LMFDB - Embedded newform 630.2.k.g.361.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.361
Dual form			630.2.k.g.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} -5.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.50000 + 6.06218i) q^{19} -1.00000 q^{20} -5.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.50000 - 4.33013i) q^{26} +(2.50000 - 0.866025i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(0.500000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{37} +(-3.50000 + 6.06218i) q^{38} +(-0.500000 - 0.866025i) q^{40} -5.00000 q^{41} +12.0000 q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(-5.50000 - 9.52628i) q^{47} +(1.00000 + 6.92820i) q^{49} -1.00000 q^{50} +(2.50000 - 4.33013i) q^{52} +(-4.50000 + 7.79423i) q^{53} -5.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(2.00000 - 3.46410i) q^{59} +(-2.00000 - 3.46410i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(6.00000 - 10.3923i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(2.50000 - 0.866025i) q^{70} -2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(12.5000 - 4.33013i) q^{77} +(6.00000 + 10.3923i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.50000 - 4.33013i) q^{82} +12.0000 q^{83} -4.00000 q^{85} +(6.00000 + 10.3923i) q^{86} +(2.50000 - 4.33013i) q^{88} +(7.00000 + 12.1244i) q^{89} +(10.0000 + 8.66025i) q^{91} -1.00000 q^{92} +(5.50000 - 9.52628i) q^{94} +(-3.50000 + 6.06218i) q^{95} -8.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + q^5 - 4 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + q^{5} - 4 q^{7} - 2 q^{8} - q^{10} - 5 q^{11} - 10 q^{13} + q^{14} - q^{16} - 4 q^{17} + 7 q^{19} - 2 q^{20} - 10 q^{22} + q^{23} - q^{25} - 5 q^{26} + 5 q^{28} + 2 q^{31} + q^{32} - 8 q^{34} + q^{35} - q^{37} - 7 q^{38} - q^{40} - 10 q^{41} + 24 q^{43} - 5 q^{44} - q^{46} - 11 q^{47} + 2 q^{49} - 2 q^{50} + 5 q^{52} - 9 q^{53} - 10 q^{55} + 4 q^{56} + 4 q^{59} - 4 q^{61} + 4 q^{62} + 2 q^{64} - 5 q^{65} + 12 q^{67} - 4 q^{68} + 5 q^{70} - 4 q^{71} - 10 q^{73} + q^{74} - 14 q^{76} + 25 q^{77} + 12 q^{79} + q^{80} - 5 q^{82} + 24 q^{83} - 8 q^{85} + 12 q^{86} + 5 q^{88} + 14 q^{89} + 20 q^{91} - 2 q^{92} + 11 q^{94} - 7 q^{95} - 16 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + q^5 - 4 * q^7 - 2 * q^8 - q^10 - 5 * q^11 - 10 * q^13 + q^14 - q^16 - 4 * q^17 + 7 * q^19 - 2 * q^20 - 10 * q^22 + q^23 - q^25 - 5 * q^26 + 5 * q^28 + 2 * q^31 + q^32 - 8 * q^34 + q^35 - q^37 - 7 * q^38 - q^40 - 10 * q^41 + 24 * q^43 - 5 * q^44 - q^46 - 11 * q^47 + 2 * q^49 - 2 * q^50 + 5 * q^52 - 9 * q^53 - 10 * q^55 + 4 * q^56 + 4 * q^59 - 4 * q^61 + 4 * q^62 + 2 * q^64 - 5 * q^65 + 12 * q^67 - 4 * q^68 + 5 * q^70 - 4 * q^71 - 10 * q^73 + q^74 - 14 * q^76 + 25 * q^77 + 12 * q^79 + q^80 - 5 * q^82 + 24 * q^83 - 8 * q^85 + 12 * q^86 + 5 * q^88 + 14 * q^89 + 20 * q^91 - 2 * q^92 + 11 * q^94 - 7 * q^95 - 16 * q^97 - 11 * 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
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$		0			0
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−5.00000			−1.06600
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$		0			0
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$		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	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−4.00000			−0.685994
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$		0			0
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−3.50000	+	6.06218i	−0.567775	+	0.983415i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−5.00000			−0.780869			−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000			−0.780869			−0.390434	+	0.920631i	$0.627675\pi$
$42$		0			0
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−5.50000	−	9.52628i	−0.802257	−	1.38955i	−0.918127	−	0.396286i	$-0.870299\pi$
$47$	−5.50000	−	9.52628i	−0.802257	−	1.38955i	0.115870	−	0.993264i	$-0.463035\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−1.00000			−0.141421
$51$		0			0
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$		0			0
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.50000	−	4.33013i	−0.310087	−	0.537086i
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		0			0
$70$	2.50000	−	0.866025i	0.298807	−	0.103510i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−7.00000			−0.802955
$77$	12.5000	−	4.33013i	1.42451	−	0.493464i
$78$		0			0
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	0.976453	+	0.215728i	$0.0692125\pi$
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	−0.301401	+	0.953498i	$0.597454\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	6.00000	+	10.3923i	0.646997	+	1.12063i
$87$		0			0
$88$	2.50000	−	4.33013i	0.266501	−	0.461593i
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$		0			0
$91$	10.0000	+	8.66025i	1.04828	+	0.907841i
$92$	−1.00000			−0.104257
$93$		0			0
$94$	5.50000	−	9.52628i	0.567282	−	0.982561i
$95$	−3.50000	+	6.06218i	−0.359092	+	0.621966i
$96$		0			0
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	−9.00000			−0.874157
$107$	−1.00000	−	1.73205i	−0.0966736	−	0.167444i	0.813632	−	0.581380i	$-0.197487\pi$
$107$	−1.00000	−	1.73205i	−0.0966736	−	0.167444i	−0.910306	+	0.413936i	$0.864154\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−2.50000	−	4.33013i	−0.238366	−	0.412861i
$111$		0			0
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$	−0.500000	+	0.866025i	−0.0466252	+	0.0807573i
$116$		0			0
$117$		0			0
$118$	4.00000			0.368230
$119$	10.0000	−	3.46410i	0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	2.00000	−	3.46410i	0.181071	−	0.313625i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	2.50000	−	4.33013i	0.219265	−	0.379777i
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$		0			0
$133$	3.50000	−	18.1865i	0.303488	−	1.57697i
$134$	12.0000			1.03664
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.00000	+	1.73205i	0.169031	+	0.146385i
$141$		0			0
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$	12.5000	−	21.6506i	1.04530	−	1.81052i
$144$		0			0
$145$		0			0
$146$	−10.0000			−0.827606
$147$		0			0
$148$	1.00000			0.0821995
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		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	$0.973745\pi$
$152$	−3.50000	−	6.06218i	−0.283887	−	0.491708i
$153$		0			0
$154$	10.0000	+	8.66025i	0.805823	+	0.697863i
$155$	2.00000			0.160644
$156$		0			0
$157$	−5.50000	+	9.52628i	−0.438948	+	0.760280i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−5.50000	+	9.52628i	−0.438948	+	0.760280i	0.558661	+	0.829396i	$0.311315\pi$
$158$	−6.00000	+	10.3923i	−0.477334	+	0.826767i
$159$		0			0
$160$	1.00000			0.0790569
$161$	0.500000	−	2.59808i	0.0394055	−	0.204757i
$162$		0			0
$163$	12.0000	+	20.7846i	0.939913	+	1.62798i	0.765631	+	0.643280i	$0.222427\pi$
$163$	12.0000	+	20.7846i	0.939913	+	1.62798i	0.174282	+	0.984696i	$0.444240\pi$
$164$	2.50000	−	4.33013i	0.195217	−	0.338126i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−11.0000			−0.851206			−0.425603	−	0.904910i	$-0.639938\pi$
$167$	−11.0000			−0.851206			−0.425603	+	0.904910i	$0.639938\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	−2.00000	−	3.46410i	−0.153393	−	0.265684i
$171$		0			0
$172$	−6.00000	+	10.3923i	−0.457496	+	0.792406i
$173$	−6.50000	−	11.2583i	−0.494186	−	0.855955i	0.505792	−	0.862656i	$-0.331200\pi$
$173$	−6.50000	−	11.2583i	−0.494186	−	0.855955i	−0.999978	+	0.00670064i	$0.997867\pi$
$174$		0			0
$175$	2.50000	−	0.866025i	0.188982	−	0.0654654i
$176$	5.00000			0.376889
$177$		0			0
$178$	−7.00000	+	12.1244i	−0.524672	+	0.908759i
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	0.0128080	+	0.999918i	$0.495923\pi$
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	−0.872358	+	0.488867i	$0.837410\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−2.50000	+	12.9904i	−0.185312	+	0.962911i
$183$		0			0
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	0.500000	−	0.866025i	0.0367607	−	0.0636715i
$186$		0			0
$187$	−10.0000	−	17.3205i	−0.731272	−	1.26660i
$188$	11.0000			0.802257
$189$		0			0
$190$	−7.00000			−0.507833
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	0.999972	+	0.00752447i	$0.00239513\pi$
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	−0.493469	+	0.869763i	$0.664272\pi$
$192$		0			0
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	−4.00000	−	6.92820i	−0.287183	−	0.497416i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$		0			0
$208$	2.50000	+	4.33013i	0.173344	+	0.300240i
$209$	−35.0000			−2.42100
$210$		0			0
$211$	17.0000			1.17033			0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000			1.17033			0.585164	+	0.810915i	$0.301030\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$		0			0
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$	6.00000	+	10.3923i	0.409197	+	0.708749i
$216$		0			0
$217$	−5.00000	+	1.73205i	−0.339422	+	0.117579i
$218$	2.00000			0.135457
$219$		0			0
$220$	2.50000	−	4.33013i	0.168550	−	0.291937i
$221$	10.0000	−	17.3205i	0.672673	−	1.16510i
$222$		0			0
$223$	−12.0000			−0.803579			−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000			−0.803579			−0.401790	+	0.915732i	$0.631612\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$	7.00000	+	12.1244i	0.465633	+	0.806500i
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		0			0
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	−1.00000			−0.0659380
$231$		0			0
$232$		0			0
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	0.540301	−	0.841472i	$-0.318310\pi$
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	−0.998886	+	0.0471787i	$0.984977\pi$
$234$		0			0
$235$	5.50000	−	9.52628i	0.358780	−	0.621426i
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$	8.00000	+	6.92820i	0.518563	+	0.449089i
$239$	22.0000			1.42306			0.711531	−	0.702655i	$-0.248002\pi$
$239$	22.0000			1.42306			0.711531	+	0.702655i	$0.248002\pi$
$240$		0			0
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$		0			0
$244$	4.00000			0.256074
$245$	−5.50000	+	4.33013i	−0.351382	+	0.276642i
$246$		0			0
$247$	−17.5000	−	30.3109i	−1.11350	−	1.92864i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−1.00000			−0.0631194			−0.0315597	−	0.999502i	$-0.510047\pi$
$251$	−1.00000			−0.0631194			−0.0315597	+	0.999502i	$0.510047\pi$
$252$		0			0
$253$	−5.00000			−0.314347
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.00000	−	13.8564i	−0.499026	−	0.864339i	0.500973	−	0.865463i	$-0.332976\pi$
$257$	−8.00000	−	13.8564i	−0.499026	−	0.864339i	−0.999999	+	0.00112398i	$0.999642\pi$
$258$		0			0
$259$	−0.500000	+	2.59808i	−0.0310685	+	0.161437i
$260$	5.00000			0.310087
$261$		0			0
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$	17.5000	−	6.06218i	1.07299	−	0.371696i
$267$		0			0
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−2.50000	−	4.33013i	−0.150756	−	0.261116i
$276$		0			0
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$		0			0
$280$	−0.500000	+	2.59808i	−0.0298807	+	0.155265i
$281$	−7.00000			−0.417585			−0.208792	−	0.977960i	$-0.566953\pi$
$281$	−7.00000			−0.417585			−0.208792	+	0.977960i	$0.566953\pi$
$282$		0			0
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$	25.0000			1.47828
$287$	10.0000	+	8.66025i	0.590281	+	0.511199i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$		0			0
$298$	−6.00000	+	10.3923i	−0.347571	+	0.602010i
$299$	−2.50000	−	4.33013i	−0.144579	−	0.250418i
$300$		0			0
$301$	−24.0000	−	20.7846i	−1.38334	−	1.19800i
$302$	−14.0000			−0.805609
$303$		0			0
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	−2.50000	+	12.9904i	−0.142451	+	0.740196i
$309$		0			0
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$		0			0
$313$	−8.00000	−	13.8564i	−0.452187	−	0.783210i	0.546335	−	0.837567i	$-0.316023\pi$
$313$	−8.00000	−	13.8564i	−0.452187	−	0.783210i	−0.998522	+	0.0543564i	$0.982689\pi$
$314$	−11.0000			−0.620766
$315$		0			0
$316$	−12.0000			−0.675053
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	−0.989882	−	0.141890i	$-0.954682\pi$
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	0.372061	−	0.928208i	$-0.378651\pi$
$318$		0			0
$319$		0			0
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	2.50000	−	0.866025i	0.139320	−	0.0482617i
$323$	−28.0000			−1.55796
$324$		0			0
$325$	2.50000	−	4.33013i	0.138675	−	0.240192i
$326$	−12.0000	+	20.7846i	−0.664619	+	1.15115i
$327$		0			0
$328$	5.00000			0.276079
$329$	−5.50000	+	28.5788i	−0.303225	+	1.57560i
$330$		0			0
$331$	−15.5000	−	26.8468i	−0.851957	−	1.47563i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−15.5000	−	26.8468i	−0.851957	−	1.47563i	0.0274825	−	0.999622i	$-0.491251\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$		0			0
$334$	−5.50000	−	9.52628i	−0.300947	−	0.521255i
$335$	12.0000			0.655630
$336$		0			0
$337$	−16.0000			−0.871576			−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000			−0.871576			−0.435788	+	0.900049i	$0.643530\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	5.00000	+	8.66025i	0.270765	+	0.468979i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−12.0000			−0.646997
$345$		0			0
$346$	6.50000	−	11.2583i	0.349442	−	0.605252i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$		0			0
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$	2.00000	+	1.73205i	0.106904	+	0.0925820i
$351$		0			0
$352$	2.50000	+	4.33013i	0.133250	+	0.230797i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	−14.0000			−0.741999
$357$		0			0
$358$	−23.0000			−1.21559
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	10.0000	+	17.3205i	0.525588	+	0.910346i
$363$		0			0
$364$	−12.5000	+	4.33013i	−0.655178	+	0.226960i
$365$	−10.0000			−0.523424
$366$		0			0
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	−0.942799	−	0.333363i	$-0.891817\pi$
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	0.760100	+	0.649806i	$0.225150\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$		0			0
$370$	1.00000			0.0519875
$371$	22.5000	−	7.79423i	1.16814	−	0.404656i
$372$		0			0
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	0.996610	+	0.0822766i	$0.0262191\pi$
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	−0.427051	+	0.904227i	$0.640448\pi$
$374$	10.0000	−	17.3205i	0.517088	−	0.895622i
$375$		0			0
$376$	5.50000	+	9.52628i	0.283641	+	0.491280i
$377$		0			0
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$	−3.50000	−	6.06218i	−0.179546	−	0.310983i
$381$		0			0
$382$	−7.00000	+	12.1244i	−0.358151	+	0.620336i
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	0.999088	+	0.0427020i	$0.0135966\pi$
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$384$		0			0
$385$	10.0000	+	8.66025i	0.509647	+	0.441367i
$386$	−10.0000			−0.508987
$387$		0			0
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$		0			0
$394$	1.50000	+	2.59808i	0.0755689	+	0.130889i
$395$	−6.00000	+	10.3923i	−0.301893	+	0.522894i
$396$		0			0
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	0.986481	−	0.163876i	$-0.0523996\pi$
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	−0.635161	+	0.772380i	$0.719066\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$		0			0
$403$	−5.00000	+	8.66025i	−0.249068	+	0.431398i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.00000			0.247841
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	2.50000	−	4.33013i	0.123466	−	0.213850i
$411$		0			0
$412$	8.00000			0.394132
$413$	−10.0000	+	3.46410i	−0.492068	+	0.170457i
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$		0			0
$418$	−17.5000	−	30.3109i	−0.855953	−	1.48255i
$419$	−15.0000			−0.732798			−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000			−0.732798			−0.366399	+	0.930458i	$0.619409\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	8.50000	+	14.7224i	0.413774	+	0.716677i
$423$		0			0
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$	−2.00000	+	10.3923i	−0.0967868	+	0.502919i
$428$	2.00000			0.0966736
$429$		0			0
$430$	−6.00000	+	10.3923i	−0.289346	+	0.501161i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	24.0000			1.15337			0.576683	−	0.816968i	$-0.304347\pi$
$433$	24.0000			1.15337			0.576683	+	0.816968i	$0.304347\pi$
$434$	−4.00000	−	3.46410i	−0.192006	−	0.166282i
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−3.50000	+	6.06218i	−0.167428	+	0.289993i
$438$		0			0
$439$	20.0000	+	34.6410i	0.954548	+	1.65333i	0.735399	+	0.677634i	$0.236995\pi$
$439$	20.0000	+	34.6410i	0.954548	+	1.65333i	0.219149	+	0.975691i	$0.429672\pi$
$440$	5.00000			0.238366
$441$		0			0
$442$	20.0000			0.951303
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	−0.979242	−	0.202695i	$-0.935030\pi$
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	0.314082	−	0.949396i	$-0.398303\pi$
$444$		0			0
$445$	−7.00000	+	12.1244i	−0.331832	+	0.574750i
$446$	−6.00000	−	10.3923i	−0.284108	−	0.492090i
$447$		0			0
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	29.0000			1.36859			0.684297	−	0.729203i	$-0.260109\pi$
$449$	29.0000			1.36859			0.684297	+	0.729203i	$0.260109\pi$
$450$		0			0
$451$	12.5000	−	21.6506i	0.588602	−	1.01949i
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$		0			0
$454$	−12.0000			−0.563188
$455$	−2.50000	+	12.9904i	−0.117202	+	0.608998i
$456$		0			0
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	0.982004	−	0.188858i	$-0.0604787\pi$
$457$	7.00000	+	12.1244i	0.327446	+	0.567153i	−0.654558	+	0.756012i	$0.727145\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$		0			0
$460$	−0.500000	−	0.866025i	−0.0233126	−	0.0403786i
$461$	4.00000			0.186299			0.0931493	−	0.995652i	$-0.470307\pi$
$461$	4.00000			0.186299			0.0931493	+	0.995652i	$0.470307\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$		0			0
$465$		0			0
$466$	7.00000	−	12.1244i	0.324269	−	0.561650i
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	0.536352	−	0.843995i	$-0.319802\pi$
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	−0.999097	+	0.0424970i	$0.986469\pi$
$468$		0			0
$469$	−30.0000	+	10.3923i	−1.38527	+	0.479872i
$470$	11.0000			0.507392
$471$		0			0
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	−30.0000	+	51.9615i	−1.37940	+	2.38919i
$474$		0			0
$475$	−7.00000			−0.321182
$476$	−2.00000	+	10.3923i	−0.0916698	+	0.476331i
$477$		0			0
$478$	11.0000	+	19.0526i	0.503128	+	0.871444i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$	−15.0000			−0.683231
$483$		0			0
$484$	14.0000			0.636364
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$487$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$488$	2.00000	+	3.46410i	0.0905357	+	0.156813i
$489$		0			0
$490$	−6.50000	−	2.59808i	−0.293640	−	0.117369i
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$		0			0
$493$		0			0
$494$	17.5000	−	30.3109i	0.787362	−	1.36375i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	4.00000	+	3.46410i	0.179425	+	0.155386i
$498$		0			0
$499$	−20.0000	−	34.6410i	−0.895323	−	1.55074i	−0.833404	−	0.552664i	$-0.813611\pi$
$499$	−20.0000	−	34.6410i	−0.895323	−	1.55074i	−0.0619186	−	0.998081i	$-0.519722\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−0.500000	−	0.866025i	−0.0223161	−	0.0386526i
$503$	20.0000			0.891756			0.445878	−	0.895094i	$-0.352892\pi$
$503$	20.0000			0.891756			0.445878	+	0.895094i	$0.352892\pi$
$504$		0			0
$505$		0			0
$506$	−2.50000	−	4.33013i	−0.111139	−	0.192498i
$507$		0			0
$508$	−4.50000	+	7.79423i	−0.199655	+	0.345813i
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$		0			0
$511$	25.0000	−	8.66025i	1.10593	−	0.383107i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	8.00000	−	13.8564i	0.352865	−	0.611180i
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$		0			0
$517$	55.0000			2.41890
$518$	−2.50000	+	0.866025i	−0.109844	+	0.0380510i
$519$		0			0
$520$	2.50000	+	4.33013i	0.109632	+	0.189889i
$521$	−16.5000	+	28.5788i	−0.722878	+	1.25206i	0.236963	+	0.971519i	$0.423848\pi$
$521$	−16.5000	+	28.5788i	−0.722878	+	1.25206i	−0.959841	+	0.280543i	$0.909485\pi$
$522$		0			0
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	0.999762	−	0.0218062i	$-0.00694167\pi$
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	−0.518766	+	0.854916i	$0.673608\pi$
$524$	9.00000			0.393167
$525$		0			0
$526$		0			0
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$		0			0
$532$	14.0000	+	12.1244i	0.606977	+	0.525657i
$533$	25.0000			1.08287
$534$		0			0
$535$	1.00000	−	1.73205i	0.0432338	−	0.0748831i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	−24.0000			−1.03471
$539$	−32.5000	−	12.9904i	−1.39987	−	0.559535i
$540$		0			0
$541$	−1.00000	−	1.73205i	−0.0429934	−	0.0744667i	0.843728	−	0.536771i	$-0.180356\pi$
$541$	−1.00000	−	1.73205i	−0.0429934	−	0.0744667i	−0.886721	+	0.462304i	$0.847023\pi$
$542$		0			0
$543$		0			0
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	2.00000			0.0856706
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−1.00000	−	1.73205i	−0.0427179	−	0.0739895i
$549$		0			0
$550$	2.50000	−	4.33013i	0.106600	−	0.184637i
$551$		0			0
$552$		0			0
$553$	6.00000	−	31.1769i	0.255146	−	1.32578i
$554$	−14.0000			−0.594803
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	−0.145802	−	0.989314i	$-0.546576\pi$
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	0.929672	−	0.368389i	$-0.120091\pi$
$558$		0			0
$559$	−60.0000			−2.53773
$560$	−2.50000	+	0.866025i	−0.105644	+	0.0365963i
$561$		0			0
$562$	−3.50000	−	6.06218i	−0.147639	−	0.255718i
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		0			0
$565$	7.00000	+	12.1244i	0.294492	+	0.510075i
$566$	10.0000			0.420331
$567$		0			0
$568$	2.00000			0.0839181
$569$	19.5000	+	33.7750i	0.817483	+	1.41592i	0.907532	+	0.419984i	$0.137964\pi$
$569$	19.5000	+	33.7750i	0.817483	+	1.41592i	−0.0900490	+	0.995937i	$0.528702\pi$
$570$		0			0
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	0.0554391	+	0.998462i	$0.482344\pi$
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	−0.892413	+	0.451219i	$0.850989\pi$
$572$	12.5000	+	21.6506i	0.522651	+	0.905259i
$573$		0			0
$574$	−2.50000	+	12.9904i	−0.104348	+	0.542208i
$575$	−1.00000			−0.0417029
$576$		0			0
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	0.457639	+	0.889138i	$0.348695\pi$
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	−0.998836	+	0.0482425i	$0.984638\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$		0			0
$580$		0			0
$581$	−24.0000	−	20.7846i	−0.995688	−	0.862291i
$582$		0			0
$583$	−22.5000	−	38.9711i	−0.931855	−	1.61402i
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$		0			0
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	30.0000			1.23823			0.619116	−	0.785299i	$-0.287491\pi$
$587$	30.0000			1.23823			0.619116	+	0.785299i	$0.287491\pi$
$588$		0			0
$589$	14.0000			0.576860
$590$	2.00000	+	3.46410i	0.0823387	+	0.142615i
$591$		0			0
$592$	−0.500000	+	0.866025i	−0.0205499	+	0.0355934i
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	0.952869	+	0.303383i	$0.0981160\pi$
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	−0.213697	+	0.976900i	$0.568551\pi$
$594$		0			0
$595$	8.00000	+	6.92820i	0.327968	+	0.284029i
$596$	−12.0000			−0.491539
$597$		0			0
$598$	2.50000	−	4.33013i	0.102233	−	0.177072i
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	−0.949908	−	0.312531i	$-0.898823\pi$
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	0.745613	+	0.666379i	$0.232157\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	6.00000	−	31.1769i	0.244542	−	1.27068i
$603$		0			0
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	0.998415	+	0.0562808i	$0.0179242\pi$
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	−0.450467	+	0.892793i	$0.648742\pi$
$608$	7.00000			0.283887
$609$		0			0
$610$	4.00000			0.161955
$611$	27.5000	+	47.6314i	1.11253	+	1.92696i
$612$		0			0
$613$	21.5000	−	37.2391i	0.868377	−	1.50407i	0.00472215	−	0.999989i	$-0.498497\pi$
$613$	21.5000	−	37.2391i	0.868377	−	1.50407i	0.863655	−	0.504084i	$-0.168170\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$	−12.5000	+	4.33013i	−0.503639	+	0.174466i
$617$	8.00000			0.322068			0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000			0.322068			0.161034	+	0.986949i	$0.448517\pi$
$618$		0			0
$619$	−12.5000	+	21.6506i	−0.502417	+	0.870212i	0.497579	+	0.867419i	$0.334223\pi$
$619$	−12.5000	+	21.6506i	−0.502417	+	0.870212i	−0.999996	+	0.00279365i	$0.999111\pi$
$620$	−1.00000	+	1.73205i	−0.0401610	+	0.0695608i
$621$		0			0
$622$	8.00000			0.320771
$623$	7.00000	−	36.3731i	0.280449	−	1.45726i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.00000	−	13.8564i	0.319744	−	0.553813i
$627$		0			0
$628$	−5.50000	−	9.52628i	−0.219474	−	0.380140i
$629$	4.00000			0.159490
$630$		0			0
$631$	6.00000			0.238856			0.119428	−	0.992843i	$-0.461894\pi$
$631$	6.00000			0.238856			0.119428	+	0.992843i	$0.461894\pi$
$632$	−6.00000	−	10.3923i	−0.238667	−	0.413384i
$633$		0			0
$634$	11.0000	−	19.0526i	0.436866	−	0.756674i
$635$	4.50000	+	7.79423i	0.178577	+	0.309305i
$636$		0			0
$637$	−5.00000	−	34.6410i	−0.198107	−	1.37253i
$638$		0			0
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	−0.580674	−	0.814136i	$-0.697211\pi$
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	0.995400	+	0.0958109i	$0.0305444\pi$
$642$		0			0
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$	2.00000	+	1.73205i	0.0788110	+	0.0682524i
$645$		0			0
$646$	−14.0000	−	24.2487i	−0.550823	−	0.954053i
$647$	−11.5000	+	19.9186i	−0.452112	+	0.783080i	−0.998517	−	0.0544405i	$-0.982662\pi$
$647$	−11.5000	+	19.9186i	−0.452112	+	0.783080i	0.546405	+	0.837521i	$0.315996\pi$
$648$		0			0
$649$	10.0000	+	17.3205i	0.392534	+	0.679889i
$650$	5.00000			0.196116
$651$		0			0
$652$	−24.0000			−0.939913
$653$	−9.50000	−	16.4545i	−0.371764	−	0.643914i	0.618073	−	0.786121i	$-0.287914\pi$
$653$	−9.50000	−	16.4545i	−0.371764	−	0.643914i	−0.989837	+	0.142207i	$0.954580\pi$
$654$		0			0
$655$	4.50000	−	7.79423i	0.175830	−	0.304546i
$656$	2.50000	+	4.33013i	0.0976086	+	0.169063i
$657$		0			0
$658$	−27.5000	+	9.52628i	−1.07206	+	0.371373i
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	15.5000	−	26.8468i	0.602425	−	1.04343i
$663$		0			0
$664$	−12.0000			−0.465690
$665$	17.5000	−	6.06218i	0.678621	−	0.235081i
$666$		0			0
$667$		0			0
$668$	5.50000	−	9.52628i	0.212801	−	0.368583i
$669$		0			0
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$	20.0000			0.772091
$672$		0			0
$673$	−4.00000			−0.154189			−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000			−0.154189			−0.0770943	+	0.997024i	$0.524564\pi$
$674$	−8.00000	−	13.8564i	−0.308148	−	0.533729i
$675$		0			0
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	0.986695	+	0.162581i	$0.0519817\pi$
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	−0.352549	+	0.935793i	$0.614685\pi$
$678$		0			0
$679$	16.0000	+	13.8564i	0.614024	+	0.531760i
$680$	4.00000			0.153393
$681$		0			0
$682$	−5.00000	+	8.66025i	−0.191460	+	0.331618i
$683$	−2.00000	+	3.46410i	−0.0765279	+	0.132550i	−0.901750	−	0.432259i	$-0.857717\pi$
$683$	−2.00000	+	3.46410i	−0.0765279	+	0.132550i	0.825222	+	0.564809i	$0.191050\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	−6.00000	−	10.3923i	−0.228748	−	0.396203i
$689$	22.5000	−	38.9711i	0.857182	−	1.48468i
$690$		0			0
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$	13.0000			0.494186
$693$		0			0
$694$	−18.0000			−0.683271
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		0			0
$697$	10.0000	−	17.3205i	0.378777	−	0.656061i
$698$	−2.00000	−	3.46410i	−0.0757011	−	0.131118i
$699$		0			0
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	3.50000	−	6.06218i	0.132005	−	0.228639i
$704$	−2.50000	+	4.33013i	−0.0942223	+	0.163198i
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$		0			0
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	−0.999549	−	0.0300298i	$-0.990440\pi$
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	0.473768	−	0.880650i	$-0.342894\pi$
$710$	1.00000	−	1.73205i	0.0375293	−	0.0650027i
$711$		0			0
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$	2.00000			0.0749006
$714$		0			0
$715$	25.0000			0.934947
$716$	−11.5000	−	19.9186i	−0.429775	−	0.744392i
$717$		0			0
$718$	10.0000	−	17.3205i	0.373197	−	0.646396i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	−4.00000	+	20.7846i	−0.148968	+	0.774059i
$722$	−30.0000			−1.11648
$723$		0			0
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$		0			0
$726$		0			0
$727$	−3.00000			−0.111264			−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000			−0.111264			−0.0556319	+	0.998451i	$0.517717\pi$
$728$	−10.0000	−	8.66025i	−0.370625	−	0.320970i
$729$		0			0
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	−24.0000	+	41.5692i	−0.887672	+	1.53749i
$732$		0			0
$733$	−4.50000	−	7.79423i	−0.166211	−	0.287886i	0.770873	−	0.636988i	$-0.219820\pi$
$733$	−4.50000	−	7.79423i	−0.166211	−	0.287886i	−0.937085	+	0.349102i	$0.886487\pi$
$734$	−7.00000			−0.258375
$735$		0			0
$736$	1.00000			0.0368605
$737$	30.0000	+	51.9615i	1.10506	+	1.91403i
$738$		0			0
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$	0.500000	+	0.866025i	0.0183804	+	0.0318357i
$741$		0			0
$742$	18.0000	+	15.5885i	0.660801	+	0.572270i
$743$	−15.0000			−0.550297			−0.275148	−	0.961402i	$-0.588727\pi$
$743$	−15.0000			−0.550297			−0.275148	+	0.961402i	$0.588727\pi$
$744$		0			0
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$	−11.0000	+	19.0526i	−0.402739	+	0.697564i
$747$		0			0
$748$	20.0000			0.731272
$749$	−1.00000	+	5.19615i	−0.0365392	+	0.189863i
$750$		0			0
$751$	25.0000	+	43.3013i	0.912263	+	1.58009i	0.810860	+	0.585240i	$0.199000\pi$
$751$	25.0000	+	43.3013i	0.912263	+	1.58009i	0.101403	+	0.994845i	$0.467667\pi$
$752$	−5.50000	+	9.52628i	−0.200564	+	0.347388i
$753$		0			0
$754$		0			0
$755$	−14.0000			−0.509512
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	0.500000	+	0.866025i	0.0181608	+	0.0314555i
$759$		0			0
$760$	3.50000	−	6.06218i	0.126958	−	0.219898i
$761$	−18.5000	−	32.0429i	−0.670624	−	1.16156i	−0.977727	−	0.209879i	$-0.932693\pi$
$761$	−18.5000	−	32.0429i	−0.670624	−	1.16156i	0.307103	−	0.951676i	$-0.400640\pi$
$762$		0			0
$763$	−5.00000	+	1.73205i	−0.181012	+	0.0627044i
$764$	−14.0000			−0.506502
$765$		0			0
$766$	−10.5000	+	18.1865i	−0.379380	+	0.657106i
$767$	−10.0000	+	17.3205i	−0.361079	+	0.625407i
$768$		0			0
$769$	−5.00000			−0.180305			−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$	−2.50000	+	12.9904i	−0.0900937	+	0.468141i
$771$		0			0
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	−2.50000	+	4.33013i	−0.0899188	+	0.155744i	−0.907477	−	0.420103i	$-0.861994\pi$
$773$	−2.50000	+	4.33013i	−0.0899188	+	0.155744i	0.817558	+	0.575846i	$0.195327\pi$
$774$		0			0
$775$	1.00000	+	1.73205i	0.0359211	+	0.0622171i
$776$	8.00000			0.287183
$777$		0			0
$778$	18.0000			0.645331
$779$	−17.5000	−	30.3109i	−0.627003	−	1.08600i
$780$		0			0
$781$	5.00000	−	8.66025i	0.178914	−	0.309888i
$782$	−2.00000	−	3.46410i	−0.0715199	−	0.123876i
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−11.0000			−0.392607
$786$		0			0
$787$	−1.00000	+	1.73205i	−0.0356462	+	0.0617409i	−0.883298	−	0.468812i	$-0.844682\pi$
$787$	−1.00000	+	1.73205i	−0.0356462	+	0.0617409i	0.847652	+	0.530553i	$0.178016\pi$
$788$	−1.50000	+	2.59808i	−0.0534353	+	0.0925526i
$789$		0			0
$790$	−12.0000			−0.426941
$791$	−28.0000	−	24.2487i	−0.995565	−	0.862185i
$792$		0			0
$793$	10.0000	+	17.3205i	0.355110	+	0.615069i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	54.0000			1.91278			0.956389	−	0.292096i	$-0.0943526\pi$
$797$	54.0000			1.91278			0.956389	+	0.292096i	$0.0943526\pi$
$798$		0			0
$799$	44.0000			1.55661
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	10.5000	−	18.1865i	0.370768	−	0.642189i
$803$	−25.0000	−	43.3013i	−0.882231	−	1.52807i
$804$		0			0
$805$	2.50000	−	0.866025i	0.0881134	−	0.0305234i
$806$	−10.0000			−0.352235
$807$		0			0
$808$		0			0
$809$	12.5000	−	21.6506i	0.439477	−	0.761196i	−0.558173	−	0.829725i	$-0.688497\pi$
$809$	12.5000	−	21.6506i	0.439477	−	0.761196i	0.997649	+	0.0685291i	$0.0218306\pi$
$810$		0			0
$811$	21.0000			0.737410			0.368705	−	0.929547i	$-0.379801\pi$
$811$	21.0000			0.737410			0.368705	+	0.929547i	$0.379801\pi$
$812$		0			0
$813$		0			0
$814$	2.50000	+	4.33013i	0.0876250	+	0.151771i
$815$	−12.0000	+	20.7846i	−0.420342	+	0.728053i
$816$		0			0
$817$	42.0000	+	72.7461i	1.46939	+	2.54507i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	5.00000			0.174608
$821$	5.00000	+	8.66025i	0.174501	+	0.302245i	0.939989	−	0.341206i	$-0.110835\pi$
$821$	5.00000	+	8.66025i	0.174501	+	0.302245i	−0.765487	+	0.643451i	$0.777502\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	−8.00000	−	6.92820i	−0.278356	−	0.241063i
$827$	6.00000			0.208640			0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000			0.208640			0.104320	+	0.994544i	$0.466733\pi$
$828$		0			0
$829$	26.0000	−	45.0333i	0.903017	−	1.56407i	0.0794606	−	0.996838i	$-0.474680\pi$
$829$	26.0000	−	45.0333i	0.903017	−	1.56407i	0.823557	−	0.567234i	$-0.191986\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$		0			0
$832$	−5.00000			−0.173344
$833$	−26.0000	−	10.3923i	−0.900847	−	0.360072i
$834$		0			0
$835$	−5.50000	−	9.52628i	−0.190335	−	0.329670i
$836$	17.5000	−	30.3109i	0.605250	−	1.04832i
$837$		0			0
$838$	−7.50000	−	12.9904i	−0.259083	−	0.448745i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	5.00000	+	8.66025i	0.172311	+	0.298452i
$843$		0			0
$844$	−8.50000	+	14.7224i	−0.292582	+	0.506767i
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	−7.00000	+	36.3731i	−0.240523	+	1.24979i
$848$	9.00000			0.309061
$849$		0			0
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	0.500000	−	0.866025i	0.0171398	−	0.0296870i
$852$		0			0
$853$	−11.0000			−0.376633			−0.188316	−	0.982108i	$-0.560303\pi$
$853$	−11.0000			−0.376633			−0.188316	+	0.982108i	$0.560303\pi$
$854$	−10.0000	+	3.46410i	−0.342193	+	0.118539i
$855$		0			0
$856$	1.00000	+	1.73205i	0.0341793	+	0.0592003i
$857$	1.00000	−	1.73205i	0.0341593	−	0.0591657i	−0.848440	−	0.529291i	$-0.822458\pi$
$857$	1.00000	−	1.73205i	0.0341593	−	0.0591657i	0.882600	+	0.470125i	$0.155791\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	−12.0000			−0.409197
$861$		0			0
$862$	12.0000			0.408722
$863$	22.5000	+	38.9711i	0.765909	+	1.32659i	0.939765	+	0.341822i	$0.111044\pi$
$863$	22.5000	+	38.9711i	0.765909	+	1.32659i	−0.173856	+	0.984771i	$0.555623\pi$
$864$		0			0
$865$	6.50000	−	11.2583i	0.221007	−	0.382795i
$866$	12.0000	+	20.7846i	0.407777	+	0.706290i
$867$		0			0
$868$	1.00000	−	5.19615i	0.0339422	−	0.176369i
$869$	−60.0000			−2.03536
$870$		0			0
$871$	−30.0000	+	51.9615i	−1.01651	+	1.76065i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$		0			0
$874$	−7.00000			−0.236779
$875$	2.00000	+	1.73205i	0.0676123	+	0.0585540i
$876$		0			0
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	0.988599	+	0.150574i	$0.0481123\pi$
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	−0.363898	+	0.931439i	$0.618554\pi$
$878$	−20.0000	+	34.6410i	−0.674967	+	1.16908i
$879$		0			0
$880$	2.50000	+	4.33013i	0.0842750	+	0.145969i
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$		0			0
$883$	−50.0000			−1.68263			−0.841317	−	0.540542i	$-0.818219\pi$
$883$	−50.0000			−1.68263			−0.841317	+	0.540542i	$0.818219\pi$
$884$	10.0000	+	17.3205i	0.336336	+	0.582552i
$885$		0			0
$886$	14.0000	−	24.2487i	0.470339	−	0.814651i
$887$	−22.0000	−	38.1051i	−0.738688	−	1.27944i	−0.953086	−	0.302698i	$-0.902113\pi$
$887$	−22.0000	−	38.1051i	−0.738688	−	1.27944i	0.214399	−	0.976746i	$-0.431221\pi$
$888$		0			0
$889$	−18.0000	−	15.5885i	−0.603701	−	0.522820i
$890$	−14.0000			−0.469281
$891$		0			0
$892$	6.00000	−	10.3923i	0.200895	−	0.347960i
$893$	38.5000	−	66.6840i	1.28835	−	2.23149i
$894$		0			0
$895$	−23.0000			−0.768805
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	14.5000	+	25.1147i	0.483871	+	0.838090i
$899$		0			0
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$	25.0000			0.832409
$903$		0			0
$904$	−14.0000			−0.465633
$905$	10.0000	+	17.3205i	0.332411	+	0.575753i
$906$		0			0
$907$	9.00000	−	15.5885i	0.298840	−	0.517606i	−0.677031	−	0.735955i	$-0.736734\pi$
$907$	9.00000	−	15.5885i	0.298840	−	0.517606i	0.975871	+	0.218348i	$0.0700669\pi$
$908$	−6.00000	−	10.3923i	−0.199117	−	0.344881i
$909$		0			0
$910$	−12.5000	+	4.33013i	−0.414371	+	0.143542i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	−30.0000	+	51.9615i	−0.992855	+	1.71968i
$914$	−7.00000	+	12.1244i	−0.231539	+	0.401038i
$915$		0			0
$916$	10.0000			0.330409
$917$	−4.50000	+	23.3827i	−0.148603	+	0.772164i
$918$		0			0
$919$	−14.0000	−	24.2487i	−0.461817	−	0.799891i	0.537234	−	0.843433i	$-0.319469\pi$
$919$	−14.0000	−	24.2487i	−0.461817	−	0.799891i	−0.999052	+	0.0435419i	$0.986136\pi$
$920$	0.500000	−	0.866025i	0.0164845	−	0.0285520i
$921$		0			0
$922$	2.00000	+	3.46410i	0.0658665	+	0.114084i
$923$	10.0000			0.329154
$924$		0			0
$925$	1.00000			0.0328798
$926$	−9.50000	−	16.4545i	−0.312189	−	0.540728i
$927$		0			0
$928$		0			0
$929$	9.50000	+	16.4545i	0.311685	+	0.539854i	0.978727	−	0.205166i	$-0.0657733\pi$
$929$	9.50000	+	16.4545i	0.311685	+	0.539854i	−0.667042	+	0.745020i	$0.732440\pi$
$930$		0			0
$931$	−38.5000	+	30.3109i	−1.26179	+	0.993399i
$932$	14.0000			0.458585
$933$		0			0
$934$	10.0000	−	17.3205i	0.327210	−	0.566744i
$935$	10.0000	−	17.3205i	0.327035	−	0.566441i
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−24.0000	−	20.7846i	−0.783628	−	0.678642i
$939$		0			0
$940$	5.50000	+	9.52628i	0.179390	+	0.310713i
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	−0.910773	−	0.412908i	$-0.864513\pi$
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	0.812975	+	0.582298i	$0.197846\pi$
$942$		0			0
$943$	−2.50000	−	4.33013i	−0.0814112	−	0.141008i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	−60.0000			−1.95077
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	−0.974244	−	0.225497i	$-0.927599\pi$
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	0.291835	−	0.956469i	$-0.405734\pi$
$948$		0			0
$949$	25.0000	−	43.3013i	0.811534	−	1.40562i
$950$	−3.50000	−	6.06218i	−0.113555	−	0.196683i
$951$		0			0
$952$	−10.0000	+	3.46410i	−0.324102	+	0.112272i
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$		0			0
$955$	−7.00000	+	12.1244i	−0.226515	+	0.392335i
$956$	−11.0000	+	19.0526i	−0.355765	+	0.616204i
$957$		0			0
$958$	18.0000			0.581554
$959$	5.00000	−	1.73205i	0.161458	−	0.0559308i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−2.50000	+	4.33013i	−0.0806032	+	0.139609i
$963$		0			0
$964$	−7.50000	−	12.9904i	−0.241559	−	0.418392i
$965$	−10.0000			−0.321911
$966$		0			0
$967$	4.00000			0.128631			0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000			0.128631			0.0643157	+	0.997930i	$0.479514\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$		0			0
$970$	4.00000	−	6.92820i	0.128432	−	0.222451i
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	8.00000	+	6.92820i	0.256468	+	0.222108i
$974$		0			0
$975$		0			0
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$		0			0
$979$	−70.0000			−2.23721
$980$	−1.00000	−	6.92820i	−0.0319438	−	0.221313i
$981$		0			0
$982$	18.0000	+	31.1769i	0.574403	+	0.994895i
$983$	−12.5000	+	21.6506i	−0.398688	+	0.690548i	−0.993564	−	0.113269i	$-0.963868\pi$
$983$	−12.5000	+	21.6506i	−0.398688	+	0.690548i	0.594876	+	0.803817i	$0.297201\pi$
$984$		0			0
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$		0			0
$987$		0			0
$988$	35.0000			1.11350
$989$	6.00000	+	10.3923i	0.190789	+	0.330456i
$990$		0			0
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	−0.388723	−	0.921355i	$-0.627084\pi$
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	0.992278	−	0.124033i	$-0.0395829\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$		0			0
$994$	−1.00000	+	5.19615i	−0.0317181	+	0.164812i
$995$	4.00000			0.126809
$996$		0			0
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	−0.637587	−	0.770378i	$-0.720067\pi$
$997$	11.0000	−	19.0526i	0.348373	−	0.603401i	0.985961	+	0.166978i	$0.0534008\pi$
$998$	20.0000	−	34.6410i	0.633089	−	1.09654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.g.361.1		2
3.2	odd	2		210.2.i.b.151.1	yes	2
7.2	even	3	inner	630.2.k.g.541.1		2
7.3	odd	6		4410.2.a.u.1.1		1
7.4	even	3		4410.2.a.j.1.1		1
12.11	even	2		1680.2.bg.d.1201.1		2
15.2	even	4		1050.2.o.g.949.2		4
15.8	even	4		1050.2.o.g.949.1		4
15.14	odd	2		1050.2.i.p.151.1		2
21.2	odd	6		210.2.i.b.121.1	✓	2
21.5	even	6		1470.2.i.e.961.1		2
21.11	odd	6		1470.2.a.l.1.1		1
21.17	even	6		1470.2.a.o.1.1		1
21.20	even	2		1470.2.i.e.361.1		2
84.23	even	6		1680.2.bg.d.961.1		2
105.2	even	12		1050.2.o.g.499.1		4
105.23	even	12		1050.2.o.g.499.2		4
105.44	odd	6		1050.2.i.p.751.1		2
105.59	even	6		7350.2.a.a.1.1		1
105.74	odd	6		7350.2.a.u.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.b.121.1	✓	2	21.2	odd	6
210.2.i.b.151.1	yes	2	3.2	odd	2
630.2.k.g.361.1		2	1.1	even	1	trivial
630.2.k.g.541.1		2	7.2	even	3	inner
1050.2.i.p.151.1		2	15.14	odd	2
1050.2.i.p.751.1		2	105.44	odd	6
1050.2.o.g.499.1		4	105.2	even	12
1050.2.o.g.499.2		4	105.23	even	12
1050.2.o.g.949.1		4	15.8	even	4
1050.2.o.g.949.2		4	15.2	even	4
1470.2.a.l.1.1		1	21.11	odd	6
1470.2.a.o.1.1		1	21.17	even	6
1470.2.i.e.361.1		2	21.20	even	2
1470.2.i.e.961.1		2	21.5	even	6
1680.2.bg.d.961.1		2	84.23	even	6
1680.2.bg.d.1201.1		2	12.11	even	2
4410.2.a.j.1.1		1	7.4	even	3
4410.2.a.u.1.1		1	7.3	odd	6
7350.2.a.a.1.1		1	105.59	even	6
7350.2.a.u.1.1		1	105.74	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} -5.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.50000 + 6.06218i) q^{19} -1.00000 q^{20} -5.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.50000 - 4.33013i) q^{26} +(2.50000 - 0.866025i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(0.500000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{37} +(-3.50000 + 6.06218i) q^{38} +(-0.500000 - 0.866025i) q^{40} -5.00000 q^{41} +12.0000 q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(-5.50000 - 9.52628i) q^{47} +(1.00000 + 6.92820i) q^{49} -1.00000 q^{50} +(2.50000 - 4.33013i) q^{52} +(-4.50000 + 7.79423i) q^{53} -5.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(2.00000 - 3.46410i) q^{59} +(-2.00000 - 3.46410i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(6.00000 - 10.3923i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(2.50000 - 0.866025i) q^{70} -2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(12.5000 - 4.33013i) q^{77} +(6.00000 + 10.3923i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.50000 - 4.33013i) q^{82} +12.0000 q^{83} -4.00000 q^{85} +(6.00000 + 10.3923i) q^{86} +(2.50000 - 4.33013i) q^{88} +(7.00000 + 12.1244i) q^{89} +(10.0000 + 8.66025i) q^{91} -1.00000 q^{92} +(5.50000 - 9.52628i) q^{94} +(-3.50000 + 6.06218i) q^{95} -8.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + q^5 - 4 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + q^{5} - 4 q^{7} - 2 q^{8} - q^{10} - 5 q^{11} - 10 q^{13} + q^{14} - q^{16} - 4 q^{17} + 7 q^{19} - 2 q^{20} - 10 q^{22} + q^{23} - q^{25} - 5 q^{26} + 5 q^{28} + 2 q^{31} + q^{32} - 8 q^{34} + q^{35} - q^{37} - 7 q^{38} - q^{40} - 10 q^{41} + 24 q^{43} - 5 q^{44} - q^{46} - 11 q^{47} + 2 q^{49} - 2 q^{50} + 5 q^{52} - 9 q^{53} - 10 q^{55} + 4 q^{56} + 4 q^{59} - 4 q^{61} + 4 q^{62} + 2 q^{64} - 5 q^{65} + 12 q^{67} - 4 q^{68} + 5 q^{70} - 4 q^{71} - 10 q^{73} + q^{74} - 14 q^{76} + 25 q^{77} + 12 q^{79} + q^{80} - 5 q^{82} + 24 q^{83} - 8 q^{85} + 12 q^{86} + 5 q^{88} + 14 q^{89} + 20 q^{91} - 2 q^{92} + 11 q^{94} - 7 q^{95} - 16 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + q^5 - 4 * q^7 - 2 * q^8 - q^10 - 5 * q^11 - 10 * q^13 + q^14 - q^16 - 4 * q^17 + 7 * q^19 - 2 * q^20 - 10 * q^22 + q^23 - q^25 - 5 * q^26 + 5 * q^28 + 2 * q^31 + q^32 - 8 * q^34 + q^35 - q^37 - 7 * q^38 - q^40 - 10 * q^41 + 24 * q^43 - 5 * q^44 - q^46 - 11 * q^47 + 2 * q^49 - 2 * q^50 + 5 * q^52 - 9 * q^53 - 10 * q^55 + 4 * q^56 + 4 * q^59 - 4 * q^61 + 4 * q^62 + 2 * q^64 - 5 * q^65 + 12 * q^67 - 4 * q^68 + 5 * q^70 - 4 * q^71 - 10 * q^73 + q^74 - 14 * q^76 + 25 * q^77 + 12 * q^79 + q^80 - 5 * q^82 + 24 * q^83 - 8 * q^85 + 12 * q^86 + 5 * q^88 + 14 * q^89 + 20 * q^91 - 2 * q^92 + 11 * q^94 - 7 * q^95 - 16 * q^97 - 11 * q^98

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