LMFDB - Embedded newform 684.3.s.a.445.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.15
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26845 - 2.71865i) q^{3} +(1.21776 + 2.10923i) q^{5} +(-1.46858 - 2.54365i) q^{7} +(-5.78207 + 6.89693i) q^{9} +O(q^{10})$	\(q+(-1.26845 - 2.71865i) q^{3} +(1.21776 + 2.10923i) q^{5} +(-1.46858 - 2.54365i) q^{7} +(-5.78207 + 6.89693i) q^{9} +(2.72603 + 4.72162i) q^{11} +5.52108i q^{13} +(4.18957 - 5.98611i) q^{15} +(10.3375 - 17.9051i) q^{17} +(18.5517 + 4.10311i) q^{19} +(-5.05247 + 7.21903i) q^{21} +4.89582 q^{23} +(9.53411 - 16.5136i) q^{25} +(26.0846 + 6.97099i) q^{27} +(-27.3832 - 15.8097i) q^{29} +(31.3417 + 18.0952i) q^{31} +(9.37858 - 13.4002i) q^{33} +(3.57675 - 6.19512i) q^{35} -41.4410i q^{37} +(15.0099 - 7.00322i) q^{39} +(12.1993 - 7.04329i) q^{41} -25.0467 q^{43} +(-21.5884 - 3.79687i) q^{45} +(-20.9277 + 36.2479i) q^{47} +(20.1866 - 34.9642i) q^{49} +(-61.7903 - 5.39232i) q^{51} +(-45.7321 + 26.4034i) q^{53} +(-6.63930 + 11.4996i) q^{55} +(-12.3770 - 55.6400i) q^{57} +(101.085 - 58.3614i) q^{59} +(47.4256 - 82.1435i) q^{61} +(26.0348 + 4.57889i) q^{63} +(-11.6452 + 6.72336i) q^{65} -15.8321i q^{67} +(-6.21010 - 13.3100i) q^{69} +(61.4316 + 35.4675i) q^{71} +(-28.8246 + 49.9256i) q^{73} +(-56.9881 - 4.97325i) q^{75} +(8.00676 - 13.8681i) q^{77} -152.320i q^{79} +(-14.1353 - 79.7571i) q^{81} +(-18.0651 - 31.2897i) q^{83} +50.3545 q^{85} +(-8.24675 + 94.4990i) q^{87} +(56.7517 - 32.7656i) q^{89} +(14.0437 - 8.10814i) q^{91} +(9.43892 - 108.160i) q^{93} +(13.9371 + 44.1263i) q^{95} +9.30418i q^{97} +(-48.3268 - 8.49950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.26845	−	2.71865i	−0.422817	−	0.906215i
$3$	−1.26845	−	2.71865i	−0.422817	−	0.906215i
$4$		0			0
$5$	1.21776	+	2.10923i	0.243552	+	0.421845i	0.961724	−	0.274021i	$-0.0883539\pi$
$5$	1.21776	+	2.10923i	0.243552	+	0.421845i	−0.718171	+	0.695866i	$0.755021\pi$
$6$		0			0
$7$	−1.46858	−	2.54365i	−0.209797	−	0.363379i	0.741854	−	0.670562i	$-0.233947\pi$
$7$	−1.46858	−	2.54365i	−0.209797	−	0.363379i	−0.951650	+	0.307183i	$0.900614\pi$
$8$		0			0
$9$	−5.78207	+	6.89693i	−0.642452	+	0.766326i
$10$		0			0
$11$	2.72603	+	4.72162i	0.247821	+	0.429238i	0.962921	−	0.269784i	$-0.0869523\pi$
$11$	2.72603	+	4.72162i	0.247821	+	0.429238i	−0.715100	+	0.699022i	$0.753619\pi$
$12$		0			0
$13$			5.52108i			0.424699i	0.977194	+	0.212349i	$0.0681115\pi$
$13$			5.52108i			0.424699i	−0.977194	+	0.212349i	$0.931889\pi$
$14$		0			0
$15$	4.18957	−	5.98611i	0.279304	−	0.399074i
$16$		0			0
$17$	10.3375	−	17.9051i	0.608089	−	1.05324i	−0.383466	−	0.923555i	$-0.625270\pi$
$17$	10.3375	−	17.9051i	0.608089	−	1.05324i	0.991555	−	0.129686i	$-0.0413971\pi$
$18$		0			0
$19$	18.5517	+	4.10311i	0.976404	+	0.215953i
$19$	18.5517	+	4.10311i	0.976404	+	0.215953i
$20$		0			0
$21$	−5.05247	+	7.21903i	−0.240594	+	0.343764i
$22$		0			0
$23$	4.89582			0.212862			0.106431	−	0.994320i	$-0.466058\pi$
$23$	4.89582			0.212862			0.106431	+	0.994320i	$0.466058\pi$
$24$		0			0
$25$	9.53411	−	16.5136i	0.381365	−	0.660543i
$26$		0			0
$27$	26.0846	+	6.97099i	0.966096	+	0.258185i
$28$		0			0
$29$	−27.3832	−	15.8097i	−0.944248	−	0.545162i	−0.0529586	−	0.998597i	$-0.516865\pi$
$29$	−27.3832	−	15.8097i	−0.944248	−	0.545162i	−0.891289	+	0.453435i	$0.850198\pi$
$30$		0			0
$31$	31.3417	+	18.0952i	1.01102	+	0.583715i	0.911491	−	0.411319i	$-0.134932\pi$
$31$	31.3417	+	18.0952i	1.01102	+	0.583715i	0.0995327	+	0.995034i	$0.468265\pi$
$32$		0			0
$33$	9.37858	−	13.4002i	0.284199	−	0.406068i
$34$		0			0
$35$	3.57675	−	6.19512i	0.102193	−	0.177003i
$36$		0			0
$37$		−	41.4410i		−	1.12003i	−0.828483	−	0.560014i	$-0.810796\pi$
$37$		−	41.4410i		−	1.12003i	0.828483	−	0.560014i	$-0.189204\pi$
$38$		0			0
$39$	15.0099	−	7.00322i	0.384868	−	0.179570i
$40$		0			0
$41$	12.1993	−	7.04329i	0.297545	−	0.171788i	−0.343795	−	0.939045i	$-0.611712\pi$
$41$	12.1993	−	7.04329i	0.297545	−	0.171788i	0.641339	+	0.767257i	$0.278379\pi$
$42$		0			0
$43$	−25.0467			−0.582481			−0.291241	−	0.956650i	$-0.594068\pi$
$43$	−25.0467			−0.582481			−0.291241	+	0.956650i	$0.594068\pi$
$44$		0			0
$45$	−21.5884	−	3.79687i	−0.479741	−	0.0843749i
$46$		0			0
$47$	−20.9277	+	36.2479i	−0.445271	+	0.771232i	−0.998071	−	0.0620820i	$-0.980226\pi$
$47$	−20.9277	+	36.2479i	−0.445271	+	0.771232i	0.552800	+	0.833314i	$0.313559\pi$
$48$		0			0
$49$	20.1866	−	34.9642i	0.411971	−	0.713554i
$50$		0			0
$51$	−61.7903	−	5.39232i	−1.21157	−	0.105732i
$52$		0			0
$53$	−45.7321	+	26.4034i	−0.862870	+	0.498178i	−0.864972	−	0.501820i	$-0.832664\pi$
$53$	−45.7321	+	26.4034i	−0.862870	+	0.498178i	0.00210252	+	0.999998i	$0.499331\pi$
$54$		0			0
$55$	−6.63930	+	11.4996i	−0.120715	+	0.209084i
$56$		0			0
$57$	−12.3770	−	55.6400i	−0.217140	−	0.976141i
$58$		0			0
$59$	101.085	−	58.3614i	1.71330	−	0.989176i	0.783286	−	0.621662i	$-0.213542\pi$
$59$	101.085	−	58.3614i	1.71330	−	0.989176i	0.930018	−	0.367515i	$-0.119791\pi$
$60$		0			0
$61$	47.4256	−	82.1435i	0.777468	−	1.34661i	−0.155929	−	0.987768i	$-0.549837\pi$
$61$	47.4256	−	82.1435i	0.777468	−	1.34661i	0.933397	−	0.358846i	$-0.116830\pi$
$62$		0			0
$63$	26.0348	+	4.57889i	0.413251	+	0.0726808i
$64$		0			0
$65$	−11.6452	+	6.72336i	−0.179157	+	0.103436i
$66$		0			0
$67$		−	15.8321i		−	0.236300i	−0.992996	−	0.118150i	$-0.962304\pi$
$67$		−	15.8321i		−	0.236300i	0.992996	−	0.118150i	$-0.0376964\pi$
$68$		0			0
$69$	−6.21010	−	13.3100i	−0.0900015	−	0.192899i
$70$		0			0
$71$	61.4316	+	35.4675i	0.865234	+	0.499543i	0.865761	−	0.500457i	$-0.166835\pi$
$71$	61.4316	+	35.4675i	0.865234	+	0.499543i	−0.000527818		1.00000i	$0.500168\pi$
$72$		0			0
$73$	−28.8246	+	49.9256i	−0.394857	+	0.683912i	−0.993083	−	0.117415i	$-0.962539\pi$
$73$	−28.8246	+	49.9256i	−0.394857	+	0.683912i	0.598226	+	0.801327i	$0.295872\pi$
$74$		0			0
$75$	−56.9881	−	4.97325i	−0.759841	−	0.0663099i
$76$		0			0
$77$	8.00676	−	13.8681i	0.103984	−	0.180105i
$78$		0			0
$79$		−	152.320i		−	1.92810i	−0.265721	−	0.964050i	$-0.585610\pi$
$79$		−	152.320i		−	1.92810i	0.265721	−	0.964050i	$-0.414390\pi$
$80$		0			0
$81$	−14.1353	−	79.7571i	−0.174510	−	0.984655i
$82$		0			0
$83$	−18.0651	−	31.2897i	−0.217652	−	0.376985i	0.736438	−	0.676506i	$-0.236507\pi$
$83$	−18.0651	−	31.2897i	−0.217652	−	0.376985i	−0.954090	+	0.299521i	$0.903173\pi$
$84$		0			0
$85$	50.3545			0.592406
$86$		0			0
$87$	−8.24675	+	94.4990i	−0.0947903	+	1.08620i
$88$		0			0
$89$	56.7517	−	32.7656i	0.637659	−	0.368153i	−0.146053	−	0.989277i	$-0.546657\pi$
$89$	56.7517	−	32.7656i	0.637659	−	0.368153i	0.783712	+	0.621124i	$0.213324\pi$
$90$		0			0
$91$	14.0437	−	8.10814i	0.154326	−	0.0891004i
$92$		0			0
$93$	9.43892	−	108.160i	0.101494	−	1.16301i
$94$		0			0
$95$	13.9371	+	44.1263i	0.146707	+	0.464487i
$96$		0			0
$97$			9.30418i			0.0959194i	0.998849	+	0.0479597i	$0.0152719\pi$
$97$			9.30418i			0.0959194i	−0.998849	+	0.0479597i	$0.984728\pi$
$98$		0			0
$99$	−48.3268	−	8.49950i	−0.488149	−	0.0858536i
$100$		0			0
$101$	58.6650	−	101.611i	0.580842	−	1.00605i	−0.414538	−	0.910032i	$-0.636057\pi$
$101$	58.6650	−	101.611i	0.580842	−	1.00605i	0.995380	−	0.0960152i	$-0.0306097\pi$
$102$		0			0
$103$	−31.5616	−	18.2221i	−0.306423	−	0.176913i	0.338902	−	0.940822i	$-0.389945\pi$
$103$	−31.5616	−	18.2221i	−0.306423	−	0.176913i	−0.645325	+	0.763908i	$0.723278\pi$
$104$		0			0
$105$	−21.3793	−	1.86573i	−0.203612	−	0.0177689i
$106$		0			0
$107$			111.398i			1.04111i	0.853829	+	0.520553i	$0.174274\pi$
$107$			111.398i			1.04111i	−0.853829	+	0.520553i	$0.825726\pi$
$108$		0			0
$109$	−151.475	−	87.4542i	−1.38968	−	0.802332i	−0.396401	−	0.918078i	$-0.629741\pi$
$109$	−151.475	−	87.4542i	−1.38968	−	0.802332i	−0.993279	+	0.115746i	$0.963074\pi$
$110$		0			0
$111$	−112.663	+	52.5659i	−1.01499	+	0.473566i
$112$		0			0
$113$	2.60574	+	1.50443i	0.0230597	+	0.0133135i	0.511486	−	0.859292i	$-0.329095\pi$
$113$	2.60574	+	1.50443i	0.0230597	+	0.0133135i	−0.488426	+	0.872605i	$0.662429\pi$
$114$		0			0
$115$	5.96194	+	10.3264i	0.0518430	+	0.0897947i
$116$		0			0
$117$	−38.0785	−	31.9233i	−0.325458	−	0.272849i
$118$		0			0
$119$	−60.7258			−0.510301
$120$		0			0
$121$	45.6376	−	79.0466i	0.377170	−	0.653277i
$122$		0			0
$123$	−34.6225	−	24.2316i	−0.281483	−	0.197005i
$124$		0			0
$125$	107.329			0.858634
$126$		0			0
$127$	103.425	−	59.7123i	0.814367	−	0.470175i	−0.0341028	−	0.999418i	$-0.510857\pi$
$127$	103.425	−	59.7123i	0.814367	−	0.470175i	0.848470	+	0.529243i	$0.177524\pi$
$128$		0			0
$129$	31.7705	+	68.0931i	0.246283	+	0.527854i
$130$		0			0
$131$	90.1674	+	156.175i	0.688301	+	1.19217i	0.972387	+	0.233374i	$0.0749765\pi$
$131$	90.1674	+	156.175i	0.688301	+	1.19217i	−0.284086	+	0.958799i	$0.591690\pi$
$132$		0			0
$133$	−16.8077	−	53.2147i	−0.126374	−	0.400110i
$134$		0			0
$135$	17.0614	+	63.5073i	0.126381	+	0.470424i
$136$		0			0
$137$	−109.812	+	190.200i	−0.801549	+	1.38832i	0.117047	+	0.993126i	$0.462657\pi$
$137$	−109.812	+	190.200i	−0.801549	+	1.38832i	−0.918596	+	0.395197i	$0.870676\pi$
$138$		0			0
$139$	82.7085			0.595025			0.297513	−	0.954718i	$-0.403843\pi$
$139$	82.7085			0.595025			0.297513	+	0.954718i	$0.403843\pi$
$140$		0			0
$141$	125.091	+	10.9165i	0.887170	+	0.0774217i
$142$		0			0
$143$	−26.0684	+	15.0506i	−0.182297	+	0.105249i
$144$		0			0
$145$		−	77.0098i		−	0.531102i
$146$		0			0
$147$	−120.661	−	10.5298i	−0.820822	−	0.0716316i
$148$		0			0
$149$	17.8414	+	30.9022i	0.119741	+	0.207397i	0.919665	−	0.392704i	$-0.128460\pi$
$149$	17.8414	+	30.9022i	0.119741	+	0.207397i	−0.799924	+	0.600101i	$0.795127\pi$
$150$		0			0
$151$	−75.9168	+	43.8306i	−0.502760	+	0.290269i	−0.729853	−	0.683605i	$-0.760411\pi$
$151$	−75.9168	+	43.8306i	−0.502760	+	0.290269i	0.227093	+	0.973873i	$0.427078\pi$
$152$		0			0
$153$	63.7180	+	174.826i	0.416458	+	1.14265i
$154$		0			0
$155$			88.1424i			0.568661i
$156$		0			0
$157$	129.436	+	224.191i	0.824436	+	1.42797i	0.902349	+	0.431005i	$0.141841\pi$
$157$	129.436	+	224.191i	0.824436	+	1.42797i	−0.0779130	+	0.996960i	$0.524826\pi$
$158$		0			0
$159$	129.790	+	90.8379i	0.816292	+	0.571308i
$160$		0			0
$161$	−7.18989	−	12.4533i	−0.0446577	−	0.0773494i
$162$		0			0
$163$	143.728			0.881769			0.440884	−	0.897564i	$-0.354665\pi$
$163$	143.728			0.881769			0.440884	+	0.897564i	$0.354665\pi$
$164$		0			0
$165$	39.6850	+	3.46324i	0.240515	+	0.0209893i
$166$		0			0
$167$		−	134.107i		−	0.803033i	−0.915852	−	0.401517i	$-0.868483\pi$
$167$		−	134.107i		−	0.803033i	0.915852	−	0.401517i	$-0.131517\pi$
$168$		0			0
$169$	138.518			0.819631
$170$		0			0
$171$	−135.566	+	104.225i	−0.792783	+	0.609504i
$172$		0			0
$173$			229.297i			1.32541i	0.748879	+	0.662707i	$0.230593\pi$
$173$			229.297i			1.32541i	−0.748879	+	0.662707i	$0.769407\pi$
$174$		0			0
$175$	−56.0063			−0.320036
$176$		0			0
$177$	−286.885	−	200.786i	−1.62082	−	1.13438i
$178$		0			0
$179$			189.800i			1.06034i	0.847893	+	0.530168i	$0.177871\pi$
$179$			189.800i			1.06034i	−0.847893	+	0.530168i	$0.822129\pi$
$180$		0			0
$181$	−149.510	+	86.3199i	−0.826025	+	0.476906i	−0.852490	−	0.522744i	$-0.824908\pi$
$181$	−149.510	+	86.3199i	−0.826025	+	0.476906i	0.0264650	+	0.999650i	$0.491575\pi$
$182$		0			0
$183$	−283.476	−	24.7384i	−1.54905	−	0.135183i
$184$		0			0
$185$	87.4085	−	50.4653i	0.472478	−	0.272785i
$186$		0			0
$187$	112.721			0.602788
$188$		0			0
$189$	−20.5755	−	76.5875i	−0.108865	−	0.405225i
$190$		0			0
$191$	115.287	+	199.683i	0.603597	+	1.04546i	0.992272	+	0.124085i	$0.0395997\pi$
$191$	115.287	+	199.683i	0.603597	+	1.04546i	−0.388675	+	0.921375i	$0.627067\pi$
$192$		0			0
$193$	−14.0638	+	8.11975i	−0.0728695	+	0.0420712i	−0.535992	−	0.844223i	$-0.680062\pi$
$193$	−14.0638	+	8.11975i	−0.0728695	+	0.0420712i	0.463123	+	0.886294i	$0.346729\pi$
$194$		0			0
$195$	33.0498	+	23.1309i	0.169486	+	0.118620i
$196$		0			0
$197$	120.492			0.611635			0.305817	−	0.952090i	$-0.401070\pi$
$197$	120.492			0.611635			0.305817	+	0.952090i	$0.401070\pi$
$198$		0			0
$199$	5.88157	+	10.1872i	0.0295556	+	0.0511918i	0.880425	−	0.474186i	$-0.157257\pi$
$199$	5.88157	+	10.1872i	0.0295556	+	0.0511918i	−0.850869	+	0.525377i	$0.823924\pi$
$200$		0			0
$201$	−43.0419	+	20.0822i	−0.214139	+	0.0999115i
$202$		0			0
$203$			92.8710i			0.457493i
$204$		0			0
$205$	29.7118	+	17.1541i	0.144936	+	0.0836786i
$206$		0			0
$207$	−28.3080	+	33.7661i	−0.136754	+	0.163121i
$208$		0			0
$209$	31.1991	+	98.7791i	0.149278	+	0.472627i
$210$		0			0
$211$	−8.73949	+	5.04575i	−0.0414194	+	0.0239135i	−0.520567	−	0.853821i	$-0.674279\pi$
$211$	−8.73949	+	5.04575i	−0.0414194	+	0.0239135i	0.479147	+	0.877734i	$0.340946\pi$
$212$		0			0
$213$	18.5008	−	212.000i	0.0868583	−	0.995303i
$214$		0			0
$215$	−30.5009	−	52.8291i	−0.141865	−	0.245717i
$216$		0			0
$217$		−	106.297i		−	0.489846i
$218$		0			0
$219$	172.292	+	15.0356i	0.786724	+	0.0686559i
$220$		0			0
$221$	98.8556	+	57.0743i	0.447310	+	0.258255i
$222$		0			0
$223$		−	291.968i		−	1.30927i	−0.755943	−	0.654637i	$-0.772821\pi$
$223$		−	291.968i		−	1.30927i	0.755943	−	0.654637i	$-0.227179\pi$
$224$		0			0
$225$	58.7660	+	161.239i	0.261182	+	0.716617i
$226$		0			0
$227$	−249.905	+	144.283i	−1.10090	+	0.635607i	−0.936458	−	0.350779i	$-0.885917\pi$
$227$	−249.905	+	144.283i	−1.10090	+	0.635607i	−0.164446	+	0.986386i	$0.552584\pi$
$228$		0			0
$229$	−0.809283	+	1.40172i	−0.00353399	+	0.00612104i	−0.867787	−	0.496936i	$-0.834458\pi$
$229$	−0.809283	+	1.40172i	−0.00353399	+	0.00612104i	0.864253	+	0.503057i	$0.167792\pi$
$230$		0			0
$231$	−47.8587	−	4.17654i	−0.207180	−	0.0180803i
$232$		0			0
$233$	88.3582	−	153.041i	0.379220	−	0.656828i	−0.611729	−	0.791067i	$-0.709526\pi$
$233$	88.3582	−	153.041i	0.379220	−	0.656828i	0.990949	+	0.134240i	$0.0428592\pi$
$234$		0			0
$235$	−101.940			−0.433787
$236$		0			0
$237$	−414.104	+	193.210i	−1.74727	+	0.815233i
$238$		0			0
$239$	−36.7670	+	63.6824i	−0.153837	+	0.266454i	−0.932635	−	0.360821i	$-0.882496\pi$
$239$	−36.7670	+	63.6824i	−0.153837	+	0.266454i	0.778798	+	0.627275i	$0.215830\pi$
$240$		0			0
$241$	−226.734	−	130.905i	−0.940805	−	0.543174i	−0.0505925	−	0.998719i	$-0.516111\pi$
$241$	−226.734	−	130.905i	−0.940805	−	0.543174i	−0.890213	+	0.455545i	$0.849444\pi$
$242$		0			0
$243$	−198.901	+	139.597i	−0.818524	+	0.574472i
$244$		0			0
$245$	98.3297			0.401346
$246$		0			0
$247$	−22.6536	+	102.425i	−0.0917150	+	0.414677i
$248$		0			0
$249$	−62.1510	+	88.8021i	−0.249602	+	0.356635i
$250$		0			0
$251$	108.392	+	187.741i	0.431841	+	0.747971i	0.997032	−	0.0769893i	$-0.0245307\pi$
$251$	108.392	+	187.741i	0.431841	+	0.747971i	−0.565191	+	0.824960i	$0.691197\pi$
$252$		0			0
$253$	13.3461	+	23.1162i	0.0527516	+	0.0913684i
$254$		0			0
$255$	−63.8722	−	136.896i	−0.250479	−	0.536848i
$256$		0			0
$257$			56.3272i			0.219172i	0.993977	+	0.109586i	$0.0349525\pi$
$257$			56.3272i			0.219172i	−0.993977	+	0.109586i	$0.965047\pi$
$258$		0			0
$259$	−105.411	+	60.8594i	−0.406994	+	0.234978i
$260$		0			0
$261$	267.370	−	97.4472i	1.02441	−	0.373361i
$262$		0			0
$263$	−399.173			−1.51777			−0.758884	−	0.651226i	$-0.774255\pi$
$263$	−399.173			−1.51777			−0.758884	+	0.651226i	$0.774255\pi$
$264$		0			0
$265$	−111.382	−	64.3062i	−0.420308	−	0.242665i
$266$		0			0
$267$	−161.065	−	112.726i	−0.603238	−	0.422195i
$268$		0			0
$269$	−307.777	−	177.695i	−1.14415	−	0.660578i	−0.196698	−	0.980464i	$-0.563022\pi$
$269$	−307.777	−	177.695i	−1.14415	−	0.660578i	−0.947456	+	0.319886i	$0.896355\pi$
$270$		0			0
$271$	90.6568	−	157.022i	0.334527	−	0.579418i	−0.648867	−	0.760902i	$-0.724757\pi$
$271$	90.6568	−	157.022i	0.334527	−	0.579418i	0.983394	+	0.181484i	$0.0580902\pi$
$272$		0			0
$273$	−39.8569	−	27.8951i	−0.145996	−	0.102180i
$274$		0			0
$275$	103.961			0.378040
$276$		0			0
$277$	148.464	+	257.147i	0.535970	+	0.928327i	0.999116	+	0.0420450i	$0.0133873\pi$
$277$	148.464	+	257.147i	0.535970	+	0.928327i	−0.463146	+	0.886282i	$0.653279\pi$
$278$		0			0
$279$	−306.021	+	111.534i	−1.09685	+	0.399765i
$280$		0			0
$281$	−74.1846	−	42.8305i	−0.264002	−	0.152422i	0.362157	−	0.932117i	$-0.382041\pi$
$281$	−74.1846	−	42.8305i	−0.264002	−	0.152422i	−0.626159	+	0.779695i	$0.715374\pi$
$282$		0			0
$283$	75.2230	+	130.290i	0.265805	+	0.460389i	0.967774	−	0.251819i	$-0.0810288\pi$
$283$	75.2230	+	130.290i	0.265805	+	0.460389i	−0.701969	+	0.712208i	$0.747695\pi$
$284$		0			0
$285$	102.285	−	93.8621i	0.358895	−	0.329341i
$286$		0			0
$287$	−35.8313	−	20.6872i	−0.124848	−	0.0720810i
$288$		0			0
$289$	−69.2285	−	119.907i	−0.239545	−	0.414904i
$290$		0			0
$291$	25.2948	−	11.8019i	0.0869236	−	0.0405563i
$292$		0			0
$293$	−115.715	−	66.8080i	−0.394931	−	0.228014i	0.289363	−	0.957219i	$-0.406556\pi$
$293$	−115.715	−	66.8080i	−0.394931	−	0.228014i	−0.684295	+	0.729206i	$0.739890\pi$
$294$		0			0
$295$	246.195	+	142.141i	0.834558	+	0.481832i
$296$		0			0
$297$	38.1929	+	142.165i	0.128596	+	0.478668i
$298$		0			0
$299$			27.0302i			0.0904021i
$300$		0			0
$301$	36.7830	+	63.7101i	0.122203	+	0.211661i
$302$		0			0
$303$	−350.657	−	30.6012i	−1.15728	−	0.100994i
$304$		0			0
$305$	231.012			0.757417
$306$		0			0
$307$	−118.668	−	68.5130i	−0.386541	−	0.223169i	0.294120	−	0.955769i	$-0.404974\pi$
$307$	−118.668	−	68.5130i	−0.386541	−	0.223169i	−0.680660	+	0.732599i	$0.738307\pi$
$308$		0			0
$309$	−9.50512	+	108.919i	−0.0307609	+	0.352487i
$310$		0			0
$311$	17.8966	−	30.9978i	0.0575453	−	0.0996715i	−0.835818	−	0.549007i	$-0.815006\pi$
$311$	17.8966	−	30.9978i	0.0575453	−	0.0996715i	0.893363	+	0.449336i	$0.148339\pi$
$312$		0			0
$313$	175.582	−	304.117i	0.560965	−	0.971620i	−0.436447	−	0.899730i	$-0.643763\pi$
$313$	175.582	−	304.117i	0.560965	−	0.971620i	0.997413	−	0.0718905i	$-0.0229032\pi$
$314$		0			0
$315$	22.0463	+	60.4892i	0.0699882	+	0.192029i
$316$		0			0
$317$	−264.410	−	152.657i	−0.834101	−	0.481569i	0.0211535	−	0.999776i	$-0.493266\pi$
$317$	−264.410	−	152.657i	−0.834101	−	0.481569i	−0.855255	+	0.518208i	$0.826599\pi$
$318$		0			0
$319$		−	172.391i		−	0.540409i
$320$		0			0
$321$	302.853	−	141.303i	0.943466	−	0.440197i
$322$		0			0
$323$	265.245	−	289.754i	0.821191	−	0.897070i
$324$		0			0
$325$	91.1728	+	52.6386i	0.280532	+	0.161965i
$326$		0			0
$327$	−45.6184	+	522.738i	−0.139506	+	1.59859i
$328$		0			0
$329$	122.936			0.373666
$330$		0			0
$331$	236.912	−	136.781i	0.715747	−	0.413237i	−0.0974383	−	0.995242i	$-0.531065\pi$
$331$	236.912	−	136.781i	0.715747	−	0.413237i	0.813185	+	0.582005i	$0.197732\pi$
$332$		0			0
$333$	285.816	+	239.615i	0.858306	+	0.719564i
$334$		0			0
$335$	33.3935	−	19.2797i	0.0996820	−	0.0575514i
$336$		0			0
$337$	412.310	−	238.047i	1.22347	−	0.706371i	0.257814	−	0.966194i	$-0.416998\pi$
$337$	412.310	−	238.047i	1.22347	−	0.706371i	0.965656	+	0.259823i	$0.0836643\pi$
$338$		0			0
$339$	0.784748	−	8.99237i	0.00231489	−	0.0265262i
$340$		0			0
$341$			197.312i			0.578626i
$342$		0			0
$343$	−262.503			−0.765314
$344$		0			0
$345$	20.5114	−	29.3069i	0.0594533	−	0.0849476i
$346$		0			0
$347$	218.957	+	379.244i	0.630999	+	1.09292i	0.987348	+	0.158570i	$0.0506883\pi$
$347$	218.957	+	379.244i	0.630999	+	1.09292i	−0.356348	+	0.934353i	$0.615978\pi$
$348$		0			0
$349$	−157.749	−	273.230i	−0.452004	−	0.782894i	0.546506	−	0.837455i	$-0.315957\pi$
$349$	−157.749	−	273.230i	−0.452004	−	0.782894i	−0.998510	+	0.0545608i	$0.982624\pi$
$350$		0			0
$351$	−38.4874	+	144.015i	−0.109651	+	0.410300i
$352$		0			0
$353$	76.2492	+	132.067i	0.216003	+	0.374129i	0.953582	−	0.301132i	$-0.0973645\pi$
$353$	76.2492	+	132.067i	0.216003	+	0.374129i	−0.737579	+	0.675261i	$0.764031\pi$
$354$		0			0
$355$			172.764i			0.486659i
$356$		0			0
$357$	77.0276	+	165.092i	0.215764	+	0.462442i
$358$		0			0
$359$	−66.4548	+	115.103i	−0.185111	+	0.320621i	−0.943614	−	0.331048i	$-0.892598\pi$
$359$	−66.4548	+	115.103i	−0.185111	+	0.320621i	0.758503	+	0.651670i	$0.225931\pi$
$360$		0			0
$361$	327.329	+	152.239i	0.906729	+	0.421715i
$362$		0			0
$363$	−272.789	−	23.8058i	−0.751484	−	0.0655806i
$364$		0			0
$365$	−140.406			−0.384673
$366$		0			0
$367$	−69.8365	+	120.960i	−0.190290	+	0.329592i	−0.945346	−	0.326068i	$-0.894276\pi$
$367$	−69.8365	+	120.960i	−0.190290	+	0.329592i	0.755056	+	0.655660i	$0.227610\pi$
$368$		0			0
$369$	−21.9603	+	124.863i	−0.0595131	+	0.338382i
$370$		0			0
$371$	134.322	+	77.5510i	0.362055	+	0.209032i
$372$		0			0
$373$	−318.040	−	183.621i	−0.852655	−	0.492280i	0.00889093	−	0.999960i	$-0.497170\pi$
$373$	−318.040	−	183.621i	−0.852655	−	0.492280i	−0.861546	+	0.507680i	$0.830503\pi$
$374$		0			0
$375$	−136.142	−	291.790i	−0.363045	−	0.778107i
$376$		0			0
$377$	87.2866	−	151.185i	0.231530	−	0.401021i
$378$		0			0
$379$			50.2751i			0.132652i	0.997798	+	0.0663259i	$0.0211277\pi$
$379$			50.2751i			0.132652i	−0.997798	+	0.0663259i	$0.978872\pi$
$380$		0			0
$381$	−293.525	−	205.433i	−0.770408	−	0.539194i
$382$		0			0
$383$	326.455	−	188.479i	0.852363	−	0.492112i	−0.00908440	−	0.999959i	$-0.502892\pi$
$383$	326.455	−	188.479i	0.852363	−	0.492112i	0.861447	+	0.507847i	$0.169558\pi$
$384$		0			0
$385$	39.0013			0.101302
$386$		0			0
$387$	144.822	−	172.745i	0.374217	−	0.446371i
$388$		0			0
$389$	−156.248	+	270.629i	−0.401666	+	0.695705i	−0.993927	−	0.110040i	$-0.964902\pi$
$389$	−156.248	+	270.629i	−0.401666	+	0.695705i	0.592261	+	0.805746i	$0.298235\pi$
$390$		0			0
$391$	50.6106	−	87.6602i	0.129439	−	0.224195i
$392$		0			0
$393$	310.210	−	443.233i	0.789340	−	1.12782i
$394$		0			0
$395$	321.277	−	185.489i	0.813359	−	0.469593i
$396$		0			0
$397$	−184.322	+	319.255i	−0.464287	+	0.804169i	−0.999169	−	0.0407578i	$-0.987023\pi$
$397$	−184.322	+	319.255i	−0.464287	+	0.804169i	0.534882	+	0.844927i	$0.320356\pi$
$398$		0			0
$399$	−123.352	+	113.194i	−0.309153	+	0.283695i
$400$		0			0
$401$	567.725	−	327.776i	1.41577	−	0.817397i	0.419849	−	0.907594i	$-0.362083\pi$
$401$	567.725	−	327.776i	1.41577	−	0.817397i	0.995924	+	0.0901967i	$0.0287496\pi$
$402$		0			0
$403$	−99.9049	+	173.040i	−0.247903	+	0.429381i
$404$		0			0
$405$	151.012	−	126.940i	0.372870	−	0.313431i
$406$		0			0
$407$	195.669	−	112.969i	0.480758	−	0.277566i
$408$		0			0
$409$		−	23.2123i		−	0.0567537i	−0.999597	−	0.0283768i	$-0.990966\pi$
$409$		−	23.2123i		−	0.0567537i	0.999597	−	0.0283768i	$-0.00903384\pi$
$410$		0			0
$411$	656.379	+	57.2810i	1.59703	+	0.139370i
$412$		0			0
$413$	−296.902	−	171.416i	−0.718891	−	0.415052i
$414$		0			0
$415$	43.9980	−	76.2069i	0.106019	−	0.183631i
$416$		0			0
$417$	−104.912	−	224.855i	−0.251587	−	0.539221i
$418$		0			0
$419$	−242.796	+	420.535i	−0.579466	+	1.00366i	0.416075	+	0.909330i	$0.363405\pi$
$419$	−242.796	+	420.535i	−0.579466	+	1.00366i	−0.995541	+	0.0943337i	$0.969928\pi$
$420$		0			0
$421$		−	256.716i		−	0.609777i	−0.952388	−	0.304888i	$-0.901381\pi$
$421$		−	256.716i		−	0.609777i	0.952388	−	0.304888i	$-0.0986192\pi$
$422$		0			0
$423$	−128.994	−	353.925i	−0.304949	−	0.836702i
$424$		0			0
$425$	−197.118	−	341.419i	−0.463807	−	0.803338i
$426$		0			0
$427$	−278.592			−0.652441
$428$		0			0
$429$	73.9838	+	51.7799i	0.172456	+	0.120699i
$430$		0			0
$431$	−347.260	+	200.491i	−0.805708	+	0.465176i	−0.845463	−	0.534034i	$-0.820676\pi$
$431$	−347.260	+	200.491i	−0.805708	+	0.465176i	0.0397552	+	0.999209i	$0.487342\pi$
$432$		0			0
$433$	−367.762	+	212.327i	−0.849334	+	0.490363i	−0.860426	−	0.509575i	$-0.829803\pi$
$433$	−367.762	+	212.327i	−0.849334	+	0.490363i	0.0110921	+	0.999938i	$0.496469\pi$
$434$		0			0
$435$	−209.362	+	97.6830i	−0.481293	+	0.224559i
$436$		0			0
$437$	90.8257	+	20.0881i	0.207839	+	0.0459682i
$438$		0			0
$439$			177.085i			0.403382i	0.979449	+	0.201691i	$0.0646436\pi$
$439$			177.085i			0.403382i	−0.979449	+	0.201691i	$0.935356\pi$
$440$		0			0
$441$	124.425	+	341.391i	0.282143	+	0.774128i
$442$		0			0
$443$	−61.6380	+	106.760i	−0.139138	+	0.240994i	−0.927170	−	0.374640i	$-0.877766\pi$
$443$	−61.6380	+	106.760i	−0.139138	+	0.240994i	0.788033	+	0.615633i	$0.211100\pi$
$444$		0			0
$445$	138.220	+	79.8014i	0.310607	+	0.179329i
$446$		0			0
$447$	61.3812	−	87.7023i	0.137318	−	0.196202i
$448$		0			0
$449$		−	547.990i		−	1.22047i	−0.792221	−	0.610234i	$-0.791075\pi$
$449$		−	547.990i		−	1.22047i	0.792221	−	0.610234i	$-0.208925\pi$
$450$		0			0
$451$	66.5115	+	38.4004i	0.147476	+	0.0851450i
$452$		0			0
$453$	215.456	+	150.794i	0.475621	+	0.332878i
$454$		0			0
$455$	34.2038	+	19.7476i	0.0751731	+	0.0434012i
$456$		0			0
$457$	375.971	+	651.201i	0.822694	+	1.42495i	0.903669	+	0.428232i	$0.140863\pi$
$457$	375.971	+	651.201i	0.822694	+	1.42495i	−0.0809747	+	0.996716i	$0.525803\pi$
$458$		0			0
$459$	394.466	−	394.984i	0.859403	−	0.860532i
$460$		0			0
$461$	55.0995			0.119522			0.0597608	−	0.998213i	$-0.480966\pi$
$461$	55.0995			0.119522			0.0597608	+	0.998213i	$0.480966\pi$
$462$		0			0
$463$	204.017	−	353.368i	0.440642	−	0.763214i	−0.557096	−	0.830448i	$-0.688084\pi$
$463$	204.017	−	353.368i	0.440642	−	0.763214i	0.997737	+	0.0672347i	$0.0214176\pi$
$464$		0			0
$465$	239.628	−	111.804i	0.515329	−	0.240439i
$466$		0			0
$467$	−486.888			−1.04259			−0.521293	−	0.853377i	$-0.674550\pi$
$467$	−486.888			−1.04259			−0.521293	+	0.853377i	$0.674550\pi$
$468$		0			0
$469$	−40.2713	+	23.2507i	−0.0858663	+	0.0495750i
$470$		0			0
$471$	445.311	−	636.267i	0.945459	−	1.35088i
$472$		0			0
$473$	−68.2780	−	118.261i	−0.144351	−	0.250023i
$474$		0			0
$475$	244.631	−	267.235i	0.515012	−	0.562600i
$476$		0			0
$477$	82.3235	−	468.078i	0.172586	−	0.981295i
$478$		0			0
$479$	−48.3446	+	83.7354i	−0.100928	+	0.174813i	−0.912067	−	0.410040i	$-0.865515\pi$
$479$	−48.3446	+	83.7354i	−0.100928	+	0.174813i	0.811139	+	0.584853i	$0.198848\pi$
$480$		0			0
$481$	228.799			0.475674
$482$		0			0
$483$	−24.7360	+	35.3431i	−0.0512132	+	0.0731741i
$484$		0			0
$485$	−19.6246	+	11.3303i	−0.0404631	+	0.0233614i
$486$		0			0
$487$			146.500i			0.300821i	0.988624	+	0.150410i	$0.0480595\pi$
$487$			146.500i			0.300821i	−0.988624	+	0.150410i	$0.951940\pi$
$488$		0			0
$489$	−182.312	−	390.746i	−0.372827	−	0.799072i
$490$		0			0
$491$	214.551	+	371.614i	0.436968	+	0.756852i	0.997454	−	0.0713127i	$-0.0227188\pi$
$491$	214.551	+	371.614i	0.436968	+	0.756852i	−0.560486	+	0.828164i	$0.689385\pi$
$492$		0			0
$493$	−566.148	+	326.866i	−1.14837	+	0.663014i
$494$		0			0
$495$	−40.9231	−	112.282i	−0.0826729	−	0.226833i
$496$		0			0
$497$		−	208.347i		−	0.419210i
$498$		0			0
$499$	−388.815	−	673.447i	−0.779188	−	1.34959i	−0.932410	−	0.361402i	$-0.882298\pi$
$499$	−388.815	−	673.447i	−0.779188	−	1.34959i	0.153222	−	0.988192i	$-0.451035\pi$
$500$		0			0
$501$	−364.588	+	170.107i	−0.727721	+	0.339536i
$502$		0			0
$503$	−338.593	−	586.460i	−0.673146	−	1.16592i	−0.977007	−	0.213207i	$-0.931609\pi$
$503$	−338.593	−	586.460i	−0.673146	−	1.16592i	0.303861	−	0.952716i	$-0.401724\pi$
$504$		0			0
$505$	285.760			0.565861
$506$		0			0
$507$	−175.703	−	376.580i	−0.346554	−	0.742762i
$508$		0			0
$509$		−	237.578i		−	0.466755i	−0.972386	−	0.233378i	$-0.925022\pi$
$509$		−	237.578i		−	0.466755i	0.972386	−	0.233378i	$-0.0749778\pi$
$510$		0			0
$511$	169.324			0.331359
$512$		0			0
$513$	455.310	+	236.351i	0.887544	+	0.460724i
$514$		0			0
$515$		−	88.7606i		−	0.172351i
$516$		0			0
$517$	−228.198			−0.441389
$518$		0			0
$519$	623.376	−	290.851i	1.20111	−	0.560407i
$520$		0			0
$521$		−	731.823i		−	1.40465i	−0.711856	−	0.702326i	$-0.752145\pi$
$521$		−	731.823i		−	1.40465i	0.711856	−	0.702326i	$-0.247855\pi$
$522$		0			0
$523$	360.598	−	208.191i	0.689479	−	0.398071i	−0.113938	−	0.993488i	$-0.536346\pi$
$523$	360.598	−	208.191i	0.689479	−	0.398071i	0.803417	+	0.595417i	$0.203013\pi$
$524$		0			0
$525$	71.0412	+	152.261i	0.135317	+	0.290022i
$526$		0			0
$527$	647.992	−	374.118i	1.22959	−	0.709902i
$528$		0			0
$529$	−505.031			−0.954690
$530$		0			0
$531$	−181.966	+	1034.63i	−0.342685	+	1.94845i
$532$		0			0
$533$	38.8866	+	67.3536i	0.0729580	+	0.126367i
$534$		0			0
$535$	−234.964	+	135.657i	−0.439185	+	0.253564i
$536$		0			0
$537$	515.999	−	240.752i	0.960892	−	0.448327i
$538$		0			0
$539$	220.116			0.408379
$540$		0			0
$541$	214.253	+	371.096i	0.396031	+	0.685945i	0.993232	−	0.116146i	$-0.0370541\pi$
$541$	214.253	+	371.096i	0.396031	+	0.685945i	−0.597202	+	0.802091i	$0.703721\pi$
$542$		0			0
$543$	424.320	+	296.974i	0.781436	+	0.546913i
$544$		0			0
$545$		−	425.993i		−	0.781639i
$546$		0			0
$547$	−479.383	−	276.772i	−0.876386	−	0.505982i	−0.00692090	−	0.999976i	$-0.502203\pi$
$547$	−479.383	−	276.772i	−0.876386	−	0.505982i	−0.869465	+	0.493994i	$0.835536\pi$
$548$		0			0
$549$	292.320	+	802.050i	0.532459	+	1.46093i
$550$		0			0
$551$	−443.135	−	405.652i	−0.804238	−	0.736211i
$552$		0			0
$553$	−387.449	+	223.694i	−0.700630	+	0.404509i
$554$		0			0
$555$	−248.071	−	173.620i	−0.446974	−	0.312829i
$556$		0			0
$557$	−165.368	−	286.425i	−0.296890	−	0.514228i	0.678533	−	0.734570i	$-0.262616\pi$
$557$	−165.368	−	286.425i	−0.296890	−	0.514228i	−0.975423	+	0.220342i	$0.929283\pi$
$558$		0			0
$559$		−	138.285i		−	0.247379i
$560$		0			0
$561$	−142.981	−	306.450i	−0.254869	−	0.546256i
$562$		0			0
$563$	720.686	+	416.088i	1.28008	+	0.739055i	0.976863	−	0.213866i	$-0.0686055\pi$
$563$	720.686	+	416.088i	1.28008	+	0.739055i	0.303218	+	0.952921i	$0.401939\pi$
$564$		0			0
$565$			7.32812i			0.0129701i
$566$		0			0
$567$	−182.115	+	153.085i	−0.321191	+	0.269991i
$568$		0			0
$569$	−835.482	+	482.365i	−1.46833	+	0.847743i	−0.999371	−	0.0354755i	$-0.988705\pi$
$569$	−835.482	+	482.365i	−1.46833	+	0.847743i	−0.468963	+	0.883218i	$0.655372\pi$
$570$		0			0
$571$	232.258	−	402.283i	0.406757	−	0.704524i	−0.587767	−	0.809030i	$-0.699993\pi$
$571$	232.258	−	402.283i	0.406757	−	0.704524i	0.994524	+	0.104506i	$0.0333262\pi$
$572$		0			0
$573$	396.631	−	566.712i	0.692202	−	0.989027i
$574$		0			0
$575$	46.6773	−	80.8475i	0.0811779	−	0.140604i
$576$		0			0
$577$	−718.841			−1.24583			−0.622913	−	0.782291i	$-0.714051\pi$
$577$	−718.841			−1.24583			−0.622913	+	0.782291i	$0.714051\pi$
$578$		0			0
$579$	39.9140	+	27.9351i	0.0689361	+	0.0482471i
$580$		0			0
$581$	−53.0601	+	91.9028i	−0.0913254	+	0.158180i
$582$		0			0
$583$	−249.334	−	143.953i	−0.427674	−	0.246918i
$584$		0			0
$585$	20.9628	−	119.191i	0.0358339	−	0.203746i
$586$		0			0
$587$	−236.225			−0.402428			−0.201214	−	0.979547i	$-0.564489\pi$
$587$	−236.225			−0.402428			−0.201214	+	0.979547i	$0.564489\pi$
$588$		0			0
$589$	507.195	+	464.294i	0.861113	+	0.788275i
$590$		0			0
$591$	−152.838	−	327.575i	−0.258609	−	0.554273i
$592$		0			0
$593$	−126.305	−	218.766i	−0.212993	−	0.368914i	0.739657	−	0.672984i	$-0.234988\pi$
$593$	−126.305	−	218.766i	−0.212993	−	0.368914i	−0.952650	+	0.304070i	$0.901654\pi$
$594$		0			0
$595$	−73.9495	−	128.084i	−0.124285	−	0.215268i
$596$		0			0
$597$	20.2349	−	28.9118i	0.0338942	−	0.0484285i
$598$		0			0
$599$			917.856i			1.53231i	0.642654	+	0.766157i	$0.277833\pi$
$599$			917.856i			1.53231i	−0.642654	+	0.766157i	$0.722167\pi$
$600$		0			0
$601$	102.444	−	59.1459i	0.170455	−	0.0984125i	−0.412345	−	0.911028i	$-0.635290\pi$
$601$	102.444	−	59.1459i	0.170455	−	0.0984125i	0.582801	+	0.812615i	$0.301957\pi$
$602$		0			0
$603$	109.193	+	91.5423i	0.181083	+	0.151811i
$604$		0			0
$605$	222.303			0.367442
$606$		0			0
$607$	−497.665	−	287.327i	−0.819876	−	0.473356i	0.0304976	−	0.999535i	$-0.490291\pi$
$607$	−497.665	−	287.327i	−0.819876	−	0.473356i	−0.850374	+	0.526179i	$0.823624\pi$
$608$		0			0
$609$	252.483	−	117.802i	0.414587	−	0.193436i
$610$		0			0
$611$	−200.128	−	115.544i	−0.327541	−	0.189106i
$612$		0			0
$613$	52.5986	−	91.1034i	0.0858052	−	0.148619i	−0.819929	−	0.572465i	$-0.805987\pi$
$613$	52.5986	−	91.1034i	0.0858052	−	0.148619i	0.905734	+	0.423847i	$0.139320\pi$
$614$		0			0
$615$	8.94803	−	102.535i	0.0145496	−	0.166723i
$616$		0			0
$617$	−1022.90			−1.65786			−0.828931	−	0.559351i	$-0.811050\pi$
$617$	−1022.90			−1.65786			−0.828931	+	0.559351i	$0.811050\pi$
$618$		0			0
$619$	214.174	+	370.960i	0.346000	+	0.599289i	0.985535	−	0.169473i	$-0.0542065\pi$
$619$	214.174	+	370.960i	0.346000	+	0.599289i	−0.639535	+	0.768762i	$0.720873\pi$
$620$		0			0
$621$	127.705	+	34.1287i	0.205645	+	0.0549577i
$622$		0			0
$623$	−166.688	−	96.2376i	−0.267558	−	0.154474i
$624$		0			0
$625$	−107.651	−	186.458i	−0.172242	−	0.298332i
$626$		0			0
$627$	228.971	−	210.115i	0.365185	−	0.335112i
$628$		0			0
$629$	−742.006	−	428.397i	−1.17966	−	0.681077i
$630$		0			0
$631$	482.528	+	835.763i	0.764703	+	1.32451i	0.940403	+	0.340061i	$0.110448\pi$
$631$	482.528	+	835.763i	0.764703	+	1.32451i	−0.175700	+	0.984444i	$0.556219\pi$
$632$		0			0
$633$	24.8032	+	17.3593i	0.0391836	+	0.0274239i
$634$		0			0
$635$	251.893	+	145.431i	0.396682	+	0.229025i
$636$		0			0
$637$	193.040	+	111.452i	0.303046	+	0.174963i
$638$		0			0
$639$	−599.819	+	218.614i	−0.938684	+	0.342118i
$640$		0			0
$641$		−	1036.62i		−	1.61719i	−0.588365	−	0.808595i	$-0.700228\pi$
$641$		−	1036.62i		−	1.61719i	0.588365	−	0.808595i	$-0.299772\pi$
$642$		0			0
$643$	584.470	+	1012.33i	0.908973	+	1.57439i	0.815494	+	0.578766i	$0.196466\pi$
$643$	584.470	+	1012.33i	0.908973	+	1.57439i	0.0934792	+	0.995621i	$0.470201\pi$
$644$		0			0
$645$	−104.935	+	149.932i	−0.162690	+	0.232453i
$646$		0			0
$647$	−314.501			−0.486090			−0.243045	−	0.970015i	$-0.578146\pi$
$647$	−314.501			−0.486090			−0.243045	+	0.970015i	$0.578146\pi$
$648$		0			0
$649$	551.120	+	318.190i	0.849184	+	0.490277i
$650$		0			0
$651$	−288.983	+	134.832i	−0.443906	+	0.207115i
$652$		0			0
$653$	105.805	−	183.260i	0.162030	−	0.280644i	−0.773567	−	0.633715i	$-0.781529\pi$
$653$	105.805	−	183.260i	0.162030	−	0.280644i	0.935596	+	0.353071i	$0.114863\pi$
$654$		0			0
$655$	−219.605	+	380.367i	−0.335275	+	0.580713i
$656$		0			0
$657$	−177.668	−	487.474i	−0.270423	−	0.741970i
$658$		0			0
$659$	491.084	+	283.528i	0.745196	+	0.430239i	0.823955	−	0.566655i	$-0.191763\pi$
$659$	491.084	+	283.528i	0.745196	+	0.430239i	−0.0787596	+	0.996894i	$0.525096\pi$
$660$		0			0
$661$			423.975i			0.641415i	0.947178	+	0.320707i	$0.103921\pi$
$661$			423.975i			0.641415i	−0.947178	+	0.320707i	$0.896079\pi$
$662$		0			0
$663$	29.7715	−	341.149i	0.0449042	−	0.514554i
$664$		0			0
$665$	91.7740	−	100.254i	0.138006	−	0.150758i
$666$		0			0
$667$	−134.063	−	77.4014i	−0.200994	−	0.116044i
$668$		0			0
$669$	−793.758	+	370.347i	−1.18648	+	0.553583i
$670$		0			0
$671$	517.133			0.770691
$672$		0			0
$673$	−907.347	+	523.857i	−1.34821	+	0.778391i	−0.987996	−	0.154478i	$-0.950630\pi$
$673$	−907.347	+	523.857i	−1.34821	+	0.778391i	−0.360216	+	0.932869i	$0.617297\pi$
$674$		0			0
$675$	363.809	−	364.287i	0.538977	−	0.539685i
$676$		0			0
$677$	−143.259	+	82.7105i	−0.211608	+	0.122172i	−0.602059	−	0.798452i	$-0.705653\pi$
$677$	−143.259	+	82.7105i	−0.211608	+	0.122172i	0.390450	+	0.920624i	$0.372319\pi$
$678$		0			0
$679$	23.6666	−	13.6639i	0.0348551	−	0.0201236i
$680$		0			0
$681$	709.246	+	496.388i	1.04148	+	0.728911i
$682$		0			0
$683$		−	1032.51i		−	1.51172i	−0.654732	−	0.755861i	$-0.727219\pi$
$683$		−	1032.51i		−	1.51172i	0.654732	−	0.755861i	$-0.272781\pi$
$684$		0			0
$685$	−534.901			−0.780877
$686$		0			0
$687$	4.83731	+	0.422143i	0.00704121	+	0.000614473i
$688$		0			0
$689$	−145.776	−	252.491i	−0.211576	−	0.366460i
$690$		0			0
$691$	15.8657	+	27.4802i	0.0229605	+	0.0397688i	0.877277	−	0.479984i	$-0.159357\pi$
$691$	15.8657	+	27.4802i	0.0229605	+	0.0397688i	−0.854317	+	0.519753i	$0.826024\pi$
$692$		0			0
$693$	49.3518	+	135.409i	0.0712147	+	0.195395i
$694$		0			0
$695$	100.719	+	174.451i	0.144920	+	0.251008i
$696$		0			0
$697$		−	291.241i		−	0.417849i
$698$		0			0
$699$	−528.142	−	46.0900i	−0.755568	−	0.0659370i
$700$		0			0
$701$	93.0345	−	161.141i	0.132717	−	0.229872i	−0.792006	−	0.610513i	$-0.790963\pi$
$701$	93.0345	−	161.141i	0.132717	−	0.229872i	0.924723	+	0.380641i	$0.124297\pi$
$702$		0			0
$703$	170.037	−	768.800i	0.241873	−	1.09360i
$704$		0			0
$705$	129.306	+	277.139i	0.183412	+	0.393105i
$706$		0			0
$707$	−344.616			−0.487435
$708$		0			0
$709$	−627.805	+	1087.39i	−0.885480	+	1.53370i	−0.0403174	+	0.999187i	$0.512837\pi$
$709$	−627.805	+	1087.39i	−0.885480	+	1.53370i	−0.845163	+	0.534509i	$0.820496\pi$
$710$		0			0
$711$	1050.54	+	880.724i	1.47755	+	1.23871i
$712$		0			0
$713$	153.444	+	88.5907i	0.215208	+	0.124251i
$714$		0			0
$715$	−63.4903	−	36.6561i	−0.0887976	−	0.0512673i
$716$		0			0
$717$	219.767	+	19.1787i	0.306509	+	0.0267485i
$718$		0			0
$719$	623.659	−	1080.21i	0.867398	−	1.50238i	0.00275185	−	0.999996i	$-0.499124\pi$
$719$	623.659	−	1080.21i	0.867398	−	1.50238i	0.864646	−	0.502381i	$-0.167543\pi$
$720$		0			0
$721$			107.042i			0.148463i
$722$		0			0
$723$	−68.2835	+	782.456i	−0.0944447	+	1.08224i
$724$		0			0
$725$	−522.149	+	301.463i	−0.720205	+	0.415811i
$726$		0			0
$727$	501.351			0.689616			0.344808	−	0.938673i	$-0.387944\pi$
$727$	501.351			0.689616			0.344808	+	0.938673i	$0.387944\pi$
$728$		0			0
$729$	631.811	+	363.671i	0.866681	+	0.498863i
$730$		0			0
$731$	−258.921	+	448.464i	−0.354201	+	0.613494i
$732$		0			0
$733$	−462.570	+	801.194i	−0.631064	+	1.09303i	0.356271	+	0.934383i	$0.384048\pi$
$733$	−462.570	+	801.194i	−0.631064	+	1.09303i	−0.987335	+	0.158652i	$0.949285\pi$
$734$		0			0
$735$	−124.726	−	267.324i	−0.169696	−	0.363706i
$736$		0			0
$737$	74.7531	−	43.1587i	0.101429	−	0.0585600i
$738$		0			0
$739$	680.499	−	1178.66i	0.920837	−	1.59494i	0.122715	−	0.992442i	$-0.460840\pi$
$739$	680.499	−	1178.66i	0.920837	−	1.59494i	0.798123	−	0.602495i	$-0.205827\pi$
$740$		0			0
$741$	307.193	−	68.3343i	0.414566	−	0.0922190i
$742$		0			0
$743$	−857.322	+	494.975i	−1.15387	+	0.666185i	−0.949826	−	0.312778i	$-0.898741\pi$
$743$	−857.322	+	494.975i	−1.15387	+	0.666185i	−0.204040	+	0.978963i	$0.565407\pi$
$744$		0			0
$745$	−43.4531	+	75.2631i	−0.0583264	+	0.101024i
$746$		0			0
$747$	320.257	+	56.3254i	0.428724	+	0.0754022i
$748$		0			0
$749$	283.358	−	163.597i	0.378315	−	0.218421i
$750$		0			0
$751$			1152.29i			1.53434i	0.641445	+	0.767169i	$0.278335\pi$
$751$			1152.29i			1.53434i	−0.641445	+	0.767169i	$0.721665\pi$
$752$		0			0
$753$	372.911	−	532.820i	0.495233	−	0.707596i
$754$		0			0
$755$	−184.897	−	106.750i	−0.244897	−	0.141391i
$756$		0			0
$757$	113.625	−	196.805i	0.150100	−	0.259980i	−0.781164	−	0.624326i	$-0.785374\pi$
$757$	113.625	−	196.805i	0.150100	−	0.259980i	0.931264	+	0.364345i	$0.118707\pi$
$758$		0			0
$759$	45.9158	−	65.6052i	0.0604952	−	0.0864363i
$760$		0			0
$761$	−28.1788	+	48.8071i	−0.0370286	+	0.0641354i	−0.883946	−	0.467589i	$-0.845123\pi$
$761$	−28.1788	+	48.8071i	−0.0370286	+	0.0641354i	0.846917	+	0.531725i	$0.178456\pi$
$762$		0			0
$763$			513.733i			0.673307i
$764$		0			0
$765$	−291.153	+	347.292i	−0.380593	+	0.453976i
$766$		0			0
$767$	322.218	+	558.098i	0.420102	+	0.727638i
$768$		0			0
$769$	−932.242			−1.21228			−0.606139	−	0.795359i	$-0.707283\pi$
$769$	−932.242			−1.21228			−0.606139	+	0.795359i	$0.707283\pi$
$770$		0			0
$771$	153.134	−	71.4483i	0.198617	−	0.0926696i
$772$		0			0
$773$	−487.159	+	281.262i	−0.630219	+	0.363857i	−0.780837	−	0.624735i	$-0.785207\pi$
$773$	−487.159	+	281.262i	−0.630219	+	0.363857i	0.150618	+	0.988592i	$0.451874\pi$
$774$		0			0
$775$	597.631	−	345.043i	0.771137	−	0.445216i
$776$		0			0
$777$	299.164	+	209.379i	0.385025	+	0.269472i
$778$		0			0
$779$	255.218	−	80.6096i	0.327622	−	0.103478i
$780$		0			0
$781$			386.742i			0.495188i
$782$		0			0
$783$	−604.070	−	603.277i	−0.771481	−	0.770469i
$784$		0			0
$785$	−315.246	+	546.021i	−0.401587	+	0.695569i
$786$		0			0
$787$	−581.484	−	335.720i	−0.738861	−	0.426582i	0.0827938	−	0.996567i	$-0.473616\pi$
$787$	−581.484	−	335.720i	−0.738861	−	0.426582i	−0.821655	+	0.569985i	$0.806949\pi$
$788$		0			0
$789$	506.331	+	1085.21i	0.641737	+	1.37542i
$790$		0			0
$791$		−	8.83746i		−	0.0111725i
$792$		0			0
$793$	453.521	+	261.840i	0.571905	+	0.330190i
$794$		0			0
$795$	−33.5438	+	384.376i	−0.0421935	+	0.483492i
$796$		0			0
$797$	464.895	+	268.407i	0.583306	+	0.336772i	0.762446	−	0.647052i	$-0.223998\pi$
$797$	464.895	+	268.407i	0.583306	+	0.336772i	−0.179140	+	0.983824i	$0.557332\pi$
$798$		0			0
$799$	432.682	+	749.427i	0.541529	+	0.937956i
$800$		0			0
$801$	−102.160	+	580.865i	−0.127541	+	0.725175i
$802$		0			0
$803$	−314.306			−0.391415
$804$		0			0
$805$	17.5112	−	30.3302i	0.0217530	−	0.0376773i
$806$		0			0
$807$	−92.6906	+	1062.14i	−0.114858	+	1.31615i
$808$		0			0
$809$	664.808			0.821765			0.410883	−	0.911688i	$-0.365221\pi$
$809$	664.808			0.821765			0.410883	+	0.911688i	$0.365221\pi$
$810$		0			0
$811$	−140.197	+	80.9429i	−0.172870	+	0.0998063i	−0.583938	−	0.811798i	$-0.698489\pi$
$811$	−140.197	+	80.9429i	−0.172870	+	0.0998063i	0.411069	+	0.911604i	$0.365156\pi$
$812$		0			0
$813$	−541.881	−	47.2890i	−0.666521	−	0.0581660i
$814$		0			0
$815$	175.027	+	303.155i	0.214757	+	0.371970i
$816$		0			0
$817$	−464.658	−	102.769i	−0.568737	−	0.125789i
$818$		0			0
$819$	−25.2804	+	143.740i	−0.0308674	+	0.175507i
$820$		0			0
$821$	−429.918	+	744.640i	−0.523652	+	0.906991i	0.475969	+	0.879462i	$0.342097\pi$
$821$	−429.918	+	744.640i	−0.523652	+	0.906991i	−0.999621	+	0.0275295i	$0.991236\pi$
$822$		0			0
$823$	−975.373			−1.18514			−0.592571	−	0.805518i	$-0.701887\pi$
$823$	−975.373			−1.18514			−0.592571	+	0.805518i	$0.701887\pi$
$824$		0			0
$825$	−131.869	−	282.633i	−0.159842	−	0.342586i
$826$		0			0
$827$	−683.380	+	394.550i	−0.826337	+	0.477086i	−0.852597	−	0.522569i	$-0.824974\pi$
$827$	−683.380	+	394.550i	−0.826337	+	0.477086i	0.0262601	+	0.999655i	$0.491640\pi$
$828$		0			0
$829$			958.236i			1.15589i	0.816075	+	0.577947i	$0.196146\pi$
$829$			958.236i			1.15589i	−0.816075	+	0.577947i	$0.803854\pi$
$830$		0			0
$831$	510.772	−	729.798i	0.614647	−	0.878216i
$832$		0			0
$833$	−417.358	−	722.885i	−0.501030	−	0.867809i
$834$		0			0
$835$	282.861	−	163.310i	0.338756	−	0.195581i
$836$		0			0
$837$	691.395	+	690.488i	0.826039	+	0.824956i
$838$		0			0
$839$		−	941.761i		−	1.12248i	−0.827653	−	0.561240i	$-0.810324\pi$
$839$		−	941.761i		−	1.12248i	0.827653	−	0.561240i	$-0.189676\pi$
$840$		0			0
$841$	79.3928	+	137.512i	0.0944029	+	0.163511i
$842$		0			0
$843$	−22.3415	+	256.010i	−0.0265024	+	0.303689i
$844$		0			0
$845$	168.681	+	292.165i	0.199623	+	0.345757i
$846$		0			0
$847$	−268.089			−0.316516
$848$		0			0
$849$	258.796	−	369.771i	0.304824	−	0.435537i
$850$		0			0
$851$		−	202.888i		−	0.238411i
$852$		0			0
$853$	1042.22			1.22183			0.610917	−	0.791695i	$-0.290801\pi$
$853$	1042.22			1.22183			0.610917	+	0.791695i	$0.290801\pi$
$854$		0			0
$855$	−384.921	−	159.018i	−0.450200	−	0.185986i
$856$		0			0
$857$			849.325i			0.991044i	0.868595	+	0.495522i	$0.165023\pi$
$857$			849.325i			0.991044i	−0.868595	+	0.495522i	$0.834977\pi$
$858$		0			0
$859$	−893.863			−1.04059			−0.520293	−	0.853988i	$-0.674177\pi$
$859$	−893.863			−1.04059			−0.520293	+	0.853988i	$0.674177\pi$
$860$		0			0
$861$	−10.7910	+	123.653i	−0.0125331	+	0.143616i
$862$		0			0
$863$		−	527.914i		−	0.611720i	−0.952077	−	0.305860i	$-0.901056\pi$
$863$		−	527.914i		−	0.611720i	0.952077	−	0.305860i	$-0.0989439\pi$
$864$		0			0
$865$	−483.638	+	279.229i	−0.559119	+	0.322808i
$866$		0			0
$867$	−238.173	+	340.304i	−0.274709	+	0.392508i
$868$		0			0
$869$	719.196	−	415.228i	0.827614	−	0.477823i
$870$		0			0
$871$	87.4103			0.100356
$872$		0			0
$873$	−64.1703	−	53.7974i	−0.0735055	−	0.0616236i
$874$		0			0
$875$	−157.621	−	273.008i	−0.180139	−	0.312009i
$876$		0			0
$877$	1034.11	−	597.044i	1.17915	−	0.680780i	0.223329	−	0.974743i	$-0.428308\pi$
$877$	1034.11	−	597.044i	1.17915	−	0.680780i	0.955817	+	0.293963i	$0.0949743\pi$
$878$		0			0
$879$	−34.8488	+	399.330i	−0.0396460	+	0.454301i
$880$		0			0
$881$	−845.187			−0.959349			−0.479675	−	0.877446i	$-0.659245\pi$
$881$	−845.187			−0.959349			−0.479675	+	0.877446i	$0.659245\pi$
$882$		0			0
$883$	−395.224	−	684.548i	−0.447592	−	0.775252i	0.550637	−	0.834745i	$-0.314385\pi$
$883$	−395.224	−	684.548i	−0.447592	−	0.775252i	−0.998229	+	0.0594929i	$0.981052\pi$
$884$		0			0
$885$	74.1443	−	849.614i	0.0837788	−	0.960016i
$886$		0			0
$887$			1125.84i			1.26927i	0.772814	+	0.634633i	$0.218849\pi$
$887$			1125.84i			1.26927i	−0.772814	+	0.634633i	$0.781151\pi$
$888$		0			0
$889$	−303.774	−	175.384i	−0.341703	−	0.197282i
$890$		0			0
$891$	338.049	−	284.162i	0.379404	−	0.318924i
$892$		0			0
$893$	−536.973	+	586.590i	−0.601314	+	0.656876i
$894$		0			0
$895$	−400.331	+	231.131i	−0.447297	+	0.258247i
$896$		0			0
$897$	73.4857	−	34.2865i	0.0819238	−	0.0382235i
$898$		0			0
$899$	−572.158	−	991.007i	−0.636438	−	1.10234i
$900$		0			0
$901$			1091.78i			1.21175i
$902$		0			0
$903$	126.548	−	180.813i	0.140141	−	0.200236i
$904$		0			0
$905$	−364.136	−	210.234i	−0.402360	−	0.232303i
$906$		0			0
$907$			53.7045i			0.0592111i	0.999562	+	0.0296056i	$0.00942512\pi$
$907$			53.7045i			0.0592111i	−0.999562	+	0.0296056i	$0.990575\pi$
$908$		0			0
$909$	361.597	+	992.129i	0.397797	+	1.09145i
$910$		0			0
$911$	−91.6127	+	52.8926i	−0.100563	+	0.0580599i	−0.549438	−	0.835535i	$-0.685158\pi$
$911$	−91.6127	+	52.8926i	−0.100563	+	0.0580599i	0.448875	+	0.893594i	$0.351825\pi$
$912$		0			0
$913$	98.4921	−	170.593i	0.107877	−	0.186849i
$914$		0			0
$915$	−293.027	−	628.040i	−0.320248	−	0.686383i
$916$		0			0
$917$	264.836	−	458.709i	0.288807	−	0.500228i
$918$		0			0
$919$	−347.202			−0.377804			−0.188902	−	0.981996i	$-0.560493\pi$
$919$	−347.202			−0.377804			−0.188902	+	0.981996i	$0.560493\pi$
$920$		0			0
$921$	−35.7382	+	409.521i	−0.0388037	+	0.444649i
$922$		0			0
$923$	−195.819	+	339.169i	−0.212155	+	0.367464i
$924$		0			0
$925$	−684.339	−	395.103i	−0.739826	−	0.427139i
$926$		0			0
$927$	308.168	−	112.317i	0.332435	−	0.121161i
$928$		0			0
$929$	286.589			0.308492			0.154246	−	0.988032i	$-0.450705\pi$
$929$	286.589			0.308492			0.154246	+	0.988032i	$0.450705\pi$
$930$		0			0
$931$	517.956	−	565.816i	0.556344	−	0.607751i
$932$		0			0
$933$	−106.973	−	9.33534i	−0.114655	−	0.0100057i
$934$		0			0
$935$	137.268	+	237.755i	0.146810	+	0.254283i
$936$		0			0
$937$	303.317	+	525.361i	0.323711	+	0.560684i	0.981251	−	0.192736i	$-0.0617361\pi$
$937$	303.317	+	525.361i	0.323711	+	0.560684i	−0.657540	+	0.753420i	$0.728403\pi$
$938$		0			0
$939$	−1049.50	−	91.5883i	−1.11768	−	0.0975381i
$940$		0			0
$941$			642.436i			0.682716i	0.939933	+	0.341358i	$0.110887\pi$
$941$			642.436i			0.682716i	−0.939933	+	0.341358i	$0.889113\pi$
$942$		0			0
$943$	59.7258	−	34.4827i	0.0633359	−	0.0365670i
$944$		0			0
$945$	136.484	−	136.664i	0.144428	−	0.144618i
$946$		0			0
$947$	1854.40			1.95818			0.979091	−	0.203424i	$-0.0652069\pi$
$947$	1854.40			1.95818			0.979091	+	0.203424i	$0.0652069\pi$
$948$		0			0
$949$	−275.643	−	159.143i	−0.290457	−	0.167695i
$950$		0			0
$951$	−79.6301	+	912.476i	−0.0837330	+	0.959491i
$952$		0			0
$953$	−224.224	−	129.456i	−0.235283	−	0.135841i	0.377724	−	0.925918i	$-0.376707\pi$
$953$	−224.224	−	129.456i	−0.235283	−	0.135841i	−0.613007	+	0.790078i	$0.710040\pi$
$954$		0			0
$955$	−280.784	+	486.333i	−0.294015	+	0.509249i
$956$		0			0
$957$	−468.669	+	218.669i	−0.489727	+	0.228494i
$958$		0			0
$959$	645.071			0.672650
$960$		0			0
$961$	174.370	+	302.018i	0.181446	+	0.314274i
$962$		0			0
$963$	−768.306	−	644.113i	−0.797826	−	0.668861i
$964$		0			0
$965$	−34.2528	−	19.7758i	−0.0354951	−	0.0204931i
$966$		0			0
$967$	551.131	+	954.587i	0.569939	+	0.987164i	0.996571	+	0.0827385i	$0.0263666\pi$
$967$	551.131	+	954.587i	0.569939	+	0.987164i	−0.426632	+	0.904425i	$0.640300\pi$
$968$		0			0
$969$	−1124.19	−	353.569i	−1.16015	−	0.364880i
$970$		0			0
$971$	1643.05	+	948.618i	1.69213	+	0.976949i	0.952799	+	0.303602i	$0.0981893\pi$
$971$	1643.05	+	948.618i	1.69213	+	0.976949i	0.739326	+	0.673347i	$0.235144\pi$
$972$		0			0
$973$	−121.464	−	210.382i	−0.124834	−	0.216219i
$974$		0			0
$975$	27.4577	−	314.636i	0.0281617	−	0.322704i
$976$		0			0
$977$	−521.457	−	301.063i	−0.533733	−	0.308151i	0.208802	−	0.977958i	$-0.433043\pi$
$977$	−521.457	−	301.063i	−0.533733	−	0.308151i	−0.742535	+	0.669807i	$0.766377\pi$
$978$		0			0
$979$	309.413	+	178.640i	0.316050	+	0.182472i
$980$		0			0
$981$	1479.01	−	539.047i	1.50765	−	0.549487i
$982$		0			0
$983$		−	1562.39i		−	1.58941i	−0.606996	−	0.794705i	$-0.707626\pi$
$983$		−	1562.39i		−	1.58941i	0.606996	−	0.794705i	$-0.292374\pi$
$984$		0			0
$985$	146.731	+	254.145i	0.148965	+	0.258015i
$986$		0			0
$987$	−155.938	−	334.219i	−0.157992	−	0.338621i
$988$		0			0
$989$	−122.624			−0.123988
$990$		0			0
$991$	−39.2689	−	22.6719i	−0.0396255	−	0.0228778i	0.480056	−	0.877238i	$-0.340616\pi$
$991$	−39.2689	−	22.6719i	−0.0396255	−	0.0228778i	−0.519682	+	0.854360i	$0.673950\pi$
$992$		0			0
$993$	−672.371	−	470.580i	−0.677111	−	0.473898i
$994$		0			0
$995$	−14.3247	+	24.8111i	−0.0143967	+	0.0249358i
$996$		0			0
$997$	−361.984	+	626.974i	−0.363073	+	0.628861i	−0.988465	−	0.151450i	$-0.951606\pi$
$997$	−361.984	+	626.974i	−0.363073	+	0.628861i	0.625392	+	0.780311i	$0.284939\pi$
$998$		0			0
$999$	288.885	−	1080.97i	0.289174	−	1.08205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.15	✓	80
3.2	odd	2		2052.3.s.a.901.17		80
9.2	odd	6		2052.3.bl.a.1585.24		80
9.7	even	3		684.3.bl.a.673.1	yes	80
19.12	odd	6		684.3.bl.a.373.1	yes	80
57.50	even	6		2052.3.bl.a.145.24		80
171.88	odd	6	inner	684.3.s.a.601.15	yes	80
171.164	even	6		2052.3.s.a.829.17		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.15	✓	80	1.1	even	1	trivial
684.3.s.a.601.15	yes	80	171.88	odd	6	inner
684.3.bl.a.373.1	yes	80	19.12	odd	6
684.3.bl.a.673.1	yes	80	9.7	even	3
2052.3.s.a.829.17		80	171.164	even	6
2052.3.s.a.901.17		80	3.2	odd	2
2052.3.bl.a.145.24		80	57.50	even	6
2052.3.bl.a.1585.24		80	9.2	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26845 - 2.71865i) q^{3} +(1.21776 + 2.10923i) q^{5} +(-1.46858 - 2.54365i) q^{7} +(-5.78207 + 6.89693i) q^{9} +O(q^{10})\)	\(q+(-1.26845 - 2.71865i) q^{3} +(1.21776 + 2.10923i) q^{5} +(-1.46858 - 2.54365i) q^{7} +(-5.78207 + 6.89693i) q^{9} +(2.72603 + 4.72162i) q^{11} +5.52108i q^{13} +(4.18957 - 5.98611i) q^{15} +(10.3375 - 17.9051i) q^{17} +(18.5517 + 4.10311i) q^{19} +(-5.05247 + 7.21903i) q^{21} +4.89582 q^{23} +(9.53411 - 16.5136i) q^{25} +(26.0846 + 6.97099i) q^{27} +(-27.3832 - 15.8097i) q^{29} +(31.3417 + 18.0952i) q^{31} +(9.37858 - 13.4002i) q^{33} +(3.57675 - 6.19512i) q^{35} -41.4410i q^{37} +(15.0099 - 7.00322i) q^{39} +(12.1993 - 7.04329i) q^{41} -25.0467 q^{43} +(-21.5884 - 3.79687i) q^{45} +(-20.9277 + 36.2479i) q^{47} +(20.1866 - 34.9642i) q^{49} +(-61.7903 - 5.39232i) q^{51} +(-45.7321 + 26.4034i) q^{53} +(-6.63930 + 11.4996i) q^{55} +(-12.3770 - 55.6400i) q^{57} +(101.085 - 58.3614i) q^{59} +(47.4256 - 82.1435i) q^{61} +(26.0348 + 4.57889i) q^{63} +(-11.6452 + 6.72336i) q^{65} -15.8321i q^{67} +(-6.21010 - 13.3100i) q^{69} +(61.4316 + 35.4675i) q^{71} +(-28.8246 + 49.9256i) q^{73} +(-56.9881 - 4.97325i) q^{75} +(8.00676 - 13.8681i) q^{77} -152.320i q^{79} +(-14.1353 - 79.7571i) q^{81} +(-18.0651 - 31.2897i) q^{83} +50.3545 q^{85} +(-8.24675 + 94.4990i) q^{87} +(56.7517 - 32.7656i) q^{89} +(14.0437 - 8.10814i) q^{91} +(9.43892 - 108.160i) q^{93} +(13.9371 + 44.1263i) q^{95} +9.30418i q^{97} +(-48.3268 - 8.49950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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