LMFDB - Embedded newform 117.4.q.f.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (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:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 32x^{10} + 823x^{8} - 5964x^{6} + 32913x^{4} - 47034x^{2} + 54756 $ x^12 - 32x^10 + 823x^8 - 5964x^6 + 32913x^4 - 47034*x^2 + 54756
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			82.2
Root			$-2.19846 + 1.26928i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.4.q.f.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19846 - 1.26928i) q^{2} +(-0.777841 - 1.34726i) q^{4} +8.18941i q^{5} +(9.33900 - 5.39187i) q^{7} +24.2577i q^{8} +O(q^{10})$	\(q+(-2.19846 - 1.26928i) q^{2} +(-0.777841 - 1.34726i) q^{4} +8.18941i q^{5} +(9.33900 - 5.39187i) q^{7} +24.2577i q^{8} +(10.3947 - 18.0041i) q^{10} +(9.51865 + 5.49559i) q^{11} +(34.4619 - 31.7707i) q^{13} -27.3753 q^{14} +(24.5672 - 42.5516i) q^{16} +(-2.42641 - 4.20267i) q^{17} +(56.5285 - 32.6367i) q^{19} +(11.0333 - 6.37006i) q^{20} +(-13.9509 - 24.1637i) q^{22} +(83.3064 - 144.291i) q^{23} +57.9336 q^{25} +(-116.089 + 26.1049i) q^{26} +(-14.5285 - 8.38804i) q^{28} +(46.2424 - 80.0942i) q^{29} -3.63236i q^{31} +(60.0423 - 34.6655i) q^{32} +12.3192i q^{34} +(44.1563 + 76.4809i) q^{35} +(35.1633 + 20.3015i) q^{37} -165.701 q^{38} -198.656 q^{40} +(210.307 + 121.421i) q^{41} +(80.7192 + 139.810i) q^{43} -17.0988i q^{44} +(-366.292 + 211.479i) q^{46} +296.631i q^{47} +(-113.355 + 196.337i) q^{49} +(-127.365 - 73.5341i) q^{50} +(-69.6093 - 21.7165i) q^{52} -662.165 q^{53} +(-45.0057 + 77.9521i) q^{55} +(130.795 + 226.543i) q^{56} +(-203.325 + 117.389i) q^{58} +(339.120 - 195.791i) q^{59} +(161.616 + 279.927i) q^{61} +(-4.61049 + 7.98561i) q^{62} -569.076 q^{64} +(260.183 + 282.222i) q^{65} +(483.723 + 279.277i) q^{67} +(-3.77472 + 6.53802i) q^{68} -224.187i q^{70} +(92.5031 - 53.4067i) q^{71} -79.5194i q^{73} +(-51.5368 - 89.2643i) q^{74} +(-87.9404 - 50.7724i) q^{76} +118.526 q^{77} +480.970 q^{79} +(348.473 + 201.191i) q^{80} +(-308.235 - 533.878i) q^{82} -1251.53i q^{83} +(34.4174 - 19.8709i) q^{85} -409.822i q^{86} +(-133.311 + 230.901i) q^{88} +(-1252.68 - 723.234i) q^{89} +(150.536 - 482.521i) q^{91} -259.197 q^{92} +(376.508 - 652.131i) q^{94} +(267.276 + 462.935i) q^{95} +(1207.87 - 697.366i) q^{97} +(498.415 - 287.760i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{4} - 18 q^{7}+O(q^{10}) $ 12 * q + 16 * q^4 - 18 * q^7	$ 12 q + 16 q^{4} - 18 q^{7} - 56 q^{10} - 154 q^{13} - 92 q^{16} - 48 q^{19} + 292 q^{22} - 92 q^{25} + 552 q^{28} - 360 q^{37} - 448 q^{40} - 810 q^{43} + 996 q^{46} - 1068 q^{49} - 700 q^{52} + 460 q^{55} + 3048 q^{58} + 1294 q^{61} - 184 q^{64} + 2658 q^{67} + 1188 q^{76} - 6380 q^{79} - 1268 q^{82} - 3768 q^{85} - 5140 q^{88} + 342 q^{91} + 1660 q^{94} + 1686 q^{97}+O(q^{100}) $ 12 * q + 16 * q^4 - 18 * q^7 - 56 * q^10 - 154 * q^13 - 92 * q^16 - 48 * q^19 + 292 * q^22 - 92 * q^25 + 552 * q^28 - 360 * q^37 - 448 * q^40 - 810 * q^43 + 996 * q^46 - 1068 * q^49 - 700 * q^52 + 460 * q^55 + 3048 * q^58 + 1294 * q^61 - 184 * q^64 + 2658 * q^67 + 1188 * q^76 - 6380 * q^79 - 1268 * q^82 - 3768 * q^85 - 5140 * q^88 + 342 * q^91 + 1660 * q^94 + 1686 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.19846	−	1.26928i	−0.777274	−	0.448759i	0.0581893	−	0.998306i	$-0.481467\pi$
$2$	−2.19846	−	1.26928i	−0.777274	−	0.448759i	−0.835463	+	0.549546i	$0.814801\pi$
$3$		0			0
$3$		0			0
$4$	−0.777841	−	1.34726i	−0.0972301	−	0.168408i
$5$			8.18941i			0.732483i	0.930520	+	0.366242i	$0.119356\pi$
$5$			8.18941i			0.732483i	−0.930520	+	0.366242i	$0.880644\pi$
$6$		0			0
$7$	9.33900	−	5.39187i	0.504258	−	0.291134i	−0.226212	−	0.974078i	$-0.572634\pi$
$7$	9.33900	−	5.39187i	0.504258	−	0.291134i	0.730470	+	0.682944i	$0.239301\pi$
$8$			24.2577i			1.07205i
$9$		0			0
$10$	10.3947	−	18.0041i	0.328709	−	0.569340i
$11$	9.51865	+	5.49559i	0.260907	+	0.150635i	0.624748	−	0.780826i	$-0.285202\pi$
$11$	9.51865	+	5.49559i	0.260907	+	0.150635i	−0.363841	+	0.931461i	$0.618535\pi$
$12$		0			0
$13$	34.4619	−	31.7707i	0.735231	−	0.677816i
$13$	34.4619	−	31.7707i	0.735231	−	0.677816i
$14$	−27.3753			−0.522596
$15$		0			0
$16$	24.5672	−	42.5516i	0.383862	−	0.664869i
$17$	−2.42641	−	4.20267i	−0.0346171	−	0.0599586i	0.848198	−	0.529680i	$-0.177688\pi$
$17$	−2.42641	−	4.20267i	−0.0346171	−	0.0599586i	−0.882815	+	0.469721i	$0.844355\pi$
$18$		0			0
$19$	56.5285	−	32.6367i	0.682554	−	0.394073i	−0.118263	−	0.992982i	$-0.537732\pi$
$19$	56.5285	−	32.6367i	0.682554	−	0.394073i	0.800817	+	0.598910i	$0.204399\pi$
$20$	11.0333	−	6.37006i	0.123356	−	0.0712194i
$21$		0			0
$22$	−13.9509	−	24.1637i	−0.135198	−	0.234169i
$23$	83.3064	−	144.291i	0.755243	−	1.30812i	−0.190010	−	0.981782i	$-0.560852\pi$
$23$	83.3064	−	144.291i	0.755243	−	1.30812i	0.945253	−	0.326338i	$-0.105815\pi$
$24$		0			0
$25$	57.9336			0.463469
$26$	−116.089	+	26.1049i	−0.875653	+	0.196907i
$27$		0			0
$28$	−14.5285	−	8.38804i	−0.0980582	−	0.0566139i
$29$	46.2424	−	80.0942i	0.296104	−	0.512866i	−0.679137	−	0.734011i	$-0.737646\pi$
$29$	46.2424	−	80.0942i	0.296104	−	0.512866i	0.975241	+	0.221145i	$0.0709793\pi$
$30$		0			0
$31$		−	3.63236i		−	0.0210449i	−0.999945	−	0.0105224i	$-0.996651\pi$
$31$		−	3.63236i		−	0.0210449i	0.999945	−	0.0105224i	$-0.00334946\pi$
$32$	60.0423	−	34.6655i	0.331690	−	0.191501i
$33$		0			0
$34$			12.3192i			0.0621390i
$35$	44.1563	+	76.4809i	0.213251	+	0.369361i
$36$		0			0
$37$	35.1633	+	20.3015i	0.156238	+	0.0902041i	0.576081	−	0.817393i	$-0.304581\pi$
$37$	35.1633	+	20.3015i	0.156238	+	0.0902041i	−0.419843	+	0.907597i	$0.637915\pi$
$38$	−165.701			−0.707375
$39$		0			0
$40$	−198.656			−0.785259
$41$	210.307	+	121.421i	0.801084	+	0.462506i	0.843850	−	0.536579i	$-0.180284\pi$
$41$	210.307	+	121.421i	0.801084	+	0.462506i	−0.0427664	+	0.999085i	$0.513617\pi$
$42$		0			0
$43$	80.7192	+	139.810i	0.286269	+	0.495832i	0.972916	−	0.231159i	$-0.0742517\pi$
$43$	80.7192	+	139.810i	0.286269	+	0.495832i	−0.686647	+	0.726991i	$0.740918\pi$
$44$		−	17.0988i		−	0.0585850i
$45$		0			0
$46$	−366.292	+	211.479i	−1.17406	+	0.677845i
$47$			296.631i			0.920596i	0.887764	+	0.460298i	$0.152257\pi$
$47$			296.631i			0.920596i	−0.887764	+	0.460298i	$0.847743\pi$
$48$		0			0
$49$	−113.355	+	196.337i	−0.330482	+	0.572412i
$50$	−127.365	−	73.5341i	−0.360242	−	0.207986i
$51$		0			0
$52$	−69.6093	−	21.7165i	−0.185636	−	0.0579143i
$53$	−662.165			−1.71614			−0.858070	−	0.513533i	$-0.828336\pi$
$53$	−662.165			−1.71614			−0.858070	+	0.513533i	$0.828336\pi$
$54$		0			0
$55$	−45.0057	+	77.9521i	−0.110338	+	0.191110i
$56$	130.795	+	226.543i	0.312110	+	0.540590i
$57$		0			0
$58$	−203.325	+	117.389i	−0.460307	+	0.265758i
$59$	339.120	−	195.791i	0.748300	−	0.432031i	−0.0767791	−	0.997048i	$-0.524464\pi$
$59$	339.120	−	195.791i	0.748300	−	0.432031i	0.825079	+	0.565017i	$0.191130\pi$
$60$		0			0
$61$	161.616	+	279.927i	0.339226	+	0.587557i	0.984287	−	0.176574i	$-0.0565015\pi$
$61$	161.616	+	279.927i	0.339226	+	0.587557i	−0.645061	+	0.764131i	$0.723168\pi$
$62$	−4.61049	+	7.98561i	−0.00944409	+	0.0163576i
$63$		0			0
$64$	−569.076			−1.11148
$65$	260.183	+	282.222i	0.496489	+	0.538544i
$66$		0			0
$67$	483.723	+	279.277i	0.882032	+	0.509241i	0.871328	−	0.490702i	$-0.163259\pi$
$67$	483.723	+	279.277i	0.882032	+	0.509241i	0.0107039	+	0.999943i	$0.496593\pi$
$68$	−3.77472	+	6.53802i	−0.00673166	+	0.0116596i
$69$		0			0
$70$		−	224.187i		−	0.382793i
$71$	92.5031	−	53.4067i	0.154621	−	0.0892705i	−0.420693	−	0.907203i	$-0.638213\pi$
$71$	92.5031	−	53.4067i	0.154621	−	0.0892705i	0.575314	+	0.817932i	$0.304880\pi$
$72$		0			0
$73$		−	79.5194i		−	0.127494i	−0.997966	−	0.0637468i	$-0.979695\pi$
$73$		−	79.5194i		−	0.127494i	0.997966	−	0.0637468i	$-0.0203050\pi$
$74$	−51.5368	−	89.2643i	−0.0809598	−	0.140227i
$75$		0			0
$76$	−87.9404	−	50.7724i	−0.132730	−	0.0766315i
$77$	118.526			0.175420
$78$		0			0
$79$	480.970			0.684980			0.342490	−	0.939522i	$-0.388730\pi$
$79$	480.970			0.684980			0.342490	+	0.939522i	$0.388730\pi$
$80$	348.473	+	201.191i	0.487006	+	0.281173i
$81$		0			0
$82$	−308.235	−	533.878i	−0.415108	−	0.718987i
$83$		−	1251.53i		−	1.65510i	−0.561392	−	0.827550i	$-0.689734\pi$
$83$		−	1251.53i		−	1.65510i	0.561392	−	0.827550i	$-0.310266\pi$
$84$		0			0
$85$	34.4174	−	19.8709i	0.0439187	−	0.0253565i
$86$		−	409.822i		−	0.513863i
$87$		0			0
$88$	−133.311	+	230.901i	−0.161488	+	0.279706i
$89$	−1252.68	−	723.234i	−1.49195	−	0.861378i	−0.491993	−	0.870599i	$-0.663731\pi$
$89$	−1252.68	−	723.234i	−1.49195	−	0.861378i	−0.999957	+	0.00922118i	$0.997065\pi$
$90$		0			0
$91$	150.536	−	482.521i	0.173411	−	0.555845i
$92$	−259.197			−0.293730
$93$		0			0
$94$	376.508	−	652.131i	0.413126	−	0.715555i
$95$	267.276	+	462.935i	0.288652	+	0.499959i
$96$		0			0
$97$	1207.87	−	697.366i	1.26434	−	0.729967i	0.290429	−	0.956897i	$-0.406202\pi$
$97$	1207.87	−	697.366i	1.26434	−	0.729967i	0.973911	+	0.226929i	$0.0728687\pi$
$98$	498.415	−	287.760i	0.513751	−	0.296614i
$99$		0			0
$100$	−45.0631	−	78.0516i	−0.0450631	−	0.0780516i
$101$	336.372	−	582.613i	0.331389	−	0.573982i	−0.651396	−	0.758738i	$-0.725816\pi$
$101$	336.372	−	582.613i	0.331389	−	0.573982i	0.982784	+	0.184756i	$0.0591495\pi$
$102$		0			0
$103$	−131.830			−0.126113			−0.0630563	−	0.998010i	$-0.520085\pi$
$103$	−131.830			−0.126113			−0.0630563	+	0.998010i	$0.520085\pi$
$104$	770.686	+	835.967i	0.726653	+	0.788205i
$105$		0			0
$106$	1455.75	+	840.475i	1.33391	+	0.770134i
$107$	−1023.30	+	1772.41i	−0.924544	+	1.60136i	−0.132250	+	0.991216i	$0.542220\pi$
$107$	−1023.30	+	1772.41i	−0.924544	+	1.60136i	−0.792293	+	0.610140i	$0.791113\pi$
$108$		0			0
$109$		−	1380.13i		−	1.21277i	−0.795170	−	0.606386i	$-0.792619\pi$
$109$		−	1380.13i		−	1.21277i	0.795170	−	0.606386i	$-0.207381\pi$
$110$	197.887	−	114.250i	0.171525	−	0.0990300i
$111$		0			0
$112$		−	529.853i		−	0.447021i
$113$	519.411	+	899.647i	0.432408	+	0.748953i	0.997080	−	0.0763627i	$-0.0243307\pi$
$113$	519.411	+	899.647i	0.432408	+	0.748953i	−0.564672	+	0.825315i	$0.690997\pi$
$114$		0			0
$115$	1181.66	+	682.231i	0.958176	+	0.553203i
$116$	−143.877			−0.115161
$117$		0			0
$118$	−994.058			−0.775513
$119$	−45.3205	−	26.1658i	−0.0349120	−	0.0201564i
$120$		0			0
$121$	−605.097	−	1048.06i	−0.454618	−	0.787422i
$122$		−	820.545i		−	0.608924i
$123$		0			0
$124$	−4.89373	+	2.82540i	−0.00354412	+	0.00204620i
$125$			1498.12i			1.07197i
$126$		0			0
$127$	−1083.73	+	1877.08i	−0.757211	+	1.31153i	0.187056	+	0.982349i	$0.440105\pi$
$127$	−1083.73	+	1877.08i	−0.757211	+	1.31153i	−0.944267	+	0.329179i	$0.893228\pi$
$128$	770.754	+	444.995i	0.532232	+	0.307284i
$129$		0			0
$130$	−213.784	−	950.702i	−0.144231	−	0.641401i
$131$	−2034.60			−1.35698			−0.678489	−	0.734611i	$-0.737365\pi$
$131$	−2034.60			−1.35698			−0.678489	+	0.734611i	$0.737365\pi$
$132$		0			0
$133$	351.946	−	609.589i	0.229456	−	0.397429i
$134$	−708.964	−	1227.96i	−0.457053	−	0.791640i
$135$		0			0
$136$	101.947	−	58.8592i	0.0642787	−	0.0371113i
$137$	−717.402	+	414.192i	−0.447385	+	0.258298i	−0.706725	−	0.707488i	$-0.749828\pi$
$137$	−717.402	+	414.192i	−0.447385	+	0.258298i	0.259340	+	0.965786i	$0.416495\pi$
$138$		0			0
$139$	739.881	+	1281.51i	0.451481	+	0.781989i	0.998478	−	0.0551460i	$-0.0175624\pi$
$139$	739.881	+	1281.51i	0.451481	+	0.781989i	−0.546997	+	0.837135i	$0.684229\pi$
$140$	68.6931	−	118.980i	0.0414688	−	0.0718260i
$141$		0			0
$142$	−271.153			−0.160244
$143$	502.630	−	113.026i	0.293930	−	0.0660958i
$144$		0			0
$145$	655.925	+	378.698i	0.375666	+	0.216891i
$146$	−100.933	+	174.820i	−0.0572140	+	0.0990975i
$147$		0			0
$148$		−	63.1654i		−	0.0350822i
$149$	2049.43	−	1183.24i	1.12682	−	0.650569i	0.183686	−	0.982985i	$-0.441197\pi$
$149$	2049.43	−	1183.24i	1.12682	−	0.650569i	0.943133	+	0.332416i	$0.107864\pi$
$150$		0			0
$151$			878.334i			0.473363i	0.971587	+	0.236681i	$0.0760598\pi$
$151$			878.334i			0.473363i	−0.971587	+	0.236681i	$0.923940\pi$
$152$	791.693	+	1371.25i	0.422466	+	0.731732i
$153$		0			0
$154$	−260.575	−	150.443i	−0.136349	−	0.0787212i
$155$	29.7469			0.0154150
$156$		0			0
$157$	−2780.63			−1.41349			−0.706746	−	0.707467i	$-0.749838\pi$
$157$	−2780.63			−1.41349			−0.706746	+	0.707467i	$0.749838\pi$
$158$	−1057.40	−	610.487i	−0.532417	−	0.307391i
$159$		0			0
$160$	283.890	+	491.711i	0.140272	+	0.242957i
$161$		−	1796.71i		−	0.879507i
$162$		0			0
$163$	−3377.44	+	1949.97i	−1.62296	+	0.937014i	−0.636832	+	0.771003i	$0.719755\pi$
$163$	−3377.44	+	1949.97i	−1.62296	+	0.937014i	−0.986124	+	0.166011i	$0.946911\pi$
$164$		−	377.784i		−	0.179878i
$165$		0			0
$166$	−1588.55	+	2751.44i	−0.742741	+	1.28647i
$167$	178.459	+	103.033i	0.0826919	+	0.0477422i	0.540776	−	0.841167i	$-0.318131\pi$
$167$	178.459	+	103.033i	0.0826919	+	0.0477422i	−0.458084	+	0.888909i	$0.651464\pi$
$168$		0			0
$169$	178.242	−	2189.76i	0.0811298	−	0.996704i
$170$	−100.887			−0.0455158
$171$		0			0
$172$	125.573	−	217.499i	0.0556679	−	0.0964196i
$173$	−126.515	−	219.130i	−0.0555995	−	0.0963012i	0.836886	−	0.547377i	$-0.184374\pi$
$173$	−126.515	−	219.130i	−0.0555995	−	0.0963012i	−0.892486	+	0.451076i	$0.851040\pi$
$174$		0			0
$175$	541.041	−	312.370i	0.233708	−	0.134931i
$176$	467.693	−	270.023i	0.200305	−	0.115646i
$177$		0			0
$178$	1835.98	+	3180.01i	0.773103	+	1.33905i
$179$	1994.61	−	3454.76i	0.832872	−	1.44258i	−0.0628796	−	0.998021i	$-0.520028\pi$
$179$	1994.61	−	3454.76i	0.832872	−	1.44258i	0.895751	−	0.444555i	$-0.146638\pi$
$180$		0			0
$181$	−3392.65			−1.39323			−0.696613	−	0.717447i	$-0.745310\pi$
$181$	−3392.65			−1.39323			−0.696613	+	0.717447i	$0.745310\pi$
$182$	−943.403	+	869.732i	−0.384229	+	0.354224i
$183$		0			0
$184$	3500.17	+	2020.83i	1.40237	+	0.809659i
$185$	−166.258	+	287.966i	−0.0660730	+	0.114442i
$186$		0			0
$187$		−	53.3383i		−	0.0208582i
$188$	399.639	−	230.731i	0.155035	−	0.0895097i
$189$		0			0
$190$		−	1356.99i		−	0.518141i
$191$	633.973	+	1098.07i	0.240171	+	0.415988i	0.960763	−	0.277371i	$-0.0894631\pi$
$191$	633.973	+	1098.07i	0.240171	+	0.415988i	−0.720592	+	0.693359i	$0.756130\pi$
$192$		0			0
$193$	−1156.37	−	667.631i	−0.431282	−	0.249001i	0.268611	−	0.963249i	$-0.413436\pi$
$193$	−1156.37	−	667.631i	−0.431282	−	0.249001i	−0.699893	+	0.714248i	$0.746769\pi$
$194$	−3540.62			−1.31032
$195$		0			0
$196$	352.690			0.128531
$197$	1277.52	+	737.576i	0.462028	+	0.266752i	0.712897	−	0.701269i	$-0.247383\pi$
$197$	1277.52	+	737.576i	0.462028	+	0.266752i	−0.250869	+	0.968021i	$0.580716\pi$
$198$		0			0
$199$	−736.650	−	1275.91i	−0.262411	−	0.454508i	0.704471	−	0.709732i	$-0.251184\pi$
$199$	−736.650	−	1275.91i	−0.262411	−	0.454508i	−0.966882	+	0.255224i	$0.917851\pi$
$200$			1405.34i			0.496862i
$201$		0			0
$202$	−1479.00	+	853.903i	−0.515160	+	0.297428i
$203$		−	997.333i		−	0.344823i
$204$		0			0
$205$	−994.364	+	1722.29i	−0.338778	+	0.586780i
$206$	289.824	+	167.330i	0.0980241	+	0.0565942i
$207$		0			0
$208$	−505.265	−	2246.93i	−0.168432	−	0.749021i
$209$	717.433			0.237445
$210$		0			0
$211$	368.711	−	638.626i	0.120299	−	0.208364i	−0.799587	−	0.600551i	$-0.794948\pi$
$211$	368.711	−	638.626i	0.120299	−	0.208364i	0.919886	+	0.392187i	$0.128281\pi$
$212$	515.059	+	892.109i	0.166860	+	0.289011i
$213$		0			0
$214$	4499.38	−	2597.72i	1.43725	−	0.829795i
$215$	−1144.96	+	661.042i	−0.363189	+	0.209687i
$216$		0			0
$217$	−19.5852	−	33.9226i	−0.00612687	−	0.0106121i
$218$	−1751.77	+	3034.16i	−0.544243	+	0.942656i
$219$		0			0
$220$	140.029			0.0429125
$221$	−217.141	−	67.7430i	−0.0660925	−	0.0206194i
$222$		0			0
$223$	4165.79	+	2405.12i	1.25095	+	0.722236i	0.971298	−	0.237865i	$-0.0764477\pi$
$223$	4165.79	+	2405.12i	1.25095	+	0.722236i	0.279652	+	0.960102i	$0.409781\pi$
$224$	373.824	−	647.481i	0.111505	−	0.193132i
$225$		0			0
$226$		−	2637.12i		−	0.776188i
$227$	−2948.21	+	1702.15i	−0.862025	+	0.497690i	−0.864690	−	0.502306i	$-0.832485\pi$
$227$	−2948.21	+	1702.15i	−0.862025	+	0.497690i	0.00266492	+	0.999996i	$0.499152\pi$
$228$		0			0
$229$		−	4254.11i		−	1.22760i	−0.789463	−	0.613798i	$-0.789641\pi$
$229$		−	4254.11i		−	1.22760i	0.789463	−	0.613798i	$-0.210359\pi$
$230$	−1731.89	−	2999.72i	−0.496510	−	0.859980i
$231$		0			0
$232$	1942.90	+	1121.74i	0.549819	+	0.317438i
$233$	5134.37			1.44362			0.721810	−	0.692091i	$-0.243310\pi$
$233$	5134.37			1.44362			0.721810	+	0.692091i	$0.243310\pi$
$234$		0			0
$235$	−2429.23			−0.674321
$236$	−527.564	−	304.589i	−0.145515	−	0.0840129i
$237$		0			0
$238$	66.4236	+	115.049i	0.0180908	+	0.0313341i
$239$			4079.91i			1.10422i	0.833773	+	0.552108i	$0.186176\pi$
$239$			4079.91i			1.10422i	−0.833773	+	0.552108i	$0.813824\pi$
$240$		0			0
$241$	−1183.88	+	683.516i	−0.316434	+	0.182693i	−0.649802	−	0.760103i	$-0.725148\pi$
$241$	−1183.88	+	683.516i	−0.316434	+	0.182693i	0.333368	+	0.942797i	$0.391815\pi$
$242$			3072.16i			0.816057i
$243$		0			0
$244$	251.423	−	435.477i	0.0659660	−	0.114256i
$245$	−1607.89	−	928.314i	−0.419282	−	0.242073i
$246$		0			0
$247$	911.185	−	2920.68i	0.234726	−	0.752381i
$248$	88.1128			0.0225612
$249$		0			0
$250$	1901.54	−	3293.56i	0.481055	−	0.833211i
$251$	1333.71	+	2310.06i	0.335391	+	0.580914i	0.983560	−	0.180582i	$-0.0577982\pi$
$251$	1333.71	+	2310.06i	0.335391	+	0.580914i	−0.648169	+	0.761497i	$0.724465\pi$
$252$		0			0
$253$	1585.93	−	915.637i	0.394097	−	0.227532i
$254$	4765.10	−	2751.13i	1.17712	−	0.679611i
$255$		0			0
$256$	1146.66	+	1986.07i	0.279945	+	0.484879i
$257$	−1721.75	+	2982.16i	−0.417898	+	0.723821i	−0.995728	−	0.0923362i	$-0.970567\pi$
$257$	−1721.75	+	2982.16i	−0.417898	+	0.723821i	0.577829	+	0.816158i	$0.303900\pi$
$258$		0			0
$259$	437.853			0.105046
$260$	177.846	−	570.059i	0.0424212	−	0.135975i
$261$		0			0
$262$	4473.00	+	2582.49i	1.05474	+	0.608956i
$263$	2534.59	−	4390.04i	0.594257	−	1.02928i	−0.399394	−	0.916779i	$-0.630780\pi$
$263$	2534.59	−	4390.04i	0.594257	−	1.02928i	0.993651	−	0.112504i	$-0.0358872\pi$
$264$		0			0
$265$		−	5422.74i		−	1.25704i
$266$	−1547.48	+	893.439i	−0.356700	+	0.205941i
$267$		0			0
$268$		−	868.933i		−	0.198054i
$269$	−2709.00	−	4692.12i	−0.614017	−	1.06351i	−0.990556	−	0.137108i	$-0.956219\pi$
$269$	−2709.00	−	4692.12i	−0.614017	−	1.06351i	0.376539	−	0.926401i	$-0.377114\pi$
$270$		0			0
$271$	2736.41	+	1579.87i	0.613376	+	0.354133i	0.774286	−	0.632836i	$-0.218109\pi$
$271$	2736.41	+	1579.87i	0.613376	+	0.354133i	−0.160909	+	0.986969i	$0.551443\pi$
$272$	−238.441			−0.0531529
$273$		0			0
$274$	2102.91			0.463655
$275$	551.449	+	318.379i	0.120922	+	0.0698145i
$276$		0			0
$277$	−2793.85	−	4839.08i	−0.606014	−	1.04965i	−0.991890	−	0.127097i	$-0.959434\pi$
$277$	−2793.85	−	4839.08i	−0.606014	−	1.04965i	0.385876	−	0.922551i	$-0.373899\pi$
$278$		−	3756.47i		−	0.810426i
$279$		0			0
$280$	−1855.25	+	1071.13i	−0.395973	+	0.228615i
$281$		−	3911.43i		−	0.830379i	−0.909735	−	0.415189i	$-0.863715\pi$
$281$		−	3911.43i		−	0.830379i	0.909735	−	0.415189i	$-0.136285\pi$
$282$		0			0
$283$	−4257.89	+	7374.89i	−0.894365	+	1.54909i	−0.0597773	+	0.998212i	$0.519039\pi$
$283$	−4257.89	+	7374.89i	−0.894365	+	1.54909i	−0.834588	+	0.550875i	$0.814294\pi$
$284$	−143.905	−	83.0838i	−0.0300676	−	0.0173596i
$285$		0			0
$286$	−1248.47	−	389.496i	−0.258125	−	0.0805293i
$287$	2618.74			0.538604
$288$		0			0
$289$	2444.73	−	4234.39i	0.497603	−	0.861874i
$290$	−961.350	−	1665.11i	−0.194664	−	0.337167i
$291$		0			0
$292$	−107.133	+	61.8534i	−0.0214709	+	0.0123962i
$293$	−4108.57	+	2372.09i	−0.819199	+	0.472965i	−0.850140	−	0.526556i	$-0.823483\pi$
$293$	−4108.57	+	2372.09i	−0.819199	+	0.472965i	0.0309410	+	0.999521i	$0.490150\pi$
$294$		0			0
$295$	1603.42	+	2777.20i	0.316456	+	0.548117i
$296$	−492.469	+	852.981i	−0.0967033	+	0.167495i
$297$		0			0
$298$	−6007.47			−1.16780
$299$	−1713.33	−	7619.24i	−0.331387	−	1.47369i
$300$		0			0
$301$	1507.67	+	870.455i	0.288707	+	0.166685i
$302$	1114.85	−	1930.98i	0.212426	−	0.367933i
$303$		0			0
$304$		−	3207.17i		−	0.605079i
$305$	−2292.44	+	1323.54i	−0.430376	+	0.248477i
$306$		0			0
$307$			7553.03i			1.40415i	0.712103	+	0.702075i	$0.247743\pi$
$307$			7553.03i			1.40415i	−0.712103	+	0.702075i	$0.752257\pi$
$308$	−92.1945	−	159.686i	−0.0170561	−	0.0295420i
$309$		0			0
$310$	−65.3974	−	37.7572i	−0.0119817	−	0.00691763i
$311$	1432.07			0.261111			0.130555	−	0.991441i	$-0.458324\pi$
$311$	1432.07			0.261111			0.130555	+	0.991441i	$0.458324\pi$
$312$		0			0
$313$	−6510.68			−1.17574			−0.587868	−	0.808957i	$-0.700033\pi$
$313$	−6510.68			−1.17574			−0.587868	+	0.808957i	$0.700033\pi$
$314$	6113.11	+	3529.40i	1.09867	+	0.634318i
$315$		0			0
$316$	−374.118	−	647.992i	−0.0666006	−	0.115356i
$317$			9640.66i			1.70812i	0.520177	+	0.854059i	$0.325866\pi$
$317$			9640.66i			1.70812i	−0.520177	+	0.854059i	$0.674134\pi$
$318$		0			0
$319$	880.331	−	508.259i	0.154511	−	0.0892071i
$320$		−	4660.40i		−	0.814138i
$321$		0			0
$322$	−2280.53	+	3950.00i	−0.394687	+	0.683618i
$323$	−274.323	−	158.380i	−0.0472561	−	0.0272833i
$324$		0			0
$325$	1996.50	−	1840.59i	0.340757	−	0.314147i
$326$	9900.25			1.68198
$327$		0			0
$328$	−2945.39	+	5101.57i	−0.495830	+	0.858802i
$329$	1599.39	+	2770.23i	0.268017	+	0.464218i
$330$		0			0
$331$	−1945.83	+	1123.42i	−0.323119	+	0.186553i	−0.652782	−	0.757546i	$-0.726398\pi$
$331$	−1945.83	+	1123.42i	−0.323119	+	0.186553i	0.329663	+	0.944099i	$0.393065\pi$
$332$	−1686.14	+	973.491i	−0.278731	+	0.160926i
$333$		0			0
$334$	−261.556	−	453.029i	−0.0428495	−	0.0742175i
$335$	−2287.12	+	3961.40i	−0.373011	+	0.646073i
$336$		0			0
$337$	−1589.67			−0.256958			−0.128479	−	0.991712i	$-0.541009\pi$
$337$	−1589.67			−0.256958			−0.128479	+	0.991712i	$0.541009\pi$
$338$	−3171.28	+	4587.86i	−0.510340	+	0.738304i
$339$		0			0
$340$	−53.5425	−	30.9128i	−0.00854044	−	0.00493082i
$341$	19.9620	−	34.5752i	0.00317009	−	0.00549076i
$342$		0			0
$343$			6143.62i			0.967126i
$344$	−3391.47	+	1958.06i	−0.531557	+	0.306895i
$345$		0			0
$346$			642.331i			0.0998032i
$347$	−489.870	−	848.480i	−0.0757856	−	0.131265i	0.825642	−	0.564194i	$-0.190813\pi$
$347$	−489.870	−	848.480i	−0.0757856	−	0.131265i	−0.901428	+	0.432930i	$0.857480\pi$
$348$		0			0
$349$	1708.61	+	986.466i	0.262062	+	0.151302i	0.625275	−	0.780404i	$-0.284987\pi$
$349$	1708.61	+	986.466i	0.262062	+	0.151302i	−0.363213	+	0.931706i	$0.618320\pi$
$350$	−1585.95			−0.242207
$351$		0			0
$352$	762.029			0.115387
$353$	−8691.34	−	5017.95i	−1.31046	−	0.756596i	−0.328290	−	0.944577i	$-0.606472\pi$
$353$	−8691.34	−	5017.95i	−1.31046	−	0.756596i	−0.982173	+	0.187981i	$0.939806\pi$
$354$		0			0
$355$	437.369	+	757.545i	0.0653891	+	0.113257i
$356$			2250.24i			0.335008i
$357$		0			0
$358$	−8770.15	+	5063.45i	−1.29474	+	0.747518i
$359$			2749.28i			0.404183i	0.979367	+	0.202091i	$0.0647738\pi$
$359$			2749.28i			0.404183i	−0.979367	+	0.202091i	$0.935226\pi$
$360$		0			0
$361$	−1299.19	+	2250.25i	−0.189413	+	0.328073i
$362$	7458.62	+	4306.24i	1.08292	+	0.625223i
$363$		0			0
$364$	−767.174	+	172.514i	−0.110469	+	0.0248411i
$365$	651.217			0.0933870
$366$		0			0
$367$	421.169	−	729.486i	0.0599042	−	0.103757i	−0.834518	−	0.550981i	$-0.814254\pi$
$367$	421.169	−	729.486i	0.0599042	−	0.103757i	0.894422	+	0.447223i	$0.147587\pi$
$368$	−4093.21	−	7089.65i	−0.579819	−	1.00428i
$369$		0			0
$370$	731.022	−	422.056i	0.102714	−	0.0593017i
$371$	−6183.96	+	3570.31i	−0.865378	+	0.499626i
$372$		0			0
$373$	−1392.66	−	2412.16i	−0.193322	−	0.334844i	0.753027	−	0.657990i	$-0.228593\pi$
$373$	−1392.66	−	2412.16i	−0.193322	−	0.334844i	−0.946349	+	0.323146i	$0.895260\pi$
$374$	−67.7014	+	117.262i	−0.00936031	+	0.0162125i
$375$		0			0
$376$	−7195.58			−0.986925
$377$	−951.051	−	4229.35i	−0.129925	−	0.577779i
$378$		0			0
$379$	6885.18	+	3975.16i	0.933161	+	0.538761i	0.887810	−	0.460210i	$-0.152226\pi$
$379$	6885.18	+	3975.16i	0.933161	+	0.538761i	0.0453512	+	0.998971i	$0.485559\pi$
$380$	415.796	−	720.180i	0.0561313	−	0.0972222i
$381$		0			0
$382$		−	3218.76i		−	0.431116i
$383$	6253.23	−	3610.30i	0.834269	−	0.481665i	−0.0210433	−	0.999779i	$-0.506699\pi$
$383$	6253.23	−	3610.30i	0.834269	−	0.481665i	0.855312	+	0.518113i	$0.173365\pi$
$384$		0			0
$385$			970.659i			0.128492i
$386$	1694.83	+	2935.52i	0.223483	+	0.387084i
$387$		0			0
$388$	−1879.07	−	1084.88i	−0.245864	−	0.141950i
$389$	−781.125			−0.101811			−0.0509057	−	0.998703i	$-0.516211\pi$
$389$	−781.125			−0.101811			−0.0509057	+	0.998703i	$0.516211\pi$
$390$		0			0
$391$	−808.543			−0.104577
$392$	−4762.70	−	2749.75i	−0.613655	−	0.354294i
$393$		0			0
$394$	−1872.39	−	3243.07i	−0.239415	−	0.414679i
$395$			3938.86i			0.501736i
$396$		0			0
$397$	5444.80	−	3143.55i	0.688329	−	0.397407i	−0.114657	−	0.993405i	$-0.536577\pi$
$397$	5444.80	−	3143.55i	0.688329	−	0.397407i	0.802986	+	0.595998i	$0.203244\pi$
$398$			3740.07i			0.471037i
$399$		0			0
$400$	1423.27	−	2465.17i	0.177908	−	0.308146i
$401$	10334.3	+	5966.50i	1.28696	+	0.743025i	0.978110	−	0.208087i	$-0.0667238\pi$
$401$	10334.3	+	5966.50i	1.28696	+	0.743025i	0.308846	+	0.951112i	$0.400057\pi$
$402$		0			0
$403$	−115.403	−	125.178i	−0.0142646	−	0.0154729i
$404$	−1046.58			−0.128884
$405$		0			0
$406$	−1265.90	+	2192.60i	−0.154743	+	0.268022i
$407$	223.138	+	386.486i	0.0271758	+	0.0470698i
$408$		0			0
$409$	6811.26	−	3932.48i	0.823460	−	0.475425i	−0.0281484	−	0.999604i	$-0.508961\pi$
$409$	6811.26	−	3932.48i	0.823460	−	0.475425i	0.851608	+	0.524179i	$0.175628\pi$
$410$	4372.15	−	2524.26i	0.526646	−	0.304059i
$411$		0			0
$412$	102.543	+	177.609i	0.0122619	+	0.0212383i
$413$	2111.36	−	3656.99i	0.251558	−	0.435711i
$414$		0			0
$415$	10249.3			1.21233
$416$	967.825	−	3102.23i	0.114066	−	0.365623i
$417$		0			0
$418$	−1577.25	−	910.626i	−0.184559	−	0.106555i
$419$	1998.67	−	3461.79i	0.233034	−	0.403627i	−0.725665	−	0.688048i	$-0.758468\pi$
$419$	1998.67	−	3461.79i	0.233034	−	0.403627i	0.958700	+	0.284421i	$0.0918013\pi$
$420$		0			0
$421$			849.972i			0.0983969i	0.998789	+	0.0491984i	$0.0156667\pi$
$421$			849.972i			0.0983969i	−0.998789	+	0.0491984i	$0.984333\pi$
$422$	−1621.19	+	935.997i	−0.187011	+	0.107971i
$423$		0			0
$424$		−	16062.6i		−	1.83979i
$425$	−140.571	−	243.476i	−0.0160440	−	0.0277889i
$426$		0			0
$427$	3018.66	+	1742.82i	0.342115	+	0.197520i
$428$	3183.86			0.359574
$429$		0			0
$430$	3356.20			0.376396
$431$	−11576.7	−	6683.84i	−1.29381	−	0.746982i	−0.314483	−	0.949263i	$-0.601831\pi$
$431$	−11576.7	−	6683.84i	−1.29381	−	0.746982i	−0.979327	+	0.202282i	$0.935164\pi$
$432$		0			0
$433$	3297.44	+	5711.34i	0.365970	+	0.633878i	0.988931	−	0.148374i	$-0.0474040\pi$
$433$	3297.44	+	5711.34i	0.365970	+	0.633878i	−0.622961	+	0.782252i	$0.714071\pi$
$434$			99.4368i			0.0109980i
$435$		0			0
$436$	−1859.39	+	1073.52i	−0.204240	+	0.117918i
$437$		−	10875.4i		−	1.19048i
$438$		0			0
$439$	5402.52	−	9357.44i	0.587354	−	1.01733i	−0.407224	−	0.913328i	$-0.633503\pi$
$439$	5402.52	−	9357.44i	0.587354	−	1.01733i	0.994577	−	0.103998i	$-0.0331636\pi$
$440$	−1890.94	−	1091.74i	−0.204880	−	0.118287i
$441$		0			0
$442$	391.390	+	424.543i	0.0421189	+	0.0456866i
$443$	11448.1			1.22780			0.613901	−	0.789383i	$-0.289599\pi$
$443$	11448.1			1.22780			0.613901	+	0.789383i	$0.289599\pi$
$444$		0			0
$445$	5922.86	−	10258.7i	0.630945	−	1.09283i
$446$	−6105.55	−	10575.1i	−0.648220	−	1.12275i
$447$		0			0
$448$	−5314.60	+	3068.39i	−0.560472	+	0.323589i
$449$	−3103.58	+	1791.85i	−0.326207	+	0.188336i	−0.654156	−	0.756360i	$-0.726976\pi$
$449$	−3103.58	+	1791.85i	−0.326207	+	0.188336i	0.327949	+	0.944695i	$0.393643\pi$
$450$		0			0
$451$	1334.56	+	2311.52i	0.139339	+	0.241342i
$452$	808.039	−	1399.56i	0.0840862	−	0.145642i
$453$		0			0
$454$	8642.04			0.893373
$455$	3951.56	+	1232.80i	0.407147	+	0.127021i
$456$		0			0
$457$	−10718.9	−	6188.54i	−1.09717	−	0.633453i	−0.161695	−	0.986841i	$-0.551696\pi$
$457$	−10718.9	−	6188.54i	−1.09717	−	0.633453i	−0.935477	+	0.353388i	$0.885030\pi$
$458$	−5399.67	+	9352.50i	−0.550895	+	0.954179i
$459$		0			0
$460$		−	2122.67i		−	0.215152i
$461$	378.996	−	218.813i	0.0382898	−	0.0221066i	−0.480733	−	0.876867i	$-0.659629\pi$
$461$	378.996	−	218.813i	0.0382898	−	0.0221066i	0.519023	+	0.854760i	$0.326296\pi$
$462$		0			0
$463$			6568.13i			0.659281i	0.944107	+	0.329640i	$0.106927\pi$
$463$			6568.13i			0.659281i	−0.944107	+	0.329640i	$0.893073\pi$
$464$	−2272.09	−	3935.38i	−0.227326	−	0.393740i
$465$		0			0
$466$	−11287.7	−	6516.96i	−1.12209	−	0.647838i
$467$	−897.583			−0.0889404			−0.0444702	−	0.999011i	$-0.514160\pi$
$467$	−897.583			−0.0889404			−0.0444702	+	0.999011i	$0.514160\pi$
$468$		0			0
$469$	6023.31			0.593029
$470$	5340.57	+	3083.38i	0.524132	+	0.302608i
$471$		0			0
$472$	4749.45	+	8226.29i	0.463159	+	0.802216i
$473$			1774.40i			0.172488i
$474$		0			0
$475$	3274.90	−	1890.76i	0.316342	−	0.182640i
$476$			81.4113i			0.00783925i
$477$		0			0
$478$	5178.57	−	8969.54i	0.495527	−	0.858279i
$479$	−6130.14	−	3539.24i	−0.584746	−	0.337603i	0.178271	−	0.983981i	$-0.442950\pi$
$479$	−6130.14	−	3539.24i	−0.584746	−	0.337603i	−0.763017	+	0.646378i	$0.776283\pi$
$480$		0			0
$481$	1856.79	−	417.534i	0.176013	−	0.0395799i
$482$	3470.30			0.327942
$483$		0			0
$484$	−941.338	+	1630.45i	−0.0884052	+	0.153122i
$485$	5711.02	+	9891.77i	0.534689	+	0.926108i
$486$		0			0
$487$	3059.99	−	1766.69i	0.284726	−	0.164387i	−0.350835	−	0.936437i	$-0.614102\pi$
$487$	3059.99	−	1766.69i	0.284726	−	0.164387i	0.635561	+	0.772051i	$0.280769\pi$
$488$	−6790.39	+	3920.43i	−0.629891	+	0.363668i
$489$		0			0
$490$	2356.59	+	4081.73i	0.217265	+	0.376314i
$491$	−1012.76	+	1754.15i	−0.0930860	+	0.161230i	−0.908808	−	0.417214i	$-0.863006\pi$
$491$	−1012.76	+	1754.15i	−0.0930860	+	0.161230i	0.815722	+	0.578444i	$0.196340\pi$
$492$		0			0
$493$	−448.813			−0.0410010
$494$	−5710.37	+	5264.44i	−0.520084	+	0.479471i
$495$		0			0
$496$	−154.563	−	89.2369i	−0.0139921	−	0.00807834i
$497$	575.924	−	997.529i	0.0519793	−	0.0900308i
$498$		0			0
$499$		−	1397.04i		−	0.125331i	−0.998035	−	0.0626653i	$-0.980040\pi$
$499$		−	1397.04i		−	0.125331i	0.998035	−	0.0626653i	$-0.0199601\pi$
$500$	2018.35	−	1165.30i	0.180527	−	0.104227i
$501$		0			0
$502$		−	6771.43i		−	0.602040i
$503$	7942.26	+	13756.4i	0.704031	+	1.21942i	0.967040	+	0.254624i	$0.0819518\pi$
$503$	7942.26	+	13756.4i	0.704031	+	1.21942i	−0.263009	+	0.964793i	$0.584715\pi$
$504$		0			0
$505$	4771.26	+	2754.69i	0.420432	+	0.242737i
$506$	−4648.81			−0.408428
$507$		0			0
$508$	3371.89			0.294495
$509$	12758.5	+	7366.10i	1.11102	+	0.641447i	0.939093	−	0.343663i	$-0.111668\pi$
$509$	12758.5	+	7366.10i	1.11102	+	0.641447i	0.171926	+	0.985110i	$0.445001\pi$
$510$		0			0
$511$	−428.758	−	742.631i	−0.0371177	−	0.0642898i
$512$		−	12941.6i		−	1.11708i
$513$		0			0
$514$	7570.41	−	4370.78i	0.649643	−	0.375072i
$515$		−	1079.61i		−	0.0923754i
$516$		0			0
$517$	−1630.16	+	2823.52i	−0.138674	+	0.240190i
$518$	−962.604	−	555.759i	−0.0816494	−	0.0471403i
$519$		0			0
$520$	−6846.08	+	6311.46i	−0.577347	+	0.532261i
$521$	−18090.5			−1.52123			−0.760613	−	0.649205i	$-0.775102\pi$
$521$	−18090.5			−1.52123			−0.760613	+	0.649205i	$0.775102\pi$
$522$		0			0
$523$	−6753.09	+	11696.7i	−0.564612	+	0.977937i	0.432473	+	0.901647i	$0.357641\pi$
$523$	−6753.09	+	11696.7i	−0.564612	+	0.977937i	−0.997086	+	0.0762904i	$0.975692\pi$
$524$	1582.60	+	2741.14i	0.131939	+	0.228525i
$525$		0			0
$526$	−11144.4	+	6434.23i	−0.923801	+	0.533357i
$527$	−15.2656	+	8.81360i	−0.00126182	+	0.000728513i
$528$		0			0
$529$	−7796.43	−	13503.8i	−0.640785	−	1.10987i
$530$	−6883.00	+	11921.7i	−0.564110	+	0.977067i
$531$		0			0
$532$	−1095.03			−0.0892401
$533$	11105.2	−	2497.22i	0.902476	−	0.202939i
$534$		0			0
$535$	−14515.0	−	8380.23i	−1.17297	−	0.677213i
$536$	−6774.63	+	11734.0i	−0.545932	+	0.945582i
$537$		0			0
$538$			13753.9i			1.10218i
$539$	−2157.98	+	1245.91i	−0.172450	+	0.0995643i
$540$		0			0
$541$			18868.5i			1.49949i	0.661730	+	0.749743i	$0.269823\pi$
$541$			18868.5i			1.49949i	−0.661730	+	0.749743i	$0.730177\pi$
$542$	−4010.60	−	6946.56i	−0.317841	−	0.550517i
$543$		0			0
$544$	−291.375	−	168.225i	−0.0229643	−	0.0132585i
$545$	11302.4			0.888335
$546$		0			0
$547$	−13405.6			−1.04786			−0.523931	−	0.851761i	$-0.675535\pi$
$547$	−13405.6			−1.04786			−0.523931	+	0.851761i	$0.675535\pi$
$548$	1116.05	+	644.351i	0.0869987	+	0.0502287i
$549$		0			0
$550$	−808.227	−	1399.89i	−0.0626599	−	0.108530i
$551$		−	6036.81i		−	0.466746i
$552$		0			0
$553$	4491.78	−	2593.33i	0.345407	−	0.199421i
$554$			14184.7i			1.08782i
$555$		0			0
$556$	1151.02	−	1993.62i	0.0877952	−	0.152066i
$557$	−10273.9	−	5931.61i	−0.781539	−	0.451222i	0.0554367	−	0.998462i	$-0.482345\pi$
$557$	−10273.9	−	5931.61i	−0.781539	−	0.451222i	−0.836975	+	0.547241i	$0.815678\pi$
$558$		0			0
$559$	7223.59	+	2253.60i	0.546557	+	0.170513i
$560$	4339.18			0.327436
$561$		0			0
$562$	−4964.71	+	8599.14i	−0.372640	+	0.645432i
$563$	2126.00	+	3682.34i	0.159148	+	0.275652i	0.934562	−	0.355801i	$-0.115792\pi$
$563$	2126.00	+	3682.34i	0.159148	+	0.275652i	−0.775414	+	0.631454i	$0.782459\pi$
$564$		0			0
$565$	−7367.58	+	4253.67i	−0.548595	+	0.316732i
$566$	18721.6	−	10808.9i	1.39033	−	0.802710i
$567$		0			0
$568$	1295.52	+	2243.91i	0.0957025	+	0.165762i
$569$	2416.36	−	4185.26i	0.178030	−	0.308357i	−0.763176	−	0.646191i	$-0.776361\pi$
$569$	2416.36	−	4185.26i	0.178030	−	0.308357i	0.941206	+	0.337834i	$0.109694\pi$
$570$		0			0
$571$	3819.95			0.279965			0.139982	−	0.990154i	$-0.455295\pi$
$571$	3819.95			0.279965			0.139982	+	0.990154i	$0.455295\pi$
$572$	−543.241	−	589.257i	−0.0397099	−	0.0430735i
$573$		0			0
$574$	−5757.20	−	3323.92i	−0.418643	−	0.241704i
$575$	4826.24	−	8359.29i	0.350031	−	0.606272i
$576$		0			0
$577$			24973.7i			1.80185i	0.433972	+	0.900926i	$0.357112\pi$
$577$			24973.7i			1.80185i	−0.433972	+	0.900926i	$0.642888\pi$
$578$	−10749.3	+	6206.10i	−0.773548	+	0.446608i
$579$		0			0
$580$		−	1178.27i		−	0.0843533i
$581$	−6748.09	−	11688.0i	−0.481855	−	0.834598i
$582$		0			0
$583$	−6302.92	−	3638.99i	−0.447753	−	0.258511i
$584$	1928.96			0.136680
$585$		0			0
$586$	12043.4			0.848990
$587$	−1271.22	−	733.940i	−0.0893849	−	0.0516064i	0.454641	−	0.890675i	$-0.349767\pi$
$587$	−1271.22	−	733.940i	−0.0893849	−	0.0516064i	−0.544026	+	0.839068i	$0.683101\pi$
$588$		0			0
$589$	−118.548	−	205.332i	−0.00829322	−	0.0143643i
$590$		−	8140.75i		−	0.568050i
$591$		0			0
$592$	1727.73	−	997.503i	0.119948	−	0.0692519i
$593$		−	6559.32i		−	0.454231i	−0.973868	−	0.227115i	$-0.927071\pi$
$593$		−	6559.32i		−	0.454231i	0.973868	−	0.227115i	$-0.0729295\pi$
$594$		0			0
$595$	214.282	−	371.148i	0.0147642	−	0.0255724i
$596$	−3188.26	−	1840.75i	−0.219121	−	0.126510i
$597$		0			0
$598$	−5904.28	+	18925.3i	−0.403752	+	1.29417i
$599$	−27069.0			−1.84642			−0.923212	−	0.384290i	$-0.874446\pi$
$599$	−27069.0			−1.84642			−0.923212	+	0.384290i	$0.874446\pi$
$600$		0			0
$601$	−4408.82	+	7636.30i	−0.299234	+	0.518288i	−0.975961	−	0.217946i	$-0.930064\pi$
$601$	−4408.82	+	7636.30i	−0.299234	+	0.518288i	0.676727	+	0.736234i	$0.263398\pi$
$602$	−2209.71	−	3827.33i	−0.149603	−	0.259120i
$603$		0			0
$604$	1183.34	−	683.204i	0.0797178	−	0.0460251i
$605$	8582.98	−	4955.39i	0.576773	−	0.333000i
$606$		0			0
$607$	−11875.0	−	20568.1i	−0.794054	−	1.37534i	−0.923438	−	0.383748i	$-0.874633\pi$
$607$	−11875.0	−	20568.1i	−0.794054	−	1.37534i	0.129383	−	0.991595i	$-0.458700\pi$
$608$	2262.74	−	3919.17i	0.150931	−	0.261420i
$609$		0			0
$610$	6719.78			0.446026
$611$	9424.17	+	10222.4i	0.623995	+	0.676851i
$612$		0			0
$613$	−20329.2	−	11737.1i	−1.33946	−	0.773338i	−0.352733	−	0.935724i	$-0.614748\pi$
$613$	−20329.2	−	11737.1i	−1.33946	−	0.773338i	−0.986727	+	0.162386i	$0.948081\pi$
$614$	9586.93	−	16605.0i	0.630125	−	1.09141i
$615$		0			0
$616$			2875.18i			0.188059i
$617$	16580.1	−	9572.54i	1.08183	−	0.624596i	0.150442	−	0.988619i	$-0.451930\pi$
$617$	16580.1	−	9572.54i	1.08183	−	0.624596i	0.931390	+	0.364022i	$0.118597\pi$
$618$		0			0
$619$			15484.0i			1.00542i	0.864455	+	0.502710i	$0.167663\pi$
$619$			15484.0i			1.00542i	−0.864455	+	0.502710i	$0.832337\pi$
$620$	−23.1384	−	40.0768i	−0.00149880	−	0.00259600i
$621$		0			0
$622$	−3148.36	−	1817.71i	−0.202955	−	0.117176i
$623$	−15598.3			−1.00310
$624$		0			0
$625$	−5027.01			−0.321728
$626$	14313.5	+	8263.90i	0.913870	+	0.527623i
$627$		0			0
$628$	2162.89	+	3746.23i	0.137434	+	0.238043i
$629$		−	197.039i		−	0.0124904i
$630$		0			0
$631$	17590.7	−	10156.0i	1.10979	−	0.640736i	0.171014	−	0.985269i	$-0.445296\pi$
$631$	17590.7	−	10156.0i	1.10979	−	0.640736i	0.938774	+	0.344532i	$0.111962\pi$
$632$			11667.2i			0.734333i
$633$		0			0
$634$	12236.7	−	21194.6i	0.766534	−	1.32768i
$635$	−15372.2	−	8875.14i	−0.960672	−	0.554644i
$636$		0			0
$637$	2331.34	+	10367.5i	0.145009	+	0.644862i
$638$	−2580.50			−0.160130
$639$		0			0
$640$	−3644.25	+	6312.02i	−0.225081	+	0.389851i
$641$	7123.61	+	12338.5i	0.438948	+	0.760280i	0.997609	−	0.0691161i	$-0.0220179\pi$
$641$	7123.61	+	12338.5i	0.438948	+	0.760280i	−0.558661	+	0.829396i	$0.688685\pi$
$642$		0			0
$643$	−16751.2	+	9671.30i	−1.02737	+	0.593155i	−0.916231	−	0.400649i	$-0.868785\pi$
$643$	−16751.2	+	9671.30i	−1.02737	+	0.593155i	−0.111143	+	0.993804i	$0.535451\pi$
$644$	−2420.64	+	1397.56i	−0.148116	+	0.0855146i
$645$		0			0
$646$	402.059	+	696.387i	0.0244873	+	0.0424133i
$647$	11740.7	−	20335.5i	0.713407	−	1.23566i	−0.250163	−	0.968204i	$-0.580484\pi$
$647$	11740.7	−	20335.5i	0.713407	−	1.23566i	0.963571	−	0.267454i	$-0.0861824\pi$
$648$		0			0
$649$	4303.96			0.260316
$650$	−6725.46	+	1512.35i	−0.405837	+	0.0912603i
$651$		0			0
$652$	5254.23	+	3033.53i	0.315600	+	0.182212i
$653$	−12147.4	+	21039.9i	−0.727969	+	1.26088i	0.229772	+	0.973245i	$0.426202\pi$
$653$	−12147.4	+	21039.9i	−0.727969	+	1.26088i	−0.957740	+	0.287634i	$0.907131\pi$
$654$		0			0
$655$		−	16662.2i		−	0.993963i
$656$	10333.3	−	5965.94i	0.615012	−	0.355077i
$657$		0			0
$658$		−	8120.34i		−	0.481100i
$659$	13720.9	+	23765.2i	0.811060	+	1.40480i	0.912123	+	0.409918i	$0.134443\pi$
$659$	13720.9	+	23765.2i	0.811060	+	1.40480i	−0.101062	+	0.994880i	$0.532224\pi$
$660$		0			0
$661$	7954.03	+	4592.26i	0.468042	+	0.270224i	0.715420	−	0.698695i	$-0.246235\pi$
$661$	7954.03	+	4592.26i	0.468042	+	0.270224i	−0.247378	+	0.968919i	$0.579569\pi$
$662$	5703.77			0.334869
$663$		0			0
$664$	30359.3			1.77435
$665$	4992.17	+	2882.23i	0.291110	+	0.168072i
$666$		0			0
$667$	−7704.58	−	13344.7i	−0.447260	−	0.774678i
$668$		−	320.574i		−	0.0185679i
$669$		0			0
$670$	10056.3	−	5806.00i	0.579863	−	0.334784i
$671$			3552.70i			0.204397i
$672$		0			0
$673$	−984.210	+	1704.70i	−0.0563722	+	0.0976396i	−0.892834	−	0.450385i	$-0.851287\pi$
$673$	−984.210	+	1704.70i	−0.0563722	+	0.0976396i	0.836462	+	0.548025i	$0.184620\pi$
$674$	3494.83	+	2017.74i	0.199727	+	0.115312i
$675$		0			0
$676$	−3088.82	+	1463.14i	−0.175741	+	0.0832467i
$677$	−14505.5			−0.823472			−0.411736	−	0.911303i	$-0.635077\pi$
$677$	−14505.5			−0.823472			−0.411736	+	0.911303i	$0.635077\pi$
$678$		0			0
$679$	7520.22	−	13025.4i	0.425036	−	0.736184i
$680$	482.022	+	834.887i	0.0271834	+	0.0470830i
$681$		0			0
$682$	−87.7713	+	50.6748i	−0.00492806	+	0.00284522i
$683$	4463.13	−	2576.79i	0.250039	−	0.144360i	−0.369743	−	0.929134i	$-0.620554\pi$
$683$	4463.13	−	2576.79i	0.250039	−	0.144360i	0.619782	+	0.784774i	$0.287221\pi$
$684$		0			0
$685$	−3391.99	−	5875.10i	−0.189199	−	0.327702i
$686$	7797.99	−	13506.5i	0.434007	−	0.751722i
$687$		0			0
$688$	7932.17			0.439551
$689$	−22819.5	+	21037.5i	−1.26176	+	1.16323i
$690$		0			0
$691$	−27907.2	−	16112.2i	−1.53638	−	0.887029i	−0.999046	−	0.0436595i	$-0.986098\pi$
$691$	−27907.2	−	16112.2i	−1.53638	−	0.887029i	−0.537333	−	0.843370i	$-0.680568\pi$
$692$	−196.816	+	340.896i	−0.0108119	+	0.0187268i
$693$		0			0
$694$			2487.14i			0.136038i
$695$	−10494.8	+	6059.19i	−0.572793	+	0.330702i
$696$		0			0
$697$		−	1178.47i		−	0.0640425i
$698$	−2504.21	−	4337.42i	−0.135796	−	0.235206i
$699$		0			0
$700$	−841.688	−	485.949i	−0.0454469	−	0.0262388i
$701$	−25310.1			−1.36370			−0.681848	−	0.731494i	$-0.738823\pi$
$701$	−25310.1			−1.36370			−0.681848	+	0.731494i	$0.738823\pi$
$702$		0			0
$703$	2650.30			0.142188
$704$	−5416.84	−	3127.41i	−0.289993	−	0.167427i
$705$		0			0
$706$	12738.4	+	22063.5i	0.679059	+	1.17616i
$707$		−	7254.70i		−	0.385914i
$708$		0			0
$709$	18246.8	−	10534.8i	0.966533	−	0.558028i	0.0683553	−	0.997661i	$-0.478225\pi$
$709$	18246.8	−	10534.8i	0.966533	−	0.558028i	0.898177	+	0.439633i	$0.144892\pi$
$710$		−	2220.58i		−	0.117376i
$711$		0			0
$712$	17544.0	−	30387.1i	0.923441	−	1.59945i
$713$	−524.117	−	302.599i	−0.0275292	−	0.0158940i
$714$		0			0
$715$	925.615	+	4116.24i	0.0484140	+	0.215299i
$716$	−6205.95			−0.323921
$717$		0			0
$718$	3489.62	−	6044.19i	0.181381	−	0.314161i
$719$	9249.51	+	16020.6i	0.479762	+	0.830972i	0.999731	−	0.0232136i	$-0.00738979\pi$
$719$	9249.51	+	16020.6i	0.479762	+	0.830972i	−0.519969	+	0.854185i	$0.674056\pi$
$720$		0			0
$721$	−1231.16	+	710.811i	−0.0635934	+	0.0367157i
$722$	5712.42	−	3298.07i	0.294452	−	0.170002i
$723$		0			0
$724$	2638.94	+	4570.78i	0.135464	+	0.234630i
$725$	2678.99	−	4640.14i	0.137235	−	0.237697i
$726$		0			0
$727$	24659.7			1.25801			0.629007	−	0.777400i	$-0.283462\pi$
$727$	24659.7			1.25801			0.629007	+	0.777400i	$0.283462\pi$
$728$	11704.9	+	3651.65i	0.595894	+	0.185906i
$729$		0			0
$730$	−1431.68	−	826.578i	−0.0725873	−	0.0419083i
$731$	391.716	−	678.472i	0.0198196	−	0.0343286i
$732$		0			0
$733$		−	1210.80i		−	0.0610119i	−0.999535	−	0.0305060i	$-0.990288\pi$
$733$		−	1210.80i		−	0.0610119i	0.999535	−	0.0305060i	$-0.00971186\pi$
$734$	−1851.85	+	1069.17i	−0.0931240	+	0.0537652i
$735$		0			0
$736$		−	11551.4i		−	0.578521i
$737$	3069.59	+	5316.69i	0.153419	+	0.265730i
$738$		0			0
$739$	−14818.7	−	8555.60i	−0.737640	−	0.425877i	0.0835706	−	0.996502i	$-0.473368\pi$
$739$	−14818.7	−	8555.60i	−0.737640	−	0.425877i	−0.821211	+	0.570625i	$0.806701\pi$
$740$	517.288			0.0256971
$741$		0			0
$742$	18126.9			0.896848
$743$	1317.72	+	760.787i	0.0650640	+	0.0375647i	0.532179	−	0.846632i	$-0.321373\pi$
$743$	1317.72	+	760.787i	0.0650640	+	0.0375647i	−0.467115	+	0.884197i	$0.654707\pi$
$744$		0			0
$745$	9690.04	+	16783.6i	0.476531	+	0.825376i
$746$			7070.71i			0.347020i
$747$		0			0
$748$	−71.8606	+	41.4887i	−0.00351268	+	0.00202804i
$749$			22070.0i			1.07666i
$750$		0			0
$751$	12961.8	−	22450.5i	0.629803	−	1.09085i	−0.357788	−	0.933803i	$-0.616469\pi$
$751$	12961.8	−	22450.5i	0.629803	−	1.09085i	0.987591	−	0.157048i	$-0.0501978\pi$
$752$	12622.1	+	7287.38i	0.612076	+	0.353382i
$753$		0			0
$754$	−3277.40	+	10505.2i	−0.158297	+	0.507398i
$755$	−7193.03			−0.346730
$756$		0			0
$757$	−12747.7	+	22079.7i	−0.612051	+	1.06010i	0.378843	+	0.925461i	$0.376322\pi$
$757$	−12747.7	+	22079.7i	−0.612051	+	1.06010i	−0.990894	+	0.134643i	$0.957011\pi$
$758$	−10091.2	−	17478.5i	−0.483548	−	0.837530i
$759$		0			0
$760$	−11229.8	+	6483.50i	−0.535982	+	0.309449i
$761$	−15307.7	+	8837.90i	−0.729177	+	0.420990i	−0.818121	−	0.575046i	$-0.804984\pi$
$761$	−15307.7	+	8837.90i	−0.729177	+	0.420990i	0.0889442	+	0.996037i	$0.471651\pi$
$762$		0			0
$763$	−7441.47	−	12889.0i	−0.353079	−	0.611551i
$764$	986.260	−	1708.25i	0.0467037	−	0.0808932i
$765$		0			0
$766$	−18330.0			−0.864607
$767$	5466.30	−	17521.4i	0.257336	−	0.824853i
$768$		0			0
$769$	−24989.0	−	14427.4i	−1.17181	−	0.676547i	−0.217707	−	0.976014i	$-0.569858\pi$
$769$	−24989.0	−	14427.4i	−1.17181	−	0.676547i	−0.954107	+	0.299467i	$0.903191\pi$
$770$	1232.04	−	2133.96i	0.0576619	−	0.0998734i
$771$		0			0
$772$			2077.24i			0.0968415i
$773$	30740.8	−	17748.2i	1.43036	−	0.825820i	0.433215	−	0.901291i	$-0.357379\pi$
$773$	30740.8	−	17748.2i	1.43036	−	0.825820i	0.997148	+	0.0754704i	$0.0240458\pi$
$774$		0			0
$775$		−	210.436i		−	0.00975364i
$776$	16916.5	+	29300.3i	0.782561	+	1.35544i
$777$		0			0
$778$	1717.27	+	991.469i	0.0791353	+	0.0456888i
$779$	15851.1			0.729044
$780$		0			0
$781$	1174.01			0.0537890
$782$	1777.55	+	1026.27i	0.0812853	+	0.0469301i
$783$		0			0
$784$	5569.65	+	9646.92i	0.253719	+	0.439455i
$785$		−	22771.7i		−	1.03536i
$786$		0			0
$787$	−11474.0	+	6624.49i	−0.519698	+	0.300048i	−0.736811	−	0.676099i	$-0.763669\pi$
$787$	−11474.0	+	6624.49i	−0.519698	+	0.300048i	0.217113	+	0.976146i	$0.430336\pi$
$788$		−	2294.87i		−	0.103745i
$789$		0			0
$790$	4999.53	−	8659.44i	0.225159	−	0.389986i
$791$	9701.56	+	5601.20i	0.436091	+	0.251777i
$792$		0			0
$793$	14463.1	+	4512.15i	0.647665	+	0.202057i
$794$	−15960.2			−0.713360
$795$		0			0
$796$	−1145.99	+	1984.92i	−0.0510284	+	0.0883838i
$797$	−16115.9	−	27913.6i	−0.716254	−	1.24059i	−0.962474	−	0.271374i	$-0.912522\pi$
$797$	−16115.9	−	27913.6i	−0.716254	−	1.24059i	0.246220	−	0.969214i	$-0.420811\pi$
$798$		0			0
$799$	1246.64	−	719.748i	0.0551977	−	0.0318684i
$800$	3478.47	−	2008.29i	0.153728	−	0.0887549i
$801$		0			0
$802$	−15146.4	−	26234.3i	−0.666879	−	1.15507i
$803$	437.006	−	756.917i	0.0192050	−	0.0332640i
$804$		0			0
$805$	14714.0			0.644224
$806$	94.8223	+	421.678i	0.00414389	+	0.0184280i
$807$		0			0
$808$	14132.9	+	8159.62i	0.615338	+	0.355265i
$809$	6318.82	−	10944.5i	0.274608	−	0.475635i	−0.695428	−	0.718596i	$-0.744785\pi$
$809$	6318.82	−	10944.5i	0.274608	−	0.475635i	0.970036	+	0.242961i	$0.0781186\pi$
$810$		0			0
$811$			41102.4i			1.77966i	0.456296	+	0.889828i	$0.349176\pi$
$811$			41102.4i			1.77966i	−0.456296	+	0.889828i	$0.650824\pi$
$812$	−1343.67	+	775.767i	−0.0580708	+	0.0335272i
$813$		0			0
$814$		−	1132.90i		−	0.0487815i
$815$	−15969.1	−	27659.3i	−0.686347	−	1.18879i
$816$		0			0
$817$	9125.87	+	5268.82i	0.390788	+	0.225621i
$818$	−19965.7			−0.853405
$819$		0			0
$820$	3093.83			0.131758
$821$	−11319.9	−	6535.54i	−0.481202	−	0.277822i	0.239715	−	0.970843i	$-0.422946\pi$
$821$	−11319.9	−	6535.54i	−0.481202	−	0.277822i	−0.720917	+	0.693021i	$0.756279\pi$
$822$		0			0
$823$	−14658.1	−	25388.5i	−0.620836	−	1.07532i	−0.989330	−	0.145689i	$-0.953460\pi$
$823$	−14658.1	−	25388.5i	−0.620836	−	1.07532i	0.368495	−	0.929630i	$-0.379873\pi$
$824$		−	3197.90i		−	0.135199i
$825$		0			0
$826$	−9283.51	+	5359.84i	−0.391059	+	0.225778i
$827$			4300.87i			0.180842i	0.995904	+	0.0904208i	$0.0288212\pi$
$827$			4300.87i			0.180842i	−0.995904	+	0.0904208i	$0.971179\pi$
$828$		0			0
$829$	−7795.26	+	13501.8i	−0.326587	+	0.565665i	−0.981832	−	0.189751i	$-0.939232\pi$
$829$	−7795.26	+	13501.8i	−0.326587	+	0.565665i	0.655245	+	0.755416i	$0.272565\pi$
$830$	−22532.7	−	13009.3i	−0.942314	−	0.544046i
$831$		0			0
$832$	−19611.4	+	18080.0i	−0.817193	+	0.753378i
$833$	1100.19			0.0457614
$834$		0			0
$835$	−843.780	+	1461.47i	−0.0349703	+	0.0605704i
$836$	−558.049	−	966.569i	−0.0230868	−	0.0399874i
$837$		0			0
$838$	−8787.99	+	5073.75i	−0.362263	+	0.209152i
$839$	16417.6	−	9478.69i	0.675563	−	0.390037i	−0.122618	−	0.992454i	$-0.539129\pi$
$839$	16417.6	−	9478.69i	0.675563	−	0.390037i	0.798181	+	0.602417i	$0.205796\pi$
$840$		0			0
$841$	7917.78	+	13714.0i	0.324645	+	0.562302i
$842$	1078.85	−	1868.63i	0.0441565	−	0.0764813i
$843$		0			0
$844$	−1147.19			−0.0467868
$845$	17932.8	+	1459.70i	0.730068	+	0.0594262i
$846$		0			0
$847$	−11302.0	−	6525.21i	−0.458490	−	0.264709i
$848$	−16267.5	+	28176.2i	−0.658762	+	1.14101i
$849$		0			0
$850$			713.696i			0.0287995i
$851$	5858.66	−	3382.50i	0.235995	−	0.136252i
$852$		0			0
$853$			36949.2i			1.48314i	0.670878	+	0.741568i	$0.265918\pi$
$853$			36949.2i			1.48314i	−0.670878	+	0.741568i	$0.734082\pi$
$854$	−4424.28	−	7663.07i	−0.177278	−	0.307055i
$855$		0			0
$856$	−42994.6	−	24822.9i	−1.71674	−	0.991157i
$857$	26643.0			1.06197			0.530985	−	0.847381i	$-0.321822\pi$
$857$	26643.0			1.06197			0.530985	+	0.847381i	$0.321822\pi$
$858$		0			0
$859$	−39165.5			−1.55566			−0.777829	−	0.628477i	$-0.783679\pi$
$859$	−39165.5			−1.55566			−0.777829	+	0.628477i	$0.783679\pi$
$860$	1781.19	+	1028.37i	0.0706257	+	0.0407758i
$861$		0			0
$862$	16967.4	+	29388.3i	0.670430	+	1.16122i
$863$		−	2483.04i		−	0.0979418i	−0.998800	−	0.0489709i	$-0.984406\pi$
$863$		−	2483.04i		−	0.0979418i	0.998800	−	0.0489709i	$-0.0155942\pi$
$864$		0			0
$865$	1794.54	−	1036.08i	0.0705390	−	0.0407257i
$866$		−	16741.5i		−	0.656929i
$867$		0			0
$868$	−30.4684	+	52.7728i	−0.00119143	+	0.00206362i
$869$	4578.19	+	2643.22i	0.178716	+	0.103182i
$870$		0			0
$871$	25542.8	−	5743.79i	0.993669	−	0.223446i
$872$	33478.8			1.30015
$873$		0			0
$874$	−13804.0	+	23909.2i	−0.534241	+	0.925332i
$875$	8077.66	+	13990.9i	0.312085	+	0.540548i
$876$		0			0
$877$	2763.63	−	1595.58i	0.106409	−	0.0614355i	−0.445851	−	0.895107i	$-0.647099\pi$
$877$	2763.63	−	1595.58i	0.106409	−	0.0614355i	0.552260	+	0.833672i	$0.313765\pi$
$878$	−23754.5	+	13714.7i	−0.913070	+	0.527161i
$879$		0			0
$880$	2211.33	+	3830.13i	0.0847089	+	0.146720i
$881$	−12157.1	+	21056.8i	−0.464908	+	0.805245i	−0.999197	−	0.0400570i	$-0.987246\pi$
$881$	−12157.1	+	21056.8i	−0.464908	+	0.805245i	0.534289	+	0.845302i	$0.320579\pi$
$882$		0			0
$883$	−7703.20			−0.293583			−0.146791	−	0.989167i	$-0.546895\pi$
$883$	−7703.20			−0.293583			−0.146791	+	0.989167i	$0.546895\pi$
$884$	77.6334	+	345.238i	0.00295372	+	0.0131353i
$885$		0			0
$886$	−25168.3	−	14530.9i	−0.954339	−	0.550988i
$887$	−17193.0	+	29779.2i	−0.650829	+	1.12727i	0.332093	+	0.943247i	$0.392245\pi$
$887$	−17193.0	+	29779.2i	−0.650829	+	1.12727i	−0.982922	+	0.184023i	$0.941088\pi$
$888$		0			0
$889$			23373.4i			0.881799i
$890$	−26042.4	+	15035.6i	−0.980834	+	0.566285i
$891$		0			0
$892$		−	7483.20i		−	0.280892i
$893$	9681.06	+	16768.1i	0.362782	+	0.628357i
$894$		0			0
$895$	28292.5	+	16334.7i	1.05666	+	0.610065i
$896$	9597.43			0.357843
$897$		0			0
$898$	9097.47			0.338070
$899$	−290.931	−	167.969i	−0.0107932	−	0.00623146i
$900$		0			0
$901$	1606.69	+	2782.86i	0.0594078	+	0.102897i
$902$		−	6775.73i		−	0.250119i
$903$		0			0
$904$	−21823.4	+	12599.7i	−0.802915	+	0.463563i
$905$		−	27783.8i		−	1.02051i
$906$		0			0
$907$	544.120	−	942.443i	0.0199197	−	0.0345020i	−0.855894	−	0.517152i	$-0.826992\pi$
$907$	544.120	−	942.443i	0.0199197	−	0.0345020i	0.875813	+	0.482650i	$0.160326\pi$
$908$	4586.48	+	2648.00i	0.167630	+	0.0967810i
$909$		0			0
$910$	−7122.59	−	7725.91i	−0.259463	−	0.281441i
$911$	38964.1			1.41705			0.708527	−	0.705683i	$-0.249360\pi$
$911$	38964.1			1.41705			0.708527	+	0.705683i	$0.249360\pi$
$912$		0			0
$913$	6877.90	−	11912.9i	0.249316	−	0.431828i
$914$	15710.0	+	27210.6i	0.568536	+	0.984732i
$915$		0			0
$916$	−5731.39	+	3309.02i	−0.206736	+	0.119359i
$917$	−19001.2	+	10970.3i	−0.684267	+	0.395062i
$918$		0			0
$919$	−11652.0	−	20181.9i	−0.418242	−	0.724416i	0.577521	−	0.816376i	$-0.304020\pi$
$919$	−11652.0	−	20181.9i	−0.418242	−	0.724416i	−0.995763	+	0.0919599i	$0.970687\pi$
$920$	−16549.4	+	28664.3i	−0.593061	+	1.02721i
$921$		0			0
$922$	−1110.94			−0.0396822
$923$	1491.06	−	4779.38i	0.0531732	−	0.170439i
$924$		0			0
$925$	2037.13	+	1176.14i	0.0724114	+	0.0418067i
$926$	8336.82	−	14439.8i	0.295858	−	0.512442i
$927$		0			0
$928$		−	6412.06i		−	0.226817i
$929$	−29579.2	+	17077.6i	−1.04463	+	0.603118i	−0.921141	−	0.389228i	$-0.872742\pi$
$929$	−29579.2	+	17077.6i	−1.04463	+	0.603118i	−0.123489	+	0.992346i	$0.539408\pi$
$930$		0			0
$931$			14798.2i			0.520936i
$932$	−3993.72	−	6917.33i	−0.140363	−	0.243116i
$933$		0			0
$934$	1973.30	+	1139.29i	0.0691311	+	0.0399128i
$935$	436.809			0.0152783
$936$		0			0
$937$	−5453.10			−0.190123			−0.0950614	−	0.995471i	$-0.530305\pi$
$937$	−5453.10			−0.190123			−0.0950614	+	0.995471i	$0.530305\pi$
$938$	−13242.0	−	7645.29i	−0.460946	−	0.266127i
$939$		0			0
$940$	1889.55	+	3272.80i	0.0655643	+	0.113561i
$941$			32998.0i			1.14315i	0.820550	+	0.571574i	$0.193667\pi$
$941$			32998.0i			1.14315i	−0.820550	+	0.571574i	$0.806333\pi$
$942$		0			0
$943$	35039.8	−	20230.3i	1.21003	−	0.698609i
$944$		−	19240.2i		−	0.663363i
$945$		0			0
$946$	2252.21	−	3900.95i	0.0774057	−	0.134071i
$947$	−6572.50	−	3794.64i	−0.225531	−	0.130210i	0.382978	−	0.923758i	$-0.374899\pi$
$947$	−6572.50	−	3794.64i	−0.225531	−	0.130210i	−0.608509	+	0.793547i	$0.708232\pi$
$948$		0			0
$949$	−2526.39	−	2740.39i	−0.0864173	−	0.0937373i
$950$	−9599.66			−0.327846
$951$		0			0
$952$	634.723	−	1099.37i	0.0216087	−	0.0374274i
$953$	−9919.60	−	17181.3i	−0.337175	−	0.584004i	0.646725	−	0.762723i	$-0.276138\pi$
$953$	−9919.60	−	17181.3i	−0.337175	−	0.584004i	−0.983900	+	0.178719i	$0.942805\pi$
$954$		0			0
$955$	−8992.57	+	5191.86i	−0.304704	+	0.175921i
$956$	5496.70	−	3173.52i	0.185958	−	0.107363i
$957$		0			0
$958$	8984.60	+	15561.8i	0.303005	+	0.524821i
$959$	−4466.54	+	7736.28i	−0.150399	+	0.260498i
$960$		0			0
$961$	29777.8			0.999557
$962$	−4612.05	−	1438.86i	−0.154572	−	0.0482230i
$963$		0			0
$964$	1841.75	+	1063.33i	0.0615339	+	0.0355266i
$965$	5467.51	−	9470.00i	0.182389	−	0.315907i
$966$		0			0
$967$		−	33260.8i		−	1.10610i	−0.833149	−	0.553049i	$-0.813464\pi$
$967$		−	33260.8i		−	1.10610i	0.833149	−	0.553049i	$-0.186536\pi$
$968$	25423.5	−	14678.3i	0.844156	−	0.487374i
$969$		0			0
$970$		−	28995.6i		−	0.959786i
$971$	−3321.58	−	5753.14i	−0.109778	−	0.190141i	0.805902	−	0.592049i	$-0.201681\pi$
$971$	−3321.58	−	5753.14i	−0.109778	−	0.190141i	−0.915680	+	0.401908i	$0.868347\pi$
$972$		0			0
$973$	13819.5	+	7978.69i	0.455327	+	0.262883i
$974$	−8969.71			−0.295080
$975$		0			0
$976$	15881.8			0.520865
$977$	9199.22	+	5311.17i	0.301237	+	0.173920i	0.642999	−	0.765867i	$-0.277690\pi$
$977$	9199.22	+	5311.17i	0.301237	+	0.173920i	−0.341761	+	0.939787i	$0.611023\pi$
$978$		0			0
$979$	−7949.20	−	13768.4i	−0.259507	−	0.449480i
$980$			2888.32i			0.0941470i
$981$		0			0
$982$	4453.03	−	2570.96i	0.144707	−	0.0835464i
$983$			9298.71i			0.301712i	0.988556	+	0.150856i	$0.0482030\pi$
$983$			9298.71i			0.301712i	−0.988556	+	0.150856i	$0.951797\pi$
$984$		0			0
$985$	−6040.31	+	10462.1i	−0.195391	+	0.338428i
$986$	986.698	+	569.670i	0.0318690	+	0.0183996i
$987$		0			0
$988$	−4643.67	+	1044.22i	−0.149529	+	0.0336245i
$989$	26897.7			0.864810
$990$		0			0
$991$	21758.7	−	37687.2i	0.697465	−	1.20805i	−0.271877	−	0.962332i	$-0.587644\pi$
$991$	21758.7	−	37687.2i	0.697465	−	1.20805i	0.969343	−	0.245713i	$-0.0790222\pi$
$992$	−125.917	−	218.095i	−0.00403012	−	0.00698038i
$993$		0			0
$994$	−2532.29	+	1462.02i	−0.0808043	+	0.0466524i
$995$	10449.0	−	6032.73i	0.332920	−	0.192211i
$996$		0			0
$997$	6049.49	+	10478.0i	0.192166	+	0.332841i	0.945968	−	0.324261i	$-0.105116\pi$
$997$	6049.49	+	10478.0i	0.192166	+	0.332841i	−0.753802	+	0.657102i	$0.771782\pi$
$998$	−1773.23	+	3071.33i	−0.0562433	+	0.0974162i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.f.82.2	yes	12
3.2	odd	2	inner	117.4.q.f.82.5	yes	12
13.6	odd	12		1521.4.a.bl.1.9		12
13.7	odd	12		1521.4.a.bl.1.4		12
13.10	even	6	inner	117.4.q.f.10.2	✓	12
39.20	even	12		1521.4.a.bl.1.10		12
39.23	odd	6	inner	117.4.q.f.10.5	yes	12
39.32	even	12		1521.4.a.bl.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.q.f.10.2	✓	12	13.10	even	6	inner
117.4.q.f.10.5	yes	12	39.23	odd	6	inner
117.4.q.f.82.2	yes	12	1.1	even	1	trivial
117.4.q.f.82.5	yes	12	3.2	odd	2	inner
1521.4.a.bl.1.3		12	39.32	even	12
1521.4.a.bl.1.4		12	13.7	odd	12
1521.4.a.bl.1.9		12	13.6	odd	12
1521.4.a.bl.1.10		12	39.20	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19846 - 1.26928i) q^{2} +(-0.777841 - 1.34726i) q^{4} +8.18941i q^{5} +(9.33900 - 5.39187i) q^{7} +24.2577i q^{8} +O(q^{10})\)	\(q+(-2.19846 - 1.26928i) q^{2} +(-0.777841 - 1.34726i) q^{4} +8.18941i q^{5} +(9.33900 - 5.39187i) q^{7} +24.2577i q^{8} +(10.3947 - 18.0041i) q^{10} +(9.51865 + 5.49559i) q^{11} +(34.4619 - 31.7707i) q^{13} -27.3753 q^{14} +(24.5672 - 42.5516i) q^{16} +(-2.42641 - 4.20267i) q^{17} +(56.5285 - 32.6367i) q^{19} +(11.0333 - 6.37006i) q^{20} +(-13.9509 - 24.1637i) q^{22} +(83.3064 - 144.291i) q^{23} +57.9336 q^{25} +(-116.089 + 26.1049i) q^{26} +(-14.5285 - 8.38804i) q^{28} +(46.2424 - 80.0942i) q^{29} -3.63236i q^{31} +(60.0423 - 34.6655i) q^{32} +12.3192i q^{34} +(44.1563 + 76.4809i) q^{35} +(35.1633 + 20.3015i) q^{37} -165.701 q^{38} -198.656 q^{40} +(210.307 + 121.421i) q^{41} +(80.7192 + 139.810i) q^{43} -17.0988i q^{44} +(-366.292 + 211.479i) q^{46} +296.631i q^{47} +(-113.355 + 196.337i) q^{49} +(-127.365 - 73.5341i) q^{50} +(-69.6093 - 21.7165i) q^{52} -662.165 q^{53} +(-45.0057 + 77.9521i) q^{55} +(130.795 + 226.543i) q^{56} +(-203.325 + 117.389i) q^{58} +(339.120 - 195.791i) q^{59} +(161.616 + 279.927i) q^{61} +(-4.61049 + 7.98561i) q^{62} -569.076 q^{64} +(260.183 + 282.222i) q^{65} +(483.723 + 279.277i) q^{67} +(-3.77472 + 6.53802i) q^{68} -224.187i q^{70} +(92.5031 - 53.4067i) q^{71} -79.5194i q^{73} +(-51.5368 - 89.2643i) q^{74} +(-87.9404 - 50.7724i) q^{76} +118.526 q^{77} +480.970 q^{79} +(348.473 + 201.191i) q^{80} +(-308.235 - 533.878i) q^{82} -1251.53i q^{83} +(34.4174 - 19.8709i) q^{85} -409.822i q^{86} +(-133.311 + 230.901i) q^{88} +(-1252.68 - 723.234i) q^{89} +(150.536 - 482.521i) q^{91} -259.197 q^{92} +(376.508 - 652.131i) q^{94} +(267.276 + 462.935i) q^{95} +(1207.87 - 697.366i) q^{97} +(498.415 - 287.760i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{4} - 18 q^{7}+O(q^{10}) \) 12 * q + 16 * q^4 - 18 * q^7	\( 12 q + 16 q^{4} - 18 q^{7} - 56 q^{10} - 154 q^{13} - 92 q^{16} - 48 q^{19} + 292 q^{22} - 92 q^{25} + 552 q^{28} - 360 q^{37} - 448 q^{40} - 810 q^{43} + 996 q^{46} - 1068 q^{49} - 700 q^{52} + 460 q^{55} + 3048 q^{58} + 1294 q^{61} - 184 q^{64} + 2658 q^{67} + 1188 q^{76} - 6380 q^{79} - 1268 q^{82} - 3768 q^{85} - 5140 q^{88} + 342 q^{91} + 1660 q^{94} + 1686 q^{97}+O(q^{100}) \) 12 * q + 16 * q^4 - 18 * q^7 - 56 * q^10 - 154 * q^13 - 92 * q^16 - 48 * q^19 + 292 * q^22 - 92 * q^25 + 552 * q^28 - 360 * q^37 - 448 * q^40 - 810 * q^43 + 996 * q^46 - 1068 * q^49 - 700 * q^52 + 460 * q^55 + 3048 * q^58 + 1294 * q^61 - 184 * q^64 + 2658 * q^67 + 1188 * q^76 - 6380 * q^79 - 1268 * q^82 - 3768 * q^85 - 5140 * q^88 + 342 * q^91 + 1660 * q^94 + 1686 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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