LMFDB - Embedded newform 3.23.b.a.2.2

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			2.2
Root			$-210.435i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.23.b.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2525.22i q^{2} +(-174303. + 31617.4i) q^{3} -2.18245e6 q^{4} +4.89124e7i q^{5} +(7.98410e7 + 4.40153e8i) q^{6} -1.80726e7 q^{7} -5.08037e9i q^{8} +(2.93817e10 - 1.10220e10i) q^{9} +O(q^{10})$	\(q-2525.22i q^{2} +(-174303. + 31617.4i) q^{3} -2.18245e6 q^{4} +4.89124e7i q^{5} +(7.98410e7 + 4.40153e8i) q^{6} -1.80726e7 q^{7} -5.08037e9i q^{8} +(2.93817e10 - 1.10220e10i) q^{9} +1.23515e11 q^{10} +3.58183e11i q^{11} +(3.80407e11 - 6.90035e10i) q^{12} +2.54848e12 q^{13} +4.56375e10i q^{14} +(-1.54648e12 - 8.52556e12i) q^{15} -2.19830e13 q^{16} +6.13126e13i q^{17} +(-2.78330e13 - 7.41955e13i) q^{18} -4.62513e13 q^{19} -1.06749e14i q^{20} +(3.15011e12 - 5.71410e11i) q^{21} +9.04492e14 q^{22} +8.34378e14i q^{23} +(1.60628e14 + 8.85522e14i) q^{24} -8.23691e12 q^{25} -6.43548e15i q^{26} +(-4.77283e15 + 2.85014e15i) q^{27} +3.94427e13 q^{28} +8.83971e14i q^{29} +(-2.15289e16 + 3.90522e15i) q^{30} +1.68992e16 q^{31} +3.42033e16i q^{32} +(-1.13248e16 - 6.24322e16i) q^{33} +1.54828e17 q^{34} -8.83976e14i q^{35} +(-6.41243e16 + 2.40550e16i) q^{36} -4.76393e16 q^{37} +1.16795e17i q^{38} +(-4.44207e17 + 8.05763e16i) q^{39} +2.48493e17 q^{40} -5.52392e17i q^{41} +(-1.44294e15 - 7.95473e15i) q^{42} -6.75626e17 q^{43} -7.81717e17i q^{44} +(5.39112e17 + 1.43713e18i) q^{45} +2.10699e18 q^{46} +2.55288e18i q^{47} +(3.83169e18 - 6.95044e17i) q^{48} -3.90949e18 q^{49} +2.08000e16i q^{50} +(-1.93855e18 - 1.06869e19i) q^{51} -5.56194e18 q^{52} +2.79624e18i q^{53} +(7.19723e18 + 1.20525e19i) q^{54} -1.75196e19 q^{55} +9.18158e16i q^{56} +(8.06172e18 - 1.46235e18i) q^{57} +2.23222e18 q^{58} -1.75779e19i q^{59} +(3.37513e18 + 1.86066e19i) q^{60} +6.98208e19 q^{61} -4.26744e19i q^{62} +(-5.31006e17 + 1.99197e17i) q^{63} -5.83230e18 q^{64} +1.24652e20i q^{65} +(-1.57655e20 + 2.85977e19i) q^{66} -1.59967e19 q^{67} -1.33812e20i q^{68} +(-2.63809e19 - 1.45434e20i) q^{69} -2.23224e18 q^{70} +1.82667e20i q^{71} +(-5.59958e19 - 1.49270e20i) q^{72} +3.16433e20 q^{73} +1.20300e20i q^{74} +(1.43572e18 - 2.60430e17i) q^{75} +1.00941e20 q^{76} -6.47331e18i q^{77} +(2.03473e20 + 1.12172e21i) q^{78} +1.39856e20 q^{79} -1.07524e21i q^{80} +(7.41802e20 - 6.47691e20i) q^{81} -1.39491e21 q^{82} -5.68668e20i q^{83} +(-6.87497e18 + 1.24708e18i) q^{84} -2.99895e21 q^{85} +1.70611e21i q^{86} +(-2.79489e19 - 1.54078e20i) q^{87} +1.81970e21 q^{88} +2.34417e21i q^{89} +(3.62908e21 - 1.36138e21i) q^{90} -4.60578e19 q^{91} -1.82099e21i q^{92} +(-2.94558e21 + 5.34310e20i) q^{93} +6.44658e21 q^{94} -2.26226e21i q^{95} +(-1.08142e21 - 5.96172e21i) q^{96} -2.75801e21 q^{97} +9.87235e21i q^{98} +(3.94789e21 + 1.05240e22i) 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 $

$2$		−	2525.22i		−	1.23302i	−0.787347	−	0.616510i	$-0.788546\pi$
$2$		−	2525.22i		−	1.23302i	0.787347	−	0.616510i	$-0.211454\pi$
$3$	−174303.	+	31617.4i	−0.983943	+	0.178481i
$3$	−174303.	+	31617.4i	−0.983943	+	0.178481i
$4$	−2.18245e6			−0.520337
$5$			4.89124e7i			1.00173i	0.865527	+	0.500863i	$0.166984\pi$
$5$			4.89124e7i			1.00173i	−0.865527	+	0.500863i	$0.833016\pi$
$6$	7.98410e7	+	4.40153e8i	0.220071	+	1.21322i
$7$	−1.80726e7			−0.00913994			−0.00456997	−	0.999990i	$-0.501455\pi$
$7$	−1.80726e7			−0.00913994			−0.00456997	+	0.999990i	$0.501455\pi$
$8$		−	5.08037e9i		−	0.591433i
$9$	2.93817e10	−	1.10220e10i	0.936289	−	0.351231i
$10$	1.23515e11			1.23515
$11$			3.58183e11i			1.25541i	0.778452	+	0.627704i	$0.216005\pi$
$11$			3.58183e11i			1.25541i	−0.778452	+	0.627704i	$0.783995\pi$
$12$	3.80407e11	−	6.90035e10i	0.511983	−	0.0928704i
$13$	2.54848e12			1.42202			0.711008	−	0.703184i	$-0.248239\pi$
$13$	2.54848e12			1.42202			0.711008	+	0.703184i	$0.248239\pi$
$14$			4.56375e10i			0.0112697i
$15$	−1.54648e12	−	8.52556e12i	−0.178789	−	0.985642i
$16$	−2.19830e13			−1.24959
$17$			6.13126e13i			1.78901i	0.447063	+	0.894503i	$0.352470\pi$
$17$			6.13126e13i			1.78901i	−0.447063	+	0.894503i	$0.647530\pi$
$18$	−2.78330e13	−	7.41955e13i	−0.433074	−	1.15446i
$19$	−4.62513e13			−0.397040			−0.198520	−	0.980097i	$-0.563613\pi$
$19$	−4.62513e13			−0.397040			−0.198520	+	0.980097i	$0.563613\pi$
$20$		−	1.06749e14i		−	0.521235i
$21$	3.15011e12	−	5.71410e11i	0.00899318	−	0.00163131i
$22$	9.04492e14			1.54794
$23$			8.34378e14i			0.875703i	0.899047	+	0.437851i	$0.144260\pi$
$23$			8.34378e14i			0.875703i	−0.899047	+	0.437851i	$0.855740\pi$
$24$	1.60628e14	+	8.85522e14i	0.105560	+	0.581937i
$25$	−8.23691e12			−0.00345481
$26$		−	6.43548e15i		−	1.75337i
$27$	−4.77283e15	+	2.85014e15i	−0.858567	+	0.512701i
$28$	3.94427e13			0.00475585
$29$			8.83971e14i			0.0724536i	0.999344	+	0.0362268i	$0.0115339\pi$
$29$			8.83971e14i			0.0724536i	−0.999344	+	0.0362268i	$0.988466\pi$
$30$	−2.15289e16	+	3.90522e15i	−1.21532	+	0.220451i
$31$	1.68992e16			0.665103			0.332551	−	0.943085i	$-0.392091\pi$
$31$	1.68992e16			0.665103			0.332551	+	0.943085i	$0.392091\pi$
$32$			3.42033e16i			0.949331i
$33$	−1.13248e16	−	6.24322e16i	−0.224067	−	1.23525i
$34$	1.54828e17			2.20588
$35$		−	8.83976e14i		−	0.00915571i
$36$	−6.41243e16	+	2.40550e16i	−0.487186	+	0.182759i
$37$	−4.76393e16			−0.267760			−0.133880	−	0.990998i	$-0.542744\pi$
$37$	−4.76393e16			−0.267760			−0.133880	+	0.990998i	$0.542744\pi$
$38$			1.16795e17i			0.489558i
$39$	−4.44207e17	+	8.05763e16i	−1.39918	+	0.253803i
$40$	2.48493e17			0.592454
$41$		−	5.52392e17i		−	1.00375i	−0.864940	−	0.501875i	$-0.832644\pi$
$41$		−	5.52392e17i		−	1.00375i	0.864940	−	0.501875i	$-0.167356\pi$
$42$	−1.44294e15	−	7.95473e15i	−0.00201143	−	0.0110888i
$43$	−6.75626e17			−0.727032			−0.363516	−	0.931588i	$-0.618424\pi$
$43$	−6.75626e17			−0.727032			−0.363516	+	0.931588i	$0.618424\pi$
$44$		−	7.81717e17i		−	0.653236i
$45$	5.39112e17	+	1.43713e18i	0.351837	+	0.937905i
$46$	2.10699e18			1.07976
$47$			2.55288e18i			1.03265i	0.856393	+	0.516325i	$0.172700\pi$
$47$			2.55288e18i			1.03265i	−0.856393	+	0.516325i	$0.827300\pi$
$48$	3.83169e18	−	6.95044e17i	1.22952	−	0.223028i
$49$	−3.90949e18			−0.999916
$50$			2.08000e16i			0.00425985i
$51$	−1.93855e18	−	1.06869e19i	−0.319304	−	1.76028i
$52$	−5.56194e18			−0.739928
$53$			2.79624e18i			0.301675i	0.988559	+	0.150838i	$0.0481970\pi$
$53$			2.79624e18i			0.301675i	−0.988559	+	0.150838i	$0.951803\pi$
$54$	7.19723e18	+	1.20525e19i	0.632171	+	1.05863i
$55$	−1.75196e19			−1.25758
$56$			9.18158e16i			0.00540566i
$57$	8.06172e18	−	1.46235e18i	0.390665	−	0.0708641i
$58$	2.23222e18			0.0893367
$59$		−	1.75779e19i		−	0.582900i	−0.956586	−	0.291450i	$-0.905862\pi$
$59$		−	1.75779e19i		−	0.582900i	0.956586	−	0.291450i	$-0.0941376\pi$
$60$	3.37513e18	+	1.86066e19i	0.0930307	+	0.512866i
$61$	6.98208e19			1.60456			0.802281	−	0.596946i	$-0.203619\pi$
$61$	6.98208e19			1.60456			0.802281	+	0.596946i	$0.203619\pi$
$62$		−	4.26744e19i		−	0.820084i
$63$	−5.31006e17	+	1.99197e17i	−0.00855762	+	0.00321023i
$64$	−5.83230e18			−0.0790424
$65$			1.24652e20i			1.42447i
$66$	−1.57655e20	+	2.85977e19i	−1.52309	+	0.276279i
$67$	−1.59967e19			−0.130981			−0.0654904	−	0.997853i	$-0.520861\pi$
$67$	−1.59967e19			−0.130981			−0.0654904	+	0.997853i	$0.520861\pi$
$68$		−	1.33812e20i		−	0.930886i
$69$	−2.63809e19	−	1.45434e20i	−0.156296	−	0.861642i
$70$	−2.23224e18			−0.0112892
$71$			1.82667e20i			0.790348i	0.918606	+	0.395174i	$0.129316\pi$
$71$			1.82667e20i			0.790348i	−0.918606	+	0.395174i	$0.870684\pi$
$72$	−5.59958e19	−	1.49270e20i	−0.207730	−	0.553753i
$73$	3.16433e20			1.00863			0.504313	−	0.863521i	$-0.331746\pi$
$73$	3.16433e20			1.00863			0.504313	+	0.863521i	$0.331746\pi$
$74$			1.20300e20i			0.330154i
$75$	1.43572e18	−	2.60430e17i	0.00339934	−	0.000616619i
$76$	1.00941e20			0.206595
$77$		−	6.47331e18i		−	0.0114744i
$78$	2.03473e20	+	1.12172e21i	0.312944	+	1.72522i
$79$	1.39856e20			0.186975			0.0934876	−	0.995620i	$-0.470198\pi$
$79$	1.39856e20			0.186975			0.0934876	+	0.995620i	$0.470198\pi$
$80$		−	1.07524e21i		−	1.25174i
$81$	7.41802e20	−	6.47691e20i	0.753274	−	0.657707i
$82$	−1.39491e21			−1.23764
$83$		−	5.68668e20i		−	0.441571i	−0.975322	−	0.220785i	$-0.929138\pi$
$83$		−	5.68668e20i		−	0.441571i	0.975322	−	0.220785i	$-0.0708620\pi$
$84$	−6.87497e18	+	1.24708e18i	−0.00467949	+	0.000848830i
$85$	−2.99895e21			−1.79209
$86$			1.70611e21i			0.896444i
$87$	−2.79489e19	−	1.54078e20i	−0.0129316	−	0.0712902i
$88$	1.81970e21			0.742491
$89$			2.34417e21i			0.844692i	0.906435	+	0.422346i	$0.138793\pi$
$89$			2.34417e21i			0.844692i	−0.906435	+	0.422346i	$0.861207\pi$
$90$	3.62908e21	−	1.36138e21i	1.15646	−	0.433822i
$91$	−4.60578e19			−0.0129971
$92$		−	1.82099e21i		−	0.455661i
$93$	−2.94558e21	+	5.34310e20i	−0.654423	+	0.118708i
$94$	6.44658e21			1.27328
$95$		−	2.26226e21i		−	0.397725i
$96$	−1.08142e21	−	5.96172e21i	−0.169438	−	0.934088i
$97$	−2.75801e21			−0.385574			−0.192787	−	0.981241i	$-0.561753\pi$
$97$	−2.75801e21			−0.385574			−0.192787	+	0.981241i	$0.561753\pi$
$98$			9.87235e21i			1.23292i
$99$	3.94789e21	+	1.05240e22i	0.440938	+	1.17543i
$100$	1.79767e19			0.00179767
$101$		−	1.14372e22i		−	1.02514i	−0.858645	−	0.512571i	$-0.828693\pi$
$101$		−	1.14372e22i		−	1.02514i	0.858645	−	0.512571i	$-0.171307\pi$
$102$	−2.69869e22	+	4.89526e21i	−2.17046	+	0.393708i
$103$	−6.06155e20			−0.0437899			−0.0218950	−	0.999760i	$-0.506970\pi$
$103$	−6.06155e20			−0.0437899			−0.0218950	+	0.999760i	$0.506970\pi$
$104$		−	1.29472e22i		−	0.841027i
$105$	2.79490e19	+	1.54079e20i	0.00163412	+	0.00900870i
$106$	7.06113e21			0.371971
$107$		−	1.27302e22i		−	0.604805i	−0.953180	−	0.302402i	$-0.902211\pi$
$107$		−	1.27302e22i		−	0.604805i	0.953180	−	0.302402i	$-0.0977886\pi$
$108$	1.04165e22	−	6.22029e21i	0.446745	−	0.266778i
$109$	2.92097e22			1.13197			0.565986	−	0.824415i	$-0.308496\pi$
$109$	2.92097e22			1.13197			0.565986	+	0.824415i	$0.308496\pi$
$110$			4.42409e22i			1.55062i
$111$	8.30366e21	−	1.50623e21i	0.263461	−	0.0477902i
$112$	3.97290e20			0.0114211
$113$			2.65216e22i			0.691411i	0.938343	+	0.345706i	$0.112360\pi$
$113$			2.65216e22i			0.691411i	−0.938343	+	0.345706i	$0.887640\pi$
$114$	−3.69275e21	−	2.03576e22i	−0.0873769	−	0.481697i
$115$	−4.08114e22			−0.877214
$116$		−	1.92923e21i		−	0.0377003i
$117$	7.48788e22	−	2.80893e22i	1.33142	−	0.499456i
$118$	−4.43880e22			−0.718727
$119$		−	1.10808e21i		−	0.0163514i
$120$	−4.33130e22	+	7.85671e21i	−0.582941	+	0.105742i
$121$	−4.68922e22			−0.576052
$122$		−	1.76313e23i		−	1.97846i
$123$	1.74652e22	+	9.62834e22i	0.179150	+	0.987632i
$124$	−3.68818e22			−0.346078
$125$			1.16213e23i			0.998265i
$126$	5.03016e20	+	1.34091e21i	0.00395827	+	0.0105517i
$127$	−9.77964e22			−0.705475			−0.352738	−	0.935722i	$-0.614749\pi$
$127$	−9.77964e22			−0.705475			−0.352738	+	0.935722i	$0.614749\pi$
$128$			1.58187e23i			1.04679i
$129$	1.17763e23	−	2.13615e22i	0.715358	−	0.129761i
$130$	3.14775e23			1.75640
$131$		−	3.36959e23i		−	1.72820i	−0.503324	−	0.864098i	$-0.667890\pi$
$131$		−	3.36959e23i		−	1.72820i	0.503324	−	0.864098i	$-0.332110\pi$
$132$	2.47159e22	+	1.36255e23i	0.116590	+	0.642747i
$133$	8.35883e20			0.00362892
$134$			4.03953e22i			0.161502i
$135$	−1.39407e23	−	2.33450e23i	−0.513586	−	0.860049i
$136$	3.11491e23			1.05808
$137$			2.34307e23i			0.734275i	0.930167	+	0.367137i	$0.119662\pi$
$137$			2.34307e23i			0.734275i	−0.930167	+	0.367137i	$0.880338\pi$
$138$	−3.67254e23	+	6.66176e22i	−1.06242	+	0.192717i
$139$	−5.37785e23			−1.43696			−0.718482	−	0.695546i	$-0.755163\pi$
$139$	−5.37785e23			−1.43696			−0.718482	+	0.695546i	$0.755163\pi$
$140$			1.92924e21i			0.00476406i
$141$	−8.07153e22	−	4.44973e23i	−0.184309	−	1.01607i
$142$	4.61275e23			0.974514
$143$			9.12822e23i			1.78521i
$144$	−6.45897e23	+	2.42296e23i	−1.16997	+	0.438893i
$145$	−4.32371e22			−0.0725787
$146$		−	7.99063e23i		−	1.24365i
$147$	6.81435e23	−	1.23608e23i	0.983861	−	0.178466i
$148$	1.03971e23			0.139326
$149$		−	1.15726e24i		−	1.44007i	−0.693938	−	0.720035i	$-0.744126\pi$
$149$		−	1.15726e24i		−	1.44007i	0.693938	−	0.720035i	$-0.255874\pi$
$150$	−6.57644e20	−	3.62550e21i	−0.000760303	−	0.00419145i
$151$	1.09553e23			0.117728			0.0588639	−	0.998266i	$-0.481252\pi$
$151$	1.09553e23			0.117728			0.0588639	+	0.998266i	$0.481252\pi$
$152$			2.34974e23i			0.234823i
$153$	6.75787e23	+	1.80147e24i	0.628354	+	1.67503i
$154$	−1.63466e22			−0.0141481
$155$			8.26582e23i			0.666250i
$156$	9.69460e23	−	1.75854e23i	0.728047	−	0.132063i
$157$	3.68423e23			0.257899			0.128950	−	0.991651i	$-0.458839\pi$
$157$	3.68423e23			0.257899			0.128950	+	0.991651i	$0.458839\pi$
$158$		−	3.53169e23i		−	0.230544i
$159$	−8.84098e22	−	4.87392e23i	−0.0538433	−	0.296831i
$160$	−1.67296e24			−0.950970
$161$		−	1.50794e22i		−	0.00800387i
$162$	−1.63556e24	−	1.87322e24i	−0.810966	−	0.928802i
$163$	−3.12317e24			−1.44721			−0.723605	−	0.690214i	$-0.757516\pi$
$163$	−3.12317e24			−1.44721			−0.723605	+	0.690214i	$0.757516\pi$
$164$			1.20557e24i			0.522288i
$165$	3.05371e24	−	5.53924e23i	1.23738	−	0.224454i
$166$	−1.43602e24			−0.544465
$167$		−	4.22382e24i		−	1.49908i	−0.661960	−	0.749539i	$-0.730275\pi$
$167$		−	4.22382e24i		−	1.49908i	0.661960	−	0.749539i	$-0.269725\pi$
$168$	−2.90298e21	−	1.60037e22i	−0.000964809	−	0.00531887i
$169$	3.28291e24			1.02213
$170$			7.57301e24i			2.20969i
$171$	−1.35894e24	+	5.09781e23i	−0.371744	+	0.139453i
$172$	1.47452e24			0.378302
$173$			2.30803e24i			0.555565i	0.960644	+	0.277782i	$0.0895994\pi$
$173$			2.30803e24i			0.555565i	−0.960644	+	0.277782i	$0.910401\pi$
$174$	−3.89083e23	+	7.05772e22i	−0.0879023	+	0.0159449i
$175$	1.48863e20			3.15768e−5
$176$		−	7.87392e24i		−	1.56874i
$177$	5.55766e23	+	3.06387e24i	0.104037	+	0.573540i
$178$	5.91955e24			1.04152
$179$		−	1.68317e24i		−	0.278448i	−0.990261	−	0.139224i	$-0.955539\pi$
$179$		−	1.68317e24i		−	0.278448i	0.990261	−	0.139224i	$-0.0444607\pi$
$180$	−1.17659e24	−	3.13647e24i	−0.183074	−	0.488027i
$181$	6.69646e24			0.980350			0.490175	−	0.871624i	$-0.336933\pi$
$181$	6.69646e24			0.980350			0.490175	+	0.871624i	$0.336933\pi$
$182$			1.16306e23i			0.0160257i
$183$	−1.21699e25	+	2.20755e24i	−1.57880	+	0.286384i
$184$	4.23895e24			0.517920
$185$		−	2.33015e24i		−	0.268223i
$186$	1.34925e24	+	7.43825e24i	0.146370	+	0.806917i
$187$	−2.19611e25			−2.24593
$188$		−	5.57153e24i		−	0.537326i
$189$	8.62576e22	−	5.15095e22i	0.00784725	−	0.00468606i
$190$	−5.71272e24			−0.490403
$191$			1.02098e25i			0.827272i	0.910442	+	0.413636i	$0.135741\pi$
$191$			1.02098e25i			0.827272i	−0.910442	+	0.413636i	$0.864259\pi$
$192$	1.01658e24	−	1.84402e23i	0.0777732	−	0.0141076i
$193$	1.64976e25			1.19204			0.596020	−	0.802970i	$-0.296748\pi$
$193$	1.64976e25			1.19204			0.596020	+	0.802970i	$0.296748\pi$
$194$			6.96460e24i			0.475420i
$195$	−3.94118e24	−	2.17272e25i	−0.254241	−	1.40160i
$196$	8.53229e24			0.520294
$197$			5.32343e24i			0.306946i	0.988153	+	0.153473i	$0.0490459\pi$
$197$			5.32343e24i			0.306946i	−0.988153	+	0.153473i	$0.950954\pi$
$198$	2.65755e25	−	9.96930e24i	1.44932	−	0.543685i
$199$	1.38053e24			0.0712298			0.0356149	−	0.999366i	$-0.488661\pi$
$199$	1.38053e24			0.0712298			0.0356149	+	0.999366i	$0.488661\pi$
$200$			4.18466e22i			0.00204329i
$201$	2.78827e24	−	5.05774e23i	0.128878	−	0.0233776i
$202$	−2.88815e25			−1.26402
$203$		−	1.59757e22i		−	0.000662221i
$204$	4.23078e24	+	2.33238e25i	0.166146	+	0.915939i
$205$	2.70188e25			1.00548
$206$			1.53068e24i			0.0539938i
$207$	9.19651e24	+	2.45155e25i	0.307574	+	0.819911i
$208$	−5.60231e25			−1.77693
$209$		−	1.65664e25i		−	0.498447i
$210$	3.89085e23	−	7.05776e22i	0.0111079	−	0.00201491i
$211$	1.63109e24			0.0441948			0.0220974	−	0.999756i	$-0.492966\pi$
$211$	1.63109e24			0.0441948			0.0220974	+	0.999756i	$0.492966\pi$
$212$		−	6.10266e24i		−	0.156973i
$213$	−5.77546e24	−	3.18393e25i	−0.141062	−	0.777657i
$214$	−3.21467e25			−0.745736
$215$		−	3.30465e25i		−	0.728286i
$216$	1.44798e25	+	2.42477e25i	0.303229	+	0.507785i
$217$	−3.05414e23			−0.00607900
$218$		−	7.37610e25i		−	1.39574i
$219$	−5.51550e25	+	1.00048e25i	−0.992430	+	0.180021i
$220$	3.82357e25			0.654364
$221$			1.56254e26i			2.54399i
$222$	−3.80357e24	−	2.09686e25i	−0.0589263	−	0.324853i
$223$	1.00453e26			1.48119			0.740596	−	0.671951i	$-0.234544\pi$
$223$	1.00453e26			1.48119			0.740596	+	0.671951i	$0.234544\pi$
$224$		−	6.18143e23i		−	0.00867683i
$225$	−2.42015e23	+	9.07872e22i	−0.00323470	+	0.00121344i
$226$	6.69729e25			0.852524
$227$		−	1.06236e25i		−	0.128821i	−0.997923	−	0.0644104i	$-0.979483\pi$
$227$		−	1.06236e25i		−	0.128821i	0.997923	−	0.0644104i	$-0.0205167\pi$
$228$	−1.75943e25	+	3.19150e24i	−0.203277	+	0.0368733i
$229$	1.65745e25			0.182494			0.0912471	−	0.995828i	$-0.470915\pi$
$229$	1.65745e25			0.182494			0.0912471	+	0.995828i	$0.470915\pi$
$230$			1.03058e26i			1.08162i
$231$	2.04669e23	+	1.12831e24i	0.00204796	+	0.0112901i
$232$	4.49090e24			0.0428515
$233$		−	1.60799e26i		−	1.46342i	−0.681616	−	0.731710i	$-0.738722\pi$
$233$		−	1.60799e26i		−	1.46342i	0.681616	−	0.731710i	$-0.261278\pi$
$234$	−7.09319e25	−	1.89086e26i	−0.615839	−	1.64166i
$235$	−1.24867e26			−1.03443
$236$			3.83629e25i			0.303305i
$237$	−2.43773e25	+	4.42189e24i	−0.183973	+	0.0333716i
$238$	−2.79815e24			−0.0201616
$239$		−	1.13665e24i		−	0.00782076i	−0.999992	−	0.00391038i	$-0.998755\pi$
$239$		−	1.13665e24i		−	0.00782076i	0.999992	−	0.00391038i	$-0.00124472\pi$
$240$	3.39963e25	+	1.87417e26i	0.223413	+	1.23164i
$241$	3.37553e25			0.211912			0.105956	−	0.994371i	$-0.466210\pi$
$241$	3.37553e25			0.211912			0.105956	+	0.994371i	$0.466210\pi$
$242$			1.18413e26i			0.710283i
$243$	−1.08820e26	+	1.36348e26i	−0.623791	+	0.781592i
$244$	−1.52381e26			−0.834914
$245$		−	1.91223e26i		−	1.00164i
$246$	2.43137e26	−	4.41036e25i	1.21777	−	0.220896i
$247$	−1.17870e26			−0.564597
$248$		−	8.58545e25i		−	0.393364i
$249$	1.79798e25	+	9.91204e25i	0.0788120	+	0.434480i
$250$	2.93465e26			1.23088
$251$		−	2.62613e26i		−	1.05416i	−0.849817	−	0.527078i	$-0.823288\pi$
$251$		−	2.62613e26i		−	1.05416i	0.849817	−	0.527078i	$-0.176712\pi$
$252$	1.15890e24	−	4.34737e23i	0.00445285	−	0.00167040i
$253$	−2.98860e26			−1.09936
$254$			2.46958e26i			0.869865i
$255$	5.22724e26	−	9.48189e25i	1.76332	−	0.319855i
$256$	3.74995e26			1.21167
$257$			3.17373e26i			0.982439i	0.871036	+	0.491220i	$0.163449\pi$
$257$			3.17373e26i			0.982439i	−0.871036	+	0.491220i	$0.836551\pi$
$258$	−5.39427e25	−	2.97379e26i	−0.159998	−	0.882050i
$259$	8.60968e23			0.00244731
$260$		−	2.72048e26i		−	0.741205i
$261$	9.74312e24	+	2.59726e25i	0.0254479	+	0.0678375i
$262$	−8.50897e26			−2.13090
$263$			7.89531e26i			1.89608i	0.318156	+	0.948039i	$0.396937\pi$
$263$			7.89531e26i			1.89608i	−0.318156	+	0.948039i	$0.603063\pi$
$264$	−3.17179e26	+	5.75343e25i	−0.730569	+	0.132521i
$265$	−1.36771e26			−0.302196
$266$		−	2.11079e24i		−	0.00447453i
$267$	−7.41165e25	−	4.08594e26i	−0.150762	−	0.831129i
$268$	3.49120e25			0.0681542
$269$		−	1.63171e26i		−	0.305751i	−0.988245	−	0.152875i	$-0.951147\pi$
$269$		−	1.63171e26i		−	0.305751i	0.988245	−	0.152875i	$-0.0488533\pi$
$270$	−5.89515e26	+	3.52034e26i	−1.06046	+	0.633262i
$271$	8.49942e26			1.46800			0.734002	−	0.679148i	$-0.237650\pi$
$271$	8.49942e26			1.46800			0.734002	+	0.679148i	$0.237650\pi$
$272$		−	1.34783e27i		−	2.23552i
$273$	8.02799e24	−	1.45623e24i	0.0127884	−	0.00231974i
$274$	5.91677e26			0.905375
$275$		−	2.95032e24i		−	0.00433720i
$276$	5.75750e25	+	3.17404e26i	0.0813269	+	0.448344i
$277$	−4.58419e26			−0.622279			−0.311139	−	0.950364i	$-0.600711\pi$
$277$	−4.58419e26			−0.622279			−0.311139	+	0.950364i	$0.600711\pi$
$278$			1.35803e27i			1.77180i
$279$	4.96529e26	−	1.86263e26i	0.622728	−	0.233604i
$280$	−4.49093e24			−0.00541499
$281$		−	3.42867e26i		−	0.397517i	−0.980048	−	0.198759i	$-0.936309\pi$
$281$		−	3.42867e26i		−	0.397517i	0.980048	−	0.198759i	$-0.0636910\pi$
$282$	−1.12366e27	+	2.03824e26i	−1.25283	+	0.227256i
$283$	9.75106e26			1.04569			0.522843	−	0.852429i	$-0.324871\pi$
$283$	9.75106e26			1.04569			0.522843	+	0.852429i	$0.324871\pi$
$284$		−	3.98662e26i		−	0.411248i
$285$	7.15268e25	+	3.94318e26i	0.0709865	+	0.391339i
$286$	2.30508e27			2.20120
$287$			9.98319e24i			0.00917421i
$288$	3.76988e26	+	1.00495e27i	0.333434	+	0.888848i
$289$	−2.58467e27			−2.20054
$290$			1.09183e26i			0.0894909i
$291$	4.80729e26	−	8.72013e25i	0.379383	−	0.0688177i
$292$	−6.90599e26			−0.524825
$293$		−	1.41193e27i		−	1.03340i	−0.856165	−	0.516702i	$-0.827159\pi$
$293$		−	1.41193e27i		−	1.03340i	0.856165	−	0.516702i	$-0.172841\pi$
$294$	−3.12138e26	−	1.72078e27i	−0.220052	−	1.21312i
$295$	8.59775e26			0.583906
$296$			2.42026e26i			0.158362i
$297$	−1.02087e27	−	1.70954e27i	−0.643650	−	1.07785i
$298$	−2.92235e27			−1.77563
$299$			2.12640e27i			1.24526i
$300$	−3.13338e24	+	5.68376e23i	−0.00176880	+	0.000320850i
$301$	1.22103e25			0.00664502
$302$		−	2.76646e26i		−	0.145161i
$303$	3.61614e26	+	1.99353e27i	0.182969	+	1.00868i
$304$	1.01674e27			0.496136
$305$			3.41510e27i			1.60733i
$306$	4.54912e27	−	1.70651e27i	2.06534	−	0.774772i
$307$	−3.33462e27			−1.46058			−0.730288	−	0.683140i	$-0.760614\pi$
$307$	−3.33462e27			−1.46058			−0.730288	+	0.683140i	$0.760614\pi$
$308$			1.41277e25i			0.00597054i
$309$	1.05654e26	−	1.91650e25i	0.0430868	−	0.00781568i
$310$	2.08731e27			0.821500
$311$		−	4.24312e27i		−	1.61184i	−0.592026	−	0.805919i	$-0.701672\pi$
$311$		−	4.24312e27i		−	1.61184i	0.592026	−	0.805919i	$-0.298328\pi$
$312$	4.09358e26	+	2.25674e27i	0.150108	+	0.827523i
$313$	2.08598e27			0.738453			0.369226	−	0.929340i	$-0.379623\pi$
$313$	2.08598e27			0.738453			0.369226	+	0.929340i	$0.379623\pi$
$314$		−	9.30350e26i		−	0.317995i
$315$	−9.74318e24	−	2.59728e25i	−0.00321577	−	0.00857239i
$316$	−3.05230e26			−0.0972902
$317$		−	1.99636e27i		−	0.614593i	−0.951614	−	0.307296i	$-0.900576\pi$
$317$		−	1.99636e27i		−	0.614593i	0.951614	−	0.307296i	$-0.0994243\pi$
$318$	−1.23077e27	+	2.23255e26i	−0.365999	+	0.0663899i
$319$	−3.16623e26			−0.0909589
$320$		−	2.85272e26i		−	0.0791788i
$321$	4.02497e26	+	2.21891e27i	0.107946	+	0.595093i
$322$	−3.80789e25			−0.00986893
$323$		−	2.83579e27i		−	0.710306i
$324$	−1.61895e27	+	1.41355e27i	−0.391957	+	0.342230i
$325$	−2.09916e25			−0.00491280
$326$			7.88670e27i			1.78444i
$327$	−5.09133e27	+	9.23535e26i	−1.11380	+	0.202036i
$328$	−2.80636e27			−0.593651
$329$		−	4.61372e25i		−	0.00943836i
$330$	−1.39878e27	−	7.71130e27i	−0.276756	−	1.52572i
$331$	7.23093e27			1.38384			0.691921	−	0.721974i	$-0.256765\pi$
$331$	7.23093e27			1.38384			0.691921	+	0.721974i	$0.256765\pi$
$332$			1.24109e27i			0.229766i
$333$	−1.39973e27	+	5.25080e26i	−0.250701	+	0.0940457i
$334$	−1.06661e28			−1.84839
$335$		−	7.82437e26i		−	0.131207i
$336$	−6.92487e25	+	1.25613e25i	−0.0112378	+	0.00203846i
$337$	1.05413e28			1.65563			0.827816	−	0.560999i	$-0.189583\pi$
$337$	1.05413e28			1.65563			0.827816	+	0.560999i	$0.189583\pi$
$338$		−	8.29009e27i		−	1.26030i
$339$	−8.38544e26	−	4.62278e27i	−0.123404	−	0.680310i
$340$	6.54506e27			0.932493
$341$			6.05302e27i			0.834976i
$342$	1.28731e27	+	3.43164e27i	0.171948	+	0.458368i
$343$	1.41316e26			0.0182791
$344$			3.43243e27i			0.429991i
$345$	7.11354e27	−	1.29035e27i	0.863129	−	0.156566i
$346$	5.82830e27			0.685022
$347$			9.96586e27i			1.13472i	0.823468	+	0.567362i	$0.192036\pi$
$347$			9.96586e27i			1.13472i	−0.823468	+	0.567362i	$0.807964\pi$
$348$	6.09971e25	+	3.36269e26i	0.00672880	+	0.0370950i
$349$	2.57296e27			0.275013			0.137507	−	0.990501i	$-0.456091\pi$
$349$	2.57296e27			0.275013			0.137507	+	0.990501i	$0.456091\pi$
$350$		−	3.75912e23i		−	3.89348e-5i
$351$	−1.21635e28	+	7.26352e27i	−1.22090	+	0.729069i
$352$	−1.22510e28			−1.19180
$353$		−	1.06691e28i		−	1.00602i	−0.864281	−	0.503010i	$-0.832226\pi$
$353$		−	1.06691e28i		−	1.00602i	0.864281	−	0.503010i	$-0.167774\pi$
$354$	7.73695e27	−	1.40343e27i	0.707186	−	0.128279i
$355$	−8.93468e27			−0.791712
$356$		−	5.11603e27i		−	0.439525i
$357$	3.50346e25	+	1.93141e26i	0.00291842	+	0.0160888i
$358$	−4.25037e27			−0.343331
$359$		−	4.56179e27i		−	0.357352i	−0.983908	−	0.178676i	$-0.942819\pi$
$359$		−	4.56179e27i		−	0.357352i	0.983908	−	0.178676i	$-0.0571814\pi$
$360$	7.30116e27	−	2.73889e27i	0.554708	−	0.208088i
$361$	−1.14308e28			−0.842359
$362$		−	1.69101e28i		−	1.20879i
$363$	8.17343e27	−	1.48261e27i	0.566802	−	0.102814i
$364$	1.00519e26			0.00676290
$365$			1.54775e28i			1.01037i
$366$	5.57457e27	+	3.07318e28i	0.353117	+	1.94669i
$367$	−1.16340e28			−0.715161			−0.357580	−	0.933882i	$-0.616398\pi$
$367$	−1.16340e28			−0.715161			−0.357580	+	0.933882i	$0.616398\pi$
$368$		−	1.83421e28i		−	1.09427i
$369$	−6.08846e27	−	1.62302e28i	−0.352548	−	0.939799i
$370$	−5.88416e27			−0.330724
$371$		−	5.05354e25i		−	0.00275729i
$372$	6.42860e27	−	1.16611e27i	0.340521	−	0.0617684i
$373$	1.29120e28			0.664042			0.332021	−	0.943272i	$-0.392270\pi$
$373$	1.29120e28			0.664042			0.332021	+	0.943272i	$0.392270\pi$
$374$			5.54568e28i			2.76928i
$375$	−3.67437e27	−	2.02563e28i	−0.178172	−	0.982236i
$376$	1.29696e28			0.610744
$377$			2.25278e27i			0.103030i
$378$	−1.30073e26	−	2.17820e26i	−0.00577800	−	0.00967581i
$379$	1.28712e28			0.555376			0.277688	−	0.960671i	$-0.410432\pi$
$379$	1.28712e28			0.555376			0.277688	+	0.960671i	$0.410432\pi$
$380$			4.93728e27i			0.206951i
$381$	1.70462e28	−	3.09207e27i	0.694148	−	0.125914i
$382$	2.57819e28			1.02004
$383$		−	2.73899e27i		−	0.105294i	−0.998613	−	0.0526470i	$-0.983234\pi$
$383$		−	2.73899e27i		−	0.105294i	0.998613	−	0.0526470i	$-0.0167658\pi$
$384$	−5.00145e27	−	2.75724e28i	−0.186833	−	1.02998i
$385$	3.16625e26			0.0114942
$386$		−	4.16602e28i		−	1.46981i
$387$	−1.98511e28	+	7.44674e27i	−0.680712	+	0.255356i
$388$	6.01924e27			0.200628
$389$		−	1.03095e28i		−	0.334035i	−0.985954	−	0.167018i	$-0.946586\pi$
$389$		−	1.03095e28i		−	0.334035i	0.985954	−	0.167018i	$-0.0534137\pi$
$390$	−5.48661e28	+	9.95237e27i	−1.72820	+	0.313484i
$391$	−5.11579e28			−1.56664
$392$			1.98617e28i			0.591384i
$393$	1.06538e28	+	5.87328e28i	0.308450	+	1.70045i
$394$	1.34428e28			0.378471
$395$			6.84071e27i			0.187298i
$396$	−8.61608e27	−	2.29682e28i	−0.229437	−	0.611618i
$397$	−3.89344e27			−0.100841			−0.0504205	−	0.998728i	$-0.516056\pi$
$397$	−3.89344e27			−0.100841			−0.0504205	+	0.998728i	$0.516056\pi$
$398$		−	3.48614e27i		−	0.0878277i
$399$	−1.45697e26	+	2.64285e25i	−0.00357065	+	0.000647694i
$400$	1.81072e26			0.00431708
$401$		−	3.03054e28i		−	0.702962i	−0.936195	−	0.351481i	$-0.885678\pi$
$401$		−	3.03054e28i		−	0.702962i	0.936195	−	0.351481i	$-0.114322\pi$
$402$	−1.27719e27	−	7.04100e27i	−0.0288250	−	0.158909i
$403$	4.30674e28			0.945786
$404$			2.49611e28i			0.533420i
$405$	3.16801e28	+	3.62833e28i	0.658842	+	0.754574i
$406$	−4.03422e25			−0.000816532
$407$		−	1.70636e28i		−	0.336149i
$408$	−5.42937e28	+	9.84854e27i	−1.04109	+	0.188847i
$409$	3.32656e28			0.620924			0.310462	−	0.950586i	$-0.399516\pi$
$409$	3.32656e28			0.620924			0.310462	+	0.950586i	$0.399516\pi$
$410$		−	6.82286e28i		−	1.23978i
$411$	−7.40817e27	−	4.08403e28i	−0.131054	−	0.722485i
$412$	1.32290e27			0.0227855
$413$			3.17678e26i			0.00532767i
$414$	6.19071e28	−	2.32232e28i	1.01097	−	0.379244i
$415$	2.78149e28			0.442333
$416$			8.71663e28i			1.34996i
$417$	9.37373e28	−	1.70034e28i	1.41389	−	0.256471i
$418$	−4.18339e28			−0.614595
$419$			8.01738e28i			1.14730i	0.819099	+	0.573652i	$0.194474\pi$
$419$			8.01738e28i			1.14730i	−0.819099	+	0.573652i	$0.805526\pi$
$420$	−6.09975e25	−	3.36271e26i	−0.000850295	−	0.00468757i
$421$	−1.22519e29			−1.66379			−0.831896	−	0.554931i	$-0.812745\pi$
$421$	−1.22519e29			−1.66379			−0.831896	+	0.554931i	$0.812745\pi$
$422$		−	4.11887e27i		−	0.0544931i
$423$	2.81378e28	+	7.50079e28i	0.362698	+	0.966859i
$424$	1.42059e28			0.178421
$425$		−	5.05026e26i		−	0.00618067i
$426$	−8.04015e28	+	1.45843e28i	−0.958867	+	0.173932i
$427$	−1.26185e27			−0.0146656
$428$			2.77832e28i			0.314702i
$429$	−2.88611e28	−	1.59107e29i	−0.318627	−	1.75655i
$430$	−8.34498e28			−0.897991
$431$		−	1.08151e29i		−	1.13443i	−0.823568	−	0.567217i	$-0.808020\pi$
$431$		−	1.08151e29i		−	1.13443i	0.823568	−	0.567217i	$-0.191980\pi$
$432$	1.04921e29	−	6.26544e28i	1.07285	−	0.640664i
$433$	−1.13707e29			−1.13350			−0.566750	−	0.823890i	$-0.691799\pi$
$433$	−1.13707e29			−1.13350			−0.566750	+	0.823890i	$0.691799\pi$
$434$			7.71239e26i			0.00749552i
$435$	7.53635e27	−	1.36705e27i	0.0714133	−	0.0129539i
$436$	−6.37488e28			−0.589007
$437$		−	3.85911e28i		−	0.347689i
$438$	2.52643e28	+	1.39279e29i	0.221969	+	1.22369i
$439$	6.21285e28			0.532330			0.266165	−	0.963927i	$-0.414243\pi$
$439$	6.21285e28			0.532330			0.266165	+	0.963927i	$0.414243\pi$
$440$			8.90060e28i			0.743772i
$441$	−1.14868e29	+	4.30904e28i	−0.936211	+	0.351201i
$442$	3.94576e29			3.13679
$443$		−	4.27219e28i		−	0.331291i	−0.986185	−	0.165646i	$-0.947029\pi$
$443$		−	4.27219e28i		−	0.331291i	0.986185	−	0.165646i	$-0.0529708\pi$
$444$	−1.81223e28	+	3.28728e27i	−0.137089	+	0.0248670i
$445$	−1.14659e29			−0.846150
$446$		−	2.53667e29i		−	1.82634i
$447$	3.65897e28	+	2.01714e29i	0.257025	+	1.41695i
$448$	1.05405e26			0.000722443
$449$			2.64309e29i			1.76768i	0.467794	+	0.883838i	$0.345049\pi$
$449$			2.64309e29i			1.76768i	−0.467794	+	0.883838i	$0.654951\pi$
$450$	2.29258e26	+	6.11142e26i	0.00149619	+	0.00398845i
$451$	1.97857e29			1.26012
$452$		−	5.78821e28i		−	0.359767i
$453$	−1.90954e28	+	3.46379e27i	−0.115837	+	0.0210122i
$454$	−2.68269e28			−0.158839
$455$		−	2.25280e27i		−	0.0130196i
$456$	−7.42926e27	−	4.09565e28i	−0.0419114	−	0.231052i
$457$	−1.57508e29			−0.867407			−0.433704	−	0.901056i	$-0.642794\pi$
$457$	−1.57508e29			−0.867407			−0.433704	+	0.901056i	$0.642794\pi$
$458$		−	4.18542e28i		−	0.225019i
$459$	−1.74749e29	−	2.92634e29i	−0.917225	−	1.53598i
$460$	8.90690e28			0.456447
$461$		−	2.77672e28i		−	0.138938i	−0.997584	−	0.0694692i	$-0.977869\pi$
$461$		−	2.77672e28i		−	0.138938i	0.997584	−	0.0694692i	$-0.0221306\pi$
$462$	2.84925e27	−	5.16836e26i	0.0139209	−	0.00252517i
$463$	3.54709e29			1.69231			0.846157	−	0.532934i	$-0.178910\pi$
$463$	3.54709e29			1.69231			0.846157	+	0.532934i	$0.178910\pi$
$464$		−	1.94323e28i		−	0.0905370i
$465$	−2.61344e28	−	1.44075e29i	−0.118913	−	0.655553i
$466$	−4.06054e29			−1.80443
$467$			2.37608e29i			1.03128i	0.856807	+	0.515638i	$0.172445\pi$
$467$			2.37608e29i			1.03128i	−0.856807	+	0.515638i	$0.827555\pi$
$468$	−1.63419e29	+	6.13036e28i	−0.692786	+	0.259885i
$469$	2.89103e26			0.00119716
$470$			3.15318e29i			1.27548i
$471$	−6.42170e28	+	1.16486e28i	−0.253758	+	0.0460302i
$472$	−8.93021e28			−0.344746
$473$		−	2.41998e29i		−	0.912722i
$474$	1.11663e28	+	6.15582e28i	0.0411478	+	0.226842i
$475$	3.80968e26			0.00137170
$476$			2.41833e27i			0.00850824i
$477$	3.08201e28	+	8.21583e28i	0.105958	+	0.282455i
$478$	−2.87029e27			−0.00964315
$479$			2.36712e28i			0.0777194i	0.999245	+	0.0388597i	$0.0123725\pi$
$479$			2.36712e28i			0.0777194i	−0.999245	+	0.0388597i	$0.987627\pi$
$480$	2.91602e29	−	5.28948e28i	0.935700	−	0.169730i
$481$	−1.21408e29			−0.380760
$482$		−	8.52398e28i		−	0.261291i
$483$	4.76772e26	+	2.62838e27i	0.00142854	+	0.00787535i
$484$	1.02340e29			0.299741
$485$		−	1.34901e29i		−	0.386239i
$486$	3.44309e29	+	2.74794e29i	0.963718	+	0.769146i
$487$	6.28916e29			1.72097			0.860487	−	0.509473i	$-0.170160\pi$
$487$	6.28916e29			1.72097			0.860487	+	0.509473i	$0.170160\pi$
$488$		−	3.54716e29i		−	0.948992i
$489$	5.44376e29	−	9.87464e28i	1.42397	−	0.258300i
$490$	−4.82880e29			−1.23504
$491$			7.44475e28i			0.186189i	0.995657	+	0.0930944i	$0.0296758\pi$
$491$			7.44475e28i			0.186189i	−0.995657	+	0.0930944i	$0.970324\pi$
$492$	−3.81170e28	−	2.10134e29i	−0.0932186	−	0.513902i
$493$	−5.41986e28			−0.129620
$494$			2.97649e29i			0.696159i
$495$	−5.14756e29	+	1.93101e29i	−1.17745	+	0.441699i
$496$	−3.71495e29			−0.831103
$497$		−	3.30128e27i		−	0.00722373i
$498$	2.50301e29	−	4.54031e28i	0.535723	−	0.0971768i
$499$	−3.83372e29			−0.802628			−0.401314	−	0.915941i	$-0.631446\pi$
$499$	−3.83372e29			−0.802628			−0.401314	+	0.915941i	$0.631446\pi$
$500$		−	2.53630e29i		−	0.519435i
$501$	1.33546e29	+	7.36223e29i	0.267557	+	1.47501i
$502$	−6.63156e29			−1.29979
$503$		−	5.41709e29i		−	1.03877i	−0.854541	−	0.519384i	$-0.826161\pi$
$503$		−	5.41709e29i		−	1.03877i	0.854541	−	0.519384i	$-0.173839\pi$
$504$	1.01199e27	+	2.69771e27i	0.00189864	+	0.00506126i
$505$	5.59420e29			1.02691
$506$			7.54688e29i			1.35554i
$507$	−5.72220e29	+	1.03797e29i	−1.00572	+	0.182431i
$508$	2.13436e29			0.367085
$509$			3.55023e29i			0.597532i	0.954326	+	0.298766i	$0.0965751\pi$
$509$			3.55023e29i			0.597532i	−0.954326	+	0.298766i	$0.903425\pi$
$510$	−2.39439e29	−	1.32000e30i	−0.394387	−	2.17421i
$511$	−5.71877e27			−0.00921877
$512$		−	2.83462e29i		−	0.447224i
$513$	2.20749e29	−	1.31822e29i	0.340885	−	0.203563i
$514$	8.01438e29			1.21137
$515$		−	2.96485e28i		−	0.0438655i
$516$	−2.57013e29	+	4.66206e28i	−0.372227	+	0.0675197i
$517$	−9.14396e29			−1.29640
$518$		−	2.17414e27i		−	0.00301759i
$519$	−7.29740e28	−	4.02296e29i	−0.0991579	−	0.546644i
$520$	6.33280e29			0.842479
$521$		−	1.98244e29i		−	0.258217i	−0.991630	−	0.129108i	$-0.958788\pi$
$521$		−	1.98244e29i		−	0.258217i	0.991630	−	0.129108i	$-0.0412115\pi$
$522$	6.55866e28	−	2.46036e28i	0.0836450	−	0.0313778i
$523$	−3.08004e29			−0.384625			−0.192312	−	0.981334i	$-0.561599\pi$
$523$	−3.08004e29			−0.384625			−0.192312	+	0.981334i	$0.561599\pi$
$524$			7.35398e29i			0.899245i
$525$	−2.59472e25	+	4.70666e24i	−3.10697e−5	+	5.63586e-6i
$526$	1.99374e30			2.33790
$527$			1.03614e30i			1.18987i
$528$	2.48953e29	+	1.37244e30i	0.279991	+	1.54355i
$529$	2.11660e29			0.233145
$530$			3.45377e29i			0.372613i
$531$	−1.93743e29	−	5.16468e29i	−0.204732	−	0.545763i
$532$	−1.82428e27			−0.00188826
$533$		−	1.40776e30i		−	1.42735i
$534$	−1.03179e30	+	1.87161e29i	−1.02480	+	0.185892i
$535$	6.22667e29			0.605848
$536$			8.12692e28i			0.0774664i
$537$	5.32173e28	+	2.93380e29i	0.0496976	+	0.273977i
$538$	−4.12043e29			−0.376997
$539$		−	1.40031e30i		−	1.25530i
$540$	3.04249e29	+	5.09495e29i	0.267238	+	0.447516i
$541$	−8.14418e29			−0.700935			−0.350467	−	0.936575i	$-0.613977\pi$
$541$	−8.14418e29			−0.700935			−0.350467	+	0.936575i	$0.613977\pi$
$542$		−	2.14629e30i		−	1.81008i
$543$	−1.16721e30	+	2.11725e29i	−0.964609	+	0.174974i
$544$	−2.09709e30			−1.69836
$545$			1.42872e30i			1.13393i
$546$	−3.67730e27	−	2.02725e28i	−0.00286029	−	0.0157684i
$547$	1.60211e29			0.122133			0.0610663	−	0.998134i	$-0.480550\pi$
$547$	1.60211e29			0.122133			0.0610663	+	0.998134i	$0.480550\pi$
$548$		−	5.11363e29i		−	0.382071i
$549$	2.05146e30	−	7.69564e29i	1.50233	−	0.563572i
$550$	−7.45022e27			−0.00534785
$551$		−	4.08848e28i		−	0.0287670i
$552$	−7.38860e29	+	1.34025e29i	−0.509604	+	0.0924389i
$553$	−2.52757e27			−0.00170894
$554$			1.15761e30i			0.767282i
$555$	7.36734e28	+	4.06152e29i	0.0478727	+	0.263916i
$556$	1.17369e30			0.747706
$557$			2.51975e30i			1.57380i	0.617080	+	0.786900i	$0.288315\pi$
$557$			2.51975e30i			1.57380i	−0.617080	+	0.786900i	$0.711685\pi$
$558$	−4.70357e29	−	1.25385e30i	−0.288039	−	0.767836i
$559$	−1.72182e30			−1.03385
$560$			1.94324e28i			0.0114409i
$561$	3.82788e30	−	6.94354e29i	2.20987	−	0.400857i
$562$	−8.65816e29			−0.490147
$563$			2.63277e30i			1.46157i	0.682607	+	0.730786i	$0.260846\pi$
$563$			2.63277e30i			1.46157i	−0.682607	+	0.730786i	$0.739154\pi$
$564$	1.76157e29	+	9.71132e29i	0.0959027	+	0.528699i
$565$	−1.29723e30			−0.692605
$566$		−	2.46236e30i		−	1.28935i
$567$	−1.34063e28	+	1.17055e28i	−0.00688488	+	0.00601140i
$568$	9.28017e29			0.467438
$569$		−	2.30096e30i		−	1.13678i	−0.822761	−	0.568388i	$-0.807567\pi$
$569$		−	2.30096e30i		−	1.13678i	0.822761	−	0.568388i	$-0.192433\pi$
$570$	9.95741e29	−	1.80621e29i	0.482529	−	0.0875277i
$571$	3.35608e30			1.59527			0.797637	−	0.603138i	$-0.206083\pi$
$571$	3.35608e30			1.59527			0.797637	+	0.603138i	$0.206083\pi$
$572$		−	1.99219e30i		−	0.928912i
$573$	−3.22806e29	−	1.77959e30i	−0.147652	−	0.813989i
$574$	2.52098e28			0.0113120
$575$		−	6.87270e27i		−	0.00302539i
$576$	−1.71363e29	+	6.42836e28i	−0.0740065	+	0.0277621i
$577$	−4.97268e29			−0.210696			−0.105348	−	0.994435i	$-0.533596\pi$
$577$	−4.97268e29			−0.210696			−0.105348	+	0.994435i	$0.533596\pi$
$578$			6.52688e30i			2.71331i
$579$	−2.87558e30	+	5.21612e29i	−1.17290	+	0.212757i
$580$	9.43630e28			0.0377654
$581$			1.02773e28i			0.00403593i
$582$	−2.20203e29	−	1.21395e30i	−0.0848535	−	0.467786i
$583$	−1.00156e30			−0.378726
$584$		−	1.60760e30i		−	0.596535i
$585$	1.37392e30	+	3.66250e30i	0.500318	+	1.33372i
$586$	−3.56545e30			−1.27421
$587$		−	3.19125e30i		−	1.11929i	−0.828733	−	0.559644i	$-0.810938\pi$
$587$		−	3.19125e30i		−	1.11929i	0.828733	−	0.559644i	$-0.189062\pi$
$588$	−1.48720e30	+	2.69769e29i	−0.511940	+	0.0928627i
$589$	−7.81612e29			−0.264072
$590$		−	2.17113e30i		−	0.719967i
$591$	−1.68313e29	−	9.27887e29i	−0.0547842	−	0.302018i
$592$	1.04725e30			0.334590
$593$			1.81917e30i			0.570520i	0.958450	+	0.285260i	$0.0920800\pi$
$593$			1.81917e30i			0.570520i	−0.958450	+	0.285260i	$0.907920\pi$
$594$	−4.31698e30	+	2.57793e30i	−1.32901	+	0.793633i
$595$	5.41989e28			0.0163796
$596$			2.52567e30i			0.749322i
$597$	−2.40630e29	+	4.36487e28i	−0.0700861	+	0.0127132i
$598$	5.36963e30			1.53543
$599$		−	6.00057e30i		−	1.68460i	−0.539007	−	0.842301i	$-0.681200\pi$
$599$		−	6.00057e30i		−	1.68460i	0.539007	−	0.842301i	$-0.318800\pi$
$600$	−1.32308e27	−	7.29397e27i	−0.000364689	−	0.00201048i
$601$	3.54183e30			0.958535			0.479267	−	0.877669i	$-0.340902\pi$
$601$	3.54183e30			0.958535			0.479267	+	0.877669i	$0.340902\pi$
$602$		−	3.08339e28i		−	0.00819345i
$603$	−4.70011e29	+	1.76316e29i	−0.122636	+	0.0460045i
$604$	−2.39095e29			−0.0612581
$605$		−	2.29361e30i		−	0.577046i
$606$	5.03411e30	−	9.13157e29i	1.24372	−	0.225604i
$607$	−2.90344e29			−0.0704429			−0.0352214	−	0.999380i	$-0.511214\pi$
$607$	−2.90344e29			−0.0704429			−0.0352214	+	0.999380i	$0.511214\pi$
$608$		−	1.58194e30i		−	0.376922i
$609$	5.05110e26	+	2.78460e27i	0.000118194	+	0.000651588i
$610$	8.62390e30			1.98187
$611$			6.50595e30i			1.46844i
$612$	−1.47487e30	−	3.93163e30i	−0.326956	−	0.871579i
$613$	−6.61501e30			−1.44034			−0.720170	−	0.693798i	$-0.755936\pi$
$613$	−6.61501e30			−1.44034			−0.720170	+	0.693798i	$0.755936\pi$
$614$			8.42066e30i			1.80092i
$615$	−4.70945e30	+	8.54265e29i	−0.989337	+	0.179460i
$616$	−3.28868e28			−0.00678632
$617$			4.72735e30i			0.958254i	0.877745	+	0.479127i	$0.159047\pi$
$617$			4.72735e30i			0.958254i	−0.877745	+	0.479127i	$0.840953\pi$
$618$	−4.83960e28	−	2.66801e29i	−0.00963688	−	0.0531269i
$619$	7.15996e30			1.40060			0.700299	−	0.713850i	$-0.253050\pi$
$619$	7.15996e30			1.40060			0.700299	+	0.713850i	$0.253050\pi$
$620$		−	1.80398e30i		−	0.346675i
$621$	−2.37809e30	−	3.98234e30i	−0.448974	−	0.751850i
$622$	−1.07148e31			−1.98743
$623$		−	4.23653e28i		−	0.00772043i
$624$	9.76498e30	−	1.77131e30i	1.74840	−	0.317149i
$625$	−5.70391e30			−1.00344
$626$		−	5.26757e30i		−	0.910526i
$627$	5.23787e29	+	2.88757e30i	0.0889635	+	0.490444i
$628$	−8.04065e29			−0.134195
$629$		−	2.92089e30i		−	0.479025i
$630$	−6.55871e28	+	2.46037e28i	−0.0105699	+	0.00396511i
$631$	2.82823e30			0.447911			0.223956	−	0.974599i	$-0.428103\pi$
$631$	2.82823e30			0.447911			0.223956	+	0.974599i	$0.428103\pi$
$632$		−	7.10523e29i		−	0.110583i
$633$	−2.84304e29	+	5.15709e28i	−0.0434852	+	0.00788794i
$634$	−5.04126e30			−0.757805
$635$		−	4.78345e30i		−	0.706693i
$636$	1.92950e29	+	1.06371e30i	0.0280167	+	0.154452i
$637$	−9.96327e30			−1.42190
$638$			7.99545e29i			0.112154i
$639$	2.01335e30	+	5.36707e30i	0.277594	+	0.739994i
$640$	−7.73729e30			−1.04860
$641$		−	7.99000e30i		−	1.06441i	−0.846616	−	0.532204i	$-0.821364\pi$
$641$		−	7.99000e30i		−	1.06441i	0.846616	−	0.532204i	$-0.178636\pi$
$642$	5.60326e30	−	1.01640e30i	0.733762	−	0.133100i
$643$	1.44424e31			1.85916			0.929582	−	0.368615i	$-0.120168\pi$
$643$	1.44424e31			1.85916			0.929582	+	0.368615i	$0.120168\pi$
$644$			3.29101e28i			0.00416471i
$645$	1.04484e30	+	5.76009e30i	0.129985	+	0.716593i
$646$	−7.16100e30			−0.875822
$647$			1.44243e31i			1.73440i	0.497961	+	0.867200i	$0.334082\pi$
$647$			1.44243e31i			1.73440i	−0.497961	+	0.867200i	$0.665918\pi$
$648$	−3.29051e30	−	3.76863e30i	−0.388990	−	0.445511i
$649$	6.29609e30			0.731778
$650$			5.30085e28i			0.00605757i
$651$	5.32345e28	−	9.65640e27i	0.00598139	−	0.00108499i
$652$	6.81616e30			0.753037
$653$		−	5.27164e30i		−	0.572665i	−0.958130	−	0.286332i	$-0.907564\pi$
$653$		−	5.27164e30i		−	0.572665i	0.958130	−	0.286332i	$-0.0924362\pi$
$654$	2.33213e30	+	1.28567e31i	0.249114	+	1.37333i
$655$	1.64815e31			1.73118
$656$			1.21432e31i			1.25427i
$657$	9.29734e30	−	3.48772e30i	0.944365	−	0.354260i
$658$	−1.16507e29			−0.0116377
$659$		−	7.41676e30i		−	0.728576i	−0.931286	−	0.364288i	$-0.881312\pi$
$659$		−	7.41676e30i		−	0.728576i	0.931286	−	0.364288i	$-0.118688\pi$
$660$	−6.66458e30	+	1.20891e30i	−0.643857	+	0.116792i
$661$	−1.27153e31			−1.20812			−0.604061	−	0.796938i	$-0.706452\pi$
$661$	−1.27153e31			−1.20812			−0.604061	+	0.796938i	$0.706452\pi$
$662$		−	1.82597e31i		−	1.70630i
$663$	−4.94034e30	−	2.72355e31i	−0.454055	−	2.50315i
$664$	−2.88905e30			−0.261160
$665$			4.08850e28i			0.00363518i
$666$	1.32595e30	+	3.53462e30i	0.115960	+	0.309119i
$667$	−7.37566e29			−0.0634478
$668$			9.21829e30i			0.780026i
$669$	−1.75093e31	+	3.17608e30i	−1.45741	+	0.264365i
$670$	−1.97583e30			−0.161781
$671$			2.50086e31i			2.01438i
$672$	1.95441e28	+	1.07744e29i	0.00154865	+	0.00853751i
$673$	1.04711e31			0.816258			0.408129	−	0.912924i	$-0.366181\pi$
$673$	1.04711e31			0.816258			0.408129	+	0.912924i	$0.366181\pi$
$674$		−	2.66191e31i		−	2.04143i
$675$	3.93134e28	−	2.34763e28i	0.00296619	−	0.00177129i
$676$	−7.16480e30			−0.531852
$677$			1.34488e31i			0.982218i	0.871098	+	0.491109i	$0.163408\pi$
$677$			1.34488e31i			0.982218i	−0.871098	+	0.491109i	$0.836592\pi$
$678$	−1.16736e31	+	2.11751e30i	−0.838835	+	0.152159i
$679$	4.98446e28			0.00352412
$680$			1.52358e31i			1.05990i
$681$	3.35890e29	+	1.85172e30i	0.0229921	+	0.126752i
$682$	1.52852e31			1.02954
$683$		−	4.81430e30i		−	0.319084i	−0.987191	−	0.159542i	$-0.948998\pi$
$683$		−	4.81430e30i		−	0.319084i	0.987191	−	0.159542i	$-0.0510018\pi$
$684$	2.96583e30	−	1.11257e30i	0.193432	−	0.0725624i
$685$	−1.14605e31			−0.735542
$686$		−	3.56854e29i		−	0.0225385i
$687$	−2.88897e30	+	5.24041e29i	−0.179564	+	0.0325718i
$688$	1.48523e31			0.908489
$689$			7.12616e30i			0.428987i
$690$	−3.25843e30	−	1.79633e31i	−0.193049	−	1.06425i
$691$	−2.80062e31			−1.63304			−0.816519	−	0.577319i	$-0.804099\pi$
$691$	−2.80062e31			−1.63304			−0.816519	+	0.577319i	$0.804099\pi$
$692$		−	5.03717e30i		−	0.289081i
$693$	−7.13488e28	−	1.90197e29i	−0.00403015	−	0.0107433i
$694$	2.51660e31			1.39914
$695$		−	2.63043e31i		−	1.43944i
$696$	−7.82776e29	+	1.41991e29i	−0.0421634	+	0.00764818i
$697$	3.38686e31			1.79571
$698$		−	6.49730e30i		−	0.339097i
$699$	5.08406e30	+	2.80278e31i	0.261193	+	1.43992i
$700$	−3.24886e26			−1.64306e−5
$701$		−	1.54016e31i		−	0.766775i	−0.923588	−	0.383388i	$-0.874757\pi$
$701$		−	1.54016e31i		−	0.766775i	0.923588	−	0.383388i	$-0.125243\pi$
$702$	1.83420e31	+	3.07154e31i	0.898956	+	1.50539i
$703$	2.20338e30			0.106312
$704$		−	2.08903e30i		−	0.0992305i
$705$	2.17647e31	−	3.94798e30i	1.01782	−	0.184627i
$706$	−2.69419e31			−1.24044
$707$			2.06700e29i			0.00936973i
$708$	−1.21293e30	−	6.68675e30i	−0.0541342	−	0.298434i
$709$	−3.05500e31			−1.34246			−0.671232	−	0.741248i	$-0.734234\pi$
$709$	−3.05500e31			−1.34246			−0.671232	+	0.741248i	$0.734234\pi$
$710$			2.25621e31i			0.976196i
$711$	4.10922e30	−	1.54150e30i	0.175063	−	0.0656715i
$712$	1.19092e31			0.499579
$713$			1.41004e31i			0.582432i
$714$	4.87725e29	−	8.84703e28i	0.0198379	−	0.00359847i
$715$	−4.46483e31			−1.78829
$716$			3.67343e30i			0.144887i
$717$	3.59378e28	+	1.98121e29i	0.00139586	+	0.00769518i
$718$	−1.15195e31			−0.440622
$719$		−	1.90690e31i		−	0.718307i	−0.933278	−	0.359154i	$-0.883065\pi$
$719$		−	1.90690e31i		−	0.718307i	0.933278	−	0.359154i	$-0.116935\pi$
$720$	−1.18513e31	−	3.15924e31i	−0.439651	−	1.17199i
$721$	1.09548e28			0.000400237
$722$			2.88653e31i			1.03865i
$723$	−5.88364e30	+	1.06726e30i	−0.208509	+	0.0378222i
$724$	−1.46147e31			−0.510113
$725$		−	7.28119e27i		−	0.000250314i
$726$	−3.74392e30	−	2.06397e31i	−0.126772	−	0.698878i
$727$	−6.44524e30			−0.214962			−0.107481	−	0.994207i	$-0.534278\pi$
$727$	−6.44524e30			−0.214962			−0.107481	+	0.994207i	$0.534278\pi$
$728$			2.33991e29i			0.00768694i
$729$	1.46566e31	−	2.72064e31i	0.474275	−	0.880377i
$730$	3.90841e31			1.24580
$731$		−	4.14244e31i		−	1.30066i
$732$	2.65603e31	−	4.81788e30i	0.821508	−	0.149016i
$733$	1.62548e31			0.495264			0.247632	−	0.968854i	$-0.420348\pi$
$733$	1.62548e31			0.495264			0.247632	+	0.968854i	$0.420348\pi$
$734$			2.93785e31i			0.881807i
$735$	6.04597e30	+	3.33306e31i	0.178774	+	0.985559i
$736$	−2.85384e31			−0.831332
$737$		−	5.72974e30i		−	0.164434i
$738$	−4.09850e31	+	1.53747e31i	−1.15879	+	0.434698i
$739$	7.38760e30			0.205785			0.102893	−	0.994692i	$-0.467190\pi$
$739$	7.38760e30			0.205785			0.102893	+	0.994692i	$0.467190\pi$
$740$			5.08545e30i			0.139566i
$741$	2.05451e31	−	3.72676e30i	0.555531	−	0.100770i
$742$	−1.27613e29			−0.00339980
$743$			7.19280e31i			1.88808i	0.329827	+	0.944041i	$0.393009\pi$
$743$			7.19280e31i			1.88808i	−0.329827	+	0.944041i	$0.606991\pi$
$744$	2.71450e30	+	1.49647e31i	0.0702080	+	0.387048i
$745$	5.66046e31			1.44256
$746$		−	3.26056e31i		−	0.818776i
$747$	−6.26786e30	−	1.67085e31i	−0.155093	−	0.413438i
$748$	4.79291e31			1.16864
$749$			2.30069e29i			0.00552788i
$750$	−5.11517e31	+	9.27860e30i	−1.21112	+	0.219689i
$751$	−1.71125e31			−0.399276			−0.199638	−	0.979870i	$-0.563977\pi$
$751$	−1.71125e31			−0.399276			−0.199638	+	0.979870i	$0.563977\pi$
$752$		−	5.61197e31i		−	1.29039i
$753$	8.30313e30	+	4.57741e31i	0.188147	+	1.03723i
$754$	5.68878e30			0.127038
$755$			5.35851e30i			0.117931i
$756$	−1.88253e29	+	1.12417e29i	−0.00408322	+	0.00243833i
$757$	−4.21418e30			−0.0900862			−0.0450431	−	0.998985i	$-0.514343\pi$
$757$	−4.21418e30			−0.0900862			−0.0450431	+	0.998985i	$0.514343\pi$
$758$		−	3.25026e31i		−	0.684790i
$759$	5.20921e31	−	9.44917e30i	1.08171	−	0.196216i
$760$	−1.14931e31			−0.235228
$761$			3.16366e31i			0.638202i	0.947721	+	0.319101i	$0.103381\pi$
$761$			3.16366e31i			0.638202i	−0.947721	+	0.319101i	$0.896619\pi$
$762$	−7.80816e30	−	4.30454e31i	−0.155254	−	0.855898i
$763$	−5.27897e29			−0.0103462
$764$		−	2.22823e31i		−	0.430461i
$765$	−8.81143e31	+	3.30544e31i	−1.67792	+	0.629438i
$766$	−6.91656e30			−0.129829
$767$		−	4.47968e31i		−	0.828892i
$768$	−6.53625e31	+	1.18564e31i	−1.19222	+	0.216261i
$769$	4.21084e31			0.757144			0.378572	−	0.925572i	$-0.376415\pi$
$769$	4.21084e31			0.757144			0.378572	+	0.925572i	$0.376415\pi$
$770$		−	7.99550e29i		−	0.0141725i
$771$	−1.00345e31	−	5.53189e31i	−0.175347	−	0.966664i
$772$	−3.60053e31			−0.620263
$773$		−	1.60007e31i		−	0.271746i	−0.990726	−	0.135873i	$-0.956616\pi$
$773$		−	1.60007e31i		−	0.271746i	0.990726	−	0.135873i	$-0.0433840\pi$
$774$	1.88047e31	+	5.01284e31i	0.314859	+	0.839331i
$775$	−1.39198e29			−0.00229780
$776$			1.40117e31i			0.228041i
$777$	−1.50069e29	+	2.72216e28i	−0.00240802	+	0.000436800i
$778$	−2.60338e31			−0.411872
$779$			2.55488e31i			0.398528i
$780$	8.60144e30	+	4.74186e31i	0.132291	+	0.729304i
$781$	−6.54282e31			−0.992210
$782$			1.29185e32i			1.93169i
$783$	−2.51944e30	−	4.21904e30i	−0.0371470	−	0.0622063i
$784$	8.59422e31			1.24948
$785$			1.80204e31i			0.258344i
$786$	1.48314e32	−	2.69032e31i	2.09668	−	0.380325i
$787$	−6.80372e31			−0.948472			−0.474236	−	0.880398i	$-0.657276\pi$
$787$	−6.80372e31			−0.948472			−0.474236	+	0.880398i	$0.657276\pi$
$788$		−	1.16181e31i		−	0.159716i
$789$	−2.49629e31	−	1.37617e32i	−0.338414	−	1.86563i
$790$	1.72743e31			0.230942
$791$		−	4.79315e29i		−	0.00631946i
$792$	5.34660e31	−	2.00567e31i	0.695186	−	0.260786i
$793$	1.77937e32			2.28171
$794$			9.83180e30i			0.124339i
$795$	2.38395e31	−	4.32433e30i	0.297344	−	0.0539363i
$796$	−3.01294e30			−0.0370635
$797$		−	1.09983e32i		−	1.33439i	−0.744881	−	0.667197i	$-0.767494\pi$
$797$		−	1.09983e32i		−	1.33439i	0.744881	−	0.667197i	$-0.232506\pi$
$798$	6.67378e28	+	3.67917e29i	0.000798619	+	0.00440268i
$799$	−1.56523e32			−1.84742
$800$		−	2.81729e29i		−	0.00327976i
$801$	2.58374e31	+	6.88757e31i	0.296682	+	0.790876i
$802$	−7.65279e31			−0.866766
$803$			1.13341e32i			1.26624i
$804$	−6.08526e30	+	1.10383e30i	−0.0670599	+	0.0121642i
$805$	7.37571e29			0.00801768
$806$		−	1.08755e32i		−	1.16617i
$807$	5.15904e30	+	2.84411e31i	0.0545708	+	0.300842i
$808$	−5.81052e31			−0.606303
$809$			1.19219e32i			1.22719i	0.789621	+	0.613595i	$0.210277\pi$
$809$			1.19219e32i			1.22719i	−0.789621	+	0.613595i	$0.789723\pi$
$810$	9.16235e31	−	7.99994e31i	0.930405	−	0.812365i
$811$	2.18511e31			0.218899			0.109449	−	0.993992i	$-0.465091\pi$
$811$	2.18511e31			0.218899			0.109449	+	0.993992i	$0.465091\pi$
$812$			3.48662e28i			0.000344579i
$813$	−1.48147e32	+	2.68730e31i	−1.44443	+	0.262011i
$814$	−4.30894e31			−0.414478
$815$		−	1.52762e32i		−	1.44971i
$816$	4.26150e31	+	2.34931e32i	0.398998	+	2.19962i
$817$	3.12486e31			0.288661
$818$		−	8.40030e31i		−	0.765612i
$819$	−1.35326e30	+	5.07648e29i	−0.0121691	+	0.00456499i
$820$	−5.89673e31			−0.523190
$821$			5.95325e31i			0.521170i	0.965451	+	0.260585i	$0.0839155\pi$
$821$			5.95325e31i			0.521170i	−0.965451	+	0.260585i	$0.916085\pi$
$822$	−1.03131e32	+	1.87073e31i	−0.890838	+	0.161592i
$823$	5.19470e31			0.442754			0.221377	−	0.975188i	$-0.428945\pi$
$823$	5.19470e31			0.442754			0.221377	+	0.975188i	$0.428945\pi$
$824$			3.07949e30i			0.0258988i
$825$	9.32815e28	+	5.14248e29i	0.000774109	+	0.00426756i
$826$	8.02209e29			0.00656912
$827$			1.16279e31i			0.0939593i	0.998896	+	0.0469797i	$0.0149596\pi$
$827$			1.16279e31i			0.0939593i	−0.998896	+	0.0469797i	$0.985040\pi$
$828$	−2.00710e31	−	5.35039e31i	−0.160042	−	0.426630i
$829$	−1.37810e32			−1.08438			−0.542189	−	0.840257i	$-0.682404\pi$
$829$	−1.37810e32			−1.08438			−0.542189	+	0.840257i	$0.682404\pi$
$830$		−	7.02390e31i		−	0.545405i
$831$	7.99036e31	−	1.44940e31i	0.612287	−	0.111065i
$832$	−1.48635e31			−0.112400
$833$		−	2.39701e32i		−	1.78886i
$834$	−4.29373e31	−	2.36708e32i	−0.316234	−	1.74335i
$835$	2.06597e32			1.50167
$836$			3.61554e31i			0.259361i
$837$	−8.06572e31	+	4.81651e31i	−0.571035	+	0.340999i
$838$	2.02457e32			1.41465
$839$			2.09997e32i			1.44821i	0.689690	+	0.724105i	$0.257747\pi$
$839$			2.09997e32i			1.44821i	−0.689690	+	0.724105i	$0.742253\pi$
$840$	7.82781e29	−	1.41992e29i	0.00532805	−	0.000966475i
$841$	1.48071e32			0.994750
$842$			3.09387e32i			2.05149i
$843$	1.08406e31	+	5.97626e31i	0.0709494	+	0.391135i
$844$	−3.55978e30			−0.0229962
$845$			1.60575e32i			1.02389i
$846$	1.89412e32	−	7.10542e31i	1.19216	−	0.447214i
$847$	8.47466e29			0.00526508
$848$		−	6.14696e31i		−	0.376969i
$849$	−1.69964e32	+	3.08303e31i	−1.02890	+	0.186635i
$850$	−1.27531e30			−0.00762089
$851$		−	3.97492e31i		−	0.234479i
$852$	1.26047e31	+	6.94879e31i	0.0733999	+	0.404644i
$853$	1.29656e32			0.745337			0.372669	−	0.927964i	$-0.378443\pi$
$853$	1.29656e32			0.745337			0.372669	+	0.927964i	$0.378443\pi$
$854$			3.18645e30i			0.0180830i
$855$	−2.49346e31	−	6.64692e31i	−0.139693	−	0.372386i
$856$	−6.46744e31			−0.357702
$857$		−	2.30671e32i		−	1.25952i	−0.776791	−	0.629758i	$-0.783154\pi$
$857$		−	2.30671e32i		−	1.25952i	0.776791	−	0.629758i	$-0.216846\pi$
$858$	−4.01781e32	+	7.28806e31i	−2.16586	+	0.392873i
$859$	1.13615e32			0.604657			0.302329	−	0.953204i	$-0.402236\pi$
$859$	1.13615e32			0.604657			0.302329	+	0.953204i	$0.402236\pi$
$860$			7.21224e31i			0.378955i
$861$	−3.15643e29	−	1.74010e30i	−0.00163742	−	0.00902690i
$862$	−2.73105e32			−1.39878
$863$		−	2.95147e32i		−	1.49252i	−0.665656	−	0.746259i	$-0.731848\pi$
$863$		−	2.95147e32i		−	1.49252i	0.665656	−	0.746259i	$-0.268152\pi$
$864$	−9.74840e31	−	1.63246e32i	−0.486723	−	0.815065i
$865$	−1.12891e32			−0.556524
$866$			2.87136e32i			1.39763i
$867$	4.50515e32	−	8.17206e31i	2.16521	−	0.392755i
$868$	6.66552e29			0.00316313
$869$			5.00941e31i			0.234730i
$870$	−3.45210e30	−	1.90310e31i	−0.0159724	−	0.0880540i
$871$	−4.07673e31			−0.186257
$872$		−	1.48396e32i		−	0.669486i
$873$	−8.10353e31	+	3.03988e31i	−0.361008	+	0.135425i
$874$	−9.74511e31			−0.428707
$875$		−	2.10028e30i		−	0.00912408i
$876$	1.20373e32	−	2.18350e31i	0.516398	−	0.0936715i
$877$	−2.67971e32			−1.13525			−0.567626	−	0.823286i	$-0.692138\pi$
$877$	−2.67971e32			−1.13525			−0.567626	+	0.823286i	$0.692138\pi$
$878$		−	1.56888e32i		−	0.656374i
$879$	4.46417e31	+	2.46104e32i	0.184443	+	1.01681i
$880$	3.85132e32			1.57145
$881$			1.13811e32i			0.458614i	0.973354	+	0.229307i	$0.0736460\pi$
$881$			1.13811e32i			0.458614i	−0.973354	+	0.229307i	$0.926354\pi$
$882$	1.08813e32	+	2.90067e32i	0.433038	+	1.15437i
$883$	−2.28006e32			−0.896145			−0.448072	−	0.893997i	$-0.647889\pi$
$883$	−2.28006e32			−0.896145			−0.448072	+	0.893997i	$0.647889\pi$
$884$		−	3.41017e32i		−	1.32373i
$885$	−1.49861e32	+	2.71839e31i	−0.574530	+	0.104216i
$886$	−1.07882e32			−0.408488
$887$			1.90154e32i			0.711123i	0.934653	+	0.355562i	$0.115710\pi$
$887$			1.90154e32i			0.711123i	−0.934653	+	0.355562i	$0.884290\pi$
$888$	−7.65222e30	−	4.21857e31i	−0.0282647	−	0.155820i
$889$	1.76744e30			0.00644800
$890$			2.89539e32i			1.04332i
$891$	2.31992e32	+	2.65701e32i	0.825691	+	0.945667i
$892$	−2.19235e32			−0.770719
$893$		−	1.18074e32i		−	0.410003i
$894$	5.09373e32	−	9.23972e31i	1.74712	−	0.316917i
$895$	8.23276e31			0.278928
$896$		−	2.85885e30i		−	0.00956761i
$897$	−6.72311e31	−	3.70636e32i	−0.222256	−	1.22527i
$898$	6.67440e32			2.17958
$899$			1.49384e31i			0.0481891i
$900$	5.28186e29	−	1.98139e29i	0.00168314	−	0.000631396i
$901$	−1.71445e32			−0.539698
$902$		−	4.99634e32i		−	1.55375i
$903$	−2.12830e30	+	3.86060e29i	−0.00653833	+	0.00118601i
$904$	1.34740e32			0.408924
$905$			3.27540e32i			0.982042i
$906$	8.74684e30	+	4.82202e31i	0.0259084	+	0.142830i
$907$	−3.66734e32			−1.07318			−0.536588	−	0.843844i	$-0.680287\pi$
$907$	−3.66734e32			−1.07318			−0.536588	+	0.843844i	$0.680287\pi$
$908$			2.31855e31i			0.0670303i
$909$	−1.26061e32	−	3.36044e32i	−0.360061	−	0.959829i
$910$	−5.68882e30			−0.0160534
$911$			1.17264e32i			0.326937i	0.986549	+	0.163468i	$0.0522682\pi$
$911$			1.17264e32i			0.326937i	−0.986549	+	0.163468i	$0.947732\pi$
$912$	−1.77220e32	+	3.21467e31i	−0.488169	+	0.0885509i
$913$	2.03687e32			0.554352
$914$			3.97742e32i			1.06953i
$915$	−1.07977e32	−	5.95261e32i	−0.286879	−	1.58152i
$916$	−3.61730e31			−0.0949585
$917$			6.08974e30i			0.0157956i
$918$	−7.38968e32	+	4.41281e32i	−1.89389	+	1.13096i
$919$	−6.75662e32			−1.71104			−0.855518	−	0.517774i	$-0.826761\pi$
$919$	−6.75662e32			−1.71104			−0.855518	+	0.517774i	$0.826761\pi$
$920$			2.07337e32i			0.518814i
$921$	5.81232e32	−	1.05432e32i	1.43712	−	0.260685i
$922$	−7.01185e31			−0.171314
$923$			4.65523e32i			1.12389i
$924$	−4.46681e29	−	2.46249e30i	−0.00106563	−	0.00587467i
$925$	3.92401e29			0.000925062
$926$		−	8.95719e32i		−	2.08666i
$927$	−1.78099e31	+	6.68104e30i	−0.0410000	+	0.0153804i
$928$	−3.02347e31			−0.0687825
$929$			3.87644e32i			0.871486i	0.900071	+	0.435743i	$0.143514\pi$
$929$			3.87644e32i			0.871486i	−0.900071	+	0.435743i	$0.856486\pi$
$930$	−3.63823e32	+	6.59952e31i	−0.808309	+	0.146622i
$931$	1.80819e32			0.397007
$932$			3.50937e32i			0.761473i
$933$	1.34157e32	+	7.39587e32i	0.287683	+	1.58596i
$934$	6.00013e32			1.27158
$935$		−	1.07417e33i		−	2.24981i
$936$	−1.42704e32	−	3.80412e32i	−0.295395	−	0.787445i
$937$	5.82105e32			1.19087			0.595437	−	0.803402i	$-0.296979\pi$
$937$	5.82105e32			1.19087			0.595437	+	0.803402i	$0.296979\pi$
$938$		−	7.30049e29i		−	0.00147612i
$939$	−3.63592e32	+	6.59533e31i	−0.726595	+	0.131800i
$940$	2.72517e32			0.538254
$941$		−	7.80346e32i		−	1.52336i	−0.647956	−	0.761678i	$-0.724376\pi$
$941$		−	7.80346e32i		−	1.52336i	0.647956	−	0.761678i	$-0.275624\pi$
$942$	2.94152e31	+	1.62162e32i	0.0567561	+	0.312889i
$943$	4.60904e32			0.878986
$944$			3.86413e32i			0.728384i
$945$	2.51945e30	+	4.21907e30i	0.00469414	+	0.00786079i
$946$	−6.11098e32			−1.12540
$947$		−	1.32860e32i		−	0.241849i	−0.992662	−	0.120925i	$-0.961414\pi$
$947$		−	1.32860e32i		−	0.241849i	0.992662	−	0.120925i	$-0.0385859\pi$
$948$	5.32024e31	−	9.65058e30i	0.0957281	−	0.0173645i
$949$	8.06422e32			1.43428
$950$		−	9.62029e29i		−	0.00169133i
$951$	6.31198e31	+	3.47971e32i	0.109693	+	0.604725i
$952$	−5.62947e30			−0.00967076
$953$			4.08946e32i			0.694454i	0.937781	+	0.347227i	$0.112877\pi$
$953$			4.08946e32i			0.694454i	−0.937781	+	0.347227i	$0.887123\pi$
$954$	2.07468e32	−	7.78277e31i	0.348273	−	0.130648i
$955$	−4.99384e32			−0.828700
$956$			2.48068e30i			0.00406943i
$957$	5.51882e31	−	1.00108e31i	0.0894984	−	0.0162345i
$958$	5.97750e31			0.0958295
$959$		−	4.23454e30i		−	0.00671122i
$960$	9.01955e30	+	4.97236e31i	0.0141319	+	0.0779075i
$961$	−3.60006e32			−0.557639
$962$			3.06582e32i			0.469484i
$963$	−1.40313e32	−	3.74037e32i	−0.212426	−	0.566272i
$964$	−7.36694e31			−0.110266
$965$			8.06938e32i			1.19410i
$966$	6.63725e30	−	1.20396e30i	0.00971047	−	0.00176142i
$967$	1.23696e30			0.00178923			0.000894614	−	1.00000i	$-0.499715\pi$
$967$	1.23696e30			0.00178923			0.000894614		1.00000i	$0.499715\pi$
$968$			2.38230e32i			0.340696i
$969$	8.96602e31	+	4.94285e32i	0.126776	+	0.698901i
$970$	−3.40656e32			−0.476241
$971$			1.43621e32i			0.198520i	0.995062	+	0.0992602i	$0.0316476\pi$
$971$			1.43621e32i			0.198520i	−0.995062	+	0.0992602i	$0.968352\pi$
$972$	2.37494e32	−	2.97573e32i	0.324582	−	0.406691i
$973$	9.71919e30			0.0131338
$974$		−	1.58815e33i		−	2.12199i
$975$	3.65889e30	−	6.63700e29i	0.00483391	−	0.000876841i
$976$	−1.53487e33			−2.00504
$977$		−	9.50799e32i		−	1.22814i	−0.789251	−	0.614071i	$-0.789531\pi$
$977$		−	9.50799e32i		−	1.22814i	0.789251	−	0.614071i	$-0.210469\pi$
$978$	−2.49357e32	−	1.37467e33i	−0.318489	−	1.75579i
$979$	−8.39640e32			−1.06043
$980$			4.17335e32i			0.521192i
$981$	8.58232e32	−	3.21949e32i	1.05985	−	0.397583i
$982$	1.87997e32			0.229574
$983$			1.24553e33i			1.50406i	0.659131	+	0.752028i	$0.270924\pi$
$983$			1.24553e33i			1.50406i	−0.659131	+	0.752028i	$0.729076\pi$
$984$	4.89156e32	−	8.87298e31i	0.584119	−	0.105955i
$985$	−2.60381e32			−0.307476
$986$			1.36863e32i			0.159824i
$987$	1.45874e30	+	8.04184e30i	0.00168457	+	0.00928681i
$988$	2.57247e32			0.293781
$989$		−	5.63727e32i		−	0.636664i
$990$	4.87623e32	+	1.29987e33i	0.544624	+	1.45182i
$991$	1.32761e32			0.146643			0.0733215	−	0.997308i	$-0.476640\pi$
$991$	1.32761e32			0.146643			0.0733215	+	0.997308i	$0.476640\pi$
$992$			5.78009e32i			0.631403i
$993$	−1.26037e33	+	2.28623e32i	−1.36162	+	0.246990i
$994$	−8.33646e30			−0.00890700
$995$			6.75250e31i			0.0713527i
$996$	−3.92401e31	−	2.16326e32i	−0.0410089	−	0.226076i
$997$	1.73525e33			1.79356			0.896778	−	0.442481i	$-0.145902\pi$
$997$	1.73525e33			1.79356			0.896778	+	0.442481i	$0.145902\pi$
$998$			9.68100e32i			0.989656i
$999$	2.27374e32	−	1.35779e32i	0.229890	−	0.137281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.23.b.a.2.2	✓	6
3.2	odd	2	inner	3.23.b.a.2.5	yes	6
4.3	odd	2		48.23.e.b.17.5		6
12.11	even	2		48.23.e.b.17.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.23.b.a.2.2	✓	6	1.1	even	1	trivial
3.23.b.a.2.5	yes	6	3.2	odd	2	inner
48.23.e.b.17.5		6	4.3	odd	2
48.23.e.b.17.6		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:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2525.22i q^{2} +(-174303. + 31617.4i) q^{3} -2.18245e6 q^{4} +4.89124e7i q^{5} +(7.98410e7 + 4.40153e8i) q^{6} -1.80726e7 q^{7} -5.08037e9i q^{8} +(2.93817e10 - 1.10220e10i) q^{9} +O(q^{10})\)	\(q-2525.22i q^{2} +(-174303. + 31617.4i) q^{3} -2.18245e6 q^{4} +4.89124e7i q^{5} +(7.98410e7 + 4.40153e8i) q^{6} -1.80726e7 q^{7} -5.08037e9i q^{8} +(2.93817e10 - 1.10220e10i) q^{9} +1.23515e11 q^{10} +3.58183e11i q^{11} +(3.80407e11 - 6.90035e10i) q^{12} +2.54848e12 q^{13} +4.56375e10i q^{14} +(-1.54648e12 - 8.52556e12i) q^{15} -2.19830e13 q^{16} +6.13126e13i q^{17} +(-2.78330e13 - 7.41955e13i) q^{18} -4.62513e13 q^{19} -1.06749e14i q^{20} +(3.15011e12 - 5.71410e11i) q^{21} +9.04492e14 q^{22} +8.34378e14i q^{23} +(1.60628e14 + 8.85522e14i) q^{24} -8.23691e12 q^{25} -6.43548e15i q^{26} +(-4.77283e15 + 2.85014e15i) q^{27} +3.94427e13 q^{28} +8.83971e14i q^{29} +(-2.15289e16 + 3.90522e15i) q^{30} +1.68992e16 q^{31} +3.42033e16i q^{32} +(-1.13248e16 - 6.24322e16i) q^{33} +1.54828e17 q^{34} -8.83976e14i q^{35} +(-6.41243e16 + 2.40550e16i) q^{36} -4.76393e16 q^{37} +1.16795e17i q^{38} +(-4.44207e17 + 8.05763e16i) q^{39} +2.48493e17 q^{40} -5.52392e17i q^{41} +(-1.44294e15 - 7.95473e15i) q^{42} -6.75626e17 q^{43} -7.81717e17i q^{44} +(5.39112e17 + 1.43713e18i) q^{45} +2.10699e18 q^{46} +2.55288e18i q^{47} +(3.83169e18 - 6.95044e17i) q^{48} -3.90949e18 q^{49} +2.08000e16i q^{50} +(-1.93855e18 - 1.06869e19i) q^{51} -5.56194e18 q^{52} +2.79624e18i q^{53} +(7.19723e18 + 1.20525e19i) q^{54} -1.75196e19 q^{55} +9.18158e16i q^{56} +(8.06172e18 - 1.46235e18i) q^{57} +2.23222e18 q^{58} -1.75779e19i q^{59} +(3.37513e18 + 1.86066e19i) q^{60} +6.98208e19 q^{61} -4.26744e19i q^{62} +(-5.31006e17 + 1.99197e17i) q^{63} -5.83230e18 q^{64} +1.24652e20i q^{65} +(-1.57655e20 + 2.85977e19i) q^{66} -1.59967e19 q^{67} -1.33812e20i q^{68} +(-2.63809e19 - 1.45434e20i) q^{69} -2.23224e18 q^{70} +1.82667e20i q^{71} +(-5.59958e19 - 1.49270e20i) q^{72} +3.16433e20 q^{73} +1.20300e20i q^{74} +(1.43572e18 - 2.60430e17i) q^{75} +1.00941e20 q^{76} -6.47331e18i q^{77} +(2.03473e20 + 1.12172e21i) q^{78} +1.39856e20 q^{79} -1.07524e21i q^{80} +(7.41802e20 - 6.47691e20i) q^{81} -1.39491e21 q^{82} -5.68668e20i q^{83} +(-6.87497e18 + 1.24708e18i) q^{84} -2.99895e21 q^{85} +1.70611e21i q^{86} +(-2.79489e19 - 1.54078e20i) q^{87} +1.81970e21 q^{88} +2.34417e21i q^{89} +(3.62908e21 - 1.36138e21i) q^{90} -4.60578e19 q^{91} -1.82099e21i q^{92} +(-2.94558e21 + 5.34310e20i) q^{93} +6.44658e21 q^{94} -2.26226e21i q^{95} +(-1.08142e21 - 5.96172e21i) q^{96} -2.75801e21 q^{97} +9.87235e21i q^{98} +(3.94789e21 + 1.05240e22i) 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

Fields

Representations

Groups

Database

Properties

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