LMFDB - Embedded newform 3150.2.bp.d.899.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("3150.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bp (of order $6$, degree $2$, not 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:	$25.1528766367$
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:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3150.899
Dual form			3150.2.bp.d.1349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.189469 + 2.63896i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.189469 + 2.63896i) q^{7} -1.00000 q^{8} +(-1.32697 - 0.766125i) q^{11} -1.48236 q^{13} +(-2.19067 + 1.48356i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.10342 + 1.21441i) q^{17} +(-4.21209 + 2.43185i) q^{19} -1.53225i q^{22} +(-0.133975 - 0.232051i) q^{23} +(-0.741181 - 1.28376i) q^{26} +(-2.38014 - 1.15539i) q^{28} -0.898979i q^{29} +(-0.717439 - 0.414214i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.42883i q^{34} +(-4.74786 + 2.74118i) q^{37} +(-4.21209 - 2.43185i) q^{38} -8.76028 q^{41} -1.86370i q^{43} +(1.32697 - 0.766125i) q^{44} +(0.133975 - 0.232051i) q^{46} +(6.46008 - 3.72973i) q^{47} +(-6.92820 + 1.00000i) q^{49} +(0.741181 - 1.28376i) q^{52} +(1.73508 - 3.00524i) q^{53} +(-0.189469 - 2.63896i) q^{56} +(0.778539 - 0.449490i) q^{58} +(-3.12837 + 5.41849i) q^{59} +(5.73445 - 3.31079i) q^{61} -0.828427i q^{62} +1.00000 q^{64} +(-13.8859 - 8.01702i) q^{67} +(-2.10342 + 1.21441i) q^{68} +12.7627i q^{71} +(0.171573 - 0.297173i) q^{73} +(-4.74786 - 2.74118i) q^{74} -4.86370i q^{76} +(1.77035 - 3.64697i) q^{77} +(-5.22438 - 9.04889i) q^{79} +(-4.38014 - 7.58662i) q^{82} +5.45001i q^{83} +(1.61401 - 0.931852i) q^{86} +(1.32697 + 0.766125i) q^{88} +(-7.98502 - 13.8305i) q^{89} +(-0.280861 - 3.91189i) q^{91} +0.267949 q^{92} +(6.46008 + 3.72973i) q^{94} -14.9481 q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 24 q^{11} - 16 q^{13} - 4 q^{16} + 24 q^{17} - 8 q^{23} - 8 q^{26} + 4 q^{32} - 32 q^{41} + 24 q^{44} + 8 q^{46} + 12 q^{47} + 8 q^{52} + 4 q^{53} - 24 q^{59} + 8 q^{64} - 48 q^{67} - 24 q^{68} + 24 q^{73} - 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} - 16 q^{89} - 20 q^{91} + 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 24 * q^11 - 16 * q^13 - 4 * q^16 + 24 * q^17 - 8 * q^23 - 8 * q^26 + 4 * q^32 - 32 * q^41 + 24 * q^44 + 8 * q^46 + 12 * q^47 + 8 * q^52 + 4 * q^53 - 24 * q^59 + 8 * q^64 - 48 * q^67 - 24 * q^68 + 24 * q^73 - 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 - 16 * q^89 - 20 * q^91 + 16 * q^92 + 12 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.189469	+	2.63896i	0.0716124	+	0.997433i
$7$	0.189469	+	2.63896i	0.0716124	+	0.997433i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	−1.32697	−	0.766125i	−0.400096	−	0.230995i	0.286430	−	0.958101i	$-0.407532\pi$
$11$	−1.32697	−	0.766125i	−0.400096	−	0.230995i	−0.686525	+	0.727106i	$0.740865\pi$
$12$		0			0
$13$	−1.48236			−0.411133			−0.205567	−	0.978643i	$-0.565904\pi$
$13$	−1.48236			−0.411133			−0.205567	+	0.978643i	$0.565904\pi$
$14$	−2.19067	+	1.48356i	−0.585481	+	0.396499i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.10342	+	1.21441i	0.510155	+	0.294538i	0.732898	−	0.680339i	$-0.238167\pi$
$17$	2.10342	+	1.21441i	0.510155	+	0.294538i	−0.222742	+	0.974877i	$0.571501\pi$
$18$		0			0
$19$	−4.21209	+	2.43185i	−0.966320	+	0.557905i	−0.898112	−	0.439766i	$-0.855061\pi$
$19$	−4.21209	+	2.43185i	−0.966320	+	0.557905i	−0.0682075	+	0.997671i	$0.521728\pi$
$20$		0			0
$21$		0			0
$22$		−	1.53225i		−	0.326677i
$23$	−0.133975	−	0.232051i	−0.0279356	−	0.0483859i	0.851720	−	0.523998i	$-0.175560\pi$
$23$	−0.133975	−	0.232051i	−0.0279356	−	0.0483859i	−0.879655	+	0.475612i	$0.842227\pi$
$24$		0			0
$25$		0			0
$26$	−0.741181	−	1.28376i	−0.145358	−	0.251767i
$27$		0			0
$28$	−2.38014	−	1.15539i	−0.449804	−	0.218349i
$29$		−	0.898979i		−	0.166936i	−0.996510	−	0.0834681i	$-0.973400\pi$
$29$		−	0.898979i		−	0.166936i	0.996510	−	0.0834681i	$-0.0265997\pi$
$30$		0			0
$31$	−0.717439	−	0.414214i	−0.128856	−	0.0743950i	0.434187	−	0.900823i	$-0.357036\pi$
$31$	−0.717439	−	0.414214i	−0.128856	−	0.0743950i	−0.563042	+	0.826428i	$0.690369\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$			2.42883i			0.416540i
$35$		0			0
$36$		0			0
$37$	−4.74786	+	2.74118i	−0.780544	+	0.450647i	−0.836623	−	0.547779i	$-0.815473\pi$
$37$	−4.74786	+	2.74118i	−0.780544	+	0.450647i	0.0560790	+	0.998426i	$0.482140\pi$
$38$	−4.21209	−	2.43185i	−0.683291	−	0.394498i
$39$		0			0
$40$		0			0
$41$	−8.76028			−1.36813			−0.684063	−	0.729423i	$-0.739789\pi$
$41$	−8.76028			−1.36813			−0.684063	+	0.729423i	$0.739789\pi$
$42$		0			0
$43$		−	1.86370i		−	0.284212i	−0.989851	−	0.142106i	$-0.954613\pi$
$43$		−	1.86370i		−	0.284212i	0.989851	−	0.142106i	$-0.0453874\pi$
$44$	1.32697	−	0.766125i	0.200048	−	0.115498i
$45$		0			0
$46$	0.133975	−	0.232051i	0.0197535	−	0.0342140i
$47$	6.46008	−	3.72973i	0.942299	−	0.544037i	0.0516191	−	0.998667i	$-0.483562\pi$
$47$	6.46008	−	3.72973i	0.942299	−	0.544037i	0.890680	+	0.454630i	$0.150229\pi$
$48$		0			0
$49$	−6.92820	+	1.00000i	−0.989743	+	0.142857i
$50$		0			0
$51$		0			0
$52$	0.741181	−	1.28376i	0.102783	−	0.178026i
$53$	1.73508	−	3.00524i	0.238331	−	0.412802i	−0.721904	−	0.691993i	$-0.756733\pi$
$53$	1.73508	−	3.00524i	0.238331	−	0.412802i	0.960236	+	0.279191i	$0.0900663\pi$
$54$		0			0
$55$		0			0
$56$	−0.189469	−	2.63896i	−0.0253188	−	0.352646i
$57$		0			0
$58$	0.778539	−	0.449490i	0.102227	−	0.0590209i
$59$	−3.12837	+	5.41849i	−0.407279	+	0.705428i	−0.994584	−	0.103938i	$-0.966856\pi$
$59$	−3.12837	+	5.41849i	−0.407279	+	0.705428i	0.587305	+	0.809366i	$0.300189\pi$
$60$		0			0
$61$	5.73445	−	3.31079i	0.734222	−	0.423903i	−0.0857429	−	0.996317i	$-0.527326\pi$
$61$	5.73445	−	3.31079i	0.734222	−	0.423903i	0.819965	+	0.572414i	$0.193993\pi$
$62$		−	0.828427i		−	0.105210i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−13.8859	−	8.01702i	−1.69643	−	0.979434i	−0.949097	−	0.314985i	$-0.898000\pi$
$67$	−13.8859	−	8.01702i	−1.69643	−	0.979434i	−0.747334	−	0.664449i	$-0.768666\pi$
$68$	−2.10342	+	1.21441i	−0.255078	+	0.147269i
$69$		0			0
$70$		0			0
$71$			12.7627i			1.51465i	0.653037	+	0.757326i	$0.273495\pi$
$71$			12.7627i			1.51465i	−0.653037	+	0.757326i	$0.726505\pi$
$72$		0			0
$73$	0.171573	−	0.297173i	0.0200811	−	0.0347815i	−0.855810	−	0.517290i	$-0.826941\pi$
$73$	0.171573	−	0.297173i	0.0200811	−	0.0347815i	0.875891	+	0.482508i	$0.160274\pi$
$74$	−4.74786	−	2.74118i	−0.551928	−	0.318656i
$75$		0			0
$76$		−	4.86370i		−	0.557905i
$77$	1.77035	−	3.64697i	0.201750	−	0.415611i
$78$		0			0
$79$	−5.22438	−	9.04889i	−0.587789	−	1.01808i	−0.994521	−	0.104533i	$-0.966665\pi$
$79$	−5.22438	−	9.04889i	−0.587789	−	1.01808i	0.406733	−	0.913547i	$-0.366668\pi$
$80$		0			0
$81$		0			0
$82$	−4.38014	−	7.58662i	−0.483705	−	0.837802i
$83$			5.45001i			0.598216i	0.954219	+	0.299108i	$0.0966891\pi$
$83$			5.45001i			0.598216i	−0.954219	+	0.299108i	$0.903311\pi$
$84$		0			0
$85$		0			0
$86$	1.61401	−	0.931852i	0.174044	−	0.100484i
$87$		0			0
$88$	1.32697	+	0.766125i	0.141455	+	0.0816692i
$89$	−7.98502	−	13.8305i	−0.846411	−	1.46603i	−0.884390	−	0.466748i	$-0.845426\pi$
$89$	−7.98502	−	13.8305i	−0.846411	−	1.46603i	0.0379795	−	0.999279i	$-0.487908\pi$
$90$		0			0
$91$	−0.280861	−	3.91189i	−0.0294423	−	0.410078i
$92$	0.267949			0.0279356
$93$		0			0
$94$	6.46008	+	3.72973i	0.666306	+	0.384692i
$95$		0			0
$96$		0			0
$97$	−14.9481			−1.51775			−0.758877	−	0.651234i	$-0.774252\pi$
$97$	−14.9481			−1.51775			−0.758877	+	0.651234i	$0.774252\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$		0			0
$100$		0			0
$101$	−1.36773	+	2.36897i	−0.136094	+	0.235721i	−0.926015	−	0.377487i	$-0.876788\pi$
$101$	−1.36773	+	2.36897i	−0.136094	+	0.235721i	0.789921	+	0.613209i	$0.210122\pi$
$102$		0			0
$103$	3.08845	+	5.34935i	0.304314	+	0.527087i	0.977108	−	0.212742i	$-0.0682395\pi$
$103$	3.08845	+	5.34935i	0.304314	+	0.527087i	−0.672794	+	0.739829i	$0.734906\pi$
$104$	1.48236			0.145358
$105$		0			0
$106$	3.47015			0.337051
$107$	2.28497	+	3.95768i	0.220896	+	0.382603i	0.955080	−	0.296347i	$-0.0957686\pi$
$107$	2.28497	+	3.95768i	0.220896	+	0.382603i	−0.734184	+	0.678950i	$0.762435\pi$
$108$		0			0
$109$	−2.97934	+	5.16036i	−0.285369	+	0.494273i	−0.972699	−	0.232072i	$-0.925449\pi$
$109$	−2.97934	+	5.16036i	−0.285369	+	0.494273i	0.687330	+	0.726345i	$0.258783\pi$
$110$		0			0
$111$		0			0
$112$	2.19067	−	1.48356i	0.206999	−	0.140184i
$113$	19.8977			1.87182			0.935911	−	0.352237i	$-0.114579\pi$
$113$	19.8977			1.87182			0.935911	+	0.352237i	$0.114579\pi$
$114$		0			0
$115$		0			0
$116$	0.778539	+	0.449490i	0.0722855	+	0.0417341i
$117$		0			0
$118$	−6.25674			−0.575979
$119$	−2.80625	+	5.78094i	−0.257249	+	0.529938i
$120$		0			0
$121$	−4.32611	−	7.49303i	−0.393282	−	0.681185i
$122$	5.73445	+	3.31079i	0.519173	+	0.299745i
$123$		0			0
$124$	0.717439	−	0.414214i	0.0644279	−	0.0371975i
$125$		0			0
$126$		0			0
$127$		−	21.2025i		−	1.88142i	−0.339219	−	0.940708i	$-0.610163\pi$
$127$		−	21.2025i		−	1.88142i	0.339219	−	0.940708i	$-0.389837\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	3.73085	+	6.46202i	0.325966	+	0.564589i	0.981707	−	0.190396i	$-0.0609772\pi$
$131$	3.73085	+	6.46202i	0.325966	+	0.564589i	−0.655742	+	0.754985i	$0.727644\pi$
$132$		0			0
$133$	−7.21561	−	10.6548i	−0.625673	−	0.923886i
$134$		−	16.0340i		−	1.38513i
$135$		0			0
$136$	−2.10342	−	1.21441i	−0.180367	−	0.104135i
$137$	0.310789	−	0.538302i	0.0265525	−	0.0459903i	−0.852444	−	0.522819i	$-0.824880\pi$
$137$	0.310789	−	0.538302i	0.0265525	−	0.0459903i	0.878996	+	0.476829i	$0.158214\pi$
$138$		0			0
$139$			18.5334i			1.57198i	0.618237	+	0.785992i	$0.287847\pi$
$139$			18.5334i			1.57198i	−0.618237	+	0.785992i	$0.712153\pi$
$140$		0			0
$141$		0			0
$142$	−11.0528	+	6.38134i	−0.927531	+	0.535510i
$143$	1.96705	+	1.13567i	0.164493	+	0.0949699i
$144$		0			0
$145$		0			0
$146$	0.343146			0.0283989
$147$		0			0
$148$		−	5.48236i		−	0.450647i
$149$	−12.1100	+	6.99171i	−0.992089	+	0.572783i	−0.905898	−	0.423496i	$-0.860803\pi$
$149$	−12.1100	+	6.99171i	−0.992089	+	0.572783i	−0.0861911	+	0.996279i	$0.527470\pi$
$150$		0			0
$151$	−9.83839	+	17.0406i	−0.800637	+	1.38674i	0.118560	+	0.992947i	$0.462172\pi$
$151$	−9.83839	+	17.0406i	−0.800637	+	1.38674i	−0.919197	+	0.393797i	$0.871161\pi$
$152$	4.21209	−	2.43185i	0.341646	−	0.197249i
$153$		0			0
$154$	4.04354	−	0.290313i	0.325838	−	0.0233941i
$155$		0			0
$156$		0			0
$157$	4.53005	−	7.84628i	0.361538	−	0.626201i	−0.626677	−	0.779279i	$-0.715585\pi$
$157$	4.53005	−	7.84628i	0.361538	−	0.626201i	0.988214	+	0.153078i	$0.0489186\pi$
$158$	5.22438	−	9.04889i	0.415629	−	0.719891i
$159$		0			0
$160$		0			0
$161$	0.586988	−	0.397520i	0.0462612	−	0.0313289i
$162$		0			0
$163$	−10.2368	+	5.91019i	−0.801804	+	0.462922i	−0.844102	−	0.536183i	$-0.819866\pi$
$163$	−10.2368	+	5.91019i	−0.801804	+	0.462922i	0.0422974	+	0.999105i	$0.486532\pi$
$164$	4.38014	−	7.58662i	0.342031	−	0.592416i
$165$		0			0
$166$	−4.71984	+	2.72500i	−0.366331	+	0.211501i
$167$		−	15.7778i		−	1.22092i	−0.792046	−	0.610462i	$-0.790984\pi$
$167$		−	15.7778i		−	1.22092i	0.792046	−	0.610462i	$-0.209016\pi$
$168$		0			0
$169$	−10.8026			−0.830969
$170$		0			0
$171$		0			0
$172$	1.61401	+	0.931852i	0.123067	+	0.0710530i
$173$	17.5129	−	10.1111i	1.33148	−	0.768730i	0.345954	−	0.938252i	$-0.387555\pi$
$173$	17.5129	−	10.1111i	1.33148	−	0.768730i	0.985527	+	0.169521i	$0.0542221\pi$
$174$		0			0
$175$		0			0
$176$			1.53225i			0.115498i
$177$		0			0
$178$	7.98502	−	13.8305i	0.598503	−	1.03664i
$179$	−5.94667	−	3.43331i	−0.444475	−	0.256618i	0.261019	−	0.965334i	$-0.415941\pi$
$179$	−5.94667	−	3.43331i	−0.444475	−	0.256618i	−0.705494	+	0.708716i	$0.749275\pi$
$180$		0			0
$181$		−	16.3066i		−	1.21206i	−0.795441	−	0.606031i	$-0.792761\pi$
$181$		−	16.3066i		−	1.21206i	0.795441	−	0.606031i	$-0.207239\pi$
$182$	3.24737	−	2.19918i	0.240711	−	0.163014i
$183$		0			0
$184$	0.133975	+	0.232051i	0.00987674	+	0.0171070i
$185$		0			0
$186$		0			0
$187$	−1.86078	−	3.22297i	−0.136074	−	0.235687i
$188$			7.45946i			0.544037i
$189$		0			0
$190$		0			0
$191$	14.8630	−	8.58114i	1.07545	−	0.620910i	0.145782	−	0.989317i	$-0.453430\pi$
$191$	14.8630	−	8.58114i	1.07545	−	0.620910i	0.929665	+	0.368407i	$0.120097\pi$
$192$		0			0
$193$	7.84204	+	4.52761i	0.564483	+	0.325904i	0.754943	−	0.655791i	$-0.227665\pi$
$193$	7.84204	+	4.52761i	0.564483	+	0.325904i	−0.190460	+	0.981695i	$0.560998\pi$
$194$	−7.47407	−	12.9455i	−0.536607	−	0.929430i
$195$		0			0
$196$	2.59808	−	6.50000i	0.185577	−	0.464286i
$197$	−21.7379			−1.54876			−0.774380	−	0.632720i	$-0.781938\pi$
$197$	−21.7379			−1.54876			−0.774380	+	0.632720i	$0.781938\pi$
$198$		0			0
$199$	7.21101	+	4.16328i	0.511175	+	0.295127i	0.733317	−	0.679887i	$-0.237971\pi$
$199$	7.21101	+	4.16328i	0.511175	+	0.295127i	−0.222141	+	0.975014i	$0.571305\pi$
$200$		0			0
$201$		0			0
$202$	−2.73545			−0.192466
$203$	2.37237	−	0.170328i	0.166508	−	0.0119547i
$204$		0			0
$205$		0			0
$206$	−3.08845	+	5.34935i	−0.215182	+	0.372707i
$207$		0			0
$208$	0.741181	+	1.28376i	0.0513917	+	0.0890130i
$209$	7.45241			0.515494
$210$		0			0
$211$	−19.9330			−1.37225			−0.686123	−	0.727486i	$-0.740689\pi$
$211$	−19.9330			−1.37225			−0.686123	+	0.727486i	$0.740689\pi$
$212$	1.73508	+	3.00524i	0.119166	+	0.206401i
$213$		0			0
$214$	−2.28497	+	3.95768i	−0.156197	+	0.270541i
$215$		0			0
$216$		0			0
$217$	0.957160	−	1.97177i	0.0649763	−	0.133853i
$218$	−5.95867			−0.403572
$219$		0			0
$220$		0			0
$221$	−3.11804	−	1.80020i	−0.209742	−	0.121094i
$222$		0			0
$223$	−7.16604			−0.479873			−0.239937	−	0.970789i	$-0.577127\pi$
$223$	−7.16604			−0.479873			−0.239937	+	0.970789i	$0.577127\pi$
$224$	2.38014	+	1.15539i	0.159030	+	0.0771980i
$225$		0			0
$226$	9.94887	+	17.2319i	0.661789	+	1.14625i
$227$	13.7303	+	7.92721i	0.911314	+	0.526147i	0.880854	−	0.473389i	$-0.156969\pi$
$227$	13.7303	+	7.92721i	0.911314	+	0.526147i	0.0304601	+	0.999536i	$0.490303\pi$
$228$		0			0
$229$	−24.4371	+	14.1087i	−1.61485	+	0.932332i	−0.626622	+	0.779323i	$0.715563\pi$
$229$	−24.4371	+	14.1087i	−1.61485	+	0.932332i	−0.988225	+	0.153009i	$0.951104\pi$
$230$		0			0
$231$		0			0
$232$			0.898979i			0.0590209i
$233$	−12.1487	−	21.0421i	−0.795886	−	1.37851i	−0.922275	−	0.386534i	$-0.873672\pi$
$233$	−12.1487	−	21.0421i	−0.795886	−	1.37851i	0.126390	−	0.991981i	$-0.459661\pi$
$234$		0			0
$235$		0			0
$236$	−3.12837	−	5.41849i	−0.203639	−	0.352714i
$237$		0			0
$238$	−6.40957	+	0.460186i	−0.415471	+	0.0298295i
$239$			19.9081i			1.28774i	0.765133	+	0.643872i	$0.222673\pi$
$239$			19.9081i			1.28774i	−0.765133	+	0.643872i	$0.777327\pi$
$240$		0			0
$241$	17.7755	+	10.2627i	1.14502	+	0.661078i	0.947669	−	0.319255i	$-0.103433\pi$
$241$	17.7755	+	10.2627i	1.14502	+	0.661078i	0.197351	+	0.980333i	$0.436766\pi$
$242$	4.32611	−	7.49303i	0.278093	−	0.481670i
$243$		0			0
$244$			6.62158i			0.423903i
$245$		0			0
$246$		0			0
$247$	6.24384	−	3.60488i	0.397286	−	0.229373i
$248$	0.717439	+	0.414214i	0.0455574	+	0.0263026i
$249$		0			0
$250$		0			0
$251$	−5.86787			−0.370376			−0.185188	−	0.982703i	$-0.559289\pi$
$251$	−5.86787			−0.370376			−0.185188	+	0.982703i	$0.559289\pi$
$252$		0			0
$253$			0.410565i			0.0258120i
$254$	18.3619	−	10.6012i	1.15213	−	0.665181i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.63519	−	3.83083i	0.413892	−	0.238961i	−0.278569	−	0.960416i	$-0.589860\pi$
$257$	6.63519	−	3.83083i	0.413892	−	0.238961i	0.692461	+	0.721456i	$0.256527\pi$
$258$		0			0
$259$	−8.13343	−	12.0100i	−0.505387	−	0.746268i
$260$		0			0
$261$		0			0
$262$	−3.73085	+	6.46202i	−0.230493	+	0.399225i
$263$	−4.23143	+	7.32905i	−0.260921	+	0.451929i	−0.966487	−	0.256716i	$-0.917360\pi$
$263$	−4.23143	+	7.32905i	−0.260921	+	0.451929i	0.705566	+	0.708644i	$0.250693\pi$
$264$		0			0
$265$		0			0
$266$	5.61950	−	11.5763i	0.344553	−	0.709788i
$267$		0			0
$268$	13.8859	−	8.01702i	0.848215	−	0.489717i
$269$	−8.52155	+	14.7598i	−0.519568	+	0.899919i	0.480173	+	0.877174i	$0.340574\pi$
$269$	−8.52155	+	14.7598i	−0.519568	+	0.899919i	−0.999741	+	0.0227449i	$0.992759\pi$
$270$		0			0
$271$	−9.12436	+	5.26795i	−0.554265	+	0.320005i	−0.750840	−	0.660484i	$-0.770351\pi$
$271$	−9.12436	+	5.26795i	−0.554265	+	0.320005i	0.196575	+	0.980489i	$0.437018\pi$
$272$		−	2.42883i		−	0.147269i
$273$		0			0
$274$	0.621578			0.0375509
$275$		0			0
$276$		0			0
$277$	7.00720	+	4.04561i	0.421022	+	0.243077i	0.695514	−	0.718512i	$-0.255177\pi$
$277$	7.00720	+	4.04561i	0.421022	+	0.243077i	−0.274493	+	0.961589i	$0.588510\pi$
$278$	−16.0504	+	9.26670i	−0.962639	+	0.555780i
$279$		0			0
$280$		0			0
$281$		−	11.1684i		−	0.666253i	−0.942882	−	0.333127i	$-0.891896\pi$
$281$		−	11.1684i		−	0.666253i	0.942882	−	0.333127i	$-0.108104\pi$
$282$		0			0
$283$	−3.60796	+	6.24917i	−0.214471	+	0.371475i	−0.953109	−	0.302628i	$-0.902136\pi$
$283$	−3.60796	+	6.24917i	−0.214471	+	0.371475i	0.738638	+	0.674103i	$0.235469\pi$
$284$	−11.0528	−	6.38134i	−0.655863	−	0.378663i
$285$		0			0
$286$			2.27135i			0.134308i
$287$	−1.65980	−	23.1180i	−0.0979748	−	1.36461i
$288$		0			0
$289$	−5.55040	−	9.61358i	−0.326494	−	0.565505i
$290$		0			0
$291$		0			0
$292$	0.171573	+	0.297173i	0.0100405	+	0.0173907i
$293$			18.2573i			1.06660i	0.845926	+	0.533300i	$0.179048\pi$
$293$			18.2573i			1.06660i	−0.845926	+	0.533300i	$0.820952\pi$
$294$		0			0
$295$		0			0
$296$	4.74786	−	2.74118i	0.275964	−	0.159328i
$297$		0			0
$298$	−12.1100	−	6.99171i	−0.701513	−	0.405019i
$299$	0.198599	+	0.343983i	0.0114853	+	0.0198931i
$300$		0			0
$301$	4.91824	−	0.353113i	0.283482	−	0.0203531i
$302$	−19.6768			−1.13227
$303$		0			0
$304$	4.21209	+	2.43185i	0.241580	+	0.139476i
$305$		0			0
$306$		0			0
$307$	3.42078			0.195234			0.0976172	−	0.995224i	$-0.468878\pi$
$307$	3.42078			0.195234			0.0976172	+	0.995224i	$0.468878\pi$
$308$	2.27319	+	3.35666i	0.129527	+	0.191263i
$309$		0			0
$310$		0			0
$311$	2.84544	−	4.92845i	0.161350	−	0.279467i	−0.774003	−	0.633182i	$-0.781748\pi$
$311$	2.84544	−	4.92845i	0.161350	−	0.279467i	0.935353	+	0.353715i	$0.115082\pi$
$312$		0			0
$313$	6.67335	+	11.5586i	0.377200	+	0.653330i	0.990654	−	0.136401i	$-0.0435535\pi$
$313$	6.67335	+	11.5586i	0.377200	+	0.653330i	−0.613453	+	0.789731i	$0.710220\pi$
$314$	9.06010			0.511291
$315$		0			0
$316$	10.4488			0.587789
$317$	6.26330	+	10.8484i	0.351782	+	0.609305i	0.986562	−	0.163389i	$-0.0522424\pi$
$317$	6.26330	+	10.8484i	0.351782	+	0.609305i	−0.634780	+	0.772693i	$0.718909\pi$
$318$		0			0
$319$	−0.688731	+	1.19292i	−0.0385615	+	0.0667905i
$320$		0			0
$321$		0			0
$322$	0.637756	+	0.309587i	0.0355408	+	0.0172526i
$323$	−11.8131			−0.657298
$324$		0			0
$325$		0			0
$326$	−10.2368	−	5.91019i	−0.566961	−	0.327335i
$327$		0			0
$328$	8.76028			0.483705
$329$	11.0666	+	16.3412i	0.610120	+	0.900920i
$330$		0			0
$331$	0.640916	+	1.11010i	0.0352279	+	0.0610166i	0.883102	−	0.469181i	$-0.155451\pi$
$331$	0.640916	+	1.11010i	0.0352279	+	0.0610166i	−0.847874	+	0.530198i	$0.822118\pi$
$332$	−4.71984	−	2.72500i	−0.259035	−	0.149554i
$333$		0			0
$334$	13.6640	−	7.88891i	0.747660	−	0.431662i
$335$		0			0
$336$		0			0
$337$		−	13.1058i		−	0.713920i	−0.934120	−	0.356960i	$-0.883813\pi$
$337$		−	13.1058i		−	0.713920i	0.934120	−	0.356960i	$-0.116187\pi$
$338$	−5.40130	−	9.35533i	−0.293792	−	0.508863i
$339$		0			0
$340$		0			0
$341$	0.634679	+	1.09930i	0.0343698	+	0.0595302i
$342$		0			0
$343$	−3.95164	−	18.0938i	−0.213368	−	0.976972i
$344$			1.86370i			0.100484i
$345$		0			0
$346$	17.5129	+	10.1111i	0.941499	+	0.543574i
$347$	7.14262	−	12.3714i	0.383436	−	0.664130i	−0.608115	−	0.793849i	$-0.708074\pi$
$347$	7.14262	−	12.3714i	0.383436	−	0.664130i	0.991551	+	0.129719i	$0.0414074\pi$
$348$		0			0
$349$			13.2713i			0.710399i	0.934791	+	0.355200i	$0.115587\pi$
$349$			13.2713i			0.710399i	−0.934791	+	0.355200i	$0.884413\pi$
$350$		0			0
$351$		0			0
$352$	−1.32697	+	0.766125i	−0.0707276	+	0.0408346i
$353$	28.2725	+	16.3232i	1.50480	+	0.868794i	0.999985	+	0.00556437i	$0.00177120\pi$
$353$	28.2725	+	16.3232i	1.50480	+	0.868794i	0.504811	+	0.863230i	$0.331562\pi$
$354$		0			0
$355$		0			0
$356$	15.9700			0.846411
$357$		0			0
$358$		−	6.86662i		−	0.362912i
$359$	5.40692	−	3.12168i	0.285366	−	0.164756i	−0.350484	−	0.936569i	$-0.613983\pi$
$359$	5.40692	−	3.12168i	0.285366	−	0.164756i	0.635850	+	0.771812i	$0.280650\pi$
$360$		0			0
$361$	2.32780	−	4.03188i	0.122516	−	0.212204i
$362$	14.1220	−	8.15331i	0.742233	−	0.428529i
$363$		0			0
$364$	3.52823	+	1.71271i	0.184929	+	0.0897705i
$365$		0			0
$366$		0			0
$367$	−6.29461	+	10.9026i	−0.328576	+	0.569110i	−0.982230	−	0.187684i	$-0.939902\pi$
$367$	−6.29461	+	10.9026i	−0.328576	+	0.569110i	0.653654	+	0.756794i	$0.273235\pi$
$368$	−0.133975	+	0.232051i	−0.00698391	+	0.0120965i
$369$		0			0
$370$		0			0
$371$	8.25945	+	4.00940i	0.428809	+	0.208158i
$372$		0			0
$373$	−31.1408	+	17.9791i	−1.61241	+	0.930924i	−0.623598	+	0.781745i	$0.714330\pi$
$373$	−31.1408	+	17.9791i	−1.61241	+	0.930924i	−0.988810	+	0.149179i	$0.952337\pi$
$374$	1.86078	−	3.22297i	0.0962188	−	0.166656i
$375$		0			0
$376$	−6.46008	+	3.72973i	−0.333153	+	0.192346i
$377$			1.33261i			0.0686331i
$378$		0			0
$379$	11.5899			0.595331			0.297666	−	0.954670i	$-0.403792\pi$
$379$	11.5899			0.595331			0.297666	+	0.954670i	$0.403792\pi$
$380$		0			0
$381$		0			0
$382$	14.8630	+	8.58114i	0.760456	+	0.439049i
$383$	−3.86897	+	2.23375i	−0.197695	+	0.114139i	−0.595580	−	0.803296i	$-0.703078\pi$
$383$	−3.86897	+	2.23375i	−0.197695	+	0.114139i	0.397885	+	0.917435i	$0.369744\pi$
$384$		0			0
$385$		0			0
$386$			9.05521i			0.460898i
$387$		0			0
$388$	7.47407	−	12.9455i	0.379438	−	0.657207i
$389$	−11.2197	−	6.47772i	−0.568863	−	0.328433i	0.187832	−	0.982201i	$-0.439854\pi$
$389$	−11.2197	−	6.47772i	−0.568863	−	0.328433i	−0.756695	+	0.653768i	$0.773187\pi$
$390$		0			0
$391$		−	0.650802i		−	0.0329125i
$392$	6.92820	−	1.00000i	0.349927	−	0.0505076i
$393$		0			0
$394$	−10.8689	−	18.8256i	−0.547570	−	0.948418i
$395$		0			0
$396$		0			0
$397$	4.63995	+	8.03664i	0.232873	+	0.403347i	0.958652	−	0.284580i	$-0.0918541\pi$
$397$	4.63995	+	8.03664i	0.232873	+	0.403347i	−0.725780	+	0.687927i	$0.758521\pi$
$398$			8.32656i			0.417373i
$399$		0			0
$400$		0			0
$401$	6.44260	−	3.71964i	0.321728	−	0.185750i	−0.330434	−	0.943829i	$-0.607195\pi$
$401$	6.44260	−	3.71964i	0.321728	−	0.185750i	0.652163	+	0.758079i	$0.273862\pi$
$402$		0			0
$403$	1.06350	+	0.614014i	0.0529769	+	0.0305862i
$404$	−1.36773	−	2.36897i	−0.0680469	−	0.117861i
$405$		0			0
$406$	1.33369	+	1.96937i	0.0661901	+	0.0977381i
$407$	8.40035			0.416390
$408$		0			0
$409$	13.8647	+	8.00481i	0.685567	+	0.395812i	0.801949	−	0.597392i	$-0.203796\pi$
$409$	13.8647	+	8.00481i	0.685567	+	0.395812i	−0.116382	+	0.993204i	$0.537130\pi$
$410$		0			0
$411$		0			0
$412$	−6.17690			−0.304314
$413$	−14.8919	−	7.22900i	−0.732783	−	0.355716i
$414$		0			0
$415$		0			0
$416$	−0.741181	+	1.28376i	−0.0363394	+	0.0629417i
$417$		0			0
$418$	3.72620	+	6.45398i	0.182255	+	0.315674i
$419$	28.4419			1.38948			0.694738	−	0.719263i	$-0.255520\pi$
$419$	28.4419			1.38948			0.694738	+	0.719263i	$0.255520\pi$
$420$		0			0
$421$	17.8345			0.869199			0.434600	−	0.900624i	$-0.356890\pi$
$421$	17.8345			0.869199			0.434600	+	0.900624i	$0.356890\pi$
$422$	−9.96651	−	17.2625i	−0.485162	−	0.840325i
$423$		0			0
$424$	−1.73508	+	3.00524i	−0.0842628	+	0.145947i
$425$		0			0
$426$		0			0
$427$	9.82353	+	14.5057i	0.475394	+	0.701980i
$428$	−4.56993			−0.220896
$429$		0			0
$430$		0			0
$431$	26.7539	+	15.4464i	1.28869	+	0.744025i	0.978420	−	0.206624i	$-0.0662477\pi$
$431$	26.7539	+	15.4464i	1.28869	+	0.744025i	0.310268	+	0.950649i	$0.399581\pi$
$432$		0			0
$433$	15.2207			0.731462			0.365731	−	0.930721i	$-0.380819\pi$
$433$	15.2207			0.731462			0.365731	+	0.930721i	$0.380819\pi$
$434$	2.18618	−	0.156961i	0.104940	−	0.00753437i
$435$		0			0
$436$	−2.97934	−	5.16036i	−0.142684	−	0.247136i
$437$	1.12863	+	0.651613i	0.0539895	+	0.0311709i
$438$		0			0
$439$	−12.4054	+	7.16228i	−0.592079	+	0.341837i	−0.765919	−	0.642937i	$-0.777716\pi$
$439$	−12.4054	+	7.16228i	−0.592079	+	0.341837i	0.173840	+	0.984774i	$0.444382\pi$
$440$		0			0
$441$		0			0
$442$		−	3.60040i		−	0.171253i
$443$	−2.57874	−	4.46651i	−0.122520	−	0.212210i	0.798241	−	0.602338i	$-0.205764\pi$
$443$	−2.57874	−	4.46651i	−0.122520	−	0.212210i	−0.920761	+	0.390128i	$0.872431\pi$
$444$		0			0
$445$		0			0
$446$	−3.58302	−	6.20597i	−0.169661	−	0.293861i
$447$		0			0
$448$	0.189469	+	2.63896i	0.00895155	+	0.124679i
$449$			19.9377i			0.940918i	0.882422	+	0.470459i	$0.155912\pi$
$449$			19.9377i			0.940918i	−0.882422	+	0.470459i	$0.844088\pi$
$450$		0			0
$451$	11.6246	+	6.71147i	0.547381	+	0.316031i
$452$	−9.94887	+	17.2319i	−0.467955	+	0.810522i
$453$		0			0
$454$			15.8544i			0.744085i
$455$		0			0
$456$		0			0
$457$	9.82065	−	5.66995i	0.459391	−	0.265229i	−0.252397	−	0.967624i	$-0.581219\pi$
$457$	9.82065	−	5.66995i	0.459391	−	0.265229i	0.711788	+	0.702394i	$0.247886\pi$
$458$	−24.4371	−	14.1087i	−1.14187	−	0.659258i
$459$		0			0
$460$		0			0
$461$	−2.01890			−0.0940298			−0.0470149	−	0.998894i	$-0.514971\pi$
$461$	−2.01890			−0.0940298			−0.0470149	+	0.998894i	$0.514971\pi$
$462$		0			0
$463$			27.2844i			1.26801i	0.773327	+	0.634007i	$0.218591\pi$
$463$			27.2844i			1.26801i	−0.773327	+	0.634007i	$0.781409\pi$
$464$	−0.778539	+	0.449490i	−0.0361428	+	0.0208670i
$465$		0			0
$466$	12.1487	−	21.0421i	0.562776	−	0.974757i
$467$	−0.599403	+	0.346065i	−0.0277370	+	0.0160140i	−0.513804	−	0.857907i	$-0.671764\pi$
$467$	−0.599403	+	0.346065i	−0.0277370	+	0.0160140i	0.486067	+	0.873921i	$0.338431\pi$
$468$		0			0
$469$	18.5256	−	38.1632i	0.855434	−	1.76221i
$470$		0			0
$471$		0			0
$472$	3.12837	−	5.41849i	0.143995	−	0.249406i
$473$	−1.42783	+	2.47307i	−0.0656517	+	0.113712i
$474$		0			0
$475$		0			0
$476$	−3.60332	−	5.32076i	−0.165158	−	0.243876i
$477$		0			0
$478$	−17.2409	+	9.95403i	−0.788580	+	0.455287i
$479$	−7.95403	+	13.7768i	−0.363429	+	0.629477i	−0.988523	−	0.151072i	$-0.951727\pi$
$479$	−7.95403	+	13.7768i	−0.363429	+	0.629477i	0.625094	+	0.780550i	$0.285061\pi$
$480$		0			0
$481$	7.03805	−	4.06342i	0.320908	−	0.185276i
$482$			20.5254i			0.934905i
$483$		0			0
$484$	8.65221			0.393282
$485$		0			0
$486$		0			0
$487$	24.8981	+	14.3749i	1.12824	+	0.651390i	0.943492	−	0.331396i	$-0.107520\pi$
$487$	24.8981	+	14.3749i	1.12824	+	0.651390i	0.184749	+	0.982786i	$0.440853\pi$
$488$	−5.73445	+	3.31079i	−0.259587	+	0.149872i
$489$		0			0
$490$		0			0
$491$			5.45753i			0.246295i	0.992388	+	0.123148i	$0.0392988\pi$
$491$			5.45753i			0.246295i	−0.992388	+	0.123148i	$0.960701\pi$
$492$		0			0
$493$	1.09173	−	1.89094i	0.0491691	−	0.0851635i
$494$	6.24384	+	3.60488i	0.280924	+	0.162191i
$495$		0			0
$496$			0.828427i			0.0371975i
$497$	−33.6802	+	2.41813i	−1.51076	+	0.108468i
$498$		0			0
$499$	−4.43148	−	7.67555i	−0.198380	−	0.343605i	0.749623	−	0.661865i	$-0.230235\pi$
$499$	−4.43148	−	7.67555i	−0.198380	−	0.343605i	−0.948003	+	0.318260i	$0.896901\pi$
$500$		0			0
$501$		0			0
$502$	−2.93393	−	5.08172i	−0.130948	−	0.226808i
$503$		−	9.36536i		−	0.417581i	−0.977960	−	0.208790i	$-0.933047\pi$
$503$		−	9.36536i		−	0.417581i	0.977960	−	0.208790i	$-0.0669526\pi$
$504$		0			0
$505$		0			0
$506$	−0.355560	+	0.205283i	−0.0158066	+	0.00912592i
$507$		0			0
$508$	18.3619	+	10.6012i	0.814677	+	0.470354i
$509$	−17.5164	−	30.3393i	−0.776400	−	1.34477i	−0.934004	−	0.357263i	$-0.883710\pi$
$509$	−17.5164	−	30.3393i	−0.776400	−	1.34477i	0.157603	−	0.987502i	$-0.449623\pi$
$510$		0			0
$511$	0.816735	+	0.396469i	0.0361302	+	0.0175387i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.63519	+	3.83083i	0.292666	+	0.168971i
$515$		0			0
$516$		0			0
$517$	−11.4298			−0.502680
$518$	6.33429	−	13.0488i	0.278313	−	0.573331i
$519$		0			0
$520$		0			0
$521$	−9.99807	+	17.3172i	−0.438023	+	0.758679i	−0.997537	−	0.0701424i	$-0.977655\pi$
$521$	−9.99807	+	17.3172i	−0.438023	+	0.758679i	0.559514	+	0.828821i	$0.310988\pi$
$522$		0			0
$523$	16.7515	+	29.0144i	0.732491	+	1.26871i	0.955816	+	0.293967i	$0.0949756\pi$
$523$	16.7515	+	29.0144i	0.732491	+	1.26871i	−0.223325	+	0.974744i	$0.571691\pi$
$524$	−7.46170			−0.325966
$525$		0			0
$526$	−8.46286			−0.368998
$527$	−1.00605	−	1.74253i	−0.0438243	−	0.0759060i
$528$		0			0
$529$	11.4641	−	19.8564i	0.498439	−	0.863322i
$530$		0			0
$531$		0			0
$532$	12.8351	−	0.921519i	0.556473	−	0.0399529i
$533$	12.9859			0.562482
$534$		0			0
$535$		0			0
$536$	13.8859	+	8.01702i	0.599779	+	0.346282i
$537$		0			0
$538$	−17.0431			−0.734781
$539$	9.95962	+	3.98090i	0.428991	+	0.171470i
$540$		0			0
$541$	−18.8766	−	32.6952i	−0.811568	−	1.40568i	−0.911766	−	0.410710i	$-0.865281\pi$
$541$	−18.8766	−	32.6952i	−0.811568	−	1.40568i	0.100198	−	0.994967i	$-0.468052\pi$
$542$	−9.12436	−	5.26795i	−0.391925	−	0.226278i
$543$		0			0
$544$	2.10342	−	1.21441i	0.0901836	−	0.0520675i
$545$		0			0
$546$		0			0
$547$			5.07130i			0.216833i	0.994106	+	0.108417i	$0.0345780\pi$
$547$			5.07130i			0.216833i	−0.994106	+	0.108417i	$0.965422\pi$
$548$	0.310789	+	0.538302i	0.0132762	+	0.0229951i
$549$		0			0
$550$		0			0
$551$	2.18618	+	3.78658i	0.0931346	+	0.161314i
$552$		0			0
$553$	22.8898	−	15.5014i	0.973373	−	0.659187i
$554$			8.09122i			0.343763i
$555$		0			0
$556$	−16.0504	−	9.26670i	−0.680689	−	0.392996i
$557$	−17.1778	+	29.7528i	−0.727846	+	1.26067i	0.229946	+	0.973203i	$0.426145\pi$
$557$	−17.1778	+	29.7528i	−0.727846	+	1.26067i	−0.957792	+	0.287463i	$0.907188\pi$
$558$		0			0
$559$			2.76268i			0.116849i
$560$		0			0
$561$		0			0
$562$	9.67215	−	5.58422i	0.407995	−	0.235556i
$563$	40.7539	+	23.5293i	1.71757	+	0.991641i	0.923300	+	0.384079i	$0.125481\pi$
$563$	40.7539	+	23.5293i	1.71757	+	0.991641i	0.794272	+	0.607562i	$0.207852\pi$
$564$		0			0
$565$		0			0
$566$	−7.21592			−0.303308
$567$		0			0
$568$		−	12.7627i		−	0.535510i
$569$	38.2670	−	22.0934i	1.60424	−	0.926206i	0.613608	−	0.789611i	$-0.289717\pi$
$569$	38.2670	−	22.0934i	1.60424	−	0.926206i	0.990627	−	0.136595i	$-0.0436159\pi$
$570$		0			0
$571$	−20.5804	+	35.6463i	−0.861263	+	1.49175i	0.00944654	+	0.999955i	$0.496993\pi$
$571$	−20.5804	+	35.6463i	−0.861263	+	1.49175i	−0.870710	+	0.491797i	$0.836340\pi$
$572$	−1.96705	+	1.13567i	−0.0822463	+	0.0474849i
$573$		0			0
$574$	19.1909	−	12.9964i	0.801012	−	0.542461i
$575$		0			0
$576$		0			0
$577$	−7.06058	+	12.2293i	−0.293936	+	0.509112i	−0.974737	−	0.223357i	$-0.928299\pi$
$577$	−7.06058	+	12.2293i	−0.293936	+	0.509112i	0.680801	+	0.732469i	$0.261632\pi$
$578$	5.55040	−	9.61358i	0.230866	−	0.399872i
$579$		0			0
$580$		0			0
$581$	−14.3823	+	1.03261i	−0.596680	+	0.0428397i
$582$		0			0
$583$	−4.60478	+	2.65857i	−0.190711	+	0.110107i
$584$	−0.171573	+	0.297173i	−0.00709974	+	0.0122971i
$585$		0			0
$586$	−15.8112	+	9.12863i	−0.653156	+	0.377100i
$587$			37.7819i			1.55942i	0.626138	+	0.779712i	$0.284635\pi$
$587$			37.7819i			1.55942i	−0.626138	+	0.779712i	$0.715365\pi$
$588$		0			0
$589$	4.02922			0.166021
$590$		0			0
$591$		0			0
$592$	4.74786	+	2.74118i	0.195136	+	0.112662i
$593$	−22.6865	+	13.0981i	−0.931623	+	0.537873i	−0.887324	−	0.461146i	$-0.847438\pi$
$593$	−22.6865	+	13.0981i	−0.931623	+	0.537873i	−0.0442982	+	0.999018i	$0.514105\pi$
$594$		0			0
$595$		0			0
$596$		−	13.9834i		−	0.572783i
$597$		0			0
$598$	−0.198599	+	0.343983i	−0.00812131	+	0.0140665i
$599$	4.15712	+	2.40012i	0.169856	+	0.0980661i	0.582518	−	0.812818i	$-0.302068\pi$
$599$	4.15712	+	2.40012i	0.169856	+	0.0980661i	−0.412662	+	0.910884i	$0.635401\pi$
$600$		0			0
$601$			37.3722i			1.52444i	0.647317	+	0.762221i	$0.275891\pi$
$601$			37.3722i			1.52444i	−0.647317	+	0.762221i	$0.724109\pi$
$602$	2.76492	+	4.08276i	0.112690	+	0.166401i
$603$		0			0
$604$	−9.83839	−	17.0406i	−0.400319	−	0.693372i
$605$		0			0
$606$		0			0
$607$	18.6195	+	32.2499i	0.755742	+	1.30898i	0.945005	+	0.327057i	$0.106057\pi$
$607$	18.6195	+	32.2499i	0.755742	+	1.30898i	−0.189263	+	0.981927i	$0.560610\pi$
$608$			4.86370i			0.197249i
$609$		0			0
$610$		0			0
$611$	−9.57618	+	5.52881i	−0.387411	+	0.223672i
$612$		0			0
$613$	−8.53861	−	4.92977i	−0.344871	−	0.199112i	0.317553	−	0.948241i	$-0.397139\pi$
$613$	−8.53861	−	4.92977i	−0.344871	−	0.199112i	−0.662424	+	0.749129i	$0.730472\pi$
$614$	1.71039	+	2.96248i	0.0690258	+	0.119556i
$615$		0			0
$616$	−1.77035	+	3.64697i	−0.0713296	+	0.146941i
$617$	−31.3545			−1.26229			−0.631143	−	0.775666i	$-0.717414\pi$
$617$	−31.3545			−1.26229			−0.631143	+	0.775666i	$0.717414\pi$
$618$		0			0
$619$	13.1943	+	7.61774i	0.530325	+	0.306183i	0.741149	−	0.671341i	$-0.234281\pi$
$619$	13.1943	+	7.61774i	0.530325	+	0.306183i	−0.210824	+	0.977524i	$0.567615\pi$
$620$		0			0
$621$		0			0
$622$	5.69089			0.228184
$623$	34.9851	−	23.6926i	1.40165	−	0.949223i
$624$		0			0
$625$		0			0
$626$	−6.67335	+	11.5586i	−0.266721	+	0.461974i
$627$		0			0
$628$	4.53005	+	7.84628i	0.180769	+	0.313101i
$629$	−13.3157			−0.530932
$630$		0			0
$631$	−1.00406			−0.0399710			−0.0199855	−	0.999800i	$-0.506362\pi$
$631$	−1.00406			−0.0399710			−0.0199855	+	0.999800i	$0.506362\pi$
$632$	5.22438	+	9.04889i	0.207815	+	0.359946i
$633$		0			0
$634$	−6.26330	+	10.8484i	−0.248748	+	0.430844i
$635$		0			0
$636$		0			0
$637$	10.2701	−	1.48236i	0.406916	−	0.0587333i
$638$	−1.37746			−0.0545342
$639$		0			0
$640$		0			0
$641$	−20.2689	−	11.7023i	−0.800574	−	0.462211i	0.0430981	−	0.999071i	$-0.486277\pi$
$641$	−20.2689	−	11.7023i	−0.800574	−	0.462211i	−0.843672	+	0.536860i	$0.819611\pi$
$642$		0			0
$643$	33.4475			1.31904			0.659521	−	0.751686i	$-0.270759\pi$
$643$	33.4475			1.31904			0.659521	+	0.751686i	$0.270759\pi$
$644$	0.0507680	+	0.707107i	0.00200054	+	0.0278639i
$645$		0			0
$646$	−5.90654	−	10.2304i	−0.232390	−	0.402511i
$647$	−14.3507	−	8.28540i	−0.564185	−	0.325733i	0.190638	−	0.981660i	$-0.438944\pi$
$647$	−14.3507	−	8.28540i	−0.564185	−	0.325733i	−0.754824	+	0.655928i	$0.772278\pi$
$648$		0			0
$649$	8.30249	−	4.79344i	0.325901	−	0.188159i
$650$		0			0
$651$		0			0
$652$		−	11.8204i		−	0.462922i
$653$	−3.01453	−	5.22132i	−0.117968	−	0.204326i	0.800994	−	0.598672i	$-0.204305\pi$
$653$	−3.01453	−	5.22132i	−0.117968	−	0.204326i	−0.918962	+	0.394346i	$0.870971\pi$
$654$		0			0
$655$		0			0
$656$	4.38014	+	7.58662i	0.171016	+	0.296208i
$657$		0			0
$658$	−8.61862	+	17.7545i	−0.335989	+	0.692144i
$659$			36.3672i			1.41666i	0.705880	+	0.708332i	$0.250552\pi$
$659$			36.3672i			1.41666i	−0.705880	+	0.708332i	$0.749448\pi$
$660$		0			0
$661$	−9.90289	−	5.71744i	−0.385178	−	0.222383i	0.294891	−	0.955531i	$-0.404717\pi$
$661$	−9.90289	−	5.71744i	−0.385178	−	0.222383i	−0.680069	+	0.733148i	$0.738050\pi$
$662$	−0.640916	+	1.11010i	−0.0249099	+	0.0431452i
$663$		0			0
$664$		−	5.45001i		−	0.211501i
$665$		0			0
$666$		0			0
$667$	−0.208609	+	0.120440i	−0.00807737	+	0.00466347i
$668$	13.6640	+	7.88891i	0.528675	+	0.305231i
$669$		0			0
$670$		0			0
$671$	−10.1459			−0.391679
$672$		0			0
$673$		−	10.8070i		−	0.416581i	−0.978067	−	0.208290i	$-0.933210\pi$
$673$		−	10.8070i		−	0.416581i	0.978067	−	0.208290i	$-0.0667899\pi$
$674$	11.3500	−	6.55291i	0.437185	−	0.252409i
$675$		0			0
$676$	5.40130	−	9.35533i	0.207742	−	0.359820i
$677$	−12.1638	+	7.02280i	−0.467494	+	0.269908i	−0.715190	−	0.698930i	$-0.753660\pi$
$677$	−12.1638	+	7.02280i	−0.467494	+	0.269908i	0.247696	+	0.968838i	$0.420327\pi$
$678$		0			0
$679$	−2.83220	−	39.4475i	−0.108690	−	1.51386i
$680$		0			0
$681$		0			0
$682$	−0.634679	+	1.09930i	−0.0243031	+	0.0420942i
$683$	−18.2385	+	31.5900i	−0.697877	+	1.20876i	0.271324	+	0.962488i	$0.412539\pi$
$683$	−18.2385	+	31.5900i	−0.697877	+	1.20876i	−0.969201	+	0.246271i	$0.920795\pi$
$684$		0			0
$685$		0			0
$686$	13.6938	−	12.4691i	0.522834	−	0.476073i
$687$		0			0
$688$	−1.61401	+	0.931852i	−0.0615337	+	0.0355265i
$689$	−2.57201	+	4.45486i	−0.0979859	+	0.169716i
$690$		0			0
$691$	−20.5831	+	11.8836i	−0.783017	+	0.452075i	−0.837498	−	0.546440i	$-0.815983\pi$
$691$	−20.5831	+	11.8836i	−0.783017	+	0.452075i	0.0544816	+	0.998515i	$0.482649\pi$
$692$			20.2221i			0.768730i
$693$		0			0
$694$	14.2852			0.542260
$695$		0			0
$696$		0			0
$697$	−18.4266	−	10.6386i	−0.697957	−	0.402965i
$698$	−11.4933	+	6.63567i	−0.435029	+	0.251164i
$699$		0			0
$700$		0			0
$701$			1.74502i			0.0659086i	0.999457	+	0.0329543i	$0.0104916\pi$
$701$			1.74502i			0.0659086i	−0.999457	+	0.0329543i	$0.989508\pi$
$702$		0			0
$703$	13.3323	−	23.0922i	0.502837	−	0.870939i
$704$	−1.32697	−	0.766125i	−0.0500120	−	0.0288744i
$705$		0			0
$706$			32.6463i			1.22866i
$707$	−6.51075	−	3.16052i	−0.244862	−	0.118864i
$708$		0			0
$709$	−6.06162	−	10.4990i	−0.227649	−	0.394299i	0.729462	−	0.684021i	$-0.239770\pi$
$709$	−6.06162	−	10.4990i	−0.227649	−	0.394299i	−0.957111	+	0.289722i	$0.906437\pi$
$710$		0			0
$711$		0			0
$712$	7.98502	+	13.8305i	0.299251	+	0.518319i
$713$			0.221976i			0.00831308i
$714$		0			0
$715$		0			0
$716$	5.94667	−	3.43331i	0.222237	−	0.128309i
$717$		0			0
$718$	5.40692	+	3.12168i	0.201784	+	0.116500i
$719$	0.893176	+	1.54703i	0.0333098	+	0.0576943i	0.882200	−	0.470875i	$-0.156062\pi$
$719$	0.893176	+	1.54703i	0.0333098	+	0.0576943i	−0.848890	+	0.528570i	$0.822729\pi$
$720$		0			0
$721$	−13.5315	+	9.16382i	−0.503941	+	0.341279i
$722$	4.65561			0.173264
$723$		0			0
$724$	14.1220	+	8.15331i	0.524838	+	0.303015i
$725$		0			0
$726$		0			0
$727$	29.8785			1.10813			0.554066	−	0.832472i	$-0.313075\pi$
$727$	29.8785			1.10813			0.554066	+	0.832472i	$0.313075\pi$
$728$	0.280861	+	3.91189i	0.0104094	+	0.144984i
$729$		0			0
$730$		0			0
$731$	2.26330	−	3.92016i	0.0837114	−	0.144992i
$732$		0			0
$733$	6.89554	+	11.9434i	0.254692	+	0.441140i	0.964812	−	0.262941i	$-0.0846924\pi$
$733$	6.89554	+	11.9434i	0.254692	+	0.441140i	−0.710119	+	0.704081i	$0.751359\pi$
$734$	−12.5892			−0.464677
$735$		0			0
$736$	−0.267949			−0.00987674
$737$	12.2841	+	21.2766i	0.452490	+	0.783735i
$738$		0			0
$739$	3.68349	−	6.37999i	0.135499	−	0.234692i	−0.790289	−	0.612735i	$-0.790069\pi$
$739$	3.68349	−	6.37999i	0.135499	−	0.234692i	0.925788	+	0.378043i	$0.123403\pi$
$740$		0			0
$741$		0			0
$742$	0.657486	+	9.15759i	0.0241371	+	0.336186i
$743$	−11.0774			−0.406389			−0.203194	−	0.979138i	$-0.565132\pi$
$743$	−11.0774			−0.406389			−0.203194	+	0.979138i	$0.565132\pi$
$744$		0			0
$745$		0			0
$746$	−31.1408	−	17.9791i	−1.14014	−	0.658263i
$747$		0			0
$748$	3.72157			0.136074
$749$	−10.0112	+	6.77978i	−0.365802	+	0.247728i
$750$		0			0
$751$	−12.1879	−	21.1100i	−0.444741	−	0.770315i	0.553293	−	0.832987i	$-0.313371\pi$
$751$	−12.1879	−	21.1100i	−0.444741	−	0.770315i	−0.998034	+	0.0626722i	$0.980038\pi$
$752$	−6.46008	−	3.72973i	−0.235575	−	0.136009i
$753$		0			0
$754$	−1.15408	+	0.666306i	−0.0420290	+	0.0242655i
$755$		0			0
$756$		0			0
$757$			19.6761i			0.715139i	0.933887	+	0.357569i	$0.116394\pi$
$757$			19.6761i			0.715139i	−0.933887	+	0.357569i	$0.883606\pi$
$758$	5.79493	+	10.0371i	0.210481	+	0.364565i
$759$		0			0
$760$		0			0
$761$	−24.9168	−	43.1572i	−0.903234	−	1.56445i	−0.823270	−	0.567650i	$-0.807853\pi$
$761$	−24.9168	−	43.1572i	−0.903234	−	1.56445i	−0.0799647	−	0.996798i	$-0.525481\pi$
$762$		0			0
$763$	−14.1825	−	6.88462i	−0.513440	−	0.249240i
$764$			17.1623i			0.620910i
$765$		0			0
$766$	−3.86897	−	2.23375i	−0.139792	−	0.0807087i
$767$	4.63737	−	8.03217i	0.167446	−	0.290025i
$768$		0			0
$769$		−	31.0584i		−	1.12000i	−0.828494	−	0.559998i	$-0.810802\pi$
$769$		−	31.0584i		−	1.12000i	0.828494	−	0.559998i	$-0.189198\pi$
$770$		0			0
$771$		0			0
$772$	−7.84204	+	4.52761i	−0.282241	+	0.162952i
$773$	3.43855	+	1.98525i	0.123676	+	0.0714043i	0.560562	−	0.828113i	$-0.310585\pi$
$773$	3.43855	+	1.98525i	0.123676	+	0.0714043i	−0.436886	+	0.899517i	$0.643919\pi$
$774$		0			0
$775$		0			0
$776$	14.9481			0.536607
$777$		0			0
$778$		−	12.9554i		−	0.464475i
$779$	36.8991	−	21.3037i	1.32205	−	0.763284i
$780$		0			0
$781$	9.77781	−	16.9357i	0.349878	−	0.606006i
$782$	0.563611	−	0.325401i	0.0201547	−	0.0116363i
$783$		0			0
$784$	4.33013	+	5.50000i	0.154647	+	0.196429i
$785$		0			0
$786$		0			0
$787$	−22.4013	+	38.8001i	−0.798519	+	1.38308i	0.122061	+	0.992523i	$0.461050\pi$
$787$	−22.4013	+	38.8001i	−0.798519	+	1.38308i	−0.920580	+	0.390553i	$0.872284\pi$
$788$	10.8689	−	18.8256i	0.387190	−	0.670633i
$789$		0			0
$790$		0			0
$791$	3.77000	+	52.5093i	0.134046	+	1.86702i
$792$		0			0
$793$	−8.50054	+	4.90779i	−0.301863	+	0.174281i
$794$	−4.63995	+	8.03664i	−0.164666	+	0.285210i
$795$		0			0
$796$	−7.21101	+	4.16328i	−0.255588	+	0.147564i
$797$			38.4813i			1.36308i	0.731781	+	0.681539i	$0.238689\pi$
$797$			38.4813i			1.36308i	−0.731781	+	0.681539i	$0.761311\pi$
$798$		0			0
$799$	18.1177			0.640959
$800$		0			0
$801$		0			0
$802$	6.44260	+	3.71964i	0.227496	+	0.131345i
$803$	−0.455343	+	0.262893i	−0.0160687	+	0.00927728i
$804$		0			0
$805$		0			0
$806$			1.22803i			0.0432555i
$807$		0			0
$808$	1.36773	−	2.36897i	0.0481164	−	0.0833401i
$809$	15.0298	+	8.67748i	0.528421	+	0.305084i	0.740373	−	0.672196i	$-0.234649\pi$
$809$	15.0298	+	8.67748i	0.528421	+	0.305084i	−0.211952	+	0.977280i	$0.567982\pi$
$810$		0			0
$811$		−	32.7270i		−	1.14920i	−0.818434	−	0.574601i	$-0.805157\pi$
$811$		−	32.7270i		−	1.14920i	0.818434	−	0.574601i	$-0.194843\pi$
$812$	−1.03868	+	2.13970i	−0.0364504	+	0.0750886i
$813$		0			0
$814$	4.20017	+	7.27492i	0.147216	+	0.254986i
$815$		0			0
$816$		0			0
$817$	4.53225	+	7.85009i	0.158563	+	0.274640i
$818$			16.0096i			0.559763i
$819$		0			0
$820$		0			0
$821$	−15.4093	+	8.89658i	−0.537789	+	0.310493i	−0.744182	−	0.667976i	$-0.767161\pi$
$821$	−15.4093	+	8.89658i	−0.537789	+	0.310493i	0.206393	+	0.978469i	$0.433827\pi$
$822$		0			0
$823$	8.50579	+	4.91082i	0.296493	+	0.171181i	0.640867	−	0.767652i	$-0.278575\pi$
$823$	8.50579	+	4.91082i	0.296493	+	0.171181i	−0.344373	+	0.938833i	$0.611909\pi$
$824$	−3.08845	−	5.34935i	−0.107591	−	0.186353i
$825$		0			0
$826$	−1.18546	−	16.5113i	−0.0412473	−	0.574501i
$827$	7.78482			0.270705			0.135352	−	0.990798i	$-0.456783\pi$
$827$	7.78482			0.270705			0.135352	+	0.990798i	$0.456783\pi$
$828$		0			0
$829$	13.1015	+	7.56413i	0.455032	+	0.262713i	0.709953	−	0.704249i	$-0.248716\pi$
$829$	13.1015	+	7.56413i	0.455032	+	0.262713i	−0.254921	+	0.966962i	$0.582049\pi$
$830$		0			0
$831$		0			0
$832$	−1.48236			−0.0513917
$833$	−15.7874	−	6.31027i	−0.547000	−	0.218638i
$834$		0			0
$835$		0			0
$836$	−3.72620	+	6.45398i	−0.128873	+	0.223215i
$837$		0			0
$838$	14.2209	+	24.6314i	0.491254	+	0.850877i
$839$	−25.2077			−0.870265			−0.435133	−	0.900366i	$-0.643299\pi$
$839$	−25.2077			−0.870265			−0.435133	+	0.900366i	$0.643299\pi$
$840$		0			0
$841$	28.1918			0.972132
$842$	8.91724	+	15.4451i	0.307308	+	0.532274i
$843$		0			0
$844$	9.96651	−	17.2625i	0.343061	−	0.594200i
$845$		0			0
$846$		0			0
$847$	18.9541	−	12.8361i	0.651272	−	0.441054i
$848$	−3.47015			−0.119166
$849$		0			0
$850$		0			0
$851$	1.27219	+	0.734497i	0.0436100	+	0.0251782i
$852$		0			0
$853$	23.3020			0.797846			0.398923	−	0.916984i	$-0.369384\pi$
$853$	23.3020			0.797846			0.398923	+	0.916984i	$0.369384\pi$
$854$	−7.65053	+	15.7603i	−0.261796	+	0.539306i
$855$		0			0
$856$	−2.28497	−	3.95768i	−0.0780985	−	0.135271i
$857$	23.0414	+	13.3030i	0.787080	+	0.454421i	0.838934	−	0.544234i	$-0.183180\pi$
$857$	23.0414	+	13.3030i	0.787080	+	0.454421i	−0.0518534	+	0.998655i	$0.516513\pi$
$858$		0			0
$859$	−49.0044	+	28.2927i	−1.67201	+	0.965334i	−0.705495	+	0.708714i	$0.749275\pi$
$859$	−49.0044	+	28.2927i	−1.67201	+	0.965334i	−0.966512	+	0.256620i	$0.917391\pi$
$860$		0			0
$861$		0			0
$862$			30.8927i			1.05221i
$863$	−17.0283	−	29.4939i	−0.579650	−	1.00398i	−0.995519	−	0.0945593i	$-0.969856\pi$
$863$	−17.0283	−	29.4939i	−0.579650	−	1.00398i	0.415869	−	0.909425i	$-0.363478\pi$
$864$		0			0
$865$		0			0
$866$	7.61037	+	13.1815i	0.258611	+	0.447927i
$867$		0			0
$868$	1.22902	+	1.81481i	0.0417158	+	0.0615987i
$869$			16.0101i			0.543106i
$870$		0			0
$871$	20.5839	+	11.8841i	0.697459	+	0.402678i
$872$	2.97934	−	5.16036i	0.100893	−	0.174752i
$873$		0			0
$874$			1.30323i			0.0440823i
$875$		0			0
$876$		0			0
$877$	20.9043	−	12.0691i	0.705888	−	0.407545i	−0.103649	−	0.994614i	$-0.533052\pi$
$877$	20.9043	−	12.0691i	0.705888	−	0.407545i	0.809537	+	0.587069i	$0.199718\pi$
$878$	−12.4054	−	7.16228i	−0.418663	−	0.241715i
$879$		0			0
$880$		0			0
$881$	−37.2609			−1.25535			−0.627676	−	0.778475i	$-0.715994\pi$
$881$	−37.2609			−1.25535			−0.627676	+	0.778475i	$0.715994\pi$
$882$		0			0
$883$		−	48.5544i		−	1.63398i	−0.576648	−	0.816992i	$-0.695640\pi$
$883$		−	48.5544i		−	1.63398i	0.576648	−	0.816992i	$-0.304360\pi$
$884$	3.11804	−	1.80020i	0.104871	−	0.0605472i
$885$		0			0
$886$	2.57874	−	4.46651i	0.0866344	−	0.150055i
$887$	15.1302	−	8.73545i	0.508024	−	0.293308i	−0.223997	−	0.974590i	$-0.571911\pi$
$887$	15.1302	−	8.73545i	0.508024	−	0.293308i	0.732021	+	0.681282i	$0.238577\pi$
$888$		0			0
$889$	55.9524	−	4.01720i	1.87658	−	0.134733i
$890$		0			0
$891$		0			0
$892$	3.58302	−	6.20597i	0.119968	−	0.207791i
$893$	−18.1403	+	31.4199i	−0.607042	+	1.05143i
$894$		0			0
$895$		0			0
$896$	−2.19067	+	1.48356i	−0.0731852	+	0.0495624i
$897$		0			0
$898$	−17.2665	+	9.96885i	−0.576192	+	0.332665i
$899$	−0.372369	+	0.644963i	−0.0124192	+	0.0215107i
$900$		0			0
$901$	7.29921	−	4.21420i	0.243172	−	0.140395i
$902$			13.4229i			0.446935i
$903$		0			0
$904$	−19.8977			−0.661789
$905$		0			0
$906$		0			0
$907$	18.5780	+	10.7260i	0.616872	+	0.356151i	0.775650	−	0.631163i	$-0.217422\pi$
$907$	18.5780	+	10.7260i	0.616872	+	0.356151i	−0.158778	+	0.987314i	$0.550756\pi$
$908$	−13.7303	+	7.92721i	−0.455657	+	0.263074i
$909$		0			0
$910$		0			0
$911$		−	42.2281i		−	1.39908i	−0.714593	−	0.699540i	$-0.753388\pi$
$911$		−	42.2281i		−	1.39908i	0.714593	−	0.699540i	$-0.246612\pi$
$912$		0			0
$913$	4.17539	−	7.23198i	0.138185	−	0.239344i
$914$	9.82065	+	5.66995i	0.324838	+	0.187545i
$915$		0			0
$916$		−	28.2175i		−	0.932332i
$917$	−16.3461	+	11.0699i	−0.539797	+	0.365560i
$918$		0			0
$919$	−28.0816	−	48.6387i	−0.926325	−	1.60444i	−0.789416	−	0.613858i	$-0.789617\pi$
$919$	−28.0816	−	48.6387i	−0.926325	−	1.60444i	−0.136908	−	0.990584i	$-0.543717\pi$
$920$		0			0
$921$		0			0
$922$	−1.00945	−	1.74842i	−0.0332445	−	0.0575812i
$923$		−	18.9189i		−	0.622724i
$924$		0			0
$925$		0			0
$926$	−23.6290	+	13.6422i	−0.776497	+	0.448311i
$927$		0			0
$928$	−0.778539	−	0.449490i	−0.0255568	−	0.0147552i
$929$	−9.26942	−	16.0551i	−0.304120	−	0.526751i	0.672945	−	0.739692i	$-0.265029\pi$
$929$	−9.26942	−	16.0551i	−0.304120	−	0.526751i	−0.977065	+	0.212941i	$0.931696\pi$
$930$		0			0
$931$	26.7504	−	21.0605i	0.876708	−	0.690228i
$932$	24.2973			0.795886
$933$		0			0
$934$	−0.599403	−	0.346065i	−0.0196131	−	0.0113236i
$935$		0			0
$936$		0			0
$937$	−39.5337			−1.29151			−0.645755	−	0.763545i	$-0.723457\pi$
$937$	−39.5337			−1.29151			−0.645755	+	0.763545i	$0.723457\pi$
$938$	42.3131	−	3.03795i	1.38157	−	0.0991925i
$939$		0			0
$940$		0			0
$941$	25.2474	−	43.7299i	0.823043	−	1.42555i	−0.0803623	−	0.996766i	$-0.525608\pi$
$941$	25.2474	−	43.7299i	0.823043	−	1.42555i	0.903406	−	0.428787i	$-0.141059\pi$
$942$		0			0
$943$	1.17365	+	2.03283i	0.0382195	+	0.0661980i
$944$	6.25674			0.203639
$945$		0			0
$946$	−2.85566			−0.0928455
$947$	−19.5814	−	33.9160i	−0.636310	−	1.10212i	−0.986236	−	0.165344i	$-0.947126\pi$
$947$	−19.5814	−	33.9160i	−0.636310	−	1.10212i	0.349926	−	0.936777i	$-0.386207\pi$
$948$		0			0
$949$	−0.254333	+	0.440518i	−0.00825600	+	0.0142998i
$950$		0			0
$951$		0			0
$952$	2.80625	−	5.78094i	0.0909511	−	0.187361i
$953$	−52.9933			−1.71662			−0.858311	−	0.513130i	$-0.828486\pi$
$953$	−52.9933			−1.71662			−0.858311	+	0.513130i	$0.828486\pi$
$954$		0			0
$955$		0			0
$956$	−17.2409	−	9.95403i	−0.557610	−	0.321936i
$957$		0			0
$958$	−15.9081			−0.513966
$959$	1.47944	+	0.718168i	0.0477737	+	0.0231909i
$960$		0			0
$961$	−15.1569	−	26.2524i	−0.488931	−	0.846853i
$962$	7.03805	+	4.06342i	0.226916	+	0.131010i
$963$		0			0
$964$	−17.7755	+	10.2627i	−0.572510	+	0.330539i
$965$		0			0
$966$		0			0
$967$			30.6208i			0.984700i	0.870397	+	0.492350i	$0.163862\pi$
$967$			30.6208i			0.984700i	−0.870397	+	0.492350i	$0.836138\pi$
$968$	4.32611	+	7.49303i	0.139046	+	0.240835i
$969$		0			0
$970$		0			0
$971$	6.03548	+	10.4538i	0.193688	+	0.335477i	0.946470	−	0.322793i	$-0.104622\pi$
$971$	6.03548	+	10.4538i	0.193688	+	0.335477i	−0.752782	+	0.658270i	$0.771288\pi$
$972$		0			0
$973$	−48.9089	+	3.51150i	−1.56795	+	0.112574i
$974$			28.7498i			0.921205i
$975$		0			0
$976$	−5.73445	−	3.31079i	−0.183555	−	0.105976i
$977$	5.61642	−	9.72792i	0.179685	−	0.311224i	−0.762088	−	0.647474i	$-0.775825\pi$
$977$	5.61642	−	9.72792i	0.179685	−	0.311224i	0.941773	+	0.336250i	$0.109159\pi$
$978$		0			0
$979$			24.4701i			0.782068i
$980$		0			0
$981$		0			0
$982$	−4.72636	+	2.72877i	−0.150824	+	0.0870784i
$983$	19.7385	+	11.3960i	0.629561	+	0.363477i	0.780582	−	0.625053i	$-0.214923\pi$
$983$	19.7385	+	11.3960i	0.629561	+	0.363477i	−0.151021	+	0.988531i	$0.548256\pi$
$984$		0			0
$985$		0			0
$986$	2.18346			0.0695357
$987$		0			0
$988$			7.20977i			0.229373i
$989$	−0.432474	+	0.249689i	−0.0137519	+	0.00793965i
$990$		0			0
$991$	4.41057	−	7.63932i	0.140106	−	0.242671i	−0.787430	−	0.616404i	$-0.788589\pi$
$991$	4.41057	−	7.63932i	0.140106	−	0.242671i	0.927536	+	0.373733i	$0.121922\pi$
$992$	−0.717439	+	0.414214i	−0.0227787	+	0.0131513i
$993$		0			0
$994$	−18.9343	−	27.9588i	−0.600558	−	0.886800i
$995$		0			0
$996$		0			0
$997$	23.2381	−	40.2497i	0.735960	−	1.27472i	−0.218342	−	0.975872i	$-0.570065\pi$
$997$	23.2381	−	40.2497i	0.735960	−	1.27472i	0.954301	−	0.298847i	$-0.0966020\pi$
$998$	4.43148	−	7.67555i	0.140276	−	0.242965i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.d.899.3		8
3.2	odd	2		3150.2.bp.c.899.3		8
5.2	odd	4		3150.2.bf.b.1151.1		8
5.3	odd	4		630.2.be.a.521.4	yes	8
5.4	even	2		3150.2.bp.a.899.2		8
7.5	odd	6		3150.2.bp.f.1349.2		8
15.2	even	4		3150.2.bf.c.1151.3		8
15.8	even	4		630.2.be.b.521.2	yes	8
15.14	odd	2		3150.2.bp.f.899.2		8
21.5	even	6		3150.2.bp.a.1349.2		8
35.3	even	12		4410.2.b.b.881.7		8
35.12	even	12		3150.2.bf.c.1601.3		8
35.18	odd	12		4410.2.b.e.881.7		8
35.19	odd	6		3150.2.bp.c.1349.3		8
35.33	even	12		630.2.be.b.341.2	yes	8
105.38	odd	12		4410.2.b.e.881.2		8
105.47	odd	12		3150.2.bf.b.1601.1		8
105.53	even	12		4410.2.b.b.881.2		8
105.68	odd	12		630.2.be.a.341.4	✓	8
105.89	even	6	inner	3150.2.bp.d.1349.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.4	✓	8	105.68	odd	12
630.2.be.a.521.4	yes	8	5.3	odd	4
630.2.be.b.341.2	yes	8	35.33	even	12
630.2.be.b.521.2	yes	8	15.8	even	4
3150.2.bf.b.1151.1		8	5.2	odd	4
3150.2.bf.b.1601.1		8	105.47	odd	12
3150.2.bf.c.1151.3		8	15.2	even	4
3150.2.bf.c.1601.3		8	35.12	even	12
3150.2.bp.a.899.2		8	5.4	even	2
3150.2.bp.a.1349.2		8	21.5	even	6
3150.2.bp.c.899.3		8	3.2	odd	2
3150.2.bp.c.1349.3		8	35.19	odd	6
3150.2.bp.d.899.3		8	1.1	even	1	trivial
3150.2.bp.d.1349.3		8	105.89	even	6	inner
3150.2.bp.f.899.2		8	15.14	odd	2
3150.2.bp.f.1349.2		8	7.5	odd	6
4410.2.b.b.881.2		8	105.53	even	12
4410.2.b.b.881.7		8	35.3	even	12
4410.2.b.e.881.2		8	105.38	odd	12
4410.2.b.e.881.7		8	35.18	odd	12

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.189469 + 2.63896i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.189469 + 2.63896i) q^{7} -1.00000 q^{8} +(-1.32697 - 0.766125i) q^{11} -1.48236 q^{13} +(-2.19067 + 1.48356i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.10342 + 1.21441i) q^{17} +(-4.21209 + 2.43185i) q^{19} -1.53225i q^{22} +(-0.133975 - 0.232051i) q^{23} +(-0.741181 - 1.28376i) q^{26} +(-2.38014 - 1.15539i) q^{28} -0.898979i q^{29} +(-0.717439 - 0.414214i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.42883i q^{34} +(-4.74786 + 2.74118i) q^{37} +(-4.21209 - 2.43185i) q^{38} -8.76028 q^{41} -1.86370i q^{43} +(1.32697 - 0.766125i) q^{44} +(0.133975 - 0.232051i) q^{46} +(6.46008 - 3.72973i) q^{47} +(-6.92820 + 1.00000i) q^{49} +(0.741181 - 1.28376i) q^{52} +(1.73508 - 3.00524i) q^{53} +(-0.189469 - 2.63896i) q^{56} +(0.778539 - 0.449490i) q^{58} +(-3.12837 + 5.41849i) q^{59} +(5.73445 - 3.31079i) q^{61} -0.828427i q^{62} +1.00000 q^{64} +(-13.8859 - 8.01702i) q^{67} +(-2.10342 + 1.21441i) q^{68} +12.7627i q^{71} +(0.171573 - 0.297173i) q^{73} +(-4.74786 - 2.74118i) q^{74} -4.86370i q^{76} +(1.77035 - 3.64697i) q^{77} +(-5.22438 - 9.04889i) q^{79} +(-4.38014 - 7.58662i) q^{82} +5.45001i q^{83} +(1.61401 - 0.931852i) q^{86} +(1.32697 + 0.766125i) q^{88} +(-7.98502 - 13.8305i) q^{89} +(-0.280861 - 3.91189i) q^{91} +0.267949 q^{92} +(6.46008 + 3.72973i) q^{94} -14.9481 q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 24 q^{11} - 16 q^{13} - 4 q^{16} + 24 q^{17} - 8 q^{23} - 8 q^{26} + 4 q^{32} - 32 q^{41} + 24 q^{44} + 8 q^{46} + 12 q^{47} + 8 q^{52} + 4 q^{53} - 24 q^{59} + 8 q^{64} - 48 q^{67} - 24 q^{68} + 24 q^{73} - 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} - 16 q^{89} - 20 q^{91} + 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 24 * q^11 - 16 * q^13 - 4 * q^16 + 24 * q^17 - 8 * q^23 - 8 * q^26 + 4 * q^32 - 32 * q^41 + 24 * q^44 + 8 * q^46 + 12 * q^47 + 8 * q^52 + 4 * q^53 - 24 * q^59 + 8 * q^64 - 48 * q^67 - 24 * q^68 + 24 * q^73 - 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 - 16 * q^89 - 20 * q^91 + 16 * q^92 + 12 * q^94 + 48 * q^97

Introduction

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