LMFDB - Embedded newform 50.15.c.b.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,15,Mod(7,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("50.7");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	50.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$62.1644840760$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 11690x^{3} + 819025x^{2} - 12217500x + 91125000 $ x^6 - 2x^5 + 2x^4 - 11690x^3 + 819025x^2 - 12217500*x + 91125000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$16.0869 - 16.0869i$ of defining polynomial
Character	$\chi$	$=$	50.43
Dual form			50.15.c.b.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(64.0000 - 64.0000i) q^{2} +(1760.67 + 1760.67i) q^{3} -8192.00i q^{4} +225366. q^{6} +(59627.2 - 59627.2i) q^{7} +(-524288. - 524288. i) q^{8} +1.41695e6i q^{9} +O(q^{10})$	\(q+(64.0000 - 64.0000i) q^{2} +(1760.67 + 1760.67i) q^{3} -8192.00i q^{4} +225366. q^{6} +(59627.2 - 59627.2i) q^{7} +(-524288. - 524288. i) q^{8} +1.41695e6i q^{9} -4.64100e6 q^{11} +(1.44234e7 - 1.44234e7i) q^{12} +(4.85144e7 + 4.85144e7i) q^{13} -7.63228e6i q^{14} -6.71089e7 q^{16} +(4.70811e8 - 4.70811e8i) q^{17} +(9.06849e7 + 9.06849e7i) q^{18} +7.64295e8i q^{19} +2.09968e8 q^{21} +(-2.97024e8 + 2.97024e8i) q^{22} +(-1.43685e9 - 1.43685e9i) q^{23} -1.84620e9i q^{24} +6.20985e9 q^{26} +(5.92645e9 - 5.92645e9i) q^{27} +(-4.88466e8 - 4.88466e8i) q^{28} +3.55005e9i q^{29} +4.07968e10 q^{31} +(-4.29497e9 + 4.29497e9i) q^{32} +(-8.17127e9 - 8.17127e9i) q^{33} -6.02638e10i q^{34} +1.16077e10 q^{36} +(1.25794e11 - 1.25794e11i) q^{37} +(4.89149e10 + 4.89149e10i) q^{38} +1.70836e11i q^{39} -1.93888e11 q^{41} +(1.34379e10 - 1.34379e10i) q^{42} +(2.99264e11 + 2.99264e11i) q^{43} +3.80191e10i q^{44} -1.83917e11 q^{46} +(-4.49650e11 + 4.49650e11i) q^{47} +(-1.18157e11 - 1.18157e11i) q^{48} +6.71112e11i q^{49} +1.65788e12 q^{51} +(3.97430e11 - 3.97430e11i) q^{52} +(8.73228e11 + 8.73228e11i) q^{53} -7.58585e11i q^{54} -6.25237e10 q^{56} +(-1.34567e12 + 1.34567e12i) q^{57} +(2.27203e11 + 2.27203e11i) q^{58} -2.30728e12i q^{59} +1.81962e12 q^{61} +(2.61099e12 - 2.61099e12i) q^{62} +(8.44889e10 + 8.44889e10i) q^{63} +5.49756e11i q^{64} -1.04592e12 q^{66} +(5.96657e12 - 5.96657e12i) q^{67} +(-3.85688e12 - 3.85688e12i) q^{68} -5.05965e12i q^{69} +5.96561e12 q^{71} +(7.42891e11 - 7.42891e11i) q^{72} +(7.19715e11 + 7.19715e11i) q^{73} -1.61016e13i q^{74} +6.26110e12 q^{76} +(-2.76730e11 + 2.76730e11i) q^{77} +(1.09335e13 + 1.09335e13i) q^{78} -3.29365e12i q^{79} +2.76463e13 q^{81} +(-1.24088e13 + 1.24088e13i) q^{82} +(6.80839e12 + 6.80839e12i) q^{83} -1.72006e12i q^{84} +3.83057e13 q^{86} +(-6.25047e12 + 6.25047e12i) q^{87} +(2.43322e12 + 2.43322e12i) q^{88} -3.40430e13i q^{89} +5.78556e12 q^{91} +(-1.17707e13 + 1.17707e13i) q^{92} +(7.18297e13 + 7.18297e13i) q^{93} +5.75552e13i q^{94} -1.51240e13 q^{96} +(7.87980e13 - 7.87980e13i) q^{97} +(4.29512e13 + 4.29512e13i) q^{98} -6.57607e12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 384 q^{2} - 2912 q^{3} - 372736 q^{6} - 943128 q^{7} - 3145728 q^{8}+O(q^{10}) $ 6 * q + 384 * q^2 - 2912 * q^3 - 372736 * q^6 - 943128 * q^7 - 3145728 * q^8	\( 6 q + 384 q^{2} - 2912 q^{3} - 372736 q^{6} - 943128 q^{7} - 3145728 q^{8} - 45566568 q^{11} - 23855104 q^{12} + 52149318 q^{13} - 402653184 q^{16} + 294348942 q^{17} + 331317376 q^{18} + 2237511512 q^{21} - 2916260352 q^{22} + 9431163408 q^{23} + 6675112704 q^{26} - 12637562360 q^{27} + 7726104576 q^{28} + 3721405392 q^{31} - 25769803776 q^{32} + 48274986136 q^{33} + 42408624128 q^{36} + 429898030002 q^{37} + 244347609600 q^{38} + 45681057912 q^{41} + 143200736768 q^{42} + 935465548368 q^{43} + 1207188916224 q^{46} + 966227586192 q^{47} + 195421011968 q^{48} + 5859939710032 q^{51} + 427207213056 q^{52} + 1868182085058 q^{53} + 988941385728 q^{56} + 134753100400 q^{57} + 2272407598080 q^{58} + 2111099930472 q^{61} + 238169945088 q^{62} + 4692600933808 q^{63} + 6179198225408 q^{66} + 8480735447712 q^{67} - 2411306532864 q^{68} + 22333649456112 q^{71} + 2714151944192 q^{72} + 6994307700378 q^{73} + 31276494028800 q^{76} - 3740771411016 q^{77} + 19625279112192 q^{78} + 140474309815186 q^{81} + 2923587706368 q^{82} + 60521791593048 q^{83} + 119739590191104 q^{86} + 54455082756640 q^{87} + 23890004803584 q^{88} + 402924178873632 q^{91} + 77260090638336 q^{92} + 290043091551016 q^{93} + 25013889531904 q^{96} + 307307370113562 q^{97} + 13656230884224 q^{98}+O(q^{100}) \) 6 * q + 384 * q^2 - 2912 * q^3 - 372736 * q^6 - 943128 * q^7 - 3145728 * q^8 - 45566568 * q^11 - 23855104 * q^12 + 52149318 * q^13 - 402653184 * q^16 + 294348942 * q^17 + 331317376 * q^18 + 2237511512 * q^21 - 2916260352 * q^22 + 9431163408 * q^23 + 6675112704 * q^26 - 12637562360 * q^27 + 7726104576 * q^28 + 3721405392 * q^31 - 25769803776 * q^32 + 48274986136 * q^33 + 42408624128 * q^36 + 429898030002 * q^37 + 244347609600 * q^38 + 45681057912 * q^41 + 143200736768 * q^42 + 935465548368 * q^43 + 1207188916224 * q^46 + 966227586192 * q^47 + 195421011968 * q^48 + 5859939710032 * q^51 + 427207213056 * q^52 + 1868182085058 * q^53 + 988941385728 * q^56 + 134753100400 * q^57 + 2272407598080 * q^58 + 2111099930472 * q^61 + 238169945088 * q^62 + 4692600933808 * q^63 + 6179198225408 * q^66 + 8480735447712 * q^67 - 2411306532864 * q^68 + 22333649456112 * q^71 + 2714151944192 * q^72 + 6994307700378 * q^73 + 31276494028800 * q^76 - 3740771411016 * q^77 + 19625279112192 * q^78 + 140474309815186 * q^81 + 2923587706368 * q^82 + 60521791593048 * q^83 + 119739590191104 * q^86 + 54455082756640 * q^87 + 23890004803584 * q^88 + 402924178873632 * q^91 + 77260090638336 * q^92 + 290043091551016 * q^93 + 25013889531904 * q^96 + 307307370113562 * q^97 + 13656230884224 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	64.0000	−	64.0000i	0.500000	−	0.500000i
$2$	64.0000	−	64.0000i	0.500000	−	0.500000i
$3$	1760.67	+	1760.67i	0.805062	+	0.805062i	0.983882	−	0.178820i	$-0.0572279\pi$
$3$	1760.67	+	1760.67i	0.805062	+	0.805062i	−0.178820	+	0.983882i	$0.557228\pi$
$4$		−	8192.00i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	225366.			0.805062
$7$	59627.2	−	59627.2i	0.0724033	−	0.0724033i	−0.669978	−	0.742381i	$-0.733696\pi$
$7$	59627.2	−	59627.2i	0.0724033	−	0.0724033i	0.742381	+	0.669978i	$0.233696\pi$
$8$	−524288.	−	524288.i	−0.250000	−	0.250000i
$9$			1.41695e6i			0.296249i
$10$		0			0
$11$	−4.64100e6			−0.238157			−0.119078	−	0.992885i	$-0.537994\pi$
$11$	−4.64100e6			−0.238157			−0.119078	+	0.992885i	$0.537994\pi$
$12$	1.44234e7	−	1.44234e7i	0.402531	−	0.402531i
$13$	4.85144e7	+	4.85144e7i	0.773157	+	0.773157i	0.978657	−	0.205500i	$-0.0658822\pi$
$13$	4.85144e7	+	4.85144e7i	0.773157	+	0.773157i	−0.205500	+	0.978657i	$0.565882\pi$
$14$		−	7.63228e6i		−	0.0724033i
$15$		0			0
$16$	−6.71089e7			−0.250000
$17$	4.70811e8	−	4.70811e8i	1.14737	−	1.14737i	0.160303	−	0.987068i	$-0.448753\pi$
$17$	4.70811e8	−	4.70811e8i	1.14737	−	1.14737i	0.987068	−	0.160303i	$-0.0512472\pi$
$18$	9.06849e7	+	9.06849e7i	0.148125	+	0.148125i
$19$			7.64295e8i			0.855038i	0.904006	+	0.427519i	$0.140612\pi$
$19$			7.64295e8i			0.855038i	−0.904006	+	0.427519i	$0.859388\pi$
$20$		0			0
$21$	2.09968e8			0.116578
$22$	−2.97024e8	+	2.97024e8i	−0.119078	+	0.119078i
$23$	−1.43685e9	−	1.43685e9i	−0.422005	−	0.422005i	0.463889	−	0.885893i	$-0.346454\pi$
$23$	−1.43685e9	−	1.43685e9i	−0.422005	−	0.422005i	−0.885893	+	0.463889i	$0.846454\pi$
$24$		−	1.84620e9i		−	0.402531i
$25$		0			0
$26$	6.20985e9			0.773157
$27$	5.92645e9	−	5.92645e9i	0.566563	−	0.566563i
$28$	−4.88466e8	−	4.88466e8i	−0.0362016	−	0.0362016i
$29$			3.55005e9i			0.205802i	0.994692	+	0.102901i	$0.0328124\pi$
$29$			3.55005e9i			0.205802i	−0.994692	+	0.102901i	$0.967188\pi$
$30$		0			0
$31$	4.07968e10			1.48284			0.741419	−	0.671042i	$-0.234153\pi$
$31$	4.07968e10			1.48284			0.741419	+	0.671042i	$0.234153\pi$
$32$	−4.29497e9	+	4.29497e9i	−0.125000	+	0.125000i
$33$	−8.17127e9	−	8.17127e9i	−0.191731	−	0.191731i
$34$		−	6.02638e10i		−	1.14737i
$35$		0			0
$36$	1.16077e10			0.148125
$37$	1.25794e11	−	1.25794e11i	1.32510	−	1.32510i	0.415507	−	0.909590i	$-0.363604\pi$
$37$	1.25794e11	−	1.25794e11i	1.32510	−	1.32510i	0.909590	−	0.415507i	$-0.136396\pi$
$38$	4.89149e10	+	4.89149e10i	0.427519	+	0.427519i
$39$			1.70836e11i			1.24488i
$40$		0			0
$41$	−1.93888e11			−0.995551			−0.497776	−	0.867306i	$-0.665850\pi$
$41$	−1.93888e11			−0.995551			−0.497776	+	0.867306i	$0.665850\pi$
$42$	1.34379e10	−	1.34379e10i	0.0582891	−	0.0582891i
$43$	2.99264e11	+	2.99264e11i	1.10097	+	1.10097i	0.994294	+	0.106674i	$0.0340201\pi$
$43$	2.99264e11	+	2.99264e11i	1.10097	+	1.10097i	0.106674	+	0.994294i	$0.465980\pi$
$44$			3.80191e10i			0.119078i
$45$		0			0
$46$	−1.83917e11			−0.422005
$47$	−4.49650e11	+	4.49650e11i	−0.887544	+	0.887544i	−0.994287	−	0.106743i	$-0.965958\pi$
$47$	−4.49650e11	+	4.49650e11i	−0.887544	+	0.887544i	0.106743	+	0.994287i	$0.465958\pi$
$48$	−1.18157e11	−	1.18157e11i	−0.201265	−	0.201265i
$49$			6.71112e11i			0.989516i
$50$		0			0
$51$	1.65788e12			1.84741
$52$	3.97430e11	−	3.97430e11i	0.386578	−	0.386578i
$53$	8.73228e11	+	8.73228e11i	0.743355	+	0.743355i	0.973222	−	0.229867i	$-0.0738290\pi$
$53$	8.73228e11	+	8.73228e11i	0.743355	+	0.743355i	−0.229867	+	0.973222i	$0.573829\pi$
$54$		−	7.58585e11i		−	0.566563i
$55$		0			0
$56$	−6.25237e10			−0.0362016
$57$	−1.34567e12	+	1.34567e12i	−0.688359	+	0.688359i
$58$	2.27203e11	+	2.27203e11i	0.102901	+	0.102901i
$59$		−	2.30728e12i		−	0.927122i	−0.886065	−	0.463561i	$-0.846572\pi$
$59$		−	2.30728e12i		−	0.927122i	0.886065	−	0.463561i	$-0.153428\pi$
$60$		0			0
$61$	1.81962e12			0.578992			0.289496	−	0.957179i	$-0.406512\pi$
$61$	1.81962e12			0.578992			0.289496	+	0.957179i	$0.406512\pi$
$62$	2.61099e12	−	2.61099e12i	0.741419	−	0.741419i
$63$	8.44889e10	+	8.44889e10i	0.0214494	+	0.0214494i
$64$			5.49756e11i			0.125000i
$65$		0			0
$66$	−1.04592e12			−0.191731
$67$	5.96657e12	−	5.96657e12i	0.984467	−	0.984467i	−0.0154143	−	0.999881i	$-0.504907\pi$
$67$	5.96657e12	−	5.96657e12i	0.984467	−	0.984467i	0.999881	+	0.0154143i	$0.00490673\pi$
$68$	−3.85688e12	−	3.85688e12i	−0.573685	−	0.573685i
$69$		−	5.05965e12i		−	0.679480i
$70$		0			0
$71$	5.96561e12			0.655913			0.327957	−	0.944693i	$-0.393640\pi$
$71$	5.96561e12			0.655913			0.327957	+	0.944693i	$0.393640\pi$
$72$	7.42891e11	−	7.42891e11i	0.0740624	−	0.0740624i
$73$	7.19715e11	+	7.19715e11i	0.0651479	+	0.0651479i	0.738930	−	0.673782i	$-0.235331\pi$
$73$	7.19715e11	+	7.19715e11i	0.0651479	+	0.0651479i	−0.673782	+	0.738930i	$0.735331\pi$
$74$		−	1.61016e13i		−	1.32510i
$75$		0			0
$76$	6.26110e12			0.427519
$77$	−2.76730e11	+	2.76730e11i	−0.0172433	+	0.0172433i
$78$	1.09335e13	+	1.09335e13i	0.622439	+	0.622439i
$79$		−	3.29365e12i		−	0.171510i	−0.996316	−	0.0857548i	$-0.972670\pi$
$79$		−	3.29365e12i		−	0.171510i	0.996316	−	0.0857548i	$-0.0273302\pi$
$80$		0			0
$81$	2.76463e13			1.20849
$82$	−1.24088e13	+	1.24088e13i	−0.497776	+	0.497776i
$83$	6.80839e12	+	6.80839e12i	0.250899	+	0.250899i	0.821339	−	0.570440i	$-0.193227\pi$
$83$	6.80839e12	+	6.80839e12i	0.250899	+	0.250899i	−0.570440	+	0.821339i	$0.693227\pi$
$84$		−	1.72006e12i		−	0.0582891i
$85$		0			0
$86$	3.83057e13			1.10097
$87$	−6.25047e12	+	6.25047e12i	−0.165683	+	0.165683i
$88$	2.43322e12	+	2.43322e12i	0.0595392	+	0.0595392i
$89$		−	3.40430e13i		−	0.769658i	−0.922988	−	0.384829i	$-0.874260\pi$
$89$		−	3.40430e13i		−	0.769658i	0.922988	−	0.384829i	$-0.125740\pi$
$90$		0			0
$91$	5.78556e12			0.111958
$92$	−1.17707e13	+	1.17707e13i	−0.211002	+	0.211002i
$93$	7.18297e13	+	7.18297e13i	1.19378	+	1.19378i
$94$			5.75552e13i			0.887544i
$95$		0			0
$96$	−1.51240e13			−0.201265
$97$	7.87980e13	−	7.87980e13i	0.975243	−	0.975243i	−0.0244574	−	0.999701i	$-0.507786\pi$
$97$	7.87980e13	−	7.87980e13i	0.975243	−	0.975243i	0.999701	+	0.0244574i	$0.00778582\pi$
$98$	4.29512e13	+	4.29512e13i	0.494758	+	0.494758i
$99$		−	6.57607e12i		−	0.0705538i
$100$		0			0
$101$	−6.15737e13			−0.574309			−0.287155	−	0.957884i	$-0.592709\pi$
$101$	−6.15737e13			−0.574309			−0.287155	+	0.957884i	$0.592709\pi$
$102$	1.06105e14	−	1.06105e14i	0.923705	−	0.923705i
$103$	−1.34320e13	−	1.34320e13i	−0.109215	−	0.109215i	0.650388	−	0.759602i	$-0.274606\pi$
$103$	−1.34320e13	−	1.34320e13i	−0.109215	−	0.109215i	−0.759602	+	0.650388i	$0.774606\pi$
$104$		−	5.08711e13i		−	0.386578i
$105$		0			0
$106$	1.11773e14			0.743355
$107$	−1.60289e13	+	1.60289e13i	−0.0998198	+	0.0998198i	−0.755253	−	0.655433i	$-0.772486\pi$
$107$	−1.60289e13	+	1.60289e13i	−0.0998198	+	0.0998198i	0.655433	+	0.755253i	$0.272486\pi$
$108$	−4.85495e13	−	4.85495e13i	−0.283281	−	0.283281i
$109$		−	1.68220e14i		−	0.920223i	−0.887861	−	0.460112i	$-0.847809\pi$
$109$		−	1.68220e14i		−	0.920223i	0.887861	−	0.460112i	$-0.152191\pi$
$110$		0			0
$111$	4.42963e14			2.13357
$112$	−4.00152e12	+	4.00152e12i	−0.0181008	+	0.0181008i
$113$	1.53279e14	+	1.53279e14i	0.651528	+	0.651528i	0.953361	−	0.301833i	$-0.0975985\pi$
$113$	1.53279e14	+	1.53279e14i	0.651528	+	0.651528i	−0.301833	+	0.953361i	$0.597599\pi$
$114$			1.72246e14i			0.688359i
$115$		0			0
$116$	2.90820e13			0.102901
$117$	−6.87426e13	+	6.87426e13i	−0.229047	+	0.229047i
$118$	−1.47666e14	−	1.47666e14i	−0.463561	−	0.463561i
$119$		−	5.61463e13i		−	0.166147i
$120$		0			0
$121$	−3.58211e14			−0.943281
$122$	1.16456e14	−	1.16456e14i	0.289496	−	0.289496i
$123$	−3.41373e14	−	3.41373e14i	−0.801480	−	0.801480i
$124$		−	3.34207e14i		−	0.741419i
$125$		0			0
$126$	1.08146e13			0.0214494
$127$	−4.15607e14	+	4.15607e14i	−0.779931	+	0.779931i	−0.979819	−	0.199888i	$-0.935942\pi$
$127$	−4.15607e14	+	4.15607e14i	−0.779931	+	0.779931i	0.199888	+	0.979819i	$0.435942\pi$
$128$	3.51844e13	+	3.51844e13i	0.0625000	+	0.0625000i
$129$			1.05381e15i			1.77269i
$130$		0			0
$131$	−1.18903e15			−1.79595			−0.897975	−	0.440047i	$-0.854962\pi$
$131$	−1.18903e15			−1.79595			−0.897975	+	0.440047i	$0.854962\pi$
$132$	−6.69390e13	+	6.69390e13i	−0.0958654	+	0.0958654i
$133$	4.55728e13	+	4.55728e13i	0.0619076	+	0.0619076i
$134$		−	7.63721e14i		−	0.984467i
$135$		0			0
$136$	−4.93681e14			−0.573685
$137$	−5.13157e14	+	5.13157e14i	−0.566509	+	0.566509i	−0.931149	−	0.364640i	$-0.881192\pi$
$137$	−5.13157e14	+	5.13157e14i	−0.566509	+	0.566509i	0.364640	+	0.931149i	$0.381192\pi$
$138$	−3.23817e14	−	3.23817e14i	−0.339740	−	0.339740i
$139$			1.82418e15i			1.81955i	0.415106	+	0.909773i	$0.363744\pi$
$139$			1.82418e15i			1.81955i	−0.415106	+	0.909773i	$0.636256\pi$
$140$		0			0
$141$	−1.58337e15			−1.42906
$142$	3.81799e14	−	3.81799e14i	0.327957	−	0.327957i
$143$	−2.25155e14	−	2.25155e14i	−0.184132	−	0.184132i
$144$		−	9.50900e13i		−	0.0740624i
$145$		0			0
$146$	9.21235e13			0.0651479
$147$	−1.18161e15	+	1.18161e15i	−0.796621	+	0.796621i
$148$	−1.03050e15	−	1.03050e15i	−0.662549	−	0.662549i
$149$		−	2.26482e15i		−	1.38909i	−0.719451	−	0.694543i	$-0.755606\pi$
$149$		−	2.26482e15i		−	1.38909i	0.719451	−	0.694543i	$-0.244394\pi$
$150$		0			0
$151$	−5.81288e13			−0.0324753			−0.0162376	−	0.999868i	$-0.505169\pi$
$151$	−5.81288e13			−0.0324753			−0.0162376	+	0.999868i	$0.505169\pi$
$152$	4.00710e14	−	4.00710e14i	0.213760	−	0.213760i
$153$	6.67116e14	+	6.67116e14i	0.339908	+	0.339908i
$154$			3.54214e13i			0.0172433i
$155$		0			0
$156$	1.39949e15			0.622439
$157$	−4.67431e14	+	4.67431e14i	−0.198802	+	0.198802i	−0.799486	−	0.600684i	$-0.794895\pi$
$157$	−4.67431e14	+	4.67431e14i	−0.198802	+	0.198802i	0.600684	+	0.799486i	$0.294895\pi$
$158$	−2.10794e14	−	2.10794e14i	−0.0857548	−	0.0857548i
$159$			3.07493e15i			1.19689i
$160$		0			0
$161$	−1.71351e14			−0.0611091
$162$	1.76936e15	−	1.76936e15i	0.604243	−	0.604243i
$163$	−2.56385e15	−	2.56385e15i	−0.838646	−	0.838646i	0.150035	−	0.988681i	$-0.452061\pi$
$163$	−2.56385e15	−	2.56385e15i	−0.838646	−	0.838646i	−0.988681	+	0.150035i	$0.952061\pi$
$164$			1.58833e15i			0.497776i
$165$		0			0
$166$	8.71474e14			0.250899
$167$	−1.70145e15	+	1.70145e15i	−0.469682	+	0.469682i	−0.901811	−	0.432130i	$-0.857762\pi$
$167$	−1.70145e15	+	1.70145e15i	−0.469682	+	0.469682i	0.432130	+	0.901811i	$0.357762\pi$
$168$	−1.10084e14	−	1.10084e14i	−0.0291446	−	0.0291446i
$169$			7.69924e14i			0.195542i
$170$		0			0
$171$	−1.08297e15			−0.253305
$172$	2.45157e15	−	2.45157e15i	0.550484	−	0.550484i
$173$	6.13238e15	+	6.13238e15i	1.32223	+	1.32223i	0.911969	+	0.410259i	$0.134562\pi$
$173$	6.13238e15	+	6.13238e15i	1.32223	+	1.32223i	0.410259	+	0.911969i	$0.365438\pi$
$174$			8.00061e14i			0.165683i
$175$		0			0
$176$	3.11452e14			0.0595392
$177$	4.06236e15	−	4.06236e15i	0.746390	−	0.746390i
$178$	−2.17875e15	−	2.17875e15i	−0.384829	−	0.384829i
$179$		−	4.12628e15i		−	0.700789i	−0.936602	−	0.350395i	$-0.886047\pi$
$179$		−	4.12628e15i		−	0.700789i	0.936602	−	0.350395i	$-0.113953\pi$
$180$		0			0
$181$	−3.82463e15			−0.600952			−0.300476	−	0.953789i	$-0.597146\pi$
$181$	−3.82463e15			−0.600952			−0.300476	+	0.953789i	$0.597146\pi$
$182$	3.70276e14	−	3.70276e14i	0.0559791	−	0.0559791i
$183$	3.20376e15	+	3.20376e15i	0.466125	+	0.466125i
$184$			1.50665e15i			0.211002i
$185$		0			0
$186$	9.19420e15			1.19378
$187$	−2.18503e15	+	2.18503e15i	−0.273254	+	0.273254i
$188$	3.68353e15	+	3.68353e15i	0.443772	+	0.443772i
$189$		−	7.06755e14i		−	0.0820420i
$190$		0			0
$191$	−4.00257e15			−0.431624			−0.215812	−	0.976435i	$-0.569240\pi$
$191$	−4.00257e15			−0.431624			−0.215812	+	0.976435i	$0.569240\pi$
$192$	−9.67939e14	+	9.67939e14i	−0.100633	+	0.100633i
$193$	−1.95374e15	−	1.95374e15i	−0.195869	−	0.195869i	0.602358	−	0.798226i	$-0.294228\pi$
$193$	−1.95374e15	−	1.95374e15i	−0.195869	−	0.195869i	−0.798226	+	0.602358i	$0.794228\pi$
$194$		−	1.00861e16i		−	0.975243i
$195$		0			0
$196$	5.49775e15			0.494758
$197$	−8.81058e15	+	8.81058e15i	−0.765140	+	0.765140i	−0.977247	−	0.212106i	$-0.931968\pi$
$197$	−8.81058e15	+	8.81058e15i	−0.765140	+	0.765140i	0.212106	+	0.977247i	$0.431968\pi$
$198$	−4.20869e14	−	4.20869e14i	−0.0352769	−	0.0352769i
$199$			8.93160e14i			0.0722700i	0.999347	+	0.0361350i	$0.0115046\pi$
$199$			8.93160e14i			0.0722700i	−0.999347	+	0.0361350i	$0.988495\pi$
$200$		0			0
$201$	2.10103e16			1.58511
$202$	−3.94072e15	+	3.94072e15i	−0.287155	+	0.287155i
$203$	2.11680e14	+	2.11680e14i	0.0149007	+	0.0149007i
$204$		−	1.35814e16i		−	0.923705i
$205$		0			0
$206$	−1.71930e15			−0.109215
$207$	2.03595e15	−	2.03595e15i	0.125019	−	0.125019i
$208$	−3.25575e15	−	3.25575e15i	−0.193289	−	0.193289i
$209$		−	3.54709e15i		−	0.203633i
$210$		0			0
$211$	−2.28838e16			−1.22900			−0.614498	−	0.788918i	$-0.710642\pi$
$211$	−2.28838e16			−1.22900			−0.614498	+	0.788918i	$0.710642\pi$
$212$	7.15348e15	−	7.15348e15i	0.371678	−	0.371678i
$213$	1.05035e16	+	1.05035e16i	0.528051	+	0.528051i
$214$			2.05170e15i			0.0998198i
$215$		0			0
$216$	−6.21433e15			−0.283281
$217$	2.43260e15	−	2.43260e15i	0.107362	−	0.107362i
$218$	−1.07661e16	−	1.07661e16i	−0.460112	−	0.460112i
$219$			2.53436e15i			0.104896i
$220$		0			0
$221$	4.56822e16			1.77419
$222$	2.83497e16	−	2.83497e16i	1.06679	−	1.06679i
$223$	1.33679e16	+	1.33679e16i	0.487449	+	0.487449i	0.907500	−	0.420051i	$-0.137988\pi$
$223$	1.33679e16	+	1.33679e16i	0.487449	+	0.487449i	−0.420051	+	0.907500i	$0.637988\pi$
$224$			5.12194e14i			0.0181008i
$225$		0			0
$226$	1.96197e16			0.651528
$227$	4.77863e15	−	4.77863e15i	0.153859	−	0.153859i	−0.625980	−	0.779839i	$-0.715301\pi$
$227$	4.77863e15	−	4.77863e15i	0.153859	−	0.153859i	0.779839	+	0.625980i	$0.215301\pi$
$228$	1.10237e16	+	1.10237e16i	0.344179	+	0.344179i
$229$		−	2.78299e16i		−	0.842681i	−0.906903	−	0.421340i	$-0.861560\pi$
$229$		−	2.78299e16i		−	0.842681i	0.906903	−	0.421340i	$-0.138440\pi$
$230$		0			0
$231$	−9.74460e14			−0.0277639
$232$	1.86125e15	−	1.86125e15i	0.0514504	−	0.0514504i
$233$	−2.21422e16	−	2.21422e16i	−0.593922	−	0.593922i	0.344766	−	0.938689i	$-0.387958\pi$
$233$	−2.21422e16	−	2.21422e16i	−0.593922	−	0.593922i	−0.938689	+	0.344766i	$0.887958\pi$
$234$			8.79905e15i			0.229047i
$235$		0			0
$236$	−1.89013e16			−0.463561
$237$	5.79904e15	−	5.79904e15i	0.138076	−	0.138076i
$238$	−3.59336e15	−	3.59336e15i	−0.0830734	−	0.0830734i
$239$			3.77217e16i			0.846848i	0.905932	+	0.423424i	$0.139172\pi$
$239$			3.77217e16i			0.846848i	−0.905932	+	0.423424i	$0.860828\pi$
$240$		0			0
$241$	2.79177e16			0.591235			0.295617	−	0.955306i	$-0.404475\pi$
$241$	2.79177e16			0.591235			0.295617	+	0.955306i	$0.404475\pi$
$242$	−2.29255e16	+	2.29255e16i	−0.471641	+	0.471641i
$243$	2.03300e16	+	2.03300e16i	0.406343	+	0.406343i
$244$		−	1.49064e16i		−	0.289496i
$245$		0			0
$246$	−4.36957e16			−0.801480
$247$	−3.70793e16	+	3.70793e16i	−0.661079	+	0.661079i
$248$	−2.13893e16	−	2.13893e16i	−0.370710	−	0.370710i
$249$			2.39747e16i			0.403978i
$250$		0			0
$251$	−7.72495e16			−1.23078			−0.615389	−	0.788224i	$-0.711001\pi$
$251$	−7.72495e16			−1.23078			−0.615389	+	0.788224i	$0.711001\pi$
$252$	6.92133e14	−	6.92133e14i	0.0107247	−	0.0107247i
$253$	6.66843e15	+	6.66843e15i	0.100503	+	0.100503i
$254$			5.31976e16i			0.779931i
$255$		0			0
$256$	4.50360e15			0.0625000
$257$	−4.29149e15	+	4.29149e15i	−0.0579530	+	0.0579530i	−0.735489	−	0.677536i	$-0.763048\pi$
$257$	−4.29149e15	+	4.29149e15i	−0.0579530	+	0.0579530i	0.677536	+	0.735489i	$0.263048\pi$
$258$	6.74438e16	+	6.74438e16i	0.886347	+	0.886347i
$259$		−	1.50015e16i		−	0.191883i
$260$		0			0
$261$	−5.03026e15			−0.0609686
$262$	−7.60980e16	+	7.60980e16i	−0.897975	+	0.897975i
$263$	−1.07016e17	−	1.07016e17i	−1.22958	−	1.22958i	−0.964121	−	0.265462i	$-0.914476\pi$
$263$	−1.07016e17	−	1.07016e17i	−1.22958	−	1.22958i	−0.265462	−	0.964121i	$-0.585524\pi$
$264$			8.56820e15i			0.0958654i
$265$		0			0
$266$	5.83331e15			0.0619076
$267$	5.99385e16	−	5.99385e16i	0.619622	−	0.619622i
$268$	−4.88781e16	−	4.88781e16i	−0.492233	−	0.492233i
$269$			8.03254e16i			0.788110i	0.919087	+	0.394055i	$0.128928\pi$
$269$			8.03254e16i			0.788110i	−0.919087	+	0.394055i	$0.871072\pi$
$270$		0			0
$271$	−1.84195e17			−1.71590			−0.857951	−	0.513731i	$-0.828263\pi$
$271$	−1.84195e17			−1.71590			−0.857951	+	0.513731i	$0.828263\pi$
$272$	−3.15956e16	+	3.15956e16i	−0.286843	+	0.286843i
$273$	1.01865e16	+	1.01865e16i	0.0901333	+	0.0901333i
$274$			6.56841e16i			0.566509i
$275$		0			0
$276$	−4.14486e16			−0.339740
$277$	1.09653e17	−	1.09653e17i	0.876319	−	0.876319i	−0.116832	−	0.993152i	$-0.537274\pi$
$277$	1.09653e17	−	1.09653e17i	0.876319	−	0.876319i	0.993152	+	0.116832i	$0.0372741\pi$
$278$	1.16747e17	+	1.16747e17i	0.909773	+	0.909773i
$279$			5.78071e16i			0.439290i
$280$		0			0
$281$	−3.66225e16			−0.264730			−0.132365	−	0.991201i	$-0.542257\pi$
$281$	−3.66225e16			−0.264730			−0.132365	+	0.991201i	$0.542257\pi$
$282$	−1.01336e17	+	1.01336e17i	−0.714528	+	0.714528i
$283$	−7.26808e16	−	7.26808e16i	−0.499936	−	0.499936i	0.411482	−	0.911418i	$-0.365011\pi$
$283$	−7.26808e16	−	7.26808e16i	−0.499936	−	0.499936i	−0.911418	+	0.411482i	$0.865011\pi$
$284$		−	4.88703e16i		−	0.327957i
$285$		0			0
$286$	−2.88199e16			−0.184132
$287$	−1.15610e16	+	1.15610e16i	−0.0720812	+	0.0720812i
$288$	−6.08576e15	−	6.08576e15i	−0.0370312	−	0.0370312i
$289$		−	2.74948e17i		−	1.63292i
$290$		0			0
$291$	2.77475e17			1.57026
$292$	5.89590e15	−	5.89590e15i	0.0325739	−	0.0325739i
$293$	−1.92332e17	−	1.92332e17i	−1.03747	−	1.03747i	−0.999270	−	0.0382043i	$-0.987836\pi$
$293$	−1.92332e17	−	1.92332e17i	−1.03747	−	1.03747i	−0.0382043	−	0.999270i	$-0.512164\pi$
$294$			1.51246e17i			0.796621i
$295$		0			0
$296$	−1.31905e17			−0.662549
$297$	−2.75046e16	+	2.75046e16i	−0.134931	+	0.134931i
$298$	−1.44948e17	−	1.44948e17i	−0.694543	−	0.694543i
$299$		−	1.39416e17i		−	0.652551i
$300$		0			0
$301$	3.56885e16			0.159427
$302$	−3.72024e15	+	3.72024e15i	−0.0162376	+	0.0162376i
$303$	−1.08411e17	−	1.08411e17i	−0.462354	−	0.462354i
$304$		−	5.12909e16i		−	0.213760i
$305$		0			0
$306$	8.53909e16			0.339908
$307$	1.26324e16	−	1.26324e16i	0.0491492	−	0.0491492i	−0.682105	−	0.731254i	$-0.738935\pi$
$307$	1.26324e16	−	1.26324e16i	0.0491492	−	0.0491492i	0.731254	+	0.682105i	$0.238935\pi$
$308$	2.26697e15	+	2.26697e15i	0.00862166	+	0.00862166i
$309$		−	4.72987e16i		−	0.175849i
$310$		0			0
$311$	2.18406e17			0.776143			0.388072	−	0.921629i	$-0.373141\pi$
$311$	2.18406e17			0.776143			0.388072	+	0.921629i	$0.373141\pi$
$312$	8.95672e16	−	8.95672e16i	0.311219	−	0.311219i
$313$	2.57557e17	+	2.57557e17i	0.875109	+	0.875109i	0.993024	−	0.117914i	$-0.0376208\pi$
$313$	2.57557e17	+	2.57557e17i	0.875109	+	0.875109i	−0.117914	+	0.993024i	$0.537621\pi$
$314$			5.98312e16i			0.198802i
$315$		0			0
$316$	−2.69816e16			−0.0857548
$317$	−9.69649e16	+	9.69649e16i	−0.301439	+	0.301439i	−0.841577	−	0.540138i	$-0.818372\pi$
$317$	−9.69649e16	+	9.69649e16i	−0.301439	+	0.301439i	0.540138	+	0.841577i	$0.318372\pi$
$318$	1.96796e17	+	1.96796e17i	0.598447	+	0.598447i
$319$		−	1.64758e16i		−	0.0490130i
$320$		0			0
$321$	−5.64432e16			−0.160722
$322$	−1.09665e16	+	1.09665e16i	−0.0305545	+	0.0305545i
$323$	3.59838e17	+	3.59838e17i	0.981046	+	0.981046i
$324$		−	2.26478e17i		−	0.604243i
$325$		0			0
$326$	−3.28172e17			−0.838646
$327$	2.96181e17	−	2.96181e17i	0.740837	−	0.740837i
$328$	1.01653e17	+	1.01653e17i	0.248888	+	0.248888i
$329$			5.36228e16i			0.128522i
$330$		0			0
$331$	5.65335e17			1.29870			0.649352	−	0.760488i	$-0.275040\pi$
$331$	5.65335e17			1.29870			0.649352	+	0.760488i	$0.275040\pi$
$332$	5.57744e16	−	5.57744e16i	0.125449	−	0.125449i
$333$	1.78244e17	+	1.78244e17i	0.392559	+	0.392559i
$334$			2.17786e17i			0.469682i
$335$		0			0
$336$	−1.40907e16			−0.0291446
$337$	3.00518e17	−	3.00518e17i	0.608781	−	0.608781i	−0.333847	−	0.942627i	$-0.608347\pi$
$337$	3.00518e17	−	3.00518e17i	0.608781	−	0.608781i	0.942627	+	0.333847i	$0.108347\pi$
$338$	4.92751e16	+	4.92751e16i	0.0977711	+	0.0977711i
$339$			5.39747e17i			1.04904i
$340$		0			0
$341$	−1.89338e17			−0.353148
$342$	−6.93100e16	+	6.93100e16i	−0.126652	+	0.126652i
$343$	8.04571e16	+	8.04571e16i	0.144047	+	0.144047i
$344$		−	3.13801e17i		−	0.550484i
$345$		0			0
$346$	7.84945e17			1.32223
$347$	−5.87282e17	+	5.87282e17i	−0.969484	+	0.969484i	−0.999548	−	0.0300638i	$-0.990429\pi$
$347$	−5.87282e17	+	5.87282e17i	−0.969484	+	0.969484i	0.0300638	+	0.999548i	$0.490429\pi$
$348$	5.12039e16	+	5.12039e16i	0.0828416	+	0.0828416i
$349$			1.17199e17i			0.185843i	0.995673	+	0.0929215i	$0.0296206\pi$
$349$			1.17199e17i			0.185843i	−0.995673	+	0.0929215i	$0.970379\pi$
$350$		0			0
$351$	5.75036e17			0.876084
$352$	1.99329e16	−	1.99329e16i	0.0297696	−	0.0297696i
$353$	3.65688e17	+	3.65688e17i	0.535412	+	0.535412i	0.922178	−	0.386766i	$-0.126408\pi$
$353$	3.65688e17	+	3.65688e17i	0.535412	+	0.535412i	−0.386766	+	0.922178i	$0.626408\pi$
$354$		−	5.19983e17i		−	0.746390i
$355$		0			0
$356$	−2.78880e17			−0.384829
$357$	9.88551e16	−	9.88551e16i	0.133759	−	0.133759i
$358$	−2.64082e17	−	2.64082e17i	−0.350395	−	0.350395i
$359$		−	4.57343e17i		−	0.595088i	−0.954708	−	0.297544i	$-0.903832\pi$
$359$		−	4.57343e17i		−	0.595088i	0.954708	−	0.297544i	$-0.0961675\pi$
$360$		0			0
$361$	2.14860e17			0.268910
$362$	−2.44777e17	+	2.44777e17i	−0.300476	+	0.300476i
$363$	−6.30691e17	−	6.30691e17i	−0.759400	−	0.759400i
$364$		−	4.73953e16i		−	0.0559791i
$365$		0			0
$366$	4.10081e17			0.466125
$367$	8.39388e17	−	8.39388e17i	0.936052	−	0.936052i	−0.0620224	−	0.998075i	$-0.519755\pi$
$367$	8.39388e17	−	8.39388e17i	0.936052	−	0.936052i	0.998075	+	0.0620224i	$0.0197550\pi$
$368$	9.64255e16	+	9.64255e16i	0.105501	+	0.105501i
$369$		−	2.74730e17i		−	0.294931i
$370$		0			0
$371$	1.04136e17			0.107643
$372$	5.88429e17	−	5.88429e17i	0.596889	−	0.596889i
$373$	−5.67215e17	−	5.67215e17i	−0.564658	−	0.564658i	0.365969	−	0.930627i	$-0.380738\pi$
$373$	−5.67215e17	−	5.67215e17i	−0.564658	−	0.564658i	−0.930627	+	0.365969i	$0.880738\pi$
$374$			2.79684e17i			0.273254i
$375$		0			0
$376$	4.71492e17			0.443772
$377$	−1.72229e17	+	1.72229e17i	−0.159117	+	0.159117i
$378$	−4.52323e16	−	4.52323e16i	−0.0410210	−	0.0410210i
$379$		−	1.03094e18i		−	0.917819i	−0.888483	−	0.458909i	$-0.848240\pi$
$379$		−	1.03094e18i		−	0.917819i	0.888483	−	0.458909i	$-0.151760\pi$
$380$		0			0
$381$	−1.46349e18			−1.25579
$382$	−2.56165e17	+	2.56165e17i	−0.215812	+	0.215812i
$383$	9.40767e17	+	9.40767e17i	0.778199	+	0.778199i	0.979524	−	0.201325i	$-0.0645249\pi$
$383$	9.40767e17	+	9.40767e17i	0.778199	+	0.778199i	−0.201325	+	0.979524i	$0.564525\pi$
$384$			1.23896e17i			0.100633i
$385$		0			0
$386$	−2.50078e17			−0.195869
$387$	−4.24042e17	+	4.24042e17i	−0.326161	+	0.326161i
$388$	−6.45513e17	−	6.45513e17i	−0.487622	−	0.487622i
$389$			1.23129e17i			0.0913513i	0.998956	+	0.0456756i	$0.0145441\pi$
$389$			1.23129e17i			0.0913513i	−0.998956	+	0.0456756i	$0.985456\pi$
$390$		0			0
$391$	−1.35297e18			−0.968392
$392$	3.51856e17	−	3.51856e17i	0.247379	−	0.247379i
$393$	−2.09349e18	−	2.09349e18i	−1.44585	−	1.44585i
$394$			1.12775e18i			0.765140i
$395$		0			0
$396$	−5.38712e16			−0.0352769
$397$	−1.57020e18	+	1.57020e18i	−1.01023	+	1.01023i	−0.0102871	+	0.999947i	$0.503275\pi$
$397$	−1.57020e18	+	1.57020e18i	−1.01023	+	1.01023i	−0.999947	+	0.0102871i	$0.996725\pi$
$398$	5.71623e16	+	5.71623e16i	0.0361350	+	0.0361350i
$399$			1.60477e17i			0.0996789i
$400$		0			0
$401$	−2.26943e18			−1.36115			−0.680575	−	0.732679i	$-0.738270\pi$
$401$	−2.26943e18			−1.36115			−0.680575	+	0.732679i	$0.738270\pi$
$402$	1.34466e18	−	1.34466e18i	0.792557	−	0.792557i
$403$	1.97923e18	+	1.97923e18i	1.14647	+	1.14647i
$404$			5.04412e17i			0.287155i
$405$		0			0
$406$	2.70950e16			0.0149007
$407$	−5.83810e17	+	5.83810e17i	−0.315581	+	0.315581i
$408$	−8.69209e17	−	8.69209e17i	−0.461852	−	0.461852i
$409$			2.56892e18i			1.34180i	0.741547	+	0.670900i	$0.234092\pi$
$409$			2.56892e18i			1.34180i	−0.741547	+	0.670900i	$0.765908\pi$
$410$		0			0
$411$	−1.80700e18			−0.912149
$412$	−1.10035e17	+	1.10035e17i	−0.0546073	+	0.0546073i
$413$	−1.37577e17	−	1.37577e17i	−0.0671266	−	0.0671266i
$414$		−	2.60602e17i		−	0.125019i
$415$		0			0
$416$	−4.16736e17			−0.193289
$417$	−3.21177e18	+	3.21177e18i	−1.46485	+	1.46485i
$418$	−2.27014e17	−	2.27014e17i	−0.101817	−	0.101817i
$419$			1.05220e18i			0.464086i	0.972705	+	0.232043i	$0.0745411\pi$
$419$			1.05220e18i			0.464086i	−0.972705	+	0.232043i	$0.925459\pi$
$420$		0			0
$421$	1.04627e18			0.446342			0.223171	−	0.974779i	$-0.428359\pi$
$421$	1.04627e18			0.446342			0.223171	+	0.974779i	$0.428359\pi$
$422$	−1.46456e18	+	1.46456e18i	−0.614498	+	0.614498i
$423$	−6.37133e17	−	6.37133e17i	−0.262934	−	0.262934i
$424$		−	9.15646e17i		−	0.371678i
$425$		0			0
$426$	1.34444e18			0.528051
$427$	1.08499e17	−	1.08499e17i	0.0419209	−	0.0419209i
$428$	1.31309e17	+	1.31309e17i	0.0499099	+	0.0499099i
$429$		−	7.92849e17i		−	0.296476i
$430$		0			0
$431$	8.35303e17			0.302345			0.151173	−	0.988507i	$-0.451695\pi$
$431$	8.35303e17			0.302345			0.151173	+	0.988507i	$0.451695\pi$
$432$	−3.97717e17	+	3.97717e17i	−0.141641	+	0.141641i
$433$	−8.99728e17	−	8.99728e17i	−0.315280	−	0.315280i	0.531671	−	0.846951i	$-0.321564\pi$
$433$	−8.99728e17	−	8.99728e17i	−0.315280	−	0.315280i	−0.846951	+	0.531671i	$0.821564\pi$
$434$		−	3.11373e17i		−	0.107362i
$435$		0			0
$436$	−1.37806e18			−0.460112
$437$	1.09818e18	−	1.09818e18i	0.360830	−	0.360830i
$438$	1.62199e17	+	1.62199e17i	0.0524481	+	0.0524481i
$439$			4.55363e18i			1.44913i	0.689209	+	0.724563i	$0.257958\pi$
$439$			4.55363e18i			1.44913i	−0.689209	+	0.724563i	$0.742042\pi$
$440$		0			0
$441$	−9.50934e17			−0.293143
$442$	2.92366e18	−	2.92366e18i	0.887097	−	0.887097i
$443$	3.00851e18	+	3.00851e18i	0.898516	+	0.898516i	0.995305	−	0.0967893i	$-0.0308573\pi$
$443$	3.00851e18	+	3.00851e18i	0.898516	+	0.898516i	−0.0967893	+	0.995305i	$0.530857\pi$
$444$		−	3.62876e18i		−	1.06679i
$445$		0			0
$446$	1.71109e18			0.487449
$447$	3.98760e18	−	3.98760e18i	1.11830	−	1.11830i
$448$	3.27804e16	+	3.27804e16i	0.00905041	+	0.00905041i
$449$			3.03670e18i			0.825425i	0.910861	+	0.412713i	$0.135419\pi$
$449$			3.03670e18i			0.825425i	−0.910861	+	0.412713i	$0.864581\pi$
$450$		0			0
$451$	8.99833e17			0.237097
$452$	1.25566e18	−	1.25566e18i	0.325764	−	0.325764i
$453$	−1.02346e17	−	1.02346e17i	−0.0261446	−	0.0261446i
$454$		−	6.11664e17i		−	0.153859i
$455$		0			0
$456$	1.41104e18			0.344179
$457$	1.78738e18	−	1.78738e18i	0.429343	−	0.429343i	−0.459062	−	0.888404i	$-0.651814\pi$
$457$	1.78738e18	−	1.78738e18i	0.429343	−	0.429343i	0.888404	+	0.459062i	$0.151814\pi$
$458$	−1.78111e18	−	1.78111e18i	−0.421340	−	0.421340i
$459$		−	5.58047e18i		−	1.30012i
$460$		0			0
$461$	−4.19270e17			−0.0947518			−0.0473759	−	0.998877i	$-0.515086\pi$
$461$	−4.19270e17			−0.0947518			−0.0473759	+	0.998877i	$0.515086\pi$
$462$	−6.23654e16	+	6.23654e16i	−0.0138819	+	0.0138819i
$463$	6.91209e17	+	6.91209e17i	0.151545	+	0.151545i	0.778808	−	0.627263i	$-0.215825\pi$
$463$	6.91209e17	+	6.91209e17i	0.151545	+	0.151545i	−0.627263	+	0.778808i	$0.715825\pi$
$464$		−	2.38240e17i		−	0.0514504i
$465$		0			0
$466$	−2.83420e18			−0.593922
$467$	−1.69375e18	+	1.69375e18i	−0.349649	+	0.349649i	−0.859979	−	0.510330i	$-0.829523\pi$
$467$	−1.69375e18	+	1.69375e18i	−0.349649	+	0.349649i	0.510330	+	0.859979i	$0.329523\pi$
$468$	5.63139e17	+	5.63139e17i	0.114524	+	0.114524i
$469$		−	7.11540e17i		−	0.142557i
$470$		0			0
$471$	−1.64599e18			−0.320096
$472$	−1.20968e18	+	1.20968e18i	−0.231780	+	0.231780i
$473$	−1.38888e18	−	1.38888e18i	−0.262203	−	0.262203i
$474$		−	7.42277e17i		−	0.138076i
$475$		0			0
$476$	−4.59950e17			−0.0830734
$477$	−1.23732e18	+	1.23732e18i	−0.220219	+	0.220219i
$478$	2.41419e18	+	2.41419e18i	0.423424	+	0.423424i
$479$			3.61673e18i			0.625126i	0.949897	+	0.312563i	$0.101187\pi$
$479$			3.61673e18i			0.625126i	−0.949897	+	0.312563i	$0.898813\pi$
$480$		0			0
$481$	1.22056e19			2.04902
$482$	1.78673e18	−	1.78673e18i	0.295617	−	0.295617i
$483$	−3.01693e17	−	3.01693e17i	−0.0491966	−	0.0491966i
$484$			2.93446e18i			0.471641i
$485$		0			0
$486$	2.60224e18			0.406343
$487$	−2.80800e18	+	2.80800e18i	−0.432210	+	0.432210i	−0.889380	−	0.457170i	$-0.848863\pi$
$487$	−2.80800e18	+	2.80800e18i	−0.432210	+	0.432210i	0.457170	+	0.889380i	$0.348863\pi$
$488$	−9.54007e17	−	9.54007e17i	−0.144748	−	0.144748i
$489$		−	9.02817e18i		−	1.35032i
$490$		0			0
$491$	8.53603e18			1.24075			0.620377	−	0.784304i	$-0.286980\pi$
$491$	8.53603e18			1.24075			0.620377	+	0.784304i	$0.286980\pi$
$492$	−2.79652e18	+	2.79652e18i	−0.400740	+	0.400740i
$493$	1.67140e18	+	1.67140e18i	0.236131	+	0.236131i
$494$			4.74615e18i			0.661079i
$495$		0			0
$496$	−2.73783e18			−0.370710
$497$	3.55713e17	−	3.55713e17i	0.0474903	−	0.0474903i
$498$	1.53438e18	+	1.53438e18i	0.201989	+	0.201989i
$499$		−	1.01549e19i		−	1.31817i	−0.752069	−	0.659084i	$-0.770944\pi$
$499$		−	1.01549e19i		−	1.31817i	0.752069	−	0.659084i	$-0.229056\pi$
$500$		0			0
$501$	−5.99138e18			−0.756246
$502$	−4.94397e18	+	4.94397e18i	−0.615389	+	0.615389i
$503$	9.79904e17	+	9.79904e17i	0.120284	+	0.120284i	0.764686	−	0.644403i	$-0.222894\pi$
$503$	9.79904e17	+	9.79904e17i	0.120284	+	0.120284i	−0.644403	+	0.764686i	$0.722894\pi$
$504$		−	8.85930e16i		−	0.0107247i
$505$		0			0
$506$	8.53559e17			0.100503
$507$	−1.35558e18	+	1.35558e18i	−0.157424	+	0.157424i
$508$	3.40465e18	+	3.40465e18i	0.389966	+	0.389966i
$509$		−	1.65546e19i		−	1.87023i	−0.354346	−	0.935114i	$-0.615296\pi$
$509$		−	1.65546e19i		−	1.87023i	0.354346	−	0.935114i	$-0.384704\pi$
$510$		0			0
$511$	8.58292e16			0.00943384
$512$	2.88230e17	−	2.88230e17i	0.0312500	−	0.0312500i
$513$	4.52955e18	+	4.52955e18i	0.484433	+	0.484433i
$514$			5.49310e17i			0.0579530i
$515$		0			0
$516$	8.63280e18			0.886347
$517$	2.08683e18	−	2.08683e18i	0.211374	−	0.211374i
$518$	−9.60095e17	−	9.60095e17i	−0.0959414	−	0.0959414i
$519$			2.15942e19i			2.12895i
$520$		0			0
$521$	−5.17021e18			−0.496186			−0.248093	−	0.968736i	$-0.579804\pi$
$521$	−5.17021e18			−0.496186			−0.248093	+	0.968736i	$0.579804\pi$
$522$	−3.21936e17	+	3.21936e17i	−0.0304843	+	0.0304843i
$523$	−2.65087e18	−	2.65087e18i	−0.247672	−	0.247672i	0.572343	−	0.820014i	$-0.306035\pi$
$523$	−2.65087e18	−	2.65087e18i	−0.247672	−	0.247672i	−0.820014	+	0.572343i	$0.806035\pi$
$524$			9.74054e18i			0.897975i
$525$		0			0
$526$	−1.36980e19			−1.22958
$527$	1.92076e19	−	1.92076e19i	1.70137	−	1.70137i
$528$	5.48365e17	+	5.48365e17i	0.0479327	+	0.0479327i
$529$		−	7.46375e18i		−	0.643824i
$530$		0			0
$531$	3.26931e18			0.274659
$532$	3.73332e17	−	3.73332e17i	0.0309538	−	0.0309538i
$533$	−9.40636e18	−	9.40636e18i	−0.769717	−	0.769717i
$534$		−	7.67213e18i		−	0.619622i
$535$		0			0
$536$	−6.25640e18			−0.492233
$537$	7.26502e18	−	7.26502e18i	0.564179	−	0.564179i
$538$	5.14083e18	+	5.14083e18i	0.394055	+	0.394055i
$539$		−	3.11463e18i		−	0.235660i
$540$		0			0
$541$	7.41169e18			0.546432			0.273216	−	0.961953i	$-0.411913\pi$
$541$	7.41169e18			0.546432			0.273216	+	0.961953i	$0.411913\pi$
$542$	−1.17885e19	+	1.17885e19i	−0.857951	+	0.857951i
$543$	−6.73392e18	−	6.73392e18i	−0.483804	−	0.483804i
$544$			4.04423e18i			0.286843i
$545$		0			0
$546$	1.30387e18			0.0901333
$547$	−2.08657e18	+	2.08657e18i	−0.142404	+	0.142404i	−0.774715	−	0.632311i	$-0.782106\pi$
$547$	−2.08657e18	+	2.08657e18i	−0.142404	+	0.142404i	0.632311	+	0.774715i	$0.282106\pi$
$548$	4.20378e18	+	4.20378e18i	0.283254	+	0.283254i
$549$			2.57832e18i			0.171526i
$550$		0			0
$551$	−2.71329e18			−0.175968
$552$	−2.65271e18	+	2.65271e18i	−0.169870	+	0.169870i
$553$	−1.96391e17	−	1.96391e17i	−0.0124179	−	0.0124179i
$554$		−	1.40356e19i		−	0.876319i
$555$		0			0
$556$	1.49436e19			0.909773
$557$	6.99419e18	−	6.99419e18i	0.420485	−	0.420485i	−0.464885	−	0.885371i	$-0.653905\pi$
$557$	6.99419e18	−	6.99419e18i	0.420485	−	0.420485i	0.885371	+	0.464885i	$0.153905\pi$
$558$	3.69965e18	+	3.69965e18i	0.219645	+	0.219645i
$559$			2.90372e19i			1.70244i
$560$		0			0
$561$	−7.69424e18			−0.439973
$562$	−2.34384e18	+	2.34384e18i	−0.132365	+	0.132365i
$563$	3.22792e18	+	3.22792e18i	0.180038	+	0.180038i	0.791372	−	0.611334i	$-0.209367\pi$
$563$	3.22792e18	+	3.22792e18i	0.180038	+	0.180038i	−0.611334	+	0.791372i	$0.709367\pi$
$564$			1.29710e19i			0.714528i
$565$		0			0
$566$	−9.30314e18			−0.499936
$567$	1.64847e18	−	1.64847e18i	0.0874983	−	0.0874983i
$568$	−3.12770e18	−	3.12770e18i	−0.163978	−	0.163978i
$569$		−	7.96619e18i		−	0.412539i	−0.978495	−	0.206269i	$-0.933868\pi$
$569$		−	7.96619e18i		−	0.412539i	0.978495	−	0.206269i	$-0.0661323\pi$
$570$		0			0
$571$	2.45235e19			1.23917			0.619583	−	0.784931i	$-0.287302\pi$
$571$	2.45235e19			1.23917			0.619583	+	0.784931i	$0.287302\pi$
$572$	−1.84447e18	+	1.84447e18i	−0.0920662	+	0.0920662i
$573$	−7.04721e18	−	7.04721e18i	−0.347484	−	0.347484i
$574$			1.47981e18i			0.0720812i
$575$		0			0
$576$	−7.78978e17			−0.0370312
$577$	−2.08177e19	+	2.08177e19i	−0.977694	+	0.977694i	−0.999757	−	0.0220629i	$-0.992977\pi$
$577$	−2.08177e19	+	2.08177e19i	−0.977694	+	0.977694i	0.0220629	+	0.999757i	$0.492977\pi$
$578$	−1.75966e19	−	1.75966e19i	−0.816460	−	0.816460i
$579$		−	6.87978e18i		−	0.315373i
$580$		0			0
$581$	8.11931e17			0.0363318
$582$	1.77584e19	−	1.77584e19i	0.785131	−	0.785131i
$583$	−4.05265e18	−	4.05265e18i	−0.177035	−	0.177035i
$584$		−	7.54675e17i		−	0.0325739i
$585$		0			0
$586$	−2.46184e19			−1.03747
$587$	−2.44656e19	+	2.44656e19i	−1.01880	+	1.01880i	−0.0189799	+	0.999820i	$0.506042\pi$
$587$	−2.44656e19	+	2.44656e19i	−1.01880	+	1.01880i	−0.999820	+	0.0189799i	$0.993958\pi$
$588$	9.67973e18	+	9.67973e18i	0.398311	+	0.398311i
$589$			3.11808e19i			1.26788i
$590$		0			0
$591$	−3.10251e19			−1.23197
$592$	−8.44189e18	+	8.44189e18i	−0.331274	+	0.331274i
$593$	9.57554e18	+	9.57554e18i	0.371348	+	0.371348i	0.867968	−	0.496620i	$-0.165426\pi$
$593$	9.57554e18	+	9.57554e18i	0.371348	+	0.371348i	−0.496620	+	0.867968i	$0.665426\pi$
$594$			3.52059e18i			0.134931i
$595$		0			0
$596$	−1.85534e19			−0.694543
$597$	−1.57256e18	+	1.57256e18i	−0.0581818	+	0.0581818i
$598$	−8.92263e18	−	8.92263e18i	−0.326276	−	0.326276i
$599$			3.35451e16i			0.00121239i	1.00000		0.000606194i	$0.000192957\pi$
$599$			3.35451e16i			0.00121239i	−1.00000		0.000606194i	$0.999807\pi$
$600$		0			0
$601$	−2.53995e19			−0.896817			−0.448409	−	0.893829i	$-0.648009\pi$
$601$	−2.53995e19			−0.896817			−0.448409	+	0.893829i	$0.648009\pi$
$602$	2.28406e18	−	2.28406e18i	0.0797137	−	0.0797137i
$603$	8.45434e18	+	8.45434e18i	0.291648	+	0.291648i
$604$			4.76191e17i			0.0162376i
$605$		0			0
$606$	−1.38766e19			−0.462354
$607$	6.37681e18	−	6.37681e18i	0.210031	−	0.210031i	−0.594250	−	0.804281i	$-0.702551\pi$
$607$	6.37681e18	−	6.37681e18i	0.210031	−	0.210031i	0.804281	+	0.594250i	$0.202551\pi$
$608$	−3.28262e18	−	3.28262e18i	−0.106880	−	0.106880i
$609$			7.45397e17i			0.0239920i
$610$		0			0
$611$	−4.36290e19			−1.37242
$612$	5.46501e18	−	5.46501e18i	0.169954	−	0.169954i
$613$	−1.47359e19	−	1.47359e19i	−0.453057	−	0.453057i	0.443311	−	0.896368i	$-0.353804\pi$
$613$	−1.47359e19	−	1.47359e19i	−0.453057	−	0.453057i	−0.896368	+	0.443311i	$0.853804\pi$
$614$		−	1.61694e18i		−	0.0491492i
$615$		0			0
$616$	2.90172e17			0.00862166
$617$	−1.67034e19	+	1.67034e19i	−0.490693	+	0.490693i	−0.908525	−	0.417831i	$-0.862790\pi$
$617$	−1.67034e19	+	1.67034e19i	−0.490693	+	0.490693i	0.417831	+	0.908525i	$0.362790\pi$
$618$	−3.02712e18	−	3.02712e18i	−0.0879245	−	0.0879245i
$619$			3.83423e19i			1.10114i	0.834788	+	0.550571i	$0.185590\pi$
$619$			3.83423e19i			1.10114i	−0.834788	+	0.550571i	$0.814410\pi$
$620$		0			0
$621$	−1.70309e19			−0.478184
$622$	1.39780e19	−	1.39780e19i	0.388072	−	0.388072i
$623$	−2.02989e18	−	2.02989e18i	−0.0557258	−	0.0557258i
$624$		−	1.14646e19i		−	0.311219i
$625$		0			0
$626$	3.29672e19			0.875109
$627$	6.24526e18	−	6.24526e18i	0.163937	−	0.163937i
$628$	3.82920e18	+	3.82920e18i	0.0994009	+	0.0994009i
$629$		−	1.18450e20i		−	3.04076i
$630$		0			0
$631$	6.44739e19			1.61875			0.809373	−	0.587296i	$-0.199807\pi$
$631$	6.44739e19			1.61875			0.809373	+	0.587296i	$0.199807\pi$
$632$	−1.72682e18	+	1.72682e18i	−0.0428774	+	0.0428774i
$633$	−4.02908e19	−	4.02908e19i	−0.989418	−	0.989418i
$634$			1.24115e19i			0.301439i
$635$		0			0
$636$	2.51898e19			0.598447
$637$	−3.25586e19	+	3.25586e19i	−0.765050	+	0.765050i
$638$	−1.05445e18	−	1.05445e18i	−0.0245065	−	0.0245065i
$639$			8.45298e18i			0.194314i
$640$		0			0
$641$	5.19649e19			1.16870			0.584351	−	0.811501i	$-0.301349\pi$
$641$	5.19649e19			1.16870			0.584351	+	0.811501i	$0.301349\pi$
$642$	−3.61236e18	+	3.61236e18i	−0.0803611	+	0.0803611i
$643$	6.17590e19	+	6.17590e19i	1.35901	+	1.35901i	0.875136	+	0.483877i	$0.160772\pi$
$643$	6.17590e19	+	6.17590e19i	1.35901	+	1.35901i	0.483877	+	0.875136i	$0.339228\pi$
$644$			1.40371e18i			0.0305545i
$645$		0			0
$646$	4.60593e19			0.981046
$647$	6.02980e19	−	6.02980e19i	1.27050	−	1.27050i	0.324668	−	0.945828i	$-0.394748\pi$
$647$	6.02980e19	−	6.02980e19i	1.27050	−	1.27050i	0.945828	−	0.324668i	$-0.105252\pi$
$648$	−1.44946e19	−	1.44946e19i	−0.302121	−	0.302121i
$649$			1.07081e19i			0.220800i
$650$		0			0
$651$	8.56601e18			0.172867
$652$	−2.10030e19	+	2.10030e19i	−0.419323	+	0.419323i
$653$	−4.70194e19	−	4.70194e19i	−0.928720	−	0.928720i	0.0689031	−	0.997623i	$-0.478050\pi$
$653$	−4.70194e19	−	4.70194e19i	−0.928720	−	0.928720i	−0.997623	+	0.0689031i	$0.978050\pi$
$654$		−	3.79111e19i		−	0.740837i
$655$		0			0
$656$	1.30116e19			0.248888
$657$	−1.01980e18	+	1.01980e18i	−0.0193000	+	0.0193000i
$658$	3.43186e18	+	3.43186e18i	0.0642611	+	0.0642611i
$659$		−	4.19923e18i		−	0.0777986i	−0.999243	−	0.0388993i	$-0.987615\pi$
$659$		−	4.19923e18i		−	0.0777986i	0.999243	−	0.0388993i	$-0.0123852\pi$
$660$		0			0
$661$	−2.57230e19			−0.466563			−0.233282	−	0.972409i	$-0.574946\pi$
$661$	−2.57230e19			−0.466563			−0.233282	+	0.972409i	$0.574946\pi$
$662$	3.61814e19	−	3.61814e19i	0.649352	−	0.649352i
$663$	8.04313e19	+	8.04313e19i	1.42834	+	1.42834i
$664$		−	7.13912e18i		−	0.125449i
$665$		0			0
$666$	2.28152e19			0.392559
$667$	5.10090e18	−	5.10090e18i	0.0868493	−	0.0868493i
$668$	1.39383e19	+	1.39383e19i	0.234841	+	0.234841i
$669$			4.70730e19i			0.784854i
$670$		0			0
$671$	−8.44487e18			−0.137891
$672$	−9.01805e17	+	9.01805e17i	−0.0145723	+	0.0145723i
$673$	−6.38829e18	−	6.38829e18i	−0.102160	−	0.102160i	0.654180	−	0.756339i	$-0.273014\pi$
$673$	−6.38829e18	−	6.38829e18i	−0.102160	−	0.102160i	−0.756339	+	0.654180i	$0.773014\pi$
$674$		−	3.84663e19i		−	0.608781i
$675$		0			0
$676$	6.30721e18			0.0977711
$677$	2.82946e19	−	2.82946e19i	0.434093	−	0.434093i	−0.455925	−	0.890018i	$-0.650692\pi$
$677$	2.82946e19	−	2.82946e19i	0.434093	−	0.434093i	0.890018	+	0.455925i	$0.150692\pi$
$678$	3.45438e19	+	3.45438e19i	0.524520	+	0.524520i
$679$		−	9.39701e18i		−	0.141222i
$680$		0			0
$681$	1.68272e19			0.247732
$682$	−1.21176e19	+	1.21176e19i	−0.176574	+	0.176574i
$683$	4.46610e19	+	4.46610e19i	0.644144	+	0.644144i	0.951572	−	0.307427i	$-0.0994681\pi$
$683$	4.46610e19	+	4.46610e19i	0.644144	+	0.644144i	−0.307427	+	0.951572i	$0.599468\pi$
$684$			8.87168e18i			0.126652i
$685$		0			0
$686$	1.02985e19			0.144047
$687$	4.89993e19	−	4.89993e19i	0.678410	−	0.678410i
$688$	−2.00832e19	−	2.00832e19i	−0.275242	−	0.275242i
$689$			8.47283e19i			1.14946i
$690$		0			0
$691$	7.31729e18			0.0972757			0.0486378	−	0.998816i	$-0.484512\pi$
$691$	7.31729e18			0.0972757			0.0486378	+	0.998816i	$0.484512\pi$
$692$	5.02365e19	−	5.02365e19i	0.661114	−	0.661114i
$693$	−3.92113e17	−	3.92113e17i	−0.00510832	−	0.00510832i
$694$			7.51722e19i			0.969484i
$695$		0			0
$696$	6.55410e18			0.0828416
$697$	−9.12845e19	+	9.12845e19i	−1.14227	+	1.14227i
$698$	7.50074e18	+	7.50074e18i	0.0929215	+	0.0929215i
$699$		−	7.79703e19i		−	0.956288i
$700$		0			0
$701$	−8.07985e19			−0.971353			−0.485676	−	0.874139i	$-0.661427\pi$
$701$	−8.07985e19			−0.971353			−0.485676	+	0.874139i	$0.661427\pi$
$702$	3.68023e19	−	3.68023e19i	0.438042	−	0.438042i
$703$	9.61436e19	+	9.61436e19i	1.13301	+	1.13301i
$704$		−	2.55142e18i		−	0.0297696i
$705$		0			0
$706$	4.68081e19			0.535412
$707$	−3.67147e18	+	3.67147e18i	−0.0415819	+	0.0415819i
$708$	−3.32789e19	−	3.32789e19i	−0.373195	−	0.373195i
$709$		−	1.11580e20i		−	1.23897i	−0.785007	−	0.619487i	$-0.787340\pi$
$709$		−	1.11580e20i		−	1.23897i	0.785007	−	0.619487i	$-0.212660\pi$
$710$		0			0
$711$	4.66695e18			0.0508096
$712$	−1.78483e19	+	1.78483e19i	−0.192414	+	0.192414i
$713$	−5.86189e19	−	5.86189e19i	−0.625765	−	0.625765i
$714$		−	1.26534e19i		−	0.133759i
$715$		0			0
$716$	−3.38025e19			−0.350395
$717$	−6.64154e19	+	6.64154e19i	−0.681765	+	0.681765i
$718$	−2.92700e19	−	2.92700e19i	−0.297544	−	0.297544i
$719$			2.18539e19i			0.220002i	0.993931	+	0.110001i	$0.0350854\pi$
$719$			2.18539e19i			0.220002i	−0.993931	+	0.110001i	$0.964915\pi$
$720$		0			0
$721$	−1.60183e18			−0.0158150
$722$	1.37511e19	−	1.37511e19i	0.134455	−	0.134455i
$723$	4.91538e19	+	4.91538e19i	0.475980	+	0.475980i
$724$			3.13314e19i			0.300476i
$725$		0			0
$726$	−8.07285e19			−0.759400
$727$	−8.83539e19	+	8.83539e19i	−0.823161	+	0.823161i	−0.986560	−	0.163399i	$-0.947754\pi$
$727$	−8.83539e19	+	8.83539e19i	−0.823161	+	0.823161i	0.163399	+	0.986560i	$0.447754\pi$
$728$	−3.03330e18	−	3.03330e18i	−0.0279895	−	0.0279895i
$729$		−	6.06425e19i		−	0.554223i
$730$		0			0
$731$	2.81793e20			2.52644
$732$	2.62452e19	−	2.62452e19i	0.233062	−	0.233062i
$733$	4.57680e19	+	4.57680e19i	0.402563	+	0.402563i	0.879135	−	0.476572i	$-0.158121\pi$
$733$	4.57680e19	+	4.57680e19i	0.402563	+	0.402563i	−0.476572	+	0.879135i	$0.658121\pi$
$734$		−	1.07442e20i		−	0.936052i
$735$		0			0
$736$	1.23425e19			0.105501
$737$	−2.76908e19	+	2.76908e19i	−0.234457	+	0.234457i
$738$	−1.75827e19	−	1.75827e19i	−0.147466	−	0.147466i
$739$			2.25447e20i			1.87298i	0.350690	+	0.936491i	$0.385947\pi$
$739$			2.25447e20i			1.87298i	−0.350690	+	0.936491i	$0.614053\pi$
$740$		0			0
$741$	−1.30569e20			−1.06442
$742$	6.66472e18	−	6.66472e18i	0.0538214	−	0.0538214i
$743$	−1.67978e20	−	1.67978e20i	−1.34379	−	1.34379i	−0.892253	−	0.451535i	$-0.850877\pi$
$743$	−1.67978e20	−	1.67978e20i	−1.34379	−	1.34379i	−0.451535	−	0.892253i	$-0.649123\pi$
$744$		−	7.53189e19i		−	0.596889i
$745$		0			0
$746$	−7.26035e19			−0.564658
$747$	−9.64717e18	+	9.64717e18i	−0.0743285	+	0.0743285i
$748$	1.78998e19	+	1.78998e19i	0.136627	+	0.136627i
$749$			1.91152e18i			0.0144546i
$750$		0			0
$751$	−8.47309e19			−0.628872			−0.314436	−	0.949279i	$-0.601815\pi$
$751$	−8.47309e19			−0.628872			−0.314436	+	0.949279i	$0.601815\pi$
$752$	3.01755e19	−	3.01755e19i	0.221886	−	0.221886i
$753$	−1.36011e20	−	1.36011e20i	−0.990852	−	0.990852i
$754$			2.20453e19i			0.159117i
$755$		0			0
$756$	−5.78974e18			−0.0410210
$757$	3.80461e19	−	3.80461e19i	0.267079	−	0.267079i	−0.560843	−	0.827922i	$-0.689523\pi$
$757$	3.80461e19	−	3.80461e19i	0.267079	−	0.267079i	0.827922	+	0.560843i	$0.189523\pi$
$758$	−6.59799e19	−	6.59799e19i	−0.458909	−	0.458909i
$759$			2.34818e19i			0.161823i
$760$		0			0
$761$	−2.26358e20			−1.53145			−0.765725	−	0.643168i	$-0.777620\pi$
$761$	−2.26358e20			−1.53145			−0.765725	+	0.643168i	$0.777620\pi$
$762$	−9.36635e19	+	9.36635e19i	−0.627893	+	0.627893i
$763$	−1.00305e19	−	1.00305e19i	−0.0666272	−	0.0666272i
$764$			3.27891e19i			0.215812i
$765$		0			0
$766$	1.20418e20			0.778199
$767$	1.11936e20	−	1.11936e20i	0.716810	−	0.716810i
$768$	7.92935e18	+	7.92935e18i	0.0503164	+	0.0503164i
$769$			2.17340e20i			1.36664i	0.730118	+	0.683321i	$0.239465\pi$
$769$			2.17340e20i			1.36664i	−0.730118	+	0.683321i	$0.760535\pi$
$770$		0			0
$771$	−1.51118e19			−0.0933115
$772$	−1.60050e19	+	1.60050e19i	−0.0979343	+	0.0979343i
$773$	−8.10237e19	−	8.10237e19i	−0.491310	−	0.491310i	0.417409	−	0.908719i	$-0.362938\pi$
$773$	−8.10237e19	−	8.10237e19i	−0.491310	−	0.491310i	−0.908719	+	0.417409i	$0.862938\pi$
$774$			5.42774e19i			0.326161i
$775$		0			0
$776$	−8.26257e19			−0.487622
$777$	2.64127e19	−	2.64127e19i	0.154478	−	0.154478i
$778$	7.88028e18	+	7.88028e18i	0.0456756	+	0.0456756i
$779$		−	1.48187e20i		−	0.851234i
$780$		0			0
$781$	−2.76864e19			−0.156210
$782$	−8.65901e19	+	8.65901e19i	−0.484196	+	0.484196i
$783$	2.10392e19	+	2.10392e19i	0.116600	+	0.116600i
$784$		−	4.50376e19i		−	0.247379i
$785$		0			0
$786$	−2.67967e20			−1.44585
$787$	1.71433e20	−	1.71433e20i	0.916793	−	0.916793i	−0.0800014	−	0.996795i	$-0.525492\pi$
$787$	1.71433e20	−	1.71433e20i	0.916793	−	0.916793i	0.996795	+	0.0800014i	$0.0254925\pi$
$788$	7.21763e19	+	7.21763e19i	0.382570	+	0.382570i
$789$		−	3.76839e20i		−	1.97978i
$790$		0			0
$791$	1.82792e19			0.0943455
$792$	−3.44776e18	+	3.44776e18i	−0.0176384	+	0.0176384i
$793$	8.82780e19	+	8.82780e19i	0.447652	+	0.447652i
$794$			2.00986e20i			1.01023i
$795$		0			0
$796$	7.31677e18			0.0361350
$797$	4.47101e19	−	4.47101e19i	0.218876	−	0.218876i	−0.589149	−	0.808025i	$-0.700537\pi$
$797$	4.47101e19	−	4.47101e19i	0.218876	−	0.218876i	0.808025	+	0.589149i	$0.200537\pi$
$798$	1.02705e19	+	1.02705e19i	0.0498394	+	0.0498394i
$799$			4.23400e20i			2.03668i
$800$		0			0
$801$	4.82373e19			0.228011
$802$	−1.45243e20	+	1.45243e20i	−0.680575	+	0.680575i
$803$	−3.34019e18	−	3.34019e18i	−0.0155154	−	0.0155154i
$804$		−	1.72117e20i		−	0.792557i
$805$		0			0
$806$	2.53342e20			1.14647
$807$	−1.41427e20	+	1.41427e20i	−0.634478	+	0.634478i
$808$	3.22824e19	+	3.22824e19i	0.143577	+	0.143577i
$809$			7.24003e19i			0.319228i	0.987180	+	0.159614i	$0.0510249\pi$
$809$			7.24003e19i			0.319228i	−0.987180	+	0.159614i	$0.948975\pi$
$810$		0			0
$811$	−9.85148e18			−0.0426929			−0.0213464	−	0.999772i	$-0.506795\pi$
$811$	−9.85148e18			−0.0426929			−0.0213464	+	0.999772i	$0.506795\pi$
$812$	1.73408e18	−	1.73408e18i	0.00745036	−	0.00745036i
$813$	−3.24306e20	−	3.24306e20i	−1.38141	−	1.38141i
$814$			7.47276e19i			0.315581i
$815$		0			0
$816$	−1.11259e20			−0.461852
$817$	−2.28726e20	+	2.28726e20i	−0.941370	+	0.941370i
$818$	1.64411e20	+	1.64411e20i	0.670900	+	0.670900i
$819$			8.19786e18i			0.0331675i
$820$		0			0
$821$	−1.47520e20			−0.586744			−0.293372	−	0.955998i	$-0.594777\pi$
$821$	−1.47520e20			−0.586744			−0.293372	+	0.955998i	$0.594777\pi$
$822$	−1.15648e20	+	1.15648e20i	−0.456075	+	0.456075i
$823$	7.76255e19	+	7.76255e19i	0.303533	+	0.303533i	0.842394	−	0.538862i	$-0.181145\pi$
$823$	7.76255e19	+	7.76255e19i	0.303533	+	0.303533i	−0.538862	+	0.842394i	$0.681145\pi$
$824$			1.40845e19i			0.0546073i
$825$		0			0
$826$	−1.76098e19			−0.0671266
$827$	1.18909e20	−	1.18909e20i	0.449443	−	0.449443i	−0.445726	−	0.895169i	$-0.647055\pi$
$827$	1.18909e20	−	1.18909e20i	0.449443	−	0.449443i	0.895169	+	0.445726i	$0.147055\pi$
$828$	−1.66785e19	−	1.66785e19i	−0.0625093	−	0.0625093i
$829$		−	2.24381e20i		−	0.833880i	−0.908934	−	0.416940i	$-0.863103\pi$
$829$		−	2.24381e20i		−	0.833880i	0.908934	−	0.416940i	$-0.136897\pi$
$830$		0			0
$831$	3.86126e20			1.41098
$832$	−2.66711e19	+	2.66711e19i	−0.0966446	+	0.0966446i
$833$	3.15967e20	+	3.15967e20i	1.13534	+	1.13534i
$834$			4.11107e20i			1.46485i
$835$		0			0
$836$	−2.90578e19			−0.101817
$837$	2.41780e20	−	2.41780e20i	0.840121	−	0.840121i
$838$	6.73406e19	+	6.73406e19i	0.232043	+	0.232043i
$839$		−	3.93890e20i		−	1.34599i	−0.739648	−	0.672994i	$-0.765008\pi$
$839$		−	3.93890e20i		−	1.34599i	0.739648	−	0.672994i	$-0.234992\pi$
$840$		0			0
$841$	2.84955e20			0.957646
$842$	6.69611e19	−	6.69611e19i	0.223171	−	0.223171i
$843$	−6.44802e19	−	6.44802e19i	−0.213124	−	0.213124i
$844$			1.87464e20i			0.614498i
$845$		0			0
$846$	−8.15530e19			−0.262934
$847$	−2.13591e19	+	2.13591e19i	−0.0682967	+	0.0682967i
$848$	−5.86013e19	−	5.86013e19i	−0.185839	−	0.185839i
$849$		−	2.55934e20i		−	0.804959i
$850$		0			0
$851$	−3.61495e20			−1.11839
$852$	8.60444e19	−	8.60444e19i	0.264025	−	0.264025i
$853$	4.26931e19	+	4.26931e19i	0.129931	+	0.129931i	0.769082	−	0.639150i	$-0.220714\pi$
$853$	4.26931e19	+	4.26931e19i	0.129931	+	0.129931i	−0.639150	+	0.769082i	$0.720714\pi$
$854$		−	1.38879e19i		−	0.0419209i
$855$		0			0
$856$	1.68075e19			0.0499099
$857$	4.92585e18	−	4.92585e18i	0.0145083	−	0.0145083i	−0.699815	−	0.714324i	$-0.746734\pi$
$857$	4.92585e18	−	4.92585e18i	0.0145083	−	0.0145083i	0.714324	+	0.699815i	$0.246734\pi$
$858$	−5.07423e19	−	5.07423e19i	−0.148238	−	0.148238i
$859$			4.12708e20i			1.19589i	0.801538	+	0.597944i	$0.204016\pi$
$859$			4.12708e20i			1.19589i	−0.801538	+	0.597944i	$0.795984\pi$
$860$		0			0
$861$	−4.07102e19			−0.116060
$862$	5.34594e19	−	5.34594e19i	0.151173	−	0.151173i
$863$	2.17087e20	+	2.17087e20i	0.608918	+	0.608918i	0.942663	−	0.333745i	$-0.108312\pi$
$863$	2.17087e20	+	2.17087e20i	0.608918	+	0.608918i	−0.333745	+	0.942663i	$0.608312\pi$
$864$			5.09078e19i			0.141641i
$865$		0			0
$866$	−1.15165e20			−0.315280
$867$	4.84092e20	−	4.84092e20i	1.31460	−	1.31460i
$868$	−1.99278e19	−	1.99278e19i	−0.0536812	−	0.0536812i
$869$			1.52858e19i			0.0408461i
$870$		0			0
$871$	5.78929e20			1.52229
$872$	−8.81959e19	+	8.81959e19i	−0.230056	+	0.230056i
$873$	1.11653e20	+	1.11653e20i	0.288915	+	0.288915i
$874$		−	1.40567e20i		−	0.360830i
$875$		0			0
$876$	2.07615e19			0.0524481
$877$	1.63936e20	−	1.63936e20i	0.410845	−	0.410845i	−0.471188	−	0.882033i	$-0.656175\pi$
$877$	1.63936e20	−	1.63936e20i	0.410845	−	0.410845i	0.882033	+	0.471188i	$0.156175\pi$
$878$	2.91432e20	+	2.91432e20i	0.724563	+	0.724563i
$879$		−	6.77265e20i		−	1.67046i
$880$		0			0
$881$	5.26752e20			1.27872			0.639359	−	0.768908i	$-0.279200\pi$
$881$	5.26752e20			1.27872			0.639359	+	0.768908i	$0.279200\pi$
$882$	−6.08598e19	+	6.08598e19i	−0.146572	+	0.146572i
$883$	−3.01806e20	−	3.01806e20i	−0.721112	−	0.721112i	0.247720	−	0.968832i	$-0.420319\pi$
$883$	−3.01806e20	−	3.01806e20i	−0.721112	−	0.721112i	−0.968832	+	0.247720i	$0.920319\pi$
$884$		−	3.74229e20i		−	0.887097i
$885$		0			0
$886$	3.85089e20			0.898516
$887$	−4.33075e20	+	4.33075e20i	−1.00253	+	1.00253i	−0.00253509	+	0.999997i	$0.500807\pi$
$887$	−4.33075e20	+	4.33075e20i	−1.00253	+	1.00253i	−0.999997	+	0.00253509i	$0.999193\pi$
$888$	−2.32240e20	−	2.32240e20i	−0.533393	−	0.533393i
$889$			4.95629e19i			0.112939i
$890$		0			0
$891$	−1.28306e20			−0.287809
$892$	1.09510e20	−	1.09510e20i	0.243725	−	0.243725i
$893$	−3.43665e20	−	3.43665e20i	−0.758884	−	0.758884i
$894$		−	5.10412e20i		−	1.11830i
$895$		0			0
$896$	4.19589e18			0.00905041
$897$	2.45466e20	−	2.45466e20i	0.525344	−	0.525344i
$898$	1.94349e20	+	1.94349e20i	0.412713	+	0.412713i
$899$			1.44831e20i			0.305171i
$900$		0			0
$901$	8.22250e20			1.70581
$902$	5.75893e19	−	5.75893e19i	0.118549	−	0.118549i
$903$	6.28357e19	+	6.28357e19i	0.128349	+	0.128349i
$904$		−	1.60724e20i		−	0.325764i
$905$		0			0
$906$	−1.31002e19			−0.0261446
$907$	−2.53171e20	+	2.53171e20i	−0.501375	+	0.501375i	−0.911865	−	0.410490i	$-0.865358\pi$
$907$	−2.53171e20	+	2.53171e20i	−0.501375	+	0.501375i	0.410490	+	0.911865i	$0.365358\pi$
$908$	−3.91465e19	−	3.91465e19i	−0.0769294	−	0.0769294i
$909$		−	8.72470e19i		−	0.170139i
$910$		0			0
$911$	−6.01030e20			−1.15416			−0.577082	−	0.816687i	$-0.695809\pi$
$911$	−6.01030e20			−1.15416			−0.577082	+	0.816687i	$0.695809\pi$
$912$	9.03064e19	−	9.03064e19i	0.172090	−	0.172090i
$913$	−3.15977e19	−	3.15977e19i	−0.0597531	−	0.0597531i
$914$		−	2.28785e20i		−	0.429343i
$915$		0			0
$916$	−2.27982e20			−0.421340
$917$	−7.08986e19	+	7.08986e19i	−0.130033	+	0.130033i
$918$	−3.57150e20	−	3.57150e20i	−0.650058	−	0.650058i
$919$			2.79389e20i			0.504662i	0.967641	+	0.252331i	$0.0811971\pi$
$919$			2.79389e20i			0.504662i	−0.967641	+	0.252331i	$0.918803\pi$
$920$		0			0
$921$	4.44829e19			0.0791363
$922$	−2.68333e19	+	2.68333e19i	−0.0473759	+	0.0473759i
$923$	2.89418e20	+	2.89418e20i	0.507124	+	0.507124i
$924$			7.98278e18i			0.0138819i
$925$		0			0
$926$	8.84747e19			0.151545
$927$	1.90325e19	−	1.90325e19i	0.0323548	−	0.0323548i
$928$	−1.52474e19	−	1.52474e19i	−0.0257252	−	0.0257252i
$929$		−	2.01079e20i		−	0.336710i	−0.985726	−	0.168355i	$-0.946155\pi$
$929$		−	2.01079e20i		−	0.336710i	0.985726	−	0.168355i	$-0.0538455\pi$
$930$		0			0
$931$	−5.12927e20			−0.846074
$932$	−1.81389e20	+	1.81389e20i	−0.296961	+	0.296961i
$933$	3.84541e20	+	3.84541e20i	0.624843	+	0.624843i
$934$			2.16800e20i			0.349649i
$935$		0			0
$936$	7.20819e19			0.114524
$937$	−6.04824e20	+	6.04824e20i	−0.953788	+	0.953788i	−0.998978	−	0.0451903i	$-0.985611\pi$
$937$	−6.04824e20	+	6.04824e20i	−0.953788	+	0.953788i	0.0451903	+	0.998978i	$0.485611\pi$
$938$	−4.55386e19	−	4.55386e19i	−0.0712786	−	0.0712786i
$939$			9.06945e20i			1.40903i
$940$		0			0
$941$	−9.20327e20			−1.40869			−0.704344	−	0.709859i	$-0.748759\pi$
$941$	−9.20327e20			−1.40869			−0.704344	+	0.709859i	$0.748759\pi$
$942$	−1.05343e20	+	1.05343e20i	−0.160048	+	0.160048i
$943$	2.78588e20	+	2.78588e20i	0.420127	+	0.420127i
$944$			1.54839e20i			0.231780i
$945$		0			0
$946$	−1.77777e20			−0.262203
$947$	−1.61084e20	+	1.61084e20i	−0.235832	+	0.235832i	−0.815122	−	0.579290i	$-0.803330\pi$
$947$	−1.61084e20	+	1.61084e20i	−0.235832	+	0.235832i	0.579290	+	0.815122i	$0.303330\pi$
$948$	−4.75057e19	−	4.75057e19i	−0.0690379	−	0.0690379i
$949$			6.98331e19i			0.100739i
$950$		0			0
$951$	−3.41446e20			−0.485354
$952$	−2.94368e19	+	2.94368e19i	−0.0415367	+	0.0415367i
$953$	−3.22901e20	−	3.22901e20i	−0.452292	−	0.452292i	0.443823	−	0.896115i	$-0.353622\pi$
$953$	−3.22901e20	−	3.22901e20i	−0.452292	−	0.452292i	−0.896115	+	0.443823i	$0.853622\pi$
$954$			1.58377e20i			0.220219i
$955$		0			0
$956$	3.09016e20			0.423424
$957$	2.90084e19	−	2.90084e19i	0.0394585	−	0.0394585i
$958$	2.31471e20	+	2.31471e20i	0.312563	+	0.312563i
$959$			6.11963e19i			0.0820342i
$960$		0			0
$961$	9.07433e20			1.19881
$962$	7.81161e20	−	7.81161e20i	1.02451	−	1.02451i
$963$	−2.27122e19	−	2.27122e19i	−0.0295716	−	0.0295716i
$964$		−	2.28702e20i		−	0.295617i
$965$		0			0
$966$	−3.86167e19			−0.0491966
$967$	2.86927e20	−	2.86927e20i	0.362899	−	0.362899i	−0.501980	−	0.864879i	$-0.667395\pi$
$967$	2.86927e20	−	2.86927e20i	0.362899	−	0.362899i	0.864879	+	0.501980i	$0.167395\pi$
$968$	1.87806e20	+	1.87806e20i	0.235820	+	0.235820i
$969$			1.26711e21i			1.57961i
$970$		0			0
$971$	−1.32844e21			−1.63233			−0.816164	−	0.577820i	$-0.803904\pi$
$971$	−1.32844e21			−1.63233			−0.816164	+	0.577820i	$0.803904\pi$
$972$	1.66543e20	−	1.66543e20i	0.203172	−	0.203172i
$973$	1.08771e20	+	1.08771e20i	0.131741	+	0.131741i
$974$			3.59424e20i			0.432210i
$975$		0			0
$976$	−1.22113e20			−0.144748
$977$	−3.97400e20	+	3.97400e20i	−0.467698	+	0.467698i	−0.901168	−	0.433470i	$-0.857289\pi$
$977$	−3.97400e20	+	3.97400e20i	−0.467698	+	0.467698i	0.433470	+	0.901168i	$0.357289\pi$
$978$	−5.77803e20	−	5.77803e20i	−0.675162	−	0.675162i
$979$			1.57993e20i			0.183299i
$980$		0			0
$981$	2.38360e20			0.272616
$982$	5.46306e20	−	5.46306e20i	0.620377	−	0.620377i
$983$	8.15034e18	+	8.15034e18i	0.00918969	+	0.00918969i	0.711687	−	0.702497i	$-0.247932\pi$
$983$	8.15034e18	+	8.15034e18i	0.00918969	+	0.00918969i	−0.702497	+	0.711687i	$0.747932\pi$
$984$			3.57955e20i			0.400740i
$985$		0			0
$986$	2.13940e20			0.236131
$987$	−9.44120e19	+	9.44120e19i	−0.103468	+	0.103468i
$988$	3.03754e20	+	3.03754e20i	0.330539	+	0.330539i
$989$		−	8.59995e20i		−	0.929227i
$990$		0			0
$991$	−6.38533e20			−0.680249			−0.340124	−	0.940380i	$-0.610469\pi$
$991$	−6.38533e20			−0.680249			−0.340124	+	0.940380i	$0.610469\pi$
$992$	−1.75221e20	+	1.75221e20i	−0.185355	+	0.185355i
$993$	9.95369e20	+	9.95369e20i	1.04554	+	1.04554i
$994$		−	4.55312e19i		−	0.0474903i
$995$		0			0
$996$	1.96401e20			0.201989
$997$	1.74291e19	−	1.74291e19i	0.0177995	−	0.0177995i	−0.698151	−	0.715951i	$-0.745994\pi$
$997$	1.74291e19	−	1.74291e19i	0.0177995	−	0.0177995i	0.715951	+	0.698151i	$0.245994\pi$
$998$	−6.49912e20	−	6.49912e20i	−0.659084	−	0.659084i
$999$		−	1.49102e21i		−	1.50150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.15.c.b.43.3		6
5.2	odd	4	inner	50.15.c.b.7.3		6
5.3	odd	4		10.15.c.a.7.1	yes	6
5.4	even	2		10.15.c.a.3.1	✓	6
15.8	even	4		90.15.g.a.37.2		6
15.14	odd	2		90.15.g.a.73.2		6
20.3	even	4		80.15.p.a.17.3		6
20.19	odd	2		80.15.p.a.33.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.15.c.a.3.1	✓	6	5.4	even	2
10.15.c.a.7.1	yes	6	5.3	odd	4
50.15.c.b.7.3		6	5.2	odd	4	inner
50.15.c.b.43.3		6	1.1	even	1	trivial
80.15.p.a.17.3		6	20.3	even	4
80.15.p.a.33.3		6	20.19	odd	2
90.15.g.a.37.2		6	15.8	even	4
90.15.g.a.73.2		6	15.14	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	50.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(64.0000 - 64.0000i) q^{2} +(1760.67 + 1760.67i) q^{3} -8192.00i q^{4} +225366. q^{6} +(59627.2 - 59627.2i) q^{7} +(-524288. - 524288. i) q^{8} +1.41695e6i q^{9} +O(q^{10})\)	\(q+(64.0000 - 64.0000i) q^{2} +(1760.67 + 1760.67i) q^{3} -8192.00i q^{4} +225366. q^{6} +(59627.2 - 59627.2i) q^{7} +(-524288. - 524288. i) q^{8} +1.41695e6i q^{9} -4.64100e6 q^{11} +(1.44234e7 - 1.44234e7i) q^{12} +(4.85144e7 + 4.85144e7i) q^{13} -7.63228e6i q^{14} -6.71089e7 q^{16} +(4.70811e8 - 4.70811e8i) q^{17} +(9.06849e7 + 9.06849e7i) q^{18} +7.64295e8i q^{19} +2.09968e8 q^{21} +(-2.97024e8 + 2.97024e8i) q^{22} +(-1.43685e9 - 1.43685e9i) q^{23} -1.84620e9i q^{24} +6.20985e9 q^{26} +(5.92645e9 - 5.92645e9i) q^{27} +(-4.88466e8 - 4.88466e8i) q^{28} +3.55005e9i q^{29} +4.07968e10 q^{31} +(-4.29497e9 + 4.29497e9i) q^{32} +(-8.17127e9 - 8.17127e9i) q^{33} -6.02638e10i q^{34} +1.16077e10 q^{36} +(1.25794e11 - 1.25794e11i) q^{37} +(4.89149e10 + 4.89149e10i) q^{38} +1.70836e11i q^{39} -1.93888e11 q^{41} +(1.34379e10 - 1.34379e10i) q^{42} +(2.99264e11 + 2.99264e11i) q^{43} +3.80191e10i q^{44} -1.83917e11 q^{46} +(-4.49650e11 + 4.49650e11i) q^{47} +(-1.18157e11 - 1.18157e11i) q^{48} +6.71112e11i q^{49} +1.65788e12 q^{51} +(3.97430e11 - 3.97430e11i) q^{52} +(8.73228e11 + 8.73228e11i) q^{53} -7.58585e11i q^{54} -6.25237e10 q^{56} +(-1.34567e12 + 1.34567e12i) q^{57} +(2.27203e11 + 2.27203e11i) q^{58} -2.30728e12i q^{59} +1.81962e12 q^{61} +(2.61099e12 - 2.61099e12i) q^{62} +(8.44889e10 + 8.44889e10i) q^{63} +5.49756e11i q^{64} -1.04592e12 q^{66} +(5.96657e12 - 5.96657e12i) q^{67} +(-3.85688e12 - 3.85688e12i) q^{68} -5.05965e12i q^{69} +5.96561e12 q^{71} +(7.42891e11 - 7.42891e11i) q^{72} +(7.19715e11 + 7.19715e11i) q^{73} -1.61016e13i q^{74} +6.26110e12 q^{76} +(-2.76730e11 + 2.76730e11i) q^{77} +(1.09335e13 + 1.09335e13i) q^{78} -3.29365e12i q^{79} +2.76463e13 q^{81} +(-1.24088e13 + 1.24088e13i) q^{82} +(6.80839e12 + 6.80839e12i) q^{83} -1.72006e12i q^{84} +3.83057e13 q^{86} +(-6.25047e12 + 6.25047e12i) q^{87} +(2.43322e12 + 2.43322e12i) q^{88} -3.40430e13i q^{89} +5.78556e12 q^{91} +(-1.17707e13 + 1.17707e13i) q^{92} +(7.18297e13 + 7.18297e13i) q^{93} +5.75552e13i q^{94} -1.51240e13 q^{96} +(7.87980e13 - 7.87980e13i) q^{97} +(4.29512e13 + 4.29512e13i) q^{98} -6.57607e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 384 q^{2} - 2912 q^{3} - 372736 q^{6} - 943128 q^{7} - 3145728 q^{8}+O(q^{10}) \) 6 * q + 384 * q^2 - 2912 * q^3 - 372736 * q^6 - 943128 * q^7 - 3145728 * q^8	\( 6 q + 384 q^{2} - 2912 q^{3} - 372736 q^{6} - 943128 q^{7} - 3145728 q^{8} - 45566568 q^{11} - 23855104 q^{12} + 52149318 q^{13} - 402653184 q^{16} + 294348942 q^{17} + 331317376 q^{18} + 2237511512 q^{21} - 2916260352 q^{22} + 9431163408 q^{23} + 6675112704 q^{26} - 12637562360 q^{27} + 7726104576 q^{28} + 3721405392 q^{31} - 25769803776 q^{32} + 48274986136 q^{33} + 42408624128 q^{36} + 429898030002 q^{37} + 244347609600 q^{38} + 45681057912 q^{41} + 143200736768 q^{42} + 935465548368 q^{43} + 1207188916224 q^{46} + 966227586192 q^{47} + 195421011968 q^{48} + 5859939710032 q^{51} + 427207213056 q^{52} + 1868182085058 q^{53} + 988941385728 q^{56} + 134753100400 q^{57} + 2272407598080 q^{58} + 2111099930472 q^{61} + 238169945088 q^{62} + 4692600933808 q^{63} + 6179198225408 q^{66} + 8480735447712 q^{67} - 2411306532864 q^{68} + 22333649456112 q^{71} + 2714151944192 q^{72} + 6994307700378 q^{73} + 31276494028800 q^{76} - 3740771411016 q^{77} + 19625279112192 q^{78} + 140474309815186 q^{81} + 2923587706368 q^{82} + 60521791593048 q^{83} + 119739590191104 q^{86} + 54455082756640 q^{87} + 23890004803584 q^{88} + 402924178873632 q^{91} + 77260090638336 q^{92} + 290043091551016 q^{93} + 25013889531904 q^{96} + 307307370113562 q^{97} + 13656230884224 q^{98}+O(q^{100}) \) 6 * q + 384 * q^2 - 2912 * q^3 - 372736 * q^6 - 943128 * q^7 - 3145728 * q^8 - 45566568 * q^11 - 23855104 * q^12 + 52149318 * q^13 - 402653184 * q^16 + 294348942 * q^17 + 331317376 * q^18 + 2237511512 * q^21 - 2916260352 * q^22 + 9431163408 * q^23 + 6675112704 * q^26 - 12637562360 * q^27 + 7726104576 * q^28 + 3721405392 * q^31 - 25769803776 * q^32 + 48274986136 * q^33 + 42408624128 * q^36 + 429898030002 * q^37 + 244347609600 * q^38 + 45681057912 * q^41 + 143200736768 * q^42 + 935465548368 * q^43 + 1207188916224 * q^46 + 966227586192 * q^47 + 195421011968 * q^48 + 5859939710032 * q^51 + 427207213056 * q^52 + 1868182085058 * q^53 + 988941385728 * q^56 + 134753100400 * q^57 + 2272407598080 * q^58 + 2111099930472 * q^61 + 238169945088 * q^62 + 4692600933808 * q^63 + 6179198225408 * q^66 + 8480735447712 * q^67 - 2411306532864 * q^68 + 22333649456112 * q^71 + 2714151944192 * q^72 + 6994307700378 * q^73 + 31276494028800 * q^76 - 3740771411016 * q^77 + 19625279112192 * q^78 + 140474309815186 * q^81 + 2923587706368 * q^82 + 60521791593048 * q^83 + 119739590191104 * q^86 + 54455082756640 * q^87 + 23890004803584 * q^88 + 402924178873632 * q^91 + 77260090638336 * q^92 + 290043091551016 * q^93 + 25013889531904 * q^96 + 307307370113562 * q^97 + 13656230884224 * q^98

Introduction

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