LMFDB - Embedded newform 510.2.l.g.137.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.6
Character	$\chi$	$=$	510.137
Dual form			510.2.l.g.443.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.44910 + 0.948737i) q^{3} -1.00000i q^{4} +(1.45929 - 1.69425i) q^{5} +(-1.69553 + 0.353812i) q^{6} +(3.19962 + 3.19962i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.19980 + 2.74963i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.44910 + 0.948737i) q^{3} -1.00000i q^{4} +(1.45929 - 1.69425i) q^{5} +(-1.69553 + 0.353812i) q^{6} +(3.19962 + 3.19962i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.19980 + 2.74963i) q^{9} +(0.166138 + 2.22989i) q^{10} -6.35238i q^{11} +(0.948737 - 1.44910i) q^{12} +(-1.37195 + 1.37195i) q^{13} -4.52495 q^{14} +(3.72206 - 1.07065i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(-2.79267 - 1.09590i) q^{18} -3.00819i q^{19} +(-1.69425 - 1.45929i) q^{20} +(1.60098 + 7.67218i) q^{21} +(4.49181 + 4.49181i) q^{22} +(0.729761 + 0.729761i) q^{23} +(0.353812 + 1.69553i) q^{24} +(-0.740938 - 4.94480i) q^{25} -1.94023i q^{26} +(-0.870049 + 5.12279i) q^{27} +(3.19962 - 3.19962i) q^{28} +0.906803 q^{29} +(-1.87483 + 3.38896i) q^{30} -2.80195 q^{31} +(0.707107 - 0.707107i) q^{32} +(6.02674 - 9.20526i) q^{33} -1.00000i q^{34} +(10.0901 - 0.751766i) q^{35} +(2.74963 - 1.19980i) q^{36} +(5.53263 + 5.53263i) q^{37} +(2.12711 + 2.12711i) q^{38} +(-3.28971 + 0.686476i) q^{39} +(2.22989 - 0.166138i) q^{40} -1.28681i q^{41} +(-6.55712 - 4.29298i) q^{42} +(-6.31079 + 6.31079i) q^{43} -6.35238 q^{44} +(6.40941 + 1.97976i) q^{45} -1.03204 q^{46} +(-5.58158 + 5.58158i) q^{47} +(-1.44910 - 0.948737i) q^{48} +13.4752i q^{49} +(4.02042 + 2.97258i) q^{50} +(-1.69553 + 0.353812i) q^{51} +(1.37195 + 1.37195i) q^{52} +(-7.23598 - 7.23598i) q^{53} +(-3.00714 - 4.23758i) q^{54} +(-10.7625 - 9.26998i) q^{55} +4.52495i q^{56} +(2.85398 - 4.35917i) q^{57} +(-0.641207 + 0.641207i) q^{58} -1.73402 q^{59} +(-1.07065 - 3.72206i) q^{60} -0.769212 q^{61} +(1.98127 - 1.98127i) q^{62} +(-4.95889 + 12.6367i) q^{63} +1.00000i q^{64} +(0.322346 + 4.32649i) q^{65} +(2.24755 + 10.7706i) q^{66} +(-3.15710 - 3.15710i) q^{67} +(0.707107 + 0.707107i) q^{68} +(0.365148 + 1.74985i) q^{69} +(-6.60322 + 7.66638i) q^{70} +15.2107i q^{71} +(-1.09590 + 2.79267i) q^{72} +(7.48444 - 7.48444i) q^{73} -7.82432 q^{74} +(3.61761 - 7.86847i) q^{75} -3.00819 q^{76} +(20.3252 - 20.3252i) q^{77} +(1.84077 - 2.81159i) q^{78} -1.01612i q^{79} +(-1.45929 + 1.69425i) q^{80} +(-6.12097 + 6.59801i) q^{81} +(0.909913 + 0.909913i) q^{82} +(-3.96539 - 3.96539i) q^{83} +(7.67218 - 1.60098i) q^{84} +(0.166138 + 2.22989i) q^{85} -8.92481i q^{86} +(1.31405 + 0.860318i) q^{87} +(4.49181 - 4.49181i) q^{88} +1.88602 q^{89} +(-5.93204 + 3.13223i) q^{90} -8.77943 q^{91} +(0.729761 - 0.729761i) q^{92} +(-4.06031 - 2.65831i) q^{93} -7.89354i q^{94} +(-5.09661 - 4.38982i) q^{95} +(1.69553 - 0.353812i) q^{96} +(9.02893 + 9.02893i) q^{97} +(-9.52838 - 9.52838i) q^{98} +(17.4667 - 7.62157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7}+O(q^{10}) $ 28 * q + 4 * q^7	$ 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) $ 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.44910	+	0.948737i	0.836640	+	0.547753i
$3$	1.44910	+	0.948737i	0.836640	+	0.547753i
$4$		−	1.00000i		−	0.500000i
$5$	1.45929	−	1.69425i	0.652615	−	0.757690i
$5$	1.45929	−	1.69425i	0.652615	−	0.757690i
$6$	−1.69553	+	0.353812i	−0.692197	+	0.144443i
$7$	3.19962	+	3.19962i	1.20934	+	1.20934i	0.971240	+	0.238104i	$0.0765258\pi$
$7$	3.19962	+	3.19962i	1.20934	+	1.20934i	0.238104	+	0.971240i	$0.423474\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.19980	+	2.74963i	0.399932	+	0.916545i
$10$	0.166138	+	2.22989i	0.0525375	+	0.705152i
$11$		−	6.35238i		−	1.91532i	−0.287909	−	0.957658i	$-0.592960\pi$
$11$		−	6.35238i		−	1.91532i	0.287909	−	0.957658i	$-0.407040\pi$
$12$	0.948737	−	1.44910i	0.273877	−	0.418320i
$13$	−1.37195	+	1.37195i	−0.380510	+	0.380510i	−0.871286	−	0.490776i	$-0.836713\pi$
$13$	−1.37195	+	1.37195i	−0.380510	+	0.380510i	0.490776	+	0.871286i	$0.336713\pi$
$14$	−4.52495			−1.20934
$15$	3.72206	−	1.07065i	0.961031	−	0.276441i
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$	−2.79267	−	1.09590i	−0.658239	−	0.258306i
$19$		−	3.00819i		−	0.690125i	−0.938580	−	0.345063i	$-0.887858\pi$
$19$		−	3.00819i		−	0.690125i	0.938580	−	0.345063i	$-0.112142\pi$
$20$	−1.69425	−	1.45929i	−0.378845	−	0.326307i
$21$	1.60098	+	7.67218i	0.349363	+	1.67421i
$22$	4.49181	+	4.49181i	0.957658	+	0.957658i
$23$	0.729761	+	0.729761i	0.152166	+	0.152166i	0.779085	−	0.626919i	$-0.215684\pi$
$23$	0.729761	+	0.729761i	0.152166	+	0.152166i	−0.626919	+	0.779085i	$0.715684\pi$
$24$	0.353812	+	1.69553i	0.0722216	+	0.346098i
$25$	−0.740938	−	4.94480i	−0.148188	−	0.988959i
$26$		−	1.94023i		−	0.380510i
$27$	−0.870049	+	5.12279i	−0.167441	+	0.985882i
$28$	3.19962	−	3.19962i	0.604672	−	0.604672i
$29$	0.906803			0.168389			0.0841946	−	0.996449i	$-0.473168\pi$
$29$	0.906803			0.168389			0.0841946	+	0.996449i	$0.473168\pi$
$30$	−1.87483	+	3.38896i	−0.342295	+	0.618736i
$31$	−2.80195			−0.503244			−0.251622	−	0.967826i	$-0.580964\pi$
$31$	−2.80195			−0.503244			−0.251622	+	0.967826i	$0.580964\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	6.02674	−	9.20526i	1.04912	−	1.60243i
$34$		−	1.00000i		−	0.171499i
$35$	10.0901	−	0.751766i	1.70554	−	0.127072i
$36$	2.74963	−	1.19980i	0.458272	−	0.199966i
$37$	5.53263	+	5.53263i	0.909559	+	0.909559i	0.996236	−	0.0866777i	$-0.0276250\pi$
$37$	5.53263	+	5.53263i	0.909559	+	0.909559i	−0.0866777	+	0.996236i	$0.527625\pi$
$38$	2.12711	+	2.12711i	0.345063	+	0.345063i
$39$	−3.28971	+	0.686476i	−0.526775	+	0.109924i
$40$	2.22989	−	0.166138i	0.352576	−	0.0262687i
$41$		−	1.28681i		−	0.200966i	−0.994939	−	0.100483i	$-0.967961\pi$
$41$		−	1.28681i		−	0.200966i	0.994939	−	0.100483i	$-0.0320388\pi$
$42$	−6.55712	−	4.29298i	−1.01178	−	0.662422i
$43$	−6.31079	+	6.31079i	−0.962387	+	0.962387i	−0.999318	−	0.0369308i	$-0.988242\pi$
$43$	−6.31079	+	6.31079i	−0.962387	+	0.962387i	0.0369308	+	0.999318i	$0.488242\pi$
$44$	−6.35238			−0.957658
$45$	6.40941	+	1.97976i	0.955458	+	0.295126i
$46$	−1.03204			−0.152166
$47$	−5.58158	+	5.58158i	−0.814156	+	0.814156i	−0.985254	−	0.171098i	$-0.945269\pi$
$47$	−5.58158	+	5.58158i	−0.814156	+	0.814156i	0.171098	+	0.985254i	$0.445269\pi$
$48$	−1.44910	−	0.948737i	−0.209160	−	0.136938i
$49$			13.4752i			1.92502i
$50$	4.02042	+	2.97258i	0.568573	+	0.420386i
$51$	−1.69553	+	0.353812i	−0.237421	+	0.0495436i
$52$	1.37195	+	1.37195i	0.190255	+	0.190255i
$53$	−7.23598	−	7.23598i	−0.993939	−	0.993939i	0.00604285	−	0.999982i	$-0.498076\pi$
$53$	−7.23598	−	7.23598i	−0.993939	−	0.993939i	−0.999982	+	0.00604285i	$0.998076\pi$
$54$	−3.00714	−	4.23758i	−0.409221	−	0.576662i
$55$	−10.7625	−	9.26998i	−1.45122	−	1.24996i
$56$			4.52495i			0.604672i
$57$	2.85398	−	4.35917i	0.378018	−	0.577386i
$58$	−0.641207	+	0.641207i	−0.0841946	+	0.0841946i
$59$	−1.73402			−0.225750			−0.112875	−	0.993609i	$-0.536006\pi$
$59$	−1.73402			−0.225750			−0.112875	+	0.993609i	$0.536006\pi$
$60$	−1.07065	−	3.72206i	−0.138221	−	0.480515i
$61$	−0.769212			−0.0984875			−0.0492438	−	0.998787i	$-0.515681\pi$
$61$	−0.769212			−0.0984875			−0.0492438	+	0.998787i	$0.515681\pi$
$62$	1.98127	−	1.98127i	0.251622	−	0.251622i
$63$	−4.95889	+	12.6367i	−0.624761	+	1.59207i
$64$			1.00000i			0.125000i
$65$	0.322346	+	4.32649i	0.0399820	+	0.536635i
$66$	2.24755	+	10.7706i	0.276654	+	1.32577i
$67$	−3.15710	−	3.15710i	−0.385701	−	0.385701i	0.487450	−	0.873151i	$-0.337927\pi$
$67$	−3.15710	−	3.15710i	−0.385701	−	0.385701i	−0.873151	+	0.487450i	$0.837927\pi$
$68$	0.707107	+	0.707107i	0.0857493	+	0.0857493i
$69$	0.365148	+	1.74985i	0.0439586	+	0.210657i
$70$	−6.60322	+	7.66638i	−0.789235	+	0.916307i
$71$			15.2107i			1.80518i	0.430502	+	0.902590i	$0.358337\pi$
$71$			15.2107i			1.80518i	−0.430502	+	0.902590i	$0.641663\pi$
$72$	−1.09590	+	2.79267i	−0.129153	+	0.329119i
$73$	7.48444	−	7.48444i	0.875988	−	0.875988i	−0.117129	−	0.993117i	$-0.537369\pi$
$73$	7.48444	−	7.48444i	0.875988	−	0.875988i	0.993117	+	0.117129i	$0.0373690\pi$
$74$	−7.82432			−0.909559
$75$	3.61761	−	7.86847i	0.417726	−	0.908573i
$76$	−3.00819			−0.345063
$77$	20.3252	−	20.3252i	2.31627	−	2.31627i
$78$	1.84077	−	2.81159i	0.208426	−	0.318350i
$79$		−	1.01612i		−	0.114322i	−0.998365	−	0.0571610i	$-0.981795\pi$
$79$		−	1.01612i		−	0.114322i	0.998365	−	0.0571610i	$-0.0182048\pi$
$80$	−1.45929	+	1.69425i	−0.163154	+	0.189422i
$81$	−6.12097	+	6.59801i	−0.680108	+	0.733112i
$82$	0.909913	+	0.909913i	0.100483	+	0.100483i
$83$	−3.96539	−	3.96539i	−0.435258	−	0.435258i	0.455154	−	0.890413i	$-0.349584\pi$
$83$	−3.96539	−	3.96539i	−0.435258	−	0.435258i	−0.890413	+	0.455154i	$0.849584\pi$
$84$	7.67218	−	1.60098i	0.837103	−	0.174681i
$85$	0.166138	+	2.22989i	0.0180202	+	0.241865i
$86$		−	8.92481i		−	0.962387i
$87$	1.31405	+	0.860318i	0.140881	+	0.0922357i
$88$	4.49181	−	4.49181i	0.478829	−	0.478829i
$89$	1.88602			0.199918			0.0999589	−	0.994992i	$-0.468129\pi$
$89$	1.88602			0.199918			0.0999589	+	0.994992i	$0.468129\pi$
$90$	−5.93204	+	3.13223i	−0.625292	+	0.330166i
$91$	−8.77943			−0.920334
$92$	0.729761	−	0.729761i	0.0760829	−	0.0760829i
$93$	−4.06031	−	2.65831i	−0.421034	−	0.275654i
$94$		−	7.89354i		−	0.814156i
$95$	−5.09661	−	4.38982i	−0.522901	−	0.450386i
$96$	1.69553	−	0.353812i	0.173049	−	0.0361108i
$97$	9.02893	+	9.02893i	0.916749	+	0.916749i	0.996791	−	0.0800423i	$-0.0255055\pi$
$97$	9.02893	+	9.02893i	0.916749	+	0.916749i	−0.0800423	+	0.996791i	$0.525506\pi$
$98$	−9.52838	−	9.52838i	−0.962511	−	0.962511i
$99$	17.4667	−	7.62157i	1.75547	−	0.765997i
$100$	−4.94480	+	0.740938i	−0.494480	+	0.0740938i
$101$		−	2.79951i		−	0.278561i	−0.990253	−	0.139281i	$-0.955521\pi$
$101$		−	2.79951i		−	0.278561i	0.990253	−	0.139281i	$-0.0444790\pi$
$102$	0.948737	−	1.44910i	0.0939389	−	0.143483i
$103$	1.56218	−	1.56218i	0.153926	−	0.153926i	−0.625943	−	0.779869i	$-0.715286\pi$
$103$	1.56218	−	1.56218i	0.153926	−	0.153926i	0.779869	+	0.625943i	$0.215286\pi$
$104$	−1.94023			−0.190255
$105$	15.3349	+	8.48349i	1.49653	+	0.827904i
$106$	10.2332			0.993939
$107$	9.90455	−	9.90455i	0.957509	−	0.957509i	−0.0416240	−	0.999133i	$-0.513253\pi$
$107$	9.90455	−	9.90455i	0.957509	−	0.957509i	0.999133	+	0.0416240i	$0.0132531\pi$
$108$	5.12279	+	0.870049i	0.492941	+	0.0837205i
$109$		−	16.8178i		−	1.61085i	−0.592694	−	0.805427i	$-0.701936\pi$
$109$		−	16.8178i		−	1.61085i	0.592694	−	0.805427i	$-0.298064\pi$
$110$	14.1651	−	1.05537i	1.35059	−	0.100626i
$111$	2.76834	+	13.2664i	0.262759	+	1.25919i
$112$	−3.19962	−	3.19962i	−0.302336	−	0.302336i
$113$	−14.0896	−	14.0896i	−1.32544	−	1.32544i	−0.909299	−	0.416144i	$-0.863381\pi$
$113$	−14.0896	−	14.0896i	−1.32544	−	1.32544i	−0.416144	−	0.909299i	$-0.636619\pi$
$114$	1.06433	+	5.10047i	0.0996839	+	0.477702i
$115$	2.30133	−	0.171461i	0.214600	−	0.0159888i
$116$		−	0.906803i		−	0.0841946i
$117$	−5.41842	−	2.12630i	−0.500933	−	0.196576i
$118$	1.22614	−	1.22614i	0.112875	−	0.112875i
$119$	−4.52495			−0.414801
$120$	3.38896	+	1.87483i	0.309368	+	0.171147i
$121$	−29.3528			−2.66843
$122$	0.543915	−	0.543915i	0.0492438	−	0.0492438i
$123$	1.22084	−	1.86472i	0.110080	−	0.168136i
$124$			2.80195i			0.251622i
$125$	−9.45895	−	5.96057i	−0.846034	−	0.533129i
$126$	−5.42902	−	12.4420i	−0.483656	−	1.10842i
$127$	−3.29168	−	3.29168i	−0.292090	−	0.292090i	0.545816	−	0.837905i	$-0.316220\pi$
$127$	−3.29168	−	3.29168i	−0.292090	−	0.292090i	−0.837905	+	0.545816i	$0.816220\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−15.1323	+	3.15771i	−1.33232	+	0.278021i
$130$	−3.28722	−	2.83136i	−0.288309	−	0.248326i
$131$			5.49121i			0.479769i	0.970801	+	0.239885i	$0.0771096\pi$
$131$			5.49121i			0.479769i	−0.970801	+	0.239885i	$0.922890\pi$
$132$	−9.20526	−	6.02674i	−0.801215	−	0.524560i
$133$	9.62506	−	9.62506i	0.834598	−	0.834598i
$134$	4.46481			0.385701
$135$	7.40962	+	8.94972i	0.637718	+	0.770270i
$136$	−1.00000			−0.0857493
$137$	−13.3734	+	13.3734i	−1.14257	+	1.14257i	−0.154592	+	0.987978i	$0.549406\pi$
$137$	−13.3734	+	13.3734i	−1.14257	+	1.14257i	−0.987978	+	0.154592i	$0.950594\pi$
$138$	−1.49553	−	0.979133i	−0.127308	−	0.0833493i
$139$		−	12.8630i		−	1.09103i	−0.838103	−	0.545513i	$-0.816335\pi$
$139$		−	12.8630i		−	1.09103i	0.838103	−	0.545513i	$-0.183665\pi$
$140$	−0.751766	−	10.0901i	−0.0635358	−	0.852771i
$141$	−13.3837	+	2.79283i	−1.12711	+	0.235199i
$142$	−10.7556	−	10.7556i	−0.902590	−	0.902590i
$143$	8.71514	+	8.71514i	0.728797	+	0.728797i
$144$	−1.19980	−	2.74963i	−0.0999831	−	0.229136i
$145$	1.32329	−	1.53635i	0.109893	−	0.127587i
$146$			10.5846i			0.875988i
$147$	−12.7844	+	19.5269i	−1.05444	+	1.61055i
$148$	5.53263	−	5.53263i	0.454779	−	0.454779i
$149$	5.16607			0.423221			0.211611	−	0.977354i	$-0.432129\pi$
$149$	5.16607			0.423221			0.211611	+	0.977354i	$0.432129\pi$
$150$	3.00581	+	8.12189i	0.245423	+	0.663150i
$151$	−1.19231			−0.0970286			−0.0485143	−	0.998822i	$-0.515449\pi$
$151$	−1.19231			−0.0970286			−0.0485143	+	0.998822i	$0.515449\pi$
$152$	2.12711	−	2.12711i	0.172531	−	0.172531i
$153$	−2.79267	−	1.09590i	−0.225774	−	0.0885983i
$154$			28.7442i			2.31627i
$155$	−4.08885	+	4.74718i	−0.328425	+	0.381303i
$156$	0.686476	+	3.28971i	0.0549621	+	0.263388i
$157$	−10.0270	−	10.0270i	−0.800244	−	0.800244i	0.182889	−	0.983133i	$-0.441455\pi$
$157$	−10.0270	−	10.0270i	−0.800244	−	0.800244i	−0.983133	+	0.182889i	$0.941455\pi$
$158$	0.718503	+	0.718503i	0.0571610	+	0.0571610i
$159$	−3.62064	−	17.3507i	−0.287135	−	1.37600i
$160$	−0.166138	−	2.22989i	−0.0131344	−	0.176288i
$161$			4.66992i			0.368041i
$162$	−0.337314	−	8.99368i	−0.0265019	−	0.706610i
$163$	−7.17303	+	7.17303i	−0.561835	+	0.561835i	−0.929828	−	0.367994i	$-0.880045\pi$
$163$	−7.17303	+	7.17303i	−0.561835	+	0.561835i	0.367994	+	0.929828i	$0.380045\pi$
$164$	−1.28681			−0.100483
$165$	−6.80120	−	23.6439i	−0.529473	−	1.84068i
$166$	5.60791			0.435258
$167$	2.71633	−	2.71633i	0.210196	−	0.210196i	−0.594155	−	0.804351i	$-0.702513\pi$
$167$	2.71633	−	2.71633i	0.210196	−	0.210196i	0.804351	+	0.594155i	$0.202513\pi$
$168$	−4.29298	+	6.55712i	−0.331211	+	0.505892i
$169$			9.23552i			0.710424i
$170$	−1.69425	−	1.45929i	−0.129943	−	0.111923i
$171$	8.27141	−	3.60921i	0.632531	−	0.276004i
$172$	6.31079	+	6.31079i	0.481194	+	0.481194i
$173$	−4.51216	−	4.51216i	−0.343053	−	0.343053i	0.514461	−	0.857514i	$-0.327992\pi$
$173$	−4.51216	−	4.51216i	−0.343053	−	0.343053i	−0.857514	+	0.514461i	$0.827992\pi$
$174$	−1.53751	+	0.320838i	−0.116558	+	0.0243227i
$175$	13.4508	−	18.1922i	1.01678	−	1.37520i
$176$			6.35238i			0.478829i
$177$	−2.51278	−	1.64513i	−0.188872	−	0.123656i
$178$	−1.33362	+	1.33362i	−0.0999589	+	0.0999589i
$179$	−3.38285			−0.252846			−0.126423	−	0.991976i	$-0.540350\pi$
$179$	−3.38285			−0.252846			−0.126423	+	0.991976i	$0.540350\pi$
$180$	1.97976	−	6.40941i	0.147563	−	0.477729i
$181$	20.5489			1.52739			0.763694	−	0.645578i	$-0.223383\pi$
$181$	20.5489			1.52739			0.763694	+	0.645578i	$0.223383\pi$
$182$	6.20800	−	6.20800i	0.460167	−	0.460167i
$183$	−1.11467	−	0.729780i	−0.0823986	−	0.0539469i
$184$			1.03204i			0.0760829i
$185$	17.4474	−	1.29992i	1.28275	−	0.0955718i
$186$	4.75078	−	0.991362i	0.348344	−	0.0726902i
$187$	4.49181	+	4.49181i	0.328474	+	0.328474i
$188$	5.58158	+	5.58158i	0.407078	+	0.407078i
$189$	−19.1748	+	13.6072i	−1.39476	+	0.989776i
$190$	6.70792	−	0.499774i	0.486643	−	0.0362574i
$191$			5.54170i			0.400983i	0.979695	+	0.200492i	$0.0642540\pi$
$191$			5.54170i			0.400983i	−0.979695	+	0.200492i	$0.935746\pi$
$192$	−0.948737	+	1.44910i	−0.0684692	+	0.104580i
$193$	5.77107	−	5.77107i	0.415411	−	0.415411i	−0.468208	−	0.883618i	$-0.655100\pi$
$193$	5.77107	−	5.77107i	0.415411	−	0.415411i	0.883618	+	0.468208i	$0.155100\pi$
$194$	−12.7688			−0.916749
$195$	−3.63759	+	6.57535i	−0.260493	+	0.470871i
$196$	13.4752			0.962511
$197$	12.4315	−	12.4315i	0.885710	−	0.885710i	−0.108398	−	0.994108i	$-0.534572\pi$
$197$	12.4315	−	12.4315i	0.885710	−	0.885710i	0.994108	+	0.108398i	$0.0345720\pi$
$198$	−6.96158	+	17.7401i	−0.494738	+	1.26073i
$199$			2.75111i			0.195021i	0.995235	+	0.0975104i	$0.0310879\pi$
$199$			2.75111i			0.195021i	−0.995235	+	0.0975104i	$0.968912\pi$
$200$	2.97258	−	4.02042i	0.210193	−	0.284287i
$201$	−1.57970	−	7.57021i	−0.111424	−	0.533962i
$202$	1.97955	+	1.97955i	0.139281	+	0.139281i
$203$	2.90143	+	2.90143i	0.203640	+	0.203640i
$204$	0.353812	+	1.69553i	0.0247718	+	0.118711i
$205$	−2.18017	−	1.87783i	−0.152270	−	0.131153i
$206$			2.20926i			0.153926i
$207$	−1.13101	+	2.88214i	−0.0786107	+	0.200323i
$208$	1.37195	−	1.37195i	0.0951275	−	0.0951275i
$209$	−19.1092			−1.32181
$210$	−16.8421	+	4.84465i	−1.16222	+	0.334313i
$211$	−11.5761			−0.796934			−0.398467	−	0.917183i	$-0.630458\pi$
$211$	−11.5761			−0.796934			−0.398467	+	0.917183i	$0.630458\pi$
$212$	−7.23598	+	7.23598i	−0.496969	+	0.496969i
$213$	−14.4310	+	22.0419i	−0.988793	+	1.51028i
$214$			14.0072i			0.957509i
$215$	1.48275	+	19.9013i	0.101123	+	1.35726i
$216$	−4.23758	+	3.00714i	−0.288331	+	0.204610i
$217$	−8.96517	−	8.96517i	−0.608595	−	0.608595i
$218$	11.8920	+	11.8920i	0.805427	+	0.805427i
$219$	17.9465	−	3.74496i	1.21271	−	0.253061i
$220$	−9.26998	+	10.7625i	−0.624982	+	0.725608i
$221$		−	1.94023i		−	0.130514i
$222$	−11.3382	−	7.42322i	−0.760973	−	0.498214i
$223$	11.5587	−	11.5587i	0.774028	−	0.774028i	−0.204780	−	0.978808i	$-0.565648\pi$
$223$	11.5587	−	11.5587i	0.774028	−	0.774028i	0.978808	+	0.204780i	$0.0656479\pi$
$224$	4.52495			0.302336
$225$	12.7074	−	7.97006i	0.847160	−	0.531337i
$226$	19.9258			1.32544
$227$	−18.4657	+	18.4657i	−1.22561	+	1.22561i	−0.260003	+	0.965608i	$0.583724\pi$
$227$	−18.4657	+	18.4657i	−1.22561	+	1.22561i	−0.965608	+	0.260003i	$0.916276\pi$
$228$	−4.35917	−	2.85398i	−0.288693	−	0.189009i
$229$		−	10.0436i		−	0.663702i	−0.943332	−	0.331851i	$-0.892327\pi$
$229$		−	10.0436i		−	0.663702i	0.943332	−	0.331851i	$-0.107673\pi$
$230$	−1.50604	+	1.74853i	−0.0993056	+	0.115294i
$231$	48.7366	−	10.1701i	3.20663	−	0.669140i
$232$	0.641207	+	0.641207i	0.0420973	+	0.0420973i
$233$	5.03975	+	5.03975i	0.330165	+	0.330165i	0.852649	−	0.522484i	$-0.174995\pi$
$233$	5.03975	+	5.03975i	0.330165	+	0.330165i	−0.522484	+	0.852649i	$0.674995\pi$
$234$	5.33492	−	2.32788i	0.348754	−	0.152178i
$235$	1.31142	+	17.6017i	0.0855474	+	1.14821i
$236$			1.73402i			0.112875i
$237$	0.964027	−	1.47246i	0.0626203	−	0.0956464i
$238$	3.19962	−	3.19962i	0.207401	−	0.207401i
$239$	−0.648149			−0.0419253			−0.0209627	−	0.999780i	$-0.506673\pi$
$239$	−0.648149			−0.0419253			−0.0209627	+	0.999780i	$0.506673\pi$
$240$	−3.72206	+	1.07065i	−0.240258	+	0.0691104i
$241$	13.1385			0.846328			0.423164	−	0.906053i	$-0.360919\pi$
$241$	13.1385			0.846328			0.423164	+	0.906053i	$0.360919\pi$
$242$	20.7555	−	20.7555i	1.33422	−	1.33422i
$243$	−15.1297	+	3.75400i	−0.970570	+	0.240819i
$244$			0.769212i			0.0492438i
$245$	22.8302	+	19.6642i	1.45857	+	1.25630i
$246$	0.455289	+	2.18182i	0.0290282	+	0.139108i
$247$	4.12708	+	4.12708i	0.262600	+	0.262600i
$248$	−1.98127	−	1.98127i	−0.125811	−	0.125811i
$249$	−1.98415	−	9.50837i	−0.125740	−	0.602569i
$250$	10.9032	−	2.47373i	0.689582	−	0.156452i
$251$		−	15.5236i		−	0.979843i	−0.871767	−	0.489922i	$-0.837025\pi$
$251$		−	15.5236i		−	0.979843i	0.871767	−	0.489922i	$-0.162975\pi$
$252$	12.6367	+	4.95889i	0.796036	+	0.312381i
$253$	4.63572	−	4.63572i	0.291445	−	0.291445i
$254$	4.65515			0.292090
$255$	−1.87483	+	3.38896i	−0.117406	+	0.212225i
$256$	1.00000			0.0625000
$257$	−12.8225	+	12.8225i	−0.799846	+	0.799846i	−0.983071	−	0.183225i	$-0.941346\pi$
$257$	−12.8225	+	12.8225i	−0.799846	+	0.799846i	0.183225	+	0.983071i	$0.441346\pi$
$258$	8.46729	−	12.9330i	0.527151	−	0.805171i
$259$			35.4046i			2.19994i
$260$	4.32649	−	0.322346i	0.268317	−	0.0199910i
$261$	1.08798	+	2.49338i	0.0673443	+	0.154336i
$262$	−3.88287	−	3.88287i	−0.239885	−	0.239885i
$263$	4.61181	+	4.61181i	0.284376	+	0.284376i	0.834851	−	0.550475i	$-0.185553\pi$
$263$	4.61181	+	4.61181i	0.284376	+	0.284376i	−0.550475	+	0.834851i	$0.685553\pi$
$264$	10.7706	−	2.24755i	0.662887	−	0.138327i
$265$	−22.8189	+	1.70013i	−1.40176	+	0.104438i
$266$			13.6119i			0.834598i
$267$	2.73304	+	1.78934i	0.167259	+	0.109506i
$268$	−3.15710	+	3.15710i	−0.192850	+	0.192850i
$269$	11.2336			0.684927			0.342464	−	0.939531i	$-0.388739\pi$
$269$	11.2336			0.684927			0.342464	+	0.939531i	$0.388739\pi$
$270$	−11.5678	−	1.08902i	−0.703994	−	0.0662757i
$271$	−13.3196			−0.809109			−0.404555	−	0.914514i	$-0.632573\pi$
$271$	−13.3196			−0.809109			−0.404555	+	0.914514i	$0.632573\pi$
$272$	0.707107	−	0.707107i	0.0428746	−	0.0428746i
$273$	−12.7223	−	8.32937i	−0.769988	−	0.504116i
$274$		−	18.9129i		−	1.14257i
$275$	−31.4112	+	4.70672i	−1.89417	+	0.283826i
$276$	1.74985	−	0.365148i	0.105329	−	0.0219793i
$277$	13.0498	+	13.0498i	0.784084	+	0.784084i	0.980517	−	0.196433i	$-0.0629358\pi$
$277$	13.0498	+	13.0498i	0.784084	+	0.784084i	−0.196433	+	0.980517i	$0.562936\pi$
$278$	9.09552	+	9.09552i	0.545513	+	0.545513i
$279$	−3.36177	−	7.70432i	−0.201264	−	0.461246i
$280$	7.66638	+	6.60322i	0.458154	+	0.394618i
$281$		−	22.2785i		−	1.32902i	−0.747279	−	0.664511i	$-0.768640\pi$
$281$		−	22.2785i		−	1.32902i	0.747279	−	0.664511i	$-0.231360\pi$
$282$	7.48889	−	11.4385i	0.445957	−	0.681156i
$283$	−7.85291	+	7.85291i	−0.466807	+	0.466807i	−0.900878	−	0.434072i	$-0.857076\pi$
$283$	−7.85291	+	7.85291i	−0.466807	+	0.466807i	0.434072	+	0.900878i	$0.357076\pi$
$284$	15.2107			0.902590
$285$	−3.22072	−	11.1966i	−0.190779	−	0.663232i
$286$	−12.3251			−0.728797
$287$	4.11731	−	4.11731i	0.243037	−	0.243037i
$288$	2.79267	+	1.09590i	0.164560	+	0.0645765i
$289$		−	1.00000i		−	0.0588235i
$290$	0.150655	+	2.02207i	0.00884674	+	0.118740i
$291$	4.51777	+	21.6499i	0.264836	+	1.26914i
$292$	−7.48444	−	7.48444i	−0.437994	−	0.437994i
$293$	14.5565	+	14.5565i	0.850400	+	0.850400i	0.990182	−	0.139782i	$-0.0446403\pi$
$293$	14.5565	+	14.5565i	0.850400	+	0.850400i	−0.139782	+	0.990182i	$0.544640\pi$
$294$	−4.76768	−	22.8475i	−0.278057	−	1.33249i
$295$	−2.53044	+	2.93786i	−0.147328	+	0.171049i
$296$			7.82432i			0.454779i
$297$	32.5419	+	5.52688i	1.88828	+	0.320702i
$298$	−3.65296	+	3.65296i	−0.211611	+	0.211611i
$299$	−2.00239			−0.115801
$300$	−7.86847	−	3.61761i	−0.454286	−	0.208863i
$301$	−40.3843			−2.32771
$302$	0.843089	−	0.843089i	0.0485143	−	0.0485143i
$303$	2.65599	−	4.05677i	0.152583	−	0.233055i
$304$			3.00819i			0.172531i
$305$	−1.12250	+	1.30323i	−0.0642744	+	0.0746230i
$306$	2.74963	−	1.19980i	0.157186	−	0.0685879i
$307$	15.3323	+	15.3323i	0.875060	+	0.875060i	0.993018	−	0.117959i	$-0.0376351\pi$
$307$	15.3323	+	15.3323i	0.875060	+	0.875060i	−0.117959	+	0.993018i	$0.537635\pi$
$308$	−20.3252	−	20.3252i	−1.15814	−	1.15814i
$309$	3.74586	−	0.781663i	0.213095	−	0.0444672i
$310$	−0.465510	−	6.24802i	−0.0264392	−	0.354864i
$311$			24.2861i			1.37714i	0.725171	+	0.688568i	$0.241760\pi$
$311$			24.2861i			1.37714i	−0.725171	+	0.688568i	$0.758240\pi$
$312$	−2.81159	−	1.84077i	−0.159175	−	0.104213i
$313$	1.38054	−	1.38054i	0.0780329	−	0.0780329i	−0.667013	−	0.745046i	$-0.732427\pi$
$313$	1.38054	−	1.38054i	0.0780329	−	0.0780329i	0.745046	+	0.667013i	$0.232427\pi$
$314$	14.1804			0.800244
$315$	14.1732	+	26.8422i	0.798569	+	1.51239i
$316$	−1.01612			−0.0571610
$317$	−8.51890	+	8.51890i	−0.478469	+	0.478469i	−0.904642	−	0.426173i	$-0.859862\pi$
$317$	−8.51890	+	8.51890i	−0.478469	+	0.478469i	0.426173	+	0.904642i	$0.359862\pi$
$318$	14.8290	+	9.70864i	0.831569	+	0.544433i
$319$		−	5.76036i		−	0.322518i
$320$	1.69425	+	1.45929i	0.0947112	+	0.0815769i
$321$	23.7495	−	4.95590i	1.32557	−	0.276611i
$322$	−3.30213	−	3.30213i	−0.184021	−	0.184021i
$323$	2.12711	+	2.12711i	0.118356	+	0.118356i
$324$	6.59801	+	6.12097i	0.366556	+	0.340054i
$325$	7.80053	+	5.76748i	0.432696	+	0.319922i
$326$		−	10.1442i		−	0.561835i
$327$	15.9557	−	24.3707i	0.882351	−	1.34771i
$328$	0.909913	−	0.909913i	0.0502415	−	0.0502415i
$329$	−35.7179			−1.96919
$330$	21.5280	+	11.9096i	1.18507	+	0.655602i
$331$	7.33597			0.403222			0.201611	−	0.979466i	$-0.435382\pi$
$331$	7.33597			0.403222			0.201611	+	0.979466i	$0.435382\pi$
$332$	−3.96539	+	3.96539i	−0.217629	+	0.217629i
$333$	−8.57467	+	21.8507i	−0.469889	+	1.19741i
$334$			3.84148i			0.210196i
$335$	−9.95602	+	0.741775i	−0.543956	+	0.0405275i
$336$	−1.60098	−	7.67218i	−0.0873407	−	0.418552i
$337$	15.7547	+	15.7547i	0.858215	+	0.858215i	0.991128	−	0.132913i	$-0.0424331\pi$
$337$	15.7547	+	15.7547i	0.858215	+	0.858215i	−0.132913	+	0.991128i	$0.542433\pi$
$338$	−6.53050	−	6.53050i	−0.355212	−	0.355212i
$339$	−7.04998	−	33.7847i	−0.382902	−	1.83493i
$340$	2.22989	−	0.166138i	0.120933	−	0.00901010i
$341$			17.7990i			0.963872i
$342$	−3.29667	+	8.40087i	−0.178264	+	0.454267i
$343$	−20.7181	+	20.7181i	−1.11867	+	1.11867i
$344$	−8.92481			−0.481194
$345$	3.49753	+	1.93489i	0.188301	+	0.104171i
$346$	6.38116			0.343053
$347$	−12.4419	+	12.4419i	−0.667915	+	0.667915i	−0.957233	−	0.289318i	$-0.906571\pi$
$347$	−12.4419	+	12.4419i	−0.667915	+	0.667915i	0.289318	+	0.957233i	$0.406571\pi$
$348$	0.860318	−	1.31405i	0.0461179	−	0.0704405i
$349$			4.96685i			0.265869i	0.991125	+	0.132935i	$0.0424400\pi$
$349$			4.96685i			0.265869i	−0.991125	+	0.132935i	$0.957560\pi$
$350$	3.35271	+	22.3749i	0.179210	+	1.19599i
$351$	−5.83455	−	8.22187i	−0.311425	−	0.438851i
$352$	−4.49181	−	4.49181i	−0.239414	−	0.239414i
$353$	−14.3035	−	14.3035i	−0.761301	−	0.761301i	0.215256	−	0.976558i	$-0.430941\pi$
$353$	−14.3035	−	14.3035i	−0.761301	−	0.761301i	−0.976558	+	0.215256i	$0.930941\pi$
$354$	2.94008	−	0.613518i	0.156264	−	0.0326081i
$355$	25.7707	+	22.1969i	1.36777	+	1.17809i
$356$		−	1.88602i		−	0.0999589i
$357$	−6.55712	−	4.29298i	−0.347039	−	0.227209i
$358$	2.39203	−	2.39203i	0.126423	−	0.126423i
$359$	−11.7038			−0.617701			−0.308850	−	0.951111i	$-0.599944\pi$
$359$	−11.7038			−0.617701			−0.308850	+	0.951111i	$0.599944\pi$
$360$	3.13223	+	5.93204i	0.165083	+	0.312646i
$361$	9.95081			0.523727
$362$	−14.5303	+	14.5303i	−0.763694	+	0.763694i
$363$	−42.5352	−	27.8481i	−2.23252	−	1.46164i
$364$			8.77943i			0.460167i
$365$	−1.75850	−	23.6025i	−0.0920443	−	1.23541i
$366$	1.30422	−	0.272157i	0.0681727	−	0.0142259i
$367$	−14.8368	−	14.8368i	−0.774475	−	0.774475i	0.204410	−	0.978885i	$-0.434472\pi$
$367$	−14.8368	−	14.8368i	−0.774475	−	0.774475i	−0.978885	+	0.204410i	$0.934472\pi$
$368$	−0.729761	−	0.729761i	−0.0380414	−	0.0380414i
$369$	3.53826	−	1.54391i	0.184194	−	0.0803729i
$370$	−11.4180	+	13.2563i	−0.593592	+	0.689163i
$371$		−	46.3048i		−	2.40403i
$372$	−2.65831	+	4.06031i	−0.137827	+	0.210517i
$373$	24.2575	−	24.2575i	1.25601	−	1.25601i	0.303025	−	0.952983i	$-0.402004\pi$
$373$	24.2575	−	24.2575i	1.25601	−	1.25601i	0.952983	−	0.303025i	$-0.0979964\pi$
$374$	−6.35238			−0.328474
$375$	−8.05197	−	17.6115i	−0.415802	−	0.909455i
$376$	−7.89354			−0.407078
$377$	−1.24409	+	1.24409i	−0.0640738	+	0.0640738i
$378$	3.93693	−	23.1804i	0.202494	−	1.19227i
$379$			19.0462i			0.978337i	0.872189	+	0.489169i	$0.162700\pi$
$379$			19.0462i			0.978337i	−0.872189	+	0.489169i	$0.837300\pi$
$380$	−4.38982	+	5.09661i	−0.225193	+	0.261450i
$381$	−1.64705	−	7.89293i	−0.0843808	−	0.404367i
$382$	−3.91857	−	3.91857i	−0.200492	−	0.200492i
$383$	15.0844	+	15.0844i	0.770778	+	0.770778i	0.978243	−	0.207465i	$-0.0665212\pi$
$383$	15.0844	+	15.0844i	0.770778	+	0.770778i	−0.207465	+	0.978243i	$0.566521\pi$
$384$	−0.353812	−	1.69553i	−0.0180554	−	0.0865246i
$385$	−4.77551	−	64.0963i	−0.243382	−	3.26665i
$386$			8.16152i			0.415411i
$387$	−24.9240	−	9.78070i	−1.26696	−	0.497181i
$388$	9.02893	−	9.02893i	0.458375	−	0.458375i
$389$	26.9072			1.36425			0.682124	−	0.731237i	$-0.261057\pi$
$389$	26.9072			1.36425			0.682124	+	0.731237i	$0.261057\pi$
$390$	−2.07731	−	7.22164i	−0.105189	−	0.365682i
$391$	−1.03204			−0.0521924
$392$	−9.52838	+	9.52838i	−0.481256	+	0.481256i
$393$	−5.20971	+	7.95732i	−0.262795	+	0.401394i
$394$			17.5808i			0.885710i
$395$	−1.72155	−	1.48281i	−0.0866206	−	0.0746082i
$396$	−7.62157	−	17.4667i	−0.382998	−	0.877736i
$397$	9.47554	+	9.47554i	0.475564	+	0.475564i	0.903710	−	0.428146i	$-0.140833\pi$
$397$	9.47554	+	9.47554i	0.475564	+	0.475564i	−0.428146	+	0.903710i	$0.640833\pi$
$398$	−1.94533	−	1.94533i	−0.0975104	−	0.0975104i
$399$	23.0793	−	4.81605i	1.15541	−	0.241104i
$400$	0.740938	+	4.94480i	0.0370469	+	0.247240i
$401$		−	7.73850i		−	0.386442i	−0.981155	−	0.193221i	$-0.938107\pi$
$401$		−	7.73850i		−	0.386442i	0.981155	−	0.193221i	$-0.0618935\pi$
$402$	6.46997	+	4.23593i	0.322693	+	0.211269i
$403$	3.84412	−	3.84412i	0.191489	−	0.191489i
$404$	−2.79951			−0.139281
$405$	2.24636	+	19.9988i	0.111623	+	0.993751i
$406$	−4.10324			−0.203640
$407$	35.1454	−	35.1454i	1.74209	−	1.74209i
$408$	−1.44910	−	0.948737i	−0.0717413	−	0.0469695i
$409$		−	19.2331i		−	0.951016i	−0.879712	−	0.475508i	$-0.842264\pi$
$409$		−	19.2331i		−	0.951016i	0.879712	−	0.475508i	$-0.157736\pi$
$410$	2.86944	−	0.213788i	0.141712	−	0.0105582i
$411$	−32.0674	+	6.69162i	−1.58177	+	0.330073i
$412$	−1.56218	−	1.56218i	−0.0769632	−	0.0769632i
$413$	−5.54822	−	5.54822i	−0.273010	−	0.273010i
$414$	−1.23824	−	2.83773i	−0.0608560	−	0.139467i
$415$	−12.5050	+	0.931687i	−0.613847	+	0.0457347i
$416$			1.94023i			0.0951275i
$417$	12.2036	−	18.6398i	0.597613	−	0.912795i
$418$	13.5122	−	13.5122i	0.660904	−	0.660904i
$419$	−10.7021			−0.522831			−0.261415	−	0.965226i	$-0.584189\pi$
$419$	−10.7021			−0.522831			−0.261415	+	0.965226i	$0.584189\pi$
$420$	8.48349	−	15.3349i	0.413952	−	0.748264i
$421$	8.04501			0.392090			0.196045	−	0.980595i	$-0.437190\pi$
$421$	8.04501			0.392090			0.196045	+	0.980595i	$0.437190\pi$
$422$	8.18556	−	8.18556i	0.398467	−	0.398467i
$423$	−22.0440	−	8.65053i	−1.07182	−	0.420603i
$424$		−	10.2332i		−	0.496969i
$425$	4.02042	+	2.97258i	0.195019	+	0.144191i
$426$	−5.38174	−	25.7902i	−0.260746	−	1.24954i
$427$	−2.46119	−	2.46119i	−0.119105	−	0.119105i
$428$	−9.90455	−	9.90455i	−0.478755	−	0.478755i
$429$	4.36076	+	20.8975i	0.210539	+	1.00894i
$430$	−15.1208	−	13.0239i	−0.729191	−	0.628068i
$431$		−	19.0787i		−	0.918991i	−0.888180	−	0.459495i	$-0.848030\pi$
$431$		−	19.0787i		−	0.918991i	0.888180	−	0.459495i	$-0.151970\pi$
$432$	0.870049	−	5.12279i	0.0418602	−	0.246471i
$433$	−6.59813	+	6.59813i	−0.317086	+	0.317086i	−0.847647	−	0.530561i	$-0.821981\pi$
$433$	−6.59813	+	6.59813i	−0.317086	+	0.317086i	0.530561	+	0.847647i	$0.321981\pi$
$434$	12.6787			0.608595
$435$	3.37517	−	0.970872i	0.161827	−	0.0465497i
$436$	−16.8178			−0.805427
$437$	2.19526	−	2.19526i	0.105013	−	0.105013i
$438$	−10.0420	+	15.3382i	−0.479825	+	0.732886i
$439$			7.94882i			0.379376i	0.981844	+	0.189688i	$0.0607477\pi$
$439$			7.94882i			0.379376i	−0.981844	+	0.189688i	$0.939252\pi$
$440$	−1.05537	−	14.1651i	−0.0503129	−	0.675295i
$441$	−37.0518	+	16.1675i	−1.76437	+	0.769879i
$442$	1.37195	+	1.37195i	0.0652569	+	0.0652569i
$443$	23.7698	+	23.7698i	1.12934	+	1.12934i	0.990285	+	0.139050i	$0.0444049\pi$
$443$	23.7698	+	23.7698i	1.12934	+	1.12934i	0.139050	+	0.990285i	$0.455595\pi$
$444$	13.2664	−	2.76834i	0.629593	−	0.131380i
$445$	2.75225	−	3.19538i	0.130469	−	0.151476i
$446$			16.3465i			0.774028i
$447$	7.48617	+	4.90124i	0.354084	+	0.231821i
$448$	−3.19962	+	3.19962i	−0.151168	+	0.151168i
$449$	34.2246			1.61516			0.807579	−	0.589760i	$-0.200778\pi$
$449$	34.2246			1.61516			0.807579	+	0.589760i	$0.200778\pi$
$450$	−3.34981	+	14.6212i	−0.157911	+	0.689249i
$451$	−8.17432			−0.384914
$452$	−14.0896	+	14.0896i	−0.662721	+	0.662721i
$453$	−1.72778	−	1.13119i	−0.0811780	−	0.0531477i
$454$		−	26.1144i		−	1.22561i
$455$	−12.8117	+	14.8745i	−0.600624	+	0.697328i
$456$	5.10047	−	1.06433i	0.238851	−	0.0498420i
$457$	−16.3735	−	16.3735i	−0.765921	−	0.765921i	0.211464	−	0.977386i	$-0.432177\pi$
$457$	−16.3735	−	16.3735i	−0.765921	−	0.765921i	−0.977386	+	0.211464i	$0.932177\pi$
$458$	7.10192	+	7.10192i	0.331851	+	0.331851i
$459$	−3.00714	−	4.23758i	−0.140361	−	0.197793i
$460$	−0.171461	−	2.30133i	−0.00799440	−	0.107300i
$461$		−	10.7499i		−	0.500671i	−0.968159	−	0.250336i	$-0.919459\pi$
$461$		−	10.7499i		−	0.500671i	0.968159	−	0.250336i	$-0.0805409\pi$
$462$	−27.2707	+	41.6533i	−1.26875	+	1.93789i
$463$	−20.6093	+	20.6093i	−0.957795	+	0.957795i	−0.999145	−	0.0413496i	$-0.986834\pi$
$463$	−20.6093	+	20.6093i	−0.957795	+	0.957795i	0.0413496	+	0.999145i	$0.486834\pi$
$464$	−0.906803			−0.0420973
$465$	−10.4290	+	2.99991i	−0.483633	+	0.139118i
$466$	−7.12728			−0.330165
$467$	3.12163	−	3.12163i	0.144452	−	0.144452i	−0.631183	−	0.775634i	$-0.717430\pi$
$467$	3.12163	−	3.12163i	0.144452	−	0.144452i	0.775634	+	0.631183i	$0.217430\pi$
$468$	−2.12630	+	5.41842i	−0.0982880	+	0.250466i
$469$		−	20.2030i		−	0.932889i
$470$	−13.3736	−	11.5190i	−0.616878	−	0.531331i
$471$	−5.01718	−	24.0432i	−0.231180	−	1.10785i
$472$	−1.22614	−	1.22614i	−0.0564376	−	0.0564376i
$473$	40.0886	+	40.0886i	1.84327	+	1.84327i
$474$	0.359514	+	1.72285i	0.0165130	+	0.0791333i
$475$	−14.8749	+	2.22888i	−0.682506	+	0.102268i
$476$			4.52495i			0.207401i
$477$	11.2146	−	28.5780i	0.513481	−	1.30850i
$478$	0.458311	−	0.458311i	0.0209627	−	0.0209627i
$479$	6.22824			0.284576			0.142288	−	0.989825i	$-0.454554\pi$
$479$	6.22824			0.284576			0.142288	+	0.989825i	$0.454554\pi$
$480$	1.87483	−	3.38896i	0.0855737	−	0.154684i
$481$	−15.1810			−0.692192
$482$	−9.29035	+	9.29035i	−0.423164	+	0.423164i
$483$	−4.43052	+	6.76719i	−0.201596	+	0.307918i
$484$			29.3528i			1.33422i
$485$	28.4731	−	2.12139i	1.29290	−	0.0963273i
$486$	8.04383	−	13.3528i	0.364875	−	0.605695i
$487$	0.539291	+	0.539291i	0.0244376	+	0.0244376i	0.719220	−	0.694782i	$-0.244499\pi$
$487$	0.539291	+	0.539291i	0.0244376	+	0.0244376i	−0.694782	+	0.719220i	$0.744499\pi$
$488$	−0.543915	−	0.543915i	−0.0246219	−	0.0246219i
$489$	−17.1998	+	3.58914i	−0.777800	+	0.162306i
$490$	−30.0481	+	2.23874i	−1.35743	+	0.101136i
$491$			21.3268i			0.962466i	0.876593	+	0.481233i	$0.159811\pi$
$491$			21.3268i			0.962466i	−0.876593	+	0.481233i	$0.840189\pi$
$492$	−1.86472	−	1.22084i	−0.0840681	−	0.0550399i
$493$	−0.641207	+	0.641207i	−0.0288785	+	0.0288785i
$494$	−5.83657			−0.262600
$495$	12.5762	−	40.7150i	0.565259	−	1.83000i
$496$	2.80195			0.125811
$497$	−48.6685	+	48.6685i	−2.18308	+	2.18308i
$498$	8.12644	+	5.32043i	0.364154	+	0.238414i
$499$			29.6201i			1.32598i	0.748629	+	0.662990i	$0.230713\pi$
$499$			29.6201i			1.32598i	−0.748629	+	0.662990i	$0.769287\pi$
$500$	−5.96057	+	9.45895i	−0.266565	+	0.423017i
$501$	6.51333	−	1.35916i	0.290994	−	0.0607228i
$502$	10.9769	+	10.9769i	0.489922	+	0.489922i
$503$	12.4659	+	12.4659i	0.555829	+	0.555829i	0.928117	−	0.372289i	$-0.121427\pi$
$503$	12.4659	+	12.4659i	0.555829	+	0.555829i	−0.372289	+	0.928117i	$0.621427\pi$
$504$	−12.4420	+	5.42902i	−0.554209	+	0.241828i
$505$	−4.74305	−	4.08529i	−0.211063	−	0.181793i
$506$			6.55590i			0.291445i
$507$	−8.76207	+	13.3832i	−0.389137	+	0.594369i
$508$	−3.29168	+	3.29168i	−0.146045	+	0.146045i
$509$	−0.282620			−0.0125269			−0.00626345	−	0.999980i	$-0.501994\pi$
$509$	−0.282620			−0.0125269			−0.00626345	+	0.999980i	$0.501994\pi$
$510$	−1.07065	−	3.72206i	−0.0474093	−	0.164815i
$511$	47.8948			2.11874
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	15.4103	+	2.61727i	0.680382	+	0.115555i
$514$		−	18.1338i		−	0.799846i
$515$	−0.367042	−	4.92640i	−0.0161738	−	0.217083i
$516$	3.15771	+	15.1323i	0.139010	+	0.666161i
$517$	35.4563	+	35.4563i	1.55937	+	1.55937i
$518$	−25.0349	−	25.0349i	−1.09997	−	1.09997i
$519$	−2.25773	−	10.8194i	−0.0991035	−	0.474921i
$520$	−2.83136	+	3.28722i	−0.124163	+	0.144154i
$521$		−	27.2183i		−	1.19246i	−0.802815	−	0.596228i	$-0.796666\pi$
$521$		−	27.2183i		−	1.19246i	0.802815	−	0.596228i	$-0.203334\pi$
$522$	−2.53240	−	0.993766i	−0.110840	−	0.0434959i
$523$	24.0189	−	24.0189i	1.05027	−	1.05027i	0.0516063	−	0.998668i	$-0.483566\pi$
$523$	24.0189	−	24.0189i	1.05027	−	1.05027i	0.998668	−	0.0516063i	$-0.0164341\pi$
$524$	5.49121			0.239885
$525$	36.7511	−	13.6011i	1.60395	−	0.593602i
$526$	−6.52208			−0.284376
$527$	1.98127	−	1.98127i	0.0863057	−	0.0863057i
$528$	−6.02674	+	9.20526i	−0.262280	+	0.400607i
$529$		−	21.9349i		−	0.953691i
$530$	14.9333	−	17.3376i	0.648659	−	0.753097i
$531$	−2.08048	−	4.76793i	−0.0902849	−	0.206910i
$532$	−9.62506	−	9.62506i	−0.417299	−	0.417299i
$533$	1.76544	+	1.76544i	0.0764696	+	0.0764696i
$534$	−3.19780	+	0.667297i	−0.138382	+	0.0288768i
$535$	−2.32712	−	31.2344i	−0.100610	−	1.35038i
$536$		−	4.46481i		−	0.192850i
$537$	−4.90209	−	3.20943i	−0.211541	−	0.138497i
$538$	−7.94338	+	7.94338i	−0.342464	+	0.342464i
$539$	85.5994			3.68703
$540$	8.94972	−	7.40962i	0.385135	−	0.318859i
$541$	−0.652289			−0.0280441			−0.0140220	−	0.999902i	$-0.504464\pi$
$541$	−0.652289			−0.0280441			−0.0140220	+	0.999902i	$0.504464\pi$
$542$	9.41839	−	9.41839i	0.404555	−	0.404555i
$543$	29.7775	+	19.4955i	1.27787	+	0.836632i
$544$			1.00000i			0.0428746i
$545$	−28.4935	−	24.5421i	−1.22053	−	1.05127i
$546$	14.8858	−	3.10627i	0.637052	−	0.132936i
$547$	−21.4505	−	21.4505i	−0.917158	−	0.917158i	0.0796635	−	0.996822i	$-0.474615\pi$
$547$	−21.4505	−	21.4505i	−0.917158	−	0.917158i	−0.996822	+	0.0796635i	$0.974615\pi$
$548$	13.3734	+	13.3734i	0.571285	+	0.571285i
$549$	−0.922899	−	2.11505i	−0.0393884	−	0.0902682i
$550$	18.8829	−	25.5393i	0.805172	−	1.08900i
$551$		−	2.72783i		−	0.116210i
$552$	−0.979133	+	1.49553i	−0.0416746	+	0.0636540i
$553$	3.25119	−	3.25119i	0.138255	−	0.138255i
$554$	−18.4552			−0.784084
$555$	26.5163	+	14.6692i	1.12555	+	0.622674i
$556$	−12.8630			−0.545513
$557$	−9.25598	+	9.25598i	−0.392188	+	0.392188i	−0.875467	−	0.483278i	$-0.839446\pi$
$557$	−9.25598	+	9.25598i	−0.392188	+	0.392188i	0.483278	+	0.875467i	$0.339446\pi$
$558$	7.82491	+	3.07065i	0.331255	+	0.129991i
$559$		−	17.3162i		−	0.732396i
$560$	−10.0901	+	0.751766i	−0.426386	+	0.0317679i
$561$	2.24755	+	10.7706i	0.0948917	+	0.454737i
$562$	15.7533	+	15.7533i	0.664511	+	0.664511i
$563$	32.0936	+	32.0936i	1.35259	+	1.35259i	0.882758	+	0.469828i	$0.155684\pi$
$563$	32.0936	+	32.0936i	1.35259	+	1.35259i	0.469828	+	0.882758i	$0.344316\pi$
$564$	2.79283	+	13.3837i	0.117599	+	0.563556i
$565$	−44.4322	+	3.31043i	−1.86928	+	0.139271i
$566$		−	11.1057i		−	0.466807i
$567$	−40.6959	+	1.52633i	−1.70907	+	0.0640998i
$568$	−10.7556	+	10.7556i	−0.451295	+	0.451295i
$569$	−24.3222			−1.01964			−0.509820	−	0.860281i	$-0.670288\pi$
$569$	−24.3222			−1.01964			−0.509820	+	0.860281i	$0.670288\pi$
$570$	10.1946	+	5.63982i	0.427005	+	0.236226i
$571$	0.175807			0.00735728			0.00367864	−	0.999993i	$-0.498829\pi$
$571$	0.175807			0.00735728			0.00367864	+	0.999993i	$0.498829\pi$
$572$	8.71514	−	8.71514i	0.364398	−	0.364398i
$573$	−5.25762	+	8.03049i	−0.219640	+	0.335479i
$574$			5.82275i			0.243037i
$575$	3.06781	−	4.14923i	0.127937	−	0.173035i
$576$	−2.74963	+	1.19980i	−0.114568	+	0.0499916i
$577$	28.0669	+	28.0669i	1.16844	+	1.16844i	0.982575	+	0.185867i	$0.0595095\pi$
$577$	28.0669	+	28.0669i	1.16844	+	1.16844i	0.185867	+	0.982575i	$0.440490\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$	13.8381	−	2.88765i	0.575092	−	0.120007i
$580$	−1.53635	−	1.32329i	−0.0637934	−	0.0549466i
$581$		−	25.3755i		−	1.05275i
$582$	−18.5034	−	12.1143i	−0.766989	−	0.502152i
$583$	−45.9657	+	45.9657i	−1.90371	+	1.90371i
$584$	10.5846			0.437994
$585$	−11.5095	+	6.07724i	−0.475860	+	0.251263i
$586$	−20.5860			−0.850400
$587$	−9.58569	+	9.58569i	−0.395644	+	0.395644i	−0.876693	−	0.481050i	$-0.840256\pi$
$587$	−9.58569	+	9.58569i	−0.395644	+	0.395644i	0.481050	+	0.876693i	$0.340256\pi$
$588$	19.5269	+	12.7844i	0.805275	+	0.527219i
$589$			8.42877i			0.347302i
$590$	−0.288087	−	3.86667i	−0.0118604	−	0.159188i
$591$	29.8088	−	6.22031i	1.22617	−	0.255870i
$592$	−5.53263	−	5.53263i	−0.227390	−	0.227390i
$593$	−9.63031	−	9.63031i	−0.395469	−	0.395469i	0.481162	−	0.876632i	$-0.340215\pi$
$593$	−9.63031	−	9.63031i	−0.395469	−	0.395469i	−0.876632	+	0.481162i	$0.840215\pi$
$594$	−26.9187	+	19.1025i	−1.10449	+	0.783787i
$595$	−6.60322	+	7.66638i	−0.270706	+	0.314291i
$596$		−	5.16607i		−	0.211611i
$597$	−2.61008	+	3.98664i	−0.106823	+	0.163162i
$598$	1.41590	−	1.41590i	0.0579006	−	0.0579006i
$599$	20.5494			0.839624			0.419812	−	0.907611i	$-0.362096\pi$
$599$	20.5494			0.839624			0.419812	+	0.907611i	$0.362096\pi$
$600$	8.12189	−	3.00581i	0.331575	−	0.122712i
$601$	19.3604			0.789728			0.394864	−	0.918740i	$-0.370792\pi$
$601$	19.3604			0.789728			0.394864	+	0.918740i	$0.370792\pi$
$602$	28.5560	−	28.5560i	1.16386	−	1.16386i
$603$	4.89298	−	12.4687i	0.199258	−	0.507766i
$604$			1.19231i			0.0485143i
$605$	−42.8342	+	49.7308i	−1.74146	+	2.02184i
$606$	0.990499	+	4.74664i	0.0402363	+	0.192819i
$607$	25.8542	+	25.8542i	1.04939	+	1.04939i	0.998715	+	0.0506749i	$0.0161372\pi$
$607$	25.8542	+	25.8542i	1.04939	+	1.04939i	0.0506749	+	0.998715i	$0.483863\pi$
$608$	−2.12711	−	2.12711i	−0.0862657	−	0.0862657i
$609$	1.45178	+	6.95716i	0.0588289	+	0.281918i
$610$	−0.127795	−	1.71526i	−0.00517428	−	0.0694487i
$611$		−	15.3153i		−	0.619589i
$612$	−1.09590	+	2.79267i	−0.0442991	+	0.112887i
$613$	12.3614	−	12.3614i	0.499271	−	0.499271i	−0.411940	−	0.911211i	$-0.635149\pi$
$613$	12.3614	−	12.3614i	0.499271	−	0.499271i	0.911211	+	0.411940i	$0.135149\pi$
$614$	−21.6831			−0.875060
$615$	−1.37773	−	4.78958i	−0.0555554	−	0.193135i
$616$	28.7442			1.15814
$617$	−6.99167	+	6.99167i	−0.281474	+	0.281474i	−0.833697	−	0.552223i	$-0.813780\pi$
$617$	−6.99167	+	6.99167i	−0.281474	+	0.281474i	0.552223	+	0.833697i	$0.313780\pi$
$618$	−2.09601	+	3.20144i	−0.0843137	+	0.128781i
$619$		−	46.6268i		−	1.87409i	−0.349210	−	0.937044i	$-0.613550\pi$
$619$		−	46.6268i		−	1.87409i	0.349210	−	0.937044i	$-0.386450\pi$
$620$	4.74718	+	4.08885i	0.190652	+	0.164212i
$621$	−4.37334	+	3.10349i	−0.175496	+	0.124539i
$622$	−17.1728	−	17.1728i	−0.688568	−	0.688568i
$623$	6.03455	+	6.03455i	0.241769	+	0.241769i
$624$	3.28971	−	0.686476i	0.131694	−	0.0274810i
$625$	−23.9020	+	7.32758i	−0.956081	+	0.293103i
$626$			1.95238i			0.0780329i
$627$	−27.6911	−	18.1296i	−1.10588	−	0.724025i
$628$	−10.0270	+	10.0270i	−0.400122	+	0.400122i
$629$	−7.82432			−0.311976
$630$	−29.0022	−	8.95833i	−1.15548	−	0.356909i
$631$	10.5313			0.419244			0.209622	−	0.977782i	$-0.432777\pi$
$631$	10.5313			0.419244			0.209622	+	0.977782i	$0.432777\pi$
$632$	0.718503	−	0.718503i	0.0285805	−	0.0285805i
$633$	−16.7750	−	10.9827i	−0.666746	−	0.436523i
$634$		−	12.0475i		−	0.478469i
$635$	−10.3805	+	0.773397i	−0.411936	+	0.0306913i
$636$	−17.3507	+	3.62064i	−0.688001	+	0.143568i
$637$	−18.4872	−	18.4872i	−0.732490	−	0.732490i
$638$	4.07319	+	4.07319i	0.161259	+	0.161259i
$639$	−41.8239	+	18.2498i	−1.65453	+	0.721950i
$640$	−2.22989	+	0.166138i	−0.0881440	+	0.00656718i
$641$		−	14.5589i		−	0.575041i	−0.957774	−	0.287521i	$-0.907169\pi$
$641$		−	14.5589i		−	0.575041i	0.957774	−	0.287521i	$-0.0928309\pi$
$642$	−13.2891	+	20.2978i	−0.524479	+	0.801090i
$643$	−3.79117	+	3.79117i	−0.149509	+	0.149509i	−0.777899	−	0.628390i	$-0.783714\pi$
$643$	−3.79117	+	3.79117i	−0.149509	+	0.149509i	0.628390	+	0.777899i	$0.283714\pi$
$644$	4.66992			0.184021
$645$	−16.7325	+	30.2458i	−0.658840	+	1.19093i
$646$	−3.00819			−0.118356
$647$	18.6319	−	18.6319i	0.732497	−	0.732497i	−0.238617	−	0.971114i	$-0.576694\pi$
$647$	18.6319	−	18.6319i	0.732497	−	0.732497i	0.971114	+	0.238617i	$0.0766940\pi$
$648$	−8.99368	+	0.337314i	−0.353305	+	0.0132510i
$649$			11.0152i			0.432383i
$650$	−9.59403	+	1.43759i	−0.376309	+	0.0563869i
$651$	−4.48586	−	21.4970i	−0.175815	−	0.842535i
$652$	7.17303	+	7.17303i	0.280917	+	0.280917i
$653$	−32.0840	−	32.0840i	−1.25554	−	1.25554i	−0.953199	−	0.302344i	$-0.902231\pi$
$653$	−32.0840	−	32.0840i	−1.25554	−	1.25554i	−0.302344	−	0.953199i	$-0.597769\pi$
$654$	5.95035	+	28.5151i	0.232677	+	1.11503i
$655$	9.30346	+	8.01327i	0.363516	+	0.313104i
$656$			1.28681i			0.0502415i
$657$	29.5593	+	11.5997i	1.15322	+	0.452546i
$658$	25.2563	−	25.2563i	0.984595	−	0.984595i
$659$	−10.5182			−0.409733			−0.204866	−	0.978790i	$-0.565676\pi$
$659$	−10.5182			−0.409733			−0.204866	+	0.978790i	$0.565676\pi$
$660$	−23.6439	+	6.80120i	−0.920339	+	0.264736i
$661$	−5.05318			−0.196546			−0.0982730	−	0.995159i	$-0.531332\pi$
$661$	−5.05318			−0.196546			−0.0982730	+	0.995159i	$0.531332\pi$
$662$	−5.18732	+	5.18732i	−0.201611	+	0.201611i
$663$	1.84077	−	2.81159i	0.0714894	−	0.109193i
$664$		−	5.60791i		−	0.217629i
$665$	−2.26145	−	30.3530i	−0.0876954	−	1.17704i
$666$	−9.38760	−	21.5140i	−0.363762	−	0.833651i
$667$	0.661750	+	0.661750i	0.0256231	+	0.0256231i
$668$	−2.71633	−	2.71633i	−0.105098	−	0.105098i
$669$	27.7159	−	5.78358i	1.07156	−	0.223606i
$670$	6.51546	−	7.56449i	0.251714	−	0.292242i
$671$			4.88633i			0.188635i
$672$	6.55712	+	4.29298i	0.252946	+	0.165605i
$673$	17.7837	−	17.7837i	0.685512	−	0.685512i	−0.275725	−	0.961237i	$-0.588918\pi$
$673$	17.7837	−	17.7837i	0.685512	−	0.685512i	0.961237	+	0.275725i	$0.0889178\pi$
$674$	−22.2805			−0.858215
$675$	25.9758	+	0.506541i	0.999810	+	0.0194968i
$676$	9.23552			0.355212
$677$	−4.06449	+	4.06449i	−0.156211	+	0.156211i	−0.780885	−	0.624674i	$-0.785232\pi$
$677$	−4.06449	+	4.06449i	−0.156211	+	0.156211i	0.624674	+	0.780885i	$0.285232\pi$
$678$	28.8745	+	18.9043i	1.10892	+	0.726016i
$679$			57.7783i			2.21733i
$680$	−1.45929	+	1.69425i	−0.0559613	+	0.0649714i
$681$	−44.2778	+	9.23960i	−1.69673	+	0.354062i
$682$	−12.5858	−	12.5858i	−0.481936	−	0.481936i
$683$	−30.4341	−	30.4341i	−1.16453	−	1.16453i	−0.983473	−	0.181056i	$-0.942049\pi$
$683$	−30.4341	−	30.4341i	−1.16453	−	1.16453i	−0.181056	−	0.983473i	$-0.557951\pi$
$684$	−3.60921	−	8.27141i	−0.138002	−	0.316265i
$685$	3.14215	+	42.1736i	0.120055	+	1.61137i
$686$		−	29.2998i		−	1.11867i
$687$	9.52876	−	14.5543i	0.363545	−	0.555280i
$688$	6.31079	−	6.31079i	0.240597	−	0.240597i
$689$	19.8548			0.756407
$690$	−3.84130	+	1.10495i	−0.146236	+	0.0420649i
$691$	−45.6672			−1.73726			−0.868631	−	0.495460i	$-0.834999\pi$
$691$	−45.6672			−1.73726			−0.868631	+	0.495460i	$0.834999\pi$
$692$	−4.51216	+	4.51216i	−0.171527	+	0.171527i
$693$	80.2731	+	31.5008i	3.04932	+	1.19662i
$694$		−	17.5955i		−	0.667915i
$695$	−21.7931	−	18.7709i	−0.826659	−	0.712020i
$696$	0.320838	+	1.53751i	0.0121613	+	0.0582792i
$697$	0.909913	+	0.909913i	0.0344654	+	0.0344654i
$698$	−3.51209	−	3.51209i	−0.132935	−	0.132935i
$699$	2.52172	+	12.0845i	0.0953802	+	0.457078i
$700$	−18.1922	−	13.4508i	−0.687601	−	0.508391i
$701$		−	0.210823i		−	0.00796266i	−0.999992	−	0.00398133i	$-0.998733\pi$
$701$		−	0.210823i		−	0.00796266i	0.999992	−	0.00398133i	$-0.00126730\pi$
$702$	9.93939	+	1.68809i	0.375138	+	0.0637130i
$703$	16.6432	−	16.6432i	0.627710	−	0.627710i
$704$	6.35238			0.239414
$705$	−14.7990	+	26.7509i	−0.557363	+	1.00750i
$706$	20.2283			0.761301
$707$	8.95736	−	8.95736i	0.336876	−	0.336876i
$708$	−1.64513	+	2.51278i	−0.0618278	+	0.0944359i
$709$			39.1602i			1.47069i	0.677693	+	0.735345i	$0.262980\pi$
$709$			39.1602i			1.47069i	−0.677693	+	0.735345i	$0.737020\pi$
$710$	−33.9182	+	2.52708i	−1.27293	+	0.0948395i
$711$	2.79395	−	1.21913i	0.104781	−	0.0457211i
$712$	1.33362	+	1.33362i	0.0499794	+	0.0499794i
$713$	−2.04475	−	2.04475i	−0.0765765	−	0.0765765i
$714$	7.67218	−	1.60098i	0.287124	−	0.0599152i
$715$	27.4835	−	2.04766i	1.02783	−	0.0765782i
$716$			3.38285i			0.126423i
$717$	−0.939235	−	0.614923i	−0.0350764	−	0.0229647i
$718$	8.27581	−	8.27581i	0.308850	−	0.308850i
$719$	−19.1624			−0.714638			−0.357319	−	0.933982i	$-0.616309\pi$
$719$	−19.1624			−0.714638			−0.357319	+	0.933982i	$0.616309\pi$
$720$	−6.40941	−	1.97976i	−0.238865	−	0.0737815i
$721$	9.99678			0.372300
$722$	−7.03629	+	7.03629i	−0.261864	+	0.261864i
$723$	19.0391	+	12.4650i	0.708072	+	0.463579i
$724$		−	20.5489i		−	0.763694i
$725$	−0.671885	−	4.48396i	−0.0249532	−	0.166530i
$726$	49.7685	−	10.3854i	1.84708	−	0.385437i
$727$	−2.08939	−	2.08939i	−0.0774913	−	0.0774913i	0.667299	−	0.744790i	$-0.267450\pi$
$727$	−2.08939	−	2.08939i	−0.0774913	−	0.0774913i	−0.744790	+	0.667299i	$0.767450\pi$
$728$	−6.20800	−	6.20800i	−0.230084	−	0.230084i
$729$	−25.4860	−	8.91416i	−0.943927	−	0.330154i
$730$	17.9329	+	15.4460i	0.663727	+	0.571683i
$731$		−	8.92481i		−	0.330096i
$732$	−0.729780	+	1.11467i	−0.0269734	+	0.0411993i
$733$	29.7175	−	29.7175i	1.09764	−	1.09764i	0.102953	−	0.994686i	$-0.467171\pi$
$733$	29.7175	−	29.7175i	1.09764	−	1.09764i	0.994686	−	0.102953i	$-0.0328292\pi$
$734$	20.9824			0.774475
$735$	14.4272	+	50.1553i	0.532156	+	1.85001i
$736$	1.03204			0.0380414
$737$	−20.0551	+	20.0551i	−0.738739	+	0.738739i
$738$	−1.41022	+	3.59364i	−0.0519108	+	0.132284i
$739$			38.7316i			1.42476i	0.701792	+	0.712382i	$0.252384\pi$
$739$			38.7316i			1.42476i	−0.701792	+	0.712382i	$0.747616\pi$
$740$	−1.29992	−	17.4474i	−0.0477859	−	0.641377i
$741$	2.06505	+	9.89607i	0.0758615	+	0.363541i
$742$	32.7425	+	32.7425i	1.20201	+	1.20201i
$743$	−25.8428	−	25.8428i	−0.948079	−	0.948079i	0.0506381	−	0.998717i	$-0.483874\pi$
$743$	−25.8428	−	25.8428i	−0.948079	−	0.948079i	−0.998717	+	0.0506381i	$0.983874\pi$
$744$	−0.991362	−	4.75078i	−0.0363451	−	0.174172i
$745$	7.53880	−	8.75260i	0.276200	−	0.320670i
$746$			34.3053i			1.25601i
$747$	6.14571	−	15.6610i	0.224860	−	0.573008i
$748$	4.49181	−	4.49181i	0.164237	−	0.164237i
$749$	63.3817			2.31592
$750$	18.1468	+	6.75962i	0.662629	+	0.246826i
$751$	0.879429			0.0320908			0.0160454	−	0.999871i	$-0.494892\pi$
$751$	0.879429			0.0320908			0.0160454	+	0.999871i	$0.494892\pi$
$752$	5.58158	−	5.58158i	0.203539	−	0.203539i
$753$	14.7278	−	22.4953i	0.536712	−	0.819776i
$754$		−	1.75941i		−	0.0640738i
$755$	−1.73992	+	2.02006i	−0.0633223	+	0.0735176i
$756$	13.6072	+	19.1748i	0.494888	+	0.697382i
$757$	23.4591	+	23.4591i	0.852637	+	0.852637i	0.990457	−	0.137821i	$-0.0440097\pi$
$757$	23.4591	+	23.4591i	0.852637	+	0.852637i	−0.137821	+	0.990457i	$0.544010\pi$
$758$	−13.4677	−	13.4677i	−0.489169	−	0.489169i
$759$	11.1157	−	2.31956i	0.403475	−	0.0841946i
$760$	−0.499774	−	6.70792i	−0.0181287	−	0.243322i
$761$			34.1689i			1.23862i	0.785146	+	0.619311i	$0.212588\pi$
$761$			34.1689i			1.23862i	−0.785146	+	0.619311i	$0.787412\pi$
$762$	6.74578	+	4.41651i	0.244374	+	0.159993i
$763$	53.8107	−	53.8107i	1.94808	−	1.94808i
$764$	5.54170			0.200492
$765$	−5.93204	+	3.13223i	−0.214473	+	0.113246i
$766$	−21.3326			−0.770778
$767$	2.37899	−	2.37899i	0.0859003	−	0.0859003i
$768$	1.44910	+	0.948737i	0.0522900	+	0.0342346i
$769$			20.0371i			0.722555i	0.932458	+	0.361278i	$0.117659\pi$
$769$			20.0371i			0.722555i	−0.932458	+	0.361278i	$0.882341\pi$
$770$	48.6998	+	41.9462i	1.75502	+	1.51164i
$771$	−30.7463	+	6.41594i	−1.10730	+	0.231065i
$772$	−5.77107	−	5.77107i	−0.207705	−	0.207705i
$773$	36.2603	+	36.2603i	1.30419	+	1.30419i	0.925538	+	0.378654i	$0.123613\pi$
$773$	36.2603	+	36.2603i	1.30419	+	1.30419i	0.378654	+	0.925538i	$0.376387\pi$
$774$	24.5400	−	10.7080i	0.882071	−	0.384890i
$775$	2.07607	+	13.8550i	0.0745746	+	0.497688i
$776$			12.7688i			0.458375i
$777$	−33.5897	+	51.3050i	−1.20502	+	1.84056i
$778$	−19.0262	+	19.0262i	−0.682124	+	0.682124i
$779$	−3.87097			−0.138692
$780$	6.57535	+	3.63759i	0.235435	+	0.130247i
$781$	96.6243			3.45749
$782$	0.729761	−	0.729761i	0.0260962	−	0.0260962i
$783$	−0.788963	+	4.64537i	−0.0281952	+	0.166012i
$784$		−	13.4752i		−	0.481256i
$785$	−31.6206	+	2.35590i	−1.12859	+	0.0840856i
$786$	−1.94286	−	9.31050i	−0.0692994	−	0.332095i
$787$	−13.8499	−	13.8499i	−0.493694	−	0.493694i	0.415774	−	0.909468i	$-0.363511\pi$
$787$	−13.8499	−	13.8499i	−0.493694	−	0.493694i	−0.909468	+	0.415774i	$0.863511\pi$
$788$	−12.4315	−	12.4315i	−0.442855	−	0.442855i
$789$	2.30759	+	11.0584i	0.0821524	+	0.393688i
$790$	2.26583	−	0.168816i	0.0806144	−	0.00600619i
$791$		−	90.1631i		−	3.20583i
$792$	17.7401	+	6.96158i	0.630367	+	0.247369i
$793$	1.05532	−	1.05532i	0.0374755	−	0.0374755i
$794$	−13.4004			−0.475564
$795$	−34.6800	−	19.1855i	−1.22997	−	0.680440i
$796$	2.75111			0.0975104
$797$	11.1438	−	11.1438i	0.394733	−	0.394733i	−0.481638	−	0.876370i	$-0.659958\pi$
$797$	11.1438	−	11.1438i	0.394733	−	0.394733i	0.876370	+	0.481638i	$0.159958\pi$
$798$	−12.9141	+	19.7250i	−0.457154	+	0.698258i
$799$		−	7.89354i		−	0.279253i
$800$	−4.02042	−	2.97258i	−0.142143	−	0.105096i
$801$	2.26284	+	5.18586i	0.0799536	+	0.183234i
$802$	5.47194	+	5.47194i	0.193221	+	0.193221i
$803$	−47.5441	−	47.5441i	−1.67779	−	1.67779i
$804$	−7.57021	+	1.57970i	−0.266981	+	0.0557119i
$805$	7.91199	+	6.81477i	0.278861	+	0.240189i
$806$			5.43641i			0.191489i
$807$	16.2787	+	10.6578i	0.573037	+	0.375171i
$808$	1.97955	−	1.97955i	0.0696403	−	0.0696403i
$809$	17.5443			0.616823			0.308412	−	0.951253i	$-0.400203\pi$
$809$	17.5443			0.616823			0.308412	+	0.951253i	$0.400203\pi$
$810$	−15.7297	−	12.5529i	−0.552687	−	0.441064i
$811$	−9.25880			−0.325121			−0.162560	−	0.986699i	$-0.551975\pi$
$811$	−9.25880			−0.325121			−0.162560	+	0.986699i	$0.551975\pi$
$812$	2.90143	−	2.90143i	0.101820	−	0.101820i
$813$	−19.3015	−	12.6368i	−0.676933	−	0.443192i
$814$			49.7031i			1.74209i
$815$	1.68534	+	22.6204i	0.0590347	+	0.792358i
$816$	1.69553	−	0.353812i	0.0593554	−	0.0123859i
$817$	18.9840	+	18.9840i	0.664168	+	0.664168i
$818$	13.5999	+	13.5999i	0.475508	+	0.475508i
$819$	−10.5335	−	24.1402i	−0.368072	−	0.843528i
$820$	−1.87783	+	2.18017i	−0.0655767	+	0.0761350i
$821$			23.4249i			0.817536i	0.912638	+	0.408768i	$0.134041\pi$
$821$			23.4249i			0.817536i	−0.912638	+	0.408768i	$0.865959\pi$
$822$	17.9434	−	27.4067i	0.625847	−	0.955920i
$823$	−3.05593	+	3.05593i	−0.106523	+	0.106523i	−0.758359	−	0.651837i	$-0.773999\pi$
$823$	−3.05593	+	3.05593i	−0.106523	+	0.106523i	0.651837	+	0.758359i	$0.273999\pi$
$824$	2.20926			0.0769632
$825$	−49.9836	−	22.9805i	−1.74020	−	0.800077i
$826$	7.84636			0.273010
$827$	−2.44030	+	2.44030i	−0.0848576	+	0.0848576i	−0.748261	−	0.663404i	$-0.769111\pi$
$827$	−2.44030	+	2.44030i	−0.0848576	+	0.0848576i	0.663404	+	0.748261i	$0.269111\pi$
$828$	2.88214	+	1.13101i	0.100161	+	0.0393053i
$829$			40.7841i			1.41649i	0.705967	+	0.708245i	$0.250513\pi$
$829$			40.7841i			1.41649i	−0.705967	+	0.708245i	$0.749487\pi$
$830$	8.18358	−	9.50118i	0.284056	−	0.329791i
$831$	6.52966	+	31.2912i	0.226511	+	1.08548i
$832$	−1.37195	−	1.37195i	−0.0475637	−	0.0475637i
$833$	−9.52838	−	9.52838i	−0.330139	−	0.330139i
$834$	4.55109	+	21.8096i	0.157591	+	0.755204i
$835$	−0.638215	−	8.56606i	−0.0220863	−	0.296441i
$836$			19.1092i			0.660904i
$837$	2.43783	−	14.3538i	0.0842637	−	0.496139i
$838$	7.56751	−	7.56751i	0.261415	−	0.261415i
$839$	17.1217			0.591108			0.295554	−	0.955326i	$-0.404496\pi$
$839$	17.1217			0.591108			0.295554	+	0.955326i	$0.404496\pi$
$840$	4.84465	+	16.8421i	0.167156	+	0.581108i
$841$	−28.1777			−0.971645
$842$	−5.68868	+	5.68868i	−0.196045	+	0.196045i
$843$	21.1364	−	32.2838i	0.727976	−	1.11191i
$844$			11.5761i			0.398467i
$845$	15.6472	+	13.4773i	0.538281	+	0.463633i
$846$	21.7043	−	9.47065i	0.746211	−	0.325608i
$847$	−93.9178	−	93.9178i	−3.22705	−	3.22705i
$848$	7.23598	+	7.23598i	0.248485	+	0.248485i
$849$	−18.8300	+	3.92933i	−0.646244	+	0.134854i
$850$	−4.94480	+	0.740938i	−0.169605	+	0.0254140i
$851$			8.07500i			0.276807i
$852$	22.0419	+	14.4310i	0.755142	+	0.494397i
$853$	−19.9577	+	19.9577i	−0.683340	+	0.683340i	−0.960751	−	0.277411i	$-0.910523\pi$
$853$	−19.9577	+	19.9577i	−0.683340	+	0.683340i	0.277411	+	0.960751i	$0.410523\pi$
$854$	3.48065			0.119105
$855$	5.95550	−	19.2807i	0.203674	−	0.659386i
$856$	14.0072			0.478755
$857$	19.0560	−	19.0560i	0.650939	−	0.650939i	−0.302280	−	0.953219i	$-0.597748\pi$
$857$	19.0560	−	19.0560i	0.650939	−	0.650939i	0.953219	+	0.302280i	$0.0977477\pi$
$858$	−17.8603	−	11.6932i	−0.609740	−	0.399201i
$859$		−	24.2637i		−	0.827867i	−0.910307	−	0.413933i	$-0.864155\pi$
$859$		−	24.2637i		−	0.827867i	0.910307	−	0.413933i	$-0.135845\pi$
$860$	19.9013	−	1.48275i	0.678629	−	0.0505614i
$861$	9.87265	−	2.06016i	0.336459	−	0.0702101i
$862$	13.4907	+	13.4907i	0.459495	+	0.459495i
$863$	8.40332	+	8.40332i	0.286052	+	0.286052i	0.835517	−	0.549465i	$-0.185168\pi$
$863$	8.40332	+	8.40332i	0.286052	+	0.286052i	−0.549465	+	0.835517i	$0.685168\pi$
$864$	3.00714	+	4.23758i	0.102305	+	0.144165i
$865$	−14.2293	+	1.06015i	−0.483810	+	0.0360463i
$866$		−	9.33116i		−	0.317086i
$867$	0.948737	−	1.44910i	0.0322208	−	0.0492141i
$868$	−8.96517	+	8.96517i	−0.304298	+	0.304298i
$869$	−6.45476			−0.218963
$870$	−1.70010	+	3.07312i	−0.0576387	+	0.104188i
$871$	8.66275			0.293526
$872$	11.8920	−	11.8920i	0.402714	−	0.402714i
$873$	−13.9934	+	35.6591i	−0.473604	+	1.20688i
$874$			3.10456i			0.105013i
$875$	−11.1935	−	49.3366i	−0.378409	−	1.66788i
$876$	−3.74496	−	17.9465i	−0.126531	−	0.606356i
$877$	−25.6120	−	25.6120i	−0.864855	−	0.864855i	0.127042	−	0.991897i	$-0.459452\pi$
$877$	−25.6120	−	25.6120i	−0.864855	−	0.864855i	−0.991897	+	0.127042i	$0.959452\pi$
$878$	−5.62066	−	5.62066i	−0.189688	−	0.189688i
$879$	7.28358	+	34.9041i	0.245669	+	1.17729i
$880$	10.7625	+	9.26998i	0.362804	+	0.312491i
$881$			28.8531i			0.972087i	0.873935	+	0.486043i	$0.161560\pi$
$881$			28.8531i			0.972087i	−0.873935	+	0.486043i	$0.838440\pi$
$882$	14.7674	−	37.6317i	0.497245	−	1.26712i
$883$	−14.9614	+	14.9614i	−0.503492	+	0.503492i	−0.912521	−	0.409030i	$-0.865867\pi$
$883$	−14.9614	+	14.9614i	−0.503492	+	0.503492i	0.409030	+	0.912521i	$0.365867\pi$
$884$	−1.94023			−0.0652569
$885$	−6.45413	+	1.85654i	−0.216953	+	0.0624068i
$886$	−33.6155			−1.12934
$887$	4.28181	−	4.28181i	0.143769	−	0.143769i	−0.631559	−	0.775328i	$-0.717585\pi$
$887$	4.28181	−	4.28181i	0.143769	−	0.143769i	0.775328	+	0.631559i	$0.217585\pi$
$888$	−7.42322	+	11.3382i	−0.249107	+	0.380487i
$889$		−	21.0643i		−	0.706474i
$890$	0.313340	+	4.20561i	0.0105032	+	0.140972i
$891$	41.9131	+	38.8828i	1.40414	+	1.30262i
$892$	−11.5587	−	11.5587i	−0.387014	−	0.387014i
$893$	16.7904	+	16.7904i	0.561870	+	0.561870i
$894$	−8.75922	+	1.82782i	−0.292952	+	0.0611314i
$895$	−4.93656	+	5.73137i	−0.165011	+	0.191579i
$896$		−	4.52495i		−	0.151168i
$897$	−2.90167	−	1.89974i	−0.0968839	−	0.0634305i
$898$	−24.2004	+	24.2004i	−0.807579	+	0.807579i
$899$	−2.54081			−0.0847409
$900$	−7.97006	−	12.7074i	−0.265669	−	0.423580i
$901$	10.2332			0.340918
$902$	5.78011	−	5.78011i	0.192457	−	0.192457i
$903$	−58.5210	−	38.3141i	−1.94746	−	1.27501i
$904$		−	19.9258i		−	0.662721i
$905$	29.9869	−	34.8149i	0.996797	−	1.15729i
$906$	2.02159	−	0.421853i	0.0671629	−	0.0140151i
$907$	31.4747	+	31.4747i	1.04510	+	1.04510i	0.998934	+	0.0461671i	$0.0147007\pi$
$907$	31.4747	+	31.4747i	1.04510	+	1.04510i	0.0461671	+	0.998934i	$0.485299\pi$
$908$	18.4657	+	18.4657i	0.612806	+	0.612806i
$909$	7.69762	−	3.35884i	0.255314	−	0.111406i
$910$	−1.45860	−	19.5771i	−0.0483520	−	0.648976i
$911$		−	15.3803i		−	0.509572i	−0.966997	−	0.254786i	$-0.917995\pi$
$911$		−	15.3803i		−	0.509572i	0.966997	−	0.254786i	$-0.0820051\pi$
$912$	−2.85398	+	4.35917i	−0.0945046	+	0.144347i
$913$	−25.1897	+	25.1897i	−0.833657	+	0.833657i
$914$	23.1557			0.765921
$915$	−2.86305	+	0.823559i	−0.0946495	+	0.0272260i
$916$	−10.0436			−0.331851
$917$	−17.5698	+	17.5698i	−0.580206	+	0.580206i
$918$	5.12279	+	0.870049i	0.169077	+	0.0287159i
$919$		−	3.58936i		−	0.118402i	−0.998246	−	0.0592010i	$-0.981145\pi$
$919$		−	3.58936i		−	0.118402i	0.998246	−	0.0592010i	$-0.0188553\pi$
$920$	1.74853	+	1.50604i	0.0576472	+	0.0496528i
$921$	7.67175	+	36.7644i	0.252793	+	1.21143i
$922$	7.60130	+	7.60130i	0.250336	+	0.250336i
$923$	−20.8683	−	20.8683i	−0.686889	−	0.686889i
$924$	−10.1701	−	48.7366i	−0.334570	−	1.60332i
$925$	23.2584	−	31.4571i	0.764731	−	1.03430i
$926$		−	29.1459i		−	0.957795i
$927$	6.16973	+	2.42113i	0.202641	+	0.0795202i
$928$	0.641207	−	0.641207i	0.0210486	−	0.0210486i
$929$	−21.7768			−0.714473			−0.357236	−	0.934014i	$-0.616281\pi$
$929$	−21.7768			−0.714473			−0.357236	+	0.934014i	$0.616281\pi$
$930$	5.25316	−	9.49567i	0.172258	−	0.311375i
$931$	40.5358			1.32851
$932$	5.03975	−	5.03975i	0.165083	−	0.165083i
$933$	−23.0411	+	35.1930i	−0.754331	+	1.15217i
$934$			4.41465i			0.144452i
$935$	14.1651	−	1.05537i	0.463248	−	0.0345144i
$936$	−2.32788	−	5.33492i	−0.0760891	−	0.174377i
$937$	20.8046	+	20.8046i	0.679658	+	0.679658i	0.959923	−	0.280265i	$-0.0904223\pi$
$937$	20.8046	+	20.8046i	0.679658	+	0.679658i	−0.280265	+	0.959923i	$0.590422\pi$
$938$	14.2857	+	14.2857i	0.466445	+	0.466445i
$939$	3.31032	−	0.690777i	0.108028	−	0.0225427i
$940$	17.6017	−	1.31142i	0.574104	−	0.0427737i
$941$		−	10.9926i		−	0.358349i	−0.983817	−	0.179174i	$-0.942657\pi$
$941$		−	10.9926i		−	0.358349i	0.983817	−	0.179174i	$-0.0573426\pi$
$942$	20.5488	+	13.4534i	0.669516	+	0.438336i
$943$	0.939065	−	0.939065i	0.0305802	−	0.0305802i
$944$	1.73402			0.0564376
$945$	−4.92776	+	52.3437i	−0.160300	+	1.70274i
$946$	−56.6938			−1.84327
$947$	−13.9569	+	13.9569i	−0.453539	+	0.453539i	−0.896527	−	0.442988i	$-0.853918\pi$
$947$	−13.9569	+	13.9569i	−0.453539	+	0.453539i	0.442988	+	0.896527i	$0.353918\pi$
$948$	−1.47246	−	0.964027i	−0.0478232	−	0.0313101i
$949$			20.5365i			0.666644i
$950$	8.94207	−	12.0942i	0.290119	−	0.392387i
$951$	−20.4269	+	4.26257i	−0.662389	+	0.138223i
$952$	−3.19962	−	3.19962i	−0.103700	−	0.103700i
$953$	13.7314	+	13.7314i	0.444803	+	0.444803i	0.893623	−	0.448819i	$-0.148155\pi$
$953$	13.7314	+	13.7314i	0.444803	+	0.444803i	−0.448819	+	0.893623i	$0.648155\pi$
$954$	12.2778	+	28.1376i	0.397508	+	0.910989i
$955$	9.38900	+	8.08696i	0.303821	+	0.261688i
$956$			0.648149i			0.0209627i
$957$	5.46507	−	8.34736i	0.176661	−	0.269832i
$958$	−4.40403	+	4.40403i	−0.142288	+	0.142288i
$959$	−85.5799			−2.76352
$960$	1.07065	+	3.72206i	0.0345552	+	0.120129i
$961$	−23.1491			−0.746745
$962$	10.7346	−	10.7346i	0.346096	−	0.346096i
$963$	39.1174	+	15.3504i	1.26054	+	0.494661i
$964$		−	13.1385i		−	0.423164i
$965$	−1.35594	−	18.1993i	−0.0436492	−	0.585856i
$966$	−1.65227	−	7.91798i	−0.0531611	−	0.254757i
$967$	14.4114	+	14.4114i	0.463440	+	0.463440i	0.899781	−	0.436341i	$-0.143726\pi$
$967$	14.4114	+	14.4114i	0.463440	+	0.463440i	−0.436341	+	0.899781i	$0.643726\pi$
$968$	−20.7555	−	20.7555i	−0.667108	−	0.667108i
$969$	1.06433	+	5.10047i	0.0341913	+	0.163851i
$970$	−18.6335	+	21.6336i	−0.598284	+	0.694612i
$971$			27.9479i			0.896891i	0.893810	+	0.448446i	$0.148022\pi$
$971$			27.9479i			0.896891i	−0.893810	+	0.448446i	$0.851978\pi$
$972$	3.75400	+	15.1297i	0.120410	+	0.485285i
$973$	41.1567	−	41.1567i	1.31942	−	1.31942i
$974$	−0.762672			−0.0244376
$975$	5.83196	+	15.7583i	0.186772	+	0.504670i
$976$	0.769212			0.0246219
$977$	−9.24508	+	9.24508i	−0.295776	+	0.295776i	−0.839357	−	0.543581i	$-0.817068\pi$
$977$	−9.24508	+	9.24508i	−0.295776	+	0.295776i	0.543581	+	0.839357i	$0.317068\pi$
$978$	9.62417	−	14.7000i	0.307747	−	0.470053i
$979$		−	11.9807i		−	0.382906i
$980$	19.6642	−	22.8302i	0.628149	−	0.729285i
$981$	46.2428	−	20.1780i	1.47642	−	0.644233i
$982$	−15.0803	−	15.0803i	−0.481233	−	0.481233i
$983$	6.78250	+	6.78250i	0.216328	+	0.216328i	0.806949	−	0.590621i	$-0.201117\pi$
$983$	6.78250	+	6.78250i	0.216328	+	0.216328i	−0.590621	+	0.806949i	$0.701117\pi$
$984$	2.18182	−	0.455289i	0.0695540	−	0.0145141i
$985$	−2.92085	−	39.2033i	−0.0930659	−	1.24912i
$986$		−	0.906803i		−	0.0288785i
$987$	−51.7588	−	33.8868i	−1.64750	−	1.07863i
$988$	4.12708	−	4.12708i	0.131300	−	0.131300i
$989$	−9.21075			−0.292885
$990$	19.8971	+	37.6826i	0.632373	+	1.19763i
$991$	31.7021			1.00705			0.503524	−	0.863981i	$-0.332036\pi$
$991$	31.7021			1.00705			0.503524	+	0.863981i	$0.332036\pi$
$992$	−1.98127	+	1.98127i	−0.0629055	+	0.0629055i
$993$	10.6306	+	6.95991i	0.337351	+	0.220866i
$994$		−	68.8277i		−	2.18308i
$995$	4.66105	+	4.01467i	0.147765	+	0.127274i
$996$	−9.50837	+	1.98415i	−0.301284	+	0.0628701i
$997$	−16.9621	−	16.9621i	−0.537196	−	0.537196i	0.385509	−	0.922704i	$-0.374026\pi$
$997$	−16.9621	−	16.9621i	−0.537196	−	0.537196i	−0.922704	+	0.385509i	$0.874026\pi$
$998$	−20.9446	−	20.9446i	−0.662990	−	0.662990i
$999$	−33.1562	+	23.5289i	−1.04902	+	0.744420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.g.137.6	✓	28
3.2	odd	2	inner	510.2.l.g.137.9	yes	28
5.3	odd	4	inner	510.2.l.g.443.9	yes	28
15.8	even	4	inner	510.2.l.g.443.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.g.137.6	✓	28	1.1	even	1	trivial
510.2.l.g.137.9	yes	28	3.2	odd	2	inner
510.2.l.g.443.6	yes	28	15.8	even	4	inner
510.2.l.g.443.9	yes	28	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.44910 + 0.948737i) q^{3} -1.00000i q^{4} +(1.45929 - 1.69425i) q^{5} +(-1.69553 + 0.353812i) q^{6} +(3.19962 + 3.19962i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.19980 + 2.74963i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.44910 + 0.948737i) q^{3} -1.00000i q^{4} +(1.45929 - 1.69425i) q^{5} +(-1.69553 + 0.353812i) q^{6} +(3.19962 + 3.19962i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.19980 + 2.74963i) q^{9} +(0.166138 + 2.22989i) q^{10} -6.35238i q^{11} +(0.948737 - 1.44910i) q^{12} +(-1.37195 + 1.37195i) q^{13} -4.52495 q^{14} +(3.72206 - 1.07065i) q^{15} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +(-2.79267 - 1.09590i) q^{18} -3.00819i q^{19} +(-1.69425 - 1.45929i) q^{20} +(1.60098 + 7.67218i) q^{21} +(4.49181 + 4.49181i) q^{22} +(0.729761 + 0.729761i) q^{23} +(0.353812 + 1.69553i) q^{24} +(-0.740938 - 4.94480i) q^{25} -1.94023i q^{26} +(-0.870049 + 5.12279i) q^{27} +(3.19962 - 3.19962i) q^{28} +0.906803 q^{29} +(-1.87483 + 3.38896i) q^{30} -2.80195 q^{31} +(0.707107 - 0.707107i) q^{32} +(6.02674 - 9.20526i) q^{33} -1.00000i q^{34} +(10.0901 - 0.751766i) q^{35} +(2.74963 - 1.19980i) q^{36} +(5.53263 + 5.53263i) q^{37} +(2.12711 + 2.12711i) q^{38} +(-3.28971 + 0.686476i) q^{39} +(2.22989 - 0.166138i) q^{40} -1.28681i q^{41} +(-6.55712 - 4.29298i) q^{42} +(-6.31079 + 6.31079i) q^{43} -6.35238 q^{44} +(6.40941 + 1.97976i) q^{45} -1.03204 q^{46} +(-5.58158 + 5.58158i) q^{47} +(-1.44910 - 0.948737i) q^{48} +13.4752i q^{49} +(4.02042 + 2.97258i) q^{50} +(-1.69553 + 0.353812i) q^{51} +(1.37195 + 1.37195i) q^{52} +(-7.23598 - 7.23598i) q^{53} +(-3.00714 - 4.23758i) q^{54} +(-10.7625 - 9.26998i) q^{55} +4.52495i q^{56} +(2.85398 - 4.35917i) q^{57} +(-0.641207 + 0.641207i) q^{58} -1.73402 q^{59} +(-1.07065 - 3.72206i) q^{60} -0.769212 q^{61} +(1.98127 - 1.98127i) q^{62} +(-4.95889 + 12.6367i) q^{63} +1.00000i q^{64} +(0.322346 + 4.32649i) q^{65} +(2.24755 + 10.7706i) q^{66} +(-3.15710 - 3.15710i) q^{67} +(0.707107 + 0.707107i) q^{68} +(0.365148 + 1.74985i) q^{69} +(-6.60322 + 7.66638i) q^{70} +15.2107i q^{71} +(-1.09590 + 2.79267i) q^{72} +(7.48444 - 7.48444i) q^{73} -7.82432 q^{74} +(3.61761 - 7.86847i) q^{75} -3.00819 q^{76} +(20.3252 - 20.3252i) q^{77} +(1.84077 - 2.81159i) q^{78} -1.01612i q^{79} +(-1.45929 + 1.69425i) q^{80} +(-6.12097 + 6.59801i) q^{81} +(0.909913 + 0.909913i) q^{82} +(-3.96539 - 3.96539i) q^{83} +(7.67218 - 1.60098i) q^{84} +(0.166138 + 2.22989i) q^{85} -8.92481i q^{86} +(1.31405 + 0.860318i) q^{87} +(4.49181 - 4.49181i) q^{88} +1.88602 q^{89} +(-5.93204 + 3.13223i) q^{90} -8.77943 q^{91} +(0.729761 - 0.729761i) q^{92} +(-4.06031 - 2.65831i) q^{93} -7.89354i q^{94} +(-5.09661 - 4.38982i) q^{95} +(1.69553 - 0.353812i) q^{96} +(9.02893 + 9.02893i) q^{97} +(-9.52838 - 9.52838i) q^{98} +(17.4667 - 7.62157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7}+O(q^{10}) \) 28 * q + 4 * q^7	\( 28 q + 4 q^{7} - 12 q^{10} - 8 q^{13} + 8 q^{15} - 28 q^{16} - 16 q^{18} + 48 q^{21} + 20 q^{22} + 40 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{31} + 8 q^{33} + 8 q^{37} - 8 q^{40} - 48 q^{42} + 48 q^{43} + 36 q^{45} - 64 q^{46} + 8 q^{52} - 36 q^{55} - 32 q^{57} + 20 q^{58} + 12 q^{60} - 16 q^{61} - 56 q^{63} + 32 q^{66} + 112 q^{67} - 28 q^{70} + 16 q^{72} + 12 q^{73} + 16 q^{75} - 8 q^{76} - 32 q^{78} - 48 q^{81} + 24 q^{82} - 12 q^{85} - 44 q^{87} + 20 q^{88} - 20 q^{90} - 80 q^{91} + 28 q^{93} + 60 q^{97}+O(q^{100}) \) 28 * q + 4 * q^7 - 12 * q^10 - 8 * q^13 + 8 * q^15 - 28 * q^16 - 16 * q^18 + 48 * q^21 + 20 * q^22 + 40 * q^25 - 36 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^31 + 8 * q^33 + 8 * q^37 - 8 * q^40 - 48 * q^42 + 48 * q^43 + 36 * q^45 - 64 * q^46 + 8 * q^52 - 36 * q^55 - 32 * q^57 + 20 * q^58 + 12 * q^60 - 16 * q^61 - 56 * q^63 + 32 * q^66 + 112 * q^67 - 28 * q^70 + 16 * q^72 + 12 * q^73 + 16 * q^75 - 8 * q^76 - 32 * q^78 - 48 * q^81 + 24 * q^82 - 12 * q^85 - 44 * q^87 + 20 * q^88 - 20 * q^90 - 80 * q^91 + 28 * q^93 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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