LMFDB - Embedded newform 378.2.m.a.125.1

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			125.1
Root			$-1.69547 - 0.354107i$ of defining polynomial
Character	$\chi$	$=$	378.125
Dual form			378.2.m.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.895175 + 1.55049i) q^{5} +(0.0213944 - 2.64566i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.895175 + 1.55049i) q^{5} +(0.0213944 - 2.64566i) q^{7} +1.00000i q^{8} -1.79035i q^{10} +(2.07976 - 1.20075i) q^{11} +(4.23601 + 2.44566i) q^{13} +(1.30430 + 2.30191i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.66466 q^{17} +3.01701i q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +(-3.26178 - 1.88319i) q^{23} +(0.897324 + 1.55421i) q^{25} -4.89133 q^{26} +(-2.28052 - 1.34136i) q^{28} +(5.68202 - 3.28052i) q^{29} +(4.02408 + 2.32330i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.17369 + 1.83233i) q^{34} +(4.08292 + 2.40150i) q^{35} +9.36404 q^{37} +(-1.50851 - 2.61281i) q^{38} +(-1.55049 - 0.895175i) q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} -2.40150i q^{44} +3.76638 q^{46} +(2.56802 + 4.44794i) q^{47} +(-6.99908 - 0.113205i) q^{49} +(-1.55421 - 0.897324i) q^{50} +(4.23601 - 2.44566i) q^{52} +4.29953i q^{55} +(2.64566 + 0.0213944i) q^{56} +(-3.28052 + 5.68202i) q^{58} +(7.29501 - 12.6353i) q^{59} +(-9.81058 + 5.66414i) q^{61} -4.64661 q^{62} -1.00000 q^{64} +(-7.58394 + 4.37859i) q^{65} +(-0.285115 + 0.493834i) q^{67} +(1.83233 - 3.17369i) q^{68} +(-4.73667 - 0.0383034i) q^{70} +5.96254i q^{71} -12.3814i q^{73} +(-8.10950 + 4.68202i) q^{74} +(2.61281 + 1.50851i) q^{76} +(-3.13229 - 5.52805i) q^{77} +(-1.51831 - 2.62979i) q^{79} +1.79035 q^{80} -8.08188i q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +(6.02973 + 3.48127i) q^{86} +(1.20075 + 2.07976i) q^{88} -3.74863 q^{89} +(6.56103 - 11.1547i) q^{91} +(-3.26178 + 1.88319i) q^{92} +(-4.44794 - 2.56802i) q^{94} +(-4.67784 - 2.70075i) q^{95} +(-4.77256 + 2.75544i) q^{97} +(6.11799 - 3.40150i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.895175	+	1.55049i	−0.400334	+	0.693399i	−0.993766	−	0.111485i	$-0.964439\pi$
$5$	−0.895175	+	1.55049i	−0.400334	+	0.693399i	0.593432	+	0.804884i	$0.297773\pi$
$6$		0			0
$7$	0.0213944	−	2.64566i	0.00808631	−	0.999967i
$7$	0.0213944	−	2.64566i	0.00808631	−	0.999967i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		−	1.79035i		−	0.566158i
$11$	2.07976	−	1.20075i	0.627072	−	0.362040i	−0.152545	−	0.988297i	$-0.548747\pi$
$11$	2.07976	−	1.20075i	0.627072	−	0.362040i	0.779617	+	0.626256i	$0.215414\pi$
$12$		0			0
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.954820	−	0.297186i	$-0.0960482\pi$
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.220039	+	0.975491i	$0.429382\pi$
$14$	1.30430	+	2.30191i	0.348590	+	0.615211i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.66466			0.888812			0.444406	−	0.895826i	$-0.353415\pi$
$17$	3.66466			0.888812			0.444406	+	0.895826i	$0.353415\pi$
$18$		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	0.119775	−	0.992801i	$-0.461783\pi$
$23$	−3.26178	−	1.88319i	−0.680129	−	0.392673i	−0.799904	+	0.600128i	$0.795116\pi$
$24$		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	0.131045	−	0.991376i	$-0.458167\pi$
$29$	5.68202	−	3.28052i	1.05512	−	0.609176i	0.924080	+	0.382200i	$0.124833\pi$
$30$		0			0
$31$	4.02408	+	2.32330i	0.722746	+	0.417278i	0.815763	−	0.578387i	$-0.196318\pi$
$31$	4.02408	+	2.32330i	0.722746	+	0.417278i	−0.0930163	+	0.995665i	$0.529651\pi$
$32$	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	0.356241	+	0.934394i	$0.384058\pi$
$41$	−4.04094	+	6.99911i	−0.631088	+	1.09308i	−0.987330	+	0.158683i	$0.949275\pi$
$42$		0			0
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	−0.999350	−	0.0360419i	$-0.988525\pi$
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	0.468462	−	0.883484i	$-0.344808\pi$
$44$		−	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	$-0.0444520\pi$
$47$	2.56802	+	4.44794i	0.374584	+	0.648799i	−0.615680	+	0.787996i	$0.711119\pi$
$48$		0			0
$49$	−6.99908	−	0.113205i	−0.999869	−	0.0161721i
$50$	−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
$56$	2.64566	+	0.0213944i	0.353542	+	0.00285894i
$57$		0			0
$58$	−3.28052	+	5.68202i	−0.430753	+	0.746086i
$59$	7.29501	−	12.6353i	0.949729	−	1.64498i	0.203735	−	0.979026i	$-0.434692\pi$
$59$	7.29501	−	12.6353i	0.949729	−	1.64498i	0.745994	−	0.665953i	$-0.231975\pi$
$60$		0			0
$61$	−9.81058	+	5.66414i	−1.25612	+	0.725219i	−0.972317	−	0.233665i	$-0.924928\pi$
$61$	−9.81058	+	5.66414i	−1.25612	+	0.725219i	−0.283799	+	0.958884i	$0.591595\pi$
$62$	−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	−0.882916	−	0.469531i	$-0.844423\pi$
$67$	−0.285115	+	0.493834i	−0.0348324	+	0.0603315i	0.848084	+	0.529862i	$0.177756\pi$
$68$	1.83233	−	3.17369i	0.222203	−	0.384867i
$69$		0			0
$70$	−4.73667	−	0.0383034i	−0.566140	−	0.00457813i
$71$			5.96254i			0.707623i	0.935317	+	0.353811i	$0.115115\pi$
$71$			5.96254i			0.707623i	−0.935317	+	0.353811i	$0.884885\pi$
$72$		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
$77$	−3.13229	−	5.52805i	−0.356958	−	0.629979i
$78$		0			0
$79$	−1.51831	−	2.62979i	−0.170824	−	0.295875i	0.767884	−	0.640588i	$-0.221309\pi$
$79$	−1.51831	−	2.62979i	−0.170824	−	0.295875i	−0.938708	+	0.344713i	$0.887976\pi$
$80$	1.79035			0.200167
$81$		0			0
$82$		−	8.08188i		−	0.892494i
$83$	−7.00270	−	12.1290i	−0.768646	−	1.33133i	−0.938297	−	0.345830i	$-0.887597\pi$
$83$	−7.00270	−	12.1290i	−0.768646	−	1.33133i	0.169651	−	0.985504i	$-0.445736\pi$
$84$		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	$-0.563664\pi$
$89$	−3.74863			−0.397354			−0.198677	+	0.980065i	$0.563664\pi$
$90$		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	$-0.756926\pi$
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	0.237743	+	0.971328i	$0.423592\pi$
$98$	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	$-0.170631\pi$
$101$	−0.125162	−	0.216787i	−0.0124541	−	0.0215711i	−0.872185	+	0.489176i	$0.837298\pi$
$102$		0			0
$103$	−0.145433	−	0.0839657i	−0.0143299	−	0.00827339i	0.492818	−	0.870132i	$-0.335967\pi$
$103$	−0.145433	−	0.0839657i	−0.0143299	−	0.00827339i	−0.507148	+	0.861859i	$0.669300\pi$
$104$	−2.44566	+	4.23601i	−0.239817	+	0.415375i
$105$		0			0
$106$		0			0
$107$		−	7.99080i		−	0.772500i	−0.922394	−	0.386250i	$-0.873770\pi$
$107$		−	7.99080i		−	0.772500i	0.922394	−	0.386250i	$-0.126230\pi$
$108$		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
$112$	−2.30191	+	1.30430i	−0.217510	+	0.123245i
$113$	1.00418	+	0.579764i	0.0944653	+	0.0545396i	0.546488	−	0.837467i	$-0.315964\pi$
$113$	1.00418	+	0.579764i	0.0944653	+	0.0545396i	−0.452023	+	0.892006i	$0.649298\pi$
$114$		0			0
$115$	5.83973	−	3.37157i	0.544558	−	0.314401i
$116$		−	6.56103i		−	0.609176i
$117$		0			0
$118$			14.5900i			1.34312i
$119$	0.0784032	−	9.69548i	0.00718721	−	0.888783i
$120$		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	$-0.984887\pi$
$131$	−5.24589	+	9.08614i	−0.458335	+	0.793860i	0.540538	+	0.841320i	$0.318221\pi$
$132$		0			0
$133$	7.98200	+	0.0645470i	0.692127	+	0.00559694i
$134$		−	0.570231i		−	0.0492604i
$135$		0			0
$136$			3.66466i			0.314242i
$137$	4.08812	−	2.36028i	0.349272	−	0.201652i	−0.315093	−	0.949061i	$-0.602036\pi$
$137$	4.08812	−	2.36028i	0.349272	−	0.201652i	0.664365	+	0.747409i	$0.268702\pi$
$138$		0			0
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	0.584296	−	0.811540i	$-0.301371\pi$
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	−0.410666	+	0.911786i	$0.634704\pi$
$140$	4.12122	−	2.33516i	0.348307	−	0.197357i
$141$		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	0.967433	−	0.253126i	$-0.0814587\pi$
$149$	15.0377	+	8.68202i	1.23194	+	0.711259i	0.264503	+	0.964385i	$0.414792\pi$
$150$		0			0
$151$	5.61639	+	9.72787i	0.457055	+	0.791643i	0.998804	−	0.0488977i	$-0.0155708\pi$
$151$	5.61639	+	9.72787i	0.457055	+	0.791643i	−0.541749	+	0.840541i	$0.682238\pi$
$152$	−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	$-0.519621\pi$
$157$	−11.9885	−	6.92154i	−0.956783	−	0.552399i	−0.895181	+	0.445702i	$0.852954\pi$
$158$	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	$-0.992826\pi$
$167$	−6.20756	+	10.7518i	−0.480355	+	0.832000i	0.519391	+	0.854537i	$0.326159\pi$
$168$		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	0.980052	+	0.198739i	$0.0636846\pi$
$173$	8.70908	+	15.0846i	0.662139	+	1.14686i	−0.317913	+	0.948120i	$0.602982\pi$
$174$		0			0
$175$	4.13112	−	2.34077i	0.312283	−	0.176945i
$176$	−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	$0.163147\pi$
$179$			13.1221i			0.980789i	−0.871501	+	0.490395i	$0.836853\pi$
$180$		0			0
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$	−0.104647	+	12.9408i	−0.00775694	+	0.959237i
$183$		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	−0.181227	−	0.983441i	$-0.558007\pi$
$191$	8.01361	−	4.62666i	0.579845	−	0.334774i	0.761072	+	0.648668i	$0.224674\pi$
$192$		0			0
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.0370176	−	0.999315i	$-0.488214\pi$
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.846923	−	0.531716i	$-0.178452\pi$
$194$	2.75544	−	4.77256i	0.197829	−	0.342650i
$195$		0			0
$196$	−3.59758	+	6.00478i	−0.256970	+	0.428913i
$197$		−	12.4861i		−	0.889598i	−0.895630	−	0.444799i	$-0.853275\pi$
$197$		−	12.4861i		−	0.889598i	0.895630	−	0.444799i	$-0.146725\pi$
$198$		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
$203$	−8.55758	−	15.1029i	−0.600625	−	1.06002i
$204$		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	−0.479192	−	0.877710i	$-0.659070\pi$
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	0.999715	−	0.0238622i	$-0.00759629\pi$
$212$		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	$-0.575970\pi$
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	0.723274	+	0.690561i	$0.242636\pi$
$224$	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	$-0.141020\pi$
$227$	1.21261	+	2.10030i	0.0804836	+	0.139402i	−0.822974	+	0.568079i	$0.807687\pi$
$228$		0			0
$229$	−1.74915	−	1.00987i	−0.115587	−	0.0667344i	0.441092	−	0.897462i	$-0.354591\pi$
$229$	−1.74915	−	1.00987i	−0.115587	−	0.0667344i	−0.556679	+	0.830728i	$0.687925\pi$
$230$	−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	$0.136901\pi$
$233$			12.7289i			0.833899i	−0.908930	+	0.416950i	$0.863099\pi$
$234$		0			0
$235$	−9.19531			−0.599836
$236$	−7.29501	−	12.6353i	−0.474864	−	0.822489i
$237$		0			0
$238$	4.77984	+	8.43573i	0.309831	+	0.546807i
$239$	−15.1117	−	8.72474i	−0.977494	−	0.564356i	−0.0759814	−	0.997109i	$-0.524209\pi$
$239$	−15.1117	−	8.72474i	−0.977494	−	0.564356i	−0.901513	+	0.432753i	$0.857542\pi$
$240$		0			0
$241$	−9.90142	+	5.71659i	−0.637807	+	0.368238i	−0.783769	−	0.621052i	$-0.786705\pi$
$241$	−9.90142	+	5.71659i	−0.637807	+	0.368238i	0.145963	+	0.989290i	$0.453372\pi$
$242$		−	5.23278i		−	0.336376i
$243$		0			0
$244$			11.3283i			0.725219i
$245$	6.44093	−	10.7507i	0.411496	−	0.686835i
$246$		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	$-0.831636\pi$
$251$	−27.3560			−1.72669			−0.863347	+	0.504611i	$0.831636\pi$
$252$		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	$-0.798549\pi$
$257$	1.74837	−	3.02826i	0.109060	−	0.188898i	0.915390	+	0.402569i	$0.131883\pi$
$258$		0			0
$259$	0.200338	−	24.7741i	0.0124484	−	1.53939i
$260$			8.75718i			0.543097i
$261$		0			0
$262$		−	10.4918i		−	0.648184i
$263$	8.35150	−	4.82174i	0.514976	−	0.297321i	−0.219901	−	0.975522i	$-0.570573\pi$
$263$	8.35150	−	4.82174i	0.514976	−	0.297321i	0.734877	+	0.678201i	$0.237240\pi$
$264$		0			0
$265$		0			0
$266$	−6.94489	+	3.93510i	−0.425818	+	0.241276i
$267$		0			0
$268$	0.285115	+	0.493834i	0.0174162	+	0.0301657i
$269$	−6.91107			−0.421376			−0.210688	−	0.977553i	$-0.567570\pi$
$269$	−6.91107			−0.421376			−0.210688	+	0.977553i	$0.567570\pi$
$270$		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	0.999250	−	0.0387296i	$-0.0123311\pi$
$277$	7.75718	+	13.4358i	0.466084	+	0.807281i	−0.533166	+	0.846011i	$0.678998\pi$
$278$	−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	−0.808275	−	0.588805i	$-0.799599\pi$
$281$	−11.7759	+	6.79883i	−0.702492	+	0.405584i	0.105783	+	0.994389i	$0.466265\pi$
$282$		0			0
$283$	4.71796	+	2.72392i	0.280454	+	0.161920i	0.633629	−	0.773637i	$-0.281565\pi$
$283$	4.71796	+	2.72392i	0.280454	+	0.161920i	−0.353175	+	0.935557i	$0.614898\pi$
$284$	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	−0.248583	−	0.968610i	$-0.579965\pi$
$293$	12.2311	−	21.1849i	0.714550	−	1.23764i	0.963133	−	0.269026i	$-0.0867017\pi$
$294$		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
$301$	−16.0271	+	9.08127i	−0.923788	+	0.523435i
$302$	−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	$-0.349978\pi$
$308$	−6.35358	−	0.0513786i	−0.362029	−	0.00292757i
$309$		0			0
$310$	4.15953	−	7.20451i	0.236245	−	0.409189i
$311$	−5.45501	+	9.44836i	−0.309325	+	0.535767i	−0.978215	−	0.207594i	$-0.933437\pi$
$311$	−5.45501	+	9.44836i	−0.309325	+	0.535767i	0.668889	+	0.743362i	$0.266770\pi$
$312$		0			0
$313$	−2.96532	+	1.71203i	−0.167610	+	0.0967694i	−0.581458	−	0.813576i	$-0.697518\pi$
$313$	−2.96532	+	1.71203i	−0.167610	+	0.0967694i	0.413849	+	0.910346i	$0.364184\pi$
$314$	13.8431			0.781210
$315$		0			0
$316$	−3.03663			−0.170824
$317$	−16.4953	+	9.52357i	−0.926468	+	0.534897i	−0.885693	−	0.464272i	$-0.846316\pi$
$317$	−16.4953	+	9.52357i	−0.926468	+	0.534897i	−0.0407755	+	0.999168i	$0.512983\pi$
$318$		0			0
$319$	7.87817	−	13.6454i	0.441093	−	0.763995i
$320$	0.895175	−	1.55049i	0.0500418	−	0.0866749i
$321$		0			0
$322$	0.0805794	−	9.96459i	0.00449051	−	0.555305i
$323$			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
$329$	11.8227	−	6.69896i	0.651807	−	0.369326i
$330$		0			0
$331$	−0.0366251	−	0.0634366i	−0.00201310	−	0.00348679i	0.865017	−	0.501742i	$-0.167307\pi$
$331$	−0.0366251	−	0.0634366i	−0.00201310	−	0.00348679i	−0.867030	+	0.498256i	$0.833974\pi$
$332$	−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	−0.834016	−	0.551741i	$-0.813964\pi$
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	0.894829	+	0.446408i	$0.147297\pi$
$338$	−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	−0.480556	−	0.876964i	$-0.659565\pi$
$347$	−27.5751	−	15.9205i	−1.48031	−	0.854656i	−0.999751	+	0.0223084i	$0.992898\pi$
$348$		0			0
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	−0.117925	−	0.993022i	$-0.537624\pi$
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	0.801020	+	0.598637i	$0.204291\pi$
$350$	−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	$-0.184970\pi$
$353$	−1.07979	−	1.87025i	−0.0574713	−	0.0995431i	−0.893330	+	0.449402i	$0.851637\pi$
$354$		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	$-0.669549\pi$
$359$		−	32.6448i		−	1.72293i	0.507820	−	0.861463i	$-0.330451\pi$
$360$		0			0
$361$	9.89765			0.520929
$362$	−6.67887	−	11.5681i	−0.351034	−	0.608008i
$363$		0			0
$364$	−6.37978	−	11.2594i	−0.334391	−	0.590153i
$365$	19.1972	+	11.0835i	1.00483	+	0.580138i
$366$		0			0
$367$	−25.7212	+	14.8501i	−1.34264	+	0.775171i	−0.987194	−	0.159527i	$-0.949003\pi$
$367$	−25.7212	+	14.8501i	−1.34264	+	0.775171i	−0.355442	+	0.934698i	$0.615670\pi$
$368$			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	−0.838739	−	0.544534i	$-0.816707\pi$
$373$	1.00836	−	1.74653i	0.0522109	−	0.0904320i	0.890950	+	0.454102i	$0.150040\pi$
$374$	−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	$-0.840137\pi$
$383$	−0.418256	+	0.724440i	−0.0213719	+	0.0370172i	0.855142	+	0.518394i	$0.173470\pi$
$384$		0			0
$385$	11.3751	+	0.0919857i	0.579730	+	0.00468803i
$386$			24.5602i			1.25008i
$387$		0			0
$388$			5.51087i			0.279772i
$389$	−21.4964	+	12.4109i	−1.08991	+	0.629260i	−0.933552	−	0.358441i	$-0.883308\pi$
$389$	−21.4964	+	12.4109i	−1.08991	+	0.629260i	−0.156357	+	0.987701i	$0.549975\pi$
$390$		0			0
$391$	−11.9533	−	6.90127i	−0.604507	−	0.349012i
$392$	0.113205	−	6.99908i	0.00571770	−	0.353507i
$393$		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	0.189822	−	0.981819i	$-0.439209\pi$
$401$	−11.3251	−	6.53854i	−0.565548	−	0.326519i	−0.755369	+	0.655300i	$0.772542\pi$
$402$		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	$-0.377284\pi$
$409$	−4.82124	−	2.78354i	−0.238395	−	0.137637i	−0.614439	+	0.788965i	$0.710618\pi$
$410$	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	$-0.702147\pi$
$419$	8.19938	−	14.2017i	0.400566	−	0.693800i	0.993794	+	0.111234i	$0.0354802\pi$
$420$		0			0
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	0.613893	−	0.789389i	$-0.289603\pi$
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	−0.990578	+	0.136952i	$0.956269\pi$
$422$			15.1221i			0.736131i
$423$		0			0
$424$		0			0
$425$	3.28839	+	5.69566i	0.159510	+	0.276280i
$426$		0			0
$427$	14.7755	+	26.0767i	0.715038	+	1.26194i
$428$	−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	$0.205926\pi$
$431$			25.0266i			1.20549i	−0.797935	+	0.602744i	$0.794074\pi$
$432$		0			0
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$	−0.0994112	+	12.2934i	−0.00477189	+	0.590101i
$435$		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	$-0.814248\pi$
$439$	−16.2293	+	9.37000i	−0.774583	+	0.447206i	0.0599239	+	0.998203i	$0.480914\pi$
$440$	−4.29953			−0.204972
$441$		0			0
$442$	−17.9251			−0.852609
$443$	1.04314	−	0.602256i	0.0495610	−	0.0286141i	−0.475015	−	0.879978i	$-0.657557\pi$
$443$	1.04314	−	0.602256i	0.0495610	−	0.0286141i	0.524576	+	0.851364i	$0.324224\pi$
$444$		0			0
$445$	3.35568	−	5.81221i	0.159074	−	0.275525i
$446$	−4.19762	+	7.27049i	−0.198763	+	0.344268i
$447$		0			0
$448$	−0.0213944	+	2.64566i	−0.00101079	+	0.124996i
$449$		−	26.8022i		−	1.26487i	−0.774612	−	0.632436i	$-0.782055\pi$
$449$		−	26.8022i		−	1.26487i	0.774612	−	0.632436i	$-0.217945\pi$
$450$		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
$455$	11.4220	+	20.1583i	0.535473	+	0.945033i
$456$		0			0
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	0.657381	−	0.753559i	$-0.271664\pi$
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	−0.981291	+	0.192529i	$0.938331\pi$
$458$	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	$-0.130976\pi$
$461$	2.40241	+	4.16110i	0.111892	+	0.193802i	−0.804641	+	0.593761i	$0.797642\pi$
$462$		0			0
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	−0.511041	−	0.859556i	$-0.670740\pi$
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	0.999918	+	0.0127960i	$0.00407321\pi$
$464$	−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	$-0.456984\pi$
$467$	5.82302			0.269457			0.134729	+	0.990883i	$0.456984\pi$
$468$		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	0.990239	+	0.139382i	$0.0445117\pi$
$479$	13.4781	+	23.3447i	0.615828	+	1.06665i	−0.374411	+	0.927263i	$0.622155\pi$
$480$		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
$490$	−0.202676	+	12.5308i	−0.00915596	+	0.566084i
$491$	33.7430	+	19.4815i	1.52280	+	0.879188i	0.999637	+	0.0269544i	$0.00858088\pi$
$491$	33.7430	+	19.4815i	1.52280	+	0.879188i	0.523162	+	0.852234i	$0.324752\pi$
$492$		0			0
$493$	20.8227	−	12.0220i	0.937807	−	0.541443i
$494$		−	14.7572i		−	0.663957i
$495$		0			0
$496$		−	4.64661i		−	0.208639i
$497$	15.7749	+	0.127565i	0.707600	+	0.00572206i
$498$		0			0
$499$	−13.0048	+	22.5250i	−0.582176	+	1.00836i	0.413045	+	0.910711i	$0.364465\pi$
$499$	−13.0048	+	22.5250i	−0.582176	+	1.00836i	−0.995221	+	0.0976483i	$0.968868\pi$
$500$	−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	$-0.424593\pi$
$503$	10.5271			0.469378			0.234689	+	0.972070i	$0.424593\pi$
$504$		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	$-0.826710\pi$
$509$	0.469435	−	0.813086i	0.0208074	−	0.0360394i	0.876242	+	0.481872i	$0.160043\pi$
$510$		0			0
$511$	−32.7571	−	0.264892i	−1.44909	−	0.0117181i
$512$		−	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
$518$	12.2136	+	21.5552i	0.536633	+	0.947080i
$519$		0			0
$520$	−4.37859	−	7.58394i	−0.192014	−	0.332578i
$521$	−39.5054			−1.73076			−0.865382	−	0.501112i	$-0.832924\pi$
$521$	−39.5054			−1.73076			−0.865382	+	0.501112i	$0.832924\pi$
$522$		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	−0.999620	−	0.0275530i	$-0.991229\pi$
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	0.475949	−	0.879473i	$-0.342105\pi$
$548$		−	4.72056i		−	0.201652i
$549$		0			0
$550$	−4.30986			−0.183773
$551$	9.89735	+	17.1427i	0.421641	+	0.730304i
$552$		0			0
$553$	−6.99004	+	3.96068i	−0.297247	+	0.168425i
$554$	−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	$0.0171662\pi$
$557$			2.54431i			0.107806i	−0.998546	+	0.0539030i	$0.982834\pi$
$558$		0			0
$559$		−	34.0560i		−	1.44042i
$560$	0.0383034	−	4.73667i	0.00161861	−	0.200161i
$561$		0			0
$562$	6.79883	−	11.7759i	0.286791	−	0.496737i
$563$	−7.90707	+	13.6954i	−0.333243	+	0.577194i	−0.983146	−	0.182823i	$-0.941476\pi$
$563$	−7.90707	+	13.6954i	−0.333243	+	0.577194i	0.649902	+	0.760018i	$0.274810\pi$
$564$		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	−0.379633	−	0.925137i	$-0.623950\pi$
$569$	5.52793	−	3.19155i	0.231743	−	0.133797i	0.611376	+	0.791340i	$0.290616\pi$
$570$		0			0
$571$	3.91188	−	6.77557i	0.163707	−	0.283549i	−0.772488	−	0.635029i	$-0.780988\pi$
$571$	3.91188	−	6.77557i	0.163707	−	0.283549i	0.936195	+	0.351480i	$0.114322\pi$
$572$	5.87327	−	10.1728i	0.245574	−	0.425346i
$573$		0			0
$574$	−21.3819	−	0.172907i	−0.892465	−	0.00721698i
$575$		−	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
$581$	−32.2392	+	18.2673i	−1.33751	+	0.757855i
$582$		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	$-0.197930\pi$
$587$	−2.37575	−	4.11492i	−0.0980577	−	0.169841i	−0.910881	+	0.412670i	$0.864596\pi$
$588$		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	$-0.476576\pi$
$593$	3.58070			0.147042			0.0735208	+	0.997294i	$0.476576\pi$
$594$		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	0.742274	−	0.670096i	$-0.233747\pi$
$599$	13.0471	+	7.53277i	0.533091	+	0.307780i	−0.209183	+	0.977877i	$0.567080\pi$
$600$		0			0
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	−0.0366096	−	0.999330i	$-0.511656\pi$
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	0.847140	+	0.531370i	$0.178322\pi$
$602$	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	$-0.498851\pi$
$607$	−21.2030	−	12.2416i	−0.860605	−	0.496870i	−0.864215	+	0.503123i	$0.832184\pi$
$608$	−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
$616$	5.52805	−	3.13229i	0.222731	−	0.126204i
$617$	11.7607	+	6.79005i	0.473468	+	0.273357i	0.717690	−	0.696362i	$-0.245199\pi$
$617$	11.7607	+	6.79005i	0.473468	+	0.273357i	−0.244222	+	0.969719i	$0.578533\pi$
$618$		0			0
$619$	30.7325	−	17.7434i	1.23524	−	0.713169i	0.267126	−	0.963662i	$-0.413926\pi$
$619$	30.7325	−	17.7434i	1.23524	−	0.713169i	0.968118	+	0.250493i	$0.0805926\pi$
$620$			8.31905i			0.334101i
$621$		0			0
$622$		−	10.9100i		−	0.437452i
$623$	−0.0801996	+	9.91762i	−0.00321313	+	0.397341i
$624$		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
$637$	−29.3714	−	17.5969i	−1.16374	−	0.697216i
$638$			15.7563i			0.623800i
$639$		0			0
$640$			1.79035i			0.0707698i
$641$	−0.932777	+	0.538539i	−0.0368425	+	0.0212710i	−0.518308	−	0.855194i	$-0.673438\pi$
$641$	−0.932777	+	0.538539i	−0.0368425	+	0.0212710i	0.481466	+	0.876465i	$0.340105\pi$
$642$		0			0
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.331010	−	0.943627i	$-0.607389\pi$
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.982710	+	0.185150i	$0.940723\pi$
$644$	4.91251	+	8.66988i	0.193580	+	0.341641i
$645$		0			0
$646$	−5.52817	−	9.57507i	−0.217503	−	0.376726i
$647$	−8.95210			−0.351943			−0.175972	−	0.984395i	$-0.556307\pi$
$647$	−8.95210			−0.351943			−0.175972	+	0.984395i	$0.556307\pi$
$648$		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	0.680350	−	0.732887i	$-0.261828\pi$
$653$	9.85934	+	5.69229i	0.385826	+	0.222757i	−0.294524	+	0.955644i	$0.595161\pi$
$654$		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	−0.965900	−	0.258915i	$-0.916635\pi$
$659$	−31.4373	+	18.1503i	−1.22462	+	0.707036i	−0.258723	+	0.965952i	$0.583302\pi$
$660$		0			0
$661$	31.2425	+	18.0379i	1.21519	+	0.701593i	0.963886	−	0.266315i	$-0.0858060\pi$
$661$	31.2425	+	18.0379i	1.21519	+	0.701593i	0.251308	+	0.967907i	$0.419139\pi$
$662$	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	0.943392	−	0.331680i	$-0.107615\pi$
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	−0.758939	+	0.651161i	$0.774282\pi$
$674$			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	$-0.0695733\pi$
$677$	7.81408	+	13.5344i	0.300320	+	0.520169i	−0.675889	+	0.737004i	$0.736240\pi$
$678$		0			0
$679$	7.18786	+	12.6855i	0.275845	+	0.486826i
$680$	−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	$-0.931689\pi$
$683$		−	11.1313i		−	0.425926i	0.977060	−	0.212963i	$-0.0683114\pi$
$684$		0			0
$685$			8.45145i			0.322913i
$686$	−8.86835	−	16.2589i	−0.338595	−	0.620768i
$687$		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	$-0.684987\pi$
$691$	−2.61903	+	1.51210i	−0.0996324	+	0.0575228i	0.449356	+	0.893353i	$0.351654\pi$
$692$	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
$700$	0.0383954	−	4.74804i	0.00145121	−	0.179459i
$701$		−	50.1486i		−	1.89409i	−0.321103	−	0.947044i	$-0.604054\pi$
$701$		−	50.1486i		−	1.89409i	0.321103	−	0.947044i	$-0.395946\pi$
$702$		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
$707$	−0.576224	+	0.326499i	−0.0216711	+	0.0122793i
$708$		0			0
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$	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	$-0.721019\pi$
$719$	−34.3161			−1.27977			−0.639887	+	0.768469i	$0.721019\pi$
$720$		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	$-0.803595\pi$
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	0.0932892	+	0.995639i	$0.470262\pi$
$728$	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	$-0.528686\pi$
$733$	−27.0065	−	15.5922i	−0.997509	−	0.575912i	−0.907510	+	0.420030i	$0.862020\pi$
$734$	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	0.532340	−	0.846531i	$-0.321313\pi$
$743$	1.78246	+	1.02910i	0.0653921	+	0.0377542i	−0.466947	+	0.884285i	$0.654646\pi$
$744$		0			0
$745$	−26.9227	+	15.5439i	−0.986373	+	0.569483i
$746$			2.01672i			0.0738374i
$747$		0			0
$748$		−	8.80071i		−	0.321786i
$749$	−21.1410	−	0.170958i	−0.772475	−	0.00624667i
$750$		0			0
$751$	−11.9053	+	20.6205i	−0.434429	+	0.752454i	−0.997249	−	0.0741262i	$-0.976383\pi$
$751$	−11.9053	+	20.6205i	−0.434429	+	0.752454i	0.562820	+	0.826580i	$0.309717\pi$
$752$	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	−0.494775	−	0.869021i	$-0.664750\pi$
$761$	13.9368	−	24.1392i	0.505207	−	0.875044i	0.999982	−	0.00602283i	$-0.00191714\pi$
$762$		0			0
$763$	−0.405495	+	50.1442i	−0.0146799	+	1.81534i
$764$		−	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	$-0.292052\pi$
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	−0.383802	+	0.923415i	$0.625385\pi$
$770$	−9.89714	+	5.60790i	−0.356668	+	0.202095i
$771$		0			0
$772$	−12.2801	−	21.2698i	−0.441970	−	0.765515i
$773$	−2.14153			−0.0770255			−0.0385128	−	0.999258i	$-0.512262\pi$
$773$	−2.14153			−0.0770255			−0.0385128	+	0.999258i	$0.512262\pi$
$774$		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	$-0.439420\pi$
$787$	−15.8961	−	9.17759i	−0.566633	−	0.327146i	−0.755804	+	0.654798i	$0.772753\pi$
$788$	−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	$-0.688301\pi$
$797$	12.4226	−	21.5166i	0.440031	−	0.762156i	0.997691	+	0.0679130i	$0.0216340\pi$
$798$		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
$805$	−8.79511	−	15.5221i	−0.309987	−	0.547082i
$806$	−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	$0.231246\pi$
$809$			37.7861i			1.32849i	−0.747516	+	0.664244i	$0.768754\pi$
$810$		0			0
$811$		−	36.5165i		−	1.28227i	−0.767429	−	0.641134i	$-0.778464\pi$
$811$		−	36.5165i		−	1.28227i	0.767429	−	0.641134i	$-0.221536\pi$
$812$	−17.3583	−	0.140369i	−0.609157	−	0.00492599i
$813$		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	−0.400547	−	0.916276i	$-0.631180\pi$
$821$	5.52142	−	3.18779i	0.192699	−	0.111255i	0.593245	+	0.805022i	$0.297846\pi$
$822$		0			0
$823$	−14.0293	+	24.2995i	−0.489032	+	0.847028i	−0.999920	−	0.0126187i	$-0.995983\pi$
$823$	−14.0293	+	24.2995i	−0.489032	+	0.847028i	0.510888	+	0.859647i	$0.329317\pi$
$824$	0.0839657	−	0.145433i	0.00292508	−	0.00506639i
$825$		0			0
$826$	38.6003	+	0.312144i	1.34308	+	0.0108609i
$827$			0.581579i			0.0202235i	0.999949	+	0.0101117i	$0.00321872\pi$
$827$			0.581579i			0.0202235i	−0.999949	+	0.0101117i	$0.996781\pi$
$828$		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
$833$	−25.6493	−	0.414857i	−0.888696	−	0.0143739i
$834$		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	$-0.203346\pi$
$839$	−3.33038	−	5.76838i	−0.114977	−	0.199147i	−0.917771	+	0.397111i	$0.870013\pi$
$840$		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	$-0.542551\pi$
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	0.791659	+	0.610964i	$0.209218\pi$
$854$	−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	$-0.250805\pi$
$857$	−7.64830	−	13.2472i	−0.261261	−	0.452517i	−0.966577	+	0.256375i	$0.917472\pi$
$858$		0			0
$859$	−3.68620	−	2.12823i	−0.125772	−	0.0726143i	0.435794	−	0.900046i	$-0.356468\pi$
$859$	−3.68620	−	2.12823i	−0.125772	−	0.0726143i	−0.561566	+	0.827432i	$0.689801\pi$
$860$	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	$0.131941\pi$
$863$			23.6624i			0.805476i	−0.915315	+	0.402738i	$0.868059\pi$
$864$		0			0
$865$	−31.1846			−1.06031
$866$	1.12584	+	1.95001i	0.0382576	+	0.0662641i
$867$		0			0
$868$	−6.06059	−	10.6961i	−0.205710	−	0.363048i
$869$	−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
$875$	−0.260258	+	32.1840i	−0.00879833	+	1.08802i
$876$		0			0
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$878$	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	$-0.315853\pi$
$881$	32.4586			1.09356			0.546780	+	0.837276i	$0.315853\pi$
$882$		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	$-0.885516\pi$
$887$	−4.86059	+	8.41879i	−0.163203	+	0.282675i	0.772813	+	0.634634i	$0.218849\pi$
$888$		0			0
$889$	0.0299843	−	3.70791i	0.00100564	−	0.124359i
$890$			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
$896$	−1.30430	−	2.30191i	−0.0435737	−	0.0769014i
$897$		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	0.968103	−	0.250551i	$-0.0806118\pi$
$907$	8.04314	+	13.9311i	0.267068	+	0.462575i	−0.701035	+	0.713127i	$0.747278\pi$
$908$	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	−0.875522	−	0.483179i	$-0.839482\pi$
$911$	−27.0087	+	15.5935i	−0.894838	+	0.516635i	−0.0193161	+	0.999813i	$0.506149\pi$
$912$		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	−0.829891	−	0.557926i	$-0.811597\pi$
$929$	−27.3744	−	47.4138i	−0.898124	−	1.55560i	−0.0682329	−	0.997669i	$-0.521736\pi$
$930$		0			0
$931$	0.341540	−	21.1163i	0.0111935	−	0.692059i
$932$	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	$0.600304\pi$
$938$	−1.50864	−	0.0121997i	−0.0492588	−	0.000398335i
$939$		0			0
$940$	−4.59766	+	7.96337i	−0.149959	+	0.259737i
$941$	16.6658	−	28.8660i	0.543289	−	0.941005i	−0.455423	−	0.890275i	$-0.650512\pi$
$941$	16.6658	−	28.8660i	0.543289	−	0.941005i	0.998712	−	0.0507297i	$-0.0161547\pi$
$942$		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	−0.389004	−	0.921236i	$-0.627181\pi$
$947$	6.59497	−	3.80761i	0.214308	−	0.123731i	0.603312	+	0.797505i	$0.293847\pi$
$948$		0			0
$949$	30.2808	−	52.4478i	0.982955	−	1.70253i
$950$	2.70724	−	4.68907i	0.0878344	−	0.152134i
$951$		0			0
$952$	9.69548	+	0.0784032i	0.314232	+	0.00254106i
$953$			55.7861i			1.80709i	0.428495	+	0.903544i	$0.359044\pi$
$953$			55.7861i			1.80709i	−0.428495	+	0.903544i	$0.640956\pi$
$954$		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
$959$	−6.15705	−	10.8663i	−0.198821	−	0.350891i
$960$		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	−0.996775	−	0.0802517i	$-0.974428\pi$
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	0.567887	+	0.823106i	$0.307761\pi$
$968$	−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	$-0.544062\pi$
$971$	−8.59942			−0.275968			−0.137984	+	0.990434i	$0.544062\pi$
$972$		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	0.690542	−	0.723293i	$-0.257372\pi$
$977$	12.7973	+	7.38854i	0.409423	+	0.236380i	−0.281119	+	0.959673i	$0.590705\pi$
$978$		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	$-0.0605818\pi$
$983$	10.2568	+	17.7652i	0.327140	+	0.566623i	−0.654803	+	0.755800i	$0.727248\pi$
$984$		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
$994$	−13.7252	+	7.77696i	−0.435338	+	0.246670i
$995$	−0.277763	−	0.160366i	−0.00880567	−	0.00508396i
$996$		0			0
$997$	0.0172917	−	0.00998339i	0.000547635	−	0.000316177i	−0.499726	−	0.866183i	$-0.666566\pi$
$997$	0.0172917	−	0.00998339i	0.000547635	−	0.000316177i	0.500274	+	0.865867i	$0.333233\pi$
$998$		−	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.125.1		16
3.2	odd	2		126.2.m.a.41.5	✓	16
4.3	odd	2		3024.2.cc.b.881.3		16
7.2	even	3		2646.2.t.a.2285.8		16
7.3	odd	6		2646.2.l.b.1097.4		16
7.4	even	3		2646.2.l.b.1097.1		16
7.5	odd	6		2646.2.t.a.2285.5		16
7.6	odd	2	inner	378.2.m.a.125.4		16
9.2	odd	6	inner	378.2.m.a.251.4		16
9.4	even	3		1134.2.d.a.1133.6		16
9.5	odd	6		1134.2.d.a.1133.11		16
9.7	even	3		126.2.m.a.83.8	yes	16
12.11	even	2		1008.2.cc.b.545.8		16
21.2	odd	6		882.2.t.b.815.3		16
21.5	even	6		882.2.t.b.815.2		16
21.11	odd	6		882.2.l.a.509.7		16
21.17	even	6		882.2.l.a.509.6		16
21.20	even	2		126.2.m.a.41.8	yes	16
28.27	even	2		3024.2.cc.b.881.6		16
36.7	odd	6		1008.2.cc.b.209.1		16
36.11	even	6		3024.2.cc.b.2897.6		16
63.2	odd	6		2646.2.l.b.521.8		16
63.11	odd	6		2646.2.t.a.1979.5		16
63.13	odd	6		1134.2.d.a.1133.3		16
63.16	even	3		882.2.l.a.227.2		16
63.20	even	6	inner	378.2.m.a.251.1		16
63.25	even	3		882.2.t.b.803.2		16
63.34	odd	6		126.2.m.a.83.5	yes	16
63.38	even	6		2646.2.t.a.1979.8		16
63.41	even	6		1134.2.d.a.1133.14		16
63.47	even	6		2646.2.l.b.521.5		16
63.52	odd	6		882.2.t.b.803.3		16
63.61	odd	6		882.2.l.a.227.3		16
84.83	odd	2		1008.2.cc.b.545.1		16
252.83	odd	6		3024.2.cc.b.2897.3		16
252.223	even	6		1008.2.cc.b.209.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	3.2	odd	2
126.2.m.a.41.8	yes	16	21.20	even	2
126.2.m.a.83.5	yes	16	63.34	odd	6
126.2.m.a.83.8	yes	16	9.7	even	3
378.2.m.a.125.1		16	1.1	even	1	trivial
378.2.m.a.125.4		16	7.6	odd	2	inner
378.2.m.a.251.1		16	63.20	even	6	inner
378.2.m.a.251.4		16	9.2	odd	6	inner
882.2.l.a.227.2		16	63.16	even	3
882.2.l.a.227.3		16	63.61	odd	6
882.2.l.a.509.6		16	21.17	even	6
882.2.l.a.509.7		16	21.11	odd	6
882.2.t.b.803.2		16	63.25	even	3
882.2.t.b.803.3		16	63.52	odd	6
882.2.t.b.815.2		16	21.5	even	6
882.2.t.b.815.3		16	21.2	odd	6
1008.2.cc.b.209.1		16	36.7	odd	6
1008.2.cc.b.209.8		16	252.223	even	6
1008.2.cc.b.545.1		16	84.83	odd	2
1008.2.cc.b.545.8		16	12.11	even	2
1134.2.d.a.1133.3		16	63.13	odd	6
1134.2.d.a.1133.6		16	9.4	even	3
1134.2.d.a.1133.11		16	9.5	odd	6
1134.2.d.a.1133.14		16	63.41	even	6
2646.2.l.b.521.5		16	63.47	even	6
2646.2.l.b.521.8		16	63.2	odd	6
2646.2.l.b.1097.1		16	7.4	even	3
2646.2.l.b.1097.4		16	7.3	odd	6
2646.2.t.a.1979.5		16	63.11	odd	6
2646.2.t.a.1979.8		16	63.38	even	6
2646.2.t.a.2285.5		16	7.5	odd	6
2646.2.t.a.2285.8		16	7.2	even	3
3024.2.cc.b.881.3		16	4.3	odd	2
3024.2.cc.b.881.6		16	28.27	even	2
3024.2.cc.b.2897.3		16	252.83	odd	6
3024.2.cc.b.2897.6		16	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.895175 + 1.55049i) q^{5} +(0.0213944 - 2.64566i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.895175 + 1.55049i) q^{5} +(0.0213944 - 2.64566i) q^{7} +1.00000i q^{8} -1.79035i q^{10} +(2.07976 - 1.20075i) q^{11} +(4.23601 + 2.44566i) q^{13} +(1.30430 + 2.30191i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.66466 q^{17} +3.01701i q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +(-3.26178 - 1.88319i) q^{23} +(0.897324 + 1.55421i) q^{25} -4.89133 q^{26} +(-2.28052 - 1.34136i) q^{28} +(5.68202 - 3.28052i) q^{29} +(4.02408 + 2.32330i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.17369 + 1.83233i) q^{34} +(4.08292 + 2.40150i) q^{35} +9.36404 q^{37} +(-1.50851 - 2.61281i) q^{38} +(-1.55049 - 0.895175i) q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} -2.40150i q^{44} +3.76638 q^{46} +(2.56802 + 4.44794i) q^{47} +(-6.99908 - 0.113205i) q^{49} +(-1.55421 - 0.897324i) q^{50} +(4.23601 - 2.44566i) q^{52} +4.29953i q^{55} +(2.64566 + 0.0213944i) q^{56} +(-3.28052 + 5.68202i) q^{58} +(7.29501 - 12.6353i) q^{59} +(-9.81058 + 5.66414i) q^{61} -4.64661 q^{62} -1.00000 q^{64} +(-7.58394 + 4.37859i) q^{65} +(-0.285115 + 0.493834i) q^{67} +(1.83233 - 3.17369i) q^{68} +(-4.73667 - 0.0383034i) q^{70} +5.96254i q^{71} -12.3814i q^{73} +(-8.10950 + 4.68202i) q^{74} +(2.61281 + 1.50851i) q^{76} +(-3.13229 - 5.52805i) q^{77} +(-1.51831 - 2.62979i) q^{79} +1.79035 q^{80} -8.08188i q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +(6.02973 + 3.48127i) q^{86} +(1.20075 + 2.07976i) q^{88} -3.74863 q^{89} +(6.56103 - 11.1547i) q^{91} +(-3.26178 + 1.88319i) q^{92} +(-4.44794 - 2.56802i) q^{94} +(-4.67784 - 2.70075i) q^{95} +(-4.77256 + 2.75544i) q^{97} +(6.11799 - 3.40150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 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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