LMFDB - Embedded newform 630.2.ba.a.529.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(499,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("630.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ba (of order $6$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.39
Character	$\chi$	$=$	630.529
Dual form			630.2.ba.a.499.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.330172 - 1.70029i) q^{3} -1.00000 q^{4} +(0.551777 - 2.16692i) q^{5} +(1.70029 + 0.330172i) q^{6} +(-0.585831 + 2.58008i) q^{7} -1.00000i q^{8} +(-2.78197 - 1.12278i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.330172 - 1.70029i) q^{3} -1.00000 q^{4} +(0.551777 - 2.16692i) q^{5} +(1.70029 + 0.330172i) q^{6} +(-0.585831 + 2.58008i) q^{7} -1.00000i q^{8} +(-2.78197 - 1.12278i) q^{9} +(2.16692 + 0.551777i) q^{10} +(-2.05292 - 3.55576i) q^{11} +(-0.330172 + 1.70029i) q^{12} +(3.36239 - 1.94128i) q^{13} +(-2.58008 - 0.585831i) q^{14} +(-3.50221 - 1.65364i) q^{15} +1.00000 q^{16} +(2.40480 + 1.38841i) q^{17} +(1.12278 - 2.78197i) q^{18} +(-1.40977 - 2.44179i) q^{19} +(-0.551777 + 2.16692i) q^{20} +(4.19346 + 1.84795i) q^{21} +(3.55576 - 2.05292i) q^{22} +(-5.13166 - 2.96277i) q^{23} +(-1.70029 - 0.330172i) q^{24} +(-4.39109 - 2.39131i) q^{25} +(1.94128 + 3.36239i) q^{26} +(-2.82758 + 4.35945i) q^{27} +(0.585831 - 2.58008i) q^{28} +(2.36090 - 4.08921i) q^{29} +(1.65364 - 3.50221i) q^{30} -3.89489 q^{31} +1.00000i q^{32} +(-6.72365 + 2.31655i) q^{33} +(-1.38841 + 2.40480i) q^{34} +(5.26758 + 2.69307i) q^{35} +(2.78197 + 1.12278i) q^{36} +(-0.356887 + 0.206049i) q^{37} +(2.44179 - 1.40977i) q^{38} +(-2.19057 - 6.35800i) q^{39} +(-2.16692 - 0.551777i) q^{40} +(-3.43052 - 5.94183i) q^{41} +(-1.84795 + 4.19346i) q^{42} +(-1.08691 - 0.627530i) q^{43} +(2.05292 + 3.55576i) q^{44} +(-3.96800 + 5.40879i) q^{45} +(2.96277 - 5.13166i) q^{46} -5.10612i q^{47} +(0.330172 - 1.70029i) q^{48} +(-6.31361 - 3.02298i) q^{49} +(2.39131 - 4.39109i) q^{50} +(3.15470 - 3.63044i) q^{51} +(-3.36239 + 1.94128i) q^{52} +(4.20182 + 2.42592i) q^{53} +(-4.35945 - 2.82758i) q^{54} +(-8.83781 + 2.48653i) q^{55} +(2.58008 + 0.585831i) q^{56} +(-4.61723 + 1.59081i) q^{57} +(4.08921 + 2.36090i) q^{58} +12.4810 q^{59} +(3.50221 + 1.65364i) q^{60} -1.08850 q^{61} -3.89489i q^{62} +(4.52662 - 6.51995i) q^{63} -1.00000 q^{64} +(-2.35131 - 8.35719i) q^{65} +(-2.31655 - 6.72365i) q^{66} +12.5268i q^{67} +(-2.40480 - 1.38841i) q^{68} +(-6.73190 + 7.74709i) q^{69} +(-2.69307 + 5.26758i) q^{70} +16.3189 q^{71} +(-1.12278 + 2.78197i) q^{72} +(11.1123 + 6.41567i) q^{73} +(-0.206049 - 0.356887i) q^{74} +(-5.51574 + 6.67657i) q^{75} +(1.40977 + 2.44179i) q^{76} +(10.3768 - 3.21362i) q^{77} +(6.35800 - 2.19057i) q^{78} +6.02746 q^{79} +(0.551777 - 2.16692i) q^{80} +(6.47874 + 6.24707i) q^{81} +(5.94183 - 3.43052i) q^{82} +(-13.4228 - 7.74967i) q^{83} +(-4.19346 - 1.84795i) q^{84} +(4.33549 - 4.44491i) q^{85} +(0.627530 - 1.08691i) q^{86} +(-6.17333 - 5.36436i) q^{87} +(-3.55576 + 2.05292i) q^{88} +(3.68803 + 6.38786i) q^{89} +(-5.40879 - 3.96800i) q^{90} +(3.03886 + 9.81250i) q^{91} +(5.13166 + 2.96277i) q^{92} +(-1.28598 + 6.62244i) q^{93} +5.10612 q^{94} +(-6.06905 + 1.70754i) q^{95} +(1.70029 + 0.330172i) q^{96} +(-3.62553 - 2.09320i) q^{97} +(3.02298 - 6.31361i) q^{98} +(1.71884 + 12.1970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9	$ 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9} + 4 q^{11} - 2 q^{14} - 2 q^{15} + 96 q^{16} + 8 q^{21} + 4 q^{24} + 24 q^{26} + 10 q^{29} + 10 q^{30} - 34 q^{35} - 8 q^{36} + 44 q^{39} + 30 q^{41} - 4 q^{44} - 44 q^{45} - 6 q^{46} - 6 q^{49} - 12 q^{50} + 28 q^{51} - 8 q^{54} + 12 q^{55} + 2 q^{56} + 48 q^{59} + 2 q^{60} + 12 q^{61} - 96 q^{64} - 36 q^{65} + 32 q^{66} + 36 q^{69} + 6 q^{70} - 32 q^{71} - 68 q^{75} - 32 q^{81} - 8 q^{84} + 4 q^{86} - 66 q^{89} - 22 q^{90} + 24 q^{94} - 60 q^{95} - 4 q^{96} - 4 q^{99}+O(q^{100}) $ 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9 + 4 * q^11 - 2 * q^14 - 2 * q^15 + 96 * q^16 + 8 * q^21 + 4 * q^24 + 24 * q^26 + 10 * q^29 + 10 * q^30 - 34 * q^35 - 8 * q^36 + 44 * q^39 + 30 * q^41 - 4 * q^44 - 44 * q^45 - 6 * q^46 - 6 * q^49 - 12 * q^50 + 28 * q^51 - 8 * q^54 + 12 * q^55 + 2 * q^56 + 48 * q^59 + 2 * q^60 + 12 * q^61 - 96 * q^64 - 36 * q^65 + 32 * q^66 + 36 * q^69 + 6 * q^70 - 32 * q^71 - 68 * q^75 - 32 * q^81 - 8 * q^84 + 4 * q^86 - 66 * q^89 - 22 * q^90 + 24 * q^94 - 60 * q^95 - 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.330172	−	1.70029i	0.190625	−	0.981663i
$3$	0.330172	−	1.70029i	0.190625	−	0.981663i
$4$	−1.00000			−0.500000
$5$	0.551777	−	2.16692i	0.246762	−	0.969076i
$5$	0.551777	−	2.16692i	0.246762	−	0.969076i
$6$	1.70029	+	0.330172i	0.694140	+	0.134792i
$7$	−0.585831	+	2.58008i	−0.221423	+	0.975178i
$7$	−0.585831	+	2.58008i	−0.221423	+	0.975178i
$8$		−	1.00000i		−	0.353553i
$9$	−2.78197	−	1.12278i	−0.927324	−	0.374259i
$10$	2.16692	+	0.551777i	0.685240	+	0.174487i
$11$	−2.05292	−	3.55576i	−0.618979	−	1.07210i	−0.989672	−	0.143348i	$-0.954213\pi$
$11$	−2.05292	−	3.55576i	−0.618979	−	1.07210i	0.370694	−	0.928755i	$-0.379120\pi$
$12$	−0.330172	+	1.70029i	−0.0953126	+	0.490831i
$13$	3.36239	−	1.94128i	0.932560	−	0.538414i	0.0449397	−	0.998990i	$-0.485690\pi$
$13$	3.36239	−	1.94128i	0.932560	−	0.538414i	0.887620	+	0.460576i	$0.152357\pi$
$14$	−2.58008	−	0.585831i	−0.689555	−	0.156570i
$15$	−3.50221	−	1.65364i	−0.904267	−	0.426967i
$16$	1.00000			0.250000
$17$	2.40480	+	1.38841i	0.583249	+	0.336739i	0.762424	−	0.647078i	$-0.224009\pi$
$17$	2.40480	+	1.38841i	0.583249	+	0.336739i	−0.179175	+	0.983817i	$0.557343\pi$
$18$	1.12278	−	2.78197i	0.264641	−	0.655717i
$19$	−1.40977	−	2.44179i	−0.323424	−	0.560186i	0.657768	−	0.753220i	$-0.271501\pi$
$19$	−1.40977	−	2.44179i	−0.323424	−	0.560186i	−0.981192	+	0.193034i	$0.938167\pi$
$20$	−0.551777	+	2.16692i	−0.123381	+	0.484538i
$21$	4.19346	+	1.84795i	0.915087	+	0.403256i
$22$	3.55576	−	2.05292i	0.758091	−	0.437684i
$23$	−5.13166	−	2.96277i	−1.07003	−	0.617780i	−0.141837	−	0.989890i	$-0.545301\pi$
$23$	−5.13166	−	2.96277i	−1.07003	−	0.617780i	−0.928188	+	0.372111i	$0.878634\pi$
$24$	−1.70029	−	0.330172i	−0.347070	−	0.0673962i
$25$	−4.39109	−	2.39131i	−0.878217	−	0.478262i
$26$	1.94128	+	3.36239i	0.380716	+	0.659420i
$27$	−2.82758	+	4.35945i	−0.544168	+	0.838976i
$28$	0.585831	−	2.58008i	0.110712	−	0.487589i
$29$	2.36090	−	4.08921i	0.438409	−	0.759346i	−0.559158	−	0.829061i	$-0.688876\pi$
$29$	2.36090	−	4.08921i	0.438409	−	0.759346i	0.997567	+	0.0697147i	$0.0222089\pi$
$30$	1.65364	−	3.50221i	0.301912	−	0.639413i
$31$	−3.89489			−0.699542			−0.349771	−	0.936835i	$-0.613741\pi$
$31$	−3.89489			−0.699542			−0.349771	+	0.936835i	$0.613741\pi$
$32$			1.00000i			0.176777i
$33$	−6.72365	+	2.31655i	−1.17044	+	0.403259i
$34$	−1.38841	+	2.40480i	−0.238110	+	0.412419i
$35$	5.26758	+	2.69307i	0.890383	+	0.455213i
$36$	2.78197	+	1.12278i	0.463662	+	0.187130i
$37$	−0.356887	+	0.206049i	−0.0586718	+	0.0338742i	−0.529049	−	0.848591i	$-0.677451\pi$
$37$	−0.356887	+	0.206049i	−0.0586718	+	0.0338742i	0.470377	+	0.882465i	$0.344118\pi$
$38$	2.44179	−	1.40977i	0.396111	−	0.228695i
$39$	−2.19057	−	6.35800i	−0.350771	−	1.01809i
$40$	−2.16692	−	0.551777i	−0.342620	−	0.0872435i
$41$	−3.43052	−	5.94183i	−0.535757	−	0.927958i	−0.999126	−	0.0417929i	$-0.986693\pi$
$41$	−3.43052	−	5.94183i	−0.535757	−	0.927958i	0.463369	−	0.886165i	$-0.346640\pi$
$42$	−1.84795	+	4.19346i	−0.285145	+	0.647064i
$43$	−1.08691	−	0.627530i	−0.165753	−	0.0956975i	0.414829	−	0.909899i	$-0.363841\pi$
$43$	−1.08691	−	0.627530i	−0.165753	−	0.0956975i	−0.580582	+	0.814202i	$0.697175\pi$
$44$	2.05292	+	3.55576i	0.309489	+	0.536051i
$45$	−3.96800	+	5.40879i	−0.591514	+	0.806295i
$46$	2.96277	−	5.13166i	0.436836	−	0.756622i
$47$		−	5.10612i		−	0.744804i	−0.928072	−	0.372402i	$-0.878534\pi$
$47$		−	5.10612i		−	0.744804i	0.928072	−	0.372402i	$-0.121466\pi$
$48$	0.330172	−	1.70029i	0.0476563	−	0.245416i
$49$	−6.31361	−	3.02298i	−0.901944	−	0.431854i
$50$	2.39131	−	4.39109i	0.338183	−	0.620993i
$51$	3.15470	−	3.63044i	0.441746	−	0.508363i
$52$	−3.36239	+	1.94128i	−0.466280	+	0.269207i
$53$	4.20182	+	2.42592i	0.577164	+	0.333226i	0.760006	−	0.649917i	$-0.225196\pi$
$53$	4.20182	+	2.42592i	0.577164	+	0.333226i	−0.182842	+	0.983142i	$0.558530\pi$
$54$	−4.35945	−	2.82758i	−0.593246	−	0.384785i
$55$	−8.83781	+	2.48653i	−1.19169	+	0.335283i
$56$	2.58008	+	0.585831i	0.344777	+	0.0782849i
$57$	−4.61723	+	1.59081i	−0.611567	+	0.210707i
$58$	4.08921	+	2.36090i	0.536939	+	0.310002i
$59$	12.4810			1.62489			0.812445	−	0.583038i	$-0.198136\pi$
$59$	12.4810			1.62489			0.812445	+	0.583038i	$0.198136\pi$
$60$	3.50221	+	1.65364i	0.452134	+	0.213484i
$61$	−1.08850			−0.139369			−0.0696843	−	0.997569i	$-0.522199\pi$
$61$	−1.08850			−0.139369			−0.0696843	+	0.997569i	$0.522199\pi$
$62$		−	3.89489i		−	0.494651i
$63$	4.52662	−	6.51995i	0.570300	−	0.821436i
$64$	−1.00000			−0.125000
$65$	−2.35131	−	8.35719i	−0.291644	−	1.03658i
$66$	−2.31655	−	6.72365i	−0.285147	−	0.827624i
$67$			12.5268i			1.53039i	0.643799	+	0.765195i	$0.277357\pi$
$67$			12.5268i			1.53039i	−0.643799	+	0.765195i	$0.722643\pi$
$68$	−2.40480	−	1.38841i	−0.291625	−	0.168369i
$69$	−6.73190	+	7.74709i	−0.810425	+	0.932640i
$70$	−2.69307	+	5.26758i	−0.321884	+	0.629596i
$71$	16.3189			1.93669			0.968346	−	0.249611i	$-0.0803028\pi$
$71$	16.3189			1.93669			0.968346	+	0.249611i	$0.0803028\pi$
$72$	−1.12278	+	2.78197i	−0.132321	+	0.327859i
$73$	11.1123	+	6.41567i	1.30059	+	0.750897i	0.980505	−	0.196492i	$-0.0629549\pi$
$73$	11.1123	+	6.41567i	1.30059	+	0.750897i	0.320086	+	0.947389i	$0.396288\pi$
$74$	−0.206049	−	0.356887i	−0.0239527	−	0.0414872i
$75$	−5.51574	+	6.67657i	−0.636903	+	0.770944i
$76$	1.40977	+	2.44179i	0.161712	+	0.280093i
$77$	10.3768	−	3.21362i	1.18255	−	0.366226i
$78$	6.35800	−	2.19057i	0.719902	−	0.248033i
$79$	6.02746			0.678142			0.339071	−	0.940761i	$-0.389887\pi$
$79$	6.02746			0.678142			0.339071	+	0.940761i	$0.389887\pi$
$80$	0.551777	−	2.16692i	0.0616905	−	0.242269i
$81$	6.47874	+	6.24707i	0.719860	+	0.694119i
$82$	5.94183	−	3.43052i	0.656165	−	0.378837i
$83$	−13.4228	−	7.74967i	−1.47335	−	0.850637i	−0.473796	−	0.880635i	$-0.657116\pi$
$83$	−13.4228	−	7.74967i	−1.47335	−	0.850637i	−0.999550	+	0.0299982i	$0.990450\pi$
$84$	−4.19346	−	1.84795i	−0.457544	−	0.201628i
$85$	4.33549	−	4.44491i	0.470249	−	0.482118i
$86$	0.627530	−	1.08691i	0.0676683	−	0.117205i
$87$	−6.17333	−	5.36436i	−0.661850	−	0.575120i
$88$	−3.55576	+	2.05292i	−0.379046	+	0.218842i
$89$	3.68803	+	6.38786i	0.390931	+	0.677112i	0.992573	−	0.121654i	$-0.0388198\pi$
$89$	3.68803	+	6.38786i	0.390931	+	0.677112i	−0.601642	+	0.798766i	$0.705487\pi$
$90$	−5.40879	−	3.96800i	−0.570136	−	0.418264i
$91$	3.03886	+	9.81250i	0.318559	+	1.02863i
$92$	5.13166	+	2.96277i	0.535013	+	0.308890i
$93$	−1.28598	+	6.62244i	−0.133350	+	0.686715i
$94$	5.10612			0.526656
$95$	−6.06905	+	1.70754i	−0.622672	+	0.175189i
$96$	1.70029	+	0.330172i	0.173535	+	0.0336981i
$97$	−3.62553	−	2.09320i	−0.368117	−	0.212532i	0.304519	−	0.952506i	$-0.401504\pi$
$97$	−3.62553	−	2.09320i	−0.368117	−	0.212532i	−0.672635	+	0.739974i	$0.734838\pi$
$98$	3.02298	−	6.31361i	0.305367	−	0.637770i
$99$	1.71884	+	12.1970i	0.172750	+	1.22585i
$100$	4.39109	+	2.39131i	0.439109	+	0.239131i
$101$	6.33196	+	10.9673i	0.630053	+	1.09128i	0.987540	+	0.157366i	$0.0503003\pi$
$101$	6.33196	+	10.9673i	0.630053	+	1.09128i	−0.357487	+	0.933918i	$0.616366\pi$
$102$	3.63044	+	3.15470i	0.359467	+	0.312362i
$103$	3.79293	+	2.18985i	0.373729	+	0.215772i	0.675086	−	0.737739i	$-0.264106\pi$
$103$	3.79293	+	2.18985i	0.373729	+	0.215772i	−0.301357	+	0.953511i	$0.597440\pi$
$104$	−1.94128	−	3.36239i	−0.190358	−	0.329710i
$105$	6.31822	−	8.06723i	0.616595	−	0.787281i
$106$	−2.42592	+	4.20182i	−0.235626	+	0.408117i
$107$	2.83265	−	1.63543i	0.273843	−	0.158103i	−0.356790	−	0.934185i	$-0.616129\pi$
$107$	2.83265	−	1.63543i	0.273843	−	0.158103i	0.630633	+	0.776081i	$0.282795\pi$
$108$	2.82758	−	4.35945i	0.272084	−	0.419488i
$109$	−1.65955	+	2.87443i	−0.158956	+	0.275321i	−0.934493	−	0.355983i	$-0.884146\pi$
$109$	−1.65955	+	2.87443i	−0.158956	+	0.275321i	0.775536	+	0.631303i	$0.217480\pi$
$110$	−2.48653	−	8.83781i	−0.237081	−	0.842652i
$111$	0.232508	+	0.674842i	0.0220687	+	0.0640532i
$112$	−0.585831	+	2.58008i	−0.0553558	+	0.243794i
$113$	6.85140	−	3.95566i	0.644526	−	0.372117i	−0.141830	−	0.989891i	$-0.545299\pi$
$113$	6.85140	−	3.95566i	0.644526	−	0.372117i	0.786356	+	0.617774i	$0.211965\pi$
$114$	−1.59081	−	4.61723i	−0.148993	−	0.432443i
$115$	−9.25161	+	9.48512i	−0.862717	+	0.884492i
$116$	−2.36090	+	4.08921i	−0.219204	+	0.379673i
$117$	−11.5337	+	1.62536i	−1.06629	+	0.150265i
$118$			12.4810i			1.14897i
$119$	−4.99101	+	5.39119i	−0.457525	+	0.494210i
$120$	−1.65364	+	3.50221i	−0.150956	+	0.319707i
$121$	−2.92897	+	5.07312i	−0.266270	+	0.461193i
$122$		−	1.08850i		−	0.0985485i
$123$	−11.2355	+	3.87105i	−1.01307	+	0.349041i
$124$	3.89489			0.349771
$125$	−7.60468	+	8.19566i	−0.680183	+	0.733042i
$126$	6.51995	+	4.52662i	0.580843	+	0.403263i
$127$		−	7.37701i		−	0.654604i	−0.944920	−	0.327302i	$-0.893861\pi$
$127$		−	7.37701i		−	0.654604i	0.944920	−	0.327302i	$-0.106139\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.42585	+	1.64088i	−0.125539	+	0.144471i
$130$	8.35719	−	2.35131i	0.732974	−	0.206223i
$131$	−5.96168	+	10.3259i	−0.520874	+	0.902181i	0.478831	+	0.877907i	$0.341061\pi$
$131$	−5.96168	+	10.3259i	−0.520874	+	0.902181i	−0.999705	+	0.0242736i	$0.992273\pi$
$132$	6.72365	−	2.31655i	0.585218	−	0.201629i
$133$	7.12591	−	2.20684i	0.617894	−	0.191357i
$134$	−12.5268			−1.08215
$135$	7.88639	+	8.53258i	0.678752	+	0.734367i
$136$	1.38841	−	2.40480i	0.119055	−	0.206210i
$137$	17.1599	−	9.90727i	1.46607	−	0.846435i	0.466788	−	0.884369i	$-0.345411\pi$
$137$	17.1599	−	9.90727i	1.46607	−	0.846435i	0.999280	+	0.0379338i	$0.0120776\pi$
$138$	−7.74709	−	6.73190i	−0.659476	−	0.573057i
$139$	2.84915	+	4.93488i	0.241662	+	0.418571i	0.961188	−	0.275895i	$-0.0889741\pi$
$139$	2.84915	+	4.93488i	0.241662	+	0.418571i	−0.719526	+	0.694466i	$0.755641\pi$
$140$	−5.26758	−	2.69307i	−0.445191	−	0.227606i
$141$	−8.68188	−	1.68590i	−0.731146	−	0.141978i
$142$			16.3189i			1.36945i
$143$	−13.8055	−	7.97058i	−1.15447	−	0.666534i
$144$	−2.78197	−	1.12278i	−0.231831	−	0.0935648i
$145$	−7.55829	−	7.37222i	−0.627682	−	0.612229i
$146$	−6.41567	+	11.1123i	−0.530964	+	0.919657i
$147$	−7.22452	+	9.73686i	−0.595868	+	0.803082i
$148$	0.356887	−	0.206049i	0.0293359	−	0.0169371i
$149$	10.4021	−	18.0169i	0.852169	−	1.47600i	−0.0270774	−	0.999633i	$-0.508620\pi$
$149$	10.4021	−	18.0169i	0.852169	−	1.47600i	0.879247	−	0.476367i	$-0.158047\pi$
$150$	−6.67657	−	5.51574i	−0.545140	−	0.450358i
$151$	−8.13217	−	14.0853i	−0.661786	−	1.14625i	−0.980146	−	0.198278i	$-0.936465\pi$
$151$	−8.13217	−	14.0853i	−0.661786	−	1.14625i	0.318359	−	0.947970i	$-0.396868\pi$
$152$	−2.44179	+	1.40977i	−0.198056	+	0.114347i
$153$	−5.13120	−	6.56257i	−0.414833	−	0.530553i
$154$	3.21362	+	10.3768i	0.258961	+	0.836187i
$155$	−2.14911	+	8.43991i	−0.172620	+	0.677910i
$156$	2.19057	+	6.35800i	0.175386	+	0.509047i
$157$		−	20.2586i		−	1.61681i	−0.588625	−	0.808406i	$-0.700331\pi$
$157$		−	20.2586i		−	1.61681i	0.588625	−	0.808406i	$-0.299669\pi$
$158$			6.02746i			0.479519i
$159$	5.51209	−	6.34334i	0.437137	−	0.503059i
$160$	2.16692	+	0.551777i	0.171310	+	0.0436218i
$161$	10.6505	−	11.5044i	0.839373	−	0.906674i
$162$	−6.24707	+	6.47874i	−0.490816	+	0.509018i
$163$	−6.81431	+	3.93424i	−0.533738	+	0.308154i	−0.742537	−	0.669805i	$-0.766378\pi$
$163$	−6.81431	+	3.93424i	−0.533738	+	0.308154i	0.208799	+	0.977958i	$0.433044\pi$
$164$	3.43052	+	5.94183i	0.267878	+	0.463979i
$165$	1.30982	+	15.8478i	0.101969	+	1.23375i
$166$	7.74967	−	13.4228i	0.601491	−	1.04181i
$167$	−18.3747	+	10.6086i	−1.42187	+	0.820919i	−0.996459	−	0.0840795i	$-0.973205\pi$
$167$	−18.3747	+	10.6086i	−1.42187	+	0.820919i	−0.425415	+	0.904999i	$0.639872\pi$
$168$	1.84795	−	4.19346i	0.142573	−	0.323532i
$169$	1.03712	−	1.79635i	0.0797788	−	0.138181i
$170$	4.44491	+	4.33549i	0.340909	+	0.332517i
$171$	1.18035	+	8.37586i	0.0902637	+	0.640518i
$172$	1.08691	+	0.627530i	0.0828764	+	0.0478487i
$173$			4.93214i			0.374984i	0.982266	+	0.187492i	$0.0600358\pi$
$173$			4.93214i			0.374984i	−0.982266	+	0.187492i	$0.939964\pi$
$174$	5.36436	−	6.17333i	0.406671	−	0.467999i
$175$	8.74220	−	9.92844i	0.660848	−	0.750519i
$176$	−2.05292	−	3.55576i	−0.154745	−	0.268026i
$177$	4.12089	−	21.2214i	0.309745	−	1.59509i
$178$	−6.38786	+	3.68803i	−0.478790	+	0.276430i
$179$	−2.63272	+	4.56000i	−0.196779	+	0.340831i	−0.947482	−	0.319809i	$-0.896381\pi$
$179$	−2.63272	+	4.56000i	−0.196779	+	0.340831i	0.750703	+	0.660639i	$0.229715\pi$
$180$	3.96800	−	5.40879i	0.295757	−	0.403147i
$181$	20.1029			1.49423			0.747117	−	0.664692i	$-0.231437\pi$
$181$	20.1029			1.49423			0.747117	+	0.664692i	$0.231437\pi$
$182$	−9.81250	+	3.03886i	−0.727351	+	0.225255i
$183$	−0.359394	+	1.85077i	−0.0265671	+	0.136813i
$184$	−2.96277	+	5.13166i	−0.218418	+	0.378311i
$185$	0.249569	+	0.887037i	0.0183487	+	0.0652163i
$186$	−6.62244	−	1.28598i	−0.485580	−	0.0942929i
$187$		−	11.4012i		−	0.833737i
$188$			5.10612i			0.372402i
$189$	−9.59124	−	9.84927i	−0.697660	−	0.716429i
$190$	−1.70754	−	6.06905i	−0.123878	−	0.440295i
$191$	−2.99287			−0.216557			−0.108278	−	0.994121i	$-0.534534\pi$
$191$	−2.99287			−0.216557			−0.108278	+	0.994121i	$0.534534\pi$
$192$	−0.330172	+	1.70029i	−0.0238281	+	0.122708i
$193$			21.4412i			1.54337i	0.636003	+	0.771687i	$0.280587\pi$
$193$			21.4412i			1.54337i	−0.636003	+	0.771687i	$0.719413\pi$
$194$	2.09320	−	3.62553i	0.150283	−	0.260298i
$195$	−14.9860	+	1.23859i	−1.07317	+	0.0886972i
$196$	6.31361	+	3.02298i	0.450972	+	0.215927i
$197$			3.13660i			0.223474i	0.993738	+	0.111737i	$0.0356414\pi$
$197$			3.13660i			0.223474i	−0.993738	+	0.111737i	$0.964359\pi$
$198$	−12.1970	+	1.71884i	−0.866804	+	0.122152i
$199$	−7.45046	+	12.9046i	−0.528149	+	0.914781i	0.471313	+	0.881966i	$0.343780\pi$
$199$	−7.45046	+	12.9046i	−0.528149	+	0.914781i	−0.999461	+	0.0328145i	$0.989553\pi$
$200$	−2.39131	+	4.39109i	−0.169091	+	0.310497i
$201$	21.2992	+	4.13600i	1.50233	+	0.291731i
$202$	−10.9673	+	6.33196i	−0.771655	+	0.445515i
$203$	9.16738	+	8.48690i	0.643424	+	0.595663i
$204$	−3.15470	+	3.63044i	−0.220873	+	0.254182i
$205$	−14.7684	+	4.15509i	−1.03147	+	0.290204i
$206$	−2.18985	+	3.79293i	−0.152574	+	0.264266i
$207$	10.9496	+	14.0040i	0.761051	+	0.973349i
$208$	3.36239	−	1.94128i	0.233140	−	0.134603i
$209$	−5.78829	+	10.0256i	−0.400385	+	0.693487i
$210$	8.06723	+	6.31822i	0.556692	+	0.435998i
$211$	7.20990	+	12.4879i	0.496350	+	0.859704i	0.999991	−	0.00420922i	$-0.00133984\pi$
$211$	7.20990	+	12.4879i	0.496350	+	0.859704i	−0.503641	+	0.863913i	$0.668007\pi$
$212$	−4.20182	−	2.42592i	−0.288582	−	0.166613i
$213$	5.38804	−	27.7468i	0.369182	−	1.90118i
$214$	1.63543	+	2.83265i	0.111796	+	0.193636i
$215$	−1.95954	+	2.00900i	−0.133640	+	0.137013i
$216$	4.35945	+	2.82758i	0.296623	+	0.192392i
$217$	2.28174	−	10.0491i	0.154895	−	0.682178i
$218$	−2.87443	−	1.65955i	−0.194681	−	0.112399i
$219$	14.5775	−	16.7758i	0.985053	−	1.13360i
$220$	8.83781	−	2.48653i	0.595845	−	0.167642i
$221$	10.7812			0.725220
$222$	−0.674842	+	0.232508i	−0.0452924	+	0.0156049i
$223$	15.8455	+	9.14843i	1.06110	+	0.612624i	0.925735	−	0.378172i	$-0.123447\pi$
$223$	15.8455	+	9.14843i	1.06110	+	0.612624i	0.135361	+	0.990796i	$0.456781\pi$
$224$	−2.58008	−	0.585831i	−0.172389	−	0.0391425i
$225$	9.53097	+	11.5828i	0.635398	+	0.772185i
$226$	3.95566	+	6.85140i	0.263126	+	0.455748i
$227$	7.81588	−	4.51250i	0.518758	−	0.299505i	−0.217668	−	0.976023i	$-0.569845\pi$
$227$	7.81588	−	4.51250i	0.518758	−	0.299505i	0.736426	+	0.676518i	$0.236512\pi$
$228$	4.61723	−	1.59081i	0.305783	−	0.105354i
$229$	−8.59266	+	14.8829i	−0.567819	+	0.983492i	0.428962	+	0.903322i	$0.358879\pi$
$229$	−8.59266	+	14.8829i	−0.567819	+	0.983492i	−0.996781	+	0.0801691i	$0.974454\pi$
$230$	−9.48512	−	9.25161i	−0.625430	−	0.610033i
$231$	−2.03795	−	18.7046i	−0.134087	−	1.23067i
$232$	−4.08921	−	2.36090i	−0.268469	−	0.155001i
$233$	−4.18657	+	2.41712i	−0.274272	+	0.158351i	−0.630827	−	0.775923i	$-0.717284\pi$
$233$	−4.18657	+	2.41712i	−0.274272	+	0.158351i	0.356556	+	0.934274i	$0.383951\pi$
$234$	−1.62536	−	11.5337i	−0.106253	−	0.753982i
$235$	−11.0645	−	2.81744i	−0.721772	−	0.183789i
$236$	−12.4810			−0.812445
$237$	1.99010	−	10.2484i	0.129271	−	0.665707i
$238$	−5.39119	−	4.99101i	−0.349459	−	0.323519i
$239$	−8.08215	−	13.9987i	−0.522791	−	0.905500i	−0.999648	−	0.0265194i	$-0.991558\pi$
$239$	−8.08215	−	13.9987i	−0.522791	−	0.905500i	0.476858	−	0.878981i	$-0.341776\pi$
$240$	−3.50221	−	1.65364i	−0.226067	−	0.106742i
$241$	4.83873	+	8.38092i	0.311690	+	0.539862i	0.978728	−	0.205161i	$-0.0657717\pi$
$241$	4.83873	+	8.38092i	0.311690	+	0.539862i	−0.667039	+	0.745023i	$0.732438\pi$
$242$	−5.07312	−	2.92897i	−0.326113	−	0.188281i
$243$	12.7609	−	8.95313i	0.818614	−	0.574343i
$244$	1.08850			0.0696843
$245$	−10.0342	+	12.0131i	−0.641065	+	0.767487i
$246$	−3.87105	−	11.2355i	−0.246809	−	0.716349i
$247$	−9.48041	−	5.47352i	−0.603224	−	0.348271i
$248$			3.89489i			0.247325i
$249$	−17.6085	+	20.2640i	−1.11590	+	1.28418i
$250$	−8.19566	−	7.60468i	−0.518339	−	0.480962i
$251$	17.3945			1.09793			0.548967	−	0.835844i	$-0.315021\pi$
$251$	17.3945			1.09793			0.548967	+	0.835844i	$0.315021\pi$
$252$	−4.52662	+	6.51995i	−0.285150	+	0.410718i
$253$			24.3293i			1.52957i
$254$	7.37701			0.462875
$255$	−6.12618	−	8.83917i	−0.383636	−	0.553530i
$256$	1.00000			0.0625000
$257$	−4.02404	−	2.32328i	−0.251013	−	0.144922i	0.369215	−	0.929344i	$-0.379627\pi$
$257$	−4.02404	−	2.32328i	−0.251013	−	0.144922i	−0.620228	+	0.784422i	$0.712960\pi$
$258$	−1.64088	−	1.42585i	−0.102157	−	0.0887697i
$259$	−0.322546	−	1.04150i	−0.0200421	−	0.0647160i
$260$	2.35131	+	8.35719i	0.145822	+	0.518291i
$261$	−11.1592	+	8.72529i	−0.690739	+	0.540082i
$262$	−10.3259	−	5.96168i	−0.637938	−	0.368314i
$263$	−24.3416	+	14.0537i	−1.50097	+	0.866586i	−0.500971	+	0.865464i	$0.667024\pi$
$263$	−24.3416	+	14.0537i	−1.50097	+	0.866586i	−0.999999	+	0.00112136i	$0.999643\pi$
$264$	2.31655	+	6.72365i	0.142574	+	0.413812i
$265$	7.57524	−	7.76644i	0.465343	−	0.477088i
$266$	2.20684	+	7.12591i	0.135310	+	0.436917i
$267$	12.0789	−	4.16163i	0.739217	−	0.254688i
$268$		−	12.5268i		−	0.765195i
$269$	14.0809	−	24.3889i	0.858529	−	1.48702i	−0.0148033	−	0.999890i	$-0.504712\pi$
$269$	14.0809	−	24.3889i	0.858529	−	1.48702i	0.873332	−	0.487125i	$-0.161954\pi$
$270$	−8.53258	+	7.88639i	−0.519276	+	0.479950i
$271$	−10.1408	−	17.5644i	−0.616009	−	1.06696i	−0.990207	−	0.139610i	$-0.955415\pi$
$271$	−10.1408	−	17.5644i	−0.616009	−	1.06696i	0.374197	−	0.927349i	$-0.377918\pi$
$272$	2.40480	+	1.38841i	0.145812	+	0.0841847i
$273$	17.6874	−	1.92712i	1.07049	−	0.116635i
$274$	9.90727	+	17.1599i	0.598520	+	1.03667i
$275$	0.511612	+	20.5228i	0.0308514	+	1.23757i
$276$	6.73190	−	7.74709i	0.405212	−	0.466320i
$277$	8.86564	−	5.11858i	0.532685	−	0.307546i	−0.209424	−	0.977825i	$-0.567159\pi$
$277$	8.86564	−	5.11858i	0.532685	−	0.307546i	0.742109	+	0.670279i	$0.233826\pi$
$278$	−4.93488	+	2.84915i	−0.295974	+	0.170881i
$279$	10.8355	+	4.37309i	0.648702	+	0.261810i
$280$	2.69307	−	5.26758i	0.160942	−	0.314798i
$281$	10.5038	−	18.1931i	0.626604	−	1.08531i	−0.361625	−	0.932324i	$-0.617778\pi$
$281$	10.5038	−	18.1931i	0.626604	−	1.08531i	0.988228	−	0.152986i	$-0.0488888\pi$
$282$	1.68590	−	8.68188i	0.100394	−	0.516999i
$283$			4.88129i			0.290162i	0.989420	+	0.145081i	$0.0463443\pi$
$283$			4.88129i			0.290162i	−0.989420	+	0.145081i	$0.953656\pi$
$284$	−16.3189			−0.968346
$285$	0.899472	+	10.8829i	0.0532801	+	0.644649i
$286$	7.97058	−	13.8055i	0.471310	−	0.816334i
$287$	17.3401	−	5.37010i	1.02355	−	0.316987i
$288$	1.12278	−	2.78197i	0.0661603	−	0.163929i
$289$	−4.64463	−	8.04474i	−0.273214	−	0.473220i
$290$	7.37222	−	7.55829i	0.432912	−	0.443838i
$291$	−4.75610	+	5.47333i	−0.278807	+	0.320852i
$292$	−11.1123	−	6.41567i	−0.650296	−	0.375448i
$293$	−3.55724	+	2.05377i	−0.207816	+	0.119983i	−0.600296	−	0.799778i	$-0.704951\pi$
$293$	−3.55724	+	2.05377i	−0.207816	+	0.119983i	0.392480	+	0.919761i	$0.371617\pi$
$294$	−9.73686	−	7.22452i	−0.567865	−	0.421342i
$295$	6.88673	−	27.0454i	0.400961	−	1.57464i
$296$	0.206049	+	0.356887i	0.0119763	+	0.0207436i
$297$	21.3060	+	1.10459i	1.23630	+	0.0640950i
$298$	18.0169	+	10.4021i	1.04369	+	0.602575i
$299$	−23.0062			−1.33048
$300$	5.51574	−	6.67657i	0.318451	−	0.385472i
$301$	2.25582	−	2.43670i	0.130024	−	0.140449i
$302$	14.0853	−	8.13217i	0.810520	−	0.467954i
$303$	20.7382	−	7.14507i	1.19138	−	0.410474i
$304$	−1.40977	−	2.44179i	−0.0808559	−	0.140047i
$305$	−0.600611	+	2.35870i	−0.0343909	+	0.135059i
$306$	6.56257	−	5.13120i	0.375157	−	0.293331i
$307$		−	7.22215i		−	0.412190i	−0.978532	−	0.206095i	$-0.933924\pi$
$307$		−	7.22215i		−	0.412190i	0.978532	−	0.206095i	$-0.0660755\pi$
$308$	−10.3768	+	3.21362i	−0.591274	+	0.183113i
$309$	4.97570	−	5.72606i	0.283058	−	0.325744i
$310$	−8.43991	−	2.14911i	−0.479354	−	0.122061i
$311$	−23.2889			−1.32059			−0.660296	−	0.751005i	$-0.729569\pi$
$311$	−23.2889			−1.32059			−0.660296	+	0.751005i	$0.729569\pi$
$312$	−6.35800	+	2.19057i	−0.359951	+	0.124016i
$313$		−	18.1702i		−	1.02704i	−0.858078	−	0.513520i	$-0.828341\pi$
$313$		−	18.1702i		−	1.02704i	0.858078	−	0.513520i	$-0.171659\pi$
$314$	20.2586			1.14326
$315$	−11.6305	−	13.4064i	−0.655306	−	0.755364i
$316$	−6.02746			−0.339071
$317$		−	0.679752i		−	0.0381787i	−0.999818	−	0.0190893i	$-0.993923\pi$
$317$		−	0.679752i		−	0.0381787i	0.999818	−	0.0190893i	$-0.00607670\pi$
$318$	6.34334	+	5.51209i	0.355717	+	0.309103i
$319$	−19.3870			−1.08546
$320$	−0.551777	+	2.16692i	−0.0308453	+	0.121135i
$321$	−1.84545	−	5.35630i	−0.103003	−	0.298960i
$322$	11.5044	+	10.6505i	0.641116	+	0.593527i
$323$		−	7.82936i		−	0.435637i
$324$	−6.47874	−	6.24707i	−0.359930	−	0.347060i
$325$	−19.4068	+	0.483790i	−1.07649	+	0.0268358i
$326$	−3.93424	−	6.81431i	−0.217898	−	0.377410i
$327$	4.33943	+	3.77078i	0.239971	+	0.208525i
$328$	−5.94183	+	3.43052i	−0.328083	+	0.189419i
$329$	13.1742	+	2.99132i	0.726316	+	0.164917i
$330$	−15.8478	+	1.30982i	−0.872394	+	0.0721032i
$331$	12.7220			0.699262			0.349631	−	0.936888i	$-0.386307\pi$
$331$	12.7220			0.699262			0.349631	+	0.936888i	$0.386307\pi$
$332$	13.4228	+	7.74967i	0.736673	+	0.425318i
$333$	1.22420	−	0.172517i	0.0670855	−	0.00945388i
$334$	−10.6086	−	18.3747i	−0.580477	−	1.00542i
$335$	27.1445	+	6.91198i	1.48306	+	0.377642i
$336$	4.19346	+	1.84795i	0.228772	+	0.100814i
$337$	14.7645	−	8.52431i	0.804276	−	0.464349i	−0.0406882	−	0.999172i	$-0.512955\pi$
$337$	14.7645	−	8.52431i	0.804276	−	0.464349i	0.844964	+	0.534823i	$0.179622\pi$
$338$	1.79635	+	1.03712i	0.0977087	+	0.0564122i
$339$	−4.46362	−	12.9554i	−0.242431	−	0.703642i
$340$	−4.33549	+	4.44491i	−0.235125	+	0.241059i
$341$	7.99589	+	13.8493i	0.433002	+	0.749981i
$342$	−8.37586	+	1.18035i	−0.452915	+	0.0638261i
$343$	11.4982	−	14.5186i	0.620846	−	0.783933i
$344$	−0.627530	+	1.08691i	−0.0338342	+	0.0586025i
$345$	13.0728	+	18.8621i	0.703817	+	1.01550i
$346$	−4.93214			−0.265154
$347$		−	25.1265i		−	1.34886i	−0.738337	−	0.674431i	$-0.764389\pi$
$347$		−	25.1265i		−	1.34886i	0.738337	−	0.674431i	$-0.235611\pi$
$348$	6.17333	+	5.36436i	0.330925	+	0.287560i
$349$	4.80323	−	8.31944i	0.257111	−	0.445329i	−0.708356	−	0.705856i	$-0.750563\pi$
$349$	4.80323	−	8.31944i	0.257111	−	0.445329i	0.965467	+	0.260526i	$0.0838961\pi$
$350$	9.92844	+	8.74220i	0.530697	+	0.467290i
$351$	−1.04452	+	20.1473i	−0.0557525	+	1.07538i
$352$	3.55576	−	2.05292i	0.189523	−	0.109421i
$353$	−23.4317	+	13.5283i	−1.24715	+	0.720040i	−0.970539	−	0.240944i	$-0.922543\pi$
$353$	−23.4317	+	13.5283i	−1.24715	+	0.720040i	−0.276606	+	0.960983i	$0.589210\pi$
$354$	21.2214	+	4.12089i	1.12790	+	0.219023i
$355$	9.00437	−	35.3617i	0.477902	−	1.87680i
$356$	−3.68803	−	6.38786i	−0.195465	−	0.338556i
$357$	7.51870	+	10.2662i	0.397932	+	0.543344i
$358$	−4.56000	−	2.63272i	−0.241004	−	0.139144i
$359$	−4.43043	−	7.67373i	−0.233829	−	0.405004i	0.725103	−	0.688641i	$-0.241792\pi$
$359$	−4.43043	−	7.67373i	−0.233829	−	0.405004i	−0.958932	+	0.283637i	$0.908459\pi$
$360$	5.40879	+	3.96800i	0.285068	+	0.209132i
$361$	5.52509	−	9.56974i	0.290794	−	0.503671i
$362$			20.1029i			1.05658i
$363$	7.65871	+	6.65510i	0.401978	+	0.349302i
$364$	−3.03886	−	9.81250i	−0.159279	−	0.514315i
$365$	20.0337	−	20.5394i	1.04861	−	1.07508i
$366$	−1.85077	−	0.359394i	−0.0967414	−	0.0187858i
$367$	9.32611	−	5.38443i	0.486819	−	0.281065i	−0.236435	−	0.971647i	$-0.575979\pi$
$367$	9.32611	−	5.38443i	0.486819	−	0.281065i	0.723254	+	0.690582i	$0.242646\pi$
$368$	−5.13166	−	2.96277i	−0.267506	−	0.154445i
$369$	2.87225	+	20.3817i	0.149523	+	1.06103i
$370$	−0.887037	+	0.249569i	−0.0461149	+	0.0129745i
$371$	−8.72062	+	9.41984i	−0.452752	+	0.489054i
$372$	1.28598	−	6.62244i	0.0666751	−	0.343357i
$373$	−4.25812	−	2.45843i	−0.220477	−	0.127293i	0.385694	−	0.922627i	$-0.373962\pi$
$373$	−4.25812	−	2.45843i	−0.220477	−	0.127293i	−0.606171	+	0.795334i	$0.707295\pi$
$374$	11.4012			0.589541
$375$	11.4241	+	15.6361i	0.589940	+	0.807447i
$376$	−5.10612			−0.263328
$377$		−	18.3327i		−	0.944181i
$378$	9.84927	−	9.59124i	0.506592	−	0.493320i
$379$	36.3873			1.86909			0.934544	−	0.355848i	$-0.115808\pi$
$379$	36.3873			1.86909			0.934544	+	0.355848i	$0.115808\pi$
$380$	6.06905	−	1.70754i	0.311336	−	0.0875947i
$381$	−12.5431	−	2.43569i	−0.642600	−	0.124784i
$382$		−	2.99287i		−	0.153129i
$383$	8.10908	+	4.68178i	0.414355	+	0.239228i	0.692659	−	0.721265i	$-0.256439\pi$
$383$	8.10908	+	4.68178i	0.414355	+	0.239228i	−0.278304	+	0.960493i	$0.589772\pi$
$384$	−1.70029	−	0.330172i	−0.0867676	−	0.0168490i
$385$	−1.23798	−	24.2589i	−0.0630932	−	1.23635i
$386$	−21.4412			−1.09133
$387$	2.31919	+	2.96613i	0.117891	+	0.150777i
$388$	3.62553	+	2.09320i	0.184058	+	0.106266i
$389$	1.02428	+	1.77411i	0.0519332	+	0.0899509i	0.890823	−	0.454350i	$-0.150128\pi$
$389$	1.02428	+	1.77411i	0.0519332	+	0.0899509i	−0.838890	+	0.544301i	$0.816795\pi$
$390$	−1.23859	−	14.9860i	−0.0627184	−	0.758845i
$391$	−8.22707	−	14.2497i	−0.416061	−	0.720639i
$392$	−3.02298	+	6.31361i	−0.152683	+	0.318885i
$393$	15.5887	+	13.5459i	0.786346	+	0.683301i
$394$	−3.13660			−0.158020
$395$	3.32581	−	13.0610i	0.167340	−	0.657171i
$396$	−1.71884	−	12.1970i	−0.0863748	−	0.612923i
$397$	−25.1640	+	14.5284i	−1.26294	+	0.729161i	−0.973643	−	0.228077i	$-0.926756\pi$
$397$	−25.1640	+	14.5284i	−1.26294	+	0.729161i	−0.289302	+	0.957238i	$0.593423\pi$
$398$	−12.9046	−	7.45046i	−0.646848	−	0.373458i
$399$	−1.39949	−	12.8447i	−0.0700622	−	0.643042i
$400$	−4.39109	−	2.39131i	−0.219554	−	0.119566i
$401$	10.0005	−	17.3213i	0.499399	−	0.864985i	−0.500601	−	0.865678i	$-0.666887\pi$
$401$	10.0005	−	17.3213i	0.499399	−	0.864985i	1.00000		0.000693636i	$0.000220791\pi$
$402$	−4.13600	+	21.2992i	−0.206285	+	1.06231i
$403$	−13.0961	+	7.56106i	−0.652365	+	0.376643i
$404$	−6.33196	−	10.9673i	−0.315027	−	0.545642i
$405$	17.1117	−	10.5919i	0.850288	−	0.526317i
$406$	−8.48690	+	9.16738i	−0.421198	+	0.454969i
$407$	1.46532	+	0.846003i	0.0726332	+	0.0419348i
$408$	−3.63044	−	3.15470i	−0.179733	−	0.156181i
$409$	−21.0715			−1.04192			−0.520959	−	0.853582i	$-0.674426\pi$
$409$	−21.0715			−1.04192			−0.520959	+	0.853582i	$0.674426\pi$
$410$	−4.15509	−	14.7684i	−0.205205	−	0.729357i
$411$	−11.1795	−	32.4479i	−0.551444	−	1.60054i
$412$	−3.79293	−	2.18985i	−0.186864	−	0.107886i
$413$	−7.31176	+	32.2020i	−0.359788	+	1.58456i
$414$	−14.0040	+	10.9496i	−0.688261	+	0.538144i
$415$	−24.1993	+	24.8101i	−1.18790	+	1.21788i
$416$	1.94128	+	3.36239i	0.0951790	+	0.164855i
$417$	9.33143	−	3.21503i	0.456962	−	0.157440i
$418$	−10.0256	−	5.78829i	−0.490369	−	0.283115i
$419$	−10.8551	−	18.8016i	−0.530306	−	0.918517i	−0.999375	−	0.0353551i	$-0.988744\pi$
$419$	−10.8551	−	18.8016i	−0.530306	−	0.918517i	0.469069	−	0.883162i	$-0.344590\pi$
$420$	−6.31822	+	8.06723i	−0.308297	+	0.393640i
$421$	−10.3520	+	17.9301i	−0.504524	+	0.873861i	0.495463	+	0.868629i	$0.334999\pi$
$421$	−10.3520	+	17.9301i	−0.504524	+	0.873861i	−0.999986	+	0.00523148i	$0.998335\pi$
$422$	−12.4879	+	7.20990i	−0.607902	+	0.350973i
$423$	−5.73304	+	14.2051i	−0.278750	+	0.690675i
$424$	2.42592	−	4.20182i	0.117813	−	0.204058i
$425$	−7.23955	−	11.8472i	−0.351170	−	0.574676i
$426$	27.7468	+	5.38804i	1.34434	+	0.261051i
$427$	0.637678	−	2.80842i	0.0308594	−	0.135909i
$428$	−2.83265	+	1.63543i	−0.136921	+	0.0790516i
$429$	−18.1105	+	20.8416i	−0.874382	+	1.00624i
$430$	−2.00900	−	1.95954i	−0.0968826	−	0.0944975i
$431$	−1.15807	+	2.00583i	−0.0557821	+	0.0966174i	−0.892568	−	0.450913i	$-0.851099\pi$
$431$	−1.15807	+	2.00583i	−0.0557821	+	0.0966174i	0.836786	+	0.547530i	$0.184432\pi$
$432$	−2.82758	+	4.35945i	−0.136042	+	0.209744i
$433$			22.2752i			1.07048i	0.844701	+	0.535238i	$0.179778\pi$
$433$			22.2752i			1.07048i	−0.844701	+	0.535238i	$0.820222\pi$
$434$	10.0491	+	2.28174i	0.482373	+	0.109527i
$435$	−15.0304	+	10.4172i	−0.720655	+	0.499466i
$436$	1.65955	−	2.87443i	0.0794782	−	0.137660i
$437$			16.7073i			0.799218i
$438$	16.7758	+	14.5775i	0.801578	+	0.696538i
$439$	20.7548			0.990575			0.495287	−	0.868729i	$-0.335063\pi$
$439$	20.7548			0.990575			0.495287	+	0.868729i	$0.335063\pi$
$440$	2.48653	+	8.83781i	0.118541	+	0.421326i
$441$	14.1701	+	15.4986i	0.674769	+	0.738029i
$442$			10.7812i			0.512808i
$443$			18.7632i			0.891467i	0.895166	+	0.445733i	$0.147057\pi$
$443$			18.7632i			0.891467i	−0.895166	+	0.445733i	$0.852943\pi$
$444$	−0.232508	−	0.674842i	−0.0110344	−	0.0320266i
$445$	15.8770	−	4.46700i	0.752640	−	0.211756i
$446$	−9.14843	+	15.8455i	−0.433191	+	0.750308i
$447$	−27.1995	−	23.6352i	−1.28649	−	1.11791i
$448$	0.585831	−	2.58008i	0.0276779	−	0.121897i
$449$	4.33662			0.204658			0.102329	−	0.994751i	$-0.467371\pi$
$449$	4.33662			0.204658			0.102329	+	0.994751i	$0.467371\pi$
$450$	−11.5828	+	9.53097i	−0.546017	+	0.449294i
$451$	−14.0852	+	24.3962i	−0.663244	+	1.14877i
$452$	−6.85140	+	3.95566i	−0.322263	+	0.186059i
$453$	−26.6342	+	9.17646i	−1.25138	+	0.431148i
$454$	4.51250	+	7.81588i	0.211782	+	0.366817i
$455$	22.9397	−	1.17065i	1.07543	−	0.0548811i
$456$	1.59081	+	4.61723i	0.0744963	+	0.216221i
$457$		−	22.7169i		−	1.06265i	−0.847168	−	0.531325i	$-0.821694\pi$
$457$		−	22.7169i		−	1.06265i	0.847168	−	0.531325i	$-0.178306\pi$
$458$	−14.8829	−	8.59266i	−0.695434	−	0.401509i
$459$	−12.8525	+	6.55775i	−0.599901	+	0.306090i
$460$	9.25161	−	9.48512i	0.431358	−	0.442246i
$461$	8.41648	−	14.5778i	0.391995	−	0.678955i	−0.600718	−	0.799461i	$-0.705118\pi$
$461$	8.41648	−	14.5778i	0.391995	−	0.678955i	0.992713	+	0.120506i	$0.0384518\pi$
$462$	18.7046	−	2.03795i	0.870218	−	0.0948141i
$463$	−24.0438	+	13.8817i	−1.11741	+	0.645138i	−0.940739	−	0.339132i	$-0.889867\pi$
$463$	−24.0438	+	13.8817i	−1.11741	+	0.645138i	−0.176673	+	0.984270i	$0.556533\pi$
$464$	2.36090	−	4.08921i	0.109602	−	0.189837i
$465$	13.6407	+	6.44073i	0.632573	+	0.298682i
$466$	−2.41712	−	4.18657i	−0.111971	−	0.193939i
$467$	−29.8191	+	17.2161i	−1.37986	+	0.796665i	−0.992143	−	0.125112i	$-0.960071\pi$
$467$	−29.8191	+	17.2161i	−1.37986	+	0.796665i	−0.387721	+	0.921777i	$0.626738\pi$
$468$	11.5337	−	1.62536i	0.533146	−	0.0751325i
$469$	−32.3201	−	7.33857i	−1.49240	−	0.338864i
$470$	2.81744	−	11.0645i	0.129959	−	0.510370i
$471$	−34.4455	−	6.68883i	−1.58716	−	0.308205i
$472$		−	12.4810i		−	0.574486i
$473$			5.15308i			0.236939i
$474$	10.2484	+	1.99010i	0.470726	+	0.0914083i
$475$	0.351332	+	14.0933i	0.0161202	+	0.646646i
$476$	4.99101	−	5.39119i	0.228763	−	0.247105i
$477$	−8.96557	−	11.4665i	−0.410505	−	0.525017i
$478$	13.9987	−	8.08215i	0.640285	−	0.369669i
$479$	5.64351	+	9.77485i	0.257859	+	0.446624i	0.965668	−	0.259779i	$-0.0836498\pi$
$479$	5.64351	+	9.77485i	0.257859	+	0.446624i	−0.707809	+	0.706403i	$0.750316\pi$
$480$	1.65364	−	3.50221i	0.0754779	−	0.159853i
$481$	−0.799995	+	1.38563i	−0.0364766	+	0.0631794i
$482$	−8.38092	+	4.83873i	−0.381740	+	0.220398i
$483$	−16.0443	−	21.9073i	−0.730043	−	0.996817i
$484$	2.92897	−	5.07312i	0.133135	−	0.230596i
$485$	−6.53628	+	6.70125i	−0.296797	+	0.304288i
$486$	8.95313	+	12.7609i	0.406122	+	0.578848i
$487$	−21.2703	−	12.2804i	−0.963848	−	0.556478i	−0.0664931	−	0.997787i	$-0.521181\pi$
$487$	−21.2703	−	12.2804i	−0.963848	−	0.556478i	−0.897355	+	0.441309i	$0.854514\pi$
$488$			1.08850i			0.0492742i
$489$	4.43946	+	12.8853i	0.200759	+	0.582692i
$490$	−12.0131	−	10.0342i	−0.542695	−	0.453301i
$491$	−9.08350	−	15.7331i	−0.409933	−	0.710024i	0.584949	−	0.811070i	$-0.301115\pi$
$491$	−9.08350	−	15.7331i	−0.409933	−	0.710024i	−0.994882	+	0.101046i	$0.967781\pi$
$492$	11.2355	−	3.87105i	0.506535	−	0.174520i
$493$	11.3550	−	6.55581i	0.511403	−	0.295259i
$494$	5.47352	−	9.48041i	0.246265	−	0.426544i
$495$	27.3784	+	3.00544i	1.23057	+	0.135084i
$496$	−3.89489			−0.174886
$497$	−9.56009	+	42.1039i	−0.428829	+	1.88862i
$498$	−20.2640	−	17.6085i	−0.908050	−	0.789057i
$499$	5.69190	−	9.85866i	0.254805	−	0.441334i	−0.710038	−	0.704164i	$-0.751322\pi$
$499$	5.69190	−	9.85866i	0.254805	−	0.441334i	0.964842	+	0.262829i	$0.0846555\pi$
$500$	7.60468	−	8.19566i	0.340092	−	0.366521i
$501$	11.9709	+	34.7449i	0.534821	+	1.55229i
$502$			17.3945i			0.776357i
$503$		−	7.11598i		−	0.317286i	−0.987336	−	0.158643i	$-0.949288\pi$
$503$		−	7.11598i		−	0.317286i	0.987336	−	0.158643i	$-0.0507118\pi$
$504$	−6.51995	−	4.52662i	−0.290422	−	0.201632i
$505$	27.2590	−	7.66936i	1.21301	−	0.341282i
$506$	−24.3293			−1.08157
$507$	−2.71189	−	2.35652i	−0.120439	−	0.104657i
$508$			7.37701i			0.327302i
$509$	−12.2001	+	21.1313i	−0.540762	+	0.936627i	0.458099	+	0.888901i	$0.348531\pi$
$509$	−12.2001	+	21.1313i	−0.540762	+	0.936627i	−0.998860	+	0.0477257i	$0.984803\pi$
$510$	8.83917	−	6.12618i	0.391405	−	0.271272i
$511$	−23.0628	+	24.9120i	−1.02024	+	1.10204i
$512$			1.00000i			0.0441942i
$513$	14.6311	+	0.758540i	0.645980	+	0.0334904i
$514$	2.32328	−	4.02404i	0.102476	−	0.177493i
$515$	6.83809	−	7.01068i	0.301322	−	0.308927i
$516$	1.42585	−	1.64088i	0.0627697	−	0.0722356i
$517$	−18.1561	+	10.4825i	−0.798506	+	0.461018i
$518$	1.04150	−	0.322546i	0.0457611	−	0.0141719i
$519$	8.38607	+	1.62846i	0.368108	+	0.0714813i
$520$	−8.35719	+	2.35131i	−0.366487	+	0.103112i
$521$	−10.6836	+	18.5046i	−0.468058	+	0.810701i	−0.999334	−	0.0364984i	$-0.988380\pi$
$521$	−10.6836	+	18.5046i	−0.468058	+	0.810701i	0.531275	+	0.847199i	$0.321713\pi$
$522$	−8.72529	−	11.1592i	−0.381895	−	0.488427i
$523$	22.4124	−	12.9398i	0.980028	−	0.565819i	0.0777491	−	0.996973i	$-0.475227\pi$
$523$	22.4124	−	12.9398i	0.980028	−	0.565819i	0.902278	+	0.431154i	$0.141893\pi$
$524$	5.96168	−	10.3259i	0.260437	−	0.451090i
$525$	−13.9948	−	18.1424i	−0.610783	−	0.791798i
$526$	−14.0537	−	24.3416i	−0.612769	−	1.06135i
$527$	−9.36641	−	5.40770i	−0.408007	−	0.235563i
$528$	−6.72365	+	2.31655i	−0.292609	+	0.100815i
$529$	6.05597	+	10.4892i	0.263303	+	0.456054i
$530$	7.76644	+	7.57524i	0.337352	+	0.329047i
$531$	−34.7219	−	14.0134i	−1.50680	−	0.608130i
$532$	−7.12591	+	2.20684i	−0.308947	+	0.0956787i
$533$	−23.0695	−	13.3192i	−0.999251	−	0.576918i
$534$	4.16163	+	12.0789i	0.180091	+	0.522705i
$535$	−1.98086	−	7.04052i	−0.0856400	−	0.304388i
$536$	12.5268			0.541075
$537$	6.88408	+	5.98197i	0.297070	+	0.258141i
$538$	24.3889	+	14.0809i	1.05148	+	0.607072i
$539$	2.21234	+	28.6556i	0.0952922	+	1.23428i
$540$	−7.88639	−	8.53258i	−0.339376	−	0.367184i
$541$	−18.0736	−	31.3045i	−0.777047	−	1.34588i	−0.933637	−	0.358221i	$-0.883384\pi$
$541$	−18.0736	−	31.3045i	−0.777047	−	1.34588i	0.156590	−	0.987664i	$-0.449950\pi$
$542$	17.5644	−	10.1408i	0.754454	−	0.435584i
$543$	6.63741	−	34.1807i	0.284839	−	1.46683i
$544$	−1.38841	+	2.40480i	−0.0595276	+	0.103105i
$545$	5.31296	+	5.18216i	0.227582	+	0.221979i
$546$	1.92712	+	17.6874i	0.0824733	+	0.756952i
$547$	8.13044	+	4.69411i	0.347633	+	0.200706i	0.663642	−	0.748050i	$-0.269010\pi$
$547$	8.13044	+	4.69411i	0.347633	+	0.200706i	−0.316010	+	0.948756i	$0.602343\pi$
$548$	−17.1599	+	9.90727i	−0.733034	+	0.423218i
$549$	3.02819	+	1.22215i	0.129240	+	0.0521600i
$550$	−20.5228	+	0.511612i	−0.875096	+	0.0218152i
$551$	−13.3133			−0.567167
$552$	7.74709	+	6.73190i	0.329738	+	0.286528i
$553$	−3.53107	+	15.5513i	−0.150156	+	0.661309i
$554$	5.11858	+	8.86564i	0.217468	+	0.376665i
$555$	1.59062	−	0.131465i	0.0675181	−	0.00558036i
$556$	−2.84915	−	4.93488i	−0.120831	−	0.209285i
$557$	18.3702	+	10.6060i	0.778370	+	0.449392i	0.835852	−	0.548955i	$-0.184974\pi$
$557$	18.3702	+	10.6060i	0.778370	+	0.449392i	−0.0574826	+	0.998347i	$0.518307\pi$
$558$	−4.37309	+	10.8355i	−0.185128	+	0.458702i
$559$	−4.87284			−0.206099
$560$	5.26758	+	2.69307i	0.222596	+	0.113803i
$561$	−19.3853	−	3.76436i	−0.818449	−	0.158931i
$562$	18.1931	+	10.5038i	0.767429	+	0.443076i
$563$			22.5552i			0.950588i	0.879827	+	0.475294i	$0.157658\pi$
$563$			22.5552i			0.950588i	−0.879827	+	0.475294i	$0.842342\pi$
$564$	8.68188	+	1.68590i	0.365573	+	0.0709892i
$565$	−4.79115	−	17.0291i	−0.201565	−	0.716419i
$566$	−4.88129			−0.205176
$567$	−19.9134	+	13.0559i	−0.836283	+	0.548298i
$568$		−	16.3189i		−	0.684724i
$569$	9.13134			0.382806			0.191403	−	0.981512i	$-0.438696\pi$
$569$	9.13134			0.382806			0.191403	+	0.981512i	$0.438696\pi$
$570$	−10.8829	+	0.899472i	−0.455836	+	0.0376747i
$571$	43.9976			1.84124			0.920621	−	0.390457i	$-0.127683\pi$
$571$	43.9976			1.84124			0.920621	+	0.390457i	$0.127683\pi$
$572$	13.8055	+	7.97058i	0.577235	+	0.333267i
$573$	−0.988163	+	5.08875i	−0.0412811	+	0.212585i
$574$	5.37010	+	17.3401i	0.224144	+	0.723761i
$575$	15.4487	+	25.2812i	0.644254	+	1.05430i
$576$	2.78197	+	1.12278i	0.115916	+	0.0467824i
$577$	16.2964	+	9.40875i	0.678429	+	0.391691i	0.799263	−	0.600981i	$-0.205223\pi$
$577$	16.2964	+	9.40875i	0.678429	+	0.391691i	−0.120834	+	0.992673i	$0.538557\pi$
$578$	8.04474	−	4.64463i	0.334617	−	0.193191i
$579$	36.4563	+	7.07930i	1.51507	+	0.294206i
$580$	7.55829	+	7.37222i	0.313841	+	0.306115i
$581$	27.8582	−	30.0919i	1.15575	−	1.24842i
$582$	−5.47333	−	4.75610i	−0.226877	−	0.197147i
$583$		−	19.9209i		−	0.825039i
$584$	6.41567	−	11.1123i	0.265482	−	0.459828i
$585$	−2.84200	+	25.8895i	−0.117502	+	1.07040i
$586$	−2.05377	−	3.55724i	−0.0848405	−	0.146948i
$587$	13.2631	+	7.65744i	0.547426	+	0.316056i	0.748083	−	0.663605i	$-0.230974\pi$
$587$	13.2631	+	7.65744i	0.547426	+	0.316056i	−0.200657	+	0.979661i	$0.564308\pi$
$588$	7.22452	−	9.73686i	0.297934	−	0.401541i
$589$	5.49090	+	9.51051i	0.226248	+	0.391874i
$590$	27.0454	+	6.88673i	1.11344	+	0.283522i
$591$	5.33313	+	1.03562i	0.219376	+	0.0425997i
$592$	−0.356887	+	0.206049i	−0.0146679	+	0.00846854i
$593$	18.6589	−	10.7727i	0.766231	−	0.442384i	−0.0652975	−	0.997866i	$-0.520800\pi$
$593$	18.6589	−	10.7727i	0.766231	−	0.442384i	0.831528	+	0.555482i	$0.187466\pi$
$594$	−1.10459	+	21.3060i	−0.0453220	+	0.874194i
$595$	8.92836	+	13.7899i	0.366027	+	0.565329i
$596$	−10.4021	+	18.0169i	−0.426085	+	0.738000i
$597$	19.4816	+	16.9287i	0.797328	+	0.692844i
$598$		−	23.0062i		−	0.940794i
$599$	−37.8675			−1.54722			−0.773612	−	0.633659i	$-0.781552\pi$
$599$	−37.8675			−1.54722			−0.773612	+	0.633659i	$0.781552\pi$
$600$	6.67657	+	5.51574i	0.272570	+	0.225179i
$601$	−16.2700	+	28.1804i	−0.663666	+	1.14950i	0.315979	+	0.948766i	$0.397667\pi$
$601$	−16.2700	+	28.1804i	−0.663666	+	1.14950i	−0.979645	+	0.200737i	$0.935666\pi$
$602$	2.43670	+	2.25582i	0.0993124	+	0.0919405i
$603$	14.0648	−	34.8492i	0.572763	−	1.41917i
$604$	8.13217	+	14.0853i	0.330893	+	0.573124i
$605$	9.37691	+	9.14607i	0.381226	+	0.371840i
$606$	7.14507	+	20.7382i	0.290249	+	0.842431i
$607$	28.9715	+	16.7267i	1.17592	+	0.678916i	0.955067	−	0.296391i	$-0.0957833\pi$
$607$	28.9715	+	16.7267i	1.17592	+	0.678916i	0.220851	+	0.975308i	$0.429117\pi$
$608$	2.44179	−	1.40977i	0.0990278	−	0.0571737i
$609$	17.4570	−	12.7851i	0.707393	−	0.518077i
$610$	−2.35870	−	0.600611i	−0.0955010	−	0.0243180i
$611$	−9.91240	−	17.1688i	−0.401013	−	0.694574i
$612$	5.13120	+	6.56257i	0.207417	+	0.265276i
$613$	−14.1077	−	8.14510i	−0.569806	−	0.328978i	0.187266	−	0.982309i	$-0.440037\pi$
$613$	−14.1077	−	8.14510i	−0.569806	−	0.328978i	−0.757072	+	0.653332i	$0.773371\pi$
$614$	7.22215			0.291462
$615$	2.18876	+	26.4824i	0.0882595	+	1.06787i
$616$	−3.21362	−	10.3768i	−0.129480	−	0.418094i
$617$	3.39147	−	1.95807i	0.136536	−	0.0788289i	−0.430176	−	0.902745i	$-0.641549\pi$
$617$	3.39147	−	1.95807i	0.136536	−	0.0788289i	0.566712	+	0.823916i	$0.308215\pi$
$618$	5.72606	+	4.97570i	0.230336	+	0.200152i
$619$	11.5743	+	20.0474i	0.465212	+	0.805771i	0.999211	−	0.0397140i	$-0.0126447\pi$
$619$	11.5743	+	20.0474i	0.465212	+	0.805771i	−0.533999	+	0.845485i	$0.679311\pi$
$620$	2.14911	−	8.43991i	0.0863102	−	0.338955i
$621$	27.4262	−	13.9938i	1.10058	−	0.561551i
$622$		−	23.2889i		−	0.933800i
$623$	−18.6417	+	5.77321i	−0.746866	+	0.231299i
$624$	−2.19057	−	6.35800i	−0.0876929	−	0.254524i
$625$	13.5633	+	21.0009i	0.542530	+	0.840036i
$626$	18.1702			0.726227
$627$	15.1353	+	13.1520i	0.604447	+	0.525239i
$628$			20.2586i			0.808406i
$629$	−1.14432			−0.0456270
$630$	13.4064	−	11.6305i	0.534123	−	0.463371i
$631$	29.9516			1.19235			0.596177	−	0.802853i	$-0.296686\pi$
$631$	29.9516			1.19235			0.596177	+	0.802853i	$0.296686\pi$
$632$		−	6.02746i		−	0.239759i
$633$	23.6136	−	8.13576i	0.938556	−	0.323367i
$634$	0.679752			0.0269964
$635$	−15.9854	−	4.07046i	−0.634361	−	0.161531i
$636$	−5.51209	+	6.34334i	−0.218569	+	0.251530i
$637$	−27.0973	+	2.09203i	−1.07363	+	0.0828892i
$638$		−	19.3870i		−	0.767538i
$639$	−45.3986	−	18.3225i	−1.79594	−	0.724825i
$640$	−2.16692	−	0.551777i	−0.0856550	−	0.0218109i
$641$	7.38355	+	12.7887i	0.291633	+	0.505123i	0.974196	−	0.225704i	$-0.0724682\pi$
$641$	7.38355	+	12.7887i	0.291633	+	0.505123i	−0.682563	+	0.730827i	$0.739135\pi$
$642$	5.35630	−	1.84545i	0.211396	−	0.0728339i
$643$	6.76719	−	3.90704i	0.266872	−	0.154078i	−0.360593	−	0.932723i	$-0.617426\pi$
$643$	6.76719	−	3.90704i	0.266872	−	0.154078i	0.627465	+	0.778645i	$0.284092\pi$
$644$	−10.6505	+	11.5044i	−0.419687	+	0.453337i
$645$	2.76890	+	3.99511i	0.109025	+	0.157307i
$646$	7.82936			0.308042
$647$	−21.1027	−	12.1837i	−0.829634	−	0.478989i	0.0240933	−	0.999710i	$-0.492330\pi$
$647$	−21.1027	−	12.1837i	−0.829634	−	0.478989i	−0.853727	+	0.520720i	$0.825663\pi$
$648$	6.24707	−	6.47874i	0.245408	−	0.254509i
$649$	−25.6225	−	44.3795i	−1.00577	−	1.74205i
$650$	−0.483790	−	19.4068i	−0.0189758	−	0.761196i
$651$	−16.3330	−	7.19756i	−0.640142	−	0.282095i
$652$	6.81431	−	3.93424i	0.266869	−	0.154077i
$653$	−17.7518	−	10.2490i	−0.694680	−	0.401074i	0.110683	−	0.993856i	$-0.464696\pi$
$653$	−17.7518	−	10.2490i	−0.694680	−	0.401074i	−0.805363	+	0.592782i	$0.798030\pi$
$654$	−3.77078	+	4.33943i	−0.147449	+	0.169685i
$655$	19.0859	+	18.6161i	0.745750	+	0.727391i
$656$	−3.43052	−	5.94183i	−0.133939	−	0.231990i
$657$	−23.7106	−	30.3248i	−0.925040	−	1.18308i
$658$	−2.99132	+	13.1742i	−0.116614	+	0.513583i
$659$	−5.19823	+	9.00360i	−0.202494	+	0.350731i	−0.949332	−	0.314276i	$-0.898238\pi$
$659$	−5.19823	+	9.00360i	−0.202494	+	0.350731i	0.746837	+	0.665007i	$0.231571\pi$
$660$	−1.30982	−	15.8478i	−0.0509846	−	0.616876i
$661$	−25.7189			−1.00035			−0.500174	−	0.865925i	$-0.666731\pi$
$661$	−25.7189			−1.00035			−0.500174	+	0.865925i	$0.666731\pi$
$662$			12.7220i			0.494453i
$663$	3.55964	−	18.3311i	0.138245	−	0.711921i
$664$	−7.74967	+	13.4228i	−0.300745	+	0.520906i
$665$	−0.850138	−	16.6590i	−0.0329669	−	0.646006i
$666$	0.172517	+	1.22420i	0.00668490	+	0.0474366i
$667$	−24.2307	+	13.9896i	−0.938217	+	0.541680i
$668$	18.3747	−	10.6086i	0.710937	−	0.410460i
$669$	20.7867	−	23.9215i	0.803662	−	0.924857i
$670$	−6.91198	+	27.1445i	−0.267033	+	1.04868i
$671$	2.23461	+	3.87046i	0.0862662	+	0.149417i
$672$	−1.84795	+	4.19346i	−0.0712863	+	0.161766i
$673$	12.4068	+	7.16309i	0.478248	+	0.276117i	0.719686	−	0.694300i	$-0.244286\pi$
$673$	12.4068	+	7.16309i	0.478248	+	0.276117i	−0.241438	+	0.970416i	$0.577619\pi$
$674$	8.52431	+	14.7645i	0.328344	+	0.568709i
$675$	22.8409	−	12.3811i	0.879148	−	0.476549i
$676$	−1.03712	+	1.79635i	−0.0398894	+	0.0690905i
$677$		−	0.895442i		−	0.0344146i	−0.999852	−	0.0172073i	$-0.994522\pi$
$677$		−	0.895442i		−	0.0344146i	0.999852	−	0.0172073i	$-0.00547753\pi$
$678$	12.9554	−	4.46362i	0.497550	−	0.171424i
$679$	7.52456	−	8.12789i	0.288766	−	0.311920i
$680$	−4.44491	−	4.33549i	−0.170455	−	0.166258i
$681$	−5.09197	−	14.7792i	−0.195125	−	0.566339i
$682$	−13.8493	+	7.99589i	−0.530317	+	0.306179i
$683$	−17.0207	−	9.82692i	−0.651280	−	0.376016i	0.137667	−	0.990479i	$-0.456040\pi$
$683$	−17.0207	−	9.82692i	−0.651280	−	0.376016i	−0.788946	+	0.614462i	$0.789373\pi$
$684$	−1.18035	−	8.37586i	−0.0451318	−	0.320259i
$685$	−11.9998	−	42.6507i	−0.458490	−	1.62960i
$686$	14.5186	+	11.4982i	0.554324	+	0.439004i
$687$	22.4682	+	19.5240i	0.857217	+	0.744885i
$688$	−1.08691	−	0.627530i	−0.0414382	−	0.0239244i
$689$	18.8375			0.717653
$690$	−18.8621	+	13.0728i	−0.718069	+	0.497674i
$691$	19.3254			0.735171			0.367586	−	0.929990i	$-0.380184\pi$
$691$	19.3254			0.735171			0.367586	+	0.929990i	$0.380184\pi$
$692$		−	4.93214i		−	0.187492i
$693$	−32.4762	−	2.71065i	−1.23367	−	0.102969i
$694$	25.1265			0.953790
$695$	12.2656	−	3.45094i	0.465260	−	0.130901i
$696$	−5.36436	+	6.17333i	−0.203336	+	0.233999i
$697$		−	19.0519i		−	0.721641i
$698$	8.31944	+	4.80323i	0.314895	+	0.181805i
$699$	2.72751	+	7.91645i	0.103164	+	0.299428i
$700$	−8.74220	+	9.92844i	−0.330424	+	0.375260i
$701$	−37.8106			−1.42809			−0.714044	−	0.700101i	$-0.753138\pi$
$701$	−37.8106			−1.42809			−0.714044	+	0.700101i	$0.753138\pi$
$702$	−20.1473	−	1.04452i	−0.760411	−	0.0394230i
$703$	1.00626	+	0.580962i	0.0379517	+	0.0219114i
$704$	2.05292	+	3.55576i	0.0773724	+	0.134013i
$705$	−8.44367	+	17.8827i	−0.318007	+	0.673502i
$706$	−13.5283	−	23.4317i	−0.509145	−	0.881865i
$707$	−32.0059	+	9.91198i	−1.20370	+	0.372778i
$708$	−4.12089	+	21.2214i	−0.154872	+	0.797547i
$709$	43.4760			1.63277			0.816387	−	0.577505i	$-0.195974\pi$
$709$	43.4760			1.63277			0.816387	+	0.577505i	$0.195974\pi$
$710$	35.3617	+	9.00437i	1.32710	+	0.337928i
$711$	−16.7682	−	6.76749i	−0.628857	−	0.253801i
$712$	6.38786	−	3.68803i	0.239395	−	0.138215i
$713$	19.9872	+	11.5396i	0.748528	+	0.432163i
$714$	−10.2662	+	7.51870i	−0.384202	+	0.281380i
$715$	−24.8891	+	25.5173i	−0.930801	+	0.954294i
$716$	2.63272	−	4.56000i	0.0983894	−	0.170415i
$717$	−26.4703	+	9.12001i	−0.988553	+	0.340593i
$718$	7.67373	−	4.43043i	0.286381	−	0.165342i
$719$	14.5195	+	25.1485i	0.541486	+	0.937881i	0.998819	+	0.0485854i	$0.0154713\pi$
$719$	14.5195	+	25.1485i	0.541486	+	0.937881i	−0.457333	+	0.889295i	$0.651195\pi$
$720$	−3.96800	+	5.40879i	−0.147879	+	0.201574i
$721$	−7.87200	+	8.50318i	−0.293169	+	0.316675i
$722$	9.56974	+	5.52509i	0.356149	+	0.205623i
$723$	15.8476	−	5.46009i	0.589379	−	0.203063i
$724$	−20.1029			−0.747117
$725$	−20.1455	+	12.3104i	−0.748185	+	0.457196i
$726$	−6.65510	+	7.65871i	−0.246994	+	0.284241i
$727$	1.94247	+	1.12149i	0.0720423	+	0.0415936i	0.535588	−	0.844479i	$-0.320090\pi$
$727$	1.94247	+	1.12149i	0.0720423	+	0.0415936i	−0.463546	+	0.886073i	$0.653423\pi$
$728$	9.81250	−	3.03886i	0.363675	−	0.112628i
$729$	−11.0096	−	24.6534i	−0.407763	−	0.913088i
$730$	20.5394	+	20.0337i	0.760196	+	0.741481i
$731$	−1.74254	−	3.01817i	−0.0644501	−	0.111631i
$732$	0.359394	−	1.85077i	0.0132836	−	0.0684065i
$733$	−0.753946	−	0.435291i	−0.0278476	−	0.0160778i	0.486012	−	0.873952i	$-0.338451\pi$
$733$	−0.753946	−	0.435291i	−0.0278476	−	0.0160778i	−0.513859	+	0.857875i	$0.671785\pi$
$734$	5.38443	+	9.32611i	0.198743	+	0.344233i
$735$	17.1127	+	21.0275i	0.631210	+	0.775612i
$736$	2.96277	−	5.13166i	0.109209	−	0.189156i
$737$	44.5423	−	25.7165i	1.64074	−	0.947279i
$738$	−20.3817	+	2.87225i	−0.750261	+	0.105729i
$739$	9.25114	−	16.0234i	0.340309	−	0.589432i	−0.644181	−	0.764873i	$-0.722802\pi$
$739$	9.25114	−	16.0234i	0.340309	−	0.589432i	0.984490	+	0.175441i	$0.0561351\pi$
$740$	−0.249569	−	0.887037i	−0.00917434	−	0.0326081i
$741$	−12.4367	+	14.3122i	−0.456875	+	0.525773i
$742$	−9.41984	−	8.72062i	−0.345813	−	0.320144i
$743$	7.22866	−	4.17347i	0.265194	−	0.153110i	−0.361508	−	0.932369i	$-0.617738\pi$
$743$	7.22866	−	4.17347i	0.265194	−	0.153110i	0.626701	+	0.779259i	$0.284405\pi$
$744$	6.62244	+	1.28598i	0.242790	+	0.0471464i
$745$	−33.3015	−	32.4817i	−1.22007	−	1.19004i
$746$	2.45843	−	4.25812i	0.0900095	−	0.155901i
$747$	28.6408	+	36.6302i	1.04791	+	1.34023i
$748$			11.4012i			0.416869i
$749$	2.56009	+	8.26655i	0.0935436	+	0.302053i
$750$	−15.6361	+	11.4241i	−0.570951	+	0.417151i
$751$	−19.5031	+	33.7804i	−0.711678	+	1.23266i	0.252548	+	0.967584i	$0.418731\pi$
$751$	−19.5031	+	33.7804i	−0.711678	+	1.23266i	−0.964227	+	0.265079i	$0.914602\pi$
$752$		−	5.10612i		−	0.186201i
$753$	5.74320	−	29.5758i	0.209294	−	1.07780i
$754$	18.3327			0.667637
$755$	−35.0089	+	9.84980i	−1.27410	+	0.358471i
$756$	9.59124	+	9.84927i	0.348830	+	0.358215i
$757$			37.6562i			1.36864i	0.729182	+	0.684320i	$0.239901\pi$
$757$			37.6562i			1.36864i	−0.729182	+	0.684320i	$0.760099\pi$
$758$			36.3873i			1.32164i
$759$	41.3669	+	8.03286i	1.50152	+	0.291574i
$760$	1.70754	+	6.06905i	0.0619388	+	0.220148i
$761$	−18.1162	+	31.3783i	−0.656714	+	1.13746i	0.324748	+	0.945801i	$0.394721\pi$
$761$	−18.1162	+	31.3783i	−0.656714	+	1.13746i	−0.981461	+	0.191661i	$0.938613\pi$
$762$	2.43569	−	12.5431i	0.0882356	−	0.454387i
$763$	−6.44404	−	5.96571i	−0.233290	−	0.215973i
$764$	2.99287			0.108278
$765$	−17.0518	+	7.49783i	−0.616511	+	0.271085i
$766$	−4.68178	+	8.10908i	−0.169160	+	0.292993i
$767$	41.9661	−	24.2291i	1.51531	−	0.874863i
$768$	0.330172	−	1.70029i	0.0119141	−	0.0613539i
$769$	6.17687	+	10.6986i	0.222744	+	0.385803i	0.955640	−	0.294537i	$-0.0951654\pi$
$769$	6.17687	+	10.6986i	0.222744	+	0.385803i	−0.732897	+	0.680340i	$0.761832\pi$
$770$	24.2589	−	1.23798i	0.874231	−	0.0446137i
$771$	−5.27888	+	6.07496i	−0.190114	+	0.218784i
$772$		−	21.4412i		−	0.771687i
$773$	−37.1712	−	21.4608i	−1.33695	−	0.771891i	−0.350600	−	0.936525i	$-0.614022\pi$
$773$	−37.1712	−	21.4608i	−1.33695	−	0.771891i	−0.986355	+	0.164634i	$0.947356\pi$
$774$	−2.96613	+	2.31919i	−0.106616	+	0.0833615i
$775$	17.1028	+	9.31389i	0.614350	+	0.334565i
$776$	−2.09320	+	3.62553i	−0.0751415	+	0.130149i
$777$	−1.87736	+	0.204546i	−0.0673498	+	0.00733805i
$778$	−1.77411	+	1.02428i	−0.0636049	+	0.0367223i
$779$	−9.67249	+	16.7532i	−0.346553	+	0.600247i
$780$	14.9860	−	1.23859i	0.536584	−	0.0443486i
$781$	−33.5013	−	58.0260i	−1.19877	−	2.07633i
$782$	14.2497	−	8.22707i	0.509568	−	0.294199i
$783$	11.1510	+	21.8548i	0.398506	+	0.781026i
$784$	−6.31361	−	3.02298i	−0.225486	−	0.107963i
$785$	−43.8988	−	11.1782i	−1.56681	−	0.398968i
$786$	−13.5459	+	15.5887i	−0.483167	+	0.556030i
$787$			32.1303i			1.14532i	0.819792	+	0.572662i	$0.194089\pi$
$787$			32.1303i			1.14532i	−0.819792	+	0.572662i	$0.805911\pi$
$788$		−	3.13660i		−	0.111737i
$789$	15.8584	+	46.0280i	0.564572	+	1.63864i
$790$	13.0610	+	3.32581i	0.464690	+	0.118327i
$791$	6.19215	+	19.9945i	0.220167	+	0.710922i
$792$	12.1970	−	1.71884i	0.433402	−	0.0610762i
$793$	−3.65998	+	2.11309i	−0.129970	+	0.0750380i
$794$	−14.5284	−	25.1640i	−0.515595	−	0.893037i
$795$	−10.7041	−	15.4444i	−0.379634	−	0.547755i
$796$	7.45046	−	12.9046i	0.264074	−	0.457390i
$797$	−31.8223	+	18.3726i	−1.12720	+	0.650791i	−0.943230	−	0.332140i	$-0.892229\pi$
$797$	−31.8223	+	18.3726i	−1.12720	+	0.650791i	−0.183973	+	0.982931i	$0.558896\pi$
$798$	12.8447	−	1.39949i	0.454699	−	0.0495414i
$799$	7.08939	−	12.2792i	0.250805	−	0.434406i
$800$	2.39131	−	4.39109i	0.0845456	−	0.155248i
$801$	−3.08786	−	21.9117i	−0.109104	−	0.774212i
$802$	17.3213	+	10.0005i	0.611637	+	0.353129i
$803$		−	52.6834i		−	1.85916i
$804$	−21.2992	−	4.13600i	−0.751163	−	0.145865i
$805$	−19.0525	−	29.4265i	−0.671511	−	1.03715i
$806$	−7.56106	−	13.0961i	−0.266327	−	0.461292i
$807$	−36.8190	−	31.9942i	−1.29609	−	1.12625i
$808$	10.9673	−	6.33196i	0.385827	−	0.222757i
$809$	1.13309	−	1.96256i	0.0398372	−	0.0690001i	−0.845419	−	0.534103i	$-0.820649\pi$
$809$	1.13309	−	1.96256i	0.0398372	−	0.0690001i	0.885257	+	0.465103i	$0.153983\pi$
$810$	10.5919	+	17.1117i	0.372162	+	0.601245i
$811$	27.0434			0.949622			0.474811	−	0.880088i	$-0.342516\pi$
$811$	27.0434			0.949622			0.474811	+	0.880088i	$0.342516\pi$
$812$	−9.16738	−	8.48690i	−0.321712	−	0.297832i
$813$	−33.2127	+	11.4430i	−1.16482	+	0.401324i
$814$	−0.846003	+	1.46532i	−0.0296524	+	0.0513594i
$815$	4.76521	+	16.9369i	0.166918	+	0.593273i
$816$	3.15470	−	3.63044i	0.110437	−	0.127091i
$817$			3.53869i			0.123803i
$818$		−	21.0715i		−	0.736747i
$819$	2.56323	−	30.7101i	0.0895667	−	1.07310i
$820$	14.7684	−	4.15509i	0.515733	−	0.145102i
$821$	10.1500			0.354238			0.177119	−	0.984189i	$-0.443322\pi$
$821$	10.1500			0.354238			0.177119	+	0.984189i	$0.443322\pi$
$822$	32.4479	−	11.1795i	1.13175	−	0.389930i
$823$		−	8.13372i		−	0.283524i	−0.989901	−	0.141762i	$-0.954723\pi$
$823$		−	8.13372i		−	0.283524i	0.989901	−	0.141762i	$-0.0452767\pi$
$824$	2.18985	−	3.79293i	0.0762871	−	0.132133i
$825$	35.0637	+	5.90618i	1.22076	+	0.205627i
$826$	−32.2020	−	7.31176i	−1.12045	−	0.254409i
$827$			2.64164i			0.0918589i	0.998945	+	0.0459294i	$0.0146249\pi$
$827$			2.64164i			0.0918589i	−0.998945	+	0.0459294i	$0.985375\pi$
$828$	−10.9496	−	14.0040i	−0.380525	−	0.486674i
$829$	14.6215	−	25.3252i	0.507827	−	0.879582i	−0.492132	−	0.870521i	$-0.663782\pi$
$829$	14.6215	−	25.3252i	0.507827	−	0.879582i	0.999959	−	0.00906143i	$-0.00288438\pi$
$830$	−24.8101	−	24.1993i	−0.861171	−	0.839970i
$831$	−5.77588	−	16.7642i	−0.200363	−	0.581543i
$832$	−3.36239	+	1.94128i	−0.116570	+	0.0673017i
$833$	−10.9858	−	16.0355i	−0.380636	−	0.555598i
$834$	3.21503	+	9.33143i	0.111327	+	0.323121i
$835$	12.8493	+	45.6700i	0.444669	+	1.58048i
$836$	5.78829	−	10.0256i	0.200192	−	0.346743i
$837$	11.0131	−	16.9796i	0.380668	−	0.586899i
$838$	18.8016	−	10.8551i	0.649489	−	0.374983i
$839$	−3.93007	+	6.80707i	−0.135681	+	0.235006i	−0.925857	−	0.377873i	$-0.876656\pi$
$839$	−3.93007	+	6.80707i	−0.135681	+	0.235006i	0.790176	+	0.612879i	$0.209989\pi$
$840$	−8.06723	−	6.31822i	−0.278346	−	0.217999i
$841$	3.35227	+	5.80630i	0.115595	+	0.200217i
$842$	−17.9301	−	10.3520i	−0.617913	−	0.356752i
$843$	−27.4655	−	23.8663i	−0.945961	−	0.822001i
$844$	−7.20990	−	12.4879i	−0.248175	−	0.429852i
$845$	−3.32029	−	3.23855i	−0.114222	−	0.111410i
$846$	−14.2051	−	5.73304i	−0.488381	−	0.197106i
$847$	−11.3732	−	10.5290i	−0.390787	−	0.361779i
$848$	4.20182	+	2.42592i	0.144291	+	0.0833064i
$849$	8.29961	+	1.61167i	0.284842	+	0.0553122i
$850$	11.8472	−	7.23955i	0.406357	−	0.248314i
$851$	2.44189			0.0837071
$852$	−5.38804	+	27.7468i	−0.184591	+	0.950590i
$853$	−6.09946	−	3.52152i	−0.208841	−	0.120575i	0.391931	−	0.919994i	$-0.371807\pi$
$853$	−6.09946	−	3.52152i	−0.208841	−	0.120575i	−0.600773	+	0.799420i	$0.705140\pi$
$854$	2.80842	+	0.637678i	0.0961023	+	0.0218209i
$855$	18.8011	+	2.06388i	0.642985	+	0.0705832i
$856$	−1.63543	−	2.83265i	−0.0558979	−	0.0968180i
$857$	2.71486	−	1.56742i	0.0927377	−	0.0535422i	−0.452914	−	0.891554i	$-0.649616\pi$
$857$	2.71486	−	1.56742i	0.0927377	−	0.0535422i	0.545652	+	0.838012i	$0.316282\pi$
$858$	−20.8416	−	18.1105i	−0.711521	−	0.618282i
$859$	−15.3632	+	26.6099i	−0.524187	+	0.907918i	0.475417	+	0.879761i	$0.342297\pi$
$859$	−15.3632	+	26.6099i	−0.524187	+	0.907918i	−0.999604	+	0.0281573i	$0.991036\pi$
$860$	1.95954	−	2.00900i	0.0668198	−	0.0685063i
$861$	−3.40550	−	31.2562i	−0.116059	−	1.06521i
$862$	−2.00583	−	1.15807i	−0.0683188	−	0.0394439i
$863$	26.0574	−	15.0443i	0.887004	−	0.512112i	0.0140430	−	0.999901i	$-0.495530\pi$
$863$	26.0574	−	15.0443i	0.887004	−	0.512112i	0.872962	+	0.487789i	$0.162196\pi$
$864$	−4.35945	−	2.82758i	−0.148311	−	0.0961962i
$865$	10.6876	+	2.72144i	0.363388	+	0.0925317i
$866$	−22.2752			−0.756941
$867$	−15.2119	+	5.24107i	−0.516624	+	0.177996i
$868$	−2.28174	+	10.0491i	−0.0774474	+	0.341089i
$869$	−12.3739	−	21.4322i	−0.419756	−	0.727038i
$870$	−10.4172	−	15.0304i	−0.353176	−	0.509580i
$871$	24.3180	+	42.1200i	0.823983	+	1.42718i
$872$	2.87443	+	1.65955i	0.0973405	+	0.0561996i
$873$	7.73592	+	9.89389i	0.261821	+	0.334857i
$874$	−16.7073			−0.565132
$875$	−16.6904	−	24.4219i	−0.564238	−	0.825612i
$876$	−14.5775	+	16.7758i	−0.492526	+	0.566801i
$877$	14.2261	+	8.21347i	0.480383	+	0.277349i	0.720576	−	0.693376i	$-0.243877\pi$
$877$	14.2261	+	8.21347i	0.480383	+	0.277349i	−0.240193	+	0.970725i	$0.577211\pi$
$878$			20.7548i			0.700442i
$879$	2.31751	+	6.72643i	0.0781676	+	0.226877i
$880$	−8.83781	+	2.48653i	−0.297922	+	0.0838209i
$881$	−33.4780			−1.12790			−0.563951	−	0.825808i	$-0.690719\pi$
$881$	−33.4780			−1.12790			−0.563951	+	0.825808i	$0.690719\pi$
$882$	−15.4986	+	14.1701i	−0.521865	+	0.477134i
$883$			44.7104i			1.50462i	0.658807	+	0.752312i	$0.271061\pi$
$883$			44.7104i			1.50462i	−0.658807	+	0.752312i	$0.728939\pi$
$884$	−10.7812			−0.362610
$885$	−43.7112	−	20.6391i	−1.46933	−	0.693775i
$886$	−18.7632			−0.630362
$887$	20.4666	+	11.8164i	0.687201	+	0.396755i	0.802562	−	0.596568i	$-0.203469\pi$
$887$	20.4666	+	11.8164i	0.687201	+	0.396755i	−0.115362	+	0.993324i	$0.536803\pi$
$888$	0.674842	−	0.232508i	0.0226462	−	0.00780246i
$889$	19.0333	+	4.32168i	0.638355	+	0.144944i
$890$	4.46700	+	15.8770i	0.149734	+	0.532197i
$891$	8.91277	−	35.8616i	0.298589	−	1.20141i
$892$	−15.8455	−	9.14843i	−0.530548	−	0.306312i
$893$	−12.4681	+	7.19846i	−0.417229	+	0.240887i
$894$	23.6352	−	27.1995i	0.790479	−	0.909686i
$895$	8.42849	+	8.22100i	0.281733	+	0.274798i
$896$	2.58008	+	0.585831i	0.0861944	+	0.0195712i
$897$	−7.59602	+	39.1172i	−0.253624	+	1.30609i
$898$			4.33662i			0.144715i
$899$	−9.19545	+	15.9270i	−0.306685	+	0.531195i
$900$	−9.53097	−	11.5828i	−0.317699	−	0.386093i
$901$	6.73635	+	11.6677i	0.224420	+	0.388707i
$902$	−24.3962	−	14.0852i	−0.812305	−	0.468985i
$903$	−3.39828	−	4.64009i	−0.113088	−	0.154412i
$904$	−3.95566	−	6.85140i	−0.131563	−	0.227874i
$905$	11.0923	−	43.5613i	0.368720	−	1.44803i
$906$	−9.17646	−	26.6342i	−0.304867	−	0.884861i
$907$	44.1604	−	25.4960i	1.46632	−	0.846582i	0.467033	−	0.884240i	$-0.345323\pi$
$907$	44.1604	−	25.4960i	1.46632	−	0.846582i	0.999291	+	0.0376579i	$0.0119897\pi$
$908$	−7.81588	+	4.51250i	−0.259379	+	0.149753i
$909$	−5.30152	−	37.6200i	−0.175840	−	1.24778i
$910$	1.17065	+	22.9397i	0.0388068	+	0.760443i
$911$	23.6679	−	40.9939i	0.784151	−	1.35819i	−0.145354	−	0.989380i	$-0.546432\pi$
$911$	23.6679	−	40.9939i	0.784151	−	1.35819i	0.929505	−	0.368810i	$-0.120235\pi$
$912$	−4.61723	+	1.59081i	−0.152892	+	0.0526768i
$913$			63.6378i			2.10610i
$914$	22.7169			0.751407
$915$	3.81217	+	1.79999i	0.126026	+	0.0595058i
$916$	8.59266	−	14.8829i	0.283910	−	0.491746i
$917$	−23.1492	−	21.4308i	−0.764453	−	0.707709i
$918$	−6.55775	−	12.8525i	−0.216438	−	0.424194i
$919$	−25.2990	−	43.8191i	−0.834536	−	1.44546i	−0.894408	−	0.447253i	$-0.852402\pi$
$919$	−25.2990	−	43.8191i	−0.834536	−	1.44546i	0.0598717	−	0.998206i	$-0.480931\pi$
$920$	9.48512	+	9.25161i	0.312715	+	0.305017i
$921$	−12.2797	−	2.38455i	−0.404631	−	0.0785737i
$922$	14.5778	+	8.41648i	0.480093	+	0.277182i
$923$	54.8704	−	31.6795i	1.80608	−	1.04274i
$924$	2.03795	+	18.7046i	0.0670437	+	0.615337i
$925$	2.05985	−	0.0513497i	0.0677273	−	0.00168837i
$926$	−13.8817	−	24.0438i	−0.456181	−	0.790129i
$927$	−8.09312	−	10.3507i	−0.265813	−	0.339963i
$928$	4.08921	+	2.36090i	0.134235	+	0.0775005i
$929$	−1.06340			−0.0348891			−0.0174446	−	0.999848i	$-0.505553\pi$
$929$	−1.06340			−0.0348891			−0.0174446	+	0.999848i	$0.505553\pi$
$930$	−6.44073	+	13.6407i	−0.211200	+	0.447297i
$931$	1.51925	+	19.6782i	0.0497913	+	0.644928i
$932$	4.18657	−	2.41712i	0.137136	−	0.0791754i
$933$	−7.68935	+	39.5979i	−0.251738	+	1.29638i
$934$	−17.2161	−	29.8191i	−0.563327	−	0.975711i
$935$	−24.7055	−	6.29091i	−0.807955	−	0.205735i
$936$	1.62536	+	11.5337i	0.0531267	+	0.376991i
$937$		−	39.6086i		−	1.29396i	−0.762508	−	0.646978i	$-0.776032\pi$
$937$		−	39.6086i		−	1.29396i	0.762508	−	0.646978i	$-0.223968\pi$
$938$	7.33857	−	32.3201i	0.239613	−	1.05529i
$939$	−30.8946	−	5.99930i	−1.00821	−	0.195780i
$940$	11.0645	+	2.81744i	0.360886	+	0.0918947i
$941$	−2.41836			−0.0788363			−0.0394182	−	0.999223i	$-0.512550\pi$
$941$	−2.41836			−0.0788363			−0.0394182	+	0.999223i	$0.512550\pi$
$942$	6.68883	−	34.4455i	0.217934	−	1.12229i
$943$			40.6553i			1.32392i
$944$	12.4810			0.406223
$945$	−26.6348	+	15.3488i	−0.866430	+	0.499298i
$946$	−5.15308			−0.167541
$947$		−	35.4602i		−	1.15230i	−0.817343	−	0.576151i	$-0.804554\pi$
$947$		−	35.4602i		−	1.15230i	0.817343	−	0.576151i	$-0.195446\pi$
$948$	−1.99010	+	10.2484i	−0.0646354	+	0.332853i
$949$	49.8184			1.61717
$950$	−14.0933	+	0.351332i	−0.457248	+	0.0113987i
$951$	−1.15578	−	0.224435i	−0.0374786	−	0.00727782i
$952$	5.39119	+	4.99101i	0.174730	+	0.161760i
$953$			50.6918i			1.64207i	0.570878	+	0.821035i	$0.306603\pi$
$953$			50.6918i			1.64207i	−0.570878	+	0.821035i	$0.693397\pi$
$954$	11.4665	−	8.96557i	0.371243	−	0.290271i
$955$	−1.65140	+	6.48531i	−0.0534379	+	0.209860i
$956$	8.08215	+	13.9987i	0.261395	+	0.452750i
$957$	−6.40105	+	32.9635i	−0.206917	+	1.06556i
$958$	−9.77485	+	5.64351i	−0.315811	+	0.182334i
$959$	15.5087	+	50.0778i	0.500803	+	1.61710i
$960$	3.50221	+	1.65364i	0.113033	+	0.0533709i
$961$	−15.8299			−0.510641
$962$	−1.38563	−	0.799995i	−0.0446746	−	0.0257929i
$963$	−9.71659	+	1.36929i	−0.313113	+	0.0441247i
$964$	−4.83873	−	8.38092i	−0.155845	−	0.269931i
$965$	46.4614	+	11.8308i	1.49565	+	0.380846i
$966$	21.9073	−	16.0443i	0.704856	−	0.516218i
$967$	−18.4021	+	10.6245i	−0.591772	+	0.341659i	−0.765798	−	0.643082i	$-0.777656\pi$
$967$	−18.4021	+	10.6245i	−0.591772	+	0.341659i	0.174026	+	0.984741i	$0.444322\pi$
$968$	5.07312	+	2.92897i	0.163056	+	0.0941406i
$969$	−13.3122	−	2.58504i	−0.427649	−	0.0830434i
$970$	−6.70125	−	6.53628i	−0.215164	−	0.209867i
$971$	−3.26795	−	5.66026i	−0.104874	−	0.181646i	0.808813	−	0.588066i	$-0.200110\pi$
$971$	−3.26795	−	5.66026i	−0.104874	−	0.181646i	−0.913687	+	0.406420i	$0.866777\pi$
$972$	−12.7609	+	8.95313i	−0.409307	+	0.287172i
$973$	−14.4015	+	4.46003i	−0.461691	+	0.142982i
$974$	12.2804	−	21.2703i	0.393489	−	0.681544i
$975$	−5.58499	+	33.1568i	−0.178863	+	1.06187i
$976$	−1.08850			−0.0348421
$977$		−	33.2788i		−	1.06468i	−0.846529	−	0.532342i	$-0.821312\pi$
$977$		−	33.2788i		−	1.06468i	0.846529	−	0.532342i	$-0.178688\pi$
$978$	−12.8853	+	4.43946i	−0.412026	+	0.141958i
$979$	15.1425	−	26.2275i	0.483956	−	0.838236i
$980$	10.0342	−	12.0131i	0.320532	−	0.383743i
$981$	7.84418	−	6.13328i	0.250445	−	0.195820i
$982$	15.7331	−	9.08350i	0.502063	−	0.289866i
$983$	20.3932	−	11.7740i	0.650441	−	0.375532i	−0.138184	−	0.990407i	$-0.544127\pi$
$983$	20.3932	−	11.7740i	0.650441	−	0.375532i	0.788625	+	0.614874i	$0.210793\pi$
$984$	3.87105	+	11.2355i	0.123404	+	0.358175i
$985$	6.79677	+	1.73070i	0.216563	+	0.0551448i
$986$	6.55581	+	11.3550i	0.208779	+	0.361617i
$987$	9.43586	−	21.4123i	0.300347	−	0.681560i
$988$	9.48041	+	5.47352i	0.301612	+	0.174136i
$989$	3.71845	+	6.44055i	0.118240	+	0.204797i
$990$	−3.00544	+	27.3784i	−0.0955192	+	0.870141i
$991$	−17.3486	+	30.0487i	−0.551097	+	0.954527i	0.447099	+	0.894484i	$0.352457\pi$
$991$	−17.3486	+	30.0487i	−0.551097	+	0.954527i	−0.998196	+	0.0600429i	$0.980876\pi$
$992$		−	3.89489i		−	0.123663i
$993$	4.20044	−	21.6310i	0.133297	−	0.686439i
$994$	−42.1039	−	9.56009i	−1.33546	−	0.303228i
$995$	23.8522	+	23.2650i	0.756165	+	0.737550i
$996$	17.6085	−	20.2640i	0.557948	−	0.642088i
$997$	−42.7308	+	24.6707i	−1.35330	+	0.781328i	−0.988710	−	0.149841i	$-0.952124\pi$
$997$	−42.7308	+	24.6707i	−1.35330	+	0.781328i	−0.364589	+	0.931168i	$0.618791\pi$
$998$	9.85866	+	5.69190i	0.312071	+	0.180174i
$999$	0.110866	−	2.13845i	0.00350766	−	0.0676575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ba.a.529.39	yes	96
3.2	odd	2		1890.2.ba.a.1369.46		96
5.4	even	2	inner	630.2.ba.a.529.10	yes	96
7.2	even	3		630.2.bq.a.79.43	yes	96
9.4	even	3		630.2.bq.a.319.6	yes	96
9.5	odd	6		1890.2.bq.a.739.47		96
15.14	odd	2		1890.2.ba.a.1369.7		96
21.2	odd	6		1890.2.bq.a.289.18		96
35.9	even	6		630.2.bq.a.79.6	yes	96
45.4	even	6		630.2.bq.a.319.43	yes	96
45.14	odd	6		1890.2.bq.a.739.18		96
63.23	odd	6		1890.2.ba.a.1549.7		96
63.58	even	3	inner	630.2.ba.a.499.34	yes	96
105.44	odd	6		1890.2.bq.a.289.47		96
315.149	odd	6		1890.2.ba.a.1549.46		96
315.184	even	6	inner	630.2.ba.a.499.15	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ba.a.499.15	✓	96	315.184	even	6	inner
630.2.ba.a.499.34	yes	96	63.58	even	3	inner
630.2.ba.a.529.10	yes	96	5.4	even	2	inner
630.2.ba.a.529.39	yes	96	1.1	even	1	trivial
630.2.bq.a.79.6	yes	96	35.9	even	6
630.2.bq.a.79.43	yes	96	7.2	even	3
630.2.bq.a.319.6	yes	96	9.4	even	3
630.2.bq.a.319.43	yes	96	45.4	even	6
1890.2.ba.a.1369.7		96	15.14	odd	2
1890.2.ba.a.1369.46		96	3.2	odd	2
1890.2.ba.a.1549.7		96	63.23	odd	6
1890.2.ba.a.1549.46		96	315.149	odd	6
1890.2.bq.a.289.18		96	21.2	odd	6
1890.2.bq.a.289.47		96	105.44	odd	6
1890.2.bq.a.739.18		96	45.14	odd	6
1890.2.bq.a.739.47		96	9.5	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.330172 - 1.70029i) q^{3} -1.00000 q^{4} +(0.551777 - 2.16692i) q^{5} +(1.70029 + 0.330172i) q^{6} +(-0.585831 + 2.58008i) q^{7} -1.00000i q^{8} +(-2.78197 - 1.12278i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.330172 - 1.70029i) q^{3} -1.00000 q^{4} +(0.551777 - 2.16692i) q^{5} +(1.70029 + 0.330172i) q^{6} +(-0.585831 + 2.58008i) q^{7} -1.00000i q^{8} +(-2.78197 - 1.12278i) q^{9} +(2.16692 + 0.551777i) q^{10} +(-2.05292 - 3.55576i) q^{11} +(-0.330172 + 1.70029i) q^{12} +(3.36239 - 1.94128i) q^{13} +(-2.58008 - 0.585831i) q^{14} +(-3.50221 - 1.65364i) q^{15} +1.00000 q^{16} +(2.40480 + 1.38841i) q^{17} +(1.12278 - 2.78197i) q^{18} +(-1.40977 - 2.44179i) q^{19} +(-0.551777 + 2.16692i) q^{20} +(4.19346 + 1.84795i) q^{21} +(3.55576 - 2.05292i) q^{22} +(-5.13166 - 2.96277i) q^{23} +(-1.70029 - 0.330172i) q^{24} +(-4.39109 - 2.39131i) q^{25} +(1.94128 + 3.36239i) q^{26} +(-2.82758 + 4.35945i) q^{27} +(0.585831 - 2.58008i) q^{28} +(2.36090 - 4.08921i) q^{29} +(1.65364 - 3.50221i) q^{30} -3.89489 q^{31} +1.00000i q^{32} +(-6.72365 + 2.31655i) q^{33} +(-1.38841 + 2.40480i) q^{34} +(5.26758 + 2.69307i) q^{35} +(2.78197 + 1.12278i) q^{36} +(-0.356887 + 0.206049i) q^{37} +(2.44179 - 1.40977i) q^{38} +(-2.19057 - 6.35800i) q^{39} +(-2.16692 - 0.551777i) q^{40} +(-3.43052 - 5.94183i) q^{41} +(-1.84795 + 4.19346i) q^{42} +(-1.08691 - 0.627530i) q^{43} +(2.05292 + 3.55576i) q^{44} +(-3.96800 + 5.40879i) q^{45} +(2.96277 - 5.13166i) q^{46} -5.10612i q^{47} +(0.330172 - 1.70029i) q^{48} +(-6.31361 - 3.02298i) q^{49} +(2.39131 - 4.39109i) q^{50} +(3.15470 - 3.63044i) q^{51} +(-3.36239 + 1.94128i) q^{52} +(4.20182 + 2.42592i) q^{53} +(-4.35945 - 2.82758i) q^{54} +(-8.83781 + 2.48653i) q^{55} +(2.58008 + 0.585831i) q^{56} +(-4.61723 + 1.59081i) q^{57} +(4.08921 + 2.36090i) q^{58} +12.4810 q^{59} +(3.50221 + 1.65364i) q^{60} -1.08850 q^{61} -3.89489i q^{62} +(4.52662 - 6.51995i) q^{63} -1.00000 q^{64} +(-2.35131 - 8.35719i) q^{65} +(-2.31655 - 6.72365i) q^{66} +12.5268i q^{67} +(-2.40480 - 1.38841i) q^{68} +(-6.73190 + 7.74709i) q^{69} +(-2.69307 + 5.26758i) q^{70} +16.3189 q^{71} +(-1.12278 + 2.78197i) q^{72} +(11.1123 + 6.41567i) q^{73} +(-0.206049 - 0.356887i) q^{74} +(-5.51574 + 6.67657i) q^{75} +(1.40977 + 2.44179i) q^{76} +(10.3768 - 3.21362i) q^{77} +(6.35800 - 2.19057i) q^{78} +6.02746 q^{79} +(0.551777 - 2.16692i) q^{80} +(6.47874 + 6.24707i) q^{81} +(5.94183 - 3.43052i) q^{82} +(-13.4228 - 7.74967i) q^{83} +(-4.19346 - 1.84795i) q^{84} +(4.33549 - 4.44491i) q^{85} +(0.627530 - 1.08691i) q^{86} +(-6.17333 - 5.36436i) q^{87} +(-3.55576 + 2.05292i) q^{88} +(3.68803 + 6.38786i) q^{89} +(-5.40879 - 3.96800i) q^{90} +(3.03886 + 9.81250i) q^{91} +(5.13166 + 2.96277i) q^{92} +(-1.28598 + 6.62244i) q^{93} +5.10612 q^{94} +(-6.06905 + 1.70754i) q^{95} +(1.70029 + 0.330172i) q^{96} +(-3.62553 - 2.09320i) q^{97} +(3.02298 - 6.31361i) q^{98} +(1.71884 + 12.1970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9	\( 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9} + 4 q^{11} - 2 q^{14} - 2 q^{15} + 96 q^{16} + 8 q^{21} + 4 q^{24} + 24 q^{26} + 10 q^{29} + 10 q^{30} - 34 q^{35} - 8 q^{36} + 44 q^{39} + 30 q^{41} - 4 q^{44} - 44 q^{45} - 6 q^{46} - 6 q^{49} - 12 q^{50} + 28 q^{51} - 8 q^{54} + 12 q^{55} + 2 q^{56} + 48 q^{59} + 2 q^{60} + 12 q^{61} - 96 q^{64} - 36 q^{65} + 32 q^{66} + 36 q^{69} + 6 q^{70} - 32 q^{71} - 68 q^{75} - 32 q^{81} - 8 q^{84} + 4 q^{86} - 66 q^{89} - 22 q^{90} + 24 q^{94} - 60 q^{95} - 4 q^{96} - 4 q^{99}+O(q^{100}) \) 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9 + 4 * q^11 - 2 * q^14 - 2 * q^15 + 96 * q^16 + 8 * q^21 + 4 * q^24 + 24 * q^26 + 10 * q^29 + 10 * q^30 - 34 * q^35 - 8 * q^36 + 44 * q^39 + 30 * q^41 - 4 * q^44 - 44 * q^45 - 6 * q^46 - 6 * q^49 - 12 * q^50 + 28 * q^51 - 8 * q^54 + 12 * q^55 + 2 * q^56 + 48 * q^59 + 2 * q^60 + 12 * q^61 - 96 * q^64 - 36 * q^65 + 32 * q^66 + 36 * q^69 + 6 * q^70 - 32 * q^71 - 68 * q^75 - 32 * q^81 - 8 * q^84 + 4 * q^86 - 66 * q^89 - 22 * q^90 + 24 * q^94 - 60 * q^95 - 4 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more