LMFDB - Embedded newform 3150.2.bf.c.1601.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

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.bf (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:	$25.1528766367$
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			1601.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.c.1151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.63896 - 0.189469i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.63896 - 0.189469i) q^{7} +1.00000i q^{8} +(1.32697 - 0.766125i) q^{11} -1.48236i q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.21441 + 2.10342i) q^{17} +(4.21209 + 2.43185i) q^{19} +1.53225 q^{22} +(0.232051 + 0.133975i) q^{23} +(0.741181 - 1.28376i) q^{26} +(-1.15539 - 2.38014i) q^{28} +0.898979i q^{29} +(-0.717439 + 0.414214i) q^{31} +(-0.866025 + 0.500000i) q^{32} +2.42883i q^{34} +(-2.74118 + 4.74786i) q^{37} +(2.43185 + 4.21209i) q^{38} +8.76028 q^{41} -1.86370 q^{43} +(1.32697 + 0.766125i) q^{44} +(0.133975 + 0.232051i) q^{46} +(-3.72973 + 6.46008i) q^{47} +(6.92820 + 1.00000i) q^{49} +(1.28376 - 0.741181i) q^{52} +(3.00524 - 1.73508i) q^{53} +(0.189469 - 2.63896i) q^{56} +(-0.449490 + 0.778539i) q^{58} +(-3.12837 - 5.41849i) q^{59} +(5.73445 + 3.31079i) q^{61} -0.828427 q^{62} -1.00000 q^{64} +(8.01702 + 13.8859i) q^{67} +(-1.21441 + 2.10342i) q^{68} +12.7627i q^{71} +(-0.297173 + 0.171573i) q^{73} +(-4.74786 + 2.74118i) q^{74} +4.86370i q^{76} +(-3.64697 + 1.77035i) q^{77} +(5.22438 - 9.04889i) q^{79} +(7.58662 + 4.38014i) q^{82} -5.45001 q^{83} +(-1.61401 - 0.931852i) q^{86} +(0.766125 + 1.32697i) q^{88} +(-7.98502 + 13.8305i) q^{89} +(-0.280861 + 3.91189i) q^{91} +0.267949i q^{92} +(-6.46008 + 3.72973i) q^{94} +14.9481i q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 24 q^{11} - 4 q^{16} - 12 q^{23} + 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} + 16 q^{83} - 16 q^{89} - 20 q^{91} - 12 q^{94} + 44 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 24 * q^11 - 4 * q^16 - 12 * q^23 + 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 + 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 $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	+	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			0
$5$		0			0
$6$		0			0
$7$	−2.63896	−	0.189469i	−0.997433	−	0.0716124i
$7$	−2.63896	−	0.189469i	−0.997433	−	0.0716124i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	1.32697	−	0.766125i	0.400096	−	0.230995i	−0.286430	−	0.958101i	$-0.592468\pi$
$11$	1.32697	−	0.766125i	0.400096	−	0.230995i	0.686525	+	0.727106i	$0.259135\pi$
$12$		0			0
$13$		−	1.48236i		−	0.411133i	−0.978643	−	0.205567i	$-0.934096\pi$
$13$		−	1.48236i		−	0.411133i	0.978643	−	0.205567i	$-0.0659037\pi$
$14$	−2.19067	−	1.48356i	−0.585481	−	0.396499i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.21441	+	2.10342i	0.294538	+	0.510155i	0.974877	−	0.222742i	$-0.0715008\pi$
$17$	1.21441	+	2.10342i	0.294538	+	0.510155i	−0.680339	+	0.732898i	$0.738167\pi$
$18$		0			0
$19$	4.21209	+	2.43185i	0.966320	+	0.557905i	0.898112	−	0.439766i	$-0.144939\pi$
$19$	4.21209	+	2.43185i	0.966320	+	0.557905i	0.0682075	+	0.997671i	$0.478272\pi$
$20$		0			0
$21$		0			0
$22$	1.53225			0.326677
$23$	0.232051	+	0.133975i	0.0483859	+	0.0279356i	0.523998	−	0.851720i	$-0.324440\pi$
$23$	0.232051	+	0.133975i	0.0483859	+	0.0279356i	−0.475612	+	0.879655i	$0.657773\pi$
$24$		0			0
$25$		0			0
$26$	0.741181	−	1.28376i	0.145358	−	0.251767i
$27$		0			0
$28$	−1.15539	−	2.38014i	−0.218349	−	0.449804i
$29$			0.898979i			0.166936i	0.996510	+	0.0834681i	$0.0265997\pi$
$29$			0.898979i			0.166936i	−0.996510	+	0.0834681i	$0.973400\pi$
$30$		0			0
$31$	−0.717439	+	0.414214i	−0.128856	+	0.0743950i	−0.563042	−	0.826428i	$-0.690369\pi$
$31$	−0.717439	+	0.414214i	−0.128856	+	0.0743950i	0.434187	+	0.900823i	$0.357036\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			2.42883i			0.416540i
$35$		0			0
$36$		0			0
$37$	−2.74118	+	4.74786i	−0.450647	+	0.780544i	−0.998426	−	0.0560790i	$-0.982140\pi$
$37$	−2.74118	+	4.74786i	−0.450647	+	0.780544i	0.547779	+	0.836623i	$0.315473\pi$
$38$	2.43185	+	4.21209i	0.394498	+	0.683291i
$39$		0			0
$40$		0			0
$41$	8.76028			1.36813			0.684063	−	0.729423i	$-0.260211\pi$
$41$	8.76028			1.36813			0.684063	+	0.729423i	$0.260211\pi$
$42$		0			0
$43$	−1.86370			−0.284212			−0.142106	−	0.989851i	$-0.545387\pi$
$43$	−1.86370			−0.284212			−0.142106	+	0.989851i	$0.545387\pi$
$44$	1.32697	+	0.766125i	0.200048	+	0.115498i
$45$		0			0
$46$	0.133975	+	0.232051i	0.0197535	+	0.0342140i
$47$	−3.72973	+	6.46008i	−0.544037	+	0.942299i	0.454630	+	0.890680i	$0.349771\pi$
$47$	−3.72973	+	6.46008i	−0.544037	+	0.942299i	−0.998667	+	0.0516191i	$0.983562\pi$
$48$		0			0
$49$	6.92820	+	1.00000i	0.989743	+	0.142857i
$50$		0			0
$51$		0			0
$52$	1.28376	−	0.741181i	0.178026	−	0.102783i
$53$	3.00524	−	1.73508i	0.412802	−	0.238331i	−0.279191	−	0.960236i	$-0.590066\pi$
$53$	3.00524	−	1.73508i	0.412802	−	0.238331i	0.691993	+	0.721904i	$0.256733\pi$
$54$		0			0
$55$		0			0
$56$	0.189469	−	2.63896i	0.0253188	−	0.352646i
$57$		0			0
$58$	−0.449490	+	0.778539i	−0.0590209	+	0.102227i
$59$	−3.12837	−	5.41849i	−0.407279	−	0.705428i	0.587305	−	0.809366i	$-0.300189\pi$
$59$	−3.12837	−	5.41849i	−0.407279	−	0.705428i	−0.994584	+	0.103938i	$0.966856\pi$
$60$		0			0
$61$	5.73445	+	3.31079i	0.734222	+	0.423903i	0.819965	−	0.572414i	$-0.193993\pi$
$61$	5.73445	+	3.31079i	0.734222	+	0.423903i	−0.0857429	+	0.996317i	$0.527326\pi$
$62$	−0.828427			−0.105210
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	8.01702	+	13.8859i	0.979434	+	1.69643i	0.664449	+	0.747334i	$0.268666\pi$
$67$	8.01702	+	13.8859i	0.979434	+	1.69643i	0.314985	+	0.949097i	$0.398000\pi$
$68$	−1.21441	+	2.10342i	−0.147269	+	0.255078i
$69$		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
$73$	−0.297173	+	0.171573i	−0.0347815	+	0.0200811i	−0.517290	−	0.855810i	$-0.673059\pi$
$73$	−0.297173	+	0.171573i	−0.0347815	+	0.0200811i	0.482508	+	0.875891i	$0.339726\pi$
$74$	−4.74786	+	2.74118i	−0.551928	+	0.318656i
$75$		0			0
$76$			4.86370i			0.557905i
$77$	−3.64697	+	1.77035i	−0.415611	+	0.201750i
$78$		0			0
$79$	5.22438	−	9.04889i	0.587789	−	1.01808i	−0.406733	−	0.913547i	$-0.633332\pi$
$79$	5.22438	−	9.04889i	0.587789	−	1.01808i	0.994521	−	0.104533i	$-0.0333347\pi$
$80$		0			0
$81$		0			0
$82$	7.58662	+	4.38014i	0.837802	+	0.483705i
$83$	−5.45001			−0.598216			−0.299108	−	0.954219i	$-0.596689\pi$
$83$	−5.45001			−0.598216			−0.299108	+	0.954219i	$0.596689\pi$
$84$		0			0
$85$		0			0
$86$	−1.61401	−	0.931852i	−0.174044	−	0.100484i
$87$		0			0
$88$	0.766125	+	1.32697i	0.0816692	+	0.141455i
$89$	−7.98502	+	13.8305i	−0.846411	+	1.46603i	0.0379795	+	0.999279i	$0.487908\pi$
$89$	−7.98502	+	13.8305i	−0.846411	+	1.46603i	−0.884390	+	0.466748i	$0.845426\pi$
$90$		0			0
$91$	−0.280861	+	3.91189i	−0.0294423	+	0.410078i
$92$			0.267949i			0.0279356i
$93$		0			0
$94$	−6.46008	+	3.72973i	−0.666306	+	0.384692i
$95$		0			0
$96$		0			0
$97$			14.9481i			1.51775i	0.651234	+	0.758877i	$0.274252\pi$
$97$			14.9481i			1.51775i	−0.651234	+	0.758877i	$0.725748\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$		0			0
$100$		0			0
$101$	1.36773	+	2.36897i	0.136094	+	0.235721i	0.926015	−	0.377487i	$-0.123212\pi$
$101$	1.36773	+	2.36897i	0.136094	+	0.235721i	−0.789921	+	0.613209i	$0.789878\pi$
$102$		0			0
$103$	5.34935	+	3.08845i	0.527087	+	0.304314i	0.739829	−	0.672794i	$-0.234906\pi$
$103$	5.34935	+	3.08845i	0.527087	+	0.304314i	−0.212742	+	0.977108i	$0.568240\pi$
$104$	1.48236			0.145358
$105$		0			0
$106$	3.47015			0.337051
$107$	3.95768	+	2.28497i	0.382603	+	0.220896i	0.678950	−	0.734184i	$-0.262435\pi$
$107$	3.95768	+	2.28497i	0.382603	+	0.220896i	−0.296347	+	0.955080i	$0.595769\pi$
$108$		0			0
$109$	2.97934	+	5.16036i	0.285369	+	0.494273i	0.972699	−	0.232072i	$-0.0745506\pi$
$109$	2.97934	+	5.16036i	0.285369	+	0.494273i	−0.687330	+	0.726345i	$0.741217\pi$
$110$		0			0
$111$		0			0
$112$	1.48356	−	2.19067i	0.140184	−	0.206999i
$113$		−	19.8977i		−	1.87182i	−0.352237	−	0.935911i	$-0.614579\pi$
$113$		−	19.8977i		−	1.87182i	0.352237	−	0.935911i	$-0.385421\pi$
$114$		0			0
$115$		0			0
$116$	−0.778539	+	0.449490i	−0.0722855	+	0.0417341i
$117$		0			0
$118$		−	6.25674i		−	0.575979i
$119$	−2.80625	−	5.78094i	−0.257249	−	0.529938i
$120$		0			0
$121$	−4.32611	+	7.49303i	−0.393282	+	0.681185i
$122$	3.31079	+	5.73445i	0.299745	+	0.519173i
$123$		0			0
$124$	−0.717439	−	0.414214i	−0.0644279	−	0.0371975i
$125$		0			0
$126$		0			0
$127$	21.2025			1.88142			0.940708	−	0.339219i	$-0.110163\pi$
$127$	21.2025			1.88142			0.940708	+	0.339219i	$0.110163\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−3.73085	+	6.46202i	−0.325966	+	0.564589i	−0.981707	−	0.190396i	$-0.939023\pi$
$131$	−3.73085	+	6.46202i	−0.325966	+	0.564589i	0.655742	+	0.754985i	$0.272356\pi$
$132$		0			0
$133$	−10.6548	−	7.21561i	−0.923886	−	0.625673i
$134$			16.0340i			1.38513i
$135$		0			0
$136$	−2.10342	+	1.21441i	−0.180367	+	0.104135i
$137$	−0.538302	+	0.310789i	−0.0459903	+	0.0265525i	−0.522819	−	0.852444i	$-0.675120\pi$
$137$	−0.538302	+	0.310789i	−0.0459903	+	0.0265525i	0.476829	+	0.878996i	$0.341786\pi$
$138$		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
$142$	−6.38134	+	11.0528i	−0.535510	+	0.927531i
$143$	−1.13567	−	1.96705i	−0.0949699	−	0.164493i
$144$		0			0
$145$		0			0
$146$	−0.343146			−0.0283989
$147$		0			0
$148$	−5.48236			−0.450647
$149$	−12.1100	−	6.99171i	−0.992089	−	0.572783i	−0.0861911	−	0.996279i	$-0.527470\pi$
$149$	−12.1100	−	6.99171i	−0.992089	−	0.572783i	−0.905898	+	0.423496i	$0.860803\pi$
$150$		0			0
$151$	−9.83839	−	17.0406i	−0.800637	−	1.38674i	−0.919197	−	0.393797i	$-0.871161\pi$
$151$	−9.83839	−	17.0406i	−0.800637	−	1.38674i	0.118560	−	0.992947i	$-0.462172\pi$
$152$	−2.43185	+	4.21209i	−0.197249	+	0.341646i
$153$		0			0
$154$	−4.04354	−	0.290313i	−0.325838	−	0.0233941i
$155$		0			0
$156$		0			0
$157$	7.84628	−	4.53005i	0.626201	−	0.361538i	−0.153078	−	0.988214i	$-0.548919\pi$
$157$	7.84628	−	4.53005i	0.626201	−	0.361538i	0.779279	+	0.626677i	$0.215585\pi$
$158$	9.04889	−	5.22438i	0.719891	−	0.415629i
$159$		0			0
$160$		0			0
$161$	−0.586988	−	0.397520i	−0.0462612	−	0.0313289i
$162$		0			0
$163$	5.91019	−	10.2368i	0.462922	−	0.801804i	−0.536183	−	0.844102i	$-0.680134\pi$
$163$	5.91019	−	10.2368i	0.462922	−	0.801804i	0.999105	+	0.0422974i	$0.0134677\pi$
$164$	4.38014	+	7.58662i	0.342031	+	0.592416i
$165$		0			0
$166$	−4.71984	−	2.72500i	−0.366331	−	0.211501i
$167$	−15.7778			−1.22092			−0.610462	−	0.792046i	$-0.709016\pi$
$167$	−15.7778			−1.22092			−0.610462	+	0.792046i	$0.709016\pi$
$168$		0			0
$169$	10.8026			0.830969
$170$		0			0
$171$		0			0
$172$	−0.931852	−	1.61401i	−0.0710530	−	0.123067i
$173$	10.1111	−	17.5129i	0.768730	−	1.33148i	−0.169521	−	0.985527i	$-0.554222\pi$
$173$	10.1111	−	17.5129i	0.768730	−	1.33148i	0.938252	−	0.345954i	$-0.112445\pi$
$174$		0			0
$175$		0			0
$176$			1.53225i			0.115498i
$177$		0			0
$178$	−13.8305	+	7.98502i	−1.03664	+	0.598503i
$179$	−5.94667	+	3.43331i	−0.444475	+	0.256618i	−0.705494	−	0.708716i	$-0.749275\pi$
$179$	−5.94667	+	3.43331i	−0.444475	+	0.256618i	0.261019	+	0.965334i	$0.415941\pi$
$180$		0			0
$181$			16.3066i			1.21206i	0.795441	+	0.606031i	$0.207239\pi$
$181$			16.3066i			1.21206i	−0.795441	+	0.606031i	$0.792761\pi$
$182$	−2.19918	+	3.24737i	−0.163014	+	0.240711i
$183$		0			0
$184$	−0.133975	+	0.232051i	−0.00987674	+	0.0171070i
$185$		0			0
$186$		0			0
$187$	3.22297	+	1.86078i	0.235687	+	0.136074i
$188$	−7.45946			−0.544037
$189$		0			0
$190$		0			0
$191$	−14.8630	−	8.58114i	−1.07545	−	0.620910i	−0.145782	−	0.989317i	$-0.546570\pi$
$191$	−14.8630	−	8.58114i	−1.07545	−	0.620910i	−0.929665	+	0.368407i	$0.879903\pi$
$192$		0			0
$193$	4.52761	+	7.84204i	0.325904	+	0.564483i	0.981695	−	0.190460i	$-0.0609980\pi$
$193$	4.52761	+	7.84204i	0.325904	+	0.564483i	−0.655791	+	0.754943i	$0.727665\pi$
$194$	−7.47407	+	12.9455i	−0.536607	+	0.929430i
$195$		0			0
$196$	2.59808	+	6.50000i	0.185577	+	0.464286i
$197$		−	21.7379i		−	1.54876i	−0.632720	−	0.774380i	$-0.718062\pi$
$197$		−	21.7379i		−	1.54876i	0.632720	−	0.774380i	$-0.281938\pi$
$198$		0			0
$199$	−7.21101	+	4.16328i	−0.511175	+	0.295127i	−0.733317	−	0.679887i	$-0.762029\pi$
$199$	−7.21101	+	4.16328i	−0.511175	+	0.295127i	0.222141	+	0.975014i	$0.428695\pi$
$200$		0			0
$201$		0			0
$202$			2.73545i			0.192466i
$203$	0.170328	−	2.37237i	0.0119547	−	0.166508i
$204$		0			0
$205$		0			0
$206$	3.08845	+	5.34935i	0.215182	+	0.372707i
$207$		0			0
$208$	1.28376	+	0.741181i	0.0890130	+	0.0513917i
$209$	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	$0.740689\pi$
$212$	3.00524	+	1.73508i	0.206401	+	0.119166i
$213$		0			0
$214$	2.28497	+	3.95768i	0.156197	+	0.270541i
$215$		0			0
$216$		0			0
$217$	1.97177	−	0.957160i	0.133853	−	0.0649763i
$218$			5.95867i			0.403572i
$219$		0			0
$220$		0			0
$221$	3.11804	−	1.80020i	0.209742	−	0.121094i
$222$		0			0
$223$		−	7.16604i		−	0.479873i	−0.970789	−	0.239937i	$-0.922873\pi$
$223$		−	7.16604i		−	0.479873i	0.970789	−	0.239937i	$-0.0771267\pi$
$224$	2.38014	−	1.15539i	0.159030	−	0.0771980i
$225$		0			0
$226$	9.94887	−	17.2319i	0.661789	−	1.14625i
$227$	7.92721	+	13.7303i	0.526147	+	0.911314i	0.999536	+	0.0304601i	$0.00969726\pi$
$227$	7.92721	+	13.7303i	0.526147	+	0.911314i	−0.473389	+	0.880854i	$0.656969\pi$
$228$		0			0
$229$	24.4371	+	14.1087i	1.61485	+	0.932332i	0.988225	+	0.153009i	$0.0488964\pi$
$229$	24.4371	+	14.1087i	1.61485	+	0.932332i	0.626622	+	0.779323i	$0.284437\pi$
$230$		0			0
$231$		0			0
$232$	−0.898979			−0.0590209
$233$	21.0421	+	12.1487i	1.37851	+	0.795886i	0.991981	−	0.126390i	$-0.0403389\pi$
$233$	21.0421	+	12.1487i	1.37851	+	0.795886i	0.386534	+	0.922275i	$0.373672\pi$
$234$		0			0
$235$		0			0
$236$	3.12837	−	5.41849i	0.203639	−	0.352714i
$237$		0			0
$238$	0.460186	−	6.40957i	0.0298295	−	0.415471i
$239$		−	19.9081i		−	1.28774i	−0.765133	−	0.643872i	$-0.777327\pi$
$239$		−	19.9081i		−	1.28774i	0.765133	−	0.643872i	$-0.222673\pi$
$240$		0			0
$241$	17.7755	−	10.2627i	1.14502	−	0.661078i	0.197351	−	0.980333i	$-0.436766\pi$
$241$	17.7755	−	10.2627i	1.14502	−	0.661078i	0.947669	+	0.319255i	$0.103433\pi$
$242$	−7.49303	+	4.32611i	−0.481670	+	0.278093i
$243$		0			0
$244$			6.62158i			0.423903i
$245$		0			0
$246$		0			0
$247$	3.60488	−	6.24384i	0.229373	−	0.397286i
$248$	−0.414214	−	0.717439i	−0.0263026	−	0.0455574i
$249$		0			0
$250$		0			0
$251$	5.86787			0.370376			0.185188	−	0.982703i	$-0.440711\pi$
$251$	5.86787			0.370376			0.185188	+	0.982703i	$0.440711\pi$
$252$		0			0
$253$	0.410565			0.0258120
$254$	18.3619	+	10.6012i	1.15213	+	0.665181i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.83083	+	6.63519i	−0.238961	+	0.413892i	−0.960416	−	0.278569i	$-0.910140\pi$
$257$	−3.83083	+	6.63519i	−0.238961	+	0.413892i	0.721456	+	0.692461i	$0.243473\pi$
$258$		0			0
$259$	8.13343	−	12.0100i	0.505387	−	0.746268i
$260$		0			0
$261$		0			0
$262$	−6.46202	+	3.73085i	−0.399225	+	0.230493i
$263$	−7.32905	+	4.23143i	−0.451929	+	0.260921i	−0.708644	−	0.705566i	$-0.750693\pi$
$263$	−7.32905	+	4.23143i	−0.451929	+	0.260921i	0.256716	+	0.966487i	$0.417360\pi$
$264$		0			0
$265$		0			0
$266$	−5.61950	−	11.5763i	−0.344553	−	0.709788i
$267$		0			0
$268$	−8.01702	+	13.8859i	−0.489717	+	0.848215i
$269$	−8.52155	−	14.7598i	−0.519568	−	0.899919i	−0.999741	−	0.0227449i	$-0.992759\pi$
$269$	−8.52155	−	14.7598i	−0.519568	−	0.899919i	0.480173	−	0.877174i	$-0.340574\pi$
$270$		0			0
$271$	−9.12436	−	5.26795i	−0.554265	−	0.320005i	0.196575	−	0.980489i	$-0.437018\pi$
$271$	−9.12436	−	5.26795i	−0.554265	−	0.320005i	−0.750840	+	0.660484i	$0.770351\pi$
$272$	−2.42883			−0.147269
$273$		0			0
$274$	−0.621578			−0.0375509
$275$		0			0
$276$		0			0
$277$	−4.04561	−	7.00720i	−0.243077	−	0.421022i	0.718512	−	0.695514i	$-0.244823\pi$
$277$	−4.04561	−	7.00720i	−0.243077	−	0.421022i	−0.961589	+	0.274493i	$0.911490\pi$
$278$	−9.26670	+	16.0504i	−0.555780	+	0.962639i
$279$		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
$283$	6.24917	−	3.60796i	0.371475	−	0.214471i	−0.302628	−	0.953109i	$-0.597864\pi$
$283$	6.24917	−	3.60796i	0.371475	−	0.214471i	0.674103	+	0.738638i	$0.264531\pi$
$284$	−11.0528	+	6.38134i	−0.655863	+	0.378663i
$285$		0			0
$286$		−	2.27135i		−	0.134308i
$287$	−23.1180	−	1.65980i	−1.36461	−	0.0979748i
$288$		0			0
$289$	5.55040	−	9.61358i	0.326494	−	0.565505i
$290$		0			0
$291$		0			0
$292$	−0.297173	−	0.171573i	−0.0173907	−	0.0100405i
$293$	−18.2573			−1.06660			−0.533300	−	0.845926i	$-0.679048\pi$
$293$	−18.2573			−1.06660			−0.533300	+	0.845926i	$0.679048\pi$
$294$		0			0
$295$		0			0
$296$	−4.74786	−	2.74118i	−0.275964	−	0.159328i
$297$		0			0
$298$	−6.99171	−	12.1100i	−0.405019	−	0.701513i
$299$	0.198599	−	0.343983i	0.0114853	−	0.0198931i
$300$		0			0
$301$	4.91824	+	0.353113i	0.283482	+	0.0203531i
$302$		−	19.6768i		−	1.13227i
$303$		0			0
$304$	−4.21209	+	2.43185i	−0.241580	+	0.139476i
$305$		0			0
$306$		0			0
$307$		−	3.42078i		−	0.195234i	−0.995224	−	0.0976172i	$-0.968878\pi$
$307$		−	3.42078i		−	0.195234i	0.995224	−	0.0976172i	$-0.0311221\pi$
$308$	−3.35666	−	2.27319i	−0.191263	−	0.129527i
$309$		0			0
$310$		0			0
$311$	−2.84544	−	4.92845i	−0.161350	−	0.279467i	0.774003	−	0.633182i	$-0.218252\pi$
$311$	−2.84544	−	4.92845i	−0.161350	−	0.279467i	−0.935353	+	0.353715i	$0.884918\pi$
$312$		0			0
$313$	11.5586	+	6.67335i	0.653330	+	0.377200i	0.789731	−	0.613453i	$-0.210220\pi$
$313$	11.5586	+	6.67335i	0.653330	+	0.377200i	−0.136401	+	0.990654i	$0.543553\pi$
$314$	9.06010			0.511291
$315$		0			0
$316$	10.4488			0.587789
$317$	10.8484	+	6.26330i	0.609305	+	0.351782i	0.772693	−	0.634780i	$-0.218909\pi$
$317$	10.8484	+	6.26330i	0.609305	+	0.351782i	−0.163389	+	0.986562i	$0.552242\pi$
$318$		0			0
$319$	0.688731	+	1.19292i	0.0385615	+	0.0667905i
$320$		0			0
$321$		0			0
$322$	−0.309587	−	0.637756i	−0.0172526	−	0.0355408i
$323$			11.8131i			0.657298i
$324$		0			0
$325$		0			0
$326$	10.2368	−	5.91019i	0.566961	−	0.327335i
$327$		0			0
$328$			8.76028i			0.483705i
$329$	11.0666	−	16.3412i	0.610120	−	0.900920i
$330$		0			0
$331$	0.640916	−	1.11010i	0.0352279	−	0.0610166i	−0.847874	−	0.530198i	$-0.822118\pi$
$331$	0.640916	−	1.11010i	0.0352279	−	0.0610166i	0.883102	+	0.469181i	$0.155451\pi$
$332$	−2.72500	−	4.71984i	−0.149554	−	0.259035i
$333$		0			0
$334$	−13.6640	−	7.88891i	−0.747660	−	0.431662i
$335$		0			0
$336$		0			0
$337$	13.1058			0.713920			0.356960	−	0.934120i	$-0.383813\pi$
$337$	13.1058			0.713920			0.356960	+	0.934120i	$0.383813\pi$
$338$	9.35533	+	5.40130i	0.508863	+	0.293792i
$339$		0			0
$340$		0			0
$341$	−0.634679	+	1.09930i	−0.0343698	+	0.0595302i
$342$		0			0
$343$	−18.0938	−	3.95164i	−0.976972	−	0.213368i
$344$		−	1.86370i		−	0.100484i
$345$		0			0
$346$	17.5129	−	10.1111i	0.941499	−	0.543574i
$347$	−12.3714	+	7.14262i	−0.664130	+	0.383436i	−0.793849	−	0.608115i	$-0.791926\pi$
$347$	−12.3714	+	7.14262i	−0.664130	+	0.383436i	0.129719	+	0.991551i	$0.458593\pi$
$348$		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
$352$	−0.766125	+	1.32697i	−0.0408346	+	0.0707276i
$353$	−16.3232	−	28.2725i	−0.868794	−	1.50480i	−0.863230	−	0.504811i	$-0.831562\pi$
$353$	−16.3232	−	28.2725i	−0.868794	−	1.50480i	−0.00556437	−	0.999985i	$-0.501771\pi$
$354$		0			0
$355$		0			0
$356$	−15.9700			−0.846411
$357$		0			0
$358$	−6.86662			−0.362912
$359$	5.40692	+	3.12168i	0.285366	+	0.164756i	0.635850	−	0.771812i	$-0.280650\pi$
$359$	5.40692	+	3.12168i	0.285366	+	0.164756i	−0.350484	+	0.936569i	$0.613983\pi$
$360$		0			0
$361$	2.32780	+	4.03188i	0.122516	+	0.212204i
$362$	−8.15331	+	14.1220i	−0.428529	+	0.742233i
$363$		0			0
$364$	−3.52823	+	1.71271i	−0.184929	+	0.0897705i
$365$		0			0
$366$		0			0
$367$	−10.9026	+	6.29461i	−0.569110	+	0.328576i	−0.756794	−	0.653654i	$-0.773235\pi$
$367$	−10.9026	+	6.29461i	−0.569110	+	0.328576i	0.187684	+	0.982230i	$0.439902\pi$
$368$	−0.232051	+	0.133975i	−0.0120965	+	0.00698391i
$369$		0			0
$370$		0			0
$371$	−8.25945	+	4.00940i	−0.428809	+	0.208158i
$372$		0			0
$373$	17.9791	−	31.1408i	0.930924	−	1.61241i	0.149179	−	0.988810i	$-0.452337\pi$
$373$	17.9791	−	31.1408i	0.930924	−	1.61241i	0.781745	−	0.623598i	$-0.214330\pi$
$374$	1.86078	+	3.22297i	0.0962188	+	0.166656i
$375$		0			0
$376$	−6.46008	−	3.72973i	−0.333153	−	0.192346i
$377$	1.33261			0.0686331
$378$		0			0
$379$	−11.5899			−0.595331			−0.297666	−	0.954670i	$-0.596208\pi$
$379$	−11.5899			−0.595331			−0.297666	+	0.954670i	$0.596208\pi$
$380$		0			0
$381$		0			0
$382$	−8.58114	−	14.8630i	−0.439049	−	0.760456i
$383$	−2.23375	+	3.86897i	−0.114139	+	0.197695i	−0.917435	−	0.397885i	$-0.869744\pi$
$383$	−2.23375	+	3.86897i	−0.114139	+	0.197695i	0.803296	+	0.595580i	$0.203078\pi$
$384$		0			0
$385$		0			0
$386$			9.05521i			0.460898i
$387$		0			0
$388$	−12.9455	+	7.47407i	−0.657207	+	0.379438i
$389$	−11.2197	+	6.47772i	−0.568863	+	0.328433i	−0.756695	−	0.653768i	$-0.773187\pi$
$389$	−11.2197	+	6.47772i	−0.568863	+	0.328433i	0.187832	+	0.982201i	$0.439854\pi$
$390$		0			0
$391$			0.650802i			0.0329125i
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$		0			0
$394$	10.8689	−	18.8256i	0.547570	−	0.948418i
$395$		0			0
$396$		0			0
$397$	−8.03664	−	4.63995i	−0.403347	−	0.232873i	0.284580	−	0.958652i	$-0.408146\pi$
$397$	−8.03664	−	4.63995i	−0.403347	−	0.232873i	−0.687927	+	0.725780i	$0.741479\pi$
$398$	−8.32656			−0.417373
$399$		0			0
$400$		0			0
$401$	−6.44260	−	3.71964i	−0.321728	−	0.185750i	0.330434	−	0.943829i	$-0.392805\pi$
$401$	−6.44260	−	3.71964i	−0.321728	−	0.185750i	−0.652163	+	0.758079i	$0.726138\pi$
$402$		0			0
$403$	0.614014	+	1.06350i	0.0305862	+	0.0529769i
$404$	−1.36773	+	2.36897i	−0.0680469	+	0.117861i
$405$		0			0
$406$	1.33369	−	1.96937i	0.0661901	−	0.0977381i
$407$			8.40035i			0.416390i
$408$		0			0
$409$	−13.8647	+	8.00481i	−0.685567	+	0.395812i	−0.801949	−	0.597392i	$-0.796204\pi$
$409$	−13.8647	+	8.00481i	−0.685567	+	0.395812i	0.116382	+	0.993204i	$0.462870\pi$
$410$		0			0
$411$		0			0
$412$			6.17690i			0.304314i
$413$	7.22900	+	14.8919i	0.355716	+	0.732783i
$414$		0			0
$415$		0			0
$416$	0.741181	+	1.28376i	0.0363394	+	0.0629417i
$417$		0			0
$418$	6.45398	+	3.72620i	0.315674	+	0.182255i
$419$	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	$0.356890\pi$
$422$	−17.2625	−	9.96651i	−0.840325	−	0.485162i
$423$		0			0
$424$	1.73508	+	3.00524i	0.0842628	+	0.145947i
$425$		0			0
$426$		0			0
$427$	−14.5057	−	9.82353i	−0.701980	−	0.475394i
$428$			4.56993i			0.220896i
$429$		0			0
$430$		0			0
$431$	−26.7539	+	15.4464i	−1.28869	+	0.744025i	−0.978420	−	0.206624i	$-0.933752\pi$
$431$	−26.7539	+	15.4464i	−1.28869	+	0.744025i	−0.310268	+	0.950649i	$0.600419\pi$
$432$		0			0
$433$			15.2207i			0.731462i	0.930721	+	0.365731i	$0.119181\pi$
$433$			15.2207i			0.731462i	−0.930721	+	0.365731i	$0.880819\pi$
$434$	2.18618	+	0.156961i	0.104940	+	0.00753437i
$435$		0			0
$436$	−2.97934	+	5.16036i	−0.142684	+	0.247136i
$437$	0.651613	+	1.12863i	0.0311709	+	0.0539895i
$438$		0			0
$439$	12.4054	+	7.16228i	0.592079	+	0.341837i	0.765919	−	0.642937i	$-0.222284\pi$
$439$	12.4054	+	7.16228i	0.592079	+	0.341837i	−0.173840	+	0.984774i	$0.555618\pi$
$440$		0			0
$441$		0			0
$442$	3.60040			0.171253
$443$	4.46651	+	2.57874i	0.212210	+	0.122520i	0.602338	−	0.798241i	$-0.294236\pi$
$443$	4.46651	+	2.57874i	0.212210	+	0.122520i	−0.390128	+	0.920761i	$0.627569\pi$
$444$		0			0
$445$		0			0
$446$	3.58302	−	6.20597i	0.169661	−	0.293861i
$447$		0			0
$448$	2.63896	+	0.189469i	0.124679	+	0.00895155i
$449$		−	19.9377i		−	0.940918i	−0.882422	−	0.470459i	$-0.844088\pi$
$449$		−	19.9377i		−	0.940918i	0.882422	−	0.470459i	$-0.155912\pi$
$450$		0			0
$451$	11.6246	−	6.71147i	0.547381	−	0.316031i
$452$	17.2319	−	9.94887i	0.810522	−	0.467955i
$453$		0			0
$454$			15.8544i			0.744085i
$455$		0			0
$456$		0			0
$457$	5.66995	−	9.82065i	0.265229	−	0.459391i	−0.702394	−	0.711788i	$-0.747886\pi$
$457$	5.66995	−	9.82065i	0.265229	−	0.459391i	0.967624	+	0.252397i	$0.0812190\pi$
$458$	14.1087	+	24.4371i	0.659258	+	1.14187i
$459$		0			0
$460$		0			0
$461$	2.01890			0.0940298			0.0470149	−	0.998894i	$-0.485029\pi$
$461$	2.01890			0.0940298			0.0470149	+	0.998894i	$0.485029\pi$
$462$		0			0
$463$	27.2844			1.26801			0.634007	−	0.773327i	$-0.281409\pi$
$463$	27.2844			1.26801			0.634007	+	0.773327i	$0.281409\pi$
$464$	−0.778539	−	0.449490i	−0.0361428	−	0.0208670i
$465$		0			0
$466$	12.1487	+	21.0421i	0.562776	+	0.974757i
$467$	0.346065	−	0.599403i	0.0160140	−	0.0277370i	−0.857907	−	0.513804i	$-0.828236\pi$
$467$	0.346065	−	0.599403i	0.0160140	−	0.0277370i	0.873921	+	0.486067i	$0.161569\pi$
$468$		0			0
$469$	−18.5256	−	38.1632i	−0.855434	−	1.76221i
$470$		0			0
$471$		0			0
$472$	5.41849	−	3.12837i	0.249406	−	0.143995i
$473$	−2.47307	+	1.42783i	−0.113712	+	0.0656517i
$474$		0			0
$475$		0			0
$476$	3.60332	−	5.32076i	0.165158	−	0.243876i
$477$		0			0
$478$	9.95403	−	17.2409i	0.455287	−	0.788580i
$479$	−7.95403	−	13.7768i	−0.363429	−	0.629477i	0.625094	−	0.780550i	$-0.285061\pi$
$479$	−7.95403	−	13.7768i	−0.363429	−	0.629477i	−0.988523	+	0.151072i	$0.951727\pi$
$480$		0			0
$481$	7.03805	+	4.06342i	0.320908	+	0.185276i
$482$	20.5254			0.934905
$483$		0			0
$484$	−8.65221			−0.393282
$485$		0			0
$486$		0			0
$487$	−14.3749	−	24.8981i	−0.651390	−	1.12824i	−0.982786	−	0.184749i	$-0.940853\pi$
$487$	−14.3749	−	24.8981i	−0.651390	−	1.12824i	0.331396	−	0.943492i	$-0.392480\pi$
$488$	−3.31079	+	5.73445i	−0.149872	+	0.259587i
$489$		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
$493$	−1.89094	+	1.09173i	−0.0851635	+	0.0491691i
$494$	6.24384	−	3.60488i	0.280924	−	0.162191i
$495$		0			0
$496$		−	0.828427i		−	0.0371975i
$497$	2.41813	−	33.6802i	0.108468	−	1.51076i
$498$		0			0
$499$	4.43148	−	7.67555i	0.198380	−	0.343605i	−0.749623	−	0.661865i	$-0.769765\pi$
$499$	4.43148	−	7.67555i	0.198380	−	0.343605i	0.948003	+	0.318260i	$0.103099\pi$
$500$		0			0
$501$		0			0
$502$	5.08172	+	2.93393i	0.226808	+	0.130948i
$503$	9.36536			0.417581			0.208790	−	0.977960i	$-0.433047\pi$
$503$	9.36536			0.417581			0.208790	+	0.977960i	$0.433047\pi$
$504$		0			0
$505$		0			0
$506$	0.355560	+	0.205283i	0.0158066	+	0.00912592i
$507$		0			0
$508$	10.6012	+	18.3619i	0.470354	+	0.814677i
$509$	−17.5164	+	30.3393i	−0.776400	+	1.34477i	0.157603	+	0.987502i	$0.449623\pi$
$509$	−17.5164	+	30.3393i	−0.776400	+	1.34477i	−0.934004	+	0.357263i	$0.883710\pi$
$510$		0			0
$511$	0.816735	−	0.396469i	0.0361302	−	0.0175387i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−6.63519	+	3.83083i	−0.292666	+	0.168971i
$515$		0			0
$516$		0			0
$517$			11.4298i			0.502680i
$518$	13.0488	−	6.33429i	0.573331	−	0.278313i
$519$		0			0
$520$		0			0
$521$	9.99807	+	17.3172i	0.438023	+	0.758679i	0.997537	−	0.0701424i	$-0.0223454\pi$
$521$	9.99807	+	17.3172i	0.438023	+	0.758679i	−0.559514	+	0.828821i	$0.689012\pi$
$522$		0			0
$523$	29.0144	+	16.7515i	1.26871	+	0.732491i	0.974744	−	0.223325i	$-0.0716911\pi$
$523$	29.0144	+	16.7515i	1.26871	+	0.732491i	0.293967	+	0.955816i	$0.405024\pi$
$524$	−7.46170			−0.325966
$525$		0			0
$526$	−8.46286			−0.368998
$527$	−1.74253	−	1.00605i	−0.0759060	−	0.0438243i
$528$		0			0
$529$	−11.4641	−	19.8564i	−0.498439	−	0.863322i
$530$		0			0
$531$		0			0
$532$	0.921519	−	12.8351i	0.0399529	−	0.556473i
$533$		−	12.9859i		−	0.562482i
$534$		0			0
$535$		0			0
$536$	−13.8859	+	8.01702i	−0.599779	+	0.346282i
$537$		0			0
$538$		−	17.0431i		−	0.734781i
$539$	9.95962	−	3.98090i	0.428991	−	0.171470i
$540$		0			0
$541$	−18.8766	+	32.6952i	−0.811568	+	1.40568i	0.100198	+	0.994967i	$0.468052\pi$
$541$	−18.8766	+	32.6952i	−0.811568	+	1.40568i	−0.911766	+	0.410710i	$0.865281\pi$
$542$	−5.26795	−	9.12436i	−0.226278	−	0.391925i
$543$		0			0
$544$	−2.10342	−	1.21441i	−0.0901836	−	0.0520675i
$545$		0			0
$546$		0			0
$547$	−5.07130			−0.216833			−0.108417	−	0.994106i	$-0.534578\pi$
$547$	−5.07130			−0.216833			−0.108417	+	0.994106i	$0.534578\pi$
$548$	−0.538302	−	0.310789i	−0.0229951	−	0.0132762i
$549$		0			0
$550$		0			0
$551$	−2.18618	+	3.78658i	−0.0931346	+	0.161314i
$552$		0			0
$553$	−15.5014	+	22.8898i	−0.659187	+	0.973373i
$554$		−	8.09122i		−	0.343763i
$555$		0			0
$556$	−16.0504	+	9.26670i	−0.680689	+	0.392996i
$557$	29.7528	−	17.1778i	1.26067	−	0.727846i	0.287463	−	0.957792i	$-0.407188\pi$
$557$	29.7528	−	17.1778i	1.26067	−	0.727846i	0.973203	+	0.229946i	$0.0738548\pi$
$558$		0			0
$559$			2.76268i			0.116849i
$560$		0			0
$561$		0			0
$562$	5.58422	−	9.67215i	0.235556	−	0.407995i
$563$	−23.5293	−	40.7539i	−0.991641	−	1.71757i	−0.607562	−	0.794272i	$-0.707852\pi$
$563$	−23.5293	−	40.7539i	−0.991641	−	1.71757i	−0.384079	−	0.923300i	$-0.625481\pi$
$564$		0			0
$565$		0			0
$566$	7.21592			0.303308
$567$		0			0
$568$	−12.7627			−0.535510
$569$	38.2670	+	22.0934i	1.60424	+	0.926206i	0.990627	+	0.136595i	$0.0436159\pi$
$569$	38.2670	+	22.0934i	1.60424	+	0.926206i	0.613608	+	0.789611i	$0.289717\pi$
$570$		0			0
$571$	−20.5804	−	35.6463i	−0.861263	−	1.49175i	−0.870710	−	0.491797i	$-0.836340\pi$
$571$	−20.5804	−	35.6463i	−0.861263	−	1.49175i	0.00944654	−	0.999955i	$-0.496993\pi$
$572$	1.13567	−	1.96705i	0.0474849	−	0.0822463i
$573$		0			0
$574$	−19.1909	−	12.9964i	−0.801012	−	0.542461i
$575$		0			0
$576$		0			0
$577$	−12.2293	+	7.06058i	−0.509112	+	0.293936i	−0.732469	−	0.680801i	$-0.761632\pi$
$577$	−12.2293	+	7.06058i	−0.509112	+	0.293936i	0.223357	+	0.974737i	$0.428299\pi$
$578$	9.61358	−	5.55040i	0.399872	−	0.230866i
$579$		0			0
$580$		0			0
$581$	14.3823	+	1.03261i	0.596680	+	0.0428397i
$582$		0			0
$583$	2.65857	−	4.60478i	0.110107	−	0.190711i
$584$	−0.171573	−	0.297173i	−0.00709974	−	0.0122971i
$585$		0			0
$586$	−15.8112	−	9.12863i	−0.653156	−	0.377100i
$587$	37.7819			1.55942			0.779712	−	0.626138i	$-0.215365\pi$
$587$	37.7819			1.55942			0.779712	+	0.626138i	$0.215365\pi$
$588$		0			0
$589$	−4.02922			−0.166021
$590$		0			0
$591$		0			0
$592$	−2.74118	−	4.74786i	−0.112662	−	0.195136i
$593$	−13.0981	+	22.6865i	−0.537873	+	0.931623i	0.461146	+	0.887324i	$0.347438\pi$
$593$	−13.0981	+	22.6865i	−0.537873	+	0.931623i	−0.999018	+	0.0442982i	$0.985895\pi$
$594$		0			0
$595$		0			0
$596$		−	13.9834i		−	0.572783i
$597$		0			0
$598$	0.343983	−	0.198599i	0.0140665	−	0.00812131i
$599$	4.15712	−	2.40012i	0.169856	−	0.0980661i	−0.412662	−	0.910884i	$-0.635401\pi$
$599$	4.15712	−	2.40012i	0.169856	−	0.0980661i	0.582518	+	0.812818i	$0.302068\pi$
$600$		0			0
$601$		−	37.3722i		−	1.52444i	−0.647317	−	0.762221i	$-0.724109\pi$
$601$		−	37.3722i		−	1.52444i	0.647317	−	0.762221i	$-0.275891\pi$
$602$	4.08276	+	2.76492i	0.166401	+	0.112690i
$603$		0			0
$604$	9.83839	−	17.0406i	0.400319	−	0.693372i
$605$		0			0
$606$		0			0
$607$	−32.2499	−	18.6195i	−1.30898	−	0.755742i	−0.327057	−	0.945005i	$-0.606057\pi$
$607$	−32.2499	−	18.6195i	−1.30898	−	0.755742i	−0.981927	+	0.189263i	$0.939390\pi$
$608$	−4.86370			−0.197249
$609$		0			0
$610$		0			0
$611$	9.57618	+	5.52881i	0.387411	+	0.223672i
$612$		0			0
$613$	−4.92977	−	8.53861i	−0.199112	−	0.344871i	0.749129	−	0.662424i	$-0.230472\pi$
$613$	−4.92977	−	8.53861i	−0.199112	−	0.344871i	−0.948241	+	0.317553i	$0.897139\pi$
$614$	1.71039	−	2.96248i	0.0690258	−	0.119556i
$615$		0			0
$616$	−1.77035	−	3.64697i	−0.0713296	−	0.146941i
$617$		−	31.3545i		−	1.26229i	−0.775666	−	0.631143i	$-0.782586\pi$
$617$		−	31.3545i		−	1.26229i	0.775666	−	0.631143i	$-0.217414\pi$
$618$		0			0
$619$	−13.1943	+	7.61774i	−0.530325	+	0.306183i	−0.741149	−	0.671341i	$-0.765719\pi$
$619$	−13.1943	+	7.61774i	−0.530325	+	0.306183i	0.210824	+	0.977524i	$0.432385\pi$
$620$		0			0
$621$		0			0
$622$		−	5.69089i		−	0.228184i
$623$	23.6926	−	34.9851i	0.949223	−	1.40165i
$624$		0			0
$625$		0			0
$626$	6.67335	+	11.5586i	0.266721	+	0.461974i
$627$		0			0
$628$	7.84628	+	4.53005i	0.313101	+	0.180769i
$629$	−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	$0.506362\pi$
$632$	9.04889	+	5.22438i	0.359946	+	0.207815i
$633$		0			0
$634$	6.26330	+	10.8484i	0.248748	+	0.430844i
$635$		0			0
$636$		0			0
$637$	1.48236	−	10.2701i	0.0587333	−	0.406916i
$638$			1.37746i			0.0545342i
$639$		0			0
$640$		0			0
$641$	20.2689	−	11.7023i	0.800574	−	0.462211i	−0.0430981	−	0.999071i	$-0.513723\pi$
$641$	20.2689	−	11.7023i	0.800574	−	0.462211i	0.843672	+	0.536860i	$0.180389\pi$
$642$		0			0
$643$			33.4475i			1.31904i	0.751686	+	0.659521i	$0.229241\pi$
$643$			33.4475i			1.31904i	−0.751686	+	0.659521i	$0.770759\pi$
$644$	0.0507680	−	0.707107i	0.00200054	−	0.0278639i
$645$		0			0
$646$	−5.90654	+	10.2304i	−0.232390	+	0.402511i
$647$	−8.28540	−	14.3507i	−0.325733	−	0.564185i	0.655928	−	0.754824i	$-0.272278\pi$
$647$	−8.28540	−	14.3507i	−0.325733	−	0.564185i	−0.981660	+	0.190638i	$0.938944\pi$
$648$		0			0
$649$	−8.30249	−	4.79344i	−0.325901	−	0.188159i
$650$		0			0
$651$		0			0
$652$	11.8204			0.462922
$653$	5.22132	+	3.01453i	0.204326	+	0.117968i	0.598672	−	0.800994i	$-0.295695\pi$
$653$	5.22132	+	3.01453i	0.204326	+	0.117968i	−0.394346	+	0.918962i	$0.629029\pi$
$654$		0			0
$655$		0			0
$656$	−4.38014	+	7.58662i	−0.171016	+	0.296208i
$657$		0			0
$658$	17.7545	−	8.61862i	0.692144	−	0.335989i
$659$		−	36.3672i		−	1.41666i	−0.705880	−	0.708332i	$-0.749448\pi$
$659$		−	36.3672i		−	1.41666i	0.705880	−	0.708332i	$-0.250552\pi$
$660$		0			0
$661$	−9.90289	+	5.71744i	−0.385178	+	0.222383i	−0.680069	−	0.733148i	$-0.738050\pi$
$661$	−9.90289	+	5.71744i	−0.385178	+	0.222383i	0.294891	+	0.955531i	$0.404717\pi$
$662$	1.11010	−	0.640916i	0.0431452	−	0.0249099i
$663$		0			0
$664$		−	5.45001i		−	0.211501i
$665$		0			0
$666$		0			0
$667$	−0.120440	+	0.208609i	−0.00466347	+	0.00807737i
$668$	−7.88891	−	13.6640i	−0.305231	−	0.528675i
$669$		0			0
$670$		0			0
$671$	10.1459			0.391679
$672$		0			0
$673$	−10.8070			−0.416581			−0.208290	−	0.978067i	$-0.566790\pi$
$673$	−10.8070			−0.416581			−0.208290	+	0.978067i	$0.566790\pi$
$674$	11.3500	+	6.55291i	0.437185	+	0.252409i
$675$		0			0
$676$	5.40130	+	9.35533i	0.207742	+	0.359820i
$677$	7.02280	−	12.1638i	0.269908	−	0.467494i	−0.698930	−	0.715190i	$-0.746340\pi$
$677$	7.02280	−	12.1638i	0.269908	−	0.467494i	0.968838	+	0.247696i	$0.0796734\pi$
$678$		0			0
$679$	2.83220	−	39.4475i	0.108690	−	1.51386i
$680$		0			0
$681$		0			0
$682$	−1.09930	+	0.634679i	−0.0420942	+	0.0243031i
$683$	−31.5900	+	18.2385i	−1.20876	+	0.697877i	−0.962488	−	0.271324i	$-0.912539\pi$
$683$	−31.5900	+	18.2385i	−1.20876	+	0.697877i	−0.246271	+	0.969201i	$0.579205\pi$
$684$		0			0
$685$		0			0
$686$	−13.6938	−	12.4691i	−0.522834	−	0.476073i
$687$		0			0
$688$	0.931852	−	1.61401i	0.0355265	−	0.0615337i
$689$	−2.57201	−	4.45486i	−0.0979859	−	0.169716i
$690$		0			0
$691$	−20.5831	−	11.8836i	−0.783017	−	0.452075i	0.0544816	−	0.998515i	$-0.482649\pi$
$691$	−20.5831	−	11.8836i	−0.783017	−	0.452075i	−0.837498	+	0.546440i	$0.815983\pi$
$692$	20.2221			0.768730
$693$		0			0
$694$	−14.2852			−0.542260
$695$		0			0
$696$		0			0
$697$	10.6386	+	18.4266i	0.402965	+	0.697957i
$698$	−6.63567	+	11.4933i	−0.251164	+	0.435029i
$699$		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
$703$	−23.0922	+	13.3323i	−0.870939	+	0.502837i
$704$	−1.32697	+	0.766125i	−0.0500120	+	0.0288744i
$705$		0			0
$706$		−	32.6463i		−	1.22866i
$707$	−3.16052	−	6.51075i	−0.118864	−	0.244862i
$708$		0			0
$709$	6.06162	−	10.4990i	0.227649	−	0.394299i	−0.729462	−	0.684021i	$-0.760230\pi$
$709$	6.06162	−	10.4990i	0.227649	−	0.394299i	0.957111	+	0.289722i	$0.0935629\pi$
$710$		0			0
$711$		0			0
$712$	−13.8305	−	7.98502i	−0.518319	−	0.299251i
$713$	−0.221976			−0.00831308
$714$		0			0
$715$		0			0
$716$	−5.94667	−	3.43331i	−0.222237	−	0.128309i
$717$		0			0
$718$	3.12168	+	5.40692i	0.116500	+	0.201784i
$719$	0.893176	−	1.54703i	0.0333098	−	0.0576943i	−0.848890	−	0.528570i	$-0.822729\pi$
$719$	0.893176	−	1.54703i	0.0333098	−	0.0576943i	0.882200	+	0.470875i	$0.156062\pi$
$720$		0			0
$721$	−13.5315	−	9.16382i	−0.503941	−	0.341279i
$722$			4.65561i			0.173264i
$723$		0			0
$724$	−14.1220	+	8.15331i	−0.524838	+	0.303015i
$725$		0			0
$726$		0			0
$727$		−	29.8785i		−	1.10813i	−0.832472	−	0.554066i	$-0.813075\pi$
$727$		−	29.8785i		−	1.10813i	0.832472	−	0.554066i	$-0.186925\pi$
$728$	−3.91189	−	0.280861i	−0.144984	−	0.0104094i
$729$		0			0
$730$		0			0
$731$	−2.26330	−	3.92016i	−0.0837114	−	0.144992i
$732$		0			0
$733$	11.9434	+	6.89554i	0.441140	+	0.254692i	0.704081	−	0.710119i	$-0.251359\pi$
$733$	11.9434	+	6.89554i	0.441140	+	0.254692i	−0.262941	+	0.964812i	$0.584692\pi$
$734$	−12.5892			−0.464677
$735$		0			0
$736$	−0.267949			−0.00987674
$737$	21.2766	+	12.2841i	0.783735	+	0.452490i
$738$		0			0
$739$	−3.68349	−	6.37999i	−0.135499	−	0.234692i	0.790289	−	0.612735i	$-0.209931\pi$
$739$	−3.68349	−	6.37999i	−0.135499	−	0.234692i	−0.925788	+	0.378043i	$0.876597\pi$
$740$		0			0
$741$		0			0
$742$	−9.15759	−	0.657486i	−0.336186	−	0.0241371i
$743$			11.0774i			0.406389i	0.979138	+	0.203194i	$0.0651323\pi$
$743$			11.0774i			0.406389i	−0.979138	+	0.203194i	$0.934868\pi$
$744$		0			0
$745$		0			0
$746$	31.1408	−	17.9791i	1.14014	−	0.658263i
$747$		0			0
$748$			3.72157i			0.136074i
$749$	−10.0112	−	6.77978i	−0.365802	−	0.247728i
$750$		0			0
$751$	−12.1879	+	21.1100i	−0.444741	+	0.770315i	−0.998034	−	0.0626722i	$-0.980038\pi$
$751$	−12.1879	+	21.1100i	−0.444741	+	0.770315i	0.553293	+	0.832987i	$0.313371\pi$
$752$	−3.72973	−	6.46008i	−0.136009	−	0.235575i
$753$		0			0
$754$	1.15408	+	0.666306i	0.0420290	+	0.0242655i
$755$		0			0
$756$		0			0
$757$	−19.6761			−0.715139			−0.357569	−	0.933887i	$-0.616394\pi$
$757$	−19.6761			−0.715139			−0.357569	+	0.933887i	$0.616394\pi$
$758$	−10.0371	−	5.79493i	−0.364565	−	0.210481i
$759$		0			0
$760$		0			0
$761$	24.9168	−	43.1572i	0.903234	−	1.56445i	0.0799647	−	0.996798i	$-0.474519\pi$
$761$	24.9168	−	43.1572i	0.903234	−	1.56445i	0.823270	−	0.567650i	$-0.192147\pi$
$762$		0			0
$763$	−6.88462	−	14.1825i	−0.249240	−	0.513440i
$764$		−	17.1623i		−	0.620910i
$765$		0			0
$766$	−3.86897	+	2.23375i	−0.139792	+	0.0807087i
$767$	−8.03217	+	4.63737i	−0.290025	+	0.167446i
$768$		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
$772$	−4.52761	+	7.84204i	−0.162952	+	0.282241i
$773$	−1.98525	−	3.43855i	−0.0714043	−	0.123676i	0.828113	−	0.560562i	$-0.189415\pi$
$773$	−1.98525	−	3.43855i	−0.0714043	−	0.123676i	−0.899517	+	0.436886i	$0.856081\pi$
$774$		0			0
$775$		0			0
$776$	−14.9481			−0.536607
$777$		0			0
$778$	−12.9554			−0.464475
$779$	36.8991	+	21.3037i	1.32205	+	0.763284i
$780$		0			0
$781$	9.77781	+	16.9357i	0.349878	+	0.606006i
$782$	−0.325401	+	0.563611i	−0.0116363	+	0.0201547i
$783$		0			0
$784$	−4.33013	+	5.50000i	−0.154647	+	0.196429i
$785$		0			0
$786$		0			0
$787$	−38.8001	+	22.4013i	−1.38308	+	0.798519i	−0.992523	−	0.122061i	$-0.961050\pi$
$787$	−38.8001	+	22.4013i	−1.38308	+	0.798519i	−0.390553	+	0.920580i	$0.627716\pi$
$788$	18.8256	−	10.8689i	0.670633	−	0.387190i
$789$		0			0
$790$		0			0
$791$	−3.77000	+	52.5093i	−0.134046	+	1.86702i
$792$		0			0
$793$	4.90779	−	8.50054i	0.174281	−	0.301863i
$794$	−4.63995	−	8.03664i	−0.164666	−	0.285210i
$795$		0			0
$796$	−7.21101	−	4.16328i	−0.255588	−	0.147564i
$797$	38.4813			1.36308			0.681539	−	0.731781i	$-0.261311\pi$
$797$	38.4813			1.36308			0.681539	+	0.731781i	$0.261311\pi$
$798$		0			0
$799$	−18.1177			−0.640959
$800$		0			0
$801$		0			0
$802$	−3.71964	−	6.44260i	−0.131345	−	0.227496i
$803$	−0.262893	+	0.455343i	−0.00927728	+	0.0160687i
$804$		0			0
$805$		0			0
$806$			1.22803i			0.0432555i
$807$		0			0
$808$	−2.36897	+	1.36773i	−0.0833401	+	0.0481164i
$809$	15.0298	−	8.67748i	0.528421	−	0.305084i	−0.211952	−	0.977280i	$-0.567982\pi$
$809$	15.0298	−	8.67748i	0.528421	−	0.305084i	0.740373	+	0.672196i	$0.234649\pi$
$810$		0			0
$811$			32.7270i			1.14920i	0.818434	+	0.574601i	$0.194843\pi$
$811$			32.7270i			1.14920i	−0.818434	+	0.574601i	$0.805157\pi$
$812$	2.13970	−	1.03868i	0.0750886	−	0.0364504i
$813$		0			0
$814$	−4.20017	+	7.27492i	−0.147216	+	0.254986i
$815$		0			0
$816$		0			0
$817$	−7.85009	−	4.53225i	−0.274640	−	0.158563i
$818$	−16.0096			−0.559763
$819$		0			0
$820$		0			0
$821$	15.4093	+	8.89658i	0.537789	+	0.310493i	0.744182	−	0.667976i	$-0.232839\pi$
$821$	15.4093	+	8.89658i	0.537789	+	0.310493i	−0.206393	+	0.978469i	$0.566173\pi$
$822$		0			0
$823$	4.91082	+	8.50579i	0.171181	+	0.296493i	0.938833	−	0.344373i	$-0.111909\pi$
$823$	4.91082	+	8.50579i	0.171181	+	0.296493i	−0.767652	+	0.640867i	$0.778575\pi$
$824$	−3.08845	+	5.34935i	−0.107591	+	0.186353i
$825$		0			0
$826$	−1.18546	+	16.5113i	−0.0412473	+	0.574501i
$827$			7.78482i			0.270705i	0.990798	+	0.135352i	$0.0432167\pi$
$827$			7.78482i			0.270705i	−0.990798	+	0.135352i	$0.956783\pi$
$828$		0			0
$829$	−13.1015	+	7.56413i	−0.455032	+	0.262713i	−0.709953	−	0.704249i	$-0.751284\pi$
$829$	−13.1015	+	7.56413i	−0.455032	+	0.262713i	0.254921	+	0.966962i	$0.417951\pi$
$830$		0			0
$831$		0			0
$832$			1.48236i			0.0513917i
$833$	6.31027	+	15.7874i	0.218638	+	0.547000i
$834$		0			0
$835$		0			0
$836$	3.72620	+	6.45398i	0.128873	+	0.223215i
$837$		0			0
$838$	24.6314	+	14.2209i	0.850877	+	0.491254i
$839$	−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
$842$	15.4451	+	8.91724i	0.532274	+	0.307308i
$843$		0			0
$844$	−9.96651	−	17.2625i	−0.343061	−	0.594200i
$845$		0			0
$846$		0			0
$847$	12.8361	−	18.9541i	0.441054	−	0.651272i
$848$			3.47015i			0.119166i
$849$		0			0
$850$		0			0
$851$	−1.27219	+	0.734497i	−0.0436100	+	0.0251782i
$852$		0			0
$853$			23.3020i			0.797846i	0.916984	+	0.398923i	$0.130616\pi$
$853$			23.3020i			0.797846i	−0.916984	+	0.398923i	$0.869384\pi$
$854$	−7.65053	−	15.7603i	−0.261796	−	0.539306i
$855$		0			0
$856$	−2.28497	+	3.95768i	−0.0780985	+	0.135271i
$857$	13.3030	+	23.0414i	0.454421	+	0.787080i	0.998655	−	0.0518534i	$-0.0165128\pi$
$857$	13.3030	+	23.0414i	0.454421	+	0.787080i	−0.544234	+	0.838934i	$0.683180\pi$
$858$		0			0
$859$	49.0044	+	28.2927i	1.67201	+	0.965334i	0.966512	+	0.256620i	$0.0826088\pi$
$859$	49.0044	+	28.2927i	1.67201	+	0.965334i	0.705495	+	0.708714i	$0.250725\pi$
$860$		0			0
$861$		0			0
$862$	−30.8927			−1.05221
$863$	29.4939	+	17.0283i	1.00398	+	0.579650i	0.909425	−	0.415869i	$-0.136522\pi$
$863$	29.4939	+	17.0283i	1.00398	+	0.579650i	0.0945593	+	0.995519i	$0.469856\pi$
$864$		0			0
$865$		0			0
$866$	−7.61037	+	13.1815i	−0.258611	+	0.447927i
$867$		0			0
$868$	1.81481	+	1.22902i	0.0615987	+	0.0417158i
$869$		−	16.0101i		−	0.543106i
$870$		0			0
$871$	20.5839	−	11.8841i	0.697459	−	0.402678i
$872$	−5.16036	+	2.97934i	−0.174752	+	0.100893i
$873$		0			0
$874$			1.30323i			0.0440823i
$875$		0			0
$876$		0			0
$877$	12.0691	−	20.9043i	0.407545	−	0.705888i	−0.587069	−	0.809537i	$-0.699718\pi$
$877$	12.0691	−	20.9043i	0.407545	−	0.705888i	0.994614	+	0.103649i	$0.0330518\pi$
$878$	7.16228	+	12.4054i	0.241715	+	0.418663i
$879$		0			0
$880$		0			0
$881$	37.2609			1.25535			0.627676	−	0.778475i	$-0.284006\pi$
$881$	37.2609			1.25535			0.627676	+	0.778475i	$0.284006\pi$
$882$		0			0
$883$	−48.5544			−1.63398			−0.816992	−	0.576648i	$-0.804360\pi$
$883$	−48.5544			−1.63398			−0.816992	+	0.576648i	$0.804360\pi$
$884$	3.11804	+	1.80020i	0.104871	+	0.0605472i
$885$		0			0
$886$	2.57874	+	4.46651i	0.0866344	+	0.150055i
$887$	−8.73545	+	15.1302i	−0.293308	+	0.508024i	−0.974590	−	0.223997i	$-0.928089\pi$
$887$	−8.73545	+	15.1302i	−0.293308	+	0.508024i	0.681282	+	0.732021i	$0.261423\pi$
$888$		0			0
$889$	−55.9524	−	4.01720i	−1.87658	−	0.134733i
$890$		0			0
$891$		0			0
$892$	6.20597	−	3.58302i	0.207791	−	0.119968i
$893$	−31.4199	+	18.1403i	−1.05143	+	0.607042i
$894$		0			0
$895$		0			0
$896$	2.19067	+	1.48356i	0.0731852	+	0.0495624i
$897$		0			0
$898$	9.96885	−	17.2665i	0.332665	−	0.576192i
$899$	−0.372369	−	0.644963i	−0.0124192	−	0.0215107i
$900$		0			0
$901$	7.29921	+	4.21420i	0.243172	+	0.140395i
$902$	13.4229			0.446935
$903$		0			0
$904$	19.8977			0.661789
$905$		0			0
$906$		0			0
$907$	−10.7260	−	18.5780i	−0.356151	−	0.616872i	0.631163	−	0.775650i	$-0.282578\pi$
$907$	−10.7260	−	18.5780i	−0.356151	−	0.616872i	−0.987314	+	0.158778i	$0.949244\pi$
$908$	−7.92721	+	13.7303i	−0.263074	+	0.455657i
$909$		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
$913$	−7.23198	+	4.17539i	−0.239344	+	0.138185i
$914$	9.82065	−	5.66995i	0.324838	−	0.187545i
$915$		0			0
$916$			28.2175i			0.932332i
$917$	11.0699	−	16.3461i	0.365560	−	0.539797i
$918$		0			0
$919$	28.0816	−	48.6387i	0.926325	−	1.60444i	0.136908	−	0.990584i	$-0.456283\pi$
$919$	28.0816	−	48.6387i	0.926325	−	1.60444i	0.789416	−	0.613858i	$-0.210383\pi$
$920$		0			0
$921$		0			0
$922$	1.74842	+	1.00945i	0.0575812	+	0.0332445i
$923$	18.9189			0.622724
$924$		0			0
$925$		0			0
$926$	23.6290	+	13.6422i	0.776497	+	0.448311i
$927$		0			0
$928$	−0.449490	−	0.778539i	−0.0147552	−	0.0255568i
$929$	−9.26942	+	16.0551i	−0.304120	+	0.526751i	−0.977065	−	0.212941i	$-0.931696\pi$
$929$	−9.26942	+	16.0551i	−0.304120	+	0.526751i	0.672945	+	0.739692i	$0.265029\pi$
$930$		0			0
$931$	26.7504	+	21.0605i	0.876708	+	0.690228i
$932$			24.2973i			0.795886i
$933$		0			0
$934$	0.599403	−	0.346065i	0.0196131	−	0.0113236i
$935$		0			0
$936$		0			0
$937$			39.5337i			1.29151i	0.763545	+	0.645755i	$0.223457\pi$
$937$			39.5337i			1.29151i	−0.763545	+	0.645755i	$0.776543\pi$
$938$	3.03795	−	42.3131i	0.0991925	−	1.38157i
$939$		0			0
$940$		0			0
$941$	−25.2474	−	43.7299i	−0.823043	−	1.42555i	−0.903406	−	0.428787i	$-0.858941\pi$
$941$	−25.2474	−	43.7299i	−0.823043	−	1.42555i	0.0803623	−	0.996766i	$-0.474392\pi$
$942$		0			0
$943$	2.03283	+	1.17365i	0.0661980	+	0.0382195i
$944$	6.25674			0.203639
$945$		0			0
$946$	−2.85566			−0.0928455
$947$	−33.9160	−	19.5814i	−1.10212	−	0.636310i	−0.165344	−	0.986236i	$-0.552874\pi$
$947$	−33.9160	−	19.5814i	−1.10212	−	0.636310i	−0.936777	+	0.349926i	$0.886207\pi$
$948$		0			0
$949$	0.254333	+	0.440518i	0.00825600	+	0.0142998i
$950$		0			0
$951$		0			0
$952$	5.78094	−	2.80625i	0.187361	−	0.0909511i
$953$			52.9933i			1.71662i	0.513130	+	0.858311i	$0.328486\pi$
$953$			52.9933i			1.71662i	−0.513130	+	0.858311i	$0.671514\pi$
$954$		0			0
$955$		0			0
$956$	17.2409	−	9.95403i	0.557610	−	0.321936i
$957$		0			0
$958$		−	15.9081i		−	0.513966i
$959$	1.47944	−	0.718168i	0.0477737	−	0.0231909i
$960$		0			0
$961$	−15.1569	+	26.2524i	−0.488931	+	0.846853i
$962$	4.06342	+	7.03805i	0.131010	+	0.226916i
$963$		0			0
$964$	17.7755	+	10.2627i	0.572510	+	0.330539i
$965$		0			0
$966$		0			0
$967$	−30.6208			−0.984700			−0.492350	−	0.870397i	$-0.663862\pi$
$967$	−30.6208			−0.984700			−0.492350	+	0.870397i	$0.663862\pi$
$968$	−7.49303	−	4.32611i	−0.240835	−	0.139046i
$969$		0			0
$970$		0			0
$971$	−6.03548	+	10.4538i	−0.193688	+	0.335477i	−0.946470	−	0.322793i	$-0.895378\pi$
$971$	−6.03548	+	10.4538i	−0.193688	+	0.335477i	0.752782	+	0.658270i	$0.228712\pi$
$972$		0			0
$973$	3.51150	−	48.9089i	0.112574	−	1.56795i
$974$		−	28.7498i		−	0.921205i
$975$		0			0
$976$	−5.73445	+	3.31079i	−0.183555	+	0.105976i
$977$	−9.72792	+	5.61642i	−0.311224	+	0.179685i	−0.647474	−	0.762088i	$-0.724175\pi$
$977$	−9.72792	+	5.61642i	−0.311224	+	0.179685i	0.336250	+	0.941773i	$0.390841\pi$
$978$		0			0
$979$			24.4701i			0.782068i
$980$		0			0
$981$		0			0
$982$	−2.72877	+	4.72636i	−0.0870784	+	0.150824i
$983$	−11.3960	−	19.7385i	−0.363477	−	0.629561i	0.625053	−	0.780582i	$-0.285077\pi$
$983$	−11.3960	−	19.7385i	−0.363477	−	0.629561i	−0.988531	+	0.151021i	$0.951744\pi$
$984$		0			0
$985$		0			0
$986$	−2.18346			−0.0695357
$987$		0			0
$988$	7.20977			0.229373
$989$	−0.432474	−	0.249689i	−0.0137519	−	0.00793965i
$990$		0			0
$991$	4.41057	+	7.63932i	0.140106	+	0.242671i	0.927536	−	0.373733i	$-0.121922\pi$
$991$	4.41057	+	7.63932i	0.140106	+	0.242671i	−0.787430	+	0.616404i	$0.788589\pi$
$992$	0.414214	−	0.717439i	0.0131513	−	0.0227787i
$993$		0			0
$994$	18.9343	−	27.9588i	0.600558	−	0.886800i
$995$		0			0
$996$		0			0
$997$	40.2497	−	23.2381i	1.27472	−	0.735960i	0.298847	−	0.954301i	$-0.403398\pi$
$997$	40.2497	−	23.2381i	1.27472	−	0.735960i	0.975872	+	0.218342i	$0.0700647\pi$
$998$	7.67555	−	4.43148i	0.242965	−	0.140276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.c.1601.3		8
3.2	odd	2		3150.2.bf.b.1601.1		8
5.2	odd	4		3150.2.bp.c.1349.3		8
5.3	odd	4		3150.2.bp.f.1349.2		8
5.4	even	2		630.2.be.b.341.2	yes	8
7.3	odd	6		3150.2.bf.b.1151.1		8
15.2	even	4		3150.2.bp.d.1349.3		8
15.8	even	4		3150.2.bp.a.1349.2		8
15.14	odd	2		630.2.be.a.341.4	✓	8
21.17	even	6	inner	3150.2.bf.c.1151.3		8
35.3	even	12		3150.2.bp.d.899.3		8
35.9	even	6		4410.2.b.b.881.7		8
35.17	even	12		3150.2.bp.a.899.2		8
35.19	odd	6		4410.2.b.e.881.7		8
35.24	odd	6		630.2.be.a.521.4	yes	8
105.17	odd	12		3150.2.bp.f.899.2		8
105.38	odd	12		3150.2.bp.c.899.3		8
105.44	odd	6		4410.2.b.e.881.2		8
105.59	even	6		630.2.be.b.521.2	yes	8
105.89	even	6		4410.2.b.b.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.4	✓	8	15.14	odd	2
630.2.be.a.521.4	yes	8	35.24	odd	6
630.2.be.b.341.2	yes	8	5.4	even	2
630.2.be.b.521.2	yes	8	105.59	even	6
3150.2.bf.b.1151.1		8	7.3	odd	6
3150.2.bf.b.1601.1		8	3.2	odd	2
3150.2.bf.c.1151.3		8	21.17	even	6	inner
3150.2.bf.c.1601.3		8	1.1	even	1	trivial
3150.2.bp.a.899.2		8	35.17	even	12
3150.2.bp.a.1349.2		8	15.8	even	4
3150.2.bp.c.899.3		8	105.38	odd	12
3150.2.bp.c.1349.3		8	5.2	odd	4
3150.2.bp.d.899.3		8	35.3	even	12
3150.2.bp.d.1349.3		8	15.2	even	4
3150.2.bp.f.899.2		8	105.17	odd	12
3150.2.bp.f.1349.2		8	5.3	odd	4
4410.2.b.b.881.2		8	105.89	even	6
4410.2.b.b.881.7		8	35.9	even	6
4410.2.b.e.881.2		8	105.44	odd	6
4410.2.b.e.881.7		8	35.19	odd	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

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

Introduction

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