LMFDB - Embedded newform 100.4.e.f.7.4

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			7.4
Character	$\chi$	$=$	100.7
Dual form			100.4.e.f.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75332 - 2.21943i) q^{2} +(-6.14790 - 6.14790i) q^{3} +(-1.85174 + 7.78274i) q^{4} +(-2.86560 + 24.4241i) q^{6} +(-16.4522 + 16.4522i) q^{7} +(20.5199 - 9.53582i) q^{8} +48.5934i q^{9} +O(q^{10})$	\(q+(-1.75332 - 2.21943i) 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} +(20.5199 - 9.53582i) q^{8} +48.5934i q^{9} -44.6211i q^{11} +(59.2319 - 36.4632i) 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} +(107.850 - 85.1997i) q^{18} +23.7025 q^{19} +202.293 q^{21} +(-99.0334 + 78.2350i) 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} +(-97.5778 - 158.508i) q^{28} +127.106i q^{29} +253.779i q^{31} +(36.2171 + 177.359i) 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} +(-41.5581 - 52.6061i) q^{38} -10.4450 q^{39} +98.0252 q^{41} +(-354.684 - 448.975i) 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} +(174.101 + 528.507i) q^{48} -198.348i q^{49} -716.719i q^{51} +(5.03825 + 8.18428i) 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} +(282.103 - 222.857i) q^{58} +12.5393 q^{59} -332.505 q^{61} +(563.246 - 444.956i) 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} +(-561.592 + 345.716i) q^{68} -134.424i q^{69} +664.410i q^{71} +(463.378 + 997.134i) 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} +(18.3135 + 23.1820i) q^{78} -703.490 q^{79} -320.295 q^{81} +(-171.869 - 217.560i) 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} +(-425.499 - 915.623i) q^{88} -386.574i q^{89} +27.9515i q^{91} +(-105.329 + 64.8407i) 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} +(-440.220 + 347.768i) 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 $

$2$	−1.75332	−	2.21943i	−0.619892	−	0.784687i
$2$	−1.75332	−	2.21943i	−0.619892	−	0.784687i
$3$	−6.14790	−	6.14790i	−1.18316	−	1.18316i	−0.978920	−	0.204244i	$-0.934526\pi$
$3$	−6.14790	−	6.14790i	−1.18316	−	1.18316i	−0.204244	−	0.978920i	$-0.565474\pi$
$4$	−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	−0.994363	−	0.106029i	$-0.966186\pi$
$7$	−16.4522	+	16.4522i	−0.888334	+	0.888334i	0.106029	+	0.994363i	$0.466186\pi$
$8$	20.5199	−	9.53582i	0.906862	−	0.421427i
$9$			48.5934i			1.79975i
$10$		0			0
$11$		−	44.6211i		−	1.22307i	−0.791217	−	0.611535i	$-0.790552\pi$
$11$		−	44.6211i		−	1.22307i	0.791217	−	0.611535i	$-0.209448\pi$
$12$	59.2319	−	36.4632i	1.42490	−	0.877168i
$13$	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	$0.549901\pi$
$18$	107.850	−	85.1997i	1.41224	−	1.11565i
$19$	23.7025			0.286197			0.143098	−	0.989708i	$-0.454293\pi$
$19$	23.7025			0.286197			0.143098	+	0.989708i	$0.454293\pi$
$20$		0			0
$21$	202.293			2.10209
$22$	−99.0334	+	78.2350i	−0.959727	+	0.758171i
$23$	10.9325	+	10.9325i	0.0991124	+	0.0991124i	0.754924	−	0.655812i	$-0.227674\pi$
$23$	10.9325	+	10.9325i	0.0991124	+	0.0991124i	−0.655812	+	0.754924i	$0.727674\pi$
$24$	−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
$28$	−97.5778	−	158.508i	−0.658588	−	1.06983i
$29$			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	$0.262894\pi$
$31$			253.779i			1.47033i	−0.677890	+	0.735163i	$0.737106\pi$
$32$	36.2171	+	177.359i	0.200073	+	0.979781i
$33$	−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	$0.844315\pi$
$38$	−41.5581	−	52.6061i	−0.177411	−	0.224575i
$39$	−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	$0.440222\pi$
$42$	−354.684	−	448.975i	−1.30307	−	1.64948i
$43$	235.212	+	235.212i	0.834173	+	0.834173i	0.988085	−	0.153911i	$-0.0491870\pi$
$43$	235.212	+	235.212i	0.834173	+	0.834173i	−0.153911	+	0.988085i	$0.549187\pi$
$44$	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	−0.979350	−	0.202172i	$-0.935200\pi$
$47$	−250.419	+	250.419i	−0.777178	+	0.777178i	0.202172	+	0.979350i	$0.435200\pi$
$48$	174.101	+	528.507i	0.523529	+	1.58924i
$49$		−	198.348i		−	0.578275i
$50$		0			0
$51$		−	716.719i		−	1.96786i
$52$	5.03825	+	8.18428i	0.0134362	+	0.0218261i
$53$	−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
$58$	282.103	−	222.857i	0.638654	−	0.504528i
$59$	12.5393			0.0276690			0.0138345	−	0.999904i	$-0.495596\pi$
$59$	12.5393			0.0276690			0.0138345	+	0.999904i	$0.495596\pi$
$60$		0			0
$61$	−332.505			−0.697916			−0.348958	−	0.937138i	$-0.613464\pi$
$61$	−332.505			−0.697916			−0.348958	+	0.937138i	$0.613464\pi$
$62$	563.246	−	444.956i	1.15375	−	0.911444i
$63$	−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	−0.865182	−	0.501459i	$-0.832797\pi$
$67$	−199.472	+	199.472i	−0.363723	+	0.363723i	0.501459	+	0.865182i	$0.332797\pi$
$68$	−561.592	+	345.716i	−1.00151	+	0.616533i
$69$		−	134.424i		−	0.234532i
$70$		0			0
$71$			664.410i			1.11058i	0.831658	+	0.555288i	$0.187392\pi$
$71$			664.410i			1.11058i	−0.831658	+	0.555288i	$0.812608\pi$
$72$	463.378	+	997.134i	0.758466	+	1.63213i
$73$	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
$78$	18.3135	+	23.1820i	0.0265845	+	0.0336518i
$79$	−703.490			−1.00188			−0.500942	−	0.865481i	$-0.667013\pi$
$79$	−703.490			−1.00188			−0.500942	+	0.865481i	$0.667013\pi$
$80$		0			0
$81$	−320.295			−0.439363
$82$	−171.869	−	217.560i	−0.231461	−	0.292994i
$83$	940.531	+	940.531i	1.24382	+	1.24382i	0.958406	+	0.285410i	$0.0921297\pi$
$83$	940.531	+	940.531i	1.24382	+	1.24382i	0.285410	+	0.958406i	$0.407870\pi$
$84$	−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
$88$	−425.499	−	915.623i	−0.515435	−	1.10916i
$89$		−	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
$92$	−105.329	+	64.8407i	−0.119362	+	0.0734794i
$93$	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	$-0.538932\pi$
$98$	−440.220	+	347.768i	−0.453765	+	0.358468i
$99$	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	$0.713808\pi$
$102$	−1590.71	+	1256.64i	−1.54415	+	1.21986i
$103$	−228.987	−	228.987i	−0.219056	−	0.219056i	0.589045	−	0.808101i	$-0.299504\pi$
$103$	−228.987	−	228.987i	−0.219056	−	0.219056i	−0.808101	+	0.589045i	$0.799504\pi$
$104$	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	−0.495464	−	0.868628i	$-0.665002\pi$
$107$	413.024	−	413.024i	0.373164	−	0.373164i	0.868628	+	0.495464i	$0.165002\pi$
$108$	787.364	+	1279.02i	0.701519	+	1.13957i
$109$			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
$112$	1414.32	−	465.907i	1.19322	−	0.393072i
$113$	−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
$118$	−21.9853	−	27.8300i	−0.0171518	−	0.0217115i
$119$	−1917.99			−1.47749
$120$		0			0
$121$	−660.042			−0.495900
$122$	582.987	+	737.971i	0.432632	+	0.547646i
$123$	−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	$0.501930\pi$
$127$	−1439.87	+	1439.87i	−1.00604	+	1.00604i	−0.999982	+	0.00606278i	$0.998070\pi$
$128$	−1447.41	−	46.5554i	−0.999483	−	0.0321481i
$129$		−	2892.12i		−	1.97393i
$130$		0			0
$131$		−	1327.53i		−	0.885393i	−0.896672	−	0.442696i	$-0.854022\pi$
$131$		−	1327.53i		−	0.885393i	0.896672	−	0.442696i	$-0.145978\pi$
$132$	−1627.03	−	2642.99i	−1.07284	−	1.74275i
$133$	−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	$0.603106\pi$
$138$	−298.344	+	235.688i	−0.184035	+	0.145385i
$139$	−1282.81			−0.782782			−0.391391	−	0.920224i	$-0.628006\pi$
$139$	−1282.81			−0.782782			−0.391391	+	0.920224i	$0.628006\pi$
$140$		0			0
$141$	3079.10			1.83906
$142$	1474.61	−	1164.92i	0.871455	−	0.688437i
$143$	−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
$148$	895.372	−	551.192i	0.497291	−	0.306133i
$149$		−	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	$-0.737642\pi$
$151$		−	2723.98i		−	1.46804i	0.679128	−	0.734020i	$-0.262358\pi$
$152$	486.375	−	226.023i	0.259541	−	0.120611i
$153$	−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	$0.892180\pi$
$158$	1233.44	+	1561.35i	0.621060	+	0.786166i
$159$	1833.62			0.914564
$160$		0			0
$161$	−359.727			−0.176090
$162$	561.580	+	710.873i	0.272357	+	0.344762i
$163$	336.009	+	336.009i	0.161462	+	0.161462i	0.783214	−	0.621752i	$-0.213579\pi$
$163$	336.009	+	336.009i	0.161462	+	0.161462i	−0.621752	+	0.783214i	$0.713579\pi$
$164$	−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	−0.316953	−	0.948441i	$-0.602660\pi$
$167$	1362.82	−	1362.82i	0.631488	−	0.631488i	0.948441	+	0.316953i	$0.102660\pi$
$168$	4151.04	−	1929.03i	1.90631	−	0.885879i
$169$			2195.56i			0.999343i
$170$		0			0
$171$			1151.79i			0.515084i
$172$	−2266.14	+	1395.04i	−1.00460	+	0.618435i
$173$	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
$178$	−857.973	+	677.787i	−0.361280	+	0.285406i
$179$	96.1861			0.0401636			0.0200818	−	0.999798i	$-0.493607\pi$
$179$	96.1861			0.0401636			0.0200818	+	0.999798i	$0.493607\pi$
$180$		0			0
$181$	2470.64			1.01459			0.507297	−	0.861771i	$-0.330645\pi$
$181$	2470.64			1.01459			0.507297	+	0.861771i	$0.330645\pi$
$182$	62.0365	−	49.0080i	0.0252662	−	0.0199600i
$183$	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
$188$	−1485.24	−	2412.66i	−0.576180	−	0.935964i
$189$			4368.18i			1.68116i
$190$		0			0
$191$			3314.57i			1.25567i	0.778345	+	0.627837i	$0.216060\pi$
$191$			3314.57i			1.25567i	−0.778345	+	0.627837i	$0.783940\pi$
$192$	−4435.62	+	376.328i	−1.66726	+	0.141454i
$193$	−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	$0.411140\pi$
$198$	−3801.70	−	4812.37i	−1.36452	−	1.72727i
$199$	3891.88			1.38637			0.693185	−	0.720759i	$-0.256207\pi$
$199$	3891.88			1.38637			0.693185	+	0.720759i	$0.256207\pi$
$200$		0			0
$201$	2452.67			0.860688
$202$	2215.05	+	2803.91i	0.771537	+	0.976646i
$203$	−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
$208$	−73.0257	+	24.0562i	−0.0243434	+	0.00801923i
$209$		−	1057.63i		−	0.350038i
$210$		0			0
$211$			5180.09i			1.69010i	0.534684	+	0.845052i	$0.320431\pi$
$211$			5180.09i			1.69010i	−0.534684	+	0.845052i	$0.679569\pi$
$212$	−884.465	−	1436.75i	−0.286534	−	0.465455i
$213$	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
$218$	3160.61	−	2496.84i	0.981944	−	0.775722i
$219$	−8600.72			−2.65380
$220$		0			0
$221$	99.0318			0.0301430
$222$	2536.14	−	2003.52i	0.766733	−	0.605708i
$223$	1451.70	+	1451.70i	0.435933	+	0.435933i	0.890641	−	0.454707i	$-0.150256\pi$
$223$	1451.70	+	1451.70i	0.435933	+	0.435933i	−0.454707	+	0.890641i	$0.650256\pi$
$224$	−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	−0.883361	−	0.468694i	$-0.844725\pi$
$227$	−1418.20	+	1418.20i	−0.414667	+	0.414667i	0.468694	+	0.883361i	$0.344725\pi$
$228$	1403.95	−	864.270i	0.407801	−	0.251042i
$229$			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
$232$	1212.06	+	2608.21i	0.342998	+	0.738092i
$233$	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
$238$	3362.84	+	4256.84i	0.915885	+	1.15937i
$239$	7017.11			1.89916			0.949580	−	0.313525i	$-0.101510\pi$
$239$	7017.11			1.89916			0.949580	+	0.313525i	$0.101510\pi$
$240$		0			0
$241$	−2758.67			−0.737351			−0.368675	−	0.929558i	$-0.620189\pi$
$241$	−2758.67			−0.737351			−0.368675	+	0.929558i	$0.620189\pi$
$242$	1157.27	+	1464.92i	0.307404	+	0.389126i
$243$	−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
$248$	2419.99	+	5207.54i	0.619636	+	1.33338i
$249$		−	11564.6i		−	2.94328i
$250$		0			0
$251$		−	4312.99i		−	1.08460i	−0.840186	−	0.542298i	$-0.817554\pi$
$251$		−	4312.99i		−	1.08460i	0.840186	−	0.542298i	$-0.182446\pi$
$252$	7702.45	−	4741.64i	1.92543	−	1.18530i
$253$	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	$0.740244\pi$
$258$	−6418.85	+	5070.80i	−1.54892	+	1.22362i
$259$	3057.94			0.733633
$260$		0			0
$261$	−6176.51			−1.46481
$262$	−2946.35	+	2327.58i	−0.694756	+	0.548848i
$263$	−950.128	−	950.128i	−0.222766	−	0.222766i	0.586896	−	0.809662i	$-0.300350\pi$
$263$	−950.128	−	950.128i	−0.222766	−	0.222766i	−0.809662	+	0.586896i	$0.800350\pi$
$264$	−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
$268$	−1183.07	−	1921.81i	−0.269655	−	0.438035i
$269$		−	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	$-0.943035\pi$
$271$		−	1588.26i		−	0.356014i	0.984029	−	0.178007i	$-0.0569649\pi$
$272$	−1650.70	−	5010.90i	−0.367972	−	1.11702i
$273$	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	$0.862709\pi$
$278$	2249.18	+	2847.11i	0.485240	+	0.614239i
$279$	−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	$0.491466\pi$
$282$	−5398.65	−	6833.86i	−1.14002	−	1.44309i
$283$	−4366.71	−	4366.71i	−0.917223	−	0.917223i	0.0796034	−	0.996827i	$-0.474635\pi$
$283$	−4366.71	−	4366.71i	−0.917223	−	0.917223i	−0.996827	+	0.0796034i	$0.974635\pi$
$284$	−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
$288$	−8618.49	+	1759.91i	−1.76337	+	0.360083i
$289$			1882.39i			0.383145i
$290$		0			0
$291$			13092.1i			2.63735i
$292$	4148.64	+	6739.17i	0.831441	+	1.35062i
$293$	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
$298$	−209.911	+	165.827i	−0.0408048	+	0.0322352i
$299$	18.5738			0.00359249
$300$		0			0
$301$	−7739.49			−1.48205
$302$	−6045.67	+	4776.00i	−1.15195	+	0.910026i
$303$	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	−0.804314	−	0.594204i	$-0.797467\pi$
$307$	−1130.20	+	1130.20i	−0.210110	+	0.210110i	0.594204	+	0.804314i	$0.297467\pi$
$308$	−7072.81	+	4354.03i	−1.30848	+	0.805500i
$309$			2815.58i			0.518358i
$310$		0			0
$311$			2093.83i			0.381769i	0.981612	+	0.190885i	$0.0611356\pi$
$311$			2093.83i			0.381769i	−0.981612	+	0.190885i	$0.938864\pi$
$312$	−214.331	+	99.6018i	−0.0388914	+	0.0180732i
$313$	−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	$0.930156\pi$
$318$	−3214.92	−	4069.60i	−0.566931	−	0.717646i
$319$	5671.61			0.995452
$320$		0			0
$321$	−5078.46			−0.883028
$322$	630.716	+	798.389i	0.109157	+	0.138175i
$323$	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
$328$	2011.47	−	934.750i	0.338613	−	0.157357i
$329$		−	8239.88i		−	1.38079i
$330$		0			0
$331$		−	2409.27i		−	0.400077i	−0.979788	−	0.200038i	$-0.935893\pi$
$331$		−	2409.27i		−	0.400077i	0.979788	−	0.200038i	$-0.0641067\pi$
$332$	−9061.53	+	5578.29i	−1.49794	+	0.922133i
$333$	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	$0.611654\pi$
$338$	4872.89	−	3849.51i	0.784172	−	0.619485i
$339$	11199.5			1.79432
$340$		0			0
$341$	11323.9			1.79831
$342$	2556.31	−	2019.45i	0.404180	−	0.319296i
$343$	−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	$-0.486107\pi$
$347$	6739.78	−	6739.78i	1.04268	−	1.04268i	0.999048	−	0.0436336i	$-0.0138934\pi$
$348$	4634.69	+	7528.72i	0.713924	+	1.15972i
$349$			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
$352$	7913.97	−	1616.05i	1.19834	−	0.244703i
$353$	−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
$358$	−168.645	−	213.478i	−0.0248971	−	0.0315159i
$359$	−7760.71			−1.14093			−0.570466	−	0.821321i	$-0.693237\pi$
$359$	−7760.71			−1.14093			−0.570466	+	0.821321i	$0.693237\pi$
$360$		0			0
$361$	−6297.19			−0.918092
$362$	−4331.83	−	5483.42i	−0.628939	−	0.796139i
$363$	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	−0.950852	−	0.309646i	$-0.899789\pi$
$367$	−4508.13	+	4508.13i	−0.641206	+	0.641206i	0.309646	+	0.950852i	$0.399789\pi$
$368$	−309.596	−	939.817i	−0.0438554	−	0.133129i
$369$			4763.38i			0.672009i
$370$		0			0
$371$		−	4906.89i		−	0.686666i
$372$	9253.60	+	15031.8i	1.28972	+	2.09506i
$373$	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
$378$	9694.88	−	7658.82i	1.31918	−	1.04214i
$379$	−8526.74			−1.15564			−0.577822	−	0.816163i	$-0.696097\pi$
$379$	−8526.74			−1.15564			−0.577822	+	0.816163i	$0.696097\pi$
$380$		0			0
$381$	17704.3			2.38063
$382$	7356.46	−	5811.50i	0.985312	−	0.778383i
$383$	−7645.72	−	7645.72i	−1.02005	−	1.02005i	−0.999795	−	0.0202520i	$-0.993553\pi$
$383$	−7645.72	−	7645.72i	−1.02005	−	1.02005i	−0.0202520	−	0.999795i	$-0.506447\pi$
$384$	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
$388$	10258.4	−	6315.08i	1.34225	−	0.826287i
$389$			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
$392$	−1891.41	−	4070.10i	−0.243701	−	0.524416i
$393$	−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	$0.989005\pi$
$398$	−6823.70	−	8637.75i	−0.859400	−	1.08787i
$399$	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	$0.338350\pi$
$402$	−4300.32	−	5443.54i	−0.533534	−	0.675371i
$403$	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
$408$	−6834.50	−	14707.0i	−0.829310	−	1.78458i
$409$			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
$412$	2206.17	−	1358.12i	0.263811	−	0.162403i
$413$	−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
$418$	−2347.34	+	1854.37i	−0.274671	+	0.216986i
$419$	−223.257			−0.0260306			−0.0130153	−	0.999915i	$-0.504143\pi$
$419$	−223.257			−0.0260306			−0.0130153	+	0.999915i	$0.504143\pi$
$420$		0			0
$421$	−9330.20			−1.08011			−0.540055	−	0.841630i	$-0.681597\pi$
$421$	−9330.20			−1.08011			−0.540055	+	0.841630i	$0.681597\pi$
$422$	11496.8	−	9082.35i	1.32620	−	1.04768i
$423$	−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
$428$	2449.64	+	3979.27i	0.276654	+	0.449405i
$429$			466.068i			0.0524522i
$430$		0			0
$431$			4319.11i			0.482701i	0.970438	+	0.241350i	$0.0775903\pi$
$431$			4319.11i			0.482701i	−0.970438	+	0.241350i	$0.922410\pi$
$432$	−11412.2	+	3759.44i	−1.27100	+	0.418695i
$433$	−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
$438$	15079.8	+	19088.7i	1.64507	+	2.08240i
$439$	−2790.65			−0.303395			−0.151697	−	0.988427i	$-0.548474\pi$
$439$	−2790.65			−0.303395			−0.151697	+	0.988427i	$0.548474\pi$
$440$		0			0
$441$	9638.42			1.04075
$442$	−173.634	−	219.794i	−0.0186854	−	0.0236528i
$443$	12801.3	+	12801.3i	1.37293	+	1.37293i	0.856077	+	0.516849i	$0.172895\pi$
$443$	12801.3	+	12801.3i	1.37293	+	1.37293i	0.516849	+	0.856077i	$0.327105\pi$
$444$	−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
$448$	1007.08	+	11870.0i	0.106205	+	1.25180i
$449$		−	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
$452$	−5402.18	−	8775.46i	−0.562162	−	0.913192i
$453$	−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	$0.786022\pi$
$458$	14103.5	−	11141.6i	1.43890	−	1.13671i
$459$	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	$0.457536\pi$
$462$	−20033.7	+	15826.4i	−2.01743	+	1.59374i
$463$	7629.96	+	7629.96i	0.765862	+	0.765862i	0.977375	−	0.211513i	$-0.0678391\pi$
$463$	7629.96	+	7629.96i	0.765862	+	0.765862i	−0.211513	+	0.977375i	$0.567839\pi$
$464$	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	−0.411280	−	0.911509i	$-0.634918\pi$
$467$	5048.30	−	5048.30i	0.500230	−	0.500230i	0.911509	+	0.411280i	$0.134918\pi$
$468$	−397.702	+	244.826i	−0.0392816	+	0.0241818i
$469$		−	6563.51i		−	0.646215i
$470$		0			0
$471$			14776.5i			1.44558i
$472$	257.305	−	119.572i	0.0250920	−	0.0116605i
$473$	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
$478$	−12303.2	−	15574.0i	−1.17727	−	1.49025i
$479$	2483.78			0.236924			0.118462	−	0.992959i	$-0.462204\pi$
$479$	2483.78			0.236924			0.118462	+	0.992959i	$0.462204\pi$
$480$		0			0
$481$	−157.891			−0.0149672
$482$	4836.83	+	6122.67i	0.457078	+	0.578590i
$483$	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	−0.502099	−	0.864810i	$-0.667439\pi$
$487$	3898.10	−	3898.10i	0.362710	−	0.362710i	0.864810	+	0.502099i	$0.167439\pi$
$488$	−6822.98	+	3170.70i	−0.632913	+	0.294121i
$489$		−	4131.50i		−	0.382071i
$490$		0			0
$491$		−	9000.53i		−	0.827267i	−0.910443	−	0.413634i	$-0.864259\pi$
$491$		−	9000.53i		−	0.827267i	0.910443	−	0.413634i	$-0.135741\pi$
$492$	5806.21	−	3574.31i	0.532041	−	0.327525i
$493$	−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
$498$	−25666.8	+	20276.4i	−2.30955	+	1.82451i
$499$	−13057.4			−1.17140			−0.585699	−	0.810528i	$-0.699180\pi$
$499$	−13057.4			−1.17140			−0.585699	+	0.810528i	$0.699180\pi$
$500$		0			0
$501$	−16757.0			−1.49431
$502$	−9572.39	+	7562.06i	−0.851069	+	0.672333i
$503$	1782.55	+	1782.55i	0.158012	+	0.158012i	0.781685	−	0.623673i	$-0.214360\pi$
$503$	1782.55	+	1782.55i	0.158012	+	0.158012i	−0.623673	+	0.781685i	$0.714360\pi$
$504$	−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
$508$	−8539.86	−	13872.4i	−0.745856	−	1.21159i
$509$		−	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
$512$	3042.55	−	11178.6i	0.262623	−	0.964898i
$513$	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
$518$	−5361.54	−	6786.88i	−0.454773	−	0.575672i
$519$	−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	$0.289258\pi$
$522$	10829.4	+	13708.3i	0.908026	+	1.14942i
$523$	3175.36	+	3175.36i	0.265486	+	0.265486i	0.827278	−	0.561793i	$-0.189888\pi$
$523$	3175.36	+	3175.36i	0.265486	+	0.265486i	−0.561793	+	0.827278i	$0.689888\pi$
$524$	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
$528$	23582.5	−	7768.60i	1.94375	−	0.640312i
$529$		−	11928.0i		−	0.980353i
$530$		0			0
$531$			609.325i			0.0497975i
$532$	−2312.84	−	3757.05i	−0.188486	−	0.306182i
$533$	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
$538$	−12647.8	+	9991.59i	−1.01354	+	0.800684i
$539$	−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	$0.413786\pi$
$542$	−3525.02	+	2784.72i	−0.279359	+	0.220690i
$543$	−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	−0.882712	−	0.469915i	$-0.844285\pi$
$547$	−5281.02	+	5281.02i	−0.412797	+	0.412797i	0.469915	+	0.882712i	$0.344285\pi$
$548$	−9728.67	+	5988.98i	−0.758372	+	0.466855i
$549$		−	16157.5i		−	1.25608i
$550$		0			0
$551$			3012.73i			0.232934i
$552$	−1281.84	−	2758.37i	−0.0988384	−	0.212689i
$553$	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	$0.583545\pi$
$558$	21621.9	+	27370.0i	1.64037	+	2.07646i
$559$	399.614			0.0302359
$560$		0			0
$561$	−31980.8			−2.40683
$562$	−442.811	−	560.531i	−0.0332364	−	0.0420722i
$563$	−7802.12	−	7802.12i	−0.584050	−	0.584050i	0.351963	−	0.936014i	$-0.385514\pi$
$563$	−7802.12	−	7802.12i	−0.584050	−	0.584050i	−0.936014	+	0.351963i	$0.885514\pi$
$564$	−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
$568$	6335.69	+	13633.7i	0.468027	+	1.00714i
$569$			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	$-0.813019\pi$
$571$		−	15123.8i		−	1.10843i	0.832375	−	0.554213i	$-0.186981\pi$
$572$	365.192	−	224.812i	0.0266948	−	0.0164334i
$573$	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	$0.649496\pi$
$578$	4177.83	−	3300.43i	0.300649	−	0.237508i
$579$	30630.8			2.19857
$580$		0			0
$581$	−30947.6			−2.20985
$582$	29056.9	−	22954.6i	2.06950	−	1.63487i
$583$	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	−0.954522	−	0.298141i	$-0.903633\pi$
$587$	−9334.98	+	9334.98i	−0.656381	+	0.656381i	0.298141	+	0.954522i	$0.403633\pi$
$588$	−7232.41	−	11748.5i	−0.507244	−	0.823982i
$589$			6015.21i			0.420802i
$590$		0			0
$591$		−	42050.2i		−	2.92676i
$592$	2631.78	+	7989.11i	0.182712	+	0.554646i
$593$	−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
$598$	−32.5659	−	41.2234i	−0.00222695	−	0.00281898i
$599$	−2384.18			−0.162629			−0.0813146	−	0.996688i	$-0.525912\pi$
$599$	−2384.18			−0.162629			−0.0813146	+	0.996688i	$0.525912\pi$
$600$		0			0
$601$	11760.3			0.798190			0.399095	−	0.916910i	$-0.369324\pi$
$601$	11760.3			0.798190			0.399095	+	0.916910i	$0.369324\pi$
$602$	13569.8	+	17177.3i	0.918710	+	1.16294i
$603$	−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	−0.835748	−	0.549113i	$-0.814966\pi$
$607$	−4286.59	+	4286.59i	−0.286635	+	0.286635i	0.549113	+	0.835748i	$0.314966\pi$
$608$	858.437	+	4203.86i	0.0572603	+	0.280410i
$609$			25712.6i			1.71088i
$610$		0			0
$611$			425.451i			0.0281701i
$612$	−16799.5	−	27289.6i	−1.10961	−	1.80248i
$613$	−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	$0.818600\pi$
$618$	6248.98	−	4936.61i	0.406749	−	0.321326i
$619$	6898.58			0.447944			0.223972	−	0.974596i	$-0.428098\pi$
$619$	6898.58			0.447944			0.223972	+	0.974596i	$0.428098\pi$
$620$		0			0
$621$	2902.67			0.187568
$622$	4647.11	−	3671.15i	0.299569	−	0.236656i
$623$	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
$628$	11578.3	−	7127.60i	0.735706	−	0.452901i
$629$		−	10834.2i		−	0.686786i
$630$		0			0
$631$			6731.96i			0.424715i	0.977192	+	0.212357i	$0.0681141\pi$
$631$			6731.96i			0.424715i	−0.977192	+	0.212357i	$0.931886\pi$
$632$	−14435.6	+	6708.35i	−0.908571	+	0.422221i
$633$	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
$638$	−9944.14	−	12587.7i	−0.617073	−	0.781118i
$639$	−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	$0.722516\pi$
$642$	8904.17	+	11271.3i	0.547382	+	0.692901i
$643$	3857.48	+	3857.48i	0.236585	+	0.236585i	0.815434	−	0.578849i	$-0.196498\pi$
$643$	3857.48	+	3857.48i	0.236585	+	0.236585i	−0.578849	+	0.815434i	$0.696498\pi$
$644$	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	−0.616659	−	0.787230i	$-0.711514\pi$
$647$	2807.13	−	2807.13i	0.170572	−	0.170572i	0.787230	+	0.616659i	$0.211514\pi$
$648$	−6572.44	+	3054.28i	−0.398441	+	0.185160i
$649$		−	559.516i		−	0.0338412i
$650$		0			0
$651$			51337.7i			3.09076i
$652$	−3237.27	+	1992.87i	−0.194450	+	0.119704i
$653$	−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
$658$	−18287.8	+	14447.1i	−1.08349	+	0.855939i
$659$	−18295.5			−1.08147			−0.540737	−	0.841191i	$-0.681855\pi$
$659$	−18295.5			−1.08147			−0.540737	+	0.841191i	$0.681855\pi$
$660$		0			0
$661$	27859.2			1.63933			0.819664	−	0.572845i	$-0.194160\pi$
$661$	27859.2			1.63933			0.819664	+	0.572845i	$0.194160\pi$
$662$	−5347.21	+	4224.22i	−0.313935	+	0.248004i
$663$	−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
$668$	8082.90	+	13130.1i	0.468169	+	0.760507i
$669$		−	17849.8i		−	1.03156i
$670$		0			0
$671$			14836.7i			0.853600i
$672$	7326.46	+	35878.5i	0.420572	+	2.05959i
$673$	−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	$0.788459\pi$
$678$	−19636.3	−	24856.5i	−1.11228	−	1.40798i
$679$	35035.2			1.98016
$680$		0			0
$681$	17437.9			0.981238
$682$	−19854.4	−	25132.6i	−1.11476	−	1.41111i
$683$	−3185.21	−	3185.21i	−0.178446	−	0.178446i	0.612232	−	0.790678i	$-0.290272\pi$
$683$	−3185.21	−	3185.21i	−0.178446	−	0.178446i	−0.790678	+	0.612232i	$0.790272\pi$
$684$	−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
$688$	−6660.92	−	20220.1i	−0.369106	−	1.12047i
$689$			253.358i			0.0140090i
$690$		0			0
$691$		−	5509.61i		−	0.303322i	−0.988433	−	0.151661i	$-0.951538\pi$
$691$		−	5509.61i		−	0.303322i	0.988433	−	0.151661i	$-0.0484622\pi$
$692$	3844.39	+	6244.93i	0.211187	+	0.343059i
$693$	−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
$698$	2756.07	−	2177.25i	0.149454	−	0.118066i
$699$	−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	$0.512206\pi$
$702$	−500.578	+	395.449i	−0.0269132	+	0.0212611i
$703$	−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
$708$	742.724	−	457.222i	0.0394255	−	0.0242704i
$709$		−	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
$712$	−3686.29	−	7932.47i	−0.194030	−	0.417531i
$713$	−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
$718$	13607.0	+	17224.4i	0.707254	+	0.895274i
$719$	35973.4			1.86590			0.932950	−	0.360006i	$-0.117225\pi$
$719$	35973.4			1.86590			0.932950	+	0.360006i	$0.117225\pi$
$720$		0			0
$721$	7534.67			0.389190
$722$	11041.0	+	13976.2i	0.569118	+	0.720415i
$723$	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	−0.903467	−	0.428658i	$-0.858987\pi$
$727$	−9307.24	+	9307.24i	−0.474809	+	0.474809i	0.428658	+	0.903467i	$0.358987\pi$
$728$	266.541	+	573.564i	0.0135696	+	0.0292001i
$729$			28508.3i			1.44837i
$730$		0			0
$731$			27420.9i			1.38741i
$732$	−19694.9	+	12124.2i	−0.994458	+	0.612189i
$733$	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
$738$	10572.0	−	8351.72i	0.527317	−	0.416573i
$739$	−24540.3			−1.22156			−0.610778	−	0.791802i	$-0.709143\pi$
$739$	−24540.3			−1.22156			−0.610778	+	0.791802i	$0.709143\pi$
$740$		0			0
$741$	−247.573			−0.0122737
$742$	−10890.5	+	8603.34i	−0.538818	+	0.425659i
$743$	25077.8	+	25077.8i	1.23825	+	1.23825i	0.960718	+	0.277528i	$0.0895152\pi$
$743$	25077.8	+	25077.8i	1.23825	+	1.23825i	0.277528	+	0.960718i	$0.410485\pi$
$744$	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
$748$	15426.2	+	25058.8i	0.754063	+	1.22492i
$749$			13590.3i			0.662989i
$750$		0			0
$751$		−	23078.2i		−	1.12135i	−0.828035	−	0.560676i	$-0.810541\pi$
$751$		−	23078.2i		−	1.12135i	0.828035	−	0.560676i	$-0.189459\pi$
$752$	21527.4	−	7091.58i	1.04391	−	0.343887i
$753$	−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	$0.554606\pi$
$758$	14950.1	+	18924.5i	0.716375	+	0.906819i
$759$	−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	$0.445750\pi$
$762$	−31041.4	−	39293.5i	−1.47573	−	1.86805i
$763$	−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
$768$	5284.77	−	35218.1i	0.248304	−	1.65472i
$769$		−	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
$772$	−14775.1	−	24001.0i	−0.688816	−	1.11893i
$773$	−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
$778$	24040.5	−	18991.7i	1.10783	−	0.875172i
$779$	2323.45			0.106863
$780$		0			0
$781$	29646.7			1.35831
$782$	2828.68	−	2234.62i	0.129352	−	0.102186i
$783$	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	−0.373894	−	0.927472i	$-0.621978\pi$
$787$	12222.0	−	12222.0i	0.553578	−	0.553578i	0.927472	+	0.373894i	$0.121978\pi$
$788$	−32948.8	+	20283.3i	−1.48953	+	0.916959i
$789$			11682.6i			0.527137i
$790$		0			0
$791$		−	29970.6i		−	1.34719i
$792$	44493.2	−	20676.4i	1.99621	−	0.927657i
$793$	−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	$0.715593\pi$
$798$	−8406.90	−	10641.8i	−0.372934	−	0.472076i
$799$	−29193.7			−1.29262
$800$		0			0
$801$	18784.9			0.828630
$802$	−13693.2	−	17333.4i	−0.602896	−	0.763173i
$803$	−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
$808$	−25923.8	+	12047.0i	−1.12871	+	0.524522i
$809$			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	$-0.939755\pi$
$811$		−	8690.30i		−	0.376273i	0.982143	−	0.188137i	$-0.0602448\pi$
$812$	20147.3	−	12402.7i	0.870730	−	0.536023i
$813$	−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
$818$	25659.4	−	20270.6i	1.09677	−	0.866435i
$819$	−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	$0.862704\pi$
$822$	−27556.4	+	21769.2i	−1.16927	+	0.923709i
$823$	−14335.6	−	14335.6i	−0.607176	−	0.607176i	0.335031	−	0.942207i	$-0.391253\pi$
$823$	−14335.6	−	14335.6i	−0.607176	−	0.607176i	−0.942207	+	0.335031i	$0.891253\pi$
$824$	−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	−0.643731	−	0.765252i	$-0.722615\pi$
$827$	2890.06	−	2890.06i	0.121520	−	0.121520i	0.765252	+	0.643731i	$0.222615\pi$
$828$	−3150.83	−	5118.29i	−0.132245	−	0.214822i
$829$		−	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
$832$	−51.9986	−	612.886i	−0.00216674	−	0.0255385i
$833$	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
$838$	391.441	+	495.504i	0.0161362	+	0.0204259i
$839$	47240.3			1.94388			0.971940	−	0.235229i	$-0.0755841\pi$
$839$	47240.3			1.94388			0.971940	+	0.235229i	$0.0755841\pi$
$840$		0			0
$841$	8233.07			0.337573
$842$	16358.8	+	20707.7i	0.669552	+	0.847548i
$843$	−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
$848$	12819.7	−	4223.07i	0.519138	−	0.171015i
$849$			53692.2i			2.17045i
$850$		0			0
$851$		−	2032.00i		−	0.0818522i
$852$	24226.5	+	39354.2i	0.974162	+	1.58246i
$853$	−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	$0.845341\pi$
$858$	1034.41	−	817.166i	0.0411585	−	0.0325147i
$859$	2068.01			0.0821416			0.0410708	−	0.999156i	$-0.486923\pi$
$859$	2068.01			0.0821416			0.0410708	+	0.999156i	$0.486923\pi$
$860$		0			0
$861$	19829.8			0.784898
$862$	9585.95	−	7572.77i	0.378769	−	0.299222i
$863$	−7493.32	−	7493.32i	−0.295568	−	0.295568i	0.543707	−	0.839275i	$-0.317020\pi$
$863$	−7493.32	−	7493.32i	−0.295568	−	0.295568i	−0.839275	+	0.543707i	$0.817020\pi$
$864$	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
$868$	40226.1	−	24763.2i	1.57300	−	0.968340i
$869$			31390.5i			1.22537i
$870$		0			0
$871$			338.895i			0.0131837i
$872$	13579.6	+	29221.7i	0.527367	+	1.13483i
$873$	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	$0.890430\pi$
$878$	4892.90	+	6193.65i	0.188072	+	0.238070i
$879$	−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	$0.467118\pi$
$882$	−16899.2	−	21391.8i	−0.645155	−	0.816666i
$883$	629.665	+	629.665i	0.0239976	+	0.0239976i	0.719004	−	0.695006i	$-0.244598\pi$
$883$	629.665	+	629.665i	0.0239976	+	0.0239976i	−0.695006	+	0.719004i	$0.744598\pi$
$884$	−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	−0.692802	−	0.721128i	$-0.743624\pi$
$887$	748.301	−	748.301i	0.0283264	−	0.0283264i	0.721128	+	0.692802i	$0.243624\pi$
$888$	10896.6	+	23448.1i	0.411785	+	0.886112i
$889$		−	47377.9i		−	1.78741i
$890$		0			0
$891$			14291.9i			0.537371i
$892$	−13986.4	+	8610.04i	−0.524999	+	0.323190i
$893$	−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
$898$	−4983.54	+	3936.93i	−0.185193	+	0.146300i
$899$	−32256.9			−1.19669
$900$		0			0
$901$	−17385.0			−0.642818
$902$	−9707.77	+	7669.00i	−0.358352	+	0.283093i
$903$	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	$-0.482430\pi$
$907$	28781.0	−	28781.0i	1.05365	−	1.05365i	0.998477	−	0.0551706i	$-0.0175703\pi$
$908$	−8411.36	−	13663.6i	−0.307424	−	0.499388i
$909$		−	61390.3i		−	2.24003i
$910$		0			0
$911$		−	15888.2i		−	0.577828i	−0.957355	−	0.288914i	$-0.906706\pi$
$911$		−	15888.2i		−	0.577828i	0.957355	−	0.288914i	$-0.0932941\pi$
$912$	4126.64	+	12526.9i	0.149832	+	0.454834i
$913$	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
$918$	−27135.1	−	34348.8i	−0.975589	−	1.23494i
$919$	47850.0			1.71755			0.858773	−	0.512356i	$-0.171227\pi$
$919$	47850.0			1.71755			0.858773	+	0.512356i	$0.171227\pi$
$920$		0			0
$921$	13896.7			0.497189
$922$	−4616.64	−	5843.95i	−0.164903	−	0.208742i
$923$	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
$928$	−22543.4	+	4603.41i	−0.797440	+	0.162839i
$929$			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
$932$	4344.59	+	7057.48i	0.152695	+	0.248042i
$933$	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	$0.545495\pi$
$938$	−14567.3	+	11507.9i	−0.507077	+	0.400584i
$939$	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	$0.648372\pi$
$942$	32795.5	−	25908.0i	1.13432	−	0.896101i
$943$	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	$-0.496092\pi$
$947$	29498.0	−	29498.0i	1.01220	−	1.01220i	0.999925	−	0.0122772i	$-0.00390806\pi$
$948$	−41669.0	+	25651.5i	−1.42758	+	0.878821i
$949$		−	1188.39i		−	0.0406500i
$950$		0			0
$951$			52628.5i			1.79453i
$952$	−39357.0	+	18289.6i	−1.33988	+	0.622656i
$953$	−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
$958$	−4354.86	−	5512.57i	−0.146867	−	0.185911i
$959$	−33226.0			−1.11879
$960$		0			0
$961$	−34613.0			−1.16186
$962$	276.833	+	350.428i	0.00927803	+	0.0117445i
$963$	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	−0.956140	−	0.292910i	$-0.905376\pi$
$967$	−19943.6	+	19943.6i	−0.663230	+	0.663230i	0.292910	+	0.956140i	$0.405376\pi$
$968$	−13544.0	+	6294.04i	−0.449713	+	0.208986i
$969$		−	16988.1i		−	0.563194i
$970$		0			0
$971$			7147.31i			0.236218i	0.993001	+	0.118109i	$0.0376833\pi$
$971$			7147.31i			0.236218i	−0.993001	+	0.118109i	$0.962317\pi$
$972$	15561.7	−	9579.82i	0.513522	−	0.316124i
$973$	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	$0.720331\pi$
$978$	−9169.57	+	7243.84i	−0.299806	+	0.236843i
$979$	−17249.3			−0.563117
$980$		0			0
$981$	−69200.1			−2.25218
$982$	−19976.1	+	15780.8i	−0.649146	+	0.512816i
$983$	−26810.4	−	26810.4i	−0.869907	−	0.869907i	0.122555	−	0.992462i	$-0.460891\pi$
$983$	−26810.4	−	26810.4i	−0.869907	−	0.869907i	−0.992462	+	0.122555i	$0.960891\pi$
$984$	−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
$988$	119.419	+	193.988i	0.00384538	+	0.00624655i
$989$			5142.91i			0.165354i
$990$		0			0
$991$			43289.7i			1.38763i	0.720153	+	0.693815i	$0.244072\pi$
$991$			43289.7i			1.38763i	−0.720153	+	0.693815i	$0.755928\pi$
$992$	−45010.1	+	9191.16i	−1.44060	+	0.294173i
$993$	−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	$-0.504659\pi$
$998$	22893.7	+	28979.9i	0.726141	+	0.919181i
$999$	−24674.7			−0.781456

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.75332 - 2.21943i) q^{2} +(-6.14790 - 6.14790i) q^{3} +(-1.85174 + 7.78274i) q^{4} +(-2.86560 + 24.4241i) q^{6} +(-16.4522 + 16.4522i) q^{7} +(20.5199 - 9.53582i) q^{8} +48.5934i q^{9} +O(q^{10})\)	\(q+(-1.75332 - 2.21943i) 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} +(20.5199 - 9.53582i) q^{8} +48.5934i q^{9} -44.6211i q^{11} +(59.2319 - 36.4632i) 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} +(107.850 - 85.1997i) q^{18} +23.7025 q^{19} +202.293 q^{21} +(-99.0334 + 78.2350i) 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} +(-97.5778 - 158.508i) q^{28} +127.106i q^{29} +253.779i q^{31} +(36.2171 + 177.359i) 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} +(-41.5581 - 52.6061i) q^{38} -10.4450 q^{39} +98.0252 q^{41} +(-354.684 - 448.975i) 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} +(174.101 + 528.507i) q^{48} -198.348i q^{49} -716.719i q^{51} +(5.03825 + 8.18428i) 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} +(282.103 - 222.857i) q^{58} +12.5393 q^{59} -332.505 q^{61} +(563.246 - 444.956i) 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} +(-561.592 + 345.716i) q^{68} -134.424i q^{69} +664.410i q^{71} +(463.378 + 997.134i) 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} +(18.3135 + 23.1820i) q^{78} -703.490 q^{79} -320.295 q^{81} +(-171.869 - 217.560i) 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} +(-425.499 - 915.623i) q^{88} -386.574i q^{89} +27.9515i q^{91} +(-105.329 + 64.8407i) 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} +(-440.220 + 347.768i) 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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