LMFDB - Embedded newform 115.7.c.c.114.16

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			114.16
Character	$\chi$	$=$	115.114
Dual form			115.7.c.c.114.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.1327i q^{2} -32.3873i q^{3} -59.9364 q^{4} +(122.088 - 26.8239i) q^{5} +360.557 q^{6} +301.337 q^{7} +45.2393i q^{8} -319.938 q^{9} +O(q^{10})$	\(q+11.1327i q^{2} -32.3873i q^{3} -59.9364 q^{4} +(122.088 - 26.8239i) q^{5} +360.557 q^{6} +301.337 q^{7} +45.2393i q^{8} -319.938 q^{9} +(298.622 + 1359.17i) q^{10} -1170.08i q^{11} +1941.18i q^{12} -1982.95i q^{13} +3354.69i q^{14} +(-868.755 - 3954.10i) q^{15} -4339.56 q^{16} -1414.70 q^{17} -3561.77i q^{18} +2353.63i q^{19} +(-7317.51 + 1607.73i) q^{20} -9759.51i q^{21} +13026.2 q^{22} +(-11822.2 - 2876.00i) q^{23} +1465.18 q^{24} +(14186.0 - 6549.75i) q^{25} +22075.5 q^{26} -13248.4i q^{27} -18061.1 q^{28} +37904.4 q^{29} +(44019.7 - 9671.56i) q^{30} +37709.9 q^{31} -45415.6i q^{32} -37895.9 q^{33} -15749.3i q^{34} +(36789.7 - 8083.05i) q^{35} +19175.9 q^{36} +26382.8 q^{37} -26202.2 q^{38} -64222.5 q^{39} +(1213.49 + 5523.17i) q^{40} -27448.3 q^{41} +108649. q^{42} -68030.4 q^{43} +70130.6i q^{44} +(-39060.6 + 8582.00i) q^{45} +(32017.5 - 131613. i) q^{46} +3618.80i q^{47} +140547. i q^{48} -26844.8 q^{49} +(72916.3 + 157928. i) q^{50} +45818.2i q^{51} +118851. i q^{52} +66265.9 q^{53} +147490. q^{54} +(-31386.3 - 142853. i) q^{55} +13632.3i q^{56} +76227.8 q^{57} +421977. i q^{58} +319056. q^{59} +(52070.0 + 236994. i) q^{60} -330862. i q^{61} +419812. i q^{62} -96409.4 q^{63} +227865. q^{64} +(-53190.5 - 242095. i) q^{65} -421883. i q^{66} +225060. q^{67} +84791.7 q^{68} +(-93145.9 + 382890. i) q^{69} +(89985.9 + 409567. i) q^{70} +119230. q^{71} -14473.8i q^{72} -305989. i q^{73} +293712. i q^{74} +(-212129. - 459445. i) q^{75} -141068. i q^{76} -352590. i q^{77} -714968. i q^{78} +865450. i q^{79} +(-529808. + 116404. i) q^{80} -662316. q^{81} -305573. i q^{82} -72268.3 q^{83} +584949. i q^{84} +(-172717. + 37947.7i) q^{85} -757361. i q^{86} -1.22762e6i q^{87} +52933.8 q^{88} -400790. i q^{89} +(-95540.6 - 434849. i) q^{90} -597537. i q^{91} +(708580. + 172377. i) q^{92} -1.22132e6i q^{93} -40286.9 q^{94} +(63133.6 + 287350. i) q^{95} -1.47089e6 q^{96} -1.46337e6 q^{97} -298854. i q^{98} +374355. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			11.1327i			1.39158i	0.718243	+	0.695792i	$0.244946\pi$
$2$			11.1327i			1.39158i	−0.718243	+	0.695792i	$0.755054\pi$
$3$		−	32.3873i		−	1.19953i	−0.800176	−	0.599765i	$-0.795261\pi$
$3$		−	32.3873i		−	1.19953i	0.800176	−	0.599765i	$-0.204739\pi$
$4$	−59.9364			−0.936505
$5$	122.088	−	26.8239i	0.976704	−	0.214591i
$5$	122.088	−	26.8239i	0.976704	−	0.214591i
$6$	360.557			1.66925
$7$	301.337			0.878535			0.439267	−	0.898356i	$-0.355238\pi$
$7$	301.337			0.878535			0.439267	+	0.898356i	$0.355238\pi$
$8$			45.2393i			0.0883580i
$9$	−319.938			−0.438873
$10$	298.622	+	1359.17i	0.298622	+	1.35917i
$11$		−	1170.08i		−	0.879102i	−0.898218	−	0.439551i	$-0.855138\pi$
$11$		−	1170.08i		−	0.879102i	0.898218	−	0.439551i	$-0.144862\pi$
$12$			1941.18i			1.12337i
$13$		−	1982.95i		−	0.902572i	−0.892379	−	0.451286i	$-0.850965\pi$
$13$		−	1982.95i		−	0.902572i	0.892379	−	0.451286i	$-0.149035\pi$
$14$			3354.69i			1.22255i
$15$	−868.755	−	3954.10i	−0.257409	−	1.17159i
$16$	−4339.56			−1.05946
$17$	−1414.70			−0.287950			−0.143975	−	0.989581i	$-0.545988\pi$
$17$	−1414.70			−0.287950			−0.143975	+	0.989581i	$0.545988\pi$
$18$		−	3561.77i		−	0.610729i
$19$			2353.63i			0.343145i	0.985171	+	0.171573i	$0.0548848\pi$
$19$			2353.63i			0.343145i	−0.985171	+	0.171573i	$0.945115\pi$
$20$	−7317.51	+	1607.73i	−0.914689	+	0.200966i
$21$		−	9759.51i		−	1.05383i
$22$	13026.2			1.22334
$23$	−11822.2	−	2876.00i	−0.971661	−	0.236377i
$23$	−11822.2	−	2876.00i	−0.971661	−	0.236377i
$24$	1465.18			0.105988
$25$	14186.0	−	6549.75i	0.907901	−	0.419184i
$26$	22075.5			1.25600
$27$		−	13248.4i		−	0.673089i
$28$	−18061.1			−0.822752
$29$	37904.4			1.55416			0.777080	−	0.629402i	$-0.216700\pi$
$29$	37904.4			1.55416			0.777080	+	0.629402i	$0.216700\pi$
$30$	44019.7	−	9671.56i	1.63036	−	0.358206i
$31$	37709.9			1.26582			0.632908	−	0.774227i	$-0.281861\pi$
$31$	37709.9			1.26582			0.632908	+	0.774227i	$0.281861\pi$
$32$		−	45415.6i		−	1.38597i
$33$	−37895.9			−1.05451
$34$		−	15749.3i		−	0.400706i
$35$	36789.7	−	8083.05i	0.858068	−	0.188526i
$36$	19175.9			0.411007
$37$	26382.8			0.520855			0.260427	−	0.965493i	$-0.416137\pi$
$37$	26382.8			0.520855			0.260427	+	0.965493i	$0.416137\pi$
$38$	−26202.2			−0.477515
$39$	−64222.5			−1.08266
$40$	1213.49	+	5523.17i	0.0189608	+	0.0862996i
$41$	−27448.3			−0.398257			−0.199129	−	0.979973i	$-0.563811\pi$
$41$	−27448.3			−0.398257			−0.199129	+	0.979973i	$0.563811\pi$
$42$	108649.			1.46649
$43$	−68030.4			−0.855654			−0.427827	−	0.903861i	$-0.640721\pi$
$43$	−68030.4			−0.855654			−0.427827	+	0.903861i	$0.640721\pi$
$44$			70130.6i			0.823284i
$45$	−39060.6	+	8582.00i	−0.428649	+	0.0941783i
$46$	32017.5	−	131613.i	0.328938	−	1.35215i
$47$			3618.80i			0.0348555i	0.999848	+	0.0174277i	$0.00554770\pi$
$47$			3618.80i			0.0348555i	−0.999848	+	0.0174277i	$0.994452\pi$
$48$			140547.i			1.27086i
$49$	−26844.8			−0.228177
$50$	72916.3	+	157928.i	0.583330	+	1.26342i
$51$			45818.2i			0.345404i
$52$			118851.i			0.845264i
$53$	66265.9			0.445105			0.222552	−	0.974921i	$-0.428561\pi$
$53$	66265.9			0.445105			0.222552	+	0.974921i	$0.428561\pi$
$54$	147490.			0.936660
$55$	−31386.3	−	142853.i	−0.188648	−	0.858623i
$56$			13632.3i			0.0776255i
$57$	76227.8			0.411613
$58$			421977.i			2.16274i
$59$	319056.			1.55350			0.776749	−	0.629810i	$-0.216867\pi$
$59$	319056.			1.55350			0.776749	+	0.629810i	$0.216867\pi$
$60$	52070.0	+	236994.i	0.241065	+	1.09720i
$61$		−	330862.i		−	1.45767i	−0.684692	−	0.728833i	$-0.740063\pi$
$61$		−	330862.i		−	1.45767i	0.684692	−	0.728833i	$-0.259937\pi$
$62$			419812.i			1.76149i
$63$	−96409.4			−0.385565
$64$	227865.			0.869235
$65$	−53190.5	−	242095.i	−0.193684	−	0.881546i
$66$		−	421883.i		−	1.46744i
$67$	225060.			0.748297			0.374148	−	0.927369i	$-0.377935\pi$
$67$	225060.			0.748297			0.374148	+	0.927369i	$0.377935\pi$
$68$	84791.7			0.269666
$69$	−93145.9	+	382890.i	−0.283541	+	1.16554i
$70$	89985.9	+	409567.i	0.262350	+	1.19407i
$71$	119230.			0.333128			0.166564	−	0.986031i	$-0.446733\pi$
$71$	119230.			0.333128			0.166564	+	0.986031i	$0.446733\pi$
$72$		−	14473.8i		−	0.0387779i
$73$		−	305989.i		−	0.786570i	−0.919417	−	0.393285i	$-0.871339\pi$
$73$		−	305989.i		−	0.786570i	0.919417	−	0.393285i	$-0.128661\pi$
$74$			293712.i			0.724813i
$75$	−212129.	−	459445.i	−0.502824	−	1.08905i
$76$		−	141068.i		−	0.321357i
$77$		−	352590.i		−	0.772322i
$78$		−	714968.i		−	1.50662i
$79$			865450.i			1.75534i	0.479268	+	0.877668i	$0.340902\pi$
$79$			865450.i			1.75534i	−0.479268	+	0.877668i	$0.659098\pi$
$80$	−529808.	+	116404.i	−1.03478	+	0.227352i
$81$	−662316.			−1.24626
$82$		−	305573.i		−	0.554209i
$83$	−72268.3			−0.126390			−0.0631952	−	0.998001i	$-0.520129\pi$
$83$	−72268.3			−0.126390			−0.0631952	+	0.998001i	$0.520129\pi$
$84$			584949.i			0.986916i
$85$	−172717.	+	37947.7i	−0.281242	+	0.0617915i
$86$		−	757361.i		−	1.19071i
$87$		−	1.22762e6i		−	1.86426i
$88$	52933.8			0.0776757
$89$		−	400790.i		−	0.568522i	−0.958747	−	0.284261i	$-0.908252\pi$
$89$		−	400790.i		−	0.568522i	0.958747	−	0.284261i	$-0.0917482\pi$
$90$	−95540.6	−	434849.i	−0.131057	−	0.596501i
$91$		−	597537.i		−	0.792941i
$92$	708580.	+	172377.i	0.909966	+	0.221368i
$93$		−	1.22132e6i		−	1.51838i
$94$	−40286.9			−0.0485043
$95$	63133.6	+	287350.i	0.0736359	+	0.335151i
$96$	−1.47089e6			−1.66252
$97$	−1.46337e6			−1.60339			−0.801694	−	0.597734i	$-0.796068\pi$
$97$	−1.46337e6			−1.60339			−0.801694	+	0.597734i	$0.796068\pi$
$98$		−	298854.i		−	0.317528i
$99$			374355.i			0.385814i
$100$	−850254.	+	392568.i	−0.850254	+	0.392568i
$101$	970049.			0.941520			0.470760	−	0.882261i	$-0.343980\pi$
$101$	970049.			0.941520			0.470760	+	0.882261i	$0.343980\pi$
$102$	−510079.			−0.480659
$103$	−249106.			−0.227968			−0.113984	−	0.993483i	$-0.536361\pi$
$103$	−249106.			−0.227968			−0.113984	+	0.993483i	$0.536361\pi$
$104$	89707.3			0.0797494
$105$	−261788.	−	1.19152e6i	−0.226142	−	1.02928i
$106$			737716.i			0.619401i
$107$	132438.			0.108109			0.0540545	−	0.998538i	$-0.482786\pi$
$107$	132438.			0.108109			0.0540545	+	0.998538i	$0.482786\pi$
$108$			794061.i			0.630351i
$109$			1.78355e6i			1.37723i	0.725127	+	0.688616i	$0.241781\pi$
$109$			1.78355e6i			1.37723i	−0.725127	+	0.688616i	$0.758219\pi$
$110$	1.59034e6	−	349413.i	1.19485	−	0.262519i
$111$		−	854470.i		−	0.624781i
$112$	−1.30767e6			−0.930775
$113$	1.08171e6			0.749679			0.374840	−	0.927090i	$-0.377698\pi$
$113$	1.08171e6			0.749679			0.374840	+	0.927090i	$0.377698\pi$
$114$			848619.i			0.572794i
$115$	−1.52049e6	−	34007.1i	−0.999750	−	0.0223602i
$116$	−2.27185e6			−1.45548
$117$			634422.i			0.396115i
$118$			3.55195e6i			2.16182i
$119$	−426301.			−0.252974
$120$	178881.	−	39301.8i	0.103519	−	0.0227441i
$121$	402462.			0.227179
$122$	3.68338e6			2.02846
$123$			888977.i			0.477722i
$124$	−2.26020e6			−1.18544
$125$	1.55624e6	−	1.18017e6i	0.796797	−	0.604247i
$126$		−	1.07329e6i		−	0.536546i
$127$			2.95295e6i			1.44160i	0.693144	+	0.720800i	$0.256225\pi$
$127$			2.95295e6i			1.44160i	−0.693144	+	0.720800i	$0.743775\pi$
$128$		−	369853.i		−	0.176360i
$129$			2.20332e6i			1.02638i
$130$	2.69516e6	−	592152.i	1.22674	−	0.269528i
$131$	−665009.			−0.295810			−0.147905	−	0.989002i	$-0.547253\pi$
$131$	−665009.			−0.295810			−0.147905	+	0.989002i	$0.547253\pi$
$132$	2.27134e6			0.987554
$133$			709237.i			0.301465i
$134$			2.50552e6i			1.04132i
$135$	−355374.	−	1.61747e6i	−0.144439	−	0.657409i
$136$		−	63999.8i		−	0.0254426i
$137$	−4.83414e6			−1.88000			−0.940000	−	0.341175i	$-0.889175\pi$
$137$	−4.83414e6			−1.88000			−0.940000	+	0.341175i	$0.889175\pi$
$138$	−4.26258e6	−	1.03696e6i	−1.62194	−	0.394572i
$139$	−2.60304e6			−0.969251			−0.484625	−	0.874722i	$-0.661044\pi$
$139$	−2.60304e6			−0.969251			−0.484625	+	0.874722i	$0.661044\pi$
$140$	−2.20504e6	+	484468.i	−0.803586	+	0.176555i
$141$	117203.			0.0418102
$142$			1.32735e6i			0.463575i
$143$	−2.32022e6			−0.793453
$144$	1.38839e6			0.464970
$145$	4.62767e6	−	1.01674e6i	1.51795	−	0.333509i
$146$	3.40648e6			1.09458
$147$			869431.i			0.273705i
$148$	−1.58129e6			−0.487783
$149$			3.62423e6i			1.09561i	0.836605	+	0.547806i	$0.184537\pi$
$149$			3.62423e6i			1.09561i	−0.836605	+	0.547806i	$0.815463\pi$
$150$	5.11485e6	−	2.36156e6i	1.51551	−	0.699722i
$151$	−956349.			−0.277770			−0.138885	−	0.990309i	$-0.544352\pi$
$151$	−956349.			−0.277770			−0.138885	+	0.990309i	$0.544352\pi$
$152$	−106477.			−0.0303196
$153$	452616.			0.126373
$154$	3.92527e6			1.07475
$155$	4.60393e6	−	1.01153e6i	1.23633	−	0.271633i
$156$	3.84926e6			1.01392
$157$	−997521.			−0.257765			−0.128882	−	0.991660i	$-0.541139\pi$
$157$	−997521.			−0.257765			−0.128882	+	0.991660i	$0.541139\pi$
$158$	−9.63476e6			−2.44270
$159$		−	2.14617e6i		−	0.533917i
$160$	−1.21822e6	−	5.54470e6i	−0.297418	−	1.35369i
$161$	−3.56247e6	−	866646.i	−0.853638	−	0.207665i
$162$		−	7.37334e6i		−	1.73428i
$163$			1.66316e6i			0.384035i	0.981392	+	0.192017i	$0.0615030\pi$
$163$			1.66316e6i			0.384035i	−0.981392	+	0.192017i	$0.938497\pi$
$164$	1.64515e6			0.372970
$165$	−4.62664e6	+	1.01652e6i	−1.02994	+	0.226289i
$166$		−	804540.i		−	0.175883i
$167$			2.24408e6i			0.481825i	0.970547	+	0.240912i	$0.0774467\pi$
$167$			2.24408e6i			0.481825i	−0.970547	+	0.240912i	$0.922553\pi$
$168$	441513.			0.0931142
$169$	894715.			0.185364
$170$	−422459.	−	1.92281e6i	−0.0859880	−	0.391371i
$171$		−	753017.i		−	0.150597i
$172$	4.07750e6			0.801324
$173$		−	7.27906e6i		−	1.40584i	−0.711268	−	0.702921i	$-0.751879\pi$
$173$		−	7.27906e6i		−	1.40584i	0.711268	−	0.702921i	$-0.248121\pi$
$174$	1.36667e7			2.59428
$175$	4.27476e6	−	1.97369e6i	0.797623	−	0.368268i
$176$			5.07765e6i			0.931376i
$177$		−	1.03334e7i		−	1.86347i
$178$	4.46186e6			0.791145
$179$	−3.50454e6			−0.611043			−0.305521	−	0.952185i	$-0.598831\pi$
$179$	−3.50454e6			−0.611043			−0.305521	+	0.952185i	$0.598831\pi$
$180$	2.34115e6	−	514374.i	0.401432	−	0.0881985i
$181$			6.02869e6i			1.01669i	0.861154	+	0.508344i	$0.169742\pi$
$181$			6.02869e6i			1.01669i	−0.861154	+	0.508344i	$0.830258\pi$
$182$	6.65218e6			1.10344
$183$	−1.07157e7			−1.74851
$184$	130108.	−	534828.i	0.0208858	−	0.0858540i
$185$	3.22103e6	−	707691.i	0.508721	−	0.111771i
$186$	1.35966e7			2.11296
$187$			1.65531e6i			0.253137i
$188$		−	216898.i		−	0.0326424i
$189$		−	3.99224e6i		−	0.591332i
$190$	−3.19897e6	+	702846.i	−0.466391	+	0.102471i
$191$			1.31131e7i			1.88194i	0.338491	+	0.940969i	$0.390083\pi$
$191$			1.31131e7i			1.88194i	−0.338491	+	0.940969i	$0.609917\pi$
$192$		−	7.37993e6i		−	1.04267i
$193$			7.93480e6i			1.10373i	0.833932	+	0.551867i	$0.186084\pi$
$193$			7.93480e6i			1.10373i	−0.833932	+	0.551867i	$0.813916\pi$
$194$		−	1.62912e7i		−	2.23125i
$195$	−7.84079e6	+	1.72270e6i	−1.05744	+	0.232330i
$196$	1.60898e6			0.213689
$197$			8.02889e6i			1.05016i	0.851052	+	0.525081i	$0.175965\pi$
$197$			8.02889e6i			1.05016i	−0.851052	+	0.525081i	$0.824035\pi$
$198$	−4.16757e6			−0.536893
$199$			5.20331e6i			0.660268i	0.943934	+	0.330134i	$0.107094\pi$
$199$			5.20331e6i			0.660268i	−0.943934	+	0.330134i	$0.892906\pi$
$200$	296306.	+	641762.i	0.0370383	+	0.0802203i
$201$		−	7.28909e6i		−	0.897605i
$202$			1.07992e7i			1.31020i
$203$	1.14220e7			1.36538
$204$		−	2.74618e6i		−	0.323473i
$205$	−3.35111e6	+	736271.i	−0.388980	+	0.0854626i
$206$		−	2.77322e6i		−	0.317236i
$207$	3.78238e6	+	920142.i	0.426436	+	0.103739i
$208$			8.60514e6i			0.956242i
$209$	2.75395e6			0.301660
$210$	1.32648e7	−	2.91440e6i	1.43233	−	0.314696i
$211$	3.00249e6			0.319620			0.159810	−	0.987148i	$-0.448912\pi$
$211$	3.00249e6			0.319620			0.159810	+	0.987148i	$0.448912\pi$
$212$	−3.97173e6			−0.416843
$213$		−	3.86154e6i		−	0.399597i
$214$			1.47439e6i			0.150443i
$215$	−8.30570e6	+	1.82484e6i	−0.835720	+	0.183616i
$216$	599348.			0.0594728
$217$	1.13634e7			1.11206
$218$	−1.98557e7			−1.91653
$219$	−9.91017e6			−0.943515
$220$	1.88118e6	+	8.56211e6i	0.176670	+	0.804105i
$221$			2.80527e6i			0.259895i
$222$	9.51253e6			0.869435
$223$			1.17138e7i			1.05629i	0.849154	+	0.528146i	$0.177112\pi$
$223$			1.17138e7i			1.05629i	−0.849154	+	0.528146i	$0.822888\pi$
$224$		−	1.36854e7i		−	1.21763i
$225$	−4.53863e6	+	2.09552e6i	−0.398453	+	0.183969i
$226$			1.20423e7i			1.04324i
$227$	−1.96308e7			−1.67826			−0.839132	−	0.543928i	$-0.816936\pi$
$227$	−1.96308e7			−1.67826			−0.839132	+	0.543928i	$0.816936\pi$
$228$	−4.56882e6			−0.385478
$229$		−	8.12925e6i		−	0.676930i	−0.940979	−	0.338465i	$-0.890092\pi$
$229$		−	8.12925e6i		−	0.676930i	0.940979	−	0.338465i	$-0.109908\pi$
$230$	378590.	−	1.69272e7i	0.0311161	−	1.39124i
$231$	−1.14195e7			−0.926423
$232$			1.71477e6i			0.137322i
$233$		−	1.29193e7i		−	1.02134i	−0.859777	−	0.510670i	$-0.829397\pi$
$233$		−	1.29193e7i		−	1.02134i	0.859777	−	0.510670i	$-0.170603\pi$
$234$	−7.06281e6			−0.551227
$235$	97070.4	+	441812.i	0.00747968	+	0.0340435i
$236$	−1.91231e7			−1.45486
$237$	2.80296e7			2.10558
$238$		−	4.74587e6i		−	0.352034i
$239$	−1.13850e7			−0.833948			−0.416974	−	0.908918i	$-0.636909\pi$
$239$	−1.13850e7			−0.833948			−0.416974	+	0.908918i	$0.636909\pi$
$240$	3.77001e6	+	1.71591e7i	0.272715	+	1.24125i
$241$			2.05804e6i			0.147029i	0.997294	+	0.0735143i	$0.0234215\pi$
$241$			2.05804e6i			0.147029i	−0.997294	+	0.0735143i	$0.976579\pi$
$242$			4.48048e6i			0.316139i
$243$			1.17925e7i			0.821842i
$244$			1.98307e7i			1.36511i
$245$	−3.27743e6	+	720083.i	−0.222861	+	0.0489648i
$246$	−9.89668e6			−0.664790
$247$	4.66714e6			0.309713
$248$			1.70597e6i			0.111845i
$249$			2.34058e6i			0.151609i
$250$	1.31384e7	+	1.73252e7i	0.840860	+	1.10881i
$251$		−	1.50804e7i		−	0.953655i	−0.878997	−	0.476827i	$-0.841787\pi$
$251$		−	1.50804e7i		−	0.953655i	0.878997	−	0.476827i	$-0.158213\pi$
$252$	5.77843e6			0.361084
$253$	−3.36516e6	+	1.38330e7i	−0.207800	+	0.854190i
$254$	−3.28742e7			−2.00611
$255$	1.22902e6	+	5.59385e6i	0.0741207	+	0.337358i
$256$	1.87008e7			1.11465
$257$		−	2.55306e7i		−	1.50405i	−0.659136	−	0.752024i	$-0.729078\pi$
$257$		−	2.55306e7i		−	1.50405i	0.659136	−	0.752024i	$-0.270922\pi$
$258$	−2.45289e7			−1.42830
$259$	7.95014e6			0.457589
$260$	3.18804e6	+	1.45103e7i	0.181386	+	0.825572i
$261$	−1.21271e7			−0.682079
$262$		−	7.40332e6i		−	0.411645i
$263$	1.19737e7			0.658203			0.329101	−	0.944295i	$-0.393254\pi$
$263$	1.19737e7			0.658203			0.329101	+	0.944295i	$0.393254\pi$
$264$		−	1.71438e6i		−	0.0931743i
$265$	8.09027e6	−	1.77751e6i	0.434736	−	0.0955156i
$266$	−7.89570e6			−0.419513
$267$	−1.29805e7			−0.681959
$268$	−1.34893e7			−0.700784
$269$	2.34634e7			1.20541			0.602705	−	0.797964i	$-0.294090\pi$
$269$	2.34634e7			1.20541			0.602705	+	0.797964i	$0.294090\pi$
$270$	1.80068e7	−	3.95626e6i	0.914839	−	0.200999i
$271$	1.93572e7			0.972599			0.486300	−	0.873792i	$-0.338346\pi$
$271$	1.93572e7			0.972599			0.486300	+	0.873792i	$0.338346\pi$
$272$	6.13916e6			0.305072
$273$	−1.93526e7			−0.951157
$274$		−	5.38169e7i		−	2.61618i
$275$	−7.66377e6	−	1.65988e7i	−0.368506	−	0.798138i
$276$	5.58282e6	−	2.29490e7i	0.265538	−	1.09153i
$277$		−	8.64069e6i		−	0.406546i	−0.979122	−	0.203273i	$-0.934842\pi$
$277$		−	8.64069e6i		−	0.406546i	0.979122	−	0.203273i	$-0.0651578\pi$
$278$		−	2.89788e7i		−	1.34879i
$279$	−1.20649e7			−0.555533
$280$	365671.	+	1.66434e6i	0.0166578	+	0.0758171i
$281$			1.47473e7i			0.664652i	0.943165	+	0.332326i	$0.107833\pi$
$281$			1.47473e7i			0.664652i	−0.943165	+	0.332326i	$0.892167\pi$
$282$			1.30479e6i			0.0581824i
$283$	82549.5			0.00364213			0.00182106	−	0.999998i	$-0.499420\pi$
$283$	82549.5			0.00364213			0.00182106	+	0.999998i	$0.499420\pi$
$284$	−7.14622e6			−0.311976
$285$	9.30650e6	−	2.04473e6i	0.402024	−	0.0883285i
$286$		−	2.58303e7i		−	1.10416i
$287$	−8.27120e6			−0.349883
$288$			1.45302e7i			0.608266i
$289$	−2.21362e7			−0.917085
$290$	1.13191e7	+	5.15184e7i	0.464106	+	2.11236i
$291$			4.73946e7i			1.92331i
$292$			1.83399e7i			0.736627i
$293$	−8.98924e6			−0.357372			−0.178686	−	0.983906i	$-0.557185\pi$
$293$	−8.98924e6			−0.357372			−0.178686	+	0.983906i	$0.557185\pi$
$294$	−9.67909e6			−0.380884
$295$	3.89529e7	−	8.55833e6i	1.51731	−	0.333367i
$296$			1.19354e6i			0.0460216i
$297$	−1.55018e7			−0.591714
$298$	−4.03473e7			−1.52464
$299$	−5.70296e6	+	2.34429e7i	−0.213347	+	0.876995i
$300$	1.27142e7	+	2.75375e7i	0.470898	+	1.01991i
$301$	−2.05001e7			−0.751721
$302$		−	1.06467e7i		−	0.386540i
$303$		−	3.14173e7i		−	1.12938i
$304$		−	1.02137e7i		−	0.363549i
$305$	−8.87502e6	−	4.03943e7i	−0.312802	−	1.42371i
$306$			5.03882e6i			0.175859i
$307$			3.74858e7i			1.29554i	0.761836	+	0.647770i	$0.224298\pi$
$307$			3.74858e7i			1.29554i	−0.761836	+	0.647770i	$0.775702\pi$
$308$			2.11330e7i			0.723283i
$309$			8.06789e6i			0.273454i
$310$	1.12610e7	+	5.12540e7i	0.378000	+	1.72045i
$311$	−1.13662e7			−0.377862			−0.188931	−	0.981990i	$-0.560502\pi$
$311$	−1.13662e7			−0.377862			−0.188931	+	0.981990i	$0.560502\pi$
$312$		−	2.90538e6i		−	0.0956619i
$313$	−5.00898e7			−1.63349			−0.816745	−	0.576999i	$-0.804224\pi$
$313$	−5.00898e7			−1.63349			−0.816745	+	0.576999i	$0.804224\pi$
$314$		−	1.11051e7i		−	0.358701i
$315$	−1.17704e7	+	2.58608e6i	−0.376583	+	0.0827389i
$316$		−	5.18719e7i		−	1.64388i
$317$		−	1.72651e7i		−	0.541991i	−0.962581	−	0.270996i	$-0.912647\pi$
$317$		−	1.72651e7i		−	0.541991i	0.962581	−	0.270996i	$-0.0873529\pi$
$318$	2.38926e7			0.742990
$319$		−	4.43514e7i		−	1.36627i
$320$	2.78196e7	−	6.11223e6i	0.848986	−	0.186530i
$321$		−	4.28932e6i		−	0.129680i
$322$	9.64808e6	−	3.96598e7i	0.288984	−	1.18791i
$323$		−	3.32967e6i		−	0.0988085i
$324$	3.96968e7			1.16713
$325$	−1.29878e7	−	2.81301e7i	−0.378344	−	0.819446i
$326$	−1.85154e7			−0.534416
$327$	5.77645e7			1.65203
$328$		−	1.24174e6i		−	0.0351892i
$329$			1.09048e6i			0.0306217i
$330$	−1.13165e7	−	5.15068e7i	−0.314900	−	1.43325i
$331$	−1.10222e7			−0.303937			−0.151968	−	0.988385i	$-0.548561\pi$
$331$	−1.10222e7			−0.303937			−0.151968	+	0.988385i	$0.548561\pi$
$332$	4.33150e6			0.118365
$333$	−8.44089e6			−0.228589
$334$	−2.49826e7			−0.670500
$335$	2.74771e7	−	6.03699e6i	0.730864	−	0.160578i
$336$			4.23520e7i			1.11649i
$337$	−3.21267e6			−0.0839415			−0.0419707	−	0.999119i	$-0.513364\pi$
$337$	−3.21267e6			−0.0839415			−0.0419707	+	0.999119i	$0.513364\pi$
$338$			9.96056e6i			0.257949i
$339$		−	3.50337e7i		−	0.899263i
$340$	1.03521e7	−	2.27445e6i	0.263384	−	0.0578681i
$341$		−	4.41238e7i		−	1.11278i
$342$	8.38309e6			0.209568
$343$	−4.35414e7			−1.07900
$344$		−	3.07765e6i		−	0.0756038i
$345$	−1.10140e6	+	4.92447e7i	−0.0268218	+	1.19923i
$346$	8.10353e7			1.95635
$347$			3.77460e7i			0.903404i	0.892169	+	0.451702i	$0.149183\pi$
$347$			3.77460e7i			0.903404i	−0.892169	+	0.451702i	$0.850817\pi$
$348$			7.35792e7i			1.74589i
$349$	8.03470e7			1.89014			0.945068	−	0.326873i	$-0.105995\pi$
$349$	8.03470e7			1.89014			0.945068	+	0.326873i	$0.105995\pi$
$350$	2.19724e7	+	4.75895e7i	0.512476	+	1.10996i
$351$	−2.62709e7			−0.607511
$352$	−5.31401e7			−1.21841
$353$			2.88730e7i			0.656398i	0.944609	+	0.328199i	$0.106442\pi$
$353$			2.88730e7i			0.656398i	−0.944609	+	0.328199i	$0.893558\pi$
$354$	1.15038e8			2.59317
$355$	1.45566e7	−	3.19822e6i	0.325367	−	0.0714863i
$356$			2.40219e7i			0.532424i
$357$			1.38067e7i			0.303450i
$358$		−	3.90149e7i		−	0.850317i
$359$			8.94094e7i			1.93241i	0.257772	+	0.966206i	$0.417012\pi$
$359$			8.94094e7i			1.93241i	−0.257772	+	0.966206i	$0.582988\pi$
$360$	−388243.	−	1.76707e6i	−0.00832140	−	0.0378745i
$361$	4.15063e7			0.882252
$362$	−6.71154e7			−1.41481
$363$		−	1.30347e7i		−	0.272509i
$364$			3.58142e7i			0.742593i
$365$	−8.20783e6	−	3.73576e7i	−0.168791	−	0.768246i
$366$		−	1.19295e8i		−	2.43320i
$367$	5.85361e7			1.18420			0.592101	−	0.805864i	$-0.298299\pi$
$367$	5.85361e7			1.18420			0.592101	+	0.805864i	$0.298299\pi$
$368$	5.13032e7	+	1.24806e7i	1.02944	+	0.250433i
$369$	8.78176e6			0.174784
$370$	7.87849e6	+	3.58587e7i	0.155539	+	0.707928i
$371$	1.99684e7			0.391040
$372$			7.32017e7i			1.42198i
$373$	6.18124e7			1.19110			0.595551	−	0.803318i	$-0.296934\pi$
$373$	6.18124e7			1.19110			0.595551	+	0.803318i	$0.296934\pi$
$374$	−1.84281e7			−0.352262
$375$	−3.82225e7	−	5.04026e7i	−0.724812	−	0.955783i
$376$	−163712.			−0.00307976
$377$		−	7.51626e7i		−	1.40274i
$378$	4.44443e7			0.822888
$379$			6.16070e7i			1.13165i	0.824525	+	0.565826i	$0.191443\pi$
$379$			6.16070e7i			1.13165i	−0.824525	+	0.565826i	$0.808557\pi$
$380$	−3.78400e6	−	1.72227e7i	−0.0689604	−	0.313871i
$381$	9.56380e7			1.72924
$382$	−1.45984e8			−2.61888
$383$	3.08970e7			0.549946			0.274973	−	0.961452i	$-0.411331\pi$
$383$	3.08970e7			0.549946			0.274973	+	0.961452i	$0.411331\pi$
$384$	−1.19785e7			−0.211549
$385$	−9.45785e6	−	4.30470e7i	−0.165733	−	0.754330i
$386$	−8.83356e7			−1.53594
$387$	2.17656e7			0.375523
$388$	8.77090e7			1.50158
$389$		−	6.81506e7i		−	1.15777i	−0.815411	−	0.578883i	$-0.803489\pi$
$389$		−	6.81506e7i		−	1.15777i	0.815411	−	0.578883i	$-0.196511\pi$
$390$	−1.91782e7	−	8.72890e7i	−0.323307	−	1.47152i
$391$	1.67248e7	+	4.06866e6i	0.279790	+	0.0680647i
$392$		−	1.21444e6i		−	0.0201613i
$393$			2.15379e7i			0.354834i
$394$	−8.93829e7			−1.46139
$395$	2.32147e7	+	1.05661e8i	0.376680	+	1.71444i
$396$		−	2.24375e7i		−	0.361317i
$397$			4.71641e7i			0.753772i	0.926260	+	0.376886i	$0.123005\pi$
$397$			4.71641e7i			0.753772i	−0.926260	+	0.376886i	$0.876995\pi$
$398$	−5.79267e7			−0.918819
$399$	2.29703e7			0.361616
$400$	−6.15608e7	+	2.84231e7i	−0.961888	+	0.444110i
$401$		−	6.09948e6i		−	0.0945931i	−0.998881	−	0.0472966i	$-0.984939\pi$
$401$		−	6.09948e6i		−	0.0945931i	0.998881	−	0.0472966i	$-0.0150606\pi$
$402$	8.11470e7			1.24909
$403$		−	7.47769e7i		−	1.14249i
$404$	−5.81412e7			−0.881739
$405$	−8.08608e7	+	1.77659e7i	−1.21723	+	0.267437i
$406$			1.27158e8i			1.90005i
$407$		−	3.08702e7i		−	0.457884i
$408$	−2.07278e6			−0.0305192
$409$	2.51440e7			0.367505			0.183753	−	0.982972i	$-0.441175\pi$
$409$	2.51440e7			0.367505			0.183753	+	0.982972i	$0.441175\pi$
$410$	−8.19666e6	−	3.73068e7i	−0.118928	−	0.541298i
$411$			1.56565e8i			2.25512i
$412$	1.49305e7			0.213493
$413$	9.61435e7			1.36480
$414$	−1.02436e7	+	4.21080e7i	−0.144362	+	0.593421i
$415$	−8.82310e6	+	1.93852e6i	−0.123446	+	0.0271223i
$416$	−9.00569e7			−1.25094
$417$			8.43054e7i			1.16265i
$418$			3.06588e7i			0.419785i
$419$		−	4.02488e7i		−	0.547156i	−0.961850	−	0.273578i	$-0.911793\pi$
$419$		−	4.02488e7i		−	0.547156i	0.961850	−	0.273578i	$-0.0882072\pi$
$420$	1.56906e7	+	7.14153e7i	0.211784	+	0.963925i
$421$			1.04142e8i			1.39566i	0.716265	+	0.697828i	$0.245850\pi$
$421$			1.04142e8i			1.39566i	−0.716265	+	0.697828i	$0.754150\pi$
$422$			3.34258e7i			0.444779i
$423$		−	1.15779e6i		−	0.0152971i
$424$			2.99782e6i			0.0393286i
$425$	−2.00688e7	+	9.26591e6i	−0.261430	+	0.120704i
$426$	4.29893e7			0.556073
$427$		−	9.97012e7i		−	1.28061i
$428$	−7.93786e6			−0.101245
$429$			7.51457e7i			0.951771i
$430$	−2.03154e7	−	9.24646e7i	−0.255517	−	1.16297i
$431$		−	1.03019e8i		−	1.28673i	−0.765561	−	0.643363i	$-0.777539\pi$
$431$		−	1.03019e8i		−	1.28673i	0.765561	−	0.643363i	$-0.222461\pi$
$432$			5.74923e7i			0.713113i
$433$	−1.02405e8			−1.26141			−0.630706	−	0.776022i	$-0.717235\pi$
$433$	−1.02405e8			−1.26141			−0.630706	+	0.776022i	$0.717235\pi$
$434$			1.26505e8i			1.54753i
$435$	−3.29296e7	−	1.49878e8i	−0.400054	−	1.82083i
$436$		−	1.06900e8i		−	1.28978i
$437$	6.76904e6	−	2.78251e7i	0.0811116	−	0.333421i
$438$		−	1.10327e8i		−	1.31298i
$439$	5.21691e7			0.616623			0.308312	−	0.951285i	$-0.400236\pi$
$439$	5.21691e7			0.616623			0.308312	+	0.951285i	$0.400236\pi$
$440$	6.46258e6	−	1.41989e6i	0.0758661	−	0.0166685i
$441$	8.58868e6			0.100141
$442$	−3.12302e7			−0.361666
$443$		−	6.12386e7i		−	0.704391i	−0.935926	−	0.352196i	$-0.885435\pi$
$443$		−	6.12386e7i		−	0.704391i	0.935926	−	0.352196i	$-0.114565\pi$
$444$			5.12138e7i			0.585111i
$445$	−1.07508e7	−	4.89317e7i	−0.122000	−	0.555277i
$446$	−1.30406e8			−1.46992
$447$	1.17379e8			1.31422
$448$	6.86642e7			0.763653
$449$	−2.69188e7			−0.297384			−0.148692	−	0.988884i	$-0.547506\pi$
$449$	−2.69188e7			−0.297384			−0.148692	+	0.988884i	$0.547506\pi$
$450$	−2.33287e7	−	5.05271e7i	−0.256008	−	0.554481i
$451$			3.21168e7i			0.350109i
$452$	−6.48337e7			−0.702079
$453$			3.09736e7i			0.333194i
$454$		−	2.18543e8i		−	2.33544i
$455$	−1.60283e7	−	7.29521e7i	−0.170158	−	0.774468i
$456$			3.44849e6i			0.0363693i
$457$	8.72372e7			0.914015			0.457008	−	0.889463i	$-0.348921\pi$
$457$	8.72372e7			0.914015			0.457008	+	0.889463i	$0.348921\pi$
$458$	9.05002e7			0.942005
$459$			1.87425e7i			0.193816i
$460$	9.11329e7	+	2.03826e6i	0.936271	+	0.0209405i
$461$	1.11418e8			1.13724			0.568620	−	0.822600i	$-0.307477\pi$
$461$	1.11418e8			1.13724			0.568620	+	0.822600i	$0.307477\pi$
$462$		−	1.27129e8i		−	1.28920i
$463$		−	2.85498e7i		−	0.287648i	−0.989603	−	0.143824i	$-0.954060\pi$
$463$		−	2.85498e7i		−	0.287648i	0.989603	−	0.143824i	$-0.0459399\pi$
$464$	−1.64488e8			−1.64657
$465$	−3.27607e7	−	1.49109e8i	−0.325832	−	1.48301i
$466$	1.43826e8			1.42128
$467$	−1.46753e8			−1.44091			−0.720454	−	0.693503i	$-0.756067\pi$
$467$	−1.46753e8			−1.44091			−0.720454	+	0.693503i	$0.756067\pi$
$468$		−	3.80250e7i		−	0.370963i
$469$	6.78190e7			0.657405
$470$	−4.91855e6	+	1.08065e6i	−0.0473744	+	0.0104086i
$471$			3.23070e7i			0.309196i
$472$			1.44339e7i			0.137264i
$473$			7.96014e7i			0.752207i
$474$			3.12044e8i			2.93009i
$475$	1.54157e7	+	3.33885e7i	0.143841	+	0.311542i
$476$	2.55509e7			0.236911
$477$	−2.12010e7			−0.195345
$478$		−	1.26745e8i		−	1.16051i
$479$		−	2.48053e7i		−	0.225703i	−0.993612	−	0.112852i	$-0.964002\pi$
$479$		−	2.48053e7i		−	0.225703i	0.993612	−	0.112852i	$-0.0359984\pi$
$480$	−1.79578e8	+	3.94550e7i	−1.62379	+	0.356762i
$481$		−	5.23159e7i		−	0.470109i
$482$	−2.29114e7			−0.204603
$483$	−2.80683e7	+	1.15379e8i	−0.249101	+	1.02396i
$484$	−2.41221e7			−0.212755
$485$	−1.78660e8	+	3.92533e7i	−1.56604	+	0.344073i
$486$	−1.31282e8			−1.14366
$487$		−	1.87555e8i		−	1.62384i	−0.583771	−	0.811918i	$-0.698424\pi$
$487$		−	1.87555e8i		−	1.62384i	0.583771	−	0.811918i	$-0.301576\pi$
$488$	1.49680e7			0.128796
$489$	5.38652e7			0.460661
$490$	−8.01644e6	−	3.64865e7i	−0.0681386	−	0.310130i
$491$	−3.74907e7			−0.316723			−0.158361	−	0.987381i	$-0.550621\pi$
$491$	−3.74907e7			−0.316723			−0.158361	+	0.987381i	$0.550621\pi$
$492$		−	5.32820e7i		−	0.447389i
$493$	−5.36232e7			−0.447520
$494$			5.19577e7i			0.430992i
$495$	1.00417e7	+	4.57043e7i	0.0827924	+	0.376826i
$496$	−1.63645e8			−1.34109
$497$	3.59285e7			0.292664
$498$	−2.60569e7			−0.210977
$499$	−2.20556e8			−1.77508			−0.887539	−	0.460733i	$-0.847586\pi$
$499$	−2.20556e8			−1.77508			−0.887539	+	0.460733i	$0.847586\pi$
$500$	−9.32756e7	+	7.07350e7i	−0.746205	+	0.565880i
$501$	7.26798e7			0.577964
$502$	1.67885e8			1.32709
$503$	−1.20697e8			−0.948401			−0.474201	−	0.880417i	$-0.657263\pi$
$503$	−1.20697e8			−0.948401			−0.474201	+	0.880417i	$0.657263\pi$
$504$		−	4.36149e6i		−	0.0340677i
$505$	1.18431e8	−	2.60205e7i	0.919586	−	0.202042i
$506$	−1.53998e8	−	3.74632e7i	−1.18868	−	0.289170i
$507$		−	2.89774e7i		−	0.222349i
$508$		−	1.76989e8i		−	1.35007i
$509$	6.16199e7			0.467270			0.233635	−	0.972324i	$-0.424938\pi$
$509$	6.16199e7			0.467270			0.233635	+	0.972324i	$0.424938\pi$
$510$	−6.22745e7	+	1.36823e7i	−0.469462	+	0.103145i
$511$		−	9.22060e7i		−	0.691029i
$512$			1.84519e8i			1.37478i
$513$	3.11819e7			0.230967
$514$	2.84224e8			2.09301
$515$	−3.04129e7	+	6.68201e6i	−0.222657	+	0.0489199i
$516$		−	1.32059e8i		−	0.961213i
$517$	4.23430e6			0.0306415
$518$			8.85063e7i			0.636773i
$519$	−2.35749e8			−1.68635
$520$	1.09522e7	−	2.40630e6i	0.0778916	−	0.0171135i
$521$			2.43886e8i			1.72454i	0.506447	+	0.862271i	$0.330959\pi$
$521$			2.43886e8i			1.72454i	−0.506447	+	0.862271i	$0.669041\pi$
$522$		−	1.35007e8i		−	0.949170i
$523$	−5.83108e7			−0.407609			−0.203805	−	0.979012i	$-0.565331\pi$
$523$	−5.83108e7			−0.407609			−0.203805	+	0.979012i	$0.565331\pi$
$524$	3.98582e7			0.277028
$525$	−6.39224e7	−	1.38448e8i	−0.441748	−	0.956772i
$526$			1.33299e8i			0.915945i
$527$	−5.33481e7			−0.364491
$528$	1.64452e8			1.11721
$529$	1.31493e8	+	6.80013e7i	0.888252	+	0.459357i
$530$	1.97884e7	+	9.00663e7i	0.132918	+	0.604971i
$531$	−1.02078e8			−0.681789
$532$		−	4.25091e7i		−	0.282323i
$533$			5.44286e7i			0.359456i
$534$		−	1.44508e8i		−	0.949003i
$535$	1.61691e7	−	3.55251e6i	0.105590	−	0.0231992i
$536$			1.01816e7i			0.0661180i
$537$			1.13503e8i			0.732964i
$538$			2.61211e8i			1.67743i
$539$			3.14107e7i			0.200591i
$540$	2.12998e7	+	9.69453e7i	0.135268	+	0.615667i
$541$	−3.58652e7			−0.226507			−0.113253	−	0.993566i	$-0.536127\pi$
$541$	−3.58652e7			−0.226507			−0.113253	+	0.993566i	$0.536127\pi$
$542$			2.15497e8i			1.35345i
$543$	1.95253e8			1.21955
$544$			6.42493e7i			0.399091i
$545$	4.78419e7	+	2.17751e8i	0.295542	+	1.34515i
$546$		−	2.15446e8i		−	1.32361i
$547$			2.27223e8i			1.38832i	0.719819	+	0.694162i	$0.244225\pi$
$547$			2.27223e8i			1.38832i	−0.719819	+	0.694162i	$0.755775\pi$
$548$	2.89741e8			1.76063
$549$			1.05856e8i			0.639730i
$550$	1.84789e8	−	8.53182e7i	1.11068	−	0.512807i
$551$			8.92130e7i			0.533302i
$552$	−1.73216e7	−	4.21385e6i	−0.102984	−	0.0250531i
$553$			2.60792e8i			1.54212i
$554$	9.61940e7			0.565742
$555$	−2.29202e7	−	1.04320e8i	−0.134073	−	0.610226i
$556$	1.56017e8			0.907708
$557$	4.96082e7			0.287070			0.143535	−	0.989645i	$-0.454153\pi$
$557$	4.96082e7			0.287070			0.143535	+	0.989645i	$0.454153\pi$
$558$		−	1.34314e8i		−	0.773070i
$559$			1.34901e8i			0.772289i
$560$	−1.59651e8	+	3.50769e7i	−0.909091	+	0.199736i
$561$	5.36112e7			0.303646
$562$	−1.64177e8			−0.924918
$563$	9.16230e7			0.513428			0.256714	−	0.966487i	$-0.417360\pi$
$563$	9.16230e7			0.513428			0.256714	+	0.966487i	$0.417360\pi$
$564$	−7.02474e6			−0.0391555
$565$	1.32064e8	−	2.90157e7i	0.732215	−	0.160875i
$566$			918996.i			0.00506832i
$567$	−1.99580e8			−1.09489
$568$			5.39388e6i			0.0294345i
$569$		−	2.70222e8i		−	1.46684i	−0.679775	−	0.733421i	$-0.737923\pi$
$569$		−	2.70222e8i		−	1.46684i	0.679775	−	0.733421i	$-0.262077\pi$
$570$	2.27633e7	+	1.03606e8i	0.122917	+	0.559450i
$571$		−	9.54975e7i		−	0.512960i	−0.966550	−	0.256480i	$-0.917437\pi$
$571$		−	9.54975e7i		−	0.512960i	0.966550	−	0.256480i	$-0.0825628\pi$
$572$	1.39066e8			0.743073
$573$	4.24698e8			2.25744
$574$		−	9.20805e7i		−	0.486891i
$575$	−1.86546e8	+	3.66338e7i	−0.981258	+	0.192698i
$576$	−7.29027e7			−0.381484
$577$			1.07817e8i			0.561254i	0.959817	+	0.280627i	$0.0905424\pi$
$577$			1.07817e8i			0.561254i	−0.959817	+	0.280627i	$0.909458\pi$
$578$		−	2.46435e8i		−	1.27620i
$579$	2.56987e8			1.32396
$580$	−2.77366e8	+	6.09399e7i	−1.42157	+	0.312333i
$581$	−2.17772e7			−0.111038
$582$	−5.27629e8			−2.67645
$583$		−	7.75367e7i		−	0.391293i
$584$	1.38427e7			0.0694997
$585$	1.70177e7	+	7.74553e7i	0.0850027	+	0.386887i
$586$		−	1.00074e8i		−	0.497313i
$587$			2.60601e8i			1.28843i	0.764842	+	0.644217i	$0.222817\pi$
$587$			2.60601e8i			1.28843i	−0.764842	+	0.644217i	$0.777183\pi$
$588$		−	5.21105e7i		−	0.256327i
$589$			8.87553e7i			0.434358i
$590$	9.52771e7	+	4.33650e8i	0.463909	+	2.11146i
$591$	2.60034e8			1.25970
$592$	−1.14490e8			−0.551826
$593$		−	1.33651e8i		−	0.640926i	−0.947261	−	0.320463i	$-0.896161\pi$
$593$		−	1.33651e8i		−	0.640926i	0.947261	−	0.320463i	$-0.103839\pi$
$594$		−	1.72576e8i		−	0.823419i
$595$	−5.20462e7	+	1.14351e7i	−0.247080	+	0.0542859i
$596$		−	2.17223e8i		−	1.02605i
$597$	1.68521e8			0.792012
$598$	−2.60982e8	−	6.34892e7i	−1.22041	−	0.296891i
$599$	−2.54413e8			−1.18375			−0.591874	−	0.806031i	$-0.701612\pi$
$599$	−2.54413e8			−1.18375			−0.591874	+	0.806031i	$0.701612\pi$
$600$	2.07850e7	−	9.59656e6i	0.0962267	−	0.0444285i
$601$	4.10166e7			0.188945			0.0944726	−	0.995527i	$-0.469884\pi$
$601$	4.10166e7			0.188945			0.0944726	+	0.995527i	$0.469884\pi$
$602$		−	2.28221e8i		−	1.04608i
$603$	−7.20053e7			−0.328407
$604$	5.73201e7			0.260133
$605$	4.91358e7	−	1.07956e7i	0.221887	−	0.0487507i
$606$	3.49758e8			1.57163
$607$			5.96674e7i			0.266791i	0.991063	+	0.133395i	$0.0425880\pi$
$607$			5.96674e7i			0.266791i	−0.991063	+	0.133395i	$0.957412\pi$
$608$	1.06892e8			0.475590
$609$		−	3.69928e8i		−	1.63782i
$610$	4.49697e8	−	9.88027e7i	1.98121	−	0.435291i
$611$	7.17590e6			0.0314596
$612$	−2.71281e7			−0.118349
$613$	2.48498e8			1.07880			0.539400	−	0.842050i	$-0.318651\pi$
$613$	2.48498e8			1.07880			0.539400	+	0.842050i	$0.318651\pi$
$614$	−4.17317e8			−1.80285
$615$	2.38458e7	+	1.08533e8i	0.102515	+	0.466593i
$616$	1.59509e7			0.0682408
$617$	−1.89216e8			−0.805569			−0.402785	−	0.915295i	$-0.631958\pi$
$617$	−1.89216e8			−0.805569			−0.402785	+	0.915295i	$0.631958\pi$
$618$	−8.98172e7			−0.380534
$619$		−	4.20153e8i		−	1.77148i	−0.464184	−	0.885739i	$-0.653652\pi$
$619$		−	4.20153e8i		−	1.77148i	0.464184	−	0.885739i	$-0.346348\pi$
$620$	−2.75943e8	+	6.06273e7i	−1.15783	+	0.254386i
$621$	−3.81024e7	+	1.56625e8i	−0.159103	+	0.654014i
$622$		−	1.26536e8i		−	0.525826i
$623$		−	1.20773e8i		−	0.499466i
$624$	2.78697e8			1.14704
$625$	1.58342e8	−	1.85829e8i	0.648569	−	0.761156i
$626$		−	5.57634e8i		−	2.27314i
$627$		−	8.91930e7i		−	0.361850i
$628$	5.97878e7			0.241398
$629$	−3.73237e7			−0.149980
$630$	−2.87899e7	−	1.31036e8i	−0.115138	−	0.524047i
$631$			2.69476e8i			1.07259i	0.844032	+	0.536293i	$0.180176\pi$
$631$			2.69476e8i			1.07259i	−0.844032	+	0.536293i	$0.819824\pi$
$632$	−3.91523e7			−0.155098
$633$		−	9.72427e7i		−	0.383394i
$634$	1.92207e8			0.754226
$635$	7.92096e7	+	3.60519e8i	0.309355	+	1.40802i
$636$			1.28634e8i			0.500016i
$637$			5.32319e7i			0.205946i
$638$	4.93749e8			1.90127
$639$	−3.81463e7			−0.146201
$640$	−9.92091e6	−	4.51546e7i	−0.0378453	−	0.172251i
$641$		−	1.02076e8i		−	0.387569i	−0.981044	−	0.193785i	$-0.937924\pi$
$641$		−	1.02076e8i		−	0.387569i	0.981044	−	0.193785i	$-0.0620763\pi$
$642$	4.77515e7			0.180461
$643$	−2.18502e7			−0.0821906			−0.0410953	−	0.999155i	$-0.513085\pi$
$643$	−2.18502e7			−0.0821906			−0.0410953	+	0.999155i	$0.513085\pi$
$644$	2.13522e8	+	5.19436e7i	0.799437	+	0.194480i
$645$	5.91018e7	+	2.68999e8i	0.220253	+	1.00247i
$646$	3.70682e7			0.137500
$647$		−	4.69217e8i		−	1.73245i	−0.499654	−	0.866225i	$-0.666539\pi$
$647$		−	4.69217e8i		−	1.73245i	0.499654	−	0.866225i	$-0.333461\pi$
$648$		−	2.99627e7i		−	0.110117i
$649$		−	3.73323e8i		−	1.36568i
$650$	3.13163e8	−	1.44589e8i	1.14033	−	0.526497i
$651$		−	3.68030e8i		−	1.33395i
$652$		−	9.96835e7i		−	0.359651i
$653$		−	4.81308e8i		−	1.72856i	−0.503015	−	0.864278i	$-0.667776\pi$
$653$		−	4.81308e8i		−	1.72856i	0.503015	−	0.864278i	$-0.332224\pi$
$654$			6.43074e8i			2.29894i
$655$	−8.11896e7	+	1.78381e7i	−0.288919	+	0.0634783i
$656$	1.19114e8			0.421939
$657$			9.78977e7i			0.345204i
$658$	−1.21400e7			−0.0426127
$659$		−	5.22660e7i		−	0.182626i	−0.995822	−	0.0913132i	$-0.970894\pi$
$659$		−	5.22660e7i		−	0.182626i	0.995822	−	0.0913132i	$-0.0291064\pi$
$660$	2.77304e8	−	6.09263e7i	0.964548	−	0.211921i
$661$			4.83832e8i			1.67529i	0.546214	+	0.837645i	$0.316068\pi$
$661$			4.83832e8i			1.67529i	−0.546214	+	0.837645i	$0.683932\pi$
$662$		−	1.22706e8i		−	0.422954i
$663$	9.08553e7			0.311752
$664$		−	3.26937e6i		−	0.0111676i
$665$	1.90245e7	+	8.65893e7i	0.0646917	+	0.294442i
$666$		−	9.39696e7i		−	0.318101i
$667$	−4.48114e8	−	1.09013e8i	−1.51012	−	0.367368i
$668$		−	1.34502e8i		−	0.451232i
$669$	3.79379e8			1.26705
$670$	6.72078e7	+	3.05894e8i	0.223458	+	1.01706i
$671$	−3.87137e8			−1.28144
$672$	−4.43234e8			−1.46058
$673$			2.44073e8i			0.800710i	0.916360	+	0.400355i	$0.131113\pi$
$673$			2.44073e8i			0.800710i	−0.916360	+	0.400355i	$0.868887\pi$
$674$		−	3.57656e7i		−	0.116812i
$675$	−8.67738e7	−	1.87941e8i	−0.282148	−	0.611098i
$676$	−5.36259e7			−0.173594
$677$	3.54963e8			1.14398			0.571989	−	0.820261i	$-0.306172\pi$
$677$	3.54963e8			1.14398			0.571989	+	0.820261i	$0.306172\pi$
$678$	3.90018e8			1.25140
$679$	−4.40968e8			−1.40863
$680$	−1.71673e6	−	7.81361e6i	−0.00545977	−	0.0248499i
$681$			6.35789e8i			2.01313i
$682$	4.91216e8			1.54853
$683$		−	8.93737e7i		−	0.280509i	−0.990115	−	0.140255i	$-0.955208\pi$
$683$		−	8.93737e7i		−	0.280509i	0.990115	−	0.140255i	$-0.0447922\pi$
$684$			4.51331e7i			0.141035i
$685$	−5.90191e8	+	1.29671e8i	−1.83620	+	0.403432i
$686$		−	4.84732e8i		−	1.50151i
$687$	−2.63285e8			−0.811998
$688$	2.95222e8			0.906533
$689$		−	1.31402e8i		−	0.401739i
$690$	−5.48226e8	−	1.22615e7i	−1.66883	−	0.0373248i
$691$	−2.91710e7			−0.0884131			−0.0442066	−	0.999022i	$-0.514076\pi$
$691$	−2.91710e7			−0.0884131			−0.0442066	+	0.999022i	$0.514076\pi$
$692$			4.36280e8i			1.31658i
$693$			1.12807e8i			0.338951i
$694$	−4.20213e8			−1.25716
$695$	−3.17800e8	+	6.98236e7i	−0.946671	+	0.207993i
$696$	5.55367e7			0.164722
$697$	3.88310e7			0.114678
$698$			8.94476e8i			2.63028i
$699$	−4.18421e8			−1.22513
$700$	−2.56213e8	+	1.18296e8i	−0.746978	+	0.344885i
$701$			2.22384e8i			0.645579i	0.946471	+	0.322789i	$0.104621\pi$
$701$			2.22384e8i			0.645579i	−0.946471	+	0.322789i	$0.895379\pi$
$702$		−	2.92466e8i		−	0.845403i
$703$			6.20955e7i			0.178729i
$704$		−	2.66621e8i		−	0.764147i
$705$	1.43091e7	−	3.14385e6i	0.0408362	−	0.00897211i
$706$	−3.21433e8			−0.913432
$707$	2.92312e8			0.827158
$708$			6.19345e8i			1.74515i
$709$		−	4.55388e8i		−	1.27774i	−0.769314	−	0.638871i	$-0.779402\pi$
$709$		−	4.55388e8i		−	1.27774i	0.769314	−	0.638871i	$-0.220598\pi$
$710$	3.56047e7	+	1.62053e8i	0.0994792	+	0.452776i
$711$		−	2.76891e8i		−	0.770370i
$712$	1.81315e7			0.0502334
$713$	−4.45814e8	−	1.08454e8i	−1.22994	−	0.299210i
$714$	−1.53706e8			−0.422276
$715$	−2.83271e8	+	6.22374e7i	−0.774969	+	0.170268i
$716$	2.10049e8			0.572245
$717$			3.68729e8i			1.00035i
$718$	−9.95365e8			−2.68911
$719$	−3.15095e8			−0.847726			−0.423863	−	0.905726i	$-0.639326\pi$
$719$	−3.15095e8			−0.847726			−0.423863	+	0.905726i	$0.639326\pi$
$720$	1.69506e8	−	3.72421e7i	0.454138	−	0.0997784i
$721$	−7.50651e7			−0.200277
$722$			4.62076e8i			1.22773i
$723$	6.66543e7			0.176365
$724$		−	3.61338e8i		−	0.952133i
$725$	5.37710e8	−	2.48265e8i	1.41102	−	0.651479i
$726$	1.45111e8			0.379218
$727$	5.80063e8			1.50964			0.754818	−	0.655934i	$-0.227725\pi$
$727$	5.80063e8			1.50964			0.754818	+	0.655934i	$0.227725\pi$
$728$	2.70321e7			0.0700626
$729$	−1.00899e8			−0.260439
$730$	4.15890e8	−	9.13750e7i	1.06908	−	0.234887i
$731$	9.62424e7			0.246385
$732$	6.42263e8			1.63749
$733$	−5.87417e8			−1.49154			−0.745769	−	0.666204i	$-0.767918\pi$
$733$	−5.87417e8			−1.49154			−0.745769	+	0.666204i	$0.767918\pi$
$734$			6.51663e8i			1.64792i
$735$	2.33215e7	+	1.06147e8i	0.0587348	+	0.267329i
$736$	−1.30615e8	+	5.36912e8i	−0.327612	+	1.34670i
$737$		−	2.63339e8i		−	0.657829i
$738$			9.77645e7i			0.243227i
$739$	−5.95450e8			−1.47541			−0.737703	−	0.675125i	$-0.764090\pi$
$739$	−5.95450e8			−1.47541			−0.737703	+	0.675125i	$0.764090\pi$
$740$	−1.93057e8	+	4.24164e7i	−0.476420	+	0.104674i
$741$		−	1.51156e8i		−	0.371510i
$742$			2.22301e8i			0.544165i
$743$	−3.26459e8			−0.795906			−0.397953	−	0.917406i	$-0.630279\pi$
$743$	−3.26459e8			−0.795906			−0.397953	+	0.917406i	$0.630279\pi$
$744$	5.52518e7			0.134161
$745$	9.72160e7	+	4.42475e8i	0.235109	+	1.07009i
$746$			6.88137e8i			1.65752i
$747$	2.31214e7			0.0554693
$748$		−	9.92135e7i		−	0.237064i
$749$	3.99086e7			0.0949775
$750$	5.61116e8	−	4.25519e8i	1.33005	−	1.00864i
$751$			2.93923e8i			0.693927i	0.937879	+	0.346963i	$0.112787\pi$
$751$			2.93923e8i			0.693927i	−0.937879	+	0.346963i	$0.887213\pi$
$752$		−	1.57040e7i		−	0.0369281i
$753$	−4.88413e8			−1.14394
$754$	8.36760e8			1.95203
$755$	−1.16759e8	+	2.56530e7i	−0.271299	+	0.0596071i
$756$			2.39280e8i			0.553785i
$757$	3.49327e8			0.805276			0.402638	−	0.915359i	$-0.368093\pi$
$757$	3.49327e8			0.805276			0.402638	+	0.915359i	$0.368093\pi$
$758$	−6.85851e8			−1.57479
$759$	4.48013e8	+	1.08989e8i	1.02463	+	0.249262i
$760$	−1.29995e7	+	2.85612e6i	−0.0296133	+	0.00650632i
$761$	−2.19514e8			−0.498090			−0.249045	−	0.968492i	$-0.580117\pi$
$761$	−2.19514e8			−0.498090			−0.249045	+	0.968492i	$0.580117\pi$
$762$			1.06471e9i			2.40638i
$763$			5.37451e8i			1.20995i
$764$		−	7.85952e8i		−	1.76245i
$765$	5.52589e7	−	1.21409e7i	0.123429	−	0.0271186i
$766$			3.43966e8i			0.765296i
$767$		−	6.32673e8i		−	1.40214i
$768$		−	6.05669e8i		−	1.33706i
$769$			3.31415e7i			0.0728775i	0.999336	+	0.0364388i	$0.0116014\pi$
$769$			3.31415e7i			0.0728775i	−0.999336	+	0.0364388i	$0.988399\pi$
$770$	4.79229e8	−	1.05291e8i	1.04971	−	0.230632i
$771$	−8.26868e8			−1.80415
$772$		−	4.75583e8i		−	1.03365i
$773$	−8.30464e7			−0.179797			−0.0898984	−	0.995951i	$-0.528654\pi$
$773$	−8.30464e7			−0.179797			−0.0898984	+	0.995951i	$0.528654\pi$
$774$			2.42309e8i			0.522572i
$775$	5.34951e8	−	2.46991e8i	1.14924	−	0.530610i
$776$		−	6.62018e7i		−	0.141672i
$777$		−	2.57484e8i		−	0.548892i
$778$	7.58698e8			1.61113
$779$		−	6.46032e7i		−	0.136660i
$780$	4.69948e8	−	1.03252e8i	0.990299	−	0.217578i
$781$		−	1.39509e8i		−	0.292853i
$782$	−4.52951e7	+	1.86192e8i	−0.0947177	+	0.389351i
$783$		−	5.02173e8i		−	1.04609i
$784$	1.16495e8			0.241745
$785$	−1.21785e8	+	2.67574e7i	−0.251760	+	0.0553140i
$786$	−2.39774e8			−0.493781
$787$	8.92867e8			1.83173			0.915867	−	0.401481i	$-0.131505\pi$
$787$	8.92867e8			1.83173			0.915867	+	0.401481i	$0.131505\pi$
$788$		−	4.81222e8i		−	0.983483i
$789$		−	3.87795e8i		−	0.789534i
$790$	−1.17629e9	+	2.58442e8i	−2.38579	+	0.524182i
$791$	3.25960e8			0.658619
$792$	−1.69356e7			−0.0340898
$793$	−6.56084e8			−1.31565
$794$	−5.25062e8			−1.04894
$795$	−5.75688e7	−	2.62022e8i	−0.114574	−	0.521479i
$796$		−	3.11867e8i		−	0.618345i
$797$	4.10301e8			0.810452			0.405226	−	0.914217i	$-0.367193\pi$
$797$	4.10301e8			0.810452			0.405226	+	0.914217i	$0.367193\pi$
$798$			2.55721e8i			0.503219i
$799$		−	5.11950e6i		−	0.0100366i
$800$	−2.97461e8	−	6.44263e8i	−0.580978	−	1.25833i
$801$			1.28228e8i			0.249509i
$802$	6.79035e7			0.131634
$803$	−3.58033e8			−0.691476
$804$			4.36881e8i			0.840612i
$805$	−4.58182e8	−	1.02476e7i	−0.878315	−	0.0196442i
$806$	8.32467e8			1.58987
$807$		−	7.59917e8i		−	1.44592i
$808$			4.38843e7i			0.0831908i
$809$	8.05042e8			1.52045			0.760226	−	0.649658i	$-0.225088\pi$
$809$	8.05042e8			1.52045			0.760226	+	0.649658i	$0.225088\pi$
$810$	−1.97782e8	−	9.00196e8i	−0.372161	−	1.69388i
$811$	−9.50793e8			−1.78247			−0.891237	−	0.453538i	$-0.850162\pi$
$811$	−9.50793e8			−1.78247			−0.891237	+	0.453538i	$0.850162\pi$
$812$	−6.84594e8			−1.27869
$813$		−	6.26927e8i		−	1.16666i
$814$	3.43667e8			0.637185
$815$	4.46124e7	+	2.03051e8i	0.0824105	+	0.375088i
$816$		−	1.98831e8i		−	0.365943i
$817$		−	1.60119e8i		−	0.293613i
$818$			2.79919e8i			0.511415i
$819$			1.91175e8i			0.348000i
$820$	2.00853e8	−	4.41294e7i	0.364281	−	0.0800362i
$821$	8.43345e8			1.52397			0.761984	−	0.647596i	$-0.224225\pi$
$821$	8.43345e8			1.52397			0.761984	+	0.647596i	$0.224225\pi$
$822$	−1.74299e9			−3.13818
$823$		−	3.80988e8i		−	0.683458i	−0.939799	−	0.341729i	$-0.888987\pi$
$823$		−	3.80988e8i		−	0.683458i	0.939799	−	0.341729i	$-0.111013\pi$
$824$		−	1.12694e7i		−	0.0201428i
$825$	−5.37590e8	+	2.48209e8i	−0.957391	+	0.442034i
$826$			1.07033e9i			1.89924i
$827$	7.29184e8			1.28920			0.644601	−	0.764519i	$-0.277024\pi$
$827$	7.29184e8			1.28920			0.644601	+	0.764519i	$0.277024\pi$
$828$	−2.26702e8	−	5.51500e7i	−0.399360	−	0.0971526i
$829$	−9.06586e8			−1.59128			−0.795638	−	0.605772i	$-0.792864\pi$
$829$	−9.06586e8			−1.59128			−0.795638	+	0.605772i	$0.792864\pi$
$830$	−2.15809e7	−	9.82246e7i	−0.0377429	−	0.171785i
$831$	−2.79849e8			−0.487664
$832$		−	4.51845e8i		−	0.784548i
$833$	3.79772e7			0.0657035
$834$	−9.38544e8			−1.61792
$835$	6.01950e7	+	2.73975e8i	0.103395	+	0.470600i
$836$	−1.65062e8			−0.282506
$837$		−	4.99597e8i		−	0.852007i
$838$	4.48077e8			0.761414
$839$			3.65557e8i			0.618969i	0.950905	+	0.309484i	$0.100156\pi$
$839$			3.65557e8i			0.618969i	−0.950905	+	0.309484i	$0.899844\pi$
$840$	5.39034e7	−	1.18431e7i	0.0909450	−	0.0199815i
$841$	8.41921e8			1.41541
$842$	−1.15938e9			−1.94217
$843$	4.77626e8			0.797270
$844$	−1.79958e8			−0.299326
$845$	1.09234e8	−	2.39997e7i	0.181045	−	0.0397774i
$846$	1.28893e7			0.0212872
$847$	1.21277e8			0.199585
$848$	−2.87565e8			−0.471572
$849$		−	2.67356e6i		−	0.00436884i
$850$	−1.03154e8	−	2.23420e8i	−0.167970	−	0.363801i
$851$	−3.11903e8	−	7.58770e7i	−0.506094	−	0.123118i
$852$			2.31447e8i			0.374225i
$853$			3.81739e8i			0.615063i	0.951538	+	0.307532i	$0.0995030\pi$
$853$			3.81739e8i			0.615063i	−0.951538	+	0.307532i	$0.900497\pi$
$854$	1.10994e9			1.78208
$855$	−2.01989e7	−	9.19344e7i	−0.0323168	−	0.147089i
$856$			5.99140e6i			0.00955229i
$857$		−	1.15806e9i		−	1.83988i	−0.392063	−	0.919939i	$-0.628238\pi$
$857$		−	1.15806e9i		−	1.83988i	0.392063	−	0.919939i	$-0.371762\pi$
$858$	−8.36573e8			−1.32447
$859$	−3.72449e7			−0.0587608			−0.0293804	−	0.999568i	$-0.509353\pi$
$859$	−3.72449e7			−0.0587608			−0.0293804	+	0.999568i	$0.509353\pi$
$860$	4.97813e8	−	1.09374e8i	0.782657	−	0.171957i
$861$			2.67882e8i			0.419695i
$862$	1.14688e9			1.79059
$863$			2.73555e8i			0.425611i	0.977095	+	0.212806i	$0.0682601\pi$
$863$			2.73555e8i			0.425611i	−0.977095	+	0.212806i	$0.931740\pi$
$864$	−6.01684e8			−0.932883
$865$	−1.95253e8	−	8.88685e8i	−0.301682	−	1.37309i
$866$		−	1.14004e9i		−	1.75536i
$867$			7.16932e8i			1.10007i
$868$	−6.81081e8			−1.04145
$869$	1.01265e9			1.54312
$870$	1.66854e9	−	3.66595e8i	2.53384	−	0.556709i
$871$		−	4.46283e8i		−	0.675392i
$872$	−8.06867e7			−0.121689
$873$	4.68188e8			0.703684
$874$	3.09768e8	+	7.53575e7i	0.463983	+	0.112874i
$875$	4.68955e8	−	3.55629e8i	0.700014	−	0.530852i
$876$	5.93979e8			0.883607
$877$			1.04129e9i			1.54373i	0.635785	+	0.771866i	$0.280677\pi$
$877$			1.04129e9i			1.54373i	−0.635785	+	0.771866i	$0.719323\pi$
$878$			5.80782e8i			0.858083i
$879$			2.91137e8i			0.428678i
$880$	1.36203e8	+	6.19921e8i	0.199865	+	0.909679i
$881$		−	1.13366e9i		−	1.65789i	−0.559329	−	0.828946i	$-0.688941\pi$
$881$		−	1.13366e9i		−	1.65789i	0.559329	−	0.828946i	$-0.311059\pi$
$882$			9.56150e7i			0.139354i
$883$			1.24792e9i			1.81261i	0.422626	+	0.906304i	$0.361108\pi$
$883$			1.24792e9i			1.81261i	−0.422626	+	0.906304i	$0.638892\pi$
$884$		−	1.68138e8i		−	0.243393i
$885$	−2.77181e8	−	1.26158e9i	−0.399884	−	1.82006i
$886$	6.81749e8			0.980220
$887$			1.92360e8i			0.275641i	0.990457	+	0.137820i	$0.0440097\pi$
$887$			1.92360e8i			0.275641i	−0.990457	+	0.137820i	$0.955990\pi$
$888$	3.86556e7			0.0552044
$889$			8.89833e8i			1.26649i
$890$	5.44740e8	−	1.19685e8i	0.772715	−	0.169773i
$891$			7.74965e8i			1.09559i
$892$		−	7.02083e8i		−	0.989222i
$893$	−8.51732e6			−0.0119605
$894$			1.30674e9i			1.82885i
$895$	−4.27862e8	+	9.40054e7i	−0.596808	+	0.131124i
$896$		−	1.11451e8i		−	0.154938i
$897$	7.59251e8	+	1.84704e8i	1.05198	+	0.255917i
$898$		−	2.99679e8i		−	0.413835i
$899$	1.42937e9			1.96728
$900$	2.72029e8	−	1.25598e8i	0.373154	−	0.172288i
$901$	−9.37461e7			−0.128168
$902$	−3.57546e8			−0.487206
$903$			6.63944e8i			0.901712i
$904$			4.89358e7i			0.0662401i
$905$	1.61713e8	+	7.36031e8i	0.218172	+	0.993002i
$906$	−3.44819e8			−0.463667
$907$	8.35479e8			1.11973			0.559866	−	0.828584i	$-0.310853\pi$
$907$	8.35479e8			1.11973			0.559866	+	0.828584i	$0.310853\pi$
$908$	1.17660e9			1.57170
$909$	−3.10356e8			−0.413208
$910$	8.12152e8	−	1.78438e8i	1.07774	−	0.236789i
$911$		−	1.21770e9i		−	1.61059i	−0.592873	−	0.805296i	$-0.702006\pi$
$911$		−	1.21770e9i		−	1.61059i	0.592873	−	0.805296i	$-0.297994\pi$
$912$	−3.30795e8			−0.436089
$913$			8.45601e7i			0.111110i
$914$			9.71183e8i			1.27193i
$915$	−1.30826e9	+	2.87438e8i	−1.70778	+	0.375216i
$916$			4.87238e8i			0.633949i
$917$	−2.00392e8			−0.259880
$918$	−2.08654e8			−0.269711
$919$			7.61659e8i			0.981328i	0.871349	+	0.490664i	$0.163246\pi$
$919$			7.61659e8i			0.981328i	−0.871349	+	0.490664i	$0.836754\pi$
$920$	1.53846e6	−	6.87861e7i	0.00197571	−	0.0883359i
$921$	1.21406e9			1.55404
$922$			1.24038e9i			1.58257i
$923$		−	2.36427e8i		−	0.300672i
$924$	6.84440e8			0.867600
$925$	3.74266e8	−	1.72801e8i	0.472884	−	0.218334i
$926$	3.17836e8			0.400286
$927$	7.96987e7			0.100049
$928$		−	1.72145e9i		−	2.15402i
$929$	7.52888e8			0.939038			0.469519	−	0.882922i	$-0.344427\pi$
$929$	7.52888e8			0.939038			0.469519	+	0.882922i	$0.344427\pi$
$930$	1.65998e9	−	3.64714e8i	2.06374	−	0.453423i
$931$		−	6.31828e7i		−	0.0782978i
$932$			7.74334e8i			0.956490i
$933$			3.68120e8i			0.453256i
$934$		−	1.63375e9i		−	2.00514i
$935$	4.44020e7	+	2.02094e8i	0.0543210	+	0.247240i
$936$	−2.87008e7			−0.0349999
$937$	−9.32956e8			−1.13408			−0.567038	−	0.823692i	$-0.691911\pi$
$937$	−9.32956e8			−1.13408			−0.567038	+	0.823692i	$0.691911\pi$
$938$			7.55006e8i			0.914834i
$939$			1.62228e9i			1.95942i
$940$	−5.81804e6	−	2.64806e7i	−0.00700476	−	0.0318819i
$941$		−	3.62166e8i		−	0.434649i	−0.976099	−	0.217325i	$-0.930267\pi$
$941$		−	3.62166e8i		−	0.434649i	0.976099	−	0.217325i	$-0.0697330\pi$
$942$	−3.59664e8			−0.430273
$943$	3.24499e8	+	7.89413e7i	0.386971	+	0.0941389i
$944$	−1.38456e9			−1.64587
$945$	−1.07087e8	−	4.87405e8i	−0.126895	−	0.577556i
$946$	−8.86176e8			−1.04676
$947$			6.78012e8i			0.798339i	0.916877	+	0.399169i	$0.130701\pi$
$947$			6.78012e8i			0.798339i	−0.916877	+	0.399169i	$0.869299\pi$
$948$	−1.67999e9			−1.97189
$949$	−6.06762e8			−0.709936
$950$	−3.71703e8	+	1.71618e8i	−0.433536	+	0.200167i
$951$	−5.59172e8			−0.650135
$952$		−	1.92855e7i		−	0.0223522i
$953$	8.74417e8			1.01028			0.505138	−	0.863039i	$-0.331442\pi$
$953$	8.74417e8			1.01028			0.505138	+	0.863039i	$0.331442\pi$
$954$		−	2.36024e8i		−	0.271838i
$955$	3.51745e8	+	1.60095e9i	0.403848	+	1.83810i
$956$	6.82375e8			0.780997
$957$	−1.43642e9			−1.63888
$958$	2.76149e8			0.314085
$959$	−1.45671e9			−1.65164
$960$	−1.97959e8	−	9.01001e8i	−0.223749	−	1.01838i
$961$	5.34535e8			0.602291
$962$	5.82416e8			0.654196
$963$	−4.23720e7			−0.0474461
$964$		−	1.23351e8i		−	0.137693i
$965$	2.12842e8	+	9.68744e8i	0.236852	+	1.07802i
$966$	−1.28448e9	−	3.12475e8i	−1.42493	−	0.346645i
$967$			1.39441e9i			1.54209i	0.636781	+	0.771045i	$0.280266\pi$
$967$			1.39441e9i			1.54209i	−0.636781	+	0.771045i	$0.719734\pi$
$968$			1.82071e7i			0.0200731i
$969$	−1.07839e8			−0.118524
$970$	−4.36994e8	−	1.98896e9i	−0.478807	−	2.17927i
$971$		−	6.57817e8i		−	0.718534i	−0.933235	−	0.359267i	$-0.883027\pi$
$971$		−	6.57817e8i		−	0.718534i	0.933235	−	0.359267i	$-0.116973\pi$
$972$		−	7.06801e8i		−	0.769660i
$973$	−7.84392e8			−0.851520
$974$	2.08799e9			2.25970
$975$	−9.11057e8	+	4.20641e8i	−0.982951	+	0.453835i
$976$			1.43580e9i			1.54434i
$977$	1.65117e9			1.77055			0.885274	−	0.465071i	$-0.153971\pi$
$977$	1.65117e9			1.77055			0.885274	+	0.465071i	$0.153971\pi$
$978$			5.99663e8i			0.641049i
$979$	−4.68958e8			−0.499789
$980$	1.96437e8	−	4.31591e7i	0.208711	−	0.0458558i
$981$		−	5.70627e8i		−	0.604430i
$982$		−	4.17372e8i		−	0.440746i
$983$	−1.28888e9			−1.35691			−0.678455	−	0.734642i	$-0.737350\pi$
$983$	−1.28888e9			−1.35691			−0.678455	+	0.734642i	$0.737350\pi$
$984$	−4.02167e7			−0.0422105
$985$	2.15366e8	+	9.80231e8i	0.225356	+	1.02570i
$986$		−	5.96970e8i		−	0.622761i
$987$	3.53177e7			0.0367317
$988$	−2.79731e8			−0.290048
$989$	8.04270e8	+	1.95655e8i	0.831406	+	0.202257i
$990$	−5.08811e8	+	1.11791e8i	−0.524385	+	0.115213i
$991$	−1.35566e9			−1.39293			−0.696467	−	0.717588i	$-0.745246\pi$
$991$	−1.35566e9			−1.39293			−0.696467	+	0.717588i	$0.745246\pi$
$992$		−	1.71262e9i		−	1.75439i
$993$			3.56979e8i			0.364582i
$994$			3.99980e8i			0.407267i
$995$	1.39573e8	+	6.35262e8i	0.141688	+	0.644887i
$996$		−	1.40286e8i		−	0.141983i
$997$		−	1.25273e8i		−	0.126408i	−0.998001	−	0.0632039i	$-0.979868\pi$
$997$		−	1.25273e8i		−	0.126408i	0.998001	−	0.0632039i	$-0.0201318\pi$
$998$		−	2.45538e9i		−	2.47017i
$999$		−	3.49531e8i		−	0.350581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.c.c.114.16	yes	68
5.4	even	2	inner	115.7.c.c.114.53	yes	68
23.22	odd	2	inner	115.7.c.c.114.54	yes	68
115.114	odd	2	inner	115.7.c.c.114.15	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.c.c.114.15	✓	68	115.114	odd	2	inner
115.7.c.c.114.16	yes	68	1.1	even	1	trivial
115.7.c.c.114.53	yes	68	5.4	even	2	inner
115.7.c.c.114.54	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)

\(f(q)\)	\(=\)	\(q+11.1327i q^{2} -32.3873i q^{3} -59.9364 q^{4} +(122.088 - 26.8239i) q^{5} +360.557 q^{6} +301.337 q^{7} +45.2393i q^{8} -319.938 q^{9} +O(q^{10})\)	\(q+11.1327i q^{2} -32.3873i q^{3} -59.9364 q^{4} +(122.088 - 26.8239i) q^{5} +360.557 q^{6} +301.337 q^{7} +45.2393i q^{8} -319.938 q^{9} +(298.622 + 1359.17i) q^{10} -1170.08i q^{11} +1941.18i q^{12} -1982.95i q^{13} +3354.69i q^{14} +(-868.755 - 3954.10i) q^{15} -4339.56 q^{16} -1414.70 q^{17} -3561.77i q^{18} +2353.63i q^{19} +(-7317.51 + 1607.73i) q^{20} -9759.51i q^{21} +13026.2 q^{22} +(-11822.2 - 2876.00i) q^{23} +1465.18 q^{24} +(14186.0 - 6549.75i) q^{25} +22075.5 q^{26} -13248.4i q^{27} -18061.1 q^{28} +37904.4 q^{29} +(44019.7 - 9671.56i) q^{30} +37709.9 q^{31} -45415.6i q^{32} -37895.9 q^{33} -15749.3i q^{34} +(36789.7 - 8083.05i) q^{35} +19175.9 q^{36} +26382.8 q^{37} -26202.2 q^{38} -64222.5 q^{39} +(1213.49 + 5523.17i) q^{40} -27448.3 q^{41} +108649. q^{42} -68030.4 q^{43} +70130.6i q^{44} +(-39060.6 + 8582.00i) q^{45} +(32017.5 - 131613. i) q^{46} +3618.80i q^{47} +140547. i q^{48} -26844.8 q^{49} +(72916.3 + 157928. i) q^{50} +45818.2i q^{51} +118851. i q^{52} +66265.9 q^{53} +147490. q^{54} +(-31386.3 - 142853. i) q^{55} +13632.3i q^{56} +76227.8 q^{57} +421977. i q^{58} +319056. q^{59} +(52070.0 + 236994. i) q^{60} -330862. i q^{61} +419812. i q^{62} -96409.4 q^{63} +227865. q^{64} +(-53190.5 - 242095. i) q^{65} -421883. i q^{66} +225060. q^{67} +84791.7 q^{68} +(-93145.9 + 382890. i) q^{69} +(89985.9 + 409567. i) q^{70} +119230. q^{71} -14473.8i q^{72} -305989. i q^{73} +293712. i q^{74} +(-212129. - 459445. i) q^{75} -141068. i q^{76} -352590. i q^{77} -714968. i q^{78} +865450. i q^{79} +(-529808. + 116404. i) q^{80} -662316. q^{81} -305573. i q^{82} -72268.3 q^{83} +584949. i q^{84} +(-172717. + 37947.7i) q^{85} -757361. i q^{86} -1.22762e6i q^{87} +52933.8 q^{88} -400790. i q^{89} +(-95540.6 - 434849. i) q^{90} -597537. i q^{91} +(708580. + 172377. i) q^{92} -1.22132e6i q^{93} -40286.9 q^{94} +(63133.6 + 287350. i) q^{95} -1.47089e6 q^{96} -1.46337e6 q^{97} -298854. i q^{98} +374355. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) \) 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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