LMFDB - Embedded newform 95.11.j.a.31.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,11,Mod(31,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.31"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	95.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$60.3589390040$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	95.31
Dual form			95.11.j.a.46.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-46.8725 + 27.0619i) q^{2} +(-321.755 + 185.765i) q^{3} +(952.688 - 1650.10i) q^{4} +(-698.771 - 1210.31i) q^{5} +(10054.3 - 17414.6i) q^{6} +6325.06 q^{7} +47703.3i q^{8} +(39493.1 - 68404.0i) q^{9} +(65506.3 + 37820.1i) q^{10} -162840. q^{11} +707906. i q^{12} +(398140. + 229866. i) q^{13} +(-296472. + 171168. i) q^{14} +(449666. + 259615. i) q^{15} +(-315388. - 546268. i) q^{16} +(332069. + 575161. i) q^{17} +4.27502e6i q^{18} +(-1.53044e6 + 1.94649e6i) q^{19} -2.66284e6 q^{20} +(-2.03512e6 + 1.17498e6i) q^{21} +(7.63273e6 - 4.40676e6i) q^{22} +(509906. - 883184. i) q^{23} +(-8.86163e6 - 1.53488e7i) q^{24} +(-976562. + 1.69146e6i) q^{25} -2.48824e7 q^{26} +7.40725e6i q^{27} +(6.02581e6 - 1.04370e7i) q^{28} +(1.64911e6 + 952114. i) q^{29} -2.81027e7 q^{30} -1.82234e7i q^{31} +(-1.27377e7 - 7.35413e6i) q^{32} +(5.23947e7 - 3.02501e7i) q^{33} +(-3.11298e7 - 1.79728e7i) q^{34} +(-4.41977e6 - 7.65527e6i) q^{35} +(-7.52491e7 - 1.30335e8i) q^{36} -1.00430e8i q^{37} +(1.90597e7 - 1.32653e8i) q^{38} -1.70805e8 q^{39} +(5.77357e7 - 3.33337e7i) q^{40} +(-5.50319e7 + 3.17727e7i) q^{41} +(6.35941e7 - 1.10148e8i) q^{42} +(5.08176e7 + 8.80186e7i) q^{43} +(-1.55136e8 + 2.68703e8i) q^{44} -1.10386e8 q^{45} +5.51961e7i q^{46} +(-1.10340e8 + 1.91114e8i) q^{47} +(2.02955e8 + 1.17176e8i) q^{48} -2.42469e8 q^{49} -1.05710e8i q^{50} +(-2.13690e8 - 1.23374e8i) q^{51} +(7.58607e8 - 4.37982e8i) q^{52} +(-1.68826e8 - 9.74716e7i) q^{53} +(-2.00454e8 - 3.47197e8i) q^{54} +(1.13788e8 + 1.97087e8i) q^{55} +3.01726e8i q^{56} +(1.30835e8 - 9.10596e8i) q^{57} -1.03064e8 q^{58} +(5.52623e8 - 3.19057e8i) q^{59} +(8.56784e8 - 4.94664e8i) q^{60} +(-5.50860e8 + 9.54118e8i) q^{61} +(4.93159e8 + 8.54176e8i) q^{62} +(2.49796e8 - 4.32659e8i) q^{63} +1.44198e9 q^{64} -6.42496e8i q^{65} +(-1.63725e9 + 2.83580e9i) q^{66} +(-3.97790e8 - 2.29664e8i) q^{67} +1.26543e9 q^{68} +3.78892e8i q^{69} +(4.14332e8 + 2.39214e8i) q^{70} +(-2.49438e9 + 1.44013e9i) q^{71} +(3.26310e9 + 1.88395e9i) q^{72} +(4.06532e8 + 7.04134e8i) q^{73} +(2.71783e9 + 4.70742e9i) q^{74} -7.25646e8i q^{75} +(1.75389e9 + 4.37978e9i) q^{76} -1.02998e9 q^{77} +(8.00605e9 - 4.62230e9i) q^{78} +(2.49622e9 - 1.44119e9i) q^{79} +(-4.40768e8 + 7.63433e8i) q^{80} +(9.56014e8 + 1.65587e9i) q^{81} +(1.71966e9 - 2.97853e9i) q^{82} -3.75075e9 q^{83} +4.47755e9i q^{84} +(4.64081e8 - 8.03812e8i) q^{85} +(-4.76389e9 - 2.75044e9i) q^{86} -7.07480e8 q^{87} -7.76802e9i q^{88} +(-9.25473e9 - 5.34322e9i) q^{89} +(5.17409e9 - 2.98726e9i) q^{90} +(2.51826e9 + 1.45392e9i) q^{91} +(-9.71563e8 - 1.68280e9i) q^{92} +(3.38528e9 + 5.86347e9i) q^{93} -1.19440e10i q^{94} +(3.42528e9 + 4.92146e8i) q^{95} +5.46457e9 q^{96} +(5.20779e9 - 3.00672e9i) q^{97} +(1.13651e10 - 6.56166e9i) q^{98} +(-6.43106e9 + 1.11389e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9} + 93750 q^{10} + 418144 q^{11} - 1256574 q^{13} + 612480 q^{14} - 20575630 q^{16} + 3635834 q^{17} + 10572814 q^{19} + 8494308 q^{21}+ \cdots - 8878413234 q^{99}+O(q^{100}) $ 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−46.8725	+	27.0619i	−1.46477	+	0.845683i	−0.999226	−	0.0393438i	$-0.987473\pi$
$2$	−46.8725	+	27.0619i	−1.46477	+	0.845683i	−0.465540	+	0.885027i	$0.654140\pi$
$3$	−321.755	+	185.765i	−1.32410	+	0.764467i	−0.984379	−	0.176061i	$-0.943664\pi$
$3$	−321.755	+	185.765i	−1.32410	+	0.764467i	−0.339716	+	0.940528i	$0.610331\pi$
$4$	952.688	−	1650.10i	0.930359	−	1.61143i
$5$	−698.771	−	1210.31i	−0.223607	−	0.387298i
$5$	−698.771	−	1210.31i	−0.223607	−	0.387298i
$6$	10054.3	−	17414.6i	1.29299	−	2.23953i
$7$	6325.06			0.376335			0.188167	−	0.982137i	$-0.439745\pi$
$7$	6325.06			0.376335			0.188167	+	0.982137i	$0.439745\pi$
$8$			47703.3i			1.45579i
$9$	39493.1	−	68404.0i	0.668818	−	1.15843i
$10$	65506.3	+	37820.1i	0.655063	+	0.378201i
$11$	−162840.			−1.01111			−0.505555	−	0.862794i	$-0.668712\pi$
$11$	−162840.			−1.01111			−0.505555	+	0.862794i	$0.668712\pi$
$12$			707906.i			2.84491i
$13$	398140.	+	229866.i	1.07231	+	0.619097i	0.928811	−	0.370554i	$-0.120832\pi$
$13$	398140.	+	229866.i	1.07231	+	0.619097i	0.143496	+	0.989651i	$0.454165\pi$
$14$	−296472.	+	171168.i	−0.551243	+	0.318260i
$15$	449666.	+	259615.i	0.592153	+	0.341880i
$16$	−315388.	−	546268.i	−0.300778	−	0.520962i
$17$	332069.	+	575161.i	0.233875	+	0.405084i	0.958945	−	0.283592i	$-0.0915260\pi$
$17$	332069.	+	575161.i	0.233875	+	0.405084i	−0.725070	+	0.688675i	$0.758193\pi$
$18$			4.27502e6i			2.26243i
$19$	−1.53044e6	+	1.94649e6i	−0.618084	+	0.786112i
$19$	−1.53044e6	+	1.94649e6i	−0.618084	+	0.786112i
$20$	−2.66284e6			−0.832139
$21$	−2.03512e6	+	1.17498e6i	−0.498303	+	0.287696i
$22$	7.63273e6	−	4.40676e6i	1.48104	−	0.855079i
$23$	509906.	−	883184.i	0.0792230	−	0.137218i	−0.823692	−	0.567038i	$-0.808089\pi$
$23$	509906.	−	883184.i	0.0792230	−	0.137218i	0.902915	+	0.429819i	$0.141423\pi$
$24$	−8.86163e6	−	1.53488e7i	−1.11290	−	1.92760i
$25$	−976562.	+	1.69146e6i	−0.100000	+	0.173205i
$26$	−2.48824e7			−2.09424
$27$			7.40725e6i			0.516224i
$28$	6.02581e6	−	1.04370e7i	0.350127	−	0.606437i
$29$	1.64911e6	+	952114.i	0.0804007	+	0.0464194i	0.539661	−	0.841882i	$-0.318552\pi$
$29$	1.64911e6	+	952114.i	0.0804007	+	0.0464194i	−0.459261	+	0.888302i	$0.651886\pi$
$30$	−2.81027e7			−1.15649
$31$		−	1.82234e7i		−	0.636533i	−0.948001	−	0.318266i	$-0.896899\pi$
$31$		−	1.82234e7i		−	0.636533i	0.948001	−	0.318266i	$-0.103101\pi$
$32$	−1.27377e7	−	7.35413e6i	−0.379614	−	0.219170i
$33$	5.23947e7	−	3.02501e7i	1.33881	−	0.772960i
$34$	−3.11298e7	−	1.79728e7i	−0.685145	−	0.395568i
$35$	−4.41977e6	−	7.65527e6i	−0.0841511	−	0.145754i
$36$	−7.52491e7	−	1.30335e8i	−1.24448	−	2.15551i
$37$		−	1.00430e8i		−	1.44829i	−0.689646	−	0.724147i	$-0.742234\pi$
$37$		−	1.00430e8i		−	1.44829i	0.689646	−	0.724147i	$-0.257766\pi$
$38$	1.90597e7	−	1.32653e8i	0.240546	−	1.67417i
$39$	−1.70805e8			−1.89312
$40$	5.77357e7	−	3.33337e7i	0.563825	−	0.325525i
$41$	−5.50319e7	+	3.17727e7i	−0.475002	+	0.274242i	−0.718331	−	0.695701i	$-0.755094\pi$
$41$	−5.50319e7	+	3.17727e7i	−0.475002	+	0.274242i	0.243329	+	0.969944i	$0.421760\pi$
$42$	6.35941e7	−	1.10148e8i	0.486598	−	0.842813i
$43$	5.08176e7	+	8.80186e7i	0.345678	+	0.598732i	0.985477	−	0.169811i	$-0.0543157\pi$
$43$	5.08176e7	+	8.80186e7i	0.345678	+	0.598732i	−0.639799	+	0.768542i	$0.720982\pi$
$44$	−1.55136e8	+	2.68703e8i	−0.940696	+	1.62933i
$45$	−1.10386e8			−0.598209
$46$			5.51961e7i			0.267990i
$47$	−1.10340e8	+	1.91114e8i	−0.481108	+	0.833303i	−0.999765	−	0.0216790i	$-0.993099\pi$
$47$	−1.10340e8	+	1.91114e8i	−0.481108	+	0.833303i	0.518657	+	0.854982i	$0.326432\pi$
$48$	2.02955e8	+	1.17176e8i	0.796516	+	0.459869i
$49$	−2.42469e8			−0.858372
$50$		−	1.05710e8i		−	0.338273i
$51$	−2.13690e8	−	1.23374e8i	−0.619346	−	0.357579i
$52$	7.58607e8	−	4.37982e8i	1.99526	−	1.15197i
$53$	−1.68826e8	−	9.74716e7i	−0.403700	−	0.233077i	0.284379	−	0.958712i	$-0.408213\pi$
$53$	−1.68826e8	−	9.74716e7i	−0.403700	−	0.233077i	−0.688079	+	0.725635i	$0.741546\pi$
$54$	−2.00454e8	−	3.47197e8i	−0.436562	−	0.756148i
$55$	1.13788e8	+	1.97087e8i	0.226091	+	0.391601i
$56$			3.01726e8i			0.547865i
$57$	1.30835e8	−	9.10596e8i	0.217445	−	1.51339i
$58$	−1.03064e8			−0.157024
$59$	5.52623e8	−	3.19057e8i	0.772981	−	0.446281i	−0.0609561	−	0.998140i	$-0.519415\pi$
$59$	5.52623e8	−	3.19057e8i	0.772981	−	0.446281i	0.833937	+	0.551860i	$0.186082\pi$
$60$	8.56784e8	−	4.94664e8i	1.10183	−	0.636142i
$61$	−5.50860e8	+	9.54118e8i	−0.652217	+	1.12967i	0.330366	+	0.943853i	$0.392828\pi$
$61$	−5.50860e8	+	9.54118e8i	−0.652217	+	1.12967i	−0.982584	+	0.185821i	$0.940506\pi$
$62$	4.93159e8	+	8.54176e8i	0.538305	+	0.932372i
$63$	2.49796e8	−	4.32659e8i	0.251700	−	0.435957i
$64$	1.44198e9			1.34295
$65$		−	6.42496e8i		−	0.553737i
$66$	−1.63725e9	+	2.83580e9i	−1.30736	+	2.26441i
$67$	−3.97790e8	−	2.29664e8i	−0.294632	−	0.170106i	0.345397	−	0.938457i	$-0.387744\pi$
$67$	−3.97790e8	−	2.29664e8i	−0.294632	−	0.170106i	−0.640029	+	0.768351i	$0.721078\pi$
$68$	1.26543e9			0.870352
$69$			3.78892e8i			0.242253i
$70$	4.14332e8	+	2.39214e8i	0.246523	+	0.142330i
$71$	−2.49438e9	+	1.44013e9i	−1.38252	+	0.798199i	−0.992457	−	0.122590i	$-0.960880\pi$
$71$	−2.49438e9	+	1.44013e9i	−1.38252	+	0.798199i	−0.390063	+	0.920788i	$0.627547\pi$
$72$	3.26310e9	+	1.88395e9i	1.68643	+	0.973659i
$73$	4.06532e8	+	7.04134e8i	0.196101	+	0.339657i	0.947261	−	0.320463i	$-0.103839\pi$
$73$	4.06532e8	+	7.04134e8i	0.196101	+	0.339657i	−0.751160	+	0.660121i	$0.770505\pi$
$74$	2.71783e9	+	4.70742e9i	1.22480	+	2.12141i
$75$		−	7.25646e8i		−	0.305787i
$76$	1.75389e9	+	4.37978e9i	0.691725	+	1.72737i
$77$	−1.02998e9			−0.380516
$78$	8.00605e9	−	4.62230e9i	2.77297	−	1.60098i
$79$	2.49622e9	−	1.44119e9i	0.811236	−	0.468367i	−0.0361490	−	0.999346i	$-0.511509\pi$
$79$	2.49622e9	−	1.44119e9i	0.811236	−	0.468367i	0.847385	+	0.530979i	$0.178176\pi$
$80$	−4.40768e8	+	7.63433e8i	−0.134512	+	0.232981i
$81$	9.56014e8	+	1.65587e9i	0.274182	+	0.474897i
$82$	1.71966e9	−	2.97853e9i	0.463844	−	0.803402i
$83$	−3.75075e9			−0.952198			−0.476099	−	0.879392i	$-0.657950\pi$
$83$	−3.75075e9			−0.952198			−0.476099	+	0.879392i	$0.657950\pi$
$84$			4.47755e9i			1.07064i
$85$	4.64081e8	−	8.03812e8i	0.104592	−	0.181159i
$86$	−4.76389e9	−	2.75044e9i	−1.01267	−	0.584668i
$87$	−7.07480e8			−0.141944
$88$		−	7.76802e9i		−	1.47196i
$89$	−9.25473e9	−	5.34322e9i	−1.65735	−	0.956870i	−0.973932	−	0.226841i	$-0.927160\pi$
$89$	−9.25473e9	−	5.34322e9i	−1.65735	−	0.956870i	−0.683416	−	0.730029i	$-0.739506\pi$
$90$	5.17409e9	−	2.98726e9i	0.876237	−	0.505896i
$91$	2.51826e9	+	1.45392e9i	0.403547	+	0.232988i
$92$	−9.71563e8	−	1.68280e9i	−0.147412	−	0.255325i
$93$	3.38528e9	+	5.86347e9i	0.486608	+	0.842830i
$94$		−	1.19440e10i		−	1.62746i
$95$	3.42528e9	+	4.92146e8i	0.442668	+	0.0636027i
$96$	5.46457e9			0.670193
$97$	5.20779e9	−	3.00672e9i	0.606450	−	0.350134i	−0.165125	−	0.986273i	$-0.552803\pi$
$97$	5.20779e9	−	3.00672e9i	0.606450	−	0.350134i	0.771575	+	0.636139i	$0.219469\pi$
$98$	1.13651e10	−	6.56166e9i	1.25731	−	0.725911i
$99$	−6.43106e9	+	1.11389e10i	−0.676249	+	1.17130i
$100$	1.86072e9	+	3.22286e9i	0.186072	+	0.322286i
$101$	1.70083e9	−	2.94593e9i	0.161828	−	0.280295i	−0.773696	−	0.633557i	$-0.781594\pi$
$101$	1.70083e9	−	2.94593e9i	0.161828	−	0.280295i	0.935524	+	0.353262i	$0.114928\pi$
$102$	1.33549e10			1.20960
$103$			7.70080e9i			0.664278i	0.943230	+	0.332139i	$0.107770\pi$
$103$			7.70080e9i			0.664278i	−0.943230	+	0.332139i	$0.892230\pi$
$104$	−1.09654e10	+	1.89926e10i	−0.901275	+	1.56105i
$105$	2.84417e9	+	1.64208e9i	0.222848	+	0.128661i
$106$	1.05510e10			0.788435
$107$			8.65089e9i			0.616797i	0.951257	+	0.308398i	$0.0997930\pi$
$107$			8.65089e9i			0.616797i	−0.951257	+	0.308398i	$0.900207\pi$
$108$	1.22227e10	+	7.05680e9i	0.831859	+	0.480274i
$109$	−2.99202e9	+	1.72744e9i	−0.194461	+	0.112272i	−0.594069	−	0.804414i	$-0.702479\pi$
$109$	−2.99202e9	+	1.72744e9i	−0.194461	+	0.112272i	0.399608	+	0.916686i	$0.369146\pi$
$110$	−1.06671e10	−	6.15864e9i	−0.662341	−	0.382403i
$111$	1.86565e10	+	3.23140e10i	1.10717	+	1.91768i
$112$	−1.99485e9	−	3.45518e9i	−0.113193	−	0.196056i
$113$		−	1.09304e10i		−	0.593257i	−0.954993	−	0.296629i	$-0.904138\pi$
$113$		−	1.09304e10i		−	0.593257i	0.954993	−	0.296629i	$-0.0958623\pi$
$114$	1.85099e10	+	4.62225e10i	0.961344	+	2.40065i
$115$	−1.42523e9			−0.0708592
$116$	3.14218e9	−	1.81414e9i	0.149603	−	0.0863734i
$117$	3.14476e10	−	1.81563e10i	1.43436	−	0.828127i
$118$	−1.72685e10	+	2.99100e10i	−0.754824	+	1.30739i
$119$	2.10036e9	+	3.63793e9i	0.0880154	+	0.152447i
$120$	−1.23845e10	+	2.14506e10i	−0.497705	+	0.862051i
$121$	5.79545e8			0.0223440
$122$		−	5.96292e10i		−	2.20628i
$123$	1.18045e10	−	2.04460e10i	0.419298	−	0.726246i
$124$	−3.00705e10	−	1.73612e10i	−1.02573	−	0.592204i
$125$	2.72958e9			0.0894427
$126$			2.70398e10i			0.851433i
$127$	1.38046e10	+	7.97011e9i	0.417836	+	0.241238i	0.694151	−	0.719829i	$-0.255780\pi$
$127$	1.38046e10	+	7.97011e9i	0.417836	+	0.241238i	−0.276315	+	0.961067i	$0.589113\pi$
$128$	−5.45458e10	+	3.14920e10i	−1.58749	+	0.916539i
$129$	−3.27016e10	−	1.88803e10i	−0.915421	−	0.528518i
$130$	1.73871e10	+	3.01154e10i	0.468286	+	0.811095i
$131$	−2.41435e10	−	4.18177e10i	−0.625811	−	1.08394i	−0.988383	−	0.151981i	$-0.951435\pi$
$131$	−2.41435e10	−	4.18177e10i	−0.625811	−	1.08394i	0.362572	−	0.931956i	$-0.381899\pi$
$132$		−	1.15276e11i		−	2.87652i
$133$	−9.68011e9	+	1.23117e10i	−0.232607	+	0.295842i
$134$	2.48605e10			0.575422
$135$	8.96505e9	−	5.17598e9i	0.199933	−	0.115431i
$136$	−2.74371e10	+	1.58408e10i	−0.589717	+	0.340473i
$137$	1.81335e10	−	3.14082e10i	0.375734	−	0.650790i	−0.614703	−	0.788759i	$-0.710724\pi$
$137$	1.81335e10	−	3.14082e10i	0.375734	−	0.650790i	0.990437	+	0.137969i	$0.0440575\pi$
$138$	−1.02535e10	−	1.77596e10i	−0.204870	−	0.354845i
$139$	−3.86191e10	+	6.68902e10i	−0.744266	+	1.28911i	0.206271	+	0.978495i	$0.433867\pi$
$139$	−3.86191e10	+	6.68902e10i	−0.744266	+	1.28911i	−0.950537	+	0.310611i	$0.899466\pi$
$140$	−1.68427e10			−0.313163
$141$		−	8.19892e10i		−	1.47116i
$142$	7.79454e10	−	1.35005e11i	1.35005	−	2.33835i
$143$	−6.48333e10	−	3.74315e10i	−1.08422	−	0.625975i
$144$	−4.98226e10			−0.804662
$145$		−	2.66124e9i		−	0.0415187i
$146$	−3.81104e10	−	2.20030e10i	−0.574485	−	0.331679i
$147$	7.80156e10	−	4.50423e10i	1.13657	−	0.656197i
$148$	−1.65721e11	−	9.56788e10i	−2.33382	−	1.34743i
$149$	−4.40884e10	−	7.63633e10i	−0.600334	−	1.03981i	−0.992770	−	0.120029i	$-0.961701\pi$
$149$	−4.40884e10	−	7.63633e10i	−0.600334	−	1.03981i	0.392437	−	0.919779i	$-0.371632\pi$
$150$	1.96373e10	+	3.40128e10i	0.258599	+	0.447906i
$151$		−	1.21266e10i		−	0.154474i	−0.997013	−	0.0772370i	$-0.975390\pi$
$151$		−	1.21266e10i		−	0.154474i	0.997013	−	0.0772370i	$-0.0246098\pi$
$152$	−9.28541e10	−	7.30069e10i	−1.14441	−	0.899800i
$153$	5.24577e10			0.625680
$154$	4.82775e10	−	2.78730e10i	0.557367	−	0.321796i
$155$	−2.20559e10	+	1.27340e10i	−0.246528	+	0.142333i
$156$	−1.62724e11	+	2.81846e11i	−1.76128	+	3.05062i
$157$	6.67399e10	+	1.15597e11i	0.699661	+	1.21185i	0.968584	+	0.248686i	$0.0799988\pi$
$157$	6.67399e10	+	1.15597e11i	0.699661	+	1.21185i	−0.268924	+	0.963162i	$0.586668\pi$
$158$	−7.80027e10	+	1.35105e11i	−0.792180	+	1.37210i
$159$	7.24274e10			0.712717
$160$			2.05554e10i			0.196032i
$161$	3.22519e9	−	5.58619e9i	0.0298144	−	0.0516400i
$162$	−8.96216e10	−	5.17430e10i	−0.803225	−	0.463742i
$163$	−1.91911e11			−1.66787			−0.833933	−	0.551866i	$-0.813916\pi$
$163$	−1.91911e11			−1.66787			−0.833933	+	0.551866i	$0.813916\pi$
$164$			1.21078e11i			1.02058i
$165$	−7.32238e10	−	4.22758e10i	−0.598732	−	0.345678i
$166$	1.75807e11	−	1.01502e11i	1.39475	−	0.805258i
$167$	7.91759e10	+	4.57122e10i	0.609552	+	0.351925i	0.772790	−	0.634662i	$-0.218861\pi$
$167$	7.91759e10	+	4.57122e10i	0.609552	+	0.351925i	−0.163238	+	0.986587i	$0.552194\pi$
$168$	−5.60503e10	−	9.70820e10i	−0.418824	−	0.725425i
$169$	3.67479e10	+	6.36492e10i	0.266562	+	0.461699i
$170$			5.02356e10i			0.353807i
$171$	7.27062e10	+	1.81561e11i	0.497268	+	1.24177i
$172$	1.93653e11			1.28642
$173$	1.94072e11	−	1.12047e11i	1.25237	−	0.723055i	0.280789	−	0.959770i	$-0.409404\pi$
$173$	1.94072e11	−	1.12047e11i	1.25237	−	0.723055i	0.971579	+	0.236714i	$0.0760706\pi$
$174$	3.31613e10	−	1.91457e10i	0.207915	−	0.120040i
$175$	−6.17682e9	+	1.06986e10i	−0.0376335	+	0.0651831i
$176$	5.13579e10	+	8.89545e10i	0.304119	+	0.526750i
$177$	−1.18539e11	+	2.05316e11i	−0.682333	+	1.18184i
$178$	5.78390e11			3.23684
$179$			1.60126e11i			0.871359i	0.900102	+	0.435679i	$0.143492\pi$
$179$			1.60126e11i			0.871359i	−0.900102	+	0.435679i	$0.856508\pi$
$180$	−1.05164e11	+	1.82149e11i	−0.556550	+	0.963972i
$181$	6.21038e10	+	3.58557e10i	0.319687	+	0.184572i	0.651253	−	0.758860i	$-0.274244\pi$
$181$	6.21038e10	+	3.58557e10i	0.319687	+	0.184572i	−0.331566	+	0.943432i	$0.607577\pi$
$182$	−1.57383e11			−0.788135
$183$		−	4.09323e11i		−	1.99439i
$184$	4.21308e10	+	2.43242e10i	0.199761	+	0.115332i
$185$	−1.21552e11	+	7.01779e10i	−0.560921	+	0.323848i
$186$	−3.17353e11	−	1.83224e11i	−1.42553	−	0.823032i
$187$	−5.40743e10	−	9.36594e10i	−0.236474	−	0.409584i
$188$	2.10239e11	+	3.64144e11i	0.895206	+	1.55054i
$189$			4.68513e10i			0.194273i
$190$	−1.73870e11	+	6.96263e10i	−0.702192	+	0.281193i
$191$	−1.21050e11			−0.476210			−0.238105	−	0.971239i	$-0.576526\pi$
$191$	−1.21050e11			−0.476210			−0.238105	+	0.971239i	$0.576526\pi$
$192$	−4.63965e11	+	2.67870e11i	−1.77819	+	1.02664i
$193$	3.92733e11	−	2.26745e11i	1.46660	−	0.846741i	0.467296	−	0.884101i	$-0.345228\pi$
$193$	3.92733e11	−	2.26745e11i	1.46660	−	0.846741i	0.999302	+	0.0373603i	$0.0118949\pi$
$194$	−1.62735e11	+	2.81865e11i	−0.592205	+	1.02573i
$195$	1.19354e11	+	2.06726e11i	0.423314	+	0.733201i
$196$	−2.30997e11	+	4.00099e11i	−0.798594	+	1.38321i
$197$	3.70111e11			1.24739			0.623693	−	0.781669i	$-0.285632\pi$
$197$	3.70111e11			1.24739			0.623693	+	0.781669i	$0.285632\pi$
$198$		−	6.96146e11i		−	2.28757i
$199$	−4.37002e10	+	7.56909e10i	−0.140029	+	0.242537i	−0.927507	−	0.373805i	$-0.878053\pi$
$199$	−4.37002e10	+	7.56909e10i	−0.140029	+	0.242537i	0.787478	+	0.616342i	$0.211386\pi$
$200$	−8.06881e10	−	4.65853e10i	−0.252150	−	0.145579i
$201$	1.70655e11			0.520161
$202$			1.84111e11i			0.547422i
$203$	1.04307e10	+	6.02218e9i	0.0302576	+	0.0174692i
$204$	−4.07160e11	+	2.35074e11i	−1.15243	+	0.665355i
$205$	7.69094e10	+	4.44037e10i	0.212427	+	0.122645i
$206$	−2.08398e11	−	3.60956e11i	−0.561768	−	0.973011i
$207$	−4.02755e10	−	6.97593e10i	−0.105972	−	0.183548i
$208$		−	2.89988e11i		−	0.744842i
$209$	2.49217e11	−	3.16967e11i	0.624951	−	0.794846i
$210$	−1.77751e11			−0.435227
$211$	6.22345e11	−	3.59311e11i	1.48806	−	0.859129i	0.488149	−	0.872760i	$-0.337672\pi$
$211$	6.22345e11	−	3.59311e11i	1.48806	−	0.859129i	0.999907	+	0.0136310i	$0.00433900\pi$
$212$	−3.21676e11	+	1.85720e11i	−0.751173	+	0.433690i
$213$	5.35054e11	−	9.26740e11i	1.22039	−	2.11378i
$214$	−2.34109e11	−	4.05489e11i	−0.521615	−	0.903463i
$215$	7.10197e10	−	1.23010e11i	0.154592	−	0.267761i
$216$	−3.53351e11			−0.751514
$217$		−	1.15264e11i		−	0.239550i
$218$	9.34956e10	−	1.61939e11i	0.189893	−	0.328904i
$219$	−2.61608e11	−	1.51039e11i	−0.519314	−	0.299826i
$220$	4.33618e11			0.841384
$221$			3.05326e11i			0.579166i
$222$	−1.74895e12	−	1.00976e12i	−3.24349	−	1.87263i
$223$	8.05103e11	−	4.64827e11i	1.45991	−	0.842882i	0.460908	−	0.887448i	$-0.347524\pi$
$223$	8.05103e11	−	4.64827e11i	1.45991	−	0.842882i	0.999006	+	0.0445660i	$0.0141905\pi$
$224$	−8.05669e10	−	4.65153e10i	−0.142862	−	0.0824814i
$225$	7.71349e10	+	1.33602e11i	0.133764	+	0.231686i
$226$	2.95796e11	+	5.12334e11i	0.501707	+	0.868983i
$227$			9.93170e11i			1.64776i	0.566764	+	0.823881i	$0.308195\pi$
$227$			9.93170e11i			1.64776i	−0.566764	+	0.823881i	$0.691805\pi$
$228$	−1.37793e12	−	1.08340e12i	−2.23642	−	1.75840i
$229$	1.07253e12			1.70307			0.851537	−	0.524294i	$-0.175671\pi$
$229$	1.07253e12			1.70307			0.851537	+	0.524294i	$0.175671\pi$
$230$	6.68042e10	−	3.85694e10i	0.103792	−	0.0599244i
$231$	3.31400e11	−	1.91334e11i	0.503840	−	0.290892i
$232$	−4.54190e10	+	7.86681e10i	−0.0675768	+	0.117047i
$233$	1.24318e11	+	2.15325e11i	0.181031	+	0.313556i	0.942232	−	0.334961i	$-0.108723\pi$
$233$	1.24318e11	+	2.15325e11i	0.181031	+	0.313556i	−0.761201	+	0.648516i	$0.775390\pi$
$234$	−9.82684e11	+	1.70206e12i	−1.40067	+	2.42602i
$235$	3.08409e11			0.430316
$236$		−	1.21585e12i		−	1.66081i
$237$	−5.35447e11	+	9.27422e11i	−0.716102	+	1.24033i
$238$	−1.96898e11	−	1.13679e11i	−0.257844	−	0.148866i
$239$	1.38518e11			0.177630			0.0888151	−	0.996048i	$-0.471692\pi$
$239$	1.38518e11			0.177630			0.0888151	+	0.996048i	$0.471692\pi$
$240$		−	3.27518e11i		−	0.411319i
$241$	−2.56873e11	−	1.48306e11i	−0.315961	−	0.182420i	0.333630	−	0.942704i	$-0.391726\pi$
$241$	−2.56873e11	−	1.48306e11i	−0.315961	−	0.182420i	−0.649591	+	0.760284i	$0.725060\pi$
$242$	−2.71647e10	+	1.56836e10i	−0.0327287	+	0.0188959i
$243$	−9.93997e11	−	5.73884e11i	−1.17315	−	0.677318i
$244$	1.04960e12	+	1.81795e12i	1.21359	+	2.10201i
$245$	1.69430e11	+	2.93462e11i	0.191938	+	0.332446i
$246$			1.27781e12i			1.41837i
$247$	−1.05676e12	+	4.23181e11i	−1.14946	+	0.460300i
$248$	8.69317e11			0.926658
$249$	1.20682e12	−	6.96759e11i	1.26080	−	0.727924i
$250$	−1.27942e11	+	7.38674e10i	−0.131013	+	0.0756402i
$251$	4.59190e11	−	7.95341e11i	0.460918	−	0.798334i	−0.538089	−	0.842888i	$-0.680853\pi$
$251$	4.59190e11	−	7.95341e11i	0.460918	−	0.798334i	0.999007	+	0.0445544i	$0.0141868\pi$
$252$	−4.75955e11	−	8.24379e11i	−0.468342	−	0.811193i
$253$	−8.30333e10	+	1.43818e11i	−0.0801032	+	0.138743i
$254$	−8.62744e11			−0.816043
$255$			3.44841e11i			0.319829i
$256$	9.66172e11	−	1.67346e12i	0.878728	−	1.52200i
$257$	2.56646e11	+	1.48175e11i	0.228912	+	0.132163i	0.610070	−	0.792347i	$-0.291141\pi$
$257$	2.56646e11	+	1.48175e11i	0.228912	+	0.132163i	−0.381158	+	0.924510i	$0.624475\pi$
$258$	2.04374e12			1.78784
$259$		−	6.35228e11i		−	0.545043i
$260$	−1.06019e12	−	6.12098e11i	−0.892308	−	0.515175i
$261$	1.30257e11	−	7.52038e10i	0.107547	−	0.0620922i
$262$	2.26333e12	+	1.30673e12i	1.83333	+	1.05848i
$263$	−8.12724e11	−	1.40768e12i	−0.645899	−	1.11873i	−0.984093	−	0.177653i	$-0.943149\pi$
$263$	−8.12724e11	−	1.40768e12i	−0.645899	−	1.11873i	0.338194	−	0.941076i	$-0.390184\pi$
$264$	1.44303e12	+	2.49940e12i	1.12527	+	1.94902i
$265$			2.72441e11i			0.208470i
$266$	1.20554e11	−	8.39041e11i	0.0905259	−	0.630050i
$267$	3.97034e12			2.92598
$268$	−7.57939e11	+	4.37596e11i	−0.548227	+	0.316519i
$269$	−1.52059e12	+	8.77910e11i	−1.07957	+	0.623288i	−0.930779	−	0.365581i	$-0.880870\pi$
$269$	−1.52059e12	+	8.77910e11i	−1.07957	+	0.623288i	−0.148787	+	0.988869i	$0.547537\pi$
$270$	−2.80143e11	+	4.85222e11i	−0.195237	+	0.338160i
$271$	−7.33167e11	−	1.26988e12i	−0.501599	−	0.868795i	−0.999998	−	0.00184742i	$-0.999412\pi$
$271$	−7.33167e11	−	1.26988e12i	−0.501599	−	0.868795i	0.498399	−	0.866948i	$-0.333921\pi$
$272$	2.09461e11	−	3.62798e11i	0.140689	−	0.243680i
$273$	−1.08035e12			−0.712446
$274$			1.96291e12i			1.27101i
$275$	1.59024e11	−	2.75437e11i	0.101111	−	0.175129i
$276$	6.25211e11	+	3.60966e11i	0.390374	+	0.225383i
$277$	2.58444e12			1.58478			0.792388	−	0.610018i	$-0.208838\pi$
$277$	2.58444e12			1.58478			0.792388	+	0.610018i	$0.208838\pi$
$278$		−	4.18042e12i		−	2.51765i
$279$	−1.24655e12	−	7.19698e11i	−0.737377	−	0.425725i
$280$	3.65182e11	−	2.10838e11i	0.212187	−	0.122506i
$281$	−1.05564e12	−	6.09476e11i	−0.602539	−	0.347876i	0.167501	−	0.985872i	$-0.446430\pi$
$281$	−1.05564e12	−	6.09476e11i	−0.602539	−	0.347876i	−0.770040	+	0.637996i	$0.779764\pi$
$282$	2.21878e12	+	3.84304e12i	1.24414	+	2.15491i
$283$	9.28997e11	+	1.60907e12i	0.511779	+	0.886427i	0.999907	+	0.0136548i	$0.00434660\pi$
$283$	9.28997e11	+	1.60907e12i	0.511779	+	0.886427i	−0.488128	+	0.872772i	$0.662320\pi$
$284$			5.48799e12i			2.97045i
$285$	−1.19352e12	+	4.77948e11i	−0.634756	+	0.254189i
$286$	4.05186e12			2.11751
$287$	−3.48080e11	+	2.00964e11i	−0.178760	+	0.103207i
$288$	−1.00610e12	+	5.80874e11i	−0.507786	+	0.293170i
$289$	7.87457e11	−	1.36392e12i	0.390605	−	0.676547i
$290$	7.20181e10	+	1.24739e11i	0.0351117	+	0.0608152i
$291$	−1.11709e12	+	1.93485e12i	−0.535331	+	0.927221i
$292$	1.54919e12			0.729779
$293$			2.09328e12i			0.969370i	0.874689	+	0.484685i	$0.161066\pi$
$293$			2.09328e12i			0.969370i	−0.874689	+	0.484685i	$0.838934\pi$
$294$	−2.43786e12	+	4.22249e12i	−1.10987	+	1.92235i
$295$	−7.72314e11	−	4.45896e11i	−0.345688	−	0.199583i
$296$	4.79086e12			2.10841
$297$		−	1.20620e12i		−	0.521960i
$298$	4.13306e12	+	2.38623e12i	1.75870	+	1.01538i
$299$	4.06029e11	−	2.34421e11i	0.169903	−	0.0980935i
$300$	−1.19739e12	−	6.91314e11i	−0.492754	−	0.284491i
$301$	3.21424e11	+	5.56723e11i	0.130091	+	0.225324i
$302$	3.28169e11	+	5.68406e11i	0.130636	+	0.226268i
$303$			1.26382e12i			0.494849i
$304$	1.54599e12	+	2.22128e11i	0.595440	+	0.0855532i
$305$	1.53970e12			0.583361
$306$	−2.45883e12	+	1.41960e12i	−0.916475	+	0.529127i
$307$	−1.25806e12	+	7.26340e11i	−0.461327	+	0.266347i	−0.712602	−	0.701568i	$-0.752483\pi$
$307$	−1.25806e12	+	7.26340e11i	−0.461327	+	0.266347i	0.251275	+	0.967916i	$0.419150\pi$
$308$	−9.81245e11	+	1.69957e12i	−0.354017	+	0.613175i
$309$	−1.43054e12	−	2.47777e12i	−0.507818	−	0.879567i
$310$	6.89211e11	−	1.19375e12i	0.240737	−	0.416969i
$311$	−9.53371e11			−0.327688			−0.163844	−	0.986486i	$-0.552389\pi$
$311$	−9.53371e11			−0.327688			−0.163844	+	0.986486i	$0.552389\pi$
$312$		−	8.14796e12i		−	2.75598i
$313$	1.19178e12	−	2.06423e12i	0.396712	−	0.687125i	−0.596606	−	0.802534i	$-0.703485\pi$
$313$	1.19178e12	−	2.06423e12i	0.396712	−	0.687125i	0.993318	+	0.115409i	$0.0368179\pi$
$314$	−6.25653e12	−	3.61221e12i	−2.04968	−	1.18338i
$315$	−6.98201e11			−0.225127
$316$		−	5.49203e12i		−	1.74300i
$317$	−2.20316e12	−	1.27199e12i	−0.688255	−	0.397364i	0.114703	−	0.993400i	$-0.463408\pi$
$317$	−2.20316e12	−	1.27199e12i	−0.688255	−	0.397364i	−0.802958	+	0.596036i	$0.796742\pi$
$318$	−3.39485e12	+	1.96002e12i	−1.04396	+	0.602733i
$319$	−2.68542e11	−	1.55043e11i	−0.0812940	−	0.0469351i
$320$	−1.00761e12	−	1.74524e12i	−0.300293	−	0.520122i
$321$	−1.60704e12	−	2.78347e12i	−0.471521	−	0.816698i
$322$			3.49119e11i			0.100854i
$323$	−1.62776e12	−	2.33877e11i	−0.462996	−	0.0665235i
$324$	3.64313e12			1.02035
$325$	−7.77618e11	+	4.48958e11i	−0.214461	+	0.123819i
$326$	8.99533e12	−	5.19346e12i	2.44303	−	1.41048i
$327$	6.41798e11	−	1.11163e12i	0.171656	−	0.297317i
$328$	−1.51566e12	−	2.62521e12i	−0.399239	−	0.691503i
$329$	−6.97905e11	+	1.20881e12i	−0.181058	+	0.313601i
$330$	4.57625e12			1.16934
$331$		−	4.22857e12i		−	1.06428i	−0.846658	−	0.532138i	$-0.821389\pi$
$331$		−	4.22857e12i		−	1.06428i	0.846658	−	0.532138i	$-0.178611\pi$
$332$	−3.57329e12	+	6.18912e12i	−0.885886	+	1.53440i
$333$	−6.86984e12	−	3.96630e12i	−1.67774	−	0.968645i
$334$	−4.94823e12			−1.19047
$335$			6.41930e11i			0.152147i
$336$	1.28371e12	+	7.41148e11i	0.299757	+	0.173065i
$337$	−3.06809e12	+	1.77136e12i	−0.705860	+	0.407529i	−0.809526	−	0.587083i	$-0.800276\pi$
$337$	−3.06809e12	+	1.77136e12i	−0.705860	+	0.407529i	0.103666	+	0.994612i	$0.466943\pi$
$338$	−3.44493e12	−	1.98893e12i	−0.780902	−	0.450854i
$339$	2.03049e12	+	3.51690e12i	0.453525	+	0.785529i
$340$	−8.84249e11	−	1.53156e12i	−0.194617	−	0.337086i
$341$			2.96750e12i			0.643605i
$342$	−8.32130e12	−	6.54265e12i	−1.77853	−	1.39837i
$343$	−3.32030e12			−0.699370
$344$	−4.19878e12	+	2.42417e12i	−0.871628	+	0.503234i
$345$	4.58576e11	−	2.64759e11i	0.0938243	−	0.0541695i
$346$	−6.06442e12	+	1.05039e13i	−1.22295	+	2.11821i
$347$	1.92663e12	+	3.33702e12i	0.382957	+	0.663302i	0.991484	−	0.130232i	$-0.0415722\pi$
$347$	1.92663e12	+	3.33702e12i	0.382957	+	0.663302i	−0.608526	+	0.793534i	$0.708239\pi$
$348$	−6.74007e11	+	1.16741e12i	−0.132059	+	0.228733i
$349$	1.25638e12			0.242657			0.121328	−	0.992612i	$-0.461285\pi$
$349$	1.25638e12			0.242657			0.121328	+	0.992612i	$0.461285\pi$
$350$		−	6.68625e11i		−	0.127304i
$351$	−1.70268e12	+	2.94913e12i	−0.319593	+	0.553551i
$352$	2.07422e12	+	1.19755e12i	0.383832	+	0.221605i
$353$	2.06106e12			0.376026			0.188013	−	0.982167i	$-0.439795\pi$
$353$	2.06106e12			0.376026			0.188013	+	0.982167i	$0.439795\pi$
$354$		−	1.28316e13i		−	2.30815i
$355$	3.48601e12	+	2.01265e12i	0.618282	+	0.356965i
$356$	−1.76337e13	+	1.01808e13i	−3.08386	+	1.78047i
$357$	−1.35160e12	−	7.80348e11i	−0.233082	−	0.134570i
$358$	−4.33331e12	−	7.50551e12i	−0.736893	−	1.27634i
$359$	−3.24710e12	−	5.62414e12i	−0.544532	−	0.943157i	−0.998636	−	0.0522087i	$-0.983374\pi$
$359$	−3.24710e12	−	5.62414e12i	−0.544532	−	0.943157i	0.454104	−	0.890949i	$-0.349959\pi$
$360$		−	5.26580e12i		−	0.870867i
$361$	−1.44660e12	−	5.95796e12i	−0.235945	−	0.971766i
$362$	−3.88128e12			−0.624356
$363$	−1.86471e11	+	1.07659e11i	−0.0295855	+	0.0170812i
$364$	4.79824e12	−	2.77026e12i	0.750887	−	0.433525i
$365$	5.68146e11	−	9.84057e11i	0.0876992	−	0.151899i
$366$	1.10770e13	+	1.91860e13i	1.68662	+	2.92132i
$367$	−6.46136e12	+	1.11914e13i	−0.970495	+	1.68095i	−0.276431	+	0.961034i	$0.589152\pi$
$367$	−6.46136e12	+	1.11914e13i	−0.970495	+	1.68095i	−0.694064	+	0.719913i	$0.744181\pi$
$368$	−6.43274e11			−0.0953140
$369$			5.01920e12i			0.733674i
$370$	3.79829e12	−	6.57882e12i	0.547746	−	0.948723i
$371$	−1.06783e12	−	6.16514e11i	−0.151927	−	0.0877149i
$372$	1.29004e13			1.81088
$373$		−	1.38357e13i		−	1.91628i	−0.286306	−	0.958138i	$-0.592427\pi$
$373$		−	1.38357e13i		−	1.91628i	0.286306	−	0.958138i	$-0.407573\pi$
$374$	5.06919e12	+	2.92670e12i	0.692757	+	0.399963i
$375$	−8.78255e11	+	5.07061e11i	−0.118431	+	0.0683760i
$376$	−9.11677e12	−	5.26357e12i	−1.21311	−	0.700392i
$377$	4.37718e11	+	7.58150e11i	0.0574762	+	0.0995516i
$378$	−1.26788e12	−	2.19604e12i	−0.164294	−	0.284565i
$379$			5.24585e12i			0.670841i	0.942069	+	0.335420i	$0.108878\pi$
$379$			5.24585e12i			0.670841i	−0.942069	+	0.335420i	$0.891122\pi$
$380$	4.07531e12	−	5.18320e12i	0.514331	−	0.654154i
$381$	−5.92228e12			−0.737673
$382$	5.67393e12	−	3.27584e12i	0.697537	−	0.402723i
$383$	−1.29935e12	+	7.50182e11i	−0.157664	+	0.0910276i	−0.576756	−	0.816916i	$-0.695682\pi$
$383$	−1.29935e12	+	7.50182e11i	−0.157664	+	0.0910276i	0.419092	+	0.907944i	$0.362348\pi$
$384$	1.17003e13	−	2.02654e13i	1.40133	−	2.42717i
$385$	7.19717e11	+	1.24659e12i	0.0850860	+	0.147373i
$386$	−1.22723e13	+	2.12562e13i	−1.43215	+	2.48055i
$387$	8.02777e12			0.924783
$388$		−	1.14579e13i		−	1.30300i
$389$	3.88291e12	−	6.72540e12i	0.435922	−	0.755040i	−0.561448	−	0.827512i	$-0.689756\pi$
$389$	3.88291e12	−	6.72540e12i	0.435922	−	0.755040i	0.997370	+	0.0724722i	$0.0230889\pi$
$390$	−1.11888e13	−	6.45986e12i	−1.24011	−	0.715978i
$391$	6.77297e11			0.0741132
$392$		−	1.15666e13i		−	1.24961i
$393$	1.55366e13	+	8.97004e12i	1.65727	+	0.956823i
$394$	−1.73480e13	+	1.00159e13i	−1.82713	+	1.05489i
$395$	−3.48857e12	−	2.01413e12i	−0.362796	−	0.209460i
$396$	1.22536e13	+	2.12238e13i	1.25831	+	2.17946i
$397$	−3.35669e12	−	5.81396e12i	−0.340376	−	0.589548i	0.644127	−	0.764919i	$-0.277221\pi$
$397$	−3.35669e12	−	5.81396e12i	−0.340376	−	0.589548i	−0.984502	+	0.175371i	$0.943888\pi$
$398$		−	4.73043e12i		−	0.473680i
$399$	8.27539e11	−	5.75957e12i	0.0818321	−	0.569542i
$400$	1.23198e12			0.120311
$401$	1.31125e13	−	7.57048e12i	1.26463	−	0.730132i	0.290660	−	0.956826i	$-0.406125\pi$
$401$	1.31125e13	−	7.57048e12i	1.26463	−	0.730132i	0.973966	+	0.226694i	$0.0727919\pi$
$402$	−7.99900e12	+	4.61823e12i	−0.761914	+	0.439891i
$403$	4.18895e12	−	7.25547e12i	0.394076	−	0.682559i
$404$	−3.24072e12	−	5.61310e12i	−0.301117	−	0.521550i
$405$	1.33607e12	−	2.31414e12i	0.122618	−	0.212381i
$406$	−6.51886e11			−0.0590937
$407$			1.63541e13i			1.46438i
$408$	5.88535e12	−	1.01937e13i	0.520561	−	0.901637i
$409$	−6.47397e12	−	3.73775e12i	−0.565658	−	0.326583i	0.189755	−	0.981831i	$-0.439231\pi$
$409$	−6.47397e12	−	3.73775e12i	−0.565658	−	0.326583i	−0.755413	+	0.655249i	$0.772564\pi$
$410$	−4.80658e12			−0.414875
$411$			1.34743e13i			1.14894i
$412$	1.27071e13	+	7.33646e12i	1.07044	+	0.618017i
$413$	3.49537e12	−	2.01805e12i	0.290900	−	0.167951i
$414$	3.77563e12	+	2.17986e12i	0.310447	+	0.179237i
$415$	2.62091e12	+	4.53956e12i	0.212918	+	0.368785i
$416$	−3.38094e12	−	5.85595e12i	−0.271375	−	0.470036i
$417$		−	2.86964e13i		−	2.27587i
$418$	−3.10369e12	+	2.16013e13i	−0.243219	+	1.69277i
$419$	−7.78219e12			−0.602604			−0.301302	−	0.953529i	$-0.597421\pi$
$419$	−7.78219e12			−0.602604			−0.301302	+	0.953529i	$0.597421\pi$
$420$	5.41921e12	−	3.12878e12i	0.414657	−	0.239403i
$421$	2.03510e13	−	1.17496e13i	1.53877	−	0.888412i	0.539864	−	0.841753i	$-0.318476\pi$
$421$	2.03510e13	−	1.17496e13i	1.53877	−	0.888412i	0.998911	−	0.0466593i	$-0.0148575\pi$
$422$	−1.94473e13	+	3.36836e13i	−1.45310	+	2.51685i
$423$	8.71531e12	+	1.50954e13i	0.643548	+	1.11466i
$424$	4.64972e12	−	8.05355e12i	0.339311	−	0.587703i
$425$	−1.29715e12			−0.0935501
$426$			5.79182e13i			4.12826i
$427$	−3.48423e12	+	6.03486e12i	−0.245452	+	0.425136i
$428$	1.42749e13	+	8.24160e12i	0.993925	+	0.573843i
$429$	2.78139e13			1.91415
$430$			7.68770e12i			0.522943i
$431$	−3.60337e12	−	2.08040e12i	−0.242282	−	0.139882i	0.373943	−	0.927452i	$-0.378006\pi$
$431$	−3.60337e12	−	2.08040e12i	−0.242282	−	0.139882i	−0.616225	+	0.787570i	$0.711339\pi$
$432$	4.04635e12	−	2.33616e12i	0.268933	−	0.155269i
$433$	−1.20998e13	−	6.98580e12i	−0.794945	−	0.458962i	0.0467554	−	0.998906i	$-0.485112\pi$
$433$	−1.20998e13	−	6.98580e12i	−0.794945	−	0.458962i	−0.841701	+	0.539945i	$0.818445\pi$
$434$	3.11926e12	+	5.40272e12i	0.202583	+	0.350884i
$435$	4.94366e11	+	8.56268e11i	0.0317397	+	0.0549748i
$436$			6.58285e12i			0.417813i
$437$	9.38731e11	+	2.34419e12i	0.0589025	+	0.147091i
$438$	1.63496e13			1.01423
$439$	3.41236e12	−	1.97013e12i	0.209282	−	0.120829i	−0.391696	−	0.920095i	$-0.628111\pi$
$439$	3.41236e12	−	1.97013e12i	0.209282	−	0.120829i	0.600978	+	0.799266i	$0.294778\pi$
$440$	−9.40170e12	+	5.42807e12i	−0.570089	+	0.329141i
$441$	−9.57584e12	+	1.65858e13i	−0.574095	+	0.994362i
$442$	−8.26269e12	−	1.43114e13i	−0.489790	−	0.848342i
$443$	2.18626e12	−	3.78672e12i	0.128140	−	0.221944i	−0.794816	−	0.606850i	$-0.792433\pi$
$443$	2.18626e12	−	3.78672e12i	0.128140	−	0.221944i	0.922956	+	0.384906i	$0.125766\pi$
$444$	7.10952e13			4.12027
$445$			1.49348e13i			0.855851i
$446$	−2.51581e13	+	4.35752e13i	−1.42562	+	2.46925i
$447$	2.83713e13	+	1.63802e13i	1.58980	+	0.917870i
$448$	9.12062e12			0.505399
$449$		−	1.43352e13i		−	0.785546i	−0.919636	−	0.392773i	$-0.871516\pi$
$449$		−	1.43352e13i		−	0.785546i	0.919636	−	0.392773i	$-0.128484\pi$
$450$	−7.23101e12	−	4.17483e12i	−0.391865	−	0.226243i
$451$	8.96141e12	−	5.17387e12i	0.480279	−	0.277289i
$452$	−1.80363e13	−	1.04132e13i	−0.955992	−	0.551942i
$453$	2.25271e12	+	3.90181e12i	0.118090	+	0.204538i
$454$	−2.68770e13	−	4.65524e13i	−1.39348	−	2.41358i
$455$		−	4.06383e12i		−	0.208391i
$456$	4.34384e13	+	6.24126e12i	2.20318	+	0.316554i
$457$	3.38664e13			1.69898			0.849490	−	0.527604i	$-0.176910\pi$
$457$	3.38664e13			1.69898			0.849490	+	0.527604i	$0.176910\pi$
$458$	−5.02723e13	+	2.90248e13i	−2.49460	+	1.44026i
$459$	−4.26036e12	+	2.45972e12i	−0.209114	+	0.120732i
$460$	−1.35780e12	+	2.35178e12i	−0.0659245	+	0.114185i
$461$	1.60288e12	+	2.77628e12i	0.0769835	+	0.133339i	0.901947	−	0.431847i	$-0.142138\pi$
$461$	1.60288e12	+	2.77628e12i	0.0769835	+	0.133339i	−0.824964	+	0.565186i	$0.808804\pi$
$462$	−1.03557e13	+	1.79366e13i	−0.492005	+	0.852177i
$463$	−2.67161e13			−1.25565			−0.627825	−	0.778354i	$-0.716055\pi$
$463$	−2.67161e13			−1.25565			−0.627825	+	0.778354i	$0.716055\pi$
$464$		−	1.20114e12i		−	0.0558476i
$465$	4.73107e12	−	8.19445e12i	0.217618	−	0.376925i
$466$	−1.16542e13	−	6.72854e12i	−0.530337	−	0.306190i
$467$	−6.61831e12			−0.297963			−0.148982	−	0.988840i	$-0.547600\pi$
$467$	−6.61831e12			−0.297963			−0.148982	+	0.988840i	$0.547600\pi$
$468$		−	6.91890e13i		−	3.08182i
$469$	−2.51604e12	−	1.45264e12i	−0.110880	−	0.0640167i
$470$	−1.44559e13	+	8.34612e12i	−0.630312	+	0.363911i
$471$	−4.29478e13	−	2.47959e13i	−1.85283	−	1.06973i
$472$	1.52201e13	+	2.63619e13i	0.649691	+	1.12530i
$473$	−8.27515e12	−	1.43330e13i	−0.349518	−	0.605384i
$474$		−	5.79608e13i		−	2.42238i
$475$	−1.79784e12	−	4.48954e12i	−0.0743503	−	0.185666i
$476$	8.00395e12			0.327544
$477$	−1.33349e13	+	7.69890e12i	−0.540005	+	0.311772i
$478$	−6.49269e12	+	3.74855e12i	−0.260187	+	0.150219i
$479$	1.81235e13	−	3.13908e13i	0.718728	−	1.24487i	−0.242776	−	0.970082i	$-0.578058\pi$
$479$	1.81235e13	−	3.13908e13i	0.718728	−	1.24487i	0.961504	−	0.274791i	$-0.0886088\pi$
$480$	−3.81849e12	−	6.61381e12i	−0.149860	−	0.259565i
$481$	2.30856e13	−	3.99854e13i	0.896634	−	1.55302i
$482$	1.60537e13			0.617078
$483$			2.39651e12i			0.0911684i
$484$	5.52125e11	−	9.56309e11i	0.0207879	−	0.0360057i
$485$	−7.27811e12	−	4.20202e12i	−0.271213	−	0.156585i
$486$	6.21215e13			2.29119
$487$		−	4.25380e13i		−	1.55286i	−0.630203	−	0.776431i	$-0.717028\pi$
$487$		−	4.25380e13i		−	1.55286i	0.630203	−	0.776431i	$-0.282972\pi$
$488$	−4.55146e13	−	2.62779e13i	−1.64457	−	0.949492i
$489$	6.17482e13	−	3.56503e13i	2.20841	−	1.27503i
$490$	−1.58832e13	−	9.17019e12i	−0.562288	−	0.324637i
$491$	1.61436e13	+	2.79616e13i	0.565710	+	0.979838i	0.996983	+	0.0776169i	$0.0247311\pi$
$491$	1.61436e13	+	2.79616e13i	0.565710	+	0.979838i	−0.431273	+	0.902221i	$0.641936\pi$
$492$	−2.24921e13	−	3.89574e13i	−0.780196	−	1.35134i
$493$			1.26467e12i			0.0434253i
$494$	3.80810e13	−	4.84335e13i	1.29442	−	1.64631i
$495$	1.79754e13			0.604856
$496$	−9.95486e12	+	5.74744e12i	−0.331609	+	0.191455i
$497$	−1.57771e13	+	9.10893e12i	−0.520291	+	0.300390i
$498$	−3.77112e13	+	6.53177e13i	−1.23119	+	2.13248i
$499$	1.66256e13	+	2.87965e13i	0.537373	+	0.930757i	0.999044	+	0.0437062i	$0.0139166\pi$
$499$	1.66256e13	+	2.87965e13i	0.537373	+	0.930757i	−0.461672	+	0.887051i	$0.652750\pi$
$500$	2.60043e12	−	4.50408e12i	0.0832139	−	0.144131i
$501$	−3.39670e13			−1.07614
$502$			4.97061e13i			1.55916i
$503$	−1.87639e13	+	3.25000e13i	−0.582751	+	1.00936i	0.412400	+	0.911003i	$0.364691\pi$
$503$	−1.87639e13	+	3.25000e13i	−0.582751	+	1.00936i	−0.995152	+	0.0983524i	$0.968643\pi$
$504$	2.06393e13	+	1.19161e13i	0.634662	+	0.366422i
$505$	−4.75397e12			−0.144744
$506$		−	8.98814e12i		−	0.270968i
$507$	−2.36476e13	−	1.36530e13i	−0.705907	−	0.407556i
$508$	2.63030e13	−	1.51861e13i	0.777476	−	0.448876i
$509$	1.92077e13	+	1.10896e13i	0.562194	+	0.324583i	0.754026	−	0.656845i	$-0.228109\pi$
$509$	1.92077e13	+	1.10896e13i	0.562194	+	0.324583i	−0.191832	+	0.981428i	$0.561443\pi$
$510$	−9.33203e12	−	1.61635e13i	−0.270474	−	0.468474i
$511$	2.57134e12	+	4.45369e12i	0.0737998	+	0.127825i
$512$			4.00899e13i			1.13942i
$513$	−1.44182e13	−	1.13363e13i	−0.405810	−	0.319070i
$514$	−1.60395e13			−0.447070
$515$	9.32033e12	−	5.38110e12i	0.257274	−	0.148537i
$516$	−6.23089e13	+	3.59741e13i	−1.70334	+	0.983424i
$517$	1.79678e13	−	3.11211e13i	0.486453	−	0.842562i
$518$	1.71905e13	+	2.97747e13i	0.460934	+	0.798361i
$519$	−4.16291e13	+	7.21037e13i	−1.10550	+	1.91479i
$520$	3.06492e13			0.806125
$521$		−	2.54700e13i		−	0.663498i	−0.943368	−	0.331749i	$-0.892361\pi$
$521$		−	2.54700e13i		−	0.663498i	0.943368	−	0.331749i	$-0.107639\pi$
$522$	−4.07031e12	+	7.04998e12i	−0.105021	+	0.181901i
$523$	6.20162e13	+	3.58051e13i	1.58488	+	0.915032i	0.994132	+	0.108178i	$0.0345017\pi$
$523$	6.20162e13	+	3.58051e13i	1.58488	+	0.915032i	0.590751	+	0.806854i	$0.298832\pi$
$524$	−9.20048e13			−2.32892
$525$		−	4.58976e12i		−	0.115078i
$526$	7.61889e13	+	4.39877e13i	1.89218	+	1.09245i
$527$	1.04814e13	−	6.05143e12i	0.257849	−	0.148869i
$528$	−3.30493e13	−	1.90810e13i	−0.805365	−	0.464978i
$529$	2.01932e13	+	3.49757e13i	0.487447	+	0.844284i
$530$	−7.37277e12	−	1.27700e13i	−0.176300	−	0.305360i
$531$		−	5.04021e13i		−	1.19392i
$532$	1.10934e13	+	2.77024e13i	0.260320	+	0.650068i
$533$	−2.92139e13			−0.679131
$534$	−1.86100e14	+	1.07445e14i	−4.28588	+	2.47445i
$535$	1.04702e13	−	6.04500e12i	0.238884	−	0.137920i
$536$	1.09557e13	−	1.89759e13i	0.247638	−	0.428922i
$537$	−2.97459e13	−	5.15214e13i	−0.666125	−	1.15376i
$538$	4.75158e13	−	8.22997e13i	1.05421	−	1.82594i
$539$	3.94837e13			0.867909
$540$		−	1.97244e13i		−	0.429570i
$541$	−1.80724e13	+	3.13022e13i	−0.389968	+	0.675444i	−0.992445	−	0.122692i	$-0.960847\pi$
$541$	−1.80724e13	+	3.13022e13i	−0.389968	+	0.675444i	0.602477	+	0.798136i	$0.294180\pi$
$542$	6.87308e13	+	3.96817e13i	1.46945	+	0.848388i
$543$	−2.66430e13			−0.564395
$544$		−	9.76832e12i		−	0.205034i
$545$	4.18147e12	+	2.41417e12i	0.0869654	+	0.0502095i
$546$	5.06388e13	−	2.92363e13i	1.04357	−	0.602503i
$547$	4.28477e13	+	2.47381e13i	0.874965	+	0.505161i	0.868995	−	0.494821i	$-0.164766\pi$
$547$	4.28477e13	+	2.47381e13i	0.874965	+	0.505161i	0.00596973	+	0.999982i	$0.498100\pi$
$548$	−3.45512e13	−	5.98445e13i	−0.699134	−	1.21094i
$549$	4.35103e13	+	7.53621e13i	0.872430	+	1.51109i
$550$			1.72139e13i			0.342031i
$551$	−4.37714e12	+	1.75283e12i	−0.0861852	+	0.0345129i
$552$	−1.80744e13			−0.352670
$553$	1.57887e13	−	9.11563e12i	0.305296	−	0.176263i
$554$	−1.21139e14	+	6.99398e13i	−2.32133	+	1.34022i
$555$	2.60732e13	−	4.51602e13i	0.495142	−	0.857612i
$556$	7.35839e13	+	1.27451e14i	1.38487	+	2.39866i
$557$	−2.29819e12	+	3.98057e12i	−0.0428656	+	0.0742454i	−0.886662	−	0.462418i	$-0.846982\pi$
$557$	−2.29819e12	+	3.98057e12i	−0.0428656	+	0.0742454i	0.843797	+	0.536663i	$0.180315\pi$
$558$	7.79054e13			1.44011
$559$			4.67250e13i			0.856033i
$560$	−2.78789e12	+	4.82876e12i	−0.0506215	+	0.0876790i
$561$	3.47973e13	+	2.00903e13i	0.626227	+	0.361552i
$562$	6.59742e13			1.17677
$563$		−	9.63803e13i		−	1.70391i	−0.523616	−	0.851954i	$-0.675417\pi$
$563$		−	9.63803e13i		−	1.70391i	0.523616	−	0.851954i	$-0.324583\pi$
$564$	−1.35291e14	−	7.81101e13i	−2.37068	−	1.36871i
$565$	−1.32291e13	+	7.63783e12i	−0.229767	+	0.132656i
$566$	−8.70889e13	−	5.02808e13i	−1.49927	−	0.865605i
$567$	6.04685e12	+	1.04734e13i	0.103184	+	0.178721i
$568$	−6.86991e13	−	1.18990e14i	−1.16201	−	2.01266i
$569$		−	1.42700e13i		−	0.239256i	−0.992819	−	0.119628i	$-0.961830\pi$
$569$		−	1.42700e13i		−	0.239256i	0.992819	−	0.119628i	$-0.0381702\pi$
$570$	4.30093e13	−	5.47016e13i	0.714806	−	0.909129i
$571$	8.35572e13			1.37659			0.688293	−	0.725433i	$-0.258360\pi$
$571$	8.35572e13			1.37659			0.688293	+	0.725433i	$0.258360\pi$
$572$	−1.23532e14	+	7.13211e13i	−2.01743	+	1.16476i
$573$	3.89485e13	−	2.24870e13i	0.630548	−	0.364047i
$574$	1.08769e13	−	1.88394e13i	0.174561	−	0.302348i
$575$	9.95911e11	+	1.72497e12i	0.0158446	+	0.0274437i
$576$	5.69482e13	−	9.86372e13i	0.898189	−	1.55571i
$577$	−3.84020e13			−0.600447			−0.300224	−	0.953869i	$-0.597061\pi$
$577$	−3.84020e13			−0.600447			−0.300224	+	0.953869i	$0.597061\pi$
$578$			8.52402e13i			1.32131i
$579$	−8.42426e13	+	1.45912e14i	−1.29461	+	2.24233i
$580$	−4.39132e12	−	2.53533e12i	−0.0669045	−	0.0386273i
$581$	−2.37237e13			−0.358345
$582$		−	1.20922e14i		−	1.81088i
$583$	2.74916e13	+	1.58723e13i	0.408186	+	0.235666i
$584$	−3.35895e13	+	1.93929e13i	−0.494470	+	0.285482i
$585$	−4.39493e13	−	2.53741e13i	−0.641464	−	0.370350i
$586$	−5.66481e13	−	9.81173e13i	−0.819779	−	1.41990i
$587$	6.31259e13	+	1.09337e14i	0.905768	+	1.56884i	0.819883	+	0.572531i	$0.194039\pi$
$587$	6.31259e13	+	1.09337e14i	0.905768	+	1.56884i	0.0858853	+	0.996305i	$0.472628\pi$
$588$		−	1.71645e14i		−	2.44199i
$589$	3.54717e13	+	2.78898e13i	0.500386	+	0.393431i
$590$	4.82670e13			0.675135
$591$	−1.19085e14	+	6.87538e13i	−1.65166	+	0.953585i
$592$	−5.48619e13	+	3.16745e13i	−0.754506	+	0.435614i
$593$	3.61524e13	−	6.26177e13i	0.493018	−	0.853933i	−0.506949	−	0.861976i	$-0.669227\pi$
$593$	3.61524e13	−	6.26177e13i	0.493018	−	0.853933i	0.999968	+	0.00804288i	$0.00256016\pi$
$594$	3.26420e13	+	5.65376e13i	0.441412	+	0.764549i
$595$	2.93534e12	−	5.08416e12i	0.0393617	−	0.0681764i
$596$	−1.68010e14			−2.23410
$597$		−	3.24719e13i		−	0.428190i
$598$	−1.26877e13	+	2.19758e13i	−0.165912	+	0.287368i
$599$	6.66650e13	+	3.84891e13i	0.864498	+	0.499118i	0.865516	−	0.500882i	$-0.166991\pi$
$599$	6.66650e13	+	3.84891e13i	0.864498	+	0.499118i	−0.00101824	+	0.999999i	$0.500324\pi$
$600$	3.46157e13			0.445161
$601$			1.01524e13i			0.129478i	0.997902	+	0.0647391i	$0.0206215\pi$
$601$			1.01524e13i			0.129478i	−0.997902	+	0.0647391i	$0.979378\pi$
$602$	−3.01319e13	−	1.73967e13i	−0.381105	−	0.220031i
$603$	−3.14199e13	+	1.81403e13i	−0.394110	+	0.227540i
$604$	−2.00102e13	−	1.15529e13i	−0.248924	−	0.143716i
$605$	−4.04969e11	−	7.01427e11i	−0.00499626	−	0.00865378i
$606$	−3.42014e13	−	5.92385e13i	−0.418485	−	0.724838i
$607$		−	1.10995e14i		−	1.34697i	−0.739199	−	0.673487i	$-0.764796\pi$
$607$		−	1.10995e14i		−	1.34697i	0.739199	−	0.673487i	$-0.235204\pi$
$608$	3.38090e13	−	1.35389e13i	0.406926	−	0.162954i
$609$	−4.47485e12			−0.0534186
$610$	−7.21697e13	+	4.16672e13i	−0.854487	+	0.493338i
$611$	−8.78614e13	+	5.07268e13i	−1.03179	+	0.595705i
$612$	4.99758e13	−	8.65607e13i	0.582107	−	1.00824i
$613$	−3.96658e13	−	6.87031e13i	−0.458261	−	0.793732i	0.540608	−	0.841275i	$-0.318194\pi$
$613$	−3.96658e13	−	6.87031e13i	−0.458261	−	0.793732i	−0.998869	+	0.0475427i	$0.984861\pi$
$614$	3.93122e13	−	6.80908e13i	0.450491	−	0.780273i
$615$	−3.29947e13			−0.375032
$616$		−	4.91332e13i		−	0.553952i
$617$	7.78261e13	−	1.34799e14i	0.870361	−	1.50751i	0.00873828	−	0.999962i	$-0.497218\pi$
$617$	7.78261e13	−	1.34799e14i	0.870361	−	1.50751i	0.861623	−	0.507548i	$-0.169448\pi$
$618$	1.34106e14	+	7.74262e13i	1.48767	+	0.858906i
$619$	−2.25788e12			−0.0248455			−0.0124227	−	0.999923i	$-0.503954\pi$
$619$	−2.25788e12			−0.0248455			−0.0124227	+	0.999923i	$0.503954\pi$
$620$			4.85261e13i			0.529684i
$621$	6.54197e12	+	3.77701e12i	0.0708354	+	0.0408968i
$622$	4.46869e13	−	2.58000e13i	0.479986	−	0.277120i
$623$	−5.85367e13	−	3.37962e13i	−0.623718	−	0.360104i
$624$	5.38698e13	+	9.33053e13i	0.569407	+	0.986241i
$625$	−1.90735e12	−	3.30362e12i	−0.0200000	−	0.0346410i
$626$			1.29007e14i			1.34197i
$627$	−2.13052e13	+	1.48282e14i	−0.219861	+	1.53021i
$628$	2.54329e14			2.60374
$629$	5.77636e13	−	3.33498e13i	0.586680	−	0.338720i
$630$	3.27264e13	−	1.88946e13i	0.329759	−	0.190386i
$631$	4.59603e13	−	7.96056e13i	0.459448	−	0.795787i	−0.539484	−	0.841996i	$-0.681381\pi$
$631$	4.59603e13	−	7.96056e13i	0.459448	−	0.795787i	0.998932	+	0.0462090i	$0.0147140\pi$
$632$	6.87497e13	+	1.19078e14i	0.681844	+	1.18099i
$633$	−1.33495e14	+	2.31220e14i	−1.31355	+	2.27514i
$634$	1.37690e14			1.34418
$635$		−	2.22771e13i		−	0.215770i
$636$	6.90007e13	−	1.19513e14i	0.663083	−	1.14849i
$637$	−9.65366e13	−	5.57354e13i	−0.920439	−	0.531416i
$638$	1.67830e13			0.158769
$639$			2.27501e14i			2.13540i
$640$	7.62301e13	+	4.40115e13i	0.709948	+	0.409889i
$641$	−1.42683e14	+	8.23779e13i	−1.31850	+	0.761238i	−0.983488	−	0.180974i	$-0.942075\pi$
$641$	−1.42683e14	+	8.23779e13i	−1.31850	+	0.761238i	−0.335016	+	0.942213i	$0.608742\pi$
$642$	1.50652e14	+	8.69788e13i	1.38133	+	0.797514i
$643$	−8.78902e13	−	1.52230e14i	−0.799624	−	1.38499i	−0.919861	−	0.392244i	$-0.871699\pi$
$643$	−8.78902e13	−	1.52230e14i	−0.799624	−	1.38499i	0.120238	−	0.992745i	$-0.461634\pi$
$644$	−6.14520e12	−	1.06438e13i	−0.0554762	−	0.0960876i
$645$			5.27720e13i			0.472721i
$646$	8.26262e13	−	3.30877e13i	0.734438	−	0.294106i
$647$	−8.77101e13			−0.773621			−0.386810	−	0.922159i	$-0.626423\pi$
$647$	−8.77101e13			−0.773621			−0.386810	+	0.922159i	$0.626423\pi$
$648$	−7.89903e13	+	4.56051e13i	−0.691351	+	0.399152i
$649$	−8.99893e13	+	5.19553e13i	−0.781569	+	0.451239i
$650$	2.42993e13	−	4.20876e13i	0.209424	−	0.362733i
$651$	2.14121e13	+	3.70868e13i	0.183128	+	0.317186i
$652$	−1.82831e14	+	3.16672e14i	−1.55171	+	2.68765i
$653$	−9.18743e13			−0.773799			−0.386900	−	0.922122i	$-0.626454\pi$
$653$	−9.18743e13			−0.773799			−0.386900	+	0.922122i	$0.626454\pi$
$654$			6.94730e13i			0.580667i
$655$	−3.37415e13	+	5.84420e13i	−0.279871	+	0.484751i
$656$	3.47128e13	+	2.00415e13i	0.285740	+	0.164972i
$657$	6.42208e13			0.524625
$658$		−	7.55465e13i		−	0.612470i
$659$	1.30331e13	+	7.52469e12i	0.104863	+	0.0605427i	0.551514	−	0.834165i	$-0.314050\pi$
$659$	1.30331e13	+	7.52469e12i	0.104863	+	0.0605427i	−0.446651	+	0.894708i	$0.647384\pi$
$660$	−1.39519e14	+	8.05513e13i	−1.11407	+	0.643210i
$661$	−1.97085e14	−	1.13787e14i	−1.56187	−	0.901748i	−0.997068	−	0.0765249i	$-0.975618\pi$
$661$	−1.97085e14	−	1.13787e14i	−1.56187	−	0.901748i	−0.564806	−	0.825223i	$-0.691049\pi$
$662$	1.14433e14	+	1.98204e14i	0.900040	+	1.55891i
$663$	−5.67190e13	−	9.82403e13i	−0.442753	−	0.766870i
$664$		−	1.78923e14i		−	1.38620i
$665$	2.16651e13	+	3.11285e12i	0.166591	+	0.0239359i
$666$	4.29342e14			3.27667
$667$	1.68178e12	−	9.70979e11i	0.0127392	−	0.00735496i
$668$	1.50860e14	−	8.70990e13i	1.13420	−	0.654833i
$669$	−1.72697e14	+	2.99121e14i	−1.28871	+	2.23211i
$670$	−1.73718e13	−	3.00889e13i	−0.128668	−	0.222860i
$671$	8.97023e13	−	1.55369e14i	0.659464	−	1.14222i
$672$	3.45638e13			0.252217
$673$		−	1.68618e14i		−	1.22132i	−0.791893	−	0.610660i	$-0.790904\pi$
$673$		−	1.68618e14i		−	1.22132i	0.791893	−	0.610660i	$-0.209096\pi$
$674$	9.58728e13	−	1.66056e14i	0.689280	−	1.19387i
$675$	−1.25290e13	−	7.23365e12i	−0.0894127	−	0.0516224i
$676$	1.40037e14			0.991995
$677$		−	3.17023e12i		−	0.0222919i	−0.999938	−	0.0111460i	$-0.996452\pi$
$677$		−	3.17023e12i		−	0.0222919i	0.999938	−	0.0111460i	$-0.00354794\pi$
$678$	−1.90348e14	−	1.09897e14i	−1.32862	−	0.767077i
$679$	3.29396e13	−	1.90177e13i	0.228228	−	0.131768i
$680$	3.83445e13	+	2.21382e13i	0.263729	+	0.152264i
$681$	−1.84497e14	−	3.19557e14i	−1.25966	−	2.18179i
$682$	−8.03062e13	−	1.39094e14i	−0.544286	−	0.942731i
$683$		−	8.42752e13i		−	0.567017i	−0.958970	−	0.283509i	$-0.908502\pi$
$683$		−	8.42752e13i		−	0.567017i	0.958970	−	0.283509i	$-0.0914984\pi$
$684$	3.68861e14	+	5.29981e13i	2.46367	+	0.353981i
$685$	−5.06848e13			−0.336066
$686$	1.55631e14	−	8.98536e13i	1.02441	−	0.591446i
$687$	−3.45093e14	+	1.99240e14i	−2.25503	+	1.30194i
$688$	3.20545e13	−	5.55200e13i	0.207944	−	0.360170i
$689$	−4.48109e13	−	7.76147e13i	−0.288594	−	0.499859i
$690$	−1.43297e13	+	2.48198e13i	−0.0916205	+	0.158691i
$691$	−1.68332e14			−1.06850			−0.534252	−	0.845325i	$-0.679407\pi$
$691$	−1.68332e14			−1.06850			−0.534252	+	0.845325i	$0.679407\pi$
$692$		−	4.26985e14i		−	2.69080i
$693$	−4.06769e13	+	7.04544e13i	−0.254496	+	0.440800i
$694$	−1.80612e14	−	1.04276e14i	−1.12189	−	0.647721i
$695$	1.07944e14			0.665692
$696$		−	3.37491e13i		−	0.206641i
$697$	−3.65488e13	−	2.11015e13i	−0.222182	−	0.128277i
$698$	−5.88894e13	+	3.39998e13i	−0.355435	+	0.205211i
$699$	−7.99998e13	−	4.61879e13i	−0.479406	−	0.276785i
$700$	1.17692e13	+	2.03848e13i	0.0700253	+	0.121287i
$701$	1.15779e14	+	2.00536e14i	0.683977	+	1.18468i	0.973757	+	0.227589i	$0.0730844\pi$
$701$	1.15779e14	+	2.00536e14i	0.683977	+	1.18468i	−0.289780	+	0.957093i	$0.593582\pi$
$702$		−	1.84311e14i		−	1.08110i
$703$	1.95487e14	+	1.53702e14i	1.13852	+	0.895166i
$704$	−2.34813e14			−1.35787
$705$	−9.92321e13	+	5.72917e13i	−0.569779	+	0.328962i
$706$	−9.66073e13	+	5.57762e13i	−0.550790	+	0.317999i
$707$	1.07579e13	−	1.86332e13i	0.0609016	−	0.105485i
$708$	2.25862e14	+	3.91205e14i	1.26963	+	2.19906i
$709$	−2.47874e13	+	4.29330e13i	−0.138356	+	0.239640i	−0.926875	−	0.375371i	$-0.877515\pi$
$709$	−2.47874e13	+	4.29330e13i	−0.138356	+	0.239640i	0.788518	+	0.615011i	$0.210849\pi$
$710$	−2.17864e14			−1.20752
$711$		−	2.27668e14i		−	1.25301i
$712$	2.54889e14	−	4.41481e14i	1.39300	−	2.41275i
$713$	−1.60946e13	−	9.29223e12i	−0.0873440	−	0.0504281i
$714$	8.44706e13			0.455213
$715$			1.04624e14i			0.559889i
$716$	2.64225e14	+	1.52550e14i	1.40413	+	0.810677i
$717$	−4.45689e13	+	2.57319e13i	−0.235199	+	0.135792i
$718$	3.04399e14	+	1.75745e14i	1.59522	+	0.921003i
$719$	5.07876e13	+	8.79666e13i	0.264310	+	0.457798i	0.967383	−	0.253320i	$-0.0815226\pi$
$719$	5.07876e13	+	8.79666e13i	0.264310	+	0.457798i	−0.703073	+	0.711118i	$0.748189\pi$
$720$	3.48146e13	+	6.03006e13i	0.179928	+	0.311644i
$721$			4.87080e13i			0.249991i
$722$	2.29039e14	+	2.40117e14i	1.16741	+	1.22388i
$723$	1.10200e14			0.557816
$724$	1.18331e14	−	6.83185e13i	0.594848	−	0.343436i
$725$	−3.22092e12	+	1.85960e12i	−0.0160801	+	0.00928387i
$726$	5.82692e12	−	1.00925e13i	0.0288906	−	0.0500399i
$727$	7.39905e13	+	1.28155e14i	0.364338	+	0.631052i	0.988670	−	0.150108i	$-0.0479620\pi$
$727$	7.39905e13	+	1.28155e14i	0.364338	+	0.631052i	−0.624332	+	0.781159i	$0.714629\pi$
$728$	−6.93568e13	+	1.20129e14i	−0.339181	+	0.587479i
$729$	3.13528e14			1.52278
$730$			6.15003e13i			0.296663i
$731$	−3.37499e13	+	5.84566e13i	−0.161691	+	0.280057i
$732$	−6.75426e14	−	3.89957e14i	−3.21383	−	1.85550i
$733$	−6.50499e13			−0.307416			−0.153708	−	0.988116i	$-0.549122\pi$
$733$	−6.50499e13			−0.307416			−0.153708	+	0.988116i	$0.549122\pi$
$734$		−	6.99425e14i		−	3.28293i
$735$	−1.09030e14	−	6.29486e13i	−0.508288	−	0.293460i
$736$	−1.29901e13	+	7.49984e12i	−0.0601483	+	0.0347266i
$737$	6.47762e13	+	3.73986e13i	0.297905	+	0.171996i
$738$	−1.35829e14	−	2.35263e14i	−0.620455	−	1.07466i
$739$	1.68586e11	+	2.91999e11i	0.000764889	+	0.00132483i	0.866408	−	0.499337i	$-0.166423\pi$
$739$	1.68586e11	+	2.91999e11i	0.000764889	+	0.00132483i	−0.865643	+	0.500662i	$0.833090\pi$
$740$			2.67430e14i			1.20518i
$741$	2.61406e14	−	3.32470e14i	1.17010	−	1.48820i
$742$	6.67360e13			0.296716
$743$	1.69278e14	−	9.77326e13i	0.747577	−	0.431614i	−0.0772406	−	0.997012i	$-0.524611\pi$
$743$	1.69278e14	−	9.77326e13i	0.747577	−	0.431614i	0.824818	+	0.565399i	$0.191278\pi$
$744$	−2.79707e14	+	1.61489e14i	−1.22698	+	0.708399i
$745$	−6.16154e13	+	1.06721e14i	−0.268477	+	0.465016i
$746$	3.74421e14	+	6.48516e14i	1.62056	+	2.80690i
$747$	−1.48128e14	+	2.56566e14i	−0.636848	+	1.10305i
$748$	−2.06064e14			−0.880021
$749$			5.47174e13i			0.232122i
$750$	2.74440e13	−	4.75344e13i	0.115649	−	0.200310i
$751$	−3.14283e14	−	1.81452e14i	−1.31559	−	0.759558i	−0.332577	−	0.943076i	$-0.607918\pi$
$751$	−3.14283e14	−	1.81452e14i	−1.31559	−	0.759558i	−0.983016	+	0.183518i	$0.941252\pi$
$752$	1.39199e14			0.578826
$753$			3.41207e14i			1.40943i
$754$	−4.10339e13	−	2.36909e13i	−0.168378	−	0.0972132i
$755$	−1.46770e13	+	8.47374e12i	−0.0598275	+	0.0345414i
$756$	7.73096e13	+	4.46347e13i	0.313058	+	0.180744i
$757$	1.94283e14	+	3.36507e14i	0.781546	+	1.35368i	0.931041	+	0.364914i	$0.118902\pi$
$757$	1.94283e14	+	3.36507e14i	0.781546	+	1.35368i	−0.149495	+	0.988762i	$0.547765\pi$
$758$	−1.41962e14	−	2.45886e14i	−0.567319	−	0.982625i
$759$		−	6.16989e13i		−	0.244945i
$760$	−2.34770e13	+	1.63397e14i	−0.0925922	+	0.644431i
$761$	1.44502e14			0.566177			0.283088	−	0.959094i	$-0.408641\pi$
$761$	1.44502e14			0.566177			0.283088	+	0.959094i	$0.408641\pi$
$762$	2.77592e14	−	1.60268e14i	1.08052	−	0.623838i
$763$	−1.89247e13	+	1.09262e13i	−0.0731823	+	0.0422518i
$764$	−1.15323e14	+	1.99746e14i	−0.443047	+	0.767380i
$765$	−3.66560e13	−	6.34900e13i	−0.139906	−	0.242325i
$766$	4.06027e13	−	7.03259e13i	0.153961	−	0.266668i
$767$	2.93362e14			1.10516
$768$			7.17925e14i			2.68703i
$769$	2.05469e14	−	3.55882e14i	0.764036	−	1.32335i	−0.176719	−	0.984261i	$-0.556548\pi$
$769$	2.05469e14	−	3.55882e14i	0.764036	−	1.32335i	0.940755	−	0.339088i	$-0.110118\pi$
$770$	−6.74699e13	−	3.89538e13i	−0.249262	−	0.143912i
$771$	−1.10103e14			−0.404135
$772$		−	8.64067e14i		−	3.15109i
$773$	7.18814e13	+	4.15007e13i	0.260447	+	0.150369i	0.624538	−	0.780994i	$-0.285287\pi$
$773$	7.18814e13	+	4.15007e13i	0.260447	+	0.150369i	−0.364092	+	0.931363i	$0.618621\pi$
$774$	−3.76281e14	+	2.17246e14i	−1.35459	+	0.782073i
$775$	3.08241e13	+	1.77963e13i	0.110251	+	0.0636533i
$776$	1.43431e14	+	2.48429e14i	0.509721	+	0.882864i
$777$	1.18003e14	+	2.04388e14i	0.416667	+	0.721689i
$778$			4.20315e14i			1.47461i
$779$	2.23776e13	−	1.55745e14i	0.0780055	−	0.542910i
$780$	4.54827e14			1.57533
$781$	4.06186e14	−	2.34512e14i	1.39788	−	0.807067i
$782$	−3.17466e13	+	1.83289e13i	−0.108558	+	0.0626762i
$783$	−7.05255e12	+	1.22154e13i	−0.0239628	+	0.0415048i
$784$	7.64718e13	+	1.32453e14i	0.258179	+	0.447179i
$785$	9.32719e13	−	1.61552e14i	0.312898	−	0.541955i
$786$	−9.70984e14			−3.23668
$787$			2.49733e14i			0.827184i	0.910462	+	0.413592i	$0.135726\pi$
$787$			2.49733e14i			0.827184i	−0.910462	+	0.413592i	$0.864274\pi$
$788$	3.52600e14	−	6.10722e14i	1.16052	−	2.01007i
$789$	5.22996e14	+	3.01952e14i	1.71046	+	0.987536i
$790$	2.18024e14			0.708548
$791$		−	6.91353e13i		−	0.223263i
$792$	−5.31364e14	−	3.06783e14i	−1.70516	−	0.984477i
$793$	−4.38639e14	+	2.53249e14i	−1.39876	+	0.807572i
$794$	3.14673e14	+	1.81676e14i	0.997141	+	0.575700i
$795$	−5.06102e13	−	8.76594e13i	−0.159368	−	0.276034i
$796$	8.32653e13	+	1.44220e14i	0.260554	+	0.451294i
$797$			6.65304e13i			0.206885i	0.994635	+	0.103442i	$0.0329858\pi$
$797$			6.65304e13i			0.206885i	−0.994635	+	0.103442i	$0.967014\pi$
$798$	1.17076e14	+	2.92360e14i	0.361787	+	0.903450i
$799$	−1.46562e14			−0.450077
$800$	2.48784e13	−	1.43635e13i	0.0759228	−	0.0438340i
$801$	−7.30995e14	+	4.22040e14i	−2.21693	+	1.27994i
$802$	−4.09742e14	+	7.09694e14i	−1.23492	+	2.13894i
$803$	−6.61998e13	−	1.14661e14i	−0.198280	−	0.343431i
$804$	1.62580e14	−	2.81598e14i	0.483936	−	0.838202i
$805$	−9.01468e12			−0.0266668
$806$			4.53443e14i			1.33305i
$807$	3.26171e14	−	5.64944e14i	0.952966	−	1.65059i
$808$	1.40530e14	+	8.11353e13i	0.408050	+	0.235588i
$809$	5.12698e14			1.47951			0.739757	−	0.672875i	$-0.234941\pi$
$809$	5.12698e14			1.47951			0.739757	+	0.672875i	$0.234941\pi$
$810$			1.44626e14i			0.414784i
$811$	9.46980e11	+	5.46739e11i	0.00269921	+	0.00155839i	0.501349	−	0.865245i	$-0.332837\pi$
$811$	9.46980e11	+	5.46739e11i	0.00269921	+	0.00155839i	−0.498650	+	0.866804i	$0.666171\pi$
$812$	1.98745e13	−	1.14745e13i	0.0563009	−	0.0325053i
$813$	4.71801e14	+	2.72394e14i	1.32833	+	0.766911i
$814$	−4.42573e14	−	7.66558e14i	−1.23840	−	2.14498i
$815$	1.34102e14	+	2.32271e14i	0.372946	+	0.645961i
$816$			1.55643e14i			0.430207i
$817$	−2.49101e14	−	3.57909e13i	−0.684328	−	0.0983246i
$818$	4.04601e14			1.10474
$819$	1.98908e14	−	1.14839e14i	0.539799	−	0.311653i
$820$	1.46541e14	−	8.46057e13i	0.395267	−	0.228208i
$821$	5.53522e13	−	9.58728e13i	0.148395	−	0.257028i	−0.782239	−	0.622978i	$-0.785923\pi$
$821$	5.53522e13	−	9.58728e13i	0.148395	−	0.257028i	0.930634	+	0.365950i	$0.119256\pi$
$822$	−3.64641e14	−	6.31576e14i	−0.971641	−	1.68293i
$823$	−2.94225e14	+	5.09613e14i	−0.779256	+	1.34971i	0.153115	+	0.988208i	$0.451070\pi$
$823$	−2.94225e14	+	5.09613e14i	−0.779256	+	1.34971i	−0.932371	+	0.361503i	$0.882264\pi$
$824$	−3.67354e14			−0.967049
$825$			1.18164e14i			0.309184i
$826$	−1.09225e14	+	1.89183e14i	−0.284067	+	0.492018i
$827$	5.15963e14	+	2.97891e14i	1.33380	+	0.770070i	0.985880	−	0.167454i	$-0.0535547\pi$
$827$	5.15963e14	+	2.97891e14i	1.33380	+	0.770070i	0.347920	+	0.937524i	$0.386888\pi$
$828$	−1.53480e14			−0.394367
$829$		−	5.09376e14i		−	1.30097i	−0.759521	−	0.650483i	$-0.774566\pi$
$829$		−	5.09376e14i		−	1.30097i	0.759521	−	0.650483i	$-0.225434\pi$
$830$	−2.45698e14	−	1.41854e14i	−0.623750	−	0.360122i
$831$	−8.31557e14	+	4.80100e14i	−2.09839	+	1.21151i
$832$	5.74110e14	+	3.31463e14i	1.44005	+	0.831416i
$833$	−8.05164e13	−	1.39459e14i	−0.200752	−	0.347712i
$834$	7.76577e14	+	1.34507e15i	1.92466	+	3.33361i
$835$		−	1.27770e14i		−	0.314771i
$836$	−2.85603e14	−	7.13204e14i	−0.699410	−	1.74656i
$837$	1.34985e14			0.328594
$838$	3.64771e14	−	2.10601e14i	0.882673	−	0.509612i
$839$	−1.87239e12	+	1.08102e12i	−0.00450388	+	0.00260031i	−0.502250	−	0.864722i	$-0.667494\pi$
$839$	−1.87239e12	+	1.08102e12i	−0.00450388	+	0.00260031i	0.497746	+	0.867323i	$0.334161\pi$
$840$	−7.83327e13	+	1.35676e14i	−0.187304	+	0.324420i
$841$	−2.08541e14	−	3.61203e14i	−0.495690	−	0.858561i
$842$	−6.35934e14	+	1.10147e15i	−1.50263	+	2.60263i
$843$	4.52878e14			1.06376
$844$		−	1.36925e15i		−	3.19720i
$845$	5.13567e13	−	8.89524e13i	0.119210	−	0.206478i
$846$	−8.17016e14	−	4.71705e14i	−1.88529	−	1.08847i
$847$	3.66566e12			0.00840881
$848$			1.22965e14i			0.280417i
$849$	−5.97819e14	−	3.45151e14i	−1.35529	−	0.782476i
$850$	6.08005e13	−	3.51032e13i	0.137029	−	0.0791137i
$851$	−8.86985e13	−	5.12101e13i	−0.198732	−	0.114738i
$852$	−1.01948e15	−	1.76579e15i	−2.27081	−	3.93315i
$853$	9.85378e13	+	1.70673e14i	0.218202	+	0.377936i	0.954258	−	0.298984i	$-0.0966476\pi$
$853$	9.85378e13	+	1.70673e14i	0.218202	+	0.377936i	−0.736057	+	0.676920i	$0.763314\pi$
$854$		−	3.77159e14i		−	0.830299i
$855$	1.68939e14	−	2.14866e14i	0.369743	−	0.470260i
$856$	−4.12676e14			−0.897927
$857$	2.57411e14	−	1.48616e14i	0.556829	−	0.321486i	−0.195043	−	0.980795i	$-0.562484\pi$
$857$	2.57411e14	−	1.48616e14i	0.556829	−	0.321486i	0.751872	+	0.659309i	$0.229151\pi$
$858$	−1.30371e15	+	7.52696e14i	−2.80378	+	1.61876i
$859$	1.01075e14	−	1.75068e14i	0.216112	−	0.374318i	−0.737504	−	0.675343i	$-0.763996\pi$
$859$	1.01075e14	−	1.75068e14i	0.216112	−	0.374318i	0.953616	+	0.301025i	$0.0973289\pi$
$860$	−1.35319e14	−	2.34380e14i	−0.287652	−	0.498228i
$861$	7.46644e13	−	1.29323e14i	0.157797	−	0.273312i
$862$	2.25198e14			0.473183
$863$		−	3.66704e14i		−	0.766058i	−0.923736	−	0.383029i	$-0.874881\pi$
$863$		−	3.66704e14i		−	0.766058i	0.923736	−	0.383029i	$-0.125119\pi$
$864$	5.44739e13	−	9.43516e13i	0.113141	−	0.195966i
$865$	−2.71224e14	−	1.56591e14i	−0.560076	−	0.323360i
$866$	7.56195e14			1.55254
$867$			5.85129e14i			1.19442i
$868$	−1.90198e14	−	1.09811e14i	−0.386017	−	0.222867i
$869$	−4.06485e14	+	2.34684e14i	−0.820249	+	0.473571i
$870$	−4.63444e13	−	2.67569e13i	−0.0929824	−	0.0536834i
$871$	−1.05584e14	−	1.82877e14i	−0.210624	−	0.364811i
$872$	−8.24047e13	−	1.42729e14i	−0.163444	−	0.283094i
$873$		−	4.74978e14i		−	0.936704i
$874$	−1.07439e14	−	8.44741e13i	−0.210670	−	0.165640i
$875$	1.72647e13			0.0336604
$876$	−4.98461e14	+	2.87786e14i	−0.966296	+	0.557891i
$877$	−3.50313e14	+	2.02253e14i	−0.675240	+	0.389850i	−0.798059	−	0.602579i	$-0.794140\pi$
$877$	−3.50313e14	+	2.02253e14i	−0.675240	+	0.389850i	0.122819	+	0.992429i	$0.460807\pi$
$878$	−1.06631e14	+	1.84690e14i	−0.204366	+	0.353973i
$879$	−3.88859e14	−	6.73524e14i	−0.741051	−	1.28354i
$880$	7.17748e13	−	1.24318e14i	0.136006	−	0.235570i
$881$	−8.75833e14			−1.65022			−0.825110	−	0.564972i	$-0.808887\pi$
$881$	−8.75833e14			−1.65022			−0.825110	+	0.564972i	$0.808887\pi$
$882$		−	1.03656e15i		−	1.94201i
$883$	3.60823e13	−	6.24964e13i	0.0672188	−	0.116426i	−0.830457	−	0.557082i	$-0.811921\pi$
$883$	3.60823e13	−	6.24964e13i	0.0672188	−	0.116426i	0.897676	+	0.440656i	$0.145254\pi$
$884$	5.03820e14	+	2.90881e14i	0.933285	+	0.538832i
$885$	3.31328e14			0.610298
$886$			2.36657e14i			0.433462i
$887$	6.80504e14	+	3.92889e14i	1.23940	+	0.715569i	0.968972	−	0.247170i	$-0.0795007\pi$
$887$	6.80504e14	+	3.92889e14i	1.23940	+	0.715569i	0.270430	+	0.962740i	$0.412834\pi$
$888$	−1.54148e15	+	8.89977e14i	−2.79174	+	1.61181i
$889$	8.73151e13	+	5.04114e13i	0.157246	+	0.0907863i
$890$	−4.04162e14	−	7.00029e14i	−0.723778	−	1.25362i
$891$	−1.55678e14	−	2.69642e14i	−0.277228	−	0.480174i
$892$		−	1.77134e15i		−	3.13673i
$893$	−2.03134e14	−	5.07263e14i	−0.357705	−	0.893256i
$894$	−1.77311e15			−3.10491
$895$	1.93802e14	−	1.11892e14i	0.337476	−	0.194842i
$896$	−3.45006e14	+	1.99189e14i	−0.597429	+	0.344926i
$897$	−8.70945e13	+	1.50852e14i	−0.149978	+	0.259770i
$898$	3.87937e14	+	6.71926e14i	0.664323	+	1.15064i
$899$	1.73508e13	−	3.00524e13i	0.0295474	−	0.0511777i
$900$	2.93942e14			0.497793
$901$		−	1.29469e14i		−	0.218043i
$902$	−2.80029e14	+	4.85025e14i	−0.468998	+	0.812328i
$903$	−2.06840e14	−	1.19419e14i	−0.344505	−	0.198900i
$904$	5.21415e14			0.863658
$905$		−	1.00220e14i		−	0.165086i
$906$	−2.11180e14	−	1.21925e14i	−0.345949	−	0.199734i
$907$	1.04469e15	−	6.03154e14i	1.70197	−	0.982633i	0.758206	−	0.652015i	$-0.226076\pi$
$907$	1.04469e15	−	6.03154e14i	1.70197	−	0.982633i	0.943765	−	0.330618i	$-0.107257\pi$
$908$	1.63883e15	+	9.46181e14i	2.65525	+	1.53301i
$909$	−1.34342e14	−	2.32687e14i	−0.216467	−	0.374933i
$910$	1.09975e14	+	1.90482e14i	0.176232	+	0.305244i
$911$		−	9.72136e13i		−	0.154930i	−0.996995	−	0.0774650i	$-0.975317\pi$
$911$		−	9.72136e13i		−	0.154930i	0.996995	−	0.0774650i	$-0.0246826\pi$
$912$	−5.38693e14	+	2.15720e14i	−0.853822	+	0.341914i
$913$	6.10773e14			0.962777
$914$	−1.58740e15	+	9.16488e14i	−2.48861	+	1.43680i
$915$	−4.95407e14	+	2.86023e14i	−0.772425	+	0.445960i
$916$	1.02179e15	−	1.76979e15i	1.58447	−	2.74438i
$917$	−1.52709e14	−	2.64500e14i	−0.235515	−	0.407923i
$918$	1.33129e14	−	2.30587e14i	0.204202	−	0.353688i
$919$	−7.58259e14			−1.15675			−0.578376	−	0.815770i	$-0.696313\pi$
$919$	−7.58259e14			−1.15675			−0.578376	+	0.815770i	$0.696313\pi$
$920$		−	6.79883e13i		−	0.103156i
$921$	2.69858e14	−	4.67407e14i	0.407227	−	0.705338i
$922$	−1.50262e14	−	8.67540e13i	−0.225526	−	0.130207i
$923$	−1.32415e15			−1.97665
$924$		−	7.29125e14i		−	1.08254i
$925$	1.69874e14	+	9.80765e13i	0.250852	+	0.144829i
$926$	1.25225e15	−	7.22988e14i	1.83923	−	1.06188i
$927$	5.26765e14	+	3.04128e14i	0.769518	+	0.444281i
$928$	−1.40039e13	−	2.42556e13i	−0.0203475	−	0.0352429i
$929$	1.50493e14	+	2.60662e14i	0.217489	+	0.376703i	0.954040	−	0.299680i	$-0.0968799\pi$
$929$	1.50493e14	+	2.60662e14i	0.217489	+	0.376703i	−0.736550	+	0.676383i	$0.763547\pi$
$930$			5.12126e14i			0.736143i
$931$	3.71083e14	−	4.71964e14i	0.530546	−	0.674777i
$932$	4.73745e14			0.673697
$933$	3.06752e14	−	1.77103e14i	0.433890	−	0.250506i
$934$	3.10217e14	−	1.79104e14i	0.436446	−	0.251982i
$935$	−7.55711e13	+	1.30893e14i	−0.105754	+	0.183172i
$936$	8.66114e14	+	1.50015e15i	1.20558	+	2.08812i
$937$	−6.58160e14	+	1.13997e15i	−0.911241	+	1.57832i	−0.0989280	+	0.995095i	$0.531541\pi$
$937$	−6.58160e14	+	1.13997e15i	−0.911241	+	1.57832i	−0.812313	+	0.583221i	$0.801792\pi$
$938$	1.57244e14			0.216551
$939$			8.85568e14i			1.21309i
$940$	2.93817e14	−	5.08907e14i	0.400348	−	0.693424i
$941$	4.76088e14	+	2.74869e14i	0.645266	+	0.372544i	0.786640	−	0.617412i	$-0.211819\pi$
$941$	4.76088e14	+	2.74869e14i	0.645266	+	0.372544i	−0.141374	+	0.989956i	$0.545152\pi$
$942$	2.68410e15			3.61862
$943$			6.48044e13i			0.0869053i
$944$	−3.48581e14	−	2.01253e14i	−0.464990	−	0.268462i
$945$	5.67045e13	−	3.27384e13i	0.0752417	−	0.0434408i
$946$	7.75754e14	+	4.47882e14i	1.02393	+	0.591164i
$947$	−2.87023e14	−	4.97139e14i	−0.376849	−	0.652722i	0.613753	−	0.789498i	$-0.289659\pi$
$947$	−2.87023e14	−	4.97139e14i	−0.376849	−	0.652722i	−0.990602	+	0.136777i	$0.956326\pi$
$948$	1.02023e15	+	1.76709e15i	1.33246	+	2.30790i
$949$			3.73792e14i			0.485623i
$950$	2.05764e14	+	1.61783e14i	0.265921	+	0.209081i
$951$	9.45169e14			1.21509
$952$	−1.73541e14	+	1.00194e14i	−0.221931	+	0.128132i
$953$	−1.00760e15	+	5.81737e14i	−1.28181	+	0.740052i	−0.977179	−	0.212419i	$-0.931866\pi$
$953$	−1.00760e15	+	5.81737e14i	−1.28181	+	0.740052i	−0.304629	+	0.952471i	$0.598533\pi$
$954$	4.16693e14	−	7.21734e14i	0.527320	−	0.913345i
$955$	8.45864e13	+	1.46508e14i	0.106484	+	0.184436i
$956$	1.31964e14	−	2.28569e14i	0.165260	−	0.286239i
$957$	1.15206e14			0.143521
$958$			1.96182e15i			2.43126i
$959$	1.14696e14	−	1.98659e14i	0.141402	−	0.244915i
$960$	6.48410e14	+	3.74360e14i	0.795232	+	0.459127i
$961$	4.87536e14			0.594826
$962$			2.49895e15i			3.03307i
$963$	5.91756e14	+	3.41650e14i	0.714514	+	0.412525i
$964$	−4.89440e14	+	2.82578e14i	−0.587914	+	0.339432i
$965$	−5.48861e14	−	3.16885e14i	−0.655882	−	0.378674i
$966$	−6.48541e13	−	1.12331e14i	−0.0770996	−	0.133540i
$967$	−5.08485e13	−	8.80722e13i	−0.0601376	−	0.104161i	0.834389	−	0.551176i	$-0.185821\pi$
$967$	−5.08485e13	−	8.80722e13i	−0.0601376	−	0.104161i	−0.894527	+	0.447014i	$0.852487\pi$
$968$			2.76462e13i			0.0325281i
$969$	5.67185e14	−	2.27130e14i	0.663905	−	0.265861i
$970$	4.54858e14			0.529684
$971$	6.30970e14	−	3.64291e14i	0.730992	−	0.422038i	−0.0877931	−	0.996139i	$-0.527981\pi$
$971$	6.30970e14	−	3.64291e14i	0.730992	−	0.422038i	0.818785	+	0.574100i	$0.194648\pi$
$972$	−1.89394e15	+	1.09347e15i	−2.18290	+	1.26030i
$973$	−2.44268e14	+	4.23085e14i	−0.280093	+	0.485136i
$974$	1.15116e15	+	1.99386e15i	1.31323	+	2.27458i
$975$	1.66802e14	−	2.88909e14i	0.189312	−	0.327897i
$976$	6.94939e14			0.784689
$977$			1.23254e15i			1.38461i	0.721605	+	0.692305i	$0.243405\pi$
$977$			1.23254e15i			1.38461i	−0.721605	+	0.692305i	$0.756595\pi$
$978$	−1.92953e15	+	3.34204e15i	−2.15654	+	3.73523i
$979$	1.50704e15	+	8.70092e14i	1.67576	+	0.967501i
$980$	6.45657e14			0.714284
$981$			2.72888e14i			0.300358i
$982$	−1.51338e15	−	8.73753e14i	−1.65726	−	0.956822i
$983$	8.83005e14	−	5.09803e14i	0.962045	−	0.555437i	0.0652432	−	0.997869i	$-0.479218\pi$
$983$	8.83005e14	−	5.09803e14i	0.962045	−	0.555437i	0.896802	+	0.442432i	$0.145884\pi$
$984$	9.75345e14	+	5.63115e14i	1.05726	+	0.610410i
$985$	−2.58623e14	−	4.47948e14i	−0.278924	−	0.483110i
$986$	−3.42244e13	−	5.92783e13i	−0.0367241	−	0.0636079i
$987$		−	5.18587e14i		−	0.553650i
$988$	−3.08471e14	+	2.14693e15i	−0.327665	+	2.28051i
$989$	1.03649e14			0.109543
$990$	−8.42550e14	+	4.86447e14i	−0.885972	+	0.511516i
$991$	6.45884e14	−	3.72901e14i	0.675750	−	0.390145i	−0.122502	−	0.992468i	$-0.539092\pi$
$991$	6.45884e14	−	3.72901e14i	0.675750	−	0.390145i	0.798252	+	0.602324i	$0.205758\pi$
$992$	−1.34017e14	+	2.32125e14i	−0.139509	+	0.241637i
$993$	7.85523e14	+	1.36057e15i	0.813603	+	1.40920i
$994$	4.93009e14	−	8.53917e14i	0.508069	−	0.880002i
$995$	1.22146e14			0.125246
$996$		−	2.65518e15i		−	2.70892i
$997$	−2.49827e14	+	4.32714e14i	−0.253609	+	0.439263i	−0.964517	−	0.264022i	$-0.914951\pi$
$997$	−2.49827e14	+	4.32714e14i	−0.253609	+	0.439263i	0.710908	+	0.703285i	$0.248284\pi$
$998$	−1.55857e15	−	8.99842e14i	−1.57425	−	0.908894i
$999$	7.43913e14			0.747644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.11.j.a.31.7	✓	136
19.8	odd	6	inner	95.11.j.a.46.7	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.11.j.a.31.7	✓	136	1.1	even	1	trivial
95.11.j.a.46.7	yes	136	19.8	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-46.8725 + 27.0619i) q^{2} +(-321.755 + 185.765i) q^{3} +(952.688 - 1650.10i) q^{4} +(-698.771 - 1210.31i) q^{5} +(10054.3 - 17414.6i) q^{6} +6325.06 q^{7} +47703.3i q^{8} +(39493.1 - 68404.0i) q^{9} +(65506.3 + 37820.1i) q^{10} -162840. q^{11} +707906. i q^{12} +(398140. + 229866. i) q^{13} +(-296472. + 171168. i) q^{14} +(449666. + 259615. i) q^{15} +(-315388. - 546268. i) q^{16} +(332069. + 575161. i) q^{17} +4.27502e6i q^{18} +(-1.53044e6 + 1.94649e6i) q^{19} -2.66284e6 q^{20} +(-2.03512e6 + 1.17498e6i) q^{21} +(7.63273e6 - 4.40676e6i) q^{22} +(509906. - 883184. i) q^{23} +(-8.86163e6 - 1.53488e7i) q^{24} +(-976562. + 1.69146e6i) q^{25} -2.48824e7 q^{26} +7.40725e6i q^{27} +(6.02581e6 - 1.04370e7i) q^{28} +(1.64911e6 + 952114. i) q^{29} -2.81027e7 q^{30} -1.82234e7i q^{31} +(-1.27377e7 - 7.35413e6i) q^{32} +(5.23947e7 - 3.02501e7i) q^{33} +(-3.11298e7 - 1.79728e7i) q^{34} +(-4.41977e6 - 7.65527e6i) q^{35} +(-7.52491e7 - 1.30335e8i) q^{36} -1.00430e8i q^{37} +(1.90597e7 - 1.32653e8i) q^{38} -1.70805e8 q^{39} +(5.77357e7 - 3.33337e7i) q^{40} +(-5.50319e7 + 3.17727e7i) q^{41} +(6.35941e7 - 1.10148e8i) q^{42} +(5.08176e7 + 8.80186e7i) q^{43} +(-1.55136e8 + 2.68703e8i) q^{44} -1.10386e8 q^{45} +5.51961e7i q^{46} +(-1.10340e8 + 1.91114e8i) q^{47} +(2.02955e8 + 1.17176e8i) q^{48} -2.42469e8 q^{49} -1.05710e8i q^{50} +(-2.13690e8 - 1.23374e8i) q^{51} +(7.58607e8 - 4.37982e8i) q^{52} +(-1.68826e8 - 9.74716e7i) q^{53} +(-2.00454e8 - 3.47197e8i) q^{54} +(1.13788e8 + 1.97087e8i) q^{55} +3.01726e8i q^{56} +(1.30835e8 - 9.10596e8i) q^{57} -1.03064e8 q^{58} +(5.52623e8 - 3.19057e8i) q^{59} +(8.56784e8 - 4.94664e8i) q^{60} +(-5.50860e8 + 9.54118e8i) q^{61} +(4.93159e8 + 8.54176e8i) q^{62} +(2.49796e8 - 4.32659e8i) q^{63} +1.44198e9 q^{64} -6.42496e8i q^{65} +(-1.63725e9 + 2.83580e9i) q^{66} +(-3.97790e8 - 2.29664e8i) q^{67} +1.26543e9 q^{68} +3.78892e8i q^{69} +(4.14332e8 + 2.39214e8i) q^{70} +(-2.49438e9 + 1.44013e9i) q^{71} +(3.26310e9 + 1.88395e9i) q^{72} +(4.06532e8 + 7.04134e8i) q^{73} +(2.71783e9 + 4.70742e9i) q^{74} -7.25646e8i q^{75} +(1.75389e9 + 4.37978e9i) q^{76} -1.02998e9 q^{77} +(8.00605e9 - 4.62230e9i) q^{78} +(2.49622e9 - 1.44119e9i) q^{79} +(-4.40768e8 + 7.63433e8i) q^{80} +(9.56014e8 + 1.65587e9i) q^{81} +(1.71966e9 - 2.97853e9i) q^{82} -3.75075e9 q^{83} +4.47755e9i q^{84} +(4.64081e8 - 8.03812e8i) q^{85} +(-4.76389e9 - 2.75044e9i) q^{86} -7.07480e8 q^{87} -7.76802e9i q^{88} +(-9.25473e9 - 5.34322e9i) q^{89} +(5.17409e9 - 2.98726e9i) q^{90} +(2.51826e9 + 1.45392e9i) q^{91} +(-9.71563e8 - 1.68280e9i) q^{92} +(3.38528e9 + 5.86347e9i) q^{93} -1.19440e10i q^{94} +(3.42528e9 + 4.92146e8i) q^{95} +5.46457e9 q^{96} +(5.20779e9 - 3.00672e9i) q^{97} +(1.13651e10 - 6.56166e9i) q^{98} +(-6.43106e9 + 1.11389e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 132 q^{3} + 37474 q^{4} - 1022 q^{6} - 76620 q^{7} + 1448988 q^{9} + 93750 q^{10} + 418144 q^{11} - 1256574 q^{13} + 612480 q^{14} - 20575630 q^{16} + 3635834 q^{17} + 10572814 q^{19} + 8494308 q^{21}+ \cdots - 8878413234 q^{99}+O(q^{100}) \) 136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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