LMFDB - Embedded newform 630.2.be.a.521.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(341,630)]

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([3, 0, 5]))

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

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

chi := DirichletCharacter("630.341");

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.be (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	630.521
Dual form			630.2.be.a.341.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.189469 + 2.63896i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.189469 + 2.63896i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +(-2.55171 - 1.47323i) q^{11} +3.93185i q^{13} +(-1.48356 - 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.199801 - 0.346065i) q^{17} +(0.0305501 - 0.0176381i) q^{19} -1.00000 q^{20} +2.94646 q^{22} +(-3.23205 + 1.86603i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.96593 - 3.40508i) q^{26} +(2.38014 + 1.15539i) q^{28} +8.89898i q^{29} +(0.717439 + 0.414214i) q^{31} +(0.866025 + 0.500000i) q^{32} +0.399602i q^{34} +(2.19067 - 1.48356i) q^{35} +(3.96593 + 6.86919i) q^{37} +(-0.0176381 + 0.0305501i) q^{38} +(0.866025 - 0.500000i) q^{40} -6.31079 q^{41} -3.03528 q^{43} +(-2.55171 + 1.47323i) q^{44} +(1.86603 - 3.23205i) q^{46} +(2.90130 + 5.02520i) q^{47} +(-6.92820 + 1.00000i) q^{49} -1.00000i q^{50} +(3.40508 + 1.96593i) q^{52} +(3.72268 + 2.14929i) q^{53} +2.94646i q^{55} +(-2.63896 + 0.189469i) q^{56} +(-4.44949 - 7.70674i) q^{58} +(-2.78522 + 4.82415i) q^{59} +(-9.97710 + 5.76028i) q^{61} -0.828427 q^{62} -1.00000 q^{64} +(3.40508 - 1.96593i) q^{65} +(6.25966 - 10.8420i) q^{67} +(-0.199801 - 0.346065i) q^{68} +(-1.15539 + 2.38014i) q^{70} +1.93426i q^{71} +(-0.297173 - 0.171573i) q^{73} +(-6.86919 - 3.96593i) q^{74} -0.0352762i q^{76} +(3.40433 - 7.01299i) q^{77} +(-4.15331 - 7.19375i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.46530 - 3.15539i) q^{82} -10.3490 q^{83} -0.399602 q^{85} +(2.62863 - 1.51764i) q^{86} +(1.47323 - 2.55171i) q^{88} +(3.08604 + 5.34519i) q^{89} +(-10.3760 + 0.744963i) q^{91} +3.73205i q^{92} +(-5.02520 - 2.90130i) q^{94} +(-0.0305501 - 0.0176381i) q^{95} +15.6344i q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^5	$ 8 q + 4 q^{4} - 4 q^{5} - 24 q^{11} - 4 q^{16} - 8 q^{20} - 12 q^{23} - 4 q^{25} - 8 q^{26} + 24 q^{37} + 4 q^{38} - 32 q^{41} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{47} - 24 q^{53} - 16 q^{58} + 24 q^{59} + 16 q^{62} - 8 q^{64} - 24 q^{67} + 16 q^{77} - 24 q^{79} - 4 q^{80} + 16 q^{83} + 16 q^{89} - 20 q^{91} - 12 q^{94} + 44 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^5 - 24 * q^11 - 4 * q^16 - 8 * q^20 - 12 * q^23 - 4 * q^25 - 8 * q^26 + 24 * q^37 + 4 * q^38 - 32 * q^41 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^47 - 24 * q^53 - 16 * q^58 + 24 * q^59 + 16 * q^62 - 8 * q^64 - 24 * q^67 + 16 * q^77 - 24 * q^79 - 4 * q^80 + 16 * q^83 + 16 * q^89 - 20 * q^91 - 12 * q^94 + 44 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	0.189469	+	2.63896i	0.0716124	+	0.997433i
$7$	0.189469	+	2.63896i	0.0716124	+	0.997433i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−2.55171	−	1.47323i	−0.769370	−	0.444196i	0.0632797	−	0.997996i	$-0.479844\pi$
$11$	−2.55171	−	1.47323i	−0.769370	−	0.444196i	−0.832650	+	0.553800i	$0.813177\pi$
$12$		0			0
$13$			3.93185i			1.09050i	0.838274	+	0.545250i	$0.183565\pi$
$13$			3.93185i			1.09050i	−0.838274	+	0.545250i	$0.816435\pi$
$14$	−1.48356	−	2.19067i	−0.396499	−	0.585481i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.199801	−	0.346065i	0.0484588	−	0.0839331i	−0.840779	−	0.541379i	$-0.817902\pi$
$17$	0.199801	−	0.346065i	0.0484588	−	0.0839331i	0.889237	+	0.457446i	$0.151236\pi$
$18$		0			0
$19$	0.0305501	−	0.0176381i	0.00700867	−	0.00404646i	−0.496492	−	0.868042i	$-0.665379\pi$
$19$	0.0305501	−	0.0176381i	0.00700867	−	0.00404646i	0.503500	+	0.863995i	$0.332045\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	2.94646			0.628188
$23$	−3.23205	+	1.86603i	−0.673929	+	0.389093i	−0.797564	−	0.603235i	$-0.793878\pi$
$23$	−3.23205	+	1.86603i	−0.673929	+	0.389093i	0.123635	+	0.992328i	$0.460545\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.96593	−	3.40508i	−0.385550	−	0.667792i
$27$		0			0
$28$	2.38014	+	1.15539i	0.449804	+	0.218349i
$29$			8.89898i			1.65250i	0.563304	+	0.826250i	$0.309530\pi$
$29$			8.89898i			1.65250i	−0.563304	+	0.826250i	$0.690470\pi$
$30$		0			0
$31$	0.717439	+	0.414214i	0.128856	+	0.0743950i	0.563042	−	0.826428i	$-0.309631\pi$
$31$	0.717439	+	0.414214i	0.128856	+	0.0743950i	−0.434187	+	0.900823i	$0.642964\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			0.399602i			0.0685311i
$35$	2.19067	−	1.48356i	0.370291	−	0.250768i
$36$		0			0
$37$	3.96593	+	6.86919i	0.651994	+	1.12929i	0.982638	+	0.185532i	$0.0594007\pi$
$37$	3.96593	+	6.86919i	0.651994	+	1.12929i	−0.330644	+	0.943756i	$0.607266\pi$
$38$	−0.0176381	+	0.0305501i	−0.00286128	+	0.00495588i
$39$		0			0
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−6.31079			−0.985580			−0.492790	−	0.870148i	$-0.664023\pi$
$41$	−6.31079			−0.985580			−0.492790	+	0.870148i	$0.664023\pi$
$42$		0			0
$43$	−3.03528			−0.462875			−0.231438	−	0.972850i	$-0.574343\pi$
$43$	−3.03528			−0.462875			−0.231438	+	0.972850i	$0.574343\pi$
$44$	−2.55171	+	1.47323i	−0.384685	+	0.222098i
$45$		0			0
$46$	1.86603	−	3.23205i	0.275130	−	0.476540i
$47$	2.90130	+	5.02520i	0.423198	+	0.733001i	0.996250	−	0.0865180i	$-0.0275740\pi$
$47$	2.90130	+	5.02520i	0.423198	+	0.733001i	−0.573052	+	0.819519i	$0.694241\pi$
$48$		0			0
$49$	−6.92820	+	1.00000i	−0.989743	+	0.142857i
$50$		−	1.00000i		−	0.141421i
$51$		0			0
$52$	3.40508	+	1.96593i	0.472200	+	0.272625i
$53$	3.72268	+	2.14929i	0.511349	+	0.295228i	0.733388	−	0.679810i	$-0.237938\pi$
$53$	3.72268	+	2.14929i	0.511349	+	0.295228i	−0.222039	+	0.975038i	$0.571271\pi$
$54$		0			0
$55$			2.94646i			0.397301i
$56$	−2.63896	+	0.189469i	−0.352646	+	0.0253188i
$57$		0			0
$58$	−4.44949	−	7.70674i	−0.584247	−	1.01194i
$59$	−2.78522	+	4.82415i	−0.362605	+	0.628050i	−0.988389	−	0.151946i	$-0.951446\pi$
$59$	−2.78522	+	4.82415i	−0.362605	+	0.628050i	0.625784	+	0.779997i	$0.284779\pi$
$60$		0			0
$61$	−9.97710	+	5.76028i	−1.27744	+	0.737528i	−0.976376	−	0.216077i	$-0.930674\pi$
$61$	−9.97710	+	5.76028i	−1.27744	+	0.737528i	−0.301060	+	0.953605i	$0.597340\pi$
$62$	−0.828427			−0.105210
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.40508	−	1.96593i	0.422349	−	0.243843i
$66$		0			0
$67$	6.25966	−	10.8420i	0.764739	−	1.32457i	−0.175646	−	0.984453i	$-0.556201\pi$
$67$	6.25966	−	10.8420i	0.764739	−	1.32457i	0.940385	−	0.340113i	$-0.110465\pi$
$68$	−0.199801	−	0.346065i	−0.0242294	−	0.0419666i
$69$		0			0
$70$	−1.15539	+	2.38014i	−0.138096	+	0.284481i
$71$			1.93426i			0.229554i	0.993391	+	0.114777i	$0.0366153\pi$
$71$			1.93426i			0.229554i	−0.993391	+	0.114777i	$0.963385\pi$
$72$		0			0
$73$	−0.297173	−	0.171573i	−0.0347815	−	0.0200811i	0.482508	−	0.875891i	$-0.339726\pi$
$73$	−0.297173	−	0.171573i	−0.0347815	−	0.0200811i	−0.517290	+	0.855810i	$0.673059\pi$
$74$	−6.86919	−	3.96593i	−0.798527	−	0.461030i
$75$		0			0
$76$		−	0.0352762i		−	0.00404646i
$77$	3.40433	−	7.01299i	0.387959	−	0.799205i
$78$		0			0
$79$	−4.15331	−	7.19375i	−0.467284	−	0.809360i	0.532017	−	0.846734i	$-0.321434\pi$
$79$	−4.15331	−	7.19375i	−0.467284	−	0.809360i	−0.999301	+	0.0373736i	$0.988101\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	5.46530	−	3.15539i	0.603542	−	0.348455i
$83$	−10.3490			−1.13595			−0.567974	−	0.823046i	$-0.692273\pi$
$83$	−10.3490			−1.13595			−0.567974	+	0.823046i	$0.692273\pi$
$84$		0			0
$85$	−0.399602			−0.0433429
$86$	2.62863	−	1.51764i	0.283452	−	0.163651i
$87$		0			0
$88$	1.47323	−	2.55171i	0.157047	−	0.272013i
$89$	3.08604	+	5.34519i	0.327120	+	0.566589i	0.981939	−	0.189197i	$-0.0605885\pi$
$89$	3.08604	+	5.34519i	0.327120	+	0.566589i	−0.654819	+	0.755786i	$0.727255\pi$
$90$		0			0
$91$	−10.3760	+	0.744963i	−1.08770	+	0.0780933i
$92$			3.73205i			0.389093i
$93$		0			0
$94$	−5.02520	−	2.90130i	−0.518310	−	0.299246i
$95$	−0.0305501	−	0.0176381i	−0.00313437	−	0.00180963i
$96$		0			0
$97$			15.6344i			1.58744i	0.608286	+	0.793718i	$0.291857\pi$
$97$			15.6344i			1.58744i	−0.608286	+	0.793718i	$0.708143\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	9.02458	−	15.6310i	0.897979	−	1.55535i	0.0679057	−	0.997692i	$-0.478368\pi$
$101$	9.02458	−	15.6310i	0.897979	−	1.55535i	0.830074	−	0.557654i	$-0.188298\pi$
$102$		0			0
$103$	−7.37857	+	4.26002i	−0.727032	+	0.419752i	−0.817336	−	0.576162i	$-0.804550\pi$
$103$	−7.37857	+	4.26002i	−0.727032	+	0.419752i	0.0903031	+	0.995914i	$0.471216\pi$
$104$	−3.93185			−0.385550
$105$		0			0
$106$	−4.29858			−0.417515
$107$	14.7702	−	8.52761i	1.42789	−	0.824395i	0.430939	−	0.902381i	$-0.358182\pi$
$107$	14.7702	−	8.52761i	1.42789	−	0.824395i	0.996954	+	0.0779862i	$0.0248490\pi$
$108$		0			0
$109$	5.84909	−	10.1309i	0.560241	−	0.970366i	−0.437234	−	0.899348i	$-0.644042\pi$
$109$	5.84909	−	10.1309i	0.560241	−	0.970366i	0.997475	−	0.0710185i	$-0.0226249\pi$
$110$	−1.47323	−	2.55171i	−0.140467	−	0.243296i
$111$		0			0
$112$	2.19067	−	1.48356i	0.206999	−	0.140184i
$113$			13.5546i			1.27511i	0.770405	+	0.637554i	$0.220054\pi$
$113$			13.5546i			1.27511i	−0.770405	+	0.637554i	$0.779946\pi$
$114$		0			0
$115$	3.23205	+	1.86603i	0.301390	+	0.174008i
$116$	7.70674	+	4.44949i	0.715553	+	0.413125i
$117$		0			0
$118$		−	5.57045i		−	0.512801i
$119$	0.951108	+	0.461698i	0.0871879	+	0.0423237i
$120$		0			0
$121$	−1.15918	−	2.00775i	−0.105380	−	0.182523i
$122$	5.76028	−	9.97710i	0.521511	−	0.903284i
$123$		0			0
$124$	0.717439	−	0.414214i	0.0644279	−	0.0371975i
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.95983			0.795056			0.397528	−	0.917590i	$-0.369868\pi$
$127$	8.95983			0.795056			0.397528	+	0.917590i	$0.369868\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.96593	+	3.40508i	−0.172423	+	0.298646i
$131$	6.39047	+	11.0686i	0.558338	+	0.967070i	0.997635	+	0.0687282i	$0.0218941\pi$
$131$	6.39047	+	11.0686i	0.558338	+	0.967070i	−0.439297	+	0.898342i	$0.644773\pi$
$132$		0			0
$133$	0.0523345	+	0.0772785i	0.00453797	+	0.00670090i
$134$			12.5193i			1.08150i
$135$		0			0
$136$	0.346065	+	0.199801i	0.0296748	+	0.0171328i
$137$	4.78094	+	2.76028i	0.408464	+	0.235827i	0.690129	−	0.723686i	$-0.257554\pi$
$137$	4.78094	+	2.76028i	0.408464	+	0.235827i	−0.281666	+	0.959513i	$0.590887\pi$
$138$		0			0
$139$		−	21.8471i		−	1.85305i	−0.376235	−	0.926524i	$-0.622782\pi$
$139$		−	21.8471i		−	1.85305i	0.376235	−	0.926524i	$-0.377218\pi$
$140$	−0.189469	−	2.63896i	−0.0160130	−	0.223033i
$141$		0			0
$142$	−0.967128	−	1.67511i	−0.0811596	−	0.140572i
$143$	5.79253	−	10.0330i	0.484396	−	0.838998i
$144$		0			0
$145$	7.70674	−	4.44949i	0.640010	−	0.369510i
$146$	0.343146			0.0283989
$147$		0			0
$148$	7.93185			0.651994
$149$	18.6179	−	10.7491i	1.52524	−	0.880598i	0.525688	−	0.850677i	$-0.323808\pi$
$149$	18.6179	−	10.7491i	1.52524	−	0.880598i	0.999552	−	0.0299204i	$-0.00952537\pi$
$150$		0			0
$151$	−1.47531	+	2.55532i	−0.120059	+	0.207949i	−0.919791	−	0.392409i	$-0.871642\pi$
$151$	−1.47531	+	2.55532i	−0.120059	+	0.207949i	0.799732	+	0.600358i	$0.204975\pi$
$152$	0.0176381	+	0.0305501i	0.00143064	+	0.00247794i
$153$		0			0
$154$	0.558263	+	7.77559i	0.0449861	+	0.626575i
$155$		−	0.828427i		−	0.0665409i
$156$		0			0
$157$	19.4823	+	11.2481i	1.55486	+	0.897698i	0.997735	+	0.0672682i	$0.0214283\pi$
$157$	19.4823	+	11.2481i	1.55486	+	0.897698i	0.557123	+	0.830430i	$0.311905\pi$
$158$	7.19375	+	4.15331i	0.572304	+	0.330420i
$159$		0			0
$160$		−	1.00000i		−	0.0790569i
$161$	−5.53674	−	8.17569i	−0.436356	−	0.644335i
$162$		0			0
$163$	−11.4035	−	19.7515i	−0.893192	−	1.54705i	−0.836026	−	0.548690i	$-0.815127\pi$
$163$	−11.4035	−	19.7515i	−0.893192	−	1.54705i	−0.0571664	−	0.998365i	$-0.518207\pi$
$164$	−3.15539	+	5.46530i	−0.246395	+	0.426769i
$165$		0			0
$166$	8.96248	−	5.17449i	0.695624	−	0.401618i
$167$	−8.84961			−0.684803			−0.342402	−	0.939554i	$-0.611240\pi$
$167$	−8.84961			−0.684803			−0.342402	+	0.939554i	$0.611240\pi$
$168$		0			0
$169$	−2.45946			−0.189189
$170$	0.346065	−	0.199801i	0.0265420	−	0.0153240i
$171$		0			0
$172$	−1.51764	+	2.62863i	−0.115719	+	0.200431i
$173$	−3.86843	−	6.70032i	−0.294111	−	0.509416i	0.680667	−	0.732593i	$-0.261690\pi$
$173$	−3.86843	−	6.70032i	−0.294111	−	0.509416i	−0.974778	+	0.223178i	$0.928357\pi$
$174$		0			0
$175$	−2.38014	−	1.15539i	−0.179922	−	0.0873396i
$176$			2.94646i			0.222098i
$177$		0			0
$178$	−5.34519	−	3.08604i	−0.400639	−	0.231309i
$179$	0.417291	+	0.240923i	0.0311898	+	0.0180074i	0.515514	−	0.856881i	$-0.327601\pi$
$179$	0.417291	+	0.240923i	0.0311898	+	0.0180074i	−0.484324	+	0.874889i	$0.660934\pi$
$180$		0			0
$181$		−	2.44876i		−	0.182015i	−0.995850	−	0.0910075i	$-0.970991\pi$
$181$		−	2.44876i		−	0.182015i	0.995850	−	0.0910075i	$-0.0290087\pi$
$182$	8.61339	−	5.83315i	0.638467	−	0.432382i
$183$		0			0
$184$	−1.86603	−	3.23205i	−0.137565	−	0.238270i
$185$	3.96593	−	6.86919i	0.291581	−	0.505033i
$186$		0			0
$187$	−1.01967	+	0.588706i	−0.0745655	+	0.0430504i
$188$	5.80260			0.423198
$189$		0			0
$190$	0.0352762			0.00255920
$191$	−3.89241	+	2.24728i	−0.281645	+	0.162608i	−0.634168	−	0.773195i	$-0.718657\pi$
$191$	−3.89241	+	2.24728i	−0.281645	+	0.162608i	0.352523	+	0.935803i	$0.385324\pi$
$192$		0			0
$193$	6.28497	−	10.8859i	0.452402	−	0.783583i	−0.546133	−	0.837698i	$-0.683901\pi$
$193$	6.28497	−	10.8859i	0.452402	−	0.783583i	0.998535	+	0.0541158i	$0.0172340\pi$
$194$	−7.81722	−	13.5398i	−0.561243	−	0.972102i
$195$		0			0
$196$	−2.59808	+	6.50000i	−0.185577	+	0.464286i
$197$		−	13.3748i		−	0.952916i	−0.879197	−	0.476458i	$-0.841920\pi$
$197$		−	13.3748i		−	0.952916i	0.879197	−	0.476458i	$-0.158080\pi$
$198$		0			0
$199$	−23.5169	−	13.5775i	−1.66707	−	0.962483i	−0.969206	−	0.246253i	$-0.920801\pi$
$199$	−23.5169	−	13.5775i	−1.66707	−	0.962483i	−0.697864	−	0.716231i	$-0.745866\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$		0			0
$202$			18.0492i			1.26993i
$203$	−23.4840	+	1.68608i	−1.64826	+	0.118339i
$204$		0			0
$205$	3.15539	+	5.46530i	0.220382	+	0.381713i
$206$	4.26002	−	7.37857i	0.296810	−	0.514090i
$207$		0			0
$208$	3.40508	−	1.96593i	0.236100	−	0.136312i
$209$	−0.103940			−0.00718968
$210$		0			0
$211$	18.4183			1.26797			0.633984	−	0.773346i	$-0.281419\pi$
$211$	18.4183			1.26797			0.633984	+	0.773346i	$0.281419\pi$
$212$	3.72268	−	2.14929i	0.255675	−	0.147614i
$213$		0			0
$214$	−8.52761	+	14.7702i	−0.582935	+	1.00967i
$215$	1.51764	+	2.62863i	0.103502	+	0.179271i
$216$		0			0
$217$	−0.957160	+	1.97177i	−0.0649763	+	0.133853i
$218$			11.6982i			0.792301i
$219$		0			0
$220$	2.55171	+	1.47323i	0.172036	+	0.0993253i
$221$	1.36068	+	0.785587i	0.0915290	+	0.0528443i
$222$		0			0
$223$			17.8045i			1.19228i	0.802881	+	0.596140i	$0.203300\pi$
$223$			17.8045i			1.19228i	−0.802881	+	0.596140i	$0.796700\pi$
$224$	−1.15539	+	2.38014i	−0.0771980	+	0.159030i
$225$		0			0
$226$	−6.77729	−	11.7386i	−0.450819	−	0.780841i
$227$	−0.856140	+	1.48288i	−0.0568240	+	0.0984220i	−0.893038	−	0.449981i	$-0.851431\pi$
$227$	−0.856140	+	1.48288i	−0.0568240	+	0.0984220i	0.836214	+	0.548403i	$0.184764\pi$
$228$		0			0
$229$	5.26142	−	3.03768i	0.347684	−	0.200736i	−0.315981	−	0.948766i	$-0.602333\pi$
$229$	5.26142	−	3.03768i	0.347684	−	0.200736i	0.663665	+	0.748030i	$0.269000\pi$
$230$	−3.73205			−0.246084
$231$		0			0
$232$	−8.89898			−0.584247
$233$	6.17109	−	3.56288i	0.404282	−	0.233412i	−0.284048	−	0.958810i	$-0.591678\pi$
$233$	6.17109	−	3.56288i	0.404282	−	0.233412i	0.688330	+	0.725398i	$0.258344\pi$
$234$		0			0
$235$	2.90130	−	5.02520i	0.189260	−	0.327808i
$236$	2.78522	+	4.82415i	0.181303	+	0.314025i
$237$		0			0
$238$	−1.05453	+	0.0757120i	−0.0683552	+	0.00490768i
$239$			18.7194i			1.21085i	0.795900	+	0.605427i	$0.206998\pi$
$239$			18.7194i			1.21085i	−0.795900	+	0.605427i	$0.793002\pi$
$240$		0			0
$241$	7.68036	+	4.43426i	0.494735	+	0.285636i	0.726537	−	0.687128i	$-0.241129\pi$
$241$	7.68036	+	4.43426i	0.494735	+	0.285636i	−0.231802	+	0.972763i	$0.574462\pi$
$242$	2.00775	+	1.15918i	0.129063	+	0.0745147i
$243$		0			0
$244$			11.5206i			0.737528i
$245$	4.33013	+	5.50000i	0.276642	+	0.351382i
$246$		0			0
$247$	0.0693504	+	0.120118i	0.00441266	+	0.00764295i
$248$	−0.414214	+	0.717439i	−0.0263026	+	0.0455574i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−22.1738			−1.39960			−0.699798	−	0.714341i	$-0.746727\pi$
$251$	−22.1738			−1.39960			−0.699798	+	0.714341i	$0.746727\pi$
$252$		0			0
$253$	10.9964			0.691335
$254$	−7.75944	+	4.47992i	−0.486871	+	0.281095i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.41662	+	14.5780i	0.525014	+	0.909351i	0.999576	+	0.0291289i	$0.00927332\pi$
$257$	8.41662	+	14.5780i	0.525014	+	0.909351i	−0.474561	+	0.880222i	$0.657393\pi$
$258$		0			0
$259$	−17.3761	+	11.7674i	−1.07970	+	0.731191i
$260$		−	3.93185i		−	0.243843i
$261$		0			0
$262$	−11.0686	−	6.39047i	−0.683822	−	0.394805i
$263$	−19.1562	−	11.0599i	−1.18122	−	0.681980i	−0.224926	−	0.974376i	$-0.572214\pi$
$263$	−19.1562	−	11.0599i	−1.18122	−	0.681980i	−0.956297	+	0.292396i	$0.905548\pi$
$264$		0			0
$265$		−	4.29858i		−	0.264060i
$266$	−0.0839622	−	0.0407579i	−0.00514805	−	0.00249903i
$267$		0			0
$268$	−6.25966	−	10.8420i	−0.382369	−	0.662283i
$269$	−1.45049	+	2.51231i	−0.0884377	+	0.153179i	−0.906851	−	0.421452i	$-0.861521\pi$
$269$	−1.45049	+	2.51231i	−0.0884377	+	0.153179i	0.818413	+	0.574630i	$0.194854\pi$
$270$		0			0
$271$	15.1244	−	8.73205i	0.918739	−	0.530434i	0.0355066	−	0.999369i	$-0.488696\pi$
$271$	15.1244	−	8.73205i	0.918739	−	0.530434i	0.883233	+	0.468935i	$0.155362\pi$
$272$	−0.399602			−0.0242294
$273$		0			0
$274$	−5.52056			−0.333509
$275$	2.55171	−	1.47323i	0.153874	−	0.0888392i
$276$		0			0
$277$	−2.28825	+	3.96336i	−0.137488	+	0.238135i	−0.926545	−	0.376184i	$-0.877236\pi$
$277$	−2.28825	+	3.96336i	−0.137488	+	0.238135i	0.789057	+	0.614319i	$0.210569\pi$
$278$	10.9236	+	18.9202i	0.655152	+	1.13476i
$279$		0			0
$280$	1.48356	+	2.19067i	0.0886599	+	0.130918i
$281$			9.55948i			0.570271i	0.958487	+	0.285135i	$0.0920386\pi$
$281$			9.55948i			0.570271i	−0.958487	+	0.285135i	$0.907961\pi$
$282$		0			0
$283$	9.46238	+	5.46311i	0.562480	+	0.324748i	0.754140	−	0.656713i	$-0.228054\pi$
$283$	9.46238	+	5.46311i	0.562480	+	0.324748i	−0.191660	+	0.981461i	$0.561387\pi$
$284$	1.67511	+	0.967128i	0.0993998	+	0.0573885i
$285$		0			0
$286$			11.5851i			0.685039i
$287$	−1.19570	−	16.6539i	−0.0705798	−	0.983049i
$288$		0			0
$289$	8.42016	+	14.5841i	0.495303	+	0.857891i
$290$	−4.44949	+	7.70674i	−0.261283	+	0.452555i
$291$		0			0
$292$	−0.297173	+	0.171573i	−0.0173907	+	0.0100405i
$293$	−16.2280			−0.948052			−0.474026	−	0.880511i	$-0.657200\pi$
$293$	−16.2280			−0.948052			−0.474026	+	0.880511i	$0.657200\pi$
$294$		0			0
$295$	5.57045			0.324324
$296$	−6.86919	+	3.96593i	−0.399263	+	0.230515i
$297$		0			0
$298$	−10.7491	+	18.6179i	−0.622677	+	1.07851i
$299$	−7.33694	−	12.7079i	−0.424306	−	0.734919i
$300$		0			0
$301$	−0.575090	−	8.00997i	−0.0331476	−	0.461687i
$302$		−	2.95063i		−	0.169790i
$303$		0			0
$304$	−0.0305501	−	0.0176381i	−0.00175217	−	0.00101161i
$305$	9.97710	+	5.76028i	0.571287	+	0.329833i
$306$		0			0
$307$			12.3782i			0.706462i	0.935536	+	0.353231i	$0.114917\pi$
$307$			12.3782i			0.706462i	−0.935536	+	0.353231i	$0.885083\pi$
$308$	−4.37127	−	6.45473i	−0.249076	−	0.367792i
$309$		0			0
$310$	0.414214	+	0.717439i	0.0235257	+	0.0407478i
$311$	−11.4312	+	19.7995i	−0.648206	+	1.12272i	0.335346	+	0.942095i	$0.391147\pi$
$311$	−11.4312	+	19.7995i	−0.648206	+	1.12272i	−0.983551	+	0.180630i	$0.942186\pi$
$312$		0			0
$313$	−30.1399	+	17.4013i	−1.70361	+	0.983578i	−0.761563	+	0.648091i	$0.775568\pi$
$313$	−30.1399	+	17.4013i	−1.70361	+	0.983578i	−0.942045	+	0.335487i	$0.891099\pi$
$314$	−22.4962			−1.26954
$315$		0			0
$316$	−8.30663			−0.467284
$317$	−5.87780	+	3.39355i	−0.330130	+	0.190601i	−0.655899	−	0.754849i	$-0.727710\pi$
$317$	−5.87780	+	3.39355i	−0.330130	+	0.190601i	0.325769	+	0.945449i	$0.394377\pi$
$318$		0			0
$319$	13.1103	−	22.7076i	0.734034	−	1.27138i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	8.88280	+	4.31199i	0.495019	+	0.240298i
$323$		−	0.0140964i		−	0.000784346i
$324$		0			0
$325$	−3.40508	−	1.96593i	−0.188880	−	0.109050i
$326$	19.7515	+	11.4035i	1.09393	+	0.631582i
$327$		0			0
$328$		−	6.31079i		−	0.348455i
$329$	−12.7116	+	8.60853i	−0.700813	+	0.474604i
$330$		0			0
$331$	−5.56985	−	9.64726i	−0.306147	−	0.530261i	0.671369	−	0.741123i	$-0.265706\pi$
$331$	−5.56985	−	9.64726i	−0.306147	−	0.530261i	−0.977516	+	0.210862i	$0.932373\pi$
$332$	−5.17449	+	8.96248i	−0.283987	+	0.491880i
$333$		0			0
$334$	7.66398	−	4.42480i	0.419355	−	0.242114i
$335$	−12.5193			−0.684003
$336$		0			0
$337$	1.59111			0.0866733			0.0433366	−	0.999061i	$-0.486201\pi$
$337$	1.59111			0.0866733			0.0433366	+	0.999061i	$0.486201\pi$
$338$	2.12995	−	1.22973i	0.115854	−	0.0668884i
$339$		0			0
$340$	−0.199801	+	0.346065i	−0.0108357	+	0.0187680i
$341$	−1.22047	−	2.11391i	−0.0660919	−	0.114475i
$342$		0			0
$343$	−3.95164	−	18.0938i	−0.213368	−	0.976972i
$344$		−	3.03528i		−	0.163651i
$345$		0			0
$346$	6.70032	+	3.86843i	0.360211	+	0.207968i
$347$	−13.3860	−	7.72840i	−0.718597	−	0.414882i	0.0956388	−	0.995416i	$-0.469511\pi$
$347$	−13.3860	−	7.72840i	−0.718597	−	0.414882i	−0.814236	+	0.580534i	$0.802844\pi$
$348$		0			0
$349$		−	0.585057i		−	0.0313174i	−0.999877	−	0.0156587i	$-0.995015\pi$
$349$		−	0.585057i		−	0.0313174i	0.999877	−	0.0156587i	$-0.00498452\pi$
$350$	2.63896	−	0.189469i	0.141058	−	0.0101275i
$351$		0			0
$352$	−1.47323	−	2.55171i	−0.0785235	−	0.136007i
$353$	1.83788	−	3.18330i	0.0978204	−	0.169430i	−0.812962	−	0.582317i	$-0.802146\pi$
$353$	1.83788	−	3.18330i	0.0978204	−	0.169430i	0.910782	+	0.412887i	$0.135480\pi$
$354$		0			0
$355$	1.67511	−	0.967128i	0.0889058	−	0.0513298i
$356$	6.17209			0.327120
$357$		0			0
$358$	−0.481846			−0.0254664
$359$	17.4069	−	10.0499i	0.918702	−	0.530413i	0.0354812	−	0.999370i	$-0.488704\pi$
$359$	17.4069	−	10.0499i	0.918702	−	0.530413i	0.883221	+	0.468958i	$0.155370\pi$
$360$		0			0
$361$	−9.49938	+	16.4534i	−0.499967	+	0.865969i
$362$	1.22438	+	2.12069i	0.0643520	+	0.111461i
$363$		0			0
$364$	−4.54284	+	9.35835i	−0.238110	+	0.490511i
$365$			0.343146i			0.0179611i
$366$		0			0
$367$	−17.2665	−	9.96885i	−0.901306	−	0.520369i	−0.0236826	−	0.999720i	$-0.507539\pi$
$367$	−17.2665	−	9.96885i	−0.901306	−	0.520369i	−0.877624	+	0.479350i	$0.840872\pi$
$368$	3.23205	+	1.86603i	0.168482	+	0.0972733i
$369$		0			0
$370$			7.93185i			0.412357i
$371$	−4.96656	+	10.2312i	−0.257851	+	0.531179i
$372$		0			0
$373$	16.9081	+	29.2856i	0.875467	+	1.51635i	0.856265	+	0.516537i	$0.172779\pi$
$373$	16.9081	+	29.2856i	0.875467	+	1.51635i	0.0192016	+	0.999816i	$0.493888\pi$
$374$	0.588706	−	1.01967i	0.0304413	−	0.0527258i
$375$		0			0
$376$	−5.02520	+	2.90130i	−0.259155	+	0.149623i
$377$	−34.9895			−1.80205
$378$		0			0
$379$	26.7614			1.37464			0.687321	−	0.726353i	$-0.258786\pi$
$379$	26.7614			1.37464			0.687321	+	0.726353i	$0.258786\pi$
$380$	−0.0305501	+	0.0176381i	−0.00156719	+	0.000904815i
$381$		0			0
$382$	2.24728	−	3.89241i	0.114981	−	0.199153i
$383$	9.89060	+	17.1310i	0.505386	+	0.875355i	0.999981	+	0.00623078i	$0.00198333\pi$
$383$	9.89060	+	17.1310i	0.505386	+	0.875355i	−0.494594	+	0.869124i	$0.664683\pi$
$384$		0			0
$385$	−7.77559	+	0.558263i	−0.396281	+	0.0284517i
$386$			12.5699i			0.639793i
$387$		0			0
$388$	13.5398	+	7.81722i	0.687380	+	0.396859i
$389$	−4.49181	−	2.59335i	−0.227744	−	0.131488i	0.381787	−	0.924250i	$-0.375309\pi$
$389$	−4.49181	−	2.59335i	−0.227744	−	0.131488i	−0.609531	+	0.792762i	$0.708642\pi$
$390$		0			0
$391$			1.49133i			0.0754200i
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$		0			0
$394$	6.68740	+	11.5829i	0.336907	+	0.583539i
$395$	−4.15331	+	7.19375i	−0.208976	+	0.361957i
$396$		0			0
$397$	4.99280	−	2.88259i	0.250581	−	0.144673i	−0.369449	−	0.929251i	$-0.620454\pi$
$397$	4.99280	−	2.88259i	0.250581	−	0.144673i	0.620030	+	0.784578i	$0.287120\pi$
$398$	27.1550			1.36116
$399$		0			0
$400$	1.00000			0.0500000
$401$	15.4361	−	8.91202i	0.770841	−	0.445045i	−0.0623335	−	0.998055i	$-0.519854\pi$
$401$	15.4361	−	8.91202i	0.770841	−	0.445045i	0.833175	+	0.553010i	$0.186521\pi$
$402$		0			0
$403$	−1.62863	+	2.82086i	−0.0811277	+	0.140517i
$404$	−9.02458	−	15.6310i	−0.448990	−	0.777673i
$405$		0			0
$406$	19.4947	−	13.2022i	0.967507	−	0.655214i
$407$		−	23.3709i		−	1.15845i
$408$		0			0
$409$	−28.5617	−	16.4901i	−1.41228	−	0.815382i	−0.416681	−	0.909053i	$-0.636807\pi$
$409$	−28.5617	−	16.4901i	−1.41228	−	0.815382i	−0.995603	+	0.0936705i	$0.970140\pi$
$410$	−5.46530	−	3.15539i	−0.269912	−	0.155834i
$411$		0			0
$412$			8.52004i			0.419752i
$413$	−13.2584	−	6.43606i	−0.652405	−	0.316698i
$414$		0			0
$415$	5.17449	+	8.96248i	0.254006	+	0.439951i
$416$	−1.96593	+	3.40508i	−0.0963874	+	0.166948i
$417$		0			0
$418$	0.0900147	−	0.0519700i	0.00440276	−	0.00254194i
$419$	15.2287			0.743969			0.371985	−	0.928239i	$-0.378677\pi$
$419$	15.2287			0.743969			0.371985	+	0.928239i	$0.378677\pi$
$420$		0			0
$421$	16.9939			0.828234			0.414117	−	0.910224i	$-0.364090\pi$
$421$	16.9939			0.828234			0.414117	+	0.910224i	$0.364090\pi$
$422$	−15.9507	+	9.20915i	−0.776468	+	0.448294i
$423$		0			0
$424$	−2.14929	+	3.72268i	−0.104379	+	0.180789i
$425$	0.199801	+	0.346065i	0.00969176	+	0.0167866i
$426$		0			0
$427$	−17.0915	−	25.2377i	−0.827115	−	1.22134i
$428$		−	17.0552i		−	0.824395i
$429$		0			0
$430$	−2.62863	−	1.51764i	−0.126764	−	0.0731870i
$431$	−15.4818	−	8.93842i	−0.745732	−	0.430549i	0.0784178	−	0.996921i	$-0.475013\pi$
$431$	−15.4818	−	8.93842i	−0.745732	−	0.430549i	−0.824150	+	0.566372i	$0.808347\pi$
$432$		0			0
$433$			5.56388i			0.267383i	0.991023	+	0.133691i	$0.0426831\pi$
$433$			5.56388i			0.267383i	−0.991023	+	0.133691i	$0.957317\pi$
$434$	−0.156961	−	2.18618i	−0.00753437	−	0.104940i
$435$		0			0
$436$	−5.84909	−	10.1309i	−0.280121	−	0.485183i
$437$	−0.0658262	+	0.114014i	−0.00314890	+	0.00545405i
$438$		0			0
$439$	9.53568	−	5.50543i	0.455113	−	0.262760i	−0.254874	−	0.966974i	$-0.582034\pi$
$439$	9.53568	−	5.50543i	0.455113	−	0.262760i	0.709987	+	0.704214i	$0.248701\pi$
$440$	−2.94646			−0.140467
$441$		0			0
$442$	−1.57117			−0.0747332
$443$	−14.7091	+	8.49233i	−0.698853	+	0.403483i	−0.806920	−	0.590661i	$-0.798867\pi$
$443$	−14.7091	+	8.49233i	−0.698853	+	0.403483i	0.108067	+	0.994144i	$0.465534\pi$
$444$		0			0
$445$	3.08604	−	5.34519i	0.146293	−	0.253386i
$446$	−8.90226	−	15.4192i	−0.421534	−	0.730119i
$447$		0			0
$448$	−0.189469	−	2.63896i	−0.00895155	−	0.124679i
$449$			12.5892i			0.594122i	0.954858	+	0.297061i	$0.0960065\pi$
$449$			12.5892i			0.594122i	−0.954858	+	0.297061i	$0.903994\pi$
$450$		0			0
$451$	16.1033	+	9.29725i	0.758276	+	0.437791i
$452$	11.7386	+	6.77729i	0.552138	+	0.318777i
$453$		0			0
$454$		−	1.71228i		−	0.0803612i
$455$	5.83315	+	8.61339i	0.273462	+	0.403802i
$456$		0			0
$457$	1.08417	+	1.87783i	0.0507153	+	0.0878414i	0.890269	−	0.455436i	$-0.150517\pi$
$457$	1.08417	+	1.87783i	0.0507153	+	0.0878414i	−0.839553	+	0.543277i	$0.817183\pi$
$458$	−3.03768	+	5.26142i	−0.141941	+	0.245850i
$459$		0			0
$460$	3.23205	−	1.86603i	0.150695	−	0.0870039i
$461$	34.3032			1.59766			0.798829	−	0.601558i	$-0.205453\pi$
$461$	34.3032			1.59766			0.798829	+	0.601558i	$0.205453\pi$
$462$		0			0
$463$	28.2133			1.31118			0.655592	−	0.755115i	$-0.272419\pi$
$463$	28.2133			1.31118			0.655592	+	0.755115i	$0.272419\pi$
$464$	7.70674	−	4.44949i	0.357777	−	0.206562i
$465$		0			0
$466$	−3.56288	+	6.17109i	−0.165047	+	0.285870i
$467$	−2.10342	−	3.64324i	−0.0973349	−	0.168589i	0.813246	−	0.581920i	$-0.197698\pi$
$467$	−2.10342	−	3.64324i	−0.0973349	−	0.168589i	−0.910581	+	0.413331i	$0.864365\pi$
$468$		0			0
$469$	29.7977	+	14.4647i	1.37593	+	0.667920i
$470$			5.80260i			0.267654i
$471$		0			0
$472$	−4.82415	−	2.78522i	−0.222049	−	0.128200i
$473$	7.74515	+	4.47167i	0.356122	+	0.205607i
$474$		0			0
$475$			0.0352762i			0.00161858i
$476$	0.875396	−	0.592835i	0.0401237	−	0.0271725i
$477$		0			0
$478$	−9.35968	−	16.2114i	−0.428102	−	0.741494i
$479$	7.35968	−	12.7473i	0.336272	−	0.582441i	−0.647456	−	0.762103i	$-0.724167\pi$
$479$	7.35968	−	12.7473i	0.336272	−	0.582441i	0.983728	+	0.179662i	$0.0575004\pi$
$480$		0			0
$481$	−27.0086	+	15.5934i	−1.23149	+	0.710999i
$482$	−8.86851			−0.403950
$483$		0			0
$484$	−2.31835			−0.105380
$485$	13.5398	−	7.81722i	0.614811	−	0.354961i
$486$		0			0
$487$	0.938784	−	1.62602i	0.0425404	−	0.0736821i	−0.843971	−	0.536388i	$-0.819788\pi$
$487$	0.938784	−	1.62602i	0.0425404	−	0.0736821i	0.886512	+	0.462706i	$0.153122\pi$
$488$	−5.76028	−	9.97710i	−0.260756	−	0.451642i
$489$		0			0
$490$	−6.50000	−	2.59808i	−0.293640	−	0.117369i
$491$			10.4281i			0.470613i	0.971921	+	0.235307i	$0.0756095\pi$
$491$			10.4281i			0.470613i	−0.971921	+	0.235307i	$0.924391\pi$
$492$		0			0
$493$	3.07963	+	1.77802i	0.138699	+	0.0800782i
$494$	−0.120118	−	0.0693504i	−0.00540438	−	0.00312022i
$495$		0			0
$496$		−	0.828427i		−	0.0371975i
$497$	−5.10442	+	0.366481i	−0.228965	+	0.0164389i
$498$		0			0
$499$	18.8822	+	32.7050i	0.845285	+	1.46408i	0.885374	+	0.464880i	$0.153903\pi$
$499$	18.8822	+	32.7050i	0.845285	+	1.46408i	−0.0400890	+	0.999196i	$0.512764\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	19.2030	−	11.0869i	0.857074	−	0.494832i
$503$	35.8895			1.60023			0.800116	−	0.599845i	$-0.204771\pi$
$503$	35.8895			1.60023			0.800116	+	0.599845i	$0.204771\pi$
$504$		0			0
$505$	−18.0492			−0.803177
$506$	−9.52312	+	5.49818i	−0.423354	+	0.244424i
$507$		0			0
$508$	4.47992	−	7.75944i	0.198764	−	0.344270i
$509$	−8.58746	−	14.8739i	−0.380633	−	0.659275i	0.610520	−	0.792001i	$-0.290960\pi$
$509$	−8.58746	−	14.8739i	−0.380633	−	0.659275i	−0.991153	+	0.132726i	$0.957627\pi$
$510$		0			0
$511$	0.396469	−	0.816735i	0.0175387	−	0.0361302i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−14.5780	−	8.41662i	−0.643008	−	0.371241i
$515$	7.37857	+	4.26002i	0.325139	+	0.187719i
$516$		0			0
$517$		−	17.0972i		−	0.751932i
$518$	9.16442	−	18.8789i	0.402661	−	0.829492i
$519$		0			0
$520$	1.96593	+	3.40508i	0.0862116	+	0.149323i
$521$	−2.26539	+	3.92377i	−0.0992484	+	0.171903i	−0.911374	−	0.411580i	$-0.864977\pi$
$521$	−2.26539	+	3.92377i	−0.0992484	+	0.171903i	0.812125	+	0.583483i	$0.198311\pi$
$522$		0			0
$523$	−22.9267	+	13.2368i	−1.00252	+	0.578803i	−0.908992	−	0.416814i	$-0.863147\pi$
$523$	−22.9267	+	13.2368i	−1.00252	+	0.578803i	−0.0935241	+	0.995617i	$0.529813\pi$
$524$	12.7809			0.558338
$525$		0			0
$526$	22.1197			0.964465
$527$	0.286690	−	0.165520i	0.0124884	−	0.00721018i
$528$		0			0
$529$	−4.53590	+	7.85641i	−0.197213	+	0.341583i
$530$	2.14929	+	3.72268i	0.0933592	+	0.161703i
$531$		0			0
$532$	0.0930924	−	0.00668373i	0.00403607	−	0.000289777i
$533$		−	24.8131i		−	1.07477i
$534$		0			0
$535$	−14.7702	−	8.52761i	−0.638573	−	0.368681i
$536$	10.8420	+	6.25966i	0.468305	+	0.270376i
$537$		0			0
$538$		−	2.90097i		−	0.125070i
$539$	19.1520	+	7.65514i	0.824936	+	0.329730i
$540$		0			0
$541$	−3.16504	−	5.48201i	−0.136076	−	0.235690i	0.789932	−	0.613194i	$-0.210116\pi$
$541$	−3.16504	−	5.48201i	−0.136076	−	0.235690i	−0.926008	+	0.377504i	$0.876782\pi$
$542$	−8.73205	+	15.1244i	−0.375074	+	0.649647i
$543$		0			0
$544$	0.346065	−	0.199801i	0.0148374	−	0.00856639i
$545$	−11.6982			−0.501095
$546$		0			0
$547$	−38.5271			−1.64730			−0.823651	−	0.567097i	$-0.808066\pi$
$547$	−38.5271			−1.64730			−0.823651	+	0.567097i	$0.808066\pi$
$548$	4.78094	−	2.76028i	0.204232	−	0.117913i
$549$		0			0
$550$	−1.47323	+	2.55171i	−0.0628188	+	0.108805i
$551$	0.156961	+	0.271864i	0.00668676	+	0.0115818i
$552$		0			0
$553$	18.1971	−	12.3234i	0.773819	−	0.524045i
$554$		−	4.57650i		−	0.194437i
$555$		0			0
$556$	−18.9202	−	10.9236i	−0.802393	−	0.463262i
$557$	8.00456	+	4.62144i	0.339164	+	0.195817i	0.659902	−	0.751351i	$-0.270598\pi$
$557$	8.00456	+	4.62144i	0.339164	+	0.195817i	−0.320738	+	0.947168i	$0.603931\pi$
$558$		0			0
$559$		−	11.9343i		−	0.504765i
$560$	−2.38014	−	1.15539i	−0.100579	−	0.0488243i
$561$		0			0
$562$	−4.77974	−	8.27875i	−0.201621	−	0.349218i
$563$	13.3871	−	23.1872i	0.564201	−	0.977225i	−0.432923	−	0.901431i	$-0.642518\pi$
$563$	13.3871	−	23.1872i	0.564201	−	0.977225i	0.997124	−	0.0757935i	$-0.0241490\pi$
$564$		0			0
$565$	11.7386	−	6.77729i	0.493847	−	0.285123i
$566$	−10.9262			−0.459263
$567$		0			0
$568$	−1.93426			−0.0811596
$569$	39.6604	−	22.8979i	1.66265	−	0.959931i	0.691207	−	0.722657i	$-0.257079\pi$
$569$	39.6604	−	22.8979i	1.66265	−	0.959931i	0.971443	−	0.237274i	$-0.0762539\pi$
$570$		0			0
$571$	−0.390149	+	0.675759i	−0.0163272	+	0.0282796i	−0.874074	−	0.485794i	$-0.838531\pi$
$571$	−0.390149	+	0.675759i	−0.0163272	+	0.0282796i	0.857746	+	0.514073i	$0.171864\pi$
$572$	−5.79253	−	10.0330i	−0.242198	−	0.419499i
$573$		0			0
$574$	9.36246	+	13.8249i	0.390781	+	0.577039i
$575$		−	3.73205i		−	0.155637i
$576$		0			0
$577$	−9.74401	−	5.62571i	−0.405648	−	0.234201i	0.283270	−	0.959040i	$-0.408581\pi$
$577$	−9.74401	−	5.62571i	−0.405648	−	0.234201i	−0.688918	+	0.724839i	$0.741914\pi$
$578$	−14.5841	−	8.42016i	−0.606620	−	0.350232i
$579$		0			0
$580$		−	8.89898i		−	0.369510i
$581$	−1.96081	−	27.3105i	−0.0813480	−	1.13303i
$582$		0			0
$583$	−6.33281	−	10.9687i	−0.262278	−	0.454279i
$584$	0.171573	−	0.297173i	0.00709974	−	0.0122971i
$585$		0			0
$586$	14.0539	−	8.11401i	0.580561	−	0.335187i
$587$	40.1593			1.65755			0.828775	−	0.559582i	$-0.189038\pi$
$587$	40.1593			1.65755			0.828775	+	0.559582i	$0.189038\pi$
$588$		0			0
$589$	0.0292237			0.00120414
$590$	−4.82415	+	2.78522i	−0.198607	+	0.114666i
$591$		0			0
$592$	3.96593	−	6.86919i	0.162999	−	0.282322i
$593$	9.54170	+	16.5267i	0.391831	+	0.678671i	0.992691	−	0.120683i	$-0.0385085\pi$
$593$	9.54170	+	16.5267i	0.391831	+	0.678671i	−0.600860	+	0.799354i	$0.705175\pi$
$594$		0			0
$595$	−0.0757120	−	1.05453i	−0.00310389	−	0.0432316i
$596$		−	21.4981i		−	0.880598i
$597$		0			0
$598$	12.7079	+	7.33694i	0.519666	+	0.300030i
$599$	24.6424	+	14.2273i	1.00686	+	0.581312i	0.910271	−	0.414013i	$-0.135873\pi$
$599$	24.6424	+	14.2273i	1.00686	+	0.581312i	0.0965902	+	0.995324i	$0.469206\pi$
$600$		0			0
$601$		−	29.2553i		−	1.19335i	−0.802484	−	0.596673i	$-0.796489\pi$
$601$		−	29.2553i		−	1.19335i	0.802484	−	0.596673i	$-0.203511\pi$
$602$	4.50303	+	6.64929i	0.183530	+	0.271005i
$603$		0			0
$604$	1.47531	+	2.55532i	0.0600297	+	0.103974i
$605$	−1.15918	+	2.00775i	−0.0471272	+	0.0816267i
$606$		0			0
$607$	−22.3712	+	12.9160i	−0.908020	+	0.524246i	−0.879794	−	0.475356i	$-0.842319\pi$
$607$	−22.3712	+	12.9160i	−0.908020	+	0.524246i	−0.0282267	+	0.999602i	$0.508986\pi$
$608$	0.0352762			0.00143064
$609$		0			0
$610$	−11.5206			−0.466454
$611$	−19.7583	+	11.4075i	−0.799337	+	0.461498i
$612$		0			0
$613$	−8.12216	+	14.0680i	−0.328051	+	0.568201i	−0.982125	−	0.188230i	$-0.939725\pi$
$613$	−8.12216	+	14.0680i	−0.328051	+	0.568201i	0.654074	+	0.756430i	$0.273058\pi$
$614$	−6.18910	−	10.7198i	−0.249772	−	0.432618i
$615$		0			0
$616$	7.01299	+	3.40433i	0.282562	+	0.137164i
$617$			31.8398i			1.28182i	0.767615	+	0.640911i	$0.221443\pi$
$617$			31.8398i			1.28182i	−0.767615	+	0.640911i	$0.778557\pi$
$618$		0			0
$619$	8.01055	+	4.62490i	0.321971	+	0.185890i	0.652271	−	0.757986i	$-0.273816\pi$
$619$	8.01055	+	4.62490i	0.321971	+	0.185890i	−0.330300	+	0.943876i	$0.607150\pi$
$620$	−0.717439	−	0.414214i	−0.0288130	−	0.0166352i
$621$		0			0
$622$		−	22.8625i		−	0.916701i
$623$	−13.5210	+	9.15669i	−0.541708	+	0.366855i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	17.4013	−	30.1399i	0.695495	−	1.20463i
$627$		0			0
$628$	19.4823	−	11.2481i	0.777429	−	0.448849i
$629$	3.16958			0.126379
$630$		0			0
$631$	−10.3096			−0.410421			−0.205210	−	0.978718i	$-0.565788\pi$
$631$	−10.3096			−0.410421			−0.205210	+	0.978718i	$0.565788\pi$
$632$	7.19375	−	4.15331i	0.286152	−	0.165210i
$633$		0			0
$634$	3.39355	−	5.87780i	0.134775	−	0.233437i
$635$	−4.47992	−	7.75944i	−0.177780	−	0.307924i
$636$		0			0
$637$	−3.93185	−	27.2407i	−0.155786	−	1.07931i
$638$			26.2205i			1.03808i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	11.1181	+	6.41906i	0.439140	+	0.253538i	0.703233	−	0.710960i	$-0.251739\pi$
$641$	11.1181	+	6.41906i	0.439140	+	0.253538i	−0.264093	+	0.964497i	$0.585072\pi$
$642$		0			0
$643$			8.96224i			0.353436i	0.984262	+	0.176718i	$0.0565481\pi$
$643$			8.96224i			0.353436i	−0.984262	+	0.176718i	$0.943452\pi$
$644$	−9.84873	+	0.707107i	−0.388094	+	0.0278639i
$645$		0			0
$646$	0.00704821	+	0.0122079i	0.000277308	+	0.000480312i
$647$	−22.6852	+	39.2919i	−0.891846	+	1.54472i	−0.0541854	+	0.998531i	$0.517256\pi$
$647$	−22.6852	+	39.2919i	−0.891846	+	1.54472i	−0.837660	+	0.546191i	$0.816077\pi$
$648$		0			0
$649$	14.2142	−	8.20656i	0.557955	−	0.322136i
$650$	3.93185			0.154220
$651$		0			0
$652$	−22.8070			−0.893192
$653$	−28.4051	+	16.3997i	−1.11158	+	0.641769i	−0.939237	−	0.343268i	$-0.888466\pi$
$653$	−28.4051	+	16.3997i	−1.11158	+	0.641769i	−0.172340	+	0.985038i	$0.555133\pi$
$654$		0			0
$655$	6.39047	−	11.0686i	0.249696	−	0.432487i
$656$	3.15539	+	5.46530i	0.123197	+	0.213384i
$657$		0			0
$658$	6.70430	−	13.8110i	0.261361	−	0.538409i
$659$		−	18.7103i		−	0.728850i	−0.931233	−	0.364425i	$-0.881266\pi$
$659$		−	18.7103i		−	0.728850i	0.931233	−	0.364425i	$-0.118734\pi$
$660$		0			0
$661$	7.41761	+	4.28256i	0.288512	+	0.166572i	0.637270	−	0.770640i	$-0.280063\pi$
$661$	7.41761	+	4.28256i	0.288512	+	0.166572i	−0.348759	+	0.937213i	$0.613397\pi$
$662$	9.64726	+	5.56985i	0.374951	+	0.216478i
$663$		0			0
$664$		−	10.3490i		−	0.401618i
$665$	0.0407579	−	0.0839622i	0.00158052	−	0.00325592i
$666$		0			0
$667$	−16.6057	−	28.7620i	−0.642976	−	1.11367i
$668$	−4.42480	+	7.66398i	−0.171201	+	0.296528i
$669$		0			0
$670$	10.8420	−	6.25966i	0.418865	−	0.241832i
$671$	33.9449			1.31043
$672$		0			0
$673$	−0.179617			−0.00692372			−0.00346186	−	0.999994i	$-0.501102\pi$
$673$	−0.179617			−0.00692372			−0.00346186	+	0.999994i	$0.501102\pi$
$674$	−1.37794	+	0.795555i	−0.0530763	+	0.0306436i
$675$		0			0
$676$	−1.22973	+	2.12995i	−0.0472973	+	0.0819213i
$677$	20.7051	+	35.8623i	0.795763	+	1.37830i	0.922354	+	0.386346i	$0.126263\pi$
$677$	20.7051	+	35.8623i	0.795763	+	1.37830i	−0.126591	+	0.991955i	$0.540404\pi$
$678$		0			0
$679$	−41.2586	+	2.96224i	−1.58336	+	0.113680i
$680$		−	0.399602i		−	0.0153240i
$681$		0			0
$682$	2.11391	+	1.22047i	0.0809457	+	0.0467340i
$683$	37.5900	+	21.7026i	1.43834	+	0.830427i	0.997735	−	0.0672723i	$-0.0214296\pi$
$683$	37.5900	+	21.7026i	1.43834	+	0.830427i	0.440608	+	0.897700i	$0.354763\pi$
$684$		0			0
$685$		−	5.52056i		−	0.210930i
$686$	12.4691	+	13.6938i	0.476073	+	0.522834i
$687$		0			0
$688$	1.51764	+	2.62863i	0.0578594	+	0.100215i
$689$	−8.45069	+	14.6370i	−0.321946	+	0.557626i
$690$		0			0
$691$	−16.8728	+	9.74150i	−0.641871	+	0.370584i	−0.785335	−	0.619071i	$-0.787509\pi$
$691$	−16.8728	+	9.74150i	−0.641871	+	0.370584i	0.143464	+	0.989656i	$0.454176\pi$
$692$	−7.73686			−0.294111
$693$		0			0
$694$	15.4568			0.586732
$695$	−18.9202	+	10.9236i	−0.717683	+	0.414354i
$696$		0			0
$697$	−1.26090	+	2.18394i	−0.0477600	+	0.0827228i
$698$	0.292529	+	0.506675i	0.0110724	+	0.0191779i
$699$		0			0
$700$	−2.19067	+	1.48356i	−0.0827996	+	0.0560734i
$701$		−	47.0245i		−	1.77609i	−0.459755	−	0.888046i	$-0.652063\pi$
$701$		−	47.0245i		−	1.77609i	0.459755	−	0.888046i	$-0.347937\pi$
$702$		0			0
$703$	0.242319	+	0.139903i	0.00913922	+	0.00527653i
$704$	2.55171	+	1.47323i	0.0961713	+	0.0555245i
$705$		0			0
$706$			3.67576i			0.138339i
$707$	42.9595	+	20.8539i	1.61566	+	0.784292i
$708$		0			0
$709$	24.2227	+	41.9549i	0.909701	+	1.57565i	0.814480	+	0.580192i	$0.197023\pi$
$709$	24.2227	+	41.9549i	0.909701	+	1.57565i	0.0952213	+	0.995456i	$0.469644\pi$
$710$	−0.967128	+	1.67511i	−0.0362957	+	0.0628659i
$711$		0			0
$712$	−5.34519	+	3.08604i	−0.200319	+	0.115654i
$713$	−3.09173			−0.115786
$714$		0			0
$715$	−11.5851			−0.433257
$716$	0.417291	−	0.240923i	0.0155949	−	0.00900372i
$717$		0			0
$718$	−10.0499	+	17.4069i	−0.375058	+	0.649620i
$719$	−20.6632	−	35.7897i	−0.770606	−	1.33473i	−0.937231	−	0.348709i	$-0.886620\pi$
$719$	−20.6632	−	35.7897i	−0.770606	−	1.33473i	0.166625	−	0.986020i	$-0.446713\pi$
$720$		0			0
$721$	−12.6400	−	18.6646i	−0.470739	−	0.695106i
$722$		−	18.9988i		−	0.707060i
$723$		0			0
$724$	−2.12069	−	1.22438i	−0.0788148	−	0.0455037i
$725$	−7.70674	−	4.44949i	−0.286221	−	0.165250i
$726$		0			0
$727$			16.7905i			0.622726i	0.950291	+	0.311363i	$0.100786\pi$
$727$			16.7905i			0.622726i	−0.950291	+	0.311363i	$0.899214\pi$
$728$	−0.744963	−	10.3760i	−0.0276102	−	0.384560i
$729$		0			0
$730$	−0.171573	−	0.297173i	−0.00635020	−	0.0109989i
$731$	−0.606451	+	1.05040i	−0.0224304	+	0.0388506i
$732$		0			0
$733$	−26.6043	+	15.3600i	−0.982652	+	0.567335i	−0.903070	−	0.429494i	$-0.858692\pi$
$733$	−26.6043	+	15.3600i	−0.982652	+	0.567335i	−0.0795826	+	0.996828i	$0.525359\pi$
$734$	19.9377			0.735914
$735$		0			0
$736$	−3.73205			−0.137565
$737$	−31.9457	+	18.4438i	−1.17673	+	0.679388i
$738$		0			0
$739$	−15.3876	+	26.6521i	−0.566041	+	0.980412i	0.430911	+	0.902395i	$0.358192\pi$
$739$	−15.3876	+	26.6521i	−0.566041	+	0.980412i	−0.996952	+	0.0780176i	$0.975141\pi$
$740$	−3.96593	−	6.86919i	−0.145790	−	0.252516i
$741$		0			0
$742$	−0.814447	−	11.3438i	−0.0298993	−	0.416443i
$743$		−	33.3616i		−	1.22392i	−0.790889	−	0.611960i	$-0.790381\pi$
$743$		−	33.3616i		−	1.22392i	0.790889	−	0.611960i	$-0.209619\pi$
$744$		0			0
$745$	−18.6179	−	10.7491i	−0.682108	−	0.393815i
$746$	−29.2856	−	16.9081i	−1.07222	−	0.619048i
$747$		0			0
$748$			1.17741i			0.0430504i
$749$	25.3025	+	37.3624i	0.924533	+	1.36519i
$750$		0			0
$751$	15.9452	+	27.6179i	0.581849	+	1.00779i	0.995260	+	0.0972480i	$0.0310040\pi$
$751$	15.9452	+	27.6179i	0.581849	+	1.00779i	−0.413411	+	0.910545i	$0.635663\pi$
$752$	2.90130	−	5.02520i	0.105800	−	0.183250i
$753$		0			0
$754$	30.3018	−	17.4947i	1.10353	−	0.637121i
$755$	2.95063			0.107384
$756$		0			0
$757$	−10.9065			−0.396404			−0.198202	−	0.980161i	$-0.563510\pi$
$757$	−10.9065			−0.396404			−0.198202	+	0.980161i	$0.563510\pi$
$758$	−23.1761	+	13.3807i	−0.841793	+	0.486010i
$759$		0			0
$760$	0.0176381	−	0.0305501i	0.000639801	−	0.00110817i
$761$	12.2097	+	21.1479i	0.442602	+	0.766610i	0.997882	−	0.0650543i	$-0.0207220\pi$
$761$	12.2097	+	21.1479i	0.442602	+	0.766610i	−0.555280	+	0.831664i	$0.687389\pi$
$762$		0			0
$763$	27.8433	+	13.5160i	1.00800	+	0.489313i
$764$			4.49457i			0.162608i
$765$		0			0
$766$	−17.1310	−	9.89060i	−0.618969	−	0.357362i
$767$	−18.9678	−	10.9511i	−0.684889	−	0.395421i
$768$		0			0
$769$		−	22.9416i		−	0.827294i	−0.910437	−	0.413647i	$-0.864255\pi$
$769$		−	22.9416i		−	0.827294i	0.910437	−	0.413647i	$-0.135745\pi$
$770$	6.45473	−	4.37127i	0.232612	−	0.157530i
$771$		0			0
$772$	−6.28497	−	10.8859i	−0.226201	−	0.391791i
$773$	22.6837	−	39.2894i	0.815877	−	1.41314i	−0.0928193	−	0.995683i	$-0.529588\pi$
$773$	22.6837	−	39.2894i	0.815877	−	1.41314i	0.908696	−	0.417458i	$-0.137079\pi$
$774$		0			0
$775$	−0.717439	+	0.414214i	−0.0257712	+	0.0148790i
$776$	−15.6344			−0.561243
$777$		0			0
$778$	5.18670			0.185952
$779$	−0.192795	+	0.111310i	−0.00690760	+	0.00398810i
$780$		0			0
$781$	2.84961	−	4.93566i	0.101967	−	0.176612i
$782$	−0.745667	−	1.29153i	−0.0266650	−	0.0461851i
$783$		0			0
$784$	4.33013	+	5.50000i	0.154647	+	0.196429i
$785$		−	22.4962i		−	0.802925i
$786$		0			0
$787$	2.89834	+	1.67335i	0.103314	+	0.0596487i	0.550767	−	0.834659i	$-0.314335\pi$
$787$	2.89834	+	1.67335i	0.103314	+	0.0596487i	−0.447452	+	0.894308i	$0.647669\pi$
$788$	−11.5829	−	6.68740i	−0.412625	−	0.238229i
$789$		0			0
$790$		−	8.30663i		−	0.295536i
$791$	−35.7700	+	2.56817i	−1.27183	+	0.0913136i
$792$		0			0
$793$	−22.6486	−	39.2285i	−0.804274	−	1.39304i
$794$	−2.88259	+	4.99280i	−0.102299	+	0.177188i
$795$		0			0
$796$	−23.5169	+	13.5775i	−0.833535	+	0.481242i
$797$	−36.5402			−1.29432			−0.647160	−	0.762354i	$-0.724044\pi$
$797$	−36.5402			−1.29432			−0.647160	+	0.762354i	$0.724044\pi$
$798$		0			0
$799$	2.31873			0.0820308
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−8.91202	+	15.4361i	−0.314695	+	0.545067i
$803$	0.505533	+	0.875609i	0.0178399	+	0.0308996i
$804$		0			0
$805$	−4.31199	+	8.88280i	−0.151978	+	0.313078i
$806$		−	3.25725i		−	0.114732i
$807$		0			0
$808$	15.6310	+	9.02458i	0.549898	+	0.317484i
$809$	−41.5179	−	23.9704i	−1.45969	−	0.842753i	−0.460696	−	0.887558i	$-0.652400\pi$
$809$	−41.5179	−	23.9704i	−1.45969	−	0.842753i	−0.998996	+	0.0448048i	$0.985733\pi$
$810$		0			0
$811$			49.6994i			1.74518i	0.488452	+	0.872591i	$0.337562\pi$
$811$			49.6994i			1.74518i	−0.488452	+	0.872591i	$0.662438\pi$
$812$	−10.2818	+	21.1808i	−0.360822	+	0.743301i
$813$		0			0
$814$	11.6855	+	20.2398i	0.409575	+	0.709405i
$815$	−11.4035	+	19.7515i	−0.399448	+	0.691864i
$816$		0			0
$817$	−0.0927279	+	0.0535365i	−0.00324414	+	0.00187300i
$818$	32.9802			1.15312
$819$		0			0
$820$	6.31079			0.220382
$821$	19.6520	−	11.3461i	0.685858	−	0.395980i	−0.116200	−	0.993226i	$-0.537071\pi$
$821$	19.6520	−	11.3461i	0.685858	−	0.395980i	0.802059	+	0.597245i	$0.203738\pi$
$822$		0			0
$823$	1.59711	−	2.76628i	0.0556719	−	0.0964266i	−0.836846	−	0.547438i	$-0.815603\pi$
$823$	1.59711	−	2.76628i	0.0556719	−	0.0964266i	0.892518	+	0.451011i	$0.148937\pi$
$824$	−4.26002	−	7.37857i	−0.148405	−	0.257045i
$825$		0			0
$826$	14.7002	−	1.05543i	0.511484	−	0.0367229i
$827$		−	29.7259i		−	1.03367i	−0.856084	−	0.516836i	$-0.827110\pi$
$827$		−	29.7259i		−	1.03367i	0.856084	−	0.516836i	$-0.172890\pi$
$828$		0			0
$829$	26.8588	+	15.5069i	0.932845	+	0.538578i	0.887710	−	0.460403i	$-0.152295\pi$
$829$	26.8588	+	15.5069i	0.932845	+	0.538578i	0.0451348	+	0.998981i	$0.485628\pi$
$830$	−8.96248	−	5.17449i	−0.311092	−	0.179609i
$831$		0			0
$832$		−	3.93185i		−	0.136312i
$833$	−1.03820	+	2.59741i	−0.0359713	+	0.0899950i
$834$		0			0
$835$	4.42480	+	7.66398i	0.153127	+	0.265223i
$836$	−0.0519700	+	0.0900147i	−0.00179742	+	0.00311322i
$837$		0			0
$838$	−13.1884	+	7.61434i	−0.455586	+	0.263033i
$839$	35.8462			1.23755			0.618773	−	0.785570i	$-0.287630\pi$
$839$	35.8462			1.23755			0.618773	+	0.785570i	$0.287630\pi$
$840$		0			0
$841$	−50.1918			−1.73075
$842$	−14.7172	+	8.49697i	−0.507188	+	0.292825i
$843$		0			0
$844$	9.20915	−	15.9507i	0.316992	−	0.549046i
$845$	1.22973	+	2.12995i	0.0423040	+	0.0732726i
$846$		0			0
$847$	5.07875	−	3.43942i	0.174508	−	0.118180i
$848$		−	4.29858i		−	0.147614i
$849$		0			0
$850$	−0.346065	−	0.199801i	−0.0118699	−	0.00685311i
$851$	−25.6361	−	14.8010i	−0.878796	−	0.507373i
$852$		0			0
$853$		−	22.8818i		−	0.783456i	−0.920081	−	0.391728i	$-0.871877\pi$
$853$		−	22.8818i		−	0.783456i	0.920081	−	0.391728i	$-0.128123\pi$
$854$	27.4205	+	13.3108i	0.938311	+	0.455486i
$855$		0			0
$856$	8.52761	+	14.7702i	0.291468	+	0.504837i
$857$	−16.8593	+	29.2012i	−0.575904	+	0.997494i	0.420039	+	0.907506i	$0.362016\pi$
$857$	−16.8593	+	29.2012i	−0.575904	+	0.997494i	−0.995943	+	0.0899883i	$0.971317\pi$
$858$		0			0
$859$	16.3926	−	9.46427i	0.559308	−	0.322917i	−0.193560	−	0.981088i	$-0.562003\pi$
$859$	16.3926	−	9.46427i	0.559308	−	0.322917i	0.752868	+	0.658172i	$0.228670\pi$
$860$	3.03528			0.103502
$861$		0			0
$862$	17.8768			0.608888
$863$	−4.55277	+	2.62854i	−0.154978	+	0.0894767i	−0.575484	−	0.817813i	$-0.695186\pi$
$863$	−4.55277	+	2.62854i	−0.154978	+	0.0894767i	0.420505	+	0.907290i	$0.361853\pi$
$864$		0			0
$865$	−3.86843	+	6.70032i	−0.131531	+	0.227818i
$866$	−2.78194	−	4.81846i	−0.0945341	−	0.163738i
$867$		0			0
$868$	1.22902	+	1.81481i	0.0417158	+	0.0615987i
$869$			24.4752i			0.830263i
$870$		0			0
$871$	42.6293	+	24.6120i	1.44444	+	0.833947i
$872$	10.1309	+	5.84909i	0.343076	+	0.198075i
$873$		0			0
$874$		−	0.131652i		−	0.00445321i
$875$	0.189469	+	2.63896i	0.00640521	+	0.0892131i
$876$		0			0
$877$	20.3326	+	35.2170i	0.686582	+	1.18919i	0.972937	+	0.231071i	$0.0742229\pi$
$877$	20.3326	+	35.2170i	0.686582	+	1.18919i	−0.286355	+	0.958124i	$0.592444\pi$
$878$	−5.50543	+	9.53568i	−0.185799	+	0.321814i
$879$		0			0
$880$	2.55171	−	1.47323i	0.0860182	−	0.0496626i
$881$	1.01828			0.0343067			0.0171533	−	0.999853i	$-0.494540\pi$
$881$	1.01828			0.0343067			0.0171533	+	0.999853i	$0.494540\pi$
$882$		0			0
$883$	11.0436			0.371647			0.185823	−	0.982583i	$-0.440505\pi$
$883$	11.0436			0.371647			0.185823	+	0.982583i	$0.440505\pi$
$884$	1.36068	−	0.785587i	0.0457645	−	0.0264222i
$885$		0			0
$886$	8.49233	−	14.7091i	0.285305	−	0.494163i
$887$	12.0492	+	20.8698i	0.404571	+	0.700738i	0.994271	−	0.106884i	$-0.0340875\pi$
$887$	12.0492	+	20.8698i	0.404571	+	0.700738i	−0.589700	+	0.807622i	$0.700754\pi$
$888$		0			0
$889$	1.69761	+	23.6446i	0.0569359	+	0.793015i
$890$			6.17209i			0.206889i
$891$		0			0
$892$	15.4192	+	8.90226i	0.516272	+	0.298070i
$893$	0.177270	+	0.102347i	0.00593211	+	0.00342491i
$894$		0			0
$895$		−	0.481846i		−	0.0161064i
$896$	1.48356	+	2.19067i	0.0495624	+	0.0731852i
$897$		0			0
$898$	−6.29461	−	10.9026i	−0.210054	−	0.363824i
$899$	−3.68608	+	6.38447i	−0.122938	+	0.212934i
$900$		0			0
$901$	1.48759	−	0.858860i	0.0495588	−	0.0286128i
$902$	−18.5945			−0.619129
$903$		0			0
$904$	−13.5546			−0.450819
$905$	−2.12069	+	1.22438i	−0.0704941	+	0.0406998i
$906$		0			0
$907$	8.10243	−	14.0338i	0.269037	−	0.465985i	−0.699577	−	0.714558i	$-0.746628\pi$
$907$	8.10243	−	14.0338i	0.269037	−	0.465985i	0.968613	+	0.248572i	$0.0799614\pi$
$908$	0.856140	+	1.48288i	0.0284120	+	0.0492110i
$909$		0			0
$910$	−9.35835	−	4.54284i	−0.310226	−	0.150594i
$911$		−	21.4586i		−	0.710955i	−0.934685	−	0.355477i	$-0.884318\pi$
$911$		−	21.4586i		−	0.710955i	0.934685	−	0.355477i	$-0.115682\pi$
$912$		0			0
$913$	26.4076	+	15.2465i	0.873965	+	0.504584i
$914$	−1.87783	−	1.08417i	−0.0621133	−	0.0358611i
$915$		0			0
$916$		−	6.07536i		−	0.200736i
$917$	−27.9988	+	18.9613i	−0.924603	+	0.626159i
$918$		0			0
$919$	29.5164	+	51.1240i	0.973657	+	1.68642i	0.684297	+	0.729203i	$0.260109\pi$
$919$	29.5164	+	51.1240i	0.973657	+	1.68642i	0.289360	+	0.957220i	$0.406558\pi$
$920$	−1.86603	+	3.23205i	−0.0615210	+	0.106558i
$921$		0			0
$922$	−29.7074	+	17.1516i	−0.978362	+	0.564857i
$923$	−7.60521			−0.250328
$924$		0			0
$925$	−7.93185			−0.260798
$926$	−24.4335	+	14.1067i	−0.802933	+	0.463574i
$927$		0			0
$928$	−4.44949	+	7.70674i	−0.146062	+	0.252986i
$929$	−12.3197	−	21.3383i	−0.404195	−	0.700087i	0.590032	−	0.807380i	$-0.299115\pi$
$929$	−12.3197	−	21.3383i	−0.404195	−	0.700087i	−0.994227	+	0.107293i	$0.965782\pi$
$930$		0			0
$931$	−0.194019	+	0.152750i	−0.00635872	+	0.00500619i
$932$		−	7.12576i		−	0.233412i
$933$		0			0
$934$	3.64324	+	2.10342i	0.119210	+	0.0688262i
$935$	1.01967	+	0.588706i	0.0333467	+	0.0192527i
$936$		0			0
$937$		−	52.5496i		−	1.71672i	−0.513048	−	0.858360i	$-0.671484\pi$
$937$		−	52.5496i		−	1.71672i	0.513048	−	0.858360i	$-0.328516\pi$
$938$	−33.0379	+	2.37202i	−1.07873	+	0.0774491i
$939$		0			0
$940$	−2.90130	−	5.02520i	−0.0946300	−	0.163904i
$941$	0.752551	−	1.30346i	0.0245325	−	0.0424915i	−0.853499	−	0.521095i	$-0.825524\pi$
$941$	0.752551	−	1.30346i	0.0245325	−	0.0424915i	0.878031	+	0.478604i	$0.158857\pi$
$942$		0			0
$943$	20.3968	−	11.7761i	0.664211	−	0.383482i
$944$	5.57045			0.181303
$945$		0			0
$946$	−8.94333			−0.290773
$947$	−9.84136	+	5.68191i	−0.319801	+	0.184637i	−0.651304	−	0.758817i	$-0.725778\pi$
$947$	−9.84136	+	5.68191i	−0.319801	+	0.184637i	0.331503	+	0.943454i	$0.392444\pi$
$948$		0			0
$949$	0.674599	−	1.16844i	0.0218984	−	0.0379292i
$950$	−0.0176381	−	0.0305501i	−0.000572255	−	0.000991175i
$951$		0			0
$952$	−0.461698	+	0.951108i	−0.0149637	+	0.0308256i
$953$			21.9184i			0.710006i	0.934865	+	0.355003i	$0.115520\pi$
$953$			21.9184i			0.710006i	−0.934865	+	0.355003i	$0.884480\pi$
$954$		0			0
$955$	3.89241	+	2.24728i	0.125955	+	0.0727204i
$956$	16.2114	+	9.35968i	0.524316	+	0.302714i
$957$		0			0
$958$			14.7194i			0.475561i
$959$	−6.37842	+	13.1397i	−0.205970	+	0.424303i
$960$		0			0
$961$	−15.1569	−	26.2524i	−0.488931	−	0.846853i
$962$	15.5934	−	27.0086i	0.502752	−	0.870793i
$963$		0			0
$964$	7.68036	−	4.43426i	0.247368	−	0.142818i
$965$	−12.5699			−0.404640
$966$		0			0
$967$	21.6634			0.696649			0.348324	−	0.937374i	$-0.386751\pi$
$967$	21.6634			0.696649			0.348324	+	0.937374i	$0.386751\pi$
$968$	2.00775	−	1.15918i	0.0645316	−	0.0372573i
$969$		0			0
$970$	−7.81722	+	13.5398i	−0.250996	+	0.434737i
$971$	0.0858379	+	0.148676i	0.00275467	+	0.00477123i	0.867399	−	0.497612i	$-0.165790\pi$
$971$	0.0858379	+	0.148676i	0.00275467	+	0.00477123i	−0.864645	+	0.502384i	$0.832456\pi$
$972$		0			0
$973$	57.6536	−	4.13934i	1.84829	−	0.132701i
$974$			1.87757i			0.0601612i
$975$		0			0
$976$	9.97710	+	5.76028i	0.319359	+	0.184382i
$977$	−9.72792	−	5.61642i	−0.311224	−	0.179685i	0.336250	−	0.941773i	$-0.390841\pi$
$977$	−9.72792	−	5.61642i	−0.311224	−	0.179685i	−0.647474	+	0.762088i	$0.724175\pi$
$978$		0			0
$979$		−	18.1858i		−	0.581222i
$980$	6.92820	−	1.00000i	0.221313	−	0.0319438i
$981$		0			0
$982$	−5.21405	−	9.03100i	−0.166387	−	0.288191i
$983$	13.3960	−	23.2026i	0.427267	−	0.740048i	−0.569362	−	0.822087i	$-0.692810\pi$
$983$	13.3960	−	23.2026i	0.427267	−	0.740048i	0.996629	+	0.0820385i	$0.0261430\pi$
$984$		0			0
$985$	−11.5829	+	6.68740i	−0.369063	+	0.213078i
$986$	−3.55605			−0.113248
$987$		0			0
$988$	0.138701			0.00441266
$989$	9.81017	−	5.66390i	0.311945	−	0.180102i
$990$		0			0
$991$	−6.99635	+	12.1180i	−0.222246	+	0.384942i	−0.955490	−	0.295024i	$-0.904672\pi$
$991$	−6.99635	+	12.1180i	−0.222246	+	0.384942i	0.733243	+	0.679966i	$0.238006\pi$
$992$	0.414214	+	0.717439i	0.0131513	+	0.0227787i
$993$		0			0
$994$	4.23732	−	2.86959i	0.134400	−	0.0910179i
$995$			27.1550i			0.860871i
$996$		0			0
$997$	34.2497	+	19.7740i	1.08470	+	0.626250i	0.932160	−	0.362047i	$-0.117922\pi$
$997$	34.2497	+	19.7740i	1.08470	+	0.626250i	0.152538	+	0.988298i	$0.451255\pi$
$998$	−32.7050	−	18.8822i	−1.03526	−	0.597707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.be.a.521.2	yes	8
3.2	odd	2		630.2.be.b.521.4	yes	8
5.2	odd	4		3150.2.bp.a.899.1		8
5.3	odd	4		3150.2.bp.d.899.4		8
5.4	even	2		3150.2.bf.b.1151.3		8
7.3	odd	6		4410.2.b.b.881.3		8
7.4	even	3		4410.2.b.e.881.3		8
7.5	odd	6		630.2.be.b.341.4	yes	8
15.2	even	4		3150.2.bp.f.899.1		8
15.8	even	4		3150.2.bp.c.899.4		8
15.14	odd	2		3150.2.bf.c.1151.1		8
21.5	even	6	inner	630.2.be.a.341.2	✓	8
21.11	odd	6		4410.2.b.b.881.6		8
21.17	even	6		4410.2.b.e.881.6		8
35.12	even	12		3150.2.bp.c.1349.4		8
35.19	odd	6		3150.2.bf.c.1601.1		8
35.33	even	12		3150.2.bp.f.1349.1		8
105.47	odd	12		3150.2.bp.d.1349.4		8
105.68	odd	12		3150.2.bp.a.1349.1		8
105.89	even	6		3150.2.bf.b.1601.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.2	✓	8	21.5	even	6	inner
630.2.be.a.521.2	yes	8	1.1	even	1	trivial
630.2.be.b.341.4	yes	8	7.5	odd	6
630.2.be.b.521.4	yes	8	3.2	odd	2
3150.2.bf.b.1151.3		8	5.4	even	2
3150.2.bf.b.1601.3		8	105.89	even	6
3150.2.bf.c.1151.1		8	15.14	odd	2
3150.2.bf.c.1601.1		8	35.19	odd	6
3150.2.bp.a.899.1		8	5.2	odd	4
3150.2.bp.a.1349.1		8	105.68	odd	12
3150.2.bp.c.899.4		8	15.8	even	4
3150.2.bp.c.1349.4		8	35.12	even	12
3150.2.bp.d.899.4		8	5.3	odd	4
3150.2.bp.d.1349.4		8	105.47	odd	12
3150.2.bp.f.899.1		8	15.2	even	4
3150.2.bp.f.1349.1		8	35.33	even	12
4410.2.b.b.881.3		8	7.3	odd	6
4410.2.b.b.881.6		8	21.11	odd	6
4410.2.b.e.881.3		8	7.4	even	3
4410.2.b.e.881.6		8	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.189469 + 2.63896i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.189469 + 2.63896i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +(-2.55171 - 1.47323i) q^{11} +3.93185i q^{13} +(-1.48356 - 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.199801 - 0.346065i) q^{17} +(0.0305501 - 0.0176381i) q^{19} -1.00000 q^{20} +2.94646 q^{22} +(-3.23205 + 1.86603i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.96593 - 3.40508i) q^{26} +(2.38014 + 1.15539i) q^{28} +8.89898i q^{29} +(0.717439 + 0.414214i) q^{31} +(0.866025 + 0.500000i) q^{32} +0.399602i q^{34} +(2.19067 - 1.48356i) q^{35} +(3.96593 + 6.86919i) q^{37} +(-0.0176381 + 0.0305501i) q^{38} +(0.866025 - 0.500000i) q^{40} -6.31079 q^{41} -3.03528 q^{43} +(-2.55171 + 1.47323i) q^{44} +(1.86603 - 3.23205i) q^{46} +(2.90130 + 5.02520i) q^{47} +(-6.92820 + 1.00000i) q^{49} -1.00000i q^{50} +(3.40508 + 1.96593i) q^{52} +(3.72268 + 2.14929i) q^{53} +2.94646i q^{55} +(-2.63896 + 0.189469i) q^{56} +(-4.44949 - 7.70674i) q^{58} +(-2.78522 + 4.82415i) q^{59} +(-9.97710 + 5.76028i) q^{61} -0.828427 q^{62} -1.00000 q^{64} +(3.40508 - 1.96593i) q^{65} +(6.25966 - 10.8420i) q^{67} +(-0.199801 - 0.346065i) q^{68} +(-1.15539 + 2.38014i) q^{70} +1.93426i q^{71} +(-0.297173 - 0.171573i) q^{73} +(-6.86919 - 3.96593i) q^{74} -0.0352762i q^{76} +(3.40433 - 7.01299i) q^{77} +(-4.15331 - 7.19375i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.46530 - 3.15539i) q^{82} -10.3490 q^{83} -0.399602 q^{85} +(2.62863 - 1.51764i) q^{86} +(1.47323 - 2.55171i) q^{88} +(3.08604 + 5.34519i) q^{89} +(-10.3760 + 0.744963i) q^{91} +3.73205i q^{92} +(-5.02520 - 2.90130i) q^{94} +(-0.0305501 - 0.0176381i) q^{95} +15.6344i q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^5	\( 8 q + 4 q^{4} - 4 q^{5} - 24 q^{11} - 4 q^{16} - 8 q^{20} - 12 q^{23} - 4 q^{25} - 8 q^{26} + 24 q^{37} + 4 q^{38} - 32 q^{41} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{47} - 24 q^{53} - 16 q^{58} + 24 q^{59} + 16 q^{62} - 8 q^{64} - 24 q^{67} + 16 q^{77} - 24 q^{79} - 4 q^{80} + 16 q^{83} + 16 q^{89} - 20 q^{91} - 12 q^{94} + 44 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^5 - 24 * q^11 - 4 * q^16 - 8 * q^20 - 12 * q^23 - 4 * q^25 - 8 * q^26 + 24 * q^37 + 4 * q^38 - 32 * q^41 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^47 - 24 * q^53 - 16 * q^58 + 24 * q^59 + 16 * q^62 - 8 * q^64 - 24 * q^67 + 16 * q^77 - 24 * q^79 - 4 * q^80 + 16 * q^83 + 16 * q^89 - 20 * q^91 - 12 * q^94 + 44 * q^98

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