LMFDB - Embedded newform 630.2.t.c.551.1

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.1
Character	$\chi$	$=$	630.551
Dual form			630.2.t.c.311.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.69665 - 0.348398i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.64354 - 0.546603i) q^{6} +(-1.74301 + 1.99046i) q^{7} +1.00000i q^{8} +(2.75724 + 1.18222i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.69665 - 0.348398i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.64354 - 0.546603i) q^{6} +(-1.74301 + 1.99046i) q^{7} +1.00000i q^{8} +(2.75724 + 1.18222i) q^{9} +(-0.866025 + 0.500000i) q^{10} -1.76481i q^{11} +(-1.15005 + 1.29514i) q^{12} +(1.79971 - 1.03906i) q^{13} +(0.514257 - 2.59529i) q^{14} +(-1.69665 - 0.348398i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.861240 + 1.49171i) q^{17} +(-2.97895 + 0.354788i) q^{18} +(-6.79557 - 3.92342i) q^{19} +(0.500000 - 0.866025i) q^{20} +(3.65074 - 2.76985i) q^{21} +(0.882407 + 1.52837i) q^{22} +7.15283i q^{23} +(0.348398 - 1.69665i) q^{24} +1.00000 q^{25} +(-1.03906 + 1.79971i) q^{26} +(-4.26618 - 2.96642i) q^{27} +(0.852286 + 2.50472i) q^{28} +(5.62132 + 3.24547i) q^{29} +(1.64354 - 0.546603i) q^{30} +(4.23286 + 2.44384i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.614858 + 2.99427i) q^{33} +(-1.49171 - 0.861240i) q^{34} +(-1.74301 + 1.99046i) q^{35} +(2.40245 - 1.79673i) q^{36} +(-5.24042 + 9.07668i) q^{37} +7.84685 q^{38} +(-3.41548 + 1.13591i) q^{39} +1.00000i q^{40} +(3.17762 + 5.50380i) q^{41} +(-1.77671 + 4.22413i) q^{42} +(1.94221 - 3.36401i) q^{43} +(-1.52837 - 0.882407i) q^{44} +(2.75724 + 1.18222i) q^{45} +(-3.57642 - 6.19453i) q^{46} +(6.01122 + 10.4117i) q^{47} +(0.546603 + 1.64354i) q^{48} +(-0.923864 - 6.93877i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-0.941513 - 2.83097i) q^{51} -2.07813i q^{52} +(-4.34949 + 2.51118i) q^{53} +(5.17784 + 0.435907i) q^{54} -1.76481i q^{55} +(-1.99046 - 1.74301i) q^{56} +(10.1628 + 9.02424i) q^{57} -6.49094 q^{58} +(-4.25453 + 7.36907i) q^{59} +(-1.15005 + 1.29514i) q^{60} +(-6.00433 + 3.46660i) q^{61} -4.88768 q^{62} +(-7.15904 + 3.42756i) q^{63} -1.00000 q^{64} +(1.79971 - 1.03906i) q^{65} +(-0.964654 - 2.90054i) q^{66} +(-2.12619 + 3.68268i) q^{67} +1.72248 q^{68} +(2.49203 - 12.1358i) q^{69} +(0.514257 - 2.59529i) q^{70} +7.97609i q^{71} +(-1.18222 + 2.75724i) q^{72} +(-9.43511 + 5.44736i) q^{73} -10.4808i q^{74} +(-1.69665 - 0.348398i) q^{75} +(-6.79557 + 3.92342i) q^{76} +(3.51279 + 3.07608i) q^{77} +(2.38994 - 2.69147i) q^{78} +(5.83721 + 10.1103i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(6.20472 + 6.51931i) q^{81} +(-5.50380 - 3.17762i) q^{82} +(5.77748 - 10.0069i) q^{83} +(-0.573393 - 4.54656i) q^{84} +(0.861240 + 1.49171i) q^{85} +3.88442i q^{86} +(-8.40669 - 7.46488i) q^{87} +1.76481 q^{88} +(4.36194 - 7.55510i) q^{89} +(-2.97895 + 0.354788i) q^{90} +(-1.06869 + 5.39334i) q^{91} +(6.19453 + 3.57642i) q^{92} +(-6.33024 - 5.62106i) q^{93} +(-10.4117 - 6.01122i) q^{94} +(-6.79557 - 3.92342i) q^{95} +(-1.29514 - 1.15005i) q^{96} +(-5.31507 - 3.06866i) q^{97} +(4.26947 + 5.54722i) q^{98} +(2.08640 - 4.86601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * 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
$3$	−1.69665	−	0.348398i	−0.979561	−	0.201148i
$3$	−1.69665	−	0.348398i	−0.979561	−	0.201148i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.64354	−	0.546603i	0.670973	−	0.223150i
$7$	−1.74301	+	1.99046i	−0.658794	+	0.752323i
$7$	−1.74301	+	1.99046i	−0.658794	+	0.752323i
$8$			1.00000i			0.353553i
$9$	2.75724	+	1.18222i	0.919079	+	0.394073i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$		−	1.76481i		−	0.532112i	−0.963958	−	0.266056i	$-0.914279\pi$
$11$		−	1.76481i		−	0.532112i	0.963958	−	0.266056i	$-0.0857206\pi$
$12$	−1.15005	+	1.29514i	−0.331990	+	0.373875i
$13$	1.79971	−	1.03906i	0.499150	−	0.288184i	−0.229213	−	0.973376i	$-0.573615\pi$
$13$	1.79971	−	1.03906i	0.499150	−	0.288184i	0.728362	+	0.685192i	$0.240282\pi$
$14$	0.514257	−	2.59529i	0.137441	−	0.693621i
$15$	−1.69665	−	0.348398i	−0.438073	−	0.0899559i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.861240	+	1.49171i	0.208881	+	0.361793i	0.951362	−	0.308074i	$-0.0996844\pi$
$17$	0.861240	+	1.49171i	0.208881	+	0.361793i	−0.742481	+	0.669867i	$0.766351\pi$
$18$	−2.97895	+	0.354788i	−0.702145	+	0.0836244i
$19$	−6.79557	−	3.92342i	−1.55901	−	0.900095i	−0.997352	−	0.0727261i	$-0.976830\pi$
$19$	−6.79557	−	3.92342i	−1.55901	−	0.900095i	−0.561659	−	0.827369i	$-0.689837\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	3.65074	−	2.76985i	0.796657	−	0.604432i
$22$	0.882407	+	1.52837i	0.188130	+	0.325851i
$23$			7.15283i			1.49147i	0.666244	+	0.745734i	$0.267901\pi$
$23$			7.15283i			1.49147i	−0.666244	+	0.745734i	$0.732099\pi$
$24$	0.348398	−	1.69665i	0.0711164	−	0.346327i
$25$	1.00000			0.200000
$26$	−1.03906	+	1.79971i	−0.203777	+	0.352952i
$27$	−4.26618	−	2.96642i	−0.821027	−	0.570889i
$28$	0.852286	+	2.50472i	0.161067	+	0.473347i
$29$	5.62132	+	3.24547i	1.04385	+	0.602669i	0.920922	−	0.389747i	$-0.127437\pi$
$29$	5.62132	+	3.24547i	1.04385	+	0.602669i	0.122931	+	0.992415i	$0.460771\pi$
$30$	1.64354	−	0.546603i	0.300068	−	0.0997957i
$31$	4.23286	+	2.44384i	0.760243	+	0.438927i	0.829383	−	0.558680i	$-0.188692\pi$
$31$	4.23286	+	2.44384i	0.760243	+	0.438927i	−0.0691397	+	0.997607i	$0.522025\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.614858	+	2.99427i	−0.107033	+	0.521236i
$34$	−1.49171	−	0.861240i	−0.255826	−	0.147701i
$35$	−1.74301	+	1.99046i	−0.294622	+	0.336449i
$36$	2.40245	−	1.79673i	0.400408	−	0.299455i
$37$	−5.24042	+	9.07668i	−0.861520	+	1.49220i	0.00894096	+	0.999960i	$0.497154\pi$
$37$	−5.24042	+	9.07668i	−0.861520	+	1.49220i	−0.870461	+	0.492237i	$0.836179\pi$
$38$	7.84685			1.27293
$39$	−3.41548	+	1.13591i	−0.546915	+	0.181891i
$40$			1.00000i			0.158114i
$41$	3.17762	+	5.50380i	0.496261	+	0.859549i	0.999991	−	0.00431191i	$-0.00137253\pi$
$41$	3.17762	+	5.50380i	0.496261	+	0.859549i	−0.503730	+	0.863861i	$0.668039\pi$
$42$	−1.77671	+	4.22413i	−0.274152	+	0.651798i
$43$	1.94221	−	3.36401i	0.296184	−	0.513006i	−0.679075	−	0.734069i	$-0.737619\pi$
$43$	1.94221	−	3.36401i	0.296184	−	0.513006i	0.975260	+	0.221062i	$0.0709524\pi$
$44$	−1.52837	−	0.882407i	−0.230411	−	0.133028i
$45$	2.75724	+	1.18222i	0.411025	+	0.176235i
$46$	−3.57642	−	6.19453i	−0.527314	−	0.913334i
$47$	6.01122	+	10.4117i	0.876826	+	1.51871i	0.854805	+	0.518950i	$0.173677\pi$
$47$	6.01122	+	10.4117i	0.876826	+	1.51871i	0.0220213	+	0.999758i	$0.492990\pi$
$48$	0.546603	+	1.64354i	0.0788954	+	0.237225i
$49$	−0.923864	−	6.93877i	−0.131981	−	0.991252i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−0.941513	−	2.83097i	−0.131838	−	0.396414i
$52$		−	2.07813i		−	0.288184i
$53$	−4.34949	+	2.51118i	−0.597449	+	0.344937i	−0.768037	−	0.640405i	$-0.778766\pi$
$53$	−4.34949	+	2.51118i	−0.597449	+	0.344937i	0.170588	+	0.985342i	$0.445433\pi$
$54$	5.17784	+	0.435907i	0.704614	+	0.0593194i
$55$		−	1.76481i		−	0.237968i
$56$	−1.99046	−	1.74301i	−0.265986	−	0.232919i
$57$	10.1628	+	9.02424i	1.34609	+	1.19529i
$58$	−6.49094			−0.852302
$59$	−4.25453	+	7.36907i	−0.553893	+	0.959371i	0.444095	+	0.895979i	$0.353525\pi$
$59$	−4.25453	+	7.36907i	−0.553893	+	0.959371i	−0.997989	+	0.0633918i	$0.979808\pi$
$60$	−1.15005	+	1.29514i	−0.148470	+	0.167202i
$61$	−6.00433	+	3.46660i	−0.768775	+	0.443853i	−0.832437	−	0.554119i	$-0.813055\pi$
$61$	−6.00433	+	3.46660i	−0.768775	+	0.443853i	0.0636623	+	0.997971i	$0.479722\pi$
$62$	−4.88768			−0.620736
$63$	−7.15904	+	3.42756i	−0.901954	+	0.431832i
$64$	−1.00000			−0.125000
$65$	1.79971	−	1.03906i	0.223226	−	0.128880i
$66$	−0.964654	−	2.90054i	−0.118741	−	0.357032i
$67$	−2.12619	+	3.68268i	−0.259756	+	0.449911i	−0.966176	−	0.257882i	$-0.916975\pi$
$67$	−2.12619	+	3.68268i	−0.259756	+	0.449911i	0.706420	+	0.707792i	$0.250309\pi$
$68$	1.72248			0.208881
$69$	2.49203	−	12.1358i	0.300005	−	1.46098i
$70$	0.514257	−	2.59529i	0.0614655	−	0.310197i
$71$			7.97609i			0.946588i	0.880905	+	0.473294i	$0.156935\pi$
$71$			7.97609i			0.946588i	−0.880905	+	0.473294i	$0.843065\pi$
$72$	−1.18222	+	2.75724i	−0.139326	+	0.324944i
$73$	−9.43511	+	5.44736i	−1.10430	+	0.637566i	−0.937346	−	0.348400i	$-0.886725\pi$
$73$	−9.43511	+	5.44736i	−1.10430	+	0.637566i	−0.166950	+	0.985965i	$0.553392\pi$
$74$		−	10.4808i		−	1.21837i
$75$	−1.69665	−	0.348398i	−0.195912	−	0.0402295i
$76$	−6.79557	+	3.92342i	−0.779505	+	0.450048i
$77$	3.51279	+	3.07608i	0.400320	+	0.350552i
$78$	2.38994	−	2.69147i	0.270607	−	0.304749i
$79$	5.83721	+	10.1103i	0.656737	+	1.13750i	0.981455	+	0.191691i	$0.0613973\pi$
$79$	5.83721	+	10.1103i	0.656737	+	1.13750i	−0.324718	+	0.945811i	$0.605269\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	6.20472	+	6.51931i	0.689414	+	0.724368i
$82$	−5.50380	−	3.17762i	−0.607793	−	0.350910i
$83$	5.77748	−	10.0069i	0.634161	−	1.09840i	−0.352531	−	0.935800i	$-0.614679\pi$
$83$	5.77748	−	10.0069i	0.634161	−	1.09840i	0.986692	−	0.162599i	$-0.0519877\pi$
$84$	−0.573393	−	4.54656i	−0.0625623	−	0.496071i
$85$	0.861240	+	1.49171i	0.0934146	+	0.161799i
$86$			3.88442i			0.418868i
$87$	−8.40669	−	7.46488i	−0.901292	−	0.800319i
$88$	1.76481			0.188130
$89$	4.36194	−	7.55510i	0.462364	−	0.800839i	−0.536714	−	0.843764i	$-0.680335\pi$
$89$	4.36194	−	7.55510i	0.462364	−	0.800839i	0.999078	+	0.0429257i	$0.0136679\pi$
$90$	−2.97895	+	0.354788i	−0.314009	+	0.0373980i
$91$	−1.06869	+	5.39334i	−0.112029	+	0.565376i
$92$	6.19453	+	3.57642i	0.645825	+	0.372867i
$93$	−6.33024	−	5.62106i	−0.656416	−	0.582877i
$94$	−10.4117	−	6.01122i	−1.07389	−	0.620010i
$95$	−6.79557	−	3.92342i	−0.697211	−	0.402535i
$96$	−1.29514	−	1.15005i	−0.132185	−	0.117376i
$97$	−5.31507	−	3.06866i	−0.539664	−	0.311575i	0.205279	−	0.978704i	$-0.434190\pi$
$97$	−5.31507	−	3.06866i	−0.539664	−	0.311575i	−0.744943	+	0.667128i	$0.767523\pi$
$98$	4.26947	+	5.54722i	0.431282	+	0.560353i
$99$	2.08640	−	4.86601i	0.209691	−	0.489053i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	6.07209			0.604195			0.302098	−	0.953277i	$-0.402313\pi$
$101$	6.07209			0.604195			0.302098	+	0.953277i	$0.402313\pi$
$102$	2.23086	+	1.98093i	0.220888	+	0.196141i
$103$		−	18.3273i		−	1.80584i	−0.429808	−	0.902920i	$-0.641419\pi$
$103$		−	18.3273i		−	1.80584i	0.429808	−	0.902920i	$-0.358581\pi$
$104$	1.03906	+	1.79971i	0.101888	+	0.176476i
$105$	3.65074	−	2.76985i	0.356276	−	0.270310i
$106$	2.51118	−	4.34949i	0.243907	−	0.422460i
$107$	−1.63586	−	0.944465i	−0.158145	−	0.0913048i	0.418839	−	0.908060i	$-0.362437\pi$
$107$	−1.63586	−	0.944465i	−0.158145	−	0.0913048i	−0.576984	+	0.816756i	$0.695770\pi$
$108$	−4.70209	+	2.21141i	−0.452459	+	0.212793i
$109$	3.31820	+	5.74730i	0.317826	+	0.550491i	0.980034	−	0.198829i	$-0.0637138\pi$
$109$	3.31820	+	5.74730i	0.317826	+	0.550491i	−0.662208	+	0.749320i	$0.730380\pi$
$110$	0.882407	+	1.52837i	0.0841342	+	0.145725i
$111$	12.0535	−	13.5742i	1.14406	−	1.28841i
$112$	2.59529	+	0.514257i	0.245232	+	0.0485927i
$113$	11.9525	−	6.90075i	1.12439	−	0.649168i	0.181874	−	0.983322i	$-0.441784\pi$
$113$	11.9525	−	6.90075i	1.12439	−	0.649168i	0.942519	+	0.334154i	$0.108450\pi$
$114$	−13.3133	−	2.73382i	−1.24691	−	0.256046i
$115$			7.15283i			0.667005i
$116$	5.62132	−	3.24547i	0.521926	−	0.301334i
$117$	6.19063	−	0.737295i	0.572324	−	0.0681629i
$118$		−	8.50907i		−	0.783323i
$119$	−4.47034	−	0.885797i	−0.409795	−	0.0812009i
$120$	0.348398	−	1.69665i	0.0318042	−	0.154882i
$121$	7.88543			0.716857
$122$	3.46660	−	6.00433i	0.313851	−	0.543606i
$123$	−3.47380	−	10.4451i	−0.313222	−	0.941803i
$124$	4.23286	−	2.44384i	0.380122	−	0.219463i
$125$	1.00000			0.0894427
$126$	4.48613	−	6.54787i	0.399656	−	0.583331i
$127$	−2.81109			−0.249444			−0.124722	−	0.992192i	$-0.539804\pi$
$127$	−2.81109			−0.249444			−0.124722	+	0.992192i	$0.539804\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−4.46726	+	5.03088i	−0.393321	+	0.442944i
$130$	−1.03906	+	1.79971i	−0.0911318	+	0.157845i
$131$	−17.0990			−1.49395			−0.746975	−	0.664852i	$-0.768495\pi$
$131$	−17.0990			−1.49395			−0.746975	+	0.664852i	$0.768495\pi$
$132$	2.28569	+	2.02962i	0.198943	+	0.176656i
$133$	19.6541	−	6.68776i	1.70423	−	0.579902i
$134$		−	4.25239i		−	0.367350i
$135$	−4.26618	−	2.96642i	−0.367175	−	0.255309i
$136$	−1.49171	+	0.861240i	−0.127913	+	0.0738507i
$137$			8.33714i			0.712290i	0.934431	+	0.356145i	$0.115909\pi$
$137$			8.33714i			0.712290i	−0.934431	+	0.356145i	$0.884091\pi$
$138$	3.90976	+	11.7560i	0.332821	+	1.00073i
$139$	8.22347	−	4.74782i	0.697505	−	0.402705i	−0.108912	−	0.994051i	$-0.534737\pi$
$139$	8.22347	−	4.74782i	0.697505	−	0.402705i	0.806418	+	0.591346i	$0.201403\pi$
$140$	0.852286	+	2.50472i	0.0720313	+	0.211687i
$141$	−6.57150	−	19.7594i	−0.553420	−	1.66404i
$142$	−3.98805	−	6.90750i	−0.334669	−	0.579664i
$143$	−1.83375	−	3.17615i	−0.153346	−	0.265603i
$144$	−0.354788	−	2.97895i	−0.0295657	−	0.248246i
$145$	5.62132	+	3.24547i	0.466825	+	0.269522i
$146$	5.44736	−	9.43511i	0.450827	−	0.780855i
$147$	−0.849978	+	12.0945i	−0.0701050	+	0.997540i
$148$	5.24042	+	9.07668i	0.430760	+	0.746098i
$149$		−	4.60451i		−	0.377216i	−0.982052	−	0.188608i	$-0.939602\pi$
$149$		−	4.60451i		−	0.377216i	0.982052	−	0.188608i	$-0.0603975\pi$
$150$	1.64354	−	0.546603i	0.134195	−	0.0446300i
$151$	5.09344			0.414498			0.207249	−	0.978288i	$-0.433549\pi$
$151$	5.09344			0.414498			0.207249	+	0.978288i	$0.433549\pi$
$152$	3.92342	−	6.79557i	0.318232	−	0.551193i
$153$	0.611116	+	5.13118i	0.0494058	+	0.414831i
$154$	−4.58021	−	0.907568i	−0.369084	−	0.0731339i
$155$	4.23286	+	2.44384i	0.339991	+	0.196294i
$156$	−0.724014	+	3.52585i	−0.0579675	+	0.282294i
$157$	−4.19746	−	2.42341i	−0.334994	−	0.193409i	0.323062	−	0.946378i	$-0.395288\pi$
$157$	−4.19746	−	2.42341i	−0.334994	−	0.193409i	−0.658056	+	0.752969i	$0.728621\pi$
$158$	−10.1103	−	5.83721i	−0.804336	−	0.464383i
$159$	8.25445	−	2.74524i	0.654621	−	0.217712i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−14.2374	−	12.4674i	−1.12207	−	0.982571i
$162$	−8.63310	−	2.54353i	−0.678281	−	0.199838i
$163$	−0.203760	+	0.352922i	−0.0159597	+	0.0276430i	−0.873895	−	0.486115i	$-0.838414\pi$
$163$	−0.203760	+	0.352922i	−0.0159597	+	0.0276430i	0.857935	+	0.513758i	$0.171747\pi$
$164$	6.35524			0.496261
$165$	−0.614858	+	2.99427i	−0.0478666	+	0.233104i
$166$			11.5550i			0.896839i
$167$	4.29226	+	7.43442i	0.332145	+	0.575293i	0.982932	−	0.183968i	$-0.0588942\pi$
$167$	4.29226	+	7.43442i	0.332145	+	0.575293i	−0.650787	+	0.759260i	$0.725561\pi$
$168$	2.76985	+	3.65074i	0.213699	+	0.281661i
$169$	−4.34070	+	7.51831i	−0.333900	+	0.578331i
$170$	−1.49171	−	0.861240i	−0.114409	−	0.0660541i
$171$	−14.0987	−	18.8517i	−1.07815	−	1.44162i
$172$	−1.94221	−	3.36401i	−0.148092	−	0.256503i
$173$	−5.28044	−	9.14598i	−0.401464	−	0.695356i	0.592439	−	0.805616i	$-0.298165\pi$
$173$	−5.28044	−	9.14598i	−0.401464	−	0.695356i	−0.993903	+	0.110259i	$0.964832\pi$
$174$	11.0128	+	2.26143i	0.834882	+	0.171438i
$175$	−1.74301	+	1.99046i	−0.131759	+	0.150465i
$176$	−1.52837	+	0.882407i	−0.115206	+	0.0665140i
$177$	9.78582	−	11.0205i	0.735547	−	0.828348i
$178$			8.72387i			0.653882i
$179$	0.503264	−	0.290560i	0.0376157	−	0.0217175i	−0.481074	−	0.876680i	$-0.659753\pi$
$179$	0.503264	−	0.290560i	0.0376157	−	0.0217175i	0.518690	+	0.854962i	$0.326420\pi$
$180$	2.40245	−	1.79673i	0.179068	−	0.133920i
$181$		−	15.6386i		−	1.16241i	−0.813757	−	0.581206i	$-0.802581\pi$
$181$		−	15.6386i		−	1.16241i	0.813757	−	0.581206i	$-0.197419\pi$
$182$	−1.77116	−	5.20512i	−0.131287	−	0.385829i
$183$	11.3950	−	3.78971i	0.842342	−	0.280143i
$184$	−7.15283			−0.527314
$185$	−5.24042	+	9.07668i	−0.385284	+	0.667331i
$186$	8.29268	+	1.70286i	0.608049	+	0.124860i
$187$	2.63259	−	1.51993i	0.192514	−	0.111148i
$188$	12.0224			0.876826
$189$	13.3405	−	3.32118i	0.970381	−	0.241580i
$190$	7.84685			0.569270
$191$	−14.8082	+	8.54950i	−1.07148	+	0.618620i	−0.928586	−	0.371118i	$-0.878975\pi$
$191$	−14.8082	+	8.54950i	−1.07148	+	0.618620i	−0.142896	+	0.989738i	$0.545641\pi$
$192$	1.69665	+	0.348398i	0.122445	+	0.0251434i
$193$	−0.407256	+	0.705389i	−0.0293150	+	0.0507750i	−0.880311	−	0.474398i	$-0.842666\pi$
$193$	−0.407256	+	0.705389i	−0.0293150	+	0.0507750i	0.850996	+	0.525173i	$0.175999\pi$
$194$	6.13732			0.440634
$195$	−3.41548	+	1.13591i	−0.244588	+	0.0813442i
$196$	−6.47108	−	2.66929i	−0.462220	−	0.190664i
$197$			15.4752i			1.10256i	0.834320	+	0.551280i	$0.185860\pi$
$197$			15.4752i			1.10256i	−0.834320	+	0.551280i	$0.814140\pi$
$198$	0.626136	+	5.25729i	0.0444975	+	0.373619i
$199$	−7.51013	+	4.33598i	−0.532379	+	0.307369i	−0.741985	−	0.670417i	$-0.766115\pi$
$199$	−7.51013	+	4.33598i	−0.532379	+	0.307369i	0.209606	+	0.977786i	$0.432782\pi$
$200$			1.00000i			0.0707107i
$201$	4.89044	−	5.50745i	0.344945	−	0.388465i
$202$	−5.25858	+	3.03604i	−0.369993	+	0.213615i
$203$	−16.2580	+	5.53214i	−1.14109	+	0.388280i
$204$	−2.92244	−	0.600108i	−0.204612	−	0.0420160i
$205$	3.17762	+	5.50380i	0.221935	+	0.384402i
$206$	9.16364	+	15.8719i	0.638461	+	1.10585i
$207$	−8.45620	+	19.7221i	−0.587747	+	1.37078i
$208$	−1.79971	−	1.03906i	−0.124787	−	0.0720460i
$209$	−6.92412	+	11.9929i	−0.478951	+	0.829568i
$210$	−1.77671	+	4.22413i	−0.122604	+	0.291493i
$211$	11.5037	+	19.9250i	0.791946	+	1.37169i	0.924760	+	0.380550i	$0.124265\pi$
$211$	11.5037	+	19.9250i	0.791946	+	1.37169i	−0.132814	+	0.991141i	$0.542401\pi$
$212$			5.02236i			0.344937i
$213$	2.77885	−	13.5326i	0.190404	−	0.927240i
$214$	1.88893			0.129125
$215$	1.94221	−	3.36401i	0.132458	−	0.229423i
$216$	2.96642	−	4.26618i	0.201840	−	0.290277i
$217$	−12.2423	+	4.16570i	−0.831059	+	0.282786i
$218$	−5.74730	−	3.31820i	−0.389256	−	0.224737i
$219$	17.9059	−	5.95510i	1.20997	−	0.402408i
$220$	−1.52837	−	0.882407i	−0.103043	−	0.0594919i
$221$	3.09996	+	1.78976i	0.208526	+	0.120393i
$222$	−3.65150	+	17.7823i	−0.245073	+	1.19347i
$223$	−7.09528	−	4.09646i	−0.475135	−	0.274320i	0.243252	−	0.969963i	$-0.421786\pi$
$223$	−7.09528	−	4.09646i	−0.475135	−	0.274320i	−0.718387	+	0.695644i	$0.755119\pi$
$224$	−2.50472	+	0.852286i	−0.167353	+	0.0569458i
$225$	2.75724	+	1.18222i	0.183816	+	0.0788145i
$226$	−6.90075	+	11.9525i	−0.459031	+	0.795066i
$227$	9.94983			0.660394			0.330197	−	0.943912i	$-0.392885\pi$
$227$	9.94983			0.660394			0.330197	+	0.943912i	$0.392885\pi$
$228$	12.8966	−	4.28911i	0.854099	−	0.284053i
$229$			3.33365i			0.220294i	0.993915	+	0.110147i	$0.0351321\pi$
$229$			3.33365i			0.220294i	−0.993915	+	0.110147i	$0.964868\pi$
$230$	−3.57642	−	6.19453i	−0.235822	−	0.408455i
$231$	−4.88828	−	6.44288i	−0.321625	−	0.423910i
$232$	−3.24547	+	5.62132i	−0.213076	+	0.369058i
$233$	−17.9721	−	10.3762i	−1.17739	−	0.679766i	−0.221980	−	0.975051i	$-0.571252\pi$
$233$	−17.9721	−	10.3762i	−1.17739	−	0.679766i	−0.955409	+	0.295285i	$0.904585\pi$
$234$	−4.99259	+	3.73383i	−0.326376	+	0.244088i
$235$	6.01122	+	10.4117i	0.392129	+	0.679187i
$236$	4.25453	+	7.36907i	0.276947	+	0.479686i
$237$	−6.38128	−	19.1874i	−0.414508	−	1.24635i
$238$	4.31432	−	1.46805i	0.279656	−	0.0951593i
$239$	13.5359	−	7.81497i	0.875567	−	0.505509i	0.00637252	−	0.999980i	$-0.497972\pi$
$239$	13.5359	−	7.81497i	0.875567	−	0.505509i	0.869194	+	0.494471i	$0.164638\pi$
$240$	0.546603	+	1.64354i	0.0352831	+	0.106090i
$241$		−	19.6492i		−	1.26571i	−0.774268	−	0.632857i	$-0.781882\pi$
$241$		−	19.6492i		−	1.26571i	0.774268	−	0.632857i	$-0.218118\pi$
$242$	−6.82898	+	3.94271i	−0.438984	+	0.253447i
$243$	−8.25592	−	13.2227i	−0.529618	−	0.848236i
$244$			6.93320i			0.443853i
$245$	−0.923864	−	6.93877i	−0.0590235	−	0.443302i
$246$	8.23095	+	7.30882i	0.524786	+	0.465993i
$247$	−16.3067			−1.03757
$248$	−2.44384	+	4.23286i	−0.155184	+	0.268787i
$249$	−13.2887	+	14.9653i	−0.842140	+	0.948389i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−4.91923			−0.310499			−0.155250	−	0.987875i	$-0.549618\pi$
$251$	−4.91923			−0.310499			−0.155250	+	0.987875i	$0.549618\pi$
$252$	−0.611165	+	7.91369i	−0.0384998	+	0.498516i
$253$	12.6234			0.793628
$254$	2.43448	−	1.40555i	0.152753	−	0.0881919i
$255$	−0.941513	−	2.83097i	−0.0589598	−	0.177282i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.8150			0.861753			0.430877	−	0.902411i	$-0.358204\pi$
$257$	13.8150			0.861753			0.430877	+	0.902411i	$0.358204\pi$
$258$	1.35332	−	6.59050i	0.0842542	−	0.410307i
$259$	−8.93268	−	26.2516i	−0.555050	−	1.63119i
$260$		−	2.07813i		−	0.128880i
$261$	11.6625	+	15.5942i	0.721888	+	0.965254i
$262$	14.8082	−	8.54952i	0.914854	−	0.528191i
$263$		−	24.9196i		−	1.53661i	−0.640084	−	0.768305i	$-0.721100\pi$
$263$		−	24.9196i		−	1.53661i	0.640084	−	0.768305i	$-0.278900\pi$
$264$	−2.99427	−	0.614858i	−0.184285	−	0.0378419i
$265$	−4.34949	+	2.51118i	−0.267187	+	0.154261i
$266$	−13.6771	+	15.6188i	−0.838597	+	0.957652i
$267$	−10.0329	+	11.2987i	−0.614001	+	0.691467i
$268$	2.12619	+	3.68268i	0.129878	+	0.224955i
$269$	−8.99870	−	15.5862i	−0.548660	−	0.950308i	−0.998367	−	0.0571312i	$-0.981805\pi$
$269$	−8.99870	−	15.5862i	−0.548660	−	0.950308i	0.449706	−	0.893176i	$-0.351529\pi$
$270$	5.17784	+	0.435907i	0.315113	+	0.0265285i
$271$	0.247998	+	0.143182i	0.0150648	+	0.00869766i	0.507513	−	0.861644i	$-0.330565\pi$
$271$	0.247998	+	0.143182i	0.0150648	+	0.00869766i	−0.492449	+	0.870341i	$0.663898\pi$
$272$	0.861240	−	1.49171i	0.0522203	−	0.0904483i
$273$	3.69222	−	8.77828i	0.223463	−	0.531286i
$274$	−4.16857	−	7.22017i	−0.251832	−	0.436187i
$275$		−	1.76481i		−	0.106422i
$276$	−9.26394	−	8.22609i	−0.557623	−	0.495152i
$277$	12.5487			0.753979			0.376990	−	0.926217i	$-0.376959\pi$
$277$	12.5487			0.753979			0.376990	+	0.926217i	$0.376959\pi$
$278$	−4.74782	+	8.22347i	−0.284755	+	0.493211i
$279$	8.78184	+	11.7424i	0.525755	+	0.703000i
$280$	−1.99046	−	1.74301i	−0.118953	−	0.104164i
$281$	−2.38434	−	1.37660i	−0.142238	−	0.0821209i	0.427192	−	0.904161i	$-0.359503\pi$
$281$	−2.38434	−	1.37660i	−0.142238	−	0.0821209i	−0.569430	+	0.822040i	$0.692836\pi$
$282$	15.5708	+	13.8264i	0.927226	+	0.823347i
$283$	15.6445	+	9.03237i	0.929970	+	0.536919i	0.886802	−	0.462149i	$-0.152922\pi$
$283$	15.6445	+	9.03237i	0.929970	+	0.536919i	0.0431681	+	0.999068i	$0.486255\pi$
$284$	6.90750	+	3.98805i	0.409885	+	0.236647i
$285$	10.1628	+	9.02424i	0.601992	+	0.534550i
$286$	3.17615	+	1.83375i	0.187810	+	0.108432i
$287$	−16.4937	−	3.26823i	−0.973593	−	0.192917i
$288$	1.79673	+	2.40245i	0.105873	+	0.141566i
$289$	7.01653	−	12.1530i	0.412737	−	0.714882i
$290$	−6.49094			−0.381161
$291$	7.94870	+	7.05820i	0.465961	+	0.413759i
$292$			10.8947i			0.637566i
$293$	5.02230	+	8.69888i	0.293406	+	0.508194i	0.974613	−	0.223897i	$-0.0718779\pi$
$293$	5.02230	+	8.69888i	0.293406	+	0.508194i	−0.681207	+	0.732091i	$0.738545\pi$
$294$	−5.31116	−	10.8992i	−0.309753	−	0.635652i
$295$	−4.25453	+	7.36907i	−0.247709	+	0.429044i
$296$	−9.07668	−	5.24042i	−0.527571	−	0.304593i
$297$	−5.23519	+	7.52902i	−0.303777	+	0.436878i
$298$	2.30225	+	3.98762i	0.133366	+	0.230997i
$299$	7.43224	+	12.8730i	0.429818	+	0.744466i
$300$	−1.15005	+	1.29514i	−0.0663979	+	0.0747751i
$301$	3.31064	+	9.72937i	0.190822	+	0.560792i
$302$	−4.41105	+	2.54672i	−0.253827	+	0.146547i
$303$	−10.3022	−	2.11550i	−0.591846	−	0.121532i
$304$			7.84685i			0.450048i
$305$	−6.00433	+	3.46660i	−0.343807	+	0.198497i
$306$	−3.09483	−	4.13817i	−0.176920	−	0.236563i
$307$		−	28.7798i		−	1.64255i	−0.570535	−	0.821274i	$-0.693264\pi$
$307$		−	28.7798i		−	1.64255i	0.570535	−	0.821274i	$-0.306736\pi$
$308$	4.42036	−	1.50413i	0.251873	−	0.0857056i
$309$	−6.38518	+	31.0950i	−0.363240	+	1.76893i
$310$	−4.88768			−0.277602
$311$	−13.5293	+	23.4335i	−0.767178	+	1.32879i	0.171910	+	0.985113i	$0.445006\pi$
$311$	−13.5293	+	23.4335i	−0.767178	+	1.32879i	−0.939088	+	0.343678i	$0.888327\pi$
$312$	−1.13591	−	3.41548i	−0.0643083	−	0.193364i
$313$	−25.8750	+	14.9390i	−1.46254	+	0.844400i	−0.999128	−	0.0417421i	$-0.986709\pi$
$313$	−25.8750	+	14.9390i	−1.46254	+	0.844400i	−0.463414	+	0.886142i	$0.653376\pi$
$314$	4.84681			0.273521
$315$	−7.15904	+	3.42756i	−0.403366	+	0.193121i
$316$	11.6744			0.656737
$317$	2.16669	−	1.25094i	0.121694	−	0.0702599i	−0.437918	−	0.899015i	$-0.644284\pi$
$317$	2.16669	−	1.25094i	0.121694	−	0.0702599i	0.559611	+	0.828755i	$0.310950\pi$
$318$	−5.77595	+	6.50467i	−0.323899	+	0.364764i
$319$	5.72765	−	9.92059i	0.320687	−	0.555446i
$320$	−1.00000			−0.0559017
$321$	2.44643	+	2.17236i	0.136547	+	0.121249i
$322$	18.5637	+	3.67839i	1.03451	+	0.204989i
$323$		−	13.5160i		−	0.752052i
$324$	8.74825	−	2.11379i	0.486014	−	0.117433i
$325$	1.79971	−	1.03906i	0.0998299	−	0.0576368i
$326$		−	0.407519i		−	0.0225704i
$327$	−3.62748	−	10.9072i	−0.200600	−	0.603170i
$328$	−5.50380	+	3.17762i	−0.303897	+	0.175455i
$329$	−31.2017	−	6.18262i	−1.72021	−	0.340859i
$330$	−0.964654	−	2.90054i	−0.0531024	−	0.159670i
$331$	−11.3861	−	19.7213i	−0.625838	−	1.08398i	−0.988378	−	0.152015i	$-0.951424\pi$
$331$	−11.3861	−	19.7213i	−0.625838	−	1.08398i	0.362541	−	0.931968i	$-0.381909\pi$
$332$	−5.77748	−	10.0069i	−0.317081	−	0.549200i
$333$	−25.1797	+	18.8312i	−1.37984	+	1.03195i
$334$	−7.43442	−	4.29226i	−0.406793	−	0.234862i
$335$	−2.12619	+	3.68268i	−0.116166	+	0.201206i
$336$	−4.22413	−	1.77671i	−0.230445	−	0.0969273i
$337$	−6.91370	−	11.9749i	−0.376613	−	0.652313i	0.613954	−	0.789342i	$-0.289578\pi$
$337$	−6.91370	−	11.9749i	−0.376613	−	0.652313i	−0.990567	+	0.137029i	$0.956245\pi$
$338$		−	8.68139i		−	0.472206i
$339$	−22.6833	+	7.54395i	−1.23199	+	0.409731i
$340$	1.72248			0.0934146
$341$	4.31293	−	7.47021i	0.233558	−	0.404534i
$342$	21.6356	+	9.27668i	1.16992	+	0.501626i
$343$	15.4216	+	10.2554i	0.832690	+	0.553739i
$344$	3.36401	+	1.94221i	0.181375	+	0.104717i
$345$	2.49203	−	12.1358i	0.134166	−	0.653372i
$346$	9.14598	+	5.28044i	0.491691	+	0.283878i
$347$	4.47611	+	2.58428i	0.240290	+	0.138732i	0.615310	−	0.788285i	$-0.289031\pi$
$347$	4.47611	+	2.58428i	0.240290	+	0.138732i	−0.375020	+	0.927017i	$0.622364\pi$
$348$	−10.6681	+	3.54797i	−0.571871	+	0.190191i
$349$	6.38127	+	3.68423i	0.341582	+	0.197212i	0.660971	−	0.750411i	$-0.270145\pi$
$349$	6.38127	+	3.68423i	0.341582	+	0.197212i	−0.319390	+	0.947623i	$0.603478\pi$
$350$	0.514257	−	2.59529i	0.0274882	−	0.138724i
$351$	−10.7602	−	0.905870i	−0.574337	−	0.0483517i
$352$	0.882407	−	1.52837i	0.0470325	−	0.0814626i
$353$	8.12499			0.432450			0.216225	−	0.976344i	$-0.430626\pi$
$353$	8.12499			0.432450			0.216225	+	0.976344i	$0.430626\pi$
$354$	−2.96454	+	14.4369i	−0.157564	+	0.767313i
$355$			7.97609i			0.423327i
$356$	−4.36194	−	7.55510i	−0.231182	−	0.400419i
$357$	7.27599	+	3.06034i	0.385086	+	0.161971i
$358$	−0.290560	+	0.503264i	−0.0153566	+	0.0265983i
$359$	14.8774	+	8.58944i	0.785197	+	0.453333i	0.838269	−	0.545257i	$-0.183568\pi$
$359$	14.8774	+	8.58944i	0.785197	+	0.453333i	−0.0530722	+	0.998591i	$0.516901\pi$
$360$	−1.18222	+	2.75724i	−0.0623083	+	0.145319i
$361$	21.2865	+	36.8693i	1.12034	+	1.94049i
$362$	7.81932	+	13.5435i	0.410974	+	0.711829i
$363$	−13.3788	−	2.74727i	−0.702205	−	0.144194i
$364$	4.13643	+	3.62218i	0.216808	+	0.189854i
$365$	−9.43511	+	5.44736i	−0.493856	+	0.285128i
$366$	−7.97350	+	8.97948i	−0.416781	+	0.469365i
$367$			13.1521i			0.686532i	0.939238	+	0.343266i	$0.111533\pi$
$367$			13.1521i			0.686532i	−0.939238	+	0.343266i	$0.888467\pi$
$368$	6.19453	−	3.57642i	0.322912	−	0.186434i
$369$	2.25477	+	18.9319i	0.117378	+	0.985557i
$370$		−	10.4808i		−	0.544873i
$371$	2.58278	−	13.0345i	0.134091	−	0.676717i
$372$	−8.03310	+	2.67162i	−0.416497	+	0.138517i
$373$	13.9681			0.723241			0.361620	−	0.932325i	$-0.382224\pi$
$373$	13.9681			0.723241			0.361620	+	0.932325i	$0.382224\pi$
$374$	−1.51993	+	2.63259i	−0.0785937	+	0.136128i
$375$	−1.69665	−	0.348398i	−0.0876146	−	0.0179912i
$376$	−10.4117	+	6.01122i	−0.536944	+	0.310005i
$377$	13.4890			0.694718
$378$	−9.89265	+	9.54649i	−0.508823	+	0.491018i
$379$	18.2898			0.939482			0.469741	−	0.882804i	$-0.344347\pi$
$379$	18.2898			0.939482			0.469741	+	0.882804i	$0.344347\pi$
$380$	−6.79557	+	3.92342i	−0.348605	+	0.201267i
$381$	4.76944	+	0.979379i	0.244346	+	0.0501751i
$382$	8.54950	−	14.8082i	0.437431	−	0.757652i
$383$	16.1857			0.827052			0.413526	−	0.910492i	$-0.364297\pi$
$383$	16.1857			0.827052			0.413526	+	0.910492i	$0.364297\pi$
$384$	−1.64354	+	0.546603i	−0.0838716	+	0.0278937i
$385$	3.51279	+	3.07608i	0.179029	+	0.156772i
$386$		−	0.814513i		−	0.0414576i
$387$	9.33212	−	6.97925i	0.474379	−	0.354775i
$388$	−5.31507	+	3.06866i	−0.269832	+	0.155788i
$389$			4.16740i			0.211295i	0.994404	+	0.105648i	$0.0336916\pi$
$389$			4.16740i			0.211295i	−0.994404	+	0.105648i	$0.966308\pi$
$390$	2.38994	−	2.69147i	0.121019	−	0.136288i
$391$	−10.6700	+	6.16030i	−0.539603	+	0.311540i
$392$	6.93877	−	0.923864i	0.350461	−	0.0466622i
$393$	29.0111	+	5.95727i	1.46342	+	0.300505i
$394$	−7.73758	−	13.4019i	−0.389814	−	0.675177i
$395$	5.83721	+	10.1103i	0.293702	+	0.508707i
$396$	−3.17089	−	4.23988i	−0.159343	−	0.213062i
$397$	−16.3535	−	9.44168i	−0.820757	−	0.473865i	0.0299201	−	0.999552i	$-0.490475\pi$
$397$	−16.3535	−	9.44168i	−0.820757	−	0.473865i	−0.850678	+	0.525688i	$0.823808\pi$
$398$	4.33598	−	7.51013i	0.217343	−	0.376449i
$399$	−35.6762	+	4.49933i	−1.78604	+	0.225248i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	4.40822i		−	0.220136i	−0.993924	−	0.110068i	$-0.964893\pi$
$401$		−	4.40822i		−	0.220136i	0.993924	−	0.110068i	$-0.0351069\pi$
$402$	−1.48152	+	7.21481i	−0.0738916	+	0.359842i
$403$	10.1572			0.505967
$404$	3.03604	−	5.25858i	0.151049	−	0.261624i
$405$	6.20472	+	6.51931i	0.308315	+	0.323947i
$406$	11.3137	−	12.9200i	0.561492	−	0.641207i
$407$	16.0187	+	9.24838i	0.794015	+	0.458425i
$408$	2.83097	−	0.941513i	0.140154	−	0.0466118i
$409$	31.9711	+	18.4585i	1.58087	+	0.912714i	0.994733	+	0.102500i	$0.0326841\pi$
$409$	31.9711	+	18.4585i	1.58087	+	0.912714i	0.586134	+	0.810214i	$0.300649\pi$
$410$	−5.50380	−	3.17762i	−0.271813	−	0.156932i
$411$	2.90464	−	14.1452i	0.143275	−	0.697731i
$412$	−15.8719	−	9.16364i	−0.781952	−	0.451460i
$413$	−7.25216	−	21.3128i	−0.356856	−	1.04873i
$414$	−2.53774	−	21.3079i	−0.124723	−	1.04723i
$415$	5.77748	−	10.0069i	0.283605	−	0.491219i
$416$	2.07813			0.101888
$417$	−15.6065	+	5.19035i	−0.764252	+	0.254173i
$418$		−	13.8482i		−	0.677339i
$419$	10.6989	+	18.5311i	0.522677	+	0.905304i	0.999652	+	0.0263867i	$0.00840012\pi$
$419$	10.6989	+	18.5311i	0.522677	+	0.905304i	−0.476974	+	0.878917i	$0.658267\pi$
$420$	−0.573393	−	4.54656i	−0.0279787	−	0.221849i
$421$	−12.6605	+	21.9286i	−0.617033	+	1.06873i	0.372991	+	0.927835i	$0.378332\pi$
$421$	−12.6605	+	21.9286i	−0.617033	+	1.06873i	−0.990024	+	0.140898i	$0.955001\pi$
$422$	−19.9250	−	11.5037i	−0.969932	−	0.559991i
$423$	4.26542	+	35.8142i	0.207392	+	1.74135i
$424$	−2.51118	−	4.34949i	−0.121954	−	0.211230i
$425$	0.861240	+	1.49171i	0.0417763	+	0.0723586i
$426$	4.35976	+	13.1090i	0.211231	+	0.635134i
$427$	3.56544	−	17.9937i	0.172544	−	0.870775i
$428$	−1.63586	+	0.944465i	−0.0790723	+	0.0456524i
$429$	2.00467	+	6.02769i	0.0967864	+	0.291020i
$430$			3.88442i			0.187323i
$431$	−22.1285	+	12.7759i	−1.06589	+	0.615393i	−0.927056	−	0.374922i	$-0.877669\pi$
$431$	−22.1285	+	12.7759i	−1.06589	+	0.615393i	−0.138836	+	0.990315i	$0.544336\pi$
$432$	−0.435907	+	5.17784i	−0.0209726	+	0.249119i
$433$		−	3.82288i		−	0.183716i	−0.995772	−	0.0918579i	$-0.970719\pi$
$433$		−	3.82288i		−	0.183716i	0.995772	−	0.0918579i	$-0.0292806\pi$
$434$	8.51926	−	9.72874i	0.408937	−	0.466994i
$435$	−8.40669	−	7.46488i	−0.403070	−	0.357914i
$436$	6.63641			0.317826
$437$	28.0636	−	48.6076i	1.34246	−	2.32522i
$438$	−12.5294	+	14.1102i	−0.598680	+	0.674213i
$439$	2.71952	−	1.57012i	0.129796	−	0.0749376i	−0.433696	−	0.901059i	$-0.642791\pi$
$439$	2.71952	−	1.57012i	0.129796	−	0.0749376i	0.563492	+	0.826122i	$0.309458\pi$
$440$	1.76481			0.0841342
$441$	5.65582	−	20.2240i	0.269325	−	0.963049i
$442$	−3.57953			−0.170261
$443$	−26.3613	+	15.2197i	−1.25246	+	0.723110i	−0.971598	−	0.236638i	$-0.923955\pi$
$443$	−26.3613	+	15.2197i	−1.25246	+	0.723110i	−0.280865	+	0.959747i	$0.590621\pi$
$444$	−5.72887	−	17.2257i	−0.271880	−	0.817495i
$445$	4.36194	−	7.55510i	0.206776	−	0.358146i
$446$	8.19293			0.387946
$447$	−1.60420	+	7.81223i	−0.0758760	+	0.369506i
$448$	1.74301	−	1.99046i	0.0823493	−	0.0940404i
$449$		−	23.6834i		−	1.11769i	−0.829273	−	0.558844i	$-0.811245\pi$
$449$		−	23.6834i		−	1.11769i	0.829273	−	0.558844i	$-0.188755\pi$
$450$	−2.97895	+	0.354788i	−0.140429	+	0.0167249i
$451$	9.71319	−	5.60791i	0.457376	−	0.264066i
$452$		−	13.8015i		−	0.649168i
$453$	−8.64178	−	1.77454i	−0.406026	−	0.0833753i
$454$	−8.61681	+	4.97492i	−0.404407	+	0.233484i
$455$	−1.06869	+	5.39334i	−0.0501010	+	0.252844i
$456$	−9.02424	+	10.1628i	−0.422599	+	0.475916i
$457$	4.33893	+	7.51524i	0.202967	+	0.351548i	0.949483	−	0.313819i	$-0.101608\pi$
$457$	4.33893	+	7.51524i	0.202967	+	0.351548i	−0.746516	+	0.665367i	$0.768275\pi$
$458$	−1.66682	−	2.88702i	−0.0778856	−	0.134902i
$459$	0.750841	−	8.91872i	0.0350463	−	0.416290i
$460$	6.19453	+	3.57642i	0.288822	+	0.166751i
$461$	−14.9611	+	25.9133i	−0.696807	+	1.20690i	0.272761	+	0.962082i	$0.412063\pi$
$461$	−14.9611	+	25.9133i	−0.696807	+	1.20690i	−0.969568	+	0.244823i	$0.921270\pi$
$462$	7.45481	+	3.13556i	0.346829	+	0.145879i
$463$	−15.7628	−	27.3020i	−0.732559	−	1.26883i	−0.955786	−	0.294063i	$-0.904992\pi$
$463$	−15.7628	−	27.3020i	−0.732559	−	1.26883i	0.223227	−	0.974767i	$-0.428341\pi$
$464$		−	6.49094i		−	0.301334i
$465$	−6.33024	−	5.62106i	−0.293558	−	0.260670i
$466$	20.7524			0.961335
$467$	15.6065	−	27.0312i	0.722181	−	1.25085i	−0.237944	−	0.971279i	$-0.576473\pi$
$467$	15.6065	−	27.0312i	0.722181	−	1.25085i	0.960124	−	0.279574i	$-0.0901933\pi$
$468$	2.45680	−	5.72989i	0.113565	−	0.264864i
$469$	−3.62425	−	10.6510i	−0.167352	−	0.491819i
$470$	−10.4117	−	6.01122i	−0.480257	−	0.277277i
$471$	6.27731	+	5.57406i	0.289243	+	0.256839i
$472$	−7.36907	−	4.25453i	−0.339189	−	0.195831i
$473$	−5.93685	−	3.42764i	−0.272977	−	0.157603i
$474$	15.1200	+	13.4261i	0.694486	+	0.616682i
$475$	−6.79557	−	3.92342i	−0.311802	−	0.180019i
$476$	−3.00229	+	3.42853i	−0.137610	+	0.157146i
$477$	−14.9613	+	1.78188i	−0.685033	+	0.0815865i
$478$	−7.81497	+	13.5359i	−0.357449	+	0.619119i
$479$	29.5666			1.35093			0.675465	−	0.737392i	$-0.263943\pi$
$479$	29.5666			1.35093			0.675465	+	0.737392i	$0.263943\pi$
$480$	−1.29514	−	1.15005i	−0.0591149	−	0.0524922i
$481$			21.7805i			0.993106i
$482$	9.82459	+	17.0167i	0.447498	+	0.775089i
$483$	19.8123	+	26.1131i	0.901491	+	1.18819i
$484$	3.94271	−	6.82898i	0.179214	−	0.310408i
$485$	−5.31507	−	3.06866i	−0.241345	−	0.139341i
$486$	13.7612	+	7.32323i	0.624220	+	0.332188i
$487$	9.02713	+	15.6354i	0.409058	+	0.708509i	0.994784	−	0.101999i	$-0.0325240\pi$
$487$	9.02713	+	15.6354i	0.409058	+	0.708509i	−0.585726	+	0.810509i	$0.699191\pi$
$488$	−3.46660	−	6.00433i	−0.156926	−	0.271803i
$489$	0.468666	−	0.527796i	0.0211938	−	0.0238677i
$490$	4.26947	+	5.54722i	0.192875	+	0.250598i
$491$	−8.24376	+	4.75953i	−0.372035	+	0.214795i	−0.674347	−	0.738414i	$-0.735575\pi$
$491$	−8.24376	+	4.75953i	−0.372035	+	0.214795i	0.302312	+	0.953209i	$0.402242\pi$
$492$	−10.7826	−	2.21415i	−0.486118	−	0.0998217i
$493$			11.1805i			0.503545i
$494$	14.1220	−	8.15337i	0.635381	−	0.366837i
$495$	2.08640	−	4.86601i	0.0937765	−	0.218711i
$496$		−	4.88768i		−	0.219463i
$497$	−15.8761	−	13.9024i	−0.712140	−	0.623606i
$498$	4.02572	−	19.6047i	0.180397	−	0.878509i
$499$	10.5398			0.471827			0.235914	−	0.971774i	$-0.424192\pi$
$499$	10.5398			0.471827			0.235914	+	0.971774i	$0.424192\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−4.69233	−	14.1090i	−0.209638	−	0.630345i
$502$	4.26018	−	2.45962i	0.190141	−	0.109778i
$503$	−16.8262			−0.750245			−0.375122	−	0.926975i	$-0.622399\pi$
$503$	−16.8262			−0.750245			−0.375122	+	0.926975i	$0.622399\pi$
$504$	−3.42756	−	7.15904i	−0.152676	−	0.318889i
$505$	6.07209			0.270204
$506$	−10.9322	+	6.31171i	−0.485996	+	0.280590i
$507$	9.98400	−	11.2436i	0.443405	−	0.499348i
$508$	−1.40555	+	2.43448i	−0.0623611	+	0.108013i
$509$	−9.17382			−0.406623			−0.203311	−	0.979114i	$-0.565170\pi$
$509$	−9.17382			−0.406623			−0.203311	+	0.979114i	$0.565170\pi$
$510$	2.23086	+	1.98093i	0.0987840	+	0.0877171i
$511$	5.60269	−	28.2750i	0.247848	−	1.25081i
$512$		−	1.00000i		−	0.0441942i
$513$	17.3526	+	36.8966i	0.766136	+	1.62902i
$514$	−11.9641	+	6.90748i	−0.527714	+	0.304676i
$515$		−	18.3273i		−	0.807597i
$516$	2.12324	+	6.38420i	0.0934703	+	0.281049i
$517$	18.3748	−	10.6087i	0.808122	−	0.466569i
$518$	20.8617	+	18.2682i	0.916611	+	0.802657i
$519$	5.77261	+	17.3572i	0.253389	+	0.761897i
$520$	1.03906	+	1.79971i	0.0455659	+	0.0789225i
$521$	−7.22962	−	12.5221i	−0.316736	−	0.548602i	0.663069	−	0.748558i	$-0.269253\pi$
$521$	−7.22962	−	12.5221i	−0.316736	−	0.548602i	−0.979805	+	0.199956i	$0.935920\pi$
$522$	−17.8971	−	7.67370i	−0.783333	−	0.335869i
$523$	23.7011	+	13.6839i	1.03638	+	0.598353i	0.918805	−	0.394711i	$-0.129155\pi$
$523$	23.7011	+	13.6839i	1.03638	+	0.598353i	0.117573	+	0.993064i	$0.462489\pi$
$524$	−8.54952	+	14.8082i	−0.373488	+	0.646900i
$525$	3.65074	−	2.76985i	0.159331	−	0.120886i
$526$	12.4598	+	21.5810i	0.543274	+	0.940978i
$527$			8.41893i			0.366734i
$528$	2.90054	−	0.964654i	0.126230	−	0.0419812i
$529$	−28.1630			−1.22448
$530$	2.51118	−	4.34949i	0.109079	−	0.188930i
$531$	−20.4426	+	15.2885i	−0.887134	+	0.663464i
$532$	4.03530	−	20.3649i	0.174952	−	0.882929i
$533$	11.4376	+	6.60350i	0.495417	+	0.286029i
$534$	3.03938	−	14.8014i	0.131527	−	0.640517i
$535$	−1.63586	−	0.944465i	−0.0707244	−	0.0408328i
$536$	−3.68268	−	2.12619i	−0.159067	−	0.0918376i
$537$	−0.955093	+	0.317642i	−0.0412153	+	0.0137073i
$538$	15.5862	+	8.99870i	0.671969	+	0.387961i
$539$	−12.2456	+	1.63045i	−0.527457	+	0.0702284i
$540$	−4.70209	+	2.21141i	−0.202346	+	0.0951640i
$541$	−5.30916	+	9.19574i	−0.228259	+	0.395356i	−0.957292	−	0.289122i	$-0.906637\pi$
$541$	−5.30916	+	9.19574i	−0.228259	+	0.395356i	0.729033	+	0.684478i	$0.239970\pi$
$542$	−0.286363			−0.0123004
$543$	−5.44847	+	26.5333i	−0.233816	+	1.13865i
$544$			1.72248i			0.0738507i
$545$	3.31820	+	5.74730i	0.142136	+	0.246187i
$546$	1.19158	+	9.44832i	0.0509950	+	0.404351i
$547$	15.7759	−	27.3247i	0.674529	−	1.16832i	−0.302077	−	0.953284i	$-0.597680\pi$
$547$	15.7759	−	27.3247i	0.674529	−	1.16832i	0.976606	−	0.215036i	$-0.0689868\pi$
$548$	7.22017	+	4.16857i	0.308430	+	0.178072i
$549$	−20.6536	+	2.45982i	−0.881475	+	0.104982i
$550$	0.882407	+	1.52837i	0.0376260	+	0.0651701i
$551$	−25.4667	−	44.1096i	−1.08492	−	1.87913i
$552$	12.1358	+	2.49203i	0.516536	+	0.106068i
$553$	−30.2985	−	6.00365i	−1.28842	−	0.255301i
$554$	−10.8675	+	6.27436i	−0.461716	+	0.266572i
$555$	12.0535	−	13.5742i	0.511641	−	0.576192i
$556$		−	9.49564i		−	0.402705i
$557$	33.3462	−	19.2524i	1.41292	−	0.815752i	0.417262	−	0.908786i	$-0.362990\pi$
$557$	33.3462	−	19.2524i	1.41292	−	0.815752i	0.995663	+	0.0930341i	$0.0296566\pi$
$558$	−13.4765	−	5.77830i	−0.570506	−	0.244615i
$559$		−	8.07231i		−	0.341422i
$560$	2.59529	+	0.514257i	0.109671	+	0.0217313i
$561$	−4.99613	+	1.66160i	−0.210937	+	0.0701527i
$562$	2.75319			0.116136
$563$	7.69592	−	13.3297i	0.324344	−	0.561781i	−0.657035	−	0.753860i	$-0.728190\pi$
$563$	7.69592	−	13.3297i	0.324344	−	0.561781i	0.981379	+	0.192079i	$0.0615230\pi$
$564$	−20.3979	−	4.18859i	−0.858905	−	0.176371i
$565$	11.9525	−	6.90075i	0.502844	−	0.290317i
$566$	−18.0647			−0.759318
$567$	−23.7913	+	0.987058i	−0.999140	+	0.0414525i
$568$	−7.97609			−0.334669
$569$	−3.43833	+	1.98512i	−0.144142	+	0.0832206i	−0.570337	−	0.821411i	$-0.693187\pi$
$569$	−3.43833	+	1.98512i	−0.144142	+	0.0832206i	0.426194	+	0.904632i	$0.359854\pi$
$570$	−13.3133	−	2.73382i	−0.557635	−	0.114507i
$571$	16.3483	−	28.3161i	0.684155	−	1.18499i	−0.289547	−	0.957164i	$-0.593505\pi$
$571$	16.3483	−	28.3161i	0.684155	−	1.18499i	0.973702	−	0.227827i	$-0.0731620\pi$
$572$	−3.66751			−0.153346
$573$	28.1029	−	9.34637i	1.17402	−	0.390450i
$574$	15.9181	−	5.41649i	0.664408	−	0.226080i
$575$			7.15283i			0.298294i
$576$	−2.75724	−	1.18222i	−0.114885	−	0.0492591i
$577$	−24.1173	+	13.9241i	−1.00402	+	0.579668i	−0.909434	−	0.415849i	$-0.863485\pi$
$577$	−24.1173	+	13.9241i	−1.00402	+	0.579668i	−0.0945813	+	0.995517i	$0.530151\pi$
$578$			14.0331i			0.583698i
$579$	0.936727	−	1.05491i	0.0389291	−	0.0438406i
$580$	5.62132	−	3.24547i	0.233413	−	0.134761i
$581$	9.84814	+	28.9419i	0.408570	+	1.20071i
$582$	−10.4129	−	2.13823i	−0.431628	−	0.0886324i
$583$	4.43177	+	7.67605i	0.183545	+	0.317909i
$584$	−5.44736	−	9.43511i	−0.225414	−	0.390428i
$585$	6.19063	−	0.737295i	0.255951	−	0.0304834i
$586$	−8.69888	−	5.02230i	−0.359348	−	0.207469i
$587$	13.5554	−	23.4786i	0.559490	−	0.969065i	−0.438049	−	0.898951i	$-0.644330\pi$
$587$	13.5554	−	23.4786i	0.559490	−	0.969065i	0.997539	−	0.0701141i	$-0.0223363\pi$
$588$	10.0492	+	6.78336i	0.414421	+	0.279741i
$589$	−19.1764	−	33.2146i	−0.790152	−	1.36858i
$590$		−	8.50907i		−	0.350313i
$591$	5.39151	−	26.2559i	0.221777	−	1.08002i
$592$	10.4808			0.430760
$593$	−10.1795	+	17.6314i	−0.418022	+	0.724035i	−0.995740	−	0.0922009i	$-0.970610\pi$
$593$	−10.1795	+	17.6314i	−0.418022	+	0.724035i	0.577719	+	0.816236i	$0.303943\pi$
$594$	0.769295	−	9.13792i	0.0315646	−	0.374933i
$595$	−4.47034	−	0.885797i	−0.183266	−	0.0363141i
$596$	−3.98762	−	2.30225i	−0.163339	−	0.0943040i
$597$	14.2527	−	4.74012i	0.583324	−	0.194000i
$598$	−12.8730	−	7.43224i	−0.526417	−	0.303927i
$599$	12.5682	+	7.25626i	0.513523	+	0.296483i	0.734281	−	0.678846i	$-0.237520\pi$
$599$	12.5682	+	7.25626i	0.513523	+	0.296483i	−0.220757	+	0.975329i	$0.570853\pi$
$600$	0.348398	−	1.69665i	0.0142233	−	0.0692654i
$601$	0.0811489	+	0.0468513i	0.00331013	+	0.00191111i	0.501654	−	0.865068i	$-0.332725\pi$
$601$	0.0811489	+	0.0468513i	0.00331013	+	0.00191111i	−0.498344	+	0.866979i	$0.666058\pi$
$602$	−7.73178	−	6.77057i	−0.315124	−	0.275948i
$603$	−10.2161	+	7.64039i	−0.416034	+	0.311141i
$604$	2.54672	−	4.41105i	0.103625	−	0.179483i
$605$	7.88543			0.320588
$606$	9.97972	−	3.31902i	0.405399	−	0.134826i
$607$		−	25.9737i		−	1.05424i	−0.849791	−	0.527119i	$-0.823272\pi$
$607$		−	25.9737i		−	1.05424i	0.849791	−	0.527119i	$-0.176728\pi$
$608$	−3.92342	−	6.79557i	−0.159116	−	0.275597i
$609$	29.5115	−	3.72186i	1.19586	−	0.150817i
$610$	3.46660	−	6.00433i	0.140358	−	0.243108i
$611$	21.6369	+	12.4921i	0.875335	+	0.505375i
$612$	4.74929	+	2.03635i	0.191979	+	0.0823144i
$613$	−15.6051	−	27.0288i	−0.630284	−	1.09168i	−0.987494	−	0.157659i	$-0.949605\pi$
$613$	−15.6051	−	27.0288i	−0.630284	−	1.09168i	0.357210	−	0.934024i	$-0.383728\pi$
$614$	14.3899	+	24.9240i	0.580728	+	1.00585i
$615$	−3.47380	−	10.4451i	−0.140077	−	0.421187i
$616$	−3.07608	+	3.51279i	−0.123939	+	0.141534i
$617$	3.21109	−	1.85393i	0.129274	−	0.0746362i	−0.433969	−	0.900928i	$-0.642887\pi$
$617$	3.21109	−	1.85393i	0.129274	−	0.0746362i	0.563242	+	0.826292i	$0.309554\pi$
$618$	−10.0178	−	30.1216i	−0.402973	−	1.21167i
$619$			12.9557i			0.520735i	0.965510	+	0.260368i	$0.0838438\pi$
$619$			12.9557i			0.520735i	−0.965510	+	0.260368i	$0.916156\pi$
$620$	4.23286	−	2.44384i	0.169996	−	0.0981470i
$621$	21.2183	−	30.5153i	0.851462	−	1.22454i
$622$		−	27.0587i		−	1.08495i
$623$	7.43524	+	21.8508i	0.297887	+	0.875435i
$624$	2.69147	+	2.38994i	0.107745	+	0.0956742i
$625$	1.00000			0.0400000
$626$	14.9390	−	25.8750i	0.597081	−	1.03417i
$627$	15.9261	−	17.9354i	0.636027	−	0.716272i
$628$	−4.19746	+	2.42341i	−0.167497	+	0.0967044i
$629$	−18.0530			−0.719822
$630$	4.48613	−	6.54787i	0.178732	−	0.260874i
$631$	−17.8680			−0.711312			−0.355656	−	0.934617i	$-0.615743\pi$
$631$	−17.8680			−0.711312			−0.355656	+	0.934617i	$0.615743\pi$
$632$	−10.1103	+	5.83721i	−0.402168	+	0.232192i
$633$	−12.5759	−	37.8135i	−0.499847	−	1.50295i
$634$	−1.25094	+	2.16669i	−0.0496812	+	0.0860504i
$635$	−2.81109			−0.111555
$636$	1.74978	−	8.52119i	0.0693833	−	0.337887i
$637$	−8.87250	−	11.5278i	−0.351541	−	0.456748i
$638$			11.4553i			0.453520i
$639$	−9.42948	+	21.9920i	−0.373024	+	0.869989i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$		−	41.0028i		−	1.61951i	−0.586766	−	0.809757i	$-0.699599\pi$
$641$		−	41.0028i		−	1.61951i	0.586766	−	0.809757i	$-0.300401\pi$
$642$	−3.20485	−	0.658099i	−0.126485	−	0.0259731i
$643$	−28.4023	+	16.3981i	−1.12008	+	0.646677i	−0.941421	−	0.337234i	$-0.890509\pi$
$643$	−28.4023	+	16.3981i	−1.12008	+	0.646677i	−0.178657	+	0.983911i	$0.557175\pi$
$644$	−17.9158	+	6.09626i	−0.705982	+	0.240226i
$645$	−4.46726	+	5.03088i	−0.175898	+	0.198091i
$646$	6.75802	+	11.7052i	0.265891	+	0.460536i
$647$	1.81054	+	3.13595i	0.0711797	+	0.123287i	0.899419	−	0.437088i	$-0.143990\pi$
$647$	1.81054	+	3.13595i	0.0711797	+	0.123287i	−0.828239	+	0.560375i	$0.810657\pi$
$648$	−6.51931	+	6.20472i	−0.256103	+	0.243745i
$649$	13.0050	+	7.50847i	0.510493	+	0.294733i
$650$	−1.03906	+	1.79971i	−0.0407554	+	0.0705904i
$651$	22.2221	−	2.80256i	0.870955	−	0.109841i
$652$	0.203760	+	0.352922i	0.00797984	+	0.0138215i
$653$			2.64800i			0.103624i	0.998657	+	0.0518121i	$0.0164997\pi$
$653$			2.64800i			0.103624i	−0.998657	+	0.0518121i	$0.983500\pi$
$654$	8.59510	+	7.63218i	0.336095	+	0.298442i
$655$	−17.0990			−0.668115
$656$	3.17762	−	5.50380i	0.124065	−	0.214887i
$657$	−32.4548	+	3.86532i	−1.26618	+	0.150801i
$658$	30.1128	−	10.2466i	1.17392	−	0.399452i
$659$	−11.8954	−	6.86782i	−0.463380	−	0.267532i	0.250085	−	0.968224i	$-0.419542\pi$
$659$	−11.8954	−	6.86782i	−0.463380	−	0.267532i	−0.713464	+	0.700692i	$0.752875\pi$
$660$	2.28569	+	2.02962i	0.0889702	+	0.0790028i
$661$	18.3413	+	10.5893i	0.713392	+	0.411877i	0.812316	−	0.583218i	$-0.198207\pi$
$661$	18.3413	+	10.5893i	0.713392	+	0.411877i	−0.0989236	+	0.995095i	$0.531540\pi$
$662$	19.7213	+	11.3861i	0.766492	+	0.442534i
$663$	−4.63600	−	4.11662i	−0.180047	−	0.159876i
$664$	10.0069	+	5.77748i	0.388343	+	0.224210i
$665$	19.6541	−	6.68776i	0.762155	−	0.259340i
$666$	12.3906	−	28.8982i	0.480128	−	1.11978i
$667$	−23.2143	+	40.2083i	−0.898861	+	1.55687i
$668$	8.58453			0.332145
$669$	10.6110	+	9.42224i	0.410245	+	0.364285i
$670$		−	4.25239i		−	0.164284i
$671$	6.11791	+	10.5965i	0.236179	+	0.409074i
$672$	4.54656	−	0.573393i	0.175387	−	0.0221191i
$673$	−12.7400	+	22.0663i	−0.491089	+	0.850591i	−0.999947	−	0.0102589i	$-0.996734\pi$
$673$	−12.7400	+	22.0663i	−0.491089	+	0.850591i	0.508858	+	0.860850i	$0.330068\pi$
$674$	11.9749	+	6.91370i	0.461255	+	0.266306i
$675$	−4.26618	−	2.96642i	−0.164205	−	0.114178i
$676$	4.34070	+	7.51831i	0.166950	+	0.289166i
$677$	−2.34586	−	4.06315i	−0.0901587	−	0.156159i	0.817419	−	0.576043i	$-0.195404\pi$
$677$	−2.34586	−	4.06315i	−0.0901587	−	0.156159i	−0.907578	+	0.419884i	$0.862071\pi$
$678$	15.8724	−	17.8749i	0.609575	−	0.686482i
$679$	15.3722	−	5.23075i	0.589933	−	0.200738i
$680$	−1.49171	+	0.861240i	−0.0572045	+	0.0330270i
$681$	−16.8814	−	3.46650i	−0.646896	−	0.132837i
$682$			8.62585i			0.330301i
$683$	−11.5223	+	6.65242i	−0.440890	+	0.254548i	−0.703975	−	0.710225i	$-0.748593\pi$
$683$	−11.5223	+	6.65242i	−0.440890	+	0.254548i	0.263085	+	0.964773i	$0.415260\pi$
$684$	−23.3753	+	2.78397i	−0.893779	+	0.106448i
$685$			8.33714i			0.318546i
$686$	−18.4832	−	1.17061i	−0.705693	−	0.0446942i
$687$	1.16144	−	5.65603i	0.0443115	−	0.215791i
$688$	−3.88442			−0.148092
$689$	−5.21855	+	9.03879i	−0.198811	+	0.344351i
$690$	3.90976	+	11.7560i	0.148842	+	0.447542i
$691$	−27.4241	+	15.8333i	−1.04326	+	0.602328i	−0.920756	−	0.390139i	$-0.872427\pi$
$691$	−27.4241	+	15.8333i	−1.04326	+	0.602328i	−0.122507	+	0.992468i	$0.539094\pi$
$692$	−10.5609			−0.401464
$693$	6.04901	+	12.6344i	0.229783	+	0.479940i
$694$	−5.16857			−0.196196
$695$	8.22347	−	4.74782i	0.311934	−	0.180095i
$696$	7.46488	−	8.40669i	0.282956	−	0.318655i
$697$	−5.47339	+	9.48019i	−0.207319	+	0.359088i
$698$	−7.36846			−0.278900
$699$	26.8773	+	23.8662i	1.01659	+	0.902701i
$700$	0.852286	+	2.50472i	0.0322134	+	0.0946694i
$701$		−	4.16751i		−	0.157405i	−0.996898	−	0.0787023i	$-0.974922\pi$
$701$		−	4.16751i		−	0.157405i	0.996898	−	0.0787023i	$-0.0250776\pi$
$702$	9.77153	−	4.59559i	0.368803	−	0.173449i
$703$	71.2233	−	41.1208i	2.68624	−	1.55090i
$704$			1.76481i			0.0665140i
$705$	−6.57150	−	19.7594i	−0.247497	−	0.744180i
$706$	−7.03645	+	4.06250i	−0.264820	+	0.152894i
$707$	−10.5837	+	12.0863i	−0.398040	+	0.454550i
$708$	−4.65109	−	13.9850i	−0.174799	−	0.525588i
$709$	−22.5799	−	39.1095i	−0.848006	−	1.46879i	−0.882985	−	0.469401i	$-0.844470\pi$
$709$	−22.5799	−	39.1095i	−0.848006	−	1.46879i	0.0349796	−	0.999388i	$-0.488863\pi$
$710$	−3.98805	−	6.90750i	−0.149669	−	0.259234i
$711$	4.14195	+	34.7775i	0.155335	+	1.30426i
$712$	7.55510	+	4.36194i	0.283139	+	0.163471i
$713$	−17.4804	+	30.2769i	−0.654645	+	1.13388i
$714$	−7.83136	+	0.987658i	−0.293081	+	0.0369622i
$715$	−1.83375	−	3.17615i	−0.0685785	−	0.118781i
$716$		−	0.581120i		−	0.0217175i
$717$	−25.6884	+	8.54338i	−0.959353	+	0.319058i
$718$	−17.1789			−0.641110
$719$	4.50906	−	7.80992i	0.168160	−	0.291261i	−0.769613	−	0.638510i	$-0.779551\pi$
$719$	4.50906	−	7.80992i	0.168160	−	0.291261i	0.937773	+	0.347249i	$0.112884\pi$
$720$	−0.354788	−	2.97895i	−0.0132222	−	0.111019i
$721$	36.4797	+	31.9446i	1.35858	+	1.18968i
$722$	−36.8693	−	21.2865i	−1.37213	−	0.792202i
$723$	−6.84573	+	33.3378i	−0.254595	+	1.23984i
$724$	−13.5435	−	7.81932i	−0.503339	−	0.290603i
$725$	5.62132	+	3.24547i	0.208771	+	0.120534i
$726$	12.9600	−	4.31020i	0.480991	−	0.159967i
$727$	−17.0192	−	9.82602i	−0.631206	−	0.364427i	0.150013	−	0.988684i	$-0.452068\pi$
$727$	−17.0192	−	9.82602i	−0.631206	−	0.364427i	−0.781219	+	0.624257i	$0.785402\pi$
$728$	−5.39334	−	1.06869i	−0.199891	−	0.0396083i
$729$	9.40065	+	25.3106i	0.348172	+	0.937431i
$730$	5.44736	−	9.43511i	0.201616	−	0.349209i
$731$	6.69084			0.247470
$732$	2.41551	−	11.7632i	0.0892799	−	0.434781i
$733$		−	39.4345i		−	1.45655i	−0.685286	−	0.728274i	$-0.740323\pi$
$733$		−	39.4345i		−	1.45655i	0.685286	−	0.728274i	$-0.259677\pi$
$734$	−6.57603	−	11.3900i	−0.242726	−	0.420413i
$735$	−0.849978	+	12.0945i	−0.0313519	+	0.446113i
$736$	−3.57642	+	6.19453i	−0.131828	+	0.228334i
$737$	6.49924	+	3.75234i	0.239403	+	0.138219i
$738$	−11.4187	−	15.2682i	−0.420326	−	0.562028i
$739$	16.3564	+	28.3302i	0.601681	+	1.04214i	0.992567	+	0.121702i	$0.0388354\pi$
$739$	16.3564	+	28.3302i	0.601681	+	1.04214i	−0.390886	+	0.920439i	$0.627831\pi$
$740$	5.24042	+	9.07668i	0.192642	+	0.333665i
$741$	27.6668	+	5.68123i	1.01637	+	0.208705i
$742$	4.28049	+	12.5796i	0.157142	+	0.461811i
$743$	25.7477	−	14.8655i	0.944593	−	0.545361i	0.0531960	−	0.998584i	$-0.483059\pi$
$743$	25.7477	−	14.8655i	0.944593	−	0.545361i	0.891397	+	0.453223i	$0.149726\pi$
$744$	5.62106	−	6.33024i	0.206078	−	0.232078i
$745$		−	4.60451i		−	0.168696i
$746$	−12.0967	+	6.98405i	−0.442893	+	0.255704i
$747$	27.7602	−	20.7611i	1.01569	−	0.759610i
$748$		−	3.03986i		−	0.111148i
$749$	4.73123	−	1.60991i	0.172876	−	0.0588248i
$750$	1.64354	−	0.546603i	0.0600136	−	0.0199591i
$751$	8.11056			0.295958			0.147979	−	0.988990i	$-0.452723\pi$
$751$	8.11056			0.295958			0.147979	+	0.988990i	$0.452723\pi$
$752$	6.01122	−	10.4117i	0.219207	−	0.379677i
$753$	8.34621	+	1.71385i	0.304153	+	0.0624562i
$754$	−11.6818	+	6.74449i	−0.425426	+	0.245620i
$755$	5.09344			0.185369
$756$	3.79404	−	13.2138i	0.137988	−	0.480582i
$757$	−44.6682			−1.62349			−0.811747	−	0.584010i	$-0.801483\pi$
$757$	−44.6682			−1.62349			−0.811747	+	0.584010i	$0.801483\pi$
$758$	−15.8394	+	9.14488i	−0.575313	+	0.332157i
$759$	−21.4175	−	4.39797i	−0.777407	−	0.159636i
$760$	3.92342	−	6.79557i	0.142318	−	0.246501i
$761$	−14.5116			−0.526043			−0.263022	−	0.964790i	$-0.584719\pi$
$761$	−14.5116			−0.526043			−0.263022	+	0.964790i	$0.584719\pi$
$762$	−4.62015	+	1.53655i	−0.167370	+	0.0556635i
$763$	−17.2234	−	3.41282i	−0.623530	−	0.123552i
$764$			17.0990i			0.618620i
$765$	0.611116	+	5.13118i	0.0220949	+	0.185518i
$766$	−14.0173	+	8.09287i	−0.506464	+	0.292407i
$767$			17.6829i			0.638493i
$768$	1.15005	−	1.29514i	0.0414987	−	0.0467344i
$769$	−14.5008	+	8.37203i	−0.522912	+	0.301903i	−0.738125	−	0.674664i	$-0.764289\pi$
$769$	−14.5008	+	8.37203i	−0.522912	+	0.301903i	0.215213	+	0.976567i	$0.430955\pi$
$770$	−4.58021	−	0.907568i	−0.165059	−	0.0327065i
$771$	−23.4391	−	4.81310i	−0.844140	−	0.173340i
$772$	0.407256	+	0.705389i	0.0146575	+	0.0253875i
$773$	17.7940	+	30.8201i	0.640005	+	1.10852i	0.985431	+	0.170075i	$0.0544010\pi$
$773$	17.7940	+	30.8201i	0.640005	+	1.10852i	−0.345426	+	0.938446i	$0.612266\pi$
$774$	−4.59223	+	10.7103i	−0.165064	+	0.384973i
$775$	4.23286	+	2.44384i	0.152049	+	0.0877854i
$776$	3.06866	−	5.31507i	0.110158	−	0.190800i
$777$	6.00965	+	47.6518i	0.215595	+	1.70950i
$778$	−2.08370	−	3.60907i	−0.0747042	−	0.129392i
$779$		−	49.8686i		−	1.78673i
$780$	−0.724014	+	3.52585i	−0.0259239	+	0.126246i
$781$	14.0763			0.503690
$782$	6.16030	−	10.6700i	0.220292	−	0.381557i
$783$	−14.3541	−	30.5210i	−0.512975	−	1.09073i
$784$	−5.54722	+	4.26947i	−0.198115	+	0.152481i
$785$	−4.19746	−	2.42341i	−0.149814	−	0.0864950i
$786$	−28.1030	+	9.34640i	−1.00240	+	0.333375i
$787$	2.54717	+	1.47061i	0.0907966	+	0.0524215i	0.544711	−	0.838624i	$-0.316639\pi$
$787$	2.54717	+	1.47061i	0.0907966	+	0.0524215i	−0.453914	+	0.891045i	$0.649973\pi$
$788$	13.4019	+	7.73758i	0.477422	+	0.275640i
$789$	−8.68195	+	42.2799i	−0.309085	+	1.50520i
$790$	−10.1103	−	5.83721i	−0.359710	−	0.207679i
$791$	−7.09752	+	35.8189i	−0.252359	+	1.27357i
$792$	4.86601	+	2.08640i	0.172906	+	0.0741368i
$793$	−7.20403	+	12.4777i	−0.255823	+	0.443098i
$794$	18.8834			0.670146
$795$	8.25445	−	2.74524i	0.292755	−	0.0973636i
$796$			8.67195i			0.307369i
$797$	2.92189	+	5.06085i	0.103499	+	0.179265i	0.913124	−	0.407682i	$-0.133663\pi$
$797$	2.92189	+	5.06085i	0.103499	+	0.179265i	−0.809625	+	0.586947i	$0.800330\pi$
$798$	28.6468	−	21.7346i	1.01409	−	0.769397i
$799$	−10.3542	+	17.9340i	−0.366305	+	0.634459i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	20.9587	−	15.6744i	0.740538	−	0.553829i
$802$	2.20411	+	3.81763i	0.0778298	+	0.134805i
$803$	9.61359	+	16.6512i	0.339256	+	0.587609i
$804$	−2.32437	−	6.98897i	−0.0819742	−	0.246482i
$805$	−14.2374	−	12.4674i	−0.501803	−	0.439419i
$806$	−8.79641	+	5.07861i	−0.309840	+	0.178886i
$807$	9.83744	+	29.5795i	0.346294	+	1.04125i
$808$			6.07209i			0.213615i
$809$	−5.11072	+	2.95068i	−0.179683	+	0.103740i	−0.587144	−	0.809483i	$-0.699748\pi$
$809$	−5.11072	+	2.95068i	−0.179683	+	0.103740i	0.407460	+	0.913223i	$0.366414\pi$
$810$	−8.63310	−	2.54353i	−0.303336	−	0.0893705i
$811$		−	14.0694i		−	0.494044i	−0.969010	−	0.247022i	$-0.920548\pi$
$811$		−	14.0694i		−	0.494044i	0.969010	−	0.247022i	$-0.0794520\pi$
$812$	−3.33801	+	16.8459i	−0.117141	+	0.591175i
$813$	−0.370881	−	0.329331i	−0.0130074	−	0.0115501i
$814$	−18.4968			−0.648311
$815$	−0.203760	+	0.352922i	−0.00713739	+	0.0123623i
$816$	−1.98093	+	2.23086i	−0.0693465	+	0.0780956i
$817$	−26.3969	+	15.2402i	−0.923509	+	0.533188i
$818$	−36.9170			−1.29077
$819$	−9.32274	+	13.6073i	−0.325763	+	0.475478i
$820$	6.35524			0.221935
$821$	27.1831	−	15.6942i	0.948698	−	0.547731i	0.0560218	−	0.998430i	$-0.482158\pi$
$821$	27.1831	−	15.6942i	0.948698	−	0.547731i	0.892676	+	0.450698i	$0.148825\pi$
$822$	4.55711	+	13.7024i	0.158947	+	0.477927i
$823$	−5.12765	+	8.88136i	−0.178739	+	0.309585i	−0.941449	−	0.337156i	$-0.890535\pi$
$823$	−5.12765	+	8.88136i	−0.178739	+	0.309585i	0.762710	+	0.646741i	$0.223868\pi$
$824$	18.3273			0.638461
$825$	−0.614858	+	2.99427i	−0.0214066	+	0.104247i
$826$	16.9370	+	14.8314i	0.589312	+	0.516049i
$827$			53.6894i			1.86696i	0.358625	+	0.933482i	$0.383246\pi$
$827$			53.6894i			1.86696i	−0.358625	+	0.933482i	$0.616754\pi$
$828$	12.8517	+	17.1843i	0.446628	+	0.597196i
$829$	−26.9613	+	15.5661i	−0.936406	+	0.540634i	−0.888832	−	0.458234i	$-0.848482\pi$
$829$	−26.9613	+	15.5661i	−0.936406	+	0.540634i	−0.0475739	+	0.998868i	$0.515149\pi$
$830$			11.5550i			0.401079i
$831$	−21.2908	−	4.37194i	−0.738569	−	0.151661i
$832$	−1.79971	+	1.03906i	−0.0623937	+	0.0360230i
$833$	9.55497	−	7.35408i	0.331060	−	0.254804i
$834$	10.9204	−	12.2982i	0.378143	−	0.425852i
$835$	4.29226	+	7.43442i	0.148540	+	0.257279i
$836$	6.92412	+	11.9929i	0.239476	+	0.414784i
$837$	−10.8087	−	22.9823i	−0.373602	−	0.794385i
$838$	−18.5311	−	10.6989i	−0.640147	−	0.369589i
$839$	−26.3146	+	45.5783i	−0.908482	+	1.57354i	−0.0923091	+	0.995730i	$0.529425\pi$
$839$	−26.3146	+	45.5783i	−0.908482	+	1.57354i	−0.816173	+	0.577807i	$0.803909\pi$
$840$	2.76985	+	3.65074i	0.0955690	+	0.125963i
$841$	6.56615	+	11.3729i	0.226419	+	0.392169i
$842$		−	25.3209i		−	0.872617i
$843$	3.56578	+	3.16630i	0.122812	+	0.109053i
$844$	23.0074			0.791946
$845$	−4.34070	+	7.51831i	−0.149325	+	0.258638i
$846$	−21.6011	−	28.8833i	−0.742660	−	0.993028i
$847$	−13.7443	+	15.6956i	−0.472261	+	0.539308i
$848$	4.34949	+	2.51118i	0.149362	+	0.0862343i
$849$	−23.3964	−	20.7753i	−0.802963	−	0.713006i
$850$	−1.49171	−	0.861240i	−0.0511653	−	0.0295403i
$851$	−64.9240	−	37.4839i	−2.22556	−	1.28493i
$852$	−10.3302	−	9.17287i	−0.353906	−	0.314257i
$853$	8.49076	+	4.90215i	0.290718	+	0.167846i	0.638266	−	0.769816i	$-0.279652\pi$
$853$	8.49076	+	4.90215i	0.290718	+	0.167846i	−0.347547	+	0.937662i	$0.612985\pi$
$854$	5.90907	+	17.3657i	0.202204	+	0.594242i
$855$	−14.0987	−	18.8517i	−0.482164	−	0.644713i
$856$	0.944465	−	1.63586i	0.0322811	−	0.0559126i
$857$	23.5187			0.803382			0.401691	−	0.915775i	$-0.368423\pi$
$857$	23.5187			0.803382			0.401691	+	0.915775i	$0.368423\pi$
$858$	−4.74994	−	4.21780i	−0.162160	−	0.143993i
$859$			46.7066i			1.59361i	0.604238	+	0.796804i	$0.293478\pi$
$859$			46.7066i			1.59361i	−0.604238	+	0.796804i	$0.706522\pi$
$860$	−1.94221	−	3.36401i	−0.0662288	−	0.114712i
$861$	26.8454	+	11.2914i	0.914889	+	0.384810i
$862$	12.7759	−	22.1285i	0.435149	−	0.753700i
$863$	46.9624	+	27.1137i	1.59862	+	0.922962i	0.991754	+	0.128156i	$0.0409059\pi$
$863$	46.9624	+	27.1137i	1.59862	+	0.922962i	0.606864	+	0.794806i	$0.292427\pi$
$864$	−2.21141	−	4.70209i	−0.0752337	−	0.159968i
$865$	−5.28044	−	9.14598i	−0.179540	−	0.310973i
$866$	1.91144	+	3.31071i	0.0649534	+	0.112503i
$867$	−16.1387	+	18.1748i	−0.548098	+	0.617249i
$868$	−2.51352	+	12.6850i	−0.0853146	+	0.430556i
$869$	17.8429	−	10.3016i	0.605278	−	0.349458i
$870$	11.0128	+	2.26143i	0.373371	+	0.0766696i
$871$			8.83700i			0.299430i
$872$	−5.74730	+	3.31820i	−0.194628	+	0.112369i
$873$	−11.0271	−	14.7446i	−0.373211	−	0.499029i
$874$			56.1272i			1.89853i
$875$	−1.74301	+	1.99046i	−0.0589243	+	0.0672898i
$876$	3.79570	−	18.4845i	0.128245	−	0.624535i
$877$	23.5981			0.796852			0.398426	−	0.917200i	$-0.369557\pi$
$877$	23.5981			0.796852			0.398426	+	0.917200i	$0.369557\pi$
$878$	−1.57012	+	2.71952i	−0.0529889	+	0.0917794i
$879$	−5.49042	−	16.5087i	−0.185187	−	0.556825i
$880$	−1.52837	+	0.882407i	−0.0515215	+	0.0297459i
$881$	20.2179			0.681159			0.340580	−	0.940216i	$-0.389377\pi$
$881$	20.2179			0.681159			0.340580	+	0.940216i	$0.389377\pi$
$882$	5.21394	+	20.3424i	0.175562	+	0.684966i
$883$	23.0406			0.775379			0.387689	−	0.921790i	$-0.373273\pi$
$883$	23.0406			0.775379			0.387689	+	0.921790i	$0.373273\pi$
$884$	3.09996	−	1.78976i	0.104263	−	0.0601963i
$885$	9.78582	−	11.0205i	0.328947	−	0.370449i
$886$	15.2197	−	26.3613i	0.511316	−	0.885625i
$887$	−24.1942			−0.812362			−0.406181	−	0.913793i	$-0.633140\pi$
$887$	−24.1942			−0.812362			−0.406181	+	0.913793i	$0.633140\pi$
$888$	13.5742	+	12.0535i	0.455520	+	0.404488i
$889$	4.89975	−	5.59537i	0.164332	−	0.187663i
$890$			8.72387i			0.292425i
$891$	11.5054	−	10.9502i	0.385445	−	0.366845i
$892$	−7.09528	+	4.09646i	−0.237568	+	0.137160i
$893$		−	94.3382i		−	3.15691i
$894$	−2.51684	−	7.56769i	−0.0841757	−	0.253101i
$895$	0.503264	−	0.290560i	0.0168223	−	0.00971234i
$896$	−0.514257	+	2.59529i	−0.0171801	+	0.0867026i
$897$	−8.12497	−	24.4304i	−0.271285	−	0.815706i
$898$	11.8417	+	20.5104i	0.395163	+	0.684442i
$899$	15.8628	+	27.4752i	0.529055	+	0.916350i
$900$	2.40245	−	1.79673i	0.0800817	−	0.0598910i
$901$	−7.49191	−	4.32546i	−0.249592	−	0.144102i
$902$	−5.60791	+	9.71319i	−0.186723	+	0.323414i
$903$	−2.22730	−	17.6608i	−0.0741199	−	0.587713i
$904$	6.90075	+	11.9525i	0.229516	+	0.397533i
$905$		−	15.6386i		−	0.519846i
$906$	8.37128	−	2.78409i	0.278117	−	0.0924953i
$907$	40.0514			1.32988			0.664942	−	0.746895i	$-0.268456\pi$
$907$	40.0514			1.32988			0.664942	+	0.746895i	$0.268456\pi$
$908$	4.97492	−	8.61681i	0.165098	−	0.285959i
$909$	16.7422	+	7.17853i	0.555304	+	0.238097i
$910$	−1.77116	−	5.20512i	−0.0587133	−	0.172548i
$911$	−0.337824	−	0.195043i	−0.0111926	−	0.00646205i	0.494393	−	0.869238i	$-0.335390\pi$
$911$	−0.337824	−	0.195043i	−0.0111926	−	0.00646205i	−0.505586	+	0.862776i	$0.668724\pi$
$912$	2.73382	−	13.3133i	0.0905260	−	0.440849i
$913$	−17.6603	−	10.1962i	−0.584471	−	0.337444i
$914$	−7.51524	−	4.33893i	−0.248582	−	0.143519i
$915$	11.3950	−	3.78971i	0.376707	−	0.125284i
$916$	2.88702	+	1.66682i	0.0953900	+	0.0550734i
$917$	29.8037	−	34.0350i	0.984206	−	1.12393i
$918$	3.80911	+	8.09926i	0.125719	+	0.267315i
$919$	27.1206	−	46.9743i	0.894627	−	1.54954i	0.0603619	−	0.998177i	$-0.480775\pi$
$919$	27.1206	−	46.9743i	0.894627	−	1.54954i	0.834265	−	0.551363i	$-0.185892\pi$
$920$	−7.15283			−0.235822
$921$	−10.0268	+	48.8291i	−0.330394	+	1.60898i
$922$		−	29.9222i		−	0.985434i
$923$	8.28766	+	14.3546i	0.272792	+	0.472489i
$924$	−8.02384	+	1.01193i	−0.263965	+	0.0332901i
$925$	−5.24042	+	9.07668i	−0.172304	+	0.298439i
$926$	27.3020	+	15.7628i	0.897198	+	0.517998i
$927$	21.6668	−	50.5327i	0.711632	−	1.65971i
$928$	3.24547	+	5.62132i	0.106538	+	0.184529i
$929$	8.56755	+	14.8394i	0.281092	+	0.486866i	0.971654	−	0.236407i	$-0.0759700\pi$
$929$	8.56755	+	14.8394i	0.281092	+	0.486866i	−0.690562	+	0.723273i	$0.742637\pi$
$930$	8.29268	+	1.70286i	0.271928	+	0.0558389i
$931$	−20.9455	+	50.7776i	−0.686462	+	1.66417i
$932$	−17.9721	+	10.3762i	−0.588695	+	0.339883i
$933$	31.1187	−	35.0448i	1.01878	−	1.14732i
$934$			31.2129i			1.02132i
$935$	2.63259	−	1.51993i	0.0860950	−	0.0497070i
$936$	0.737295	+	6.19063i	0.0240992	+	0.202347i
$937$		−	6.23344i		−	0.203638i	−0.994803	−	0.101819i	$-0.967534\pi$
$937$		−	6.23344i		−	0.203638i	0.994803	−	0.101819i	$-0.0324662\pi$
$938$	8.46421	+	7.41194i	0.276366	+	0.242008i
$939$	49.1055	−	16.3314i	1.60250	−	0.532954i
$940$	12.0224			0.392129
$941$	14.4227	−	24.9809i	0.470167	−	0.814354i	−0.529251	−	0.848465i	$-0.677527\pi$
$941$	14.4227	−	24.9809i	0.470167	−	0.814354i	0.999418	+	0.0341119i	$0.0108603\pi$
$942$	−8.22334	−	1.68862i	−0.267931	−	0.0550182i
$943$	−39.3678	+	22.7290i	−1.28199	+	0.740158i
$944$	8.50907			0.276947
$945$	13.3405	−	3.32118i	0.433968	−	0.108038i
$946$	6.85528			0.222884
$947$	9.28868	−	5.36282i	0.301842	−	0.174268i	−0.341428	−	0.939908i	$-0.610911\pi$
$947$	9.28868	−	5.36282i	0.301842	−	0.174268i	0.643270	+	0.765639i	$0.277577\pi$
$948$	−19.8074	−	4.06734i	−0.643314	−	0.132101i
$949$	−11.3203	+	19.6073i	−0.367473	+	0.636481i
$950$	7.84685			0.254585
$951$	−4.11195	+	1.36754i	−0.133339	+	0.0443454i
$952$	0.885797	−	4.47034i	0.0287088	−	0.144884i
$953$			23.9523i			0.775891i	0.921682	+	0.387946i	$0.126815\pi$
$953$			23.9523i			0.775891i	−0.921682	+	0.387946i	$0.873185\pi$
$954$	12.0660	−	9.02382i	0.390650	−	0.292157i
$955$	−14.8082	+	8.54950i	−0.479181	+	0.276655i
$956$		−	15.6299i		−	0.505509i
$957$	−13.1741	+	14.8363i	−0.425859	+	0.479588i
$958$	−25.6054	+	14.7833i	−0.827273	+	0.477626i
$959$	−16.5947	−	14.5317i	−0.535872	−	0.469252i
$960$	1.69665	+	0.348398i	0.0547591	+	0.0112445i
$961$	−3.55528	−	6.15793i	−0.114687	−	0.198643i
$962$	−10.8903	−	18.8625i	−0.351116	−	0.608151i
$963$	−3.39389	−	4.53806i	−0.109367	−	0.146237i
$964$	−17.0167	−	9.82459i	−0.548071	−	0.316429i
$965$	−0.407256	+	0.705389i	−0.0131100	+	0.0227073i
$966$	−30.2145	−	12.7085i	−0.972136	−	0.408889i
$967$	−22.5636	−	39.0812i	−0.725595	−	1.25677i	−0.958729	−	0.284323i	$-0.908231\pi$
$967$	−22.5636	−	39.0812i	−0.725595	−	1.25677i	0.233133	−	0.972445i	$-0.425102\pi$
$968$			7.88543i			0.253447i
$969$	−4.70896	+	22.9320i	−0.151274	+	0.736681i
$970$	6.13732			0.197057
$971$	−6.67403	+	11.5598i	−0.214180	+	0.370971i	−0.953019	−	0.302912i	$-0.902041\pi$
$971$	−6.67403	+	11.5598i	−0.214180	+	0.370971i	0.738839	+	0.673882i	$0.235375\pi$
$972$	−15.5792	+	0.538492i	−0.499702	+	0.0172721i
$973$	−4.88320	+	24.6440i	−0.156548	+	0.790049i
$974$	−15.6354	−	9.02713i	−0.500992	−	0.289248i
$975$	−3.41548	+	1.13591i	−0.109383	+	0.0363782i
$976$	6.00433	+	3.46660i	0.192194	+	0.110963i
$977$	−45.1236	−	26.0521i	−1.44363	−	0.833482i	−0.445543	−	0.895260i	$-0.646990\pi$
$977$	−45.1236	−	26.0521i	−1.44363	−	0.833482i	−0.998090	+	0.0617782i	$0.980323\pi$
$978$	−0.141979	+	0.691417i	−0.00453998	+	0.0221091i
$979$	−13.3333	−	7.69801i	−0.426136	−	0.246030i
$980$	−6.47108	−	2.66929i	−0.206711	−	0.0852674i
$981$	2.35452	+	19.7695i	0.0751741	+	0.631192i
$982$	4.75953	−	8.24376i	0.151883	−	0.263069i
$983$	36.7441			1.17195			0.585977	−	0.810327i	$-0.300711\pi$
$983$	36.7441			1.17195			0.585977	+	0.810327i	$0.300711\pi$
$984$	10.4451	−	3.47380i	0.332978	−	0.110741i
$985$			15.4752i			0.493080i
$986$	−5.59026	−	9.68261i	−0.178030	−	0.308357i
$987$	50.7844	+	21.3603i	1.61648	+	0.679907i
$988$	−8.15337	+	14.1220i	−0.259393	+	0.449282i
$989$	24.0622	+	13.8923i	0.765133	+	0.441750i
$990$	0.626136	+	5.25729i	0.0198999	+	0.167088i
$991$	−13.8366	−	23.9658i	−0.439536	−	0.761298i	0.558118	−	0.829762i	$-0.311524\pi$
$991$	−13.8366	−	23.9658i	−0.439536	−	0.761298i	−0.997654	+	0.0684637i	$0.978190\pi$
$992$	2.44384	+	4.23286i	0.0775920	+	0.134393i
$993$	12.4474	+	37.4271i	0.395006	+	1.18771i
$994$	20.7003	+	4.10176i	0.656573	+	0.130100i
$995$	−7.51013	+	4.33598i	−0.238087	+	0.137460i
$996$	6.31598	+	18.9910i	0.200130	+	0.601754i
$997$			27.9324i			0.884629i	0.896860	+	0.442314i	$0.145842\pi$
$997$			27.9324i			0.884629i	−0.896860	+	0.442314i	$0.854158\pi$
$998$	−9.12775	+	5.26991i	−0.288934	+	0.166816i
$999$	49.2819	−	23.1775i	1.55921	−	0.733302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.551.1	yes	32
3.2	odd	2		1890.2.t.c.1601.12		32
7.3	odd	6		630.2.bk.c.101.3	yes	32
9.4	even	3		1890.2.bk.c.341.11		32
9.5	odd	6		630.2.bk.c.131.11	yes	32
21.17	even	6		1890.2.bk.c.521.11		32
63.31	odd	6		1890.2.t.c.1151.12		32
63.59	even	6	inner	630.2.t.c.311.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.1	✓	32	63.59	even	6	inner
630.2.t.c.551.1	yes	32	1.1	even	1	trivial
630.2.bk.c.101.3	yes	32	7.3	odd	6
630.2.bk.c.131.11	yes	32	9.5	odd	6
1890.2.t.c.1151.12		32	63.31	odd	6
1890.2.t.c.1601.12		32	3.2	odd	2
1890.2.bk.c.341.11		32	9.4	even	3
1890.2.bk.c.521.11		32	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.69665 - 0.348398i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.64354 - 0.546603i) q^{6} +(-1.74301 + 1.99046i) q^{7} +1.00000i q^{8} +(2.75724 + 1.18222i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.69665 - 0.348398i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(1.64354 - 0.546603i) q^{6} +(-1.74301 + 1.99046i) q^{7} +1.00000i q^{8} +(2.75724 + 1.18222i) q^{9} +(-0.866025 + 0.500000i) q^{10} -1.76481i q^{11} +(-1.15005 + 1.29514i) q^{12} +(1.79971 - 1.03906i) q^{13} +(0.514257 - 2.59529i) q^{14} +(-1.69665 - 0.348398i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.861240 + 1.49171i) q^{17} +(-2.97895 + 0.354788i) q^{18} +(-6.79557 - 3.92342i) q^{19} +(0.500000 - 0.866025i) q^{20} +(3.65074 - 2.76985i) q^{21} +(0.882407 + 1.52837i) q^{22} +7.15283i q^{23} +(0.348398 - 1.69665i) q^{24} +1.00000 q^{25} +(-1.03906 + 1.79971i) q^{26} +(-4.26618 - 2.96642i) q^{27} +(0.852286 + 2.50472i) q^{28} +(5.62132 + 3.24547i) q^{29} +(1.64354 - 0.546603i) q^{30} +(4.23286 + 2.44384i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.614858 + 2.99427i) q^{33} +(-1.49171 - 0.861240i) q^{34} +(-1.74301 + 1.99046i) q^{35} +(2.40245 - 1.79673i) q^{36} +(-5.24042 + 9.07668i) q^{37} +7.84685 q^{38} +(-3.41548 + 1.13591i) q^{39} +1.00000i q^{40} +(3.17762 + 5.50380i) q^{41} +(-1.77671 + 4.22413i) q^{42} +(1.94221 - 3.36401i) q^{43} +(-1.52837 - 0.882407i) q^{44} +(2.75724 + 1.18222i) q^{45} +(-3.57642 - 6.19453i) q^{46} +(6.01122 + 10.4117i) q^{47} +(0.546603 + 1.64354i) q^{48} +(-0.923864 - 6.93877i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-0.941513 - 2.83097i) q^{51} -2.07813i q^{52} +(-4.34949 + 2.51118i) q^{53} +(5.17784 + 0.435907i) q^{54} -1.76481i q^{55} +(-1.99046 - 1.74301i) q^{56} +(10.1628 + 9.02424i) q^{57} -6.49094 q^{58} +(-4.25453 + 7.36907i) q^{59} +(-1.15005 + 1.29514i) q^{60} +(-6.00433 + 3.46660i) q^{61} -4.88768 q^{62} +(-7.15904 + 3.42756i) q^{63} -1.00000 q^{64} +(1.79971 - 1.03906i) q^{65} +(-0.964654 - 2.90054i) q^{66} +(-2.12619 + 3.68268i) q^{67} +1.72248 q^{68} +(2.49203 - 12.1358i) q^{69} +(0.514257 - 2.59529i) q^{70} +7.97609i q^{71} +(-1.18222 + 2.75724i) q^{72} +(-9.43511 + 5.44736i) q^{73} -10.4808i q^{74} +(-1.69665 - 0.348398i) q^{75} +(-6.79557 + 3.92342i) q^{76} +(3.51279 + 3.07608i) q^{77} +(2.38994 - 2.69147i) q^{78} +(5.83721 + 10.1103i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(6.20472 + 6.51931i) q^{81} +(-5.50380 - 3.17762i) q^{82} +(5.77748 - 10.0069i) q^{83} +(-0.573393 - 4.54656i) q^{84} +(0.861240 + 1.49171i) q^{85} +3.88442i q^{86} +(-8.40669 - 7.46488i) q^{87} +1.76481 q^{88} +(4.36194 - 7.55510i) q^{89} +(-2.97895 + 0.354788i) q^{90} +(-1.06869 + 5.39334i) q^{91} +(6.19453 + 3.57642i) q^{92} +(-6.33024 - 5.62106i) q^{93} +(-10.4117 - 6.01122i) q^{94} +(-6.79557 - 3.92342i) q^{95} +(-1.29514 - 1.15005i) q^{96} +(-5.31507 - 3.06866i) q^{97} +(4.26947 + 5.54722i) q^{98} +(2.08640 - 4.86601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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