LMFDB - Embedded newform 378.2.m.a.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(125,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("378.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.4
Root			$1.69547 - 0.354107i$ of defining polynomial
Character	$\chi$	$=$	378.251
Dual form			378.2.m.a.125.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.895175 + 1.55049i) q^{5} +(-2.30191 + 1.30430i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.895175 + 1.55049i) q^{5} +(-2.30191 + 1.30430i) q^{7} -1.00000i q^{8} -1.79035i q^{10} +(2.07976 + 1.20075i) q^{11} +(-4.23601 + 2.44566i) q^{13} +(2.64566 + 0.0213944i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.66466 q^{17} +3.01701i q^{19} +(-0.895175 + 1.55049i) q^{20} +(-1.20075 - 2.07976i) q^{22} +(-3.26178 + 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +4.89133 q^{26} +(-2.28052 - 1.34136i) q^{28} +(5.68202 + 3.28052i) q^{29} +(-4.02408 + 2.32330i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.17369 + 1.83233i) q^{34} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +(1.50851 - 2.61281i) q^{38} +(1.55049 - 0.895175i) q^{40} +(4.04094 + 6.99911i) q^{41} +(-3.48127 + 6.02973i) q^{43} +2.40150i q^{44} +3.76638 q^{46} +(-2.56802 + 4.44794i) q^{47} +(3.59758 - 6.00478i) q^{49} +(-1.55421 + 0.897324i) q^{50} +(-4.23601 - 2.44566i) q^{52} +4.29953i q^{55} +(1.30430 + 2.30191i) q^{56} +(-3.28052 - 5.68202i) q^{58} +(-7.29501 - 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} +4.64661 q^{62} -1.00000 q^{64} +(-7.58394 - 4.37859i) q^{65} +(-0.285115 - 0.493834i) q^{67} +(-1.83233 - 3.17369i) q^{68} +(2.33516 + 4.12122i) q^{70} -5.96254i q^{71} -12.3814i q^{73} +(-8.10950 - 4.68202i) q^{74} +(-2.61281 + 1.50851i) q^{76} +(-6.35358 - 0.0513786i) q^{77} +(-1.51831 + 2.62979i) q^{79} -1.79035 q^{80} -8.08188i q^{82} +(7.00270 - 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} +(6.02973 - 3.48127i) q^{86} +(1.20075 - 2.07976i) q^{88} +3.74863 q^{89} +(6.56103 - 11.1547i) q^{91} +(-3.26178 - 1.88319i) q^{92} +(4.44794 - 2.56802i) q^{94} +(-4.67784 + 2.70075i) q^{95} +(4.77256 + 2.75544i) q^{97} +(-6.11799 + 3.40150i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{14} - 8 q^{16} + 48 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{29} - 8 q^{37} + 4 q^{43} + 24 q^{46} - 8 q^{49} - 60 q^{50} + 6 q^{56} - 12 q^{58} - 16 q^{64} - 84 q^{65} - 28 q^{67} - 36 q^{74} - 78 q^{77} - 4 q^{79} - 12 q^{85} + 24 q^{86} + 24 q^{91} + 48 q^{92} - 12 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^14 - 8 * q^16 + 48 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^29 - 8 * q^37 + 4 * q^43 + 24 * q^46 - 8 * q^49 - 60 * q^50 + 6 * q^56 - 12 * q^58 - 16 * q^64 - 84 * q^65 - 28 * q^67 - 36 * q^74 - 78 * q^77 - 4 * q^79 - 12 * q^85 + 24 * q^86 + 24 * q^91 + 48 * q^92 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.895175	+	1.55049i	0.400334	+	0.693399i	0.993766	−	0.111485i	$-0.0355607\pi$
$5$	0.895175	+	1.55049i	0.400334	+	0.693399i	−0.593432	+	0.804884i	$0.702227\pi$
$6$		0			0
$7$	−2.30191	+	1.30430i	−0.870040	+	0.492981i
$7$	−2.30191	+	1.30430i	−0.870040	+	0.492981i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		−	1.79035i		−	0.566158i
$11$	2.07976	+	1.20075i	0.627072	+	0.362040i	0.779617	−	0.626256i	$-0.215414\pi$
$11$	2.07976	+	1.20075i	0.627072	+	0.362040i	−0.152545	+	0.988297i	$0.548747\pi$
$12$		0			0
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.954820	−	0.297186i	$-0.903952\pi$
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.220039	+	0.975491i	$0.570618\pi$
$14$	2.64566	+	0.0213944i	0.707084	+	0.00571788i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.66466			−0.888812			−0.444406	−	0.895826i	$-0.646585\pi$
$17$	−3.66466			−0.888812			−0.444406	+	0.895826i	$0.646585\pi$
$18$		0			0
$19$			3.01701i			0.692150i	0.938207	+	0.346075i	$0.112486\pi$
$19$			3.01701i			0.692150i	−0.938207	+	0.346075i	$0.887514\pi$
$20$	−0.895175	+	1.55049i	−0.200167	+	0.346700i
$21$		0			0
$22$	−1.20075	−	2.07976i	−0.256001	−	0.443407i
$23$	−3.26178	+	1.88319i	−0.680129	+	0.392673i	−0.799904	−	0.600128i	$-0.795116\pi$
$23$	−3.26178	+	1.88319i	−0.680129	+	0.392673i	0.119775	+	0.992801i	$0.461783\pi$
$24$		0			0
$25$	0.897324	−	1.55421i	0.179465	−	0.310842i
$26$	4.89133			0.959268
$27$		0			0
$28$	−2.28052	−	1.34136i	−0.430977	−	0.253493i
$29$	5.68202	+	3.28052i	1.05512	+	0.609176i	0.924080	−	0.382200i	$-0.124833\pi$
$29$	5.68202	+	3.28052i	1.05512	+	0.609176i	0.131045	+	0.991376i	$0.458167\pi$
$30$		0			0
$31$	−4.02408	+	2.32330i	−0.722746	+	0.417278i	−0.815763	−	0.578387i	$-0.803682\pi$
$31$	−4.02408	+	2.32330i	−0.722746	+	0.417278i	0.0930163	+	0.995665i	$0.470349\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	3.17369	+	1.83233i	0.544284	+	0.314242i
$35$	−4.08292	−	2.40150i	−0.690140	−	0.405928i
$36$		0			0
$37$	9.36404			1.53944			0.769719	−	0.638382i	$-0.220396\pi$
$37$	9.36404			1.53944			0.769719	+	0.638382i	$0.220396\pi$
$38$	1.50851	−	2.61281i	0.244712	−	0.423853i
$39$		0			0
$40$	1.55049	−	0.895175i	0.245154	−	0.141540i
$41$	4.04094	+	6.99911i	0.631088	+	1.09308i	0.987330	+	0.158683i	$0.0507248\pi$
$41$	4.04094	+	6.99911i	0.631088	+	1.09308i	−0.356241	+	0.934394i	$0.615942\pi$
$42$		0			0
$43$	−3.48127	+	6.02973i	−0.530888	+	0.919526i	0.468462	+	0.883484i	$0.344808\pi$
$43$	−3.48127	+	6.02973i	−0.530888	+	0.919526i	−0.999350	+	0.0360419i	$0.988525\pi$
$44$			2.40150i			0.362040i
$45$		0			0
$46$	3.76638			0.555323
$47$	−2.56802	+	4.44794i	−0.374584	+	0.648799i	−0.990265	−	0.139197i	$-0.955548\pi$
$47$	−2.56802	+	4.44794i	−0.374584	+	0.648799i	0.615680	+	0.787996i	$0.288881\pi$
$48$		0			0
$49$	3.59758	−	6.00478i	0.513940	−	0.857826i
$50$	−1.55421	+	0.897324i	−0.219799	+	0.126901i
$51$		0			0
$52$	−4.23601	−	2.44566i	−0.587429	−	0.339152i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$			4.29953i			0.579749i
$56$	1.30430	+	2.30191i	0.174295	+	0.307606i
$57$		0			0
$58$	−3.28052	−	5.68202i	−0.430753	−	0.746086i
$59$	−7.29501	−	12.6353i	−0.949729	−	1.64498i	−0.745994	−	0.665953i	$-0.768025\pi$
$59$	−7.29501	−	12.6353i	−0.949729	−	1.64498i	−0.203735	−	0.979026i	$-0.565308\pi$
$60$		0			0
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.972317	−	0.233665i	$-0.0750718\pi$
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.283799	+	0.958884i	$0.408405\pi$
$62$	4.64661			0.590120
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.58394	−	4.37859i	−0.940672	−	0.543097i
$66$		0			0
$67$	−0.285115	−	0.493834i	−0.0348324	−	0.0603315i	0.848084	−	0.529862i	$-0.177756\pi$
$67$	−0.285115	−	0.493834i	−0.0348324	−	0.0603315i	−0.882916	+	0.469531i	$0.844423\pi$
$68$	−1.83233	−	3.17369i	−0.222203	−	0.384867i
$69$		0			0
$70$	2.33516	+	4.12122i	0.279105	+	0.492580i
$71$		−	5.96254i		−	0.707623i	−0.935317	−	0.353811i	$-0.884885\pi$
$71$		−	5.96254i		−	0.707623i	0.935317	−	0.353811i	$-0.115115\pi$
$72$		0			0
$73$		−	12.3814i		−	1.44913i	−0.689204	−	0.724567i	$-0.742040\pi$
$73$		−	12.3814i		−	1.44913i	0.689204	−	0.724567i	$-0.257960\pi$
$74$	−8.10950	−	4.68202i	−0.942710	−	0.544274i
$75$		0			0
$76$	−2.61281	+	1.50851i	−0.299710	+	0.173037i
$77$	−6.35358	−	0.0513786i	−0.724057	−	0.00585514i
$78$		0			0
$79$	−1.51831	+	2.62979i	−0.170824	+	0.295875i	−0.938708	−	0.344713i	$-0.887976\pi$
$79$	−1.51831	+	2.62979i	−0.170824	+	0.295875i	0.767884	+	0.640588i	$0.221309\pi$
$80$	−1.79035			−0.200167
$81$		0			0
$82$		−	8.08188i		−	0.892494i
$83$	7.00270	−	12.1290i	0.768646	−	1.33133i	−0.169651	−	0.985504i	$-0.554264\pi$
$83$	7.00270	−	12.1290i	0.768646	−	1.33133i	0.938297	−	0.345830i	$-0.112403\pi$
$84$		0			0
$85$	−3.28052	−	5.68202i	−0.355822	−	0.616302i
$86$	6.02973	−	3.48127i	0.650203	−	0.375395i
$87$		0			0
$88$	1.20075	−	2.07976i	0.128001	−	0.221704i
$89$	3.74863			0.397354			0.198677	−	0.980065i	$-0.436336\pi$
$89$	3.74863			0.397354			0.198677	+	0.980065i	$0.436336\pi$
$90$		0			0
$91$	6.56103	−	11.1547i	0.687783	−	1.16934i
$92$	−3.26178	−	1.88319i	−0.340064	−	0.196336i
$93$		0			0
$94$	4.44794	−	2.56802i	0.458770	−	0.264871i
$95$	−4.67784	+	2.70075i	−0.479936	+	0.277091i
$96$		0			0
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	0.722323	−	0.691556i	$-0.243074\pi$
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	−0.237743	+	0.971328i	$0.576408\pi$
$98$	−6.11799	+	3.40150i	−0.618010	+	0.343604i
$99$		0			0
$100$	1.79465			0.179465
$101$	0.125162	−	0.216787i	0.0124541	−	0.0215711i	−0.859731	−	0.510747i	$-0.829369\pi$
$101$	0.125162	−	0.216787i	0.0124541	−	0.0215711i	0.872185	+	0.489176i	$0.162702\pi$
$102$		0			0
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	−0.492818	−	0.870132i	$-0.664033\pi$
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	0.507148	+	0.861859i	$0.330700\pi$
$104$	2.44566	+	4.23601i	0.239817	+	0.415375i
$105$		0			0
$106$		0			0
$107$			7.99080i			0.772500i	0.922394	+	0.386250i	$0.126230\pi$
$107$			7.99080i			0.772500i	−0.922394	+	0.386250i	$0.873770\pi$
$108$		0			0
$109$	−18.9533			−1.81540			−0.907700	−	0.419619i	$-0.862164\pi$
$109$	−18.9533			−1.81540			−0.907700	+	0.419619i	$0.862164\pi$
$110$	2.14977	−	3.72350i	0.204972	−	0.355022i
$111$		0			0
$112$	0.0213944	−	2.64566i	0.00202158	−	0.249992i
$113$	1.00418	−	0.579764i	0.0944653	−	0.0545396i	−0.452023	−	0.892006i	$-0.649298\pi$
$113$	1.00418	−	0.579764i	0.0944653	−	0.0545396i	0.546488	+	0.837467i	$0.315964\pi$
$114$		0			0
$115$	−5.83973	−	3.37157i	−0.544558	−	0.314401i
$116$			6.56103i			0.609176i
$117$		0			0
$118$			14.5900i			1.34312i
$119$	8.43573	−	4.77984i	0.773302	−	0.438167i
$120$		0			0
$121$	−2.61639	−	4.53172i	−0.237854	−	0.411974i
$122$	−5.66414	−	9.81058i	−0.512807	−	0.888208i
$123$		0			0
$124$	−4.02408	−	2.32330i	−0.361373	−	0.208639i
$125$	12.1648			1.08805
$126$		0			0
$127$	1.40150			0.124363			0.0621817	−	0.998065i	$-0.480194\pi$
$127$	1.40150			0.124363			0.0621817	+	0.998065i	$0.480194\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	4.37859	+	7.58394i	0.384028	+	0.665156i
$131$	5.24589	+	9.08614i	0.458335	+	0.793860i	0.998873	−	0.0474597i	$-0.0151126\pi$
$131$	5.24589	+	9.08614i	0.458335	+	0.793860i	−0.540538	+	0.841320i	$0.681779\pi$
$132$		0			0
$133$	−3.93510	−	6.94489i	−0.341216	−	0.602198i
$134$			0.570231i			0.0492604i
$135$		0			0
$136$			3.66466i			0.314242i
$137$	4.08812	+	2.36028i	0.349272	+	0.201652i	0.664365	−	0.747409i	$-0.268702\pi$
$137$	4.08812	+	2.36028i	0.349272	+	0.201652i	−0.315093	+	0.949061i	$0.602036\pi$
$138$		0			0
$139$	−2.04707	+	1.18187i	−0.173630	+	0.100245i	−0.584296	−	0.811540i	$-0.698629\pi$
$139$	−2.04707	+	1.18187i	−0.173630	+	0.100245i	0.410666	+	0.911786i	$0.365296\pi$
$140$	0.0383034	−	4.73667i	0.00323723	−	0.400321i
$141$		0			0
$142$	−2.98127	+	5.16371i	−0.250182	+	0.433329i
$143$	−11.7465			−0.982295
$144$		0			0
$145$			11.7465i			0.975497i
$146$	−6.19070	+	10.7226i	−0.512346	+	0.887410i
$147$		0			0
$148$	4.68202	+	8.10950i	0.384860	+	0.666597i
$149$	15.0377	−	8.68202i	1.23194	−	0.711259i	0.264503	−	0.964385i	$-0.414792\pi$
$149$	15.0377	−	8.68202i	1.23194	−	0.711259i	0.967433	+	0.253126i	$0.0814587\pi$
$150$		0			0
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	−0.541749	−	0.840541i	$-0.682238\pi$
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	0.998804	+	0.0488977i	$0.0155708\pi$
$152$	3.01701			0.244712
$153$		0			0
$154$	5.47667	+	3.22128i	0.441322	+	0.259578i
$155$	−7.20451	−	4.15953i	−0.578680	−	0.334101i
$156$		0			0
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.0616014	−	0.998101i	$-0.480379\pi$
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.895181	+	0.445702i	$0.147046\pi$
$158$	2.62979	−	1.51831i	0.209215	−	0.120790i
$159$		0			0
$160$	1.55049	+	0.895175i	0.122577	+	0.0707698i
$161$	5.05208	−	8.58930i	0.398159	−	0.676931i
$162$		0			0
$163$	−4.33577			−0.339604			−0.169802	−	0.985478i	$-0.554313\pi$
$163$	−4.33577			−0.339604			−0.169802	+	0.985478i	$0.554313\pi$
$164$	−4.04094	+	6.99911i	−0.315544	+	0.546539i
$165$		0			0
$166$	−12.1290	+	7.00270i	−0.941395	+	0.543515i
$167$	6.20756	+	10.7518i	0.480355	+	0.832000i	0.999746	−	0.0225370i	$-0.00717435\pi$
$167$	6.20756	+	10.7518i	0.480355	+	0.832000i	−0.519391	+	0.854537i	$0.673841\pi$
$168$		0			0
$169$	5.46254	−	9.46139i	0.420195	−	0.727799i
$170$			6.56103i			0.503208i
$171$		0			0
$172$	−6.96254			−0.530888
$173$	−8.70908	+	15.0846i	−0.662139	+	1.14686i	0.317913	+	0.948120i	$0.397018\pi$
$173$	−8.70908	+	15.0846i	−0.662139	+	1.14686i	−0.980052	+	0.198739i	$0.936315\pi$
$174$		0			0
$175$	−0.0383954	+	4.74804i	−0.00290242	+	0.358918i
$176$	−2.07976	+	1.20075i	−0.156768	+	0.0905101i
$177$		0			0
$178$	−3.24641	−	1.87432i	−0.243329	−	0.140486i
$179$		−	13.1221i		−	0.980789i	−0.871501	−	0.490395i	$-0.836853\pi$
$179$		−	13.1221i		−	0.980789i	0.871501	−	0.490395i	$-0.163147\pi$
$180$		0			0
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$	−11.2594	+	6.37978i	−0.834602	+	0.472901i
$183$		0			0
$184$	1.88319	+	3.26178i	0.138831	+	0.240462i
$185$	8.38245	+	14.5188i	0.616290	+	1.06745i
$186$		0			0
$187$	−7.62164	−	4.40035i	−0.557349	−	0.321786i
$188$	−5.13604			−0.374584
$189$		0			0
$190$	5.40150			0.391866
$191$	8.01361	+	4.62666i	0.579845	+	0.334774i	0.761072	−	0.648668i	$-0.224674\pi$
$191$	8.01361	+	4.62666i	0.579845	+	0.334774i	−0.181227	+	0.983441i	$0.558007\pi$
$192$		0			0
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.846923	+	0.531716i	$0.178452\pi$
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.0370176	+	0.999315i	$0.488214\pi$
$194$	−2.75544	−	4.77256i	−0.197829	−	0.342650i
$195$		0			0
$196$	6.99908	+	0.113205i	0.499935	+	0.00808604i
$197$			12.4861i			0.889598i	0.895630	+	0.444799i	$0.146725\pi$
$197$			12.4861i			0.889598i	−0.895630	+	0.444799i	$0.853275\pi$
$198$		0			0
$199$			0.179145i			0.0126993i	0.999980	+	0.00634964i	$0.00202117\pi$
$199$			0.179145i			0.0126993i	−0.999980	+	0.00634964i	$0.997979\pi$
$200$	−1.55421	−	0.897324i	−0.109899	−	0.0634504i
$201$		0			0
$202$	−0.216787	+	0.125162i	−0.0152531	+	0.00880637i
$203$	−17.3583	−	0.140369i	−1.21831	−	0.00985198i
$204$		0			0
$205$	−7.23469	+	12.5309i	−0.505293	+	0.875193i
$206$	−0.167931			−0.0117003
$207$		0			0
$208$		−	4.89133i		−	0.339152i
$209$	−3.62268	+	6.27467i	−0.250586	+	0.434028i
$210$		0			0
$211$	7.56103	+	13.0961i	0.520523	+	0.901572i	0.999715	+	0.0238622i	$0.00759629\pi$
$211$	7.56103	+	13.0961i	0.520523	+	0.901572i	−0.479192	+	0.877710i	$0.659070\pi$
$212$		0			0
$213$		0			0
$214$	3.99540	−	6.92024i	0.273120	−	0.473058i
$215$	−12.4654			−0.850131
$216$		0			0
$217$	6.23278	−	10.5967i	0.423109	−	0.719348i
$218$	16.4141	+	9.47667i	1.11170	+	0.641841i
$219$		0			0
$220$	−3.72350	+	2.14977i	−0.251039	+	0.144937i
$221$	15.5236	−	8.96254i	1.04423	−	0.602885i
$222$		0			0
$223$	−7.27049	−	4.19762i	−0.486868	−	0.281093i	0.236406	−	0.971654i	$-0.424030\pi$
$223$	−7.27049	−	4.19762i	−0.486868	−	0.281093i	−0.723274	+	0.690561i	$0.757364\pi$
$224$	−1.34136	+	2.28052i	−0.0896234	+	0.152373i
$225$		0			0
$226$	−1.15953			−0.0771306
$227$	−1.21261	+	2.10030i	−0.0804836	+	0.139402i	−0.903458	−	0.428677i	$-0.858980\pi$
$227$	−1.21261	+	2.10030i	−0.0804836	+	0.139402i	0.822974	+	0.568079i	$0.192313\pi$
$228$		0			0
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	−0.441092	−	0.897462i	$-0.645409\pi$
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	0.556679	+	0.830728i	$0.312075\pi$
$230$	3.37157	+	5.83973i	0.222315	+	0.385061i
$231$		0			0
$232$	3.28052	−	5.68202i	0.215376	−	0.373043i
$233$		−	12.7289i		−	0.833899i	−0.908930	−	0.416950i	$-0.863099\pi$
$233$		−	12.7289i		−	0.833899i	0.908930	−	0.416950i	$-0.136901\pi$
$234$		0			0
$235$	−9.19531			−0.599836
$236$	7.29501	−	12.6353i	0.474864	−	0.822489i
$237$		0			0
$238$	−9.69548	−	0.0784032i	−0.628464	−	0.00508212i
$239$	−15.1117	+	8.72474i	−0.977494	+	0.564356i	−0.901513	−	0.432753i	$-0.857542\pi$
$239$	−15.1117	+	8.72474i	−0.977494	+	0.564356i	−0.0759814	+	0.997109i	$0.524209\pi$
$240$		0			0
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	0.783769	−	0.621052i	$-0.213295\pi$
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	−0.145963	+	0.989290i	$0.546628\pi$
$242$			5.23278i			0.336376i
$243$		0			0
$244$			11.3283i			0.725219i
$245$	12.5308	+	0.202676i	0.800564	+	0.0129485i
$246$		0			0
$247$	−7.37859	−	12.7801i	−0.469489	−	0.813178i
$248$	2.32330	+	4.02408i	0.147530	+	0.255529i
$249$		0			0
$250$	−10.5350	−	6.08240i	−0.666293	−	0.384685i
$251$	27.3560			1.72669			0.863347	−	0.504611i	$-0.168364\pi$
$251$	27.3560			1.72669			0.863347	+	0.504611i	$0.168364\pi$
$252$		0			0
$253$	−9.04499			−0.568653
$254$	−1.21374	−	0.700752i	−0.0761567	−	0.0439691i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.74837	−	3.02826i	−0.109060	−	0.188898i	0.806330	−	0.591466i	$-0.201451\pi$
$257$	−1.74837	−	3.02826i	−0.109060	−	0.188898i	−0.915390	+	0.402569i	$0.868117\pi$
$258$		0			0
$259$	−21.5552	+	12.2136i	−1.33937	+	0.758914i
$260$		−	8.75718i		−	0.543097i
$261$		0			0
$262$		−	10.4918i		−	0.648184i
$263$	8.35150	+	4.82174i	0.514976	+	0.297321i	0.734877	−	0.678201i	$-0.237240\pi$
$263$	8.35150	+	4.82174i	0.514976	+	0.297321i	−0.219901	+	0.975522i	$0.570573\pi$
$264$		0			0
$265$		0			0
$266$	−0.0645470	+	7.98200i	−0.00395763	+	0.489408i
$267$		0			0
$268$	0.285115	−	0.493834i	0.0174162	−	0.0301657i
$269$	6.91107			0.421376			0.210688	−	0.977553i	$-0.432430\pi$
$269$	6.91107			0.421376			0.210688	+	0.977553i	$0.432430\pi$
$270$		0			0
$271$			20.6312i			1.25326i	0.779318	+	0.626629i	$0.215566\pi$
$271$			20.6312i			1.25326i	−0.779318	+	0.626629i	$0.784434\pi$
$272$	1.83233	−	3.17369i	0.111101	−	0.192433i
$273$		0			0
$274$	−2.36028	−	4.08812i	−0.142590	−	0.246973i
$275$	3.73244	−	2.15493i	0.225075	−	0.129947i
$276$		0			0
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	−0.533166	−	0.846011i	$-0.678998\pi$
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	0.999250	+	0.0387296i	$0.0123311\pi$
$278$	2.36375			0.141768
$279$		0			0
$280$	−2.40150	+	4.08292i	−0.143517	+	0.244001i
$281$	−11.7759	−	6.79883i	−0.702492	−	0.405584i	0.105783	−	0.994389i	$-0.466265\pi$
$281$	−11.7759	−	6.79883i	−0.702492	−	0.405584i	−0.808275	+	0.588805i	$0.799599\pi$
$282$		0			0
$283$	−4.71796	+	2.72392i	−0.280454	+	0.161920i	−0.633629	−	0.773637i	$-0.718435\pi$
$283$	−4.71796	+	2.72392i	−0.280454	+	0.161920i	0.353175	+	0.935557i	$0.385102\pi$
$284$	5.16371	−	2.98127i	0.306410	−	0.176906i
$285$		0			0
$286$	10.1728	+	5.87327i	0.601530	+	0.347294i
$287$	−18.4308	−	10.8407i	−1.08794	−	0.639907i
$288$		0			0
$289$	−3.57023			−0.210014
$290$	5.87327	−	10.1728i	0.344890	−	0.597368i
$291$		0			0
$292$	10.7226	−	6.19070i	0.627493	−	0.362284i
$293$	−12.2311	−	21.1849i	−0.714550	−	1.23764i	−0.963133	−	0.269026i	$-0.913298\pi$
$293$	−12.2311	−	21.1849i	−0.714550	−	1.23764i	0.248583	−	0.968610i	$-0.420035\pi$
$294$		0			0
$295$	13.0606	−	22.6216i	0.760418	−	1.31708i
$296$		−	9.36404i		−	0.544274i
$297$		0			0
$298$	−17.3640			−1.00587
$299$	9.21130	−	15.9544i	0.532703	−	0.922670i
$300$		0			0
$301$	0.148959	−	18.4205i	0.00858585	−	1.06174i
$302$	−9.72787	+	5.61639i	−0.559776	+	0.323187i
$303$		0			0
$304$	−2.61281	−	1.50851i	−0.149855	−	0.0865187i
$305$			20.2816i			1.16132i
$306$		0			0
$307$		−	31.2223i		−	1.78195i	−0.454053	−	0.890975i	$-0.650022\pi$
$307$		−	31.2223i		−	1.78195i	0.454053	−	0.890975i	$-0.349978\pi$
$308$	−3.13229	−	5.52805i	−0.178479	−	0.314990i
$309$		0			0
$310$	4.15953	+	7.20451i	0.236245	+	0.409189i
$311$	5.45501	+	9.44836i	0.309325	+	0.535767i	0.978215	−	0.207594i	$-0.0665634\pi$
$311$	5.45501	+	9.44836i	0.309325	+	0.535767i	−0.668889	+	0.743362i	$0.733230\pi$
$312$		0			0
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	0.581458	−	0.813576i	$-0.302482\pi$
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	−0.413849	+	0.910346i	$0.635816\pi$
$314$	−13.8431			−0.781210
$315$		0			0
$316$	−3.03663			−0.170824
$317$	−16.4953	−	9.52357i	−0.926468	−	0.534897i	−0.0407755	−	0.999168i	$-0.512983\pi$
$317$	−16.4953	−	9.52357i	−0.926468	−	0.534897i	−0.885693	+	0.464272i	$0.846316\pi$
$318$		0			0
$319$	7.87817	+	13.6454i	0.441093	+	0.763995i
$320$	−0.895175	−	1.55049i	−0.0500418	−	0.0866749i
$321$		0			0
$322$	−8.66988	+	4.91251i	−0.483153	+	0.273763i
$323$		−	11.0563i		−	0.615191i
$324$		0			0
$325$			8.77821i			0.486927i
$326$	3.75489	+	2.16789i	0.207964	+	0.120068i
$327$		0			0
$328$	6.99911	−	4.04094i	0.386461	−	0.223123i
$329$	0.109882	−	13.5882i	0.00605801	−	0.749144i
$330$		0			0
$331$	−0.0366251	+	0.0634366i	−0.00201310	+	0.00348679i	−0.867030	−	0.498256i	$-0.833974\pi$
$331$	−0.0366251	+	0.0634366i	−0.00201310	+	0.00348679i	0.865017	+	0.501742i	$0.167307\pi$
$332$	14.0054			0.768646
$333$		0			0
$334$		−	12.4151i		−	0.679325i
$335$	0.510456	−	0.884136i	0.0278892	−	0.0483055i
$336$		0			0
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	0.894829	−	0.446408i	$-0.147297\pi$
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	−0.834016	+	0.551741i	$0.813964\pi$
$338$	−9.46139	+	5.46254i	−0.514632	+	0.297123i
$339$		0			0
$340$	3.28052	−	5.68202i	0.177911	−	0.308151i
$341$	−11.1589			−0.604286
$342$		0			0
$343$	−0.449242	+	18.5148i	−0.0242568	+	0.999706i
$344$	6.02973	+	3.48127i	0.325101	+	0.187697i
$345$		0			0
$346$	15.0846	−	8.70908i	0.810952	−	0.468203i
$347$	−27.5751	+	15.9205i	−1.48031	+	0.854656i	−0.999751	−	0.0223084i	$-0.992898\pi$
$347$	−27.5751	+	15.9205i	−1.48031	+	0.854656i	−0.480556	+	0.876964i	$0.659565\pi$
$348$		0			0
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	0.117925	−	0.993022i	$-0.462376\pi$
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	−0.801020	+	0.598637i	$0.795709\pi$
$350$	2.40727	−	4.09272i	0.128674	−	0.218765i
$351$		0			0
$352$	2.40150			0.128001
$353$	1.07979	−	1.87025i	0.0574713	−	0.0995431i	−0.835858	−	0.548945i	$-0.815030\pi$
$353$	1.07979	−	1.87025i	0.0574713	−	0.0995431i	0.893330	+	0.449402i	$0.148363\pi$
$354$		0			0
$355$	9.24484	−	5.33751i	0.490665	−	0.283286i
$356$	1.87432	+	3.24641i	0.0993385	+	0.172059i
$357$		0			0
$358$	−6.56103	+	11.3640i	−0.346761	+	0.600608i
$359$			32.6448i			1.72293i	0.507820	+	0.861463i	$0.330451\pi$
$359$			32.6448i			1.72293i	−0.507820	+	0.861463i	$0.669549\pi$
$360$		0			0
$361$	9.89765			0.520929
$362$	6.67887	−	11.5681i	0.351034	−	0.608008i
$363$		0			0
$364$	12.9408	+	0.104647i	0.678283	+	0.00548498i
$365$	19.1972	−	11.0835i	1.00483	−	0.580138i
$366$		0			0
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.987194	−	0.159527i	$-0.0509969\pi$
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.355442	+	0.934698i	$0.384330\pi$
$368$		−	3.76638i		−	0.196336i
$369$		0			0
$370$		−	16.7649i		−	0.871566i
$371$		0			0
$372$		0			0
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	0.890950	−	0.454102i	$-0.150040\pi$
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	−0.838739	+	0.544534i	$0.816707\pi$
$374$	4.40035	+	7.62164i	0.227537	+	0.394105i
$375$		0			0
$376$	4.44794	+	2.56802i	0.229385	+	0.132436i
$377$	−32.0921			−1.65283
$378$		0			0
$379$	−18.8709			−0.969332			−0.484666	−	0.874699i	$-0.661059\pi$
$379$	−18.8709			−0.969332			−0.484666	+	0.874699i	$0.661059\pi$
$380$	−4.67784	−	2.70075i	−0.239968	−	0.138546i
$381$		0			0
$382$	−4.62666	−	8.01361i	−0.236721	−	0.410012i
$383$	0.418256	+	0.724440i	0.0213719	+	0.0370172i	0.876514	−	0.481377i	$-0.159863\pi$
$383$	0.418256	+	0.724440i	0.0213719	+	0.0370172i	−0.855142	+	0.518394i	$0.826530\pi$
$384$		0			0
$385$	−5.60790	−	9.89714i	−0.285805	−	0.504405i
$386$		−	24.5602i		−	1.25008i
$387$		0			0
$388$			5.51087i			0.279772i
$389$	−21.4964	−	12.4109i	−1.08991	−	0.629260i	−0.156357	−	0.987701i	$-0.549975\pi$
$389$	−21.4964	−	12.4109i	−1.08991	−	0.629260i	−0.933552	+	0.358441i	$0.883308\pi$
$390$		0			0
$391$	11.9533	−	6.90127i	0.604507	−	0.349012i
$392$	−6.00478	−	3.59758i	−0.303287	−	0.181705i
$393$		0			0
$394$	6.24305	−	10.8133i	0.314520	−	0.544765i
$395$	−5.43662			−0.273546
$396$		0			0
$397$		−	3.03390i		−	0.152267i	−0.997098	−	0.0761336i	$-0.975742\pi$
$397$		−	3.03390i		−	0.152267i	0.997098	−	0.0761336i	$-0.0242575\pi$
$398$	0.0895727	−	0.155144i	0.00448987	−	0.00777669i
$399$		0			0
$400$	0.897324	+	1.55421i	0.0448662	+	0.0777105i
$401$	−11.3251	+	6.53854i	−0.565548	+	0.326519i	−0.755369	−	0.655300i	$-0.772542\pi$
$401$	−11.3251	+	6.53854i	−0.565548	+	0.326519i	0.189822	+	0.981819i	$0.439209\pi$
$402$		0			0
$403$	11.3640	−	19.6831i	0.566083	−	0.980485i
$404$	0.250324			0.0124541
$405$		0			0
$406$	14.9625	+	8.80071i	0.742578	+	0.436772i
$407$	19.4750	+	11.2439i	0.965339	+	0.557339i
$408$		0			0
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	−0.376044	−	0.926602i	$-0.622716\pi$
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	0.614439	+	0.788965i	$0.289382\pi$
$410$	12.5309	−	7.23469i	0.618855	−	0.357296i
$411$		0			0
$412$	0.145433	+	0.0839657i	0.00716496	+	0.00413669i
$413$	33.2728	+	19.5705i	1.63725	+	0.963000i
$414$		0			0
$415$	25.0746			1.23086
$416$	−2.44566	+	4.23601i	−0.119908	+	0.207688i
$417$		0			0
$418$	6.27467	−	3.62268i	0.306904	−	0.177191i
$419$	−8.19938	−	14.2017i	−0.400566	−	0.693800i	0.593228	−	0.805034i	$-0.297853\pi$
$419$	−8.19938	−	14.2017i	−0.400566	−	0.693800i	−0.993794	+	0.111234i	$0.964520\pi$
$420$		0			0
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	−0.990578	−	0.136952i	$-0.956269\pi$
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	0.613893	+	0.789389i	$0.289603\pi$
$422$		−	15.1221i		−	0.736131i
$423$		0			0
$424$		0			0
$425$	−3.28839	+	5.69566i	−0.159510	+	0.276280i
$426$		0			0
$427$	−29.9708	−	0.242361i	−1.45039	−	0.0117287i
$428$	−6.92024	+	3.99540i	−0.334502	+	0.193125i
$429$		0			0
$430$	10.7953	+	6.23269i	0.520597	+	0.300567i
$431$		−	25.0266i		−	1.20549i	−0.797935	−	0.602744i	$-0.794074\pi$
$431$		−	25.0266i		−	1.20549i	0.797935	−	0.602744i	$-0.205926\pi$
$432$		0			0
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$	−10.6961	+	6.06059i	−0.513428	+	0.290918i
$435$		0			0
$436$	−9.47667	−	16.4141i	−0.453850	−	0.786091i
$437$	−5.68161	−	9.84084i	−0.271788	−	0.470751i
$438$		0			0
$439$	16.2293	+	9.37000i	0.774583	+	0.447206i	0.834507	−	0.550997i	$-0.185752\pi$
$439$	16.2293	+	9.37000i	0.774583	+	0.447206i	−0.0599239	+	0.998203i	$0.519086\pi$
$440$	4.29953			0.204972
$441$		0			0
$442$	−17.9251			−0.852609
$443$	1.04314	+	0.602256i	0.0495610	+	0.0286141i	0.524576	−	0.851364i	$-0.324224\pi$
$443$	1.04314	+	0.602256i	0.0495610	+	0.0286141i	−0.475015	+	0.879978i	$0.657557\pi$
$444$		0			0
$445$	3.35568	+	5.81221i	0.159074	+	0.275525i
$446$	4.19762	+	7.27049i	0.198763	+	0.344268i
$447$		0			0
$448$	2.30191	−	1.30430i	0.108755	−	0.0616226i
$449$			26.8022i			1.26487i	0.774612	+	0.632436i	$0.217945\pi$
$449$			26.8022i			1.26487i	−0.774612	+	0.632436i	$0.782055\pi$
$450$		0			0
$451$			19.4087i			0.913918i
$452$	1.00418	+	0.579764i	0.0472327	+	0.0272698i
$453$		0			0
$454$	2.10030	−	1.21261i	0.0985719	−	0.0569105i
$455$	23.1686	+	0.187354i	1.08616	+	0.00878331i
$456$		0			0
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	−0.981291	−	0.192529i	$-0.938331\pi$
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	0.657381	+	0.753559i	$0.271664\pi$
$458$	−2.01975			−0.0943766
$459$		0			0
$460$		−	6.74314i		−	0.314401i
$461$	−2.40241	+	4.16110i	−0.111892	+	0.193802i	−0.916533	−	0.399959i	$-0.869024\pi$
$461$	−2.40241	+	4.16110i	−0.111892	+	0.193802i	0.804641	+	0.593761i	$0.202358\pi$
$462$		0			0
$463$	10.5194	+	18.2201i	0.488877	+	0.846760i	0.999918	−	0.0127960i	$-0.00407321\pi$
$463$	10.5194	+	18.2201i	0.488877	+	0.846760i	−0.511041	+	0.859556i	$0.670740\pi$
$464$	−5.68202	+	3.28052i	−0.263781	+	0.152294i
$465$		0			0
$466$	−6.36446	+	11.0236i	−0.294828	+	0.510657i
$467$	−5.82302			−0.269457			−0.134729	−	0.990883i	$-0.543016\pi$
$467$	−5.82302			−0.269457			−0.134729	+	0.990883i	$0.543016\pi$
$468$		0			0
$469$	1.30042	+	0.764885i	0.0600478	+	0.0353191i
$470$	7.96337	+	4.59766i	0.367323	+	0.212074i
$471$		0			0
$472$	−12.6353	+	7.29501i	−0.581588	+	0.335780i
$473$	−14.4804	+	8.36028i	−0.665811	+	0.384406i
$474$		0			0
$475$	4.68907	+	2.70724i	0.215149	+	0.124217i
$476$	8.35733	+	4.91564i	0.383057	+	0.225308i
$477$		0			0
$478$	17.4495			0.798121
$479$	−13.4781	+	23.3447i	−0.615828	+	1.06665i	0.374411	+	0.927263i	$0.377845\pi$
$479$	−13.4781	+	23.3447i	−0.615828	+	1.06665i	−0.990239	+	0.139382i	$0.955488\pi$
$480$		0			0
$481$	−39.6662	+	22.9013i	−1.80862	+	1.04421i
$482$	−5.71659	−	9.90142i	−0.260383	−	0.450997i
$483$		0			0
$484$	2.61639	−	4.53172i	0.118927	−	0.205987i
$485$			9.86639i			0.448010i
$486$		0			0
$487$	−13.6268			−0.617487			−0.308744	−	0.951145i	$-0.599909\pi$
$487$	−13.6268			−0.617487			−0.308744	+	0.951145i	$0.599909\pi$
$488$	5.66414	−	9.81058i	0.256404	−	0.444104i
$489$		0			0
$490$	−10.7507	−	6.44093i	−0.485665	−	0.290971i
$491$	33.7430	−	19.4815i	1.52280	−	0.879188i	0.523162	−	0.852234i	$-0.324752\pi$
$491$	33.7430	−	19.4815i	1.52280	−	0.879188i	0.999637	−	0.0269544i	$-0.00858088\pi$
$492$		0			0
$493$	−20.8227	−	12.0220i	−0.937807	−	0.541443i
$494$			14.7572i			0.663957i
$495$		0			0
$496$		−	4.64661i		−	0.208639i
$497$	7.77696	+	13.7252i	0.348844	+	0.615660i
$498$		0			0
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	−0.995221	−	0.0976483i	$-0.968868\pi$
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	0.413045	−	0.910711i	$-0.364465\pi$
$500$	6.08240	+	10.5350i	0.272013	+	0.471141i
$501$		0			0
$502$	−23.6910	−	13.6780i	−1.05738	−	0.610478i
$503$	−10.5271			−0.469378			−0.234689	−	0.972070i	$-0.575407\pi$
$503$	−10.5271			−0.469378			−0.234689	+	0.972070i	$0.575407\pi$
$504$		0			0
$505$	0.448168			0.0199432
$506$	7.83319	+	4.52249i	0.348228	+	0.201049i
$507$		0			0
$508$	0.700752	+	1.21374i	0.0310908	+	0.0538509i
$509$	−0.469435	−	0.813086i	−0.0208074	−	0.0360394i	0.855434	−	0.517911i	$-0.173290\pi$
$509$	−0.469435	−	0.813086i	−0.0208074	−	0.0360394i	−0.876242	+	0.481872i	$0.839957\pi$
$510$		0			0
$511$	16.1491	+	28.5009i	0.714395	+	1.26081i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$			3.49673i			0.154234i
$515$	0.260376	+	0.150328i	0.0114735	+	0.00662424i
$516$		0			0
$517$	−10.6818	+	6.16711i	−0.469783	+	0.271229i
$518$	24.7741	+	0.200338i	1.08851	+	0.00880233i
$519$		0			0
$520$	−4.37859	+	7.58394i	−0.192014	+	0.332578i
$521$	39.5054			1.73076			0.865382	−	0.501112i	$-0.167076\pi$
$521$	39.5054			1.73076			0.865382	+	0.501112i	$0.167076\pi$
$522$		0			0
$523$		−	24.3292i		−	1.06384i	−0.846794	−	0.531922i	$-0.821470\pi$
$523$		−	24.3292i		−	1.06384i	0.846794	−	0.531922i	$-0.178530\pi$
$524$	−5.24589	+	9.08614i	−0.229168	+	0.396930i
$525$		0			0
$526$	−4.82174	−	8.35150i	−0.210238	−	0.364143i
$527$	14.7469	−	8.51413i	0.642385	−	0.370881i
$528$		0			0
$529$	−4.40718	+	7.63346i	−0.191616	+	0.331889i
$530$		0			0
$531$		0			0
$532$	4.04690	−	6.88034i	0.175455	−	0.298301i
$533$	−34.2349	−	19.7655i	−1.48288	−	0.856141i
$534$		0			0
$535$	−12.3896	+	7.15316i	−0.535651	+	0.309258i
$536$	−0.493834	+	0.285115i	−0.0213304	+	0.0123151i
$537$		0			0
$538$	−5.98517	−	3.45554i	−0.258039	−	0.148979i
$539$	14.6924	−	8.16873i	0.632845	−	0.351852i
$540$		0			0
$541$	42.7281			1.83702			0.918512	−	0.395394i	$-0.129392\pi$
$541$	42.7281			1.83702			0.918512	+	0.395394i	$0.129392\pi$
$542$	10.3156	−	17.8672i	0.443093	−	0.767460i
$543$		0			0
$544$	−3.17369	+	1.83233i	−0.136071	+	0.0785606i
$545$	−16.9665	−	29.3869i	−0.726767	−	1.25880i
$546$		0			0
$547$	−12.2477	+	21.2136i	−0.523672	+	0.907026i	0.475949	+	0.879473i	$0.342105\pi$
$547$	−12.2477	+	21.2136i	−0.523672	+	0.907026i	−0.999620	+	0.0275530i	$0.991229\pi$
$548$			4.72056i			0.201652i
$549$		0			0
$550$	−4.30986			−0.183773
$551$	−9.89735	+	17.1427i	−0.421641	+	0.730304i
$552$		0			0
$553$	0.0649667	−	8.03389i	0.00276266	−	0.341636i
$554$	−13.4358	+	7.75718i	−0.570834	+	0.329571i
$555$		0			0
$556$	−2.04707	−	1.18187i	−0.0868150	−	0.0501227i
$557$		−	2.54431i		−	0.107806i	−0.998546	−	0.0539030i	$-0.982834\pi$
$557$		−	2.54431i		−	0.107806i	0.998546	−	0.0539030i	$-0.0171662\pi$
$558$		0			0
$559$		−	34.0560i		−	1.44042i
$560$	4.12122	−	2.33516i	0.174153	−	0.0986786i
$561$		0			0
$562$	6.79883	+	11.7759i	0.286791	+	0.496737i
$563$	7.90707	+	13.6954i	0.333243	+	0.577194i	0.983146	−	0.182823i	$-0.0585236\pi$
$563$	7.90707	+	13.6954i	0.333243	+	0.577194i	−0.649902	+	0.760018i	$0.725190\pi$
$564$		0			0
$565$	1.79783	+	1.03798i	0.0756354	+	0.0436681i
$566$	5.44783			0.228990
$567$		0			0
$568$	−5.96254			−0.250182
$569$	5.52793	+	3.19155i	0.231743	+	0.133797i	0.611376	−	0.791340i	$-0.290616\pi$
$569$	5.52793	+	3.19155i	0.231743	+	0.133797i	−0.379633	+	0.925137i	$0.623950\pi$
$570$		0			0
$571$	3.91188	+	6.77557i	0.163707	+	0.283549i	0.936195	−	0.351480i	$-0.114322\pi$
$571$	3.91188	+	6.77557i	0.163707	+	0.283549i	−0.772488	+	0.635029i	$0.780988\pi$
$572$	−5.87327	−	10.1728i	−0.245574	−	0.425346i
$573$		0			0
$574$	10.5412	+	18.6038i	0.439982	+	0.776506i
$575$			6.75933i			0.281884i
$576$		0			0
$577$			14.3197i			0.596138i	0.954544	+	0.298069i	$0.0963425\pi$
$577$			14.3197i			0.596138i	−0.954544	+	0.298069i	$0.903657\pi$
$578$	3.09191	+	1.78512i	0.128607	+	0.0742510i
$579$		0			0
$580$	−10.1728	+	5.87327i	−0.422403	+	0.243874i
$581$	−0.299637	+	37.0536i	−0.0124310	+	1.53724i
$582$		0			0
$583$		0			0
$584$	−12.3814			−0.512346
$585$		0			0
$586$			24.4622i			1.01053i
$587$	2.37575	−	4.11492i	0.0980577	−	0.169841i	−0.812823	−	0.582511i	$-0.802070\pi$
$587$	2.37575	−	4.11492i	0.0980577	−	0.169841i	0.910881	+	0.412670i	$0.135404\pi$
$588$		0			0
$589$	−7.00943	−	12.1407i	−0.288819	−	0.500249i
$590$	−22.6216	+	13.0606i	−0.931318	+	0.537697i
$591$		0			0
$592$	−4.68202	+	8.10950i	−0.192430	+	0.333298i
$593$	−3.58070			−0.147042			−0.0735208	−	0.997294i	$-0.523424\pi$
$593$	−3.58070			−0.147042			−0.0735208	+	0.997294i	$0.523424\pi$
$594$		0			0
$595$	14.9625	+	8.80071i	0.613404	+	0.360794i
$596$	15.0377	+	8.68202i	0.615968	+	0.355629i
$597$		0			0
$598$	−15.9544	+	9.21130i	−0.652426	+	0.376678i
$599$	13.0471	−	7.53277i	0.533091	−	0.307780i	−0.209183	−	0.977877i	$-0.567080\pi$
$599$	13.0471	−	7.53277i	0.533091	−	0.307780i	0.742274	+	0.670096i	$0.233747\pi$
$600$		0			0
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	0.0366096	−	0.999330i	$-0.488344\pi$
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	−0.847140	+	0.531370i	$0.821678\pi$
$602$	−9.33927	+	15.8782i	−0.380640	+	0.647146i
$603$		0			0
$604$	11.2328			0.457055
$605$	4.68425	−	8.11336i	0.190442	−	0.329855i
$606$		0			0
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	−0.00360990	−	0.999993i	$-0.501149\pi$
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	0.864215	+	0.503123i	$0.167816\pi$
$608$	1.50851	+	2.61281i	0.0611780	+	0.105963i
$609$		0			0
$610$	10.1408	−	17.5644i	0.410589	−	0.711161i
$611$		−	25.1221i		−	1.01633i
$612$		0			0
$613$	−0.880086			−0.0355463			−0.0177732	−	0.999842i	$-0.505658\pi$
$613$	−0.880086			−0.0355463			−0.0177732	+	0.999842i	$0.505658\pi$
$614$	−15.6111	+	27.0393i	−0.630014	+	1.09122i
$615$		0			0
$616$	−0.0513786	+	6.35358i	−0.00207010	+	0.255993i
$617$	11.7607	−	6.79005i	0.473468	−	0.273357i	−0.244222	−	0.969719i	$-0.578533\pi$
$617$	11.7607	−	6.79005i	0.473468	−	0.273357i	0.717690	+	0.696362i	$0.245199\pi$
$618$		0			0
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.267126	−	0.963662i	$-0.586074\pi$
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.968118	+	0.250493i	$0.919407\pi$
$620$		−	8.31905i		−	0.334101i
$621$		0			0
$622$		−	10.9100i		−	0.437452i
$623$	−8.62901	+	4.88936i	−0.345714	+	0.195888i
$624$		0			0
$625$	6.40300	+	11.0903i	0.256120	+	0.443613i
$626$	−1.71203	−	2.96532i	−0.0684263	−	0.118518i
$627$		0			0
$628$	11.9885	+	6.92154i	0.478391	+	0.276199i
$629$	−34.3161			−1.36827
$630$		0			0
$631$	26.9822			1.07415			0.537073	−	0.843536i	$-0.319530\pi$
$631$	26.9822			1.07415			0.537073	+	0.843536i	$0.319530\pi$
$632$	2.62979	+	1.51831i	0.104608	+	0.0603952i
$633$		0			0
$634$	9.52357	+	16.4953i	0.378229	+	0.655112i
$635$	1.25459	+	2.17302i	0.0497869	+	0.0862335i
$636$		0			0
$637$	−0.553721	+	34.2348i	−0.0219392	+	1.35643i
$638$		−	15.7563i		−	0.623800i
$639$		0			0
$640$			1.79035i			0.0707698i
$641$	−0.932777	−	0.538539i	−0.0368425	−	0.0212710i	0.481466	−	0.876465i	$-0.340105\pi$
$641$	−0.932777	−	0.538539i	−0.0368425	−	0.0212710i	−0.518308	+	0.855194i	$0.673438\pi$
$642$		0			0
$643$	33.3126	−	19.2330i	1.31372	−	0.758477i	0.331010	−	0.943627i	$-0.392611\pi$
$643$	33.3126	−	19.2330i	1.31372	−	0.758477i	0.982710	+	0.185150i	$0.0592773\pi$
$644$	9.96459	+	0.0805794i	0.392660	+	0.00317527i
$645$		0			0
$646$	−5.52817	+	9.57507i	−0.217503	+	0.376726i
$647$	8.95210			0.351943			0.175972	−	0.984395i	$-0.443693\pi$
$647$	8.95210			0.351943			0.175972	+	0.984395i	$0.443693\pi$
$648$		0			0
$649$		−	35.0380i		−	1.37536i
$650$	4.38910	−	7.60215i	0.172155	−	0.298181i
$651$		0			0
$652$	−2.16789	−	3.75489i	−0.0849010	−	0.147053i
$653$	9.85934	−	5.69229i	0.385826	−	0.222757i	−0.294524	−	0.955644i	$-0.595161\pi$
$653$	9.85934	−	5.69229i	0.385826	−	0.222757i	0.680350	+	0.732887i	$0.261828\pi$
$654$		0			0
$655$	−9.39197	+	16.2674i	−0.366975	+	0.635619i
$656$	−8.08188			−0.315544
$657$		0			0
$658$	−6.88929	+	11.7128i	−0.268572	+	0.456614i
$659$	−31.4373	−	18.1503i	−1.22462	−	0.707036i	−0.258723	−	0.965952i	$-0.583302\pi$
$659$	−31.4373	−	18.1503i	−1.22462	−	0.707036i	−0.965900	+	0.258915i	$0.916635\pi$
$660$		0			0
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.963886	−	0.266315i	$-0.914194\pi$
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.251308	+	0.967907i	$0.580861\pi$
$662$	0.0634366	−	0.0366251i	0.00246553	−	0.00142348i
$663$		0			0
$664$	−12.1290	−	7.00270i	−0.470698	−	0.271757i
$665$	7.24536	−	12.3182i	0.280963	−	0.477680i
$666$		0			0
$667$	−24.7114			−0.956828
$668$	−6.20756	+	10.7518i	−0.240178	+	0.416000i
$669$		0			0
$670$	−0.884136	+	0.510456i	−0.0341572	+	0.0197206i
$671$	13.6025	+	23.5602i	0.525117	+	0.909530i
$672$		0			0
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	−0.758939	−	0.651161i	$-0.774282\pi$
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	0.943392	+	0.331680i	$0.107615\pi$
$674$		−	2.23278i		−	0.0860034i
$675$		0			0
$676$	10.9251			0.420195
$677$	−7.81408	+	13.5344i	−0.300320	+	0.520169i	−0.976208	−	0.216835i	$-0.930427\pi$
$677$	−7.81408	+	13.5344i	−0.300320	+	0.520169i	0.675889	+	0.737004i	$0.263760\pi$
$678$		0			0
$679$	−14.5799	−	0.117902i	−0.559526	−	0.00452465i
$680$	−5.68202	+	3.28052i	−0.217896	+	0.125802i
$681$		0			0
$682$	9.66385	+	5.57943i	0.370048	+	0.213647i
$683$			11.1313i			0.425926i	0.977060	+	0.212963i	$0.0683114\pi$
$683$			11.1313i			0.425926i	−0.977060	+	0.212963i	$0.931689\pi$
$684$		0			0
$685$			8.45145i			0.322913i
$686$	9.64646	−	15.8097i	0.368304	−	0.603616i
$687$		0			0
$688$	−3.48127	−	6.02973i	−0.132722	−	0.229881i
$689$		0			0
$690$		0			0
$691$	2.61903	+	1.51210i	0.0996324	+	0.0575228i	0.548988	−	0.835830i	$-0.315013\pi$
$691$	2.61903	+	1.51210i	0.0996324	+	0.0575228i	−0.449356	+	0.893353i	$0.648346\pi$
$692$	−17.4182			−0.662139
$693$		0			0
$694$	31.8409			1.20867
$695$	−3.66497	−	2.11597i	−0.139020	−	0.0802633i
$696$		0			0
$697$	−14.8087	−	25.6494i	−0.560919	−	0.971540i
$698$	7.36772	+	12.7613i	0.278872	+	0.483021i
$699$		0			0
$700$	−4.13112	+	2.34077i	−0.156142	+	0.0884727i
$701$			50.1486i			1.89409i	0.321103	+	0.947044i	$0.395946\pi$
$701$			50.1486i			1.89409i	−0.321103	+	0.947044i	$0.604054\pi$
$702$		0			0
$703$			28.2514i			1.06552i
$704$	−2.07976	−	1.20075i	−0.0783840	−	0.0452550i
$705$		0			0
$706$	−1.87025	+	1.07979i	−0.0703876	+	0.0406383i
$707$	−0.00535553	+	0.662274i	−0.000201415	+	0.0249074i
$708$		0			0
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	−0.830163	−	0.557520i	$-0.811753\pi$
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	0.897908	+	0.440183i	$0.145086\pi$
$710$	−10.6750			−0.400626
$711$		0			0
$712$		−	3.74863i		−	0.140486i
$713$	8.75046	−	15.1562i	0.327707	−	0.567605i
$714$		0			0
$715$	−10.5152	−	18.2129i	−0.393246	−	0.681123i
$716$	11.3640	−	6.56103i	0.424694	−	0.245197i
$717$		0			0
$718$	16.3224	−	28.2712i	0.609146	−	1.05507i
$719$	34.3161			1.27977			0.639887	−	0.768469i	$-0.278981\pi$
$719$	34.3161			1.27977			0.639887	+	0.768469i	$0.278981\pi$
$720$		0			0
$721$	−0.225257	+	0.382970i	−0.00838899	+	0.0142626i
$722$	−8.57161	−	4.94882i	−0.319002	−	0.184176i
$723$		0			0
$724$	−11.5681	+	6.67887i	−0.429927	+	0.248218i
$725$	10.1972	−	5.88737i	0.378716	−	0.218651i
$726$		0			0
$727$	19.4757	+	11.2443i	0.722315	+	0.417029i	0.815604	−	0.578610i	$-0.196405\pi$
$727$	19.4757	+	11.2443i	0.722315	+	0.417029i	−0.0932892	+	0.995639i	$0.529738\pi$
$728$	−11.1547	−	6.56103i	−0.413422	−	0.243168i
$729$		0			0
$730$	−22.1670			−0.820439
$731$	12.7577	−	22.0970i	0.471860	−	0.817285i
$732$		0			0
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.0899987	−	0.995942i	$-0.471314\pi$
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.907510	+	0.420030i	$0.137980\pi$
$734$	−14.8501	−	25.7212i	−0.548129	−	0.949387i
$735$		0			0
$736$	−1.88319	+	3.26178i	−0.0694154	+	0.120231i
$737$		−	1.36941i		−	0.0504429i
$738$		0			0
$739$	4.08628			0.150316			0.0751581	−	0.997172i	$-0.476054\pi$
$739$	4.08628			0.150316			0.0751581	+	0.997172i	$0.476054\pi$
$740$	−8.38245	+	14.5188i	−0.308145	+	0.533723i
$741$		0			0
$742$		0			0
$743$	1.78246	−	1.02910i	0.0653921	−	0.0377542i	−0.466947	−	0.884285i	$-0.654646\pi$
$743$	1.78246	−	1.02910i	0.0653921	−	0.0377542i	0.532340	+	0.846531i	$0.321313\pi$
$744$		0			0
$745$	26.9227	+	15.5439i	0.986373	+	0.569483i
$746$		−	2.01672i		−	0.0738374i
$747$		0			0
$748$		−	8.80071i		−	0.321786i
$749$	−10.4224	−	18.3941i	−0.380828	−	0.672106i
$750$		0			0
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	0.562820	−	0.826580i	$-0.309717\pi$
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	−0.997249	+	0.0741262i	$0.976383\pi$
$752$	−2.56802	−	4.44794i	−0.0936461	−	0.162200i
$753$		0			0
$754$	27.7926	+	16.0461i	1.01215	+	0.584363i
$755$	20.1106			0.731900
$756$		0			0
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$	16.3427	+	9.43544i	0.593592	+	0.342711i
$759$		0			0
$760$	2.70075	+	4.67784i	0.0979666	+	0.169683i
$761$	−13.9368	−	24.1392i	−0.505207	−	0.875044i	−0.999982	−	0.00602283i	$-0.998083\pi$
$761$	−13.9368	−	24.1392i	−0.505207	−	0.875044i	0.494775	−	0.869021i	$-0.335250\pi$
$762$		0			0
$763$	43.6289	−	24.7209i	1.57947	−	0.894957i
$764$			9.25333i			0.334774i
$765$		0			0
$766$		−	0.836511i		−	0.0302244i
$767$	61.8035	+	35.6823i	2.23159	+	1.28841i
$768$		0			0
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	−0.607800	−	0.794090i	$-0.707948\pi$
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	0.383802	+	0.923415i	$0.374615\pi$
$770$	−0.0919857	+	11.3751i	−0.00331494	+	0.409931i
$771$		0			0
$772$	−12.2801	+	21.2698i	−0.441970	+	0.765515i
$773$	2.14153			0.0770255			0.0385128	−	0.999258i	$-0.487738\pi$
$773$	2.14153			0.0770255			0.0385128	+	0.999258i	$0.487738\pi$
$774$		0			0
$775$			8.33903i			0.299547i
$776$	2.75544	−	4.77256i	0.0989144	−	0.171325i
$777$		0			0
$778$	12.4109	+	21.4964i	0.444954	+	0.770682i
$779$	−21.1164	+	12.1916i	−0.756573	+	0.436808i
$780$		0			0
$781$	7.15953	−	12.4007i	0.256188	−	0.443731i
$782$	−13.8025			−0.493578
$783$		0			0
$784$	3.40150	+	6.11799i	0.121482	+	0.218500i
$785$	21.4635	+	12.3920i	0.766066	+	0.442288i
$786$		0			0
$787$	15.8961	−	9.17759i	0.566633	−	0.327146i	−0.189170	−	0.981944i	$-0.560580\pi$
$787$	15.8961	−	9.17759i	0.566633	−	0.327146i	0.755804	+	0.654798i	$0.227247\pi$
$788$	−10.8133	+	6.24305i	−0.385207	+	0.222400i
$789$		0			0
$790$	4.70825	+	2.71831i	0.167512	+	0.0967131i
$791$	−1.55534	+	2.64432i	−0.0553017	+	0.0940212i
$792$		0			0
$793$	−55.4103			−1.96768
$794$	−1.51695	+	2.62744i	−0.0538346	+	0.0932442i
$795$		0			0
$796$	−0.155144	+	0.0895727i	−0.00549895	+	0.00317482i
$797$	−12.4226	−	21.5166i	−0.440031	−	0.762156i	0.557660	−	0.830069i	$-0.311699\pi$
$797$	−12.4226	−	21.5166i	−0.440031	−	0.762156i	−0.997691	+	0.0679130i	$0.978366\pi$
$798$		0			0
$799$	9.41094	−	16.3002i	0.332935	−	0.576660i
$800$		−	1.79465i		−	0.0634504i
$801$		0			0
$802$	13.0771			0.461768
$803$	14.8670	−	25.7504i	0.524645	−	0.908712i
$804$		0			0
$805$	17.8401	+	0.144265i	0.628781	+	0.00508468i
$806$	−19.6831	+	11.3640i	−0.693307	+	0.400281i
$807$		0			0
$808$	−0.216787	−	0.125162i	−0.00762654	−	0.00440319i
$809$		−	37.7861i		−	1.32849i	−0.747516	−	0.664244i	$-0.768754\pi$
$809$		−	37.7861i		−	1.32849i	0.747516	−	0.664244i	$-0.231246\pi$
$810$		0			0
$811$		−	36.5165i		−	1.28227i	−0.767429	−	0.641134i	$-0.778464\pi$
$811$		−	36.5165i		−	1.28227i	0.767429	−	0.641134i	$-0.221536\pi$
$812$	−8.55758	−	15.1029i	−0.300312	−	0.530008i
$813$		0			0
$814$	−11.2439	−	19.4750i	−0.394098	−	0.682598i
$815$	−3.88128	−	6.72257i	−0.135955	−	0.235481i
$816$		0			0
$817$	−18.1918	−	10.5030i	−0.636449	−	0.367454i
$818$	−5.56709			−0.194649
$819$		0			0
$820$	−14.4694			−0.505293
$821$	5.52142	+	3.18779i	0.192699	+	0.111255i	0.593245	−	0.805022i	$-0.297846\pi$
$821$	5.52142	+	3.18779i	0.192699	+	0.111255i	−0.400547	+	0.916276i	$0.631180\pi$
$822$		0			0
$823$	−14.0293	−	24.2995i	−0.489032	−	0.847028i	0.510888	−	0.859647i	$-0.329317\pi$
$823$	−14.0293	−	24.2995i	−0.489032	−	0.847028i	−0.999920	+	0.0126187i	$0.995983\pi$
$824$	−0.0839657	−	0.145433i	−0.00292508	−	0.00506639i
$825$		0			0
$826$	−19.0298	−	33.5849i	−0.662132	−	1.16857i
$827$		−	0.581579i		−	0.0202235i	−0.999949	−	0.0101117i	$-0.996781\pi$
$827$		−	0.581579i		−	0.0202235i	0.999949	−	0.0101117i	$-0.00321872\pi$
$828$		0			0
$829$		−	51.9246i		−	1.80342i	−0.432346	−	0.901708i	$-0.642314\pi$
$829$		−	51.9246i		−	1.80342i	0.432346	−	0.901708i	$-0.357686\pi$
$830$	−21.7152	−	12.5373i	−0.753746	−	0.435175i
$831$		0			0
$832$	4.23601	−	2.44566i	0.146857	−	0.0847881i
$833$	−13.1839	+	22.0055i	−0.456796	+	0.762446i
$834$		0			0
$835$	−11.1137	+	19.2495i	−0.384606	+	0.666156i
$836$	−7.24536			−0.250586
$837$		0			0
$838$			16.3988i			0.566486i
$839$	3.33038	−	5.76838i	0.114977	−	0.199147i	−0.802793	−	0.596257i	$-0.796654\pi$
$839$	3.33038	−	5.76838i	0.114977	−	0.199147i	0.917771	+	0.397111i	$0.129987\pi$
$840$		0			0
$841$	7.02357	+	12.1652i	0.242192	+	0.419489i
$842$	13.3869	−	7.72892i	0.461342	−	0.266356i
$843$		0			0
$844$	−7.56103	+	13.0961i	−0.260261	+	0.450786i
$845$	19.5597			0.672874
$846$		0			0
$847$	11.9334	+	7.01904i	0.410038	+	0.241177i
$848$		0			0
$849$		0			0
$850$	5.69566	−	3.28839i	0.195360	−	0.112791i
$851$	−30.5435	+	17.6343i	−1.04702	+	0.604495i
$852$		0			0
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	0.133281	−	0.991078i	$-0.457449\pi$
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	−0.791659	+	0.610964i	$0.790782\pi$
$854$	25.8343	+	15.1953i	0.884033	+	0.519973i
$855$		0			0
$856$	7.99080			0.273120
$857$	7.64830	−	13.2472i	0.261261	−	0.452517i	−0.705316	−	0.708893i	$-0.749195\pi$
$857$	7.64830	−	13.2472i	0.261261	−	0.452517i	0.966577	+	0.256375i	$0.0825283\pi$
$858$		0			0
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	−0.435794	−	0.900046i	$-0.643532\pi$
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	0.561566	+	0.827432i	$0.310199\pi$
$860$	−6.23269	−	10.7953i	−0.212533	−	0.368118i
$861$		0			0
$862$	−12.5133	+	21.6737i	−0.426204	+	0.738208i
$863$		−	23.6624i		−	0.805476i	−0.915315	−	0.402738i	$-0.868059\pi$
$863$		−	23.6624i		−	0.805476i	0.915315	−	0.402738i	$-0.131941\pi$
$864$		0			0
$865$	−31.1846			−1.06031
$866$	−1.12584	+	1.95001i	−0.0382576	+	0.0662641i
$867$		0			0
$868$	12.2934	+	0.0994112i	0.417264	+	0.00337424i
$869$	−6.31546	+	3.64623i	−0.214237	+	0.123690i
$870$		0			0
$871$	2.41551	+	1.39459i	0.0818463	+	0.0472540i
$872$			18.9533i			0.641841i
$873$		0			0
$874$			11.3632i			0.384367i
$875$	−28.0023	+	15.8666i	−0.946649	+	0.536389i
$876$		0			0
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$	−9.37000	−	16.2293i	−0.316222	−	0.547713i
$879$		0			0
$880$	−3.72350	−	2.14977i	−0.125519	−	0.0724686i
$881$	−32.4586			−1.09356			−0.546780	−	0.837276i	$-0.684147\pi$
$881$	−32.4586			−1.09356			−0.546780	+	0.837276i	$0.684147\pi$
$882$		0			0
$883$	−24.8311			−0.835632			−0.417816	−	0.908532i	$-0.637204\pi$
$883$	−24.8311			−0.835632			−0.417816	+	0.908532i	$0.637204\pi$
$884$	15.5236	+	8.96254i	0.522114	+	0.301443i
$885$		0			0
$886$	−0.602256	−	1.04314i	−0.0202332	−	0.0350449i
$887$	4.86059	+	8.41879i	0.163203	+	0.282675i	0.936016	−	0.351959i	$-0.114484\pi$
$887$	4.86059	+	8.41879i	0.163203	+	0.282675i	−0.772813	+	0.634634i	$0.781151\pi$
$888$		0			0
$889$	−3.22614	+	1.82799i	−0.108201	+	0.0613088i
$890$		−	6.71136i		−	0.224965i
$891$		0			0
$892$		−	8.39524i		−	0.281093i
$893$	−13.4195	−	7.74775i	−0.449066	−	0.259269i
$894$		0			0
$895$	20.3456	−	11.7465i	0.680079	−	0.392644i
$896$	−2.64566	−	0.0213944i	−0.0883855	−	0.000714735i
$897$		0			0
$898$	13.4011	−	23.2114i	0.447200	−	0.774573i
$899$	−30.4865			−1.01678
$900$		0			0
$901$		0			0
$902$	9.70433	−	16.8084i	0.323119	−	0.559658i
$903$		0			0
$904$	−0.579764	−	1.00418i	−0.0192827	−	0.0333985i
$905$	−20.7110	+	11.9575i	−0.688458	+	0.397481i
$906$		0			0
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	−0.701035	−	0.713127i	$-0.747278\pi$
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	0.968103	+	0.250551i	$0.0806118\pi$
$908$	−2.42522			−0.0804836
$909$		0			0
$910$	−19.9709	−	11.7465i	−0.662029	−	0.389394i
$911$	−27.0087	−	15.5935i	−0.894838	−	0.516635i	−0.0193161	−	0.999813i	$-0.506149\pi$
$911$	−27.0087	−	15.5935i	−0.894838	−	0.516635i	−0.875522	+	0.483179i	$0.839482\pi$
$912$		0			0
$913$	29.1279	−	16.8170i	0.963993	−	0.556562i
$914$	11.9934	−	6.92442i	0.396708	−	0.229039i
$915$		0			0
$916$	1.74915	+	1.00987i	0.0577936	+	0.0333672i
$917$	−23.9267	−	14.0733i	−0.790128	−	0.464740i
$918$		0			0
$919$	25.7664			0.849955			0.424977	−	0.905204i	$-0.360282\pi$
$919$	25.7664			0.849955			0.424977	+	0.905204i	$0.360282\pi$
$920$	−3.37157	+	5.83973i	−0.111157	+	0.192530i
$921$		0			0
$922$	4.16110	−	2.40241i	0.137039	−	0.0791193i
$923$	14.5824	+	25.2574i	0.479984	+	0.831357i
$924$		0			0
$925$	8.40258	−	14.5537i	0.276275	−	0.478522i
$926$		−	21.0388i		−	0.691377i
$927$		0			0
$928$	6.56103			0.215376
$929$	27.3744	−	47.4138i	0.898124	−	1.55560i	0.0682329	−	0.997669i	$-0.478264\pi$
$929$	27.3744	−	47.4138i	0.898124	−	1.55560i	0.829891	−	0.557926i	$-0.188403\pi$
$930$		0			0
$931$	18.1165	+	10.8539i	0.593744	+	0.355723i
$932$	11.0236	−	6.36446i	0.361089	−	0.208475i
$933$		0			0
$934$	5.04288	+	2.91151i	0.165008	+	0.0952675i
$935$		−	15.7563i		−	0.515288i
$936$		0			0
$937$			58.2065i			1.90152i	0.309924	+	0.950761i	$0.399696\pi$
$937$			58.2065i			1.90152i	−0.309924	+	0.950761i	$0.600304\pi$
$938$	−0.743755	−	1.31262i	−0.0242844	−	0.0428586i
$939$		0			0
$940$	−4.59766	−	7.96337i	−0.149959	−	0.259737i
$941$	−16.6658	−	28.8660i	−0.543289	−	0.941005i	−0.998712	−	0.0507297i	$-0.983845\pi$
$941$	−16.6658	−	28.8660i	−0.543289	−	0.941005i	0.455423	−	0.890275i	$-0.349488\pi$
$942$		0			0
$943$	−26.3613	−	15.2197i	−0.858443	−	0.495622i
$944$	14.5900			0.474864
$945$		0			0
$946$	16.7206			0.543632
$947$	6.59497	+	3.80761i	0.214308	+	0.123731i	0.603312	−	0.797505i	$-0.293847\pi$
$947$	6.59497	+	3.80761i	0.214308	+	0.123731i	−0.389004	+	0.921236i	$0.627181\pi$
$948$		0			0
$949$	30.2808	+	52.4478i	0.982955	+	1.70253i
$950$	−2.70724	−	4.68907i	−0.0878344	−	0.152134i
$951$		0			0
$952$	−4.77984	−	8.43573i	−0.154915	−	0.273404i
$953$		−	55.7861i		−	1.80709i	−0.428495	−	0.903544i	$-0.640956\pi$
$953$		−	55.7861i		−	1.80709i	0.428495	−	0.903544i	$-0.359044\pi$
$954$		0			0
$955$			16.5667i			0.536085i
$956$	−15.1117	−	8.72474i	−0.488747	−	0.282178i
$957$		0			0
$958$	23.3447	−	13.4781i	0.754232	−	0.435456i
$959$	−12.4890	−	0.100993i	−0.403291	−	0.00326125i
$960$		0			0
$961$	−4.70451	+	8.14845i	−0.151758	+	0.262853i
$962$	45.8026			1.47673
$963$		0			0
$964$			11.4332i			0.368238i
$965$	−21.9857	+	38.0803i	−0.707744	+	1.22585i
$966$		0			0
$967$	−13.3369	−	23.1003i	−0.428887	−	0.742855i	0.567887	−	0.823106i	$-0.307761\pi$
$967$	−13.3369	−	23.1003i	−0.428887	−	0.742855i	−0.996775	+	0.0802517i	$0.974428\pi$
$968$	−4.53172	+	2.61639i	−0.145655	+	0.0840939i
$969$		0			0
$970$	4.93320	−	8.54455i	0.158395	−	0.274349i
$971$	8.59942			0.275968			0.137984	−	0.990434i	$-0.455938\pi$
$971$	8.59942			0.275968			0.137984	+	0.990434i	$0.455938\pi$
$972$		0			0
$973$	3.17064	−	5.39057i	0.101646	−	0.172814i
$974$	11.8011	+	6.81338i	0.378132	+	0.218315i
$975$		0			0
$976$	−9.81058	+	5.66414i	−0.314029	+	0.181305i
$977$	12.7973	−	7.38854i	0.409423	−	0.236380i	−0.281119	−	0.959673i	$-0.590705\pi$
$977$	12.7973	−	7.38854i	0.409423	−	0.236380i	0.690542	+	0.723293i	$0.257372\pi$
$978$		0			0
$979$	7.79627	+	4.50118i	0.249170	+	0.143858i
$980$	6.08988	+	10.9533i	0.194534	+	0.349891i
$981$		0			0
$982$	−38.9630			−1.24336
$983$	−10.2568	+	17.7652i	−0.327140	+	0.566623i	−0.981943	−	0.189176i	$-0.939418\pi$
$983$	−10.2568	+	17.7652i	−0.327140	+	0.566623i	0.654803	+	0.755800i	$0.272752\pi$
$984$		0			0
$985$	−19.3596	+	11.1772i	−0.616847	+	0.356137i
$986$	12.0220	+	20.8227i	0.382858	+	0.663130i
$987$		0			0
$988$	7.37859	−	12.7801i	0.234744	−	0.406589i
$989$		−	26.2236i		−	0.833861i
$990$		0			0
$991$	−9.29294			−0.295200			−0.147600	−	0.989047i	$-0.547155\pi$
$991$	−9.29294			−0.295200			−0.147600	+	0.989047i	$0.547155\pi$
$992$	−2.32330	+	4.02408i	−0.0737650	+	0.127765i
$993$		0			0
$994$	0.127565	−	15.7749i	0.00404610	−	0.500349i
$995$	−0.277763	+	0.160366i	−0.00880567	+	0.00508396i
$996$		0			0
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	0.499726	−	0.866183i	$-0.333434\pi$
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	−0.500274	+	0.865867i	$0.666767\pi$
$998$			26.0097i			0.823322i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.m.a.251.4		16
3.2	odd	2		126.2.m.a.83.8	yes	16
4.3	odd	2		3024.2.cc.b.2897.6		16
7.2	even	3		2646.2.l.b.521.8		16
7.3	odd	6		2646.2.t.a.1979.8		16
7.4	even	3		2646.2.t.a.1979.5		16
7.5	odd	6		2646.2.l.b.521.5		16
7.6	odd	2	inner	378.2.m.a.251.1		16
9.2	odd	6		1134.2.d.a.1133.6		16
9.4	even	3		126.2.m.a.41.5	✓	16
9.5	odd	6	inner	378.2.m.a.125.1		16
9.7	even	3		1134.2.d.a.1133.11		16
12.11	even	2		1008.2.cc.b.209.1		16
21.2	odd	6		882.2.l.a.227.2		16
21.5	even	6		882.2.l.a.227.3		16
21.11	odd	6		882.2.t.b.803.2		16
21.17	even	6		882.2.t.b.803.3		16
21.20	even	2		126.2.m.a.83.5	yes	16
28.27	even	2		3024.2.cc.b.2897.3		16
36.23	even	6		3024.2.cc.b.881.3		16
36.31	odd	6		1008.2.cc.b.545.8		16
63.4	even	3		882.2.l.a.509.7		16
63.5	even	6		2646.2.t.a.2285.5		16
63.13	odd	6		126.2.m.a.41.8	yes	16
63.20	even	6		1134.2.d.a.1133.3		16
63.23	odd	6		2646.2.t.a.2285.8		16
63.31	odd	6		882.2.l.a.509.6		16
63.32	odd	6		2646.2.l.b.1097.1		16
63.34	odd	6		1134.2.d.a.1133.14		16
63.40	odd	6		882.2.t.b.815.2		16
63.41	even	6	inner	378.2.m.a.125.4		16
63.58	even	3		882.2.t.b.815.3		16
63.59	even	6		2646.2.l.b.1097.4		16
84.83	odd	2		1008.2.cc.b.209.8		16
252.139	even	6		1008.2.cc.b.545.1		16
252.167	odd	6		3024.2.cc.b.881.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	9.4	even	3
126.2.m.a.41.8	yes	16	63.13	odd	6
126.2.m.a.83.5	yes	16	21.20	even	2
126.2.m.a.83.8	yes	16	3.2	odd	2
378.2.m.a.125.1		16	9.5	odd	6	inner
378.2.m.a.125.4		16	63.41	even	6	inner
378.2.m.a.251.1		16	7.6	odd	2	inner
378.2.m.a.251.4		16	1.1	even	1	trivial
882.2.l.a.227.2		16	21.2	odd	6
882.2.l.a.227.3		16	21.5	even	6
882.2.l.a.509.6		16	63.31	odd	6
882.2.l.a.509.7		16	63.4	even	3
882.2.t.b.803.2		16	21.11	odd	6
882.2.t.b.803.3		16	21.17	even	6
882.2.t.b.815.2		16	63.40	odd	6
882.2.t.b.815.3		16	63.58	even	3
1008.2.cc.b.209.1		16	12.11	even	2
1008.2.cc.b.209.8		16	84.83	odd	2
1008.2.cc.b.545.1		16	252.139	even	6
1008.2.cc.b.545.8		16	36.31	odd	6
1134.2.d.a.1133.3		16	63.20	even	6
1134.2.d.a.1133.6		16	9.2	odd	6
1134.2.d.a.1133.11		16	9.7	even	3
1134.2.d.a.1133.14		16	63.34	odd	6
2646.2.l.b.521.5		16	7.5	odd	6
2646.2.l.b.521.8		16	7.2	even	3
2646.2.l.b.1097.1		16	63.32	odd	6
2646.2.l.b.1097.4		16	63.59	even	6
2646.2.t.a.1979.5		16	7.4	even	3
2646.2.t.a.1979.8		16	7.3	odd	6
2646.2.t.a.2285.5		16	63.5	even	6
2646.2.t.a.2285.8		16	63.23	odd	6
3024.2.cc.b.881.3		16	36.23	even	6
3024.2.cc.b.881.6		16	252.167	odd	6
3024.2.cc.b.2897.3		16	28.27	even	2
3024.2.cc.b.2897.6		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.895175 + 1.55049i) q^{5} +(-2.30191 + 1.30430i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.895175 + 1.55049i) q^{5} +(-2.30191 + 1.30430i) q^{7} -1.00000i q^{8} -1.79035i q^{10} +(2.07976 + 1.20075i) q^{11} +(-4.23601 + 2.44566i) q^{13} +(2.64566 + 0.0213944i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.66466 q^{17} +3.01701i q^{19} +(-0.895175 + 1.55049i) q^{20} +(-1.20075 - 2.07976i) q^{22} +(-3.26178 + 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +4.89133 q^{26} +(-2.28052 - 1.34136i) q^{28} +(5.68202 + 3.28052i) q^{29} +(-4.02408 + 2.32330i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.17369 + 1.83233i) q^{34} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +(1.50851 - 2.61281i) q^{38} +(1.55049 - 0.895175i) q^{40} +(4.04094 + 6.99911i) q^{41} +(-3.48127 + 6.02973i) q^{43} +2.40150i q^{44} +3.76638 q^{46} +(-2.56802 + 4.44794i) q^{47} +(3.59758 - 6.00478i) q^{49} +(-1.55421 + 0.897324i) q^{50} +(-4.23601 - 2.44566i) q^{52} +4.29953i q^{55} +(1.30430 + 2.30191i) q^{56} +(-3.28052 - 5.68202i) q^{58} +(-7.29501 - 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} +4.64661 q^{62} -1.00000 q^{64} +(-7.58394 - 4.37859i) q^{65} +(-0.285115 - 0.493834i) q^{67} +(-1.83233 - 3.17369i) q^{68} +(2.33516 + 4.12122i) q^{70} -5.96254i q^{71} -12.3814i q^{73} +(-8.10950 - 4.68202i) q^{74} +(-2.61281 + 1.50851i) q^{76} +(-6.35358 - 0.0513786i) q^{77} +(-1.51831 + 2.62979i) q^{79} -1.79035 q^{80} -8.08188i q^{82} +(7.00270 - 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} +(6.02973 - 3.48127i) q^{86} +(1.20075 - 2.07976i) q^{88} +3.74863 q^{89} +(6.56103 - 11.1547i) q^{91} +(-3.26178 - 1.88319i) q^{92} +(4.44794 - 2.56802i) q^{94} +(-4.67784 + 2.70075i) q^{95} +(4.77256 + 2.75544i) q^{97} +(-6.11799 + 3.40150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{14} - 8 q^{16} + 48 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{29} - 8 q^{37} + 4 q^{43} + 24 q^{46} - 8 q^{49} - 60 q^{50} + 6 q^{56} - 12 q^{58} - 16 q^{64} - 84 q^{65} - 28 q^{67} - 36 q^{74} - 78 q^{77} - 4 q^{79} - 12 q^{85} + 24 q^{86} + 24 q^{91} + 48 q^{92} - 12 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^14 - 8 * q^16 + 48 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^29 - 8 * q^37 + 4 * q^43 + 24 * q^46 - 8 * q^49 - 60 * q^50 + 6 * q^56 - 12 * q^58 - 16 * q^64 - 84 * q^65 - 28 * q^67 - 36 * q^74 - 78 * q^77 - 4 * q^79 - 12 * q^85 + 24 * q^86 + 24 * q^91 + 48 * q^92 - 12 * q^95

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