LMFDB - Embedded newform 867.2.h.g.688.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("867.688");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not 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:	$6.92302985525$
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:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			688.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	867.688
Dual form			867.2.h.g.712.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.541196 + 0.541196i) q^{2} +(0.382683 - 0.923880i) q^{3} +1.41421i q^{4} +(0.0761205 + 0.0315301i) q^{5} +(0.292893 + 0.707107i) q^{6} +(-2.55487 + 1.05826i) q^{7} +(-1.84776 - 1.84776i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(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} +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} -0.227845 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} +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} -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} +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}+O(q^{10}) $ 8 * q + 8 * q^5 + 8 * q^6	$ 8 q + 8 q^{5} + 8 q^{6} - 8 q^{11} + 16 q^{14} + 16 q^{16} - 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} + 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} - 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}+O(q^{100}) $ 8 * q + 8 * q^5 + 8 * q^6 - 8 * q^11 + 16 * q^14 + 16 * q^16 - 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 + 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 - 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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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	0.399640	−	0.916672i	$-0.369135\pi$
$5$	0.0761205	+	0.0315301i	0.0340421	+	0.0141007i	−0.365597	+	0.930773i	$0.619135\pi$
$6$	0.292893	+	0.707107i	0.119573	+	0.288675i
$7$	−2.55487	+	1.05826i	−0.965649	+	0.399985i	−0.809091	−	0.587684i	$-0.800040\pi$
$7$	−2.55487	+	1.05826i	−0.965649	+	0.399985i	−0.156558	+	0.987669i	$0.550040\pi$
$8$	−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	0.957729	−	0.287673i	$-0.0928816\pi$
$11$	0.255701	+	0.617317i	0.0770967	+	0.186128i	−0.880632	+	0.473801i	$0.842882\pi$
$12$	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
$17$		0			0
$17$		0			0
$18$	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	$-0.702517\pi$
$23$	−3.56226	−	8.60007i	−0.742783	−	1.79324i	−0.148618	−	0.988895i	$-0.547483\pi$
$24$	−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	0.847339	−	0.531052i	$-0.178203\pi$
$29$	5.76745	+	2.38896i	1.07099	+	0.443618i	0.223649	+	0.974670i	$0.428203\pi$
$30$			0.0630603i			0.0115132i
$31$	1.93015	−	4.65980i	0.346665	−	0.836924i	−0.650344	−	0.759640i	$-0.725375\pi$
$31$	1.93015	−	4.65980i	0.346665	−	0.836924i	0.997009	−	0.0772842i	$-0.0246249\pi$
$32$	4.14386	−	4.14386i	0.732538	−	0.732538i
$33$	0.668179			0.116315
$34$		0			0
$35$	−0.227845			−0.0385128
$36$	1.00000	−	1.00000i	0.166667	−	0.166667i
$37$	−0.920815	+	2.22304i	−0.151381	+	0.365466i	−0.981318	−	0.192390i	$-0.938376\pi$
$37$	−0.920815	+	2.22304i	−0.151381	+	0.365466i	0.829937	+	0.557857i	$0.188376\pi$
$38$		−	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	−0.347770	−	0.937580i	$-0.613061\pi$
$41$	0.443663	−	0.183771i	0.0692885	−	0.0287002i	0.417059	+	0.908880i	$0.363061\pi$
$42$	−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
$51$		0			0
$52$	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	−0.530408	−	0.847743i	$-0.677961\pi$
$61$	−2.39008	+	0.990004i	−0.306019	+	0.126757i	0.224389	+	0.974500i	$0.427961\pi$
$62$	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	$0.481616\pi$
$68$		0			0
$69$	−9.30864			−1.12063
$70$	0.123309	−	0.123309i	0.0147382	−	0.0147382i
$71$	1.25830	−	3.03780i	0.149333	−	0.360521i	−0.831457	−	0.555589i	$-0.812493\pi$
$71$	1.25830	−	3.03780i	0.149333	−	0.360521i	0.980790	+	0.195068i	$0.0624928\pi$
$72$			2.61313i			0.307960i
$73$	−14.4882	−	6.00122i	−1.69572	−	0.702390i	−0.695843	−	0.718194i	$-0.744969\pi$
$73$	−14.4882	−	6.00122i	−1.69572	−	0.702390i	−0.999875	+	0.0158041i	$0.994969\pi$
$74$	−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	$-0.968913\pi$
$79$	−3.20371	−	7.73445i	−0.360446	−	0.870193i	0.634789	−	0.772686i	$-0.281087\pi$
$80$	−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			0
$86$	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	−0.196817	−	0.980440i	$-0.563060\pi$
$97$	−10.1371	−	4.19891i	−1.02926	−	0.426335i	−0.832447	+	0.554105i	$0.813060\pi$
$98$			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	$0.447875\pi$
$102$		0			0
$103$	−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	0.736776	−	0.676137i	$-0.236347\pi$
$107$	8.06480	+	3.34055i	0.779653	+	0.322943i	0.0428777	+	0.999080i	$0.486347\pi$
$108$	−0.541196	−	1.30656i	−0.0520766	−	0.125724i
$109$	3.94495	−	1.63405i	0.377857	−	0.156514i	−0.185668	−	0.982613i	$-0.559445\pi$
$109$	3.94495	−	1.63405i	0.377857	−	0.156514i	0.563525	+	0.826099i	$0.309445\pi$
$110$	−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	$0.100952\pi$
$113$	5.30237	+	12.8011i	0.498805	+	1.20422i	−0.451322	+	0.892361i	$0.649048\pi$
$114$	−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
$119$		0			0
$120$	−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	−0.327780	−	0.944754i	$-0.606300\pi$
$131$	−14.0505	−	5.81990i	−1.22760	−	0.508487i	−0.899817	+	0.436267i	$0.856300\pi$
$132$			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
$136$		0			0
$137$	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	−0.947917	−	0.318518i	$-0.896815\pi$
$139$	−0.617926	+	1.49181i	−0.0524118	+	0.126533i	0.895505	+	0.445052i	$0.146815\pi$
$140$		−	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
$153$		0			0
$154$	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	−0.445281	−	0.895391i	$-0.646896\pi$
$163$	−1.62151	+	0.671650i	−0.127006	+	0.0526077i	0.318275	+	0.947998i	$0.396896\pi$
$164$	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	−0.997144	−	0.0755188i	$-0.975939\pi$
$167$	−3.08413	+	7.44574i	−0.238657	+	0.576169i	0.758487	+	0.651688i	$0.225939\pi$
$168$	5.10973	−	5.10973i	0.394224	−	0.394224i
$169$	2.23304			0.171772
$170$		0			0
$171$	3.64047			0.278393
$172$	8.27452	−	8.27452i	0.630926	−	0.630926i
$173$	−2.20151	+	5.31492i	−0.167378	+	0.404086i	−0.985205	−	0.171378i	$-0.945178\pi$
$173$	−2.20151	+	5.31492i	−0.167378	+	0.404086i	0.817828	+	0.575463i	$0.195178\pi$
$174$			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	$0.0505692\pi$
$181$	5.39584	+	13.0267i	0.401069	+	0.968267i	−0.586338	+	0.810067i	$0.699431\pi$
$182$	−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
$187$		0			0
$188$	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	0.974448	−	0.224611i	$-0.0721112\pi$
$193$	1.75858	+	4.24558i	0.126585	+	0.305604i	−0.847863	+	0.530215i	$0.822111\pi$
$194$	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	0.445384	−	0.895340i	$-0.353067\pi$
$197$	19.5576	−	8.10101i	1.39342	−	0.577173i	0.948035	+	0.318167i	$0.103067\pi$
$198$	0.195705	+	0.472474i	0.0139081	+	0.0335772i
$199$	−2.14840	−	0.889895i	−0.152296	−	0.0630830i	0.305234	−	0.952278i	$-0.401265\pi$
$199$	−2.14840	−	0.889895i	−0.152296	−	0.0630830i	−0.457529	+	0.889195i	$0.651265\pi$
$200$			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
$204$		0			0
$205$	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	−0.610634	−	0.791913i	$-0.709085\pi$
$211$	−7.00801	+	2.90281i	−0.482451	+	0.199838i	0.128183	+	0.991751i	$0.459085\pi$
$212$	−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
$221$		0			0
$222$	−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	$-0.963615\pi$
$227$	−5.59920	−	13.5177i	−0.371632	−	0.897200i	0.621842	−	0.783143i	$-0.286385\pi$
$228$	−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	0.371829	−	0.928301i	$-0.378731\pi$
$233$	−0.330574	−	0.136928i	−0.0216566	−	0.00897046i	−0.393485	+	0.919331i	$0.628731\pi$
$234$		−	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
$238$		0			0
$239$	−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	−0.996269	−	0.0863041i	$-0.972494\pi$
$241$	−3.58258	+	8.64911i	−0.230774	+	0.557138i	0.765495	+	0.643442i	$0.222494\pi$
$242$			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			0
$256$	−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	−0.852035	−	0.523486i	$-0.824631\pi$
$269$	1.97807	−	4.77548i	0.120605	−	0.291166i	0.972640	+	0.232319i	$0.0746314\pi$
$270$	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	$0.434908\pi$
$272$		0			0
$273$	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	0.300692	−	0.953721i	$-0.402782\pi$
$277$	−2.68072	−	1.11039i	−0.161069	−	0.0667170i	−0.461761	+	0.887004i	$0.652782\pi$
$278$	−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	$0.183216\pi$
$283$	10.6083	+	25.6108i	0.630600	+	1.52240i	−0.208271	+	0.978071i	$0.566784\pi$
$284$	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
$289$		0			0
$290$	−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
$306$		0			0
$307$	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	0.519969	−	0.854185i	$-0.325944\pi$
$311$	5.00208	+	2.07193i	0.283642	+	0.117488i	−0.236327	+	0.971674i	$0.575944\pi$
$312$	3.28130	+	7.92177i	0.185767	+	0.448482i
$313$	0.878944	−	0.364070i	0.0496808	−	0.0205785i	−0.357705	−	0.933835i	$-0.616441\pi$
$313$	0.878944	−	0.364070i	0.0496808	−	0.0205785i	0.407386	+	0.913256i	$0.366441\pi$
$314$	−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	$-0.917935\pi$
$317$	−8.25244	−	19.9232i	−0.463503	−	1.11900i	0.503446	−	0.864027i	$-0.332065\pi$
$318$	−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
$323$		0			0
$324$	−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	−0.999993	−	0.00361586i	$-0.998849\pi$
$337$	−5.32983	+	12.8674i	−0.290335	+	0.700930i	0.709659	+	0.704545i	$0.248849\pi$
$338$	−1.20851	+	1.20851i	−0.0657344	+	0.0657344i
$339$	13.8558			0.752542
$340$		0			0
$341$	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	−0.744145	−	0.668018i	$-0.767143\pi$
$347$	−14.8646	+	6.15713i	−0.797975	+	0.330532i	−0.0538302	+	0.998550i	$0.517143\pi$
$348$	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
$357$		0			0
$358$	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	−0.276045	−	0.961145i	$-0.589024\pi$
$367$	3.99226	−	1.65365i	0.208394	−	0.0863197i	0.484439	+	0.874825i	$0.339024\pi$
$368$	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	$0.429881\pi$
$374$		0			0
$375$	−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	0.556880	−	0.830593i	$-0.311998\pi$
$379$	7.07337	+	2.92989i	0.363335	+	0.150498i	−0.193545	+	0.981091i	$0.561998\pi$
$380$	−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
$391$		0			0
$392$	−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	0.890850	−	0.454297i	$-0.150110\pi$
$397$	−1.20172	−	2.90122i	−0.0603128	−	0.145608i	−0.951163	+	0.308689i	$0.900110\pi$
$398$	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	0.323323	−	0.946289i	$-0.395200\pi$
$401$	24.4520	−	10.1283i	1.22107	−	0.505785i	0.897751	+	0.440503i	$0.145200\pi$
$402$	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
$408$		0			0
$409$	−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	$-0.729816\pi$
$419$	−14.8249	−	35.7906i	−0.724246	−	1.74848i	−0.0633678	−	0.997990i	$-0.520184\pi$
$420$	−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
$425$		0			0
$426$	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	0.994814	−	0.101710i	$-0.0324314\pi$
$431$	4.55599	+	10.9991i	0.219454	+	0.529810i	−0.775360	+	0.631520i	$0.782431\pi$
$432$	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	$-0.706269\pi$
$439$	8.10801	−	19.5745i	0.386974	−	0.934238i	0.990577	−	0.136953i	$-0.0437311\pi$
$440$	0.101724	−	0.101724i	0.00484951	−	0.00484951i
$441$	−0.647254			−0.0308216
$442$		0			0
$443$	−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	−0.987988	−	0.154530i	$-0.950614\pi$
$449$	−33.4231	+	13.8443i	−1.57733	+	0.653352i	−0.589344	+	0.807882i	$0.700614\pi$
$450$	−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
$459$		0			0
$460$	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
$476$		0			0
$477$	11.3524			0.519789
$478$	5.25584	−	5.25584i	0.240397	−	0.240397i
$479$	5.95122	−	14.3675i	0.271918	−	0.656468i	−0.727647	−	0.685952i	$-0.759386\pi$
$479$	5.95122	−	14.3675i	0.271918	−	0.656468i	0.999565	+	0.0294832i	$0.00938615\pi$
$480$		−	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	$-0.974722\pi$
$487$	−7.68112	−	18.5439i	−0.348065	−	0.840302i	0.648784	−	0.760973i	$-0.275278\pi$
$488$	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
$493$		0			0
$494$	−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	$-0.908793\pi$
$499$	−10.7403	−	25.9294i	−0.480802	−	1.16076i	0.478426	−	0.878128i	$-0.341207\pi$
$500$	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	−0.194681	−	0.980867i	$-0.562367\pi$
$503$	8.10170	−	3.35583i	0.361237	−	0.149629i	0.555917	+	0.831238i	$0.312367\pi$
$504$	−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			0
$511$	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	0.826247	−	0.563308i	$-0.190471\pi$
$521$	−3.56799	−	8.61389i	−0.156316	−	0.377381i	−0.982564	+	0.185926i	$0.940471\pi$
$522$	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
$527$		0			0
$528$	−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	−0.889425	−	0.457081i	$-0.848895\pi$
$541$	1.45834	−	3.52074i	0.0626988	−	0.151368i	0.952124	+	0.305713i	$0.0988948\pi$
$542$	−3.61839	+	3.61839i	−0.155423	+	0.155423i
$543$	14.1000			0.605089
$544$		0			0
$545$	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	$0.313307\pi$
$547$	−9.98266	+	24.1003i	−0.426828	+	1.03045i	−0.980287	+	0.197577i	$0.936693\pi$
$548$			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
$561$		0			0
$562$	−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	−0.665112	−	0.746743i	$-0.731616\pi$
$571$	−14.5140	+	6.01188i	−0.607391	+	0.251590i	0.0577217	+	0.998333i	$0.481616\pi$
$572$	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	$0.707168\pi$
$578$		0			0
$579$	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			0
$596$	−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	0.899007	−	0.437935i	$-0.144290\pi$
$601$	−1.13638	−	2.74347i	−0.0463539	−	0.111908i	−0.945361	+	0.326027i	$0.894290\pi$
$602$	−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	0.861531	−	0.507705i	$-0.169506\pi$
$607$	27.3900	+	11.3453i	1.11172	+	0.460491i	0.250193	+	0.968196i	$0.419506\pi$
$608$			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			0
$613$	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	−0.391886	−	0.920014i	$-0.628177\pi$
$617$	−32.7767	−	13.5765i	−1.31954	−	0.546571i	−0.927653	+	0.373443i	$0.878177\pi$
$618$	−3.52140	−	8.50141i	−0.141651	−	0.341977i
$619$	24.2079	−	10.0272i	0.972997	−	0.403028i	0.161170	−	0.986927i	$-0.448473\pi$
$619$	24.2079	−	10.0272i	0.972997	−	0.403028i	0.811827	+	0.583898i	$0.198473\pi$
$620$	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
$629$		0			0
$630$	−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	0.468327	−	0.883555i	$-0.344857\pi$
$641$	4.42347	+	1.83226i	0.174717	+	0.0723699i	−0.293611	+	0.955925i	$0.594857\pi$
$642$			6.68110i			0.263682i
$643$	−7.85802	+	18.9709i	−0.309890	+	0.748141i	0.689818	+	0.723983i	$0.257690\pi$
$643$	−7.85802	+	18.9709i	−0.309890	+	0.748141i	−0.999708	+	0.0241580i	$0.992310\pi$
$644$	−25.7418	+	25.7418i	−1.01437	+	1.01437i
$645$	−0.681756			−0.0268441
$646$		0			0
$647$	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	−0.624591	−	0.780952i	$-0.714734\pi$
$653$	−13.1354	+	5.44085i	−0.514027	+	0.212917i	0.110564	+	0.993869i	$0.464734\pi$
$654$	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
$663$		0			0
$664$	−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	0.313066	−	0.949731i	$-0.398644\pi$
$673$	31.2863	−	12.9592i	1.20600	−	0.499541i	0.892933	+	0.450190i	$0.148644\pi$
$674$	−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	$0.365583\pi$
$677$	−13.6588	+	32.9752i	−0.524950	+	1.26734i	−0.934795	+	0.355186i	$0.884417\pi$
$678$	−7.49869	+	7.49869i	−0.287985	+	0.287985i
$679$	30.3424			1.16443
$680$		0			0
$681$	−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	$-0.734922\pi$
$683$	8.52097	−	20.5715i	0.326046	−	0.787145i	0.998878	−	0.0473497i	$-0.0150775\pi$
$684$			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	$-0.938875\pi$
$691$	−11.1052	−	26.8103i	−0.422462	−	1.01991i	0.559157	−	0.829061i	$-0.311125\pi$
$692$	−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			0
$698$	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	−0.486048	−	0.873932i	$-0.661562\pi$
$709$	−38.5480	−	15.9671i	−1.44770	−	0.599657i	−0.961651	+	0.274275i	$0.911562\pi$
$710$			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
$714$		0			0
$715$	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	$0.0185541\pi$
$719$	46.8015	+	19.3858i	1.74540	+	0.722969i	0.747099	+	0.664712i	$0.231446\pi$
$720$	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
$731$		0			0
$732$	−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	0.130705	−	0.991421i	$-0.458276\pi$
$743$	−13.0270	−	5.39595i	−0.477913	−	0.197958i	−0.608618	+	0.793463i	$0.708276\pi$
$744$			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
$748$		0			0
$749$	−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	$-0.741232\pi$
$751$	8.55723	−	20.6590i	0.312258	−	0.753857i	0.999621	−	0.0275426i	$-0.00876820\pi$
$752$			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			0
$766$	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
$782$		0			0
$783$	−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	0.857750	−	0.514067i	$-0.171862\pi$
$787$	30.8805	+	12.7911i	1.10077	+	0.455954i	0.243020	+	0.970021i	$0.421862\pi$
$788$	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
$799$		0			0
$800$	−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	−0.313177	−	0.949695i	$-0.601393\pi$
$809$	3.89409	−	1.61298i	0.136909	−	0.0567095i	0.450086	+	0.892985i	$0.351393\pi$
$810$	−0.0241321	−	0.0582601i	−0.000847916	−	0.00204705i
$811$	−23.1219	−	9.57741i	−0.811920	−	0.336308i	−0.0622001	−	0.998064i	$-0.519812\pi$
$811$	−23.1219	−	9.57741i	−0.811920	−	0.336308i	−0.749720	+	0.661756i	$0.769812\pi$
$812$		−	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			0
$817$	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	0.696151	−	0.717895i	$-0.254894\pi$
$821$	19.5063	+	8.07979i	0.680776	+	0.281987i	−0.0153751	+	0.999882i	$0.504894\pi$
$822$	0.699566	+	1.68890i	0.0244002	+	0.0589072i
$823$	23.3711	−	9.68061i	0.814664	−	0.337445i	0.0638509	−	0.997959i	$-0.479662\pi$
$823$	23.3711	−	9.68061i	0.814664	−	0.337445i	0.750813	+	0.660515i	$0.229662\pi$
$824$	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	0.997025	−	0.0770744i	$-0.0245579\pi$
$827$	6.83057	+	16.4904i	0.237522	+	0.573429i	−0.759503	+	0.650504i	$0.774558\pi$
$828$	−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			0
$834$	−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	0.845487	−	0.533995i	$-0.179310\pi$
$839$	−3.76419	−	9.08756i	−0.129954	−	0.313737i	−0.975442	+	0.220258i	$0.929310\pi$
$840$	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
$850$		0			0
$851$	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	$0.485537\pi$
$853$	−20.2420	+	48.8685i	−0.693073	+	1.67323i	−0.738496	+	0.674258i	$0.764463\pi$
$854$			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	0.539545	−	0.841957i	$-0.318596\pi$
$857$	44.3924	−	18.3879i	1.51641	−	0.628119i	0.976869	+	0.213837i	$0.0685962\pi$
$858$	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
$867$		0			0
$868$	−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	0.251853	−	0.967765i	$-0.418960\pi$
$877$	32.9977	−	13.6681i	1.11425	−	0.461539i	0.862401	+	0.506227i	$0.168960\pi$
$878$	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	−0.967655	−	0.252275i	$-0.918821\pi$
$881$	−3.11758	+	7.52651i	−0.105034	+	0.253575i	0.862621	+	0.505850i	$0.168821\pi$
$882$	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	$0.658136\pi$
$884$		0			0
$885$	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	$-0.638550\pi$
$887$	15.4177	−	37.2216i	0.517675	−	1.24978i	0.939328	−	0.343020i	$-0.111450\pi$
$888$		−	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
$901$		0			0
$902$	−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	$0.131428\pi$
$907$	16.6247	+	40.1356i	0.552015	+	1.33268i	−0.363949	+	0.931419i	$0.618572\pi$
$908$	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	−0.416473	−	0.909148i	$-0.636734\pi$
$911$	−2.05540	+	0.851374i	−0.0680984	+	0.0282073i	0.348374	+	0.937356i	$0.386734\pi$
$912$	−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			0
$919$	−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	$-0.948720\pi$
$929$	−12.2687	−	29.6194i	−0.402525	−	0.971780i	0.584527	−	0.811375i	$-0.301280\pi$
$930$	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			0
$936$	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	0.987460	−	0.157866i	$-0.0504615\pi$
$941$	5.44777	+	13.1521i	0.177592	+	0.428745i	−0.809868	+	0.586612i	$0.800462\pi$
$942$	−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	−0.279924	−	0.960022i	$-0.590309\pi$
$947$	−35.5955	−	14.7441i	−1.15670	−	0.479120i	−0.876774	+	0.480902i	$0.840309\pi$
$948$		−	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
$952$		0			0
$953$	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
$969$		0			0
$970$	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	$-0.709596\pi$
$983$	11.9157	−	28.7670i	0.380052	−	0.917526i	0.991955	−	0.126593i	$-0.0404043\pi$
$984$	−0.887325	+	0.887325i	−0.0282869	+	0.0282869i
$985$	1.74416			0.0555734
$986$		0			0
$987$	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	0.393876	−	0.919164i	$-0.371134\pi$
$991$	0.706469	+	0.292629i	0.0224417	+	0.00929567i	−0.371434	+	0.928459i	$0.621134\pi$
$992$	−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	0.916445	−	0.400161i	$-0.131046\pi$
$997$	−0.458984	−	1.10809i	−0.0145362	−	0.0350934i	−0.930981	+	0.365068i	$0.881046\pi$
$998$	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	867.2.h.g.688.1		8
17.2	even	8		51.2.h.a.49.1	yes	8
17.3	odd	16		867.2.e.h.616.3		8
17.4	even	4		867.2.h.b.757.2		8
17.5	odd	16		867.2.e.h.829.2		8
17.6	odd	16		867.2.d.e.577.3		8
17.7	odd	16		867.2.a.m.1.3		4
17.8	even	8		867.2.h.b.733.2		8
17.9	even	8		867.2.h.f.733.2		8
17.10	odd	16		867.2.a.n.1.3		4
17.11	odd	16		867.2.d.e.577.4		8
17.12	odd	16		867.2.e.i.829.2		8
17.13	even	4		867.2.h.f.757.2		8
17.14	odd	16		867.2.e.i.616.3		8
17.15	even	8	inner	867.2.h.g.712.1		8
17.16	even	2		51.2.h.a.25.1	✓	8
51.2	odd	8		153.2.l.e.100.2		8
51.41	even	16		2601.2.a.bc.1.2		4
51.44	even	16		2601.2.a.bd.1.2		4
51.50	odd	2		153.2.l.e.127.2		8
68.19	odd	8		816.2.bq.a.49.2		8
68.67	odd	2		816.2.bq.a.433.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.25.1	✓	8	17.16	even	2
51.2.h.a.49.1	yes	8	17.2	even	8
153.2.l.e.100.2		8	51.2	odd	8
153.2.l.e.127.2		8	51.50	odd	2
816.2.bq.a.49.2		8	68.19	odd	8
816.2.bq.a.433.2		8	68.67	odd	2
867.2.a.m.1.3		4	17.7	odd	16
867.2.a.n.1.3		4	17.10	odd	16
867.2.d.e.577.3		8	17.6	odd	16
867.2.d.e.577.4		8	17.11	odd	16
867.2.e.h.616.3		8	17.3	odd	16
867.2.e.h.829.2		8	17.5	odd	16
867.2.e.i.616.3		8	17.14	odd	16
867.2.e.i.829.2		8	17.12	odd	16
867.2.h.b.733.2		8	17.8	even	8
867.2.h.b.757.2		8	17.4	even	4
867.2.h.f.733.2		8	17.9	even	8
867.2.h.f.757.2		8	17.13	even	4
867.2.h.g.688.1		8	1.1	even	1	trivial
867.2.h.g.712.1		8	17.15	even	8	inner
2601.2.a.bc.1.2		4	51.41	even	16
2601.2.a.bd.1.2		4	51.44	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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.541196 + 0.541196i) q^{2} +(0.382683 - 0.923880i) q^{3} +1.41421i q^{4} +(0.0761205 + 0.0315301i) q^{5} +(0.292893 + 0.707107i) q^{6} +(-2.55487 + 1.05826i) q^{7} +(-1.84776 - 1.84776i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(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} +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} -0.227845 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} +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} -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} +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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5} + 8 q^{6}+O(q^{10}) \) 8 * q + 8 * q^5 + 8 * q^6	\( 8 q + 8 q^{5} + 8 q^{6} - 8 q^{11} + 16 q^{14} + 16 q^{16} - 8 q^{19} - 16 q^{20} + 8 q^{22} - 8 q^{23} - 8 q^{24} - 16 q^{25} + 16 q^{26} + 8 q^{28} - 8 q^{31} + 8 q^{33} + 32 q^{35} + 8 q^{36} + 8 q^{37} - 16 q^{39} + 8 q^{40} + 24 q^{41} + 8 q^{42} - 8 q^{43} + 8 q^{45} - 8 q^{49} - 32 q^{50} - 16 q^{52} - 32 q^{53} + 8 q^{54} + 16 q^{56} + 16 q^{57} - 24 q^{58} + 16 q^{59} - 8 q^{60} - 16 q^{61} - 16 q^{62} - 24 q^{65} - 16 q^{66} - 16 q^{67} - 24 q^{69} + 40 q^{70} + 16 q^{71} - 48 q^{73} - 64 q^{74} - 16 q^{75} + 24 q^{76} - 8 q^{78} + 16 q^{80} + 8 q^{82} + 32 q^{83} - 32 q^{86} + 24 q^{87} + 8 q^{88} + 16 q^{91} + 32 q^{92} - 32 q^{93} + 40 q^{95} + 16 q^{96} - 8 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^5 + 8 * q^6 - 8 * q^11 + 16 * q^14 + 16 * q^16 - 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 + 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 - 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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