LMFDB - Embedded newform 630.2.k.i.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(361,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	630.361
Dual form			630.2.k.i.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.32288 + 4.02334i) q^{11} +0.645751 q^{13} +(-1.32288 - 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.64575 + 2.85052i) q^{17} +(2.14575 + 3.71655i) q^{19} -1.00000 q^{20} +4.64575 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.322876 - 0.559237i) q^{26} +(-1.32288 + 2.29129i) q^{28} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.29150 q^{34} +(1.32288 + 2.29129i) q^{35} +(2.96863 + 5.14181i) q^{37} +(2.14575 - 3.71655i) q^{38} +(0.500000 + 0.866025i) q^{40} +1.35425 q^{41} +11.2915 q^{43} +(-2.32288 - 4.02334i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(4.79150 + 8.29913i) q^{47} +7.00000 q^{49} +1.00000 q^{50} +(-0.322876 + 0.559237i) q^{52} +(0.145751 - 0.252449i) q^{53} -4.64575 q^{55} +2.64575 q^{56} +(4.64575 - 8.04668i) q^{59} +(-5.64575 - 9.77873i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(0.322876 + 0.559237i) q^{65} +(-2.35425 + 4.07768i) q^{67} +(-1.64575 - 2.85052i) q^{68} +(1.32288 - 2.29129i) q^{70} -2.70850 q^{71} +(-1.00000 + 1.73205i) q^{73} +(2.96863 - 5.14181i) q^{74} -4.29150 q^{76} +(-6.14575 + 10.6448i) q^{77} +(-5.64575 - 9.77873i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.677124 - 1.17281i) q^{82} +15.2915 q^{83} -3.29150 q^{85} +(-5.64575 - 9.77873i) q^{86} +(-2.32288 + 4.02334i) q^{88} +(-3.29150 - 5.70105i) q^{89} +1.70850 q^{91} +3.00000 q^{92} +(4.79150 - 8.29913i) q^{94} +(-2.14575 + 3.71655i) q^{95} -4.00000 q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 4 q^{11} - 8 q^{13} - 2 q^{16} + 4 q^{17} - 2 q^{19} - 4 q^{20} + 8 q^{22} - 6 q^{23} - 2 q^{25} + 4 q^{26} - 4 q^{31} - 2 q^{32} - 8 q^{34} - 4 q^{37} - 2 q^{38} + 2 q^{40} + 16 q^{41} + 24 q^{43} - 4 q^{44} - 6 q^{46} - 2 q^{47} + 28 q^{49} + 4 q^{50} + 4 q^{52} - 10 q^{53} - 8 q^{55} + 8 q^{59} - 12 q^{61} + 8 q^{62} + 4 q^{64} - 4 q^{65} - 20 q^{67} + 4 q^{68} - 32 q^{71} - 4 q^{73} - 4 q^{74} + 4 q^{76} - 14 q^{77} - 12 q^{79} + 2 q^{80} - 8 q^{82} + 40 q^{83} + 8 q^{85} - 12 q^{86} - 4 q^{88} + 8 q^{89} + 28 q^{91} + 12 q^{92} - 2 q^{94} + 2 q^{95} - 16 q^{97} - 14 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 - 4 * q^11 - 8 * q^13 - 2 * q^16 + 4 * q^17 - 2 * q^19 - 4 * q^20 + 8 * q^22 - 6 * q^23 - 2 * q^25 + 4 * q^26 - 4 * q^31 - 2 * q^32 - 8 * q^34 - 4 * q^37 - 2 * q^38 + 2 * q^40 + 16 * q^41 + 24 * q^43 - 4 * q^44 - 6 * q^46 - 2 * q^47 + 28 * q^49 + 4 * q^50 + 4 * q^52 - 10 * q^53 - 8 * q^55 + 8 * q^59 - 12 * q^61 + 8 * q^62 + 4 * q^64 - 4 * q^65 - 20 * q^67 + 4 * q^68 - 32 * q^71 - 4 * q^73 - 4 * q^74 + 4 * q^76 - 14 * q^77 - 12 * q^79 + 2 * q^80 - 8 * q^82 + 40 * q^83 + 8 * q^85 - 12 * q^86 - 4 * q^88 + 8 * q^89 + 28 * q^91 + 12 * q^92 - 2 * q^94 + 2 * q^95 - 16 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.64575			1.00000
$7$	2.64575			1.00000
$8$	1.00000			0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.32288	+	4.02334i	−0.700373	+	1.21308i	0.267962	+	0.963429i	$0.413650\pi$
$11$	−2.32288	+	4.02334i	−0.700373	+	1.21308i	−0.968335	+	0.249653i	$0.919684\pi$
$12$		0			0
$13$	0.645751			0.179099			0.0895496	−	0.995982i	$-0.471457\pi$
$13$	0.645751			0.179099			0.0895496	+	0.995982i	$0.471457\pi$
$14$	−1.32288	−	2.29129i	−0.353553	−	0.612372i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.64575	+	2.85052i	−0.399153	+	0.691354i	−0.993622	−	0.112765i	$-0.964029\pi$
$17$	−1.64575	+	2.85052i	−0.399153	+	0.691354i	0.594468	+	0.804119i	$0.297363\pi$
$18$		0			0
$19$	2.14575	+	3.71655i	0.492269	+	0.852635i	0.999960	−	0.00890397i	$-0.00283426\pi$
$19$	2.14575	+	3.71655i	0.492269	+	0.852635i	−0.507691	+	0.861539i	$0.669501\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	4.64575			0.990478
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.322876	−	0.559237i	−0.0633211	−	0.109675i
$27$		0			0
$28$	−1.32288	+	2.29129i	−0.250000	+	0.433013i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.29150			0.564488
$35$	1.32288	+	2.29129i	0.223607	+	0.387298i
$36$		0			0
$37$	2.96863	+	5.14181i	0.488039	+	0.845309i	0.999905	−	0.0137564i	$-0.00437895\pi$
$37$	2.96863	+	5.14181i	0.488039	+	0.845309i	−0.511866	+	0.859065i	$0.671046\pi$
$38$	2.14575	−	3.71655i	0.348087	−	0.602904i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	1.35425			0.211498			0.105749	−	0.994393i	$-0.466276\pi$
$41$	1.35425			0.211498			0.105749	+	0.994393i	$0.466276\pi$
$42$		0			0
$43$	11.2915			1.72194			0.860969	−	0.508657i	$-0.169858\pi$
$43$	11.2915			1.72194			0.860969	+	0.508657i	$0.169858\pi$
$44$	−2.32288	−	4.02334i	−0.350187	−	0.606541i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	4.79150	+	8.29913i	0.698912	+	1.21055i	0.968844	+	0.247672i	$0.0796657\pi$
$47$	4.79150	+	8.29913i	0.698912	+	1.21055i	−0.269931	+	0.962880i	$0.587001\pi$
$48$		0			0
$49$	7.00000			1.00000
$50$	1.00000			0.141421
$51$		0			0
$52$	−0.322876	+	0.559237i	−0.0447748	+	0.0775522i
$53$	0.145751	−	0.252449i	0.0200205	−	0.0346765i	−0.855842	−	0.517238i	$-0.826960\pi$
$53$	0.145751	−	0.252449i	0.0200205	−	0.0346765i	0.875862	+	0.482562i	$0.160294\pi$
$54$		0			0
$55$	−4.64575			−0.626433
$56$	2.64575			0.353553
$57$		0			0
$58$		0			0
$59$	4.64575	−	8.04668i	0.604825	−	1.04759i	−0.387254	−	0.921973i	$-0.626576\pi$
$59$	4.64575	−	8.04668i	0.604825	−	1.04759i	0.992079	−	0.125615i	$-0.0400904\pi$
$60$		0			0
$61$	−5.64575	−	9.77873i	−0.722864	−	1.25204i	−0.959847	−	0.280524i	$-0.909492\pi$
$61$	−5.64575	−	9.77873i	−0.722864	−	1.25204i	0.236983	−	0.971514i	$-0.423842\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	0.322876	+	0.559237i	0.0400478	+	0.0693648i
$66$		0			0
$67$	−2.35425	+	4.07768i	−0.287617	+	0.498168i	−0.973241	−	0.229789i	$-0.926196\pi$
$67$	−2.35425	+	4.07768i	−0.287617	+	0.498168i	0.685623	+	0.727957i	$0.259530\pi$
$68$	−1.64575	−	2.85052i	−0.199577	−	0.345677i
$69$		0			0
$70$	1.32288	−	2.29129i	0.158114	−	0.273861i
$71$	−2.70850			−0.321440			−0.160720	−	0.987000i	$-0.551382\pi$
$71$	−2.70850			−0.321440			−0.160720	+	0.987000i	$0.551382\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	2.96863	−	5.14181i	0.345096	−	0.597724i
$75$		0			0
$76$	−4.29150			−0.492269
$77$	−6.14575	+	10.6448i	−0.700373	+	1.21308i
$78$		0			0
$79$	−5.64575	−	9.77873i	−0.635197	−	1.10019i	−0.986473	−	0.163921i	$-0.947586\pi$
$79$	−5.64575	−	9.77873i	−0.635197	−	1.10019i	0.351277	−	0.936272i	$-0.385748\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−0.677124	−	1.17281i	−0.0747759	−	0.129516i
$83$	15.2915			1.67846			0.839230	−	0.543776i	$-0.183006\pi$
$83$	15.2915			1.67846			0.839230	+	0.543776i	$0.183006\pi$
$84$		0			0
$85$	−3.29150			−0.357014
$86$	−5.64575	−	9.77873i	−0.608797	−	1.05447i
$87$		0			0
$88$	−2.32288	+	4.02334i	−0.247619	+	0.428889i
$89$	−3.29150	−	5.70105i	−0.348899	−	0.604310i	0.637156	−	0.770735i	$-0.280111\pi$
$89$	−3.29150	−	5.70105i	−0.348899	−	0.604310i	−0.986054	+	0.166425i	$0.946778\pi$
$90$		0			0
$91$	1.70850			0.179099
$92$	3.00000			0.312772
$93$		0			0
$94$	4.79150	−	8.29913i	0.494206	−	0.855989i
$95$	−2.14575	+	3.71655i	−0.220149	+	0.381310i
$96$		0			0
$97$	−4.00000			−0.406138			−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000			−0.406138			−0.203069	+	0.979164i	$0.565092\pi$
$98$	−3.50000	−	6.06218i	−0.353553	−	0.612372i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$		0			0
$103$	−8.64575	−	14.9749i	−0.851891	−	1.47552i	−0.879499	−	0.475900i	$-0.842122\pi$
$103$	−8.64575	−	14.9749i	−0.851891	−	1.47552i	0.0276082	−	0.999619i	$-0.491211\pi$
$104$	0.645751			0.0633211
$105$		0			0
$106$	−0.291503			−0.0283132
$107$	7.93725	+	13.7477i	0.767323	+	1.32904i	0.939009	+	0.343891i	$0.111745\pi$
$107$	7.93725	+	13.7477i	0.767323	+	1.32904i	−0.171686	+	0.985152i	$0.554922\pi$
$108$		0			0
$109$	−10.2915	+	17.8254i	−0.985747	+	1.70736i	−0.347179	+	0.937799i	$0.612860\pi$
$109$	−10.2915	+	17.8254i	−0.985747	+	1.70736i	−0.638568	+	0.769565i	$0.720473\pi$
$110$	2.32288	+	4.02334i	0.221478	+	0.383610i
$111$		0			0
$112$	−1.32288	−	2.29129i	−0.125000	−	0.216506i
$113$	−12.5830			−1.18371			−0.591855	−	0.806045i	$-0.701604\pi$
$113$	−12.5830			−1.18371			−0.591855	+	0.806045i	$0.701604\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$		0			0
$117$		0			0
$118$	−9.29150			−0.855352
$119$	−4.35425	+	7.54178i	−0.399153	+	0.691354i
$120$		0			0
$121$	−5.29150	−	9.16515i	−0.481046	−	0.833196i
$122$	−5.64575	+	9.77873i	−0.511142	+	0.885324i
$123$		0			0
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	9.35425			0.830055			0.415028	−	0.909809i	$-0.363772\pi$
$127$	9.35425			0.830055			0.415028	+	0.909809i	$0.363772\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	0.322876	−	0.559237i	0.0283181	−	0.0490483i
$131$	2.32288	+	4.02334i	0.202951	+	0.351521i	0.949478	−	0.313834i	$-0.101614\pi$
$131$	2.32288	+	4.02334i	0.202951	+	0.351521i	−0.746527	+	0.665355i	$0.768280\pi$
$132$		0			0
$133$	5.67712	+	9.83307i	0.492269	+	0.852635i
$134$	4.70850			0.406752
$135$		0			0
$136$	−1.64575	+	2.85052i	−0.141122	+	0.244430i
$137$	−7.93725	+	13.7477i	−0.678125	+	1.17455i	0.297419	+	0.954747i	$0.403874\pi$
$137$	−7.93725	+	13.7477i	−0.678125	+	1.17455i	−0.975545	+	0.219801i	$0.929459\pi$
$138$		0			0
$139$	−10.5830			−0.897639			−0.448819	−	0.893622i	$-0.648155\pi$
$139$	−10.5830			−0.897639			−0.448819	+	0.893622i	$0.648155\pi$
$140$	−2.64575			−0.223607
$141$		0			0
$142$	1.35425	+	2.34563i	0.113646	+	0.196841i
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$		0			0
$145$		0			0
$146$	2.00000			0.165521
$147$		0			0
$148$	−5.93725			−0.488039
$149$	−10.9373	−	18.9439i	−0.896015	−	1.55194i	−0.832544	−	0.553959i	$-0.813116\pi$
$149$	−10.9373	−	18.9439i	−0.896015	−	1.55194i	−0.0634711	−	0.997984i	$-0.520217\pi$
$150$		0			0
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	0.426948	+	0.904276i	$0.359589\pi$
$151$	−7.00000	+	12.1244i	−0.569652	+	0.986666i	−0.996600	+	0.0823900i	$0.973745\pi$
$152$	2.14575	+	3.71655i	0.174043	+	0.301452i
$153$		0			0
$154$	12.2915			0.990478
$155$	−2.00000			−0.160644
$156$		0			0
$157$	10.3229	−	17.8797i	0.823855	−	1.42696i	−0.0789359	−	0.996880i	$-0.525152\pi$
$157$	10.3229	−	17.8797i	0.823855	−	1.42696i	0.902791	−	0.430079i	$-0.141514\pi$
$158$	−5.64575	+	9.77873i	−0.449152	+	0.777954i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−3.96863	−	6.87386i	−0.312772	−	0.541736i
$162$		0			0
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	0.665771	−	0.746156i	$-0.268103\pi$
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	−0.677124	+	1.17281i	−0.0528745	+	0.0915814i
$165$		0			0
$166$	−7.64575	−	13.2428i	−0.593425	−	1.02784i
$167$	9.00000			0.696441			0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000			0.696441			0.348220	+	0.937413i	$0.386786\pi$
$168$		0			0
$169$	−12.5830			−0.967923
$170$	1.64575	+	2.85052i	0.126223	+	0.218625i
$171$		0			0
$172$	−5.64575	+	9.77873i	−0.430485	+	0.745621i
$173$	−9.14575	−	15.8409i	−0.695339	−	1.20436i	−0.970066	−	0.242840i	$-0.921921\pi$
$173$	−9.14575	−	15.8409i	−0.695339	−	1.20436i	0.274728	−	0.961522i	$-0.411412\pi$
$174$		0			0
$175$	−1.32288	+	2.29129i	−0.100000	+	0.173205i
$176$	4.64575			0.350187
$177$		0			0
$178$	−3.29150	+	5.70105i	−0.246709	+	0.427312i
$179$	12.9686	−	22.4623i	0.969321	−	1.67891i	0.271792	−	0.962356i	$-0.412384\pi$
$179$	12.9686	−	22.4623i	0.969321	−	1.67891i	0.697529	−	0.716557i	$-0.254283\pi$
$180$		0			0
$181$	−0.708497			−0.0526622			−0.0263311	−	0.999653i	$-0.508382\pi$
$181$	−0.708497			−0.0526622			−0.0263311	+	0.999653i	$0.508382\pi$
$182$	−0.854249	−	1.47960i	−0.0633211	−	0.109675i
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	−2.96863	+	5.14181i	−0.218258	+	0.378034i
$186$		0			0
$187$	−7.64575	−	13.2428i	−0.559113	−	0.968412i
$188$	−9.58301			−0.698912
$189$		0			0
$190$	4.29150			0.311338
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	3.93725	−	6.81952i	0.283410	−	0.490880i	−0.688813	−	0.724939i	$-0.741868\pi$
$193$	3.93725	−	6.81952i	0.283410	−	0.490880i	0.972222	+	0.234059i	$0.0752010\pi$
$194$	2.00000	+	3.46410i	0.143592	+	0.248708i
$195$		0			0
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	6.29150			0.448251			0.224126	−	0.974560i	$-0.428047\pi$
$197$	6.29150			0.448251			0.224126	+	0.974560i	$0.428047\pi$
$198$		0			0
$199$	−8.93725	+	15.4798i	−0.633545	+	1.09733i	0.353276	+	0.935519i	$0.385068\pi$
$199$	−8.93725	+	15.4798i	−0.633545	+	1.09733i	−0.986821	+	0.161813i	$0.948266\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	−12.0000			−0.844317
$203$		0			0
$204$		0			0
$205$	0.677124	+	1.17281i	0.0472924	+	0.0819129i
$206$	−8.64575	+	14.9749i	−0.602378	+	1.04335i
$207$		0			0
$208$	−0.322876	−	0.559237i	−0.0223874	−	0.0387761i
$209$	−19.9373			−1.37909
$210$		0			0
$211$	8.29150			0.570811			0.285405	−	0.958407i	$-0.407872\pi$
$211$	8.29150			0.570811			0.285405	+	0.958407i	$0.407872\pi$
$212$	0.145751	+	0.252449i	0.0100102	+	0.0173382i
$213$		0			0
$214$	7.93725	−	13.7477i	0.542580	−	0.939775i
$215$	5.64575	+	9.77873i	0.385037	+	0.666904i
$216$		0			0
$217$	−2.64575	+	4.58258i	−0.179605	+	0.311086i
$218$	20.5830			1.39406
$219$		0			0
$220$	2.32288	−	4.02334i	0.156608	−	0.271253i
$221$	−1.06275	+	1.84073i	−0.0714880	+	0.123821i
$222$		0			0
$223$	5.29150			0.354345			0.177173	−	0.984180i	$-0.443305\pi$
$223$	5.29150			0.354345			0.177173	+	0.984180i	$0.443305\pi$
$224$	−1.32288	+	2.29129i	−0.0883883	+	0.153093i
$225$		0			0
$226$	6.29150	+	10.8972i	0.418505	+	0.724871i
$227$	−1.64575	+	2.85052i	−0.109232	+	0.189196i	−0.915459	−	0.402410i	$-0.868173\pi$
$227$	−1.64575	+	2.85052i	−0.109232	+	0.189196i	0.806227	+	0.591606i	$0.201506\pi$
$228$		0			0
$229$	−8.64575	−	14.9749i	−0.571327	−	0.989568i	−0.996430	−	0.0844228i	$-0.973095\pi$
$229$	−8.64575	−	14.9749i	−0.571327	−	0.989568i	0.425103	−	0.905145i	$-0.360238\pi$
$230$	−3.00000			−0.197814
$231$		0			0
$232$		0			0
$233$	−1.93725	−	3.35542i	−0.126914	−	0.219821i	0.795566	−	0.605867i	$-0.207174\pi$
$233$	−1.93725	−	3.35542i	−0.126914	−	0.219821i	−0.922479	+	0.386046i	$0.873840\pi$
$234$		0			0
$235$	−4.79150	+	8.29913i	−0.312563	+	0.541375i
$236$	4.64575	+	8.04668i	0.302413	+	0.523794i
$237$		0			0
$238$	8.70850			0.564488
$239$	12.5830			0.813927			0.406963	−	0.913444i	$-0.366588\pi$
$239$	12.5830			0.813927			0.406963	+	0.913444i	$0.366588\pi$
$240$		0			0
$241$	12.7915	−	22.1555i	0.823973	−	1.42716i	−0.0787285	−	0.996896i	$-0.525086\pi$
$241$	12.7915	−	22.1555i	0.823973	−	1.42716i	0.902702	−	0.430267i	$-0.141581\pi$
$242$	−5.29150	+	9.16515i	−0.340151	+	0.589158i
$243$		0			0
$244$	11.2915			0.722864
$245$	3.50000	+	6.06218i	0.223607	+	0.387298i
$246$		0			0
$247$	1.38562	+	2.39997i	0.0881650	+	0.152706i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	13.9373			0.879712			0.439856	−	0.898068i	$-0.355030\pi$
$251$	13.9373			0.879712			0.439856	+	0.898068i	$0.355030\pi$
$252$		0			0
$253$	13.9373			0.876228
$254$	−4.67712	−	8.10102i	−0.293469	−	0.508303i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.6458	−	23.6351i	−0.851199	−	1.47432i	−0.880127	−	0.474738i	$-0.842543\pi$
$257$	−13.6458	−	23.6351i	−0.851199	−	1.47432i	0.0289287	−	0.999581i	$-0.490790\pi$
$258$		0			0
$259$	7.85425	+	13.6040i	0.488039	+	0.845309i
$260$	−0.645751			−0.0400478
$261$		0			0
$262$	2.32288	−	4.02334i	0.143508	−	0.248563i
$263$	3.29150	−	5.70105i	0.202963	−	0.351542i	−0.746519	−	0.665364i	$-0.768276\pi$
$263$	3.29150	−	5.70105i	0.202963	−	0.351542i	0.949482	+	0.313822i	$0.101610\pi$
$264$		0			0
$265$	0.291503			0.0179069
$266$	5.67712	−	9.83307i	0.348087	−	0.602904i
$267$		0			0
$268$	−2.35425	−	4.07768i	−0.143809	−	0.249084i
$269$	10.9373	−	18.9439i	0.666856	−	1.15503i	−0.311922	−	0.950108i	$-0.600973\pi$
$269$	10.9373	−	18.9439i	0.666856	−	1.15503i	0.978778	−	0.204921i	$-0.0656938\pi$
$270$		0			0
$271$	8.58301	+	14.8662i	0.521380	+	0.903057i	0.999691	+	0.0248665i	$0.00791608\pi$
$271$	8.58301	+	14.8662i	0.521380	+	0.903057i	−0.478310	+	0.878191i	$0.658751\pi$
$272$	3.29150			0.199577
$273$		0			0
$274$	15.8745			0.959014
$275$	−2.32288	−	4.02334i	−0.140075	−	0.242616i
$276$		0			0
$277$	−13.2915	+	23.0216i	−0.798609	+	1.38323i	0.121913	+	0.992541i	$0.461097\pi$
$277$	−13.2915	+	23.0216i	−0.798609	+	1.38323i	−0.920522	+	0.390691i	$0.872236\pi$
$278$	5.29150	+	9.16515i	0.317363	+	0.549689i
$279$		0			0
$280$	1.32288	+	2.29129i	0.0790569	+	0.136931i
$281$	−26.5203			−1.58207			−0.791033	−	0.611773i	$-0.790456\pi$
$281$	−26.5203			−1.58207			−0.791033	+	0.611773i	$0.790456\pi$
$282$		0			0
$283$	3.93725	−	6.81952i	0.234045	−	0.405379i	−0.724949	−	0.688802i	$-0.758137\pi$
$283$	3.93725	−	6.81952i	0.234045	−	0.405379i	0.958995	+	0.283424i	$0.0914702\pi$
$284$	1.35425	−	2.34563i	0.0803599	−	0.139187i
$285$		0			0
$286$	3.00000			0.177394
$287$	3.58301			0.211498
$288$		0			0
$289$	3.08301	+	5.33992i	0.181353	+	0.314113i
$290$		0			0
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	11.7085			0.684018			0.342009	−	0.939697i	$-0.388893\pi$
$293$	11.7085			0.684018			0.342009	+	0.939697i	$0.388893\pi$
$294$		0			0
$295$	9.29150			0.540972
$296$	2.96863	+	5.14181i	0.172548	+	0.298862i
$297$		0			0
$298$	−10.9373	+	18.9439i	−0.633578	+	1.09739i
$299$	−0.968627	−	1.67771i	−0.0560171	−	0.0970245i
$300$		0			0
$301$	29.8745			1.72194
$302$	14.0000			0.805609
$303$		0			0
$304$	2.14575	−	3.71655i	0.123067	−	0.213159i
$305$	5.64575	−	9.77873i	0.323275	−	0.559928i
$306$		0			0
$307$	−12.7085			−0.725312			−0.362656	−	0.931923i	$-0.618130\pi$
$307$	−12.7085			−0.725312			−0.362656	+	0.931923i	$0.618130\pi$
$308$	−6.14575	−	10.6448i	−0.350187	−	0.606541i
$309$		0			0
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	10.9373	−	18.9439i	0.620195	−	1.07421i	−0.369254	−	0.929328i	$-0.620387\pi$
$311$	10.9373	−	18.9439i	0.620195	−	1.07421i	0.989449	−	0.144880i	$-0.0462798\pi$
$312$		0			0
$313$	0.937254	+	1.62337i	0.0529767	+	0.0917584i	0.891298	−	0.453419i	$-0.149796\pi$
$313$	0.937254	+	1.62337i	0.0529767	+	0.0917584i	−0.838321	+	0.545177i	$0.816462\pi$
$314$	−20.6458			−1.16511
$315$		0			0
$316$	11.2915			0.635197
$317$	5.70850	+	9.88741i	0.320621	+	0.555332i	0.980616	−	0.195938i	$-0.0627750\pi$
$317$	5.70850	+	9.88741i	0.320621	+	0.555332i	−0.659995	+	0.751270i	$0.729442\pi$
$318$		0			0
$319$		0			0
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−3.96863	+	6.87386i	−0.221163	+	0.383065i
$323$	−14.1255			−0.785963
$324$		0			0
$325$	−0.322876	+	0.559237i	−0.0179099	+	0.0310209i
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$		0			0
$328$	1.35425			0.0747759
$329$	12.6771	+	21.9574i	0.698912	+	1.21055i
$330$		0			0
$331$	11.7288	+	20.3148i	0.644671	+	1.11660i	0.984377	+	0.176071i	$0.0563389\pi$
$331$	11.7288	+	20.3148i	0.644671	+	1.11660i	−0.339707	+	0.940531i	$0.610328\pi$
$332$	−7.64575	+	13.2428i	−0.419615	+	0.726795i
$333$		0			0
$334$	−4.50000	−	7.79423i	−0.246229	−	0.426481i
$335$	−4.70850			−0.257253
$336$		0			0
$337$	11.2915			0.615087			0.307544	−	0.951534i	$-0.400493\pi$
$337$	11.2915			0.615087			0.307544	+	0.951534i	$0.400493\pi$
$338$	6.29150	+	10.8972i	0.342213	+	0.592730i
$339$		0			0
$340$	1.64575	−	2.85052i	0.0892534	−	0.154591i
$341$	−4.64575	−	8.04668i	−0.251582	−	0.435752i
$342$		0			0
$343$	18.5203			1.00000
$344$	11.2915			0.608797
$345$		0			0
$346$	−9.14575	+	15.8409i	−0.491679	+	0.851612i
$347$	4.64575	−	8.04668i	0.249397	−	0.431968i	−0.713962	−	0.700185i	$-0.753101\pi$
$347$	4.64575	−	8.04668i	0.249397	−	0.431968i	0.963359	+	0.268217i	$0.0864343\pi$
$348$		0			0
$349$	1.41699			0.0758500			0.0379250	−	0.999281i	$-0.487925\pi$
$349$	1.41699			0.0758500			0.0379250	+	0.999281i	$0.487925\pi$
$350$	2.64575			0.141421
$351$		0			0
$352$	−2.32288	−	4.02334i	−0.123810	−	0.214445i
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	−0.661004	−	0.750382i	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$		0			0
$355$	−1.35425	−	2.34563i	−0.0718761	−	0.124493i
$356$	6.58301			0.348899
$357$		0			0
$358$	−25.9373			−1.37083
$359$	9.29150	+	16.0934i	0.490387	+	0.849375i	0.999939	−	0.0110651i	$-0.00352220\pi$
$359$	9.29150	+	16.0934i	0.490387	+	0.849375i	−0.509552	+	0.860440i	$0.670189\pi$
$360$		0			0
$361$	0.291503	−	0.504897i	0.0153422	−	0.0265735i
$362$	0.354249	+	0.613577i	0.0186189	+	0.0322489i
$363$		0			0
$364$	−0.854249	+	1.47960i	−0.0447748	+	0.0775522i
$365$	−2.00000			−0.104685
$366$		0			0
$367$	13.3229	−	23.0759i	0.695448	−	1.20455i	−0.274581	−	0.961564i	$-0.588539\pi$
$367$	13.3229	−	23.0759i	0.695448	−	1.20455i	0.970029	−	0.242988i	$-0.0781276\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$		0			0
$370$	5.93725			0.308663
$371$	0.385622	−	0.667916i	0.0200205	−	0.0346765i
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	−7.64575	+	13.2428i	−0.395352	+	0.684770i
$375$		0			0
$376$	4.79150	+	8.29913i	0.247103	+	0.427995i
$377$		0			0
$378$		0			0
$379$	1.70850			0.0877596			0.0438798	−	0.999037i	$-0.486028\pi$
$379$	1.70850			0.0877596			0.0438798	+	0.999037i	$0.486028\pi$
$380$	−2.14575	−	3.71655i	−0.110075	−	0.190655i
$381$		0			0
$382$	3.00000	−	5.19615i	0.153493	−	0.265858i
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$		0			0
$385$	−12.2915			−0.626433
$386$	−7.87451			−0.400802
$387$		0			0
$388$	2.00000	−	3.46410i	0.101535	−	0.175863i
$389$	7.35425	−	12.7379i	0.372875	−	0.645839i	−0.617131	−	0.786860i	$-0.711705\pi$
$389$	7.35425	−	12.7379i	0.372875	−	0.645839i	0.990007	+	0.141021i	$0.0450386\pi$
$390$		0			0
$391$	9.87451			0.499375
$392$	7.00000			0.353553
$393$		0			0
$394$	−3.14575	−	5.44860i	−0.158481	−	0.274497i
$395$	5.64575	−	9.77873i	0.284069	−	0.492021i
$396$		0			0
$397$	11.2915	+	19.5575i	0.566704	+	0.981561i	0.996889	+	0.0788197i	$0.0251151\pi$
$397$	11.2915	+	19.5575i	0.566704	+	0.981561i	−0.430185	+	0.902741i	$0.641552\pi$
$398$	17.8745			0.895968
$399$		0			0
$400$	1.00000			0.0500000
$401$	8.61438	+	14.9205i	0.430182	+	0.745096i	0.996889	−	0.0788231i	$-0.0251162\pi$
$401$	8.61438	+	14.9205i	0.430182	+	0.745096i	−0.566707	+	0.823919i	$0.691783\pi$
$402$		0			0
$403$	−0.645751	+	1.11847i	−0.0321672	+	0.0557152i
$404$	6.00000	+	10.3923i	0.298511	+	0.517036i
$405$		0			0
$406$		0			0
$407$	−27.5830			−1.36724
$408$		0			0
$409$	−16.2915	+	28.2177i	−0.805563	+	1.39528i	0.110347	+	0.993893i	$0.464804\pi$
$409$	−16.2915	+	28.2177i	−0.805563	+	1.39528i	−0.915910	+	0.401383i	$0.868530\pi$
$410$	0.677124	−	1.17281i	0.0334408	−	0.0579211i
$411$		0			0
$412$	17.2915			0.851891
$413$	12.2915	−	21.2895i	0.604825	−	1.04759i
$414$		0			0
$415$	7.64575	+	13.2428i	0.375315	+	0.650065i
$416$	−0.322876	+	0.559237i	−0.0158303	+	0.0274189i
$417$		0			0
$418$	9.96863	+	17.2662i	0.487581	+	0.844516i
$419$	−22.0627			−1.07784			−0.538918	−	0.842358i	$-0.681167\pi$
$419$	−22.0627			−1.07784			−0.538918	+	0.842358i	$0.681167\pi$
$420$		0			0
$421$	−0.125492			−0.00611611			−0.00305806	−	0.999995i	$-0.500973\pi$
$421$	−0.125492			−0.00611611			−0.00305806	+	0.999995i	$0.500973\pi$
$422$	−4.14575	−	7.18065i	−0.201812	−	0.349549i
$423$		0			0
$424$	0.145751	−	0.252449i	0.00707831	−	0.0122600i
$425$	−1.64575	−	2.85052i	−0.0798307	−	0.138271i
$426$		0			0
$427$	−14.9373	−	25.8721i	−0.722864	−	1.25204i
$428$	−15.8745			−0.767323
$429$		0			0
$430$	5.64575	−	9.77873i	0.272262	−	0.471572i
$431$	1.06275	−	1.84073i	0.0511907	−	0.0886649i	−0.839295	−	0.543677i	$-0.817032\pi$
$431$	1.06275	−	1.84073i	0.0511907	−	0.0886649i	0.890485	+	0.455012i	$0.150365\pi$
$432$		0			0
$433$	8.00000			0.384455			0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000			0.384455			0.192228	+	0.981350i	$0.438429\pi$
$434$	5.29150			0.254000
$435$		0			0
$436$	−10.2915	−	17.8254i	−0.492874	−	0.853682i
$437$	6.43725	−	11.1497i	0.307936	−	0.533360i
$438$		0			0
$439$	−16.5830	−	28.7226i	−0.791464	−	1.37086i	−0.925061	−	0.379820i	$-0.875986\pi$
$439$	−16.5830	−	28.7226i	−0.791464	−	1.37086i	0.133597	−	0.991036i	$-0.457347\pi$
$440$	−4.64575			−0.221478
$441$		0			0
$442$	2.12549			0.101099
$443$	19.6458	+	34.0274i	0.933398	+	1.61669i	0.777466	+	0.628925i	$0.216505\pi$
$443$	19.6458	+	34.0274i	0.933398	+	1.61669i	0.155931	+	0.987768i	$0.450162\pi$
$444$		0			0
$445$	3.29150	−	5.70105i	0.156032	−	0.270256i
$446$	−2.64575	−	4.58258i	−0.125280	−	0.216991i
$447$		0			0
$448$	2.64575			0.125000
$449$	−23.8118			−1.12375			−0.561873	−	0.827223i	$-0.689919\pi$
$449$	−23.8118			−1.12375			−0.561873	+	0.827223i	$0.689919\pi$
$450$		0			0
$451$	−3.14575	+	5.44860i	−0.148128	+	0.256565i
$452$	6.29150	−	10.8972i	0.295927	−	0.512561i
$453$		0			0
$454$	3.29150			0.154478
$455$	0.854249	+	1.47960i	0.0400478	+	0.0693648i
$456$		0			0
$457$	3.35425	+	5.80973i	0.156905	+	0.271768i	0.933751	−	0.357923i	$-0.116515\pi$
$457$	3.35425	+	5.80973i	0.156905	+	0.271768i	−0.776846	+	0.629691i	$0.783182\pi$
$458$	−8.64575	+	14.9749i	−0.403989	+	0.699730i
$459$		0			0
$460$	1.50000	+	2.59808i	0.0699379	+	0.121136i
$461$	−25.1660			−1.17210			−0.586049	−	0.810276i	$-0.699317\pi$
$461$	−25.1660			−1.17210			−0.586049	+	0.810276i	$0.699317\pi$
$462$		0			0
$463$	0.0627461			0.00291606			0.00145803	−	0.999999i	$-0.499536\pi$
$463$	0.0627461			0.00291606			0.00145803	+	0.999999i	$0.499536\pi$
$464$		0			0
$465$		0			0
$466$	−1.93725	+	3.35542i	−0.0897416	+	0.155437i
$467$	4.35425	+	7.54178i	0.201491	+	0.348992i	0.949009	−	0.315249i	$-0.102088\pi$
$467$	4.35425	+	7.54178i	0.201491	+	0.348992i	−0.747518	+	0.664241i	$0.768755\pi$
$468$		0			0
$469$	−6.22876	+	10.7885i	−0.287617	+	0.498168i
$470$	9.58301			0.442031
$471$		0			0
$472$	4.64575	−	8.04668i	0.213838	−	0.370378i
$473$	−26.2288	+	45.4295i	−1.20600	+	2.08885i
$474$		0			0
$475$	−4.29150			−0.196908
$476$	−4.35425	−	7.54178i	−0.199577	−	0.345677i
$477$		0			0
$478$	−6.29150	−	10.8972i	−0.287767	−	0.498426i
$479$	−12.8745	+	22.2993i	−0.588251	+	1.01888i	0.406210	+	0.913780i	$0.366850\pi$
$479$	−12.8745	+	22.2993i	−0.588251	+	1.01888i	−0.994462	+	0.105101i	$0.966483\pi$
$480$		0			0
$481$	1.91699	+	3.32033i	0.0874074	+	0.151394i
$482$	−25.5830			−1.16527
$483$		0			0
$484$	10.5830			0.481046
$485$	−2.00000	−	3.46410i	−0.0908153	−	0.157297i
$486$		0			0
$487$	3.93725	−	6.81952i	0.178414	−	0.309022i	−0.762923	−	0.646489i	$-0.776237\pi$
$487$	3.93725	−	6.81952i	0.178414	−	0.309022i	0.941337	+	0.337467i	$0.109570\pi$
$488$	−5.64575	−	9.77873i	−0.255571	−	0.442662i
$489$		0			0
$490$	3.50000	−	6.06218i	0.158114	−	0.273861i
$491$	−8.12549			−0.366698			−0.183349	−	0.983048i	$-0.558694\pi$
$491$	−8.12549			−0.366698			−0.183349	+	0.983048i	$0.558694\pi$
$492$		0			0
$493$		0			0
$494$	1.38562	−	2.39997i	0.0623421	−	0.107980i
$495$		0			0
$496$	2.00000			0.0898027
$497$	−7.16601			−0.321440
$498$		0			0
$499$	−7.29150	−	12.6293i	−0.326412	−	0.565363i	0.655385	−	0.755295i	$-0.272507\pi$
$499$	−7.29150	−	12.6293i	−0.326412	−	0.565363i	−0.981797	+	0.189932i	$0.939173\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−6.96863	−	12.0700i	−0.311025	−	0.538711i
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	−6.96863	−	12.0700i	−0.309793	−	0.536578i
$507$		0			0
$508$	−4.67712	+	8.10102i	−0.207514	+	0.359425i
$509$	20.5203	+	35.5421i	0.909544	+	1.57538i	0.814698	+	0.579885i	$0.196903\pi$
$509$	20.5203	+	35.5421i	0.909544	+	1.57538i	0.0948464	+	0.995492i	$0.469764\pi$
$510$		0			0
$511$	−2.64575	+	4.58258i	−0.117041	+	0.202721i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−13.6458	+	23.6351i	−0.601888	+	1.04250i
$515$	8.64575	−	14.9749i	0.380977	−	0.659872i
$516$		0			0
$517$	−44.5203			−1.95800
$518$	7.85425	−	13.6040i	0.345096	−	0.597724i
$519$		0			0
$520$	0.322876	+	0.559237i	0.0141590	+	0.0245242i
$521$	−8.61438	+	14.9205i	−0.377403	+	0.653681i	−0.990684	−	0.136184i	$-0.956516\pi$
$521$	−8.61438	+	14.9205i	−0.377403	+	0.653681i	0.613281	+	0.789865i	$0.289849\pi$
$522$		0			0
$523$	−7.58301	−	13.1342i	−0.331582	−	0.574316i	0.651240	−	0.758871i	$-0.274249\pi$
$523$	−7.58301	−	13.1342i	−0.331582	−	0.574316i	−0.982822	+	0.184555i	$0.940916\pi$
$524$	−4.64575			−0.202951
$525$		0			0
$526$	−6.58301			−0.287033
$527$	−3.29150	−	5.70105i	−0.143380	−	0.248342i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−0.145751	−	0.252449i	−0.00633103	−	0.0109657i
$531$		0			0
$532$	−11.3542			−0.492269
$533$	0.874508			0.0378791
$534$		0			0
$535$	−7.93725	+	13.7477i	−0.343157	+	0.594366i
$536$	−2.35425	+	4.07768i	−0.101688	+	0.176129i
$537$		0			0
$538$	−21.8745			−0.943077
$539$	−16.2601	+	28.1634i	−0.700373	+	1.21308i
$540$		0			0
$541$	−21.2288	−	36.7693i	−0.912696	−	1.58084i	−0.810241	−	0.586097i	$-0.800664\pi$
$541$	−21.2288	−	36.7693i	−0.912696	−	1.58084i	−0.102455	−	0.994738i	$-0.532670\pi$
$542$	8.58301	−	14.8662i	0.368672	−	0.638558i
$543$		0			0
$544$	−1.64575	−	2.85052i	−0.0705610	−	0.122215i
$545$	−20.5830			−0.881679
$546$		0			0
$547$	−19.2915			−0.824845			−0.412423	−	0.910993i	$-0.635317\pi$
$547$	−19.2915			−0.824845			−0.412423	+	0.910993i	$0.635317\pi$
$548$	−7.93725	−	13.7477i	−0.339063	−	0.587274i
$549$		0			0
$550$	−2.32288	+	4.02334i	−0.0990478	+	0.171556i
$551$		0			0
$552$		0			0
$553$	−14.9373	−	25.8721i	−0.635197	−	1.10019i
$554$	26.5830			1.12940
$555$		0			0
$556$	5.29150	−	9.16515i	0.224410	−	0.388689i
$557$	19.0203	−	32.9441i	0.805914	−	1.39588i	−0.109758	−	0.993958i	$-0.535008\pi$
$557$	19.0203	−	32.9441i	0.805914	−	1.39588i	0.915672	−	0.401926i	$-0.131659\pi$
$558$		0			0
$559$	7.29150			0.308398
$560$	1.32288	−	2.29129i	0.0559017	−	0.0968246i
$561$		0			0
$562$	13.2601	+	22.9672i	0.559345	+	0.968814i
$563$	−15.5830	+	26.9906i	−0.656745	+	1.13752i	0.324708	+	0.945814i	$0.394734\pi$
$563$	−15.5830	+	26.9906i	−0.656745	+	1.13752i	−0.981453	+	0.191702i	$0.938599\pi$
$564$		0			0
$565$	−6.29150	−	10.8972i	−0.264686	−	0.458449i
$566$	−7.87451			−0.330990
$567$		0			0
$568$	−2.70850			−0.113646
$569$	5.90588	+	10.2293i	0.247587	+	0.428834i	0.962856	−	0.270016i	$-0.0870289\pi$
$569$	5.90588	+	10.2293i	0.247587	+	0.428834i	−0.715268	+	0.698850i	$0.753696\pi$
$570$		0			0
$571$	4.70850	−	8.15536i	0.197044	−	0.341291i	−0.750524	−	0.660843i	$-0.770199\pi$
$571$	4.70850	−	8.15536i	0.197044	−	0.341291i	0.947569	+	0.319552i	$0.103532\pi$
$572$	−1.50000	−	2.59808i	−0.0627182	−	0.108631i
$573$		0			0
$574$	−1.79150	−	3.10297i	−0.0747759	−	0.129516i
$575$	3.00000			0.125109
$576$		0			0
$577$	−7.58301	+	13.1342i	−0.315685	+	0.546782i	−0.979583	−	0.201041i	$-0.935567\pi$
$577$	−7.58301	+	13.1342i	−0.315685	+	0.546782i	0.663898	+	0.747823i	$0.268901\pi$
$578$	3.08301	−	5.33992i	0.128236	−	0.222111i
$579$		0			0
$580$		0			0
$581$	40.4575			1.67846
$582$		0			0
$583$	0.677124	+	1.17281i	0.0280436	+	0.0485730i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−5.85425	−	10.1399i	−0.241837	−	0.418874i
$587$	−12.5830			−0.519356			−0.259678	−	0.965695i	$-0.583616\pi$
$587$	−12.5830			−0.519356			−0.259678	+	0.965695i	$0.583616\pi$
$588$		0			0
$589$	−8.58301			−0.353657
$590$	−4.64575	−	8.04668i	−0.191263	−	0.331276i
$591$		0			0
$592$	2.96863	−	5.14181i	0.122010	−	0.211327i
$593$	−1.06275	−	1.84073i	−0.0436418	−	0.0755897i	0.843379	−	0.537318i	$-0.180563\pi$
$593$	−1.06275	−	1.84073i	−0.0436418	−	0.0755897i	−0.887021	+	0.461729i	$0.847229\pi$
$594$		0			0
$595$	−8.70850			−0.357014
$596$	21.8745			0.896015
$597$		0			0
$598$	−0.968627	+	1.67771i	−0.0396101	+	0.0686067i
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$		0			0
$601$	−11.1660			−0.455471			−0.227736	−	0.973723i	$-0.573132\pi$
$601$	−11.1660			−0.455471			−0.227736	+	0.973723i	$0.573132\pi$
$602$	−14.9373	−	25.8721i	−0.608797	−	1.05447i
$603$		0			0
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	5.29150	−	9.16515i	0.215130	−	0.372616i
$606$		0			0
$607$	5.38562	+	9.32817i	0.218596	+	0.378619i	0.954379	−	0.298598i	$-0.0965191\pi$
$607$	5.38562	+	9.32817i	0.218596	+	0.378619i	−0.735783	+	0.677217i	$0.763186\pi$
$608$	−4.29150			−0.174043
$609$		0			0
$610$	−11.2915			−0.457180
$611$	3.09412	+	5.35917i	0.125175	+	0.216809i
$612$		0			0
$613$	5.67712	−	9.83307i	0.229297	−	0.397154i	−0.728303	−	0.685255i	$-0.759691\pi$
$613$	5.67712	−	9.83307i	0.229297	−	0.397154i	0.957600	+	0.288101i	$0.0930240\pi$
$614$	6.35425	+	11.0059i	0.256437	+	0.444161i
$615$		0			0
$616$	−6.14575	+	10.6448i	−0.247619	+	0.428889i
$617$	15.2915			0.615613			0.307806	−	0.951449i	$-0.400405\pi$
$617$	15.2915			0.615613			0.307806	+	0.951449i	$0.400405\pi$
$618$		0			0
$619$	2.43725	−	4.22145i	0.0979615	−	0.169674i	−0.812879	−	0.582432i	$-0.802101\pi$
$619$	2.43725	−	4.22145i	0.0979615	−	0.169674i	0.910841	+	0.412758i	$0.135434\pi$
$620$	1.00000	−	1.73205i	0.0401610	−	0.0695608i
$621$		0			0
$622$	−21.8745			−0.877088
$623$	−8.70850	−	15.0836i	−0.348899	−	0.604310i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.937254	−	1.62337i	0.0374602	−	0.0648830i
$627$		0			0
$628$	10.3229	+	17.8797i	0.411928	+	0.713480i
$629$	−19.5425			−0.779210
$630$		0			0
$631$	−29.7490			−1.18429			−0.592145	−	0.805832i	$-0.701719\pi$
$631$	−29.7490			−1.18429			−0.592145	+	0.805832i	$0.701719\pi$
$632$	−5.64575	−	9.77873i	−0.224576	−	0.388977i
$633$		0			0
$634$	5.70850	−	9.88741i	0.226713	−	0.392679i
$635$	4.67712	+	8.10102i	0.185606	+	0.321479i
$636$		0			0
$637$	4.52026			0.179099
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−22.5516	+	39.0606i	−0.890736	+	1.54280i	−0.0517411	+	0.998661i	$0.516477\pi$
$641$	−22.5516	+	39.0606i	−0.890736	+	1.54280i	−0.838995	+	0.544139i	$0.816856\pi$
$642$		0			0
$643$	17.2915			0.681910			0.340955	−	0.940080i	$-0.389250\pi$
$643$	17.2915			0.681910			0.340955	+	0.940080i	$0.389250\pi$
$644$	7.93725			0.312772
$645$		0			0
$646$	7.06275	+	12.2330i	0.277880	+	0.481302i
$647$	14.0830	−	24.3925i	0.553660	−	0.958967i	−0.444346	−	0.895855i	$-0.646564\pi$
$647$	14.0830	−	24.3925i	0.553660	−	0.958967i	0.998006	−	0.0631123i	$-0.0201026\pi$
$648$		0			0
$649$	21.5830	+	37.3829i	0.847207	+	1.46741i
$650$	0.645751			0.0253285
$651$		0			0
$652$	8.00000			0.313304
$653$	18.7288	+	32.4392i	0.732913	+	1.26944i	0.955633	+	0.294560i	$0.0951731\pi$
$653$	18.7288	+	32.4392i	0.732913	+	1.26944i	−0.222720	+	0.974882i	$0.571494\pi$
$654$		0			0
$655$	−2.32288	+	4.02334i	−0.0907623	+	0.157205i
$656$	−0.677124	−	1.17281i	−0.0264373	−	0.0457907i
$657$		0			0
$658$	12.6771	−	21.9574i	0.494206	−	0.855989i
$659$	2.70850			0.105508			0.0527540	−	0.998608i	$-0.483200\pi$
$659$	2.70850			0.105508			0.0527540	+	0.998608i	$0.483200\pi$
$660$		0			0
$661$	−0.708497	+	1.22715i	−0.0275574	+	0.0477307i	−0.879475	−	0.475945i	$-0.842106\pi$
$661$	−0.708497	+	1.22715i	−0.0275574	+	0.0477307i	0.851918	+	0.523675i	$0.175440\pi$
$662$	11.7288	−	20.3148i	0.455851	−	0.789557i
$663$		0			0
$664$	15.2915			0.593425
$665$	−5.67712	+	9.83307i	−0.220149	+	0.381310i
$666$		0			0
$667$		0			0
$668$	−4.50000	+	7.79423i	−0.174110	+	0.301568i
$669$		0			0
$670$	2.35425	+	4.07768i	0.0909526	+	0.157534i
$671$	52.4575			2.02510
$672$		0			0
$673$	−22.5830			−0.870511			−0.435255	−	0.900307i	$-0.643342\pi$
$673$	−22.5830			−0.870511			−0.435255	+	0.900307i	$0.643342\pi$
$674$	−5.64575	−	9.77873i	−0.217466	−	0.376663i
$675$		0			0
$676$	6.29150	−	10.8972i	0.241981	−	0.419123i
$677$	−24.4373	−	42.3266i	−0.939200	−	1.62674i	−0.766968	−	0.641686i	$-0.778235\pi$
$677$	−24.4373	−	42.3266i	−0.939200	−	1.62674i	−0.172232	−	0.985056i	$-0.555098\pi$
$678$		0			0
$679$	−10.5830			−0.406138
$680$	−3.29150			−0.126223
$681$		0			0
$682$	−4.64575	+	8.04668i	−0.177895	+	0.308123i
$683$	−6.58301	+	11.4021i	−0.251892	+	0.436289i	−0.964047	−	0.265733i	$-0.914386\pi$
$683$	−6.58301	+	11.4021i	−0.251892	+	0.436289i	0.712155	+	0.702022i	$0.247719\pi$
$684$		0			0
$685$	−15.8745			−0.606534
$686$	−9.26013	−	16.0390i	−0.353553	−	0.612372i
$687$		0			0
$688$	−5.64575	−	9.77873i	−0.215242	−	0.372811i
$689$	0.0941191	−	0.163019i	0.00358565	−	0.00621053i
$690$		0			0
$691$	17.2915	+	29.9498i	0.657800	+	1.13934i	0.981184	+	0.193075i	$0.0618460\pi$
$691$	17.2915	+	29.9498i	0.657800	+	1.13934i	−0.323384	+	0.946268i	$0.604821\pi$
$692$	18.2915			0.695339
$693$		0			0
$694$	−9.29150			−0.352701
$695$	−5.29150	−	9.16515i	−0.200718	−	0.347654i
$696$		0			0
$697$	−2.22876	+	3.86032i	−0.0844202	+	0.146220i
$698$	−0.708497	−	1.22715i	−0.0268170	−	0.0464484i
$699$		0			0
$700$	−1.32288	−	2.29129i	−0.0500000	−	0.0866025i
$701$	22.4575			0.848209			0.424104	−	0.905613i	$-0.360589\pi$
$701$	22.4575			0.848209			0.424104	+	0.905613i	$0.360589\pi$
$702$		0			0
$703$	−12.7399	+	22.0661i	−0.480493	+	0.832239i
$704$	−2.32288	+	4.02334i	−0.0875467	+	0.151635i
$705$		0			0
$706$	−12.0000			−0.451626
$707$	15.8745	−	27.4955i	0.597022	−	1.03407i
$708$		0			0
$709$	−10.5830	−	18.3303i	−0.397453	−	0.688409i	0.595958	−	0.803016i	$-0.296773\pi$
$709$	−10.5830	−	18.3303i	−0.397453	−	0.688409i	−0.993411	+	0.114607i	$0.963439\pi$
$710$	−1.35425	+	2.34563i	−0.0508240	+	0.0880298i
$711$		0			0
$712$	−3.29150	−	5.70105i	−0.123354	−	0.213656i
$713$	6.00000			0.224702
$714$		0			0
$715$	−3.00000			−0.112194
$716$	12.9686	+	22.4623i	0.484660	+	0.839456i
$717$		0			0
$718$	9.29150	−	16.0934i	0.346756	−	0.600599i
$719$	25.9373	+	44.9246i	0.967296	+	1.67541i	0.703315	+	0.710879i	$0.251703\pi$
$719$	25.9373	+	44.9246i	0.967296	+	1.67541i	0.263982	+	0.964528i	$0.414964\pi$
$720$		0			0
$721$	−22.8745	−	39.6198i	−0.851891	−	1.47552i
$722$	−0.583005			−0.0216972
$723$		0			0
$724$	0.354249	−	0.613577i	0.0131655	−	0.0228034i
$725$		0			0
$726$		0			0
$727$	30.6458			1.13659			0.568294	−	0.822826i	$-0.307604\pi$
$727$	30.6458			1.13659			0.568294	+	0.822826i	$0.307604\pi$
$728$	1.70850			0.0633211
$729$		0			0
$730$	1.00000	+	1.73205i	0.0370117	+	0.0641061i
$731$	−18.5830	+	32.1867i	−0.687317	+	1.19047i
$732$		0			0
$733$	−5.73987	−	9.94175i	−0.212007	−	0.367207i	0.740336	−	0.672237i	$-0.234667\pi$
$733$	−5.73987	−	9.94175i	−0.212007	−	0.367207i	−0.952343	+	0.305031i	$0.901333\pi$
$734$	−26.6458			−0.983513
$735$		0			0
$736$	3.00000			0.110581
$737$	−10.9373	−	18.9439i	−0.402879	−	0.697807i
$738$		0			0
$739$	10.8542	−	18.8001i	0.399280	−	0.691573i	−0.594357	−	0.804201i	$-0.702593\pi$
$739$	10.8542	−	18.8001i	0.399280	−	0.691573i	0.993637	+	0.112628i	$0.0359268\pi$
$740$	−2.96863	−	5.14181i	−0.109129	−	0.189017i
$741$		0			0
$742$	−0.771243			−0.0283132
$743$	−28.7490			−1.05470			−0.527350	−	0.849648i	$-0.676814\pi$
$743$	−28.7490			−1.05470			−0.527350	+	0.849648i	$0.676814\pi$
$744$		0			0
$745$	10.9373	−	18.9439i	0.400710	−	0.694050i
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$		0			0
$748$	15.2915			0.559113
$749$	21.0000	+	36.3731i	0.767323	+	1.32904i
$750$		0			0
$751$	−2.06275	−	3.57278i	−0.0752707	−	0.130373i	0.825933	−	0.563768i	$-0.190649\pi$
$751$	−2.06275	−	3.57278i	−0.0752707	−	0.130373i	−0.901204	+	0.433395i	$0.857315\pi$
$752$	4.79150	−	8.29913i	0.174728	−	0.302638i
$753$		0			0
$754$		0			0
$755$	−14.0000			−0.509512
$756$		0			0
$757$	33.1660			1.20544			0.602720	−	0.797953i	$-0.294084\pi$
$757$	33.1660			1.20544			0.602720	+	0.797953i	$0.294084\pi$
$758$	−0.854249	−	1.47960i	−0.0310277	−	0.0537416i
$759$		0			0
$760$	−2.14575	+	3.71655i	−0.0778346	+	0.134813i
$761$	−21.9686	−	38.0508i	−0.796362	−	1.37934i	−0.921971	−	0.387260i	$-0.873422\pi$
$761$	−21.9686	−	38.0508i	−0.796362	−	1.37934i	0.125609	−	0.992080i	$-0.459912\pi$
$762$		0			0
$763$	−27.2288	+	47.1616i	−0.985747	+	1.70736i
$764$	−6.00000			−0.217072
$765$		0			0
$766$	−10.5000	+	18.1865i	−0.379380	+	0.657106i
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$		0			0
$769$	30.1660			1.08781			0.543907	−	0.839145i	$-0.316944\pi$
$769$	30.1660			1.08781			0.543907	+	0.839145i	$0.316944\pi$
$770$	6.14575	+	10.6448i	0.221478	+	0.383610i
$771$		0			0
$772$	3.93725	+	6.81952i	0.141705	+	0.245440i
$773$	6.43725	−	11.1497i	0.231532	−	0.401025i	−0.726727	−	0.686926i	$-0.758960\pi$
$773$	6.43725	−	11.1497i	0.231532	−	0.401025i	0.958259	+	0.285901i	$0.0922929\pi$
$774$		0			0
$775$	−1.00000	−	1.73205i	−0.0359211	−	0.0622171i
$776$	−4.00000			−0.143592
$777$		0			0
$778$	−14.7085			−0.527325
$779$	2.90588	+	5.03313i	0.104114	+	0.180331i
$780$		0			0
$781$	6.29150	−	10.8972i	0.225128	−	0.389933i
$782$	−4.93725	−	8.55157i	−0.176556	−	0.305804i
$783$		0			0
$784$	−3.50000	−	6.06218i	−0.125000	−	0.216506i
$785$	20.6458			0.736878
$786$		0			0
$787$	19.2288	−	33.3052i	0.685431	−	1.18720i	−0.287870	−	0.957670i	$-0.592947\pi$
$787$	19.2288	−	33.3052i	0.685431	−	1.18720i	0.973301	−	0.229532i	$-0.0737196\pi$
$788$	−3.14575	+	5.44860i	−0.112063	+	0.194098i
$789$		0			0
$790$	−11.2915			−0.401734
$791$	−33.2915			−1.18371
$792$		0			0
$793$	−3.64575	−	6.31463i	−0.129464	−	0.224239i
$794$	11.2915	−	19.5575i	0.400720	−	0.694068i
$795$		0			0
$796$	−8.93725	−	15.4798i	−0.316773	−	0.548666i
$797$	37.7490			1.33714			0.668569	−	0.743650i	$-0.266907\pi$
$797$	37.7490			1.33714			0.668569	+	0.743650i	$0.266907\pi$
$798$		0			0
$799$	−31.5425			−1.11589
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	8.61438	−	14.9205i	0.304184	−	0.526863i
$803$	−4.64575	−	8.04668i	−0.163945	−	0.283961i
$804$		0			0
$805$	3.96863	−	6.87386i	0.139876	−	0.242272i
$806$	1.29150			0.0454912
$807$		0			0
$808$	6.00000	−	10.3923i	0.211079	−	0.365600i
$809$	−5.90588	+	10.2293i	−0.207640	+	0.359643i	−0.950971	−	0.309281i	$-0.899911\pi$
$809$	−5.90588	+	10.2293i	−0.207640	+	0.359643i	0.743331	+	0.668924i	$0.233245\pi$
$810$		0			0
$811$	−16.8745			−0.592544			−0.296272	−	0.955104i	$-0.595744\pi$
$811$	−16.8745			−0.592544			−0.296272	+	0.955104i	$0.595744\pi$
$812$		0			0
$813$		0			0
$814$	13.7915	+	23.8876i	0.483392	+	0.837259i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$	24.2288	+	41.9654i	0.847657	+	1.46818i
$818$	32.5830			1.13924
$819$		0			0
$820$	−1.35425			−0.0472924
$821$	7.93725	+	13.7477i	0.277012	+	0.479799i	0.970641	−	0.240534i	$-0.0773225\pi$
$821$	7.93725	+	13.7477i	0.277012	+	0.479799i	−0.693629	+	0.720333i	$0.743989\pi$
$822$		0			0
$823$	9.35425	−	16.2020i	0.326069	−	0.564767i	−0.655659	−	0.755057i	$-0.727609\pi$
$823$	9.35425	−	16.2020i	0.326069	−	0.564767i	0.981728	+	0.190289i	$0.0609426\pi$
$824$	−8.64575	−	14.9749i	−0.301189	−	0.521675i
$825$		0			0
$826$	−24.5830			−0.855352
$827$	−48.5830			−1.68940			−0.844698	−	0.535243i	$-0.820220\pi$
$827$	−48.5830			−1.68940			−0.844698	+	0.535243i	$0.820220\pi$
$828$		0			0
$829$	−5.06275	+	8.76893i	−0.175836	+	0.304558i	−0.940450	−	0.339931i	$-0.889596\pi$
$829$	−5.06275	+	8.76893i	−0.175836	+	0.304558i	0.764614	+	0.644489i	$0.222930\pi$
$830$	7.64575	−	13.2428i	0.265388	−	0.459665i
$831$		0			0
$832$	0.645751			0.0223874
$833$	−11.5203	+	19.9537i	−0.399153	+	0.691354i
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	9.96863	−	17.2662i	0.344772	−	0.597163i
$837$		0			0
$838$	11.0314	+	19.1069i	0.381072	+	0.660037i
$839$	−40.4575			−1.39675			−0.698374	−	0.715733i	$-0.746093\pi$
$839$	−40.4575			−1.39675			−0.698374	+	0.715733i	$0.746093\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	0.0627461	+	0.108679i	0.00216237	+	0.00374534i
$843$		0			0
$844$	−4.14575	+	7.18065i	−0.142703	+	0.247168i
$845$	−6.29150	−	10.8972i	−0.216434	−	0.374875i
$846$		0			0
$847$	−14.0000	−	24.2487i	−0.481046	−	0.833196i
$848$	−0.291503			−0.0100102
$849$		0			0
$850$	−1.64575	+	2.85052i	−0.0564488	+	0.0977722i
$851$	8.90588	−	15.4254i	0.305290	−	0.528777i
$852$		0			0
$853$	49.8118			1.70552			0.852761	−	0.522301i	$-0.174926\pi$
$853$	49.8118			1.70552			0.852761	+	0.522301i	$0.174926\pi$
$854$	−14.9373	+	25.8721i	−0.511142	+	0.885324i
$855$		0			0
$856$	7.93725	+	13.7477i	0.271290	+	0.469888i
$857$	−7.93725	+	13.7477i	−0.271131	+	0.469613i	−0.969152	−	0.246464i	$-0.920731\pi$
$857$	−7.93725	+	13.7477i	−0.271131	+	0.469613i	0.698020	+	0.716078i	$0.254064\pi$
$858$		0			0
$859$	20.5830	+	35.6508i	0.702283	+	1.21639i	0.967663	+	0.252246i	$0.0811692\pi$
$859$	20.5830	+	35.6508i	0.702283	+	1.21639i	−0.265380	+	0.964144i	$0.585497\pi$
$860$	−11.2915			−0.385037
$861$		0			0
$862$	−2.12549			−0.0723945
$863$	11.0830	+	19.1963i	0.377270	+	0.653451i	0.990664	−	0.136326i	$-0.0435296\pi$
$863$	11.0830	+	19.1963i	0.377270	+	0.653451i	−0.613394	+	0.789777i	$0.710196\pi$
$864$		0			0
$865$	9.14575	−	15.8409i	0.310965	−	0.538607i
$866$	−4.00000	−	6.92820i	−0.135926	−	0.235430i
$867$		0			0
$868$	−2.64575	−	4.58258i	−0.0898027	−	0.155543i
$869$	52.4575			1.77950
$870$		0			0
$871$	−1.52026	+	2.63317i	−0.0515120	+	0.0892214i
$872$	−10.2915	+	17.8254i	−0.348514	+	0.603644i
$873$		0			0
$874$	−12.8745			−0.435487
$875$	−2.64575			−0.0894427
$876$		0			0
$877$	24.8431	+	43.0296i	0.838893	+	1.45301i	0.890821	+	0.454355i	$0.150130\pi$
$877$	24.8431	+	43.0296i	0.838893	+	1.45301i	−0.0519279	+	0.998651i	$0.516537\pi$
$878$	−16.5830	+	28.7226i	−0.559649	+	0.969341i
$879$		0			0
$880$	2.32288	+	4.02334i	0.0783041	+	0.135627i
$881$	37.3542			1.25850			0.629248	−	0.777204i	$-0.283363\pi$
$881$	37.3542			1.25850			0.629248	+	0.777204i	$0.283363\pi$
$882$		0			0
$883$	32.5830			1.09651			0.548253	−	0.836313i	$-0.315293\pi$
$883$	32.5830			1.09651			0.548253	+	0.836313i	$0.315293\pi$
$884$	−1.06275	−	1.84073i	−0.0357440	−	0.0619105i
$885$		0			0
$886$	19.6458	−	34.0274i	0.660012	−	1.14317i
$887$	−0.583005	−	1.00979i	−0.0195754	−	0.0339056i	0.856072	−	0.516857i	$-0.172898\pi$
$887$	−0.583005	−	1.00979i	−0.0195754	−	0.0339056i	−0.875647	+	0.482951i	$0.839565\pi$
$888$		0			0
$889$	24.7490			0.830055
$890$	−6.58301			−0.220663
$891$		0			0
$892$	−2.64575	+	4.58258i	−0.0885863	+	0.153436i
$893$	−20.5627	+	35.6157i	−0.688106	+	1.19183i
$894$		0			0
$895$	25.9373			0.866987
$896$	−1.32288	−	2.29129i	−0.0441942	−	0.0765466i
$897$		0			0
$898$	11.9059	+	20.6216i	0.397304	+	0.688151i
$899$		0			0
$900$		0			0
$901$	0.479741	+	0.830935i	0.0159825	+	0.0276825i
$902$	6.29150			0.209484
$903$		0			0
$904$	−12.5830			−0.418505
$905$	−0.354249	−	0.613577i	−0.0117756	−	0.0203960i
$906$		0			0
$907$	20.8745	−	36.1557i	0.693127	−	1.20053i	−0.277681	−	0.960673i	$-0.589566\pi$
$907$	20.8745	−	36.1557i	0.693127	−	1.20053i	0.970808	−	0.239857i	$-0.0771007\pi$
$908$	−1.64575	−	2.85052i	−0.0546162	−	0.0945980i
$909$		0			0
$910$	0.854249	−	1.47960i	0.0283181	−	0.0490483i
$911$	−47.6235			−1.57784			−0.788919	−	0.614497i	$-0.789359\pi$
$911$	−47.6235			−1.57784			−0.788919	+	0.614497i	$0.789359\pi$
$912$		0			0
$913$	−35.5203	+	61.5229i	−1.17555	+	2.03611i
$914$	3.35425	−	5.80973i	0.110949	−	0.192169i
$915$		0			0
$916$	17.2915			0.571327
$917$	6.14575	+	10.6448i	0.202951	+	0.351521i
$918$		0			0
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$	1.50000	−	2.59808i	0.0494535	−	0.0856560i
$921$		0			0
$922$	12.5830	+	21.7944i	0.414399	+	0.717760i
$923$	−1.74902			−0.0575696
$924$		0			0
$925$	−5.93725			−0.195216
$926$	−0.0313730	−	0.0543397i	−0.00103098	−	0.00178571i
$927$		0			0
$928$		0			0
$929$	22.5516	+	39.0606i	0.739895	+	1.28154i	0.952542	+	0.304407i	$0.0984582\pi$
$929$	22.5516	+	39.0606i	0.739895	+	1.28154i	−0.212647	+	0.977129i	$0.568208\pi$
$930$		0			0
$931$	15.0203	+	26.0159i	0.492269	+	0.852635i
$932$	3.87451			0.126914
$933$		0			0
$934$	4.35425	−	7.54178i	0.142475	−	0.246775i
$935$	7.64575	−	13.2428i	0.250043	−	0.433087i
$936$		0			0
$937$	37.6235			1.22911			0.614553	−	0.788875i	$-0.289336\pi$
$937$	37.6235			1.22911			0.614553	+	0.788875i	$0.289336\pi$
$938$	12.4575			0.406752
$939$		0			0
$940$	−4.79150	−	8.29913i	−0.156282	−	0.270688i
$941$	12.2915	−	21.2895i	0.400692	−	0.694018i	−0.593118	−	0.805116i	$-0.702103\pi$
$941$	12.2915	−	21.2895i	0.400692	−	0.694018i	0.993810	+	0.111097i	$0.0354366\pi$
$942$		0			0
$943$	−2.03137	−	3.51844i	−0.0661506	−	0.114576i
$944$	−9.29150			−0.302413
$945$		0			0
$946$	52.4575			1.70554
$947$	−14.5203	−	25.1498i	−0.471845	−	0.817260i	0.527636	−	0.849471i	$-0.323078\pi$
$947$	−14.5203	−	25.1498i	−0.471845	−	0.817260i	−0.999481	+	0.0322110i	$0.989745\pi$
$948$		0			0
$949$	−0.645751	+	1.11847i	−0.0209620	+	0.0363072i
$950$	2.14575	+	3.71655i	0.0696174	+	0.120581i
$951$		0			0
$952$	−4.35425	+	7.54178i	−0.141122	+	0.244430i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$	−6.29150	+	10.8972i	−0.203482	+	0.352441i
$957$		0			0
$958$	25.7490			0.831913
$959$	−21.0000	+	36.3731i	−0.678125	+	1.17455i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	1.91699	−	3.32033i	0.0618064	−	0.107052i
$963$		0			0
$964$	12.7915	+	22.1555i	0.411987	+	0.713582i
$965$	7.87451			0.253489
$966$		0			0
$967$	−18.7085			−0.601625			−0.300812	−	0.953683i	$-0.597258\pi$
$967$	−18.7085			−0.601625			−0.300812	+	0.953683i	$0.597258\pi$
$968$	−5.29150	−	9.16515i	−0.170075	−	0.294579i
$969$		0			0
$970$	−2.00000	+	3.46410i	−0.0642161	+	0.111226i
$971$	−3.09412	−	5.35917i	−0.0992950	−	0.171984i	0.812098	−	0.583521i	$-0.198325\pi$
$971$	−3.09412	−	5.35917i	−0.0992950	−	0.171984i	−0.911393	+	0.411537i	$0.864992\pi$
$972$		0			0
$973$	−28.0000			−0.897639
$974$	−7.87451			−0.252316
$975$		0			0
$976$	−5.64575	+	9.77873i	−0.180716	+	0.313009i
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$		0			0
$979$	30.5830			0.977437
$980$	−7.00000			−0.223607
$981$		0			0
$982$	4.06275	+	7.03688i	0.129647	+	0.224556i
$983$	17.6660	−	30.5984i	0.563458	−	0.975938i	−0.433733	−	0.901041i	$-0.642804\pi$
$983$	17.6660	−	30.5984i	0.563458	−	0.975938i	0.997191	−	0.0748969i	$-0.0238628\pi$
$984$		0			0
$985$	3.14575	+	5.44860i	0.100232	+	0.173607i
$986$		0			0
$987$		0			0
$988$	−2.77124			−0.0881650
$989$	−16.9373	−	29.3362i	−0.538573	−	0.932836i
$990$		0			0
$991$	−2.64575	+	4.58258i	−0.0840451	+	0.145570i	−0.904984	−	0.425446i	$-0.860117\pi$
$991$	−2.64575	+	4.58258i	−0.0840451	+	0.145570i	0.820939	+	0.571016i	$0.193451\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$		0			0
$994$	3.58301	+	6.20595i	0.113646	+	0.196841i
$995$	−17.8745			−0.566660
$996$		0			0
$997$	−7.87451	+	13.6390i	−0.249388	+	0.431953i	−0.963356	−	0.268225i	$-0.913563\pi$
$997$	−7.87451	+	13.6390i	−0.249388	+	0.431953i	0.713968	+	0.700178i	$0.246896\pi$
$998$	−7.29150	+	12.6293i	−0.230808	+	0.399772i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.i.361.2	✓	4
3.2	odd	2		630.2.k.j.361.2	yes	4
7.2	even	3	inner	630.2.k.i.541.2	yes	4
7.3	odd	6		4410.2.a.ca.1.2		2
7.4	even	3		4410.2.a.bv.1.2		2
21.2	odd	6		630.2.k.j.541.2	yes	4
21.11	odd	6		4410.2.a.bq.1.1		2
21.17	even	6		4410.2.a.bo.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.k.i.361.2	✓	4	1.1	even	1	trivial
630.2.k.i.541.2	yes	4	7.2	even	3	inner
630.2.k.j.361.2	yes	4	3.2	odd	2
630.2.k.j.541.2	yes	4	21.2	odd	6
4410.2.a.bo.1.1		2	21.17	even	6
4410.2.a.bq.1.1		2	21.11	odd	6
4410.2.a.bv.1.2		2	7.4	even	3
4410.2.a.ca.1.2		2	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.32288 + 4.02334i) q^{11} +0.645751 q^{13} +(-1.32288 - 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.64575 + 2.85052i) q^{17} +(2.14575 + 3.71655i) q^{19} -1.00000 q^{20} +4.64575 q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.322876 - 0.559237i) q^{26} +(-1.32288 + 2.29129i) q^{28} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.29150 q^{34} +(1.32288 + 2.29129i) q^{35} +(2.96863 + 5.14181i) q^{37} +(2.14575 - 3.71655i) q^{38} +(0.500000 + 0.866025i) q^{40} +1.35425 q^{41} +11.2915 q^{43} +(-2.32288 - 4.02334i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(4.79150 + 8.29913i) q^{47} +7.00000 q^{49} +1.00000 q^{50} +(-0.322876 + 0.559237i) q^{52} +(0.145751 - 0.252449i) q^{53} -4.64575 q^{55} +2.64575 q^{56} +(4.64575 - 8.04668i) q^{59} +(-5.64575 - 9.77873i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(0.322876 + 0.559237i) q^{65} +(-2.35425 + 4.07768i) q^{67} +(-1.64575 - 2.85052i) q^{68} +(1.32288 - 2.29129i) q^{70} -2.70850 q^{71} +(-1.00000 + 1.73205i) q^{73} +(2.96863 - 5.14181i) q^{74} -4.29150 q^{76} +(-6.14575 + 10.6448i) q^{77} +(-5.64575 - 9.77873i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.677124 - 1.17281i) q^{82} +15.2915 q^{83} -3.29150 q^{85} +(-5.64575 - 9.77873i) q^{86} +(-2.32288 + 4.02334i) q^{88} +(-3.29150 - 5.70105i) q^{89} +1.70850 q^{91} +3.00000 q^{92} +(4.79150 - 8.29913i) q^{94} +(-2.14575 + 3.71655i) q^{95} -4.00000 q^{97} +(-3.50000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 4 q^{11} - 8 q^{13} - 2 q^{16} + 4 q^{17} - 2 q^{19} - 4 q^{20} + 8 q^{22} - 6 q^{23} - 2 q^{25} + 4 q^{26} - 4 q^{31} - 2 q^{32} - 8 q^{34} - 4 q^{37} - 2 q^{38} + 2 q^{40} + 16 q^{41} + 24 q^{43} - 4 q^{44} - 6 q^{46} - 2 q^{47} + 28 q^{49} + 4 q^{50} + 4 q^{52} - 10 q^{53} - 8 q^{55} + 8 q^{59} - 12 q^{61} + 8 q^{62} + 4 q^{64} - 4 q^{65} - 20 q^{67} + 4 q^{68} - 32 q^{71} - 4 q^{73} - 4 q^{74} + 4 q^{76} - 14 q^{77} - 12 q^{79} + 2 q^{80} - 8 q^{82} + 40 q^{83} + 8 q^{85} - 12 q^{86} - 4 q^{88} + 8 q^{89} + 28 q^{91} + 12 q^{92} - 2 q^{94} + 2 q^{95} - 16 q^{97} - 14 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 - 4 * q^11 - 8 * q^13 - 2 * q^16 + 4 * q^17 - 2 * q^19 - 4 * q^20 + 8 * q^22 - 6 * q^23 - 2 * q^25 + 4 * q^26 - 4 * q^31 - 2 * q^32 - 8 * q^34 - 4 * q^37 - 2 * q^38 + 2 * q^40 + 16 * q^41 + 24 * q^43 - 4 * q^44 - 6 * q^46 - 2 * q^47 + 28 * q^49 + 4 * q^50 + 4 * q^52 - 10 * q^53 - 8 * q^55 + 8 * q^59 - 12 * q^61 + 8 * q^62 + 4 * q^64 - 4 * q^65 - 20 * q^67 + 4 * q^68 - 32 * q^71 - 4 * q^73 - 4 * q^74 + 4 * q^76 - 14 * q^77 - 12 * q^79 + 2 * q^80 - 8 * q^82 + 40 * q^83 + 8 * q^85 - 12 * q^86 - 4 * q^88 + 8 * q^89 + 28 * q^91 + 12 * q^92 - 2 * q^94 + 2 * q^95 - 16 * q^97 - 14 * q^98

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