LMFDB - Embedded newform 405.2.k.a.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(46,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("405.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$405 = 3^{4} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	405.k (of order $9$ , degree $6$ , not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	405.91
Dual form			405.2.k.a.316.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.130038 + 0.737480i) q^{2} +(1.35242 - 0.492240i) q^{4} +(0.766044 + 0.642788i) q^{5} +(0.498180 + 0.181323i) q^{7} +(1.28774 + 2.23043i) q^{8} +(-0.374428 + 0.648529i) q^{10} +(0.148674 - 0.124752i) q^{11} +(0.315087 - 1.78695i) q^{13} +(-0.0689397 + 0.390976i) q^{14} +(0.727561 - 0.610496i) q^{16} +(-0.226222 + 0.391829i) q^{17} +(1.93374 + 3.34934i) q^{19} +(1.35242 + 0.492240i) q^{20} +(0.111336 + 0.0934217i) q^{22} +(-3.74433 + 1.36283i) q^{23} +(0.173648 + 0.984808i) q^{25} +1.35881 q^{26} +0.763002 q^{28} +(-1.67673 - 9.50919i) q^{29} +(8.56046 - 3.11575i) q^{31} +(4.49070 + 3.76814i) q^{32} +(-0.318383 - 0.115882i) q^{34} +(0.265076 + 0.459125i) q^{35} +(-5.33354 + 9.23795i) q^{37} +(-2.21861 + 1.86164i) q^{38} +(-0.447227 + 2.53635i) q^{40} +(-1.24032 + 7.03423i) q^{41} +(-0.876764 + 0.735692i) q^{43} +(0.139662 - 0.241901i) q^{44} +(-1.49196 - 2.58415i) q^{46} +(-3.81750 - 1.38946i) q^{47} +(-5.14701 - 4.31885i) q^{49} +(-0.703695 + 0.256124i) q^{50} +(-0.453478 - 2.57180i) q^{52} +3.04103 q^{53} +0.194080 q^{55} +(0.237098 + 1.34465i) q^{56} +(6.79480 - 2.47311i) q^{58} +(-2.03716 - 1.70938i) q^{59} +(-11.2031 - 4.07760i) q^{61} +(3.41099 + 5.90800i) q^{62} +(-1.24521 + 2.15676i) q^{64} +(1.39000 - 1.16635i) q^{65} +(-1.01879 + 5.77785i) q^{67} +(-0.113074 + 0.641272i) q^{68} +(-0.304126 + 0.255192i) q^{70} +(4.55517 - 7.88979i) q^{71} +(-2.99330 - 5.18454i) q^{73} +(-7.50637 - 2.73209i) q^{74} +(4.26391 + 3.57785i) q^{76} +(0.0966869 - 0.0351912i) q^{77} +(-2.17315 - 12.3246i) q^{79} +0.949763 q^{80} -5.34889 q^{82} +(-2.37738 - 13.4828i) q^{83} +(-0.425159 + 0.154745i) q^{85} +(-0.656570 - 0.550928i) q^{86} +(0.469705 + 0.170959i) q^{88} +(-1.94800 - 3.37404i) q^{89} +(0.480985 - 0.833090i) q^{91} +(-4.39307 + 3.68622i) q^{92} +(0.528278 - 2.99601i) q^{94} +(-0.671582 + 3.80873i) q^{95} +(-6.47950 + 5.43694i) q^{97} +(2.51576 - 4.35743i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$30 q + 9 q^{8} + 3 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} + 12 q^{16} + 12 q^{17} + 24 q^{19} - 51 q^{22} - 18 q^{23} + 18 q^{26} - 60 q^{28} - 18 q^{29} + 12 q^{31} - 36 q^{32} - 69 q^{34} + 12 q^{35}+ \cdots + 15 q^{98}+O(q^{100})$ 30 * q + 9 * q^8 + 3 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 + 12 * q^16 + 12 * q^17 + 24 * q^19 - 51 * q^22 - 18 * q^23 + 18 * q^26 - 60 * q^28 - 18 * q^29 + 12 * q^31 - 36 * q^32 - 69 * q^34 + 12 * q^35 + 24 * q^37 + 24 * q^38 + 9 * q^40 + 75 * q^41 + 6 * q^43 - 12 * q^44 + 30 * q^46 - 45 * q^47 - 36 * q^49 + 30 * q^52 - 36 * q^53 - 30 * q^56 + 27 * q^58 + 27 * q^59 - 12 * q^61 - 36 * q^62 + 27 * q^64 - 6 * q^65 - 30 * q^67 - 69 * q^68 + 27 * q^70 - 12 * q^71 + 21 * q^73 - 30 * q^76 + 36 * q^77 + 54 * q^79 - 6 * q^80 - 48 * q^82 + 87 * q^83 + 27 * q^85 - 18 * q^86 - 18 * q^88 - 9 * q^89 + 51 * q^91 - 24 * q^92 + 15 * q^94 - 21 * q^95 - 75 * q^97 + 15 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$ .

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.130038	+	0.737480i	0.0919505	+	0.521477i	0.995639	+	0.0932871i	$0.0297375\pi$
$2$	0.130038	+	0.737480i	0.0919505	+	0.521477i	−0.903689	+	0.428190i	$0.859151\pi$
$3$		0			0
$3$		0			0
$4$	1.35242	−	0.492240i	0.676209	−	0.246120i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$6$		0			0
$7$	0.498180	+	0.181323i	0.188294	+	0.0685335i	0.434446	−	0.900698i	$-0.356944\pi$
$7$	0.498180	+	0.181323i	0.188294	+	0.0685335i	−0.246152	+	0.969231i	$0.579166\pi$
$8$	1.28774	+	2.23043i	0.455285	+	0.788576i
$9$		0			0
$10$	−0.374428	+	0.648529i	−0.118405	+	0.205083i
$11$	0.148674	−	0.124752i	0.0448270	−	0.0376143i	−0.620099	−	0.784524i	$-0.712908\pi$
$11$	0.148674	−	0.124752i	0.0448270	−	0.0376143i	0.664926	+	0.746909i	$0.268463\pi$
$12$		0			0
$13$	0.315087	−	1.78695i	0.0873895	−	0.495611i	−0.909426	−	0.415866i	$-0.863478\pi$
$13$	0.315087	−	1.78695i	0.0873895	−	0.495611i	0.996815	−	0.0797445i	$-0.0254104\pi$
$14$	−0.0689397	+	0.390976i	−0.0184249	+	0.104493i
$15$		0			0
$16$	0.727561	−	0.610496i	0.181890	−	0.152624i
$17$	−0.226222	+	0.391829i	−0.0548670	+	0.0950324i	−0.892154	−	0.451731i	$-0.850807\pi$
$17$	−0.226222	+	0.391829i	−0.0548670	+	0.0950324i	0.837287	+	0.546763i	$0.184140\pi$
$18$		0			0
$19$	1.93374	+	3.34934i	0.443631	+	0.768392i	0.997956	−	0.0639089i	$-0.0203567\pi$
$19$	1.93374	+	3.34934i	0.443631	+	0.768392i	−0.554325	+	0.832301i	$0.687023\pi$
$20$	1.35242	+	0.492240i	0.302410	+	0.110068i
$21$		0			0
$22$	0.111336	+	0.0934217i	0.0237368	+	0.0199176i
$23$	−3.74433	+	1.36283i	−0.780747	+	0.284169i	−0.701484	−	0.712685i	$-0.747479\pi$
$23$	−3.74433	+	1.36283i	−0.780747	+	0.284169i	−0.0792630	+	0.996854i	$0.525257\pi$
$24$		0			0
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	1.35881			0.266485
$27$		0			0
$28$	0.763002			0.144194
$29$	−1.67673	−	9.50919i	−0.311360	−	1.76581i	−0.591940	−	0.805982i	$-0.701638\pi$
$29$	−1.67673	−	9.50919i	−0.311360	−	1.76581i	0.280579	−	0.959831i	$-0.409473\pi$
$30$		0			0
$31$	8.56046	−	3.11575i	1.53750	−	0.559606i	0.572059	−	0.820213i	$-0.306145\pi$
$31$	8.56046	−	3.11575i	1.53750	−	0.559606i	0.965445	+	0.260607i	$0.0839226\pi$
$32$	4.49070	+	3.76814i	0.793851	+	0.666120i
$33$		0			0
$34$	−0.318383	−	0.115882i	−0.0546023	−	0.0198736i
$35$	0.265076	+	0.459125i	0.0448060	+	0.0776063i
$36$		0			0
$37$	−5.33354	+	9.23795i	−0.876828	+	1.51871i	−0.0220251	+	0.999757i	$0.507011\pi$
$37$	−5.33354	+	9.23795i	−0.876828	+	1.51871i	−0.854803	+	0.518953i	$0.826322\pi$
$38$	−2.21861	+	1.86164i	−0.359907	+	0.301997i
$39$		0			0
$40$	−0.447227	+	2.53635i	−0.0707128	+	0.401032i
$41$	−1.24032	+	7.03423i	−0.193706	+	1.09856i	0.720543	+	0.693410i	$0.243893\pi$
$41$	−1.24032	+	7.03423i	−0.193706	+	1.09856i	−0.914249	+	0.405152i	$0.867219\pi$
$42$		0			0
$43$	−0.876764	+	0.735692i	−0.133705	+	0.112192i	−0.707188	−	0.707026i	$-0.750036\pi$
$43$	−0.876764	+	0.735692i	−0.133705	+	0.112192i	0.573483	+	0.819218i	$0.305592\pi$
$44$	0.139662	−	0.241901i	0.0210548	−	0.0364679i
$45$		0			0
$46$	−1.49196	−	2.58415i	−0.219978	−	0.381012i
$47$	−3.81750	−	1.38946i	−0.556840	−	0.202673i	0.0482429	−	0.998836i	$-0.484638\pi$
$47$	−3.81750	−	1.38946i	−0.556840	−	0.202673i	−0.605083	+	0.796162i	$0.706860\pi$
$48$		0			0
$49$	−5.14701	−	4.31885i	−0.735287	−	0.616979i
$50$	−0.703695	+	0.256124i	−0.0995175	+	0.0362214i
$51$		0			0
$52$	−0.453478	−	2.57180i	−0.0628861	−	0.356645i
$53$	3.04103			0.417717			0.208859	−	0.977946i	$-0.433025\pi$
$53$	3.04103			0.417717			0.208859	+	0.977946i	$0.433025\pi$
$54$		0			0
$55$	0.194080			0.0261698
$56$	0.237098	+	1.34465i	0.0316836	+	0.179687i
$57$		0			0
$58$	6.79480	−	2.47311i	0.892201	−	0.324735i
$59$	−2.03716	−	1.70938i	−0.265215	−	0.222542i	0.500476	−	0.865751i	$-0.333158\pi$
$59$	−2.03716	−	1.70938i	−0.265215	−	0.222542i	−0.765691	+	0.643208i	$0.777603\pi$
$60$		0			0
$61$	−11.2031	−	4.07760i	−1.43441	−	0.522084i	−0.496220	−	0.868197i	$-0.665279\pi$
$61$	−11.2031	−	4.07760i	−1.43441	−	0.522084i	−0.938193	+	0.346113i	$0.887501\pi$
$62$	3.41099	+	5.90800i	0.433196	+	0.750317i
$63$		0			0
$64$	−1.24521	+	2.15676i	−0.155651	+	0.269595i
$65$	1.39000	−	1.16635i	0.172408	−	0.144668i
$66$		0			0
$67$	−1.01879	+	5.77785i	−0.124465	+	0.705877i	0.857159	+	0.515052i	$0.172227\pi$
$67$	−1.01879	+	5.77785i	−0.124465	+	0.705877i	−0.981624	+	0.190825i	$0.938884\pi$
$68$	−0.113074	+	0.641272i	−0.0137122	+	0.0777656i
$69$		0			0
$70$	−0.304126	+	0.255192i	−0.0363500	+	0.0305012i
$71$	4.55517	−	7.88979i	0.540599	−	0.936346i	−0.458270	−	0.888813i	$-0.651531\pi$
$71$	4.55517	−	7.88979i	0.540599	−	0.936346i	0.998870	−	0.0475327i	$-0.0151358\pi$
$72$		0			0
$73$	−2.99330	−	5.18454i	−0.350339	−	0.606804i	0.635970	−	0.771714i	$-0.280600\pi$
$73$	−2.99330	−	5.18454i	−0.350339	−	0.606804i	−0.986309	+	0.164909i	$0.947267\pi$
$74$	−7.50637	−	2.73209i	−0.872597	−	0.317599i
$75$		0			0
$76$	4.26391	+	3.57785i	0.489104	+	0.410407i
$77$	0.0966869	−	0.0351912i	0.0110185	−	0.00401041i
$78$		0			0
$79$	−2.17315	−	12.3246i	−0.244499	−	1.38662i	−0.821653	−	0.569987i	$-0.806948\pi$
$79$	−2.17315	−	12.3246i	−0.244499	−	1.38662i	0.577154	−	0.816635i	$-0.304163\pi$
$80$	0.949763			0.106187
$81$		0			0
$82$	−5.34889			−0.590686
$83$	−2.37738	−	13.4828i	−0.260951	−	1.47993i	−0.780322	−	0.625378i	$-0.784945\pi$
$83$	−2.37738	−	13.4828i	−0.260951	−	1.47993i	0.519371	−	0.854549i	$-0.326166\pi$
$84$		0			0
$85$	−0.425159	+	0.154745i	−0.0461150	+	0.0167845i
$86$	−0.656570	−	0.550928i	−0.0707998	−	0.0594081i
$87$		0			0
$88$	0.469705	+	0.170959i	0.0500707	+	0.0182243i
$89$	−1.94800	−	3.37404i	−0.206488	−	0.357648i	0.744118	−	0.668048i	$-0.232870\pi$
$89$	−1.94800	−	3.37404i	−0.206488	−	0.357648i	−0.950606	+	0.310401i	$0.899537\pi$
$90$		0			0
$91$	0.480985	−	0.833090i	0.0504209	−	0.0873316i
$92$	−4.39307	+	3.68622i	−0.458009	+	0.384315i
$93$		0			0
$94$	0.528278	−	2.99601i	0.0544877	−	0.309015i
$95$	−0.671582	+	3.80873i	−0.0689029	+	0.390768i
$96$		0			0
$97$	−6.47950	+	5.43694i	−0.657893	+	0.552038i	−0.909455	−	0.415803i	$-0.863500\pi$
$97$	−6.47950	+	5.43694i	−0.657893	+	0.552038i	0.251561	+	0.967841i	$0.419056\pi$
$98$	2.51576	−	4.35743i	0.254130	−	0.440167i
$99$		0			0
$100$	0.719607	+	1.24640i	0.0719607	+	0.124640i
$101$	4.71752	+	1.71704i	0.469411	+	0.170852i	0.565885	−	0.824484i	$-0.308534\pi$
$101$	4.71752	+	1.71704i	0.469411	+	0.170852i	−0.0964746	+	0.995335i	$0.530757\pi$
$102$		0			0
$103$	−8.67406	−	7.27840i	−0.854680	−	0.717162i	0.106135	−	0.994352i	$-0.466152\pi$
$103$	−8.67406	−	7.27840i	−0.854680	−	0.717162i	−0.960815	+	0.277190i	$0.910597\pi$
$104$	4.39142	−	1.59834i	0.430614	−	0.156731i
$105$		0			0
$106$	0.395448	+	2.24270i	0.0384093	+	0.217830i
$107$	10.1961			0.985690			0.492845	−	0.870117i	$-0.335957\pi$
$107$	10.1961			0.985690			0.492845	+	0.870117i	$0.335957\pi$
$108$		0			0
$109$	1.18543			0.113544			0.0567718	−	0.998387i	$-0.481919\pi$
$109$	1.18543			0.113544			0.0567718	+	0.998387i	$0.481919\pi$
$110$	0.0252377	+	0.143130i	0.00240632	+	0.0136469i
$111$		0			0
$112$	0.473153	−	0.172214i	0.0447087	−	0.0162727i
$113$	−14.4355	−	12.1128i	−1.35797	−	1.13948i	−0.976602	−	0.215054i	$-0.931007\pi$
$113$	−14.4355	−	12.1128i	−1.35797	−	1.13948i	−0.381372	−	0.924422i	$-0.624548\pi$
$114$		0			0
$115$	−3.74433	−	1.36283i	−0.349161	−	0.127084i
$116$	−6.94844	−	12.0351i	−0.645147	−	1.11743i
$117$		0			0
$118$	0.995725	−	1.72465i	0.0916639	−	0.158767i
$119$	−0.183747	+	0.154182i	−0.0168440	+	0.0141338i
$120$		0			0
$121$	−1.90359	+	10.7958i	−0.173054	+	0.981435i
$122$	1.55032	−	8.79232i	0.140360	−	0.796019i
$123$		0			0
$124$	10.0436	−	8.42760i	0.901944	−	0.756821i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	9.57059	+	16.5768i	0.849253	+	1.47095i	0.881876	+	0.471481i	$0.156281\pi$
$127$	9.57059	+	16.5768i	0.849253	+	1.47095i	−0.0326233	+	0.999468i	$0.510386\pi$
$128$	9.26483	+	3.37212i	0.818903	+	0.298056i
$129$		0			0
$130$	1.04091	+	0.873428i	0.0912939	+	0.0766047i
$131$	−9.43779	+	3.43507i	−0.824583	+	0.300124i	−0.719634	−	0.694354i	$-0.755690\pi$
$131$	−9.43779	+	3.43507i	−0.824583	+	0.300124i	−0.104949	+	0.994478i	$0.533468\pi$
$132$		0			0
$133$	0.356040	+	2.01921i	0.0308726	+	0.175087i
$134$	−4.39353			−0.379543
$135$		0			0
$136$	−1.16526			−0.0999203
$137$	0.145522	+	0.825297i	0.0124328	+	0.0705099i	0.990393	−	0.138282i	$-0.0441580\pi$
$137$	0.145522	+	0.825297i	0.0124328	+	0.0705099i	−0.977960	+	0.208792i	$0.933047\pi$
$138$		0			0
$139$	7.81972	−	2.84614i	0.663260	−	0.241407i	0.0116166	−	0.999933i	$-0.496302\pi$
$139$	7.81972	−	2.84614i	0.663260	−	0.241407i	0.651643	+	0.758526i	$0.274080\pi$
$140$	0.584493	+	0.490448i	0.0493987	+	0.0414504i
$141$		0			0
$142$	6.41090	+	2.33338i	0.537991	+	0.195813i
$143$	−0.176081	−	0.304981i	−0.0147246	−	0.0255038i
$144$		0			0
$145$	4.82794	−	8.36225i	0.400939	−	0.694447i
$146$	3.43425	−	2.88168i	0.284221	−	0.238490i
$147$		0			0
$148$	−2.66588	+	15.1190i	−0.219134	+	1.24277i
$149$	−0.504757	+	2.86262i	−0.0413513	+	0.234515i	−0.998478	−	0.0551555i	$-0.982435\pi$
$149$	−0.504757	+	2.86262i	−0.0413513	+	0.234515i	0.957126	+	0.289670i	$0.0935457\pi$
$150$		0			0
$151$	−8.94423	+	7.50510i	−0.727871	+	0.610757i	−0.929550	−	0.368695i	$-0.879805\pi$
$151$	−8.94423	+	7.50510i	−0.727871	+	0.610757i	0.201679	+	0.979452i	$0.435360\pi$
$152$	−4.98031	+	8.62616i	−0.403957	+	0.699674i
$153$		0			0
$154$	0.0385257	+	0.0667285i	0.00310449	+	0.00537714i
$155$	8.56046	+	3.11575i	0.687593	+	0.250263i
$156$		0			0
$157$	−17.2442	−	14.4696i	−1.37624	−	1.15480i	−0.970580	−	0.240777i	$-0.922598\pi$
$157$	−17.2442	−	14.4696i	−1.37624	−	1.15480i	−0.405659	−	0.914025i	$-0.632958\pi$
$158$	8.80653	−	3.20532i	0.700610	−	0.255001i
$159$		0			0
$160$	1.01796	+	5.77313i	0.0804767	+	0.456406i
$161$	−2.11246			−0.166485
$162$		0			0
$163$	9.62546			0.753924			0.376962	−	0.926229i	$-0.376969\pi$
$163$	9.62546			0.753924			0.376962	+	0.926229i	$0.376969\pi$
$164$	1.78509	+	10.1238i	0.139392	+	0.790533i
$165$		0			0
$166$	9.63412	−	3.50653i	0.747753	−	0.272160i
$167$	12.2334	+	10.2651i	0.946651	+	0.794334i	0.978730	−	0.205151i	$-0.0657685\pi$
$167$	12.2334	+	10.2651i	0.946651	+	0.794334i	−0.0320795	+	0.999485i	$0.510213\pi$
$168$		0			0
$169$	9.12209	+	3.32017i	0.701700	+	0.255398i
$170$	−0.169408	−	0.293423i	−0.0129930	−	0.0225046i
$171$		0			0
$172$	−0.823614	+	1.42654i	−0.0628000	+	0.108773i
$173$	−4.38627	+	3.68052i	−0.333482	+	0.279825i	−0.794117	−	0.607765i	$-0.792066\pi$
$173$	−4.38627	+	3.68052i	−0.333482	+	0.279825i	0.460635	+	0.887590i	$0.347622\pi$
$174$		0			0
$175$	−0.0920599	+	0.522098i	−0.00695908	+	0.0394669i
$176$	0.0320086	−	0.181530i	0.00241274	−	0.0136833i
$177$		0			0
$178$	2.23497	−	1.87537i	0.167518	−	0.140565i
$179$	−6.34218	+	10.9850i	−0.474037	+	0.821056i	−0.999558	−	0.0297242i	$-0.990537\pi$
$179$	−6.34218	+	10.9850i	−0.474037	+	0.821056i	0.525521	+	0.850781i	$0.323870\pi$
$180$		0			0
$181$	−4.56381	−	7.90474i	−0.339225	−	0.587555i	0.645062	−	0.764130i	$-0.276831\pi$
$181$	−4.56381	−	7.90474i	−0.339225	−	0.587555i	−0.984287	+	0.176575i	$0.943498\pi$
$182$	0.676933	+	0.246384i	0.0501776	+	0.0182632i
$183$		0			0
$184$	−7.86141	−	6.59651i	−0.579551	−	0.486301i
$185$	−10.0238	+	3.64835i	−0.736962	+	0.268232i
$186$		0			0
$187$	0.0152482	+	0.0864766i	0.00111506	+	0.00632380i
$188$	−5.84681			−0.426422
$189$		0			0
$190$	−2.89619			−0.210112
$191$	4.29300	+	24.3468i	0.310631	+	1.76167i	0.595738	+	0.803179i	$0.296860\pi$
$191$	4.29300	+	24.3468i	0.310631	+	1.76167i	−0.285108	+	0.958496i	$0.592029\pi$
$192$		0			0
$193$	−4.52691	+	1.64766i	−0.325854	+	0.118601i	−0.499767	−	0.866160i	$-0.666581\pi$
$193$	−4.52691	+	1.64766i	−0.325854	+	0.118601i	0.173913	+	0.984761i	$0.444359\pi$
$194$	−4.85222	−	4.07149i	−0.348369	−	0.292316i
$195$		0			0
$196$	−9.08682	−	3.30733i	−0.649058	−	0.236238i
$197$	8.57097	+	14.8454i	0.610656	+	1.05769i	0.991130	+	0.132896i	$0.0424276\pi$
$197$	8.57097	+	14.8454i	0.610656	+	1.05769i	−0.380474	+	0.924792i	$0.624239\pi$
$198$		0			0
$199$	9.54372	−	16.5302i	0.676537	−	1.17180i	−0.299481	−	0.954102i	$-0.596813\pi$
$199$	9.54372	−	16.5302i	0.676537	−	1.17180i	0.976017	−	0.217693i	$-0.0698533\pi$
$200$	−1.97293	+	1.65549i	−0.139507	+	0.117060i
$201$		0			0
$202$	−0.652825	+	3.70236i	−0.0459326	+	0.260497i
$203$	0.888920	−	5.04132i	0.0623900	−	0.353831i
$204$		0			0
$205$	−5.47166	+	4.59127i	−0.382157	+	0.320668i
$206$	4.23972	−	7.34341i	0.295395	−	0.511639i
$207$		0			0
$208$	−0.861681	−	1.49247i	−0.0597468	−	0.103484i
$209$	0.705336	+	0.256721i	0.0487891	+	0.0177578i
$210$		0			0
$211$	6.00165	+	5.03598i	0.413171	+	0.346691i	0.825558	−	0.564317i	$-0.190861\pi$
$211$	6.00165	+	5.03598i	0.413171	+	0.346691i	−0.412387	+	0.911009i	$0.635305\pi$
$212$	4.11274	−	1.49692i	0.282464	−	0.102809i
$213$		0			0
$214$	1.32587	+	7.51939i	0.0906346	+	0.514015i
$215$	−1.14453			−0.0780565
$216$		0			0
$217$	4.82960			0.327855
$218$	0.154151	+	0.874231i	0.0104404	+	0.0592104i
$219$		0			0
$220$	0.262478	−	0.0955341i	0.0176963	−	0.00644091i
$221$	0.628898	+	0.527708i	0.0423043	+	0.0354975i
$222$		0			0
$223$	13.6246	+	4.95897i	0.912374	+	0.332077i	0.755200	−	0.655494i	$-0.227540\pi$
$223$	13.6246	+	4.95897i	0.912374	+	0.332077i	0.157174	+	0.987571i	$0.449762\pi$
$224$	1.55393	+	2.69148i	0.103826	+	0.179832i
$225$		0			0
$226$	7.05579	−	12.2210i	0.469344	−	0.812928i
$227$	−0.344364	+	0.288955i	−0.0228562	+	0.0191786i	−0.654144	−	0.756370i	$-0.726971\pi$
$227$	−0.344364	+	0.288955i	−0.0228562	+	0.0191786i	0.631288	+	0.775549i	$0.282527\pi$
$228$		0			0
$229$	−2.41140	+	13.6757i	−0.159350	+	0.903716i	0.795351	+	0.606149i	$0.207286\pi$
$229$	−2.41140	+	13.6757i	−0.159350	+	0.903716i	−0.954701	+	0.297567i	$0.903825\pi$
$230$	0.518152	−	2.93859i	0.0341660	−	0.193765i
$231$		0			0
$232$	19.0504	−	15.9852i	1.25072	−	1.04948i
$233$	−9.85639	+	17.0718i	−0.645713	+	1.11841i	0.338423	+	0.940994i	$0.390107\pi$
$233$	−9.85639	+	17.0718i	−0.645713	+	1.11841i	−0.984136	+	0.177414i	$0.943227\pi$
$234$		0			0
$235$	−2.03125	−	3.51823i	−0.132504	−	0.229504i
$236$	−3.59652	−	1.30902i	−0.234113	−	0.0852102i
$237$		0			0
$238$	−0.137600	−	0.115460i	−0.00891928	−	0.00748417i
$239$	18.7092	−	6.80960i	1.21020	−	0.440477i	0.343427	−	0.939180i	$-0.388412\pi$
$239$	18.7092	−	6.80960i	1.21020	−	0.440477i	0.866773	+	0.498703i	$0.166190\pi$
$240$		0			0
$241$	1.30157	+	7.38156i	0.0838414	+	0.475488i	0.997601	+	0.0692320i	$0.0220549\pi$
$241$	1.30157	+	7.38156i	0.0838414	+	0.475488i	−0.913759	+	0.406256i	$0.866834\pi$
$242$	−8.20922			−0.527708
$243$		0			0
$244$	−17.1585			−1.09846
$245$	−1.16673	−	6.61686i	−0.0745397	−	0.422736i
$246$		0			0
$247$	6.59440	−	2.40017i	0.419592	−	0.152719i
$248$	17.9731	+	15.0812i	1.14129	+	0.957659i
$249$		0			0
$250$	−0.703695	−	0.256124i	−0.0445056	−	0.0161987i
$251$	−7.99942	−	13.8554i	−0.504919	−	0.874545i	−0.999984	−	0.00568921i	$-0.998189\pi$
$251$	−7.99942	−	13.8554i	−0.504919	−	0.874545i	0.495065	−	0.868856i	$-0.335144\pi$
$252$		0			0
$253$	−0.386670	+	0.669732i	−0.0243097	+	0.0421057i
$254$	−10.9805	+	9.21372i	−0.688977	+	0.578120i
$255$		0			0
$256$	−2.14701	+	12.1763i	−0.134188	+	0.761018i
$257$	2.82207	−	16.0048i	0.176036	−	0.998350i	−0.760905	−	0.648863i	$-0.775245\pi$
$257$	2.82207	−	16.0048i	0.176036	−	0.998350i	0.936941	−	0.349487i	$-0.113644\pi$
$258$		0			0
$259$	−4.33211	+	3.63507i	−0.269184	+	0.225872i
$260$	1.30574	−	2.26161i	0.0809785	−	0.140259i
$261$		0			0
$262$	−3.76056	−	6.51349i	−0.232328	−	0.402405i
$263$	8.91004	+	3.24299i	0.549417	+	0.199971i	0.601787	−	0.798656i	$-0.294456\pi$
$263$	8.91004	+	3.24299i	0.549417	+	0.199971i	−0.0523707	+	0.998628i	$0.516678\pi$
$264$		0			0
$265$	2.32956	+	1.95473i	0.143104	+	0.120078i
$266$	−1.44283	+	0.525145i	−0.0884653	+	0.0321987i
$267$		0			0
$268$	1.46626	+	8.31556i	0.0895660	+	0.507954i
$269$	7.66734			0.467486			0.233743	−	0.972298i	$-0.424903\pi$
$269$	7.66734			0.467486			0.233743	+	0.972298i	$0.424903\pi$
$270$		0			0
$271$	4.50868			0.273883			0.136941	−	0.990579i	$-0.456273\pi$
$271$	4.50868			0.273883			0.136941	+	0.990579i	$0.456273\pi$
$272$	0.0746193	+	0.423187i	0.00452446	+	0.0256595i
$273$		0			0
$274$	−0.589716	+	0.214639i	−0.0356261	+	0.0129668i
$275$	0.148674	+	0.124752i	0.00896539	+	0.00752286i
$276$		0			0
$277$	21.0211	+	7.65104i	1.26303	+	0.459707i	0.884786	−	0.465998i	$-0.154305\pi$
$277$	21.0211	+	7.65104i	1.26303	+	0.459707i	0.378248	+	0.925704i	$0.376527\pi$
$278$	3.11583	+	5.39678i	0.186875	+	0.323677i
$279$		0			0
$280$	−0.682697	+	1.18247i	−0.0407990	+	0.0706659i
$281$	21.4261	−	17.9786i	1.27817	−	1.07252i	0.284681	−	0.958622i	$-0.408112\pi$
$281$	21.4261	−	17.9786i	1.27817	−	1.07252i	0.993493	−	0.113893i	$-0.0363320\pi$
$282$		0			0
$283$	1.06339	−	6.03078i	0.0632119	−	0.358493i	−0.936752	−	0.349994i	$-0.886184\pi$
$283$	1.06339	−	6.03078i	0.0632119	−	0.358493i	0.999964	−	0.00849869i	$-0.00270525\pi$
$284$	2.27683	−	12.9125i	0.135105	−	0.766218i
$285$		0			0
$286$	0.202020	−	0.169515i	0.0119457	−	0.0100236i
$287$	−1.89337	+	3.27941i	−0.111762	+	0.193578i
$288$		0			0
$289$	8.39765	+	14.5452i	0.493979	+	0.855597i
$290$	6.79480	+	2.47311i	0.399004	+	0.145226i
$291$		0			0
$292$	−6.60023	−	5.53825i	−0.386249	−	0.324101i
$293$	−4.43261	+	1.61334i	−0.258956	+	0.0942523i	−0.468236	−	0.883604i	$-0.655110\pi$
$293$	−4.43261	+	1.61334i	−0.258956	+	0.0942523i	0.209280	+	0.977856i	$0.432888\pi$
$294$		0			0
$295$	−0.461786	−	2.61892i	−0.0268862	−	0.152479i
$296$	−27.4728			−1.59682
$297$		0			0
$298$	−2.17676			−0.126096
$299$	1.25551	+	7.12034i	0.0726079	+	0.411780i
$300$		0			0
$301$	−0.570184	+	0.207530i	−0.0328648	+	0.0119618i
$302$	−6.69795	−	5.62025i	−0.385424	−	0.323409i
$303$		0			0
$304$	3.45168	+	1.25631i	0.197967	+	0.0720542i
$305$	−5.96106	−	10.3249i	−0.341329	−	0.591200i
$306$		0			0
$307$	−3.57293	+	6.18850i	−0.203918	+	0.353196i	−0.949787	−	0.312896i	$-0.898701\pi$
$307$	−3.57293	+	6.18850i	−0.203918	+	0.353196i	0.745870	+	0.666092i	$0.232034\pi$
$308$	0.113439	−	0.0951864i	0.00646377	−	0.00542375i
$309$		0			0
$310$	−1.18462	+	6.71833i	−0.0672821	+	0.381576i
$311$	−2.13051	+	12.0827i	−0.120810	+	0.685147i	0.862899	+	0.505377i	$0.168647\pi$
$311$	−2.13051	+	12.0827i	−0.120810	+	0.685147i	−0.983709	+	0.179770i	$0.942465\pi$
$312$		0			0
$313$	3.81932	−	3.20479i	0.215881	−	0.181146i	−0.528434	−	0.848974i	$-0.677221\pi$
$313$	3.81932	−	3.20479i	0.215881	−	0.181146i	0.744315	+	0.667829i	$0.232776\pi$
$314$	8.42866	−	14.5989i	0.475657	−	0.823862i
$315$		0			0
$316$	−9.00566	−	15.5983i	−0.506608	−	0.877471i
$317$	−28.8548	−	10.5023i	−1.62065	−	0.589868i	−0.637144	−	0.770745i	$-0.719884\pi$
$317$	−28.8548	−	10.5023i	−1.62065	−	0.589868i	−0.983506	+	0.180877i	$0.942106\pi$
$318$		0			0
$319$	−1.43558	−	1.20460i	−0.0803771	−	0.0674444i
$320$	−2.34023	+	0.851772i	−0.130823	+	0.0476155i
$321$		0			0
$322$	−0.274699	−	1.55790i	−0.0153084	−	0.0868183i
$323$	−1.74982			−0.0973628
$324$		0			0
$325$	1.81452			0.100651
$326$	1.25167	+	7.09858i	0.0693237	+	0.393154i
$327$		0			0
$328$	−17.2866	+	6.29180i	−0.954491	+	0.347406i
$329$	−1.64986	−	1.38440i	−0.0909599	−	0.0763244i
$330$		0			0
$331$	8.70541	+	3.16851i	0.478493	+	0.174157i	0.569996	−	0.821648i	$-0.306945\pi$
$331$	8.70541	+	3.16851i	0.478493	+	0.174157i	−0.0915030	+	0.995805i	$0.529167\pi$
$332$	−9.85197	−	17.0641i	−0.540697	−	0.936515i
$333$		0			0
$334$	−5.97947	+	10.3567i	−0.327182	+	0.566696i
$335$	−4.49437	+	3.77123i	−0.245554	+	0.206044i
$336$		0			0
$337$	2.94490	−	16.7013i	0.160419	−	0.909780i	−0.793244	−	0.608904i	$-0.791610\pi$
$337$	2.94490	−	16.7013i	0.160419	−	0.909780i	0.953663	−	0.300877i	$-0.0972792\pi$
$338$	−1.26234	+	7.15911i	−0.0686625	+	0.389404i
$339$		0			0
$340$	−0.498821	+	0.418561i	−0.0270524	+	0.0226996i
$341$	0.884022	−	1.53117i	0.0478725	−	0.0829175i
$342$		0			0
$343$	−3.63656	−	6.29871i	−0.196356	−	0.340098i
$344$	−2.76995	−	1.00818i	−0.149346	−	0.0543574i
$345$		0			0
$346$	−3.28469	−	2.75618i	−0.176586	−	0.148173i
$347$	20.8779	−	7.59893i	1.12078	−	0.407932i	0.285845	−	0.958276i	$-0.407726\pi$
$347$	20.8779	−	7.59893i	1.12078	−	0.407932i	0.834938	+	0.550344i	$0.185503\pi$
$348$		0			0
$349$	3.49006	+	19.7931i	0.186819	+	1.05950i	0.923596	+	0.383367i	$0.125235\pi$
$349$	3.49006	+	19.7931i	0.186819	+	1.05950i	−0.736777	+	0.676135i	$0.763653\pi$
$350$	−0.397008			−0.0212210
$351$		0			0
$352$	1.13774			0.0606416
$353$	−2.28369	−	12.9515i	−0.121549	−	0.689337i	−0.983298	−	0.182003i	$-0.941742\pi$
$353$	−2.28369	−	12.9515i	−0.121549	−	0.689337i	0.861749	−	0.507334i	$-0.169369\pi$
$354$		0			0
$355$	8.56092	−	3.11592i	0.454367	−	0.165376i
$356$	−4.29536	−	3.60423i	−0.227653	−	0.191024i
$357$		0			0
$358$	−8.92593	−	3.24877i	−0.471750	−	0.171703i
$359$	10.1145	+	17.5188i	0.533822	+	0.924608i	0.999219	+	0.0395056i	$0.0125783\pi$
$359$	10.1145	+	17.5188i	0.533822	+	0.924608i	−0.465397	+	0.885102i	$0.654088\pi$
$360$		0			0
$361$	2.02127	−	3.50095i	0.106383	−	0.184260i
$362$	5.23612	−	4.39363i	0.275204	−	0.230924i
$363$		0			0
$364$	0.240412	−	1.36345i	0.0126010	−	0.0714640i
$365$	1.03956	−	5.89564i	0.0544131	−	0.308592i
$366$		0			0
$367$	15.3312	−	12.8644i	0.800285	−	0.671519i	−0.147983	−	0.988990i	$-0.547278\pi$
$367$	15.3312	−	12.8644i	0.800285	−	0.671519i	0.948268	+	0.317471i	$0.102834\pi$
$368$	−1.89223	+	3.27744i	−0.0986393	+	0.170848i
$369$		0			0
$370$	−3.99405	−	6.91790i	−0.207641	−	0.359645i
$371$	1.51498	+	0.551407i	0.0786538	+	0.0286276i
$372$		0			0
$373$	−17.7658	−	14.9073i	−0.919877	−	0.771869i	0.0540952	−	0.998536i	$-0.482773\pi$
$373$	−17.7658	−	14.9073i	−0.919877	−	0.771869i	−0.973972	+	0.226667i	$0.927217\pi$
$374$	−0.0617919	+	0.0224904i	−0.00319518	+	0.00116295i
$375$		0			0
$376$	−1.81686	−	10.3039i	−0.0936974	−	0.531385i
$377$	−17.5208			−0.902366
$378$		0			0
$379$	−16.0635			−0.825125			−0.412562	−	0.910929i	$-0.635366\pi$
$379$	−16.0635			−0.825125			−0.412562	+	0.910929i	$0.635366\pi$
$380$	0.966550	+	5.48158i	0.0495830	+	0.281199i
$381$		0			0
$382$	−17.3970	+	6.33200i	−0.890110	+	0.323974i
$383$	−3.84624	−	3.22738i	−0.196534	−	0.164911i	0.539210	−	0.842171i	$-0.318723\pi$
$383$	−3.84624	−	3.22738i	−0.196534	−	0.164911i	−0.735744	+	0.677260i	$0.763167\pi$
$384$		0			0
$385$	0.0966869	+	0.0351912i	0.00492762	+	0.00179351i
$386$	−1.80378	−	3.12425i	−0.0918102	−	0.159020i
$387$		0			0
$388$	−6.08671	+	10.5425i	−0.309006	+	0.535214i
$389$	23.2082	−	19.4740i	1.17670	−	0.987371i	0.176707	−	0.984263i	$-0.443455\pi$
$389$	23.2082	−	19.4740i	1.17670	−	0.987371i	0.999995	−	0.00310704i	$-0.000989004\pi$
$390$		0			0
$391$	0.313058	−	1.77544i	0.0158320	−	0.0897878i
$392$	3.00489	−	17.0416i	0.151770	−	0.860730i
$393$		0			0
$394$	−9.83360	+	8.25137i	−0.495410	+	0.415698i
$395$	6.25735	−	10.8380i	0.314841	−	0.545321i
$396$		0			0
$397$	−7.31880	−	12.6765i	−0.367320	−	0.636217i	0.621826	−	0.783156i	$-0.286391\pi$
$397$	−7.31880	−	12.6765i	−0.367320	−	0.636217i	−0.989146	+	0.146939i	$0.953058\pi$
$398$	13.4317	+	4.88875i	0.673272	+	0.245051i
$399$		0			0
$400$	0.727561	+	0.610496i	0.0363780	+	0.0305248i
$401$	−10.4806	+	3.81464i	−0.523378	+	0.190494i	−0.590179	−	0.807272i	$-0.700943\pi$
$401$	−10.4806	+	3.81464i	−0.523378	+	0.190494i	0.0668011	+	0.997766i	$0.478721\pi$
$402$		0			0
$403$	−2.87040	−	16.2788i	−0.142985	−	0.810907i
$404$	7.22526			0.359470
$405$		0			0
$406$	3.83346			0.190252
$407$	0.359498	+	2.03882i	0.0178197	+	0.101060i
$408$		0			0
$409$	−16.7073	+	6.08096i	−0.826123	+	0.300684i	−0.720267	−	0.693697i	$-0.755981\pi$
$409$	−16.7073	+	6.08096i	−0.826123	+	0.300684i	−0.105856	+	0.994381i	$0.533758\pi$
$410$	−4.09749	−	3.43820i	−0.202361	−	0.169801i
$411$		0			0
$412$	−15.3137	−	5.57372i	−0.754451	−	0.274598i
$413$	−0.704922	−	1.22096i	−0.0346870	−	0.0600796i
$414$		0			0
$415$	6.84538	−	11.8565i	0.336027	−	0.582015i
$416$	8.14845	−	6.83736i	0.399511	−	0.335229i
$417$		0			0
$418$	−0.0976066	+	0.553555i	−0.00477410	+	0.0270753i
$419$	−1.90918	+	10.8275i	−0.0932697	+	0.528959i	0.901994	+	0.431748i	$0.142103\pi$
$419$	−1.90918	+	10.8275i	−0.0932697	+	0.528959i	−0.995264	+	0.0972104i	$0.969008\pi$
$420$		0			0
$421$	−28.0171	+	23.5092i	−1.36547	+	1.14577i	−0.391221	+	0.920297i	$0.627947\pi$
$421$	−28.0171	+	23.5092i	−1.36547	+	1.14577i	−0.974250	+	0.225469i	$0.927608\pi$
$422$	−2.93350	+	5.08096i	−0.142800	+	0.247337i
$423$		0			0
$424$	3.91605	+	6.78280i	0.190180	+	0.329402i
$425$	−0.425159	−	0.154745i	−0.0206232	−	0.00750624i
$426$		0			0
$427$	−4.84181	−	4.06276i	−0.234312	−	0.196611i
$428$	13.7893	−	5.01891i	0.666533	−	0.242598i
$429$		0			0
$430$	−0.148832	−	0.844070i	−0.00717734	−	0.0407047i
$431$	25.0324			1.20577			0.602883	−	0.797829i	$-0.294018\pi$
$431$	25.0324			1.20577			0.602883	+	0.797829i	$0.294018\pi$
$432$		0			0
$433$	8.75430			0.420705			0.210352	−	0.977626i	$-0.432539\pi$
$433$	8.75430			0.420705			0.210352	+	0.977626i	$0.432539\pi$
$434$	0.628030	+	3.56174i	0.0301464	+	0.170969i
$435$		0			0
$436$	1.60320	−	0.583516i	0.0767793	−	0.0279454i
$437$	−11.8051	−	9.90569i	−0.564717	−	0.473854i
$438$		0			0
$439$	−9.76542	−	3.55432i	−0.466078	−	0.169638i	0.0982969	−	0.995157i	$-0.468661\pi$
$439$	−9.76542	−	3.55432i	−0.466078	−	0.169638i	−0.564375	+	0.825519i	$0.690883\pi$
$440$	0.249925	+	0.432883i	0.0119147	+	0.0206369i
$441$		0			0
$442$	−0.307394	+	0.532422i	−0.0146212	+	0.0253247i
$443$	−30.3175	+	25.4394i	−1.44043	+	1.20866i	−0.501217	+	0.865322i	$0.667114\pi$
$443$	−30.3175	+	25.4394i	−1.44043	+	1.20866i	−0.939211	+	0.343340i	$0.888442\pi$
$444$		0			0
$445$	0.676535	−	3.83682i	0.0320708	−	0.181883i
$446$	−1.88542	+	10.6928i	−0.0892773	+	0.506317i
$447$		0			0
$448$	−1.01141	+	0.848672i	−0.0477845	+	0.0400960i
$449$	−9.88388	+	17.1194i	−0.466449	+	0.807914i	−0.999266	−	0.0383171i	$-0.987800\pi$
$449$	−9.88388	+	17.1194i	−0.466449	+	0.807914i	0.532816	+	0.846231i	$0.321134\pi$
$450$		0			0
$451$	0.693133	+	1.20054i	0.0326384	+	0.0565313i
$452$	−25.4852	−	9.27585i	−1.19872	−	0.436299i
$453$		0			0
$454$	−0.257879	−	0.216386i	−0.0121029	−	0.0101555i
$455$	0.903956	−	0.329013i	0.0423781	−	0.0154244i
$456$		0			0
$457$	−1.84752	−	10.4778i	−0.0864232	−	0.490131i	−0.997040	−	0.0768795i	$-0.975504\pi$
$457$	−1.84752	−	10.4778i	−0.0864232	−	0.490131i	0.910617	−	0.413251i	$-0.135607\pi$
$458$	−10.3991			−0.485919
$459$		0			0
$460$	−5.73474			−0.267384
$461$	4.81686	+	27.3178i	0.224343	+	1.27231i	0.863936	+	0.503601i	$0.167992\pi$
$461$	4.81686	+	27.3178i	0.224343	+	1.27231i	−0.639593	+	0.768714i	$0.720897\pi$
$462$		0			0
$463$	23.3502	−	8.49879i	1.08518	−	0.394972i	0.263345	−	0.964702i	$-0.415174\pi$
$463$	23.3502	−	8.49879i	1.08518	−	0.394972i	0.821832	+	0.569730i	$0.192952\pi$
$464$	−7.02525	−	5.89488i	−0.326139	−	0.273663i
$465$		0			0
$466$	−13.8718	−	5.04892i	−0.642598	−	0.233886i
$467$	4.20002	+	7.27465i	0.194354	+	0.336630i	0.946688	−	0.322151i	$-0.104406\pi$
$467$	4.20002	+	7.27465i	0.194354	+	0.336630i	−0.752335	+	0.658781i	$0.771072\pi$
$468$		0			0
$469$	−1.55520	+	2.69368i	−0.0718123	+	0.124383i
$470$	2.33048	−	1.95551i	0.107497	−	0.0902009i
$471$		0			0
$472$	1.18932	−	6.74497i	0.0547429	−	0.310463i
$473$	−0.0385727	+	0.218757i	−0.00177358	+	0.0100585i
$474$		0			0
$475$	−2.96267	+	2.48597i	−0.135936	+	0.114064i
$476$	−0.172608	+	0.298966i	−0.00791148	+	0.0137031i
$477$		0			0
$478$	7.45485	+	12.9122i	0.340977	+	0.590589i
$479$	−1.81040	−	0.658932i	−0.0827193	−	0.0301074i	0.300329	−	0.953836i	$-0.402904\pi$
$479$	−1.81040	−	0.658932i	−0.0827193	−	0.0301074i	−0.383048	+	0.923728i	$0.625126\pi$
$480$		0			0
$481$	14.8272	+	12.4415i	0.676064	+	0.567285i
$482$	−5.27450	+	1.91976i	−0.240247	+	0.0874427i
$483$		0			0
$484$	2.73967	+	15.5374i	0.124531	+	0.706248i
$485$	−8.45838			−0.384075
$486$		0			0
$487$	6.91110			0.313172			0.156586	−	0.987664i	$-0.449951\pi$
$487$	6.91110			0.313172			0.156586	+	0.987664i	$0.449951\pi$
$488$	−5.33189	−	30.2387i	−0.241364	−	1.36884i
$489$		0			0
$490$	4.72808	−	1.72088i	0.213593	−	0.0777415i
$491$	9.83941	+	8.25624i	0.444046	+	0.372599i	0.837221	−	0.546865i	$-0.184179\pi$
$491$	9.83941	+	8.25624i	0.444046	+	0.372599i	−0.393175	+	0.919464i	$0.628623\pi$
$492$		0			0
$493$	4.10529	+	1.49420i	0.184893	+	0.0672955i
$494$	2.62760	+	4.55113i	0.118221	+	0.204765i
$495$		0			0
$496$	4.32610	−	7.49303i	0.194248	−	0.336447i
$497$	3.69989	−	3.10458i	0.165963	−	0.139259i
$498$		0			0
$499$	0.867688	−	4.92090i	0.0388431	−	0.220290i	−0.959207	−	0.282704i	$-0.908769\pi$
$499$	0.867688	−	4.92090i	0.0388431	−	0.220290i	0.998050	+	0.0624137i	$0.0198798\pi$
$500$	−0.249917	+	1.41735i	−0.0111766	+	0.0633858i
$501$		0			0
$502$	9.17785	−	7.70113i	0.409628	−	0.343718i
$503$	11.2981	−	19.5689i	0.503757	−	0.872532i	−0.496234	−	0.868189i	$-0.665284\pi$
$503$	11.2981	−	19.5689i	0.503757	−	0.872532i	0.999991	−	0.00434323i	$-0.00138250\pi$
$504$		0			0
$505$	2.51014	+	4.34769i	0.111700	+	0.193470i
$506$	−0.544195	−	0.198071i	−0.0241924	−	0.00880532i
$507$		0			0
$508$	21.1032	+	17.7077i	0.936303	+	0.785651i
$509$	−9.21782	+	3.35501i	−0.408573	+	0.148708i	−0.538127	−	0.842864i	$-0.680868\pi$
$509$	−9.21782	+	3.35501i	−0.408573	+	0.148708i	0.129554	+	0.991572i	$0.458646\pi$
$510$		0			0
$511$	−0.551125	−	3.12559i	−0.0243803	−	0.138268i
$512$	10.4599			0.462266
$513$		0			0
$514$	12.1702			0.536803
$515$	−1.96625	−	11.1512i	−0.0866433	−	0.491378i
$516$		0			0
$517$	−0.740902	+	0.269666i	−0.0325849	+	0.0118599i
$518$	−3.24413	−	2.72215i	−0.142539	−	0.119604i
$519$		0			0
$520$	4.39142	+	1.59834i	0.192576	+	0.0700921i
$521$	8.46385	+	14.6598i	0.370808	+	0.642258i	0.989690	−	0.143226i	$-0.0457474\pi$
$521$	8.46385	+	14.6598i	0.370808	+	0.642258i	−0.618882	+	0.785484i	$0.712414\pi$
$522$		0			0
$523$	−18.8074	+	32.5754i	−0.822390	+	1.42442i	0.0815076	+	0.996673i	$0.474027\pi$
$523$	−18.8074	+	32.5754i	−0.822390	+	1.42442i	−0.903898	+	0.427749i	$0.859307\pi$
$524$	−11.0730	+	9.29131i	−0.483724	+	0.405893i
$525$		0			0
$526$	−1.23300	+	6.99268i	−0.0537613	+	0.304896i
$527$	−0.715726	+	4.05909i	−0.0311775	+	0.176817i
$528$		0			0
$529$	−5.45629	+	4.57837i	−0.237230	+	0.199060i
$530$	−1.13865	+	1.97219i	−0.0494597	+	0.0856666i
$531$		0			0
$532$	1.47545	+	2.55555i	0.0639689	+	0.110797i
$533$	12.1790	+	4.43280i	0.527531	+	0.192006i
$534$		0			0
$535$	7.81063	+	6.55390i	0.337683	+	0.283350i
$536$	−14.1990	+	5.16802i	−0.613305	+	0.223225i
$537$		0			0
$538$	0.997042	+	5.65451i	0.0429855	+	0.243783i
$539$	−1.30401			−0.0561679
$540$		0			0
$541$	17.1610			0.737810			0.368905	−	0.929467i	$-0.379733\pi$
$541$	17.1610			0.737810			0.368905	+	0.929467i	$0.379733\pi$
$542$	0.586298	+	3.32506i	0.0251837	+	0.142824i
$543$		0			0
$544$	−2.49236	+	0.907146i	−0.106859	+	0.0388936i
$545$	0.908093	+	0.761980i	0.0388984	+	0.0326396i
$546$		0			0
$547$	−12.1470	−	4.42115i	−0.519368	−	0.189035i	0.0690169	−	0.997615i	$-0.478014\pi$
$547$	−12.1470	−	4.42115i	−0.519368	−	0.189035i	−0.588385	+	0.808581i	$0.700236\pi$
$548$	0.603051	+	1.04451i	0.0257611	+	0.0446195i
$549$		0			0
$550$	−0.0726692	+	0.125867i	−0.00309862	+	0.00536698i
$551$	28.6072	−	24.0043i	1.21871	−	1.02262i
$552$		0			0
$553$	1.15210	−	6.53389i	0.0489924	−	0.277849i
$554$	−2.90896	+	16.4975i	−0.123590	+	0.700913i
$555$		0			0
$556$	9.17454	−	7.69836i	0.389087	−	0.326483i
$557$	6.44842	−	11.1690i	0.273229	−	0.473246i	−0.696458	−	0.717597i	$-0.745242\pi$
$557$	6.44842	−	11.1690i	0.273229	−	0.473246i	0.969687	+	0.244352i	$0.0785751\pi$
$558$		0			0
$559$	1.03839	+	1.79854i	0.0439191	+	0.0760701i
$560$	0.473153	+	0.172214i	0.0199944	+	0.00727735i
$561$		0			0
$562$	16.0451	+	13.4634i	0.676821	+	0.567920i
$563$	2.66099	−	0.968522i	0.112147	−	0.0408183i	−0.285337	−	0.958427i	$-0.592106\pi$
$563$	2.66099	−	0.968522i	0.112147	−	0.0408183i	0.397484	+	0.917609i	$0.369883\pi$
$564$		0			0
$565$	−3.27225	−	18.5579i	−0.137665	−	0.780736i
$566$	4.58586			0.192758
$567$		0			0
$568$	23.4635			0.984506
$569$	0.717987	+	4.07191i	0.0300996	+	0.170703i	0.996152	−	0.0876432i	$-0.0279335\pi$
$569$	0.717987	+	4.07191i	0.0300996	+	0.170703i	−0.966052	+	0.258346i	$0.916822\pi$
$570$		0			0
$571$	−5.29347	+	1.92667i	−0.221525	+	0.0806285i	−0.450398	−	0.892828i	$-0.648718\pi$
$571$	−5.29347	+	1.92667i	−0.221525	+	0.0806285i	0.228873	+	0.973456i	$0.426496\pi$
$572$	−0.388259	−	0.325788i	−0.0162339	−	0.0136219i
$573$		0			0
$574$	−2.66471	−	0.969875i	−0.111223	−	0.0404818i
$575$	−1.99232	−	3.45080i	−0.0830854	−	0.143908i
$576$		0			0
$577$	3.00546	−	5.20561i	0.125119	−	0.216712i	−0.796661	−	0.604427i	$-0.793402\pi$
$577$	3.00546	−	5.20561i	0.125119	−	0.216712i	0.921779	+	0.387715i	$0.126735\pi$
$578$	−9.63475	+	8.08451i	−0.400753	+	0.336271i
$579$		0			0
$580$	2.41317	−	13.6858i	0.100201	−	0.568270i
$581$	1.26037	−	7.14792i	0.0522890	−	0.296546i
$582$		0			0
$583$	0.452122	−	0.379376i	0.0187250	−	0.0157121i
$584$	7.70917	−	13.3527i	0.319008	−	0.552537i
$585$		0			0
$586$	−1.76621	−	3.05917i	−0.0729615	−	0.126373i
$587$	−12.7934	−	4.65641i	−0.528039	−	0.192190i	0.0642236	−	0.997936i	$-0.479543\pi$
$587$	−12.7934	−	4.65641i	−0.528039	−	0.192190i	−0.592262	+	0.805745i	$0.701765\pi$
$588$		0			0
$589$	26.9895	+	22.6468i	1.11208	+	0.933147i
$590$	1.87135	−	0.681116i	0.0770423	−	0.0280411i
$591$		0			0
$592$	1.75926	+	9.97728i	0.0723053	+	0.410064i
$593$	38.9303			1.59868			0.799338	−	0.600882i	$-0.205184\pi$
$593$	38.9303			1.59868			0.799338	+	0.600882i	$0.205184\pi$
$594$		0			0
$595$	−0.239864			−0.00983348
$596$	0.726453	+	4.11992i	0.0297567	+	0.168758i
$597$		0			0
$598$	−5.08785	+	1.85182i	−0.208058	+	0.0757267i
$599$	27.2995	+	22.9070i	1.11543	+	0.935954i	0.998364	−	0.0571711i	$-0.0182081\pi$
$599$	27.2995	+	22.9070i	1.11543	+	0.935954i	0.117062	+	0.993125i	$0.462653\pi$
$600$		0			0
$601$	35.5884	+	12.9531i	1.45168	+	0.528369i	0.943060	−	0.332622i	$-0.107933\pi$
$601$	35.5884	+	12.9531i	1.45168	+	0.528369i	0.508621	+	0.860991i	$0.330156\pi$
$602$	−0.227194	−	0.393512i	−0.00925975	−	0.0160384i
$603$		0			0
$604$	−8.40203	+	14.5528i	−0.341874	+	0.592143i
$605$	−8.39763	+	7.04645i	−0.341412	+	0.286479i
$606$		0			0
$607$	3.11194	−	17.6487i	0.126310	−	0.716338i	−0.854212	−	0.519925i	$-0.825960\pi$
$607$	3.11194	−	17.6487i	0.126310	−	0.716338i	0.980521	−	0.196412i	$-0.0629291\pi$
$608$	−3.93694	+	22.3275i	−0.159664	+	0.905500i
$609$		0			0
$610$	6.83921	−	5.73878i	0.276912	−	0.232356i
$611$	−3.68574	+	6.38389i	−0.149109	+	0.258264i
$612$		0			0
$613$	−6.89087	−	11.9353i	−0.278320	−	0.482064i	0.692648	−	0.721276i	$-0.256444\pi$
$613$	−6.89087	−	11.9353i	−0.278320	−	0.482064i	−0.970967	+	0.239212i	$0.923111\pi$
$614$	−5.02851	−	1.83023i	−0.202934	−	0.0738620i
$615$		0			0
$616$	0.202999	+	0.170336i	0.00817906	+	0.00686305i
$617$	−36.2761	+	13.2034i	−1.46042	+	0.531550i	−0.945481	−	0.325677i	$-0.894408\pi$
$617$	−36.2761	+	13.2034i	−1.46042	+	0.531550i	−0.514940	+	0.857226i	$0.672186\pi$
$618$		0			0
$619$	−6.89620	−	39.1103i	−0.277182	−	1.57198i	−0.731945	−	0.681364i	$-0.761387\pi$
$619$	−6.89620	−	39.1103i	−0.277182	−	1.57198i	0.454763	−	0.890612i	$-0.349724\pi$
$620$	13.1110			0.526551
$621$		0			0
$622$	−9.18780			−0.368397
$623$	−0.358666	−	2.03410i	−0.0143697	−	0.0814944i
$624$		0			0
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	2.86012	+	2.39993i	0.114314	+	0.0959205i
$627$		0			0
$628$	−30.4439	−	11.0807i	−1.21485	−	0.442168i
$629$	−2.41313	−	4.17966i	−0.0962178	−	0.166654i
$630$		0			0
$631$	−9.71146	+	16.8207i	−0.386607	+	0.669623i	−0.991991	−	0.126311i	$-0.959686\pi$
$631$	−9.71146	+	16.8207i	−0.386607	+	0.669623i	0.605384	+	0.795934i	$0.293020\pi$
$632$	24.6906	−	20.7179i	0.982141	−	0.824114i
$633$		0			0
$634$	3.99302	−	22.6456i	0.158583	−	0.899370i
$635$	−3.32383	+	18.8504i	−0.131902	+	0.748055i
$636$		0			0
$637$	−9.33933	+	7.83663i	−0.370038	+	0.310498i
$638$	0.701686	−	1.21536i	0.0277800	−	0.0481164i
$639$		0			0
$640$	4.92971	+	8.53851i	0.194864	+	0.337514i
$641$	−32.2397	−	11.7343i	−1.27339	−	0.463476i	−0.385149	−	0.922854i	$-0.625850\pi$
$641$	−32.2397	−	11.7343i	−1.27339	−	0.463476i	−0.888241	+	0.459378i	$0.848072\pi$
$642$		0			0
$643$	24.8918	+	20.8867i	0.981637	+	0.823691i	0.984336	−	0.176305i	$-0.0564146\pi$
$643$	24.8918	+	20.8867i	0.981637	+	0.823691i	−0.00269885	+	0.999996i	$0.500859\pi$
$644$	−2.85693	+	1.03984i	−0.112579	+	0.0409754i
$645$		0			0
$646$	−0.227543	−	1.29046i	−0.00895256	−	0.0507725i
$647$	19.6313			0.771787			0.385894	−	0.922543i	$-0.373893\pi$
$647$	19.6313			0.771787			0.385894	+	0.922543i	$0.373893\pi$
$648$		0			0
$649$	−0.516122			−0.0202596
$650$	0.235955	+	1.33817i	0.00925493	+	0.0524873i
$651$		0			0
$652$	13.0176	−	4.73804i	0.509810	−	0.185556i
$653$	9.18189	+	7.70452i	0.359315	+	0.301501i	0.804518	−	0.593929i	$-0.202424\pi$
$653$	9.18189	+	7.70452i	0.359315	+	0.301501i	−0.445202	+	0.895430i	$0.646868\pi$
$654$		0			0
$655$	−9.43779	−	3.43507i	−0.368765	−	0.134219i
$656$	3.39196	+	5.87505i	0.132434	+	0.229382i
$657$		0			0
$658$	0.806422	−	1.39676i	0.0314376	−	0.0544516i
$659$	−14.3096	+	12.0072i	−0.557423	+	0.467733i	−0.877445	−	0.479677i	$-0.840754\pi$
$659$	−14.3096	+	12.0072i	−0.557423	+	0.467733i	0.320022	+	0.947410i	$0.396310\pi$
$660$		0			0
$661$	3.73208	−	21.1657i	0.145161	−	0.823250i	−0.822077	−	0.569377i	$-0.807184\pi$
$661$	3.73208	−	21.1657i	0.145161	−	0.823250i	0.967238	−	0.253873i	$-0.0817044\pi$
$662$	−1.20468	+	6.83209i	−0.0468213	+	0.265537i
$663$		0			0
$664$	27.0109	−	22.6649i	1.04823	−	0.879567i
$665$	−1.02518	+	1.77566i	−0.0397547	+	0.0688571i
$666$		0			0
$667$	19.2376	+	33.3205i	0.744883	+	1.29017i
$668$	21.5976	+	7.86088i	0.835636	+	0.304147i
$669$		0			0
$670$	−3.36564	−	2.82411i	−0.130026	−	0.109105i
$671$	−2.17431	+	0.791383i	−0.0839382	+	0.0305510i
$672$		0			0
$673$	−1.40383	−	7.96152i	−0.0541137	−	0.306894i	0.945723	−	0.324974i	$-0.105356\pi$
$673$	−1.40383	−	7.96152i	−0.0541137	−	0.306894i	−0.999837	+	0.0180803i	$0.994245\pi$
$674$	12.6999			0.489180
$675$		0			0
$676$	13.9712			0.537354
$677$	−1.86299	−	10.5656i	−0.0716006	−	0.406067i	−0.999452	−	0.0331158i	$-0.989457\pi$
$677$	−1.86299	−	10.5656i	−0.0716006	−	0.406067i	0.927851	−	0.372951i	$-0.121654\pi$
$678$		0			0
$679$	−4.21380	+	1.53370i	−0.161711	+	0.0588579i
$680$	−0.892642	−	0.749016i	−0.0342313	−	0.0287234i
$681$		0			0
$682$	1.24416	+	0.452838i	0.0476415	+	0.0173401i
$683$	−7.36365	−	12.7542i	−0.281762	−	0.488027i	0.690057	−	0.723755i	$-0.257586\pi$
$683$	−7.36365	−	12.7542i	−0.281762	−	0.488027i	−0.971819	+	0.235729i	$0.924252\pi$
$684$		0			0
$685$	−0.419014	+	0.725754i	−0.0160097	+	0.0277296i
$686$	4.17228	−	3.50096i	0.159298	−	0.133667i
$687$		0			0
$688$	−0.188762	+	1.07052i	−0.00719648	+	0.0408132i
$689$	0.958190	−	5.43416i	0.0365041	−	0.207025i
$690$		0			0
$691$	−5.28360	+	4.43347i	−0.200998	+	0.168657i	−0.737731	−	0.675095i	$-0.764103\pi$
$691$	−5.28360	+	4.43347i	−0.200998	+	0.168657i	0.536733	+	0.843752i	$0.319658\pi$
$692$	−4.12038	+	7.13671i	−0.156633	+	0.271297i
$693$		0			0
$694$	8.31897	+	14.4089i	0.315784	+	0.546953i
$695$	7.81972	+	2.84614i	0.296619	+	0.107960i
$696$		0			0
$697$	−2.47562	−	2.07730i	−0.0937710	−	0.0786832i
$698$	−14.1432	+	5.14770i	−0.535328	+	0.194843i
$699$		0			0
$700$	0.132494	+	0.751410i	0.00500780	+	0.0284006i
$701$	21.5524			0.814024			0.407012	−	0.913423i	$-0.366571\pi$
$701$	21.5524			0.814024			0.407012	+	0.913423i	$0.366571\pi$
$702$		0			0
$703$	−41.2548			−1.55595
$704$	0.0839313	+	0.475998i	0.00316328	+	0.0179398i
$705$		0			0
$706$	9.25448	−	3.36835i	0.348297	−	0.126770i
$707$	2.03884	+	1.71079i	0.0766783	+	0.0643407i
$708$		0			0
$709$	−8.74711	−	3.18369i	−0.328505	−	0.119566i	0.172502	−	0.985009i	$-0.444815\pi$
$709$	−8.74711	−	3.18369i	−0.328505	−	0.119566i	−0.501007	+	0.865443i	$0.667037\pi$
$710$	3.41117	+	5.90832i	0.128019	+	0.221735i
$711$		0			0
$712$	5.01704	−	8.68977i	0.188022	−	0.325663i
$713$	−27.8070	+	23.3328i	−1.04138	+	0.873821i
$714$		0			0
$715$	0.0611523	−	0.346812i	0.00228697	−	0.0129700i
$716$	−3.17004	+	17.9782i	−0.118470	+	0.671876i
$717$		0			0
$718$	−11.6045	+	9.73734i	−0.433076	+	0.363394i
$719$	−8.27715	+	14.3364i	−0.308686	+	0.534659i	−0.978075	−	0.208252i	$-0.933222\pi$
$719$	−8.27715	+	14.3364i	−0.308686	+	0.534659i	0.669389	+	0.742912i	$0.266556\pi$
$720$		0			0
$721$	−3.00150	−	5.19875i	−0.111782	−	0.193612i
$722$	2.84472	+	1.03539i	0.105870	+	0.0385334i
$723$		0			0
$724$	−10.0632	−	8.44403i	−0.373996	−	0.313820i
$725$	9.07357	−	3.30251i	0.336984	−	0.122652i
$726$		0			0
$727$	0.00349359	+	0.0198131i	0.000129570	+	0.000734829i	0.984872	−	0.173281i	$-0.0554368\pi$
$727$	0.00349359	+	0.0198131i	0.000129570	+	0.000734829i	−0.984743	+	0.174016i	$0.944326\pi$
$728$	2.47753			0.0918234
$729$		0			0
$730$	4.48310			0.165927
$731$	−0.0899217	−	0.509971i	−0.00332587	−	0.0188620i
$732$		0			0
$733$	−6.82912	+	2.48559i	−0.252239	+	0.0918075i	−0.465045	−	0.885287i	$-0.653962\pi$
$733$	−6.82912	+	2.48559i	−0.252239	+	0.0918075i	0.212806	+	0.977094i	$0.431740\pi$
$734$	11.4809	+	9.63363i	0.423768	+	0.355584i
$735$		0			0
$736$	−21.9500	−	7.98915i	−0.809088	−	0.294484i
$737$	0.569333	+	0.986114i	0.0209717	+	0.0363240i
$738$		0			0
$739$	12.5613	−	21.7568i	0.462074	−	0.800336i	−0.536990	−	0.843589i	$-0.680439\pi$
$739$	12.5613	−	21.7568i	0.462074	−	0.800336i	0.999064	+	0.0432525i	$0.0137720\pi$
$740$	−11.7605	+	9.86820i	−0.432323	+	0.362762i
$741$		0			0
$742$	−0.209647	+	1.18897i	−0.00769640	+	0.0436485i
$743$	5.15289	−	29.2235i	0.189041	−	1.07211i	−0.731611	−	0.681722i	$-0.761231\pi$
$743$	5.15289	−	29.2235i	0.189041	−	1.07211i	0.920652	−	0.390383i	$-0.127658\pi$
$744$		0			0
$745$	−2.22672	+	1.86844i	−0.0815808	+	0.0684544i
$746$	8.68358	−	15.0404i	0.317929	−	0.550668i
$747$		0			0
$748$	0.0631891	+	0.109447i	0.00231042	+	0.00400177i
$749$	5.07947	+	1.84878i	0.185600	+	0.0675528i
$750$		0			0
$751$	22.2113	+	18.6375i	0.810502	+	0.680092i	0.950728	−	0.310028i	$-0.100338\pi$
$751$	22.2113	+	18.6375i	0.810502	+	0.680092i	−0.140226	+	0.990120i	$0.544783\pi$
$752$	−3.62572	+	1.31966i	−0.132217	+	0.0481229i
$753$		0			0
$754$	−2.27836	−	12.9212i	−0.0829729	−	0.470563i
$755$	−11.6759			−0.424928
$756$		0			0
$757$	−0.0752608			−0.00273540			−0.00136770	−	0.999999i	$-0.500435\pi$
$757$	−0.0752608			−0.00273540			−0.00136770	+	0.999999i	$0.500435\pi$
$758$	−2.08885	−	11.8465i	−0.0758706	−	0.430284i
$759$		0			0
$760$	−9.35993	+	3.40674i	−0.339520	+	0.123575i
$761$	−35.5809	−	29.8559i	−1.28981	−	1.08228i	−0.991812	−	0.127709i	$-0.959238\pi$
$761$	−35.5809	−	29.8559i	−1.28981	−	1.08228i	−0.297996	−	0.954567i	$-0.596318\pi$
$762$		0			0
$763$	0.590558	+	0.214945i	0.0213796	+	0.00778155i
$764$	17.7904	+	30.8139i	0.643635	+	1.11481i
$765$		0			0
$766$	1.87997	−	3.25621i	0.0679261	−	0.117652i
$767$	−3.69646	+	3.10170i	−0.133471	+	0.111996i
$768$		0			0
$769$	−5.06818	+	28.7431i	−0.182763	+	1.03650i	0.746032	+	0.665910i	$0.231957\pi$
$769$	−5.06818	+	28.7431i	−0.182763	+	1.03650i	−0.928795	+	0.370593i	$0.879155\pi$
$770$	−0.0133798	+	0.0758808i	−0.000482176	+	0.00273456i
$771$		0			0
$772$	−5.31123	+	4.45665i	−0.191155	+	0.160398i
$773$	5.94544	−	10.2978i	0.213843	−	0.370387i	−0.739071	−	0.673627i	$-0.764735\pi$
$773$	5.94544	−	10.2978i	0.213843	−	0.370387i	0.952914	+	0.303241i	$0.0980687\pi$
$774$		0			0
$775$	4.55493	+	7.88936i	0.163618	+	0.283394i
$776$	−20.4706	−	7.45070i	−0.734853	−	0.267464i
$777$		0			0
$778$	17.3796	+	14.5832i	0.623089	+	0.522834i
$779$	−25.9585	+	9.44813i	−0.930060	+	0.338514i
$780$		0			0
$781$	−0.307034	−	1.74128i	−0.0109865	−	0.0623078i
$782$	1.35006			0.0482780
$783$		0			0
$784$	−6.38140			−0.227907
$785$	−3.90895	−	22.1688i	−0.139516	−	0.791237i
$786$		0			0
$787$	−12.7571	+	4.64320i	−0.454741	+	0.165512i	−0.559228	−	0.829014i	$-0.688902\pi$
$787$	−12.7571	+	4.64320i	−0.454741	+	0.165512i	0.104486	+	0.994526i	$0.466680\pi$
$788$	18.8990	+	15.8582i	0.673249	+	0.564923i
$789$		0			0
$790$	8.80653	+	3.20532i	0.313322	+	0.114040i
$791$	−4.99513	−	8.65183i	−0.177607	−	0.307623i
$792$		0			0
$793$	−10.8164	+	18.7346i	−0.384103	+	0.665286i
$794$	8.39697	−	7.04589i	0.297997	−	0.250049i
$795$		0			0
$796$	4.77027	−	27.0536i	0.169078	−	0.958888i
$797$	−5.91972	+	33.5724i	−0.209687	+	1.18919i	0.680204	+	0.733022i	$0.261891\pi$
$797$	−5.91972	+	33.5724i	−0.209687	+	1.18919i	−0.889892	+	0.456172i	$0.849220\pi$
$798$		0			0
$799$	1.40803	−	1.18148i	0.0498126	−	0.0417978i
$800$	−2.93110	+	5.07681i	−0.103630	+	0.179492i
$801$		0			0
$802$	−4.17610	−	7.23321i	−0.147463	−	0.255414i
$803$	−1.09181	−	0.397386i	−0.0385291	−	0.0140235i
$804$		0			0
$805$	−1.61824	−	1.35786i	−0.0570355	−	0.0478584i
$806$	11.6321	−	4.23372i	0.409722	−	0.149127i
$807$		0			0
$808$	2.24521	+	12.7332i	0.0789860	+	0.447952i
$809$	−33.2161			−1.16781			−0.583907	−	0.811821i	$-0.698477\pi$
$809$	−33.2161			−1.16781			−0.583907	+	0.811821i	$0.698477\pi$
$810$		0			0
$811$	−45.6200			−1.60194			−0.800968	−	0.598708i	$-0.795681\pi$
$811$	−45.6200			−1.60194			−0.800968	+	0.598708i	$0.795681\pi$
$812$	−1.27935	−	7.25553i	−0.0448962	−	0.254619i
$813$		0			0
$814$	−1.45684	+	0.530246i	−0.0510622	+	0.0185851i
$815$	7.37353	+	6.18712i	0.258283	+	0.216725i
$816$		0			0
$817$	−4.15952	−	1.51394i	−0.145523	−	0.0529661i
$818$	−6.65717	−	11.5305i	−0.232762	−	0.403156i
$819$		0			0
$820$	−5.13997	+	8.90269i	−0.179496	+	0.310895i
$821$	−1.74217	+	1.46185i	−0.0608021	+	0.0510190i	−0.672682	−	0.739931i	$-0.734858\pi$
$821$	−1.74217	+	1.46185i	−0.0608021	+	0.0510190i	0.611880	+	0.790950i	$0.290413\pi$
$822$		0			0
$823$	6.20317	−	35.1799i	0.216229	−	1.22629i	−0.662533	−	0.749033i	$-0.730518\pi$
$823$	6.20317	−	35.1799i	0.216229	−	1.22629i	0.878761	−	0.477261i	$-0.158371\pi$
$824$	5.06403	−	28.7195i	0.176414	−	1.00049i
$825$		0			0
$826$	0.808768	−	0.678637i	0.0281406	−	0.0236128i
$827$	6.66996	−	11.5527i	0.231937	−	0.401727i	−0.726441	−	0.687229i	$-0.758827\pi$
$827$	6.66996	−	11.5527i	0.231937	−	0.401727i	0.958378	+	0.285502i	$0.0921602\pi$
$828$		0			0
$829$	−5.82120	−	10.0826i	−0.202179	−	0.350184i	0.747051	−	0.664766i	$-0.231469\pi$
$829$	−5.82120	−	10.0826i	−0.202179	−	0.350184i	−0.949230	+	0.314582i	$0.898136\pi$
$830$	9.63412	+	3.50653i	0.334405	+	0.121714i
$831$		0			0
$832$	3.46168	+	2.90469i	0.120012	+	0.100702i
$833$	2.85662	−	1.03972i	0.0989759	−	0.0360243i
$834$		0			0
$835$	2.77309	+	15.7270i	0.0959668	+	0.544255i
$836$	1.08028			0.0373622
$837$		0			0
$838$	−8.23334			−0.284416
$839$	−6.96649	−	39.5089i	−0.240510	−	1.36400i	−0.830694	−	0.556730i	$-0.812056\pi$
$839$	−6.96649	−	39.5089i	−0.240510	−	1.36400i	0.590184	−	0.807269i	$-0.299055\pi$
$840$		0			0
$841$	−60.3623	+	21.9701i	−2.08146	+	0.757589i
$842$	−20.9808	−	17.6050i	−0.723046	−	0.606708i
$843$		0			0
$844$	10.5957	+	3.85650i	0.364718	+	0.132746i
$845$	4.85376	+	8.40697i	0.166975	+	0.289208i
$846$		0			0
$847$	−2.90585	+	5.03308i	−0.0998462	+	0.172939i
$848$	2.21253	−	1.85654i	0.0759787	−	0.0637537i
$849$		0			0
$850$	0.0588348	−	0.333669i	0.00201802	−	0.0114447i
$851$	7.38081	−	41.8586i	0.253011	−	1.43490i
$852$		0			0
$853$	−1.23431	+	1.03571i	−0.0422621	+	0.0354621i	−0.663674	−	0.748022i	$-0.731004\pi$
$853$	−1.23431	+	1.03571i	−0.0422621	+	0.0354621i	0.621412	+	0.783484i	$0.286559\pi$
$854$	2.36659	−	4.09905i	0.0809829	−	0.140267i
$855$		0			0
$856$	13.1299	+	22.7416i	0.448769	+	0.777291i
$857$	23.2290	+	8.45466i	0.793487	+	0.288806i	0.706785	−	0.707429i	$-0.250145\pi$
$857$	23.2290	+	8.45466i	0.793487	+	0.288806i	0.0867023	+	0.996234i	$0.472367\pi$
$858$		0			0
$859$	−2.74608	−	2.30424i	−0.0936951	−	0.0786196i	0.594737	−	0.803920i	$-0.297256\pi$
$859$	−2.74608	−	2.30424i	−0.0936951	−	0.0786196i	−0.688432	+	0.725301i	$0.741701\pi$
$860$	−1.54789	+	0.563385i	−0.0527826	+	0.0192113i
$861$		0			0
$862$	3.25515	+	18.4609i	0.110871	+	0.628779i
$863$	−30.2496			−1.02971			−0.514853	−	0.857278i	$-0.672154\pi$
$863$	−30.2496			−1.02971			−0.514853	+	0.857278i	$0.672154\pi$
$864$		0			0
$865$	−5.72588			−0.194686
$866$	1.13839	+	6.45612i	0.0386840	+	0.219388i
$867$		0			0
$868$	6.53165	−	2.37732i	0.221699	−	0.0806917i
$869$	−1.86061	−	1.56124i	−0.0631170	−	0.0529614i
$870$		0			0
$871$	10.0037	+	3.64106i	0.338963	+	0.123373i
$872$	1.52653	+	2.64402i	0.0516947	+	0.0895378i
$873$		0			0
$874$	5.77014	−	9.99417i	0.195178	−	0.338058i
$875$	−0.406120	+	0.340775i	−0.0137294	+	0.0115203i
$876$		0			0
$877$	1.47134	−	8.34440i	0.0496837	−	0.281771i	−0.949836	−	0.312747i	$-0.898751\pi$
$877$	1.47134	−	8.34440i	0.0496837	−	0.281771i	0.999520	+	0.0309768i	$0.00986180\pi$
$878$	1.35137	−	7.66399i	0.0456065	−	0.258647i
$879$		0			0
$880$	0.141205	−	0.118485i	0.00476003	−	0.00399414i
$881$	−13.2335	+	22.9211i	−0.445848	+	0.772232i	−0.998111	−	0.0614383i	$-0.980431\pi$
$881$	−13.2335	+	22.9211i	−0.445848	+	0.772232i	0.552263	+	0.833670i	$0.313765\pi$
$882$		0			0
$883$	4.54571	+	7.87340i	0.152975	+	0.264961i	0.932320	−	0.361635i	$-0.117781\pi$
$883$	4.54571	+	7.87340i	0.152975	+	0.264961i	−0.779345	+	0.626595i	$0.784448\pi$
$884$	1.11029	+	0.404114i	0.0373432	+	0.0135918i
$885$		0			0
$886$	−22.7035	−	19.0505i	−0.762738	−	0.640013i
$887$	47.5180	−	17.2951i	1.59550	−	0.580714i	0.616998	−	0.786964i	$-0.288349\pi$
$887$	47.5180	−	17.2951i	1.59550	−	0.580714i	0.978499	+	0.206251i	$0.0661263\pi$
$888$		0			0
$889$	1.76214	+	9.99357i	0.0591001	+	0.335174i
$890$	2.91755			0.0977966
$891$		0			0
$892$	20.8672			0.698686
$893$	−2.72830	−	15.4730i	−0.0912992	−	0.517783i
$894$		0			0
$895$	−11.9194	+	4.33831i	−0.398422	+	0.145014i
$896$	4.00411	+	3.35984i	0.133768	+	0.112245i
$897$		0			0
$898$	−13.9105	−	5.06300i	−0.464199	−	0.168955i
$899$	−43.9819	−	76.1788i	−1.46688	−	2.54071i
$900$		0			0
$901$	−0.687948	+	1.19156i	−0.0229189	+	0.0396967i
$902$	−0.795242	+	0.667288i	−0.0264787	+	0.0222182i
$903$		0			0
$904$	8.42762	−	47.7954i	0.280298	−	1.58965i
$905$	1.58499	−	8.98894i	0.0526869	−	0.298803i
$906$		0			0
$907$	−34.2189	+	28.7131i	−1.13622	+	0.953403i	−0.999309	−	0.0371802i	$-0.988162\pi$
$907$	−34.2189	+	28.7131i	−1.13622	+	0.953403i	−0.136913	+	0.990583i	$0.543718\pi$
$908$	−0.323488	+	0.560298i	−0.0107353	+	0.0185942i
$909$		0			0
$910$	0.360189	+	0.623865i	0.0119401	+	0.0206809i
$911$	−17.1655	−	6.24774i	−0.568719	−	0.206997i	0.0416249	−	0.999133i	$-0.486747\pi$
$911$	−17.1655	−	6.24774i	−0.568719	−	0.206997i	−0.610344	+	0.792136i	$0.708969\pi$
$912$		0			0
$913$	−2.03546	−	1.70796i	−0.0673640	−	0.0565251i
$914$	7.48692	−	2.72501i	0.247645	−	0.0901355i
$915$		0			0
$916$	3.47051	+	19.6823i	0.114669	+	0.650320i
$917$	−5.32457			−0.175833
$918$		0			0
$919$	−15.3472			−0.506259			−0.253129	−	0.967432i	$-0.581460\pi$
$919$	−15.3472			−0.506259			−0.253129	+	0.967432i	$0.581460\pi$
$920$	−1.78204	−	10.1064i	−0.0587520	−	0.333199i
$921$		0			0
$922$	−19.5199	+	7.10467i	−0.642854	+	0.233980i
$923$	−12.6634	−	10.6258i	−0.416820	−	0.349754i
$924$		0			0
$925$	−10.0238	−	3.64835i	−0.329579	−	0.119957i
$926$	9.30409	+	16.1152i	0.305751	+	0.529577i
$927$		0			0
$928$	28.3023	−	49.0211i	0.929070	−	1.60920i
$929$	41.2347	−	34.6000i	1.35287	−	1.13519i	0.374751	−	0.927125i	$-0.377728\pi$
$929$	41.2347	−	34.6000i	1.35287	−	1.13519i	0.978115	−	0.208064i	$-0.0667163\pi$
$930$		0			0
$931$	4.51232	−	25.5906i	0.147885	−	0.838699i
$932$	−4.92655	+	27.9399i	−0.161375	+	0.915201i
$933$		0			0
$934$	−4.81874	+	4.04341i	−0.157674	+	0.132304i
$935$	−0.0439053	+	0.0760462i	−0.00143586	+	0.00248698i
$936$		0			0
$937$	−29.8115	−	51.6351i	−0.973900	−	1.68684i	−0.683519	−	0.729932i	$-0.739552\pi$
$937$	−29.8115	−	51.6351i	−0.973900	−	1.68684i	−0.290380	−	0.956911i	$-0.593782\pi$
$938$	−2.18877	−	0.796647i	−0.0714658	−	0.0260114i
$939$		0			0
$940$	−4.47891	−	3.75826i	−0.146086	−	0.122581i
$941$	31.2201	−	11.3632i	1.01775	−	0.370430i	0.221344	−	0.975196i	$-0.428956\pi$
$941$	31.2201	−	11.3632i	1.01775	−	0.370430i	0.796403	+	0.604766i	$0.206733\pi$
$942$		0			0
$943$	−4.94224	−	28.0288i	−0.160942	−	0.912745i
$944$	−2.52573			−0.0822054
$945$		0			0
$946$	−0.166345			−0.00540833
$947$	8.65820	+	49.1031i	0.281354	+	1.59564i	0.718026	+	0.696016i	$0.245046\pi$
$947$	8.65820	+	49.1031i	0.281354	+	1.59564i	−0.436673	+	0.899620i	$0.643843\pi$
$948$		0			0
$949$	−10.2077	+	3.71529i	−0.331355	+	0.120603i
$950$	−2.21861	−	1.86164i	−0.0719813	−	0.0603995i
$951$		0			0
$952$	−0.580510	−	0.211288i	−0.0188144	−	0.00684789i
$953$	4.87188	+	8.43834i	0.157816	+	0.273345i	0.934081	−	0.357062i	$-0.116222\pi$
$953$	4.87188	+	8.43834i	0.157816	+	0.273345i	−0.776265	+	0.630407i	$0.782888\pi$
$954$		0			0
$955$	−12.3612	+	21.4102i	−0.399999	+	0.692819i
$956$	21.9508	−	18.4189i	0.709938	−	0.595709i
$957$		0			0
$958$	0.250529	−	1.42082i	0.00809422	−	0.0459046i
$959$	−0.0771488	+	0.437533i	−0.00249127	+	0.0141287i
$960$		0			0
$961$	39.8262	−	33.4181i	1.28472	−	1.07800i
$962$	−7.24728	+	12.5527i	−0.233662	+	0.404714i
$963$		0			0
$964$	5.39377	+	9.34228i	0.173722	+	0.300895i
$965$	−4.52691	−	1.64766i	−0.145726	−	0.0530401i
$966$		0			0
$967$	36.8948	+	30.9584i	1.18646	+	0.995554i	0.999914	+	0.0131071i	$0.00417224\pi$
$967$	36.8948	+	30.9584i	1.18646	+	0.995554i	0.186541	+	0.982447i	$0.440272\pi$
$968$	−26.5306	+	9.65634i	−0.852725	+	0.310367i
$969$		0			0
$970$	−1.09991	−	6.23789i	−0.0353159	−	0.200287i
$971$	−41.0170			−1.31630			−0.658149	−	0.752888i	$-0.728660\pi$
$971$	−41.0170			−1.31630			−0.658149	+	0.752888i	$0.728660\pi$
$972$		0			0
$973$	4.41170			0.141432
$974$	0.898702	+	5.09679i	0.0287963	+	0.163312i
$975$		0			0
$976$	−10.6403	+	3.87276i	−0.340588	+	0.123964i
$977$	5.88186	+	4.93546i	0.188177	+	0.157899i	0.732009	−	0.681295i	$-0.238583\pi$
$977$	5.88186	+	4.93546i	0.188177	+	0.157899i	−0.543832	+	0.839194i	$0.683027\pi$
$978$		0			0
$979$	−0.710538	−	0.258615i	−0.0227089	−	0.00826536i
$980$	−4.83499	−	8.37446i	−0.154448	−	0.267512i
$981$		0			0
$982$	−4.80932	+	8.32999i	−0.153472	+	0.265821i
$983$	−42.6130	+	35.7566i	−1.35914	+	1.14046i	−0.382899	+	0.923790i	$0.625074\pi$
$983$	−42.6130	+	35.7566i	−1.35914	+	1.14046i	−0.976245	+	0.216668i	$0.930481\pi$
$984$		0			0
$985$	−2.97667	+	16.8815i	−0.0948445	+	0.537890i
$986$	−0.568103	+	3.22187i	−0.0180921	+	0.102605i
$987$		0			0
$988$	7.73694	−	6.49206i	0.246145	−	0.206540i
$989$	2.28027	−	3.94955i	0.0725085	−	0.125588i
$990$		0			0
$991$	0.876303	+	1.51780i	0.0278367	+	0.0482145i	0.879608	−	0.475699i	$-0.157805\pi$
$991$	0.876303	+	1.51780i	0.0278367	+	0.0482145i	−0.851771	+	0.523914i	$0.824471\pi$
$992$	50.1831	+	18.2651i	1.59331	+	0.579919i
$993$		0			0
$994$	2.77069	+	2.32488i	0.0878809	+	0.0737408i
$995$	17.9363	−	6.52829i	0.568620	−	0.206961i
$996$		0			0
$997$	1.48133	+	8.40103i	0.0469141	+	0.266063i	0.999238	−	0.0390249i	$-0.0124252\pi$
$997$	1.48133	+	8.40103i	0.0469141	+	0.266063i	−0.952324	+	0.305088i	$0.901314\pi$
$998$	3.74190			0.118448
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.k.a.91.4		30
3.2	odd	2		135.2.k.a.121.2	yes	30
15.2	even	4		675.2.u.c.499.7		60
15.8	even	4		675.2.u.c.499.4		60
15.14	odd	2		675.2.l.d.526.4		30
27.2	odd	18		135.2.k.a.106.2	✓	30
27.5	odd	18		3645.2.a.h.1.5		15
27.22	even	9		3645.2.a.g.1.11		15
27.25	even	9	inner	405.2.k.a.316.4		30
135.2	even	36		675.2.u.c.349.4		60
135.29	odd	18		675.2.l.d.376.4		30
135.83	even	36		675.2.u.c.349.7		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.106.2	✓	30	27.2	odd	18
135.2.k.a.121.2	yes	30	3.2	odd	2
405.2.k.a.91.4		30	1.1	even	1	trivial
405.2.k.a.316.4		30	27.25	even	9	inner
675.2.l.d.376.4		30	135.29	odd	18
675.2.l.d.526.4		30	15.14	odd	2
675.2.u.c.349.4		60	135.2	even	36
675.2.u.c.349.7		60	135.83	even	36
675.2.u.c.499.4		60	15.8	even	4
675.2.u.c.499.7		60	15.2	even	4
3645.2.a.g.1.11		15	27.22	even	9
3645.2.a.h.1.5		15	27.5	odd	18

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	405.2.k.a.91.4

Level	$405$
Weight	$2$
Character	405.91
Analytic conductor	$3.234$
Analytic rank	$0$
Dimension	$30$
Inner twists	$2$