LMFDB - Embedded newform 102.2.h.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,2,Mod(19,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("102.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	102.h (of order $8$, degree $4$, 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:	$0.814474100617$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.2
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	102.49
Dual form			102.2.h.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.400544 - 0.165911i) q^{5} +(0.382683 - 0.923880i) q^{6} +(3.15432 + 1.30656i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.400544 - 0.165911i) q^{10} +(0.648847 - 1.56645i) q^{11} +(-0.923880 + 0.382683i) q^{12} +0.331821i q^{13} +(-1.30656 - 3.15432i) q^{14} +(0.306563 + 0.306563i) q^{15} -1.00000 q^{16} +(-3.94495 - 1.19891i) q^{17} +1.00000 q^{18} +(-1.51594 - 1.51594i) q^{19} +(0.165911 + 0.400544i) q^{20} +3.41421i q^{21} +(-1.56645 + 0.648847i) q^{22} +(0.720777 - 1.74011i) q^{23} +(0.923880 + 0.382683i) q^{24} +(-3.40262 + 3.40262i) q^{25} +(0.234633 - 0.234633i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(-1.30656 + 3.15432i) q^{28} +(-7.88877 + 3.26763i) q^{29} -0.433546i q^{30} +(-0.989538 - 2.38896i) q^{31} +(0.707107 + 0.707107i) q^{32} +1.69552 q^{33} +(1.94174 + 3.63726i) q^{34} +1.48022 q^{35} +(-0.707107 - 0.707107i) q^{36} +(-4.06193 - 9.80638i) q^{37} +2.14386i q^{38} +(-0.306563 + 0.126983i) q^{39} +(0.165911 - 0.400544i) q^{40} +(11.1953 + 4.63726i) q^{41} +(2.41421 - 2.41421i) q^{42} +(7.13707 - 7.13707i) q^{43} +(1.56645 + 0.648847i) q^{44} +(-0.165911 + 0.400544i) q^{45} +(-1.74011 + 0.720777i) q^{46} -2.38009i q^{47} +(-0.382683 - 0.923880i) q^{48} +(3.29289 + 3.29289i) q^{49} +4.81204 q^{50} +(-0.402015 - 4.10346i) q^{51} -0.331821 q^{52} +(2.21371 + 2.21371i) q^{53} +(0.382683 + 0.923880i) q^{54} -0.735084i q^{55} +(3.15432 - 1.30656i) q^{56} +(0.820420 - 1.98067i) q^{57} +(7.88877 + 3.26763i) q^{58} +(-5.42676 + 5.42676i) q^{59} +(-0.306563 + 0.306563i) q^{60} +(-7.42788 - 3.07673i) q^{61} +(-0.989538 + 2.38896i) q^{62} +(-3.15432 + 1.30656i) q^{63} -1.00000i q^{64} +(0.0550527 + 0.132909i) q^{65} +(-1.19891 - 1.19891i) q^{66} +15.7711 q^{67} +(1.19891 - 3.94495i) q^{68} +1.88348 q^{69} +(-1.04667 - 1.04667i) q^{70} +(0.0867259 + 0.209375i) q^{71} +1.00000i q^{72} +(-11.2147 + 4.64527i) q^{73} +(-4.06193 + 9.80638i) q^{74} +(-4.44574 - 1.84149i) q^{75} +(1.51594 - 1.51594i) q^{76} +(4.09334 - 4.09334i) q^{77} +(0.306563 + 0.126983i) q^{78} +(-4.79863 + 11.5849i) q^{79} +(-0.400544 + 0.165911i) q^{80} -1.00000i q^{81} +(-4.63726 - 11.1953i) q^{82} +(-0.738027 - 0.738027i) q^{83} -3.41421 q^{84} +(-1.77904 + 0.174292i) q^{85} -10.0933 q^{86} +(-6.03780 - 6.03780i) q^{87} +(-0.648847 - 1.56645i) q^{88} +13.8281i q^{89} +(0.400544 - 0.165911i) q^{90} +(-0.433546 + 1.04667i) q^{91} +(1.74011 + 0.720777i) q^{92} +(1.82843 - 1.82843i) q^{93} +(-1.68297 + 1.68297i) q^{94} +(-0.858710 - 0.355689i) q^{95} +(-0.382683 + 0.923880i) q^{96} +(3.46953 - 1.43713i) q^{97} -4.65685i q^{98} +(0.648847 + 1.56645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{5} - 8 q^{10} - 8 q^{15} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{22} - 16 q^{23} + 8 q^{25} + 8 q^{26} - 16 q^{33} + 16 q^{34} - 16 q^{35} + 8 q^{39} + 16 q^{41} + 8 q^{42} - 16 q^{43} + 16 q^{44}+ \cdots + 16 q^{97}+O(q^{100}) $ 8 * q + 8 * q^5 - 8 * q^10 - 8 * q^15 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^22 - 16 * q^23 + 8 * q^25 + 8 * q^26 - 16 * q^33 + 16 * q^34 - 16 * q^35 + 8 * q^39 + 16 * q^41 + 8 * q^42 - 16 * q^43 + 16 * q^44 + 32 * q^49 + 8 * q^50 - 8 * q^51 + 8 * q^53 + 24 * q^57 + 8 * q^60 - 32 * q^61 + 24 * q^65 + 48 * q^67 + 16 * q^69 + 16 * q^70 - 16 * q^71 - 24 * q^73 - 16 * q^75 - 16 * q^77 - 8 * q^78 - 8 * q^80 - 8 * q^82 - 32 * q^83 - 16 * q^84 + 8 * q^85 - 32 * q^86 - 24 * q^87 + 8 * q^90 - 8 * q^93 - 16 * q^94 + 48 * q^95 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$			1.00000i			0.500000i
$5$	0.400544	−	0.165911i	0.179129	−	0.0741975i	−0.291317	−	0.956627i	$-0.594093\pi$
$5$	0.400544	−	0.165911i	0.179129	−	0.0741975i	0.470445	+	0.882429i	$0.344093\pi$
$6$	0.382683	−	0.923880i	0.156230	−	0.377172i
$7$	3.15432	+	1.30656i	1.19222	+	0.493834i	0.888478	−	0.458919i	$-0.151763\pi$
$7$	3.15432	+	1.30656i	1.19222	+	0.493834i	0.303744	+	0.952754i	$0.401763\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	−0.400544	−	0.165911i	−0.126663	−	0.0524656i
$11$	0.648847	−	1.56645i	0.195635	−	0.472304i	−0.795371	−	0.606123i	$-0.792724\pi$
$11$	0.648847	−	1.56645i	0.195635	−	0.472304i	0.991006	+	0.133819i	$0.0427240\pi$
$12$	−0.923880	+	0.382683i	−0.266701	+	0.110471i
$13$			0.331821i			0.0920307i	0.998941	+	0.0460153i	$0.0146523\pi$
$13$			0.331821i			0.0920307i	−0.998941	+	0.0460153i	$0.985348\pi$
$14$	−1.30656	−	3.15432i	−0.349194	−	0.843028i
$15$	0.306563	+	0.306563i	0.0791542	+	0.0791542i
$16$	−1.00000			−0.250000
$17$	−3.94495	−	1.19891i	−0.956790	−	0.290779i
$17$	−3.94495	−	1.19891i	−0.956790	−	0.290779i
$18$	1.00000			0.235702
$19$	−1.51594	−	1.51594i	−0.347780	−	0.347780i	0.511502	−	0.859282i	$-0.329089\pi$
$19$	−1.51594	−	1.51594i	−0.347780	−	0.347780i	−0.859282	+	0.511502i	$0.829089\pi$
$20$	0.165911	+	0.400544i	0.0370988	+	0.0895643i
$21$			3.41421i			0.745042i
$22$	−1.56645	+	0.648847i	−0.333969	+	0.138335i
$23$	0.720777	−	1.74011i	0.150292	−	0.362838i	−0.830746	−	0.556652i	$-0.812086\pi$
$23$	0.720777	−	1.74011i	0.150292	−	0.362838i	0.981038	+	0.193814i	$0.0620858\pi$
$24$	0.923880	+	0.382683i	0.188586	+	0.0781149i
$25$	−3.40262	+	3.40262i	−0.680525	+	0.680525i
$26$	0.234633	−	0.234633i	0.0460153	−	0.0460153i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	−1.30656	+	3.15432i	−0.246917	+	0.596111i
$29$	−7.88877	+	3.26763i	−1.46491	+	0.606785i	−0.965691	−	0.259693i	$-0.916379\pi$
$29$	−7.88877	+	3.26763i	−1.46491	+	0.606785i	−0.499216	+	0.866477i	$0.666379\pi$
$30$		−	0.433546i		−	0.0791542i
$31$	−0.989538	−	2.38896i	−0.177726	−	0.429069i	0.809763	−	0.586758i	$-0.199596\pi$
$31$	−0.989538	−	2.38896i	−0.177726	−	0.429069i	−0.987489	+	0.157688i	$0.949596\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.69552			0.295152
$34$	1.94174	+	3.63726i	0.333006	+	0.623785i
$35$	1.48022			0.250202
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	−4.06193	−	9.80638i	−0.667778	−	1.61216i	−0.785320	−	0.619090i	$-0.787501\pi$
$37$	−4.06193	−	9.80638i	−0.667778	−	1.61216i	0.117542	−	0.993068i	$-0.462499\pi$
$38$			2.14386i			0.347780i
$39$	−0.306563	+	0.126983i	−0.0490894	+	0.0203335i
$40$	0.165911	−	0.400544i	0.0262328	−	0.0633315i
$41$	11.1953	+	4.63726i	1.74842	+	0.724218i	0.997997	+	0.0632564i	$0.0201486\pi$
$41$	11.1953	+	4.63726i	1.74842	+	0.724218i	0.750420	+	0.660962i	$0.229851\pi$
$42$	2.41421	−	2.41421i	0.372521	−	0.372521i
$43$	7.13707	−	7.13707i	1.08839	−	1.08839i	0.0926990	−	0.995694i	$-0.470451\pi$
$43$	7.13707	−	7.13707i	1.08839	−	1.08839i	0.995694	−	0.0926990i	$-0.0295494\pi$
$44$	1.56645	+	0.648847i	0.236152	+	0.0978173i
$45$	−0.165911	+	0.400544i	−0.0247325	+	0.0597095i
$46$	−1.74011	+	0.720777i	−0.256565	+	0.106273i
$47$		−	2.38009i		−	0.347171i	−0.984819	−	0.173586i	$-0.944465\pi$
$47$		−	2.38009i		−	0.347171i	0.984819	−	0.173586i	$-0.0555353\pi$
$48$	−0.382683	−	0.923880i	−0.0552356	−	0.133351i
$49$	3.29289	+	3.29289i	0.470413	+	0.470413i
$50$	4.81204			0.680525
$51$	−0.402015	−	4.10346i	−0.0562934	−	0.574599i
$52$	−0.331821			−0.0460153
$53$	2.21371	+	2.21371i	0.304076	+	0.304076i	0.842606	−	0.538530i	$-0.181020\pi$
$53$	2.21371	+	2.21371i	0.304076	+	0.304076i	−0.538530	+	0.842606i	$0.681020\pi$
$54$	0.382683	+	0.923880i	0.0520766	+	0.125724i
$55$		−	0.735084i		−	0.0991187i
$56$	3.15432	−	1.30656i	0.421514	−	0.174597i
$57$	0.820420	−	1.98067i	0.108667	−	0.262346i
$58$	7.88877	+	3.26763i	1.03585	+	0.429061i
$59$	−5.42676	+	5.42676i	−0.706504	+	0.706504i	−0.965798	−	0.259295i	$-0.916510\pi$
$59$	−5.42676	+	5.42676i	−0.706504	+	0.706504i	0.259295	+	0.965798i	$0.416510\pi$
$60$	−0.306563	+	0.306563i	−0.0395771	+	0.0395771i
$61$	−7.42788	−	3.07673i	−0.951043	−	0.393935i	−0.147420	−	0.989074i	$-0.547097\pi$
$61$	−7.42788	−	3.07673i	−0.951043	−	0.393935i	−0.803623	+	0.595139i	$0.797097\pi$
$62$	−0.989538	+	2.38896i	−0.125671	+	0.303398i
$63$	−3.15432	+	1.30656i	−0.397407	+	0.164611i
$64$		−	1.00000i		−	0.125000i
$65$	0.0550527	+	0.132909i	0.00682845	+	0.0164853i
$66$	−1.19891	−	1.19891i	−0.147576	−	0.147576i
$67$	15.7711			1.92675			0.963375	−	0.268159i	$-0.0864153\pi$
$67$	15.7711			1.92675			0.963375	+	0.268159i	$0.0864153\pi$
$68$	1.19891	−	3.94495i	0.145389	−	0.478395i
$69$	1.88348			0.226744
$70$	−1.04667	−	1.04667i	−0.125101	−	0.125101i
$71$	0.0867259	+	0.209375i	0.0102925	+	0.0248482i	0.928942	−	0.370225i	$-0.120719\pi$
$71$	0.0867259	+	0.209375i	0.0102925	+	0.0248482i	−0.918650	+	0.395073i	$0.870719\pi$
$72$			1.00000i			0.117851i
$73$	−11.2147	+	4.64527i	−1.31258	+	0.543687i	−0.925635	−	0.378417i	$-0.876469\pi$
$73$	−11.2147	+	4.64527i	−1.31258	+	0.543687i	−0.386942	+	0.922104i	$0.626469\pi$
$74$	−4.06193	+	9.80638i	−0.472190	+	1.13997i
$75$	−4.44574	−	1.84149i	−0.513350	−	0.212637i
$76$	1.51594	−	1.51594i	0.173890	−	0.173890i
$77$	4.09334	−	4.09334i	0.466480	−	0.466480i
$78$	0.306563	+	0.126983i	0.0347114	+	0.0143779i
$79$	−4.79863	+	11.5849i	−0.539888	+	1.30341i	0.384912	+	0.922953i	$0.374232\pi$
$79$	−4.79863	+	11.5849i	−0.539888	+	1.30341i	−0.924800	+	0.380453i	$0.875768\pi$
$80$	−0.400544	+	0.165911i	−0.0447822	+	0.0185494i
$81$		−	1.00000i		−	0.111111i
$82$	−4.63726	−	11.1953i	−0.512099	−	1.23632i
$83$	−0.738027	−	0.738027i	−0.0810090	−	0.0810090i	0.665441	−	0.746450i	$-0.268243\pi$
$83$	−0.738027	−	0.738027i	−0.0810090	−	0.0810090i	−0.746450	+	0.665441i	$0.768243\pi$
$84$	−3.41421			−0.372521
$85$	−1.77904	+	0.174292i	−0.192964	+	0.0189046i
$86$	−10.0933			−1.08839
$87$	−6.03780	−	6.03780i	−0.647320	−	0.647320i
$88$	−0.648847	−	1.56645i	−0.0691673	−	0.166985i
$89$			13.8281i			1.46577i	0.680352	+	0.732885i	$0.261827\pi$
$89$			13.8281i			1.46577i	−0.680352	+	0.732885i	$0.738173\pi$
$90$	0.400544	−	0.165911i	0.0422210	−	0.0174885i
$91$	−0.433546	+	1.04667i	−0.0454479	+	0.109721i
$92$	1.74011	+	0.720777i	0.181419	+	0.0751461i
$93$	1.82843	−	1.82843i	0.189599	−	0.189599i
$94$	−1.68297	+	1.68297i	−0.173586	+	0.173586i
$95$	−0.858710	−	0.355689i	−0.0881018	−	0.0364929i
$96$	−0.382683	+	0.923880i	−0.0390575	+	0.0942931i
$97$	3.46953	−	1.43713i	0.352277	−	0.145918i	−0.199525	−	0.979893i	$-0.563940\pi$
$97$	3.46953	−	1.43713i	0.352277	−	0.145918i	0.551803	+	0.833975i	$0.313940\pi$
$98$		−	4.65685i		−	0.470413i
$99$	0.648847	+	1.56645i	0.0652115	+	0.157435i
$100$	−3.40262	−	3.40262i	−0.340262	−	0.340262i
$101$	−0.636303			−0.0633145			−0.0316573	−	0.999499i	$-0.510079\pi$
$101$	−0.636303			−0.0633145			−0.0316573	+	0.999499i	$0.510079\pi$
$102$	−2.61732	+	3.18585i	−0.259153	+	0.315446i
$103$	8.59955			0.847339			0.423669	−	0.905817i	$-0.360742\pi$
$103$	8.59955			0.847339			0.423669	+	0.905817i	$0.360742\pi$
$104$	0.234633	+	0.234633i	0.0230077	+	0.0230077i
$105$	0.566454	+	1.36754i	0.0552803	+	0.133458i
$106$		−	3.13066i		−	0.304076i
$107$	2.00000	−	0.828427i	0.193347	−	0.0800871i	−0.283909	−	0.958851i	$-0.591631\pi$
$107$	2.00000	−	0.828427i	0.193347	−	0.0800871i	0.477256	+	0.878764i	$0.341631\pi$
$108$	0.382683	−	0.923880i	0.0368237	−	0.0889003i
$109$	−7.31136	−	3.02847i	−0.700302	−	0.290074i	0.00398311	−	0.999992i	$-0.498732\pi$
$109$	−7.31136	−	3.02847i	−0.700302	−	0.290074i	−0.704285	+	0.709918i	$0.748732\pi$
$110$	−0.519783	+	0.519783i	−0.0495594	+	0.0495594i
$111$	7.50548	−	7.50548i	0.712388	−	0.712388i
$112$	−3.15432	−	1.30656i	−0.298055	−	0.123459i
$113$	3.51620	−	8.48886i	0.330776	−	0.798565i	−0.667755	−	0.744382i	$-0.732744\pi$
$113$	3.51620	−	8.48886i	0.330776	−	0.798565i	0.998531	−	0.0541835i	$-0.0172556\pi$
$114$	−1.98067	+	0.820420i	−0.185507	+	0.0768393i
$115$		−	0.816574i		−	0.0761459i
$116$	−3.26763	−	7.88877i	−0.303392	−	0.732454i
$117$	−0.234633	−	0.234633i	−0.0216918	−	0.0216918i
$118$	7.67459			0.706504
$119$	−10.8772	−	8.93608i	−0.997109	−	0.819169i
$120$	0.433546			0.0395771
$121$	5.74540	+	5.74540i	0.522309	+	0.522309i
$122$	3.07673	+	7.42788i	0.278554	+	0.672489i
$123$			12.1177i			1.09262i
$124$	2.38896	−	0.989538i	0.214535	−	0.0888631i
$125$	−1.62792	+	3.93015i	−0.145606	+	0.351523i
$126$	3.15432	+	1.30656i	0.281009	+	0.116398i
$127$	−8.54487	+	8.54487i	−0.758235	+	0.758235i	−0.976001	−	0.217766i	$-0.930123\pi$
$127$	−8.54487	+	8.54487i	−0.758235	+	0.758235i	0.217766	+	0.976001i	$0.430123\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	9.32503	+	3.86256i	0.821023	+	0.340079i
$130$	0.0550527	−	0.132909i	0.00482844	−	0.0116569i
$131$	−0.828427	+	0.343146i	−0.0723800	+	0.0299808i	−0.418580	−	0.908180i	$-0.637472\pi$
$131$	−0.828427	+	0.343146i	−0.0723800	+	0.0299808i	0.346200	+	0.938161i	$0.387472\pi$
$132$			1.69552i			0.147576i
$133$	−2.80109	−	6.76242i	−0.242885	−	0.586377i
$134$	−11.1519	−	11.1519i	−0.963375	−	0.963375i
$135$	−0.433546			−0.0373137
$136$	−3.63726	+	1.94174i	−0.311892	+	0.166503i
$137$	12.6109			1.07742			0.538710	−	0.842491i	$-0.318912\pi$
$137$	12.6109			1.07742			0.538710	+	0.842491i	$0.318912\pi$
$138$	−1.33182	−	1.33182i	−0.113372	−	0.113372i
$139$	6.52273	+	15.7473i	0.553250	+	1.33566i	0.915024	+	0.403399i	$0.132171\pi$
$139$	6.52273	+	15.7473i	0.553250	+	1.33566i	−0.361774	+	0.932266i	$0.617829\pi$
$140$			1.48022i			0.125101i
$141$	2.19891	−	0.910819i	0.185182	−	0.0767048i
$142$	0.0867259	−	0.209375i	0.00727787	−	0.0175703i
$143$	0.519783	+	0.215301i	0.0434664	+	0.0180044i
$144$	0.707107	−	0.707107i	0.0589256	−	0.0589256i
$145$	−2.61766	+	2.61766i	−0.217385	+	0.217385i
$146$	11.2147	+	4.64527i	0.928132	+	0.384445i
$147$	−1.78210	+	4.30237i	−0.146985	+	0.354854i
$148$	9.80638	−	4.06193i	0.806079	−	0.333889i
$149$		−	17.5004i		−	1.43369i	−0.697234	−	0.716844i	$-0.745586\pi$
$149$		−	17.5004i		−	1.43369i	0.697234	−	0.716844i	$-0.254414\pi$
$150$	1.84149	+	4.44574i	0.150357	+	0.362993i
$151$	6.81657	+	6.81657i	0.554725	+	0.554725i	0.927801	−	0.373076i	$-0.121697\pi$
$151$	6.81657	+	6.81657i	0.554725	+	0.554725i	−0.373076	+	0.927801i	$0.621697\pi$
$152$	−2.14386			−0.173890
$153$	3.63726	−	1.94174i	0.294055	−	0.156980i
$154$	−5.78886			−0.466480
$155$	−0.792706	−	0.792706i	−0.0636717	−	0.0636717i
$156$	−0.126983	−	0.306563i	−0.0101667	−	0.0245447i
$157$		−	4.78976i		−	0.382265i	−0.981564	−	0.191132i	$-0.938784\pi$
$157$		−	4.78976i		−	0.382265i	0.981564	−	0.191132i	$-0.0612160\pi$
$158$	11.5849	−	4.79863i	0.921647	−	0.381759i
$159$	−1.19805	+	2.89235i	−0.0950116	+	0.229378i
$160$	0.400544	+	0.165911i	0.0316658	+	0.0131164i
$161$	4.54712	−	4.54712i	0.358363	−	0.358363i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−16.4496	−	6.81363i	−1.28843	−	0.533685i	−0.369912	−	0.929067i	$-0.620612\pi$
$163$	−16.4496	−	6.81363i	−1.28843	−	0.533685i	−0.918517	+	0.395382i	$0.870612\pi$
$164$	−4.63726	+	11.1953i	−0.362109	+	0.874208i
$165$	0.679129	−	0.281305i	0.0528701	−	0.0218995i
$166$			1.04373i			0.0810090i
$167$	6.73332	+	16.2557i	0.521040	+	1.25790i	0.937258	+	0.348637i	$0.113355\pi$
$167$	6.73332	+	16.2557i	0.521040	+	1.25790i	−0.416218	+	0.909265i	$0.636645\pi$
$168$	2.41421	+	2.41421i	0.186261	+	0.186261i
$169$	12.8899			0.991530
$170$	1.38121	+	1.13473i	0.105934	+	0.0870295i
$171$	2.14386			0.163945
$172$	7.13707	+	7.13707i	0.544197	+	0.544197i
$173$	−7.40349	−	17.8736i	−0.562877	−	1.35890i	−0.907456	−	0.420147i	$-0.861978\pi$
$173$	−7.40349	−	17.8736i	−0.562877	−	1.35890i	0.344579	−	0.938757i	$-0.388022\pi$
$174$			8.53874i			0.647320i
$175$	−15.1787	+	6.28723i	−1.14740	+	0.475270i
$176$	−0.648847	+	1.56645i	−0.0489087	+	0.118076i
$177$	−7.09040	−	2.93694i	−0.532947	−	0.220754i
$178$	9.77791	−	9.77791i	0.732885	−	0.732885i
$179$	6.44834	−	6.44834i	0.481972	−	0.481972i	−0.423789	−	0.905761i	$-0.639300\pi$
$179$	6.44834	−	6.44834i	0.481972	−	0.481972i	0.905761	+	0.423789i	$0.139300\pi$
$180$	−0.400544	−	0.165911i	−0.0298548	−	0.0123663i
$181$	0.297227	−	0.717569i	0.0220927	−	0.0533365i	−0.912448	−	0.409192i	$-0.865811\pi$
$181$	0.297227	−	0.717569i	0.0220927	−	0.0533365i	0.934541	+	0.355856i	$0.115811\pi$
$182$	1.04667	−	0.433546i	0.0775844	−	0.0321365i
$183$		−	8.03988i		−	0.594325i
$184$	−0.720777	−	1.74011i	−0.0531364	−	0.128282i
$185$	−3.25397	−	3.25397i	−0.239236	−	0.239236i
$186$	−2.58579			−0.189599
$187$	−4.43771	+	5.40167i	−0.324517	+	0.395009i
$188$	2.38009			0.173586
$189$	−2.41421	−	2.41421i	−0.175608	−	0.175608i
$190$	0.355689	+	0.858710i	0.0258044	+	0.0622974i
$191$		−	13.4248i		−	0.971384i	−0.874130	−	0.485692i	$-0.838568\pi$
$191$		−	13.4248i		−	0.971384i	0.874130	−	0.485692i	$-0.161432\pi$
$192$	0.923880	−	0.382683i	0.0666753	−	0.0276178i
$193$	1.94749	−	4.70167i	0.140184	−	0.338434i	−0.838159	−	0.545426i	$-0.816368\pi$
$193$	1.94749	−	4.70167i	0.140184	−	0.338434i	0.978342	+	0.206993i	$0.0663677\pi$
$194$	−3.46953	−	1.43713i	−0.249098	−	0.103180i
$195$	−0.101724	+	0.101724i	−0.00728462	+	0.00728462i
$196$	−3.29289	+	3.29289i	−0.235207	+	0.235207i
$197$	3.83825	+	1.58986i	0.273464	+	0.113273i	0.515201	−	0.857069i	$-0.327717\pi$
$197$	3.83825	+	1.58986i	0.273464	+	0.113273i	−0.241737	+	0.970342i	$0.577717\pi$
$198$	0.648847	−	1.56645i	0.0461115	−	0.111323i
$199$	9.89357	−	4.09805i	0.701336	−	0.290503i	−0.00337780	−	0.999994i	$-0.501075\pi$
$199$	9.89357	−	4.09805i	0.701336	−	0.290503i	0.704714	+	0.709491i	$0.251075\pi$
$200$			4.81204i			0.340262i
$201$	6.03535	+	14.5706i	0.425701	+	1.02773i
$202$	0.449934	+	0.449934i	0.0316573	+	0.0316573i
$203$	−29.1531			−2.04615
$204$	4.10346	−	0.402015i	0.287300	−	0.0281467i
$205$	5.25359			0.366927
$206$	−6.08080	−	6.08080i	−0.423669	−	0.423669i
$207$	0.720777	+	1.74011i	0.0500974	+	0.120946i
$208$		−	0.331821i		−	0.0230077i
$209$	−3.35826	+	1.39104i	−0.232296	+	0.0962200i
$210$	0.566454	−	1.36754i	0.0390891	−	0.0943694i
$211$	−4.36210	−	1.80684i	−0.300300	−	0.124388i	0.227446	−	0.973791i	$-0.426963\pi$
$211$	−4.36210	−	1.80684i	−0.300300	−	0.124388i	−0.527746	+	0.849403i	$0.676963\pi$
$212$	−2.21371	+	2.21371i	−0.152038	+	0.152038i
$213$	−0.160248	+	0.160248i	−0.0109800	+	0.0109800i
$214$	−2.00000	−	0.828427i	−0.136717	−	0.0566301i
$215$	1.67459	−	4.04283i	0.114206	−	0.275718i
$216$	−0.923880	+	0.382683i	−0.0628620	+	0.0260383i
$217$		−	8.82843i		−	0.599313i
$218$	3.02847	+	7.31136i	0.205114	+	0.495188i
$219$	−8.58333	−	8.58333i	−0.580008	−	0.580008i
$220$	0.735084			0.0495594
$221$	0.397825	−	1.30902i	0.0267606	−	0.0880541i
$222$	−10.6143			−0.712388
$223$	11.0563	+	11.0563i	0.740383	+	0.740383i	0.972652	−	0.232269i	$-0.0746149\pi$
$223$	11.0563	+	11.0563i	0.740383	+	0.740383i	−0.232269	+	0.972652i	$0.574615\pi$
$224$	1.30656	+	3.15432i	0.0872984	+	0.210757i
$225$		−	4.81204i		−	0.320803i
$226$	−8.48886	+	3.51620i	−0.564671	+	0.233894i
$227$	−4.23304	+	10.2195i	−0.280957	+	0.678290i	−0.999858	−	0.0168221i	$-0.994645\pi$
$227$	−4.23304	+	10.2195i	−0.280957	+	0.678290i	0.718902	+	0.695112i	$0.244645\pi$
$228$	1.98067	+	0.820420i	0.131173	+	0.0543336i
$229$	−10.8789	+	10.8789i	−0.718901	+	0.718901i	−0.968380	−	0.249479i	$-0.919741\pi$
$229$	−10.8789	+	10.8789i	−0.718901	+	0.718901i	0.249479	+	0.968380i	$0.419741\pi$
$230$	−0.577405	+	0.577405i	−0.0380730	+	0.0380730i
$231$	5.34821	+	2.21530i	0.351886	+	0.145756i
$232$	−3.26763	+	7.88877i	−0.214531	+	0.517923i
$233$	−9.58764	+	3.97133i	−0.628107	+	0.260171i	−0.673949	−	0.738778i	$-0.735403\pi$
$233$	−9.58764	+	3.97133i	−0.628107	+	0.260171i	0.0458413	+	0.998949i	$0.485403\pi$
$234$			0.331821i			0.0216918i
$235$	−0.394882	−	0.953329i	−0.0257592	−	0.0621883i
$236$	−5.42676	−	5.42676i	−0.353252	−	0.353252i
$237$	−12.5394			−0.814524
$238$	1.37257	+	14.0101i	0.0889703	+	0.908139i
$239$	−24.7803			−1.60291			−0.801454	−	0.598057i	$-0.795940\pi$
$239$	−24.7803			−1.60291			−0.801454	+	0.598057i	$0.795940\pi$
$240$	−0.306563	−	0.306563i	−0.0197886	−	0.0197886i
$241$	−1.64752	−	3.97746i	−0.106126	−	0.256211i	0.861892	−	0.507092i	$-0.169280\pi$
$241$	−1.64752	−	3.97746i	−0.106126	−	0.256211i	−0.968018	+	0.250881i	$0.919280\pi$
$242$		−	8.12522i		−	0.522309i
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$	3.07673	−	7.42788i	0.196967	−	0.475522i
$245$	1.86527	+	0.772622i	0.119168	+	0.0493610i
$246$	8.56854	−	8.56854i	0.546310	−	0.546310i
$247$	0.503021	−	0.503021i	0.0320064	−	0.0320064i
$248$	−2.38896	−	0.989538i	−0.151699	−	0.0628357i
$249$	0.399418	−	0.964279i	0.0253121	−	0.0611087i
$250$	3.93015	−	1.62792i	0.248565	−	0.102959i
$251$			19.0639i			1.20330i	0.798759	+	0.601652i	$0.205490\pi$
$251$			19.0639i			1.20330i	−0.798759	+	0.601652i	$0.794510\pi$
$252$	−1.30656	−	3.15432i	−0.0823057	−	0.198704i
$253$	−2.25813	−	2.25813i	−0.141967	−	0.141967i
$254$	12.0843			0.758235
$255$	−0.841833	−	1.57692i	−0.0527176	−	0.0987504i
$256$	1.00000			0.0625000
$257$	18.9218	+	18.9218i	1.18031	+	1.18031i	0.979664	+	0.200643i	$0.0643032\pi$
$257$	18.9218	+	18.9218i	1.18031	+	1.18031i	0.200643	+	0.979664i	$0.435697\pi$
$258$	−3.86256	−	9.32503i	−0.240472	−	0.580551i
$259$		−	36.2396i		−	2.25182i
$260$	−0.132909	+	0.0550527i	−0.00824267	+	0.00341422i
$261$	3.26763	−	7.88877i	0.202262	−	0.488302i
$262$	0.828427	+	0.343146i	0.0511804	+	0.0211996i
$263$	19.4541	−	19.4541i	1.19959	−	1.19959i	0.225302	−	0.974289i	$-0.427663\pi$
$263$	19.4541	−	19.4541i	1.19959	−	1.19959i	0.974289	−	0.225302i	$-0.0723369\pi$
$264$	1.19891	−	1.19891i	0.0737880	−	0.0737880i
$265$	1.25397	+	0.519409i	0.0770305	+	0.0319071i
$266$	−2.80109	+	6.76242i	−0.171746	+	0.414631i
$267$	−12.7755	+	5.29177i	−0.781845	+	0.323851i
$268$			15.7711i			0.963375i
$269$	3.83250	+	9.25247i	0.233671	+	0.564133i	0.996604	−	0.0823455i	$-0.0262411\pi$
$269$	3.83250	+	9.25247i	0.233671	+	0.564133i	−0.762932	+	0.646478i	$0.776241\pi$
$270$	0.306563	+	0.306563i	0.0186568	+	0.0186568i
$271$	−9.20949			−0.559437			−0.279718	−	0.960082i	$-0.590241\pi$
$271$	−9.20949			−0.559437			−0.279718	+	0.960082i	$0.590241\pi$
$272$	3.94495	+	1.19891i	0.239198	+	0.0726947i
$273$	−1.13291			−0.0685668
$274$	−8.91723	−	8.91723i	−0.538710	−	0.538710i
$275$	3.12228	+	7.53784i	0.188280	+	0.454549i
$276$			1.88348i			0.113372i
$277$	−7.72852	+	3.20126i	−0.464362	+	0.192345i	−0.602583	−	0.798056i	$-0.705862\pi$
$277$	−7.72852	+	3.20126i	−0.464362	+	0.192345i	0.138221	+	0.990401i	$0.455862\pi$
$278$	6.52273	−	15.7473i	0.391207	−	0.944458i
$279$	2.38896	+	0.989538i	0.143023	+	0.0592421i
$280$	1.04667	−	1.04667i	0.0625506	−	0.0625506i
$281$	−7.77791	+	7.77791i	−0.463991	+	0.463991i	−0.899961	−	0.435970i	$-0.856405\pi$
$281$	−7.77791	+	7.77791i	−0.463991	+	0.463991i	0.435970	+	0.899961i	$0.356405\pi$
$282$	−2.19891	−	0.910819i	−0.130943	−	0.0542385i
$283$	8.08918	−	19.5290i	0.480852	−	1.16088i	−0.478353	−	0.878168i	$-0.658766\pi$
$283$	8.08918	−	19.5290i	0.480852	−	1.16088i	0.959205	−	0.282712i	$-0.0912339\pi$
$284$	−0.209375	+	0.0867259i	−0.0124241	+	0.00514623i
$285$		−	0.929461i		−	0.0550565i
$286$	−0.215301	−	0.519783i	−0.0127310	−	0.0307354i
$287$	29.2548	+	29.2548i	1.72686	+	1.72686i
$288$	−1.00000			−0.0589256
$289$	14.1252	+	9.45929i	0.830895	+	0.556429i
$290$	3.70193			0.217385
$291$	2.65546	+	2.65546i	0.155666	+	0.155666i
$292$	−4.64527	−	11.2147i	−0.271844	−	0.656289i
$293$			25.1277i			1.46797i	0.679164	+	0.733987i	$0.262343\pi$
$293$			25.1277i			1.46797i	−0.679164	+	0.733987i	$0.737657\pi$
$294$	4.30237	−	1.78210i	0.250919	−	0.103934i
$295$	−1.27330	+	3.07401i	−0.0741342	+	0.178976i
$296$	−9.80638	−	4.06193i	−0.569984	−	0.236095i
$297$	−1.19891	+	1.19891i	−0.0695680	+	0.0695680i
$298$	−12.3746	+	12.3746i	−0.716844	+	0.716844i
$299$	0.577405	+	0.239169i	0.0333922	+	0.0138315i
$300$	1.84149	−	4.44574i	0.106318	−	0.256675i
$301$	31.8377	−	13.1876i	1.83509	−	0.760120i
$302$		−	9.64009i		−	0.554725i
$303$	−0.243503	−	0.587868i	−0.0139889	−	0.0337721i
$304$	1.51594	+	1.51594i	0.0869450	+	0.0869450i
$305$	−3.48566			−0.199588
$306$	−3.94495	−	1.19891i	−0.225518	−	0.0685373i
$307$	15.3433			0.875688			0.437844	−	0.899051i	$-0.355742\pi$
$307$	15.3433			0.875688			0.437844	+	0.899051i	$0.355742\pi$
$308$	4.09334	+	4.09334i	0.233240	+	0.233240i
$309$	3.29090	+	7.94495i	0.187213	+	0.451972i
$310$			1.12106i			0.0636717i
$311$	20.0320	−	8.29752i	1.13591	−	0.470509i	0.266124	−	0.963939i	$-0.414257\pi$
$311$	20.0320	−	8.29752i	1.13591	−	0.470509i	0.869786	+	0.493429i	$0.164257\pi$
$312$	−0.126983	+	0.306563i	−0.00718897	+	0.0173557i
$313$	−7.74993	−	3.21013i	−0.438052	−	0.181447i	0.152748	−	0.988265i	$-0.451188\pi$
$313$	−7.74993	−	3.21013i	−0.438052	−	0.181447i	−0.590800	+	0.806818i	$0.701188\pi$
$314$	−3.38687	+	3.38687i	−0.191132	+	0.191132i
$315$	−1.04667	+	1.04667i	−0.0589733	+	0.0589733i
$316$	−11.5849	−	4.79863i	−0.651703	−	0.269944i
$317$	9.17686	−	22.1549i	0.515424	−	1.24434i	−0.425264	−	0.905069i	$-0.639819\pi$
$317$	9.17686	−	22.1549i	0.515424	−	1.24434i	0.940688	−	0.339274i	$-0.110181\pi$
$318$	2.89235	−	1.19805i	0.162195	−	0.0671833i
$319$			14.4776i			0.810589i
$320$	−0.165911	−	0.400544i	−0.00927469	−	0.0223911i
$321$	1.53073	+	1.53073i	0.0854372	+	0.0854372i
$322$	−6.43060			−0.358363
$323$	4.16282	+	7.79777i	0.231625	+	0.433880i
$324$	1.00000			0.0555556
$325$	−1.12906	−	1.12906i	−0.0626292	−	0.0626292i
$326$	6.81363	+	16.4496i	0.377372	+	0.911057i
$327$		−	7.91376i		−	0.437632i
$328$	11.1953	−	4.63726i	0.618159	−	0.256050i
$329$	3.10973	−	7.50756i	0.171445	−	0.413905i
$330$	−0.679129	−	0.281305i	−0.0373848	−	0.0154853i
$331$	−2.88311	+	2.88311i	−0.158470	+	0.158470i	−0.781888	−	0.623418i	$-0.785743\pi$
$331$	−2.88311	+	2.88311i	−0.158470	+	0.158470i	0.623418	+	0.781888i	$0.285743\pi$
$332$	0.738027	−	0.738027i	0.0405045	−	0.0405045i
$333$	9.80638	+	4.06193i	0.537386	+	0.222593i
$334$	6.73332	−	16.2557i	0.368431	−	0.889471i
$335$	6.31703	−	2.61660i	0.345136	−	0.142960i
$336$		−	3.41421i		−	0.186261i
$337$	−3.83323	−	9.25423i	−0.208809	−	0.504110i	0.784427	−	0.620221i	$-0.212957\pi$
$337$	−3.83323	−	9.25423i	−0.208809	−	0.504110i	−0.993236	+	0.116111i	$0.962957\pi$
$338$	−9.11453	−	9.11453i	−0.495765	−	0.495765i
$339$	9.18828			0.499039
$340$	−0.174292	−	1.77904i	−0.00945231	−	0.0964818i
$341$	−4.38425			−0.237420
$342$	−1.51594	−	1.51594i	−0.0819725	−	0.0819725i
$343$	−3.06147	−	7.39104i	−0.165304	−	0.399078i
$344$		−	10.0933i		−	0.544197i
$345$	0.754416	−	0.312489i	0.0406164	−	0.0168239i
$346$	−7.40349	+	17.8736i	−0.398014	+	0.960891i
$347$	−7.98618	−	3.30798i	−0.428721	−	0.177582i	0.157880	−	0.987458i	$-0.449534\pi$
$347$	−7.98618	−	3.30798i	−0.428721	−	0.177582i	−0.586601	+	0.809876i	$0.699534\pi$
$348$	6.03780	−	6.03780i	0.323660	−	0.323660i
$349$	−14.7167	+	14.7167i	−0.787768	+	0.787768i	−0.981128	−	0.193360i	$-0.938062\pi$
$349$	−14.7167	+	14.7167i	−0.787768	+	0.787768i	0.193360	+	0.981128i	$0.438062\pi$
$350$	15.1787	+	6.28723i	0.811337	+	0.336067i
$351$	0.126983	−	0.306563i	0.00677783	−	0.0163631i
$352$	1.56645	−	0.648847i	0.0834923	−	0.0345836i
$353$			20.1049i			1.07007i	0.844829	+	0.535037i	$0.179702\pi$
$353$			20.1049i			1.07007i	−0.844829	+	0.535037i	$0.820298\pi$
$354$	2.93694	+	7.09040i	0.156097	+	0.376850i
$355$	0.0694750	+	0.0694750i	0.00368735	+	0.00368735i
$356$	−13.8281			−0.732885
$357$	4.09334	−	13.4689i	0.216643	−	0.712849i
$358$	−9.11933			−0.481972
$359$	−17.8899	−	17.8899i	−0.944193	−	0.944193i	0.0543305	−	0.998523i	$-0.482698\pi$
$359$	−17.8899	−	17.8899i	−0.944193	−	0.944193i	−0.998523	+	0.0543305i	$0.982698\pi$
$360$	0.165911	+	0.400544i	0.00874426	+	0.0211105i
$361$		−	14.4039i		−	0.758098i
$362$	−0.717569	+	0.297227i	−0.0377146	+	0.0156219i
$363$	−3.10939	+	7.50672i	−0.163200	+	0.394001i
$364$	−1.04667	−	0.433546i	−0.0548605	−	0.0227240i
$365$	−3.72126	+	3.72126i	−0.194780	+	0.194780i
$366$	−5.68506	+	5.68506i	−0.297163	+	0.297163i
$367$	−9.53441	−	3.94928i	−0.497692	−	0.206151i	0.119694	−	0.992811i	$-0.461809\pi$
$367$	−9.53441	−	3.94928i	−0.497692	−	0.206151i	−0.617386	+	0.786660i	$0.711809\pi$
$368$	−0.720777	+	1.74011i	−0.0375731	+	0.0907094i
$369$	−11.1953	+	4.63726i	−0.582806	+	0.241406i
$370$			4.60180i			0.239236i
$371$	4.09040	+	9.87510i	0.212363	+	0.512690i
$372$	1.82843	+	1.82843i	0.0947995	+	0.0947995i
$373$	−18.2719			−0.946083			−0.473041	−	0.881040i	$-0.656844\pi$
$373$	−18.2719			−0.946083			−0.473041	+	0.881040i	$0.656844\pi$
$374$	6.95749	−	0.681624i	0.359763	−	0.0352460i
$375$	−4.25397			−0.219674
$376$	−1.68297	−	1.68297i	−0.0867928	−	0.0867928i
$377$	−1.08427	−	2.61766i	−0.0558428	−	0.134816i
$378$			3.41421i			0.175608i
$379$	19.3386	−	8.01029i	0.993355	−	0.411461i	0.173999	−	0.984746i	$-0.444331\pi$
$379$	19.3386	−	8.01029i	0.993355	−	0.411461i	0.819356	+	0.573285i	$0.194331\pi$
$380$	0.355689	−	0.858710i	0.0182465	−	0.0440509i
$381$	−11.1644	−	4.62445i	−0.571970	−	0.236918i
$382$	−9.49276	+	9.49276i	−0.485692	+	0.485692i
$383$	−16.2616	+	16.2616i	−0.830929	+	0.830929i	−0.987644	−	0.156715i	$-0.949910\pi$
$383$	−16.2616	+	16.2616i	−0.830929	+	0.830929i	0.156715	+	0.987644i	$0.449910\pi$
$384$	−0.923880	−	0.382683i	−0.0471465	−	0.0195287i
$385$	0.960434	−	2.31869i	0.0489482	−	0.118172i
$386$	−4.70167	+	1.94749i	−0.239309	+	0.0991249i
$387$			10.0933i			0.513073i
$388$	1.43713	+	3.46953i	0.0729590	+	0.176139i
$389$	−6.41875	−	6.41875i	−0.325444	−	0.325444i	0.525407	−	0.850851i	$-0.323913\pi$
$389$	−6.41875	−	6.41875i	−0.325444	−	0.325444i	−0.850851	+	0.525407i	$0.823913\pi$
$390$	0.143860			0.00728462
$391$	−4.92966	+	6.00049i	−0.249304	+	0.303458i
$392$	4.65685			0.235207
$393$	−0.634051	−	0.634051i	−0.0319836	−	0.0319836i
$394$	−1.58986	−	3.83825i	−0.0800958	−	0.193368i
$395$			5.43641i			0.273536i
$396$	−1.56645	+	0.648847i	−0.0787173	+	0.0326058i
$397$	−2.98821	+	7.21417i	−0.149974	+	0.362069i	−0.980956	−	0.194230i	$-0.937779\pi$
$397$	−2.98821	+	7.21417i	−0.149974	+	0.362069i	0.830982	+	0.556299i	$0.187779\pi$
$398$	−9.89357	−	4.09805i	−0.495920	−	0.205417i
$399$	5.17574	−	5.17574i	0.259111	−	0.259111i
$400$	3.40262	−	3.40262i	0.170131	−	0.170131i
$401$	−16.0392	−	6.64367i	−0.800962	−	0.331769i	−0.0556201	−	0.998452i	$-0.517714\pi$
$401$	−16.0392	−	6.64367i	−0.800962	−	0.331769i	−0.745342	+	0.666683i	$0.767714\pi$
$402$	6.03535	−	14.5706i	0.301016	−	0.726716i
$403$	0.792706	−	0.328350i	0.0394875	−	0.0163563i
$404$		−	0.636303i		−	0.0316573i
$405$	−0.165911	−	0.400544i	−0.00824417	−	0.0199032i
$406$	20.6143	+	20.6143i	1.02307	+	1.02307i
$407$	−17.9968			−0.892069
$408$	−3.18585	−	2.61732i	−0.157723	−	0.129576i
$409$	4.42153			0.218631			0.109315	−	0.994007i	$-0.465134\pi$
$409$	4.42153			0.218631			0.109315	+	0.994007i	$0.465134\pi$
$410$	−3.71485	−	3.71485i	−0.183463	−	0.183463i
$411$	4.82597	+	11.6509i	0.238048	+	0.574698i
$412$			8.59955i			0.423669i
$413$	−24.2081	+	10.0273i	−1.19120	+	0.493413i
$414$	0.720777	−	1.74011i	0.0354242	−	0.0855217i
$415$	−0.418059	−	0.173166i	−0.0205217	−	0.00850037i
$416$	−0.234633	+	0.234633i	−0.0115038	+	0.0115038i
$417$	−12.0524	+	12.0524i	−0.590210	+	0.590210i
$418$	3.35826	+	1.39104i	0.164258	+	0.0680378i
$419$	8.86537	−	21.4029i	0.433102	−	1.04560i	−0.545180	−	0.838319i	$-0.683539\pi$
$419$	8.86537	−	21.4029i	0.433102	−	1.04560i	0.978282	−	0.207281i	$-0.0664613\pi$
$420$	−1.36754	+	0.566454i	−0.0667292	+	0.0276401i
$421$			20.0524i			0.977295i	0.872481	+	0.488648i	$0.162510\pi$
$421$			20.0524i			0.977295i	−0.872481	+	0.488648i	$0.837490\pi$
$422$	1.80684	+	4.36210i	0.0879557	+	0.212344i
$423$	1.68297	+	1.68297i	0.0818290	+	0.0818290i
$424$	3.13066			0.152038
$425$	17.5026	−	9.34373i	0.849002	−	0.453237i
$426$	0.226626			0.0109800
$427$	−19.4100	−	19.4100i	−0.939315	−	0.939315i
$428$	0.828427	+	2.00000i	0.0400435	+	0.0966736i
$429$			0.562609i			0.0271630i
$430$	−4.04283	+	1.67459i	−0.194962	+	0.0807561i
$431$	15.3635	−	37.0908i	0.740033	−	1.78660i	0.134285	−	0.990943i	$-0.457126\pi$
$431$	15.3635	−	37.0908i	0.740033	−	1.78660i	0.605749	−	0.795656i	$-0.292874\pi$
$432$	0.923880	+	0.382683i	0.0444502	+	0.0184119i
$433$	−15.4502	+	15.4502i	−0.742490	+	0.742490i	−0.973057	−	0.230566i	$-0.925942\pi$
$433$	−15.4502	+	15.4502i	−0.742490	+	0.742490i	0.230566	+	0.973057i	$0.425942\pi$
$434$	−6.24264	+	6.24264i	−0.299656	+	0.299656i
$435$	−3.42014	−	1.41667i	−0.163983	−	0.0679240i
$436$	3.02847	−	7.31136i	0.145037	−	0.350151i
$437$	−3.73055	+	1.54524i	−0.178456	+	0.0739190i
$438$			12.1387i			0.580008i
$439$	0.320985	+	0.774927i	0.0153198	+	0.0369852i	0.931354	−	0.364114i	$-0.118628\pi$
$439$	0.320985	+	0.774927i	0.0153198	+	0.0369852i	−0.916035	+	0.401099i	$0.868628\pi$
$440$	−0.519783	−	0.519783i	−0.0247797	−	0.0247797i
$441$	−4.65685			−0.221755
$442$	−1.20692	+	0.644311i	−0.0574073	+	0.0306467i
$443$	−3.21267			−0.152639			−0.0763194	−	0.997083i	$-0.524317\pi$
$443$	−3.21267			−0.152639			−0.0763194	+	0.997083i	$0.524317\pi$
$444$	7.50548	+	7.50548i	0.356194	+	0.356194i
$445$	2.29422	+	5.53874i	0.108757	+	0.262562i
$446$		−	15.6359i		−	0.740383i
$447$	16.1683	−	6.69711i	0.764732	−	0.316762i
$448$	1.30656	−	3.15432i	0.0617293	−	0.149028i
$449$	−26.5599	−	11.0015i	−1.25344	−	0.519192i	−0.345550	−	0.938400i	$-0.612308\pi$
$449$	−26.5599	−	11.0015i	−1.25344	−	0.519192i	−0.907890	+	0.419208i	$0.862308\pi$
$450$	−3.40262	+	3.40262i	−0.160401	+	0.160401i
$451$	14.5281	−	14.5281i	0.684102	−	0.684102i
$452$	8.48886	+	3.51620i	0.399283	+	0.165388i
$453$	−3.68910	+	8.90628i	−0.173329	+	0.418454i
$454$	10.2195	−	4.23304i	0.479623	−	0.198666i
$455$			0.491168i			0.0230263i
$456$	−0.820420	−	1.98067i	−0.0384197	−	0.0927533i
$457$	−5.26863	−	5.26863i	−0.246456	−	0.246456i	0.573058	−	0.819515i	$-0.305757\pi$
$457$	−5.26863	−	5.26863i	−0.246456	−	0.246456i	−0.819515	+	0.573058i	$0.805757\pi$
$458$	15.3852			0.718901
$459$	3.18585	+	2.61732i	0.148703	+	0.122166i
$460$	0.816574			0.0380730
$461$	−18.1287	−	18.1287i	−0.844337	−	0.844337i	0.145082	−	0.989420i	$-0.453655\pi$
$461$	−18.1287	−	18.1287i	−0.844337	−	0.844337i	−0.989420	+	0.145082i	$0.953655\pi$
$462$	−2.21530	−	5.34821i	−0.103065	−	0.248821i
$463$		−	10.7747i		−	0.500744i	−0.968150	−	0.250372i	$-0.919447\pi$
$463$		−	10.7747i		−	0.500744i	0.968150	−	0.250372i	$-0.0805529\pi$
$464$	7.88877	−	3.26763i	0.366227	−	0.151696i
$465$	0.429010	−	1.03572i	0.0198948	−	0.0480304i
$466$	9.58764	+	3.97133i	0.444139	+	0.183968i
$467$	25.2078	−	25.2078i	1.16648	−	1.16648i	0.183447	−	0.983030i	$-0.441275\pi$
$467$	25.2078	−	25.2078i	1.16648	−	1.16648i	0.983030	−	0.183447i	$-0.0587254\pi$
$468$	0.234633	−	0.234633i	0.0108459	−	0.0108459i
$469$	49.7472	+	20.6060i	2.29711	+	0.951495i
$470$	−0.394882	+	0.953329i	−0.0182145	+	0.0439738i
$471$	4.42516	−	1.83296i	0.203901	−	0.0844585i
$472$			7.67459i			0.353252i
$473$	−6.54903	−	15.8108i	−0.301125	−	0.726980i
$474$	8.86672	+	8.86672i	0.407262	+	0.407262i
$475$	10.3163			0.473346
$476$	8.93608	−	10.8772i	0.409584	−	0.498555i
$477$	−3.13066			−0.143343
$478$	17.5224	+	17.5224i	0.801454	+	0.801454i
$479$	−5.38442	−	12.9991i	−0.246020	−	0.593946i	0.751839	−	0.659347i	$-0.229167\pi$
$479$	−5.38442	−	12.9991i	−0.246020	−	0.593946i	−0.997859	+	0.0654014i	$0.979167\pi$
$480$			0.433546i			0.0197886i
$481$	3.25397	−	1.34784i	0.148368	−	0.0614561i
$482$	−1.64752	+	3.97746i	−0.0750424	+	0.181168i
$483$	5.94110	+	2.46088i	0.270329	+	0.111974i
$484$	−5.74540	+	5.74540i	−0.261154	+	0.261154i
$485$	1.15126	−	1.15126i	0.0522762	−	0.0522762i
$486$	−0.923880	−	0.382683i	−0.0419080	−	0.0173589i
$487$	−9.23512	+	22.2956i	−0.418483	+	1.01031i	0.564304	+	0.825567i	$0.309145\pi$
$487$	−9.23512	+	22.2956i	−0.418483	+	1.01031i	−0.982787	+	0.184741i	$0.940855\pi$
$488$	−7.42788	+	3.07673i	−0.336244	+	0.139277i
$489$		−	17.8049i		−	0.805164i
$490$	−0.772622	−	1.86527i	−0.0349035	−	0.0842645i
$491$	18.7525	+	18.7525i	0.846288	+	0.846288i	0.989668	−	0.143380i	$-0.0457971\pi$
$491$	18.7525	+	18.7525i	0.846288	+	0.846288i	−0.143380	+	0.989668i	$0.545797\pi$
$492$	−12.1177			−0.546310
$493$	35.0384	−	3.43271i	1.57805	−	0.154601i
$494$	−0.711378			−0.0320064
$495$	0.519783	+	0.519783i	0.0233625	+	0.0233625i
$496$	0.989538	+	2.38896i	0.0444316	+	0.107267i
$497$			0.773748i			0.0347073i
$498$	−0.964279	+	0.399418i	−0.0432104	+	0.0178983i
$499$	−1.73737	+	4.19438i	−0.0777753	+	0.187766i	−0.957985	−	0.286819i	$-0.907402\pi$
$499$	−1.73737	+	4.19438i	−0.0777753	+	0.187766i	0.880209	+	0.474585i	$0.157402\pi$
$500$	−3.93015	−	1.62792i	−0.175762	−	0.0728029i
$501$	−12.4416	+	12.4416i	−0.555848	+	0.555848i
$502$	13.4802	−	13.4802i	0.601652	−	0.601652i
$503$	3.69306	+	1.52972i	0.164666	+	0.0682067i	0.463494	−	0.886100i	$-0.346596\pi$
$503$	3.69306	+	1.52972i	0.164666	+	0.0682067i	−0.298828	+	0.954307i	$0.596596\pi$
$504$	−1.30656	+	3.15432i	−0.0581989	+	0.140505i
$505$	−0.254867	+	0.105570i	−0.0113414	+	0.00469778i
$506$			3.19347i			0.141967i
$507$	4.93275	+	11.9087i	0.219071	+	0.528884i
$508$	−8.54487	−	8.54487i	−0.379117	−	0.379117i
$509$	22.9751			1.01835			0.509176	−	0.860662i	$-0.329950\pi$
$509$	22.9751			1.01835			0.509176	+	0.860662i	$0.329950\pi$
$510$	−0.519783	+	1.71031i	−0.0230164	+	0.0757340i
$511$	−41.4440			−1.83337
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.820420	+	1.98067i	0.0362224	+	0.0874486i
$514$		−	26.7594i		−	1.18031i
$515$	3.44450	−	1.42676i	0.151783	−	0.0628704i
$516$	−3.86256	+	9.32503i	−0.170040	+	0.410512i
$517$	−3.72830	−	1.54431i	−0.163970	−	0.0679187i
$518$	−25.6253	+	25.6253i	−1.12591	+	1.12591i
$519$	13.6799	−	13.6799i	0.600479	−	0.600479i
$520$	0.132909	+	0.0550527i	0.00582844	+	0.00241422i
$521$	−6.46078	+	15.5977i	−0.283052	+	0.683347i	−0.999904	−	0.0138781i	$-0.995582\pi$
$521$	−6.46078	+	15.5977i	−0.283052	+	0.683347i	0.716852	+	0.697225i	$0.245582\pi$
$522$	−7.88877	+	3.26763i	−0.345282	+	0.143020i
$523$			15.5903i			0.681717i	0.940115	+	0.340859i	$0.110718\pi$
$523$			15.5903i			0.681717i	−0.940115	+	0.340859i	$0.889282\pi$
$524$	−0.343146	−	0.828427i	−0.0149904	−	0.0361900i
$525$	−11.6173	−	11.6173i	−0.507020	−	0.507020i
$526$	−27.5122			−1.19959
$527$	1.03953	+	10.6107i	0.0452825	+	0.462208i
$528$	−1.69552			−0.0737880
$529$	13.7550	+	13.7550i	0.598043	+	0.598043i
$530$	−0.519409	−	1.25397i	−0.0225617	−	0.0544688i
$531$		−	7.67459i		−	0.333049i
$532$	6.76242	−	2.80109i	0.293188	−	0.121443i
$533$	−1.53874	+	3.71485i	−0.0666503	+	0.160908i
$534$	12.7755	+	5.29177i	0.552848	+	0.228997i
$535$	0.663643	−	0.663643i	0.0286918	−	0.0286918i
$536$	11.1519	−	11.1519i	0.481687	−	0.481687i
$537$	8.42516	+	3.48982i	0.363573	+	0.150597i
$538$	3.83250	−	9.25247i	0.165231	−	0.398902i
$539$	7.29475	−	3.02158i	0.314207	−	0.130149i
$540$		−	0.433546i		−	0.0186568i
$541$	5.79023	+	13.9789i	0.248941	+	0.600998i	0.998115	−	0.0613763i	$-0.0195490\pi$
$541$	5.79023	+	13.9789i	0.248941	+	0.600998i	−0.749173	+	0.662374i	$0.769549\pi$
$542$	6.51209	+	6.51209i	0.279718	+	0.279718i
$543$	0.776691			0.0333310
$544$	−1.94174	−	3.63726i	−0.0832514	−	0.155946i
$545$	−3.43098			−0.146967
$546$	0.801088	+	0.801088i	0.0342834	+	0.0342834i
$547$	−1.01292	−	2.44540i	−0.0433092	−	0.104558i	0.900745	−	0.434349i	$-0.143022\pi$
$547$	−1.01292	−	2.44540i	−0.0433092	−	0.104558i	−0.944054	+	0.329791i	$0.893022\pi$
$548$			12.6109i			0.538710i
$549$	7.42788	−	3.07673i	0.317014	−	0.131312i
$550$	3.12228	−	7.53784i	0.133134	−	0.321415i
$551$	16.9124	+	7.00535i	0.720493	+	0.298438i
$552$	1.33182	−	1.33182i	0.0566861	−	0.0566861i
$553$	−30.2729	+	30.2729i	−1.28733	+	1.28733i
$554$	7.72852	+	3.20126i	0.328353	+	0.136008i
$555$	1.76103	−	4.25151i	0.0747517	−	0.180467i
$556$	−15.7473	+	6.52273i	−0.667832	+	0.276625i
$557$			12.4900i			0.529217i	0.964356	+	0.264609i	$0.0852427\pi$
$557$			12.4900i			0.529217i	−0.964356	+	0.264609i	$0.914757\pi$
$558$	−0.989538	−	2.38896i	−0.0418905	−	0.101133i
$559$	2.36823	+	2.36823i	0.100166	+	0.100166i
$560$	−1.48022			−0.0625506
$561$	−6.68873	−	2.03278i	−0.282398	−	0.0858239i
$562$	10.9996			0.463991
$563$	−1.40167	−	1.40167i	−0.0590734	−	0.0590734i	0.676953	−	0.736026i	$-0.263300\pi$
$563$	−1.40167	−	1.40167i	−0.0590734	−	0.0590734i	−0.736026	+	0.676953i	$0.763300\pi$
$564$	0.910819	+	2.19891i	0.0383524	+	0.0925909i
$565$		−	3.98354i		−	0.167589i
$566$	−19.5290	+	8.08918i	−0.820866	+	0.340014i
$567$	1.30656	−	3.15432i	0.0548705	−	0.132469i
$568$	0.209375	+	0.0867259i	0.00878517	+	0.00363894i
$569$	11.8558	−	11.8558i	0.497020	−	0.497020i	−0.413489	−	0.910509i	$-0.635690\pi$
$569$	11.8558	−	11.8558i	0.497020	−	0.497020i	0.910509	+	0.413489i	$0.135690\pi$
$570$	−0.657228	+	0.657228i	−0.0275283	+	0.0275283i
$571$	−27.8300	−	11.5275i	−1.16465	−	0.482413i	−0.285228	−	0.958460i	$-0.592069\pi$
$571$	−27.8300	−	11.5275i	−1.16465	−	0.482413i	−0.879420	+	0.476047i	$0.842069\pi$
$572$	−0.215301	+	0.519783i	−0.00900220	+	0.0217332i
$573$	12.4029	−	5.13744i	0.518138	−	0.214620i
$574$		−	41.3725i		−	1.72686i
$575$	3.46840	+	8.37347i	0.144642	+	0.349198i
$576$	0.707107	+	0.707107i	0.0294628	+	0.0294628i
$577$	19.8204			0.825132			0.412566	−	0.910928i	$-0.364633\pi$
$577$	19.8204			0.825132			0.412566	+	0.910928i	$0.364633\pi$
$578$	−3.29931	−	16.6768i	−0.137233	−	0.693662i
$579$	5.08905			0.211494
$580$	−2.61766	−	2.61766i	−0.108692	−	0.108692i
$581$	−1.36370	−	3.29226i	−0.0565757	−	0.136586i
$582$		−	3.75539i		−	0.155666i
$583$	4.90403	−	2.03132i	0.203104	−	0.0841285i
$584$	−4.64527	+	11.2147i	−0.192222	+	0.464066i
$585$	−0.132909	−	0.0550527i	−0.00549511	−	0.00227615i
$586$	17.7679	−	17.7679i	0.733987	−	0.733987i
$587$	−9.09425	+	9.09425i	−0.375360	+	0.375360i	−0.869425	−	0.494065i	$-0.835510\pi$
$587$	−9.09425	+	9.09425i	−0.375360	+	0.375360i	0.494065	+	0.869425i	$0.335510\pi$
$588$	−4.30237	−	1.78210i	−0.177427	−	0.0734926i
$589$	−2.12143	+	5.12158i	−0.0874120	+	0.211031i
$590$	3.07401	−	1.27330i	0.126555	−	0.0524208i
$591$			4.15449i			0.170893i
$592$	4.06193	+	9.80638i	0.166944	+	0.403040i
$593$	−25.3356	−	25.3356i	−1.04041	−	1.04041i	−0.999148	−	0.0412617i	$-0.986862\pi$
$593$	−25.3356	−	25.3356i	−1.04041	−	1.04041i	−0.0412617	−	0.999148i	$-0.513138\pi$
$594$	1.69552			0.0695680
$595$	−5.83938	−	1.77465i	−0.239391	−	0.0727536i
$596$	17.5004			0.716844
$597$	7.57221	+	7.57221i	0.309910	+	0.309910i
$598$	−0.239169	−	0.577405i	−0.00978035	−	0.0236119i
$599$		−	21.1148i		−	0.862728i	−0.902178	−	0.431364i	$-0.858032\pi$
$599$		−	21.1148i		−	0.862728i	0.902178	−	0.431364i	$-0.141968\pi$
$600$	−4.44574	+	1.84149i	−0.181497	+	0.0751784i
$601$	5.83004	−	14.0750i	0.237812	−	0.574130i	−0.759244	−	0.650806i	$-0.774431\pi$
$601$	5.83004	−	14.0750i	0.237812	−	0.574130i	0.997056	+	0.0766767i	$0.0244309\pi$
$602$	−31.8377	−	13.1876i	−1.29761	−	0.537486i
$603$	−11.1519	+	11.1519i	−0.454139	+	0.454139i
$604$	−6.81657	+	6.81657i	−0.277362	+	0.277362i
$605$	3.25451	+	1.34806i	0.132314	+	0.0548065i
$606$	−0.243503	+	0.587868i	−0.00989162	+	0.0238805i
$607$	−35.4629	+	14.6892i	−1.43940	+	0.596217i	−0.959652	−	0.281192i	$-0.909270\pi$
$607$	−35.4629	+	14.6892i	−1.43940	+	0.596217i	−0.479743	+	0.877409i	$0.659270\pi$
$608$		−	2.14386i		−	0.0869450i
$609$	−11.1564	−	26.9339i	−0.452080	−	1.09142i
$610$	2.46473	+	2.46473i	0.0997940	+	0.0997940i
$611$	0.789763			0.0319504
$612$	1.94174	+	3.63726i	0.0784902	+	0.147027i
$613$	−1.39554			−0.0563654			−0.0281827	−	0.999603i	$-0.508972\pi$
$613$	−1.39554			−0.0563654			−0.0281827	+	0.999603i	$0.508972\pi$
$614$	−10.8494	−	10.8494i	−0.437844	−	0.437844i
$615$	2.01046	+	4.85369i	0.0810697	+	0.195719i
$616$		−	5.78886i		−	0.233240i
$617$	7.77433	−	3.22023i	0.312983	−	0.129642i	−0.220662	−	0.975350i	$-0.570822\pi$
$617$	7.77433	−	3.22023i	0.312983	−	0.129642i	0.533645	+	0.845709i	$0.320822\pi$
$618$	3.29090	−	7.94495i	0.132380	−	0.319593i
$619$	−4.93657	−	2.04479i	−0.198417	−	0.0821872i	0.281262	−	0.959631i	$-0.409247\pi$
$619$	−4.93657	−	2.04479i	−0.198417	−	0.0821872i	−0.479679	+	0.877444i	$0.659247\pi$
$620$	0.792706	−	0.792706i	0.0318359	−	0.0318359i
$621$	−1.33182	+	1.33182i	−0.0534442	+	0.0534442i
$622$	−20.0320	−	8.29752i	−0.803210	−	0.332700i
$623$	−18.0672	+	43.6181i	−0.723848	+	1.74752i
$624$	0.306563	−	0.126983i	0.0122723	−	0.00508337i
$625$		−	22.2159i		−	0.888636i
$626$	3.21013	+	7.74993i	0.128302	+	0.309750i
$627$	−2.57030	−	2.57030i	−0.102648	−	0.102648i
$628$	4.78976			0.191132
$629$	4.26713	+	43.5555i	0.170142	+	1.73667i
$630$	1.48022			0.0589733
$631$	1.03437	+	1.03437i	0.0411776	+	0.0411776i	0.727396	−	0.686218i	$-0.240730\pi$
$631$	1.03437	+	1.03437i	0.0411776	+	0.0411776i	−0.686218	+	0.727396i	$0.740730\pi$
$632$	4.79863	+	11.5849i	0.190879	+	0.460824i
$633$		−	4.72151i		−	0.187663i
$634$	−22.1549	+	9.17686i	−0.879884	+	0.364460i
$635$	−2.00491	+	4.84028i	−0.0795624	+	0.192081i
$636$	−2.89235	−	1.19805i	−0.114689	−	0.0475058i
$637$	−1.09265	+	1.09265i	−0.0432925	+	0.0432925i
$638$	10.2372	−	10.2372i	0.405295	−	0.405295i
$639$	−0.209375	−	0.0867259i	−0.00828274	−	0.00343082i
$640$	−0.165911	+	0.400544i	−0.00655820	+	0.0158329i
$641$	−0.442882	+	0.183448i	−0.0174928	+	0.00724574i	−0.391413	−	0.920215i	$-0.628013\pi$
$641$	−0.442882	+	0.183448i	−0.0174928	+	0.00724574i	0.373920	+	0.927461i	$0.378013\pi$
$642$		−	2.16478i		−	0.0854372i
$643$	−12.2860	−	29.6610i	−0.484512	−	1.16972i	−0.957444	−	0.288617i	$-0.906804\pi$
$643$	−12.2860	−	29.6610i	−0.484512	−	1.16972i	0.472932	−	0.881099i	$-0.343196\pi$
$644$	4.54712	+	4.54712i	0.179182	+	0.179182i
$645$	4.37592			0.172302
$646$	2.57030	−	8.45741i	0.101127	−	0.332752i
$647$	23.4802			0.923103			0.461551	−	0.887114i	$-0.347293\pi$
$647$	23.4802			0.923103			0.461551	+	0.887114i	$0.347293\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	4.97963	+	12.0219i	0.195468	+	0.471901i
$650$			1.59674i			0.0626292i
$651$	8.15640	−	3.37849i	0.319675	−	0.132414i
$652$	6.81363	−	16.4496i	0.266842	−	0.644215i
$653$	41.9154	+	17.3619i	1.64027	+	0.679424i	0.996326	−	0.0856443i	$-0.0272949\pi$
$653$	41.9154	+	17.3619i	1.64027	+	0.679424i	0.643949	+	0.765068i	$0.277295\pi$
$654$	−5.59588	+	5.59588i	−0.218816	+	0.218816i
$655$	−0.274890	+	0.274890i	−0.0107408	+	0.0107408i
$656$	−11.1953	−	4.63726i	−0.437104	−	0.181055i
$657$	4.64527	−	11.2147i	0.181229	−	0.437526i
$658$	−7.50756	+	3.10973i	−0.292675	+	0.121230i
$659$		−	12.8417i		−	0.500240i	−0.968215	−	0.250120i	$-0.919530\pi$
$659$		−	12.8417i		−	0.500240i	0.968215	−	0.250120i	$-0.0804701\pi$
$660$	0.281305	+	0.679129i	0.0109498	+	0.0264351i
$661$	−19.2247	−	19.2247i	−0.747753	−	0.747753i	0.226304	−	0.974057i	$-0.427336\pi$
$661$	−19.2247	−	19.2247i	−0.747753	−	0.747753i	−0.974057	+	0.226304i	$0.927336\pi$
$662$	4.07733			0.158470
$663$	1.36162	−	0.133397i	0.0528808	−	0.00518072i
$664$	−1.04373			−0.0405045
$665$	−2.24392	−	2.24392i	−0.0870154	−	0.0870154i
$666$	−4.06193	−	9.80638i	−0.157397	−	0.379989i
$667$			16.0825i			0.622719i
$668$	−16.2557	+	6.73332i	−0.628951	+	0.260520i
$669$	−5.98361	+	14.4457i	−0.231340	+	0.558504i
$670$	−6.31703	−	2.61660i	−0.244048	−	0.101088i
$671$	−9.63912	+	9.63912i	−0.372114	+	0.372114i
$672$	−2.41421	+	2.41421i	−0.0931303	+	0.0931303i
$673$	15.4077	+	6.38207i	0.593923	+	0.246011i	0.659337	−	0.751847i	$-0.270837\pi$
$673$	15.4077	+	6.38207i	0.593923	+	0.246011i	−0.0654145	+	0.997858i	$0.520837\pi$
$674$	−3.83323	+	9.25423i	−0.147650	+	0.356460i
$675$	4.44574	−	1.84149i	0.171117	−	0.0708789i
$676$			12.8899i			0.495765i
$677$	0.996062	+	2.40471i	0.0382818	+	0.0924204i	0.941864	−	0.335994i	$-0.109072\pi$
$677$	0.996062	+	2.40471i	0.0382818	+	0.0924204i	−0.903582	+	0.428415i	$0.859072\pi$
$678$	−6.49709	−	6.49709i	−0.249519	−	0.249519i
$679$	12.8217			0.492052
$680$	−1.13473	+	1.38121i	−0.0435147	+	0.0529671i
$681$	−11.0615			−0.423876
$682$	3.10013	+	3.10013i	0.118710	+	0.118710i
$683$	4.68507	+	11.3108i	0.179269	+	0.432794i	0.987814	−	0.155641i	$-0.0497442\pi$
$683$	4.68507	+	11.3108i	0.179269	+	0.432794i	−0.808544	+	0.588435i	$0.799744\pi$
$684$			2.14386i			0.0819725i
$685$	5.05121	−	2.09228i	0.192997	−	0.0799419i
$686$	−3.06147	+	7.39104i	−0.116887	+	0.282191i
$687$	−14.2140	−	5.88764i	−0.542299	−	0.224628i
$688$	−7.13707	+	7.13707i	−0.272098	+	0.272098i
$689$	−0.734556	+	0.734556i	−0.0279843	+	0.0279843i
$690$	−0.754416	−	0.312489i	−0.0287201	−	0.0118963i
$691$	−5.99803	+	14.4805i	−0.228176	+	0.550865i	−0.995955	−	0.0898487i	$-0.971362\pi$
$691$	−5.99803	+	14.4805i	−0.228176	+	0.550865i	0.767779	+	0.640714i	$0.221362\pi$
$692$	17.8736	−	7.40349i	0.679452	−	0.281438i
$693$			5.78886i			0.219901i
$694$	3.30798	+	7.98618i	0.125569	+	0.303151i
$695$	5.22528	+	5.22528i	0.198206	+	0.198206i
$696$	−8.53874			−0.323660
$697$	−38.6053	−	31.7160i	−1.46228	−	1.20133i
$698$	20.8126			0.787768
$699$	−7.33806	−	7.33806i	−0.277551	−	0.277551i
$700$	−6.28723	−	15.1787i	−0.237635	−	0.573702i
$701$			30.8222i			1.16414i	0.813139	+	0.582070i	$0.197757\pi$
$701$			30.8222i			1.16414i	−0.813139	+	0.582070i	$0.802243\pi$
$702$	−0.306563	+	0.126983i	−0.0115705	+	0.00479265i
$703$	−8.70822	+	21.0235i	−0.328437	+	0.792916i
$704$	−1.56645	−	0.648847i	−0.0590380	−	0.0244543i
$705$	0.729646	−	0.729646i	0.0274801	−	0.0274801i
$706$	14.2163	−	14.2163i	0.535037	−	0.535037i
$707$	−2.00711	−	0.831370i	−0.0754850	−	0.0312669i
$708$	2.93694	−	7.09040i	0.110377	−	0.266474i
$709$	0.364823	−	0.151115i	0.0137012	−	0.00567523i	−0.375822	−	0.926692i	$-0.622640\pi$
$709$	0.364823	−	0.151115i	0.0137012	−	0.00567523i	0.389524	+	0.921017i	$0.372640\pi$
$710$		−	0.0982525i		−	0.00368735i
$711$	−4.79863	−	11.5849i	−0.179963	−	0.434469i
$712$	9.77791	+	9.77791i	0.366443	+	0.366443i
$713$	−4.87028			−0.182393
$714$	−12.4184	+	6.62951i	−0.464746	+	0.248103i
$715$	0.243917			0.00912197
$716$	6.44834	+	6.44834i	0.240986	+	0.240986i
$717$	−9.48303	−	22.8941i	−0.354150	−	0.854994i
$718$			25.3001i			0.944193i
$719$	−10.2515	+	4.24631i	−0.382317	+	0.158361i	−0.565561	−	0.824707i	$-0.691340\pi$
$719$	−10.2515	+	4.24631i	−0.382317	+	0.158361i	0.183244	+	0.983067i	$0.441340\pi$
$720$	0.165911	−	0.400544i	0.00618313	−	0.0149274i
$721$	27.1257	+	11.2359i	1.01022	+	0.418445i
$722$	−10.1851	+	10.1851i	−0.379049	+	0.379049i
$723$	3.04422	−	3.04422i	0.113216	−	0.113216i
$724$	0.717569	+	0.297227i	0.0266682	+	0.0110463i
$725$	15.7240	−	37.9611i	0.583974	−	1.40984i
$726$	7.50672	−	3.10939i	0.278601	−	0.115400i
$727$		−	27.2866i		−	1.01200i	−0.862533	−	0.506001i	$-0.831123\pi$
$727$		−	27.2866i		−	1.01200i	0.862533	−	0.506001i	$-0.168877\pi$
$728$	0.433546	+	1.04667i	0.0160683	+	0.0387922i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	5.26266			0.194780
$731$	−36.7121	+	19.5986i	−1.35785	+	0.724882i
$732$	8.03988			0.297163
$733$	20.7090	+	20.7090i	0.764906	+	0.764906i	0.977205	−	0.212299i	$-0.0680951\pi$
$733$	20.7090	+	20.7090i	0.764906	+	0.764906i	−0.212299	+	0.977205i	$0.568095\pi$
$734$	3.94928	+	9.53441i	0.145771	+	0.351921i
$735$			2.01896i			0.0744704i
$736$	1.74011	−	0.720777i	0.0641412	−	0.0265682i
$737$	10.2330	−	24.7047i	0.376939	−	0.910011i
$738$	11.1953	+	4.63726i	0.412106	+	0.170700i
$739$	26.2007	−	26.2007i	0.963810	−	0.963810i	−0.0355580	−	0.999368i	$-0.511321\pi$
$739$	26.2007	−	26.2007i	0.963810	−	0.963810i	0.999368	+	0.0355580i	$0.0113209\pi$
$740$	3.25397	−	3.25397i	0.119618	−	0.119618i
$741$	0.657228	+	0.272233i	0.0241439	+	0.0100007i
$742$	4.09040	−	9.87510i	0.150163	−	0.362526i
$743$	13.3844	−	5.54401i	0.491027	−	0.203390i	−0.123410	−	0.992356i	$-0.539383\pi$
$743$	13.3844	−	5.54401i	0.491027	−	0.203390i	0.614437	+	0.788966i	$0.289383\pi$
$744$		−	2.58579i		−	0.0947995i
$745$	−2.90350	−	7.00967i	−0.106376	−	0.256815i
$746$	12.9202	+	12.9202i	0.473041	+	0.473041i
$747$	1.04373			0.0381880
$748$	−5.40167	−	4.43771i	−0.197505	−	0.162259i
$749$	7.39104			0.270063
$750$	3.00801	+	3.00801i	0.109837	+	0.109837i
$751$	16.8240	+	40.6167i	0.613917	+	1.48213i	0.858664	+	0.512539i	$0.171295\pi$
$751$	16.8240	+	40.6167i	0.613917	+	1.48213i	−0.244747	+	0.969587i	$0.578705\pi$
$752$			2.38009i			0.0867928i
$753$	−17.6128	+	7.29544i	−0.641844	+	0.265861i
$754$	−1.08427	+	2.61766i	−0.0394868	+	0.0953296i
$755$	3.86128	+	1.59939i	0.140526	+	0.0582079i
$756$	2.41421	−	2.41421i	0.0878041	−	0.0878041i
$757$	26.7702	−	26.7702i	0.972980	−	0.972980i	−0.0266643	−	0.999644i	$-0.508489\pi$
$757$	26.7702	−	26.7702i	0.972980	−	0.972980i	0.999644	+	0.0266643i	$0.00848850\pi$
$758$	−19.3386	−	8.01029i	−0.702408	−	0.290947i
$759$	1.22209	−	2.95039i	0.0443590	−	0.107092i
$760$	−0.858710	+	0.355689i	−0.0311487	+	0.0129022i
$761$			9.82880i			0.356294i	0.984004	+	0.178147i	$0.0570102\pi$
$761$			9.82880i			0.356294i	−0.984004	+	0.178147i	$0.942990\pi$
$762$	4.62445	+	11.1644i	0.167526	+	0.404444i
$763$	−19.1055	−	19.1055i	−0.691666	−	0.691666i
$764$	13.4248			0.485692
$765$	1.13473	−	1.38121i	0.0410261	−	0.0499378i
$766$	22.9974			0.830929
$767$	−1.80071	−	1.80071i	−0.0650200	−	0.0650200i
$768$	0.382683	+	0.923880i	0.0138089	+	0.0333376i
$769$			41.1522i			1.48398i	0.670408	+	0.741992i	$0.266119\pi$
$769$			41.1522i			1.48398i	−0.670408	+	0.741992i	$0.733881\pi$
$770$	−2.31869	+	0.960434i	−0.0835599	+	0.0346116i
$771$	−10.2404	+	24.7225i	−0.368799	+	0.890359i
$772$	4.70167	+	1.94749i	0.169217	+	0.0700919i
$773$	15.3765	−	15.3765i	0.553054	−	0.553054i	−0.374267	−	0.927321i	$-0.622106\pi$
$773$	15.3765	−	15.3765i	0.553054	−	0.553054i	0.927321	+	0.374267i	$0.122106\pi$
$774$	7.13707	−	7.13707i	0.256537	−	0.256537i
$775$	11.4957	+	4.76169i	0.412939	+	0.171045i
$776$	1.43713	−	3.46953i	0.0515898	−	0.124549i
$777$	33.4811	−	13.8683i	1.20113	−	0.497523i
$778$			9.07748i			0.325444i
$779$	−9.94163	−	24.0012i	−0.356196	−	0.859933i
$780$	−0.101724	−	0.101724i	−0.00364231	−	0.00364231i
$781$	0.384248			0.0137495
$782$	7.72878	−	0.757188i	0.276381	−	0.0270770i
$783$	8.53874			0.305150
$784$	−3.29289	−	3.29289i	−0.117603	−	0.117603i
$785$	−0.794673	−	1.91851i	−0.0283631	−	0.0684746i
$786$			0.896683i			0.0319836i
$787$	43.9786	−	18.2165i	1.56767	−	0.649349i	0.581267	−	0.813713i	$-0.302557\pi$
$787$	43.9786	−	18.2165i	1.56767	−	0.649349i	0.986400	+	0.164364i	$0.0525572\pi$
$788$	−1.58986	+	3.83825i	−0.0566363	+	0.136732i
$789$	25.4180	+	10.5285i	0.904905	+	0.374824i
$790$	3.84413	−	3.84413i	0.136768	−	0.136768i
$791$	22.1825	−	22.1825i	0.788718	−	0.788718i
$792$	1.56645	+	0.648847i	0.0556615	+	0.0230558i
$793$	1.02092	−	2.46473i	0.0362541	−	0.0875251i
$794$	7.21417	−	2.98821i	0.256021	−	0.106048i
$795$			1.35728i			0.0481378i
$796$	4.09805	+	9.89357i	0.145252	+	0.350668i
$797$	−26.7982	−	26.7982i	−0.949242	−	0.949242i	0.0495310	−	0.998773i	$-0.484227\pi$
$797$	−26.7982	−	26.7982i	−0.949242	−	0.949242i	−0.998773	+	0.0495310i	$0.984227\pi$
$798$	−7.31959			−0.259111
$799$	−2.85351	+	9.38931i	−0.100950	+	0.332170i
$800$	−4.81204			−0.170131
$801$	−9.77791	−	9.77791i	−0.345485	−	0.345485i
$802$	6.64367	+	16.0392i	0.234596	+	0.566365i
$803$			20.5813i			0.726299i
$804$	−14.5706	+	6.03535i	−0.513866	+	0.212850i
$805$	1.06691	−	2.57574i	0.0376035	−	0.0907828i
$806$	−0.792706	−	0.328350i	−0.0279219	−	0.0115656i
$807$	−7.08153	+	7.08153i	−0.249282	+	0.249282i
$808$	−0.449934	+	0.449934i	−0.0158286	+	0.0158286i
$809$	−35.6369	−	14.7613i	−1.25293	−	0.518979i	−0.345195	−	0.938531i	$-0.612187\pi$
$809$	−35.6369	−	14.7613i	−1.25293	−	0.518979i	−0.907731	+	0.419552i	$0.862187\pi$
$810$	−0.165911	+	0.400544i	−0.00582951	+	0.0140737i
$811$	−17.9596	+	7.43911i	−0.630647	+	0.261223i	−0.675028	−	0.737792i	$-0.735869\pi$
$811$	−17.9596	+	7.43911i	−0.630647	+	0.261223i	0.0443808	+	0.999015i	$0.485869\pi$
$812$		−	29.1531i		−	1.02307i
$813$	−3.52432	−	8.50846i	−0.123603	−	0.298405i
$814$	12.7257	+	12.7257i	0.446034	+	0.446034i
$815$	−7.71922			−0.270393
$816$	0.402015	+	4.10346i	0.0140734	+	0.143650i
$817$	−21.6387			−0.757043
$818$	−3.12649	−	3.12649i	−0.109315	−	0.109315i
$819$	−0.433546	−	1.04667i	−0.0151493	−	0.0365737i
$820$			5.25359i			0.183463i
$821$	0.214175	−	0.0887142i	0.00747476	−	0.00309615i	−0.378943	−	0.925420i	$-0.623712\pi$
$821$	0.214175	−	0.0887142i	0.00747476	−	0.00309615i	0.386418	+	0.922324i	$0.373712\pi$
$822$	4.82597	−	11.6509i	0.168325	−	0.406373i
$823$	−20.7809	−	8.60773i	−0.724376	−	0.300047i	−0.0101376	−	0.999949i	$-0.503227\pi$
$823$	−20.7809	−	8.60773i	−0.724376	−	0.300047i	−0.714239	+	0.699902i	$0.753227\pi$
$824$	6.08080	−	6.08080i	0.211835	−	0.211835i
$825$	−5.76921	+	5.76921i	−0.200858	+	0.200858i
$826$	24.2081	+	10.0273i	0.842309	+	0.348896i
$827$	−20.0190	+	48.3300i	−0.696127	+	1.68060i	0.0359274	+	0.999354i	$0.488561\pi$
$827$	−20.0190	+	48.3300i	−0.696127	+	1.68060i	−0.732055	+	0.681246i	$0.761439\pi$
$828$	−1.74011	+	0.720777i	−0.0604729	+	0.0250487i
$829$		−	23.3260i		−	0.810144i	−0.914285	−	0.405072i	$-0.867246\pi$
$829$		−	23.3260i		−	0.810144i	0.914285	−	0.405072i	$-0.132754\pi$
$830$	0.173166	+	0.418059i	0.00601067	+	0.0145110i
$831$	−5.91515	−	5.91515i	−0.205194	−	0.205194i
$832$	0.331821			0.0115038
$833$	−9.04240	−	16.9382i	−0.313301	−	0.586873i
$834$	17.0447			0.590210
$835$	5.39398	+	5.39398i	0.186666	+	0.186666i
$836$	−1.39104	−	3.35826i	−0.0481100	−	0.116148i
$837$			2.58579i			0.0893779i
$838$	−21.4029	+	8.86537i	−0.739351	+	0.306249i
$839$	−5.13605	+	12.3995i	−0.177316	+	0.428079i	−0.987402	−	0.158232i	$-0.949421\pi$
$839$	−5.13605	+	12.3995i	−0.177316	+	0.428079i	0.810086	+	0.586312i	$0.199421\pi$
$840$	1.36754	+	0.566454i	0.0471847	+	0.0195445i
$841$	31.0491	−	31.0491i	1.07066	−	1.07066i
$842$	14.1792	−	14.1792i	0.488648	−	0.488648i
$843$	−10.1623	−	4.20937i	−0.350009	−	0.144979i
$844$	1.80684	−	4.36210i	0.0621941	−	0.150150i
$845$	5.16297	−	2.13857i	0.177611	−	0.0735691i
$846$		−	2.38009i		−	0.0818290i
$847$	10.6161	+	25.6296i	0.364774	+	0.880642i
$848$	−2.21371	−	2.21371i	−0.0760191	−	0.0760191i
$849$	21.1380			0.725456
$850$	−18.9832	−	5.76921i	−0.651120	−	0.197882i
$851$	−19.9919			−0.685314
$852$	−0.160248	−	0.160248i	−0.00549002	−	0.00549002i
$853$	−19.1093	−	46.1339i	−0.654290	−	1.57960i	−0.806491	−	0.591246i	$-0.798636\pi$
$853$	−19.1093	−	46.1339i	−0.654290	−	1.57960i	0.152202	−	0.988349i	$-0.451364\pi$
$854$			27.4499i			0.939315i
$855$	0.858710	−	0.355689i	0.0293673	−	0.0121643i
$856$	0.828427	−	2.00000i	0.0283151	−	0.0683586i
$857$	15.8686	+	6.57298i	0.542060	+	0.224529i	0.636876	−	0.770966i	$-0.280226\pi$
$857$	15.8686	+	6.57298i	0.542060	+	0.224529i	−0.0948160	+	0.995495i	$0.530226\pi$
$858$	0.397825	−	0.397825i	0.0135815	−	0.0135815i
$859$	−6.19681	+	6.19681i	−0.211433	+	0.211433i	−0.804876	−	0.593443i	$-0.797768\pi$
$859$	−6.19681	+	6.19681i	−0.211433	+	0.211433i	0.593443	+	0.804876i	$0.297768\pi$
$860$	4.04283	+	1.67459i	0.137859	+	0.0571032i
$861$	−15.8326	+	38.2233i	−0.539573	+	1.30264i
$862$	−37.0908	+	15.3635i	−1.26332	+	0.523283i
$863$		−	35.9177i		−	1.22265i	−0.791379	−	0.611326i	$-0.790636\pi$
$863$		−	35.9177i		−	1.22265i	0.791379	−	0.611326i	$-0.209364\pi$
$864$	−0.382683	−	0.923880i	−0.0130192	−	0.0314310i
$865$	−5.93084	−	5.93084i	−0.201655	−	0.201655i
$866$	21.8499			0.742490
$867$	−3.33376	+	16.6699i	−0.113220	+	0.566140i
$868$	8.82843			0.299656
$869$	15.0337	+	15.0337i	0.509983	+	0.509983i
$870$	1.41667	+	3.42014i	0.0480296	+	0.115954i
$871$			5.23320i			0.177320i
$872$	−7.31136	+	3.02847i	−0.247594	+	0.102557i
$873$	−1.43713	+	3.46953i	−0.0486394	+	0.117426i
$874$	3.73055	+	1.54524i	0.126188	+	0.0522686i
$875$	−10.2700	+	10.2700i	−0.347189	+	0.347189i
$876$	8.58333	−	8.58333i	0.290004	−	0.290004i
$877$	−3.90356	−	1.61691i	−0.131814	−	0.0545991i	0.315801	−	0.948825i	$-0.397727\pi$
$877$	−3.90356	−	1.61691i	−0.131814	−	0.0545991i	−0.447615	+	0.894226i	$0.647727\pi$
$878$	0.320985	−	0.774927i	0.0108327	−	0.0261525i
$879$	−23.2149	+	9.61594i	−0.783020	+	0.324338i
$880$			0.735084i			0.0247797i
$881$	−11.4789	−	27.7125i	−0.386734	−	0.933657i	−0.990627	−	0.136593i	$-0.956385\pi$
$881$	−11.4789	−	27.7125i	−0.386734	−	0.933657i	0.603894	−	0.797065i	$-0.293615\pi$
$882$	3.29289	+	3.29289i	0.110877	+	0.110877i
$883$	−13.9714			−0.470175			−0.235087	−	0.971974i	$-0.575538\pi$
$883$	−13.9714			−0.470175			−0.235087	+	0.971974i	$0.575538\pi$
$884$	1.30902	+	0.397825i	0.0440270	+	0.0133803i
$885$	−3.32729			−0.111845
$886$	2.27170	+	2.27170i	0.0763194	+	0.0763194i
$887$	−8.42959	−	20.3508i	−0.283038	−	0.683314i	0.716866	−	0.697211i	$-0.245576\pi$
$887$	−8.42959	−	20.3508i	−0.283038	−	0.683314i	−0.999903	+	0.0138977i	$0.995576\pi$
$888$		−	10.6143i		−	0.356194i
$889$	−38.1177	+	15.7889i	−1.27843	+	0.529541i
$890$	2.29422	−	5.53874i	0.0769025	−	0.185659i
$891$	−1.56645	−	0.648847i	−0.0524782	−	0.0217372i
$892$	−11.0563	+	11.0563i	−0.370191	+	0.370191i
$893$	−3.60806	+	3.60806i	−0.120739	+	0.120739i
$894$	−16.1683	−	6.69711i	−0.540747	−	0.223985i
$895$	1.51299	−	3.65269i	0.0505738	−	0.122096i
$896$	−3.15432	+	1.30656i	−0.105379	+	0.0436492i
$897$			0.624979i			0.0208674i
$898$	11.0015	+	26.5599i	0.367124	+	0.886316i
$899$	15.6125	+	15.6125i	0.520705	+	0.520705i
$900$	4.81204			0.160401
$901$	−6.07892	−	11.3870i	−0.202518	−	0.379356i
$902$	−20.5458			−0.684102
$903$	24.3675	+	24.3675i	0.810899	+	0.810899i
$904$	−3.51620	−	8.48886i	−0.116947	−	0.282335i
$905$		−	0.336731i		−	0.0111933i
$906$	8.90628	−	3.68910i	0.295891	−	0.122562i
$907$	−10.2983	+	24.8622i	−0.341948	+	0.825535i	0.655571	+	0.755134i	$0.272428\pi$
$907$	−10.2983	+	24.8622i	−0.341948	+	0.825535i	−0.997519	+	0.0704015i	$0.977572\pi$
$908$	−10.2195	−	4.23304i	−0.339145	−	0.140478i
$909$	0.449934	−	0.449934i	0.0149234	−	0.0149234i
$910$	0.347308	−	0.347308i	0.0115131	−	0.0115131i
$911$	−32.7838	−	13.5795i	−1.08618	−	0.449908i	−0.233504	−	0.972356i	$-0.575019\pi$
$911$	−32.7838	−	13.5795i	−1.08618	−	0.449908i	−0.852671	+	0.522447i	$0.825019\pi$
$912$	−0.820420	+	1.98067i	−0.0271668	+	0.0655865i
$913$	−1.63495	+	0.677220i	−0.0541090	+	0.0224127i
$914$			7.45097i			0.246456i
$915$	−1.33390	−	3.22033i	−0.0440975	−	0.106461i
$916$	−10.8789	−	10.8789i	−0.359450	−	0.359450i
$917$	−3.06147			−0.101099
$918$	−0.402015	−	4.10346i	−0.0132685	−	0.135434i
$919$	−38.6107			−1.27365			−0.636824	−	0.771009i	$-0.719752\pi$
$919$	−38.6107			−1.27365			−0.636824	+	0.771009i	$0.719752\pi$
$920$	−0.577405	−	0.577405i	−0.0190365	−	0.0190365i
$921$	5.87163	+	14.1754i	0.193477	+	0.467094i
$922$			25.6378i			0.844337i
$923$	−0.0694750	+	0.0287775i	−0.00228680	+	0.000947223i
$924$	−2.21530	+	5.34821i	−0.0728781	+	0.175943i
$925$	47.1887	+	19.5462i	1.55155	+	0.642675i
$926$	−7.61888	+	7.61888i	−0.250372	+	0.250372i
$927$	−6.08080	+	6.08080i	−0.199720	+	0.199720i
$928$	−7.88877	−	3.26763i	−0.258962	−	0.107265i
$929$	8.76150	−	21.1521i	0.287455	−	0.693979i	−0.712515	−	0.701657i	$-0.752444\pi$
$929$	8.76150	−	21.1521i	0.287455	−	0.693979i	0.999971	+	0.00767791i	$0.00244398\pi$
$930$	−1.03572	+	0.429010i	−0.0339626	+	0.0140678i
$931$		−	9.98364i		−	0.327201i
$932$	−3.97133	−	9.58764i	−0.130085	−	0.314054i
$933$	15.3318	+	15.3318i	0.501941	+	0.501941i
$934$	−35.6492			−1.16648
$935$	−0.881302	+	2.89987i	−0.0288216	+	0.0948358i
$936$	−0.331821			−0.0108459
$937$	−28.0575	−	28.0575i	−0.916598	−	0.916598i	0.0801820	−	0.996780i	$-0.474450\pi$
$937$	−28.0575	−	28.0575i	−0.916598	−	0.916598i	−0.996780	+	0.0801820i	$0.974450\pi$
$938$	−20.6060	−	49.7472i	−0.672809	−	1.62430i
$939$		−	8.38847i		−	0.273747i
$940$	0.953329	−	0.394882i	0.0310941	−	0.0128796i
$941$	−20.1541	+	48.6562i	−0.657004	+	1.58615i	0.145405	+	0.989372i	$0.453551\pi$
$941$	−20.1541	+	48.6562i	−0.657004	+	1.58615i	−0.802409	+	0.596775i	$0.796449\pi$
$942$	−4.42516	−	1.83296i	−0.144180	−	0.0597212i
$943$	16.1387	−	16.1387i	0.525547	−	0.525547i
$944$	5.42676	−	5.42676i	0.176626	−	0.176626i
$945$	−1.36754	−	0.566454i	−0.0444861	−	0.0184268i
$946$	−6.54903	+	15.8108i	−0.212927	+	0.514052i
$947$	−1.41074	+	0.584348i	−0.0458430	+	0.0189888i	−0.405487	−	0.914101i	$-0.632898\pi$
$947$	−1.41074	+	0.584348i	−0.0458430	+	0.0189888i	0.359644	+	0.933090i	$0.382898\pi$
$948$		−	12.5394i		−	0.407262i
$949$	−1.54140	−	3.72126i	−0.0500359	−	0.120797i
$950$	−7.29475	−	7.29475i	−0.236673	−	0.236673i
$951$	23.9803			0.777614
$952$	−14.0101	+	1.37257i	−0.454070	+	0.0444851i
$953$	9.95360			0.322429			0.161214	−	0.986919i	$-0.448459\pi$
$953$	9.95360			0.322429			0.161214	+	0.986919i	$0.448459\pi$
$954$	2.21371	+	2.21371i	0.0716715	+	0.0716715i
$955$	−2.22732	−	5.37722i	−0.0720743	−	0.174003i
$956$		−	24.7803i		−	0.801454i
$957$	−13.3755	+	5.54033i	−0.432370	+	0.179094i
$958$	−5.38442	+	12.9991i	−0.173963	+	0.419983i
$959$	39.7788	+	16.4769i	1.28452	+	0.532067i
$960$	0.306563	−	0.306563i	0.00989428	−	0.00989428i
$961$	17.1924	−	17.1924i	0.554593	−	0.554593i
$962$	−3.25397	−	1.34784i	−0.104912	−	0.0434560i
$963$	−0.828427	+	2.00000i	−0.0266957	+	0.0644491i
$964$	3.97746	−	1.64752i	0.128105	−	0.0530630i
$965$		−	2.20633i		−	0.0710244i
$966$	−2.46088	−	5.94110i	−0.0791777	−	0.191152i
$967$	4.16375	+	4.16375i	0.133897	+	0.133897i	0.770879	−	0.636982i	$-0.219817\pi$
$967$	4.16375	+	4.16375i	0.133897	+	0.133897i	−0.636982	+	0.770879i	$0.719817\pi$
$968$	8.12522			0.261154
$969$	−5.61116	+	6.83002i	−0.180256	+	0.219412i
$970$	−1.62813			−0.0522762
$971$	−13.4117	−	13.4117i	−0.430403	−	0.430403i	0.458363	−	0.888765i	$-0.348436\pi$
$971$	−13.4117	−	13.4117i	−0.430403	−	0.430403i	−0.888765	+	0.458363i	$0.848436\pi$
$972$	0.382683	+	0.923880i	0.0122746	+	0.0296334i
$973$			58.1943i			1.86562i
$974$	22.2956	−	9.23512i	0.714396	−	0.295912i
$975$	0.611045	−	1.47519i	0.0195691	−	0.0472440i
$976$	7.42788	+	3.07673i	0.237761	+	0.0984837i
$977$	22.8517	−	22.8517i	0.731090	−	0.731090i	−0.239746	−	0.970836i	$-0.577064\pi$
$977$	22.8517	−	22.8517i	0.731090	−	0.731090i	0.970836	+	0.239746i	$0.0770641\pi$
$978$	−12.5899	+	12.5899i	−0.402582	+	0.402582i
$979$	21.6610	+	8.97229i	0.692289	+	0.286756i
$980$	−0.772622	+	1.86527i	−0.0246805	+	0.0595840i
$981$	7.31136	−	3.02847i	0.233434	−	0.0966915i
$982$		−	26.5200i		−	0.846288i
$983$	−12.4128	−	29.9672i	−0.395908	−	0.955805i	−0.988626	−	0.150396i	$-0.951945\pi$
$983$	−12.4128	−	29.9672i	−0.395908	−	0.955805i	0.592718	−	0.805410i	$-0.298055\pi$
$984$	8.56854	+	8.56854i	0.273155	+	0.273155i
$985$	1.80116			0.0573898
$986$	−27.2032	−	22.3486i	−0.866325	−	0.711724i
$987$	8.12612			0.258657
$988$	0.503021	+	0.503021i	0.0160032	+	0.0160032i
$989$	−7.27504	−	17.5635i	−0.231333	−	0.558487i
$990$		−	0.735084i		−	0.0233625i
$991$	43.3309	−	17.9482i	1.37645	−	0.570145i	0.432921	−	0.901432i	$-0.357483\pi$
$991$	43.3309	−	17.9482i	1.37645	−	0.570145i	0.943530	+	0.331287i	$0.107483\pi$
$992$	0.989538	−	2.38896i	0.0314179	−	0.0758494i
$993$	−3.76696	−	1.56033i	−0.119541	−	0.0495154i
$994$	0.547123	−	0.547123i	0.0173537	−	0.0173537i
$995$	3.28290	−	3.28290i	0.104075	−	0.104075i
$996$	0.964279	+	0.399418i	0.0305544	+	0.0126560i
$997$	−18.1610	+	43.8446i	−0.575166	+	1.38857i	0.321941	+	0.946760i	$0.395665\pi$
$997$	−18.1610	+	43.8446i	−0.575166	+	1.38857i	−0.897107	+	0.441813i	$0.854335\pi$
$998$	4.19438	−	1.73737i	0.132771	−	0.0549954i
$999$			10.6143i			0.335823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.2.h.a.49.2	yes	8
3.2	odd	2		306.2.l.d.253.2		8
4.3	odd	2		816.2.bq.b.49.1		8
17.3	odd	16		1734.2.b.k.577.6		8
17.5	odd	16		1734.2.a.v.1.3		4
17.6	odd	16		1734.2.f.m.829.3		8
17.7	odd	16		1734.2.f.m.1483.3		8
17.8	even	8	inner	102.2.h.a.25.2	✓	8
17.10	odd	16		1734.2.f.j.1483.2		8
17.11	odd	16		1734.2.f.j.829.2		8
17.12	odd	16		1734.2.a.w.1.2		4
17.14	odd	16		1734.2.b.k.577.3		8
51.5	even	16		5202.2.a.br.1.2		4
51.8	odd	8		306.2.l.d.127.2		8
51.29	even	16		5202.2.a.bt.1.3		4
68.59	odd	8		816.2.bq.b.433.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.h.a.25.2	✓	8	17.8	even	8	inner
102.2.h.a.49.2	yes	8	1.1	even	1	trivial
306.2.l.d.127.2		8	51.8	odd	8
306.2.l.d.253.2		8	3.2	odd	2
816.2.bq.b.49.1		8	4.3	odd	2
816.2.bq.b.433.1		8	68.59	odd	8
1734.2.a.v.1.3		4	17.5	odd	16
1734.2.a.w.1.2		4	17.12	odd	16
1734.2.b.k.577.3		8	17.14	odd	16
1734.2.b.k.577.6		8	17.3	odd	16
1734.2.f.j.829.2		8	17.11	odd	16
1734.2.f.j.1483.2		8	17.10	odd	16
1734.2.f.m.829.3		8	17.6	odd	16
1734.2.f.m.1483.3		8	17.7	odd	16
5202.2.a.br.1.2		4	51.5	even	16
5202.2.a.bt.1.3		4	51.29	even	16

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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	102.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.400544 - 0.165911i) q^{5} +(0.382683 - 0.923880i) q^{6} +(3.15432 + 1.30656i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.400544 - 0.165911i) q^{10} +(0.648847 - 1.56645i) q^{11} +(-0.923880 + 0.382683i) q^{12} +0.331821i q^{13} +(-1.30656 - 3.15432i) q^{14} +(0.306563 + 0.306563i) q^{15} -1.00000 q^{16} +(-3.94495 - 1.19891i) q^{17} +1.00000 q^{18} +(-1.51594 - 1.51594i) q^{19} +(0.165911 + 0.400544i) q^{20} +3.41421i q^{21} +(-1.56645 + 0.648847i) q^{22} +(0.720777 - 1.74011i) q^{23} +(0.923880 + 0.382683i) q^{24} +(-3.40262 + 3.40262i) q^{25} +(0.234633 - 0.234633i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(-1.30656 + 3.15432i) q^{28} +(-7.88877 + 3.26763i) q^{29} -0.433546i q^{30} +(-0.989538 - 2.38896i) q^{31} +(0.707107 + 0.707107i) q^{32} +1.69552 q^{33} +(1.94174 + 3.63726i) q^{34} +1.48022 q^{35} +(-0.707107 - 0.707107i) q^{36} +(-4.06193 - 9.80638i) q^{37} +2.14386i q^{38} +(-0.306563 + 0.126983i) q^{39} +(0.165911 - 0.400544i) q^{40} +(11.1953 + 4.63726i) q^{41} +(2.41421 - 2.41421i) q^{42} +(7.13707 - 7.13707i) q^{43} +(1.56645 + 0.648847i) q^{44} +(-0.165911 + 0.400544i) q^{45} +(-1.74011 + 0.720777i) q^{46} -2.38009i q^{47} +(-0.382683 - 0.923880i) q^{48} +(3.29289 + 3.29289i) q^{49} +4.81204 q^{50} +(-0.402015 - 4.10346i) q^{51} -0.331821 q^{52} +(2.21371 + 2.21371i) q^{53} +(0.382683 + 0.923880i) q^{54} -0.735084i q^{55} +(3.15432 - 1.30656i) q^{56} +(0.820420 - 1.98067i) q^{57} +(7.88877 + 3.26763i) q^{58} +(-5.42676 + 5.42676i) q^{59} +(-0.306563 + 0.306563i) q^{60} +(-7.42788 - 3.07673i) q^{61} +(-0.989538 + 2.38896i) q^{62} +(-3.15432 + 1.30656i) q^{63} -1.00000i q^{64} +(0.0550527 + 0.132909i) q^{65} +(-1.19891 - 1.19891i) q^{66} +15.7711 q^{67} +(1.19891 - 3.94495i) q^{68} +1.88348 q^{69} +(-1.04667 - 1.04667i) q^{70} +(0.0867259 + 0.209375i) q^{71} +1.00000i q^{72} +(-11.2147 + 4.64527i) q^{73} +(-4.06193 + 9.80638i) q^{74} +(-4.44574 - 1.84149i) q^{75} +(1.51594 - 1.51594i) q^{76} +(4.09334 - 4.09334i) q^{77} +(0.306563 + 0.126983i) q^{78} +(-4.79863 + 11.5849i) q^{79} +(-0.400544 + 0.165911i) q^{80} -1.00000i q^{81} +(-4.63726 - 11.1953i) q^{82} +(-0.738027 - 0.738027i) q^{83} -3.41421 q^{84} +(-1.77904 + 0.174292i) q^{85} -10.0933 q^{86} +(-6.03780 - 6.03780i) q^{87} +(-0.648847 - 1.56645i) q^{88} +13.8281i q^{89} +(0.400544 - 0.165911i) q^{90} +(-0.433546 + 1.04667i) q^{91} +(1.74011 + 0.720777i) q^{92} +(1.82843 - 1.82843i) q^{93} +(-1.68297 + 1.68297i) q^{94} +(-0.858710 - 0.355689i) q^{95} +(-0.382683 + 0.923880i) q^{96} +(3.46953 - 1.43713i) q^{97} -4.65685i q^{98} +(0.648847 + 1.56645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5} - 8 q^{10} - 8 q^{15} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{22} - 16 q^{23} + 8 q^{25} + 8 q^{26} - 16 q^{33} + 16 q^{34} - 16 q^{35} + 8 q^{39} + 16 q^{41} + 8 q^{42} - 16 q^{43} + 16 q^{44}+ \cdots + 16 q^{97}+O(q^{100}) \) 8 * q + 8 * q^5 - 8 * q^10 - 8 * q^15 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^22 - 16 * q^23 + 8 * q^25 + 8 * q^26 - 16 * q^33 + 16 * q^34 - 16 * q^35 + 8 * q^39 + 16 * q^41 + 8 * q^42 - 16 * q^43 + 16 * q^44 + 32 * q^49 + 8 * q^50 - 8 * q^51 + 8 * q^53 + 24 * q^57 + 8 * q^60 - 32 * q^61 + 24 * q^65 + 48 * q^67 + 16 * q^69 + 16 * q^70 - 16 * q^71 - 24 * q^73 - 16 * q^75 - 16 * q^77 - 8 * q^78 - 8 * q^80 - 8 * q^82 - 32 * q^83 - 16 * q^84 + 8 * q^85 - 32 * q^86 - 24 * q^87 + 8 * q^90 - 8 * q^93 - 16 * q^94 + 48 * q^95 + 16 * q^97

Introduction

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