LMFDB - Embedded newform 48.9.l.a.43.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.21
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.57965 - 14.9956i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-193.735 - 167.340i) q^{4} +(214.689 + 214.689i) q^{5} +(-680.384 + 311.367i) q^{6} -321.411 q^{7} +(-3590.34 + 1971.47i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(5.57965 - 14.9956i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-193.735 - 167.340i) q^{4} +(214.689 + 214.689i) q^{5} +(-680.384 + 311.367i) q^{6} -321.411 q^{7} +(-3590.34 + 1971.47i) q^{8} +2187.00i q^{9} +(4417.27 - 2021.50i) q^{10} +(-13451.1 + 13451.1i) q^{11} +(872.821 + 11940.1i) q^{12} +(-3434.55 + 3434.55i) q^{13} +(-1793.36 + 4819.74i) q^{14} -14198.7i q^{15} +(9530.45 + 64839.3i) q^{16} +65954.5 q^{17} +(32795.3 + 12202.7i) q^{18} +(113520. + 113520. i) q^{19} +(-5666.64 - 77518.8i) q^{20} +(10628.4 + 10628.4i) q^{21} +(126654. + 276759. i) q^{22} -99132.9 q^{23} +(183918. + 53533.0i) q^{24} -298442. i q^{25} +(32339.5 + 70666.7i) q^{26} +(72320.0 - 72320.0i) q^{27} +(62268.5 + 53784.9i) q^{28} +(74218.8 - 74218.8i) q^{29} +(-212918. - 79223.9i) q^{30} +783672. i q^{31} +(1.02548e6 + 218866. i) q^{32} +889604. q^{33} +(368003. - 989027. i) q^{34} +(-69003.3 - 69003.3i) q^{35} +(365973. - 423698. i) q^{36} +(385145. + 385145. i) q^{37} +(2.33569e6 - 1.06889e6i) q^{38} +227148. q^{39} +(-1.19406e6 - 347554. i) q^{40} +2.10509e6i q^{41} +(218683. - 100077. i) q^{42} +(-2.77452e6 + 2.77452e6i) q^{43} +(4.85685e6 - 355037. i) q^{44} +(-469525. + 469525. i) q^{45} +(-553127. + 1.48655e6i) q^{46} +6.61433e6i q^{47} +(1.82896e6 - 2.45927e6i) q^{48} -5.66150e6 q^{49} +(-4.47532e6 - 1.66520e6i) q^{50} +(-2.18099e6 - 2.18099e6i) q^{51} +(1.24013e6 - 90653.7i) q^{52} +(873055. + 873055. i) q^{53} +(-680960. - 1.48800e6i) q^{54} -5.77560e6 q^{55} +(1.15397e6 - 633650. i) q^{56} -7.50775e6i q^{57} +(-698839. - 1.52707e6i) q^{58} +(-1.79884e6 + 1.79884e6i) q^{59} +(-2.37602e6 + 2.75079e6i) q^{60} +(-1.03492e7 + 1.03492e7i) q^{61} +(1.17516e7 + 4.37262e6i) q^{62} -702925. i q^{63} +(9.00385e6 - 1.41565e7i) q^{64} -1.47472e6 q^{65} +(4.96368e6 - 1.33401e7i) q^{66} +(-1.57263e7 - 1.57263e7i) q^{67} +(-1.27777e7 - 1.10369e7i) q^{68} +(3.27814e6 + 3.27814e6i) q^{69} +(-1.41976e6 + 649730. i) q^{70} -4.51284e7 q^{71} +(-4.31160e6 - 7.85207e6i) q^{72} -1.41319e7i q^{73} +(7.92444e6 - 3.62650e6i) q^{74} +(-9.86893e6 + 9.86893e6i) q^{75} +(-2.99631e6 - 4.09891e7i) q^{76} +(4.32332e6 - 4.32332e6i) q^{77} +(1.26741e6 - 3.40622e6i) q^{78} +5.93775e6i q^{79} +(-1.18742e7 + 1.59664e7i) q^{80} -4.78297e6 q^{81} +(3.15671e7 + 1.17457e7i) q^{82} +(4.07467e7 + 4.07467e7i) q^{83} +(-280534. - 3.83767e6i) q^{84} +(1.41597e7 + 1.41597e7i) q^{85} +(2.61247e7 + 5.70864e7i) q^{86} -4.90855e6 q^{87} +(2.17756e7 - 7.48123e7i) q^{88} +3.55568e7i q^{89} +(4.42101e6 + 9.66058e6i) q^{90} +(1.10390e6 - 1.10390e6i) q^{91} +(1.92055e7 + 1.65889e7i) q^{92} +(2.59146e7 - 2.59146e7i) q^{93} +(9.91857e7 + 3.69057e7i) q^{94} +4.87428e7i q^{95} +(-2.66732e7 - 4.11482e7i) q^{96} -1.43728e7 q^{97} +(-3.15892e7 + 8.48974e7i) q^{98} +(-2.94175e7 - 2.94175e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * 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 $

$2$	5.57965	−	14.9956i	0.348728	−	0.937224i
$2$	5.57965	−	14.9956i	0.348728	−	0.937224i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$4$	−193.735	−	167.340i	−0.756777	−	0.653673i
$5$	214.689	+	214.689i	0.343502	+	0.343502i	0.857682	−	0.514180i	$-0.171904\pi$
$5$	214.689	+	214.689i	0.343502	+	0.343502i	−0.514180	+	0.857682i	$0.671904\pi$
$6$	−680.384	+	311.367i	−0.524988	+	0.240252i
$7$	−321.411			−0.133865			−0.0669326	−	0.997757i	$-0.521321\pi$
$7$	−321.411			−0.133865			−0.0669326	+	0.997757i	$0.521321\pi$
$8$	−3590.34	+	1971.47i	−0.876548	+	0.481315i
$9$			2187.00i			0.333333i
$10$	4417.27	−	2021.50i	0.441727	−	0.202150i
$11$	−13451.1	+	13451.1i	−0.918727	+	0.918727i	−0.996937	−	0.0782097i	$-0.975080\pi$
$11$	−13451.1	+	13451.1i	−0.918727	+	0.918727i	0.0782097	+	0.996937i	$0.475080\pi$
$12$	872.821	+	11940.1i	0.0420921	+	0.575814i
$13$	−3434.55	+	3434.55i	−0.120253	+	0.120253i	−0.764672	−	0.644419i	$-0.777099\pi$
$13$	−3434.55	+	3434.55i	−0.120253	+	0.120253i	0.644419	+	0.764672i	$0.277099\pi$
$14$	−1793.36	+	4819.74i	−0.0466826	+	0.125462i
$15$		−	14198.7i		−	0.280468i
$16$	9530.45	+	64839.3i	0.145423	+	0.989370i
$17$	65954.5			0.789676			0.394838	−	0.918751i	$-0.370801\pi$
$17$	65954.5			0.789676			0.394838	+	0.918751i	$0.370801\pi$
$18$	32795.3	+	12202.7i	0.312408	+	0.116243i
$19$	113520.	+	113520.i	0.871076	+	0.871076i	0.992590	−	0.121514i	$-0.0387748\pi$
$19$	113520.	+	113520.i	0.871076	+	0.871076i	−0.121514	+	0.992590i	$0.538775\pi$
$20$	−5666.64	−	77518.8i	−0.0354165	−	0.484493i
$21$	10628.4	+	10628.4i	0.0546503	+	0.0546503i
$22$	126654.	+	276759.i	0.540667	+	1.18144i
$23$	−99132.9			−0.354247			−0.177124	−	0.984189i	$-0.556679\pi$
$23$	−99132.9			−0.354247			−0.177124	+	0.984189i	$0.556679\pi$
$24$	183918.	+	53533.0i	0.554345	+	0.161353i
$25$		−	298442.i		−	0.764012i
$26$	32339.5	+	70666.7i	0.0707684	+	0.154640i
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$	62268.5	+	53784.9i	0.101306	+	0.0875041i
$29$	74218.8	−	74218.8i	0.104935	−	0.104935i	−0.652690	−	0.757625i	$-0.726360\pi$
$29$	74218.8	−	74218.8i	0.104935	−	0.104935i	0.757625	+	0.652690i	$0.226360\pi$
$30$	−212918.	−	79223.9i	−0.262862	−	0.0978073i
$31$			783672.i			0.848570i	0.905529	+	0.424285i	$0.139475\pi$
$31$			783672.i			0.848570i	−0.905529	+	0.424285i	$0.860525\pi$
$32$	1.02548e6	+	218866.i	0.977974	+	0.208727i
$33$	889604.			0.750138
$34$	368003.	−	989027.i	0.275382	−	0.740103i
$35$	−69003.3	−	69003.3i	−0.0459830	−	0.0459830i
$36$	365973.	−	423698.i	0.217891	−	0.252259i
$37$	385145.	+	385145.i	0.205502	+	0.205502i	0.802353	−	0.596850i	$-0.203581\pi$
$37$	385145.	+	385145.i	0.205502	+	0.205502i	−0.596850	+	0.802353i	$0.703581\pi$
$38$	2.33569e6	−	1.06889e6i	1.12016	−	0.512624i
$39$	227148.			0.0981863
$40$	−1.19406e6	−	347554.i	−0.466429	−	0.135763i
$41$			2.10509e6i			0.744964i	0.928039	+	0.372482i	$0.121493\pi$
$41$			2.10509e6i			0.744964i	−0.928039	+	0.372482i	$0.878507\pi$
$42$	218683.	−	100077.i	0.0702776	−	0.0321614i
$43$	−2.77452e6	+	2.77452e6i	−0.811548	+	0.811548i	−0.984866	−	0.173318i	$-0.944551\pi$
$43$	−2.77452e6	+	2.77452e6i	−0.811548	+	0.811548i	0.173318	+	0.984866i	$0.444551\pi$
$44$	4.85685e6	−	355037.i	1.29582	−	0.0947245i
$45$	−469525.	+	469525.i	−0.114501	+	0.114501i
$46$	−553127.	+	1.48655e6i	−0.123536	+	0.332009i
$47$			6.61433e6i			1.35548i	0.735300	+	0.677742i	$0.237041\pi$
$47$			6.61433e6i			1.35548i	−0.735300	+	0.677742i	$0.762959\pi$
$48$	1.82896e6	−	2.45927e6i	0.344540	−	0.463277i
$49$	−5.66150e6			−0.982080
$50$	−4.47532e6	−	1.66520e6i	−0.716051	−	0.266433i
$51$	−2.18099e6	−	2.18099e6i	−0.322384	−	0.322384i
$52$	1.24013e6	−	90653.7i	0.169611	−	0.0123986i
$53$	873055.	+	873055.i	0.110647	+	0.110647i	0.760263	−	0.649616i	$-0.225070\pi$
$53$	873055.	+	873055.i	0.110647	+	0.110647i	−0.649616	+	0.760263i	$0.725070\pi$
$54$	−680960.	−	1.48800e6i	−0.0800841	−	0.174996i
$55$	−5.77560e6			−0.631170
$56$	1.15397e6	−	633650.i	0.117339	−	0.0644314i
$57$		−	7.50775e6i		−	0.711231i
$58$	−698839.	−	1.52707e6i	−0.0617540	−	0.134942i
$59$	−1.79884e6	+	1.79884e6i	−0.148451	+	0.148451i	−0.777426	−	0.628975i	$-0.783475\pi$
$59$	−1.79884e6	+	1.79884e6i	−0.148451	+	0.148451i	0.628975	+	0.777426i	$0.283475\pi$
$60$	−2.37602e6	+	2.75079e6i	−0.183335	+	0.212252i
$61$	−1.03492e7	+	1.03492e7i	−0.747458	+	0.747458i	−0.974001	−	0.226543i	$-0.927258\pi$
$61$	−1.03492e7	+	1.03492e7i	−0.747458	+	0.747458i	0.226543	+	0.974001i	$0.427258\pi$
$62$	1.17516e7	+	4.37262e6i	0.795300	+	0.295920i
$63$		−	702925.i		−	0.0446218i
$64$	9.00385e6	−	1.41565e7i	0.536671	−	0.843791i
$65$	−1.47472e6			−0.0826144
$66$	4.96368e6	−	1.33401e7i	0.261594	−	0.703047i
$67$	−1.57263e7	−	1.57263e7i	−0.780418	−	0.780418i	0.199483	−	0.979901i	$-0.436074\pi$
$67$	−1.57263e7	−	1.57263e7i	−0.780418	−	0.780418i	−0.979901	+	0.199483i	$0.936074\pi$
$68$	−1.27777e7	−	1.10369e7i	−0.597609	−	0.516190i
$69$	3.27814e6	+	3.27814e6i	0.144621	+	0.144621i
$70$	−1.41976e6	+	649730.i	−0.0591320	+	0.0270608i
$71$	−4.51284e7			−1.77589			−0.887945	−	0.459949i	$-0.847868\pi$
$71$	−4.51284e7			−1.77589			−0.887945	+	0.459949i	$0.847868\pi$
$72$	−4.31160e6	−	7.85207e6i	−0.160438	−	0.292183i
$73$		−	1.41319e7i		−	0.497631i	−0.968551	−	0.248816i	$-0.919959\pi$
$73$		−	1.41319e7i		−	0.497631i	0.968551	−	0.248816i	$-0.0800413\pi$
$74$	7.92444e6	−	3.62650e6i	0.264266	−	0.120937i
$75$	−9.86893e6	+	9.86893e6i	−0.311907	+	0.311907i
$76$	−2.99631e6	−	4.09891e7i	−0.0898115	−	1.22861i
$77$	4.32332e6	−	4.32332e6i	0.122986	−	0.122986i
$78$	1.26741e6	−	3.40622e6i	0.0342403	−	0.0920225i
$79$			5.93775e6i			0.152445i	0.997091	+	0.0762225i	$0.0242859\pi$
$79$			5.93775e6i			0.152445i	−0.997091	+	0.0762225i	$0.975714\pi$
$80$	−1.18742e7	+	1.59664e7i	−0.289897	+	0.389804i
$81$	−4.78297e6			−0.111111
$82$	3.15671e7	+	1.17457e7i	0.698198	+	0.259790i
$83$	4.07467e7	+	4.07467e7i	0.858579	+	0.858579i	0.991171	−	0.132592i	$-0.0423300\pi$
$83$	4.07467e7	+	4.07467e7i	0.858579	+	0.858579i	−0.132592	+	0.991171i	$0.542330\pi$
$84$	−280534.	−	3.83767e6i	−0.00563467	−	0.0770815i
$85$	1.41597e7	+	1.41597e7i	0.271255	+	0.271255i
$86$	2.61247e7	+	5.70864e7i	0.477592	+	1.04361i
$87$	−4.90855e6			−0.0856794
$88$	2.17756e7	−	7.48123e7i	0.363111	−	1.24751i
$89$			3.55568e7i			0.566712i	0.959015	+	0.283356i	$0.0914478\pi$
$89$			3.55568e7i			0.566712i	−0.959015	+	0.283356i	$0.908552\pi$
$90$	4.42101e6	+	9.66058e6i	0.0673832	+	0.147242i
$91$	1.10390e6	−	1.10390e6i	0.0160977	−	0.0160977i
$92$	1.92055e7	+	1.65889e7i	0.268086	+	0.231562i
$93$	2.59146e7	−	2.59146e7i	0.346427	−	0.346427i
$94$	9.91857e7	+	3.69057e7i	1.27039	+	0.472696i
$95$			4.87428e7i			0.598433i
$96$	−2.66732e7	−	4.11482e7i	−0.314044	−	0.484469i
$97$	−1.43728e7			−0.162351			−0.0811755	−	0.996700i	$-0.525867\pi$
$97$	−1.43728e7			−0.162351			−0.0811755	+	0.996700i	$0.525867\pi$
$98$	−3.15892e7	+	8.48974e7i	−0.342479	+	0.920429i
$99$	−2.94175e7	−	2.94175e7i	−0.306242	−	0.306242i
$100$	−4.99414e7	+	5.78187e7i	−0.499414	+	0.578187i
$101$	1.27428e8	+	1.27428e8i	1.22456	+	1.22456i	0.965994	+	0.258565i	$0.0832495\pi$
$101$	1.27428e8	+	1.27428e8i	1.22456	+	1.22456i	0.258565	+	0.965994i	$0.416750\pi$
$102$	−4.48744e7	+	2.05361e7i	−0.414570	+	0.189721i
$103$	−7.05349e7			−0.626694			−0.313347	−	0.949639i	$-0.601450\pi$
$103$	−7.05349e7			−0.626694			−0.313347	+	0.949639i	$0.601450\pi$
$104$	5.56009e6	−	1.91023e7i	0.0475279	−	0.163287i
$105$			4.56362e6i			0.0375450i
$106$	1.79633e7	−	8.22062e6i	0.142286	−	0.0651150i
$107$	−4.30920e7	+	4.30920e7i	−0.328746	+	0.328746i	−0.852110	−	0.523363i	$-0.824677\pi$
$107$	−4.30920e7	+	4.30920e7i	−0.328746	+	0.328746i	0.523363	+	0.852110i	$0.324677\pi$
$108$	−2.61129e7	+	1.90886e6i	−0.191938	+	0.0140307i
$109$	1.74484e8	−	1.74484e8i	1.23609	−	1.23609i	0.274502	−	0.961586i	$-0.411487\pi$
$109$	1.74484e8	−	1.74484e8i	1.23609	−	1.23609i	0.961586	−	0.274502i	$-0.0885131\pi$
$110$	−3.22258e7	+	8.66084e7i	−0.220107	+	0.591547i
$111$		−	2.54720e7i		−	0.167792i
$112$	−3.06319e6	−	2.08400e7i	−0.0194671	−	0.132442i
$113$	1.52983e8			0.938275			0.469138	−	0.883125i	$-0.344565\pi$
$113$	1.52983e8			0.938275			0.469138	+	0.883125i	$0.344565\pi$
$114$	−1.12583e8	−	4.18906e7i	−0.666582	−	0.248026i
$115$	−2.12827e7	−	2.12827e7i	−0.121685	−	0.121685i
$116$	−2.67986e7	+	1.95898e6i	−0.148006	+	0.0108193i
$117$	−7.51136e6	−	7.51136e6i	−0.0400844	−	0.0400844i
$118$	1.69377e7	+	3.70115e7i	0.0873629	+	0.190901i
$119$	−2.11985e7			−0.105710
$120$	2.79923e7	+	5.09782e7i	0.134994	+	0.245844i
$121$		−	1.47504e8i		−	0.688119i
$122$	9.74472e7	+	2.12937e8i	0.439876	+	0.961196i
$123$	6.96114e7	−	6.96114e7i	0.304130	−	0.304130i
$124$	1.31140e8	−	1.51825e8i	0.554687	−	0.642178i
$125$	1.47935e8	−	1.47935e8i	0.605942	−	0.605942i
$126$	−1.05408e7	−	3.92208e6i	−0.0418206	−	0.0155609i
$127$		−	2.43669e8i		−	0.936667i	−0.883552	−	0.468334i	$-0.844855\pi$
$127$		−	2.43669e8i		−	0.936667i	0.883552	−	0.468334i	$-0.155145\pi$
$128$	−1.62046e8	−	2.14006e8i	−0.603669	−	0.797235i
$129$	1.83496e8			0.662626
$130$	−8.22842e6	+	2.21143e7i	−0.0288100	+	0.0774282i
$131$	−1.01426e7	−	1.01426e7i	−0.0344401	−	0.0344401i	0.689677	−	0.724117i	$-0.257753\pi$
$131$	−1.01426e7	−	1.01426e7i	−0.0344401	−	0.0344401i	−0.724117	+	0.689677i	$0.757753\pi$
$132$	−1.72347e8	−	1.48867e8i	−0.567687	−	0.490345i
$133$	−3.64864e7	−	3.64864e7i	−0.116607	−	0.116607i
$134$	−3.23572e8	+	1.48078e8i	−1.00358	+	0.459272i
$135$	3.10526e7			0.0934895
$136$	−2.36799e8	+	1.30027e8i	−0.692189	+	0.380083i
$137$		−	5.43447e8i		−	1.54268i	−0.636425	−	0.771339i	$-0.719587\pi$
$137$		−	5.43447e8i		−	1.54268i	0.636425	−	0.771339i	$-0.280413\pi$
$138$	6.74484e7	−	3.08667e7i	0.185975	−	0.0851087i
$139$	−5.06935e8	+	5.06935e8i	−1.35798	+	1.35798i	−0.481572	+	0.876407i	$0.659934\pi$
$139$	−5.06935e8	+	5.06935e8i	−1.35798	+	1.35798i	−0.876407	+	0.481572i	$0.840066\pi$
$140$	1.82132e6	+	2.49154e7i	0.00474104	+	0.0648568i
$141$	2.18723e8	−	2.18723e8i	0.553374	−	0.553374i
$142$	−2.51801e8	+	6.76726e8i	−0.619303	+	1.66441i
$143$		−	9.23968e7i		−	0.220960i
$144$	−1.41804e8	+	2.08431e7i	−0.329790	+	0.0484744i
$145$	3.18679e7			0.0720911
$146$	−2.11915e8	−	7.88508e7i	−0.466392	−	0.173538i
$147$	1.87215e8	+	1.87215e8i	0.400933	+	0.400933i
$148$	−1.01658e7	−	1.39066e8i	−0.0211881	−	0.289851i
$149$	1.51435e8	+	1.51435e8i	0.307241	+	0.307241i	0.843839	−	0.536597i	$-0.180290\pi$
$149$	1.51435e8	+	1.51435e8i	0.307241	+	0.307241i	−0.536597	+	0.843839i	$0.680290\pi$
$150$	9.29251e7	+	2.03055e8i	0.183556	+	0.401097i
$151$	−7.95362e8			−1.52988			−0.764939	−	0.644103i	$-0.777231\pi$
$151$	−7.95362e8			−1.52988			−0.764939	+	0.644103i	$0.777231\pi$
$152$	−6.31373e8	−	1.83773e8i	−1.18280	−	0.344277i
$153$			1.44243e8i			0.263225i
$154$	−4.07081e7	−	8.89533e7i	−0.0723765	−	0.158154i
$155$	−1.68246e8	+	1.68246e8i	−0.291486	+	0.291486i
$156$	−4.40065e7	−	3.80110e7i	−0.0743051	−	0.0641817i
$157$	6.55541e7	−	6.55541e7i	0.107895	−	0.107895i	−0.651098	−	0.758993i	$-0.725691\pi$
$157$	6.55541e7	−	6.55541e7i	0.107895	−	0.107895i	0.758993	+	0.651098i	$0.225691\pi$
$158$	8.90400e7	+	3.31306e7i	0.142875	+	0.0531619i
$159$		−	5.77405e7i		−	0.0903425i
$160$	1.73171e8	+	2.67147e8i	0.264238	+	0.407634i
$161$	3.18623e7			0.0474214
$162$	−2.66873e7	+	7.17234e7i	−0.0387476	+	0.104136i
$163$	−4.97850e8	−	4.97850e8i	−0.705258	−	0.705258i	0.260277	−	0.965534i	$-0.416186\pi$
$163$	−4.97850e8	−	4.97850e8i	−0.705258	−	0.705258i	−0.965534	+	0.260277i	$0.916186\pi$
$164$	3.52267e8	−	4.07830e8i	0.486963	−	0.563772i
$165$	1.90988e8	+	1.90988e8i	0.257674	+	0.257674i
$166$	8.38373e8	−	3.83668e8i	1.10409	−	0.505270i
$167$	6.10230e8			0.784563			0.392282	−	0.919845i	$-0.371686\pi$
$167$	6.10230e8			0.784563			0.392282	+	0.919845i	$0.371686\pi$
$168$	−5.91133e7	−	1.72061e7i	−0.0742076	−	0.0215996i
$169$			7.92138e8i			0.971078i
$170$	2.91339e8	−	1.33327e8i	0.348822	−	0.159633i
$171$	−2.48267e8	+	2.48267e8i	−0.290359	+	0.290359i
$172$	1.00181e9	−	7.32325e7i	1.14465	−	0.0836739i
$173$	3.08198e8	−	3.08198e8i	0.344068	−	0.344068i	−0.513826	−	0.857894i	$-0.671772\pi$
$173$	3.08198e8	−	3.08198e8i	0.344068	−	0.344068i	0.857894	+	0.513826i	$0.171772\pi$
$174$	−2.73880e7	+	7.36066e7i	−0.0298788	+	0.0803007i
$175$			9.59225e7i			0.102275i
$176$	−1.00035e9	−	7.43964e8i	−1.04256	−	0.775356i
$177$	1.18968e8			0.121210
$178$	5.33195e8	+	1.98395e8i	0.531136	+	0.197629i
$179$	7.53399e8	+	7.53399e8i	0.733859	+	0.733859i	0.971382	−	0.237523i	$-0.0763354\pi$
$179$	7.53399e8	+	7.53399e8i	0.733859	+	0.733859i	−0.237523	+	0.971382i	$0.576335\pi$
$180$	1.69534e8	−	1.23929e7i	0.161498	−	0.0118055i
$181$	1.14962e8	+	1.14962e8i	0.107112	+	0.107112i	0.758632	−	0.651520i	$-0.225868\pi$
$181$	1.14962e8	+	1.14962e8i	0.107112	+	0.107112i	−0.651520	+	0.758632i	$0.725868\pi$
$182$	−1.03942e7	−	2.27130e7i	−0.00947344	−	0.0207009i
$183$	6.84456e8			0.610297
$184$	3.55921e8	−	1.95437e8i	0.310514	−	0.170505i
$185$			1.65373e8i			0.141181i
$186$	−2.44010e8	−	5.33198e8i	−0.203871	−	0.445489i
$187$	−8.87160e8	+	8.87160e8i	−0.725497	+	0.725497i
$188$	1.10684e9	−	1.28143e9i	0.886043	−	1.02580i
$189$	−2.32444e7	+	2.32444e7i	−0.0182168	+	0.0182168i
$190$	7.30926e8	+	2.71968e8i	0.560866	+	0.208691i
$191$		−	1.97297e9i		−	1.48247i	−0.671245	−	0.741236i	$-0.734240\pi$
$191$		−	1.97297e9i		−	1.48247i	0.671245	−	0.741236i	$-0.265760\pi$
$192$	−7.65868e8	+	1.70387e8i	−0.563572	+	0.125381i
$193$	−2.10182e9			−1.51484			−0.757419	−	0.652929i	$-0.773540\pi$
$193$	−2.10182e9			−1.51484			−0.757419	+	0.652929i	$0.773540\pi$
$194$	−8.01953e7	+	2.15529e8i	−0.0566164	+	0.152159i
$195$	4.87662e7	+	4.87662e7i	0.0337272	+	0.0337272i
$196$	1.09683e9	+	9.47396e8i	0.743216	+	0.641959i
$197$	9.25864e7	+	9.25864e7i	0.0614727	+	0.0614727i	0.737175	−	0.675702i	$-0.236159\pi$
$197$	9.25864e7	+	9.25864e7i	0.0614727	+	0.0614727i	−0.675702	+	0.737175i	$0.736159\pi$
$198$	−6.05272e8	+	2.76993e8i	−0.393813	+	0.180222i
$199$	3.75161e8			0.239225			0.119612	−	0.992821i	$-0.461835\pi$
$199$	3.75161e8			0.239225			0.119612	+	0.992821i	$0.461835\pi$
$200$	5.88369e8	+	1.07151e9i	0.367731	+	0.669693i
$201$			1.04008e9i			0.637208i
$202$	2.62186e9	−	1.19985e9i	1.57472	−	0.720647i
$203$	−2.38547e7	+	2.38547e7i	−0.0140472	+	0.0140472i
$204$	5.75665e7	+	7.87502e8i	0.0332391	+	0.454706i
$205$	−4.51940e8	+	4.51940e8i	−0.255897	+	0.255897i
$206$	−3.93561e8	+	1.05771e9i	−0.218546	+	0.587352i
$207$		−	2.16804e8i		−	0.118082i
$208$	−2.55427e8	−	1.89961e8i	−0.136462	−	0.101487i
$209$	−3.05392e9			−1.60056
$210$	6.84341e7	+	2.54634e7i	0.0351881	+	0.0130930i
$211$	8.36177e8	+	8.36177e8i	0.421860	+	0.421860i	0.885844	−	0.463984i	$-0.153580\pi$
$211$	8.36177e8	+	8.36177e8i	0.421860	+	0.421860i	−0.463984	+	0.885844i	$0.653580\pi$
$212$	−2.30440e7	−	3.15238e8i	−0.0114081	−	0.156061i
$213$	1.49231e9	+	1.49231e9i	0.725004	+	0.725004i
$214$	4.05751e8	+	8.86627e8i	0.193466	+	0.422752i
$215$	−1.19132e9			−0.557537
$216$	−1.17077e8	+	4.02230e8i	−0.0537843	+	0.184782i
$217$		−	2.51881e8i		−	0.113594i
$218$	−1.64293e9	−	3.59005e9i	−0.727433	−	1.58955i
$219$	−4.67314e8	+	4.67314e8i	−0.203157	+	0.203157i
$220$	1.11893e9	+	9.66490e8i	0.477655	+	0.412579i
$221$	−2.26524e8	+	2.26524e8i	−0.0949610	+	0.0949610i
$222$	−3.81968e8	−	1.42125e8i	−0.157259	−	0.0585138i
$223$		−	3.15369e9i		−	1.27526i	−0.770342	−	0.637631i	$-0.779914\pi$
$223$		−	3.15369e9i		−	1.27526i	0.770342	−	0.637631i	$-0.220086\pi$
$224$	−3.29600e8	−	7.03459e7i	−0.130917	−	0.0279413i
$225$	6.52693e8			0.254671
$226$	8.53594e8	−	2.29407e9i	0.327203	−	0.879374i
$227$	2.85405e9	+	2.85405e9i	1.07487	+	1.07487i	0.996960	+	0.0779139i	$0.0248259\pi$
$227$	2.85405e9	+	2.85405e9i	1.07487	+	1.07487i	0.0779139	+	0.996960i	$0.475174\pi$
$228$	−1.25635e9	+	1.45451e9i	−0.464912	+	0.538243i
$229$	4.08940e8	+	4.08940e8i	0.148702	+	0.148702i	0.777538	−	0.628836i	$-0.216468\pi$
$229$	4.08940e8	+	4.08940e8i	0.148702	+	0.148702i	−0.628836	+	0.777538i	$0.716468\pi$
$230$	−4.37897e8	+	2.00397e8i	−0.156481	+	0.0716109i
$231$	−2.85928e8			−0.100417
$232$	−1.20151e8	+	4.12790e8i	−0.0414738	+	0.142488i
$233$			3.36265e8i			0.114093i	0.998372	+	0.0570463i	$0.0181683\pi$
$233$			3.36265e8i			0.114093i	−0.998372	+	0.0570463i	$0.981832\pi$
$234$	−1.54548e8	+	7.07264e7i	−0.0515466	+	0.0235895i
$235$	−1.42002e9	+	1.42002e9i	−0.465612	+	0.465612i
$236$	6.49516e8	−	4.74797e7i	0.209383	−	0.0153059i
$237$	1.96350e8	−	1.96350e8i	0.0622354	−	0.0622354i
$238$	−1.18280e8	+	3.17884e8i	−0.0368641	+	0.0990741i
$239$		−	4.68464e8i		−	0.143577i	−0.997420	−	0.0717885i	$-0.977129\pi$
$239$		−	4.68464e8i		−	0.143577i	0.997420	−	0.0717885i	$-0.0228707\pi$
$240$	9.20635e8	−	1.35320e8i	0.277487	−	0.0407866i
$241$	−6.11577e9			−1.81294			−0.906469	−	0.422273i	$-0.861232\pi$
$241$	−6.11577e9			−1.81294			−0.906469	+	0.422273i	$0.861232\pi$
$242$	−2.21192e9	−	8.23024e8i	−0.644922	−	0.239967i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$	3.73684e9	−	2.73163e8i	1.05425	−	0.0770660i
$245$	−1.21546e9	−	1.21546e9i	−0.337347	−	0.337347i
$246$	−6.55456e8	−	1.43227e9i	−0.178979	−	0.391097i
$247$	−7.79777e8			−0.209499
$248$	−1.54498e9	−	2.81365e9i	−0.408430	−	0.743812i
$249$		−	2.69483e9i		−	0.701027i
$250$	−1.39295e9	−	3.04380e9i	−0.356594	−	0.779213i
$251$	8.62591e8	−	8.62591e8i	0.217325	−	0.217325i	−0.590045	−	0.807370i	$-0.700890\pi$
$251$	8.62591e8	−	8.62591e8i	0.217325	−	0.217325i	0.807370	+	0.590045i	$0.200890\pi$
$252$	−1.17628e8	+	1.36181e8i	−0.0291680	+	0.0337687i
$253$	1.33344e9	−	1.33344e9i	0.325456	−	0.325456i
$254$	−3.65396e9	−	1.35959e9i	−0.877867	−	0.326642i
$255$		−	9.36469e8i		−	0.221479i
$256$	−4.11331e9	+	1.23590e9i	−0.957704	+	0.287755i
$257$	−6.89191e9			−1.57982			−0.789909	−	0.613223i	$-0.789873\pi$
$257$	−6.89191e9			−1.57982			−0.789909	+	0.613223i	$0.789873\pi$
$258$	1.02385e9	−	2.75163e9i	0.231076	−	0.621029i
$259$	−1.23790e8	−	1.23790e8i	−0.0275096	−	0.0275096i
$260$	2.85705e8	+	2.46780e8i	0.0625207	+	0.0540028i
$261$	1.62316e8	+	1.62316e8i	0.0349785	+	0.0349785i
$262$	−2.08687e8	+	9.55021e7i	−0.0442883	+	0.0202679i
$263$	8.36743e9			1.74892			0.874459	−	0.485100i	$-0.161217\pi$
$263$	8.36743e9			1.74892			0.874459	+	0.485100i	$0.161217\pi$
$264$	−3.19398e9	+	1.75383e9i	−0.657531	+	0.361053i
$265$			3.74870e8i			0.0760147i
$266$	−7.50716e8	+	3.43553e8i	−0.149951	+	0.0686226i
$267$	1.17580e9	−	1.17580e9i	0.231359	−	0.231359i
$268$	4.15090e8	+	5.67837e9i	0.0804643	+	1.10074i
$269$	4.28997e9	−	4.28997e9i	0.819304	−	0.819304i	−0.166703	−	0.986007i	$-0.553312\pi$
$269$	4.28997e9	−	4.28997e9i	0.819304	−	0.819304i	0.986007	+	0.166703i	$0.0533122\pi$
$270$	1.73263e8	−	4.65652e8i	0.0326024	−	0.0876206i
$271$		−	6.13114e9i		−	1.13675i	−0.822770	−	0.568374i	$-0.807573\pi$
$271$		−	6.13114e9i		−	1.13675i	0.822770	−	0.568374i	$-0.192427\pi$
$272$	6.28577e8	+	4.27645e9i	0.114837	+	0.781281i
$273$	−7.30078e7			−0.0131437
$274$	−8.14931e9	−	3.03225e9i	−1.44583	−	0.537976i
$275$	4.01437e9	+	4.01437e9i	0.701919	+	0.701919i
$276$	−8.65253e7	−	1.18365e9i	−0.0149110	−	0.203980i
$277$	4.63135e9	+	4.63135e9i	0.786662	+	0.786662i	0.980945	−	0.194283i	$-0.0622381\pi$
$277$	4.63135e9	+	4.63135e9i	0.786662	+	0.786662i	−0.194283	+	0.980945i	$0.562238\pi$
$278$	4.77326e9	+	1.04303e10i	0.799164	+	1.74630i
$279$	−1.71389e9			−0.282857
$280$	3.83783e8	+	1.11707e8i	0.0624386	+	0.0181740i
$281$		−	2.92015e9i		−	0.468361i	−0.972193	−	0.234180i	$-0.924759\pi$
$281$		−	2.92015e9i		−	0.468361i	0.972193	−	0.234180i	$-0.0752406\pi$
$282$	−2.05948e9	−	4.50028e9i	−0.325658	−	0.711612i
$283$	4.73143e9	−	4.73143e9i	0.737644	−	0.737644i	−0.234477	−	0.972122i	$-0.575338\pi$
$283$	4.73143e9	−	4.73143e9i	0.737644	−	0.737644i	0.972122	+	0.234477i	$0.0753378\pi$
$284$	8.74294e9	+	7.55179e9i	1.34395	+	1.16085i
$285$	1.61183e9	−	1.61183e9i	0.244309	−	0.244309i
$286$	−1.38554e9	−	5.15542e8i	−0.207089	−	0.0770549i
$287$		−	6.76598e8i		−	0.0997249i
$288$	−4.78660e8	+	2.24272e9i	−0.0695757	+	0.325991i
$289$	−2.62576e9			−0.376412
$290$	1.77812e8	−	4.77878e8i	0.0251402	−	0.0675655i
$291$	4.75282e8	+	4.75282e8i	0.0662795	+	0.0662795i
$292$	−2.36483e9	+	2.73783e9i	−0.325288	+	0.376596i
$293$	4.99670e9	+	4.99670e9i	0.677973	+	0.677973i	0.959541	−	0.281568i	$-0.0908546\pi$
$293$	4.99670e9	+	4.99670e9i	0.677973	+	0.677973i	−0.281568	+	0.959541i	$0.590855\pi$
$294$	3.85199e9	−	1.76280e9i	0.515580	−	0.235947i
$295$	−7.72381e8			−0.101987
$296$	−2.14210e9	−	6.23500e8i	−0.279044	−	0.0812212i
$297$			1.94556e9i			0.250046i
$298$	3.11580e9	−	1.42590e9i	0.395098	−	0.180810i
$299$	3.40477e8	−	3.40477e8i	0.0425993	−	0.0425993i
$300$	3.56342e9	−	2.60487e8i	0.439929	−	0.0321589i
$301$	8.91760e8	−	8.91760e8i	0.108638	−	0.108638i
$302$	−4.43784e9	+	1.19269e10i	−0.533512	+	1.43384i
$303$		−	8.42761e9i		−	0.999848i
$304$	−6.27864e9	+	8.44242e9i	−0.735141	+	0.988491i
$305$	−4.44371e9			−0.513507
$306$	2.16300e9	+	8.04823e8i	0.246701	+	0.0917941i
$307$	2.24003e9	+	2.24003e9i	0.252174	+	0.252174i	0.821861	−	0.569687i	$-0.192936\pi$
$307$	2.24003e9	+	2.24003e9i	0.252174	+	0.252174i	−0.569687	+	0.821861i	$0.692936\pi$
$308$	−1.56104e9	+	1.14113e8i	−0.173465	+	0.0126803i
$309$	2.33246e9	+	2.33246e9i	0.255847	+	0.255847i
$310$	1.58419e9	+	3.46170e9i	0.171538	+	0.374837i
$311$	1.74578e10			1.86616			0.933080	−	0.359669i	$-0.117110\pi$
$311$	1.74578e10			1.86616			0.933080	+	0.359669i	$0.117110\pi$
$312$	−8.15539e8	+	4.47815e8i	−0.0860649	+	0.0472585i
$313$		−	5.39649e8i		−	0.0562256i	−0.999605	−	0.0281128i	$-0.991050\pi$
$313$		−	5.39649e8i		−	0.0562256i	0.999605	−	0.0281128i	$-0.00894976\pi$
$314$	−6.17253e8	−	1.34879e9i	−0.0634957	−	0.138748i
$315$	1.50910e8	−	1.50910e8i	0.0153277	−	0.0153277i
$316$	9.93624e8	−	1.15035e9i	0.0996492	−	0.115367i
$317$	−1.14777e10	+	1.14777e10i	−1.13663	+	1.13663i	−0.147581	+	0.989050i	$0.547149\pi$
$317$	−1.14777e10	+	1.14777e10i	−1.13663	+	1.13663i	−0.989050	+	0.147581i	$0.952851\pi$
$318$	−8.65853e8	−	3.22172e8i	−0.0846712	−	0.0315050i
$319$			1.99665e9i			0.192814i
$320$	4.97226e9	−	1.10621e9i	0.474192	−	0.105496i
$321$	2.84994e9			0.268420
$322$	1.77781e8	−	4.77794e8i	0.0165372	−	0.0444445i
$323$	7.48713e9	+	7.48713e9i	0.687868	+	0.687868i
$324$	9.26628e8	+	8.00383e8i	0.0840863	+	0.0726303i
$325$	1.02502e9	+	1.02502e9i	0.0918749	+	0.0918749i
$326$	−1.02434e10	+	4.68772e9i	−0.906927	+	0.415041i
$327$	−1.15397e10			−1.00926
$328$	−4.15012e9	−	7.55799e9i	−0.358563	−	0.652997i
$329$		−	2.12591e9i		−	0.181452i
$330$	3.92962e9	−	1.79833e9i	0.331356	−	0.151640i
$331$	−4.68871e9	+	4.68871e9i	−0.390608	+	0.390608i	−0.874904	−	0.484296i	$-0.839076\pi$
$331$	−4.68871e9	+	4.68871e9i	−0.390608	+	0.390608i	0.484296	+	0.874904i	$0.339076\pi$
$332$	−1.07549e9	−	1.47126e10i	−0.0885230	−	1.21098i
$333$	−8.42312e8	+	8.42312e8i	−0.0685008	+	0.0685008i
$334$	3.40487e9	−	9.15076e9i	0.273599	−	0.735311i
$335$		−	6.75252e9i		−	0.536150i
$336$	−5.87847e8	+	7.90435e8i	−0.0461219	+	0.0620167i
$337$	1.49622e10			1.16005			0.580025	−	0.814599i	$-0.303043\pi$
$337$	1.49622e10			1.16005			0.580025	+	0.814599i	$0.303043\pi$
$338$	1.18786e10	+	4.41986e9i	0.910118	+	0.338643i
$339$	−5.05887e9	−	5.05887e9i	−0.383049	−	0.383049i
$340$	−3.73740e8	−	5.11272e9i	−0.0279676	−	0.382592i
$341$	−1.05412e10	−	1.05412e10i	−0.779604	−	0.779604i
$342$	2.33767e9	+	5.10816e9i	0.170875	+	0.373387i
$343$	3.67253e9			0.265332
$344$	4.49159e9	−	1.54313e10i	0.320750	−	1.10197i
$345$			1.40756e9i			0.0993551i
$346$	−2.90197e9	−	6.34124e9i	−0.202483	−	0.442456i
$347$	−1.34112e10	+	1.34112e10i	−0.925016	+	0.925016i	−0.997378	−	0.0723626i	$-0.976946\pi$
$347$	−1.34112e10	+	1.34112e10i	−0.925016	+	0.925016i	0.0723626	+	0.997378i	$0.476946\pi$
$348$	9.50958e8	+	8.21398e8i	0.0648402	+	0.0560063i
$349$	1.93059e10	−	1.93059e10i	1.30134	−	1.30134i	0.373843	−	0.927492i	$-0.378040\pi$
$349$	1.93059e10	−	1.93059e10i	1.30134	−	1.30134i	0.927492	−	0.373843i	$-0.121960\pi$
$350$	1.43841e9	+	5.35214e8i	0.0958543	+	0.0356661i
$351$			4.96773e8i			0.0327288i
$352$	−1.67378e10	+	1.08498e10i	−1.09025	+	0.706728i
$353$	−2.03892e10			−1.31311			−0.656555	−	0.754278i	$-0.727987\pi$
$353$	−2.03892e10			−1.31311			−0.656555	+	0.754278i	$0.727987\pi$
$354$	6.63802e8	−	1.78400e9i	0.0422693	−	0.113601i
$355$	−9.68856e9	−	9.68856e9i	−0.610022	−	0.610022i
$356$	5.95008e9	−	6.88859e9i	0.370444	−	0.428875i
$357$	7.00994e8	+	7.00994e8i	0.0431560	+	0.0431560i
$358$	1.55014e10	−	7.09395e9i	0.943708	−	0.431873i
$359$	−2.14611e10			−1.29203			−0.646016	−	0.763324i	$-0.723566\pi$
$359$	−2.14611e10			−1.29203			−0.646016	+	0.763324i	$0.723566\pi$
$360$	7.60100e8	−	2.61140e9i	0.0452544	−	0.155476i
$361$			8.78979e9i			0.517547i
$362$	2.36537e9	−	1.08247e9i	0.137741	−	0.0630351i
$363$	−4.87769e9	+	4.87769e9i	−0.280924	+	0.280924i
$364$	−3.98591e8	+	2.91371e7i	−0.0227050	+	0.00165974i
$365$	3.03395e9	−	3.03395e9i	0.170937	−	0.170937i
$366$	3.81903e9	−	1.02638e10i	0.212828	−	0.571985i
$367$		−	5.54772e9i		−	0.305809i	−0.988241	−	0.152905i	$-0.951137\pi$
$367$		−	5.54772e9i		−	0.305809i	0.988241	−	0.152905i	$-0.0488627\pi$
$368$	−9.44781e8	−	6.42771e9i	−0.0515157	−	0.350481i
$369$	−4.60383e9			−0.248321
$370$	2.47986e9	+	9.22722e8i	0.132318	+	0.0492339i
$371$	−2.80609e8	−	2.80609e8i	−0.0148117	−	0.0148117i
$372$	−9.35711e9	+	6.84006e8i	−0.488618	+	0.0357181i
$373$	2.11197e10	+	2.11197e10i	1.09107	+	1.09107i	0.995414	+	0.0956566i	$0.0304951\pi$
$373$	2.11197e10	+	2.11197e10i	1.09107	+	1.09107i	0.0956566	+	0.995414i	$0.469505\pi$
$374$	8.35344e9	+	1.82535e10i	0.426952	+	0.932954i
$375$	−9.78387e9			−0.494750
$376$	−1.30399e10	−	2.37477e10i	−0.652415	−	1.18815i
$377$			5.09816e8i			0.0252376i
$378$	2.18868e8	+	4.78259e8i	0.0107205	+	0.0234259i
$379$	−1.43672e10	+	1.43672e10i	−0.696329	+	0.696329i	−0.963617	−	0.267288i	$-0.913873\pi$
$379$	−1.43672e10	+	1.43672e10i	−0.696329	+	0.696329i	0.267288	+	0.963617i	$0.413873\pi$
$380$	8.15663e9	−	9.44317e9i	0.391180	−	0.452881i
$381$	−8.05767e9	+	8.05767e9i	−0.382393	+	0.382393i
$382$	−2.95858e10	−	1.10085e10i	−1.38941	−	0.516980i
$383$			2.68615e10i			1.24835i	0.781285	+	0.624174i	$0.214565\pi$
$383$			2.68615e10i			1.24835i	−0.781285	+	0.624174i	$0.785435\pi$
$384$	−1.71822e9	+	1.24353e10i	−0.0790230	+	0.571917i
$385$	1.85634e9			0.0844917
$386$	−1.17274e10	+	3.15180e10i	−0.528267	+	1.41974i
$387$	−6.06788e9	−	6.06788e9i	−0.270516	−	0.270516i
$388$	2.78452e9	+	2.40515e9i	0.122863	+	0.106124i
$389$	−2.88548e10	−	2.88548e10i	−1.26014	−	1.26014i	−0.951023	−	0.309121i	$-0.899965\pi$
$389$	−2.88548e10	−	2.88548e10i	−1.26014	−	1.26014i	−0.309121	−	0.951023i	$-0.600035\pi$
$390$	1.00338e9	−	4.59179e8i	0.0433716	−	0.0198483i
$391$	−6.53826e9			−0.279740
$392$	2.03267e10	−	1.11615e10i	0.860840	−	0.472690i
$393$			6.70794e8i			0.0281202i
$394$	1.90499e9	−	8.71787e8i	0.0790509	−	0.0361764i
$395$	−1.27477e9	+	1.27477e9i	−0.0523652	+	0.0523652i
$396$	7.76465e8	+	1.06219e10i	0.0315748	+	0.431940i
$397$	9.47205e9	−	9.47205e9i	0.381313	−	0.381313i	−0.490262	−	0.871575i	$-0.663099\pi$
$397$	9.47205e9	−	9.47205e9i	0.381313	−	0.381313i	0.871575	+	0.490262i	$0.163099\pi$
$398$	2.09327e9	−	5.62576e9i	0.0834244	−	0.224207i
$399$			2.41307e9i			0.0952091i
$400$	1.93508e10	−	2.84429e9i	0.755891	−	0.111105i
$401$	1.16717e10			0.451397			0.225698	−	0.974197i	$-0.427534\pi$
$401$	1.16717e10			0.451397			0.225698	+	0.974197i	$0.427534\pi$
$402$	1.55966e10	+	5.80327e9i	0.597207	+	0.222213i
$403$	−2.69156e9	−	2.69156e9i	−0.102043	−	0.102043i
$404$	−3.36342e9	−	4.60111e10i	−0.126257	−	1.72718i
$405$	−1.02685e9	−	1.02685e9i	−0.0381669	−	0.0381669i
$406$	2.24614e8	+	4.90816e8i	0.00826672	+	0.0180640i
$407$	−1.03612e10			−0.377601
$408$	1.21303e10	+	3.53075e9i	0.437753	+	0.127417i
$409$			2.04558e10i			0.731008i	0.930810	+	0.365504i	$0.119103\pi$
$409$			2.04558e10i			0.731008i	−0.930810	+	0.365504i	$0.880897\pi$
$410$	4.25543e9	+	9.29876e9i	0.150594	+	0.329071i
$411$	−1.79708e10	+	1.79708e10i	−0.629796	+	0.629796i
$412$	1.36651e10	+	1.18033e10i	0.474268	+	0.409653i
$413$	5.78165e8	−	5.78165e8i	0.0198725	−	0.0198725i
$414$	−3.25110e9	−	1.20969e9i	−0.110670	−	0.0411787i
$415$			1.74957e10i			0.589847i
$416$	−4.27377e9	+	2.77035e9i	−0.142705	+	0.0925043i
$417$	3.35268e10			1.10878
$418$	−1.70398e10	+	4.57953e10i	−0.558162	+	1.50009i
$419$	1.07657e10	+	1.07657e10i	0.349291	+	0.349291i	0.859845	−	0.510554i	$-0.170560\pi$
$419$	1.07657e10	+	1.07657e10i	0.349291	+	0.349291i	−0.510554	+	0.859845i	$0.670560\pi$
$420$	7.63677e8	−	8.84132e8i	0.0245421	−	0.0284132i
$421$	1.52423e9	+	1.52423e9i	0.0485203	+	0.0485203i	0.730951	−	0.682430i	$-0.239077\pi$
$421$	1.52423e9	+	1.52423e9i	0.0485203	+	0.0485203i	−0.682430	+	0.730951i	$0.739077\pi$
$422$	1.72045e10	−	7.87338e9i	0.542492	−	0.248263i
$423$	−1.44655e10			−0.451828
$424$	−4.85576e9	−	1.41336e9i	−0.150243	−	0.0437311i
$425$		−	1.96836e10i		−	0.603322i
$426$	3.07046e10	−	1.40515e10i	0.932321	−	0.426662i
$427$	3.32634e9	−	3.32634e9i	0.100059	−	0.100059i
$428$	1.55594e10	−	1.13740e9i	0.463680	−	0.0338951i
$429$	−3.05539e9	+	3.05539e9i	−0.0902064	+	0.0902064i
$430$	−6.64714e9	+	1.78645e10i	−0.194429	+	0.522537i
$431$		−	1.69058e10i		−	0.489923i	−0.969533	−	0.244962i	$-0.921225\pi$
$431$		−	1.69058e10i		−	0.489923i	0.969533	−	0.244962i	$-0.0787753\pi$
$432$	5.37842e9	+	3.99994e9i	0.154426	+	0.114847i
$433$	6.20156e10			1.76421			0.882103	−	0.471057i	$-0.156128\pi$
$433$	6.20156e10			1.76421			0.882103	+	0.471057i	$0.156128\pi$
$434$	−3.77709e9	−	1.40541e9i	−0.106463	−	0.0396135i
$435$	−1.05381e9	−	1.05381e9i	−0.0294311	−	0.0294311i
$436$	−6.30019e10	+	4.60544e9i	−1.74344	+	0.127446i
$437$	−1.12535e10	−	1.12535e10i	−0.308576	−	0.308576i
$438$	4.40019e9	+	9.61509e9i	0.119557	+	0.261250i
$439$	1.12319e10			0.302408			0.151204	−	0.988503i	$-0.451685\pi$
$439$	1.12319e10			0.302408			0.151204	+	0.988503i	$0.451685\pi$
$440$	2.07363e10	−	1.13864e10i	0.553250	−	0.303792i
$441$		−	1.23817e10i		−	0.327360i
$442$	2.13293e9	+	4.66079e9i	0.0558841	+	0.122115i
$443$	3.31396e10	−	3.31396e10i	0.860464	−	0.860464i	−0.130928	−	0.991392i	$-0.541796\pi$
$443$	3.31396e10	−	3.31396e10i	0.860464	−	0.860464i	0.991392	+	0.130928i	$0.0417957\pi$
$444$	−4.26249e9	+	4.93482e9i	−0.109681	+	0.126981i
$445$	−7.63365e9	+	7.63365e9i	−0.194667	+	0.194667i
$446$	−4.72914e10	−	1.75965e10i	−1.19521	−	0.444720i
$447$		−	1.00153e10i		−	0.250862i
$448$	−2.89393e9	+	4.55004e9i	−0.0718416	+	0.112954i
$449$	1.60349e10			0.394531			0.197266	−	0.980350i	$-0.436794\pi$
$449$	1.60349e10			0.394531			0.197266	+	0.980350i	$0.436794\pi$
$450$	3.64180e9	−	9.78752e9i	0.0888109	−	0.238684i
$451$	−2.83158e10	−	2.83158e10i	−0.684419	−	0.684419i
$452$	−2.96382e10	−	2.56003e10i	−0.710065	−	0.613325i
$453$	2.63011e10	+	2.63011e10i	0.624570	+	0.624570i
$454$	5.87227e10	−	2.68735e10i	1.38224	−	0.632559i
$455$	4.73990e8			0.0110592
$456$	1.48013e10	+	2.69554e10i	0.342326	+	0.623427i
$457$			1.43942e9i			0.0330008i	0.999864	+	0.0165004i	$0.00525247\pi$
$457$			1.43942e9i			0.0330008i	−0.999864	+	0.0165004i	$0.994748\pi$
$458$	8.41404e9	−	3.85055e9i	0.191224	−	0.0875106i
$459$	4.76983e9	−	4.76983e9i	0.107461	−	0.107461i
$460$	5.61750e8	+	7.68466e9i	0.0125462	+	0.171630i
$461$	−9.71534e8	+	9.71534e8i	−0.0215107	+	0.0215107i	−0.717780	−	0.696270i	$-0.754842\pi$
$461$	−9.71534e8	+	9.71534e8i	−0.0215107	+	0.0215107i	0.696270	+	0.717780i	$0.254842\pi$
$462$	−1.59538e9	+	4.28766e9i	−0.0350184	+	0.0941136i
$463$			8.99701e10i			1.95783i	0.204278	+	0.978913i	$0.434515\pi$
$463$			8.99701e10i			1.95783i	−0.204278	+	0.978913i	$0.565485\pi$
$464$	5.51963e9	+	4.10496e9i	0.119080	+	0.0885598i
$465$	1.11271e10			0.237997
$466$	5.04248e9	+	1.87624e9i	0.106930	+	0.0397873i
$467$	5.62958e9	+	5.62958e9i	0.118361	+	0.118361i	0.763806	−	0.645445i	$-0.223328\pi$
$467$	5.62958e9	+	5.62958e9i	0.118361	+	0.118361i	−0.645445	+	0.763806i	$0.723328\pi$
$468$	1.98260e8	+	2.71217e9i	0.00413286	+	0.0565370i
$469$	5.05460e9	+	5.05460e9i	0.104471	+	0.104471i
$470$	1.33708e10	+	2.92173e10i	0.274010	+	0.598754i
$471$	−4.33550e9			−0.0880959
$472$	2.91209e9	−	1.00048e10i	0.0586727	−	0.201576i
$473$		−	7.46406e10i		−	1.49118i
$474$	−1.84882e9	−	4.03995e9i	−0.0366253	−	0.0800318i
$475$	3.38790e10	−	3.38790e10i	0.665513	−	0.665513i
$476$	4.10689e9	+	3.54736e9i	0.0799991	+	0.0690999i
$477$	−1.90937e9	+	1.90937e9i	−0.0368822	+	0.0368822i
$478$	−7.02490e9	−	2.61387e9i	−0.134564	−	0.0500694i
$479$			2.84189e10i			0.539841i	0.962883	+	0.269921i	$0.0869974\pi$
$479$			2.84189e10i			0.539841i	−0.962883	+	0.269921i	$0.913003\pi$
$480$	3.10762e9	−	1.45605e10i	0.0585414	−	0.274291i
$481$	−2.64560e9			−0.0494246
$482$	−3.41239e10	+	9.17095e10i	−0.632223	+	1.69913i
$483$	−1.05363e9	−	1.05363e9i	−0.0193597	−	0.0193597i
$484$	−2.46834e10	+	2.85768e10i	−0.449805	+	0.520753i
$485$	−3.08568e9	−	3.08568e9i	−0.0557679	−	0.0557679i
$486$	3.25426e9	−	1.48926e9i	0.0583320	−	0.0266947i
$487$	4.99046e10			0.887206			0.443603	−	0.896223i	$-0.353700\pi$
$487$	4.99046e10			0.887206			0.443603	+	0.896223i	$0.353700\pi$
$488$	1.67540e10	−	5.75602e10i	0.295420	−	1.01495i
$489$			3.29259e10i			0.575840i
$490$	−2.50084e10	+	1.14447e10i	−0.433812	+	0.198527i
$491$	2.50716e10	−	2.50716e10i	0.431376	−	0.431376i	−0.457720	−	0.889096i	$-0.651334\pi$
$491$	2.50716e10	−	2.50716e10i	0.431376	−	0.431376i	0.889096	+	0.457720i	$0.151334\pi$
$492$	−2.51349e10	+	1.83737e9i	−0.428961	+	0.0313571i
$493$	4.89507e9	−	4.89507e9i	0.0828649	−	0.0828649i
$494$	−4.35088e9	+	1.16932e10i	−0.0730583	+	0.196348i
$495$		−	1.26312e10i		−	0.210390i
$496$	−5.08128e10	+	7.46875e9i	−0.839549	+	0.123402i
$497$	1.45047e10			0.237730
$498$	−4.04106e10	−	1.50362e10i	−0.657019	−	0.244468i
$499$	−6.45686e10	−	6.45686e10i	−1.04140	−	1.04140i	−0.999105	−	0.0422994i	$-0.986532\pi$
$499$	−6.45686e10	−	6.45686e10i	−1.04140	−	1.04140i	−0.0422994	−	0.999105i	$-0.513468\pi$
$500$	−5.34157e10	+	3.90470e9i	−0.854651	+	0.0624751i
$501$	−2.01792e10	−	2.01792e10i	−0.320297	−	0.320297i
$502$	−8.12210e9	−	1.77480e10i	−0.127895	−	0.279470i
$503$	3.98044e10			0.621813			0.310906	−	0.950441i	$-0.399367\pi$
$503$	3.98044e10			0.621813			0.310906	+	0.950441i	$0.399367\pi$
$504$	1.38579e9	+	2.52374e9i	0.0214771	+	0.0391131i
$505$			5.47148e10i			0.841277i
$506$	−1.25556e10	−	2.74359e10i	−0.191530	−	0.418521i
$507$	2.61945e10	−	2.61945e10i	0.396441	−	0.396441i
$508$	−4.07756e10	+	4.72072e10i	−0.612274	+	0.708848i
$509$	−8.83621e10	+	8.83621e10i	−1.31642	+	1.31642i	−0.399832	+	0.916588i	$0.630932\pi$
$509$	−8.83621e10	+	8.83621e10i	−1.31642	+	1.31642i	−0.916588	+	0.399832i	$0.869068\pi$
$510$	−1.40429e10	−	5.22517e9i	−0.207576	−	0.0772361i
$511$			4.54213e9i			0.0666156i
$512$	−4.41785e9	+	6.85773e10i	−0.0642881	+	0.997931i
$513$	1.64195e10			0.237077
$514$	−3.84545e10	+	1.03348e11i	−0.550928	+	1.48064i
$515$	−1.51431e10	−	1.51431e10i	−0.215271	−	0.215271i
$516$	−3.55496e10	−	3.07063e10i	−0.501460	−	0.433141i
$517$	−8.89699e10	−	8.89699e10i	−1.24532	−	1.24532i
$518$	−2.54700e9	+	1.16559e9i	−0.0353761	+	0.0161893i
$519$	−2.03830e10			−0.280931
$520$	5.29474e9	−	2.90736e9i	0.0724155	−	0.0397636i
$521$		−	3.23543e9i		−	0.0439118i	−0.999759	−	0.0219559i	$-0.993011\pi$
$521$		−	3.23543e9i		−	0.0439118i	0.999759	−	0.0219559i	$-0.00698935\pi$
$522$	3.33970e9	−	1.52836e9i	0.0449806	−	0.0205847i
$523$	5.28959e10	−	5.28959e10i	0.706994	−	0.706994i	−0.258908	−	0.965902i	$-0.583363\pi$
$523$	5.28959e10	−	5.28959e10i	0.706994	−	0.706994i	0.965902	+	0.258908i	$0.0833627\pi$
$524$	2.67711e8	+	3.66225e9i	0.00355092	+	0.0485761i
$525$	3.17198e9	−	3.17198e9i	0.0417535	−	0.0417535i
$526$	4.66874e10	−	1.25475e11i	0.609897	−	1.63913i
$527$			5.16867e10i			0.670095i
$528$	8.47833e9	+	5.76813e10i	0.109087	+	0.742163i
$529$	−6.84837e10			−0.874509
$530$	5.62140e9	+	2.09165e9i	0.0712428	+	0.0265085i
$531$	−3.93406e9	−	3.93406e9i	−0.0494838	−	0.0494838i
$532$	9.63045e8	+	1.31743e10i	0.0120226	+	0.164468i
$533$	−7.23004e9	−	7.23004e9i	−0.0895843	−	0.0895843i
$534$	−1.10712e10	−	2.41923e10i	−0.136154	−	0.297517i
$535$	−1.85027e10			−0.225850
$536$	8.74666e10	+	2.54588e10i	1.05970	+	0.308446i
$537$		−	4.98270e10i		−	0.599194i
$538$	−4.03940e10	−	8.82671e10i	−0.482157	−	1.05359i
$539$	7.61533e10	−	7.61533e10i	0.902264	−	0.902264i
$540$	−6.01597e9	−	5.19635e9i	−0.0707507	−	0.0611115i
$541$	7.06245e10	−	7.06245e10i	0.824454	−	0.824454i	−0.162289	−	0.986743i	$-0.551888\pi$
$541$	7.06245e10	−	7.06245e10i	0.824454	−	0.824454i	0.986743	+	0.162289i	$0.0518878\pi$
$542$	−9.19401e10	−	3.42097e10i	−1.06539	−	0.396416i
$543$		−	7.60314e9i		−	0.0874568i
$544$	6.76351e10	+	1.44352e10i	0.772283	+	0.164827i
$545$	7.49196e10			0.849199
$546$	−4.07358e8	+	1.09479e9i	−0.00458359	+	0.0123186i
$547$	−6.56817e10	−	6.56817e10i	−0.733660	−	0.733660i	0.237683	−	0.971343i	$-0.423612\pi$
$547$	−6.56817e10	−	6.56817e10i	−0.733660	−	0.733660i	−0.971343	+	0.237683i	$0.923612\pi$
$548$	−9.09407e10	+	1.05285e11i	−1.00841	+	1.16746i
$549$	−2.26337e10	−	2.26337e10i	−0.249153	−	0.249153i
$550$	8.25967e10	−	3.77991e10i	0.902634	−	0.413076i
$551$	1.68506e10			0.182813
$552$	−1.82324e10	−	5.30688e9i	−0.196375	−	0.0571588i
$553$		−	1.90845e9i		−	0.0204071i
$554$	9.52911e10	−	4.36084e10i	1.01161	−	0.462947i
$555$	5.46856e9	−	5.46856e9i	0.0576369	−	0.0576369i
$556$	1.83042e11	−	1.33804e10i	1.91536	−	0.140013i
$557$	−1.17862e11	+	1.17862e11i	−1.22449	+	1.22449i	−0.258468	+	0.966020i	$0.583218\pi$
$557$	−1.17862e11	+	1.17862e11i	−1.22449	+	1.22449i	−0.966020	+	0.258468i	$0.916782\pi$
$558$	−9.56292e9	+	2.57008e10i	−0.0986401	+	0.265100i
$559$		−	1.90585e10i		−	0.195182i
$560$	3.81649e9	−	5.13176e9i	0.0388072	−	0.0521812i
$561$	5.86734e10			0.592366
$562$	−4.37894e10	−	1.62934e10i	−0.438959	−	0.163331i
$563$	1.16659e11	+	1.16659e11i	1.16114	+	1.16114i	0.984226	+	0.176917i	$0.0566123\pi$
$563$	1.16659e11	+	1.16659e11i	1.16114	+	1.16114i	0.176917	+	0.984226i	$0.443388\pi$
$564$	−7.89756e10	+	5.77313e9i	−0.780506	+	0.0570551i
$565$	3.28438e10	+	3.28438e10i	0.322300	+	0.322300i
$566$	−4.45508e10	−	9.73504e10i	−0.434100	−	0.948575i
$567$	1.53730e9			0.0148739
$568$	1.62026e11	−	8.89691e10i	1.55665	−	0.854763i
$569$		−	1.87613e9i		−	0.0178984i	−0.999960	−	0.00894921i	$-0.997151\pi$
$569$		−	1.87613e9i		−	0.0178984i	0.999960	−	0.00894921i	$-0.00284866\pi$
$570$	−1.51769e10	−	3.31638e10i	−0.143775	−	0.314170i
$571$	4.05487e10	−	4.05487e10i	0.381445	−	0.381445i	−0.490177	−	0.871623i	$-0.663068\pi$
$571$	4.05487e10	−	4.05487e10i	0.381445	−	0.381445i	0.871623	+	0.490177i	$0.163068\pi$
$572$	−1.54617e10	+	1.79005e10i	−0.144435	+	0.167217i
$573$	−6.52423e10	+	6.52423e10i	−0.605216	+	0.605216i
$574$	−1.01460e10	−	3.77518e9i	−0.0934645	−	0.0347769i
$575$			2.95854e10i			0.270649i
$576$	3.09602e10	+	1.96914e10i	0.281264	+	0.178890i
$577$	−1.27347e11			−1.14891			−0.574456	−	0.818536i	$-0.694786\pi$
$577$	−1.27347e11			−1.14891			−0.574456	+	0.818536i	$0.694786\pi$
$578$	−1.46508e10	+	3.93748e10i	−0.131265	+	0.352782i
$579$	6.95032e10	+	6.95032e10i	0.618430	+	0.618430i
$580$	−6.17393e9	−	5.33278e9i	−0.0545569	−	0.0471240i
$581$	−1.30964e10	−	1.30964e10i	−0.114934	−	0.114934i
$582$	9.77903e9	−	4.47522e9i	0.0852323	−	0.0390052i
$583$	−2.34871e10			−0.203308
$584$	2.78605e10	+	5.07381e10i	0.239518	+	0.436198i
$585$		−	3.22521e9i		−	0.0275381i
$586$	1.02808e11	−	4.70485e10i	0.871841	−	0.398984i
$587$	−9.06324e10	+	9.06324e10i	−0.763363	+	0.763363i	−0.976929	−	0.213566i	$-0.931492\pi$
$587$	−9.06324e10	+	9.06324e10i	−0.763363	+	0.763363i	0.213566	+	0.976929i	$0.431492\pi$
$588$	−4.94147e9	−	6.75987e10i	−0.0413378	−	0.565495i
$589$	−8.89621e10	+	8.89621e10i	−0.739169	+	0.739169i
$590$	−4.30962e9	+	1.15823e10i	−0.0355657	+	0.0955844i
$591$		−	6.12331e9i		−	0.0501922i
$592$	−2.13019e10	+	2.86431e10i	−0.173433	+	0.233203i
$593$	−4.31542e10			−0.348983			−0.174491	−	0.984659i	$-0.555828\pi$
$593$	−4.31542e10			−0.348983			−0.174491	+	0.984659i	$0.555828\pi$
$594$	2.91749e10	+	1.08556e10i	0.234349	+	0.0871981i
$595$	−4.55108e9	−	4.55108e9i	−0.0363117	−	0.0363117i
$596$	−3.99706e9	−	5.46793e10i	−0.0316779	−	0.433349i
$597$	−1.24059e10	−	1.24059e10i	−0.0976630	−	0.0976630i
$598$	−3.20590e9	−	7.00539e9i	−0.0250695	−	0.0547807i
$599$	1.08451e10			0.0842415			0.0421207	−	0.999113i	$-0.486589\pi$
$599$	1.08451e10			0.0842415			0.0421207	+	0.999113i	$0.486589\pi$
$600$	1.59765e10	−	5.48890e10i	0.123276	−	0.423527i
$601$			1.29082e11i			0.989387i	0.869068	+	0.494693i	$0.164720\pi$
$601$			1.29082e11i			0.989387i	−0.869068	+	0.494693i	$0.835280\pi$
$602$	−8.39675e9	−	1.83482e10i	−0.0639330	−	0.139703i
$603$	3.43934e10	−	3.43934e10i	0.260139	−	0.260139i
$604$	1.54089e11	+	1.33096e11i	1.15778	+	1.00004i
$605$	3.16676e10	−	3.16676e10i	0.236371	−	0.236371i
$606$	−1.26377e11	−	4.70231e10i	−0.937081	−	0.348675i
$607$			2.41012e11i			1.77535i	0.460468	+	0.887676i	$0.347681\pi$
$607$			2.41012e11i			1.77535i	−0.460468	+	0.887676i	$0.652319\pi$
$608$	9.15664e10	+	1.41258e11i	0.670073	+	1.03371i
$609$	1.57766e9			0.0114695
$610$	−2.47944e10	+	6.66361e10i	−0.179075	+	0.481271i
$611$	−2.27172e10	−	2.27172e10i	−0.163001	−	0.163001i
$612$	2.41376e10	−	2.79448e10i	0.172063	−	0.199203i
$613$	−6.99206e10	−	6.99206e10i	−0.495180	−	0.495180i	0.414754	−	0.909934i	$-0.363868\pi$
$613$	−6.99206e10	−	6.99206e10i	−0.495180	−	0.495180i	−0.909934	+	0.414754i	$0.863868\pi$
$614$	4.60891e10	−	2.10920e10i	0.324284	−	0.148403i
$615$	2.98896e10			0.208939
$616$	−6.99890e9	+	2.40455e10i	−0.0486079	+	0.166998i
$617$			2.02589e11i			1.39790i	0.715171	+	0.698949i	$0.246349\pi$
$617$			2.02589e11i			1.39790i	−0.715171	+	0.698949i	$0.753651\pi$
$618$	4.79909e10	−	2.19623e10i	0.329007	−	0.150565i
$619$	−1.56596e11	+	1.56596e11i	−1.06664	+	1.06664i	−0.0690266	+	0.997615i	$0.521989\pi$
$619$	−1.56596e11	+	1.56596e11i	−1.06664	+	1.06664i	−0.997615	+	0.0690266i	$0.978011\pi$
$620$	6.07494e10	−	4.44079e9i	0.411126	−	0.0300534i
$621$	−7.16928e9	+	7.16928e9i	−0.0482069	+	0.0482069i
$622$	9.74087e10	−	2.61790e11i	0.650783	−	1.74901i
$623$		−	1.14283e10i		−	0.0758631i
$624$	2.16482e9	+	1.47281e10i	0.0142786	+	0.0971425i
$625$	−5.30590e10			−0.347727
$626$	−8.09235e9	−	3.01105e9i	−0.0526959	−	0.0196074i
$627$	1.00987e11	+	1.00987e11i	0.653427	+	0.653427i
$628$	−2.36700e10	+	1.73028e9i	−0.152181	+	0.0111244i
$629$	2.54020e10	+	2.54020e10i	0.162280	+	0.162280i
$630$	−1.42096e9	−	3.10501e9i	−0.00902027	−	0.0197107i
$631$	1.60818e11			1.01442			0.507210	−	0.861823i	$-0.330677\pi$
$631$	1.60818e11			1.01442			0.507210	+	0.861823i	$0.330677\pi$
$632$	−1.17061e10	−	2.13185e10i	−0.0733741	−	0.133625i
$633$		−	5.53016e10i		−	0.344447i
$634$	1.08074e11	+	2.36157e11i	0.668902	+	1.46165i
$635$	5.23130e10	−	5.23130e10i	0.321747	−	0.321747i
$636$	−9.66232e9	+	1.11864e10i	−0.0590545	+	0.0683692i
$637$	1.94447e10	−	1.94447e10i	0.118098	−	0.118098i
$638$	2.99409e10	+	1.11406e10i	0.180710	+	0.0672397i
$639$		−	9.86957e10i		−	0.591964i
$640$	1.11552e10	−	8.07343e10i	0.0664904	−	0.481214i
$641$	2.42585e11			1.43692			0.718459	−	0.695569i	$-0.244848\pi$
$641$	2.42585e11			1.43692			0.718459	+	0.695569i	$0.244848\pi$
$642$	1.59017e10	−	4.27365e10i	0.0936058	−	0.251570i
$643$	−2.09870e11	−	2.09870e11i	−1.22774	−	1.22774i	−0.964817	−	0.262923i	$-0.915313\pi$
$643$	−2.09870e11	−	2.09870e11i	−1.22774	−	1.22774i	−0.262923	−	0.964817i	$-0.584687\pi$
$644$	−6.17285e9	−	5.33185e9i	−0.0358874	−	0.0309981i
$645$	3.93946e10	+	3.93946e10i	0.227614	+	0.227614i
$646$	1.54049e11	−	7.04982e10i	0.884565	−	0.404807i
$647$	−5.01468e10			−0.286171			−0.143086	−	0.989710i	$-0.545702\pi$
$647$	−5.01468e10			−0.286171			−0.143086	+	0.989710i	$0.545702\pi$
$648$	1.71725e10	−	9.42947e9i	0.0973942	−	0.0534795i
$649$		−	4.83926e10i		−	0.272772i
$650$	2.10899e10	−	9.65147e9i	0.118147	−	0.0540680i
$651$	−8.32921e9	+	8.32921e9i	−0.0463746	+	0.0463746i
$652$	1.31406e10	+	1.79761e11i	0.0727149	+	0.994731i
$653$	9.32411e10	−	9.32411e10i	0.512808	−	0.512808i	−0.402578	−	0.915386i	$-0.631886\pi$
$653$	9.32411e10	−	9.32411e10i	0.512808	−	0.512808i	0.915386	+	0.402578i	$0.131886\pi$
$654$	−6.43876e10	+	1.73045e11i	−0.351958	+	0.945905i
$655$		−	4.35501e9i		−	0.0236605i
$656$	−1.36493e11	+	2.00625e10i	−0.737045	+	0.108335i
$657$	3.09064e10			0.165877
$658$	−3.18793e10	−	1.18619e10i	−0.170061	−	0.0632775i
$659$	−3.78176e9	−	3.78176e9i	−0.0200517	−	0.0200517i	0.697010	−	0.717062i	$-0.254513\pi$
$659$	−3.78176e9	−	3.78176e9i	−0.0200517	−	0.0200517i	−0.717062	+	0.697010i	$0.754513\pi$
$660$	−5.04106e9	−	6.89611e10i	−0.0265672	−	0.363436i
$661$	−1.89156e11	−	1.89156e11i	−0.990864	−	0.990864i	0.00909472	−	0.999959i	$-0.497105\pi$
$661$	−1.89156e11	−	1.89156e11i	−0.990864	−	0.990864i	−0.999959	+	0.00909472i	$0.997105\pi$
$662$	4.41486e10	+	9.64713e10i	0.229871	+	0.502304i
$663$	1.49814e10			0.0775353
$664$	−2.26625e11	−	6.59637e10i	−1.16583	−	0.339338i
$665$		−	1.56664e10i		−	0.0801094i
$666$	7.93114e9	+	1.73308e10i	0.0403124	+	0.0880888i
$667$	−7.35752e9	+	7.35752e9i	−0.0371730	+	0.0371730i
$668$	−1.18223e11	−	1.02116e11i	−0.593740	−	0.512848i
$669$	−1.04287e11	+	1.04287e11i	−0.520624	+	0.520624i
$670$	−1.01258e11	−	3.76767e10i	−0.502493	−	0.186971i
$671$		−	2.78416e11i		−	1.37342i
$672$	8.57305e9	+	1.32255e10i	0.0420396	+	0.0648535i
$673$	−3.72954e11			−1.81801			−0.909003	−	0.416789i	$-0.863155\pi$
$673$	−3.72954e11			−1.81801			−0.909003	+	0.416789i	$0.863155\pi$
$674$	8.34841e10	−	2.24367e11i	0.404542	−	1.08723i
$675$	−2.15833e10	−	2.15833e10i	−0.103969	−	0.103969i
$676$	1.32557e11	−	1.53465e11i	0.634768	−	0.734890i
$677$	6.10238e10	+	6.10238e10i	0.290499	+	0.290499i	0.837277	−	0.546778i	$-0.184146\pi$
$677$	6.10238e10	+	6.10238e10i	0.290499	+	0.290499i	−0.546778	+	0.837277i	$0.684146\pi$
$678$	−1.04087e11	+	4.76339e10i	−0.492583	+	0.225423i
$679$	4.61957e9			0.0217332
$680$	−7.87535e10	−	2.29227e10i	−0.368328	−	0.107209i
$681$		−	1.88756e11i		−	0.877631i
$682$	−2.16889e11	+	9.92556e10i	−1.00253	+	0.458794i
$683$	−1.46023e10	+	1.46023e10i	−0.0671023	+	0.0671023i	−0.739862	−	0.672759i	$-0.765109\pi$
$683$	−1.46023e10	+	1.46023e10i	−0.0671023	+	0.0671023i	0.672759	+	0.739862i	$0.265109\pi$
$684$	8.96431e10	−	6.55293e9i	0.409536	−	0.0299372i
$685$	1.16672e11	−	1.16672e11i	0.529913	−	0.529913i
$686$	2.04915e10	−	5.50718e10i	0.0925287	−	0.248675i
$687$		−	2.70457e10i		−	0.121415i
$688$	−2.06340e11	−	1.53456e11i	−0.920939	−	0.684903i
$689$	−5.99710e9			−0.0266112
$690$	2.11072e10	+	7.85369e9i	0.0931180	+	0.0346479i
$691$	−1.40475e9	−	1.40475e9i	−0.00616152	−	0.00616152i	0.704019	−	0.710181i	$-0.251387\pi$
$691$	−1.40475e9	−	1.40475e9i	−0.00616152	−	0.00616152i	−0.710181	+	0.704019i	$0.751387\pi$
$692$	−1.11283e11	+	8.13477e9i	−0.485291	+	0.0354749i
$693$	9.45510e9	+	9.45510e9i	0.0409952	+	0.0409952i
$694$	1.26279e11	+	2.75938e11i	0.544368	+	1.18953i
$695$	−2.17667e11			−0.932937
$696$	1.76234e10	−	9.67705e9i	0.0751020	−	0.0412388i
$697$			1.38840e11i			0.588280i
$698$	−1.81783e11	−	3.97224e11i	−0.765830	−	1.67345i
$699$	1.11196e10	−	1.11196e10i	0.0465781	−	0.0465781i
$700$	1.60517e10	−	1.85835e10i	0.0668542	−	0.0773992i
$701$	4.98964e10	−	4.98964e10i	0.206632	−	0.206632i	−0.596202	−	0.802834i	$-0.703324\pi$
$701$	4.98964e10	−	4.98964e10i	0.206632	−	0.206632i	0.802834	+	0.596202i	$0.203324\pi$
$702$	7.44940e9	+	2.77182e9i	0.0306742	+	0.0114134i
$703$			8.74429e10i			0.358017i
$704$	6.93084e10	+	3.11531e11i	0.282160	+	1.26827i
$705$	9.39149e10			0.380170
$706$	−1.13765e11	+	3.05748e11i	−0.457919	+	1.23068i
$707$	−4.09567e10	−	4.09567e10i	−0.163926	−	0.163926i
$708$	−2.30483e10	−	1.99082e10i	−0.0917289	−	0.0792317i
$709$	1.81955e11	+	1.81955e11i	0.720076	+	0.720076i	0.968620	−	0.248545i	$-0.0799523\pi$
$709$	1.81955e11	+	1.81955e11i	0.720076	+	0.720076i	−0.248545	+	0.968620i	$0.579952\pi$
$710$	−1.99344e11	+	9.12268e10i	−0.784460	+	0.358995i
$711$	−1.29858e10			−0.0508150
$712$	−7.00991e10	−	1.27661e11i	−0.272767	−	0.496750i
$713$		−	7.76877e10i		−	0.300603i
$714$	1.44231e10	−	6.60051e9i	0.0554966	−	0.0253971i
$715$	1.98366e10	−	1.98366e10i	0.0759001	−	0.0759001i
$716$	−1.98857e10	−	2.72034e11i	−0.0756639	−	1.03507i
$717$	−1.54912e10	+	1.54912e10i	−0.0586151	+	0.0586151i
$718$	−1.19745e11	+	3.21821e11i	−0.450568	+	1.21092i
$719$		−	4.21431e11i		−	1.57692i	−0.615084	−	0.788462i	$-0.710878\pi$
$719$		−	4.21431e11i		−	1.57692i	0.615084	−	0.788462i	$-0.289122\pi$
$720$	−3.49184e10	−	2.59689e10i	−0.129935	−	0.0966325i
$721$	2.26707e10			0.0838926
$722$	1.31808e11	+	4.90440e10i	0.485058	+	0.180483i
$723$	2.02237e11	+	2.02237e11i	0.740129	+	0.740129i
$724$	−3.03438e9	−	4.15099e10i	−0.0110437	−	0.151077i
$725$	−2.21500e10	−	2.21500e10i	−0.0801719	−	0.0801719i
$726$	4.59280e10	+	1.00360e11i	0.165322	+	0.361254i
$727$	3.61832e11			1.29530			0.647649	−	0.761939i	$-0.275752\pi$
$727$	3.61832e11			1.29530			0.647649	+	0.761939i	$0.275752\pi$
$728$	−1.78707e9	+	6.13968e9i	−0.00636234	+	0.0218585i
$729$		−	1.04604e10i		−	0.0370370i
$730$	−2.85675e10	−	6.24243e10i	−0.100596	−	0.219817i
$731$	−1.82992e11	+	1.82992e11i	−0.640860	+	0.640860i
$732$	−1.32603e11	−	1.14537e11i	−0.461859	−	0.398935i
$733$	2.27256e11	−	2.27256e11i	0.787227	−	0.787227i	−0.193812	−	0.981039i	$-0.562085\pi$
$733$	2.27256e11	−	2.27256e11i	0.787227	−	0.787227i	0.981039	+	0.193812i	$0.0620851\pi$
$734$	−8.31913e10	−	3.09544e10i	−0.286612	−	0.106644i
$735$			8.03860e10i			0.275442i
$736$	−1.01659e11	−	2.16968e10i	−0.346444	−	0.0739410i
$737$	4.23071e11			1.43398
$738$	−2.56878e10	+	6.90372e10i	−0.0865967	+	0.232733i
$739$	8.64797e10	+	8.64797e10i	0.289959	+	0.289959i	0.837064	−	0.547105i	$-0.184270\pi$
$739$	8.64797e10	+	8.64797e10i	0.289959	+	0.289959i	−0.547105	+	0.837064i	$0.684270\pi$
$740$	2.76735e10	−	3.20384e10i	0.0922863	−	0.106843i
$741$	2.57857e10	+	2.57857e10i	0.0855277	+	0.0855277i
$742$	−5.77360e9	+	2.64219e9i	−0.0190472	+	0.00871664i
$743$	−4.53548e11			−1.48822			−0.744112	−	0.668055i	$-0.767127\pi$
$743$	−4.53548e11			−1.48822			−0.744112	+	0.668055i	$0.767127\pi$
$744$	−4.19523e10	+	1.44132e11i	−0.136919	+	0.470401i
$745$			6.50226e10i			0.211076i
$746$	4.34543e11	−	1.98862e11i	1.40307	−	0.642090i
$747$	−8.91130e10	+	8.91130e10i	−0.286193	+	0.286193i
$748$	3.20332e11	−	2.34163e10i	1.02328	−	0.0748017i
$749$	1.38502e10	−	1.38502e10i	0.0440077	−	0.0440077i
$750$	−5.45906e10	+	1.46715e11i	−0.172533	+	0.463691i
$751$		−	1.33549e11i		−	0.419836i	−0.977719	−	0.209918i	$-0.932680\pi$
$751$		−	1.33549e11i		−	0.419836i	0.977719	−	0.209918i	$-0.0673198\pi$
$752$	−4.28869e11	+	6.30376e10i	−1.34107	+	0.197119i
$753$	−5.70485e10			−0.177445
$754$	7.64499e9	+	2.84460e9i	0.0236533	+	0.00880107i
$755$	−1.70755e11	−	1.70755e11i	−0.525517	−	0.525517i
$756$	8.39298e9	−	6.13528e8i	0.0256938	−	0.00187822i
$757$	4.18661e11	+	4.18661e11i	1.27491	+	1.27491i	0.943481	+	0.331427i	$0.107530\pi$
$757$	4.18661e11	+	4.18661e11i	1.27491	+	1.27491i	0.331427	+	0.943481i	$0.392470\pi$
$758$	1.35280e11	+	2.95608e11i	0.409787	+	0.895446i
$759$	−8.81890e10			−0.265734
$760$	−9.60948e10	−	1.75003e11i	−0.288035	−	0.524555i
$761$		−	3.87386e11i		−	1.15506i	−0.816368	−	0.577532i	$-0.804016\pi$
$761$		−	3.87386e11i		−	1.15506i	0.816368	−	0.577532i	$-0.195984\pi$
$762$	7.58705e10	+	1.65789e11i	0.225036	+	0.491739i
$763$	−5.60810e10	+	5.60810e10i	−0.165469	+	0.165469i
$764$	−3.30157e11	+	3.82233e11i	−0.969051	+	1.12190i
$765$	−3.09673e10	+	3.09673e10i	−0.0904185	+	0.0904185i
$766$	4.02805e11	+	1.49878e11i	1.16998	+	0.435335i
$767$		−	1.23564e10i		−	0.0357035i
$768$	1.76888e11	+	9.51506e10i	0.508456	+	0.273506i
$769$	−1.11931e11			−0.320070			−0.160035	−	0.987111i	$-0.551161\pi$
$769$	−1.11931e11			−0.320070			−0.160035	+	0.987111i	$0.551161\pi$
$770$	1.03577e10	−	2.78369e10i	0.0294647	−	0.0791876i
$771$	2.27903e11	+	2.27903e11i	0.644958	+	0.644958i
$772$	4.07196e11	+	3.51719e11i	1.14640	+	0.990209i
$773$	3.26989e11	+	3.26989e11i	0.915829	+	0.915829i	0.996723	−	0.0808934i	$-0.0257773\pi$
$773$	3.26989e11	+	3.26989e11i	0.915829	+	0.915829i	−0.0808934	+	0.996723i	$0.525777\pi$
$774$	−1.24848e11	+	5.71347e10i	−0.347871	+	0.159197i
$775$	2.33881e11			0.648318
$776$	5.16033e10	−	2.83355e10i	0.142308	−	0.0781420i
$777$			8.18698e9i			0.0224615i
$778$	−5.93695e11	+	2.71695e11i	−1.62048	+	0.741589i
$779$	−2.38969e11	+	2.38969e11i	−0.648921	+	0.648921i
$780$	−1.28717e9	−	1.76083e10i	−0.00347741	−	0.0475705i
$781$	6.07025e11	−	6.07025e11i	1.63156	−	1.63156i
$782$	−3.64812e10	+	9.80450e10i	−0.0975534	+	0.262179i
$783$		−	1.07350e10i		−	0.0285598i
$784$	−5.39566e10	−	3.67088e11i	−0.142817	−	0.971640i
$785$	2.81475e10			0.0741244
$786$	1.00589e10	+	3.74280e9i	0.0263550	+	0.00980632i
$787$	−3.95177e10	−	3.95177e10i	−0.103013	−	0.103013i	0.653722	−	0.756735i	$-0.273207\pi$
$787$	−3.95177e10	−	3.95177e10i	−0.103013	−	0.103013i	−0.756735	+	0.653722i	$0.773207\pi$
$788$	−2.44379e9	−	3.34307e10i	−0.00633809	−	0.0867042i
$789$	−2.76695e11	−	2.76695e11i	−0.713993	−	0.713993i
$790$	1.20031e10	+	2.62287e10i	0.0308167	+	0.0673391i
$791$	−4.91704e10			−0.125602
$792$	1.63615e11	+	4.76232e10i	0.415835	+	0.121037i
$793$		−	7.10896e10i		−	0.179768i
$794$	−8.91882e10	−	1.94890e11i	−0.224401	−	0.490351i
$795$	1.23963e10	−	1.23963e10i	0.0310329	−	0.0310329i
$796$	−7.26819e10	−	6.27796e10i	−0.181040	−	0.156375i
$797$	2.90803e11	−	2.90803e11i	0.720718	−	0.720718i	−0.248034	−	0.968751i	$-0.579784\pi$
$797$	2.90803e11	−	2.90803e11i	0.720718	−	0.720718i	0.968751	+	0.248034i	$0.0797844\pi$
$798$	3.61854e10	+	1.34641e10i	0.0892322	+	0.0332021i
$799$			4.36245e11i			1.07039i
$800$	6.53190e10	−	3.06047e11i	0.159470	−	0.747184i
$801$	−7.77627e10			−0.188904
$802$	6.51243e10	−	1.75025e11i	0.157415	−	0.423060i
$803$	1.90089e11	+	1.90089e11i	0.457187	+	0.457187i
$804$	1.74047e11	−	2.01499e11i	0.416526	−	0.482225i
$805$	6.84049e9	+	6.84049e9i	0.0162894	+	0.0162894i
$806$	−5.53795e10	+	2.53435e10i	−0.131223	+	0.0600520i
$807$	−2.83722e11			−0.668959
$808$	−7.08730e11	−	2.06290e11i	−1.66278	−	0.483985i
$809$		−	3.45805e11i		−	0.807304i	−0.914913	−	0.403652i	$-0.867741\pi$
$809$		−	3.45805e11i		−	0.807304i	0.914913	−	0.403652i	$-0.132259\pi$
$810$	−2.11277e10	+	9.66875e9i	−0.0490808	+	0.0224611i
$811$	2.27058e11	−	2.27058e11i	0.524871	−	0.524871i	−0.394167	−	0.919039i	$-0.628967\pi$
$811$	2.27058e11	−	2.27058e11i	0.524871	−	0.524871i	0.919039	+	0.394167i	$0.128967\pi$
$812$	8.61334e9	−	6.29637e8i	0.0198129	−	0.00144832i
$813$	−2.02745e11	+	2.02745e11i	−0.464076	+	0.464076i
$814$	−5.78121e10	+	1.55373e11i	−0.131680	+	0.353897i
$815$		−	2.13766e11i		−	0.484515i
$816$	1.20628e11	−	1.62200e11i	0.272075	−	0.365839i
$817$	−6.29924e11			−1.41384
$818$	3.06746e11	+	1.14136e11i	0.685119	+	0.254923i
$819$	2.41423e9	+	2.41423e9i	0.00536591	+	0.00536591i
$820$	1.63184e11	−	1.19288e10i	0.360930	−	0.0263840i
$821$	6.01905e11	+	6.01905e11i	1.32481	+	1.32481i	0.909827	+	0.414988i	$0.136214\pi$
$821$	6.01905e11	+	6.01905e11i	1.32481	+	1.32481i	0.414988	+	0.909827i	$0.363786\pi$
$822$	1.69212e11	+	3.69753e11i	0.370632	+	0.809887i
$823$	2.08094e10			0.0453586			0.0226793	−	0.999743i	$-0.492780\pi$
$823$	2.08094e10			0.0453586			0.0226793	+	0.999743i	$0.492780\pi$
$824$	2.53244e11	−	1.39057e11i	0.549327	−	0.301637i
$825$		−	2.65495e11i		−	0.573114i
$826$	−5.44396e9	−	1.18959e10i	−0.0116949	−	0.0255551i
$827$	−2.85750e11	+	2.85750e11i	−0.610892	+	0.610892i	−0.943178	−	0.332287i	$-0.892180\pi$
$827$	−2.85750e11	+	2.85750e11i	−0.610892	+	0.610892i	0.332287	+	0.943178i	$0.392180\pi$
$828$	−3.62800e10	+	4.20024e10i	−0.0771873	+	0.0893620i
$829$	6.34081e11	−	6.34081e11i	1.34254	−	1.34254i	0.449014	−	0.893525i	$-0.351776\pi$
$829$	6.34081e11	−	6.34081e11i	1.34254	−	1.34254i	0.893525	−	0.449014i	$-0.148224\pi$
$830$	2.62359e11	+	9.76201e10i	0.552819	+	0.205696i
$831$		−	3.06300e11i		−	0.642307i
$832$	1.76969e10	+	7.95453e10i	0.0369322	+	0.166005i
$833$	−3.73401e11			−0.775525
$834$	1.87068e11	−	5.02753e11i	0.386665	−	1.03918i
$835$	1.31010e11	+	1.31010e11i	0.269499	+	0.269499i
$836$	5.91651e11	+	5.11044e11i	1.21127	+	1.04624i
$837$	5.66751e10	+	5.66751e10i	0.115476	+	0.115476i
$838$	2.21507e11	−	1.01369e11i	0.449172	−	0.205556i
$839$	−3.96094e11			−0.799375			−0.399688	−	0.916651i	$-0.630881\pi$
$839$	−3.96094e11			−0.799375			−0.399688	+	0.916651i	$0.630881\pi$
$840$	−8.99702e9	−	1.63849e10i	−0.0180710	−	0.0329100i
$841$			4.89230e11i			0.977977i
$842$	3.13615e10	−	1.43521e10i	0.0623947	−	0.0285540i
$843$	−9.65640e10	+	9.65640e10i	−0.191207	+	0.191207i
$844$	−2.20706e10	−	3.01923e11i	−0.0434955	−	0.595012i
$845$	−1.70063e11	+	1.70063e11i	−0.333568	+	0.333568i
$846$	−8.07127e10	+	2.16919e11i	−0.157565	+	0.423464i
$847$			4.74095e10i			0.0921153i
$848$	−4.82877e10	+	6.49289e10i	−0.0933798	+	0.125561i
$849$	−3.12919e11			−0.602284
$850$	−2.95167e11	−	1.09828e11i	−0.565448	−	0.210396i
$851$	−3.81805e10	−	3.81805e10i	−0.0727987	−	0.0727987i
$852$	−3.93890e10	−	5.38836e11i	−0.0747509	−	1.02258i
$853$	−2.36449e11	−	2.36449e11i	−0.446624	−	0.446624i	0.447607	−	0.894231i	$-0.352276\pi$
$853$	−2.36449e11	−	2.36449e11i	−0.446624	−	0.446624i	−0.894231	+	0.447607i	$0.852276\pi$
$854$	−3.13206e10	−	6.84402e10i	−0.0588841	−	0.128671i
$855$	−1.06600e11			−0.199478
$856$	6.97603e10	−	2.39669e11i	0.129931	−	0.446393i
$857$			5.75350e11i			1.06662i	0.845921	+	0.533309i	$0.179052\pi$
$857$			5.75350e11i			1.06662i	−0.845921	+	0.533309i	$0.820948\pi$
$858$	2.87693e10	+	6.28653e10i	0.0530861	+	0.116001i
$859$	−4.54656e11	+	4.54656e11i	−0.835046	+	0.835046i	−0.988202	−	0.153156i	$-0.951056\pi$
$859$	−4.54656e11	+	4.54656e11i	−0.835046	+	0.835046i	0.153156	+	0.988202i	$0.451056\pi$
$860$	2.30800e11	+	1.99355e11i	0.421931	+	0.364447i
$861$	−2.23738e10	+	2.23738e10i	−0.0407125	+	0.0407125i
$862$	−2.53513e11	−	9.43288e10i	−0.459168	−	0.170850i
$863$		−	5.63595e11i		−	1.01607i	−0.861336	−	0.508035i	$-0.830372\pi$
$863$		−	5.63595e11i		−	1.01607i	0.861336	−	0.508035i	$-0.169628\pi$
$864$	8.99911e10	−	5.83343e10i	0.161490	−	0.104681i
$865$	1.32333e11			0.236377
$866$	3.46025e11	−	9.29959e11i	0.615228	−	1.65346i
$867$	8.68288e10	+	8.68288e10i	0.153669	+	0.153669i
$868$	−4.21498e10	+	4.87981e10i	−0.0742534	+	0.0859654i
$869$	−7.98691e10	−	7.98691e10i	−0.140055	−	0.140055i
$870$	−2.16824e10	+	9.92261e9i	−0.0378469	+	0.0173200i
$871$	1.08025e11			0.187695
$872$	−2.82467e11	+	9.70446e11i	−0.488542	+	1.67844i
$873$		−	3.14333e10i		−	0.0541170i
$874$	−2.31544e11	+	1.05962e11i	−0.396814	+	0.181596i
$875$	−4.75479e10	+	4.75479e10i	−0.0811146	+	0.0811146i
$876$	1.68735e11	−	1.23346e10i	0.286543	−	0.0209463i
$877$	−4.72278e11	+	4.72278e11i	−0.798361	+	0.798361i	−0.982837	−	0.184476i	$-0.940941\pi$
$877$	−4.72278e11	+	4.72278e11i	−0.798361	+	0.798361i	0.184476	+	0.982837i	$0.440941\pi$
$878$	6.26699e10	−	1.68428e11i	0.105458	−	0.283424i
$879$		−	3.30463e11i		−	0.553563i
$880$	−5.50441e10	−	3.74486e11i	−0.0917867	−	0.624460i
$881$	−1.91927e11			−0.318590			−0.159295	−	0.987231i	$-0.550922\pi$
$881$	−1.91927e11			−0.318590			−0.159295	+	0.987231i	$0.550922\pi$
$882$	−1.85671e11	−	6.90855e10i	−0.306810	−	0.114160i
$883$	5.35958e10	+	5.35958e10i	0.0881634	+	0.0881634i	0.749813	−	0.661650i	$-0.230143\pi$
$883$	5.35958e10	+	5.35958e10i	0.0881634	+	0.0881634i	−0.661650	+	0.749813i	$0.730143\pi$
$884$	8.17922e10	−	5.97902e9i	0.133938	−	0.00979087i
$885$	2.55412e10	+	2.55412e10i	0.0416359	+	0.0416359i
$886$	−3.12040e11	−	6.81856e11i	−0.506379	−	1.10652i
$887$	−5.32731e11			−0.860623			−0.430312	−	0.902680i	$-0.641596\pi$
$887$	−5.32731e11			−0.860623			−0.430312	+	0.902680i	$0.641596\pi$
$888$	5.02173e10	+	9.14532e10i	0.0807609	+	0.147078i
$889$			7.83178e10i			0.125387i
$890$	7.18779e10	+	1.57064e11i	0.114561	+	0.250332i
$891$	6.43361e10	−	6.43361e10i	0.102081	−	0.102081i
$892$	−5.27740e11	+	6.10980e11i	−0.833605	+	0.965090i
$893$	−7.50855e11	+	7.50855e11i	−1.18073	+	1.18073i
$894$	−1.50185e11	−	5.58819e10i	−0.235113	−	0.0874825i
$895$			3.23493e11i			0.504165i
$896$	5.20833e10	+	6.87838e10i	0.0808103	+	0.106722i
$897$	−2.25178e10			−0.0347822
$898$	8.94693e10	−	2.40453e11i	0.137584	−	0.369764i
$899$	5.81632e10	+	5.81632e10i	0.0890450	+	0.0890450i
$900$	−1.26450e11	−	1.09222e11i	−0.192729	−	0.166471i
$901$	5.75819e10	+	5.75819e10i	0.0873750	+	0.0873750i
$902$	−5.82603e11	+	2.66619e11i	−0.880130	+	0.402777i
$903$	−5.89776e10			−0.0887026
$904$	−5.49262e11	+	3.01602e11i	−0.822443	+	0.451606i
$905$			4.93621e10i			0.0735866i
$906$	5.41151e11	−	2.47649e11i	0.803167	−	0.367557i
$907$	1.14644e11	−	1.14644e11i	0.169403	−	0.169403i	−0.617314	−	0.786717i	$-0.711779\pi$
$907$	1.14644e11	−	1.14644e11i	0.169403	−	0.169403i	0.786717	+	0.617314i	$0.211779\pi$
$908$	−7.53316e10	−	1.03053e12i	−0.110824	−	1.51606i
$909$	−2.78685e11	+	2.78685e11i	−0.408186	+	0.408186i
$910$	2.64470e9	−	7.10776e9i	0.00385666	−	0.0103650i
$911$		−	6.94812e10i		−	0.100877i	−0.998727	−	0.0504387i	$-0.983938\pi$
$911$		−	6.94812e10i		−	0.100877i	0.998727	−	0.0504387i	$-0.0160620\pi$
$912$	4.86798e11	−	7.15523e10i	0.703670	−	0.103429i
$913$	−1.09617e12			−1.57760
$914$	2.15850e10	+	8.03149e9i	0.0309291	+	0.0115083i
$915$	1.46945e11	+	1.46945e11i	0.209638	+	0.209638i
$916$	−1.07938e10	−	1.47658e11i	−0.0153318	−	0.209737i
$917$	3.25994e9	+	3.25994e9i	0.00461034	+	0.00461034i
$918$	−4.49124e10	−	9.81404e10i	−0.0632405	−	0.138190i
$919$	9.17244e11			1.28595			0.642973	−	0.765889i	$-0.277701\pi$
$919$	9.17244e11			1.28595			0.642973	+	0.765889i	$0.277701\pi$
$920$	1.18370e11	+	3.44540e10i	0.165231	+	0.0480937i
$921$		−	1.48147e11i		−	0.205899i
$922$	9.14790e9	+	1.99895e10i	0.0126589	+	0.0276617i
$923$	1.54996e11	−	1.54996e11i	0.213556	−	0.213556i
$924$	5.53943e10	+	4.78473e10i	0.0759936	+	0.0656401i
$925$	1.14943e11	−	1.14943e11i	0.157006	−	0.157006i
$926$	1.34915e12	+	5.02002e11i	1.83492	+	0.682749i
$927$		−	1.54260e11i		−	0.208898i
$928$	9.23539e10	−	5.98659e10i	0.124527	−	0.0807212i
$929$	−2.02150e11			−0.271400			−0.135700	−	0.990750i	$-0.543328\pi$
$929$	−2.02150e11			−0.271400			−0.135700	+	0.990750i	$0.543328\pi$
$930$	6.20856e10	−	1.66858e11i	0.0829963	−	0.223057i
$931$	−6.42690e11	−	6.42690e11i	−0.855466	−	0.855466i
$932$	5.62706e10	−	6.51462e10i	0.0745792	−	0.0863426i
$933$	−5.77298e11	−	5.77298e11i	−0.761857	−	0.761857i
$934$	1.15830e11	−	5.30077e10i	0.152206	−	0.0696549i
$935$	−3.80927e11			−0.498420
$936$	4.17767e10	+	1.21599e10i	0.0544291	+	0.0158426i
$937$			4.55072e11i			0.590367i	0.955441	+	0.295184i	$0.0953808\pi$
$937$			4.55072e11i			0.590367i	−0.955441	+	0.295184i	$0.904619\pi$
$938$	1.04000e11	−	4.75937e10i	0.134345	−	0.0614806i
$939$	−1.78452e10	+	1.78452e10i	−0.0229540	+	0.0229540i
$940$	5.12735e11	−	3.74810e10i	0.656722	−	0.0480065i
$941$	−2.30280e11	+	2.30280e11i	−0.293696	+	0.293696i	−0.838539	−	0.544842i	$-0.816590\pi$
$941$	−2.30280e11	+	2.30280e11i	−0.293696	+	0.293696i	0.544842	+	0.838539i	$0.316590\pi$
$942$	−2.41906e10	+	6.50134e10i	−0.0307215	+	0.0825656i
$943$		−	2.08684e11i		−	0.263901i
$944$	−1.33779e11	−	9.94917e10i	−0.168461	−	0.125285i
$945$	−9.98063e9			−0.0125150
$946$	−1.11928e12	−	4.16469e11i	−1.39757	−	0.520017i
$947$	9.29338e11	+	9.29338e11i	1.15551	+	1.15551i	0.985430	+	0.170080i	$0.0544027\pi$
$947$	9.29338e11	+	9.29338e11i	1.15551	+	1.15551i	0.170080	+	0.985430i	$0.445597\pi$
$948$	−7.08971e10	+	5.18259e9i	−0.0877800	+	0.00641673i
$949$	4.85366e10	+	4.85366e10i	0.0598417	+	0.0598417i
$950$	−3.19003e11	−	6.97069e11i	−0.391651	−	0.855818i
$951$	7.59095e11			0.928055
$952$	7.61097e10	−	4.17921e10i	0.0926600	−	0.0508799i
$953$			2.94264e11i			0.356751i	0.983962	+	0.178376i	$0.0570842\pi$
$953$			2.94264e11i			0.356751i	−0.983962	+	0.178376i	$0.942916\pi$
$954$	1.79785e10	+	3.92857e10i	0.0217050	+	0.0474287i
$955$	4.23574e11	−	4.23574e11i	0.509232	−	0.509232i
$956$	−7.83930e10	+	9.07579e10i	−0.0938525	+	0.108656i
$957$	6.60253e10	−	6.60253e10i	0.0787160	−	0.0787160i
$958$	4.26159e11	+	1.58568e11i	0.505952	+	0.188258i
$959$			1.74670e11i			0.206511i
$960$	−2.01004e11	−	1.27843e11i	−0.236657	−	0.150519i
$961$	2.38749e11			0.279929
$962$	−1.47615e10	+	3.96723e10i	−0.0172358	+	0.0463219i
$963$	−9.42421e10	−	9.42421e10i	−0.109582	−	0.109582i
$964$	1.18484e12	+	1.02341e12i	1.37199	+	1.18507i
$965$	−4.51238e11	−	4.51238e11i	−0.520350	−	0.520350i
$966$	−2.16786e10	+	9.92088e9i	−0.0248956	+	0.0113931i
$967$	1.17556e12			1.34443			0.672216	−	0.740355i	$-0.265343\pi$
$967$	1.17556e12			1.34443			0.672216	+	0.740355i	$0.265343\pi$
$968$	2.90800e11	+	5.29591e11i	0.331202	+	0.603169i
$969$		−	4.95170e11i		−	0.561642i
$970$	−6.34887e10	+	2.90546e10i	−0.0717149	+	0.0328192i
$971$	2.62616e11	−	2.62616e11i	0.295423	−	0.295423i	−0.543795	−	0.839218i	$-0.683013\pi$
$971$	2.62616e11	−	2.62616e11i	0.295423	−	0.295423i	0.839218	+	0.543795i	$0.183013\pi$
$972$	−4.17468e9	−	5.71090e10i	−0.00467690	−	0.0639793i
$973$	1.62934e11	−	1.62934e11i	0.181786	−	0.181786i
$974$	2.78450e11	−	7.48348e11i	0.309394	−	0.831511i
$975$		−	6.77906e10i		−	0.0750155i
$976$	−7.69667e11	−	5.72402e11i	−0.848210	−	0.630815i
$977$	6.52580e11			0.716235			0.358117	−	0.933677i	$-0.383419\pi$
$977$	6.52580e11			0.716235			0.358117	+	0.933677i	$0.383419\pi$
$978$	4.93743e11	+	1.83715e11i	0.539691	+	0.200812i
$979$	−4.78277e11	−	4.78277e11i	−0.520654	−	0.520654i
$980$	3.20817e10	+	4.38873e11i	0.0347818	+	0.475811i
$981$	3.81597e11	+	3.81597e11i	0.412030	+	0.412030i
$982$	−2.36072e11	−	5.15854e11i	−0.253863	−	0.554729i
$983$	1.10301e12			1.18132			0.590659	−	0.806922i	$-0.298868\pi$
$983$	1.10301e12			1.18132			0.590659	+	0.806922i	$0.298868\pi$
$984$	−1.12692e11	+	3.87165e11i	−0.120202	+	0.412967i
$985$			3.97545e10i			0.0422320i
$986$	−4.60916e10	−	1.00717e11i	−0.0487656	−	0.106560i
$987$	−7.03000e10	+	7.03000e10i	−0.0740776	+	0.0740776i
$988$	1.51070e11	+	1.30488e11i	0.158544	+	0.136944i
$989$	2.75046e11	−	2.75046e11i	0.287488	−	0.287488i
$990$	−1.89413e11	−	7.04779e10i	−0.197182	−	0.0733689i
$991$		−	3.11647e11i		−	0.323124i	−0.986863	−	0.161562i	$-0.948347\pi$
$991$		−	3.11647e11i		−	0.323124i	0.986863	−	0.161562i	$-0.0516531\pi$
$992$	−1.71519e11	+	8.03640e11i	−0.177120	+	0.829879i
$993$	3.10094e11			0.318930
$994$	8.09314e10	−	2.17507e11i	0.0829032	−	0.222806i
$995$	8.05430e10	+	8.05430e10i	0.0821742	+	0.0821742i
$996$	−4.50954e11	+	5.22083e11i	−0.458242	+	0.530521i
$997$	1.44432e11	+	1.44432e11i	0.146178	+	0.146178i	0.776408	−	0.630230i	$-0.217039\pi$
$997$	1.44432e11	+	1.44432e11i	0.146178	+	0.146178i	−0.630230	+	0.776408i	$0.717039\pi$
$998$	−1.32851e12	+	6.07974e11i	−1.33920	+	0.612862i
$999$	5.57073e10			0.0559307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.21	yes	64
4.3	odd	2		192.9.l.a.79.25		64
16.3	odd	4	inner	48.9.l.a.19.21	✓	64
16.13	even	4		192.9.l.a.175.25		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.21	✓	64	16.3	odd	4	inner
48.9.l.a.43.21	yes	64	1.1	even	1	trivial
192.9.l.a.79.25		64	4.3	odd	2
192.9.l.a.175.25		64	16.13	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.57965 - 14.9956i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-193.735 - 167.340i) q^{4} +(214.689 + 214.689i) q^{5} +(-680.384 + 311.367i) q^{6} -321.411 q^{7} +(-3590.34 + 1971.47i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(5.57965 - 14.9956i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-193.735 - 167.340i) q^{4} +(214.689 + 214.689i) q^{5} +(-680.384 + 311.367i) q^{6} -321.411 q^{7} +(-3590.34 + 1971.47i) q^{8} +2187.00i q^{9} +(4417.27 - 2021.50i) q^{10} +(-13451.1 + 13451.1i) q^{11} +(872.821 + 11940.1i) q^{12} +(-3434.55 + 3434.55i) q^{13} +(-1793.36 + 4819.74i) q^{14} -14198.7i q^{15} +(9530.45 + 64839.3i) q^{16} +65954.5 q^{17} +(32795.3 + 12202.7i) q^{18} +(113520. + 113520. i) q^{19} +(-5666.64 - 77518.8i) q^{20} +(10628.4 + 10628.4i) q^{21} +(126654. + 276759. i) q^{22} -99132.9 q^{23} +(183918. + 53533.0i) q^{24} -298442. i q^{25} +(32339.5 + 70666.7i) q^{26} +(72320.0 - 72320.0i) q^{27} +(62268.5 + 53784.9i) q^{28} +(74218.8 - 74218.8i) q^{29} +(-212918. - 79223.9i) q^{30} +783672. i q^{31} +(1.02548e6 + 218866. i) q^{32} +889604. q^{33} +(368003. - 989027. i) q^{34} +(-69003.3 - 69003.3i) q^{35} +(365973. - 423698. i) q^{36} +(385145. + 385145. i) q^{37} +(2.33569e6 - 1.06889e6i) q^{38} +227148. q^{39} +(-1.19406e6 - 347554. i) q^{40} +2.10509e6i q^{41} +(218683. - 100077. i) q^{42} +(-2.77452e6 + 2.77452e6i) q^{43} +(4.85685e6 - 355037. i) q^{44} +(-469525. + 469525. i) q^{45} +(-553127. + 1.48655e6i) q^{46} +6.61433e6i q^{47} +(1.82896e6 - 2.45927e6i) q^{48} -5.66150e6 q^{49} +(-4.47532e6 - 1.66520e6i) q^{50} +(-2.18099e6 - 2.18099e6i) q^{51} +(1.24013e6 - 90653.7i) q^{52} +(873055. + 873055. i) q^{53} +(-680960. - 1.48800e6i) q^{54} -5.77560e6 q^{55} +(1.15397e6 - 633650. i) q^{56} -7.50775e6i q^{57} +(-698839. - 1.52707e6i) q^{58} +(-1.79884e6 + 1.79884e6i) q^{59} +(-2.37602e6 + 2.75079e6i) q^{60} +(-1.03492e7 + 1.03492e7i) q^{61} +(1.17516e7 + 4.37262e6i) q^{62} -702925. i q^{63} +(9.00385e6 - 1.41565e7i) q^{64} -1.47472e6 q^{65} +(4.96368e6 - 1.33401e7i) q^{66} +(-1.57263e7 - 1.57263e7i) q^{67} +(-1.27777e7 - 1.10369e7i) q^{68} +(3.27814e6 + 3.27814e6i) q^{69} +(-1.41976e6 + 649730. i) q^{70} -4.51284e7 q^{71} +(-4.31160e6 - 7.85207e6i) q^{72} -1.41319e7i q^{73} +(7.92444e6 - 3.62650e6i) q^{74} +(-9.86893e6 + 9.86893e6i) q^{75} +(-2.99631e6 - 4.09891e7i) q^{76} +(4.32332e6 - 4.32332e6i) q^{77} +(1.26741e6 - 3.40622e6i) q^{78} +5.93775e6i q^{79} +(-1.18742e7 + 1.59664e7i) q^{80} -4.78297e6 q^{81} +(3.15671e7 + 1.17457e7i) q^{82} +(4.07467e7 + 4.07467e7i) q^{83} +(-280534. - 3.83767e6i) q^{84} +(1.41597e7 + 1.41597e7i) q^{85} +(2.61247e7 + 5.70864e7i) q^{86} -4.90855e6 q^{87} +(2.17756e7 - 7.48123e7i) q^{88} +3.55568e7i q^{89} +(4.42101e6 + 9.66058e6i) q^{90} +(1.10390e6 - 1.10390e6i) q^{91} +(1.92055e7 + 1.65889e7i) q^{92} +(2.59146e7 - 2.59146e7i) q^{93} +(9.91857e7 + 3.69057e7i) q^{94} +4.87428e7i q^{95} +(-2.66732e7 - 4.11482e7i) q^{96} -1.43728e7 q^{97} +(-3.15892e7 + 8.48974e7i) q^{98} +(-2.94175e7 - 2.94175e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

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Database

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