LMFDB - Embedded newform 48.8.k.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,8,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	48.k (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:	$14.9944812232$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	48.11
Dual form			48.8.k.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.1336 + 2.01052i) q^{2} +(1.90114 + 46.7267i) q^{3} +(119.916 - 44.7688i) q^{4} +(277.365 - 277.365i) q^{5} +(-115.112 - 516.416i) q^{6} +418.647 q^{7} +(-1245.09 + 739.532i) q^{8} +(-2179.77 + 177.668i) q^{9} +O(q^{10})$	\(q+(-11.1336 + 2.01052i) q^{2} +(1.90114 + 46.7267i) q^{3} +(119.916 - 44.7688i) q^{4} +(277.365 - 277.365i) q^{5} +(-115.112 - 516.416i) q^{6} +418.647 q^{7} +(-1245.09 + 739.532i) q^{8} +(-2179.77 + 177.668i) q^{9} +(-2530.44 + 3645.73i) q^{10} +(-5506.90 - 5506.90i) q^{11} +(2319.88 + 5518.15i) q^{12} +(1588.08 - 1588.08i) q^{13} +(-4661.06 + 841.699i) q^{14} +(13487.7 + 12433.1i) q^{15} +(12375.5 - 10737.0i) q^{16} +15876.2i q^{17} +(23911.6 - 6360.57i) q^{18} +(-38149.1 - 38149.1i) q^{19} +(20843.1 - 45677.8i) q^{20} +(795.908 + 19562.0i) q^{21} +(72383.6 + 50240.1i) q^{22} -107309. i q^{23} +(-36923.0 - 56772.9i) q^{24} -75738.2i q^{25} +(-14488.2 + 20873.9i) q^{26} +(-12445.9 - 101516. i) q^{27} +(50202.3 - 18742.3i) q^{28} +(124918. + 124918. i) q^{29} +(-175164. - 111308. i) q^{30} +13594.2i q^{31} +(-116198. + 144423. i) q^{32} +(246850. - 267789. i) q^{33} +(-31919.5 - 176760. i) q^{34} +(116118. - 116118. i) q^{35} +(-253435. + 118891. i) q^{36} +(-137258. - 137258. i) q^{37} +(501438. + 348039. i) q^{38} +(77224.8 + 71186.5i) q^{39} +(-140224. + 550465. i) q^{40} +23734.4 q^{41} +(-48191.2 - 216196. i) q^{42} +(380018. - 380018. i) q^{43} +(-906901. - 413826. i) q^{44} +(-555314. + 653872. i) q^{45} +(215748. + 1.19474e6i) q^{46} +748140. q^{47} +(525230. + 557854. i) q^{48} -648278. q^{49} +(152273. + 843241. i) q^{50} +(-741844. + 30183.0i) q^{51} +(119339. - 261532. i) q^{52} +(249051. - 249051. i) q^{53} +(342668. + 1.10522e6i) q^{54} -3.05485e6 q^{55} +(-521253. + 309603. i) q^{56} +(1.71006e6 - 1.85511e6i) q^{57} +(-1.64194e6 - 1.13964e6i) q^{58} +(283853. + 283853. i) q^{59} +(2.17400e6 + 887091. i) q^{60} +(286681. - 286681. i) q^{61} +(-27331.4 - 151353. i) q^{62} +(-912555. + 74380.3i) q^{63} +(1.00334e6 - 1.84157e6i) q^{64} -880955. i q^{65} +(-2.20994e6 + 3.47776e6i) q^{66} +(-1.01238e6 - 1.01238e6i) q^{67} +(710759. + 1.90381e6i) q^{68} +(5.01421e6 - 204010. i) q^{69} +(-1.05936e6 + 1.52628e6i) q^{70} -596500. i q^{71} +(2.58262e6 - 1.83322e6i) q^{72} +1.34997e6i q^{73} +(1.80414e6 + 1.25222e6i) q^{74} +(3.53899e6 - 143989. i) q^{75} +(-6.28257e6 - 2.86679e6i) q^{76} +(-2.30545e6 - 2.30545e6i) q^{77} +(-1.00291e6 - 637302. i) q^{78} -3.25061e6i q^{79} +(454479. - 6.41060e6i) q^{80} +(4.71984e6 - 774552. i) q^{81} +(-264250. + 47718.4i) q^{82} +(-2.80904e6 + 2.80904e6i) q^{83} +(971209. + 2.31016e6i) q^{84} +(4.40352e6 + 4.40352e6i) q^{85} +(-3.46695e6 + 4.99501e6i) q^{86} +(-5.59953e6 + 6.07450e6i) q^{87} +(1.09291e7 + 2.78405e6i) q^{88} -3.56934e6 q^{89} +(4.86804e6 - 8.39644e6i) q^{90} +(664844. - 664844. i) q^{91} +(-4.80411e6 - 1.28681e7i) q^{92} +(-635211. + 25844.4i) q^{93} +(-8.32952e6 + 1.50415e6i) q^{94} -2.11625e7 q^{95} +(-6.96930e6 - 5.15496e6i) q^{96} +608540. q^{97} +(7.21769e6 - 1.30338e6i) q^{98} +(1.29822e7 + 1.10254e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−11.1336	+	2.01052i	−0.984084	+	0.177707i
$2$	−11.1336	+	2.01052i	−0.984084	+	0.177707i
$3$	1.90114	+	46.7267i	0.0406528	+	0.999173i
$3$	1.90114	+	46.7267i	0.0406528	+	0.999173i
$4$	119.916	−	44.7688i	0.936841	−	0.349756i
$5$	277.365	−	277.365i	0.992333	−	0.992333i	−0.00763814	−	0.999971i	$-0.502431\pi$
$5$	277.365	−	277.365i	0.992333	−	0.992333i	0.999971	+	0.00763814i	$0.00243132\pi$
$6$	−115.112	−	516.416i	−0.217565	−	0.976046i
$7$	418.647			0.461323			0.230661	−	0.973034i	$-0.425911\pi$
$7$	418.647			0.461323			0.230661	+	0.973034i	$0.425911\pi$
$8$	−1245.09	+	739.532i	−0.859776	+	0.510672i
$9$	−2179.77	+	177.668i	−0.996695	+	0.0812383i
$10$	−2530.44	+	3645.73i	−0.800194	+	1.15288i
$11$	−5506.90	−	5506.90i	−1.24748	−	1.24748i	−0.956830	−	0.290649i	$-0.906129\pi$
$11$	−5506.90	−	5506.90i	−1.24748	−	1.24748i	−0.290649	−	0.956830i	$-0.593871\pi$
$12$	2319.88	+	5518.15i	0.387552	+	0.921848i
$13$	1588.08	−	1588.08i	0.200479	−	0.200479i	−0.599726	−	0.800205i	$-0.704724\pi$
$13$	1588.08	−	1588.08i	0.200479	−	0.200479i	0.800205	+	0.599726i	$0.204724\pi$
$14$	−4661.06	+	841.699i	−0.453980	+	0.0819801i
$15$	13487.7	+	12433.1i	1.03185	+	0.951171i
$16$	12375.5	−	10737.0i	0.755341	−	0.655332i
$17$			15876.2i			0.783747i	0.920019	+	0.391874i	$0.128173\pi$
$17$			15876.2i			0.783747i	−0.920019	+	0.391874i	$0.871827\pi$
$18$	23911.6	−	6360.57i	0.966394	−	0.257064i
$19$	−38149.1	−	38149.1i	−1.27599	−	1.27599i	−0.942893	−	0.333097i	$-0.891906\pi$
$19$	−38149.1	−	38149.1i	−1.27599	−	1.27599i	−0.333097	−	0.942893i	$-0.608094\pi$
$20$	20843.1	−	45677.8i	0.582583	−	1.27673i
$21$	795.908	+	19562.0i	0.0187540	+	0.460942i
$22$	72383.6	+	50240.1i	1.44931	+	1.00594i
$23$		−	107309.i		−	1.83904i	−0.393049	−	0.919518i	$-0.628580\pi$
$23$		−	107309.i		−	1.83904i	0.393049	−	0.919518i	$-0.371420\pi$
$24$	−36923.0	−	56772.9i	−0.545202	−	0.838305i
$25$		−	75738.2i		−	0.969448i
$26$	−14488.2	+	20873.9i	−0.161662	+	0.232915i
$27$	−12445.9	−	101516.i	−0.121690	−	0.992568i
$28$	50202.3	−	18742.3i	0.432186	−	0.161351i
$29$	124918.	+	124918.i	0.951114	+	0.951114i	0.998860	−	0.0477453i	$-0.0152036\pi$
$29$	124918.	+	124918.i	0.951114	+	0.951114i	−0.0477453	+	0.998860i	$0.515204\pi$
$30$	−175164.	−	111308.i	−1.18446	−	0.752665i
$31$			13594.2i			0.0819572i	0.999160	+	0.0409786i	$0.0130475\pi$
$31$			13594.2i			0.0819572i	−0.999160	+	0.0409786i	$0.986952\pi$
$32$	−116198.	+	144423.i	−0.626862	+	0.779130i
$33$	246850.	−	267789.i	1.19573	−	1.29716i
$34$	−31919.5	−	176760.i	−0.139277	−	0.771273i
$35$	116118.	−	116118.i	0.457786	−	0.457786i
$36$	−253435.	+	118891.i	−0.905331	+	0.424708i
$37$	−137258.	−	137258.i	−0.445484	−	0.445484i	0.448366	−	0.893850i	$-0.352006\pi$
$37$	−137258.	−	137258.i	−0.445484	−	0.445484i	−0.893850	+	0.448366i	$0.852006\pi$
$38$	501438.	+	348039.i	1.48243	+	1.02893i
$39$	77224.8	+	71186.5i	0.208464	+	0.192164i
$40$	−140224.	+	550465.i	−0.346427	+	1.35994i
$41$	23734.4			0.0537816			0.0268908	−	0.999638i	$-0.491439\pi$
$41$	23734.4			0.0537816			0.0268908	+	0.999638i	$0.491439\pi$
$42$	−48191.2	−	216196.i	−0.100368	−	0.450272i
$43$	380018.	−	380018.i	0.728894	−	0.728894i	−0.241506	−	0.970399i	$-0.577641\pi$
$43$	380018.	−	380018.i	0.728894	−	0.728894i	0.970399	+	0.241506i	$0.0776412\pi$
$44$	−906901.	−	413826.i	−1.60500	−	0.732375i
$45$	−555314.	+	653872.i	−0.908437	+	1.06967i
$46$	215748.	+	1.19474e6i	0.326809	+	1.80976i
$47$	748140.			1.05109			0.525546	−	0.850765i	$-0.323861\pi$
$47$	748140.			1.05109			0.525546	+	0.850765i	$0.323861\pi$
$48$	525230.	+	557854.i	0.685497	+	0.728076i
$49$	−648278.			−0.787181
$50$	152273.	+	843241.i	0.172277	+	0.954018i
$51$	−741844.	+	30183.0i	−0.783099	+	0.0318615i
$52$	119339.	−	261532.i	0.117698	−	0.257936i
$53$	249051.	−	249051.i	0.229786	−	0.229786i	−0.582817	−	0.812603i	$-0.698050\pi$
$53$	249051.	−	249051.i	0.229786	−	0.229786i	0.812603	+	0.582817i	$0.198050\pi$
$54$	342668.	+	1.10522e6i	0.296139	+	0.955145i
$55$	−3.05485e6			−2.47583
$56$	−521253.	+	309603.i	−0.396634	+	0.235585i
$57$	1.71006e6	−	1.85511e6i	1.22306	−	1.32681i
$58$	−1.64194e6	−	1.13964e6i	−1.10500	−	0.766957i
$59$	283853.	+	283853.i	0.179934	+	0.179934i	0.791327	−	0.611393i	$-0.209391\pi$
$59$	283853.	+	283853.i	0.179934	+	0.179934i	−0.611393	+	0.791327i	$0.709391\pi$
$60$	2.17400e6	+	887091.i	1.29936	+	0.530199i
$61$	286681.	−	286681.i	0.161713	−	0.161713i	−0.621612	−	0.783325i	$-0.713522\pi$
$61$	286681.	−	286681.i	0.161713	−	0.161713i	0.783325	+	0.621612i	$0.213522\pi$
$62$	−27331.4	−	151353.i	−0.0145643	−	0.0806527i
$63$	−912555.	+	74380.3i	−0.459798	+	0.0374771i
$64$	1.00334e6	−	1.84157e6i	0.478428	−	0.878127i
$65$		−	880955.i		−	0.397885i
$66$	−2.20994e6	+	3.47776e6i	−0.946188	+	1.48900i
$67$	−1.01238e6	−	1.01238e6i	−0.411228	−	0.411228i	0.470938	−	0.882166i	$-0.343915\pi$
$67$	−1.01238e6	−	1.01238e6i	−0.411228	−	0.411228i	−0.882166	+	0.470938i	$0.843915\pi$
$68$	710759.	+	1.90381e6i	0.274120	+	0.734246i
$69$	5.01421e6	−	204010.i	1.83751	−	0.0747619i
$70$	−1.05936e6	+	1.52628e6i	−0.369148	+	0.531851i
$71$		−	596500.i		−	0.197791i	−0.995098	−	0.0988954i	$-0.968469\pi$
$71$		−	596500.i		−	0.197791i	0.995098	−	0.0988954i	$-0.0315309\pi$
$72$	2.58262e6	−	1.83322e6i	0.815448	−	0.578831i
$73$			1.34997e6i			0.406156i	0.979163	+	0.203078i	$0.0650945\pi$
$73$			1.34997e6i			0.406156i	−0.979163	+	0.203078i	$0.934906\pi$
$74$	1.80414e6	+	1.25222e6i	0.517559	+	0.359228i
$75$	3.53899e6	−	143989.i	0.968647	−	0.0394108i
$76$	−6.28257e6	−	2.86679e6i	−1.64168	−	0.749114i
$77$	−2.30545e6	−	2.30545e6i	−0.575490	−	0.575490i
$78$	−1.00291e6	−	637302.i	−0.239294	−	0.152060i
$79$		−	3.25061e6i		−	0.741772i	−0.928678	−	0.370886i	$-0.879054\pi$
$79$		−	3.25061e6i		−	0.741772i	0.928678	−	0.370886i	$-0.120946\pi$
$80$	454479.	−	6.41060e6i	0.0992427	−	1.39986i
$81$	4.71984e6	−	774552.i	0.986801	−	0.161940i
$82$	−264250.	+	47718.4i	−0.0529256	+	0.00955735i
$83$	−2.80904e6	+	2.80904e6i	−0.539242	+	0.539242i	−0.923306	−	0.384064i	$-0.874524\pi$
$83$	−2.80904e6	+	2.80904e6i	−0.539242	+	0.539242i	0.384064	+	0.923306i	$0.374524\pi$
$84$	971209.	+	2.31016e6i	0.178787	+	0.425269i
$85$	4.40352e6	+	4.40352e6i	0.777738	+	0.777738i
$86$	−3.46695e6	+	4.99501e6i	−0.587763	+	0.846822i
$87$	−5.59953e6	+	6.07450e6i	−0.911663	+	0.988993i
$88$	1.09291e7	+	2.78405e6i	1.70960	+	0.435499i
$89$	−3.56934e6			−0.536689			−0.268344	−	0.963323i	$-0.586476\pi$
$89$	−3.56934e6			−0.536689			−0.268344	+	0.963323i	$0.586476\pi$
$90$	4.86804e6	−	8.39644e6i	0.703891	−	1.21408i
$91$	664844.	−	664844.i	0.0924858	−	0.0924858i
$92$	−4.80411e6	−	1.28681e7i	−0.643214	−	1.72288i
$93$	−635211.	+	25844.4i	−0.0818894	+	0.00333178i
$94$	−8.32952e6	+	1.50415e6i	−1.03436	+	0.186786i
$95$	−2.11625e7			−2.53241
$96$	−6.96930e6	−	5.15496e6i	−0.803970	−	0.594670i
$97$	608540.			0.0676999			0.0338500	−	0.999427i	$-0.489223\pi$
$97$	608540.			0.0676999			0.0338500	+	0.999427i	$0.489223\pi$
$98$	7.21769e6	−	1.30338e6i	0.774652	−	0.139887i
$99$	1.29822e7	+	1.10254e7i	1.34470	+	1.14201i
$100$	−3.39071e6	−	9.08219e6i	−0.339071	−	0.908219i
$101$	7.57513e6	−	7.57513e6i	0.731586	−	0.731586i	−0.239348	−	0.970934i	$-0.576934\pi$
$101$	7.57513e6	−	7.57513e6i	0.731586	−	0.731586i	0.970934	+	0.239348i	$0.0769336\pi$
$102$	8.19873e6	−	1.82754e6i	0.764973	−	0.170516i
$103$	2.63682e6			0.237766			0.118883	−	0.992908i	$-0.462069\pi$
$103$	2.63682e6			0.237766			0.118883	+	0.992908i	$0.462069\pi$
$104$	−802862.	+	3.15173e6i	−0.0699881	+	0.274747i
$105$	5.64658e6	+	5.20507e6i	0.476018	+	0.438797i
$106$	−2.27212e6	+	3.27357e6i	−0.185294	+	0.266963i
$107$	2.83654e6	+	2.83654e6i	0.223844	+	0.223844i	0.810115	−	0.586271i	$-0.199405\pi$
$107$	2.83654e6	+	2.83654e6i	0.223844	+	0.223844i	−0.586271	+	0.810115i	$0.699405\pi$
$108$	−6.03720e6	−	1.16161e7i	−0.461161	−	0.887317i
$109$	2.64308e6	−	2.64308e6i	0.195487	−	0.195487i	−0.602575	−	0.798062i	$-0.705859\pi$
$109$	2.64308e6	−	2.64308e6i	0.195487	−	0.195487i	0.798062	+	0.602575i	$0.205859\pi$
$110$	3.40116e7	−	6.14184e6i	2.43642	−	0.439971i
$111$	6.15268e6	−	6.67457e6i	0.427006	−	0.463226i
$112$	5.18097e6	−	4.49500e6i	0.348456	−	0.302320i
$113$			7.87979e6i			0.513736i	0.966446	+	0.256868i	$0.0826906\pi$
$113$			7.87979e6i			0.513736i	−0.966446	+	0.256868i	$0.917309\pi$
$114$	−1.53094e7	+	2.40922e7i	−0.967813	+	1.52304i
$115$	−2.97639e7	−	2.97639e7i	−1.82493	−	1.82493i
$116$	2.05721e7	+	9.38721e6i	1.22370	+	0.558384i
$117$	−3.17949e6	+	3.74380e6i	−0.183530	+	0.216103i
$118$	−3.73101e6	−	2.58963e6i	−0.209045	−	0.145094i
$119$			6.64654e6i			0.361561i
$120$	−2.59880e7	−	5.50568e6i	−1.37290	−	0.290855i
$121$			4.11648e7i			2.11241i
$122$	−2.61542e6	+	3.76818e6i	−0.130401	+	0.187876i
$123$	45122.4	+	1.10903e6i	0.00218637	+	0.0537372i
$124$	608595.	+	1.63015e6i	0.0286650	+	0.0767808i
$125$	662029.	+	662029.i	0.0303174	+	0.0303174i
$126$	1.00105e7	−	2.66283e6i	0.445820	−	0.118590i
$127$			3.48412e7i			1.50931i	0.656120	+	0.754657i	$0.272197\pi$
$127$			3.48412e7i			1.50931i	−0.656120	+	0.754657i	$0.727803\pi$
$128$	−7.46828e6	+	2.25205e7i	−0.314764	+	0.949170i
$129$	1.84794e7	+	1.70345e7i	0.757923	+	0.698660i
$130$	1.77118e6	+	9.80823e6i	0.0707067	+	0.391552i
$131$	−2.71952e7	+	2.71952e7i	−1.05692	+	1.05692i	−0.0586436	+	0.998279i	$0.518678\pi$
$131$	−2.71952e7	+	2.71952e7i	−1.05692	+	1.05692i	−0.998279	+	0.0586436i	$0.981322\pi$
$132$	1.76126e7	−	4.31633e7i	0.666522	−	1.63345i
$133$	−1.59710e7	−	1.59710e7i	−0.588643	−	0.588643i
$134$	1.33069e7	+	9.23607e6i	0.477760	+	0.331605i
$135$	−3.16090e7	−	2.47049e7i	−1.10571	−	0.864201i
$136$	−1.17410e7	−	1.97673e7i	−0.400238	−	0.673847i
$137$	−1.68253e7			−0.559038			−0.279519	−	0.960140i	$-0.590175\pi$
$137$	−1.68253e7			−0.559038			−0.279519	+	0.960140i	$0.590175\pi$
$138$	−5.54162e7	+	1.23525e7i	−1.79498	+	0.400110i
$139$	7.30622e6	−	7.30622e6i	0.230750	−	0.230750i	−0.582256	−	0.813006i	$-0.697830\pi$
$139$	7.30622e6	−	7.30622e6i	0.230750	−	0.230750i	0.813006	+	0.582256i	$0.197830\pi$
$140$	8.72592e6	−	1.91229e7i	0.268759	−	0.588986i
$141$	1.42232e6	+	3.49581e7i	0.0427298	+	1.05022i
$142$	1.19927e6	+	6.64121e6i	0.0351487	+	0.194643i
$143$	−1.74908e7			−0.500188
$144$	−2.50682e7	+	2.56028e7i	−0.699607	+	0.714528i
$145$	6.92960e7			1.88764
$146$	−2.71413e6	−	1.50300e7i	−0.0721766	−	0.399691i
$147$	−1.23247e6	−	3.02919e7i	−0.0320011	−	0.786530i
$148$	−2.26043e7	−	1.03145e7i	−0.573159	−	0.261537i
$149$	1.60311e7	−	1.60311e7i	0.397020	−	0.397020i	−0.480160	−	0.877181i	$-0.659422\pi$
$149$	1.60311e7	−	1.60311e7i	0.397020	−	0.397020i	0.877181	+	0.480160i	$0.159422\pi$
$150$	−3.91124e7	+	8.71834e6i	−0.946226	+	0.210918i
$151$	5.53418e7			1.30808			0.654040	−	0.756460i	$-0.273073\pi$
$151$	5.53418e7			1.30808			0.654040	+	0.756460i	$0.273073\pi$
$152$	7.57115e7	+	1.92865e7i	1.74868	+	0.445452i
$153$	−2.82070e6	−	3.46065e7i	−0.0636703	−	0.781157i
$154$	3.03032e7	+	2.10329e7i	0.668599	+	0.464062i
$155$	3.77055e6	+	3.77055e6i	0.0813288	+	0.0813288i
$156$	1.24474e7	+	5.07911e6i	0.262508	+	0.107115i
$157$	1.01404e7	−	1.01404e7i	0.209125	−	0.209125i	−0.594770	−	0.803896i	$-0.702757\pi$
$157$	1.01404e7	−	1.01404e7i	0.209125	−	0.209125i	0.803896	+	0.594770i	$0.202757\pi$
$158$	6.53542e6	+	3.61911e7i	0.131818	+	0.729965i
$159$	1.21108e7	+	1.11639e7i	0.238937	+	0.220254i
$160$	7.82864e6	+	7.22870e7i	0.151101	+	1.39521i
$161$		−	4.49247e7i		−	0.848389i
$162$	−5.09917e7	+	1.81129e7i	−0.942317	+	0.334723i
$163$	−6.07062e6	−	6.07062e6i	−0.109794	−	0.109794i	0.650076	−	0.759869i	$-0.274737\pi$
$163$	−6.07062e6	−	6.07062e6i	−0.109794	−	0.109794i	−0.759869	+	0.650076i	$0.774737\pi$
$164$	2.84612e6	−	1.06256e6i	0.0503848	−	0.0188105i
$165$	−5.80770e6	−	1.42743e8i	−0.100649	−	2.47378i
$166$	2.56272e7	−	3.69224e7i	0.434833	−	0.626487i
$167$		−	3.26849e7i		−	0.543050i	−0.962431	−	0.271525i	$-0.912472\pi$
$167$		−	3.26849e7i		−	0.543050i	0.962431	−	0.271525i	$-0.0875280\pi$
$168$	−1.54577e7	−	2.37678e7i	−0.251514	−	0.386729i
$169$			5.77045e7i			0.919616i
$170$	−5.78805e7	−	4.01738e7i	−0.903568	−	0.627150i
$171$	8.99343e7	+	7.63785e7i	1.37543	+	1.16811i
$172$	2.85571e7	−	6.25830e7i	0.427922	−	0.937793i
$173$	−5.54142e7	−	5.54142e7i	−0.813691	−	0.813691i	0.171494	−	0.985185i	$-0.445141\pi$
$173$	−5.54142e7	−	5.54142e7i	−0.813691	−	0.813691i	−0.985185	+	0.171494i	$0.945141\pi$
$174$	5.01302e7	−	7.88893e7i	0.721402	−	1.13526i
$175$		−	3.17076e7i		−	0.447229i
$176$	−1.27278e8	−	9.02337e6i	−1.75978	−	0.124760i
$177$	−1.27239e7	+	1.38032e7i	−0.172470	+	0.187100i
$178$	3.97397e7	−	7.17622e6i	0.528146	−	0.0953731i
$179$	7.32112e7	−	7.32112e7i	0.954096	−	0.954096i	−0.0448958	−	0.998992i	$-0.514296\pi$
$179$	7.32112e7	−	7.32112e7i	0.954096	−	0.954096i	0.998992	+	0.0448958i	$0.0142956\pi$
$180$	−3.73178e7	+	1.03270e8i	−0.476938	+	1.31984i
$181$	−5.67328e7	−	5.67328e7i	−0.711146	−	0.711146i	0.255629	−	0.966775i	$-0.417717\pi$
$181$	−5.67328e7	−	5.67328e7i	−0.711146	−	0.711146i	−0.966775	+	0.255629i	$0.917717\pi$
$182$	−6.06545e6	+	8.73881e6i	−0.0745784	+	0.107449i
$183$	1.39407e7	+	1.28506e7i	0.168153	+	0.155005i
$184$	7.93587e7	+	1.33610e8i	0.939144	+	1.58116i
$185$	−7.61413e7			−0.884137
$186$	7.02025e6	−	1.56485e6i	0.0799939	−	0.0178310i
$187$	8.74288e7	−	8.74288e7i	0.977708	−	0.977708i
$188$	8.97137e7	−	3.34933e7i	0.984705	−	0.367626i
$189$	−5.21044e6	−	4.24993e7i	−0.0561382	−	0.457894i
$190$	2.35616e8	−	4.25476e7i	2.49211	−	0.450026i
$191$	−1.26381e8			−1.31240			−0.656200	−	0.754587i	$-0.727837\pi$
$191$	−1.26381e8			−1.31240			−0.656200	+	0.754587i	$0.727837\pi$
$192$	8.79578e7	+	4.33815e7i	0.896850	+	0.442334i
$193$	−1.26027e8			−1.26187			−0.630934	−	0.775836i	$-0.717328\pi$
$193$	−1.26027e8			−1.26187			−0.630934	+	0.775836i	$0.717328\pi$
$194$	−6.77527e6	+	1.22348e6i	−0.0666224	+	0.0120307i
$195$	4.11641e7	−	1.67482e6i	0.397556	−	0.0161751i
$196$	−7.77386e7	+	2.90226e7i	−0.737463	+	0.275322i
$197$	1.96745e7	−	1.96745e7i	0.183346	−	0.183346i	−0.609466	−	0.792812i	$-0.708616\pi$
$197$	1.96745e7	−	1.96745e7i	0.183346	−	0.183346i	0.792812	+	0.609466i	$0.208616\pi$
$198$	−1.66706e8	−	9.66517e7i	−1.52624	−	0.884874i
$199$	−1.94555e8			−1.75008			−0.875038	−	0.484055i	$-0.839164\pi$
$199$	−1.94555e8			−1.75008			−0.875038	+	0.484055i	$0.839164\pi$
$200$	5.60108e7	+	9.43007e7i	0.495070	+	0.833508i
$201$	4.53806e7	−	4.92299e7i	0.394170	−	0.427605i
$202$	−6.91088e7	+	9.95687e7i	−0.589934	+	0.849949i
$203$	5.22966e7	+	5.22966e7i	0.438771	+	0.438771i
$204$	−8.76074e7	+	3.68309e7i	−0.722496	+	0.303743i
$205$	6.58309e6	−	6.58309e6i	0.0533693	−	0.0533693i
$206$	−2.93574e7	+	5.30137e6i	−0.233982	+	0.0422526i
$207$	1.90655e7	+	2.33910e8i	0.149400	+	1.83296i
$208$	2.60215e6	−	3.67044e7i	0.0200498	−	0.282811i
$209$			4.20167e8i			3.18354i
$210$	−7.33319e7	−	4.65987e7i	−0.546418	−	0.347222i
$211$	1.10451e8	+	1.10451e8i	0.809430	+	0.809430i	0.984548	−	0.175117i	$-0.0560305\pi$
$211$	1.10451e8	+	1.10451e8i	0.809430	+	0.809430i	−0.175117	+	0.984548i	$0.556030\pi$
$212$	1.87154e7	−	4.10149e7i	0.134904	−	0.295642i
$213$	2.78725e7	−	1.13403e6i	0.197627	−	0.00804074i
$214$	−3.72839e7	−	2.58781e7i	−0.260060	−	0.180503i
$215$		−	2.10808e8i		−	1.44661i
$216$	9.05704e7	+	1.17192e8i	0.611503	+	0.791242i
$217$			5.69116e6i			0.0378087i
$218$	−2.41131e7	+	3.47410e7i	−0.157636	+	0.227115i
$219$	−6.30795e7	+	2.56648e6i	−0.405820	+	0.0165114i
$220$	−3.66324e8	+	1.36762e8i	−2.31946	+	0.865936i
$221$	2.52127e7	+	2.52127e7i	0.157125	+	0.157125i
$222$	−5.50823e7	+	8.66823e7i	−0.337891	+	0.531735i
$223$			2.63107e7i			0.158879i	0.996840	+	0.0794393i	$0.0253130\pi$
$223$			2.63107e7i			0.158879i	−0.996840	+	0.0794393i	$0.974687\pi$
$224$	−4.86458e7	+	6.04621e7i	−0.289186	+	0.359431i
$225$	1.34563e7	+	1.65092e8i	0.0787563	+	0.966244i
$226$	−1.58425e7	−	8.77307e7i	−0.0912943	−	0.505559i
$227$	1.82460e8	−	1.82460e8i	1.03533	−	1.03533i	0.0359731	−	0.999353i	$-0.488547\pi$
$227$	1.82460e8	−	1.82460e8i	1.03533	−	1.03533i	0.999353	−	0.0359731i	$-0.0114531\pi$
$228$	1.22011e8	−	2.99014e8i	0.681756	−	1.67078i
$229$	−6.95614e6	−	6.95614e6i	−0.0382776	−	0.0382776i	0.687709	−	0.725987i	$-0.258617\pi$
$229$	−6.95614e6	−	6.95614e6i	−0.0382776	−	0.0382776i	−0.725987	+	0.687709i	$0.758617\pi$
$230$	3.91221e8	+	2.71539e8i	2.12019	+	1.47159i
$231$	1.03343e8	−	1.12109e8i	0.551619	−	0.598410i
$232$	−2.47915e8	−	6.31531e7i	−1.30345	−	0.332037i
$233$	−2.72572e8			−1.41168			−0.705839	−	0.708373i	$-0.749430\pi$
$233$	−2.72572e8			−1.41168			−0.705839	+	0.708373i	$0.749430\pi$
$234$	2.78723e7	−	4.80745e7i	0.142206	−	0.245278i
$235$	2.07508e8	−	2.07508e8i	1.04303	−	1.04303i
$236$	4.67462e7	+	2.13307e7i	0.231502	+	0.105636i
$237$	1.51890e8	−	6.17987e6i	0.741158	−	0.0301551i
$238$	−1.33630e7	−	7.40001e7i	−0.0642517	−	0.355806i
$239$	−1.69594e7			−0.0803561			−0.0401780	−	0.999193i	$-0.512793\pi$
$239$	−1.69594e7			−0.0803561			−0.0401780	+	0.999193i	$0.512793\pi$
$240$	3.00410e8	+	9.04883e6i	1.40273	+	0.0422526i
$241$	3.10241e8			1.42771			0.713854	−	0.700294i	$-0.246948\pi$
$241$	3.10241e8			1.42771			0.713854	+	0.700294i	$0.246948\pi$
$242$	−8.27627e7	−	4.58314e8i	−0.375388	−	2.07878i
$243$	4.51653e7	+	2.19070e8i	0.201922	+	0.979402i
$244$	2.15431e7	−	4.72118e7i	0.0949390	−	0.208059i
$245$	−1.79810e8	+	1.79810e8i	−0.781146	+	0.781146i
$246$	−2.73210e6	−	1.22568e7i	−0.0117010	−	0.0524933i
$247$	−1.21168e8			−0.511619
$248$	−1.00533e7	−	1.69259e7i	−0.0418532	−	0.0704648i
$249$	−1.36597e8	−	1.25917e8i	−0.560718	−	0.516875i
$250$	−8.70182e6	−	6.03977e6i	−0.0352225	−	0.0244473i
$251$	2.46790e8	+	2.46790e8i	0.985074	+	0.985074i	0.999890	−	0.0148160i	$-0.00471624\pi$
$251$	2.46790e8	+	2.46790e8i	0.985074	+	0.985074i	−0.0148160	+	0.999890i	$0.504716\pi$
$252$	−1.06100e8	+	4.97733e7i	−0.417650	+	0.195927i
$253$	−5.90942e8	+	5.90942e8i	−2.29416	+	2.29416i
$254$	−7.00489e7	−	3.87909e8i	−0.268215	−	1.48529i
$255$	−1.97390e8	+	2.14134e8i	−0.745478	+	0.808712i
$256$	3.78711e7	−	2.65751e8i	0.141081	−	0.989998i
$257$		−	3.64469e8i		−	1.33935i	−0.742654	−	0.669676i	$-0.766433\pi$
$257$		−	3.64469e8i		−	1.33935i	0.742654	−	0.669676i	$-0.233567\pi$
$258$	−2.39992e8	−	1.52503e8i	−0.870016	−	0.552852i
$259$	−5.74627e7	−	5.74627e7i	−0.205512	−	0.205512i
$260$	−3.94393e7	−	1.05640e8i	−0.139163	−	0.372755i
$261$	−2.94487e8	−	2.50099e8i	−1.02524	−	0.870704i
$262$	2.48105e8	−	3.57458e8i	0.852278	−	1.22792i
$263$			7.78799e7i			0.263986i	0.991251	+	0.131993i	$0.0421376\pi$
$263$			7.78799e7i			0.263986i	−0.991251	+	0.131993i	$0.957862\pi$
$264$	−1.09312e8	+	5.15974e8i	−0.365639	+	1.72589i
$265$		−	1.38156e8i		−	0.456048i
$266$	2.09926e8	+	1.45706e8i	0.683880	+	0.474668i
$267$	−6.78581e6	−	1.66783e8i	−0.0218179	−	0.536245i
$268$	−1.66723e8	−	7.60773e7i	−0.529084	−	0.241425i
$269$	1.20191e8	+	1.20191e8i	0.376476	+	0.376476i	0.869829	−	0.493353i	$-0.164229\pi$
$269$	1.20191e8	+	1.20191e8i	0.376476	+	0.376476i	−0.493353	+	0.869829i	$0.664229\pi$
$270$	4.01593e8	+	2.11505e8i	1.24169	+	0.653954i
$271$			2.28277e8i			0.696740i	0.937357	+	0.348370i	$0.113265\pi$
$271$			2.28277e8i			0.696740i	−0.937357	+	0.348370i	$0.886735\pi$
$272$	1.70462e8	+	1.96476e8i	0.513614	+	0.591997i
$273$	3.23299e7	+	2.98020e7i	0.0961691	+	0.0886495i
$274$	1.87327e8	−	3.38277e7i	0.550140	−	0.0993448i
$275$	−4.17083e8	+	4.17083e8i	−1.20937	+	1.20937i
$276$	5.92149e8	−	2.48944e8i	1.69531	−	0.712722i
$277$	1.69674e8	+	1.69674e8i	0.479663	+	0.479663i	0.905024	−	0.425361i	$-0.139853\pi$
$277$	1.69674e8	+	1.69674e8i	0.479663	+	0.479663i	−0.425361	+	0.905024i	$0.639853\pi$
$278$	−6.66555e7	+	9.60341e7i	−0.186071	+	0.268083i
$279$	−2.41525e6	−	2.96322e7i	−0.00665806	−	0.0816863i
$280$	−5.87043e7	+	2.30451e8i	−0.159815	+	0.627371i
$281$	3.98626e8			1.07175			0.535875	−	0.844297i	$-0.319982\pi$
$281$	3.98626e8			1.07175			0.535875	+	0.844297i	$0.319982\pi$
$282$	−8.61196e7	−	3.86351e8i	−0.228681	−	1.02591i
$283$	1.93442e8	−	1.93442e8i	0.507340	−	0.507340i	−0.406369	−	0.913709i	$-0.633205\pi$
$283$	1.93442e8	−	1.93442e8i	0.507340	−	0.507340i	0.913709	+	0.406369i	$0.133205\pi$
$284$	−2.67046e7	−	7.15296e7i	−0.0691785	−	0.185298i
$285$	−4.02329e7	−	9.88854e8i	−0.102950	−	2.53032i
$286$	1.94736e8	−	3.51656e7i	0.492226	−	0.0888866i
$287$	9.93632e6			0.0248107
$288$	2.27625e8	−	3.35453e8i	0.561495	−	0.827480i
$289$	1.58284e8			0.385740
$290$	−7.71516e8	+	1.39321e8i	−1.85760	+	0.335447i
$291$	1.15692e6	+	2.84351e7i	0.00275219	+	0.0676440i
$292$	6.04363e7	+	1.61882e8i	0.142056	+	0.380503i
$293$	5.98979e8	−	5.98979e8i	1.39115	−	1.39115i	0.568406	−	0.822749i	$-0.307560\pi$
$293$	5.98979e8	−	5.98979e8i	1.39115	−	1.39115i	0.822749	−	0.568406i	$-0.192440\pi$
$294$	7.46243e7	+	3.34781e8i	0.171263	+	0.768325i
$295$	1.57462e8			0.357108
$296$	2.72405e8	+	6.93917e7i	0.610513	+	0.155520i
$297$	−4.90499e8	+	6.27576e8i	−1.08640	+	1.39001i
$298$	−1.46254e8	+	2.10716e8i	−0.320148	+	0.461254i
$299$	−1.70415e8	−	1.70415e8i	−0.368689	−	0.368689i
$300$	4.17935e8	−	1.75703e8i	0.893684	−	0.375712i
$301$	1.59093e8	−	1.59093e8i	0.336255	−	0.336255i
$302$	−6.16156e8	+	1.11266e8i	−1.28726	+	0.232454i
$303$	3.68362e8	+	3.39560e8i	0.760722	+	0.701240i
$304$	−8.81721e8	−	6.25095e7i	−1.80000	−	0.127611i
$305$		−	1.59031e8i		−	0.320946i
$306$	1.00982e8	+	3.79625e8i	0.201474	+	0.757409i
$307$	−5.56809e8	−	5.56809e8i	−1.09830	−	1.09830i	−0.994609	−	0.103692i	$-0.966934\pi$
$307$	−5.56809e8	−	5.56809e8i	−1.09830	−	1.09830i	−0.103692	−	0.994609i	$-0.533066\pi$
$308$	−3.79672e8	−	1.73247e8i	−0.740424	−	0.337862i
$309$	5.01296e6	+	1.23210e8i	0.00966584	+	0.237569i
$310$	−4.95607e7	−	3.43992e7i	−0.0944870	−	0.0655816i
$311$			4.89520e8i			0.922803i	0.887191	+	0.461402i	$0.152653\pi$
$311$			4.89520e8i			0.922803i	−0.887191	+	0.461402i	$0.847347\pi$
$312$	−1.48796e8	−	3.15232e7i	−0.277365	−	0.0587610i
$313$			4.81058e8i			0.886732i	0.896341	+	0.443366i	$0.146216\pi$
$313$			4.81058e8i			0.886732i	−0.896341	+	0.443366i	$0.853784\pi$
$314$	−9.25121e7	+	1.33287e8i	−0.168634	+	0.242960i
$315$	−2.32481e8	+	2.73742e8i	−0.419083	+	0.493462i
$316$	−1.45526e8	−	3.89799e8i	−0.259439	−	0.694922i
$317$	2.58744e8	+	2.58744e8i	0.456208	+	0.456208i	0.897408	−	0.441201i	$-0.145447\pi$
$317$	2.58744e8	+	2.58744e8i	0.456208	+	0.456208i	−0.441201	+	0.897408i	$0.645447\pi$
$318$	−1.57283e8	−	9.99453e7i	−0.274275	−	0.174288i
$319$		−	1.37582e9i		−	2.37299i
$320$	−2.32496e8	−	7.89077e8i	−0.396634	−	1.34615i
$321$	−1.27150e8	+	1.37935e8i	−0.214559	+	0.232759i
$322$	9.03221e7	+	5.00176e8i	0.150764	+	0.834886i
$323$	6.05664e8	−	6.05664e8i	1.00005	−	1.00005i
$324$	5.31306e8	−	3.04182e8i	0.867836	−	0.496851i
$325$	−1.20278e8	−	1.20278e8i	−0.194354	−	0.194354i
$326$	7.97932e7	+	5.53830e7i	0.127557	+	0.0885350i
$327$	1.28527e8	+	1.18477e8i	0.203272	+	0.187378i
$328$	−2.95514e7	+	1.75523e7i	−0.0462401	+	0.0274648i
$329$	3.13207e8			0.484893
$330$	3.51649e8	+	1.57757e9i	0.538654	+	2.41652i
$331$	−5.85533e8	+	5.85533e8i	−0.887469	+	0.887469i	−0.994279	−	0.106811i	$-0.965936\pi$
$331$	−5.85533e8	+	5.85533e8i	−0.887469	+	0.887469i	0.106811	+	0.994279i	$0.465936\pi$
$332$	−2.11090e8	+	4.62605e8i	−0.316581	+	0.693788i
$333$	3.23578e8	+	2.74805e8i	0.480202	+	0.407821i
$334$	6.57137e7	+	3.63902e8i	0.0965036	+	0.534407i
$335$	−5.61599e8			−0.816149
$336$	2.19886e8	+	2.33544e8i	0.316235	+	0.335878i
$337$	3.16703e6			0.00450762			0.00225381	−	0.999997i	$-0.499283\pi$
$337$	3.16703e6			0.00450762			0.00225381	+	0.999997i	$0.499283\pi$
$338$	−1.16016e8	−	6.42461e8i	−0.163422	−	0.904979i
$339$	−3.68197e8	+	1.49806e7i	−0.513312	+	0.0208848i
$340$	7.25190e8	+	3.30910e8i	1.00064	+	0.456598i
$341$	7.48618e7	−	7.48618e7i	0.102240	−	0.102240i
$342$	−1.15486e9	−	6.69556e8i	−1.56112	−	0.905097i
$343$	−6.16173e8			−0.824468
$344$	−1.92120e8	+	7.54191e8i	−0.254459	+	0.998911i
$345$	1.33418e9	−	1.44735e9i	1.74924	−	1.89761i
$346$	7.28372e8	+	5.05550e8i	0.945338	+	0.656142i
$347$	7.62960e8	+	7.62960e8i	0.980277	+	0.980277i	0.999809	−	0.0195327i	$-0.00621784\pi$
$347$	7.62960e8	+	7.62960e8i	0.980277	+	0.980277i	−0.0195327	+	0.999809i	$0.506218\pi$
$348$	−3.99523e8	+	9.79112e8i	−0.508176	+	1.24539i
$349$	2.53972e8	−	2.53972e8i	0.319814	−	0.319814i	−0.528882	−	0.848695i	$-0.677389\pi$
$349$	2.53972e8	−	2.53972e8i	0.319814	−	0.319814i	0.848695	+	0.528882i	$0.177389\pi$
$350$	6.37487e7	+	3.53020e8i	0.0794755	+	0.440110i
$351$	−1.80980e8	−	1.41450e8i	−0.223386	−	0.174593i
$352$	1.43521e9	−	1.55432e8i	1.75395	−	0.189951i
$353$		−	7.40280e8i		−	0.895745i	−0.894097	−	0.447872i	$-0.852182\pi$
$353$		−	7.40280e8i		−	0.895745i	0.894097	−	0.447872i	$-0.147818\pi$
$354$	1.13912e8	−	1.79261e8i	0.136476	−	0.214771i
$355$	−1.65448e8	−	1.65448e8i	−0.196274	−	0.196274i
$356$	−4.28019e8	+	1.59795e8i	−0.502792	+	0.187710i
$357$	−3.10571e8	+	1.26360e7i	−0.361262	+	0.0146984i
$358$	−6.67914e8	+	9.62300e8i	−0.769361	+	1.10846i
$359$		−	2.95266e8i		−	0.336808i	−0.985718	−	0.168404i	$-0.946139\pi$
$359$		−	2.95266e8i		−	0.336808i	0.985718	−	0.168404i	$-0.0538614\pi$
$360$	2.07856e8	−	1.22480e9i	0.234803	−	1.38359i
$361$			2.01684e9i			2.25630i
$362$	7.45704e8	+	5.17579e8i	0.826203	+	0.573452i
$363$	−1.92350e9	+	7.82601e7i	−2.11066	+	0.0858751i
$364$	4.99609e7	−	1.09489e8i	0.0542970	−	0.118992i
$365$	3.74434e8	+	3.74434e8i	0.403042	+	0.403042i
$366$	−1.81047e8	−	1.15046e8i	−0.193022	−	0.122656i
$367$		−	1.39363e9i		−	1.47169i	−0.677152	−	0.735843i	$-0.736786\pi$
$367$		−	1.39363e9i		−	1.47169i	0.677152	−	0.735843i	$-0.263214\pi$
$368$	−1.15218e9	−	1.32801e9i	−1.20518	−	1.38910i
$369$	−5.17355e7	+	4.21684e6i	−0.0536039	+	0.00436913i
$370$	8.47730e8	−	1.53084e8i	0.870065	−	0.157117i
$371$	1.04265e8	−	1.04265e8i	0.106005	−	0.106005i
$372$	−7.50147e7	+	3.15368e7i	−0.0755520	+	0.0317627i
$373$	1.11848e9	+	1.11848e9i	1.11595	+	1.11595i	0.992329	+	0.123625i	$0.0394521\pi$
$373$	1.11848e9	+	1.11848e9i	1.11595	+	1.11595i	0.123625	+	0.992329i	$0.460548\pi$
$374$	−7.97623e8	+	1.14918e9i	−0.788401	+	1.13589i
$375$	−2.96758e7	+	3.21931e7i	−0.0290599	+	0.0315248i
$376$	−9.31500e8	+	5.53274e8i	−0.903703	+	0.536763i
$377$	3.96759e8			0.381358
$378$	1.43457e8	+	4.62696e8i	0.136615	+	0.440630i
$379$	4.08499e8	−	4.08499e8i	0.385438	−	0.385438i	−0.487619	−	0.873057i	$-0.662134\pi$
$379$	4.08499e8	−	4.08499e8i	0.385438	−	0.385438i	0.873057	+	0.487619i	$0.162134\pi$
$380$	−2.53771e9	+	9.47420e8i	−2.37247	+	0.885727i
$381$	−1.62801e9	+	6.62380e7i	−1.50807	+	0.0613578i
$382$	1.40708e9	−	2.54092e8i	1.29151	−	0.233222i
$383$	5.58122e8			0.507614			0.253807	−	0.967255i	$-0.418317\pi$
$383$	5.58122e8			0.507614			0.253807	+	0.967255i	$0.418317\pi$
$384$	−1.06651e9	−	3.06153e8i	−0.961181	−	0.275918i
$385$	−1.27890e9			−1.14216
$386$	1.40314e9	−	2.53380e8i	1.24178	−	0.224242i
$387$	−7.60835e8	+	8.95869e8i	−0.667271	+	0.785699i
$388$	7.29735e7	−	2.72436e7i	0.0634241	−	0.0236785i
$389$	−5.14187e8	+	5.14187e8i	−0.442892	+	0.442892i	−0.892983	−	0.450091i	$-0.851392\pi$
$389$	−5.14187e8	+	5.14187e8i	−0.442892	+	0.442892i	0.450091	+	0.892983i	$0.351392\pi$
$390$	−4.54939e8	+	1.01408e8i	−0.388354	+	0.0865659i
$391$	1.70367e9			1.44134
$392$	8.07163e8	−	4.79422e8i	0.676799	−	0.401991i
$393$	−1.32245e9	−	1.21904e9i	−1.09902	−	1.01308i
$394$	−1.79493e8	+	2.58605e8i	−0.147846	+	0.213010i
$395$	−9.01607e8	−	9.01607e8i	−0.736084	−	0.736084i
$396$	2.05036e9	+	7.40919e8i	1.65919	+	0.599567i
$397$	1.00430e9	−	1.00430e9i	0.805561	−	0.805561i	−0.178398	−	0.983958i	$-0.557091\pi$
$397$	1.00430e9	−	1.00430e9i	0.805561	−	0.805561i	0.983958	+	0.178398i	$0.0570914\pi$
$398$	2.16610e9	−	3.91157e8i	1.72222	−	0.311000i
$399$	7.15910e8	−	7.76637e8i	0.564227	−	0.612087i
$400$	−8.13197e8	−	9.37298e8i	−0.635310	−	0.732264i
$401$		−	6.70792e8i		−	0.519497i	−0.965676	−	0.259748i	$-0.916360\pi$
$401$		−	6.70792e8i		−	0.519497i	0.965676	−	0.259748i	$-0.0836396\pi$
$402$	−4.06273e8	+	6.39347e8i	−0.311908	+	0.490846i
$403$	2.15886e7	+	2.15886e7i	0.0164307	+	0.0164307i
$404$	5.69247e8	−	1.24751e9i	0.429503	−	0.941256i
$405$	1.09429e9	−	1.52395e9i	0.818537	−	1.13993i
$406$	−6.87395e8	−	4.77108e8i	−0.509760	−	0.353815i
$407$			1.51174e9i			1.11146i
$408$	9.01340e8	−	5.86198e8i	0.657019	−	0.427301i
$409$		−	7.37911e8i		−	0.533301i	−0.963793	−	0.266651i	$-0.914083\pi$
$409$		−	7.37911e8i		−	0.533301i	0.963793	−	0.266651i	$-0.0859170\pi$
$410$	−6.00583e7	+	8.65291e7i	−0.0430358	+	0.0620039i
$411$	−3.19873e7	−	7.86192e8i	−0.0227265	−	0.558576i
$412$	3.16196e8	−	1.18047e8i	0.222749	−	0.0831601i
$413$	1.18834e8	+	1.18834e8i	0.0830075	+	0.0830075i
$414$	−6.82548e8	−	2.56593e9i	−0.472751	−	1.77723i
$415$			1.55826e9i			1.07022i
$416$	4.48235e7	+	4.13885e8i	0.0305266	+	0.281873i
$417$	3.55286e8	+	3.27505e8i	0.239939	+	0.221178i
$418$	−8.44755e8	−	4.67799e9i	−0.565736	−	3.13287i
$419$	2.81581e8	−	2.81581e8i	0.187005	−	0.187005i	−0.607395	−	0.794400i	$-0.707785\pi$
$419$	2.81581e8	−	2.81581e8i	0.187005	−	0.187005i	0.794400	+	0.607395i	$0.207785\pi$
$420$	9.10138e8	+	3.71378e8i	0.599425	+	0.244593i
$421$	1.61340e9	+	1.61340e9i	1.05379	+	1.05379i	0.998468	+	0.0553258i	$0.0176197\pi$
$421$	1.61340e9	+	1.61340e9i	1.05379	+	1.05379i	0.0553258	+	0.998468i	$0.482380\pi$
$422$	−1.45178e9	−	1.00765e9i	−0.940388	−	0.652706i
$423$	−1.63077e9	+	1.32921e8i	−1.04762	+	0.0853889i
$424$	−1.25909e8	+	4.94272e8i	−0.0802190	+	0.314909i
$425$	1.20244e9			0.759802
$426$	−3.08042e8	+	6.86640e7i	−0.193053	+	0.0430324i
$427$	1.20018e8	−	1.20018e8i	0.0746018	−	0.0746018i
$428$	4.67134e8	+	2.13157e8i	0.287997	+	0.131416i
$429$	−3.32524e7	−	8.17286e8i	−0.0203340	−	0.499774i
$430$	4.23833e8	+	2.34705e9i	0.257072	+	1.42359i
$431$	1.28716e9			0.774391			0.387196	−	0.921998i	$-0.373444\pi$
$431$	1.28716e9			0.774391			0.387196	+	0.921998i	$0.373444\pi$
$432$	−1.24399e9	−	1.12268e9i	−0.742379	−	0.669981i
$433$	2.08018e8			0.123138			0.0615691	−	0.998103i	$-0.480390\pi$
$433$	2.08018e8			0.123138			0.0615691	+	0.998103i	$0.480390\pi$
$434$	−1.14422e7	−	6.33633e7i	−0.00671886	−	0.0372069i
$435$	1.31741e8	+	3.23797e9i	0.0767379	+	1.88608i
$436$	1.98619e8	−	4.35274e8i	0.114767	−	0.251513i
$437$	−4.09376e9	+	4.09376e9i	−2.34659	+	2.34659i
$438$	6.97144e8	−	1.55397e8i	0.396427	−	0.0883655i
$439$	1.07671e9			0.607396			0.303698	−	0.952768i	$-0.401779\pi$
$439$	1.07671e9			0.607396			0.303698	+	0.952768i	$0.401779\pi$
$440$	3.80356e9	−	2.25916e9i	2.12866	−	1.26434i
$441$	1.41310e9	−	1.15178e8i	0.784579	−	0.0639493i
$442$	−3.31399e8	−	2.30018e8i	−0.182547	−	0.126702i
$443$	−1.00399e9	−	1.00399e9i	−0.548675	−	0.548675i	0.377383	−	0.926057i	$-0.376824\pi$
$443$	−1.00399e9	−	1.00399e9i	−0.548675	−	0.548675i	−0.926057	+	0.377383i	$0.876824\pi$
$444$	4.38990e8	−	1.07583e9i	0.238020	−	0.583317i
$445$	−9.90010e8	+	9.90010e8i	−0.532574	+	0.532574i
$446$	−5.28982e7	−	2.92934e8i	−0.0282338	−	0.156350i
$447$	7.79560e8	+	7.18605e8i	0.412832	+	0.380552i
$448$	4.20044e8	−	7.70966e8i	0.220710	−	0.405100i
$449$		−	3.39704e9i		−	1.77108i	−0.464564	−	0.885540i	$-0.653789\pi$
$449$		−	3.39704e9i		−	1.77108i	0.464564	−	0.885540i	$-0.346211\pi$
$450$	−4.81738e8	−	1.81102e9i	−0.249211	−	0.936869i
$451$	−1.30703e8	−	1.30703e8i	−0.0670914	−	0.0670914i
$452$	3.52769e8	+	9.44910e8i	0.179682	+	0.481289i
$453$	1.05213e8	+	2.58594e9i	0.0531770	+	1.30700i
$454$	−1.66460e9	+	2.39828e9i	−0.834863	+	1.20283i
$455$		−	3.68809e8i		−	0.183553i
$456$	−7.57257e8	+	3.57442e9i	−0.373996	+	1.76534i
$457$		−	1.62455e9i		−	0.796209i	−0.917340	−	0.398105i	$-0.869668\pi$
$457$		−	1.62455e9i		−	0.796209i	0.917340	−	0.398105i	$-0.130332\pi$
$458$	9.14326e7	+	6.34617e7i	0.0444705	+	0.0308662i
$459$	1.61169e9	−	1.97594e8i	0.777923	−	0.0953738i
$460$	−4.90165e9	−	2.23666e9i	−2.34796	−	1.07139i
$461$	2.13207e9	+	2.13207e9i	1.01356	+	1.01356i	0.999907	+	0.0136489i	$0.00434470\pi$
$461$	2.13207e9	+	2.13207e9i	1.01356	+	1.01356i	0.0136489	+	0.999907i	$0.495655\pi$
$462$	−9.25187e8	+	1.45595e9i	−0.436498	+	0.686912i
$463$			1.53100e8i			0.0716872i	0.999357	+	0.0358436i	$0.0114118\pi$
$463$			1.53100e8i			0.0716872i	−0.999357	+	0.0358436i	$0.988588\pi$
$464$	2.88717e9	+	2.04685e8i	1.34171	+	0.0951204i
$465$	−1.69017e8	+	1.83354e8i	−0.0779553	+	0.0845678i
$466$	3.03472e9	−	5.48011e8i	1.38921	−	0.250864i
$467$	3.14335e8	−	3.14335e8i	0.142818	−	0.142818i	−0.632083	−	0.774901i	$-0.717800\pi$
$467$	3.14335e8	−	3.14335e8i	0.142818	−	0.142818i	0.774901	+	0.632083i	$0.217800\pi$
$468$	−2.13666e8	+	5.91282e8i	−0.0963551	+	0.266645i
$469$	−4.23831e8	−	4.23831e8i	−0.189709	−	0.189709i
$470$	−1.89312e9	+	2.72752e9i	−0.841077	+	1.21178i
$471$	4.93106e8	+	4.54549e8i	0.217454	+	0.200451i
$472$	−5.63341e8	−	1.43504e8i	−0.246590	−	0.0628154i
$473$	−4.18544e9			−1.81856
$474$	−1.67867e9	+	3.74183e8i	−0.724003	+	0.161384i
$475$	−2.88935e9	+	2.88935e9i	−1.23701	+	1.23701i
$476$	2.97557e8	+	7.97024e8i	0.126458	+	0.338725i
$477$	−4.98626e8	+	5.87123e8i	−0.210359	+	0.247694i
$478$	1.88820e8	−	3.40973e7i	0.0790771	−	0.0142798i
$479$	−3.77227e9			−1.56830			−0.784150	−	0.620572i	$-0.786901\pi$
$479$	−3.77227e9			−1.56830			−0.784150	+	0.620572i	$0.786901\pi$
$480$	−3.36285e9	+	5.03234e8i	−1.38792	+	0.207695i
$481$	−4.35953e8			−0.178621
$482$	−3.45411e9	+	6.23746e8i	−1.40498	+	0.253713i
$483$	2.09919e9	−	8.54083e7i	0.847688	−	0.0344894i
$484$	1.84290e9	+	4.93630e9i	0.738827	+	1.97899i
$485$	1.68788e8	−	1.68788e8i	0.0671809	−	0.0671809i
$486$	−9.43299e8	−	2.34824e9i	−0.372754	−	0.927930i
$487$	−8.51354e8			−0.334010			−0.167005	−	0.985956i	$-0.553410\pi$
$487$	−8.51354e8			−0.334010			−0.167005	+	0.985956i	$0.553410\pi$
$488$	−1.44933e8	+	5.68952e8i	−0.0564545	+	0.221619i
$489$	2.72119e8	−	2.95201e8i	0.105239	−	0.114166i
$490$	1.64043e9	−	2.36345e9i	0.629898	−	0.907527i
$491$	−5.19791e8	−	5.19791e8i	−0.198172	−	0.198172i	0.601044	−	0.799216i	$-0.294752\pi$
$491$	−5.19791e8	−	5.19791e8i	−0.198172	−	0.198172i	−0.799216	+	0.601044i	$0.794752\pi$
$492$	5.50607e7	+	1.30970e8i	0.0208432	+	0.0495785i
$493$	−1.98323e9	+	1.98323e9i	−0.745433	+	0.745433i
$494$	1.34904e9	−	2.43610e8i	0.503476	−	0.0909181i
$495$	6.65887e9	−	5.42750e8i	2.46764	−	0.201132i
$496$	1.45960e8	+	1.68235e8i	0.0537091	+	0.0619056i
$497$		−	2.49723e8i		−	0.0912454i
$498$	1.77398e9	+	1.12728e9i	0.643646	+	0.409005i
$499$	4.92094e7	+	4.92094e7i	0.0177295	+	0.0177295i	0.715916	−	0.698186i	$-0.246009\pi$
$499$	4.92094e7	+	4.92094e7i	0.0177295	+	0.0177295i	−0.698186	+	0.715916i	$0.746009\pi$
$500$	1.09026e8	+	4.97494e7i	0.0390063	+	0.0177989i
$501$	1.52726e9	−	6.21387e7i	0.542601	−	0.0220765i
$502$	−3.24384e9	−	2.25149e9i	−1.14445	−	0.794341i
$503$			3.52165e9i			1.23384i	0.787027	+	0.616918i	$0.211619\pi$
$503$			3.52165e9i			1.23384i	−0.787027	+	0.616918i	$0.788381\pi$
$504$	1.08120e9	−	7.67474e8i	0.376185	−	0.267028i
$505$		−	4.20216e9i		−	1.45195i
$506$	5.39123e9	−	7.76743e9i	1.84996	−	2.66533i
$507$	−2.69634e9	+	1.09704e8i	−0.918856	+	0.0373849i
$508$	1.55980e9	+	4.17800e9i	0.527892	+	1.41399i
$509$	−1.02925e9	−	1.02925e9i	−0.345945	−	0.345945i	0.512652	−	0.858597i	$-0.328663\pi$
$509$	−1.02925e9	−	1.02925e9i	−0.345945	−	0.345945i	−0.858597	+	0.512652i	$0.828663\pi$
$510$	1.76715e9	−	2.78094e9i	0.589899	−	0.928317i
$511$			5.65159e8i			0.187369i
$512$	1.12654e8	+	3.03491e9i	0.0370940	+	0.999312i
$513$	−3.39794e9	+	4.34754e9i	−1.11123	+	1.42178i
$514$	7.32772e8	+	4.05786e9i	0.238012	+	1.31803i
$515$	7.31362e8	−	7.31362e8i	0.235943	−	0.235943i
$516$	2.97859e9	+	1.21540e9i	0.954414	+	0.389445i
$517$	−4.11994e9	−	4.11994e9i	−1.31121	−	1.31121i
$518$	7.55299e8	+	5.24239e8i	0.238762	+	0.165720i
$519$	2.48397e9	−	2.69467e9i	0.779940	−	0.846097i
$520$	6.51495e8	+	1.09687e9i	0.203189	+	0.342091i
$521$	1.09501e9			0.339222			0.169611	−	0.985511i	$-0.445749\pi$
$521$	1.09501e9			0.339222			0.169611	+	0.985511i	$0.445749\pi$
$522$	3.78154e9	+	2.19244e9i	1.16365	+	0.674654i
$523$	2.64709e9	−	2.64709e9i	0.809121	−	0.809121i	−0.175380	−	0.984501i	$-0.556115\pi$
$523$	2.64709e9	−	2.64709e9i	0.809121	−	0.809121i	0.984501	+	0.175380i	$0.0561153\pi$
$524$	−2.04364e9	+	4.47863e9i	−0.620503	+	1.35983i
$525$	1.48159e9	−	6.02806e7i	0.446859	−	0.0181811i
$526$	−1.56579e8	−	8.67086e8i	−0.0469120	−	0.259784i
$527$	−2.15824e8			−0.0642337
$528$	1.79659e8	−	5.96444e9i	0.0531165	−	1.76340i
$529$	−8.11046e9			−2.38205
$530$	2.77766e8	+	1.53818e9i	0.0810427	+	0.448789i
$531$	−6.69167e8	−	5.68304e8i	−0.193956	−	0.164721i
$532$	−2.63018e9	−	1.20017e9i	−0.757347	−	0.345583i
$533$	3.76920e7	−	3.76920e7i	0.0107821	−	0.0107821i
$534$	4.10872e8	+	1.84326e9i	0.116765	+	0.523833i
$535$	1.57352e9			0.444256
$536$	2.00919e9	+	5.11815e8i	0.563566	+	0.143561i
$537$	3.56010e9	+	3.28173e9i	0.992094	+	0.914521i
$538$	−1.57980e9	−	1.09651e9i	−0.437386	−	0.303582i
$539$	3.57000e9	+	3.57000e9i	0.981992	+	0.981992i
$540$	−4.89642e9	−	1.54741e9i	−1.33814	−	0.422889i
$541$	4.02353e9	−	4.02353e9i	1.09249	−	1.09249i	0.0972258	−	0.995262i	$-0.469003\pi$
$541$	4.02353e9	−	4.02353e9i	1.09249	−	1.09249i	0.995262	−	0.0972258i	$-0.0309969\pi$
$542$	−4.58957e8	−	2.54156e9i	−0.123815	−	0.685650i
$543$	2.54308e9	−	2.75879e9i	0.681648	−	0.739468i
$544$	−2.29288e9	−	1.84478e9i	−0.610641	−	0.491301i
$545$		−	1.46620e9i		−	0.387976i
$546$	−4.19867e8	−	2.66805e8i	−0.110392	−	0.0701486i
$547$	3.04406e9	+	3.04406e9i	0.795238	+	0.795238i	0.982340	−	0.187103i	$-0.0599097\pi$
$547$	3.04406e9	+	3.04406e9i	0.795238	+	0.795238i	−0.187103	+	0.982340i	$0.559910\pi$
$548$	−2.01762e9	+	7.53250e8i	−0.523730	+	0.195527i
$549$	−5.73964e8	+	6.75832e8i	−0.148041	+	0.174315i
$550$	3.80509e9	−	5.48220e9i	0.975205	−	1.40503i
$551$		−	9.53104e9i		−	2.42722i
$552$	−6.09226e9	+	3.96218e9i	−1.54167	+	1.00265i
$553$		−	1.36086e9i		−	0.342196i
$554$	−2.23022e9	−	1.54795e9i	−0.557267	−	0.386789i
$555$	−1.44755e8	−	3.55783e9i	−0.0359426	−	0.883406i
$556$	5.49039e8	−	1.20322e9i	0.135469	−	0.296882i
$557$	−2.86440e9	−	2.86440e9i	−0.702329	−	0.702329i	0.262581	−	0.964910i	$-0.415426\pi$
$557$	−2.86440e9	−	2.86440e9i	−0.702329	−	0.702329i	−0.964910	+	0.262581i	$0.915426\pi$
$558$	8.64667e7	+	3.25058e8i	0.0210683	+	0.0792029i
$559$		−	1.20700e9i		−	0.292256i
$560$	1.90266e8	−	2.68378e9i	0.0457829	−	0.645786i
$561$	4.25148e9	+	3.91905e9i	1.01665	+	0.937153i
$562$	−4.43816e9	+	8.01446e8i	−1.05469	+	0.190457i
$563$	4.29266e9	−	4.29266e9i	1.01379	−	1.01379i	0.0138848	−	0.999904i	$-0.495580\pi$
$563$	4.29266e9	−	4.29266e9i	1.01379	−	1.01379i	0.999904	−	0.0138848i	$-0.00441981\pi$
$564$	1.73559e9	+	4.12835e9i	0.407353	+	0.968946i
$565$	2.18558e9	+	2.18558e9i	0.509797	+	0.509797i
$566$	−1.76480e9	+	2.54263e9i	−0.409107	+	0.589422i
$567$	1.97595e9	−	3.24264e8i	0.455234	−	0.0747064i
$568$	4.41131e8	+	7.42694e8i	0.101006	+	0.170056i
$569$	−2.15353e9			−0.490071			−0.245035	−	0.969514i	$-0.578800\pi$
$569$	−2.15353e9			−0.490071			−0.245035	+	0.969514i	$0.578800\pi$
$570$	2.43605e9	+	1.09287e10i	0.550965	+	2.47175i
$571$	−3.46028e9	+	3.46028e9i	−0.777831	+	0.777831i	−0.979462	−	0.201631i	$-0.935376\pi$
$571$	−3.46028e9	+	3.46028e9i	−0.777831	+	0.777831i	0.201631	+	0.979462i	$0.435376\pi$
$572$	−2.09742e9	+	7.83041e8i	−0.468596	+	0.174944i
$573$	−2.40269e8	−	5.90538e9i	−0.0533527	−	1.31131i
$574$	−1.10627e8	+	1.99772e7i	−0.0244158	+	0.00440902i
$575$	−8.12741e9			−1.78285
$576$	−1.85986e9	+	4.19245e9i	−0.405509	+	0.914091i
$577$	7.48337e9			1.62174			0.810872	−	0.585224i	$-0.198993\pi$
$577$	7.48337e9			1.62174			0.810872	+	0.585224i	$0.198993\pi$
$578$	−1.76228e9	+	3.18234e8i	−0.379601	+	0.0685486i
$579$	−2.39596e8	−	5.88884e9i	−0.0512984	−	1.26082i
$580$	8.30967e9	−	3.10230e9i	1.76842	−	0.660215i
$581$	−1.17600e9	+	1.17600e9i	−0.248765	+	0.248765i
$582$	−7.00501e7	−	3.14260e8i	−0.0147292	−	0.0660782i
$583$	−2.74300e9			−0.573306
$584$	−9.98343e8	−	1.68083e9i	−0.207412	−	0.349203i
$585$	1.56518e8	+	1.92028e9i	0.0323235	+	0.396569i
$586$	−5.46456e9	+	7.87308e9i	−1.12179	+	1.61623i
$587$	−4.10378e9	−	4.10378e9i	−0.837434	−	0.837434i	0.151086	−	0.988521i	$-0.451723\pi$
$587$	−4.10378e9	−	4.10378e9i	−0.837434	−	0.837434i	−0.988521	+	0.151086i	$0.951723\pi$
$588$	−1.50392e9	−	3.57729e9i	−0.305074	−	0.725661i
$589$	5.18606e8	−	5.18606e8i	0.104576	−	0.104576i
$590$	−1.75313e9	+	3.16581e8i	−0.351424	+	0.0634604i
$591$	9.56730e8	+	8.81922e8i	0.190648	+	0.175741i
$592$	−3.17238e9	−	2.24905e8i	−0.628432	−	0.0445526i
$593$		−	1.67412e9i		−	0.329683i	−0.986320	−	0.164841i	$-0.947289\pi$
$593$		−	1.67412e9i		−	0.329683i	0.986320	−	0.164841i	$-0.0527112\pi$
$594$	4.19928e9	−	7.97336e9i	0.822096	−	1.56095i
$595$	1.84352e9	+	1.84352e9i	0.358788	+	0.358788i
$596$	1.20469e9	−	2.64008e9i	0.233084	−	0.510805i
$597$	−3.69877e8	−	9.09092e9i	−0.0711454	−	1.74863i
$598$	2.23997e9	+	1.55472e9i	0.428339	+	0.297302i
$599$			7.94576e9i			1.51057i	0.655395	+	0.755286i	$0.272502\pi$
$599$			7.94576e9i			1.51057i	−0.655395	+	0.755286i	$0.727498\pi$
$600$	−4.29988e9	+	2.79648e9i	−0.812693	+	0.528545i
$601$			5.61464e9i			1.05502i	0.849548	+	0.527511i	$0.176875\pi$
$601$			5.61464e9i			1.05502i	−0.849548	+	0.527511i	$0.823125\pi$
$602$	−1.45143e9	+	2.09115e9i	−0.271149	+	0.390658i
$603$	2.38663e9	+	2.02689e9i	0.443276	+	0.376461i
$604$	6.63635e9	−	2.47759e9i	1.22546	−	0.457509i
$605$	1.14177e10	+	1.14177e10i	2.09621	+	2.09621i
$606$	−4.78390e9	−	3.03993e9i	−0.873229	−	0.554894i
$607$		−	2.72163e9i		−	0.493933i	−0.969024	−	0.246966i	$-0.920566\pi$
$607$		−	2.72163e9i		−	0.493933i	0.969024	−	0.246966i	$-0.0794337\pi$
$608$	9.94243e9	−	1.07676e9i	1.79403	−	0.194293i
$609$	−2.34423e9	+	2.54307e9i	−0.420571	+	0.456245i
$610$	3.19734e8	+	1.77059e9i	0.0570341	+	0.315837i
$611$	1.18810e9	−	1.18810e9i	0.210722	−	0.210722i
$612$	−1.88754e9	−	4.02359e9i	−0.332863	−	0.709550i
$613$	−4.42976e9	−	4.42976e9i	−0.776727	−	0.776727i	0.202546	−	0.979273i	$-0.435079\pi$
$613$	−4.42976e9	−	4.42976e9i	−0.776727	−	0.776727i	−0.979273	+	0.202546i	$0.935079\pi$
$614$	7.31878e9	+	5.07983e9i	1.27600	+	0.885645i
$615$	3.20122e8	+	2.95091e8i	0.0554948	+	0.0511555i
$616$	4.57544e9	+	1.16553e9i	0.788679	+	0.200906i
$617$	1.13122e9			0.193888			0.0969438	−	0.995290i	$-0.469093\pi$
$617$	1.13122e9			0.193888			0.0969438	+	0.995290i	$0.469093\pi$
$618$	−3.03528e8	−	1.36169e9i	−0.0517296	−	0.232070i
$619$	−3.02880e9	+	3.02880e9i	−0.513279	+	0.513279i	−0.915530	−	0.402250i	$-0.868228\pi$
$619$	−3.02880e9	+	3.02880e9i	−0.513279	+	0.513279i	0.402250	+	0.915530i	$0.368228\pi$
$620$	6.20951e8	+	2.83345e8i	0.104637	+	0.0477469i
$621$	−1.08936e10	+	1.33556e9i	−1.82537	+	0.223791i
$622$	−9.84190e8	−	5.45014e9i	−0.163988	−	0.908115i
$623$	−1.49429e9			−0.247587
$624$	1.72002e9	+	5.18098e7i	0.283392	+	0.00853623i
$625$	6.28429e9			1.02962
$626$	−9.67178e8	−	5.35593e9i	−0.157578	−	0.872619i
$627$	−1.96330e10	+	7.98797e8i	−3.18091	+	0.129420i
$628$	7.62019e8	−	1.66997e9i	0.122774	−	0.269060i
$629$	2.17914e9	−	2.17914e9i	0.349147	−	0.349147i
$630$	2.03799e9	−	3.51515e9i	0.324721	−	0.560082i
$631$	−4.09691e9			−0.649162			−0.324581	−	0.945858i	$-0.605223\pi$
$631$	−4.09691e9			−0.649162			−0.324581	+	0.945858i	$0.605223\pi$
$632$	2.40393e9	+	4.04730e9i	0.378802	+	0.637757i
$633$	−4.95101e9	+	5.37097e9i	−0.775856	+	0.841667i
$634$	−3.40097e9	−	2.36055e9i	−0.530017	−	0.367875i
$635$	9.66373e9	+	9.66373e9i	1.49774	+	1.49774i
$636$	1.95207e9	+	7.96535e8i	0.300882	+	0.122774i
$637$	−1.02951e9	+	1.02951e9i	−0.157814	+	0.157814i
$638$	2.76612e9	+	1.53179e10i	0.421696	+	2.33522i
$639$	1.05979e8	+	1.30023e9i	0.0160682	+	0.197137i
$640$	4.17498e9	+	8.31786e9i	0.629541	+	1.25424i
$641$		−	6.14724e9i		−	0.921886i	−0.887430	−	0.460943i	$-0.847511\pi$
$641$		−	6.14724e9i		−	0.921886i	0.887430	−	0.460943i	$-0.152489\pi$
$642$	1.13832e9	−	1.79135e9i	0.169782	−	0.267183i
$643$	−6.93362e8	−	6.93362e8i	−0.102854	−	0.102854i	0.653807	−	0.756661i	$-0.273171\pi$
$643$	−6.93362e8	−	6.93362e8i	−0.102854	−	0.102854i	−0.756661	+	0.653807i	$0.773171\pi$
$644$	−2.01123e9	−	5.38718e9i	−0.296729	−	0.794805i
$645$	9.85035e9	−	4.00775e8i	1.44541	−	0.0588087i
$646$	−5.52554e9	+	7.96094e9i	−0.806420	+	1.16185i
$647$			1.65557e9i			0.240317i	0.992755	+	0.120158i	$0.0383402\pi$
$647$			1.65557e9i			0.240317i	−0.992755	+	0.120158i	$0.961660\pi$
$648$	−5.30381e9	+	4.45486e9i	−0.765729	+	0.643163i
$649$		−	3.12631e9i		−	0.448926i
$650$	1.58095e9	+	1.09731e9i	0.225799	+	0.156723i
$651$	−2.65929e8	+	1.08197e7i	−0.0377775	+	0.00153703i
$652$	−9.99737e8	−	4.56188e8i	−0.141260	−	0.0644581i
$653$	−1.99854e9	−	1.99854e9i	−0.280877	−	0.280877i	0.552582	−	0.833459i	$-0.313643\pi$
$653$	−1.99854e9	−	1.99854e9i	−0.280877	−	0.280877i	−0.833459	+	0.552582i	$0.813643\pi$
$654$	−1.66918e9	−	1.06068e9i	−0.233335	−	0.148273i
$655$			1.50860e10i			2.09764i
$656$	2.93725e8	−	2.54835e8i	0.0406235	−	0.0352448i
$657$	−2.39846e8	−	2.94262e9i	−0.0329954	−	0.404813i
$658$	−3.48713e9	+	6.29709e8i	−0.477175	+	0.0861686i
$659$	−4.41480e9	+	4.41480e9i	−0.600914	+	0.600914i	−0.940555	−	0.339641i	$-0.889694\pi$
$659$	−4.41480e9	+	4.41480e9i	−0.600914	+	0.600914i	0.339641	+	0.940555i	$0.389694\pi$
$660$	−7.08687e9	−	1.68571e10i	−0.959512	−	2.28234i
$661$	−4.43062e9	−	4.43062e9i	−0.596705	−	0.596705i	0.342729	−	0.939434i	$-0.388649\pi$
$661$	−4.43062e9	−	4.43062e9i	−0.596705	−	0.596705i	−0.939434	+	0.342729i	$0.888649\pi$
$662$	5.34188e9	−	7.69633e9i	0.715634	−	1.03105i
$663$	−1.13017e9	+	1.22604e9i	−0.150608	+	0.163383i
$664$	1.42013e9	−	5.57487e9i	0.188251	−	0.739004i
$665$	−8.85962e9			−1.16826
$666$	−4.15510e9	−	2.40902e9i	−0.545031	−	0.315995i
$667$	1.34049e10	−	1.34049e10i	1.74913	−	1.74913i
$668$	−1.46327e9	−	3.91943e9i	−0.189935	−	0.508752i
$669$	−1.22941e9	+	5.00204e7i	−0.158747	+	0.00645885i
$670$	6.25264e9	−	1.12911e9i	0.803159	−	0.145035i
$671$	−3.15745e9			−0.403466
$672$	−2.91768e9	−	2.15811e9i	−0.370890	−	0.274335i
$673$	9.92386e9			1.25495			0.627477	−	0.778635i	$-0.284087\pi$
$673$	9.92386e9			1.25495			0.627477	+	0.778635i	$0.284087\pi$
$674$	−3.52606e7	+	6.36738e6i	−0.00443588	+	0.000801034i
$675$	−7.68862e9	+	9.42630e8i	−0.962244	+	0.117972i
$676$	2.58336e9	+	6.91968e9i	0.321641	+	0.861534i
$677$	−1.40454e9	+	1.40454e9i	−0.173969	+	0.173969i	−0.788721	−	0.614751i	$-0.789256\pi$
$677$	−1.40454e9	+	1.40454e9i	−0.173969	+	0.173969i	0.614751	+	0.788721i	$0.289256\pi$
$678$	4.06925e9	−	9.07056e8i	0.501430	−	0.111771i
$679$	2.54764e8			0.0312315
$680$	−8.73931e9	−	2.22622e9i	−1.06585	−	0.271511i
$681$	8.87264e9	+	8.17887e9i	1.07656	+	0.992381i
$682$	−6.82973e8	+	9.83995e8i	−0.0824438	+	0.118781i
$683$	4.87810e9	+	4.87810e9i	0.585839	+	0.585839i	0.936502	−	0.350663i	$-0.114044\pi$
$683$	4.87810e9	+	4.87810e9i	0.585839	+	0.585839i	−0.350663	+	0.936502i	$0.614044\pi$
$684$	1.42039e10	+	5.13273e9i	1.69711	+	0.613270i
$685$	−4.66676e9	+	4.66676e9i	−0.554752	+	0.554752i
$686$	6.86025e9	−	1.23883e9i	0.811345	−	0.146513i
$687$	3.11813e8	−	3.38262e8i	0.0366898	−	0.0398020i
$688$	6.22680e8	−	8.78315e9i	0.0728963	−	1.02823i
$689$		−	7.91025e8i		−	0.0921347i
$690$	−1.19444e10	+	1.87967e10i	−1.38418	+	2.17826i
$691$	2.92288e9	+	2.92288e9i	0.337006	+	0.337006i	0.855239	−	0.518233i	$-0.173410\pi$
$691$	2.92288e9	+	2.92288e9i	0.337006	+	0.337006i	−0.518233	+	0.855239i	$0.673410\pi$
$692$	−9.12585e9	−	4.16420e9i	−1.04689	−	0.477705i
$693$	5.43496e9	+	4.61575e9i	0.620340	+	0.526836i
$694$	−1.00285e10	−	6.96057e9i	−1.13888	−	0.790472i
$695$		−	4.05298e9i		−	0.457961i
$696$	2.47962e9	−	1.17043e10i	0.278774	−	1.31587i
$697$			3.76812e8i			0.0421512i
$698$	−2.31702e9	+	3.33825e9i	−0.257890	+	0.371556i
$699$	−5.18198e8	−	1.27364e10i	−0.0573886	−	1.41051i
$700$	−1.41951e9	−	3.80223e9i	−0.156421	−	0.418982i
$701$	−8.67396e8	−	8.67396e8i	−0.0951052	−	0.0951052i	0.657953	−	0.753059i	$-0.271422\pi$
$701$	−8.67396e8	−	8.67396e8i	−0.0951052	−	0.0951052i	−0.753059	+	0.657953i	$0.771422\pi$
$702$	2.29935e9	+	1.21099e9i	0.250857	+	0.132117i
$703$			1.04726e10i			1.13687i
$704$	−1.56666e10	+	4.61605e9i	−1.69227	+	0.498615i
$705$	1.00907e10	+	9.30167e9i	1.08457	+	0.999768i
$706$	1.48835e9	+	8.24200e9i	0.159180	+	0.881488i
$707$	3.17131e9	−	3.17131e9i	0.337497	−	0.337497i
$708$	−9.07842e8	+	2.22485e9i	−0.0961377	+	0.235605i
$709$	7.32198e9	+	7.32198e9i	0.771555	+	0.771555i	0.978378	−	0.206824i	$-0.0663126\pi$
$709$	7.32198e9	+	7.32198e9i	0.771555	+	0.771555i	−0.206824	+	0.978378i	$0.566313\pi$
$710$	2.17468e9	+	1.50940e9i	0.228029	+	0.158271i
$711$	5.77530e8	+	7.08559e9i	0.0602603	+	0.739320i
$712$	4.44414e9	−	2.63964e9i	0.461432	−	0.274072i
$713$	1.45878e9			0.150722
$714$	3.43238e9	−	7.65094e8i	0.352900	−	0.0786631i
$715$	−4.85134e9	+	4.85134e9i	−0.496352	+	0.496352i
$716$	5.50159e9	−	1.20567e10i	0.560135	−	1.22754i
$717$	−3.22423e7	−	7.92458e8i	−0.00326670	−	0.0802896i
$718$	5.93638e8	+	3.28738e9i	0.0598530	+	0.331448i
$719$	−1.88825e10			−1.89456			−0.947280	−	0.320407i	$-0.896180\pi$
$719$	−1.88825e10			−1.89456			−0.947280	+	0.320407i	$0.896180\pi$
$720$	1.48300e8	+	1.40544e10i	0.0148074	+	1.40329i
$721$	1.10390e9			0.109687
$722$	−4.05490e9	−	2.24548e10i	−0.400959	−	2.22039i
$723$	5.89812e8	+	1.44965e10i	0.0580403	+	1.42653i
$724$	−9.34300e9	−	4.26329e9i	−0.914958	−	0.417503i
$725$	9.46107e9	−	9.46107e9i	0.922056	−	0.922056i
$726$	2.12582e10	−	4.73855e9i	2.06180	−	0.459586i
$727$	−9.03782e9			−0.872355			−0.436178	−	0.899861i	$-0.643668\pi$
$727$	−9.03782e9			−0.872355			−0.436178	+	0.899861i	$0.643668\pi$
$728$	−3.36116e8	+	1.31946e9i	−0.0322871	+	0.126747i
$729$	−1.01506e10	+	2.52691e9i	−0.970383	+	0.241570i
$730$	−4.92162e9	−	3.41600e9i	−0.468250	−	0.325004i
$731$	6.03325e9	+	6.03325e9i	0.571269	+	0.571269i
$732$	2.24701e9	+	9.16884e8i	0.211747	+	0.0864024i
$733$	7.72123e9	−	7.72123e9i	0.724140	−	0.724140i	−0.245305	−	0.969446i	$-0.578888\pi$
$733$	7.72123e9	−	7.72123e9i	0.724140	−	0.724140i	0.969446	+	0.245305i	$0.0788882\pi$
$734$	2.80191e9	+	1.55161e10i	0.261528	+	1.44826i
$735$	−8.74376e9	−	8.06008e9i	−0.812256	−	0.748744i
$736$	1.54979e10	+	1.24691e10i	1.43285	+	1.15282i
$737$			1.11502e10i			1.02600i
$738$	5.67526e8	−	1.50964e8i	0.0519743	−	0.0138253i
$739$	−3.39226e9	−	3.39226e9i	−0.309196	−	0.309196i	0.535402	−	0.844597i	$-0.320160\pi$
$739$	−3.39226e9	−	3.39226e9i	−0.309196	−	0.309196i	−0.844597	+	0.535402i	$0.820160\pi$
$740$	−9.13054e9	+	3.40876e9i	−0.828295	+	0.309232i
$741$	−2.30357e8	−	5.66176e9i	−0.0207987	−	0.511196i
$742$	−9.51218e8	+	1.37047e9i	−0.0854803	+	0.123156i
$743$		−	2.45394e9i		−	0.219484i	−0.993960	−	0.109742i	$-0.964997\pi$
$743$		−	2.45394e9i		−	0.219484i	0.993960	−	0.109742i	$-0.0350025\pi$
$744$	7.71781e8	−	5.01938e8i	0.0687051	−	0.0446832i
$745$		−	8.89297e9i		−	0.787952i
$746$	−1.47014e10	−	1.02040e10i	−1.29650	−	0.899880i
$747$	5.62398e9	−	6.62213e9i	0.493653	−	0.581267i
$748$	6.57000e9	−	1.43982e10i	0.573997	−	1.25792i
$749$	1.18751e9	+	1.18751e9i	0.103264	+	0.103264i
$750$	2.65675e8	−	4.18090e8i	0.0229952	−	0.0361872i
$751$		−	1.18513e10i		−	1.02100i	−0.859878	−	0.510500i	$-0.829460\pi$
$751$		−	1.18513e10i		−	1.02100i	0.859878	−	0.510500i	$-0.170540\pi$
$752$	9.25862e9	−	8.03275e9i	0.793933	−	0.688814i
$753$	−1.10625e10	+	1.20009e10i	−0.944214	+	1.02431i
$754$	−4.41737e9	+	7.97693e8i	−0.375288	+	0.0677698i
$755$	1.53499e10	−	1.53499e10i	1.29805	−	1.29805i
$756$	−2.52746e9	−	4.86306e9i	−0.212744	−	0.409339i
$757$	2.71222e9	+	2.71222e9i	0.227242	+	0.227242i	0.811540	−	0.584298i	$-0.198630\pi$
$757$	2.71222e9	+	2.71222e9i	0.227242	+	0.227242i	−0.584298	+	0.811540i	$0.698630\pi$
$758$	−3.72679e9	+	5.36938e9i	−0.310808	+	0.447798i
$759$	−2.87362e10	−	2.64893e10i	−2.38552	−	2.19900i
$760$	2.63492e10	−	1.56504e10i	2.17731	−	1.29323i
$761$	8.64977e9			0.711472			0.355736	−	0.934586i	$-0.384230\pi$
$761$	8.64977e9			0.711472			0.355736	+	0.934586i	$0.384230\pi$
$762$	1.79925e10	−	4.01062e9i	1.47316	−	0.328374i
$763$	1.10652e9	−	1.10652e9i	0.0901825	−	0.0901825i
$764$	−1.51551e10	+	5.65794e9i	−1.22951	+	0.459020i
$765$	−1.03810e10	−	8.81629e9i	−0.838349	−	0.711985i
$766$	−6.21392e9	+	1.12211e9i	−0.499534	+	0.0902063i
$767$	9.01562e8			0.0721460
$768$	1.24896e10	+	1.26436e9i	0.994915	+	0.100718i
$769$	5.42850e9			0.430465			0.215232	−	0.976563i	$-0.430949\pi$
$769$	5.42850e9			0.430465			0.215232	+	0.976563i	$0.430949\pi$
$770$	1.42388e10	−	2.57126e9i	1.12398	−	0.202969i
$771$	1.70304e10	−	6.92907e8i	1.33824	−	0.0544483i
$772$	−1.51126e10	+	5.64209e9i	−1.18217	+	0.441346i
$773$	−6.20778e9	+	6.20778e9i	−0.483402	+	0.483402i	−0.906216	−	0.422815i	$-0.861042\pi$
$773$	−6.20778e9	+	6.20778e9i	−0.483402	+	0.483402i	0.422815	+	0.906216i	$0.361042\pi$
$774$	6.66969e9	−	1.15040e10i	0.517026	−	0.891772i
$775$	1.02960e9			0.0794532
$776$	−7.57686e8	+	4.50035e8i	−0.0582068	+	0.0345725i
$777$	2.57580e9	−	2.79429e9i	0.196987	−	0.213697i
$778$	4.69099e9	−	6.75855e9i	0.357138	−	0.514547i
$779$	−9.05445e8	−	9.05445e8i	−0.0686248	−	0.0686248i
$780$	4.86124e9	−	2.04371e9i	0.366789	−	0.154201i
$781$	−3.28487e9	+	3.28487e9i	−0.246740	+	0.246740i
$782$	−1.89680e10	+	3.42526e9i	−1.41840	+	0.256135i
$783$	1.11264e10	−	1.42359e10i	0.828305	−	1.05979i
$784$	−8.02277e9	+	6.96053e9i	−0.594590	+	0.515865i
$785$		−	5.62519e9i		−	0.415044i
$786$	1.71745e10	+	1.09136e10i	1.26155	+	0.801655i
$787$	−1.39269e9	−	1.39269e9i	−0.101846	−	0.101846i	0.654348	−	0.756194i	$-0.272943\pi$
$787$	−1.39269e9	−	1.39269e9i	−0.101846	−	0.101846i	−0.756194	+	0.654348i	$0.772943\pi$
$788$	1.47848e9	−	3.24009e9i	0.107640	−	0.235893i
$789$	−3.63907e9	+	1.48061e8i	−0.263767	+	0.0107317i
$790$	1.18509e10	+	8.22547e9i	0.855175	+	0.593561i
$791$			3.29885e9i			0.236998i
$792$	−2.43176e10	−	4.12683e9i	−1.73933	−	0.295174i
$793$		−	9.10542e8i		−	0.0648401i
$794$	−9.16238e9	+	1.32007e10i	−0.649586	+	0.935893i
$795$	6.45559e9	−	2.62655e8i	0.455671	−	0.0185396i
$796$	−2.33302e10	+	8.71000e9i	−1.63954	+	0.612100i
$797$	7.89412e9	+	7.89412e9i	0.552331	+	0.552331i	0.927113	−	0.374782i	$-0.122282\pi$
$797$	7.89412e9	+	7.89412e9i	0.552331	+	0.552331i	−0.374782	+	0.927113i	$0.622282\pi$
$798$	−6.40924e9	+	1.00861e10i	−0.446474	+	0.702611i
$799$			1.18776e10i			0.823790i
$800$	1.09383e10	+	8.80059e9i	0.755327	+	0.607710i
$801$	7.78034e9	−	6.34157e8i	0.534915	−	0.0435997i
$802$	1.34864e9	+	7.46836e9i	0.0923180	+	0.511228i
$803$	7.43413e9	−	7.43413e9i	0.506671	−	0.506671i
$804$	3.23788e9	−	7.93507e9i	0.219717	−	0.538462i
$805$	−1.24606e10	−	1.24606e10i	−0.841884	−	0.841884i
$806$	−2.83764e8	−	1.96955e8i	−0.0190891	−	0.0132494i
$807$	−5.38761e9	+	5.84461e9i	−0.360860	+	0.391470i
$808$	−3.82965e9	+	1.50338e10i	−0.255399	+	1.00260i
$809$	8.80211e9			0.584476			0.292238	−	0.956346i	$-0.405600\pi$
$809$	8.80211e9			0.584476			0.292238	+	0.956346i	$0.405600\pi$
$810$	−9.11944e9	+	1.91672e10i	−0.602935	+	1.26725i
$811$	−2.27038e8	+	2.27038e8i	−0.0149460	+	0.0149460i	−0.714540	−	0.699594i	$-0.753364\pi$
$811$	−2.27038e8	+	2.27038e8i	−0.0149460	+	0.0149460i	0.699594	+	0.714540i	$0.253364\pi$
$812$	8.61244e9	+	3.92993e9i	0.564521	+	0.257596i
$813$	−1.06667e10	+	4.33988e8i	−0.696164	+	0.0283244i
$814$	−3.03937e9	−	1.68311e10i	−0.197514	−	1.09377i
$815$	−3.36756e9			−0.217903
$816$	−8.85662e9	+	8.33867e9i	−0.570627	+	0.537256i
$817$	−2.89947e10			−1.86012
$818$	1.48359e9	+	8.21564e9i	0.0947711	+	0.524813i
$819$	−1.33109e9	+	1.56733e9i	−0.0846667	+	0.0996934i
$820$	4.94698e8	−	1.08413e9i	0.0313323	−	0.0686647i
$821$	1.64939e10	−	1.64939e10i	1.04021	−	1.04021i	0.0410554	−	0.999157i	$-0.486928\pi$
$821$	1.64939e10	−	1.64939e10i	1.04021	−	1.04021i	0.999157	−	0.0410554i	$-0.0130720\pi$
$822$	1.93679e9	+	8.68887e9i	0.121627	+	0.545647i
$823$	1.62855e10			1.01836			0.509180	−	0.860660i	$-0.329949\pi$
$823$	1.62855e10			1.01836			0.509180	+	0.860660i	$0.329949\pi$
$824$	−3.28307e9	+	1.95001e9i	−0.204425	+	0.121420i
$825$	−2.02818e10	−	1.86960e10i	−1.25753	−	1.15920i
$826$	−1.56198e9	−	1.08414e9i	−0.0964373	−	0.0669353i
$827$	4.41808e9	+	4.41808e9i	0.271622	+	0.271622i	0.829753	−	0.558131i	$-0.188481\pi$
$827$	4.41808e9	+	4.41808e9i	0.271622	+	0.271622i	−0.558131	+	0.829753i	$0.688481\pi$
$828$	1.27581e10	+	2.71959e10i	0.781052	+	1.66493i
$829$	2.94421e9	−	2.94421e9i	0.179485	−	0.179485i	−0.611646	−	0.791131i	$-0.709493\pi$
$829$	2.94421e9	−	2.94421e9i	0.179485	−	0.179485i	0.791131	+	0.611646i	$0.209493\pi$
$830$	−3.13291e9	−	1.73491e10i	−0.190184	−	1.05318i
$831$	−7.60573e9	+	8.25088e9i	−0.459767	+	0.498766i
$832$	−1.33117e9	−	4.51792e9i	−0.0801314	−	0.271961i
$833$		−	1.02922e10i		−	0.616951i
$834$	−4.61408e9	−	2.93202e9i	−0.275425	−	0.175019i
$835$	−9.06567e9	−	9.06567e9i	−0.538887	−	0.538887i
$836$	1.88104e10	+	5.03846e10i	1.11346	+	2.98247i
$837$	1.38002e9	−	1.69192e8i	0.0813481	−	0.00997333i
$838$	−2.56889e9	+	3.70114e9i	−0.150797	+	0.217261i
$839$			2.38323e9i			0.139315i	0.997571	+	0.0696576i	$0.0221907\pi$
$839$			2.38323e9i			0.139315i	−0.997571	+	0.0696576i	$0.977809\pi$
$840$	−1.08798e10	−	2.30494e9i	−0.633350	−	0.134178i
$841$			1.39592e10i			0.809237i
$842$	−2.12068e10	−	1.47193e10i	−1.22429	−	0.849755i
$843$	7.57845e8	+	1.86265e10i	0.0435696	+	1.07086i
$844$	1.81895e10	+	8.30001e9i	1.04141	+	0.475204i
$845$	1.60052e10	+	1.60052e10i	0.912565	+	0.912565i
$846$	1.78892e10	−	4.75860e9i	1.01577	−	0.270198i
$847$			1.72335e10i			0.974501i
$848$	4.08084e8	−	5.75619e9i	0.0229808	−	0.324153i
$849$	9.40668e9	+	8.67116e9i	0.527545	+	0.486295i
$850$	−1.33875e10	+	2.41752e9i	−0.747709	+	0.135022i
$851$	−1.47291e10	+	1.47291e10i	−0.819261	+	0.819261i
$852$	3.29157e9	−	1.38380e9i	0.182333	−	0.0766542i
$853$	−1.81651e10	−	1.81651e10i	−1.00211	−	1.00211i	−0.999998	−	0.00211131i	$-0.999328\pi$
$853$	−1.81651e10	−	1.81651e10i	−1.00211	−	1.00211i	−0.00211131	−	0.999998i	$-0.500672\pi$
$854$	−1.09494e9	+	1.57754e9i	−0.0601571	+	0.0866716i
$855$	4.61294e10	−	3.75990e9i	2.52404	−	0.205729i
$856$	−5.62946e9	−	1.43403e9i	−0.306767	−	0.0781448i
$857$	7.81954e9			0.424374			0.212187	−	0.977229i	$-0.431941\pi$
$857$	7.81954e9			0.424374			0.212187	+	0.977229i	$0.431941\pi$
$858$	2.01339e9	+	9.03251e9i	0.108823	+	0.488206i
$859$	−9.41882e9	+	9.41882e9i	−0.507015	+	0.507015i	−0.913609	−	0.406594i	$-0.866716\pi$
$859$	−9.41882e9	+	9.41882e9i	−0.507015	+	0.507015i	0.406594	+	0.913609i	$0.366716\pi$
$860$	−9.43760e9	−	2.52791e10i	−0.505961	−	1.35524i
$861$	1.88904e7	+	4.64292e8i	0.00100862	+	0.0247902i
$862$	−1.43307e10	+	2.58785e9i	−0.762066	+	0.137614i
$863$	3.33703e10			1.76735			0.883674	−	0.468102i	$-0.155062\pi$
$863$	3.33703e10			1.76735			0.883674	+	0.468102i	$0.155062\pi$
$864$	1.61073e10	+	9.99841e9i	0.849622	+	0.527391i
$865$	−3.07400e10			−1.61490
$866$	−2.31599e9	+	4.18224e8i	−0.121178	+	0.0218825i
$867$	3.00921e8	+	7.39610e9i	0.0156814	+	0.385421i
$868$	2.54786e8	+	6.82459e8i	0.0132238	+	0.0354207i
$869$	−1.79008e10	+	1.79008e10i	−0.925344	+	0.925344i
$870$	−7.97677e9	−	3.57855e10i	−0.410686	−	1.84243i
$871$	−3.21548e9			−0.164885
$872$	−1.33622e9	+	5.24551e9i	−0.0682451	+	0.267904i
$873$	−1.32648e9	+	1.08118e8i	−0.0674762	+	0.00549983i
$874$	3.73478e10	−	5.38090e10i	1.89224	−	2.72624i
$875$	2.77157e8	+	2.77157e8i	0.0139861	+	0.0139861i
$876$	−7.44931e9	+	3.13175e9i	−0.374414	+	0.157407i
$877$	1.61503e10	−	1.61503e10i	0.808502	−	0.808502i	−0.175905	−	0.984407i	$-0.556285\pi$
$877$	1.61503e10	−	1.61503e10i	0.808502	−	0.808502i	0.984407	+	0.175905i	$0.0562852\pi$
$878$	−1.19877e10	+	2.16474e9i	−0.597728	+	0.107938i
$879$	2.91271e10	+	2.68496e10i	1.44656	+	1.33345i
$880$	−3.78053e10	+	3.27998e10i	−1.87009	+	1.62249i
$881$		−	1.69706e10i		−	0.836146i	−0.908413	−	0.418073i	$-0.862706\pi$
$881$		−	1.69706e10i		−	0.836146i	0.908413	−	0.418073i	$-0.137294\pi$
$882$	−1.55013e10	+	4.12341e9i	−0.760727	+	0.202356i
$883$	−1.28793e10	−	1.28793e10i	−0.629551	−	0.629551i	0.318404	−	0.947955i	$-0.396853\pi$
$883$	−1.28793e10	−	1.28793e10i	−0.629551	−	0.629551i	−0.947955	+	0.318404i	$0.896853\pi$
$884$	4.15213e9	+	1.89465e9i	0.202157	+	0.0922458i
$885$	2.99358e8	+	7.35769e9i	0.0145174	+	0.356813i
$886$	1.31966e10	+	9.15948e9i	0.637445	+	0.442438i
$887$			2.17928e10i			1.04853i	0.851556	+	0.524264i	$0.175659\pi$
$887$			2.17928e10i			1.04853i	−0.851556	+	0.524264i	$0.824341\pi$
$888$	−2.72456e9	+	1.28605e10i	−0.130572	+	0.616330i
$889$			1.45862e10i			0.696281i
$890$	9.03198e9	−	1.30128e10i	0.429455	−	0.618739i
$891$	−3.02571e10	−	2.17263e10i	−1.43303	−	1.02900i
$892$	1.17790e9	+	3.15506e9i	0.0555688	+	0.148844i
$893$	−2.85409e10	−	2.85409e10i	−1.34118	−	1.34118i
$894$	−1.01241e10	−	6.43337e9i	−0.473888	−	0.301132i
$895$		−	4.06125e10i		−	1.89356i
$896$	−3.12657e9	+	9.42816e9i	−0.145208	+	0.437874i
$897$	7.63897e9	−	8.28694e9i	0.353396	−	0.383372i
$898$	6.82981e9	+	3.78214e10i	0.314732	+	1.74289i
$899$	−1.69816e9	+	1.69816e9i	−0.0779506	+	0.0779506i
$900$	9.00458e9	+	1.91947e10i	0.411732	+	0.877671i
$901$	3.95399e9	+	3.95399e9i	0.180094	+	0.180094i
$902$	1.71798e9	+	1.19242e9i	0.0779462	+	0.0541010i
$903$	7.73637e9	+	7.13145e9i	0.349647	+	0.322308i
$904$	−5.82736e9	−	9.81104e9i	−0.262351	−	0.441698i
$905$	−3.14714e10			−1.41139
$906$	−6.37049e9	−	2.85794e10i	−0.284593	−	1.27675i
$907$	1.74005e10	−	1.74005e10i	0.774349	−	0.774349i	−0.204515	−	0.978864i	$-0.565562\pi$
$907$	1.74005e10	−	1.74005e10i	0.774349	−	0.774349i	0.978864	+	0.204515i	$0.0655616\pi$
$908$	1.37113e10	−	3.00483e10i	0.607824	−	1.33205i
$909$	−1.51662e10	+	1.78579e10i	−0.669735	+	0.788601i
$910$	7.41499e8	+	4.10619e9i	0.0326186	+	0.180632i
$911$	−1.77844e9			−0.0779338			−0.0389669	−	0.999241i	$-0.512407\pi$
$911$	−1.77844e9			−0.0779338			−0.0389669	+	0.999241i	$0.512407\pi$
$912$	1.24459e9	−	4.13187e10i	0.0543304	−	1.80370i
$913$	3.09382e10			1.34539
$914$	3.26620e9	+	1.80872e10i	0.141492	+	0.783537i
$915$	7.43098e9	−	3.02340e8i	0.320680	−	0.0130473i
$916$	−1.14557e9	−	5.22732e8i	−0.0492478	−	0.0224722i
$917$	−1.13852e10	+	1.13852e10i	−0.487583	+	0.487583i
$918$	−1.75467e10	+	5.44027e9i	−0.748592	+	0.232098i
$919$	6.75772e9			0.287208			0.143604	−	0.989635i	$-0.454131\pi$
$919$	6.75772e9			0.287208			0.143604	+	0.989635i	$0.454131\pi$
$920$	5.90700e10	+	1.50473e10i	2.50098	+	0.637091i
$921$	2.49593e10	−	2.70764e10i	1.05274	−	1.14204i
$922$	−2.80242e10	−	1.94511e10i	−1.17754	−	0.817308i
$923$	−9.47287e8	−	9.47287e8i	−0.0396530	−	0.0396530i
$924$	7.37346e9	−	1.80702e10i	0.307482	−	0.753547i
$925$	−1.03957e10	+	1.03957e10i	−0.431874	+	0.431874i
$926$	−3.07811e8	−	1.70456e9i	−0.0127393	−	0.0705462i
$927$	−5.74766e9	+	4.68478e8i	−0.236980	+	0.0193157i
$928$	−3.25562e10	+	3.52582e9i	−1.33726	+	0.144824i
$929$			3.78153e9i			0.154744i	0.997002	+	0.0773718i	$0.0246528\pi$
$929$			3.78153e9i			0.154744i	−0.997002	+	0.0773718i	$0.975347\pi$
$930$	1.51314e9	−	2.38121e9i	0.0616863	−	0.0970749i
$931$	2.47312e10	+	2.47312e10i	1.00443	+	1.00443i
$932$	−3.26856e10	+	1.22027e10i	−1.32252	+	0.493743i
$933$	−2.28737e10	+	9.30647e8i	−0.922040	+	0.0375145i
$934$	−2.86771e9	+	4.13166e9i	−0.115165	+	0.165925i
$935$		−	4.84995e10i		−	1.94042i
$936$	1.19009e9	−	7.01269e9i	0.0474368	−	0.279524i
$937$			2.77490e8i			0.0110194i	0.999985	+	0.00550970i	$0.00175380\pi$
$937$			2.77490e8i			0.0110194i	−0.999985	+	0.00550970i	$0.998246\pi$
$938$	5.57090e9	+	3.86666e9i	0.220402	+	0.152977i
$939$	−2.24783e10	+	9.14560e8i	−0.885999	+	0.0360481i
$940$	1.55936e10	−	3.41734e10i	0.612348	−	1.34196i
$941$	3.15823e10	+	3.15823e10i	1.23561	+	1.23561i	0.961778	+	0.273830i	$0.0882906\pi$
$941$	3.15823e10	+	3.15823e10i	1.23561	+	1.23561i	0.273830	+	0.961778i	$0.411709\pi$
$942$	−6.40394e9	−	4.06939e9i	−0.249614	−	0.158617i
$943$		−	2.54692e9i		−	0.0989063i
$944$	6.56055e9	+	4.65110e8i	0.253827	+	0.0179951i
$945$	−1.32330e10	−	1.03426e10i	−0.510091	−	0.398676i
$946$	4.65992e10	−	8.41492e9i	1.78961	−	0.323170i
$947$	3.36790e10	−	3.36790e10i	1.28865	−	1.28865i	0.353039	−	0.935609i	$-0.385148\pi$
$947$	3.36790e10	−	3.36790e10i	1.28865	−	1.28865i	0.935609	−	0.353039i	$-0.114852\pi$
$948$	1.79374e10	−	7.54101e9i	0.683801	−	0.287475i
$949$	2.14385e9	+	2.14385e9i	0.0814259	+	0.0814259i
$950$	2.63598e10	−	3.79780e10i	0.997493	−	1.43714i
$951$	−1.15983e10	+	1.25822e10i	−0.437284	+	0.474377i
$952$	−4.91533e9	−	8.27552e9i	−0.184639	−	0.310861i
$953$	−1.66123e10			−0.621734			−0.310867	−	0.950453i	$-0.600619\pi$
$953$	−1.66123e10			−0.621734			−0.310867	+	0.950453i	$0.600619\pi$
$954$	4.37110e9	−	7.53931e9i	0.162994	−	0.281133i
$955$	−3.50538e10	+	3.50538e10i	−1.30234	+	1.30234i
$956$	−2.03370e9	+	7.59253e8i	−0.0752808	+	0.0281050i
$957$	6.42878e10	−	2.61564e9i	2.37103	−	0.0964686i
$958$	4.19991e10	−	7.58423e9i	1.54334	−	0.278697i
$959$	−7.04388e9			−0.257897
$960$	3.64290e10	−	1.23639e10i	1.32892	−	0.451031i
$961$	2.73278e10			0.993283
$962$	4.85374e9	−	8.76493e8i	0.175778	−	0.0317421i
$963$	−6.68698e9	−	5.67905e9i	−0.241289	−	0.204920i
$964$	3.72027e10	−	1.38891e10i	1.33754	−	0.499350i
$965$	−3.49556e10	+	3.49556e10i	−1.25219	+	1.25219i
$966$	−2.31998e10	+	5.17136e9i	−0.828066	+	0.184580i
$967$	2.97766e10			1.05897			0.529483	−	0.848321i	$-0.322386\pi$
$967$	2.97766e10			1.05897			0.529483	+	0.848321i	$0.322386\pi$
$968$	−3.04427e10	−	5.12538e10i	−1.07875	−	1.81619i
$969$	2.94522e10	+	2.71492e10i	1.03988	+	0.958572i
$970$	−1.53987e9	+	2.21858e9i	−0.0541731	+	0.0780501i
$971$	−3.32240e10	−	3.32240e10i	−1.16462	−	1.16462i	−0.983452	−	0.181171i	$-0.942011\pi$
$971$	−3.32240e10	−	3.32240e10i	−1.16462	−	1.16462i	−0.181171	−	0.983452i	$-0.557989\pi$
$972$	1.52235e10	+	2.42479e10i	0.531720	+	0.846920i
$973$	3.05873e9	−	3.05873e9i	0.106450	−	0.106450i
$974$	9.47867e9	−	1.71166e9i	0.328693	−	0.0593557i
$975$	5.39153e9	−	5.84886e9i	0.186293	−	0.202095i
$976$	4.69742e8	−	6.62590e9i	0.0161728	−	0.228124i
$977$			3.35927e10i			1.15243i	0.817299	+	0.576214i	$0.195471\pi$
$977$			3.35927e10i			1.15243i	−0.817299	+	0.576214i	$0.804529\pi$
$978$	−2.43617e9	+	3.83377e9i	−0.0832762	+	0.131051i
$979$	1.96560e10	+	1.96560e10i	0.669508	+	0.669508i
$980$	−1.35121e10	+	2.96119e10i	−0.458599	+	1.00502i
$981$	−5.29171e9	+	6.23090e9i	−0.178960	+	0.210722i
$982$	6.83221e9	+	4.74211e9i	0.230235	+	0.159802i
$983$			4.69821e8i			0.0157759i	0.999969	+	0.00788796i	$0.00251084\pi$
$983$			4.69821e8i			0.0157759i	−0.999969	+	0.00788796i	$0.997489\pi$
$984$	−8.76344e8	−	1.34747e9i	−0.0293219	−	0.0450854i
$985$		−	1.09141e10i		−	0.363881i
$986$	1.80932e10	−	2.60679e10i	0.601100	−	0.866037i
$987$	5.95450e8	+	1.46351e10i	0.0197122	+	0.484492i
$988$	−1.45299e10	+	5.42452e9i	−0.479306	+	0.178942i
$989$	−4.07794e10	−	4.07794e10i	−1.34046	−	1.34046i
$990$	−7.30462e10	+	1.94306e10i	−2.39263	+	0.636447i
$991$		−	9.44028e9i		−	0.308125i	−0.988061	−	0.154063i	$-0.950764\pi$
$991$		−	9.44028e9i		−	0.308125i	0.988061	−	0.154063i	$-0.0492357\pi$
$992$	−1.96331e9	−	1.57961e9i	−0.0638553	−	0.0513758i
$993$	−2.84732e10	−	2.62468e10i	−0.922813	−	0.850657i
$994$	5.02073e8	+	2.78032e9i	0.0162149	+	0.0897931i
$995$	−5.39628e10	+	5.39628e10i	−1.73666	+	1.73666i
$996$	−2.20173e10	−	8.98407e9i	−0.706084	−	0.288115i
$997$	3.20572e10	+	3.20572e10i	1.02445	+	1.02445i	0.999693	+	0.0247598i	$0.00788208\pi$
$997$	3.20572e10	+	3.20572e10i	1.02445	+	1.02445i	0.0247598	+	0.999693i	$0.492118\pi$
$998$	−6.46816e8	−	4.48943e8i	−0.0205979	−	0.0142966i
$999$	−1.22256e10	+	1.56422e10i	−0.387963	+	0.496384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.8.k.a.11.2	✓	108
3.2	odd	2	inner	48.8.k.a.11.53	yes	108
16.3	odd	4	inner	48.8.k.a.35.53	yes	108
48.35	even	4	inner	48.8.k.a.35.2	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.8.k.a.11.2	✓	108	1.1	even	1	trivial
48.8.k.a.11.53	yes	108	3.2	odd	2	inner
48.8.k.a.35.2	yes	108	48.35	even	4	inner
48.8.k.a.35.53	yes	108	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.1336 + 2.01052i) q^{2} +(1.90114 + 46.7267i) q^{3} +(119.916 - 44.7688i) q^{4} +(277.365 - 277.365i) q^{5} +(-115.112 - 516.416i) q^{6} +418.647 q^{7} +(-1245.09 + 739.532i) q^{8} +(-2179.77 + 177.668i) q^{9} +O(q^{10})\)	\(q+(-11.1336 + 2.01052i) q^{2} +(1.90114 + 46.7267i) q^{3} +(119.916 - 44.7688i) q^{4} +(277.365 - 277.365i) q^{5} +(-115.112 - 516.416i) q^{6} +418.647 q^{7} +(-1245.09 + 739.532i) q^{8} +(-2179.77 + 177.668i) q^{9} +(-2530.44 + 3645.73i) q^{10} +(-5506.90 - 5506.90i) q^{11} +(2319.88 + 5518.15i) q^{12} +(1588.08 - 1588.08i) q^{13} +(-4661.06 + 841.699i) q^{14} +(13487.7 + 12433.1i) q^{15} +(12375.5 - 10737.0i) q^{16} +15876.2i q^{17} +(23911.6 - 6360.57i) q^{18} +(-38149.1 - 38149.1i) q^{19} +(20843.1 - 45677.8i) q^{20} +(795.908 + 19562.0i) q^{21} +(72383.6 + 50240.1i) q^{22} -107309. i q^{23} +(-36923.0 - 56772.9i) q^{24} -75738.2i q^{25} +(-14488.2 + 20873.9i) q^{26} +(-12445.9 - 101516. i) q^{27} +(50202.3 - 18742.3i) q^{28} +(124918. + 124918. i) q^{29} +(-175164. - 111308. i) q^{30} +13594.2i q^{31} +(-116198. + 144423. i) q^{32} +(246850. - 267789. i) q^{33} +(-31919.5 - 176760. i) q^{34} +(116118. - 116118. i) q^{35} +(-253435. + 118891. i) q^{36} +(-137258. - 137258. i) q^{37} +(501438. + 348039. i) q^{38} +(77224.8 + 71186.5i) q^{39} +(-140224. + 550465. i) q^{40} +23734.4 q^{41} +(-48191.2 - 216196. i) q^{42} +(380018. - 380018. i) q^{43} +(-906901. - 413826. i) q^{44} +(-555314. + 653872. i) q^{45} +(215748. + 1.19474e6i) q^{46} +748140. q^{47} +(525230. + 557854. i) q^{48} -648278. q^{49} +(152273. + 843241. i) q^{50} +(-741844. + 30183.0i) q^{51} +(119339. - 261532. i) q^{52} +(249051. - 249051. i) q^{53} +(342668. + 1.10522e6i) q^{54} -3.05485e6 q^{55} +(-521253. + 309603. i) q^{56} +(1.71006e6 - 1.85511e6i) q^{57} +(-1.64194e6 - 1.13964e6i) q^{58} +(283853. + 283853. i) q^{59} +(2.17400e6 + 887091. i) q^{60} +(286681. - 286681. i) q^{61} +(-27331.4 - 151353. i) q^{62} +(-912555. + 74380.3i) q^{63} +(1.00334e6 - 1.84157e6i) q^{64} -880955. i q^{65} +(-2.20994e6 + 3.47776e6i) q^{66} +(-1.01238e6 - 1.01238e6i) q^{67} +(710759. + 1.90381e6i) q^{68} +(5.01421e6 - 204010. i) q^{69} +(-1.05936e6 + 1.52628e6i) q^{70} -596500. i q^{71} +(2.58262e6 - 1.83322e6i) q^{72} +1.34997e6i q^{73} +(1.80414e6 + 1.25222e6i) q^{74} +(3.53899e6 - 143989. i) q^{75} +(-6.28257e6 - 2.86679e6i) q^{76} +(-2.30545e6 - 2.30545e6i) q^{77} +(-1.00291e6 - 637302. i) q^{78} -3.25061e6i q^{79} +(454479. - 6.41060e6i) q^{80} +(4.71984e6 - 774552. i) q^{81} +(-264250. + 47718.4i) q^{82} +(-2.80904e6 + 2.80904e6i) q^{83} +(971209. + 2.31016e6i) q^{84} +(4.40352e6 + 4.40352e6i) q^{85} +(-3.46695e6 + 4.99501e6i) q^{86} +(-5.59953e6 + 6.07450e6i) q^{87} +(1.09291e7 + 2.78405e6i) q^{88} -3.56934e6 q^{89} +(4.86804e6 - 8.39644e6i) q^{90} +(664844. - 664844. i) q^{91} +(-4.80411e6 - 1.28681e7i) q^{92} +(-635211. + 25844.4i) q^{93} +(-8.32952e6 + 1.50415e6i) q^{94} -2.11625e7 q^{95} +(-6.96930e6 - 5.15496e6i) q^{96} +608540. q^{97} +(7.21769e6 - 1.30338e6i) q^{98} +(1.29822e7 + 1.10254e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Introduction

L-functions

Modular forms

Varieties

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