LMFDB - Embedded newform 630.2.bi.a.479.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(479,630)]

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([1, 3, 1]))

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

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

chi := DirichletCharacter("630.479");

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.bi (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			479.12
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.a.509.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.241929 - 1.71507i) q^{3} +1.00000 q^{4} +(-1.71718 + 1.43224i) q^{5} +(0.241929 + 1.71507i) q^{6} +(-2.63972 - 0.178501i) q^{7} -1.00000 q^{8} +(-2.88294 + 0.829851i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.241929 - 1.71507i) q^{3} +1.00000 q^{4} +(-1.71718 + 1.43224i) q^{5} +(0.241929 + 1.71507i) q^{6} +(-2.63972 - 0.178501i) q^{7} -1.00000 q^{8} +(-2.88294 + 0.829851i) q^{9} +(1.71718 - 1.43224i) q^{10} +(3.12718 - 1.80548i) q^{11} +(-0.241929 - 1.71507i) q^{12} +(-1.68621 - 2.92060i) q^{13} +(2.63972 + 0.178501i) q^{14} +(2.87183 + 2.59858i) q^{15} +1.00000 q^{16} +(6.40634 + 3.69870i) q^{17} +(2.88294 - 0.829851i) q^{18} +(-4.15471 + 2.39873i) q^{19} +(-1.71718 + 1.43224i) q^{20} +(0.332483 + 4.57050i) q^{21} +(-3.12718 + 1.80548i) q^{22} +(-3.99454 + 6.91875i) q^{23} +(0.241929 + 1.71507i) q^{24} +(0.897383 - 4.91881i) q^{25} +(1.68621 + 2.92060i) q^{26} +(2.12072 + 4.74368i) q^{27} +(-2.63972 - 0.178501i) q^{28} +(7.66188 + 4.42359i) q^{29} +(-2.87183 - 2.59858i) q^{30} +6.44913i q^{31} -1.00000 q^{32} +(-3.85308 - 4.92653i) q^{33} +(-6.40634 - 3.69870i) q^{34} +(4.78852 - 3.47420i) q^{35} +(-2.88294 + 0.829851i) q^{36} +(5.56251 - 3.21152i) q^{37} +(4.15471 - 2.39873i) q^{38} +(-4.60109 + 3.59855i) q^{39} +(1.71718 - 1.43224i) q^{40} +(-1.31158 - 2.27173i) q^{41} +(-0.332483 - 4.57050i) q^{42} +(0.660123 + 0.381122i) q^{43} +(3.12718 - 1.80548i) q^{44} +(3.76197 - 5.55406i) q^{45} +(3.99454 - 6.91875i) q^{46} +8.22805i q^{47} +(-0.241929 - 1.71507i) q^{48} +(6.93627 + 0.942388i) q^{49} +(-0.897383 + 4.91881i) q^{50} +(4.79366 - 11.8821i) q^{51} +(-1.68621 - 2.92060i) q^{52} +(-1.47706 + 2.55834i) q^{53} +(-2.12072 - 4.74368i) q^{54} +(-2.78404 + 7.57918i) q^{55} +(2.63972 + 0.178501i) q^{56} +(5.11913 + 6.54531i) q^{57} +(-7.66188 - 4.42359i) q^{58} +1.12529 q^{59} +(2.87183 + 2.59858i) q^{60} -1.68162i q^{61} -6.44913i q^{62} +(7.75829 - 1.67597i) q^{63} +1.00000 q^{64} +(7.07851 + 2.60013i) q^{65} +(3.85308 + 4.92653i) q^{66} +4.74896i q^{67} +(6.40634 + 3.69870i) q^{68} +(12.8325 + 5.17708i) q^{69} +(-4.78852 + 3.47420i) q^{70} +1.40979i q^{71} +(2.88294 - 0.829851i) q^{72} +(-2.78262 + 4.81964i) q^{73} +(-5.56251 + 3.21152i) q^{74} +(-8.65322 - 0.349073i) q^{75} +(-4.15471 + 2.39873i) q^{76} +(-8.57716 + 4.20775i) q^{77} +(4.60109 - 3.59855i) q^{78} +0.172505 q^{79} +(-1.71718 + 1.43224i) q^{80} +(7.62270 - 4.78482i) q^{81} +(1.31158 + 2.27173i) q^{82} +(-11.5262 - 6.65467i) q^{83} +(0.332483 + 4.57050i) q^{84} +(-16.2982 + 2.82409i) q^{85} +(-0.660123 - 0.381122i) q^{86} +(5.73314 - 14.2109i) q^{87} +(-3.12718 + 1.80548i) q^{88} +(-7.08044 - 12.2637i) q^{89} +(-3.76197 + 5.55406i) q^{90} +(3.92979 + 8.01056i) q^{91} +(-3.99454 + 6.91875i) q^{92} +(11.0607 - 1.56023i) q^{93} -8.22805i q^{94} +(3.69883 - 10.0696i) q^{95} +(0.241929 + 1.71507i) q^{96} +(-4.18720 + 7.25244i) q^{97} +(-6.93627 - 0.942388i) q^{98} +(-7.51719 + 7.80017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8	$ 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} + 42 q^{55} + 3 q^{56} + 22 q^{57} + 3 q^{58} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 q^{70} + 18 q^{73} + 18 q^{75} + 12 q^{77} + 18 q^{78} + 8 q^{81} + 3 q^{82} - 9 q^{83} + 8 q^{84} + 33 q^{85} + 15 q^{87} - 6 q^{88} - 33 q^{89} - 15 q^{90} - 3 q^{92} + 8 q^{93} + 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.241929	−	1.71507i	−0.139678	−	0.990197i
$3$	−0.241929	−	1.71507i	−0.139678	−	0.990197i
$4$	1.00000			0.500000
$5$	−1.71718	+	1.43224i	−0.767944	+	0.640517i
$5$	−1.71718	+	1.43224i	−0.767944	+	0.640517i
$6$	0.241929	+	1.71507i	0.0987671	+	0.700175i
$7$	−2.63972	−	0.178501i	−0.997721	−	0.0674671i
$7$	−2.63972	−	0.178501i	−0.997721	−	0.0674671i
$8$	−1.00000			−0.353553
$9$	−2.88294	+	0.829851i	−0.960980	+	0.276617i
$10$	1.71718	−	1.43224i	0.543019	−	0.452914i
$11$	3.12718	−	1.80548i	0.942879	−	0.544372i	0.0520175	−	0.998646i	$-0.483435\pi$
$11$	3.12718	−	1.80548i	0.942879	−	0.544372i	0.890862	+	0.454275i	$0.150102\pi$
$12$	−0.241929	−	1.71507i	−0.0698389	−	0.495099i
$13$	−1.68621	−	2.92060i	−0.467670	−	0.810028i	0.531647	−	0.846966i	$-0.321573\pi$
$13$	−1.68621	−	2.92060i	−0.467670	−	0.810028i	−0.999318	+	0.0369373i	$0.988240\pi$
$14$	2.63972	+	0.178501i	0.705496	+	0.0477065i
$15$	2.87183	+	2.59858i	0.741502	+	0.670950i
$16$	1.00000			0.250000
$17$	6.40634	+	3.69870i	1.55377	+	0.897067i	0.997830	+	0.0658408i	$0.0209729\pi$
$17$	6.40634	+	3.69870i	1.55377	+	0.897067i	0.555935	+	0.831226i	$0.312360\pi$
$18$	2.88294	−	0.829851i	0.679516	−	0.195598i
$19$	−4.15471	+	2.39873i	−0.953157	+	0.550305i	−0.894060	−	0.447947i	$-0.852155\pi$
$19$	−4.15471	+	2.39873i	−0.953157	+	0.550305i	−0.0590966	+	0.998252i	$0.518822\pi$
$20$	−1.71718	+	1.43224i	−0.383972	+	0.320258i
$21$	0.332483	+	4.57050i	0.0725537	+	0.997365i
$22$	−3.12718	+	1.80548i	−0.666716	+	0.384929i
$23$	−3.99454	+	6.91875i	−0.832920	+	1.44266i	0.0627930	+	0.998027i	$0.479999\pi$
$23$	−3.99454	+	6.91875i	−0.832920	+	1.44266i	−0.895713	+	0.444633i	$0.853334\pi$
$24$	0.241929	+	1.71507i	0.0493835	+	0.350088i
$25$	0.897383	−	4.91881i	0.179477	−	0.983762i
$26$	1.68621	+	2.92060i	0.330693	+	0.572777i
$27$	2.12072	+	4.74368i	0.408133	+	0.912923i
$28$	−2.63972	−	0.178501i	−0.498861	−	0.0337336i
$29$	7.66188	+	4.42359i	1.42278	+	0.821440i	0.996535	−	0.0831703i	$-0.0265045\pi$
$29$	7.66188	+	4.42359i	1.42278	+	0.821440i	0.426240	+	0.904610i	$0.359838\pi$
$30$	−2.87183	−	2.59858i	−0.524321	−	0.474433i
$31$			6.44913i			1.15830i	0.815222	+	0.579149i	$0.196615\pi$
$31$			6.44913i			1.15830i	−0.815222	+	0.579149i	$0.803385\pi$
$32$	−1.00000			−0.176777
$33$	−3.85308	−	4.92653i	−0.670734	−	0.857600i
$34$	−6.40634	−	3.69870i	−1.09868	−	0.634322i
$35$	4.78852	−	3.47420i	0.809408	−	0.587246i
$36$	−2.88294	+	0.829851i	−0.480490	+	0.138308i
$37$	5.56251	−	3.21152i	0.914471	−	0.527970i	0.0326040	−	0.999468i	$-0.489620\pi$
$37$	5.56251	−	3.21152i	0.914471	−	0.527970i	0.881867	+	0.471498i	$0.156287\pi$
$38$	4.15471	−	2.39873i	0.673984	−	0.389125i
$39$	−4.60109	+	3.59855i	−0.736765	+	0.576229i
$40$	1.71718	−	1.43224i	0.271509	−	0.226457i
$41$	−1.31158	−	2.27173i	−0.204835	−	0.354785i	0.745245	−	0.666791i	$-0.232332\pi$
$41$	−1.31158	−	2.27173i	−0.204835	−	0.354785i	−0.950080	+	0.312006i	$0.898999\pi$
$42$	−0.332483	−	4.57050i	−0.0513032	−	0.705243i
$43$	0.660123	+	0.381122i	0.100668	+	0.0581206i	0.549489	−	0.835501i	$-0.314823\pi$
$43$	0.660123	+	0.381122i	0.100668	+	0.0581206i	−0.448821	+	0.893622i	$0.648156\pi$
$44$	3.12718	−	1.80548i	0.471440	−	0.272186i
$45$	3.76197	−	5.55406i	0.560801	−	0.827950i
$46$	3.99454	−	6.91875i	0.588963	−	1.02011i
$47$			8.22805i			1.20018i	0.799931	+	0.600092i	$0.204869\pi$
$47$			8.22805i			1.20018i	−0.799931	+	0.600092i	$0.795131\pi$
$48$	−0.241929	−	1.71507i	−0.0349194	−	0.247549i
$49$	6.93627	+	0.942388i	0.990896	+	0.134627i
$50$	−0.897383	+	4.91881i	−0.126909	+	0.695625i
$51$	4.79366	−	11.8821i	0.671246	−	1.66383i
$52$	−1.68621	−	2.92060i	−0.233835	−	0.405014i
$53$	−1.47706	+	2.55834i	−0.202889	+	0.351415i	−0.949458	−	0.313893i	$-0.898367\pi$
$53$	−1.47706	+	2.55834i	−0.202889	+	0.351415i	0.746569	+	0.665308i	$0.231700\pi$
$54$	−2.12072	−	4.74368i	−0.288593	−	0.645534i
$55$	−2.78404	+	7.57918i	−0.375399	+	1.02198i
$56$	2.63972	+	0.178501i	0.352748	+	0.0238532i
$57$	5.11913	+	6.54531i	0.678045	+	0.866948i
$58$	−7.66188	−	4.42359i	−1.00605	−	0.580846i
$59$	1.12529			0.146500			0.0732502	−	0.997314i	$-0.476663\pi$
$59$	1.12529			0.146500			0.0732502	+	0.997314i	$0.476663\pi$
$60$	2.87183	+	2.59858i	0.370751	+	0.335475i
$61$		−	1.68162i		−	0.215310i	−0.994188	−	0.107655i	$-0.965666\pi$
$61$		−	1.68162i		−	0.215310i	0.994188	−	0.107655i	$-0.0343341\pi$
$62$		−	6.44913i		−	0.819040i
$63$	7.75829	−	1.67597i	0.977453	−	0.211152i
$64$	1.00000			0.125000
$65$	7.07851	+	2.60013i	0.877981	+	0.322506i
$66$	3.85308	+	4.92653i	0.474281	+	0.606414i
$67$			4.74896i			0.580177i	0.957000	+	0.290089i	$0.0936848\pi$
$67$			4.74896i			0.580177i	−0.957000	+	0.290089i	$0.906315\pi$
$68$	6.40634	+	3.69870i	0.776883	+	0.448533i
$69$	12.8325	+	5.17708i	1.54486	+	0.623247i
$70$	−4.78852	+	3.47420i	−0.572338	+	0.415246i
$71$			1.40979i			0.167311i	0.996495	+	0.0836554i	$0.0266595\pi$
$71$			1.40979i			0.167311i	−0.996495	+	0.0836554i	$0.973341\pi$
$72$	2.88294	−	0.829851i	0.339758	−	0.0977989i
$73$	−2.78262	+	4.81964i	−0.325681	+	0.564096i	−0.981650	−	0.190692i	$-0.938927\pi$
$73$	−2.78262	+	4.81964i	−0.325681	+	0.564096i	0.655969	+	0.754788i	$0.272260\pi$
$74$	−5.56251	+	3.21152i	−0.646629	+	0.373331i
$75$	−8.65322	−	0.349073i	−0.999187	−	0.0403075i
$76$	−4.15471	+	2.39873i	−0.476578	+	0.275153i
$77$	−8.57716	+	4.20775i	−0.977458	+	0.479518i
$78$	4.60109	−	3.59855i	0.520971	−	0.407455i
$79$	0.172505			0.0194083			0.00970417	−	0.999953i	$-0.496911\pi$
$79$	0.172505			0.0194083			0.00970417	+	0.999953i	$0.496911\pi$
$80$	−1.71718	+	1.43224i	−0.191986	+	0.160129i
$81$	7.62270	−	4.78482i	0.846966	−	0.531647i
$82$	1.31158	+	2.27173i	0.144840	+	0.250871i
$83$	−11.5262	−	6.65467i	−1.26517	−	0.730445i	−0.291098	−	0.956693i	$-0.594020\pi$
$83$	−11.5262	−	6.65467i	−1.26517	−	0.730445i	−0.974070	+	0.226249i	$0.927354\pi$
$84$	0.332483	+	4.57050i	0.0362769	+	0.498682i
$85$	−16.2982	+	2.82409i	−1.76779	+	0.306315i
$86$	−0.660123	−	0.381122i	−0.0711829	−	0.0410975i
$87$	5.73314	−	14.2109i	0.614657	−	1.52356i
$88$	−3.12718	+	1.80548i	−0.333358	+	0.192464i
$89$	−7.08044	−	12.2637i	−0.750525	−	1.29995i	−0.947568	−	0.319553i	$-0.896467\pi$
$89$	−7.08044	−	12.2637i	−0.750525	−	1.29995i	0.197043	−	0.980395i	$-0.436866\pi$
$90$	−3.76197	+	5.55406i	−0.396547	+	0.585449i
$91$	3.92979	+	8.01056i	0.411954	+	0.839735i
$92$	−3.99454	+	6.91875i	−0.416460	+	0.721330i
$93$	11.0607	−	1.56023i	1.14694	−	0.161788i
$94$		−	8.22805i		−	0.848658i
$95$	3.69883	−	10.0696i	0.379491	−	1.03312i
$96$	0.241929	+	1.71507i	0.0246918	+	0.175044i
$97$	−4.18720	+	7.25244i	−0.425145	+	0.736373i	−0.996434	−	0.0843759i	$-0.973110\pi$
$97$	−4.18720	+	7.25244i	−0.425145	+	0.736373i	0.571289	+	0.820749i	$0.306444\pi$
$98$	−6.93627	−	0.942388i	−0.700670	−	0.0951955i
$99$	−7.51719	+	7.80017i	−0.755506	+	0.783947i
$100$	0.897383	−	4.91881i	0.0897383	−	0.491881i
$101$	7.88869	+	13.6636i	0.784954	+	1.35958i	0.929026	+	0.370014i	$0.120647\pi$
$101$	7.88869	+	13.6636i	0.784954	+	1.35958i	−0.144072	+	0.989567i	$0.546020\pi$
$102$	−4.79366	+	11.8821i	−0.474643	+	1.17651i
$103$	−2.00208	+	3.46771i	−0.197271	+	0.341683i	−0.947643	−	0.319333i	$-0.896541\pi$
$103$	−2.00208	+	3.46771i	−0.197271	+	0.341683i	0.750372	+	0.661016i	$0.229875\pi$
$104$	1.68621	+	2.92060i	0.165346	+	0.286388i
$105$	−7.11698	−	7.37215i	−0.694546	−	0.719448i
$106$	1.47706	−	2.55834i	0.143465	−	0.248488i
$107$	1.60810	+	2.78531i	0.155461	+	0.269266i	0.933227	−	0.359288i	$-0.116980\pi$
$107$	1.60810	+	2.78531i	0.155461	+	0.269266i	−0.777766	+	0.628554i	$0.783647\pi$
$108$	2.12072	+	4.74368i	0.204066	+	0.456461i
$109$	3.65311	−	6.32737i	0.349904	−	0.606052i	−0.636328	−	0.771419i	$-0.719547\pi$
$109$	3.65311	−	6.32737i	0.349904	−	0.606052i	0.986232	+	0.165367i	$0.0528808\pi$
$110$	2.78404	−	7.57918i	0.265448	−	0.722647i
$111$	−6.85371	−	8.76314i	−0.650526	−	0.831761i
$112$	−2.63972	−	0.178501i	−0.249430	−	0.0168668i
$113$	6.81995	+	11.8125i	0.641567	+	1.11123i	0.985083	+	0.172079i	$0.0550485\pi$
$113$	6.81995	+	11.8125i	0.641567	+	1.11123i	−0.343517	+	0.939147i	$0.611618\pi$
$114$	−5.11913	−	6.54531i	−0.479451	−	0.613025i
$115$	−3.04997	−	17.6019i	−0.284412	−	1.64138i
$116$	7.66188	+	4.42359i	0.711388	+	0.410720i
$117$	7.28490	+	7.02061i	0.673489	+	0.649056i
$118$	−1.12529			−0.103591
$119$	−16.2507	−	10.9071i	−1.48970	−	0.999851i
$120$	−2.87183	−	2.59858i	−0.262161	−	0.237217i
$121$	1.01949	−	1.76581i	0.0926807	−	0.160528i
$122$			1.68162i			0.152247i
$123$	−3.57887	+	2.79906i	−0.322696	+	0.252383i
$124$			6.44913i			0.579149i
$125$	5.50395	+	9.73173i	0.492288	+	0.870432i
$126$	−7.75829	+	1.67597i	−0.691164	+	0.149307i
$127$		−	8.41042i		−	0.746304i	−0.927770	−	0.373152i	$-0.878277\pi$
$127$		−	8.41042i		−	0.746304i	0.927770	−	0.373152i	$-0.121723\pi$
$128$	−1.00000			−0.0883883
$129$	0.493949	−	1.22436i	0.0434898	−	0.107799i
$130$	−7.07851	−	2.60013i	−0.620827	−	0.228046i
$131$	−2.89711	+	5.01795i	−0.253122	+	0.438420i	−0.964384	−	0.264507i	$-0.914791\pi$
$131$	−2.89711	+	5.01795i	−0.253122	+	0.438420i	0.711262	+	0.702927i	$0.248124\pi$
$132$	−3.85308	−	4.92653i	−0.335367	−	0.428800i
$133$	11.3955	−	5.59035i	0.988113	−	0.484745i
$134$		−	4.74896i		−	0.410247i
$135$	−10.4357	−	5.10836i	−0.898165	−	0.439658i
$136$	−6.40634	−	3.69870i	−0.549339	−	0.317161i
$137$	−3.72838	−	6.45775i	−0.318537	−	0.551722i	0.661646	−	0.749816i	$-0.269858\pi$
$137$	−3.72838	−	6.45775i	−0.318537	−	0.551722i	−0.980183	+	0.198094i	$0.936525\pi$
$138$	−12.8325	−	5.17708i	−1.09238	−	0.440702i
$139$	−7.19444	+	4.15371i	−0.610225	+	0.352313i	−0.773053	−	0.634341i	$-0.781272\pi$
$139$	−7.19444	+	4.15371i	−0.610225	+	0.352313i	0.162829	+	0.986654i	$0.447938\pi$
$140$	4.78852	−	3.47420i	0.404704	−	0.293623i
$141$	14.1117	−	1.99060i	1.18842	−	0.167639i
$142$		−	1.40979i		−	0.118307i
$143$	−10.5461	−	6.08882i	−0.881913	−	0.509173i
$144$	−2.88294	+	0.829851i	−0.240245	+	0.0691542i
$145$	−19.4924	+	3.37757i	−1.61876	+	0.280492i
$146$	2.78262	−	4.81964i	0.230291	−	0.398876i
$147$	−0.0618228	−	12.1242i	−0.00509906	−	0.999987i
$148$	5.56251	−	3.21152i	0.457236	−	0.263985i
$149$	−10.1240	−	5.84511i	−0.829393	−	0.478850i	0.0242521	−	0.999706i	$-0.492280\pi$
$149$	−10.1240	−	5.84511i	−0.829393	−	0.478850i	−0.853645	+	0.520856i	$0.825613\pi$
$150$	8.65322	+	0.349073i	0.706532	+	0.0285017i
$151$	4.53199	+	7.84964i	0.368808	+	0.638795i	0.989380	−	0.145355i	$-0.0464326\pi$
$151$	4.53199	+	7.84964i	0.368808	+	0.638795i	−0.620571	+	0.784150i	$0.713099\pi$
$152$	4.15471	−	2.39873i	0.336992	−	0.194562i
$153$	−21.5385	−	5.34683i	−1.74128	−	0.432266i
$154$	8.57716	−	4.20775i	0.691167	−	0.339070i
$155$	−9.23669	−	11.0743i	−0.741909	−	0.889508i
$156$	−4.60109	+	3.59855i	−0.368382	+	0.288114i
$157$	−19.7804			−1.57864			−0.789322	−	0.613979i	$-0.789568\pi$
$157$	−19.7804			−1.57864			−0.789322	+	0.613979i	$0.789568\pi$
$158$	−0.172505			−0.0137238
$159$	4.74508	+	1.91432i	0.376309	+	0.151816i
$160$	1.71718	−	1.43224i	0.135755	−	0.113228i
$161$	11.7795	−	17.5506i	0.928354	−	1.38318i
$162$	−7.62270	+	4.78482i	−0.598896	+	0.375931i
$163$	11.4067	−	6.58566i	0.893442	−	0.515829i	0.0183750	−	0.999831i	$-0.494151\pi$
$163$	11.4067	−	6.58566i	0.893442	−	0.515829i	0.875067	+	0.484002i	$0.160817\pi$
$164$	−1.31158	−	2.27173i	−0.102418	−	0.177392i
$165$	13.6724	+	2.94120i	1.06439	+	0.228972i
$166$	11.5262	+	6.65467i	0.894608	+	0.516502i
$167$	−1.88823	+	1.09017i	−0.146116	+	0.0843601i	−0.571276	−	0.820758i	$-0.693551\pi$
$167$	−1.88823	+	1.09017i	−0.146116	+	0.0843601i	0.425160	+	0.905118i	$0.360218\pi$
$168$	−0.332483	−	4.57050i	−0.0256516	−	0.352622i
$169$	0.813400	−	1.40885i	0.0625692	−	0.108373i
$170$	16.2982	−	2.82409i	1.25002	−	0.216598i
$171$	9.98721	−	10.3632i	0.763741	−	0.792492i
$172$	0.660123	+	0.381122i	0.0503339	+	0.0290603i
$173$			25.9317i			1.97155i	0.168079	+	0.985773i	$0.446243\pi$
$173$			25.9317i			1.97155i	−0.168079	+	0.985773i	$0.553757\pi$
$174$	−5.73314	+	14.2109i	−0.434628	+	1.07732i
$175$	−3.24686	+	12.8241i	−0.245439	+	0.969412i
$176$	3.12718	−	1.80548i	0.235720	−	0.136093i
$177$	−0.272240	−	1.92995i	−0.0204628	−	0.145064i
$178$	7.08044	+	12.2637i	0.530702	+	0.919202i
$179$	−12.3911	−	7.15401i	−0.926155	−	0.534716i	−0.0405613	−	0.999177i	$-0.512915\pi$
$179$	−12.3911	−	7.15401i	−0.926155	−	0.534716i	−0.885593	+	0.464461i	$0.846248\pi$
$180$	3.76197	−	5.55406i	0.280401	−	0.413975i
$181$		−	4.19706i		−	0.311965i	−0.987760	−	0.155982i	$-0.950146\pi$
$181$		−	4.19706i		−	0.311965i	0.987760	−	0.155982i	$-0.0498543\pi$
$182$	−3.92979	−	8.01056i	−0.291296	−	0.593782i
$183$	−2.88410	+	0.406833i	−0.213199	+	0.0300740i
$184$	3.99454	−	6.91875i	0.294482	−	0.510057i
$185$	−4.95215	+	13.4816i	−0.364089	+	0.991186i
$186$	−11.0607	+	1.56023i	−0.811011	+	0.114402i
$187$	26.7117			1.95335
$188$			8.22805i			0.600092i
$189$	−4.75136	−	12.9006i	−0.345611	−	0.938378i
$190$	−3.69883	+	10.0696i	−0.268341	+	0.730524i
$191$			18.8086i			1.36094i	0.732775	+	0.680471i	$0.238225\pi$
$191$			18.8086i			1.36094i	−0.732775	+	0.680471i	$0.761775\pi$
$192$	−0.241929	−	1.71507i	−0.0174597	−	0.123775i
$193$		−	5.50601i		−	0.396331i	−0.980169	−	0.198166i	$-0.936502\pi$
$193$		−	5.50601i		−	0.396331i	0.980169	−	0.198166i	$-0.0634984\pi$
$194$	4.18720	−	7.25244i	0.300623	−	0.520695i
$195$	2.74691	−	12.7692i	0.196710	−	0.914421i
$196$	6.93627	+	0.942388i	0.495448	+	0.0673134i
$197$	13.1218			0.934888			0.467444	−	0.884023i	$-0.345175\pi$
$197$	13.1218			0.934888			0.467444	+	0.884023i	$0.345175\pi$
$198$	7.51719	−	7.80017i	0.534223	−	0.554334i
$199$	−9.55302	−	5.51544i	−0.677195	−	0.390979i	0.121602	−	0.992579i	$-0.461197\pi$
$199$	−9.55302	−	5.51544i	−0.677195	−	0.390979i	−0.798797	+	0.601600i	$0.794530\pi$
$200$	−0.897383	+	4.91881i	−0.0634546	+	0.347812i
$201$	8.14480	−	1.14891i	0.574490	−	0.0810379i
$202$	−7.88869	−	13.6636i	−0.555047	−	0.961369i
$203$	−19.4356	−	13.0447i	−1.36411	−	0.915559i
$204$	4.79366	−	11.8821i	0.335623	−	0.831917i
$205$	5.50588	+	2.02246i	0.384547	+	0.141255i
$206$	2.00208	−	3.46771i	0.139492	−	0.241607i
$207$	5.77450	−	23.2612i	0.401355	−	1.61677i
$208$	−1.68621	−	2.92060i	−0.116918	−	0.202507i
$209$	−8.66168	+	15.0025i	−0.599141	+	1.03774i
$210$	7.11698	+	7.37215i	0.491118	+	0.508727i
$211$	7.09074	+	12.2815i	0.488147	+	0.845495i	0.999907	−	0.0136335i	$-0.00433983\pi$
$211$	7.09074	+	12.2815i	0.488147	+	0.845495i	−0.511761	+	0.859128i	$0.671006\pi$
$212$	−1.47706	+	2.55834i	−0.101445	+	0.175707i
$213$	2.41788	−	0.341068i	0.165671	−	0.0233696i
$214$	−1.60810	−	2.78531i	−0.109927	−	0.190400i
$215$	−1.67941	+	0.291000i	−0.114535	+	0.0198461i
$216$	−2.12072	−	4.74368i	−0.144297	−	0.322767i
$217$	1.15118	−	17.0239i	0.0781470	−	1.15566i
$218$	−3.65311	+	6.32737i	−0.247420	+	0.428543i
$219$	8.93922	+	3.60638i	0.604056	+	0.243697i
$220$	−2.78404	+	7.57918i	−0.187700	+	0.510988i
$221$		−	24.9471i		−	1.67813i
$222$	6.85371	+	8.76314i	0.459991	+	0.588144i
$223$	−1.85603	+	3.21474i	−0.124289	+	0.215275i	−0.921455	−	0.388485i	$-0.872998\pi$
$223$	−1.85603	+	3.21474i	−0.124289	+	0.215275i	0.797166	+	0.603761i	$0.206332\pi$
$224$	2.63972	+	0.178501i	0.176374	+	0.0119266i
$225$	1.49478	+	14.9253i	0.0996518	+	0.995022i
$226$	−6.81995	−	11.8125i	−0.453656	−	0.785755i
$227$	13.9721	−	8.06681i	0.927362	−	0.535413i	0.0413858	−	0.999143i	$-0.486823\pi$
$227$	13.9721	−	8.06681i	0.927362	−	0.535413i	0.885976	+	0.463730i	$0.153489\pi$
$228$	5.11913	+	6.54531i	0.339023	+	0.433474i
$229$	−6.70713	−	3.87236i	−0.443220	−	0.255893i	0.261743	−	0.965138i	$-0.415703\pi$
$229$	−6.70713	−	3.87236i	−0.443220	−	0.255893i	−0.704962	+	0.709245i	$0.749036\pi$
$230$	3.04997	+	17.6019i	0.201109	+	1.16063i
$231$	9.29166	+	13.6925i	0.611346	+	0.900898i
$232$	−7.66188	−	4.42359i	−0.503027	−	0.290423i
$233$	−8.53036	−	14.7750i	−0.558842	−	0.967944i	−0.997593	−	0.0693349i	$-0.977912\pi$
$233$	−8.53036	−	14.7750i	−0.558842	−	0.967944i	0.438751	−	0.898609i	$-0.355421\pi$
$234$	−7.28490	−	7.02061i	−0.476229	−	0.458952i
$235$	−11.7845	−	14.1290i	−0.768738	−	0.921675i
$236$	1.12529			0.0732502
$237$	−0.0417340	−	0.295859i	−0.00271091	−	0.0192181i
$238$	16.2507	+	10.9071i	1.05338	+	0.707001i
$239$	−11.0069	+	6.35481i	−0.711975	+	0.411059i	−0.811792	−	0.583947i	$-0.801508\pi$
$239$	−11.0069	+	6.35481i	−0.711975	+	0.411059i	0.0998171	+	0.995006i	$0.468174\pi$
$240$	2.87183	+	2.59858i	0.185376	+	0.167738i
$241$	−5.49087	+	3.17016i	−0.353698	+	0.204208i	−0.666313	−	0.745672i	$-0.732129\pi$
$241$	−5.49087	+	3.17016i	−0.353698	+	0.204208i	0.312615	+	0.949880i	$0.398795\pi$
$242$	−1.01949	+	1.76581i	−0.0655352	+	0.113510i
$243$	−10.0505	−	11.9159i	−0.644737	−	0.764404i
$244$		−	1.68162i		−	0.107655i
$245$	−13.2605	+	8.31616i	−0.847184	+	0.531300i
$246$	3.57887	−	2.79906i	0.228180	−	0.178461i
$247$	14.0114	+	8.08950i	0.891526	+	0.514723i
$248$		−	6.44913i		−	0.409520i
$249$	−8.62470	+	21.3782i	−0.546568	+	1.35479i
$250$	−5.50395	−	9.73173i	−0.348100	−	0.615489i
$251$	16.1974			1.02237			0.511186	−	0.859470i	$-0.329206\pi$
$251$	16.1974			1.02237			0.511186	+	0.859470i	$0.329206\pi$
$252$	7.75829	−	1.67597i	0.488727	−	0.105576i
$253$			28.8482i			1.81367i
$254$			8.41042i			0.527717i
$255$	8.78653	+	27.2694i	0.550234	+	1.70768i
$256$	1.00000			0.0625000
$257$	0.827880	+	0.477977i	0.0516417	+	0.0298154i	0.525599	−	0.850733i	$-0.323841\pi$
$257$	0.827880	+	0.477977i	0.0516417	+	0.0298154i	−0.473957	+	0.880548i	$0.657175\pi$
$258$	−0.493949	+	1.22436i	−0.0307519	+	0.0762255i
$259$	−15.2567	+	7.48460i	−0.948008	+	0.465070i
$260$	7.07851	+	2.60013i	0.438991	+	0.161253i
$261$	−25.7597	−	6.39473i	−1.59448	−	0.395824i
$262$	2.89711	−	5.01795i	0.178984	−	0.310010i
$263$	8.23669	+	14.2664i	0.507896	+	0.879701i	0.999958	+	0.00914143i	$0.00290985\pi$
$263$	8.23669	+	14.2664i	0.507896	+	0.879701i	−0.492062	+	0.870560i	$0.663757\pi$
$264$	3.85308	+	4.92653i	0.237140	+	0.303207i
$265$	−1.12779	−	6.50862i	−0.0692793	−	0.399821i
$266$	−11.3955	+	5.59035i	−0.698701	+	0.342766i
$267$	−19.3201	+	15.1104i	−1.18237	+	0.924742i
$268$			4.74896i			0.290089i
$269$	−8.79451	+	15.2325i	−0.536210	+	0.928744i	0.462893	+	0.886414i	$0.346811\pi$
$269$	−8.79451	+	15.2325i	−0.536210	+	0.928744i	−0.999104	+	0.0423298i	$0.986522\pi$
$270$	10.4357	+	5.10836i	0.635099	+	0.310885i
$271$	−5.44818	+	3.14551i	−0.330953	+	0.191076i	−0.656264	−	0.754531i	$-0.727864\pi$
$271$	−5.44818	+	3.14551i	−0.330953	+	0.191076i	0.325311	+	0.945607i	$0.394531\pi$
$272$	6.40634	+	3.69870i	0.388441	+	0.224267i
$273$	12.7880	−	8.67786i	0.773962	−	0.525208i
$274$	3.72838	+	6.45775i	0.225240	+	0.390127i
$275$	−6.07452	−	17.0022i	−0.366307	−	1.02527i
$276$	12.8325	+	5.17708i	0.772429	+	0.311624i
$277$	−2.39658	+	1.38367i	−0.143997	+	0.0831365i	−0.570267	−	0.821459i	$-0.693160\pi$
$277$	−2.39658	+	1.38367i	−0.143997	+	0.0831365i	0.426271	+	0.904596i	$0.359827\pi$
$278$	7.19444	−	4.15371i	0.431494	−	0.249123i
$279$	−5.35181	−	18.5925i	−0.320405	−	1.11310i
$280$	−4.78852	+	3.47420i	−0.286169	+	0.207623i
$281$	3.01229	+	1.73915i	0.179698	+	0.103749i	0.587151	−	0.809477i	$-0.300249\pi$
$281$	3.01229	+	1.73915i	0.179698	+	0.103749i	−0.407453	+	0.913226i	$0.633583\pi$
$282$	−14.1117	+	1.99060i	−0.840339	+	0.118539i
$283$	12.2282			0.726889			0.363444	−	0.931616i	$-0.381601\pi$
$283$	12.2282			0.726889			0.363444	+	0.931616i	$0.381601\pi$
$284$			1.40979i			0.0836554i
$285$	−18.1649	−	3.90763i	−1.07600	−	0.231468i
$286$	10.5461	+	6.08882i	0.623607	+	0.360039i
$287$	3.05671	+	6.23086i	0.180432	+	0.367796i
$288$	2.88294	−	0.829851i	0.169879	−	0.0488994i
$289$	18.8608	+	32.6678i	1.10946	+	1.92164i
$290$	19.4924	−	3.37757i	1.14463	−	0.198337i
$291$	13.4515	+	5.42677i	0.788538	+	0.318123i
$292$	−2.78262	+	4.81964i	−0.162840	+	0.282048i
$293$	10.8450	−	6.26137i	0.633572	−	0.365793i	−0.148562	−	0.988903i	$-0.547464\pi$
$293$	10.8450	−	6.26137i	0.633572	−	0.365793i	0.782134	+	0.623110i	$0.214131\pi$
$294$	0.0618228	+	12.1242i	0.00360558	+	0.707098i
$295$	−1.93232	+	1.61169i	−0.112504	+	0.0938359i
$296$	−5.56251	+	3.21152i	−0.323314	+	0.186666i
$297$	15.1965	+	11.0054i	0.881789	+	0.638600i
$298$	10.1240	+	5.84511i	0.586469	+	0.338598i
$299$	26.9425			1.55813
$300$	−8.65322	−	0.349073i	−0.499594	−	0.0201538i
$301$	−1.67451	−	1.12389i	−0.0965173	−	0.0647800i
$302$	−4.53199	−	7.84964i	−0.260787	−	0.451696i
$303$	21.5256	−	16.8353i	1.23661	−	0.967163i
$304$	−4.15471	+	2.39873i	−0.238289	+	0.137576i
$305$	2.40848	+	2.88764i	0.137909	+	0.165346i
$306$	21.5385	+	5.34683i	1.23127	+	0.305658i
$307$	−7.45350			−0.425394			−0.212697	−	0.977118i	$-0.568225\pi$
$307$	−7.45350			−0.425394			−0.212697	+	0.977118i	$0.568225\pi$
$308$	−8.57716	+	4.20775i	−0.488729	+	0.239759i
$309$	6.43173	+	2.59478i	0.365888	+	0.147612i
$310$	9.23669	+	11.0743i	0.524609	+	0.628977i
$311$	−22.5224			−1.27713			−0.638563	−	0.769570i	$-0.720471\pi$
$311$	−22.5224			−1.27713			−0.638563	+	0.769570i	$0.720471\pi$
$312$	4.60109	−	3.59855i	0.260486	−	0.203728i
$313$	20.5931			1.16399			0.581995	−	0.813193i	$-0.302272\pi$
$313$	20.5931			1.16399			0.581995	+	0.813193i	$0.302272\pi$
$314$	19.7804			1.11627
$315$	−10.9220	+	13.9897i	−0.615383	+	0.788228i
$316$	0.172505			0.00970417
$317$	8.71515			0.489492			0.244746	−	0.969587i	$-0.421295\pi$
$317$	8.71515			0.489492			0.244746	+	0.969587i	$0.421295\pi$
$318$	−4.74508	−	1.91432i	−0.266091	−	0.107350i
$319$	31.9467			1.78867
$320$	−1.71718	+	1.43224i	−0.0959930	+	0.0800646i
$321$	4.38796	−	3.43185i	0.244912	−	0.191547i
$322$	−11.7795	+	17.5506i	−0.656446	+	0.978054i
$323$	−35.4887			−1.97464
$324$	7.62270	−	4.78482i	0.423483	−	0.265823i
$325$	−15.8791	+	5.67325i	−0.880811	+	0.314695i
$326$	−11.4067	+	6.58566i	−0.631759	+	0.364746i
$327$	−11.7357	−	4.73457i	−0.648985	−	0.261822i
$328$	1.31158	+	2.27173i	0.0724201	+	0.125435i
$329$	1.46872	−	21.7198i	0.0809730	−	1.19745i
$330$	−13.6724	−	2.94120i	−0.752640	−	0.161908i
$331$	−14.3647			−0.789557			−0.394779	−	0.918776i	$-0.629179\pi$
$331$	−14.3647			−0.789557			−0.394779	+	0.918776i	$0.629179\pi$
$332$	−11.5262	−	6.65467i	−0.632584	−	0.365222i
$333$	−13.3713	+	13.8747i	−0.732743	+	0.760327i
$334$	1.88823	−	1.09017i	0.103320	−	0.0596516i
$335$	−6.80164	−	8.15479i	−0.371613	−	0.445544i
$336$	0.332483	+	4.57050i	0.0181384	+	0.249341i
$337$	9.09613	−	5.25165i	0.495498	−	0.286076i	−0.231355	−	0.972870i	$-0.574316\pi$
$337$	9.09613	−	5.25165i	0.495498	−	0.286076i	0.726852	+	0.686794i	$0.240982\pi$
$338$	−0.813400	+	1.40885i	−0.0442431	+	0.0766313i
$339$	18.6093	−	14.5545i	1.01072	−	0.790491i
$340$	−16.2982	+	2.82409i	−0.883896	+	0.153158i
$341$	11.6437	+	20.1676i	0.630544	+	1.09213i
$342$	−9.98721	+	10.3632i	−0.540046	+	0.560376i
$343$	−18.1416	−	3.72578i	−0.979556	−	0.201173i
$344$	−0.660123	−	0.381122i	−0.0355915	−	0.0205487i
$345$	−29.4506	+	9.48932i	−1.58556	+	0.510888i
$346$		−	25.9317i		−	1.39409i
$347$	13.6614			0.733381			0.366691	−	0.930343i	$-0.380491\pi$
$347$	13.6614			0.733381			0.366691	+	0.930343i	$0.380491\pi$
$348$	5.73314	−	14.2109i	0.307329	−	0.761782i
$349$	30.2742	+	17.4788i	1.62054	+	0.935620i	0.986775	+	0.162095i	$0.0518249\pi$
$349$	30.2742	+	17.4788i	1.62054	+	0.935620i	0.633766	+	0.773525i	$0.281508\pi$
$350$	3.24686	−	12.8241i	0.173552	−	0.685478i
$351$	10.2784	−	14.1926i	0.548622	−	0.757546i
$352$	−3.12718	+	1.80548i	−0.166679	+	0.0962322i
$353$	8.71536	−	5.03181i	0.463872	−	0.267816i	−0.249799	−	0.968298i	$-0.580365\pi$
$353$	8.71536	−	5.03181i	0.463872	−	0.267816i	0.713671	+	0.700481i	$0.247031\pi$
$354$	0.272240	+	1.92995i	0.0144694	+	0.102576i
$355$	−2.01915	−	2.42085i	−0.107165	−	0.128485i
$356$	−7.08044	−	12.2637i	−0.375263	−	0.649974i
$357$	−14.7749	+	30.5099i	−0.781971	+	1.61476i
$358$	12.3911	+	7.15401i	0.654890	+	0.378101i
$359$	−3.51811	+	2.03118i	−0.185679	+	0.107202i	−0.589958	−	0.807434i	$-0.700856\pi$
$359$	−3.51811	+	2.03118i	−0.185679	+	0.107202i	0.404279	+	0.914636i	$0.367522\pi$
$360$	−3.76197	+	5.55406i	−0.198273	+	0.292725i
$361$	2.00777	−	3.47755i	0.105672	−	0.183029i
$362$			4.19706i			0.220592i
$363$	−3.27513	−	1.32130i	−0.171900	−	0.0693500i
$364$	3.92979	+	8.01056i	0.205977	+	0.419868i
$365$	−2.12463	−	12.2615i	−0.111208	−	0.641798i
$366$	2.88410	−	0.406833i	0.150754	−	0.0212655i
$367$	−7.70236	−	13.3409i	−0.402060	−	0.696388i	0.591914	−	0.806001i	$-0.298372\pi$
$367$	−7.70236	−	13.3409i	−0.402060	−	0.696388i	−0.993974	+	0.109613i	$0.965039\pi$
$368$	−3.99454	+	6.91875i	−0.208230	+	0.360665i
$369$	5.66642	+	5.46084i	0.294982	+	0.284280i
$370$	4.95215	−	13.4816i	0.257450	−	0.700874i
$371$	4.35569	−	6.48965i	0.226136	−	0.336926i
$372$	11.0607	−	1.56023i	0.573471	−	0.0808942i
$373$	25.3219	+	14.6196i	1.31112	+	0.756974i	0.982281	−	0.187412i	$-0.0600100\pi$
$373$	25.3219	+	14.6196i	1.31112	+	0.756974i	0.328837	+	0.944387i	$0.393343\pi$
$374$	−26.7117			−1.38123
$375$	15.3590	−	11.7941i	0.793138	−	0.609042i
$376$		−	8.22805i		−	0.424329i
$377$		−	29.8364i		−	1.53665i
$378$	4.75136	+	12.9006i	0.244384	+	0.663533i
$379$	32.1478			1.65132			0.825662	−	0.564166i	$-0.190802\pi$
$379$	32.1478			1.65132			0.825662	+	0.564166i	$0.190802\pi$
$380$	3.69883	−	10.0696i	0.189746	−	0.516558i
$381$	−14.4245	+	2.03472i	−0.738988	+	0.104242i
$382$		−	18.8086i		−	0.962332i
$383$	−5.49320	−	3.17150i	−0.280690	−	0.162056i	0.353046	−	0.935606i	$-0.385146\pi$
$383$	−5.49320	−	3.17150i	−0.280690	−	0.162056i	−0.633736	+	0.773550i	$0.718479\pi$
$384$	0.241929	+	1.71507i	0.0123459	+	0.0875219i
$385$	8.70198	−	19.5100i	0.443494	−	0.994321i
$386$			5.50601i			0.280249i
$387$	−2.21937	−	0.550949i	−0.112817	−	0.0280063i
$388$	−4.18720	+	7.25244i	−0.212573	+	0.368187i
$389$	−21.0192	+	12.1355i	−1.06572	+	0.615292i	−0.927008	−	0.375041i	$-0.877629\pi$
$389$	−21.0192	+	12.1355i	−1.06572	+	0.615292i	−0.138709	+	0.990333i	$0.544295\pi$
$390$	−2.74691	+	12.7692i	−0.139095	+	0.646594i
$391$	−51.1808	+	29.5492i	−2.58832	+	1.49437i
$392$	−6.93627	−	0.942388i	−0.350335	−	0.0475978i
$393$	9.30703	+	3.75477i	0.469478	+	0.189403i
$394$	−13.1218			−0.661066
$395$	−0.296222	+	0.247069i	−0.0149045	+	0.0124314i
$396$	−7.51719	+	7.80017i	−0.377753	+	0.391973i
$397$	3.23274	+	5.59927i	0.162246	+	0.281019i	0.935674	−	0.352866i	$-0.114793\pi$
$397$	3.23274	+	5.59927i	0.162246	+	0.281019i	−0.773428	+	0.633885i	$0.781459\pi$
$398$	9.55302	+	5.51544i	0.478849	+	0.276464i
$399$	−12.3447	−	18.1916i	−0.618010	−	0.910718i
$400$	0.897383	−	4.91881i	0.0448692	−	0.245941i
$401$	31.2348	+	18.0334i	1.55979	+	0.900547i	0.997276	+	0.0737608i	$0.0235001\pi$
$401$	31.2348	+	18.0334i	1.55979	+	0.900547i	0.562517	+	0.826786i	$0.309833\pi$
$402$	−8.14480	+	1.14891i	−0.406226	+	0.0573024i
$403$	18.8353	−	10.8746i	0.938254	−	0.541701i
$404$	7.88869	+	13.6636i	0.392477	+	0.679790i
$405$	−6.23650	+	19.1339i	−0.309894	+	0.950771i
$406$	19.4356	+	13.0447i	0.964574	+	0.647398i
$407$	11.5966	−	20.0860i	0.574824	−	0.995624i
$408$	−4.79366	+	11.8821i	−0.237321	+	0.588254i
$409$		−	35.5824i		−	1.75944i	−0.475496	−	0.879718i	$-0.657731\pi$
$409$		−	35.5824i		−	1.75944i	0.475496	−	0.879718i	$-0.342269\pi$
$410$	−5.50588	−	2.02246i	−0.271916	−	0.0998821i
$411$	−10.1735	+	7.95676i	−0.501821	+	0.392478i
$412$	−2.00208	+	3.46771i	−0.0986355	+	0.170842i
$413$	−2.97046	−	0.200866i	−0.146167	−	0.00988396i
$414$	−5.77450	+	23.2612i	−0.283801	+	1.14323i
$415$	29.3236	−	5.08107i	1.43944	−	0.249420i
$416$	1.68621	+	2.92060i	0.0826732	+	0.143194i
$417$	8.86446	+	11.3341i	0.434094	+	0.555032i
$418$	8.66168	−	15.0025i	0.423657	−	0.733795i
$419$	−9.77575	−	16.9321i	−0.477576	−	0.827187i	0.522093	−	0.852888i	$-0.325151\pi$
$419$	−9.77575	−	16.9321i	−0.477576	−	0.827187i	−0.999670	+	0.0257018i	$0.991818\pi$
$420$	−7.11698	−	7.37215i	−0.347273	−	0.359724i
$421$	6.82851	−	11.8273i	0.332801	−	0.576428i	−0.650259	−	0.759713i	$-0.725340\pi$
$421$	6.82851	−	11.8273i	0.332801	−	0.576428i	0.983060	+	0.183284i	$0.0586729\pi$
$422$	−7.09074	−	12.2815i	−0.345172	−	0.597855i
$423$	−6.82805	−	23.7210i	−0.331991	−	1.15335i
$424$	1.47706	−	2.55834i	0.0717323	−	0.124244i
$425$	23.9421	−	28.1924i	1.16136	−	1.36753i
$426$	−2.41788	+	0.341068i	−0.117147	+	0.0165248i
$427$	−0.300172	+	4.43902i	−0.0145263	+	0.214819i
$428$	1.60810	+	2.78531i	0.0777304	+	0.134633i
$429$	−7.89134	+	19.5605i	−0.380998	+	0.944388i
$430$	1.67941	−	0.291000i	0.0809881	−	0.0140333i
$431$	−6.33629	−	3.65826i	−0.305208	−	0.176212i	0.339572	−	0.940580i	$-0.389718\pi$
$431$	−6.33629	−	3.65826i	−0.305208	−	0.176212i	−0.644780	+	0.764368i	$0.723051\pi$
$432$	2.12072	+	4.74368i	0.102033	+	0.228231i
$433$	−7.45007			−0.358027			−0.179014	−	0.983847i	$-0.557291\pi$
$433$	−7.45007			−0.358027			−0.179014	+	0.983847i	$0.557291\pi$
$434$	−1.15118	+	17.0239i	−0.0552583	+	0.817174i
$435$	10.5085	+	32.6138i	0.503846	+	1.56371i
$436$	3.65311	−	6.32737i	0.174952	−	0.303026i
$437$		−	38.3272i		−	1.83344i
$438$	−8.93922	−	3.60638i	−0.427132	−	0.172320i
$439$		−	15.2426i		−	0.727490i	−0.931498	−	0.363745i	$-0.881498\pi$
$439$		−	15.2426i		−	0.727490i	0.931498	−	0.363745i	$-0.118502\pi$
$440$	2.78404	−	7.57918i	0.132724	−	0.361323i
$441$	−20.7789	+	3.03922i	−0.989472	+	0.144725i
$442$			24.9471i			1.18661i
$443$	−2.19726			−0.104395			−0.0521974	−	0.998637i	$-0.516623\pi$
$443$	−2.19726			−0.104395			−0.0521974	+	0.998637i	$0.516623\pi$
$444$	−6.85371	−	8.76314i	−0.325263	−	0.415880i
$445$	29.7229	+	10.9180i	1.40900	+	0.517564i
$446$	1.85603	−	3.21474i	0.0878857	−	0.152222i
$447$	−7.57549	+	18.7775i	−0.358308	+	0.888147i
$448$	−2.63972	−	0.178501i	−0.124715	−	0.00843339i
$449$		−	11.6919i		−	0.551773i	−0.961190	−	0.275886i	$-0.911029\pi$
$449$		−	11.6919i		−	0.551773i	0.961190	−	0.275886i	$-0.0889713\pi$
$450$	−1.49478	−	14.9253i	−0.0704645	−	0.703587i
$451$	−8.20311	−	4.73607i	−0.386269	−	0.223013i
$452$	6.81995	+	11.8125i	0.320783	+	0.555613i
$453$	12.3663	−	9.67175i	0.581018	−	0.454418i
$454$	−13.9721	+	8.06681i	−0.655744	+	0.378594i
$455$	−18.2212	−	8.12714i	−0.854222	−	0.381006i
$456$	−5.11913	−	6.54531i	−0.239725	−	0.306512i
$457$			21.7463i			1.01725i	0.860988	+	0.508625i	$0.169846\pi$
$457$			21.7463i			1.01725i	−0.860988	+	0.508625i	$0.830154\pi$
$458$	6.70713	+	3.87236i	0.313404	+	0.180944i
$459$	−3.95942	+	38.2336i	−0.184810	+	1.78459i
$460$	−3.04997	−	17.6019i	−0.142206	−	0.820691i
$461$	7.88022	−	13.6489i	0.367019	−	0.635695i	−0.622079	−	0.782954i	$-0.713712\pi$
$461$	7.88022	−	13.6489i	0.367019	−	0.635695i	0.989098	+	0.147259i	$0.0470452\pi$
$462$	−9.29166	−	13.6925i	−0.432287	−	0.637031i
$463$	6.80572	−	3.92928i	0.316288	−	0.182609i	−0.333449	−	0.942768i	$-0.608212\pi$
$463$	6.80572	−	3.92928i	0.316288	−	0.182609i	0.649737	+	0.760159i	$0.274879\pi$
$464$	7.66188	+	4.42359i	0.355694	+	0.205360i
$465$	−16.7586	+	18.5208i	−0.777160	+	0.858881i
$466$	8.53036	+	14.7750i	0.395161	+	0.684439i
$467$	22.1423	−	12.7839i	1.02462	−	0.591567i	0.109184	−	0.994022i	$-0.465176\pi$
$467$	22.1423	−	12.7839i	1.02462	−	0.591567i	0.915440	+	0.402455i	$0.131843\pi$
$468$	7.28490	+	7.02061i	0.336745	+	0.324528i
$469$	0.847695	−	12.5359i	0.0391429	−	0.578855i
$470$	11.7845	+	14.1290i	0.543580	+	0.651722i
$471$	4.78544	+	33.9247i	0.220501	+	1.56317i
$472$	−1.12529			−0.0517957
$473$	2.75243			0.126557
$474$	0.0417340	+	0.295859i	0.00191691	+	0.0135892i
$475$	8.07051	+	22.5888i	0.370300	+	1.03645i
$476$	−16.2507	−	10.9071i	−0.744851	−	0.499925i
$477$	2.13523	−	8.60128i	0.0977655	−	0.393825i
$478$	11.0069	−	6.35481i	0.503442	−	0.290662i
$479$	−3.98318	−	6.89907i	−0.181996	−	0.315227i	0.760564	−	0.649263i	$-0.224923\pi$
$479$	−3.98318	−	6.89907i	−0.181996	−	0.315227i	−0.942560	+	0.334036i	$0.891589\pi$
$480$	−2.87183	−	2.59858i	−0.131080	−	0.118608i
$481$	−18.7591	−	10.8306i	−0.855342	−	0.493832i
$482$	5.49087	−	3.17016i	0.250102	−	0.144397i
$483$	−32.9503	−	15.9567i	−1.49929	−	0.726054i
$484$	1.01949	−	1.76581i	0.0463404	−	0.0802639i
$485$	−3.19707	−	18.4508i	−0.145172	−	0.837806i
$486$	10.0505	+	11.9159i	0.455898	+	0.540515i
$487$	1.35301	+	0.781161i	0.0613108	+	0.0353978i	0.530342	−	0.847784i	$-0.322064\pi$
$487$	1.35301	+	0.781161i	0.0613108	+	0.0353978i	−0.469031	+	0.883182i	$0.655397\pi$
$488$			1.68162i			0.0761235i
$489$	−14.0545	−	17.9700i	−0.635566	−	0.812633i
$490$	13.2605	−	8.31616i	0.599049	−	0.375686i
$491$	−3.63710	+	2.09988i	−0.164140	+	0.0947663i	−0.579820	−	0.814745i	$-0.696877\pi$
$491$	−3.63710	+	2.09988i	−0.164140	+	0.0947663i	0.415680	+	0.909511i	$0.363544\pi$
$492$	−3.57887	+	2.79906i	−0.161348	+	0.126191i
$493$	32.7231	+	56.6780i	1.47377	+	2.55265i
$494$	−14.0114	−	8.08950i	−0.630404	−	0.363964i
$495$	1.73662	−	24.1607i	0.0780554	−	1.08594i
$496$			6.44913i			0.289574i
$497$	0.251648	−	3.72144i	0.0112880	−	0.166929i
$498$	8.62470	−	21.3782i	0.386482	−	0.957982i
$499$	5.57817	−	9.66168i	0.249713	−	0.432516i	−0.713733	−	0.700418i	$-0.752997\pi$
$499$	5.57817	−	9.66168i	0.249713	−	0.432516i	0.963446	+	0.267902i	$0.0863303\pi$
$500$	5.50395	+	9.73173i	0.246144	+	0.435216i
$501$	2.32654	+	2.97471i	0.103942	+	0.132900i
$502$	−16.1974			−0.722926
$503$		−	15.9146i		−	0.709598i	−0.934943	−	0.354799i	$-0.884549\pi$
$503$		−	15.9146i		−	0.709598i	0.934943	−	0.354799i	$-0.115451\pi$
$504$	−7.75829	+	1.67597i	−0.345582	+	0.0746535i
$505$	−33.1158	−	12.1643i	−1.47364	−	0.541306i
$506$		−	28.8482i		−	1.28246i
$507$	−2.61306	−	1.05420i	−0.116050	−	0.0468186i
$508$		−	8.41042i		−	0.373152i
$509$	−7.03825	+	12.1906i	−0.311965	+	0.540339i	−0.978788	−	0.204877i	$-0.934321\pi$
$509$	−7.03825	+	12.1906i	−0.311965	+	0.540339i	0.666823	+	0.745216i	$0.267654\pi$
$510$	−8.78653	−	27.2694i	−0.389074	−	1.20751i
$511$	8.20565	−	12.2258i	0.362997	−	0.540838i
$512$	−1.00000			−0.0441942
$513$	−20.1898	−	14.6216i	−0.891401	−	0.645561i
$514$	−0.827880	−	0.477977i	−0.0365162	−	0.0210827i
$515$	−1.52866	−	8.82212i	−0.0673608	−	0.388749i
$516$	0.493949	−	1.22436i	0.0217449	−	0.0538996i
$517$	14.8555	+	25.7306i	0.653346	+	1.13163i
$518$	15.2567	−	7.48460i	0.670343	−	0.328854i
$519$	44.4746	−	6.27362i	1.95222	−	0.275381i
$520$	−7.07851	−	2.60013i	−0.310413	−	0.114023i
$521$	−15.9369	+	27.6036i	−0.698209	+	1.20933i	0.270877	+	0.962614i	$0.412686\pi$
$521$	−15.9369	+	27.6036i	−0.698209	+	1.20933i	−0.969087	+	0.246720i	$0.920647\pi$
$522$	25.7597	+	6.39473i	1.12747	+	0.279890i
$523$	−5.99562	−	10.3847i	−0.262170	−	0.454092i	0.704648	−	0.709557i	$-0.251105\pi$
$523$	−5.99562	−	10.3847i	−0.262170	−	0.454092i	−0.966818	+	0.255465i	$0.917771\pi$
$524$	−2.89711	+	5.01795i	−0.126561	+	0.219210i
$525$	22.7798	+	2.46607i	0.994191	+	0.107628i
$526$	−8.23669	−	14.2664i	−0.359137	−	0.622043i
$527$	−23.8534	+	41.3153i	−1.03907	+	1.79972i
$528$	−3.85308	−	4.92653i	−0.167684	−	0.214400i
$529$	−20.4128	−	35.3559i	−0.887511	−	1.53721i
$530$	1.12779	+	6.50862i	0.0489879	+	0.282716i
$531$	−3.24415	+	0.933823i	−0.140784	+	0.0405245i
$532$	11.3955	−	5.59035i	0.494056	−	0.242372i
$533$	−4.42321	+	7.66122i	−0.191590	+	0.331844i
$534$	19.3201	−	15.1104i	0.836064	−	0.653891i
$535$	−6.75062	−	2.47968i	−0.291855	−	0.107206i
$536$		−	4.74896i		−	0.205124i
$537$	−9.27187	+	22.9824i	−0.400111	+	0.991763i
$538$	8.79451	−	15.2325i	0.379158	−	0.656721i
$539$	23.3924	−	9.57627i	1.00758	−	0.412479i
$540$	−10.4357	−	5.10836i	−0.449083	−	0.219829i
$541$	−8.92677	−	15.4616i	−0.383792	−	0.664747i	0.607809	−	0.794083i	$-0.292049\pi$
$541$	−8.92677	−	15.4616i	−0.383792	−	0.664747i	−0.991601	+	0.129336i	$0.958715\pi$
$542$	5.44818	−	3.14551i	0.234019	−	0.135111i
$543$	−7.19825	+	1.01539i	−0.308907	+	0.0435745i
$544$	−6.40634	−	3.69870i	−0.274669	−	0.158580i
$545$	2.78928	+	16.0973i	0.119479	+	0.689534i
$546$	−12.7880	+	8.67786i	−0.547274	+	0.371378i
$547$	−16.3179	−	9.42113i	−0.697702	−	0.402818i	0.108789	−	0.994065i	$-0.465303\pi$
$547$	−16.3179	−	9.42113i	−0.697702	−	0.402818i	−0.806491	+	0.591247i	$0.798636\pi$
$548$	−3.72838	−	6.45775i	−0.159269	−	0.275861i
$549$	1.39550	+	4.84802i	0.0595583	+	0.206908i
$550$	6.07452	+	17.0022i	0.259018	+	0.724976i
$551$	−42.4439			−1.80817
$552$	−12.8325	−	5.17708i	−0.546190	−	0.220351i
$553$	−0.455366	−	0.0307924i	−0.0193641	−	0.00130943i
$554$	2.39658	−	1.38367i	0.101821	−	0.0587864i
$555$	24.3199	+	5.23170i	1.03232	+	0.222073i
$556$	−7.19444	+	4.15371i	−0.305112	+	0.176157i
$557$	−16.8982	+	29.2685i	−0.716000	+	1.24015i	0.246573	+	0.969124i	$0.420696\pi$
$557$	−16.8982	+	29.2685i	−0.716000	+	1.24015i	−0.962573	+	0.271024i	$0.912638\pi$
$558$	5.35181	+	18.5925i	0.226560	+	0.787081i
$559$		−	2.57061i		−	0.108725i
$560$	4.78852	−	3.47420i	0.202352	−	0.146812i
$561$	−6.46232	−	45.8124i	−0.272840	−	1.93420i
$562$	−3.01229	−	1.73915i	−0.127066	−	0.0733616i
$563$			22.6063i			0.952743i	0.879244	+	0.476371i	$0.158048\pi$
$563$			22.6063i			0.952743i	−0.879244	+	0.476371i	$0.841952\pi$
$564$	14.1117	−	1.99060i	0.594209	−	0.0838195i
$565$	−28.6294	−	10.5163i	−1.20445	−	0.442425i
$566$	−12.2282			−0.513988
$567$	−20.9759	+	11.2699i	−0.880905	+	0.473293i
$568$		−	1.40979i		−	0.0591533i
$569$		−	13.1152i		−	0.549818i	−0.961470	−	0.274909i	$-0.911352\pi$
$569$		−	13.1152i		−	0.549818i	0.961470	−	0.274909i	$-0.0886477\pi$
$570$	18.1649	+	3.90763i	0.760844	+	0.163673i
$571$	37.4357			1.56663			0.783317	−	0.621623i	$-0.213526\pi$
$571$	37.4357			1.56663			0.783317	+	0.621623i	$0.213526\pi$
$572$	−10.5461	−	6.08882i	−0.440956	−	0.254586i
$573$	32.2581	−	4.55035i	1.34760	−	0.190093i
$574$	−3.05671	−	6.23086i	−0.127585	−	0.260071i
$575$	30.4474	+	25.8572i	1.26974	+	1.07832i
$576$	−2.88294	+	0.829851i	−0.120123	+	0.0345771i
$577$	9.64764	−	16.7102i	0.401636	−	0.695655i	−0.592287	−	0.805727i	$-0.701775\pi$
$577$	9.64764	−	16.7102i	0.401636	−	0.695655i	0.993924	+	0.110072i	$0.0351082\pi$
$578$	−18.8608	−	32.6678i	−0.784505	−	1.35880i
$579$	−9.44320	+	1.33206i	−0.392446	+	0.0553587i
$580$	−19.4924	+	3.37757i	−0.809379	+	0.140246i
$581$	29.2382	+	19.6239i	1.21300	+	0.814137i
$582$	−13.4515	−	5.42677i	−0.557581	−	0.224947i
$583$			10.6672i			0.441789i
$584$	2.78262	−	4.81964i	0.115146	−	0.199438i
$585$	−22.5646	−	1.62190i	−0.932933	−	0.0670575i
$586$	−10.8450	+	6.26137i	−0.448003	+	0.258655i
$587$	20.0370	+	11.5683i	0.827014	+	0.477477i	0.852829	−	0.522190i	$-0.174885\pi$
$587$	20.0370	+	11.5683i	0.827014	+	0.477477i	−0.0258152	+	0.999667i	$0.508218\pi$
$588$	−0.0618228	−	12.1242i	−0.00254953	−	0.499993i
$589$	−15.4697	−	26.7943i	−0.637417	−	1.10404i
$590$	1.93232	−	1.61169i	0.0795524	−	0.0663520i
$591$	−3.17454	−	22.5048i	−0.130583	−	0.925724i
$592$	5.56251	−	3.21152i	0.228618	−	0.131993i
$593$	−12.4103	+	7.16507i	−0.509629	+	0.294234i	−0.732681	−	0.680572i	$-0.761731\pi$
$593$	−12.4103	+	7.16507i	−0.509629	+	0.294234i	0.223052	+	0.974806i	$0.428398\pi$
$594$	−15.1965	−	11.0054i	−0.623519	−	0.451558i
$595$	43.5269	−	4.54556i	1.78443	−	0.186350i
$596$	−10.1240	−	5.84511i	−0.414696	−	0.239425i
$597$	−7.14822	+	17.7184i	−0.292557	+	0.725168i
$598$	−26.9425			−1.10176
$599$			5.64734i			0.230744i	0.993322	+	0.115372i	$0.0368060\pi$
$599$			5.64734i			0.230744i	−0.993322	+	0.115372i	$0.963194\pi$
$600$	8.65322	+	0.349073i	0.353266	+	0.0142509i
$601$	−11.9185	−	6.88116i	−0.486167	−	0.280688i	0.236816	−	0.971554i	$-0.423896\pi$
$601$	−11.9185	−	6.88116i	−0.486167	−	0.280688i	−0.722983	+	0.690866i	$0.757229\pi$
$602$	1.67451	+	1.12389i	0.0682480	+	0.0458063i
$603$	−3.94093	−	13.6910i	−0.160487	−	0.557539i
$604$	4.53199	+	7.84964i	0.184404	+	0.319397i
$605$	0.778415	+	4.49235i	0.0316471	+	0.182640i
$606$	−21.5256	+	16.8353i	−0.874417	+	0.683887i
$607$	−2.83266	+	4.90632i	−0.114974	+	0.199141i	−0.917769	−	0.397114i	$-0.870012\pi$
$607$	−2.83266	+	4.90632i	−0.114974	+	0.199141i	0.802795	+	0.596255i	$0.203345\pi$
$608$	4.15471	−	2.39873i	0.168496	−	0.0972812i
$609$	−17.6706	+	36.4894i	−0.716047	+	1.47862i
$610$	−2.40848	−	2.88764i	−0.0975167	−	0.116917i
$611$	24.0308	−	13.8742i	0.972183	−	0.561290i
$612$	−21.5385	−	5.34683i	−0.870641	−	0.216133i
$613$	4.30137	+	2.48340i	0.173731	+	0.100304i	0.584344	−	0.811506i	$-0.301352\pi$
$613$	4.30137	+	2.48340i	0.173731	+	0.100304i	−0.410613	+	0.911810i	$0.634685\pi$
$614$	7.45350			0.300799
$615$	2.13663	−	9.93227i	0.0861571	−	0.400508i
$616$	8.57716	−	4.20775i	0.345584	−	0.169535i
$617$	−12.3417	−	21.3765i	−0.496858	−	0.860584i	0.503135	−	0.864208i	$-0.332180\pi$
$617$	−12.3417	−	21.3765i	−0.496858	−	0.860584i	−0.999993	+	0.00362388i	$0.998846\pi$
$618$	−6.43173	−	2.59478i	−0.258722	−	0.104377i
$619$	−27.6626	+	15.9710i	−1.11186	+	0.641930i	−0.939309	−	0.343071i	$-0.888533\pi$
$619$	−27.6626	+	15.9710i	−1.11186	+	0.641930i	−0.172546	+	0.985001i	$0.555199\pi$
$620$	−9.23669	−	11.0743i	−0.370955	−	0.444754i
$621$	−41.2917	−	4.27612i	−1.65698	−	0.171595i
$622$	22.5224			0.903064
$623$	16.5013	+	33.6366i	0.661112	+	1.34762i
$624$	−4.60109	+	3.59855i	−0.184191	+	0.144057i
$625$	−23.3894	−	8.82812i	−0.935576	−	0.353125i
$626$	−20.5931			−0.823065
$627$	27.8258	+	11.2259i	1.11126	+	0.448318i
$628$	−19.7804			−0.789322
$629$	47.5138			1.89450
$630$	10.9220	−	13.9897i	0.435142	−	0.557361i
$631$	−29.5217			−1.17524			−0.587620	−	0.809137i	$-0.699935\pi$
$631$	−29.5217			−1.17524			−0.587620	+	0.809137i	$0.699935\pi$
$632$	−0.172505			−0.00686189
$633$	19.3482	−	15.1324i	0.769023	−	0.601458i
$634$	−8.71515			−0.346123
$635$	12.0457	+	14.4422i	0.478020	+	0.573120i
$636$	4.74508	+	1.91432i	0.188155	+	0.0759079i
$637$	−8.94367	−	21.8471i	−0.354361	−	0.865615i
$638$	−31.9467			−1.26478
$639$	−1.16991	−	4.06433i	−0.0462810	−	0.160782i
$640$	1.71718	−	1.43224i	0.0678773	−	0.0566142i
$641$	−26.5658	+	15.3377i	−1.04928	+	0.605804i	−0.922449	−	0.386119i	$-0.873815\pi$
$641$	−26.5658	+	15.3377i	−1.04928	+	0.605804i	−0.126835	+	0.991924i	$0.540482\pi$
$642$	−4.38796	+	3.43185i	−0.173179	+	0.135444i
$643$	9.01650	+	15.6170i	0.355576	+	0.615876i	0.987216	−	0.159386i	$-0.0509514\pi$
$643$	9.01650	+	15.6170i	0.355576	+	0.615876i	−0.631640	+	0.775262i	$0.717618\pi$
$644$	11.7795	−	17.5506i	0.464177	−	0.691589i
$645$	0.905383	+	2.80990i	0.0356494	+	0.110640i
$646$	35.4887			1.39628
$647$	0.566867	+	0.327281i	0.0222858	+	0.0128667i	0.511102	−	0.859520i	$-0.329238\pi$
$647$	0.566867	+	0.327281i	0.0222858	+	0.0128667i	−0.488816	+	0.872387i	$0.662571\pi$
$648$	−7.62270	+	4.78482i	−0.299448	+	0.187966i
$649$	3.51898	−	2.03169i	0.138132	−	0.0797506i
$650$	15.8791	−	5.67325i	0.622828	−	0.222523i
$651$	−29.4757	+	2.14422i	−1.15525	+	0.0840388i
$652$	11.4067	−	6.58566i	0.446721	−	0.257914i
$653$	4.16491	−	7.21384i	0.162986	−	0.282299i	−0.772952	−	0.634464i	$-0.781221\pi$
$653$	4.16491	−	7.21384i	0.162986	−	0.282299i	0.935938	+	0.352165i	$0.114554\pi$
$654$	11.7357	+	4.73457i	0.458901	+	0.185136i
$655$	−2.21205	−	12.7661i	−0.0864319	−	0.498811i
$656$	−1.31158	−	2.27173i	−0.0512088	−	0.0886962i
$657$	4.02255	−	16.2039i	0.156934	−	0.632174i
$658$	−1.46872	+	21.7198i	−0.0572566	+	0.846725i
$659$	32.1220	+	18.5456i	1.25129	+	0.722435i	0.971367	−	0.237586i	$-0.0763561\pi$
$659$	32.1220	+	18.5456i	1.25129	+	0.722435i	0.279928	+	0.960021i	$0.409689\pi$
$660$	13.6724	+	2.94120i	0.532197	+	0.114486i
$661$		−	13.2188i		−	0.514154i	−0.966391	−	0.257077i	$-0.917241\pi$
$661$		−	13.2188i		−	0.514154i	0.966391	−	0.257077i	$-0.0827593\pi$
$662$	14.3647			0.558301
$663$	−42.7861	+	6.03543i	−1.66167	+	0.234397i
$664$	11.5262	+	6.65467i	0.447304	+	0.258251i
$665$	−11.5613	+	25.9206i	−0.448328	+	1.00516i
$666$	13.3713	−	13.8747i	0.518128	−	0.537632i
$667$	−61.2114	+	35.3404i	−2.37012	+	1.36839i
$668$	−1.88823	+	1.09017i	−0.0730580	+	0.0421800i
$669$	5.96254	+	2.40549i	0.230525	+	0.0930016i
$670$	6.80164	+	8.15479i	0.262770	+	0.315047i
$671$	−3.03613	−	5.25873i	−0.117208	−	0.203011i
$672$	−0.332483	−	4.57050i	−0.0128258	−	0.176311i
$673$	−25.9475	−	14.9808i	−1.00020	−	0.577466i	−0.0918934	−	0.995769i	$-0.529292\pi$
$673$	−25.9475	−	14.9808i	−1.00020	−	0.577466i	−0.908308	+	0.418302i	$0.862625\pi$
$674$	−9.09613	+	5.25165i	−0.350370	+	0.202286i
$675$	25.2364	−	6.17452i	0.971349	−	0.237657i
$676$	0.813400	−	1.40885i	0.0312846	−	0.0541865i
$677$			41.9473i			1.61217i	0.591802	+	0.806083i	$0.298417\pi$
$677$			41.9473i			1.61217i	−0.591802	+	0.806083i	$0.701583\pi$
$678$	−18.6093	+	14.5545i	−0.714687	+	0.558961i
$679$	12.3476	−	18.3970i	0.473858	−	0.706012i
$680$	16.2982	−	2.82409i	0.625009	−	0.108299i
$681$	−17.2154	−	22.0116i	−0.659696	−	0.843486i
$682$	−11.6437	−	20.1676i	−0.445862	−	0.772256i
$683$	−17.3451	+	30.0426i	−0.663691	+	1.14955i	0.315947	+	0.948777i	$0.397678\pi$
$683$	−17.3451	+	30.0426i	−0.663691	+	1.14955i	−0.979638	+	0.200770i	$0.935656\pi$
$684$	9.98721	−	10.3632i	0.381871	−	0.396246i
$685$	15.6513	+	5.74915i	0.598006	+	0.219664i
$686$	18.1416	+	3.72578i	0.692650	+	0.142251i
$687$	−5.01873	+	12.4400i	−0.191477	+	0.474617i
$688$	0.660123	+	0.381122i	0.0251670	+	0.0145302i
$689$	9.96251			0.379541
$690$	29.4506	−	9.48932i	1.12116	−	0.361252i
$691$		−	11.7917i		−	0.448577i	−0.974523	−	0.224288i	$-0.927994\pi$
$691$		−	11.7917i		−	0.448577i	0.974523	−	0.224288i	$-0.0720058\pi$
$692$			25.9317i			0.985773i
$693$	21.2356	−	19.2485i	0.806675	−	0.731189i
$694$	−13.6614			−0.518579
$695$	6.40501	−	17.4368i	0.242956	−	0.661416i
$696$	−5.73314	+	14.2109i	−0.217314	+	0.538662i
$697$		−	19.4046i		−	0.735003i
$698$	−30.2742	−	17.4788i	−1.14590	−	0.661583i
$699$	−23.2765	+	18.2047i	−0.880397	+	0.688564i
$700$	−3.24686	+	12.8241i	−0.122720	+	0.484706i
$701$		−	32.3472i		−	1.22174i	−0.791732	−	0.610869i	$-0.790820\pi$
$701$		−	32.3472i		−	1.22174i	0.791732	−	0.610869i	$-0.209180\pi$
$702$	−10.2784	+	14.1926i	−0.387934	+	0.535666i
$703$	−15.4071	+	26.6859i	−0.581089	+	1.00648i
$704$	3.12718	−	1.80548i	0.117860	−	0.0680464i
$705$	−21.3812	+	23.6295i	−0.805264	+	0.889940i
$706$	−8.71536	+	5.03181i	−0.328007	+	0.189375i
$707$	−18.3850	−	37.4763i	−0.691439	−	1.40944i
$708$	−0.272240	−	1.92995i	−0.0102314	−	0.0725321i
$709$	−23.9548			−0.899640			−0.449820	−	0.893119i	$-0.648512\pi$
$709$	−23.9548			−0.899640			−0.449820	+	0.893119i	$0.648512\pi$
$710$	2.01915	+	2.42085i	0.0757773	+	0.0908528i
$711$	−0.497322	+	0.143154i	−0.0186510	+	0.00536868i
$712$	7.08044	+	12.2637i	0.265351	+	0.459601i
$713$	−44.6199	−	25.7613i	−1.67103	−	0.964769i
$714$	14.7749	−	30.5099i	0.552937	−	1.14180i
$715$	26.8302	−	4.64903i	1.00339	−	0.173864i
$716$	−12.3911	−	7.15401i	−0.463077	−	0.267358i
$717$	13.5618	+	17.3401i	0.506476	+	0.647579i
$718$	3.51811	−	2.03118i	0.131295	−	0.0758030i
$719$	−10.7973	−	18.7015i	−0.402672	−	0.697448i	0.591376	−	0.806396i	$-0.298585\pi$
$719$	−10.7973	−	18.7015i	−0.402672	−	0.697448i	−0.994047	+	0.108948i	$0.965252\pi$
$720$	3.76197	−	5.55406i	0.140200	−	0.206988i
$721$	5.90393	−	8.79642i	0.219874	−	0.327596i
$722$	−2.00777	+	3.47755i	−0.0747213	+	0.129421i
$723$	6.76545	+	8.65029i	0.251610	+	0.321708i
$724$		−	4.19706i		−	0.155982i
$725$	28.6344	−	33.7177i	1.06346	−	1.25224i
$726$	3.27513	+	1.32130i	0.121551	+	0.0490379i
$727$	16.1191	−	27.9190i	0.597823	−	1.03546i	−0.395319	−	0.918544i	$-0.629366\pi$
$727$	16.1191	−	27.9190i	0.597823	−	1.03546i	0.993142	−	0.116916i	$-0.0373008\pi$
$728$	−3.92979	−	8.01056i	−0.145648	−	0.296891i
$729$	−18.0051	+	20.1201i	−0.666855	+	0.745187i
$730$	2.12463	+	12.2615i	0.0786360	+	0.453820i
$731$	2.81931	+	4.88320i	0.104276	+	0.180612i
$732$	−2.88410	+	0.406833i	−0.106599	+	0.0150370i
$733$	9.81994	−	17.0086i	0.362708	−	0.628229i	−0.625698	−	0.780066i	$-0.715186\pi$
$733$	9.81994	−	17.0086i	0.362708	−	0.628229i	0.988406	+	0.151837i	$0.0485189\pi$
$734$	7.70236	+	13.3409i	0.284299	+	0.492421i
$735$	17.4709	+	20.7308i	0.644424	+	0.764668i
$736$	3.99454	−	6.91875i	0.147241	−	0.255029i
$737$	8.57413	+	14.8508i	0.315832	+	0.547037i
$738$	−5.66642	−	5.46084i	−0.208584	−	0.201016i
$739$	−18.6678	+	32.3336i	−0.686706	+	1.18941i	0.286191	+	0.958172i	$0.407611\pi$
$739$	−18.6678	+	32.3336i	−0.686706	+	1.18941i	−0.972897	+	0.231237i	$0.925723\pi$
$740$	−4.95215	+	13.4816i	−0.182045	+	0.495593i
$741$	10.4843	−	25.9877i	0.385151	−	0.954682i
$742$	−4.35569	+	6.48965i	−0.159902	+	0.238242i
$743$	6.11862	+	10.5978i	0.224470	+	0.388794i	0.956160	−	0.292843i	$-0.0946015\pi$
$743$	6.11862	+	10.5978i	0.224470	+	0.388794i	−0.731690	+	0.681637i	$0.761268\pi$
$744$	−11.0607	+	1.56023i	−0.405506	+	0.0572008i
$745$	25.7563	−	4.46295i	0.943639	−	0.163510i
$746$	−25.3219	−	14.6196i	−0.927101	−	0.535262i
$747$	38.7518	+	9.61997i	1.41785	+	0.351976i
$748$	26.7117			0.976675
$749$	−3.74775	−	7.63949i	−0.136940	−	0.279141i
$750$	−15.3590	+	11.7941i	−0.560833	+	0.430658i
$751$	−8.02163	+	13.8939i	−0.292713	+	0.506994i	−0.974450	−	0.224603i	$-0.927892\pi$
$751$	−8.02163	+	13.8939i	−0.292713	+	0.506994i	0.681737	+	0.731597i	$0.261225\pi$
$752$			8.22805i			0.300046i
$753$	−3.91862	−	27.7797i	−0.142803	−	1.01235i
$754$			29.8364i			1.08658i
$755$	−19.0248	−	6.98831i	−0.692383	−	0.254331i
$756$	−4.75136	−	12.9006i	−0.172805	−	0.469189i
$757$		−	5.92914i		−	0.215498i	−0.994178	−	0.107749i	$-0.965636\pi$
$757$		−	5.92914i		−	0.215498i	0.994178	−	0.107749i	$-0.0343643\pi$
$758$	−32.1478			−1.16766
$759$	49.4767	−	6.97922i	1.79589	−	0.253329i
$760$	−3.69883	+	10.0696i	−0.134170	+	0.365262i
$761$	−7.29361	+	12.6329i	−0.264393	+	0.457942i	−0.967404	−	0.253236i	$-0.918505\pi$
$761$	−7.29361	+	12.6329i	−0.264393	+	0.457942i	0.703011	+	0.711179i	$0.251838\pi$
$762$	14.4245	−	2.03472i	0.522544	−	0.0737103i
$763$	−10.7726	+	16.0504i	−0.389996	+	0.581064i
$764$			18.8086i			0.680471i
$765$	44.6433	−	21.6668i	1.61408	−	0.783364i
$766$	5.49320	+	3.17150i	0.198478	+	0.114591i
$767$	−1.89748	−	3.28652i	−0.0685139	−	0.118669i
$768$	−0.241929	−	1.71507i	−0.00872986	−	0.0618873i
$769$	28.3116	−	16.3457i	1.02094	−	0.589441i	0.106565	−	0.994306i	$-0.466015\pi$
$769$	28.3116	−	16.3457i	1.02094	−	0.589441i	0.914377	+	0.404865i	$0.132681\pi$
$770$	−8.70198	+	19.5100i	−0.313598	+	0.703091i
$771$	0.619476	−	1.53551i	0.0223099	−	0.0553000i
$772$		−	5.50601i		−	0.198166i
$773$	14.5424	+	8.39605i	0.523053	+	0.301985i	0.738183	−	0.674601i	$-0.235684\pi$
$773$	14.5424	+	8.39605i	0.523053	+	0.301985i	−0.215130	+	0.976585i	$0.569017\pi$
$774$	2.21937	+	0.550949i	0.0797736	+	0.0198035i
$775$	31.7220	+	5.78734i	1.13949	+	0.207887i
$776$	4.18720	−	7.25244i	0.150312	−	0.260347i
$777$	16.5277	+	24.3557i	0.592927	+	0.873755i
$778$	21.0192	−	12.1355i	0.753576	−	0.435077i
$779$	10.8985	+	6.29226i	0.390480	+	0.225444i
$780$	2.74691	−	12.7692i	0.0983551	−	0.457211i
$781$	2.54533	+	4.40865i	0.0910792	+	0.157754i
$782$	51.1808	−	29.5492i	1.83022	−	1.05668i
$783$	−4.73541	+	45.7267i	−0.169230	+	1.63414i
$784$	6.93627	+	0.942388i	0.247724	+	0.0336567i
$785$	33.9663	−	28.3302i	1.21231	−	1.01115i
$786$	−9.30703	−	3.75477i	−0.331971	−	0.133928i
$787$	21.9307			0.781744			0.390872	−	0.920445i	$-0.372173\pi$
$787$	21.9307			0.781744			0.390872	+	0.920445i	$0.372173\pi$
$788$	13.1218			0.467444
$789$	22.4751	−	17.5780i	0.800136	−	0.625792i
$790$	0.296222	−	0.247069i	0.0105391	−	0.00879031i
$791$	−15.8942	−	32.3991i	−0.565133	−	1.15198i
$792$	7.51719	−	7.80017i	0.267112	−	0.277167i
$793$	−4.91134	+	2.83557i	−0.174407	+	0.100694i
$794$	−3.23274	−	5.59927i	−0.114726	−	0.198711i
$795$	−10.8899	+	3.50885i	−0.386225	+	0.124446i
$796$	−9.55302	−	5.51544i	−0.338598	−	0.195489i
$797$	19.5566	−	11.2910i	0.692730	−	0.399948i	−0.111904	−	0.993719i	$-0.535695\pi$
$797$	19.5566	−	11.2910i	0.692730	−	0.399948i	0.804634	+	0.593771i	$0.202362\pi$
$798$	12.3447	+	18.1916i	0.436999	+	0.643975i
$799$	−30.4331	+	52.7117i	−1.07665	+	1.86480i
$800$	−0.897383	+	4.91881i	−0.0317273	+	0.173906i
$801$	30.5895	+	29.4798i	1.08083	+	1.04162i
$802$	−31.2348	−	18.0334i	−1.10294	−	0.636783i
$803$			20.0958i			0.709166i
$804$	8.14480	−	1.14891i	0.287245	−	0.0405189i
$805$	4.90913	+	47.0084i	0.173024	+	1.65683i
$806$	−18.8353	+	10.8746i	−0.663446	+	0.383041i
$807$	28.2525	+	11.3980i	0.994536	+	0.401229i
$808$	−7.88869	−	13.6636i	−0.277523	−	0.480684i
$809$	13.7016	+	7.91060i	0.481721	+	0.278122i	0.721133	−	0.692796i	$-0.243621\pi$
$809$	13.7016	+	7.91060i	0.481721	+	0.278122i	−0.239412	+	0.970918i	$0.576955\pi$
$810$	6.23650	−	19.1339i	0.219128	−	0.672297i
$811$			20.5447i			0.721421i	0.932678	+	0.360710i	$0.117466\pi$
$811$			20.5447i			0.721421i	−0.932678	+	0.360710i	$0.882534\pi$
$812$	−19.4356	−	13.0447i	−0.682057	−	0.457779i
$813$	6.71284	+	8.58302i	0.235430	+	0.301020i
$814$	−11.5966	+	20.0860i	−0.406462	+	0.704012i
$815$	−10.1551	+	27.6459i	−0.355716	+	0.968392i
$816$	4.79366	−	11.8821i	0.167812	−	0.415958i
$817$	−3.65683			−0.127936
$818$			35.5824i			1.24411i
$819$	−17.9769	−	19.8328i	−0.628165	−	0.693015i
$820$	5.50588	+	2.02246i	0.192274	+	0.0706273i
$821$			13.5685i			0.473542i	0.971565	+	0.236771i	$0.0760892\pi$
$821$			13.5685i			0.473542i	−0.971565	+	0.236771i	$0.923911\pi$
$822$	10.1735	−	7.95676i	0.354841	−	0.277524i
$823$		−	18.9960i		−	0.662159i	−0.943603	−	0.331079i	$-0.892587\pi$
$823$		−	18.9960i		−	0.662159i	0.943603	−	0.331079i	$-0.107413\pi$
$824$	2.00208	−	3.46771i	0.0697458	−	0.120803i
$825$	−27.6904	+	14.5316i	−0.964055	+	0.505924i
$826$	2.97046	+	0.200866i	0.103355	+	0.00698902i
$827$	45.9391			1.59746			0.798730	−	0.601689i	$-0.205505\pi$
$827$	45.9391			1.59746			0.798730	+	0.601689i	$0.205505\pi$
$828$	5.77450	−	23.2612i	0.200678	−	0.808384i
$829$	23.0544	+	13.3105i	0.800714	+	0.462292i	0.843721	−	0.536782i	$-0.180360\pi$
$829$	23.0544	+	13.3105i	0.800714	+	0.462292i	−0.0430068	+	0.999075i	$0.513694\pi$
$830$	−29.3236	+	5.08107i	−1.01784	+	0.176367i
$831$	2.95289	+	3.77556i	0.102435	+	0.130973i
$832$	−1.68621	−	2.92060i	−0.0584588	−	0.101254i
$833$	40.9505	+	31.6925i	1.41885	+	1.09808i
$834$	−8.86446	−	11.3341i	−0.306951	−	0.392467i
$835$	1.68104	−	4.57642i	0.0581748	−	0.158374i
$836$	−8.66168	+	15.0025i	−0.299571	+	0.518871i
$837$	−30.5926	+	13.6768i	−1.05744	+	0.472739i
$838$	9.77575	+	16.9321i	0.337698	+	0.584909i
$839$	11.2983	−	19.5693i	0.390062	−	0.675607i	−0.602396	−	0.798198i	$-0.705787\pi$
$839$	11.2983	−	19.5693i	0.390062	−	0.675607i	0.992457	+	0.122591i	$0.0391204\pi$
$840$	7.11698	+	7.37215i	0.245559	+	0.254363i
$841$	24.6363	+	42.6713i	0.849527	+	1.47142i
$842$	−6.82851	+	11.8273i	−0.235326	+	0.407596i
$843$	2.25400	−	5.58705i	0.0776320	−	0.192428i
$844$	7.09074	+	12.2815i	0.244073	+	0.422747i
$845$	0.621060	+	3.58423i	0.0213651	+	0.123301i
$846$	6.82805	+	23.7210i	0.234753	+	0.815544i
$847$	−3.00636	+	4.47926i	−0.103300	+	0.153909i
$848$	−1.47706	+	2.55834i	−0.0507224	+	0.0878537i
$849$	−2.95835	−	20.9722i	−0.101530	−	0.719763i
$850$	−23.9421	+	28.1924i	−0.821209	+	0.966992i
$851$			51.3142i			1.75903i
$852$	2.41788	−	0.341068i	0.0828353	−	0.0116848i
$853$	5.34386	−	9.25584i	0.182970	−	0.316914i	−0.759920	−	0.650016i	$-0.774762\pi$
$853$	5.34386	−	9.25584i	0.182970	−	0.316914i	0.942891	+	0.333102i	$0.108095\pi$
$854$	0.300172	−	4.43902i	0.0102717	−	0.151900i
$855$	−2.30725	+	32.0995i	−0.0789062	+	1.09778i
$856$	−1.60810	−	2.78531i	−0.0549637	−	0.0951999i
$857$	−23.5848	+	13.6167i	−0.805640	+	0.465137i	−0.845440	−	0.534071i	$-0.820661\pi$
$857$	−23.5848	+	13.6167i	−0.805640	+	0.465137i	0.0397993	+	0.999208i	$0.487328\pi$
$858$	7.89134	−	19.5605i	0.269406	−	0.667783i
$859$	−22.6509	−	13.0775i	−0.772838	−	0.446198i	0.0610478	−	0.998135i	$-0.480556\pi$
$859$	−22.6509	−	13.0775i	−0.772838	−	0.446198i	−0.833886	+	0.551936i	$0.813889\pi$
$860$	−1.67941	+	0.291000i	−0.0572673	+	0.00992303i
$861$	9.94686	−	6.74990i	0.338988	−	0.230036i
$862$	6.33629	+	3.65826i	0.215815	+	0.124601i
$863$	−25.1857	−	43.6229i	−0.857331	−	1.48494i	−0.874466	−	0.485087i	$-0.838788\pi$
$863$	−25.1857	−	43.6229i	−0.857331	−	1.48494i	0.0171355	−	0.999853i	$-0.494545\pi$
$864$	−2.12072	−	4.74368i	−0.0721484	−	0.161383i
$865$	−37.1403	−	44.5292i	−1.26281	−	1.51404i
$866$	7.45007			0.253164
$867$	51.4647	−	40.2509i	1.74783	−	1.36699i
$868$	1.15118	−	17.0239i	0.0390735	−	0.577829i
$869$	0.539454	−	0.311454i	0.0182997	−	0.0105653i
$870$	−10.5085	−	32.6138i	−0.356273	−	1.10571i
$871$	13.8698	−	8.00773i	0.469960	−	0.271332i
$872$	−3.65311	+	6.32737i	−0.123710	+	0.214272i
$873$	6.05300	−	24.3831i	0.204863	−	0.825243i
$874$			38.3272i			1.29644i
$875$	−12.7918	−	26.6715i	−0.432441	−	0.901662i
$876$	8.93922	+	3.60638i	0.302028	+	0.121848i
$877$	−29.6735	−	17.1320i	−1.00200	−	0.578507i	−0.0931630	−	0.995651i	$-0.529698\pi$
$877$	−29.6735	−	17.1320i	−1.00200	−	0.578507i	−0.908840	+	0.417144i	$0.863031\pi$
$878$			15.2426i			0.514413i
$879$	−13.3624	−	17.0852i	−0.450703	−	0.576268i
$880$	−2.78404	+	7.57918i	−0.0938499	+	0.255494i
$881$	8.34204			0.281050			0.140525	−	0.990077i	$-0.455121\pi$
$881$	8.34204			0.281050			0.140525	+	0.990077i	$0.455121\pi$
$882$	20.7789	−	3.03922i	0.699662	−	0.102336i
$883$		−	32.5885i		−	1.09669i	−0.836252	−	0.548345i	$-0.815258\pi$
$883$		−	32.5885i		−	1.09669i	0.836252	−	0.548345i	$-0.184742\pi$
$884$		−	24.9471i		−	0.839063i
$885$	3.23164	+	2.92416i	0.108630	+	0.0982945i
$886$	2.19726			0.0738183
$887$	19.5822	+	11.3058i	0.657506	+	0.379611i	0.791326	−	0.611394i	$-0.209391\pi$
$887$	19.5822	+	11.3058i	0.657506	+	0.379611i	−0.133820	+	0.991006i	$0.542724\pi$
$888$	6.85371	+	8.76314i	0.229996	+	0.294072i
$889$	−1.50127	+	22.2012i	−0.0503510	+	0.744604i
$890$	−29.7229	−	10.9180i	−0.996314	−	0.365973i
$891$	15.1986	−	28.7256i	0.509173	−	0.962343i
$892$	−1.85603	+	3.21474i	−0.0621446	+	0.107638i
$893$	−19.7368	−	34.1852i	−0.660468	−	1.14396i
$894$	7.57549	−	18.7775i	0.253362	−	0.628015i
$895$	31.5239	−	5.46234i	1.05373	−	0.182586i
$896$	2.63972	+	0.178501i	0.0881870	+	0.00596331i
$897$	−6.51818	−	46.2084i	−0.217636	−	1.54285i
$898$			11.6919i			0.390162i
$899$	−28.5283	+	49.4125i	−0.951472	+	1.64800i
$900$	1.49478	+	14.9253i	0.0498259	+	0.497511i
$901$	−18.9251	+	10.9264i	−0.630485	+	0.364011i
$902$	8.20311	+	4.73607i	0.273134	+	0.157694i
$903$	−1.52244	+	3.14381i	−0.0506636	+	0.104619i
$904$	−6.81995	−	11.8125i	−0.226828	−	0.392878i
$905$	6.01119	+	7.20708i	0.199819	+	0.239572i
$906$	−12.3663	+	9.67175i	−0.410842	+	0.321322i
$907$	−4.12913	+	2.38395i	−0.137105	+	0.0791578i	−0.566984	−	0.823729i	$-0.691890\pi$
$907$	−4.12913	+	2.38395i	−0.137105	+	0.0791578i	0.429878	+	0.902887i	$0.358556\pi$
$908$	13.9721	−	8.06681i	0.463681	−	0.267706i
$909$	−34.0814	−	32.8450i	−1.13041	−	1.08940i
$910$	18.2212	+	8.12714i	0.604026	+	0.269412i
$911$	−45.4053	−	26.2148i	−1.50434	−	0.868534i	−0.999987	−	0.00503892i	$-0.998396\pi$
$911$	−45.4053	−	26.2148i	−1.50434	−	0.868534i	−0.504357	−	0.863495i	$-0.668271\pi$
$912$	5.11913	+	6.54531i	0.169511	+	0.216737i
$913$	−48.0594			−1.59053
$914$		−	21.7463i		−	0.719304i
$915$	4.36983	−	4.82933i	0.144462	−	0.159653i
$916$	−6.70713	−	3.87236i	−0.221610	−	0.127946i
$917$	8.54328	−	12.7289i	0.282124	−	0.420344i
$918$	3.95942	−	38.2336i	0.130680	−	1.26190i
$919$	11.9138	+	20.6354i	0.393001	+	0.680698i	0.992844	−	0.119420i	$-0.0381034\pi$
$919$	11.9138	+	20.6354i	0.393001	+	0.680698i	−0.599842	+	0.800118i	$0.704770\pi$
$920$	3.04997	+	17.6019i	0.100555	+	0.580316i
$921$	1.80322	+	12.7833i	0.0594180	+	0.421223i
$922$	−7.88022	+	13.6489i	−0.259521	+	0.449504i
$923$	4.11742	−	2.37719i	0.135526	−	0.0782462i
$924$	9.29166	+	13.6925i	0.305673	+	0.450449i
$925$	−10.8051	−	30.2429i	−0.355271	−	0.994380i
$926$	−6.80572	+	3.92928i	−0.223650	+	0.129124i
$927$	2.89420	−	11.6586i	0.0950581	−	0.382920i
$928$	−7.66188	−	4.42359i	−0.251514	−	0.145211i
$929$	10.4976			0.344415			0.172207	−	0.985061i	$-0.444910\pi$
$929$	10.4976			0.344415			0.172207	+	0.985061i	$0.444910\pi$
$930$	16.7586	−	18.5208i	0.549535	−	0.607320i
$931$	−31.0788	+	12.7229i	−1.01857	+	0.416975i
$932$	−8.53036	−	14.7750i	−0.279421	−	0.483972i
$933$	5.44881	+	38.6274i	0.178386	+	1.26461i
$934$	−22.1423	+	12.7839i	−0.724518	+	0.418301i
$935$	−45.8686	+	38.2575i	−1.50006	+	1.25115i
$936$	−7.28490	−	7.02061i	−0.238114	−	0.229476i
$937$	21.2575			0.694452			0.347226	−	0.937781i	$-0.387124\pi$
$937$	21.2575			0.694452			0.347226	+	0.937781i	$0.387124\pi$
$938$	−0.847695	+	12.5359i	−0.0276782	+	0.409313i
$939$	−4.98206	−	35.3186i	−0.162583	−	1.15258i
$940$	−11.7845	−	14.1290i	−0.384369	−	0.460837i
$941$	60.1465			1.96072			0.980361	−	0.197213i	$-0.0631891\pi$
$941$	60.1465			1.96072			0.980361	+	0.197213i	$0.0631891\pi$
$942$	−4.78544	−	33.9247i	−0.155918	−	1.10533i
$943$	20.9567			0.682445
$944$	1.12529			0.0366251
$945$	26.6356	+	15.3475i	0.866456	+	0.499253i
$946$	−2.75243			−0.0894892
$947$	−51.5780			−1.67606			−0.838030	−	0.545624i	$-0.816293\pi$
$947$	−51.5780			−1.67606			−0.838030	+	0.545624i	$0.816293\pi$
$948$	−0.0417340	−	0.295859i	−0.00135546	−	0.00960904i
$949$	18.7683			0.609245
$950$	−8.07051	−	22.5888i	−0.261842	−	0.732878i
$951$	−2.10845	−	14.9471i	−0.0683711	−	0.484693i
$952$	16.2507	+	10.9071i	0.526689	+	0.353501i
$953$	21.6816			0.702337			0.351169	−	0.936312i	$-0.385784\pi$
$953$	21.6816			0.702337			0.351169	+	0.936312i	$0.385784\pi$
$954$	−2.13523	+	8.60128i	−0.0691306	+	0.278477i
$955$	−26.9384	−	32.2977i	−0.871707	−	1.04513i
$956$	−11.0069	+	6.35481i	−0.355987	+	0.205529i
$957$	−7.72884	−	54.7909i	−0.249838	−	1.77114i
$958$	3.98318	+	6.89907i	0.128691	+	0.222899i
$959$	8.68918	+	17.7122i	0.280588	+	0.571956i
$960$	2.87183	+	2.59858i	0.0926878	+	0.0838688i
$961$	−10.5913			−0.341654
$962$	18.7591	+	10.8306i	0.604818	+	0.349192i
$963$	−6.94744	−	6.69540i	−0.223878	−	0.215756i
$964$	−5.49087	+	3.17016i	−0.176849	+	0.102104i
$965$	7.88592	+	9.45479i	0.253857	+	0.304360i
$966$	32.9503	+	15.9567i	1.06016	+	0.513398i
$967$	−24.9910	+	14.4286i	−0.803657	+	0.463992i	−0.844748	−	0.535164i	$-0.820250\pi$
$967$	−24.9910	+	14.4286i	−0.803657	+	0.463992i	0.0410912	+	0.999155i	$0.486917\pi$
$968$	−1.01949	+	1.76581i	−0.0327676	+	0.0567551i
$969$	8.58573	+	60.8656i	0.275814	+	1.95528i
$970$	3.19707	+	18.4508i	0.102652	+	0.592419i
$971$	14.9307	+	25.8608i	0.479150	+	0.829911i	0.999714	−	0.0239109i	$-0.00761181\pi$
$971$	14.9307	+	25.8608i	0.479150	+	0.829911i	−0.520565	+	0.853822i	$0.674278\pi$
$972$	−10.0505	−	11.9159i	−0.322369	−	0.382202i
$973$	19.7328	−	9.68043i	0.632604	−	0.310340i
$974$	−1.35301	−	0.781161i	−0.0433533	−	0.0250300i
$975$	13.5716	+	25.8612i	0.434640	+	0.828221i
$976$		−	1.68162i		−	0.0538274i
$977$	−0.430019			−0.0137575			−0.00687877	−	0.999976i	$-0.502190\pi$
$977$	−0.430019			−0.0137575			−0.00687877	+	0.999976i	$0.502190\pi$
$978$	14.0545	+	17.9700i	0.449413	+	0.574619i
$979$	−44.2836	−	25.5671i	−1.41531	−	0.817129i
$980$	−13.2605	+	8.31616i	−0.423592	+	0.265650i
$981$	−5.28092	+	21.2730i	−0.168607	+	0.679193i
$982$	3.63710	−	2.09988i	0.116065	−	0.0670099i
$983$	−6.91899	+	3.99468i	−0.220682	+	0.127411i	−0.606266	−	0.795262i	$-0.707333\pi$
$983$	−6.91899	+	3.99468i	−0.220682	+	0.127411i	0.385584	+	0.922673i	$0.374000\pi$
$984$	3.57887	−	2.79906i	0.114090	−	0.0892307i
$985$	−22.5324	+	18.7935i	−0.717942	+	0.598812i
$986$	−32.7231	−	56.6780i	−1.04211	−	1.80500i
$987$	−37.6063	+	2.73569i	−1.19702	+	0.0870778i
$988$	14.0114	+	8.08950i	0.445763	+	0.257361i
$989$	−5.27378	+	3.04482i	−0.167697	+	0.0968196i
$990$	−1.73662	+	24.1607i	−0.0551935	+	0.767877i
$991$	28.7067	−	49.7215i	0.911900	−	1.57946i	0.100522	−	0.994935i	$-0.467949\pi$
$991$	28.7067	−	49.7215i	0.911900	−	1.57946i	0.811378	−	0.584522i	$-0.198718\pi$
$992$		−	6.44913i		−	0.204760i
$993$	3.47524	+	24.6366i	0.110284	+	0.781817i
$994$	−0.251648	+	3.72144i	−0.00798180	+	0.118037i
$995$	24.3036	−	4.21123i	0.770477	−	0.133505i
$996$	−8.62470	+	21.3782i	−0.273284	+	0.677396i
$997$	−12.6379	−	21.8894i	−0.400245	−	0.693245i	0.593510	−	0.804827i	$-0.297742\pi$
$997$	−12.6379	−	21.8894i	−0.400245	−	0.693245i	−0.993755	+	0.111582i	$0.964408\pi$
$998$	−5.57817	+	9.66168i	−0.176574	+	0.305835i
$999$	27.0310	+	19.5761i	0.855221	+	0.619359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.a.479.12	yes	48
3.2	odd	2		1890.2.bi.b.899.18		48
5.4	even	2		630.2.bi.b.479.13	yes	48
7.5	odd	6		630.2.r.b.299.3	yes	48
9.4	even	3		1890.2.r.b.1529.23		48
9.5	odd	6		630.2.r.a.59.22	✓	48
15.14	odd	2		1890.2.bi.a.899.15		48
21.5	even	6		1890.2.r.a.89.23		48
35.19	odd	6		630.2.r.a.299.22	yes	48
45.4	even	6		1890.2.r.a.1529.23		48
45.14	odd	6		630.2.r.b.59.3	yes	48
63.5	even	6		630.2.bi.b.509.13	yes	48
63.40	odd	6		1890.2.bi.a.719.15		48
105.89	even	6		1890.2.r.b.89.23		48
315.194	even	6	inner	630.2.bi.a.509.12	yes	48
315.229	odd	6		1890.2.bi.b.719.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.22	✓	48	9.5	odd	6
630.2.r.a.299.22	yes	48	35.19	odd	6
630.2.r.b.59.3	yes	48	45.14	odd	6
630.2.r.b.299.3	yes	48	7.5	odd	6
630.2.bi.a.479.12	yes	48	1.1	even	1	trivial
630.2.bi.a.509.12	yes	48	315.194	even	6	inner
630.2.bi.b.479.13	yes	48	5.4	even	2
630.2.bi.b.509.13	yes	48	63.5	even	6
1890.2.r.a.89.23		48	21.5	even	6
1890.2.r.a.1529.23		48	45.4	even	6
1890.2.r.b.89.23		48	105.89	even	6
1890.2.r.b.1529.23		48	9.4	even	3
1890.2.bi.a.719.15		48	63.40	odd	6
1890.2.bi.a.899.15		48	15.14	odd	2
1890.2.bi.b.719.18		48	315.229	odd	6
1890.2.bi.b.899.18		48	3.2	odd	2

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.241929 - 1.71507i) q^{3} +1.00000 q^{4} +(-1.71718 + 1.43224i) q^{5} +(0.241929 + 1.71507i) q^{6} +(-2.63972 - 0.178501i) q^{7} -1.00000 q^{8} +(-2.88294 + 0.829851i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.241929 - 1.71507i) q^{3} +1.00000 q^{4} +(-1.71718 + 1.43224i) q^{5} +(0.241929 + 1.71507i) q^{6} +(-2.63972 - 0.178501i) q^{7} -1.00000 q^{8} +(-2.88294 + 0.829851i) q^{9} +(1.71718 - 1.43224i) q^{10} +(3.12718 - 1.80548i) q^{11} +(-0.241929 - 1.71507i) q^{12} +(-1.68621 - 2.92060i) q^{13} +(2.63972 + 0.178501i) q^{14} +(2.87183 + 2.59858i) q^{15} +1.00000 q^{16} +(6.40634 + 3.69870i) q^{17} +(2.88294 - 0.829851i) q^{18} +(-4.15471 + 2.39873i) q^{19} +(-1.71718 + 1.43224i) q^{20} +(0.332483 + 4.57050i) q^{21} +(-3.12718 + 1.80548i) q^{22} +(-3.99454 + 6.91875i) q^{23} +(0.241929 + 1.71507i) q^{24} +(0.897383 - 4.91881i) q^{25} +(1.68621 + 2.92060i) q^{26} +(2.12072 + 4.74368i) q^{27} +(-2.63972 - 0.178501i) q^{28} +(7.66188 + 4.42359i) q^{29} +(-2.87183 - 2.59858i) q^{30} +6.44913i q^{31} -1.00000 q^{32} +(-3.85308 - 4.92653i) q^{33} +(-6.40634 - 3.69870i) q^{34} +(4.78852 - 3.47420i) q^{35} +(-2.88294 + 0.829851i) q^{36} +(5.56251 - 3.21152i) q^{37} +(4.15471 - 2.39873i) q^{38} +(-4.60109 + 3.59855i) q^{39} +(1.71718 - 1.43224i) q^{40} +(-1.31158 - 2.27173i) q^{41} +(-0.332483 - 4.57050i) q^{42} +(0.660123 + 0.381122i) q^{43} +(3.12718 - 1.80548i) q^{44} +(3.76197 - 5.55406i) q^{45} +(3.99454 - 6.91875i) q^{46} +8.22805i q^{47} +(-0.241929 - 1.71507i) q^{48} +(6.93627 + 0.942388i) q^{49} +(-0.897383 + 4.91881i) q^{50} +(4.79366 - 11.8821i) q^{51} +(-1.68621 - 2.92060i) q^{52} +(-1.47706 + 2.55834i) q^{53} +(-2.12072 - 4.74368i) q^{54} +(-2.78404 + 7.57918i) q^{55} +(2.63972 + 0.178501i) q^{56} +(5.11913 + 6.54531i) q^{57} +(-7.66188 - 4.42359i) q^{58} +1.12529 q^{59} +(2.87183 + 2.59858i) q^{60} -1.68162i q^{61} -6.44913i q^{62} +(7.75829 - 1.67597i) q^{63} +1.00000 q^{64} +(7.07851 + 2.60013i) q^{65} +(3.85308 + 4.92653i) q^{66} +4.74896i q^{67} +(6.40634 + 3.69870i) q^{68} +(12.8325 + 5.17708i) q^{69} +(-4.78852 + 3.47420i) q^{70} +1.40979i q^{71} +(2.88294 - 0.829851i) q^{72} +(-2.78262 + 4.81964i) q^{73} +(-5.56251 + 3.21152i) q^{74} +(-8.65322 - 0.349073i) q^{75} +(-4.15471 + 2.39873i) q^{76} +(-8.57716 + 4.20775i) q^{77} +(4.60109 - 3.59855i) q^{78} +0.172505 q^{79} +(-1.71718 + 1.43224i) q^{80} +(7.62270 - 4.78482i) q^{81} +(1.31158 + 2.27173i) q^{82} +(-11.5262 - 6.65467i) q^{83} +(0.332483 + 4.57050i) q^{84} +(-16.2982 + 2.82409i) q^{85} +(-0.660123 - 0.381122i) q^{86} +(5.73314 - 14.2109i) q^{87} +(-3.12718 + 1.80548i) q^{88} +(-7.08044 - 12.2637i) q^{89} +(-3.76197 + 5.55406i) q^{90} +(3.92979 + 8.01056i) q^{91} +(-3.99454 + 6.91875i) q^{92} +(11.0607 - 1.56023i) q^{93} -8.22805i q^{94} +(3.69883 - 10.0696i) q^{95} +(0.241929 + 1.71507i) q^{96} +(-4.18720 + 7.25244i) q^{97} +(-6.93627 - 0.942388i) q^{98} +(-7.51719 + 7.80017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} + 42 q^{55} + 3 q^{56} + 22 q^{57} + 3 q^{58} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 q^{70} + 18 q^{73} + 18 q^{75} + 12 q^{77} + 18 q^{78} + 8 q^{81} + 3 q^{82} - 9 q^{83} + 8 q^{84} + 33 q^{85} + 15 q^{87} - 6 q^{88} - 33 q^{89} - 15 q^{90} - 3 q^{92} + 8 q^{93} + 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

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