LMFDB - Embedded newform 3.23.b.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,23,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, 23, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 23 $
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:	$9.20122304526$
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} + 126474x^{4} + 3861674040x^{2} + 9831214131200 $ x^6 + 126474x^4 + 3861674040x^2 + 9831214131200
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{21}\cdot 3^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.6
Root			$281.771i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.23.b.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3381.25i q^{2} +(169408. - 51788.6i) q^{3} -7.23853e6 q^{4} +6.36810e7i q^{5} +(1.75110e8 + 5.72810e8i) q^{6} -2.60308e9 q^{7} -1.02933e10i q^{8} +(2.60170e10 - 1.75468e10i) q^{9} +O(q^{10})$	\(q+3381.25i q^{2} +(169408. - 51788.6i) q^{3} -7.23853e6 q^{4} +6.36810e7i q^{5} +(1.75110e8 + 5.72810e8i) q^{6} -2.60308e9 q^{7} -1.02933e10i q^{8} +(2.60170e10 - 1.75468e10i) q^{9} -2.15321e11 q^{10} +2.74891e10i q^{11} +(-1.22626e12 + 3.74873e11i) q^{12} -6.09922e9 q^{13} -8.80165e12i q^{14} +(3.29794e12 + 1.07881e13i) q^{15} +4.44356e12 q^{16} +8.12449e12i q^{17} +(5.93300e13 + 8.79698e13i) q^{18} +7.54682e13 q^{19} -4.60957e14i q^{20} +(-4.40982e14 + 1.34810e14i) q^{21} -9.29473e13 q^{22} +1.66353e15i q^{23} +(-5.33075e14 - 1.74376e15i) q^{24} -1.67108e15 q^{25} -2.06230e13i q^{26} +(3.49875e15 - 4.31994e15i) q^{27} +1.88425e16 q^{28} +1.26684e16i q^{29} +(-3.64771e16 + 1.11512e16i) q^{30} +1.69379e16 q^{31} -2.81484e16i q^{32} +(1.42362e15 + 4.65686e15i) q^{33} -2.74709e16 q^{34} -1.65766e17i q^{35} +(-1.88325e17 + 1.27013e17i) q^{36} +1.59704e17 q^{37} +2.55177e17i q^{38} +(-1.03325e15 + 3.15870e14i) q^{39} +6.55487e17 q^{40} +4.83588e17i q^{41} +(-4.55825e17 - 1.49107e18i) q^{42} +4.91968e17 q^{43} -1.98980e17i q^{44} +(1.11740e18 + 1.65678e18i) q^{45} -5.62480e18 q^{46} +7.73166e17i q^{47} +(7.52774e17 - 2.30126e17i) q^{48} +2.86619e18 q^{49} -5.65033e18i q^{50} +(4.20756e17 + 1.37635e18i) q^{51} +4.41494e16 q^{52} -5.90402e18i q^{53} +(1.46068e19 + 1.18302e19i) q^{54} -1.75053e18 q^{55} +2.67942e19i q^{56} +(1.27849e19 - 3.90839e18i) q^{57} -4.28351e19 q^{58} -2.68658e19i q^{59} +(-2.38723e19 - 7.80897e19i) q^{60} +2.43398e19 q^{61} +5.72711e19i q^{62} +(-6.77241e19 + 4.56756e19i) q^{63} +1.13814e20 q^{64} -3.88404e17i q^{65} +(-1.57460e19 + 4.81361e18i) q^{66} -1.30406e20 q^{67} -5.88094e19i q^{68} +(8.61517e19 + 2.81815e20i) q^{69} +5.60498e20 q^{70} -4.07363e20i q^{71} +(-1.80614e20 - 2.67800e20i) q^{72} -4.04873e20 q^{73} +5.39998e20i q^{74} +(-2.83094e20 + 8.65427e19i) q^{75} -5.46279e20 q^{76} -7.15562e19i q^{77} +(-1.06803e18 - 3.49369e18i) q^{78} +1.11027e21 q^{79} +2.82970e20i q^{80} +(3.68993e20 - 9.13027e20i) q^{81} -1.63513e21 q^{82} +1.31903e19i q^{83} +(3.19206e21 - 9.75824e20i) q^{84} -5.17375e20 q^{85} +1.66347e21i q^{86} +(6.56080e20 + 2.14613e21i) q^{87} +2.82953e20 q^{88} -2.62916e20i q^{89} +(-5.60200e21 + 3.77819e21i) q^{90} +1.58767e19 q^{91} -1.20415e22i q^{92} +(2.86941e21 - 8.77187e20i) q^{93} -2.61427e21 q^{94} +4.80589e21i q^{95} +(-1.45777e21 - 4.76856e21i) q^{96} -1.92665e21 q^{97} +9.69131e21i q^{98} +(4.82344e20 + 7.15181e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9}+O(q^{10}) $ 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9	$ 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9} - 186869600640 q^{10} - 1325972980800 q^{12} + 2025132496860 q^{13} + 2628031314240 q^{15} - 9703467227136 q^{16} + 42127150135680 q^{18} + 100485688668636 q^{19} - 789079193287812 q^{21} + 10\!\cdots\!00 q^{22}+ \cdots - 60\!\cdots\!60 q^{99}+O(q^{100}) $ 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9 - 186869600640 * q^10 - 1325972980800 * q^12 + 2025132496860 * q^13 + 2628031314240 * q^15 - 9703467227136 * q^16 + 42127150135680 * q^18 + 100485688668636 * q^19 - 789079193287812 * q^21 + 1045890315676800 * q^22 - 2472467233277952 * q^24 + 1396569263732790 * q^25 - 10731657558901410 * q^27 + 44570708098492800 * q^28 - 116169123436801920 * q^30 + 114109662401153292 * q^31 - 174850022773609920 * q^33 + 319017868488396288 * q^34 - 707589966262651200 * q^36 + 683782874080661820 * q^37 - 1038045209126993748 * q^39 + 1781949720499015680 * q^40 - 1108714403505421440 * q^42 + 273273330169769340 * q^43 + 3228622736179443840 * q^45 - 8349686917048426752 * q^46 + 10392767955626526720 * q^48 - 8294807529216677070 * q^49 + 14237699192275302144 * q^51 - 22636595958302682240 * q^52 + 48383805955937626944 * q^54 - 40874587160137441920 * q^55 + 43721391850797114540 * q^57 - 67285958146132360320 * q^58 - 44311576503733309440 * q^60 + 121649250388145492892 * q^61 - 184494903535705683060 * q^63 + 285203601894474055680 * q^64 - 374640791614422030720 * q^66 + 75701571086175260700 * q^67 - 233446021721582921856 * q^69 + 1113607014897000234240 * q^70 - 639860863731149721600 * q^72 - 57178481309533986900 * q^73 - 333973626119358339330 * q^75 - 731229802672243966080 * q^76 + 735750453969076417920 * q^78 + 384537395891327736396 * q^79 + 3109769787236091157926 * q^81 - 5166859472437001068800 * q^82 + 6698665889827068753792 * q^84 - 6772579853411844011520 * q^85 + 4995406256507248236480 * q^87 - 404168025320661381120 * q^88 - 3858783621100493362560 * q^90 - 2806742501496183911304 * q^91 + 2087220280517252053020 * q^93 + 8135725180445469439488 * q^94 - 15069021592890694238208 * q^96 + 1565231688506989945740 * q^97 - 6095367699696122981760 * 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 $

$2$			3381.25i			1.65100i	0.564402	+	0.825500i	$0.309107\pi$
$2$			3381.25i			1.65100i	−0.564402	+	0.825500i	$0.690893\pi$
$3$	169408.	−	51788.6i	0.956312	−	0.292348i
$3$	169408.	−	51788.6i	0.956312	−	0.292348i
$4$	−7.23853e6			−1.72580
$5$			6.36810e7i			1.30419i	0.758139	+	0.652093i	$0.226109\pi$
$5$			6.36810e7i			1.30419i	−0.758139	+	0.652093i	$0.773891\pi$
$6$	1.75110e8	+	5.72810e8i	0.482666	+	1.57887i
$7$	−2.60308e9			−1.31646			−0.658232	−	0.752816i	$-0.728695\pi$
$7$	−2.60308e9			−1.31646			−0.658232	+	0.752816i	$0.728695\pi$
$8$		−	1.02933e10i		−	1.19830i
$9$	2.60170e10	−	1.75468e10i	0.829065	−	0.559152i
$10$	−2.15321e11			−2.15321
$11$			2.74891e10i			0.0963475i	0.998839	+	0.0481737i	$0.0153401\pi$
$11$			2.74891e10i			0.0963475i	−0.998839	+	0.0481737i	$0.984660\pi$
$12$	−1.22626e12	+	3.74873e11i	−1.65040	+	0.504534i
$13$	−6.09922e9			−0.00340328			−0.00170164	−	0.999999i	$-0.500542\pi$
$13$	−6.09922e9			−0.00340328			−0.00170164	+	0.999999i	$0.500542\pi$
$14$		−	8.80165e12i		−	2.17348i
$15$	3.29794e12	+	1.07881e13i	0.381276	+	1.24721i
$16$	4.44356e12			0.252587
$17$			8.12449e12i			0.237060i	0.992950	+	0.118530i	$0.0378182\pi$
$17$			8.12449e12i			0.237060i	−0.992950	+	0.118530i	$0.962182\pi$
$18$	5.93300e13	+	8.79698e13i	0.923159	+	1.36879i
$19$	7.54682e13			0.647850			0.323925	−	0.946083i	$-0.394997\pi$
$19$	7.54682e13			0.647850			0.323925	+	0.946083i	$0.394997\pi$
$20$		−	4.60957e14i		−	2.25076i
$21$	−4.40982e14	+	1.34810e14i	−1.25895	+	0.384865i
$22$	−9.29473e13			−0.159070
$23$			1.66353e15i			1.74592i	0.487794	+	0.872959i	$0.337802\pi$
$23$			1.66353e15i			1.74592i	−0.487794	+	0.872959i	$0.662198\pi$
$24$	−5.33075e14	−	1.74376e15i	−0.350320	−	1.14595i
$25$	−1.67108e15			−0.700901
$26$		−	2.06230e13i		−	0.00561881i
$27$	3.49875e15	−	4.31994e15i	0.629378	−	0.777099i
$28$	1.88425e16			2.27195
$29$			1.26684e16i			1.03835i	0.854667	+	0.519176i	$0.173761\pi$
$29$			1.26684e16i			1.03835i	−0.854667	+	0.519176i	$0.826239\pi$
$30$	−3.64771e16	+	1.11512e16i	−2.05914	+	0.629487i
$31$	1.69379e16			0.666622			0.333311	−	0.942817i	$-0.391834\pi$
$31$	1.69379e16			0.666622			0.333311	+	0.942817i	$0.391834\pi$
$32$		−	2.81484e16i		−	0.781275i
$33$	1.42362e15	+	4.65686e15i	0.0281670	+	0.0921382i
$34$	−2.74709e16			−0.391386
$35$		−	1.65766e17i		−	1.71691i
$36$	−1.88325e17	+	1.27013e17i	−1.43080	+	0.964984i
$37$	1.59704e17			0.897628			0.448814	−	0.893625i	$-0.351847\pi$
$37$	1.59704e17			0.897628			0.448814	+	0.893625i	$0.351847\pi$
$38$			2.55177e17i			1.06960i
$39$	−1.03325e15	+	3.15870e14i	−0.00325459	+	0.000994940i
$40$	6.55487e17			1.56280
$41$			4.83588e17i			0.878726i	0.898310	+	0.439363i	$0.144796\pi$
$41$			4.83588e17i			0.878726i	−0.898310	+	0.439363i	$0.855204\pi$
$42$	−4.55825e17	−	1.49107e18i	−0.635412	−	2.07853i
$43$	4.91968e17			0.529400			0.264700	−	0.964331i	$-0.414727\pi$
$43$	4.91968e17			0.529400			0.264700	+	0.964331i	$0.414727\pi$
$44$		−	1.98980e17i		−	0.166277i
$45$	1.11740e18	+	1.65678e18i	0.729238	+	1.08126i
$46$	−5.62480e18			−2.88251
$47$			7.73166e17i			0.312749i	0.987698	+	0.156375i	$0.0499807\pi$
$47$			7.73166e17i			0.312749i	−0.987698	+	0.156375i	$0.950019\pi$
$48$	7.52774e17	−	2.30126e17i	0.241552	−	0.0738433i
$49$	2.86619e18			0.733075
$50$		−	5.65033e18i		−	1.15719i
$51$	4.20756e17	+	1.37635e18i	0.0693039	+	0.226703i
$52$	4.41494e16			0.00587337
$53$		−	5.90402e18i		−	0.636962i	−0.947929	−	0.318481i	$-0.896827\pi$
$53$		−	5.90402e18i		−	0.636962i	0.947929	−	0.318481i	$-0.103173\pi$
$54$	1.46068e19	+	1.18302e19i	1.28299	+	1.03910i
$55$	−1.75053e18			−0.125655
$56$			2.67942e19i			1.57751i
$57$	1.27849e19	−	3.90839e18i	0.619547	−	0.189398i
$58$	−4.28351e19			−1.71432
$59$		−	2.68658e19i		−	0.890897i	−0.895308	−	0.445449i	$-0.853044\pi$
$59$		−	2.68658e19i		−	0.890897i	0.895308	−	0.445449i	$-0.146956\pi$
$60$	−2.38723e19	−	7.80897e19i	−0.658006	−	2.15243i
$61$	2.43398e19			0.559357			0.279678	−	0.960094i	$-0.409772\pi$
$61$	2.43398e19			0.559357			0.279678	+	0.960094i	$0.409772\pi$
$62$			5.72711e19i			1.10059i
$63$	−6.77241e19	+	4.56756e19i	−1.09143	+	0.736102i
$64$	1.13814e20			1.54247
$65$		−	3.88404e17i		−	0.00443850i
$66$	−1.57460e19	+	4.81361e18i	−0.152120	+	0.0465037i
$67$	−1.30406e20			−1.06776			−0.533882	−	0.845559i	$-0.679267\pi$
$67$	−1.30406e20			−1.06776			−0.533882	+	0.845559i	$0.679267\pi$
$68$		−	5.88094e19i		−	0.409118i
$69$	8.61517e19	+	2.81815e20i	0.510415	+	1.66964i
$70$	5.60498e20			2.83462
$71$		−	4.07363e20i		−	1.76254i	−0.472609	−	0.881272i	$-0.656688\pi$
$71$		−	4.07363e20i		−	1.76254i	0.472609	−	0.881272i	$-0.343312\pi$
$72$	−1.80614e20	−	2.67800e20i	−0.670030	−	0.993466i
$73$	−4.04873e20			−1.29053			−0.645263	−	0.763960i	$-0.723252\pi$
$73$	−4.04873e20			−1.29053			−0.645263	+	0.763960i	$0.723252\pi$
$74$			5.39998e20i			1.48198i
$75$	−2.83094e20	+	8.65427e19i	−0.670280	+	0.204907i
$76$	−5.46279e20			−1.11806
$77$		−	7.15562e19i		−	0.126838i
$78$	−1.06803e18	−	3.49369e18i	−0.00164265	−	0.00537333i
$79$	1.11027e21			1.48433			0.742167	−	0.670215i	$-0.233798\pi$
$79$	1.11027e21			1.48433			0.742167	+	0.670215i	$0.233798\pi$
$80$			2.82970e20i			0.329421i
$81$	3.68993e20	−	9.13027e20i	0.374699	−	0.927147i
$82$	−1.63513e21			−1.45078
$83$			1.31903e19i			0.0102422i	0.999987	+	0.00512112i	$0.00163011\pi$
$83$			1.31903e19i			0.0102422i	−0.999987	+	0.00512112i	$0.998370\pi$
$84$	3.19206e21	−	9.75824e20i	2.17270	−	0.664201i
$85$	−5.17375e20			−0.309170
$86$			1.66347e21i			0.874040i
$87$	6.56080e20	+	2.14613e21i	0.303560	+	0.992989i
$88$	2.82953e20			0.115453
$89$		−	2.62916e20i		−	0.0947384i	−0.998877	−	0.0473692i	$-0.984916\pi$
$89$		−	2.62916e20i		−	0.0947384i	0.998877	−	0.0473692i	$-0.0150837\pi$
$90$	−5.60200e21	+	3.77819e21i	−1.78515	+	1.20397i
$91$	1.58767e19			0.00448029
$92$		−	1.20415e22i		−	3.01311i
$93$	2.86941e21	−	8.77187e20i	0.637499	−	0.194886i
$94$	−2.61427e21			−0.516349
$95$			4.80589e21i			0.844917i
$96$	−1.45777e21	−	4.76856e21i	−0.228404	−	0.747143i
$97$	−1.92665e21			−0.269348			−0.134674	−	0.990890i	$-0.542999\pi$
$97$	−1.92665e21			−0.269348			−0.134674	+	0.990890i	$0.542999\pi$
$98$			9.69131e21i			1.21031i
$99$	4.82344e20	+	7.15181e20i	0.0538728	+	0.0798784i
$100$	1.20962e22			1.20962
$101$			1.07496e22i			0.963512i	0.876305	+	0.481756i	$0.160001\pi$
$101$			1.07496e22i			0.963512i	−0.876305	+	0.481756i	$0.839999\pi$
$102$	−4.65379e21	+	1.42268e21i	−0.374287	+	0.114421i
$103$	1.33938e22			0.967595			0.483797	−	0.875180i	$-0.339257\pi$
$103$	1.33938e22			0.967595			0.483797	+	0.875180i	$0.339257\pi$
$104$			6.27810e19i			0.00407813i
$105$	−8.58481e21	−	2.80821e22i	−0.501936	−	1.64190i
$106$	1.99630e22			1.05162
$107$		−	2.24306e22i		−	1.06566i	−0.846221	−	0.532832i	$-0.821128\pi$
$107$		−	2.24306e22i		−	1.06566i	0.846221	−	0.532832i	$-0.178872\pi$
$108$	−2.53258e22	+	3.12700e22i	−1.08618	+	1.34112i
$109$	−2.63116e22			−1.01966			−0.509831	−	0.860275i	$-0.670292\pi$
$109$	−2.63116e22			−1.01966			−0.509831	+	0.860275i	$0.670292\pi$
$110$		−	5.91897e21i		−	0.207456i
$111$	2.70551e22	−	8.27083e21i	0.858412	−	0.262420i
$112$	−1.15669e22			−0.332522
$113$			4.24878e22i			1.10765i	0.832634	+	0.553823i	$0.186832\pi$
$113$			4.24878e22i			1.10765i	−0.832634	+	0.553823i	$0.813168\pi$
$114$	1.32152e22	+	4.32289e22i	0.312695	+	1.02287i
$115$	−1.05935e23			−2.27700
$116$		−	9.17008e22i		−	1.79199i
$117$	−1.58683e20	+	1.07022e20i	−0.00282154	+	0.00190295i
$118$	9.08399e22			1.47087
$119$		−	2.11487e22i		−	0.312081i
$120$	1.11045e23	−	3.39467e22i	1.49453	−	0.456882i
$121$	8.06471e22			0.990717
$122$			8.22989e22i			0.923498i
$123$	2.50443e22	+	8.19237e22i	0.256894	+	0.840336i
$124$	−1.22605e23			−1.15046
$125$			4.54114e22i			0.390081i
$126$	−1.54441e23	−	2.28992e23i	−1.21531	−	1.80196i
$127$	−5.07164e22			−0.365853			−0.182927	−	0.983127i	$-0.558557\pi$
$127$	−5.07164e22			−0.365853			−0.182927	+	0.983127i	$0.558557\pi$
$128$			2.66772e23i			1.76535i
$129$	8.33433e22	−	2.54783e22i	0.506272	−	0.154769i
$130$	1.31329e21			0.00732797
$131$		−	8.53623e22i		−	0.437806i	−0.975747	−	0.218903i	$-0.929752\pi$
$131$		−	8.53623e22i		−	0.437806i	0.975747	−	0.218903i	$-0.0702478\pi$
$132$	−1.03049e22	−	3.37088e22i	−0.0486106	−	0.159012i
$133$	−1.96450e23			−0.852870
$134$		−	4.40936e23i		−	1.76288i
$135$	2.75098e23	+	2.22804e23i	1.01348	+	0.820827i
$136$	8.36277e22			0.284068
$137$		−	5.86882e23i		−	1.83918i	−0.392878	−	0.919590i	$-0.628521\pi$
$137$		−	5.86882e23i		−	1.83918i	0.392878	−	0.919590i	$-0.371479\pi$
$138$	−9.52885e23	+	2.91300e23i	−2.75658	+	0.842696i
$139$	5.05196e23			1.34989			0.674943	−	0.737870i	$-0.264168\pi$
$139$	5.05196e23			1.34989			0.674943	+	0.737870i	$0.264168\pi$
$140$			1.19991e24i			2.96305i
$141$	4.00412e22	+	1.30980e23i	0.0914316	+	0.299086i
$142$	1.37740e24			2.90996
$143$		−	1.67662e20i		−	0.000327897i
$144$	1.15608e23	−	7.79702e22i	0.209411	−	0.141235i
$145$	−8.06738e23			−1.35420
$146$		−	1.36897e24i		−	2.13066i
$147$	4.85555e23	−	1.48436e23i	0.701048	−	0.214313i
$148$	−1.15602e24			−1.54913
$149$			1.20360e24i			1.49773i	0.662723	+	0.748865i	$0.269401\pi$
$149$			1.20360e24i			1.49773i	−0.662723	+	0.748865i	$0.730599\pi$
$150$	−2.92622e23	−	9.57210e23i	−0.338301	−	1.10663i
$151$	9.34709e22			0.100445			0.0502227	−	0.998738i	$-0.484007\pi$
$151$	9.34709e22			0.100445			0.0502227	+	0.998738i	$0.484007\pi$
$152$		−	7.76816e23i		−	0.776316i
$153$	1.42559e23	+	2.11374e23i	0.132552	+	0.196538i
$154$	2.41949e23			0.209409
$155$			1.07862e24i			0.869400i
$156$	7.47925e21	−	2.28643e21i	0.00561678	−	0.00171707i
$157$	−2.65459e24			−1.85824			−0.929118	−	0.369783i	$-0.879432\pi$
$157$	−2.65459e24			−1.85824			−0.929118	+	0.369783i	$0.879432\pi$
$158$			3.75411e24i			2.45064i
$159$	−3.05761e23	−	1.00019e24i	−0.186214	−	0.609134i
$160$	1.79252e24			1.01893
$161$		−	4.33029e24i		−	2.29844i
$162$	3.08717e24	+	1.24766e24i	1.53072	+	0.618628i
$163$	1.54342e24			0.715187			0.357593	−	0.933877i	$-0.383597\pi$
$163$	1.54342e24			0.715187			0.357593	+	0.933877i	$0.383597\pi$
$164$		−	3.50047e24i		−	1.51651i
$165$	−2.96553e23	+	9.06574e22i	−0.120165	+	0.0367350i
$166$	−4.45996e22			−0.0169099
$167$			2.90075e24i			1.02951i	0.857338	+	0.514754i	$0.172117\pi$
$167$			2.90075e24i			1.02951i	−0.857338	+	0.514754i	$0.827883\pi$
$168$	1.38763e24	+	4.53915e24i	0.461183	+	1.50860i
$169$	−3.21180e24			−0.999988
$170$		−	1.74937e24i		−	0.510440i
$171$	1.96345e24	−	1.32422e24i	0.537110	−	0.362246i
$172$	−3.56113e24			−0.913639
$173$			5.31439e23i			0.127922i	0.997952	+	0.0639611i	$0.0203734\pi$
$173$			5.31439e23i			0.127922i	−0.997952	+	0.0639611i	$0.979627\pi$
$174$	−7.25660e24	+	2.21837e24i	−1.63942	+	0.501178i
$175$	4.34995e24			0.922710
$176$			1.22149e23i			0.0243361i
$177$	−1.39134e24	−	4.55128e24i	−0.260452	−	0.851976i
$178$	8.88983e23			0.156413
$179$			3.21962e24i			0.532624i	0.963887	+	0.266312i	$0.0858052\pi$
$179$			3.21962e24i			0.532624i	−0.963887	+	0.266312i	$0.914195\pi$
$180$	−8.08830e24	−	1.19927e25i	−1.25852	−	1.86603i
$181$	2.29263e24			0.335637			0.167818	−	0.985818i	$-0.446328\pi$
$181$	2.29263e24			0.335637			0.167818	+	0.985818i	$0.446328\pi$
$182$			5.36832e22i			0.00739695i
$183$	4.12335e24	−	1.26052e24i	0.534919	−	0.163527i
$184$	1.71232e25			2.09213
$185$			1.01701e25i			1.17067i
$186$	2.96599e24	+	9.70217e24i	0.321756	+	1.05251i
$187$	−2.23335e23			−0.0228401
$188$		−	5.59659e24i		−	0.539743i
$189$	−9.10753e24	+	1.12451e25i	−0.828553	+	1.02302i
$190$	−1.62499e25			−1.39496
$191$			1.89558e24i			0.153595i	0.997047	+	0.0767973i	$0.0244694\pi$
$191$			1.89558e24i			0.153595i	−0.997047	+	0.0767973i	$0.975531\pi$
$192$	1.92810e25	−	5.89428e24i	1.47509	−	0.450939i
$193$	5.59039e24			0.403935			0.201967	−	0.979392i	$-0.435266\pi$
$193$	5.59039e24			0.403935			0.201967	+	0.979392i	$0.435266\pi$
$194$		−	6.51448e24i		−	0.444694i
$195$	−2.01149e22	−	6.57986e22i	−0.00129759	−	0.00424459i
$196$	−2.07470e25			−1.26514
$197$		−	2.86286e25i		−	1.65072i	−0.564610	−	0.825358i	$-0.690973\pi$
$197$		−	2.86286e25i		−	1.65072i	0.564610	−	0.825358i	$-0.309027\pi$
$198$	−2.41821e24	+	1.63093e24i	−0.131879	+	0.0889441i
$199$	3.46992e25			1.79034			0.895171	−	0.445722i	$-0.147053\pi$
$199$	3.46992e25			1.79034			0.895171	+	0.445722i	$0.147053\pi$
$200$			1.72009e25i			0.839887i
$201$	−2.20918e25	+	6.75355e24i	−1.02112	+	0.312159i
$202$	−3.63470e25			−1.59076
$203$		−	3.29769e25i		−	1.36695i
$204$	−3.04565e24	−	9.96277e24i	−0.119605	−	0.391244i
$205$	−3.07954e25			−1.14602
$206$			4.52877e25i			1.59750i
$207$	2.91895e25	+	4.32799e25i	0.976233	+	1.44748i
$208$	−2.71022e22			−0.000859624
$209$			2.07455e24i			0.0624187i
$210$	9.49527e25	−	2.90274e25i	2.71078	−	0.828696i
$211$	−3.16564e24			−0.0857738			−0.0428869	−	0.999080i	$-0.513656\pi$
$211$	−3.16564e24			−0.0857738			−0.0428869	+	0.999080i	$0.513656\pi$
$212$			4.27365e25i			1.09927i
$213$	−2.10968e25	−	6.90105e25i	−0.515276	−	1.68554i
$214$	7.58435e25			1.75941
$215$			3.13290e25i			0.690436i
$216$	−4.44664e25	−	3.60137e25i	−0.931195	−	0.754182i
$217$	−4.40906e25			−0.877584
$218$		−	8.89661e25i		−	1.68346i
$219$	−6.85886e25	+	2.09678e25i	−1.23415	+	0.377283i
$220$	1.26713e25			0.216856
$221$		−	4.95530e22i		−	0.000806780i
$222$	2.79657e25	+	9.14799e25i	0.433255	+	1.41724i
$223$	1.01616e26			1.49833			0.749165	−	0.662383i	$-0.230455\pi$
$223$	1.01616e26			1.49833			0.749165	+	0.662383i	$0.230455\pi$
$224$			7.32725e25i			1.02852i
$225$	−4.34764e25	+	2.93220e25i	−0.581093	+	0.391910i
$226$	−1.43662e26			−1.82872
$227$			2.81242e25i			0.341032i	0.985355	+	0.170516i	$0.0545435\pi$
$227$			2.81242e25i			0.341032i	−0.985355	+	0.170516i	$0.945457\pi$
$228$	−9.25439e25	+	2.82910e25i	−1.06921	+	0.326862i
$229$	2.37376e25			0.261364			0.130682	−	0.991424i	$-0.458283\pi$
$229$	2.37376e25			0.261364			0.130682	+	0.991424i	$0.458283\pi$
$230$		−	3.58193e26i		−	3.75933i
$231$	−3.70579e24	−	1.21222e25i	−0.0370808	−	0.121297i
$232$	1.30400e26			1.24425
$233$			5.50447e25i			0.500957i	0.968122	+	0.250479i	$0.0805880\pi$
$233$			5.50447e25i			0.500957i	−0.968122	+	0.250479i	$0.919412\pi$
$234$	−3.61866e23	−	5.36546e23i	−0.00314177	−	0.00465836i
$235$	−4.92360e25			−0.407883
$236$			1.94469e26i			1.53751i
$237$	1.88089e26	−	5.74994e25i	1.41949	−	0.433942i
$238$	7.15089e25			0.515245
$239$		−	5.89602e25i		−	0.405679i	−0.979212	−	0.202839i	$-0.934983\pi$
$239$		−	5.89602e25i		−	0.405679i	0.979212	−	0.202839i	$-0.0650169\pi$
$240$	1.46546e25	+	4.79374e25i	0.0963055	+	0.315029i
$241$	1.23102e26			0.772818			0.386409	−	0.922328i	$-0.373715\pi$
$241$	1.23102e26			0.772818			0.386409	+	0.922328i	$0.373715\pi$
$242$			2.72688e26i			1.63567i
$243$	1.52259e25	−	1.73783e26i	0.0872797	−	0.996184i
$244$	−1.76184e26			−0.965338
$245$			1.82522e26i			0.956066i
$246$	−2.77004e26	+	8.46811e25i	−1.38740	+	0.424132i
$247$	−4.60297e23			−0.00220481
$248$		−	1.74346e26i		−	0.798811i
$249$	6.83106e23	+	2.23454e24i	0.00299430	+	0.00979478i
$250$	−1.53547e26			−0.644023
$251$		−	2.15323e26i		−	0.864332i	−0.901794	−	0.432166i	$-0.857750\pi$
$251$		−	2.15323e26i		−	0.864332i	0.901794	−	0.432166i	$-0.142250\pi$
$252$	4.90223e26	−	3.30624e26i	1.88360	−	1.27037i
$253$	−4.57288e25			−0.168215
$254$		−	1.71485e26i		−	0.604024i
$255$	−8.76474e25	+	2.67941e25i	−0.295663	+	0.0903852i
$256$	−4.24649e26			−1.37211
$257$			6.83596e25i			0.211609i	0.994387	+	0.105805i	$0.0337418\pi$
$257$			6.83596e25i			0.211609i	−0.994387	+	0.105805i	$0.966258\pi$
$258$	8.61485e25	+	2.81804e26i	0.255524	+	0.835855i
$259$	−4.15721e26			−1.18169
$260$			2.81147e24i			0.00765997i
$261$	2.22290e26	+	3.29594e26i	0.580596	+	0.860862i
$262$	2.88631e26			0.722817
$263$			6.08879e26i			1.46224i	0.682250	+	0.731119i	$0.261001\pi$
$263$			6.08879e26i			1.46224i	−0.682250	+	0.731119i	$0.738999\pi$
$264$	4.79344e25	−	1.46537e25i	0.110409	−	0.0337524i
$265$	3.75974e26			0.830717
$266$		−	6.64245e26i		−	1.40809i
$267$	−1.36160e25	−	4.45399e25i	−0.0276966	−	0.0905995i
$268$	9.43949e26			1.84275
$269$		−	6.14042e26i		−	1.15060i	−0.817944	−	0.575298i	$-0.804886\pi$
$269$		−	6.14042e26i		−	1.15060i	0.817944	−	0.575298i	$-0.195114\pi$
$270$	−7.53355e26	+	9.30174e26i	−1.35518	+	1.67326i
$271$	−8.66689e26			−1.49693			−0.748464	−	0.663175i	$-0.769208\pi$
$271$	−8.66689e26			−1.49693			−0.748464	+	0.663175i	$0.769208\pi$
$272$			3.61017e25i			0.0598783i
$273$	2.68964e24	−	8.22233e23i	0.00428455	−	0.00130980i
$274$	1.98439e27			3.03649
$275$		−	4.59364e25i		−	0.0675300i
$276$	−6.23612e26	−	2.03992e27i	−0.880875	−	2.88147i
$277$	−1.44952e26			−0.196764			−0.0983821	−	0.995149i	$-0.531367\pi$
$277$	−1.44952e26			−0.196764			−0.0983821	+	0.995149i	$0.531367\pi$
$278$			1.70819e27i			2.22866i
$279$	4.40671e26	−	2.97205e26i	0.552674	−	0.372743i
$280$	−1.70628e27			−2.05737
$281$		−	1.01210e27i		−	1.17343i	−0.809795	−	0.586713i	$-0.800422\pi$
$281$		−	1.01210e27i		−	1.17343i	0.809795	−	0.586713i	$-0.199578\pi$
$282$	−4.42877e26	+	1.35389e26i	−0.493791	+	0.150954i
$283$	−1.22710e27			−1.31592			−0.657960	−	0.753053i	$-0.728581\pi$
$283$	−1.22710e27			−1.31592			−0.657960	+	0.753053i	$0.728581\pi$
$284$			2.94871e27i			3.04180i
$285$	2.48890e26	+	8.14155e26i	0.247010	+	0.808004i
$286$	5.66906e23			0.000541358
$287$		−	1.25882e27i		−	1.15681i
$288$	−4.93914e26	−	7.32336e26i	−0.436851	−	0.647728i
$289$	1.10856e27			0.943803
$290$		−	2.72778e27i		−	2.23579i
$291$	−3.26390e26	+	9.97784e25i	−0.257581	+	0.0787433i
$292$	2.93068e27			2.22719
$293$			1.23894e27i			0.906790i	0.891310	+	0.453395i	$0.149787\pi$
$293$			1.23894e27i			0.906790i	−0.891310	+	0.453395i	$0.850213\pi$
$294$	5.01899e26	+	1.64178e27i	0.353831	+	1.15743i
$295$	1.71084e27			1.16190
$296$		−	1.64388e27i		−	1.07562i
$297$	1.18751e26	+	9.61774e25i	0.0748715	+	0.0606390i
$298$	−4.06967e27			−2.47275
$299$		−	1.01462e25i		−	0.00594184i
$300$	2.04918e27	−	6.26442e26i	1.15677	−	0.353629i
$301$	−1.28063e27			−0.696936
$302$			3.16048e26i			0.165835i
$303$	5.56706e26	+	1.82107e27i	0.281681	+	0.921418i
$304$	3.35348e26			0.163639
$305$			1.54998e27i			0.729505i
$306$	−7.14709e26	+	4.82026e26i	−0.324484	+	0.218844i
$307$	−1.07440e26			−0.0470590			−0.0235295	−	0.999723i	$-0.507490\pi$
$307$	−1.07440e26			−0.0470590			−0.0235295	+	0.999723i	$0.507490\pi$
$308$			5.17962e26i			0.218897i
$309$	2.26901e27	−	6.93644e26i	0.925322	−	0.282874i
$310$	−3.64708e27			−1.43538
$311$			1.57800e27i			0.599436i	0.954028	+	0.299718i	$0.0968927\pi$
$311$			1.57800e27i			0.599436i	−0.954028	+	0.299718i	$0.903107\pi$
$312$	3.25134e24	+	1.06356e25i	0.00119223	+	0.00389997i
$313$	2.12037e27			0.750625			0.375313	−	0.926898i	$-0.377535\pi$
$313$	2.12037e27			0.750625			0.375313	+	0.926898i	$0.377535\pi$
$314$		−	8.97582e27i		−	3.06795i
$315$	−2.90867e27	−	4.31274e27i	−0.960014	−	1.42343i
$316$	−8.03675e27			−2.56167
$317$			2.48006e27i			0.763501i	0.924265	+	0.381750i	$0.124679\pi$
$317$			2.48006e27i			0.763501i	−0.924265	+	0.381750i	$0.875321\pi$
$318$	3.38188e27	−	1.03385e27i	1.00568	−	0.307440i
$319$	−3.48243e26			−0.100043
$320$			7.24781e27i			2.01167i
$321$	−1.16165e27	−	3.79992e27i	−0.311544	−	1.01911i
$322$	1.46418e28			3.79472
$323$			6.13141e26i			0.153579i
$324$	−2.67096e27	+	6.60898e27i	−0.646656	+	1.60007i
$325$	1.01923e25			0.00238536
$326$			5.21867e27i			1.18077i
$327$	−4.45739e27	+	1.36264e27i	−0.975114	+	0.298096i
$328$	4.97772e27			1.05297
$329$		−	2.01261e27i		−	0.411723i
$330$	−3.06535e26	−	1.00272e27i	−0.0606494	−	0.198393i
$331$	1.14762e27			0.219630			0.109815	−	0.993952i	$-0.464974\pi$
$331$	1.14762e27			0.219630			0.109815	+	0.993952i	$0.464974\pi$
$332$		−	9.54783e25i		−	0.0176761i
$333$	4.15500e27	−	2.80229e27i	0.744192	−	0.501910i
$334$	−9.80817e27			−1.69972
$335$		−	8.30439e27i		−	1.39256i
$336$	−1.95953e27	+	5.99035e26i	−0.317995	+	0.0972120i
$337$	9.17701e26			0.144136			0.0720679	−	0.997400i	$-0.477040\pi$
$337$	9.17701e26			0.144136			0.0720679	+	0.997400i	$0.477040\pi$
$338$		−	1.08599e28i		−	1.65098i
$339$	2.20038e27	+	7.19776e27i	0.323818	+	1.05926i
$340$	3.74504e27			0.533566
$341$			4.65606e26i			0.0642274i
$342$	4.47753e27	+	6.63892e27i	0.598069	+	0.886768i
$343$	2.71665e27			0.351397
$344$		−	5.06397e27i		−	0.634379i
$345$	−1.79462e28	+	5.48622e27i	−2.17752	+	0.665677i
$346$	−1.79693e27			−0.211200
$347$			6.91877e27i			0.787779i	0.919158	+	0.393890i	$0.128871\pi$
$347$			6.91877e27i			0.787779i	−0.919158	+	0.393890i	$0.871129\pi$
$348$	−4.74905e27	−	1.55348e28i	−0.523884	−	1.71370i
$349$	−1.49774e28			−1.60087			−0.800437	−	0.599417i	$-0.795399\pi$
$349$	−1.49774e28			−1.60087			−0.800437	+	0.599417i	$0.795399\pi$
$350$			1.47082e28i			1.52339i
$351$	−2.13396e25	+	2.63482e25i	−0.00214195	+	0.00264468i
$352$	7.73773e26			0.0752739
$353$			4.56597e27i			0.430538i	0.976555	+	0.215269i	$0.0690628\pi$
$353$			4.56597e27i			0.430538i	−0.976555	+	0.215269i	$0.930937\pi$
$354$	1.53890e28	−	4.70447e27i	1.40661	−	0.430006i
$355$	2.59413e28			2.29869
$356$			1.90312e27i			0.163500i
$357$	−1.09526e27	−	3.58275e27i	−0.0912361	−	0.298446i
$358$	−1.08863e28			−0.879362
$359$		−	8.52502e26i		−	0.0667816i	−0.999442	−	0.0333908i	$-0.989369\pi$
$359$		−	8.52502e26i		−	0.0667816i	0.999442	−	0.0333908i	$-0.0106306\pi$
$360$	1.70538e28	−	1.15017e28i	1.29566	−	0.873843i
$361$	−7.87453e27			−0.580291
$362$			7.75195e27i			0.554136i
$363$	1.36622e28	−	4.17660e27i	0.947435	−	0.289634i
$364$	−1.14924e26			−0.00773208
$365$		−	2.57827e28i		−	1.68309i
$366$	4.26214e27	+	1.39421e28i	0.269983	+	0.883152i
$367$	−4.97496e27			−0.305818			−0.152909	−	0.988240i	$-0.548864\pi$
$367$	−4.97496e27			−0.305818			−0.152909	+	0.988240i	$0.548864\pi$
$368$			7.39199e27i			0.440996i
$369$	8.48542e27	+	1.25815e28i	0.491341	+	0.728521i
$370$	−3.43876e28			−1.93278
$371$			1.53686e28i			0.838537i
$372$	−2.07703e28	+	6.34955e27i	−1.10020	+	0.336334i
$373$	7.77252e27			0.399728			0.199864	−	0.979824i	$-0.435950\pi$
$373$	7.77252e27			0.399728			0.199864	+	0.979824i	$0.435950\pi$
$374$		−	7.55150e26i		−	0.0377090i
$375$	2.35179e27	+	7.69304e27i	0.114039	+	0.373039i
$376$	7.95842e27			0.374766
$377$		−	7.72675e25i		−	0.00353380i
$378$	−3.80226e28	−	3.07948e28i	−1.68901	−	1.36794i
$379$	1.81644e28			0.783771			0.391885	−	0.920014i	$-0.371823\pi$
$379$	1.81644e28			0.783771			0.391885	+	0.920014i	$0.371823\pi$
$380$		−	3.47876e28i		−	1.45816i
$381$	−8.59175e27	+	2.62653e27i	−0.349870	+	0.106956i
$382$	−6.40944e27			−0.253585
$383$		−	2.52550e28i		−	0.970871i	−0.874273	−	0.485435i	$-0.838661\pi$
$383$		−	2.52550e28i		−	0.970871i	0.874273	−	0.485435i	$-0.161339\pi$
$384$	1.38157e28	+	4.51932e28i	0.516095	+	1.68822i
$385$	4.55676e27			0.165420
$386$			1.89025e28i			0.666896i
$387$	1.27995e28	−	8.63245e27i	0.438907	−	0.296015i
$388$	1.39461e28			0.464841
$389$		−	2.07224e28i		−	0.671419i	−0.941966	−	0.335709i	$-0.891024\pi$
$389$		−	2.07224e28i		−	0.671419i	0.941966	−	0.335709i	$-0.108976\pi$
$390$	2.22482e26	−	6.80134e25i	0.00700783	−	0.00214232i
$391$	−1.35153e28			−0.413887
$392$		−	2.95026e28i		−	0.878441i
$393$	−4.42079e27	−	1.44610e28i	−0.127992	−	0.418679i
$394$	9.68005e28			2.72533
$395$			7.07033e28i			1.93585i
$396$	−3.49146e27	−	5.17686e27i	−0.0929738	−	0.137854i
$397$	−5.09414e28			−1.31940			−0.659698	−	0.751531i	$-0.729316\pi$
$397$	−5.09414e28			−1.31940			−0.659698	+	0.751531i	$0.729316\pi$
$398$			1.17327e29i			2.95586i
$399$	−3.32801e28	+	1.01738e28i	−0.815610	+	0.249335i
$400$	−7.42554e27			−0.177039
$401$			9.15869e27i			0.212444i	0.994342	+	0.106222i	$0.0338755\pi$
$401$			9.15869e27i			0.212444i	−0.994342	+	0.106222i	$0.966124\pi$
$402$	−2.28354e28	−	7.46979e28i	−0.515374	−	1.68586i
$403$	−1.03308e26			−0.00226870
$404$		−	7.78113e28i		−	1.66283i
$405$	5.81424e28	+	2.34978e28i	1.20917	+	0.488677i
$406$	1.11503e29			2.25684
$407$			4.39011e27i			0.0864841i
$408$	1.41672e28	−	4.33096e27i	0.271658	−	0.0830467i
$409$	−8.43773e28			−1.57496			−0.787479	−	0.616341i	$-0.788614\pi$
$409$	−8.43773e28			−1.57496			−0.787479	+	0.616341i	$0.788614\pi$
$410$		−	1.04127e29i		−	1.89208i
$411$	−3.03938e28	−	9.94224e28i	−0.537681	−	1.75883i
$412$	−9.69513e28			−1.66988
$413$			6.99338e28i			1.17283i
$414$	−1.46340e29	+	9.86970e28i	−2.38979	+	1.61176i
$415$	−8.39970e26			−0.0133578
$416$			1.71683e26i			0.00265889i
$417$	8.55842e28	−	2.61634e28i	1.29091	−	0.394637i
$418$	−7.01457e27			−0.103053
$419$		−	6.84490e28i		−	0.979519i	−0.871857	−	0.489760i	$-0.837085\pi$
$419$		−	6.84490e28i		−	0.979519i	0.871857	−	0.489760i	$-0.162915\pi$
$420$	6.21414e28	+	2.03273e29i	0.866241	+	2.83360i
$421$	5.64315e28			0.766334			0.383167	−	0.923679i	$-0.374833\pi$
$421$	5.64315e28			0.766334			0.383167	+	0.923679i	$0.374833\pi$
$422$		−	1.07038e28i		−	0.141612i
$423$	1.35666e28	+	2.01154e28i	0.174874	+	0.259290i
$424$	−6.07718e28			−0.763269
$425$		−	1.35767e28i		−	0.166155i
$426$	2.33342e29	−	7.13334e28i	2.78283	−	0.850721i
$427$	−6.33584e28			−0.736372
$428$			1.62365e29i			1.83912i
$429$	−8.68296e24	−	2.84032e25i	−9.58600e−5	−	0.000313572i
$430$	−1.05931e29			−1.13991
$431$		−	1.34048e29i		−	1.40608i	−0.711151	−	0.703040i	$-0.751826\pi$
$431$		−	1.34048e29i		−	1.40608i	0.711151	−	0.703040i	$-0.248174\pi$
$432$	1.55469e28	−	1.91959e28i	0.158973	−	0.196285i
$433$	5.41506e28			0.539804			0.269902	−	0.962888i	$-0.413009\pi$
$433$	5.41506e28			0.539804			0.269902	+	0.962888i	$0.413009\pi$
$434$		−	1.49081e29i		−	1.44889i
$435$	−1.36668e29	+	4.17798e28i	−1.29504	+	0.395899i
$436$	1.90457e29			1.75973
$437$			1.25543e29i			1.13109i
$438$	−7.08972e28	−	2.31915e29i	−0.622894	−	2.03758i
$439$	9.15985e28			0.784836			0.392418	−	0.919787i	$-0.371639\pi$
$439$	9.15985e28			0.784836			0.392418	+	0.919787i	$0.371639\pi$
$440$			1.80187e28i			0.150572i
$441$	7.45696e28	−	5.02924e28i	0.607767	−	0.409900i
$442$	1.67551e26			0.00133199
$443$			1.52046e29i			1.17905i	0.807749	+	0.589526i	$0.200685\pi$
$443$			1.52046e29i			1.17905i	−0.807749	+	0.589526i	$0.799315\pi$
$444$	−1.95839e29	+	5.98686e28i	−1.48145	+	0.452884i
$445$	1.67427e28			0.123557
$446$			3.43588e29i			2.47374i
$447$	6.23327e28	+	2.03899e29i	0.437858	+	1.43230i
$448$	−2.96268e29			−2.03061
$449$		−	2.11279e29i		−	1.41301i	−0.707707	−	0.706506i	$-0.750270\pi$
$449$		−	2.11279e29i		−	1.41301i	0.707707	−	0.706506i	$-0.249730\pi$
$450$	−9.91450e28	−	1.47004e29i	−0.647043	−	0.959384i
$451$	−1.32934e28			−0.0846630
$452$		−	3.07549e29i		−	1.91158i
$453$	1.58347e28	−	4.84072e27i	0.0960571	−	0.0293650i
$454$	−9.50948e28			−0.563044
$455$			1.01105e27i			0.00584313i
$456$	−4.02302e28	−	1.31599e29i	−0.226954	−	0.742401i
$457$	−1.25653e29			−0.691982			−0.345991	−	0.938238i	$-0.612457\pi$
$457$	−1.25653e29			−0.691982			−0.345991	+	0.938238i	$0.612457\pi$
$458$			8.02627e28i			0.431512i
$459$	3.50973e28	+	2.84256e28i	0.184219	+	0.149200i
$460$	7.66814e29			3.92965
$461$			8.00496e28i			0.400543i	0.979740	+	0.200271i	$0.0641824\pi$
$461$			8.00496e28i			0.400543i	−0.979740	+	0.200271i	$0.935818\pi$
$462$	4.09881e28	−	1.25302e28i	0.200261	−	0.0612204i
$463$	1.02477e29			0.488918			0.244459	−	0.969660i	$-0.421390\pi$
$463$	1.02477e29			0.488918			0.244459	+	0.969660i	$0.421390\pi$
$464$			5.62929e28i			0.262275i
$465$	5.58601e28	+	1.82726e29i	0.254167	+	0.831417i
$466$	−1.86120e29			−0.827080
$467$		−	2.34893e29i		−	1.01949i	−0.860325	−	0.509746i	$-0.829739\pi$
$467$		−	2.34893e29i		−	1.01949i	0.860325	−	0.509746i	$-0.170261\pi$
$468$	1.14863e27	−	7.74679e26i	0.00486941	−	0.00328411i
$469$	3.39457e29			1.40567
$470$		−	1.66479e29i		−	0.673415i
$471$	−4.49708e29	+	1.37477e29i	−1.77705	+	0.543251i
$472$	−2.76537e29			−1.06756
$473$			1.35237e28i			0.0510064i
$474$	1.94420e29	+	6.35975e29i	0.716438	+	2.34357i
$475$	−1.26113e29			−0.454079
$476$			1.53085e29i			0.538589i
$477$	−1.03597e29	−	1.53605e29i	−0.356158	−	0.528083i
$478$	1.99359e29			0.669776
$479$		−	2.40723e29i		−	0.790365i	−0.918603	−	0.395182i	$-0.870681\pi$
$479$		−	2.40723e29i		−	0.790365i	0.918603	−	0.395182i	$-0.129319\pi$
$480$	3.03666e29	−	9.28319e28i	0.974413	−	0.297882i
$481$	−9.74068e26			−0.00305487
$482$			4.16238e29i			1.27592i
$483$	−2.24259e29	−	7.33585e29i	−0.671943	−	2.19802i
$484$	−5.83767e29			−1.70978
$485$		−	1.22691e29i		−	0.351280i
$486$	5.87605e29	+	5.14825e28i	1.64470	+	0.144099i
$487$	−1.92933e29			−0.527943			−0.263971	−	0.964531i	$-0.585032\pi$
$487$	−1.92933e29			−0.527943			−0.263971	+	0.964531i	$0.585032\pi$
$488$		−	2.50537e29i		−	0.670275i
$489$	2.61467e29	−	7.99313e28i	0.683942	−	0.209083i
$490$	−6.17152e29			−1.57847
$491$			2.56167e29i			0.640658i	0.947306	+	0.320329i	$0.103794\pi$
$491$			2.56167e29i			0.640658i	−0.947306	+	0.320329i	$0.896206\pi$
$492$	−1.81284e29	−	5.93007e29i	−0.443347	−	1.45025i
$493$	−1.02925e29			−0.246152
$494$		−	1.55638e27i		−	0.00364014i
$495$	−4.55434e28	+	3.07161e28i	−0.104176	+	0.0702602i
$496$	7.52644e28			0.168380
$497$			1.06040e30i			2.32032i
$498$	−7.55553e27	+	2.30975e27i	−0.0161712	+	0.00494359i
$499$	3.69485e29			0.773554			0.386777	−	0.922173i	$-0.373588\pi$
$499$	3.69485e29			0.773554			0.386777	+	0.922173i	$0.373588\pi$
$500$		−	3.28712e29i		−	0.673202i
$501$	1.50226e29	+	4.91410e29i	0.300975	+	0.984531i
$502$	7.28062e29			1.42701
$503$			1.47551e29i			0.282940i	0.989943	+	0.141470i	$0.0451829\pi$
$503$			1.47551e29i			0.282940i	−0.989943	+	0.141470i	$0.954817\pi$
$504$	4.70152e29	+	6.97104e29i	0.882069	+	1.30786i
$505$	−6.84545e29			−1.25660
$506$		−	1.54620e29i		−	0.277723i
$507$	−5.44104e29	+	1.66335e29i	−0.956301	+	0.292345i
$508$	3.67112e29			0.631390
$509$		−	9.75884e29i		−	1.64249i	−0.570576	−	0.821245i	$-0.693280\pi$
$509$		−	9.75884e29i		−	1.64249i	0.570576	−	0.821245i	$-0.306720\pi$
$510$	−9.05975e28	−	2.96358e29i	−0.149226	−	0.488140i
$511$	1.05392e30			1.69893
$512$		−	3.16922e29i		−	0.500015i
$513$	2.64045e29	−	3.26018e29i	0.407743	−	0.503443i
$514$	−2.31141e29			−0.349367
$515$			8.52928e29i			1.26192i
$516$	−6.03283e29	+	1.84426e29i	−0.873724	+	0.267100i
$517$	−2.12536e28			−0.0301326
$518$		−	1.40566e30i		−	1.95098i
$519$	2.75225e28	+	9.00299e28i	0.0373978	+	0.122334i
$520$	−3.99795e27			−0.00531864
$521$		−	5.11220e29i		−	0.665876i	−0.942949	−	0.332938i	$-0.891960\pi$
$521$		−	5.11220e29i		−	0.665876i	0.942949	−	0.332938i	$-0.108040\pi$
$522$	−1.11444e30	+	7.51618e29i	−1.42128	+	0.958565i
$523$	7.39983e29			0.924066			0.462033	−	0.886863i	$-0.347120\pi$
$523$	7.39983e29			0.924066			0.462033	+	0.886863i	$0.347120\pi$
$524$			6.17897e29i			0.755566i
$525$	7.36915e29	−	2.25277e29i	0.882399	−	0.269752i
$526$	−2.05877e30			−2.41415
$527$			1.37611e29i			0.158029i
$528$	6.32594e27	+	2.06930e28i	0.00711462	+	0.0232729i
$529$	−1.85948e30			−2.04823
$530$			1.27126e30i			1.37151i
$531$	−4.71408e29	−	6.98966e29i	−0.498147	−	0.738612i
$532$	1.42201e30			1.47188
$533$		−	2.94951e27i		−	0.00299055i
$534$	1.50601e29	−	4.60391e28i	0.149580	−	0.0457271i
$535$	1.42840e30			1.38982
$536$			1.34231e30i			1.27950i
$537$	1.66739e29	+	5.45428e29i	0.155712	+	0.509355i
$538$	2.07623e30			1.89963
$539$			7.87889e28i			0.0706299i
$540$	−1.99131e30	−	1.61277e30i	−1.74907	−	1.41658i
$541$	1.14061e28			0.00981676			0.00490838	−	0.999988i	$-0.498438\pi$
$541$	1.14061e28			0.00981676			0.00490838	+	0.999988i	$0.498438\pi$
$542$		−	2.93049e30i		−	2.47143i
$543$	3.88389e29	−	1.18732e29i	0.320974	−	0.0981227i
$544$	2.28691e29			0.185209
$545$		−	1.67555e30i		−	1.32983i
$546$	2.78017e27	+	9.09435e27i	0.00216248	+	0.00707379i
$547$	8.07862e29			0.615852			0.307926	−	0.951410i	$-0.400365\pi$
$547$	8.07862e29			0.615852			0.307926	+	0.951410i	$0.400365\pi$
$548$			4.24816e30i			3.17406i
$549$	6.33247e29	−	4.27085e29i	0.463743	−	0.312765i
$550$	1.55322e29			0.111492
$551$			9.56063e29i			0.672696i
$552$	2.90080e30	−	8.86784e29i	2.00073	−	0.611629i
$553$	−2.89013e30			−1.95407
$554$		−	4.90118e29i		−	0.324858i
$555$	5.26694e29	+	1.72289e30i	0.342244	+	1.11953i
$556$	−3.65688e30			−2.32964
$557$			2.05598e30i			1.28414i	0.766647	+	0.642069i	$0.221924\pi$
$557$			2.05598e30i			1.28414i	−0.766647	+	0.642069i	$0.778076\pi$
$558$	1.00492e30	+	1.49002e30i	0.615399	+	0.912464i
$559$	−3.00062e27			−0.00180169
$560$		−	7.36593e29i		−	0.433670i
$561$	−3.78346e28	+	1.15662e28i	−0.0218423	+	0.00667726i
$562$	3.42218e30			1.93733
$563$		−	3.18768e30i		−	1.76963i	−0.465944	−	0.884814i	$-0.654285\pi$
$563$		−	3.18768e30i		−	1.76963i	0.465944	−	0.884814i	$-0.345715\pi$
$564$	−2.89839e29	−	9.48106e29i	−0.157793	−	0.516163i
$565$	−2.70566e30			−1.44458
$566$		−	4.14913e30i		−	2.17258i
$567$	−9.60516e29	+	2.37668e30i	−0.493277	+	1.22055i
$568$	−4.19311e30			−2.11205
$569$		−	2.11635e28i		−	0.0104557i	−0.999986	−	0.00522784i	$-0.998336\pi$
$569$		−	2.11635e28i		−	0.0104557i	0.999986	−	0.00522784i	$-0.00166408\pi$
$570$	−2.75286e30	+	8.41558e29i	−1.33401	+	0.407813i
$571$	−2.03671e29			−0.0968124			−0.0484062	−	0.998828i	$-0.515414\pi$
$571$	−2.03671e29			−0.0968124			−0.0484062	+	0.998828i	$0.515414\pi$
$572$			1.21362e27i			0.000565885i
$573$	9.81696e28	+	3.21127e29i	0.0449031	+	0.146884i
$574$	4.25638e30			1.90989
$575$		−	2.77988e30i		−	1.22372i
$576$	2.96110e30	−	1.99708e30i	1.27881	−	0.862476i
$577$	−7.10098e29			−0.300874			−0.150437	−	0.988620i	$-0.548068\pi$
$577$	−7.10098e29			−0.300874			−0.150437	+	0.988620i	$0.548068\pi$
$578$			3.74830e30i			1.55822i
$579$	9.47055e29	−	2.89518e29i	0.386288	−	0.118090i
$580$	5.83960e30			2.33709
$581$		−	3.43353e28i		−	0.0134835i
$582$	−3.37376e29	−	1.10360e30i	−0.130005	−	0.425266i
$583$	1.62296e29			0.0613697
$584$			4.16747e30i			1.54643i
$585$	−6.81523e27	−	1.01051e28i	−0.00248180	−	0.00367981i
$586$	−4.18917e30			−1.49711
$587$			4.23524e30i			1.48545i	0.669594	+	0.742727i	$0.266468\pi$
$587$			4.23524e30i			1.48545i	−0.669594	+	0.742727i	$0.733532\pi$
$588$	−3.51471e30	+	1.07446e30i	−1.20987	+	0.369861i
$589$	1.27827e30			0.431871
$590$			5.78477e30i			1.91829i
$591$	−1.48264e30	−	4.84992e30i	−0.482583	−	1.57860i
$592$	7.09653e29			0.226729
$593$		−	1.89823e30i		−	0.595316i	−0.954673	−	0.297658i	$-0.903795\pi$
$593$		−	1.89823e30i		−	0.595316i	0.954673	−	0.297658i	$-0.0962055\pi$
$594$	−3.25200e29	+	4.01527e29i	−0.100115	+	0.123613i
$595$	1.34677e30			0.407011
$596$		−	8.71230e30i		−	2.58478i
$597$	5.87832e30	−	1.79702e30i	1.71213	−	0.523403i
$598$	3.43069e28			0.00980997
$599$			1.20877e29i			0.0339352i	0.999856	+	0.0169676i	$0.00540121\pi$
$599$			1.20877e29i			0.0339352i	−0.999856	+	0.0169676i	$0.994599\pi$
$600$	8.90809e29	+	2.91397e30i	0.245539	+	0.803194i
$601$	4.57436e30			1.23797			0.618987	−	0.785401i	$-0.287543\pi$
$601$	4.57436e30			1.23797			0.618987	+	0.785401i	$0.287543\pi$
$602$		−	4.33013e30i		−	1.15064i
$603$	−3.39277e30	+	2.28821e30i	−0.885246	+	0.597042i
$604$	−6.76592e29			−0.173349
$605$			5.13568e30i			1.29208i
$606$	−6.15747e30	+	1.88236e30i	−1.52126	+	0.465055i
$607$	−1.54217e30			−0.374159			−0.187080	−	0.982345i	$-0.559902\pi$
$607$	−1.54217e30			−0.374159			−0.187080	+	0.982345i	$0.559902\pi$
$608$		−	2.12431e30i		−	0.506149i
$609$	−1.70783e30	−	5.58655e30i	−0.399626	−	1.30723i
$610$	−5.24087e30			−1.20441
$611$		−	4.71571e27i		−	0.00106437i
$612$	−1.03191e30	−	1.53004e30i	−0.228759	−	0.339186i
$613$	1.07192e30			0.233398			0.116699	−	0.993167i	$-0.462769\pi$
$613$	1.07192e30			0.233398			0.116699	+	0.993167i	$0.462769\pi$
$614$		−	3.63280e29i		−	0.0776944i
$615$	−5.21698e30	+	1.59485e30i	−1.09595	+	0.335037i
$616$	−7.36548e29			−0.151989
$617$			2.87077e30i			0.581918i	0.956736	+	0.290959i	$0.0939743\pi$
$617$			2.87077e30i			0.581918i	−0.956736	+	0.290959i	$0.906026\pi$
$618$	2.34538e30	+	7.67208e30i	0.467025	+	1.52771i
$619$	7.00164e30			1.36963			0.684814	−	0.728718i	$-0.259884\pi$
$619$	7.00164e30			1.36963			0.684814	+	0.728718i	$0.259884\pi$
$620$		−	7.80762e30i		−	1.50041i
$621$	7.18634e30	+	5.82027e30i	1.35675	+	1.09884i
$622$	−5.33561e30			−0.989669
$623$			6.84390e29i			0.124720i
$624$	−4.59133e27	+	1.40359e27i	−0.000822069	+	0.000251309i
$625$	−6.87600e30			−1.20964
$626$			7.16948e30i			1.23928i
$627$	1.07438e29	+	3.51445e29i	0.0182480	+	0.0596917i
$628$	1.92153e31			3.20695
$629$			1.29751e30i			0.212791i
$630$	1.45824e31	−	9.83492e30i	2.35009	−	1.58498i
$631$	−6.42277e30			−1.01718			−0.508592	−	0.861008i	$-0.669834\pi$
$631$	−6.42277e30			−1.01718			−0.508592	+	0.861008i	$0.669834\pi$
$632$		−	1.14284e31i		−	1.77867i
$633$	−5.36284e29	+	1.63944e29i	−0.0820265	+	0.0250758i
$634$	−8.38568e30			−1.26054
$635$		−	3.22967e30i		−	0.477141i
$636$	2.21326e30	+	7.23989e30i	0.321369	+	1.05124i
$637$	−1.74815e28			−0.00249486
$638$		−	1.17750e30i		−	0.165170i
$639$	−7.14791e30	−	1.05984e31i	−0.985530	−	1.46126i
$640$	−1.69883e31			−2.30234
$641$		−	5.36151e29i		−	0.0714248i	−0.999362	−	0.0357124i	$-0.988630\pi$
$641$		−	5.36151e29i		−	0.0714248i	0.999362	−	0.0357124i	$-0.0113700\pi$
$642$	1.28485e31	−	3.92783e30i	1.68255	−	0.514360i
$643$	1.20075e31			1.54573			0.772864	−	0.634572i	$-0.218823\pi$
$643$	1.20075e31			1.54573			0.772864	+	0.634572i	$0.218823\pi$
$644$			3.13450e31i			3.96664i
$645$	1.62248e30	+	5.30738e30i	0.201848	+	0.660273i
$646$	−2.07318e30			−0.253559
$647$			5.19437e30i			0.624577i	0.949987	+	0.312288i	$0.101096\pi$
$647$			5.19437e30i			0.624577i	−0.949987	+	0.312288i	$0.898904\pi$
$648$	−9.39805e30	−	3.79815e30i	−1.11100	−	0.449001i
$649$	7.38515e29			0.0858357
$650$			3.44626e28i			0.00393823i
$651$	−7.46929e30	+	2.28339e30i	−0.839244	+	0.256560i
$652$	−1.11721e31			−1.23427
$653$		−	1.52058e31i		−	1.65183i	−0.563794	−	0.825916i	$-0.690659\pi$
$653$		−	1.52058e31i		−	1.65183i	0.563794	−	0.825916i	$-0.309341\pi$
$654$	−4.60742e30	−	1.50715e31i	−0.492156	−	1.60991i
$655$	5.43595e30			0.570980
$656$			2.14886e30i			0.221955i
$657$	−1.05336e31	+	7.10421e30i	−1.06993	+	0.721600i
$658$	6.80514e30			0.679754
$659$		−	5.32045e30i		−	0.522648i	−0.965251	−	0.261324i	$-0.915841\pi$
$659$		−	5.32045e30i		−	0.522648i	0.965251	−	0.261324i	$-0.0841591\pi$
$660$	2.14661e30	−	6.56226e29i	0.207382	−	0.0633973i
$661$	8.18313e30			0.777505			0.388753	−	0.921342i	$-0.372906\pi$
$661$	8.18313e30			0.777505			0.388753	+	0.921342i	$0.372906\pi$
$662$			3.88040e30i			0.362609i
$663$	−2.56628e27	−	8.39467e27i	−0.000235860	−	0.000771533i
$664$	1.35771e29			0.0122733
$665$		−	1.25101e31i		−	1.11230i
$666$	9.47522e30	+	1.40491e31i	0.828653	+	1.22866i
$667$	−2.10743e31			−1.81288
$668$		−	2.09972e31i		−	1.77673i
$669$	1.72145e31	−	5.26253e30i	1.43287	−	0.438034i
$670$	2.80792e31			2.29912
$671$			6.69078e29i			0.0538926i
$672$	3.79468e30	+	1.24129e31i	0.300686	+	0.983586i
$673$	−2.13511e31			−1.66439			−0.832194	−	0.554484i	$-0.812916\pi$
$673$	−2.13511e31			−1.66439			−0.832194	+	0.554484i	$0.812916\pi$
$674$			3.10297e30i			0.237968i
$675$	−5.84669e30	+	7.21896e30i	−0.441132	+	0.544669i
$676$	2.32487e31			1.72578
$677$			1.73132e31i			1.26445i	0.774783	+	0.632227i	$0.217859\pi$
$677$			1.73132e31i			1.26445i	−0.774783	+	0.632227i	$0.782141\pi$
$678$	−2.43374e31	+	7.44003e30i	−1.74883	+	0.534624i
$679$	5.01522e30			0.354587
$680$			5.32549e30i			0.370478i
$681$	1.45651e30	+	4.76445e30i	0.0997000	+	0.326133i
$682$	−1.57433e30			−0.106039
$683$		−	7.74068e30i		−	0.513040i	−0.966539	−	0.256520i	$-0.917424\pi$
$683$		−	7.74068e30i		−	0.513040i	0.966539	−	0.256520i	$-0.0825760\pi$
$684$	−1.42125e31	+	9.58543e30i	−0.926945	+	0.625165i
$685$	3.73732e31			2.39863
$686$			9.18566e30i			0.580156i
$687$	4.02133e30	−	1.22934e30i	0.249946	−	0.0764093i
$688$	2.18609e30			0.133720
$689$			3.60099e28i			0.00216776i
$690$	−1.85503e31	−	6.06806e31i	−1.09903	−	3.59509i
$691$	−1.61533e31			−0.941897			−0.470948	−	0.882161i	$-0.656088\pi$
$691$	−1.61533e31			−0.941897			−0.470948	+	0.882161i	$0.656088\pi$
$692$		−	3.84684e30i		−	0.220768i
$693$	−1.25558e30	−	1.86167e30i	−0.0709216	−	0.105157i
$694$	−2.33941e31			−1.30062
$695$			3.21714e31i			1.76050i
$696$	2.20907e31	−	6.75322e30i	1.18990	−	0.363755i
$697$	−3.92891e30			−0.208311
$698$		−	5.06424e31i		−	2.64304i
$699$	2.85069e30	+	9.32501e30i	0.146454	+	0.479071i
$700$	−3.14872e31			−1.59241
$701$			4.58185e30i			0.228109i	0.993475	+	0.114054i	$0.0363838\pi$
$701$			4.58185e30i			0.228109i	−0.993475	+	0.114054i	$0.963616\pi$
$702$	−8.90899e28	−	7.21546e28i	−0.00436637	−	0.00353636i
$703$	1.20526e31			0.581528
$704$			3.12865e30i			0.148613i
$705$	−8.34095e30	+	2.54986e30i	−0.390064	+	0.119244i
$706$	−1.54387e31			−0.710818
$707$		−	2.79820e31i		−	1.26843i
$708$	1.00713e31	+	3.29446e31i	0.449488	+	1.47034i
$709$	1.19148e31			0.523573			0.261787	−	0.965126i	$-0.415688\pi$
$709$	1.19148e31			0.523573			0.261787	+	0.965126i	$0.415688\pi$
$710$			8.77139e31i			3.79513i
$711$	2.88859e31	−	1.94817e31i	1.23061	−	0.829968i
$712$	−2.70627e30			−0.113525
$713$			2.81766e31i			1.16387i
$714$	1.21142e31	−	3.70334e30i	0.492735	−	0.150631i
$715$	1.06769e28			0.000427639
$716$		−	2.33053e31i		−	0.919203i
$717$	−3.05347e30	−	9.98832e30i	−0.118599	−	0.387955i
$718$	2.88252e30			0.110256
$719$		−	2.53712e31i		−	0.955702i	−0.878441	−	0.477851i	$-0.841416\pi$
$719$		−	2.53712e31i		−	0.955702i	0.878441	−	0.477851i	$-0.158584\pi$
$720$	4.96521e30	+	7.36202e30i	0.184196	+	0.273111i
$721$	−3.48650e31			−1.27380
$722$		−	2.66257e31i		−	0.958060i
$723$	2.08544e31	−	6.37527e30i	0.739055	−	0.225932i
$724$	−1.65953e31			−0.579242
$725$		−	2.11699e31i		−	0.727782i
$726$	1.41221e31	+	4.61954e31i	0.478186	+	1.56421i
$727$	1.92745e31			0.642844			0.321422	−	0.946936i	$-0.395839\pi$
$727$	1.92745e31			0.642844			0.321422	+	0.946936i	$0.395839\pi$
$728$		−	1.63424e29i		−	0.00536871i
$729$	−6.42061e30	−	3.02288e31i	−0.207766	−	0.978179i
$730$	8.71776e31			2.77878
$731$			3.99699e30i			0.125500i
$732$	−2.98470e31	+	9.12434e30i	−0.923164	+	0.282215i
$733$	−2.69272e31			−0.820441			−0.410221	−	0.911986i	$-0.634548\pi$
$733$	−2.69272e31			−0.820441			−0.410221	+	0.911986i	$0.634548\pi$
$734$		−	1.68216e31i		−	0.504905i
$735$	9.45254e30	+	3.09206e31i	0.279504	+	0.914298i
$736$	4.68256e31			1.36404
$737$		−	3.58474e30i		−	0.102876i
$738$	−4.25412e31	+	2.86913e31i	−1.20279	+	0.811204i
$739$	−2.50535e31			−0.697879			−0.348939	−	0.937145i	$-0.613458\pi$
$739$	−2.50535e31			−0.697879			−0.348939	+	0.937145i	$0.613458\pi$
$740$		−	7.36165e31i		−	2.02035i
$741$	−7.79779e28	+	2.38381e28i	−0.00210849	+	0.000644572i
$742$	−5.19651e31			−1.38442
$743$			4.91616e31i			1.29047i	0.763982	+	0.645237i	$0.223241\pi$
$743$			4.91616e31i			1.29047i	−0.763982	+	0.645237i	$0.776759\pi$
$744$	−9.02914e30	−	2.95356e31i	−0.233531	−	0.763913i
$745$	−7.66464e31			−1.95332
$746$			2.62808e31i			0.659951i
$747$	2.31447e29	+	3.43171e29i	0.00572697	+	0.00849149i
$748$	1.61661e30			0.0394175
$749$			5.83887e31i			1.40291i
$750$	−2.60121e31	+	7.95198e30i	−0.615887	+	0.188279i
$751$	−3.14313e30			−0.0733370			−0.0366685	−	0.999327i	$-0.511675\pi$
$751$	−3.14313e30			−0.0733370			−0.0366685	+	0.999327i	$0.511675\pi$
$752$			3.43561e30i			0.0789965i
$753$	−1.11513e31	−	3.64775e31i	−0.252686	−	0.826571i
$754$	2.61260e29			0.00583430
$755$			5.95231e30i			0.130999i
$756$	6.59251e31	−	8.13983e31i	1.42992	−	1.76553i
$757$	7.54271e31			1.61240			0.806200	−	0.591643i	$-0.201520\pi$
$757$	7.54271e31			1.61240			0.806200	+	0.591643i	$0.201520\pi$
$758$			6.14182e31i			1.29401i
$759$	−7.74682e30	+	2.36823e30i	−0.160866	+	0.0491772i
$760$	4.94684e31			1.01246
$761$		−	6.42228e31i		−	1.29556i	−0.761827	−	0.647781i	$-0.775697\pi$
$761$		−	6.42228e31i		−	1.29556i	0.761827	−	0.647781i	$-0.224303\pi$
$762$	−8.88094e30	−	2.90508e31i	−0.176585	−	0.577635i
$763$	6.84912e31			1.34235
$764$		−	1.37213e31i		−	0.265074i
$765$	−1.34605e31	+	9.07826e30i	−0.256322	+	0.172873i
$766$	8.53935e31			1.60291
$767$			1.63860e29i			0.00303197i
$768$	−7.19389e31	+	2.19920e31i	−1.31217	+	0.401135i
$769$	−5.92659e31			−1.06565			−0.532825	−	0.846225i	$-0.678870\pi$
$769$	−5.92659e31			−1.06565			−0.532825	+	0.846225i	$0.678870\pi$
$770$			1.54075e31i			0.273109i
$771$	3.54024e30	+	1.15806e31i	0.0618636	+	0.202365i
$772$	−4.04662e31			−0.697111
$773$			1.03663e31i			0.176055i	0.996118	+	0.0880273i	$0.0280563\pi$
$773$			1.03663e31i			0.176055i	−0.996118	+	0.0880273i	$0.971944\pi$
$774$	2.91885e31	+	4.32783e31i	0.488721	+	0.724636i
$775$	−2.83045e31			−0.467236
$776$			1.98316e31i			0.322759i
$777$	−7.04264e31	+	2.15296e31i	−1.13007	+	0.345466i
$778$	7.00674e31			1.10851
$779$			3.64955e31i			0.569283i
$780$	1.45602e29	+	4.76286e29i	0.00223938	+	0.00732532i
$781$	1.11980e31			0.169817
$782$		−	4.56986e31i		−	0.683327i
$783$	5.47269e31	+	4.43237e31i	0.806903	+	0.653517i
$784$	1.27361e31			0.185165
$785$		−	1.69047e32i		−	2.42349i
$786$	4.88963e31	−	1.49478e31i	0.691239	−	0.211314i
$787$	2.60427e31			0.363048			0.181524	−	0.983387i	$-0.441897\pi$
$787$	2.60427e31			0.363048			0.181524	+	0.983387i	$0.441897\pi$
$788$			2.07229e32i			2.84881i
$789$	3.15330e31	+	1.03149e32i	0.427482	+	1.39836i
$790$	−2.39065e32			−3.19609
$791$		−	1.10599e32i		−	1.45818i
$792$	7.36157e30	−	4.96491e30i	0.0957180	−	0.0645557i
$793$	−1.48454e29			−0.00190364
$794$		−	1.72246e32i		−	2.17832i
$795$	6.36929e31	−	1.94711e31i	0.794424	−	0.242858i
$796$	−2.51172e32			−3.08977
$797$		−	2.42229e31i		−	0.293889i	−0.989145	−	0.146945i	$-0.953056\pi$
$797$		−	2.42229e31i		−	0.293889i	0.989145	−	0.146945i	$-0.0469439\pi$
$798$	−3.44003e31	−	1.12528e32i	−0.411652	−	1.34657i
$799$	−6.28158e30			−0.0741403
$800$			4.70382e31i			0.547597i
$801$	−4.61332e30	−	6.84026e30i	−0.0529731	−	0.0785444i
$802$	−3.09678e31			−0.350746
$803$		−	1.11296e31i		−	0.124339i
$804$	1.59912e32	−	4.88858e31i	1.76224	−	0.538723i
$805$	2.75757e32			2.99759
$806$		−	3.49309e29i		−	0.00374562i
$807$	−3.18003e31	−	1.04023e32i	−0.336374	−	1.10033i
$808$	1.10649e32			1.15457
$809$			1.57502e32i			1.62126i	0.585561	+	0.810628i	$0.300874\pi$
$809$			1.57502e32i			1.62126i	−0.585561	+	0.810628i	$0.699126\pi$
$810$	−7.94519e31	+	1.96594e32i	−0.806806	+	1.99634i
$811$	−1.02490e32			−1.02672			−0.513361	−	0.858173i	$-0.671600\pi$
$811$	−1.02490e32			−1.02672			−0.513361	+	0.858173i	$0.671600\pi$
$812$			2.38704e32i			2.35909i
$813$	−1.46824e32	+	4.48846e31i	−1.43153	+	0.437624i
$814$	−1.48440e31			−0.142785
$815$			9.82862e31i			0.932736i
$816$	1.86965e30	+	6.11590e30i	0.0175053	+	0.0572623i
$817$	3.71280e31			0.342972
$818$		−	2.85301e32i		−	2.60026i
$819$	4.13064e29	−	2.78585e29i	0.00371445	−	0.00250516i
$820$	2.22913e32			1.97781
$821$			1.81814e32i			1.59167i	0.605512	+	0.795836i	$0.292968\pi$
$821$			1.81814e32i			1.59167i	−0.605512	+	0.795836i	$0.707032\pi$
$822$	3.36172e32	−	1.02769e32i	2.90383	−	0.887711i
$823$	−9.73130e31			−0.829417			−0.414708	−	0.909954i	$-0.636116\pi$
$823$	−9.73130e31			−0.829417			−0.414708	+	0.909954i	$0.636116\pi$
$824$		−	1.37866e32i		−	1.15947i
$825$	−2.37898e30	−	7.78198e30i	−0.0197423	−	0.0645798i
$826$	−2.36463e32			−1.93635
$827$			1.29618e31i			0.104738i	0.998628	+	0.0523689i	$0.0166772\pi$
$827$			1.29618e31i			0.104738i	−0.998628	+	0.0523689i	$0.983323\pi$
$828$	−2.11289e32	−	3.13283e32i	−1.68478	−	2.49806i
$829$	1.84340e32			1.45050			0.725252	−	0.688484i	$-0.241723\pi$
$829$	1.84340e32			1.45050			0.725252	+	0.688484i	$0.241723\pi$
$830$		−	2.84015e30i		−	0.0220537i
$831$	−2.45560e31	+	7.50684e30i	−0.188168	+	0.0575236i
$832$	−6.94178e29			−0.00524946
$833$			2.32863e31i			0.173783i
$834$	8.84649e31	+	2.89381e32i	0.651545	+	2.13130i
$835$	−1.84723e32			−1.34267
$836$		−	1.50167e31i		−	0.107722i
$837$	5.92614e31	−	7.31705e31i	0.419558	−	0.518032i
$838$	2.31443e32			1.61719
$839$		−	1.79761e32i		−	1.23969i	−0.784724	−	0.619845i	$-0.787195\pi$
$839$		−	1.79761e32i		−	1.23969i	0.784724	−	0.619845i	$-0.212805\pi$
$840$	−2.89058e32	+	8.83659e31i	−1.96749	+	0.601468i
$841$	−1.16367e31			−0.0781758
$842$			1.90809e32i			1.26522i
$843$	−5.24154e31	−	1.71458e32i	−0.343049	−	1.12216i
$844$	2.29146e31			0.148028
$845$		−	2.04531e32i		−	1.30417i
$846$	−6.80152e31	+	4.58719e31i	−0.428087	+	0.288717i
$847$	−2.09931e32			−1.30424
$848$		−	2.62349e31i		−	0.160888i
$849$	−2.07881e32	+	6.35498e31i	−1.25843	+	0.384707i
$850$	4.59060e31			0.274323
$851$			2.65672e32i			1.56718i
$852$	1.52710e32	+	4.99535e32i	0.889264	+	2.90891i
$853$	1.78802e32			1.02786			0.513930	−	0.857832i	$-0.328189\pi$
$853$	1.78802e32			1.02786			0.513930	+	0.857832i	$0.328189\pi$
$854$		−	2.14230e32i		−	1.21575i
$855$	8.43278e31	+	1.25035e32i	0.472436	+	0.700491i
$856$	−2.30885e32			−1.27698
$857$		−	1.90019e32i		−	1.03755i	−0.854912	−	0.518773i	$-0.826389\pi$
$857$		−	1.90019e32i		−	1.03755i	0.854912	−	0.518773i	$-0.173611\pi$
$858$	9.60383e28	−	2.93592e28i	0.000517707	−	0.000158265i
$859$	1.06484e32			0.566711			0.283355	−	0.959015i	$-0.408552\pi$
$859$	1.06484e32			0.566711			0.283355	+	0.959015i	$0.408552\pi$
$860$		−	2.26776e32i		−	1.19156i
$861$	−6.51924e31	−	2.13254e32i	−0.338191	−	1.10627i
$862$	4.53249e32			2.32144
$863$			6.46783e31i			0.327070i	0.986538	+	0.163535i	$0.0522896\pi$
$863$			6.46783e31i			0.327070i	−0.986538	+	0.163535i	$0.947710\pi$
$864$	−1.21599e32	−	9.84843e31i	−0.607128	−	0.491718i
$865$	−3.38425e31			−0.166834
$866$			1.83096e32i			0.891216i
$867$	1.87798e32	−	5.74105e31i	0.902570	−	0.275919i
$868$	3.19151e32			1.51453
$869$			3.05204e31i			0.143012i
$870$	−1.41268e32	−	4.62107e32i	−0.653629	−	2.13811i
$871$	7.95375e29			0.00363389
$872$			2.70833e32i			1.22186i
$873$	−5.01256e31	+	3.38065e31i	−0.223307	+	0.150606i
$874$	−4.24493e32			−1.86743
$875$		−	1.18209e32i		−	0.513527i
$876$	4.96481e32	−	1.51776e32i	2.12989	−	0.651115i
$877$	−8.00076e31			−0.338950			−0.169475	−	0.985534i	$-0.554207\pi$
$877$	−8.00076e31			−0.338950			−0.169475	+	0.985534i	$0.554207\pi$
$878$			3.09717e32i			1.29576i
$879$	6.41629e31	+	2.09886e32i	0.265098	+	0.867174i
$880$	−7.77859e30			−0.0317389
$881$			4.43743e32i			1.78812i	0.447948	+	0.894060i	$0.352155\pi$
$881$			4.43743e32i			1.78812i	−0.447948	+	0.894060i	$0.647845\pi$
$882$	1.70051e32	+	2.52138e32i	0.676745	+	1.00342i
$883$	−1.57479e32			−0.618949			−0.309474	−	0.950908i	$-0.600153\pi$
$883$	−1.57479e32			−0.618949			−0.309474	+	0.950908i	$0.600153\pi$
$884$			3.58691e29i			0.00139234i
$885$	2.89830e32	−	8.86019e31i	1.11113	−	0.339678i
$886$	−5.14104e32			−1.94661
$887$		−	3.61043e32i		−	1.35020i	−0.737725	−	0.675102i	$-0.764100\pi$
$887$		−	3.61043e32i		−	1.35020i	0.737725	−	0.675102i	$-0.235900\pi$
$888$	−8.51340e31	−	2.78486e32i	−0.314456	−	1.02863i
$889$	1.32019e32			0.481633
$890$			5.66113e31i			0.203992i
$891$	2.50983e31	+	1.01433e31i	0.0893282	+	0.0361013i
$892$	−7.35549e32			−2.58582
$893$			5.83494e31i			0.202615i
$894$	−6.89434e32	+	2.10762e32i	−2.36472	+	0.722904i
$895$	−2.05028e32			−0.694641
$896$		−	6.94427e32i		−	2.32401i
$897$	−5.25458e29	−	1.71885e30i	−0.00173708	−	0.00568225i
$898$	7.14386e32			2.33288
$899$			2.14576e32i			0.692189i
$900$	3.14705e32	−	2.12248e32i	1.00285	−	0.676358i
$901$	4.79672e31			0.150998
$902$		−	4.49483e31i		−	0.139779i
$903$	−2.16949e32	+	6.63221e31i	−0.666488	+	0.203748i
$904$	4.37339e32			1.32729
$905$			1.45997e32i			0.437733i
$906$	1.63677e31	+	5.35410e31i	0.0484816	+	0.158590i
$907$	9.61787e31			0.281448			0.140724	−	0.990049i	$-0.455057\pi$
$907$	9.61787e31			0.281448			0.140724	+	0.990049i	$0.455057\pi$
$908$		−	2.03578e32i		−	0.588553i
$909$	1.88621e32	+	2.79672e32i	0.538749	+	0.798814i
$910$	−3.41859e30			−0.00964700
$911$		−	4.61504e32i		−	1.28669i	−0.765577	−	0.643344i	$-0.777546\pi$
$911$		−	4.61504e32i		−	1.28669i	0.765577	−	0.643344i	$-0.222454\pi$
$912$	5.68105e31	−	1.73672e31i	0.156490	−	0.0478394i
$913$	−3.62589e29			−0.000986815
$914$		−	4.24864e32i		−	1.14246i
$915$	8.02713e31	+	2.62579e32i	0.213269	+	0.697634i
$916$	−1.71825e32			−0.451063
$917$			2.22205e32i			0.576355i
$918$	−9.61139e31	+	1.18673e32i	−0.246330	+	0.304145i
$919$	1.82792e32			0.462899			0.231450	−	0.972847i	$-0.425653\pi$
$919$	1.82792e32			0.462899			0.231450	+	0.972847i	$0.425653\pi$
$920$			1.09042e33i			2.72852i
$921$	−1.82011e31	+	5.56415e30i	−0.0450031	+	0.0137576i
$922$	−2.70667e32			−0.661296
$923$			2.48460e30i			0.00599842i
$924$	2.68245e31	+	8.77467e31i	0.0639941	+	0.209334i
$925$	−2.66877e32			−0.629148
$926$			3.46501e32i			0.807204i
$927$	3.48465e32	−	2.35017e32i	0.802199	−	0.541032i
$928$	3.56596e32			0.811239
$929$		−	7.69269e32i		−	1.72944i	−0.502255	−	0.864719i	$-0.667496\pi$
$929$		−	7.69269e32i		−	1.72944i	0.502255	−	0.864719i	$-0.332504\pi$
$930$	−6.17844e32	+	1.88877e32i	−1.37267	+	0.419630i
$931$	2.16306e32			0.474923
$932$		−	3.98443e32i		−	0.864552i
$933$	8.17224e31	+	2.67326e32i	0.175244	+	0.573248i
$934$	7.94231e32			1.68318
$935$		−	1.42222e31i		−	0.0297878i
$936$	1.10160e30	+	1.63337e30i	0.00228030	+	0.00338104i
$937$	5.05414e31			0.103398			0.0516989	−	0.998663i	$-0.483536\pi$
$937$	5.05414e31			0.103398			0.0516989	+	0.998663i	$0.483536\pi$
$938$			1.14779e33i			2.32076i
$939$	3.59207e32	−	1.09811e32i	0.717832	−	0.219444i
$940$	3.56396e32			0.703925
$941$		−	6.49725e32i		−	1.26836i	−0.773184	−	0.634182i	$-0.781337\pi$
$941$		−	6.49725e32i		−	1.26836i	0.773184	−	0.634182i	$-0.218663\pi$
$942$	−4.64845e32	−	1.52057e33i	−0.896908	−	2.93392i
$943$	−8.04463e32			−1.53418
$944$		−	1.19380e32i		−	0.225029i
$945$	−7.16101e32	−	5.79976e32i	−1.33421	−	1.08059i
$946$	−4.57271e31			−0.0842115
$947$			4.73368e31i			0.0861685i	0.999071	+	0.0430843i	$0.0137184\pi$
$947$			4.73368e31i			0.0861685i	−0.999071	+	0.0430843i	$0.986282\pi$
$948$	−1.36149e33	+	4.16212e32i	−2.44975	+	0.748898i
$949$	2.46941e30			0.00439202
$950$		−	4.26420e32i		−	0.749684i
$951$	1.28438e32	+	4.20141e32i	0.223208	+	0.730145i
$952$	−2.17689e32			−0.373965
$953$			2.95640e32i			0.502044i	0.967981	+	0.251022i	$0.0807666\pi$
$953$			2.95640e32i			0.502044i	−0.967981	+	0.251022i	$0.919233\pi$
$954$	5.19375e32	−	3.50286e32i	0.871865	−	0.588017i
$955$	−1.20713e32			−0.200316
$956$			4.26786e32i			0.700121i
$957$	−5.89951e31	+	1.80350e31i	−0.0956720	+	0.0292473i
$958$	8.13945e32			1.30489
$959$			1.52770e33i			2.42121i
$960$	3.75354e32	+	1.22784e33i	0.588108	+	1.92379i
$961$	−3.58700e32			−0.555615
$962$		−	3.29356e30i		−	0.00504360i
$963$	−3.93585e32	−	5.83577e32i	−0.595867	−	0.883505i
$964$	−8.91077e32			−1.33373
$965$			3.56001e32i			0.526806i
$966$	2.48043e33	−	7.58277e32i	3.62893	−	1.10938i
$967$	7.29083e32			1.05459			0.527297	−	0.849681i	$-0.323205\pi$
$967$	7.29083e32			1.05459			0.527297	+	0.849681i	$0.323205\pi$
$968$		−	8.30124e32i		−	1.18717i
$969$	3.17537e31	+	1.03871e32i	0.0448985	+	0.146870i
$970$	4.14848e32			0.579963
$971$		−	8.36746e32i		−	1.15660i	−0.815825	−	0.578299i	$-0.803717\pi$
$971$		−	8.36746e32i		−	1.15660i	0.815825	−	0.578299i	$-0.196283\pi$
$972$	−1.10213e32	+	1.25794e33i	−0.150627	+	1.71921i
$973$	−1.31507e33			−1.77708
$974$		−	6.52353e32i		−	0.871634i
$975$	1.72665e30	−	5.27843e29i	0.00228115	−	0.000697355i
$976$	1.08155e32			0.141286
$977$		−	4.51728e32i		−	0.583494i	−0.956495	−	0.291747i	$-0.905763\pi$
$977$		−	4.51728e32i		−	0.583494i	0.956495	−	0.291747i	$-0.0942366\pi$
$978$	2.70268e32	+	8.84084e32i	0.345197	+	1.12919i
$979$	7.22730e30			0.00912781
$980$		−	1.32119e33i		−	1.64998i
$981$	−6.84548e32	+	4.61684e32i	−0.845366	+	0.570145i
$982$	−8.66163e32			−1.05773
$983$		−	1.89765e32i		−	0.229154i	−0.993414	−	0.114577i	$-0.963449\pi$
$983$		−	1.89765e32i		−	0.229154i	0.993414	−	0.114577i	$-0.0365513\pi$
$984$	8.43264e32	−	2.57789e32i	1.00697	−	0.307835i
$985$	1.82310e33			2.15284
$986$		−	3.48013e32i		−	0.406396i
$987$	−1.04230e32	−	3.40952e32i	−0.120366	−	0.393736i
$988$	3.33187e30			0.00380506
$989$			8.18403e32i			0.924289i
$990$	−1.03859e32	−	1.53994e32i	−0.116000	−	0.171995i
$991$	1.41092e33			1.55844			0.779222	−	0.626748i	$-0.215615\pi$
$991$	1.41092e33			1.55844			0.779222	+	0.626748i	$0.215615\pi$
$992$		−	4.76774e32i		−	0.520816i
$993$	1.94416e32	−	5.94337e31i	0.210035	−	0.0642083i
$994$	−3.58547e33			−3.83086
$995$			2.20968e33i			2.33494i
$996$	−4.94468e30	−	1.61748e31i	−0.00516756	−	0.0169038i
$997$	−5.89392e32			−0.609197			−0.304598	−	0.952481i	$-0.598522\pi$
$997$	−5.89392e32			−0.609197			−0.304598	+	0.952481i	$0.598522\pi$
$998$			1.24932e33i			1.27714i
$999$	5.58764e32	−	6.89911e32i	0.564947	−	0.697545i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.23.b.a.2.6	yes	6
3.2	odd	2	inner	3.23.b.a.2.1	✓	6
4.3	odd	2		48.23.e.b.17.2		6
12.11	even	2		48.23.e.b.17.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.23.b.a.2.1	✓	6	3.2	odd	2	inner
3.23.b.a.2.6	yes	6	1.1	even	1	trivial
48.23.e.b.17.1		6	12.11	even	2
48.23.e.b.17.2		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3381.25i q^{2} +(169408. - 51788.6i) q^{3} -7.23853e6 q^{4} +6.36810e7i q^{5} +(1.75110e8 + 5.72810e8i) q^{6} -2.60308e9 q^{7} -1.02933e10i q^{8} +(2.60170e10 - 1.75468e10i) q^{9} +O(q^{10})\)	\(q+3381.25i q^{2} +(169408. - 51788.6i) q^{3} -7.23853e6 q^{4} +6.36810e7i q^{5} +(1.75110e8 + 5.72810e8i) q^{6} -2.60308e9 q^{7} -1.02933e10i q^{8} +(2.60170e10 - 1.75468e10i) q^{9} -2.15321e11 q^{10} +2.74891e10i q^{11} +(-1.22626e12 + 3.74873e11i) q^{12} -6.09922e9 q^{13} -8.80165e12i q^{14} +(3.29794e12 + 1.07881e13i) q^{15} +4.44356e12 q^{16} +8.12449e12i q^{17} +(5.93300e13 + 8.79698e13i) q^{18} +7.54682e13 q^{19} -4.60957e14i q^{20} +(-4.40982e14 + 1.34810e14i) q^{21} -9.29473e13 q^{22} +1.66353e15i q^{23} +(-5.33075e14 - 1.74376e15i) q^{24} -1.67108e15 q^{25} -2.06230e13i q^{26} +(3.49875e15 - 4.31994e15i) q^{27} +1.88425e16 q^{28} +1.26684e16i q^{29} +(-3.64771e16 + 1.11512e16i) q^{30} +1.69379e16 q^{31} -2.81484e16i q^{32} +(1.42362e15 + 4.65686e15i) q^{33} -2.74709e16 q^{34} -1.65766e17i q^{35} +(-1.88325e17 + 1.27013e17i) q^{36} +1.59704e17 q^{37} +2.55177e17i q^{38} +(-1.03325e15 + 3.15870e14i) q^{39} +6.55487e17 q^{40} +4.83588e17i q^{41} +(-4.55825e17 - 1.49107e18i) q^{42} +4.91968e17 q^{43} -1.98980e17i q^{44} +(1.11740e18 + 1.65678e18i) q^{45} -5.62480e18 q^{46} +7.73166e17i q^{47} +(7.52774e17 - 2.30126e17i) q^{48} +2.86619e18 q^{49} -5.65033e18i q^{50} +(4.20756e17 + 1.37635e18i) q^{51} +4.41494e16 q^{52} -5.90402e18i q^{53} +(1.46068e19 + 1.18302e19i) q^{54} -1.75053e18 q^{55} +2.67942e19i q^{56} +(1.27849e19 - 3.90839e18i) q^{57} -4.28351e19 q^{58} -2.68658e19i q^{59} +(-2.38723e19 - 7.80897e19i) q^{60} +2.43398e19 q^{61} +5.72711e19i q^{62} +(-6.77241e19 + 4.56756e19i) q^{63} +1.13814e20 q^{64} -3.88404e17i q^{65} +(-1.57460e19 + 4.81361e18i) q^{66} -1.30406e20 q^{67} -5.88094e19i q^{68} +(8.61517e19 + 2.81815e20i) q^{69} +5.60498e20 q^{70} -4.07363e20i q^{71} +(-1.80614e20 - 2.67800e20i) q^{72} -4.04873e20 q^{73} +5.39998e20i q^{74} +(-2.83094e20 + 8.65427e19i) q^{75} -5.46279e20 q^{76} -7.15562e19i q^{77} +(-1.06803e18 - 3.49369e18i) q^{78} +1.11027e21 q^{79} +2.82970e20i q^{80} +(3.68993e20 - 9.13027e20i) q^{81} -1.63513e21 q^{82} +1.31903e19i q^{83} +(3.19206e21 - 9.75824e20i) q^{84} -5.17375e20 q^{85} +1.66347e21i q^{86} +(6.56080e20 + 2.14613e21i) q^{87} +2.82953e20 q^{88} -2.62916e20i q^{89} +(-5.60200e21 + 3.77819e21i) q^{90} +1.58767e19 q^{91} -1.20415e22i q^{92} +(2.86941e21 - 8.77187e20i) q^{93} -2.61427e21 q^{94} +4.80589e21i q^{95} +(-1.45777e21 - 4.76856e21i) q^{96} -1.92665e21 q^{97} +9.69131e21i q^{98} +(4.82344e20 + 7.15181e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9}+O(q^{10}) \) 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9	\( 6 q + 86670 q^{3} - 11258688 q^{4} + 293575104 q^{6} - 3447063060 q^{7} + 57339715158 q^{9} - 186869600640 q^{10} - 1325972980800 q^{12} + 2025132496860 q^{13} + 2628031314240 q^{15} - 9703467227136 q^{16} + 42127150135680 q^{18} + 100485688668636 q^{19} - 789079193287812 q^{21} + 10\!\cdots\!00 q^{22}+ \cdots - 60\!\cdots\!60 q^{99}+O(q^{100}) \) 6 * q + 86670 * q^3 - 11258688 * q^4 + 293575104 * q^6 - 3447063060 * q^7 + 57339715158 * q^9 - 186869600640 * q^10 - 1325972980800 * q^12 + 2025132496860 * q^13 + 2628031314240 * q^15 - 9703467227136 * q^16 + 42127150135680 * q^18 + 100485688668636 * q^19 - 789079193287812 * q^21 + 1045890315676800 * q^22 - 2472467233277952 * q^24 + 1396569263732790 * q^25 - 10731657558901410 * q^27 + 44570708098492800 * q^28 - 116169123436801920 * q^30 + 114109662401153292 * q^31 - 174850022773609920 * q^33 + 319017868488396288 * q^34 - 707589966262651200 * q^36 + 683782874080661820 * q^37 - 1038045209126993748 * q^39 + 1781949720499015680 * q^40 - 1108714403505421440 * q^42 + 273273330169769340 * q^43 + 3228622736179443840 * q^45 - 8349686917048426752 * q^46 + 10392767955626526720 * q^48 - 8294807529216677070 * q^49 + 14237699192275302144 * q^51 - 22636595958302682240 * q^52 + 48383805955937626944 * q^54 - 40874587160137441920 * q^55 + 43721391850797114540 * q^57 - 67285958146132360320 * q^58 - 44311576503733309440 * q^60 + 121649250388145492892 * q^61 - 184494903535705683060 * q^63 + 285203601894474055680 * q^64 - 374640791614422030720 * q^66 + 75701571086175260700 * q^67 - 233446021721582921856 * q^69 + 1113607014897000234240 * q^70 - 639860863731149721600 * q^72 - 57178481309533986900 * q^73 - 333973626119358339330 * q^75 - 731229802672243966080 * q^76 + 735750453969076417920 * q^78 + 384537395891327736396 * q^79 + 3109769787236091157926 * q^81 - 5166859472437001068800 * q^82 + 6698665889827068753792 * q^84 - 6772579853411844011520 * q^85 + 4995406256507248236480 * q^87 - 404168025320661381120 * q^88 - 3858783621100493362560 * q^90 - 2806742501496183911304 * q^91 + 2087220280517252053020 * q^93 + 8135725180445469439488 * q^94 - 15069021592890694238208 * q^96 + 1565231688506989945740 * q^97 - 6095367699696122981760 * q^99

Introduction

L-functions

Modular forms

Varieties

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