LMFDB - Embedded newform 100.7.b.f.51.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,7,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, 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:	$23.0054083620$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} - 10x^{8} + 1775x^{6} - 1000x^{4} - 160000x^{2} + 1000000 $ x^12 - 16x^10 - 10x^8 + 1775x^6 - 1000x^4 - 160000*x^2 + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.6
Root			$-3.05235 - 0.826519i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.7.b.f.51.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.98770 + 7.42116i) q^{2} +6.08848i q^{3} +(-46.1473 - 44.3444i) q^{4} +(-45.1836 - 18.1905i) q^{6} +422.345i q^{7} +(466.961 - 209.979i) q^{8} +691.930 q^{9} +O(q^{10})$	\(q+(-2.98770 + 7.42116i) q^{2} +6.08848i q^{3} +(-46.1473 - 44.3444i) q^{4} +(-45.1836 - 18.1905i) q^{6} +422.345i q^{7} +(466.961 - 209.979i) q^{8} +691.930 q^{9} -1743.93i q^{11} +(269.990 - 280.967i) q^{12} +898.704 q^{13} +(-3134.29 - 1261.84i) q^{14} +(163.152 + 4092.75i) q^{16} +5542.94 q^{17} +(-2067.28 + 5134.93i) q^{18} +8906.74i q^{19} -2571.44 q^{21} +(12942.0 + 5210.33i) q^{22} +3740.11i q^{23} +(1278.46 + 2843.09i) q^{24} +(-2685.06 + 6669.43i) q^{26} +8651.31i q^{27} +(18728.6 - 19490.1i) q^{28} -31180.3 q^{29} +22647.9i q^{31} +(-30860.4 - 11017.1i) q^{32} +10617.9 q^{33} +(-16560.6 + 41135.1i) q^{34} +(-31930.7 - 30683.2i) q^{36} -14997.5 q^{37} +(-66098.4 - 26610.7i) q^{38} +5471.75i q^{39} +6598.75 q^{41} +(7682.68 - 19083.1i) q^{42} +81078.0i q^{43} +(-77333.4 + 80477.6i) q^{44} +(-27756.0 - 11174.3i) q^{46} -30231.0i q^{47} +(-24918.6 + 993.349i) q^{48} -60726.1 q^{49} +33748.1i q^{51} +(-41472.8 - 39852.5i) q^{52} +17256.7 q^{53} +(-64202.8 - 25847.5i) q^{54} +(88683.7 + 197219. i) q^{56} -54228.6 q^{57} +(93157.4 - 231394. i) q^{58} +294323. i q^{59} -211992. q^{61} +(-168074. - 67665.1i) q^{62} +292233. i q^{63} +(173961. - 196104. i) q^{64} +(-31723.0 + 78797.0i) q^{66} +452884. i q^{67} +(-255792. - 245798. i) q^{68} -22771.6 q^{69} -246386. i q^{71} +(323105. - 145291. i) q^{72} +476862. q^{73} +(44807.9 - 111299. i) q^{74} +(394964. - 411022. i) q^{76} +736539. q^{77} +(-40606.7 - 16347.9i) q^{78} -680467. i q^{79} +451744. q^{81} +(-19715.1 + 48970.4i) q^{82} +1.03860e6i q^{83} +(118665. + 114029. i) q^{84} +(-601693. - 242237. i) q^{86} -189841. i q^{87} +(-366189. - 814346. i) q^{88} +937027. q^{89} +379563. i q^{91} +(165853. - 172596. i) q^{92} -137891. q^{93} +(224349. + 90321.0i) q^{94} +(67077.6 - 187893. i) q^{96} -957172. q^{97} +(181431. - 450659. i) q^{98} -1.20668e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9}+O(q^{10}) $ 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9	$ 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9} - 512 q^{14} - 20928 q^{16} + 51216 q^{21} + 20928 q^{24} + 14496 q^{26} + 16072 q^{29} - 257216 q^{34} - 144960 q^{36} - 192136 q^{41} + 165120 q^{44} - 49472 q^{46} - 145796 q^{49} + 118656 q^{54} + 1078208 q^{56} + 215384 q^{61} + 6656 q^{64} - 1403520 q^{66} - 1015824 q^{69} + 1020384 q^{74} + 2515200 q^{76} - 2327652 q^{81} - 424704 q^{84} - 5268832 q^{86} + 4346152 q^{89} - 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) $ 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9 - 512 * q^14 - 20928 * q^16 + 51216 * q^21 + 20928 * q^24 + 14496 * q^26 + 16072 * q^29 - 257216 * q^34 - 144960 * q^36 - 192136 * q^41 + 165120 * q^44 - 49472 * q^46 - 145796 * q^49 + 118656 * q^54 + 1078208 * q^56 + 215384 * q^61 + 6656 * q^64 - 1403520 * q^66 - 1015824 * q^69 + 1020384 * q^74 + 2515200 * q^76 - 2327652 * q^81 - 424704 * q^84 - 5268832 * q^86 + 4346152 * q^89 - 4292992 * q^94 + 7673088 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.98770	+	7.42116i	−0.373462	+	0.927645i
$2$	−2.98770	+	7.42116i	−0.373462	+	0.927645i
$3$			6.08848i			0.225499i	0.993623	+	0.112750i	$0.0359658\pi$
$3$			6.08848i			0.225499i	−0.993623	+	0.112750i	$0.964034\pi$
$4$	−46.1473	−	44.3444i	−0.721052	−	0.692881i
$5$		0			0
$5$		0			0
$6$	−45.1836	−	18.1905i	−0.209184	−	0.0842155i
$7$			422.345i			1.23133i	0.788010	+	0.615663i	$0.211112\pi$
$7$			422.345i			1.23133i	−0.788010	+	0.615663i	$0.788888\pi$
$8$	466.961	−	209.979i	0.912033	−	0.410116i
$9$	691.930			0.949150
$10$		0			0
$11$		−	1743.93i		−	1.31024i	−0.755526	−	0.655119i	$-0.772618\pi$
$11$		−	1743.93i		−	1.31024i	0.755526	−	0.655119i	$-0.227382\pi$
$12$	269.990	−	280.967i	0.156244	−	0.162597i
$13$	898.704			0.409060			0.204530	−	0.978860i	$-0.434433\pi$
$13$	898.704			0.409060			0.204530	+	0.978860i	$0.434433\pi$
$14$	−3134.29	−	1261.84i	−1.14223	−	0.459854i
$15$		0			0
$16$	163.152	+	4092.75i	0.0398321	+	0.999206i
$17$	5542.94			1.12822			0.564110	−	0.825700i	$-0.309219\pi$
$17$	5542.94			1.12822			0.564110	+	0.825700i	$0.309219\pi$
$18$	−2067.28	+	5134.93i	−0.354472	+	0.880475i
$19$			8906.74i			1.29855i	0.760554	+	0.649274i	$0.224927\pi$
$19$			8906.74i			1.29855i	−0.760554	+	0.649274i	$0.775073\pi$
$20$		0			0
$21$	−2571.44			−0.277663
$22$	12942.0	+	5210.33i	1.21544	+	0.489324i
$23$			3740.11i			0.307398i	0.988118	+	0.153699i	$0.0491186\pi$
$23$			3740.11i			0.307398i	−0.988118	+	0.153699i	$0.950881\pi$
$24$	1278.46	+	2843.09i	0.0924809	+	0.205663i
$25$		0			0
$26$	−2685.06	+	6669.43i	−0.152768	+	0.379462i
$27$			8651.31i			0.439532i
$28$	18728.6	−	19490.1i	0.853162	−	0.887850i
$29$	−31180.3			−1.27846			−0.639229	−	0.769016i	$-0.720747\pi$
$29$	−31180.3			−1.27846			−0.639229	+	0.769016i	$0.720747\pi$
$30$		0			0
$31$			22647.9i			0.760227i	0.924940	+	0.380113i	$0.124115\pi$
$31$			22647.9i			0.760227i	−0.924940	+	0.380113i	$0.875885\pi$
$32$	−30860.4	−	11017.1i	−0.941785	−	0.336216i
$33$	10617.9			0.295458
$34$	−16560.6	+	41135.1i	−0.421347	+	1.04659i
$35$		0			0
$36$	−31930.7	−	30683.2i	−0.684387	−	0.657648i
$37$	−14997.5			−0.296082			−0.148041	−	0.988981i	$-0.547297\pi$
$37$	−14997.5			−0.296082			−0.148041	+	0.988981i	$0.547297\pi$
$38$	−66098.4	−	26610.7i	−1.20459	−	0.484959i
$39$			5471.75i			0.0922427i
$40$		0			0
$41$	6598.75			0.0957436			0.0478718	−	0.998853i	$-0.484756\pi$
$41$	6598.75			0.0957436			0.0478718	+	0.998853i	$0.484756\pi$
$42$	7682.68	−	19083.1i	0.103697	−	0.257573i
$43$			81078.0i			1.01976i	0.860246	+	0.509880i	$0.170310\pi$
$43$			81078.0i			1.01976i	−0.860246	+	0.509880i	$0.829690\pi$
$44$	−77333.4	+	80477.6i	−0.907839	+	0.944750i
$45$		0			0
$46$	−27756.0	−	11174.3i	−0.285156	−	0.114802i
$47$		−	30231.0i		−	0.291178i	−0.989345	−	0.145589i	$-0.953492\pi$
$47$		−	30231.0i		−	0.291178i	0.989345	−	0.145589i	$-0.0465077\pi$
$48$	−24918.6	+	993.349i	−0.225320	+	0.00898211i
$49$	−60726.1			−0.516164
$50$		0			0
$51$			33748.1i			0.254413i
$52$	−41472.8	−	39852.5i	−0.294953	−	0.283430i
$53$	17256.7			0.115913			0.0579563	−	0.998319i	$-0.481542\pi$
$53$	17256.7			0.115913			0.0579563	+	0.998319i	$0.481542\pi$
$54$	−64202.8	−	25847.5i	−0.407730	−	0.164149i
$55$		0			0
$56$	88683.7	+	197219.i	0.504986	+	1.12301i
$57$	−54228.6			−0.292822
$58$	93157.4	−	231394.i	0.477456	−	1.18596i
$59$			294323.i			1.43307i	0.697550	+	0.716536i	$0.254273\pi$
$59$			294323.i			1.43307i	−0.697550	+	0.716536i	$0.745727\pi$
$60$		0			0
$61$	−211992.			−0.933963			−0.466982	−	0.884267i	$-0.654659\pi$
$61$	−211992.			−0.933963			−0.466982	+	0.884267i	$0.654659\pi$
$62$	−168074.	−	67665.1i	−0.705221	−	0.283916i
$63$			292233.i			1.16871i
$64$	173961.	−	196104.i	0.663610	−	0.748079i
$65$		0			0
$66$	−31723.0	+	78797.0i	−0.110342	+	0.274080i
$67$			452884.i			1.50578i	0.658145	+	0.752891i	$0.271341\pi$
$67$			452884.i			1.50578i	−0.658145	+	0.752891i	$0.728659\pi$
$68$	−255792.	−	245798.i	−0.813505	−	0.781722i
$69$	−22771.6			−0.0693181
$70$		0			0
$71$		−	246386.i		−	0.688401i	−0.938896	−	0.344201i	$-0.888150\pi$
$71$		−	246386.i		−	0.688401i	0.938896	−	0.344201i	$-0.111850\pi$
$72$	323105.	−	145291.i	0.865657	−	0.389261i
$73$	476862.			1.22581			0.612907	−	0.790155i	$-0.290000\pi$
$73$	476862.			1.22581			0.612907	+	0.790155i	$0.290000\pi$
$74$	44807.9	−	111299.i	0.110576	−	0.274659i
$75$		0			0
$76$	394964.	−	411022.i	0.899740	−	0.936321i
$77$	736539.			1.61333
$78$	−40606.7	−	16347.9i	−0.0855686	−	0.0344492i
$79$		−	680467.i		−	1.38015i	−0.723738	−	0.690075i	$-0.757578\pi$
$79$		−	680467.i		−	1.38015i	0.723738	−	0.690075i	$-0.242422\pi$
$80$		0			0
$81$	451744.			0.850036
$82$	−19715.1	+	48970.4i	−0.0357566	+	0.0888161i
$83$			1.03860e6i			1.81641i	0.418521	+	0.908207i	$0.362549\pi$
$83$			1.03860e6i			1.81641i	−0.418521	+	0.908207i	$0.637451\pi$
$84$	118665.	+	114029.i	0.200210	+	0.192388i
$85$		0			0
$86$	−601693.	−	242237.i	−0.945975	−	0.380842i
$87$		−	189841.i		−	0.288292i
$88$	−366189.	−	814346.i	−0.537349	−	1.19498i
$89$	937027.			1.32918			0.664588	−	0.747210i	$-0.268607\pi$
$89$	937027.			1.32918			0.664588	+	0.747210i	$0.268607\pi$
$90$		0			0
$91$			379563.i			0.503686i
$92$	165853.	−	172596.i	0.212990	−	0.221650i
$93$	−137891.			−0.171431
$94$	224349.	+	90321.0i	0.270110	+	0.108744i
$95$		0			0
$96$	67077.6	−	187893.i	0.0758165	−	0.212372i
$97$	−957172.			−1.04876			−0.524379	−	0.851485i	$-0.675702\pi$
$97$	−957172.			−1.04876			−0.524379	+	0.851485i	$0.675702\pi$
$98$	181431.	−	450659.i	0.192768	−	0.478817i
$99$		−	1.20668e6i		−	1.24361i
$100$		0			0
$101$	561162.			0.544658			0.272329	−	0.962204i	$-0.412206\pi$
$101$	561162.			0.544658			0.272329	+	0.962204i	$0.412206\pi$
$102$	−250450.	−	100829.i	−0.236005	−	0.0950136i
$103$			649255.i			0.594161i	0.954852	+	0.297080i	$0.0960129\pi$
$103$			649255.i			0.594161i	−0.954852	+	0.297080i	$0.903987\pi$
$104$	419660.	−	188709.i	0.373076	−	0.167762i
$105$		0			0
$106$	−51557.9	+	128065.i	−0.0432890	+	0.107526i
$107$			1.01005e6i			0.824501i	0.911070	+	0.412251i	$0.135257\pi$
$107$			1.01005e6i			0.824501i	−0.911070	+	0.412251i	$0.864743\pi$
$108$	383637.	−	399235.i	0.304543	−	0.316926i
$109$	−202984.			−0.156741			−0.0783703	−	0.996924i	$-0.524972\pi$
$109$	−202984.			−0.156741			−0.0783703	+	0.996924i	$0.524972\pi$
$110$		0			0
$111$		−	91311.8i		−	0.0667664i
$112$	−1.72855e6	+	68906.4i	−1.23035	+	0.0490462i
$113$	1.50469e6			1.04283			0.521413	−	0.853305i	$-0.325405\pi$
$113$	1.50469e6			1.04283			0.521413	+	0.853305i	$0.325405\pi$
$114$	162019.	−	402439.i	0.109358	−	0.271635i
$115$		0			0
$116$	1.43889e6	+	1.38267e6i	0.921835	+	0.885820i
$117$	621841.			0.388259
$118$	−2.18422e6	−	879347.i	−1.32938	−	0.535198i
$119$			2.34103e6i			1.38921i
$120$		0			0
$121$	−1.26972e6			−0.716725
$122$	633368.	−	1.57323e6i	0.348800	−	0.866387i
$123$			40176.4i			0.0215901i
$124$	1.00431e6	−	1.04514e6i	0.526747	−	0.548163i
$125$		0			0
$126$	−2.16871e6	−	873104.i	−1.08415	−	0.436470i
$127$		−	1.14744e6i		−	0.560168i	−0.959975	−	0.280084i	$-0.909638\pi$
$127$		−	1.14744e6i		−	0.560168i	0.959975	−	0.280084i	$-0.0903623\pi$
$128$	935578.	+	1.87690e6i	0.446118	+	0.894974i
$129$	−493642.			−0.229955
$130$		0			0
$131$		−	2.85296e6i		−	1.26906i	−0.772899	−	0.634529i	$-0.781194\pi$
$131$		−	2.85296e6i		−	1.26906i	0.772899	−	0.634529i	$-0.218806\pi$
$132$	−489987.	−	470843.i	−0.213041	−	0.204717i
$133$	−3.76172e6			−1.59894
$134$	−3.36092e6	−	1.35308e6i	−1.39683	−	0.562353i
$135$		0			0
$136$	2.58834e6	−	1.16390e6i	1.02897	−	0.462701i
$137$	−1.39333e6			−0.541866			−0.270933	−	0.962598i	$-0.587332\pi$
$137$	−1.39333e6			−0.541866			−0.270933	+	0.962598i	$0.587332\pi$
$138$	68034.7	−	168992.i	0.0258877	−	0.0643026i
$139$			489730.i			0.182353i	0.995835	+	0.0911764i	$0.0290627\pi$
$139$			489730.i			0.182353i	−0.995835	+	0.0911764i	$0.970937\pi$
$140$		0			0
$141$	184061.			0.0656605
$142$	1.82847e6	+	736128.i	0.638592	+	0.257092i
$143$		−	1.56727e6i		−	0.535966i
$144$	112890.	+	2.83190e6i	0.0378066	+	0.948397i
$145$		0			0
$146$	−1.42472e6	+	3.53887e6i	−0.457795	+	1.13712i
$147$		−	369730.i		−	0.116395i
$148$	692093.	+	665053.i	0.213491	+	0.205150i
$149$	−1.02592e6			−0.310138			−0.155069	−	0.987904i	$-0.549560\pi$
$149$	−1.02592e6			−0.310138			−0.155069	+	0.987904i	$0.549560\pi$
$150$		0			0
$151$			4.68243e6i			1.36000i	0.733210	+	0.680002i	$0.238021\pi$
$151$			4.68243e6i			1.36000i	−0.733210	+	0.680002i	$0.761979\pi$
$152$	1.87023e6	+	4.15910e6i	0.532555	+	1.18432i
$153$	3.83533e6			1.07085
$154$	−2.20055e6	+	5.46597e6i	−0.602518	+	1.49660i
$155$		0			0
$156$	242641.	−	252507.i	0.0639132	−	0.0665118i
$157$	3.46076e6			0.894278			0.447139	−	0.894464i	$-0.352443\pi$
$157$	3.46076e6			0.894278			0.447139	+	0.894464i	$0.352443\pi$
$158$	5.04986e6	+	2.03303e6i	1.28029	+	0.515433i
$159$			105067.i			0.0261382i
$160$		0			0
$161$	−1.57962e6			−0.378507
$162$	−1.34967e6	+	3.35246e6i	−0.317456	+	0.788532i
$163$		−	5.02544e6i		−	1.16041i	−0.814471	−	0.580205i	$-0.802972\pi$
$163$		−	5.02544e6i		−	1.16041i	0.814471	−	0.580205i	$-0.197028\pi$
$164$	−304514.	−	292617.i	−0.0690361	−	0.0663389i
$165$		0			0
$166$	−7.70764e6	−	3.10303e6i	−1.68499	−	0.678362i
$167$			1.81735e6i			0.390201i	0.980783	+	0.195101i	$0.0625033\pi$
$167$			1.81735e6i			0.390201i	−0.980783	+	0.195101i	$0.937497\pi$
$168$	−1.20076e6	+	539949.i	−0.253238	+	0.113874i
$169$	−4.01914e6			−0.832670
$170$		0			0
$171$			6.16285e6i			1.23252i
$172$	3.59535e6	−	3.74153e6i	0.706572	−	0.735300i
$173$	−2.12346e6			−0.410115			−0.205058	−	0.978750i	$-0.565738\pi$
$173$	−2.12346e6			−0.410115			−0.205058	+	0.978750i	$0.565738\pi$
$174$	1.40884e6	+	567187.i	0.267432	+	0.107666i
$175$		0			0
$176$	7.13746e6	−	284525.i	1.30920	−	0.0521895i
$177$	−1.79198e6			−0.323157
$178$	−2.79955e6	+	6.95383e6i	−0.496397	+	1.23300i
$179$			1.28491e6i			0.224034i	0.993706	+	0.112017i	$0.0357312\pi$
$179$			1.28491e6i			0.224034i	−0.993706	+	0.112017i	$0.964269\pi$
$180$		0			0
$181$	1.89832e6			0.320136			0.160068	−	0.987106i	$-0.448829\pi$
$181$	1.89832e6			0.320136			0.160068	+	0.987106i	$0.448829\pi$
$182$	−2.81680e6	−	1.13402e6i	−0.467242	−	0.188108i
$183$		−	1.29071e6i		−	0.210608i
$184$	785346.	+	1.74649e6i	0.126069	+	0.280357i
$185$		0			0
$186$	411978.	−	1.02332e6i	0.0640229	−	0.159027i
$187$		−	9.66649e6i		−	1.47824i
$188$	−1.34057e6	+	1.39508e6i	−0.201752	+	0.209955i
$189$	−3.65384e6			−0.541207
$190$		0			0
$191$		−	1.10365e7i		−	1.58391i	−0.610581	−	0.791954i	$-0.709064\pi$
$191$		−	1.10365e7i		−	1.58391i	0.610581	−	0.791954i	$-0.290936\pi$
$192$	1.19398e6	+	1.05916e6i	0.168691	+	0.149644i
$193$	−9.60496e6			−1.33605			−0.668027	−	0.744137i	$-0.732861\pi$
$193$	−9.60496e6			−1.33605			−0.668027	+	0.744137i	$0.732861\pi$
$194$	2.85974e6	−	7.10333e6i	0.391671	−	0.972875i
$195$		0			0
$196$	2.80235e6	+	2.69286e6i	0.372181	+	0.357640i
$197$	−3.52707e6			−0.461334			−0.230667	−	0.973033i	$-0.574091\pi$
$197$	−3.52707e6			−0.461334			−0.230667	+	0.973033i	$0.574091\pi$
$198$	8.95494e6	+	3.60518e6i	1.15363	+	0.464442i
$199$		−	1.68919e6i		−	0.214347i	−0.994240	−	0.107174i	$-0.965820\pi$
$199$		−	1.68919e6i		−	0.214347i	0.994240	−	0.107174i	$-0.0341801\pi$
$200$		0			0
$201$	−2.75738e6			−0.339553
$202$	−1.67658e6	+	4.16448e6i	−0.203409	+	0.505250i
$203$		−	1.31688e7i		−	1.57420i
$204$	1.49654e6	−	1.55739e6i	0.176278	−	0.183445i
$205$		0			0
$206$	−4.81823e6	−	1.93978e6i	−0.551170	−	0.221897i
$207$			2.58790e6i			0.291767i
$208$	146625.	+	3.67817e6i	0.0162937	+	0.408735i
$209$	1.55327e7			1.70141
$210$		0			0
$211$		−	5.46799e6i		−	0.582077i	−0.956711	−	0.291038i	$-0.905999\pi$
$211$		−	5.46799e6i		−	0.582077i	0.956711	−	0.291038i	$-0.0940007\pi$
$212$	−796352.	−	765239.i	−0.0835790	−	0.0803136i
$213$	1.50012e6			0.155234
$214$	−7.49574e6	−	3.01772e6i	−0.764845	−	0.307920i
$215$		0			0
$216$	1.81660e6	+	4.03983e6i	0.180259	+	0.400868i
$217$	−9.56523e6			−0.936087
$218$	606453.	−	1.50637e6i	0.0585367	−	0.145400i
$219$			2.90337e6i			0.276420i
$220$		0			0
$221$	4.98147e6			0.461509
$222$	677640.	+	272812.i	0.0619355	+	0.0249347i
$223$		−	6.77154e6i		−	0.610622i	−0.952253	−	0.305311i	$-0.901240\pi$
$223$		−	6.77154e6i		−	0.610622i	0.952253	−	0.305311i	$-0.0987605\pi$
$224$	4.65302e6	−	1.30337e7i	0.413991	−	1.15964i
$225$		0			0
$226$	−4.49556e6	+	1.11665e7i	−0.389456	+	0.967372i
$227$		−	5.17157e6i		−	0.442125i	−0.975260	−	0.221062i	$-0.929048\pi$
$227$		−	5.17157e6i		−	0.442125i	0.975260	−	0.221062i	$-0.0709524\pi$
$228$	2.50250e6	+	2.40473e6i	0.211140	+	0.202891i
$229$	1.14858e7			0.956432			0.478216	−	0.878242i	$-0.341284\pi$
$229$	1.14858e7			0.956432			0.478216	+	0.878242i	$0.341284\pi$
$230$		0			0
$231$			4.48440e6i			0.363805i
$232$	−1.45600e7	+	6.54722e6i	−1.16600	+	0.524316i
$233$	611879.			0.0483724			0.0241862	−	0.999707i	$-0.492301\pi$
$233$	611879.			0.0483724			0.0241862	+	0.999707i	$0.492301\pi$
$234$	−1.85787e6	+	4.61478e6i	−0.145000	+	0.360167i
$235$		0			0
$236$	1.30516e7	−	1.35822e7i	0.992948	−	1.03332i
$237$	4.14301e6			0.311223
$238$	−1.73732e7	−	6.99430e6i	−1.28869	−	0.518816i
$239$		−	1.88564e7i		−	1.38123i	−0.723225	−	0.690613i	$-0.757341\pi$
$239$		−	1.88564e7i		−	1.38123i	0.723225	−	0.690613i	$-0.242659\pi$
$240$		0			0
$241$	1.19579e7			0.854285			0.427143	−	0.904184i	$-0.359520\pi$
$241$	1.19579e7			0.854285			0.427143	+	0.904184i	$0.359520\pi$
$242$	3.79354e6	−	9.42281e6i	0.267670	−	0.664866i
$243$			9.05724e6i			0.631215i
$244$	9.78286e6	+	9.40065e6i	0.673436	+	0.647125i
$245$		0			0
$246$	−298155.	−	120035.i	−0.0200280	−	0.00806310i
$247$			8.00453e6i			0.531184i
$248$	4.75559e6	+	1.05757e7i	0.311781	+	0.693352i
$249$	−6.32351e6			−0.409600
$250$		0			0
$251$			4.43941e6i			0.280740i	0.990099	+	0.140370i	$0.0448292\pi$
$251$			4.43941e6i			0.280740i	−0.990099	+	0.140370i	$0.955171\pi$
$252$	1.29589e7	−	1.34858e7i	0.809779	−	0.842703i
$253$	6.52249e6			0.402765
$254$	8.51533e6	+	3.42820e6i	0.519637	+	0.209202i
$255$		0			0
$256$	−1.67240e7	+	1.33548e6i	−0.996827	+	0.0796009i
$257$	3.02099e7			1.77971			0.889857	−	0.456240i	$-0.150804\pi$
$257$	3.02099e7			1.77971			0.889857	+	0.456240i	$0.150804\pi$
$258$	1.47485e6	−	3.66340e6i	0.0858796	−	0.213317i
$259$		−	6.33410e6i		−	0.364574i
$260$		0			0
$261$	−2.15746e7			−1.21345
$262$	2.11723e7	+	8.52378e6i	1.17724	+	0.473946i
$263$			2.91425e7i			1.60199i	0.598673	+	0.800994i	$0.295695\pi$
$263$			2.91425e7i			1.60199i	−0.598673	+	0.800994i	$0.704305\pi$
$264$	4.95813e6	−	2.22953e6i	0.269468	−	0.121172i
$265$		0			0
$266$	1.12389e7	−	2.79163e7i	0.597142	−	1.48325i
$267$			5.70508e6i			0.299728i
$268$	2.00828e7	−	2.08994e7i	1.04333	−	1.08575i
$269$	−2.25831e7			−1.16018			−0.580091	−	0.814552i	$-0.696983\pi$
$269$	−2.25831e7			−1.16018			−0.580091	+	0.814552i	$0.696983\pi$
$270$		0			0
$271$			7.50243e6i			0.376959i	0.982077	+	0.188479i	$0.0603559\pi$
$271$			7.50243e6i			0.376959i	−0.982077	+	0.188479i	$0.939644\pi$
$272$	904343.	+	2.26859e7i	0.0449393	+	1.12732i
$273$	−2.31096e6			−0.113581
$274$	4.16284e6	−	1.03401e7i	0.202366	−	0.502659i
$275$		0			0
$276$	1.05085e6	+	1.00979e6i	0.0499820	+	0.0480292i
$277$	−2.36803e7			−1.11416			−0.557080	−	0.830459i	$-0.688078\pi$
$277$	−2.36803e7			−1.11416			−0.557080	+	0.830459i	$0.688078\pi$
$278$	−3.63437e6	−	1.46317e6i	−0.169159	−	0.0681019i
$279$			1.56708e7i			0.721569i
$280$		0			0
$281$	2.22984e7			1.00498			0.502488	−	0.864584i	$-0.332418\pi$
$281$	2.22984e7			1.00498			0.502488	+	0.864584i	$0.332418\pi$
$282$	−549918.	+	1.36595e6i	−0.0245217	+	0.0609097i
$283$			2.01491e6i			0.0888988i	0.999012	+	0.0444494i	$0.0141533\pi$
$283$			2.01491e6i			0.0888988i	−0.999012	+	0.0444494i	$0.985847\pi$
$284$	−1.09258e7	+	1.13701e7i	−0.476980	+	0.496373i
$285$		0			0
$286$	1.16310e7	+	4.68254e6i	0.497186	+	0.200163i
$287$			2.78695e6i			0.117892i
$288$	−2.13533e7	−	7.62308e6i	−0.893895	−	0.319119i
$289$	6.58667e6			0.272880
$290$		0			0
$291$		−	5.82773e6i		−	0.236494i
$292$	−2.20059e7	−	2.11462e7i	−0.883875	−	0.849343i
$293$	3.19886e7			1.27172			0.635861	−	0.771804i	$-0.280645\pi$
$293$	3.19886e7			1.27172			0.635861	+	0.771804i	$0.280645\pi$
$294$	2.74383e6	+	1.10464e6i	0.107973	+	0.0434690i
$295$		0			0
$296$	−7.00323e6	+	3.14916e6i	−0.270037	+	0.121428i
$297$	1.50873e7			0.575892
$298$	3.06514e6	−	7.61353e6i	0.115825	−	0.287698i
$299$			3.36126e6i			0.125744i
$300$		0			0
$301$	−3.42429e7			−1.25566
$302$	−3.47491e7	−	1.39897e7i	−1.26160	−	0.507910i
$303$			3.41663e6i			0.122820i
$304$	−3.64531e7	+	1.45315e6i	−1.29752	+	0.0517239i
$305$		0			0
$306$	−1.14588e7	+	2.84626e7i	−0.399922	+	0.993369i
$307$			1.45346e7i			0.502328i	0.967945	+	0.251164i	$0.0808134\pi$
$307$			1.45346e7i			0.502328i	−0.967945	+	0.251164i	$0.919187\pi$
$308$	−3.39893e7	−	3.26613e7i	−1.16330	−	1.11785i
$309$	−3.95298e6			−0.133983
$310$		0			0
$311$		−	5.75145e6i		−	0.191204i	−0.995420	−	0.0956018i	$-0.969522\pi$
$311$		−	5.75145e6i		−	0.191204i	0.995420	−	0.0956018i	$-0.0304776\pi$
$312$	1.14895e6	+	2.55509e6i	0.0378302	+	0.0841285i
$313$	−8.24901e6			−0.269010			−0.134505	−	0.990913i	$-0.542944\pi$
$313$	−8.24901e6			−0.269010			−0.134505	+	0.990913i	$0.542944\pi$
$314$	−1.03397e7	+	2.56829e7i	−0.333979	+	0.829573i
$315$		0			0
$316$	−3.01749e7	+	3.14018e7i	−0.956279	+	0.995159i
$317$	−2.38162e7			−0.747643			−0.373821	−	0.927501i	$-0.621953\pi$
$317$	−2.38162e7			−0.747643			−0.373821	+	0.927501i	$0.621953\pi$
$318$	−779721.	−	313909.i	−0.0242470	−	0.00976164i
$319$			5.43762e7i			1.67509i
$320$		0			0
$321$	−6.14967e6			−0.185925
$322$	4.71942e6	−	1.17226e7i	0.141358	−	0.351121i
$323$			4.93696e7i			1.46505i
$324$	−2.08468e7	−	2.00323e7i	−0.612920	−	0.588974i
$325$		0			0
$326$	3.72946e7	+	1.50145e7i	1.07645	+	0.433369i
$327$		−	1.23586e6i		−	0.0353449i
$328$	3.08136e6	−	1.38560e6i	0.0873214	−	0.0392660i
$329$	1.27679e7			0.358535
$330$		0			0
$331$			467508.i			0.0128915i	0.999979	+	0.00644577i	$0.00205177\pi$
$331$			467508.i			0.0128915i	−0.999979	+	0.00644577i	$0.997948\pi$
$332$	4.60562e7	−	4.79287e7i	1.25856	−	1.30973i
$333$	−1.03772e7			−0.281026
$334$	−1.34868e7	−	5.42968e6i	−0.361968	−	0.145725i
$335$		0			0
$336$	−419536.	−	1.05243e7i	−0.0110599	−	0.277443i
$337$	2.14399e7			0.560186			0.280093	−	0.959973i	$-0.409635\pi$
$337$	2.14399e7			0.560186			0.280093	+	0.959973i	$0.409635\pi$
$338$	1.20080e7	−	2.98267e7i	0.310971	−	0.772423i
$339$			9.16128e6i			0.235156i
$340$		0			0
$341$	3.94963e7			0.996078
$342$	−4.57355e7	−	1.84127e7i	−1.14334	−	0.460299i
$343$			2.40411e7i			0.595760i
$344$	1.70247e7	+	3.78603e7i	0.418219	+	0.930055i
$345$		0			0
$346$	6.34425e6	−	1.57585e7i	0.153162	−	0.380441i
$347$			2.74539e7i			0.657077i	0.944491	+	0.328538i	$0.106556\pi$
$347$			2.74539e7i			0.657077i	−0.944491	+	0.328538i	$0.893444\pi$
$348$	−8.41838e6	+	8.76065e6i	−0.199752	+	0.207873i
$349$	−5.59712e7			−1.31670			−0.658352	−	0.752710i	$-0.728746\pi$
$349$	−5.59712e7			−1.31670			−0.658352	+	0.752710i	$0.728746\pi$
$350$		0			0
$351$			7.77497e6i			0.179795i
$352$	−1.92131e7	+	5.38183e7i	−0.440523	+	1.23396i
$353$	−2.18485e7			−0.496704			−0.248352	−	0.968670i	$-0.579889\pi$
$353$	−2.18485e7			−0.496704			−0.248352	+	0.968670i	$0.579889\pi$
$354$	5.35389e6	−	1.32986e7i	0.120687	−	0.299775i
$355$		0			0
$356$	−4.32413e7	−	4.15519e7i	−0.958404	−	0.920960i
$357$	−1.42533e7			−0.313265
$358$	−9.53554e6	−	3.83893e6i	−0.207824	−	0.0836683i
$359$		−	5.17942e7i		−	1.11943i	−0.828685	−	0.559716i	$-0.810910\pi$
$359$		−	5.17942e7i		−	1.11943i	0.828685	−	0.559716i	$-0.189090\pi$
$360$		0			0
$361$	−3.22842e7			−0.686228
$362$	−5.67162e6	+	1.40878e7i	−0.119559	+	0.296973i
$363$		−	7.73068e6i		−	0.161621i
$364$	1.68315e7	−	1.75158e7i	0.348994	−	0.363184i
$365$		0			0
$366$	9.57857e6	+	3.85625e6i	0.195370	+	0.0786542i
$367$		−	6.56443e7i		−	1.32800i	−0.747732	−	0.664001i	$-0.768857\pi$
$367$		−	6.56443e7i		−	1.32800i	0.747732	−	0.664001i	$-0.231143\pi$
$368$	−1.53073e7	+	610207.i	−0.307154	+	0.0122443i
$369$	4.56587e6			0.0908750
$370$		0			0
$371$			7.28829e6i			0.142726i
$372$	6.36332e6	+	6.11471e6i	0.123610	+	0.118781i
$373$	8.58466e7			1.65423			0.827116	−	0.562031i	$-0.189980\pi$
$373$	8.58466e7			1.65423			0.827116	+	0.562031i	$0.189980\pi$
$374$	7.17366e7	+	2.88806e7i	1.37128	+	0.552066i
$375$		0			0
$376$	−6.34788e6	−	1.41167e7i	−0.119417	−	0.265564i
$377$	−2.80219e7			−0.522966
$378$	1.09166e7	−	2.71157e7i	0.202120	−	0.502049i
$379$		−	4.15395e7i		−	0.763034i	−0.924362	−	0.381517i	$-0.875402\pi$
$379$		−	4.15395e7i		−	0.763034i	0.924362	−	0.381517i	$-0.124598\pi$
$380$		0			0
$381$	6.98616e6			0.126318
$382$	8.19034e7	+	3.29736e7i	1.46930	+	0.591530i
$383$		−	4.94031e7i		−	0.879343i	−0.898159	−	0.439671i	$-0.855095\pi$
$383$		−	4.94031e7i		−	0.879343i	0.898159	−	0.439671i	$-0.144905\pi$
$384$	−1.14275e7	+	5.69625e6i	−0.201816	+	0.100599i
$385$		0			0
$386$	2.86967e7	−	7.12800e7i	0.498965	−	1.23938i
$387$			5.61003e7i			0.967905i
$388$	4.41709e7	+	4.24452e7i	0.756208	+	0.726664i
$389$	2.48999e7			0.423008			0.211504	−	0.977377i	$-0.432164\pi$
$389$	2.48999e7			0.423008			0.211504	+	0.977377i	$0.432164\pi$
$390$		0			0
$391$			2.07312e7i			0.346813i
$392$	−2.83567e7	+	1.27512e7i	−0.470759	+	0.211687i
$393$	1.73702e7			0.286172
$394$	1.05378e7	−	2.61750e7i	0.172291	−	0.427955i
$395$		0			0
$396$	−5.35093e7	+	5.56849e7i	−0.861676	+	0.896710i
$397$	1.03578e8			1.65537			0.827687	−	0.561190i	$-0.189656\pi$
$397$	1.03578e8			1.65537			0.827687	+	0.561190i	$0.189656\pi$
$398$	1.25357e7	+	5.04678e6i	0.198838	+	0.0800507i
$399$		−	2.29032e7i		−	0.360559i
$400$		0			0
$401$	8.14381e7			1.26297			0.631487	−	0.775386i	$-0.282445\pi$
$401$	8.14381e7			1.26297			0.631487	+	0.775386i	$0.282445\pi$
$402$	8.23820e6	−	2.04629e7i	0.126810	−	0.314985i
$403$			2.03538e7i			0.310978i
$404$	−2.58961e7	−	2.48844e7i	−0.392727	−	0.377383i
$405$		0			0
$406$	9.77282e7	+	3.93445e7i	1.46030	+	0.587904i
$407$			2.61545e7i			0.387938i
$408$	7.08641e6	+	1.57591e7i	0.104339	+	0.232033i
$409$	9.56658e7			1.39826			0.699128	−	0.714996i	$-0.253572\pi$
$409$	9.56658e7			1.39826			0.699128	+	0.714996i	$0.253572\pi$
$410$		0			0
$411$		−	8.48325e6i		−	0.122190i
$412$	2.87908e7	−	2.99614e7i	0.411683	−	0.428421i
$413$	−1.24306e8			−1.76458
$414$	−1.92052e7	−	7.73186e6i	−0.270656	−	0.108964i
$415$		0			0
$416$	−2.77344e7	−	9.90113e6i	−0.385246	−	0.137532i
$417$	−2.98171e6			−0.0411205
$418$	−4.64071e7	+	1.15271e8i	−0.635412	+	1.57830i
$419$			2.42825e6i			0.0330105i	0.999864	+	0.0165053i	$0.00525402\pi$
$419$			2.42825e6i			0.0330105i	−0.999864	+	0.0165053i	$0.994746\pi$
$420$		0			0
$421$	−5.13368e7			−0.687991			−0.343995	−	0.938971i	$-0.611780\pi$
$421$	−5.13368e7			−0.687991			−0.343995	+	0.938971i	$0.611780\pi$
$422$	4.05788e7	+	1.63367e7i	0.539961	+	0.217384i
$423$		−	2.09177e7i		−	0.276372i
$424$	8.05822e6	−	3.62355e6i	0.105716	−	0.0475376i
$425$		0			0
$426$	−4.48190e6	+	1.11326e7i	−0.0579740	+	0.144002i
$427$		−	8.95337e7i		−	1.15001i
$428$	4.47900e7	−	4.66111e7i	0.571281	−	0.594508i
$429$	9.54233e6			0.120860
$430$		0			0
$431$		−	8.99001e7i		−	1.12287i	−0.827522	−	0.561434i	$-0.810250\pi$
$431$		−	8.99001e7i		−	1.12287i	0.827522	−	0.561434i	$-0.189750\pi$
$432$	−3.54077e7	+	1.41148e6i	−0.439183	+	0.0175075i
$433$	−3.62806e7			−0.446900			−0.223450	−	0.974715i	$-0.571732\pi$
$433$	−3.62806e7			−0.446900			−0.223450	+	0.974715i	$0.571732\pi$
$434$	2.85780e7	−	7.09851e7i	0.349593	−	0.868357i
$435$		0			0
$436$	9.36715e6	+	9.00118e6i	0.113018	+	0.108603i
$437$	−3.33122e7			−0.399171
$438$	−2.15464e7	−	8.67439e6i	−0.256420	−	0.103232i
$439$			2.02544e7i			0.239401i	0.992810	+	0.119701i	$0.0381935\pi$
$439$			2.02544e7i			0.239401i	−0.992810	+	0.119701i	$0.961806\pi$
$440$		0			0
$441$	−4.20183e7			−0.489917
$442$	−1.48831e7	+	3.69683e7i	−0.172356	+	0.428117i
$443$		−	1.42522e8i		−	1.63935i	−0.572828	−	0.819676i	$-0.694154\pi$
$443$		−	1.42522e8i		−	1.63935i	0.572828	−	0.819676i	$-0.305846\pi$
$444$	−4.04916e6	+	4.21379e6i	−0.0462612	+	0.0481420i
$445$		0			0
$446$	5.02527e7	+	2.02313e7i	0.566441	+	0.228044i
$447$		−	6.24631e6i		−	0.0699360i
$448$	8.28236e7	+	7.34717e7i	0.921129	+	0.817120i
$449$	8.30869e7			0.917896			0.458948	−	0.888463i	$-0.348226\pi$
$449$	8.30869e7			0.917896			0.458948	+	0.888463i	$0.348226\pi$
$450$		0			0
$451$		−	1.15077e7i		−	0.125447i
$452$	−6.94374e7	−	6.67245e7i	−0.751931	−	0.722554i
$453$	−2.85089e7			−0.306680
$454$	3.83790e7	+	1.54511e7i	0.410135	+	0.165117i
$455$		0			0
$456$	−2.53226e7	+	1.13869e7i	−0.267063	+	0.120091i
$457$	−1.72794e8			−1.81043			−0.905214	−	0.424956i	$-0.860289\pi$
$457$	−1.72794e8			−1.81043			−0.905214	+	0.424956i	$0.860289\pi$
$458$	−3.43160e7	+	8.52378e7i	−0.357191	+	0.887229i
$459$			4.79537e7i			0.495889i
$460$		0			0
$461$	1.94634e7			0.198663			0.0993315	−	0.995054i	$-0.468330\pi$
$461$	1.94634e7			0.198663			0.0993315	+	0.995054i	$0.468330\pi$
$462$	−3.32795e7	−	1.33980e7i	−0.337482	−	0.135867i
$463$		−	1.61739e8i		−	1.62957i	−0.579763	−	0.814785i	$-0.696855\pi$
$463$		−	1.61739e8i		−	1.62957i	0.579763	−	0.814785i	$-0.303145\pi$
$464$	−5.08714e6	−	1.27613e8i	−0.0509236	−	1.27744i
$465$		0			0
$466$	−1.82811e6	+	4.54085e6i	−0.0180653	+	0.0448725i
$467$		−	5.34609e7i		−	0.524911i	−0.964944	−	0.262455i	$-0.915468\pi$
$467$		−	5.34609e7i		−	0.524911i	0.964944	−	0.262455i	$-0.0845323\pi$
$468$	−2.86963e7	−	2.75751e7i	−0.279955	−	0.269017i
$469$	−1.91273e8			−1.85411
$470$		0			0
$471$			2.10708e7i			0.201659i
$472$	6.18017e7	+	1.37437e8i	0.587725	+	1.30701i
$473$	1.41394e8			1.33613
$474$	−1.23781e7	+	3.07460e7i	−0.116230	+	0.288704i
$475$		0			0
$476$	1.03812e8	−	1.08032e8i	0.962555	−	1.00169i
$477$	1.19404e7			0.110018
$478$	1.39936e8	+	5.63371e7i	1.28129	+	0.515835i
$479$		−	5.20964e7i		−	0.474024i	−0.971507	−	0.237012i	$-0.923832\pi$
$479$		−	5.20964e7i		−	0.474024i	0.971507	−	0.237012i	$-0.0761682\pi$
$480$		0			0
$481$	−1.34783e7			−0.121115
$482$	−3.57265e7	+	8.87413e7i	−0.319043	+	0.792474i
$483$		−	9.61748e6i		−	0.0853532i
$484$	5.85943e7	+	5.63050e7i	0.516796	+	0.496605i
$485$		0			0
$486$	−6.72153e7	−	2.70603e7i	−0.585544	−	0.235735i
$487$		−	4.49422e7i		−	0.389105i	−0.980892	−	0.194553i	$-0.937674\pi$
$487$		−	4.49422e7i		−	0.389105i	0.980892	−	0.194553i	$-0.0623255\pi$
$488$	−9.89920e7	+	4.45139e7i	−0.851806	+	0.383033i
$489$	3.05973e7			0.261672
$490$		0			0
$491$		−	2.58692e7i		−	0.218543i	−0.994012	−	0.109272i	$-0.965148\pi$
$491$		−	2.58692e7i		−	0.218543i	0.994012	−	0.109272i	$-0.0348519\pi$
$492$	1.78160e6	−	1.85403e6i	0.0149594	−	0.0155676i
$493$	−1.72831e8			−1.44238
$494$	−5.94029e7	−	2.39151e7i	−0.492750	−	0.198377i
$495$		0			0
$496$	−9.26922e7	+	3.69506e6i	−0.759623	+	0.0302814i
$497$	1.04060e8			0.847646
$498$	1.88927e7	−	4.69278e7i	0.152970	−	0.379964i
$499$			2.14540e7i			0.172666i	0.996266	+	0.0863329i	$0.0275149\pi$
$499$			2.14540e7i			0.172666i	−0.996266	+	0.0863329i	$0.972485\pi$
$500$		0			0
$501$	−1.10649e7			−0.0879901
$502$	−3.29456e7	−	1.32636e7i	−0.260427	−	0.104846i
$503$			1.02143e8i			0.802607i	0.915945	+	0.401303i	$0.131443\pi$
$503$			1.02143e8i			0.802607i	−0.915945	+	0.401303i	$0.868557\pi$
$504$	6.13629e7	+	1.36462e8i	0.479308	+	1.06591i
$505$		0			0
$506$	−1.94872e7	+	4.84044e7i	−0.150417	+	0.373623i
$507$		−	2.44705e7i		−	0.187767i
$508$	−5.08825e7	+	5.29512e7i	−0.388130	+	0.403910i
$509$	−1.68263e8			−1.27595			−0.637976	−	0.770056i	$-0.720228\pi$
$509$	−1.68263e8			−1.27595			−0.637976	+	0.770056i	$0.720228\pi$
$510$		0			0
$511$			2.01400e8i			1.50938i
$512$	4.00554e7	−	1.28101e8i	0.298436	−	0.954430i
$513$	−7.70550e7			−0.570754
$514$	−9.02581e7	+	2.24193e8i	−0.664656	+	1.65094i
$515$		0			0
$516$	2.27803e7	+	2.18903e7i	0.165810	+	0.159332i
$517$	−5.27206e7			−0.381513
$518$	4.70064e7	+	1.89244e7i	0.338195	+	0.136155i
$519$		−	1.29287e7i		−	0.0924807i
$520$		0			0
$521$	7.03931e7			0.497756			0.248878	−	0.968535i	$-0.419938\pi$
$521$	7.03931e7			0.497756			0.248878	+	0.968535i	$0.419938\pi$
$522$	6.44584e7	−	1.60109e8i	0.453177	−	1.12565i
$523$		−	1.32429e7i		−	0.0925719i	−0.998928	−	0.0462859i	$-0.985261\pi$
$523$		−	1.32429e7i		−	0.0925719i	0.998928	−	0.0462859i	$-0.0147385\pi$
$524$	−1.26513e8	+	1.31656e8i	−0.879307	+	0.915058i
$525$		0			0
$526$	−2.16271e8	−	8.70689e7i	−1.48608	−	0.598282i
$527$			1.25536e8i			0.857703i
$528$	1.73233e6	+	4.34563e7i	0.0117687	+	0.295224i
$529$	1.34047e8			0.905506
$530$		0			0
$531$			2.03651e8i			1.36020i
$532$	1.73593e8	+	1.66811e8i	1.15292	+	1.10787i
$533$	5.93032e6			0.0391649
$534$	−4.23383e7	−	1.70450e7i	−0.278042	−	0.111937i
$535$		0			0
$536$	9.50962e7	+	2.11479e8i	0.617545	+	1.37332i
$537$	−7.82317e6			−0.0505196
$538$	6.74713e7	−	1.67593e8i	0.433284	−	1.07624i
$539$			1.05902e8i			0.676297i
$540$		0			0
$541$	8.75392e6			0.0552855			0.0276427	−	0.999618i	$-0.491200\pi$
$541$	8.75392e6			0.0552855			0.0276427	+	0.999618i	$0.491200\pi$
$542$	−5.56767e7	−	2.24150e7i	−0.349684	−	0.140780i
$543$			1.15579e7i			0.0721905i
$544$	−1.71058e8	−	6.10673e7i	−1.06254	−	0.379325i
$545$		0			0
$546$	6.90446e6	−	1.71500e7i	0.0424182	−	0.105363i
$547$		−	1.27352e8i		−	0.778114i	−0.921214	−	0.389057i	$-0.872801\pi$
$547$		−	1.27352e8i		−	0.778114i	0.921214	−	0.389057i	$-0.127199\pi$
$548$	6.42983e7	+	6.17862e7i	0.390713	+	0.375448i
$549$	−1.46684e8			−0.886471
$550$		0			0
$551$		−	2.77715e8i		−	1.66014i
$552$	−1.06335e7	+	4.78157e6i	−0.0632204	+	0.0284284i
$553$	2.87392e8			1.69941
$554$	7.07495e7	−	1.75735e8i	0.416096	−	1.03354i
$555$		0			0
$556$	2.17168e7	−	2.25997e7i	0.126349	−	0.131486i
$557$	2.82592e8			1.63529			0.817645	−	0.575723i	$-0.195279\pi$
$557$	2.82592e8			1.63529			0.817645	+	0.575723i	$0.195279\pi$
$558$	−1.16295e8	−	4.68196e7i	−0.669360	−	0.269479i
$559$			7.28652e7i			0.417143i
$560$		0			0
$561$	5.88543e7			0.333342
$562$	−6.66210e7	+	1.65480e8i	−0.375320	+	0.932261i
$563$			2.23747e7i			0.125381i	0.998033	+	0.0626905i	$0.0199681\pi$
$563$			2.23747e7i			0.125381i	−0.998033	+	0.0626905i	$0.980032\pi$
$564$	−8.49392e6	−	8.16207e6i	−0.0473446	−	0.0454949i
$565$		0			0
$566$	−1.49530e7	−	6.01993e6i	−0.0824665	−	0.0332003i
$567$			1.90792e8i			1.04667i
$568$	−5.17360e7	−	1.15053e8i	−0.282324	−	0.627845i
$569$	2.06789e8			1.12251			0.561256	−	0.827642i	$-0.310318\pi$
$569$	2.06789e8			1.12251			0.561256	+	0.827642i	$0.310318\pi$
$570$		0			0
$571$		−	1.67454e8i		−	0.899473i	−0.893161	−	0.449737i	$-0.851518\pi$
$571$		−	1.67454e8i		−	0.899473i	0.893161	−	0.449737i	$-0.148482\pi$
$572$	−6.94998e7	+	7.23256e7i	−0.371360	+	0.386459i
$573$	6.71954e7			0.357170
$574$	−2.06824e7	−	8.32655e6i	−0.109362	−	0.0440280i
$575$		0			0
$576$	1.20369e8	−	1.35691e8i	0.629865	−	0.710039i
$577$	−1.29395e8			−0.673583			−0.336792	−	0.941579i	$-0.609342\pi$
$577$	−1.29395e8			−0.673583			−0.336792	+	0.941579i	$0.609342\pi$
$578$	−1.96790e7	+	4.88807e7i	−0.101910	+	0.253136i
$579$		−	5.84797e7i		−	0.301279i
$580$		0			0
$581$	−4.38648e8			−2.23660
$582$	4.32485e7	+	1.74115e7i	0.219383	+	0.0883216i
$583$		−	3.00945e7i		−	0.151873i
$584$	2.22676e8	−	1.00131e8i	1.11798	−	0.502725i
$585$		0			0
$586$	−9.55722e7	+	2.37393e8i	−0.474940	+	1.17971i
$587$			1.84946e8i			0.914386i	0.889367	+	0.457193i	$0.151145\pi$
$587$			1.84946e8i			0.914386i	−0.889367	+	0.457193i	$0.848855\pi$
$588$	−1.63955e7	+	1.70621e7i	−0.0806476	+	0.0839266i
$589$	−2.01719e8			−0.987191
$590$		0			0
$591$		−	2.14745e7i		−	0.104031i
$592$	−2.44687e6	−	6.13808e7i	−0.0117936	−	0.295847i
$593$	−1.51763e8			−0.727784			−0.363892	−	0.931441i	$-0.618552\pi$
$593$	−1.51763e8			−0.727784			−0.363892	+	0.931441i	$0.618552\pi$
$594$	−4.50762e7	+	1.11965e8i	−0.215074	+	0.534224i
$595$		0			0
$596$	4.73436e7	+	4.54939e7i	0.223626	+	0.214889i
$597$	1.02846e7			0.0483352
$598$	−2.49444e7	−	1.00424e7i	−0.116646	−	0.0469607i
$599$			2.67870e8i			1.24636i	0.782079	+	0.623180i	$0.214159\pi$
$599$			2.67870e8i			1.24636i	−0.782079	+	0.623180i	$0.785841\pi$
$600$		0			0
$601$	2.92898e8			1.34925			0.674626	−	0.738160i	$-0.264305\pi$
$601$	2.92898e8			1.34925			0.674626	+	0.738160i	$0.264305\pi$
$602$	1.02307e8	−	2.54122e8i	0.468940	−	1.16480i
$603$			3.13364e8i			1.42921i
$604$	2.07639e8	−	2.16082e8i	0.942322	−	0.980634i
$605$		0			0
$606$	−2.53553e7	−	1.02078e7i	−0.113934	−	0.0458687i
$607$		−	2.54116e8i		−	1.13623i	−0.822949	−	0.568115i	$-0.807673\pi$
$607$		−	2.54116e8i		−	1.13623i	0.822949	−	0.568115i	$-0.192327\pi$
$608$	9.81267e7	−	2.74866e8i	0.436592	−	1.22295i
$609$	8.01783e7			0.354981
$610$		0			0
$611$		−	2.71687e7i		−	0.119109i
$612$	−1.76990e8	−	1.70075e8i	−0.772139	−	0.741972i
$613$	−3.65576e7			−0.158707			−0.0793534	−	0.996847i	$-0.525286\pi$
$613$	−3.65576e7			−0.158707			−0.0793534	+	0.996847i	$0.525286\pi$
$614$	−1.07864e8	−	4.34249e7i	−0.465982	−	0.187601i
$615$		0			0
$616$	3.43935e8	−	1.54658e8i	1.47141	−	0.661652i
$617$	−1.37267e8			−0.584400			−0.292200	−	0.956357i	$-0.594387\pi$
$617$	−1.37267e8			−0.584400			−0.292200	+	0.956357i	$0.594387\pi$
$618$	1.18103e7	−	2.93357e7i	0.0500375	−	0.124289i
$619$		−	2.41038e8i		−	1.01628i	−0.861275	−	0.508140i	$-0.830333\pi$
$619$		−	2.41038e8i		−	1.01628i	0.861275	−	0.508140i	$-0.169667\pi$
$620$		0			0
$621$	−3.23569e7			−0.135111
$622$	4.26825e7	+	1.71836e7i	0.177369	+	0.0714073i
$623$			3.95749e8i			1.63665i
$624$	−2.23945e7	+	892727.i	−0.0921695	+	0.00367422i
$625$		0			0
$626$	2.46455e7	−	6.12172e7i	0.100465	−	0.249546i
$627$			9.45707e7i			0.383667i
$628$	−1.59705e8	−	1.53465e8i	−0.644821	−	0.619628i
$629$	−8.31301e7			−0.334046
$630$		0			0
$631$			2.23847e8i			0.890968i	0.895290	+	0.445484i	$0.146968\pi$
$631$			2.23847e8i			0.890968i	−0.895290	+	0.445484i	$0.853032\pi$
$632$	−1.42884e8	−	3.17752e8i	−0.566021	−	1.25874i
$633$	3.32918e7			0.131258
$634$	7.11555e7	−	1.76744e8i	0.279216	−	0.693547i
$635$		0			0
$636$	4.65914e6	−	4.84857e6i	0.0181107	−	0.0188470i
$637$	−5.45748e7			−0.211142
$638$	−4.03535e8	−	1.62460e8i	−1.55389	−	0.625581i
$639$		−	1.70482e8i		−	0.653396i
$640$		0			0
$641$	5.85061e7			0.222140			0.111070	−	0.993813i	$-0.464572\pi$
$641$	5.85061e7			0.222140			0.111070	+	0.993813i	$0.464572\pi$
$642$	1.83734e7	−	4.56377e7i	0.0694358	−	0.172472i
$643$			2.24198e7i			0.0843331i	0.999111	+	0.0421666i	$0.0134260\pi$
$643$			2.24198e7i			0.0843331i	−0.999111	+	0.0421666i	$0.986574\pi$
$644$	7.28951e7	+	7.00472e7i	0.272923	+	0.262260i
$645$		0			0
$646$	−3.66380e8	−	1.47501e8i	−1.35905	−	0.547140i
$647$			1.77477e8i			0.655283i	0.944802	+	0.327641i	$0.106254\pi$
$647$			1.77477e8i			0.655283i	−0.944802	+	0.327641i	$0.893746\pi$
$648$	2.10947e8	−	9.48569e7i	0.775261	−	0.348613i
$649$	5.13278e8			1.87767
$650$		0			0
$651$		−	5.82378e7i		−	0.211087i
$652$	−2.22850e8	+	2.31911e8i	−0.804026	+	0.836716i
$653$	3.43085e8			1.23215			0.616073	−	0.787689i	$-0.288723\pi$
$653$	3.43085e8			1.23215			0.616073	+	0.787689i	$0.288723\pi$
$654$	9.17153e6	+	3.69238e6i	0.0327875	+	0.0132000i
$655$		0			0
$656$	1.07660e6	+	2.70070e7i	0.00381366	+	0.0956676i
$657$	3.29955e8			1.16348
$658$	−3.81466e7	+	9.47527e7i	−0.133899	+	0.332594i
$659$		−	2.57705e8i		−	0.900465i	−0.892911	−	0.450233i	$-0.851341\pi$
$659$		−	2.57705e8i		−	0.900465i	0.892911	−	0.450233i	$-0.148659\pi$
$660$		0			0
$661$	1.58848e8			0.550018			0.275009	−	0.961442i	$-0.411319\pi$
$661$	1.58848e8			0.550018			0.275009	+	0.961442i	$0.411319\pi$
$662$	−3.46945e6	−	1.39677e6i	−0.0119588	−	0.00481450i
$663$			3.03296e7i			0.104070i
$664$	2.18085e8	+	4.84987e8i	0.744940	+	1.65663i
$665$		0			0
$666$	3.10039e7	−	7.70109e7i	0.104953	−	0.260693i
$667$		−	1.16618e8i		−	0.392996i
$668$	8.05891e7	−	8.38657e7i	0.270363	−	0.281355i
$669$	4.12284e7			0.137695
$670$		0			0
$671$			3.69699e8i			1.22371i
$672$	7.93557e7	+	2.83299e7i	0.261499	+	0.0933548i
$673$	−2.76715e8			−0.907793			−0.453897	−	0.891054i	$-0.649966\pi$
$673$	−2.76715e8			−0.907793			−0.453897	+	0.891054i	$0.649966\pi$
$674$	−6.40558e7	+	1.59109e8i	−0.209208	+	0.519654i
$675$		0			0
$676$	1.85473e8	+	1.78226e8i	0.600398	+	0.576941i
$677$	−4.19801e8			−1.35294			−0.676468	−	0.736472i	$-0.736490\pi$
$677$	−4.19801e8			−1.35294			−0.676468	+	0.736472i	$0.736490\pi$
$678$	−6.79873e7	−	2.73711e7i	−0.218142	−	0.0878220i
$679$		−	4.04257e8i		−	1.29136i
$680$		0			0
$681$	3.14870e7			0.0996988
$682$	−1.18003e8	+	2.93109e8i	−0.371998	+	0.924008i
$683$			9.99621e7i			0.313742i	0.987619	+	0.156871i	$0.0501408\pi$
$683$			9.99621e7i			0.313742i	−0.987619	+	0.156871i	$0.949859\pi$
$684$	2.73288e8	−	2.84399e8i	0.853988	−	0.888709i
$685$		0			0
$686$	−1.78413e8	−	7.18275e7i	−0.552654	−	0.222494i
$687$			6.99310e7i			0.215675i
$688$	−3.31832e8	+	1.32280e7i	−1.01895	+	0.0406191i
$689$	1.55087e7			0.0474152
$690$		0			0
$691$		−	2.78223e8i		−	0.843254i	−0.906769	−	0.421627i	$-0.861459\pi$
$691$		−	2.78223e8i		−	0.843254i	0.906769	−	0.421627i	$-0.138541\pi$
$692$	9.79920e7	+	9.41635e7i	0.295714	+	0.284161i
$693$	5.09633e8			1.53129
$694$	−2.03740e8	−	8.20241e7i	−0.609534	−	0.245393i
$695$		0			0
$696$	−3.98627e7	−	8.86483e7i	−0.118233	−	0.262932i
$697$	3.65765e7			0.108020
$698$	1.67225e8	−	4.15372e8i	0.491739	−	1.22144i
$699$			3.72542e6i			0.0109080i
$700$		0			0
$701$	1.43797e8			0.417443			0.208721	−	0.977975i	$-0.433070\pi$
$701$	1.43797e8			0.417443			0.208721	+	0.977975i	$0.433070\pi$
$702$	−5.76993e7	−	2.32293e7i	−0.166786	−	0.0671466i
$703$		−	1.33579e8i		−	0.384477i
$704$	−3.41992e8	−	3.03376e8i	−0.980161	−	0.869487i
$705$		0			0
$706$	6.52767e7	−	1.62141e8i	0.185500	−	0.460765i
$707$			2.37004e8i			0.670652i
$708$	8.26951e7	+	7.94642e7i	0.233013	+	0.223909i
$709$	−3.30939e8			−0.928558			−0.464279	−	0.885689i	$-0.653686\pi$
$709$	−3.30939e8			−0.928558			−0.464279	+	0.885689i	$0.653686\pi$
$710$		0			0
$711$		−	4.70836e8i		−	1.30997i
$712$	4.37555e8	−	1.96756e8i	1.21225	−	0.545116i
$713$	−8.47058e7			−0.233692
$714$	4.25847e7	−	1.05776e8i	0.116993	−	0.290599i
$715$		0			0
$716$	5.69786e7	−	5.92953e7i	0.155229	−	0.161540i
$717$	1.14807e8			0.311466
$718$	3.84373e8	+	1.54745e8i	1.03844	+	0.418065i
$719$			3.88053e8i			1.04401i	0.852943	+	0.522004i	$0.174815\pi$
$719$			3.88053e8i			1.04401i	−0.852943	+	0.522004i	$0.825185\pi$
$720$		0			0
$721$	−2.74210e8			−0.731605
$722$	9.64555e7	−	2.39586e8i	0.256280	−	0.636577i
$723$			7.28053e7i			0.192641i
$724$	−8.76026e7	−	8.41800e7i	−0.230835	−	0.221816i
$725$		0			0
$726$	5.73706e7	+	2.30969e7i	0.149927	+	0.0603593i
$727$		−	6.94954e8i		−	1.80864i	−0.426852	−	0.904322i	$-0.640377\pi$
$727$		−	6.94954e8i		−	1.80864i	0.426852	−	0.904322i	$-0.359623\pi$
$728$	7.97004e7	+	1.77241e8i	0.206570	+	0.459378i
$729$	2.74176e8			0.707697
$730$		0			0
$731$			4.49411e8i			1.15051i
$732$	−5.72357e7	+	5.95628e7i	−0.145926	+	0.151859i
$733$	−6.03758e8			−1.53303			−0.766515	−	0.642226i	$-0.778011\pi$
$733$	−6.03758e8			−1.53303			−0.766515	+	0.642226i	$0.778011\pi$
$734$	4.87157e8	+	1.96125e8i	1.23191	+	0.495958i
$735$		0			0
$736$	4.12053e7	−	1.15421e8i	0.103352	−	0.289503i
$737$	7.89796e8			1.97293
$738$	−1.36414e7	+	3.38841e7i	−0.0339384	+	0.0842998i
$739$			7.73026e8i			1.91540i	0.287760	+	0.957702i	$0.407089\pi$
$739$			7.73026e8i			1.91540i	−0.287760	+	0.957702i	$0.592911\pi$
$740$		0			0
$741$	−4.87355e7			−0.119782
$742$	−5.40876e7	−	2.17752e7i	−0.132399	−	0.0533028i
$743$		−	6.42826e7i		−	0.156721i	−0.996925	−	0.0783605i	$-0.975031\pi$
$743$		−	6.42826e7i		−	0.156721i	0.996925	−	0.0783605i	$-0.0249685\pi$
$744$	−6.43900e7	+	2.89544e7i	−0.156351	+	0.0703064i
$745$		0			0
$746$	−2.56484e8	+	6.37082e8i	−0.617793	+	1.53454i
$747$			7.18640e8i			1.72405i
$748$	−4.28655e8	+	4.46083e8i	−1.02424	+	1.06589i
$749$	−4.26589e8			−1.01523
$750$		0			0
$751$		−	6.17586e8i		−	1.45807i	−0.684477	−	0.729034i	$-0.739970\pi$
$751$		−	6.17586e8i		−	1.45807i	0.684477	−	0.729034i	$-0.260030\pi$
$752$	1.23728e8	−	4.93225e6i	0.290947	−	0.0115982i
$753$	−2.70293e7			−0.0633067
$754$	8.37209e7	−	2.07955e8i	0.195308	−	0.485127i
$755$		0			0
$756$	1.68615e8	+	1.62027e8i	0.390239	+	0.374992i
$757$	−3.20889e8			−0.739719			−0.369859	−	0.929088i	$-0.620594\pi$
$757$	−3.20889e8			−0.739719			−0.369859	+	0.929088i	$0.620594\pi$
$758$	3.08271e8	+	1.24107e8i	0.707825	+	0.284964i
$759$			3.97121e7i			0.0908232i
$760$		0			0
$761$	−7.08784e7			−0.160827			−0.0804136	−	0.996762i	$-0.525624\pi$
$761$	−7.08784e7			−0.160827			−0.0804136	+	0.996762i	$0.525624\pi$
$762$	−2.08725e7	+	5.18455e7i	−0.0471748	+	0.117178i
$763$		−	8.57290e7i		−	0.192999i
$764$	−4.89405e8	+	5.09303e8i	−1.09746	+	1.14208i
$765$		0			0
$766$	3.66629e8	+	1.47602e8i	0.815718	+	0.328401i
$767$			2.64509e8i			0.586212i
$768$	−8.13106e6	−	1.01824e8i	−0.0179500	−	0.224784i
$769$	−2.07387e8			−0.456040			−0.228020	−	0.973656i	$-0.573225\pi$
$769$	−2.07387e8			−0.456040			−0.228020	+	0.973656i	$0.573225\pi$
$770$		0			0
$771$			1.83933e8i			0.401324i
$772$	4.43243e8	+	4.25926e8i	0.963364	+	0.925726i
$773$	4.62098e8			1.00045			0.500226	−	0.865895i	$-0.333250\pi$
$773$	4.62098e8			1.00045			0.500226	+	0.865895i	$0.333250\pi$
$774$	−4.16330e8	−	1.67611e8i	−0.897872	−	0.361476i
$775$		0			0
$776$	−4.46962e8	+	2.00986e8i	−0.956502	+	0.430112i
$777$	3.85651e7			0.0822112
$778$	−7.43934e7	+	1.84786e8i	−0.157978	+	0.392402i
$779$			5.87733e7i			0.124328i
$780$		0			0
$781$	−4.29680e8			−0.901970
$782$	−1.53850e8	−	6.19387e7i	−0.321719	−	0.129521i
$783$		−	2.69751e8i		−	0.561924i
$784$	−9.90760e6	−	2.48537e8i	−0.0205599	−	0.515754i
$785$		0			0
$786$	−5.18969e7	+	1.28907e8i	−0.106874	+	0.265466i
$787$		−	6.57367e8i		−	1.34860i	−0.738457	−	0.674301i	$-0.764445\pi$
$787$		−	6.57367e8i		−	1.34860i	0.738457	−	0.674301i	$-0.235555\pi$
$788$	1.62765e8	+	1.56406e8i	0.332646	+	0.319650i
$789$	−1.77433e8			−0.361247
$790$		0			0
$791$			6.35498e8i			1.28406i
$792$	−2.53377e8	−	5.63471e8i	−0.510025	−	1.13422i
$793$	−1.90518e8			−0.382047
$794$	−3.09460e8	+	7.68669e8i	−0.618219	+	1.53560i
$795$		0			0
$796$	−7.49059e7	+	7.79515e7i	−0.148517	+	0.154556i
$797$	−3.81335e8			−0.753238			−0.376619	−	0.926368i	$-0.622913\pi$
$797$	−3.81335e8			−0.753238			−0.376619	+	0.926368i	$0.622913\pi$
$798$	1.69968e8	+	6.84277e7i	0.334471	+	0.134655i
$799$		−	1.67569e8i		−	0.328513i
$800$		0			0
$801$	6.48358e8			1.26159
$802$	−2.43313e8	+	6.04366e8i	−0.471673	+	1.17159i
$803$		−	8.31613e8i		−	1.60611i
$804$	1.27245e8	+	1.22274e8i	0.244835	+	0.235270i
$805$		0			0
$806$	−1.51049e8	−	6.08109e7i	−0.288477	−	0.116139i
$807$		−	1.37497e8i		−	0.261620i
$808$	2.62041e8	−	1.17832e8i	0.496747	−	0.223373i
$809$	2.89351e8			0.546487			0.273243	−	0.961945i	$-0.411904\pi$
$809$	2.89351e8			0.546487			0.273243	+	0.961945i	$0.411904\pi$
$810$		0			0
$811$			2.32956e8i			0.436729i	0.975867	+	0.218364i	$0.0700721\pi$
$811$			2.32956e8i			0.436729i	−0.975867	+	0.218364i	$0.929928\pi$
$812$	−5.83964e8	+	6.07707e8i	−1.09073	+	1.13508i
$813$	−4.56784e7			−0.0850040
$814$	−1.94097e8	−	7.81416e7i	−0.359869	−	0.144880i
$815$		0			0
$816$	−1.38123e8	+	5.50608e6i	−0.254211	+	0.0101338i
$817$	−7.22141e8			−1.32421
$818$	−2.85821e8	+	7.09952e8i	−0.522196	+	1.29709i
$819$			2.62631e8i			0.478073i
$820$		0			0
$821$	−4.41895e8			−0.798528			−0.399264	−	0.916836i	$-0.630734\pi$
$821$	−4.41895e8			−0.798528			−0.399264	+	0.916836i	$0.630734\pi$
$822$	6.29556e7	+	2.53454e7i	0.113349	+	0.0456335i
$823$		−	8.93586e8i		−	1.60301i	−0.597987	−	0.801506i	$-0.704032\pi$
$823$		−	8.93586e8i		−	1.60301i	0.597987	−	0.801506i	$-0.295968\pi$
$824$	1.36330e8	+	3.03177e8i	0.243675	+	0.541894i
$825$		0			0
$826$	3.71388e8	−	9.22493e8i	0.659003	−	1.63690i
$827$		−	5.74698e8i		−	1.01607i	−0.861337	−	0.508034i	$-0.830372\pi$
$827$		−	5.74698e8i		−	1.01607i	0.861337	−	0.508034i	$-0.169628\pi$
$828$	1.14759e8	−	1.19425e8i	0.202160	−	0.210379i
$829$	5.62396e7			0.0987139			0.0493570	−	0.998781i	$-0.484283\pi$
$829$	5.62396e7			0.0987139			0.0493570	+	0.998781i	$0.484283\pi$
$830$		0			0
$831$		−	1.44177e8i		−	0.251242i
$832$	1.56340e8	−	1.76240e8i	0.271456	−	0.306009i
$833$	−3.36602e8			−0.582346
$834$	8.90846e6	−	2.21278e7i	0.0153569	−	0.0381452i
$835$		0			0
$836$	−7.16793e8	−	6.88789e8i	−1.22680	−	1.17887i
$837$	−1.95934e8			−0.334144
$838$	−1.80205e7	−	7.25489e6i	−0.0306220	−	0.0123282i
$839$		−	6.14216e8i		−	1.04001i	−0.854165	−	0.520003i	$-0.825931\pi$
$839$		−	6.14216e8i		−	1.04001i	0.854165	−	0.520003i	$-0.174069\pi$
$840$		0			0
$841$	3.77390e8			0.634457
$842$	1.53379e8	−	3.80979e8i	0.256938	−	0.638211i
$843$			1.35764e8i			0.226621i
$844$	−2.42475e8	+	2.52333e8i	−0.403310	+	0.419708i
$845$		0			0
$846$	1.55234e8	+	6.24959e7i	0.256375	+	0.103214i
$847$		−	5.36260e8i		−	0.882522i
$848$	2.81547e6	+	7.06274e7i	0.00461704	+	0.115821i
$849$	−1.22677e7			−0.0200466
$850$		0			0
$851$		−	5.60922e7i		−	0.0910151i
$852$	−6.92265e7	−	6.65219e7i	−0.111932	−	0.107559i
$853$	−7.29239e8			−1.17496			−0.587480	−	0.809239i	$-0.699880\pi$
$853$	−7.29239e8			−1.17496			−0.587480	+	0.809239i	$0.699880\pi$
$854$	6.64444e8	+	2.67500e8i	1.06680	+	0.429486i
$855$		0			0
$856$	2.12089e8	+	4.71654e8i	0.338141	+	0.751973i
$857$	5.93996e6			0.00943716			0.00471858	−	0.999989i	$-0.498498\pi$
$857$	5.93996e6			0.00943716			0.00471858	+	0.999989i	$0.498498\pi$
$858$	−2.85096e7	+	7.08152e7i	−0.0451366	+	0.112115i
$859$		−	2.37950e8i		−	0.375410i	−0.982225	−	0.187705i	$-0.939895\pi$
$859$		−	2.37950e8i		−	0.375410i	0.982225	−	0.187705i	$-0.0601049\pi$
$860$		0			0
$861$	−1.69683e7			−0.0265845
$862$	6.67163e8	+	2.68594e8i	1.04162	+	0.419348i
$863$			9.36443e8i			1.45696i	0.685065	+	0.728482i	$0.259774\pi$
$863$			9.36443e8i			1.45696i	−0.685065	+	0.728482i	$0.740226\pi$
$864$	9.53125e7	−	2.66983e8i	0.147778	−	0.413945i
$865$		0			0
$866$	1.08395e8	−	2.69244e8i	0.166900	−	0.414565i
$867$			4.01028e7i			0.0615344i
$868$	4.41410e8	+	4.24164e8i	0.674967	+	0.648597i
$869$	−1.18669e9			−1.80832
$870$		0			0
$871$			4.07008e8i			0.615955i
$872$	−9.47854e7	+	4.26223e7i	−0.142953	+	0.0642818i
$873$	−6.62297e8			−0.995428
$874$	9.95269e7	−	2.47216e8i	0.149075	−	0.370290i
$875$		0			0
$876$	1.28748e8	−	1.33983e8i	0.191526	−	0.199313i
$877$	4.37126e8			0.648050			0.324025	−	0.946049i	$-0.394964\pi$
$877$	4.37126e8			0.648050			0.324025	+	0.946049i	$0.394964\pi$
$878$	−1.50312e8	−	6.05141e7i	−0.222080	−	0.0894074i
$879$			1.94762e8i			0.286773i
$880$		0			0
$881$	−3.67911e8			−0.538041			−0.269020	−	0.963134i	$-0.586700\pi$
$881$	−3.67911e8			−0.538041			−0.269020	+	0.963134i	$0.586700\pi$
$882$	1.25538e8	−	3.11824e8i	0.182965	−	0.454469i
$883$		−	9.70524e8i		−	1.40969i	−0.709360	−	0.704846i	$-0.751016\pi$
$883$		−	9.70524e8i		−	1.40969i	0.709360	−	0.704846i	$-0.248984\pi$
$884$	−2.29881e8	−	2.20900e8i	−0.332772	−	0.319771i
$885$		0			0
$886$	1.05768e9	+	4.25814e8i	1.52074	+	0.612236i
$887$			8.13859e8i			1.16621i	0.812395	+	0.583107i	$0.198163\pi$
$887$			8.13859e8i			1.16621i	−0.812395	+	0.583107i	$0.801837\pi$
$888$	−1.91736e7	−	4.26390e7i	−0.0273819	−	0.0608932i
$889$	4.84615e8			0.689750
$890$		0			0
$891$		−	7.87808e8i		−	1.11375i
$892$	−3.00280e8	+	3.12488e8i	−0.423089	+	0.440290i
$893$	2.69260e8			0.378109
$894$	4.63549e7	+	1.86621e7i	0.0648758	+	0.0261185i
$895$		0			0
$896$	−7.92697e8	+	3.95137e8i	−1.10200	+	0.549317i
$897$	−2.04650e7			−0.0283552
$898$	−2.48239e8	+	6.16602e8i	−0.342800	+	0.851482i
$899$		−	7.06169e8i		−	0.971919i
$900$		0			0
$901$	9.56531e7			0.130775
$902$	8.54008e7	+	3.43816e7i	0.116370	+	0.0468497i
$903$		−	2.08487e8i		−	0.283150i
$904$	7.02631e8	−	3.15954e8i	0.951091	−	0.427679i
$905$		0			0
$906$	8.51760e7	−	2.11569e8i	0.114534	−	0.284491i
$907$		−	1.02901e8i		−	0.137910i	−0.997620	−	0.0689551i	$-0.978033\pi$
$907$		−	1.02901e8i		−	0.137910i	0.997620	−	0.0689551i	$-0.0219665\pi$
$908$	−2.29330e8	+	2.38654e8i	−0.306340	+	0.318795i
$909$	3.88285e8			0.516962
$910$		0			0
$911$			1.62697e8i			0.215191i	0.994195	+	0.107596i	$0.0343152\pi$
$911$			1.62697e8i			0.215191i	−0.994195	+	0.107596i	$0.965685\pi$
$912$	−8.84751e6	−	2.21944e8i	−0.0116637	−	0.292590i
$913$	1.81125e9			2.37994
$914$	5.16258e8	−	1.28234e9i	0.676126	−	1.67944i
$915$		0			0
$916$	−5.30038e8	−	5.09330e8i	−0.689637	−	0.662693i
$917$	1.20493e9			1.56263
$918$	−3.55873e8	−	1.43271e8i	−0.460009	−	0.185196i
$919$			1.40533e9i			1.81064i	0.424730	+	0.905320i	$0.360369\pi$
$919$			1.40533e9i			1.81064i	−0.424730	+	0.905320i	$0.639631\pi$
$920$		0			0
$921$	−8.84936e7			−0.113275
$922$	−5.81509e7	+	1.44441e8i	−0.0741931	+	0.184289i
$923$		−	2.21428e8i		−	0.281597i
$924$	1.98858e8	−	2.06943e8i	0.252074	−	0.262322i
$925$		0			0
$926$	1.20030e9	+	4.83229e8i	1.51166	+	0.608583i
$927$			4.49239e8i			0.563948i
$928$	9.62238e8	+	3.43517e8i	1.20403	+	0.429838i
$929$	1.57221e9			1.96093			0.980467	−	0.196685i	$-0.0630178\pi$
$929$	1.57221e9			1.96093			0.980467	+	0.196685i	$0.0630178\pi$
$930$		0			0
$931$		−	5.40872e8i		−	0.670264i
$932$	−2.82366e7	−	2.71334e7i	−0.0348790	−	0.0335163i
$933$	3.50176e7			0.0431163
$934$	3.96742e8	+	1.59725e8i	0.486931	+	0.196034i
$935$		0			0
$936$	2.90375e8	−	1.30574e8i	0.354105	−	0.159231i
$937$	−5.23220e8			−0.636013			−0.318006	−	0.948089i	$-0.603013\pi$
$937$	−5.23220e8			−0.636013			−0.318006	+	0.948089i	$0.603013\pi$
$938$	5.71466e8	−	1.41947e9i	0.692440	−	1.71996i
$939$		−	5.02239e7i		−	0.0606616i
$940$		0			0
$941$	3.00726e8			0.360912			0.180456	−	0.983583i	$-0.442243\pi$
$941$	3.00726e8			0.360912			0.180456	+	0.983583i	$0.442243\pi$
$942$	−1.56370e8	−	6.29531e7i	−0.187068	−	0.0753121i
$943$			2.46801e7i			0.0294314i
$944$	−1.20459e9	+	4.80194e7i	−1.43193	+	0.0570822i
$945$		0			0
$946$	−4.22443e8	+	1.04931e9i	−0.498993	+	1.23945i
$947$		−	4.73433e8i		−	0.557453i	−0.960370	−	0.278727i	$-0.910088\pi$
$947$		−	4.73433e8i		−	0.557453i	0.960370	−	0.278727i	$-0.0899123\pi$
$948$	−1.91189e8	−	1.83719e8i	−0.224408	−	0.215640i
$949$	4.28558e8			0.501431
$950$		0			0
$951$		−	1.45004e8i		−	0.168593i
$952$	4.91569e8	+	1.09317e9i	0.569736	+	1.26700i
$953$	−6.45528e8			−0.745824			−0.372912	−	0.927867i	$-0.621641\pi$
$953$	−6.45528e8			−0.745824			−0.372912	+	0.927867i	$0.621641\pi$
$954$	−3.56744e7	+	8.86120e7i	−0.0410877	+	0.102058i
$955$		0			0
$956$	−8.36174e8	+	8.70171e8i	−0.957025	+	0.995935i
$957$	−3.31069e8			−0.377731
$958$	3.86616e8	+	1.55648e8i	0.439727	+	0.177030i
$959$		−	5.88465e8i		−	0.667213i
$960$		0			0
$961$	3.74576e8			0.422055
$962$	4.02690e7	−	1.00024e8i	0.0452320	−	0.112352i
$963$			6.98884e8i			0.782575i
$964$	−5.51824e8	−	5.30264e8i	−0.615984	−	0.591918i
$965$		0			0
$966$	7.13729e7	+	2.87341e7i	0.0791775	+	0.0318762i
$967$			6.01748e8i			0.665481i	0.943018	+	0.332740i	$0.107973\pi$
$967$			6.01748e8i			0.665481i	−0.943018	+	0.332740i	$0.892027\pi$
$968$	−5.92911e8	+	2.66615e8i	−0.653677	+	0.293940i
$969$	−3.00586e8			−0.330368
$970$		0			0
$971$			3.59534e8i			0.392719i	0.980532	+	0.196360i	$0.0629120\pi$
$971$			3.59534e8i			0.392719i	−0.980532	+	0.196360i	$0.937088\pi$
$972$	4.01638e8	−	4.17968e8i	0.437357	−	0.455139i
$973$	−2.06835e8			−0.224536
$974$	3.33523e8	+	1.34274e8i	0.360952	+	0.145316i
$975$		0			0
$976$	−3.45869e7	−	8.67630e8i	−0.0372017	−	0.933222i
$977$	−3.41034e8			−0.365691			−0.182845	−	0.983142i	$-0.558531\pi$
$977$	−3.41034e8			−0.365691			−0.182845	+	0.983142i	$0.558531\pi$
$978$	−9.14155e7	+	2.27068e8i	−0.0977245	+	0.242739i
$979$		−	1.63411e9i		−	1.74154i
$980$		0			0
$981$	−1.40450e8			−0.148770
$982$	1.91979e8	+	7.72892e7i	0.202731	+	0.0816177i
$983$			7.22351e8i			0.760480i	0.924888	+	0.380240i	$0.124159\pi$
$983$			7.22351e8i			0.760480i	−0.924888	+	0.380240i	$0.875841\pi$
$984$	8.43620e6	+	1.87608e7i	0.00885445	+	0.0196909i
$985$		0			0
$986$	5.16366e8	−	1.28261e9i	0.538675	−	1.33802i
$987$			7.77372e7i			0.0808495i
$988$	3.54956e8	−	3.69388e8i	0.368047	−	0.383011i
$989$	−3.03241e8			−0.313472
$990$		0			0
$991$		−	1.09281e9i		−	1.12286i	−0.827526	−	0.561428i	$-0.810252\pi$
$991$		−	1.09281e9i		−	1.12286i	0.827526	−	0.561428i	$-0.189748\pi$
$992$	2.49515e8	−	6.98924e8i	0.255600	−	0.715970i
$993$	−2.84641e6			−0.00290703
$994$	−3.10900e8	+	7.72246e8i	−0.316564	+	0.786315i
$995$		0			0
$996$	2.91813e8	+	2.80412e8i	0.295343	+	0.283804i
$997$	9.59556e8			0.968245			0.484122	−	0.875000i	$-0.339139\pi$
$997$	9.59556e8			0.968245			0.484122	+	0.875000i	$0.339139\pi$
$998$	−1.59213e8	−	6.40980e7i	−0.160173	−	0.0644841i
$999$		−	1.29748e8i		−	0.130138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.7.b.f.51.6		12
4.3	odd	2	inner	100.7.b.f.51.5		12
5.2	odd	4		20.7.d.d.19.1	✓	12
5.3	odd	4		20.7.d.d.19.12	yes	12
5.4	even	2	inner	100.7.b.f.51.7		12
15.2	even	4		180.7.f.e.19.12		12
15.8	even	4		180.7.f.e.19.1		12
20.3	even	4		20.7.d.d.19.2	yes	12
20.7	even	4		20.7.d.d.19.11	yes	12
20.19	odd	2	inner	100.7.b.f.51.8		12
40.3	even	4		320.7.h.f.319.5		12
40.13	odd	4		320.7.h.f.319.7		12
40.27	even	4		320.7.h.f.319.8		12
40.37	odd	4		320.7.h.f.319.6		12
60.23	odd	4		180.7.f.e.19.11		12
60.47	odd	4		180.7.f.e.19.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.d.d.19.1	✓	12	5.2	odd	4
20.7.d.d.19.2	yes	12	20.3	even	4
20.7.d.d.19.11	yes	12	20.7	even	4
20.7.d.d.19.12	yes	12	5.3	odd	4
100.7.b.f.51.5		12	4.3	odd	2	inner
100.7.b.f.51.6		12	1.1	even	1	trivial
100.7.b.f.51.7		12	5.4	even	2	inner
100.7.b.f.51.8		12	20.19	odd	2	inner
180.7.f.e.19.1		12	15.8	even	4
180.7.f.e.19.2		12	60.47	odd	4
180.7.f.e.19.11		12	60.23	odd	4
180.7.f.e.19.12		12	15.2	even	4
320.7.h.f.319.5		12	40.3	even	4
320.7.h.f.319.6		12	40.37	odd	4
320.7.h.f.319.7		12	40.13	odd	4
320.7.h.f.319.8		12	40.27	even	4

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.98770 + 7.42116i) q^{2} +6.08848i q^{3} +(-46.1473 - 44.3444i) q^{4} +(-45.1836 - 18.1905i) q^{6} +422.345i q^{7} +(466.961 - 209.979i) q^{8} +691.930 q^{9} +O(q^{10})\)	\(q+(-2.98770 + 7.42116i) q^{2} +6.08848i q^{3} +(-46.1473 - 44.3444i) q^{4} +(-45.1836 - 18.1905i) q^{6} +422.345i q^{7} +(466.961 - 209.979i) q^{8} +691.930 q^{9} -1743.93i q^{11} +(269.990 - 280.967i) q^{12} +898.704 q^{13} +(-3134.29 - 1261.84i) q^{14} +(163.152 + 4092.75i) q^{16} +5542.94 q^{17} +(-2067.28 + 5134.93i) q^{18} +8906.74i q^{19} -2571.44 q^{21} +(12942.0 + 5210.33i) q^{22} +3740.11i q^{23} +(1278.46 + 2843.09i) q^{24} +(-2685.06 + 6669.43i) q^{26} +8651.31i q^{27} +(18728.6 - 19490.1i) q^{28} -31180.3 q^{29} +22647.9i q^{31} +(-30860.4 - 11017.1i) q^{32} +10617.9 q^{33} +(-16560.6 + 41135.1i) q^{34} +(-31930.7 - 30683.2i) q^{36} -14997.5 q^{37} +(-66098.4 - 26610.7i) q^{38} +5471.75i q^{39} +6598.75 q^{41} +(7682.68 - 19083.1i) q^{42} +81078.0i q^{43} +(-77333.4 + 80477.6i) q^{44} +(-27756.0 - 11174.3i) q^{46} -30231.0i q^{47} +(-24918.6 + 993.349i) q^{48} -60726.1 q^{49} +33748.1i q^{51} +(-41472.8 - 39852.5i) q^{52} +17256.7 q^{53} +(-64202.8 - 25847.5i) q^{54} +(88683.7 + 197219. i) q^{56} -54228.6 q^{57} +(93157.4 - 231394. i) q^{58} +294323. i q^{59} -211992. q^{61} +(-168074. - 67665.1i) q^{62} +292233. i q^{63} +(173961. - 196104. i) q^{64} +(-31723.0 + 78797.0i) q^{66} +452884. i q^{67} +(-255792. - 245798. i) q^{68} -22771.6 q^{69} -246386. i q^{71} +(323105. - 145291. i) q^{72} +476862. q^{73} +(44807.9 - 111299. i) q^{74} +(394964. - 411022. i) q^{76} +736539. q^{77} +(-40606.7 - 16347.9i) q^{78} -680467. i q^{79} +451744. q^{81} +(-19715.1 + 48970.4i) q^{82} +1.03860e6i q^{83} +(118665. + 114029. i) q^{84} +(-601693. - 242237. i) q^{86} -189841. i q^{87} +(-366189. - 814346. i) q^{88} +937027. q^{89} +379563. i q^{91} +(165853. - 172596. i) q^{92} -137891. q^{93} +(224349. + 90321.0i) q^{94} +(67077.6 - 187893. i) q^{96} -957172. q^{97} +(181431. - 450659. i) q^{98} -1.20668e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9}+O(q^{10}) \) 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9	\( 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9} - 512 q^{14} - 20928 q^{16} + 51216 q^{21} + 20928 q^{24} + 14496 q^{26} + 16072 q^{29} - 257216 q^{34} - 144960 q^{36} - 192136 q^{41} + 165120 q^{44} - 49472 q^{46} - 145796 q^{49} + 118656 q^{54} + 1078208 q^{56} + 215384 q^{61} + 6656 q^{64} - 1403520 q^{66} - 1015824 q^{69} + 1020384 q^{74} + 2515200 q^{76} - 2327652 q^{81} - 424704 q^{84} - 5268832 q^{86} + 4346152 q^{89} - 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) \) 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9 - 512 * q^14 - 20928 * q^16 + 51216 * q^21 + 20928 * q^24 + 14496 * q^26 + 16072 * q^29 - 257216 * q^34 - 144960 * q^36 - 192136 * q^41 + 165120 * q^44 - 49472 * q^46 - 145796 * q^49 + 118656 * q^54 + 1078208 * q^56 + 215384 * q^61 + 6656 * q^64 - 1403520 * q^66 - 1015824 * q^69 + 1020384 * q^74 + 2515200 * q^76 - 2327652 * q^81 - 424704 * q^84 - 5268832 * q^86 + 4346152 * q^89 - 4292992 * q^94 + 7673088 * q^96

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