LMFDB - Embedded newform 370.2.q.f.103.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(97,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("370.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,16,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	370.103
Dual form			370.2.q.f.97.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.418603 - 1.56225i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.09367 + 0.785216i) q^{5} +(1.14364 - 1.14364i) q^{6} +(-0.298699 - 1.11476i) q^{7} -1.00000 q^{8} +(0.332689 - 0.192078i) q^{9} +(-1.72685 - 1.42056i) q^{10} -5.41958i q^{11} +(1.56225 + 0.418603i) q^{12} +(2.03941 - 3.53236i) q^{13} +(0.816061 - 0.816061i) q^{14} +(2.10312 + 2.94213i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.37280 - 1.94729i) q^{17} +(0.332689 + 0.192078i) q^{18} +(-5.80123 + 1.55443i) q^{19} +(0.366816 - 2.20578i) q^{20} +(-1.61650 + 0.933284i) q^{21} +(4.69349 - 2.70979i) q^{22} +0.383468 q^{23} +(0.418603 + 1.56225i) q^{24} +(3.76687 - 3.28796i) q^{25} +4.07882 q^{26} +(-3.87027 - 3.87027i) q^{27} +(1.11476 + 0.298699i) q^{28} +(-5.82137 + 5.82137i) q^{29} +(-1.49640 + 3.29242i) q^{30} +(-3.43124 - 3.43124i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-8.46672 + 2.26865i) q^{33} +(3.37280 + 1.94729i) q^{34} +(1.50070 + 2.09939i) q^{35} +0.384156i q^{36} +(5.44223 - 2.71702i) q^{37} +(-4.24679 - 4.24679i) q^{38} +(-6.37212 - 1.70740i) q^{39} +(2.09367 - 0.785216i) q^{40} +(7.78143 + 4.49261i) q^{41} +(-1.61650 - 0.933284i) q^{42} +1.57247 q^{43} +(4.69349 + 2.70979i) q^{44} +(-0.545717 + 0.663380i) q^{45} +(0.191734 + 0.332093i) q^{46} +(-3.06744 + 3.06744i) q^{47} +(-1.14364 + 1.14364i) q^{48} +(4.90871 - 2.83404i) q^{49} +(4.73089 + 1.61823i) q^{50} +(-4.45401 - 4.45401i) q^{51} +(2.03941 + 3.53236i) q^{52} +(-2.04146 + 7.61884i) q^{53} +(1.41662 - 5.28689i) q^{54} +(4.25554 + 11.3468i) q^{55} +(0.298699 + 1.11476i) q^{56} +(4.85682 + 8.41226i) q^{57} +(-7.95215 - 2.13077i) q^{58} +(-2.84475 + 10.6168i) q^{59} +(-3.59952 + 0.350287i) q^{60} +(-8.58880 + 2.30136i) q^{61} +(1.25592 - 4.68716i) q^{62} +(-0.313495 - 0.313495i) q^{63} +1.00000 q^{64} +(-1.49617 + 8.99695i) q^{65} +(-6.19807 - 6.19807i) q^{66} +(10.0190 - 2.68457i) q^{67} +3.89458i q^{68} +(-0.160521 - 0.599071i) q^{69} +(-1.06778 + 2.34934i) q^{70} +(2.42276 - 4.19634i) q^{71} +(-0.332689 + 0.192078i) q^{72} +(9.61059 - 9.61059i) q^{73} +(5.07412 + 3.35460i) q^{74} +(-6.71343 - 4.50843i) q^{75} +(1.55443 - 5.80123i) q^{76} +(-6.04153 + 1.61882i) q^{77} +(-1.70740 - 6.37212i) q^{78} +(8.53421 - 2.28673i) q^{79} +(1.72685 + 1.42056i) q^{80} +(-3.84998 + 6.66836i) q^{81} +8.98522i q^{82} +(3.22265 - 12.0271i) q^{83} -1.86657i q^{84} +(-5.53248 + 6.72535i) q^{85} +(0.786233 + 1.36180i) q^{86} +(11.5313 + 6.65758i) q^{87} +5.41958i q^{88} +(-14.3038 - 3.83268i) q^{89} +(-0.847362 - 0.140915i) q^{90} +(-4.54690 - 1.21834i) q^{91} +(-0.191734 + 0.332093i) q^{92} +(-3.92412 + 6.79677i) q^{93} +(-4.19020 - 1.12276i) q^{94} +(10.9253 - 7.80968i) q^{95} +(-1.56225 - 0.418603i) q^{96} +4.38333i q^{97} +(4.90871 + 2.83404i) q^{98} +(-1.04098 - 1.80304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9} + 6 q^{10} + 10 q^{12} + 10 q^{13} - 8 q^{14} - 8 q^{15} - 16 q^{16} - 12 q^{17} + 12 q^{18} + 2 q^{19} - 54 q^{21}+ \cdots - 26 q^{99}+O(q^{100}) $ 32 * q + 16 * q^2 - 2 * q^3 - 16 * q^4 + 6 * q^5 + 8 * q^6 - 10 * q^7 - 32 * q^8 + 12 * q^9 + 6 * q^10 + 10 * q^12 + 10 * q^13 - 8 * q^14 - 8 * q^15 - 16 * q^16 - 12 * q^17 + 12 * q^18 + 2 * q^19 - 54 * q^21 + 6 * q^22 + 12 * q^23 + 2 * q^24 - 16 * q^25 + 20 * q^26 + 40 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^30 - 4 * q^31 + 16 * q^32 + 26 * q^33 - 12 * q^34 - 12 * q^35 + 20 * q^37 - 26 * q^38 - 58 * q^39 - 6 * q^40 + 18 * q^41 - 54 * q^42 - 32 * q^43 + 6 * q^44 + 56 * q^45 + 6 * q^46 + 18 * q^47 - 8 * q^48 - 12 * q^49 - 14 * q^50 - 4 * q^51 + 10 * q^52 - 24 * q^53 + 20 * q^54 - 32 * q^55 + 10 * q^56 + 8 * q^57 + 36 * q^58 + 42 * q^59 + 16 * q^60 - 46 * q^61 - 14 * q^62 + 32 * q^64 - 18 * q^65 + 4 * q^66 + 50 * q^67 - 66 * q^69 + 12 * q^70 - 12 * q^71 - 12 * q^72 - 28 * q^73 + 16 * q^74 - 20 * q^75 - 28 * q^76 + 12 * q^77 - 26 * q^78 + 38 * q^79 - 6 * q^80 + 56 * q^81 - 8 * q^85 - 16 * q^86 + 18 * q^87 + 18 * q^89 + 4 * q^90 + 4 * q^91 - 6 * q^92 + 32 * q^93 + 30 * q^94 + 96 * q^95 - 10 * q^96 - 12 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.418603	−	1.56225i	−0.241680	−	0.901964i	−0.975023	−	0.222104i	$-0.928707\pi$
$3$	−0.418603	−	1.56225i	−0.241680	−	0.901964i	0.733342	−	0.679859i	$-0.237959\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.09367	+	0.785216i	−0.936316	+	0.351159i
$5$	−2.09367	+	0.785216i	−0.936316	+	0.351159i
$6$	1.14364	−	1.14364i	0.466891	−	0.466891i
$7$	−0.298699	−	1.11476i	−0.112898	−	0.421340i	0.886223	−	0.463258i	$-0.153320\pi$
$7$	−0.298699	−	1.11476i	−0.112898	−	0.421340i	−0.999121	+	0.0419183i	$0.986653\pi$
$8$	−1.00000			−0.353553
$9$	0.332689	−	0.192078i	0.110896	−	0.0640260i
$10$	−1.72685	−	1.42056i	−0.546078	−	0.449220i
$11$		−	5.41958i		−	1.63406i	−0.576592	−	0.817032i	$-0.695618\pi$
$11$		−	5.41958i		−	1.63406i	0.576592	−	0.817032i	$-0.304382\pi$
$12$	1.56225	+	0.418603i	0.450982	+	0.120840i
$13$	2.03941	−	3.53236i	0.565630	−	0.979700i	−0.431361	−	0.902179i	$-0.641966\pi$
$13$	2.03941	−	3.53236i	0.565630	−	0.979700i	0.996991	−	0.0775203i	$-0.0247003\pi$
$14$	0.816061	−	0.816061i	0.218102	−	0.218102i
$15$	2.10312	+	2.94213i	0.543022	+	0.759654i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.37280	−	1.94729i	0.818025	−	0.472287i	−0.0317102	−	0.999497i	$-0.510095\pi$
$17$	3.37280	−	1.94729i	0.818025	−	0.472287i	0.849735	+	0.527210i	$0.176762\pi$
$18$	0.332689	+	0.192078i	0.0784156	+	0.0452732i
$19$	−5.80123	+	1.55443i	−1.33089	+	0.356612i	−0.853048	−	0.521833i	$-0.825249\pi$
$19$	−5.80123	+	1.55443i	−1.33089	+	0.356612i	−0.477845	+	0.878444i	$0.658582\pi$
$20$	0.366816	−	2.20578i	0.0820225	−	0.493226i
$21$	−1.61650	+	0.933284i	−0.352748	+	0.203659i
$22$	4.69349	−	2.70979i	1.00066	−	0.577729i
$23$	0.383468			0.0799586			0.0399793	−	0.999201i	$-0.487271\pi$
$23$	0.383468			0.0799586			0.0399793	+	0.999201i	$0.487271\pi$
$24$	0.418603	+	1.56225i	0.0854469	+	0.318892i
$25$	3.76687	−	3.28796i	0.753374	−	0.657592i
$26$	4.07882			0.799922
$27$	−3.87027	−	3.87027i	−0.744834	−	0.744834i
$28$	1.11476	+	0.298699i	0.210670	+	0.0564488i
$29$	−5.82137	+	5.82137i	−1.08100	+	1.08100i	−0.0845860	+	0.996416i	$0.526957\pi$
$29$	−5.82137	+	5.82137i	−1.08100	+	1.08100i	−0.996416	+	0.0845860i	$0.973043\pi$
$30$	−1.49640	+	3.29242i	−0.273204	+	0.601110i
$31$	−3.43124	−	3.43124i	−0.616269	−	0.616269i	0.328304	−	0.944572i	$-0.393523\pi$
$31$	−3.43124	−	3.43124i	−0.616269	−	0.616269i	−0.944572	+	0.328304i	$0.893523\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−8.46672	+	2.26865i	−1.47387	+	0.394922i
$34$	3.37280	+	1.94729i	0.578431	+	0.333957i
$35$	1.50070	+	2.09939i	0.253665	+	0.354862i
$36$			0.384156i			0.0640260i
$37$	5.44223	−	2.71702i	0.894696	−	0.446675i
$37$	5.44223	−	2.71702i	0.894696	−	0.446675i
$38$	−4.24679	−	4.24679i	−0.688921	−	0.688921i
$39$	−6.37212	−	1.70740i	−1.02036	−	0.273403i
$40$	2.09367	−	0.785216i	0.331038	−	0.124154i
$41$	7.78143	+	4.49261i	1.21526	+	0.701628i	0.963899	−	0.266267i	$-0.0857901\pi$
$41$	7.78143	+	4.49261i	1.21526	+	0.701628i	0.251356	+	0.967895i	$0.419123\pi$
$42$	−1.61650	−	0.933284i	−0.249431	−	0.144009i
$43$	1.57247			0.239799			0.119899	−	0.992786i	$-0.461743\pi$
$43$	1.57247			0.239799			0.119899	+	0.992786i	$0.461743\pi$
$44$	4.69349	+	2.70979i	0.707571	+	0.408516i
$45$	−0.545717	+	0.663380i	−0.0813507	+	0.0988909i
$46$	0.191734	+	0.332093i	0.0282696	+	0.0489644i
$47$	−3.06744	+	3.06744i	−0.447432	+	0.447432i	−0.894500	−	0.447068i	$-0.852468\pi$
$47$	−3.06744	+	3.06744i	−0.447432	+	0.447432i	0.447068	+	0.894500i	$0.352468\pi$
$48$	−1.14364	+	1.14364i	−0.165071	+	0.165071i
$49$	4.90871	−	2.83404i	0.701244	−	0.404863i
$50$	4.73089	+	1.61823i	0.669049	+	0.228852i
$51$	−4.45401	−	4.45401i	−0.623686	−	0.623686i
$52$	2.03941	+	3.53236i	0.282815	+	0.489850i
$53$	−2.04146	+	7.61884i	−0.280416	+	1.04653i	0.671708	+	0.740816i	$0.265561\pi$
$53$	−2.04146	+	7.61884i	−0.280416	+	1.04653i	−0.952124	+	0.305712i	$0.901106\pi$
$54$	1.41662	−	5.28689i	0.192777	−	0.719454i
$55$	4.25554	+	11.3468i	0.573817	+	1.53000i
$56$	0.298699	+	1.11476i	0.0399154	+	0.148966i
$57$	4.85682	+	8.41226i	0.643302	+	1.11423i
$58$	−7.95215	−	2.13077i	−1.04417	−	0.279784i
$59$	−2.84475	+	10.6168i	−0.370355	+	1.38218i	0.489659	+	0.871914i	$0.337121\pi$
$59$	−2.84475	+	10.6168i	−0.370355	+	1.38218i	−0.860014	+	0.510270i	$0.829546\pi$
$60$	−3.59952	+	0.350287i	−0.464696	+	0.0452219i
$61$	−8.58880	+	2.30136i	−1.09968	+	0.294659i	−0.762635	−	0.646829i	$-0.776095\pi$
$61$	−8.58880	+	2.30136i	−1.09968	+	0.294659i	−0.337047	+	0.941488i	$0.609428\pi$
$62$	1.25592	−	4.68716i	0.159502	−	0.595270i
$63$	−0.313495	−	0.313495i	−0.0394967	−	0.0394967i
$64$	1.00000			0.125000
$65$	−1.49617	+	8.99695i	−0.185578	+	1.11593i
$66$	−6.19807	−	6.19807i	−0.762930	−	0.762930i
$67$	10.0190	−	2.68457i	1.22401	−	0.327973i	0.411766	−	0.911290i	$-0.364912\pi$
$67$	10.0190	−	2.68457i	1.22401	−	0.327973i	0.812245	+	0.583317i	$0.198245\pi$
$68$			3.89458i			0.472287i
$69$	−0.160521	−	0.599071i	−0.0193244	−	0.0721197i
$70$	−1.06778	+	2.34934i	−0.127624	+	0.280800i
$71$	2.42276	−	4.19634i	0.287528	−	0.498013i	−0.685691	−	0.727893i	$-0.740500\pi$
$71$	2.42276	−	4.19634i	0.287528	−	0.498013i	0.973219	+	0.229879i	$0.0738332\pi$
$72$	−0.332689	+	0.192078i	−0.0392078	+	0.0226366i
$73$	9.61059	−	9.61059i	1.12483	−	1.12483i	0.133830	−	0.991004i	$-0.457272\pi$
$73$	9.61059	−	9.61059i	1.12483	−	1.12483i	0.991004	−	0.133830i	$-0.0427275\pi$
$74$	5.07412	+	3.35460i	0.589854	+	0.389964i
$75$	−6.71343	−	4.50843i	−0.775200	−	0.520589i
$76$	1.55443	−	5.80123i	0.178306	−	0.665446i
$77$	−6.04153	+	1.61882i	−0.688497	+	0.184482i
$78$	−1.70740	−	6.37212i	−0.193325	−	0.721500i
$79$	8.53421	−	2.28673i	0.960174	−	0.257278i	0.255500	−	0.966809i	$-0.417760\pi$
$79$	8.53421	−	2.28673i	0.960174	−	0.257278i	0.704674	+	0.709531i	$0.251093\pi$
$80$	1.72685	+	1.42056i	0.193068	+	0.158823i
$81$	−3.84998	+	6.66836i	−0.427775	+	0.740929i
$82$			8.98522i			0.992252i
$83$	3.22265	−	12.0271i	0.353731	−	1.32014i	−0.528342	−	0.849032i	$-0.677186\pi$
$83$	3.22265	−	12.0271i	0.353731	−	1.32014i	0.882073	−	0.471112i	$-0.156147\pi$
$84$		−	1.86657i		−	0.203659i
$85$	−5.53248	+	6.72535i	−0.600081	+	0.729466i
$86$	0.786233	+	1.36180i	0.0847817	+	0.146846i
$87$	11.5313	+	6.65758i	1.23628	+	0.713768i
$88$			5.41958i			0.577729i
$89$	−14.3038	−	3.83268i	−1.51620	−	0.406264i	−0.597709	−	0.801713i	$-0.703922\pi$
$89$	−14.3038	−	3.83268i	−1.51620	−	0.406264i	−0.918488	+	0.395449i	$0.870589\pi$
$90$	−0.847362	−	0.140915i	−0.0893198	−	0.0148537i
$91$	−4.54690	−	1.21834i	−0.476645	−	0.127717i
$92$	−0.191734	+	0.332093i	−0.0199896	+	0.0346231i
$93$	−3.92412	+	6.79677i	−0.406912	+	0.704792i
$94$	−4.19020	−	1.12276i	−0.432186	−	0.115804i
$95$	10.9253	−	7.80968i	1.12091	−	0.801256i
$96$	−1.56225	−	0.418603i	−0.159446	−	0.0427235i
$97$			4.38333i			0.445060i	0.974926	+	0.222530i	$0.0714315\pi$
$97$			4.38333i			0.445060i	−0.974926	+	0.222530i	$0.928569\pi$
$98$	4.90871	+	2.83404i	0.495854	+	0.286282i
$99$	−1.04098	−	1.80304i	−0.104623	−	0.181212i
$100$	0.964021	+	4.90619i	0.0964021	+	0.490619i
$101$			7.97874i			0.793914i	0.917837	+	0.396957i	$0.129934\pi$
$101$			7.97874i			0.793914i	−0.917837	+	0.396957i	$0.870066\pi$
$102$	1.63028	−	6.08429i	0.161422	−	0.602434i
$103$			4.69150i			0.462267i	0.972922	+	0.231134i	$0.0742435\pi$
$103$			4.69150i			0.462267i	−0.972922	+	0.231134i	$0.925757\pi$
$104$	−2.03941	+	3.53236i	−0.199980	+	0.346376i
$105$	2.65157	−	3.22328i	0.258767	−	0.314560i
$106$	−7.61884	+	2.04146i	−0.740007	+	0.198284i
$107$	−0.868218	−	3.24023i	−0.0839338	−	0.313245i	0.911176	−	0.412017i	$-0.135175\pi$
$107$	−0.868218	−	3.24023i	−0.0839338	−	0.313245i	−0.995110	+	0.0987714i	$0.968509\pi$
$108$	5.28689	−	1.41662i	0.508731	−	0.136314i
$109$	2.16115	−	8.06551i	0.207000	−	0.772536i	−0.781830	−	0.623491i	$-0.785714\pi$
$109$	2.16115	−	8.06551i	0.207000	−	0.772536i	0.988831	−	0.149044i	$-0.0476197\pi$
$110$	−7.69884	+	9.35880i	−0.734055	+	0.892327i
$111$	−6.52278	−	7.36475i	−0.619115	−	0.699031i
$112$	−0.816061	+	0.816061i	−0.0771106	+	0.0771106i
$113$	5.90335	−	3.40830i	0.555340	−	0.320626i	−0.195933	−	0.980617i	$-0.562773\pi$
$113$	5.90335	−	3.40830i	0.555340	−	0.320626i	0.751273	+	0.659992i	$0.229440\pi$
$114$	−4.85682	+	8.41226i	−0.454883	+	0.787880i
$115$	−0.802853	+	0.301105i	−0.0748665	+	0.0280782i
$116$	−2.13077	−	7.95215i	−0.197837	−	0.738338i
$117$		−	1.56690i		−	0.144860i
$118$	−10.6168	+	2.84475i	−0.977351	+	0.261881i
$119$	−3.17821	−	3.17821i	−0.291346	−	0.291346i
$120$	−2.10312	−	2.94213i	−0.191987	−	0.268578i
$121$	−18.3719			−1.67017
$122$	−6.28744	−	6.28744i	−0.569238	−	0.569238i
$123$	3.76124	−	14.0371i	0.339140	−	1.26569i
$124$	4.68716	−	1.25592i	0.420919	−	0.112785i
$125$	−5.30481	+	9.84170i	−0.474477	+	0.880268i
$126$	0.114747	−	0.428242i	0.0102225	−	0.0381508i
$127$	1.49703	+	0.401127i	0.132840	+	0.0355943i	0.324626	−	0.945842i	$-0.394761\pi$
$127$	1.49703	+	0.401127i	0.132840	+	0.0355943i	−0.191787	+	0.981437i	$0.561428\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.658239	−	2.45658i	−0.0579547	−	0.216290i
$130$	−8.53968	+	3.20275i	−0.748979	+	0.280900i
$131$	−3.77026	+	14.0708i	−0.329409	+	1.22937i	0.580396	+	0.814334i	$0.302898\pi$
$131$	−3.77026	+	14.0708i	−0.329409	+	1.22937i	−0.909805	+	0.415036i	$0.863769\pi$
$132$	2.26865	−	8.46672i	0.197461	−	0.736934i
$133$	3.46564	+	6.00267i	0.300509	+	0.520498i
$134$	7.33439	+	7.33439i	0.633595	+	0.633595i
$135$	11.1421	+	5.06405i	0.958955	+	0.435844i
$136$	−3.37280	+	1.94729i	−0.289215	+	0.166979i
$137$	−8.51418	+	8.51418i	−0.727416	+	0.727416i	−0.970104	−	0.242689i	$-0.921971\pi$
$137$	−8.51418	+	8.51418i	−0.727416	+	0.727416i	0.242689	+	0.970104i	$0.421971\pi$
$138$	0.438551	−	0.438551i	0.0373319	−	0.0373319i
$139$	−5.04939	−	8.74580i	−0.428284	−	0.741809i	0.568437	−	0.822727i	$-0.307548\pi$
$139$	−5.04939	−	8.74580i	−0.428284	−	0.741809i	−0.996721	+	0.0809175i	$0.974215\pi$
$140$	−2.56848	+	0.249952i	−0.217076	+	0.0211248i
$141$	6.07614	+	3.50806i	0.511703	+	0.295432i
$142$	4.84551			0.406626
$143$	−19.1439	−	11.0527i	−1.60089	−	0.924276i
$144$	−0.332689	−	0.192078i	−0.0277241	−	0.0160065i
$145$	7.61698	−	16.7590i	0.632555	−	1.39176i
$146$	13.1283	+	3.51772i	1.08651	+	0.291128i
$147$	−6.48228	−	6.48228i	−0.534649	−	0.534649i
$148$	−0.368107	+	6.07161i	−0.0302582	+	0.499084i
$149$		−	7.20201i		−	0.590012i	−0.955495	−	0.295006i	$-0.904678\pi$
$149$		−	7.20201i		−	0.590012i	0.955495	−	0.295006i	$-0.0953216\pi$
$150$	0.547705	−	8.06822i	0.0447199	−	0.658767i
$151$	5.82441	+	3.36272i	0.473984	+	0.273655i	0.717906	−	0.696140i	$-0.245101\pi$
$151$	5.82441	+	3.36272i	0.473984	+	0.273655i	−0.243922	+	0.969795i	$0.578434\pi$
$152$	5.80123	−	1.55443i	0.470542	−	0.126081i
$153$	0.748063	−	1.29568i	0.0604773	−	0.104750i
$154$	−4.42271	−	4.42271i	−0.356392	−	0.356392i
$155$	9.87813	+	4.48960i	0.793430	+	0.360614i
$156$	4.66471	−	4.66471i	0.373476	−	0.373476i
$157$	12.8692	+	3.44829i	1.02707	+	0.275204i	0.732747	−	0.680501i	$-0.238238\pi$
$157$	12.8692	+	3.44829i	1.02707	+	0.275204i	0.294327	+	0.955705i	$0.404905\pi$
$158$	6.24748	+	6.24748i	0.497022	+	0.497022i
$159$	12.7571			1.01170
$160$	−0.366816	+	2.20578i	−0.0289993	+	0.174382i
$161$	−0.114542	−	0.427475i	−0.00902714	−	0.0336897i
$162$	−7.69996			−0.604966
$163$	3.89013	−	2.24597i	0.304699	−	0.175918i	−0.339853	−	0.940479i	$-0.610377\pi$
$163$	3.89013	−	2.24597i	0.304699	−	0.175918i	0.644552	+	0.764561i	$0.277044\pi$
$164$	−7.78143	+	4.49261i	−0.607628	+	0.350814i
$165$	15.9451	−	11.3980i	1.24132	−	0.887333i
$166$	12.0271	−	3.22265i	0.933483	−	0.250126i
$167$	3.82275	+	2.20707i	0.295813	+	0.170788i	0.640561	−	0.767908i	$-0.278702\pi$
$167$	3.82275	+	2.20707i	0.295813	+	0.170788i	−0.344747	+	0.938696i	$0.612035\pi$
$168$	1.61650	−	0.933284i	0.124715	−	0.0720044i
$169$	−1.81837	−	3.14951i	−0.139874	−	0.242270i
$170$	−8.59056	−	1.42859i	−0.658866	−	0.109568i
$171$	−1.63143	+	1.63143i	−0.124759	+	0.124759i
$172$	−0.786233	+	1.36180i	−0.0599497	+	0.103836i
$173$	19.6886	+	5.27554i	1.49690	+	0.401092i	0.912059	−	0.410058i	$-0.134492\pi$
$173$	19.6886	+	5.27554i	1.49690	+	0.401092i	0.584837	+	0.811151i	$0.301158\pi$
$174$			13.3152i			1.00942i
$175$	−4.79045	−	3.21705i	−0.362124	−	0.243186i
$176$	−4.69349	+	2.70979i	−0.353785	+	0.204258i
$177$	17.7768			1.33619
$178$	−3.83268	−	14.3038i	−0.287272	−	1.07211i
$179$	14.7689	−	14.7689i	1.10388	−	1.10388i	0.109943	−	0.993938i	$-0.464933\pi$
$179$	14.7689	−	14.7689i	1.10388	−	1.10388i	0.993938	−	0.109943i	$-0.0350667\pi$
$180$	−0.301646	−	0.804295i	−0.0224833	−	0.0599486i
$181$	−2.80922	+	4.86571i	−0.208808	+	0.361665i	−0.951339	−	0.308146i	$-0.900292\pi$
$181$	−2.80922	+	4.86571i	−0.208808	+	0.361665i	0.742532	+	0.669811i	$0.233625\pi$
$182$	−1.21834	−	4.54690i	−0.0903093	−	0.337039i
$183$	7.19059	+	12.4545i	0.531544	+	0.920661i
$184$	−0.383468			−0.0282696
$185$	−9.26076	+	9.96185i	−0.680864	+	0.732410i
$186$	−7.84823			−0.575460
$187$	−10.5535	−	18.2792i	−0.771747	−	1.33671i
$188$	−1.12276	−	4.19020i	−0.0818857	−	0.305602i
$189$	−3.15838	+	5.47047i	−0.229738	+	0.397918i
$190$	12.2260	+	5.55672i	0.886968	+	0.403126i
$191$	6.46180	−	6.46180i	0.467559	−	0.467559i	−0.433564	−	0.901123i	$-0.642744\pi$
$191$	6.46180	−	6.46180i	0.467559	−	0.467559i	0.901123	+	0.433564i	$0.142744\pi$
$192$	−0.418603	−	1.56225i	−0.0302101	−	0.112745i
$193$	10.6806			0.768808			0.384404	−	0.923165i	$-0.374407\pi$
$193$	10.6806			0.768808			0.384404	+	0.923165i	$0.374407\pi$
$194$	−3.79607	+	2.19166i	−0.272542	+	0.157352i
$195$	14.6818	−	1.42876i	1.05138	−	0.102315i
$196$			5.66809i			0.404863i
$197$	−1.67820	−	0.449673i	−0.119567	−	0.0320379i	0.198539	−	0.980093i	$-0.436380\pi$
$197$	−1.67820	−	0.449673i	−0.119567	−	0.0320379i	−0.318106	+	0.948055i	$0.603047\pi$
$198$	1.04098	−	1.80304i	0.0739794	−	0.128136i
$199$	10.8607	−	10.8607i	0.769891	−	0.769891i	−0.208196	−	0.978087i	$-0.566759\pi$
$199$	10.8607	−	10.8607i	0.769891	−	0.769891i	0.978087	+	0.208196i	$0.0667591\pi$
$200$	−3.76687	+	3.28796i	−0.266358	+	0.232494i
$201$	−8.38793	−	14.5283i	−0.591639	−	1.02475i
$202$	−6.90979	+	3.98937i	−0.486171	+	0.280691i
$203$	8.22828	+	4.75060i	0.577512	+	0.333427i
$204$	6.08429	−	1.63028i	0.425985	−	0.114142i
$205$	−19.8194	−	3.29592i	−1.38425	−	0.230197i
$206$	−4.06296	+	2.34575i	−0.283080	+	0.163436i
$207$	0.127576	−	0.0736558i	0.00886711	−	0.00511943i
$208$	−4.07882			−0.282815
$209$	8.42438	+	31.4402i	0.582727	+	2.17477i
$210$	4.11723	+	0.684687i	0.284116	+	0.0472479i
$211$	15.7228			1.08240			0.541200	−	0.840894i	$-0.317970\pi$
$211$	15.7228			1.08240			0.541200	+	0.840894i	$0.317970\pi$
$212$	−5.57738	−	5.57738i	−0.383056	−	0.383056i
$213$	−7.56989	−	2.02834i	−0.518680	−	0.138980i
$214$	2.37202	−	2.37202i	0.162148	−	0.162148i
$215$	−3.29222	+	1.23473i	−0.224528	+	0.0842076i
$216$	3.87027	+	3.87027i	0.263339	+	0.263339i
$217$	−2.80010	+	4.84992i	−0.190083	+	0.329234i
$218$	8.06551	−	2.16115i	0.546265	−	0.146371i
$219$	−19.0371	−	10.9911i	−1.28641	−	0.742709i
$220$	−11.9544	−	1.98799i	−0.805964	−	0.134030i
$221$		−	15.8853i		−	1.06856i
$222$	3.11667	−	9.33127i	0.209177	−	0.626274i
$223$	−7.88096	−	7.88096i	−0.527748	−	0.527748i	0.392152	−	0.919900i	$-0.371731\pi$
$223$	−7.88096	−	7.88096i	−0.527748	−	0.527748i	−0.919900	+	0.392152i	$0.871731\pi$
$224$	−1.11476	−	0.298699i	−0.0744831	−	0.0199577i
$225$	0.621652	−	1.81740i	0.0414435	−	0.121160i
$226$	5.90335	+	3.40830i	0.392685	+	0.226717i
$227$	3.07951	+	1.77796i	0.204394	+	0.118007i	0.598704	−	0.800971i	$-0.295683\pi$
$227$	3.07951	+	1.77796i	0.204394	+	0.118007i	−0.394309	+	0.918978i	$0.629016\pi$
$228$	−9.71364			−0.643302
$229$	11.7656	+	6.79287i	0.777492	+	0.448885i	0.835541	−	0.549428i	$-0.185154\pi$
$229$	11.7656	+	6.79287i	0.777492	+	0.448885i	−0.0580484	+	0.998314i	$0.518488\pi$
$230$	−0.662191	−	0.544739i	−0.0436636	−	0.0359190i
$231$	5.05801	+	8.76072i	0.332792	+	0.576413i
$232$	5.82137	−	5.82137i	0.382192	−	0.382192i
$233$	−7.60963	+	7.60963i	−0.498523	+	0.498523i	−0.910978	−	0.412455i	$-0.864672\pi$
$233$	−7.60963	+	7.60963i	−0.498523	+	0.498523i	0.412455	+	0.910978i	$0.364672\pi$
$234$	1.35698	−	0.783451i	0.0887084	−	0.0512158i
$235$	4.01359	−	8.83079i	0.261818	−	0.576057i
$236$	−7.77200	−	7.77200i	−0.505914	−	0.505914i
$237$	−7.14489	−	12.3753i	−0.464110	−	0.803863i
$238$	1.16331	−	4.34152i	0.0754060	−	0.281419i
$239$	−5.53867	+	20.6706i	−0.358267	+	1.33707i	0.518056	+	0.855347i	$0.326656\pi$
$239$	−5.53867	+	20.6706i	−0.358267	+	1.33707i	−0.876323	+	0.481724i	$0.840011\pi$
$240$	1.49640	−	3.29242i	0.0965923	−	0.212525i
$241$	−1.88845	−	7.04781i	−0.121646	−	0.453989i	0.878052	−	0.478565i	$-0.158843\pi$
$241$	−1.88845	−	7.04781i	−0.121646	−	0.453989i	−0.999698	+	0.0245762i	$0.992176\pi$
$242$	−9.18593	−	15.9105i	−0.590494	−	1.02277i
$243$	−3.83143	−	1.02663i	−0.245786	−	0.0658583i
$244$	2.30136	−	8.58880i	0.147330	−	0.549841i
$245$	−8.05186	+	9.78794i	−0.514414	+	0.625328i
$246$	14.0371	−	3.76124i	0.894975	−	0.239808i
$247$	−6.34025	+	23.6621i	−0.403420	+	1.50559i
$248$	3.43124	+	3.43124i	0.217884	+	0.217884i
$249$	−20.1383			−1.27621
$250$	−11.1756	+	0.326747i	−0.706805	+	0.0206653i
$251$	4.53943	+	4.53943i	0.286526	+	0.286526i	0.835705	−	0.549179i	$-0.185059\pi$
$251$	4.53943	+	4.53943i	0.286526	+	0.286526i	−0.549179	+	0.835705i	$0.685059\pi$
$252$	0.428242	−	0.114747i	0.0269767	−	0.00722839i
$253$		−	2.07823i		−	0.130657i
$254$	0.401127	+	1.49703i	0.0251690	+	0.0939319i
$255$	12.8226	+	5.82785i	0.802980	+	0.364954i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.8740	−	6.27813i	0.678304	−	0.391619i	−0.120912	−	0.992663i	$-0.538582\pi$
$257$	10.8740	−	6.27813i	0.678304	−	0.391619i	0.799216	+	0.601044i	$0.205248\pi$
$258$	1.79834	−	1.79834i	0.111960	−	0.111960i
$259$	−4.65441	−	5.25521i	−0.289211	−	0.326543i
$260$	−7.04350	−	5.79420i	−0.436819	−	0.359341i
$261$	−0.818549	+	3.05487i	−0.0506669	+	0.189091i
$262$	−14.0708	+	3.77026i	−0.869296	+	0.232927i
$263$	1.78743	+	6.67077i	0.110218	+	0.411337i	0.998885	−	0.0472153i	$-0.0150347\pi$
$263$	1.78743	+	6.67077i	0.110218	+	0.411337i	−0.888667	+	0.458553i	$0.848368\pi$
$264$	8.46672	−	2.26865i	0.521091	−	0.139626i
$265$	−1.70830	−	17.5543i	−0.104940	−	1.07835i
$266$	−3.46564	+	6.00267i	−0.212492	+	0.368047i
$267$			23.9504i			1.46574i
$268$	−2.68457	+	10.0190i	−0.163986	+	0.612005i
$269$		−	25.0622i		−	1.52807i	−0.645174	−	0.764036i	$-0.723215\pi$
$269$		−	25.0622i		−	1.52807i	0.645174	−	0.764036i	$-0.276785\pi$
$270$	1.18543	+	12.1813i	0.0721427	+	0.741332i
$271$	8.90741	+	15.4281i	0.541087	+	0.937189i	0.998842	+	0.0481113i	$0.0153202\pi$
$271$	8.90741	+	15.4281i	0.541087	+	0.937189i	−0.457755	+	0.889078i	$0.651346\pi$
$272$	−3.37280	−	1.94729i	−0.204506	−	0.118072i
$273$			7.61339i			0.460783i
$274$	−11.6306	−	3.11641i	−0.702629	−	0.188269i
$275$	−17.8194	−	20.4149i	−1.07455	−	1.23106i
$276$	0.599071	+	0.160521i	0.0360599	+	0.00966221i
$277$	−7.89869	+	13.6809i	−0.474586	+	0.822008i	−0.999576	−	0.0291008i	$-0.990736\pi$
$277$	−7.89869	+	13.6809i	−0.474586	+	0.822008i	0.524990	+	0.851108i	$0.324069\pi$
$278$	5.04939	−	8.74580i	0.302842	−	0.524538i
$279$	−1.80060	−	0.482470i	−0.107799	−	0.0288847i
$280$	−1.50070	−	2.09939i	−0.0896842	−	0.125463i
$281$	9.74564	+	2.61134i	0.581376	+	0.155779i	0.537509	−	0.843258i	$-0.319366\pi$
$281$	9.74564	+	2.61134i	0.581376	+	0.155779i	0.0438671	+	0.999037i	$0.486032\pi$
$282$			7.01612i			0.417804i
$283$	−16.0443	−	9.26316i	−0.953733	−	0.550638i	−0.0594941	−	0.998229i	$-0.518949\pi$
$283$	−16.0443	−	9.26316i	−0.953733	−	0.550638i	−0.894238	+	0.447591i	$0.852282\pi$
$284$	2.42276	+	4.19634i	0.143764	+	0.249007i
$285$	−16.7740	−	13.7988i	−0.993606	−	0.817371i
$286$		−	22.1055i		−	1.30712i
$287$	2.68388	−	10.0164i	0.158424	−	0.591248i
$288$		−	0.384156i		−	0.0226366i
$289$	−0.916138	+	1.58680i	−0.0538905	+	0.0933410i
$290$	18.3223	−	1.78303i	1.07592	−	0.104703i
$291$	6.84784	−	1.83487i	0.401428	−	0.107562i
$292$	3.51772	+	13.1283i	0.205859	+	0.768276i
$293$	−8.84889	+	2.37105i	−0.516957	+	0.138518i	−0.507859	−	0.861440i	$-0.669563\pi$
$293$	−8.84889	+	2.37105i	−0.516957	+	0.138518i	−0.00909855	+	0.999959i	$0.502896\pi$
$294$	2.37268	−	8.85495i	0.138377	−	0.516431i
$295$	−2.38049	−	24.4617i	−0.138597	−	1.42421i
$296$	−5.44223	+	2.71702i	−0.316323	+	0.157923i
$297$	−20.9752	+	20.9752i	−1.21711	+	1.21711i
$298$	6.23713	−	3.60101i	0.361307	−	0.208601i
$299$	0.782047	−	1.35455i	0.0452270	−	0.0783354i
$300$	7.26113	−	3.55978i	0.419222	−	0.205524i
$301$	−0.469695	−	1.75292i	−0.0270727	−	0.101037i
$302$			6.72545i			0.387006i
$303$	12.4648	−	3.33992i	0.716082	−	0.191874i
$304$	4.24679	+	4.24679i	0.243570	+	0.243570i
$305$	16.1750	−	11.5623i	0.926178	−	0.662058i
$306$	1.49613			0.0855278
$307$	−24.1075	−	24.1075i	−1.37589	−	1.37589i	−0.851450	−	0.524435i	$-0.824276\pi$
$307$	−24.1075	−	24.1075i	−1.37589	−	1.37589i	−0.524435	−	0.851450i	$-0.675724\pi$
$308$	1.61882	−	6.04153i	0.0922411	−	0.344248i
$309$	7.32928	−	1.96388i	0.416948	−	0.111721i
$310$	1.05095	+	10.7995i	0.0596902	+	0.613371i
$311$	−6.07987	+	22.6904i	−0.344758	+	1.28665i	0.548137	+	0.836389i	$0.315337\pi$
$311$	−6.07987	+	22.6904i	−0.344758	+	1.28665i	−0.892895	+	0.450266i	$0.851329\pi$
$312$	6.37212	+	1.70740i	0.360750	+	0.0966627i
$313$	−6.03304	−	10.4495i	−0.341008	−	0.590643i	0.643612	−	0.765352i	$-0.277435\pi$
$313$	−6.03304	−	10.4495i	−0.341008	−	0.590643i	−0.984620	+	0.174709i	$0.944102\pi$
$314$	3.44829	+	12.8692i	0.194598	+	0.726251i
$315$	0.902515	+	0.410193i	0.0508510	+	0.0231117i
$316$	−2.28673	+	8.53421i	−0.128639	+	0.480087i
$317$	4.10260	−	15.3111i	0.230425	−	0.859959i	−0.749733	−	0.661741i	$-0.769818\pi$
$317$	4.10260	−	15.3111i	0.230425	−	0.859959i	0.980158	−	0.198218i	$-0.0635154\pi$
$318$	6.37854	+	11.0479i	0.357691	+	0.619538i
$319$	31.5494	+	31.5494i	1.76643	+	1.76643i
$320$	−2.09367	+	0.785216i	−0.117039	+	0.0438949i
$321$	−4.69861	+	2.71274i	−0.262251	+	0.151410i
$322$	0.312933	−	0.312933i	0.0174391	−	0.0174391i
$323$	−16.5395	+	16.5395i	−0.920280	+	0.920280i
$324$	−3.84998	−	6.66836i	−0.213888	−	0.370464i
$325$	−3.93206	−	20.0114i	−0.218112	−	1.11003i
$326$	3.89013	+	2.24597i	0.215454	+	0.124393i
$327$	−13.5050			−0.746827
$328$	−7.78143	−	4.49261i	−0.429658	−	0.248063i
$329$	4.33570	+	2.50322i	0.239035	+	0.138007i
$330$	17.8435	+	8.10986i	0.982253	+	0.446433i
$331$	0.522368	+	0.139968i	0.0287119	+	0.00769334i	0.273146	−	0.961972i	$-0.411936\pi$
$331$	0.522368	+	0.139968i	0.0287119	+	0.00769334i	−0.244434	+	0.969666i	$0.578602\pi$
$332$	8.80443	+	8.80443i	0.483206	+	0.483206i
$333$	1.28869	−	1.94925i	0.0706197	−	0.106818i
$334$			4.41413i			0.241531i
$335$	−18.8684	+	13.4876i	−1.03089	+	0.736909i
$336$	1.61650	+	0.933284i	0.0881870	+	0.0509148i
$337$	26.6162	−	7.13180i	1.44988	−	0.388494i	0.553897	−	0.832585i	$-0.313140\pi$
$337$	26.6162	−	7.13180i	1.44988	−	0.388494i	0.895981	+	0.444092i	$0.146474\pi$
$338$	1.81837	−	3.14951i	0.0989062	−	0.171311i
$339$	−7.79576	−	7.79576i	−0.423408	−	0.423408i
$340$	−3.05808	−	8.15394i	−0.165848	−	0.442210i
$341$	−18.5959	+	18.5959i	−1.00702	+	1.00702i
$342$	−2.22858	−	0.597146i	−0.120508	−	0.0322899i
$343$	−10.3379	−	10.3379i	−0.558196	−	0.558196i
$344$	−1.57247			−0.0847817
$345$	0.806477	+	1.12821i	0.0434193	+	0.0607409i
$346$	5.27554	+	19.6886i	0.283615	+	1.05847i
$347$	2.69381			0.144611			0.0723056	−	0.997383i	$-0.476964\pi$
$347$	2.69381			0.144611			0.0723056	+	0.997383i	$0.476964\pi$
$348$	−11.5313	+	6.65758i	−0.618141	+	0.356884i
$349$	−13.6101	+	7.85782i	−0.728535	+	0.420620i	−0.817886	−	0.575381i	$-0.804854\pi$
$349$	−13.6101	+	7.85782i	−0.728535	+	0.420620i	0.0893513	+	0.996000i	$0.471521\pi$
$350$	0.390822	−	5.75718i	0.0208903	−	0.307734i
$351$	−21.5642	+	5.77812i	−1.15101	+	0.308413i
$352$	−4.69349	−	2.70979i	−0.250164	−	0.144432i
$353$	−10.2119	+	5.89584i	−0.543525	+	0.313804i	−0.746506	−	0.665378i	$-0.768270\pi$
$353$	−10.2119	+	5.89584i	−0.543525	+	0.313804i	0.202982	+	0.979183i	$0.434937\pi$
$354$	8.88841	+	15.3952i	0.472413	+	0.818244i
$355$	−1.77741	+	10.6881i	−0.0943351	+	0.567266i
$356$	10.4711	−	10.4711i	0.554967	−	0.554967i
$357$	−3.63475	+	6.29556i	−0.192371	+	0.333197i
$358$	20.1747	+	5.40580i	1.06627	+	0.285705i
$359$			12.6671i			0.668543i	0.942477	+	0.334272i	$0.108490\pi$
$359$			12.6671i			0.668543i	−0.942477	+	0.334272i	$0.891510\pi$
$360$	0.545717	−	0.663380i	0.0287618	−	0.0349632i
$361$	14.7835	−	8.53525i	0.778079	−	0.449224i
$362$	−5.61844			−0.295299
$363$	7.69051	+	28.7014i	0.403647	+	1.50643i
$364$	3.32856	−	3.32856i	0.174464	−	0.174464i
$365$	−12.5750	+	27.6677i	−0.658204	+	1.44820i
$366$	−7.19059	+	12.4545i	−0.375858	+	0.651005i
$367$	5.34154	+	19.9349i	0.278826	+	1.04059i	0.953234	+	0.302234i	$0.0977324\pi$
$367$	5.34154	+	19.9349i	0.278826	+	1.04059i	−0.674408	+	0.738359i	$0.735601\pi$
$368$	−0.191734	−	0.332093i	−0.00999482	−	0.0173115i
$369$	3.45173			0.179690
$370$	−13.2576	−	3.03913i	−0.689229	−	0.157997i
$371$	9.10297			0.472603
$372$	−3.92412	−	6.79677i	−0.203456	−	0.352396i
$373$	8.93048	+	33.3290i	0.462403	+	1.72571i	0.665360	+	0.746523i	$0.268278\pi$
$373$	8.93048	+	33.3290i	0.462403	+	1.72571i	−0.202957	+	0.979188i	$0.565055\pi$
$374$	10.5535	−	18.2792i	0.545708	−	0.945193i
$375$	17.5958	+	4.16766i	0.908642	+	0.215217i
$376$	3.06744	−	3.06744i	0.158191	−	0.158191i
$377$	8.69102	+	32.4353i	0.447610	+	1.67050i
$378$	−6.31676			−0.324899
$379$	4.64897	−	2.68408i	0.238802	−	0.137872i	−0.375824	−	0.926691i	$-0.622640\pi$
$379$	4.64897	−	2.68408i	0.238802	−	0.137872i	0.614626	+	0.788819i	$0.289307\pi$
$380$	1.30075	+	13.3664i	0.0667271	+	0.685682i
$381$		−	2.50664i		−	0.128419i
$382$	8.82698	+	2.36518i	0.451628	+	0.121013i
$383$	17.0195	−	29.4786i	0.869656	−	1.50629i	0.00730659	−	0.999973i	$-0.497674\pi$
$383$	17.0195	−	29.4786i	0.869656	−	1.50629i	0.862349	−	0.506314i	$-0.168992\pi$
$384$	1.14364	−	1.14364i	0.0583613	−	0.0583613i
$385$	11.3778	−	8.13319i	0.579868	−	0.414506i
$386$	5.34031	+	9.24969i	0.271815	+	0.470797i
$387$	0.523143	−	0.302036i	0.0265928	−	0.0153534i
$388$	−3.79607	−	2.19166i	−0.192716	−	0.111265i
$389$	17.5552	−	4.70391i	0.890086	−	0.238498i	0.215332	−	0.976541i	$-0.430917\pi$
$389$	17.5552	−	4.70391i	0.890086	−	0.238498i	0.674754	+	0.738043i	$0.264250\pi$
$390$	8.57822	+	12.0004i	0.434375	+	0.607664i
$391$	1.29336	−	0.746722i	0.0654081	−	0.0377634i
$392$	−4.90871	+	2.83404i	−0.247927	+	0.143141i
$393$	23.5603			1.18846
$394$	−0.449673	−	1.67820i	−0.0226542	−	0.0845466i
$395$	−16.0722	+	11.4889i	−0.808680	+	0.578067i
$396$	2.08197			0.104623
$397$	−22.8690	−	22.8690i	−1.14776	−	1.14776i	−0.986992	−	0.160770i	$-0.948602\pi$
$397$	−22.8690	−	22.8690i	−1.14776	−	1.14776i	−0.160770	−	0.986992i	$-0.551398\pi$
$398$	14.8359	+	3.97528i	0.743658	+	0.199263i
$399$	7.92693	−	7.92693i	0.396843	−	0.396843i
$400$	−4.73089	−	1.61823i	−0.236545	−	0.0809113i
$401$	18.7127	+	18.7127i	0.934468	+	0.934468i	0.997981	−	0.0635130i	$-0.0202304\pi$
$401$	18.7127	+	18.7127i	0.934468	+	0.934468i	−0.0635130	+	0.997981i	$0.520230\pi$
$402$	8.38793	−	14.5283i	0.418352	−	0.724607i
$403$	−19.1181	+	5.12267i	−0.952338	+	0.255178i
$404$	−6.90979	−	3.98937i	−0.343775	−	0.198479i
$405$	2.82447	−	16.9844i	0.140349	−	0.843960i
$406$			9.50120i			0.471537i
$407$	−14.7251	−	29.4946i	−0.729896	−	1.46199i
$408$	4.45401	+	4.45401i	0.220506	+	0.220506i
$409$	−33.4605	−	8.96573i	−1.65452	−	0.443327i	−0.693645	−	0.720317i	$-0.743996\pi$
$409$	−33.4605	−	8.96573i	−1.65452	−	0.443327i	−0.960873	+	0.276990i	$0.910663\pi$
$410$	−7.05534	−	18.8121i	−0.348438	−	0.929061i
$411$	16.8653	+	9.73719i	0.831905	+	0.480300i
$412$	−4.06296	−	2.34575i	−0.200168	−	0.115567i
$413$	12.6849			0.624181
$414$	0.127576	+	0.0736558i	0.00626999	+	0.00361998i
$415$	2.69671	+	27.7112i	0.132376	+	1.36029i
$416$	−2.03941	−	3.53236i	−0.0999902	−	0.173188i
$417$	−11.5494	+	11.5494i	−0.565577	+	0.565577i
$418$	−23.0158	+	23.0158i	−1.12574	+	1.12574i
$419$	−15.3378	+	8.85527i	−0.749300	+	0.432608i	−0.825441	−	0.564489i	$-0.809073\pi$
$419$	−15.3378	+	8.85527i	−0.749300	+	0.432608i	0.0761412	+	0.997097i	$0.475740\pi$
$420$	1.46566	+	3.90797i	0.0715168	+	0.190689i
$421$	−12.5994	−	12.5994i	−0.614057	−	0.614057i	0.329944	−	0.944001i	$-0.392970\pi$
$421$	−12.5994	−	12.5994i	−0.614057	−	0.614057i	−0.944001	+	0.329944i	$0.892970\pi$
$422$	7.86139	+	13.6163i	0.382686	+	0.662832i
$423$	−0.431315	+	1.60969i	−0.0209713	+	0.0782659i
$424$	2.04146	−	7.61884i	0.0991422	−	0.370004i
$425$	6.30231	−	18.4248i	0.305707	−	0.893735i
$426$	−2.02834	−	7.56989i	−0.0982736	−	0.366762i
$427$	5.13093	+	8.88704i	0.248303	+	0.430074i
$428$	3.24023	+	0.868218i	0.156623	+	0.0419669i
$429$	−9.25341	+	34.5342i	−0.446759	+	1.66733i
$430$	−2.71541	−	2.23378i	−0.130949	−	0.107723i
$431$	−10.8241	+	2.90031i	−0.521380	+	0.139703i	−0.509905	−	0.860231i	$-0.670319\pi$
$431$	−10.8241	+	2.90031i	−0.521380	+	0.139703i	−0.0114749	+	0.999934i	$0.503653\pi$
$432$	−1.41662	+	5.28689i	−0.0681570	+	0.254366i
$433$	−3.62400	−	3.62400i	−0.174158	−	0.174158i	0.614645	−	0.788804i	$-0.289299\pi$
$433$	−3.62400	−	3.62400i	−0.174158	−	0.174158i	−0.788804	+	0.614645i	$0.789299\pi$
$434$	−5.60020			−0.268818
$435$	−29.3703	−	4.88421i	−1.40820	−	0.234180i
$436$	5.90436	+	5.90436i	0.282768	+	0.282768i
$437$	−2.22458	+	0.596075i	−0.106416	+	0.0285142i
$438$		−	21.9822i		−	1.05035i
$439$	−4.65935	−	17.3889i	−0.222378	−	0.829928i	−0.983438	−	0.181245i	$-0.941987\pi$
$439$	−4.65935	−	17.3889i	−0.222378	−	0.829928i	0.761059	−	0.648682i	$-0.224680\pi$
$440$	−4.25554	−	11.3468i	−0.202875	−	0.540937i
$441$	1.08872	−	1.88571i	0.0518436	−	0.0897957i
$442$	13.7570	−	7.94263i	0.654356	−	0.377792i
$443$	−9.53895	+	9.53895i	−0.453209	+	0.453209i	−0.896418	−	0.443209i	$-0.853840\pi$
$443$	−9.53895	+	9.53895i	−0.453209	+	0.453209i	0.443209	+	0.896418i	$0.353840\pi$
$444$	9.63945	−	1.96652i	0.457468	−	0.0933270i
$445$	32.9568	−	3.20719i	1.56230	−	0.152035i
$446$	2.88463	−	10.7656i	0.136591	−	0.509766i
$447$	−11.2513	+	3.01478i	−0.532169	+	0.142594i
$448$	−0.298699	−	1.11476i	−0.0141122	−	0.0526675i
$449$	20.0298	−	5.36698i	0.945267	−	0.253283i	0.246914	−	0.969037i	$-0.420583\pi$
$449$	20.0298	−	5.36698i	0.945267	−	0.253283i	0.698353	+	0.715754i	$0.253917\pi$
$450$	1.88474	−	0.370335i	0.0888476	−	0.0174577i
$451$	24.3481	−	42.1721i	1.14651	−	1.98581i
$452$			6.81660i			0.320626i
$453$	2.81529	−	10.5068i	0.132274	−	0.493653i
$454$			3.55591i			0.166887i
$455$	10.4764	−	1.01951i	0.491139	−	0.0477952i
$456$	−4.85682	−	8.41226i	−0.227441	−	0.393940i
$457$	−3.68504	−	2.12756i	−0.172379	−	0.0995230i	0.411328	−	0.911487i	$-0.365065\pi$
$457$	−3.68504	−	2.12756i	−0.172379	−	0.0995230i	−0.583707	+	0.811964i	$0.698398\pi$
$458$			13.5857i			0.634820i
$459$	−20.5902	−	5.51712i	−0.961068	−	0.257517i
$460$	0.140662	−	0.845844i	0.00655840	−	0.0394377i
$461$	22.9371	+	6.14596i	1.06829	+	0.286246i	0.749788	−	0.661678i	$-0.230155\pi$
$461$	22.9371	+	6.14596i	1.06829	+	0.286246i	0.318497	+	0.947924i	$0.396822\pi$
$462$	−5.05801	+	8.76072i	−0.235320	+	0.407586i
$463$	−13.1877	+	22.8418i	−0.612886	+	1.06155i	0.377866	+	0.925860i	$0.376658\pi$
$463$	−13.1877	+	22.8418i	−0.612886	+	1.06155i	−0.990752	+	0.135689i	$0.956675\pi$
$464$	7.95215	+	2.13077i	0.369169	+	0.0989186i
$465$	2.87886	−	17.3114i	0.133504	−	0.802799i
$466$	−10.3949	−	2.78532i	−0.481537	−	0.129027i
$467$		−	4.82320i		−	0.223191i	−0.993754	−	0.111596i	$-0.964404\pi$
$467$		−	4.82320i		−	0.223191i	0.993754	−	0.111596i	$-0.0355961\pi$
$468$	1.35698	+	0.783451i	0.0627263	+	0.0362150i
$469$	−5.98531	−	10.3669i	−0.276376	−	0.478697i
$470$	9.65449	−	0.939526i	0.445328	−	0.0433371i
$471$		−	21.5483i		−	0.992895i
$472$	2.84475	−	10.6168i	0.130940	−	0.488676i
$473$		−	8.52211i		−	0.391847i
$474$	7.14489	−	12.3753i	0.328176	−	0.568417i
$475$	−16.7416	+	24.9296i	−0.768156	+	1.14385i
$476$	4.34152	−	1.16331i	0.198993	−	0.0533201i
$477$	0.784240	+	2.92683i	0.0359079	+	0.134010i
$478$	−20.6706	+	5.53867i	−0.945452	+	0.253333i
$479$	10.5344	−	39.3150i	0.481330	−	1.79635i	−0.114716	−	0.993398i	$-0.536596\pi$
$479$	10.5344	−	39.3150i	0.481330	−	1.79635i	0.596046	−	0.802950i	$-0.296738\pi$
$480$	3.59952	−	0.350287i	0.164295	−	0.0159883i
$481$	1.50144	−	24.7650i	0.0684598	−	1.12919i
$482$	5.15935	−	5.15935i	0.235002	−	0.235002i
$483$	−0.619874	+	0.357884i	−0.0282052	+	0.0162843i
$484$	9.18593	−	15.9105i	0.417542	−	0.723204i
$485$	−3.44186	−	9.17722i	−0.156287	−	0.416716i
$486$	−1.02663	−	3.83143i	−0.0465688	−	0.173797i
$487$			14.0068i			0.634709i	0.948307	+	0.317355i	$0.102795\pi$
$487$			14.0068i			0.634709i	−0.948307	+	0.317355i	$0.897205\pi$
$488$	8.58880	−	2.30136i	0.388797	−	0.104178i
$489$	−5.13718	−	5.13718i	−0.232311	−	0.232311i
$490$	−12.5025	−	2.07914i	−0.564807	−	0.0939262i
$491$	14.8170			0.668683			0.334342	−	0.942452i	$-0.391486\pi$
$491$	14.8170			0.668683			0.334342	+	0.942452i	$0.391486\pi$
$492$	10.2759	+	10.2759i	0.463273	+	0.463273i
$493$	−8.29845	+	30.9702i	−0.373743	+	1.39483i
$494$	−23.6621	+	6.34025i	−1.06461	+	0.285261i
$495$	3.59524	+	2.95756i	0.161594	+	0.132932i
$496$	−1.25592	+	4.68716i	−0.0563925	+	0.210460i
$497$	−5.40159	−	1.44735i	−0.242294	−	0.0649225i
$498$	−10.0691	−	17.4403i	−0.451209	−	0.781517i
$499$	8.81869	+	32.9118i	0.394779	+	1.47333i	0.822157	+	0.569261i	$0.192771\pi$
$499$	8.81869	+	32.9118i	0.394779	+	1.47333i	−0.427378	+	0.904073i	$0.640563\pi$
$500$	−5.87075	−	9.51495i	−0.262548	−	0.425521i
$501$	1.84777	−	6.89596i	0.0825522	−	0.308089i
$502$	−1.66155	+	6.20098i	−0.0741585	+	0.276763i
$503$	−7.13645	−	12.3607i	−0.318199	−	0.551136i	0.661914	−	0.749580i	$-0.269745\pi$
$503$	−7.13645	−	12.3607i	−0.318199	−	0.551136i	−0.980112	+	0.198444i	$0.936411\pi$
$504$	0.313495	+	0.313495i	0.0139642	+	0.0139642i
$505$	−6.26503	−	16.7048i	−0.278790	−	0.743354i
$506$	1.79980	−	1.03912i	0.0800110	−	0.0461944i
$507$	−4.15913	+	4.15913i	−0.184714	+	0.184714i
$508$	−1.09590	+	1.09590i	−0.0486227	+	0.0486227i
$509$	8.11064	+	14.0480i	0.359498	+	0.622669i	0.987877	−	0.155239i	$-0.0496147\pi$
$509$	8.11064	+	14.0480i	0.359498	+	0.622669i	−0.628379	+	0.777907i	$0.716281\pi$
$510$	1.36422	+	14.0186i	0.0604087	+	0.620754i
$511$	−13.5842	−	7.84283i	−0.600929	−	0.346946i
$512$	−1.00000			−0.0441942
$513$	28.4684	+	16.4362i	1.25691	+	0.725678i
$514$	10.8740	+	6.27813i	0.479633	+	0.276917i
$515$	−3.68384	−	9.82243i	−0.162329	−	0.432828i
$516$	2.45658	+	0.658239i	0.108145	+	0.0289774i
$517$	16.6242	+	16.6242i	0.731133	+	0.731133i
$518$	2.22394	−	6.65844i	0.0977142	−	0.292555i
$519$		−	32.9668i		−	1.44708i
$520$	1.49617	−	8.99695i	0.0656116	−	0.394542i
$521$	−13.4673	−	7.77533i	−0.590012	−	0.340643i	0.175090	−	0.984552i	$-0.443978\pi$
$521$	−13.4673	−	7.77533i	−0.590012	−	0.340643i	−0.765102	+	0.643909i	$0.777312\pi$
$522$	−3.05487	+	0.818549i	−0.133708	+	0.0358269i
$523$	−13.9061	+	24.0862i	−0.608073	+	1.05321i	0.383484	+	0.923547i	$0.374724\pi$
$523$	−13.9061	+	24.0862i	−0.608073	+	1.05321i	−0.991558	+	0.129666i	$0.958609\pi$
$524$	−10.3005	−	10.3005i	−0.449981	−	0.449981i
$525$	−3.02053	+	8.83053i	−0.131827	+	0.385396i
$526$	−4.88334	+	4.88334i	−0.212924	+	0.212924i
$527$	−18.2545	−	4.89128i	−0.795178	−	0.213067i
$528$	6.19807	+	6.19807i	0.269736	+	0.269736i
$529$	−22.8530			−0.993607
$530$	14.3483	−	10.2566i	0.623251	−	0.445517i
$531$	1.09283	+	4.07849i	0.0474247	+	0.176991i
$532$	−6.93129			−0.300509
$533$	31.7390	−	18.3245i	1.37477	−	0.793724i
$534$	−20.7417	+	11.9752i	−0.897579	+	0.518217i
$535$	4.36204	+	6.10223i	0.188587	+	0.263822i
$536$	−10.0190	+	2.68457i	−0.432753	+	0.115956i
$537$	−29.2550	−	16.8904i	−1.26245	−	0.728874i
$538$	21.7045	−	12.5311i	0.935749	−	0.540255i
$539$	−15.3593	−	26.6031i	−0.661573	−	1.14588i
$540$	−9.95662	+	7.11727i	−0.428465	+	0.306279i
$541$	1.73685	−	1.73685i	0.0746729	−	0.0746729i	−0.668784	−	0.743457i	$-0.733185\pi$
$541$	1.73685	−	1.73685i	0.0746729	−	0.0746729i	0.743457	+	0.668784i	$0.233185\pi$
$542$	−8.90741	+	15.4281i	−0.382606	+	0.662693i
$543$	8.77739	+	2.35189i	0.376674	+	0.100929i
$544$		−	3.89458i		−	0.166979i
$545$	1.80845	+	18.5834i	0.0774654	+	0.796027i
$546$	−6.59339	+	3.80669i	−0.282171	+	0.162911i
$547$	−7.95342			−0.340064			−0.170032	−	0.985439i	$-0.554387\pi$
$547$	−7.95342			−0.340064			−0.170032	+	0.985439i	$0.554387\pi$
$548$	−3.11641	−	11.6306i	−0.133126	−	0.496834i
$549$	−2.41536	+	2.41536i	−0.103085	+	0.103085i
$550$	8.77011	−	25.6395i	0.373959	−	1.09327i
$551$	24.7222	−	42.8201i	1.05320	−	1.82420i
$552$	0.160521	+	0.599071i	0.00683221	+	0.0254982i
$553$	−5.09832	−	8.83056i	−0.216803	−	0.375513i
$554$	−15.7974			−0.671166
$555$	19.4394	+	10.2975i	0.825158	+	0.437106i
$556$	10.0988			0.428284
$557$	−13.6937	−	23.7183i	−0.580223	−	1.00498i	−0.995453	−	0.0952586i	$-0.969632\pi$
$557$	−13.6937	−	23.7183i	−0.580223	−	1.00498i	0.415230	−	0.909716i	$-0.363701\pi$
$558$	−0.482470	−	1.80060i	−0.0204246	−	0.0762255i
$559$	3.20690	−	5.55452i	0.135637	−	0.234931i
$560$	1.06778	−	2.34934i	0.0451217	−	0.0992779i
$561$	−24.1389	+	24.1389i	−1.01914	+	1.01914i
$562$	2.61134	+	9.74564i	0.110153	+	0.411095i
$563$	−3.30187			−0.139157			−0.0695785	−	0.997576i	$-0.522165\pi$
$563$	−3.30187			−0.139157			−0.0695785	+	0.997576i	$0.522165\pi$
$564$	−6.07614	+	3.50806i	−0.255851	+	0.147716i
$565$	−9.68338	+	11.7712i	−0.407383	+	0.495220i
$566$		−	18.5263i		−	0.778719i
$567$	8.58361	+	2.29997i	0.360478	+	0.0965897i
$568$	−2.42276	+	4.19634i	−0.101657	+	0.176074i
$569$	9.43733	−	9.43733i	0.395633	−	0.395633i	−0.481056	−	0.876690i	$-0.659747\pi$
$569$	9.43733	−	9.43733i	0.395633	−	0.395633i	0.876690	+	0.481056i	$0.159747\pi$
$570$	3.56312	−	21.4261i	0.149243	−	0.897441i
$571$	−3.05157	−	5.28548i	−0.127704	−	0.221190i	0.795083	−	0.606501i	$-0.207428\pi$
$571$	−3.05157	−	5.28548i	−0.127704	−	0.221190i	−0.922787	+	0.385311i	$0.874094\pi$
$572$	19.1439	−	11.0527i	0.800447	−	0.462138i
$573$	−12.7999	−	7.39000i	−0.534722	−	0.308722i
$574$	10.0164	−	2.68388i	0.418075	−	0.112023i
$575$	1.44447	−	1.26083i	0.0602387	−	0.0525801i
$576$	0.332689	−	0.192078i	0.0138620	−	0.00800325i
$577$	−1.25068	+	0.722081i	−0.0520665	+	0.0300606i	−0.525807	−	0.850604i	$-0.676237\pi$
$577$	−1.25068	+	0.722081i	−0.0520665	+	0.0300606i	0.473741	+	0.880664i	$0.342903\pi$
$578$	−1.83228			−0.0762126
$579$	−4.47094	−	16.6858i	−0.185806	−	0.693437i
$580$	10.7053	+	14.9760i	0.444512	+	0.621845i
$581$	−14.3699			−0.596165
$582$	5.01297	+	5.01297i	0.207794	+	0.207794i
$583$	41.2909	+	11.0639i	1.71010	+	0.458219i
$584$	−9.61059	+	9.61059i	−0.397689	+	0.397689i
$585$	1.23036	+	3.28057i	0.0508690	+	0.135635i
$586$	−6.47783	−	6.47783i	−0.267597	−	0.267597i
$587$	4.55674	−	7.89250i	0.188077	−	0.325758i	−0.756532	−	0.653956i	$-0.773108\pi$
$587$	4.55674	−	7.89250i	0.188077	−	0.325758i	0.944609	+	0.328198i	$0.106441\pi$
$588$	8.85495	−	2.37268i	0.365172	−	0.0978476i
$589$	25.2390	+	14.5718i	1.03996	+	0.600419i
$590$	19.9942	−	14.2924i	0.823148	−	0.588409i
$591$			2.81000i			0.115588i
$592$	−5.07412	−	3.35460i	−0.208545	−	0.137873i
$593$	−12.0803	−	12.0803i	−0.496078	−	0.496078i	0.414136	−	0.910215i	$-0.364084\pi$
$593$	−12.0803	−	12.0803i	−0.496078	−	0.496078i	−0.910215	+	0.414136i	$0.864084\pi$
$594$	−28.6527	−	7.67747i	−1.17564	−	0.315010i
$595$	9.14970	+	4.15853i	0.375101	+	0.170483i
$596$	6.23713	+	3.60101i	0.255483	+	0.147503i
$597$	−21.5133	−	12.4207i	−0.880482	−	0.508346i
$598$	1.56409			0.0639606
$599$	−17.9905	−	10.3868i	−0.735073	−	0.424395i	0.0852021	−	0.996364i	$-0.472846\pi$
$599$	−17.9905	−	10.3868i	−0.735073	−	0.424395i	−0.820275	+	0.571969i	$0.806180\pi$
$600$	6.71343	+	4.50843i	0.274075	+	0.184056i
$601$	14.4319	+	24.9968i	0.588690	+	1.01964i	0.994404	+	0.105641i	$0.0336893\pi$
$601$	14.4319	+	24.9968i	0.588690	+	1.01964i	−0.405715	+	0.914000i	$0.632977\pi$
$602$	1.28323	−	1.28323i	0.0523005	−	0.0523005i
$603$	2.81755	−	2.81755i	0.114740	−	0.114740i
$604$	−5.82441	+	3.36272i	−0.236992	+	0.136827i
$605$	38.4645	−	14.4259i	1.56380	−	0.586495i
$606$	9.12484	+	9.12484i	0.370671	+	0.370671i
$607$	22.1786	+	38.4145i	0.900203	+	1.55920i	0.827231	+	0.561863i	$0.189915\pi$
$607$	22.1786	+	38.4145i	0.900203	+	1.55920i	0.0729719	+	0.997334i	$0.476752\pi$
$608$	−1.55443	+	5.80123i	−0.0630406	+	0.235271i
$609$	3.97723	−	14.8432i	0.161165	−	0.601478i
$610$	18.1008	+	8.22679i	0.732879	+	0.333093i
$611$	4.57953	+	17.0911i	0.185268	+	0.691430i
$612$	0.748063	+	1.29568i	0.0302386	+	0.0523749i
$613$	11.0465	+	2.95989i	0.446163	+	0.119549i	0.474903	−	0.880038i	$-0.342483\pi$
$613$	11.0465	+	2.95989i	0.446163	+	0.119549i	−0.0287405	+	0.999587i	$0.509150\pi$
$614$	8.82394	−	32.9314i	0.356105	−	1.32900i
$615$	3.14741	+	32.3425i	0.126916	+	1.30417i
$616$	6.04153	−	1.61882i	0.243420	−	0.0652243i
$617$	1.82356	−	6.80561i	0.0734136	−	0.273983i	−0.919455	−	0.393195i	$-0.871370\pi$
$617$	1.82356	−	6.80561i	0.0734136	−	0.273983i	0.992869	+	0.119211i	$0.0380365\pi$
$618$	5.36541	+	5.36541i	0.215828	+	0.215828i
$619$	16.6861			0.670672			0.335336	−	0.942099i	$-0.391150\pi$
$619$	16.6861			0.670672			0.335336	+	0.942099i	$0.391150\pi$
$620$	−8.82717	+	6.30991i	−0.354508	+	0.253412i
$621$	−1.48412	−	1.48412i	−0.0595558	−	0.0595558i
$622$	−22.6904	+	6.07987i	−0.909802	+	0.243781i
$623$			17.0901i			0.684700i
$624$	1.70740	+	6.37212i	0.0683508	+	0.255089i
$625$	3.37864	−	24.7706i	0.135146	−	0.990826i
$626$	6.03304	−	10.4495i	0.241129	−	0.417647i
$627$	45.5909	−	26.3219i	1.82073	−	1.05120i
$628$	−9.42091	+	9.42091i	−0.375935	+	0.375935i
$629$	13.0647	−	19.7615i	0.520925	−	0.787944i
$630$	0.0960205	+	0.986697i	0.00382555	+	0.0393110i
$631$	0.508184	−	1.89657i	0.0202305	−	0.0755012i	−0.955073	−	0.296372i	$-0.904223\pi$
$631$	0.508184	−	1.89657i	0.0202305	−	0.0755012i	0.975303	+	0.220871i	$0.0708899\pi$
$632$	−8.53421	+	2.28673i	−0.339473	+	0.0909614i
$633$	−6.58160	−	24.5629i	−0.261595	−	0.976286i
$634$	15.3111	−	4.10260i	0.608083	−	0.162935i
$635$	−3.44925	+	0.335664i	−0.136879	+	0.0133204i
$636$	−6.37854	+	11.0479i	−0.252925	+	0.438080i
$637$		−	23.1191i		−	0.916011i
$638$	−11.5479	+	43.0973i	−0.457185	+	1.70624i
$639$		−	1.86143i		−	0.0736372i
$640$	−1.72685	−	1.42056i	−0.0682597	−	0.0561525i
$641$	−0.691853	−	1.19832i	−0.0273265	−	0.0473309i	0.852039	−	0.523479i	$-0.175366\pi$
$641$	−0.691853	−	1.19832i	−0.0273265	−	0.0473309i	−0.879365	+	0.476148i	$0.842033\pi$
$642$	−4.69861	−	2.71274i	−0.185439	−	0.107063i
$643$		−	5.02728i		−	0.198256i	−0.995075	−	0.0991282i	$-0.968395\pi$
$643$		−	5.02728i		−	0.198256i	0.995075	−	0.0991282i	$-0.0316054\pi$
$644$	0.427475	+	0.114542i	0.0168449	+	0.00451357i
$645$	3.30708	+	4.62640i	0.130216	+	0.182164i
$646$	−22.5933	−	6.05386i	−0.888922	−	0.238186i
$647$	−19.6120	+	33.9690i	−0.771029	+	1.33546i	0.165971	+	0.986131i	$0.446924\pi$
$647$	−19.6120	+	33.9690i	−0.771029	+	1.33546i	−0.937000	+	0.349330i	$0.886409\pi$
$648$	3.84998	−	6.66836i	0.151241	−	0.261958i
$649$	57.5384	+	15.4174i	2.25858	+	0.605184i
$650$	15.3644	−	13.4110i	0.602640	−	0.526022i
$651$	8.74890	+	2.34426i	0.342896	+	0.0918788i
$652$			4.49194i			0.175918i
$653$	−9.91638	−	5.72522i	−0.388058	−	0.224045i	0.293260	−	0.956033i	$-0.405260\pi$
$653$	−9.91638	−	5.72522i	−0.388058	−	0.224045i	−0.681318	+	0.731987i	$0.738593\pi$
$654$	−6.75249	−	11.6957i	−0.264043	−	0.457336i
$655$	−3.15495	−	32.4200i	−0.123274	−	1.26675i
$656$		−	8.98522i		−	0.350814i
$657$	1.35135	−	5.04332i	0.0527213	−	0.196759i
$658$			5.00644i			0.195171i
$659$	−21.5298	+	37.2907i	−0.838683	+	1.45264i	0.0523138	+	0.998631i	$0.483340\pi$
$659$	−21.5298	+	37.2907i	−0.838683	+	1.45264i	−0.890996	+	0.454010i	$0.849993\pi$
$660$	1.89841	+	19.5079i	0.0738955	+	0.759343i
$661$	−35.8756	+	9.61285i	−1.39540	+	0.373896i	−0.876691	−	0.481054i	$-0.840254\pi$
$661$	−35.8756	+	9.61285i	−1.39540	+	0.373896i	−0.518710	+	0.854950i	$0.673587\pi$
$662$	0.139968	+	0.522368i	0.00544001	+	0.0203024i
$663$	−24.8167	+	6.64961i	−0.963801	+	0.258250i
$664$	−3.22265	+	12.0271i	−0.125063	+	0.466741i
$665$	−11.9693	−	9.84631i	−0.464149	−	0.381823i
$666$	2.33245	+	0.141411i	0.0903805	+	0.00547955i
$667$	−2.23231	+	2.23231i	−0.0864354	+	0.0864354i
$668$	−3.82275	+	2.20707i	−0.147907	+	0.0853939i
$669$	−9.01302	+	15.6110i	−0.348463	+	0.603556i
$670$	−21.1148	−	9.59668i	−0.815737	−	0.370752i
$671$	12.4724	+	46.5477i	0.481492	+	1.79695i
$672$			1.86657i			0.0720044i
$673$	23.5841	−	6.31935i	0.909102	−	0.243593i	0.226181	−	0.974085i	$-0.427376\pi$
$673$	23.5841	−	6.31935i	0.909102	−	0.243593i	0.682921	+	0.730492i	$0.260709\pi$
$674$	19.4844	+	19.4844i	0.750512	+	0.750512i
$675$	−27.3041	−	1.85352i	−1.05094	−	0.0713420i
$676$	3.63674			0.139874
$677$	−26.0351	−	26.0351i	−1.00061	−	1.00061i	−1.00000		0.000608497i	$-0.999806\pi$
$677$	−26.0351	−	26.0351i	−1.00061	−	1.00061i	−0.000608497	−	1.00000i	$-0.500194\pi$
$678$	2.85345	−	10.6492i	0.109586	−	0.408980i
$679$	4.88636	−	1.30930i	0.187521	−	0.0502462i
$680$	5.53248	−	6.72535i	0.212161	−	0.257905i
$681$	1.48851	−	5.55521i	0.0570400	−	0.212876i
$682$	−25.4024	−	6.80656i	−0.972710	−	0.260637i
$683$	−25.4771	−	44.1277i	−0.974855	−	1.68850i	−0.680413	−	0.732829i	$-0.738199\pi$
$683$	−25.4771	−	44.1277i	−0.974855	−	1.68850i	−0.294442	−	0.955669i	$-0.595134\pi$
$684$	−0.597146	−	2.22858i	−0.0228324	−	0.0852118i
$685$	11.1404	−	24.5113i	0.425652	−	0.936529i
$686$	3.78395	−	14.1219i	0.144472	−	0.539176i
$687$	5.68703	−	21.2243i	0.216974	−	0.809757i
$688$	−0.786233	−	1.36180i	−0.0299749	−	0.0519180i
$689$	22.7491	+	22.7491i	0.866672	+	0.866672i
$690$	−0.573821	+	1.26254i	−0.0218450	+	0.0480639i
$691$	15.6154	−	9.01555i	0.594038	−	0.342968i	−0.172655	−	0.984982i	$-0.555234\pi$
$691$	15.6154	−	9.01555i	0.594038	−	0.342968i	0.766692	+	0.642015i	$0.221901\pi$
$692$	−14.4131	+	14.4131i	−0.547902	+	0.547902i
$693$	−1.69901	+	1.69901i	−0.0645401	+	0.0645401i
$694$	1.34690	+	2.33291i	0.0511278	+	0.0885559i
$695$	17.4391	+	14.3459i	0.661502	+	0.544172i
$696$	−11.5313	−	6.65758i	−0.437092	−	0.252355i
$697$	34.9936			1.32548
$698$	−13.6101	−	7.85782i	−0.515152	−	0.297423i
$699$	15.0735	+	8.70271i	0.570133	+	0.329167i
$700$	5.18127	−	2.54013i	0.195834	−	0.0960077i
$701$	−6.34539	−	1.70024i	−0.239662	−	0.0642173i	0.136989	−	0.990573i	$-0.456258\pi$
$701$	−6.34539	−	1.70024i	−0.239662	−	0.0642173i	−0.376651	+	0.926355i	$0.622924\pi$
$702$	−15.7861	−	15.7861i	−0.595809	−	0.595809i
$703$	−27.3482	+	24.2216i	−1.03146	+	0.913536i
$704$		−	5.41958i		−	0.204258i
$705$	−15.4760	−	2.57362i	−0.582859	−	0.0969282i
$706$	−10.2119	−	5.89584i	−0.384330	−	0.221893i
$707$	8.89438	−	2.38324i	0.334508	−	0.0896311i
$708$	−8.88841	+	15.3952i	−0.334047	+	0.578586i
$709$	−2.12914	−	2.12914i	−0.0799615	−	0.0799615i	0.665995	−	0.745956i	$-0.268007\pi$
$709$	−2.12914	−	2.12914i	−0.0799615	−	0.0799615i	−0.745956	+	0.665995i	$0.768007\pi$
$710$	−10.1449	+	3.80477i	−0.380731	+	0.142791i
$711$	2.40001	−	2.40001i	0.0900073	−	0.0900073i
$712$	14.3038	+	3.83268i	0.536056	+	0.143636i
$713$	−1.31577	−	1.31577i	−0.0492759	−	0.0492759i
$714$	−7.26949			−0.272054
$715$	48.7597	+	8.10864i	1.82351	+	0.303246i
$716$	5.40580	+	20.1747i	0.202024	+	0.753964i
$717$	34.6111			1.29258
$718$	−10.9700	+	6.33354i	−0.409397	+	0.236366i
$719$	−14.1884	+	8.19165i	−0.529137	+	0.305497i	−0.740665	−	0.671875i	$-0.765489\pi$
$719$	−14.1884	+	8.19165i	−0.529137	+	0.305497i	0.211528	+	0.977372i	$0.432156\pi$
$720$	0.847362	+	0.140915i	0.0315793	+	0.00525158i
$721$	5.22990	−	1.40135i	0.194772	−	0.0521889i
$722$	14.7835	+	8.53525i	0.550185	+	0.317649i
$723$	−10.2199	+	5.90046i	−0.380082	+	0.219441i
$724$	−2.80922	−	4.86571i	−0.104404	−	0.180833i
$725$	−2.78793	+	41.0688i	−0.103541	+	1.52526i
$726$	−21.0109	+	21.0109i	−0.779786	+	0.779786i
$727$	−10.0281	+	17.3691i	−0.371920	+	0.644184i	−0.989861	−	0.142040i	$-0.954634\pi$
$727$	−10.0281	+	17.3691i	−0.371920	+	0.644184i	0.617941	+	0.786225i	$0.287967\pi$
$728$	4.54690	+	1.21834i	0.168519	+	0.0451546i
$729$			29.5153i			1.09316i
$730$	−30.2484	+	2.94363i	−1.11955	+	0.108949i
$731$	5.30362	−	3.06205i	0.196161	−	0.113254i
$732$	−14.3812			−0.531544
$733$	2.61340	+	9.75335i	0.0965283	+	0.360248i	0.997247	−	0.0741549i	$-0.0236259\pi$
$733$	2.61340	+	9.75335i	0.0965283	+	0.360248i	−0.900718	+	0.434403i	$0.856959\pi$
$734$	−14.5934	+	14.5934i	−0.538651	+	0.538651i
$735$	18.6617	+	8.48173i	0.688347	+	0.312853i
$736$	0.191734	−	0.332093i	0.00706740	−	0.0122411i
$737$	−14.5493	−	54.2986i	−0.535929	−	2.00011i
$738$	1.72586	+	2.98929i	0.0635300	+	0.110037i
$739$	−10.7871			−0.396811			−0.198405	−	0.980120i	$-0.563576\pi$
$739$	−10.7871			−0.396811			−0.198405	+	0.980120i	$0.563576\pi$
$740$	−3.99684	−	13.0010i	−0.146927	−	0.477925i
$741$	39.6201			1.45548
$742$	4.55148	+	7.88340i	0.167090	+	0.289409i
$743$	−7.13337	−	26.6221i	−0.261698	−	0.976669i	−0.964241	−	0.265028i	$-0.914619\pi$
$743$	−7.13337	−	26.6221i	−0.261698	−	0.976669i	0.702543	−	0.711641i	$-0.252048\pi$
$744$	3.92412	−	6.79677i	0.143865	−	0.249182i
$745$	5.65514	+	15.0786i	0.207188	+	0.552437i
$746$	−24.3985	+	24.3985i	−0.893293	+	0.893293i
$747$	−1.23800	−	4.62028i	−0.0452960	−	0.169047i
$748$	21.1070			0.771747
$749$	−3.35275	+	1.93571i	−0.122507	+	0.0707293i
$750$	5.18858	+	17.3222i	0.189460	+	0.632518i
$751$			21.2874i			0.776790i	0.921493	+	0.388395i	$0.126970\pi$
$751$			21.2874i			0.776790i	−0.921493	+	0.388395i	$0.873030\pi$
$752$	4.19020	+	1.12276i	0.152801	+	0.0409429i
$753$	5.19149	−	8.99193i	0.189188	−	0.327684i
$754$	−23.7443	+	23.7443i	−0.864717	+	0.864717i
$755$	−14.8348	−	2.46700i	−0.539895	−	0.0897833i
$756$	−3.15838	−	5.47047i	−0.114869	−	0.198959i
$757$	26.0820	−	15.0584i	0.947966	−	0.547308i	0.0555175	−	0.998458i	$-0.482319\pi$
$757$	26.0820	−	15.0584i	0.947966	−	0.547308i	0.892448	+	0.451149i	$0.148986\pi$
$758$	4.64897	+	2.68408i	0.168858	+	0.0974904i
$759$	−3.24672	+	0.869955i	−0.117848	+	0.0315774i
$760$	−10.9253	+	7.80968i	−0.396301	+	0.283287i
$761$	−38.3547	+	22.1441i	−1.39036	+	0.802723i	−0.993355	−	0.115094i	$-0.963283\pi$
$761$	−38.3547	+	22.1441i	−1.39036	+	0.802723i	−0.397003	+	0.917817i	$0.629950\pi$
$762$	2.17081	−	1.25332i	0.0786403	−	0.0454030i
$763$	−9.63664			−0.348870
$764$	2.36518	+	8.82698i	0.0855693	+	0.319349i
$765$	−0.548803	+	3.30012i	−0.0198420	+	0.119316i
$766$	34.0390			1.22988
$767$	31.7006	+	31.7006i	1.14464	+	1.14464i
$768$	1.56225	+	0.418603i	0.0563727	+	0.0151050i
$769$	17.1063	−	17.1063i	0.616870	−	0.616870i	−0.327857	−	0.944727i	$-0.606327\pi$
$769$	17.1063	−	17.1063i	0.616870	−	0.616870i	0.944727	+	0.327857i	$0.106327\pi$
$770$	12.7325	+	5.78689i	0.458846	+	0.208545i
$771$	−14.3599	−	14.3599i	−0.517159	−	0.517159i
$772$	−5.34031	+	9.24969i	−0.192202	+	0.332904i
$773$	10.0159	−	2.68374i	0.360246	−	0.0965276i	−0.0741563	−	0.997247i	$-0.523626\pi$
$773$	10.0159	−	2.68374i	0.360246	−	0.0965276i	0.434402	+	0.900719i	$0.356960\pi$
$774$	0.523143	+	0.302036i	0.0188040	+	0.0108565i
$775$	−24.2068	−	1.64326i	−0.869534	−	0.0590277i
$776$		−	4.38333i		−	0.157352i
$777$	−6.26158	+	9.47119i	−0.224633	+	0.339777i
$778$	12.8513	+	12.8513i	0.460742	+	0.460742i
$779$	−52.1253	−	13.9669i	−1.86758	−	0.500418i
$780$	−6.10354	+	13.4292i	−0.218542	+	0.480841i
$781$	−22.7424	−	13.1303i	−0.813786	−	0.469840i
$782$	1.29336	+	0.746722i	0.0462505	+	0.0267027i
$783$	45.0606			1.61033
$784$	−4.90871	−	2.83404i	−0.175311	−	0.101216i
$785$	−29.6515	+	2.88553i	−1.05831	+	0.102989i
$786$	11.7801	+	20.4038i	0.420184	+	0.727779i
$787$	24.1983	−	24.1983i	0.862577	−	0.862577i	−0.129060	−	0.991637i	$-0.541196\pi$
$787$	24.1983	−	24.1983i	0.862577	−	0.862577i	0.991637	+	0.129060i	$0.0411959\pi$
$788$	1.22853	−	1.22853i	0.0437645	−	0.0437645i
$789$	9.67317	−	5.58481i	0.344374	−	0.198824i
$790$	−17.9857	−	8.17451i	−0.639904	−	0.290836i
$791$	−5.56276	−	5.56276i	−0.197789	−	0.197789i
$792$	1.04098	+	1.80304i	0.0369897	+	0.0640681i
$793$	−9.38683	+	35.0321i	−0.333336	+	1.24403i
$794$	8.37064	−	31.2396i	0.297063	−	1.10865i
$795$	−26.7090	+	10.0171i	−0.947272	+	0.355268i
$796$	3.97528	+	14.8359i	0.140900	+	0.525846i
$797$	20.2061	+	34.9981i	0.715738	+	1.23969i	0.962674	+	0.270663i	$0.0872429\pi$
$797$	20.2061	+	34.9981i	0.715738	+	1.23969i	−0.246936	+	0.969032i	$0.579424\pi$
$798$	10.8284	+	2.90146i	0.383321	+	0.102710i
$799$	−4.37268	+	16.3191i	−0.154694	+	0.577327i
$800$	−0.964021	−	4.90619i	−0.0340833	−	0.173460i
$801$	−5.49488	+	1.47235i	−0.194152	+	0.0520229i
$802$	−6.84933	+	25.5620i	−0.241858	+	0.902627i
$803$	−52.0853	−	52.0853i	−1.83805	−	1.83805i
$804$	16.7759			0.591639
$805$	0.575472	+	0.805049i	0.0202827	+	0.0283743i
$806$	−13.9954	−	13.9954i	−0.492967	−	0.492967i
$807$	−39.1534	+	10.4911i	−1.37826	+	0.369305i
$808$		−	7.97874i		−	0.280691i
$809$	11.8811	+	44.3407i	0.417716	+	1.55894i	0.779333	+	0.626610i	$0.215558\pi$
$809$	11.8811	+	44.3407i	0.417716	+	1.55894i	−0.361618	+	0.932327i	$0.617775\pi$
$810$	16.1211	−	6.04613i	0.566439	−	0.212439i
$811$	−19.0531	+	33.0009i	−0.669044	+	1.15882i	0.309128	+	0.951021i	$0.399963\pi$
$811$	−19.0531	+	33.0009i	−0.669044	+	1.15882i	−0.978172	+	0.207798i	$0.933370\pi$
$812$	−8.22828	+	4.75060i	−0.288756	+	0.166713i
$813$	20.3738	−	20.3738i	0.714541	−	0.714541i
$814$	18.1805	−	27.4996i	0.637226	−	0.963860i
$815$	−6.38106	+	7.75690i	−0.223519	+	0.271712i
$816$	−1.63028	+	6.08429i	−0.0570712	+	0.212993i
$817$	−9.12224	+	2.44430i	−0.319147	+	0.0855151i
$818$	−8.96573	−	33.4605i	−0.313479	−	1.16992i
$819$	−1.74672	+	0.468032i	−0.0610354	+	0.0163544i
$820$	12.7640	−	15.5161i	0.445740	−	0.541847i
$821$	17.6107	−	30.5026i	0.614618	−	1.06455i	−0.375834	−	0.926687i	$-0.622644\pi$
$821$	17.6107	−	30.5026i	0.614618	−	1.06455i	0.990451	−	0.137862i	$-0.0440231\pi$
$822$			19.4744i			0.679247i
$823$	2.02938	−	7.57375i	0.0707397	−	0.264004i	−0.921494	−	0.388393i	$-0.873030\pi$
$823$	2.02938	−	7.57375i	0.0707397	−	0.264004i	0.992234	+	0.124389i	$0.0396970\pi$
$824$		−	4.69150i		−	0.163436i
$825$	−24.4338	+	36.3840i	−0.850677	+	1.26673i
$826$	6.34243	+	10.9854i	0.220681	+	0.382231i
$827$	20.3129	+	11.7277i	0.706349	+	0.407811i	0.809708	−	0.586834i	$-0.199626\pi$
$827$	20.3129	+	11.7277i	0.706349	+	0.407811i	−0.103359	+	0.994644i	$0.532959\pi$
$828$			0.147312i			0.00511943i
$829$	22.4913	+	6.02652i	0.781155	+	0.209310i	0.627294	−	0.778783i	$-0.284163\pi$
$829$	22.4913	+	6.02652i	0.781155	+	0.209310i	0.153861	+	0.988093i	$0.450829\pi$
$830$	−22.6502	+	16.1910i	−0.786200	+	0.561998i
$831$	24.6794	+	6.61283i	0.856119	+	0.229396i
$832$	2.03941	−	3.53236i	0.0707037	−	0.122462i
$833$	11.0374	−	19.1173i	0.382423	−	0.662376i
$834$	−15.7768	−	4.22738i	−0.546306	−	0.146382i
$835$	−9.73658	−	1.61917i	−0.336948	−	0.0560338i
$836$	−31.4402	−	8.42438i	−1.08738	−	0.291363i
$837$			26.5596i			0.918036i
$838$	−15.3378	−	8.85527i	−0.529835	−	0.305900i
$839$	13.6978	+	23.7253i	0.472900	+	0.819087i	0.999519	−	0.0310147i	$-0.00987385\pi$
$839$	13.6978	+	23.7253i	0.472900	+	0.819087i	−0.526619	+	0.850101i	$0.676541\pi$
$840$	−2.65157	+	3.22328i	−0.0914879	+	0.111214i
$841$		−	38.7768i		−	1.33713i
$842$	4.61170	−	17.2111i	0.158930	−	0.593133i
$843$		−	16.3182i		−	0.562029i
$844$	−7.86139	+	13.6163i	−0.270600	+	0.468693i
$845$	6.28010	+	5.16620i	0.216042	+	0.177723i
$846$	−1.60969	+	0.431315i	−0.0553423	+	0.0148289i
$847$	5.48766	+	20.4802i	0.188558	+	0.703709i
$848$	7.61884	−	2.04146i	0.261632	−	0.0701041i
$849$	−7.75517	+	28.9427i	−0.266157	+	0.993310i
$850$	19.1075	−	3.75445i	0.655382	−	0.128777i
$851$	2.08692	−	1.04189i	0.0715386	−	0.0357155i
$852$	5.54154	−	5.54154i	0.189850	−	0.189850i
$853$	16.2872	−	9.40340i	0.557662	−	0.321966i	−0.194544	−	0.980894i	$-0.562323\pi$
$853$	16.2872	−	9.40340i	0.557662	−	0.321966i	0.752207	+	0.658927i	$0.228990\pi$
$854$	−5.13093	+	8.88704i	−0.175577	+	0.304108i
$855$	2.13465	−	4.69670i	0.0730034	−	0.160624i
$856$	0.868218	+	3.24023i	0.0296751	+	0.110749i
$857$		−	33.0001i		−	1.12726i	−0.826027	−	0.563631i	$-0.809404\pi$
$857$		−	33.0001i		−	1.12726i	0.826027	−	0.563631i	$-0.190596\pi$
$858$	−34.5342	+	9.25341i	−1.17898	+	0.315906i
$859$	14.9683	+	14.9683i	0.510713	+	0.510713i	0.914745	−	0.404032i	$-0.132392\pi$
$859$	14.9683	+	14.9683i	0.510713	+	0.510713i	−0.404032	+	0.914745i	$0.632392\pi$
$860$	0.576806	−	3.46851i	0.0196689	−	0.118275i
$861$	−16.7715			−0.571572
$862$	−7.92381	−	7.92381i	−0.269886	−	0.269886i
$863$	2.61347	−	9.75362i	0.0889637	−	0.332017i	−0.907072	−	0.420977i	$-0.861687\pi$
$863$	2.61347	−	9.75362i	0.0889637	−	0.332017i	0.996035	+	0.0889594i	$0.0283541\pi$
$864$	−5.28689	+	1.41662i	−0.179864	+	0.0481943i
$865$	−45.3638	+	4.41458i	−1.54241	+	0.150100i
$866$	1.32648	−	4.95048i	0.0450755	−	0.168224i
$867$	2.86247	+	0.766996i	0.0972145	+	0.0260485i
$868$	−2.80010	−	4.84992i	−0.0950416	−	0.164617i
$869$	−12.3931	−	46.2518i	−0.420409	−	1.56899i
$870$	−10.4553	−	27.8775i	−0.354467	−	0.945136i
$871$	10.9499	−	40.8655i	0.371022	−	1.38467i
$872$	−2.16115	+	8.06551i	−0.0731857	+	0.273133i
$873$	0.841941	+	1.45829i	0.0284954	+	0.0493555i
$874$	−1.62851	−	1.62851i	−0.0550851	−	0.0550851i
$875$	12.5557	+	2.97389i	0.424459	+	0.100536i
$876$	19.0371	−	10.9911i	0.643205	−	0.371355i
$877$	12.2589	−	12.2589i	0.413952	−	0.413952i	−0.469161	−	0.883113i	$-0.655444\pi$
$877$	12.2589	−	12.2589i	0.413952	−	0.413952i	0.883113	+	0.469161i	$0.155444\pi$
$878$	12.7296	−	12.7296i	0.429602	−	0.429602i
$879$	7.40834	+	12.8316i	0.249877	+	0.432800i
$880$	7.69884	−	9.35880i	0.259528	−	0.315485i
$881$	−4.48347	−	2.58853i	−0.151052	−	0.0872099i	0.422569	−	0.906331i	$-0.361128\pi$
$881$	−4.48347	−	2.58853i	−0.151052	−	0.0872099i	−0.573621	+	0.819121i	$0.694462\pi$
$882$	2.17743			0.0733179
$883$	27.7939	+	16.0468i	0.935338	+	0.540017i	0.888496	−	0.458885i	$-0.151751\pi$
$883$	27.7939	+	16.0468i	0.935338	+	0.540017i	0.0468420	+	0.998902i	$0.485084\pi$
$884$	13.7570	+	7.94263i	0.462699	+	0.267140i
$885$	−37.2187	+	13.9586i	−1.25109	+	0.469214i
$886$	−13.0304	−	3.49150i	−0.437766	−	0.117299i
$887$	28.3782	+	28.3782i	0.952845	+	0.952845i	0.998937	−	0.0460918i	$-0.0146767\pi$
$887$	28.3782	+	28.3782i	0.952845	+	0.952845i	−0.0460918	+	0.998937i	$0.514677\pi$
$888$	6.52278	+	7.36475i	0.218890	+	0.247145i
$889$		−	1.78864i		−	0.0599892i
$890$	19.2559	+	26.9378i	0.645460	+	0.902958i
$891$	36.1397	+	20.8653i	1.21073	+	0.699013i
$892$	10.7656	−	2.88463i	0.360459	−	0.0965846i
$893$	13.0268	−	22.5630i	0.435925	−	0.755043i
$894$	−8.23654	−	8.23654i	−0.275471	−	0.275471i
$895$	−19.3244	+	42.5180i	−0.645943	+	1.42122i
$896$	0.816061	−	0.816061i	0.0272627	−	0.0272627i
$897$	−2.44350	−	0.654734i	−0.0815861	−	0.0218609i
$898$	14.6629	+	14.6629i	0.489306	+	0.489306i
$899$	39.9491			1.33238
$900$	1.26309	+	1.44707i	0.0421030	+	0.0482356i
$901$	7.95063	+	29.6722i	0.264874	+	0.988523i
$902$	48.6961			1.62140
$903$	−2.54188	+	1.46756i	−0.0845886	+	0.0488373i
$904$	−5.90335	+	3.40830i	−0.196342	+	0.113358i
$905$	2.06093	−	12.3930i	0.0685077	−	0.411958i
$906$	10.5068	−	2.81529i	0.349065	−	0.0935318i
$907$	−1.66040	−	0.958632i	−0.0551326	−	0.0318308i	0.472180	−	0.881502i	$-0.343467\pi$
$907$	−1.66040	−	0.958632i	−0.0551326	−	0.0318308i	−0.527313	+	0.849671i	$0.676800\pi$
$908$	−3.07951	+	1.77796i	−0.102197	+	0.0590035i
$909$	1.53254	+	2.65444i	0.0508312	+	0.0880422i
$910$	6.12110	+	8.56304i	0.202912	+	0.283862i
$911$	−16.5788	+	16.5788i	−0.549281	+	0.549281i	−0.926233	−	0.376952i	$-0.876972\pi$
$911$	−16.5788	+	16.5788i	−0.549281	+	0.549281i	0.376952	+	0.926233i	$0.376972\pi$
$912$	4.85682	−	8.41226i	0.160825	−	0.278558i
$913$	−65.1817	−	17.4654i	−2.15720	−	0.578020i
$914$		−	4.25512i		−	0.140747i
$915$	−24.8341	−	20.4293i	−0.820991	−	0.675373i
$916$	−11.7656	+	6.79287i	−0.388746	+	0.224443i
$917$	16.8117			0.555172
$918$	−5.51712	−	20.5902i	−0.182092	−	0.679577i
$919$	36.7182	−	36.7182i	1.21122	−	1.21122i	0.240594	−	0.970626i	$-0.422658\pi$
$919$	36.7182	−	36.7182i	1.21122	−	1.21122i	0.970626	−	0.240594i	$-0.0773423\pi$
$920$	0.802853	−	0.301105i	0.0264693	−	0.00992714i
$921$	−27.5704	+	47.7533i	−0.908474	+	1.57352i
$922$	6.14596	+	22.9371i	0.202407	+	0.755392i
$923$	−9.88197	−	17.1161i	−0.325269	−	0.563383i
$924$	−10.1160			−0.332792
$925$	11.5667	−	28.1285i	0.380311	−	0.924858i
$926$	−26.3755			−0.866751
$927$	0.901135	+	1.56081i	0.0295971	+	0.0512638i
$928$	2.13077	+	7.95215i	0.0699460	+	0.261042i
$929$	−10.8007	+	18.7074i	−0.354360	+	0.613770i	−0.987008	−	0.160670i	$-0.948635\pi$
$929$	−10.8007	+	18.7074i	−0.354360	+	0.613770i	0.632648	+	0.774439i	$0.281968\pi$
$930$	16.4316	−	6.16256i	0.538813	−	0.202078i
$931$	−24.0712	+	24.0712i	−0.788902	+	0.788902i
$932$	−2.78532	−	10.3949i	−0.0912361	−	0.340498i
$933$	37.9931			1.24384
$934$	4.17701	−	2.41160i	0.136676	−	0.0789100i
$935$	36.4486	+	29.9837i	1.19200	+	0.980572i
$936$			1.56690i			0.0512158i
$937$	−10.1589	−	2.72206i	−0.331876	−	0.0889258i	0.0890335	−	0.996029i	$-0.471622\pi$
$937$	−10.1589	−	2.72206i	−0.331876	−	0.0889258i	−0.420909	+	0.907103i	$0.638289\pi$
$938$	5.98531	−	10.3669i	0.195427	−	0.338490i
$939$	−13.7993	+	13.7993i	−0.450323	+	0.450323i
$940$	5.64090	+	7.89127i	0.183986	+	0.257385i
$941$	−20.8136	−	36.0502i	−0.678504	−	1.17520i	−0.975431	−	0.220304i	$-0.929295\pi$
$941$	−20.8136	−	36.0502i	−0.678504	−	1.17520i	0.296927	−	0.954900i	$-0.404038\pi$
$942$	18.6614	−	10.7742i	0.608021	−	0.351041i
$943$	2.98393	+	1.72277i	0.0971701	+	0.0561012i
$944$	10.6168	−	2.84475i	0.345546	−	0.0925887i
$945$	2.31709	−	13.9333i	0.0753748	−	0.453252i
$946$	7.38036	−	4.26106i	0.239956	−	0.138539i
$947$	−20.1967	+	11.6606i	−0.656304	+	0.378917i	−0.790867	−	0.611988i	$-0.790370\pi$
$947$	−20.1967	+	11.6606i	−0.656304	+	0.378917i	0.134564	+	0.990905i	$0.457037\pi$
$948$	14.2898			0.464110
$949$	−14.3481	−	53.5479i	−0.465760	−	1.73824i
$950$	−29.9604	−	2.03384i	−0.972044	−	0.0659865i
$951$	−25.6371			−0.831341
$952$	3.17821	+	3.17821i	0.103006	+	0.103006i
$953$	−10.0369	−	2.68937i	−0.325126	−	0.0871174i	0.0925641	−	0.995707i	$-0.470494\pi$
$953$	−10.0369	−	2.68937i	−0.325126	−	0.0871174i	−0.417690	+	0.908589i	$0.637160\pi$
$954$	−2.14258	+	2.14258i	−0.0693687	+	0.0693687i
$955$	−8.45494	+	18.6028i	−0.273595	+	0.601971i
$956$	−15.1319	−	15.1319i	−0.489402	−	0.489402i
$957$	36.0813	−	62.4946i	1.16634	−	2.02016i
$958$	39.3150	−	10.5344i	1.27021	−	0.340352i
$959$	12.0345	+	6.94809i	0.388613	+	0.224366i
$960$	2.10312	+	2.94213i	0.0678778	+	0.0949568i
$961$		−	7.45320i		−	0.240426i
$962$	22.1978	−	11.0822i	0.715687	−	0.357305i
$963$	−0.911225	−	0.911225i	−0.0293638	−	0.0293638i
$964$	7.04781	+	1.88845i	0.226995	+	0.0608230i
$965$	−22.3617	+	8.38660i	−0.719847	+	0.269974i
$966$	−0.619874	−	0.357884i	−0.0199441	−	0.0115147i
$967$	−19.2414	−	11.1090i	−0.618761	−	0.357242i	0.157625	−	0.987499i	$-0.449616\pi$
$967$	−19.2414	−	11.1090i	−0.618761	−	0.357242i	−0.776387	+	0.630257i	$0.782950\pi$
$968$	18.3719			0.590494
$969$	32.7622	+	18.9153i	1.05247	+	0.607646i
$970$	6.22678	−	7.56935i	0.199930	−	0.243037i
$971$	−5.81973	−	10.0801i	−0.186764	−	0.323485i	0.757405	−	0.652945i	$-0.226467\pi$
$971$	−5.81973	−	10.0801i	−0.186764	−	0.323485i	−0.944170	+	0.329460i	$0.893133\pi$
$972$	2.80480	−	2.80480i	0.0899641	−	0.0899641i
$973$	−8.24123	+	8.24123i	−0.264202	+	0.264202i
$974$	−12.1303	+	7.00341i	−0.388679	+	0.224404i
$975$	−29.6168	+	14.5197i	−0.948497	+	0.465002i
$976$	6.28744	+	6.28744i	0.201256	+	0.201256i
$977$	−27.2295	−	47.1628i	−0.871147	−	1.50887i	−0.860811	−	0.508925i	$-0.830043\pi$
$977$	−27.2295	−	47.1628i	−0.871147	−	1.50887i	−0.0103367	−	0.999947i	$-0.503290\pi$
$978$	1.88034	−	7.01751i	0.0601266	−	0.224395i
$979$	−20.7715	+	77.5204i	−0.663861	+	2.47756i
$980$	−4.45067	−	11.8671i	−0.142172	−	0.379080i
$981$	−0.830218	−	3.09842i	−0.0265068	−	0.0989248i
$982$	7.40852	+	12.8319i	0.236415	+	0.409483i
$983$	−15.4801	−	4.14789i	−0.493740	−	0.132297i	0.00335334	−	0.999994i	$-0.498933\pi$
$983$	−15.4801	−	4.14789i	−0.493740	−	0.132297i	−0.497093	+	0.867697i	$0.665599\pi$
$984$	−3.76124	+	14.0371i	−0.119904	+	0.447488i
$985$	3.86668	−	0.376286i	0.123203	−	0.0119895i
$986$	−30.9702	+	8.29845i	−0.986293	+	0.264277i
$987$	2.09571	−	7.82129i	0.0667071	−	0.248954i
$988$	−17.3219	−	17.3219i	−0.551083	−	0.551083i
$989$	0.602990			0.0191740
$990$	−0.763698	+	4.59235i	−0.0242719	+	0.145954i
$991$	−18.9057	−	18.9057i	−0.600559	−	0.600559i	0.339902	−	0.940461i	$-0.389606\pi$
$991$	−18.9057	−	18.9057i	−0.600559	−	0.600559i	−0.940461	+	0.339902i	$0.889606\pi$
$992$	−4.68716	+	1.25592i	−0.148817	+	0.0398755i
$993$		−	0.874659i		−	0.0277565i
$994$	−1.44735	−	5.40159i	−0.0459072	−	0.171328i
$995$	−14.2106	+	31.2665i	−0.450507	+	0.991216i
$996$	10.0691	−	17.4403i	0.319053	−	0.552616i
$997$	22.4744	−	12.9756i	0.711772	−	0.410942i	−0.0999446	−	0.994993i	$-0.531867\pi$
$997$	22.4744	−	12.9756i	0.711772	−	0.410942i	0.811717	+	0.584051i	$0.198533\pi$
$998$	−24.0931	+	24.0931i	−0.762654	+	0.762654i
$999$	−31.5785	−	10.5473i	−0.999099	−	0.333702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.f.103.4	yes	32
5.2	odd	4		370.2.r.f.177.4	yes	32
37.23	odd	12		370.2.r.f.23.4	yes	32
185.97	even	12	inner	370.2.q.f.97.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.f.97.4	✓	32	185.97	even	12	inner
370.2.q.f.103.4	yes	32	1.1	even	1	trivial
370.2.r.f.23.4	yes	32	37.23	odd	12
370.2.r.f.177.4	yes	32	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.418603 - 1.56225i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.09367 + 0.785216i) q^{5} +(1.14364 - 1.14364i) q^{6} +(-0.298699 - 1.11476i) q^{7} -1.00000 q^{8} +(0.332689 - 0.192078i) q^{9} +(-1.72685 - 1.42056i) q^{10} -5.41958i q^{11} +(1.56225 + 0.418603i) q^{12} +(2.03941 - 3.53236i) q^{13} +(0.816061 - 0.816061i) q^{14} +(2.10312 + 2.94213i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.37280 - 1.94729i) q^{17} +(0.332689 + 0.192078i) q^{18} +(-5.80123 + 1.55443i) q^{19} +(0.366816 - 2.20578i) q^{20} +(-1.61650 + 0.933284i) q^{21} +(4.69349 - 2.70979i) q^{22} +0.383468 q^{23} +(0.418603 + 1.56225i) q^{24} +(3.76687 - 3.28796i) q^{25} +4.07882 q^{26} +(-3.87027 - 3.87027i) q^{27} +(1.11476 + 0.298699i) q^{28} +(-5.82137 + 5.82137i) q^{29} +(-1.49640 + 3.29242i) q^{30} +(-3.43124 - 3.43124i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-8.46672 + 2.26865i) q^{33} +(3.37280 + 1.94729i) q^{34} +(1.50070 + 2.09939i) q^{35} +0.384156i q^{36} +(5.44223 - 2.71702i) q^{37} +(-4.24679 - 4.24679i) q^{38} +(-6.37212 - 1.70740i) q^{39} +(2.09367 - 0.785216i) q^{40} +(7.78143 + 4.49261i) q^{41} +(-1.61650 - 0.933284i) q^{42} +1.57247 q^{43} +(4.69349 + 2.70979i) q^{44} +(-0.545717 + 0.663380i) q^{45} +(0.191734 + 0.332093i) q^{46} +(-3.06744 + 3.06744i) q^{47} +(-1.14364 + 1.14364i) q^{48} +(4.90871 - 2.83404i) q^{49} +(4.73089 + 1.61823i) q^{50} +(-4.45401 - 4.45401i) q^{51} +(2.03941 + 3.53236i) q^{52} +(-2.04146 + 7.61884i) q^{53} +(1.41662 - 5.28689i) q^{54} +(4.25554 + 11.3468i) q^{55} +(0.298699 + 1.11476i) q^{56} +(4.85682 + 8.41226i) q^{57} +(-7.95215 - 2.13077i) q^{58} +(-2.84475 + 10.6168i) q^{59} +(-3.59952 + 0.350287i) q^{60} +(-8.58880 + 2.30136i) q^{61} +(1.25592 - 4.68716i) q^{62} +(-0.313495 - 0.313495i) q^{63} +1.00000 q^{64} +(-1.49617 + 8.99695i) q^{65} +(-6.19807 - 6.19807i) q^{66} +(10.0190 - 2.68457i) q^{67} +3.89458i q^{68} +(-0.160521 - 0.599071i) q^{69} +(-1.06778 + 2.34934i) q^{70} +(2.42276 - 4.19634i) q^{71} +(-0.332689 + 0.192078i) q^{72} +(9.61059 - 9.61059i) q^{73} +(5.07412 + 3.35460i) q^{74} +(-6.71343 - 4.50843i) q^{75} +(1.55443 - 5.80123i) q^{76} +(-6.04153 + 1.61882i) q^{77} +(-1.70740 - 6.37212i) q^{78} +(8.53421 - 2.28673i) q^{79} +(1.72685 + 1.42056i) q^{80} +(-3.84998 + 6.66836i) q^{81} +8.98522i q^{82} +(3.22265 - 12.0271i) q^{83} -1.86657i q^{84} +(-5.53248 + 6.72535i) q^{85} +(0.786233 + 1.36180i) q^{86} +(11.5313 + 6.65758i) q^{87} +5.41958i q^{88} +(-14.3038 - 3.83268i) q^{89} +(-0.847362 - 0.140915i) q^{90} +(-4.54690 - 1.21834i) q^{91} +(-0.191734 + 0.332093i) q^{92} +(-3.92412 + 6.79677i) q^{93} +(-4.19020 - 1.12276i) q^{94} +(10.9253 - 7.80968i) q^{95} +(-1.56225 - 0.418603i) q^{96} +4.38333i q^{97} +(4.90871 + 2.83404i) q^{98} +(-1.04098 - 1.80304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 2 q^{3} - 16 q^{4} + 6 q^{5} + 8 q^{6} - 10 q^{7} - 32 q^{8} + 12 q^{9} + 6 q^{10} + 10 q^{12} + 10 q^{13} - 8 q^{14} - 8 q^{15} - 16 q^{16} - 12 q^{17} + 12 q^{18} + 2 q^{19} - 54 q^{21}+ \cdots - 26 q^{99}+O(q^{100}) \) 32 * q + 16 * q^2 - 2 * q^3 - 16 * q^4 + 6 * q^5 + 8 * q^6 - 10 * q^7 - 32 * q^8 + 12 * q^9 + 6 * q^10 + 10 * q^12 + 10 * q^13 - 8 * q^14 - 8 * q^15 - 16 * q^16 - 12 * q^17 + 12 * q^18 + 2 * q^19 - 54 * q^21 + 6 * q^22 + 12 * q^23 + 2 * q^24 - 16 * q^25 + 20 * q^26 + 40 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^30 - 4 * q^31 + 16 * q^32 + 26 * q^33 - 12 * q^34 - 12 * q^35 + 20 * q^37 - 26 * q^38 - 58 * q^39 - 6 * q^40 + 18 * q^41 - 54 * q^42 - 32 * q^43 + 6 * q^44 + 56 * q^45 + 6 * q^46 + 18 * q^47 - 8 * q^48 - 12 * q^49 - 14 * q^50 - 4 * q^51 + 10 * q^52 - 24 * q^53 + 20 * q^54 - 32 * q^55 + 10 * q^56 + 8 * q^57 + 36 * q^58 + 42 * q^59 + 16 * q^60 - 46 * q^61 - 14 * q^62 + 32 * q^64 - 18 * q^65 + 4 * q^66 + 50 * q^67 - 66 * q^69 + 12 * q^70 - 12 * q^71 - 12 * q^72 - 28 * q^73 + 16 * q^74 - 20 * q^75 - 28 * q^76 + 12 * q^77 - 26 * q^78 + 38 * q^79 - 6 * q^80 + 56 * q^81 - 8 * q^85 - 16 * q^86 + 18 * q^87 + 18 * q^89 + 4 * q^90 + 4 * q^91 - 6 * q^92 + 32 * q^93 + 30 * q^94 + 96 * q^95 - 10 * q^96 - 12 * q^98 - 26 * q^99

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