LMFDB - Embedded newform 51.2.h.a.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,2,Mod(19,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.407237050309$
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			25.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	51.25
Dual form			51.2.h.a.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.541196 + 0.541196i) q^{2} +(-0.382683 + 0.923880i) q^{3} +1.41421i q^{4} +(-0.0761205 - 0.0315301i) q^{5} +(-0.292893 - 0.707107i) q^{6} +(2.55487 - 1.05826i) q^{7} +(-1.84776 - 1.84776i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(0.0582601 - 0.0241321i) q^{10} +(-0.255701 - 0.617317i) q^{11} +(-1.30656 - 0.541196i) q^{12} -3.28130i q^{13} +(-0.809957 + 1.95541i) q^{14} +(0.0582601 - 0.0582601i) q^{15} -0.828427 q^{16} +(3.18585 - 2.61732i) q^{17} +0.765367 q^{18} +(-2.57420 + 2.57420i) q^{19} +(0.0445903 - 0.107651i) q^{20} +2.76537i q^{21} +(0.472474 + 0.195705i) q^{22} +(3.56226 + 8.60007i) q^{23} +(2.41421 - 1.00000i) q^{24} +(-3.53073 - 3.53073i) q^{25} +(1.77583 + 1.77583i) q^{26} +(0.923880 - 0.382683i) q^{27} +(1.49661 + 3.61313i) q^{28} +(-5.76745 - 2.38896i) q^{29} +0.0630603i q^{30} +(-1.93015 + 4.65980i) q^{31} +(4.14386 - 4.14386i) q^{32} +0.668179 q^{33} +(-0.307689 + 3.14065i) q^{34} -0.227845 q^{35} +(1.00000 - 1.00000i) q^{36} +(0.920815 - 2.22304i) q^{37} -2.78629i q^{38} +(3.03153 + 1.25570i) q^{39} +(0.0823922 + 0.198912i) q^{40} +(-0.443663 + 0.183771i) q^{41} +(-1.49661 - 1.49661i) q^{42} +(-5.85097 - 5.85097i) q^{43} +(0.873017 - 0.361616i) q^{44} +(0.0315301 + 0.0761205i) q^{45} +(-6.58221 - 2.72644i) q^{46} -8.88311i q^{47} +(0.317025 - 0.765367i) q^{48} +(0.457678 - 0.457678i) q^{49} +3.82164 q^{50} +(1.19891 + 3.94495i) q^{51} +4.64047 q^{52} +(-8.02734 + 8.02734i) q^{53} +(-0.292893 + 0.707107i) q^{54} +0.0550527i q^{55} +(-6.67619 - 2.76537i) q^{56} +(-1.39315 - 3.36335i) q^{57} +(4.41421 - 1.82843i) q^{58} +(6.78384 + 6.78384i) q^{59} +(0.0823922 + 0.0823922i) q^{60} +(2.39008 - 0.990004i) q^{61} +(-1.47727 - 3.56645i) q^{62} +(-2.55487 - 1.05826i) q^{63} +2.82843i q^{64} +(-0.103460 + 0.249774i) q^{65} +(-0.361616 + 0.361616i) q^{66} +0.944947 q^{67} +(3.70144 + 4.50548i) q^{68} -9.30864 q^{69} +(0.123309 - 0.123309i) q^{70} +(-1.25830 + 3.03780i) q^{71} +2.61313i q^{72} +(14.4882 + 6.00122i) q^{73} +(0.704761 + 1.70144i) q^{74} +(4.61313 - 1.91082i) q^{75} +(-3.64047 - 3.64047i) q^{76} +(-1.30656 - 1.30656i) q^{77} +(-2.32023 + 0.961072i) q^{78} +(3.20371 + 7.73445i) q^{79} +(0.0630603 + 0.0261204i) q^{80} +1.00000i q^{81} +(0.140652 - 0.339565i) q^{82} +(0.636303 - 0.636303i) q^{83} -3.91082 q^{84} +(-0.325033 + 0.0987810i) q^{85} +6.33304 q^{86} +(4.41421 - 4.41421i) q^{87} +(-0.668179 + 1.61313i) q^{88} -5.64431i q^{89} +(-0.0582601 - 0.0241321i) q^{90} +(-3.47247 - 8.38329i) q^{91} +(-12.1623 + 5.03780i) q^{92} +(-3.56645 - 3.56645i) q^{93} +(4.80750 + 4.80750i) q^{94} +(0.277114 - 0.114784i) q^{95} +(2.24264 + 5.41421i) q^{96} +(10.1371 + 4.19891i) q^{97} +0.495387i q^{98} +(-0.255701 + 0.617317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5} - 8 q^{6} + 8 q^{11} - 16 q^{14} + 16 q^{16} - 8 q^{17} - 8 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{23} + 8 q^{24} - 16 q^{25} + 16 q^{26} - 8 q^{28} + 8 q^{31} + 8 q^{33} - 8 q^{34} + 32 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^6 + 8 * q^11 - 16 * q^14 + 16 * q^16 - 8 * q^17 - 8 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^23 + 8 * q^24 - 16 * q^25 + 16 * q^26 - 8 * q^28 + 8 * q^31 + 8 * q^33 - 8 * q^34 + 32 * q^35 + 8 * q^36 - 8 * q^37 + 16 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^50 - 16 * q^52 - 32 * q^53 - 8 * q^54 - 16 * q^56 - 16 * q^57 + 24 * q^58 + 16 * q^59 - 8 * q^60 + 16 * q^61 + 16 * q^62 + 24 * q^65 - 16 * q^66 - 16 * q^67 - 24 * q^69 + 40 * q^70 - 16 * q^71 + 48 * q^73 + 64 * q^74 + 16 * q^75 + 24 * q^76 + 8 * q^78 - 16 * q^80 - 8 * q^82 + 32 * q^83 + 40 * q^85 - 32 * q^86 + 24 * q^87 - 8 * q^88 - 16 * q^91 - 32 * q^92 - 32 * q^93 - 40 * q^95 - 16 * q^96 + 8 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−0.541196	+	0.541196i	−0.382683	+	0.382683i	−0.872068	−	0.489385i	$-0.837221\pi$
$2$	−0.541196	+	0.541196i	−0.382683	+	0.382683i	0.489385	+	0.872068i	$0.337221\pi$
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$			1.41421i			0.707107i
$5$	−0.0761205	−	0.0315301i	−0.0340421	−	0.0141007i	0.365597	−	0.930773i	$-0.380865\pi$
$5$	−0.0761205	−	0.0315301i	−0.0340421	−	0.0141007i	−0.399640	+	0.916672i	$0.630865\pi$
$6$	−0.292893	−	0.707107i	−0.119573	−	0.288675i
$7$	2.55487	−	1.05826i	0.965649	−	0.399985i	0.156558	−	0.987669i	$-0.449960\pi$
$7$	2.55487	−	1.05826i	0.965649	−	0.399985i	0.809091	+	0.587684i	$0.199960\pi$
$8$	−1.84776	−	1.84776i	−0.653281	−	0.653281i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	0.0582601	−	0.0241321i	0.0184235	−	0.00763125i
$11$	−0.255701	−	0.617317i	−0.0770967	−	0.186128i	0.880632	−	0.473801i	$-0.157118\pi$
$11$	−0.255701	−	0.617317i	−0.0770967	−	0.186128i	−0.957729	+	0.287673i	$0.907118\pi$
$12$	−1.30656	−	0.541196i	−0.377172	−	0.156230i
$13$		−	3.28130i		−	0.910070i	−0.890474	−	0.455035i	$-0.849627\pi$
$13$		−	3.28130i		−	0.910070i	0.890474	−	0.455035i	$-0.150373\pi$
$14$	−0.809957	+	1.95541i	−0.216470	+	0.522605i
$15$	0.0582601	−	0.0582601i	0.0150427	−	0.0150427i
$16$	−0.828427			−0.207107
$17$	3.18585	−	2.61732i	0.772683	−	0.634793i
$17$	3.18585	−	2.61732i	0.772683	−	0.634793i
$18$	0.765367			0.180399
$19$	−2.57420	+	2.57420i	−0.590561	+	0.590561i	−0.937783	−	0.347222i	$-0.887125\pi$
$19$	−2.57420	+	2.57420i	−0.590561	+	0.590561i	0.347222	+	0.937783i	$0.387125\pi$
$20$	0.0445903	−	0.107651i	0.00997070	−	0.0240714i
$21$			2.76537i			0.603453i
$22$	0.472474	+	0.195705i	0.100732	+	0.0417244i
$23$	3.56226	+	8.60007i	0.742783	+	1.79324i	0.594165	+	0.804343i	$0.297483\pi$
$23$	3.56226	+	8.60007i	0.742783	+	1.79324i	0.148618	+	0.988895i	$0.452517\pi$
$24$	2.41421	−	1.00000i	0.492799	−	0.204124i
$25$	−3.53073	−	3.53073i	−0.706147	−	0.706147i
$26$	1.77583	+	1.77583i	0.348269	+	0.348269i
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$	1.49661	+	3.61313i	0.282832	+	0.682817i
$29$	−5.76745	−	2.38896i	−1.07099	−	0.443618i	−0.223649	−	0.974670i	$-0.571797\pi$
$29$	−5.76745	−	2.38896i	−1.07099	−	0.443618i	−0.847339	+	0.531052i	$0.821797\pi$
$30$			0.0630603i			0.0115132i
$31$	−1.93015	+	4.65980i	−0.346665	+	0.836924i	0.650344	+	0.759640i	$0.274625\pi$
$31$	−1.93015	+	4.65980i	−0.346665	+	0.836924i	−0.997009	+	0.0772842i	$0.975375\pi$
$32$	4.14386	−	4.14386i	0.732538	−	0.732538i
$33$	0.668179			0.116315
$34$	−0.307689	+	3.14065i	−0.0527683	+	0.538617i
$35$	−0.227845			−0.0385128
$36$	1.00000	−	1.00000i	0.166667	−	0.166667i
$37$	0.920815	−	2.22304i	0.151381	−	0.365466i	−0.829937	−	0.557857i	$-0.811624\pi$
$37$	0.920815	−	2.22304i	0.151381	−	0.365466i	0.981318	+	0.192390i	$0.0616239\pi$
$38$		−	2.78629i		−	0.451996i
$39$	3.03153	+	1.25570i	0.485433	+	0.201073i
$40$	0.0823922	+	0.198912i	0.0130274	+	0.0314508i
$41$	−0.443663	+	0.183771i	−0.0692885	+	0.0287002i	−0.417059	−	0.908880i	$-0.636939\pi$
$41$	−0.443663	+	0.183771i	−0.0692885	+	0.0287002i	0.347770	+	0.937580i	$0.386939\pi$
$42$	−1.49661	−	1.49661i	−0.230931	−	0.230931i
$43$	−5.85097	−	5.85097i	−0.892264	−	0.892264i	0.102472	−	0.994736i	$-0.467325\pi$
$43$	−5.85097	−	5.85097i	−0.892264	−	0.892264i	−0.994736	+	0.102472i	$0.967325\pi$
$44$	0.873017	−	0.361616i	0.131612	−	0.0545156i
$45$	0.0315301	+	0.0761205i	0.00470023	+	0.0113474i
$46$	−6.58221	−	2.72644i	−0.970493	−	0.401991i
$47$		−	8.88311i		−	1.29573i	−0.761753	−	0.647867i	$-0.775661\pi$
$47$		−	8.88311i		−	1.29573i	0.761753	−	0.647867i	$-0.224339\pi$
$48$	0.317025	−	0.765367i	0.0457587	−	0.110471i
$49$	0.457678	−	0.457678i	0.0653825	−	0.0653825i
$50$	3.82164			0.540461
$51$	1.19891	+	3.94495i	0.167881	+	0.552403i
$52$	4.64047			0.643517
$53$	−8.02734	+	8.02734i	−1.10264	+	1.10264i	−0.108549	+	0.994091i	$0.534620\pi$
$53$	−8.02734	+	8.02734i	−1.10264	+	1.10264i	−0.994091	+	0.108549i	$0.965380\pi$
$54$	−0.292893	+	0.707107i	−0.0398577	+	0.0962250i
$55$			0.0550527i			0.00742331i
$56$	−6.67619	−	2.76537i	−0.892143	−	0.369538i
$57$	−1.39315	−	3.36335i	−0.184527	−	0.445487i
$58$	4.41421	−	1.82843i	0.579615	−	0.240084i
$59$	6.78384	+	6.78384i	0.883180	+	0.883180i	0.993857	−	0.110676i	$-0.0353016\pi$
$59$	6.78384	+	6.78384i	0.883180	+	0.883180i	−0.110676	+	0.993857i	$0.535302\pi$
$60$	0.0823922	+	0.0823922i	0.0106368	+	0.0106368i
$61$	2.39008	−	0.990004i	0.306019	−	0.126757i	−0.224389	−	0.974500i	$-0.572039\pi$
$61$	2.39008	−	0.990004i	0.306019	−	0.126757i	0.530408	+	0.847743i	$0.322039\pi$
$62$	−1.47727	−	3.56645i	−0.187614	−	0.452940i
$63$	−2.55487	−	1.05826i	−0.321883	−	0.133328i
$64$			2.82843i			0.353553i
$65$	−0.103460	+	0.249774i	−0.0128326	+	0.0309807i
$66$	−0.361616	+	0.361616i	−0.0445118	+	0.0445118i
$67$	0.944947			0.115444			0.0577218	−	0.998333i	$-0.481616\pi$
$67$	0.944947			0.115444			0.0577218	+	0.998333i	$0.481616\pi$
$68$	3.70144	+	4.50548i	0.448866	+	0.546369i
$69$	−9.30864			−1.12063
$70$	0.123309	−	0.123309i	0.0147382	−	0.0147382i
$71$	−1.25830	+	3.03780i	−0.149333	+	0.360521i	−0.980790	−	0.195068i	$-0.937507\pi$
$71$	−1.25830	+	3.03780i	−0.149333	+	0.360521i	0.831457	+	0.555589i	$0.187507\pi$
$72$			2.61313i			0.307960i
$73$	14.4882	+	6.00122i	1.69572	+	0.702390i	0.999875	−	0.0158041i	$-0.00503080\pi$
$73$	14.4882	+	6.00122i	1.69572	+	0.702390i	0.695843	+	0.718194i	$0.255031\pi$
$74$	0.704761	+	1.70144i	0.0819269	+	0.197789i
$75$	4.61313	−	1.91082i	0.532678	−	0.220642i
$76$	−3.64047	−	3.64047i	−0.417590	−	0.417590i
$77$	−1.30656	−	1.30656i	−0.148897	−	0.148897i
$78$	−2.32023	+	0.961072i	−0.262715	+	0.108820i
$79$	3.20371	+	7.73445i	0.360446	+	0.870193i	0.995235	+	0.0975076i	$0.0310870\pi$
$79$	3.20371	+	7.73445i	0.360446	+	0.870193i	−0.634789	+	0.772686i	$0.718913\pi$
$80$	0.0630603	+	0.0261204i	0.00705035	+	0.00292035i
$81$			1.00000i			0.111111i
$82$	0.140652	−	0.339565i	0.0155324	−	0.0374986i
$83$	0.636303	−	0.636303i	0.0698434	−	0.0698434i	−0.671322	−	0.741166i	$-0.734273\pi$
$83$	0.636303	−	0.636303i	0.0698434	−	0.0698434i	0.741166	+	0.671322i	$0.234273\pi$
$84$	−3.91082			−0.426705
$85$	−0.325033	+	0.0987810i	−0.0352548	+	0.0107143i
$86$	6.33304			0.682909
$87$	4.41421	−	4.41421i	0.473253	−	0.473253i
$88$	−0.668179	+	1.61313i	−0.0712281	+	0.171960i
$89$		−	5.64431i		−	0.598296i	−0.954207	−	0.299148i	$-0.903298\pi$
$89$		−	5.64431i		−	0.598296i	0.954207	−	0.299148i	$-0.0967024\pi$
$90$	−0.0582601	−	0.0241321i	−0.00614115	−	0.00254375i
$91$	−3.47247	−	8.38329i	−0.364014	−	0.878808i
$92$	−12.1623	+	5.03780i	−1.26801	+	0.525227i
$93$	−3.56645	−	3.56645i	−0.369824	−	0.369824i
$94$	4.80750	+	4.80750i	0.495856	+	0.495856i
$95$	0.277114	−	0.114784i	0.0284313	−	0.0117766i
$96$	2.24264	+	5.41421i	0.228889	+	0.552586i
$97$	10.1371	+	4.19891i	1.02926	+	0.426335i	0.832447	−	0.554105i	$-0.186940\pi$
$97$	10.1371	+	4.19891i	1.02926	+	0.426335i	0.196817	+	0.980440i	$0.436940\pi$
$98$			0.495387i			0.0500416i
$99$	−0.255701	+	0.617317i	−0.0256989	+	0.0620426i
$100$	4.99321	−	4.99321i	0.499321	−	0.499321i
$101$	3.27677			0.326051			0.163025	−	0.986622i	$-0.447875\pi$
$101$	3.27677			0.326051			0.163025	+	0.986622i	$0.447875\pi$
$102$	−2.78384	−	1.48614i	−0.275641	−	0.147150i
$103$	−12.0228			−1.18464			−0.592321	−	0.805702i	$-0.701788\pi$
$103$	−12.0228			−1.18464			−0.592321	+	0.805702i	$0.701788\pi$
$104$	−6.06306	+	6.06306i	−0.594532	+	0.594532i
$105$	0.0871924	−	0.210501i	0.00850910	−	0.0205428i
$106$		−	8.68873i		−	0.843924i
$107$	−8.06480	−	3.34055i	−0.779653	−	0.322943i	−0.0428777	−	0.999080i	$-0.513653\pi$
$107$	−8.06480	−	3.34055i	−0.779653	−	0.322943i	−0.736776	+	0.676137i	$0.763653\pi$
$108$	0.541196	+	1.30656i	0.0520766	+	0.125724i
$109$	−3.94495	+	1.63405i	−0.377857	+	0.156514i	−0.563525	−	0.826099i	$-0.690555\pi$
$109$	−3.94495	+	1.63405i	−0.377857	+	0.156514i	0.185668	+	0.982613i	$0.440555\pi$
$110$	−0.0297943	−	0.0297943i	−0.00284078	−	0.00284078i
$111$	1.70144	+	1.70144i	0.161494	+	0.161494i
$112$	−2.11652	+	0.876691i	−0.199992	+	0.0828395i
$113$	−5.30237	−	12.8011i	−0.498805	−	1.20422i	−0.950128	−	0.311861i	$-0.899048\pi$
$113$	−5.30237	−	12.8011i	−0.498805	−	1.20422i	0.451322	−	0.892361i	$-0.350952\pi$
$114$	2.57420	+	1.06627i	0.241096	+	0.0998651i
$115$		−	0.766960i		−	0.0715194i
$116$	3.37849	−	8.15640i	0.313685	−	0.757303i
$117$	−2.32023	+	2.32023i	−0.214506	+	0.214506i
$118$	−7.34277			−0.675957
$119$	5.36962	−	10.0584i	0.492233	−	0.922048i
$120$	−0.215301			−0.0196542
$121$	7.46248	−	7.46248i	0.678407	−	0.678407i
$122$	−0.757716	+	1.82929i	−0.0686004	+	0.165616i
$123$		−	0.480217i		−	0.0432997i
$124$	−6.58995	−	2.72965i	−0.591795	−	0.245129i
$125$	0.315087	+	0.760688i	0.0281823	+	0.0680380i
$126$	1.95541	−	0.809957i	0.174202	−	0.0721567i
$127$	0.448077	+	0.448077i	0.0397604	+	0.0397604i	0.726707	−	0.686947i	$-0.241050\pi$
$127$	0.448077	+	0.448077i	0.0397604	+	0.0397604i	−0.686947	+	0.726707i	$0.741050\pi$
$128$	6.75699	+	6.75699i	0.597239	+	0.597239i
$129$	7.64466	−	3.16652i	0.673074	−	0.278797i
$130$	−0.0791848	−	0.191169i	−0.00694497	−	0.0167666i
$131$	14.0505	+	5.81990i	1.22760	+	0.508487i	0.899817	−	0.436267i	$-0.143700\pi$
$131$	14.0505	+	5.81990i	1.22760	+	0.508487i	0.327780	+	0.944754i	$0.393700\pi$
$132$			0.944947i			0.0822471i
$133$	−3.85256	+	9.30090i	−0.334059	+	0.806490i
$134$	−0.511402	+	0.511402i	−0.0441784	+	0.0441784i
$135$	−0.0823922			−0.00709119
$136$	−10.7229	−	1.05052i	−0.919477	−	0.0900811i
$137$	2.38847			0.204060			0.102030	−	0.994781i	$-0.467466\pi$
$137$	2.38847			0.204060			0.102030	+	0.994781i	$0.467466\pi$
$138$	5.03780	−	5.03780i	0.428846	−	0.428846i
$139$	0.617926	−	1.49181i	0.0524118	−	0.126533i	−0.895505	−	0.445052i	$-0.853185\pi$
$139$	0.617926	−	1.49181i	0.0524118	−	0.126533i	0.947917	+	0.318518i	$0.103185\pi$
$140$		−	0.322221i		−	0.0272326i
$141$	8.20692	+	3.39942i	0.691147	+	0.286283i
$142$	−0.963060	−	2.32503i	−0.0808182	−	0.195112i
$143$	−2.02560	+	0.839033i	−0.169389	+	0.0701634i
$144$	0.585786	+	0.585786i	0.0488155	+	0.0488155i
$145$	0.363697	+	0.363697i	0.0302034	+	0.0302034i
$146$	−11.0888	+	4.59313i	−0.917716	+	0.380130i
$147$	0.247693	+	0.597985i	0.0204294	+	0.0493209i
$148$	3.14386	+	1.30223i	0.258424	+	0.107043i
$149$			10.8082i			0.885442i	0.896660	+	0.442721i	$0.145987\pi$
$149$			10.8082i			0.885442i	−0.896660	+	0.442721i	$0.854013\pi$
$150$	−1.46248	+	3.53073i	−0.119411	+	0.288283i
$151$	−15.3842	+	15.3842i	−1.25195	+	1.25195i	−0.297109	+	0.954844i	$0.596022\pi$
$151$	−15.3842	+	15.3842i	−1.25195	+	1.25195i	−0.954844	+	0.297109i	$0.903978\pi$
$152$	9.51299			0.771606
$153$	−4.10346	−	0.402015i	−0.331745	−	0.0325010i
$154$	1.41421			0.113961
$155$	0.293848	−	0.293848i	0.0236024	−	0.0236024i
$156$	−1.77583	+	4.28723i	−0.142180	+	0.343253i
$157$			19.8535i			1.58448i	0.610208	+	0.792241i	$0.291086\pi$
$157$			19.8535i			1.58448i	−0.610208	+	0.792241i	$0.708914\pi$
$158$	−5.91969	−	2.45202i	−0.470945	−	0.195072i
$159$	−4.34436	−	10.4882i	−0.344531	−	0.831770i
$160$	−0.446089	+	0.184776i	−0.0352664	+	0.0146078i
$161$	18.2022	+	18.2022i	1.43454	+	1.43454i
$162$	−0.541196	−	0.541196i	−0.0425204	−	0.0425204i
$163$	1.62151	−	0.671650i	0.127006	−	0.0526077i	−0.318275	−	0.947998i	$-0.603104\pi$
$163$	1.62151	−	0.671650i	0.127006	−	0.0526077i	0.445281	+	0.895391i	$0.353104\pi$
$164$	−0.259892	−	0.627434i	−0.0202941	−	0.0489943i
$165$	−0.0508621	−	0.0210678i	−0.00395961	−	0.00164012i
$166$			0.688730i			0.0534558i
$167$	3.08413	−	7.44574i	0.238657	−	0.576169i	−0.758487	−	0.651688i	$-0.774061\pi$
$167$	3.08413	−	7.44574i	0.238657	−	0.576169i	0.997144	+	0.0755188i	$0.0240613\pi$
$168$	5.10973	−	5.10973i	0.394224	−	0.394224i
$169$	2.23304			0.171772
$170$	0.122447	−	0.229366i	0.00939123	−	0.0175916i
$171$	3.64047			0.278393
$172$	8.27452	−	8.27452i	0.630926	−	0.630926i
$173$	2.20151	−	5.31492i	0.167378	−	0.404086i	−0.817828	−	0.575463i	$-0.804822\pi$
$173$	2.20151	−	5.31492i	0.167378	−	0.404086i	0.985205	+	0.171378i	$0.0548218\pi$
$174$			4.77791i			0.362212i
$175$	−12.7570	−	5.28412i	−0.964337	−	0.399442i
$176$	0.211830	+	0.511402i	0.0159673	+	0.0385484i
$177$	−8.86351	+	3.67139i	−0.666222	+	0.275958i
$178$	3.05468	+	3.05468i	0.228958	+	0.228958i
$179$	−10.3360	−	10.3360i	−0.772548	−	0.772548i	0.206004	−	0.978551i	$-0.433954\pi$
$179$	−10.3360	−	10.3360i	−0.772548	−	0.772548i	−0.978551	+	0.206004i	$0.933954\pi$
$180$	−0.107651	+	0.0445903i	−0.00802380	+	0.00332357i
$181$	−5.39584	−	13.0267i	−0.401069	−	0.968267i	−0.987407	−	0.158200i	$-0.949431\pi$
$181$	−5.39584	−	13.0267i	−0.401069	−	0.968267i	0.586338	−	0.810067i	$-0.300569\pi$
$182$	6.41629	+	2.65772i	0.475607	+	0.197003i
$183$			2.58701i			0.191237i
$184$	9.30864	−	22.4731i	0.686242	−	1.65674i
$185$	−0.140186	+	0.140186i	−0.0103067	+	0.0103067i
$186$	3.86030			0.283051
$187$	−2.43034	−	1.29743i	−0.177724	−	0.0948774i
$188$	12.5626			0.916222
$189$	1.95541	−	1.95541i	0.142235	−	0.142235i
$190$	−0.0878521	+	0.212094i	−0.00637346	+	0.0153869i
$191$		−	16.0167i		−	1.15893i	−0.814998	−	0.579464i	$-0.803262\pi$
$191$		−	16.0167i		−	1.15893i	0.814998	−	0.579464i	$-0.196738\pi$
$192$	−2.61313	−	1.08239i	−0.188586	−	0.0781149i
$193$	−1.75858	−	4.24558i	−0.126585	−	0.305604i	0.847863	−	0.530215i	$-0.177889\pi$
$193$	−1.75858	−	4.24558i	−0.126585	−	0.305604i	−0.974448	+	0.224611i	$0.927889\pi$
$194$	−7.75858	+	3.21371i	−0.557033	+	0.230731i
$195$	−0.191169	−	0.191169i	−0.0136899	−	0.0136899i
$196$	0.647254	+	0.647254i	0.0462324	+	0.0462324i
$197$	−19.5576	+	8.10101i	−1.39342	+	0.577173i	−0.948035	−	0.318167i	$-0.896933\pi$
$197$	−19.5576	+	8.10101i	−1.39342	+	0.577173i	−0.445384	+	0.895340i	$0.646933\pi$
$198$	−0.195705	−	0.472474i	−0.0139081	−	0.0335772i
$199$	2.14840	+	0.889895i	0.152296	+	0.0630830i	0.457529	−	0.889195i	$-0.348735\pi$
$199$	2.14840	+	0.889895i	0.152296	+	0.0630830i	−0.305234	+	0.952278i	$0.598735\pi$
$200$			13.0479i			0.922625i
$201$	−0.361616	+	0.873017i	−0.0255064	+	0.0615779i
$202$	−1.77337	+	1.77337i	−0.124774	+	0.124774i
$203$	−17.2632			−1.21164
$204$	−5.57900	+	1.69552i	−0.390608	+	0.118710i
$205$	0.0395661			0.00276342
$206$	6.50669	−	6.50669i	0.453343	−	0.453343i
$207$	3.56226	−	8.60007i	0.247594	−	0.597746i
$208$			2.71832i			0.188482i
$209$	2.24732	+	0.930870i	0.155450	+	0.0643896i
$210$	0.0667342	+	0.161111i	0.00460509	+	0.0111177i
$211$	7.00801	−	2.90281i	0.482451	−	0.199838i	−0.128183	−	0.991751i	$-0.540915\pi$
$211$	7.00801	−	2.90281i	0.482451	−	0.199838i	0.610634	+	0.791913i	$0.290915\pi$
$212$	−11.3524	−	11.3524i	−0.779684	−	0.779684i
$213$	−2.32503	−	2.32503i	−0.159309	−	0.159309i
$214$	6.17253	−	2.55674i	0.421945	−	0.174775i
$215$	0.260897	+	0.629860i	0.0177930	+	0.0429561i
$216$	−2.41421	−	1.00000i	−0.164266	−	0.0680414i
$217$			13.9478i			0.946836i
$218$	1.25065	−	3.01933i	0.0847046	−	0.204495i
$219$	−11.0888	+	11.0888i	−0.749312	+	0.749312i
$220$	−0.0778563			−0.00524907
$221$	−8.58821	−	10.4538i	−0.577706	−	0.703195i
$222$	−1.84163			−0.123602
$223$	11.0750	−	11.0750i	0.741635	−	0.741635i	−0.231258	−	0.972892i	$-0.574284\pi$
$223$	11.0750	−	11.0750i	0.741635	−	0.741635i	0.972892	+	0.231258i	$0.0742841\pi$
$224$	6.20172	−	14.9723i	0.414370	−	1.00038i
$225$			4.99321i			0.332881i
$226$	9.79751	+	4.05826i	0.651720	+	0.269951i
$227$	5.59920	+	13.5177i	0.371632	+	0.897200i	0.993474	+	0.114057i	$0.0363846\pi$
$227$	5.59920	+	13.5177i	0.371632	+	0.897200i	−0.621842	+	0.783143i	$0.713615\pi$
$228$	4.75650	−	1.97021i	0.315007	−	0.130480i
$229$	11.5577	+	11.5577i	0.763754	+	0.763754i	0.976999	−	0.213245i	$-0.0684031\pi$
$229$	11.5577	+	11.5577i	0.763754	+	0.763754i	−0.213245	+	0.976999i	$0.568403\pi$
$230$	0.415076	+	0.415076i	0.0273693	+	0.0273693i
$231$	1.70711	−	0.707107i	0.112319	−	0.0465242i
$232$	6.24264	+	15.0711i	0.409849	+	0.989464i
$233$	0.330574	+	0.136928i	0.0216566	+	0.00897046i	0.393485	−	0.919331i	$-0.371269\pi$
$233$	0.330574	+	0.136928i	0.0216566	+	0.00897046i	−0.371829	+	0.928301i	$0.621269\pi$
$234$		−	2.51140i		−	0.164175i
$235$	−0.280085	+	0.676186i	−0.0182708	+	0.0441095i
$236$	−9.59379	+	9.59379i	−0.624503	+	0.624503i
$237$	−8.37170			−0.543801
$238$	2.53752	+	8.34956i	0.164483	+	0.541222i
$239$	−9.71153			−0.628187			−0.314093	−	0.949392i	$-0.601701\pi$
$239$	−9.71153			−0.628187			−0.314093	+	0.949392i	$0.601701\pi$
$240$	−0.0482642	+	0.0482642i	−0.00311544	+	0.00311544i
$241$	3.58258	−	8.64911i	0.230774	−	0.557138i	−0.765495	−	0.643442i	$-0.777506\pi$
$241$	3.58258	−	8.64911i	0.230774	−	0.557138i	0.996269	+	0.0863041i	$0.0275057\pi$
$242$			8.07733i			0.519230i
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$	1.40008	+	3.38009i	0.0896308	+	0.216388i
$245$	−0.0492693	+	0.0204080i	−0.00314770	+	0.00130382i
$246$	0.259892	+	0.259892i	0.0165701	+	0.0165701i
$247$	8.44673	+	8.44673i	0.537452	+	0.537452i
$248$	12.1766	−	5.04373i	0.773217	−	0.320277i
$249$	0.344365	+	0.831370i	0.0218232	+	0.0526859i
$250$	−0.582205	−	0.241157i	−0.0368219	−	0.0152521i
$251$			3.28196i			0.207156i	0.994621	+	0.103578i	$0.0330291\pi$
$251$			3.28196i			0.207156i	−0.994621	+	0.103578i	$0.966971\pi$
$252$	1.49661	−	3.61313i	0.0942773	−	0.227606i
$253$	4.39809	−	4.39809i	0.276505	−	0.276505i
$254$	−0.484995			−0.0304313
$255$	0.0331229	−	0.338093i	0.00207424	−	0.0211722i
$256$	−12.9706			−0.810660
$257$	−2.50669	+	2.50669i	−0.156363	+	0.156363i	−0.780953	−	0.624590i	$-0.785266\pi$
$257$	−2.50669	+	2.50669i	−0.156363	+	0.156363i	0.624590	+	0.780953i	$0.285266\pi$
$258$	−2.42355	+	5.85097i	−0.150884	+	0.364265i
$259$		−	6.65404i		−	0.413462i
$260$	−0.353234	−	0.146314i	−0.0219067	−	0.00907404i
$261$	2.38896	+	5.76745i	0.147873	+	0.356996i
$262$	−10.7538	+	4.45436i	−0.664371	+	0.275191i
$263$	9.55533	+	9.55533i	0.589207	+	0.589207i	0.937417	−	0.348210i	$-0.113210\pi$
$263$	9.55533	+	9.55533i	0.589207	+	0.589207i	−0.348210	+	0.937417i	$0.613210\pi$
$264$	−1.23463	−	1.23463i	−0.0759864	−	0.0759864i
$265$	0.864148	−	0.357942i	0.0530842	−	0.0219882i
$266$	−2.94862	−	7.11860i	−0.180792	−	0.436469i
$267$	5.21466	+	2.15998i	0.319132	+	0.132189i
$268$			1.33636i			0.0816310i
$269$	−1.97807	+	4.77548i	−0.120605	+	0.291166i	−0.972640	−	0.232319i	$-0.925369\pi$
$269$	−1.97807	+	4.77548i	−0.120605	+	0.291166i	0.852035	+	0.523486i	$0.175369\pi$
$270$	0.0445903	−	0.0445903i	0.00271368	−	0.00271368i
$271$	6.68592			0.406141			0.203070	−	0.979164i	$-0.434908\pi$
$271$	6.68592			0.406141			0.203070	+	0.979164i	$0.434908\pi$
$272$	−2.63925	+	2.16826i	−0.160028	+	0.131470i
$273$	9.07401			0.549184
$274$	−1.29263	+	1.29263i	−0.0780906	+	0.0780906i
$275$	−1.27677	+	3.08239i	−0.0769920	+	0.185875i
$276$		−	13.1644i		−	0.792404i
$277$	2.68072	+	1.11039i	0.161069	+	0.0667170i	0.461761	−	0.887004i	$-0.347218\pi$
$277$	2.68072	+	1.11039i	0.161069	+	0.0667170i	−0.300692	+	0.953721i	$0.597218\pi$
$278$	0.472940	+	1.14178i	0.0283651	+	0.0684793i
$279$	4.65980	−	1.93015i	0.278975	−	0.115555i
$280$	0.421002	+	0.421002i	0.0251597	+	0.0251597i
$281$	16.2074	+	16.2074i	0.966853	+	0.966853i	0.999468	−	0.0326151i	$-0.0103835\pi$
$281$	16.2074	+	16.2074i	0.966853	+	0.966853i	−0.0326151	+	0.999468i	$0.510384\pi$
$282$	−6.28130	+	2.60180i	−0.374046	+	0.154935i
$283$	−10.6083	−	25.6108i	−0.630600	−	1.52240i	−0.838871	−	0.544331i	$-0.816784\pi$
$283$	−10.6083	−	25.6108i	−0.630600	−	1.52240i	0.208271	−	0.978071i	$-0.433216\pi$
$284$	−4.29610	−	1.77950i	−0.254927	−	0.105594i
$285$			0.299946i			0.0177673i
$286$	0.642168	−	1.55033i	0.0379722	−	0.0916729i
$287$	−0.939021	+	0.939021i	−0.0554286	+	0.0554286i
$288$	−5.86030			−0.345322
$289$	3.29931	−	16.6768i	0.194077	−	0.980986i
$290$	−0.393663			−0.0231167
$291$	−7.75858	+	7.75858i	−0.454816	+	0.454816i
$292$	−8.48701	+	20.4894i	−0.496664	+	1.19905i
$293$		−	11.4677i		−	0.669949i	−0.942227	−	0.334974i	$-0.891272\pi$
$293$		−	11.4677i		−	0.669949i	0.942227	−	0.334974i	$-0.108728\pi$
$294$	−0.457678	−	0.189576i	−0.0266923	−	0.0110563i
$295$	−0.302494	−	0.730284i	−0.0176119	−	0.0425188i
$296$	−5.80910	+	2.40621i	−0.337647	+	0.139858i
$297$	−0.472474	−	0.472474i	−0.0274157	−	0.0274157i
$298$	−5.84935	−	5.84935i	−0.338844	−	0.338844i
$299$	28.2194	−	11.6889i	1.63197	−	0.675985i
$300$	2.70231	+	6.52395i	0.156018	+	0.376660i
$301$	−21.1403	−	8.75659i	−1.21851	−	0.504721i
$302$		−	16.6518i		−	0.958203i
$303$	−1.25397	+	3.02734i	−0.0720384	+	0.173916i
$304$	2.13254	−	2.13254i	0.122309	−	0.122309i
$305$	−0.213149			−0.0122049
$306$	2.43835	−	2.00321i	0.139391	−	0.114516i
$307$	10.5245			0.600663			0.300332	−	0.953835i	$-0.402903\pi$
$307$	10.5245			0.600663			0.300332	+	0.953835i	$0.402903\pi$
$308$	1.84776	−	1.84776i	0.105286	−	0.105286i
$309$	4.60093	−	11.1076i	0.261738	−	0.631891i
$310$			0.318059i			0.0180645i
$311$	−5.00208	−	2.07193i	−0.283642	−	0.117488i	0.236327	−	0.971674i	$-0.424056\pi$
$311$	−5.00208	−	2.07193i	−0.283642	−	0.117488i	−0.519969	+	0.854185i	$0.674056\pi$
$312$	−3.28130	−	7.92177i	−0.185767	−	0.448482i
$313$	−0.878944	+	0.364070i	−0.0496808	+	0.0205785i	−0.407386	−	0.913256i	$-0.633559\pi$
$313$	−0.878944	+	0.364070i	−0.0496808	+	0.0205785i	0.357705	+	0.933835i	$0.383559\pi$
$314$	−10.7446	−	10.7446i	−0.606355	−	0.606355i
$315$	0.161111	+	0.161111i	0.00907755	+	0.00907755i
$316$	−10.9382	+	4.53073i	−0.615320	+	0.254874i
$317$	8.25244	+	19.9232i	0.463503	+	1.11900i	0.966949	+	0.254969i	$0.0820654\pi$
$317$	8.25244	+	19.9232i	0.463503	+	1.11900i	−0.503446	+	0.864027i	$0.667935\pi$
$318$	8.02734	+	3.32503i	0.450151	+	0.186459i
$319$			4.17120i			0.233542i
$320$	0.0891807	−	0.215301i	0.00498535	−	0.0120357i
$321$	6.17253	−	6.17253i	0.344517	−	0.344517i
$322$	−19.7019			−1.09795
$323$	−1.46352	+	14.9385i	−0.0814326	+	0.831201i
$324$	−1.41421			−0.0785674
$325$	−11.5854	+	11.5854i	−0.642643	+	0.642643i
$326$	−0.514059	+	1.24105i	−0.0284711	+	0.0687353i
$327$		−	4.26998i		−	0.236130i
$328$	1.15935	+	0.480217i	0.0640142	+	0.0265155i
$329$	−9.40064	−	22.6951i	−0.518274	−	1.25122i
$330$	0.0389281	−	0.0161246i	0.00214292	−	0.000887628i
$331$	−14.6630	−	14.6630i	−0.805952	−	0.805952i	0.178067	−	0.984018i	$-0.443016\pi$
$331$	−14.6630	−	14.6630i	−0.805952	−	0.805952i	−0.984018	+	0.178067i	$0.943016\pi$
$332$	0.899869	+	0.899869i	0.0493867	+	0.0493867i
$333$	−2.22304	+	0.920815i	−0.121822	+	0.0504604i
$334$	2.36049	+	5.69873i	0.129160	+	0.311820i
$335$	−0.0719298	−	0.0297943i	−0.00392995	−	0.00162784i
$336$		−	2.29090i		−	0.124979i
$337$	5.32983	−	12.8674i	0.290335	−	0.700930i	−0.709659	−	0.704545i	$-0.751151\pi$
$337$	5.32983	−	12.8674i	0.290335	−	0.700930i	0.999993	+	0.00361586i	$0.00115097\pi$
$338$	−1.20851	+	1.20851i	−0.0657344	+	0.0657344i
$339$	13.8558			0.752542
$340$	−0.139697	−	0.459666i	−0.00757616	−	0.0249289i
$341$	3.37011			0.182502
$342$	−1.97021	+	1.97021i	−0.106537	+	0.106537i
$343$	−6.72286	+	16.2304i	−0.363000	+	0.876360i
$344$			21.6224i			1.16580i
$345$	0.708578	+	0.293503i	0.0381486	+	0.0158017i
$346$	1.68496	+	4.06786i	0.0905842	+	0.218690i
$347$	14.8646	−	6.15713i	0.797975	−	0.330532i	0.0538302	−	0.998550i	$-0.482857\pi$
$347$	14.8646	−	6.15713i	0.797975	−	0.330532i	0.744145	+	0.668018i	$0.232857\pi$
$348$	6.24264	+	6.24264i	0.334641	+	0.334641i
$349$	−6.57645	−	6.57645i	−0.352029	−	0.352029i	0.508835	−	0.860864i	$-0.330076\pi$
$349$	−6.57645	−	6.57645i	−0.352029	−	0.352029i	−0.860864	+	0.508835i	$0.830076\pi$
$350$	9.76377	−	4.04429i	0.521896	−	0.216176i
$351$	−1.25570	−	3.03153i	−0.0670244	−	0.161811i
$352$	−3.61766	−	1.49848i	−0.192822	−	0.0798695i
$353$		−	27.8142i		−	1.48040i	−0.672385	−	0.740201i	$-0.734730\pi$
$353$		−	27.8142i		−	1.48040i	0.672385	−	0.740201i	$-0.265270\pi$
$354$	2.80996	−	6.78384i	0.149348	−	0.360557i
$355$	0.191565	−	0.191565i	0.0101672	−	0.0101672i
$356$	7.98226			0.423059
$357$	7.23784	+	8.81005i	0.383067	+	0.466277i
$358$	11.1876			0.591282
$359$	−3.28113	+	3.28113i	−0.173172	+	0.173172i	−0.788371	−	0.615200i	$-0.789075\pi$
$359$	−3.28113	+	3.28113i	−0.173172	+	0.173172i	0.615200	+	0.788371i	$0.289075\pi$
$360$	0.0823922	−	0.198912i	0.00434245	−	0.0104836i
$361$			5.74701i			0.302474i
$362$	9.97021	+	4.12979i	0.524022	+	0.217057i
$363$	4.03866	+	9.75020i	0.211975	+	0.511753i
$364$	11.8558	−	4.91082i	0.621411	−	0.257397i
$365$	−0.913631	−	0.913631i	−0.0478216	−	0.0478216i
$366$	−1.40008	−	1.40008i	−0.0731832	−	0.0731832i
$367$	−3.99226	+	1.65365i	−0.208394	+	0.0863197i	−0.484439	−	0.874825i	$-0.660976\pi$
$367$	−3.99226	+	1.65365i	−0.208394	+	0.0863197i	0.276045	+	0.961145i	$0.410976\pi$
$368$	−2.95108	−	7.12453i	−0.153835	−	0.371392i
$369$	0.443663	+	0.183771i	0.0230962	+	0.00956674i
$370$		−	0.151736i		−	0.00788838i
$371$	−12.0138	+	29.0038i	−0.623723	+	1.50580i
$372$	5.04373	−	5.04373i	0.261505	−	0.261505i
$373$	8.44020			0.437017			0.218509	−	0.975835i	$-0.429881\pi$
$373$	8.44020			0.437017			0.218509	+	0.975835i	$0.429881\pi$
$374$	2.01745	−	0.613126i	0.104320	−	0.0317040i
$375$	−0.823363			−0.0425183
$376$	−16.4138	+	16.4138i	−0.846479	+	0.846479i
$377$	−7.83889	+	18.9248i	−0.403723	+	0.974674i
$378$			2.11652i			0.108862i
$379$	−7.07337	−	2.92989i	−0.363335	−	0.150498i	0.193545	−	0.981091i	$-0.438002\pi$
$379$	−7.07337	−	2.92989i	−0.363335	−	0.150498i	−0.556880	+	0.830593i	$0.688002\pi$
$380$	0.162330	+	0.391898i	0.00832733	+	0.0201040i
$381$	−0.585441	+	0.242498i	−0.0299931	+	0.0124235i
$382$	8.66818	+	8.66818i	0.443503	+	0.443503i
$383$	−13.1001	−	13.1001i	−0.669385	−	0.669385i	0.288188	−	0.957574i	$-0.406947\pi$
$383$	−13.1001	−	13.1001i	−0.669385	−	0.669385i	−0.957574	+	0.288188i	$0.906947\pi$
$384$	−8.82843	+	3.65685i	−0.450524	+	0.186613i
$385$	0.0582601	+	0.140652i	0.00296921	+	0.00716830i
$386$	3.24943	+	1.34596i	0.165392	+	0.0685074i
$387$			8.27452i			0.420617i
$388$	−5.93816	+	14.3360i	−0.301464	+	0.727799i
$389$	18.9592	−	18.9592i	0.961270	−	0.961270i	−0.0380079	−	0.999277i	$-0.512101\pi$
$389$	18.9592	−	18.9592i	0.961270	−	0.961270i	0.999277	+	0.0380079i	$0.0121012\pi$
$390$	0.206920			0.0104778
$391$	33.8579	+	18.0750i	1.71227	+	0.914090i
$392$	−1.69136			−0.0854264
$393$	−10.7538	+	10.7538i	−0.542456	+	0.542456i
$394$	6.20024	−	14.9687i	0.312364	−	0.754112i
$395$		−	0.689763i		−	0.0347058i
$396$	−0.873017	−	0.361616i	−0.0438708	−	0.0181719i
$397$	1.20172	+	2.90122i	0.0603128	+	0.145608i	0.951163	−	0.308689i	$-0.0998904\pi$
$397$	1.20172	+	2.90122i	0.0603128	+	0.145608i	−0.890850	+	0.454297i	$0.849890\pi$
$398$	−1.64431	+	0.681096i	−0.0824219	+	0.0341402i
$399$	−7.11860	−	7.11860i	−0.356376	−	0.356376i
$400$	2.92496	+	2.92496i	0.146248	+	0.146248i
$401$	−24.4520	+	10.1283i	−1.22107	+	0.505785i	−0.897751	−	0.440503i	$-0.854800\pi$
$401$	−24.4520	+	10.1283i	−1.22107	+	0.505785i	−0.323323	+	0.946289i	$0.604800\pi$
$402$	−0.276769	−	0.668179i	−0.0138040	−	0.0333257i
$403$	15.2902	+	6.33341i	0.761660	+	0.315490i
$404$			4.63405i			0.230553i
$405$	0.0315301	−	0.0761205i	0.00156674	−	0.00378246i
$406$	9.34277	−	9.34277i	0.463674	−	0.463674i
$407$	−1.60778			−0.0796945
$408$	5.07401	−	9.50461i	0.251201	−	0.470548i
$409$	−31.0443			−1.53504			−0.767521	−	0.641024i	$-0.778510\pi$
$409$	−31.0443			−1.53504			−0.767521	+	0.641024i	$0.778510\pi$
$410$	−0.0214130	+	0.0214130i	−0.00105751	+	0.00105751i
$411$	−0.914027	+	2.20666i	−0.0450856	+	0.108846i
$412$		−	17.0028i		−	0.837668i
$413$	24.5109	+	10.1527i	1.20610	+	0.499583i
$414$	2.72644	+	6.58221i	0.133997	+	0.323498i
$415$	−0.0684984	+	0.0283730i	−0.00336246	+	0.00139277i
$416$	−13.5973	−	13.5973i	−0.666661	−	0.666661i
$417$	1.14178	+	1.14178i	0.0559131	+	0.0559131i
$418$	−1.72002	+	0.712457i	−0.0841291	+	0.0348474i
$419$	14.8249	+	35.7906i	0.724246	+	1.74848i	0.660878	+	0.750493i	$0.270184\pi$
$419$	14.8249	+	35.7906i	0.724246	+	1.74848i	0.0633678	+	0.997990i	$0.479816\pi$
$420$	0.297693	+	0.123309i	0.0145260	+	0.00601685i
$421$		−	19.0379i		−	0.927851i	−0.885874	−	0.463926i	$-0.846440\pi$
$421$		−	19.0379i		−	0.927851i	0.885874	−	0.463926i	$-0.153560\pi$
$422$	−2.22172	+	5.36370i	−0.108151	+	0.261101i
$423$	−6.28130	+	6.28130i	−0.305407	+	0.305407i
$424$	29.6652			1.44067
$425$	−20.4894	−	2.00735i	−0.993884	−	0.0973707i
$426$	2.51660			0.121930
$427$	5.05866	−	5.05866i	0.244806	−	0.244806i
$428$	4.72425	−	11.4053i	0.228355	−	0.551298i
$429$		−	2.19250i		−	0.105855i
$430$	−0.482074	−	0.199682i	−0.0232477	−	0.00962950i
$431$	−4.55599	−	10.9991i	−0.219454	−	0.529810i	0.775360	−	0.631520i	$-0.217569\pi$
$431$	−4.55599	−	10.9991i	−0.219454	−	0.529810i	−0.994814	+	0.101710i	$0.967569\pi$
$432$	−0.765367	+	0.317025i	−0.0368237	+	0.0152529i
$433$	−15.1091	−	15.1091i	−0.726097	−	0.726097i	0.243743	−	0.969840i	$-0.421625\pi$
$433$	−15.1091	−	15.1091i	−0.726097	−	0.726097i	−0.969840	+	0.243743i	$0.921625\pi$
$434$	−7.54847	−	7.54847i	−0.362338	−	0.362338i
$435$	−0.475193	+	0.196831i	−0.0227837	+	0.00943734i
$436$	−2.31090	−	5.57900i	−0.110672	−	0.267186i
$437$	−31.3082	−	12.9683i	−1.49768	−	0.620358i
$438$		−	12.0024i		−	0.573499i
$439$	−8.10801	+	19.5745i	−0.386974	+	0.934238i	0.603603	+	0.797285i	$0.293731\pi$
$439$	−8.10801	+	19.5745i	−0.386974	+	0.934238i	−0.990577	+	0.136953i	$0.956269\pi$
$440$	0.101724	−	0.101724i	0.00484951	−	0.00484951i
$441$	−0.647254			−0.0308216
$442$	10.3054	+	1.00962i	0.490180	+	0.0480228i
$443$	−21.5467			−1.02372			−0.511858	−	0.859070i	$-0.671043\pi$
$443$	−21.5467			−1.02372			−0.511858	+	0.859070i	$0.671043\pi$
$444$	−2.40621	+	2.40621i	−0.114193	+	0.114193i
$445$	−0.177966	+	0.429648i	−0.00843639	+	0.0203672i
$446$			11.9875i			0.567623i
$447$	−9.98547	−	4.13612i	−0.472296	−	0.195632i
$448$	2.99321	+	7.22625i	0.141416	+	0.341408i
$449$	33.4231	−	13.8443i	1.57733	−	0.653352i	0.589344	−	0.807882i	$-0.299386\pi$
$449$	33.4231	−	13.8443i	1.57733	−	0.653352i	0.987988	+	0.154530i	$0.0493863\pi$
$450$	−2.70231	−	2.70231i	−0.127388	−	0.127388i
$451$	0.226890	+	0.226890i	0.0106838	+	0.0106838i
$452$	18.1034	−	7.49869i	0.851514	−	0.352709i
$453$	−8.32589	−	20.1005i	−0.391185	−	0.944403i
$454$	−10.3460	−	4.28544i	−0.485561	−	0.201126i
$455$			0.747628i			0.0350493i
$456$	−3.64047	+	8.78886i	−0.170480	+	0.411576i
$457$	19.9517	−	19.9517i	0.933299	−	0.933299i	−0.0646113	−	0.997911i	$-0.520581\pi$
$457$	19.9517	−	19.9517i	0.933299	−	0.933299i	0.997911	+	0.0646113i	$0.0205808\pi$
$458$	−12.5100			−0.584552
$459$	1.94174	−	3.63726i	0.0906327	−	0.169773i
$460$	1.08464			0.0505718
$461$	20.1202	−	20.1202i	0.937091	−	0.937091i	−0.0610442	−	0.998135i	$-0.519443\pi$
$461$	20.1202	−	20.1202i	0.937091	−	0.937091i	0.998135	+	0.0610442i	$0.0194431\pi$
$462$	−0.541196	+	1.30656i	−0.0251787	+	0.0607868i
$463$			6.05277i			0.281296i	0.990060	+	0.140648i	$0.0449186\pi$
$463$			6.05277i			0.281296i	−0.990060	+	0.140648i	$0.955081\pi$
$464$	4.77791	+	1.97908i	0.221809	+	0.0918763i
$465$	0.159029	+	0.383931i	0.00737481	+	0.0178044i
$466$	−0.253010	+	0.104800i	−0.0117205	+	0.00485478i
$467$	−22.7284	−	22.7284i	−1.05175	−	1.05175i	−0.998586	−	0.0531594i	$-0.983071\pi$
$467$	−22.7284	−	22.7284i	−1.05175	−	1.05175i	−0.0531594	−	0.998586i	$-0.516929\pi$
$468$	−3.28130	−	3.28130i	−0.151678	−	0.151678i
$469$	2.41421	−	1.00000i	0.111478	−	0.0461757i
$470$	−0.214368	−	0.517531i	−0.00988807	−	0.0238719i
$471$	−18.3423	−	7.59761i	−0.845167	−	0.350079i
$472$		−	25.0698i		−	1.15393i
$473$	−2.11580	+	5.10800i	−0.0972846	+	0.234866i
$474$	4.53073	−	4.53073i	0.208103	−	0.208103i
$475$	18.1776			0.834046
$476$	14.2247	+	7.59379i	0.651986	+	0.348061i
$477$	11.3524			0.519789
$478$	5.25584	−	5.25584i	0.240397	−	0.240397i
$479$	−5.95122	+	14.3675i	−0.271918	+	0.656468i	−0.999565	−	0.0294832i	$-0.990614\pi$
$479$	−5.95122	+	14.3675i	−0.271918	+	0.656468i	0.727647	+	0.685952i	$0.240614\pi$
$480$		−	0.482843i		−	0.0220387i
$481$	−7.29449	−	3.02148i	−0.332600	−	0.137767i
$482$	2.74199	+	6.61974i	0.124894	+	0.301521i
$483$	−23.7823	+	9.85097i	−1.08213	+	0.448234i
$484$	10.5535	+	10.5535i	0.479706	+	0.479706i
$485$	−0.639246	−	0.639246i	−0.0290267	−	0.0290267i
$486$	0.707107	−	0.292893i	0.0320750	−	0.0132859i
$487$	7.68112	+	18.5439i	0.348065	+	0.840302i	0.996848	+	0.0793296i	$0.0252780\pi$
$487$	7.68112	+	18.5439i	0.348065	+	0.840302i	−0.648784	+	0.760973i	$0.724722\pi$
$488$	−6.24558	−	2.58701i	−0.282724	−	0.117108i
$489$			1.75511i			0.0793687i
$490$	0.0156196	−	0.0377091i	0.000705622	−	0.00170352i
$491$	3.79777	−	3.79777i	0.171391	−	0.171391i	−0.616199	−	0.787590i	$-0.711328\pi$
$491$	3.79777	−	3.79777i	0.171391	−	0.171391i	0.787590	+	0.616199i	$0.211328\pi$
$492$	0.679129			0.0306175
$493$	−24.6269	+	7.48438i	−1.10914	+	0.337079i
$494$	−9.14267			−0.411348
$495$	0.0389281	−	0.0389281i	0.00174969	−	0.00174969i
$496$	1.59899	−	3.86030i	0.0717968	−	0.173333i
$497$			9.09278i			0.407867i
$498$	−0.636303	−	0.263565i	−0.0285134	−	0.0118106i
$499$	10.7403	+	25.9294i	0.480802	+	1.16076i	0.959228	+	0.282632i	$0.0912074\pi$
$499$	10.7403	+	25.9294i	0.480802	+	1.16076i	−0.478426	+	0.878128i	$0.658793\pi$
$500$	−1.07578	+	0.445601i	−0.0481101	+	0.0199279i
$501$	5.69873	+	5.69873i	0.254600	+	0.254600i
$502$	−1.77619	−	1.77619i	−0.0792751	−	0.0792751i
$503$	−8.10170	+	3.35583i	−0.361237	+	0.149629i	−0.555917	−	0.831238i	$-0.687633\pi$
$503$	−8.10170	+	3.35583i	−0.361237	+	0.149629i	0.194681	+	0.980867i	$0.437633\pi$
$504$	2.76537	+	6.67619i	0.123179	+	0.297381i
$505$	−0.249429	−	0.103317i	−0.0110995	−	0.00459754i
$506$			4.76046i			0.211628i
$507$	−0.854548	+	2.06306i	−0.0379518	+	0.0916237i
$508$	−0.633677	+	0.633677i	−0.0281149	+	0.0281149i
$509$	13.5248			0.599475			0.299737	−	0.954022i	$-0.403101\pi$
$509$	13.5248			0.599475			0.299737	+	0.954022i	$0.403101\pi$
$510$	0.165049	+	0.200901i	0.00730848	+	0.00889603i
$511$	43.3663			1.91841
$512$	−6.49435	+	6.49435i	−0.287013	+	0.287013i
$513$	−1.39315	+	3.36335i	−0.0615089	+	0.148496i
$514$		−	2.71323i		−	0.119675i
$515$	0.915181	+	0.379081i	0.0403277	+	0.0167043i
$516$	4.47814	+	10.8112i	0.197139	+	0.475935i
$517$	−5.48369	+	2.27142i	−0.241172	+	0.0998969i
$518$	3.60114	+	3.60114i	0.158225	+	0.158225i
$519$	4.06786	+	4.06786i	0.178559	+	0.178559i
$520$	0.652692	−	0.270354i	0.0286224	−	0.0118558i
$521$	3.56799	+	8.61389i	0.156316	+	0.377381i	0.982564	−	0.185926i	$-0.0595286\pi$
$521$	3.56799	+	8.61389i	0.156316	+	0.377381i	−0.826247	+	0.563308i	$0.809529\pi$
$522$	−4.41421	−	1.82843i	−0.193205	−	0.0800281i
$523$		−	17.0634i		−	0.746129i	−0.927805	−	0.373065i	$-0.878307\pi$
$523$		−	17.0634i		−	0.746129i	0.927805	−	0.373065i	$-0.121693\pi$
$524$	−8.23059	+	19.8704i	−0.359555	+	0.868042i
$525$	9.76377	−	9.76377i	0.426126	−	0.426126i
$526$	−10.3426			−0.450960
$527$	6.04699	+	19.8972i	0.263411	+	0.866737i
$528$	−0.553537			−0.0240896
$529$	−45.0080	+	45.0080i	−1.95687	+	1.95687i
$530$	−0.273957	+	0.661390i	−0.0118999	+	0.0287290i
$531$		−	9.59379i		−	0.416335i
$532$	−13.1535	−	5.44834i	−0.570275	−	0.236216i
$533$	0.603009	+	1.45579i	0.0261192	+	0.0630574i
$534$	−3.99113	+	1.65318i	−0.172713	+	0.0715401i
$535$	0.508568	+	0.508568i	0.0219873	+	0.0219873i
$536$	−1.74603	−	1.74603i	−0.0754172	−	0.0754172i
$537$	13.5046	−	5.59379i	0.582767	−	0.241390i
$538$	−1.51395	−	3.65500i	−0.0652710	−	0.157578i
$539$	−0.399561	−	0.165503i	−0.0172103	−	0.00712874i
$540$		−	0.116520i		−	0.00501423i
$541$	−1.45834	+	3.52074i	−0.0626988	+	0.151368i	−0.952124	−	0.305713i	$-0.901105\pi$
$541$	−1.45834	+	3.52074i	−0.0626988	+	0.151368i	0.889425	+	0.457081i	$0.151105\pi$
$542$	−3.61839	+	3.61839i	−0.155423	+	0.155423i
$543$	14.1000			0.605089
$544$	2.35593	−	24.0475i	0.101010	−	1.03103i
$545$	0.351813			0.0150700
$546$	−4.91082	+	4.91082i	−0.210164	+	0.210164i
$547$	9.98266	−	24.1003i	0.426828	−	1.03045i	−0.553460	−	0.832876i	$-0.686693\pi$
$547$	9.98266	−	24.1003i	0.426828	−	1.03045i	0.980287	−	0.197577i	$-0.0633072\pi$
$548$			3.37780i			0.144293i
$549$	−2.39008	−	0.990004i	−0.102006	−	0.0422523i
$550$	−0.977196	−	2.35916i	−0.0416678	−	0.100595i
$551$	20.9962	−	8.69691i	0.894468	−	0.370501i
$552$	17.2001	+	17.2001i	0.732086	+	0.732086i
$553$	16.3701	+	16.3701i	0.696128	+	0.696128i
$554$	−2.05174	+	0.849857i	−0.0871699	+	0.0361070i
$555$	−0.0758680	−	0.183162i	−0.00322042	−	0.00777477i
$556$	2.10973	+	0.873879i	0.0894726	+	0.0370607i
$557$			2.00763i			0.0850662i	0.999095	+	0.0425331i	$0.0135428\pi$
$557$			2.00763i			0.0850662i	−0.999095	+	0.0425331i	$0.986457\pi$
$558$	−1.47727	+	3.56645i	−0.0625380	+	0.150980i
$559$	−19.1988	+	19.1988i	−0.812023	+	0.812023i
$560$	0.188753			0.00797626
$561$	2.12872	−	1.74884i	0.0898746	−	0.0738359i
$562$	−17.5428			−0.739997
$563$	19.7305	−	19.7305i	0.831541	−	0.831541i	−0.156187	−	0.987728i	$-0.549920\pi$
$563$	19.7305	−	19.7305i	0.831541	−	0.831541i	0.987728	+	0.156187i	$0.0499201\pi$
$564$	−4.80750	+	11.6063i	−0.202432	+	0.488715i
$565$			1.14161i			0.0480278i
$566$	19.6016	+	8.11926i	0.823918	+	0.341278i
$567$	1.05826	+	2.55487i	0.0444427	+	0.107294i
$568$	7.93816	−	3.28809i	0.333078	−	0.137965i
$569$	−16.1310	−	16.1310i	−0.676246	−	0.676246i	0.282903	−	0.959149i	$-0.408703\pi$
$569$	−16.1310	−	16.1310i	−0.676246	−	0.676246i	−0.959149	+	0.282903i	$0.908703\pi$
$570$	−0.162330	−	0.162330i	−0.00679924	−	0.00679924i
$571$	14.5140	−	6.01188i	0.607391	−	0.251590i	−0.0577217	−	0.998333i	$-0.518384\pi$
$571$	14.5140	−	6.01188i	0.607391	−	0.251590i	0.665112	+	0.746743i	$0.268384\pi$
$572$	−1.18657	−	2.86464i	−0.0496130	−	0.119776i
$573$	14.7975	+	6.12933i	0.618175	+	0.256056i
$574$		−	1.01639i		−	0.0424233i
$575$	17.7871	−	42.9419i	0.741775	−	1.79080i
$576$	2.00000	−	2.00000i	0.0833333	−	0.0833333i
$577$	−29.1062			−1.21171			−0.605853	−	0.795577i	$-0.707168\pi$
$577$	−29.1062			−1.21171			−0.605853	+	0.795577i	$0.707168\pi$
$578$	7.23983	+	10.8110i	0.301137	+	0.449677i
$579$	4.59539			0.190978
$580$	−0.514345	+	0.514345i	−0.0213570	+	0.0213570i
$581$	0.952295	−	2.29904i	0.0395079	−	0.0953804i
$582$		−	8.39782i		−	0.348101i
$583$	7.00801	+	2.90281i	0.290242	+	0.120222i
$584$	−15.6819	−	37.8596i	−0.648923	−	1.56664i
$585$	0.249774	−	0.103460i	0.0103269	−	0.00427754i
$586$	6.20626	+	6.20626i	0.256378	+	0.256378i
$587$	−13.4482	−	13.4482i	−0.555067	−	0.555067i	0.372832	−	0.927899i	$-0.378387\pi$
$587$	−13.4482	−	13.4482i	−0.555067	−	0.555067i	−0.927899	+	0.372832i	$0.878387\pi$
$588$	−0.845678	+	0.350291i	−0.0348752	+	0.0144458i
$589$	−7.02665	−	16.9638i	−0.289528	−	0.698982i
$590$	0.558935	+	0.231519i	0.0230110	+	0.00953147i
$591$		−	21.1689i		−	0.870774i
$592$	−0.762828	+	1.84163i	−0.0313520	+	0.0756905i
$593$	−7.38393	+	7.38393i	−0.303222	+	0.303222i	−0.842273	−	0.539051i	$-0.818783\pi$
$593$	−7.38393	+	7.38393i	−0.303222	+	0.303222i	0.539051	+	0.842273i	$0.318783\pi$
$594$	0.511402			0.0209831
$595$	−0.725879	+	0.596342i	−0.0297582	+	0.0244476i
$596$	−15.2851			−0.626102
$597$	−1.64431	+	1.64431i	−0.0672972	+	0.0672972i
$598$	−8.94628	+	21.5982i	−0.365840	+	0.883217i
$599$			22.1338i			0.904361i	0.891927	+	0.452180i	$0.149354\pi$
$599$			22.1338i			0.904361i	−0.891927	+	0.452180i	$0.850646\pi$
$600$	−12.0547	−	4.99321i	−0.492130	−	0.203847i
$601$	1.13638	+	2.74347i	0.0463539	+	0.111908i	0.945361	−	0.326027i	$-0.105710\pi$
$601$	1.13638	+	2.74347i	0.0463539	+	0.111908i	−0.899007	+	0.437935i	$0.855710\pi$
$602$	16.1801	−	6.70200i	0.659450	−	0.273153i
$603$	−0.668179	−	0.668179i	−0.0272103	−	0.0272103i
$604$	−21.7566	−	21.7566i	−0.885264	−	0.885264i
$605$	−0.803340	+	0.332754i	−0.0326604	+	0.0135284i
$606$	−0.959743	−	2.31703i	−0.0389869	−	0.0941227i
$607$	−27.3900	−	11.3453i	−1.11172	−	0.460491i	−0.250193	−	0.968196i	$-0.580494\pi$
$607$	−27.3900	−	11.3453i	−1.11172	−	0.460491i	−0.861531	+	0.507705i	$0.830494\pi$
$608$			21.3342i			0.865217i
$609$	6.60634	−	15.9491i	0.267702	−	0.646291i
$610$	0.115355	−	0.115355i	0.00467061	−	0.00467061i
$611$	−29.1482			−1.17921
$612$	0.568536	−	5.80317i	0.0229817	−	0.234579i
$613$	30.3538			1.22598			0.612988	−	0.790092i	$-0.289967\pi$
$613$	30.3538			1.22598			0.612988	+	0.790092i	$0.289967\pi$
$614$	−5.69580	+	5.69580i	−0.229864	+	0.229864i
$615$	−0.0151413	+	0.0365543i	−0.000610556	+	0.00147401i
$616$			4.82843i			0.194543i
$617$	32.7767	+	13.5765i	1.31954	+	0.546571i	0.927653	−	0.373443i	$-0.121823\pi$
$617$	32.7767	+	13.5765i	1.31954	+	0.546571i	0.391886	+	0.920014i	$0.371823\pi$
$618$	3.52140	+	8.50141i	0.141651	+	0.341977i
$619$	−24.2079	+	10.0272i	−0.972997	+	0.403028i	−0.811827	−	0.583898i	$-0.801527\pi$
$619$	−24.2079	+	10.0272i	−0.972997	+	0.403028i	−0.161170	+	0.986927i	$0.551527\pi$
$620$	0.415564	+	0.415564i	0.0166894	+	0.0166894i
$621$	6.58221	+	6.58221i	0.264135	+	0.264135i
$622$	3.82843	−	1.58579i	0.153506	−	0.0635842i
$623$	−5.97315	−	14.4205i	−0.239309	−	0.577743i
$624$	−2.51140	−	1.04026i	−0.100537	−	0.0416436i
$625$			24.8982i			0.995929i
$626$	0.278647	−	0.672715i	0.0111370	−	0.0268871i
$627$	−1.72002	+	1.72002i	−0.0686911	+	0.0686911i
$628$	−28.0771			−1.12040
$629$	−2.88483	−	9.49236i	−0.115026	−	0.378485i
$630$	−0.174385			−0.00694765
$631$	0.310259	−	0.310259i	0.0123512	−	0.0123512i	−0.700904	−	0.713255i	$-0.747220\pi$
$631$	0.310259	−	0.310259i	0.0123512	−	0.0123512i	0.713255	+	0.700904i	$0.247220\pi$
$632$	8.37170	−	20.2111i	0.333009	−	0.803954i
$633$			7.58541i			0.301493i
$634$	−15.2485	−	6.31615i	−0.605596	−	0.250846i
$635$	−0.0199799	−	0.0482358i	−0.000792879	−	0.00191418i
$636$	14.8326	−	6.14386i	0.588150	−	0.243620i
$637$	−1.50178	−	1.50178i	−0.0595027	−	0.0595027i
$638$	−2.25744	−	2.25744i	−0.0893728	−	0.0893728i
$639$	3.03780	−	1.25830i	0.120174	−	0.0497775i
$640$	−0.301296	−	0.727394i	−0.0119098	−	0.0287528i
$641$	−4.42347	−	1.83226i	−0.174717	−	0.0723699i	0.293611	−	0.955925i	$-0.405143\pi$
$641$	−4.42347	−	1.83226i	−0.174717	−	0.0723699i	−0.468327	+	0.883555i	$0.655143\pi$
$642$			6.68110i			0.263682i
$643$	7.85802	−	18.9709i	0.309890	−	0.748141i	−0.689818	−	0.723983i	$-0.742310\pi$
$643$	7.85802	−	18.9709i	0.309890	−	0.748141i	0.999708	−	0.0241580i	$-0.00769048\pi$
$644$	−25.7418	+	25.7418i	−1.01437	+	1.01437i
$645$	−0.681756			−0.0268441
$646$	−7.29261	−	8.87671i	−0.286924	−	0.349250i
$647$	18.7594			0.737508			0.368754	−	0.929527i	$-0.379784\pi$
$647$	18.7594			0.737508			0.368754	+	0.929527i	$0.379784\pi$
$648$	1.84776	−	1.84776i	0.0725868	−	0.0725868i
$649$	2.45314	−	5.92241i	0.0962942	−	0.232475i
$650$		−	12.5400i		−	0.491858i
$651$	−12.8860	−	5.33758i	−0.505044	−	0.209196i
$652$	0.949857	+	2.29316i	0.0371993	+	0.0898070i
$653$	13.1354	−	5.44085i	0.514027	−	0.212917i	−0.110564	−	0.993869i	$-0.535266\pi$
$653$	13.1354	−	5.44085i	0.514027	−	0.212917i	0.624591	+	0.780952i	$0.285266\pi$
$654$	2.31090	+	2.31090i	0.0903632	+	0.0903632i
$655$	−0.886027	−	0.886027i	−0.0346200	−	0.0346200i
$656$	0.367542	−	0.152241i	0.0143501	−	0.00594401i
$657$	−6.00122	−	14.4882i	−0.234130	−	0.565239i
$658$	17.3701	+	7.19494i	0.677157	+	0.280488i
$659$			34.5061i			1.34417i	0.740475	+	0.672084i	$0.234601\pi$
$659$			34.5061i			1.34417i	−0.740475	+	0.672084i	$0.765399\pi$
$660$	0.0297943	−	0.0719298i	0.00115974	−	0.00279986i
$661$	9.03386	−	9.03386i	0.351377	−	0.351377i	−0.509245	−	0.860622i	$-0.670075\pi$
$661$	9.03386	−	9.03386i	0.351377	−	0.351377i	0.860622	+	0.509245i	$0.170075\pi$
$662$	15.8711			0.616849
$663$	12.9446	−	3.93400i	0.502726	−	0.152784i
$664$	−2.35147			−0.0912547
$665$	0.586517	−	0.586517i	0.0227442	−	0.0227442i
$666$	0.704761	−	1.70144i	0.0273090	−	0.0659296i
$667$		−	58.1105i		−	2.25005i
$668$	10.5299	+	4.36162i	0.407413	+	0.168756i
$669$	5.99373	+	14.4701i	0.231731	+	0.559448i
$670$	0.0550527	−	0.0228036i	0.00212687	−	0.000880979i
$671$	−1.22229	−	1.22229i	−0.0471861	−	0.0471861i
$672$	11.4593	+	11.4593i	0.442052	+	0.442052i
$673$	−31.2863	+	12.9592i	−1.20600	+	0.499541i	−0.892933	−	0.450190i	$-0.851356\pi$
$673$	−31.2863	+	12.9592i	−1.20600	+	0.499541i	−0.313066	+	0.949731i	$0.601356\pi$
$674$	4.07928	+	9.84825i	0.157128	+	0.379340i
$675$	−4.61313	−	1.91082i	−0.177559	−	0.0735475i
$676$			3.15800i			0.121461i
$677$	13.6588	−	32.9752i	0.524950	−	1.26734i	−0.409845	−	0.912155i	$-0.634417\pi$
$677$	13.6588	−	32.9752i	0.524950	−	1.26734i	0.934795	−	0.355186i	$-0.115583\pi$
$678$	−7.49869	+	7.49869i	−0.287985	+	0.287985i
$679$	30.3424			1.16443
$680$	0.783106	+	0.418059i	0.0300307	+	0.0160318i
$681$	−14.6314			−0.560677
$682$	−1.82389	+	1.82389i	−0.0698404	+	0.0698404i
$683$	−8.52097	+	20.5715i	−0.326046	+	0.787145i	0.672832	+	0.739795i	$0.265078\pi$
$683$	−8.52097	+	20.5715i	−0.326046	+	0.787145i	−0.998878	+	0.0473497i	$0.984922\pi$
$684$			5.14840i			0.196854i
$685$	−0.181811	−	0.0753087i	−0.00694665	−	0.00287740i
$686$	−5.14545	−	12.4222i	−0.196454	−	0.474283i
$687$	−15.1009	+	6.25498i	−0.576134	+	0.238642i
$688$	4.84710	+	4.84710i	0.184794	+	0.184794i
$689$	26.3401	+	26.3401i	1.00348	+	1.00348i
$690$	−0.542322	+	0.224637i	−0.0206459	+	0.00855180i
$691$	11.1052	+	26.8103i	0.422462	+	1.01991i	0.981619	+	0.190851i	$0.0611247\pi$
$691$	11.1052	+	26.8103i	0.422462	+	1.01991i	−0.559157	+	0.829061i	$0.688875\pi$
$692$	7.51643	+	3.11341i	0.285732	+	0.118354i
$693$			1.84776i			0.0701906i
$694$	−4.71247	+	11.3769i	−0.178883	+	0.431861i
$695$	−0.0940736	+	0.0940736i	−0.00356842	+	0.00356842i
$696$	−16.3128			−0.618335
$697$	−0.932456	+	1.74667i	−0.0353193	+	0.0661600i
$698$	7.11830			0.269432
$699$	−0.253010	+	0.253010i	−0.00956973	+	0.00956973i
$700$	7.47287	−	18.0411i	0.282448	−	0.681890i
$701$			33.5632i			1.26766i	0.773471	+	0.633832i	$0.218519\pi$
$701$			33.5632i			1.26766i	−0.773471	+	0.633832i	$0.781481\pi$
$702$	2.32023	+	0.961072i	0.0875715	+	0.0362733i
$703$	3.35220	+	8.09292i	0.126430	+	0.305230i
$704$	1.74603	−	0.723231i	0.0658062	−	0.0272578i
$705$	−0.517531	−	0.517531i	−0.0194913	−	0.0194913i
$706$	15.0530	+	15.0530i	0.566525	+	0.566525i
$707$	8.37170	−	3.46767i	0.314850	−	0.130415i
$708$	−5.19212	−	12.5349i	−0.195132	−	0.471090i
$709$	38.5480	+	15.9671i	1.44770	+	0.599657i	0.961651	−	0.274275i	$-0.0884380\pi$
$709$	38.5480	+	15.9671i	1.44770	+	0.599657i	0.486048	+	0.873932i	$0.338438\pi$
$710$			0.207348i			0.00778163i
$711$	3.20371	−	7.73445i	0.120149	−	0.290064i
$712$	−10.4293	+	10.4293i	−0.390856	+	0.390856i
$713$	−46.9503			−1.75830
$714$	−8.68506	−	0.850874i	−0.325030	−	0.0318431i
$715$	0.180645			0.00675573
$716$	14.6173	−	14.6173i	0.546274	−	0.546274i
$717$	3.71644	−	8.97229i	0.138793	−	0.335076i
$718$		−	3.55147i		−	0.132540i
$719$	−46.8015	−	19.3858i	−1.74540	−	0.722969i	−0.998302	−	0.0582565i	$-0.981446\pi$
$719$	−46.8015	−	19.3858i	−1.74540	−	0.722969i	−0.747099	−	0.664712i	$-0.768554\pi$
$720$	−0.0261204	−	0.0630603i	−0.000973450	−	0.00235012i
$721$	−30.7167	+	12.7233i	−1.14395	+	0.473839i
$722$	−3.11026	−	3.11026i	−0.115752	−	0.115752i
$723$	6.61974	+	6.61974i	0.246191	+	0.246191i
$724$	18.4225	−	7.63087i	0.684668	−	0.283599i
$725$	11.9286	+	28.7981i	0.443016	+	1.06953i
$726$	−7.46248	−	3.09106i	−0.276959	−	0.114720i
$727$			11.4948i			0.426317i	0.977018	+	0.213159i	$0.0683751\pi$
$727$			11.4948i			0.426317i	−0.977018	+	0.213159i	$0.931625\pi$
$728$	−9.07401	+	21.9066i	−0.336305	+	0.811913i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	0.988907			0.0366011
$731$	−33.9541	−	3.32648i	−1.25584	−	0.123034i
$732$	−3.65858			−0.135225
$733$	34.2720	−	34.2720i	1.26587	−	1.26587i	0.317663	−	0.948204i	$-0.397102\pi$
$733$	34.2720	−	34.2720i	1.26587	−	1.26587i	0.948204	−	0.317663i	$-0.102898\pi$
$734$	1.26565	−	3.05554i	0.0467159	−	0.112782i
$735$		−	0.0533287i		−	0.00196706i
$736$	50.3990	+	20.8759i	1.85773	+	0.769498i
$737$	−0.241624	−	0.583332i	−0.00890033	−	0.0214873i
$738$	−0.339565	+	0.140652i	−0.0124995	+	0.00517748i
$739$	1.77139	+	1.77139i	0.0651615	+	0.0651615i	0.738937	−	0.673775i	$-0.235328\pi$
$739$	1.77139	+	1.77139i	0.0651615	+	0.0651615i	−0.673775	+	0.738937i	$0.735328\pi$
$740$	−0.198253	−	0.198253i	−0.00728791	−	0.00728791i
$741$	−11.0362	+	4.57134i	−0.405424	+	0.167932i
$742$	−9.19494	−	22.1985i	−0.337557	−	0.814934i
$743$	13.0270	+	5.39595i	0.477913	+	0.197958i	0.608618	−	0.793463i	$-0.291724\pi$
$743$	13.0270	+	5.39595i	0.477913	+	0.197958i	−0.130705	+	0.991421i	$0.541724\pi$
$744$			13.1799i			0.483198i
$745$	0.340784	−	0.822725i	0.0124853	−	0.0301423i
$746$	−4.56780	+	4.56780i	−0.167239	+	0.167239i
$747$	−0.899869			−0.0329245
$748$	1.83484	−	3.43702i	0.0670885	−	0.125670i
$749$	−24.1396			−0.882043
$750$	0.445601	−	0.445601i	0.0162710	−	0.0162710i
$751$	−8.55723	+	20.6590i	−0.312258	+	0.753857i	0.687363	+	0.726314i	$0.258768\pi$
$751$	−8.55723	+	20.6590i	−0.312258	+	0.753857i	−0.999621	+	0.0275426i	$0.991232\pi$
$752$			7.35901i			0.268355i
$753$	−3.03214	−	1.25595i	−0.110497	−	0.0457695i
$754$	−5.99963	−	14.4844i	−0.218494	−	0.527490i
$755$	1.65612	−	0.685989i	0.0602725	−	0.0249657i
$756$	2.76537	+	2.76537i	0.100575	+	0.100575i
$757$	6.47088	+	6.47088i	0.235188	+	0.235188i	0.814854	−	0.579666i	$-0.196817\pi$
$757$	6.47088	+	6.47088i	0.235188	+	0.235188i	−0.579666	+	0.814854i	$0.696817\pi$
$758$	5.41373	−	2.24244i	0.196635	−	0.0814490i
$759$	2.38023	+	5.74638i	0.0863968	+	0.208580i
$760$	−0.724134	−	0.299946i	−0.0262671	−	0.0108802i
$761$		−	29.3561i		−	1.06416i	−0.846694	−	0.532079i	$-0.821411\pi$
$761$		−	29.3561i		−	1.06416i	0.846694	−	0.532079i	$-0.178589\pi$
$762$	0.185600	−	0.448077i	0.00672357	−	0.0162321i
$763$	−8.34956	+	8.34956i	−0.302274	+	0.302274i
$764$	22.6510			0.819486
$765$	0.299682	+	0.159984i	0.0108350	+	0.00578424i
$766$	14.1795			0.512325
$767$	22.2598	−	22.2598i	0.803756	−	0.803756i
$768$	4.96362	−	11.9832i	0.179109	−	0.432408i
$769$			17.3301i			0.624939i	0.949928	+	0.312470i	$0.101156\pi$
$769$			17.3301i			0.624939i	−0.949928	+	0.312470i	$0.898844\pi$
$770$	−0.107651	−	0.0445903i	−0.00387946	−	0.00160692i
$771$	−1.35661	−	3.27515i	−0.0488572	−	0.117952i
$772$	6.00416	−	2.48701i	0.216095	−	0.0895093i
$773$	32.2079	+	32.2079i	1.15844	+	1.15844i	0.984812	+	0.173626i	$0.0555483\pi$
$773$	32.2079	+	32.2079i	1.15844	+	1.15844i	0.173626	+	0.984812i	$0.444452\pi$
$774$	−4.47814	−	4.47814i	−0.160963	−	0.160963i
$775$	23.2674	−	9.63765i	0.835788	−	0.346195i
$776$	−10.9723	−	26.4894i	−0.393882	−	0.950916i
$777$	6.14753	+	2.54639i	0.220542	+	0.0913513i
$778$			20.5213i			0.735724i
$779$	0.669012	−	1.61514i	0.0239698	−	0.0578683i
$780$	0.270354	−	0.270354i	0.00968022	−	0.00968022i
$781$	2.19703			0.0786160
$782$	−28.1059	+	8.54168i	−1.00506	+	0.305450i
$783$	−6.24264			−0.223094
$784$	−0.379153	+	0.379153i	−0.0135412	+	0.0135412i
$785$	0.625984	−	1.51126i	0.0223423	−	0.0539391i
$786$		−	11.6398i		−	0.415178i
$787$	−30.8805	−	12.7911i	−1.10077	−	0.455954i	−0.243020	−	0.970021i	$-0.578138\pi$
$787$	−30.8805	−	12.7911i	−1.10077	−	0.455954i	−0.857750	+	0.514067i	$0.828138\pi$
$788$	−11.4566	−	27.6586i	−0.408123	−	0.985295i
$789$	−12.4846	+	5.17131i	−0.444465	+	0.184103i
$790$	0.373297	+	0.373297i	0.0132813	+	0.0132813i
$791$	−27.0937	−	27.0937i	−0.963341	−	0.963341i
$792$	1.61313	−	0.668179i	0.0573199	−	0.0237427i
$793$	−3.24851	−	7.84259i	−0.115358	−	0.278498i
$794$	−2.22050	−	0.919760i	−0.0788025	−	0.0326411i
$795$			0.935347i			0.0331733i
$796$	−1.25850	+	3.03829i	−0.0446064	+	0.107689i
$797$	−7.00506	+	7.00506i	−0.248132	+	0.248132i	−0.820204	−	0.572072i	$-0.806140\pi$
$797$	−7.00506	+	7.00506i	−0.248132	+	0.248132i	0.572072	+	0.820204i	$0.306140\pi$
$798$	7.70512			0.272758
$799$	−23.2499	−	28.3003i	−0.822522	−	1.00119i
$800$	−29.2617			−1.03456
$801$	−3.99113	+	3.99113i	−0.141020	+	0.141020i
$802$	7.75190	−	18.7147i	0.273729	−	0.660840i
$803$		−	10.4783i		−	0.369773i
$804$	−1.23463	−	0.511402i	−0.0435422	−	0.0180358i
$805$	−0.811643	−	1.95948i	−0.0286066	−	0.0690626i
$806$	−11.7026	+	4.84739i	−0.412207	+	0.170742i
$807$	−3.65500	−	3.65500i	−0.128662	−	0.128662i
$808$	−6.05468	−	6.05468i	−0.213003	−	0.213003i
$809$	−3.89409	+	1.61298i	−0.136909	+	0.0567095i	−0.450086	−	0.892985i	$-0.648607\pi$
$809$	−3.89409	+	1.61298i	−0.136909	+	0.0567095i	0.313177	+	0.949695i	$0.398607\pi$
$810$	0.0241321	+	0.0582601i	0.000847916	+	0.00204705i
$811$	23.1219	+	9.57741i	0.811920	+	0.336308i	0.749720	−	0.661756i	$-0.230188\pi$
$811$	23.1219	+	9.57741i	0.811920	+	0.336308i	0.0622001	+	0.998064i	$0.480188\pi$
$812$		−	24.4138i		−	0.856758i
$813$	−2.55859	+	6.17698i	−0.0897337	+	0.216636i
$814$	0.870122	−	0.870122i	0.0304978	−	0.0304978i
$815$	−0.144607			−0.00506537
$816$	−0.993212	−	3.26810i	−0.0347694	−	0.114406i
$817$	30.1231			1.05387
$818$	16.8010	−	16.8010i	0.587435	−	0.587435i
$819$	−3.47247	+	8.38329i	−0.121338	+	0.292936i
$820$			0.0559550i			0.00195403i
$821$	−19.5063	−	8.07979i	−0.680776	−	0.281987i	0.0153751	−	0.999882i	$-0.495106\pi$
$821$	−19.5063	−	8.07979i	−0.680776	−	0.281987i	−0.696151	+	0.717895i	$0.745106\pi$
$822$	−0.699566	−	1.68890i	−0.0244002	−	0.0589072i
$823$	−23.3711	+	9.68061i	−0.814664	+	0.337445i	−0.750813	−	0.660515i	$-0.770338\pi$
$823$	−23.3711	+	9.68061i	−0.814664	+	0.337445i	−0.0638509	+	0.997959i	$0.520338\pi$
$824$	22.2152	+	22.2152i	0.773905	+	0.773905i
$825$	−2.35916	−	2.35916i	−0.0821354	−	0.0821354i
$826$	−18.7598	+	7.77056i	−0.652737	+	0.270372i
$827$	−6.83057	−	16.4904i	−0.237522	−	0.573429i	0.759503	−	0.650504i	$-0.225442\pi$
$827$	−6.83057	−	16.4904i	−0.237522	−	0.573429i	−0.997025	+	0.0770744i	$0.975442\pi$
$828$	12.1623	+	5.03780i	0.422670	+	0.175076i
$829$			8.81114i			0.306023i	0.988224	+	0.153012i	$0.0488972\pi$
$829$			8.81114i			0.306023i	−0.988224	+	0.153012i	$0.951103\pi$
$830$	0.0217157	−	0.0524264i	0.000753764	−	0.00181975i
$831$	−2.05174	+	2.05174i	−0.0711739	+	0.0711739i
$832$	9.28093			0.321758
$833$	0.260206	−	2.65598i	0.00901560	−	0.0920243i
$834$	−1.23585			−0.0427941
$835$	−0.469531	+	0.469531i	−0.0162488	+	0.0162488i
$836$	−1.31645	+	3.17819i	−0.0455304	+	0.109920i
$837$			5.04373i			0.174337i
$838$	−27.3929	−	11.3465i	−0.946273	−	0.391959i
$839$	3.76419	+	9.08756i	0.129954	+	0.313737i	0.975442	−	0.220258i	$-0.0706899\pi$
$839$	3.76419	+	9.08756i	0.129954	+	0.313737i	−0.845487	+	0.533995i	$0.820690\pi$
$840$	−0.550066	+	0.227845i	−0.0189791	+	0.00786139i
$841$	7.05025	+	7.05025i	0.243112	+	0.243112i
$842$	10.3032	+	10.3032i	0.355073	+	0.355073i
$843$	−21.1760	+	8.77139i	−0.729340	+	0.302103i
$844$	4.10520	+	9.91082i	0.141307	+	0.341144i
$845$	−0.169980	−	0.0704081i	−0.00584749	−	0.00242211i
$846$		−	6.79884i		−	0.233749i
$847$	11.1684	−	26.9629i	0.383750	−	0.926455i
$848$	6.65007	−	6.65007i	0.228364	−	0.228364i
$849$	27.7209			0.951379
$850$	12.1752	−	10.0024i	0.417605	−	0.343081i
$851$	22.3985			0.767811
$852$	3.28809	−	3.28809i	0.112648	−	0.112648i
$853$	20.2420	−	48.8685i	0.693073	−	1.67323i	−0.0454226	−	0.998968i	$-0.514463\pi$
$853$	20.2420	−	48.8685i	0.693073	−	1.67323i	0.738496	−	0.674258i	$-0.235537\pi$
$854$			5.47545i			0.187366i
$855$	−0.277114	−	0.114784i	−0.00947710	−	0.00392554i
$856$	8.72927	+	21.0743i	0.298360	+	0.720306i
$857$	−44.3924	+	18.3879i	−1.51641	+	0.628119i	−0.976869	−	0.213837i	$-0.931404\pi$
$857$	−44.3924	+	18.3879i	−1.51641	+	0.628119i	−0.539545	+	0.841957i	$0.681404\pi$
$858$	1.18657	+	1.18657i	0.0405089	+	0.0405089i
$859$	−12.7938	−	12.7938i	−0.436518	−	0.436518i	0.454320	−	0.890838i	$-0.349882\pi$
$859$	−12.7938	−	12.7938i	−0.436518	−	0.436518i	−0.890838	+	0.454320i	$0.849882\pi$
$860$	−0.890757	+	0.368963i	−0.0303745	+	0.0125815i
$861$	−0.508194	−	1.22689i	−0.0173192	−	0.0418123i
$862$	8.41838	+	3.48701i	0.286731	+	0.118768i
$863$			29.4477i			1.00241i	0.865328	+	0.501206i	$0.167110\pi$
$863$			29.4477i			1.00241i	−0.865328	+	0.501206i	$0.832890\pi$
$864$	2.24264	−	5.41421i	0.0762962	−	0.184195i
$865$	−0.335160	+	0.335160i	−0.0113958	+	0.0113958i
$866$	16.3540			0.555730
$867$	14.1447	+	9.43009i	0.480380	+	0.320262i
$868$	−19.7251			−0.669514
$869$	3.95541	−	3.95541i	0.134178	−	0.134178i
$870$	0.150648	−	0.363697i	0.00510745	−	0.0123305i
$871$		−	3.10066i		−	0.105062i
$872$	10.3086	+	4.26998i	0.349095	+	0.144600i
$873$	−4.19891	−	10.1371i	−0.142112	−	0.343088i
$874$	23.9623	−	9.92551i	0.810537	−	0.335735i
$875$	1.61001	+	1.61001i	0.0544283	+	0.0544283i
$876$	−15.6819	−	15.6819i	−0.529844	−	0.529844i
$877$	−32.9977	+	13.6681i	−1.11425	+	0.461539i	−0.862401	−	0.506227i	$-0.831040\pi$
$877$	−32.9977	+	13.6681i	−1.11425	+	0.461539i	−0.251853	+	0.967765i	$0.581040\pi$
$878$	−6.20560	−	14.9816i	−0.209429	−	0.505606i
$879$	10.5947	+	4.38849i	0.357352	+	0.148020i
$880$		−	0.0456072i		−	0.00153742i
$881$	3.11758	−	7.52651i	0.105034	−	0.253575i	−0.862621	−	0.505850i	$-0.831179\pi$
$881$	3.11758	−	7.52651i	0.105034	−	0.253575i	0.967655	+	0.252275i	$0.0811789\pi$
$882$	0.350291	−	0.350291i	0.0117949	−	0.0117949i
$883$	−28.3255			−0.953228			−0.476614	−	0.879113i	$-0.658136\pi$
$883$	−28.3255			−0.953228			−0.476614	+	0.879113i	$0.658136\pi$
$884$	14.7838	−	12.1456i	0.497234	−	0.408500i
$885$	0.790454			0.0265708
$886$	11.6610	−	11.6610i	0.391760	−	0.391760i
$887$	−15.4177	+	37.2216i	−0.517675	+	1.24978i	0.421653	+	0.906757i	$0.361450\pi$
$887$	−15.4177	+	37.2216i	−0.517675	+	1.24978i	−0.939328	+	0.343020i	$0.888550\pi$
$888$		−	6.28772i		−	0.211002i
$889$	1.61896	+	0.670595i	0.0542982	+	0.0224910i
$890$	−0.136209	−	0.328838i	−0.00456574	−	0.0110227i
$891$	0.617317	−	0.255701i	0.0206809	−	0.00856630i
$892$	15.6624	+	15.6624i	0.524415	+	0.524415i
$893$	22.8669	+	22.8669i	0.765211	+	0.765211i
$894$	7.64255	−	3.16565i	0.255605	−	0.105875i
$895$	0.460885	+	1.11267i	0.0154057	+	0.0371926i
$896$	24.4138	+	10.1125i	0.815609	+	0.337836i
$897$			30.5445i			1.01985i
$898$	−10.5960	+	25.5809i	−0.353592	+	0.853646i
$899$	22.2641	−	22.2641i	0.742549	−	0.742549i
$900$	−7.06147			−0.235382
$901$	−4.56383	+	46.5840i	−0.152043	+	1.55194i
$902$	−0.245584			−0.00817705
$903$	16.1801	−	16.1801i	0.538439	−	0.538439i
$904$	−13.8558	+	33.4508i	−0.460836	+	1.11256i
$905$			1.16173i			0.0386172i
$906$	15.3842	+	6.37236i	0.511107	+	0.211708i
$907$	−16.6247	−	40.1356i	−0.552015	−	1.33268i	−0.915963	−	0.401262i	$-0.868572\pi$
$907$	−16.6247	−	40.1356i	−0.552015	−	1.33268i	0.363949	−	0.931419i	$-0.381428\pi$
$908$	−19.1169	+	7.91847i	−0.634416	+	0.262784i
$909$	−2.31703	−	2.31703i	−0.0768509	−	0.0768509i
$910$	−0.404613	−	0.404613i	−0.0134128	−	0.0134128i
$911$	2.05540	−	0.851374i	0.0680984	−	0.0282073i	−0.348374	−	0.937356i	$-0.613266\pi$
$911$	2.05540	−	0.851374i	0.0680984	−	0.0282073i	0.416473	+	0.909148i	$0.363266\pi$
$912$	1.15412	+	2.78629i	0.0382167	+	0.0922633i
$913$	−0.555504	−	0.230097i	−0.0183845	−	0.00761511i
$914$			21.5955i			0.714316i
$915$	0.0815686	−	0.196924i	0.00269658	−	0.00651011i
$916$	−16.3451	+	16.3451i	−0.540056	+	0.540056i
$917$	42.0561			1.38881
$918$	0.917608	+	3.01933i	0.0302856	+	0.0996528i
$919$	−47.4595			−1.56554			−0.782772	−	0.622308i	$-0.786195\pi$
$919$	−47.4595			−1.56554			−0.782772	+	0.622308i	$0.786195\pi$
$920$	−1.41716	+	1.41716i	−0.0467223	+	0.0467223i
$921$	−4.02754	+	9.72335i	−0.132712	+	0.320395i
$922$			21.7779i			0.717218i
$923$	9.96795	+	4.12886i	0.328099	+	0.135903i
$924$	1.00000	+	2.41421i	0.0328976	+	0.0794218i
$925$	−11.1001	+	4.59782i	−0.364970	+	0.151176i
$926$	−3.27574	−	3.27574i	−0.107647	−	0.107647i
$927$	8.50141	+	8.50141i	0.279223	+	0.279223i
$928$	−33.7990	+	14.0000i	−1.10951	+	0.459573i
$929$	12.2687	+	29.6194i	0.402525	+	0.971780i	0.987051	+	0.160406i	$0.0512803\pi$
$929$	12.2687	+	29.6194i	0.402525	+	0.971780i	−0.584527	+	0.811375i	$0.698720\pi$
$930$	−0.293848	−	0.121716i	−0.00963566	−	0.00399122i
$931$			2.35631i			0.0772248i
$932$	−0.193646	+	0.467502i	−0.00634307	+	0.0153135i
$933$	3.82843	−	3.82843i	0.125337	−	0.125337i
$934$	24.6011			0.804971
$935$	0.144090	+	0.175390i	0.00471226	+	0.00573586i
$936$	8.57446			0.280265
$937$	−12.0024	+	12.0024i	−0.392103	+	0.392103i	−0.875436	−	0.483334i	$-0.839426\pi$
$937$	−12.0024	+	12.0024i	−0.392103	+	0.392103i	0.483334	+	0.875436i	$0.339426\pi$
$938$	−0.765367	+	1.84776i	−0.0249901	+	0.0603315i
$939$		−	0.951362i		−	0.0310465i
$940$	−0.956272	−	0.396101i	−0.0311901	−	0.0129194i
$941$	−5.44777	−	13.1521i	−0.177592	−	0.428745i	0.809868	−	0.586612i	$-0.199538\pi$
$941$	−5.44777	−	13.1521i	−0.177592	−	0.428745i	−0.987460	+	0.157866i	$0.949538\pi$
$942$	14.0386	−	5.81496i	0.457401	−	0.189462i
$943$	−3.16089	−	3.16089i	−0.102933	−	0.102933i
$944$	−5.61991	−	5.61991i	−0.182913	−	0.182913i
$945$	−0.210501	+	0.0871924i	−0.00684760	+	0.00283637i
$946$	−1.61936	−	3.90949i	−0.0526501	−	0.127109i
$947$	35.5955	+	14.7441i	1.15670	+	0.479120i	0.876774	−	0.480902i	$-0.159691\pi$
$947$	35.5955	+	14.7441i	1.15670	+	0.479120i	0.279924	+	0.960022i	$0.409691\pi$
$948$		−	11.8394i		−	0.384525i
$949$	19.6918	−	47.5403i	0.639224	−	1.54322i
$950$	−9.83765	+	9.83765i	−0.319176	+	0.319176i
$951$	−21.5647			−0.699282
$952$	−28.5072	+	8.66364i	−0.923923	+	0.280790i
$953$	17.8637			0.578663			0.289331	−	0.957229i	$-0.406567\pi$
$953$	17.8637			0.578663			0.289331	+	0.957229i	$0.406567\pi$
$954$	−6.14386	+	6.14386i	−0.198915	+	0.198915i
$955$	−0.505009	+	1.21920i	−0.0163417	+	0.0394524i
$956$		−	13.7342i		−	0.444195i
$957$	−3.85369	−	1.59625i	−0.124572	−	0.0515994i
$958$	−4.55487	−	10.9964i	−0.147161	−	0.355278i
$959$	6.10221	−	2.52762i	0.197051	−	0.0816211i
$960$	0.164784	+	0.164784i	0.00531839	+	0.00531839i
$961$	3.93208	+	3.93208i	0.126841	+	0.126841i
$962$	5.58296	−	2.31254i	0.180002	−	0.0745592i
$963$	3.34055	+	8.06480i	0.107648	+	0.259884i
$964$	12.2317	+	5.06653i	0.393956	+	0.163182i
$965$			0.378624i			0.0121883i
$966$	7.53960	−	18.2022i	0.242583	−	0.585647i
$967$	15.7440	−	15.7440i	0.506294	−	0.506294i	−0.407093	−	0.913387i	$-0.633457\pi$
$967$	15.7440	−	15.7440i	0.506294	−	0.506294i	0.913387	+	0.407093i	$0.133457\pi$
$968$	−27.5777			−0.886382
$969$	−13.2413	−	7.06884i	−0.425372	−	0.227084i
$970$	0.691915			0.0222161
$971$	3.09891	−	3.09891i	0.0994488	−	0.0994488i	−0.655632	−	0.755081i	$-0.727598\pi$
$971$	3.09891	−	3.09891i	0.0994488	−	0.0994488i	0.755081	+	0.655632i	$0.227598\pi$
$972$	0.541196	−	1.30656i	0.0173589	−	0.0419080i
$973$		−	4.46529i		−	0.143151i
$974$	−14.1929	−	5.87887i	−0.454768	−	0.188371i
$975$	−6.26998	−	15.1371i	−0.200800	−	0.484774i
$976$	−1.98001	+	0.820146i	−0.0633785	+	0.0262522i
$977$	−19.4485	−	19.4485i	−0.622211	−	0.622211i	0.323885	−	0.946096i	$-0.395011\pi$
$977$	−19.4485	−	19.4485i	−0.622211	−	0.622211i	−0.946096	+	0.323885i	$0.895011\pi$
$978$	−0.949857	−	0.949857i	−0.0303731	−	0.0303731i
$979$	−3.48433	+	1.44326i	−0.111360	+	0.0461266i
$980$	−0.0288613	−	0.0696773i	−0.000921939	−	0.00222576i
$981$	3.94495	+	1.63405i	0.125952	+	0.0521712i
$982$			4.11068i			0.131177i
$983$	−11.9157	+	28.7670i	−0.380052	+	0.917526i	0.611903	+	0.790933i	$0.290404\pi$
$983$	−11.9157	+	28.7670i	−0.380052	+	0.917526i	−0.991955	+	0.126593i	$0.959596\pi$
$984$	−0.887325	+	0.887325i	−0.0282869	+	0.0282869i
$985$	1.74416			0.0555734
$986$	9.27746	−	17.3785i	0.295454	−	0.553444i
$987$	24.5650			0.781914
$988$	−11.9455	+	11.9455i	−0.380036	+	0.380036i
$989$	29.4760	−	71.1614i	0.937283	−	2.26280i
$990$			0.0421355i			0.00133915i
$991$	−0.706469	−	0.292629i	−0.0224417	−	0.00929567i	0.371434	−	0.928459i	$-0.378866\pi$
$991$	−0.706469	−	0.292629i	−0.0224417	−	0.00929567i	−0.393876	+	0.919164i	$0.628866\pi$
$992$	11.3113	+	27.3078i	0.359133	+	0.867024i
$993$	19.1581	−	7.93556i	0.607965	−	0.251827i
$994$	−4.92098	−	4.92098i	−0.156084	−	0.156084i
$995$	−0.135478	−	0.135478i	−0.00429495	−	0.00429495i
$996$	−1.17574	+	0.487005i	−0.0372546	+	0.0154314i
$997$	0.458984	+	1.10809i	0.0145362	+	0.0350934i	0.930981	−	0.365068i	$-0.118954\pi$
$997$	0.458984	+	1.10809i	0.0145362	+	0.0350934i	−0.916445	+	0.400161i	$0.868954\pi$
$998$	−19.8455	−	8.22028i	−0.628199	−	0.260208i
$999$		−	2.40621i		−	0.0761290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.2.h.a.25.1	✓	8
3.2	odd	2		153.2.l.e.127.2		8
4.3	odd	2		816.2.bq.a.433.2		8
17.2	even	8		867.2.h.g.712.1		8
17.3	odd	16		867.2.e.i.616.3		8
17.4	even	4		867.2.h.f.757.2		8
17.5	odd	16		867.2.e.i.829.2		8
17.6	odd	16		867.2.d.e.577.4		8
17.7	odd	16		867.2.a.n.1.3		4
17.8	even	8		867.2.h.f.733.2		8
17.9	even	8		867.2.h.b.733.2		8
17.10	odd	16		867.2.a.m.1.3		4
17.11	odd	16		867.2.d.e.577.3		8
17.12	odd	16		867.2.e.h.829.2		8
17.13	even	4		867.2.h.b.757.2		8
17.14	odd	16		867.2.e.h.616.3		8
17.15	even	8	inner	51.2.h.a.49.1	yes	8
17.16	even	2		867.2.h.g.688.1		8
51.32	odd	8		153.2.l.e.100.2		8
51.41	even	16		2601.2.a.bd.1.2		4
51.44	even	16		2601.2.a.bc.1.2		4
68.15	odd	8		816.2.bq.a.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.25.1	✓	8	1.1	even	1	trivial
51.2.h.a.49.1	yes	8	17.15	even	8	inner
153.2.l.e.100.2		8	51.32	odd	8
153.2.l.e.127.2		8	3.2	odd	2
816.2.bq.a.49.2		8	68.15	odd	8
816.2.bq.a.433.2		8	4.3	odd	2
867.2.a.m.1.3		4	17.10	odd	16
867.2.a.n.1.3		4	17.7	odd	16
867.2.d.e.577.3		8	17.11	odd	16
867.2.d.e.577.4		8	17.6	odd	16
867.2.e.h.616.3		8	17.14	odd	16
867.2.e.h.829.2		8	17.12	odd	16
867.2.e.i.616.3		8	17.3	odd	16
867.2.e.i.829.2		8	17.5	odd	16
867.2.h.b.733.2		8	17.9	even	8
867.2.h.b.757.2		8	17.13	even	4
867.2.h.f.733.2		8	17.8	even	8
867.2.h.f.757.2		8	17.4	even	4
867.2.h.g.688.1		8	17.16	even	2
867.2.h.g.712.1		8	17.2	even	8
2601.2.a.bc.1.2		4	51.44	even	16
2601.2.a.bd.1.2		4	51.41	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.541196 + 0.541196i) q^{2} +(-0.382683 + 0.923880i) q^{3} +1.41421i q^{4} +(-0.0761205 - 0.0315301i) q^{5} +(-0.292893 - 0.707107i) q^{6} +(2.55487 - 1.05826i) q^{7} +(-1.84776 - 1.84776i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(0.0582601 - 0.0241321i) q^{10} +(-0.255701 - 0.617317i) q^{11} +(-1.30656 - 0.541196i) q^{12} -3.28130i q^{13} +(-0.809957 + 1.95541i) q^{14} +(0.0582601 - 0.0582601i) q^{15} -0.828427 q^{16} +(3.18585 - 2.61732i) q^{17} +0.765367 q^{18} +(-2.57420 + 2.57420i) q^{19} +(0.0445903 - 0.107651i) q^{20} +2.76537i q^{21} +(0.472474 + 0.195705i) q^{22} +(3.56226 + 8.60007i) q^{23} +(2.41421 - 1.00000i) q^{24} +(-3.53073 - 3.53073i) q^{25} +(1.77583 + 1.77583i) q^{26} +(0.923880 - 0.382683i) q^{27} +(1.49661 + 3.61313i) q^{28} +(-5.76745 - 2.38896i) q^{29} +0.0630603i q^{30} +(-1.93015 + 4.65980i) q^{31} +(4.14386 - 4.14386i) q^{32} +0.668179 q^{33} +(-0.307689 + 3.14065i) q^{34} -0.227845 q^{35} +(1.00000 - 1.00000i) q^{36} +(0.920815 - 2.22304i) q^{37} -2.78629i q^{38} +(3.03153 + 1.25570i) q^{39} +(0.0823922 + 0.198912i) q^{40} +(-0.443663 + 0.183771i) q^{41} +(-1.49661 - 1.49661i) q^{42} +(-5.85097 - 5.85097i) q^{43} +(0.873017 - 0.361616i) q^{44} +(0.0315301 + 0.0761205i) q^{45} +(-6.58221 - 2.72644i) q^{46} -8.88311i q^{47} +(0.317025 - 0.765367i) q^{48} +(0.457678 - 0.457678i) q^{49} +3.82164 q^{50} +(1.19891 + 3.94495i) q^{51} +4.64047 q^{52} +(-8.02734 + 8.02734i) q^{53} +(-0.292893 + 0.707107i) q^{54} +0.0550527i q^{55} +(-6.67619 - 2.76537i) q^{56} +(-1.39315 - 3.36335i) q^{57} +(4.41421 - 1.82843i) q^{58} +(6.78384 + 6.78384i) q^{59} +(0.0823922 + 0.0823922i) q^{60} +(2.39008 - 0.990004i) q^{61} +(-1.47727 - 3.56645i) q^{62} +(-2.55487 - 1.05826i) q^{63} +2.82843i q^{64} +(-0.103460 + 0.249774i) q^{65} +(-0.361616 + 0.361616i) q^{66} +0.944947 q^{67} +(3.70144 + 4.50548i) q^{68} -9.30864 q^{69} +(0.123309 - 0.123309i) q^{70} +(-1.25830 + 3.03780i) q^{71} +2.61313i q^{72} +(14.4882 + 6.00122i) q^{73} +(0.704761 + 1.70144i) q^{74} +(4.61313 - 1.91082i) q^{75} +(-3.64047 - 3.64047i) q^{76} +(-1.30656 - 1.30656i) q^{77} +(-2.32023 + 0.961072i) q^{78} +(3.20371 + 7.73445i) q^{79} +(0.0630603 + 0.0261204i) q^{80} +1.00000i q^{81} +(0.140652 - 0.339565i) q^{82} +(0.636303 - 0.636303i) q^{83} -3.91082 q^{84} +(-0.325033 + 0.0987810i) q^{85} +6.33304 q^{86} +(4.41421 - 4.41421i) q^{87} +(-0.668179 + 1.61313i) q^{88} -5.64431i q^{89} +(-0.0582601 - 0.0241321i) q^{90} +(-3.47247 - 8.38329i) q^{91} +(-12.1623 + 5.03780i) q^{92} +(-3.56645 - 3.56645i) q^{93} +(4.80750 + 4.80750i) q^{94} +(0.277114 - 0.114784i) q^{95} +(2.24264 + 5.41421i) q^{96} +(10.1371 + 4.19891i) q^{97} +0.495387i q^{98} +(-0.255701 + 0.617317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5} - 8 q^{6} + 8 q^{11} - 16 q^{14} + 16 q^{16} - 8 q^{17} - 8 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{23} + 8 q^{24} - 16 q^{25} + 16 q^{26} - 8 q^{28} + 8 q^{31} + 8 q^{33} - 8 q^{34} + 32 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^6 + 8 * q^11 - 16 * q^14 + 16 * q^16 - 8 * q^17 - 8 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^23 + 8 * q^24 - 16 * q^25 + 16 * q^26 - 8 * q^28 + 8 * q^31 + 8 * q^33 - 8 * q^34 + 32 * q^35 + 8 * q^36 - 8 * q^37 + 16 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^49 - 32 * q^50 - 16 * q^52 - 32 * q^53 - 8 * q^54 - 16 * q^56 - 16 * q^57 + 24 * q^58 + 16 * q^59 - 8 * q^60 + 16 * q^61 + 16 * q^62 + 24 * q^65 - 16 * q^66 - 16 * q^67 - 24 * q^69 + 40 * q^70 - 16 * q^71 + 48 * q^73 + 64 * q^74 + 16 * q^75 + 24 * q^76 + 8 * q^78 - 16 * q^80 - 8 * q^82 + 32 * q^83 + 40 * q^85 - 32 * q^86 + 24 * q^87 - 8 * q^88 - 16 * q^91 - 32 * q^92 - 32 * q^93 - 40 * q^95 - 16 * q^96 + 8 * q^97 + 8 * q^99

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