LMFDB - Embedded newform 1680.2.bg.d.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(961,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.4148675396$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1680.961
Dual form			1680.2.bg.d.1201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} -5.00000 q^{13} +1.00000 q^{15} +(2.00000 + 3.46410i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-2.50000 - 0.866025i) q^{21} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{31} +(-2.50000 + 4.33013i) q^{33} +(0.500000 + 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(2.50000 + 4.33013i) q^{39} +5.00000 q^{41} -12.0000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-5.50000 + 9.52628i) q^{47} +(1.00000 - 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{51} +(4.50000 + 7.79423i) q^{53} +5.00000 q^{55} +7.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(0.500000 + 2.59808i) q^{63} +(2.50000 - 4.33013i) q^{65} +(-6.00000 - 10.3923i) q^{67} -1.00000 q^{69} -2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(-12.5000 - 4.33013i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -4.00000 q^{85} +(-7.00000 + 12.1244i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-1.00000 + 1.73205i) q^{93} +(-3.50000 - 6.06218i) q^{95} -8.00000 q^{97} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - q^{5} + 4 q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 - q^5 + 4 * q^7 - q^9	$ 2 q - q^{3} - q^{5} + 4 q^{7} - q^{9} - 5 q^{11} - 10 q^{13} + 2 q^{15} + 4 q^{17} - 7 q^{19} - 5 q^{21} + q^{23} - q^{25} + 2 q^{27} - 2 q^{31} - 5 q^{33} + q^{35} - q^{37} + 5 q^{39} + 10 q^{41} - 24 q^{43} - q^{45} - 11 q^{47} + 2 q^{49} + 4 q^{51} + 9 q^{53} + 10 q^{55} + 14 q^{57} + 4 q^{59} - 4 q^{61} + q^{63} + 5 q^{65} - 12 q^{67} - 2 q^{69} - 4 q^{71} - 10 q^{73} - q^{75} - 25 q^{77} - 12 q^{79} - q^{81} + 24 q^{83} - 8 q^{85} - 14 q^{89} - 20 q^{91} - 2 q^{93} - 7 q^{95} - 16 q^{97} + 10 q^{99}+O(q^{100}) $ 2 * q - q^3 - q^5 + 4 * q^7 - q^9 - 5 * q^11 - 10 * q^13 + 2 * q^15 + 4 * q^17 - 7 * q^19 - 5 * q^21 + q^23 - q^25 + 2 * q^27 - 2 * q^31 - 5 * q^33 + q^35 - q^37 + 5 * q^39 + 10 * q^41 - 24 * q^43 - q^45 - 11 * q^47 + 2 * q^49 + 4 * q^51 + 9 * q^53 + 10 * q^55 + 14 * q^57 + 4 * q^59 - 4 * q^61 + q^63 + 5 * q^65 - 12 * q^67 - 2 * q^69 - 4 * q^71 - 10 * q^73 - q^75 - 25 * q^77 - 12 * q^79 - q^81 + 24 * q^83 - 8 * q^85 - 14 * q^89 - 20 * q^91 - 2 * q^93 - 7 * q^95 - 16 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	−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
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		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			0
$15$	1.00000			0.258199
$16$		0			0
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−2.50000	−	0.866025i	−0.545545	−	0.188982i
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		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	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$		0			0
$33$	−2.50000	+	4.33013i	−0.435194	+	0.753778i
$34$		0			0
$35$	0.500000	+	2.59808i	0.0845154	+	0.439155i
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	2.50000	+	4.33013i	0.400320	+	0.693375i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$	−12.0000			−1.82998			−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000			−1.82998			−0.914991	+	0.403473i	$0.867803\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	−5.50000	+	9.52628i	−0.802257	+	1.38955i	0.115870	+	0.993264i	$0.463035\pi$
$47$	−5.50000	+	9.52628i	−0.802257	+	1.38955i	−0.918127	+	0.396286i	$0.870299\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$		0			0
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$		0			0
$57$	7.00000			0.927173
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$		0			0
$63$	0.500000	+	2.59808i	0.0629941	+	0.327327i
$64$		0			0
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		0			0
$69$	−1.00000			−0.120386
$70$		0			0
$71$	−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	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	0.409644	−	0.912245i	$-0.365653\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$	−12.5000	−	4.33013i	−1.42451	−	0.493464i
$78$		0			0
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	0.301401	+	0.953498i	$0.402546\pi$
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	−0.976453	+	0.215728i	$0.930788\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	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
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$		0			0
$91$	−10.0000	+	8.66025i	−1.04828	+	0.907841i
$92$		0			0
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$		0			0
$95$	−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	$0.633125\pi$
$98$		0			0
$99$	5.00000			0.502519
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$		0			0
$105$	2.00000	−	1.73205i	0.195180	−	0.169031i
$106$		0			0
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	1.00000			0.0949158
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$		0			0
$117$	2.50000	−	4.33013i	0.231125	−	0.400320i
$118$		0			0
$119$	10.0000	+	3.46410i	0.916698	+	0.317554i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$	−2.50000	−	4.33013i	−0.225417	−	0.390434i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$		0			0
$129$	6.00000	+	10.3923i	0.528271	+	0.914991i
$130$		0			0
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		0			0
$133$	3.50000	+	18.1865i	0.303488	+	1.57697i
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	11.0000			0.926367
$142$		0			0
$143$	12.5000	+	21.6506i	1.04530	+	1.81052i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$		0			0
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$		0			0
$151$	7.00000	+	12.1244i	0.569652	+	0.986666i	0.996600	+	0.0823900i	$0.0262553\pi$
$151$	7.00000	+	12.1244i	0.569652	+	0.986666i	−0.426948	+	0.904276i	$0.640411\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	2.00000			0.160644
$156$		0			0
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	0.558661	−	0.829396i	$-0.311315\pi$
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	4.50000	−	7.79423i	0.356873	−	0.618123i
$160$		0			0
$161$	−0.500000	−	2.59808i	−0.0394055	−	0.204757i
$162$		0			0
$163$	−12.0000	+	20.7846i	−0.939913	+	1.62798i	−0.174282	+	0.984696i	$0.555760\pi$
$163$	−12.0000	+	20.7846i	−0.939913	+	1.62798i	−0.765631	+	0.643280i	$0.777573\pi$
$164$		0			0
$165$	−2.50000	−	4.33013i	−0.194625	−	0.337100i
$166$		0			0
$167$	−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
$170$		0			0
$171$	−3.50000	−	6.06218i	−0.267652	−	0.463586i
$172$		0			0
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	−0.505792	−	0.862656i	$-0.668800\pi$
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	0.999978	+	0.00670064i	$0.00213290\pi$
$174$		0			0
$175$	−2.50000	−	0.866025i	−0.188982	−	0.0654654i
$176$		0			0
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$		0			0
$179$	−11.5000	−	19.9186i	−0.859550	−	1.48878i	−0.872358	−	0.488867i	$-0.837410\pi$
$179$	−11.5000	−	19.9186i	−0.859550	−	1.48878i	0.0128080	−	0.999918i	$-0.495923\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$	4.00000			0.295689
$184$		0			0
$185$	−0.500000	−	0.866025i	−0.0367607	−	0.0636715i
$186$		0			0
$187$	10.0000	−	17.3205i	0.731272	−	1.26660i
$188$		0			0
$189$	2.00000	−	1.73205i	0.145479	−	0.125988i
$190$		0			0
$191$	7.00000	−	12.1244i	0.506502	−	0.877288i	−0.493469	−	0.869763i	$-0.664272\pi$
$191$	7.00000	−	12.1244i	0.506502	−	0.877288i	0.999972	−	0.00752447i	$-0.00239513\pi$
$192$		0			0
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	0.628037	−	0.778183i	$-0.283859\pi$
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	−0.987945	+	0.154805i	$0.950525\pi$
$194$		0			0
$195$	−5.00000			−0.358057
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$		0			0
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$		0			0
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$		0			0
$209$	35.0000			2.42100
$210$		0			0
$211$	−17.0000			−1.17033			−0.585164	−	0.810915i	$-0.698970\pi$
$211$	−17.0000			−1.17033			−0.585164	+	0.810915i	$0.698970\pi$
$212$		0			0
$213$	1.00000	+	1.73205i	0.0685189	+	0.118678i
$214$		0			0
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$		0			0
$217$	−5.00000	−	1.73205i	−0.339422	−	0.117579i
$218$		0			0
$219$	−5.00000	+	8.66025i	−0.337869	+	0.585206i
$220$		0			0
$221$	−10.0000	−	17.3205i	−0.672673	−	1.16510i
$222$		0			0
$223$	12.0000			0.803579			0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000			0.803579			0.401790	+	0.915732i	$0.368388\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$		0			0
$231$	2.50000	+	12.9904i	0.164488	+	0.854704i
$232$		0			0
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	−0.540301	−	0.841472i	$-0.681690\pi$
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	0.998886	+	0.0471787i	$0.0150230\pi$
$234$		0			0
$235$	−5.50000	−	9.52628i	−0.358780	−	0.621426i
$236$		0			0
$237$	12.0000			0.779484
$238$		0			0
$239$	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	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$	17.5000	−	30.3109i	1.11350	−	1.92864i
$248$		0			0
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$	−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
$254$		0			0
$255$	2.00000	+	3.46410i	0.125245	+	0.216930i
$256$		0			0
$257$	8.00000	−	13.8564i	0.499026	−	0.864339i	−0.500973	−	0.865463i	$-0.667024\pi$
$257$	8.00000	−	13.8564i	0.499026	−	0.864339i	0.999999	+	0.00112398i	$0.000357774\pi$
$258$		0			0
$259$	0.500000	+	2.59808i	0.0310685	+	0.161437i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$		0			0
$267$	14.0000			0.856786
$268$		0			0
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$		0			0
$273$	12.5000	+	4.33013i	0.756534	+	0.262071i
$274$		0			0
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$		0			0
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	0.575408	−	0.817867i	$-0.304843\pi$
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	−0.995997	+	0.0893846i	$0.971510\pi$
$278$		0			0
$279$	2.00000			0.119737
$280$		0			0
$281$	7.00000			0.417585			0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000			0.417585			0.208792	+	0.977960i	$0.433047\pi$
$282$		0			0
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	0.678280	−	0.734804i	$-0.262726\pi$
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	−0.975499	+	0.220005i	$0.929393\pi$
$284$		0			0
$285$	−3.50000	+	6.06218i	−0.207322	+	0.359092i
$286$		0			0
$287$	10.0000	−	8.66025i	0.590281	−	0.511199i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	4.00000	+	6.92820i	0.234484	+	0.406138i
$292$		0			0
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$	−2.50000	−	4.33013i	−0.145065	−	0.251259i
$298$		0			0
$299$	−2.50000	+	4.33013i	−0.144579	+	0.250418i
$300$		0			0
$301$	−24.0000	+	20.7846i	−1.38334	+	1.19800i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.00000	−	3.46410i	−0.114520	−	0.198354i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$		0			0
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	0.956864	−	0.290537i	$-0.0938340\pi$
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	−0.730044	+	0.683400i	$0.760501\pi$
$312$		0			0
$313$	−8.00000	+	13.8564i	−0.452187	+	0.783210i	−0.998522	−	0.0543564i	$-0.982689\pi$
$313$	−8.00000	+	13.8564i	−0.452187	+	0.783210i	0.546335	+	0.837567i	$0.316023\pi$
$314$		0			0
$315$	−2.50000	−	0.866025i	−0.140859	−	0.0487950i
$316$		0			0
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	−0.372061	−	0.928208i	$-0.621349\pi$
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	0.989882	−	0.141890i	$-0.0453179\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	2.00000			0.111629
$322$		0			0
$323$	−28.0000			−1.55796
$324$		0			0
$325$	2.50000	+	4.33013i	0.138675	+	0.240192i
$326$		0			0
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$	5.50000	+	28.5788i	0.303225	+	1.57560i
$330$		0			0
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	0.879440	−	0.476011i	$-0.157918\pi$
$332$		0			0
$333$	−0.500000	−	0.866025i	−0.0273998	−	0.0474579i
$334$		0			0
$335$	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	$0.643530\pi$
$338$		0			0
$339$	7.00000	+	12.1244i	0.380188	+	0.658505i
$340$		0			0
$341$	−5.00000	+	8.66025i	−0.270765	+	0.468979i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	0.500000	−	0.866025i	0.0269191	−	0.0466252i
$346$		0			0
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$		0			0
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$		0			0
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$		0			0
$357$	−2.00000	−	10.3923i	−0.105851	−	0.550019i
$358$		0			0
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	14.0000			0.734809
$364$		0			0
$365$	10.0000			0.523424
$366$		0			0
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$		0			0
$369$	−2.50000	+	4.33013i	−0.130145	+	0.225417i
$370$		0			0
$371$	22.5000	+	7.79423i	1.16814	+	0.404656i
$372$		0			0
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	−0.427051	−	0.904227i	$-0.640448\pi$
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	0.996610	−	0.0822766i	$-0.0262191\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	4.50000	+	7.79423i	0.230542	+	0.399310i
$382$		0			0
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$		0			0
$385$	10.0000	−	8.66025i	0.509647	−	0.441367i
$386$		0			0
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$		0			0
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$		0			0
$393$	9.00000			0.453990
$394$		0			0
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$		0			0
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$		0			0
$399$	14.0000	−	12.1244i	0.700877	−	0.606977i
$400$		0			0
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	−0.475253	−	0.879849i	$-0.657644\pi$
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	0.999598	−	0.0283431i	$-0.00902310\pi$
$402$		0			0
$403$	5.00000	+	8.66025i	0.249068	+	0.431398i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	5.00000			0.247841
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$	1.00000	−	1.73205i	0.0493264	−	0.0854358i
$412$		0			0
$413$	10.0000	+	3.46410i	0.492068	+	0.170457i
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	−2.00000	−	3.46410i	−0.0979404	−	0.169638i
$418$		0			0
$419$	−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	$0.421644\pi$
$422$		0			0
$423$	−5.50000	−	9.52628i	−0.267419	−	0.463184i
$424$		0			0
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	2.00000	+	10.3923i	0.0967868	+	0.502919i
$428$		0			0
$429$	12.5000	−	21.6506i	0.603506	−	1.04530i
$430$		0			0
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	24.0000			1.15337			0.576683	−	0.816968i	$-0.304347\pi$
$433$	24.0000			1.15337			0.576683	+	0.816968i	$0.304347\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.50000	+	6.06218i	0.167428	+	0.289993i
$438$		0			0
$439$	−20.0000	+	34.6410i	−0.954548	+	1.65333i	−0.219149	+	0.975691i	$0.570328\pi$
$439$	−20.0000	+	34.6410i	−0.954548	+	1.65333i	−0.735399	+	0.677634i	$0.763005\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	0.314082	+	0.949396i	$0.398303\pi$
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	−0.979242	+	0.202695i	$0.935030\pi$
$444$		0			0
$445$	−7.00000	−	12.1244i	−0.331832	−	0.574750i
$446$		0			0
$447$	12.0000			0.567581
$448$		0			0
$449$	−29.0000			−1.36859			−0.684297	−	0.729203i	$-0.739891\pi$
$449$	−29.0000			−1.36859			−0.684297	+	0.729203i	$0.739891\pi$
$450$		0			0
$451$	−12.5000	−	21.6506i	−0.588602	−	1.01949i
$452$		0			0
$453$	7.00000	−	12.1244i	0.328889	−	0.569652i
$454$		0			0
$455$	−2.50000	−	12.9904i	−0.117202	−	0.608998i
$456$		0			0
$457$	7.00000	−	12.1244i	0.327446	−	0.567153i	−0.654558	−	0.756012i	$-0.727145\pi$
$457$	7.00000	−	12.1244i	0.327446	−	0.567153i	0.982004	+	0.188858i	$0.0604787\pi$
$458$		0			0
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	−4.00000			−0.186299			−0.0931493	−	0.995652i	$-0.529693\pi$
$461$	−4.00000			−0.186299			−0.0931493	+	0.995652i	$0.529693\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$		0			0
$465$	−1.00000	−	1.73205i	−0.0463739	−	0.0803219i
$466$		0			0
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	−0.999097	−	0.0424970i	$-0.986469\pi$
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	0.536352	+	0.843995i	$0.319802\pi$
$468$		0			0
$469$	−30.0000	−	10.3923i	−1.38527	−	0.479872i
$470$		0			0
$471$	−5.50000	+	9.52628i	−0.253427	+	0.438948i
$472$		0			0
$473$	30.0000	+	51.9615i	1.37940	+	2.38919i
$474$		0			0
$475$	7.00000			0.321182
$476$		0			0
$477$	−9.00000			−0.412082
$478$		0			0
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$		0			0
$483$	−2.00000	+	1.73205i	−0.0910032	+	0.0788110i
$484$		0			0
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$		0			0
$487$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$487$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$488$		0			0
$489$	24.0000			1.08532
$490$		0			0
$491$	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
$494$		0			0
$495$	−2.50000	+	4.33013i	−0.112367	+	0.194625i
$496$		0			0
$497$	−4.00000	+	3.46410i	−0.179425	+	0.155386i
$498$		0			0
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$		0			0
$501$	5.50000	+	9.52628i	0.245722	+	0.425603i
$502$		0			0
$503$	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
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$		0			0
$513$	−3.50000	+	6.06218i	−0.154529	+	0.267652i
$514$		0			0
$515$	4.00000	+	6.92820i	0.176261	+	0.305293i
$516$		0			0
$517$	55.0000			2.41890
$518$		0			0
$519$	−13.0000			−0.570637
$520$		0			0
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	0.959841	+	0.280543i	$0.0905145\pi$
$521$	16.5000	+	28.5788i	0.722878	+	1.25206i	−0.236963	+	0.971519i	$0.576152\pi$
$522$		0			0
$523$	−11.0000	+	19.0526i	−0.480996	+	0.833110i	−0.999762	−	0.0218062i	$-0.993058\pi$
$523$	−11.0000	+	19.0526i	−0.480996	+	0.833110i	0.518766	+	0.854916i	$0.326392\pi$
$524$		0			0
$525$	0.500000	+	2.59808i	0.0218218	+	0.113389i
$526$		0			0
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−25.0000			−1.08287
$534$		0			0
$535$	−1.00000	−	1.73205i	−0.0432338	−	0.0748831i
$536$		0			0
$537$	−11.5000	+	19.9186i	−0.496262	+	0.859550i
$538$		0			0
$539$	−32.5000	+	12.9904i	−1.39987	+	0.559535i
$540$		0			0
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$		0			0
$543$	−10.0000	−	17.3205i	−0.429141	−	0.743294i
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	−2.00000	−	3.46410i	−0.0853579	−	0.147844i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	6.00000	+	31.1769i	0.255146	+	1.32578i
$554$		0			0
$555$	−0.500000	+	0.866025i	−0.0212238	+	0.0367607i
$556$		0			0
$557$	−18.5000	−	32.0429i	−0.783870	−	1.35770i	−0.929672	−	0.368389i	$-0.879909\pi$
$557$	−18.5000	−	32.0429i	−0.783870	−	1.35770i	0.145802	−	0.989314i	$-0.453424\pi$
$558$		0			0
$559$	60.0000			2.53773
$560$		0			0
$561$	−20.0000			−0.844401
$562$		0			0
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$		0			0
$565$	7.00000	−	12.1244i	0.294492	−	0.510075i
$566$		0			0
$567$	−2.50000	−	0.866025i	−0.104990	−	0.0363696i
$568$		0			0
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	0.0900490	+	0.995937i	$0.471298\pi$
$569$	−19.5000	+	33.7750i	−0.817483	+	1.41592i	−0.907532	+	0.419984i	$0.862036\pi$
$570$		0			0
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	0.892413	+	0.451219i	$0.149011\pi$
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	−0.0554391	+	0.998462i	$0.517656\pi$
$572$		0			0
$573$	−14.0000			−0.584858
$574$		0			0
$575$	−1.00000			−0.0417029
$576$		0			0
$577$	−13.0000	−	22.5167i	−0.541197	−	0.937381i	−0.998836	−	0.0482425i	$-0.984638\pi$
$577$	−13.0000	−	22.5167i	−0.541197	−	0.937381i	0.457639	−	0.889138i	$-0.348695\pi$
$578$		0			0
$579$	−5.00000	+	8.66025i	−0.207793	+	0.359908i
$580$		0			0
$581$	24.0000	−	20.7846i	0.995688	−	0.862291i
$582$		0			0
$583$	22.5000	−	38.9711i	0.931855	−	1.61402i
$584$		0			0
$585$	2.50000	+	4.33013i	0.103362	+	0.179029i
$586$		0			0
$587$	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
$590$		0			0
$591$	1.50000	+	2.59808i	0.0617018	+	0.106871i
$592$		0			0
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$		0			0
$595$	−8.00000	+	6.92820i	−0.327968	+	0.284029i
$596$		0			0
$597$	−2.00000	+	3.46410i	−0.0818546	+	0.141776i
$598$		0			0
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	0.745613	−	0.666379i	$-0.232157\pi$
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	−0.949908	+	0.312531i	$0.898823\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	0.450467	+	0.892793i	$0.351258\pi$
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	−0.998415	+	0.0562808i	$0.982076\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	27.5000	−	47.6314i	1.11253	−	1.92696i
$612$		0			0
$613$	21.5000	+	37.2391i	0.868377	+	1.50407i	0.863655	+	0.504084i	$0.168170\pi$
$613$	21.5000	+	37.2391i	0.868377	+	1.50407i	0.00472215	+	0.999989i	$0.498497\pi$
$614$		0			0
$615$	5.00000			0.201619
$616$		0			0
$617$	−8.00000			−0.322068			−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000			−0.322068			−0.161034	+	0.986949i	$0.551483\pi$
$618$		0			0
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	0.999996	+	0.00279365i	$0.000889247\pi$
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	−0.497579	+	0.867419i	$0.665777\pi$
$620$		0			0
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$		0			0
$623$	7.00000	+	36.3731i	0.280449	+	1.45726i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−17.5000	−	30.3109i	−0.698883	−	1.21050i
$628$		0			0
$629$	−4.00000			−0.159490
$630$		0			0
$631$	−6.00000			−0.238856			−0.119428	−	0.992843i	$-0.538106\pi$
$631$	−6.00000			−0.238856			−0.119428	+	0.992843i	$0.538106\pi$
$632$		0			0
$633$	8.50000	+	14.7224i	0.337845	+	0.585164i
$634$		0			0
$635$	4.50000	−	7.79423i	0.178577	−	0.309305i
$636$		0			0
$637$	−5.00000	+	34.6410i	−0.198107	+	1.37253i
$638$		0			0
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$		0			0
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	0.580674	−	0.814136i	$-0.302789\pi$
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	−0.995400	+	0.0958109i	$0.969456\pi$
$642$		0			0
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$		0			0
$645$	−12.0000			−0.472500
$646$		0			0
$647$	−11.5000	−	19.9186i	−0.452112	−	0.783080i	0.546405	−	0.837521i	$-0.315996\pi$
$647$	−11.5000	−	19.9186i	−0.452112	−	0.783080i	−0.998517	+	0.0544405i	$0.982662\pi$
$648$		0			0
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$		0			0
$651$	1.00000	+	5.19615i	0.0391931	+	0.203653i
$652$		0			0
$653$	9.50000	−	16.4545i	0.371764	−	0.643914i	−0.618073	−	0.786121i	$-0.712086\pi$
$653$	9.50000	−	16.4545i	0.371764	−	0.643914i	0.989837	+	0.142207i	$0.0454198\pi$
$654$		0			0
$655$	−4.50000	−	7.79423i	−0.175830	−	0.304546i
$656$		0			0
$657$	10.0000			0.390137
$658$		0			0
$659$	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	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$		0			0
$663$	−10.0000	+	17.3205i	−0.388368	+	0.672673i
$664$		0			0
$665$	−17.5000	−	6.06218i	−0.678621	−	0.235081i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$		0			0
$671$	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	$0.524564\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	0.352549	+	0.935793i	$0.385315\pi$
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	−0.986695	+	0.162581i	$0.948018\pi$
$678$		0			0
$679$	−16.0000	+	13.8564i	−0.614024	+	0.531760i
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	0.825222	−	0.564809i	$-0.191050\pi$
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	−0.901750	+	0.432259i	$0.857717\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$		0			0
$687$	10.0000			0.381524
$688$		0			0
$689$	−22.5000	−	38.9711i	−0.857182	−	1.48468i
$690$		0			0
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$		0			0
$693$	10.0000	−	8.66025i	0.379869	−	0.328976i
$694$		0			0
$695$	−2.00000	+	3.46410i	−0.0758643	+	0.131401i
$696$		0			0
$697$	10.0000	+	17.3205i	0.378777	+	0.656061i
$698$		0			0
$699$	−14.0000			−0.529529
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$		0			0
$705$	−5.50000	+	9.52628i	−0.207142	+	0.358780i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−14.0000	+	24.2487i	−0.525781	+	0.910679i	0.473768	+	0.880650i	$0.342894\pi$
$709$	−14.0000	+	24.2487i	−0.525781	+	0.910679i	−0.999549	+	0.0300298i	$0.990440\pi$
$710$		0			0
$711$	−6.00000	−	10.3923i	−0.225018	−	0.389742i
$712$		0			0
$713$	−2.00000			−0.0749006
$714$		0			0
$715$	−25.0000			−0.934947
$716$		0			0
$717$	−11.0000	−	19.0526i	−0.410803	−	0.711531i
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	−4.00000	−	20.7846i	−0.148968	−	0.774059i
$722$		0			0
$723$	−7.50000	+	12.9904i	−0.278928	+	0.483117i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	3.00000			0.111264			0.0556319	−	0.998451i	$-0.482283\pi$
$727$	3.00000			0.111264			0.0556319	+	0.998451i	$0.482283\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$		0			0
$733$	−4.50000	+	7.79423i	−0.166211	+	0.287886i	−0.937085	−	0.349102i	$-0.886487\pi$
$733$	−4.50000	+	7.79423i	−0.166211	+	0.287886i	0.770873	+	0.636988i	$0.219820\pi$
$734$		0			0
$735$	1.00000	−	6.92820i	0.0368856	−	0.255551i
$736$		0			0
$737$	−30.0000	+	51.9615i	−1.10506	+	1.91403i
$738$		0			0
$739$	−7.50000	−	12.9904i	−0.275892	−	0.477859i	0.694468	−	0.719524i	$-0.255640\pi$
$739$	−7.50000	−	12.9904i	−0.275892	−	0.477859i	−0.970360	+	0.241665i	$0.922307\pi$
$740$		0			0
$741$	−35.0000			−1.28576
$742$		0			0
$743$	−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
$746$		0			0
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$	1.00000	+	5.19615i	0.0365392	+	0.189863i
$750$		0			0
$751$	−25.0000	+	43.3013i	−0.912263	+	1.58009i	−0.101403	+	0.994845i	$0.532333\pi$
$751$	−25.0000	+	43.3013i	−0.912263	+	1.58009i	−0.810860	+	0.585240i	$0.801000\pi$
$752$		0			0
$753$	0.500000	+	0.866025i	0.0182210	+	0.0315597i
$754$		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			0
$759$	2.50000	+	4.33013i	0.0907443	+	0.157174i
$760$		0			0
$761$	18.5000	−	32.0429i	0.670624	−	1.16156i	−0.307103	−	0.951676i	$-0.599360\pi$
$761$	18.5000	−	32.0429i	0.670624	−	1.16156i	0.977727	−	0.209879i	$-0.0673071\pi$
$762$		0			0
$763$	5.00000	+	1.73205i	0.181012	+	0.0627044i
$764$		0			0
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$		0			0
$767$	−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	$0.528735\pi$
$770$		0			0
$771$	−16.0000			−0.576226
$772$		0			0
$773$	2.50000	+	4.33013i	0.0899188	+	0.155744i	0.907477	−	0.420103i	$-0.138006\pi$
$773$	2.50000	+	4.33013i	0.0899188	+	0.155744i	−0.817558	+	0.575846i	$0.804673\pi$
$774$		0			0
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$		0			0
$777$	2.00000	−	1.73205i	0.0717496	−	0.0621370i
$778$		0			0
$779$	−17.5000	+	30.3109i	−0.627003	+	1.08600i
$780$		0			0
$781$	5.00000	+	8.66025i	0.178914	+	0.309888i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	11.0000			0.392607
$786$		0			0
$787$	1.00000	+	1.73205i	0.0356462	+	0.0617409i	0.883298	−	0.468812i	$-0.155318\pi$
$787$	1.00000	+	1.73205i	0.0356462	+	0.0617409i	−0.847652	+	0.530553i	$0.821984\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−28.0000	+	24.2487i	−0.995565	+	0.862185i
$792$		0			0
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$		0			0
$795$	4.50000	+	7.79423i	0.159599	+	0.276433i
$796$		0			0
$797$	−54.0000			−1.91278			−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000			−1.91278			−0.956389	+	0.292096i	$0.905647\pi$
$798$		0			0
$799$	−44.0000			−1.55661
$800$		0			0
$801$	−7.00000	−	12.1244i	−0.247333	−	0.428393i
$802$		0			0
$803$	−25.0000	+	43.3013i	−0.882231	+	1.52807i
$804$		0			0
$805$	2.50000	+	0.866025i	0.0881134	+	0.0305234i
$806$		0			0
$807$	12.0000	−	20.7846i	0.422420	−	0.731653i
$808$		0			0
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	0.558173	−	0.829725i	$-0.311503\pi$
$809$	−12.5000	−	21.6506i	−0.439477	−	0.761196i	−0.997649	+	0.0685291i	$0.978169\pi$
$810$		0			0
$811$	−21.0000			−0.737410			−0.368705	−	0.929547i	$-0.620199\pi$
$811$	−21.0000			−0.737410			−0.368705	+	0.929547i	$0.620199\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−12.0000	−	20.7846i	−0.420342	−	0.728053i
$816$		0			0
$817$	42.0000	−	72.7461i	1.46939	−	2.54507i
$818$		0			0
$819$	−2.50000	−	12.9904i	−0.0873571	−	0.453921i
$820$		0			0
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	−0.939989	−	0.341206i	$-0.889165\pi$
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	0.765487	+	0.643451i	$0.222498\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$		0			0
$825$	5.00000			0.174078
$826$		0			0
$827$	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	0.823557	+	0.567234i	$0.191986\pi$
$829$	26.0000	+	45.0333i	0.903017	+	1.56407i	0.0794606	+	0.996838i	$0.474680\pi$
$830$		0			0
$831$	−7.00000	+	12.1244i	−0.242827	+	0.420589i
$832$		0			0
$833$	26.0000	−	10.3923i	0.900847	−	0.360072i
$834$		0			0
$835$	5.50000	−	9.52628i	0.190335	−	0.329670i
$836$		0			0
$837$	−1.00000	−	1.73205i	−0.0345651	−	0.0598684i
$838$		0			0
$839$	−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
$842$		0			0
$843$	−3.50000	−	6.06218i	−0.120546	−	0.208792i
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	7.00000	+	36.3731i	0.240523	+	1.24979i
$848$		0			0
$849$	−5.00000	+	8.66025i	−0.171600	+	0.297219i
$850$		0			0
$851$	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	$0.560303\pi$
$854$		0			0
$855$	7.00000			0.239395
$856$		0			0
$857$	−1.00000	−	1.73205i	−0.0341593	−	0.0591657i	0.848440	−	0.529291i	$-0.177542\pi$
$857$	−1.00000	−	1.73205i	−0.0341593	−	0.0591657i	−0.882600	+	0.470125i	$0.844209\pi$
$858$		0			0
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$		0			0
$861$	−12.5000	−	4.33013i	−0.425999	−	0.147570i
$862$		0			0
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	−0.173856	−	0.984771i	$-0.555623\pi$
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	0.939765	−	0.341822i	$-0.111044\pi$
$864$		0			0
$865$	6.50000	+	11.2583i	0.221007	+	0.382795i
$866$		0			0
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	60.0000			2.03536
$870$		0			0
$871$	30.0000	+	51.9615i	1.01651	+	1.76065i
$872$		0			0
$873$	4.00000	−	6.92820i	0.135379	−	0.234484i
$874$		0			0
$875$	2.00000	−	1.73205i	0.0676123	−	0.0585540i
$876$		0			0
$877$	18.5000	−	32.0429i	0.624701	−	1.08201i	−0.363898	−	0.931439i	$-0.618554\pi$
$877$	18.5000	−	32.0429i	0.624701	−	1.08201i	0.988599	−	0.150574i	$-0.0481123\pi$
$878$		0			0
$879$	−4.50000	−	7.79423i	−0.151781	−	0.262893i
$880$		0			0
$881$	3.00000			0.101073			0.0505363	−	0.998722i	$-0.483907\pi$
$881$	3.00000			0.101073			0.0505363	+	0.998722i	$0.483907\pi$
$882$		0			0
$883$	50.0000			1.68263			0.841317	−	0.540542i	$-0.181781\pi$
$883$	50.0000			1.68263			0.841317	+	0.540542i	$0.181781\pi$
$884$		0			0
$885$	2.00000	+	3.46410i	0.0672293	+	0.116445i
$886$		0			0
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	0.214399	+	0.976746i	$0.431221\pi$
$887$	−22.0000	+	38.1051i	−0.738688	+	1.27944i	−0.953086	+	0.302698i	$0.902113\pi$
$888$		0			0
$889$	−18.0000	+	15.5885i	−0.603701	+	0.522820i
$890$		0			0
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$		0			0
$893$	−38.5000	−	66.6840i	−1.28835	−	2.23149i
$894$		0			0
$895$	23.0000			0.768805
$896$		0			0
$897$	5.00000			0.166945
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$	30.0000	+	10.3923i	0.998337	+	0.345834i
$904$		0			0
$905$	−10.0000	+	17.3205i	−0.332411	+	0.575753i
$906$		0			0
$907$	−9.00000	−	15.5885i	−0.298840	−	0.517606i	0.677031	−	0.735955i	$-0.263266\pi$
$907$	−9.00000	−	15.5885i	−0.298840	−	0.517606i	−0.975871	+	0.218348i	$0.929933\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−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
$914$		0			0
$915$	−2.00000	+	3.46410i	−0.0661180	+	0.114520i
$916$		0			0
$917$	4.50000	+	23.3827i	0.148603	+	0.772164i
$918$		0			0
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	−0.537234	−	0.843433i	$-0.680531\pi$
$919$	14.0000	−	24.2487i	0.461817	−	0.799891i	0.999052	+	0.0435419i	$0.0138642\pi$
$920$		0			0
$921$	4.00000	+	6.92820i	0.131804	+	0.228292i
$922$		0			0
$923$	10.0000			0.329154
$924$		0			0
$925$	1.00000			0.0328798
$926$		0			0
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	−9.50000	+	16.4545i	−0.311685	+	0.539854i	−0.978727	−	0.205166i	$-0.934227\pi$
$929$	−9.50000	+	16.4545i	−0.311685	+	0.539854i	0.667042	+	0.745020i	$0.267560\pi$
$930$		0			0
$931$	38.5000	+	30.3109i	1.26179	+	0.993399i
$932$		0			0
$933$	4.00000	−	6.92820i	0.130954	−	0.226819i
$934$		0			0
$935$	10.0000	+	17.3205i	0.327035	+	0.566441i
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$	16.0000			0.522140
$940$		0			0
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	0.910773	−	0.412908i	$-0.135487\pi$
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	−0.812975	+	0.582298i	$0.802154\pi$
$942$		0			0
$943$	2.50000	−	4.33013i	0.0814112	−	0.141008i
$944$		0			0
$945$	0.500000	+	2.59808i	0.0162650	+	0.0845154i
$946$		0			0
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	0.291835	+	0.956469i	$0.405734\pi$
$947$	−21.0000	+	36.3731i	−0.682408	+	1.18197i	−0.974244	+	0.225497i	$0.927599\pi$
$948$		0			0
$949$	25.0000	+	43.3013i	0.811534	+	1.40562i
$950$		0			0
$951$	−22.0000			−0.713399
$952$		0			0
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$		0			0
$955$	7.00000	+	12.1244i	0.226515	+	0.392335i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.00000	+	1.73205i	0.161458	+	0.0559308i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$	−1.00000	−	1.73205i	−0.0322245	−	0.0558146i
$964$		0			0
$965$	10.0000			0.321911
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		0			0
$969$	14.0000	+	24.2487i	0.449745	+	0.778981i
$970$		0			0
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	8.00000	−	6.92820i	0.256468	−	0.222108i
$974$		0			0
$975$	2.50000	−	4.33013i	0.0800641	−	0.138675i
$976$		0			0
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$		0			0
$979$	70.0000			2.23721
$980$		0			0
$981$	−2.00000			−0.0638551
$982$		0			0
$983$	−12.5000	−	21.6506i	−0.398688	−	0.690548i	0.594876	−	0.803817i	$-0.297201\pi$
$983$	−12.5000	−	21.6506i	−0.398688	−	0.690548i	−0.993564	+	0.113269i	$0.963868\pi$
$984$		0			0
$985$	1.50000	−	2.59808i	0.0477940	−	0.0827816i
$986$		0			0
$987$	22.0000	−	19.0526i	0.700268	−	0.606450i
$988$		0			0
$989$	−6.00000	+	10.3923i	−0.190789	+	0.330456i
$990$		0			0
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	−0.992278	−	0.124033i	$-0.960417\pi$
$991$	−19.0000	−	32.9090i	−0.603555	−	1.04539i	0.388723	−	0.921355i	$-0.372916\pi$
$992$		0			0
$993$	−31.0000			−0.983755
$994$		0			0
$995$	4.00000			0.126809
$996$		0			0
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$		0			0
$999$	−0.500000	+	0.866025i	−0.0158193	+	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.d.961.1		2
4.3	odd	2		210.2.i.b.121.1	✓	2
7.4	even	3	inner	1680.2.bg.d.1201.1		2
12.11	even	2		630.2.k.g.541.1		2
20.3	even	4		1050.2.o.g.499.2		4
20.7	even	4		1050.2.o.g.499.1		4
20.19	odd	2		1050.2.i.p.751.1		2
28.3	even	6		1470.2.i.e.361.1		2
28.11	odd	6		210.2.i.b.151.1	yes	2
28.19	even	6		1470.2.a.o.1.1		1
28.23	odd	6		1470.2.a.l.1.1		1
28.27	even	2		1470.2.i.e.961.1		2
84.11	even	6		630.2.k.g.361.1		2
84.23	even	6		4410.2.a.j.1.1		1
84.47	odd	6		4410.2.a.u.1.1		1
140.19	even	6		7350.2.a.a.1.1		1
140.39	odd	6		1050.2.i.p.151.1		2
140.67	even	12		1050.2.o.g.949.2		4
140.79	odd	6		7350.2.a.u.1.1		1
140.123	even	12		1050.2.o.g.949.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.b.121.1	✓	2	4.3	odd	2
210.2.i.b.151.1	yes	2	28.11	odd	6
630.2.k.g.361.1		2	84.11	even	6
630.2.k.g.541.1		2	12.11	even	2
1050.2.i.p.151.1		2	140.39	odd	6
1050.2.i.p.751.1		2	20.19	odd	2
1050.2.o.g.499.1		4	20.7	even	4
1050.2.o.g.499.2		4	20.3	even	4
1050.2.o.g.949.1		4	140.123	even	12
1050.2.o.g.949.2		4	140.67	even	12
1470.2.a.l.1.1		1	28.23	odd	6
1470.2.a.o.1.1		1	28.19	even	6
1470.2.i.e.361.1		2	28.3	even	6
1470.2.i.e.961.1		2	28.27	even	2
1680.2.bg.d.961.1		2	1.1	even	1	trivial
1680.2.bg.d.1201.1		2	7.4	even	3	inner
4410.2.a.j.1.1		1	84.23	even	6
4410.2.a.u.1.1		1	84.47	odd	6
7350.2.a.a.1.1		1	140.19	even	6
7350.2.a.u.1.1		1	140.79	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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} -5.00000 q^{13} +1.00000 q^{15} +(2.00000 + 3.46410i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-2.50000 - 0.866025i) q^{21} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{31} +(-2.50000 + 4.33013i) q^{33} +(0.500000 + 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(2.50000 + 4.33013i) q^{39} +5.00000 q^{41} -12.0000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-5.50000 + 9.52628i) q^{47} +(1.00000 - 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{51} +(4.50000 + 7.79423i) q^{53} +5.00000 q^{55} +7.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(0.500000 + 2.59808i) q^{63} +(2.50000 - 4.33013i) q^{65} +(-6.00000 - 10.3923i) q^{67} -1.00000 q^{69} -2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(-12.5000 - 4.33013i) q^{77} +(-6.00000 + 10.3923i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -4.00000 q^{85} +(-7.00000 + 12.1244i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-1.00000 + 1.73205i) q^{93} +(-3.50000 - 6.06218i) q^{95} -8.00000 q^{97} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - q^{5} + 4 q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 - q^5 + 4 * q^7 - q^9	\( 2 q - q^{3} - q^{5} + 4 q^{7} - q^{9} - 5 q^{11} - 10 q^{13} + 2 q^{15} + 4 q^{17} - 7 q^{19} - 5 q^{21} + q^{23} - q^{25} + 2 q^{27} - 2 q^{31} - 5 q^{33} + q^{35} - q^{37} + 5 q^{39} + 10 q^{41} - 24 q^{43} - q^{45} - 11 q^{47} + 2 q^{49} + 4 q^{51} + 9 q^{53} + 10 q^{55} + 14 q^{57} + 4 q^{59} - 4 q^{61} + q^{63} + 5 q^{65} - 12 q^{67} - 2 q^{69} - 4 q^{71} - 10 q^{73} - q^{75} - 25 q^{77} - 12 q^{79} - q^{81} + 24 q^{83} - 8 q^{85} - 14 q^{89} - 20 q^{91} - 2 q^{93} - 7 q^{95} - 16 q^{97} + 10 q^{99}+O(q^{100}) \) 2 * q - q^3 - q^5 + 4 * q^7 - q^9 - 5 * q^11 - 10 * q^13 + 2 * q^15 + 4 * q^17 - 7 * q^19 - 5 * q^21 + q^23 - q^25 + 2 * q^27 - 2 * q^31 - 5 * q^33 + q^35 - q^37 + 5 * q^39 + 10 * q^41 - 24 * q^43 - q^45 - 11 * q^47 + 2 * q^49 + 4 * q^51 + 9 * q^53 + 10 * q^55 + 14 * q^57 + 4 * q^59 - 4 * q^61 + q^63 + 5 * q^65 - 12 * q^67 - 2 * q^69 - 4 * q^71 - 10 * q^73 - q^75 - 25 * q^77 - 12 * q^79 - q^81 + 24 * q^83 - 8 * q^85 - 14 * q^89 - 20 * q^91 - 2 * q^93 - 7 * q^95 - 16 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

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