LMFDB - Embedded newform 117.4.q.d.82.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 17x^{2} + 289 $ x^4 - 17*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			82.1
Root			$-3.57071 - 2.06155i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.4.q.d.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.57071 - 2.06155i) q^{2} +(4.50000 + 7.79423i) q^{4} -3.05006i q^{5} +(-5.78786 + 3.34162i) q^{7} -4.12311i q^{8} +O(q^{10})$	\(q+(-3.57071 - 2.06155i) q^{2} +(4.50000 + 7.79423i) q^{4} -3.05006i q^{5} +(-5.78786 + 3.34162i) q^{7} -4.12311i q^{8} +(-6.28786 + 10.8909i) q^{10} +(27.9293 + 16.1250i) q^{11} +(-22.1364 + 41.3156i) q^{13} +27.5557 q^{14} +(27.5000 - 47.6314i) q^{16} +(14.4293 + 24.9923i) q^{17} +(87.6364 - 50.5969i) q^{19} +(23.7729 - 13.7253i) q^{20} +(-66.4850 - 115.155i) q^{22} +(59.4950 - 103.048i) q^{23} +115.697 q^{25} +(164.217 - 101.891i) q^{26} +(-52.0907 - 30.0746i) q^{28} +(80.0557 - 138.661i) q^{29} +38.0705i q^{31} +(-224.955 + 129.878i) q^{32} -118.987i q^{34} +(10.1921 + 17.6533i) q^{35} +(283.682 + 163.784i) q^{37} -417.233 q^{38} -12.5757 q^{40} +(-48.5707 - 28.0423i) q^{41} +(63.9393 + 110.746i) q^{43} +290.250i q^{44} +(-424.879 + 245.304i) q^{46} +517.983i q^{47} +(-149.167 + 258.365i) q^{49} +(-413.121 - 238.516i) q^{50} +(-421.637 + 13.3838i) q^{52} +695.546 q^{53} +(49.1821 - 85.1860i) q^{55} +(13.7779 + 23.8639i) q^{56} +(-571.712 + 330.078i) q^{58} +(-568.566 + 328.262i) q^{59} +(-350.652 - 607.347i) q^{61} +(78.4843 - 135.939i) q^{62} +631.000 q^{64} +(126.015 + 67.5174i) q^{65} +(-49.5150 - 28.5875i) q^{67} +(-129.864 + 224.930i) q^{68} -84.0465i q^{70} +(267.798 - 154.613i) q^{71} -389.711i q^{73} +(-675.299 - 1169.65i) q^{74} +(788.728 + 455.372i) q^{76} -215.534 q^{77} +901.820 q^{79} +(-145.279 - 83.8766i) q^{80} +(115.621 + 200.262i) q^{82} +687.095i q^{83} +(76.2279 - 44.0102i) q^{85} -527.257i q^{86} +(66.4850 - 115.155i) q^{88} +(927.113 + 535.269i) q^{89} +(-9.93858 - 313.100i) q^{91} +1070.91 q^{92} +(1067.85 - 1849.57i) q^{94} +(-154.324 - 267.296i) q^{95} +(-1519.43 + 877.242i) q^{97} +(1065.27 - 615.032i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{4} - 66 q^{7}+O(q^{10}) $ 4 * q + 18 * q^4 - 66 * q^7	$ 4 q + 18 q^{4} - 66 q^{7} - 68 q^{10} + 126 q^{11} + 40 q^{13} - 204 q^{14} + 110 q^{16} + 72 q^{17} + 222 q^{19} - 162 q^{20} + 34 q^{22} + 138 q^{23} + 120 q^{25} + 714 q^{26} - 594 q^{28} + 6 q^{29} - 402 q^{35} + 492 q^{37} - 612 q^{38} - 136 q^{40} - 180 q^{41} + 470 q^{43} - 714 q^{46} + 346 q^{49} - 1224 q^{50} - 144 q^{52} + 2268 q^{53} - 446 q^{55} - 102 q^{56} - 2244 q^{58} - 2160 q^{59} - 160 q^{61} + 1428 q^{62} + 2524 q^{64} + 804 q^{65} - 498 q^{67} - 648 q^{68} + 1314 q^{71} - 1530 q^{74} + 1998 q^{76} - 2976 q^{77} + 8 q^{79} + 990 q^{80} + 34 q^{82} - 852 q^{85} - 34 q^{88} + 252 q^{89} - 1668 q^{91} + 2484 q^{92} + 2686 q^{94} + 54 q^{95} - 336 q^{97} + 6732 q^{98}+O(q^{100}) $ 4 * q + 18 * q^4 - 66 * q^7 - 68 * q^10 + 126 * q^11 + 40 * q^13 - 204 * q^14 + 110 * q^16 + 72 * q^17 + 222 * q^19 - 162 * q^20 + 34 * q^22 + 138 * q^23 + 120 * q^25 + 714 * q^26 - 594 * q^28 + 6 * q^29 - 402 * q^35 + 492 * q^37 - 612 * q^38 - 136 * q^40 - 180 * q^41 + 470 * q^43 - 714 * q^46 + 346 * q^49 - 1224 * q^50 - 144 * q^52 + 2268 * q^53 - 446 * q^55 - 102 * q^56 - 2244 * q^58 - 2160 * q^59 - 160 * q^61 + 1428 * q^62 + 2524 * q^64 + 804 * q^65 - 498 * q^67 - 648 * q^68 + 1314 * q^71 - 1530 * q^74 + 1998 * q^76 - 2976 * q^77 + 8 * q^79 + 990 * q^80 + 34 * q^82 - 852 * q^85 - 34 * q^88 + 252 * q^89 - 1668 * q^91 + 2484 * q^92 + 2686 * q^94 + 54 * q^95 - 336 * q^97 + 6732 * q^98

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 $

$2$	−3.57071	−	2.06155i	−1.26244	−	0.728869i	−0.288892	−	0.957362i	$-0.593287\pi$
$2$	−3.57071	−	2.06155i	−1.26244	−	0.728869i	−0.973546	+	0.228493i	$0.926620\pi$
$3$		0			0
$3$		0			0
$4$	4.50000	+	7.79423i	0.562500	+	0.974279i
$5$		−	3.05006i		−	0.272806i	−0.990653	−	0.136403i	$-0.956446\pi$
$5$		−	3.05006i		−	0.272806i	0.990653	−	0.136403i	$-0.0435541\pi$
$6$		0			0
$7$	−5.78786	+	3.34162i	−0.312515	+	0.180431i	−0.648051	−	0.761597i	$-0.724416\pi$
$7$	−5.78786	+	3.34162i	−0.312515	+	0.180431i	0.335536	+	0.942027i	$0.391082\pi$
$8$		−	4.12311i		−	0.182217i
$9$		0			0
$10$	−6.28786	+	10.8909i	−0.198840	+	0.344400i
$11$	27.9293	+	16.1250i	0.765545	+	0.441988i	0.831283	−	0.555849i	$-0.187607\pi$
$11$	27.9293	+	16.1250i	0.765545	+	0.441988i	−0.0657380	+	0.997837i	$0.520940\pi$
$12$		0			0
$13$	−22.1364	+	41.3156i	−0.472272	+	0.881453i
$13$	−22.1364	+	41.3156i	−0.472272	+	0.881453i
$14$	27.5557			0.526041
$15$		0			0
$16$	27.5000	−	47.6314i	0.429688	−	0.744241i
$17$	14.4293	+	24.9923i	0.205860	+	0.356560i	0.950406	−	0.311011i	$-0.100668\pi$
$17$	14.4293	+	24.9923i	0.205860	+	0.356560i	−0.744547	+	0.667571i	$0.767334\pi$
$18$		0			0
$19$	87.6364	−	50.5969i	1.05817	−	0.610933i	0.133242	−	0.991083i	$-0.457461\pi$
$19$	87.6364	−	50.5969i	1.05817	−	0.610933i	0.924925	+	0.380150i	$0.124128\pi$
$20$	23.7729	−	13.7253i	0.265789	−	0.153453i
$21$		0			0
$22$	−66.4850	−	115.155i	−0.644302	−	1.11596i
$23$	59.4950	−	103.048i	0.539372	−	0.934220i	−0.459566	−	0.888144i	$-0.651995\pi$
$23$	59.4950	−	103.048i	0.539372	−	0.934220i	0.998938	−	0.0460765i	$-0.0146718\pi$
$24$		0			0
$25$	115.697			0.925577
$26$	164.217	−	101.891i	1.23868	−	0.768555i
$27$		0			0
$28$	−52.0907	−	30.0746i	−0.351579	−	0.202984i
$29$	80.0557	−	138.661i	0.512620	−	0.887883i	−0.487273	−	0.873250i	$-0.662008\pi$
$29$	80.0557	−	138.661i	0.512620	−	0.887883i	0.999893	−	0.0146339i	$-0.00465827\pi$
$30$		0			0
$31$			38.0705i			0.220570i	0.993900	+	0.110285i	$0.0351763\pi$
$31$			38.0705i			0.220570i	−0.993900	+	0.110285i	$0.964824\pi$
$32$	−224.955	+	129.878i	−1.24271	+	0.717480i
$33$		0			0
$34$		−	118.987i		−	0.600179i
$35$	10.1921	+	17.6533i	0.0492225	+	0.0852558i
$36$		0			0
$37$	283.682	+	163.784i	1.26046	+	0.727727i	0.973164	−	0.230114i	$-0.0739099\pi$
$37$	283.682	+	163.784i	1.26046	+	0.727727i	0.287297	+	0.957841i	$0.407243\pi$
$38$	−417.233			−1.78116
$39$		0			0
$40$	−12.5757			−0.0497099
$41$	−48.5707	−	28.0423i	−0.185011	−	0.106816i	0.404634	−	0.914479i	$-0.367399\pi$
$41$	−48.5707	−	28.0423i	−0.185011	−	0.106816i	−0.589645	+	0.807662i	$0.700732\pi$
$42$		0			0
$43$	63.9393	+	110.746i	0.226759	+	0.392759i	0.956846	−	0.290596i	$-0.0938536\pi$
$43$	63.9393	+	110.746i	0.226759	+	0.392759i	−0.730087	+	0.683355i	$0.760520\pi$
$44$			290.250i			0.994472i
$45$		0			0
$46$	−424.879	+	245.304i	−1.36185	+	0.786264i
$47$			517.983i			1.60757i	0.594923	+	0.803783i	$0.297183\pi$
$47$			517.983i			1.60757i	−0.594923	+	0.803783i	$0.702817\pi$
$48$		0			0
$49$	−149.167	+	258.365i	−0.434890	+	0.753251i
$50$	−413.121	−	238.516i	−1.16848	−	0.674624i
$51$		0			0
$52$	−421.637	+	13.3838i	−1.12443	+	0.0356923i
$53$	695.546			1.80265			0.901326	−	0.433141i	$-0.142595\pi$
$53$	695.546			1.80265			0.901326	+	0.433141i	$0.142595\pi$
$54$		0			0
$55$	49.1821	−	85.1860i	0.120577	−	0.208845i
$56$	13.7779	+	23.8639i	0.0328776	+	0.0569456i
$57$		0			0
$58$	−571.712	+	330.078i	−1.29430	+	0.747265i
$59$	−568.566	+	328.262i	−1.25459	+	0.724339i	−0.972018	−	0.234906i	$-0.924522\pi$
$59$	−568.566	+	328.262i	−1.25459	+	0.724339i	−0.282574	+	0.959245i	$0.591188\pi$
$60$		0			0
$61$	−350.652	−	607.347i	−0.736007	−	1.27480i	−0.954280	−	0.298913i	$-0.903376\pi$
$61$	−350.652	−	607.347i	−0.736007	−	1.27480i	0.218274	−	0.975888i	$-0.429957\pi$
$62$	78.4843	−	135.939i	0.160766	−	0.278456i
$63$		0			0
$64$	631.000			1.23242
$65$	126.015	+	67.5174i	0.240465	+	0.128839i
$66$		0			0
$67$	−49.5150	−	28.5875i	−0.0902869	−	0.0521271i	0.454177	−	0.890912i	$-0.349933\pi$
$67$	−49.5150	−	28.5875i	−0.0902869	−	0.0521271i	−0.544464	+	0.838784i	$0.683267\pi$
$68$	−129.864	+	224.930i	−0.231592	+	0.401130i
$69$		0			0
$70$		−	84.0465i		−	0.143507i
$71$	267.798	−	154.613i	0.447630	−	0.258440i	−0.259199	−	0.965824i	$-0.583458\pi$
$71$	267.798	−	154.613i	0.447630	−	0.258440i	0.706829	+	0.707385i	$0.250125\pi$
$72$		0			0
$73$		−	389.711i		−	0.624826i	−0.949946	−	0.312413i	$-0.898863\pi$
$73$		−	389.711i		−	0.624826i	0.949946	−	0.312413i	$-0.101137\pi$
$74$	−675.299	−	1169.65i	−1.06084	−	1.83742i
$75$		0			0
$76$	788.728	+	455.372i	1.19044	+	0.687300i
$77$	−215.534			−0.318992
$78$		0			0
$79$	901.820			1.28434			0.642169	−	0.766563i	$-0.278035\pi$
$79$	901.820			1.28434			0.642169	+	0.766563i	$0.278035\pi$
$80$	−145.279	−	83.8766i	−0.203033	−	0.117221i
$81$		0			0
$82$	115.621	+	200.262i	0.155710	+	0.269698i
$83$			687.095i			0.908657i	0.890834	+	0.454328i	$0.150121\pi$
$83$			687.095i			0.908657i	−0.890834	+	0.454328i	$0.849879\pi$
$84$		0			0
$85$	76.2279	−	44.0102i	0.0972714	−	0.0561597i
$86$		−	527.257i		−	0.661111i
$87$		0			0
$88$	66.4850	−	115.155i	0.0805378	−	0.139496i
$89$	927.113	+	535.269i	1.10420	+	0.637510i	0.937321	−	0.348467i	$-0.113298\pi$
$89$	927.113	+	535.269i	1.10420	+	0.637510i	0.166879	+	0.985977i	$0.446631\pi$
$90$		0			0
$91$	−9.93858	−	313.100i	−0.0114489	−	0.360679i
$92$	1070.91			1.21359
$93$		0			0
$94$	1067.85	−	1849.57i	1.17170	−	2.02945i
$95$	−154.324	−	267.296i	−0.166666	−	0.288674i
$96$		0			0
$97$	−1519.43	+	877.242i	−1.59046	+	0.918251i	−0.597230	+	0.802070i	$0.703732\pi$
$97$	−1519.43	+	877.242i	−1.59046	+	0.918251i	−0.993228	+	0.116182i	$0.962935\pi$
$98$	1065.27	−	615.032i	1.09804	−	0.633955i
$99$		0			0
$100$	520.637	+	901.770i	0.520637	+	0.901770i
$101$	320.420	−	554.984i	0.315673	−	0.546762i	−0.663907	−	0.747815i	$-0.731103\pi$
$101$	320.420	−	554.984i	0.315673	−	0.546762i	0.979580	+	0.201053i	$0.0644364\pi$
$102$		0			0
$103$	693.153			0.663091			0.331546	−	0.943439i	$-0.392430\pi$
$103$	693.153			0.663091			0.331546	+	0.943439i	$0.392430\pi$
$104$	170.349	+	91.2708i	0.160616	+	0.0860562i
$105$		0			0
$106$	−2483.59	−	1433.90i	−2.27574	−	1.31390i
$107$	−202.838	+	351.325i	−0.183262	+	0.317420i	−0.942990	−	0.332822i	$-0.891999\pi$
$107$	−202.838	+	351.325i	−0.183262	+	0.317420i	0.759727	+	0.650242i	$0.225332\pi$
$108$		0			0
$109$			479.516i			0.421370i	0.977554	+	0.210685i	$0.0675694\pi$
$109$			479.516i			0.421370i	−0.977554	+	0.210685i	$0.932431\pi$
$110$	−351.231	+	202.783i	−0.304441	+	0.175769i
$111$		0			0
$112$			367.578i			0.310115i
$113$	−773.602	−	1339.92i	−0.644021	−	1.11548i	−0.984527	−	0.175235i	$-0.943932\pi$
$113$	−773.602	−	1339.92i	−0.644021	−	1.11548i	0.340506	−	0.940242i	$-0.389402\pi$
$114$		0			0
$115$	−314.304	−	181.463i	−0.254861	−	0.147144i
$116$	1441.00			1.15339
$117$		0			0
$118$	2706.91			2.11179
$119$	−167.029	−	96.4344i	−0.128668	−	0.0742868i
$120$		0			0
$121$	−145.470	−	251.961i	−0.109294	−	0.189302i
$122$			2891.55i			2.14581i
$123$		0			0
$124$	−296.730	+	171.317i	−0.214896	+	0.124070i
$125$		−	734.140i		−	0.525308i
$126$		0			0
$127$	−1247.58	+	2160.87i	−0.871690	+	1.50981i	−0.0114416	+	0.999935i	$0.503642\pi$
$127$	−1247.58	+	2160.87i	−0.871690	+	1.50981i	−0.860248	+	0.509876i	$0.829691\pi$
$128$	−453.481	−	261.817i	−0.313144	−	0.180794i
$129$		0			0
$130$	−310.773	−	500.872i	−0.209666	−	0.337918i
$131$	−43.7571			−0.0291838			−0.0145919	−	0.999894i	$-0.504645\pi$
$131$	−43.7571			−0.0291838			−0.0145919	+	0.999894i	$0.504645\pi$
$132$		0			0
$133$	−338.151	+	585.695i	−0.220462	+	0.381851i
$134$	117.869	+	204.156i	0.0759877	+	0.131615i
$135$		0			0
$136$	103.046	−	59.4935i	0.0649713	−	0.0375112i
$137$	178.569	−	103.097i	0.111359	−	0.0642932i	−0.443286	−	0.896380i	$-0.646187\pi$
$137$	178.569	−	103.097i	0.111359	−	0.0642932i	0.554645	+	0.832087i	$0.312854\pi$
$138$		0			0
$139$	50.0000	+	86.6025i	0.0305104	+	0.0528456i	0.880877	−	0.473344i	$-0.156953\pi$
$139$	50.0000	+	86.6025i	0.0305104	+	0.0528456i	−0.850367	+	0.526190i	$0.823620\pi$
$140$	−91.7293	+	158.880i	−0.0553753	+	0.0959128i
$141$		0			0
$142$	−1274.97			−0.753474
$143$	−1284.47	+	796.966i	−0.751137	+	0.466053i
$144$		0			0
$145$	−422.923	−	244.175i	−0.242220	−	0.139846i
$146$	−803.411	+	1391.55i	−0.455416	+	0.788804i
$147$		0			0
$148$			2948.11i			1.63739i
$149$	329.480	−	190.225i	0.181155	−	0.104590i	−0.406680	−	0.913571i	$-0.633314\pi$
$149$	329.480	−	190.225i	0.181155	−	0.104590i	0.587835	+	0.808981i	$0.299980\pi$
$150$		0			0
$151$		−	1517.45i		−	0.817805i	−0.912578	−	0.408902i	$-0.865912\pi$
$151$		−	1517.45i		−	0.817805i	0.912578	−	0.408902i	$-0.134088\pi$
$152$	−208.616	−	361.334i	−0.111323	−	0.192816i
$153$		0			0
$154$	769.611	+	444.335i	0.402708	+	0.232504i
$155$	116.117			0.0601726
$156$		0			0
$157$	1450.16			0.737166			0.368583	−	0.929595i	$-0.379843\pi$
$157$	1450.16			0.737166			0.368583	+	0.929595i	$0.379843\pi$
$158$	−3220.14	−	1859.15i	−1.62140	−	0.936114i
$159$		0			0
$160$	396.135	+	686.126i	0.195733	+	0.339019i
$161$			795.239i			0.389277i
$162$		0			0
$163$	2028.54	−	1171.18i	0.974772	−	0.562785i	0.0740844	−	0.997252i	$-0.476397\pi$
$163$	2028.54	−	1171.18i	0.974772	−	0.562785i	0.900688	+	0.434467i	$0.143063\pi$
$164$		−	504.762i		−	0.240337i
$165$		0			0
$166$	1416.48	−	2453.42i	0.662292	−	1.14712i
$167$	−34.7043	−	20.0365i	−0.0160808	−	0.00928428i	0.491938	−	0.870630i	$-0.336289\pi$
$167$	−34.7043	−	20.0365i	−0.0160808	−	0.00928428i	−0.508019	+	0.861346i	$0.669622\pi$
$168$		0			0
$169$	−1216.96	−	1829.16i	−0.553918	−	0.832571i
$170$	−362.917			−0.163732
$171$		0			0
$172$	−575.454	+	996.715i	−0.255104	+	0.441853i
$173$	−954.770	−	1653.71i	−0.419594	−	0.726759i	0.576304	−	0.817235i	$-0.304494\pi$
$173$	−954.770	−	1653.71i	−0.419594	−	0.726759i	−0.995899	+	0.0904765i	$0.971161\pi$
$174$		0			0
$175$	−669.639	+	386.616i	−0.289257	+	0.167002i
$176$	1536.11	−	886.874i	0.657890	−	0.379833i
$177$		0			0
$178$	−2206.97	−	3822.58i	−0.929322	−	1.60963i
$179$	254.979	−	441.637i	0.106470	−	0.184411i	−0.807868	−	0.589363i	$-0.799379\pi$
$179$	254.979	−	441.637i	0.106470	−	0.184411i	0.914338	+	0.404953i	$0.132712\pi$
$180$		0			0
$181$	2136.88			0.877531			0.438766	−	0.898602i	$-0.355416\pi$
$181$	2136.88			0.877531			0.438766	+	0.898602i	$0.355416\pi$
$182$	−609.985	+	1138.48i	−0.248435	+	0.463680i
$183$		0			0
$184$	−424.879	−	245.304i	−0.170231	−	0.0982830i
$185$	499.551	−	865.247i	0.198528	−	0.343861i
$186$		0			0
$187$			930.688i			0.363950i
$188$	−4037.28	+	2330.92i	−1.56622	+	0.904256i
$189$		0			0
$190$			1272.58i			0.485911i
$191$	2028.87	+	3514.11i	0.768607	+	1.33127i	0.938318	+	0.345773i	$0.112383\pi$
$191$	2028.87	+	3514.11i	0.768607	+	1.33127i	−0.169711	+	0.985494i	$0.554283\pi$
$192$		0			0
$193$	−756.381	−	436.697i	−0.282101	−	0.162871i	0.352273	−	0.935897i	$-0.385409\pi$
$193$	−756.381	−	436.697i	−0.282101	−	0.162871i	−0.634374	+	0.773026i	$0.718742\pi$
$194$	7233.92			2.67714
$195$		0			0
$196$	−2685.01			−0.978502
$197$	−3591.62	−	2073.62i	−1.29895	−	0.749947i	−0.318724	−	0.947848i	$-0.603254\pi$
$197$	−3591.62	−	2073.62i	−1.29895	−	0.749947i	−0.980222	+	0.197901i	$0.936588\pi$
$198$		0			0
$199$	−1202.03	−	2081.98i	−0.428189	−	0.741646i	0.568523	−	0.822667i	$-0.307515\pi$
$199$	−1202.03	−	2081.98i	−0.428189	−	0.741646i	−0.996712	+	0.0810216i	$0.974182\pi$
$200$		−	477.032i		−	0.168656i
$201$		0			0
$202$	−2288.26	+	1321.13i	−0.797035	+	0.460169i
$203$			1070.06i			0.369969i
$204$		0			0
$205$	−85.5307	+	148.144i	−0.0291401	+	0.0504722i
$206$	−2475.05	−	1428.97i	−0.837111	−	0.483307i
$207$		0			0
$208$	1359.17	+	2190.57i	0.453083	+	0.730233i
$209$	3263.50			1.08010
$210$		0			0
$211$	−1934.43	+	3350.53i	−0.631144	+	1.09317i	0.356174	+	0.934420i	$0.384081\pi$
$211$	−1934.43	+	3350.53i	−0.631144	+	1.09317i	−0.987318	+	0.158754i	$0.949252\pi$
$212$	3129.96	+	5421.24i	1.01399	+	1.75629i
$213$		0			0
$214$	1448.55	−	836.322i	0.462715	−	0.267149i
$215$	337.782	−	195.019i	0.107147	−	0.0618612i
$216$		0			0
$217$	−127.217	−	220.346i	−0.0397975	−	0.0689313i
$218$	988.547	−	1712.21i	0.307123	−	0.531953i
$219$		0			0
$220$	885.279			0.271298
$221$	−1351.98	+	42.9153i	−0.411512	+	0.0130624i
$222$		0			0
$223$	2436.61	+	1406.78i	0.731692	+	0.422443i	0.819041	−	0.573735i	$-0.194506\pi$
$223$	2436.61	+	1406.78i	0.731692	+	0.422443i	−0.0873487	+	0.996178i	$0.527839\pi$
$224$	868.005	−	1503.43i	0.258911	−	0.448447i
$225$		0			0
$226$			6379.29i			1.87763i
$227$	−3913.02	+	2259.19i	−1.14413	+	0.660561i	−0.947449	−	0.319907i	$-0.896348\pi$
$227$	−3913.02	+	2259.19i	−1.14413	+	0.660561i	−0.196677	+	0.980468i	$0.563015\pi$
$228$		0			0
$229$		−	1305.27i		−	0.376658i	−0.982106	−	0.188329i	$-0.939693\pi$
$229$		−	1305.27i		−	0.376658i	0.982106	−	0.188329i	$-0.0603070\pi$
$230$	748.192	+	1295.91i	0.214497	+	0.371520i
$231$		0			0
$232$	−571.712	−	330.078i	−0.161788	−	0.0934082i
$233$	−3360.55			−0.944879			−0.472440	−	0.881363i	$-0.656627\pi$
$233$	−3360.55			−0.944879			−0.472440	+	0.881363i	$0.656627\pi$
$234$		0			0
$235$	1579.88			0.438553
$236$	−5117.09	−	2954.35i	−1.41142	−	0.814882i
$237$		0			0
$238$	397.609	+	688.679i	0.108291	+	0.187565i
$239$		−	4737.17i		−	1.28210i	−0.767499	−	0.641050i	$-0.778499\pi$
$239$		−	4737.17i		−	1.28210i	0.767499	−	0.641050i	$-0.221501\pi$
$240$		0			0
$241$	4144.17	−	2392.64i	1.10767	−	0.639516i	0.169448	−	0.985539i	$-0.445801\pi$
$241$	4144.17	−	2392.64i	1.10767	−	0.639516i	0.938226	+	0.346023i	$0.112468\pi$
$242$			1199.58i			0.318643i
$243$		0			0
$244$	3155.87	−	5466.13i	0.828007	−	1.43415i
$245$	788.029	+	454.969i	0.205491	+	0.118640i
$246$		0			0
$247$	150.484	+	4740.79i	0.0387655	+	1.22125i
$248$	156.969			0.0401916
$249$		0			0
$250$	−1513.47	+	2621.41i	−0.382881	+	0.663169i
$251$	1636.93	+	2835.25i	0.411642	+	0.712985i	0.995069	−	0.0991805i	$-0.0316221\pi$
$251$	1636.93	+	2835.25i	0.411642	+	0.712985i	−0.583428	+	0.812165i	$0.698289\pi$
$252$		0			0
$253$	3323.31	−	1918.71i	0.825828	−	0.476792i
$254$	8909.48	−	5143.89i	2.20091	−	1.27069i
$255$		0			0
$256$	−1444.50	−	2501.95i	−0.352661	−	0.610827i
$257$	3272.91	−	5668.84i	0.794390	−	1.37592i	−0.128835	−	0.991666i	$-0.541124\pi$
$257$	3272.91	−	5668.84i	0.794390	−	1.37592i	0.923226	−	0.384258i	$-0.125543\pi$
$258$		0			0
$259$	−2189.22			−0.525217
$260$	40.8214	+	1286.02i	0.00973706	+	0.306752i
$261$		0			0
$262$	156.244	+	90.2077i	0.0368428	+	0.0212712i
$263$	44.1007	−	76.3847i	0.0103398	−	0.0179091i	−0.860809	−	0.508928i	$-0.830042\pi$
$263$	44.1007	−	76.3847i	0.0103398	−	0.0179091i	0.871149	+	0.491019i	$0.163375\pi$
$264$		0			0
$265$		−	2121.46i		−	0.491773i
$266$	2414.88	−	1394.23i	0.556639	−	0.321376i
$267$		0			0
$268$		−	514.575i		−	0.117286i
$269$	−2263.80	−	3921.01i	−0.513109	−	0.888730i	−0.999884	−	0.0152033i	$-0.995160\pi$
$269$	−2263.80	−	3921.01i	−0.513109	−	0.888730i	0.486776	−	0.873527i	$-0.338173\pi$
$270$		0			0
$271$	−7206.91	−	4160.91i	−1.61546	−	0.932684i	−0.988075	−	0.153971i	$-0.950794\pi$
$271$	−7206.91	−	4160.91i	−1.61546	−	0.932684i	−0.627380	−	0.778713i	$-0.715873\pi$
$272$	1587.22			0.353821
$273$		0			0
$274$	−850.160			−0.187445
$275$	3231.34	+	1865.61i	0.708571	+	0.409094i
$276$		0			0
$277$	−1440.65	−	2495.29i	−0.312493	−	0.541254i	0.666408	−	0.745587i	$-0.267831\pi$
$277$	−1440.65	−	2495.29i	−0.312493	−	0.541254i	−0.978901	+	0.204333i	$0.934497\pi$
$278$		−	412.311i		−	0.0889523i
$279$		0			0
$280$	72.7864	−	42.0233i	0.0155351	−	0.00896918i
$281$			2817.99i			0.598247i	0.954214	+	0.299123i	$0.0966942\pi$
$281$			2817.99i			0.598247i	−0.954214	+	0.299123i	$0.903306\pi$
$282$		0			0
$283$	132.301	−	229.152i	0.0277896	−	0.0481330i	−0.851796	−	0.523873i	$-0.824486\pi$
$283$	132.301	−	229.152i	0.0277896	−	0.0481330i	0.879586	+	0.475740i	$0.157820\pi$
$284$	2410.18	+	1391.52i	0.503584	+	0.290744i
$285$		0			0
$286$	6229.45	−	197.738i	1.28796	−	0.0408829i
$287$	374.827			0.0770918
$288$		0			0
$289$	2040.09	−	3533.54i	0.415244	−	0.719223i
$290$	1006.76	+	1743.76i	0.203858	+	0.353093i
$291$		0			0
$292$	3037.50	−	1753.70i	0.608754	−	0.351464i
$293$	−3717.43	+	2146.26i	−0.741211	+	0.427938i	−0.822509	−	0.568751i	$-0.807427\pi$
$293$	−3717.43	+	2146.26i	−0.741211	+	0.427938i	0.0812984	+	0.996690i	$0.474093\pi$
$294$		0			0
$295$	1001.22	+	1734.16i	0.197604	+	0.342260i
$296$	675.299	−	1169.65i	0.132604	−	0.229678i
$297$		0			0
$298$	−1568.64			−0.304929
$299$	2940.50	+	4739.19i	0.568740	+	0.916638i
$300$		0			0
$301$	−740.143	−	427.322i	−0.141731	−	0.0818286i
$302$	−3128.31	+	5418.39i	−0.596072	+	1.03243i
$303$		0			0
$304$		−	5565.66i		−	1.05004i
$305$	−1852.45	+	1069.51i	−0.347773	+	0.200787i
$306$		0			0
$307$			7026.26i			1.30622i	0.757263	+	0.653110i	$0.226536\pi$
$307$			7026.26i			1.30622i	−0.757263	+	0.653110i	$0.773464\pi$
$308$	−969.904	−	1679.92i	−0.179433	−	0.310787i
$309$		0			0
$310$	−414.621	−	239.382i	−0.0759642	−	0.0438580i
$311$	−1133.21			−0.206618			−0.103309	−	0.994649i	$-0.532943\pi$
$311$	−1133.21			−0.206618			−0.103309	+	0.994649i	$0.532943\pi$
$312$		0			0
$313$	−5285.95			−0.954566			−0.477283	−	0.878750i	$-0.658378\pi$
$313$	−5285.95			−0.954566			−0.477283	+	0.878750i	$0.658378\pi$
$314$	−5178.09	−	2989.57i	−0.930626	−	0.537297i
$315$		0			0
$316$	4058.19	+	7028.99i	0.722440	+	1.25130i
$317$		−	4782.16i		−	0.847296i	−0.905827	−	0.423648i	$-0.860749\pi$
$317$		−	4782.16i		−	0.847296i	0.905827	−	0.423648i	$-0.139251\pi$
$318$		0			0
$319$	4471.80	−	2581.79i	0.784867	−	0.453143i
$320$		−	1924.59i		−	0.336212i
$321$		0			0
$322$	1639.43	−	2839.57i	0.283732	−	0.491438i
$323$	2529.06	+	1460.15i	0.435668	+	0.251533i
$324$		0			0
$325$	−2561.12	+	4780.10i	−0.437124	+	0.815852i
$326$	−9657.80			−1.64079
$327$		0			0
$328$	−115.621	+	200.262i	−0.0194638	+	0.0337123i
$329$	−1730.90	−	2998.01i	−0.290054	−	0.502388i
$330$		0			0
$331$	−7508.43	+	4334.99i	−1.24683	+	0.719857i	−0.970476	−	0.241199i	$-0.922459\pi$
$331$	−7508.43	+	4334.99i	−1.24683	+	0.719857i	−0.276353	+	0.961056i	$0.589126\pi$
$332$	−5355.38	+	3091.93i	−0.885285	+	0.511120i
$333$		0			0
$334$	82.6128	+	143.090i	0.0135340	+	0.0234417i
$335$	−87.1936	+	151.024i	−0.0142206	+	0.0246308i
$336$		0			0
$337$	−8526.59			−1.37826			−0.689129	−	0.724639i	$-0.742007\pi$
$337$	−8526.59			−1.37826			−0.689129	+	0.724639i	$0.742007\pi$
$338$	574.497	+	9040.23i	0.0924513	+	1.45480i
$339$		0			0
$340$	686.051	+	396.092i	0.109430	+	0.0631796i
$341$	−613.886	+	1063.28i	−0.0974891	+	0.168856i
$342$		0			0
$343$		−	4286.19i		−	0.674731i
$344$	456.618	−	263.628i	0.0715674	−	0.0413195i
$345$		0			0
$346$			7873.23i			1.22332i
$347$	−6290.74	−	10895.9i	−0.973213	−	1.68565i	−0.685711	−	0.727874i	$-0.740509\pi$
$347$	−6290.74	−	10895.9i	−0.973213	−	1.68565i	−0.287501	−	0.957780i	$-0.592825\pi$
$348$		0			0
$349$	7760.61	+	4480.59i	1.19030	+	0.687222i	0.958375	−	0.285511i	$-0.0921633\pi$
$349$	7760.61	+	4480.59i	1.19030	+	0.687222i	0.231928	+	0.972733i	$0.425497\pi$
$350$	3188.12			0.486892
$351$		0			0
$352$	−8377.11			−1.26847
$353$	4640.16	+	2679.00i	0.699634	+	0.403934i	0.807211	−	0.590263i	$-0.200976\pi$
$353$	4640.16	+	2679.00i	0.699634	+	0.403934i	−0.107577	+	0.994197i	$0.534309\pi$
$354$		0			0
$355$	−471.579	−	816.799i	−0.0705037	−	0.122116i
$356$			9634.84i			1.43440i
$357$		0			0
$358$	−1820.92	+	1051.31i	−0.268822	+	0.155205i
$359$			2705.40i			0.397731i	0.980027	+	0.198866i	$0.0637257\pi$
$359$			2705.40i			0.397731i	−0.980027	+	0.198866i	$0.936274\pi$
$360$		0			0
$361$	1690.60	−	2928.20i	0.246478	−	0.426913i
$362$	−7630.19	−	4405.29i	−1.10783	−	0.639605i
$363$		0			0
$364$	2395.65	−	1486.42i	0.344962	−	0.214037i
$365$	−1188.64			−0.170456
$366$		0			0
$367$	−5236.88	+	9070.54i	−0.744858	+	1.29013i	0.205403	+	0.978678i	$0.434150\pi$
$367$	−5236.88	+	9070.54i	−0.744858	+	1.29013i	−0.950261	+	0.311455i	$0.899184\pi$
$368$	−3272.22	−	5667.66i	−0.463523	−	0.802846i
$369$		0			0
$370$	−3567.51	+	2059.70i	−0.501259	+	0.289402i
$371$	−4025.72	+	2324.25i	−0.563356	+	0.325254i
$372$		0			0
$373$	6381.51	+	11053.1i	0.885850	+	1.53434i	0.844737	+	0.535182i	$0.179757\pi$
$373$	6381.51	+	11053.1i	0.885850	+	1.53434i	0.0411127	+	0.999155i	$0.486910\pi$
$374$	1918.66	−	3323.22i	0.265272	−	0.459464i
$375$		0			0
$376$	2135.70			0.292926
$377$	3956.70	+	6377.00i	0.540531	+	0.871173i
$378$		0			0
$379$	−2007.47	−	1159.01i	−0.272076	−	0.157083i	0.357755	−	0.933816i	$-0.383542\pi$
$379$	−2007.47	−	1159.01i	−0.272076	−	0.157083i	−0.629831	+	0.776733i	$0.716876\pi$
$380$	1388.91	−	2405.67i	0.187499	−	0.324758i
$381$		0			0
$382$		−	16730.5i		−	2.24086i
$383$	1717.63	−	991.672i	0.229156	−	0.132303i	−0.381027	−	0.924564i	$-0.624429\pi$
$383$	1717.63	−	991.672i	0.229156	−	0.132303i	0.610183	+	0.792261i	$0.291096\pi$
$384$		0			0
$385$			657.392i			0.0870229i
$386$	1800.55	+	3118.64i	0.237424	+	0.411230i
$387$		0			0
$388$	−13674.8	−	7895.17i	−1.78927	−	1.03303i
$389$	−3244.51			−0.422887			−0.211444	−	0.977390i	$-0.567816\pi$
$389$	−3244.51			−0.422887			−0.211444	+	0.977390i	$0.567816\pi$
$390$		0			0
$391$	3433.88			0.444140
$392$	1065.27	+	615.032i	0.137255	+	0.0792444i
$393$		0			0
$394$	8549.77	+	14808.6i	1.09323	+	1.89352i
$395$		−	2750.60i		−	0.350374i
$396$		0			0
$397$	3256.02	−	1879.86i	0.411624	−	0.237651i	−0.279863	−	0.960040i	$-0.590289\pi$
$397$	3256.02	−	1879.86i	0.411624	−	0.237651i	0.691487	+	0.722389i	$0.256956\pi$
$398$			9912.20i			1.24838i
$399$		0			0
$400$	3181.67	−	5510.82i	0.397709	−	0.688852i
$401$	−1729.93	−	998.773i	−0.215432	−	0.124380i	0.388401	−	0.921490i	$-0.373027\pi$
$401$	−1729.93	−	998.773i	−0.215432	−	0.124380i	−0.603833	+	0.797110i	$0.706361\pi$
$402$		0			0
$403$	−1572.90	−	842.744i	−0.194422	−	0.104169i
$404$	5767.56			0.710264
$405$		0			0
$406$	2205.99	−	3820.89i	0.269659	−	0.467063i
$407$	5282.03	+	9148.74i	0.643293	+	1.11422i
$408$		0			0
$409$	4499.20	−	2597.62i	0.543940	−	0.314044i	−0.202735	−	0.979234i	$-0.564983\pi$
$409$	4499.20	−	2597.62i	0.543940	−	0.314044i	0.746674	+	0.665190i	$0.231650\pi$
$410$	610.811	−	352.652i	0.0735752	−	0.0424787i
$411$		0			0
$412$	3119.19	+	5402.59i	0.372989	+	0.646035i
$413$	2193.85	−	3799.86i	0.261386	−	0.452734i
$414$		0			0
$415$	2095.68			0.247887
$416$	−386.280	−	12169.2i	−0.0455263	−	1.43424i
$417$		0			0
$418$	−11653.0	−	6727.87i	−1.36356	−	0.787251i
$419$	−3411.05	+	5908.12i	−0.397711	+	0.688855i	−0.993443	−	0.114328i	$-0.963529\pi$
$419$	−3411.05	+	5908.12i	−0.397711	+	0.688855i	0.595732	+	0.803183i	$0.296862\pi$
$420$		0			0
$421$		−	7537.70i		−	0.872601i	−0.899801	−	0.436300i	$-0.856288\pi$
$421$		−	7537.70i		−	0.872601i	0.899801	−	0.436300i	$-0.143712\pi$
$422$	13814.6	−	7975.85i	1.59356	−	0.920043i
$423$		0			0
$424$		−	2867.81i		−	0.328474i
$425$	1669.43	+	2891.53i	0.190539	+	0.330023i
$426$		0			0
$427$	4059.05	+	2343.49i	0.460026	+	0.265596i
$428$	−3651.08			−0.412340
$429$		0			0
$430$	−1608.16			−0.180355
$431$	11608.4	+	6702.10i	1.29735	+	0.749023i	0.979945	−	0.199268i	$-0.0638565\pi$
$431$	11608.4	+	6702.10i	1.29735	+	0.749023i	0.317401	+	0.948291i	$0.397190\pi$
$432$		0			0
$433$	−8857.97	−	15342.5i	−0.983110	−	1.70280i	−0.650050	−	0.759892i	$-0.725252\pi$
$433$	−8857.97	−	15342.5i	−0.983110	−	1.70280i	−0.333061	−	0.942905i	$-0.608081\pi$
$434$			1049.06i			0.116029i
$435$		0			0
$436$	−3737.46	+	2157.82i	−0.410531	+	0.237020i
$437$		−	12041.1i		−	1.31808i
$438$		0			0
$439$	3581.73	−	6203.75i	0.389401	−	0.674462i	−0.602968	−	0.797765i	$-0.706015\pi$
$439$	3581.73	−	6203.75i	0.389401	−	0.674462i	0.992369	+	0.123303i	$0.0393488\pi$
$440$	−351.231	−	202.783i	−0.0380552	−	0.0219712i
$441$		0			0
$442$	4916.02	+	2633.95i	0.529030	+	0.283448i
$443$	10169.2			1.09064			0.545321	−	0.838227i	$-0.316408\pi$
$443$	10169.2			1.09064			0.545321	+	0.838227i	$0.316408\pi$
$444$		0			0
$445$	1632.60	−	2827.75i	0.173916	−	0.301232i
$446$	−5800.29	−	10046.4i	−0.615811	−	1.06662i
$447$		0			0
$448$	−3652.14	+	2108.56i	−0.385150	+	0.222367i
$449$	14845.8	−	8571.24i	1.56040	−	0.900895i	0.563179	−	0.826335i	$-0.309578\pi$
$449$	14845.8	−	8571.24i	1.56040	−	0.900895i	0.997217	−	0.0745603i	$-0.0237553\pi$
$450$		0			0
$451$	−904.364	−	1566.40i	−0.0944231	−	0.163546i
$452$	6962.42	−	12059.3i	0.724524	−	1.25491i
$453$		0			0
$454$	18629.7			1.92585
$455$	−954.974	+	30.3133i	−0.0983954	+	0.00312331i
$456$		0			0
$457$	12203.3	+	7045.57i	1.24912	+	0.721177i	0.970933	−	0.239351i	$-0.0769346\pi$
$457$	12203.3	+	7045.57i	1.24912	+	0.721177i	0.278183	+	0.960528i	$0.410268\pi$
$458$	−2690.88	+	4660.74i	−0.274534	+	0.475507i
$459$		0			0
$460$		−	3266.34i		−	0.331074i
$461$	−2530.72	+	1461.11i	−0.255678	+	0.147616i	−0.622361	−	0.782730i	$-0.713826\pi$
$461$	−2530.72	+	1461.11i	−0.255678	+	0.147616i	0.366684	+	0.930346i	$0.380493\pi$
$462$		0			0
$463$		−	2072.61i		−	0.208040i	−0.994575	−	0.104020i	$-0.966829\pi$
$463$		−	2072.61i		−	0.208040i	0.994575	−	0.104020i	$-0.0331706\pi$
$464$	−4403.06	−	7626.33i	−0.440533	−	0.763025i
$465$		0			0
$466$	11999.6	+	6927.95i	1.19285	+	0.688693i
$467$	−2664.19			−0.263992			−0.131996	−	0.991250i	$-0.542139\pi$
$467$	−2664.19			−0.263992			−0.131996	+	0.991250i	$0.542139\pi$
$468$		0			0
$469$	382.114			0.0376213
$470$	−5641.29	−	3257.00i	−0.553646	−	0.319648i
$471$		0			0
$472$	1353.46	+	2344.26i	0.131987	+	0.228608i
$473$			4124.08i			0.400899i
$474$		0			0
$475$	10139.3	−	5853.92i	0.979415	−	0.565466i
$476$		−	1735.82i		−	0.167145i
$477$		0			0
$478$	−9765.92	+	16915.1i	−0.934483	+	1.61857i
$479$	−4521.26	−	2610.35i	−0.431277	−	0.248998i	0.268614	−	0.963248i	$-0.413434\pi$
$479$	−4521.26	−	2610.35i	−0.431277	−	0.248998i	−0.699890	+	0.714250i	$0.746768\pi$
$480$		0			0
$481$	−13046.5	+	8094.91i	−1.23674	+	0.767351i
$482$	−19730.2			−1.86449
$483$		0			0
$484$	1309.23	−	2267.65i	0.122955	−	0.212965i
$485$	2675.64	+	4634.34i	0.250504	+	0.433886i
$486$		0			0
$487$	10586.8	−	6112.30i	0.985081	−	0.568737i	0.0812808	−	0.996691i	$-0.474099\pi$
$487$	10586.8	−	6112.30i	0.985081	−	0.568737i	0.903800	+	0.427954i	$0.140766\pi$
$488$	−2504.16	+	1445.78i	−0.232291	+	0.134113i
$489$		0			0
$490$	−1875.88	−	3249.13i	−0.172946	−	0.299552i
$491$	−9826.61	+	17020.2i	−0.903195	+	1.56438i	−0.0798720	+	0.996805i	$0.525451\pi$
$491$	−9826.61	+	17020.2i	−0.903195	+	1.56438i	−0.823323	+	0.567574i	$0.807882\pi$
$492$		0			0
$493$	4620.59			0.422111
$494$	9236.04	−	17238.2i	0.841193	−	1.57001i
$495$		0			0
$496$	1813.35	+	1046.94i	0.164157	+	0.0947760i
$497$	−1033.32	+	1789.76i	−0.0932608	+	0.161532i
$498$		0			0
$499$			11713.6i			1.05084i	0.850842	+	0.525422i	$0.176093\pi$
$499$			11713.6i			1.05084i	−0.850842	+	0.525422i	$0.823907\pi$
$500$	5722.06	−	3303.63i	0.511796	−	0.295486i
$501$		0			0
$502$		−	13498.5i		−	1.20013i
$503$	6501.67	+	11261.2i	0.576332	+	0.998236i	0.995896	+	0.0905104i	$0.0288498\pi$
$503$	6501.67	+	11261.2i	0.576332	+	0.998236i	−0.419563	+	0.907726i	$0.637817\pi$
$504$		0			0
$505$	−1692.73	−	977.300i	−0.149160	−	0.0861174i
$506$	−15822.1			−1.39008
$507$		0			0
$508$	−22456.4			−1.96130
$509$	4614.99	+	2664.47i	0.401878	+	0.232024i	0.687294	−	0.726379i	$-0.258798\pi$
$509$	4614.99	+	2664.47i	0.401878	+	0.232024i	−0.285416	+	0.958404i	$0.592132\pi$
$510$		0			0
$511$	1302.27	+	2255.59i	0.112738	+	0.195267i
$512$			16100.7i			1.38976i
$513$		0			0
$514$	−23373.2	+	13494.5i	−2.00574	+	1.15801i
$515$		−	2114.16i		−	0.180895i
$516$		0			0
$517$	−8352.47	+	14466.9i	−0.710524	+	1.23066i
$518$	7817.06	+	4513.18i	0.663054	+	0.382814i
$519$		0			0
$520$	278.381	−	519.573i	0.0234766	−	0.0438169i
$521$	11700.3			0.983876			0.491938	−	0.870630i	$-0.336289\pi$
$521$	11700.3			0.983876			0.491938	+	0.870630i	$0.336289\pi$
$522$		0			0
$523$	2267.52	−	3927.46i	0.189583	−	0.328367i	−0.755528	−	0.655116i	$-0.772620\pi$
$523$	2267.52	−	3927.46i	0.189583	−	0.328367i	0.945111	+	0.326749i	$0.105953\pi$
$524$	−196.907	−	341.053i	−0.0164159	−	0.0284332i
$525$		0			0
$526$	−314.942	+	181.832i	−0.0261067	+	0.0150727i
$527$	−951.467	+	549.330i	−0.0786462	+	0.0454064i
$528$		0			0
$529$	−995.810	−	1724.79i	−0.0818451	−	0.141760i
$530$	−4373.49	+	7575.11i	−0.358438	+	0.620834i
$531$		0			0
$532$	−6086.73			−0.496040
$533$	2233.77	−	1385.97i	0.181529	−	0.112632i
$534$		0			0
$535$	1071.56	+	618.667i	0.0865939	+	0.0499950i
$536$	−117.869	+	204.156i	−0.00949847	+	0.0164518i
$537$		0			0
$538$			18667.8i			1.49596i
$539$	−8332.26	+	4810.63i	−0.665855	+	0.384432i
$540$		0			0
$541$		−	5184.89i		−	0.412044i	−0.978547	−	0.206022i	$-0.933948\pi$
$541$		−	5184.89i		−	0.412044i	0.978547	−	0.206022i	$-0.0660519\pi$
$542$	17155.9	+	29714.8i	1.35961	+	2.35491i
$543$		0			0
$544$	−6491.88	−	3748.09i	−0.511649	−	0.295401i
$545$	1462.55			0.114952
$546$		0			0
$547$	5609.12			0.438443			0.219222	−	0.975675i	$-0.429648\pi$
$547$	5609.12			0.438443			0.219222	+	0.975675i	$0.429648\pi$
$548$	1607.12	+	927.873i	0.125279	+	0.0723299i
$549$		0			0
$550$	−7692.12	−	13323.2i	−0.596351	−	1.03291i
$551$		−	16202.3i		−	1.25271i
$552$		0			0
$553$	−5219.61	+	3013.54i	−0.401375	+	0.231734i
$554$			11879.9i			0.911066i
$555$		0			0
$556$	−450.000	+	779.423i	−0.0343242	+	0.0594512i
$557$	−17450.9	−	10075.3i	−1.32750	−	0.766432i	−0.342586	−	0.939486i	$-0.611303\pi$
$557$	−17450.9	−	10075.3i	−1.32750	−	0.766432i	−0.984912	+	0.173055i	$0.944636\pi$
$558$		0			0
$559$	−5990.93	+	190.167i	−0.453290	+	0.0143886i
$560$	1121.14			0.0846011
$561$		0			0
$562$	5809.44	−	10062.2i	0.436044	−	0.755250i
$563$	−8146.10	−	14109.5i	−0.609800	−	1.05620i	−0.991273	−	0.131824i	$-0.957917\pi$
$563$	−8146.10	−	14109.5i	−0.609800	−	1.05620i	0.381474	−	0.924380i	$-0.375417\pi$
$564$		0			0
$565$	−4086.83	+	2359.53i	−0.304308	+	0.175692i
$566$	−944.816	+	545.490i	−0.0701654	+	0.0405100i
$567$		0			0
$568$	−637.486	−	1104.16i	−0.0470921	−	0.0815660i
$569$	−5230.27	+	9059.09i	−0.385350	+	0.667446i	−0.991818	−	0.127662i	$-0.959253\pi$
$569$	−5230.27	+	9059.09i	−0.385350	+	0.667446i	0.606468	+	0.795108i	$0.292586\pi$
$570$		0			0
$571$	−2225.96			−0.163141			−0.0815705	−	0.996668i	$-0.525994\pi$
$571$	−2225.96			−0.163141			−0.0815705	+	0.996668i	$0.525994\pi$
$572$	−11991.8	−	6425.09i	−0.876580	−	0.469662i
$573$		0			0
$574$	−1338.40	−	772.726i	−0.0973236	−	0.0561898i
$575$	6883.40	−	11922.4i	0.499231	−	0.864693i
$576$		0			0
$577$		−	4686.23i		−	0.338112i	−0.985606	−	0.169056i	$-0.945928\pi$
$577$		−	4686.23i		−	0.338112i	0.985606	−	0.169056i	$-0.0540718\pi$
$578$	−14569.2	+	8411.51i	−1.04844	+	0.605316i
$579$		0			0
$580$		−	4395.14i		−	0.314652i
$581$	−2296.01	−	3976.81i	−0.163949	−	0.283969i
$582$		0			0
$583$	19426.1	+	11215.7i	1.38001	+	0.796750i
$584$	−1606.82			−0.113854
$585$		0			0
$586$	17698.5			1.24764
$587$	−10470.7	−	6045.28i	−0.736241	−	0.425069i	0.0844601	−	0.996427i	$-0.473083\pi$
$587$	−10470.7	−	6045.28i	−0.736241	−	0.425069i	−0.820701	+	0.571358i	$0.806417\pi$
$588$		0			0
$589$	1926.25	+	3336.36i	0.134753	+	0.233400i
$590$		−	8256.25i		−	0.576109i
$591$		0			0
$592$	15602.5	−	9008.12i	1.08321	−	0.625391i
$593$		−	6135.97i		−	0.424914i	−0.977170	−	0.212457i	$-0.931853\pi$
$593$		−	6135.97i		−	0.424914i	0.977170	−	0.212457i	$-0.0681466\pi$
$594$		0			0
$595$	−294.131	+	509.449i	−0.0202658	+	0.0351015i
$596$	2965.32	+	1712.03i	0.203799	+	0.117663i
$597$		0			0
$598$	−729.579	−	22984.3i	−0.0498908	−	1.57174i
$599$	6198.80			0.422831			0.211416	−	0.977396i	$-0.432193\pi$
$599$	6198.80			0.422831			0.211416	+	0.977396i	$0.432193\pi$
$600$		0			0
$601$	−9172.69	+	15887.6i	−0.622565	+	1.07831i	0.366441	+	0.930441i	$0.380576\pi$
$601$	−9172.69	+	15887.6i	−0.622565	+	1.07831i	−0.989006	+	0.147873i	$0.952757\pi$
$602$	1761.89	+	3051.69i	0.119285	+	0.206607i
$603$		0			0
$604$	11827.4	−	6828.53i	0.796770	−	0.460015i
$605$	−768.497	+	443.692i	−0.0516427	+	0.0298159i
$606$		0			0
$607$	−5194.06	−	8996.38i	−0.347315	−	0.601568i	0.638456	−	0.769658i	$-0.279573\pi$
$607$	−5194.06	−	8996.38i	−0.347315	−	0.601568i	−0.985772	+	0.168090i	$0.946240\pi$
$608$	−13142.8	+	22764.1i	−0.876665	+	1.51843i
$609$		0			0
$610$	8819.40			0.585389
$611$	−21400.8	−	11466.3i	−1.41699	−	0.759209i
$612$		0			0
$613$	−696.701	−	402.240i	−0.0459045	−	0.0265030i	0.476872	−	0.878973i	$-0.341770\pi$
$613$	−696.701	−	402.240i	−0.0459045	−	0.0265030i	−0.522777	+	0.852470i	$0.675104\pi$
$614$	14485.0	−	25088.8i	0.952064	−	1.64902i
$615$		0			0
$616$			888.671i			0.0581259i
$617$	13179.4	−	7609.13i	0.859940	−	0.496486i	−0.00405239	−	0.999992i	$-0.501290\pi$
$617$	13179.4	−	7609.13i	0.859940	−	0.496486i	0.863992	+	0.503505i	$0.167957\pi$
$618$		0			0
$619$		−	11462.5i		−	0.744291i	−0.928174	−	0.372145i	$-0.878622\pi$
$619$		−	11462.5i		−	0.744291i	0.928174	−	0.372145i	$-0.121378\pi$
$620$	522.527	+	905.044i	0.0338471	+	0.0586249i
$621$		0			0
$622$	4046.36	+	2336.17i	0.260843	+	0.150598i
$623$	−7154.66			−0.460105
$624$		0			0
$625$	12223.0			0.782270
$626$	18874.6	+	10897.3i	1.20508	+	0.695754i
$627$		0			0
$628$	6525.70	+	11302.8i	0.414656	+	0.718205i
$629$			9453.14i			0.599239i
$630$		0			0
$631$	−3869.99	+	2234.34i	−0.244155	+	0.140963i	−0.617085	−	0.786896i	$-0.711687\pi$
$631$	−3869.99	+	2234.34i	−0.244155	+	0.140963i	0.372930	+	0.927860i	$0.378353\pi$
$632$		−	3718.30i		−	0.234028i
$633$		0			0
$634$	−9858.67	+	17075.7i	−0.617568	+	1.06966i
$635$	6590.77	+	3805.18i	0.411885	+	0.237802i
$636$		0			0
$637$	−7372.48	−	11882.2i	−0.458569	−	0.739074i
$638$	−21290.0			−1.32113
$639$		0			0
$640$	−798.558	+	1383.14i	−0.0493215	+	0.0854274i
$641$	−3071.18	−	5319.44i	−0.189242	−	0.327777i	0.755756	−	0.654854i	$-0.227270\pi$
$641$	−3071.18	−	5319.44i	−0.189242	−	0.327777i	−0.944998	+	0.327077i	$0.893936\pi$
$642$		0			0
$643$	−17959.8	+	10369.1i	−1.10150	+	0.635951i	−0.936615	−	0.350361i	$-0.886059\pi$
$643$	−17959.8	+	10369.1i	−1.10150	+	0.635951i	−0.164886	+	0.986313i	$0.552726\pi$
$644$	−6198.27	+	3578.58i	−0.379264	+	0.218968i
$645$		0			0
$646$	−6020.37	−	10427.6i	−0.366669	−	0.635090i
$647$	−426.379	+	738.509i	−0.0259083	+	0.0448745i	−0.878689	−	0.477395i	$-0.841581\pi$
$647$	−426.379	+	738.509i	−0.0259083	+	0.0448745i	0.852781	+	0.522269i	$0.174914\pi$
$648$		0			0
$649$	−21172.8			−1.28060
$650$	18999.5	−	11788.5i	1.14649	−	0.711357i
$651$		0			0
$652$	18256.9	+	10540.6i	1.09662	+	0.633133i
$653$	−3672.88	+	6361.61i	−0.220108	+	0.381239i	−0.954841	−	0.297118i	$-0.903974\pi$
$653$	−3672.88	+	6361.61i	−0.220108	+	0.381239i	0.734732	+	0.678357i	$0.237308\pi$
$654$		0			0
$655$			133.462i			0.00796151i
$656$	−2671.39	+	1542.33i	−0.158994	+	0.0917954i
$657$		0			0
$658$			14273.4i			0.845645i
$659$	6270.33	+	10860.5i	0.370648	+	0.641982i	0.989665	−	0.143396i	$-0.0458022\pi$
$659$	6270.33	+	10860.5i	0.370648	+	0.641982i	−0.619017	+	0.785378i	$0.712469\pi$
$660$		0			0
$661$	1942.45	+	1121.48i	0.114301	+	0.0659915i	0.556060	−	0.831142i	$-0.312312\pi$
$661$	1942.45	+	1121.48i	0.114301	+	0.0659915i	−0.441760	+	0.897133i	$0.645646\pi$
$662$	35747.3			2.09873
$663$		0			0
$664$	2832.97			0.165573
$665$	1786.41	+	1031.38i	0.104171	+	0.0601433i
$666$		0			0
$667$	−9525.83	−	16499.2i	−0.552986	−	0.957800i
$668$		−	360.658i		−	0.0208896i
$669$		0			0
$670$	622.687	−	359.508i	0.0359052	−	0.0207299i
$671$		−	22617.0i		−	1.30122i
$672$		0			0
$673$	−2388.23	+	4136.53i	−0.136790	+	0.236927i	−0.926280	−	0.376837i	$-0.877012\pi$
$673$	−2388.23	+	4136.53i	−0.136790	+	0.236927i	0.789490	+	0.613763i	$0.210345\pi$
$674$	30446.0	+	17578.0i	1.73997	+	1.00457i
$675$		0			0
$676$	8780.58	−	17716.5i	0.499578	−	1.00799i
$677$	7933.57			0.450387			0.225193	−	0.974314i	$-0.427699\pi$
$677$	7933.57			0.450387			0.225193	+	0.974314i	$0.427699\pi$
$678$		0			0
$679$	5862.82	−	10154.7i	0.331361	−	0.573935i
$680$	−181.459	−	314.295i	−0.0102333	−	0.0177245i
$681$		0			0
$682$	4384.02	−	2531.12i	0.246148	−	0.142114i
$683$	−20415.5	+	11786.9i	−1.14374	+	0.660340i	−0.947355	−	0.320186i	$-0.896255\pi$
$683$	−20415.5	+	11786.9i	−1.14374	+	0.660340i	−0.196388	+	0.980526i	$0.562921\pi$
$684$		0			0
$685$	−314.452	−	544.647i	−0.0175396	−	0.0303794i
$686$	−8836.21	+	15304.8i	−0.491790	+	0.851806i
$687$		0			0
$688$	7033.32			0.389743
$689$	−15396.9	+	28736.9i	−0.851343	+	1.58895i
$690$		0			0
$691$	−10863.2	−	6271.89i	−0.598056	−	0.345288i	0.170221	−	0.985406i	$-0.445552\pi$
$691$	−10863.2	−	6271.89i	−0.598056	−	0.345288i	−0.768276	+	0.640118i	$0.778885\pi$
$692$	8592.93	−	14883.4i	0.472044	−	0.817604i
$693$		0			0
$694$			51874.8i			2.83738i
$695$	264.143	−	152.503i	0.0144166	−	0.00832340i
$696$		0			0
$697$		−	1618.52i		−	0.0879568i
$698$	−18473.9	−	31997.8i	−1.00179	−	1.73515i
$699$		0			0
$700$	−6026.75	−	3479.54i	−0.325414	−	0.187878i
$701$	−581.786			−0.0313463			−0.0156731	−	0.999877i	$-0.504989\pi$
$701$	−581.786			−0.0313463			−0.0156731	+	0.999877i	$0.504989\pi$
$702$		0			0
$703$	33147.9			1.77837
$704$	17623.4	+	10174.9i	0.943475	+	0.544715i
$705$		0			0
$706$	−11045.8	−	19131.9i	−0.588830	−	1.01988i
$707$			4282.89i			0.227828i
$708$		0			0
$709$	−17963.1	+	10371.0i	−0.951507	+	0.549353i	−0.893549	−	0.448966i	$-0.851792\pi$
$709$	−17963.1	+	10371.0i	−0.951507	+	0.549353i	−0.0579583	+	0.998319i	$0.518459\pi$
$710$			3888.74i			0.205552i
$711$		0			0
$712$	2206.97	−	3822.58i	0.116165	−	0.201204i
$713$	3923.10	+	2265.00i	0.206061	+	0.118969i
$714$		0			0
$715$	2430.79	+	3917.70i	0.127142	+	0.204914i
$716$	4589.63			0.239556
$717$		0			0
$718$	5577.32	−	9660.21i	0.289894	−	0.502111i
$719$	−12675.1	−	21953.9i	−0.657443	−	1.13872i	−0.981275	−	0.192610i	$-0.938305\pi$
$719$	−12675.1	−	21953.9i	−0.657443	−	1.13872i	0.323832	−	0.946114i	$-0.395029\pi$
$720$		0			0
$721$	−4011.87	+	2316.25i	−0.207226	+	0.119642i
$722$	−12073.3	+	6970.50i	−0.622328	+	0.359301i
$723$		0			0
$724$	9615.97	+	16655.3i	0.493611	+	0.854960i
$725$	9262.22	−	16042.6i	0.474469	−	0.821805i
$726$		0			0
$727$	−33428.2			−1.70534			−0.852672	−	0.522447i	$-0.825019\pi$
$727$	−33428.2			−1.70534			−0.852672	+	0.522447i	$0.825019\pi$
$728$	−1290.95	+	40.9778i	−0.0657220	+	0.00208618i
$729$		0			0
$730$	4244.30	+	2450.45i	0.215190	+	0.124240i
$731$	−1845.20	+	3195.97i	−0.0933612	+	0.161706i
$732$		0			0
$733$			3842.67i			0.193632i	0.995302	+	0.0968160i	$0.0308658\pi$
$733$			3842.67i			0.193632i	−0.995302	+	0.0968160i	$0.969134\pi$
$734$	37398.8	−	21592.2i	1.88067	−	1.08581i
$735$		0			0
$736$			30908.3i			1.54796i
$737$	−921.946	−	1596.86i	−0.0460791	−	0.0798114i
$738$		0			0
$739$	−25140.4	−	14514.8i	−1.25143	−	0.722511i	−0.280034	−	0.959990i	$-0.590346\pi$
$739$	−25140.4	−	14514.8i	−1.25143	−	0.722511i	−0.971393	+	0.237479i	$0.923679\pi$
$740$	8991.91			0.446688
$741$		0			0
$742$	19166.3			0.948269
$743$	30308.0	+	17498.3i	1.49649	+	0.864000i	0.999992	−	0.00403656i	$-0.00128488\pi$
$743$	30308.0	+	17498.3i	1.49649	+	0.864000i	0.496500	+	0.868037i	$0.334618\pi$
$744$		0			0
$745$	−580.199	−	1004.93i	−0.0285327	−	0.0494200i
$746$		−	52623.2i		−	2.58267i
$747$		0			0
$748$	−7253.99	+	4188.10i	−0.354589	+	0.204722i
$749$		−	2711.23i		−	0.132265i
$750$		0			0
$751$	5227.06	−	9053.52i	0.253979	−	0.439904i	−0.710639	−	0.703557i	$-0.751594\pi$
$751$	5227.06	−	9053.52i	0.253979	−	0.439904i	0.964618	+	0.263653i	$0.0849274\pi$
$752$	24672.3	+	14244.5i	1.19642	+	0.690751i
$753$		0			0
$754$	−981.712	−	30927.4i	−0.0474162	−	1.49378i
$755$	−4628.32			−0.223102
$756$		0			0
$757$	14065.2	−	24361.6i	0.675308	−	1.16967i	−0.301071	−	0.953602i	$-0.597344\pi$
$757$	14065.2	−	24361.6i	0.675308	−	1.16967i	0.976379	−	0.216065i	$-0.0693225\pi$
$758$	4778.73	+	8277.00i	0.228986	+	0.396615i
$759$		0			0
$760$	−1102.09	+	636.292i	−0.0526014	+	0.0303694i
$761$	−18261.9	+	10543.5i	−0.869899	+	0.502236i	−0.867315	−	0.497761i	$-0.834156\pi$
$761$	−18261.9	+	10543.5i	−0.869899	+	0.502236i	−0.00258400	+	0.999997i	$0.500823\pi$
$762$		0			0
$763$	−1602.36	−	2775.37i	−0.0760280	−	0.131684i
$764$	−18259.8	+	31627.0i	−0.864683	+	1.49768i
$765$		0			0
$766$	−8177.54			−0.385727
$767$	−976.309	−	30757.2i	−0.0459615	−	1.44795i
$768$		0			0
$769$	16911.7	+	9763.96i	0.793044	+	0.457864i	0.841033	−	0.540984i	$-0.181948\pi$
$769$	16911.7	+	9763.96i	0.793044	+	0.457864i	−0.0479893	+	0.998848i	$0.515281\pi$
$770$	1355.25	−	2347.36i	0.0634283	−	0.109861i
$771$		0			0
$772$		−	7860.55i		−	0.366460i
$773$	−25419.6	+	14676.0i	−1.18277	+	0.682870i	−0.956653	−	0.291231i	$-0.905935\pi$
$773$	−25419.6	+	14676.0i	−1.18277	+	0.682870i	−0.226113	+	0.974101i	$0.572602\pi$
$774$		0			0
$775$			4404.64i			0.204154i
$776$	3616.96	+	6264.76i	0.167321	+	0.289809i
$777$		0			0
$778$	11585.2	+	6688.73i	0.533869	+	0.308229i
$779$	−5675.42			−0.261031
$780$		0			0
$781$	9972.54			0.456908
$782$	−12261.4	−	7079.13i	−0.560700	−	0.323720i
$783$		0			0
$784$	8204.19	+	14210.1i	0.373733	+	0.647325i
$785$		−	4423.06i		−	0.201103i
$786$		0			0
$787$	3865.18	−	2231.56i	0.175068	−	0.101076i	−0.409905	−	0.912128i	$-0.634438\pi$
$787$	3865.18	−	2231.56i	0.175068	−	0.101076i	0.584974	+	0.811052i	$0.301105\pi$
$788$		−	37325.2i		−	1.68738i
$789$		0			0
$790$	−5670.52	+	9821.62i	−0.255377	+	0.442326i
$791$	8955.00	+	5170.17i	0.402532	+	0.232402i
$792$		0			0
$793$	32855.1	−	1042.90i	1.47127	−	0.0467018i
$794$	−15501.7			−0.692866
$795$		0			0
$796$	10818.3	−	18737.8i	0.481713	−	0.834352i
$797$	17392.7	+	30125.1i	0.773002	+	1.33888i	0.935911	+	0.352237i	$0.114579\pi$
$797$	17392.7	+	30125.1i	0.773002	+	1.33888i	−0.162909	+	0.986641i	$0.552088\pi$
$798$		0			0
$799$	−12945.6	+	7474.12i	−0.573193	+	0.330933i
$800$	−26026.6	+	15026.5i	−1.15023	+	0.664083i
$801$		0			0
$802$	4118.05	+	7132.66i	0.181313	+	0.314044i
$803$	6284.09	−	10884.4i	0.276165	−	0.478332i
$804$		0			0
$805$	2425.53			0.106197
$806$	3879.03	+	6251.82i	0.169520	+	0.273215i
$807$		0			0
$808$	−2288.26	−	1321.13i	−0.0996294	−	0.0575211i
$809$	−5309.98	+	9197.15i	−0.230765	+	0.399697i	−0.958033	−	0.286656i	$-0.907456\pi$
$809$	−5309.98	+	9197.15i	−0.230765	+	0.399697i	0.727268	+	0.686353i	$0.240790\pi$
$810$		0			0
$811$		−	5497.87i		−	0.238047i	−0.992891	−	0.119024i	$-0.962024\pi$
$811$		−	5497.87i		−	0.238047i	0.992891	−	0.119024i	$-0.0379764\pi$
$812$	−8340.32	+	4815.29i	−0.360453	+	0.208108i
$813$		0			0
$814$		−	43556.7i		−	1.87551i
$815$	−3572.17	−	6187.18i	−0.153531	−	0.265923i
$816$		0			0
$817$	11206.8	+	6470.26i	0.479898	+	0.277070i
$818$	−21420.5			−0.915587
$819$		0			0
$820$	−1539.55			−0.0655653
$821$	−18451.0	−	10652.7i	−0.784340	−	0.452839i	0.0536261	−	0.998561i	$-0.482922\pi$
$821$	−18451.0	−	10652.7i	−0.784340	−	0.452839i	−0.837966	+	0.545722i	$0.816255\pi$
$822$		0			0
$823$	8671.28	+	15019.1i	0.367268	+	0.636127i	0.989137	−	0.146994i	$-0.0469597\pi$
$823$	8671.28	+	15019.1i	0.367268	+	0.636127i	−0.621869	+	0.783121i	$0.713626\pi$
$824$		−	2857.94i		−	0.120827i
$825$		0			0
$826$	−15667.2	+	9045.48i	−0.659967	+	0.381032i
$827$		−	5129.96i		−	0.215703i	−0.994167	−	0.107851i	$-0.965603\pi$
$827$		−	5129.96i		−	0.215703i	0.994167	−	0.107851i	$-0.0343971\pi$
$828$		0			0
$829$	−4235.90	+	7336.80i	−0.177466	+	0.307380i	−0.941012	−	0.338374i	$-0.890123\pi$
$829$	−4235.90	+	7336.80i	−0.177466	+	0.307380i	0.763546	+	0.645753i	$0.223457\pi$
$830$	−7483.08	−	4320.36i	−0.312942	−	0.180677i
$831$		0			0
$832$	−13968.1	+	26070.1i	−0.582039	+	1.08632i
$833$	−8609.50			−0.358105
$834$		0			0
$835$	−61.1126	+	105.850i	−0.00253280	+	0.00438694i
$836$	14685.7	+	25436.4i	0.607556	+	1.05232i
$837$		0			0
$838$	24359.8	−	14064.1i	1.00417	−	0.579758i
$839$	16588.8	−	9577.52i	0.682607	−	0.394103i	−0.118230	−	0.992986i	$-0.537722\pi$
$839$	16588.8	−	9577.52i	0.682607	−	0.394103i	0.800837	+	0.598883i	$0.204389\pi$
$840$		0			0
$841$	−623.334	−	1079.65i	−0.0255580	−	0.0442678i
$842$	−15539.4	+	26915.0i	−0.636012	+	1.10160i
$843$		0			0
$844$	−34819.7			−1.42007
$845$	−5579.04	+	3711.79i	−0.227130	+	0.151112i
$846$		0			0
$847$	1683.92	+	972.211i	0.0683119	+	0.0394399i
$848$	19127.5	−	33129.8i	0.774577	−	1.34161i
$849$		0			0
$850$		−	13766.4i		−	0.555512i
$851$	33755.3	−	19488.7i	1.35972	−	0.785032i
$852$		0			0
$853$		−	18075.1i		−	0.725532i	−0.931880	−	0.362766i	$-0.881832\pi$
$853$		−	18075.1i		−	0.725532i	0.931880	−	0.362766i	$-0.118168\pi$
$854$	−9662.47	−	16735.9i	−0.387170	−	0.670598i
$855$		0			0
$856$	1448.55	+	836.322i	0.0578394	+	0.0333936i
$857$	−21054.6			−0.839219			−0.419609	−	0.907705i	$-0.637833\pi$
$857$	−21054.6			−0.839219			−0.419609	+	0.907705i	$0.637833\pi$
$858$		0			0
$859$	920.322			0.0365553			0.0182776	−	0.999833i	$-0.494182\pi$
$859$	920.322			0.0365553			0.0182776	+	0.999833i	$0.494182\pi$
$860$	3040.04	+	1755.17i	0.120540	+	0.0695938i
$861$		0			0
$862$	−27633.5	−	47862.6i	−1.09188	−	1.89119i
$863$		−	19427.5i		−	0.766304i	−0.923685	−	0.383152i	$-0.874839\pi$
$863$		−	19427.5i		−	0.766304i	0.923685	−	0.383152i	$-0.125161\pi$
$864$		0			0
$865$	−5043.91	+	2912.10i	−0.198264	+	0.114468i
$866$			73044.7i			2.86623i
$867$		0			0
$868$	1144.95	−	1983.12i	0.0447722	−	0.0775477i
$869$	25187.2	+	14541.8i	0.983218	+	0.567661i
$870$		0			0
$871$	2277.19	−	1412.92i	0.0885876	−	0.0549654i
$872$	1977.09			0.0767808
$873$		0			0
$874$	−24823.3	+	42995.2i	−0.960709	+	1.66400i
$875$	2453.22	+	4249.10i	0.0947816	+	0.164167i
$876$		0			0
$877$	−12879.7	+	7436.09i	−0.495914	+	0.286316i	−0.727024	−	0.686612i	$-0.759097\pi$
$877$	−12879.7	+	7436.09i	−0.495914	+	0.286316i	0.231111	+	0.972927i	$0.425764\pi$
$878$	−25578.7	+	14767.9i	−0.983188	+	0.567644i
$879$		0			0
$880$	−2705.02	−	4685.23i	−0.103621	−	0.179476i
$881$	6470.30	−	11206.9i	0.247435	−	0.428570i	−0.715379	−	0.698737i	$-0.753746\pi$
$881$	6470.30	−	11206.9i	0.247435	−	0.428570i	0.962813	+	0.270167i	$0.0870791\pi$
$882$		0			0
$883$	25585.5			0.975108			0.487554	−	0.873093i	$-0.337889\pi$
$883$	25585.5			0.975108			0.487554	+	0.873093i	$0.337889\pi$
$884$	−6418.41	−	10344.5i	−0.244202	−	0.393580i
$885$		0			0
$886$	−36311.4	−	20964.4i	−1.37687	−	0.794935i
$887$	1858.23	−	3218.55i	0.0703418	−	0.121836i	−0.828709	−	0.559679i	$-0.810924\pi$
$887$	1858.23	−	3218.55i	0.0703418	−	0.121836i	0.899051	+	0.437844i	$0.144258\pi$
$888$		0			0
$889$		−	16675.7i		−	0.629118i
$890$	−11659.1	+	6731.39i	−0.439117	+	0.253524i
$891$		0			0
$892$			25322.0i			0.950496i
$893$	26208.3	+	45394.2i	0.982115	+	1.70107i
$894$		0			0
$895$	−1347.02	−	777.702i	−0.0503082	−	0.0290455i
$896$	3499.58			0.130483
$897$		0			0
$898$	−70680.3			−2.62654
$899$	5278.87	+	3047.76i	0.195840	+	0.113068i
$900$		0			0
$901$	10036.2	+	17383.3i	0.371093	+	0.642753i
$902$			7457.57i			0.275288i
$903$		0			0
$904$	−5524.62	+	3189.64i	−0.203259	+	0.117352i
$905$		−	6517.61i		−	0.239395i
$906$		0			0
$907$	−6480.21	+	11224.0i	−0.237235	+	0.410902i	−0.959920	−	0.280275i	$-0.909574\pi$
$907$	−6480.21	+	11224.0i	−0.237235	+	0.410902i	0.722685	+	0.691177i	$0.242908\pi$
$908$	−35217.2	−	20332.7i	−1.28714	−	0.743131i
$909$		0			0
$910$	3472.43	+	1860.49i	0.126495	+	0.0677743i
$911$	36607.1			1.33134			0.665668	−	0.746248i	$-0.268147\pi$
$911$	36607.1			1.33134			0.665668	+	0.746248i	$0.268147\pi$
$912$		0			0
$913$	−11079.4	+	19190.1i	−0.401615	+	0.695618i
$914$	−29049.6	−	50315.5i	−1.05129	−	1.82088i
$915$		0			0
$916$	10173.6	−	5873.71i	0.366969	−	0.211870i
$917$	253.260	−	146.220i	0.00912038	−	0.00526565i
$918$		0			0
$919$	−10178.1	−	17629.0i	−0.365338	−	0.632784i	0.623492	−	0.781830i	$-0.285713\pi$
$919$	−10178.1	−	17629.0i	−0.365338	−	0.632784i	−0.988830	+	0.149045i	$0.952380\pi$
$920$	−748.192	+	1295.91i	−0.0268121	+	0.0464400i
$921$		0			0
$922$	12048.6			0.430370
$923$	459.847	+	14486.8i	0.0163988	+	0.516619i
$924$		0			0
$925$	32821.2	+	18949.3i	1.16665	+	0.673568i
$926$	−4272.80	+	7400.71i	−0.151634	+	0.262638i
$927$		0			0
$928$			41589.8i			1.47118i
$929$	−39031.5	+	22534.8i	−1.37845	+	0.795849i	−0.991973	−	0.126449i	$-0.959642\pi$
$929$	−39031.5	+	22534.8i	−1.37845	+	0.795849i	−0.386478	+	0.922298i	$0.626309\pi$
$930$		0			0
$931$			30189.6i			1.06275i
$932$	−15122.5	−	26192.9i	−0.531495	−	0.920576i
$933$		0			0
$934$	9513.07	+	5492.37i	0.333273	+	0.192415i
$935$	2838.65			0.0992876
$936$		0			0
$937$	−6771.10			−0.236075			−0.118037	−	0.993009i	$-0.537660\pi$
$937$	−6771.10			−0.236075			−0.118037	+	0.993009i	$0.537660\pi$
$938$	−1364.42	−	787.749i	−0.0474946	−	0.0274210i
$939$		0			0
$940$	7109.45	+	12313.9i	0.246686	+	0.427273i
$941$			36690.7i			1.27108i	0.772070	+	0.635538i	$0.219222\pi$
$941$			36690.7i			1.27108i	−0.772070	+	0.635538i	$0.780778\pi$
$942$		0			0
$943$	−5779.43	+	3336.76i	−0.199580	+	0.115228i
$944$			36108.8i			1.24496i
$945$		0			0
$946$	8502.01	−	14725.9i	0.292203	−	0.506111i
$947$	−44047.1	−	25430.6i	−1.51145	−	0.872634i	−0.999911	−	0.0133718i	$-0.995744\pi$
$947$	−44047.1	−	25430.6i	−1.51145	−	0.872634i	−0.511536	−	0.859262i	$-0.670923\pi$
$948$		0			0
$949$	16101.2	+	8626.82i	0.550754	+	0.295088i
$950$	−48272.6			−1.64860
$951$		0			0
$952$	−397.609	+	688.679i	−0.0135363	+	0.0234456i
$953$	−5927.79	−	10267.2i	−0.201490	−	0.348991i	0.747519	−	0.664241i	$-0.231245\pi$
$953$	−5927.79	−	10267.2i	−0.201490	−	0.348991i	−0.949009	+	0.315250i	$0.897912\pi$
$954$		0			0
$955$	10718.2	−	6188.18i	0.363177	−	0.209680i
$956$	36922.6	−	21317.3i	1.24912	−	0.721181i
$957$		0			0
$958$	10762.7	+	18641.6i	0.362973	+	0.628688i
$959$	−689.022	+	1193.42i	−0.0232009	+	0.0401852i
$960$		0			0
$961$	28341.6			0.951349
$962$	63273.5	−	2008.46i	2.12060	−	0.0673132i
$963$		0			0
$964$	37297.5	+	21533.7i	1.24613	+	0.719455i
$965$	−1331.95	+	2307.01i	−0.0444322	+	0.0769588i
$966$		0			0
$967$		−	40661.7i		−	1.35221i	−0.736803	−	0.676107i	$-0.763666\pi$
$967$		−	40661.7i		−	1.35221i	0.736803	−	0.676107i	$-0.236334\pi$
$968$	−1038.86	+	599.788i	−0.0344942	+	0.0199152i
$969$		0			0
$970$		−	22063.9i		−	0.730339i
$971$	28659.1	+	49639.1i	0.947184	+	1.64057i	0.751318	+	0.659940i	$0.229418\pi$
$971$	28659.1	+	49639.1i	0.947184	+	1.64057i	0.195866	+	0.980631i	$0.437248\pi$
$972$		0			0
$973$	−578.786	−	334.162i	−0.0190699	−	0.0110100i
$974$	−50403.3			−1.65814
$975$		0			0
$976$	−38571.7			−1.26501
$977$	2621.23	+	1513.37i	0.0858347	+	0.0495567i	0.542303	−	0.840183i	$-0.317552\pi$
$977$	2621.23	+	1513.37i	0.0858347	+	0.0495567i	−0.456468	+	0.889740i	$0.650886\pi$
$978$		0			0
$979$	17262.4	+	29899.4i	0.563543	+	0.976085i
$980$			8189.43i			0.266941i
$981$		0			0
$982$	70176.0	−	40516.1i	2.28045	−	1.31662i
$983$		−	33942.5i		−	1.10132i	−0.834730	−	0.550659i	$-0.814376\pi$
$983$		−	33942.5i		−	1.10132i	0.834730	−	0.550659i	$-0.185624\pi$
$984$		0			0
$985$	−6324.67	+	10954.7i	−0.204590	+	0.354360i
$986$	−16498.8	−	9525.58i	−0.532889	−	0.307664i
$987$		0			0
$988$	−36273.6	+	22506.4i	−1.16803	+	0.724722i
$989$	15216.3			0.489231
$990$		0			0
$991$	−10818.7	+	18738.6i	−0.346790	+	0.600658i	−0.985677	−	0.168642i	$-0.946062\pi$
$991$	−10818.7	+	18738.6i	−0.346790	+	0.600658i	0.638887	+	0.769300i	$0.279395\pi$
$992$	−4944.51	−	8564.14i	−0.158254	−	0.274105i
$993$		0			0
$994$	7379.36	−	4260.48i	0.235472	−	0.135950i
$995$	−6350.16	+	3666.26i	−0.202325	+	0.116812i
$996$		0			0
$997$	−9812.31	−	16995.4i	−0.311694	−	0.539870i	0.667035	−	0.745026i	$-0.267563\pi$
$997$	−9812.31	−	16995.4i	−0.311694	−	0.539870i	−0.978729	+	0.205156i	$0.934230\pi$
$998$	24148.1	−	41825.8i	0.765928	−	1.32663i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.d.82.1		4
3.2	odd	2		39.4.j.b.4.2	✓	4
12.11	even	2		624.4.bv.c.433.2		4
13.6	odd	12		1521.4.a.z.1.4		4
13.7	odd	12		1521.4.a.z.1.1		4
13.10	even	6	inner	117.4.q.d.10.1		4
39.17	odd	6		507.4.b.e.337.4		4
39.20	even	12		507.4.a.k.1.4		4
39.23	odd	6		39.4.j.b.10.2	yes	4
39.32	even	12		507.4.a.k.1.1		4
39.35	odd	6		507.4.b.e.337.1		4
156.23	even	6		624.4.bv.c.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.b.4.2	✓	4	3.2	odd	2
39.4.j.b.10.2	yes	4	39.23	odd	6
117.4.q.d.10.1		4	13.10	even	6	inner
117.4.q.d.82.1		4	1.1	even	1	trivial
507.4.a.k.1.1		4	39.32	even	12
507.4.a.k.1.4		4	39.20	even	12
507.4.b.e.337.1		4	39.35	odd	6
507.4.b.e.337.4		4	39.17	odd	6
624.4.bv.c.49.1		4	156.23	even	6
624.4.bv.c.433.2		4	12.11	even	2
1521.4.a.z.1.1		4	13.7	odd	12
1521.4.a.z.1.4		4	13.6	odd	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)

\(f(q)\)	\(=\)	\(q+(-3.57071 - 2.06155i) q^{2} +(4.50000 + 7.79423i) q^{4} -3.05006i q^{5} +(-5.78786 + 3.34162i) q^{7} -4.12311i q^{8} +O(q^{10})\)	\(q+(-3.57071 - 2.06155i) q^{2} +(4.50000 + 7.79423i) q^{4} -3.05006i q^{5} +(-5.78786 + 3.34162i) q^{7} -4.12311i q^{8} +(-6.28786 + 10.8909i) q^{10} +(27.9293 + 16.1250i) q^{11} +(-22.1364 + 41.3156i) q^{13} +27.5557 q^{14} +(27.5000 - 47.6314i) q^{16} +(14.4293 + 24.9923i) q^{17} +(87.6364 - 50.5969i) q^{19} +(23.7729 - 13.7253i) q^{20} +(-66.4850 - 115.155i) q^{22} +(59.4950 - 103.048i) q^{23} +115.697 q^{25} +(164.217 - 101.891i) q^{26} +(-52.0907 - 30.0746i) q^{28} +(80.0557 - 138.661i) q^{29} +38.0705i q^{31} +(-224.955 + 129.878i) q^{32} -118.987i q^{34} +(10.1921 + 17.6533i) q^{35} +(283.682 + 163.784i) q^{37} -417.233 q^{38} -12.5757 q^{40} +(-48.5707 - 28.0423i) q^{41} +(63.9393 + 110.746i) q^{43} +290.250i q^{44} +(-424.879 + 245.304i) q^{46} +517.983i q^{47} +(-149.167 + 258.365i) q^{49} +(-413.121 - 238.516i) q^{50} +(-421.637 + 13.3838i) q^{52} +695.546 q^{53} +(49.1821 - 85.1860i) q^{55} +(13.7779 + 23.8639i) q^{56} +(-571.712 + 330.078i) q^{58} +(-568.566 + 328.262i) q^{59} +(-350.652 - 607.347i) q^{61} +(78.4843 - 135.939i) q^{62} +631.000 q^{64} +(126.015 + 67.5174i) q^{65} +(-49.5150 - 28.5875i) q^{67} +(-129.864 + 224.930i) q^{68} -84.0465i q^{70} +(267.798 - 154.613i) q^{71} -389.711i q^{73} +(-675.299 - 1169.65i) q^{74} +(788.728 + 455.372i) q^{76} -215.534 q^{77} +901.820 q^{79} +(-145.279 - 83.8766i) q^{80} +(115.621 + 200.262i) q^{82} +687.095i q^{83} +(76.2279 - 44.0102i) q^{85} -527.257i q^{86} +(66.4850 - 115.155i) q^{88} +(927.113 + 535.269i) q^{89} +(-9.93858 - 313.100i) q^{91} +1070.91 q^{92} +(1067.85 - 1849.57i) q^{94} +(-154.324 - 267.296i) q^{95} +(-1519.43 + 877.242i) q^{97} +(1065.27 - 615.032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{4} - 66 q^{7}+O(q^{10}) \) 4 * q + 18 * q^4 - 66 * q^7	\( 4 q + 18 q^{4} - 66 q^{7} - 68 q^{10} + 126 q^{11} + 40 q^{13} - 204 q^{14} + 110 q^{16} + 72 q^{17} + 222 q^{19} - 162 q^{20} + 34 q^{22} + 138 q^{23} + 120 q^{25} + 714 q^{26} - 594 q^{28} + 6 q^{29} - 402 q^{35} + 492 q^{37} - 612 q^{38} - 136 q^{40} - 180 q^{41} + 470 q^{43} - 714 q^{46} + 346 q^{49} - 1224 q^{50} - 144 q^{52} + 2268 q^{53} - 446 q^{55} - 102 q^{56} - 2244 q^{58} - 2160 q^{59} - 160 q^{61} + 1428 q^{62} + 2524 q^{64} + 804 q^{65} - 498 q^{67} - 648 q^{68} + 1314 q^{71} - 1530 q^{74} + 1998 q^{76} - 2976 q^{77} + 8 q^{79} + 990 q^{80} + 34 q^{82} - 852 q^{85} - 34 q^{88} + 252 q^{89} - 1668 q^{91} + 2484 q^{92} + 2686 q^{94} + 54 q^{95} - 336 q^{97} + 6732 q^{98}+O(q^{100}) \) 4 * q + 18 * q^4 - 66 * q^7 - 68 * q^10 + 126 * q^11 + 40 * q^13 - 204 * q^14 + 110 * q^16 + 72 * q^17 + 222 * q^19 - 162 * q^20 + 34 * q^22 + 138 * q^23 + 120 * q^25 + 714 * q^26 - 594 * q^28 + 6 * q^29 - 402 * q^35 + 492 * q^37 - 612 * q^38 - 136 * q^40 - 180 * q^41 + 470 * q^43 - 714 * q^46 + 346 * q^49 - 1224 * q^50 - 144 * q^52 + 2268 * q^53 - 446 * q^55 - 102 * q^56 - 2244 * q^58 - 2160 * q^59 - 160 * q^61 + 1428 * q^62 + 2524 * q^64 + 804 * q^65 - 498 * q^67 - 648 * q^68 + 1314 * q^71 - 1530 * q^74 + 1998 * q^76 - 2976 * q^77 + 8 * q^79 + 990 * q^80 + 34 * q^82 - 852 * q^85 - 34 * q^88 + 252 * q^89 - 1668 * q^91 + 2484 * q^92 + 2686 * q^94 + 54 * q^95 - 336 * q^97 + 6732 * q^98

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