LMFDB - Embedded newform 115.7.c.c.114.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.c (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:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.14
Character	$\chi$	$=$	115.114
Dual form			115.7.c.c.114.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.35786i q^{2} -24.6249i q^{3} +45.0090 q^{4} +(108.536 - 62.0072i) q^{5} +107.312 q^{6} -356.743 q^{7} +475.046i q^{8} +122.613 q^{9} +O(q^{10})$	\(q+4.35786i q^{2} -24.6249i q^{3} +45.0090 q^{4} +(108.536 - 62.0072i) q^{5} +107.312 q^{6} -356.743 q^{7} +475.046i q^{8} +122.613 q^{9} +(270.219 + 472.986i) q^{10} +2460.25i q^{11} -1108.34i q^{12} +3886.94i q^{13} -1554.64i q^{14} +(-1526.92 - 2672.70i) q^{15} +810.390 q^{16} +5678.93 q^{17} +534.332i q^{18} -4274.93i q^{19} +(4885.11 - 2790.88i) q^{20} +8784.77i q^{21} -10721.5 q^{22} +(-11955.6 + 2258.26i) q^{23} +11698.0 q^{24} +(7935.21 - 13460.1i) q^{25} -16938.7 q^{26} -20970.9i q^{27} -16056.7 q^{28} +31948.2 q^{29} +(11647.2 - 6654.12i) q^{30} +27146.6 q^{31} +33934.5i q^{32} +60583.6 q^{33} +24748.0i q^{34} +(-38719.5 + 22120.6i) q^{35} +5518.71 q^{36} -6032.87 q^{37} +18629.6 q^{38} +95715.5 q^{39} +(29456.3 + 51559.7i) q^{40} +103770. q^{41} -38282.8 q^{42} -105331. q^{43} +110734. i q^{44} +(13308.0 - 7602.91i) q^{45} +(-9841.21 - 52100.8i) q^{46} +6782.07i q^{47} -19955.8i q^{48} +9616.64 q^{49} +(58657.1 + 34580.6i) q^{50} -139843. i q^{51} +174947. i q^{52} -47948.2 q^{53} +91388.4 q^{54} +(152554. + 267027. i) q^{55} -169470. i q^{56} -105270. q^{57} +139226. i q^{58} -275854. q^{59} +(-68725.3 - 120295. i) q^{60} -44668.5i q^{61} +118301. i q^{62} -43741.5 q^{63} -96017.2 q^{64} +(241018. + 421873. i) q^{65} +264015. i q^{66} -120875. q^{67} +255603. q^{68} +(55609.6 + 294405. i) q^{69} +(-96398.8 - 168734. i) q^{70} +493278. q^{71} +58247.0i q^{72} -37898.7i q^{73} -26290.4i q^{74} +(-331453. - 195404. i) q^{75} -192411. i q^{76} -877679. i q^{77} +417115. i q^{78} -532286. i q^{79} +(87956.6 - 50250.0i) q^{80} -427022. q^{81} +452216. i q^{82} +610329. q^{83} +395394. i q^{84} +(616369. - 352135. i) q^{85} -459020. i q^{86} -786722. i q^{87} -1.16874e6 q^{88} +1.02095e6i q^{89} +(33132.5 + 57994.4i) q^{90} -1.38664e6i q^{91} +(-538109. + 101642. i) q^{92} -668484. i q^{93} -29555.3 q^{94} +(-265077. - 463985. i) q^{95} +835635. q^{96} +837437. q^{97} +41908.0i q^{98} +301660. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$			4.35786i			0.544733i	0.962194	+	0.272366i	$0.0878063\pi$
$2$			4.35786i			0.544733i	−0.962194	+	0.272366i	$0.912194\pi$
$3$		−	24.6249i		−	0.912034i	−0.889971	−	0.456017i	$-0.849276\pi$
$3$		−	24.6249i		−	0.912034i	0.889971	−	0.456017i	$-0.150724\pi$
$4$	45.0090			0.703266
$5$	108.536	−	62.0072i	0.868290	−	0.496058i
$5$	108.536	−	62.0072i	0.868290	−	0.496058i
$6$	107.312			0.496815
$7$	−356.743			−1.04007			−0.520034	−	0.854146i	$-0.674081\pi$
$7$	−356.743			−1.04007			−0.520034	+	0.854146i	$0.674081\pi$
$8$			475.046i			0.927825i
$9$	122.613			0.168194
$10$	270.219	+	472.986i	0.270219	+	0.472986i
$11$			2460.25i			1.84843i	0.381878	+	0.924213i	$0.375277\pi$
$11$			2460.25i			1.84843i	−0.381878	+	0.924213i	$0.624723\pi$
$12$		−	1108.34i		−	0.641403i
$13$			3886.94i			1.76920i	0.466348	+	0.884601i	$0.345569\pi$
$13$			3886.94i			1.76920i	−0.466348	+	0.884601i	$0.654431\pi$
$14$		−	1554.64i		−	0.566559i
$15$	−1526.92	−	2672.70i	−0.452422	−	0.791910i
$16$	810.390			0.197849
$17$	5678.93			1.15590			0.577949	−	0.816073i	$-0.303853\pi$
$17$	5678.93			1.15590			0.577949	+	0.816073i	$0.303853\pi$
$18$			534.332i			0.0916208i
$19$		−	4274.93i		−	0.623259i	−0.950204	−	0.311629i	$-0.899125\pi$
$19$		−	4274.93i		−	0.623259i	0.950204	−	0.311629i	$-0.100875\pi$
$20$	4885.11	−	2790.88i	0.610639	−	0.348861i
$21$			8784.77i			0.948577i
$22$	−10721.5			−1.00690
$23$	−11955.6	+	2258.26i	−0.982624	+	0.185606i
$23$	−11955.6	+	2258.26i	−0.982624	+	0.185606i
$24$	11698.0			0.846208
$25$	7935.21	−	13460.1i	0.507854	−	0.861443i
$26$	−16938.7			−0.963743
$27$		−	20970.9i		−	1.06543i
$28$	−16056.7			−0.731444
$29$	31948.2			1.30994			0.654972	−	0.755653i	$-0.272680\pi$
$29$	31948.2			1.30994			0.654972	+	0.755653i	$0.272680\pi$
$30$	11647.2	−	6654.12i	0.431379	−	0.246449i
$31$	27146.6			0.911236			0.455618	−	0.890175i	$-0.349418\pi$
$31$	27146.6			0.911236			0.455618	+	0.890175i	$0.349418\pi$
$32$			33934.5i			1.03560i
$33$	60583.6			1.68583
$34$			24748.0i			0.629656i
$35$	−38719.5	+	22120.6i	−0.903080	+	0.515933i
$36$	5518.71			0.118285
$37$	−6032.87			−0.119102			−0.0595510	−	0.998225i	$-0.518967\pi$
$37$	−6032.87			−0.119102			−0.0595510	+	0.998225i	$0.518967\pi$
$38$	18629.6			0.339510
$39$	95715.5			1.61357
$40$	29456.3	+	51559.7i	0.460255	+	0.805621i
$41$	103770.			1.50564			0.752819	−	0.658227i	$-0.228693\pi$
$41$	103770.			1.50564			0.752819	+	0.658227i	$0.228693\pi$
$42$	−38282.8			−0.516721
$43$	−105331.			−1.32481			−0.662403	−	0.749148i	$-0.730463\pi$
$43$	−105331.			−1.32481			−0.662403	+	0.749148i	$0.730463\pi$
$44$			110734.i			1.29993i
$45$	13308.0	−	7602.91i	0.146041	−	0.0834339i
$46$	−9841.21	−	52100.8i	−0.101106	−	0.535268i
$47$			6782.07i			0.0653234i	0.999466	+	0.0326617i	$0.0103984\pi$
$47$			6782.07i			0.0653234i	−0.999466	+	0.0326617i	$0.989602\pi$
$48$		−	19955.8i		−	0.180445i
$49$	9616.64			0.0817401
$50$	58657.1	+	34580.6i	0.469257	+	0.276645i
$51$		−	139843.i		−	1.05422i
$52$			174947.i			1.24422i
$53$	−47948.2			−0.322066			−0.161033	−	0.986949i	$-0.551483\pi$
$53$	−47948.2			−0.322066			−0.161033	+	0.986949i	$0.551483\pi$
$54$	91388.4			0.580376
$55$	152554.	+	267027.i	0.916926	+	1.60497i
$56$		−	169470.i		−	0.965001i
$57$	−105270.			−0.568433
$58$			139226.i			0.713570i
$59$	−275854.			−1.34315			−0.671574	−	0.740938i	$-0.734381\pi$
$59$	−275854.			−1.34315			−0.671574	+	0.740938i	$0.734381\pi$
$60$	−68725.3	−	120295.i	−0.318173	−	0.556923i
$61$		−	44668.5i		−	0.196794i	−0.995147	−	0.0983971i	$-0.968628\pi$
$61$		−	44668.5i		−	0.196794i	0.995147	−	0.0983971i	$-0.0313715\pi$
$62$			118301.i			0.496380i
$63$	−43741.5			−0.174933
$64$	−96017.2			−0.366276
$65$	241018.	+	421873.i	0.877626	+	1.53618i
$66$			264015.i			0.918326i
$67$	−120875.			−0.401895			−0.200947	−	0.979602i	$-0.564402\pi$
$67$	−120875.			−0.401895			−0.200947	+	0.979602i	$0.564402\pi$
$68$	255603.			0.812904
$69$	55609.6	+	294405.i	0.169279	+	0.896187i
$70$	−96398.8	−	168734.i	−0.281046	−	0.491937i
$71$	493278.			1.37821			0.689107	−	0.724660i	$-0.258003\pi$
$71$	493278.			1.37821			0.689107	+	0.724660i	$0.258003\pi$
$72$			58247.0i			0.156055i
$73$		−	37898.7i		−	0.0974218i	−0.998813	−	0.0487109i	$-0.984489\pi$
$73$		−	37898.7i		−	0.0974218i	0.998813	−	0.0487109i	$-0.0155113\pi$
$74$		−	26290.4i		−	0.0648787i
$75$	−331453.	−	195404.i	−0.785666	−	0.463180i
$76$		−	192411.i		−	0.438317i
$77$		−	877679.i		−	1.92249i
$78$			417115.i			0.878966i
$79$		−	532286.i		−	1.07960i	−0.841793	−	0.539801i	$-0.818500\pi$
$79$		−	532286.i		−	1.07960i	0.841793	−	0.539801i	$-0.181500\pi$
$80$	87956.6	−	50250.0i	0.171790	−	0.0981445i
$81$	−427022.			−0.803517
$82$			452216.i			0.820171i
$83$	610329.			1.06741			0.533703	−	0.845672i	$-0.320800\pi$
$83$	610329.			1.06741			0.533703	+	0.845672i	$0.320800\pi$
$84$			395394.i			0.667102i
$85$	616369.	−	352135.i	1.00365	−	0.573392i
$86$		−	459020.i		−	0.721665i
$87$		−	786722.i		−	1.19471i
$88$	−1.16874e6			−1.71502
$89$			1.02095e6i			1.44822i	0.689684	+	0.724111i	$0.257750\pi$
$89$			1.02095e6i			1.44822i	−0.689684	+	0.724111i	$0.742250\pi$
$90$	33132.5	+	57994.4i	0.0454492	+	0.0795533i
$91$		−	1.38664e6i		−	1.84009i
$92$	−538109.	+	101642.i	−0.691046	+	0.130530i
$93$		−	668484.i		−	0.831079i
$94$	−29555.3			−0.0355838
$95$	−265077.	−	463985.i	−0.309172	−	0.541169i
$96$	835635.			0.944503
$97$	837437.			0.917566			0.458783	−	0.888548i	$-0.348286\pi$
$97$	837437.			0.917566			0.458783	+	0.888548i	$0.348286\pi$
$98$			41908.0i			0.0445265i
$99$			301660.i			0.310894i
$100$	357156.	−	605824.i	0.357156	−	0.605824i
$101$	−1.04596e6			−1.01519			−0.507597	−	0.861595i	$-0.669466\pi$
$101$	−1.04596e6			−1.01519			−0.507597	+	0.861595i	$0.669466\pi$
$102$	609417.			0.574268
$103$	234877.			0.214945			0.107473	−	0.994208i	$-0.465724\pi$
$103$	234877.			0.214945			0.107473	+	0.994208i	$0.465724\pi$
$104$	−1.84648e6			−1.64151
$105$	544719.	+	953466.i	0.470549	+	0.823639i
$106$		−	208952.i		−	0.175440i
$107$	−86713.5			−0.0707841			−0.0353920	−	0.999374i	$-0.511268\pi$
$107$	−86713.5			−0.0707841			−0.0353920	+	0.999374i	$0.511268\pi$
$108$		−	943880.i		−	0.749283i
$109$			363988.i			0.281066i	0.990076	+	0.140533i	$0.0448816\pi$
$109$			363988.i			0.281066i	−0.990076	+	0.140533i	$0.955118\pi$
$110$	−1.16367e6	+	664807.i	−0.874279	+	0.499480i
$111$			148559.i			0.108625i
$112$	−289101.			−0.205776
$113$	−454665.			−0.315106			−0.157553	−	0.987511i	$-0.550360\pi$
$113$	−454665.			−0.315106			−0.157553	+	0.987511i	$0.550360\pi$
$114$		−	458752.i		−	0.309644i
$115$	−1.15759e6	+	986436.i	−0.761131	+	0.648598i
$116$	1.43796e6			0.921239
$117$			476590.i			0.297569i
$118$		−	1.20214e6i		−	0.731657i
$119$	−2.02592e6			−1.20221
$120$	1.26965e6	−	725359.i	0.734754	−	0.419768i
$121$	−4.28129e6			−2.41668
$122$	194659.			0.107200
$123$		−	2.55533e6i		−	1.37319i
$124$	1.22184e6			0.640841
$125$	26637.2	−	1.95294e6i	0.0136382	−	0.999907i
$126$		−	190619.i		−	0.0952918i
$127$			961934.i			0.469606i	0.972043	+	0.234803i	$0.0754446\pi$
$127$			961934.i			0.469606i	−0.972043	+	0.234803i	$0.924555\pi$
$128$			1.75338e6i			0.836077i
$129$			2.59378e6i			1.20827i
$130$	−1.83847e6	+	1.05032e6i	−0.836808	+	0.478072i
$131$	−1.68559e6			−0.749786			−0.374893	−	0.927068i	$-0.622321\pi$
$131$	−1.68559e6			−0.749786			−0.374893	+	0.927068i	$0.622321\pi$
$132$	2.72681e6			1.18558
$133$			1.52505e6i			0.648231i
$134$		−	526757.i		−	0.218925i
$135$	−1.30035e6	−	2.27610e6i	−0.528516	−	0.925104i
$136$			2.69775e6i			1.07247i
$137$	773225.			0.300708			0.150354	−	0.988632i	$-0.451959\pi$
$137$	773225.			0.300708			0.150354	+	0.988632i	$0.451959\pi$
$138$	−1.28298e6	+	242339.i	−0.488183	+	0.0922117i
$139$	3.65378e6			1.36050			0.680249	−	0.732981i	$-0.261871\pi$
$139$	3.65378e6			1.36050			0.680249	+	0.732981i	$0.261871\pi$
$140$	−1.74273e6	+	995629.i	−0.635105	+	0.362838i
$141$	167008.			0.0595771
$142$			2.14964e6i			0.750758i
$143$	−9.56285e6			−3.27024
$144$	99364.6			0.0332770
$145$	3.46754e6	−	1.98102e6i	1.13741	−	0.649808i
$146$	165158.			0.0530689
$147$		−	236809.i		−	0.0745498i
$148$	−271534.			−0.0837603
$149$		−	1.76101e6i		−	0.532358i	−0.963924	−	0.266179i	$-0.914239\pi$
$149$		−	1.76101e6i		−	0.532358i	0.963924	−	0.266179i	$-0.0857612\pi$
$150$	851544.	−	1.44443e6i	0.252309	−	0.427978i
$151$	467646.			0.135827			0.0679135	−	0.997691i	$-0.478366\pi$
$151$	467646.			0.135827			0.0679135	+	0.997691i	$0.478366\pi$
$152$	2.03079e6			0.578275
$153$	696312.			0.194415
$154$	3.82480e6			1.04724
$155$	2.94639e6	−	1.68329e6i	0.791217	−	0.452026i
$156$	4.30806e6			1.13477
$157$	2.91729e6			0.753842			0.376921	−	0.926245i	$-0.376983\pi$
$157$	2.91729e6			0.753842			0.376921	+	0.926245i	$0.376983\pi$
$158$	2.31963e6			0.588095
$159$			1.18072e6i			0.293735i
$160$	2.10419e6	+	3.68313e6i	0.513717	+	0.899201i
$161$	4.26507e6	−	805620.i	1.02200	−	0.193042i
$162$		−	1.86090e6i		−	0.437702i
$163$			4.35741e6i			1.00616i	0.864241	+	0.503079i	$0.167799\pi$
$163$			4.35741e6i			1.00616i	−0.864241	+	0.503079i	$0.832201\pi$
$164$	4.67059e6			1.05886
$165$	6.57551e6	−	3.75662e6i	1.46379	−	0.836267i
$166$			2.65973e6i			0.581451i
$167$		−	8.54229e6i		−	1.83411i	−0.398763	−	0.917054i	$-0.630561\pi$
$167$		−	8.54229e6i		−	1.83411i	0.398763	−	0.917054i	$-0.369439\pi$
$168$	−4.17317e6			−0.880113
$169$	−1.02815e7			−2.13008
$170$	1.53455e6	+	2.68605e6i	0.312346	+	0.546724i
$171$		−	524164.i		−	0.104828i
$172$	−4.74086e6			−0.931691
$173$		−	2.83226e6i		−	0.547010i	−0.961871	−	0.273505i	$-0.911817\pi$
$173$		−	2.83226e6i		−	0.547010i	0.961871	−	0.273505i	$-0.0881829\pi$
$174$	3.42843e6			0.650800
$175$	−2.83083e6	+	4.80178e6i	−0.528202	+	0.895959i
$176$			1.99376e6i			0.365709i
$177$			6.79289e6i			1.22500i
$178$	−4.44917e6			−0.788894
$179$	−4.47118e6			−0.779585			−0.389792	−	0.920903i	$-0.627453\pi$
$179$	−4.47118e6			−0.779585			−0.389792	+	0.920903i	$0.627453\pi$
$180$	598979.	−	342200.i	0.102706	−	0.0586762i
$181$		−	1.11610e6i		−	0.188220i	−0.995562	−	0.0941101i	$-0.969999\pi$
$181$		−	1.11610e6i		−	0.188220i	0.995562	−	0.0941101i	$-0.0300006\pi$
$182$	6.04278e6			1.00236
$183$	−1.09996e6			−0.179483
$184$	−1.07278e6	−	5.67946e6i	−0.172210	−	0.911704i
$185$	−654785.	+	374081.i	−0.103415	+	0.0590814i
$186$	2.91316e6			0.452716
$187$			1.39716e7i			2.13659i
$188$			305254.i			0.0459397i
$189$			7.48123e6i			1.10812i
$190$	2.02198e6	−	1.15517e6i	0.294793	−	0.168416i
$191$		−	2.93034e6i		−	0.420550i	−0.977642	−	0.210275i	$-0.932564\pi$
$191$		−	2.93034e6i		−	0.420550i	0.977642	−	0.210275i	$-0.0674359\pi$
$192$			2.36442e6i			0.334057i
$193$		−	2.11862e6i		−	0.294701i	−0.989084	−	0.147351i	$-0.952925\pi$
$193$		−	2.11862e6i		−	0.294701i	0.989084	−	0.147351i	$-0.0470746\pi$
$194$			3.64944e6i			0.499828i
$195$	1.03886e7	−	5.93505e6i	1.40105	−	0.800425i
$196$	432836.			0.0574850
$197$		−	7.08008e6i		−	0.926061i	−0.886342	−	0.463031i	$-0.846762\pi$
$197$		−	7.08008e6i		−	0.926061i	0.886342	−	0.463031i	$-0.153238\pi$
$198$	−1.31459e6			−0.169354
$199$			3.90889e6i			0.496015i	0.968758	+	0.248007i	$0.0797757\pi$
$199$			3.90889e6i			0.496015i	−0.968758	+	0.248007i	$0.920224\pi$
$200$	6.39415e6	+	3.76959e6i	0.799269	+	0.471199i
$201$			2.97654e6i			0.366542i
$202$		−	4.55813e6i		−	0.553010i
$203$	−1.13973e7			−1.36243
$204$		−	6.29420e6i		−	0.741396i
$205$	1.12628e7	−	6.43450e6i	1.30733	−	0.746884i
$206$			1.02356e6i			0.117088i
$207$	−1.46591e6	+	276893.i	−0.165271	+	0.0312177i
$208$			3.14993e6i			0.350035i
$209$	1.05174e7			1.15205
$210$	−4.15507e6	+	2.37381e6i	−0.448664	+	0.256323i
$211$	−2.29079e6			−0.243858			−0.121929	−	0.992539i	$-0.538908\pi$
$211$	−2.29079e6			−0.243858			−0.121929	+	0.992539i	$0.538908\pi$
$212$	−2.15810e6			−0.226498
$213$		−	1.21469e7i		−	1.25698i
$214$		−	377886.i		−	0.0385584i
$215$	−1.14323e7	+	6.53130e6i	−1.15032	+	0.657180i
$216$	9.96216e6			0.988535
$217$	−9.68438e6			−0.947747
$218$	−1.58621e6			−0.153106
$219$	−933253.			−0.0888520
$220$	6.86628e6	+	1.20186e7i	0.644843	+	1.12872i
$221$			2.20736e7i			2.04502i
$222$	−647399.			−0.0591716
$223$			1.12421e7i			1.01375i	0.862019	+	0.506877i	$0.169200\pi$
$223$			1.12421e7i			1.01375i	−0.862019	+	0.506877i	$0.830800\pi$
$224$		−	1.21059e7i		−	1.07709i
$225$	972963.	−	1.65038e6i	0.0854179	−	0.144890i
$226$		−	1.98137e6i		−	0.171648i
$227$	1.25244e7			1.07073			0.535366	−	0.844620i	$-0.320174\pi$
$227$	1.25244e7			1.07073			0.535366	+	0.844620i	$0.320174\pi$
$228$	−4.73809e6			−0.399760
$229$		−	1.34835e7i		−	1.12278i	−0.827551	−	0.561391i	$-0.810266\pi$
$229$		−	1.34835e7i		−	1.12278i	0.827551	−	0.561391i	$-0.189734\pi$
$230$	−4.29875e6	−	5.04460e6i	−0.353313	−	0.414613i
$231$	−2.16128e7			−1.75337
$232$			1.51769e7i			1.21540i
$233$		−	1.98445e6i		−	0.156882i	−0.996919	−	0.0784408i	$-0.975006\pi$
$233$		−	1.98445e6i		−	0.156882i	0.996919	−	0.0784408i	$-0.0249942\pi$
$234$	−2.07692e6			−0.162096
$235$	420537.	+	736100.i	0.0324042	+	0.0567196i
$236$	−1.24159e7			−0.944590
$237$	−1.31075e7			−0.984633
$238$		−	8.82868e6i		−	0.654885i
$239$	3.91064e6			0.286454			0.143227	−	0.989690i	$-0.454252\pi$
$239$	3.91064e6			0.286454			0.143227	+	0.989690i	$0.454252\pi$
$240$	−1.23740e6	−	2.16592e6i	−0.0895112	−	0.156679i
$241$			1.91337e7i			1.36693i	0.729982	+	0.683467i	$0.239529\pi$
$241$			1.91337e7i			1.36693i	−0.729982	+	0.683467i	$0.760471\pi$
$242$		−	1.86573e7i		−	1.31644i
$243$		−	4.77241e6i		−	0.332598i
$244$		−	2.01049e6i		−	0.138399i
$245$	1.04375e6	−	596301.i	0.0709741	−	0.0405478i
$246$	1.11358e7			0.748024
$247$	1.66164e7			1.10267
$248$			1.28959e7i			0.845468i
$249$		−	1.50293e7i		−	0.973510i
$250$	8.51066e6	+	116081.i	0.544682	+	0.00742920i
$251$		−	2.21200e7i		−	1.39882i	−0.714719	−	0.699412i	$-0.753445\pi$
$251$		−	2.21200e7i		−	1.39882i	0.714719	−	0.699412i	$-0.246555\pi$
$252$	−1.96876e6			−0.123024
$253$	−5.55591e6	−	2.94138e7i	−0.343078	−	1.81631i
$254$	−4.19198e6			−0.255810
$255$	−8.67128e6	−	1.51780e7i	−0.522953	−	0.915367i
$256$	−1.37861e7			−0.821715
$257$		−	2.05607e6i		−	0.121126i	−0.998164	−	0.0605631i	$-0.980710\pi$
$257$		−	2.05607e6i		−	0.121126i	0.998164	−	0.0605631i	$-0.0192896\pi$
$258$	−1.13033e7			−0.658183
$259$	2.15218e6			0.123874
$260$	1.08480e7	+	1.89881e7i	0.617205	+	1.08034i
$261$	3.91728e6			0.220325
$262$		−	7.34556e6i		−	0.408433i
$263$	3.64508e6			0.200373			0.100187	−	0.994969i	$-0.468056\pi$
$263$	3.64508e6			0.200373			0.100187	+	0.994969i	$0.468056\pi$
$264$			2.87800e7i			1.56415i
$265$	−5.20411e6	+	2.97313e6i	−0.279646	+	0.159763i
$266$	−6.64597e6			−0.353113
$267$	2.51408e7			1.32083
$268$	−5.44047e6			−0.282639
$269$	−3.78860e7			−1.94635			−0.973176	−	0.230061i	$-0.926107\pi$
$269$	−3.78860e7			−1.94635			−0.973176	+	0.230061i	$0.926107\pi$
$270$	9.91895e6	−	5.66674e6i	0.503935	−	0.287900i
$271$	−1.07476e7			−0.540011			−0.270006	−	0.962859i	$-0.587026\pi$
$271$	−1.07476e7			−0.540011			−0.270006	+	0.962859i	$0.587026\pi$
$272$	4.60214e6			0.228693
$273$	−3.41459e7			−1.67822
$274$			3.36961e6i			0.163805i
$275$	3.31152e7	+	1.95226e7i	1.59231	+	0.938729i
$276$	2.50293e6	+	1.32509e7i	0.119048	+	0.630258i
$277$		−	5.12768e6i		−	0.241258i	−0.992698	−	0.120629i	$-0.961509\pi$
$277$		−	5.12768e6i		−	0.241258i	0.992698	−	0.120629i	$-0.0384911\pi$
$278$			1.59227e7i			0.741109i
$279$	3.32854e6			0.153264
$280$	−1.05083e7	−	1.83936e7i	−0.478696	−	0.837900i
$281$		−	3.59117e7i		−	1.61852i	−0.587452	−	0.809259i	$-0.699869\pi$
$281$		−	3.59117e7i		−	1.61852i	0.587452	−	0.809259i	$-0.300131\pi$
$282$			727798.i			0.0324536i
$283$	−1.46282e7			−0.645402			−0.322701	−	0.946501i	$-0.604591\pi$
$283$	−1.46282e7			−0.645402			−0.322701	+	0.946501i	$0.604591\pi$
$284$	2.22020e7			0.969251
$285$	−1.14256e7	+	6.52749e6i	−0.493565	+	0.281976i
$286$		−	4.16736e7i		−	1.78141i
$287$	−3.70193e7			−1.56597
$288$			4.16083e6i			0.174182i
$289$	8.11266e6			0.336101
$290$	8.63302e6	+	1.51111e7i	0.353972	+	0.619585i
$291$		−	2.06218e7i		−	0.836851i
$292$		−	1.70579e6i		−	0.0685134i
$293$	−1.11366e7			−0.442742			−0.221371	−	0.975190i	$-0.571053\pi$
$293$	−1.11366e7			−0.442742			−0.221371	+	0.975190i	$0.571053\pi$
$294$	1.03198e6			0.0406097
$295$	−2.99402e7	+	1.71050e7i	−1.16624	+	0.666279i
$296$		−	2.86589e6i		−	0.110506i
$297$	5.15938e7			1.96937
$298$	7.67425e6			0.289993
$299$	−8.77773e6	−	4.64706e7i	−0.328374	−	1.73846i
$300$	−1.49184e7	−	8.79494e6i	−0.552532	−	0.325739i
$301$	3.75762e7			1.37789
$302$			2.03794e6i			0.0739895i
$303$			2.57566e7i			0.925892i
$304$		−	3.46436e6i		−	0.123311i
$305$	−2.76977e6	−	4.84815e6i	−0.0976212	−	0.170874i
$306$			3.03443e6i			0.105904i
$307$		−	1.31452e7i		−	0.454311i	−0.973859	−	0.227155i	$-0.927057\pi$
$307$		−	1.31452e7i		−	0.454311i	0.973859	−	0.227155i	$-0.0729425\pi$
$308$		−	3.95035e7i		−	1.35202i
$309$		−	5.78382e6i		−	0.196037i
$310$	7.33554e6	+	1.28400e7i	0.246233	+	0.431002i
$311$	3.84386e6			0.127787			0.0638935	−	0.997957i	$-0.479648\pi$
$311$	3.84386e6			0.127787			0.0638935	+	0.997957i	$0.479648\pi$
$312$			4.54693e7i			1.49711i
$313$	−5.42766e7			−1.77003			−0.885013	−	0.465566i	$-0.845851\pi$
$313$	−5.42766e7			−1.77003			−0.885013	+	0.465566i	$0.845851\pi$
$314$			1.27131e7i			0.410643i
$315$	−4.74753e6	+	2.71229e6i	−0.151892	+	0.0867768i
$316$		−	2.39577e7i		−	0.759247i
$317$		−	2.12458e7i		−	0.666954i	−0.942758	−	0.333477i	$-0.891778\pi$
$317$		−	2.12458e7i		−	0.666954i	0.942758	−	0.333477i	$-0.108222\pi$
$318$	−5.14542e6			−0.160007
$319$			7.86008e7i			2.42133i
$320$	−1.04213e7	+	5.95376e6i	−0.318034	+	0.181694i
$321$			2.13531e6i			0.0645575i
$322$	3.51078e6	+	1.85866e7i	0.105157	+	0.556715i
$323$		−	2.42770e7i		−	0.720424i
$324$	−1.92198e7			−0.565086
$325$	5.23184e7	+	3.08437e7i	1.52407	+	0.898496i
$326$	−1.89890e7			−0.548087
$327$	8.96319e6			0.256342
$328$			4.92956e7i			1.39697i
$329$		−	2.41946e6i		−	0.0679407i
$330$	1.63708e7	+	2.86552e7i	0.455542	+	0.797373i
$331$	−2.69439e7			−0.742979			−0.371490	−	0.928437i	$-0.621153\pi$
$331$	−2.69439e7			−0.742979			−0.371490	+	0.928437i	$0.621153\pi$
$332$	2.74703e7			0.750670
$333$	−739710.			−0.0200322
$334$	3.72261e7			0.999099
$335$	−1.31193e7	+	7.49512e6i	−0.348961	+	0.199363i
$336$			7.11909e6i			0.187675i
$337$	4.90414e7			1.28137			0.640683	−	0.767806i	$-0.278651\pi$
$337$	4.90414e7			1.28137			0.640683	+	0.767806i	$0.278651\pi$
$338$		−	4.48053e7i		−	1.16032i
$339$			1.11961e7i			0.287387i
$340$	2.77422e7	−	1.58492e7i	0.705836	−	0.403247i
$341$			6.67876e7i			1.68435i
$342$	2.28423e6			0.0571034
$343$	3.85398e7			0.955052
$344$		−	5.00373e7i		−	1.22919i
$345$	2.42909e7	+	2.85055e7i	0.591543	+	0.694178i
$346$	1.23426e7			0.297974
$347$		−	4.12918e7i		−	0.988270i	−0.869385	−	0.494135i	$-0.835485\pi$
$347$		−	4.12918e7i		−	0.988270i	0.869385	−	0.494135i	$-0.164515\pi$
$348$		−	3.54096e7i		−	0.840201i
$349$	1.20243e7			0.282867			0.141434	−	0.989948i	$-0.454829\pi$
$349$	1.20243e7			0.282867			0.141434	+	0.989948i	$0.454829\pi$
$350$	−2.09255e7	−	1.23364e7i	−0.488059	−	0.287729i
$351$	8.15126e7			1.88497
$352$	−8.34876e7			−1.91423
$353$		−	5.15907e7i		−	1.17286i	−0.809999	−	0.586431i	$-0.800532\pi$
$353$		−	5.15907e7i		−	1.17286i	0.809999	−	0.586431i	$-0.199468\pi$
$354$	−2.96025e7			−0.667296
$355$	5.35385e7	−	3.05868e7i	1.19669	−	0.683674i
$356$			4.59520e7i			1.01848i
$357$			4.98881e7i			1.09646i
$358$		−	1.94848e7i		−	0.424666i
$359$			1.62740e7i			0.351732i	0.984414	+	0.175866i	$0.0562725\pi$
$359$			1.62740e7i			0.351732i	−0.984414	+	0.175866i	$0.943728\pi$
$360$	3.61174e6	+	6.32191e6i	0.0774120	+	0.135500i
$361$	2.87708e7			0.611548
$362$	4.86380e6			0.102530
$363$			1.05426e8i			2.20409i
$364$		−	6.24112e7i		−	1.29407i
$365$	−2.35000e6	−	4.11339e6i	−0.0483268	−	0.0845903i
$366$		−	4.79347e6i		−	0.0977703i
$367$	−1.09260e7			−0.221036			−0.110518	−	0.993874i	$-0.535251\pi$
$367$	−1.09260e7			−0.221036			−0.110518	+	0.993874i	$0.535251\pi$
$368$	−9.68869e6	+	1.83007e6i	−0.194411	+	0.0367219i
$369$	1.27236e7			0.253239
$370$	−1.63020e6	−	2.85346e6i	−0.0321836	−	0.0563335i
$371$	1.71052e7			0.334970
$372$		−	3.00878e7i		−	0.584469i
$373$	4.32586e7			0.833578			0.416789	−	0.909003i	$-0.363155\pi$
$373$	4.32586e7			0.833578			0.416789	+	0.909003i	$0.363155\pi$
$374$	−6.08864e7			−1.16387
$375$	−4.80911e7	−	655939.i	−0.911949	−	0.0124385i
$376$	−3.22180e6			−0.0606087
$377$			1.24181e8i			2.31756i
$378$	−3.26022e7			−0.603630
$379$			7.86169e7i			1.44410i	0.691839	+	0.722052i	$0.256801\pi$
$379$			7.86169e7i			1.44410i	−0.691839	+	0.722052i	$0.743199\pi$
$380$	−1.19308e7	−	2.08835e7i	−0.217430	−	0.380586i
$381$	2.36875e7			0.428297
$382$	1.27700e7			0.229087
$383$	−8.68806e7			−1.54642			−0.773208	−	0.634152i	$-0.781349\pi$
$383$	−8.68806e7			−1.54642			−0.773208	+	0.634152i	$0.781349\pi$
$384$	4.31769e7			0.762531
$385$	−5.44224e7	−	9.52599e7i	−0.953665	−	1.66928i
$386$	9.23267e6			0.160533
$387$	−1.29150e7			−0.222824
$388$	3.76922e7			0.645293
$389$		−	1.11129e8i		−	1.88790i	−0.330095	−	0.943948i	$-0.607081\pi$
$389$		−	1.11129e8i		−	1.88790i	0.330095	−	0.943948i	$-0.392919\pi$
$390$	2.58642e7	+	4.52721e7i	0.436018	+	0.763197i
$391$	−6.78949e7	+	1.28245e7i	−1.13581	+	0.214541i
$392$			4.56835e6i			0.0758405i
$393$			4.15075e7i			0.683830i
$394$	3.08540e7			0.504456
$395$	−3.30055e7	−	5.77723e7i	−0.535545	−	0.937407i
$396$			1.35774e7i			0.218641i
$397$		−	2.70597e7i		−	0.432465i	−0.976342	−	0.216233i	$-0.930623\pi$
$397$		−	2.70597e7i		−	0.432465i	0.976342	−	0.216233i	$-0.0693770\pi$
$398$	−1.70344e7			−0.270196
$399$	3.75543e7			0.591209
$400$	6.43061e6	−	1.09079e7i	0.100478	−	0.170436i
$401$			5.03622e7i			0.781036i	0.920595	+	0.390518i	$0.127704\pi$
$401$			5.03622e7i			0.781036i	−0.920595	+	0.390518i	$0.872296\pi$
$402$	−1.29713e7			−0.199667
$403$			1.05517e8i			1.61216i
$404$	−4.70774e7			−0.713951
$405$	−4.63473e7	+	2.64784e7i	−0.697685	+	0.398591i
$406$		−	4.96679e7i		−	0.742160i
$407$		−	1.48424e7i		−	0.220151i
$408$	6.64320e7			0.978131
$409$	1.10084e8			1.60900			0.804500	−	0.593953i	$-0.202434\pi$
$409$	1.10084e8			1.60900			0.804500	+	0.593953i	$0.202434\pi$
$410$	2.80407e7	+	4.90818e7i	0.406852	+	0.712146i
$411$		−	1.90406e7i		−	0.274256i
$412$	1.05716e7			0.151164
$413$	9.84091e7			1.39696
$414$	−1.20666e6	−	6.38826e6i	−0.0170053	−	0.0900288i
$415$	6.62427e7	−	3.78448e7i	0.926817	−	0.529495i
$416$	−1.31901e8			−1.83219
$417$		−	8.99741e7i		−	1.24082i
$418$			4.58335e7i			0.627558i
$419$			1.05835e8i			1.43876i	0.694617	+	0.719380i	$0.255574\pi$
$419$			1.05835e8i			1.43876i	−0.694617	+	0.719380i	$0.744426\pi$
$420$	2.45173e7	+	4.29146e7i	0.330921	+	0.579238i
$421$			1.42758e6i			0.0191317i	0.999954	+	0.00956587i	$0.00304496\pi$
$421$			1.42758e6i			0.0191317i	−0.999954	+	0.00956587i	$0.996955\pi$
$422$		−	9.98295e6i		−	0.132838i
$423$			831572.i			0.0109870i
$424$		−	2.27776e7i		−	0.298821i
$425$	4.50635e7	−	7.64387e7i	0.587027	−	0.995741i
$426$	5.29347e7			0.684717
$427$			1.59352e7i			0.204679i
$428$	−3.90289e6			−0.0497800
$429$			2.35485e8i			2.98257i
$430$	−2.84625e7	−	4.98202e7i	−0.357988	−	0.626615i
$431$		−	1.40897e8i		−	1.75982i	−0.475138	−	0.879912i	$-0.657602\pi$
$431$		−	1.40897e8i		−	1.75982i	0.475138	−	0.879912i	$-0.342398\pi$
$432$		−	1.69946e7i		−	0.210795i
$433$	6.90311e7			0.850318			0.425159	−	0.905119i	$-0.360218\pi$
$433$	6.90311e7			0.850318			0.425159	+	0.905119i	$0.360218\pi$
$434$		−	4.22032e7i		−	0.516269i
$435$	−4.87825e7	−	8.53879e7i	−0.592647	−	1.03736i
$436$			1.63828e7i			0.197664i
$437$	9.65393e6	+	5.11093e7i	0.115680	+	0.612429i
$438$		−	4.06699e6i		−	0.0484006i
$439$	−1.53760e7			−0.181740			−0.0908698	−	0.995863i	$-0.528965\pi$
$439$	−1.53760e7			−0.181740			−0.0908698	+	0.995863i	$0.528965\pi$
$440$	−1.26850e8	+	7.24700e7i	−1.48913	+	0.850747i
$441$	1.17913e6			0.0137482
$442$	−9.61939e7			−1.11399
$443$			3.41033e7i			0.392270i	0.980577	+	0.196135i	$0.0628391\pi$
$443$			3.41033e7i			0.392270i	−0.980577	+	0.196135i	$0.937161\pi$
$444$			6.68649e6i			0.0763923i
$445$	6.33063e7	+	1.10810e8i	0.718401	+	1.25748i
$446$	−4.89915e7			−0.552225
$447$	−4.33648e7			−0.485529
$448$	3.42535e7			0.380952
$449$	−1.16340e8			−1.28526			−0.642628	−	0.766178i	$-0.722156\pi$
$449$	−1.16340e8			−1.28526			−0.642628	+	0.766178i	$0.722156\pi$
$450$	7.19214e6	+	4.24004e6i	0.0789261	+	0.0465299i
$451$			2.55301e8i			2.78306i
$452$	−2.04640e7			−0.221603
$453$		−	1.15157e7i		−	0.123879i
$454$			5.45798e7i			0.583262i
$455$	−8.59816e7	−	1.50500e8i	−0.912791	−	1.59773i
$456$		−	5.00081e7i		−	0.527407i
$457$	−9.39087e7			−0.983914			−0.491957	−	0.870619i	$-0.663718\pi$
$457$	−9.39087e7			−0.983914			−0.491957	+	0.870619i	$0.663718\pi$
$458$	5.87591e7			0.611616
$459$		−	1.19092e8i		−	1.23153i
$460$	−5.21018e7	+	4.43985e7i	−0.535278	+	0.456137i
$461$	8.25346e7			0.842429			0.421215	−	0.906961i	$-0.361604\pi$
$461$	8.25346e7			0.842429			0.421215	+	0.906961i	$0.361604\pi$
$462$		−	9.41855e7i		−	0.955120i
$463$		−	1.26626e8i		−	1.27579i	−0.770124	−	0.637895i	$-0.779806\pi$
$463$		−	1.26626e8i		−	1.27579i	0.770124	−	0.637895i	$-0.220194\pi$
$464$	2.58905e7			0.259171
$465$	−4.14508e7	−	7.25547e7i	−0.412263	−	0.721617i
$466$	8.64796e6			0.0854586
$467$	1.17457e8			1.15326			0.576631	−	0.817005i	$-0.304367\pi$
$467$	1.17457e8			1.15326			0.576631	+	0.817005i	$0.304367\pi$
$468$			2.14509e7i			0.209270i
$469$	4.31213e7			0.417997
$470$	−3.20782e6	+	1.83264e6i	−0.0308970	+	0.0176516i
$471$		−	7.18380e7i		−	0.687530i
$472$		−	1.31044e8i		−	1.24621i
$473$		−	2.59142e8i		−	2.44881i
$474$		−	5.71207e7i		−	0.536362i
$475$	−5.75408e7	−	3.39225e7i	−0.536902	−	0.316524i
$476$	−9.11846e7			−0.845475
$477$	−5.87909e6			−0.0541695
$478$			1.70421e7i			0.156041i
$479$		−	9.17861e7i		−	0.835161i	−0.908640	−	0.417581i	$-0.862878\pi$
$479$		−	9.17861e7i		−	0.835161i	0.908640	−	0.417581i	$-0.137122\pi$
$480$	9.06967e7	−	5.18154e7i	0.820102	−	0.468528i
$481$		−	2.34494e7i		−	0.210715i
$482$	−8.33820e7			−0.744614
$483$	−1.98383e7	−	1.05027e8i	−0.176061	−	0.932095i
$484$	−1.92697e8			−1.69957
$485$	9.08923e7	−	5.19272e7i	0.796713	−	0.455166i
$486$	2.07975e7			0.181177
$487$		−	3.44496e7i		−	0.298262i	−0.988817	−	0.149131i	$-0.952352\pi$
$487$		−	3.44496e7i		−	0.298262i	0.988817	−	0.149131i	$-0.0476475\pi$
$488$	2.12196e7			0.182591
$489$	1.07301e8			0.917650
$490$	2.59860e6	+	4.54854e6i	0.0220877	+	0.0386619i
$491$	−9.71931e7			−0.821090			−0.410545	−	0.911840i	$-0.634662\pi$
$491$	−9.71931e7			−0.821090			−0.410545	+	0.911840i	$0.634662\pi$
$492$		−	1.15013e8i		−	0.965720i
$493$	1.81432e8			1.51416
$494$			7.24120e7i			0.600661i
$495$	1.87051e7	+	3.27410e7i	0.154221	+	0.269946i
$496$	2.19994e7			0.180287
$497$	−1.75973e8			−1.43344
$498$	6.54956e7			0.530303
$499$	−3.80414e6			−0.0306164			−0.0153082	−	0.999883i	$-0.504873\pi$
$499$	−3.80414e6			−0.0306164			−0.0153082	+	0.999883i	$0.504873\pi$
$500$	1.19891e6	−	8.79001e7i	0.00959132	−	0.703201i
$501$	−2.10353e8			−1.67277
$502$	9.63957e7			0.761985
$503$	1.14172e8			0.897128			0.448564	−	0.893751i	$-0.351936\pi$
$503$	1.14172e8			0.897128			0.448564	+	0.893751i	$0.351936\pi$
$504$		−	2.07792e7i		−	0.162307i
$505$	−1.13524e8	+	6.48568e7i	−0.881482	+	0.503595i
$506$	1.28181e8	−	2.42119e7i	0.989403	−	0.186886i
$507$			2.53180e8i			1.94270i
$508$			4.32957e7i			0.330258i
$509$	−2.24320e8			−1.70104			−0.850521	−	0.525941i	$-0.823713\pi$
$509$	−2.24320e8			−1.70104			−0.850521	+	0.525941i	$0.823713\pi$
$510$	6.61438e7	−	3.77883e7i	0.498631	−	0.284870i
$511$			1.35201e7i			0.101325i
$512$			5.21385e7i			0.388462i
$513$	−8.96492e7			−0.664040
$514$	8.96006e6			0.0659814
$515$	2.54926e7	−	1.45640e7i	0.186635	−	0.106625i
$516$			1.16743e8i			0.849734i
$517$	−1.66856e7			−0.120745
$518$			9.37893e6i			0.0674783i
$519$	−6.97442e7			−0.498891
$520$	−2.00409e8	+	1.14495e8i	−1.42531	+	0.814284i
$521$			1.06077e8i			0.750080i	0.927009	+	0.375040i	$0.122371\pi$
$521$			1.06077e8i			0.750080i	−0.927009	+	0.375040i	$0.877629\pi$
$522$			1.70710e7i			0.120018i
$523$	5.79765e7			0.405272			0.202636	−	0.979254i	$-0.435049\pi$
$523$	5.79765e7			0.405272			0.202636	+	0.979254i	$0.435049\pi$
$524$	−7.58666e7			−0.527299
$525$	1.18243e8	+	6.97090e7i	0.817145	+	0.481738i
$526$			1.58847e7i			0.109150i
$527$	1.54164e8			1.05330
$528$	4.90963e7			0.333539
$529$	1.37836e8	−	5.39978e7i	0.931101	−	0.364761i
$530$	−1.29565e7	−	2.26788e7i	−0.0870283	−	0.152333i
$531$	−3.38234e7			−0.225909
$532$			6.86411e7i			0.455879i
$533$			4.03348e8i			2.66378i
$534$			1.09560e8i			0.719498i
$535$	−9.41156e6	+	5.37686e6i	−0.0614611	+	0.0351130i
$536$		−	5.74212e7i		−	0.372888i
$537$			1.10103e8i			0.711008i
$538$		−	1.65102e8i		−	1.06024i
$539$			2.36594e7i			0.151090i
$540$	−5.85274e7	−	1.02445e8i	−0.371687	−	0.650594i
$541$	1.09975e7			0.0694545			0.0347272	−	0.999397i	$-0.488944\pi$
$541$	1.09975e7			0.0694545			0.0347272	+	0.999397i	$0.488944\pi$
$542$		−	4.68365e7i		−	0.294162i
$543$	−2.74838e7			−0.171663
$544$			1.92712e8i			1.19705i
$545$	2.25699e7	+	3.95059e7i	0.139425	+	0.244047i
$546$		−	1.48803e8i		−	0.914184i
$547$		−	1.41932e8i		−	0.867200i	−0.901105	−	0.433600i	$-0.857243\pi$
$547$		−	1.41932e8i		−	0.867200i	0.901105	−	0.433600i	$-0.142757\pi$
$548$	3.48021e7			0.211477
$549$		−	5.47696e6i		−	0.0330996i
$550$	−8.50770e7	+	1.44311e8i	−0.511357	+	0.867386i
$551$		−	1.36576e8i		−	0.816434i
$552$	−1.39856e8	+	2.64171e7i	−0.831505	+	0.157061i
$553$			1.89889e8i			1.12286i
$554$	2.23457e7			0.131421
$555$	9.21172e6	+	1.61240e7i	0.0538843	+	0.0943179i
$556$	1.64453e8			0.956792
$557$	−1.27913e8			−0.740201			−0.370101	−	0.928992i	$-0.620677\pi$
$557$	−1.27913e8			−0.740201			−0.370101	+	0.928992i	$0.620677\pi$
$558$			1.45053e7i			0.0834882i
$559$		−	4.09416e8i		−	2.34385i
$560$	−3.13779e7	+	1.79263e7i	−0.178673	+	0.102077i
$561$	3.44050e8			1.94864
$562$	1.56498e8			0.881660
$563$	1.30431e8			0.730898			0.365449	−	0.930831i	$-0.380915\pi$
$563$	1.30431e8			0.730898			0.365449	+	0.930831i	$0.380915\pi$
$564$	7.51686e6			0.0418986
$565$	−4.93476e7	+	2.81925e7i	−0.273603	+	0.156311i
$566$		−	6.37475e7i		−	0.351572i
$567$	1.52337e8			0.835712
$568$			2.34330e8i			1.27874i
$569$			2.35725e8i			1.27958i	0.768548	+	0.639792i	$0.220979\pi$
$569$			2.35725e8i			1.27958i	−0.768548	+	0.639792i	$0.779021\pi$
$570$	−2.84459e7	−	4.97912e7i	−0.153601	−	0.268861i
$571$			2.64145e7i			0.141884i	0.997480	+	0.0709422i	$0.0226006\pi$
$571$			2.64145e7i			0.141884i	−0.997480	+	0.0709422i	$0.977399\pi$
$572$	−4.30415e8			−2.29985
$573$	−7.21593e7			−0.383556
$574$		−	1.61325e8i		−	0.853033i
$575$	−6.44738e7	+	1.78843e8i	−0.339140	+	0.940736i
$576$	−1.17730e7			−0.0616055
$577$			1.93402e8i			1.00678i	0.864060	+	0.503389i	$0.167914\pi$
$577$			1.93402e8i			1.00678i	−0.864060	+	0.503389i	$0.832086\pi$
$578$			3.53539e7i			0.183085i
$579$	−5.21709e7			−0.268778
$580$	1.56071e8	−	8.91638e7i	0.799902	−	0.456988i
$581$	−2.17731e8			−1.11017
$582$	8.98671e7			0.455860
$583$		−	1.17965e8i		−	0.595314i
$584$	1.80037e7			0.0903904
$585$	2.95520e7	+	5.17273e7i	0.147611	+	0.258376i
$586$		−	4.85318e7i		−	0.241176i
$587$		−	3.42598e8i		−	1.69383i	−0.531725	−	0.846917i	$-0.678456\pi$
$587$		−	3.42598e8i		−	1.69383i	0.531725	−	0.846917i	$-0.321544\pi$
$588$		−	1.06585e7i		−	0.0524283i
$589$		−	1.16050e8i		−	0.567936i
$590$	−7.45411e7	−	1.30475e8i	−0.362944	−	0.635290i
$591$	−1.74346e8			−0.844599
$592$	−4.88897e6			−0.0235642
$593$			2.68518e8i			1.28768i	0.765159	+	0.643842i	$0.222661\pi$
$593$			2.68518e8i			1.28768i	−0.765159	+	0.643842i	$0.777339\pi$
$594$			2.24839e8i			1.07278i
$595$	−2.19885e8	+	1.25622e8i	−1.04387	+	0.596367i
$596$		−	7.92615e7i		−	0.374389i
$597$	9.62562e7			0.452382
$598$	2.02513e8	−	3.82522e7i	0.946997	−	0.178876i
$599$	3.92104e8			1.82441			0.912203	−	0.409739i	$-0.134380\pi$
$599$	3.92104e8			1.82441			0.912203	+	0.409739i	$0.134380\pi$
$600$	9.28260e7	−	1.57455e8i	0.429750	−	0.728960i
$601$	1.70258e8			0.784302			0.392151	−	0.919901i	$-0.371731\pi$
$601$	1.70258e8			0.784302			0.392151	+	0.919901i	$0.371731\pi$
$602$			1.63752e8i			0.750581i
$603$	−1.48209e7			−0.0675962
$604$	2.10483e7			0.0955225
$605$	−4.64675e8	+	2.65471e8i	−2.09838	+	1.19881i
$606$	−1.12244e8			−0.504364
$607$			7.37280e6i			0.0329660i	0.999864	+	0.0164830i	$0.00524694\pi$
$607$			7.37280e6i			0.0329660i	−0.999864	+	0.0164830i	$0.994753\pi$
$608$	1.45068e8			0.645447
$609$			2.80658e8i			1.24258i
$610$	2.11276e7	−	1.20703e7i	0.0930808	−	0.0531775i
$611$	−2.63615e7			−0.115570
$612$	3.13403e7			0.136725
$613$	2.46648e8			1.07077			0.535386	−	0.844608i	$-0.320166\pi$
$613$	2.46648e8			1.07077			0.535386	+	0.844608i	$0.320166\pi$
$614$	5.72851e7			0.247478
$615$	−1.58449e8	−	2.77346e8i	−0.681183	−	1.19233i
$616$	4.16938e8			1.78373
$617$	1.82302e8			0.776134			0.388067	−	0.921631i	$-0.373143\pi$
$617$	1.82302e8			0.776134			0.388067	+	0.921631i	$0.373143\pi$
$618$	2.52051e7			0.106788
$619$		−	1.52689e8i		−	0.643780i	−0.946777	−	0.321890i	$-0.895682\pi$
$619$		−	1.52689e8i		−	0.643780i	0.946777	−	0.321890i	$-0.104318\pi$
$620$	1.32614e8	−	7.57631e7i	0.556436	−	0.317894i
$621$	4.73579e7	+	2.50720e8i	0.197750	+	1.04692i
$622$			1.67510e7i			0.0696098i
$623$		−	3.64217e8i		−	1.50625i
$624$	7.75669e7			0.319244
$625$	−1.18205e8	−	2.13617e8i	−0.484170	−	0.874974i
$626$		−	2.36530e8i		−	0.964192i
$627$		−	2.58991e8i		−	1.05071i
$628$	1.31304e8			0.530151
$629$	−3.42602e7			−0.137670
$630$	−1.18198e7	−	2.06891e7i	−0.0472702	−	0.0827408i
$631$			1.07826e8i			0.429175i	0.976705	+	0.214587i	$0.0688407\pi$
$631$			1.07826e8i			0.429175i	−0.976705	+	0.214587i	$0.931159\pi$
$632$	2.52860e8			1.00168
$633$			5.64105e7i			0.222407i
$634$	9.25865e7			0.363312
$635$	5.96468e7	+	1.04405e8i	0.232952	+	0.407754i
$636$			5.31430e7i			0.206574i
$637$			3.73793e7i			0.144615i
$638$	−3.42531e8			−1.31898
$639$	6.04824e7			0.231807
$640$	1.08722e8	+	1.90305e8i	0.414743	+	0.725957i
$641$		−	2.29008e8i		−	0.869513i	−0.900548	−	0.434757i	$-0.856834\pi$
$641$		−	2.29008e8i		−	0.869513i	0.900548	−	0.434757i	$-0.143166\pi$
$642$	−9.30541e6			−0.0351666
$643$	−1.48088e8			−0.557041			−0.278520	−	0.960430i	$-0.589844\pi$
$643$	−1.48088e8			−0.557041			−0.278520	+	0.960430i	$0.589844\pi$
$644$	1.91967e8	−	3.62602e7i	0.718735	−	0.135760i
$645$	1.60833e8	+	2.81519e8i	0.599371	+	1.04913i
$646$	1.05796e8			0.392439
$647$			1.48933e8i			0.549893i	0.961459	+	0.274947i	$0.0886602\pi$
$647$			1.48933e8i			0.549893i	−0.961459	+	0.274947i	$0.911340\pi$
$648$		−	2.02855e8i		−	0.745523i
$649$		−	6.78672e8i		−	2.48271i
$650$	−1.34413e8	+	2.27996e8i	−0.489440	+	0.830210i
$651$			2.38477e8i			0.864378i
$652$			1.96123e8i			0.707596i
$653$			4.40549e8i			1.58218i	0.611703	+	0.791088i	$0.290485\pi$
$653$			4.40549e8i			1.58218i	−0.611703	+	0.791088i	$0.709515\pi$
$654$			3.90603e7i			0.139638i
$655$	−1.82947e8	+	1.04519e8i	−0.651031	+	0.371937i
$656$	8.40942e7			0.297889
$657$		−	4.64689e6i		−	0.0163858i
$658$	1.05437e7			0.0370095
$659$			3.25083e8i			1.13589i	0.823065	+	0.567947i	$0.192262\pi$
$659$			3.25083e8i			1.13589i	−0.823065	+	0.567947i	$0.807738\pi$
$660$	2.95957e8	−	1.69082e8i	1.02943	−	0.588118i
$661$			3.66487e7i			0.126898i	0.997985	+	0.0634489i	$0.0202100\pi$
$661$			3.66487e7i			0.126898i	−0.997985	+	0.0634489i	$0.979790\pi$
$662$		−	1.17418e8i		−	0.404725i
$663$	5.43562e8			1.86513
$664$			2.89934e8i			0.990366i
$665$	9.45643e7	+	1.65523e8i	0.321560	+	0.562852i
$666$		−	3.22356e6i		−	0.0109122i
$667$	−3.81960e8	+	7.21475e7i	−1.28718	+	0.243133i
$668$		−	3.84480e8i		−	1.28987i
$669$	2.76836e8			0.924578
$670$	−3.26627e7	−	5.71722e7i	−0.108600	−	0.190090i
$671$	1.09896e8			0.363759
$672$	−2.98107e8			−0.982346
$673$		−	2.87968e8i		−	0.944712i	−0.881408	−	0.472356i	$-0.843404\pi$
$673$		−	2.87968e8i		−	0.944712i	0.881408	−	0.472356i	$-0.156596\pi$
$674$			2.13716e8i			0.698002i
$675$	−2.82270e8	−	1.66409e8i	−0.917810	−	0.541084i
$676$	−4.62759e8			−1.49801
$677$	5.61644e7			0.181007			0.0905035	−	0.995896i	$-0.471152\pi$
$677$	5.61644e7			0.181007			0.0905035	+	0.995896i	$0.471152\pi$
$678$	−4.87910e7			−0.156549
$679$	−2.98750e8			−0.954330
$680$	1.67280e8	+	2.92804e8i	0.532008	+	0.931216i
$681$		−	3.08413e8i		−	0.976543i
$682$	−2.91051e8			−0.917522
$683$		−	1.77141e8i		−	0.555976i	−0.960585	−	0.277988i	$-0.910332\pi$
$683$		−	1.77141e8i		−	0.555976i	0.960585	−	0.277988i	$-0.0896675\pi$
$684$		−	2.35921e7i		−	0.0737222i
$685$	8.39229e7	−	4.79455e7i	0.261101	−	0.149168i
$686$			1.67951e8i			0.520248i
$687$	−3.32029e8			−1.02402
$688$	−8.53594e7			−0.262112
$689$		−	1.86372e8i		−	0.569799i
$690$	−1.24223e8	+	1.05856e8i	−0.378141	+	0.322233i
$691$	−2.95017e8			−0.894155			−0.447078	−	0.894495i	$-0.647535\pi$
$691$	−2.95017e8			−0.894155			−0.447078	+	0.894495i	$0.647535\pi$
$692$		−	1.27477e8i		−	0.384693i
$693$		−	1.07615e8i		−	0.323351i
$694$	1.79944e8			0.538343
$695$	3.96568e8	−	2.26561e8i	1.18131	−	0.674886i
$696$	3.73730e8			1.10849
$697$	5.89303e8			1.74037
$698$			5.24002e7i			0.154087i
$699$	−4.88669e7			−0.143081
$700$	−1.27413e8	+	2.16123e8i	−0.371466	+	0.630098i
$701$		−	9.95401e7i		−	0.288964i	−0.989507	−	0.144482i	$-0.953848\pi$
$701$		−	9.95401e7i		−	0.288964i	0.989507	−	0.144482i	$-0.0461516\pi$
$702$			3.55221e8i			1.02680i
$703$			2.57901e7i			0.0742313i
$704$		−	2.36227e8i		−	0.677035i
$705$	1.81264e7	−	1.03557e7i	0.0517302	−	0.0295537i
$706$	2.24825e8			0.638897
$707$	3.73137e8			1.05587
$708$			3.05741e8i			0.861498i
$709$		−	5.67813e8i		−	1.59319i	−0.604517	−	0.796593i	$-0.706634\pi$
$709$		−	5.67813e8i		−	1.59319i	0.604517	−	0.796593i	$-0.293366\pi$
$710$	1.33293e8	+	2.33313e8i	0.372420	+	0.651876i
$711$		−	6.52653e7i		−	0.181582i
$712$	−4.84999e8			−1.34370
$713$	−3.24554e8	+	6.13043e7i	−0.895403	+	0.169131i
$714$	−2.17405e8			−0.597277
$715$	−1.03792e9	+	5.92966e8i	−2.83951	+	1.62223i
$716$	−2.01244e8			−0.548255
$717$		−	9.62993e7i		−	0.261256i
$718$	−7.09199e7			−0.191600
$719$	−5.08780e8			−1.36881			−0.684405	−	0.729102i	$-0.739938\pi$
$719$	−5.08780e8			−1.36881			−0.684405	+	0.729102i	$0.739938\pi$
$720$	1.07847e7	−	6.16132e6i	0.0288941	−	0.0165073i
$721$	−8.37906e7			−0.223558
$722$			1.25379e8i			0.333131i
$723$	4.71165e8			1.24669
$724$		−	5.02344e7i		−	0.132369i
$725$	2.53516e8	−	4.30025e8i	0.665260	−	1.12844i
$726$	−4.59434e8			−1.20064
$727$	2.73772e8			0.712503			0.356251	−	0.934390i	$-0.384055\pi$
$727$	2.73772e8			0.712503			0.356251	+	0.934390i	$0.384055\pi$
$728$	6.58718e8			1.70728
$729$	−4.28819e8			−1.10686
$730$	1.79256e7	−	1.02410e7i	0.0460791	−	0.0263252i
$731$	−5.98169e8			−1.53134
$732$	−4.95081e7			−0.126224
$733$	−6.84631e8			−1.73838			−0.869190	−	0.494479i	$-0.835359\pi$
$733$	−6.84631e8			−1.73838			−0.869190	+	0.494479i	$0.835359\pi$
$734$		−	4.76141e7i		−	0.120406i
$735$	−1.46839e7	−	2.57023e7i	−0.0369810	−	0.0647308i
$736$	−7.66332e7	−	4.05707e8i	−0.192213	−	1.01761i
$737$		−	2.97383e8i		−	0.742872i
$738$			5.54477e7i			0.137948i
$739$	3.13451e8			0.776669			0.388335	−	0.921518i	$-0.373050\pi$
$739$	3.13451e8			0.776669			0.388335	+	0.921518i	$0.373050\pi$
$740$	−2.94712e7	+	1.68370e7i	−0.0727282	+	0.0415499i
$741$		−	4.09177e8i		−	1.00567i
$742$			7.45420e7i			0.182469i
$743$	−6.52445e8			−1.59066			−0.795330	−	0.606176i	$-0.792703\pi$
$743$	−6.52445e8			−1.59066			−0.795330	+	0.606176i	$0.792703\pi$
$744$	3.17561e8			0.771096
$745$	−1.09196e8	−	1.91134e8i	−0.264080	−	0.462241i
$746$			1.88515e8i			0.454078i
$747$	7.48344e7			0.179531
$748$			6.28848e8i			1.50259i
$749$	3.09345e7			0.0736202
$750$	2.85849e6	−	2.09574e8i	0.00677569	−	0.496769i
$751$			4.00386e8i			0.945277i	0.881256	+	0.472638i	$0.156698\pi$
$751$			4.00386e8i			0.945277i	−0.881256	+	0.472638i	$0.843302\pi$
$752$			5.49612e6i			0.0129242i
$753$	−5.44702e8			−1.27577
$754$	−5.41163e8			−1.26245
$755$	5.07565e7	−	2.89974e7i	0.117937	−	0.0673781i
$756$			3.36723e8i			0.779304i
$757$	2.95647e8			0.681532			0.340766	−	0.940148i	$-0.389314\pi$
$757$	2.95647e8			0.681532			0.340766	+	0.940148i	$0.389314\pi$
$758$	−3.42602e8			−0.786651
$759$	−7.24312e8	+	1.36814e8i	−1.65653	+	0.312899i
$760$	2.20414e8	−	1.25924e8i	0.502110	−	0.286858i
$761$	4.67608e8			1.06103			0.530516	−	0.847675i	$-0.321998\pi$
$761$	4.67608e8			1.06103			0.530516	+	0.847675i	$0.321998\pi$
$762$			1.03227e8i			0.233308i
$763$		−	1.29850e8i		−	0.292327i
$764$		−	1.31892e8i		−	0.295758i
$765$	7.55751e7	−	4.31764e7i	0.168809	−	0.0964411i
$766$		−	3.78614e8i		−	0.842384i
$767$		−	1.07223e9i		−	2.37630i
$768$			3.39481e8i			0.749432i
$769$			5.90805e8i			1.29917i	0.760290	+	0.649584i	$0.225057\pi$
$769$			5.90805e8i			1.29917i	−0.760290	+	0.649584i	$0.774943\pi$
$770$	4.15130e8	−	2.37165e8i	0.909309	−	0.519493i
$771$	−5.06305e7			−0.110471
$772$		−	9.53572e7i		−	0.207253i
$773$	−2.37718e8			−0.514664			−0.257332	−	0.966323i	$-0.582843\pi$
$773$	−2.37718e8			−0.514664			−0.257332	+	0.966323i	$0.582843\pi$
$774$		−	5.62819e7i		−	0.121380i
$775$	2.15414e8	−	3.65395e8i	0.462775	−	0.784979i
$776$			3.97822e8i			0.851340i
$777$		−	5.29974e7i		−	0.112977i
$778$	4.84284e8			1.02840
$779$		−	4.43610e8i		−	0.938403i
$780$	4.67581e8	−	2.67131e8i	0.985310	−	0.562912i
$781$			1.21359e9i			2.54753i
$782$	−5.58875e7	−	2.95877e8i	−0.116868	−	0.618715i
$783$		−	6.69983e8i		−	1.39566i
$784$	7.79323e6			0.0161722
$785$	3.16631e8	−	1.80893e8i	0.654553	−	0.373949i
$786$	−1.80884e8			−0.372505
$787$	−6.53890e8			−1.34147			−0.670734	−	0.741698i	$-0.734021\pi$
$787$	−6.53890e8			−1.34147			−0.670734	+	0.741698i	$0.734021\pi$
$788$		−	3.18668e8i		−	0.651267i
$789$		−	8.97597e7i		−	0.182747i
$790$	2.51764e8	−	1.43834e8i	0.510636	−	0.291729i
$791$	1.62199e8			0.327731
$792$	−1.43303e8			−0.288455
$793$	1.73624e8			0.348169
$794$	1.17922e8			0.235578
$795$	7.32131e7	+	1.28151e8i	0.145709	+	0.255047i
$796$			1.75936e8i			0.348830i
$797$	8.07485e8			1.59500			0.797498	−	0.603322i	$-0.206157\pi$
$797$	8.07485e8			1.59500			0.797498	+	0.603322i	$0.206157\pi$
$798$			1.63657e8i			0.322051i
$799$			3.85149e7i			0.0755072i
$800$	4.56761e8	+	2.69278e8i	0.892111	+	0.525933i
$801$			1.25182e8i			0.243582i
$802$	−2.19471e8			−0.425456
$803$	9.32405e7			0.180077
$804$			1.33971e8i			0.257776i
$805$	4.12961e8	−	3.51904e8i	0.791628	−	0.674585i
$806$	−4.59830e8			−0.878197
$807$			9.32939e8i			1.77514i
$808$		−	4.96877e8i		−	0.941923i
$809$	−3.45032e8			−0.651649			−0.325825	−	0.945430i	$-0.605642\pi$
$809$	−3.45032e8			−0.651649			−0.325825	+	0.945430i	$0.605642\pi$
$810$	−1.15389e8	−	2.01975e8i	−0.217126	−	0.380052i
$811$	−2.38949e8			−0.447964			−0.223982	−	0.974593i	$-0.571906\pi$
$811$	−2.38949e8			−0.447964			−0.223982	+	0.974593i	$0.571906\pi$
$812$	−5.12982e8			−0.958151
$813$			2.64658e8i			0.492509i
$814$	6.46811e7			0.119924
$815$	2.70191e8	+	4.72937e8i	0.499112	+	0.873636i
$816$		−	1.13327e8i		−	0.208576i
$817$			4.50284e8i			0.825697i
$818$			4.79733e8i			0.876475i
$819$		−	1.70020e8i		−	0.309492i
$820$	5.06928e8	−	2.89610e8i	0.919401	−	0.525258i
$821$	6.24654e8			1.12878			0.564391	−	0.825507i	$-0.309111\pi$
$821$	6.24654e8			1.12878			0.564391	+	0.825507i	$0.309111\pi$
$822$	8.29764e7			0.149396
$823$		−	4.88424e8i		−	0.876189i	−0.898929	−	0.438094i	$-0.855654\pi$
$823$		−	4.88424e8i		−	0.876189i	0.898929	−	0.438094i	$-0.144346\pi$
$824$			1.11577e8i			0.199432i
$825$	4.80743e8	−	8.15458e8i	0.856153	−	1.45224i
$826$			4.28853e8i			0.760972i
$827$	2.40129e7			0.0424550			0.0212275	−	0.999775i	$-0.493243\pi$
$827$	2.40129e7			0.0424550			0.0212275	+	0.999775i	$0.493243\pi$
$828$	−6.59794e7	+	1.24627e7i	−0.116230	+	0.0219544i
$829$	−8.77054e7			−0.153944			−0.0769720	−	0.997033i	$-0.524525\pi$
$829$	−8.77054e7			−0.153944			−0.0769720	+	0.997033i	$0.524525\pi$
$830$	1.64922e8	+	2.88677e8i	0.288433	+	0.504868i
$831$	−1.26269e8			−0.220035
$832$		−	3.73213e8i		−	0.648017i
$833$	5.46122e7			0.0944832
$834$	3.92095e8			0.675916
$835$	−5.29683e8	−	9.27147e8i	−0.909823	−	1.59254i
$836$	4.73379e8			0.810196
$837$		−	5.69290e8i		−	0.970861i
$838$	−4.61216e8			−0.783740
$839$		−	4.89140e8i		−	0.828222i	−0.910226	−	0.414111i	$-0.864092\pi$
$839$		−	4.89140e8i		−	0.828222i	0.910226	−	0.414111i	$-0.135908\pi$
$840$	−4.52940e8	+	2.58767e8i	−0.764193	+	0.436587i
$841$	4.25866e8			0.715953
$842$	−6.22120e6			−0.0104217
$843$	−8.84324e8			−1.47614
$844$	−1.03106e8			−0.171497
$845$	−1.11591e9	+	6.37525e8i	−1.84952	+	1.05664i
$846$	−3.62388e6			−0.00598498
$847$	1.52732e9			2.51351
$848$	−3.88567e7			−0.0637204
$849$			3.60217e8i			0.588629i
$850$	3.33109e8	+	1.96381e8i	0.542413	+	0.319773i
$851$	7.21265e7	−	1.36238e7i	0.117032	−	0.0221060i
$852$		−	5.46721e8i		−	0.883990i
$853$		−	6.50958e8i		−	1.04883i	−0.851462	−	0.524416i	$-0.824284\pi$
$853$		−	6.50958e8i		−	1.04883i	0.851462	−	0.524416i	$-0.175716\pi$
$854$	−6.94434e7			−0.111495
$855$	−3.25019e7	−	5.68907e7i	−0.0520009	−	0.0910213i
$856$		−	4.11930e7i		−	0.0656752i
$857$			9.76530e8i			1.55147i	0.631059	+	0.775735i	$0.282621\pi$
$857$			9.76530e8i			1.55147i	−0.631059	+	0.775735i	$0.717379\pi$
$858$	−1.02621e9			−1.62470
$859$	3.68168e8			0.580853			0.290427	−	0.956897i	$-0.406203\pi$
$859$	3.68168e8			0.580853			0.290427	+	0.956897i	$0.406203\pi$
$860$	−5.14555e8	+	2.93968e8i	−0.808978	+	0.462172i
$861$			9.11597e8i			1.42821i
$862$	6.14009e8			0.958634
$863$		−	9.21893e8i		−	1.43433i	−0.696905	−	0.717163i	$-0.745440\pi$
$863$		−	9.21893e8i		−	1.43433i	0.696905	−	0.717163i	$-0.254560\pi$
$864$	7.11638e8			1.10336
$865$	−1.75621e8	−	3.07403e8i	−0.271348	−	0.474963i
$866$			3.00828e8i			0.463196i
$867$		−	1.99774e8i		−	0.306535i
$868$	−4.35884e8			−0.666518
$869$	1.30956e9			1.99556
$870$	3.72109e8	−	2.12587e8i	0.565083	−	0.322834i
$871$		−	4.69834e8i		−	0.711033i
$872$	−1.72911e8			−0.260780
$873$	1.02681e8			0.154329
$874$	−2.22728e8	+	4.20705e7i	−0.333610	+	0.0630149i
$875$	−9.50264e6	+	6.96699e8i	−0.0141847	+	1.03997i
$876$	−4.20048e7			−0.0624866
$877$			1.07484e8i			0.159347i	0.996821	+	0.0796737i	$0.0253878\pi$
$877$			1.07484e8i			0.159347i	−0.996821	+	0.0796737i	$0.974612\pi$
$878$		−	6.70065e7i		−	0.0989996i
$879$			2.74238e8i			0.403795i
$880$	1.23628e8	+	2.16396e8i	0.181413	+	0.317541i
$881$		−	8.94812e7i		−	0.130859i	−0.997857	−	0.0654295i	$-0.979158\pi$
$881$		−	8.94812e7i		−	0.130859i	0.997857	−	0.0654295i	$-0.0208418\pi$
$882$			5.13848e6i			0.00748909i
$883$			2.15585e8i			0.313139i	0.987667	+	0.156570i	$0.0500435\pi$
$883$			2.15585e8i			0.313139i	−0.987667	+	0.156570i	$0.949956\pi$
$884$			9.93513e8i			1.43819i
$885$	4.21208e8	+	7.37274e8i	0.607669	+	1.06365i
$886$	−1.48617e8			−0.213682
$887$			1.32026e9i			1.89185i	0.324380	+	0.945927i	$0.394844\pi$
$887$			1.32026e9i			1.89185i	−0.324380	+	0.945927i	$0.605156\pi$
$888$	−7.05724e7			−0.100785
$889$		−	3.43163e8i		−	0.488422i
$890$	−4.82896e8	+	2.75880e8i	−0.684988	+	0.391337i
$891$		−	1.05058e9i		−	1.48524i
$892$			5.05995e8i			0.712938i
$893$	2.89929e7			0.0407134
$894$		−	1.88978e8i		−	0.264483i
$895$	−4.85285e8	+	2.77246e8i	−0.676905	+	0.386719i
$896$		−	6.25507e8i		−	0.869577i
$897$	−1.14434e9	+	2.16151e8i	−1.58554	+	0.299488i
$898$		−	5.06994e8i		−	0.700122i
$899$	8.67287e8			1.19367
$900$	4.37921e7	−	7.42821e7i	0.0600715	−	0.101896i
$901$	−2.72294e8			−0.372275
$902$	−1.11257e9			−1.51603
$903$		−	9.25312e8i		−	1.25668i
$904$		−	2.15987e8i		−	0.292363i
$905$	−6.92061e7	−	1.21137e8i	−0.0933681	−	0.163430i
$906$	5.01840e7			0.0674809
$907$	1.36986e9			1.83592			0.917960	−	0.396673i	$-0.129835\pi$
$907$	1.36986e9			1.83592			0.917960	+	0.396673i	$0.129835\pi$
$908$	5.63712e8			0.753009
$909$	−1.28248e8			−0.170749
$910$	6.55860e8	−	3.74696e8i	0.870336	−	0.497227i
$911$		−	9.16919e8i		−	1.21276i	−0.795174	−	0.606381i	$-0.792621\pi$
$911$		−	9.16919e8i		−	1.21276i	0.795174	−	0.606381i	$-0.207379\pi$
$912$	−8.53096e7			−0.112464
$913$			1.50156e9i			1.97302i
$914$		−	4.09241e8i		−	0.535971i
$915$	−1.19385e8	+	6.82054e7i	−0.155843	+	0.0890339i
$916$		−	6.06878e8i		−	0.789614i
$917$	6.01322e8			0.779828
$918$	5.18988e8			0.670856
$919$			1.23505e9i			1.59125i	0.605790	+	0.795625i	$0.292857\pi$
$919$			1.23505e9i			1.59125i	−0.605790	+	0.795625i	$0.707143\pi$
$920$	−4.68603e8	−	5.49907e8i	−0.601785	−	0.706197i
$921$	−3.23700e8			−0.414347
$922$			3.59675e8i			0.458899i
$923$			1.91734e9i			2.43834i
$924$	−9.72770e8			−1.23309
$925$	−4.78721e7	+	8.12027e7i	−0.0604863	+	0.102600i
$926$	5.51818e8			0.694965
$927$	2.87990e7			0.0361525
$928$			1.08415e9i			1.35658i
$929$	8.18771e8			1.02121			0.510605	−	0.859815i	$-0.329421\pi$
$929$	8.18771e8			1.02121			0.510605	+	0.859815i	$0.329421\pi$
$930$	3.16183e8	−	1.80637e8i	0.393088	−	0.224573i
$931$		−	4.11105e7i		−	0.0509452i
$932$		−	8.93181e7i		−	0.110330i
$933$		−	9.46548e7i		−	0.116546i
$934$			5.11861e8i			0.628220i
$935$	8.66340e8	+	1.51643e9i	1.05987	+	1.85518i
$936$	−2.26403e8			−0.276092
$937$	−3.58530e8			−0.435819			−0.217910	−	0.975969i	$-0.569924\pi$
$937$	−3.58530e8			−0.435819			−0.217910	+	0.975969i	$0.569924\pi$
$938$			1.87917e8i			0.227697i
$939$			1.33656e9i			1.61432i
$940$	1.89280e7	+	3.31311e7i	0.0227887	+	0.0398890i
$941$		−	1.69067e8i		−	0.202903i	−0.994840	−	0.101452i	$-0.967651\pi$
$941$		−	1.69067e8i		−	0.202903i	0.994840	−	0.101452i	$-0.0323487\pi$
$942$	3.13060e8			0.374520
$943$	−1.24063e9	+	2.34340e8i	−1.47948	+	0.279455i
$944$	−2.23549e8			−0.265740
$945$	4.63890e8	+	8.11984e8i	0.549692	+	0.962170i
$946$	1.12931e9			1.33394
$947$		−	3.49591e8i		−	0.411633i	−0.978591	−	0.205816i	$-0.934015\pi$
$947$		−	3.49591e8i		−	0.411633i	0.978591	−	0.205816i	$-0.0659849\pi$
$948$	−5.89955e8			−0.692459
$949$	1.47310e8			0.172359
$950$	1.47830e8	−	2.50755e8i	0.172421	−	0.292468i
$951$	−5.23177e8			−0.608285
$952$		−	9.62405e8i		−	1.11544i
$953$	−7.46030e8			−0.861941			−0.430970	−	0.902366i	$-0.641829\pi$
$953$	−7.46030e8			−0.861941			−0.430970	+	0.902366i	$0.641829\pi$
$954$		−	2.56203e7i		−	0.0295079i
$955$	−1.81702e8	−	3.18048e8i	−0.208617	−	0.365159i
$956$	1.76014e8			0.201453
$957$	1.93554e9			2.20834
$958$	3.99991e8			0.454940
$959$	−2.75843e8			−0.312756
$960$	1.46611e8	+	2.56625e8i	0.165711	+	0.290058i
$961$	−1.50564e8			−0.169648
$962$	1.02189e8			0.114784
$963$	−1.06322e7			−0.0119054
$964$			8.61188e8i			0.961318i
$965$	−1.31370e8	−	2.29947e8i	−0.146189	−	0.255886i
$966$	4.57694e8	−	8.64528e7i	0.507743	−	0.0959064i
$967$			5.12211e8i			0.566460i	0.959052	+	0.283230i	$0.0914060\pi$
$967$			5.12211e8i			0.566460i	−0.959052	+	0.283230i	$0.908594\pi$
$968$		−	2.03381e9i		−	2.24225i
$969$	−5.97820e8			−0.657051
$970$	2.26291e8	+	3.96096e8i	0.247944	+	0.433996i
$971$		−	9.05048e8i		−	0.988585i	−0.869296	−	0.494293i	$-0.835427\pi$
$971$		−	9.05048e8i		−	0.988585i	0.869296	−	0.494293i	$-0.164573\pi$
$972$		−	2.14802e8i		−	0.233905i
$973$	−1.30346e9			−1.41501
$974$	1.50127e8			0.162473
$975$	7.59523e8	−	1.28834e9i	0.819459	−	1.39000i
$976$		−	3.61989e7i		−	0.0389355i
$977$	−1.98357e8			−0.212698			−0.106349	−	0.994329i	$-0.533916\pi$
$977$	−1.98357e8			−0.212698			−0.106349	+	0.994329i	$0.533916\pi$
$978$			4.67603e8i			0.499874i
$979$	−2.51180e9			−2.67693
$980$	4.69783e7	−	2.68389e7i	0.0499137	−	0.0285159i
$981$			4.46298e7i			0.0472736i
$982$		−	4.23554e8i		−	0.447275i
$983$	−1.31713e9			−1.38666			−0.693330	−	0.720621i	$-0.743857\pi$
$983$	−1.31713e9			−1.38666			−0.693330	+	0.720621i	$0.743857\pi$
$984$	1.21390e9			1.27408
$985$	−4.39016e8	−	7.68445e8i	−0.459380	−	0.804089i
$986$			7.90654e8i			0.824814i
$987$	−5.95789e7			−0.0619642
$988$	7.47888e8			0.775471
$989$	1.25930e9	−	2.37866e8i	1.30179	−	0.245892i
$990$	−1.42681e8	+	8.15143e7i	−0.147048	+	0.0840094i
$991$	−2.78887e8			−0.286555			−0.143277	−	0.989683i	$-0.545764\pi$
$991$	−2.78887e8			−0.286555			−0.143277	+	0.989683i	$0.545764\pi$
$992$			9.21209e8i			0.943676i
$993$			6.63492e8i			0.677623i
$994$		−	7.66868e8i		−	0.780839i
$995$	2.42380e8	+	4.24257e8i	0.246052	+	0.430685i
$996$		−	6.76454e8i		−	0.684637i
$997$			4.83529e8i			0.487907i	0.969787	+	0.243953i	$0.0784444\pi$
$997$			4.83529e8i			0.487907i	−0.969787	+	0.243953i	$0.921556\pi$
$998$		−	1.65779e7i		−	0.0166778i
$999$			1.26515e8i			0.126895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.c.c.114.14	yes	68
5.4	even	2	inner	115.7.c.c.114.55	yes	68
23.22	odd	2	inner	115.7.c.c.114.56	yes	68
115.114	odd	2	inner	115.7.c.c.114.13	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.c.c.114.13	✓	68	115.114	odd	2	inner
115.7.c.c.114.14	yes	68	1.1	even	1	trivial
115.7.c.c.114.55	yes	68	5.4	even	2	inner
115.7.c.c.114.56	yes	68	23.22	odd	2	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.35786i q^{2} -24.6249i q^{3} +45.0090 q^{4} +(108.536 - 62.0072i) q^{5} +107.312 q^{6} -356.743 q^{7} +475.046i q^{8} +122.613 q^{9} +O(q^{10})\)	\(q+4.35786i q^{2} -24.6249i q^{3} +45.0090 q^{4} +(108.536 - 62.0072i) q^{5} +107.312 q^{6} -356.743 q^{7} +475.046i q^{8} +122.613 q^{9} +(270.219 + 472.986i) q^{10} +2460.25i q^{11} -1108.34i q^{12} +3886.94i q^{13} -1554.64i q^{14} +(-1526.92 - 2672.70i) q^{15} +810.390 q^{16} +5678.93 q^{17} +534.332i q^{18} -4274.93i q^{19} +(4885.11 - 2790.88i) q^{20} +8784.77i q^{21} -10721.5 q^{22} +(-11955.6 + 2258.26i) q^{23} +11698.0 q^{24} +(7935.21 - 13460.1i) q^{25} -16938.7 q^{26} -20970.9i q^{27} -16056.7 q^{28} +31948.2 q^{29} +(11647.2 - 6654.12i) q^{30} +27146.6 q^{31} +33934.5i q^{32} +60583.6 q^{33} +24748.0i q^{34} +(-38719.5 + 22120.6i) q^{35} +5518.71 q^{36} -6032.87 q^{37} +18629.6 q^{38} +95715.5 q^{39} +(29456.3 + 51559.7i) q^{40} +103770. q^{41} -38282.8 q^{42} -105331. q^{43} +110734. i q^{44} +(13308.0 - 7602.91i) q^{45} +(-9841.21 - 52100.8i) q^{46} +6782.07i q^{47} -19955.8i q^{48} +9616.64 q^{49} +(58657.1 + 34580.6i) q^{50} -139843. i q^{51} +174947. i q^{52} -47948.2 q^{53} +91388.4 q^{54} +(152554. + 267027. i) q^{55} -169470. i q^{56} -105270. q^{57} +139226. i q^{58} -275854. q^{59} +(-68725.3 - 120295. i) q^{60} -44668.5i q^{61} +118301. i q^{62} -43741.5 q^{63} -96017.2 q^{64} +(241018. + 421873. i) q^{65} +264015. i q^{66} -120875. q^{67} +255603. q^{68} +(55609.6 + 294405. i) q^{69} +(-96398.8 - 168734. i) q^{70} +493278. q^{71} +58247.0i q^{72} -37898.7i q^{73} -26290.4i q^{74} +(-331453. - 195404. i) q^{75} -192411. i q^{76} -877679. i q^{77} +417115. i q^{78} -532286. i q^{79} +(87956.6 - 50250.0i) q^{80} -427022. q^{81} +452216. i q^{82} +610329. q^{83} +395394. i q^{84} +(616369. - 352135. i) q^{85} -459020. i q^{86} -786722. i q^{87} -1.16874e6 q^{88} +1.02095e6i q^{89} +(33132.5 + 57994.4i) q^{90} -1.38664e6i q^{91} +(-538109. + 101642. i) q^{92} -668484. i q^{93} -29555.3 q^{94} +(-265077. - 463985. i) q^{95} +835635. q^{96} +837437. q^{97} +41908.0i q^{98} +301660. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

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