836i	$-0.656308\pi$
$317$	1.00341	−	0.579319i	0.0563571	−	0.0325378i	0.527914	+	0.849298i	$0.322974\pi$
$318$	2.30587	+	1.33129i	0.129307	+	0.0746552i
$319$	−17.2673	+	29.9079i	−0.966785	+	1.67452i
$320$	11.4025	−	5.97334i	0.637418	−	0.333920i
$321$	−6.91596			−0.386011
$322$	−27.1818	−	9.66969i	−1.51478	−	0.538871i
$323$		−	0.833827i		−	0.0463954i
$324$	0.204988	+	0.355049i	0.0113882	+	0.0197249i
$325$	−7.12138	−	4.93167i	−0.395023	−	0.273560i
$326$	4.18886	−	7.25532i	0.231999	−	0.401835i
$327$	3.82952	−	2.21097i	0.211773	−	0.122267i
$328$			16.5766i			0.915292i
$329$	3.11598	+	3.65901i	0.171790	+	0.201728i
$330$	−0.631092	+	15.3675i	−0.0347404	+	0.845953i
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	0.932459	+	0.361277i	$0.117659\pi$
$331$	14.1746	+	24.5511i	0.779104	+	1.34945i	−0.153355	+	0.988171i	$0.549008\pi$
$332$	−1.81056	−	1.04533i	−0.0993673	−	0.0573697i
$333$	−3.18183	−	1.83703i	−0.174363	−	0.100669i
$334$	0.242603	+	0.420201i	0.0132746	+	0.0229924i
$335$	−18.7321	−	0.769266i	−1.02345	−	0.0420295i
$336$	−12.1048	+	2.22546i	−0.660372	+	0.121409i
$337$			15.9729i			0.870101i	0.900406	+	0.435051i	$0.143270\pi$
$337$			15.9729i			0.870101i	−0.900406	+	0.435051i	$0.856730\pi$
$338$	−13.4424	+	7.76095i	−0.731168	+	0.422140i
$339$	1.43075	−	2.47814i	0.0777079	−	0.134594i
$340$	−1.34042	+	2.11612i	−0.0726947	+	0.114763i
$341$	11.7080	+	20.2788i	0.634023	+	1.09816i
$342$			0.473727i			0.0256162i
$343$	−9.60845	−	15.8328i	−0.518808	−	0.854891i
$344$	23.9817			1.29301
$345$	−13.9131	+	7.28858i	−0.749059	+	0.392404i
$346$	7.46301	−	12.9263i	0.401214	−	0.694923i
$347$	−11.2687	−	6.50599i	−0.604935	−	0.349260i	0.166045	−	0.986118i	$-0.446900\pi$
$347$	−11.2687	−	6.50599i	−0.604935	−	0.349260i	−0.770981	+	0.636859i	$0.780234\pi$
$348$	2.76736	−	1.59774i	0.148346	−	0.0856476i
$349$	−32.0724			−1.71680			−0.858398	−	0.512984i	$-0.828540\pi$
$349$	−32.0724			−1.71680			−0.858398	+	0.512984i	$0.828540\pi$
$350$	−20.4344	+	2.04473i	−1.09226	+	0.109296i
$351$	1.73246			0.0924718
$352$	8.76737	−	5.06185i	0.467303	−	0.269797i
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	0.775398	−	0.631473i	$-0.217549\pi$
$353$	11.5778	+	6.68445i	0.616225	+	0.355778i	−0.159173	+	0.987251i	$0.550883\pi$
$354$	0.886763	−	1.53592i	0.0471309	−	0.0816331i
$355$	−20.3794	+	10.6760i	−1.08163	+	0.566624i
$356$	1.66887			0.0884498
$357$	−5.50404	+	4.68720i	−0.291305	+	0.248073i
$358$		−	13.7460i		−	0.726497i
$359$	−6.55974	−	11.3618i	−0.346210	−	0.599653i	0.639363	−	0.768905i	$-0.279198\pi$
$359$	−6.55974	−	11.3618i	−0.346210	−	0.599653i	−0.985573	+	0.169252i	$0.945865\pi$
$360$	−2.95353	+	4.66271i	−0.155665	+	0.245747i
$361$	9.45344	−	16.3738i	0.497549	−	0.861781i
$362$	22.7522	−	13.1360i	1.19583	−	0.690412i
$363$		−	8.63158i		−	0.453041i
$364$	0.629837	−	1.77049i	0.0330124	−	0.0927990i
$365$	28.6432	+	1.17628i	1.49926	+	0.0615694i
$366$	7.41769	+	12.8478i	0.387729	+	0.671566i
$367$	−11.3761	−	6.56798i	−0.593826	−	0.342846i	0.172783	−	0.984960i	$-0.444724\pi$
$367$	−11.3761	−	6.56798i	−0.593826	−	0.342846i	−0.766609	+	0.642114i	$0.778057\pi$
$368$	28.2981	+	16.3379i	1.47514	+	0.851672i
$369$	−3.35781	−	5.81590i	−0.174801	−	0.302764i
$370$	−0.523313	+	12.7430i	−0.0272057	+	0.662478i
$371$	1.52091	−	4.27534i	0.0789620	−	0.221965i
$372$		−	2.16666i		−	0.112336i
$373$	25.6514	−	14.8099i	1.32818	−	0.766826i	0.343163	−	0.939276i	$-0.388502\pi$
$373$	25.6514	−	14.8099i	1.32818	−	0.766826i	0.985018	+	0.172450i	$0.0551682\pi$
$374$	9.39740	−	16.2768i	0.485928	−	0.841652i
$375$	−6.73704	+	8.92257i	−0.347900	+	0.460759i
$376$	−2.24190	−	3.88308i	−0.115617	−	0.200254i
$377$		−	13.5033i		−	0.695456i
$378$	3.12705	−	2.66297i	0.160838	−	0.136968i
$379$	−7.47689			−0.384062			−0.192031	−	0.981389i	$-0.561507\pi$
$379$	−7.47689			−0.384062			−0.192031	+	0.981389i	$0.561507\pi$
$380$	0.247803	−	0.129815i	0.0127120	−	0.00665936i
$381$	6.86623	−	11.8927i	0.351768	−	0.609279i
$382$	0.428255	+	0.247253i	0.0219114	+	0.0126506i
$383$	20.5586	−	11.8695i	1.05050	−	0.606505i	0.127709	−	0.991812i	$-0.459238\pi$
$383$	20.5586	−	11.8695i	1.05050	−	0.606505i	0.922789	+	0.385307i	$0.125904\pi$
$384$	13.5065			0.689250
$385$	25.9534	−	3.67791i	1.32271	−	0.187444i
$386$	−3.24972			−0.165406
$387$	−8.41398	+	4.85781i	−0.427706	+	0.246936i
$388$	−1.02195	−	0.590025i	−0.0518818	−	0.0299540i
$389$	−7.06523	+	12.2373i	−0.358221	+	0.620458i	−0.987664	−	0.156589i	$-0.949950\pi$
$389$	−7.06523	+	12.2373i	−0.358221	+	0.620458i	0.629442	+	0.777047i	$0.283283\pi$
$390$	−2.79070	−	5.32716i	−0.141313	−	0.269751i
$391$	19.1934			0.970653
$392$	6.14558	+	16.1487i	0.310398	+	0.815634i
$393$		−	21.9817i		−	1.10883i
$394$	17.5265	+	30.3569i	0.882975	+	1.52936i
$395$	−12.6821	−	8.03330i	−0.638106	−	0.404199i
$396$	−0.908250	+	1.57313i	−0.0456413	+	0.0790530i
$397$	9.75974	−	5.63479i	0.489827	−	0.282802i	−0.234676	−	0.972074i	$-0.575403\pi$
$397$	9.75974	−	5.63479i	0.489827	−	0.282802i	0.724503	+	0.689272i	$0.242069\pi$
$398$		−	11.6494i		−	0.583932i
$399$	0.794059	−	0.145987i	0.0397527	−	0.00730849i
$400$	23.1810	+	1.90715i	1.15905	+	0.0953576i
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	−0.995279	−	0.0970583i	$-0.969057\pi$
$401$	−11.6484	−	20.1757i	−0.581694	−	1.00752i	0.413584	−	0.910466i	$-0.364277\pi$
$402$	−11.2721	−	6.50796i	−0.562202	−	0.324587i
$403$	−7.92917	−	4.57791i	−0.394980	−	0.228042i
$404$	1.47953	+	2.56262i	0.0736094	+	0.127495i
$405$	0.0917505	−	2.23418i	0.00455912	−	0.111018i
$406$	−20.7560	−	24.3732i	−1.03010	−	1.20962i
$407$		−	16.2789i		−	0.806914i
$408$	5.84110	−	3.37236i	0.289177	−	0.166957i
$409$	10.3239	−	17.8815i	0.510484	−	0.884184i	−0.489443	−	0.872036i	$-0.662800\pi$
$409$	10.3239	−	17.8815i	0.510484	−	0.884184i	0.999926	−	0.0121481i	$-0.00386695\pi$
$410$	−12.4745	+	19.6934i	−0.616072	+	0.972589i
$411$	1.50095	+	2.59973i	0.0740366	+	0.128235i
$412$		−	4.62181i		−	0.227700i
$413$	−2.84777	−	1.01307i	−0.140130	−	0.0498498i
$414$	−10.9045			−0.535926
$415$	5.29138	+	10.1007i	0.259743	+	0.495823i
$416$	−1.97922	+	3.42811i	−0.0970393	+	0.168077i
$417$	18.8243	+	10.8682i	0.921829	+	0.532218i
$418$	−1.81776	+	1.04948i	−0.0889096	+	0.0513320i
$419$	5.48254			0.267839			0.133920	−	0.990992i	$-0.457244\pi$
$419$	5.48254			0.267839			0.133920	+	0.990992i	$0.457244\pi$
$420$	−2.24988	−	0.906004i	−0.109783	−	0.0442085i
$421$	−3.78079			−0.184264			−0.0921322	−	0.995747i	$-0.529368\pi$
$421$	−3.78079			−0.184264			−0.0921322	+	0.995747i	$0.529368\pi$
$422$	−10.3146	+	5.95517i	−0.502109	+	0.289893i
$423$	1.57313	+	0.908250i	0.0764884	+	0.0441606i
$424$	−2.11679	+	3.66639i	−0.102800	+	0.178055i
$425$	12.3522	−	5.83799i	0.599168	−	0.283184i
$426$	−15.9724			−0.773868
$427$	19.2495	−	16.3927i	0.931551	−	0.793301i
$428$			2.83537i			0.137053i
$429$	3.83805	+	6.64770i	0.185303	+	0.320954i
$430$	28.4909	+	18.0471i	1.37395	+	0.870310i
$431$	13.7564	−	23.8267i	0.662621	−	1.14769i	−0.317303	−	0.948324i	$-0.602777\pi$
$431$	13.7564	−	23.8267i	0.662621	−	1.14769i	0.979924	−	0.199369i	$-0.0638894\pi$
$432$	−4.02864	+	2.32594i	−0.193828	+	0.111907i
$433$		−	8.75514i		−	0.420745i	−0.977621	−	0.210373i	$-0.932532\pi$
$433$		−	8.75514i		−	0.420745i	0.977621	−	0.210373i	$-0.0674677\pi$
$434$	−21.3487	+	3.92493i	−1.02477	+	0.188403i
$435$	−17.4139	−	0.715131i	−0.834933	−	0.0342879i
$436$	−0.906444	−	1.57001i	−0.0434108	−	0.0751897i
$437$	−1.85631	−	1.07174i	−0.0887996	−	0.0512685i
$438$	17.2361	+	9.95129i	0.823574	+	0.475491i
$439$	−5.30636	−	9.19088i	−0.253259	−	0.438657i	0.711163	−	0.703028i	$-0.248169\pi$
$439$	−5.30636	−	9.19088i	−0.253259	−	0.438657i	−0.964421	+	0.264371i	$0.914836\pi$
$440$	−24.4347	−	1.00345i	−1.16488	−	0.0478377i
$441$	−5.42730	−	4.42090i	−0.258443	−	0.210519i
$442$			7.34891i			0.349552i
$443$	−17.3080	+	9.99278i	−0.822328	+	0.474771i	−0.851219	−	0.524811i	$-0.824136\pi$
$443$	−17.3080	+	9.99278i	−0.822328	+	0.474771i	0.0288905	+	0.999583i	$0.490803\pi$
$444$	−0.753138	+	1.30447i	−0.0357423	+	0.0619075i
$445$	−7.68941	−	4.87074i	−0.364513	−	0.230895i
$446$	5.35743	+	9.27934i	0.253682	+	0.439390i
$447$		−	5.21309i		−	0.246571i
$448$	−2.75400	−	14.9797i	−0.130114	−	0.707725i
$449$	−3.02578			−0.142795			−0.0713976	−	0.997448i	$-0.522746\pi$
$449$	−3.02578			−0.142795			−0.0713976	+	0.997448i	$0.522746\pi$
$450$	−7.01772	+	3.31677i	−0.330818	+	0.156354i
$451$	14.8776	−	25.7688i	0.700561	−	1.21341i
$452$	−1.01598	−	0.586574i	−0.0477875	−	0.0275901i
$453$	8.41233	−	4.85686i	0.395246	−	0.228195i
$454$	9.85346			0.462446
$455$	−8.06936	+	6.31941i	−0.378297	+	0.296259i
$456$	−0.753238			−0.0352736
$457$	−1.97570	+	1.14067i	−0.0924195	+	0.0533584i	−0.545497	−	0.838112i	$-0.683659\pi$
$457$	−1.97570	+	1.14067i	−0.0924195	+	0.0533584i	0.453078	+	0.891471i	$0.350326\pi$
$458$	−9.08387	−	5.24457i	−0.424461	−	0.245063i
$459$	−1.36623	+	2.36638i	−0.0637701	+	0.110453i
$460$	2.98814	+	5.70404i	0.139323	+	0.265952i
$461$	−24.0678			−1.12095			−0.560475	−	0.828171i	$-0.689381\pi$
$461$	−24.0678			−1.12095			−0.560475	+	0.828171i	$0.689381\pi$
$462$	17.1458	+	6.09946i	0.797694	+	0.283773i
$463$			11.1290i			0.517211i	0.965983	+	0.258605i	$0.0832629\pi$
$463$			11.1290i			0.517211i	−0.965983	+	0.258605i	$0.916737\pi$
$464$	18.1290	+	31.4004i	0.841620	+	1.45773i
$465$	−6.32361	+	9.98304i	−0.293251	+	0.462952i
$466$	5.75324	−	9.96490i	0.266514	−	0.461615i
$467$	−24.7481	+	14.2883i	−1.14521	+	0.661185i	−0.947714	−	0.319120i	$-0.896613\pi$
$467$	−24.7481	+	14.2883i	−1.14521	+	0.661185i	−0.197491	+	0.980305i	$0.563279\pi$
$468$		−	0.710265i		−	0.0328320i
$469$	−7.43491	+	20.8998i	−0.343312	+	0.965062i
$470$	0.258732	−	6.30029i	0.0119344	−	0.290611i
$471$	4.73591	+	8.20284i	0.218219	+	0.377967i
$472$	2.44215	+	1.40998i	0.112409	+	0.0648994i
$473$	−37.2803	−	21.5238i	−1.71415	−	0.989664i
$474$	−5.21122	−	9.02610i	−0.239359	−	0.414582i
$475$	−1.52064	−	0.125106i	−0.0697719	−	0.00574028i
$476$	1.92163	+	2.25652i	0.0880780	+	0.103427i
$477$		−	1.71513i		−	0.0785305i
$478$	9.89975	−	5.71562i	0.452804	−	0.261427i
$479$	−2.79005	+	4.83250i	−0.127480	+	0.220803i	−0.922700	−	0.385519i	$-0.874022\pi$
$479$	−2.79005	+	4.83250i	−0.127480	+	0.220803i	0.795219	+	0.606322i	$0.207356\pi$
$480$	4.31608	+	2.73396i	0.197001	+	0.124788i
$481$	3.18258	+	5.51240i	0.145113	+	0.251344i
$482$		−	21.2370i		−	0.967320i
$483$	3.36040	+	18.2780i	0.152903	+	0.831679i
$484$	−3.53873			−0.160852
$485$	2.98667	+	5.70124i	0.135618	+	0.258880i
$486$	0.776205	−	1.34443i	0.0352094	−	0.0609844i
$487$	7.22858	+	4.17342i	0.327558	+	0.189116i	0.654756	−	0.755840i	$-0.272771\pi$
$487$	7.22858	+	4.17342i	0.327558	+	0.189116i	−0.327198	+	0.944956i	$0.606105\pi$
$488$	−20.4283	+	11.7943i	−0.924747	+	0.533903i
$489$	−5.39659			−0.244042
$490$	−4.85141	+	23.8098i	−0.219165	+	1.07562i
$491$	0.557405			0.0251554			0.0125777	−	0.999921i	$-0.495996\pi$
$491$	0.557405			0.0251554			0.0125777	+	0.999921i	$0.495996\pi$
$492$	−2.38437	+	1.37662i	−0.107496	+	0.0620628i
$493$	18.4443	+	10.6488i	0.830689	+	0.479598i
$494$	0.410357	−	0.710759i	0.0184628	−	0.0319785i
$495$	8.77615	−	4.59750i	0.394459	−	0.206642i
$496$	24.5845			1.10388
$497$	4.92217	+	26.7729i	0.220790	+	1.20093i
$498$			7.91645i			0.354745i
$499$	−13.0168	−	22.5458i	−0.582713	−	1.00929i	−0.995156	−	0.0983057i	$-0.968658\pi$
$499$	−13.0168	−	22.5458i	−0.582713	−	1.00929i	0.412443	−	0.910983i	$-0.364676\pi$
$500$	3.65803	+	2.76202i	0.163592	+	0.123521i
$501$	0.156275	−	0.270676i	0.00698186	−	0.0120929i
$502$	−31.5729	+	18.2286i	−1.40917	+	0.813583i
$503$			5.52409i			0.246307i	0.992388	+	0.123154i	$0.0393008\pi$
$503$			5.52409i			0.246307i	−0.992388	+	0.123154i	$0.960699\pi$
$504$	4.23418	+	4.97208i	0.188606	+	0.221474i
$505$	0.662224	−	16.1256i	0.0294686	−	0.717580i
$506$	−24.1575	−	41.8421i	−1.07393	−	1.86011i
$507$	8.65903	+	4.99929i	0.384561	+	0.222026i
$508$	−4.87569	−	2.81498i	−0.216324	−	0.124895i
$509$	11.4446	+	19.8227i	0.507274	+	0.878625i	0.999965	+	0.00842016i	$0.00268025\pi$
$509$	11.4446	+	19.8227i	0.507274	+	0.878625i	−0.492690	+	0.870205i	$0.663986\pi$
$510$	9.47718	+	0.389196i	0.419657	+	0.0172339i
$511$	11.3687	−	31.9578i	0.502921	−	1.41373i
$512$			12.3362i			0.545186i
$513$	0.264273	−	0.152578i	0.0116679	−	0.00673649i
$514$	−11.3306	+	19.6251i	−0.499771	+	0.865628i
$515$	−13.4892	+	21.2953i	−0.594404	+	0.938382i
$516$	1.99158	+	3.44952i	0.0876745	+	0.151857i
$517$			8.04846i			0.353971i
$518$	14.2176	+	5.05779i	0.624686	+	0.222226i
$519$	−9.61475			−0.422041
$520$	8.47032	−	4.43729i	0.371448	−	0.194588i
$521$	−13.0995	+	22.6889i	−0.573898	+	0.994020i	0.422263	+	0.906474i	$0.361236\pi$
$521$	−13.0995	+	22.6889i	−0.573898	+	0.994020i	−0.996160	+	0.0875466i	$0.972097\pi$
$522$	−10.4789	−	6.04998i	−0.458648	−	0.264800i
$523$	−23.2753	+	13.4380i	−1.01776	+	0.587603i	−0.913454	−	0.406943i	$-0.866595\pi$
$523$	−23.2753	+	13.4380i	−1.01776	+	0.587603i	−0.104304	+	0.994545i	$0.533262\pi$
$524$	−9.01197			−0.393690
$525$	7.72218	+	10.7409i	0.337024	+	0.468773i
$526$	7.90083			0.344493
$527$	12.5060	−	7.22034i	0.544770	−	0.314523i
$528$	−17.8499	−	10.3056i	−0.776817	−	0.448496i
$529$	13.1699	−	22.8109i	0.572605	−	0.991780i
$530$	−5.27388	+	2.76279i	−0.229083	+	0.120008i
$531$	−1.14243			−0.0495774
$532$	−0.0598510	−	0.325545i	−0.00259487	−	0.0141141i
$533$			11.6345i			0.503948i
$534$	−3.15966	−	5.47269i	−0.136732	−	0.236827i
$535$	8.27530	−	13.0641i	0.357772	−	0.564812i
$536$	10.3478	−	17.9229i	0.446957	−	0.774153i
$537$	−7.66831	+	4.42730i	−0.330912	+	0.191052i
$538$			47.3639i			2.04200i
$539$	4.94013	−	30.6193i	0.212786	−	1.31887i
$540$	−0.915960	−	0.0376154i	−0.0394167	−	0.00161871i
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	0.994181	−	0.107719i	$-0.0343547\pi$
$541$	9.39222	+	16.2678i	0.403803	+	0.699408i	−0.590378	+	0.807127i	$0.701021\pi$
$542$	−26.2002	−	15.1267i	−1.12540	−	0.649747i
$543$	−14.6561	−	8.46168i	−0.628952	−	0.363125i
$544$	−3.12166	−	5.40687i	−0.133840	−	0.231817i
$545$	−0.405716	+	9.87944i	−0.0173789	+	0.423189i
$546$	−6.99842	+	1.28665i	−0.299505	+	0.0550636i
$547$			13.4126i			0.573483i	0.958008	+	0.286742i	$0.0925721\pi$
$547$			13.4126i			0.573483i	−0.958008	+	0.286742i	$0.907428\pi$
$548$	1.06582	−	0.615353i	0.0455297	−	0.0262866i
$549$	4.77818	−	8.27604i	0.203928	−	0.353213i
$550$	−28.2738	−	19.5801i	−1.20560	−	0.834899i
$551$	−1.18924	−	2.05982i	−0.0506633	−	0.0877515i
$552$		−	17.3384i		−	0.737971i
$553$	−13.5236	+	11.5166i	−0.575081	+	0.489734i
$554$	39.5557			1.68056
$555$	7.27735	−	3.81233i	0.308906	−	0.161825i
$556$	4.45569	−	7.71749i	0.188963	−	0.327294i
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.999589	−	0.0286677i	$-0.00912646\pi$
$557$	34.8008	+	20.0922i	1.47456	+	0.851336i	0.474968	+	0.880003i	$0.342460\pi$
$558$	−7.10511	+	4.10214i	−0.300784	+	0.173657i
$559$	16.8319			0.711914
$560$	10.2802	−	25.5287i	0.434417	−	1.07878i
$561$	−12.1069			−0.511152
$562$	29.8347	−	17.2251i	1.25850	−	0.726595i
$563$	21.8134	+	12.5940i	0.919325	+	0.530772i	0.883420	−	0.468583i	$-0.155235\pi$
$563$	21.8134	+	12.5940i	0.919325	+	0.530772i	0.0359052	+	0.999355i	$0.488569\pi$
$564$	0.372360	−	0.644946i	0.0156792	−	0.0271571i
$565$	2.96920	+	5.66789i	0.124915	+	0.238450i
$566$	28.1362			1.18265
$567$	−2.49272	−	0.886763i	−0.104684	−	0.0372405i
$568$		−	25.3966i		−	1.06562i
$569$	−5.51757	−	9.55672i	−0.231309	−	0.400638i	0.726885	−	0.686759i	$-0.240967\pi$
$569$	−5.51757	−	9.55672i	−0.231309	−	0.400638i	−0.958194	+	0.286121i	$0.907634\pi$
$570$	−0.894864	−	0.566839i	−0.0374817	−	0.0237423i
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	0.391858	+	0.920026i	$0.371832\pi$
$571$	−14.3573	+	24.8677i	−0.600836	+	1.04068i	−0.992695	+	0.120654i	$0.961501\pi$
$572$	2.72539	−	1.57351i	0.113954	−	0.0657916i
$573$		−	0.318541i		−	0.0133073i
$574$	17.8835	+	21.0001i	0.746442	+	0.876526i
$575$	2.87976	−	35.0029i	0.120094	−	1.45972i
$576$	−2.87834	−	4.98544i	−0.119931	−	0.207727i
$577$	−5.94444	−	3.43202i	−0.247470	−	0.142877i	0.371135	−	0.928579i	$-0.378969\pi$
$577$	−5.94444	−	3.43202i	−0.247470	−	0.142877i	−0.618605	+	0.785702i	$0.712302\pi$
$578$	12.8173	+	7.40008i	0.533130	+	0.307803i
$579$	1.04667	+	1.81289i	0.0434981	+	0.0753410i
$580$	−0.293186	+	7.13927i	−0.0121739	+	0.296442i
$581$	13.2695	−	2.43959i	0.550512	−	0.101211i
$582$			4.46837i			0.185220i
$583$	6.58121	−	3.79966i	0.272566	−	0.157366i
$584$	−15.8228	+	27.4059i	−0.654752	+	1.13406i
$585$	−2.07298	+	3.27259i	−0.0857070	+	0.135305i
$586$	−10.7860	−	18.6819i	−0.445565	−	0.771741i
$587$		−	9.03965i		−	0.373106i	−0.982445	−	0.186553i	$-0.940268\pi$
$587$		−	9.03965i		−	0.373106i	0.982445	−	0.186553i	$-0.0597317\pi$
$588$	−1.81246	+	2.22506i	−0.0747446	+	0.0917599i
$589$	−1.61271			−0.0664506
$590$	1.84027	+	3.51289i	0.0757628	+	0.144623i
$591$	11.2899	−	19.5547i	0.464404	−	0.804372i
$592$	−14.8015	−	8.54564i	−0.608337	−	0.351224i
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	−0.588071	−	0.808809i	$-0.700112\pi$
$593$	−4.42364	+	2.55399i	−0.181657	+	0.104880i	0.406414	+	0.913689i	$0.366779\pi$
$594$	6.87834			0.282222
$595$	−2.26818	−	16.0055i	−0.0929864	−	0.656163i
$596$	−2.13724			−0.0875446
$597$	−6.49872	+	3.75204i	−0.265975	+	0.153561i
$598$	16.3606	+	9.44578i	0.669034	+	0.386267i
$599$	−14.9721	+	25.9325i	−0.611745	+	1.05957i	0.379202	+	0.925314i	$0.376199\pi$
$599$	−14.9721	+	25.9325i	−0.611745	+	1.05957i	−0.990946	+	0.134259i	$0.957135\pi$
$600$	−5.27375	−	11.1583i	−0.215300	−	0.455538i
$601$	−12.5387			−0.511466			−0.255733	−	0.966747i	$-0.582317\pi$
$601$	−12.5387			−0.511466			−0.255733	+	0.966747i	$0.582317\pi$
$602$	30.3812	−	25.8724i	1.23825	−	1.05448i
$603$			8.38433i			0.341436i
$604$	−1.99119	−	3.44884i	−0.0810204	−	0.140331i
$605$	16.3049	+	10.3281i	0.662890	+	0.419898i
$606$	5.60239	−	9.70362i	0.227581	−	0.394182i
$607$	−8.31216	+	4.79903i	−0.337380	+	0.194786i	−0.659113	−	0.752044i	$-0.729068\pi$
$607$	−8.31216	+	4.79903i	−0.337380	+	0.194786i	0.321733	+	0.946831i	$0.395735\pi$
$608$			0.697242i			0.0282769i
$609$	−6.91170	+	19.4290i	−0.280076	+	0.787304i
$610$	−33.1450	−	1.36115i	−1.34200	−	0.0551115i
$611$	−1.57351	−	2.72539i	−0.0636572	−	0.110258i
$612$	0.970157	+	0.560120i	0.0392163	+	0.0226415i
$613$	−23.9583	−	13.8323i	−0.967665	−	0.558682i	−0.0691416	−	0.997607i	$-0.522026\pi$
$613$	−23.9583	−	13.8323i	−0.967665	−	0.558682i	−0.898524	+	0.438925i	$0.855359\pi$
$614$	−23.1567	−	40.1085i	−0.934527	−	1.61865i
$615$	15.0039	+	0.616162i	0.605017	+	0.0248460i
$616$	−9.69830	+	27.2622i	−0.390755	+	1.09843i
$617$			20.4155i			0.821896i	0.911659	+	0.410948i	$0.134802\pi$
$617$			20.4155i			0.821896i	−0.911659	+	0.410948i	$0.865198\pi$
$618$	−15.1562	+	8.75046i	−0.609673	+	0.351995i
$619$	−7.72112	+	13.3734i	−0.310338	+	0.537521i	−0.978435	−	0.206553i	$-0.933776\pi$
$619$	−7.72112	+	13.3734i	−0.310338	+	0.537521i	0.668098	+	0.744074i	$0.267109\pi$
$620$	4.09280	+	2.59252i	0.164371	+	0.104118i
$621$	3.51212	+	6.08316i	0.140936	+	0.244109i
$622$		−	20.9781i		−	0.841145i
$623$	−8.19960	+	6.98271i	−0.328510	+	0.279756i
$624$	8.05918			0.322625
$625$	−8.79339	−	23.4025i	−0.351735	−	0.936099i
$626$	−22.4988	+	38.9691i	−0.899234	+	1.55752i
$627$	1.17093	+	0.676036i	0.0467624	+	0.0269983i
$628$	3.36296	−	1.94161i	0.134197	−	0.0774785i
$629$	−10.0392			−0.400290
$630$	1.28864	+	9.09332i	0.0513405	+	0.362287i
$631$	−38.1722			−1.51961			−0.759805	−	0.650151i	$-0.774705\pi$
$631$	−38.1722			−1.51961			−0.759805	+	0.650151i	$0.774705\pi$
$632$	14.3517	−	8.28597i	0.570881	−	0.329598i
$633$	6.64428	+	3.83608i	0.264087	+	0.152470i
$634$	−0.899340	+	1.55770i	−0.0357173	+	0.0618643i
$635$	14.2493	+	27.2004i	0.565465	+	1.07941i
$636$	−0.703161			−0.0278822
$637$	4.31336	+	11.3342i	0.170901	+	0.449078i
$638$		−	53.6119i		−	2.12252i
$639$	5.14441	+	8.91037i	0.203510	+	0.352489i
$640$	−16.1612	+	25.5135i	−0.638827	+	1.00851i
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	−0.651396	−	0.758738i	$-0.725816\pi$
$641$	8.39007	−	14.5320i	0.331388	−	0.573981i	0.982784	+	0.184757i	$0.0591498\pi$
$642$	9.29800	−	5.36820i	0.366963	−	0.211866i
$643$		−	14.2002i		−	0.560001i	−0.960000	−	0.280001i	$-0.909665\pi$
$643$		−	14.2002i		−	0.560001i	0.960000	−	0.280001i	$-0.0903346\pi$
$644$	7.49354	−	1.37768i	0.295287	−	0.0542882i
$645$	0.891413	−	21.7065i	0.0350994	−	0.854692i
$646$	0.647220	+	1.12102i	0.0254645	+	0.0441059i
$647$	12.5474	+	7.24426i	0.493290	+	0.284801i	0.725938	−	0.687760i	$-0.241406\pi$
$647$	12.5474	+	7.24426i	0.493290	+	0.284801i	−0.232648	+	0.972561i	$0.574739\pi$
$648$	2.13767	+	1.23418i	0.0839756	+	0.0484834i
$649$	−2.53092	−	4.38369i	−0.0993474	−	0.172075i
$650$	13.4021	+	1.10262i	0.525676	+	0.0432484i
$651$	9.06554	+	10.6454i	0.355307	+	0.417227i
$652$			2.21247i			0.0866469i
$653$	8.90562	−	5.14166i	0.348504	−	0.201209i	−0.315522	−	0.948918i	$-0.602180\pi$
$653$	8.90562	−	5.14166i	0.348504	−	0.201209i	0.664026	+	0.747709i	$0.268846\pi$
$654$	−3.43233	+	5.94498i	−0.134215	+	0.232467i
$655$	41.5232	+	26.3023i	1.62245	+	1.02771i
$656$	−15.6201	−	27.0548i	−0.609863	−	1.05631i
$657$		−	12.8204i		−	0.500173i
$658$	−7.02935	−	2.50063i	−0.274032	−	0.0974846i
$659$	−14.9773			−0.583433			−0.291717	−	0.956505i	$-0.594226\pi$
$659$	−14.9773			−0.583433			−0.291717	+	0.956505i	$0.594226\pi$
$660$	−1.88486	−	3.59801i	−0.0733681	−	0.140052i
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	−0.888834	−	0.458230i	$-0.848484\pi$
$661$	−1.22323	+	2.11870i	−0.0475782	+	0.0824079i	0.841256	+	0.540638i	$0.181817\pi$
$662$	−38.1133	−	22.0047i	−1.48131	−	0.855238i
$663$	4.09966	−	2.36694i	0.159217	−	0.0919242i
$664$	−12.5874			−0.488484
$665$	−0.674365	+	1.67465i	−0.0261507	+	0.0649400i
$666$	5.70365			0.221012
$667$	47.4140	−	27.3745i	1.83588	−	1.05994i
$668$	−0.110971	−	0.0640689i	−0.00429358	−	0.00247890i
$669$	3.45104	−	5.97738i	0.133425	−	0.231099i
$670$	25.7811	−	13.5058i	0.996010	−	0.521773i
$671$	42.3418			1.63459
$672$	4.60245	−	3.91941i	0.177544	−	0.151195i
$673$			17.2596i			0.665310i	0.943049	+	0.332655i	$0.107945\pi$
$673$			17.2596i			0.665310i	−0.943049	+	0.332655i	$0.892055\pi$
$674$	−12.3983	−	21.4744i	−0.477564	−	0.827164i
$675$	4.11056	+	2.84663i	0.158215	+	0.109567i
$676$	2.04959	−	3.54999i	0.0788302	−	0.136538i
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	−0.681021	−	0.732264i	$-0.738464\pi$
$677$	−10.0791	+	5.81918i	−0.387372	+	0.223649i	0.293649	+	0.955913i	$0.405130\pi$
$678$			4.44223i			0.170603i
$679$	7.48986	−	1.37700i	0.287434	−	0.0528445i
$680$	−0.618831	+	15.0689i	−0.0237311	+	0.577868i
$681$	−3.17360	−	5.49684i	−0.121613	−	0.210639i
$682$	−31.4810	−	18.1756i	−1.20547	−	0.695979i
$683$	26.9299	+	15.5480i	1.03044	+	0.594928i	0.917112	−	0.398629i	$-0.130514\pi$
$683$	26.9299	+	15.5480i	1.03044	+	0.594928i	0.113333	+	0.993557i	$0.463847\pi$
$684$	−0.0625532	−	0.108345i	−0.00239178	−	0.00414269i
$685$	−6.70681	−	0.275426i	−0.256254	−	0.0105235i
$686$	25.2073	+	13.8279i	0.962421	+	0.527952i
$687$			6.75669i			0.257784i
$688$	−39.1407	+	22.5979i	−1.49223	+	0.861537i
$689$	−1.48570	+	2.57330i	−0.0566006	+	0.0980351i
$690$	13.0478	−	20.5984i	0.496720	−	0.784168i
$691$	8.96695	+	15.5312i	0.341119	+	0.590835i	0.984641	−	0.174592i	$-0.0558607\pi$
$691$	8.96695	+	15.5312i	0.341119	+	0.590835i	−0.643522	+	0.765428i	$0.722527\pi$
$692$			3.94181i			0.149845i
$693$	−2.11968	−	11.5294i	−0.0805198	−	0.437967i
$694$	20.1999			0.766778
$695$	−43.0541	+	22.5544i	−1.63313	+	0.855538i
$696$	9.61961	−	16.6617i	0.364630	−	0.631559i
$697$	−15.8917	−	9.17508i	−0.601941	−	0.347531i
$698$	43.1190	−	24.8947i	1.63208	−	0.942280i
$699$	−7.41201			−0.280348
$700$	4.40352	−	3.16590i	0.166437	−	0.119660i
$701$	7.04488			0.266081			0.133041	−	0.991111i	$-0.457526\pi$
$701$	7.04488			0.266081			0.133041	+	0.991111i	$0.457526\pi$
$702$	−2.32916	+	1.34474i	−0.0879086	+	0.0507541i
$703$	0.970956	+	0.560582i	0.0366203	+	0.0211427i
$704$	12.7532	−	22.0893i	0.480656	−	0.832520i
$705$	−3.59801	+	1.88486i	−0.135509	+	0.0709880i
$706$	−20.7540			−0.781088
$707$	−17.9916	−	6.40036i	−0.676644	−	0.240710i
$708$			0.468370i			0.0176024i
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	0.513080	−	0.858341i	$-0.328504\pi$
$709$	−12.9622	−	22.4511i	−0.486804	−	0.843170i	−0.999885	+	0.0151705i	$0.995171\pi$
$710$	19.1118	−	30.1717i	0.717255	−	1.13232i
$711$	−3.35686	+	5.81425i	−0.125892	+	0.218051i
$712$	8.70172	−	5.02394i	0.326111	−	0.188280i
$713$		−	37.1221i		−	1.39023i
$714$	3.76156	−	10.5739i	0.140773	−	0.395717i
$715$	−17.1498	−	0.704286i	−0.641367	−	0.0263388i
$716$	1.81508	+	3.14382i	0.0678329	+	0.117490i
$717$	−6.37702	−	3.68178i	−0.238154	−	0.137498i
$718$	17.6382	+	10.1834i	0.658251	+	0.380041i
$719$	15.6427	+	27.0940i	0.583376	+	1.01044i	0.995076	+	0.0991173i	$0.0316019\pi$
$719$	15.6427	+	27.0940i	0.583376	+	1.01044i	−0.411700	+	0.911320i	$0.635065\pi$
$720$	0.426811	−	10.3931i	0.0159063	−	0.387329i
$721$	19.3381	+	22.7082i	0.720189	+	0.845698i
$722$			29.3512i			1.09234i
$723$	−11.8473	+	6.84002i	−0.440605	+	0.254383i
$724$	−3.46908	+	6.00862i	−0.128927	+	0.223309i
$725$	22.1875	−	32.0389i	0.824023	−	1.18990i
$726$	6.69988	+	11.6045i	0.248656	+	0.430684i
$727$			22.8312i			0.846761i	0.905952	+	0.423380i	$0.139157\pi$
$727$			22.8312i			0.846761i	−0.905952	+	0.423380i	$0.860843\pi$
$728$	−2.04581	−	11.1277i	−0.0758227	−	0.412419i
$729$	−1.00000			−0.0370370
$730$	−39.4217	+	20.6516i	−1.45906	+	0.764350i
$731$	−13.2738	+	22.9908i	−0.490948	+	0.850347i
$732$	−3.39297	−	1.95893i	−0.125408	−	0.0724043i
$733$	5.15661	−	2.97717i	0.190464	−	0.109964i	−0.401736	−	0.915756i	$-0.631593\pi$
$733$	5.15661	−	2.97717i	0.190464	−	0.109964i	0.592200	+	0.805791i	$0.298260\pi$
$734$	20.3924			0.752696
$735$	14.8451	−	4.96226i	0.547568	−	0.183036i
$736$	−16.0494			−0.591590
$737$	−32.1719	+	18.5745i	−1.18507	+	0.684199i
$738$	9.02866	+	5.21270i	0.332350	+	0.191882i
$739$	20.7539	−	35.9469i	0.763446	−	1.32233i	−0.177618	−	0.984099i	$-0.556839\pi$
$739$	20.7539	−	35.9469i	0.763446	−	1.32233i	0.941064	−	0.338228i	$-0.109827\pi$
$740$	−1.56296	−	2.98353i	−0.0574556	−	0.109677i
$741$	−0.528671			−0.0194212
$742$	1.27378	+	6.92842i	0.0467620	+	0.254350i
$743$			6.80015i			0.249473i	0.992190	+	0.124737i	$0.0398086\pi$
$743$			6.80015i			0.249473i	−0.992190	+	0.124737i	$0.960191\pi$
$744$	−6.52250	−	11.2973i	−0.239127	−	0.414179i
$745$	9.84745	+	6.23773i	0.360783	+	0.228533i
$746$	−22.9910	+	39.8216i	−0.841760	+	1.45797i
$747$	4.41626	−	2.54973i	0.161583	−	0.0932898i
$748$			4.96351i			0.181484i
$749$	−11.8635	−	13.9310i	−0.433482	−	0.509026i
$750$	2.13172	−	17.2251i	0.0778394	−	0.628970i
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	0.566148	−	0.824304i	$-0.308433\pi$
$751$	−11.8056	−	20.4480i	−0.430794	−	0.746157i	−0.996942	+	0.0781464i	$0.975100\pi$
$752$	7.31802	+	4.22506i	0.266861	+	0.154072i
$753$	20.3380	+	11.7421i	0.741157	+	0.427907i
$754$	10.4813	+	18.1542i	0.381708	+	0.661137i
$755$	−0.891238	+	21.7022i	−0.0324355	+	0.789825i
$756$	−0.363551	+	1.02195i	−0.0132222	+	0.0371681i
$757$			16.2267i			0.589769i	0.955533	+	0.294884i	$0.0952811\pi$
$757$			16.2267i			0.589769i	−0.955533	+	0.294884i	$0.904719\pi$
$758$	10.0521	−	5.80360i	0.365110	−	0.210796i
$759$	−15.5613	+	26.9530i	−0.564840	+	0.978332i
$760$	0.901288	−	1.42286i	0.0326931	−	0.0516124i
$761$	1.27754	+	2.21276i	0.0463108	+	0.0802126i	0.888252	−	0.459357i	$-0.151920\pi$
$761$	1.27754	+	2.21276i	0.0463108	+	0.0802126i	−0.841941	+	0.539570i	$0.818587\pi$
$762$			21.3184i			0.772284i
$763$	11.0227	+	3.92122i	0.399047	+	0.141958i
$764$	−0.130594			−0.00472473
$765$	−2.83529	−	5.41228i	−0.102510	−	0.195681i
$766$	−18.4264	+	31.9154i	−0.665772	+	1.15315i
$767$	1.71406	+	0.989610i	0.0618910	+	0.0357328i
$768$	−8.18758	+	4.72710i	−0.295444	+	0.170575i
$769$	45.4525			1.63906			0.819530	−	0.573037i	$-0.194235\pi$
$769$	45.4525			1.63906			0.819530	+	0.573037i	$0.194235\pi$
$770$	−32.0376	+	25.0898i	−1.15455	+	0.904175i
$771$	14.5974			0.525713
$772$	0.743238	−	0.429109i	0.0267497	−	0.0154440i
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.990713	−	0.135970i	$-0.956585\pi$
$773$	−44.5909	−	25.7446i	−1.60382	−	0.925968i	−0.613110	−	0.789997i	$-0.710082\pi$
$774$	7.54131	−	13.0619i	0.271067	−	0.469502i
$775$	−11.2913	−	23.8904i	−0.405595	−	0.858170i
$776$	−7.10482			−0.255048
$777$	−1.75767	−	9.56043i	−0.0630562	−	0.342979i
$778$		−	21.9363i		−	0.786453i
$779$	1.02466	+	1.77476i	0.0367121	+	0.0635873i
$780$	1.34168	+	0.849868i	0.0480399	+	0.0304302i
$781$	−22.7936	+	39.4797i	−0.815619	+	1.41269i
$782$	−25.8041	+	14.8980i	−0.922754	+	0.532752i
$783$			7.79430i			0.278546i
$784$	−25.2471	−	20.5655i	−0.901683	−	0.734481i
$785$	−21.1618	−	0.869044i	−0.755297	−	0.0310175i
$786$	17.0623	+	29.5528i	0.608593	+	1.05411i
$787$	−17.4517	−	10.0757i	−0.622085	−	0.359161i	0.155596	−	0.987821i	$-0.450270\pi$
$787$	−17.4517	−	10.0757i	−0.622085	−	0.359161i	−0.777680	+	0.628660i	$0.783604\pi$
$788$	−8.01693	−	4.62858i	−0.285591	−	0.164886i
$789$	−2.54470	−	4.40755i	−0.0905937	−	0.156913i
$790$	23.2857	+	0.956264i	0.828466	+	0.0340223i
$791$	7.44605	−	1.36895i	0.264751	−	0.0486742i
$792$			10.9367i			0.388620i
$793$	−14.3379	+	8.27800i	−0.509154	+	0.293960i
$794$	−8.74750	+	15.1511i	−0.310437	+	0.537693i
$795$	3.23986	+	2.05224i	0.114906	+	0.0727855i
$796$	1.53824	+	2.66431i	0.0545216	+	0.0944341i
$797$		−	13.0702i		−	0.462971i	−0.972838	−	0.231486i	$-0.925641\pi$
$797$		−	13.0702i		−	0.462971i	0.972838	−	0.231486i	$-0.0743587\pi$
$798$	−0.954238	+	0.812621i	−0.0337797	+	0.0287665i
$799$	4.96351			0.175596
$800$	−10.3288	+	4.88170i	−0.365179	+	0.172594i
$801$	−2.03533	+	3.52529i	−0.0719148	+	0.124560i
$802$	31.3209	+	18.0831i	1.10598	+	0.638537i
$803$	49.1939	−	28.4021i	1.73602	−	1.00229i
$804$	3.43737			0.121227
$805$	−38.5478	−	15.5229i	−1.35863	−	0.547109i
$806$	14.2136			0.500652
$807$	26.4224	−	15.2550i	0.930112	−	0.537000i
$808$	15.4290	+	8.90793i	0.542790	+	0.313380i
$809$	−0.868598	+	1.50446i	−0.0305383	+	0.0528938i	−0.880891	−	0.473320i	$-0.843055\pi$
$809$	−0.868598	+	1.50446i	−0.0305383	+	0.0528938i	0.850352	+	0.526214i	$0.176389\pi$
$810$	1.61083	+	3.07491i	0.0565989	+	0.108041i
$811$	−27.9004			−0.979715			−0.489858	−	0.871802i	$-0.662951\pi$
$811$	−27.9004			−0.979715			−0.489858	+	0.871802i	$0.662951\pi$
$812$	7.96541	+	2.83363i	0.279531	+	0.0994408i
$813$			19.4880i			0.683475i
$814$	12.6357	+	21.8857i	0.442883	+	0.767095i
$815$	6.45729	−	10.1941i	0.226189	−	0.357083i
$816$	−6.35552	+	11.0081i	−0.222488	+	0.385360i
$817$	2.56758	−	1.48239i	0.0898282	−	0.0518623i
$818$			32.0538i			1.12074i
$819$	2.97182	+	3.48973i	0.103844	+	0.121941i
$820$	0.252611	−	6.15124i	0.00882156	−	0.214811i
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	0.679574	−	0.733607i	$-0.262165\pi$
$821$	−8.46799	−	14.6670i	−0.295535	−	0.511881i	−0.975109	+	0.221725i	$0.928831\pi$
$822$	−4.03584	−	2.33009i	−0.140766	−	0.0812714i
$823$	8.56526	+	4.94516i	0.298566	+	0.172377i	0.641799	−	0.766873i	$-0.278188\pi$
$823$	8.56526	+	4.94516i	0.298566	+	0.172377i	−0.343232	+	0.939251i	$0.611522\pi$
$824$	−13.9134	−	24.0988i	−0.484698	−	0.839521i
$825$	−1.81650	+	22.0792i	−0.0632424	+	0.768698i
$826$	4.61496	−	0.848456i	0.160575	−	0.0295216i
$827$			35.3201i			1.22820i	0.789228	+	0.614101i	$0.210481\pi$
$827$			35.3201i			1.22820i	−0.789228	+	0.614101i	$0.789519\pi$
$828$	2.49395	−	1.43988i	0.0866706	−	0.0500393i
$829$	4.64975	−	8.05361i	0.161493	−	0.279713i	−0.773912	−	0.633294i	$-0.781703\pi$
$829$	4.64975	−	8.05361i	0.161493	−	0.279713i	0.935404	+	0.353580i	$0.115036\pi$
$830$	−14.9541	−	9.47244i	−0.519063	−	0.328793i
$831$	−12.7401	−	22.0665i	−0.441949	−	0.765478i
$832$			9.97323i			0.345760i
$833$	−18.8830	−	3.04659i	−0.654258	−	0.105558i
$834$	−33.7438			−1.16845
$835$	0.324313	+	0.619080i	0.0112233	+	0.0214241i
$836$	0.277158	−	0.480052i	0.00958571	−	0.0166029i
$837$	4.57683	+	2.64243i	0.158198	+	0.0913359i
$838$	−7.37086	+	4.25557i	−0.254622	+	0.147006i
$839$	7.93405			0.273914			0.136957	−	0.990577i	$-0.456268\pi$
$839$	7.93405			0.273914			0.136957	+	0.990577i	$0.456268\pi$
$840$	−14.4586	+	2.04896i	−0.498870	+	0.0706960i
$841$	31.7512			1.09487
$842$	5.08299	−	2.93467i	0.175171	−	0.101135i
$843$	−19.2183	−	11.0957i	−0.661914	−	0.382156i
$844$	1.57270	−	2.72399i	0.0541345	−	0.0937636i
$845$	−19.8046	+	10.3749i	−0.681298	+	0.356906i
$846$	−2.81995			−0.0969519
$847$	17.3868	−	14.8064i	0.597416	−	0.508755i
$848$		−	7.97857i		−	0.273985i
$849$	−9.06209	−	15.6960i	−0.311010	−	0.538685i
$850$	−12.0751	+	17.4366i	−0.414173	+	0.598069i
$851$	−12.9037	+	22.3499i	−0.442334	+	0.766146i
$852$	3.65303	−	2.10908i	0.125151	−	0.0722558i
$853$		−	30.0757i		−	1.02977i	−0.857258	−	0.514887i	$-0.827834\pi$
$853$		−	30.0757i		−	1.02977i	0.857258	−	0.514887i	$-0.172166\pi$
$854$	−13.1555	+	36.9804i	−0.450170	+	1.26544i
$855$	−0.0279982	+	0.681775i	−0.000957519	+	0.0233162i
$856$	8.53557	+	14.7840i	0.291740	+	0.505308i
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.400652	−	0.916230i	$-0.631216\pi$
$857$	−40.8221	−	23.5686i	−1.39446	−	0.805090i	−0.993805	+	0.111141i	$0.964550\pi$
$858$	−10.3199	−	5.95823i	−0.352317	−	0.203410i
$859$	−16.3183	−	28.2642i	−0.556774	−	0.964361i	−0.997763	−	0.0668485i	$-0.978706\pi$
$859$	−16.3183	−	28.2642i	−0.556774	−	0.964361i	0.440989	−	0.897512i	$-0.354628\pi$
$860$	−8.89912	−	0.365457i	−0.303458	−	0.0124620i
$861$	5.95517	−	16.7402i	0.202951	−	0.570503i
$862$			42.7110i			1.45474i
$863$	32.3982	−	18.7051i	1.10285	−	0.636728i	0.165879	−	0.986146i	$-0.446954\pi$
$863$	32.3982	−	18.7051i	1.10285	−	0.636728i	0.936967	+	0.349418i	$0.113621\pi$
$864$	1.14243	−	1.97875i	0.0388664	−	0.0673186i
$865$	11.5045	−	18.1621i	0.391166	−	0.617531i
$866$	6.79578	+	11.7706i	0.230930	+	0.399983i
$867$		−	9.53367i		−	0.323780i
$868$	4.36435	−	3.71665i	0.148136	−	0.126151i
$869$	−29.7468			−1.00909
$870$	23.9668	−	12.5553i	0.812551	−	0.425665i
$871$	7.26275	−	12.5795i	0.246089	−	0.426239i
$872$	−9.45266	−	5.45750i	−0.320108	−	0.184814i
$873$	2.49272	−	1.43917i	0.0843658	−	0.0487086i
$874$	3.32757			0.112557
$875$	−29.5295	+	1.73501i	−0.998278	+	0.0586541i
$876$	−5.25606			−0.177586
$877$	−29.0687	+	16.7828i	−0.981581	+	0.566716i	−0.902747	−	0.430172i	$-0.858453\pi$
$877$	−29.0687	+	16.7828i	−0.981581	+	0.566716i	−0.0788336	+	0.996888i	$0.525120\pi$
$878$	14.2680	+	8.23764i	0.481522	+	0.278007i
$879$	−6.94790	+	12.0341i	−0.234347	+	0.405901i
$880$	40.8255	−	21.3870i	1.37623	−	0.720955i
$881$	−12.1952			−0.410867			−0.205433	−	0.978671i	$-0.565860\pi$
$881$	−12.1952			−0.410867			−0.205433	+	0.978671i	$0.565860\pi$
$882$	10.7281	+	1.73088i	0.361235	+	0.0582817i
$883$		−	11.0408i		−	0.371552i	−0.982592	−	0.185776i	$-0.940520\pi$
$883$		−	11.0408i		−	0.371552i	0.982592	−	0.185776i	$-0.0594799\pi$
$884$	−0.970385	−	1.68076i	−0.0326376	−	0.0565300i
$885$	1.36698	−	2.15804i	0.0459505	−	0.0725418i
$886$	15.5129	−	26.8691i	0.521166	−	0.902685i
$887$	−1.35180	+	0.780464i	−0.0453891	+	0.0262054i	−0.522523	−	0.852625i	$-0.675009\pi$
$887$	−1.35180	+	0.780464i	−0.0453891	+	0.0262054i	0.477134	+	0.878831i	$0.341676\pi$
$888$			9.06895i			0.304334i
$889$	35.7338	−	6.56962i	1.19847	−	0.220338i
$890$	14.1185	+	0.579801i	0.473254	+	0.0194350i
$891$	−2.21538	−	3.83715i	−0.0742179	−	0.128549i
$892$	−2.45058	−	1.41484i	−0.0820514	−	0.0473724i
$893$	−0.480052	−	0.277158i	−0.0160643	−	0.00927474i
$894$	4.04642	+	7.00861i	0.135333	+	0.234403i
$895$	0.812414	−	19.7828i	0.0271560	−	0.661267i
$896$	23.1687	+	27.2064i	0.774012	+	0.908900i
$897$		−	12.1692i		−	0.406318i
$898$	4.06793	−	2.34862i	0.135749	−	0.0783745i
$899$	20.5959	−	35.6732i	0.686913	−	1.18977i
$900$	1.16705	−	1.68523i	0.0389016	−	0.0561742i
$901$	−2.34326	−	4.05865i	−0.0780654	−	0.135213i
$902$			46.1924i			1.53804i
$903$	−24.2183	−	8.61545i	−0.805935	−	0.286704i
$904$	−7.06326			−0.234921
$905$	33.5207	−	17.5603i	1.11427	−	0.583722i
$906$	−7.53983	+	13.0594i	−0.250494	+	0.433869i
$907$	−15.0756	−	8.70390i	−0.500577	−	0.289008i	0.228375	−	0.973573i	$-0.426659\pi$
$907$	−15.0756	−	8.70390i	−0.500577	−	0.289008i	−0.728952	+	0.684565i	$0.759992\pi$
$908$	−2.25357	+	1.30110i	−0.0747873	+	0.0431785i
$909$	−7.21767			−0.239395
$910$	5.94350	−	14.7595i	0.197025	−	0.489271i
$911$	−18.3203			−0.606978			−0.303489	−	0.952835i	$-0.598152\pi$
$911$	−18.3203			−0.606978			−0.303489	+	0.952835i	$0.598152\pi$
$912$	1.22936	−	0.709774i	0.0407083	−	0.0235030i
$913$	19.5674	+	11.2972i	0.647586	+	0.373884i
$914$	1.77079	−	3.06710i	0.0585726	−	0.101451i
$915$	9.91600	+	18.9286i	0.327813	+	0.625761i
$916$	2.77007			0.0915258
$917$	44.2783	−	37.7070i	1.46220	−	1.24519i
$918$		−	4.24190i		−	0.140003i
$919$	11.2963	+	19.5658i	0.372632	+	0.645417i	0.989970	−	0.141281i	$-0.0451221\pi$
$919$	11.2963	+	19.5658i	0.372632	+	0.645417i	−0.617338	+	0.786698i	$0.711789\pi$
$920$	32.7520	+	20.7463i	1.07980	+	0.683984i
$921$	−14.9166	+	25.8363i	−0.491519	+	0.851335i
$922$	32.3574	−	18.6816i	1.06563	−	0.615244i
$923$		−	17.8249i		−	0.586715i
$924$	−4.72678	+	0.869014i	−0.155500	+	0.0285885i
$925$	−1.50628	+	18.3085i	−0.0495260	+	0.601979i
$926$	−8.63842	−	14.9622i	−0.283876	−	0.491688i
$927$	9.76304	+	5.63670i	0.320660	+	0.185133i
$928$	−15.4230	−	8.90448i	−0.506285	−	0.292304i
$929$	19.3356	+	33.4903i	0.634381	+	1.09878i	0.986646	+	0.162880i	$0.0520783\pi$
$929$	19.3356	+	33.4903i	0.634381	+	1.09878i	−0.352265	+	0.935900i	$0.614588\pi$
$930$	0.752747	−	18.3299i	0.0246835	−	0.601060i
$931$	1.65618	+	1.34907i	0.0542790	+	0.0442139i
$932$			3.03874i			0.0995372i
$933$	−11.7028	+	6.75662i	−0.383133	+	0.221202i
$934$	22.1813	−	38.4192i	0.725795	−	1.25711i
$935$	14.4865	−	22.8697i	0.473758	−	0.747918i
$936$	−2.13817	−	3.70343i	−0.0698884	−	0.121050i
$937$		−	46.7921i		−	1.52863i	−0.644842	−	0.764316i	$-0.723077\pi$
$937$		−	46.7921i		−	1.52863i	0.644842	−	0.764316i	$-0.276923\pi$
$938$	−6.22682	−	33.8692i	−0.203313	−	1.10587i
$939$	28.9857			0.945912
$940$	0.772746	+	1.47509i	0.0252042	+	0.0481122i
$941$	20.9461	−	36.2797i	0.682824	−	1.18268i	−0.291292	−	0.956634i	$-0.594085\pi$
$941$	20.9461	−	36.2797i	0.682824	−	1.18268i	0.974116	−	0.226051i	$-0.0725815\pi$
$942$	−12.7342	−	7.35207i	−0.414901	−	0.239543i
$943$	−40.8522	+	23.5860i	−1.33033	+	0.768067i
$944$	−5.31446			−0.172971
$945$	4.65775	−	3.64765i	0.151517	−	0.118658i
$946$	66.8274			2.17275
$947$	48.5967	−	28.0573i	1.57918	−	0.911740i	0.584206	−	0.811605i	$-0.301406\pi$
$947$	48.5967	−	28.0573i	1.57918	−	0.911740i	0.994974	−	0.100134i	$-0.0319273\pi$
$948$	2.38370	+	1.37623i	0.0774189	+	0.0446978i
$949$	−11.1054	+	19.2352i	−0.360498	+	0.624401i
$950$	2.14150	−	1.01213i	0.0694795	−	0.0328380i
$951$	1.15864			0.0375714
$952$	16.8127	+	5.98097i	0.544903	+	0.193844i
$953$		−	17.7705i		−	0.575643i	−0.957684	−	0.287821i	$-0.907069\pi$
$953$		−	17.7705i		−	0.575643i	0.957684	−	0.287821i	$-0.0929309\pi$
$954$	1.33129	+	2.30587i	0.0431022	+	0.0746552i
$955$	0.601720	+	0.381151i	0.0194712	+	0.0123337i
$956$	−1.50944	+	2.61442i	−0.0488187	+	0.0845564i
$957$	−29.9079	+	17.2673i	−0.966785	+	0.558173i
$958$		−	8.66259i		−	0.279875i
$959$	−2.66198	+	7.48291i	−0.0859598	+	0.241636i
$960$	12.8615	+	0.528179i	0.415103	+	0.0170469i
$961$	1.53508	+	2.65884i	0.0495188	+	0.0857690i
$962$	−8.55750	−	4.94067i	−0.275905	−	0.159294i
$963$	−5.98940	−	3.45798i	−0.193006	−	0.111432i
$964$	2.80424	+	4.85708i	0.0903185	+	0.156436i
$965$	−4.67691	−	0.192065i	−0.150555	−	0.00618279i
$966$	−18.7053	−	21.9651i	−0.601833	−	0.706716i
$967$		−	22.5942i		−	0.726579i	−0.931676	−	0.363290i	$-0.881654\pi$
$967$		−	22.5942i		−	0.726579i	0.931676	−	0.363290i	$-0.118346\pi$
$968$	−18.4515	+	10.6530i	−0.593053	+	0.342399i
$969$	0.416913	−	0.722115i	0.0133932	−	0.0231977i
$970$	−8.44069	−	5.34663i	−0.271014	−	0.171670i
$971$	−20.5244	−	35.5493i	−0.658660	−	1.14083i	−0.980963	−	0.194196i	$-0.937790\pi$
$971$	−20.5244	−	35.5493i	−0.658660	−	1.14083i	0.322303	−	0.946637i	$-0.395543\pi$
$972$			0.409975i			0.0131500i
$973$	10.3987	+	56.5612i	0.333367	+	1.81327i
$974$	−12.9577			−0.415192
$975$	−3.70146	−	7.83164i	−0.118541	−	0.250813i
$976$	22.2275	−	38.4991i	0.711484	−	1.23233i
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	0.744893	−	0.667184i	$-0.232501\pi$
$977$	16.8644	+	9.73668i	0.539541	+	0.311504i	−0.205352	+	0.978688i	$0.565834\pi$
$978$	7.25532	−	4.18886i	0.231999	−	0.133945i
$979$	−18.0361			−0.576435
$980$	−2.03440	−	6.08611i	−0.0649867	−	0.194414i
$981$	4.42195			0.141182
$982$	−0.749390	+	0.432661i	−0.0239140	+	0.0138068i
$983$	44.7970	+	25.8636i	1.42880	+	0.824920i	0.997026	−	0.0770602i	$-0.0245534\pi$
$983$	44.7970	+	25.8636i	1.42880	+	0.824920i	0.431777	+	0.901980i	$0.357887\pi$
$984$	−8.28832	+	14.3558i	−0.264222	+	0.457646i
$985$	23.4296	+	44.7246i	0.746528	+	1.42505i
$986$	−33.0626			−1.05293
$987$	0.869014	+	4.72678i	0.0276610	+	0.150455i
$988$			0.216742i			0.00689548i
$989$	34.1224	+	59.1017i	1.08503	+	1.87932i
$990$	−8.23029	+	12.9931i	−0.261576	+	0.412948i
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	0.425472	+	0.904972i	$0.360108\pi$
$991$	−17.9749	+	31.1335i	−0.570992	+	0.988988i	−0.996464	+	0.0840162i	$0.973225\pi$
$992$	−10.4575	+	6.03762i	−0.332025	+	0.191694i
$993$			28.3491i			0.899632i
$994$	−27.3988	−	32.1736i	−0.869036	−	1.02048i
$995$	0.688503	−	16.7655i	0.0218270	−	0.531502i
$996$	−1.04533	−	1.81056i	−0.0331224	−	0.0573697i
$997$	−48.5493	−	28.0300i	−1.53757	−	0.887718i	−0.998980	−	0.0451513i	$-0.985623\pi$
$997$	−48.5493	−	28.0300i	−1.53757	−	0.887718i	−0.538592	−	0.842567i	$-0.681044\pi$
$998$	35.0003	+	20.2075i	1.10792	+	0.639656i
$999$	−1.83703	−	3.18183i	−0.0581211	−	0.100669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.q.a.4.3	✓	16
3.2	odd	2		315.2.bf.b.109.6		16
4.3	odd	2		1680.2.di.d.529.1		16
5.2	odd	4		525.2.i.h.151.2		8
5.3	odd	4		525.2.i.k.151.3		8
5.4	even	2	inner	105.2.q.a.4.6	yes	16
7.2	even	3	inner	105.2.q.a.79.6	yes	16
7.3	odd	6		735.2.d.e.589.3		8
7.4	even	3		735.2.d.d.589.3		8
7.5	odd	6		735.2.q.g.79.6		16
7.6	odd	2		735.2.q.g.214.3		16
15.14	odd	2		315.2.bf.b.109.3		16
20.19	odd	2		1680.2.di.d.529.8		16
21.2	odd	6		315.2.bf.b.289.3		16
21.11	odd	6		2205.2.d.s.1324.6		8
21.17	even	6		2205.2.d.o.1324.6		8
28.23	odd	6		1680.2.di.d.289.8		16
35.2	odd	12		525.2.i.h.226.2		8
35.3	even	12		3675.2.a.bn.1.2		4
35.4	even	6		735.2.d.d.589.6		8
35.9	even	6	inner	105.2.q.a.79.3	yes	16
35.17	even	12		3675.2.a.cb.1.3		4
35.18	odd	12		3675.2.a.bp.1.2		4
35.19	odd	6		735.2.q.g.79.3		16
35.23	odd	12		525.2.i.k.226.3		8
35.24	odd	6		735.2.d.e.589.6		8
35.32	odd	12		3675.2.a.bz.1.3		4
35.34	odd	2		735.2.q.g.214.6		16
105.44	odd	6		315.2.bf.b.289.6		16
105.59	even	6		2205.2.d.o.1324.3		8
105.74	odd	6		2205.2.d.s.1324.3		8
140.79	odd	6		1680.2.di.d.289.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	1.1	even	1	trivial
105.2.q.a.4.6	yes	16	5.4	even	2	inner
105.2.q.a.79.3	yes	16	35.9	even	6	inner
105.2.q.a.79.6	yes	16	7.2	even	3	inner
315.2.bf.b.109.3		16	15.14	odd	2
315.2.bf.b.109.6		16	3.2	odd	2
315.2.bf.b.289.3		16	21.2	odd	6
315.2.bf.b.289.6		16	105.44	odd	6
525.2.i.h.151.2		8	5.2	odd	4
525.2.i.h.226.2		8	35.2	odd	12
525.2.i.k.151.3		8	5.3	odd	4
525.2.i.k.226.3		8	35.23	odd	12
735.2.d.d.589.3		8	7.4	even	3
735.2.d.d.589.6		8	35.4	even	6
735.2.d.e.589.3		8	7.3	odd	6
735.2.d.e.589.6		8	35.24	odd	6
735.2.q.g.79.3		16	35.19	odd	6
735.2.q.g.79.6		16	7.5	odd	6
735.2.q.g.214.3		16	7.6	odd	2
735.2.q.g.214.6		16	35.34	odd	2
1680.2.di.d.289.1		16	140.79	odd	6
1680.2.di.d.289.8		16	28.23	odd	6
1680.2.di.d.529.1		16	4.3	odd	2
1680.2.di.d.529.8		16	20.19	odd	2
2205.2.d.o.1324.3		8	105.59	even	6
2205.2.d.o.1324.6		8	21.17	even	6
2205.2.d.s.1324.3		8	105.74	odd	6
2205.2.d.s.1324.6		8	21.11	odd	6
3675.2.a.bn.1.2		4	35.3	even	12
3675.2.a.bp.1.2		4	35.18	odd	12
3675.2.a.bz.1.3		4	35.32	odd	12
3675.2.a.cb.1.3		4	35.17	even	12

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34443 + 0.776205i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.204988 - 0.355049i) q^{4} +(-1.98074 + 1.03763i) q^{5} -1.55241 q^{6} +(0.478401 + 2.60214i) q^{7} -2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.34443 + 0.776205i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.204988 - 0.355049i) q^{4} +(-1.98074 + 1.03763i) q^{5} -1.55241 q^{6} +(0.478401 + 2.60214i) q^{7} -2.46837i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.85754 - 2.93248i) q^{10} +(-2.21538 + 3.83715i) q^{11} +(0.355049 - 0.204988i) q^{12} -1.73246i q^{13} +(-2.66297 - 3.12705i) q^{14} +(-2.23418 - 0.0917505i) q^{15} +(2.32594 + 4.02864i) q^{16} +(2.36638 + 1.36623i) q^{17} +(-1.34443 - 0.776205i) q^{18} +(-0.152578 - 0.264273i) q^{19} +(-0.0376154 + 0.915960i) q^{20} +(-0.886763 + 2.49272i) q^{21} -6.87834i q^{22} +(6.08316 - 3.51212i) q^{23} +(1.23418 - 2.13767i) q^{24} +(2.84663 - 4.11056i) q^{25} +(1.34474 + 2.32916i) q^{26} +1.00000i q^{27} +(1.02195 + 0.363551i) q^{28} +7.79430 q^{29} +(3.07491 - 1.61083i) q^{30} +(2.64243 - 4.57683i) q^{31} +(-1.97875 - 1.14243i) q^{32} +(-3.83715 + 2.21538i) q^{33} -4.24190 q^{34} +(-3.64765 - 4.65775i) q^{35} +0.409975 q^{36} +(-3.18183 + 1.83703i) q^{37} +(0.410260 + 0.236864i) q^{38} +(0.866230 - 1.50035i) q^{39} +(2.56126 + 4.88919i) q^{40} -6.71562 q^{41} +(-0.742674 - 4.03959i) q^{42} +9.71562i q^{43} +(0.908250 + 1.57313i) q^{44} +(-1.88899 - 1.19655i) q^{45} +(-5.45224 + 9.44356i) q^{46} +(1.57313 - 0.908250i) q^{47} +4.65187i q^{48} +(-6.54227 + 2.48973i) q^{49} +(-0.636449 + 7.73591i) q^{50} +(1.36623 + 2.36638i) q^{51} +(-0.615108 - 0.355133i) q^{52} +(-1.48535 - 0.857566i) q^{53} +(-0.776205 - 1.34443i) q^{54} +(0.406524 - 9.89912i) q^{55} +(6.42304 - 1.18087i) q^{56} -0.305156i q^{57} +(-10.4789 + 6.04998i) q^{58} +(-0.571217 + 0.989377i) q^{59} +(-0.490556 + 0.774437i) q^{60} +(-4.77818 - 8.27604i) q^{61} +8.20428i q^{62} +(-2.01432 + 1.71538i) q^{63} -5.75669 q^{64} +(1.79766 + 3.43154i) q^{65} +(3.43917 - 5.95682i) q^{66} +(7.26104 + 4.19216i) q^{67} +(0.970157 - 0.560120i) q^{68} +7.02423 q^{69} +(8.51937 + 3.43067i) q^{70} +10.2888 q^{71} +(2.13767 - 1.23418i) q^{72} +(-11.1028 - 6.41022i) q^{73} +(2.85183 - 4.93951i) q^{74} +(4.52053 - 2.13653i) q^{75} -0.125106 q^{76} +(-11.0446 - 3.92903i) q^{77} +2.68949i q^{78} +(3.35686 + 5.81425i) q^{79} +(-8.78732 - 5.56620i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.02866 - 5.21270i) q^{82} -5.09946i q^{83} +(0.703262 + 0.825821i) q^{84} +(-6.10482 - 0.250704i) q^{85} +(-7.54131 - 13.0619i) q^{86} +(6.75007 + 3.89715i) q^{87} +(9.47149 + 5.46837i) q^{88} +(2.03533 + 3.52529i) q^{89} +(3.46837 + 0.142434i) q^{90} +(4.50810 - 0.828810i) q^{91} -2.87976i q^{92} +(4.57683 - 2.64243i) q^{93} +(-1.40998 + 2.44215i) q^{94} +(0.576436 + 0.365135i) q^{95} +(-1.14243 - 1.97875i) q^{96} -2.87834i q^{97} +(6.86305 - 8.42540i) q^{98} -4.43075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9	\( 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9} - 4 q^{10} - 24 q^{14} - 4 q^{15} - 24 q^{19} - 8 q^{20} - 4 q^{21} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 24 q^{29} - 12 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35} + 16 q^{36} - 4 q^{39} + 32 q^{40} + 16 q^{41} + 20 q^{44} - 2 q^{45} - 32 q^{46} - 40 q^{49} - 40 q^{50} + 4 q^{51} - 4 q^{54} + 8 q^{55} + 84 q^{56} + 4 q^{59} + 16 q^{60} + 16 q^{61} + 16 q^{64} + 30 q^{65} + 28 q^{66} + 40 q^{69} + 16 q^{70} - 56 q^{71} + 40 q^{74} + 8 q^{75} - 64 q^{76} - 16 q^{79} + 52 q^{80} - 8 q^{81} + 12 q^{84} - 64 q^{85} - 48 q^{86} + 16 q^{89} - 8 q^{90} + 8 q^{91} - 32 q^{94} - 22 q^{95} + 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9 - 4 * q^10 - 24 * q^14 - 4 * q^15 - 24 * q^19 - 8 * q^20 - 4 * q^21 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 24 * q^29 - 12 * q^30 + 16 * q^31 + 16 * q^34 - 10 * q^35 + 16 * q^36 - 4 * q^39 + 32 * q^40 + 16 * q^41 + 20 * q^44 - 2 * q^45 - 32 * q^46 - 40 * q^49 - 40 * q^50 + 4 * q^51 - 4 * q^54 + 8 * q^55 + 84 * q^56 + 4 * q^59 + 16 * q^60 + 16 * q^61 + 16 * q^64 + 30 * q^65 + 28 * q^66 + 40 * q^69 + 16 * q^70 - 56 * q^71 + 40 * q^74 + 8 * q^75 - 64 * q^76 - 16 * q^79 + 52 * q^80 - 8 * q^81 + 12 * q^84 - 64 * q^85 - 48 * q^86 + 16 * q^89 - 8 * q^90 + 8 * q^91 - 32 * q^94 - 22 * q^95 + 8 * q^96

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