LMFDB - Embedded newform 1008.2.v.e.323.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (of order $4$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.18
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37088 + 0.347400i) q^{2} +(1.75863 + 0.952488i) q^{4} +(-0.111394 - 0.111394i) q^{5} +1.00000 q^{7} +(2.07997 + 1.91669i) q^{8} +O(q^{10})$	\(q+(1.37088 + 0.347400i) q^{2} +(1.75863 + 0.952488i) q^{4} +(-0.111394 - 0.111394i) q^{5} +1.00000 q^{7} +(2.07997 + 1.91669i) q^{8} +(-0.114009 - 0.191406i) q^{10} +(3.61173 - 3.61173i) q^{11} +(-1.94473 - 1.94473i) q^{13} +(1.37088 + 0.347400i) q^{14} +(2.18553 + 3.35014i) q^{16} +4.79732i q^{17} +(3.03275 - 3.03275i) q^{19} +(-0.0897988 - 0.302001i) q^{20} +(6.20596 - 3.69654i) q^{22} +6.58652i q^{23} -4.97518i q^{25} +(-1.99040 - 3.34160i) q^{26} +(1.75863 + 0.952488i) q^{28} +(1.53154 - 1.53154i) q^{29} +3.26529i q^{31} +(1.83227 + 5.35190i) q^{32} +(-1.66659 + 6.57655i) q^{34} +(-0.111394 - 0.111394i) q^{35} +(1.05597 - 1.05597i) q^{37} +(5.21112 - 3.10396i) q^{38} +(-0.0181883 - 0.445204i) q^{40} -1.26613 q^{41} +(0.484499 + 0.484499i) q^{43} +(9.79181 - 2.91156i) q^{44} +(-2.28816 + 9.02934i) q^{46} -11.2247 q^{47} +1.00000 q^{49} +(1.72838 - 6.82038i) q^{50} +(-1.56772 - 5.27239i) q^{52} +(4.00870 + 4.00870i) q^{53} -0.804648 q^{55} +(2.07997 + 1.91669i) q^{56} +(2.63161 - 1.56750i) q^{58} +(-7.61474 + 7.61474i) q^{59} +(5.44215 + 5.44215i) q^{61} +(-1.13436 + 4.47632i) q^{62} +(0.652573 + 7.97334i) q^{64} +0.433262i q^{65} +(-0.897143 + 0.897143i) q^{67} +(-4.56939 + 8.43670i) q^{68} +(-0.114009 - 0.191406i) q^{70} +2.83052i q^{71} -15.7394i q^{73} +(1.81446 - 1.08077i) q^{74} +(8.22214 - 2.44482i) q^{76} +(3.61173 - 3.61173i) q^{77} -15.4151i q^{79} +(0.129730 - 0.616640i) q^{80} +(-1.73572 - 0.439855i) q^{82} +(-7.57988 - 7.57988i) q^{83} +(0.534392 - 0.534392i) q^{85} +(0.495876 + 0.832506i) q^{86} +(14.4349 - 0.589720i) q^{88} +13.1420 q^{89} +(-1.94473 - 1.94473i) q^{91} +(-6.27358 + 11.5832i) q^{92} +(-15.3877 - 3.89946i) q^{94} -0.675660 q^{95} -10.4839 q^{97} +(1.37088 + 0.347400i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{7}+O(q^{10}) $ 40 * q + 40 * q^7	$ 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) $ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.37088	+	0.347400i	0.969359	+	0.245649i
$2$	1.37088	+	0.347400i	0.969359	+	0.245649i
$3$		0			0
$3$		0			0
$4$	1.75863	+	0.952488i	0.879313	+	0.476244i
$5$	−0.111394	−	0.111394i	−0.0498168	−	0.0498168i	0.681760	−	0.731576i	$-0.261215\pi$
$5$	−0.111394	−	0.111394i	−0.0498168	−	0.0498168i	−0.731576	+	0.681760i	$0.761215\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.07997	+	1.91669i	0.735381	+	0.677653i
$9$		0			0
$10$	−0.114009	−	0.191406i	−0.0360529	−	0.0605278i
$11$	3.61173	−	3.61173i	1.08898	−	1.08898i	0.0933436	−	0.995634i	$-0.470245\pi$
$11$	3.61173	−	3.61173i	1.08898	−	1.08898i	0.995634	−	0.0933436i	$-0.0297555\pi$
$12$		0			0
$13$	−1.94473	−	1.94473i	−0.539372	−	0.539372i	0.383973	−	0.923344i	$-0.374556\pi$
$13$	−1.94473	−	1.94473i	−0.539372	−	0.539372i	−0.923344	+	0.383973i	$0.874556\pi$
$14$	1.37088	+	0.347400i	0.366383	+	0.0928465i
$15$		0			0
$16$	2.18553	+	3.35014i	0.546384	+	0.837535i
$17$			4.79732i			1.16352i	0.813360	+	0.581761i	$0.197636\pi$
$17$			4.79732i			1.16352i	−0.813360	+	0.581761i	$0.802364\pi$
$18$		0			0
$19$	3.03275	−	3.03275i	0.695761	−	0.695761i	−0.267732	−	0.963493i	$-0.586274\pi$
$19$	3.03275	−	3.03275i	0.695761	−	0.695761i	0.963493	+	0.267732i	$0.0862742\pi$
$20$	−0.0897988	−	0.302001i	−0.0200796	−	0.0675295i
$21$		0			0
$22$	6.20596	−	3.69654i	1.32312	−	0.788104i
$23$			6.58652i			1.37339i	0.726948	+	0.686693i	$0.240938\pi$
$23$			6.58652i			1.37339i	−0.726948	+	0.686693i	$0.759062\pi$
$24$		0			0
$25$		−	4.97518i		−	0.995037i
$26$	−1.99040	−	3.34160i	−0.390349	−	0.655341i
$27$		0			0
$28$	1.75863	+	0.952488i	0.332349	+	0.180003i
$29$	1.53154	−	1.53154i	0.284399	−	0.284399i	−0.550462	−	0.834861i	$-0.685548\pi$
$29$	1.53154	−	1.53154i	0.284399	−	0.284399i	0.834861	+	0.550462i	$0.185548\pi$
$30$		0			0
$31$			3.26529i			0.586464i	0.956041	+	0.293232i	$0.0947308\pi$
$31$			3.26529i			0.586464i	−0.956041	+	0.293232i	$0.905269\pi$
$32$	1.83227	+	5.35190i	0.323902	+	0.946091i
$33$		0			0
$34$	−1.66659	+	6.57655i	−0.285818	+	1.12787i
$35$	−0.111394	−	0.111394i	−0.0188290	−	0.0188290i
$36$		0			0
$37$	1.05597	−	1.05597i	0.173601	−	0.173601i	−0.614959	−	0.788559i	$-0.710827\pi$
$37$	1.05597	−	1.05597i	0.173601	−	0.173601i	0.788559	+	0.614959i	$0.210827\pi$
$38$	5.21112	−	3.10396i	0.845355	−	0.503530i
$39$		0			0
$40$	−0.0181883	−	0.445204i	−0.00287582	−	0.0703929i
$41$	−1.26613			−0.197737			−0.0988684	−	0.995101i	$-0.531522\pi$
$41$	−1.26613			−0.197737			−0.0988684	+	0.995101i	$0.531522\pi$
$42$		0			0
$43$	0.484499	+	0.484499i	0.0738855	+	0.0738855i	0.743084	−	0.669198i	$-0.233362\pi$
$43$	0.484499	+	0.484499i	0.0738855	+	0.0738855i	−0.669198	+	0.743084i	$0.733362\pi$
$44$	9.79181	−	2.91156i	1.47617	−	0.438934i
$45$		0			0
$46$	−2.28816	+	9.02934i	−0.337371	+	1.33130i
$47$	−11.2247			−1.63729			−0.818644	−	0.574301i	$-0.805274\pi$
$47$	−11.2247			−1.63729			−0.818644	+	0.574301i	$0.805274\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	1.72838	−	6.82038i	0.244430	−	0.964548i
$51$		0			0
$52$	−1.56772	−	5.27239i	−0.217404	−	0.731149i
$53$	4.00870	+	4.00870i	0.550637	+	0.550637i	0.926625	−	0.375988i	$-0.122697\pi$
$53$	4.00870	+	4.00870i	0.550637	+	0.550637i	−0.375988	+	0.926625i	$0.622697\pi$
$54$		0			0
$55$	−0.804648			−0.108499
$56$	2.07997	+	1.91669i	0.277948	+	0.256129i
$57$		0			0
$58$	2.63161	−	1.56750i	0.345547	−	0.205822i
$59$	−7.61474	+	7.61474i	−0.991354	+	0.991354i	−0.999963	−	0.00860874i	$-0.997260\pi$
$59$	−7.61474	+	7.61474i	−0.991354	+	0.991354i	0.00860874	+	0.999963i	$0.497260\pi$
$60$		0			0
$61$	5.44215	+	5.44215i	0.696796	+	0.696796i	0.963718	−	0.266922i	$-0.0860066\pi$
$61$	5.44215	+	5.44215i	0.696796	+	0.696796i	−0.266922	+	0.963718i	$0.586007\pi$
$62$	−1.13436	+	4.47632i	−0.144064	+	0.568494i
$63$		0			0
$64$	0.652573	+	7.97334i	0.0815716	+	0.996667i
$65$			0.433262i			0.0537395i
$66$		0			0
$67$	−0.897143	+	0.897143i	−0.109603	+	0.109603i	−0.759782	−	0.650178i	$-0.774694\pi$
$67$	−0.897143	+	0.897143i	−0.109603	+	0.109603i	0.650178	+	0.759782i	$0.274694\pi$
$68$	−4.56939	+	8.43670i	−0.554120	+	1.02310i
$69$		0			0
$70$	−0.114009	−	0.191406i	−0.0136267	−	0.0228774i
$71$			2.83052i			0.335921i	0.985794	+	0.167960i	$0.0537181\pi$
$71$			2.83052i			0.335921i	−0.985794	+	0.167960i	$0.946282\pi$
$72$		0			0
$73$		−	15.7394i		−	1.84216i	−0.389372	−	0.921080i	$-0.627308\pi$
$73$		−	15.7394i		−	1.84216i	0.389372	−	0.921080i	$-0.372692\pi$
$74$	1.81446	−	1.08077i	0.210926	−	0.125637i
$75$		0			0
$76$	8.22214	−	2.44482i	0.943144	−	0.280440i
$77$	3.61173	−	3.61173i	0.411595	−	0.411595i
$78$		0			0
$79$		−	15.4151i		−	1.73433i	−0.498020	−	0.867165i	$-0.665939\pi$
$79$		−	15.4151i		−	1.73433i	0.498020	−	0.867165i	$-0.334061\pi$
$80$	0.129730	−	0.616640i	0.0145042	−	0.0689424i
$81$		0			0
$82$	−1.73572	−	0.439855i	−0.191678	−	0.0485738i
$83$	−7.57988	−	7.57988i	−0.832000	−	0.832000i	0.155790	−	0.987790i	$-0.450208\pi$
$83$	−7.57988	−	7.57988i	−0.832000	−	0.832000i	−0.987790	+	0.155790i	$0.950208\pi$
$84$		0			0
$85$	0.534392	−	0.534392i	0.0579629	−	0.0579629i
$86$	0.495876	+	0.832506i	0.0534717	+	0.0897714i
$87$		0			0
$88$	14.4349	−	0.589720i	1.53876	−	0.0628644i
$89$	13.1420			1.39305			0.696525	−	0.717532i	$-0.254728\pi$
$89$	13.1420			1.39305			0.696525	+	0.717532i	$0.254728\pi$
$90$		0			0
$91$	−1.94473	−	1.94473i	−0.203863	−	0.203863i
$92$	−6.27358	+	11.5832i	−0.654066	+	1.20764i
$93$		0			0
$94$	−15.3877	−	3.89946i	−1.58712	−	0.402198i
$95$	−0.675660			−0.0693212
$96$		0			0
$97$	−10.4839			−1.06447			−0.532237	−	0.846595i	$-0.678648\pi$
$97$	−10.4839			−1.06447			−0.532237	+	0.846595i	$0.678648\pi$
$98$	1.37088	+	0.347400i	0.138480	+	0.0350927i
$99$		0			0
$100$	4.73880	−	8.74949i	0.473880	−	0.874949i
$101$	0.472060	+	0.472060i	0.0469717	+	0.0469717i	0.730202	−	0.683231i	$-0.239426\pi$
$101$	0.472060	+	0.472060i	0.0469717	+	0.0469717i	−0.683231	+	0.730202i	$0.739426\pi$
$102$		0			0
$103$	−16.5554			−1.63125			−0.815624	−	0.578583i	$-0.803606\pi$
$103$	−16.5554			−1.63125			−0.815624	+	0.578583i	$0.803606\pi$
$104$	−0.317534	−	7.77245i	−0.0311368	−	0.762151i
$105$		0			0
$106$	4.10282	+	6.88806i	0.398501	+	0.669028i
$107$	−7.98789	+	7.98789i	−0.772218	+	0.772218i	−0.978494	−	0.206276i	$-0.933866\pi$
$107$	−7.98789	+	7.98789i	−0.772218	+	0.772218i	0.206276	+	0.978494i	$0.433866\pi$
$108$		0			0
$109$	−6.01886	−	6.01886i	−0.576502	−	0.576502i	0.357436	−	0.933938i	$-0.383651\pi$
$109$	−6.01886	−	6.01886i	−0.576502	−	0.576502i	−0.933938	+	0.357436i	$0.883651\pi$
$110$	−1.10308	−	0.279535i	−0.105174	−	0.0266526i
$111$		0			0
$112$	2.18553	+	3.35014i	0.206514	+	0.316558i
$113$		−	7.81071i		−	0.734770i	−0.930069	−	0.367385i	$-0.880253\pi$
$113$		−	7.81071i		−	0.734770i	0.930069	−	0.367385i	$-0.119747\pi$
$114$		0			0
$115$	0.733698	−	0.733698i	0.0684177	−	0.0684177i
$116$	4.15217	−	1.23463i	0.385519	−	0.114633i
$117$		0			0
$118$	−13.0843	+	7.79353i	−1.20450	+	0.717453i
$119$			4.79732i			0.439770i
$120$		0			0
$121$		−	15.0892i		−	1.37174i
$122$	5.56994	+	9.35114i	0.504278	+	0.846613i
$123$		0			0
$124$	−3.11015	+	5.74243i	−0.279300	+	0.515685i
$125$	−1.11117	+	1.11117i	−0.0993863	+	0.0993863i
$126$		0			0
$127$			6.59439i			0.585157i	0.956241	+	0.292579i	$0.0945133\pi$
$127$			6.59439i			0.585157i	−0.956241	+	0.292579i	$0.905487\pi$
$128$	−1.87534	+	11.1572i	−0.165758	+	0.986166i
$129$		0			0
$130$	−0.150515	+	0.593951i	−0.0132011	+	0.0520929i
$131$	6.27211	+	6.27211i	0.547997	+	0.547997i	0.925861	−	0.377864i	$-0.123341\pi$
$131$	6.27211	+	6.27211i	0.547997	+	0.547997i	−0.377864	+	0.925861i	$0.623341\pi$
$132$		0			0
$133$	3.03275	−	3.03275i	0.262973	−	0.262973i
$134$	−1.54154	+	0.918209i	−0.133169	+	0.0793211i
$135$		0			0
$136$	−9.19499	+	9.97830i	−0.788464	+	0.855632i
$137$	−22.4152			−1.91506			−0.957530	−	0.288333i	$-0.906899\pi$
$137$	−22.4152			−1.91506			−0.957530	+	0.288333i	$0.906899\pi$
$138$		0			0
$139$	9.44120	+	9.44120i	0.800792	+	0.800792i	0.983219	−	0.182427i	$-0.0583953\pi$
$139$	9.44120	+	9.44120i	0.800792	+	0.800792i	−0.182427	+	0.983219i	$0.558395\pi$
$140$	−0.0897988	−	0.302001i	−0.00758939	−	0.0255238i
$141$		0			0
$142$	−0.983322	+	3.88030i	−0.0825186	+	0.325628i
$143$	−14.0477			−1.17473
$144$		0			0
$145$	−0.341207			−0.0283357
$146$	5.46788	−	21.5769i	0.452525	−	1.78572i
$147$		0			0
$148$	2.86286	−	0.851261i	0.235326	−	0.0699732i
$149$	10.6024	+	10.6024i	0.868581	+	0.868581i	0.992315	−	0.123735i	$-0.0394872\pi$
$149$	10.6024	+	10.6024i	0.868581	+	0.868581i	−0.123735	+	0.992315i	$0.539487\pi$
$150$		0			0
$151$	−0.651929			−0.0530532			−0.0265266	−	0.999648i	$-0.508445\pi$
$151$	−0.651929			−0.0530532			−0.0265266	+	0.999648i	$0.508445\pi$
$152$	12.1209	−	0.495186i	0.983135	−	0.0401649i
$153$		0			0
$154$	6.20596	−	3.69654i	0.500091	−	0.297875i
$155$	0.363733	−	0.363733i	0.0292157	−	0.0292157i
$156$		0			0
$157$	−15.6768	−	15.6768i	−1.25114	−	1.25114i	−0.955209	−	0.295934i	$-0.904369\pi$
$157$	−15.6768	−	15.6768i	−1.25114	−	1.25114i	−0.295934	−	0.955209i	$-0.595631\pi$
$158$	5.35519	−	21.1322i	0.426036	−	1.68119i
$159$		0			0
$160$	0.392065	−	0.800271i	0.0309954	−	0.0632670i
$161$			6.58652i			0.519091i
$162$		0			0
$163$	−4.07211	+	4.07211i	−0.318952	+	0.318952i	−0.848365	−	0.529412i	$-0.822412\pi$
$163$	−4.07211	+	4.07211i	−0.318952	+	0.318952i	0.529412	+	0.848365i	$0.322412\pi$
$164$	−2.22666	−	1.20598i	−0.173873	−	0.0941709i
$165$		0			0
$166$	−7.75786	−	13.0244i	−0.602127	−	1.01089i
$167$		−	8.04509i		−	0.622548i	−0.950320	−	0.311274i	$-0.899244\pi$
$167$		−	8.04509i		−	0.622548i	0.950320	−	0.311274i	$-0.100756\pi$
$168$		0			0
$169$		−	5.43603i		−	0.418156i
$170$	0.918235	−	0.546939i	0.0704254	−	0.0419483i
$171$		0			0
$172$	0.390574	+	1.31353i	0.0297810	+	0.100156i
$173$	−0.546907	+	0.546907i	−0.0415806	+	0.0415806i	−0.727591	−	0.686011i	$-0.759360\pi$
$173$	−0.546907	+	0.546907i	−0.0415806	+	0.0415806i	0.686011	+	0.727591i	$0.259360\pi$
$174$		0			0
$175$		−	4.97518i		−	0.376088i
$176$	19.9934	+	4.20624i	1.50706	+	0.317057i
$177$		0			0
$178$	18.0161	+	4.56554i	1.35037	+	0.342201i
$179$	−15.4071	−	15.4071i	−1.15158	−	1.15158i	−0.986236	−	0.165345i	$-0.947126\pi$
$179$	−15.4071	−	15.4071i	−1.15158	−	1.15158i	−0.165345	−	0.986236i	$-0.552874\pi$
$180$		0			0
$181$	−4.10925	+	4.10925i	−0.305438	+	0.305438i	−0.843137	−	0.537699i	$-0.819294\pi$
$181$	−4.10925	+	4.10925i	−0.305438	+	0.305438i	0.537699	+	0.843137i	$0.319294\pi$
$182$	−1.99040	−	3.34160i	−0.147538	−	0.247696i
$183$		0			0
$184$	−12.6243	+	13.6998i	−0.930679	+	1.00996i
$185$	−0.235257			−0.0172965
$186$		0			0
$187$	17.3266	+	17.3266i	1.26705	+	1.26705i
$188$	−19.7400	−	10.6914i	−1.43969	−	0.779749i
$189$		0			0
$190$	−0.926249	−	0.234724i	−0.0671971	−	0.0170287i
$191$	−7.56461			−0.547356			−0.273678	−	0.961821i	$-0.588240\pi$
$191$	−7.56461			−0.547356			−0.273678	+	0.961821i	$0.588240\pi$
$192$		0			0
$193$	14.0355			1.01030			0.505149	−	0.863032i	$-0.331438\pi$
$193$	14.0355			1.01030			0.505149	+	0.863032i	$0.331438\pi$
$194$	−14.3721	−	3.64209i	−1.03186	−	0.261487i
$195$		0			0
$196$	1.75863	+	0.952488i	0.125616	+	0.0680348i
$197$	9.59894	+	9.59894i	0.683896	+	0.683896i	0.960876	−	0.276980i	$-0.0893335\pi$
$197$	9.59894	+	9.59894i	0.683896	+	0.683896i	−0.276980	+	0.960876i	$0.589334\pi$
$198$		0			0
$199$	−12.5176			−0.887349			−0.443675	−	0.896188i	$-0.646325\pi$
$199$	−12.5176			−0.887349			−0.443675	+	0.896188i	$0.646325\pi$
$200$	9.53590	−	10.3482i	0.674290	−	0.731731i
$201$		0			0
$202$	0.483144	+	0.811131i	0.0339939	+	0.0570710i
$203$	1.53154	−	1.53154i	0.107493	−	0.107493i
$204$		0			0
$205$	0.141039	+	0.141039i	0.00985062	+	0.00985062i
$206$	−22.6954	−	5.75133i	−1.58126	−	0.400714i
$207$		0			0
$208$	2.26485	−	10.7654i	0.157039	−	0.746447i
$209$		−	21.9070i		−	1.51534i
$210$		0			0
$211$	6.19384	−	6.19384i	0.426401	−	0.426401i	−0.460999	−	0.887401i	$-0.652509\pi$
$211$	6.19384	−	6.19384i	0.426401	−	0.426401i	0.887401	+	0.460999i	$0.152509\pi$
$212$	3.23157	+	10.8680i	0.221945	+	0.746420i
$213$		0			0
$214$	−13.7254	+	8.17545i	−0.938251	+	0.558862i
$215$		−	0.107940i		−	0.00736148i
$216$		0			0
$217$			3.26529i			0.221662i
$218$	−6.16018	−	10.3421i	−0.417220	−	0.700455i
$219$		0			0
$220$	−1.41508	−	0.766418i	−0.0954044	−	0.0516719i
$221$	9.32951	−	9.32951i	0.627571	−	0.627571i
$222$		0			0
$223$			23.4809i			1.57240i	0.617972	+	0.786200i	$0.287955\pi$
$223$			23.4809i			1.57240i	−0.617972	+	0.786200i	$0.712045\pi$
$224$	1.83227	+	5.35190i	0.122424	+	0.357589i
$225$		0			0
$226$	2.71344	−	10.7076i	0.180495	−	0.712256i
$227$	−13.8869	−	13.8869i	−0.921707	−	0.921707i	0.0754430	−	0.997150i	$-0.475963\pi$
$227$	−13.8869	−	13.8869i	−0.921707	−	0.921707i	−0.997150	+	0.0754430i	$0.975963\pi$
$228$		0			0
$229$	−2.96200	+	2.96200i	−0.195735	+	0.195735i	−0.798169	−	0.602434i	$-0.794198\pi$
$229$	−2.96200	+	2.96200i	−0.195735	+	0.195735i	0.602434	+	0.798169i	$0.294198\pi$
$230$	1.26070	−	0.750925i	0.0831280	−	0.0495145i
$231$		0			0
$232$	6.12104	−	0.250068i	0.401866	−	0.0164178i
$233$	1.94090			0.127153			0.0635763	−	0.997977i	$-0.479749\pi$
$233$	1.94090			0.127153			0.0635763	+	0.997977i	$0.479749\pi$
$234$		0			0
$235$	1.25036	+	1.25036i	0.0815645	+	0.0815645i
$236$	−20.6444	+	6.13854i	−1.34384	+	0.399585i
$237$		0			0
$238$	−1.66659	+	6.57655i	−0.108029	+	0.426295i
$239$	3.73260			0.241442			0.120721	−	0.992686i	$-0.461479\pi$
$239$	3.73260			0.241442			0.120721	+	0.992686i	$0.461479\pi$
$240$		0			0
$241$	−6.72519			−0.433208			−0.216604	−	0.976260i	$-0.569498\pi$
$241$	−6.72519			−0.433208			−0.216604	+	0.976260i	$0.569498\pi$
$242$	5.24198	−	20.6855i	0.336967	−	1.32971i
$243$		0			0
$244$	4.38713	+	14.7543i	0.280857	+	0.944547i
$245$	−0.111394	−	0.111394i	−0.00711669	−	0.00711669i
$246$		0			0
$247$	−11.7958			−0.750548
$248$	−6.25856	+	6.79172i	−0.397419	+	0.431275i
$249$		0			0
$250$	−1.90931	+	1.13726i	−0.120755	+	0.0719269i
$251$	7.29389	−	7.29389i	0.460387	−	0.460387i	−0.438396	−	0.898782i	$-0.644453\pi$
$251$	7.29389	−	7.29389i	0.460387	−	0.460387i	0.898782	+	0.438396i	$0.144453\pi$
$252$		0			0
$253$	23.7887	+	23.7887i	1.49559	+	1.49559i
$254$	−2.29089	+	9.04012i	−0.143743	+	0.567227i
$255$		0			0
$256$	−6.44688	+	14.6437i	−0.402930	+	0.915231i
$257$		−	3.33778i		−	0.208205i	−0.994567	−	0.104103i	$-0.966803\pi$
$257$		−	3.33778i		−	0.208205i	0.994567	−	0.104103i	$-0.0331970\pi$
$258$		0			0
$259$	1.05597	−	1.05597i	0.0656149	−	0.0656149i
$260$	−0.412677	+	0.761946i	−0.0255931	+	0.0472539i
$261$		0			0
$262$	6.41939	+	10.7772i	0.396591	+	0.665821i
$263$			16.2784i			1.00377i	0.864934	+	0.501886i	$0.167360\pi$
$263$			16.2784i			1.00377i	−0.864934	+	0.501886i	$0.832640\pi$
$264$		0			0
$265$		−	0.893087i		−	0.0548619i
$266$	5.21112	−	3.10396i	0.319514	−	0.190316i
$267$		0			0
$268$	−2.43226	+	0.723222i	−0.148574	+	0.0441778i
$269$	16.6895	−	16.6895i	1.01758	−	1.01758i	0.0177322	−	0.999843i	$-0.494355\pi$
$269$	16.6895	−	16.6895i	1.01758	−	1.01758i	0.999843	−	0.0177322i	$-0.00564465\pi$
$270$		0			0
$271$			19.4291i			1.18023i	0.807318	+	0.590116i	$0.200918\pi$
$271$			19.4291i			1.18023i	−0.807318	+	0.590116i	$0.799082\pi$
$272$	−16.0717	+	10.4847i	−0.974490	+	0.635729i
$273$		0			0
$274$	−30.7286	−	7.78704i	−1.85638	−	0.470432i
$275$	−17.9690	−	17.9690i	−1.08357	−	1.08357i
$276$		0			0
$277$	−20.2943	+	20.2943i	−1.21937	+	1.21937i	−0.251511	+	0.967854i	$0.580927\pi$
$277$	−20.2943	+	20.2943i	−1.21937	+	1.21937i	−0.967854	+	0.251511i	$0.919073\pi$
$278$	9.66289	+	16.2226i	0.579541	+	0.972969i
$279$		0			0
$280$	−0.0181883	−	0.445204i	−0.00108696	−	0.0266060i
$281$	8.67930			0.517763			0.258882	−	0.965909i	$-0.416646\pi$
$281$	8.67930			0.517763			0.258882	+	0.965909i	$0.416646\pi$
$282$		0			0
$283$	−5.11240	−	5.11240i	−0.303901	−	0.303901i	0.538637	−	0.842538i	$-0.318939\pi$
$283$	−5.11240	−	5.11240i	−0.303901	−	0.303901i	−0.842538	+	0.538637i	$0.818939\pi$
$284$	−2.69604	+	4.97783i	−0.159980	+	0.295380i
$285$		0			0
$286$	−19.2577	−	4.88017i	−1.13873	−	0.288570i
$287$	−1.26613			−0.0747375
$288$		0			0
$289$	−6.01430			−0.353782
$290$	−0.467754	−	0.118535i	−0.0274675	−	0.00696063i
$291$		0			0
$292$	14.9916	−	27.6798i	0.877318	−	1.61984i
$293$	−4.21225	−	4.21225i	−0.246082	−	0.246082i	0.573279	−	0.819361i	$-0.305671\pi$
$293$	−4.21225	−	4.21225i	−0.246082	−	0.246082i	−0.819361	+	0.573279i	$0.805671\pi$
$294$		0			0
$295$	1.69647			0.0987722
$296$	4.22037	−	0.172418i	0.245304	−	0.0100216i
$297$		0			0
$298$	10.8513	+	18.2179i	0.628600	+	1.05533i
$299$	12.8090	−	12.8090i	0.740765	−	0.740765i
$300$		0			0
$301$	0.484499	+	0.484499i	0.0279261	+	0.0279261i
$302$	−0.893716	−	0.226480i	−0.0514276	−	0.0130325i
$303$		0			0
$304$	16.7883	+	3.53196i	0.962877	+	0.202572i
$305$		−	1.21244i		−	0.0694243i
$306$		0			0
$307$	5.47769	−	5.47769i	0.312628	−	0.312628i	−0.533299	−	0.845927i	$-0.679048\pi$
$307$	5.47769	−	5.47769i	0.312628	−	0.312628i	0.845927	+	0.533299i	$0.179048\pi$
$308$	9.79181	−	2.91156i	0.557940	−	0.165901i
$309$		0			0
$310$	0.624995	−	0.372274i	0.0354974	−	0.0211437i
$311$			10.8058i			0.612740i	0.951913	+	0.306370i	$0.0991144\pi$
$311$			10.8058i			0.612740i	−0.951913	+	0.306370i	$0.900886\pi$
$312$		0			0
$313$		−	26.1747i		−	1.47948i	−0.672893	−	0.739740i	$-0.734949\pi$
$313$		−	26.1747i		−	1.47948i	0.672893	−	0.739740i	$-0.265051\pi$
$314$	−16.0449	−	26.9371i	−0.905464	−	1.52015i
$315$		0			0
$316$	14.6827	−	27.1093i	0.825964	−	1.52502i
$317$	14.7908	−	14.7908i	0.830735	−	0.830735i	−0.156883	−	0.987617i	$-0.550144\pi$
$317$	14.7908	−	14.7908i	0.830735	−	0.830735i	0.987617	+	0.156883i	$0.0501444\pi$
$318$		0			0
$319$		−	11.0630i		−	0.619408i
$320$	0.815488	−	0.960873i	0.0455872	−	0.0537144i
$321$		0			0
$322$	−2.28816	+	9.02934i	−0.127514	+	0.503185i
$323$	14.5491	+	14.5491i	0.809533	+	0.809533i
$324$		0			0
$325$	−9.67540	+	9.67540i	−0.536695	+	0.536695i
$326$	−6.99703	+	4.16773i	−0.387530	+	0.230829i
$327$		0			0
$328$	−2.63352	−	2.42679i	−0.145412	−	0.133997i
$329$	−11.2247			−0.618837
$330$		0			0
$331$	12.8239	+	12.8239i	0.704868	+	0.704868i	0.965451	−	0.260583i	$-0.0839149\pi$
$331$	12.8239	+	12.8239i	0.704868	+	0.704868i	−0.260583	+	0.965451i	$0.583915\pi$
$332$	−6.11044	−	20.5499i	−0.335354	−	1.12782i
$333$		0			0
$334$	2.79486	−	11.0289i	0.152928	−	0.603472i
$335$	0.199872			0.0109202
$336$		0			0
$337$	11.5576			0.629582			0.314791	−	0.949161i	$-0.398066\pi$
$337$	11.5576			0.629582			0.314791	+	0.949161i	$0.398066\pi$
$338$	1.88848	−	7.45215i	0.102720	−	0.405344i
$339$		0			0
$340$	1.44880	−	0.430794i	0.0785720	−	0.0233631i
$341$	11.7934	+	11.7934i	0.638646	+	0.638646i
$342$		0			0
$343$	1.00000			0.0539949
$344$	0.0791087	+	1.93638i	0.00426526	+	0.104403i
$345$		0			0
$346$	−0.939740	+	0.559749i	−0.0505207	+	0.0300923i
$347$	−2.89704	+	2.89704i	−0.155521	+	0.155521i	−0.780579	−	0.625058i	$-0.785076\pi$
$347$	−2.89704	+	2.89704i	−0.155521	+	0.155521i	0.625058	+	0.780579i	$0.285076\pi$
$348$		0			0
$349$	8.35296	+	8.35296i	0.447124	+	0.447124i	0.894397	−	0.447273i	$-0.147605\pi$
$349$	8.35296	+	8.35296i	0.447124	+	0.447124i	−0.447273	+	0.894397i	$0.647605\pi$
$350$	1.72838	−	6.82038i	0.0923857	−	0.364565i
$351$		0			0
$352$	25.9473	+	12.7119i	1.38299	+	0.677549i
$353$		−	11.6486i		−	0.619993i	−0.950738	−	0.309996i	$-0.899672\pi$
$353$		−	11.6486i		−	0.619993i	0.950738	−	0.309996i	$-0.100328\pi$
$354$		0			0
$355$	0.315302	−	0.315302i	0.0167345	−	0.0167345i
$356$	23.1119	+	12.5176i	1.22493	+	0.663432i
$357$		0			0
$358$	−15.7689	−	26.4737i	−0.833411	−	1.39918i
$359$			24.0137i			1.26739i	0.773582	+	0.633696i	$0.218463\pi$
$359$			24.0137i			1.26739i	−0.773582	+	0.633696i	$0.781537\pi$
$360$		0			0
$361$			0.604810i			0.0318321i
$362$	−7.06084	+	4.20574i	−0.371110	+	0.221049i
$363$		0			0
$364$	−1.56772	−	5.27239i	−0.0821711	−	0.276348i
$365$	−1.75327	+	1.75327i	−0.0917706	+	0.0917706i
$366$		0			0
$367$			12.1938i			0.636510i	0.948005	+	0.318255i	$0.103097\pi$
$367$			12.1938i			0.636510i	−0.948005	+	0.318255i	$0.896903\pi$
$368$	−22.0658	+	14.3951i	−1.15026	+	0.750395i
$369$		0			0
$370$	−0.322510	−	0.0817284i	−0.0167665	−	0.00424886i
$371$	4.00870	+	4.00870i	0.208121	+	0.208121i
$372$		0			0
$373$	17.3599	−	17.3599i	0.898859	−	0.898859i	−0.0964762	−	0.995335i	$-0.530757\pi$
$373$	17.3599	−	17.3599i	0.898859	−	0.898859i	0.995335	+	0.0964762i	$0.0307572\pi$
$374$	17.7335	+	29.7720i	0.916976	+	1.53947i
$375$		0			0
$376$	−23.3470	−	21.5143i	−1.20403	−	1.10951i
$377$	−5.95685			−0.306794
$378$		0			0
$379$	16.2388	+	16.2388i	0.834130	+	0.834130i	0.988079	−	0.153949i	$-0.0491991\pi$
$379$	16.2388	+	16.2388i	0.834130	+	0.834130i	−0.153949	+	0.988079i	$0.549199\pi$
$380$	−1.18823	−	0.643557i	−0.0609551	−	0.0330138i
$381$		0			0
$382$	−10.3702	−	2.62795i	−0.530585	−	0.134457i
$383$	12.0190			0.614141			0.307070	−	0.951687i	$-0.400651\pi$
$383$	12.0190			0.614141			0.307070	+	0.951687i	$0.400651\pi$
$384$		0			0
$385$	−0.804648			−0.0410087
$386$	19.2410	+	4.87593i	0.979340	+	0.248178i
$387$		0			0
$388$	−18.4372	−	9.98574i	−0.936006	−	0.506949i
$389$	−13.2292	−	13.2292i	−0.670749	−	0.670749i	0.287140	−	0.957889i	$-0.407296\pi$
$389$	−13.2292	−	13.2292i	−0.670749	−	0.670749i	−0.957889	+	0.287140i	$0.907296\pi$
$390$		0			0
$391$	−31.5977			−1.59796
$392$	2.07997	+	1.91669i	0.105054	+	0.0968076i
$393$		0			0
$394$	9.82432	+	16.4937i	0.494942	+	0.830939i
$395$	−1.71714	+	1.71714i	−0.0863988	+	0.0863988i
$396$		0			0
$397$	21.8846	+	21.8846i	1.09836	+	1.09836i	0.994603	+	0.103756i	$0.0330860\pi$
$397$	21.8846	+	21.8846i	1.09836	+	1.09836i	0.103756	+	0.994603i	$0.466914\pi$
$398$	−17.1601	−	4.34861i	−0.860160	−	0.217976i
$399$		0			0
$400$	16.6676	−	10.8734i	0.833378	−	0.543672i
$401$			27.8646i			1.39149i	0.718288	+	0.695746i	$0.244926\pi$
$401$			27.8646i			1.39149i	−0.718288	+	0.695746i	$0.755074\pi$
$402$		0			0
$403$	6.35012	−	6.35012i	0.316322	−	0.316322i
$404$	0.380546	+	1.27981i	0.0189329	+	0.0636728i
$405$		0			0
$406$	2.63161	−	1.56750i	0.130604	−	0.0777935i
$407$		−	7.62778i		−	0.378095i
$408$		0			0
$409$		−	9.57933i		−	0.473667i	−0.971550	−	0.236834i	$-0.923890\pi$
$409$		−	9.57933i		−	0.473667i	0.971550	−	0.236834i	$-0.0761097\pi$
$410$	0.144351	+	0.242345i	0.00712899	+	0.0119686i
$411$		0			0
$412$	−29.1147	−	15.7688i	−1.43438	−	0.776872i
$413$	−7.61474	+	7.61474i	−0.374697	+	0.374697i
$414$		0			0
$415$			1.68870i			0.0828952i
$416$	6.84473	−	13.9713i	0.335591	−	0.684998i
$417$		0			0
$418$	7.61048	−	30.0318i	0.372241	−	1.46891i
$419$	−6.53866	−	6.53866i	−0.319435	−	0.319435i	0.529115	−	0.848550i	$-0.322524\pi$
$419$	−6.53866	−	6.53866i	−0.319435	−	0.319435i	−0.848550	+	0.529115i	$0.822524\pi$
$420$		0			0
$421$	−17.8801	+	17.8801i	−0.871424	+	0.871424i	−0.992628	−	0.121204i	$-0.961325\pi$
$421$	−17.8801	+	17.8801i	−0.871424	+	0.871424i	0.121204	+	0.992628i	$0.461325\pi$
$422$	10.6427	−	6.33927i	0.518081	−	0.308591i
$423$		0			0
$424$	0.654537	+	16.0214i	0.0317871	+	0.778069i
$425$	23.8676			1.15775
$426$		0			0
$427$	5.44215	+	5.44215i	0.263364	+	0.263364i
$428$	−21.6561	+	6.43935i	−1.04679	+	0.311258i
$429$		0			0
$430$	0.0374985	−	0.147973i	0.00180834	−	0.00713591i
$431$	3.02619			0.145766			0.0728832	−	0.997340i	$-0.476780\pi$
$431$	3.02619			0.145766			0.0728832	+	0.997340i	$0.476780\pi$
$432$		0			0
$433$	33.3339			1.60192			0.800962	−	0.598715i	$-0.204322\pi$
$433$	33.3339			1.60192			0.800962	+	0.598715i	$0.204322\pi$
$434$	−1.13436	+	4.47632i	−0.0544511	+	0.214870i
$435$		0			0
$436$	−4.85204	−	16.3178i	−0.232370	−	0.781482i
$437$	19.9753	+	19.9753i	0.955549	+	0.955549i
$438$		0			0
$439$	25.0388			1.19504			0.597519	−	0.801855i	$-0.296153\pi$
$439$	25.0388			1.19504			0.597519	+	0.801855i	$0.296153\pi$
$440$	−1.67365	−	1.54226i	−0.0797880	−	0.0735246i
$441$		0			0
$442$	16.0307	−	9.54857i	0.762503	−	0.454179i
$443$	11.5230	−	11.5230i	0.547473	−	0.547473i	−0.378236	−	0.925709i	$-0.623469\pi$
$443$	11.5230	−	11.5230i	0.547473	−	0.547473i	0.925709	+	0.378236i	$0.123469\pi$
$444$		0			0
$445$	−1.46394	−	1.46394i	−0.0693973	−	0.0693973i
$446$	−8.15728	+	32.1896i	−0.386258	+	1.52422i
$447$		0			0
$448$	0.652573	+	7.97334i	0.0308312	+	0.376705i
$449$			24.9666i			1.17825i	0.808042	+	0.589124i	$0.200527\pi$
$449$			24.9666i			1.17825i	−0.808042	+	0.589124i	$0.799473\pi$
$450$		0			0
$451$	−4.57293	+	4.57293i	−0.215331	+	0.215331i
$452$	7.43961	−	13.7361i	0.349930	−	0.646093i
$453$		0			0
$454$	−14.2130	−	23.8616i	−0.667049	−	1.11988i
$455$			0.433262i			0.0203116i
$456$		0			0
$457$		−	15.0783i		−	0.705333i	−0.935749	−	0.352666i	$-0.885275\pi$
$457$		−	15.0783i		−	0.705333i	0.935749	−	0.352666i	$-0.114725\pi$
$458$	−5.08955	+	3.03155i	−0.237819	+	0.141655i
$459$		0			0
$460$	1.98914	−	0.591462i	0.0927440	−	0.0275771i
$461$	−1.98842	+	1.98842i	−0.0926101	+	0.0926101i	−0.751894	−	0.659284i	$-0.770860\pi$
$461$	−1.98842	+	1.98842i	−0.0926101	+	0.0926101i	0.659284	+	0.751894i	$0.270860\pi$
$462$		0			0
$463$		−	13.8131i		−	0.641949i	−0.947088	−	0.320975i	$-0.895990\pi$
$463$		−	13.8131i		−	0.641949i	0.947088	−	0.320975i	$-0.104010\pi$
$464$	8.47808	+	1.78363i	0.393585	+	0.0828031i
$465$		0			0
$466$	2.66074	+	0.674268i	0.123256	+	0.0312349i
$467$	27.8035	+	27.8035i	1.28659	+	1.28659i	0.936842	+	0.349753i	$0.113734\pi$
$467$	27.8035	+	27.8035i	1.28659	+	1.28659i	0.349753	+	0.936842i	$0.386266\pi$
$468$		0			0
$469$	−0.897143	+	0.897143i	−0.0414262	+	0.0414262i
$470$	1.27972	+	2.14847i	0.0590290	+	0.0991015i
$471$		0			0
$472$	−30.4336	+	1.24333i	−1.40082	+	0.0572288i
$473$	3.49976			0.160919
$474$		0			0
$475$	−15.0885	−	15.0885i	−0.692308	−	0.692308i
$476$	−4.56939	+	8.43670i	−0.209438	+	0.386695i
$477$		0			0
$478$	5.11695	+	1.29670i	0.234044	+	0.0593099i
$479$	−21.4026			−0.977909			−0.488954	−	0.872309i	$-0.662622\pi$
$479$	−21.4026			−0.977909			−0.488954	+	0.872309i	$0.662622\pi$
$480$		0			0
$481$	−4.10717			−0.187271
$482$	−9.21944	−	2.33633i	−0.419934	−	0.106417i
$483$		0			0
$484$	14.3723	−	26.5362i	0.653285	−	1.20619i
$485$	1.16784	+	1.16784i	0.0530287	+	0.0530287i
$486$		0			0
$487$	−27.9883			−1.26827			−0.634136	−	0.773222i	$-0.718644\pi$
$487$	−27.9883			−1.26827			−0.634136	+	0.773222i	$0.718644\pi$
$488$	0.888590	+	21.7505i	0.0402246	+	0.984597i
$489$		0			0
$490$	−0.114009	−	0.191406i	−0.00515042	−	0.00864683i
$491$	22.0491	−	22.0491i	0.995063	−	0.995063i	−0.00492464	−	0.999988i	$-0.501568\pi$
$491$	22.0491	−	22.0491i	0.995063	−	0.995063i	0.999988	+	0.00492464i	$0.00156757\pi$
$492$		0			0
$493$	7.34727	+	7.34727i	0.330904	+	0.330904i
$494$	−16.1706	−	4.09786i	−0.727550	−	0.184371i
$495$		0			0
$496$	−10.9392	+	7.13641i	−0.491184	+	0.320434i
$497$			2.83052i			0.126966i
$498$		0			0
$499$	5.60480	−	5.60480i	0.250905	−	0.250905i	−0.570436	−	0.821342i	$-0.693226\pi$
$499$	5.60480	−	5.60480i	0.250905	−	0.250905i	0.821342	+	0.570436i	$0.193226\pi$
$500$	−3.01252	+	0.895760i	−0.134724	+	0.0400596i
$501$		0			0
$502$	12.5330	−	7.46516i	0.559373	−	0.333186i
$503$			5.02371i			0.223996i	0.993708	+	0.111998i	$0.0357250\pi$
$503$			5.02371i			0.223996i	−0.993708	+	0.111998i	$0.964275\pi$
$504$		0			0
$505$		−	0.105169i		−	0.00467996i
$506$	24.3473	+	40.8757i	1.08237	+	1.81715i
$507$		0			0
$508$	−6.28107	+	11.5971i	−0.278678	+	0.514537i
$509$	26.3372	−	26.3372i	1.16738	−	1.16738i	0.184555	−	0.982822i	$-0.440915\pi$
$509$	26.3372	−	26.3372i	1.16738	−	1.16738i	0.982822	−	0.184555i	$-0.0590845\pi$
$510$		0			0
$511$		−	15.7394i		−	0.696271i
$512$	−13.9251	+	17.8351i	−0.615409	+	0.788208i
$513$		0			0
$514$	1.15955	−	4.57570i	0.0511454	−	0.201826i
$515$	1.84416	+	1.84416i	0.0812635	+	0.0812635i
$516$		0			0
$517$	−40.5405	+	40.5405i	−1.78297	+	1.78297i
$518$	1.81446	−	1.08077i	0.0797227	−	0.0474862i
$519$		0			0
$520$	−0.830431	+	0.901173i	−0.0364168	+	0.0395191i
$521$	0.453686			0.0198763			0.00993817	−	0.999951i	$-0.496837\pi$
$521$	0.453686			0.0198763			0.00993817	+	0.999951i	$0.496837\pi$
$522$		0			0
$523$	26.5974	+	26.5974i	1.16302	+	1.16302i	0.983810	+	0.179214i	$0.0573554\pi$
$523$	26.5974	+	26.5974i	1.16302	+	1.16302i	0.179214	+	0.983810i	$0.442645\pi$
$524$	5.05619	+	17.0044i	0.220881	+	0.742841i
$525$		0			0
$526$	−5.65513	+	22.3158i	−0.246575	+	0.973015i
$527$	−15.6647			−0.682363
$528$		0			0
$529$	−20.3823			−0.886187
$530$	0.310259	−	1.22432i	0.0134768	−	0.0531809i
$531$		0			0
$532$	8.22214	−	2.44482i	0.356475	−	0.105996i
$533$	2.46229	+	2.46229i	0.106654	+	0.106654i
$534$		0			0
$535$	1.77960			0.0769389
$536$	−3.58558	+	0.146485i	−0.154874	+	0.00632718i
$537$		0			0
$538$	28.6772	−	17.0813i	1.23636	−	0.736429i
$539$	3.61173	−	3.61173i	0.155568	−	0.155568i
$540$		0			0
$541$	−17.5559	−	17.5559i	−0.754785	−	0.754785i	0.220583	−	0.975368i	$-0.429204\pi$
$541$	−17.5559	−	17.5559i	−0.754785	−	0.754785i	−0.975368	+	0.220583i	$0.929204\pi$
$542$	−6.74966	+	26.6349i	−0.289923	+	1.14407i
$543$		0			0
$544$	−25.6748	+	8.78998i	−1.10080	+	0.376867i
$545$			1.34093i			0.0574390i
$546$		0			0
$547$	6.76713	−	6.76713i	0.289342	−	0.289342i	−0.547478	−	0.836820i	$-0.684412\pi$
$547$	6.76713	−	6.76713i	0.289342	−	0.289342i	0.836820	+	0.547478i	$0.184412\pi$
$548$	−39.4200	−	21.3502i	−1.68394	−	0.912036i
$549$		0			0
$550$	−18.3909	−	30.8758i	−0.784192	−	1.31655i
$551$		−	9.28954i		−	0.395748i
$552$		0			0
$553$		−	15.4151i		−	0.655515i
$554$	−34.8713	+	20.7708i	−1.48154	+	0.882467i
$555$		0			0
$556$	7.61092	+	25.5962i	0.322775	+	1.08552i
$557$	−29.6889	+	29.6889i	−1.25796	+	1.25796i	−0.305893	+	0.952066i	$0.598955\pi$
$557$	−29.6889	+	29.6889i	−1.25796	+	1.25796i	−0.952066	+	0.305893i	$0.901045\pi$
$558$		0			0
$559$		−	1.88444i		−	0.0797035i
$560$	0.129730	−	0.616640i	0.00548208	−	0.0260578i
$561$		0			0
$562$	11.8983	+	3.01519i	0.501899	+	0.127188i
$563$	−25.1503	−	25.1503i	−1.05996	−	1.05996i	−0.998084	−	0.0618753i	$-0.980292\pi$
$563$	−25.1503	−	25.1503i	−1.05996	−	1.05996i	−0.0618753	−	0.998084i	$-0.519708\pi$
$564$		0			0
$565$	−0.870065	+	0.870065i	−0.0366039	+	0.0366039i
$566$	−5.23244	−	8.78454i	−0.219936	−	0.369242i
$567$		0			0
$568$	−5.42524	+	5.88740i	−0.227638	+	0.247030i
$569$	−17.4528			−0.731660			−0.365830	−	0.930682i	$-0.619215\pi$
$569$	−17.4528			−0.731660			−0.365830	+	0.930682i	$0.619215\pi$
$570$		0			0
$571$	−22.4569	−	22.4569i	−0.939793	−	0.939793i	0.0584947	−	0.998288i	$-0.481370\pi$
$571$	−22.4569	−	22.4569i	−0.939793	−	0.939793i	−0.998288	+	0.0584947i	$0.981370\pi$
$572$	−24.7047	−	13.3803i	−1.03295	−	0.559457i
$573$		0			0
$574$	−1.73572	−	0.439855i	−0.0724474	−	0.0183592i
$575$	32.7692			1.36657
$576$		0			0
$577$	40.6265			1.69130			0.845652	−	0.533734i	$-0.179212\pi$
$577$	40.6265			1.69130			0.845652	+	0.533734i	$0.179212\pi$
$578$	−8.24488	−	2.08937i	−0.342942	−	0.0869062i
$579$		0			0
$580$	−0.600056	−	0.324995i	−0.0249160	−	0.0134947i
$581$	−7.57988	−	7.57988i	−0.314466	−	0.314466i
$582$		0			0
$583$	28.9567			1.19926
$584$	30.1677	−	32.7376i	1.24835	−	1.35469i
$585$		0			0
$586$	−4.31115	−	7.23782i	−0.178092	−	0.298992i
$587$	−1.79577	+	1.79577i	−0.0741194	+	0.0741194i	−0.743195	−	0.669075i	$-0.766690\pi$
$587$	−1.79577	+	1.79577i	−0.0741194	+	0.0741194i	0.669075	+	0.743195i	$0.266690\pi$
$588$		0			0
$589$	9.90283	+	9.90283i	0.408039	+	0.408039i
$590$	2.32565	+	0.589353i	0.0957457	+	0.0242633i
$591$		0			0
$592$	5.84552	+	1.22979i	0.240249	+	0.0505441i
$593$		−	11.4046i		−	0.468331i	−0.972197	−	0.234165i	$-0.924764\pi$
$593$		−	11.4046i		−	0.468331i	0.972197	−	0.234165i	$-0.0752357\pi$
$594$		0			0
$595$	0.534392	−	0.534392i	0.0219079	−	0.0219079i
$596$	8.54699	+	28.7443i	0.350098	+	1.17741i
$597$		0			0
$598$	22.0095	−	13.1098i	0.900035	−	0.536099i
$599$		−	7.81649i		−	0.319373i	−0.987168	−	0.159687i	$-0.948952\pi$
$599$		−	7.81649i		−	0.319373i	0.987168	−	0.159687i	$-0.0510484\pi$
$600$		0			0
$601$			22.2752i			0.908625i	0.890842	+	0.454313i	$0.150115\pi$
$601$			22.2752i			0.908625i	−0.890842	+	0.454313i	$0.849885\pi$
$602$	0.495876	+	0.832506i	0.0202104	+	0.0339304i
$603$		0			0
$604$	−1.14650	−	0.620954i	−0.0466504	−	0.0252663i
$605$	−1.68084	+	1.68084i	−0.0683359	+	0.0683359i
$606$		0			0
$607$			11.5129i			0.467293i	0.972322	+	0.233646i	$0.0750658\pi$
$607$			11.5129i			0.467293i	−0.972322	+	0.233646i	$0.924934\pi$
$608$	21.7878	+	10.6742i	0.883612	+	0.432895i
$609$		0			0
$610$	0.421203	−	1.66211i	0.0170540	−	0.0672971i
$611$	21.8290	+	21.8290i	0.883107	+	0.883107i
$612$		0			0
$613$	24.6256	−	24.6256i	0.994618	−	0.994618i	−0.00536742	−	0.999986i	$-0.501709\pi$
$613$	24.6256	−	24.6256i	0.994618	−	0.994618i	0.999986	+	0.00536742i	$0.00170851\pi$
$614$	9.41221	−	5.60631i	0.379846	−	0.226252i
$615$		0			0
$616$	14.4349	−	0.589720i	0.581598	−	0.0237605i
$617$	−29.3630			−1.18211			−0.591054	−	0.806632i	$-0.701288\pi$
$617$	−29.3630			−1.18211			−0.591054	+	0.806632i	$0.701288\pi$
$618$		0			0
$619$	32.5316	+	32.5316i	1.30756	+	1.30756i	0.923173	+	0.384384i	$0.125586\pi$
$619$	32.5316	+	32.5316i	1.30756	+	1.30756i	0.384384	+	0.923173i	$0.374414\pi$
$620$	0.986122	−	0.293219i	0.0396036	−	0.0117760i
$621$		0			0
$622$	−3.75393	+	14.8134i	−0.150519	+	0.593965i
$623$	13.1420			0.526524
$624$		0			0
$625$	−24.6284			−0.985134
$626$	9.09308	−	35.8823i	0.363433	−	1.43415i
$627$		0			0
$628$	−12.6377	−	42.5015i	−0.504297	−	1.69599i
$629$	5.06584	+	5.06584i	0.201988	+	0.201988i
$630$		0			0
$631$	−10.4307			−0.415240			−0.207620	−	0.978210i	$-0.566572\pi$
$631$	−10.4307			−0.415240			−0.207620	+	0.978210i	$0.566572\pi$
$632$	29.5460	−	32.0629i	1.17528	−	1.27539i
$633$		0			0
$634$	25.4148	−	15.1381i	1.00935	−	0.601211i
$635$	0.734574	−	0.734574i	0.0291507	−	0.0291507i
$636$		0			0
$637$	−1.94473	−	1.94473i	−0.0770531	−	0.0770531i
$638$	3.84328	−	15.1660i	0.152157	−	0.600429i
$639$		0			0
$640$	1.45174	−	1.03394i	0.0573852	−	0.0408701i
$641$		−	26.3287i		−	1.03992i	−0.854191	−	0.519960i	$-0.825947\pi$
$641$		−	26.3287i		−	1.03992i	0.854191	−	0.519960i	$-0.174053\pi$
$642$		0			0
$643$	10.1662	−	10.1662i	0.400917	−	0.400917i	−0.477639	−	0.878556i	$-0.658507\pi$
$643$	10.1662	−	10.1662i	0.400917	−	0.400917i	0.878556	+	0.477639i	$0.158507\pi$
$644$	−6.27358	+	11.5832i	−0.247214	+	0.456443i
$645$		0			0
$646$	14.8907	+	24.9994i	0.585867	+	0.983589i
$647$			30.4560i			1.19735i	0.800992	+	0.598675i	$0.204306\pi$
$647$			30.4560i			1.19735i	−0.800992	+	0.598675i	$0.795694\pi$
$648$		0			0
$649$			55.0047i			2.15912i
$650$	−16.6250	+	9.90258i	−0.652088	+	0.388411i
$651$		0			0
$652$	−11.0400	+	3.28269i	−0.432358	+	0.128560i
$653$	0.424352	−	0.424352i	0.0166062	−	0.0166062i	−0.698755	−	0.715361i	$-0.746262\pi$
$653$	0.424352	−	0.424352i	0.0166062	−	0.0166062i	0.715361	+	0.698755i	$0.246262\pi$
$654$		0			0
$655$		−	1.39735i		−	0.0545989i
$656$	−2.76718	−	4.24172i	−0.108040	−	0.165611i
$657$		0			0
$658$	−15.3877	−	3.89946i	−0.599875	−	0.152017i
$659$	21.4421	+	21.4421i	0.835268	+	0.835268i	0.988232	−	0.152964i	$-0.0488819\pi$
$659$	21.4421	+	21.4421i	0.835268	+	0.835268i	−0.152964	+	0.988232i	$0.548882\pi$
$660$		0			0
$661$	29.6529	−	29.6529i	1.15337	−	1.15337i	0.167492	−	0.985873i	$-0.446433\pi$
$661$	29.6529	−	29.6529i	1.15337	−	1.15337i	0.985873	−	0.167492i	$-0.0535668\pi$
$662$	13.1251	+	22.0351i	0.510120	+	0.856420i
$663$		0			0
$664$	−1.23764	−	30.2943i	−0.0480296	−	1.17564i
$665$	−0.675660			−0.0262010
$666$		0			0
$667$	10.0875	+	10.0875i	0.390589	+	0.390589i
$668$	7.66285	−	14.1483i	0.296484	−	0.547414i
$669$		0			0
$670$	0.274001	+	0.0694356i	0.0105856	+	0.00268253i
$671$	39.3112			1.51759
$672$		0			0
$673$	−33.5720			−1.29410			−0.647052	−	0.762446i	$-0.723998\pi$
$673$	−33.5720			−1.29410			−0.647052	+	0.762446i	$0.723998\pi$
$674$	15.8441	+	4.01511i	0.610291	+	0.154656i
$675$		0			0
$676$	5.17775	−	9.55995i	0.199144	−	0.367690i
$677$	23.4845	+	23.4845i	0.902584	+	0.902584i	0.995659	−	0.0930751i	$-0.0296697\pi$
$677$	23.4845	+	23.4845i	0.902584	+	0.902584i	−0.0930751	+	0.995659i	$0.529670\pi$
$678$		0			0
$679$	−10.4839			−0.402333
$680$	2.13579	−	0.0872551i	0.0819036	−	0.00334608i
$681$		0			0
$682$	12.0703	+	20.2643i	0.462194	+	0.775960i
$683$	−4.90491	+	4.90491i	−0.187681	+	0.187681i	−0.794693	−	0.607012i	$-0.792368\pi$
$683$	−4.90491	+	4.90491i	−0.187681	+	0.187681i	0.607012	+	0.794693i	$0.292368\pi$
$684$		0			0
$685$	2.49691	+	2.49691i	0.0954022	+	0.0954022i
$686$	1.37088	+	0.347400i	0.0523405	+	0.0132638i
$687$		0			0
$688$	−0.564251	+	2.68203i	−0.0215119	+	0.102251i
$689$		−	15.5917i		−	0.593996i
$690$		0			0
$691$	−19.1177	+	19.1177i	−0.727272	+	0.727272i	−0.970075	−	0.242804i	$-0.921933\pi$
$691$	−19.1177	+	19.1177i	−0.727272	+	0.727272i	0.242804	+	0.970075i	$0.421933\pi$
$692$	−1.48273	+	0.440883i	−0.0563649	+	0.0167599i
$693$		0			0
$694$	−4.97792	+	2.96506i	−0.188959	+	0.112552i
$695$		−	2.10338i		−	0.0797858i
$696$		0			0
$697$		−	6.07405i		−	0.230071i
$698$	8.54909	+	14.3527i	0.323588	+	0.543259i
$699$		0			0
$700$	4.73880	−	8.74949i	0.179110	−	0.330700i
$701$	6.01355	−	6.01355i	0.227129	−	0.227129i	−0.584363	−	0.811492i	$-0.698656\pi$
$701$	6.01355	−	6.01355i	0.227129	−	0.227129i	0.811492	+	0.584363i	$0.198656\pi$
$702$		0			0
$703$		−	6.40501i		−	0.241570i
$704$	31.1545	+	26.4406i	1.17418	+	0.996519i
$705$		0			0
$706$	4.04672	−	15.9688i	0.152300	−	0.600995i
$707$	0.472060	+	0.472060i	0.0177536	+	0.0177536i
$708$		0			0
$709$	−6.33448	+	6.33448i	−0.237896	+	0.237896i	−0.815979	−	0.578082i	$-0.803801\pi$
$709$	−6.33448	+	6.33448i	−0.237896	+	0.237896i	0.578082	+	0.815979i	$0.303801\pi$
$710$	0.541778	−	0.322706i	0.0203326	−	0.0121109i
$711$		0			0
$712$	27.3350	+	25.1892i	1.02442	+	0.944006i
$713$	−21.5069			−0.805441
$714$		0			0
$715$	1.56483	+	1.56483i	0.0585212	+	0.0585212i
$716$	−12.4203	−	41.7704i	−0.464167	−	1.56103i
$717$		0			0
$718$	−8.34234	+	32.9199i	−0.311334	+	1.22856i
$719$	19.8643			0.740814			0.370407	−	0.928869i	$-0.379218\pi$
$719$	19.8643			0.740814			0.370407	+	0.928869i	$0.379218\pi$
$720$		0			0
$721$	−16.5554			−0.616554
$722$	−0.210111	+	0.829123i	−0.00781953	+	0.0308568i
$723$		0			0
$724$	−11.1406	+	3.31263i	−0.414039	+	0.123113i
$725$	−7.61967	−	7.61967i	−0.282987	−	0.282987i
$726$		0			0
$727$	−17.0880			−0.633759			−0.316879	−	0.948466i	$-0.602635\pi$
$727$	−17.0880			−0.633759			−0.316879	+	0.948466i	$0.602635\pi$
$728$	−0.317534	−	7.77245i	−0.0117686	−	0.288066i
$729$		0			0
$730$	−3.01262	+	1.79444i	−0.111502	+	0.0664153i
$731$	−2.32430	+	2.32430i	−0.0859673	+	0.0859673i
$732$		0			0
$733$	27.4896	+	27.4896i	1.01535	+	1.01535i	0.999880	+	0.0154724i	$0.00492520\pi$
$733$	27.4896	+	27.4896i	1.01535	+	1.01535i	0.0154724	+	0.999880i	$0.495075\pi$
$734$	−4.23612	+	16.7162i	−0.156358	+	0.617007i
$735$		0			0
$736$	−35.2504	+	12.0683i	−1.29935	+	0.444843i
$737$			6.48048i			0.238711i
$738$		0			0
$739$	33.4666	−	33.4666i	1.23109	−	1.23109i	0.267542	−	0.963546i	$-0.413788\pi$
$739$	33.4666	−	33.4666i	1.23109	−	1.23109i	0.963546	−	0.267542i	$-0.0862115\pi$
$740$	−0.413730	−	0.224080i	−0.0152090	−	0.00823734i
$741$		0			0
$742$	4.10282	+	6.88806i	0.150619	+	0.252869i
$743$		−	0.720828i		−	0.0264446i	−0.999913	−	0.0132223i	$-0.995791\pi$
$743$		−	0.720828i		−	0.0264446i	0.999913	−	0.0132223i	$-0.00420892\pi$
$744$		0			0
$745$		−	2.36208i		−	0.0865398i
$746$	29.8291	−	17.7675i	1.09212	−	0.650513i
$747$		0			0
$748$	13.9677	+	46.9745i	0.510709	+	1.71756i
$749$	−7.98789	+	7.98789i	−0.291871	+	0.291871i
$750$		0			0
$751$		−	8.54158i		−	0.311687i	−0.987782	−	0.155843i	$-0.950190\pi$
$751$		−	8.54158i		−	0.311687i	0.987782	−	0.155843i	$-0.0498095\pi$
$752$	−24.5319	−	37.6043i	−0.894588	−	1.37129i
$753$		0			0
$754$	−8.16613	−	2.06941i	−0.297393	−	0.0753635i
$755$	0.0726208	+	0.0726208i	0.00264294	+	0.00264294i
$756$		0			0
$757$	5.80744	−	5.80744i	0.211075	−	0.211075i	−0.593649	−	0.804724i	$-0.702313\pi$
$757$	5.80744	−	5.80744i	0.211075	−	0.211075i	0.804724	+	0.593649i	$0.202313\pi$
$758$	16.6201	+	27.9028i	0.603668	+	1.01347i
$759$		0			0
$760$	−1.40535	−	1.29503i	−0.0509775	−	0.0469758i
$761$	−19.8670			−0.720179			−0.360090	−	0.932918i	$-0.617254\pi$
$761$	−19.8670			−0.720179			−0.360090	+	0.932918i	$0.617254\pi$
$762$		0			0
$763$	−6.01886	−	6.01886i	−0.217897	−	0.217897i
$764$	−13.3033	−	7.20520i	−0.481298	−	0.260675i
$765$		0			0
$766$	16.4766	+	4.17539i	0.595323	+	0.150863i
$767$	29.6172			1.06942
$768$		0			0
$769$	51.4781			1.85635			0.928173	−	0.372148i	$-0.121379\pi$
$769$	51.4781			1.85635			0.928173	+	0.372148i	$0.121379\pi$
$770$	−1.10308	−	0.279535i	−0.0397521	−	0.0100737i
$771$		0			0
$772$	24.6832	+	13.3686i	0.888368	+	0.481148i
$773$	17.8748	+	17.8748i	0.642913	+	0.642913i	0.951271	−	0.308358i	$-0.0997793\pi$
$773$	17.8748	+	17.8748i	0.642913	+	0.642913i	−0.308358	+	0.951271i	$0.599779\pi$
$774$		0			0
$775$	16.2454			0.583553
$776$	−21.8061	−	20.0943i	−0.782794	−	0.721344i
$777$		0			0
$778$	−13.5399	−	22.7315i	−0.485428	−	0.814965i
$779$	−3.83987	+	3.83987i	−0.137578	+	0.137578i
$780$		0			0
$781$	10.2231	+	10.2231i	0.365810	+	0.365810i
$782$	−43.3166	−	10.9770i	−1.54900	−	0.392538i
$783$		0			0
$784$	2.18553	+	3.35014i	0.0780548	+	0.119648i
$785$			3.49259i			0.124656i
$786$		0			0
$787$	−9.93955	+	9.93955i	−0.354307	+	0.354307i	−0.861709	−	0.507403i	$-0.830606\pi$
$787$	−9.93955	+	9.93955i	−0.354307	+	0.354307i	0.507403	+	0.861709i	$0.330606\pi$
$788$	7.73808	+	26.0238i	0.275658	+	0.927060i
$789$		0			0
$790$	−2.95053	+	1.75746i	−0.104975	+	0.0625277i
$791$		−	7.81071i		−	0.277717i
$792$		0			0
$793$		−	21.1671i		−	0.751664i
$794$	22.3985	+	37.6039i	0.794893	+	1.33451i
$795$		0			0
$796$	−22.0138	−	11.9229i	−0.780258	−	0.422595i
$797$	−1.30890	+	1.30890i	−0.0463636	+	0.0463636i	−0.729908	−	0.683545i	$-0.760437\pi$
$797$	−1.30890	+	1.30890i	−0.0463636	+	0.0463636i	0.683545	+	0.729908i	$0.260437\pi$
$798$		0			0
$799$		−	53.8484i		−	1.90502i
$800$	26.6267	−	9.11587i	0.941395	−	0.322295i
$801$		0			0
$802$	−9.68016	+	38.1990i	−0.341818	+	1.34885i
$803$	−56.8466	−	56.8466i	−2.00607	−	2.00607i
$804$		0			0
$805$	0.733698	−	0.733698i	0.0258594	−	0.0258594i
$806$	10.9113	−	6.49922i	0.384334	−	0.228925i
$807$		0			0
$808$	0.0770775	+	1.88666i	0.00271158	+	0.0663726i
$809$	−38.4014			−1.35012			−0.675060	−	0.737763i	$-0.735882\pi$
$809$	−38.4014			−1.35012			−0.675060	+	0.737763i	$0.735882\pi$
$810$		0			0
$811$	−32.4504	−	32.4504i	−1.13949	−	1.13949i	−0.988542	−	0.150946i	$-0.951768\pi$
$811$	−32.4504	−	32.4504i	−1.13949	−	1.13949i	−0.150946	−	0.988542i	$-0.548232\pi$
$812$	4.15217	−	1.23463i	0.145713	−	0.0433270i
$813$		0			0
$814$	2.64989	−	10.4568i	0.0928786	−	0.366510i
$815$	0.907215			0.0317784
$816$		0			0
$817$	2.93873			0.102813
$818$	3.32786	−	13.1321i	0.116356	−	0.459154i
$819$		0			0
$820$	0.113697	+	0.382374i	0.00397048	+	0.0133531i
$821$	−13.9023	−	13.9023i	−0.485194	−	0.485194i	0.421592	−	0.906786i	$-0.361472\pi$
$821$	−13.9023	−	13.9023i	−0.485194	−	0.485194i	−0.906786	+	0.421592i	$0.861472\pi$
$822$		0			0
$823$	−15.7710			−0.549744			−0.274872	−	0.961481i	$-0.588635\pi$
$823$	−15.7710			−0.549744			−0.274872	+	0.961481i	$0.588635\pi$
$824$	−34.4347	−	31.7315i	−1.19959	−	1.10542i
$825$		0			0
$826$	−13.0843	+	7.79353i	−0.455259	+	0.271172i
$827$	25.4573	−	25.4573i	0.885237	−	0.885237i	−0.108824	−	0.994061i	$-0.534709\pi$
$827$	25.4573	−	25.4573i	0.885237	−	0.885237i	0.994061	+	0.108824i	$0.0347085\pi$
$828$		0			0
$829$	−18.0084	−	18.0084i	−0.625459	−	0.625459i	0.321463	−	0.946922i	$-0.395825\pi$
$829$	−18.0084	−	18.0084i	−0.625459	−	0.625459i	−0.946922	+	0.321463i	$0.895825\pi$
$830$	−0.586655	+	2.31501i	−0.0203631	+	0.0803552i
$831$		0			0
$832$	14.2369	−	16.7751i	0.493577	−	0.581572i
$833$			4.79732i			0.166217i
$834$		0			0
$835$	−0.896173	+	0.896173i	−0.0310133	+	0.0310133i
$836$	20.8661	−	38.5262i	0.721670	−	1.33246i
$837$		0			0
$838$	−6.69219	−	11.2353i	−0.231178	−	0.388115i
$839$		−	6.91080i		−	0.238587i	−0.992859	−	0.119294i	$-0.961937\pi$
$839$		−	6.91080i		−	0.238587i	0.992859	−	0.119294i	$-0.0380630\pi$
$840$		0			0
$841$			24.3088i			0.838234i
$842$	−30.7231	+	18.3000i	−1.05879	+	0.630658i
$843$		0			0
$844$	16.7922	−	4.99309i	0.578011	−	0.171869i
$845$	−0.605540	+	0.605540i	−0.0208312	+	0.0208312i
$846$		0			0
$847$		−	15.0892i		−	0.518471i
$848$	−4.66855	+	22.1908i	−0.160319	+	0.762037i
$849$		0			0
$850$	32.7196	+	8.29159i	1.12227	+	0.284399i
$851$	6.95519	+	6.95519i	0.238421	+	0.238421i
$852$		0			0
$853$	−8.91240	+	8.91240i	−0.305155	+	0.305155i	−0.843027	−	0.537872i	$-0.819228\pi$
$853$	−8.91240	+	8.91240i	−0.305155	+	0.305155i	0.537872	+	0.843027i	$0.319228\pi$
$854$	5.56994	+	9.35114i	0.190599	+	0.319990i
$855$		0			0
$856$	−31.9249	+	1.30426i	−1.09117	+	0.0445786i
$857$	29.4916			1.00741			0.503706	−	0.863875i	$-0.331969\pi$
$857$	29.4916			1.00741			0.503706	+	0.863875i	$0.331969\pi$
$858$		0			0
$859$	−11.9280	−	11.9280i	−0.406977	−	0.406977i	0.473706	−	0.880683i	$-0.342916\pi$
$859$	−11.9280	−	11.9280i	−0.406977	−	0.406977i	−0.880683	+	0.473706i	$0.842916\pi$
$860$	0.102812	−	0.189827i	0.00350586	−	0.00647304i
$861$		0			0
$862$	4.14854	+	1.05130i	0.141300	+	0.0358073i
$863$	−45.3343			−1.54320			−0.771598	−	0.636110i	$-0.780542\pi$
$863$	−45.3343			−1.54320			−0.771598	+	0.636110i	$0.780542\pi$
$864$		0			0
$865$	0.121844			0.00414282
$866$	45.6968	+	11.5802i	1.55284	+	0.393511i
$867$		0			0
$868$	−3.11015	+	5.74243i	−0.105565	+	0.194911i
$869$	−55.6751	−	55.6751i	−1.88865	−	1.88865i
$870$		0			0
$871$	3.48941			0.118234
$872$	−0.982755	−	24.0554i	−0.0332803	−	0.814618i
$873$		0			0
$874$	20.4443	+	34.3232i	0.691540	+	1.16100i
$875$	−1.11117	+	1.11117i	−0.0375645	+	0.0375645i
$876$		0			0
$877$	31.3609	+	31.3609i	1.05898	+	1.05898i	0.998148	+	0.0608358i	$0.0193766\pi$
$877$	31.3609	+	31.3609i	1.05898	+	1.05898i	0.0608358	+	0.998148i	$0.480623\pi$
$878$	34.3252	+	8.69849i	1.15842	+	0.293560i
$879$		0			0
$880$	−1.75859	−	2.69568i	−0.0592819	−	0.0908715i
$881$		−	51.6409i		−	1.73983i	−0.493204	−	0.869913i	$-0.664175\pi$
$881$		−	51.6409i		−	1.73983i	0.493204	−	0.869913i	$-0.335825\pi$
$882$		0			0
$883$	−21.8785	+	21.8785i	−0.736269	+	0.736269i	−0.971854	−	0.235585i	$-0.924299\pi$
$883$	−21.8785	+	21.8785i	−0.736269	+	0.736269i	0.235585	+	0.971854i	$0.424299\pi$
$884$	25.2934	−	7.52088i	0.850708	−	0.252955i
$885$		0			0
$886$	19.7997	−	11.7935i	0.665184	−	0.396212i
$887$			19.7592i			0.663449i	0.943376	+	0.331725i	$0.107630\pi$
$887$			19.7592i			0.663449i	−0.943376	+	0.331725i	$0.892370\pi$
$888$		0			0
$889$			6.59439i			0.221169i
$890$	−1.49831	−	2.51546i	−0.0502236	−	0.0843183i
$891$		0			0
$892$	−22.3653	+	41.2942i	−0.748846	+	1.38263i
$893$	−34.0417	+	34.0417i	−1.13916	+	1.13916i
$894$		0			0
$895$			3.43251i			0.114736i
$896$	−1.87534	+	11.1572i	−0.0626507	+	0.372736i
$897$		0			0
$898$	−8.67341	+	34.2263i	−0.289435	+	1.14215i
$899$	5.00091	+	5.00091i	0.166790	+	0.166790i
$900$		0			0
$901$	−19.2310	+	19.2310i	−0.640678	+	0.640678i
$902$	−7.85758	+	4.68031i	−0.261629	+	0.155837i
$903$		0			0
$904$	14.9707	−	16.2461i	0.497920	−	0.540336i
$905$	0.915490			0.0304319
$906$		0			0
$907$	−31.5036	−	31.5036i	−1.04606	−	1.04606i	−0.998887	−	0.0471723i	$-0.984979\pi$
$907$	−31.5036	−	31.5036i	−1.04606	−	1.04606i	−0.0471723	−	0.998887i	$-0.515021\pi$
$908$	−11.1948	−	37.6490i	−0.371512	−	1.24943i
$909$		0			0
$910$	−0.150515	+	0.593951i	−0.00498953	+	0.0196893i
$911$	−15.7479			−0.521752			−0.260876	−	0.965372i	$-0.584011\pi$
$911$	−15.7479			−0.521752			−0.260876	+	0.965372i	$0.584011\pi$
$912$		0			0
$913$	−54.7530			−1.81206
$914$	5.23820	−	20.6705i	0.173264	−	0.683721i
$915$		0			0
$916$	−8.03033	+	2.38779i	−0.265330	+	0.0788947i
$917$	6.27211	+	6.27211i	0.207123	+	0.207123i
$918$		0			0
$919$	−31.5809			−1.04176			−0.520880	−	0.853630i	$-0.674396\pi$
$919$	−31.5809			−1.04176			−0.520880	+	0.853630i	$0.674396\pi$
$920$	2.93234	−	0.119798i	0.0966765	−	0.00394961i
$921$		0			0
$922$	−3.41667	+	2.03511i	−0.112522	+	0.0670229i
$923$	5.50460	−	5.50460i	0.181186	−	0.181186i
$924$		0			0
$925$	−5.25366	−	5.25366i	−0.172739	−	0.172739i
$926$	4.79867	−	18.9361i	0.157694	−	0.622279i
$927$		0			0
$928$	11.0028	+	5.39043i	0.361185	+	0.176950i
$929$			31.4061i			1.03040i	0.857070	+	0.515200i	$0.172282\pi$
$929$			31.4061i			1.03040i	−0.857070	+	0.515200i	$0.827718\pi$
$930$		0			0
$931$	3.03275	−	3.03275i	0.0993945	−	0.0993945i
$932$	3.41332	+	1.84868i	0.111807	+	0.0605556i
$933$		0			0
$934$	28.4564	+	47.7743i	0.931121	+	1.56322i
$935$		−	3.86016i		−	0.126241i
$936$		0			0
$937$			14.9239i			0.487544i	0.969833	+	0.243772i	$0.0783848\pi$
$937$			14.9239i			0.487544i	−0.969833	+	0.243772i	$0.921615\pi$
$938$	−1.54154	+	0.918209i	−0.0503332	+	0.0299806i
$939$		0			0
$940$	1.00796	+	3.38987i	0.0328762	+	0.110565i
$941$	13.4870	−	13.4870i	0.439664	−	0.439664i	−0.452235	−	0.891899i	$-0.649373\pi$
$941$	13.4870	−	13.4870i	0.439664	−	0.439664i	0.891899	+	0.452235i	$0.149373\pi$
$942$		0			0
$943$		−	8.33942i		−	0.271569i
$944$	−42.1527	−	8.86816i	−1.37195	−	0.288634i
$945$		0			0
$946$	4.79776	+	1.21582i	0.155988	+	0.0395296i
$947$	28.6554	+	28.6554i	0.931174	+	0.931174i	0.997779	−	0.0666054i	$-0.0212169\pi$
$947$	28.6554	+	28.6554i	0.931174	+	0.931174i	−0.0666054	+	0.997779i	$0.521217\pi$
$948$		0			0
$949$	−30.6090	+	30.6090i	−0.993609	+	0.993609i
$950$	−15.4428	−	25.9263i	−0.501030	−	0.841160i
$951$		0			0
$952$	−9.19499	+	9.97830i	−0.298011	+	0.323398i
$953$	−48.9378			−1.58525			−0.792626	−	0.609709i	$-0.791286\pi$
$953$	−48.9378			−1.58525			−0.792626	+	0.609709i	$0.791286\pi$
$954$		0			0
$955$	0.842651	+	0.842651i	0.0272675	+	0.0272675i
$956$	6.56425	+	3.55525i	0.212303	+	0.114985i
$957$		0			0
$958$	−29.3404	−	7.43525i	−0.947945	−	0.240222i
$959$	−22.4152			−0.723825
$960$		0			0
$961$	20.3379			0.656060
$962$	−5.63044	−	1.42683i	−0.181533	−	0.0460028i
$963$		0			0
$964$	−11.8271	−	6.40566i	−0.380925	−	0.206313i
$965$	−1.56347	−	1.56347i	−0.0503298	−	0.0503298i
$966$		0			0
$967$	−8.50595			−0.273533			−0.136767	−	0.990603i	$-0.543671\pi$
$967$	−8.50595			−0.273533			−0.136767	+	0.990603i	$0.543671\pi$
$968$	28.9213	−	31.3851i	0.929567	−	1.00876i
$969$		0			0
$970$	1.19526	+	2.00667i	0.0383774	+	0.0644303i
$971$	8.52407	−	8.52407i	0.273550	−	0.273550i	−0.556977	−	0.830528i	$-0.688039\pi$
$971$	8.52407	−	8.52407i	0.273550	−	0.273550i	0.830528	+	0.556977i	$0.188039\pi$
$972$		0			0
$973$	9.44120	+	9.44120i	0.302671	+	0.302671i
$974$	−38.3686	−	9.72314i	−1.22941	−	0.311549i
$975$		0			0
$976$	−6.33796	+	30.1260i	−0.202873	+	0.964309i
$977$			30.2469i			0.967685i	0.875155	+	0.483842i	$0.160759\pi$
$977$			30.2469i			0.967685i	−0.875155	+	0.483842i	$0.839241\pi$
$978$		0			0
$979$	47.4654	−	47.4654i	1.51700	−	1.51700i
$980$	−0.0897988	−	0.302001i	−0.00286852	−	0.00964707i
$981$		0			0
$982$	37.8866	−	22.5669i	1.20901	−	0.720137i
$983$		−	49.8151i		−	1.58886i	−0.607358	−	0.794428i	$-0.707771\pi$
$983$		−	49.8151i		−	1.58886i	0.607358	−	0.794428i	$-0.292229\pi$
$984$		0			0
$985$		−	2.13852i		−	0.0681390i
$986$	7.51979	+	12.6247i	0.239479	+	0.402051i
$987$		0			0
$988$	−20.7444	−	11.2353i	−0.659967	−	0.357444i
$989$	−3.19117	+	3.19117i	−0.101473	+	0.101473i
$990$		0			0
$991$		−	26.1968i		−	0.832167i	−0.909326	−	0.416084i	$-0.863402\pi$
$991$		−	26.1968i		−	0.832167i	0.909326	−	0.416084i	$-0.136598\pi$
$992$	−17.4755	+	5.98289i	−0.554848	+	0.189957i
$993$		0			0
$994$	−0.983322	+	3.88030i	−0.0311891	+	0.123076i
$995$	1.39438	+	1.39438i	0.0442049	+	0.0442049i
$996$		0			0
$997$	−5.13429	+	5.13429i	−0.162604	+	0.162604i	−0.783719	−	0.621115i	$-0.786680\pi$
$997$	−5.13429	+	5.13429i	−0.162604	+	0.162604i	0.621115	+	0.783719i	$0.286680\pi$
$998$	9.63062	−	5.73640i	0.304852	−	0.181583i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.18	yes	40
3.2	odd	2	inner	1008.2.v.e.323.3	✓	40
4.3	odd	2		4032.2.v.e.1583.9		40
12.11	even	2		4032.2.v.e.1583.12		40
16.5	even	4		4032.2.v.e.3599.12		40
16.11	odd	4	inner	1008.2.v.e.827.3	yes	40
48.5	odd	4		4032.2.v.e.3599.9		40
48.11	even	4	inner	1008.2.v.e.827.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.3	✓	40	3.2	odd	2	inner
1008.2.v.e.323.18	yes	40	1.1	even	1	trivial
1008.2.v.e.827.3	yes	40	16.11	odd	4	inner
1008.2.v.e.827.18	yes	40	48.11	even	4	inner
4032.2.v.e.1583.9		40	4.3	odd	2
4032.2.v.e.1583.12		40	12.11	even	2
4032.2.v.e.3599.9		40	48.5	odd	4
4032.2.v.e.3599.12		40	16.5	even	4

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37088 + 0.347400i) q^{2} +(1.75863 + 0.952488i) q^{4} +(-0.111394 - 0.111394i) q^{5} +1.00000 q^{7} +(2.07997 + 1.91669i) q^{8} +O(q^{10})\)	\(q+(1.37088 + 0.347400i) q^{2} +(1.75863 + 0.952488i) q^{4} +(-0.111394 - 0.111394i) q^{5} +1.00000 q^{7} +(2.07997 + 1.91669i) q^{8} +(-0.114009 - 0.191406i) q^{10} +(3.61173 - 3.61173i) q^{11} +(-1.94473 - 1.94473i) q^{13} +(1.37088 + 0.347400i) q^{14} +(2.18553 + 3.35014i) q^{16} +4.79732i q^{17} +(3.03275 - 3.03275i) q^{19} +(-0.0897988 - 0.302001i) q^{20} +(6.20596 - 3.69654i) q^{22} +6.58652i q^{23} -4.97518i q^{25} +(-1.99040 - 3.34160i) q^{26} +(1.75863 + 0.952488i) q^{28} +(1.53154 - 1.53154i) q^{29} +3.26529i q^{31} +(1.83227 + 5.35190i) q^{32} +(-1.66659 + 6.57655i) q^{34} +(-0.111394 - 0.111394i) q^{35} +(1.05597 - 1.05597i) q^{37} +(5.21112 - 3.10396i) q^{38} +(-0.0181883 - 0.445204i) q^{40} -1.26613 q^{41} +(0.484499 + 0.484499i) q^{43} +(9.79181 - 2.91156i) q^{44} +(-2.28816 + 9.02934i) q^{46} -11.2247 q^{47} +1.00000 q^{49} +(1.72838 - 6.82038i) q^{50} +(-1.56772 - 5.27239i) q^{52} +(4.00870 + 4.00870i) q^{53} -0.804648 q^{55} +(2.07997 + 1.91669i) q^{56} +(2.63161 - 1.56750i) q^{58} +(-7.61474 + 7.61474i) q^{59} +(5.44215 + 5.44215i) q^{61} +(-1.13436 + 4.47632i) q^{62} +(0.652573 + 7.97334i) q^{64} +0.433262i q^{65} +(-0.897143 + 0.897143i) q^{67} +(-4.56939 + 8.43670i) q^{68} +(-0.114009 - 0.191406i) q^{70} +2.83052i q^{71} -15.7394i q^{73} +(1.81446 - 1.08077i) q^{74} +(8.22214 - 2.44482i) q^{76} +(3.61173 - 3.61173i) q^{77} -15.4151i q^{79} +(0.129730 - 0.616640i) q^{80} +(-1.73572 - 0.439855i) q^{82} +(-7.57988 - 7.57988i) q^{83} +(0.534392 - 0.534392i) q^{85} +(0.495876 + 0.832506i) q^{86} +(14.4349 - 0.589720i) q^{88} +13.1420 q^{89} +(-1.94473 - 1.94473i) q^{91} +(-6.27358 + 11.5832i) q^{92} +(-15.3877 - 3.89946i) q^{94} -0.675660 q^{95} -10.4839 q^{97} +(1.37088 + 0.347400i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 40 * q + 40 * q^7	\( 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) \) 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

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