LMFDB - Embedded newform 630.2.t.b.551.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

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.t (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.3
Character	$\chi$	$=$	630.551
Dual form			630.2.t.b.311.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.790256 - 1.54126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.45501 + 0.939646i) q^{6} +(-1.82075 - 1.91960i) q^{7} +1.00000i q^{8} +(-1.75099 + 2.43599i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.790256 - 1.54126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.45501 + 0.939646i) q^{6} +(-1.82075 - 1.91960i) q^{7} +1.00000i q^{8} +(-1.75099 + 2.43599i) q^{9} +(0.866025 - 0.500000i) q^{10} +3.07697i q^{11} +(-1.72990 - 0.0862508i) q^{12} +(-0.449846 + 0.259719i) q^{13} +(2.53662 + 0.752047i) q^{14} +(0.790256 + 1.54126i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.44423 - 4.23353i) q^{17} +(0.298411 - 2.98512i) q^{18} +(0.713627 + 0.412013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.51975 + 4.32323i) q^{21} +(-1.53849 - 2.66474i) q^{22} +8.94137i q^{23} +(1.54126 - 0.790256i) q^{24} +1.00000 q^{25} +(0.259719 - 0.449846i) q^{26} +(5.13823 + 0.773690i) q^{27} +(-2.57280 + 0.617016i) q^{28} +(5.55412 + 3.20667i) q^{29} +(-1.45501 - 0.939646i) q^{30} +(-0.784474 - 0.452916i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.74243 - 2.43160i) q^{33} +(4.23353 + 2.44423i) q^{34} +(1.82075 + 1.91960i) q^{35} +(1.23413 + 2.73440i) q^{36} +(2.53840 - 4.39664i) q^{37} -0.824025 q^{38} +(0.755788 + 0.488087i) q^{39} -1.00000i q^{40} +(2.18596 + 3.78619i) q^{41} +(-0.845472 - 4.50391i) q^{42} +(-1.84515 + 3.19589i) q^{43} +(2.66474 + 1.53849i) q^{44} +(1.75099 - 2.43599i) q^{45} +(-4.47068 - 7.74345i) q^{46} +(1.89222 + 3.27742i) q^{47} +(-0.939646 + 1.45501i) q^{48} +(-0.369732 + 6.99023i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-4.59342 + 7.11278i) q^{51} +0.519437i q^{52} +(4.69700 - 2.71181i) q^{53} +(-4.83668 + 1.89908i) q^{54} -3.07697i q^{55} +(1.91960 - 1.82075i) q^{56} +(0.0710728 - 1.42548i) q^{57} -6.41334 q^{58} +(-5.29109 + 9.16443i) q^{59} +(1.72990 + 0.0862508i) q^{60} +(-8.24872 + 4.76240i) q^{61} +0.905833 q^{62} +(7.86424 - 1.07412i) q^{63} -1.00000 q^{64} +(0.449846 - 0.259719i) q^{65} +(-2.89127 + 4.47704i) q^{66} +(-3.95287 + 6.84657i) q^{67} -4.88846 q^{68} +(13.7810 - 7.06596i) q^{69} +(-2.53662 - 0.752047i) q^{70} +10.6760i q^{71} +(-2.43599 - 1.75099i) q^{72} +(5.78211 - 3.33830i) q^{73} +5.07681i q^{74} +(-0.790256 - 1.54126i) q^{75} +(0.713627 - 0.412013i) q^{76} +(5.90656 - 5.60240i) q^{77} +(-0.898575 - 0.0448019i) q^{78} +(-1.73049 - 2.99730i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.86805 - 8.53078i) q^{81} +(-3.78619 - 2.18596i) q^{82} +(-3.32033 + 5.75098i) q^{83} +(2.98415 + 3.47776i) q^{84} +(2.44423 + 4.23353i) q^{85} -3.69030i q^{86} +(0.553156 - 11.0945i) q^{87} -3.07697 q^{88} +(0.771960 - 1.33707i) q^{89} +(-0.298411 + 2.98512i) q^{90} +(1.31761 + 0.390641i) q^{91} +(7.74345 + 4.47068i) q^{92} +(-0.0781288 + 1.56700i) q^{93} +(-3.27742 - 1.89222i) q^{94} +(-0.713627 - 0.412013i) q^{95} +(0.0862508 - 1.72990i) q^{96} +(1.93786 + 1.11882i) q^{97} +(-3.17492 - 6.23858i) q^{98} +(-7.49547 - 5.38776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.790256	−	1.54126i	−0.456254	−	0.889849i
$3$	−0.790256	−	1.54126i	−0.456254	−	0.889849i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.45501	+	0.939646i	0.594007	+	0.383609i
$7$	−1.82075	−	1.91960i	−0.688179	−	0.725541i
$7$	−1.82075	−	1.91960i	−0.688179	−	0.725541i
$8$			1.00000i			0.353553i
$9$	−1.75099	+	2.43599i	−0.583664	+	0.811995i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$			3.07697i			0.927743i	0.885903	+	0.463871i	$0.153540\pi$
$11$			3.07697i			0.927743i	−0.885903	+	0.463871i	$0.846460\pi$
$12$	−1.72990	−	0.0862508i	−0.499380	−	0.0248984i
$13$	−0.449846	+	0.259719i	−0.124765	+	0.0720330i	−0.561084	−	0.827759i	$-0.689615\pi$
$13$	−0.449846	+	0.259719i	−0.124765	+	0.0720330i	0.436319	+	0.899792i	$0.356282\pi$
$14$	2.53662	+	0.752047i	0.677939	+	0.200993i
$15$	0.790256	+	1.54126i	0.204043	+	0.397953i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.44423	−	4.23353i	−0.592813	−	1.02678i	−0.993852	−	0.110721i	$-0.964684\pi$
$17$	−2.44423	−	4.23353i	−0.592813	−	1.02678i	0.401039	−	0.916061i	$-0.368649\pi$
$18$	0.298411	−	2.98512i	0.0703361	−	0.703600i
$19$	0.713627	+	0.412013i	0.163717	+	0.0945222i	0.579620	−	0.814887i	$-0.303201\pi$
$19$	0.713627	+	0.412013i	0.163717	+	0.0945222i	−0.415903	+	0.909409i	$0.636534\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−1.51975	+	4.32323i	−0.331637	+	0.943407i
$22$	−1.53849	−	2.66474i	−0.328007	−	0.568124i
$23$			8.94137i			1.86440i	0.361939	+	0.932202i	$0.382115\pi$
$23$			8.94137i			1.86440i	−0.361939	+	0.932202i	$0.617885\pi$
$24$	1.54126	−	0.790256i	0.314609	−	0.161310i
$25$	1.00000			0.200000
$26$	0.259719	−	0.449846i	0.0509350	−	0.0882220i
$27$	5.13823	+	0.773690i	0.988853	+	0.148897i
$28$	−2.57280	+	0.617016i	−0.486213	+	0.116605i
$29$	5.55412	+	3.20667i	1.03137	+	0.595464i	0.917378	−	0.398017i	$-0.130302\pi$
$29$	5.55412	+	3.20667i	1.03137	+	0.595464i	0.113996	+	0.993481i	$0.463635\pi$
$30$	−1.45501	−	0.939646i	−0.265648	−	0.171555i
$31$	−0.784474	−	0.452916i	−0.140896	−	0.0813462i	0.427895	−	0.903828i	$-0.359255\pi$
$31$	−0.784474	−	0.452916i	−0.140896	−	0.0813462i	−0.568791	+	0.822482i	$0.692589\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	4.74243	−	2.43160i	0.825551	−	0.423287i
$34$	4.23353	+	2.44423i	0.726045	+	0.419182i
$35$	1.82075	+	1.91960i	0.307763	+	0.324472i
$36$	1.23413	+	2.73440i	0.205688	+	0.455733i
$37$	2.53840	−	4.39664i	0.417311	−	0.722804i	−0.578357	−	0.815784i	$-0.696306\pi$
$37$	2.53840	−	4.39664i	0.417311	−	0.722804i	0.995668	+	0.0929800i	$0.0296392\pi$
$38$	−0.824025			−0.133675
$39$	0.755788	+	0.488087i	0.121023	+	0.0781565i
$40$		−	1.00000i		−	0.158114i
$41$	2.18596	+	3.78619i	0.341389	+	0.591304i	0.984691	−	0.174309i	$-0.0557692\pi$
$41$	2.18596	+	3.78619i	0.341389	+	0.591304i	−0.643302	+	0.765613i	$0.722436\pi$
$42$	−0.845472	−	4.50391i	−0.130459	−	0.694968i
$43$	−1.84515	+	3.19589i	−0.281383	+	0.487369i	−0.971726	−	0.236113i	$-0.924126\pi$
$43$	−1.84515	+	3.19589i	−0.281383	+	0.487369i	0.690343	+	0.723482i	$0.257460\pi$
$44$	2.66474	+	1.53849i	0.401724	+	0.231936i
$45$	1.75099	−	2.43599i	0.261022	−	0.363135i
$46$	−4.47068	−	7.74345i	−0.659166	−	1.14171i
$47$	1.89222	+	3.27742i	0.276008	+	0.478060i	0.970389	−	0.241547i	$-0.0776549\pi$
$47$	1.89222	+	3.27742i	0.276008	+	0.478060i	−0.694381	+	0.719608i	$0.744322\pi$
$48$	−0.939646	+	1.45501i	−0.135626	+	0.210013i
$49$	−0.369732	+	6.99023i	−0.0528188	+	0.998604i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−4.59342	+	7.11278i	−0.643208	+	0.995988i
$52$			0.519437i			0.0720330i
$53$	4.69700	−	2.71181i	0.645182	−	0.372496i	−0.141426	−	0.989949i	$-0.545169\pi$
$53$	4.69700	−	2.71181i	0.645182	−	0.372496i	0.786608	+	0.617453i	$0.211835\pi$
$54$	−4.83668	+	1.89908i	−0.658189	+	0.258432i
$55$		−	3.07697i		−	0.414899i
$56$	1.91960	−	1.82075i	0.256517	−	0.243308i
$57$	0.0710728	−	1.42548i	0.00941382	−	0.188810i
$58$	−6.41334			−0.842113
$59$	−5.29109	+	9.16443i	−0.688841	+	1.19311i	0.283372	+	0.959010i	$0.408547\pi$
$59$	−5.29109	+	9.16443i	−0.688841	+	1.19311i	−0.972213	+	0.234097i	$0.924787\pi$
$60$	1.72990	+	0.0862508i	0.223329	+	0.0111349i
$61$	−8.24872	+	4.76240i	−1.05614	+	0.609763i	−0.924362	−	0.381516i	$-0.875402\pi$
$61$	−8.24872	+	4.76240i	−1.05614	+	0.609763i	−0.131779	+	0.991279i	$0.542069\pi$
$62$	0.905833			0.115041
$63$	7.86424	−	1.07412i	0.990801	−	0.135326i
$64$	−1.00000			−0.125000
$65$	0.449846	−	0.259719i	0.0557965	−	0.0322141i
$66$	−2.89127	+	4.47704i	−0.355891	+	0.551086i
$67$	−3.95287	+	6.84657i	−0.482920	+	0.836442i	−0.999808	−	0.0196114i	$-0.993757\pi$
$67$	−3.95287	+	6.84657i	−0.482920	+	0.836442i	0.516888	+	0.856053i	$0.327090\pi$
$68$	−4.88846			−0.592813
$69$	13.7810	−	7.06596i	1.65904	−	0.850642i
$70$	−2.53662	−	0.752047i	−0.303184	−	0.0898868i
$71$			10.6760i			1.26701i	0.773741	+	0.633503i	$0.218383\pi$
$71$			10.6760i			1.26701i	−0.773741	+	0.633503i	$0.781617\pi$
$72$	−2.43599	−	1.75099i	−0.287084	−	0.206356i
$73$	5.78211	−	3.33830i	0.676744	−	0.390719i	−0.121883	−	0.992544i	$-0.538893\pi$
$73$	5.78211	−	3.33830i	0.676744	−	0.390719i	0.798627	+	0.601826i	$0.205560\pi$
$74$			5.07681i			0.590167i
$75$	−0.790256	−	1.54126i	−0.0912509	−	0.177970i
$76$	0.713627	−	0.412013i	0.0818586	−	0.0472611i
$77$	5.90656	−	5.60240i	0.673115	−	0.638453i
$78$	−0.898575	−	0.0448019i	−0.101744	−	0.00507281i
$79$	−1.73049	−	2.99730i	−0.194696	−	0.337223i	0.752105	−	0.659043i	$-0.229039\pi$
$79$	−1.73049	−	2.99730i	−0.194696	−	0.337223i	−0.946801	+	0.321820i	$0.895705\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−2.86805	−	8.53078i	−0.318673	−	0.947865i
$82$	−3.78619	−	2.18596i	−0.418115	−	0.241399i
$83$	−3.32033	+	5.75098i	−0.364454	+	0.631252i	−0.988688	−	0.149985i	$-0.952078\pi$
$83$	−3.32033	+	5.75098i	−0.364454	+	0.631252i	0.624235	+	0.781237i	$0.285411\pi$
$84$	2.98415	+	3.47776i	0.325598	+	0.379455i
$85$	2.44423	+	4.23353i	0.265114	+	0.459191i
$86$		−	3.69030i		−	0.397935i
$87$	0.553156	−	11.0945i	0.0593045	−	1.18945i
$88$	−3.07697			−0.328007
$89$	0.771960	−	1.33707i	0.0818276	−	0.141729i	−0.822207	−	0.569188i	$-0.807258\pi$
$89$	0.771960	−	1.33707i	0.0818276	−	0.141729i	0.904035	+	0.427459i	$0.140591\pi$
$90$	−0.298411	+	2.98512i	−0.0314553	+	0.314659i
$91$	1.31761	+	0.390641i	0.138123	+	0.0409503i
$92$	7.74345	+	4.47068i	0.807310	+	0.466101i
$93$	−0.0781288	+	1.56700i	−0.00810158	+	0.162491i
$94$	−3.27742	−	1.89222i	−0.338040	−	0.195167i
$95$	−0.713627	−	0.412013i	−0.0732166	−	0.0422716i
$96$	0.0862508	−	1.72990i	0.00880293	−	0.176557i
$97$	1.93786	+	1.11882i	0.196759	+	0.113599i	0.595143	−	0.803620i	$-0.297095\pi$
$97$	1.93786	+	1.11882i	0.196759	+	0.113599i	−0.398384	+	0.917219i	$0.630429\pi$
$98$	−3.17492	−	6.23858i	−0.320715	−	0.630192i
$99$	−7.49547	−	5.38776i	−0.753323	−	0.541490i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−4.19679			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$101$	−4.19679			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$102$	0.421633	−	8.45656i	0.0417479	−	0.837324i
$103$			0.701137i			0.0690851i	0.999403	+	0.0345426i	$0.0109974\pi$
$103$			0.701137i			0.0690851i	−0.999403	+	0.0345426i	$0.989003\pi$
$104$	−0.259719	−	0.449846i	−0.0254675	−	0.0441110i
$105$	1.51975	−	4.32323i	0.148313	−	0.421904i
$106$	−2.71181	+	4.69700i	−0.263395	+	0.456213i
$107$	−17.8959	−	10.3322i	−1.73006	−	0.998851i	−0.888990	−	0.457927i	$-0.848592\pi$
$107$	−17.8959	−	10.3322i	−1.73006	−	0.998851i	−0.841072	−	0.540924i	$-0.818075\pi$
$108$	3.23915	−	4.06299i	0.311687	−	0.390962i
$109$	−0.903287	−	1.56454i	−0.0865192	−	0.149856i	0.819518	−	0.573053i	$-0.194241\pi$
$109$	−0.903287	−	1.56454i	−0.0865192	−	0.149856i	−0.906038	+	0.423197i	$0.860908\pi$
$110$	1.53849	+	2.66474i	0.146689	+	0.254073i
$111$	−8.78238	−	0.437878i	−0.833587	−	0.0415616i
$112$	−0.752047	+	2.53662i	−0.0710618	+	0.239688i
$113$	−16.2514	+	9.38276i	−1.52881	+	0.882656i	−0.529393	+	0.848377i	$0.677580\pi$
$113$	−16.2514	+	9.38276i	−1.52881	+	0.882656i	−0.999412	+	0.0342794i	$0.989086\pi$
$114$	0.651191	+	1.27004i	0.0609896	+	0.118950i
$115$		−	8.94137i		−	0.833787i
$116$	5.55412	−	3.20667i	0.515687	−	0.297732i
$117$	0.155006	−	1.55058i	0.0143303	−	0.143351i
$118$		−	10.5822i		−	0.974168i
$119$	−3.67635	+	12.4002i	−0.337011	+	1.13672i
$120$	−1.54126	+	0.790256i	−0.140698	+	0.0721401i
$121$	1.53223			0.139293
$122$	4.76240	−	8.24872i	0.431168	−	0.746804i
$123$	4.10805	−	6.36120i	0.370411	−	0.573570i
$124$	−0.784474	+	0.452916i	−0.0704479	+	0.0406731i
$125$	−1.00000			−0.0894427
$126$	−6.27357	+	4.86233i	−0.558894	+	0.433171i
$127$	1.53891			0.136556			0.0682779	−	0.997666i	$-0.478250\pi$
$127$	1.53891			0.136556			0.0682779	+	0.997666i	$0.478250\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	6.38386	+	0.318291i	0.562067	+	0.0280240i
$130$	−0.259719	+	0.449846i	−0.0227788	+	0.0394541i
$131$	10.5223			0.919335			0.459668	−	0.888091i	$-0.347969\pi$
$131$	10.5223			0.919335			0.459668	+	0.888091i	$0.347969\pi$
$132$	0.265391	−	5.32286i	0.0230994	−	0.463296i
$133$	−0.508437	−	2.12005i	−0.0440871	−	0.183832i
$134$		−	7.90574i		−	0.682952i
$135$	−5.13823	−	0.773690i	−0.442228	−	0.0665887i
$136$	4.23353	−	2.44423i	0.363022	−	0.209591i
$137$		−	0.00335499i		−	0.000286636i	−1.00000		0.000143318i	$-0.999954\pi$
$137$		−	0.00335499i		−	0.000286636i	1.00000		0.000143318i	$-4.56196e-5\pi$
$138$	−8.40172	+	13.0098i	−0.715202	+	1.10747i
$139$	16.6324	−	9.60272i	1.41074	−	0.814492i	0.415284	−	0.909692i	$-0.363682\pi$
$139$	16.6324	−	9.60272i	1.41074	−	0.814492i	0.995458	+	0.0951995i	$0.0303489\pi$
$140$	2.57280	−	0.617016i	0.217441	−	0.0521474i
$141$	3.55603	−	5.50641i	0.299472	−	0.463723i
$142$	−5.33799	−	9.24567i	−0.447954	−	0.775879i
$143$	−0.799148	−	1.38416i	−0.0668281	−	0.115750i
$144$	2.98512	+	0.298411i	0.248760	+	0.0248676i
$145$	−5.55412	−	3.20667i	−0.461244	−	0.266300i
$146$	−3.33830	+	5.78211i	−0.276280	+	0.478530i
$147$	11.0660	−	4.95421i	0.912706	−	0.408617i
$148$	−2.53840	−	4.39664i	−0.208655	−	0.361402i
$149$		−	12.0662i		−	0.988502i	−0.869319	−	0.494251i	$-0.835442\pi$
$149$		−	12.0662i		−	0.988502i	0.869319	−	0.494251i	$-0.164558\pi$
$150$	1.45501	+	0.939646i	0.118801	+	0.0767218i
$151$	−14.6605			−1.19305			−0.596527	−	0.802593i	$-0.703453\pi$
$151$	−14.6605			−1.19305			−0.596527	+	0.802593i	$0.703453\pi$
$152$	−0.412013	+	0.713627i	−0.0334186	+	0.0578828i
$153$	14.5927	+	1.45877i	1.17975	+	0.117934i
$154$	−2.31403	+	7.80511i	−0.186470	+	0.628953i
$155$	0.784474	+	0.452916i	0.0630105	+	0.0363791i
$156$	0.800590	−	0.410488i	0.0640985	−	0.0328654i
$157$	−0.502653	−	0.290207i	−0.0401161	−	0.0231610i	0.479808	−	0.877374i	$-0.340706\pi$
$157$	−0.502653	−	0.290207i	−0.0401161	−	0.0231610i	−0.519924	+	0.854213i	$0.674040\pi$
$158$	2.99730	+	1.73049i	0.238453	+	0.137671i
$159$	−7.89145	−	5.09629i	−0.625833	−	0.404162i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	17.1638	−	16.2800i	1.35270	−	1.28304i
$162$	6.74920	+	5.95385i	0.530267	+	0.467779i
$163$	0.0642633	−	0.111307i	0.00503349	−	0.00871827i	−0.863498	−	0.504353i	$-0.831731\pi$
$163$	0.0642633	−	0.111307i	0.00503349	−	0.00871827i	0.868531	+	0.495635i	$0.165064\pi$
$164$	4.37192			0.341389
$165$	−4.74243	+	2.43160i	−0.369198	+	0.189300i
$166$		−	6.64066i		−	0.515415i
$167$	−12.6749	−	21.9535i	−0.980811	−	1.69881i	−0.659247	−	0.751927i	$-0.729125\pi$
$167$	−12.6749	−	21.9535i	−0.980811	−	1.69881i	−0.321564	−	0.946888i	$-0.604209\pi$
$168$	−4.32323	−	1.51975i	−0.333545	−	0.117252i
$169$	−6.36509	+	11.0247i	−0.489622	+	0.848051i
$170$	−4.23353	−	2.44423i	−0.324697	−	0.187464i
$171$	−2.25321	+	1.01695i	−0.172307	+	0.0777684i
$172$	1.84515	+	3.19589i	0.140691	+	0.243685i
$173$	2.36631	+	4.09857i	0.179907	+	0.311609i	0.941849	−	0.336037i	$-0.109087\pi$
$173$	2.36631	+	4.09857i	0.179907	+	0.311609i	−0.761941	+	0.647646i	$0.775754\pi$
$174$	5.06818	+	9.88466i	0.384218	+	0.749354i
$175$	−1.82075	−	1.91960i	−0.137636	−	0.145108i
$176$	2.66474	−	1.53849i	0.200862	−	0.115968i
$177$	18.3061	+	0.912720i	1.37597	+	0.0686043i
$178$			1.54392i			0.115722i
$179$	−6.52127	+	3.76505i	−0.487422	+	0.281413i	−0.723504	−	0.690320i	$-0.757470\pi$
$179$	−6.52127	+	3.76505i	−0.487422	+	0.281413i	0.236082	+	0.971733i	$0.424137\pi$
$180$	−1.23413	−	2.73440i	−0.0919866	−	0.203810i
$181$		−	12.3791i		−	0.920133i	−0.887884	−	0.460067i	$-0.847825\pi$
$181$		−	12.3791i		−	0.920133i	0.887884	−	0.460067i	$-0.152175\pi$
$182$	−1.33641	+	0.320501i	−0.0990611	+	0.0237571i
$183$	13.8587	+	8.94995i	1.02447	+	0.661599i
$184$	−8.94137			−0.659166
$185$	−2.53840	+	4.39664i	−0.186627	+	0.323248i
$186$	−0.715840	−	1.39613i	−0.0524879	−	0.102369i
$187$	13.0265	−	7.52084i	0.952590	−	0.549978i
$188$	3.78444			0.276008
$189$	−7.87026	−	11.2720i	−0.572477	−	0.819921i
$190$	0.824025			0.0597811
$191$	16.6514	−	9.61366i	1.20485	−	0.695620i	0.243220	−	0.969971i	$-0.421796\pi$
$191$	16.6514	−	9.61366i	1.20485	−	0.695620i	0.961630	+	0.274351i	$0.0884630\pi$
$192$	0.790256	+	1.54126i	0.0570318	+	0.111231i
$193$	−11.8348	+	20.4985i	−0.851889	+	1.47551i	0.0276128	+	0.999619i	$0.491209\pi$
$193$	−11.8348	+	20.4985i	−0.851889	+	1.47551i	−0.879502	+	0.475896i	$0.842124\pi$
$194$	−2.23764			−0.160653
$195$	−0.755788	−	0.488087i	−0.0541231	−	0.0349527i
$196$	5.86885	+	3.81531i	0.419204	+	0.272522i
$197$			5.93788i			0.423057i	0.977372	+	0.211528i	$0.0678441\pi$
$197$			5.93788i			0.423057i	−0.977372	+	0.211528i	$0.932156\pi$
$198$	9.18514	+	0.918202i	0.652760	+	0.0652538i
$199$	−14.4039	+	8.31608i	−1.02106	+	0.589511i	−0.914412	−	0.404785i	$-0.867346\pi$
$199$	−14.4039	+	8.31608i	−1.02106	+	0.589511i	−0.106652	+	0.994296i	$0.534013\pi$
$200$			1.00000i			0.0707107i
$201$	13.6762	+	0.681876i	0.964641	+	0.0480958i
$202$	3.63453	−	2.09840i	0.255725	−	0.147643i
$203$	−3.95714	−	16.5002i	−0.277737	−	1.15809i
$204$	3.86313	+	7.53441i	0.270473	+	0.527514i
$205$	−2.18596	−	3.78619i	−0.152674	−	0.264439i
$206$	−0.350569	−	0.607203i	−0.0244253	−	0.0423058i
$207$	−21.7810	−	15.6563i	−1.51389	−	1.08819i
$208$	0.449846	+	0.259719i	0.0311912	+	0.0180082i
$209$	−1.26775	+	2.19581i	−0.0876923	+	0.151888i
$210$	0.845472	+	4.50391i	0.0583431	+	0.310799i
$211$	10.7108	+	18.5516i	0.737360	+	1.27714i	0.953680	+	0.300822i	$0.0972611\pi$
$211$	10.7108	+	18.5516i	0.737360	+	1.27714i	−0.216320	+	0.976322i	$0.569406\pi$
$212$		−	5.42363i		−	0.372496i
$213$	16.4545	−	8.43675i	1.12744	−	0.578077i
$214$	20.6644			1.41259
$215$	1.84515	−	3.19589i	0.125838	−	0.217958i
$216$	−0.773690	+	5.13823i	−0.0526430	+	0.349612i
$217$	0.558914	+	2.33053i	0.0379415	+	0.158206i
$218$	1.56454	+	0.903287i	0.105964	+	0.0611783i
$219$	−9.71455	−	6.27364i	−0.656448	−	0.423934i
$220$	−2.66474	−	1.53849i	−0.179657	−	0.103725i
$221$	2.19905	+	1.26962i	0.147924	+	0.0854042i
$222$	7.82470	−	4.01198i	0.525160	−	0.269266i
$223$	23.0028	+	13.2807i	1.54038	+	0.889340i	0.998814	+	0.0486838i	$0.0155027\pi$
$223$	23.0028	+	13.2807i	1.54038	+	0.889340i	0.541569	+	0.840657i	$0.317831\pi$
$224$	−0.617016	−	2.57280i	−0.0412261	−	0.171902i
$225$	−1.75099	+	2.43599i	−0.116733	+	0.162399i
$226$	9.38276	−	16.2514i	0.624132	−	1.08103i
$227$	−26.7377			−1.77464			−0.887321	−	0.461152i	$-0.847436\pi$
$227$	−26.7377			−1.77464			−0.887321	+	0.461152i	$0.847436\pi$
$228$	−1.19897	−	0.774292i	−0.0794036	−	0.0512788i
$229$		−	7.93372i		−	0.524275i	−0.965031	−	0.262137i	$-0.915573\pi$
$229$		−	7.93372i		−	0.524275i	0.965031	−	0.262137i	$-0.0844274\pi$
$230$	4.47068	+	7.74345i	0.294788	+	0.510588i
$231$	−13.3025	−	4.67624i	−0.875239	−	0.307674i
$232$	−3.20667	+	5.55412i	−0.210528	+	0.364646i
$233$	24.2871	+	14.0222i	1.59110	+	0.918623i	0.993118	+	0.117114i	$0.0373644\pi$
$233$	24.2871	+	14.0222i	1.59110	+	0.918623i	0.597983	+	0.801509i	$0.295969\pi$
$234$	0.641053	+	1.42035i	0.0419069	+	0.0928510i
$235$	−1.89222	−	3.27742i	−0.123435	−	0.213795i
$236$	5.29109	+	9.16443i	0.344420	+	0.596554i
$237$	−3.25210	+	5.03578i	−0.211247	+	0.327109i
$238$	−3.01626	−	12.5770i	−0.195515	−	0.815247i
$239$	−24.5540	+	14.1762i	−1.58826	+	0.916985i	−0.594671	+	0.803969i	$0.702718\pi$
$239$	−24.5540	+	14.1762i	−1.58826	+	0.916985i	−0.993593	+	0.113016i	$0.963949\pi$
$240$	0.939646	−	1.45501i	0.0606539	−	0.0939207i
$241$			0.954238i			0.0614679i	0.999528	+	0.0307339i	$0.00978446\pi$
$241$			0.954238i			0.0614679i	−0.999528	+	0.0307339i	$0.990216\pi$
$242$	−1.32695	+	0.766113i	−0.0852994	+	0.0492476i
$243$	−10.8817	+	11.1619i	−0.698061	+	0.716038i
$244$			9.52480i			0.609763i
$245$	0.369732	−	6.99023i	0.0236213	−	0.446589i
$246$	−0.377081	+	7.56299i	−0.0240418	+	0.482198i
$247$	−0.428029			−0.0272349
$248$	0.452916	−	0.784474i	0.0287602	−	0.0498142i
$249$	11.4877	+	0.572762i	0.728003	+	0.0362973i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	6.84608			0.432121			0.216060	−	0.976380i	$-0.430679\pi$
$251$	6.84608			0.432121			0.216060	+	0.976380i	$0.430679\pi$
$252$	3.00191	−	7.34769i	0.189102	−	0.462861i
$253$	−27.5124			−1.72969
$254$	−1.33273	+	0.769453i	−0.0836230	+	0.0482798i
$255$	4.59342	−	7.11278i	0.287651	−	0.445419i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−26.4342			−1.64892			−0.824459	−	0.565922i	$-0.808521\pi$
$257$	−26.4342			−1.64892			−0.824459	+	0.565922i	$0.808521\pi$
$258$	−5.68773	+	2.91628i	−0.354102	+	0.181560i
$259$	−13.0616	+	3.13247i	−0.811608	+	0.194642i
$260$		−	0.519437i		−	0.0322141i
$261$	−17.5366	+	7.91490i	−1.08549	+	0.489920i
$262$	−9.11256	+	5.26114i	−0.562976	+	0.325034i
$263$			25.7323i			1.58672i	0.608750	+	0.793362i	$0.291671\pi$
$263$			25.7323i			1.58672i	−0.608750	+	0.793362i	$0.708329\pi$
$264$	2.43160	+	4.74243i	0.149654	+	0.291877i
$265$	−4.69700	+	2.71181i	−0.288534	+	0.166585i
$266$	1.50035	+	1.58180i	0.0919921	+	0.0969864i
$267$	−2.67083	−	0.133164i	−0.163452	−	0.00814952i
$268$	3.95287	+	6.84657i	0.241460	+	0.418221i
$269$	−4.44806	−	7.70427i	−0.271203	−	0.469738i	0.697967	−	0.716130i	$-0.254088\pi$
$269$	−4.44806	−	7.70427i	−0.271203	−	0.469738i	−0.969170	+	0.246392i	$0.920755\pi$
$270$	4.83668	−	1.89908i	0.294351	−	0.115574i
$271$	19.2172	+	11.0951i	1.16736	+	0.673978i	0.953058	−	0.302789i	$-0.0979176\pi$
$271$	19.2172	+	11.0951i	1.16736	+	0.673978i	0.214306	+	0.976767i	$0.431251\pi$
$272$	−2.44423	+	4.23353i	−0.148203	+	0.256696i
$273$	−0.439170	−	2.33950i	−0.0265798	−	0.141593i
$274$	0.00167750	+	0.00290551i	0.000101341	+	0.000175528i
$275$			3.07697i			0.185549i
$276$	0.771200	−	15.4677i	0.0464208	−	0.931045i
$277$	12.6086			0.757576			0.378788	−	0.925484i	$-0.376341\pi$
$277$	12.6086			0.757576			0.378788	+	0.925484i	$0.376341\pi$
$278$	−9.60272	+	16.6324i	−0.575933	+	0.997545i
$279$	2.47691	−	1.11792i	0.148289	−	0.0669278i
$280$	−1.91960	+	1.82075i	−0.114718	+	0.108811i
$281$	−6.81401	−	3.93407i	−0.406490	−	0.234687i	0.282791	−	0.959182i	$-0.408740\pi$
$281$	−6.81401	−	3.93407i	−0.406490	−	0.234687i	−0.689280	+	0.724495i	$0.742073\pi$
$282$	−0.326410	+	6.54670i	−0.0194375	+	0.389850i
$283$	−25.5885	−	14.7735i	−1.52108	−	0.878193i	−0.999691	−	0.0248719i	$-0.992082\pi$
$283$	−25.5885	−	14.7735i	−1.52108	−	0.878193i	−0.521385	−	0.853322i	$-0.674584\pi$
$284$	9.24567	+	5.33799i	0.548629	+	0.316751i
$285$	−0.0710728	+	1.42548i	−0.00420999	+	0.0844383i
$286$	1.38416	+	0.799148i	0.0818474	+	0.0472546i
$287$	3.28789	−	11.0899i	0.194078	−	0.654615i
$288$	−2.73440	+	1.23413i	−0.161126	+	0.0727218i
$289$	−3.44853	+	5.97302i	−0.202854	+	0.351354i
$290$	6.41334			0.376605
$291$	0.192998	−	3.87090i	0.0113138	−	0.226916i
$292$		−	6.67660i		−	0.390719i
$293$	−3.97830	−	6.89061i	−0.232415	−	0.402554i	0.726104	−	0.687585i	$-0.241329\pi$
$293$	−3.97830	−	6.89061i	−0.232415	−	0.402554i	−0.958518	+	0.285031i	$0.907996\pi$
$294$	−7.10631	+	9.82346i	−0.414448	+	0.572916i
$295$	5.29109	−	9.16443i	0.308059	−	0.533574i
$296$	4.39664	+	2.53840i	0.255550	+	0.147542i
$297$	−2.38063	+	15.8102i	−0.138138	+	0.917401i
$298$	6.03310	+	10.4496i	0.349488	+	0.605332i
$299$	−2.32224	−	4.02224i	−0.134299	−	0.232612i
$300$	−1.72990	−	0.0862508i	−0.0998759	−	0.00497969i
$301$	9.49440	−	2.27698i	0.547248	−	0.131243i
$302$	12.6964	−	7.33025i	0.730593	−	0.421808i
$303$	3.31654	+	6.46837i	0.190530	+	0.371598i
$304$		−	0.824025i		−	0.0472611i
$305$	8.24872	−	4.76240i	0.472320	−	0.272694i
$306$	−13.3670	+	6.03299i	−0.764140	+	0.344883i
$307$			33.8175i			1.93006i	0.262132	+	0.965032i	$0.415574\pi$
$307$			33.8175i			1.93006i	−0.262132	+	0.965032i	$0.584426\pi$
$308$	−1.89854	−	7.91644i	−0.108180	−	0.451081i
$309$	1.08064	−	0.554078i	0.0614754	−	0.0315204i
$310$	−0.905833			−0.0514479
$311$	−11.6897	+	20.2471i	−0.662861	+	1.14811i	0.316999	+	0.948426i	$0.397325\pi$
$311$	−11.6897	+	20.2471i	−0.662861	+	1.14811i	−0.979860	+	0.199684i	$0.936009\pi$
$312$	−0.488087	+	0.755788i	−0.0276325	+	0.0427881i
$313$	14.9966	−	8.65830i	0.847659	−	0.489396i	−0.0122014	−	0.999926i	$-0.503884\pi$
$313$	14.9966	−	8.65830i	0.847659	−	0.489396i	0.859860	+	0.510529i	$0.170551\pi$
$314$	0.580414			0.0327546
$315$	−7.86424	+	1.07412i	−0.443100	+	0.0605197i
$316$	−3.46099			−0.194696
$317$	13.8006	−	7.96781i	0.775121	−	0.447517i	−0.0595771	−	0.998224i	$-0.518975\pi$
$317$	13.8006	−	7.96781i	0.775121	−	0.447517i	0.834699	+	0.550707i	$0.185642\pi$
$318$	9.38234	+	0.467792i	0.526136	+	0.0262325i
$319$	−9.86685	+	17.0899i	−0.552437	+	0.956850i
$320$	1.00000			0.0559017
$321$	−1.78232	+	35.7474i	−0.0994794	+	1.99522i
$322$	−6.72433	+	22.6808i	−0.374732	+	1.26395i
$323$		−	4.02822i		−	0.224136i
$324$	−8.82190	−	1.78158i	−0.490106	−	0.0989769i
$325$	−0.449846	+	0.259719i	−0.0249530	+	0.0144066i
$326$			0.128527i			0.00711843i
$327$	−1.69754	+	2.62859i	−0.0938743	+	0.145361i
$328$	−3.78619	+	2.18596i	−0.209057	+	0.120699i
$329$	2.84607	−	9.59966i	0.156909	−	0.529247i
$330$	2.89127	−	4.47704i	0.159159	−	0.246453i
$331$	−4.20318	−	7.28013i	−0.231028	−	0.400152i	0.727083	−	0.686550i	$-0.240876\pi$
$331$	−4.20318	−	7.28013i	−0.231028	−	0.400152i	−0.958111	+	0.286398i	$0.907542\pi$
$332$	3.32033	+	5.75098i	0.182227	+	0.315626i
$333$	6.26544	+	13.8820i	0.343344	+	0.760729i
$334$	21.9535	+	12.6749i	1.20124	+	0.693538i
$335$	3.95287	−	6.84657i	0.215968	−	0.374068i
$336$	4.50391	−	0.845472i	0.245708	−	0.0461243i
$337$	7.68218	+	13.3059i	0.418475	+	0.724820i	0.995786	−	0.0917044i	$-0.0292315\pi$
$337$	7.68218	+	13.3059i	0.418475	+	0.724820i	−0.577311	+	0.816524i	$0.695898\pi$
$338$		−	12.7302i		−	0.692431i
$339$	27.3041	+	17.6330i	1.48296	+	0.957691i
$340$	4.88846			0.265114
$341$	1.39361	−	2.41381i	0.0754684	−	0.130715i
$342$	1.44286	−	2.00731i	0.0780210	−	0.108543i
$343$	14.0916	−	12.0177i	0.760877	−	0.648896i
$344$	−3.19589	−	1.84515i	−0.172311	−	0.0994838i
$345$	−13.7810	+	7.06596i	−0.741945	+	0.380419i
$346$	−4.09857	−	2.36631i	−0.220341	−	0.127214i
$347$	−9.56913	−	5.52474i	−0.513698	−	0.296584i	0.220654	−	0.975352i	$-0.429181\pi$
$347$	−9.56913	−	5.52474i	−0.513698	−	0.296584i	−0.734352	+	0.678768i	$0.762514\pi$
$348$	−9.33150	−	6.02628i	−0.500221	−	0.323042i
$349$	13.7644	+	7.94687i	0.736791	+	0.425386i	0.820901	−	0.571070i	$-0.193472\pi$
$349$	13.7644	+	7.94687i	0.736791	+	0.425386i	−0.0841107	+	0.996456i	$0.526805\pi$
$350$	2.53662	+	0.752047i	0.135588	+	0.0401986i
$351$	−2.51235	+	0.986452i	−0.134099	+	0.0526529i
$352$	−1.53849	+	2.66474i	−0.0820017	+	0.142031i
$353$	−11.9879			−0.638053			−0.319026	−	0.947746i	$-0.603356\pi$
$353$	−11.9879			−0.638053			−0.319026	+	0.947746i	$0.603356\pi$
$354$	−16.3099	+	8.36262i	−0.866863	+	0.444468i
$355$		−	10.6760i		−	0.566622i
$356$	−0.771960	−	1.33707i	−0.0409138	−	0.0708647i
$357$	22.0172	−	4.13306i	1.16527	−	0.218745i
$358$	3.76505	−	6.52127i	0.198989	−	0.344660i
$359$	−11.7767	−	6.79925i	−0.621548	−	0.358851i	0.155923	−	0.987769i	$-0.450165\pi$
$359$	−11.7767	−	6.79925i	−0.621548	−	0.358851i	−0.777471	+	0.628918i	$0.783498\pi$
$360$	2.43599	+	1.75099i	0.128388	+	0.0922854i
$361$	−9.16049	−	15.8664i	−0.482131	−	0.835076i
$362$	6.18956	+	10.7206i	0.325316	+	0.563464i
$363$	−1.21085	−	2.36157i	−0.0635532	−	0.123950i
$364$	0.997112	−	0.945766i	0.0522629	−	0.0495716i
$365$	−5.78211	+	3.33830i	−0.302649	+	0.174735i
$366$	−16.4770	−	0.821522i	−0.861265	−	0.0429416i
$367$			5.63278i			0.294029i	0.989134	+	0.147014i	$0.0469664\pi$
$367$			5.63278i			0.294029i	−0.989134	+	0.147014i	$0.953034\pi$
$368$	7.74345	−	4.47068i	0.403655	−	0.233050i
$369$	−13.0507	−	1.30463i	−0.679392	−	0.0679161i
$370$		−	5.07681i		−	0.263931i
$371$	−13.7577	−	4.07882i	−0.714262	−	0.211762i
$372$	1.31800	+	0.851163i	0.0683351	+	0.0441307i
$373$	5.72999			0.296687			0.148344	−	0.988936i	$-0.452606\pi$
$373$	5.72999			0.296687			0.148344	+	0.988936i	$0.452606\pi$
$374$	−7.52084	+	13.0265i	−0.388893	+	0.673583i
$375$	0.790256	+	1.54126i	0.0408086	+	0.0795906i
$376$	−3.27742	+	1.89222i	−0.169020	+	0.0975837i
$377$	−3.33133			−0.171572
$378$	12.4519	+	5.82675i	0.640455	+	0.299696i
$379$	−12.0397			−0.618437			−0.309219	−	0.950991i	$-0.600067\pi$
$379$	−12.0397			−0.618437			−0.309219	+	0.950991i	$0.600067\pi$
$380$	−0.713627	+	0.412013i	−0.0366083	+	0.0211358i
$381$	−1.21613	−	2.37186i	−0.0623042	−	0.121514i
$382$	−9.61366	+	16.6514i	−0.491878	+	0.851957i
$383$	20.5060			1.04781			0.523903	−	0.851778i	$-0.324475\pi$
$383$	20.5060			1.04781			0.523903	+	0.851778i	$0.324475\pi$
$384$	−1.45501	−	0.939646i	−0.0742509	−	0.0479511i
$385$	−5.90656	+	5.60240i	−0.301026	+	0.285525i
$386$		−	23.6696i		−	1.20475i
$387$	−4.55431	−	10.0907i	−0.231508	−	0.512941i
$388$	1.93786	−	1.11882i	0.0983797	−	0.0567995i
$389$		−	25.8396i		−	1.31012i	−0.755577	−	0.655060i	$-0.772643\pi$
$389$		−	25.8396i		−	1.31012i	0.755577	−	0.655060i	$-0.227357\pi$
$390$	0.898575	+	0.0448019i	0.0455011	+	0.00226863i
$391$	37.8536	−	21.8548i	1.91434	−	1.10524i
$392$	−6.99023	−	0.369732i	−0.353060	−	0.0186743i
$393$	−8.31529	−	16.2176i	−0.419451	−	0.818070i
$394$	−2.96894	−	5.14236i	−0.149573	−	0.259068i
$395$	1.73049	+	2.99730i	0.0870706	+	0.150811i
$396$	−8.41367	+	3.79739i	−0.422803	+	0.190826i
$397$	5.58453	+	3.22423i	0.280279	+	0.161819i	0.633550	−	0.773702i	$-0.281597\pi$
$397$	5.58453	+	3.22423i	0.280279	+	0.161819i	−0.353271	+	0.935521i	$0.614930\pi$
$398$	8.31608	−	14.4039i	0.416848	−	0.722001i
$399$	−2.86576	+	2.45902i	−0.143468	+	0.123105i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$			12.1434i			0.606413i	0.952925	+	0.303206i	$0.0980571\pi$
$401$			12.1434i			0.606413i	−0.952925	+	0.303206i	$0.901943\pi$
$402$	−12.1848	+	6.24755i	−0.607724	+	0.311600i
$403$	0.470523			0.0234384
$404$	−2.09840	+	3.63453i	−0.104399	+	0.180825i
$405$	2.86805	+	8.53078i	0.142515	+	0.423898i
$406$	11.6771	+	12.3111i	0.579525	+	0.610988i
$407$	13.5284	+	7.81060i	0.670576	+	0.387157i
$408$	−7.11278	−	4.59342i	−0.352135	−	0.227408i
$409$	19.2077	+	11.0896i	0.949761	+	0.548345i	0.893007	−	0.450043i	$-0.148591\pi$
$409$	19.2077	+	11.0896i	0.949761	+	0.548345i	0.0567546	+	0.998388i	$0.481925\pi$
$410$	3.78619	+	2.18596i	0.186987	+	0.107957i
$411$	−0.00517093	+	0.00265130i	−0.000255063	+	0.000130779i
$412$	0.607203	+	0.350569i	0.0299147	+	0.0172713i
$413$	27.2258	−	6.52937i	1.33969	−	0.321289i
$414$	26.6911	+	2.66820i	1.31179	+	0.131135i
$415$	3.32033	−	5.75098i	0.162989	−	0.282305i
$416$	−0.519437			−0.0254675
$417$	−27.9442	−	18.0463i	−1.36843	−	0.883732i
$418$		−	2.53551i		−	0.124016i
$419$	−7.31349	−	12.6673i	−0.357287	−	0.618840i	0.630219	−	0.776417i	$-0.282965\pi$
$419$	−7.31349	−	12.6673i	−0.357287	−	0.618840i	−0.987507	+	0.157577i	$0.949632\pi$
$420$	−2.98415	−	3.47776i	−0.145612	−	0.169697i
$421$	17.6810	−	30.6243i	0.861717	−	1.49254i	−0.00855262	−	0.999963i	$-0.502722\pi$
$421$	17.6810	−	30.6243i	0.861717	−	1.49254i	0.870270	−	0.492575i	$-0.163944\pi$
$422$	−18.5516	−	10.7108i	−0.903078	−	0.521392i
$423$	−11.2970	−	1.12932i	−0.549279	−	0.0549092i
$424$	2.71181	+	4.69700i	0.131697	+	0.228106i
$425$	−2.44423	−	4.23353i	−0.118563	−	0.205356i
$426$	−10.0316	+	15.5337i	−0.486035	+	0.752610i
$427$	24.1608	+	7.16310i	1.16922	+	0.346647i
$428$	−17.8959	+	10.3322i	−0.865031	+	0.499426i
$429$	−1.50183	+	2.32554i	−0.0725091	+	0.112278i
$430$			3.69030i			0.177962i
$431$	14.2396	−	8.22125i	0.685898	−	0.396003i	−0.116175	−	0.993229i	$-0.537063\pi$
$431$	14.2396	−	8.22125i	0.685898	−	0.396003i	0.802074	+	0.597225i	$0.203730\pi$
$432$	−1.89908	−	4.83668i	−0.0913695	−	0.232705i
$433$			22.0355i			1.05896i	0.848323	+	0.529479i	$0.177612\pi$
$433$			22.0355i			1.05896i	−0.848323	+	0.529479i	$0.822388\pi$
$434$	−1.64930	−	1.73884i	−0.0791687	−	0.0834669i
$435$	−0.553156	+	11.0945i	−0.0265218	+	0.531938i
$436$	−1.80657			−0.0865192
$437$	−3.68396	+	6.38080i	−0.176228	+	0.305235i
$438$	11.5499	+	0.575862i	0.551874	+	0.0275157i
$439$	21.4924	−	12.4087i	1.02578	−	0.592233i	0.110006	−	0.993931i	$-0.464913\pi$
$439$	21.4924	−	12.4087i	1.02578	−	0.592233i	0.915772	+	0.401697i	$0.131580\pi$
$440$	3.07697			0.146689
$441$	−16.3807	−	13.1405i	−0.780033	−	0.625738i
$442$	−2.53925			−0.120780
$443$	−14.3967	+	8.31193i	−0.684007	+	0.394912i	−0.801363	−	0.598178i	$-0.795891\pi$
$443$	−14.3967	+	8.31193i	−0.684007	+	0.394912i	0.117356	+	0.993090i	$0.462558\pi$
$444$	−4.77040	+	7.38682i	−0.226393	+	0.350563i
$445$	−0.771960	+	1.33707i	−0.0365944	+	0.0633834i
$446$	−26.5614			−1.25772
$447$	−18.5972	+	9.53539i	−0.879618	+	0.451008i
$448$	1.82075	+	1.91960i	0.0860224	+	0.0906926i
$449$		−	12.5154i		−	0.590638i	−0.955399	−	0.295319i	$-0.904574\pi$
$449$		−	12.5154i		−	0.590638i	0.955399	−	0.295319i	$-0.0954260\pi$
$450$	0.298411	−	2.98512i	0.0140672	−	0.140720i
$451$	−11.6500	+	6.72614i	−0.548578	+	0.316721i
$452$			18.7655i			0.882656i
$453$	11.5855	+	22.5957i	0.544336	+	1.06164i
$454$	23.1555	−	13.3688i	1.08674	−	0.627431i
$455$	−1.31761	−	0.390641i	−0.0617707	−	0.0183135i
$456$	1.42548	+	0.0710728i	0.0667544	+	0.00332829i
$457$	16.3501	+	28.3193i	0.764827	+	1.32472i	0.940338	+	0.340242i	$0.110509\pi$
$457$	16.3501	+	28.3193i	0.764827	+	1.32472i	−0.175511	+	0.984478i	$0.556158\pi$
$458$	3.96686	+	6.87080i	0.185359	+	0.321051i
$459$	−9.28358	−	23.6439i	−0.433320	−	1.10360i
$460$	−7.74345	−	4.47068i	−0.361040	−	0.208447i
$461$	2.69005	−	4.65931i	0.125288	−	0.217006i	−0.796557	−	0.604563i	$-0.793348\pi$
$461$	2.69005	−	4.65931i	0.125288	−	0.217006i	0.921846	+	0.387557i	$0.126681\pi$
$462$	13.8584	−	2.60150i	0.644751	−	0.121033i
$463$	5.41835	+	9.38485i	0.251812	+	0.436151i	0.964025	−	0.265813i	$-0.0856402\pi$
$463$	5.41835	+	9.38485i	0.251812	+	0.436151i	−0.712213	+	0.701964i	$0.752307\pi$
$464$		−	6.41334i		−	0.297732i
$465$	0.0781288	−	1.56700i	0.00362314	−	0.0726680i
$466$	−28.0443			−1.29913
$467$	−2.76713	+	4.79281i	−0.128048	+	0.221785i	−0.922920	−	0.384992i	$-0.874204\pi$
$467$	−2.76713	+	4.79281i	−0.128048	+	0.221785i	0.794872	+	0.606777i	$0.207538\pi$
$468$	−1.26534	−	0.909530i	−0.0584904	−	0.0420431i
$469$	20.3399	−	4.87797i	0.939208	−	0.225244i
$470$	3.27742	+	1.89222i	0.151176	+	0.0872815i
$471$	−0.0500611	+	1.00406i	−0.00230670	+	0.0462646i
$472$	−9.16443	−	5.29109i	−0.421827	−	0.243542i
$473$	−9.83368	−	5.67748i	−0.452153	−	0.261051i
$474$	0.298513	−	5.98717i	0.0137111	−	0.275000i
$475$	0.713627	+	0.412013i	0.0327434	+	0.0189044i
$476$	8.90067	+	9.38389i	0.407962	+	0.430110i
$477$	−1.61847	+	16.1902i	−0.0741046	+	0.741298i
$478$	14.1762	−	24.5540i	0.648406	−	1.12307i
$479$	39.8255			1.81968			0.909838	−	0.414964i	$-0.136206\pi$
$479$	39.8255			1.81968			0.909838	+	0.414964i	$0.136206\pi$
$480$	−0.0862508	+	1.72990i	−0.00393679	+	0.0789589i
$481$			2.63708i			0.120241i
$482$	−0.477119	−	0.826394i	−0.0217322	−	0.0376412i
$483$	−38.6556	−	13.5887i	−1.75889	−	0.618306i
$484$	0.766113	−	1.32695i	0.0348233	−	0.0603158i
$485$	−1.93786	−	1.11882i	−0.0879935	−	0.0508031i
$486$	3.84286	−	15.1074i	0.174316	−	0.685284i
$487$	19.7936	+	34.2835i	0.896934	+	1.55354i	0.831393	+	0.555685i	$0.187544\pi$
$487$	19.7936	+	34.2835i	0.896934	+	1.55354i	0.0655411	+	0.997850i	$0.479123\pi$
$488$	−4.76240	−	8.24872i	−0.215584	−	0.373402i
$489$	−0.222339	−	0.0110855i	−0.0100545	−	0.000501305i
$490$	3.17492	+	6.23858i	0.143428	+	0.281830i
$491$	27.1823	−	15.6937i	1.22672	−	0.708247i	0.260377	−	0.965507i	$-0.416153\pi$
$491$	27.1823	−	15.6937i	1.22672	−	0.708247i	0.966342	+	0.257260i	$0.0828197\pi$
$492$	−3.45493	−	6.73828i	−0.155760	−	0.303785i
$493$		−	31.3514i		−	1.41200i
$494$	0.370684	−	0.214015i	0.0166779	−	0.00962898i
$495$	7.49547	+	5.38776i	0.336896	+	0.242162i
$496$			0.905833i			0.0406731i
$497$	20.4936	−	19.4383i	0.919264	−	0.871927i
$498$	−10.2350	+	5.24782i	−0.458642	+	0.235160i
$499$	−29.6748			−1.32843			−0.664214	−	0.747542i	$-0.731234\pi$
$499$	−29.6748			−1.32843			−0.664214	+	0.747542i	$0.731234\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−23.8198	+	36.8842i	−1.06419	+	1.64787i
$502$	−5.92888	+	3.42304i	−0.264619	+	0.152778i
$503$	−31.4939			−1.40424			−0.702121	−	0.712058i	$-0.747764\pi$
$503$	−31.4939			−1.40424			−0.702121	+	0.712058i	$0.747764\pi$
$504$	1.07412	+	7.86424i	0.0478450	+	0.350301i
$505$	4.19679			0.186755
$506$	23.8264	−	13.7562i	1.05921	−	0.611537i
$507$	22.0220	+	1.09799i	0.978030	+	0.0487634i
$508$	0.769453	−	1.33273i	0.0341390	−	0.0591304i
$509$	12.4151			0.550290			0.275145	−	0.961403i	$-0.411274\pi$
$509$	12.4151			0.550290			0.275145	+	0.961403i	$0.411274\pi$
$510$	−0.421633	+	8.45656i	−0.0186702	+	0.374463i
$511$	−16.9360	−	5.02112i	−0.749204	−	0.222121i
$512$		−	1.00000i		−	0.0441942i
$513$	3.34801	+	2.66914i	0.147818	+	0.117846i
$514$	22.8927	−	13.2171i	1.00975	−	0.582981i
$515$		−	0.701137i		−	0.0308958i
$516$	3.46758	−	5.36944i	0.152652	−	0.236376i
$517$	−10.0845	+	5.82231i	−0.443517	+	0.256065i
$518$	9.74544	−	9.24360i	0.428190	−	0.406141i
$519$	4.44699	−	6.88603i	0.195201	−	0.302263i
$520$	0.259719	+	0.449846i	0.0113894	+	0.0197270i
$521$	20.9931	+	36.3610i	0.919722	+	1.59301i	0.799836	+	0.600218i	$0.204920\pi$
$521$	20.9931	+	36.3610i	0.919722	+	1.59301i	0.119886	+	0.992788i	$0.461747\pi$
$522$	11.2297	−	15.6228i	0.491511	−	0.683792i
$523$	−20.1026	−	11.6062i	−0.879024	−	0.507505i	−0.00868774	−	0.999962i	$-0.502765\pi$
$523$	−20.1026	−	11.6062i	−0.879024	−	0.507505i	−0.870337	+	0.492457i	$0.836099\pi$
$524$	5.26114	−	9.11256i	0.229834	−	0.398084i
$525$	−1.51975	+	4.32323i	−0.0663275	+	0.188681i
$526$	−12.8662	−	22.2849i	−0.560992	−	0.971666i
$527$			4.42813i			0.192892i
$528$	−4.47704	−	2.89127i	−0.194838	−	0.125826i
$529$	−56.9480			−2.47600
$530$	2.71181	−	4.69700i	0.117794	−	0.204025i
$531$	−13.0598	−	28.9359i	−0.566746	−	1.25571i
$532$	−2.09024	−	0.619706i	−0.0906233	−	0.0268677i
$533$	−1.96669	−	1.13547i	−0.0851867	−	0.0491826i
$534$	2.37959	−	1.22009i	0.102975	−	0.0527985i
$535$	17.8959	+	10.3322i	0.773707	+	0.446700i
$536$	−6.84657	−	3.95287i	−0.295727	−	0.170738i
$537$	10.9564	+	7.07564i	0.472804	+	0.305336i
$538$	7.70427	+	4.44806i	0.332155	+	0.191770i
$539$	−21.5088	−	1.13766i	−0.926448	−	0.0490023i
$540$	−3.23915	+	4.06299i	−0.139391	+	0.174843i
$541$	3.91386	−	6.77900i	0.168270	−	0.291452i	−0.769542	−	0.638596i	$-0.779515\pi$
$541$	3.91386	−	6.77900i	0.168270	−	0.291452i	0.937812	+	0.347145i	$0.112849\pi$
$542$	−22.1902			−0.953149
$543$	−19.0795	+	9.78268i	−0.818780	+	0.419815i
$544$		−	4.88846i		−	0.209591i
$545$	0.903287	+	1.56454i	0.0386926	+	0.0670175i
$546$	1.55008	+	1.80648i	0.0663373	+	0.0773102i
$547$	20.3459	−	35.2402i	0.869930	−	1.50676i	0.00786205	−	0.999969i	$-0.497497\pi$
$547$	20.3459	−	35.2402i	0.869930	−	1.50676i	0.862068	−	0.506793i	$-0.169169\pi$
$548$	−0.00290551	−	0.00167750i	−0.000124117	−	7.16591e-5i
$549$	2.84230	−	28.4327i	0.121307	−	1.21348i
$550$	−1.53849	−	2.66474i	−0.0656013	−	0.113625i
$551$	2.64238	+	4.57674i	0.112569	+	0.194975i
$552$	7.06596	+	13.7810i	0.300747	+	0.586559i
$553$	−2.60283	+	8.77920i	−0.110683	+	0.373330i
$554$	−10.9193	+	6.30428i	−0.463918	+	0.267843i
$555$	8.78238	+	0.437878i	0.372791	+	0.0185869i
$556$		−	19.2054i		−	0.814492i
$557$	26.3951	−	15.2392i	1.11840	−	0.645707i	0.177406	−	0.984138i	$-0.443229\pi$
$557$	26.3951	−	15.2392i	1.11840	−	0.645707i	0.940991	+	0.338430i	$0.109896\pi$
$558$	−1.58611	+	2.20660i	−0.0671452	+	0.0934127i
$559$		−	1.91688i		−	0.0810754i
$560$	0.752047	−	2.53662i	0.0317798	−	0.107192i
$561$	−21.8858	−	14.1339i	−0.924021	−	0.596732i
$562$	7.86814			0.331898
$563$	4.87559	−	8.44476i	0.205481	−	0.355904i	−0.744805	−	0.667283i	$-0.767457\pi$
$563$	4.87559	−	8.44476i	0.205481	−	0.355904i	0.950286	+	0.311378i	$0.100791\pi$
$564$	−2.99067	−	5.83282i	−0.125930	−	0.245606i
$565$	16.2514	−	9.38276i	0.683703	−	0.394736i
$566$	29.5470			1.24195
$567$	−11.1537	+	21.0379i	−0.468411	+	0.883511i
$568$	−10.6760			−0.447954
$569$	28.8139	−	16.6357i	1.20794	−	0.697405i	0.245632	−	0.969363i	$-0.421004\pi$
$569$	28.8139	−	16.6357i	1.20794	−	0.697405i	0.962309	+	0.271958i	$0.0876711\pi$
$570$	−0.651191	−	1.27004i	−0.0272754	−	0.0531962i
$571$	18.9605	−	32.8406i	0.793473	−	1.37434i	−0.130332	−	0.991470i	$-0.541604\pi$
$571$	18.9605	−	32.8406i	0.793473	−	1.37434i	0.923804	−	0.382865i	$-0.125062\pi$
$572$	−1.59830			−0.0668281
$573$	−27.9760	−	18.0669i	−1.16872	−	0.754755i
$574$	2.69754	+	11.2481i	0.112593	+	0.469485i
$575$			8.94137i			0.372881i
$576$	1.75099	−	2.43599i	0.0729580	−	0.101499i
$577$	−11.5550	+	6.67129i	−0.481042	+	0.277730i	−0.720850	−	0.693091i	$-0.756249\pi$
$577$	−11.5550	+	6.67129i	−0.481042	+	0.277730i	0.239809	+	0.970820i	$0.422915\pi$
$578$		−	6.89705i		−	0.286880i
$579$	40.9461	+	2.04152i	1.70166	+	0.0848428i
$580$	−5.55412	+	3.20667i	−0.230622	+	0.133150i
$581$	17.0851	−	4.09740i	0.708809	−	0.169989i
$582$	1.76831	+	3.44880i	0.0732988	+	0.142957i
$583$	8.34418	+	14.4525i	0.345581	+	0.598563i
$584$	3.33830	+	5.78211i	0.138140	+	0.239265i
$585$	−0.155006	+	1.55058i	−0.00640869	+	0.0641087i
$586$	6.89061	+	3.97830i	0.284649	+	0.164342i
$587$	−8.76612	+	15.1834i	−0.361817	+	0.626685i	−0.988260	−	0.152782i	$-0.951177\pi$
$587$	−8.76612	+	15.1834i	−0.361817	+	0.626685i	0.626443	+	0.779467i	$0.284510\pi$
$588$	1.24251	−	12.0605i	0.0512403	−	0.497367i
$589$	−0.373215	−	0.646427i	−0.0153780	−	0.0266356i
$590$			10.5822i			0.435661i
$591$	9.15185	−	4.69245i	0.376457	−	0.193021i
$592$	−5.07681			−0.208655
$593$	−13.1868	+	22.8403i	−0.541519	+	0.937938i	0.457298	+	0.889313i	$0.348817\pi$
$593$	−13.1868	+	22.8403i	−0.541519	+	0.937938i	−0.998817	+	0.0486245i	$0.984516\pi$
$594$	−5.84342	−	14.8824i	−0.239758	−	0.610630i
$595$	3.67635	−	12.4002i	0.150716	−	0.508357i
$596$	−10.4496	−	6.03310i	−0.428034	−	0.247126i
$597$	24.2000	+	15.6284i	0.990441	+	0.639626i
$598$	4.02224	+	2.32224i	0.164481	+	0.0949634i
$599$	24.1184	+	13.9248i	0.985452	+	0.568951i	0.903912	−	0.427719i	$-0.140683\pi$
$599$	24.1184	+	13.9248i	0.985452	+	0.568951i	0.0815405	+	0.996670i	$0.474016\pi$
$600$	1.54126	−	0.790256i	0.0629219	−	0.0322621i
$601$	−23.8076	−	13.7453i	−0.971131	−	0.560683i	−0.0715503	−	0.997437i	$-0.522795\pi$
$601$	−23.8076	−	13.7453i	−0.971131	−	0.560683i	−0.899581	+	0.436754i	$0.856128\pi$
$602$	−7.08390	+	6.71912i	−0.288718	+	0.273851i
$603$	−9.75671	−	21.6174i	−0.397324	−	0.880330i
$604$	−7.33025	+	12.6964i	−0.298263	+	0.516607i
$605$	−1.53223			−0.0622938
$606$	−6.10639	−	3.94350i	−0.248055	−	0.160194i
$607$		−	39.3814i		−	1.59844i	−0.601037	−	0.799221i	$-0.705246\pi$
$607$		−	39.3814i		−	1.59844i	0.601037	−	0.799221i	$-0.294754\pi$
$608$	0.412013	+	0.713627i	0.0167093	+	0.0289414i
$609$	−22.3041	+	19.1384i	−0.903807	+	0.775527i
$610$	−4.76240	+	8.24872i	−0.192824	+	0.333981i
$611$	−1.70241	−	0.982888i	−0.0688722	−	0.0397634i
$612$	8.55966	−	11.9082i	0.346004	−	0.481361i
$613$	−0.989576	−	1.71400i	−0.0399686	−	0.0692277i	0.845349	−	0.534214i	$-0.179392\pi$
$613$	−0.989576	−	1.71400i	−0.0399686	−	0.0692277i	−0.885318	+	0.464987i	$0.846059\pi$
$614$	−16.9087	−	29.2868i	−0.682381	−	1.18192i
$615$	−4.10805	+	6.36120i	−0.165653	+	0.256508i
$616$	5.60240	+	5.90656i	0.225727	+	0.237982i
$617$	−33.1061	+	19.1138i	−1.33280	+	0.769493i	−0.985728	−	0.168346i	$-0.946158\pi$
$617$	−33.1061	+	19.1138i	−1.33280	+	0.769493i	−0.347072	+	0.937838i	$0.612824\pi$
$618$	−0.658821	+	1.02016i	−0.0265017	+	0.0410370i
$619$			26.6725i			1.07206i	0.844200	+	0.536028i	$0.180076\pi$
$619$			26.6725i			1.07206i	−0.844200	+	0.536028i	$0.819924\pi$
$620$	0.784474	−	0.452916i	0.0315052	−	0.0181896i
$621$	−6.91785	+	45.9428i	−0.277604	+	1.84362i
$622$		−	23.3794i		−	0.937427i
$623$	−3.97219	+	0.952623i	−0.159143	+	0.0381661i
$624$	0.0448019	−	0.898575i	0.00179351	−	0.0359718i
$625$	1.00000			0.0400000
$626$	−8.65830	+	14.9966i	−0.346055	+	0.599385i
$627$	4.38618	+	0.218689i	0.175167	+	0.00873361i
$628$	−0.502653	+	0.290207i	−0.0200580	+	0.0115805i
$629$	−24.8178			−0.989549
$630$	6.27357	−	4.86233i	0.249945	−	0.193720i
$631$	8.55537			0.340584			0.170292	−	0.985394i	$-0.445529\pi$
$631$	8.55537			0.340584			0.170292	+	0.985394i	$0.445529\pi$
$632$	2.99730	−	1.73049i	0.119226	−	0.0688353i
$633$	20.1287	−	31.1686i	0.800043	−	1.23884i
$634$	−7.96781	+	13.8006i	−0.316442	+	0.548094i
$635$	−1.53891			−0.0610696
$636$	−8.35924	+	4.28605i	−0.331466	+	0.169953i
$637$	−1.64917	−	3.24055i	−0.0653425	−	0.128395i
$638$		−	19.7337i		−	0.781265i
$639$	−26.0065	−	18.6936i	−1.02880	−	0.739505i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$			24.1197i			0.952672i	0.879263	+	0.476336i	$0.158035\pi$
$641$			24.1197i			0.952672i	−0.879263	+	0.476336i	$0.841965\pi$
$642$	−16.3302	−	31.8493i	−0.644500	−	1.25699i
$643$	13.4384	−	7.75864i	0.529957	−	0.305971i	−0.211042	−	0.977477i	$-0.567686\pi$
$643$	13.4384	−	7.75864i	0.529957	−	0.305971i	0.740999	+	0.671506i	$0.234352\pi$
$644$	−5.51697	−	23.0043i	−0.217399	−	0.906498i
$645$	−6.38386	−	0.318291i	−0.251364	−	0.0125327i
$646$	2.01411	+	3.48854i	0.0792440	+	0.137255i
$647$	−3.88442	−	6.72802i	−0.152712	−	0.264506i	0.779511	−	0.626388i	$-0.215467\pi$
$647$	−3.88442	−	6.72802i	−0.152712	−	0.264506i	−0.932224	+	0.361883i	$0.882134\pi$
$648$	8.53078	−	2.86805i	0.335121	−	0.112668i
$649$	−28.1987	−	16.2805i	−1.10690	−	0.639067i
$650$	0.259719	−	0.449846i	0.0101870	−	0.0176444i
$651$	3.15027	−	2.70314i	0.123469	−	0.105945i
$652$	−0.0642633	−	0.111307i	−0.00251675	−	0.00435913i
$653$		−	17.3302i		−	0.678184i	−0.940753	−	0.339092i	$-0.889880\pi$
$653$		−	17.3302i		−	0.678184i	0.940753	−	0.339092i	$-0.110120\pi$
$654$	0.155818	−	3.12520i	0.00609298	−	0.122205i
$655$	−10.5223			−0.411139
$656$	2.18596	−	3.78619i	0.0853473	−	0.147826i
$657$	−1.99237	+	19.9305i	−0.0777297	+	0.777562i
$658$	2.33506	+	9.73659i	0.0910301	+	0.379572i
$659$	3.46721	+	2.00179i	0.135063	+	0.0779787i	0.566009	−	0.824399i	$-0.308487\pi$
$659$	3.46721	+	2.00179i	0.135063	+	0.0779787i	−0.430946	+	0.902378i	$0.641820\pi$
$660$	−0.265391	+	5.32286i	−0.0103303	+	0.207192i
$661$	−33.8131	−	19.5220i	−1.31518	−	0.759317i	−0.332228	−	0.943199i	$-0.607800\pi$
$661$	−33.8131	−	19.5220i	−1.31518	−	0.759317i	−0.982948	+	0.183882i	$0.941134\pi$
$662$	7.28013	+	4.20318i	0.282950	+	0.163361i
$663$	0.219012	−	4.39265i	0.00850573	−	0.170596i
$664$	−5.75098	−	3.32033i	−0.223181	−	0.128854i
$665$	0.508437	+	2.12005i	0.0197163	+	0.0822121i
$666$	−12.3670	−	8.88945i	−0.479213	−	0.344459i
$667$	−28.6720	+	49.6614i	−1.11019	+	1.92290i
$668$	−25.3497			−0.980811
$669$	2.29094	−	45.9486i	0.0885728	−	1.77647i
$670$			7.90574i			0.305425i
$671$	−14.6538	−	25.3811i	−0.565703	−	0.979827i
$672$	−3.47776	+	2.98415i	−0.134158	+	0.115116i
$673$	5.02582	−	8.70498i	0.193731	−	0.335552i	−0.752753	−	0.658303i	$-0.771274\pi$
$673$	5.02582	−	8.70498i	0.193731	−	0.335552i	0.946484	+	0.322751i	$0.104608\pi$
$674$	−13.3059	−	7.68218i	−0.512525	−	0.295906i
$675$	5.13823	+	0.773690i	0.197771	+	0.0297794i
$676$	6.36509	+	11.0247i	0.244811	+	0.424026i
$677$	−11.3646	−	19.6840i	−0.436776	−	0.756519i	0.560663	−	0.828044i	$-0.310547\pi$
$677$	−11.3646	−	19.6840i	−0.436776	−	0.756519i	−0.997439	+	0.0715258i	$0.977213\pi$
$678$	−32.4625	−	1.61854i	−1.24672	−	0.0621597i
$679$	−1.38066	−	5.75700i	−0.0529849	−	0.220933i
$680$	−4.23353	+	2.44423i	−0.162349	+	0.0937320i
$681$	21.1296	+	41.2098i	0.809688	+	1.57916i
$682$			2.78723i			0.106728i
$683$	−6.28399	+	3.62806i	−0.240450	+	0.138824i	−0.615384	−	0.788228i	$-0.710999\pi$
$683$	−6.28399	+	3.62806i	−0.240450	+	0.138824i	0.374933	+	0.927052i	$0.377666\pi$
$684$	−0.245898	+	2.45982i	−0.00940215	+	0.0940534i
$685$			0.00335499i			0.000128188i
$686$	−6.19485	+	17.4535i	−0.236520	+	0.666377i
$687$	−12.2280	+	6.26966i	−0.466526	+	0.239203i
$688$	3.69030			0.140691
$689$	−1.40862	+	2.43980i	−0.0536640	+	0.0929488i
$690$	8.40172	−	13.0098i	0.319848	−	0.495275i
$691$	−8.38246	+	4.83962i	−0.318884	+	0.184108i	−0.650895	−	0.759168i	$-0.725606\pi$
$691$	−8.38246	+	4.83962i	−0.318884	+	0.184108i	0.332011	+	0.943275i	$0.392273\pi$
$692$	4.73262			0.179907
$693$	3.30503	+	24.1981i	0.125548	+	0.919209i
$694$	11.0495			0.419433
$695$	−16.6324	+	9.60272i	−0.630903	+	0.364252i
$696$	11.0945	+	0.553156i	0.420534	+	0.0209673i
$697$	10.6860	−	18.5086i	0.404760	−	0.701065i
$698$	−15.8937			−0.601587
$699$	2.41885	−	48.5140i	0.0914891	−	1.83497i
$700$	−2.57280	+	0.617016i	−0.0972426	+	0.0233210i
$701$		−	5.56860i		−	0.210323i	−0.994455	−	0.105162i	$-0.966464\pi$
$701$		−	5.56860i		−	0.210323i	0.994455	−	0.105162i	$-0.0335360\pi$
$702$	1.68254	−	2.11047i	0.0635032	−	0.0796545i
$703$	3.62295	−	2.09171i	0.136642	−	0.0788903i
$704$		−	3.07697i		−	0.115968i
$705$	−3.55603	+	5.50641i	−0.133928	+	0.207383i
$706$	10.3818	−	5.99396i	0.390726	−	0.225586i
$707$	7.64132	+	8.05617i	0.287381	+	0.302983i
$708$	9.94350	−	15.3972i	0.373700	−	0.578662i
$709$	−12.6267	−	21.8702i	−0.474207	−	0.821351i	0.525357	−	0.850882i	$-0.323932\pi$
$709$	−12.6267	−	21.8702i	−0.474207	−	0.821351i	−0.999564	+	0.0295310i	$0.990599\pi$
$710$	5.33799	+	9.24567i	0.200331	+	0.346984i
$711$	10.3315	+	1.03280i	0.387460	+	0.0387329i
$712$	1.33707	+	0.771960i	0.0501089	+	0.0289304i
$713$	4.04969	−	7.01427i	0.151662	−	0.262687i
$714$	−17.0009	+	14.5879i	−0.636243	+	0.545939i
$715$	0.799148	+	1.38416i	0.0298864	+	0.0517648i
$716$			7.53011i			0.281413i
$717$	41.2533	+	26.6413i	1.54063	+	0.994938i
$718$	13.5985			0.507492
$719$	−3.56765	+	6.17935i	−0.133051	+	0.230451i	−0.924851	−	0.380329i	$-0.875811\pi$
$719$	−3.56765	+	6.17935i	−0.133051	+	0.230451i	0.791800	+	0.610780i	$0.209144\pi$
$720$	−2.98512	−	0.298411i	−0.111249	−	0.0111211i
$721$	1.34590	−	1.27660i	0.0501241	−	0.0475429i
$722$	15.8664	+	9.16049i	0.590488	+	0.340918i
$723$	1.47073	−	0.754092i	0.0546971	−	0.0280450i
$724$	−10.7206	−	6.18956i	−0.398429	−	0.230033i
$725$	5.55412	+	3.20667i	0.206275	+	0.119093i
$726$	2.22941	+	1.43975i	0.0827412	+	0.0534342i
$727$	−7.48124	−	4.31930i	−0.277464	−	0.160194i	0.354811	−	0.934938i	$-0.384545\pi$
$727$	−7.48124	−	4.31930i	−0.277464	−	0.160194i	−0.632275	+	0.774744i	$0.717879\pi$
$728$	−0.390641	+	1.31761i	−0.0144781	+	0.0488340i
$729$	25.8028	+	7.95080i	0.955660	+	0.294474i
$730$	3.33830	−	5.78211i	0.123556	−	0.214005i
$731$	18.0399			0.667229
$732$	14.6802	−	7.52703i	0.542597	−	0.278207i
$733$			36.2890i			1.34037i	0.742196	+	0.670183i	$0.233784\pi$
$733$			36.2890i			1.34037i	−0.742196	+	0.670183i	$0.766216\pi$
$734$	−2.81639	−	4.87813i	−0.103955	−	0.180055i
$735$	−11.0660	+	4.95421i	−0.408175	+	0.182739i
$736$	−4.47068	+	7.74345i	−0.164792	+	0.285427i
$737$	−21.0667	−	12.1629i	−0.776003	−	0.448025i
$738$	11.9546	−	5.39551i	0.440053	−	0.198611i
$739$	5.37054	+	9.30205i	0.197558	+	0.342181i	0.947736	−	0.319055i	$-0.103365\pi$
$739$	5.37054	+	9.30205i	0.197558	+	0.342181i	−0.750178	+	0.661236i	$0.770032\pi$
$740$	2.53840	+	4.39664i	0.0933136	+	0.161624i
$741$	0.338253	+	0.659707i	0.0124260	+	0.0242349i
$742$	13.9539	−	3.34647i	0.512264	−	0.122853i
$743$	9.06518	−	5.23379i	0.332569	−	0.192009i	−0.324412	−	0.945916i	$-0.605166\pi$
$743$	9.06518	−	5.23379i	0.332569	−	0.192009i	0.656981	+	0.753907i	$0.271833\pi$
$744$	−1.56700	−	0.0781288i	−0.0574491	−	0.00286434i
$745$			12.0662i			0.442072i
$746$	−4.96231	+	2.86499i	−0.181683	+	0.104895i
$747$	−8.19544	−	18.1582i	−0.299855	−	0.664374i
$748$		−	15.0417i		−	0.549978i
$749$	12.7503	+	53.1653i	0.465885	+	1.94262i
$750$	−1.45501	−	0.939646i	−0.0531296	−	0.0343110i
$751$	18.5461			0.676758			0.338379	−	0.941010i	$-0.390121\pi$
$751$	18.5461			0.676758			0.338379	+	0.941010i	$0.390121\pi$
$752$	1.89222	−	3.27742i	0.0690021	−	0.119515i
$753$	−5.41016	−	10.5516i	−0.197157	−	0.384523i
$754$	2.88502	−	1.66566i	0.105066	−	0.0606599i
$755$	14.6605			0.533550
$756$	−13.6970	+	1.17982i	−0.498155	+	0.0429097i
$757$	−8.57410			−0.311631			−0.155816	−	0.987786i	$-0.549801\pi$
$757$	−8.57410			−0.311631			−0.155816	+	0.987786i	$0.549801\pi$
$758$	10.4267	−	6.01984i	0.378714	−	0.218651i
$759$	21.7418	+	42.4038i	0.789177	+	1.53916i
$760$	0.412013	−	0.713627i	0.0149453	−	0.0258860i
$761$	−3.68978			−0.133755			−0.0668773	−	0.997761i	$-0.521304\pi$
$761$	−3.68978			−0.133755			−0.0668773	+	0.997761i	$0.521304\pi$
$762$	2.23913	+	1.44603i	0.0811151	+	0.0523841i
$763$	−1.35863	+	4.58259i	−0.0491857	+	0.165901i
$764$		−	19.2273i		−	0.695620i
$765$	−14.5927	−	1.45877i	−0.527598	−	0.0527419i
$766$	−17.7587	+	10.2530i	−0.641648	+	0.370456i
$767$		−	5.49677i		−	0.198477i
$768$	1.72990	+	0.0862508i	0.0624225	+	0.00311231i
$769$	−1.09328	+	0.631204i	−0.0394246	+	0.0227618i	−0.519583	−	0.854420i	$-0.673913\pi$
$769$	−1.09328	+	0.631204i	−0.0394246	+	0.0227618i	0.480158	+	0.877182i	$0.340579\pi$
$770$	2.31403	−	7.80511i	0.0833919	−	0.281276i
$771$	20.8898	+	40.7420i	0.752326	+	1.46729i
$772$	11.8348	+	20.4985i	0.425944	+	0.737757i
$773$	−1.80204	−	3.12123i	−0.0648150	−	0.112263i	0.831797	−	0.555080i	$-0.187312\pi$
$773$	−1.80204	−	3.12123i	−0.0648150	−	0.112263i	−0.896612	+	0.442817i	$0.853979\pi$
$774$	8.98952	+	6.46169i	0.323122	+	0.232261i
$775$	−0.784474	−	0.452916i	−0.0281791	−	0.0162692i
$776$	−1.11882	+	1.93786i	−0.0401633	+	0.0695649i
$777$	15.1500	+	17.6559i	0.543502	+	0.633403i
$778$	12.9198	+	22.3778i	0.463197	+	0.802282i
$779$			3.60257i			0.129075i
$780$	−0.800590	+	0.410488i	−0.0286657	+	0.0146978i
$781$	−32.8497			−1.17546
$782$	−21.8548	+	37.8536i	−0.781525	+	1.35364i
$783$	26.0574	+	20.7738i	0.931214	+	0.742395i
$784$	6.23858	−	3.17492i	0.222806	−	0.113390i
$785$	0.502653	+	0.290207i	0.0179405	+	0.0103579i
$786$	15.3101	+	9.88722i	0.546092	+	0.352665i
$787$	−12.5305	−	7.23448i	−0.446664	−	0.257882i	0.259756	−	0.965674i	$-0.416358\pi$
$787$	−12.5305	−	7.23448i	−0.446664	−	0.257882i	−0.706420	+	0.707793i	$0.749691\pi$
$788$	5.14236	+	2.96894i	0.183189	+	0.105764i
$789$	39.6604	−	20.3351i	1.41195	−	0.723950i
$790$	−2.99730	−	1.73049i	−0.106639	−	0.0615682i
$791$	47.6010	+	14.1126i	1.69249	+	0.501785i
$792$	5.38776	−	7.49547i	0.191446	−	0.266340i
$793$	2.47377	−	4.28469i	0.0878461	−	0.152154i
$794$	−6.44846			−0.228847
$795$	7.89145	+	5.09629i	0.279881	+	0.180747i
$796$			16.6322i			0.589511i
$797$	−13.9972	−	24.2439i	−0.495808	−	0.858764i	0.504180	−	0.863598i	$-0.331795\pi$
$797$	−13.9972	−	24.2439i	−0.495808	−	0.858764i	−0.999988	+	0.00483393i	$0.998461\pi$
$798$	1.25232	−	3.56245i	0.0443315	−	0.126110i
$799$	9.25003	−	16.0215i	0.327243	−	0.566801i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	1.90540	+	4.22169i	0.0673239	+	0.149166i
$802$	−6.07170	−	10.5165i	−0.214399	−	0.371350i
$803$	10.2719	+	17.7914i	0.362486	+	0.627845i
$804$	7.42860	−	11.5030i	0.261986	−	0.405678i
$805$	−17.1638	+	16.2800i	−0.604946	+	0.573795i
$806$	−0.407485	+	0.235262i	−0.0143531	+	0.00828674i
$807$	−8.35922	+	12.9440i	−0.294258	+	0.455650i
$808$		−	4.19679i		−	0.147643i
$809$	37.0756	−	21.4056i	1.30351	−	0.752582i	0.322505	−	0.946568i	$-0.395475\pi$
$809$	37.0756	−	21.4056i	1.30351	−	0.752582i	0.981004	+	0.193986i	$0.0621416\pi$
$810$	−6.74920	−	5.95385i	−0.237143	−	0.209197i
$811$			7.75794i			0.272418i	0.990680	+	0.136209i	$0.0434919\pi$
$811$			7.75794i			0.272418i	−0.990680	+	0.136209i	$0.956508\pi$
$812$	−16.2682	−	4.82314i	−0.570902	−	0.169259i
$813$	1.91392	−	38.3868i	0.0671240	−	1.34628i
$814$	−15.6212			−0.547523
$815$	−0.0642633	+	0.111307i	−0.00225105	+	0.00389893i
$816$	8.45656	+	0.421633i	0.296039	+	0.0147601i
$817$	−2.63350	+	1.52045i	−0.0921344	+	0.0531938i
$818$	−22.1792			−0.775477
$819$	−3.25873	+	2.52568i	−0.113869	+	0.0882543i
$820$	−4.37192			−0.152674
$821$	−21.1360	+	12.2029i	−0.737650	+	0.425883i	−0.821214	−	0.570620i	$-0.806703\pi$
$821$	−21.1360	+	12.2029i	−0.737650	+	0.425883i	0.0835640	+	0.996502i	$0.473370\pi$
$822$	0.00315251	−	0.00488156i	0.000109956	−	0.000170264i
$823$	−11.5997	+	20.0913i	−0.404342	+	0.700340i	−0.994245	−	0.107134i	$-0.965833\pi$
$823$	−11.5997	+	20.0913i	−0.404342	+	0.700340i	0.589903	+	0.807474i	$0.299166\pi$
$824$	−0.701137			−0.0244253
$825$	4.74243	−	2.43160i	0.165110	−	0.0846573i
$826$	−20.3135	+	19.2675i	−0.706799	+	0.670402i
$827$			29.3259i			1.01976i	0.860245	+	0.509881i	$0.170311\pi$
$827$			29.3259i			1.01976i	−0.860245	+	0.509881i	$0.829689\pi$
$828$	−24.4492	+	11.0348i	−0.849670	+	0.383486i
$829$	26.1269	−	15.0844i	0.907424	−	0.523901i	0.0278223	−	0.999613i	$-0.491143\pi$
$829$	26.1269	−	15.0844i	0.907424	−	0.523901i	0.879601	+	0.475712i	$0.157809\pi$
$830$			6.64066i			0.230501i
$831$	−9.96399	−	19.4331i	−0.345647	−	0.674128i
$832$	0.449846	−	0.259719i	0.0155956	−	0.00900412i
$833$	30.4971	−	15.5205i	1.05666	−	0.537752i
$834$	33.2235	+	1.65648i	1.15044	+	0.0573594i
$835$	12.6749	+	21.9535i	0.438632	+	0.759733i
$836$	1.26775	+	2.19581i	0.0438461	+	0.0759438i
$837$	−3.68039	−	2.93413i	−0.127213	−	0.101418i
$838$	12.6673	+	7.31349i	0.437586	+	0.252640i
$839$	−18.2437	+	31.5990i	−0.629843	+	1.09092i	0.357740	+	0.933821i	$0.383547\pi$
$839$	−18.2437	+	31.5990i	−0.629843	+	1.09092i	−0.987583	+	0.157098i	$0.949786\pi$
$840$	4.32323	+	1.51975i	0.149166	+	0.0524365i
$841$	6.06549	+	10.5057i	0.209155	+	0.362267i
$842$			35.3619i			1.21865i
$843$	−0.678633	+	13.6111i	−0.0233734	+	0.468792i
$844$	21.4215			0.737360
$845$	6.36509	−	11.0247i	0.218966	−	0.379260i
$846$	10.3481	−	4.67048i	0.355777	−	0.160575i
$847$	−2.78980	−	2.94126i	−0.0958587	−	0.101063i
$848$	−4.69700	−	2.71181i	−0.161296	−	0.0931241i
$849$	−2.54845	+	51.1134i	−0.0874626	+	1.75421i
$850$	4.23353	+	2.44423i	0.145209	+	0.0838364i
$851$	39.3120	+	22.6968i	1.34760	+	0.778036i
$852$	0.920811	−	18.4684i	0.0315465	−	0.632717i
$853$	−2.99449	−	1.72887i	−0.102530	−	0.0591954i	0.447858	−	0.894104i	$-0.352187\pi$
$853$	−2.99449	−	1.72887i	−0.102530	−	0.0591954i	−0.550388	+	0.834909i	$0.685520\pi$
$854$	−24.5054	+	5.87696i	−0.838558	+	0.201105i
$855$	2.25321	−	1.01695i	0.0770582	−	0.0347791i
$856$	10.3322	−	17.8959i	0.353147	−	0.611669i
$857$	−26.1122			−0.891977			−0.445989	−	0.895039i	$-0.647148\pi$
$857$	−26.1122			−0.891977			−0.445989	+	0.895039i	$0.647148\pi$
$858$	0.137854	−	2.76489i	0.00470626	−	0.0943919i
$859$		−	26.6217i		−	0.908319i	−0.890920	−	0.454160i	$-0.849940\pi$
$859$		−	26.6217i		−	0.908319i	0.890920	−	0.454160i	$-0.150060\pi$
$860$	−1.84515	−	3.19589i	−0.0629191	−	0.108979i
$861$	−19.6907	+	3.69633i	−0.671057	+	0.125971i
$862$	−8.22125	+	14.2396i	−0.280017	+	0.485003i
$863$	20.3839	+	11.7687i	0.693877	+	0.400610i	0.805063	−	0.593189i	$-0.202131\pi$
$863$	20.3839	+	11.7687i	0.693877	+	0.400610i	−0.111186	+	0.993800i	$0.535465\pi$
$864$	4.06299	+	3.23915i	0.138226	+	0.110198i
$865$	−2.36631	−	4.09857i	−0.0804570	−	0.139356i
$866$	−11.0177	−	19.0833i	−0.374398	−	0.648476i
$867$	11.9312	+	0.594876i	0.405206	+	0.0202030i
$868$	2.29775	+	0.681229i	0.0779908	+	0.0231224i
$869$	9.22263	−	5.32469i	0.312856	−	0.180628i
$870$	−5.06818	−	9.88466i	−0.171827	−	0.335121i
$871$		−	4.10653i		−	0.139145i
$872$	1.56454	−	0.903287i	0.0529820	−	0.0305892i
$873$	−6.11860	+	2.76154i	−0.207083	+	0.0934640i
$874$		−	7.36791i		−	0.249223i
$875$	1.82075	+	1.91960i	0.0615526	+	0.0648943i
$876$	−10.2904	+	5.27622i	−0.347681	+	0.178267i
$877$	7.21212			0.243536			0.121768	−	0.992559i	$-0.461144\pi$
$877$	7.21212			0.243536			0.121768	+	0.992559i	$0.461144\pi$
$878$	−12.4087	+	21.4924i	−0.418772	+	0.725335i
$879$	−7.47639	+	11.5770i	−0.252172	+	0.390481i
$880$	−2.66474	+	1.53849i	−0.0898283	+	0.0518624i
$881$	−57.4455			−1.93539			−0.967694	−	0.252129i	$-0.918869\pi$
$881$	−57.4455			−1.93539			−0.967694	+	0.252129i	$0.918869\pi$
$882$	20.7564	+	3.18965i	0.698903	+	0.107401i
$883$	15.0734			0.507262			0.253631	−	0.967301i	$-0.418375\pi$
$883$	15.0734			0.507262			0.253631	+	0.967301i	$0.418375\pi$
$884$	2.19905	−	1.26962i	0.0739622	−	0.0427021i
$885$	−18.3061	−	0.912720i	−0.615354	−	0.0306808i
$886$	8.31193	−	14.3967i	0.279245	−	0.483666i
$887$	35.1323			1.17963			0.589814	−	0.807539i	$-0.299201\pi$
$887$	35.1323			1.17963			0.589814	+	0.807539i	$0.299201\pi$
$888$	0.437878	−	8.78238i	0.0146942	−	0.294717i
$889$	−2.80197	−	2.95409i	−0.0939749	−	0.0990768i
$890$		−	1.54392i		−	0.0517523i
$891$	26.2490	−	8.82493i	0.879375	−	0.295646i
$892$	23.0028	−	13.2807i	0.770191	−	0.444670i
$893$			3.11847i			0.104356i
$894$	11.3380	−	17.5565i	0.379198	−	0.587177i
$895$	6.52127	−	3.76505i	0.217982	−	0.125852i
$896$	−2.53662	−	0.752047i	−0.0847424	−	0.0251241i
$897$	−4.36417	+	6.75778i	−0.145715	+	0.225636i
$898$	6.25770	+	10.8387i	0.208822	+	0.361691i
$899$	−2.90471	−	5.03110i	−0.0968775	−	0.167797i
$900$	1.23413	+	2.73440i	0.0411377	+	0.0911466i
$901$	−22.9611	−	13.2566i	−0.764945	−	0.441641i
$902$	6.72614	−	11.6500i	0.223956	−	0.387903i
$903$	−11.0124	−	12.8340i	−0.366470	−	0.427088i
$904$	−9.38276	−	16.2514i	−0.312066	−	0.540514i
$905$			12.3791i			0.411496i
$906$	−21.3312	−	13.7757i	−0.708682	−	0.457666i
$907$	9.56489			0.317597			0.158799	−	0.987311i	$-0.449238\pi$
$907$	9.56489			0.317597			0.158799	+	0.987311i	$0.449238\pi$
$908$	−13.3688	+	23.1555i	−0.443661	+	0.768443i
$909$	7.34855	−	10.2233i	0.243736	−	0.339086i
$910$	1.33641	−	0.320501i	0.0443015	−	0.0106245i
$911$	−10.5695	−	6.10232i	−0.350184	−	0.202179i	0.314582	−	0.949230i	$-0.398136\pi$
$911$	−10.5695	−	6.10232i	−0.350184	−	0.202179i	−0.664766	+	0.747051i	$0.731469\pi$
$912$	−1.27004	+	0.651191i	−0.0420553	+	0.0215631i
$913$	−17.6956	−	10.2166i	−0.585640	−	0.338119i
$914$	−28.3193	−	16.3501i	−0.936718	−	0.540814i
$915$	−13.8587	−	8.94995i	−0.458155	−	0.295876i
$916$	−6.87080	−	3.96686i	−0.227018	−	0.131069i
$917$	−19.1584	−	20.1986i	−0.632668	−	0.667015i
$918$	19.8618	+	15.8345i	0.655536	+	0.522615i
$919$	−5.75745	+	9.97219i	−0.189921	+	0.328952i	−0.945224	−	0.326424i	$-0.894156\pi$
$919$	−5.75745	+	9.97219i	−0.189921	+	0.328952i	0.755303	+	0.655376i	$0.227490\pi$
$920$	8.94137			0.294788
$921$	52.1216	−	26.7244i	1.71747	−	0.880600i
$922$			5.38010i			0.177184i
$923$	−2.77275	−	4.80254i	−0.0912662	−	0.158078i
$924$	−10.7010	+	9.18217i	−0.352037	+	0.302071i
$925$	2.53840	−	4.39664i	0.0834622	−	0.144561i
$926$	−9.38485	−	5.41835i	−0.308405	−	0.178058i
$927$	−1.70796	−	1.22769i	−0.0560968	−	0.0403225i
$928$	3.20667	+	5.55412i	0.105264	+	0.182323i
$929$	−7.79341	−	13.4986i	−0.255694	−	0.442874i	0.709390	−	0.704816i	$-0.248970\pi$
$929$	−7.79341	−	13.4986i	−0.255694	−	0.442874i	−0.965084	+	0.261942i	$0.915637\pi$
$930$	0.715840	+	1.39613i	0.0234733	+	0.0457808i
$931$	−3.14391	+	4.83608i	−0.103038	+	0.158496i
$932$	24.2871	−	14.0222i	0.795551	−	0.459311i
$933$	40.4440	+	2.01649i	1.32408	+	0.0660169i
$934$		−	5.53426i		−	0.181087i
$935$	−13.0265	+	7.52084i	−0.426011	+	0.245958i
$936$	1.55058	+	0.155006i	0.0506824	+	0.00506652i
$937$			52.6446i			1.71982i	0.510442	+	0.859912i	$0.329482\pi$
$937$			52.6446i			1.71982i	−0.510442	+	0.859912i	$0.670518\pi$
$938$	−15.1759	+	14.3944i	−0.495509	+	0.469993i
$939$	−25.1959	−	16.2715i	−0.822237	−	0.531000i
$940$	−3.78444			−0.123435
$941$	1.60723	−	2.78380i	0.0523942	−	0.0907494i	−0.838639	−	0.544688i	$-0.816648\pi$
$941$	1.60723	−	2.78380i	0.0523942	−	0.0907494i	0.891033	+	0.453939i	$0.149981\pi$
$942$	−0.458675	−	0.894571i	−0.0149444	−	0.0291467i
$943$	−33.8537	+	19.5454i	−1.10243	+	0.636487i
$944$	10.5822			0.344420
$945$	7.87026	+	11.2720i	0.256020	+	0.366680i
$946$	11.3550			0.369182
$947$	3.02017	−	1.74370i	0.0981423	−	0.0566625i	−0.450126	−	0.892965i	$-0.648621\pi$
$947$	3.02017	−	1.74370i	0.0981423	−	0.0566625i	0.548268	+	0.836303i	$0.315287\pi$
$948$	2.73506	+	5.33430i	0.0888308	+	0.173250i
$949$	−1.73404	+	3.00344i	−0.0562892	+	0.0974958i
$950$	−0.824025			−0.0267349
$951$	−23.1865	−	14.9738i	−0.751875	−	0.485560i
$952$	−12.4002	−	3.67635i	−0.401891	−	0.119151i
$953$		−	45.7759i		−	1.48283i	−0.671049	−	0.741413i	$-0.734156\pi$
$953$		−	45.7759i		−	1.48283i	0.671049	−	0.741413i	$-0.265844\pi$
$954$	−6.69346	−	14.8303i	−0.216709	−	0.480150i
$955$	−16.6514	+	9.61366i	−0.538825	+	0.311091i
$956$			28.3525i			0.916985i
$957$	34.1374	+	1.70205i	1.10350	+	0.0550193i
$958$	−34.4899	+	19.9128i	−1.11432	+	0.643353i
$959$	−0.00644025	+	0.00610861i	−0.000207966	+	0.000197257i
$960$	−0.790256	−	1.54126i	−0.0255054	−	0.0497441i
$961$	−15.0897	−	26.1362i	−0.486766	−	0.843103i
$962$	−1.31854	−	2.28378i	−0.0425115	−	0.0736320i
$963$	56.5047	−	25.5025i	1.82084	−	0.821808i
$964$	0.826394	+	0.477119i	0.0266164	+	0.0153670i
$965$	11.8348	−	20.4985i	0.380976	−	0.659870i
$966$	40.2711	−	7.55967i	1.29570	−	0.243229i
$967$	−25.9697	−	44.9808i	−0.835129	−	1.44649i	−0.893925	−	0.448216i	$-0.852060\pi$
$967$	−25.9697	−	44.9808i	−0.835129	−	1.44649i	0.0587965	−	0.998270i	$-0.481274\pi$
$968$			1.53223i			0.0492476i
$969$	−6.20855	+	3.18332i	−0.199447	+	0.102263i
$970$	2.23764			0.0718464
$971$	−13.0616	+	22.6234i	−0.419167	+	0.726019i	−0.995856	−	0.0909448i	$-0.971011\pi$
$971$	−13.0616	+	22.6234i	−0.419167	+	0.726019i	0.576688	+	0.816964i	$0.304345\pi$
$972$	4.22566	+	15.0048i	0.135538	+	0.481279i
$973$	−48.7169	−	14.4434i	−1.56179	−	0.463034i
$974$	−34.2835	−	19.7936i	−1.09852	−	0.634228i
$975$	0.755788	+	0.488087i	0.0242046	+	0.0156313i
$976$	8.24872	+	4.76240i	0.264035	+	0.152441i
$977$	35.7603	+	20.6462i	1.14407	+	0.660532i	0.947436	−	0.319944i	$-0.103664\pi$
$977$	35.7603	+	20.6462i	1.14407	+	0.660532i	0.196638	+	0.980476i	$0.436998\pi$
$978$	0.198094	−	0.101569i	0.00633433	−	0.00324782i
$979$	4.11414	+	2.37530i	0.131489	+	0.0759149i
$980$	−5.86885	−	3.81531i	−0.187474	−	0.121876i
$981$	5.39285	+	0.539101i	0.172180	+	0.0172122i
$982$	−15.6937	+	27.1823i	−0.500806	+	0.867422i
$983$	15.2552			0.486567			0.243283	−	0.969955i	$-0.421776\pi$
$983$	15.2552			0.486567			0.243283	+	0.969955i	$0.421776\pi$
$984$	6.36120	+	4.10805i	0.202788	+	0.130960i
$985$		−	5.93788i		−	0.189197i
$986$	15.6757	+	27.1511i	0.499216	+	0.864667i
$987$	−17.0447	+	3.19963i	−0.542540	+	0.101845i
$988$	−0.214015	+	0.370684i	−0.00680872	+	0.0117930i
$989$	−28.5757	−	16.4982i	−0.908653	−	0.524611i
$990$	−9.18514	−	0.918202i	−0.291923	−	0.0291824i
$991$	1.36395	+	2.36244i	0.0433274	+	0.0750453i	0.886876	−	0.462008i	$-0.152871\pi$
$991$	1.36395	+	2.36244i	0.0433274	+	0.0750453i	−0.843548	+	0.537053i	$0.819537\pi$
$992$	−0.452916	−	0.784474i	−0.0143801	−	0.0249071i
$993$	−7.89901	+	12.2314i	−0.250668	+	0.388151i
$994$	−8.02884	+	27.0809i	−0.254659	+	0.858953i
$995$	14.4039	−	8.31608i	0.456634	−	0.263638i
$996$	6.23987	−	9.66225i	0.197718	−	0.306160i
$997$			0.196236i			0.00621485i	0.999995	+	0.00310743i	$0.000989126\pi$
$997$			0.196236i			0.00621485i	−0.999995	+	0.00310743i	$0.999011\pi$
$998$	25.6992	−	14.8374i	0.813493	−	0.469670i
$999$	16.4445	−	20.6270i	0.520282	−	0.652610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.551.3	yes	28
3.2	odd	2		1890.2.t.b.1601.12		28
7.3	odd	6		630.2.bk.b.101.5	yes	28
9.4	even	3		1890.2.bk.b.341.11		28
9.5	odd	6		630.2.bk.b.131.12	yes	28
21.17	even	6		1890.2.bk.b.521.11		28
63.31	odd	6		1890.2.t.b.1151.12		28
63.59	even	6	inner	630.2.t.b.311.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.3	✓	28	63.59	even	6	inner
630.2.t.b.551.3	yes	28	1.1	even	1	trivial
630.2.bk.b.101.5	yes	28	7.3	odd	6
630.2.bk.b.131.12	yes	28	9.5	odd	6
1890.2.t.b.1151.12		28	63.31	odd	6
1890.2.t.b.1601.12		28	3.2	odd	2
1890.2.bk.b.341.11		28	9.4	even	3
1890.2.bk.b.521.11		28	21.17	even	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.790256 - 1.54126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.45501 + 0.939646i) q^{6} +(-1.82075 - 1.91960i) q^{7} +1.00000i q^{8} +(-1.75099 + 2.43599i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.790256 - 1.54126i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.45501 + 0.939646i) q^{6} +(-1.82075 - 1.91960i) q^{7} +1.00000i q^{8} +(-1.75099 + 2.43599i) q^{9} +(0.866025 - 0.500000i) q^{10} +3.07697i q^{11} +(-1.72990 - 0.0862508i) q^{12} +(-0.449846 + 0.259719i) q^{13} +(2.53662 + 0.752047i) q^{14} +(0.790256 + 1.54126i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.44423 - 4.23353i) q^{17} +(0.298411 - 2.98512i) q^{18} +(0.713627 + 0.412013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.51975 + 4.32323i) q^{21} +(-1.53849 - 2.66474i) q^{22} +8.94137i q^{23} +(1.54126 - 0.790256i) q^{24} +1.00000 q^{25} +(0.259719 - 0.449846i) q^{26} +(5.13823 + 0.773690i) q^{27} +(-2.57280 + 0.617016i) q^{28} +(5.55412 + 3.20667i) q^{29} +(-1.45501 - 0.939646i) q^{30} +(-0.784474 - 0.452916i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.74243 - 2.43160i) q^{33} +(4.23353 + 2.44423i) q^{34} +(1.82075 + 1.91960i) q^{35} +(1.23413 + 2.73440i) q^{36} +(2.53840 - 4.39664i) q^{37} -0.824025 q^{38} +(0.755788 + 0.488087i) q^{39} -1.00000i q^{40} +(2.18596 + 3.78619i) q^{41} +(-0.845472 - 4.50391i) q^{42} +(-1.84515 + 3.19589i) q^{43} +(2.66474 + 1.53849i) q^{44} +(1.75099 - 2.43599i) q^{45} +(-4.47068 - 7.74345i) q^{46} +(1.89222 + 3.27742i) q^{47} +(-0.939646 + 1.45501i) q^{48} +(-0.369732 + 6.99023i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-4.59342 + 7.11278i) q^{51} +0.519437i q^{52} +(4.69700 - 2.71181i) q^{53} +(-4.83668 + 1.89908i) q^{54} -3.07697i q^{55} +(1.91960 - 1.82075i) q^{56} +(0.0710728 - 1.42548i) q^{57} -6.41334 q^{58} +(-5.29109 + 9.16443i) q^{59} +(1.72990 + 0.0862508i) q^{60} +(-8.24872 + 4.76240i) q^{61} +0.905833 q^{62} +(7.86424 - 1.07412i) q^{63} -1.00000 q^{64} +(0.449846 - 0.259719i) q^{65} +(-2.89127 + 4.47704i) q^{66} +(-3.95287 + 6.84657i) q^{67} -4.88846 q^{68} +(13.7810 - 7.06596i) q^{69} +(-2.53662 - 0.752047i) q^{70} +10.6760i q^{71} +(-2.43599 - 1.75099i) q^{72} +(5.78211 - 3.33830i) q^{73} +5.07681i q^{74} +(-0.790256 - 1.54126i) q^{75} +(0.713627 - 0.412013i) q^{76} +(5.90656 - 5.60240i) q^{77} +(-0.898575 - 0.0448019i) q^{78} +(-1.73049 - 2.99730i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.86805 - 8.53078i) q^{81} +(-3.78619 - 2.18596i) q^{82} +(-3.32033 + 5.75098i) q^{83} +(2.98415 + 3.47776i) q^{84} +(2.44423 + 4.23353i) q^{85} -3.69030i q^{86} +(0.553156 - 11.0945i) q^{87} -3.07697 q^{88} +(0.771960 - 1.33707i) q^{89} +(-0.298411 + 2.98512i) q^{90} +(1.31761 + 0.390641i) q^{91} +(7.74345 + 4.47068i) q^{92} +(-0.0781288 + 1.56700i) q^{93} +(-3.27742 - 1.89222i) q^{94} +(-0.713627 - 0.412013i) q^{95} +(0.0862508 - 1.72990i) q^{96} +(1.93786 + 1.11882i) q^{97} +(-3.17492 - 6.23858i) q^{98} +(-7.49547 - 5.38776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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