LMFDB - Embedded newform 100.4.e.f.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(7,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("100.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	100.7
Dual form			100.4.e.f.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21943 - 1.75332i) q^{2} +(6.14790 + 6.14790i) q^{3} +(1.85174 + 7.78274i) q^{4} +(-2.86560 - 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(9.53582 - 20.5199i) q^{8} +48.5934i q^{9} +O(q^{10})$	\(q+(-2.21943 - 1.75332i) q^{2} +(6.14790 + 6.14790i) q^{3} +(1.85174 + 7.78274i) q^{4} +(-2.86560 - 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(9.53582 - 20.5199i) q^{8} +48.5934i q^{9} +44.6211i q^{11} +(-36.4632 + 59.2319i) q^{12} +(0.849478 - 0.849478i) q^{13} +(-65.3604 + 7.66854i) q^{14} +(-57.1421 + 28.8233i) q^{16} +(58.2897 + 58.2897i) q^{17} +(85.1997 - 107.850i) q^{18} -23.7025 q^{19} +202.293 q^{21} +(78.2350 - 99.0334i) q^{22} +(-10.9325 - 10.9325i) q^{23} +(184.780 - 67.5294i) q^{24} +(-3.37476 + 0.395951i) q^{26} +(-132.754 + 132.754i) q^{27} +(158.508 + 97.5778i) q^{28} +127.106i q^{29} -253.779i q^{31} +(177.359 + 36.2171i) q^{32} +(-274.326 + 274.326i) q^{33} +(-27.1695 - 231.571i) q^{34} +(-378.190 + 89.9824i) q^{36} +(-92.9341 - 92.9341i) q^{37} +(52.6061 + 41.5581i) q^{38} +10.4450 q^{39} +98.0252 q^{41} +(-448.975 - 354.684i) q^{42} +(-235.212 - 235.212i) q^{43} +(-347.274 + 82.6268i) q^{44} +(5.09576 + 43.4321i) q^{46} +(250.419 - 250.419i) q^{47} +(-528.507 - 174.101i) q^{48} -198.348i q^{49} +716.719i q^{51} +(8.18428 + 5.03825i) q^{52} +(-149.126 + 149.126i) q^{53} +(527.398 - 61.8781i) q^{54} +(-180.713 - 494.483i) q^{56} +(-145.721 - 145.721i) q^{57} +(222.857 - 282.103i) q^{58} -12.5393 q^{59} -332.505 q^{61} +(-444.956 + 563.246i) q^{62} +(799.467 + 799.467i) q^{63} +(-330.136 - 391.349i) q^{64} +(1089.83 - 127.866i) q^{66} +(199.472 - 199.472i) q^{67} +(-345.716 + 561.592i) q^{68} -134.424i q^{69} -664.410i q^{71} +(997.134 + 463.378i) q^{72} +(699.484 - 699.484i) q^{73} +(43.3176 + 369.204i) q^{74} +(-43.8910 - 184.471i) q^{76} +(734.114 + 734.114i) q^{77} +(-23.1820 - 18.3135i) q^{78} +703.490 q^{79} -320.295 q^{81} +(-217.560 - 171.869i) q^{82} +(-940.531 - 940.531i) q^{83} +(374.594 + 1574.39i) q^{84} +(109.635 + 934.437i) q^{86} +(-781.435 + 781.435i) q^{87} +(915.623 + 425.499i) q^{88} -386.574i q^{89} -27.9515i q^{91} +(64.8407 - 105.329i) q^{92} +(1560.21 - 1560.21i) q^{93} +(-994.852 + 116.723i) q^{94} +(867.728 + 1313.05i) q^{96} +(-1064.76 - 1064.76i) q^{97} +(-347.768 + 440.220i) q^{98} -2168.29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{6}+O(q^{10}) $ 24 * q + 36 * q^6	$ 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) $ 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.21943	−	1.75332i	−0.784687	−	0.619892i
$2$	−2.21943	−	1.75332i	−0.784687	−	0.619892i
$3$	6.14790	+	6.14790i	1.18316	+	1.18316i	0.978920	+	0.204244i	$0.0654737\pi$
$3$	6.14790	+	6.14790i	1.18316	+	1.18316i	0.204244	+	0.978920i	$0.434526\pi$
$4$	1.85174	+	7.78274i	0.231468	+	0.972843i
$5$		0			0
$5$		0			0
$6$	−2.86560	−	24.4241i	−0.194980	−	1.66185i
$7$	16.4522	−	16.4522i	0.888334	−	0.888334i	−0.106029	−	0.994363i	$-0.533814\pi$
$7$	16.4522	−	16.4522i	0.888334	−	0.888334i	0.994363	+	0.106029i	$0.0338136\pi$
$8$	9.53582	−	20.5199i	0.421427	−	0.906862i
$9$			48.5934i			1.79975i
$10$		0			0
$11$			44.6211i			1.22307i	0.791217	+	0.611535i	$0.209448\pi$
$11$			44.6211i			1.22307i	−0.791217	+	0.611535i	$0.790552\pi$
$12$	−36.4632	+	59.2319i	−0.877168	+	1.42490i
$13$	0.849478	−	0.849478i	0.0181233	−	0.0181233i	−0.697987	−	0.716110i	$-0.745921\pi$
$13$	0.849478	−	0.849478i	0.0181233	−	0.0181233i	0.716110	+	0.697987i	$0.245921\pi$
$14$	−65.3604	+	7.66854i	−1.24774	+	0.146393i
$15$		0			0
$16$	−57.1421	+	28.8233i	−0.892845	+	0.450364i
$17$	58.2897	+	58.2897i	0.831608	+	0.831608i	0.987737	−	0.156128i	$-0.0499014\pi$
$17$	58.2897	+	58.2897i	0.831608	+	0.831608i	−0.156128	+	0.987737i	$0.549901\pi$
$18$	85.1997	−	107.850i	1.11565	−	1.41224i
$19$	−23.7025			−0.286197			−0.143098	−	0.989708i	$-0.545707\pi$
$19$	−23.7025			−0.286197			−0.143098	+	0.989708i	$0.545707\pi$
$20$		0			0
$21$	202.293			2.10209
$22$	78.2350	−	99.0334i	0.758171	−	0.959727i
$23$	−10.9325	−	10.9325i	−0.0991124	−	0.0991124i	0.655812	−	0.754924i	$-0.272326\pi$
$23$	−10.9325	−	10.9325i	−0.0991124	−	0.0991124i	−0.754924	+	0.655812i	$0.772326\pi$
$24$	184.780	−	67.5294i	1.57158	−	0.574349i
$25$		0			0
$26$	−3.37476	+	0.395951i	−0.0254556	+	0.00298663i
$27$	−132.754	+	132.754i	−0.946241	+	0.946241i
$28$	158.508	+	97.5778i	1.06983	+	0.658588i
$29$			127.106i			0.813896i	0.913451	+	0.406948i	$0.133407\pi$
$29$			127.106i			0.813896i	−0.913451	+	0.406948i	$0.866593\pi$
$30$		0			0
$31$		−	253.779i		−	1.47033i	−0.677890	−	0.735163i	$-0.737106\pi$
$31$		−	253.779i		−	1.47033i	0.677890	−	0.735163i	$-0.262894\pi$
$32$	177.359	+	36.2171i	0.979781	+	0.200073i
$33$	−274.326	+	274.326i	−1.44709	+	1.44709i
$34$	−27.1695	−	231.571i	−0.137045	−	1.16806i
$35$		0			0
$36$	−378.190	+	89.9824i	−1.75088	+	0.416585i
$37$	−92.9341	−	92.9341i	−0.412926	−	0.412926i	0.469830	−	0.882757i	$-0.344315\pi$
$37$	−92.9341	−	92.9341i	−0.412926	−	0.412926i	−0.882757	+	0.469830i	$0.844315\pi$
$38$	52.6061	+	41.5581i	0.224575	+	0.177411i
$39$	10.4450			0.0428857
$40$		0			0
$41$	98.0252			0.373389			0.186695	−	0.982418i	$-0.440222\pi$
$41$	98.0252			0.373389			0.186695	+	0.982418i	$0.440222\pi$
$42$	−448.975	−	354.684i	−1.64948	−	1.30307i
$43$	−235.212	−	235.212i	−0.834173	−	0.834173i	0.153911	−	0.988085i	$-0.450813\pi$
$43$	−235.212	−	235.212i	−0.834173	−	0.834173i	−0.988085	+	0.153911i	$0.950813\pi$
$44$	−347.274	+	82.6268i	−1.18985	+	0.283101i
$45$		0			0
$46$	5.09576	+	43.4321i	0.0163332	+	0.139211i
$47$	250.419	−	250.419i	0.777178	−	0.777178i	−0.202172	−	0.979350i	$-0.564800\pi$
$47$	250.419	−	250.419i	0.777178	−	0.777178i	0.979350	+	0.202172i	$0.0648000\pi$
$48$	−528.507	−	174.101i	−1.58924	−	0.523529i
$49$		−	198.348i		−	0.578275i
$50$		0			0
$51$			716.719i			1.96786i
$52$	8.18428	+	5.03825i	0.0218261	+	0.0134362i
$53$	−149.126	+	149.126i	−0.386491	+	0.386491i	−0.873434	−	0.486943i	$-0.838112\pi$
$53$	−149.126	+	149.126i	−0.386491	+	0.386491i	0.486943	+	0.873434i	$0.338112\pi$
$54$	527.398	−	61.8781i	1.32907	−	0.155936i
$55$		0			0
$56$	−180.713	−	494.483i	−0.431228	−	1.17996i
$57$	−145.721	−	145.721i	−0.338618	−	0.338618i
$58$	222.857	−	282.103i	0.504528	−	0.638654i
$59$	−12.5393			−0.0276690			−0.0138345	−	0.999904i	$-0.504404\pi$
$59$	−12.5393			−0.0276690			−0.0138345	+	0.999904i	$0.504404\pi$
$60$		0			0
$61$	−332.505			−0.697916			−0.348958	−	0.937138i	$-0.613464\pi$
$61$	−332.505			−0.697916			−0.348958	+	0.937138i	$0.613464\pi$
$62$	−444.956	+	563.246i	−0.911444	+	1.15375i
$63$	799.467	+	799.467i	1.59878	+	1.59878i
$64$	−330.136	−	391.349i	−0.644798	−	0.764353i
$65$		0			0
$66$	1089.83	−	127.866i	2.03256	−	0.238474i
$67$	199.472	−	199.472i	0.363723	−	0.363723i	−0.501459	−	0.865182i	$-0.667203\pi$
$67$	199.472	−	199.472i	0.363723	−	0.363723i	0.865182	+	0.501459i	$0.167203\pi$
$68$	−345.716	+	561.592i	−0.616533	+	1.00151i
$69$		−	134.424i		−	0.234532i
$70$		0			0
$71$		−	664.410i		−	1.11058i	−0.831658	−	0.555288i	$-0.812608\pi$
$71$		−	664.410i		−	1.11058i	0.831658	−	0.555288i	$-0.187392\pi$
$72$	997.134	+	463.378i	1.63213	+	0.758466i
$73$	699.484	−	699.484i	1.12149	−	1.12149i	0.129967	−	0.991518i	$-0.458513\pi$
$73$	699.484	−	699.484i	1.12149	−	1.12149i	0.991518	−	0.129967i	$-0.0414871\pi$
$74$	43.3176	+	369.204i	0.0680482	+	0.579987i
$75$		0			0
$76$	−43.8910	−	184.471i	−0.0662453	−	0.278424i
$77$	734.114	+	734.114i	1.08649	+	1.08649i
$78$	−23.1820	−	18.3135i	−0.0336518	−	0.0265845i
$79$	703.490			1.00188			0.500942	−	0.865481i	$-0.332987\pi$
$79$	703.490			1.00188			0.500942	+	0.865481i	$0.332987\pi$
$80$		0			0
$81$	−320.295			−0.439363
$82$	−217.560	−	171.869i	−0.292994	−	0.231461i
$83$	−940.531	−	940.531i	−1.24382	−	1.24382i	−0.958406	−	0.285410i	$-0.907870\pi$
$83$	−940.531	−	940.531i	−1.24382	−	1.24382i	−0.285410	−	0.958406i	$-0.592130\pi$
$84$	374.594	+	1574.39i	0.486566	+	2.04500i
$85$		0			0
$86$	109.635	+	934.437i	0.137468	+	1.17166i
$87$	−781.435	+	781.435i	−0.962973	+	0.962973i
$88$	915.623	+	425.499i	1.10916	+	0.515435i
$89$		−	386.574i		−	0.460413i	−0.973142	−	0.230206i	$-0.926060\pi$
$89$		−	386.574i		−	0.460413i	0.973142	−	0.230206i	$-0.0739401\pi$
$90$		0			0
$91$		−	27.9515i		−	0.0321991i
$92$	64.8407	−	105.329i	0.0734794	−	0.119362i
$93$	1560.21	−	1560.21i	1.73964	−	1.73964i
$94$	−994.852	+	116.723i	−1.09161	+	0.128075i
$95$		0			0
$96$	867.728	+	1313.05i	0.922522	+	1.39596i
$97$	−1064.76	−	1064.76i	−1.11453	−	1.11453i	−0.992530	−	0.122005i	$-0.961068\pi$
$97$	−1064.76	−	1064.76i	−1.11453	−	1.11453i	−0.122005	−	0.992530i	$-0.538932\pi$
$98$	−347.768	+	440.220i	−0.358468	+	0.453765i
$99$	−2168.29			−2.20123
$100$		0			0
$101$	−1263.35			−1.24463			−0.622316	−	0.782766i	$-0.713808\pi$
$101$	−1263.35			−1.24463			−0.622316	+	0.782766i	$0.713808\pi$
$102$	1256.64	−	1590.71i	1.21986	−	1.54415i
$103$	228.987	+	228.987i	0.219056	+	0.219056i	0.808101	−	0.589045i	$-0.200496\pi$
$103$	228.987	+	228.987i	0.219056	+	0.219056i	−0.589045	+	0.808101i	$0.700496\pi$
$104$	−9.33078	−	25.5317i	−0.00879768	−	0.0240730i
$105$		0			0
$106$	592.440	−	69.5092i	0.542857	−	0.0636918i
$107$	−413.024	+	413.024i	−0.373164	+	0.373164i	−0.868628	−	0.495464i	$-0.834998\pi$
$107$	−413.024	+	413.024i	−0.373164	+	0.373164i	0.495464	+	0.868628i	$0.334998\pi$
$108$	−1279.02	−	787.364i	−1.13957	−	0.701519i
$109$			1424.06i			1.25138i	0.780071	+	0.625691i	$0.215183\pi$
$109$			1424.06i			1.25138i	−0.780071	+	0.625691i	$0.784817\pi$
$110$		0			0
$111$		−	1142.70i		−	0.977119i
$112$	−465.907	+	1414.32i	−0.393072	+	1.19322i
$113$	−910.839	+	910.839i	−0.758270	+	0.758270i	−0.976007	−	0.217737i	$-0.930132\pi$
$113$	−910.839	+	910.839i	−0.758270	+	0.758270i	0.217737	+	0.976007i	$0.430132\pi$
$114$	67.9221	+	578.912i	0.0558025	+	0.475615i
$115$		0			0
$116$	−989.233	+	235.368i	−0.791793	+	0.188391i
$117$	41.2790	+	41.2790i	0.0326175	+	0.0326175i
$118$	27.8300	+	21.9853i	0.0217115	+	0.0171518i
$119$	1917.99			1.47749
$120$		0			0
$121$	−660.042			−0.495900
$122$	737.971	+	582.987i	0.547646	+	0.432632i
$123$	602.649	+	602.649i	0.441781	+	0.441781i
$124$	1975.10	−	469.934i	1.43040	−	0.340333i
$125$		0			0
$126$	−372.640	−	3176.08i	−0.263472	−	2.24562i
$127$	1439.87	−	1439.87i	1.00604	−	1.00604i	0.00606278	−	0.999982i	$-0.498070\pi$
$127$	1439.87	−	1439.87i	1.00604	−	1.00604i	0.999982	−	0.00606278i	$-0.00192986\pi$
$128$	46.5554	+	1447.41i	0.0321481	+	0.999483i
$129$		−	2892.12i		−	1.97393i
$130$		0			0
$131$			1327.53i			0.885393i	0.896672	+	0.442696i	$0.145978\pi$
$131$			1327.53i			0.885393i	−0.896672	+	0.442696i	$0.854022\pi$
$132$	−2642.99	−	1627.03i	−1.74275	−	1.07284i
$133$	−389.958	+	389.958i	−0.254238	+	0.254238i
$134$	−792.454	+	92.9763i	−0.510878	+	0.0599398i
$135$		0			0
$136$	1751.94	−	640.262i	1.10462	−	0.403691i
$137$	1009.78	+	1009.78i	0.629715	+	0.629715i	0.947996	−	0.318281i	$-0.103106\pi$
$137$	1009.78	+	1009.78i	0.629715	+	0.629715i	−0.318281	+	0.947996i	$0.603106\pi$
$138$	−235.688	+	298.344i	−0.145385	+	0.184035i
$139$	1282.81			0.782782			0.391391	−	0.920224i	$-0.371994\pi$
$139$	1282.81			0.782782			0.391391	+	0.920224i	$0.371994\pi$
$140$		0			0
$141$	3079.10			1.83906
$142$	−1164.92	+	1474.61i	−0.688437	+	0.871455i
$143$	37.9047	+	37.9047i	0.0221661	+	0.0221661i
$144$	−1400.62	−	2776.73i	−0.810544	−	1.60690i
$145$		0			0
$146$	−2778.88	+	326.037i	−1.57521	+	0.184815i
$147$	1219.43	−	1219.43i	0.684194	−	0.684194i
$148$	551.192	−	895.372i	0.306133	−	0.497291i
$149$		−	94.5789i		−	0.0520014i	−0.999662	−	0.0260007i	$-0.991723\pi$
$149$		−	94.5789i		−	0.0520014i	0.999662	−	0.0260007i	$-0.00827721\pi$
$150$		0			0
$151$			2723.98i			1.46804i	0.679128	+	0.734020i	$0.262358\pi$
$151$			2723.98i			1.46804i	−0.679128	+	0.734020i	$0.737642\pi$
$152$	−226.023	+	486.375i	−0.120611	+	0.259541i
$153$	−2832.50	+	2832.50i	−1.49669	+	1.49669i
$154$	−342.179	−	2916.45i	−0.179049	−	1.52607i
$155$		0			0
$156$	19.3415	+	81.2909i	0.00992665	+	0.0417210i
$157$	−1201.75	−	1201.75i	−0.610894	−	0.610894i	0.332285	−	0.943179i	$-0.392180\pi$
$157$	−1201.75	−	1201.75i	−0.610894	−	0.610894i	−0.943179	+	0.332285i	$0.892180\pi$
$158$	−1561.35	−	1233.44i	−0.786166	−	0.621060i
$159$	−1833.62			−0.914564
$160$		0			0
$161$	−359.727			−0.176090
$162$	710.873	+	561.580i	0.344762	+	0.272357i
$163$	−336.009	−	336.009i	−0.161462	−	0.161462i	0.621752	−	0.783214i	$-0.286421\pi$
$163$	−336.009	−	336.009i	−0.161462	−	0.161462i	−0.783214	+	0.621752i	$0.786421\pi$
$164$	181.517	+	762.905i	0.0864276	+	0.363249i
$165$		0			0
$166$	438.392	+	3736.49i	0.204975	+	1.74704i
$167$	−1362.82	+	1362.82i	−0.631488	+	0.631488i	−0.948441	−	0.316953i	$-0.897340\pi$
$167$	−1362.82	+	1362.82i	−0.631488	+	0.631488i	0.316953	+	0.948441i	$0.397340\pi$
$168$	1929.03	−	4151.04i	0.885879	−	1.90631i
$169$			2195.56i			0.999343i
$170$		0			0
$171$		−	1151.79i		−	0.515084i
$172$	1395.04	−	2266.14i	0.618435	−	1.00460i
$173$	648.186	−	648.186i	0.284859	−	0.284859i	−0.550184	−	0.835043i	$-0.685442\pi$
$173$	648.186	−	648.186i	0.284859	−	0.284859i	0.835043	+	0.550184i	$0.185442\pi$
$174$	3104.45	−	364.235i	1.35257	−	0.158693i
$175$		0			0
$176$	−1286.13	−	2549.74i	−0.550826	−	1.09201i
$177$	−77.0902	−	77.0902i	−0.0327370	−	0.0327370i
$178$	−677.787	+	857.973i	−0.285406	+	0.361280i
$179$	−96.1861			−0.0401636			−0.0200818	−	0.999798i	$-0.506393\pi$
$179$	−96.1861			−0.0401636			−0.0200818	+	0.999798i	$0.506393\pi$
$180$		0			0
$181$	2470.64			1.01459			0.507297	−	0.861771i	$-0.330645\pi$
$181$	2470.64			1.01459			0.507297	+	0.861771i	$0.330645\pi$
$182$	−49.0080	+	62.0365i	−0.0199600	+	0.0252662i
$183$	−2044.21	−	2044.21i	−0.825749	−	0.825749i
$184$	−328.585	+	120.084i	−0.131650	+	0.0481126i
$185$		0			0
$186$	−6198.33	+	727.231i	−2.44346	+	0.286684i
$187$	−2600.95	+	2600.95i	−1.01711	+	1.01711i
$188$	2412.66	+	1485.24i	0.935964	+	0.576180i
$189$			4368.18i			1.68116i
$190$		0			0
$191$		−	3314.57i		−	1.25567i	−0.778345	−	0.627837i	$-0.783940\pi$
$191$		−	3314.57i		−	1.25567i	0.778345	−	0.627837i	$-0.216060\pi$
$192$	376.328	−	4435.62i	0.141454	−	1.66726i
$193$	−2491.16	+	2491.16i	−0.929106	+	0.929106i	−0.997648	−	0.0685419i	$-0.978165\pi$
$193$	−2491.16	+	2491.16i	−0.929106	+	0.929106i	0.0685419	+	0.997648i	$0.478165\pi$
$194$	496.296	+	4230.02i	0.183670	+	1.56545i
$195$		0			0
$196$	1543.69	−	367.290i	0.562571	−	0.133852i
$197$	3419.89	+	3419.89i	1.23684	+	1.23684i	0.961287	+	0.275550i	$0.0888598\pi$
$197$	3419.89	+	3419.89i	1.23684	+	1.23684i	0.275550	+	0.961287i	$0.411140\pi$
$198$	4812.37	+	3801.70i	1.72727	+	1.36452i
$199$	−3891.88			−1.38637			−0.693185	−	0.720759i	$-0.743793\pi$
$199$	−3891.88			−1.38637			−0.693185	+	0.720759i	$0.743793\pi$
$200$		0			0
$201$	2452.67			0.860688
$202$	2803.91	+	2215.05i	0.976646	+	0.771537i
$203$	2091.17	+	2091.17i	0.723012	+	0.723012i
$204$	−5578.04	+	1327.18i	−1.91442	+	0.455496i
$205$		0			0
$206$	−106.733	−	909.708i	−0.0360994	−	0.307681i
$207$	531.247	−	531.247i	0.178378	−	0.178378i
$208$	−24.0562	+	73.0257i	−0.00801923	+	0.0243434i
$209$		−	1057.63i		−	0.350038i
$210$		0			0
$211$		−	5180.09i		−	1.69010i	−0.534684	−	0.845052i	$-0.679569\pi$
$211$		−	5180.09i		−	1.69010i	0.534684	−	0.845052i	$-0.320431\pi$
$212$	−1436.75	−	884.465i	−0.465455	−	0.286534i
$213$	4084.73	−	4084.73i	1.31399	−	1.31399i
$214$	1640.84	−	192.515i	0.524138	−	0.0614956i
$215$		0			0
$216$	1458.19	+	3990.02i	0.459338	+	1.25688i
$217$	−4175.22	−	4175.22i	−1.30614	−	1.30614i
$218$	2496.84	−	3160.61i	0.775722	−	0.981944i
$219$	8600.72			2.65380
$220$		0			0
$221$	99.0318			0.0301430
$222$	−2003.52	+	2536.14i	−0.605708	+	0.766733i
$223$	−1451.70	−	1451.70i	−0.435933	−	0.435933i	0.454707	−	0.890641i	$-0.349744\pi$
$223$	−1451.70	−	1451.70i	−0.435933	−	0.435933i	−0.890641	+	0.454707i	$0.849744\pi$
$224$	3513.80	−	2322.10i	1.04810	−	0.692641i
$225$		0			0
$226$	3618.53	−	424.552i	1.06505	−	0.124959i
$227$	1418.20	−	1418.20i	0.414667	−	0.414667i	−0.468694	−	0.883361i	$-0.655275\pi$
$227$	1418.20	−	1418.20i	0.414667	−	0.414667i	0.883361	+	0.468694i	$0.155275\pi$
$228$	864.270	−	1403.95i	0.251042	−	0.407801i
$229$			6354.57i			1.83372i	0.399208	+	0.916860i	$0.369285\pi$
$229$			6354.57i			1.83372i	−0.399208	+	0.916860i	$0.630715\pi$
$230$		0			0
$231$			9026.52i			2.57100i
$232$	2608.21	+	1212.06i	0.738092	+	0.342998i
$233$	732.523	−	732.523i	0.205962	−	0.205962i	−0.596587	−	0.802549i	$-0.703477\pi$
$233$	732.523	−	732.523i	0.205962	−	0.205962i	0.802549	+	0.596587i	$0.203477\pi$
$234$	−19.2406	−	163.991i	−0.00537520	−	0.0458139i
$235$		0			0
$236$	−23.2195	−	97.5899i	−0.00640449	−	0.0269176i
$237$	4324.99	+	4324.99i	1.18539	+	1.18539i
$238$	−4256.84	−	3362.84i	−1.15937	−	0.915885i
$239$	−7017.11			−1.89916			−0.949580	−	0.313525i	$-0.898490\pi$
$239$	−7017.11			−1.89916			−0.949580	+	0.313525i	$0.898490\pi$
$240$		0			0
$241$	−2758.67			−0.737351			−0.368675	−	0.929558i	$-0.620189\pi$
$241$	−2758.67			−0.737351			−0.368675	+	0.929558i	$0.620189\pi$
$242$	1464.92	+	1157.27i	0.389126	+	0.307404i
$243$	1615.21	+	1615.21i	0.426403	+	0.426403i
$244$	−615.713	−	2587.80i	−0.161545	−	0.678962i
$245$		0			0
$246$	−280.901	−	2394.17i	−0.0728033	−	0.620516i
$247$	−20.1348	+	20.1348i	−0.00518683	+	0.00518683i
$248$	−5207.54	−	2419.99i	−1.33338	−	0.619636i
$249$		−	11564.6i		−	2.94328i
$250$		0			0
$251$			4312.99i			1.08460i	0.840186	+	0.542298i	$0.182446\pi$
$251$			4312.99i			1.08460i	−0.840186	+	0.542298i	$0.817554\pi$
$252$	−4741.64	+	7702.45i	−1.18530	+	1.92543i
$253$	487.820	−	487.820i	0.121221	−	0.121221i
$254$	−5720.24	+	671.138i	−1.41307	+	0.165791i
$255$		0			0
$256$	2434.44	−	3294.04i	0.594345	−	0.804210i
$257$	178.554	+	178.554i	0.0433382	+	0.0433382i	0.728444	−	0.685106i	$-0.240244\pi$
$257$	178.554	+	178.554i	0.0433382	+	0.0433382i	−0.685106	+	0.728444i	$0.740244\pi$
$258$	−5070.80	+	6418.85i	−1.22362	+	1.54892i
$259$	−3057.94			−0.733633
$260$		0			0
$261$	−6176.51			−1.46481
$262$	2327.58	−	2946.35i	0.548848	−	0.694756i
$263$	950.128	+	950.128i	0.222766	+	0.222766i	0.809662	−	0.586896i	$-0.199650\pi$
$263$	950.128	+	950.128i	0.222766	+	0.222766i	−0.586896	+	0.809662i	$0.699650\pi$
$264$	3013.23	+	8245.08i	0.702469	+	1.92216i
$265$		0			0
$266$	1549.21	−	181.764i	0.357098	−	0.0418972i
$267$	2376.62	−	2376.62i	0.544744	−	0.544744i
$268$	1921.81	+	1183.07i	0.438035	+	0.269655i
$269$		−	5698.67i		−	1.29165i	−0.763485	−	0.645826i	$-0.776513\pi$
$269$		−	5698.67i		−	1.29165i	0.763485	−	0.645826i	$-0.223487\pi$
$270$		0			0
$271$			1588.26i			0.356014i	0.984029	+	0.178007i	$0.0569649\pi$
$271$			1588.26i			0.356014i	−0.984029	+	0.178007i	$0.943035\pi$
$272$	−5010.90	−	1650.70i	−1.11702	−	0.367972i
$273$	171.843	−	171.843i	0.0380968	−	0.0380968i
$274$	−470.668	−	4011.59i	−0.103774	−	0.884484i
$275$		0			0
$276$	1046.19	−	248.918i	0.228163	−	0.0542867i
$277$	−2260.64	−	2260.64i	−0.490355	−	0.490355i	0.418063	−	0.908418i	$-0.362709\pi$
$277$	−2260.64	−	2260.64i	−0.490355	−	0.490355i	−0.908418	+	0.418063i	$0.862709\pi$
$278$	−2847.11	−	2249.18i	−0.614239	−	0.485240i
$279$	12332.0			2.64623
$280$		0			0
$281$	252.556			0.0536165			0.0268082	−	0.999641i	$-0.491466\pi$
$281$	252.556			0.0536165			0.0268082	+	0.999641i	$0.491466\pi$
$282$	−6833.86	−	5398.65i	−1.44309	−	1.14002i
$283$	4366.71	+	4366.71i	0.917223	+	0.917223i	0.996827	−	0.0796034i	$-0.0253654\pi$
$283$	4366.71	+	4366.71i	0.917223	+	0.917223i	−0.0796034	+	0.996827i	$0.525365\pi$
$284$	5170.93	−	1230.32i	1.08042	−	0.257063i
$285$		0			0
$286$	−17.6678	−	150.586i	−0.00365286	−	0.0311340i
$287$	1612.73	−	1612.73i	0.331694	−	0.331694i
$288$	−1759.91	+	8618.49i	−0.360083	+	1.76337i
$289$			1882.39i			0.383145i
$290$		0			0
$291$		−	13092.1i		−	2.63735i
$292$	6739.17	+	4148.64i	1.35062	+	0.831441i
$293$	1484.31	−	1484.31i	0.295954	−	0.295954i	−0.543473	−	0.839427i	$-0.682891\pi$
$293$	1484.31	−	1484.31i	0.295954	−	0.295954i	0.839427	+	0.543473i	$0.182891\pi$
$294$	−4844.47	+	568.388i	−0.961005	+	0.112752i
$295$		0			0
$296$	−2793.20	+	1020.80i	−0.548486	+	0.200449i
$297$	−5923.63	−	5923.63i	−1.15732	−	1.15732i
$298$	−165.827	+	209.911i	−0.0322352	+	0.0408048i
$299$	−18.5738			−0.00359249
$300$		0			0
$301$	−7739.49			−1.48205
$302$	4776.00	−	6045.67i	0.910026	−	1.15195i
$303$	−7766.93	−	7766.93i	−1.47260	−	1.47260i
$304$	1354.41	−	683.184i	0.255529	−	0.128892i
$305$		0			0
$306$	11252.8	−	1320.26i	2.10222	−	0.246647i
$307$	1130.20	−	1130.20i	0.210110	−	0.210110i	−0.594204	−	0.804314i	$-0.702533\pi$
$307$	1130.20	−	1130.20i	0.210110	−	0.210110i	0.804314	+	0.594204i	$0.202533\pi$
$308$	−4354.03	+	7072.81i	−0.805500	+	1.30848i
$309$			2815.58i			0.518358i
$310$		0			0
$311$		−	2093.83i		−	0.381769i	−0.981612	−	0.190885i	$-0.938864\pi$
$311$		−	2093.83i		−	0.381769i	0.981612	−	0.190885i	$-0.0611356\pi$
$312$	99.6018	−	214.331i	0.0180732	−	0.0388914i
$313$	−2420.68	+	2420.68i	−0.437140	+	0.437140i	−0.891048	−	0.453908i	$-0.850029\pi$
$313$	−2420.68	+	2420.68i	−0.437140	+	0.437140i	0.453908	+	0.891048i	$0.350029\pi$
$314$	560.151	+	4774.27i	0.100672	+	0.858049i
$315$		0			0
$316$	1302.68	+	5475.08i	0.231904	+	0.974675i
$317$	−4280.20	−	4280.20i	−0.758360	−	0.758360i	0.217664	−	0.976024i	$-0.430156\pi$
$317$	−4280.20	−	4280.20i	−0.758360	−	0.758360i	−0.976024	+	0.217664i	$0.930156\pi$
$318$	4069.60	+	3214.92i	0.717646	+	0.566931i
$319$	−5671.61			−0.995452
$320$		0			0
$321$	−5078.46			−0.883028
$322$	798.389	+	630.716i	0.138175	+	0.109157i
$323$	−1381.61	−	1381.61i	−0.238003	−	0.238003i
$324$	−593.105	−	2492.78i	−0.101698	−	0.427431i
$325$		0			0
$326$	156.617	+	1334.88i	0.0266081	+	0.226786i
$327$	−8755.01	+	8755.01i	−1.48059	+	1.48059i
$328$	934.750	−	2011.47i	0.157357	−	0.338613i
$329$		−	8239.88i		−	1.38079i
$330$		0			0
$331$			2409.27i			0.400077i	0.979788	+	0.200038i	$0.0641067\pi$
$331$			2409.27i			0.400077i	−0.979788	+	0.200038i	$0.935893\pi$
$332$	5578.29	−	9061.53i	0.922133	−	1.49794i
$333$	4515.98	−	4515.98i	0.743166	−	0.743166i
$334$	5414.16	−	635.227i	0.886974	−	0.104066i
$335$		0			0
$336$	−11559.4	+	5830.74i	−1.87684	+	0.946705i
$337$	3683.97	+	3683.97i	0.595486	+	0.595486i	0.939108	−	0.343622i	$-0.111654\pi$
$337$	3683.97	+	3683.97i	0.595486	+	0.595486i	−0.343622	+	0.939108i	$0.611654\pi$
$338$	3849.51	−	4872.89i	0.619485	−	0.784172i
$339$	−11199.5			−1.79432
$340$		0			0
$341$	11323.9			1.79831
$342$	−2019.45	+	2556.31i	−0.319296	+	0.404180i
$343$	2379.83	+	2379.83i	0.374633	+	0.374633i
$344$	−7069.47	+	2583.60i	−1.10802	+	0.404937i
$345$		0			0
$346$	−2575.08	+	302.127i	−0.400107	+	0.0469434i
$347$	−6739.78	+	6739.78i	−1.04268	+	1.04268i	−0.0436336	+	0.999048i	$0.513893\pi$
$347$	−6739.78	+	6739.78i	−1.04268	+	1.04268i	−0.999048	+	0.0436336i	$0.986107\pi$
$348$	−7528.72	−	4634.69i	−1.15972	−	0.713924i
$349$			1241.79i			0.190463i	0.995455	+	0.0952313i	$0.0303591\pi$
$349$			1241.79i			0.190463i	−0.995455	+	0.0952313i	$0.969641\pi$
$350$		0			0
$351$			225.543i			0.0342980i
$352$	−1616.05	+	7913.97i	−0.244703	+	1.19834i
$353$	−1393.38	+	1393.38i	−0.210090	+	0.210090i	−0.804306	−	0.594215i	$-0.797463\pi$
$353$	−1393.38	+	1393.38i	−0.210090	+	0.210090i	0.594215	+	0.804306i	$0.297463\pi$
$354$	35.9326	+	306.260i	0.00539490	+	0.0459817i
$355$		0			0
$356$	3008.60	−	715.835i	0.447909	−	0.106571i
$357$	11791.6	+	11791.6i	1.74812	+	1.74812i
$358$	213.478	+	168.645i	0.0315159	+	0.0248971i
$359$	7760.71			1.14093			0.570466	−	0.821321i	$-0.306763\pi$
$359$	7760.71			1.14093			0.570466	+	0.821321i	$0.306763\pi$
$360$		0			0
$361$	−6297.19			−0.918092
$362$	−5483.42	−	4331.83i	−0.796139	−	0.628939i
$363$	−4057.88	−	4057.88i	−0.586731	−	0.586731i
$364$	217.540	−	51.7591i	0.0313246	−	0.00745305i
$365$		0			0
$366$	952.827	+	8121.12i	0.136079	+	1.15983i
$367$	4508.13	−	4508.13i	0.641206	−	0.641206i	−0.309646	−	0.950852i	$-0.600211\pi$
$367$	4508.13	−	4508.13i	0.641206	−	0.641206i	0.950852	+	0.309646i	$0.100211\pi$
$368$	939.817	+	309.596i	0.133129	+	0.0438554i
$369$			4763.38i			0.672009i
$370$		0			0
$371$			4906.89i			0.686666i
$372$	15031.8	+	9253.60i	2.09506	+	1.28972i
$373$	5363.66	−	5363.66i	0.744557	−	0.744557i	−0.228894	−	0.973451i	$-0.573511\pi$
$373$	5363.66	−	5363.66i	0.744557	−	0.744557i	0.973451	+	0.228894i	$0.0735110\pi$
$374$	10332.9	−	1212.33i	1.42862	−	0.167616i
$375$		0			0
$376$	−2750.64	−	7526.54i	−0.377269	−	1.03232i
$377$	107.974	+	107.974i	0.0147505	+	0.0147505i
$378$	7658.82	−	9694.88i	1.04214	−	1.31918i
$379$	8526.74			1.15564			0.577822	−	0.816163i	$-0.303903\pi$
$379$	8526.74			1.15564			0.577822	+	0.816163i	$0.303903\pi$
$380$		0			0
$381$	17704.3			2.38063
$382$	−5811.50	+	7356.46i	−0.778383	+	0.985312i
$383$	7645.72	+	7645.72i	1.02005	+	1.02005i	0.999795	+	0.0202520i	$0.00644685\pi$
$383$	7645.72	+	7645.72i	1.02005	+	1.02005i	0.0202520	+	0.999795i	$0.493553\pi$
$384$	−8612.29	+	9184.73i	−1.14452	+	1.22059i
$385$		0			0
$386$	9896.75	−	1161.16i	1.30500	−	0.153112i
$387$	11429.7	−	11429.7i	1.50131	−	1.50131i
$388$	6315.08	−	10258.4i	0.826287	−	1.34225i
$389$			10831.8i			1.41181i	0.708304	+	0.705907i	$0.249460\pi$
$389$			10831.8i			1.41181i	−0.708304	+	0.705907i	$0.750540\pi$
$390$		0			0
$391$		−	1274.51i		−	0.164845i
$392$	−4070.10	−	1891.41i	−0.524416	−	0.243701i
$393$	−8161.50	+	8161.50i	−1.04756	+	1.04756i
$394$	−1594.05	−	13586.4i	−0.203825	−	1.73723i
$395$		0			0
$396$	−4015.12	−	16875.2i	−0.509513	−	2.14145i
$397$	−7632.28	−	7632.28i	−0.964870	−	0.964870i	0.0345340	−	0.999404i	$-0.489005\pi$
$397$	−7632.28	−	7632.28i	−0.964870	−	0.964870i	−0.999404	+	0.0345340i	$0.989005\pi$
$398$	8637.75	+	6823.70i	1.08787	+	0.859400i
$399$	−4794.85			−0.601611
$400$		0			0
$401$	7809.85			0.972582			0.486291	−	0.873797i	$-0.338350\pi$
$401$	7809.85			0.972582			0.486291	+	0.873797i	$0.338350\pi$
$402$	−5443.54	−	4300.32i	−0.675371	−	0.533534i
$403$	−215.580	−	215.580i	−0.0266472	−	0.0266472i
$404$	−2339.39	−	9832.30i	−0.288092	−	1.21083i
$405$		0			0
$406$	−974.718	−	8307.70i	−0.119149	−	1.01553i
$407$	4146.82	−	4146.82i	0.505038	−	0.505038i
$408$	14707.0	+	6834.50i	1.78458	+	0.829310i
$409$			11561.3i			1.39772i	0.715259	+	0.698860i	$0.246309\pi$
$409$			11561.3i			1.39772i	−0.715259	+	0.698860i	$0.753691\pi$
$410$		0			0
$411$			12416.0i			1.49011i
$412$	−1358.12	+	2206.17i	−0.162403	+	0.263811i
$413$	−206.298	+	206.298i	−0.0245794	+	0.0245794i
$414$	−2110.51	+	247.620i	−0.250546	+	0.0293958i
$415$		0			0
$416$	181.429	−	119.897i	0.0213828	−	0.0141309i
$417$	7886.60	+	7886.60i	0.926160	+	0.926160i
$418$	−1854.37	+	2347.34i	−0.216986	+	0.274671i
$419$	223.257			0.0260306			0.0130153	−	0.999915i	$-0.495857\pi$
$419$	223.257			0.0260306			0.0130153	+	0.999915i	$0.495857\pi$
$420$		0			0
$421$	−9330.20			−1.08011			−0.540055	−	0.841630i	$-0.681597\pi$
$421$	−9330.20			−1.08011			−0.540055	+	0.841630i	$0.681597\pi$
$422$	−9082.35	+	11496.8i	−1.04768	+	1.32620i
$423$	12168.7	+	12168.7i	1.39873	+	1.39873i
$424$	1638.02	+	4482.09i	0.187616	+	0.513372i
$425$		0			0
$426$	−16227.6	+	1903.94i	−1.84561	+	0.216540i
$427$	−5470.43	+	5470.43i	−0.619982	+	0.619982i
$428$	−3979.27	−	2449.64i	−0.449405	−	0.276654i
$429$			466.068i			0.0524522i
$430$		0			0
$431$		−	4319.11i		−	0.482701i	−0.970438	−	0.241350i	$-0.922410\pi$
$431$		−	4319.11i		−	0.482701i	0.970438	−	0.241350i	$-0.0775903\pi$
$432$	3759.44	−	11412.2i	0.418695	−	1.27100i
$433$	−3860.89	+	3860.89i	−0.428505	+	0.428505i	−0.888119	−	0.459614i	$-0.847988\pi$
$433$	−3860.89	+	3860.89i	−0.428505	+	0.428505i	0.459614	+	0.888119i	$0.347988\pi$
$434$	1946.12	+	16587.1i	0.215246	+	1.83458i
$435$		0			0
$436$	−11083.1	+	2637.00i	−1.21740	+	0.289655i
$437$	259.128	+	259.128i	0.0283656	+	0.0283656i
$438$	−19088.7	−	15079.8i	−2.08240	−	1.64507i
$439$	2790.65			0.303395			0.151697	−	0.988427i	$-0.451526\pi$
$439$	2790.65			0.303395			0.151697	+	0.988427i	$0.451526\pi$
$440$		0			0
$441$	9638.42			1.04075
$442$	−219.794	−	173.634i	−0.0236528	−	0.0186854i
$443$	−12801.3	−	12801.3i	−1.37293	−	1.37293i	−0.856077	−	0.516849i	$-0.827105\pi$
$443$	−12801.3	−	12801.3i	−1.37293	−	1.37293i	−0.516849	−	0.856077i	$-0.672895\pi$
$444$	8893.33	−	2115.98i	0.950583	−	0.226172i
$445$		0			0
$446$	676.654	+	5767.25i	0.0718397	+	0.612303i
$447$	581.462	−	581.462i	0.0615262	−	0.0615262i
$448$	−11870.0	−	1007.08i	−1.25180	−	0.106205i
$449$		−	2245.42i		−	0.236008i	−0.993013	−	0.118004i	$-0.962350\pi$
$449$		−	2245.42i		−	0.236008i	0.993013	−	0.118004i	$-0.0376496\pi$
$450$		0			0
$451$			4373.99i			0.456681i
$452$	−8775.46	−	5402.18i	−0.913192	−	0.562162i
$453$	−16746.7	+	16746.7i	−1.73693	+	1.73693i
$454$	−5634.16	+	661.040i	−0.582433	+	0.0683351i
$455$		0			0
$456$	−4379.75	+	1600.62i	−0.449782	+	0.164377i
$457$	−1560.21	−	1560.21i	−0.159701	−	0.159701i	0.622733	−	0.782434i	$-0.286022\pi$
$457$	−1560.21	−	1560.21i	−0.159701	−	0.159701i	−0.782434	+	0.622733i	$0.786022\pi$
$458$	11141.6	−	14103.5i	1.13671	−	1.43890i
$459$	−15476.4			−1.57380
$460$		0			0
$461$	2633.09			0.266020			0.133010	−	0.991115i	$-0.457536\pi$
$461$	2633.09			0.266020			0.133010	+	0.991115i	$0.457536\pi$
$462$	15826.4	−	20033.7i	1.59374	−	2.01743i
$463$	−7629.96	−	7629.96i	−0.765862	−	0.765862i	0.211513	−	0.977375i	$-0.432161\pi$
$463$	−7629.96	−	7629.96i	−0.765862	−	0.765862i	−0.977375	+	0.211513i	$0.932161\pi$
$464$	−3663.61	−	7263.10i	−0.366549	−	0.726683i
$465$		0			0
$466$	−2910.13	+	341.437i	−0.289290	+	0.0339416i
$467$	−5048.30	+	5048.30i	−0.500230	+	0.500230i	−0.911509	−	0.411280i	$-0.865082\pi$
$467$	−5048.30	+	5048.30i	−0.500230	+	0.500230i	0.411280	+	0.911509i	$0.365082\pi$
$468$	−244.826	+	397.702i	−0.0241818	+	0.0392816i
$469$		−	6563.51i		−	0.646215i
$470$		0			0
$471$		−	14776.5i		−	1.44558i
$472$	−119.572	+	257.305i	−0.0116605	+	0.0250920i
$473$	10495.4	−	10495.4i	1.02025	−	1.02025i
$474$	−2015.93	−	17182.1i	−0.195347	−	1.66498i
$475$		0			0
$476$	3551.62	+	14927.2i	0.341992	+	1.43737i
$477$	−7246.53	−	7246.53i	−0.695588	−	0.695588i
$478$	15574.0	+	12303.2i	1.49025	+	1.17727i
$479$	−2483.78			−0.236924			−0.118462	−	0.992959i	$-0.537796\pi$
$479$	−2483.78			−0.236924			−0.118462	+	0.992959i	$0.537796\pi$
$480$		0			0
$481$	−157.891			−0.0149672
$482$	6122.67	+	4836.83i	0.578590	+	0.457078i
$483$	−2211.57	−	2211.57i	−0.208343	−	0.208343i
$484$	−1222.23	−	5136.94i	−0.114785	−	0.482432i
$485$		0			0
$486$	−752.869	−	6416.84i	−0.0702692	−	0.598917i
$487$	−3898.10	+	3898.10i	−0.362710	+	0.362710i	−0.864810	−	0.502099i	$-0.832561\pi$
$487$	−3898.10	+	3898.10i	−0.362710	+	0.362710i	0.502099	+	0.864810i	$0.332561\pi$
$488$	−3170.70	+	6822.98i	−0.294121	+	0.632913i
$489$		−	4131.50i		−	0.382071i
$490$		0			0
$491$			9000.53i			0.827267i	0.910443	+	0.413634i	$0.135741\pi$
$491$			9000.53i			0.827267i	−0.910443	+	0.413634i	$0.864259\pi$
$492$	−3574.31	+	5806.21i	−0.327525	+	0.532041i
$493$	−7408.98	+	7408.98i	−0.676843	+	0.676843i
$494$	79.9905	−	9.38505i	0.00728531	−	0.000854764i
$495$		0			0
$496$	7314.75	+	14501.5i	0.662181	+	1.31277i
$497$	−10931.0	−	10931.0i	−0.986563	−	0.986563i
$498$	−20276.4	+	25666.8i	−1.82451	+	2.30955i
$499$	13057.4			1.17140			0.585699	−	0.810528i	$-0.300820\pi$
$499$	13057.4			1.17140			0.585699	+	0.810528i	$0.300820\pi$
$500$		0			0
$501$	−16757.0			−1.49431
$502$	7562.06	−	9572.39i	0.672333	−	0.851069i
$503$	−1782.55	−	1782.55i	−0.158012	−	0.158012i	0.623673	−	0.781685i	$-0.285640\pi$
$503$	−1782.55	−	1782.55i	−0.158012	−	0.158012i	−0.781685	+	0.623673i	$0.785640\pi$
$504$	24028.6	−	8781.45i	2.12365	−	0.776105i
$505$		0			0
$506$	−1937.99	+	227.378i	−0.170265	+	0.0199767i
$507$	−13498.1	+	13498.1i	−1.18239	+	1.18239i
$508$	13872.4	+	8539.86i	1.21159	+	0.745856i
$509$		−	6098.28i		−	0.531044i	−0.964105	−	0.265522i	$-0.914456\pi$
$509$		−	6098.28i		−	0.531044i	0.964105	−	0.265522i	$-0.0855443\pi$
$510$		0			0
$511$		−	23016.1i		−	1.99251i
$512$	−11178.6	+	3042.55i	−0.964898	+	0.262623i
$513$	3146.61	−	3146.61i	0.270811	−	0.270811i
$514$	−83.2262	−	709.352i	−0.00714193	−	0.0608720i
$515$		0			0
$516$	22508.6	−	5355.46i	1.92032	−	0.456901i
$517$	11174.0	+	11174.0i	0.950543	+	0.950543i
$518$	6786.88	+	5361.54i	0.575672	+	0.454773i
$519$	7969.96			0.674070
$520$		0			0
$521$	14621.2			1.22949			0.614746	−	0.788725i	$-0.289258\pi$
$521$	14621.2			1.22949			0.614746	+	0.788725i	$0.289258\pi$
$522$	13708.3	+	10829.4i	1.14942	+	0.908026i
$523$	−3175.36	−	3175.36i	−0.265486	−	0.265486i	0.561793	−	0.827278i	$-0.310112\pi$
$523$	−3175.36	−	3175.36i	−0.265486	−	0.265486i	−0.827278	+	0.561793i	$0.810112\pi$
$524$	−10331.8	+	2458.24i	−0.861348	+	0.204940i
$525$		0			0
$526$	−442.865	−	3774.62i	−0.0367107	−	0.312892i
$527$	14792.7	−	14792.7i	1.22274	−	1.22274i
$528$	7768.60	−	23582.5i	0.640312	−	1.94375i
$529$		−	11928.0i		−	0.980353i
$530$		0			0
$531$		−	609.325i		−	0.0497975i
$532$	−3757.05	−	2312.84i	−0.306182	−	0.188486i
$533$	83.2703	−	83.2703i	0.00676705	−	0.00676705i
$534$	−9441.70	+	1107.77i	−0.765135	+	0.0897711i
$535$		0			0
$536$	−2191.03	−	5995.30i	−0.176564	−	0.483130i
$537$	−591.343	−	591.343i	−0.0475202	−	0.0475202i
$538$	−9991.59	+	12647.8i	−0.800684	+	1.01354i
$539$	8850.52			0.707271
$540$		0			0
$541$	6733.34			0.535099			0.267550	−	0.963544i	$-0.413786\pi$
$541$	6733.34			0.535099			0.267550	+	0.963544i	$0.413786\pi$
$542$	2784.72	−	3525.02i	0.220690	−	0.279359i
$543$	15189.3	+	15189.3i	1.20043	+	1.20043i
$544$	8227.14	+	12449.3i	0.648411	+	0.981176i
$545$		0			0
$546$	−682.690	+	80.0981i	−0.0535100	+	0.00627817i
$547$	5281.02	−	5281.02i	0.412797	−	0.412797i	−0.469915	−	0.882712i	$-0.655715\pi$
$547$	5281.02	−	5281.02i	0.412797	−	0.412797i	0.882712	+	0.469915i	$0.155715\pi$
$548$	−5988.98	+	9728.67i	−0.466855	+	0.758372i
$549$		−	16157.5i		−	1.25608i
$550$		0			0
$551$		−	3012.73i		−	0.232934i
$552$	−2758.37	−	1281.84i	−0.212689	−	0.0988384i
$553$	11573.9	−	11573.9i	0.890008	−	0.890008i
$554$	1053.71	+	8980.94i	0.0808082	+	0.688743i
$555$		0			0
$556$	2375.44	+	9983.79i	0.181189	+	0.761524i
$557$	9284.66	+	9284.66i	0.706290	+	0.706290i	0.965753	−	0.259463i	$-0.0835455\pi$
$557$	9284.66	+	9284.66i	0.706290	+	0.706290i	−0.259463	+	0.965753i	$0.583545\pi$
$558$	−27370.0	−	21621.9i	−2.07646	−	1.64037i
$559$	−399.614			−0.0302359
$560$		0			0
$561$	−31980.8			−2.40683
$562$	−560.531	−	442.811i	−0.0420722	−	0.0332364i
$563$	7802.12	+	7802.12i	0.584050	+	0.584050i	0.936014	−	0.351963i	$-0.114486\pi$
$563$	7802.12	+	7802.12i	0.584050	+	0.584050i	−0.351963	+	0.936014i	$0.614486\pi$
$564$	5701.71	+	23963.9i	0.425683	+	1.78911i
$565$		0			0
$566$	−2035.37	−	17347.9i	−0.151154	−	1.28831i
$567$	−5269.56	+	5269.56i	−0.390301	+	0.390301i
$568$	−13633.7	−	6335.69i	−1.00714	−	0.468027i
$569$			15179.2i			1.11836i	0.829046	+	0.559180i	$0.188884\pi$
$569$			15179.2i			1.11836i	−0.829046	+	0.559180i	$0.811116\pi$
$570$		0			0
$571$			15123.8i			1.10843i	0.832375	+	0.554213i	$0.186981\pi$
$571$			15123.8i			1.10843i	−0.832375	+	0.554213i	$0.813019\pi$
$572$	−224.812	+	365.192i	−0.0164334	+	0.0266948i
$573$	20377.6	−	20377.6i	1.48567	−	1.48567i
$574$	−6406.96	+	751.710i	−0.465891	+	0.0546616i
$575$		0			0
$576$	19017.0	−	16042.4i	1.37565	−	1.16048i
$577$	6086.54	+	6086.54i	0.439144	+	0.439144i	0.891724	−	0.452580i	$-0.149496\pi$
$577$	6086.54	+	6086.54i	0.439144	+	0.439144i	−0.452580	+	0.891724i	$0.649496\pi$
$578$	3300.43	−	4177.83i	0.237508	−	0.300649i
$579$	−30630.8			−2.19857
$580$		0			0
$581$	−30947.6			−2.20985
$582$	−22954.6	+	29056.9i	−1.63487	+	2.06950i
$583$	−6654.16	−	6654.16i	−0.472705	−	0.472705i
$584$	−7683.22	−	21023.5i	−0.544408	−	1.48966i
$585$		0			0
$586$	−5896.80	+	691.854i	−0.415691	+	0.0487718i
$587$	9334.98	−	9334.98i	0.656381	−	0.656381i	−0.298141	−	0.954522i	$-0.596367\pi$
$587$	9334.98	−	9334.98i	0.656381	−	0.656381i	0.954522	+	0.298141i	$0.0963665\pi$
$588$	11748.5	+	7232.41i	0.823982	+	0.507244i
$589$			6015.21i			0.420802i
$590$		0			0
$591$			42050.2i			2.92676i
$592$	7989.11	+	2631.78i	0.554646	+	0.182712i
$593$	−801.327	+	801.327i	−0.0554917	+	0.0554917i	−0.734308	−	0.678816i	$-0.762493\pi$
$593$	−801.327	+	801.327i	−0.0554917	+	0.0554917i	0.678816	+	0.734308i	$0.262493\pi$
$594$	2761.07	+	23533.1i	0.190721	+	1.62555i
$595$		0			0
$596$	736.083	−	175.136i	0.0505892	−	0.0120366i
$597$	−23926.9	−	23926.9i	−1.64030	−	1.64030i
$598$	41.2234	+	32.5659i	0.00281898	+	0.00222695i
$599$	2384.18			0.162629			0.0813146	−	0.996688i	$-0.474088\pi$
$599$	2384.18			0.162629			0.0813146	+	0.996688i	$0.474088\pi$
$600$		0			0
$601$	11760.3			0.798190			0.399095	−	0.916910i	$-0.369324\pi$
$601$	11760.3			0.798190			0.399095	+	0.916910i	$0.369324\pi$
$602$	17177.3	+	13569.8i	1.16294	+	0.918710i
$603$	9693.04	+	9693.04i	0.654612	+	0.654612i
$604$	−21200.0	+	5044.10i	−1.42817	+	0.339804i
$605$		0			0
$606$	3620.25	+	30856.1i	0.242678	+	2.06839i
$607$	4286.59	−	4286.59i	0.286635	−	0.286635i	−0.549113	−	0.835748i	$-0.685034\pi$
$607$	4286.59	−	4286.59i	0.286635	−	0.286635i	0.835748	+	0.549113i	$0.185034\pi$
$608$	−4203.86	−	858.437i	−0.280410	−	0.0572603i
$609$			25712.6i			1.71088i
$610$		0			0
$611$		−	425.451i		−	0.0281701i
$612$	−27289.6	−	16799.5i	−1.80248	−	1.10961i
$613$	−2911.11	+	2911.11i	−0.191808	+	0.191808i	−0.796477	−	0.604669i	$-0.793305\pi$
$613$	−2911.11	+	2911.11i	−0.191808	+	0.191808i	0.604669	+	0.796477i	$0.293305\pi$
$614$	−4489.99	+	526.797i	−0.295116	+	0.0346251i
$615$		0			0
$616$	22064.4	−	8063.61i	1.44318	−	0.527422i
$617$	−4635.01	−	4635.01i	−0.302429	−	0.302429i	0.539535	−	0.841963i	$-0.318600\pi$
$617$	−4635.01	−	4635.01i	−0.302429	−	0.302429i	−0.841963	+	0.539535i	$0.818600\pi$
$618$	4936.61	−	6248.98i	0.321326	−	0.406749i
$619$	−6898.58			−0.447944			−0.223972	−	0.974596i	$-0.571902\pi$
$619$	−6898.58			−0.447944			−0.223972	+	0.974596i	$0.571902\pi$
$620$		0			0
$621$	2902.67			0.187568
$622$	−3671.15	+	4647.11i	−0.236656	+	0.299569i
$623$	−6359.98	−	6359.98i	−0.409000	−	0.409000i
$624$	−596.850	+	301.059i	−0.0382903	+	0.0193141i
$625$		0			0
$626$	9616.75	−	1128.30i	0.613998	−	0.0720385i
$627$	6502.22	−	6502.22i	0.414153	−	0.414153i
$628$	7127.60	−	11578.3i	0.452901	−	0.735706i
$629$		−	10834.2i		−	0.686786i
$630$		0			0
$631$		−	6731.96i		−	0.424715i	−0.977192	−	0.212357i	$-0.931886\pi$
$631$		−	6731.96i		−	0.424715i	0.977192	−	0.212357i	$-0.0681141\pi$
$632$	6708.35	−	14435.6i	0.422221	−	0.908571i
$633$	31846.7	−	31846.7i	1.99967	−	1.99967i
$634$	1995.05	+	17004.2i	0.124974	+	1.06518i
$635$		0			0
$636$	−3395.40	−	14270.6i	−0.211692	−	0.889727i
$637$	−168.493	−	168.493i	−0.0104803	−	0.0104803i
$638$	12587.7	+	9944.14i	0.781118	+	0.617073i
$639$	32285.9			1.99877
$640$		0			0
$641$	−20886.3			−1.28699			−0.643495	−	0.765450i	$-0.722516\pi$
$641$	−20886.3			−1.28699			−0.643495	+	0.765450i	$0.722516\pi$
$642$	11271.3	+	8904.17i	0.692901	+	0.547382i
$643$	−3857.48	−	3857.48i	−0.236585	−	0.236585i	0.578849	−	0.815434i	$-0.303502\pi$
$643$	−3857.48	−	3857.48i	−0.236585	−	0.236585i	−0.815434	+	0.578849i	$0.803502\pi$
$644$	−666.122	−	2799.66i	−0.0407591	−	0.171308i
$645$		0			0
$646$	643.986	+	5488.81i	0.0392218	+	0.334295i
$647$	−2807.13	+	2807.13i	−0.170572	+	0.170572i	−0.787230	−	0.616659i	$-0.788486\pi$
$647$	−2807.13	+	2807.13i	−0.170572	+	0.170572i	0.616659	+	0.787230i	$0.288486\pi$
$648$	−3054.28	+	6572.44i	−0.185160	+	0.398441i
$649$		−	559.516i		−	0.0338412i
$650$		0			0
$651$		−	51337.7i		−	3.09076i
$652$	1992.87	−	3237.27i	0.119704	−	0.194450i
$653$	−9353.51	+	9353.51i	−0.560538	+	0.560538i	−0.929460	−	0.368922i	$-0.879727\pi$
$653$	−9353.51	+	9353.51i	−0.560538	+	0.560538i	0.368922	+	0.929460i	$0.379727\pi$
$654$	34781.5	−	4080.81i	2.07961	−	0.243994i
$655$		0			0
$656$	−5601.36	+	2825.41i	−0.333379	+	0.168161i
$657$	33990.3	+	33990.3i	2.01840	+	2.01840i
$658$	−14447.1	+	18287.8i	−0.855939	+	1.08349i
$659$	18295.5			1.08147			0.540737	−	0.841191i	$-0.318145\pi$
$659$	18295.5			1.08147			0.540737	+	0.841191i	$0.318145\pi$
$660$		0			0
$661$	27859.2			1.63933			0.819664	−	0.572845i	$-0.194160\pi$
$661$	27859.2			1.63933			0.819664	+	0.572845i	$0.194160\pi$
$662$	4224.22	−	5347.21i	0.248004	−	0.313935i
$663$	608.837	+	608.837i	0.0356641	+	0.0356641i
$664$	−28268.4	+	10330.9i	−1.65215	+	0.603791i
$665$		0			0
$666$	−17940.9	+	2104.95i	−1.04384	+	0.122470i
$667$	1389.59	−	1389.59i	0.0806672	−	0.0806672i
$668$	−13130.1	−	8082.90i	−0.760507	−	0.468169i
$669$		−	17849.8i		−	1.03156i
$670$		0			0
$671$		−	14836.7i		−	0.853600i
$672$	35878.5	+	7326.46i	2.05959	+	0.420572i
$673$	−4252.85	+	4252.85i	−0.243589	+	0.243589i	−0.818333	−	0.574744i	$-0.805102\pi$
$673$	−4252.85	+	4252.85i	−0.243589	+	0.243589i	0.574744	+	0.818333i	$0.305102\pi$
$674$	−1717.14	−	14635.5i	−0.0981332	−	0.836407i
$675$		0			0
$676$	−17087.4	+	4065.61i	−0.972203	+	0.231316i
$677$	−3002.52	−	3002.52i	−0.170453	−	0.170453i	0.616726	−	0.787178i	$-0.288459\pi$
$677$	−3002.52	−	3002.52i	−0.170453	−	0.170453i	−0.787178	+	0.616726i	$0.788459\pi$
$678$	24856.5	+	19636.3i	1.40798	+	1.11228i
$679$	−35035.2			−1.98016
$680$		0			0
$681$	17437.9			0.981238
$682$	−25132.6	−	19854.4i	−1.41111	−	1.11476i
$683$	3185.21	+	3185.21i	0.178446	+	0.178446i	0.790678	−	0.612232i	$-0.209728\pi$
$683$	3185.21	+	3185.21i	0.178446	+	0.178446i	−0.612232	+	0.790678i	$0.709728\pi$
$684$	8964.05	−	2132.81i	0.501095	−	0.119225i
$685$		0			0
$686$	−1109.27	−	9454.49i	−0.0617376	−	0.526201i
$687$	−39067.3	+	39067.3i	−2.16959	+	2.16959i
$688$	20220.1	+	6660.92i	1.12047	+	0.369106i
$689$			253.358i			0.0140090i
$690$		0			0
$691$			5509.61i			0.303322i	0.988433	+	0.151661i	$0.0484622\pi$
$691$			5509.61i			0.303322i	−0.988433	+	0.151661i	$0.951538\pi$
$692$	6244.93	+	3844.39i	0.343059	+	0.211187i
$693$	−35673.1	+	35673.1i	−1.95542	+	1.95542i
$694$	26775.5	−	3141.49i	1.46453	−	0.171829i
$695$		0			0
$696$	8583.38	+	23486.6i	0.467460	+	1.27911i
$697$	5713.86	+	5713.86i	0.310514	+	0.310514i
$698$	2177.25	−	2756.07i	0.118066	−	0.149454i
$699$	9006.96			0.487374
$700$		0			0
$701$	−1423.05			−0.0766731			−0.0383365	−	0.999265i	$-0.512206\pi$
$701$	−1423.05			−0.0766731			−0.0383365	+	0.999265i	$0.512206\pi$
$702$	395.449	−	500.578i	0.0212611	−	0.0269132i
$703$	2202.77	+	2202.77i	0.118178	+	0.118178i
$704$	17462.4	−	14731.1i	0.934857	−	0.788633i
$705$		0			0
$706$	5535.53	−	649.468i	0.295089	−	0.0346219i
$707$	−20784.8	+	20784.8i	−1.10565	+	1.10565i
$708$	457.222	−	742.724i	0.0242704	−	0.0394255i
$709$		−	26914.2i		−	1.42565i	−0.701343	−	0.712824i	$-0.747416\pi$
$709$		−	26914.2i		−	1.42565i	0.701343	−	0.712824i	$-0.252584\pi$
$710$		0			0
$711$			34185.0i			1.80315i
$712$	−7932.47	−	3686.29i	−0.417531	−	0.194030i
$713$	−2774.44	+	2774.44i	−0.145728	+	0.145728i
$714$	−5496.19	−	46845.0i	−0.288081	−	2.45537i
$715$		0			0
$716$	−178.112	−	748.592i	−0.00929659	−	0.0390729i
$717$	−43140.5	−	43140.5i	−2.24702	−	2.24702i
$718$	−17224.4	−	13607.0i	−0.895274	−	0.707254i
$719$	−35973.4			−1.86590			−0.932950	−	0.360006i	$-0.882775\pi$
$719$	−35973.4			−1.86590			−0.932950	+	0.360006i	$0.882775\pi$
$720$		0			0
$721$	7534.67			0.389190
$722$	13976.2	+	11041.0i	0.720415	+	0.569118i
$723$	−16960.0	−	16960.0i	−0.872407	−	0.872407i
$724$	4575.00	+	19228.4i	0.234846	+	0.987040i
$725$		0			0
$726$	1891.42	+	16120.9i	0.0966904	+	0.824110i
$727$	9307.24	−	9307.24i	0.474809	−	0.474809i	−0.428658	−	0.903467i	$-0.641013\pi$
$727$	9307.24	−	9307.24i	0.474809	−	0.474809i	0.903467	+	0.428658i	$0.141013\pi$
$728$	−573.564	−	266.541i	−0.0292001	−	0.0135696i
$729$			28508.3i			1.44837i
$730$		0			0
$731$		−	27420.9i		−	1.38741i
$732$	12124.2	−	19694.9i	0.612189	−	0.994458i
$733$	7372.92	−	7372.92i	0.371521	−	0.371521i	−0.496510	−	0.868031i	$-0.665385\pi$
$733$	7372.92	−	7372.92i	0.371521	−	0.371521i	0.868031	+	0.496510i	$0.165385\pi$
$734$	−17909.7	+	2101.29i	−0.900624	+	0.105668i
$735$		0			0
$736$	−1543.04	−	2334.92i	−0.0772787	−	0.116938i
$737$	8900.68	+	8900.68i	0.444859	+	0.444859i
$738$	8351.72	−	10572.0i	0.416573	−	0.527317i
$739$	24540.3			1.22156			0.610778	−	0.791802i	$-0.290857\pi$
$739$	24540.3			1.22156			0.610778	+	0.791802i	$0.290857\pi$
$740$		0			0
$741$	−247.573			−0.0122737
$742$	8603.34	−	10890.5i	0.425659	−	0.538818i
$743$	−25077.8	−	25077.8i	−1.23825	−	1.23825i	−0.960718	−	0.277528i	$-0.910485\pi$
$743$	−25077.8	−	25077.8i	−1.23825	−	1.23825i	−0.277528	−	0.960718i	$-0.589515\pi$
$744$	−17137.6	−	46893.3i	−0.844480	−	2.31074i
$745$		0			0
$746$	−21308.5	+	2500.06i	−1.04579	+	0.122699i
$747$	45703.6	−	45703.6i	2.23856	−	2.23856i
$748$	−25058.8	−	15426.2i	−1.22492	−	0.754063i
$749$			13590.3i			0.662989i
$750$		0			0
$751$			23078.2i			1.12135i	0.828035	+	0.560676i	$0.189459\pi$
$751$			23078.2i			1.12135i	−0.828035	+	0.560676i	$0.810541\pi$
$752$	−7091.58	+	21527.4i	−0.343887	+	1.04391i
$753$	−26515.9	+	26515.9i	−1.28326	+	1.28326i
$754$	−50.3278	−	428.953i	−0.00243081	−	0.0207182i
$755$		0			0
$756$	−33996.4	+	8088.75i	−1.63550	+	0.389134i
$757$	16966.6	+	16966.6i	0.814613	+	0.814613i	0.985322	−	0.170708i	$-0.0546056\pi$
$757$	16966.6	+	16966.6i	0.814613	+	0.814613i	−0.170708	+	0.985322i	$0.554606\pi$
$758$	−18924.5	−	14950.1i	−0.906819	−	0.716375i
$759$	5998.14			0.286849
$760$		0			0
$761$	7121.15			0.339213			0.169607	−	0.985512i	$-0.445750\pi$
$761$	7121.15			0.339213			0.169607	+	0.985512i	$0.445750\pi$
$762$	−39293.5	−	31041.4i	−1.86805	−	1.47573i
$763$	23429.0	+	23429.0i	1.11165	+	1.11165i
$764$	25796.4	−	6137.73i	1.22157	−	0.290648i
$765$		0			0
$766$	−3563.75	−	30374.5i	−0.168099	−	1.43274i
$767$	−10.6518	+	10.6518i	−0.000501454	+	0.000501454i
$768$	35218.1	−	5284.77i	1.65472	−	0.248304i
$769$		−	10040.5i		−	0.470831i	−0.971895	−	0.235415i	$-0.924355\pi$
$769$		−	10040.5i		−	0.470831i	0.971895	−	0.235415i	$-0.0756451\pi$
$770$		0			0
$771$			2195.47i			0.102552i
$772$	−24001.0	−	14775.1i	−1.11893	−	0.688816i
$773$	−18388.2	+	18388.2i	−0.855599	+	0.855599i	−0.990816	−	0.135217i	$-0.956827\pi$
$773$	−18388.2	+	18388.2i	−0.855599	+	0.855599i	0.135217	+	0.990816i	$0.456827\pi$
$774$	−45407.5	+	5327.52i	−2.10870	+	0.247408i
$775$		0			0
$776$	−32002.1	+	11695.4i	−1.48042	+	0.541033i
$777$	−18799.9	−	18799.9i	−0.868008	−	0.868008i
$778$	18991.7	−	24040.5i	0.875172	−	1.10783i
$779$	−2323.45			−0.106863
$780$		0			0
$781$	29646.7			1.35831
$782$	−2234.62	+	2828.68i	−0.102186	+	0.129352i
$783$	−16873.8	−	16873.8i	−0.770142	−	0.770142i
$784$	5717.05	+	11334.0i	0.260434	+	0.516310i
$785$		0			0
$786$	32423.6	−	3804.16i	1.47139	−	0.172634i
$787$	−12222.0	+	12222.0i	−0.553578	+	0.553578i	−0.927472	−	0.373894i	$-0.878022\pi$
$787$	−12222.0	+	12222.0i	−0.553578	+	0.553578i	0.373894	+	0.927472i	$0.378022\pi$
$788$	−20283.3	+	32948.8i	−0.916959	+	1.48953i
$789$			11682.6i			0.527137i
$790$		0			0
$791$			29970.6i			1.34719i
$792$	−20676.4	+	44493.2i	−0.927657	+	1.99621i
$793$	−282.456	+	282.456i	−0.0126485	+	0.0126485i
$794$	3557.49	+	30321.1i	0.159006	+	1.35524i
$795$		0			0
$796$	−7206.75	−	30289.5i	−0.320900	−	1.34872i
$797$	3432.79	+	3432.79i	0.152567	+	0.152567i	0.779263	−	0.626697i	$-0.215593\pi$
$797$	3432.79	+	3432.79i	0.152567	+	0.152567i	−0.626697	+	0.779263i	$0.715593\pi$
$798$	10641.8	+	8406.90i	0.472076	+	0.372934i
$799$	29193.7			1.29262
$800$		0			0
$801$	18784.9			0.828630
$802$	−17333.4	−	13693.2i	−0.763173	−	0.602896i
$803$	31211.7	+	31211.7i	1.37165	+	1.37165i
$804$	4541.72	+	19088.5i	0.199222	+	0.837314i
$805$		0			0
$806$	100.484	+	856.446i	0.00439132	+	0.0374281i
$807$	35034.9	−	35034.9i	1.52824	−	1.52824i
$808$	−12047.0	+	25923.8i	−0.524522	+	1.12871i
$809$			21193.7i			0.921053i	0.887646	+	0.460526i	$0.152339\pi$
$809$			21193.7i			0.921053i	−0.887646	+	0.460526i	$0.847661\pi$
$810$		0			0
$811$			8690.30i			0.376273i	0.982143	+	0.188137i	$0.0602448\pi$
$811$			8690.30i			0.376273i	−0.982143	+	0.188137i	$0.939755\pi$
$812$	−12402.7	+	20147.3i	−0.536023	+	0.870730i
$813$	−9764.44	+	9764.44i	−0.421222	+	0.421222i
$814$	−16474.3	+	1932.88i	−0.709365	+	0.0832277i
$815$		0			0
$816$	−20658.2	−	40954.8i	−0.886252	−	1.75699i
$817$	5575.11	+	5575.11i	0.238738	+	0.238738i
$818$	20270.6	−	25659.4i	0.866435	−	1.09677i
$819$	1358.26			0.0579505
$820$		0			0
$821$	−42739.3			−1.81682			−0.908411	−	0.418077i	$-0.862704\pi$
$821$	−42739.3			−1.81682			−0.908411	+	0.418077i	$0.862704\pi$
$822$	21769.2	−	27556.4i	0.923709	−	1.16927i
$823$	14335.6	+	14335.6i	0.607176	+	0.607176i	0.942207	−	0.335031i	$-0.108747\pi$
$823$	14335.6	+	14335.6i	0.607176	+	0.607176i	−0.335031	+	0.942207i	$0.608747\pi$
$824$	6882.38	−	2515.22i	0.290970	−	0.106337i
$825$		0			0
$826$	819.571	−	96.1579i	0.0345237	−	0.00405056i
$827$	−2890.06	+	2890.06i	−0.121520	+	0.121520i	−0.765252	−	0.643731i	$-0.777385\pi$
$827$	−2890.06	+	2890.06i	−0.121520	+	0.121520i	0.643731	+	0.765252i	$0.277385\pi$
$828$	5118.29	+	3150.83i	0.214822	+	0.132245i
$829$		−	22098.9i		−	0.925847i	−0.886398	−	0.462924i	$-0.846800\pi$
$829$		−	22098.9i		−	0.925847i	0.886398	−	0.462924i	$-0.153200\pi$
$830$		0			0
$831$		−	27796.3i		−	1.16034i
$832$	−612.886	−	51.9986i	−0.0255385	−	0.00216674i
$833$	11561.7	−	11561.7i	0.480898	−	0.480898i
$834$	−3676.03	−	31331.5i	−0.152627	−	1.30086i
$835$		0			0
$836$	8231.28	−	1958.46i	0.340532	−	0.0810226i
$837$	33690.2	+	33690.2i	1.39128	+	1.39128i
$838$	−495.504	−	391.441i	−0.0204259	−	0.0161362i
$839$	−47240.3			−1.94388			−0.971940	−	0.235229i	$-0.924416\pi$
$839$	−47240.3			−1.94388			−0.971940	+	0.235229i	$0.924416\pi$
$840$		0			0
$841$	8233.07			0.337573
$842$	20707.7	+	16358.8i	0.847548	+	0.669552i
$843$	1552.69	+	1552.69i	0.0634371	+	0.0634371i
$844$	40315.3	−	9592.19i	1.64421	−	0.391205i
$845$		0			0
$846$	−5671.97	−	48343.2i	−0.230504	−	1.96463i
$847$	−10859.1	+	10859.1i	−0.440525	+	0.440525i
$848$	4223.07	−	12819.7i	0.171015	−	0.519138i
$849$			53692.2i			2.17045i
$850$		0			0
$851$			2032.00i			0.0818522i
$852$	39354.2	+	24226.5i	1.58246	+	0.974162i
$853$	−9572.36	+	9572.36i	−0.384234	+	0.384234i	−0.872625	−	0.488391i	$-0.837584\pi$
$853$	−9572.36	+	9572.36i	−0.384234	+	0.384234i	0.488391	+	0.872625i	$0.337584\pi$
$854$	21732.6	−	2549.83i	0.870814	−	0.102170i
$855$		0			0
$856$	4536.71	+	12413.8i	0.181147	+	0.495670i
$857$	−10468.9	−	10468.9i	−0.417284	−	0.417284i	0.466983	−	0.884266i	$-0.345341\pi$
$857$	−10468.9	−	10468.9i	−0.417284	−	0.417284i	−0.884266	+	0.466983i	$0.845341\pi$
$858$	817.166	−	1034.41i	0.0325147	−	0.0411585i
$859$	−2068.01			−0.0821416			−0.0410708	−	0.999156i	$-0.513077\pi$
$859$	−2068.01			−0.0821416			−0.0410708	+	0.999156i	$0.513077\pi$
$860$		0			0
$861$	19829.8			0.784898
$862$	−7572.77	+	9585.95i	−0.299222	+	0.378769i
$863$	7493.32	+	7493.32i	0.295568	+	0.295568i	0.839275	−	0.543707i	$-0.182980\pi$
$863$	7493.32	+	7493.32i	0.295568	+	0.295568i	−0.543707	+	0.839275i	$0.682980\pi$
$864$	−28353.1	+	18737.2i	−1.11643	+	0.737792i
$865$		0			0
$866$	15338.3	−	1799.60i	0.601869	−	0.0706155i
$867$	−11572.7	+	11572.7i	−0.453323	+	0.453323i
$868$	24763.2	−	40226.1i	0.968340	−	1.57300i
$869$			31390.5i			1.22537i
$870$		0			0
$871$		−	338.895i		−	0.0131837i
$872$	29221.7	+	13579.6i	1.13483	+	0.527367i
$873$	51740.2	−	51740.2i	2.00589	−	2.00589i
$874$	−120.782	−	1029.45i	−0.00467452	−	0.0398418i
$875$		0			0
$876$	15926.3	+	66937.2i	0.614270	+	2.58173i
$877$	−15683.5	−	15683.5i	−0.603872	−	0.603872i	0.337466	−	0.941338i	$-0.390430\pi$
$877$	−15683.5	−	15683.5i	−0.603872	−	0.603872i	−0.941338	+	0.337466i	$0.890430\pi$
$878$	−6193.65	−	4892.90i	−0.238070	−	0.188072i
$879$	18250.8			0.700324
$880$		0			0
$881$	5393.01			0.206237			0.103119	−	0.994669i	$-0.467118\pi$
$881$	5393.01			0.206237			0.103119	+	0.994669i	$0.467118\pi$
$882$	−21391.8	−	16899.2i	−0.816666	−	0.645155i
$883$	−629.665	−	629.665i	−0.0239976	−	0.0239976i	0.695006	−	0.719004i	$-0.255402\pi$
$883$	−629.665	−	629.665i	−0.0239976	−	0.0239976i	−0.719004	+	0.695006i	$0.755402\pi$
$884$	183.381	+	770.738i	0.00697713	+	0.0293244i
$885$		0			0
$886$	5966.81	+	50856.2i	0.226251	+	1.92838i
$887$	−748.301	+	748.301i	−0.0283264	+	0.0283264i	−0.721128	−	0.692802i	$-0.756376\pi$
$887$	−748.301	+	748.301i	−0.0283264	+	0.0283264i	0.692802	+	0.721128i	$0.256376\pi$
$888$	−23448.1	−	10896.6i	−0.886112	−	0.411785i
$889$		−	47377.9i		−	1.78741i
$890$		0			0
$891$		−	14291.9i		−	0.537371i
$892$	8610.04	−	13986.4i	0.323190	−	0.524999i
$893$	−5935.57	+	5935.57i	−0.222426	+	0.222426i
$894$	−2310.00	+	271.026i	−0.0864184	+	0.0101392i
$895$		0			0
$896$	24578.9	+	23047.0i	0.916433	+	0.859317i
$897$	−114.190	−	114.190i	−0.00425050	−	0.00425050i
$898$	−3936.93	+	4983.54i	−0.146300	+	0.185193i
$899$	32256.9			1.19669
$900$		0			0
$901$	−17385.0			−0.642818
$902$	7669.00	−	9707.77i	0.283093	−	0.358352i
$903$	−47581.6	−	47581.6i	−1.75351	−	1.75351i
$904$	10004.8	+	27376.0i	0.368090	+	1.00720i
$905$		0			0
$906$	66530.6	−	7805.84i	2.43966	−	0.286238i
$907$	−28781.0	+	28781.0i	−1.05365	+	1.05365i	−0.0551706	+	0.998477i	$0.517570\pi$
$907$	−28781.0	+	28781.0i	−1.05365	+	1.05365i	−0.998477	+	0.0551706i	$0.982430\pi$
$908$	13663.6	+	8411.36i	0.499388	+	0.307424i
$909$		−	61390.3i		−	2.24003i
$910$		0			0
$911$			15888.2i			0.577828i	0.957355	+	0.288914i	$0.0932941\pi$
$911$			15888.2i			0.577828i	−0.957355	+	0.288914i	$0.906706\pi$
$912$	12526.9	+	4126.64i	0.454834	+	0.149832i
$913$	41967.5	−	41967.5i	1.52127	−	1.52127i
$914$	727.229	+	6198.30i	0.0263179	+	0.224313i
$915$		0			0
$916$	−49456.0	+	11767.0i	−1.78392	+	0.424447i
$917$	21840.7	+	21840.7i	0.786525	+	0.786525i
$918$	34348.8	+	27135.1i	1.23494	+	0.975589i
$919$	−47850.0			−1.71755			−0.858773	−	0.512356i	$-0.828773\pi$
$919$	−47850.0			−1.71755			−0.858773	+	0.512356i	$0.828773\pi$
$920$		0			0
$921$	13896.7			0.497189
$922$	−5843.95	−	4616.64i	−0.208742	−	0.164903i
$923$	−564.402	−	564.402i	−0.0201273	−	0.0201273i
$924$	−70251.1	+	16714.8i	−2.50118	+	0.595104i
$925$		0			0
$926$	3556.41	+	30311.9i	0.126210	+	1.07571i
$927$	−11127.3	+	11127.3i	−0.394247	+	0.394247i
$928$	−4603.41	+	22543.4i	−0.162839	+	0.797440i
$929$			19071.0i			0.673517i	0.941591	+	0.336759i	$0.109331\pi$
$929$			19071.0i			0.673517i	−0.941591	+	0.336759i	$0.890669\pi$
$930$		0			0
$931$			4701.36i			0.165500i
$932$	7057.48	+	4344.59i	0.248042	+	0.152695i
$933$	12872.7	−	12872.7i	0.451696	−	0.451696i
$934$	20055.6	−	2353.07i	0.702612	−	0.0824354i
$935$		0			0
$936$	1240.67	−	453.414i	0.0433255	−	0.0158337i
$937$	24304.0	+	24304.0i	0.847362	+	0.847362i	0.989803	−	0.142441i	$-0.0454952\pi$
$937$	24304.0	+	24304.0i	0.847362	+	0.847362i	−0.142441	+	0.989803i	$0.545495\pi$
$938$	−11507.9	+	14567.3i	−0.400584	+	0.507077i
$939$	−29764.2			−1.03442
$940$		0			0
$941$	−25946.3			−0.898856			−0.449428	−	0.893316i	$-0.648372\pi$
$941$	−25946.3			−0.898856			−0.449428	+	0.893316i	$0.648372\pi$
$942$	−25908.0	+	32795.5i	−0.896101	+	1.13432i
$943$	−1071.66	−	1071.66i	−0.0370075	−	0.0370075i
$944$	716.520	−	361.423i	0.0247042	−	0.0124611i
$945$		0			0
$946$	−41695.6	+	4892.02i	−1.43302	+	0.168133i
$947$	−29498.0	+	29498.0i	−1.01220	+	1.01220i	−0.0122772	+	0.999925i	$0.503908\pi$
$947$	−29498.0	+	29498.0i	−1.01220	+	1.01220i	−0.999925	+	0.0122772i	$0.996092\pi$
$948$	−25651.5	+	41669.0i	−0.878821	+	1.42758i
$949$		−	1188.39i		−	0.0406500i
$950$		0			0
$951$		−	52628.5i		−	1.79453i
$952$	18289.6	−	39357.0i	0.622656	−	1.33988i
$953$	−22625.2	+	22625.2i	−0.769048	+	0.769048i	−0.977939	−	0.208891i	$-0.933015\pi$
$953$	−22625.2	+	22625.2i	−0.769048	+	0.769048i	0.208891	+	0.977939i	$0.433015\pi$
$954$	3377.69	+	28788.6i	0.114630	+	0.977009i
$955$		0			0
$956$	−12993.9	−	54612.4i	−0.439594	−	1.84758i
$957$	−34868.5	−	34868.5i	−1.17778	−	1.17778i
$958$	5512.57	+	4354.86i	0.185911	+	0.146867i
$959$	33226.0			1.11879
$960$		0			0
$961$	−34613.0			−1.16186
$962$	350.428	+	276.833i	0.0117445	+	0.00927803i
$963$	−20070.2	−	20070.2i	−0.671604	−	0.671604i
$964$	−5108.35	−	21470.0i	−0.170673	−	0.717326i
$965$		0			0
$966$	1030.84	+	8786.00i	0.0343339	+	0.292634i
$967$	19943.6	−	19943.6i	0.663230	−	0.663230i	−0.292910	−	0.956140i	$-0.594624\pi$
$967$	19943.6	−	19943.6i	0.663230	−	0.663230i	0.956140	+	0.292910i	$0.0946235\pi$
$968$	−6294.04	+	13544.0i	−0.208986	+	0.449713i
$969$		−	16988.1i		−	0.563194i
$970$		0			0
$971$		−	7147.31i		−	0.236218i	−0.993001	−	0.118109i	$-0.962317\pi$
$971$		−	7147.31i		−	0.236218i	0.993001	−	0.118109i	$-0.0376833\pi$
$972$	−9579.82	+	15561.7i	−0.316124	+	0.513522i
$973$	21105.1	−	21105.1i	0.695372	−	0.695372i
$974$	15486.2	−	1816.95i	0.509455	−	0.0597729i
$975$		0			0
$976$	19000.0	−	9583.87i	0.623131	−	0.314316i
$977$	4019.53	+	4019.53i	0.131623	+	0.131623i	0.769849	−	0.638226i	$-0.220331\pi$
$977$	4019.53	+	4019.53i	0.131623	+	0.131623i	−0.638226	+	0.769849i	$0.720331\pi$
$978$	−7243.84	+	9169.57i	−0.236843	+	0.299806i
$979$	17249.3			0.563117
$980$		0			0
$981$	−69200.1			−2.25218
$982$	15780.8	−	19976.1i	0.512816	−	0.649146i
$983$	26810.4	+	26810.4i	0.869907	+	0.869907i	0.992462	−	0.122555i	$-0.0391086\pi$
$983$	26810.4	+	26810.4i	0.869907	+	0.869907i	−0.122555	+	0.992462i	$0.539109\pi$
$984$	18113.1	−	6619.58i	0.586813	−	0.214456i
$985$		0			0
$986$	29434.0	−	3453.41i	0.950679	−	0.111540i
$987$	50658.0	−	50658.0i	1.63370	−	1.63370i
$988$	−193.988	−	119.419i	−0.00624655	−	0.00384538i
$989$			5142.91i			0.165354i
$990$		0			0
$991$		−	43289.7i		−	1.38763i	−0.720153	−	0.693815i	$-0.755928\pi$
$991$		−	43289.7i		−	1.38763i	0.720153	−	0.693815i	$-0.244072\pi$
$992$	9191.16	−	45010.1i	0.294173	−	1.44060i
$993$	−14812.0	+	14812.0i	−0.473357	+	0.473357i
$994$	5095.05	+	43426.1i	0.162581	+	1.38571i
$995$		0			0
$996$	90004.1	−	21414.6i	2.86334	−	0.681274i
$997$	−31938.0	−	31938.0i	−1.01453	−	1.01453i	−0.999893	−	0.0146370i	$-0.995341\pi$
$997$	−31938.0	−	31938.0i	−1.01453	−	1.01453i	−0.0146370	−	0.999893i	$-0.504659\pi$
$998$	−28979.9	−	22893.7i	−0.919181	−	0.726141i
$999$	24674.7			0.781456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.f.7.3	✓	24
4.3	odd	2	inner	100.4.e.f.7.4	yes	24
5.2	odd	4	inner	100.4.e.f.43.9	yes	24
5.3	odd	4	inner	100.4.e.f.43.4	yes	24
5.4	even	2	inner	100.4.e.f.7.10	yes	24
20.3	even	4	inner	100.4.e.f.43.3	yes	24
20.7	even	4	inner	100.4.e.f.43.10	yes	24
20.19	odd	2	inner	100.4.e.f.7.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.e.f.7.3	✓	24	1.1	even	1	trivial
100.4.e.f.7.4	yes	24	4.3	odd	2	inner
100.4.e.f.7.9	yes	24	20.19	odd	2	inner
100.4.e.f.7.10	yes	24	5.4	even	2	inner
100.4.e.f.43.3	yes	24	20.3	even	4	inner
100.4.e.f.43.4	yes	24	5.3	odd	4	inner
100.4.e.f.43.9	yes	24	5.2	odd	4	inner
100.4.e.f.43.10	yes	24	20.7	even	4	inner

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21943 - 1.75332i) q^{2} +(6.14790 + 6.14790i) q^{3} +(1.85174 + 7.78274i) q^{4} +(-2.86560 - 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(9.53582 - 20.5199i) q^{8} +48.5934i q^{9} +O(q^{10})\)	\(q+(-2.21943 - 1.75332i) q^{2} +(6.14790 + 6.14790i) q^{3} +(1.85174 + 7.78274i) q^{4} +(-2.86560 - 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(9.53582 - 20.5199i) q^{8} +48.5934i q^{9} +44.6211i q^{11} +(-36.4632 + 59.2319i) q^{12} +(0.849478 - 0.849478i) q^{13} +(-65.3604 + 7.66854i) q^{14} +(-57.1421 + 28.8233i) q^{16} +(58.2897 + 58.2897i) q^{17} +(85.1997 - 107.850i) q^{18} -23.7025 q^{19} +202.293 q^{21} +(78.2350 - 99.0334i) q^{22} +(-10.9325 - 10.9325i) q^{23} +(184.780 - 67.5294i) q^{24} +(-3.37476 + 0.395951i) q^{26} +(-132.754 + 132.754i) q^{27} +(158.508 + 97.5778i) q^{28} +127.106i q^{29} -253.779i q^{31} +(177.359 + 36.2171i) q^{32} +(-274.326 + 274.326i) q^{33} +(-27.1695 - 231.571i) q^{34} +(-378.190 + 89.9824i) q^{36} +(-92.9341 - 92.9341i) q^{37} +(52.6061 + 41.5581i) q^{38} +10.4450 q^{39} +98.0252 q^{41} +(-448.975 - 354.684i) q^{42} +(-235.212 - 235.212i) q^{43} +(-347.274 + 82.6268i) q^{44} +(5.09576 + 43.4321i) q^{46} +(250.419 - 250.419i) q^{47} +(-528.507 - 174.101i) q^{48} -198.348i q^{49} +716.719i q^{51} +(8.18428 + 5.03825i) q^{52} +(-149.126 + 149.126i) q^{53} +(527.398 - 61.8781i) q^{54} +(-180.713 - 494.483i) q^{56} +(-145.721 - 145.721i) q^{57} +(222.857 - 282.103i) q^{58} -12.5393 q^{59} -332.505 q^{61} +(-444.956 + 563.246i) q^{62} +(799.467 + 799.467i) q^{63} +(-330.136 - 391.349i) q^{64} +(1089.83 - 127.866i) q^{66} +(199.472 - 199.472i) q^{67} +(-345.716 + 561.592i) q^{68} -134.424i q^{69} -664.410i q^{71} +(997.134 + 463.378i) q^{72} +(699.484 - 699.484i) q^{73} +(43.3176 + 369.204i) q^{74} +(-43.8910 - 184.471i) q^{76} +(734.114 + 734.114i) q^{77} +(-23.1820 - 18.3135i) q^{78} +703.490 q^{79} -320.295 q^{81} +(-217.560 - 171.869i) q^{82} +(-940.531 - 940.531i) q^{83} +(374.594 + 1574.39i) q^{84} +(109.635 + 934.437i) q^{86} +(-781.435 + 781.435i) q^{87} +(915.623 + 425.499i) q^{88} -386.574i q^{89} -27.9515i q^{91} +(64.8407 - 105.329i) q^{92} +(1560.21 - 1560.21i) q^{93} +(-994.852 + 116.723i) q^{94} +(867.728 + 1313.05i) q^{96} +(-1064.76 - 1064.76i) q^{97} +(-347.768 + 440.220i) q^{98} -2168.29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{6}+O(q^{10}) \) 24 * q + 36 * q^6	\( 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) \) 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * q^96

Introduction

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