LMFDB - Embedded newform 48.9.l.a.19.5

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			19.5
Character	$\chi$	$=$	48.19
Dual form			48.9.l.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.3280 - 8.85242i) q^{2} +(33.0681 - 33.0681i) q^{3} +(99.2693 + 235.970i) q^{4} +(-642.261 + 642.261i) q^{5} +(-733.463 + 147.998i) q^{6} -3321.99 q^{7} +(765.844 - 4023.77i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-13.3280 - 8.85242i) q^{2} +(33.0681 - 33.0681i) q^{3} +(99.2693 + 235.970i) q^{4} +(-642.261 + 642.261i) q^{5} +(-733.463 + 147.998i) q^{6} -3321.99 q^{7} +(765.844 - 4023.77i) q^{8} -2187.00i q^{9} +(14245.6 - 2874.47i) q^{10} +(2818.91 + 2818.91i) q^{11} +(11085.7 + 4520.42i) q^{12} +(-2766.38 - 2766.38i) q^{13} +(44275.3 + 29407.6i) q^{14} +42476.7i q^{15} +(-45827.2 + 46849.0i) q^{16} +30162.9 q^{17} +(-19360.2 + 29148.3i) q^{18} +(106294. - 106294. i) q^{19} +(-215311. - 87797.3i) q^{20} +(-109852. + 109852. i) q^{21} +(-12616.2 - 62524.6i) q^{22} +443611. q^{23} +(-107733. - 158383. i) q^{24} -434375. i q^{25} +(12381.0 + 61359.3i) q^{26} +(-72320.0 - 72320.0i) q^{27} +(-329771. - 783888. i) q^{28} +(314973. + 314973. i) q^{29} +(376022. - 566129. i) q^{30} -1.41498e6i q^{31} +(1.02551e6 - 218721. i) q^{32} +186432. q^{33} +(-402010. - 267015. i) q^{34} +(2.13358e6 - 2.13358e6i) q^{35} +(516065. - 217102. i) q^{36} +(-1.67007e6 + 1.67007e6i) q^{37} +(-2.35764e6 + 475722. i) q^{38} -182958. q^{39} +(2.09244e6 + 3.07618e6i) q^{40} -4.98022e6i q^{41} +(2.43656e6 - 491647. i) q^{42} +(-2.03856e6 - 2.03856e6i) q^{43} +(-385346. + 945009. i) q^{44} +(1.40463e6 + 1.40463e6i) q^{45} +(-5.91244e6 - 3.92703e6i) q^{46} +6.72352e6i q^{47} +(33789.9 + 3.06463e6i) q^{48} +5.27080e6 q^{49} +(-3.84527e6 + 5.78933e6i) q^{50} +(997430. - 997430. i) q^{51} +(378164. - 927397. i) q^{52} +(2.92612e6 - 2.92612e6i) q^{53} +(323671. + 1.60408e6i) q^{54} -3.62096e6 q^{55} +(-2.54412e6 + 1.33669e7i) q^{56} -7.02987e6i q^{57} +(-1.40968e6 - 6.98623e6i) q^{58} +(1.69351e7 + 1.69351e7i) q^{59} +(-1.00232e7 + 4.21664e6i) q^{60} +(2.92298e6 + 2.92298e6i) q^{61} +(-1.25260e7 + 1.88588e7i) q^{62} +7.26519e6i q^{63} +(-1.56042e7 - 6.16316e6i) q^{64} +3.55347e6 q^{65} +(-2.48476e6 - 1.65038e6i) q^{66} +(1.68235e7 - 1.68235e7i) q^{67} +(2.99425e6 + 7.11752e6i) q^{68} +(1.46694e7 - 1.46694e7i) q^{69} +(-4.73237e7 + 9.54895e6i) q^{70} +831221. q^{71} +(-8.79998e6 - 1.67490e6i) q^{72} -9.05852e6i q^{73} +(3.70427e7 - 7.47446e6i) q^{74} +(-1.43639e7 - 1.43639e7i) q^{75} +(3.56338e7 + 1.45304e7i) q^{76} +(-9.36440e6 - 9.36440e6i) q^{77} +(2.43845e6 + 1.61962e6i) q^{78} -2.11866e7i q^{79} +(-656281. - 5.95224e7i) q^{80} -4.78297e6 q^{81} +(-4.40870e7 + 6.63762e7i) q^{82} +(-1.73371e7 + 1.73371e7i) q^{83} +(-3.68266e7 - 1.50168e7i) q^{84} +(-1.93725e7 + 1.93725e7i) q^{85} +(9.12368e6 + 4.52161e7i) q^{86} +2.08311e7 q^{87} +(1.35015e7 - 9.18380e6i) q^{88} +9.27589e6i q^{89} +(-6.28646e6 - 3.11551e7i) q^{90} +(9.18987e6 + 9.18987e6i) q^{91} +(4.40370e7 + 1.04679e8i) q^{92} +(-4.67906e7 - 4.67906e7i) q^{93} +(5.95194e7 - 8.96108e7i) q^{94} +1.36537e8i q^{95} +(2.66790e7 - 4.11444e7i) q^{96} +1.18939e8 q^{97} +(-7.02491e7 - 4.66594e7i) q^{98} +(6.16497e6 - 6.16497e6i) 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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−13.3280	−	8.85242i	−0.832998	−	0.553276i
$2$	−13.3280	−	8.85242i	−0.832998	−	0.553276i
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$4$	99.2693	+	235.970i	0.387771	+	0.921756i
$5$	−642.261	+	642.261i	−1.02762	+	1.02762i	−0.0280107	+	0.999608i	$0.508917\pi$
$5$	−642.261	+	642.261i	−1.02762	+	1.02762i	−0.999608	+	0.0280107i	$0.991083\pi$
$6$	−733.463	+	147.998i	−0.565944	+	0.114196i
$7$	−3321.99			−1.38359			−0.691793	−	0.722096i	$-0.743179\pi$
$7$	−3321.99			−1.38359			−0.691793	+	0.722096i	$0.743179\pi$
$8$	765.844	−	4023.77i	0.186974	−	0.982365i
$9$		−	2187.00i		−	0.333333i
$10$	14245.6	−	2874.47i	1.42456	−	0.287447i
$11$	2818.91	+	2818.91i	0.192536	+	0.192536i	0.796791	−	0.604255i	$-0.206529\pi$
$11$	2818.91	+	2818.91i	0.192536	+	0.192536i	−0.604255	+	0.796791i	$0.706529\pi$
$12$	11085.7	+	4520.42i	0.534612	+	0.217999i
$13$	−2766.38	−	2766.38i	−0.0968585	−	0.0968585i	0.657017	−	0.753876i	$-0.271818\pi$
$13$	−2766.38	−	2766.38i	−0.0968585	−	0.0968585i	−0.753876	+	0.657017i	$0.771818\pi$
$14$	44275.3	+	29407.6i	1.15252	+	0.765505i
$15$			42476.7i			0.839047i
$16$	−45827.2	+	46849.0i	−0.699268	+	0.714860i
$17$	30162.9			0.361141			0.180571	−	0.983562i	$-0.442206\pi$
$17$	30162.9			0.361141			0.180571	+	0.983562i	$0.442206\pi$
$18$	−19360.2	+	29148.3i	−0.184425	+	0.277666i
$19$	106294.	−	106294.i	0.815630	−	0.815630i	−0.169841	−	0.985471i	$-0.554325\pi$
$19$	106294.	−	106294.i	0.815630	−	0.815630i	0.985471	+	0.169841i	$0.0543254\pi$
$20$	−215311.	−	87797.3i	−1.34569	−	0.548733i
$21$	−109852.	+	109852.i	−0.564846	+	0.564846i
$22$	−12616.2	−	62524.6i	−0.0538563	−	0.266907i
$23$	443611.			1.58523			0.792613	−	0.609725i	$-0.208720\pi$
$23$	443611.			1.58523			0.792613	+	0.609725i	$0.208720\pi$
$24$	−107733.	−	158383.i	−0.324717	−	0.477380i
$25$		−	434375.i		−	1.11200i
$26$	12381.0	+	61359.3i	0.0270934	+	0.134272i
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$	−329771.	−	783888.i	−0.536514	−	1.27533i
$29$	314973.	+	314973.i	0.445330	+	0.445330i	0.893798	−	0.448469i	$-0.148031\pi$
$29$	314973.	+	314973.i	0.445330	+	0.445330i	−0.448469	+	0.893798i	$0.648031\pi$
$30$	376022.	−	566129.i	0.464225	−	0.698924i
$31$		−	1.41498e6i		−	1.53215i	−0.642749	−	0.766077i	$-0.722206\pi$
$31$		−	1.41498e6i		−	1.53215i	0.642749	−	0.766077i	$-0.277794\pi$
$32$	1.02551e6	−	218721.i	0.978004	−	0.208588i
$33$	186432.			0.157205
$34$	−402010.	−	267015.i	−0.300830	−	0.199811i
$35$	2.13358e6	−	2.13358e6i	1.42180	−	1.42180i
$36$	516065.	−	217102.i	0.307252	−	0.129257i
$37$	−1.67007e6	+	1.67007e6i	−0.891101	+	0.891101i	−0.994627	−	0.103526i	$-0.966988\pi$
$37$	−1.67007e6	+	1.67007e6i	−0.891101	+	0.891101i	0.103526	+	0.994627i	$0.466988\pi$
$38$	−2.35764e6	+	475722.i	−1.13069	+	0.228149i
$39$	−182958.			−0.0790847
$40$	2.09244e6	+	3.07618e6i	0.817359	+	1.20163i
$41$		−	4.98022e6i		−	1.76243i	−0.472712	−	0.881217i	$-0.656725\pi$
$41$		−	4.98022e6i		−	1.76243i	0.472712	−	0.881217i	$-0.343275\pi$
$42$	2.43656e6	−	491647.i	0.783032	−	0.158000i
$43$	−2.03856e6	−	2.03856e6i	−0.596280	−	0.596280i	0.343040	−	0.939321i	$-0.388543\pi$
$43$	−2.03856e6	−	2.03856e6i	−0.596280	−	0.596280i	−0.939321	+	0.343040i	$0.888543\pi$
$44$	−385346.	+	945009.i	−0.102811	+	0.252131i
$45$	1.40463e6	+	1.40463e6i	0.342539	+	0.342539i
$46$	−5.91244e6	−	3.92703e6i	−1.32049	−	0.877068i
$47$			6.72352e6i			1.37786i	0.724828	+	0.688930i	$0.241919\pi$
$47$			6.72352e6i			1.37786i	−0.724828	+	0.688930i	$0.758081\pi$
$48$	33789.9	+	3.06463e6i	0.00636535	+	0.577315i
$49$	5.27080e6			0.914308
$50$	−3.84527e6	+	5.78933e6i	−0.615243	+	0.926292i
$51$	997430.	−	997430.i	0.147435	−	0.147435i
$52$	378164.	−	927397.i	0.0517210	−	0.126839i
$53$	2.92612e6	−	2.92612e6i	0.370841	−	0.370841i	−0.496942	−	0.867784i	$-0.665544\pi$
$53$	2.92612e6	−	2.92612e6i	0.370841	−	0.370841i	0.867784	+	0.496942i	$0.165544\pi$
$54$	323671.	+	1.60408e6i	0.0380653	+	0.188648i
$55$	−3.62096e6			−0.395706
$56$	−2.54412e6	+	1.33669e7i	−0.258694	+	1.35919i
$57$		−	7.02987e6i		−	0.665959i
$58$	−1.40968e6	−	6.98623e6i	−0.124568	−	0.617349i
$59$	1.69351e7	+	1.69351e7i	1.39759	+	1.39759i	0.806904	+	0.590682i	$0.201141\pi$
$59$	1.69351e7	+	1.69351e7i	1.39759	+	1.39759i	0.590682	+	0.806904i	$0.298859\pi$
$60$	−1.00232e7	+	4.21664e6i	−0.773396	+	0.325358i
$61$	2.92298e6	+	2.92298e6i	0.211109	+	0.211109i	0.804739	−	0.593629i	$-0.202306\pi$
$61$	2.92298e6	+	2.92298e6i	0.211109	+	0.211109i	−0.593629	+	0.804739i	$0.702306\pi$
$62$	−1.25260e7	+	1.88588e7i	−0.847704	+	1.27628i
$63$			7.26519e6i			0.461195i
$64$	−1.56042e7	−	6.16316e6i	−0.930082	−	0.367353i
$65$	3.55347e6			0.199067
$66$	−2.48476e6	−	1.65038e6i	−0.130951	−	0.0869776i
$67$	1.68235e7	−	1.68235e7i	0.834865	−	0.834865i	−0.153313	−	0.988178i	$-0.548994\pi$
$67$	1.68235e7	−	1.68235e7i	0.834865	−	0.834865i	0.988178	+	0.153313i	$0.0489942\pi$
$68$	2.99425e6	+	7.11752e6i	0.140040	+	0.332884i
$69$	1.46694e7	−	1.46694e7i	0.647166	−	0.647166i
$70$	−4.73237e7	+	9.54895e6i	−1.97100	+	0.397707i
$71$	831221.			0.0327102			0.0163551	−	0.999866i	$-0.494794\pi$
$71$	831221.			0.0327102			0.0163551	+	0.999866i	$0.494794\pi$
$72$	−8.79998e6	−	1.67490e6i	−0.327455	−	0.0623245i
$73$		−	9.05852e6i		−	0.318982i	−0.987199	−	0.159491i	$-0.949015\pi$
$73$		−	9.05852e6i		−	0.318982i	0.987199	−	0.159491i	$-0.0509853\pi$
$74$	3.70427e7	−	7.47446e6i	1.23531	−	0.249260i
$75$	−1.43639e7	−	1.43639e7i	−0.453972	−	0.453972i
$76$	3.56338e7	+	1.45304e7i	1.06809	+	0.435535i
$77$	−9.36440e6	−	9.36440e6i	−0.266389	−	0.266389i
$78$	2.43845e6	+	1.61962e6i	0.0658774	+	0.0437557i
$79$		−	2.11866e7i		−	0.543942i	−0.962305	−	0.271971i	$-0.912324\pi$
$79$		−	2.11866e7i		−	0.543942i	0.962305	−	0.271971i	$-0.0876755\pi$
$80$	−656281.	−	5.95224e7i	−0.0160225	−	1.45318i
$81$	−4.78297e6			−0.111111
$82$	−4.40870e7	+	6.63762e7i	−0.975113	+	1.46810i
$83$	−1.73371e7	+	1.73371e7i	−0.365312	+	0.365312i	−0.865764	−	0.500452i	$-0.833167\pi$
$83$	−1.73371e7	+	1.73371e7i	−0.365312	+	0.365312i	0.500452	+	0.865764i	$0.333167\pi$
$84$	−3.68266e7	−	1.50168e7i	−0.739681	−	0.301620i
$85$	−1.93725e7	+	1.93725e7i	−0.371116	+	0.371116i
$86$	9.12368e6	+	4.52161e7i	0.166792	+	0.826608i
$87$	2.08311e7			0.363610
$88$	1.35015e7	−	9.18380e6i	0.225139	−	0.153141i
$89$			9.27589e6i			0.147841i	0.997264	+	0.0739206i	$0.0235511\pi$
$89$			9.27589e6i			0.147841i	−0.997264	+	0.0739206i	$0.976449\pi$
$90$	−6.28646e6	−	3.11551e7i	−0.0958156	−	0.474854i
$91$	9.18987e6	+	9.18987e6i	0.134012	+	0.134012i
$92$	4.40370e7	+	1.04679e8i	0.614704	+	1.46119i
$93$	−4.67906e7	−	4.67906e7i	−0.625499	−	0.625499i
$94$	5.95194e7	−	8.96108e7i	0.762337	−	1.14775i
$95$			1.36537e8i			1.67631i
$96$	2.66790e7	−	4.11444e7i	0.314112	−	0.484424i
$97$	1.18939e8			1.34350			0.671752	−	0.740776i	$-0.265542\pi$
$97$	1.18939e8			1.34350			0.671752	+	0.740776i	$0.265542\pi$
$98$	−7.02491e7	−	4.66594e7i	−0.761617	−	0.505865i
$99$	6.16497e6	−	6.16497e6i	0.0641785	−	0.0641785i
$100$	1.02499e8	−	4.31200e7i	1.02499	−	0.431200i
$101$	1.27132e8	−	1.27132e8i	1.22171	−	1.22171i	0.254688	−	0.967023i	$-0.418027\pi$
$101$	1.27132e8	−	1.27132e8i	1.22171	−	1.22171i	0.967023	−	0.254688i	$-0.0819727\pi$
$102$	−2.21234e7	+	4.46404e6i	−0.204386	+	0.0412408i
$103$	7.02155e7			0.623855			0.311928	−	0.950106i	$-0.399025\pi$
$103$	7.02155e7			0.623855			0.311928	+	0.950106i	$0.399025\pi$
$104$	−1.32499e7	+	9.01264e6i	−0.113260	+	0.0770404i
$105$		−	1.41107e8i		−	1.16089i
$106$	−6.49024e7	+	1.30960e7i	−0.514088	+	0.103732i
$107$	−1.07892e7	−	1.07892e7i	−0.0823102	−	0.0823102i	0.664753	−	0.747063i	$-0.268537\pi$
$107$	−1.07892e7	−	1.07892e7i	−0.0823102	−	0.0823102i	−0.747063	+	0.664753i	$0.768537\pi$
$108$	9.88615e6	−	2.42445e7i	0.0726662	−	0.178204i
$109$	−1.29604e8	−	1.29604e8i	−0.918145	−	0.918145i	0.0787494	−	0.996894i	$-0.474907\pi$
$109$	−1.29604e8	−	1.29604e8i	−0.918145	−	0.918145i	−0.996894	+	0.0787494i	$0.974907\pi$
$110$	4.82600e7	+	3.20543e7i	0.329622	+	0.218935i
$111$			1.10452e8i			0.727581i
$112$	1.52237e8	−	1.55632e8i	0.967497	−	0.989069i
$113$	−1.02763e8			−0.630262			−0.315131	−	0.949048i	$-0.602048\pi$
$113$	−1.02763e8			−0.630262			−0.315131	+	0.949048i	$0.602048\pi$
$114$	−6.22314e7	+	9.36938e7i	−0.368460	+	0.554743i
$115$	−2.84914e8	+	2.84914e8i	−1.62901	+	1.62901i
$116$	−4.30569e7	+	1.05591e8i	−0.237799	+	0.583171i
$117$	−6.05007e6	+	6.05007e6i	−0.0322862	+	0.0322862i
$118$	−7.57936e7	−	3.75626e8i	−0.390935	−	1.93744i
$119$	−1.00201e8			−0.499670
$120$	1.70917e8	+	3.25306e7i	0.824250	+	0.156880i
$121$		−	1.98466e8i		−	0.925860i
$122$	−1.30819e7	−	6.48329e7i	−0.0590517	−	0.292655i
$123$	−1.64686e8	−	1.64686e8i	−0.719511	−	0.719511i
$124$	3.33891e8	−	1.40464e8i	1.41227	−	0.594124i
$125$	2.80986e7	+	2.80986e7i	0.115092	+	0.115092i
$126$	6.43145e7	−	9.68302e7i	0.255168	−	0.384174i
$127$			4.64840e8i			1.78685i	0.449210	+	0.893426i	$0.351706\pi$
$127$			4.64840e8i			1.78685i	−0.449210	+	0.893426i	$0.648294\pi$
$128$	1.53413e8	+	2.20277e8i	0.571508	+	0.820596i
$129$	−1.34823e8			−0.486861
$130$	−4.73606e7	−	3.14569e7i	−0.165823	−	0.110139i
$131$	9.86235e7	−	9.86235e7i	0.334885	−	0.334885i	−0.519553	−	0.854438i	$-0.673902\pi$
$131$	9.86235e7	−	9.86235e7i	0.334885	−	0.334885i	0.854438	+	0.519553i	$0.173902\pi$
$132$	1.85070e7	+	4.39923e7i	0.0609594	+	0.144904i
$133$	−3.53107e8	+	3.53107e8i	−1.12849	+	1.12849i
$134$	−3.73151e8	+	7.52941e7i	−1.15735	+	0.233530i
$135$	9.28966e7			0.279682
$136$	2.31001e7	−	1.21368e8i	0.0675239	−	0.354773i
$137$			1.45634e8i			0.413410i	0.978403	+	0.206705i	$0.0662741\pi$
$137$			1.45634e8i			0.413410i	−0.978403	+	0.206705i	$0.933726\pi$
$138$	−3.25373e8	+	6.56535e7i	−0.897150	+	0.181026i
$139$	2.39964e8	+	2.39964e8i	0.642816	+	0.642816i	0.951247	−	0.308431i	$-0.0998039\pi$
$139$	2.39964e8	+	2.39964e8i	0.642816	+	0.642816i	−0.308431	+	0.951247i	$0.599804\pi$
$140$	7.15260e8	+	2.91662e8i	1.86188	+	0.759219i
$141$	2.22334e8	+	2.22334e8i	0.562509	+	0.562509i
$142$	−1.10785e7	−	7.35832e6i	−0.0272475	−	0.0180978i
$143$		−	1.55964e7i		−	0.0372974i
$144$	1.02459e8	+	1.00224e8i	0.238287	+	0.233089i
$145$	−4.04590e8			−0.915258
$146$	−8.01898e7	+	1.20732e8i	−0.176485	+	0.265711i
$147$	1.74296e8	−	1.74296e8i	0.373265	−	0.373265i
$148$	−5.59871e8	−	2.28299e8i	−1.16692	−	0.475835i
$149$	4.02530e8	−	4.02530e8i	0.816683	−	0.816683i	−0.168943	−	0.985626i	$-0.554035\pi$
$149$	4.02530e8	−	4.02530e8i	0.816683	−	0.816683i	0.985626	+	0.168943i	$0.0540354\pi$
$150$	6.42865e7	+	3.18598e8i	0.126986	+	0.629329i
$151$	−6.49957e8			−1.25019			−0.625096	−	0.780548i	$-0.714940\pi$
$151$	−6.49957e8			−1.25019			−0.625096	+	0.780548i	$0.714940\pi$
$152$	−3.46297e8	−	5.09106e8i	−0.648745	−	0.953748i
$153$		−	6.59663e7i		−	0.120380i
$154$	4.19108e7	+	2.07706e8i	0.0745148	+	0.369289i
$155$	9.08785e8	+	9.08785e8i	1.57447	+	1.57447i
$156$	−1.81621e7	−	4.31724e7i	−0.0306667	−	0.0728968i
$157$	4.40501e8	+	4.40501e8i	0.725017	+	0.725017i	0.969623	−	0.244606i	$-0.0786585\pi$
$157$	4.40501e8	+	4.40501e8i	0.725017	+	0.725017i	−0.244606	+	0.969623i	$0.578658\pi$
$158$	−1.87553e8	+	2.82374e8i	−0.300950	+	0.453103i
$159$		−	1.93522e8i		−	0.302791i
$160$	−5.18170e8	+	7.99122e8i	−0.790665	+	1.21936i
$161$	−1.47367e9			−2.19330
$162$	6.37472e7	+	4.23409e7i	0.0925553	+	0.0614751i
$163$	1.18343e8	−	1.18343e8i	0.167646	−	0.167646i	−0.618298	−	0.785944i	$-0.712178\pi$
$163$	1.18343e8	−	1.18343e8i	0.167646	−	0.167646i	0.785944	+	0.618298i	$0.212178\pi$
$164$	1.17518e9	−	4.94383e8i	1.62453	−	0.683420i
$165$	−1.19738e8	+	1.19738e8i	−0.161546	+	0.161546i
$166$	3.84544e8	−	7.75930e7i	0.506423	−	0.102186i
$167$	−1.32515e9			−1.70372			−0.851861	−	0.523768i	$-0.824526\pi$
$167$	−1.32515e9			−1.70372			−0.851861	+	0.523768i	$0.824526\pi$
$168$	3.57889e8	+	5.26148e8i	0.449274	+	0.660497i
$169$		−	8.00425e8i		−	0.981237i
$170$	4.29689e8	−	8.67023e7i	0.514468	−	0.103809i
$171$	−2.32464e8	−	2.32464e8i	−0.271877	−	0.271877i
$172$	2.78672e8	−	6.83406e8i	0.318405	−	0.780845i
$173$	−2.88853e8	−	2.88853e8i	−0.322472	−	0.322472i	0.527243	−	0.849715i	$-0.323226\pi$
$173$	−2.88853e8	−	2.88853e8i	−0.322472	−	0.322472i	−0.849715	+	0.527243i	$0.823226\pi$
$174$	−2.77637e8	−	1.84406e8i	−0.302886	−	0.201177i
$175$			1.44299e9i			1.53855i
$176$	−2.61246e8	+	2.88045e6i	−0.272270	+	0.00300199i
$177$	1.12002e9			1.14112
$178$	8.21141e7	−	1.23629e8i	0.0817970	−	0.123151i
$179$	8.46841e8	−	8.46841e8i	0.824878	−	0.824878i	−0.161925	−	0.986803i	$-0.551770\pi$
$179$	8.46841e8	−	8.46841e8i	0.824878	−	0.824878i	0.986803	+	0.161925i	$0.0517704\pi$
$180$	−1.92013e8	+	4.70885e8i	−0.182911	+	0.448564i
$181$	1.03102e9	−	1.03102e9i	0.960626	−	0.960626i	−0.0386273	−	0.999254i	$-0.512299\pi$
$181$	1.03102e9	−	1.03102e9i	0.960626	−	0.960626i	0.999254	+	0.0386273i	$0.0122985\pi$
$182$	−4.11297e7	−	2.03835e8i	−0.0374860	−	0.185777i
$183$	1.93315e8			0.172370
$184$	3.39737e8	−	1.78499e9i	0.296396	−	1.55727i
$185$		−	2.14524e9i		−	1.83142i
$186$	2.09413e8	+	1.03783e9i	0.174966	+	0.867113i
$187$	8.50266e7	+	8.50266e7i	0.0695326	+	0.0695326i
$188$	−1.58654e9	+	6.67439e8i	−1.27005	+	0.534294i
$189$	2.40246e8	+	2.40246e8i	0.188282	+	0.188282i
$190$	1.20868e9	−	1.81976e9i	0.927465	−	1.39637i
$191$		−	8.68915e8i		−	0.652895i	−0.945215	−	0.326448i	$-0.894148\pi$
$191$		−	8.68915e8i		−	0.652895i	0.945215	−	0.326448i	$-0.105852\pi$
$192$	−7.19805e8	+	3.12197e8i	−0.529675	+	0.229733i
$193$	−2.81048e8			−0.202559			−0.101279	−	0.994858i	$-0.532294\pi$
$193$	−2.81048e8			−0.202559			−0.101279	+	0.994858i	$0.532294\pi$
$194$	−1.58522e9	−	1.05290e9i	−1.11914	−	0.743328i
$195$	1.17507e8	−	1.17507e8i	0.0812689	−	0.0812689i
$196$	5.23229e8	+	1.24375e9i	0.354542	+	0.842769i
$197$	1.66138e9	−	1.66138e9i	1.10308	−	1.10308i	0.109038	−	0.994038i	$-0.465223\pi$
$197$	1.66138e9	−	1.66138e9i	1.10308	−	1.10308i	0.994038	−	0.109038i	$-0.0347769\pi$
$198$	−1.36741e8	+	2.75916e7i	−0.0889691	+	0.0179521i
$199$	5.34908e8			0.341089			0.170544	−	0.985350i	$-0.445447\pi$
$199$	5.34908e8			0.341089			0.170544	+	0.985350i	$0.445447\pi$
$200$	−1.74782e9	−	3.32663e8i	−1.09239	−	0.207914i
$201$		−	1.11264e9i		−	0.681664i
$202$	−2.81983e9	+	5.68984e8i	−1.69363	+	0.341739i
$203$	−1.04634e9	−	1.04634e9i	−0.616151	−	0.616151i
$204$	3.34377e8	+	1.36349e8i	0.193071	+	0.0787283i
$205$	3.19860e9	+	3.19860e9i	1.81111	+	1.81111i
$206$	−9.35829e8	−	6.21577e8i	−0.519670	−	0.345164i
$207$		−	9.70178e8i		−	0.528409i
$208$	2.56377e8	−	2.82676e6i	0.136970	−	0.00151021i
$209$	5.99266e8			0.314076
$210$	−1.24914e9	+	1.88067e9i	−0.642294	+	0.967021i
$211$	9.61799e8	−	9.61799e8i	0.485238	−	0.485238i	−0.421562	−	0.906800i	$-0.638518\pi$
$211$	9.61799e8	−	9.61799e8i	0.485238	−	0.485238i	0.906800	+	0.421562i	$0.138518\pi$
$212$	9.80948e8	+	4.00001e8i	0.485626	+	0.198024i
$213$	2.74869e7	−	2.74869e7i	0.0133539	−	0.0133539i
$214$	4.82875e7	+	2.39308e8i	0.0230239	+	0.114105i
$215$	2.61858e9			1.22550
$216$	−3.46384e8	+	2.35613e8i	−0.159127	+	0.108239i
$217$			4.70053e9i			2.11987i
$218$	5.80047e8	+	2.87466e9i	0.256825	+	1.27280i
$219$	−2.99548e8	−	2.99548e8i	−0.130224	−	0.130224i
$220$	−3.59450e8	−	8.54436e8i	−0.153443	−	0.364745i
$221$	−8.34419e7	−	8.34419e7i	−0.0349796	−	0.0349796i
$222$	9.77767e8	−	1.47210e9i	0.402553	−	0.606073i
$223$			3.25473e9i			1.31612i	0.752966	+	0.658059i	$0.228622\pi$
$223$			3.25473e9i			1.31612i	−0.752966	+	0.658059i	$0.771378\pi$
$224$	−3.40674e9	+	7.26587e8i	−1.35315	+	0.288600i
$225$	−9.49977e8			−0.370666
$226$	1.36962e9	+	9.09698e8i	0.525007	+	0.348709i
$227$	2.09780e9	−	2.09780e9i	0.790061	−	0.790061i	−0.191443	−	0.981504i	$-0.561317\pi$
$227$	2.09780e9	−	2.09780e9i	0.790061	−	0.790061i	0.981504	+	0.191443i	$0.0613166\pi$
$228$	1.65883e9	−	6.97850e8i	0.613852	−	0.258240i
$229$	−3.15202e9	+	3.15202e9i	−1.14617	+	1.14617i	−0.158865	+	0.987300i	$0.550784\pi$
$229$	−3.15202e9	+	3.15202e9i	−1.14617	+	1.14617i	−0.987300	+	0.158865i	$0.949216\pi$
$230$	6.31951e9	−	1.27515e9i	2.25825	−	0.455668i
$231$	−6.19326e8			−0.217506
$232$	1.50860e9	−	1.02616e9i	0.520741	−	0.354211i
$233$		−	9.88788e8i		−	0.335490i	−0.985830	−	0.167745i	$-0.946351\pi$
$233$		−	9.88788e8i		−	0.335490i	0.985830	−	0.167745i	$-0.0536485\pi$
$234$	1.34193e8	−	2.70773e7i	0.0447575	−	0.00903114i
$235$	−4.31826e9	−	4.31826e9i	−1.41591	−	1.41591i
$236$	−2.31503e9	+	5.67729e9i	−0.746291	+	1.83018i
$237$	−7.00601e8	−	7.00601e8i	−0.222064	−	0.222064i
$238$	1.33547e9	+	8.87020e8i	0.416224	+	0.276456i
$239$			1.74940e8i			0.0536164i	0.999641	+	0.0268082i	$0.00853434\pi$
$239$			1.74940e8i			0.0536164i	−0.999641	+	0.0268082i	$0.991466\pi$
$240$	−1.99000e9	−	1.94659e9i	−0.599801	−	0.586718i
$241$	−3.74568e9			−1.11036			−0.555178	−	0.831732i	$-0.687350\pi$
$241$	−3.74568e9			−1.11036			−0.555178	+	0.831732i	$0.687350\pi$
$242$	−1.75691e9	+	2.64515e9i	−0.512256	+	0.771239i
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$	−3.99572e8	+	9.79897e8i	−0.112729	+	0.276453i
$245$	−3.38523e9	+	3.38523e9i	−0.939560	+	0.939560i
$246$	7.37061e8	+	3.65281e9i	0.201263	+	0.997439i
$247$	−5.88097e8			−0.158002
$248$	−5.69353e9	−	1.08365e9i	−1.50513	−	0.286472i
$249$			1.14661e9i			0.298276i
$250$	−1.25757e8	−	6.23238e8i	−0.0321937	−	0.159549i
$251$	1.82386e8	+	1.82386e8i	0.0459512	+	0.0459512i	0.729709	−	0.683758i	$-0.239656\pi$
$251$	1.82386e8	+	1.82386e8i	0.0459512	+	0.0459512i	−0.683758	+	0.729709i	$0.739656\pi$
$252$	−1.71436e9	+	7.21210e8i	−0.425109	+	0.178838i
$253$	1.25050e9	+	1.25050e9i	0.305213	+	0.305213i
$254$	4.11496e9	−	6.19537e9i	0.988623	−	1.48844i
$255$			1.28122e9i			0.303015i
$256$	−9.46993e7	−	4.29392e9i	−0.0220489	−	0.999757i
$257$	−3.81357e9			−0.874176			−0.437088	−	0.899419i	$-0.643990\pi$
$257$	−3.81357e9			−0.874176			−0.437088	+	0.899419i	$0.643990\pi$
$258$	1.79691e9	+	1.19351e9i	0.405554	+	0.269369i
$259$	5.54794e9	−	5.54794e9i	1.23291	−	1.23291i
$260$	3.52751e8	+	8.38512e8i	0.0771924	+	0.183491i
$261$	6.88846e8	−	6.88846e8i	0.148443	−	0.148443i
$262$	−2.18751e9	+	4.41394e8i	−0.464242	+	0.0936744i
$263$	−4.11275e9			−0.859627			−0.429813	−	0.902918i	$-0.641421\pi$
$263$	−4.11275e9			−0.859627			−0.429813	+	0.902918i	$0.641421\pi$
$264$	1.42778e8	−	7.50160e8i	0.0293931	−	0.154432i
$265$			3.75866e9i			0.762166i
$266$	7.83204e9	−	1.58034e9i	1.56440	−	0.315664i
$267$	3.06736e8	+	3.06736e8i	0.0603559	+	0.0603559i
$268$	5.63988e9	+	2.29977e9i	1.09328	+	0.445806i
$269$	4.34863e9	+	4.34863e9i	0.830507	+	0.830507i	0.987586	−	0.157079i	$-0.0502077\pi$
$269$	4.34863e9	+	4.34863e9i	0.830507	+	0.830507i	−0.157079	+	0.987586i	$0.550208\pi$
$270$	−1.23812e9	−	8.22360e8i	−0.232975	−	0.154742i
$271$		−	6.01493e9i		−	1.11520i	−0.830109	−	0.557601i	$-0.811722\pi$
$271$		−	6.01493e9i		−	1.11520i	0.830109	−	0.557601i	$-0.188278\pi$
$272$	−1.38228e9	+	1.41310e9i	−0.252535	+	0.258166i
$273$	6.07783e8			0.109420
$274$	1.28922e9	−	1.94101e9i	0.228730	−	0.344370i
$275$	1.22446e9	−	1.22446e9i	0.214099	−	0.214099i
$276$	4.91775e9	+	2.00531e9i	0.847481	+	0.345577i
$277$	3.62486e9	−	3.62486e9i	0.615704	−	0.615704i	−0.328723	−	0.944426i	$-0.606618\pi$
$277$	3.62486e9	−	3.62486e9i	0.615704	−	0.615704i	0.944426	+	0.328723i	$0.106618\pi$
$278$	−1.07397e9	−	5.32249e9i	−0.179809	−	0.891119i
$279$	−3.09455e9			−0.510718
$280$	−6.95105e9	−	1.02190e10i	−1.13089	−	1.66256i
$281$		−	1.58515e9i		−	0.254241i	−0.991887	−	0.127121i	$-0.959426\pi$
$281$		−	1.58515e9i		−	0.254241i	0.991887	−	0.127121i	$-0.0405735\pi$
$282$	−9.95066e8	−	4.93145e9i	−0.157346	−	0.779792i
$283$	1.80875e9	+	1.80875e9i	0.281990	+	0.281990i	0.833902	−	0.551912i	$-0.186102\pi$
$283$	1.80875e9	+	1.80875e9i	0.281990	+	0.281990i	−0.551912	+	0.833902i	$0.686102\pi$
$284$	8.25147e7	+	1.96143e8i	0.0126841	+	0.0301508i
$285$	4.51501e9	+	4.51501e9i	0.684352	+	0.684352i
$286$	−1.38066e8	+	2.07868e8i	−0.0206358	+	0.0310687i
$287$			1.65442e10i			2.43848i
$288$	−4.78342e8	−	2.24279e9i	−0.0695294	−	0.326001i
$289$	−6.06596e9			−0.869577
$290$	5.39236e9	+	3.58160e9i	0.762408	+	0.506390i
$291$	3.93310e9	−	3.93310e9i	0.548483	−	0.548483i
$292$	2.13753e9	−	8.99233e8i	0.294023	−	0.123692i
$293$	−7.03436e9	+	7.03436e9i	−0.954453	+	0.954453i	−0.999007	−	0.0445544i	$-0.985813\pi$
$293$	−7.03436e9	+	7.03436e9i	−0.954453	+	0.954453i	0.0445544	+	0.999007i	$0.485813\pi$
$294$	−3.86594e9	+	7.80067e8i	−0.517447	+	0.104410i
$295$	−2.17535e10			−2.87237
$296$	5.44095e9	+	7.99897e9i	0.708774	+	1.04200i
$297$		−	4.07728e8i		−	0.0524016i
$298$	−8.92828e9	+	1.80154e9i	−1.13215	+	0.228444i
$299$	−1.22720e9	−	1.22720e9i	−0.153543	−	0.153543i
$300$	1.96355e9	−	4.81535e9i	0.242414	−	0.594488i
$301$	6.77208e9	+	6.77208e9i	0.825004	+	0.825004i
$302$	8.66261e9	+	5.75369e9i	1.04141	+	0.691702i
$303$		−	8.40801e9i		−	0.997523i
$304$	1.08614e8	+	9.85091e9i	0.0127172	+	1.15341i
$305$	−3.75464e9			−0.433879
$306$	−5.83961e8	+	8.79196e8i	−0.0666037	+	0.100277i
$307$	2.97287e9	−	2.97287e9i	0.334674	−	0.334674i	−0.519684	−	0.854358i	$-0.673950\pi$
$307$	2.97287e9	−	2.97287e9i	0.334674	−	0.334674i	0.854358	+	0.519684i	$0.173950\pi$
$308$	1.28012e9	−	3.13931e9i	0.142248	−	0.348844i
$309$	2.32189e9	−	2.32189e9i	0.254688	−	0.254688i
$310$	−4.06731e9	−	2.01572e10i	−0.440413	−	2.18265i
$311$	1.31373e10			1.40432			0.702158	−	0.712021i	$-0.252220\pi$
$311$	1.31373e10			1.40432			0.702158	+	0.712021i	$0.252220\pi$
$312$	−1.40117e8	+	7.36179e8i	−0.0147867	+	0.0776900i
$313$		−	1.14009e10i		−	1.18785i	−0.804521	−	0.593924i	$-0.797578\pi$
$313$		−	1.14009e10i		−	1.18785i	0.804521	−	0.593924i	$-0.202422\pi$
$314$	−1.97148e9	−	9.77048e9i	−0.202803	−	1.00507i
$315$	−4.66615e9	−	4.66615e9i	−0.473932	−	0.473932i
$316$	4.99939e9	−	2.10318e9i	0.501382	−	0.210925i
$317$	−1.59061e9	−	1.59061e9i	−0.157517	−	0.157517i	0.623949	−	0.781465i	$-0.285527\pi$
$317$	−1.59061e9	−	1.59061e9i	−0.157517	−	0.157517i	−0.781465	+	0.623949i	$0.785527\pi$
$318$	−1.71314e9	+	2.57926e9i	−0.167527	+	0.252224i
$319$			1.77576e9i			0.171484i
$320$	1.39803e10	−	6.06361e9i	1.33327	−	0.578271i
$321$	−7.13557e8			−0.0672060
$322$	1.96410e10	+	1.30456e10i	1.82701	+	1.21350i
$323$	3.20613e9	−	3.20613e9i	0.294558	−	0.294558i
$324$	−4.74802e8	−	1.12863e9i	−0.0430856	−	0.102417i
$325$	−1.20164e9	+	1.20164e9i	−0.107707	+	0.107707i
$326$	−2.62490e9	+	5.29650e8i	−0.232403	+	0.0468941i
$327$	−8.57150e9			−0.749662
$328$	−2.00392e10	−	3.81407e9i	−1.73135	−	0.329529i
$329$		−	2.23354e10i		−	1.90639i
$330$	2.65584e9	−	5.35894e8i	0.223948	−	0.0451880i
$331$	−4.52678e8	−	4.52678e8i	−0.0377118	−	0.0377118i	0.687999	−	0.725711i	$-0.258489\pi$
$331$	−4.52678e8	−	4.52678e8i	−0.0377118	−	0.0377118i	−0.725711	+	0.687999i	$0.758489\pi$
$332$	−5.81207e9	−	2.36999e9i	−0.478386	−	0.195071i
$333$	3.65244e9	+	3.65244e9i	0.297034	+	0.297034i
$334$	1.76615e10	+	1.17308e10i	1.41920	+	0.942629i
$335$			2.16101e10i			1.71584i
$336$	−1.12250e8	−	1.01807e10i	−0.00880701	−	0.798765i
$337$	1.94981e10			1.51173			0.755863	−	0.654730i	$-0.227217\pi$
$337$	1.94981e10			1.51173			0.755863	+	0.654730i	$0.227217\pi$
$338$	−7.08570e9	+	1.06680e10i	−0.542895	+	0.817368i
$339$	−3.39816e9	+	3.39816e9i	−0.257303	+	0.257303i
$340$	−6.49440e9	−	2.64822e9i	−0.485986	−	0.198170i
$341$	3.98870e9	−	3.98870e9i	0.294994	−	0.294994i
$342$	1.04040e9	+	5.15615e9i	0.0760498	+	0.376896i
$343$	1.64105e9			0.118562
$344$	−9.76393e9	+	6.64148e9i	−0.697253	+	0.474276i
$345$			1.88432e10i			1.33008i
$346$	1.29277e9	+	6.40687e9i	0.0902024	+	0.447035i
$347$	5.59073e9	+	5.59073e9i	0.385612	+	0.385612i	0.873119	−	0.487507i	$-0.162094\pi$
$347$	5.59073e9	+	5.59073e9i	0.385612	+	0.385612i	−0.487507	+	0.873119i	$0.662094\pi$
$348$	2.06789e9	+	4.91551e9i	0.140997	+	0.335160i
$349$	−1.39382e10	−	1.39382e10i	−0.939520	−	0.939520i	0.0587529	−	0.998273i	$-0.481288\pi$
$349$	−1.39382e10	−	1.39382e10i	−0.939520	−	0.939520i	−0.998273	+	0.0587529i	$0.981288\pi$
$350$	1.27739e10	−	1.92321e10i	0.851241	−	1.28160i
$351$			4.00129e8i			0.0263616i
$352$	3.50738e9	+	2.27427e9i	0.228461	+	0.148140i
$353$	−2.54889e10			−1.64154			−0.820771	−	0.571257i	$-0.806456\pi$
$353$	−2.54889e10			−1.64154			−0.820771	+	0.571257i	$0.806456\pi$
$354$	−1.49276e10	−	9.91490e9i	−0.950554	−	0.631357i
$355$	−5.33861e8	+	5.33861e8i	−0.0336136	+	0.0336136i
$356$	−2.18883e9	+	9.20811e8i	−0.136273	+	0.0573285i
$357$	−3.31345e9	+	3.31345e9i	−0.203989	+	0.203989i
$358$	−1.87833e10	+	3.79007e9i	−1.14351	+	0.230736i
$359$	2.59116e10			1.55997			0.779985	−	0.625798i	$-0.215226\pi$
$359$	2.59116e10			1.55997			0.779985	+	0.625798i	$0.215226\pi$
$360$	6.72761e9	−	4.57616e9i	0.400545	−	0.272453i
$361$		−	5.61317e9i		−	0.330506i
$362$	−2.28685e10	+	4.61439e9i	−1.33169	+	0.268708i
$363$	−6.56291e9	−	6.56291e9i	−0.377981	−	0.377981i
$364$	−1.25626e9	+	3.08080e9i	−0.0715605	+	0.175492i
$365$	5.81794e9	+	5.81794e9i	0.327791	+	0.327791i
$366$	−2.57650e9	−	1.71131e9i	−0.143584	−	0.0953681i
$367$		−	1.52203e10i		−	0.838992i	−0.907757	−	0.419496i	$-0.862207\pi$
$367$		−	1.52203e10i		−	0.838992i	0.907757	−	0.419496i	$-0.137793\pi$
$368$	−2.03295e10	+	2.07828e10i	−1.10850	+	1.13321i
$369$	−1.08917e10			−0.587478
$370$	−1.89906e10	+	2.85917e10i	−1.01328	+	1.52557i
$371$	−9.72052e9	+	9.72052e9i	−0.513090	+	0.513090i
$372$	6.39629e9	−	1.56860e10i	0.334007	−	0.819108i
$373$	2.17994e10	−	2.17994e10i	1.12619	−	1.12619i	0.135393	−	0.990792i	$-0.456770\pi$
$373$	2.17994e10	−	2.17994e10i	1.12619	−	1.12619i	0.990792	−	0.135393i	$-0.0432298\pi$
$374$	−3.80540e8	−	1.88592e9i	−0.0194498	−	0.0963912i
$375$	1.85834e9			0.0939722
$376$	2.70539e10	+	5.14916e9i	1.35356	+	0.257623i
$377$		−	1.74267e9i		−	0.0862679i
$378$	−1.07523e9	−	5.32875e9i	−0.0526665	−	0.261011i
$379$	1.43873e10	+	1.43873e10i	0.697306	+	0.697306i	0.963829	−	0.266523i	$-0.0858748\pi$
$379$	1.43873e10	+	1.43873e10i	0.697306	+	0.697306i	−0.266523	+	0.963829i	$0.585875\pi$
$380$	−3.22185e10	+	1.35539e10i	−1.54515	+	0.650025i
$381$	1.53714e10	+	1.53714e10i	0.729480	+	0.729480i
$382$	−7.69200e9	+	1.15809e10i	−0.361232	+	0.543860i
$383$		−	1.23809e10i		−	0.575382i	−0.957723	−	0.287691i	$-0.907112\pi$
$383$		−	1.23809e10i		−	0.575382i	0.957723	−	0.287691i	$-0.0928876\pi$
$384$	1.23572e10	+	2.21106e9i	0.568324	+	0.101690i
$385$	1.20288e10			0.547493
$386$	3.74580e9	+	2.48795e9i	0.168731	+	0.112071i
$387$	−4.45834e9	+	4.45834e9i	−0.198760	+	0.198760i
$388$	1.18070e10	+	2.80661e10i	0.520971	+	1.23838i
$389$	−1.38519e9	+	1.38519e9i	−0.0604940	+	0.0604940i	−0.736707	−	0.676213i	$-0.763620\pi$
$389$	−1.38519e9	+	1.38519e9i	−0.0604940	+	0.0604940i	0.676213	+	0.736707i	$0.263620\pi$
$390$	−2.60634e9	+	5.25906e8i	−0.112661	+	0.0227326i
$391$	1.33806e10			0.572491
$392$	4.03661e9	−	2.12085e10i	0.170951	−	0.898184i
$393$		−	6.52259e9i		−	0.273432i
$394$	−3.68501e10	+	7.43560e9i	−1.52916	+	0.308554i
$395$	1.36073e10	+	1.36073e10i	0.558965	+	0.558965i
$396$	2.06674e9	+	8.42752e8i	0.0840435	+	0.0342704i
$397$	−1.03563e10	−	1.03563e10i	−0.416911	−	0.416911i	0.467226	−	0.884138i	$-0.345253\pi$
$397$	−1.03563e10	−	1.03563e10i	−0.416911	−	0.416911i	−0.884138	+	0.467226i	$0.845253\pi$
$398$	−7.12924e9	−	4.73523e9i	−0.284126	−	0.188716i
$399$			2.33531e10i			0.921412i
$400$	2.03500e10	+	1.99062e10i	0.794923	+	0.777585i
$401$	2.64412e10			1.02259			0.511297	−	0.859404i	$-0.329165\pi$
$401$	2.64412e10			1.02259			0.511297	+	0.859404i	$0.329165\pi$
$402$	−9.84956e9	+	1.48292e10i	−0.377149	+	0.567825i
$403$	−3.91436e9	+	3.91436e9i	−0.148402	+	0.148402i
$404$	4.26195e10	+	1.73789e10i	1.59986	+	0.652376i
$405$	3.07192e9	−	3.07192e9i	0.114180	−	0.114180i
$406$	4.68293e9	+	2.32082e10i	0.172351	+	0.854155i
$407$	−9.41555e9			−0.343137
$408$	−3.24955e9	−	4.77730e9i	−0.117269	−	0.172402i
$409$			3.91923e10i			1.40058i	0.713860	+	0.700289i	$0.246945\pi$
$409$			3.91923e10i			1.40058i	−0.713860	+	0.700289i	$0.753055\pi$
$410$	−1.43155e10	−	7.09462e10i	−0.506606	−	2.51069i
$411$	4.81585e9	+	4.81585e9i	0.168774	+	0.168774i
$412$	6.97024e9	+	1.65687e10i	0.241913	+	0.575042i
$413$	−5.62581e10	−	5.62581e10i	−1.93368	−	1.93368i
$414$	−8.58843e9	+	1.29305e10i	−0.292356	+	0.440163i
$415$		−	2.22699e10i		−	0.750803i
$416$	−3.44201e9	−	2.23189e9i	−0.114932	−	0.0745244i
$417$	1.58703e10			0.524857
$418$	−7.98700e9	−	5.30495e9i	−0.261624	−	0.173771i
$419$	−1.87056e10	+	1.87056e10i	−0.606898	+	0.606898i	−0.942134	−	0.335236i	$-0.891184\pi$
$419$	−1.87056e10	+	1.87056e10i	−0.606898	+	0.606898i	0.335236	+	0.942134i	$0.391184\pi$
$420$	3.32970e10	−	1.40076e10i	1.07006	−	0.450160i
$421$	2.64186e10	−	2.64186e10i	0.840972	−	0.840972i	−0.148013	−	0.988985i	$-0.547288\pi$
$421$	2.64186e10	−	2.64186e10i	0.840972	−	0.840972i	0.988985	+	0.148013i	$0.0472877\pi$
$422$	−2.13331e10	+	4.30457e9i	−0.672672	+	0.135731i
$423$	1.47043e10			0.459287
$424$	−9.53306e9	−	1.40150e10i	−0.294964	−	0.433639i
$425$		−	1.31020e10i		−	0.401589i
$426$	−6.09670e8	+	1.23019e8i	−0.0185121	+	0.00373537i
$427$	−9.71011e9	−	9.71011e9i	−0.292087	−	0.292087i
$428$	1.47489e9	−	3.61696e9i	0.0439525	−	0.107787i
$429$	−5.15742e8	−	5.15742e8i	−0.0152266	−	0.0152266i
$430$	−3.49004e10	−	2.31808e10i	−1.02084	−	0.678038i
$431$			4.48620e9i			0.130008i	0.997885	+	0.0650039i	$0.0207060\pi$
$431$			4.48620e9i			0.130008i	−0.997885	+	0.0650039i	$0.979294\pi$
$432$	6.70234e9	−	7.38986e7i	0.192438	−	0.00212178i
$433$	8.15879e8			0.0232100			0.0116050	−	0.999933i	$-0.496306\pi$
$433$	8.15879e8			0.0232100			0.0116050	+	0.999933i	$0.496306\pi$
$434$	4.16111e10	−	6.26486e10i	1.17287	−	1.76584i
$435$	−1.33790e10	+	1.33790e10i	−0.373652	+	0.373652i
$436$	1.77169e10	−	4.34482e10i	0.490276	−	1.20234i
$437$	4.71531e10	−	4.71531e10i	1.29296	−	1.29296i
$438$	1.34064e9	+	6.64409e9i	0.0364264	+	0.180526i
$439$	−1.26915e10			−0.341708			−0.170854	−	0.985296i	$-0.554653\pi$
$439$	−1.26915e10			−0.341708			−0.170854	+	0.985296i	$0.554653\pi$
$440$	−2.77309e9	+	1.45699e10i	−0.0739866	+	0.388728i
$441$		−	1.15272e10i		−	0.304769i
$442$	3.73448e8	+	1.85077e9i	0.00978456	+	0.0484914i
$443$	3.64322e10	+	3.64322e10i	0.945955	+	0.945955i	0.998613	−	0.0526580i	$-0.0167693\pi$
$443$	3.64322e10	+	3.64322e10i	0.945955	+	0.945955i	−0.0526580	+	0.998613i	$0.516769\pi$
$444$	−2.60633e10	+	1.09645e10i	−0.670652	+	0.282135i
$445$	−5.95755e9	−	5.95755e9i	−0.151924	−	0.151924i
$446$	2.88122e10	−	4.33789e10i	0.728177	−	1.09632i
$447$		−	2.66218e10i		−	0.666819i
$448$	5.18369e10	+	2.04739e10i	1.28685	+	0.508264i
$449$	−4.99421e10			−1.22880			−0.614400	−	0.788995i	$-0.710602\pi$
$449$	−4.99421e10			−1.22880			−0.614400	+	0.788995i	$0.710602\pi$
$450$	1.26613e10	+	8.40960e9i	0.308764	+	0.205081i
$451$	1.40388e10	−	1.40388e10i	0.339331	−	0.339331i
$452$	−1.02012e10	−	2.42488e10i	−0.244397	−	0.580948i
$453$	−2.14929e10	+	2.14929e10i	−0.510389	+	0.510389i
$454$	−4.65300e10	+	9.38880e9i	−1.09524	+	0.220997i
$455$	−1.18046e10			−0.275426
$456$	−2.82866e10	−	5.38378e9i	−0.654215	−	0.124517i
$457$		−	4.16526e10i		−	0.954942i	−0.878647	−	0.477471i	$-0.841553\pi$
$457$		−	4.16526e10i		−	0.954942i	0.878647	−	0.477471i	$-0.158447\pi$
$458$	6.99131e10	−	1.41070e10i	1.58890	−	0.320607i
$459$	−2.18138e9	−	2.18138e9i	−0.0491451	−	0.0491451i
$460$	−9.55144e10	−	3.89479e10i	−2.13323	−	0.869866i
$461$	2.35675e9	+	2.35675e9i	0.0521807	+	0.0521807i	0.732716	−	0.680535i	$-0.238253\pi$
$461$	2.35675e9	+	2.35675e9i	0.0521807	+	0.0521807i	−0.680535	+	0.732716i	$0.738253\pi$
$462$	8.25435e9	+	5.48253e9i	0.181182	+	0.120341i
$463$			1.66399e10i			0.362099i	0.983474	+	0.181049i	$0.0579494\pi$
$463$			1.66399e10i			0.362099i	−0.983474	+	0.181049i	$0.942051\pi$
$464$	−2.91905e10	+	3.21849e8i	−0.629753	+	0.00694352i
$465$	6.01036e10			1.28555
$466$	−8.75317e9	+	1.31785e10i	−0.185619	+	0.279462i
$467$	−2.06774e10	+	2.06774e10i	−0.434740	+	0.434740i	−0.890237	−	0.455498i	$-0.849461\pi$
$467$	−2.06774e10	+	2.06774e10i	−0.434740	+	0.434740i	0.455498	+	0.890237i	$0.349461\pi$
$468$	−2.02822e9	−	8.27045e8i	−0.0422796	−	0.0172403i
$469$	−5.58873e10	+	5.58873e10i	−1.15511	+	1.15511i
$470$	1.93265e10	+	9.57806e10i	0.396062	+	1.96284i
$471$	2.91331e10			0.591974
$472$	8.11123e10	−	5.51731e10i	1.63425	−	1.11163i
$473$		−	1.14931e10i		−	0.229610i
$474$	3.13557e9	+	1.55396e10i	0.0621159	+	0.307841i
$475$	−4.61713e10	−	4.61713e10i	−0.906980	−	0.906980i
$476$	−9.94686e9	−	2.36443e10i	−0.193757	−	0.460574i
$477$	−6.39942e9	−	6.39942e9i	−0.123614	−	0.123614i
$478$	1.54864e9	−	2.33160e9i	0.0296647	−	0.0446624i
$479$		−	8.37310e9i		−	0.159054i	−0.996833	−	0.0795269i	$-0.974659\pi$
$479$		−	8.37310e9i		−	0.159054i	0.996833	−	0.0795269i	$-0.0253410\pi$
$480$	9.29054e9	+	4.35604e10i	0.175015	+	0.820591i
$481$	9.24007e9			0.172622
$482$	4.99223e10	+	3.31583e10i	0.924924	+	0.614334i
$483$	−4.87315e10	+	4.87315e10i	−0.895409	+	0.895409i
$484$	4.68320e10	−	1.97016e10i	0.853417	−	0.359021i
$485$	−7.63902e10	+	7.63902e10i	−1.38061	+	1.38061i
$486$	3.50813e9	−	7.07869e8i	0.0628827	−	0.0126884i
$487$	−5.95303e10			−1.05833			−0.529166	−	0.848518i	$-0.677495\pi$
$487$	−5.95303e10			−1.05833			−0.529166	+	0.848518i	$0.677495\pi$
$488$	1.39999e10	−	9.52285e9i	0.246858	−	0.167914i
$489$		−	7.82676e9i		−	0.136882i
$490$	7.50858e10	−	1.51508e10i	1.30249	−	0.262815i
$491$	2.73699e10	+	2.73699e10i	0.470921	+	0.470921i	0.902212	−	0.431292i	$-0.141942\pi$
$491$	2.73699e10	+	2.73699e10i	0.470921	+	0.470921i	−0.431292	+	0.902212i	$0.641942\pi$
$492$	2.25127e10	−	5.52093e10i	0.384208	−	0.942218i
$493$	9.50050e9	+	9.50050e9i	0.160827	+	0.160827i
$494$	7.83814e9	+	5.20608e9i	0.131615	+	0.0874185i
$495$			7.91904e9i			0.131902i
$496$	6.62903e10	+	6.48444e10i	1.09528	+	1.07139i
$497$	−2.76131e9			−0.0452574
$498$	1.01503e10	−	1.52820e10i	0.165029	−	0.248464i
$499$	4.06734e10	−	4.06734e10i	0.656006	−	0.656006i	−0.298427	−	0.954433i	$-0.596462\pi$
$499$	4.06734e10	−	4.06734e10i	0.656006	−	0.656006i	0.954433	+	0.298427i	$0.0964618\pi$
$500$	−3.84109e9	+	9.41975e9i	−0.0614574	+	0.150716i
$501$	−4.38202e10	+	4.38202e10i	−0.695541	+	0.695541i
$502$	−8.16277e8	−	4.04539e9i	−0.0128535	−	0.0637009i
$503$	5.23840e10			0.818327			0.409164	−	0.912461i	$-0.365821\pi$
$503$	5.23840e10			0.818327			0.409164	+	0.912461i	$0.365821\pi$
$504$	2.92334e10	+	5.56400e9i	0.453062	+	0.0862313i
$505$			1.63304e11i			2.51091i
$506$	−5.59668e9	−	2.77366e10i	−0.0853745	−	0.423108i
$507$	−2.64685e10	−	2.64685e10i	−0.400588	−	0.400588i
$508$	−1.09688e11	+	4.61443e10i	−1.64704	+	0.692889i
$509$	−5.57041e10	−	5.57041e10i	−0.829881	−	0.829881i	0.157619	−	0.987500i	$-0.449618\pi$
$509$	−5.57041e10	−	5.57041e10i	−0.829881	−	0.829881i	−0.987500	+	0.157619i	$0.949618\pi$
$510$	1.13419e10	−	1.70761e10i	0.167651	−	0.252411i
$511$			3.00923e10i			0.441338i
$512$	−3.67495e10	+	5.80676e10i	−0.534775	+	0.844994i
$513$	−1.53743e10			−0.221986
$514$	5.08271e10	+	3.37593e10i	0.728187	+	0.483661i
$515$	−4.50967e10	+	4.50967e10i	−0.641085	+	0.641085i
$516$	−1.33838e10	−	3.18141e10i	−0.188790	−	0.448767i
$517$	−1.89530e10	+	1.89530e10i	−0.265287	+	0.265287i
$518$	−1.23056e11	+	2.48301e10i	−1.70916	+	0.344873i
$519$	−1.91036e10			−0.263298
$520$	2.72141e9	−	1.42984e10i	0.0372203	−	0.195557i
$521$			2.70246e10i			0.366782i	0.983040	+	0.183391i	$0.0587075\pi$
$521$			2.70246e10i			0.366782i	−0.983040	+	0.183391i	$0.941293\pi$
$522$	−1.52789e10	+	3.08296e9i	−0.205783	+	0.0415227i
$523$	−2.48643e10	−	2.48643e10i	−0.332330	−	0.332330i	0.521141	−	0.853471i	$-0.325507\pi$
$523$	−2.48643e10	−	2.48643e10i	−0.332330	−	0.332330i	−0.853471	+	0.521141i	$0.825507\pi$
$524$	3.30624e10	+	1.34819e10i	0.438540	+	0.178823i
$525$	4.77169e10	+	4.77169e10i	0.628108	+	0.628108i
$526$	5.48147e10	+	3.64078e10i	0.716067	+	0.475611i
$527$		−	4.26798e10i		−	0.553324i
$528$	−8.54368e9	+	8.73418e9i	−0.109928	+	0.112379i
$529$	1.18480e11			1.51294
$530$	3.32733e10	−	5.00953e10i	0.421689	−	0.634883i
$531$	3.70370e10	−	3.70370e10i	0.465862	−	0.465862i
$532$	−1.18375e11	−	4.82698e10i	−1.47779	−	0.602599i
$533$	−1.37772e10	+	1.37772e10i	−0.170707	+	0.170707i
$534$	−1.37281e9	−	6.80353e9i	−0.0168828	−	0.0836698i
$535$	1.38590e10			0.169167
$536$	−5.48095e10	−	8.05778e10i	−0.664044	−	0.976240i
$537$		−	5.60068e10i		−	0.673510i
$538$	−1.94625e10	−	9.64543e10i	−0.232311	−	1.15131i
$539$	1.48579e10	+	1.48579e10i	0.176037	+	0.176037i
$540$	9.22178e9	+	2.19208e10i	0.108453	+	0.257799i
$541$	−4.80828e10	−	4.80828e10i	−0.561307	−	0.561307i	0.368372	−	0.929679i	$-0.379915\pi$
$541$	−4.80828e10	−	4.80828e10i	−0.561307	−	0.561307i	−0.929679	+	0.368372i	$0.879915\pi$
$542$	−5.32467e10	+	8.01668e10i	−0.617015	+	0.928961i
$543$		−	6.81880e10i		−	0.784348i
$544$	3.09324e10	−	6.59725e9i	0.353198	−	0.0753299i
$545$	1.66479e11			1.88701
$546$	−8.10052e9	−	5.38035e9i	−0.0911469	−	0.0605397i
$547$	−9.79264e10	+	9.79264e10i	−1.09383	+	1.09383i	−0.0987158	+	0.995116i	$0.531473\pi$
$547$	−9.79264e10	+	9.79264e10i	−1.09383	+	1.09383i	−0.995116	+	0.0987158i	$0.968527\pi$
$548$	−3.43652e10	+	1.44570e10i	−0.381063	+	0.160308i
$549$	6.39256e9	−	6.39256e9i	0.0703697	−	0.0703697i
$550$	−2.71591e10	+	5.48014e9i	−0.296800	+	0.0598882i
$551$	6.69594e10			0.726449
$552$	−4.77917e10	−	7.02607e10i	−0.514750	−	0.756756i
$553$			7.03816e10i			0.752591i
$554$	−8.04007e10	+	1.62232e10i	−0.853534	+	0.172226i
$555$	−7.09390e10	−	7.09390e10i	−0.747676	−	0.747676i
$556$	−3.28031e10	+	8.04452e10i	−0.343254	+	0.841784i
$557$	1.48427e10	+	1.48427e10i	0.154203	+	0.154203i	0.779992	−	0.625789i	$-0.215223\pi$
$557$	1.48427e10	+	1.48427e10i	0.154203	+	0.154203i	−0.625789	+	0.779992i	$0.715223\pi$
$558$	4.12441e10	+	2.73943e10i	0.425427	+	0.282568i
$559$			1.12789e10i			0.115510i
$560$	2.18016e9	+	1.97733e11i	0.0221685	+	2.01060i
$561$	5.62334e9			0.0567731
$562$	−1.40324e10	+	2.11269e10i	−0.140666	+	0.211782i
$563$	1.36341e10	−	1.36341e10i	0.135704	−	0.135704i	−0.635992	−	0.771696i	$-0.719409\pi$
$563$	1.36341e10	−	1.36341e10i	0.135704	−	0.135704i	0.771696	+	0.635992i	$0.219409\pi$
$564$	−3.03931e10	+	7.45350e10i	−0.300371	+	0.736620i
$565$	6.60004e10	−	6.60004e10i	0.647669	−	0.647669i
$566$	−8.09516e9	−	4.01189e10i	−0.0788787	−	0.390915i
$567$	1.58890e10			0.153732
$568$	6.36586e8	−	3.34464e9i	0.00611595	−	0.0321334i
$569$			1.58350e10i			0.151067i	0.997143	+	0.0755336i	$0.0240660\pi$
$569$			1.58350e10i			0.151067i	−0.997143	+	0.0755336i	$0.975934\pi$
$570$	−2.02071e10	−	1.00145e11i	−0.191428	−	0.948700i
$571$	1.11746e11	+	1.11746e11i	1.05120	+	1.05120i	0.998616	+	0.0525866i	$0.0167466\pi$
$571$	1.11746e11	+	1.11746e11i	1.05120	+	1.05120i	0.0525866	+	0.998616i	$0.483253\pi$
$572$	3.68026e9	−	1.54824e9i	0.0343791	−	0.0144629i
$573$	−2.87334e10	−	2.87334e10i	−0.266543	−	0.266543i
$574$	1.46456e11	−	2.20501e11i	1.34915	−	2.03125i
$575$		−	1.92693e11i		−	1.76277i
$576$	−1.34788e10	+	3.41263e10i	−0.122451	+	0.310027i
$577$	−6.43529e10			−0.580583			−0.290292	−	0.956938i	$-0.593752\pi$
$577$	−6.43529e10			−0.580583			−0.290292	+	0.956938i	$0.593752\pi$
$578$	8.08469e10	+	5.36984e10i	0.724356	+	0.481116i
$579$	−9.29372e9	+	9.29372e9i	−0.0826943	+	0.0826943i
$580$	−4.01634e10	−	9.54710e10i	−0.354910	−	0.843644i
$581$	5.75937e10	−	5.75937e10i	0.505441	−	0.505441i
$582$	−8.72377e10	+	1.76028e10i	−0.760348	+	0.153422i
$583$	1.64969e10			0.142800
$584$	−3.64494e10	−	6.93741e9i	−0.313356	−	0.0596412i
$585$		−	7.77145e9i		−	0.0663557i
$586$	1.56025e11	−	3.14826e10i	1.32313	−	0.266981i
$587$	−7.52668e10	−	7.52668e10i	−0.633944	−	0.633944i	0.315111	−	0.949055i	$-0.397958\pi$
$587$	−7.52668e10	−	7.52668e10i	−0.633944	−	0.633944i	−0.949055	+	0.315111i	$0.897958\pi$
$588$	5.84306e10	+	2.38262e10i	0.488800	+	0.199318i
$589$	−1.50403e11	−	1.50403e11i	−1.24967	−	1.24967i
$590$	2.89930e11	+	1.92571e11i	2.39268	+	1.58921i
$591$		−	1.09878e11i		−	0.900657i
$592$	−1.70652e9	−	1.54776e11i	−0.0138939	−	1.26013i
$593$	−1.49438e11			−1.20848			−0.604242	−	0.796801i	$-0.706524\pi$
$593$	−1.49438e11			−1.20848			−0.604242	+	0.796801i	$0.706524\pi$
$594$	−3.60938e9	+	5.43418e9i	−0.0289925	+	0.0436504i
$595$	6.43551e10	−	6.43551e10i	0.513470	−	0.513470i
$596$	1.34944e11	+	5.50260e10i	1.06947	+	0.436097i
$597$	1.76884e10	−	1.76884e10i	0.139249	−	0.139249i
$598$	5.49237e9	+	2.72197e10i	0.0429492	+	0.212852i
$599$	8.48939e10			0.659430			0.329715	−	0.944080i	$-0.393047\pi$
$599$	8.48939e10			0.659430			0.329715	+	0.944080i	$0.393047\pi$
$600$	−6.87977e10	+	4.67966e10i	−0.530846	+	0.361085i
$601$			1.87711e11i			1.43877i	0.694612	+	0.719385i	$0.255576\pi$
$601$			1.87711e11i			1.43877i	−0.694612	+	0.719385i	$0.744424\pi$
$602$	−3.03088e10	−	1.50207e11i	−0.230771	−	1.14368i
$603$	−3.67929e10	−	3.67929e10i	−0.278288	−	0.278288i
$604$	−6.45208e10	−	1.53370e11i	−0.484788	−	1.15237i
$605$	1.27467e11	+	1.27467e11i	0.951431	+	0.951431i
$606$	−7.44313e10	+	1.12062e11i	−0.551906	+	0.830934i
$607$		−	2.18676e11i		−	1.61082i	−0.592721	−	0.805408i	$-0.701946\pi$
$607$		−	2.18676e11i		−	1.61082i	0.592721	−	0.805408i	$-0.298054\pi$
$608$	8.57568e10	−	1.32254e11i	0.627559	−	0.967820i
$609$	−6.92008e10			−0.503086
$610$	5.00417e10	+	3.32376e10i	0.361420	+	0.240055i
$611$	1.85998e10	−	1.85998e10i	0.133458	−	0.133458i
$612$	1.55660e10	−	6.54842e9i	0.110961	−	0.0466800i
$613$	3.28307e10	−	3.28307e10i	0.232508	−	0.232508i	−0.581231	−	0.813739i	$-0.697429\pi$
$613$	3.28307e10	−	3.28307e10i	0.232508	−	0.232508i	0.813739	+	0.581231i	$0.197429\pi$
$614$	−6.59393e10	+	1.33052e10i	−0.463950	+	0.0936155i
$615$	2.11543e11			1.47876
$616$	−4.48518e10	+	3.05085e10i	−0.311499	+	0.211884i
$617$			2.76340e11i			1.90679i	0.301726	+	0.953395i	$0.402437\pi$
$617$			2.76340e11i			1.90679i	−0.301726	+	0.953395i	$0.597563\pi$
$618$	−5.15005e10	+	1.03917e10i	−0.353067	+	0.0712417i
$619$	1.58672e11	+	1.58672e11i	1.08078	+	1.08078i	0.996437	+	0.0843452i	$0.0268798\pi$
$619$	1.58672e11	+	1.58672e11i	1.08078	+	1.08078i	0.0843452	+	0.996437i	$0.473120\pi$
$620$	−1.24231e11	+	3.04660e11i	−0.840743	+	2.06181i
$621$	−3.20820e10	−	3.20820e10i	−0.215722	−	0.215722i
$622$	−1.75094e11	−	1.16297e11i	−1.16979	−	0.776975i
$623$		−	3.08144e10i		−	0.204551i
$624$	8.38444e9	−	8.57139e9i	0.0553014	−	0.0565344i
$625$	1.33584e11			0.875458
$626$	−1.00925e11	+	1.51950e11i	−0.657208	+	0.989474i
$627$	1.98166e10	−	1.98166e10i	0.128221	−	0.128221i
$628$	−6.02166e10	+	1.47673e11i	−0.387148	+	0.949429i
$629$	−5.03741e10	+	5.03741e10i	−0.321814	+	0.321814i
$630$	2.08836e10	+	1.03497e11i	0.132569	+	0.657000i
$631$	−1.36033e11			−0.858079			−0.429040	−	0.903286i	$-0.641148\pi$
$631$	−1.36033e11			−0.858079			−0.429040	+	0.903286i	$0.641148\pi$
$632$	−8.52499e10	−	1.62256e10i	−0.534350	−	0.101703i
$633$		−	6.36098e10i		−	0.396195i
$634$	7.11884e9	+	3.52803e10i	0.0440608	+	0.218361i
$635$	−2.98549e11	−	2.98549e11i	−1.83620	−	1.83620i
$636$	4.56653e10	−	1.92108e10i	0.279099	−	0.117413i
$637$	−1.45810e10	−	1.45810e10i	−0.0885585	−	0.0885585i
$638$	1.57198e10	−	2.36673e10i	0.0948778	−	0.142845i
$639$		−	1.81788e9i		−	0.0109034i
$640$	−2.40007e11	−	4.29441e10i	−1.43055	−	0.255967i
$641$	1.78662e11			1.05828			0.529139	−	0.848535i	$-0.322515\pi$
$641$	1.78662e11			1.05828			0.529139	+	0.848535i	$0.322515\pi$
$642$	9.51026e9	+	6.31670e9i	0.0559825	+	0.0371835i
$643$	9.66166e10	−	9.66166e10i	0.565207	−	0.565207i	−0.365575	−	0.930782i	$-0.619127\pi$
$643$	9.66166e10	−	9.66166e10i	0.565207	−	0.565207i	0.930782	+	0.365575i	$0.119127\pi$
$644$	−1.46290e11	−	3.47742e11i	−0.850496	−	2.02168i
$645$	8.65915e10	−	8.65915e10i	0.500307	−	0.500307i
$646$	−7.11132e10	+	1.43492e10i	−0.408338	+	0.0823942i
$647$	1.80838e11			1.03198			0.515992	−	0.856593i	$-0.327423\pi$
$647$	1.80838e11			1.03198			0.515992	+	0.856593i	$0.327423\pi$
$648$	−3.66301e9	+	1.92456e10i	−0.0207748	+	0.109152i
$649$			9.54770e10i			0.538170i
$650$	2.66529e10	−	5.37801e9i	0.149311	−	0.0301278i
$651$	1.55438e11	+	1.55438e11i	0.865431	+	0.865431i
$652$	3.96732e10	+	1.61775e10i	0.219537	+	0.0895203i
$653$	1.42463e11	+	1.42463e11i	0.783521	+	0.783521i	0.980423	−	0.196902i	$-0.0630881\pi$
$653$	1.42463e11	+	1.42463e11i	0.783521	+	0.783521i	−0.196902	+	0.980423i	$0.563088\pi$
$654$	1.14241e11	+	7.58785e10i	0.624467	+	0.414770i
$655$			1.26684e11i			0.688267i
$656$	2.33318e11	+	2.28230e11i	1.25989	+	1.23241i
$657$	−1.98110e10			−0.106327
$658$	−1.97723e11	+	2.97686e11i	−1.05476	+	1.58802i
$659$	5.81000e10	−	5.81000e10i	0.308059	−	0.308059i	−0.536097	−	0.844156i	$-0.680102\pi$
$659$	5.81000e10	−	5.81000e10i	0.308059	−	0.308059i	0.844156	+	0.536097i	$0.180102\pi$
$660$	−4.01409e10	−	1.63683e10i	−0.211549	−	0.0862634i
$661$	−3.65977e10	+	3.65977e10i	−0.191711	+	0.191711i	−0.796435	−	0.604724i	$-0.793283\pi$
$661$	−3.65977e10	+	3.65977e10i	−0.191711	+	0.191711i	0.604724	+	0.796435i	$0.293283\pi$
$662$	2.02598e9	+	1.00406e10i	0.0105488	+	0.0522789i
$663$	−5.51853e9			−0.0285608
$664$	5.64830e10	+	8.30380e10i	0.290566	+	0.427174i
$665$		−	4.53574e11i		−	2.31932i
$666$	−1.63466e10	−	8.10125e10i	−0.0830867	−	0.411770i
$667$	1.39726e11	+	1.39726e11i	0.705948	+	0.705948i
$668$	−1.31547e11	−	3.12695e11i	−0.660653	−	1.57042i
$669$	1.07628e11	+	1.07628e11i	0.537303	+	0.537303i
$670$	1.91302e11	−	2.88019e11i	0.949336	−	1.42930i
$671$			1.64793e10i			0.0812920i
$672$	−8.86274e10	+	1.36681e11i	−0.434601	+	0.670242i
$673$	−1.32411e11			−0.645452			−0.322726	−	0.946493i	$-0.604599\pi$
$673$	−1.32411e11			−0.645452			−0.322726	+	0.946493i	$0.604599\pi$
$674$	−2.59870e11	−	1.72606e11i	−1.25926	−	0.836402i
$675$	−3.14139e10	+	3.14139e10i	−0.151324	+	0.151324i
$676$	1.88876e11	−	7.94576e10i	0.904461	−	0.380495i
$677$	−1.80078e11	+	1.80078e11i	−0.857248	+	0.857248i	−0.991013	−	0.133765i	$-0.957293\pi$
$677$	−1.80078e11	+	1.80078e11i	−0.857248	+	0.857248i	0.133765	+	0.991013i	$0.457293\pi$
$678$	7.53726e10	−	1.52086e10i	0.356693	−	0.0719733i
$679$	−3.95115e11			−1.85885
$680$	6.31140e10	+	9.27866e10i	0.295182	+	0.433960i
$681$		−	1.38741e11i		−	0.645082i
$682$	−8.84708e10	+	1.78516e10i	−0.408943	+	0.0825162i
$683$	3.55401e10	+	3.55401e10i	0.163319	+	0.163319i	0.784035	−	0.620717i	$-0.213158\pi$
$683$	3.55401e10	+	3.55401e10i	0.163319	+	0.163319i	−0.620717	+	0.784035i	$0.713158\pi$
$684$	3.17779e10	−	7.79311e10i	0.145178	−	0.356030i
$685$	−9.35353e10	−	9.35353e10i	−0.424828	−	0.424828i
$686$	−2.18719e10	−	1.45273e10i	−0.0987620	−	0.0655976i
$687$			2.08463e11i			0.935840i
$688$	1.88926e11	−	2.08306e9i	0.843216	−	0.00929712i
$689$	−1.61895e10			−0.0718383
$690$	1.66808e11	−	2.51141e11i	0.735901	−	1.10795i
$691$	−3.83205e10	+	3.83205e10i	−0.168081	+	0.168081i	−0.786135	−	0.618054i	$-0.787921\pi$
$691$	−3.83205e10	+	3.83205e10i	−0.168081	+	0.168081i	0.618054	+	0.786135i	$0.287921\pi$
$692$	3.94863e10	−	9.68347e10i	0.172195	−	0.422286i
$693$	−2.04799e10	+	2.04799e10i	−0.0887965	+	0.0887965i
$694$	−2.50216e10	−	1.24005e11i	−0.107864	−	0.534564i
$695$	−3.08239e11			−1.32114
$696$	1.59534e10	−	8.38196e10i	0.0679855	−	0.357198i
$697$		−	1.50218e11i		−	0.636488i
$698$	6.23811e10	+	3.09155e11i	0.262804	+	1.30243i
$699$	−3.26973e10	−	3.26973e10i	−0.136963	−	0.136963i
$700$	−3.40501e11	+	1.43244e11i	−1.41816	+	0.596603i
$701$	1.59199e11	+	1.59199e11i	0.659279	+	0.659279i	0.955210	−	0.295930i	$-0.0956296\pi$
$701$	1.59199e11	+	1.59199e11i	0.659279	+	0.659279i	−0.295930	+	0.955210i	$0.595630\pi$
$702$	3.54211e9	−	5.33290e9i	0.0145852	−	0.0219591i
$703$			3.55035e11i			1.45362i
$704$	−2.66134e10	−	6.13603e10i	−0.108345	−	0.249802i
$705$	−2.85593e11			−1.15609
$706$	3.39715e11	+	2.25638e11i	1.36740	+	0.908226i
$707$	−4.22330e11	+	4.22330e11i	−1.69034	+	1.69034i
$708$	1.11184e11	+	2.64291e11i	0.442495	+	1.05184i
$709$	1.32304e11	−	1.32304e11i	0.523587	−	0.523587i	−0.395066	−	0.918653i	$-0.629278\pi$
$709$	1.32304e11	−	1.32304e11i	0.523587	−	0.523587i	0.918653	+	0.395066i	$0.129278\pi$
$710$	1.18413e10	−	2.38932e9i	0.0465977	−	0.00940245i
$711$	−4.63351e10			−0.181314
$712$	3.73240e10	+	7.10388e9i	0.145234	+	0.0276424i
$713$		−	6.27700e11i		−	2.42881i
$714$	7.34936e10	−	1.48295e10i	0.282785	−	0.0570602i
$715$	1.00169e10	+	1.00169e10i	0.0383275	+	0.0383275i
$716$	2.83894e11	+	1.15763e11i	1.08020	+	0.440473i
$717$	5.78494e9	+	5.78494e9i	0.0218888	+	0.0218888i
$718$	−3.45349e11	−	2.29380e11i	−1.29945	−	0.863095i
$719$			4.13697e11i			1.54798i	0.633195	+	0.773992i	$0.281743\pi$
$719$			4.13697e11i			1.54798i	−0.633195	+	0.773992i	$0.718257\pi$
$720$	−1.30175e11	+	1.43529e9i	−0.484394	+	0.00534083i
$721$	−2.33255e11			−0.863157
$722$	−4.96901e10	+	7.48121e10i	−0.182861	+	0.275311i
$723$	−1.23862e11	+	1.23862e11i	−0.453301	+	0.453301i
$724$	3.45639e11	+	1.40941e11i	1.25797	+	0.512960i
$725$	1.36816e11	−	1.36816e11i	0.495206	−	0.495206i
$726$	2.93726e10	+	1.45568e11i	0.105729	+	0.523985i
$727$	−1.30030e11			−0.465487			−0.232743	−	0.972538i	$-0.574770\pi$
$727$	−1.30030e11			−0.465487			−0.232743	+	0.972538i	$0.574770\pi$
$728$	4.40159e10	−	2.99399e10i	0.156705	−	0.106592i
$729$			1.04604e10i			0.0370370i
$730$	−2.60384e10	−	1.29044e11i	−0.0916903	−	0.454409i
$731$	−6.14890e10	−	6.14890e10i	−0.215342	−	0.215342i
$732$	1.91902e10	+	4.56165e10i	0.0668400	+	0.158883i
$733$	−4.68031e9	−	4.68031e9i	−0.0162128	−	0.0162128i	0.698954	−	0.715167i	$-0.253649\pi$
$733$	−4.68031e9	−	4.68031e9i	−0.0162128	−	0.0162128i	−0.715167	+	0.698954i	$0.753649\pi$
$734$	−1.34736e11	+	2.02855e11i	−0.464195	+	0.698879i
$735$			2.23887e11i			0.767147i
$736$	4.54928e11	−	9.70270e10i	1.55036	−	0.330660i
$737$	9.48478e10			0.321482
$738$	1.45165e11	+	9.64182e10i	0.489368	+	0.325038i
$739$	2.41836e11	−	2.41836e11i	0.810856	−	0.810856i	−0.173906	−	0.984762i	$-0.555639\pi$
$739$	2.41836e11	−	2.41836e11i	0.810856	−	0.810856i	0.984762	+	0.173906i	$0.0556389\pi$
$740$	5.06211e11	−	2.12956e11i	1.68813	−	0.710172i
$741$	−1.94473e10	+	1.94473e10i	−0.0645039	+	0.0645039i
$742$	2.15605e11	−	4.35046e10i	0.711284	−	0.143522i
$743$	−1.69004e10			−0.0554550			−0.0277275	−	0.999616i	$-0.508827\pi$
$743$	−1.69004e10			−0.0554550			−0.0277275	+	0.999616i	$0.508827\pi$
$744$	−2.24109e11	+	1.52440e11i	−0.731420	+	0.497517i
$745$			5.17059e11i			1.67848i
$746$	−4.83520e11	+	9.75643e10i	−1.56120	+	0.315018i
$747$	3.79163e10	+	3.79163e10i	0.121771	+	0.121771i
$748$	−1.16232e10	+	2.85042e10i	−0.0371294	+	0.0910548i
$749$	3.58416e10	+	3.58416e10i	0.113883	+	0.113883i
$750$	−2.47678e10	−	1.64508e10i	−0.0782786	−	0.0519926i
$751$			5.69730e10i			0.179106i	0.995982	+	0.0895529i	$0.0285438\pi$
$751$			5.69730e10i			0.179106i	−0.995982	+	0.0895529i	$0.971456\pi$
$752$	−3.14990e11	−	3.08120e11i	−0.984977	−	0.963493i
$753$	1.20623e10			0.0375190
$754$	−1.54268e10	+	2.32262e10i	−0.0477300	+	0.0718610i
$755$	4.17442e11	−	4.17442e11i	1.28472	−	1.28472i
$756$	−3.28417e10	+	8.05398e10i	−0.100540	+	0.246560i
$757$	−1.67293e11	+	1.67293e11i	−0.509442	+	0.509442i	−0.914355	−	0.404913i	$-0.867302\pi$
$757$	−1.67293e11	+	1.67293e11i	−0.509442	+	0.509442i	0.404913	+	0.914355i	$0.367302\pi$
$758$	−6.43911e10	−	3.19116e11i	−0.195051	−	0.966657i
$759$	8.27035e10			0.249205
$760$	5.49392e11	+	1.04566e11i	1.64675	+	0.313426i
$761$		−	1.67385e11i		−	0.499087i	−0.968364	−	0.249544i	$-0.919719\pi$
$761$		−	1.67385e11i		−	0.499087i	0.968364	−	0.249544i	$-0.0802806\pi$
$762$	−6.87953e10	−	3.40943e11i	−0.204051	−	1.01126i
$763$	4.30542e11	+	4.30542e11i	1.27033	+	1.27033i
$764$	2.05037e11	−	8.62565e10i	0.601810	−	0.253174i
$765$	4.23676e10	+	4.23676e10i	0.123705	+	0.123705i
$766$	−1.09601e11	+	1.65012e11i	−0.318345	+	0.479292i
$767$		−	9.36975e10i		−	0.270736i
$768$	−1.45123e11	−	1.38860e11i	−0.417150	−	0.399148i
$769$	5.53997e10			0.158417			0.0792086	−	0.996858i	$-0.474761\pi$
$769$	5.53997e10			0.158417			0.0792086	+	0.996858i	$0.474761\pi$
$770$	−1.60319e11	−	1.06484e11i	−0.456061	−	0.302915i
$771$	−1.26107e11	+	1.26107e11i	−0.356881	+	0.356881i
$772$	−2.78994e10	−	6.63187e10i	−0.0785464	−	0.186710i
$773$	−1.48712e11	+	1.48712e11i	−0.416512	+	0.416512i	−0.884000	−	0.467487i	$-0.845159\pi$
$773$	−1.48712e11	+	1.48712e11i	−0.416512	+	0.416512i	0.467487	+	0.884000i	$0.345159\pi$
$774$	9.88877e10	−	1.99535e10i	0.275536	−	0.0555975i
$775$	−6.14630e11			−1.70375
$776$	9.10890e10	−	4.78584e11i	0.251200	−	1.31981i
$777$		−	3.66920e11i		−	1.00667i
$778$	3.07241e10	−	6.19949e9i	0.0838612	−	0.0169215i
$779$	−5.29366e11	−	5.29366e11i	−1.43749	−	1.43749i
$780$	3.93928e10	+	1.60632e10i	0.106424	+	0.0433964i
$781$	2.34314e9	+	2.34314e9i	0.00629788	+	0.00629788i
$782$	−1.78336e11	−	1.18451e11i	−0.476884	−	0.316746i
$783$		−	4.55577e10i		−	0.121203i
$784$	−2.41546e11	+	2.46932e11i	−0.639346	+	0.653602i
$785$	−5.65834e11			−1.49008
$786$	−5.77407e10	+	8.69328e10i	−0.151284	+	0.227768i
$787$	3.30946e11	−	3.30946e11i	0.862698	−	0.862698i	−0.128953	−	0.991651i	$-0.541162\pi$
$787$	3.30946e11	−	3.30946e11i	0.862698	−	0.862698i	0.991651	+	0.128953i	$0.0411615\pi$
$788$	5.56960e11	+	2.27112e11i	1.44451	+	0.589026i
$789$	−1.36001e11	+	1.36001e11i	−0.350941	+	0.350941i
$790$	−6.09002e10	−	3.01816e11i	−0.156355	−	0.774879i
$791$	3.41376e11			0.872021
$792$	−2.00850e10	−	2.95278e10i	−0.0510471	−	0.0750464i
$793$		−	1.61721e10i		−	0.0408954i
$794$	4.63502e10	+	2.29707e11i	0.116619	+	0.577953i
$795$	1.24292e11	+	1.24292e11i	0.311153	+	0.311153i
$796$	5.31000e10	+	1.26222e11i	0.132264	+	0.314400i
$797$	1.02183e10	+	1.02183e10i	0.0253247	+	0.0253247i	0.719656	−	0.694331i	$-0.244300\pi$
$797$	1.02183e10	+	1.02183e10i	0.0253247	+	0.0253247i	−0.694331	+	0.719656i	$0.744300\pi$
$798$	2.06732e11	−	3.11250e11i	0.509795	−	0.767534i
$799$			2.02801e11i			0.497602i
$800$	−9.50067e10	−	4.45456e11i	−0.231950	−	1.08754i
$801$	2.02864e10			0.0492804
$802$	−3.52407e11	−	2.34068e11i	−0.851819	−	0.565777i
$803$	2.55352e10	−	2.55352e10i	0.0614154	−	0.0614154i
$804$	2.62549e11	−	1.10451e11i	0.628328	−	0.264329i
$805$	9.46483e11	−	9.46483e11i	2.25387	−	2.25387i
$806$	8.68220e10	−	1.75189e10i	0.205726	−	0.0415113i
$807$	2.87602e11			0.678106
$808$	−4.14185e11	−	6.08912e11i	−0.971738	−	1.42859i
$809$			6.69517e11i			1.56303i	0.623885	+	0.781516i	$0.285553\pi$
$809$			6.69517e11i			1.56303i	−0.623885	+	0.781516i	$0.714447\pi$
$810$	−6.81363e10	+	1.37485e10i	−0.158285	+	0.0319385i
$811$	−3.00358e11	−	3.00358e11i	−0.694315	−	0.694315i	0.268864	−	0.963178i	$-0.413352\pi$
$811$	−3.00358e11	−	3.00358e11i	−0.694315	−	0.694315i	−0.963178	+	0.268864i	$0.913352\pi$
$812$	1.43035e11	−	3.50773e11i	0.329016	−	0.806867i
$813$	−1.98902e11	−	1.98902e11i	−0.455279	−	0.455279i
$814$	1.25490e11	+	8.33504e10i	0.285833	+	0.189850i
$815$			1.52014e11i			0.344552i
$816$	1.01920e9	+	9.24381e10i	0.00229879	+	0.208492i
$817$	−4.33373e11			−0.972689
$818$	3.46946e11	−	5.22353e11i	0.774906	−	1.16668i
$819$	2.00982e10	−	2.00982e10i	0.0446707	−	0.0446707i
$820$	−4.37250e11	+	1.07230e12i	−0.967106	+	2.37170i
$821$	7.92528e10	−	7.92528e10i	0.174438	−	0.174438i	−0.614488	−	0.788926i	$-0.710637\pi$
$821$	7.92528e10	−	7.92528e10i	0.174438	−	0.174438i	0.788926	+	0.614488i	$0.210637\pi$
$822$	−2.15535e10	−	1.06817e11i	−0.0472097	−	0.233967i
$823$	7.48485e11			1.63149			0.815743	−	0.578414i	$-0.196328\pi$
$823$	7.48485e11			1.63149			0.815743	+	0.578414i	$0.196328\pi$
$824$	5.37741e10	−	2.82531e11i	0.116645	−	0.612854i
$825$		−	8.09815e10i		−	0.174811i
$826$	2.51785e11	+	1.24783e12i	0.540892	+	2.68061i
$827$	3.51285e11	+	3.51285e11i	0.750996	+	0.750996i	0.974665	−	0.223669i	$-0.0718034\pi$
$827$	3.51285e11	+	3.51285e11i	0.750996	+	0.750996i	−0.223669	+	0.974665i	$0.571803\pi$
$828$	2.28932e11	−	9.63089e10i	0.487064	−	0.204901i
$829$	−5.82469e11	−	5.82469e11i	−1.23326	−	1.23326i	−0.962704	−	0.270556i	$-0.912792\pi$
$829$	−5.82469e11	−	5.82469e11i	−1.23326	−	1.23326i	−0.270556	−	0.962704i	$-0.587208\pi$
$830$	−1.97143e11	+	2.96813e11i	−0.415402	+	0.625418i
$831$		−	2.39734e11i		−	0.502720i
$832$	2.61174e10	+	6.02167e10i	0.0545051	+	0.125668i
$833$	1.58983e11			0.330195
$834$	−2.11519e11	−	1.40491e11i	−0.437205	−	0.290391i
$835$	8.51092e11	−	8.51092e11i	1.75078	−	1.75078i
$836$	5.94887e10	+	1.41409e11i	0.121789	+	0.289501i
$837$	−1.02331e11	+	1.02331e11i	−0.208500	+	0.208500i
$838$	4.14898e11	−	8.37178e10i	0.841327	−	0.169762i
$839$	−8.39048e11			−1.69332			−0.846659	−	0.532135i	$-0.821390\pi$
$839$	−8.39048e11			−1.69332			−0.846659	+	0.532135i	$0.821390\pi$
$840$	−5.67783e11	−	1.08066e11i	−1.14042	−	0.217056i
$841$		−	3.01830e11i		−	0.603363i
$842$	−5.85975e11	+	1.18238e11i	−1.16582	+	0.235238i
$843$	−5.24180e10	−	5.24180e10i	−0.103794	−	0.103794i
$844$	3.22432e11	+	1.31478e11i	0.635432	+	0.259110i
$845$	5.14082e11	+	5.14082e11i	1.00834	+	1.00834i
$846$	−1.95979e11	−	1.30169e11i	−0.382585	−	0.254112i
$847$			6.59303e11i			1.28101i
$848$	2.98999e9	+	2.71181e11i	0.00578211	+	0.524417i
$849$	1.19624e11			0.230244
$850$	−1.15984e11	+	1.74623e11i	−0.222190	+	0.334523i
$851$	−7.40861e11	+	7.40861e11i	−1.41260	+	1.41260i
$852$	9.21468e9	+	3.75747e9i	0.0174873	+	0.00713078i
$853$	1.42652e11	−	1.42652e11i	0.269453	−	0.269453i	−0.559427	−	0.828880i	$-0.688979\pi$
$853$	1.42652e11	−	1.42652e11i	0.269453	−	0.269453i	0.828880	+	0.559427i	$0.188979\pi$
$854$	4.34580e10	+	2.15374e11i	0.0817031	+	0.404913i
$855$	2.98606e11			0.558771
$856$	−5.16760e10	+	3.51504e10i	−0.0962485	+	0.0654689i
$857$		−	6.57834e10i		−	0.121953i	−0.998139	−	0.0609766i	$-0.980579\pi$
$857$		−	6.57834e10i		−	0.121953i	0.998139	−	0.0609766i	$-0.0194215\pi$
$858$	2.30823e9	+	1.14394e10i	0.00425921	+	0.0211083i
$859$	−1.46389e11	−	1.46389e11i	−0.268867	−	0.268867i	0.559777	−	0.828643i	$-0.310887\pi$
$859$	−1.46389e11	−	1.46389e11i	−0.268867	−	0.268867i	−0.828643	+	0.559777i	$0.810887\pi$
$860$	2.59945e11	+	6.17905e11i	0.475212	+	1.12961i
$861$	5.47086e11	+	5.47086e11i	0.995504	+	0.995504i
$862$	3.97137e10	−	5.97919e10i	0.0719303	−	0.108296i
$863$		−	3.05540e11i		−	0.550839i	−0.961324	−	0.275420i	$-0.911183\pi$
$863$		−	3.05540e11i		−	0.550839i	0.961324	−	0.275420i	$-0.0888168\pi$
$864$	−8.99828e10	−	5.83471e10i	−0.161475	−	0.104704i
$865$	3.71038e11			0.662757
$866$	−1.08740e10	−	7.22251e9i	−0.0193338	−	0.0128415i
$867$	−2.00590e11	+	2.00590e11i	−0.355003	+	0.355003i
$868$	−1.10918e12	+	4.66619e11i	−1.95400	+	0.822022i
$869$	5.97232e10	−	5.97232e10i	0.104728	−	0.104728i
$870$	2.96752e11	−	5.98784e10i	0.517985	−	0.104519i
$871$	−9.30801e10			−0.161728
$872$	−6.20751e11	+	4.22239e11i	−1.07362	+	0.730285i
$873$		−	2.60120e11i		−	0.447834i
$874$	−1.04587e12	+	2.11036e11i	−1.79240	+	0.361668i
$875$	−9.33433e10	−	9.33433e10i	−0.159240	−	0.159240i
$876$	4.09483e10	−	1.00420e11i	0.0695376	−	0.170531i
$877$	−3.56193e11	−	3.56193e11i	−0.602126	−	0.602126i	0.338750	−	0.940876i	$-0.389996\pi$
$877$	−3.56193e11	−	3.56193e11i	−0.602126	−	0.602126i	−0.940876	+	0.338750i	$0.889996\pi$
$878$	1.69152e11	+	1.12351e11i	0.284642	+	0.189059i
$879$			4.65226e11i			0.779307i
$880$	1.65939e11	−	1.69639e11i	0.276705	−	0.282874i
$881$	4.96299e11			0.823834			0.411917	−	0.911221i	$-0.364859\pi$
$881$	4.96299e11			0.823834			0.411917	+	0.911221i	$0.364859\pi$
$882$	−1.02044e11	+	1.53635e11i	−0.168622	+	0.253872i
$883$	−2.26020e11	+	2.26020e11i	−0.371795	+	0.371795i	−0.868131	−	0.496336i	$-0.834678\pi$
$883$	−2.26020e11	+	2.26020e11i	−0.371795	+	0.371795i	0.496336	+	0.868131i	$0.334678\pi$
$884$	1.14065e10	−	2.79730e10i	0.0186786	−	0.0458068i
$885$	−7.19346e11	+	7.19346e11i	−1.17264	+	1.17264i
$886$	−1.63054e11	−	8.08080e11i	−0.264604	−	1.31135i
$887$	3.06301e11			0.494828			0.247414	−	0.968910i	$-0.420419\pi$
$887$	3.06301e11			0.494828			0.247414	+	0.968910i	$0.420419\pi$
$888$	4.44433e11	+	8.45889e10i	0.714750	+	0.136038i
$889$		−	1.54419e12i		−	2.47226i
$890$	2.66633e10	+	1.32141e11i	0.0424965	+	0.210609i
$891$	−1.34828e10	−	1.34828e10i	−0.0213928	−	0.0213928i
$892$	−7.68016e11	+	3.23094e11i	−1.21314	+	0.510352i
$893$	7.14668e11	+	7.14668e11i	1.12382	+	1.12382i
$894$	−2.35668e11	+	3.54815e11i	−0.368935	+	0.555458i
$895$			1.08779e12i			1.69532i
$896$	−5.09637e11	−	7.31758e11i	−0.790731	−	1.13536i
$897$	−8.11621e10			−0.125367
$898$	6.65626e11	+	4.42108e11i	1.02359	+	0.679866i
$899$	4.45680e11	−	4.45680e11i	0.682313	−	0.682313i
$900$	−9.43035e10	−	2.24166e11i	−0.143733	−	0.341664i
$901$	8.82601e10	−	8.82601e10i	0.133926	−	0.133926i
$902$	−3.11386e11	+	6.28313e10i	−0.470406	+	0.0949183i
$903$	4.47880e11			0.673613
$904$	−7.87001e10	+	4.13493e11i	−0.117842	+	0.619147i
$905$			1.32437e12i			1.97431i
$906$	4.76720e11	−	9.61922e10i	0.707539	−	0.142767i
$907$	−3.89554e11	−	3.89554e11i	−0.575624	−	0.575624i	0.358070	−	0.933695i	$-0.383435\pi$
$907$	−3.89554e11	−	3.89554e11i	−0.575624	−	0.575624i	−0.933695	+	0.358070i	$0.883435\pi$
$908$	7.03264e11	+	2.86770e11i	1.03461	+	0.421881i
$909$	−2.78037e11	−	2.78037e11i	−0.407237	−	0.407237i
$910$	1.57331e11	+	1.04499e11i	0.229430	+	0.152387i
$911$		−	3.51605e11i		−	0.510484i	−0.966877	−	0.255242i	$-0.917845\pi$
$911$		−	3.51605e11i		−	0.510484i	0.966877	−	0.255242i	$-0.0821551\pi$
$912$	3.29343e11	+	3.22159e11i	0.476068	+	0.465684i
$913$	−9.77437e10			−0.140671
$914$	−3.68726e11	+	5.55144e11i	−0.528347	+	0.795465i
$915$	−1.24159e11	+	1.24159e11i	−0.177130	+	0.177130i
$916$	−1.05668e12	−	4.30882e11i	−1.50093	−	0.612035i
$917$	−3.27626e11	+	3.27626e11i	−0.463341	+	0.463341i
$918$	9.76286e9	+	4.83838e10i	0.0137469	+	0.0681286i
$919$	−9.02461e11			−1.26522			−0.632610	−	0.774470i	$-0.718016\pi$
$919$	−9.02461e11			−1.26522			−0.632610	+	0.774470i	$0.718016\pi$
$920$	9.28229e11	+	1.36463e12i	1.29570	+	1.90486i
$921$		−	1.96614e11i		−	0.273260i
$922$	−1.05477e10	−	5.22736e10i	−0.0145961	−	0.0723368i
$923$	−2.29947e9	−	2.29947e9i	−0.00316826	−	0.00316826i
$924$	−6.14800e10	−	1.46142e11i	−0.0843425	−	0.200488i
$925$	7.25435e11	+	7.25435e11i	0.990903	+	0.990903i
$926$	1.47303e11	−	2.21776e11i	0.200341	−	0.301627i
$927$		−	1.53561e11i		−	0.207952i
$928$	3.91900e11	+	2.54117e11i	0.528424	+	0.342643i
$929$	4.07441e11			0.547018			0.273509	−	0.961869i	$-0.411816\pi$
$929$	4.07441e11			0.547018			0.273509	+	0.961869i	$0.411816\pi$
$930$	−8.01059e11	−	5.32062e11i	−1.07086	−	0.711264i
$931$	5.60254e11	−	5.60254e11i	0.745737	−	0.745737i
$932$	2.33324e11	−	9.81562e10i	0.309240	−	0.130093i
$933$	4.34426e11	−	4.34426e11i	0.573310	−	0.573310i
$934$	4.58633e11	−	9.25428e10i	0.602668	−	0.121606i
$935$	−1.09219e11			−0.142906
$936$	1.97106e10	+	2.89775e10i	0.0256801	+	0.0377535i
$937$			6.80883e11i			0.883312i	0.897185	+	0.441656i	$0.145609\pi$
$937$			6.80883e11i			0.883312i	−0.897185	+	0.441656i	$0.854391\pi$
$938$	1.23960e12	−	2.50126e11i	1.60129	−	0.323108i
$939$	−3.77005e11	−	3.77005e11i	−0.484937	−	0.484937i
$940$	5.90307e11	−	1.44765e12i	0.756077	−	1.85418i
$941$	7.92749e11	+	7.92749e11i	1.01106	+	1.01106i	0.999938	+	0.0111227i	$0.00354055\pi$
$941$	7.92749e11	+	7.92749e11i	1.01106	+	1.01106i	0.0111227	+	0.999938i	$0.496459\pi$
$942$	−3.88285e11	−	2.57898e11i	−0.493113	−	0.327525i
$943$		−	2.20928e12i		−	2.79386i
$944$	−1.56948e12	+	1.73047e10i	−1.97637	+	0.0217910i
$945$	−3.08602e11			−0.386964
$946$	−1.01741e11	+	1.53179e11i	−0.127038	+	0.191265i
$947$	8.89223e11	−	8.89223e11i	1.10563	−	1.10563i	0.111914	−	0.993718i	$-0.464302\pi$
$947$	8.89223e11	−	8.89223e11i	1.10563	−	1.10563i	0.993718	−	0.111914i	$-0.0356983\pi$
$948$	9.57723e10	−	2.34869e11i	0.118579	−	0.290798i
$949$	−2.50593e10	+	2.50593e10i	−0.0308961	+	0.0308961i
$950$	2.06642e11	+	1.02410e12i	0.253702	+	1.25732i
$951$	−1.05197e11			−0.128612
$952$	−7.67382e10	+	4.03185e11i	−0.0934251	+	0.490858i
$953$		−	9.53216e11i		−	1.15563i	−0.816167	−	0.577816i	$-0.803905\pi$
$953$		−	9.53216e11i		−	1.15563i	0.816167	−	0.577816i	$-0.196095\pi$
$954$	2.86409e10	+	1.41941e11i	0.0345774	+	0.171363i
$955$	5.58070e11	+	5.58070e11i	0.670927	+	0.670927i
$956$	−4.12805e10	+	1.73662e10i	−0.0494213	+	0.0207909i
$957$	5.87212e10	+	5.87212e10i	0.0700079	+	0.0700079i
$958$	−7.41222e10	+	1.11596e11i	−0.0880007	+	0.132491i
$959$		−	4.83795e11i		−	0.571988i
$960$	2.61791e11	−	6.62815e11i	0.308226	−	0.780382i
$961$	−1.14927e12			−1.34750
$962$	−1.23151e11	−	8.17970e10i	−0.143793	−	0.0955074i
$963$	−2.35960e10	+	2.35960e10i	−0.0274367	+	0.0274367i
$964$	−3.71831e11	−	8.83866e11i	−0.430563	−	1.02348i
$965$	1.80506e11	−	1.80506e11i	0.208153	−	0.208153i
$966$	1.08088e12	−	2.18100e11i	1.24128	−	0.250465i
$967$	−9.15719e11			−1.04726			−0.523632	−	0.851945i	$-0.675423\pi$
$967$	−9.15719e11			−1.04726			−0.523632	+	0.851945i	$0.675423\pi$
$968$	−7.98582e11	−	1.51994e11i	−0.909532	−	0.173111i
$969$		−	2.12041e11i		−	0.240506i
$970$	1.69436e12	−	3.41888e11i	1.91390	−	0.386186i
$971$	6.03084e11	+	6.03084e11i	0.678423	+	0.678423i	0.959643	−	0.281220i	$-0.0907391\pi$
$971$	6.03084e11	+	6.03084e11i	0.678423	+	0.678423i	−0.281220	+	0.959643i	$0.590739\pi$
$972$	−5.30226e10	−	2.16210e10i	−0.0594013	−	0.0242221i
$973$	−7.97157e11	−	7.97157e11i	−0.889390	−	0.889390i
$974$	7.93418e11	+	5.26987e11i	0.881589	+	0.585551i
$975$			7.94722e10i			0.0879421i
$976$	−2.70891e11	+	2.98679e9i	−0.298535	+	0.00329158i
$977$	−7.46917e11			−0.819773			−0.409887	−	0.912136i	$-0.634432\pi$
$977$	−7.46917e11			−0.819773			−0.409887	+	0.912136i	$0.634432\pi$
$978$	−6.92858e10	+	1.04315e11i	−0.0757337	+	0.114023i
$979$	−2.61479e10	+	2.61479e10i	−0.0284647	+	0.0284647i
$980$	−1.13486e12	−	4.62762e11i	−1.23038	−	0.501711i
$981$	−2.83443e11	+	2.83443e11i	−0.306048	+	0.306048i
$982$	−1.22495e11	−	6.07076e11i	−0.131727	−	0.652825i
$983$	−6.70852e11			−0.718477			−0.359238	−	0.933246i	$-0.616964\pi$
$983$	−6.70852e11			−0.718477			−0.359238	+	0.933246i	$0.616964\pi$
$984$	−7.88784e11	+	5.36536e11i	−0.841352	+	0.572293i
$985$			2.13409e12i			2.26708i
$986$	−4.25199e10	−	2.10725e11i	−0.0449868	−	0.222950i
$987$	−7.38591e11	−	7.38591e11i	−0.778279	−	0.778279i
$988$	−5.83800e10	−	1.38773e11i	−0.0612684	−	0.145639i
$989$	−9.04330e11	−	9.04330e11i	−0.945239	−	0.945239i
$990$	7.01027e10	−	1.05545e11i	0.0729783	−	0.109874i
$991$			5.38280e10i			0.0558102i	0.999611	+	0.0279051i	$0.00888363\pi$
$991$			5.38280e10i			0.0558102i	−0.999611	+	0.0279051i	$0.991116\pi$
$992$	−3.09484e11	−	1.45107e12i	−0.319589	−	1.49845i
$993$	−2.99384e10			−0.0307916
$994$	3.68026e10	+	2.44443e10i	0.0376993	+	0.0250398i
$995$	−3.43551e11	+	3.43551e11i	−0.350509	+	0.350509i
$996$	−2.70565e11	+	1.13823e11i	−0.274938	+	0.115663i
$997$	−8.19738e11	+	8.19738e11i	−0.829649	+	0.829649i	−0.987468	−	0.157819i	$-0.949554\pi$
$997$	−8.19738e11	+	8.19738e11i	−0.829649	+	0.829649i	0.157819	+	0.987468i	$0.449554\pi$
$998$	−9.02151e11	+	1.82035e11i	−0.909404	+	0.183499i
$999$	2.41558e11			0.242527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.19.5	✓	64
4.3	odd	2		192.9.l.a.175.3		64
16.5	even	4		192.9.l.a.79.3		64
16.11	odd	4	inner	48.9.l.a.43.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.5	✓	64	1.1	even	1	trivial
48.9.l.a.43.5	yes	64	16.11	odd	4	inner
192.9.l.a.79.3		64	16.5	even	4
192.9.l.a.175.3		64	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-13.3280 - 8.85242i) q^{2} +(33.0681 - 33.0681i) q^{3} +(99.2693 + 235.970i) q^{4} +(-642.261 + 642.261i) q^{5} +(-733.463 + 147.998i) q^{6} -3321.99 q^{7} +(765.844 - 4023.77i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-13.3280 - 8.85242i) q^{2} +(33.0681 - 33.0681i) q^{3} +(99.2693 + 235.970i) q^{4} +(-642.261 + 642.261i) q^{5} +(-733.463 + 147.998i) q^{6} -3321.99 q^{7} +(765.844 - 4023.77i) q^{8} -2187.00i q^{9} +(14245.6 - 2874.47i) q^{10} +(2818.91 + 2818.91i) q^{11} +(11085.7 + 4520.42i) q^{12} +(-2766.38 - 2766.38i) q^{13} +(44275.3 + 29407.6i) q^{14} +42476.7i q^{15} +(-45827.2 + 46849.0i) q^{16} +30162.9 q^{17} +(-19360.2 + 29148.3i) q^{18} +(106294. - 106294. i) q^{19} +(-215311. - 87797.3i) q^{20} +(-109852. + 109852. i) q^{21} +(-12616.2 - 62524.6i) q^{22} +443611. q^{23} +(-107733. - 158383. i) q^{24} -434375. i q^{25} +(12381.0 + 61359.3i) q^{26} +(-72320.0 - 72320.0i) q^{27} +(-329771. - 783888. i) q^{28} +(314973. + 314973. i) q^{29} +(376022. - 566129. i) q^{30} -1.41498e6i q^{31} +(1.02551e6 - 218721. i) q^{32} +186432. q^{33} +(-402010. - 267015. i) q^{34} +(2.13358e6 - 2.13358e6i) q^{35} +(516065. - 217102. i) q^{36} +(-1.67007e6 + 1.67007e6i) q^{37} +(-2.35764e6 + 475722. i) q^{38} -182958. q^{39} +(2.09244e6 + 3.07618e6i) q^{40} -4.98022e6i q^{41} +(2.43656e6 - 491647. i) q^{42} +(-2.03856e6 - 2.03856e6i) q^{43} +(-385346. + 945009. i) q^{44} +(1.40463e6 + 1.40463e6i) q^{45} +(-5.91244e6 - 3.92703e6i) q^{46} +6.72352e6i q^{47} +(33789.9 + 3.06463e6i) q^{48} +5.27080e6 q^{49} +(-3.84527e6 + 5.78933e6i) q^{50} +(997430. - 997430. i) q^{51} +(378164. - 927397. i) q^{52} +(2.92612e6 - 2.92612e6i) q^{53} +(323671. + 1.60408e6i) q^{54} -3.62096e6 q^{55} +(-2.54412e6 + 1.33669e7i) q^{56} -7.02987e6i q^{57} +(-1.40968e6 - 6.98623e6i) q^{58} +(1.69351e7 + 1.69351e7i) q^{59} +(-1.00232e7 + 4.21664e6i) q^{60} +(2.92298e6 + 2.92298e6i) q^{61} +(-1.25260e7 + 1.88588e7i) q^{62} +7.26519e6i q^{63} +(-1.56042e7 - 6.16316e6i) q^{64} +3.55347e6 q^{65} +(-2.48476e6 - 1.65038e6i) q^{66} +(1.68235e7 - 1.68235e7i) q^{67} +(2.99425e6 + 7.11752e6i) q^{68} +(1.46694e7 - 1.46694e7i) q^{69} +(-4.73237e7 + 9.54895e6i) q^{70} +831221. q^{71} +(-8.79998e6 - 1.67490e6i) q^{72} -9.05852e6i q^{73} +(3.70427e7 - 7.47446e6i) q^{74} +(-1.43639e7 - 1.43639e7i) q^{75} +(3.56338e7 + 1.45304e7i) q^{76} +(-9.36440e6 - 9.36440e6i) q^{77} +(2.43845e6 + 1.61962e6i) q^{78} -2.11866e7i q^{79} +(-656281. - 5.95224e7i) q^{80} -4.78297e6 q^{81} +(-4.40870e7 + 6.63762e7i) q^{82} +(-1.73371e7 + 1.73371e7i) q^{83} +(-3.68266e7 - 1.50168e7i) q^{84} +(-1.93725e7 + 1.93725e7i) q^{85} +(9.12368e6 + 4.52161e7i) q^{86} +2.08311e7 q^{87} +(1.35015e7 - 9.18380e6i) q^{88} +9.27589e6i q^{89} +(-6.28646e6 - 3.11551e7i) q^{90} +(9.18987e6 + 9.18987e6i) q^{91} +(4.40370e7 + 1.04679e8i) q^{92} +(-4.67906e7 - 4.67906e7i) q^{93} +(5.95194e7 - 8.96108e7i) q^{94} +1.36537e8i q^{95} +(2.66790e7 - 4.11444e7i) q^{96} +1.18939e8 q^{97} +(-7.02491e7 - 4.66594e7i) q^{98} +(6.16497e6 - 6.16497e6i) 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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