LMFDB - Embedded newform 3.25.b.b.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,25,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 25, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 25);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, 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:	$10.9490145677$
Analytic rank:	$0$
Dimension:	$6$
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} + 253102x^{4} + 17425276096x^{2} + 250659115499520 $ x^6 + 253102x^4 + 17425276096x^2 + 250659115499520
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{13}\cdot 3^{24}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.2
Root			$-298.476i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.25.b.b.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5372.56i q^{2} +(-24323.9 + 530884. i) q^{3} -1.20872e7 q^{4} -5.28531e7i q^{5} +(2.85221e9 + 1.30681e8i) q^{6} +2.07202e10 q^{7} -2.51975e10i q^{8} +(-2.81246e11 - 2.58263e10i) q^{9} +O(q^{10})$	\(q-5372.56i q^{2} +(-24323.9 + 530884. i) q^{3} -1.20872e7 q^{4} -5.28531e7i q^{5} +(2.85221e9 + 1.30681e8i) q^{6} +2.07202e10 q^{7} -2.51975e10i q^{8} +(-2.81246e11 - 2.58263e10i) q^{9} -2.83957e11 q^{10} -3.54125e12i q^{11} +(2.94007e11 - 6.41689e12i) q^{12} +1.35964e13 q^{13} -1.11321e14i q^{14} +(2.80589e13 + 1.28559e12i) q^{15} -3.38164e14 q^{16} -3.86175e14i q^{17} +(-1.38753e14 + 1.51101e15i) q^{18} +3.34561e15 q^{19} +6.38845e14i q^{20} +(-5.03995e14 + 1.10000e16i) q^{21} -1.90256e16 q^{22} -2.15008e16i q^{23} +(1.33770e16 + 6.12901e14i) q^{24} +5.68112e16 q^{25} -7.30474e16i q^{26} +(2.05518e16 - 1.48681e17i) q^{27} -2.50449e17 q^{28} +4.45640e17i q^{29} +(6.90692e15 - 1.50748e17i) q^{30} +1.28791e17 q^{31} +1.39406e18i q^{32} +(1.87999e18 + 8.61369e16i) q^{33} -2.07475e18 q^{34} -1.09513e18i q^{35} +(3.39947e18 + 3.12167e17i) q^{36} -7.59778e18 q^{37} -1.79745e19i q^{38} +(-3.30717e17 + 7.21811e18i) q^{39} -1.33177e18 q^{40} +3.81470e18i q^{41} +(5.90983e19 + 2.70774e18i) q^{42} -4.20156e19 q^{43} +4.28037e19i q^{44} +(-1.36500e18 + 1.48647e19i) q^{45} -1.15514e20 q^{46} +1.58270e20i q^{47} +(8.22546e18 - 1.79526e20i) q^{48} +2.37745e20 q^{49} -3.05222e20i q^{50} +(2.05014e20 + 9.39326e18i) q^{51} -1.64342e20 q^{52} -9.55171e18i q^{53} +(-7.98797e20 - 1.10416e20i) q^{54} -1.87166e20 q^{55} -5.22097e20i q^{56} +(-8.13783e19 + 1.77613e21i) q^{57} +2.39423e21 q^{58} +1.20754e21i q^{59} +(-3.39153e20 - 1.55392e19i) q^{60} +6.21416e20 q^{61} -6.91938e20i q^{62} +(-5.82748e21 - 5.35126e20i) q^{63} +1.81624e21 q^{64} -7.18612e20i q^{65} +(4.62776e20 - 1.01004e22i) q^{66} -7.90979e20 q^{67} +4.66776e21i q^{68} +(1.14144e22 + 5.22982e20i) q^{69} -5.88364e21 q^{70} -7.83792e21i q^{71} +(-6.50758e20 + 7.08670e21i) q^{72} +6.11332e21 q^{73} +4.08195e22i q^{74} +(-1.38187e21 + 3.01602e22i) q^{75} -4.04390e22 q^{76} -7.33754e22i q^{77} +(3.87797e22 + 1.77680e21i) q^{78} -3.59198e22 q^{79} +1.78730e22i q^{80} +(7.84324e22 + 1.45271e22i) q^{81} +2.04947e22 q^{82} -1.44479e23i q^{83} +(6.09188e21 - 1.32959e23i) q^{84} -2.04105e22 q^{85} +2.25731e23i q^{86} +(-2.36583e23 - 1.08397e22i) q^{87} -8.92307e22 q^{88} +1.68834e23i q^{89} +(7.98617e22 + 7.33355e21i) q^{90} +2.81720e23 q^{91} +2.59884e23i q^{92} +(-3.13270e21 + 6.83732e22i) q^{93} +8.50312e23 q^{94} -1.76826e23i q^{95} +(-7.40086e23 - 3.39090e22i) q^{96} -6.67785e23 q^{97} -1.27730e24i q^{98} +(-9.14574e22 + 9.95963e23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9}+O(q^{10}) $ 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9	$ 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9} + 2770823311200 q^{10} - 18492861842352 q^{12} - 73542438063924 q^{13} + 227151045057600 q^{15} - 433335898904448 q^{16} - 12\!\cdots\!40 q^{18}+ \cdots - 18\!\cdots\!20 q^{99}+O(q^{100}) $ 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9 + 2770823311200 * q^10 - 18492861842352 * q^12 - 73542438063924 * q^13 + 227151045057600 * q^15 - 433335898904448 * q^16 - 1227888881468640 * q^18 + 6095219493474156 * q^19 + 2706110098936524 * q^21 - 4132747004902560 * q^22 + 79223562819483264 * q^24 - 206274704562968250 * q^25 - 153687400093414602 * q^27 + 11425252275435936 * q^28 + 1679034252186079200 * q^30 - 1137843910975220628 * q^31 + 7067811391497299520 * q^33 - 15440589345121992576 * q^34 + 23041875850704576144 * q^36 - 14032623495718823604 * q^37 + 25380736596180392364 * q^39 - 121930725979226707200 * q^40 + 209343891033396594720 * q^42 - 114603298148542353684 * q^43 + 311304965429932790400 * q^45 - 346860905830754272704 * q^46 + 51162839242132733568 * q^48 + 107947782097205854482 * q^49 - 479022139696737883392 * q^51 - 124107229893322470624 * q^52 - 1113391638534691344528 * q^54 + 1679273232066520675200 * q^55 - 1140401446469855973684 * q^57 + 7395366373865537628960 * q^58 - 14436777252623118393600 * q^60 + 10013078414594836175052 * q^61 - 8325410033672205875604 * q^63 + 11741892494977734042624 * q^64 - 5418873997530695523360 * q^66 - 5445087092431082846484 * q^67 + 11943290073056639859072 * q^69 - 55632387081854182017600 * q^70 + 63773250138227244591360 * q^72 + 7228988839203443040396 * q^73 + 37723327374597984717750 * q^75 - 4244116415001816243552 * q^76 + 235720510135983845200800 * q^78 - 423484844106082827915924 * q^79 + 102726090691231740574086 * q^81 - 272255725325320387035840 * q^82 + 200996808333809534079264 * q^84 + 319008824808936798988800 * q^85 - 252430535429613815803200 * q^87 + 160152458683551892335360 * q^88 - 1246806301659161625597600 * q^90 + 1497033316223591396871768 * q^91 - 501165623869166897253684 * q^93 + 1979316836866080826257024 * q^94 - 1420600675222724601424896 * q^96 - 1411607470255832450422644 * q^97 - 1834460043482282449115520 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	5372.56i		−	1.31166i	−0.754909	−	0.655830i	$-0.772319\pi$
$2$		−	5372.56i		−	1.31166i	0.754909	−	0.655830i	$-0.227681\pi$
$3$	−24323.9	+	530884.i	−0.0457696	+	0.998952i
$3$	−24323.9	+	530884.i	−0.0457696	+	0.998952i
$4$	−1.20872e7			−0.720452
$5$		−	5.28531e7i		−	0.216486i	−0.994124	−	0.108243i	$-0.965477\pi$
$5$		−	5.28531e7i		−	0.216486i	0.994124	−	0.108243i	$-0.0345225\pi$
$6$	2.85221e9	+	1.30681e8i	1.31029	+	0.0600342i
$7$	2.07202e10			1.49699			0.748493	−	0.663143i	$-0.230778\pi$
$7$	2.07202e10			1.49699			0.748493	+	0.663143i	$0.230778\pi$
$8$		−	2.51975e10i		−	0.366672i
$9$	−2.81246e11	−	2.58263e10i	−0.995810	−	0.0914433i
$10$	−2.83957e11			−0.283957
$11$		−	3.54125e12i		−	1.12835i	−0.825655	−	0.564176i	$-0.809194\pi$
$11$		−	3.54125e12i		−	1.12835i	0.825655	−	0.564176i	$-0.190806\pi$
$12$	2.94007e11	−	6.41689e12i	0.0329748	−	0.719697i
$13$	1.35964e13			0.583584			0.291792	−	0.956482i	$-0.405748\pi$
$13$	1.35964e13			0.583584			0.291792	+	0.956482i	$0.405748\pi$
$14$		−	1.11321e14i		−	1.96354i
$15$	2.80589e13	+	1.28559e12i	0.216260	+	0.00990850i
$16$	−3.38164e14			−1.20140
$17$		−	3.86175e14i		−	0.662822i	−0.943487	−	0.331411i	$-0.892475\pi$
$17$		−	3.86175e14i		−	0.662822i	0.943487	−	0.331411i	$-0.107525\pi$
$18$	−1.38753e14	+	1.51101e15i	−0.119943	+	1.30616i
$19$	3.34561e15			1.51159			0.755793	−	0.654811i	$-0.227252\pi$
$19$	3.34561e15			1.51159			0.755793	+	0.654811i	$0.227252\pi$
$20$			6.38845e14i			0.155968i
$21$	−5.03995e14	+	1.10000e16i	−0.0685165	+	1.49542i
$22$	−1.90256e16			−1.48001
$23$		−	2.15008e16i		−	0.981115i	−0.871409	−	0.490558i	$-0.836793\pi$
$23$		−	2.15008e16i		−	0.981115i	0.871409	−	0.490558i	$-0.163207\pi$
$24$	1.33770e16	+	6.12901e14i	0.366288	+	0.0167824i
$25$	5.68112e16			0.953134
$26$		−	7.30474e16i		−	0.765464i
$27$	2.05518e16	−	1.48681e17i	0.136925	−	0.990581i
$28$	−2.50449e17			−1.07851
$29$			4.45640e17i			1.25953i	0.776786	+	0.629765i	$0.216849\pi$
$29$			4.45640e17i			1.25953i	−0.776786	+	0.629765i	$0.783151\pi$
$30$	6.90692e15	−	1.50748e17i	0.0129966	−	0.283659i
$31$	1.28791e17			0.163511			0.0817553	−	0.996652i	$-0.473947\pi$
$31$	1.28791e17			0.163511			0.0817553	+	0.996652i	$0.473947\pi$
$32$			1.39406e18i			1.20916i
$33$	1.87999e18	+	8.61369e16i	1.12717	+	0.0516442i
$34$	−2.07475e18			−0.869397
$35$		−	1.09513e18i		−	0.324077i
$36$	3.39947e18	+	3.12167e17i	0.717434	+	0.0658805i
$37$	−7.59778e18			−1.15416			−0.577080	−	0.816687i	$-0.695808\pi$
$37$	−7.59778e18			−1.15416			−0.577080	+	0.816687i	$0.695808\pi$
$38$		−	1.79745e19i		−	1.98269i
$39$	−3.30717e17	+	7.21811e18i	−0.0267104	+	0.582973i
$40$	−1.33177e18			−0.0793795
$41$			3.81470e18i			0.169065i	0.996421	+	0.0845325i	$0.0269397\pi$
$41$			3.81470e18i			0.169065i	−0.996421	+	0.0845325i	$0.973060\pi$
$42$	5.90983e19	+	2.70774e18i	1.96148	+	0.0898703i
$43$	−4.20156e19			−1.05145			−0.525725	−	0.850654i	$-0.676206\pi$
$43$	−4.20156e19			−1.05145			−0.525725	+	0.850654i	$0.676206\pi$
$44$			4.28037e19i			0.812923i
$45$	−1.36500e18	+	1.48647e19i	−0.0197962	+	0.215579i
$46$	−1.15514e20			−1.28689
$47$			1.58270e20i			1.36214i	0.732217	+	0.681072i	$0.238486\pi$
$47$			1.58270e20i			1.36214i	−0.732217	+	0.681072i	$0.761514\pi$
$48$	8.22546e18	−	1.79526e20i	0.0549877	−	1.20014i
$49$	2.37745e20			1.24096
$50$		−	3.05222e20i		−	1.25019i
$51$	2.05014e20	+	9.39326e18i	0.662127	+	0.0303371i
$52$	−1.64342e20			−0.420444
$53$		−	9.55171e18i		−	0.0194433i	−0.999953	−	0.00972166i	$-0.996905\pi$
$53$		−	9.55171e18i		−	0.0194433i	0.999953	−	0.00972166i	$-0.00309455\pi$
$54$	−7.98797e20	−	1.10416e20i	−1.29931	−	0.179600i
$55$	−1.87166e20			−0.244273
$56$		−	5.22097e20i		−	0.548902i
$57$	−8.13783e19	+	1.77613e21i	−0.0691847	+	1.51000i
$58$	2.39423e21			1.65207
$59$			1.20754e21i			0.678698i	0.940661	+	0.339349i	$0.110207\pi$
$59$			1.20754e21i			0.678698i	−0.940661	+	0.339349i	$0.889793\pi$
$60$	−3.39153e20	−	1.55392e19i	−0.155805	−	0.00713860i
$61$	6.21416e20			0.234112			0.117056	−	0.993125i	$-0.462654\pi$
$61$	6.21416e20			0.234112			0.117056	+	0.993125i	$0.462654\pi$
$62$		−	6.91938e20i		−	0.214470i
$63$	−5.82748e21	−	5.35126e20i	−1.49071	−	0.136889i
$64$	1.81624e21			0.384603
$65$		−	7.18612e20i		−	0.126338i
$66$	4.62776e20	−	1.01004e22i	0.0677397	−	1.47846i
$67$	−7.90979e20			−0.0966645			−0.0483323	−	0.998831i	$-0.515391\pi$
$67$	−7.90979e20			−0.0966645			−0.0483323	+	0.998831i	$0.515391\pi$
$68$			4.66776e21i			0.477531i
$69$	1.14144e22	+	5.22982e20i	0.980087	+	0.0449053i
$70$	−5.88364e21			−0.425079
$71$		−	7.83792e21i		−	0.477640i	−0.971064	−	0.238820i	$-0.923239\pi$
$71$		−	7.83792e21i		−	0.477640i	0.971064	−	0.238820i	$-0.0767606\pi$
$72$	−6.50758e20	+	7.08670e21i	−0.0335297	+	0.365136i
$73$	6.11332e21			0.266933			0.133467	−	0.991053i	$-0.457389\pi$
$73$	6.11332e21			0.266933			0.133467	+	0.991053i	$0.457389\pi$
$74$			4.08195e22i			1.51387i
$75$	−1.38187e21	+	3.01602e22i	−0.0436246	+	0.952135i
$76$	−4.04390e22			−1.08902
$77$		−	7.33754e22i		−	1.68913i
$78$	3.87797e22	+	1.77680e21i	0.764662	+	0.0350350i
$79$	−3.59198e22			−0.607868			−0.303934	−	0.952693i	$-0.598300\pi$
$79$	−3.59198e22			−0.607868			−0.303934	+	0.952693i	$0.598300\pi$
$80$			1.78730e22i			0.260087i
$81$	7.84324e22	+	1.45271e22i	0.983276	+	0.182120i
$82$	2.04947e22			0.221756
$83$		−	1.44479e23i		−	1.35166i	−0.737058	−	0.675829i	$-0.763786\pi$
$83$		−	1.44479e23i		−	1.35166i	0.737058	−	0.675829i	$-0.236214\pi$
$84$	6.09188e21	−	1.32959e23i	0.0493628	−	1.07738i
$85$	−2.04105e22			−0.143492
$86$			2.25731e23i			1.37915i
$87$	−2.36583e23	−	1.08397e22i	−1.25821	−	0.0576482i
$88$	−8.92307e22			−0.413735
$89$			1.68834e23i			0.683566i	0.939779	+	0.341783i	$0.111031\pi$
$89$			1.68834e23i			0.683566i	−0.939779	+	0.341783i	$0.888969\pi$
$90$	7.98617e22	+	7.33355e21i	0.282767	+	0.0259659i
$91$	2.81720e23			0.873617
$92$			2.59884e23i			0.706846i
$93$	−3.13270e21	+	6.83732e22i	−0.00748382	+	0.163339i
$94$	8.50312e23			1.78667
$95$		−	1.76826e23i		−	0.327238i
$96$	−7.40086e23	−	3.39090e22i	−1.20789	−	0.0553427i
$97$	−6.67785e23			−0.962445			−0.481222	−	0.876599i	$-0.659807\pi$
$97$	−6.67785e23			−0.962445			−0.481222	+	0.876599i	$0.659807\pi$
$98$		−	1.27730e24i		−	1.62772i
$99$	−9.14574e22	+	9.95963e23i	−0.103180	+	1.12362i
$100$	−6.86687e23			−0.686687
$101$		−	4.87793e23i		−	0.432892i	−0.976295	−	0.216446i	$-0.930554\pi$
$101$		−	4.87793e23i		−	0.432892i	0.976295	−	0.216446i	$-0.0694465\pi$
$102$	5.04658e22	−	1.10145e24i	0.0397920	−	0.868486i
$103$	2.17648e24			1.52654			0.763269	−	0.646081i	$-0.223593\pi$
$103$	2.17648e24			1.52654			0.763269	+	0.646081i	$0.223593\pi$
$104$		−	3.42595e23i		−	0.213984i
$105$	5.81386e23	+	2.66377e22i	0.323737	+	0.0148329i
$106$	−5.13171e22			−0.0255030
$107$			3.42273e24i			1.51974i	0.650078	+	0.759868i	$0.274736\pi$
$107$			3.42273e24i			1.51974i	−0.650078	+	0.759868i	$0.725264\pi$
$108$	−2.48413e23	+	1.79713e24i	−0.0986482	+	0.713666i
$109$	−1.25999e24			−0.447970			−0.223985	−	0.974593i	$-0.571907\pi$
$109$	−1.25999e24			−0.447970			−0.223985	+	0.974593i	$0.571907\pi$
$110$			1.00556e24i			0.320403i
$111$	1.84807e23	−	4.03354e24i	0.0528255	−	1.15295i
$112$	−7.00683e24			−1.79848
$113$			4.34828e24i			1.00317i	0.865107	+	0.501587i	$0.167250\pi$
$113$			4.34828e24i			1.00317i	−0.865107	+	0.501587i	$0.832750\pi$
$114$	9.54238e24	+	4.37210e23i	1.98061	+	0.0907468i
$115$	−1.13638e24			−0.212398
$116$		−	5.38653e24i		−	0.907431i
$117$	−3.82393e24	−	3.51145e23i	−0.581139	−	0.0533649i
$118$	6.48757e24			0.890221
$119$		−	8.00162e24i		−	0.992234i
$120$	3.23937e22	−	7.07014e23i	0.00363317	−	0.0792963i
$121$	−2.69073e24			−0.273178
$122$		−	3.33859e24i		−	0.307076i
$123$	−2.02516e24	−	9.27881e22i	−0.168888	−	0.00773804i
$124$	−1.55672e24			−0.117802
$125$		−	6.15294e24i		−	0.422827i
$126$	−2.87500e24	+	3.13085e25i	−0.179552	+	1.95531i
$127$	−1.25873e24			−0.0714970			−0.0357485	−	0.999361i	$-0.511382\pi$
$127$	−1.25873e24			−0.0714970			−0.0357485	+	0.999361i	$0.511382\pi$
$128$			1.36307e25i			0.704690i
$129$	1.02198e24	−	2.23054e25i	0.0481245	−	1.05035i
$130$	−3.86078e24			−0.165713
$131$			2.41316e25i			0.944780i	0.881390	+	0.472390i	$0.156609\pi$
$131$			2.41316e25i			0.944780i	−0.881390	+	0.472390i	$0.843391\pi$
$132$	−2.27238e25	−	1.04115e24i	−0.812071	−	0.0372072i
$133$	6.93218e25			2.26282
$134$			4.24958e24i			0.126791i
$135$	−7.85825e24	−	1.08623e24i	−0.214447	−	0.0296425i
$136$	−9.73064e24			−0.243038
$137$		−	2.06918e25i		−	0.473317i	−0.971593	−	0.236659i	$-0.923948\pi$
$137$		−	2.06918e25i		−	0.473317i	0.971593	−	0.236659i	$-0.0760523\pi$
$138$	2.80975e24	−	6.13246e25i	0.0589005	−	1.28554i
$139$	−1.34700e25			−0.258935			−0.129467	−	0.991584i	$-0.541327\pi$
$139$	−1.34700e25			−0.258935			−0.129467	+	0.991584i	$0.541327\pi$
$140$			1.32370e25i			0.233482i
$141$	−8.40228e25	−	3.84973e24i	−1.36072	−	0.0623448i
$142$	−4.21097e25			−0.626501
$143$		−	4.81482e25i		−	0.658488i
$144$	9.51074e25	+	8.73353e24i	1.19637	+	0.109860i
$145$	2.35535e25			0.272671
$146$		−	3.28442e25i		−	0.350126i
$147$	−5.78289e24	+	1.26215e26i	−0.0567985	+	1.23966i
$148$	9.18358e25			0.831517
$149$			1.15098e26i			0.961237i	0.876930	+	0.480619i	$0.159588\pi$
$149$			1.15098e26i			0.961237i	−0.876930	+	0.480619i	$0.840412\pi$
$150$	1.62037e26	+	7.42417e24i	1.24888	+	0.0572206i
$151$	−1.03694e26			−0.737955			−0.368978	−	0.929438i	$-0.620292\pi$
$151$	−1.03694e26			−0.737955			−0.368978	+	0.929438i	$0.620292\pi$
$152$		−	8.43011e25i		−	0.554256i
$153$	−9.97346e24	+	1.08610e26i	−0.0606106	+	0.660045i
$154$	−3.94214e26			−2.21556
$155$		−	6.80702e24i		−	0.0353978i
$156$	3.99743e24	−	8.72466e25i	0.0192436	−	0.420004i
$157$	8.11385e25			0.361769			0.180884	−	0.983504i	$-0.442104\pi$
$157$	8.11385e25			0.361769			0.180884	+	0.983504i	$0.442104\pi$
$158$			1.92982e26i			0.797316i
$159$	5.07085e24	+	2.32334e23i	0.0194229	+	0.000889914i
$160$	7.36806e25			0.261766
$161$		−	4.45500e26i		−	1.46871i
$162$	7.80477e25	−	4.21383e26i	0.238880	−	1.28972i
$163$	6.89069e26			1.95890			0.979449	−	0.201693i	$-0.0646444\pi$
$163$	6.89069e26			1.95890			0.979449	+	0.201693i	$0.0646444\pi$
$164$		−	4.61089e25i		−	0.121803i
$165$	4.55260e24	−	9.93635e25i	0.0111803	−	0.244017i
$166$	−7.76221e26			−1.77292
$167$			8.62977e26i			1.83401i	0.398877	+	0.917004i	$0.369400\pi$
$167$			8.62977e26i			1.83401i	−0.398877	+	0.917004i	$0.630600\pi$
$168$	2.77173e26	+	1.26994e25i	0.548327	+	0.0251231i
$169$	−3.57939e26			−0.659430
$170$			1.09657e26i			0.188213i
$171$	−9.40941e26	−	8.64048e25i	−1.50525	−	0.138224i
$172$	5.07850e26			0.757520
$173$		−	8.85100e26i		−	1.23151i	−0.787936	−	0.615757i	$-0.788850\pi$
$173$		−	8.85100e26i		−	1.23151i	0.787936	−	0.615757i	$-0.211150\pi$
$174$	−5.82369e25	+	1.27106e27i	−0.0756149	+	1.65034i
$175$	1.17714e27			1.42683
$176$			1.19752e27i			1.35560i
$177$	−6.41063e26	−	2.93720e25i	−0.677987	−	0.0310638i
$178$	9.07071e26			0.896606
$179$		−	1.01430e27i		−	0.937408i	−0.883355	−	0.468704i	$-0.844721\pi$
$179$		−	1.01430e27i		−	0.937408i	0.883355	−	0.468704i	$-0.155279\pi$
$180$	1.64990e25	−	1.79673e26i	0.0142622	−	0.155315i
$181$	−3.12948e26			−0.253122			−0.126561	−	0.991959i	$-0.540394\pi$
$181$	−3.12948e26			−0.253122			−0.126561	+	0.991959i	$0.540394\pi$
$182$		−	1.51356e27i		−	1.14589i
$183$	−1.51152e25	+	3.29900e26i	−0.0107152	+	0.233867i
$184$	−5.41766e26			−0.359747
$185$			4.01567e26i			0.249860i
$186$	3.67339e26	+	1.68306e25i	0.214246	+	0.00981623i
$187$	−1.36754e27			−0.747896
$188$		−	1.91303e27i		−	0.981359i
$189$	4.25837e26	−	3.08070e27i	0.204975	−	1.48289i
$190$	−9.50009e26			−0.429225
$191$			3.12120e27i			1.32410i	0.749459	+	0.662051i	$0.230314\pi$
$191$			3.12120e27i			1.32410i	−0.749459	+	0.662051i	$0.769686\pi$
$192$	−4.41779e25	+	9.64210e26i	−0.0176031	+	0.384200i
$193$	2.37406e27			0.888801			0.444401	−	0.895828i	$-0.353417\pi$
$193$	2.37406e27			0.888801			0.444401	+	0.895828i	$0.353417\pi$
$194$			3.58771e27i			1.26240i
$195$	3.81500e26	+	1.74794e25i	0.126206	+	0.00578245i
$196$	−2.87367e27			−0.894055
$197$		−	4.35660e26i		−	0.127513i	−0.997965	−	0.0637563i	$-0.979692\pi$
$197$		−	4.35660e26i		−	0.127513i	0.997965	−	0.0637563i	$-0.0203080\pi$
$198$	5.35087e27	+	4.91360e26i	1.47381	+	0.135337i
$199$	2.66734e26			0.0691578			0.0345789	−	0.999402i	$-0.488991\pi$
$199$	2.66734e26			0.0691578			0.0345789	+	0.999402i	$0.488991\pi$
$200$		−	1.43150e27i		−	0.349487i
$201$	1.92397e25	−	4.19918e26i	0.00442430	−	0.0965632i
$202$	−2.62070e27			−0.567807
$203$			9.23375e27i			1.88550i
$204$	−2.47804e27	−	1.13538e26i	−0.477031	−	0.0218564i
$205$	2.01619e26			0.0366003
$206$		−	1.16933e28i		−	2.00230i
$207$	−5.55285e26	+	6.04701e27i	−0.0897164	+	0.977004i
$208$	−4.59781e27			−0.701118
$209$		−	1.18477e28i		−	1.70560i
$210$	1.43113e26	−	3.12353e27i	0.0194557	−	0.424633i
$211$	−3.71009e27			−0.476426			−0.238213	−	0.971213i	$-0.576562\pi$
$211$	−3.71009e27			−0.476426			−0.238213	+	0.971213i	$0.576562\pi$
$212$			1.15453e26i			0.0140080i
$213$	4.16103e27	+	1.90648e26i	0.477139	+	0.0218614i
$214$	1.83888e28			1.99338
$215$			2.22065e27i			0.227625i
$216$	−3.74639e27	−	5.17853e26i	−0.363218	−	0.0502067i
$217$	2.66858e27			0.244773
$218$			6.76937e27i			0.587585i
$219$	−1.48699e26	+	3.24546e27i	−0.0122174	+	0.266653i
$220$	2.26231e27			0.175987
$221$		−	5.25058e27i		−	0.386812i
$222$	−2.16704e28	−	9.92889e26i	−1.51228	−	0.0692891i
$223$	−1.17423e28			−0.776414			−0.388207	−	0.921572i	$-0.626905\pi$
$223$	−1.17423e28			−0.776414			−0.388207	+	0.921572i	$0.626905\pi$
$224$			2.88853e28i			1.81009i
$225$	−1.59779e28	−	1.46722e27i	−0.949140	−	0.0871577i
$226$	2.33614e28			1.31582
$227$			1.53934e28i			0.822291i	0.911570	+	0.411146i	$0.134871\pi$
$227$			1.53934e28i			0.822291i	−0.911570	+	0.411146i	$0.865129\pi$
$228$	9.83634e26	−	2.14684e28i	0.0498443	−	1.08788i
$229$	−7.52008e27			−0.361574			−0.180787	−	0.983522i	$-0.557864\pi$
$229$	−7.52008e27			−0.361574			−0.180787	+	0.983522i	$0.557864\pi$
$230$			6.10528e27i			0.278594i
$231$	3.89538e28	+	1.78477e27i	1.68736	+	0.0773107i
$232$	1.12290e28			0.461834
$233$		−	4.31427e28i		−	1.68514i	−0.538586	−	0.842571i	$-0.681041\pi$
$233$		−	4.31427e28i		−	1.68514i	0.538586	−	0.842571i	$-0.318959\pi$
$234$	−1.88654e27	+	2.05443e28i	−0.0699966	+	0.762257i
$235$	8.36504e27			0.294886
$236$		−	1.45957e28i		−	0.488969i
$237$	8.73709e26	−	1.90693e28i	0.0278219	−	0.607231i
$238$	−4.29892e28			−1.30147
$239$		−	2.88384e28i		−	0.830226i	−0.909770	−	0.415113i	$-0.863742\pi$
$239$		−	2.88384e28i		−	0.830226i	0.909770	−	0.415113i	$-0.136258\pi$
$240$	−9.48851e27	−	4.34741e26i	−0.259814	−	0.0119041i
$241$	−2.56842e28			−0.669055			−0.334528	−	0.942386i	$-0.608577\pi$
$241$	−2.56842e28			−0.669055			−0.334528	+	0.942386i	$0.608577\pi$
$242$			1.44561e28i			0.358316i
$243$	−9.61999e27	+	4.12852e28i	−0.226934	+	0.973910i
$244$	−7.51117e27			−0.168667
$245$		−	1.25656e28i		−	0.268652i
$246$	−4.98510e26	+	1.08803e28i	−0.0101497	+	0.221523i
$247$	4.54883e28			0.882137
$248$		−	3.24522e27i		−	0.0599547i
$249$	7.67015e28	+	3.51428e27i	1.35024	+	0.0618649i
$250$	−3.30570e28			−0.554605
$251$			7.85609e28i			1.25638i	0.778059	+	0.628191i	$0.216204\pi$
$251$			7.85609e28i			1.25638i	−0.778059	+	0.628191i	$0.783796\pi$
$252$	7.04378e28	+	6.46817e27i	1.07399	+	0.0986222i
$253$	−7.61396e28			−1.10704
$254$			6.76260e27i			0.0937797i
$255$	4.96463e26	−	1.08356e28i	0.00656757	−	0.143342i
$256$	1.03703e29			1.30892
$257$			1.81147e28i			0.218190i	0.994031	+	0.109095i	$0.0347952\pi$
$257$			1.81147e28i			0.218190i	−0.994031	+	0.109095i	$0.965205\pi$
$258$	−1.19837e29	−	5.49065e27i	−1.37770	−	0.0631230i
$259$	−1.57428e29			−1.72776
$260$			8.68599e27i			0.0910205i
$261$	1.15092e28	−	1.25335e29i	0.115176	−	1.25425i
$262$	1.29648e29			1.23923
$263$			1.12981e29i			1.03166i	0.856691	+	0.515829i	$0.172516\pi$
$263$			1.12981e29i			1.03166i	−0.856691	+	0.515829i	$0.827484\pi$
$264$	2.17043e27	−	4.73711e28i	0.0189365	−	0.413301i
$265$	−5.04838e26			−0.00420922
$266$		−	3.72435e29i		−	2.96805i
$267$	−8.96314e28	−	4.10670e27i	−0.682849	−	0.0312865i
$268$	9.56070e27			0.0696421
$269$			1.43924e29i			1.00255i	0.865287	+	0.501276i	$0.167136\pi$
$269$			1.43924e29i			1.00255i	−0.865287	+	0.501276i	$0.832864\pi$
$270$	−5.83581e27	+	4.22189e28i	−0.0388809	+	0.281282i
$271$	2.42358e29			1.54464			0.772318	−	0.635236i	$-0.219097\pi$
$271$	2.42358e29			1.54464			0.772318	+	0.635236i	$0.219097\pi$
$272$			1.30590e29i			0.796315i
$273$	−6.85252e27	+	1.49561e29i	−0.0399851	+	0.872701i
$274$	−1.11168e29			−0.620832
$275$		−	2.01183e29i		−	1.07547i
$276$	−1.37968e29	−	6.32137e27i	−0.706106	−	0.0323521i
$277$	2.50185e29			1.22604			0.613020	−	0.790068i	$-0.289955\pi$
$277$	2.50185e29			1.22604			0.613020	+	0.790068i	$0.289955\pi$
$278$			7.23684e28i			0.339634i
$279$	−3.62220e28	−	3.32620e27i	−0.162826	−	0.0149520i
$280$	−2.75945e28			−0.118830
$281$		−	1.57192e28i		−	0.0648566i	−0.999474	−	0.0324283i	$-0.989676\pi$
$281$		−	1.57192e28i		−	0.0648566i	0.999474	−	0.0324283i	$-0.0103241\pi$
$282$	−2.06829e28	+	4.51417e29i	−0.0817752	+	1.78480i
$283$	−2.24189e29			−0.849529			−0.424764	−	0.905304i	$-0.639643\pi$
$283$	−2.24189e29			−0.849529			−0.424764	+	0.905304i	$0.639643\pi$
$284$			9.47383e28i			0.344117i
$285$	9.38742e28	+	4.30110e27i	0.326895	+	0.0149775i
$286$	−2.58679e29			−0.863713
$287$			7.90412e28i			0.253088i
$288$	3.60035e28	−	3.92075e29i	0.110569	−	1.20409i
$289$	1.90318e29			0.560667
$290$		−	1.26542e29i		−	0.357652i
$291$	1.62431e28	−	3.54516e29i	0.0440507	−	0.961436i
$292$	−7.38927e28			−0.192313
$293$		−	1.77181e29i		−	0.442595i	−0.975206	−	0.221297i	$-0.928971\pi$
$293$		−	1.77181e29i		−	0.442595i	0.975206	−	0.221297i	$-0.0710292\pi$
$294$	6.78099e29	+	3.10689e28i	1.62602	+	0.0745003i
$295$	6.38221e28			0.146929
$296$			1.91445e29i			0.423198i
$297$	−5.26517e29	−	7.27790e28i	−1.11772	−	0.154500i
$298$	6.18368e29			1.26082
$299$		−	2.92333e29i		−	0.572563i
$300$	1.67029e28	−	3.64551e29i	0.0314294	−	0.685967i
$301$	−8.70571e29			−1.57401
$302$			5.57102e29i			0.967946i
$303$	2.58962e29	+	1.18650e28i	0.432438	+	0.0198133i
$304$	−1.13137e30			−1.81602
$305$		−	3.28438e28i		−	0.0506822i
$306$	5.83515e29	+	5.35830e28i	0.865754	+	0.0795005i
$307$	−2.24039e29			−0.319642			−0.159821	−	0.987146i	$-0.551092\pi$
$307$	−2.24039e29			−0.319642			−0.159821	+	0.987146i	$0.551092\pi$
$308$			8.86902e29i			1.21693i
$309$	−5.29403e28	+	1.15546e30i	−0.0698690	+	1.52494i
$310$	−3.65711e28			−0.0464299
$311$		−	1.07347e30i		−	1.31119i	−0.755114	−	0.655594i	$-0.772418\pi$
$311$		−	1.07347e30i		−	1.31119i	0.755114	−	0.655594i	$-0.227582\pi$
$312$	1.81878e29	+	8.33324e27i	0.213760	+	0.00979397i
$313$	1.48917e30			1.68427			0.842135	−	0.539268i	$-0.181299\pi$
$313$	1.48917e30			1.68427			0.842135	+	0.539268i	$0.181299\pi$
$314$		−	4.35921e29i		−	0.474518i
$315$	−2.82831e28	+	3.08000e29i	−0.0296347	+	0.322719i
$316$	4.34170e29			0.437940
$317$			9.48590e29i			0.921228i	0.887601	+	0.460614i	$0.152371\pi$
$317$			9.48590e29i			0.921228i	−0.887601	+	0.460614i	$0.847629\pi$
$318$	1.24823e27	−	2.72434e28i	0.00116726	−	0.0254763i
$319$	1.57812e30			1.42119
$320$		−	9.59937e28i		−	0.0832613i
$321$	−1.81708e30	−	8.32541e28i	−1.51814	−	0.0695577i
$322$	−2.39348e30			−1.92645
$323$		−	1.29199e30i		−	1.00191i
$324$	−9.48027e29	−	1.75592e29i	−0.708403	−	0.131209i
$325$	7.72427e29			0.556234
$326$		−	3.70207e30i		−	2.56941i
$327$	3.06478e28	−	6.68909e29i	0.0205034	−	0.447501i
$328$	9.61208e28			0.0619914
$329$			3.27938e30i			2.03911i
$330$	−5.33836e29	−	2.44591e28i	−0.320067	−	0.0146647i
$331$	−1.20405e30			−0.696160			−0.348080	−	0.937465i	$-0.613166\pi$
$331$	−1.20405e30			−0.696160			−0.348080	+	0.937465i	$0.613166\pi$
$332$			1.74634e30i			0.973805i
$333$	2.13685e30	+	1.96223e29i	1.14933	+	0.105540i
$334$	4.63639e30			2.40560
$335$			4.18057e28i			0.0209266i
$336$	1.70433e29	−	3.71982e30i	0.0823157	−	1.79659i
$337$	−8.99923e29			−0.419417			−0.209709	−	0.977764i	$-0.567252\pi$
$337$	−8.99923e29			−0.419417			−0.209709	+	0.977764i	$0.567252\pi$
$338$			1.92305e30i			0.864947i
$339$	−2.30843e30	−	1.05767e29i	−1.00212	−	0.0459149i
$340$	2.46706e29			0.103379
$341$		−	4.56082e29i		−	0.184497i
$342$	−4.64215e29	+	5.05526e30i	−0.181303	+	1.97438i
$343$	9.56533e29			0.360720
$344$			1.05869e30i			0.385537i
$345$	2.76412e28	−	6.03287e29i	0.00972138	−	0.212175i
$346$	−4.75525e30			−1.61533
$347$			3.93285e30i			1.29049i	0.763977	+	0.645244i	$0.223244\pi$
$347$			3.93285e30i			1.29049i	−0.763977	+	0.645244i	$0.776756\pi$
$348$	2.85962e30	+	1.31021e29i	0.906480	+	0.0415328i
$349$	−4.16588e30			−1.27586			−0.637929	−	0.770095i	$-0.720209\pi$
$349$	−4.16588e30			−1.27586			−0.637929	+	0.770095i	$0.720209\pi$
$350$		−	6.32425e30i		−	1.87151i
$351$	2.79430e29	−	2.02152e30i	0.0799075	−	0.578088i
$352$	4.93673e30			1.36436
$353$		−	1.95068e30i		−	0.521063i	−0.965465	−	0.260532i	$-0.916102\pi$
$353$		−	1.95068e30i		−	0.521063i	0.965465	−	0.260532i	$-0.0838978\pi$
$354$	−1.57803e29	+	3.44415e30i	−0.0407451	+	0.889288i
$355$	−4.14259e29			−0.103403
$356$		−	2.04073e30i		−	0.492476i
$357$	4.24793e30	+	1.94630e29i	0.991194	+	0.0454142i
$358$	−5.44937e30			−1.22956
$359$		−	6.24546e30i		−	1.36280i	−0.731912	−	0.681399i	$-0.761372\pi$
$359$		−	6.24546e30i		−	1.36280i	0.731912	−	0.681399i	$-0.238628\pi$
$360$	3.74554e29	+	3.43946e28i	0.0790469	+	0.00725873i
$361$	6.29437e30			1.28489
$362$			1.68133e30i			0.332010i
$363$	6.54488e28	−	1.42846e30i	0.0125032	−	0.272891i
$364$	−3.40520e30			−0.629399
$365$		−	3.23108e29i		−	0.0577874i
$366$	1.77241e30	+	8.12075e28i	0.306754	+	0.0140548i
$367$	−6.85802e30			−1.14870			−0.574349	−	0.818610i	$-0.694745\pi$
$367$	−6.85802e30			−1.14870			−0.574349	+	0.818610i	$0.694745\pi$
$368$			7.27079e30i			1.17871i
$369$	9.85195e28	−	1.07287e30i	0.0154599	−	0.168357i
$370$	2.15744e30			0.327731
$371$		−	1.97913e29i		−	0.0291064i
$372$	3.78655e28	−	8.26439e29i	0.00539173	−	0.117678i
$373$	−3.93519e30			−0.542575			−0.271287	−	0.962498i	$-0.587449\pi$
$373$	−3.93519e30			−0.542575			−0.271287	+	0.962498i	$0.587449\pi$
$374$			7.34720e30i			0.980985i
$375$	3.26650e30	+	1.49663e29i	0.422384	+	0.0193526i
$376$	3.98800e30			0.499460
$377$			6.05910e30i			0.735041i
$378$	−1.65512e31	−	2.28783e30i	−1.94504	−	0.268858i
$379$	6.29783e30			0.717002			0.358501	−	0.933529i	$-0.383288\pi$
$379$	6.29783e30			0.717002			0.358501	+	0.933529i	$0.383288\pi$
$380$			2.13733e30i			0.235759i
$381$	3.06172e28	−	6.68239e29i	0.00327239	−	0.0714220i
$382$	1.67688e31			1.73677
$383$			6.83982e30i			0.686530i	0.939239	+	0.343265i	$0.111533\pi$
$383$			6.83982e30i			0.686530i	−0.939239	+	0.343265i	$0.888467\pi$
$384$	−7.23631e30	−	3.31551e29i	−0.703951	−	0.0322534i
$385$	−3.87812e30			−0.365673
$386$		−	1.27548e31i		−	1.16581i
$387$	1.18167e31	+	1.08511e30i	1.04705	+	0.0961481i
$388$	8.07163e30			0.693395
$389$		−	1.46728e31i		−	1.22213i	−0.791581	−	0.611064i	$-0.790742\pi$
$389$		−	1.46728e31i		−	1.22213i	0.791581	−	0.611064i	$-0.209258\pi$
$390$	9.39092e28	−	2.04963e30i	0.00758460	−	0.165539i
$391$	−8.30305e30			−0.650304
$392$		−	5.99059e30i		−	0.455027i
$393$	−1.28111e31	−	5.86974e29i	−0.943790	−	0.0432422i
$394$	−2.34061e30			−0.167253
$395$			1.89848e30i			0.131595i
$396$	1.10546e30	−	1.20384e31i	0.0743364	−	0.809517i
$397$	−2.83411e30			−0.184897			−0.0924487	−	0.995717i	$-0.529469\pi$
$397$	−2.83411e30			−0.184897			−0.0924487	+	0.995717i	$0.529469\pi$
$398$		−	1.43304e30i		−	0.0907116i
$399$	−1.68617e30	+	3.68018e31i	−0.103568	+	2.26045i
$400$	−1.92115e31			−1.14510
$401$		−	2.22807e31i		−	1.28883i	−0.764675	−	0.644416i	$-0.777101\pi$
$401$		−	2.22807e31i		−	1.28883i	0.764675	−	0.644416i	$-0.222899\pi$
$402$	−2.25603e30	−	1.03366e29i	−0.126658	−	0.00580318i
$403$	1.75110e30			0.0954222
$404$			5.89604e30i			0.311878i
$405$	7.67803e29	−	4.14540e30i	0.0394266	−	0.212866i
$406$	4.96089e31			2.47313
$407$			2.69057e31i			1.30230i
$408$	2.36687e29	−	5.16584e30i	0.0111238	−	0.242783i
$409$	7.89674e30			0.360386			0.180193	−	0.983631i	$-0.442328\pi$
$409$	7.89674e30			0.360386			0.180193	+	0.983631i	$0.442328\pi$
$410$		−	1.08321e30i		−	0.0480071i
$411$	1.09850e31	+	5.03306e29i	0.472821	+	0.0216636i
$412$	−2.63075e31			−1.09980
$413$			2.50204e31i			1.01600i
$414$	3.24879e31	+	2.98330e30i	1.28150	+	0.117677i
$415$	−7.63615e30			−0.292616
$416$			1.89542e31i			0.705645i
$417$	3.27642e29	−	7.15101e30i	0.0118513	−	0.258663i
$418$	−6.36523e31			−2.23717
$419$		−	1.84985e31i		−	0.631783i	−0.948795	−	0.315892i	$-0.897696\pi$
$419$		−	1.84985e31i		−	0.631783i	0.948795	−	0.315892i	$-0.102304\pi$
$420$	−7.02731e30	−	3.21975e29i	−0.233237	−	0.0106864i
$421$	−1.89060e31			−0.609838			−0.304919	−	0.952378i	$-0.598629\pi$
$421$	−1.89060e31			−0.609838			−0.304919	+	0.952378i	$0.598629\pi$
$422$			1.99327e31i			0.624908i
$423$	4.08752e30	−	4.45127e31i	0.124559	−	1.35644i
$424$	−2.40679e29			−0.00712932
$425$		−	2.19390e31i		−	0.631758i
$426$	1.02427e30	−	2.23554e31i	0.0286747	−	0.625845i
$427$	1.28759e31			0.350463
$428$		−	4.13712e31i		−	1.09490i
$429$	2.55611e31	+	1.17115e30i	0.657798	+	0.0301388i
$430$	1.19306e31			0.298566
$431$			2.61841e31i			0.637250i	0.947881	+	0.318625i	$0.103221\pi$
$431$			2.61841e31i			0.637250i	−0.947881	+	0.318625i	$0.896779\pi$
$432$	−6.94987e30	+	5.02786e31i	−0.164502	+	1.19009i
$433$	6.56673e31			1.51180			0.755900	−	0.654687i	$-0.227200\pi$
$433$	6.56673e31			1.51180			0.755900	+	0.654687i	$0.227200\pi$
$434$		−	1.43371e31i		−	0.321059i
$435$	−5.72911e29	+	1.25042e31i	−0.0124801	+	0.272385i
$436$	1.52297e31			0.322741
$437$		−	7.19333e31i		−	1.48304i
$438$	1.74364e31	+	7.98897e29i	0.349759	+	0.0160251i
$439$	−4.85617e31			−0.947806			−0.473903	−	0.880577i	$-0.657155\pi$
$439$	−4.85617e31			−0.947806			−0.473903	+	0.880577i	$0.657155\pi$
$440$			4.71612e30i			0.0895680i
$441$	−6.68650e31	−	6.14009e30i	−1.23577	−	0.113478i
$442$	−2.82091e31			−0.507366
$443$			7.67254e31i			1.34306i	0.740979	+	0.671528i	$0.234362\pi$
$443$			7.67254e31i			1.34306i	−0.740979	+	0.671528i	$0.765638\pi$
$444$	−2.23380e30	+	4.87541e31i	−0.0380582	+	0.830646i
$445$	8.92341e30			0.147983
$446$			6.30860e31i			1.01839i
$447$	−6.11034e31	−	2.79962e30i	−0.960230	−	0.0439955i
$448$	3.76328e31			0.575745
$449$		−	4.11870e31i		−	0.613485i	−0.951793	−	0.306743i	$-0.900761\pi$
$449$		−	4.11870e31i		−	0.613485i	0.951793	−	0.306743i	$-0.0992391\pi$
$450$	−7.88274e30	+	8.58424e31i	−0.114321	+	1.24495i
$451$	1.35088e31			0.190765
$452$		−	5.25584e31i		−	0.722738i
$453$	2.52224e30	−	5.50495e31i	0.0337759	−	0.737182i
$454$	8.27022e31			1.07857
$455$		−	1.48898e31i		−	0.189126i
$456$	4.47541e31	+	2.05053e30i	0.553675	+	0.0253681i
$457$	2.61744e31			0.315415			0.157708	−	0.987486i	$-0.449590\pi$
$457$	2.61744e31			0.315415			0.157708	+	0.987486i	$0.449590\pi$
$458$			4.04021e31i			0.474262i
$459$	−5.74168e31	−	7.93657e30i	−0.656579	−	0.0907571i
$460$	1.37357e31			0.153023
$461$			1.36067e32i			1.47687i	0.674323	+	0.738436i	$0.264436\pi$
$461$			1.36067e32i			1.47687i	−0.674323	+	0.738436i	$0.735564\pi$
$462$	9.58880e30	−	2.09282e32i	0.101405	−	2.21324i
$463$	6.72415e31			0.692892			0.346446	−	0.938070i	$-0.387388\pi$
$463$	6.72415e31			0.692892			0.346446	+	0.938070i	$0.387388\pi$
$464$		−	1.50700e32i		−	1.51320i
$465$	3.61374e30	+	1.65573e29i	0.0353607	+	0.00162015i
$466$	−2.31787e32			−2.21033
$467$		−	3.28080e31i		−	0.304913i	−0.988310	−	0.152457i	$-0.951282\pi$
$467$		−	3.28080e31i		−	0.304913i	0.988310	−	0.152457i	$-0.0487185\pi$
$468$	4.62206e31	+	4.24435e30i	0.418683	+	0.0384468i
$469$	−1.63892e31			−0.144705
$470$		−	4.49417e31i		−	0.386790i
$471$	−1.97360e30	+	4.30751e31i	−0.0165580	+	0.361390i
$472$	3.04269e31			0.248860
$473$			1.48788e32i			1.18641i
$474$	−1.02451e32	−	4.69406e30i	−0.796481	−	0.0364929i
$475$	1.90068e32			1.44074
$476$			9.67170e31i			0.714857i
$477$	−2.46685e29	+	2.68638e30i	−0.00177796	+	0.0193619i
$478$	−1.54936e32			−1.08897
$479$		−	2.12659e32i		−	1.45766i	−0.684693	−	0.728831i	$-0.740064\pi$
$479$		−	2.12659e32i		−	1.45766i	0.684693	−	0.728831i	$-0.259936\pi$
$480$	−1.79220e30	+	3.91159e31i	−0.0119809	+	0.261492i
$481$	−1.03302e32			−0.673550
$482$			1.37990e32i			0.877573i
$483$	2.36509e32	+	1.08363e31i	1.46718	+	0.0672225i
$484$	3.25233e31			0.196811
$485$			3.52945e31i			0.208356i
$486$	2.21807e32	+	5.16839e31i	1.27744	+	0.297660i
$487$	−1.74666e32			−0.981431			−0.490715	−	0.871320i	$-0.663265\pi$
$487$	−1.74666e32			−0.981431			−0.490715	+	0.871320i	$0.663265\pi$
$488$		−	1.56581e31i		−	0.0858425i
$489$	−1.67608e31	+	3.65816e32i	−0.0896580	+	1.95684i
$490$	−6.75094e31			−0.352380
$491$			3.55957e31i			0.181309i	0.995882	+	0.0906546i	$0.0288959\pi$
$491$			3.55957e31i			0.181309i	−0.995882	+	0.0906546i	$0.971104\pi$
$492$	2.44785e31	+	1.12155e30i	0.121676	+	0.00557489i
$493$	1.72095e32			0.834844
$494$		−	2.44389e32i		−	1.15706i
$495$	5.26398e31	+	4.83381e30i	0.243249	+	0.0223371i
$496$	−4.35526e31			−0.196442
$497$		−	1.62403e32i		−	0.715020i
$498$	1.88807e31	−	4.12083e32i	0.0811457	−	1.77106i
$499$	−4.00755e32			−1.68140			−0.840702	−	0.541498i	$-0.817857\pi$
$499$	−4.00755e32			−1.68140			−0.840702	+	0.541498i	$0.817857\pi$
$500$			7.43717e31i			0.304626i
$501$	−4.58141e32	−	2.09909e31i	−1.83209	−	0.0839419i
$502$	4.22073e32			1.64795
$503$		−	2.31914e32i		−	0.884120i	−0.896985	−	0.442060i	$-0.854248\pi$
$503$		−	2.31914e32i		−	0.884120i	0.896985	−	0.442060i	$-0.145752\pi$
$504$	−1.34838e31	+	1.46838e32i	−0.0501935	+	0.546603i
$505$	−2.57814e31			−0.0937152
$506$			4.09065e32i			1.45206i
$507$	8.70646e30	−	1.90024e32i	0.0301819	−	0.658739i
$508$	1.52145e31			0.0515101
$509$			1.25787e32i			0.415932i	0.978136	+	0.207966i	$0.0666844\pi$
$509$			1.25787e32i			0.415932i	−0.978136	+	0.207966i	$0.933316\pi$
$510$	−5.82151e31	−	2.66728e30i	−0.188015	−	0.00861442i
$511$	1.26669e32			0.399595
$512$		−	3.28466e32i		−	1.01216i
$513$	6.87583e31	−	4.97429e32i	0.206974	−	1.49735i
$514$	9.73224e31			0.286191
$515$		−	1.15034e32i		−	0.330474i
$516$	−1.23529e31	+	2.69609e32i	−0.0346714	+	0.756726i
$517$	5.60472e32			1.53698
$518$			8.45789e32i			2.26624i
$519$	4.69885e32	+	2.15290e31i	1.23022	+	0.0563659i
$520$	−1.81072e31			−0.0463246
$521$			2.59982e32i			0.649966i	0.945720	+	0.324983i	$0.105359\pi$
$521$			2.59982e32i			0.649966i	−0.945720	+	0.324983i	$0.894641\pi$
$522$	−6.73368e32	−	6.18341e31i	−1.64515	−	0.151071i
$523$	−6.55109e32			−1.56420			−0.782102	−	0.623150i	$-0.785852\pi$
$523$	−6.55109e32			−1.56420			−0.782102	+	0.623150i	$0.785852\pi$
$524$		−	2.91683e32i		−	0.680669i
$525$	−2.86326e31	+	6.24924e32i	−0.0653053	+	1.42533i
$526$	6.06997e32			1.35319
$527$		−	4.97359e31i		−	0.108378i
$528$	−6.35747e32	−	2.91284e31i	−1.35418	−	0.0620454i
$529$	1.79678e31			0.0374133
$530$			2.71227e30i			0.00552106i
$531$	3.11862e31	−	3.39615e32i	0.0620624	−	0.675855i
$532$	−8.37905e32			−1.63025
$533$			5.18661e31i			0.0986636i
$534$	−2.20635e31	+	4.81550e32i	−0.0410373	+	0.895666i
$535$	1.80902e32			0.329002
$536$			1.99307e31i			0.0354442i
$537$	5.38474e32	+	2.46716e31i	0.936425	+	0.0429048i
$538$	7.73243e32			1.31501
$539$		−	8.41916e32i		−	1.40024i
$540$	9.49841e31	+	1.31294e31i	0.154499	+	0.0213560i
$541$	1.68377e32			0.267865			0.133933	−	0.990990i	$-0.457239\pi$
$541$	1.68377e32			0.267865			0.133933	+	0.990990i	$0.457239\pi$
$542$		−	1.30208e33i		−	2.02604i
$543$	7.61211e30	−	1.66139e32i	0.0115853	−	0.252857i
$544$	5.38352e32			0.801456
$545$			6.65944e31i			0.0969795i
$546$	8.03523e32	+	3.68156e31i	1.14469	+	0.0524469i
$547$	−7.51689e32			−1.04759			−0.523794	−	0.851845i	$-0.675484\pi$
$547$	−7.51689e32			−1.04759			−0.523794	+	0.851845i	$0.675484\pi$
$548$			2.50106e32i			0.341002i
$549$	−1.74771e32	−	1.60489e31i	−0.233132	−	0.0214080i
$550$	−1.08087e33			−1.41065
$551$			1.49094e33i			1.90389i
$552$	1.31778e31	−	2.87615e32i	0.0164655	−	0.359370i
$553$	−7.44266e32			−0.909970
$554$		−	1.34413e33i		−	1.60815i
$555$	−2.13185e32	−	9.76765e30i	−0.249598	−	0.0114360i
$556$	1.62814e32			0.186550
$557$			8.19903e32i			0.919391i	0.888077	+	0.459695i	$0.152041\pi$
$557$			8.19903e32i			0.919391i	−0.888077	+	0.459695i	$0.847959\pi$
$558$	−1.78702e31	+	1.94605e32i	−0.0196119	+	0.213572i
$559$	−5.71260e32			−0.613610
$560$			3.70333e32i			0.389346i
$561$	3.32639e31	−	7.26006e32i	0.0342309	−	0.747112i
$562$	−8.44523e31			−0.0850698
$563$			9.09259e32i			0.896576i	0.893889	+	0.448288i	$0.147966\pi$
$563$			9.09259e32i			0.896576i	−0.893889	+	0.448288i	$0.852034\pi$
$564$	1.01560e33	+	4.65323e31i	0.980331	+	0.0449165i
$565$	2.29820e32			0.217173
$566$			1.20447e33i			1.11429i
$567$	1.62514e33	+	3.01004e32i	1.47195	+	0.272632i
$568$	−1.97496e32			−0.175137
$569$			4.18516e32i			0.363383i	0.983356	+	0.181692i	$0.0581572\pi$
$569$			4.18516e32i			0.363383i	−0.983356	+	0.181692i	$0.941843\pi$
$570$	2.31079e31	−	5.04345e32i	0.0196455	−	0.428775i
$571$	1.11459e33			0.927856			0.463928	−	0.885873i	$-0.346440\pi$
$571$	1.11459e33			0.927856			0.463928	+	0.885873i	$0.346440\pi$
$572$			5.81976e32i			0.474409i
$573$	−1.65700e33	−	7.59196e31i	−1.32271	−	0.0606036i
$574$	4.24654e32			0.331965
$575$		−	1.22148e33i		−	0.935134i
$576$	−5.10809e32	−	4.69066e31i	−0.382991	−	0.0351694i
$577$	3.90924e32			0.287066			0.143533	−	0.989645i	$-0.454154\pi$
$577$	3.90924e32			0.287066			0.143533	+	0.989645i	$0.454154\pi$
$578$		−	1.02249e33i		−	0.735405i
$579$	−5.77464e31	+	1.26035e33i	−0.0406801	+	0.887870i
$580$	−2.84695e32			−0.196446
$581$		−	2.99363e33i		−	2.02341i
$582$	−1.90466e33	−	8.72670e31i	−1.26108	−	0.0577796i
$583$	−3.38250e31			−0.0219389
$584$		−	1.54040e32i		−	0.0978769i
$585$	−1.85591e31	+	2.02107e32i	−0.0115528	+	0.125809i
$586$	−9.51917e32			−0.580534
$587$			1.31542e33i			0.785970i	0.919545	+	0.392985i	$0.128558\pi$
$587$			1.31542e33i			0.785970i	−0.919545	+	0.392985i	$0.871442\pi$
$588$	6.98988e31	−	1.52559e33i	0.0409206	−	0.893118i
$589$	4.30886e32			0.247160
$590$		−	3.42888e32i		−	0.192721i
$591$	2.31285e32	+	1.05969e31i	0.127379	+	0.00583621i
$592$	2.56930e33			1.38661
$593$		−	9.40105e32i		−	0.497187i	−0.968608	−	0.248594i	$-0.920032\pi$
$593$		−	9.40105e32i		−	0.497187i	0.968608	−	0.248594i	$-0.0799683\pi$
$594$	−3.91009e32	+	2.82874e33i	−0.202651	+	1.46607i
$595$	−4.22910e32			−0.214805
$596$		−	1.39120e33i		−	0.692525i
$597$	−6.48800e30	+	1.41605e32i	−0.00316533	+	0.0690854i
$598$	−1.57058e33			−0.751008
$599$		−	2.02550e33i		−	0.949315i	−0.880170	−	0.474658i	$-0.842572\pi$
$599$		−	2.02550e33i		−	0.949315i	0.880170	−	0.474658i	$-0.157428\pi$
$600$	7.59961e32	+	3.48196e31i	0.349121	+	0.0159959i
$601$	2.02528e33			0.911993			0.455996	−	0.889982i	$-0.349283\pi$
$601$	2.02528e33			0.911993			0.455996	+	0.889982i	$0.349283\pi$
$602$			4.67719e33i			2.06456i
$603$	2.22460e32	+	2.04281e31i	0.0962595	+	0.00883933i
$604$	1.25337e33			0.531661
$605$			1.42213e32i			0.0591392i
$606$	6.37455e31	−	1.39129e33i	0.0259883	−	0.567212i
$607$	2.58616e32			0.103369			0.0516847	−	0.998663i	$-0.483541\pi$
$607$	2.58616e32			0.103369			0.0516847	+	0.998663i	$0.483541\pi$
$608$			4.66400e33i			1.82774i
$609$	−4.90205e33	−	2.24601e32i	−1.88352	−	0.0862985i
$610$	−1.76455e32			−0.0664778
$611$			2.15189e33i			0.794926i
$612$	1.20551e32	−	1.31279e33i	0.0436671	−	0.475531i
$613$	2.66778e33			0.947600			0.473800	−	0.880632i	$-0.342882\pi$
$613$	2.66778e33			0.947600			0.473800	+	0.880632i	$0.342882\pi$
$614$			1.20366e33i			0.419261i
$615$	−4.90414e30	+	1.07036e32i	−0.00167518	+	0.0365619i
$616$	−1.84888e33			−0.619355
$617$		−	5.82313e33i		−	1.91309i	−0.291592	−	0.956543i	$-0.594185\pi$
$617$		−	5.82313e33i		−	1.91309i	0.291592	−	0.956543i	$-0.405815\pi$
$618$	6.20776e33	+	2.84425e32i	2.00020	+	0.0916444i
$619$	−3.87997e33			−1.22614			−0.613070	−	0.790029i	$-0.710066\pi$
$619$	−3.87997e33			−1.22614			−0.613070	+	0.790029i	$0.710066\pi$
$620$			8.22776e31i			0.0255024i
$621$	−3.19675e33	−	4.41879e32i	−0.971874	−	0.134340i
$622$	−5.76727e33			−1.71983
$623$			3.49828e33i			1.02329i
$624$	1.11837e32	−	2.44091e33i	0.0320899	−	0.700384i
$625$	3.06101e33			0.861597
$626$		−	8.00064e33i		−	2.20919i
$627$	6.28973e33	+	2.88181e32i	1.70381	+	0.0780647i
$628$	−9.80736e32			−0.260637
$629$			2.93407e33i			0.765003i
$630$	1.65475e33	+	1.51953e32i	0.423298	+	0.0388706i
$631$	−4.23917e33			−1.06397			−0.531984	−	0.846755i	$-0.678553\pi$
$631$	−4.23917e33			−1.06397			−0.531984	+	0.846755i	$0.678553\pi$
$632$			9.05091e32i			0.222888i
$633$	9.02437e31	−	1.96963e33i	0.0218058	−	0.475926i
$634$	5.09635e33			1.20834
$635$			6.65278e31i			0.0154781i
$636$	−6.12923e31	−	2.80827e30i	−0.0139933	−	0.000641140i
$637$	3.23248e33			0.724207
$638$		−	8.47856e33i		−	1.86412i
$639$	−2.02424e32	+	2.20439e33i	−0.0436770	+	0.475639i
$640$	7.20424e32			0.152556
$641$		−	1.58254e33i		−	0.328895i	−0.986386	−	0.164448i	$-0.947416\pi$
$641$		−	1.58254e33i		−	0.328895i	0.986386	−	0.164448i	$-0.0525841\pi$
$642$	−4.47288e32	+	9.76235e33i	−0.0912361	+	1.99129i
$643$	−5.10649e33			−1.02233			−0.511164	−	0.859483i	$-0.670786\pi$
$643$	−5.10649e33			−1.02233			−0.511164	+	0.859483i	$0.670786\pi$
$644$			5.38484e33i			1.05814i
$645$	−1.17891e33	−	5.40149e31i	−0.227386	−	0.0104183i
$646$	−6.94130e33			−1.31417
$647$			2.51993e33i			0.468314i	0.972199	+	0.234157i	$0.0752330\pi$
$647$			2.51993e33i			0.468314i	−0.972199	+	0.234157i	$0.924767\pi$
$648$	3.66047e32	−	1.97630e33i	0.0667785	−	0.360540i
$649$	4.27619e33			0.765810
$650$		−	4.14991e33i		−	0.729589i
$651$	−6.49102e31	+	1.41671e33i	−0.0112032	+	0.244516i
$652$	−8.32890e33			−1.41129
$653$			8.74673e33i			1.45508i	0.686064	+	0.727541i	$0.259337\pi$
$653$			8.74673e33i			1.45508i	−0.686064	+	0.727541i	$0.740663\pi$
$654$	−3.59375e33	−	1.64657e32i	−0.586969	−	0.0268935i
$655$	1.27543e33			0.204532
$656$		−	1.28999e33i		−	0.203115i
$657$	−1.71935e33	−	1.57884e32i	−0.265815	−	0.0244093i
$658$	1.76186e34			2.67462
$659$			1.45934e33i			0.217536i	0.994067	+	0.108768i	$0.0346906\pi$
$659$			1.45934e33i			0.217536i	−0.994067	+	0.108768i	$0.965309\pi$
$660$	−5.50281e31	+	1.20102e33i	−0.00805485	+	0.175802i
$661$	3.52478e33			0.506658			0.253329	−	0.967380i	$-0.418475\pi$
$661$	3.52478e33			0.506658			0.253329	+	0.967380i	$0.418475\pi$
$662$			6.46884e33i			0.913125i
$663$	2.78745e33	+	1.27714e32i	0.386407	+	0.0177043i
$664$	−3.64050e33			−0.495615
$665$		−	3.66387e33i		−	0.489870i
$666$	1.05422e33	−	1.14803e34i	0.138433	−	1.50752i
$667$	9.58161e33			1.23574
$668$		−	1.04310e34i		−	1.32132i
$669$	2.85617e32	−	6.23378e33i	0.0355362	−	0.775601i
$670$	2.24604e32			0.0274485
$671$		−	2.20059e33i		−	0.264161i
$672$	−1.53347e34	−	7.02602e32i	−1.80819	−	0.0828472i
$673$	−6.95635e33			−0.805751			−0.402875	−	0.915255i	$-0.631989\pi$
$673$	−6.95635e33			−0.805751			−0.402875	+	0.915255i	$0.631989\pi$
$674$			4.83489e33i			0.550133i
$675$	1.16757e33	−	8.44674e33i	0.130508	−	0.944156i
$676$	4.32647e33			0.475087
$677$			1.30853e34i			1.41163i	0.708397	+	0.705814i	$0.249419\pi$
$677$			1.30853e34i			1.41163i	−0.708397	+	0.705814i	$0.750581\pi$
$678$	−5.68239e32	+	1.24022e34i	−0.0602247	+	1.31444i
$679$	−1.38366e34			−1.44077
$680$			5.14295e32i			0.0526144i
$681$	−8.17214e33	−	3.74428e32i	−0.821429	−	0.0376360i
$682$	−2.45033e33			−0.241998
$683$		−	1.71940e34i		−	1.66851i	−0.551381	−	0.834254i	$-0.685899\pi$
$683$		−	1.71940e34i		−	1.66851i	0.551381	−	0.834254i	$-0.314101\pi$
$684$	1.13733e34	+	1.04439e33i	1.08446	+	0.0995841i
$685$	−1.09363e33			−0.102467
$686$		−	5.13903e33i		−	0.473142i
$687$	1.82917e32	−	3.99229e33i	0.0165491	−	0.361195i
$688$	1.42082e34			1.26321
$689$		−	1.29869e32i		−	0.0113468i
$690$	−3.24120e33	−	1.48504e32i	−0.278302	−	0.0127511i
$691$	4.81889e33			0.406640			0.203320	−	0.979112i	$-0.434827\pi$
$691$	4.81889e33			0.406640			0.203320	+	0.979112i	$0.434827\pi$
$692$			1.06984e34i			0.887246i
$693$	−1.89502e33	+	2.06366e34i	−0.154459	+	1.68205i
$694$	2.11295e34			1.69268
$695$			7.11932e32i			0.0560558i
$696$	−2.73133e32	+	5.96131e33i	−0.0211380	+	0.461350i
$697$	1.47314e33			0.112060
$698$			2.23815e34i			1.67349i
$699$	2.29038e34	+	1.04940e33i	1.68338	+	0.0771283i
$700$	−1.42283e34			−1.02796
$701$		−	1.86159e34i		−	1.32211i	−0.750337	−	0.661055i	$-0.770109\pi$
$701$		−	1.86159e34i		−	1.32211i	0.750337	−	0.661055i	$-0.229891\pi$
$702$	−1.08608e34	−	1.50125e33i	−0.758254	−	0.104811i
$703$	−2.54193e34			−1.74461
$704$		−	6.43174e33i		−	0.433967i
$705$	−2.03470e32	+	4.44087e33i	−0.0134968	+	0.294577i
$706$	−1.04802e34			−0.683458
$707$		−	1.01072e34i		−	0.648032i
$708$	7.74864e33	+	3.55024e32i	0.488457	+	0.0223800i
$709$	−1.75378e34			−1.08697			−0.543487	−	0.839417i	$-0.682896\pi$
$709$	−1.75378e34			−1.08697			−0.543487	+	0.839417i	$0.682896\pi$
$710$			2.22563e33i			0.135629i
$711$	1.01023e34	+	9.27677e32i	0.605321	+	0.0555855i
$712$	4.25420e33			0.250644
$713$		−	2.76911e33i		−	0.160423i
$714$	1.04566e33	−	2.28223e34i	0.0595680	−	1.30011i
$715$	−2.54478e33			−0.142554
$716$			1.22600e34i			0.675357i
$717$	1.53098e34	+	7.01461e32i	0.829356	+	0.0379991i
$718$	−3.35541e34			−1.78753
$719$		−	6.76613e32i		−	0.0354482i	−0.999843	−	0.0177241i	$-0.994358\pi$
$719$		−	6.76613e32i		−	0.0354482i	0.999843	−	0.0177241i	$-0.00564205\pi$
$720$	4.61594e32	−	5.02672e33i	0.0237832	−	0.258997i
$721$	4.50970e34			2.28520
$722$		−	3.38169e34i		−	1.68534i
$723$	6.24740e32	−	1.36353e34i	0.0306224	−	0.668354i
$724$	3.78266e33			0.182362
$725$			2.53174e34i			1.20050i
$726$	−7.67450e33	−	3.51628e32i	−0.357941	−	0.0164000i
$727$	1.93368e34			0.887098			0.443549	−	0.896250i	$-0.353719\pi$
$727$	1.93368e34			0.887098			0.443549	+	0.896250i	$0.353719\pi$
$728$		−	7.09864e33i		−	0.320331i
$729$	−2.16836e34	−	6.11131e33i	−0.962503	−	0.271271i
$730$	−1.73592e33			−0.0757974
$731$			1.62253e34i			0.696924i
$732$	1.82701e32	−	3.98756e33i	0.00771982	−	0.168490i
$733$	−1.02410e34			−0.425693			−0.212847	−	0.977086i	$-0.568273\pi$
$733$	−1.02410e34			−0.425693			−0.212847	+	0.977086i	$0.568273\pi$
$734$			3.68451e34i			1.50670i
$735$	6.67087e33	+	3.05644e32i	0.268370	+	0.0122961i
$736$	2.99734e34			1.18632
$737$			2.80105e33i			0.109072i
$738$	−5.76405e33	−	5.29302e32i	−0.220827	−	0.0202781i
$739$	−4.24541e34			−1.60025			−0.800123	−	0.599837i	$-0.795232\pi$
$739$	−4.24541e34			−1.60025			−0.800123	+	0.599837i	$0.795232\pi$
$740$		−	4.85381e33i		−	0.180012i
$741$	−1.10645e33	+	2.41490e34i	−0.0403751	+	0.881213i
$742$	−1.06330e33			−0.0381777
$743$		−	4.57683e34i		−	1.61696i	−0.588524	−	0.808480i	$-0.700291\pi$
$743$		−	4.57683e34i		−	1.61696i	0.588524	−	0.808480i	$-0.299709\pi$
$744$	1.72283e33	+	7.89362e31i	0.0598919	+	0.00274411i
$745$	6.08326e33			0.208095
$746$			2.11420e34i			0.711673i
$747$	−3.73135e33	+	4.06341e34i	−0.123600	+	1.34600i
$748$	1.65297e34			0.538823
$749$			7.09198e34i			2.27502i
$750$	8.04075e32	−	1.75495e34i	0.0253841	−	0.554024i
$751$	−2.60713e34			−0.809998			−0.404999	−	0.914317i	$-0.632728\pi$
$751$	−2.60713e34			−0.809998			−0.404999	+	0.914317i	$0.632728\pi$
$752$		−	5.35211e34i		−	1.63648i
$753$	−4.17067e34	−	1.91090e33i	−1.25506	−	0.0575041i
$754$	3.25529e34			0.964124
$755$			5.48055e33i			0.159757i
$756$	−5.14716e33	+	3.72370e34i	−0.147675	+	1.06835i
$757$	5.97556e34			1.68744			0.843719	−	0.536785i	$-0.180361\pi$
$757$	5.97556e34			1.68744			0.843719	+	0.536785i	$0.180361\pi$
$758$		−	3.38355e34i		−	0.940463i
$759$	1.85201e33	−	4.04213e34i	0.0506689	−	1.10588i
$760$	−4.45558e33			−0.119989
$761$		−	6.68680e34i		−	1.77257i	−0.463144	−	0.886283i	$-0.653279\pi$
$761$		−	6.68680e34i		−	1.77257i	0.463144	−	0.886283i	$-0.346721\pi$
$762$	−3.59015e33	−	1.64492e32i	−0.0936814	−	0.00429226i
$763$	−2.61073e34			−0.670605
$764$		−	3.77265e34i		−	0.953951i
$765$	5.74039e33	+	5.27129e32i	0.142891	+	0.0131214i
$766$	3.67473e34			0.900494
$767$			1.64182e34i			0.396077i
$768$	−2.52246e33	+	5.50543e34i	−0.0599086	+	1.30754i
$769$	2.56976e34			0.600864			0.300432	−	0.953803i	$-0.402869\pi$
$769$	2.56976e34			0.600864			0.300432	+	0.953803i	$0.402869\pi$
$770$			2.08354e34i			0.479638i
$771$	−9.61682e33	−	4.40620e32i	−0.217961	−	0.00998646i
$772$	−2.86957e34			−0.640339
$773$			2.00267e34i			0.440004i	0.975499	+	0.220002i	$0.0706063\pi$
$773$			2.00267e34i			0.440004i	−0.975499	+	0.220002i	$0.929394\pi$
$774$	5.82980e33	−	6.34860e34i	0.126114	−	1.37337i
$775$	7.31678e33			0.155847
$776$			1.68265e34i			0.352901i
$777$	3.82925e33	−	8.35758e34i	0.0790790	−	1.72595i
$778$	−7.88303e34			−1.60302
$779$			1.27625e34i			0.255556i
$780$	−4.61125e33	−	2.11277e32i	−0.0909251	−	0.00416597i
$781$	−2.77560e34			−0.538946
$782$			4.46086e34i			0.852978i
$783$	6.62582e34	+	9.15869e33i	1.24767	+	0.172462i
$784$	−8.03970e34			−1.49090
$785$		−	4.28842e33i		−	0.0783180i
$786$	−3.15355e33	+	6.88283e34i	−0.0567191	+	1.23793i
$787$	8.09658e34			1.43418			0.717092	−	0.696979i	$-0.245473\pi$
$787$	8.09658e34			1.43418			0.717092	+	0.696979i	$0.245473\pi$
$788$			5.26591e33i			0.0918668i
$789$	−5.99798e34	−	2.74813e33i	−1.03058	−	0.0472186i
$790$	1.01997e34			0.172608
$791$			9.00972e34i			1.50174i
$792$	2.50958e34	+	2.30450e33i	0.412001	+	0.0378333i
$793$	8.44902e33			0.136624
$794$			1.52264e34i			0.242523i
$795$	1.22796e31	−	2.68010e32i	0.000192654	−	0.00420480i
$796$	−3.22406e33			−0.0498249
$797$		−	7.00599e34i		−	1.06652i	−0.845951	−	0.533261i	$-0.820967\pi$
$797$		−	7.00599e34i		−	1.06652i	0.845951	−	0.533261i	$-0.179033\pi$
$798$	1.97720e35	+	9.05907e33i	2.96494	+	0.135847i
$799$	6.11197e34			0.902859
$800$			7.91984e34i			1.15249i
$801$	4.36036e33	−	4.74840e34i	0.0625075	−	0.680702i
$802$	−1.19704e35			−1.69051
$803$		−	2.16488e34i		−	0.301194i
$804$	−2.32553e32	+	5.07562e33i	−0.00318750	+	0.0695692i
$805$	−2.35461e34			−0.317957
$806$		−	9.40787e33i		−	0.125161i
$807$	−7.64072e34	−	3.50080e33i	−1.00150	−	0.0458865i
$808$	−1.22912e34			−0.158729
$809$		−	1.15058e35i		−	1.46398i	−0.681316	−	0.731989i	$-0.738592\pi$
$809$		−	1.15058e35i		−	1.46398i	0.681316	−	0.731989i	$-0.261408\pi$
$810$	−2.22714e34	−	4.12507e33i	−0.279208	−	0.0517143i
$811$	−8.60608e34			−1.06305			−0.531527	−	0.847041i	$-0.678382\pi$
$811$	−8.60608e34			−1.06305			−0.531527	+	0.847041i	$0.678382\pi$
$812$		−	1.11610e35i		−	1.35841i
$813$	−5.89508e33	+	1.28664e35i	−0.0706974	+	1.54302i
$814$	1.44552e35			1.70817
$815$		−	3.64195e34i		−	0.424075i
$816$	−6.93284e34	−	3.17647e33i	−0.795480	−	0.0364470i
$817$	−1.40568e35			−1.58936
$818$		−	4.24257e34i		−	0.472704i
$819$	−7.92327e34	−	7.27578e33i	−0.869956	−	0.0798864i
$820$	−2.43700e33			−0.0263687
$821$			1.04318e35i			1.11235i	0.831066	+	0.556173i	$0.187731\pi$
$821$			1.04318e35i			1.11235i	−0.831066	+	0.556173i	$0.812269\pi$
$822$	2.70404e33	−	5.90174e34i	0.0284152	−	0.620181i
$823$	1.29959e35			1.34589			0.672944	−	0.739694i	$-0.265030\pi$
$823$	1.29959e35			1.34589			0.672944	+	0.739694i	$0.265030\pi$
$824$		−	5.48418e34i		−	0.559738i
$825$	1.06805e35	+	4.89354e33i	1.07434	+	0.0492239i
$826$	1.34424e35			1.33265
$827$		−	1.73426e34i		−	0.169453i	−0.996404	−	0.0847265i	$-0.972998\pi$
$827$		−	1.73426e34i		−	0.169453i	0.996404	−	0.0847265i	$-0.0270016\pi$
$828$	6.71183e33	−	7.30913e34i	0.0646364	−	0.703885i
$829$	4.84844e34			0.460201			0.230101	−	0.973167i	$-0.426094\pi$
$829$	4.84844e34			0.460201			0.230101	+	0.973167i	$0.426094\pi$
$830$			4.10257e34i			0.383812i
$831$	−6.08547e33	+	1.32819e35i	−0.0561154	+	1.22475i
$832$	2.46942e34			0.224448
$833$		−	9.18113e34i		−	0.822538i
$834$	−3.84192e34	−	1.76028e33i	−0.339278	−	0.0155449i
$835$	4.56110e34			0.397038
$836$			1.43205e35i			1.22880i
$837$	2.64689e33	−	1.91488e34i	0.0223888	−	0.161971i
$838$	−9.93843e34			−0.828685
$839$			1.56426e35i			1.28578i	0.765959	+	0.642889i	$0.222264\pi$
$839$			1.56426e35i			1.28578i	−0.765959	+	0.642889i	$0.777736\pi$
$840$	6.71204e32	−	1.46495e34i	0.00543880	−	0.118705i
$841$	−7.34103e34			−0.586415
$842$			1.01574e35i			0.799900i
$843$	8.34506e33	+	3.82351e32i	0.0647886	+	0.00296846i
$844$	4.48445e34			0.343242
$845$			1.89182e34i			0.142758i
$846$	−2.39147e35	−	2.19604e34i	−1.77918	−	0.163379i
$847$	−5.57524e34			−0.408943
$848$			3.23005e33i			0.0233592i
$849$	5.45315e33	−	1.19019e35i	0.0388826	−	0.848638i
$850$	−1.17869e35			−0.828651
$851$			1.63358e35i			1.13236i
$852$	−5.02951e34	−	2.30440e33i	−0.343756	−	0.0157501i
$853$	2.80714e35			1.89180			0.945901	−	0.324454i	$-0.105181\pi$
$853$	2.80714e35			1.89180			0.945901	+	0.324454i	$0.105181\pi$
$854$		−	6.91764e34i		−	0.459688i
$855$	−4.56677e33	+	4.97317e34i	−0.0299237	+	0.325867i
$856$	8.62444e34			0.557244
$857$		−	1.04775e35i		−	0.667557i	−0.942652	−	0.333779i	$-0.891676\pi$
$857$		−	1.04775e35i		−	0.667557i	0.942652	−	0.333779i	$-0.108324\pi$
$858$	6.29208e33	−	1.37329e35i	0.0395318	−	0.862807i
$859$	−3.22031e34			−0.199517			−0.0997585	−	0.995012i	$-0.531807\pi$
$859$	−3.22031e34			−0.199517			−0.0997585	+	0.995012i	$0.531807\pi$
$860$		−	2.68414e34i		−	0.163993i
$861$	−4.19617e34	−	1.92259e33i	−0.252822	−	0.0115837i
$862$	1.40675e35			0.835855
$863$		−	1.23171e35i		−	0.721739i	−0.932616	−	0.360870i	$-0.882480\pi$
$863$		−	1.23171e35i		−	0.721739i	0.932616	−	0.360870i	$-0.117520\pi$
$864$	2.07271e35	+	2.86505e34i	1.19777	+	0.165564i
$865$	−4.67803e34			−0.266606
$866$		−	3.52801e35i		−	1.98297i
$867$	−4.62926e33	+	1.01037e35i	−0.0256615	+	0.560080i
$868$	−3.22556e34			−0.176347
$869$			1.27201e35i			0.685889i
$870$	6.71794e34	+	3.07800e33i	0.357277	+	0.0163696i
$871$	−1.07545e34			−0.0564119
$872$			3.17486e34i			0.164258i
$873$	1.87812e35	+	1.72464e34i	0.958412	+	0.0880091i
$874$	−3.86466e35			−1.94524
$875$		−	1.27490e35i		−	0.632965i
$876$	1.79736e33	−	3.92285e34i	0.00880207	−	0.192111i
$877$	−2.10105e35			−1.01494			−0.507472	−	0.861668i	$-0.669420\pi$
$877$	−2.10105e35			−1.01494			−0.507472	+	0.861668i	$0.669420\pi$
$878$			2.60901e35i			1.24320i
$879$	9.40627e34	+	4.30973e33i	0.442131	+	0.0202574i
$880$	6.32929e34			0.293470
$881$		−	3.92932e35i		−	1.79724i	−0.438726	−	0.898621i	$-0.644570\pi$
$881$		−	3.92932e35i		−	1.79724i	0.438726	−	0.898621i	$-0.355430\pi$
$882$	−3.29880e34	+	3.59236e35i	−0.148844	+	1.62090i
$883$	−3.99273e35			−1.77722			−0.888612	−	0.458660i	$-0.848329\pi$
$883$	−3.99273e35			−1.77722			−0.888612	+	0.458660i	$0.848329\pi$
$884$			6.34647e34i			0.278680i
$885$	−1.55240e33	+	3.38822e34i	−0.00672488	+	0.146775i
$886$	4.12212e35			1.76163
$887$		−	3.48394e34i		−	0.146888i	−0.997299	−	0.0734441i	$-0.976601\pi$
$887$		−	3.48394e34i		−	0.146888i	0.997299	−	0.0734441i	$-0.0233991\pi$
$888$	−1.01635e35	−	4.65669e33i	−0.422755	−	0.0193696i
$889$	−2.60811e34			−0.107030
$890$		−	4.79416e34i		−	0.194103i
$891$	5.14441e34	−	2.77749e35i	0.205496	−	1.10948i
$892$	1.41931e35			0.559369
$893$			5.29509e35i			2.05900i
$894$	−1.50411e34	+	3.28282e35i	−0.0577071	+	1.25950i
$895$	−5.36087e34			−0.202936
$896$			2.82430e35i			1.05491i
$897$	1.55195e35	+	7.11066e33i	0.571963	+	0.0262060i
$898$	−2.21280e35			−0.804684
$899$			5.73945e34i			0.205946i
$900$	1.93128e35	+	1.77346e34i	0.683810	+	0.0627930i
$901$	−3.68863e33			−0.0128875
$902$		−	7.25768e34i		−	0.250218i
$903$	2.11756e34	−	4.62172e35i	0.0720417	−	1.57236i
$904$	1.09566e35			0.367836
$905$			1.65403e34i			0.0547974i
$906$	−2.95757e35	−	1.35509e34i	−0.966932	−	0.0443026i
$907$	4.87653e35			1.57334			0.786671	−	0.617373i	$-0.211803\pi$
$907$	4.87653e35			1.57334			0.786671	+	0.617373i	$0.211803\pi$
$908$		−	1.86063e35i		−	0.592421i
$909$	−1.25979e34	+	1.37190e35i	−0.0395851	+	0.431078i
$910$	−7.99962e34			−0.248069
$911$		−	2.38593e35i		−	0.730192i	−0.930970	−	0.365096i	$-0.881036\pi$
$911$		−	2.38593e35i		−	0.730192i	0.930970	−	0.365096i	$-0.118964\pi$
$912$	2.75192e34	−	6.00625e35i	0.0831186	−	1.81412i
$913$	−5.11636e35			−1.52515
$914$		−	1.40624e35i		−	0.413718i
$915$	1.74362e34	+	7.98888e32i	0.0506290	+	0.00231970i
$916$	9.08965e34			0.260496
$917$			5.00012e35i			1.41432i
$918$	−4.26397e34	+	3.08475e35i	−0.119042	+	0.861208i
$919$	1.34436e35			0.370449			0.185224	−	0.982696i	$-0.440699\pi$
$919$	1.34436e35			0.370449			0.185224	+	0.982696i	$0.440699\pi$
$920$			2.86340e34i			0.0778804i
$921$	5.44950e33	−	1.18939e35i	0.0146299	−	0.319307i
$922$	7.31030e35			1.93716
$923$		−	1.06567e35i		−	0.278743i
$924$	−4.70842e35	−	2.15729e34i	−1.21566	−	0.0556986i
$925$	−4.31639e35			−1.10007
$926$		−	3.61259e35i		−	0.908839i
$927$	−6.12126e35	−	5.62103e34i	−1.52014	−	0.139592i
$928$	−6.21251e35			−1.52297
$929$		−	7.07852e35i		−	1.71299i	−0.516158	−	0.856493i	$-0.672638\pi$
$929$		−	7.07852e35i		−	1.71299i	0.516158	−	0.856493i	$-0.327362\pi$
$930$	8.89551e32	−	1.94150e34i	0.00212508	−	0.0463812i
$931$	7.95405e35			1.87582
$932$			5.21474e35i			1.21406i
$933$	5.69887e35	+	2.61109e34i	1.30981	+	0.0600126i
$934$	−1.76263e35			−0.399943
$935$			7.22788e34i			0.161909i
$936$	−8.84797e33	+	9.63536e34i	−0.0195674	+	0.213087i
$937$	3.88231e35			0.847648			0.423824	−	0.905745i	$-0.360688\pi$
$937$	3.88231e35			0.847648			0.423824	+	0.905745i	$0.360688\pi$
$938$			8.80521e34i			0.189804i
$939$	−3.62223e34	+	7.90575e35i	−0.0770884	+	1.68250i
$940$	−1.01110e35			−0.212451
$941$			6.86827e35i			1.42486i	0.701743	+	0.712430i	$0.252405\pi$
$941$			6.86827e35i			1.42486i	−0.701743	+	0.712430i	$0.747595\pi$
$942$	2.31424e35	+	1.06033e34i	0.474020	+	0.0217185i
$943$	8.20189e34			0.165872
$944$		−	4.08346e35i		−	0.815389i
$945$	−1.62825e35	−	2.25068e34i	−0.321025	−	0.0443744i
$946$	7.99371e35			1.55616
$947$			1.75347e35i			0.337054i	0.985697	+	0.168527i	$0.0539010\pi$
$947$			1.75347e35i			0.337054i	−0.985697	+	0.168527i	$0.946099\pi$
$948$	−1.05607e34	+	2.30494e35i	−0.0200443	+	0.437481i
$949$	8.31190e34			0.155778
$950$		−	1.02115e36i		−	1.88976i
$951$	−5.03591e35	−	2.30734e34i	−0.920263	−	0.0421643i
$952$	−2.01621e35			−0.363824
$953$			4.62990e35i			0.825005i	0.910956	+	0.412503i	$0.135345\pi$
$953$			4.62990e35i			0.825005i	−0.910956	+	0.412503i	$0.864655\pi$
$954$	1.44327e34	+	1.32533e33i	0.0253962	+	0.00233208i
$955$	1.64965e35			0.286650
$956$			3.48575e35i			0.598138i
$957$	−3.83861e34	+	8.37801e35i	−0.0650475	+	1.41970i
$958$	−1.14252e36			−1.91196
$959$		−	4.28739e35i		−	0.708549i
$960$	5.09615e34	+	2.33494e33i	0.0831740	+	0.00381084i
$961$	−6.03825e35			−0.973264
$962$			5.54999e35i			0.883468i
$963$	8.83966e34	−	9.62631e35i	0.138970	−	1.51337i
$964$	3.10450e35			0.482022
$965$		−	1.25477e35i		−	0.192413i
$966$	5.82186e34	−	1.27066e36i	0.0881731	−	1.92444i
$967$	−6.74786e35			−1.00936			−0.504682	−	0.863305i	$-0.668390\pi$
$967$	−6.74786e35			−1.00936			−0.504682	+	0.863305i	$0.668390\pi$
$968$			6.77996e34i			0.100167i
$969$	6.85898e35	+	3.14262e34i	1.00086	+	0.0458571i
$970$	1.89622e35			0.273292
$971$		−	1.08989e36i		−	1.55150i	−0.631043	−	0.775748i	$-0.717373\pi$
$971$		−	1.08989e36i		−	1.55150i	0.631043	−	0.775748i	$-0.282627\pi$
$972$	1.16278e35	−	4.99021e35i	0.163495	−	0.701656i
$973$	−2.79101e35			−0.387621
$974$			9.38401e35i			1.28730i
$975$	−1.87884e34	+	4.10069e35i	−0.0254586	+	0.555651i
$976$	−2.10141e35			−0.281263
$977$		−	1.19976e35i		−	0.158621i	−0.996850	−	0.0793103i	$-0.974728\pi$
$977$		−	1.19976e35i		−	0.158621i	0.996850	−	0.0793103i	$-0.0252718\pi$
$978$	1.96537e36	+	9.00485e34i	2.56671	+	0.117601i
$979$	5.97884e35			0.771302
$980$			1.51883e35i			0.193551i
$981$	3.54368e35	+	3.25409e34i	0.446093	+	0.0409639i
$982$	1.91240e35			0.237816
$983$			1.67619e35i			0.205911i	0.994686	+	0.102956i	$0.0328300\pi$
$983$			1.67619e35i			0.205911i	−0.994686	+	0.102956i	$0.967170\pi$
$984$	−2.33803e33	+	5.10290e34i	−0.00283732	+	0.0619264i
$985$	−2.30260e34			−0.0276048
$986$		−	9.24590e35i		−	1.09503i
$987$	−1.74097e36	−	7.97671e34i	−2.03697	−	0.0933293i
$988$	−5.49825e35			−0.635537
$989$			9.03367e35i			1.03159i
$990$	2.59699e34	−	2.82810e35i	0.0292987	−	0.319060i
$991$	6.85685e35			0.764260			0.382130	−	0.924109i	$-0.375191\pi$
$991$	6.85685e35			0.764260			0.382130	+	0.924109i	$0.375191\pi$
$992$			1.79543e35i			0.197710i
$993$	2.92872e34	−	6.39212e35i	0.0318630	−	0.695430i
$994$	−8.72521e35			−0.937863
$995$		−	1.40977e34i		−	0.0149717i
$996$	−9.27104e35	−	4.24777e34i	−0.972784	−	0.0445707i
$997$	−3.99999e35			−0.414684			−0.207342	−	0.978268i	$-0.566481\pi$
$997$	−3.99999e35			−0.414684			−0.207342	+	0.978268i	$0.566481\pi$
$998$			2.15308e36i			2.20543i
$999$	−1.56148e35	+	1.12965e36i	−0.158034	+	1.14329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.25.b.b.2.2	✓	6
3.2	odd	2	inner	3.25.b.b.2.5	yes	6
4.3	odd	2		48.25.e.b.17.3		6
12.11	even	2		48.25.e.b.17.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.25.b.b.2.2	✓	6	1.1	even	1	trivial
3.25.b.b.2.5	yes	6	3.2	odd	2	inner
48.25.e.b.17.3		6	4.3	odd	2
48.25.e.b.17.4		6	12.11	even	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5372.56i q^{2} +(-24323.9 + 530884. i) q^{3} -1.20872e7 q^{4} -5.28531e7i q^{5} +(2.85221e9 + 1.30681e8i) q^{6} +2.07202e10 q^{7} -2.51975e10i q^{8} +(-2.81246e11 - 2.58263e10i) q^{9} +O(q^{10})\)	\(q-5372.56i q^{2} +(-24323.9 + 530884. i) q^{3} -1.20872e7 q^{4} -5.28531e7i q^{5} +(2.85221e9 + 1.30681e8i) q^{6} +2.07202e10 q^{7} -2.51975e10i q^{8} +(-2.81246e11 - 2.58263e10i) q^{9} -2.83957e11 q^{10} -3.54125e12i q^{11} +(2.94007e11 - 6.41689e12i) q^{12} +1.35964e13 q^{13} -1.11321e14i q^{14} +(2.80589e13 + 1.28559e12i) q^{15} -3.38164e14 q^{16} -3.86175e14i q^{17} +(-1.38753e14 + 1.51101e15i) q^{18} +3.34561e15 q^{19} +6.38845e14i q^{20} +(-5.03995e14 + 1.10000e16i) q^{21} -1.90256e16 q^{22} -2.15008e16i q^{23} +(1.33770e16 + 6.12901e14i) q^{24} +5.68112e16 q^{25} -7.30474e16i q^{26} +(2.05518e16 - 1.48681e17i) q^{27} -2.50449e17 q^{28} +4.45640e17i q^{29} +(6.90692e15 - 1.50748e17i) q^{30} +1.28791e17 q^{31} +1.39406e18i q^{32} +(1.87999e18 + 8.61369e16i) q^{33} -2.07475e18 q^{34} -1.09513e18i q^{35} +(3.39947e18 + 3.12167e17i) q^{36} -7.59778e18 q^{37} -1.79745e19i q^{38} +(-3.30717e17 + 7.21811e18i) q^{39} -1.33177e18 q^{40} +3.81470e18i q^{41} +(5.90983e19 + 2.70774e18i) q^{42} -4.20156e19 q^{43} +4.28037e19i q^{44} +(-1.36500e18 + 1.48647e19i) q^{45} -1.15514e20 q^{46} +1.58270e20i q^{47} +(8.22546e18 - 1.79526e20i) q^{48} +2.37745e20 q^{49} -3.05222e20i q^{50} +(2.05014e20 + 9.39326e18i) q^{51} -1.64342e20 q^{52} -9.55171e18i q^{53} +(-7.98797e20 - 1.10416e20i) q^{54} -1.87166e20 q^{55} -5.22097e20i q^{56} +(-8.13783e19 + 1.77613e21i) q^{57} +2.39423e21 q^{58} +1.20754e21i q^{59} +(-3.39153e20 - 1.55392e19i) q^{60} +6.21416e20 q^{61} -6.91938e20i q^{62} +(-5.82748e21 - 5.35126e20i) q^{63} +1.81624e21 q^{64} -7.18612e20i q^{65} +(4.62776e20 - 1.01004e22i) q^{66} -7.90979e20 q^{67} +4.66776e21i q^{68} +(1.14144e22 + 5.22982e20i) q^{69} -5.88364e21 q^{70} -7.83792e21i q^{71} +(-6.50758e20 + 7.08670e21i) q^{72} +6.11332e21 q^{73} +4.08195e22i q^{74} +(-1.38187e21 + 3.01602e22i) q^{75} -4.04390e22 q^{76} -7.33754e22i q^{77} +(3.87797e22 + 1.77680e21i) q^{78} -3.59198e22 q^{79} +1.78730e22i q^{80} +(7.84324e22 + 1.45271e22i) q^{81} +2.04947e22 q^{82} -1.44479e23i q^{83} +(6.09188e21 - 1.32959e23i) q^{84} -2.04105e22 q^{85} +2.25731e23i q^{86} +(-2.36583e23 - 1.08397e22i) q^{87} -8.92307e22 q^{88} +1.68834e23i q^{89} +(7.98617e22 + 7.33355e21i) q^{90} +2.81720e23 q^{91} +2.59884e23i q^{92} +(-3.13270e21 + 6.83732e22i) q^{93} +8.50312e23 q^{94} -1.76826e23i q^{95} +(-7.40086e23 - 3.39090e22i) q^{96} -6.67785e23 q^{97} -1.27730e24i q^{98} +(-9.14574e22 + 9.95963e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9}+O(q^{10}) \) 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9	\( 6 q - 616842 q^{3} - 63346800 q^{4} - 2673890352 q^{6} + 1988064876 q^{7} - 791186949882 q^{9} + 2770823311200 q^{10} - 18492861842352 q^{12} - 73542438063924 q^{13} + 227151045057600 q^{15} - 433335898904448 q^{16} - 12\!\cdots\!40 q^{18}+ \cdots - 18\!\cdots\!20 q^{99}+O(q^{100}) \) 6 * q - 616842 * q^3 - 63346800 * q^4 - 2673890352 * q^6 + 1988064876 * q^7 - 791186949882 * q^9 + 2770823311200 * q^10 - 18492861842352 * q^12 - 73542438063924 * q^13 + 227151045057600 * q^15 - 433335898904448 * q^16 - 1227888881468640 * q^18 + 6095219493474156 * q^19 + 2706110098936524 * q^21 - 4132747004902560 * q^22 + 79223562819483264 * q^24 - 206274704562968250 * q^25 - 153687400093414602 * q^27 + 11425252275435936 * q^28 + 1679034252186079200 * q^30 - 1137843910975220628 * q^31 + 7067811391497299520 * q^33 - 15440589345121992576 * q^34 + 23041875850704576144 * q^36 - 14032623495718823604 * q^37 + 25380736596180392364 * q^39 - 121930725979226707200 * q^40 + 209343891033396594720 * q^42 - 114603298148542353684 * q^43 + 311304965429932790400 * q^45 - 346860905830754272704 * q^46 + 51162839242132733568 * q^48 + 107947782097205854482 * q^49 - 479022139696737883392 * q^51 - 124107229893322470624 * q^52 - 1113391638534691344528 * q^54 + 1679273232066520675200 * q^55 - 1140401446469855973684 * q^57 + 7395366373865537628960 * q^58 - 14436777252623118393600 * q^60 + 10013078414594836175052 * q^61 - 8325410033672205875604 * q^63 + 11741892494977734042624 * q^64 - 5418873997530695523360 * q^66 - 5445087092431082846484 * q^67 + 11943290073056639859072 * q^69 - 55632387081854182017600 * q^70 + 63773250138227244591360 * q^72 + 7228988839203443040396 * q^73 + 37723327374597984717750 * q^75 - 4244116415001816243552 * q^76 + 235720510135983845200800 * q^78 - 423484844106082827915924 * q^79 + 102726090691231740574086 * q^81 - 272255725325320387035840 * q^82 + 200996808333809534079264 * q^84 + 319008824808936798988800 * q^85 - 252430535429613815803200 * q^87 + 160152458683551892335360 * q^88 - 1246806301659161625597600 * q^90 + 1497033316223591396871768 * q^91 - 501165623869166897253684 * q^93 + 1979316836866080826257024 * q^94 - 1420600675222724601424896 * q^96 - 1411607470255832450422644 * q^97 - 1834460043482282449115520 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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