LMFDB - Embedded newform 5.9.c.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,9,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.03689305031$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 $ x^6 - 2x^5 + 2x^4 - 30x^3 + 1089x^2 - 3168*x + 4608
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.3
Root			$1.52966 - 1.52966i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.9.c.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.2610 + 15.2610i) q^{2} +(-20.3321 + 20.3321i) q^{3} +209.796i q^{4} +(558.542 - 280.457i) q^{5} -620.576 q^{6} +(-2415.21 - 2415.21i) q^{7} +(705.116 - 705.116i) q^{8} +5734.21i q^{9} +O(q^{10})$	\(q+(15.2610 + 15.2610i) q^{2} +(-20.3321 + 20.3321i) q^{3} +209.796i q^{4} +(558.542 - 280.457i) q^{5} -620.576 q^{6} +(-2415.21 - 2415.21i) q^{7} +(705.116 - 705.116i) q^{8} +5734.21i q^{9} +(12804.0 + 4243.86i) q^{10} -981.878 q^{11} +(-4265.60 - 4265.60i) q^{12} +(-26582.1 + 26582.1i) q^{13} -73717.1i q^{14} +(-5654.06 + 17058.6i) q^{15} +75229.4 q^{16} +(-18503.9 - 18503.9i) q^{17} +(-87509.8 + 87509.8i) q^{18} -50374.1i q^{19} +(58838.8 + 117180. i) q^{20} +98212.6 q^{21} +(-14984.4 - 14984.4i) q^{22} +(13652.5 - 13652.5i) q^{23} +28673.0i q^{24} +(233313. - 313294. i) q^{25} -811340. q^{26} +(-249988. - 249988. i) q^{27} +(506702. - 506702. i) q^{28} +1.05137e6i q^{29} +(-346618. + 174045. i) q^{30} +1.09477e6 q^{31} +(967566. + 967566. i) q^{32} +(19963.6 - 19963.6i) q^{33} -564775. i q^{34} +(-2.02636e6 - 671634. i) q^{35} -1.20302e6 q^{36} +(77885.1 + 77885.1i) q^{37} +(768759. - 768759. i) q^{38} -1.08094e6i q^{39} +(196082. - 591591. i) q^{40} +554897. q^{41} +(1.49882e6 + 1.49882e6i) q^{42} +(-1.07414e6 + 1.07414e6i) q^{43} -205994. i q^{44} +(1.60820e6 + 3.20280e6i) q^{45} +416702. q^{46} +(-4.06986e6 - 4.06986e6i) q^{47} +(-1.52957e6 + 1.52957e6i) q^{48} +5.90168e6i q^{49} +(8.34176e6 - 1.22058e6i) q^{50} +752445. q^{51} +(-5.57683e6 - 5.57683e6i) q^{52} +(1.88025e6 - 1.88025e6i) q^{53} -7.63012e6i q^{54} +(-548420. + 275374. i) q^{55} -3.40601e6 q^{56} +(1.02421e6 + 1.02421e6i) q^{57} +(-1.60450e7 + 1.60450e7i) q^{58} -1.27248e7i q^{59} +(-3.57883e6 - 1.18620e6i) q^{60} +1.40038e7 q^{61} +(1.67073e7 + 1.67073e7i) q^{62} +(1.38493e7 - 1.38493e7i) q^{63} +1.02733e7i q^{64} +(-7.39210e6 + 2.23024e7i) q^{65} +609330. q^{66} +(-9.54151e6 - 9.54151e6i) q^{67} +(3.88204e6 - 3.88204e6i) q^{68} +555168. i q^{69} +(-2.06744e7 - 4.11741e7i) q^{70} -2.82034e7 q^{71} +(4.04328e6 + 4.04328e6i) q^{72} +(1.11578e7 - 1.11578e7i) q^{73} +2.37721e6i q^{74} +(1.62617e6 + 1.11137e7i) q^{75} +1.05683e7 q^{76} +(2.37144e6 + 2.37144e6i) q^{77} +(1.64963e7 - 1.64963e7i) q^{78} +6.87542e7i q^{79} +(4.20188e7 - 2.10986e7i) q^{80} -2.74566e7 q^{81} +(8.46828e6 + 8.46828e6i) q^{82} +(-3.29194e6 + 3.29194e6i) q^{83} +2.06046e7i q^{84} +(-1.55247e7 - 5.14565e6i) q^{85} -3.27850e7 q^{86} +(-2.13766e7 - 2.13766e7i) q^{87} +(-692338. + 692338. i) q^{88} -7.97635e7i q^{89} +(-2.43352e7 + 7.34206e7i) q^{90} +1.28403e8 q^{91} +(2.86424e6 + 2.86424e6i) q^{92} +(-2.22591e7 + 2.22591e7i) q^{93} -1.24220e8i q^{94} +(-1.41278e7 - 2.81360e7i) q^{95} -3.93453e7 q^{96} +(-1.96546e7 - 1.96546e7i) q^{97} +(-9.00656e7 + 9.00656e7i) q^{98} -5.63029e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8	\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8} + 30870 q^{10} + 23192 q^{11} - 45912 q^{12} - 119142 q^{13} + 241440 q^{15} + 218616 q^{16} - 265502 q^{17} - 454062 q^{18} + 412260 q^{20} + 231672 q^{21} - 35664 q^{22} + 28888 q^{23} - 340350 q^{25} - 801388 q^{26} + 392040 q^{27} + 1305192 q^{28} - 2549760 q^{30} - 747648 q^{31} + 3033928 q^{32} + 4269096 q^{33} - 4971680 q^{35} - 3972804 q^{36} - 454002 q^{37} + 1443720 q^{38} + 2683500 q^{40} + 2489432 q^{41} + 4223856 q^{42} + 792648 q^{43} + 210690 q^{45} - 3149928 q^{46} - 15313352 q^{47} - 21677712 q^{48} + 29537650 q^{50} + 35567712 q^{51} - 735732 q^{52} - 13509122 q^{53} + 4448040 q^{55} - 18454800 q^{56} - 34625520 q^{57} - 23903520 q^{58} + 13688520 q^{60} + 24111192 q^{61} + 53913416 q^{62} + 44837688 q^{63} - 30943610 q^{65} - 55047936 q^{66} - 32827752 q^{67} + 8118692 q^{68} - 44156280 q^{70} - 13992928 q^{71} + 82596420 q^{72} + 111859638 q^{73} - 126793200 q^{75} - 56470800 q^{76} + 26260136 q^{77} + 31125576 q^{78} + 23045920 q^{80} + 65834226 q^{81} + 38023056 q^{82} - 14768432 q^{83} - 19713030 q^{85} - 135560008 q^{86} - 133207680 q^{87} - 44555040 q^{88} + 135147990 q^{90} + 167542032 q^{91} + 69931048 q^{92} - 96798024 q^{93} + 239661000 q^{95} + 184867872 q^{96} - 186656202 q^{97} - 345959698 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8 + 30870 * q^10 + 23192 * q^11 - 45912 * q^12 - 119142 * q^13 + 241440 * q^15 + 218616 * q^16 - 265502 * q^17 - 454062 * q^18 + 412260 * q^20 + 231672 * q^21 - 35664 * q^22 + 28888 * q^23 - 340350 * q^25 - 801388 * q^26 + 392040 * q^27 + 1305192 * q^28 - 2549760 * q^30 - 747648 * q^31 + 3033928 * q^32 + 4269096 * q^33 - 4971680 * q^35 - 3972804 * q^36 - 454002 * q^37 + 1443720 * q^38 + 2683500 * q^40 + 2489432 * q^41 + 4223856 * q^42 + 792648 * q^43 + 210690 * q^45 - 3149928 * q^46 - 15313352 * q^47 - 21677712 * q^48 + 29537650 * q^50 + 35567712 * q^51 - 735732 * q^52 - 13509122 * q^53 + 4448040 * q^55 - 18454800 * q^56 - 34625520 * q^57 - 23903520 * q^58 + 13688520 * q^60 + 24111192 * q^61 + 53913416 * q^62 + 44837688 * q^63 - 30943610 * q^65 - 55047936 * q^66 - 32827752 * q^67 + 8118692 * q^68 - 44156280 * q^70 - 13992928 * q^71 + 82596420 * q^72 + 111859638 * q^73 - 126793200 * q^75 - 56470800 * q^76 + 26260136 * q^77 + 31125576 * q^78 + 23045920 * q^80 + 65834226 * q^81 + 38023056 * q^82 - 14768432 * q^83 - 19713030 * q^85 - 135560008 * q^86 - 133207680 * q^87 - 44555040 * q^88 + 135147990 * q^90 + 167542032 * q^91 + 69931048 * q^92 - 96798024 * q^93 + 239661000 * q^95 + 184867872 * q^96 - 186656202 * q^97 - 345959698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	15.2610	+	15.2610i	0.953812	+	0.953812i	0.998979	−	0.0451670i	$-0.0143820\pi$
$2$	15.2610	+	15.2610i	0.953812	+	0.953812i	−0.0451670	+	0.998979i	$0.514382\pi$
$3$	−20.3321	+	20.3321i	−0.251014	+	0.251014i	−0.821386	−	0.570373i	$-0.806799\pi$
$3$	−20.3321	+	20.3321i	−0.251014	+	0.251014i	0.570373	+	0.821386i	$0.306799\pi$
$4$			209.796i			0.819516i
$5$	558.542	−	280.457i	0.893667	−	0.448731i
$5$	558.542	−	280.457i	0.893667	−	0.448731i
$6$	−620.576			−0.478840
$7$	−2415.21	−	2415.21i	−1.00592	−	1.00592i	−0.999982	−	0.00593626i	$-0.998110\pi$
$7$	−2415.21	−	2415.21i	−1.00592	−	1.00592i	−0.00593626	−	0.999982i	$-0.501890\pi$
$8$	705.116	−	705.116i	0.172147	−	0.172147i
$9$			5734.21i			0.873984i
$10$	12804.0	+	4243.86i	1.28040	+	0.424386i
$11$	−981.878			−0.0670636			−0.0335318	−	0.999438i	$-0.510675\pi$
$11$	−981.878			−0.0670636			−0.0335318	+	0.999438i	$0.510675\pi$
$12$	−4265.60	−	4265.60i	−0.205710	−	0.205710i
$13$	−26582.1	+	26582.1i	−0.930715	+	0.930715i	−0.997751	−	0.0670358i	$-0.978646\pi$
$13$	−26582.1	+	26582.1i	−0.930715	+	0.930715i	0.0670358	+	0.997751i	$0.478646\pi$
$14$		−	73717.1i		−	1.91892i
$15$	−5654.06	+	17058.6i	−0.111685	+	0.336960i
$16$	75229.4			1.14791
$17$	−18503.9	−	18503.9i	−0.221547	−	0.221547i	0.587602	−	0.809150i	$-0.300072\pi$
$17$	−18503.9	−	18503.9i	−0.221547	−	0.221547i	−0.809150	+	0.587602i	$0.800072\pi$
$18$	−87509.8	+	87509.8i	−0.833617	+	0.833617i
$19$		−	50374.1i		−	0.386539i	−0.981146	−	0.193269i	$-0.938091\pi$
$19$		−	50374.1i		−	0.386539i	0.981146	−	0.193269i	$-0.0619091\pi$
$20$	58838.8	+	117180.i	0.367742	+	0.732375i
$21$	98212.6			0.504999
$22$	−14984.4	−	14984.4i	−0.0639661	−	0.0639661i
$23$	13652.5	−	13652.5i	0.0487866	−	0.0487866i	−0.682293	−	0.731079i	$-0.739017\pi$
$23$	13652.5	−	13652.5i	0.0487866	−	0.0487866i	0.731079	+	0.682293i	$0.239017\pi$
$24$			28673.0i			0.0864227i
$25$	233313.	−	313294.i	0.597281	−	0.802032i
$26$	−811340.			−1.77545
$27$	−249988.	−	249988.i	−0.470396	−	0.470396i
$28$	506702.	−	506702.i	0.824367	−	0.824367i
$29$			1.05137e6i			1.48650i	0.669015	+	0.743249i	$0.266716\pi$
$29$			1.05137e6i			1.48650i	−0.669015	+	0.743249i	$0.733284\pi$
$30$	−346618.	+	174045.i	−0.427923	+	0.214870i
$31$	1.09477e6			1.18543			0.592717	−	0.805411i	$-0.298055\pi$
$31$	1.09477e6			1.18543			0.592717	+	0.805411i	$0.298055\pi$
$32$	967566.	+	967566.i	0.922743	+	0.922743i
$33$	19963.6	−	19963.6i	0.0168339	−	0.0168339i
$34$		−	564775.i		−	0.422629i
$35$	−2.02636e6	−	671634.i	−1.35034	−	0.447570i
$36$	−1.20302e6			−0.716244
$37$	77885.1	+	77885.1i	0.0415573	+	0.0415573i	0.727580	−	0.686023i	$-0.240645\pi$
$37$	77885.1	+	77885.1i	0.0415573	+	0.0415573i	−0.686023	+	0.727580i	$0.740645\pi$
$38$	768759.	−	768759.i	0.368685	−	0.368685i
$39$		−	1.08094e6i		−	0.467244i
$40$	196082.	−	591591.i	0.0765947	−	0.231090i
$41$	554897.			0.196371			0.0981854	−	0.995168i	$-0.468696\pi$
$41$	554897.			0.196371			0.0981854	+	0.995168i	$0.468696\pi$
$42$	1.49882e6	+	1.49882e6i	0.481674	+	0.481674i
$43$	−1.07414e6	+	1.07414e6i	−0.314187	+	0.314187i	−0.846529	−	0.532342i	$-0.821312\pi$
$43$	−1.07414e6	+	1.07414e6i	−0.314187	+	0.314187i	0.532342	+	0.846529i	$0.321312\pi$
$44$		−	205994.i		−	0.0549597i
$45$	1.60820e6	+	3.20280e6i	0.392184	+	0.781051i
$46$	416702.			0.0930666
$47$	−4.06986e6	−	4.06986e6i	−0.834043	−	0.834043i	0.154024	−	0.988067i	$-0.450777\pi$
$47$	−4.06986e6	−	4.06986e6i	−0.834043	−	0.834043i	−0.988067	+	0.154024i	$0.950777\pi$
$48$	−1.52957e6	+	1.52957e6i	−0.288141	+	0.288141i
$49$			5.90168e6i			1.02374i
$50$	8.34176e6	−	1.22058e6i	1.33468	−	0.195293i
$51$	752445.			0.111223
$52$	−5.57683e6	−	5.57683e6i	−0.762736	−	0.762736i
$53$	1.88025e6	−	1.88025e6i	0.238294	−	0.238294i	−0.577850	−	0.816143i	$-0.696108\pi$
$53$	1.88025e6	−	1.88025e6i	0.238294	−	0.238294i	0.816143	+	0.577850i	$0.196108\pi$
$54$		−	7.63012e6i		−	0.897338i
$55$	−548420.	+	275374.i	−0.0599325	+	0.0300935i
$56$	−3.40601e6			−0.346333
$57$	1.02421e6	+	1.02421e6i	0.0970265	+	0.0970265i
$58$	−1.60450e7	+	1.60450e7i	−1.41784	+	1.41784i
$59$		−	1.27248e7i		−	1.05013i	−0.851063	−	0.525063i	$-0.824042\pi$
$59$		−	1.27248e7i		−	1.05013i	0.851063	−	0.525063i	$-0.175958\pi$
$60$	−3.57883e6	−	1.18620e6i	−0.276144	−	0.0915277i
$61$	1.40038e7			1.01141			0.505705	−	0.862707i	$-0.331233\pi$
$61$	1.40038e7			1.01141			0.505705	+	0.862707i	$0.331233\pi$
$62$	1.67073e7	+	1.67073e7i	1.13068	+	1.13068i
$63$	1.38493e7	−	1.38493e7i	0.879157	−	0.879157i
$64$			1.02733e7i			0.612338i
$65$	−7.39210e6	+	2.23024e7i	−0.414109	+	1.24939i
$66$	609330.			0.0321127
$67$	−9.54151e6	−	9.54151e6i	−0.473498	−	0.473498i	0.429547	−	0.903045i	$-0.358673\pi$
$67$	−9.54151e6	−	9.54151e6i	−0.473498	−	0.473498i	−0.903045	+	0.429547i	$0.858673\pi$
$68$	3.88204e6	−	3.88204e6i	0.181562	−	0.181562i
$69$			555168.i			0.0244922i
$70$	−2.06744e7	−	4.11741e7i	−0.861076	−	1.71487i
$71$	−2.82034e7			−1.10986			−0.554930	−	0.831897i	$-0.687255\pi$
$71$	−2.82034e7			−1.10986			−0.554930	+	0.831897i	$0.687255\pi$
$72$	4.04328e6	+	4.04328e6i	0.150454	+	0.150454i
$73$	1.11578e7	−	1.11578e7i	0.392905	−	0.392905i	−0.482817	−	0.875721i	$-0.660386\pi$
$73$	1.11578e7	−	1.11578e7i	0.392905	−	0.392905i	0.875721	+	0.482817i	$0.160386\pi$
$74$			2.37721e6i			0.0792758i
$75$	1.62617e6	+	1.11137e7i	0.0513951	+	0.351247i
$76$	1.05683e7			0.316775
$77$	2.37144e6	+	2.37144e6i	0.0674605	+	0.0674605i
$78$	1.64963e7	−	1.64963e7i	0.445663	−	0.445663i
$79$			6.87542e7i			1.76519i	0.470136	+	0.882594i	$0.344205\pi$
$79$			6.87542e7i			1.76519i	−0.470136	+	0.882594i	$0.655795\pi$
$80$	4.20188e7	−	2.10986e7i	1.02585	−	0.515102i
$81$	−2.74566e7			−0.637833
$82$	8.46828e6	+	8.46828e6i	0.187301	+	0.187301i
$83$	−3.29194e6	+	3.29194e6i	−0.0693649	+	0.0693649i	−0.740938	−	0.671573i	$-0.765619\pi$
$83$	−3.29194e6	+	3.29194e6i	−0.0693649	+	0.0693649i	0.671573	+	0.740938i	$0.265619\pi$
$84$			2.06046e7i			0.413855i
$85$	−1.55247e7	−	5.14565e6i	−0.297405	−	0.0985745i
$86$	−3.27850e7			−0.599351
$87$	−2.13766e7	−	2.13766e7i	−0.373131	−	0.373131i
$88$	−692338.	+	692338.i	−0.0115448	+	0.0115448i
$89$		−	7.97635e7i		−	1.27129i	−0.771982	−	0.635645i	$-0.780734\pi$
$89$		−	7.97635e7i		−	1.27129i	0.771982	−	0.635645i	$-0.219266\pi$
$90$	−2.43352e7	+	7.34206e7i	−0.370906	+	1.11905i
$91$	1.28403e8			1.87245
$92$	2.86424e6	+	2.86424e6i	0.0399814	+	0.0399814i
$93$	−2.22591e7	+	2.22591e7i	−0.297560	+	0.297560i
$94$		−	1.24220e8i		−	1.59104i
$95$	−1.41278e7	−	2.81360e7i	−0.173452	−	0.345437i
$96$	−3.93453e7			−0.463242
$97$	−1.96546e7	−	1.96546e7i	−0.222012	−	0.222012i	0.587333	−	0.809345i	$-0.300178\pi$
$97$	−1.96546e7	−	1.96546e7i	−0.222012	−	0.222012i	−0.809345	+	0.587333i	$0.800178\pi$
$98$	−9.00656e7	+	9.00656e7i	−0.976460	+	0.976460i
$99$		−	5.63029e6i		−	0.0586125i
$100$	6.57278e7	+	4.89482e7i	0.657278	+	0.489482i
$101$	3.02468e7			0.290666			0.145333	−	0.989383i	$-0.453575\pi$
$101$	3.02468e7			0.290666			0.145333	+	0.989383i	$0.453575\pi$
$102$	1.14831e7	+	1.14831e7i	0.106086	+	0.106086i
$103$	−4.28162e7	+	4.28162e7i	−0.380416	+	0.380416i	−0.871252	−	0.490836i	$-0.836691\pi$
$103$	−4.28162e7	+	4.28162e7i	−0.380416	+	0.380416i	0.490836	+	0.871252i	$0.336691\pi$
$104$			3.74870e7i			0.320440i
$105$	5.48559e7	−	2.75444e7i	0.451301	−	0.226608i
$106$	5.73890e7			0.454575
$107$	8.84746e7	+	8.84746e7i	0.674969	+	0.674969i	0.958857	−	0.283888i	$-0.0916246\pi$
$107$	8.84746e7	+	8.84746e7i	0.674969	+	0.674969i	−0.283888	+	0.958857i	$0.591625\pi$
$108$	5.24464e7	−	5.24464e7i	0.385497	−	0.385497i
$109$			4.49302e7i			0.318297i	0.987255	+	0.159148i	$0.0508749\pi$
$109$			4.49302e7i			0.318297i	−0.987255	+	0.159148i	$0.949125\pi$
$110$	−1.25719e7	−	4.16695e6i	−0.0858679	−	0.0284608i
$111$	−3.16714e6			−0.0208629
$112$	−1.81695e8	−	1.81695e8i	−1.15470	−	1.15470i
$113$	9.24017e6	−	9.24017e6i	0.0566717	−	0.0566717i	−0.678203	−	0.734875i	$-0.737241\pi$
$113$	9.24017e6	−	9.24017e6i	0.0566717	−	0.0566717i	0.734875	+	0.678203i	$0.237241\pi$
$114$			3.12610e7i			0.185090i
$115$	3.79656e6	−	1.14544e7i	0.0217069	−	0.0654911i
$116$	−2.20574e8			−1.21821
$117$	−1.52428e8	−	1.52428e8i	−0.813430	−	0.813430i
$118$	1.94193e8	−	1.94193e8i	1.00162	−	1.00162i
$119$			8.93815e7i			0.445717i
$120$	8.04153e6	+	1.60151e7i	0.0387805	+	0.0772331i
$121$	−2.13395e8			−0.995502
$122$	2.13712e8	+	2.13712e8i	0.964695	+	0.964695i
$123$	−1.12822e7	+	1.12822e7i	−0.0492917	+	0.0492917i
$124$			2.29679e8i			0.971483i
$125$	4.24498e7	−	2.40422e8i	0.173874	−	0.984768i
$126$	4.22709e8			1.67710
$127$	2.89529e8	+	2.89529e8i	1.11295	+	1.11295i	0.992749	+	0.120204i	$0.0383548\pi$
$127$	2.89529e8	+	2.89529e8i	1.11295	+	1.11295i	0.120204	+	0.992749i	$0.461645\pi$
$128$	9.09157e7	−	9.09157e7i	0.338687	−	0.338687i
$129$		−	4.36792e7i		−	0.157731i
$130$	−4.53167e8	+	2.27546e8i	−1.58667	+	0.796701i
$131$	−1.84509e8			−0.626516			−0.313258	−	0.949668i	$-0.601420\pi$
$131$	−1.84509e8			−0.626516			−0.313258	+	0.949668i	$0.601420\pi$
$132$	4.18830e6	+	4.18830e6i	0.0137956	+	0.0137956i
$133$	−1.21664e8	+	1.21664e8i	−0.388826	+	0.388826i
$134$		−	2.91226e8i		−	0.903256i
$135$	−2.09739e8	−	6.95178e7i	−0.631458	−	0.209296i
$136$	−2.60947e7			−0.0762777
$137$	1.60104e8	+	1.60104e8i	0.454484	+	0.454484i	0.896840	−	0.442356i	$-0.145857\pi$
$137$	1.60104e8	+	1.60104e8i	0.454484	+	0.454484i	−0.442356	+	0.896840i	$0.645857\pi$
$138$	−8.47242e6	+	8.47242e6i	−0.0233610	+	0.0233610i
$139$		−	2.86303e8i		−	0.766949i	−0.923551	−	0.383475i	$-0.874727\pi$
$139$		−	2.86303e8i		−	0.766949i	0.923551	−	0.383475i	$-0.125273\pi$
$140$	1.40906e8	−	4.25122e8i	0.366791	−	1.10663i
$141$	1.65498e8			0.418712
$142$	−4.30412e8	−	4.30412e8i	−1.05860	−	1.05860i
$143$	2.61004e7	−	2.61004e7i	0.0624171	−	0.0624171i
$144$			4.31381e8i			1.00325i
$145$	2.94864e8	+	5.87235e8i	0.667037	+	1.32843i
$146$	3.40558e8			0.749515
$147$	−1.19994e8	−	1.19994e8i	−0.256974	−	0.256974i
$148$	−1.63400e7	+	1.63400e7i	−0.0340569	+	0.0340569i
$149$		−	1.84894e8i		−	0.375127i	−0.982253	−	0.187563i	$-0.939941\pi$
$149$		−	1.84894e8i		−	0.375127i	0.982253	−	0.187563i	$-0.0600590\pi$
$150$	−1.44789e8	+	1.94423e8i	−0.286002	+	0.384045i
$151$	−6.16679e8			−1.18618			−0.593091	−	0.805135i	$-0.702093\pi$
$151$	−6.16679e8			−1.18618			−0.593091	+	0.805135i	$0.702093\pi$
$152$	−3.55196e7	−	3.55196e7i	−0.0665416	−	0.0665416i
$153$	1.06105e8	−	1.06105e8i	0.193629	−	0.193629i
$154$			7.23811e7i			0.128689i
$155$	6.11477e8	−	3.07037e8i	1.05938	−	0.531941i
$156$	2.26778e8			0.382914
$157$	2.91004e8	+	2.91004e8i	0.478961	+	0.478961i	0.904799	−	0.425838i	$-0.140021\pi$
$157$	2.91004e8	+	2.91004e8i	0.478961	+	0.478961i	−0.425838	+	0.904799i	$0.640021\pi$
$158$	−1.04926e9	+	1.04926e9i	−1.68366	+	1.68366i
$159$			7.64589e7i			0.119630i
$160$	8.11786e8	+	2.69066e8i	1.23869	+	0.410562i
$161$	−6.59473e7			−0.0981508
$162$	−4.19015e8	−	4.19015e8i	−0.608373	−	0.608373i
$163$	7.65254e8	−	7.65254e8i	1.08406	−	1.08406i	0.0879389	−	0.996126i	$-0.471972\pi$
$163$	7.65254e8	−	7.65254e8i	1.08406	−	1.08406i	0.996126	−	0.0879389i	$-0.0280280\pi$
$164$			1.16415e8i			0.160929i
$165$	5.55159e6	−	1.67495e7i	0.00749000	−	0.0225978i
$166$	−1.00477e8			−0.132322
$167$	−4.23551e8	−	4.23551e8i	−0.544552	−	0.544552i	0.380308	−	0.924860i	$-0.375818\pi$
$167$	−4.23551e8	−	4.23551e8i	−0.544552	−	0.544552i	−0.924860	+	0.380308i	$0.875818\pi$
$168$	6.92513e7	−	6.92513e7i	0.0869342	−	0.0869342i
$169$		−	5.97490e8i		−	0.732460i
$170$	−1.58395e8	−	3.15450e8i	−0.189647	−	0.377690i
$171$	2.88856e8			0.337829
$172$	−2.25351e8	−	2.25351e8i	−0.257482	−	0.257482i
$173$	−1.22912e9	+	1.22912e9i	−1.37217	+	1.37217i	−0.514955	+	0.857217i	$0.672191\pi$
$173$	−1.22912e9	+	1.22912e9i	−1.37217	+	1.37217i	−0.857217	+	0.514955i	$0.827809\pi$
$174$		−	6.52457e8i		−	0.711795i
$175$	−1.32017e9	+	1.93170e8i	−1.40760	+	0.205962i
$176$	−7.38661e7			−0.0769829
$177$	2.58721e8	+	2.58721e8i	0.263596	+	0.263596i
$178$	1.21727e9	−	1.21727e9i	1.21257	−	1.21257i
$179$			4.39309e8i			0.427916i	0.976843	+	0.213958i	$0.0686355\pi$
$179$			4.39309e8i			0.427916i	−0.976843	+	0.213958i	$0.931364\pi$
$180$	−6.71935e8	+	3.37394e8i	−0.640084	+	0.321401i
$181$	1.68623e9			1.57110			0.785549	−	0.618799i	$-0.212380\pi$
$181$	1.68623e9			1.57110			0.785549	+	0.618799i	$0.212380\pi$
$182$	1.95956e9	+	1.95956e9i	1.78596	+	1.78596i
$183$	−2.84727e8	+	2.84727e8i	−0.253877	+	0.253877i
$184$		−	1.92532e7i		−	0.0167970i
$185$	6.53455e7	+	2.16587e7i	0.0557865	+	0.0184904i
$186$	−6.79391e8			−0.567633
$187$	1.81685e7	+	1.81685e7i	0.0148578	+	0.0148578i
$188$	8.53842e8	−	8.53842e8i	0.683512	−	0.683512i
$189$			1.20755e9i			0.946359i
$190$	2.13780e8	−	6.44988e8i	0.164041	−	0.494922i
$191$	−1.52273e9			−1.14416			−0.572082	−	0.820196i	$-0.693864\pi$
$191$	−1.52273e9			−1.14416			−0.572082	+	0.820196i	$0.693864\pi$
$192$	−2.08878e8	−	2.08878e8i	−0.153705	−	0.153705i
$193$	−1.96356e8	+	1.96356e8i	−0.141519	+	0.141519i	−0.774317	−	0.632798i	$-0.781906\pi$
$193$	−1.96356e8	+	1.96356e8i	−0.141519	+	0.141519i	0.632798	+	0.774317i	$0.281906\pi$
$194$		−	5.99897e8i		−	0.423516i
$195$	−3.03157e8	−	6.03751e8i	−0.209667	−	0.417561i
$196$	−1.23815e9			−0.838976
$197$	−1.25390e9	−	1.25390e9i	−0.832525	−	0.832525i	0.155337	−	0.987862i	$-0.450354\pi$
$197$	−1.25390e9	−	1.25390e9i	−0.832525	−	0.832525i	−0.987862	+	0.155337i	$0.950354\pi$
$198$	8.59239e7	−	8.59239e7i	0.0559053	−	0.0559053i
$199$			1.10010e9i			0.701489i	0.936471	+	0.350745i	$0.114071\pi$
$199$			1.10010e9i			0.701489i	−0.936471	+	0.350745i	$0.885929\pi$
$200$	−5.63956e7	−	3.85421e8i	−0.0352473	−	0.240888i
$201$	3.87998e8			0.237709
$202$	4.61597e8	+	4.61597e8i	0.277241	+	0.277241i
$203$	2.53928e9	−	2.53928e9i	1.49530	−	1.49530i
$204$			1.57860e8i			0.0911490i
$205$	3.09933e8	−	1.55625e8i	0.175490	−	0.0881176i
$206$	−1.30684e9			−0.725691
$207$	7.82863e7	+	7.82863e7i	0.0426388	+	0.0426388i
$208$	−1.99976e9	+	1.99976e9i	−1.06838	+	1.06838i
$209$			4.94612e7i			0.0259227i
$210$	1.25751e9	+	4.16800e8i	0.646598	+	0.214314i
$211$	2.62708e9			1.32539			0.662695	−	0.748889i	$-0.269412\pi$
$211$	2.62708e9			1.32539			0.662695	+	0.748889i	$0.269412\pi$
$212$	3.94470e8	+	3.94470e8i	0.195286	+	0.195286i
$213$	5.73434e8	−	5.73434e8i	0.278590	−	0.278590i
$214$			2.70042e9i			1.28759i
$215$	−2.98703e8	+	9.01205e8i	−0.139793	+	0.421764i
$216$	−3.52540e8			−0.161955
$217$	−2.64411e9	−	2.64411e9i	−1.19245	−	1.19245i
$218$	−6.85680e8	+	6.85680e8i	−0.303596	+	0.303596i
$219$			4.53723e8i			0.197249i
$220$	−5.77725e7	−	1.15056e8i	−0.0246621	−	0.0491157i
$221$	9.83745e8			0.412395
$222$	−4.83337e7	−	4.83337e7i	−0.0198993	−	0.0198993i
$223$	−2.23974e9	+	2.23974e9i	−0.905687	+	0.905687i	−0.995921	−	0.0902332i	$-0.971239\pi$
$223$	−2.23974e9	+	2.23974e9i	−0.905687	+	0.905687i	0.0902332	+	0.995921i	$0.471239\pi$
$224$		−	4.67375e9i		−	1.85641i
$225$	1.79649e9	+	1.33787e9i	0.700963	+	0.522015i
$226$	2.82028e8			0.108108
$227$	2.86595e9	+	2.86595e9i	1.07936	+	1.07936i	0.996567	+	0.0827897i	$0.0263830\pi$
$227$	2.86595e9	+	2.86595e9i	1.07936	+	1.07936i	0.0827897	+	0.996567i	$0.473617\pi$
$228$	−2.14876e8	+	2.14876e8i	−0.0795148	+	0.0795148i
$229$		−	4.21694e9i		−	1.53340i	−0.642005	−	0.766701i	$-0.721897\pi$
$229$		−	4.21694e9i		−	1.53340i	0.642005	−	0.766701i	$-0.278103\pi$
$230$	2.32745e8	−	1.16867e8i	0.0831705	−	0.0417618i
$231$	−9.64328e7			−0.0338670
$232$	7.41339e8	+	7.41339e8i	0.255897	+	0.255897i
$233$	−1.39423e9	+	1.39423e9i	−0.473052	+	0.473052i	−0.902901	−	0.429849i	$-0.858567\pi$
$233$	−1.39423e9	+	1.39423e9i	−0.473052	+	0.473052i	0.429849	+	0.902901i	$0.358567\pi$
$234$		−	4.65240e9i		−	1.55172i
$235$	−3.41461e9	−	1.13177e9i	−1.11962	−	0.371096i
$236$	2.66961e9			0.860596
$237$	−1.39792e9	−	1.39792e9i	−0.443086	−	0.443086i
$238$	−1.36405e9	+	1.36405e9i	−0.425131	+	0.425131i
$239$			2.78614e9i			0.853907i	0.904274	+	0.426954i	$0.140413\pi$
$239$			2.78614e9i			0.853907i	−0.904274	+	0.426954i	$0.859587\pi$
$240$	−4.25351e8	+	1.28331e9i	−0.128204	+	0.386800i
$241$	−1.82461e9			−0.540881			−0.270441	−	0.962737i	$-0.587169\pi$
$241$	−1.82461e9			−0.540881			−0.270441	+	0.962737i	$0.587169\pi$
$242$	−3.25662e9	−	3.25662e9i	−0.949523	−	0.949523i
$243$	2.19842e9	−	2.19842e9i	0.630500	−	0.630500i
$244$			2.93795e9i			0.828866i
$245$	1.65517e9	+	3.29634e9i	0.459386	+	0.914887i
$246$	−3.44356e8			−0.0940301
$247$	1.33905e9	+	1.33905e9i	0.359757	+	0.359757i
$248$	7.71943e8	−	7.71943e8i	0.204070	−	0.204070i
$249$		−	1.33864e8i		−	0.0348230i
$250$	4.31690e9	−	3.02125e9i	1.10513	−	0.773440i
$251$	−1.08818e9			−0.274162			−0.137081	−	0.990560i	$-0.543772\pi$
$251$	−1.08818e9			−0.274162			−0.137081	+	0.990560i	$0.543772\pi$
$252$	2.90554e9	+	2.90554e9i	0.720484	+	0.720484i
$253$	−1.34051e7	+	1.34051e7i	−0.00327181	+	0.00327181i
$254$			8.83700e9i			2.12310i
$255$	4.20272e8	−	2.11028e8i	0.0993962	−	0.0499091i
$256$	5.40490e9			1.25843
$257$	−1.38793e9	−	1.38793e9i	−0.318151	−	0.318151i	0.529905	−	0.848057i	$-0.322227\pi$
$257$	−1.38793e9	−	1.38793e9i	−0.318151	−	0.318151i	−0.848057	+	0.529905i	$0.822227\pi$
$258$	6.66588e8	−	6.66588e8i	0.150445	−	0.150445i
$259$		−	3.76218e8i		−	0.0836066i
$260$	−4.67896e9	−	1.55083e9i	−1.02390	−	0.339369i
$261$	−6.02879e9			−1.29918
$262$	−2.81579e9	−	2.81579e9i	−0.597578	−	0.597578i
$263$	3.30796e9	−	3.30796e9i	0.691412	−	0.691412i	−0.271130	−	0.962543i	$-0.587397\pi$
$263$	3.30796e9	−	3.30796e9i	0.691412	−	0.691412i	0.962543	+	0.271130i	$0.0873974\pi$
$264$		−	2.81534e7i		−	0.00579582i
$265$	5.22870e8	−	1.57753e9i	0.106025	−	0.319885i
$266$	−3.71343e9			−0.741735
$267$	1.62176e9	+	1.62176e9i	0.319111	+	0.319111i
$268$	2.00177e9	−	2.00177e9i	0.388039	−	0.388039i
$269$		−	4.82096e9i		−	0.920713i	−0.887734	−	0.460356i	$-0.847722\pi$
$269$		−	4.82096e9i		−	0.920713i	0.887734	−	0.460356i	$-0.152278\pi$
$270$	−2.13992e9	−	4.26174e9i	−0.402663	−	0.801922i
$271$	−5.54038e9			−1.02722			−0.513609	−	0.858025i	$-0.671692\pi$
$271$	−5.54038e9			−1.02722			−0.513609	+	0.858025i	$0.671692\pi$
$272$	−1.39203e9	−	1.39203e9i	−0.254316	−	0.254316i
$273$	−2.61070e9	+	2.61070e9i	−0.470010	+	0.470010i
$274$			4.88668e9i			0.866985i
$275$	−2.29085e8	+	3.07616e8i	−0.0400558	+	0.0537871i
$276$	−1.16472e8			−0.0200718
$277$	6.27804e9	+	6.27804e9i	1.06636	+	1.06636i	0.997635	+	0.0687272i	$0.0218938\pi$
$277$	6.27804e9	+	6.27804e9i	1.06636	+	1.06636i	0.0687272	+	0.997635i	$0.478106\pi$
$278$	4.36927e9	−	4.36927e9i	0.731526	−	0.731526i
$279$			6.27766e9i			1.03605i
$280$	−1.90240e9	+	9.55238e8i	−0.309506	+	0.155410i
$281$	9.60308e9			1.54023			0.770114	−	0.637906i	$-0.220199\pi$
$281$	9.60308e9			1.54023			0.770114	+	0.637906i	$0.220199\pi$
$282$	2.52566e9	+	2.52566e9i	0.399373	+	0.399373i
$283$	2.69661e9	−	2.69661e9i	0.420409	−	0.420409i	−0.464936	−	0.885344i	$-0.653923\pi$
$283$	2.69661e9	−	2.69661e9i	0.420409	−	0.420409i	0.885344	+	0.464936i	$0.153923\pi$
$284$		−	5.91696e9i		−	0.909548i
$285$	8.59312e8	+	2.84818e8i	0.130248	+	0.0431706i
$286$	7.96637e8			0.119068
$287$	−1.34019e9	−	1.34019e9i	−0.197533	−	0.197533i
$288$	−5.54823e9	+	5.54823e9i	−0.806463	+	0.806463i
$289$		−	6.29097e9i		−	0.901833i
$290$	−4.46187e9	+	1.34617e10i	−0.630849	+	1.90331i
$291$	7.99238e8			0.111456
$292$	2.34086e9	+	2.34086e9i	0.321992	+	0.321992i
$293$	−6.28799e9	+	6.28799e9i	−0.853182	+	0.853182i	−0.990524	−	0.137342i	$-0.956144\pi$
$293$	−6.28799e9	+	6.28799e9i	−0.853182	+	0.853182i	0.137342	+	0.990524i	$0.456144\pi$
$294$		−	3.66245e9i		−	0.490210i
$295$	−3.56875e9	−	7.10731e9i	−0.471224	−	0.938464i
$296$	1.09836e8			0.0143080
$297$	2.45457e8	+	2.45457e8i	0.0315464	+	0.0315464i
$298$	2.82167e9	−	2.82167e9i	0.357800	−	0.357800i
$299$			7.25825e8i			0.0908129i
$300$	−2.33160e9	+	3.41165e8i	−0.287852	+	0.0421192i
$301$	5.18856e9			0.632093
$302$	−9.41114e9	−	9.41114e9i	−1.13140	−	1.13140i
$303$	−6.14981e8	+	6.14981e8i	−0.0729611	+	0.0729611i
$304$		−	3.78961e9i		−	0.443711i
$305$	7.82171e9	−	3.92746e9i	0.903863	−	0.453850i
$306$	3.23854e9			0.369371
$307$	−4.34115e8	−	4.34115e8i	−0.0488710	−	0.0488710i	0.682249	−	0.731120i	$-0.261002\pi$
$307$	−4.34115e8	−	4.34115e8i	−0.0488710	−	0.0488710i	−0.731120	+	0.682249i	$0.761002\pi$
$308$	−4.97519e8	+	4.97519e8i	−0.0552850	+	0.0552850i
$309$		−	1.74109e9i		−	0.190979i
$310$	1.40174e10	+	4.64606e9i	1.51783	+	0.503082i
$311$	−5.29907e9			−0.566445			−0.283223	−	0.959054i	$-0.591404\pi$
$311$	−5.29907e9			−0.566445			−0.283223	+	0.959054i	$0.591404\pi$
$312$	−7.62190e8	−	7.62190e8i	−0.0804349	−	0.0804349i
$313$	−5.51999e9	+	5.51999e9i	−0.575123	+	0.575123i	−0.933556	−	0.358433i	$-0.883311\pi$
$313$	−5.51999e9	+	5.51999e9i	−0.575123	+	0.575123i	0.358433	+	0.933556i	$0.383311\pi$
$314$			8.88202e9i			0.913678i
$315$	3.85129e9	−	1.16196e10i	0.391169	−	1.18018i
$316$	−1.44244e10			−1.44660
$317$	−3.86039e9	−	3.86039e9i	−0.382291	−	0.382291i	0.489636	−	0.871927i	$-0.337130\pi$
$317$	−3.86039e9	−	3.86039e9i	−0.382291	−	0.382291i	−0.871927	+	0.489636i	$0.837130\pi$
$318$	−1.16684e9	+	1.16684e9i	−0.114104	+	0.114104i
$319$		−	1.03232e9i		−	0.0996899i
$320$	2.88122e9	+	5.73808e9i	0.274775	+	0.547226i
$321$	−3.59775e9			−0.338853
$322$	−1.00642e9	−	1.00642e9i	−0.0936174	−	0.0936174i
$323$	−9.32115e8	+	9.32115e8i	−0.0856366	+	0.0856366i
$324$		−	5.76029e9i		−	0.522715i
$325$	2.12606e9	+	1.45300e10i	0.190564	+	1.30236i
$326$	2.33571e10			2.06799
$327$	−9.13526e8	−	9.13526e8i	−0.0798969	−	0.0798969i
$328$	3.91267e8	−	3.91267e8i	0.0338047	−	0.0338047i
$329$			1.96591e10i			1.67796i
$330$	3.40336e8	−	1.70891e8i	0.0286981	−	0.0144100i
$331$	−4.43747e9			−0.369678			−0.184839	−	0.982769i	$-0.559176\pi$
$331$	−4.43747e9			−0.369678			−0.184839	+	0.982769i	$0.559176\pi$
$332$	−6.90636e8	−	6.90636e8i	−0.0568456	−	0.0568456i
$333$	−4.46610e8	+	4.46610e8i	−0.0363204	+	0.0363204i
$334$		−	1.29276e10i		−	1.03880i
$335$	−8.00532e9	−	2.65335e9i	−0.635622	−	0.210676i
$336$	7.38848e9			0.579693
$337$	5.03851e9	+	5.03851e9i	0.390645	+	0.390645i	0.874917	−	0.484272i	$-0.160916\pi$
$337$	5.03851e9	+	5.03851e9i	0.390645	+	0.390645i	−0.484272	+	0.874917i	$0.660916\pi$
$338$	9.11830e9	−	9.11830e9i	0.698630	−	0.698630i
$339$			3.75744e8i			0.0284507i
$340$	1.07954e9	−	3.25703e9i	0.0807834	−	0.243728i
$341$	−1.07493e9			−0.0794995
$342$	4.40823e9	+	4.40823e9i	0.322225	+	0.322225i
$343$	3.30601e8	−	3.30601e8i	0.0238852	−	0.0238852i
$344$			1.51479e9i			0.108173i
$345$	1.55701e8	+	3.10085e8i	0.0109904	+	0.0218879i
$346$	−3.75151e10			−2.61759
$347$	−2.80674e9	−	2.80674e9i	−0.193590	−	0.193590i	0.603655	−	0.797246i	$-0.293710\pi$
$347$	−2.80674e9	−	2.80674e9i	−0.193590	−	0.193590i	−0.797246	+	0.603655i	$0.793710\pi$
$348$	4.48473e9	−	4.48473e9i	0.305787	−	0.305787i
$349$		−	1.32267e10i		−	0.891561i	−0.895142	−	0.445780i	$-0.852926\pi$
$349$		−	1.32267e10i		−	0.891561i	0.895142	−	0.445780i	$-0.147074\pi$
$350$	−2.30951e10	−	1.71992e10i	−1.53903	−	1.14613i
$351$	1.32904e10			0.875608
$352$	−9.50031e8	−	9.50031e8i	−0.0618824	−	0.0618824i
$353$	−1.16376e9	+	1.16376e9i	−0.0749489	+	0.0749489i	−0.743587	−	0.668639i	$-0.766877\pi$
$353$	−1.16376e9	+	1.16376e9i	−0.0749489	+	0.0749489i	0.668639	+	0.743587i	$0.266877\pi$
$354$			7.89669e9i			0.502843i
$355$	−1.57528e10	+	7.90983e9i	−0.991845	+	0.498028i
$356$	1.67341e10			1.04184
$357$	−1.81731e9	−	1.81731e9i	−0.111881	−	0.111881i
$358$	−6.70430e9	+	6.70430e9i	−0.408151	+	0.408151i
$359$		−	1.99414e10i		−	1.20054i	−0.799797	−	0.600270i	$-0.795060\pi$
$359$		−	1.99414e10i		−	1.20054i	0.799797	−	0.600270i	$-0.204940\pi$
$360$	3.39231e9	+	1.12438e9i	0.201969	+	0.0669425i
$361$	1.44460e10			0.850588
$362$	2.57336e10	+	2.57336e10i	1.49853	+	1.49853i
$363$	4.33877e9	−	4.33877e9i	0.249885	−	0.249885i
$364$			2.69385e10i			1.53450i
$365$	3.10282e9	−	9.36138e9i	0.174817	−	0.527434i
$366$	−8.69043e9			−0.484303
$367$	2.26918e10	+	2.26918e10i	1.25085	+	1.25085i	0.955341	+	0.295506i	$0.0954881\pi$
$367$	2.26918e10	+	2.26918e10i	1.25085	+	1.25085i	0.295506	+	0.955341i	$0.404512\pi$
$368$	1.02707e9	−	1.02707e9i	0.0560026	−	0.0560026i
$369$			3.18190e9i			0.171625i
$370$	6.66704e8	+	1.32777e9i	0.0355735	+	0.0708461i
$371$	−9.08241e9			−0.479408
$372$	−4.66987e9	−	4.66987e9i	−0.243856	−	0.243856i
$373$	1.70421e10	−	1.70421e10i	0.880417	−	0.880417i	−0.113160	−	0.993577i	$-0.536097\pi$
$373$	1.70421e10	−	1.70421e10i	0.880417	−	0.880417i	0.993577	+	0.113160i	$0.0360971\pi$
$374$			5.54540e8i			0.0283430i
$375$	4.02519e9	+	5.75138e9i	0.203545	+	0.290835i
$376$	−5.73945e9			−0.287157
$377$	−2.79477e10	−	2.79477e10i	−1.38351	−	1.38351i
$378$	−1.84283e10	+	1.84283e10i	−0.902649	+	0.902649i
$379$			2.63026e10i			1.27480i	0.770534	+	0.637399i	$0.219990\pi$
$379$			2.63026e10i			1.27480i	−0.770534	+	0.637399i	$0.780010\pi$
$380$	5.90283e9	−	2.96395e9i	0.283091	−	0.142147i
$381$	−1.17735e10			−0.558733
$382$	−2.32383e10	−	2.32383e10i	−1.09132	−	1.09132i
$383$	2.24947e10	−	2.24947e10i	1.04541	−	1.04541i	0.0464865	−	0.998919i	$-0.485198\pi$
$383$	2.24947e10	−	2.24947e10i	1.04541	−	1.04541i	0.998919	−	0.0464865i	$-0.0148024\pi$
$384$			3.69702e9i			0.170030i
$385$	1.98964e9	+	6.59463e8i	0.0905588	+	0.0300156i
$386$	−5.99317e9			−0.269965
$387$	−6.15936e9	−	6.15936e9i	−0.274595	−	0.274595i
$388$	4.12345e9	−	4.12345e9i	0.181943	−	0.181943i
$389$			5.72221e9i			0.249900i	0.992163	+	0.124950i	$0.0398770\pi$
$389$			5.72221e9i			0.249900i	−0.992163	+	0.124950i	$0.960123\pi$
$390$	4.58736e9	−	1.38403e10i	0.198292	−	0.598257i
$391$	−5.05248e8			−0.0216171
$392$	4.16137e9	+	4.16137e9i	0.176235	+	0.176235i
$393$	3.75145e9	−	3.75145e9i	0.157264	−	0.157264i
$394$		−	3.82715e10i		−	1.58814i
$395$	1.92826e10	+	3.84021e10i	0.792094	+	1.57749i
$396$	1.18121e9			0.0480339
$397$	2.97350e9	+	2.97350e9i	0.119703	+	0.119703i	0.764421	−	0.644718i	$-0.223025\pi$
$397$	2.97350e9	+	2.97350e9i	0.119703	+	0.119703i	−0.644718	+	0.764421i	$0.723025\pi$
$398$	−1.67887e10	+	1.67887e10i	−0.669089	+	0.669089i
$399$		−	4.94737e9i		−	0.195201i
$400$	1.75520e10	−	2.35689e10i	0.685625	−	0.920660i
$401$	−1.77762e10			−0.687481			−0.343741	−	0.939065i	$-0.611694\pi$
$401$	−1.77762e10			−0.687481			−0.343741	+	0.939065i	$0.611694\pi$
$402$	5.92124e9	+	5.92124e9i	0.226730	+	0.226730i
$403$	−2.91014e10	+	2.91014e10i	−1.10330	+	1.10330i
$404$			6.34567e9i			0.238205i
$405$	−1.53357e10	+	7.70039e9i	−0.570010	+	0.286215i
$406$	7.75040e10			2.85246
$407$	−7.64737e7	−	7.64737e7i	−0.00278698	−	0.00278698i
$408$	5.30561e8	−	5.30561e8i	0.0191467	−	0.0191467i
$409$		−	2.57868e10i		−	0.921519i	−0.887525	−	0.460759i	$-0.847577\pi$
$409$		−	2.57868e10i		−	0.921519i	0.887525	−	0.460759i	$-0.152423\pi$
$410$	7.10487e9	+	2.35490e9i	0.251432	+	0.0833369i
$411$	−6.51048e9			−0.228163
$412$	−8.98267e9	−	8.98267e9i	−0.311757	−	0.311757i
$413$	−3.07330e10	+	3.07330e10i	−1.05634	+	1.05634i
$414$			2.38945e9i			0.0813387i
$415$	−9.15439e8	+	2.76193e9i	−0.0308629	+	0.0931152i
$416$	−5.14399e10			−1.71762
$417$	5.82114e9	+	5.82114e9i	0.192515	+	0.192515i
$418$	−7.54827e8	+	7.54827e8i	−0.0247254	+	0.0247254i
$419$		−	2.80387e9i		−	0.0909707i	−0.998965	−	0.0454853i	$-0.985517\pi$
$419$		−	2.80387e9i		−	0.0909707i	0.998965	−	0.0454853i	$-0.0144834\pi$
$420$	5.77871e9	+	1.15086e10i	0.185709	+	0.369848i
$421$	3.39054e10			1.07929			0.539647	−	0.841891i	$-0.318558\pi$
$421$	3.39054e10			1.07929			0.539647	+	0.841891i	$0.318558\pi$
$422$	4.00919e10	+	4.00919e10i	1.26417	+	1.26417i
$423$	2.33374e10	−	2.33374e10i	0.728940	−	0.728940i
$424$		−	2.65159e9i		−	0.0820433i
$425$	−1.01143e10	+	1.47995e9i	−0.310014	+	0.0453619i
$426$	1.75024e10			0.531445
$427$	−3.38221e10	−	3.38221e10i	−1.01740	−	1.01740i
$428$	−1.85616e10	+	1.85616e10i	−0.553148	+	0.553148i
$429$			1.06135e9i			0.0313351i
$430$	−1.83118e10	+	9.19477e9i	−0.535620	+	0.268947i
$431$	4.74314e10			1.37454			0.687269	−	0.726403i	$-0.258810\pi$
$431$	4.74314e10			1.37454			0.687269	+	0.726403i	$0.258810\pi$
$432$	−1.88064e10	−	1.88064e10i	−0.539971	−	0.539971i
$433$	2.85545e10	−	2.85545e10i	0.812313	−	0.812313i	−0.172667	−	0.984980i	$-0.555238\pi$
$433$	2.85545e10	−	2.85545e10i	0.812313	−	0.812313i	0.984980	+	0.172667i	$0.0552384\pi$
$434$		−	8.07035e10i		−	2.27475i
$435$	−1.79349e10	−	5.94452e9i	−0.500891	−	0.166020i
$436$	−9.42619e9			−0.260850
$437$	−6.87732e8	−	6.87732e8i	−0.0188579	−	0.0188579i
$438$	−6.92427e9	+	6.92427e9i	−0.188138	+	0.188138i
$439$			4.70888e10i			1.26783i	0.773404	+	0.633913i	$0.218552\pi$
$439$			4.70888e10i			1.26783i	−0.773404	+	0.633913i	$0.781448\pi$
$440$	−1.92529e8	+	5.80870e8i	−0.00513671	+	0.0154977i
$441$	−3.38415e10			−0.894737
$442$	1.50129e10	+	1.50129e10i	0.393347	+	0.393347i
$443$	−2.13908e10	+	2.13908e10i	−0.555407	+	0.555407i	−0.927996	−	0.372589i	$-0.878470\pi$
$443$	−2.13908e10	+	2.13908e10i	−0.555407	+	0.555407i	0.372589	+	0.927996i	$0.378470\pi$
$444$		−	6.64453e8i		−	0.0170975i
$445$	−2.23702e10	−	4.45513e10i	−0.570467	−	1.13611i
$446$	−6.83614e10			−1.72771
$447$	3.75928e9	+	3.75928e9i	0.0941619	+	0.0941619i
$448$	2.48122e10	−	2.48122e10i	0.615962	−	0.615962i
$449$			1.99035e9i			0.0489717i	0.999700	+	0.0244858i	$0.00779487\pi$
$449$			1.99035e9i			0.0489717i	−0.999700	+	0.0244858i	$0.992205\pi$
$450$	6.99909e9	+	4.78334e10i	0.170683	+	1.16649i
$451$	−5.44841e8			−0.0131693
$452$	1.93855e9	+	1.93855e9i	0.0464434	+	0.0464434i
$453$	1.25384e10	−	1.25384e10i	0.297748	−	0.297748i
$454$			8.74745e10i			2.05901i
$455$	7.17184e10	−	3.60115e10i	1.67334	−	0.840224i
$456$	1.44438e9			0.0334057
$457$	1.28799e10	+	1.28799e10i	0.295290	+	0.295290i	0.839166	−	0.543876i	$-0.183044\pi$
$457$	1.28799e10	+	1.28799e10i	0.295290	+	0.295290i	−0.543876	+	0.839166i	$0.683044\pi$
$458$	6.43548e10	−	6.43548e10i	1.46258	−	1.46258i
$459$			9.25147e9i			0.208430i
$460$	2.40310e9	+	7.96503e8i	0.0536710	+	0.0177892i
$461$	2.95032e10			0.653229			0.326615	−	0.945158i	$-0.394092\pi$
$461$	2.95032e10			0.653229			0.326615	+	0.945158i	$0.394092\pi$
$462$	−1.47166e9	−	1.47166e9i	−0.0323028	−	0.0323028i
$463$	−2.68794e10	+	2.68794e10i	−0.584919	+	0.584919i	−0.936251	−	0.351332i	$-0.885729\pi$
$463$	−2.68794e10	+	2.68794e10i	−0.584919	+	0.584919i	0.351332	+	0.936251i	$0.385729\pi$
$464$			7.90941e10i			1.70636i
$465$	−6.18991e9	+	1.86753e10i	−0.132395	+	0.399444i
$466$	−4.25545e10			−0.902407
$467$	2.41860e10	+	2.41860e10i	0.508507	+	0.508507i	0.914068	−	0.405561i	$-0.132924\pi$
$467$	2.41860e10	+	2.41860e10i	0.508507	+	0.508507i	−0.405561	+	0.914068i	$0.632924\pi$
$468$	3.19787e10	−	3.19787e10i	0.666619	−	0.666619i
$469$			4.60895e10i			0.952601i
$470$	−3.48384e10	−	6.93822e10i	−0.713949	−	1.42186i
$471$	−1.18334e10			−0.240451
$472$	−8.97244e9	−	8.97244e9i	−0.180777	−	0.180777i
$473$	1.05468e9	−	1.05468e9i	0.0210705	−	0.0210705i
$474$		−	4.26672e10i		−	0.845242i
$475$	−1.57819e10	−	1.17529e10i	−0.310016	−	0.230872i
$476$	−1.87519e10			−0.365273
$477$	1.07818e10	+	1.07818e10i	0.208265	+	0.208265i
$478$	−4.25192e10	+	4.25192e10i	−0.814467	+	0.814467i
$479$		−	1.00060e11i		−	1.90073i	−0.311144	−	0.950363i	$-0.600712\pi$
$479$		−	1.00060e11i		−	1.90073i	0.311144	−	0.950363i	$-0.399288\pi$
$480$	−2.19760e10	+	1.10347e10i	−0.413984	+	0.207871i
$481$	−4.14071e9			−0.0773560
$482$	−2.78454e10	−	2.78454e10i	−0.515899	−	0.515899i
$483$	1.34085e9	−	1.34085e9i	0.0246372	−	0.0246372i
$484$		−	4.47694e10i		−	0.815831i
$485$	−1.64902e10	−	5.46564e9i	−0.298029	−	0.0987812i
$486$	6.71001e10			1.20276
$487$	−4.35298e10	−	4.35298e10i	−0.773875	−	0.773875i	0.204907	−	0.978782i	$-0.434311\pi$
$487$	−4.35298e10	−	4.35298e10i	−0.773875	−	0.773875i	−0.978782	+	0.204907i	$0.934311\pi$
$488$	9.87431e9	−	9.87431e9i	0.174112	−	0.174112i
$489$			3.11185e10i			0.544230i
$490$	−2.50459e10	+	7.55649e10i	−0.434463	+	1.31080i
$491$	−1.74821e10			−0.300794			−0.150397	−	0.988626i	$-0.548055\pi$
$491$	−1.74821e10			−0.300794			−0.150397	+	0.988626i	$0.548055\pi$
$492$	−2.36697e9	−	2.36697e9i	−0.0403954	−	0.0403954i
$493$	1.94544e10	−	1.94544e10i	0.329330	−	0.329330i
$494$			4.08705e10i			0.686282i
$495$	−1.57905e9	−	3.14475e9i	−0.0263012	−	0.0523801i
$496$	8.23592e10			1.36077
$497$	6.81171e10	+	6.81171e10i	1.11643	+	1.11643i
$498$	2.04290e9	−	2.04290e9i	0.0332147	−	0.0332147i
$499$		−	6.18997e10i		−	0.998358i	−0.866499	−	0.499179i	$-0.833635\pi$
$499$		−	6.18997e10i		−	0.998358i	0.866499	−	0.499179i	$-0.166365\pi$
$500$	5.04396e10	+	8.90581e9i	0.807033	+	0.142493i
$501$	1.72234e10			0.273380
$502$	−1.66068e10	−	1.66068e10i	−0.261499	−	0.261499i
$503$	−5.48962e10	+	5.48962e10i	−0.857571	+	0.857571i	−0.991051	−	0.133480i	$-0.957385\pi$
$503$	−5.48962e10	+	5.48962e10i	−0.857571	+	0.857571i	0.133480	+	0.991051i	$0.457385\pi$
$504$		−	1.95308e10i		−	0.302689i
$505$	1.68941e10	−	8.48292e9i	0.259759	−	0.130431i
$506$	−4.09150e8			−0.00624138
$507$	1.21482e10	+	1.21482e10i	0.183857	+	0.183857i
$508$	−6.07420e10	+	6.07420e10i	−0.912083	+	0.912083i
$509$		−	2.78975e9i		−	0.0415618i	−0.999784	−	0.0207809i	$-0.993385\pi$
$509$		−	2.78975e9i		−	0.0415618i	0.999784	−	0.0207809i	$-0.00661524\pi$
$510$	9.63427e9	+	3.19327e9i	0.142409	+	0.0472014i
$511$	−5.38969e10			−0.790460
$512$	5.92097e10	+	5.92097e10i	0.861615	+	0.861615i
$513$	−1.25929e10	+	1.25929e10i	−0.181826	+	0.181826i
$514$		−	4.23623e10i		−	0.606914i
$515$	−1.19065e10	+	3.59227e10i	−0.169261	+	0.510670i
$516$	9.16373e9			0.129263
$517$	3.99611e9	+	3.99611e9i	0.0559339	+	0.0559339i
$518$	5.74146e9	−	5.74146e9i	0.0797450	−	0.0797450i
$519$		−	4.99810e10i		−	0.688868i
$520$	1.05135e10	+	2.09381e10i	0.143791	+	0.286367i
$521$	−7.48087e10			−1.01532			−0.507658	−	0.861559i	$-0.669489\pi$
$521$	−7.48087e10			−1.01532			−0.507658	+	0.861559i	$0.669489\pi$
$522$	−9.20053e10	−	9.20053e10i	−1.23917	−	1.23917i
$523$	−1.13284e10	+	1.13284e10i	−0.151412	+	0.151412i	−0.778748	−	0.627336i	$-0.784145\pi$
$523$	−1.13284e10	+	1.13284e10i	−0.151412	+	0.151412i	0.627336	+	0.778748i	$0.284145\pi$
$524$		−	3.87093e10i		−	0.513440i
$525$	2.29143e10	−	3.07694e10i	0.301626	−	0.405025i
$526$	1.00966e11			1.31896
$527$	−2.02575e10	−	2.02575e10i	−0.262630	−	0.262630i
$528$	1.50185e9	−	1.50185e9i	0.0193238	−	0.0193238i
$529$			7.79382e10i			0.995240i
$530$	3.20542e10	−	1.60951e10i	0.406239	−	0.203982i
$531$	7.29665e10			0.917794
$532$	−2.55247e10	−	2.55247e10i	−0.318650	−	0.318650i
$533$	−1.47503e10	+	1.47503e10i	−0.182765	+	0.182765i
$534$			4.94994e10i			0.608744i
$535$	7.42301e10	+	2.46035e10i	0.906077	+	0.300318i
$536$	−1.34557e10			−0.163023
$537$	−8.93208e9	−	8.93208e9i	−0.107413	−	0.107413i
$538$	7.35726e10	−	7.35726e10i	0.878187	−	0.878187i
$539$		−	5.79473e9i		−	0.0686560i
$540$	1.45846e10	−	4.40025e10i	0.171522	−	0.517490i
$541$	−1.41419e11			−1.65090			−0.825448	−	0.564479i	$-0.809077\pi$
$541$	−1.41419e11			−1.65090			−0.825448	+	0.564479i	$0.809077\pi$
$542$	−8.45517e10	−	8.45517e10i	−0.979773	−	0.979773i
$543$	−3.42847e10	+	3.42847e10i	−0.394367	+	0.394367i
$544$		−	3.58074e10i		−	0.408863i
$545$	1.26010e10	+	2.50954e10i	0.142830	+	0.284452i
$546$	−7.96839e10			−0.896602
$547$	−2.99290e10	−	2.99290e10i	−0.334305	−	0.334305i	0.519914	−	0.854219i	$-0.325964\pi$
$547$	−2.99290e10	−	2.99290e10i	−0.334305	−	0.334305i	−0.854219	+	0.519914i	$0.825964\pi$
$548$	−3.35891e10	+	3.35891e10i	−0.372457	+	0.372457i
$549$			8.03008e10i			0.883956i
$550$	−8.19059e9	+	1.19846e9i	−0.0895086	+	0.0130971i
$551$	5.29619e10			0.574589
$552$	3.91458e8	+	3.91458e8i	0.00421627	+	0.00421627i
$553$	1.66056e11	−	1.66056e11i	1.77564	−	1.77564i
$554$			1.91618e11i			2.03422i
$555$	−1.76898e9	+	8.88245e8i	−0.0186445	+	0.00936183i
$556$	6.00653e10			0.628527
$557$	5.59400e10	+	5.59400e10i	0.581168	+	0.581168i	0.935224	−	0.354056i	$-0.115198\pi$
$557$	5.59400e10	+	5.59400e10i	0.581168	+	0.581168i	−0.354056	+	0.935224i	$0.615198\pi$
$558$	−9.58034e10	+	9.58034e10i	−0.988199	+	0.988199i
$559$		−	5.71061e10i		−	0.584837i
$560$	−1.52442e11	−	5.05266e10i	−1.55007	−	0.513769i
$561$	−7.38809e8			−0.00745900
$562$	1.46553e11	+	1.46553e11i	1.46909	+	1.46909i
$563$	5.76816e9	−	5.76816e9i	0.0574121	−	0.0574121i	−0.677818	−	0.735230i	$-0.737074\pi$
$563$	5.76816e9	−	5.76816e9i	0.0574121	−	0.0574121i	0.735230	+	0.677818i	$0.237074\pi$
$564$			3.47208e10i			0.343141i
$565$	2.56955e9	−	7.75249e9i	0.0252153	−	0.0760759i
$566$	8.23058e10			0.801982
$567$	6.63135e10	+	6.63135e10i	0.641608	+	0.641608i
$568$	−1.98867e10	+	1.98867e10i	−0.191059	+	0.191059i
$569$		−	1.53674e11i		−	1.46606i	−0.680196	−	0.733031i	$-0.738105\pi$
$569$		−	1.53674e11i		−	1.46606i	0.680196	−	0.733031i	$-0.261895\pi$
$570$	8.76735e9	+	1.74606e10i	0.0830556	+	0.165409i
$571$	−3.33206e10			−0.313450			−0.156725	−	0.987642i	$-0.550094\pi$
$571$	−3.33206e10			−0.313450			−0.156725	+	0.987642i	$0.550094\pi$
$572$	5.47577e9	+	5.47577e9i	0.0511518	+	0.0511518i
$573$	3.09602e10	−	3.09602e10i	0.287201	−	0.287201i
$574$		−	4.09054e10i		−	0.376819i
$575$	−1.09194e9	−	7.46255e9i	−0.00998908	−	0.0682678i
$576$	−5.89094e10			−0.535173
$577$	6.01902e10	+	6.01902e10i	0.543029	+	0.543029i	0.924416	−	0.381387i	$-0.124553\pi$
$577$	6.01902e10	+	6.01902e10i	0.543029	+	0.543029i	−0.381387	+	0.924416i	$0.624553\pi$
$578$	9.60065e10	−	9.60065e10i	0.860180	−	0.860180i
$579$		−	7.98465e9i		−	0.0710464i
$580$	−1.23200e11	+	6.18614e10i	−1.08867	+	0.546648i
$581$	1.59015e10			0.139551
$582$	1.21972e10	+	1.21972e10i	0.106308	+	0.106308i
$583$	−1.84618e9	+	1.84618e9i	−0.0159808	+	0.0159808i
$584$		−	1.57351e10i		−	0.135275i
$585$	−1.27887e11	−	4.23879e10i	−1.09195	−	0.361925i
$586$	−1.91922e11			−1.62755
$587$	−1.49796e11	−	1.49796e11i	−1.26168	−	1.26168i	−0.950280	−	0.311397i	$-0.899203\pi$
$587$	−1.49796e11	−	1.49796e11i	−1.26168	−	1.26168i	−0.311397	−	0.950280i	$-0.600797\pi$
$588$	2.51742e10	−	2.51742e10i	0.210594	−	0.210594i
$589$		−	5.51482e10i		−	0.458216i
$590$	5.40021e10	−	1.62927e11i	0.445659	−	1.34458i
$591$	5.09887e10			0.417950
$592$	5.85925e9	+	5.85925e9i	0.0477040	+	0.0477040i
$593$	−9.15532e10	+	9.15532e10i	−0.740381	+	0.740381i	−0.972651	−	0.232271i	$-0.925384\pi$
$593$	−9.15532e10	+	9.15532e10i	−0.740381	+	0.740381i	0.232271	+	0.972651i	$0.425384\pi$
$594$			7.49184e9i			0.0601787i
$595$	2.50676e10	+	4.99233e10i	0.200007	+	0.398323i
$596$	3.87901e10			0.307422
$597$	−2.23674e10	−	2.23674e10i	−0.176083	−	0.176083i
$598$	−1.10768e10	+	1.10768e10i	−0.0866185	+	0.0866185i
$599$			1.74821e11i			1.35796i	0.734158	+	0.678979i	$0.237577\pi$
$599$			1.74821e11i			1.35796i	−0.734158	+	0.678979i	$0.762423\pi$
$600$	8.98307e9	+	6.68978e9i	0.0693138	+	0.0516187i
$601$	6.55639e10			0.502536			0.251268	−	0.967918i	$-0.419153\pi$
$601$	6.55639e10			0.502536			0.251268	+	0.967918i	$0.419153\pi$
$602$	7.91827e10	+	7.91827e10i	0.602899	+	0.602899i
$603$	5.47130e10	−	5.47130e10i	0.413830	−	0.413830i
$604$		−	1.29377e11i		−	0.972096i
$605$	−1.19190e11	+	5.98480e10i	−0.889648	+	0.446713i
$606$	−1.87705e10			−0.139182
$607$	8.22746e10	+	8.22746e10i	0.606054	+	0.606054i	0.941912	−	0.335859i	$-0.109026\pi$
$607$	8.22746e10	+	8.22746e10i	0.606054	+	0.606054i	−0.335859	+	0.941912i	$0.609026\pi$
$608$	4.87402e10	−	4.87402e10i	0.356676	−	0.356676i
$609$			1.03258e11i			0.750679i
$610$	1.79304e11	+	5.94302e10i	1.29500	+	0.429228i
$611$	2.16371e11			1.55251
$612$	2.22604e10	+	2.22604e10i	0.158682	+	0.158682i
$613$	3.09061e10	−	3.09061e10i	0.218878	−	0.218878i	−0.589148	−	0.808026i	$-0.700536\pi$
$613$	3.09061e10	−	3.09061e10i	0.218878	−	0.218878i	0.808026	+	0.589148i	$0.200536\pi$
$614$		−	1.32501e10i		−	0.0932276i
$615$	−3.13742e9	+	9.46577e9i	−0.0219317	+	0.0661691i
$616$	3.34428e9			0.0232263
$617$	−1.72051e11	−	1.72051e11i	−1.18718	−	1.18718i	−0.977844	−	0.209337i	$-0.932870\pi$
$617$	−1.72051e11	−	1.72051e11i	−1.18718	−	1.18718i	−0.209337	−	0.977844i	$-0.567130\pi$
$618$	2.65707e10	−	2.65707e10i	0.182158	−	0.182158i
$619$			2.58123e11i			1.75818i	0.476652	+	0.879092i	$0.341850\pi$
$619$			2.58123e11i			1.75818i	−0.476652	+	0.879092i	$0.658150\pi$
$620$	6.44151e10	+	1.28286e11i	0.435934	+	0.868182i
$621$	−6.82591e9			−0.0458980
$622$	−8.08691e10	−	8.08691e10i	−0.540283	−	0.540283i
$623$	−1.92646e11	+	1.92646e11i	−1.27881	+	1.27881i
$624$		−	8.13186e10i		−	0.536354i
$625$	−4.37179e10	−	1.46191e11i	−0.286510	−	0.958077i
$626$	−1.68481e11			−1.09712
$627$	−1.00565e9	−	1.00565e9i	−0.00650694	−	0.00650694i
$628$	−6.10515e10	+	6.10515e10i	−0.392516	+	0.392516i
$629$		−	2.88235e9i		−	0.0184138i
$630$	2.36101e11	−	1.18552e11i	1.49877	−	0.752567i
$631$	−2.49622e11			−1.57458			−0.787292	−	0.616580i	$-0.788518\pi$
$631$	−2.49622e11			−1.57458			−0.787292	+	0.616580i	$0.788518\pi$
$632$	4.84797e10	+	4.84797e10i	0.303873	+	0.303873i
$633$	−5.34141e10	+	5.34141e10i	−0.332691	+	0.332691i
$634$		−	1.17827e11i		−	0.729267i
$635$	2.42914e11	+	8.05136e10i	1.49403	+	0.495193i
$636$	−1.60408e10			−0.0980387
$637$	−1.56879e11	−	1.56879e11i	−0.952814	−	0.952814i
$638$	1.57542e10	−	1.57542e10i	0.0950854	−	0.0950854i
$639$		−	1.61724e11i		−	0.970000i
$640$	2.52823e10	−	7.62781e10i	0.150694	−	0.454653i
$641$	1.95384e11			1.15733			0.578666	−	0.815565i	$-0.303573\pi$
$641$	1.95384e11			1.15733			0.578666	+	0.815565i	$0.303573\pi$
$642$	−5.49053e10	−	5.49053e10i	−0.323202	−	0.323202i
$643$	4.31377e10	−	4.31377e10i	0.252355	−	0.252355i	−0.569580	−	0.821936i	$-0.692894\pi$
$643$	4.31377e10	−	4.31377e10i	0.252355	−	0.252355i	0.821936	+	0.569580i	$0.192894\pi$
$644$		−	1.38355e10i		−	0.0804362i
$645$	−1.22501e10	−	2.43967e10i	−0.0707785	−	0.140959i
$646$	−2.84500e10			−0.163363
$647$	−5.34194e10	−	5.34194e10i	−0.304847	−	0.304847i	0.538060	−	0.842907i	$-0.319158\pi$
$647$	−5.34194e10	−	5.34194e10i	−0.304847	−	0.304847i	−0.842907	+	0.538060i	$0.819158\pi$
$648$	−1.93601e10	+	1.93601e10i	−0.109801	+	0.109801i
$649$			1.24942e10i			0.0704252i
$650$	−1.89296e11	+	2.54188e11i	−1.06045	+	1.42397i
$651$	1.07521e11			0.598643
$652$	1.60547e11	+	1.60547e11i	0.888409	+	0.888409i
$653$	1.68747e11	−	1.68747e11i	0.928074	−	0.928074i	−0.0695077	−	0.997581i	$-0.522143\pi$
$653$	1.68747e11	−	1.68747e11i	0.928074	−	0.928074i	0.997581	+	0.0695077i	$0.0221429\pi$
$654$		−	2.78826e10i		−	0.152413i
$655$	−1.03056e11	+	5.17467e10i	−0.559896	+	0.281137i
$656$	4.17445e10			0.225416
$657$	6.39812e10	+	6.39812e10i	0.343392	+	0.343392i
$658$	−3.00018e11	+	3.00018e11i	−1.60046	+	1.60046i
$659$		−	2.23769e11i		−	1.18647i	−0.805028	−	0.593237i	$-0.797850\pi$
$659$		−	2.23769e11i		−	1.18647i	0.805028	−	0.593237i	$-0.202150\pi$
$660$	3.51397e9	+	1.16470e9i	0.0185192	+	0.00613818i
$661$	1.49226e11			0.781700			0.390850	−	0.920454i	$-0.372181\pi$
$661$	1.49226e11			0.781700			0.390850	+	0.920454i	$0.372181\pi$
$662$	−6.77202e10	−	6.77202e10i	−0.352603	−	0.352603i
$663$	−2.00016e10	+	2.00016e10i	−0.103517	+	0.103517i
$664$			4.64240e9i			0.0238820i
$665$	−3.38330e10	+	1.02076e11i	−0.173003	+	0.521960i
$666$	−1.36314e10			−0.0692858
$667$	1.43539e10	+	1.43539e10i	0.0725212	+	0.0725212i
$668$	8.88594e10	−	8.88594e10i	0.446270	−	0.446270i
$669$		−	9.10773e10i		−	0.454680i
$670$	−8.16763e10	−	1.62662e11i	−0.405319	−	0.807210i
$671$	−1.37500e10			−0.0678287
$672$	9.50272e10	+	9.50272e10i	0.465984	+	0.465984i
$673$	−1.20787e11	+	1.20787e11i	−0.588791	+	0.588791i	−0.937304	−	0.348513i	$-0.886687\pi$
$673$	−1.20787e11	+	1.20787e11i	−0.588791	+	0.588791i	0.348513	+	0.937304i	$0.386687\pi$
$674$			1.53785e11i			0.745204i
$675$	−1.36645e11	+	1.99942e10i	−0.658231	+	0.0963137i
$676$	1.25351e11			0.600263
$677$	1.59570e11	+	1.59570e11i	0.759621	+	0.759621i	0.976253	−	0.216632i	$-0.0695072\pi$
$677$	1.59570e11	+	1.59570e11i	0.759621	+	0.759621i	−0.216632	+	0.976253i	$0.569507\pi$
$678$	−5.73423e9	+	5.73423e9i	−0.0271367	+	0.0271367i
$679$			9.49399e10i			0.446652i
$680$	−1.45750e10	+	7.31845e9i	−0.0681668	+	0.0342281i
$681$	−1.16542e11			−0.541867
$682$	−1.64046e10	−	1.64046e10i	−0.0758276	−	0.0758276i
$683$	2.73157e11	−	2.73157e11i	1.25525	−	1.25525i	0.301913	−	0.953336i	$-0.402375\pi$
$683$	2.73157e11	−	2.73157e11i	1.25525	−	1.25525i	0.953336	−	0.301913i	$-0.0976252\pi$
$684$			6.06008e10i			0.276856i
$685$	1.34327e11	+	4.45224e10i	0.610098	+	0.202216i
$686$	1.00906e10			0.0455639
$687$	8.57393e10	+	8.57393e10i	0.384905	+	0.384905i
$688$	−8.08071e10	+	8.08071e10i	−0.360658	+	0.360658i
$689$			9.99622e10i			0.443567i
$690$	−2.35605e9	+	7.10835e9i	−0.0103941	+	0.0313597i
$691$	1.64854e11			0.723082			0.361541	−	0.932356i	$-0.382251\pi$
$691$	1.64854e11			0.723082			0.361541	+	0.932356i	$0.382251\pi$
$692$	−2.57864e11	−	2.57864e11i	−1.12452	−	1.12452i
$693$	−1.35983e10	+	1.35983e10i	−0.0589594	+	0.0589594i
$694$		−	8.56672e10i		−	0.369298i
$695$	−8.02956e10	−	1.59912e11i	−0.344154	−	0.685397i
$696$	−3.01460e10			−0.128467
$697$	−1.02677e10	−	1.02677e10i	−0.0435054	−	0.0435054i
$698$	2.01853e11	−	2.01853e11i	0.850382	−	0.850382i
$699$		−	5.66951e10i		−	0.237485i
$700$	−4.05263e10	−	2.76967e11i	−0.168789	−	1.15355i
$701$	−4.11487e11			−1.70406			−0.852028	−	0.523496i	$-0.824627\pi$
$701$	−4.11487e11			−1.70406			−0.852028	+	0.523496i	$0.824627\pi$
$702$	2.02825e11	+	2.02825e11i	0.835166	+	0.835166i
$703$	3.92339e9	−	3.92339e9i	0.0160635	−	0.0160635i
$704$		−	1.00871e10i		−	0.0410655i
$705$	9.24374e10	−	4.64149e10i	0.374189	−	0.187889i
$706$	−3.55203e10			−0.142974
$707$	−7.30524e10	−	7.30524e10i	−0.292386	−	0.292386i
$708$	−5.42787e10	+	5.42787e10i	−0.216021	+	0.216021i
$709$			3.55785e11i			1.40800i	0.710201	+	0.703999i	$0.248604\pi$
$709$			3.55785e11i			1.40800i	−0.710201	+	0.703999i	$0.751396\pi$
$710$	−3.61115e11	−	1.19691e11i	−1.42106	−	0.471008i
$711$	−3.94251e11			−1.54275
$712$	−5.62426e10	−	5.62426e10i	−0.218849	−	0.218849i
$713$	1.49464e10	−	1.49464e10i	0.0578334	−	0.0578334i
$714$		−	5.54680e10i		−	0.213427i
$715$	7.25814e9	−	2.18982e10i	0.0277716	−	0.0837885i
$716$	−9.21654e10			−0.350684
$717$	−5.66480e10	−	5.66480e10i	−0.214342	−	0.214342i
$718$	3.04325e11	−	3.04325e11i	1.14509	−	1.14509i
$719$			1.68430e10i			0.0630238i	0.999503	+	0.0315119i	$0.0100322\pi$
$719$			1.68430e10i			0.0630238i	−0.999503	+	0.0315119i	$0.989968\pi$
$720$	1.20984e11	+	2.40944e11i	0.450191	+	0.896576i
$721$	2.06820e11			0.765335
$722$	2.20461e11	+	2.20461e11i	0.811301	+	0.811301i
$723$	3.70982e10	−	3.70982e10i	0.135769	−	0.135769i
$724$			3.53765e11i			1.28754i
$725$	3.29388e11	+	2.45299e11i	1.19222	+	0.887858i
$726$	1.32428e11			0.476686
$727$	−7.96403e9	−	7.96403e9i	−0.0285099	−	0.0285099i	0.692708	−	0.721218i	$-0.256417\pi$
$727$	−7.96403e9	−	7.96403e9i	−0.0285099	−	0.0285099i	−0.721218	+	0.692708i	$0.756417\pi$
$728$	9.05390e10	−	9.05390e10i	0.322337	−	0.322337i
$729$		−	9.07459e10i		−	0.321304i
$730$	1.90216e11	−	9.55119e10i	0.669816	−	0.336330i
$731$	3.97516e10			0.139215
$732$	−5.97346e10	−	5.97346e10i	−0.208057	−	0.208057i
$733$	−3.27099e10	+	3.27099e10i	−0.113309	+	0.113309i	−0.761488	−	0.648179i	$-0.775531\pi$
$733$	−3.27099e10	+	3.27099e10i	−0.113309	+	0.113309i	0.648179	+	0.761488i	$0.275531\pi$
$734$			6.92598e11i			2.38615i
$735$	−1.00675e11	−	3.33685e10i	−0.344961	−	0.114337i
$736$	2.64194e10			0.0900350
$737$	9.36860e9	+	9.36860e9i	0.0317545	+	0.0317545i
$738$	−4.85589e10	+	4.85589e10i	−0.163698	+	0.163698i
$739$		−	2.49954e11i		−	0.838075i	−0.907969	−	0.419038i	$-0.862368\pi$
$739$		−	2.49954e11i		−	0.838075i	0.907969	−	0.419038i	$-0.137632\pi$
$740$	−4.54391e9	+	1.37092e10i	−0.0151532	+	0.0457179i
$741$	−5.44515e10			−0.180608
$742$	−1.38607e11	−	1.38607e11i	−0.457265	−	0.457265i
$743$	−2.19494e11	+	2.19494e11i	−0.720224	+	0.720224i	−0.968651	−	0.248427i	$-0.920086\pi$
$743$	−2.19494e11	+	2.19494e11i	−0.720224	+	0.720224i	0.248427	+	0.968651i	$0.420086\pi$
$744$			3.13904e10i			0.102449i
$745$	−5.18548e10	−	1.03271e11i	−0.168331	−	0.335238i
$746$	5.20160e11			1.67951
$747$	−1.88767e10	−	1.88767e10i	−0.0606238	−	0.0606238i
$748$	−3.81169e9	+	3.81169e9i	−0.0121762	+	0.0121762i
$749$		−	4.27370e11i		−	1.35793i
$750$	−2.63433e10	+	1.49200e11i	−0.0832580	+	0.471546i
$751$	−3.34163e11			−1.05051			−0.525253	−	0.850946i	$-0.676029\pi$
$751$	−3.34163e11			−1.05051			−0.525253	+	0.850946i	$0.676029\pi$
$752$	−3.06173e11	−	3.06173e11i	−0.957405	−	0.957405i
$753$	2.21250e10	−	2.21250e10i	0.0688183	−	0.0688183i
$754$		−	8.53020e11i		−	2.63921i
$755$	−3.44441e11	+	1.72952e11i	−1.06005	+	0.532276i
$756$	−2.53338e11			−0.775557
$757$	3.61172e11	+	3.61172e11i	1.09984	+	1.09984i	0.994428	+	0.105414i	$0.0336168\pi$
$757$	3.61172e11	+	3.61172e11i	1.09984	+	1.09984i	0.105414	+	0.994428i	$0.466383\pi$
$758$	−4.01403e11	+	4.01403e11i	−1.21592	+	1.21592i
$759$		−	5.45107e8i		−	0.00164254i
$760$	−2.98009e10	−	9.87747e9i	−0.0893254	−	0.0296068i
$761$	1.43773e10			0.0428685			0.0214342	−	0.999770i	$-0.493177\pi$
$761$	1.43773e10			0.0428685			0.0214342	+	0.999770i	$0.493177\pi$
$762$	−1.79675e11	−	1.79675e11i	−0.532926	−	0.532926i
$763$	1.08516e11	−	1.08516e11i	0.320181	−	0.320181i
$764$		−	3.19462e11i		−	0.937661i
$765$	2.95062e10	−	8.90220e10i	0.0861525	−	0.259927i
$766$	6.86583e11			1.99424
$767$	3.38252e11	+	3.38252e11i	0.977368	+	0.977368i
$768$	−1.09893e11	+	1.09893e11i	−0.315882	+	0.315882i
$769$		−	4.36097e10i		−	0.124703i	−0.998054	−	0.0623517i	$-0.980140\pi$
$769$		−	4.36097e10i		−	0.124703i	0.998054	−	0.0623517i	$-0.0198600\pi$
$770$	2.02998e10	+	4.04279e10i	0.0577469	+	0.115005i
$771$	5.64389e10			0.159721
$772$	−4.11947e10	−	4.11947e10i	−0.115977	−	0.115977i
$773$	−4.23792e11	+	4.23792e11i	−1.18696	+	1.18696i	−0.209051	+	0.977905i	$0.567037\pi$
$773$	−4.23792e11	+	4.23792e11i	−1.18696	+	1.18696i	−0.977905	+	0.209051i	$0.932963\pi$
$774$		−	1.87996e11i		−	0.523824i
$775$	2.55425e11	−	3.42986e11i	0.708038	−	0.950756i
$776$	−2.77175e10			−0.0764377
$777$	7.64930e9	+	7.64930e9i	0.0209864	+	0.0209864i
$778$	−8.73267e10	+	8.73267e10i	−0.238357	+	0.238357i
$779$		−	2.79524e10i		−	0.0759049i
$780$	1.26665e11	−	6.36013e10i	0.342198	−	0.171825i
$781$	2.76923e10			0.0744311
$782$	−7.71059e9	−	7.71059e9i	−0.0206187	−	0.0206187i
$783$	2.62830e11	−	2.62830e11i	0.699242	−	0.699242i
$784$			4.43980e11i			1.17517i
$785$	2.44152e11	+	8.09238e10i	0.642956	+	0.213107i
$786$	1.14502e11			0.300001
$787$	−6.89291e10	−	6.89291e10i	−0.179682	−	0.179682i	0.611535	−	0.791217i	$-0.290552\pi$
$787$	−6.89291e10	−	6.89291e10i	−0.179682	−	0.179682i	−0.791217	+	0.611535i	$0.790552\pi$
$788$	2.63063e11	−	2.63063e11i	0.682268	−	0.682268i
$789$			1.34516e11i			0.347108i
$790$	−2.91783e11	+	8.80326e11i	−0.749120	+	2.26014i
$791$	−4.46339e10			−0.114014
$792$	−3.97001e9	−	3.97001e9i	−0.0100900	−	0.0100900i
$793$	−3.72251e11	+	3.72251e11i	−0.941333	+	0.941333i
$794$			9.07571e10i			0.228349i
$795$	2.14434e10	+	4.27055e10i	0.0536816	+	0.106909i
$796$	−2.30797e11			−0.574882
$797$	−4.21172e11	−	4.21172e11i	−1.04382	−	1.04382i	−0.998995	−	0.0448261i	$-0.985727\pi$
$797$	−4.21172e11	−	4.21172e11i	−1.04382	−	1.04382i	−0.0448261	−	0.998995i	$-0.514273\pi$
$798$	7.55018e10	−	7.55018e10i	0.186186	−	0.186186i
$799$			1.50616e11i			0.369560i
$800$	5.28878e11	−	7.73865e10i	1.29121	−	0.188932i
$801$	4.57381e11			1.11109
$802$	−2.71282e11	−	2.71282e11i	−0.655728	−	0.655728i
$803$	−1.09556e10	+	1.09556e10i	−0.0263496	+	0.0263496i
$804$			8.14005e10i			0.194806i
$805$	−3.68343e10	+	1.84954e10i	−0.0877141	+	0.0440433i
$806$	−8.88234e11			−2.10469
$807$	9.80202e10	+	9.80202e10i	0.231111	+	0.231111i
$808$	2.13275e10	−	2.13275e10i	0.0500374	−	0.0500374i
$809$		−	3.91293e11i		−	0.913499i	−0.889595	−	0.456750i	$-0.849014\pi$
$809$		−	3.91293e11i		−	0.913499i	0.889595	−	0.456750i	$-0.150986\pi$
$810$	−3.51553e11	−	1.16522e11i	−0.816678	−	0.270687i
$811$	1.43185e11			0.330989			0.165495	−	0.986211i	$-0.447078\pi$
$811$	1.43185e11			0.330989			0.165495	+	0.986211i	$0.447078\pi$
$812$	5.32732e11	+	5.32732e11i	1.22542	+	1.22542i
$813$	1.12648e11	−	1.12648e11i	0.257846	−	0.257846i
$814$		−	2.33413e9i		−	0.00531652i
$815$	2.12806e11	−	6.42047e11i	0.482340	−	1.45525i
$816$	5.66060e10			0.127674
$817$	5.41090e10	+	5.41090e10i	0.121445	+	0.121445i
$818$	3.93532e11	−	3.93532e11i	0.878956	−	0.878956i
$819$			7.36290e11i			1.63649i
$820$	3.26494e10	+	6.50228e10i	0.0722138	+	0.143817i
$821$	5.36389e11			1.18061			0.590306	−	0.807180i	$-0.299007\pi$
$821$	5.36389e11			1.18061			0.590306	+	0.807180i	$0.299007\pi$
$822$	−9.93565e10	−	9.93565e10i	−0.217625	−	0.217625i
$823$	2.70833e11	−	2.70833e11i	0.590339	−	0.590339i	−0.347384	−	0.937723i	$-0.612930\pi$
$823$	2.70833e11	−	2.70833e11i	0.590339	−	0.590339i	0.937723	+	0.347384i	$0.112930\pi$
$824$			6.03807e10i			0.130975i
$825$	−1.59670e9	−	1.09123e10i	−0.00344674	−	0.0235559i
$826$	−9.38032e11			−2.01510
$827$	−2.55449e11	−	2.55449e11i	−0.546113	−	0.546113i	0.379201	−	0.925314i	$-0.376199\pi$
$827$	−2.55449e11	−	2.55449e11i	−0.546113	−	0.546113i	−0.925314	+	0.379201i	$0.876199\pi$
$828$	−1.64242e10	+	1.64242e10i	−0.0349432	+	0.0349432i
$829$		−	3.10375e11i		−	0.657157i	−0.944477	−	0.328579i	$-0.893430\pi$
$829$		−	3.10375e11i		−	0.657157i	0.944477	−	0.328579i	$-0.106570\pi$
$830$	−5.61204e10	+	2.81793e10i	−0.118252	+	0.0593770i
$831$	−2.55292e11			−0.535343
$832$	−2.73087e11	−	2.73087e11i	−0.569912	−	0.569912i
$833$	1.09204e11	−	1.09204e11i	0.226808	−	0.226808i
$834$			1.77673e11i			0.367246i
$835$	−3.55359e11	−	1.17783e11i	−0.731006	−	0.242291i
$836$	−1.03768e10			−0.0212440
$837$	−2.73680e11	−	2.73680e11i	−0.557623	−	0.557623i
$838$	4.27898e10	−	4.27898e10i	0.0867690	−	0.0867690i
$839$			3.11103e11i			0.627851i	0.949448	+	0.313925i	$0.101644\pi$
$839$			3.11103e11i			0.627851i	−0.949448	+	0.313925i	$0.898356\pi$
$840$	1.92578e10	−	5.81018e10i	0.0386802	−	0.116700i
$841$	−6.05136e11			−1.20968
$842$	5.17430e11	+	5.17430e11i	1.02944	+	1.02944i
$843$	−1.95251e11	+	1.95251e11i	−0.386618	+	0.386618i
$844$			5.51152e11i			1.08618i
$845$	−1.67570e11	−	3.33723e11i	−0.328677	−	0.654575i
$846$	7.12305e11			1.39054
$847$	5.15393e11	+	5.15393e11i	1.00139	+	1.00139i
$848$	1.41450e11	−	1.41450e11i	0.273539	−	0.273539i
$849$			1.09655e11i			0.211057i
$850$	−1.76940e11	−	1.31769e11i	−0.338962	−	0.252429i
$851$	2.12665e9			0.00405488
$852$	1.20304e11	+	1.20304e11i	0.228309	+	0.228309i
$853$	−7.97714e10	+	7.97714e10i	−0.150678	+	0.150678i	−0.778421	−	0.627743i	$-0.783979\pi$
$853$	−7.97714e10	+	7.97714e10i	−0.150678	+	0.150678i	0.627743	+	0.778421i	$0.283979\pi$
$854$		−	1.03232e12i		−	1.94081i
$855$	1.61338e11	−	8.10115e10i	0.301906	−	0.151594i
$856$	1.24770e11			0.232388
$857$	4.72560e10	+	4.72560e10i	0.0876060	+	0.0876060i	0.749552	−	0.661946i	$-0.230269\pi$
$857$	4.72560e10	+	4.72560e10i	0.0876060	+	0.0876060i	−0.661946	+	0.749552i	$0.730269\pi$
$858$	−1.61973e10	+	1.61973e10i	−0.0298878	+	0.0298878i
$859$			6.23299e11i			1.14478i	0.819980	+	0.572392i	$0.193984\pi$
$859$			6.23299e11i			1.14478i	−0.819980	+	0.572392i	$0.806016\pi$
$860$	−1.89069e11	−	6.26668e10i	−0.345643	−	0.114563i
$861$	5.44979e10			0.0991669
$862$	7.23850e11	+	7.23850e11i	1.31105	+	1.31105i
$863$	−3.76731e11	+	3.76731e11i	−0.679185	+	0.679185i	−0.959816	−	0.280631i	$-0.909456\pi$
$863$	−3.76731e11	+	3.76731e11i	−0.679185	+	0.679185i	0.280631	+	0.959816i	$0.409456\pi$
$864$		−	4.83759e11i		−	0.868108i
$865$	−3.41799e11	+	1.03123e12i	−0.610529	+	1.84200i
$866$	8.71542e11			1.54959
$867$	1.27909e11	+	1.27909e11i	0.226373	+	0.226373i
$868$	5.54724e11	−	5.54724e11i	0.977233	−	0.977233i
$869$		−	6.75082e10i		−	0.118380i
$870$	−1.82986e11	−	3.64424e11i	−0.319404	−	0.636107i
$871$	5.07268e11			0.881383
$872$	3.16810e10	+	3.16810e10i	0.0547940	+	0.0547940i
$873$	1.12703e11	−	1.12703e11i	0.194035	−	0.194035i
$874$		−	2.09910e10i		−	0.0359738i
$875$	−6.83195e11	+	4.78144e11i	−1.16550	+	0.815693i
$876$	−9.51894e10			−0.161649
$877$	−6.00059e11	−	6.00059e11i	−1.01437	−	1.01437i	−0.999895	−	0.0144728i	$-0.995393\pi$
$877$	−6.00059e11	−	6.00059e11i	−1.01437	−	1.01437i	−0.0144728	−	0.999895i	$-0.504607\pi$
$878$	−7.18623e11	+	7.18623e11i	−1.20927	+	1.20927i
$879$		−	2.55696e11i		−	0.428320i
$880$	−4.12573e10	+	2.07162e10i	−0.0687971	+	0.0345446i
$881$	−5.01925e11			−0.833174			−0.416587	−	0.909096i	$-0.636774\pi$
$881$	−5.01925e11			−0.833174			−0.416587	+	0.909096i	$0.636774\pi$
$882$	−5.16455e11	−	5.16455e11i	−0.853411	−	0.853411i
$883$	7.06343e11	−	7.06343e11i	1.16191	−	1.16191i	0.177854	−	0.984057i	$-0.443085\pi$
$883$	7.06343e11	−	7.06343e11i	1.16191	−	1.16191i	0.984057	−	0.177854i	$-0.0569153\pi$
$884$			2.06386e11i			0.337964i
$885$	2.17067e11	+	7.19465e10i	0.353851	+	0.117283i
$886$	−6.52889e11			−1.05951
$887$	2.38573e11	+	2.38573e11i	0.385414	+	0.385414i	0.873048	−	0.487634i	$-0.162140\pi$
$887$	2.38573e11	+	2.38573e11i	0.385414	+	0.385414i	−0.487634	+	0.873048i	$0.662140\pi$
$888$	−2.23320e9	+	2.23320e9i	−0.00359150	+	0.00359150i
$889$		−	1.39855e12i		−	2.23908i
$890$	3.38505e11	−	1.02129e12i	0.539517	−	1.62775i
$891$	2.69590e10			0.0427753
$892$	−4.69889e11	−	4.69889e11i	−0.742226	−	0.742226i
$893$	−2.05016e11	+	2.05016e11i	−0.322390	+	0.322390i
$894$			1.14741e11i			0.179626i
$895$	1.23207e11	+	2.45373e11i	0.192019	+	0.382414i
$896$	−4.39161e11			−0.681384
$897$	−1.47576e10	−	1.47576e10i	−0.0227953	−	0.0227953i
$898$	−3.03748e10	+	3.03748e10i	−0.0467098	+	0.0467098i
$899$			1.15101e12i			1.76215i
$900$	−2.80679e11	+	3.76897e11i	−0.427800	+	0.574451i
$901$	−6.95838e10			−0.105587
$902$	−8.31481e9	−	8.31481e9i	−0.0125611	−	0.0125611i
$903$	−1.05494e11	+	1.05494e11i	−0.158664	+	0.158664i
$904$		−	1.30308e10i		−	0.0195118i
$905$	9.41832e11	−	4.72916e11i	1.40404	−	0.705000i
$906$	3.82696e11			0.567991
$907$	−4.12169e11	−	4.12169e11i	−0.609040	−	0.609040i	0.333655	−	0.942695i	$-0.391718\pi$
$907$	−4.12169e11	−	4.12169e11i	−0.609040	−	0.609040i	−0.942695	+	0.333655i	$0.891718\pi$
$908$	−6.01265e11	+	6.01265e11i	−0.884551	+	0.884551i
$909$			1.73442e11i			0.254037i
$910$	1.64407e12	+	5.44924e11i	2.39747	+	0.794640i
$911$	−6.90488e10			−0.100250			−0.0501248	−	0.998743i	$-0.515962\pi$
$911$	−6.90488e10			−0.100250			−0.0501248	+	0.998743i	$0.515962\pi$
$912$	7.70508e10	+	7.70508e10i	0.111378	+	0.111378i
$913$	3.23228e9	−	3.23228e9i	0.00465185	−	0.00465185i
$914$			3.93121e11i			0.563302i
$915$	−7.91783e10	+	2.38885e11i	−0.112959	+	0.340805i
$916$	8.84699e11			1.25665
$917$	4.45628e11	+	4.45628e11i	0.630224	+	0.630224i
$918$	−1.41187e11	+	1.41187e11i	−0.198803	+	0.198803i
$919$		−	1.35037e12i		−	1.89317i	−0.322447	−	0.946587i	$-0.604505\pi$
$919$		−	1.35037e12i		−	1.89317i	0.322447	−	0.946587i	$-0.395495\pi$
$920$	−5.39969e9	−	1.07537e10i	−0.00753733	−	0.0150109i
$921$	1.76529e10			0.0245346
$922$	4.50248e11	+	4.50248e11i	0.623058	+	0.623058i
$923$	7.49707e11	−	7.49707e11i	1.03296	−	1.03296i
$924$		−	2.02312e10i		−	0.0277546i
$925$	4.25725e10	−	6.22930e9i	0.0581517	−	0.00850888i
$926$	−8.20414e11			−1.11581
$927$	−2.45517e11	−	2.45517e11i	−0.332478	−	0.332478i
$928$	−1.01727e12	+	1.01727e12i	−1.37166	+	1.37166i
$929$			8.74727e11i			1.17438i	0.809448	+	0.587191i	$0.199766\pi$
$929$			8.74727e11i			1.17438i	−0.809448	+	0.587191i	$0.800234\pi$
$930$	−3.79468e11	+	1.90540e11i	−0.507275	+	0.254715i
$931$	2.97292e11			0.395717
$932$	−2.92503e11	−	2.92503e11i	−0.387674	−	0.387674i
$933$	1.07741e11	−	1.07741e11i	0.142186	−	0.142186i
$934$			7.38206e11i			0.970041i
$935$	1.52434e10	+	5.05240e9i	0.0199450	+	0.00661076i
$936$	−2.14958e11			−0.280060
$937$	−8.71252e11	−	8.71252e11i	−1.13028	−	1.13028i	−0.990131	−	0.140148i	$-0.955242\pi$
$937$	−8.71252e11	−	8.71252e11i	−1.13028	−	1.13028i	−0.140148	−	0.990131i	$-0.544758\pi$
$938$	−7.03372e11	+	7.03372e11i	−0.908602	+	0.908602i
$939$		−	2.24466e11i		−	0.288727i
$940$	2.37441e11	−	7.16372e11i	0.304119	−	0.917544i
$941$	7.43237e11			0.947914			0.473957	−	0.880548i	$-0.342825\pi$
$941$	7.43237e11			0.947914			0.473957	+	0.880548i	$0.342825\pi$
$942$	−1.80590e11	−	1.80590e11i	−0.229346	−	0.229346i
$943$	7.57573e9	−	7.57573e9i	0.00958027	−	0.00958027i
$944$		−	9.57276e11i		−	1.20545i
$945$	3.38664e11	+	6.74464e11i	0.424661	+	0.845730i
$946$	3.21909e10			0.0401946
$947$	−2.14562e11	−	2.14562e11i	−0.266780	−	0.266780i	0.561022	−	0.827801i	$-0.310408\pi$
$947$	−2.14562e11	−	2.14562e11i	−0.266780	−	0.266780i	−0.827801	+	0.561022i	$0.810408\pi$
$948$	2.93278e11	−	2.93278e11i	0.363116	−	0.363116i
$949$			5.93196e11i			0.731364i
$950$	−6.14858e10	−	4.20209e11i	−0.0754884	−	0.515906i
$951$	1.56980e11			0.191920
$952$	6.30243e10	+	6.30243e10i	0.0767291	+	0.0767291i
$953$	3.76794e11	−	3.76794e11i	0.456807	−	0.456807i	−0.440799	−	0.897606i	$-0.645305\pi$
$953$	3.76794e11	−	3.76794e11i	0.456807	−	0.456807i	0.897606	+	0.440799i	$0.145305\pi$
$954$			3.29081e11i			0.397291i
$955$	−8.50506e11	+	4.27059e11i	−1.02250	+	0.513422i
$956$	−5.84521e11			−0.699791
$957$	2.09892e10	+	2.09892e10i	0.0250235	+	0.0250235i
$958$	1.52702e12	−	1.52702e12i	1.81294	−	1.81294i
$959$		−	7.73367e11i		−	0.914348i
$960$	−1.75249e11	−	5.80859e10i	−0.206333	−	0.0683890i
$961$	3.45639e11			0.405255
$962$	−6.31913e10	−	6.31913e10i	−0.0737831	−	0.0737831i
$963$	−5.07332e11	+	5.07332e11i	−0.589912	+	0.589912i
$964$		−	3.82796e11i		−	0.443261i
$965$	−5.46036e10	+	1.64742e11i	−0.0629669	+	0.189975i
$966$	4.09254e10			0.0469985
$967$	1.15307e12	+	1.15307e12i	1.31871	+	1.31871i	0.914798	+	0.403911i	$0.132349\pi$
$967$	1.15307e12	+	1.15307e12i	1.31871	+	1.31871i	0.403911	+	0.914798i	$0.367651\pi$
$968$	−1.50468e11	+	1.50468e11i	−0.171373	+	0.171373i
$969$		−	3.79037e10i		−	0.0429919i
$970$	−1.68245e11	−	3.35067e11i	−0.190045	−	0.378482i
$971$	−1.14897e12			−1.29250			−0.646250	−	0.763126i	$-0.723664\pi$
$971$	−1.14897e12			−1.29250			−0.646250	+	0.763126i	$0.723664\pi$
$972$	4.61220e11	+	4.61220e11i	0.516705	+	0.516705i
$973$	−6.91482e11	+	6.91482e11i	−0.771488	+	0.771488i
$974$		−	1.32862e12i		−	1.47626i
$975$	−3.38652e11	−	2.52198e11i	−0.374745	−	0.279076i
$976$	1.05350e12			1.16101
$977$	4.00572e11	+	4.00572e11i	0.439646	+	0.439646i	0.891893	−	0.452247i	$-0.149377\pi$
$977$	4.00572e11	+	4.00572e11i	0.439646	+	0.439646i	−0.452247	+	0.891893i	$0.649377\pi$
$978$	−4.74899e11	+	4.74899e11i	−0.519093	+	0.519093i
$979$			7.83180e10i			0.0852572i
$980$	−6.91559e11	+	3.47248e11i	−0.749765	+	0.376474i
$981$	−2.57639e11			−0.278187
$982$	−2.66795e11	−	2.66795e11i	−0.286901	−	0.286901i
$983$	6.04096e11	−	6.04096e11i	0.646982	−	0.646982i	−0.305281	−	0.952262i	$-0.598750\pi$
$983$	6.04096e11	−	6.04096e11i	0.646982	−	0.646982i	0.952262	+	0.305281i	$0.0987503\pi$
$984$			1.59105e10i			0.0169709i
$985$	−1.05202e12	−	3.48690e11i	−1.11758	−	0.370420i
$986$	5.93788e11			0.628238
$987$	−3.99712e11	−	3.99712e11i	−0.421190	−	0.421190i
$988$	−2.80928e11	+	2.80928e11i	−0.294827	+	0.294827i
$989$			2.93295e10i			0.0306563i
$990$	2.38942e10	−	7.20900e10i	0.0248743	−	0.0750472i
$991$	4.34203e10			0.0450193			0.0225096	−	0.999747i	$-0.492834\pi$
$991$	4.34203e10			0.0450193			0.0225096	+	0.999747i	$0.492834\pi$
$992$	1.05927e12	+	1.05927e12i	1.09385	+	1.09385i
$993$	9.02231e10	−	9.02231e10i	0.0927942	−	0.0927942i
$994$			2.07907e12i			2.12973i
$995$	3.08531e11	+	6.14454e11i	0.314780	+	0.626898i
$996$	2.80842e10			0.0285381
$997$	5.58826e11	+	5.58826e11i	0.565582	+	0.565582i	0.930888	−	0.365305i	$-0.119035\pi$
$997$	5.58826e11	+	5.58826e11i	0.565582	+	0.565582i	−0.365305	+	0.930888i	$0.619035\pi$
$998$	9.44651e11	−	9.44651e11i	0.952246	−	0.952246i
$999$		−	3.89406e10i		−	0.0390968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.9.c.a.2.3	✓	6
3.2	odd	2		45.9.g.a.37.1		6
4.3	odd	2		80.9.p.c.17.2		6
5.2	odd	4		25.9.c.b.18.1		6
5.3	odd	4	inner	5.9.c.a.3.3	yes	6
5.4	even	2		25.9.c.b.7.1		6
15.8	even	4		45.9.g.a.28.1		6
20.3	even	4		80.9.p.c.33.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.9.c.a.2.3	✓	6	1.1	even	1	trivial
5.9.c.a.3.3	yes	6	5.3	odd	4	inner
25.9.c.b.7.1		6	5.4	even	2
25.9.c.b.18.1		6	5.2	odd	4
45.9.g.a.28.1		6	15.8	even	4
45.9.g.a.37.1		6	3.2	odd	2
80.9.p.c.17.2		6	4.3	odd	2
80.9.p.c.33.2		6	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(15.2610 + 15.2610i) q^{2} +(-20.3321 + 20.3321i) q^{3} +209.796i q^{4} +(558.542 - 280.457i) q^{5} -620.576 q^{6} +(-2415.21 - 2415.21i) q^{7} +(705.116 - 705.116i) q^{8} +5734.21i q^{9} +O(q^{10})\)	\(q+(15.2610 + 15.2610i) q^{2} +(-20.3321 + 20.3321i) q^{3} +209.796i q^{4} +(558.542 - 280.457i) q^{5} -620.576 q^{6} +(-2415.21 - 2415.21i) q^{7} +(705.116 - 705.116i) q^{8} +5734.21i q^{9} +(12804.0 + 4243.86i) q^{10} -981.878 q^{11} +(-4265.60 - 4265.60i) q^{12} +(-26582.1 + 26582.1i) q^{13} -73717.1i q^{14} +(-5654.06 + 17058.6i) q^{15} +75229.4 q^{16} +(-18503.9 - 18503.9i) q^{17} +(-87509.8 + 87509.8i) q^{18} -50374.1i q^{19} +(58838.8 + 117180. i) q^{20} +98212.6 q^{21} +(-14984.4 - 14984.4i) q^{22} +(13652.5 - 13652.5i) q^{23} +28673.0i q^{24} +(233313. - 313294. i) q^{25} -811340. q^{26} +(-249988. - 249988. i) q^{27} +(506702. - 506702. i) q^{28} +1.05137e6i q^{29} +(-346618. + 174045. i) q^{30} +1.09477e6 q^{31} +(967566. + 967566. i) q^{32} +(19963.6 - 19963.6i) q^{33} -564775. i q^{34} +(-2.02636e6 - 671634. i) q^{35} -1.20302e6 q^{36} +(77885.1 + 77885.1i) q^{37} +(768759. - 768759. i) q^{38} -1.08094e6i q^{39} +(196082. - 591591. i) q^{40} +554897. q^{41} +(1.49882e6 + 1.49882e6i) q^{42} +(-1.07414e6 + 1.07414e6i) q^{43} -205994. i q^{44} +(1.60820e6 + 3.20280e6i) q^{45} +416702. q^{46} +(-4.06986e6 - 4.06986e6i) q^{47} +(-1.52957e6 + 1.52957e6i) q^{48} +5.90168e6i q^{49} +(8.34176e6 - 1.22058e6i) q^{50} +752445. q^{51} +(-5.57683e6 - 5.57683e6i) q^{52} +(1.88025e6 - 1.88025e6i) q^{53} -7.63012e6i q^{54} +(-548420. + 275374. i) q^{55} -3.40601e6 q^{56} +(1.02421e6 + 1.02421e6i) q^{57} +(-1.60450e7 + 1.60450e7i) q^{58} -1.27248e7i q^{59} +(-3.57883e6 - 1.18620e6i) q^{60} +1.40038e7 q^{61} +(1.67073e7 + 1.67073e7i) q^{62} +(1.38493e7 - 1.38493e7i) q^{63} +1.02733e7i q^{64} +(-7.39210e6 + 2.23024e7i) q^{65} +609330. q^{66} +(-9.54151e6 - 9.54151e6i) q^{67} +(3.88204e6 - 3.88204e6i) q^{68} +555168. i q^{69} +(-2.06744e7 - 4.11741e7i) q^{70} -2.82034e7 q^{71} +(4.04328e6 + 4.04328e6i) q^{72} +(1.11578e7 - 1.11578e7i) q^{73} +2.37721e6i q^{74} +(1.62617e6 + 1.11137e7i) q^{75} +1.05683e7 q^{76} +(2.37144e6 + 2.37144e6i) q^{77} +(1.64963e7 - 1.64963e7i) q^{78} +6.87542e7i q^{79} +(4.20188e7 - 2.10986e7i) q^{80} -2.74566e7 q^{81} +(8.46828e6 + 8.46828e6i) q^{82} +(-3.29194e6 + 3.29194e6i) q^{83} +2.06046e7i q^{84} +(-1.55247e7 - 5.14565e6i) q^{85} -3.27850e7 q^{86} +(-2.13766e7 - 2.13766e7i) q^{87} +(-692338. + 692338. i) q^{88} -7.97635e7i q^{89} +(-2.43352e7 + 7.34206e7i) q^{90} +1.28403e8 q^{91} +(2.86424e6 + 2.86424e6i) q^{92} +(-2.22591e7 + 2.22591e7i) q^{93} -1.24220e8i q^{94} +(-1.41278e7 - 2.81360e7i) q^{95} -3.93453e7 q^{96} +(-1.96546e7 - 1.96546e7i) q^{97} +(-9.00656e7 + 9.00656e7i) q^{98} -5.63029e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8	\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8} + 30870 q^{10} + 23192 q^{11} - 45912 q^{12} - 119142 q^{13} + 241440 q^{15} + 218616 q^{16} - 265502 q^{17} - 454062 q^{18} + 412260 q^{20} + 231672 q^{21} - 35664 q^{22} + 28888 q^{23} - 340350 q^{25} - 801388 q^{26} + 392040 q^{27} + 1305192 q^{28} - 2549760 q^{30} - 747648 q^{31} + 3033928 q^{32} + 4269096 q^{33} - 4971680 q^{35} - 3972804 q^{36} - 454002 q^{37} + 1443720 q^{38} + 2683500 q^{40} + 2489432 q^{41} + 4223856 q^{42} + 792648 q^{43} + 210690 q^{45} - 3149928 q^{46} - 15313352 q^{47} - 21677712 q^{48} + 29537650 q^{50} + 35567712 q^{51} - 735732 q^{52} - 13509122 q^{53} + 4448040 q^{55} - 18454800 q^{56} - 34625520 q^{57} - 23903520 q^{58} + 13688520 q^{60} + 24111192 q^{61} + 53913416 q^{62} + 44837688 q^{63} - 30943610 q^{65} - 55047936 q^{66} - 32827752 q^{67} + 8118692 q^{68} - 44156280 q^{70} - 13992928 q^{71} + 82596420 q^{72} + 111859638 q^{73} - 126793200 q^{75} - 56470800 q^{76} + 26260136 q^{77} + 31125576 q^{78} + 23045920 q^{80} + 65834226 q^{81} + 38023056 q^{82} - 14768432 q^{83} - 19713030 q^{85} - 135560008 q^{86} - 133207680 q^{87} - 44555040 q^{88} + 135147990 q^{90} + 167542032 q^{91} + 69931048 q^{92} - 96798024 q^{93} + 239661000 q^{95} + 184867872 q^{96} - 186656202 q^{97} - 345959698 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8 + 30870 * q^10 + 23192 * q^11 - 45912 * q^12 - 119142 * q^13 + 241440 * q^15 + 218616 * q^16 - 265502 * q^17 - 454062 * q^18 + 412260 * q^20 + 231672 * q^21 - 35664 * q^22 + 28888 * q^23 - 340350 * q^25 - 801388 * q^26 + 392040 * q^27 + 1305192 * q^28 - 2549760 * q^30 - 747648 * q^31 + 3033928 * q^32 + 4269096 * q^33 - 4971680 * q^35 - 3972804 * q^36 - 454002 * q^37 + 1443720 * q^38 + 2683500 * q^40 + 2489432 * q^41 + 4223856 * q^42 + 792648 * q^43 + 210690 * q^45 - 3149928 * q^46 - 15313352 * q^47 - 21677712 * q^48 + 29537650 * q^50 + 35567712 * q^51 - 735732 * q^52 - 13509122 * q^53 + 4448040 * q^55 - 18454800 * q^56 - 34625520 * q^57 - 23903520 * q^58 + 13688520 * q^60 + 24111192 * q^61 + 53913416 * q^62 + 44837688 * q^63 - 30943610 * q^65 - 55047936 * q^66 - 32827752 * q^67 + 8118692 * q^68 - 44156280 * q^70 - 13992928 * q^71 + 82596420 * q^72 + 111859638 * q^73 - 126793200 * q^75 - 56470800 * q^76 + 26260136 * q^77 + 31125576 * q^78 + 23045920 * q^80 + 65834226 * q^81 + 38023056 * q^82 - 14768432 * q^83 - 19713030 * q^85 - 135560008 * q^86 - 133207680 * q^87 - 44555040 * q^88 + 135147990 * q^90 + 167542032 * q^91 + 69931048 * q^92 - 96798024 * q^93 + 239661000 * q^95 + 184867872 * q^96 - 186656202 * q^97 - 345959698 * q^98

Introduction

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