LMFDB - Embedded newform 25.9.c.b.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,9,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	25.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:	$10.1844652515$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 $ x^6 - 2x^5 + 2x^4 - 30x^3 + 1089x^2 - 3168*x + 4608
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.3
Root			$3.70505 - 3.70505i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.9.c.b.18.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.8649 + 11.8649i) q^{2} +(90.9660 - 90.9660i) q^{3} +25.5528i q^{4} +2158.61 q^{6} +(-508.219 - 508.219i) q^{7} +(2734.24 - 2734.24i) q^{8} -9988.61i q^{9} +O(q^{10})$	\(q+(11.8649 + 11.8649i) q^{2} +(90.9660 - 90.9660i) q^{3} +25.5528i q^{4} +2158.61 q^{6} +(-508.219 - 508.219i) q^{7} +(2734.24 - 2734.24i) q^{8} -9988.61i q^{9} -7021.93 q^{11} +(2324.44 + 2324.44i) q^{12} +(8073.75 - 8073.75i) q^{13} -12060.0i q^{14} +71424.6 q^{16} +(102958. + 102958. i) q^{17} +(118514. - 118514. i) q^{18} +59599.0i q^{19} -92461.2 q^{21} +(-83314.7 - 83314.7i) q^{22} +(-132866. + 132866. i) q^{23} -497445. i q^{24} +191589. q^{26} +(-311796. - 311796. i) q^{27} +(12986.4 - 12986.4i) q^{28} +392047. i q^{29} -507883. q^{31} +(147482. + 147482. i) q^{32} +(-638757. + 638757. i) q^{33} +2.44319e6i q^{34} +255237. q^{36} +(61012.9 + 61012.9i) q^{37} +(-707137. + 707137. i) q^{38} -1.46887e6i q^{39} -1.81765e6 q^{41} +(-1.09705e6 - 1.09705e6i) q^{42} +(-1.47723e6 + 1.47723e6i) q^{43} -179430. i q^{44} -3.15288e6 q^{46} +(1.79287e6 + 1.79287e6i) q^{47} +(6.49721e6 - 6.49721e6i) q^{48} -5.24823e6i q^{49} +1.87314e7 q^{51} +(206307. + 206307. i) q^{52} +(5.66320e6 - 5.66320e6i) q^{53} -7.39887e6i q^{54} -2.77918e6 q^{56} +(5.42148e6 + 5.42148e6i) q^{57} +(-4.65161e6 + 4.65161e6i) q^{58} +1.74855e7i q^{59} -1.96459e7 q^{61} +(-6.02599e6 - 6.02599e6i) q^{62} +(-5.07640e6 + 5.07640e6i) q^{63} -1.47850e7i q^{64} -1.51576e7 q^{66} +(1.12859e7 + 1.12859e7i) q^{67} +(-2.63088e6 + 2.63088e6i) q^{68} +2.41725e7i q^{69} +3.01001e7 q^{71} +(-2.73112e7 - 2.73112e7i) q^{72} +(-2.52645e7 + 2.52645e7i) q^{73} +1.44783e6i q^{74} -1.52292e6 q^{76} +(3.56868e6 + 3.56868e6i) q^{77} +(1.74281e7 - 1.74281e7i) q^{78} +8.14025e6i q^{79} +8.80962e6 q^{81} +(-2.15663e7 - 2.15663e7i) q^{82} +(1.99635e7 - 1.99635e7i) q^{83} -2.36265e6i q^{84} -3.50545e7 q^{86} +(3.56630e7 + 3.56630e7i) q^{87} +(-1.91996e7 + 1.91996e7i) q^{88} -8.20905e7i q^{89} -8.20646e6 q^{91} +(-3.39509e6 - 3.39509e6i) q^{92} +(-4.62000e7 + 4.62000e7i) q^{93} +4.25446e7i q^{94} +2.68317e7 q^{96} +(-3.37379e7 - 3.37379e7i) q^{97} +(6.22698e7 - 6.22698e7i) q^{98} +7.01393e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8	$ 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8} + 23192 q^{11} + 45912 q^{12} + 119142 q^{13} + 218616 q^{16} + 265502 q^{17} + 454062 q^{18} + 231672 q^{21} + 35664 q^{22} - 28888 q^{23} - 801388 q^{26} - 392040 q^{27} - 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} - 4269096 q^{33} - 3972804 q^{36} + 454002 q^{37} - 1443720 q^{38} + 2489432 q^{41} - 4223856 q^{42} - 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} + 21677712 q^{48} + 35567712 q^{51} + 735732 q^{52} + 13509122 q^{53} - 18454800 q^{56} + 34625520 q^{57} + 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} - 44837688 q^{63} - 55047936 q^{66} + 32827752 q^{67} - 8118692 q^{68} - 13992928 q^{71} - 82596420 q^{72} - 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 31125576 q^{78} + 65834226 q^{81} - 38023056 q^{82} + 14768432 q^{83} - 135560008 q^{86} + 133207680 q^{87} + 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} + 96798024 q^{93} + 184867872 q^{96} + 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8 + 23192 * q^11 + 45912 * q^12 + 119142 * q^13 + 218616 * q^16 + 265502 * q^17 + 454062 * q^18 + 231672 * q^21 + 35664 * q^22 - 28888 * q^23 - 801388 * q^26 - 392040 * q^27 - 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 - 4269096 * q^33 - 3972804 * q^36 + 454002 * q^37 - 1443720 * q^38 + 2489432 * q^41 - 4223856 * q^42 - 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 + 21677712 * q^48 + 35567712 * q^51 + 735732 * q^52 + 13509122 * q^53 - 18454800 * q^56 + 34625520 * q^57 + 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 - 44837688 * q^63 - 55047936 * q^66 + 32827752 * q^67 - 8118692 * q^68 - 13992928 * q^71 - 82596420 * q^72 - 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 31125576 * q^78 + 65834226 * q^81 - 38023056 * q^82 + 14768432 * q^83 - 135560008 * q^86 + 133207680 * q^87 + 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 + 96798024 * q^93 + 184867872 * q^96 + 186656202 * q^97 + 345959698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	11.8649	+	11.8649i	0.741558	+	0.741558i	0.972878	−	0.231320i	$-0.0743044\pi$
$2$	11.8649	+	11.8649i	0.741558	+	0.741558i	−0.231320	+	0.972878i	$0.574304\pi$
$3$	90.9660	−	90.9660i	1.12304	−	1.12304i	0.131754	−	0.991282i	$-0.457939\pi$
$3$	90.9660	−	90.9660i	1.12304	−	1.12304i	0.991282	−	0.131754i	$-0.0420609\pi$
$4$			25.5528i			0.0998158i
$5$		0			0
$5$		0			0
$6$	2158.61			1.66559
$7$	−508.219	−	508.219i	−0.211670	−	0.211670i	0.593307	−	0.804976i	$-0.297822\pi$
$7$	−508.219	−	508.219i	−0.211670	−	0.211670i	−0.804976	+	0.593307i	$0.797822\pi$
$8$	2734.24	−	2734.24i	0.667539	−	0.667539i
$9$		−	9988.61i		−	1.52242i
$10$		0			0
$11$	−7021.93			−0.479607			−0.239804	−	0.970821i	$-0.577083\pi$
$11$	−7021.93			−0.479607			−0.239804	+	0.970821i	$0.577083\pi$
$12$	2324.44	+	2324.44i	0.112097	+	0.112097i
$13$	8073.75	−	8073.75i	0.282684	−	0.282684i	−0.551494	−	0.834179i	$-0.685942\pi$
$13$	8073.75	−	8073.75i	0.282684	−	0.282684i	0.834179	+	0.551494i	$0.185942\pi$
$14$		−	12060.0i		−	0.313930i
$15$		0			0
$16$	71424.6			1.08985
$17$	102958.	+	102958.i	1.23273	+	1.23273i	0.962913	+	0.269813i	$0.0869619\pi$
$17$	102958.	+	102958.i	1.23273	+	1.23273i	0.269813	+	0.962913i	$0.413038\pi$
$18$	118514.	−	118514.i	1.12896	−	1.12896i
$19$			59599.0i			0.457324i	0.973506	+	0.228662i	$0.0734351\pi$
$19$			59599.0i			0.457324i	−0.973506	+	0.228662i	$0.926565\pi$
$20$		0			0
$21$	−92461.2			−0.475425
$22$	−83314.7	−	83314.7i	−0.355657	−	0.355657i
$23$	−132866.	+	132866.i	−0.474790	+	0.474790i	−0.903461	−	0.428671i	$-0.858982\pi$
$23$	−132866.	+	132866.i	−0.474790	+	0.474790i	0.428671	+	0.903461i	$0.358982\pi$
$24$		−	497445.i		−	1.49934i
$25$		0			0
$26$	191589.			0.419254
$27$	−311796.	−	311796.i	−0.586699	−	0.586699i
$28$	12986.4	−	12986.4i	0.0211280	−	0.0211280i
$29$			392047.i			0.554302i	0.960826	+	0.277151i	$0.0893902\pi$
$29$			392047.i			0.554302i	−0.960826	+	0.277151i	$0.910610\pi$
$30$		0			0
$31$	−507883.			−0.549942			−0.274971	−	0.961453i	$-0.588668\pi$
$31$	−507883.			−0.549942			−0.274971	+	0.961453i	$0.588668\pi$
$32$	147482.	+	147482.i	0.140650	+	0.140650i
$33$	−638757.	+	638757.i	−0.538617	+	0.538617i
$34$			2.44319e6i			1.82827i
$35$		0			0
$36$	255237.			0.151962
$37$	61012.9	+	61012.9i	0.0325548	+	0.0325548i	0.723197	−	0.690642i	$-0.242672\pi$
$37$	61012.9	+	61012.9i	0.0325548	+	0.0325548i	−0.690642	+	0.723197i	$0.742672\pi$
$38$	−707137.	+	707137.i	−0.339132	+	0.339132i
$39$		−	1.46887e6i		−	0.634930i
$40$		0			0
$41$	−1.81765e6			−0.643242			−0.321621	−	0.946868i	$-0.604228\pi$
$41$	−1.81765e6			−0.643242			−0.321621	+	0.946868i	$0.604228\pi$
$42$	−1.09705e6	−	1.09705e6i	−0.352555	−	0.352555i
$43$	−1.47723e6	+	1.47723e6i	−0.432090	+	0.432090i	−0.889339	−	0.457249i	$-0.848835\pi$
$43$	−1.47723e6	+	1.47723e6i	−0.432090	+	0.432090i	0.457249	+	0.889339i	$0.348835\pi$
$44$		−	179430.i		−	0.0478724i
$45$		0			0
$46$	−3.15288e6			−0.704168
$47$	1.79287e6	+	1.79287e6i	0.367416	+	0.367416i	0.866534	−	0.499118i	$-0.166343\pi$
$47$	1.79287e6	+	1.79287e6i	0.367416	+	0.367416i	−0.499118	+	0.866534i	$0.666343\pi$
$48$	6.49721e6	−	6.49721e6i	1.22394	−	1.22394i
$49$		−	5.24823e6i		−	0.910392i
$50$		0			0
$51$	1.87314e7			2.76879
$52$	206307.	+	206307.i	0.0282164	+	0.0282164i
$53$	5.66320e6	−	5.66320e6i	0.717725	−	0.717725i	−0.250414	−	0.968139i	$-0.580567\pi$
$53$	5.66320e6	−	5.66320e6i	0.717725	−	0.717725i	0.968139	+	0.250414i	$0.0805666\pi$
$54$		−	7.39887e6i		−	0.870143i
$55$		0			0
$56$	−2.77918e6			−0.282595
$57$	5.42148e6	+	5.42148e6i	0.513592	+	0.513592i
$58$	−4.65161e6	+	4.65161e6i	−0.411047	+	0.411047i
$59$			1.74855e7i			1.44301i	0.692410	+	0.721504i	$0.256549\pi$
$59$			1.74855e7i			1.44301i	−0.692410	+	0.721504i	$0.743451\pi$
$60$		0			0
$61$	−1.96459e7			−1.41890			−0.709452	−	0.704754i	$-0.751057\pi$
$61$	−1.96459e7			−1.41890			−0.709452	+	0.704754i	$0.751057\pi$
$62$	−6.02599e6	−	6.02599e6i	−0.407814	−	0.407814i
$63$	−5.07640e6	+	5.07640e6i	−0.322251	+	0.322251i
$64$		−	1.47850e7i		−	0.881252i
$65$		0			0
$66$	−1.51576e7			−0.798831
$67$	1.12859e7	+	1.12859e7i	0.560061	+	0.560061i	0.929325	−	0.369264i	$-0.120390\pi$
$67$	1.12859e7	+	1.12859e7i	0.560061	+	0.560061i	−0.369264	+	0.929325i	$0.620390\pi$
$68$	−2.63088e6	+	2.63088e6i	−0.123045	+	0.123045i
$69$			2.41725e7i			1.06641i
$70$		0			0
$71$	3.01001e7			1.18450			0.592249	−	0.805755i	$-0.298240\pi$
$71$	3.01001e7			1.18450			0.592249	+	0.805755i	$0.298240\pi$
$72$	−2.73112e7	−	2.73112e7i	−1.01628	−	1.01628i
$73$	−2.52645e7	+	2.52645e7i	−0.889649	+	0.889649i	−0.994489	−	0.104840i	$-0.966567\pi$
$73$	−2.52645e7	+	2.52645e7i	−0.889649	+	0.889649i	0.104840	+	0.994489i	$0.466567\pi$
$74$			1.44783e6i			0.0482825i
$75$		0			0
$76$	−1.52292e6			−0.0456482
$77$	3.56868e6	+	3.56868e6i	0.101518	+	0.101518i
$78$	1.74281e7	−	1.74281e7i	0.470837	−	0.470837i
$79$			8.14025e6i			0.208992i	0.994525	+	0.104496i	$0.0333229\pi$
$79$			8.14025e6i			0.208992i	−0.994525	+	0.104496i	$0.966677\pi$
$80$		0			0
$81$	8.80962e6			0.204653
$82$	−2.15663e7	−	2.15663e7i	−0.477001	−	0.477001i
$83$	1.99635e7	−	1.99635e7i	0.420652	−	0.420652i	−0.464776	−	0.885428i	$-0.653865\pi$
$83$	1.99635e7	−	1.99635e7i	0.420652	−	0.420652i	0.885428	+	0.464776i	$0.153865\pi$
$84$		−	2.36265e6i		−	0.0474550i
$85$		0			0
$86$	−3.50545e7			−0.640840
$87$	3.56630e7	+	3.56630e7i	0.622501	+	0.622501i
$88$	−1.91996e7	+	1.91996e7i	−0.320156	+	0.320156i
$89$		−	8.20905e7i		−	1.30838i	−0.756332	−	0.654189i	$-0.773010\pi$
$89$		−	8.20905e7i		−	1.30838i	0.756332	−	0.654189i	$-0.226990\pi$
$90$		0			0
$91$	−8.20646e6			−0.119671
$92$	−3.39509e6	−	3.39509e6i	−0.0473915	−	0.0473915i
$93$	−4.62000e7	+	4.62000e7i	−0.617605	+	0.617605i
$94$			4.25446e7i			0.544920i
$95$		0			0
$96$	2.68317e7			0.315910
$97$	−3.37379e7	−	3.37379e7i	−0.381093	−	0.381093i	0.490403	−	0.871496i	$-0.336850\pi$
$97$	−3.37379e7	−	3.37379e7i	−0.381093	−	0.381093i	−0.871496	+	0.490403i	$0.836850\pi$
$98$	6.22698e7	−	6.22698e7i	0.675108	−	0.675108i
$99$			7.01393e7i			0.730165i
$100$		0			0
$101$	−1.91592e7			−0.184116			−0.0920582	−	0.995754i	$-0.529345\pi$
$101$	−1.91592e7			−0.184116			−0.0920582	+	0.995754i	$0.529345\pi$
$102$	2.22247e8	+	2.22247e8i	2.05322	+	2.05322i
$103$	1.35177e8	−	1.35177e8i	1.20103	−	1.20103i	0.227173	−	0.973854i	$-0.427052\pi$
$103$	1.35177e8	−	1.35177e8i	1.20103	−	1.20103i	0.973854	−	0.227173i	$-0.0729483\pi$
$104$		−	4.41511e7i		−	0.377405i
$105$		0			0
$106$	1.34387e8			1.06447
$107$	−1.22825e8	−	1.22825e8i	−0.937029	−	0.937029i	0.0611024	−	0.998132i	$-0.480538\pi$
$107$	−1.22825e8	−	1.22825e8i	−0.937029	−	0.937029i	−0.998132	+	0.0611024i	$0.980538\pi$
$108$	7.96728e6	−	7.96728e6i	0.0585619	−	0.0585619i
$109$		−	1.66780e8i		−	1.18151i	−0.806850	−	0.590757i	$-0.798829\pi$
$109$		−	1.66780e8i		−	1.18151i	0.806850	−	0.590757i	$-0.201171\pi$
$110$		0			0
$111$	1.11002e7			0.0731204
$112$	−3.62993e7	−	3.62993e7i	−0.230689	−	0.230689i
$113$	−3.23356e7	+	3.23356e7i	−0.198320	+	0.198320i	−0.799280	−	0.600959i	$-0.794785\pi$
$113$	−3.23356e7	+	3.23356e7i	−0.198320	+	0.198320i	0.600959	+	0.799280i	$0.294785\pi$
$114$			1.28651e8i			0.761716i
$115$		0			0
$116$	−1.00179e7			−0.0553281
$117$	−8.06456e7	−	8.06456e7i	−0.430365	−	0.430365i
$118$	−2.07464e8	+	2.07464e8i	−1.07007	+	1.07007i
$119$		−	1.04651e8i		−	0.521861i
$120$		0			0
$121$	−1.65051e8			−0.769977
$122$	−2.33097e8	−	2.33097e8i	−1.05220	−	1.05220i
$123$	−1.65344e8	+	1.65344e8i	−0.722385	+	0.722385i
$124$		−	1.29778e7i		−	0.0548929i
$125$		0			0
$126$	−1.20462e8			−0.477935
$127$	2.93412e8	+	2.93412e8i	1.12788	+	1.12788i	0.990522	+	0.137357i	$0.0438608\pi$
$127$	2.93412e8	+	2.93412e8i	1.12788	+	1.12788i	0.137357	+	0.990522i	$0.456139\pi$
$128$	2.13178e8	−	2.13178e8i	0.794150	−	0.794150i
$129$			2.68756e8i			0.970507i
$130$		0			0
$131$	−3.37671e8			−1.14659			−0.573295	−	0.819349i	$-0.694335\pi$
$131$	−3.37671e8			−1.14659			−0.573295	+	0.819349i	$0.694335\pi$
$132$	−1.63220e7	−	1.63220e7i	−0.0537624	−	0.0537624i
$133$	3.02893e7	−	3.02893e7i	0.0968017	−	0.0968017i
$134$			2.67812e8i			0.830635i
$135$		0			0
$136$	5.63026e8			1.64578
$137$	−1.06123e8	−	1.06123e8i	−0.301249	−	0.301249i	0.540253	−	0.841502i	$-0.318328\pi$
$137$	−1.06123e8	−	1.06123e8i	−0.301249	−	0.301249i	−0.841502	+	0.540253i	$0.818328\pi$
$138$	−2.86805e8	+	2.86805e8i	−0.790806	+	0.790806i
$139$			5.86652e8i			1.57153i	0.618528	+	0.785763i	$0.287729\pi$
$139$			5.86652e8i			1.57153i	−0.618528	+	0.785763i	$0.712271\pi$
$140$		0			0
$141$	3.26181e8			0.825243
$142$	3.57135e8	+	3.57135e8i	0.878373	+	0.878373i
$143$	−5.66933e7	+	5.66933e7i	−0.135577	+	0.135577i
$144$		−	7.13432e8i		−	1.65922i
$145$		0			0
$146$	−5.99522e8			−1.31945
$147$	−4.77410e8	−	4.77410e8i	−1.02240	−	1.02240i
$148$	−1.55905e6	+	1.55905e6i	−0.00324948	+	0.00324948i
$149$		−	5.45945e8i		−	1.10765i	−0.832632	−	0.553827i	$-0.813167\pi$
$149$		−	5.45945e8i		−	1.10765i	0.832632	−	0.553827i	$-0.186833\pi$
$150$		0			0
$151$	8.88293e7			0.170863			0.0854316	−	0.996344i	$-0.472773\pi$
$151$	8.88293e7			0.170863			0.0854316	+	0.996344i	$0.472773\pi$
$152$	1.62958e8	+	1.62958e8i	0.305282	+	0.305282i
$153$	1.02841e9	−	1.02841e9i	1.87673	−	1.87673i
$154$			8.46841e7i			0.150563i
$155$		0			0
$156$	3.75339e7			0.0633760
$157$	3.21072e8	+	3.21072e8i	0.528450	+	0.528450i	0.920110	−	0.391660i	$-0.128099\pi$
$157$	3.21072e8	+	3.21072e8i	0.528450	+	0.528450i	−0.391660	+	0.920110i	$0.628099\pi$
$158$	−9.65834e7	+	9.65834e7i	−0.154979	+	0.154979i
$159$		−	1.03032e9i		−	1.61206i
$160$		0			0
$161$	1.35050e8			0.200997
$162$	1.04526e8	+	1.04526e8i	0.151762	+	0.151762i
$163$	−2.14053e8	+	2.14053e8i	−0.303229	+	0.303229i	−0.842276	−	0.539047i	$-0.818785\pi$
$163$	−2.14053e8	+	2.14053e8i	−0.303229	+	0.303229i	0.539047	+	0.842276i	$0.318785\pi$
$164$		−	4.64461e7i		−	0.0642057i
$165$		0			0
$166$	4.73730e8			0.623876
$167$	−6.91005e8	−	6.91005e8i	−0.888414	−	0.888414i	0.105957	−	0.994371i	$-0.466209\pi$
$167$	−6.91005e8	−	6.91005e8i	−0.888414	−	0.888414i	−0.994371	+	0.105957i	$0.966209\pi$
$168$	−2.52811e8	+	2.52811e8i	−0.317365	+	0.317365i
$169$			6.85360e8i			0.840179i
$170$		0			0
$171$	5.95311e8			0.696241
$172$	−3.77475e7	−	3.77475e7i	−0.0431294	−	0.0431294i
$173$	3.40367e8	−	3.40367e8i	0.379982	−	0.379982i	−0.491114	−	0.871095i	$-0.663410\pi$
$173$	3.40367e8	−	3.40367e8i	0.379982	−	0.379982i	0.871095	+	0.491114i	$0.163410\pi$
$174$			8.46276e8i			0.923241i
$175$		0			0
$176$	−5.01538e8			−0.522701
$177$	1.59058e9	+	1.59058e9i	1.62055	+	1.62055i
$178$	9.73998e8	−	9.73998e8i	0.970237	−	0.970237i
$179$			7.51587e7i			0.0732094i	0.999330	+	0.0366047i	$0.0116542\pi$
$179$			7.51587e7i			0.0732094i	−0.999330	+	0.0366047i	$0.988346\pi$
$180$		0			0
$181$	1.46153e8			0.136174			0.0680870	−	0.997679i	$-0.478310\pi$
$181$	1.46153e8			0.136174			0.0680870	+	0.997679i	$0.478310\pi$
$182$	−9.73690e7	−	9.73690e7i	−0.0887432	−	0.0887432i
$183$	−1.78711e9	+	1.78711e9i	−1.59348	+	1.59348i
$184$			7.26573e8i			0.633881i
$185$		0			0
$186$	−1.09632e9			−0.915979
$187$	−7.22967e8	−	7.22967e8i	−0.591224	−	0.591224i
$188$	−4.58130e7	+	4.58130e7i	−0.0366739	+	0.0366739i
$189$			3.16921e8i			0.248373i
$190$		0			0
$191$	−2.54450e9			−1.91191			−0.955957	−	0.293506i	$-0.905178\pi$
$191$	−2.54450e9			−1.91191			−0.955957	+	0.293506i	$0.905178\pi$
$192$	−1.34493e9	−	1.34493e9i	−0.989679	−	0.989679i
$193$	−9.46964e8	+	9.46964e8i	−0.682503	+	0.682503i	−0.960563	−	0.278061i	$-0.910308\pi$
$193$	−9.46964e8	+	9.46964e8i	−0.682503	+	0.682503i	0.278061	+	0.960563i	$0.410308\pi$
$194$		−	8.00595e8i		−	0.565205i
$195$		0			0
$196$	1.34107e8			0.0908715
$197$	−6.42356e8	−	6.42356e8i	−0.426492	−	0.426492i	0.460940	−	0.887432i	$-0.347513\pi$
$197$	−6.42356e8	−	6.42356e8i	−0.426492	−	0.426492i	−0.887432	+	0.460940i	$0.847513\pi$
$198$	−8.32198e8	+	8.32198e8i	−0.541459	+	0.541459i
$199$		−	3.47565e8i		−	0.221628i	−0.993841	−	0.110814i	$-0.964654\pi$
$199$		−	3.47565e8i		−	0.221628i	0.993841	−	0.110814i	$-0.0353457\pi$
$200$		0			0
$201$	2.05326e9			1.25794
$202$	−2.27323e8	−	2.27323e8i	−0.136533	−	0.136533i
$203$	1.99246e8	−	1.99246e8i	0.117329	−	0.117329i
$204$			4.78641e8i			0.276369i
$205$		0			0
$206$	3.20772e9			1.78126
$207$	1.32714e9	+	1.32714e9i	0.722831	+	0.722831i
$208$	5.76664e8	−	5.76664e8i	0.308084	−	0.308084i
$209$		−	4.18500e8i		−	0.219336i
$210$		0			0
$211$	−1.32439e9			−0.668168			−0.334084	−	0.942543i	$-0.608427\pi$
$211$	−1.32439e9			−0.668168			−0.334084	+	0.942543i	$0.608427\pi$
$212$	1.44711e8	+	1.44711e8i	0.0716403	+	0.0716403i
$213$	2.73808e9	−	2.73808e9i	1.33023	−	1.33023i
$214$		−	2.91463e9i		−	1.38972i
$215$		0			0
$216$	−1.70505e9			−0.783289
$217$	2.58115e8	+	2.58115e8i	0.116406	+	0.116406i
$218$	1.97883e9	−	1.97883e9i	0.876160	−	0.876160i
$219$			4.59641e9i			1.99822i
$220$		0			0
$221$	1.66252e9			0.696945
$222$	1.31703e8	+	1.31703e8i	0.0542230	+	0.0542230i
$223$	−2.96426e9	+	2.96426e9i	−1.19866	+	1.19866i	−0.224096	+	0.974567i	$0.571943\pi$
$223$	−2.96426e9	+	2.96426e9i	−1.19866	+	1.19866i	−0.974567	+	0.224096i	$0.928057\pi$
$224$		−	1.49906e8i		−	0.0595427i
$225$		0			0
$226$	−7.67318e8			−0.294132
$227$	8.37535e8	+	8.37535e8i	0.315428	+	0.315428i	0.847008	−	0.531580i	$-0.178402\pi$
$227$	8.37535e8	+	8.37535e8i	0.315428	+	0.315428i	−0.531580	+	0.847008i	$0.678402\pi$
$228$	−1.38534e8	+	1.38534e8i	−0.0512646	+	0.0512646i
$229$		−	2.66676e9i		−	0.969709i	−0.874595	−	0.484854i	$-0.838873\pi$
$229$		−	2.66676e9i		−	0.969709i	0.874595	−	0.484854i	$-0.161127\pi$
$230$		0			0
$231$	6.49256e8			0.228017
$232$	1.07195e9	+	1.07195e9i	0.370018	+	0.370018i
$233$	−9.91964e8	+	9.91964e8i	−0.336568	+	0.336568i	−0.855074	−	0.518506i	$-0.826488\pi$
$233$	−9.91964e8	+	9.91964e8i	−0.336568	+	0.336568i	0.518506	+	0.855074i	$0.326488\pi$
$234$		−	1.91371e9i		−	0.638281i
$235$		0			0
$236$	−4.46803e8			−0.144035
$237$	7.40485e8	+	7.40485e8i	0.234705	+	0.234705i
$238$	1.24167e9	−	1.24167e9i	0.386990	−	0.386990i
$239$			1.26088e9i			0.386440i	0.981155	+	0.193220i	$0.0618931\pi$
$239$			1.26088e9i			0.386440i	−0.981155	+	0.193220i	$0.938107\pi$
$240$		0			0
$241$	−1.40173e9			−0.415524			−0.207762	−	0.978179i	$-0.566618\pi$
$241$	−1.40173e9			−0.415524			−0.207762	+	0.978179i	$0.566618\pi$
$242$	−1.95832e9	−	1.95832e9i	−0.570982	−	0.570982i
$243$	2.84707e9	−	2.84707e9i	0.816532	−	0.816532i
$244$		−	5.02009e8i		−	0.141629i
$245$		0			0
$246$	−3.92359e9			−1.07138
$247$	4.81187e8	+	4.81187e8i	0.129278	+	0.129278i
$248$	−1.38867e9	+	1.38867e9i	−0.367107	+	0.367107i
$249$		−	3.63199e9i		−	0.944816i
$250$		0			0
$251$	5.24024e9			1.32025			0.660126	−	0.751155i	$-0.270503\pi$
$251$	5.24024e9			1.32025			0.660126	+	0.751155i	$0.270503\pi$
$252$	−1.29716e8	−	1.29716e8i	−0.0321657	−	0.0321657i
$253$	9.32973e8	−	9.32973e8i	0.227713	−	0.227713i
$254$			6.96261e9i			1.67277i
$255$		0			0
$256$	1.27373e9			0.296563
$257$	2.38954e9	+	2.38954e9i	0.547749	+	0.547749i	0.925789	−	0.378040i	$-0.123402\pi$
$257$	2.38954e9	+	2.38954e9i	0.547749	+	0.547749i	−0.378040	+	0.925789i	$0.623402\pi$
$258$	−3.18876e9	+	3.18876e9i	−0.719687	+	0.719687i
$259$		−	6.20158e7i		−	0.0137817i
$260$		0			0
$261$	3.91601e9			0.843882
$262$	−4.00644e9	−	4.00644e9i	−0.850263	−	0.850263i
$263$	1.29445e9	−	1.29445e9i	0.270559	−	0.270559i	−0.558766	−	0.829325i	$-0.688725\pi$
$263$	1.29445e9	−	1.29445e9i	0.270559	−	0.270559i	0.829325	+	0.558766i	$0.188725\pi$
$264$			3.49303e9i			0.719095i
$265$		0			0
$266$	7.18761e8			0.143568
$267$	−7.46744e9	−	7.46744e9i	−1.46936	−	1.46936i
$268$	−2.88386e8	+	2.88386e8i	−0.0559029	+	0.0559029i
$269$		−	6.14346e9i		−	1.17329i	−0.809845	−	0.586643i	$-0.800449\pi$
$269$		−	6.14346e9i		−	1.17329i	0.809845	−	0.586643i	$-0.199551\pi$
$270$		0			0
$271$	−5.21208e9			−0.966349			−0.483174	−	0.875524i	$-0.660516\pi$
$271$	−5.21208e9			−0.966349			−0.483174	+	0.875524i	$0.660516\pi$
$272$	7.35377e9	+	7.35377e9i	1.34349	+	1.34349i
$273$	−7.46509e8	+	7.46509e8i	−0.134395	+	0.134395i
$274$		−	2.51828e9i		−	0.446787i
$275$		0			0
$276$	−6.17676e8			−0.106445
$277$	−5.42598e9	−	5.42598e9i	−0.921635	−	0.921635i	0.0755097	−	0.997145i	$-0.475942\pi$
$277$	−5.42598e9	−	5.42598e9i	−0.921635	−	0.921635i	−0.997145	+	0.0755097i	$0.975942\pi$
$278$	−6.96058e9	+	6.96058e9i	−1.16538	+	1.16538i
$279$			5.07304e9i			0.837243i
$280$		0			0
$281$	−7.13397e9			−1.14421			−0.572106	−	0.820180i	$-0.693873\pi$
$281$	−7.13397e9			−1.14421			−0.572106	+	0.820180i	$0.693873\pi$
$282$	3.87011e9	+	3.87011e9i	0.611965	+	0.611965i
$283$	−2.63941e9	+	2.63941e9i	−0.411492	+	0.411492i	−0.882258	−	0.470766i	$-0.843978\pi$
$283$	−2.63941e9	+	2.63941e9i	−0.411492	+	0.411492i	0.470766	+	0.882258i	$0.343978\pi$
$284$			7.69142e8i			0.118232i
$285$		0			0
$286$	−1.34532e9			−0.201077
$287$	9.23763e8	+	9.23763e8i	0.136155	+	0.136155i
$288$	1.47314e9	−	1.47314e9i	0.214129	−	0.214129i
$289$			1.42251e10i			2.03923i
$290$		0			0
$291$	−6.13800e9			−0.855963
$292$	−6.45579e8	−	6.45579e8i	−0.0888010	−	0.0888010i
$293$	2.26873e9	−	2.26873e9i	0.307831	−	0.307831i	−0.536237	−	0.844068i	$-0.680155\pi$
$293$	2.26873e9	−	2.26873e9i	0.307831	−	0.307831i	0.844068	+	0.536237i	$0.180155\pi$
$294$		−	1.13289e10i		−	1.51634i
$295$		0			0
$296$	3.33648e8			0.0434631
$297$	2.18941e9	+	2.18941e9i	0.281385	+	0.281385i
$298$	6.47760e9	−	6.47760e9i	0.821390	−	0.821390i
$299$			2.14545e9i			0.268431i
$300$		0			0
$301$	1.50151e9			0.182921
$302$	1.05395e9	+	1.05395e9i	0.126705	+	0.126705i
$303$	−1.74284e9	+	1.74284e9i	−0.206769	+	0.206769i
$304$			4.25683e9i			0.498416i
$305$		0			0
$306$	2.44041e10			2.78341
$307$	5.16937e9	+	5.16937e9i	0.581948	+	0.581948i	0.935438	−	0.353490i	$-0.115005\pi$
$307$	5.16937e9	+	5.16937e9i	0.581948	+	0.581948i	−0.353490	+	0.935438i	$0.615005\pi$
$308$	−9.11898e7	+	9.11898e7i	−0.0101331	+	0.0101331i
$309$		−	2.45930e10i		−	2.69760i
$310$		0			0
$311$	1.32155e10			1.41268			0.706340	−	0.707873i	$-0.250345\pi$
$311$	1.32155e10			1.41268			0.706340	+	0.707873i	$0.250345\pi$
$312$	−4.01625e9	−	4.01625e9i	−0.423840	−	0.423840i
$313$	9.02814e9	−	9.02814e9i	0.940635	−	0.940635i	−0.0576992	−	0.998334i	$-0.518376\pi$
$313$	9.02814e9	−	9.02814e9i	0.940635	−	0.940635i	0.998334	+	0.0576992i	$0.0183764\pi$
$314$			7.61899e9i			0.783753i
$315$		0			0
$316$	−2.08006e8			−0.0208607
$317$	4.91807e9	+	4.91807e9i	0.487032	+	0.487032i	0.907369	−	0.420336i	$-0.138088\pi$
$317$	4.91807e9	+	4.91807e9i	0.487032	+	0.487032i	−0.420336	+	0.907369i	$0.638088\pi$
$318$	1.22246e10	−	1.22246e10i	1.19544	−	1.19544i
$319$		−	2.75293e9i		−	0.265847i
$320$		0			0
$321$	−2.23459e10			−2.10464
$322$	1.60235e9	+	1.60235e9i	0.149051	+	0.149051i
$323$	−6.13622e9	+	6.13622e9i	−0.563756	+	0.563756i
$324$			2.25111e8i			0.0204276i
$325$		0			0
$326$	−5.07944e9			−0.449723
$327$	−1.51713e10	−	1.51713e10i	−1.32688	−	1.32688i
$328$	−4.96989e9	+	4.96989e9i	−0.429389	+	0.429389i
$329$		−	1.82234e9i		−	0.155541i
$330$		0			0
$331$	1.72045e9			0.143327			0.0716637	−	0.997429i	$-0.477169\pi$
$331$	1.72045e9			0.143327			0.0716637	+	0.997429i	$0.477169\pi$
$332$	5.10123e8	+	5.10123e8i	0.0419877	+	0.0419877i
$333$	6.09434e8	−	6.09434e8i	0.0495621	−	0.0495621i
$334$		−	1.63974e10i		−	1.31762i
$335$		0			0
$336$	−6.60400e9			−0.518144
$337$	5.92808e9	+	5.92808e9i	0.459615	+	0.459615i	0.898529	−	0.438914i	$-0.144637\pi$
$337$	5.92808e9	+	5.92808e9i	0.459615	+	0.459615i	−0.438914	+	0.898529i	$0.644637\pi$
$338$	−8.13174e9	+	8.13174e9i	−0.623041	+	0.623041i
$339$			5.88287e9i			0.445442i
$340$		0			0
$341$	3.56632e9			0.263756
$342$	7.06332e9	+	7.06332e9i	0.516303	+	0.516303i
$343$	−5.59703e9	+	5.59703e9i	−0.404372	+	0.404372i
$344$			8.07820e9i			0.576874i
$345$		0			0
$346$	8.07685e9			0.563557
$347$	−4.12838e9	−	4.12838e9i	−0.284749	−	0.284749i	0.550251	−	0.834999i	$-0.314532\pi$
$347$	−4.12838e9	−	4.12838e9i	−0.284749	−	0.284749i	−0.834999	+	0.550251i	$0.814532\pi$
$348$	−9.11290e8	+	9.11290e8i	−0.0621355	+	0.0621355i
$349$			3.79762e9i			0.255983i	0.991775	+	0.127991i	$0.0408530\pi$
$349$			3.79762e9i			0.255983i	−0.991775	+	0.127991i	$0.959147\pi$
$350$		0			0
$351$	−5.03473e9			−0.331702
$352$	−1.03561e9	−	1.03561e9i	−0.0674568	−	0.0674568i
$353$	4.46363e9	−	4.46363e9i	0.287468	−	0.287468i	−0.548610	−	0.836078i	$-0.684843\pi$
$353$	4.46363e9	−	4.46363e9i	0.287468	−	0.287468i	0.836078	+	0.548610i	$0.184843\pi$
$354$			3.77443e10i			2.40347i
$355$		0			0
$356$	2.09765e9			0.130597
$357$	−9.51967e9	−	9.51967e9i	−0.586069	−	0.586069i
$358$	−8.91752e8	+	8.91752e8i	−0.0542890	+	0.0542890i
$359$		−	9.04307e8i		−	0.0544425i	−0.999629	−	0.0272213i	$-0.991334\pi$
$359$		−	9.04307e8i		−	0.0544425i	0.999629	−	0.0272213i	$-0.00866586\pi$
$360$		0			0
$361$	1.34315e10			0.790854
$362$	1.73410e9	+	1.73410e9i	0.100981	+	0.100981i
$363$	−1.50141e10	+	1.50141e10i	−0.864712	+	0.864712i
$364$		−	2.09698e8i		−	0.0119451i
$365$		0			0
$366$	−4.24078e10			−2.36332
$367$	9.88793e9	+	9.88793e9i	0.545056	+	0.545056i	0.925007	−	0.379951i	$-0.124059\pi$
$367$	9.88793e9	+	9.88793e9i	0.545056	+	0.545056i	−0.379951	+	0.925007i	$0.624059\pi$
$368$	−9.48987e9	+	9.48987e9i	−0.517451	+	0.517451i
$369$			1.81558e10i			0.979287i
$370$		0			0
$371$	−5.75629e9			−0.303841
$372$	−1.18054e9	−	1.18054e9i	−0.0616467	−	0.0616467i
$373$	1.56902e10	−	1.56902e10i	0.810575	−	0.810575i	−0.174145	−	0.984720i	$-0.555716\pi$
$373$	1.56902e10	−	1.56902e10i	0.810575	−	0.810575i	0.984720	+	0.174145i	$0.0557163\pi$
$374$		−	1.71559e10i		−	0.876854i
$375$		0			0
$376$	9.80428e9			0.490528
$377$	3.16529e9	+	3.16529e9i	0.156692	+	0.156692i
$378$	−3.76025e9	+	3.76025e9i	−0.184183	+	0.184183i
$379$		−	4.03797e8i		−	0.0195707i	−0.999952	−	0.00978534i	$-0.996885\pi$
$379$		−	4.03797e8i		−	0.0195707i	0.999952	−	0.00978534i	$-0.00311482\pi$
$380$		0			0
$381$	5.33809e10			2.53330
$382$	−3.01903e10	−	3.01903e10i	−1.41779	−	1.41779i
$383$	1.94253e10	−	1.94253e10i	0.902761	−	0.902761i	−0.0929130	−	0.995674i	$-0.529618\pi$
$383$	1.94253e10	−	1.94253e10i	0.902761	−	0.902761i	0.995674	+	0.0929130i	$0.0296178\pi$
$384$		−	3.87839e10i		−	1.78372i
$385$		0			0
$386$	−2.24713e10			−1.01223
$387$	1.47555e10	+	1.47555e10i	0.657824	+	0.657824i
$388$	8.62099e8	−	8.62099e8i	0.0380391	−	0.0380391i
$389$		−	1.00547e10i		−	0.439109i	−0.975600	−	0.219555i	$-0.929540\pi$
$389$		−	1.00547e10i		−	0.439109i	0.975600	−	0.219555i	$-0.0704604\pi$
$390$		0			0
$391$	−2.73593e10			−1.17057
$392$	−1.43499e10	−	1.43499e10i	−0.607722	−	0.607722i
$393$	−3.07165e10	+	3.07165e10i	−1.28766	+	1.28766i
$394$		−	1.52430e10i		−	0.632537i
$395$		0			0
$396$	−1.79226e9			−0.0728820
$397$	−4.59921e9	−	4.59921e9i	−0.185149	−	0.185149i	0.608446	−	0.793595i	$-0.291793\pi$
$397$	−4.59921e9	−	4.59921e9i	−0.185149	−	0.185149i	−0.793595	+	0.608446i	$0.791793\pi$
$398$	4.12383e9	−	4.12383e9i	0.164350	−	0.164350i
$399$		−	5.51059e9i		−	0.217424i
$400$		0			0
$401$	3.93282e10			1.52099			0.760496	−	0.649343i	$-0.224956\pi$
$401$	3.93282e10			1.52099			0.760496	+	0.649343i	$0.224956\pi$
$402$	2.43617e10	+	2.43617e10i	0.932834	+	0.932834i
$403$	−4.10052e9	+	4.10052e9i	−0.155460	+	0.155460i
$404$		−	4.89572e8i		−	0.0183777i
$405$		0			0
$406$	4.72807e9			0.174012
$407$	−4.28428e8	−	4.28428e8i	−0.0156135	−	0.0156135i
$408$	5.12162e10	−	5.12162e10i	1.84828	−	1.84828i
$409$			3.53396e10i			1.26290i	0.775417	+	0.631450i	$0.217540\pi$
$409$			3.53396e10i			1.26290i	−0.775417	+	0.631450i	$0.782460\pi$
$410$		0			0
$411$	−1.93071e10			−0.676628
$412$	3.45415e9	+	3.45415e9i	0.119881	+	0.119881i
$413$	8.88644e9	−	8.88644e9i	0.305441	−	0.305441i
$414$			3.14929e10i			1.07204i
$415$		0			0
$416$	2.38147e9			0.0795191
$417$	5.33654e10	+	5.33654e10i	1.76488	+	1.76488i
$418$	4.96547e9	−	4.96547e9i	0.162650	−	0.162650i
$419$		−	1.65282e10i		−	0.536251i	−0.963384	−	0.268126i	$-0.913596\pi$
$419$		−	1.65282e10i		−	0.536251i	0.963384	−	0.268126i	$-0.0864042\pi$
$420$		0			0
$421$	−2.05277e10			−0.653449			−0.326725	−	0.945120i	$-0.605945\pi$
$421$	−2.05277e10			−0.653449			−0.326725	+	0.945120i	$0.605945\pi$
$422$	−1.57138e10	−	1.57138e10i	−0.495485	−	0.495485i
$423$	1.79083e10	−	1.79083e10i	0.559362	−	0.559362i
$424$		−	3.09691e10i		−	0.958219i
$425$		0			0
$426$	6.49743e10			1.97289
$427$	9.98442e9	+	9.98442e9i	0.300339	+	0.300339i
$428$	3.13854e9	−	3.13854e9i	0.0935303	−	0.0935303i
$429$			1.03143e10i			0.304517i
$430$		0			0
$431$	2.06955e9			0.0599745			0.0299873	−	0.999550i	$-0.490453\pi$
$431$	2.06955e9			0.0599745			0.0299873	+	0.999550i	$0.490453\pi$
$432$	−2.22699e10	−	2.22699e10i	−0.639416	−	0.639416i
$433$	−2.90398e10	+	2.90398e10i	−0.826118	+	0.826118i	−0.986977	−	0.160860i	$-0.948573\pi$
$433$	−2.90398e10	+	2.90398e10i	−0.826118	+	0.826118i	0.160860	+	0.986977i	$0.448573\pi$
$434$			6.12504e9i			0.172643i
$435$		0			0
$436$	4.26171e9			0.117934
$437$	−7.91866e9	−	7.91866e9i	−0.217133	−	0.217133i
$438$	−5.45361e10	+	5.45361e10i	−1.48179	+	1.48179i
$439$			1.56289e10i			0.420795i	0.977616	+	0.210398i	$0.0674758\pi$
$439$			1.56289e10i			0.420795i	−0.977616	+	0.210398i	$0.932524\pi$
$440$		0			0
$441$	−5.24225e10			−1.38600
$442$	1.97257e10	+	1.97257e10i	0.516825	+	0.516825i
$443$	−7.72628e9	+	7.72628e9i	−0.200611	+	0.200611i	−0.800262	−	0.599651i	$-0.795306\pi$
$443$	−7.72628e9	+	7.72628e9i	−0.200611	+	0.200611i	0.599651	+	0.800262i	$0.295306\pi$
$444$			2.83641e8i			0.00729857i
$445$		0			0
$446$	−7.03415e10			−1.77776
$447$	−4.96625e10	−	4.96625e10i	−1.24394	−	1.24394i
$448$	−7.51399e9	+	7.51399e9i	−0.186534	+	0.186534i
$449$		−	1.21836e10i		−	0.299771i	−0.988703	−	0.149886i	$-0.952109\pi$
$449$		−	1.21836e10i		−	0.299771i	0.988703	−	0.149886i	$-0.0478905\pi$
$450$		0			0
$451$	1.27634e10			0.308504
$452$	−8.26266e8	−	8.26266e8i	−0.0197955	−	0.0197955i
$453$	8.08045e9	−	8.08045e9i	0.191886	−	0.191886i
$454$			1.98746e10i			0.467816i
$455$		0			0
$456$	2.96472e10			0.685685
$457$	−4.53311e10	−	4.53311e10i	−1.03928	−	1.03928i	−0.999196	−	0.0400801i	$-0.987239\pi$
$457$	−4.53311e10	−	4.53311e10i	−1.03928	−	1.03928i	−0.0400801	−	0.999196i	$-0.512761\pi$
$458$	3.16409e10	−	3.16409e10i	0.719095	−	0.719095i
$459$		−	6.42041e10i		−	1.44648i
$460$		0			0
$461$	−3.53353e9			−0.0782357			−0.0391178	−	0.999235i	$-0.512455\pi$
$461$	−3.53353e9			−0.0782357			−0.0391178	+	0.999235i	$0.512455\pi$
$462$	7.70337e9	+	7.70337e9i	0.169088	+	0.169088i
$463$	−1.72557e10	+	1.72557e10i	−0.375499	+	0.375499i	−0.869475	−	0.493976i	$-0.835543\pi$
$463$	−1.72557e10	+	1.72557e10i	−0.375499	+	0.375499i	0.493976	+	0.869475i	$0.335543\pi$
$464$			2.80018e10i			0.604107i
$465$		0			0
$466$	−2.35392e10			−0.499169
$467$	2.45996e10	+	2.45996e10i	0.517203	+	0.517203i	0.916724	−	0.399521i	$-0.130823\pi$
$467$	2.45996e10	+	2.45996e10i	0.517203	+	0.517203i	−0.399521	+	0.916724i	$0.630823\pi$
$468$	2.06072e9	−	2.06072e9i	0.0429572	−	0.0429572i
$469$		−	1.14714e10i		−	0.237096i
$470$		0			0
$471$	5.84133e10			1.18694
$472$	4.78094e10	+	4.78094e10i	0.963264	+	0.963264i
$473$	1.03730e10	−	1.03730e10i	0.207234	−	0.207234i
$474$			1.75716e10i			0.348095i
$475$		0			0
$476$	2.67413e9			0.0520900
$477$	−5.65675e10	−	5.65675e10i	−1.09268	−	1.09268i
$478$	−1.49602e10	+	1.49602e10i	−0.286568	+	0.286568i
$479$			7.37614e10i			1.40116i	0.713575	+	0.700579i	$0.247075\pi$
$479$			7.37614e10i			1.40116i	−0.713575	+	0.700579i	$0.752925\pi$
$480$		0			0
$481$	9.85206e8			0.0184055
$482$	−1.66314e10	−	1.66314e10i	−0.308135	−	0.308135i
$483$	1.22849e10	−	1.22849e10i	0.225727	−	0.225727i
$484$		−	4.21753e9i		−	0.0768558i
$485$		0			0
$486$	6.75605e10			1.21101
$487$	2.80441e10	+	2.80441e10i	0.498569	+	0.498569i	0.910992	−	0.412423i	$-0.135318\pi$
$487$	2.80441e10	+	2.80441e10i	0.498569	+	0.498569i	−0.412423	+	0.910992i	$0.635318\pi$
$488$	−5.37166e10	+	5.37166e10i	−0.947173	+	0.947173i
$489$			3.89430e10i			0.681074i
$490$		0			0
$491$	−1.16769e10			−0.200911			−0.100455	−	0.994942i	$-0.532030\pi$
$491$	−1.16769e10			−0.200911			−0.100455	+	0.994942i	$0.532030\pi$
$492$	−4.22501e9	−	4.22501e9i	−0.0721054	−	0.0721054i
$493$	−4.03646e10	+	4.03646e10i	−0.683302	+	0.683302i
$494$			1.14185e10i			0.191735i
$495$		0			0
$496$	−3.62753e10			−0.599355
$497$	−1.52974e10	−	1.52974e10i	−0.250722	−	0.250722i
$498$	4.30933e10	−	4.30933e10i	0.700635	−	0.700635i
$499$		−	7.08522e10i		−	1.14275i	−0.820689	−	0.571375i	$-0.806410\pi$
$499$		−	7.08522e10i		−	1.14275i	0.820689	−	0.571375i	$-0.193590\pi$
$500$		0			0
$501$	−1.25716e11			−1.99544
$502$	6.21751e10	+	6.21751e10i	0.979043	+	0.979043i
$503$	7.32217e10	−	7.32217e10i	1.14385	−	1.14385i	0.156107	−	0.987740i	$-0.450106\pi$
$503$	7.32217e10	−	7.32217e10i	1.14385	−	1.14385i	0.987740	−	0.156107i	$-0.0498944\pi$
$504$			2.77602e10i			0.430229i
$505$		0			0
$506$	2.21393e10			0.337724
$507$	6.23444e10	+	6.23444e10i	0.943552	+	0.943552i
$508$	−7.49750e9	+	7.49750e9i	−0.112580	+	0.112580i
$509$		−	1.10598e11i		−	1.64769i	−0.566813	−	0.823846i	$-0.691824\pi$
$509$		−	1.10598e11i		−	1.64769i	0.566813	−	0.823846i	$-0.308176\pi$
$510$		0			0
$511$	2.56797e10			0.376623
$512$	−3.94608e10	−	3.94608e10i	−0.574231	−	0.574231i
$513$	1.85827e10	−	1.85827e10i	0.268312	−	0.268312i
$514$			5.67034e10i			0.812376i
$515$		0			0
$516$	−6.86747e9			−0.0968719
$517$	−1.25894e10	−	1.25894e10i	−0.176215	−	0.176215i
$518$	7.35813e8	−	7.35813e8i	0.0102199	−	0.0102199i
$519$		−	6.19236e10i		−	0.853467i
$520$		0			0
$521$	−8.07216e10			−1.09557			−0.547783	−	0.836620i	$-0.684528\pi$
$521$	−8.07216e10			−1.09557			−0.547783	+	0.836620i	$0.684528\pi$
$522$	4.64631e10	+	4.64631e10i	0.625787	+	0.625787i
$523$	3.77792e10	−	3.77792e10i	0.504948	−	0.504948i	−0.408024	−	0.912971i	$-0.633782\pi$
$523$	3.77792e10	−	3.77792e10i	0.504948	−	0.504948i	0.912971	+	0.408024i	$0.133782\pi$
$524$		−	8.62844e9i		−	0.114448i
$525$		0			0
$526$	3.07170e10			0.401270
$527$	−5.22908e10	−	5.22908e10i	−0.677927	−	0.677927i
$528$	−4.56229e10	+	4.56229e10i	−0.587013	+	0.587013i
$529$			4.30044e10i			0.549149i
$530$		0			0
$531$	1.74655e11			2.19687
$532$	7.73978e8	+	7.73978e8i	0.00966233	+	0.00966233i
$533$	−1.46752e10	+	1.46752e10i	−0.181835	+	0.181835i
$534$		−	1.77201e11i		−	2.17922i
$535$		0			0
$536$	6.17164e10			0.747725
$537$	6.83688e9	+	6.83688e9i	0.0822169	+	0.0822169i
$538$	7.28917e10	−	7.28917e10i	0.870060	−	0.870060i
$539$			3.68527e10i			0.436631i
$540$		0			0
$541$	7.53948e10			0.880141			0.440071	−	0.897963i	$-0.354953\pi$
$541$	7.53948e10			0.880141			0.440071	+	0.897963i	$0.354953\pi$
$542$	−6.18409e10	−	6.18409e10i	−0.716604	−	0.716604i
$543$	1.32950e10	−	1.32950e10i	0.152928	−	0.152928i
$544$			3.03691e10i			0.346766i
$545$		0			0
$546$	−1.77145e10			−0.199324
$547$	−2.20178e10	−	2.20178e10i	−0.245937	−	0.245937i	0.573364	−	0.819301i	$-0.305638\pi$
$547$	−2.20178e10	−	2.20178e10i	−0.245937	−	0.245937i	−0.819301	+	0.573364i	$0.805638\pi$
$548$	2.71174e9	−	2.71174e9i	0.0300694	−	0.0300694i
$549$			1.96235e11i			2.16017i
$550$		0			0
$551$	−2.33656e10			−0.253496
$552$	6.60934e10	+	6.60934e10i	0.711871	+	0.711871i
$553$	4.13703e9	−	4.13703e9i	0.0442372	−	0.0442372i
$554$		−	1.28758e11i		−	1.36689i
$555$		0			0
$556$	−1.49906e10			−0.156863
$557$	1.03428e11	+	1.03428e11i	1.07453	+	1.07453i	0.996990	+	0.0775357i	$0.0247052\pi$
$557$	1.03428e11	+	1.03428e11i	1.07453	+	1.07453i	0.0775357	+	0.996990i	$0.475295\pi$
$558$	−6.01913e10	+	6.01913e10i	−0.620864	+	0.620864i
$559$			2.38536e10i			0.244290i
$560$		0			0
$561$	−1.31531e11			−1.32793
$562$	−8.46441e10	−	8.46441e10i	−0.848499	−	0.848499i
$563$	7.70545e10	−	7.70545e10i	0.766945	−	0.766945i	−0.210623	−	0.977567i	$-0.567549\pi$
$563$	7.70545e10	−	7.70545e10i	0.766945	−	0.766945i	0.977567	+	0.210623i	$0.0675491\pi$
$564$			8.33484e9i			0.0823722i
$565$		0			0
$566$	−6.26329e10			−0.610290
$567$	−4.47721e9	−	4.47721e9i	−0.0433187	−	0.0433187i
$568$	8.23008e10	−	8.23008e10i	0.790698	−	0.790698i
$569$		−	6.19669e10i		−	0.591168i	−0.955317	−	0.295584i	$-0.904486\pi$
$569$		−	6.19669e10i		−	0.591168i	0.955317	−	0.295584i	$-0.0955142\pi$
$570$		0			0
$571$	2.38428e10			0.224292			0.112146	−	0.993692i	$-0.464228\pi$
$571$	2.38428e10			0.224292			0.112146	+	0.993692i	$0.464228\pi$
$572$	−1.44867e9	−	1.44867e9i	−0.0135328	−	0.0135328i
$573$	−2.31463e11	+	2.31463e11i	−2.14715	+	2.14715i
$574$			2.19208e10i			0.201933i
$575$		0			0
$576$	−1.47681e11			−1.34164
$577$	−1.08821e11	−	1.08821e11i	−0.981772	−	0.981772i	0.0180652	−	0.999837i	$-0.494249\pi$
$577$	−1.08821e11	−	1.08821e11i	−0.981772	−	0.981772i	−0.999837	+	0.0180652i	$0.994249\pi$
$578$	−1.68780e11	+	1.68780e11i	−1.51220	+	1.51220i
$579$			1.72283e11i			1.53295i
$580$		0			0
$581$	−2.02916e10			−0.178079
$582$	−7.28269e10	−	7.28269e10i	−0.634746	−	0.634746i
$583$	−3.97666e10	+	3.97666e10i	−0.344226	+	0.344226i
$584$			1.38158e11i			1.18775i
$585$		0			0
$586$	5.38366e10			0.456549
$587$	9.61187e10	+	9.61187e10i	0.809572	+	0.809572i	0.984569	−	0.174997i	$-0.0559916\pi$
$587$	9.61187e10	+	9.61187e10i	0.809572	+	0.809572i	−0.174997	+	0.984569i	$0.555992\pi$
$588$	1.21992e10	−	1.21992e10i	0.102052	−	0.102052i
$589$		−	3.02693e10i		−	0.251502i
$590$		0			0
$591$	−1.16865e11			−0.957932
$592$	4.35782e9	+	4.35782e9i	0.0354799	+	0.0354799i
$593$	−1.01154e10	+	1.01154e10i	−0.0818021	+	0.0818021i	−0.746824	−	0.665022i	$-0.768422\pi$
$593$	−1.01154e10	+	1.01154e10i	−0.0818021	+	0.0818021i	0.665022	+	0.746824i	$0.268422\pi$
$594$			5.19544e10i			0.417327i
$595$		0			0
$596$	1.39505e10			0.110561
$597$	−3.16166e10	−	3.16166e10i	−0.248896	−	0.248896i
$598$	−2.54556e10	+	2.54556e10i	−0.199057	+	0.199057i
$599$		−	1.61079e11i		−	1.25121i	−0.780139	−	0.625606i	$-0.784852\pi$
$599$		−	1.61079e11i		−	1.25121i	0.780139	−	0.625606i	$-0.215148\pi$
$600$		0			0
$601$	2.16088e11			1.65627			0.828137	−	0.560526i	$-0.189401\pi$
$601$	2.16088e11			1.65627			0.828137	+	0.560526i	$0.189401\pi$
$602$	1.78153e10	+	1.78153e10i	0.135646	+	0.135646i
$603$	1.12730e11	−	1.12730e11i	0.852649	−	0.852649i
$604$			2.26984e9i			0.0170548i
$605$		0			0
$606$	−4.13573e10			−0.306663
$607$	8.94773e10	+	8.94773e10i	0.659111	+	0.659111i	0.955170	−	0.296059i	$-0.0956725\pi$
$607$	8.94773e10	+	8.94773e10i	0.659111	+	0.659111i	−0.296059	+	0.955170i	$0.595673\pi$
$608$	−8.78979e9	+	8.78979e9i	−0.0643227	+	0.0643227i
$609$		−	3.62492e10i		−	0.263529i
$610$		0			0
$611$	2.89504e10			0.207725
$612$	2.62789e10	+	2.62789e10i	0.187327	+	0.187327i
$613$	1.23726e11	−	1.23726e11i	0.876229	−	0.876229i	−0.116913	−	0.993142i	$-0.537300\pi$
$613$	1.23726e11	−	1.23726e11i	0.876229	−	0.876229i	0.993142	+	0.116913i	$0.0373000\pi$
$614$			1.22668e11i			0.863096i
$615$		0			0
$616$	1.95152e10			0.135535
$617$	−1.10854e11	−	1.10854e11i	−0.764908	−	0.764908i	0.212297	−	0.977205i	$-0.431906\pi$
$617$	−1.10854e11	−	1.10854e11i	−0.764908	−	0.764908i	−0.977205	+	0.212297i	$0.931906\pi$
$618$	2.91794e11	−	2.91794e11i	2.00042	−	2.00042i
$619$		−	1.30648e11i		−	0.889897i	−0.895556	−	0.444949i	$-0.853222\pi$
$619$		−	1.30648e11i		−	0.889897i	0.895556	−	0.444949i	$-0.146778\pi$
$620$		0			0
$621$	8.28540e10			0.557118
$622$	1.56801e11	+	1.56801e11i	1.04758	+	1.04758i
$623$	−4.17199e10	+	4.17199e10i	−0.276944	+	0.276944i
$624$		−	1.04914e11i		−	0.691980i
$625$		0			0
$626$	2.14236e11			1.39507
$627$	−3.80692e10	−	3.80692e10i	−0.246323	−	0.246323i
$628$	−8.20431e9	+	8.20431e9i	−0.0527477	+	0.0527477i
$629$			1.25636e10i			0.0802622i
$630$		0			0
$631$	−2.21106e11			−1.39470			−0.697352	−	0.716729i	$-0.745639\pi$
$631$	−2.21106e11			−1.39470			−0.697352	+	0.716729i	$0.745639\pi$
$632$	2.22574e10	+	2.22574e10i	0.139510	+	0.139510i
$633$	−1.20474e11	+	1.20474e11i	−0.750377	+	0.750377i
$634$			1.16705e11i			0.722325i
$635$		0			0
$636$	2.63275e10			0.160909
$637$	−4.23729e10	−	4.23729e10i	−0.257354	−	0.257354i
$638$	3.26633e10	−	3.26633e10i	0.197141	−	0.197141i
$639$		−	3.00658e11i		−	1.80331i
$640$		0			0
$641$	2.04377e11			1.21060			0.605298	−	0.795999i	$-0.293054\pi$
$641$	2.04377e11			1.21060			0.605298	+	0.795999i	$0.293054\pi$
$642$	−2.65132e11	−	2.65132e11i	−1.56071	−	1.56071i
$643$	−1.72443e11	+	1.72443e11i	−1.00879	+	1.00879i	−0.00882849	+	0.999961i	$0.502810\pi$
$643$	−1.72443e11	+	1.72443e11i	−1.00879	+	1.00879i	−0.999961	+	0.00882849i	$0.997190\pi$
$644$			3.45090e9i			0.0200627i
$645$		0			0
$646$	−1.45612e11			−0.836115
$647$	1.33246e11	+	1.33246e11i	0.760392	+	0.760392i	0.976393	−	0.216001i	$-0.0693014\pi$
$647$	1.33246e11	+	1.33246e11i	0.760392	+	0.760392i	−0.216001	+	0.976393i	$0.569301\pi$
$648$	2.40876e10	−	2.40876e10i	0.136614	−	0.136614i
$649$		−	1.22782e11i		−	0.692078i
$650$		0			0
$651$	4.69594e10			0.261456
$652$	−5.46966e9	−	5.46966e9i	−0.0302670	−	0.0302670i
$653$	7.89023e10	−	7.89023e10i	0.433947	−	0.433947i	−0.456022	−	0.889969i	$-0.650726\pi$
$653$	7.89023e10	−	7.89023e10i	0.433947	−	0.433947i	0.889969	+	0.456022i	$0.150726\pi$
$654$		−	3.60013e11i		−	1.96792i
$655$		0			0
$656$	−1.29825e11			−0.701039
$657$	2.52357e11	+	2.52357e11i	1.35442	+	1.35442i
$658$	2.16219e10	−	2.16219e10i	0.115343	−	0.115343i
$659$			3.33275e11i			1.76710i	0.468339	+	0.883549i	$0.344853\pi$
$659$			3.33275e11i			1.76710i	−0.468339	+	0.883549i	$0.655147\pi$
$660$		0			0
$661$	−2.67623e11			−1.40190			−0.700951	−	0.713209i	$-0.747241\pi$
$661$	−2.67623e11			−1.40190			−0.700951	+	0.713209i	$0.747241\pi$
$662$	2.04130e10	+	2.04130e10i	0.106286	+	0.106286i
$663$	1.51233e11	−	1.51233e11i	0.782694	−	0.782694i
$664$		−	1.09170e11i		−	0.561603i
$665$		0			0
$666$	1.44618e10			0.0735064
$667$	−5.20896e10	−	5.20896e10i	−0.263177	−	0.263177i
$668$	1.76571e10	−	1.76571e10i	0.0886777	−	0.0886777i
$669$			5.39294e11i			2.69228i
$670$		0			0
$671$	1.37952e11			0.680517
$672$	−1.36364e10	−	1.36364e10i	−0.0668686	−	0.0668686i
$673$	4.65870e10	−	4.65870e10i	0.227093	−	0.227093i	−0.584384	−	0.811477i	$-0.698664\pi$
$673$	4.65870e10	−	4.65870e10i	0.227093	−	0.227093i	0.811477	+	0.584384i	$0.198664\pi$
$674$			1.40672e11i			0.681662i
$675$		0			0
$676$	−1.75129e10			−0.0838631
$677$	2.04905e11	+	2.04905e11i	0.975432	+	0.975432i	0.999705	−	0.0242736i	$-0.00772728\pi$
$677$	2.04905e11	+	2.04905e11i	0.975432	+	0.975432i	−0.0242736	+	0.999705i	$0.507727\pi$
$678$	−6.97998e10	+	6.97998e10i	−0.330321	+	0.330321i
$679$			3.42925e10i			0.161332i
$680$		0			0
$681$	1.52374e11			0.708473
$682$	4.23141e10	+	4.23141e10i	0.195590	+	0.195590i
$683$	−2.26392e11	+	2.26392e11i	−1.04035	+	1.04035i	−0.0411961	+	0.999151i	$0.513117\pi$
$683$	−2.26392e11	+	2.26392e11i	−1.04035	+	1.04035i	−0.999151	+	0.0411961i	$0.986883\pi$
$684$			1.52119e10i			0.0694958i
$685$		0			0
$686$	−1.32817e11			−0.599730
$687$	−2.42584e11	−	2.42584e11i	−1.08902	−	1.08902i
$688$	−1.05511e11	+	1.05511e11i	−0.470915	+	0.470915i
$689$		−	9.14465e10i		−	0.405779i
$690$		0			0
$691$	−1.15111e11			−0.504900			−0.252450	−	0.967610i	$-0.581236\pi$
$691$	−1.15111e11			−0.504900			−0.252450	+	0.967610i	$0.581236\pi$
$692$	8.69734e9	+	8.69734e9i	0.0379282	+	0.0379282i
$693$	3.56461e10	−	3.56461e10i	0.154554	−	0.154554i
$694$		−	9.79658e10i		−	0.422315i
$695$		0			0
$696$	1.95022e11			0.831087
$697$	−1.87142e11	−	1.87142e11i	−0.792941	−	0.792941i
$698$	−4.50585e10	+	4.50585e10i	−0.189826	+	0.189826i
$699$			1.80470e11i			0.755956i
$700$		0			0
$701$	3.26439e10			0.135185			0.0675927	−	0.997713i	$-0.478468\pi$
$701$	3.26439e10			0.135185			0.0675927	+	0.997713i	$0.478468\pi$
$702$	−5.97367e10	−	5.97367e10i	−0.245976	−	0.245976i
$703$	−3.63631e9	+	3.63631e9i	−0.0148881	+	0.0148881i
$704$			1.03819e11i			0.422655i
$705$		0			0
$706$	1.05921e11			0.426349
$707$	9.73707e9	+	9.73707e9i	0.0389718	+	0.0389718i
$708$	−4.06439e10	+	4.06439e10i	−0.161757	+	0.161757i
$709$			1.10106e11i			0.435737i	0.975978	+	0.217869i	$0.0699104\pi$
$709$			1.10106e11i			0.435737i	−0.975978	+	0.217869i	$0.930090\pi$
$710$		0			0
$711$	8.13098e10			0.318174
$712$	−2.24455e11	−	2.24455e11i	−0.873392	−	0.873392i
$713$	6.74802e10	−	6.74802e10i	0.261107	−	0.261107i
$714$		−	2.25900e11i		−	0.869208i
$715$		0			0
$716$	−1.92052e9			−0.00730746
$717$	1.14697e11	+	1.14697e11i	0.433986	+	0.433986i
$718$	1.07295e10	−	1.07295e10i	0.0403723	−	0.0403723i
$719$		−	2.80995e11i		−	1.05144i	−0.850658	−	0.525719i	$-0.823796\pi$
$719$		−	2.80995e11i		−	1.05144i	0.850658	−	0.525719i	$-0.176204\pi$
$720$		0			0
$721$	−1.37399e11			−0.508442
$722$	1.59364e11	+	1.59364e11i	0.586464	+	0.586464i
$723$	−1.27510e11	+	1.27510e11i	−0.466649	+	0.466649i
$724$			3.73463e9i			0.0135923i
$725$		0			0
$726$	−3.56281e11			−1.28247
$727$	−7.91155e10	−	7.91155e10i	−0.283220	−	0.283220i	0.551172	−	0.834392i	$-0.314181\pi$
$727$	−7.91155e10	−	7.91155e10i	−0.283220	−	0.283220i	−0.834392	+	0.551172i	$0.814181\pi$
$728$	−2.24384e10	+	2.24384e10i	−0.0798853	+	0.0798853i
$729$		−	4.60173e11i		−	1.62934i
$730$		0			0
$731$	−3.04187e11			−1.06530
$732$	−4.56657e10	−	4.56657e10i	−0.159055	−	0.159055i
$733$	1.00588e11	−	1.00588e11i	0.348441	−	0.348441i	−0.511088	−	0.859529i	$-0.670757\pi$
$733$	1.00588e11	−	1.00588e11i	0.348441	−	0.348441i	0.859529	+	0.511088i	$0.170757\pi$
$734$			2.34639e11i			0.808381i
$735$		0			0
$736$	−3.91906e10			−0.133558
$737$	−7.92485e10	−	7.92485e10i	−0.268609	−	0.268609i
$738$	−2.15417e11	+	2.15417e11i	−0.726197	+	0.726197i
$739$			1.06947e11i			0.358584i	0.983796	+	0.179292i	$0.0573806\pi$
$739$			1.06947e11i			0.358584i	−0.983796	+	0.179292i	$0.942619\pi$
$740$		0			0
$741$	8.75433e10			0.290369
$742$	−6.82979e10	−	6.82979e10i	−0.225316	−	0.225316i
$743$	−5.96783e10	+	5.96783e10i	−0.195822	+	0.195822i	−0.798206	−	0.602384i	$-0.794218\pi$
$743$	−5.96783e10	+	5.96783e10i	−0.195822	+	0.195822i	0.602384	+	0.798206i	$0.294218\pi$
$744$			2.52644e11i			0.824550i
$745$		0			0
$746$	3.72326e11			1.20218
$747$	−1.99407e11	−	1.99407e11i	−0.640410	−	0.640410i
$748$	1.84739e10	−	1.84739e10i	0.0590135	−	0.0590135i
$749$			1.24844e11i			0.396681i
$750$		0			0
$751$	−2.90374e11			−0.912846			−0.456423	−	0.889763i	$-0.650870\pi$
$751$	−2.90374e11			−0.912846			−0.456423	+	0.889763i	$0.650870\pi$
$752$	1.28055e11	+	1.28055e11i	0.400429	+	0.400429i
$753$	4.76684e11	−	4.76684e11i	1.48269	−	1.48269i
$754$			7.51119e10i			0.232393i
$755$		0			0
$756$	−8.09824e9			−0.0247915
$757$	2.22407e11	+	2.22407e11i	0.677274	+	0.677274i	0.959383	−	0.282108i	$-0.0910338\pi$
$757$	2.22407e11	+	2.22407e11i	0.677274	+	0.677274i	−0.282108	+	0.959383i	$0.591034\pi$
$758$	4.79102e9	−	4.79102e9i	0.0145128	−	0.0145128i
$759$		−	1.69738e11i		−	0.511459i
$760$		0			0
$761$	5.59405e11			1.66797			0.833984	−	0.551788i	$-0.186054\pi$
$761$	5.59405e11			1.66797			0.833984	+	0.551788i	$0.186054\pi$
$762$	6.33361e11	+	6.33361e11i	1.87859	+	1.87859i
$763$	−8.47608e10	+	8.47608e10i	−0.250090	+	0.250090i
$764$		−	6.50191e10i		−	0.190839i
$765$		0			0
$766$	4.60960e11			1.33890
$767$	1.41173e11	+	1.41173e11i	0.407916	+	0.407916i
$768$	1.15866e11	−	1.15866e11i	0.333051	−	0.333051i
$769$		−	3.07549e10i		−	0.0879446i	−0.999033	−	0.0439723i	$-0.985999\pi$
$769$		−	3.07549e10i		−	0.0879446i	0.999033	−	0.0439723i	$-0.0140013\pi$
$770$		0			0
$771$	4.34734e11			1.23029
$772$	−2.41976e10	−	2.41976e10i	−0.0681245	−	0.0681245i
$773$	1.21896e11	−	1.21896e11i	0.341405	−	0.341405i	−0.515490	−	0.856896i	$-0.672390\pi$
$773$	1.21896e11	−	1.21896e11i	0.341405	−	0.341405i	0.856896	+	0.515490i	$0.172390\pi$
$774$			3.50146e11i			0.975629i
$775$		0			0
$776$	−1.84495e11			−0.508789
$777$	−5.64133e9	−	5.64133e9i	−0.0154774	−	0.0154774i
$778$	1.19299e11	−	1.19299e11i	0.325625	−	0.325625i
$779$		−	1.08330e11i		−	0.294170i
$780$		0			0
$781$	−2.11361e11			−0.568094
$782$	−3.24616e11	−	3.24616e11i	−0.868046	−	0.868046i
$783$	1.22239e11	−	1.22239e11i	0.325209	−	0.325209i
$784$		−	3.74853e11i		−	0.992193i
$785$		0			0
$786$	−7.28899e11			−1.90975
$787$	2.26235e9	+	2.26235e9i	0.00589741	+	0.00589741i	0.710049	−	0.704152i	$-0.248673\pi$
$787$	2.26235e9	+	2.26235e9i	0.00589741	+	0.00589741i	−0.704152	+	0.710049i	$0.748673\pi$
$788$	1.64140e10	−	1.64140e10i	0.0425706	−	0.0425706i
$789$		−	2.35501e11i		−	0.607695i
$790$		0			0
$791$	3.28671e10			0.0839567
$792$	1.91778e11	+	1.91778e11i	0.487413	+	0.487413i
$793$	−1.58616e11	+	1.58616e11i	−0.401102	+	0.401102i
$794$		−	1.09139e11i		−	0.274597i
$795$		0			0
$796$	8.88127e9			0.0221219
$797$	−3.08554e11	−	3.08554e11i	−0.764711	−	0.764711i	0.212459	−	0.977170i	$-0.431853\pi$
$797$	−3.08554e11	−	3.08554e11i	−0.764711	−	0.764711i	−0.977170	+	0.212459i	$0.931853\pi$
$798$	6.53828e10	−	6.53828e10i	0.161232	−	0.161232i
$799$			3.69183e11i			0.905846i
$800$		0			0
$801$	−8.19970e11			−1.99190
$802$	4.66626e11	+	4.66626e11i	1.12790	+	1.12790i
$803$	1.77405e11	−	1.77405e11i	0.426682	−	0.426682i
$804$			5.24666e10i			0.125562i
$805$		0			0
$806$	−9.73047e10			−0.230565
$807$	−5.58846e11	−	5.58846e11i	−1.31764	−	1.31764i
$808$	−5.23859e10	+	5.23859e10i	−0.122905	+	0.122905i
$809$		−	3.71836e11i		−	0.868076i	−0.900895	−	0.434038i	$-0.857088\pi$
$809$		−	3.71836e11i		−	0.868076i	0.900895	−	0.434038i	$-0.142912\pi$
$810$		0			0
$811$	7.35802e11			1.70090			0.850448	−	0.526060i	$-0.176331\pi$
$811$	7.35802e11			1.70090			0.850448	+	0.526060i	$0.176331\pi$
$812$	5.09129e9	+	5.09129e9i	0.0117113	+	0.0117113i
$813$	−4.74122e11	+	4.74122e11i	−1.08525	+	1.08525i
$814$		−	1.01665e10i		−	0.0231566i
$815$		0			0
$816$	1.33789e12			3.01758
$817$	−8.80415e10	−	8.80415e10i	−0.197606	−	0.197606i
$818$	−4.19302e11	+	4.19302e11i	−0.936513	+	0.936513i
$819$			8.19712e10i			0.182190i
$820$		0			0
$821$	−5.89174e11			−1.29679			−0.648397	−	0.761303i	$-0.724560\pi$
$821$	−5.89174e11			−1.29679			−0.648397	+	0.761303i	$0.724560\pi$
$822$	−2.29077e11	−	2.29077e11i	−0.501759	−	0.501759i
$823$	6.93799e10	−	6.93799e10i	0.151229	−	0.151229i	−0.627438	−	0.778667i	$-0.715896\pi$
$823$	6.93799e10	−	6.93799e10i	0.151229	−	0.151229i	0.778667	+	0.627438i	$0.215896\pi$
$824$		−	7.39211e11i		−	1.60346i
$825$		0			0
$826$	2.10874e11			0.453004
$827$	6.01415e10	+	6.01415e10i	0.128574	+	0.128574i	0.768465	−	0.639891i	$-0.221021\pi$
$827$	6.01415e10	+	6.01415e10i	0.128574	+	0.128574i	−0.639891	+	0.768465i	$0.721021\pi$
$828$	−3.39123e10	+	3.39123e10i	−0.0721499	+	0.0721499i
$829$		−	8.00261e11i		−	1.69439i	−0.531282	−	0.847195i	$-0.678289\pi$
$829$		−	8.00261e11i		−	1.69439i	0.531282	−	0.847195i	$-0.321711\pi$
$830$		0			0
$831$	−9.87159e11			−2.07006
$832$	−1.19370e11	−	1.19370e11i	−0.249116	−	0.249116i
$833$	5.40350e11	−	5.40350e11i	1.12226	−	1.12226i
$834$			1.26635e12i			2.61752i
$835$		0			0
$836$	1.06939e10			0.0218932
$837$	1.58356e11	+	1.58356e11i	0.322650	+	0.322650i
$838$	1.96105e11	−	1.96105e11i	0.397661	−	0.397661i
$839$			6.08689e11i			1.22842i	0.789142	+	0.614211i	$0.210526\pi$
$839$			6.08689e11i			1.22842i	−0.789142	+	0.614211i	$0.789474\pi$
$840$		0			0
$841$	3.46545e11			0.692749
$842$	−2.43560e11	−	2.43560e11i	−0.484570	−	0.484570i
$843$	−6.48949e11	+	6.48949e11i	−1.28499	+	1.28499i
$844$		−	3.38419e10i		−	0.0666937i
$845$		0			0
$846$	4.24961e11			0.829598
$847$	8.38822e10	+	8.38822e10i	0.162981	+	0.162981i
$848$	4.04492e11	−	4.04492e11i	0.782215	−	0.782215i
$849$			4.80193e11i			0.924241i
$850$		0			0
$851$	−1.62130e10			−0.0309134
$852$	6.99658e10	+	6.99658e10i	0.132778	+	0.132778i
$853$	−3.37705e11	+	3.37705e11i	−0.637883	+	0.637883i	−0.950033	−	0.312150i	$-0.898951\pi$
$853$	−3.37705e11	+	3.37705e11i	−0.637883	+	0.637883i	0.312150	+	0.950033i	$0.398951\pi$
$854$			2.36929e11i			0.445437i
$855$		0			0
$856$	−6.71668e11			−1.25101
$857$	−2.05118e11	−	2.05118e11i	−0.380260	−	0.380260i	0.490935	−	0.871196i	$-0.336655\pi$
$857$	−2.05118e11	−	2.05118e11i	−0.380260	−	0.380260i	−0.871196	+	0.490935i	$0.836655\pi$
$858$	−1.22379e11	+	1.22379e11i	−0.225817	+	0.225817i
$859$			1.00757e12i			1.85056i	0.379281	+	0.925282i	$0.376171\pi$
$859$			1.00757e12i			1.85056i	−0.379281	+	0.925282i	$0.623829\pi$
$860$		0			0
$861$	1.68062e11			0.305814
$862$	2.45550e10	+	2.45550e10i	0.0444746	+	0.0444746i
$863$	−1.70651e11	+	1.70651e11i	−0.307656	+	0.307656i	−0.844000	−	0.536344i	$-0.819805\pi$
$863$	−1.70651e11	+	1.70651e11i	−0.307656	+	0.307656i	0.536344	+	0.844000i	$0.319805\pi$
$864$		−	9.19688e10i		−	0.165039i
$865$		0			0
$866$	−6.89110e11			−1.22523
$867$	1.29400e12	+	1.29400e12i	2.29013	+	2.29013i
$868$	−6.59558e9	+	6.59558e9i	−0.0116191	+	0.0116191i
$869$		−	5.71602e10i		−	0.100234i
$870$		0			0
$871$	1.82238e11			0.316641
$872$	−4.56017e11	−	4.56017e11i	−0.788706	−	0.788706i
$873$	−3.36995e11	+	3.36995e11i	−0.580185	+	0.580185i
$874$		−	1.87909e11i		−	0.322033i
$875$		0			0
$876$	−1.17451e11			−0.199454
$877$	1.79019e11	+	1.79019e11i	0.302623	+	0.302623i	0.842039	−	0.539416i	$-0.181355\pi$
$877$	1.79019e11	+	1.79019e11i	0.302623	+	0.302623i	−0.539416	+	0.842039i	$0.681355\pi$
$878$	−1.85436e11	+	1.85436e11i	−0.312044	+	0.312044i
$879$		−	4.12754e11i		−	0.691411i
$880$		0			0
$881$	−4.12168e10			−0.0684180			−0.0342090	−	0.999415i	$-0.510891\pi$
$881$	−4.12168e10			−0.0684180			−0.0342090	+	0.999415i	$0.510891\pi$
$882$	−6.21989e11	−	6.21989e11i	−1.02780	−	1.02780i
$883$	4.90367e11	−	4.90367e11i	0.806638	−	0.806638i	−0.177486	−	0.984123i	$-0.556796\pi$
$883$	4.90367e11	−	4.90367e11i	0.806638	−	0.806638i	0.984123	+	0.177486i	$0.0567964\pi$
$884$			4.24822e10i			0.0695661i
$885$		0			0
$886$	−1.83344e11			−0.297530
$887$	−5.99973e11	−	5.99973e11i	−0.969253	−	0.969253i	0.0302885	−	0.999541i	$-0.490357\pi$
$887$	−5.99973e11	−	5.99973e11i	−0.969253	−	0.969253i	−0.999541	+	0.0302885i	$0.990357\pi$
$888$	3.03506e10	−	3.03506e10i	0.0488107	−	0.0488107i
$889$		−	2.98235e11i		−	0.477475i
$890$		0			0
$891$	−6.18606e10			−0.0981529
$892$	−7.57453e10	−	7.57453e10i	−0.119645	−	0.119645i
$893$	−1.06853e11	+	1.06853e11i	−0.168028	+	0.168028i
$894$		−	1.17848e12i		−	1.84490i
$895$		0			0
$896$	−2.16682e11			−0.336195
$897$	1.95163e11	+	1.95163e11i	0.301458	+	0.301458i
$898$	1.44557e11	−	1.44557e11i	0.222298	−	0.222298i
$899$		−	1.99114e11i		−	0.304834i
$900$		0			0
$901$	1.16615e12			1.76952
$902$	1.51437e11	+	1.51437e11i	0.228773	+	0.228773i
$903$	1.36587e11	−	1.36587e11i	0.205427	−	0.205427i
$904$			1.76826e11i			0.264773i
$905$		0			0
$906$	1.91748e11			0.284589
$907$	5.29755e11	+	5.29755e11i	0.782791	+	0.782791i	0.980301	−	0.197510i	$-0.0632854\pi$
$907$	5.29755e11	+	5.29755e11i	0.782791	+	0.782791i	−0.197510	+	0.980301i	$0.563285\pi$
$908$	−2.14014e10	+	2.14014e10i	−0.0314847	+	0.0314847i
$909$			1.91374e11i			0.280303i
$910$		0			0
$911$	−4.06858e11			−0.590703			−0.295351	−	0.955389i	$-0.595437\pi$
$911$	−4.06858e11			−0.590703			−0.295351	+	0.955389i	$0.595437\pi$
$912$	3.87227e11	+	3.87227e11i	0.559740	+	0.559740i
$913$	−1.40182e11	+	1.40182e11i	−0.201748	+	0.201748i
$914$		−	1.07570e12i		−	1.54137i
$915$		0			0
$916$	6.81432e10			0.0967922
$917$	1.71611e11	+	1.71611e11i	0.242698	+	0.242698i
$918$	7.61777e11	−	7.61777e11i	1.07265	−	1.07265i
$919$			1.03523e12i			1.45135i	0.688036	+	0.725676i	$0.258473\pi$
$919$			1.03523e12i			1.45135i	−0.688036	+	0.725676i	$0.741527\pi$
$920$		0			0
$921$	9.40473e11			1.30710
$922$	−4.19250e10	−	4.19250e10i	−0.0580163	−	0.0580163i
$923$	2.43020e11	−	2.43020e11i	0.334839	−	0.334839i
$924$			1.65903e10i			0.0227597i
$925$		0			0
$926$	−4.09476e11			−0.556909
$927$	−1.35023e12	−	1.35023e12i	−1.82847	−	1.82847i
$928$	−5.78200e10	+	5.78200e10i	−0.0779626	+	0.0779626i
$929$		−	5.10944e11i		−	0.685978i	−0.939339	−	0.342989i	$-0.888561\pi$
$929$		−	5.10944e11i		−	0.685978i	0.939339	−	0.342989i	$-0.111439\pi$
$930$		0			0
$931$	3.12789e11			0.416345
$932$	−2.53475e10	−	2.53475e10i	−0.0335948	−	0.0335948i
$933$	1.20217e12	−	1.20217e12i	1.58649	−	1.58649i
$934$			5.83746e11i			0.767072i
$935$		0			0
$936$	−4.41008e11			−0.574571
$937$	6.26235e11	+	6.26235e11i	0.812417	+	0.812417i	0.984996	−	0.172579i	$-0.0552099\pi$
$937$	6.26235e11	+	6.26235e11i	0.812417	+	0.812417i	−0.172579	+	0.984996i	$0.555210\pi$
$938$	1.36107e11	−	1.36107e11i	0.175820	−	0.175820i
$939$		−	1.64251e12i		−	2.11273i
$940$		0			0
$941$	5.32097e11			0.678628			0.339314	−	0.940673i	$-0.389805\pi$
$941$	5.32097e11			0.678628			0.339314	+	0.940673i	$0.389805\pi$
$942$	6.93069e11	+	6.93069e11i	0.880183	+	0.880183i
$943$	2.41503e11	−	2.41503e11i	0.305405	−	0.305405i
$944$			1.24889e12i			1.57267i
$945$		0			0
$946$	2.46150e11			0.307352
$947$	6.94903e11	+	6.94903e11i	0.864021	+	0.864021i	0.991802	−	0.127781i	$-0.0407855\pi$
$947$	6.94903e11	+	6.94903e11i	0.864021	+	0.864021i	−0.127781	+	0.991802i	$0.540786\pi$
$948$	−1.89215e10	+	1.89215e10i	−0.0234273	+	0.0234273i
$949$			4.07958e11i			0.502980i
$950$		0			0
$951$	8.94754e11			1.09391
$952$	−2.86140e11	−	2.86140e11i	−0.348362	−	0.348362i
$953$	−1.46903e11	+	1.46903e11i	−0.178098	+	0.178098i	−0.790526	−	0.612428i	$-0.790193\pi$
$953$	−1.46903e11	+	1.46903e11i	−0.178098	+	0.178098i	0.612428	+	0.790526i	$0.290193\pi$
$954$		−	1.34234e12i		−	1.62057i
$955$		0			0
$956$	−3.22191e10			−0.0385728
$957$	−2.50423e11	−	2.50423e11i	−0.298556	−	0.298556i
$958$	−8.75174e11	+	8.75174e11i	−1.03904	+	1.03904i
$959$			1.07867e11i			0.127531i
$960$		0			0
$961$	−5.94946e11			−0.697564
$962$	1.16894e10	+	1.16894e10i	0.0136487	+	0.0136487i
$963$	−1.22686e12	+	1.22686e12i	−1.42655	+	1.42655i
$964$		−	3.58182e10i		−	0.0414758i
$965$		0			0
$966$	2.91519e11			0.334779
$967$	−8.32464e11	−	8.32464e11i	−0.952050	−	0.952050i	0.0468522	−	0.998902i	$-0.485081\pi$
$967$	−8.32464e11	−	8.32464e11i	−0.952050	−	0.952050i	−0.998902	+	0.0468522i	$0.985081\pi$
$968$	−4.51290e11	+	4.51290e11i	−0.513989	+	0.513989i
$969$			1.11637e12i			1.26624i
$970$		0			0
$971$	1.00239e11			0.112761			0.0563804	−	0.998409i	$-0.482044\pi$
$971$	1.00239e11			0.112761			0.0563804	+	0.998409i	$0.482044\pi$
$972$	7.27507e10	+	7.27507e10i	0.0815027	+	0.0815027i
$973$	2.98148e11	−	2.98148e11i	0.332644	−	0.332644i
$974$			6.65481e11i			0.739435i
$975$		0			0
$976$	−1.40320e12			−1.54640
$977$	1.07451e11	+	1.07451e11i	0.117932	+	0.117932i	0.763610	−	0.645678i	$-0.223425\pi$
$977$	1.07451e11	+	1.07451e11i	0.117932	+	0.117932i	−0.645678	+	0.763610i	$0.723425\pi$
$978$	−4.62056e11	+	4.62056e11i	−0.505056	+	0.505056i
$979$			5.76434e11i			0.627507i
$980$		0			0
$981$	−1.66590e12			−1.79876
$982$	−1.38546e11	−	1.38546e11i	−0.148987	−	0.148987i
$983$	−5.36756e10	+	5.36756e10i	−0.0574861	+	0.0574861i	−0.735265	−	0.677779i	$-0.762942\pi$
$983$	−5.36756e10	+	5.36756e10i	−0.0574861	+	0.0574861i	0.677779	+	0.735265i	$0.262942\pi$
$984$			9.04181e11i			0.964439i
$985$		0			0
$986$	−9.57846e11			−1.01342
$987$	−1.65771e11	−	1.65771e11i	−0.174679	−	0.174679i
$988$	−1.22957e10	+	1.22957e10i	−0.0129040	+	0.0129040i
$989$		−	3.92547e11i		−	0.410304i
$990$		0			0
$991$	−1.54321e12			−1.60004			−0.800019	−	0.599974i	$-0.795177\pi$
$991$	−1.54321e12			−1.60004			−0.800019	+	0.599974i	$0.795177\pi$
$992$	−7.49037e10	−	7.49037e10i	−0.0773493	−	0.0773493i
$993$	1.56502e11	−	1.56502e11i	0.160962	−	0.160962i
$994$		−	3.63005e11i		−	0.371850i
$995$		0			0
$996$	9.28076e10			0.0943075
$997$	7.69594e11	+	7.69594e11i	0.778898	+	0.778898i	0.979644	−	0.200745i	$-0.0643363\pi$
$997$	7.69594e11	+	7.69594e11i	0.778898	+	0.778898i	−0.200745	+	0.979644i	$0.564336\pi$
$998$	8.40656e11	−	8.40656e11i	0.847415	−	0.847415i
$999$		−	3.80472e10i		−	0.0381997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.c.b.7.3		6
5.2	odd	4		5.9.c.a.3.1	yes	6
5.3	odd	4	inner	25.9.c.b.18.3		6
5.4	even	2		5.9.c.a.2.1	✓	6
15.2	even	4		45.9.g.a.28.3		6
15.14	odd	2		45.9.g.a.37.3		6
20.7	even	4		80.9.p.c.33.3		6
20.19	odd	2		80.9.p.c.17.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.9.c.a.2.1	✓	6	5.4	even	2
5.9.c.a.3.1	yes	6	5.2	odd	4
25.9.c.b.7.3		6	1.1	even	1	trivial
25.9.c.b.18.3		6	5.3	odd	4	inner
45.9.g.a.28.3		6	15.2	even	4
45.9.g.a.37.3		6	15.14	odd	2
80.9.p.c.17.3		6	20.19	odd	2
80.9.p.c.33.3		6	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.8649 + 11.8649i) q^{2} +(90.9660 - 90.9660i) q^{3} +25.5528i q^{4} +2158.61 q^{6} +(-508.219 - 508.219i) q^{7} +(2734.24 - 2734.24i) q^{8} -9988.61i q^{9} +O(q^{10})\)	\(q+(11.8649 + 11.8649i) q^{2} +(90.9660 - 90.9660i) q^{3} +25.5528i q^{4} +2158.61 q^{6} +(-508.219 - 508.219i) q^{7} +(2734.24 - 2734.24i) q^{8} -9988.61i q^{9} -7021.93 q^{11} +(2324.44 + 2324.44i) q^{12} +(8073.75 - 8073.75i) q^{13} -12060.0i q^{14} +71424.6 q^{16} +(102958. + 102958. i) q^{17} +(118514. - 118514. i) q^{18} +59599.0i q^{19} -92461.2 q^{21} +(-83314.7 - 83314.7i) q^{22} +(-132866. + 132866. i) q^{23} -497445. i q^{24} +191589. q^{26} +(-311796. - 311796. i) q^{27} +(12986.4 - 12986.4i) q^{28} +392047. i q^{29} -507883. q^{31} +(147482. + 147482. i) q^{32} +(-638757. + 638757. i) q^{33} +2.44319e6i q^{34} +255237. q^{36} +(61012.9 + 61012.9i) q^{37} +(-707137. + 707137. i) q^{38} -1.46887e6i q^{39} -1.81765e6 q^{41} +(-1.09705e6 - 1.09705e6i) q^{42} +(-1.47723e6 + 1.47723e6i) q^{43} -179430. i q^{44} -3.15288e6 q^{46} +(1.79287e6 + 1.79287e6i) q^{47} +(6.49721e6 - 6.49721e6i) q^{48} -5.24823e6i q^{49} +1.87314e7 q^{51} +(206307. + 206307. i) q^{52} +(5.66320e6 - 5.66320e6i) q^{53} -7.39887e6i q^{54} -2.77918e6 q^{56} +(5.42148e6 + 5.42148e6i) q^{57} +(-4.65161e6 + 4.65161e6i) q^{58} +1.74855e7i q^{59} -1.96459e7 q^{61} +(-6.02599e6 - 6.02599e6i) q^{62} +(-5.07640e6 + 5.07640e6i) q^{63} -1.47850e7i q^{64} -1.51576e7 q^{66} +(1.12859e7 + 1.12859e7i) q^{67} +(-2.63088e6 + 2.63088e6i) q^{68} +2.41725e7i q^{69} +3.01001e7 q^{71} +(-2.73112e7 - 2.73112e7i) q^{72} +(-2.52645e7 + 2.52645e7i) q^{73} +1.44783e6i q^{74} -1.52292e6 q^{76} +(3.56868e6 + 3.56868e6i) q^{77} +(1.74281e7 - 1.74281e7i) q^{78} +8.14025e6i q^{79} +8.80962e6 q^{81} +(-2.15663e7 - 2.15663e7i) q^{82} +(1.99635e7 - 1.99635e7i) q^{83} -2.36265e6i q^{84} -3.50545e7 q^{86} +(3.56630e7 + 3.56630e7i) q^{87} +(-1.91996e7 + 1.91996e7i) q^{88} -8.20905e7i q^{89} -8.20646e6 q^{91} +(-3.39509e6 - 3.39509e6i) q^{92} +(-4.62000e7 + 4.62000e7i) q^{93} +4.25446e7i q^{94} +2.68317e7 q^{96} +(-3.37379e7 - 3.37379e7i) q^{97} +(6.22698e7 - 6.22698e7i) q^{98} +7.01393e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8	\( 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8} + 23192 q^{11} + 45912 q^{12} + 119142 q^{13} + 218616 q^{16} + 265502 q^{17} + 454062 q^{18} + 231672 q^{21} + 35664 q^{22} - 28888 q^{23} - 801388 q^{26} - 392040 q^{27} - 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} - 4269096 q^{33} - 3972804 q^{36} + 454002 q^{37} - 1443720 q^{38} + 2489432 q^{41} - 4223856 q^{42} - 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} + 21677712 q^{48} + 35567712 q^{51} + 735732 q^{52} + 13509122 q^{53} - 18454800 q^{56} + 34625520 q^{57} + 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} - 44837688 q^{63} - 55047936 q^{66} + 32827752 q^{67} - 8118692 q^{68} - 13992928 q^{71} - 82596420 q^{72} - 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 31125576 q^{78} + 65834226 q^{81} - 38023056 q^{82} + 14768432 q^{83} - 135560008 q^{86} + 133207680 q^{87} + 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} + 96798024 q^{93} + 184867872 q^{96} + 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8 + 23192 * q^11 + 45912 * q^12 + 119142 * q^13 + 218616 * q^16 + 265502 * q^17 + 454062 * q^18 + 231672 * q^21 + 35664 * q^22 - 28888 * q^23 - 801388 * q^26 - 392040 * q^27 - 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 - 4269096 * q^33 - 3972804 * q^36 + 454002 * q^37 - 1443720 * q^38 + 2489432 * q^41 - 4223856 * q^42 - 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 + 21677712 * q^48 + 35567712 * q^51 + 735732 * q^52 + 13509122 * q^53 - 18454800 * q^56 + 34625520 * q^57 + 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 - 44837688 * q^63 - 55047936 * q^66 + 32827752 * q^67 - 8118692 * q^68 - 13992928 * q^71 - 82596420 * q^72 - 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 31125576 * q^78 + 65834226 * q^81 - 38023056 * q^82 + 14768432 * q^83 - 135560008 * q^86 + 133207680 * q^87 + 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 + 96798024 * q^93 + 184867872 * q^96 + 186656202 * q^97 + 345959698 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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