LMFDB - Embedded newform 3.33.b.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,33,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, 33, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 33 $
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:	$19.4599965427$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 954745942 x^{8} + \cdots + 31\!\cdots\!00 $ x^10 + 954745942x^8 + 302468338607088448x^6 + 37939920124077893929140224x^4 + 1938513915962148831841211918581760x^2 + 31225030372218346257929044634944667648000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{61}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.8
Root			$9879.94i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.33.b.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+59279.7i q^{2} +(-4.29008e7 + 3.54120e6i) q^{3} +7.80890e8 q^{4} +2.23415e11i q^{5} +(-2.09921e11 - 2.54315e12i) q^{6} +4.13333e13 q^{7} +3.00895e14i q^{8} +(1.82794e15 - 3.03841e14i) q^{9} +O(q^{10})$	\(q+59279.7i q^{2} +(-4.29008e7 + 3.54120e6i) q^{3} +7.80890e8 q^{4} +2.23415e11i q^{5} +(-2.09921e11 - 2.54315e12i) q^{6} +4.13333e13 q^{7} +3.00895e14i q^{8} +(1.82794e15 - 3.03841e14i) q^{9} -1.32440e16 q^{10} +7.52532e16i q^{11} +(-3.35008e16 + 2.76529e15i) q^{12} +3.61912e17 q^{13} +2.45022e18i q^{14} +(-7.91159e17 - 9.58470e18i) q^{15} -1.44831e19 q^{16} -4.65302e19i q^{17} +(1.80116e19 + 1.08360e20i) q^{18} -2.35200e20 q^{19} +1.74463e20i q^{20} +(-1.77323e21 + 1.46370e20i) q^{21} -4.46098e21 q^{22} -1.16904e21i q^{23} +(-1.06553e21 - 1.29086e22i) q^{24} -2.66313e22 q^{25} +2.14540e22i q^{26} +(-7.73442e22 + 1.95081e22i) q^{27} +3.22768e22 q^{28} +6.23293e22i q^{29} +(5.68178e23 - 4.68996e22i) q^{30} +5.99047e23 q^{31} +4.33784e23i q^{32} +(-2.66487e23 - 3.22842e24i) q^{33} +2.75829e24 q^{34} +9.23449e24i q^{35} +(1.42742e24 - 2.37266e23i) q^{36} -5.06861e24 q^{37} -1.39426e25i q^{38} +(-1.55263e25 + 1.28160e24i) q^{39} -6.72246e25 q^{40} +1.64115e25i q^{41} +(-8.67674e24 - 1.05117e26i) q^{42} +7.52091e25 q^{43} +5.87645e25i q^{44} +(6.78827e25 + 4.08390e26i) q^{45} +6.93006e25 q^{46} -3.86340e26i q^{47} +(6.21335e26 - 5.12874e25i) q^{48} +6.04014e26 q^{49} -1.57870e27i q^{50} +(1.64773e26 + 1.99618e27i) q^{51} +2.82614e26 q^{52} +1.18574e27i q^{53} +(-1.15643e27 - 4.58493e27i) q^{54} -1.68127e28 q^{55} +1.24370e28i q^{56} +(1.00903e28 - 8.32892e26i) q^{57} -3.69486e27 q^{58} -2.66209e28i q^{59} +(-6.17808e26 - 7.48460e27i) q^{60} +1.94501e28 q^{61} +3.55113e28i q^{62} +(7.55548e28 - 1.25587e28i) q^{63} -8.79188e28 q^{64} +8.08568e28i q^{65} +(1.91380e29 - 1.57972e28i) q^{66} +3.59652e28 q^{67} -3.63350e28i q^{68} +(4.13982e27 + 5.01530e28i) q^{69} -5.47418e29 q^{70} -7.06445e29i q^{71} +(9.14242e28 + 5.50018e29i) q^{72} -1.05315e30 q^{73} -3.00466e29i q^{74} +(1.14251e30 - 9.43069e28i) q^{75} -1.83666e29 q^{76} +3.11046e30i q^{77} +(-7.59731e28 - 9.20396e29i) q^{78} +1.00731e30 q^{79} -3.23574e30i q^{80} +(3.24905e30 - 1.11081e30i) q^{81} -9.72866e29 q^{82} +1.77768e30i q^{83} +(-1.38470e30 + 1.14299e29i) q^{84} +1.03956e31 q^{85} +4.45837e30i q^{86} +(-2.20720e29 - 2.67398e30i) q^{87} -2.26433e31 q^{88} +1.02841e30i q^{89} +(-2.42092e31 + 4.02406e30i) q^{90} +1.49590e31 q^{91} -9.12895e29i q^{92} +(-2.56996e31 + 2.12135e30i) q^{93} +2.29021e31 q^{94} -5.25474e31i q^{95} +(-1.53612e30 - 1.86097e31i) q^{96} +8.20379e31 q^{97} +3.58058e31i q^{98} +(2.28650e31 + 1.37558e32i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9}+O(q^{10}) $ 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9	$ 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 70\!\cdots\!40 q^{10}+ \cdots - 33\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9 - 7003812786596640 * q^10 - 279007424380502640 * q^12 + 567697557679805780 * q^13 - 20342205597863242080 * q^15 + 93452609752238437504 * q^16 - 546532439317269948000 * q^18 + 571007688520350419876 * q^19 - 202809296674597359852 * q^21 - 7726803521259943913760 * q^22 + 40966888307328818303616 * q^24 - 68909708350780834128950 * q^25 - 72967926462080465281230 * q^27 + 205937256056975756717600 * q^28 - 1107420825536697507876000 * q^30 + 2337947500037502285593540 * q^31 + 2522449071689961111334560 * q^33 - 6060358314194999366692224 * q^34 + 19880961335883894024618192 * q^36 - 35307903416851790686359340 * q^37 - 31624005377757923978634972 * q^39 + 103824872020641394026996480 * q^40 - 141365101025586253616004960 * q^42 + 20133134465218107006792740 * q^43 + 324508325822765233105320000 * q^45 - 1081312096716791246752963776 * q^46 + 3981901930430244196770990720 * q^48 - 2767041101974767237639509154 * q^49 + 1958591008210563208705802112 * q^51 - 5054272042223836449280397920 * q^52 + 8609682620485865645134310448 * q^54 - 11870374622399979665591304000 * q^55 + 40568829971233106153298510900 * q^57 - 126691224865576416891245282400 * q^58 + 279833341447916827662753642240 * q^60 - 196667345182223458343232398380 * q^61 + 349775312774222889759843110340 * q^63 - 738816306154787409411488427008 * q^64 + 939413077861687418842822458720 * q^66 - 442550741350999501345614861340 * q^67 + 1096443581430237499419700598208 * q^69 - 3084260511067452830890360584000 * q^70 + 5478956649034785201935062114560 * q^72 - 4530286149796751043896742263020 * q^73 + 5689646867484953837977805651250 * q^75 - 10804853453030293252172855440096 * q^76 + 9245617327241370897996048982560 * q^78 - 2115110787448996851533482223164 * q^79 - 454653247801524309158818752630 * q^81 + 6754240700896495824250705604160 * q^82 - 10589261014798101343390846457952 * q^84 + 8783873758902640422771709896960 * q^85 - 12893796544943502316879779198240 * q^87 + 15416255855088684041150976480000 * q^88 - 76437416541013126109366518121760 * q^90 + 59544256621898576615810233543816 * q^91 - 105131728169400940473110940107820 * q^93 + 301803894289991891760064059517056 * q^94 - 522680019947351351608967407401984 * q^96 + 390148965222370670128665882607700 * q^97 - 333895893109019690643343683610560 * 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 $

$2$			59279.7i			0.904536i	0.891882	+	0.452268i	$0.149385\pi$
$2$			59279.7i			0.904536i	−0.891882	+	0.452268i	$0.850615\pi$
$3$	−4.29008e7	+	3.54120e6i	−0.996611	+	0.0822641i
$3$	−4.29008e7	+	3.54120e6i	−0.996611	+	0.0822641i
$4$	7.80890e8			0.181815
$5$			2.23415e11i			1.46417i	0.681211	+	0.732087i	$0.261454\pi$
$5$			2.23415e11i			1.46417i	−0.681211	+	0.732087i	$0.738546\pi$
$6$	−2.09921e11	−	2.54315e12i	−0.0744109	−	0.901470i
$7$	4.13333e13			1.24375			0.621873	−	0.783118i	$-0.286372\pi$
$7$	4.13333e13			1.24375			0.621873	+	0.783118i	$0.286372\pi$
$8$			3.00895e14i			1.06899i
$9$	1.82794e15	−	3.03841e14i	0.986465	−	0.163971i
$10$	−1.32440e16			−1.32440
$11$			7.52532e16i			1.63773i	0.573987	+	0.818864i	$0.305396\pi$
$11$			7.52532e16i			1.63773i	−0.573987	+	0.818864i	$0.694604\pi$
$12$	−3.35008e16	+	2.76529e15i	−0.181199	+	0.0149569i
$13$	3.61912e17			0.543888			0.271944	−	0.962313i	$-0.412333\pi$
$13$	3.61912e17			0.543888			0.271944	+	0.962313i	$0.412333\pi$
$14$			2.45022e18i			1.12501i
$15$	−7.91159e17	−	9.58470e18i	−0.120449	−	1.45921i
$16$	−1.44831e19			−0.785128
$17$		−	4.65302e19i		−	0.956208i	−0.878303	−	0.478104i	$-0.841324\pi$
$17$		−	4.65302e19i		−	0.956208i	0.878303	−	0.478104i	$-0.158676\pi$
$18$	1.80116e19	+	1.08360e20i	0.148317	+	0.892293i
$19$	−2.35200e20			−0.815418			−0.407709	−	0.913112i	$-0.633672\pi$
$19$	−2.35200e20			−0.815418			−0.407709	+	0.913112i	$0.633672\pi$
$20$			1.74463e20i			0.266209i
$21$	−1.77323e21	+	1.46370e20i	−1.23953	+	0.102316i
$22$	−4.46098e21			−1.48138
$23$		−	1.16904e21i		−	0.190628i	−0.995447	−	0.0953138i	$-0.969615\pi$
$23$		−	1.16904e21i		−	0.190628i	0.995447	−	0.0953138i	$-0.0303854\pi$
$24$	−1.06553e21	−	1.29086e22i	−0.0879399	−	1.06537i
$25$	−2.66313e22			−1.14381
$26$			2.14540e22i			0.491966i
$27$	−7.73442e22	+	1.95081e22i	−0.969633	+	0.244566i
$28$	3.22768e22			0.226132
$29$			6.23293e22i			0.249072i	0.992215	+	0.124536i	$0.0397441\pi$
$29$			6.23293e22i			0.249072i	−0.992215	+	0.124536i	$0.960256\pi$
$30$	5.68178e23	−	4.68996e22i	1.31991	−	0.108950i
$31$	5.99047e23			0.823520			0.411760	−	0.911292i	$-0.364914\pi$
$31$	5.99047e23			0.823520			0.411760	+	0.911292i	$0.364914\pi$
$32$			4.33784e23i			0.358818i
$33$	−2.66487e23	−	3.22842e24i	−0.134726	−	1.63218i
$34$	2.75829e24			0.864924
$35$			9.23449e24i			1.82106i
$36$	1.42742e24	−	2.37266e23i	0.179354	−	0.0298123i
$37$	−5.06861e24			−0.410829			−0.205415	−	0.978675i	$-0.565854\pi$
$37$	−5.06861e24			−0.410829			−0.205415	+	0.978675i	$0.565854\pi$
$38$		−	1.39426e25i		−	0.737575i
$39$	−1.55263e25	+	1.28160e24i	−0.542045	+	0.0447425i
$40$	−6.72246e25			−1.56519
$41$			1.64115e25i			0.257398i	0.991684	+	0.128699i	$0.0410802\pi$
$41$			1.64115e25i			0.257398i	−0.991684	+	0.128699i	$0.958920\pi$
$42$	−8.67674e24	−	1.05117e26i	−0.0925482	−	1.12120i
$43$	7.52091e25			0.550522			0.275261	−	0.961369i	$-0.411236\pi$
$43$	7.52091e25			0.550522			0.275261	+	0.961369i	$0.411236\pi$
$44$			5.87645e25i			0.297764i
$45$	6.78827e25	+	4.08390e26i	0.240082	+	1.44436i
$46$	6.93006e25			0.172429
$47$		−	3.86340e26i		−	0.681403i	−0.940172	−	0.340701i	$-0.889335\pi$
$47$		−	3.86340e26i		−	0.681403i	0.940172	−	0.340701i	$-0.110665\pi$
$48$	6.21335e26	−	5.12874e25i	0.782467	−	0.0645879i
$49$	6.04014e26			0.546902
$50$		−	1.57870e27i		−	1.03461i
$51$	1.64773e26	+	1.99618e27i	0.0786616	+	0.952967i
$52$	2.82614e26			0.0988871
$53$			1.18574e27i			0.305898i	0.988234	+	0.152949i	$0.0488770\pi$
$53$			1.18574e27i			0.305898i	−0.988234	+	0.152949i	$0.951123\pi$
$54$	−1.15643e27	−	4.58493e27i	−0.221218	−	0.877067i
$55$	−1.68127e28			−2.39792
$56$			1.24370e28i			1.32956i
$57$	1.00903e28	−	8.32892e26i	0.812654	−	0.0670797i
$58$	−3.69486e27			−0.225294
$59$		−	2.66209e28i		−	1.23478i	−0.786657	−	0.617391i	$-0.788190\pi$
$59$		−	2.66209e28i		−	1.23478i	0.786657	−	0.617391i	$-0.211810\pi$
$60$	−6.17808e26	−	7.48460e27i	−0.0218995	−	0.265307i
$61$	1.94501e28			0.529230			0.264615	−	0.964354i	$-0.414755\pi$
$61$	1.94501e28			0.529230			0.264615	+	0.964354i	$0.414755\pi$
$62$			3.55113e28i			0.744903i
$63$	7.55548e28	−	1.25587e28i	1.22691	−	0.203938i
$64$	−8.79188e28			−1.10969
$65$			8.08568e28i			0.796347i
$66$	1.91380e29	−	1.57972e28i	1.47636	−	0.121865i
$67$	3.59652e28			0.218115			0.109058	−	0.994035i	$-0.465217\pi$
$67$	3.59652e28			0.218115			0.109058	+	0.994035i	$0.465217\pi$
$68$		−	3.63350e28i		−	0.173853i
$69$	4.13982e27	+	5.01530e28i	0.0156818	+	0.189981i
$70$	−5.47418e29			−1.64721
$71$		−	7.06445e29i		−	1.69412i	−0.531496	−	0.847061i	$-0.678370\pi$
$71$		−	7.06445e29i		−	1.69412i	0.531496	−	0.847061i	$-0.321630\pi$
$72$	9.14242e28	+	5.50018e29i	0.175284	+	1.05453i
$73$	−1.05315e30			−1.61929			−0.809644	−	0.586921i	$-0.800340\pi$
$73$	−1.05315e30			−1.61929			−0.809644	+	0.586921i	$0.800340\pi$
$74$		−	3.00466e29i		−	0.371610i
$75$	1.14251e30	−	9.43069e28i	1.13993	−	0.0940943i
$76$	−1.83666e29			−0.148255
$77$			3.11046e30i			2.03692i
$78$	−7.59731e28	−	9.20396e29i	−0.0404712	−	0.490299i
$79$	1.00731e30			0.437651			0.218825	−	0.975764i	$-0.429777\pi$
$79$	1.00731e30			0.437651			0.218825	+	0.975764i	$0.429777\pi$
$80$		−	3.23574e30i		−	1.14956i
$81$	3.24905e30	−	1.11081e30i	0.946227	−	0.323503i
$82$	−9.72866e29			−0.232826
$83$			1.77768e30i			0.350433i	0.984530	+	0.175216i	$0.0560625\pi$
$83$			1.77768e30i			0.350433i	−0.984530	+	0.175216i	$0.943938\pi$
$84$	−1.38470e30	+	1.14299e29i	−0.225365	+	0.0186025i
$85$	1.03956e31			1.40005
$86$			4.45837e30i			0.497967i
$87$	−2.20720e29	−	2.67398e30i	−0.0204897	−	0.248227i
$88$	−2.26433e31			−1.75072
$89$			1.02841e30i			0.0663628i	0.999449	+	0.0331814i	$0.0105639\pi$
$89$			1.02841e30i			0.0663628i	−0.999449	+	0.0331814i	$0.989436\pi$
$90$	−2.42092e31	+	4.02406e30i	−1.30647	+	0.217162i
$91$	1.49590e31			0.676459
$92$		−	9.12895e29i		−	0.0346590i
$93$	−2.56996e31	+	2.12135e30i	−0.820729	+	0.0677461i
$94$	2.29021e31			0.616353
$95$		−	5.25474e31i		−	1.19391i
$96$	−1.53612e30	−	1.86097e31i	−0.0295178	−	0.357601i
$97$	8.20379e31			1.33557			0.667785	−	0.744354i	$-0.267243\pi$
$97$	8.20379e31			1.33557			0.667785	+	0.744354i	$0.267243\pi$
$98$			3.58058e31i			0.494693i
$99$	2.28650e31	+	1.37558e32i	0.268539	+	1.61556i
$100$	−2.07961e31			−0.207961
$101$		−	7.39513e31i		−	0.630672i	−0.948980	−	0.315336i	$-0.897883\pi$
$101$		−	7.39513e31i		−	0.630672i	0.948980	−	0.315336i	$-0.102117\pi$
$102$	−1.18333e32	+	9.76768e30i	−0.861992	+	0.0711522i
$103$	2.71418e32			1.69139			0.845693	−	0.533669i	$-0.179187\pi$
$103$	2.71418e32			1.69139			0.845693	+	0.533669i	$0.179187\pi$
$104$			1.08898e32i			0.581413i
$105$	−3.27012e31	−	3.96167e32i	−0.149808	−	1.81489i
$106$	−7.02904e31			−0.276695
$107$			4.68813e32i			1.58803i	0.607897	+	0.794016i	$0.292013\pi$
$107$			4.68813e32i			1.58803i	−0.607897	+	0.794016i	$0.707987\pi$
$108$	−6.03973e31	+	1.52337e31i	−0.176294	+	0.0444657i
$109$	−5.91727e32			−1.49038			−0.745191	−	0.666851i	$-0.767642\pi$
$109$	−5.91727e32			−1.49038			−0.745191	+	0.666851i	$0.767642\pi$
$110$		−	9.96652e32i		−	2.16900i
$111$	2.17448e32	−	1.79490e31i	0.409437	−	0.0337965i
$112$	−5.98633e32			−0.976499
$113$			1.05367e33i			1.49091i	0.666557	+	0.745454i	$0.267767\pi$
$113$			1.05367e33i			1.49091i	−0.666557	+	0.745454i	$0.732233\pi$
$114$	4.93735e31	+	5.98149e32i	0.0606760	+	0.735075i
$115$	2.61182e32			0.279112
$116$			4.86723e31i			0.0452850i
$117$	6.61554e32	−	1.09964e32i	0.536527	−	0.0891817i
$118$	1.57808e33			1.11690
$119$		−	1.92325e33i		−	1.18928i
$120$	2.88399e33	−	2.38056e32i	1.55989	−	0.128759i
$121$	−3.55167e33			−1.68216
$122$			1.15300e33i			0.478708i
$123$	−5.81163e31	−	7.04065e32i	−0.0211747	−	0.256526i
$124$	4.67790e32			0.149728
$125$		−	7.48054e32i		−	0.210559i
$126$	7.44478e32	+	4.47886e33i	0.184469	+	1.10979i
$127$	1.54393e32			0.0337107			0.0168554	−	0.999858i	$-0.494635\pi$
$127$	1.54393e32			0.0337107			0.0168554	+	0.999858i	$0.494635\pi$
$128$		−	3.34871e33i		−	0.644938i
$129$	−3.22653e33	+	2.66330e32i	−0.548656	+	0.0452882i
$130$	−4.79316e33			−0.720325
$131$			6.36918e33i			0.846726i	0.905960	+	0.423363i	$0.139150\pi$
$131$			6.36918e33i			0.846726i	−0.905960	+	0.423363i	$0.860850\pi$
$132$	−2.08097e32	−	2.52104e33i	−0.0244953	−	0.296755i
$133$	−9.72161e33			−1.01417
$134$			2.13201e33i			0.197293i
$135$	−4.35841e33	−	1.72799e34i	−0.358087	−	1.41971i
$136$	1.40007e34			1.02218
$137$		−	1.70940e33i		−	0.110998i	−0.998459	−	0.0554988i	$-0.982325\pi$
$137$		−	1.70940e33i		−	0.110998i	0.998459	−	0.0554988i	$-0.0176749\pi$
$138$	−2.97305e33	+	2.45407e32i	−0.171845	+	0.0141848i
$139$	2.43736e34			1.25511			0.627557	−	0.778570i	$-0.284055\pi$
$139$	2.43736e34			1.25511			0.627557	+	0.778570i	$0.284055\pi$
$140$			7.21112e33i			0.331096i
$141$	1.36811e33	+	1.65743e34i	0.0560550	+	0.679093i
$142$	4.18778e34			1.53239
$143$			2.72351e34i			0.890742i
$144$	−2.64742e34	+	4.40055e33i	−0.774502	+	0.128738i
$145$	−1.39253e34			−0.364684
$146$		−	6.24303e34i		−	1.46470i
$147$	−2.59127e34	+	2.13894e33i	−0.545049	+	0.0449905i
$148$	−3.95803e33			−0.0746950
$149$		−	1.43527e34i		−	0.243193i	−0.992580	−	0.121597i	$-0.961199\pi$
$149$		−	1.43527e34i		−	0.243193i	0.992580	−	0.121597i	$-0.0388015\pi$
$150$	5.59048e33	+	6.77274e34i	0.0851117	+	1.03111i
$151$	2.88137e34			0.394429			0.197214	−	0.980360i	$-0.436810\pi$
$151$	2.88137e34			0.394429			0.197214	+	0.980360i	$0.436810\pi$
$152$		−	7.07706e34i		−	0.871677i
$153$	−1.41378e34	−	8.50544e34i	−0.156790	−	0.943266i
$154$	−1.84387e35			−1.84246
$155$			1.33836e35i			1.20578i
$156$	−1.21244e34	+	1.00079e33i	−0.0985520	+	0.00813486i
$157$	1.23711e35			0.907846			0.453923	−	0.891041i	$-0.350024\pi$
$157$	1.23711e35			0.907846			0.453923	+	0.891041i	$0.350024\pi$
$158$			5.97127e34i			0.395871i
$159$	−4.19895e33	−	5.08693e34i	−0.0251644	−	0.304861i
$160$	−9.69139e34			−0.525371
$161$		−	4.83205e34i		−	0.237092i
$162$	6.58482e34	+	1.92602e35i	0.292620	+	0.855896i
$163$	1.52139e35			0.612687			0.306344	−	0.951921i	$-0.400894\pi$
$163$	1.52139e35			0.612687			0.306344	+	0.951921i	$0.400894\pi$
$164$			1.28155e34i			0.0467989i
$165$	7.21279e35	−	5.95372e34i	2.38979	−	0.197263i
$166$	−1.05380e35			−0.316979
$167$		−	2.90713e35i		−	0.794329i	−0.917748	−	0.397164i	$-0.869994\pi$
$167$		−	2.90713e35i		−	0.794329i	0.917748	−	0.397164i	$-0.130006\pi$
$168$	−4.40419e34	−	5.33557e35i	−0.109375	−	1.32505i
$169$	−3.11799e35			−0.704185
$170$			6.16245e35i			1.26640i
$171$	−4.29932e35	+	7.14635e34i	−0.804382	+	0.133705i
$172$	5.87300e34			0.100093
$173$			6.17095e35i			0.958548i	0.877665	+	0.479274i	$0.159100\pi$
$173$			6.17095e35i			0.958548i	−0.877665	+	0.479274i	$0.840900\pi$
$174$	1.58512e35	−	1.30842e34i	0.224530	−	0.0185336i
$175$	−1.10076e36			−1.42260
$176$		−	1.08990e36i		−	1.28583i
$177$	9.42699e34	+	1.14206e36i	0.101578	+	1.23060i
$178$	−6.09636e34			−0.0600275
$179$		−	1.36201e36i		−	1.22612i	−0.790036	−	0.613060i	$-0.789938\pi$
$179$		−	1.36201e36i		−	1.22612i	0.790036	−	0.613060i	$-0.210062\pi$
$180$	5.30089e34	+	3.18907e35i	0.0436505	+	0.262606i
$181$	4.25956e35			0.321002			0.160501	−	0.987036i	$-0.448689\pi$
$181$	4.25956e35			0.321002			0.160501	+	0.987036i	$0.448689\pi$
$182$			8.86766e35i			0.611881i
$183$	−8.34425e35	+	6.88767e34i	−0.527436	+	0.0435367i
$184$	3.51760e35			0.203780
$185$		−	1.13241e36i		−	0.601526i
$186$	−1.25753e35	−	1.52346e36i	−0.0612788	−	0.742378i
$187$	3.50155e36			1.56601
$188$		−	3.01689e35i		−	0.123889i
$189$	−3.19689e36	+	8.06335e35i	−1.20598	+	0.304177i
$190$	3.11499e36			1.07994
$191$			4.74091e36i			1.51122i	0.655021	+	0.755611i	$0.272660\pi$
$191$			4.74091e36i			1.51122i	−0.655021	+	0.755611i	$0.727340\pi$
$192$	3.77179e36	−	3.11338e35i	1.10593	−	0.0912878i
$193$	−3.26228e35			−0.0880245			−0.0440123	−	0.999031i	$-0.514014\pi$
$193$	−3.26228e35			−0.0880245			−0.0440123	+	0.999031i	$0.514014\pi$
$194$			4.86318e36i			1.20807i
$195$	−2.86330e35	−	3.46882e36i	−0.0655108	−	0.793648i
$196$	4.71669e35			0.0994351
$197$		−	5.99182e36i		−	1.16439i	−0.813048	−	0.582196i	$-0.802194\pi$
$197$		−	5.99182e36i		−	1.16439i	0.813048	−	0.582196i	$-0.197806\pi$
$198$	−8.15441e36	+	1.35543e36i	−1.46133	+	0.242903i
$199$	−7.16734e36			−1.18497			−0.592487	−	0.805580i	$-0.701854\pi$
$199$	−7.16734e36			−1.18497			−0.592487	+	0.805580i	$0.701854\pi$
$200$		−	8.01324e36i		−	1.22272i
$201$	−1.54294e36	+	1.27360e35i	−0.217376	+	0.0179431i
$202$	4.38381e36			0.570466
$203$			2.57627e36i			0.309782i
$204$	1.28669e35	+	1.55880e36i	0.0143019	+	0.173264i
$205$	−3.66657e36			−0.376876
$206$			1.60896e37i			1.52992i
$207$	−3.55204e35	−	2.13694e36i	−0.0312573	−	0.188047i
$208$	−5.24160e36			−0.427022
$209$		−	1.76996e37i		−	1.33543i
$210$	2.34847e37	−	1.93852e36i	1.64163	−	0.135507i
$211$	1.13918e37			0.738027			0.369014	−	0.929424i	$-0.379696\pi$
$211$	1.13918e37			0.738027			0.369014	+	0.929424i	$0.379696\pi$
$212$			9.25934e35i			0.0556168i
$213$	2.50166e36	+	3.03071e37i	0.139365	+	1.68838i
$214$	−2.77911e37			−1.43643
$215$			1.68029e37i			0.806061i
$216$	−5.86990e36	−	2.32725e37i	−0.261439	−	1.03653i
$217$	2.47606e37			1.02425
$218$		−	3.50774e37i		−	1.34810i
$219$	4.51809e37	−	3.72941e36i	1.61380	−	0.133209i
$220$	−1.31289e37			−0.435978
$221$		−	1.68399e37i		−	0.520070i
$222$	1.06401e36	+	1.28902e37i	0.0305702	+	0.370350i
$223$	5.72956e36			0.153195			0.0765974	−	0.997062i	$-0.475594\pi$
$223$	5.72956e36			0.153195			0.0765974	+	0.997062i	$0.475594\pi$
$224$			1.79297e37i			0.446278i
$225$	−4.86805e37	+	8.09169e36i	−1.12833	+	0.187551i
$226$	−6.24614e37			−1.34858
$227$			6.19550e37i			1.24642i	0.782057	+	0.623208i	$0.214171\pi$
$227$			6.19550e37i			1.24642i	−0.782057	+	0.623208i	$0.785829\pi$
$228$	7.87940e36	−	6.50397e35i	0.147753	−	0.0121961i
$229$	−3.39981e37			−0.594411			−0.297206	−	0.954814i	$-0.596055\pi$
$229$	−3.39981e37			−0.594411			−0.297206	+	0.954814i	$0.596055\pi$
$230$			1.54828e37i			0.252467i
$231$	−1.10148e37	−	1.33441e38i	−0.167565	−	2.03001i
$232$	−1.87546e37			−0.266256
$233$			3.53083e37i			0.467931i	0.972245	+	0.233966i	$0.0751703\pi$
$233$			3.53083e37i			0.467931i	−0.972245	+	0.233966i	$0.924830\pi$
$234$	6.51861e36	+	3.92167e37i	0.0806681	+	0.485308i
$235$	8.63143e37			0.997693
$236$		−	2.07880e37i		−	0.224502i
$237$	−4.32142e37	+	3.56707e36i	−0.436168	+	0.0360030i
$238$	1.14009e38			1.07575
$239$		−	9.61019e37i		−	0.847941i	−0.905676	−	0.423970i	$-0.860636\pi$
$239$		−	9.61019e37i		−	0.847941i	0.905676	−	0.423970i	$-0.139364\pi$
$240$	1.14584e37	+	1.38816e38i	0.0945679	+	1.14567i
$241$	1.78150e38			1.37567			0.687835	−	0.725867i	$-0.258561\pi$
$241$	1.78150e38			1.37567			0.687835	+	0.725867i	$0.258561\pi$
$242$		−	2.10542e38i		−	1.52157i
$243$	−1.35453e38	+	5.91600e37i	−0.916407	+	0.400247i
$244$	1.51884e37			0.0962220
$245$			1.34946e38i			0.800761i
$246$	4.17367e37	−	3.44511e36i	0.232037	−	0.0191532i
$247$	−8.51219e37			−0.443496
$248$			1.80250e38i			0.880338i
$249$	−6.29513e36	−	7.62640e37i	−0.0288280	−	0.349245i
$250$	4.43444e37			0.190458
$251$			5.62504e37i			0.226645i	0.993558	+	0.113323i	$0.0361493\pi$
$251$			5.62504e37i			0.226645i	−0.993558	+	0.113323i	$0.963851\pi$
$252$	5.90000e37	−	9.80700e36i	0.223071	−	0.0370790i
$253$	8.79743e37			0.312196
$254$			9.15236e36i			0.0304925i
$255$	−4.45978e38	+	3.68128e37i	−1.39531	+	0.115174i
$256$	−1.79098e38			−0.526322
$257$		−	6.70968e38i		−	1.85256i	−0.376839	−	0.926279i	$-0.622989\pi$
$257$		−	6.70968e38i		−	1.85256i	0.376839	−	0.926279i	$-0.377011\pi$
$258$	−1.57880e37	−	1.91268e38i	−0.0409648	−	0.496279i
$259$	−2.09502e38			−0.510967
$260$			6.31402e37i			0.144788i
$261$	1.89382e37	+	1.13934e38i	0.0408404	+	0.245700i
$262$	−3.77563e38			−0.765894
$263$			9.93014e38i			1.89524i	0.319406	+	0.947618i	$0.396517\pi$
$263$			9.93014e38i			1.89524i	−0.319406	+	0.947618i	$0.603483\pi$
$264$	9.71417e38	−	8.01845e37i	1.74479	−	0.144022i
$265$	−2.64913e38			−0.447888
$266$		−	5.76294e38i		−	0.917355i
$267$	−3.64180e36	−	4.41195e37i	−0.00545928	−	0.0661379i
$268$	2.80849e37			0.0396566
$269$			7.86234e38i			1.04596i	0.852345	+	0.522981i	$0.175180\pi$
$269$			7.86234e38i			1.04596i	−0.852345	+	0.522981i	$0.824820\pi$
$270$	1.02434e39	−	2.58365e38i	1.28418	−	0.323902i
$271$	1.12500e39			1.32936			0.664681	−	0.747127i	$-0.268567\pi$
$271$	1.12500e39			1.32936			0.664681	+	0.747127i	$0.268567\pi$
$272$			6.73900e38i			0.750746i
$273$	−6.41755e38	+	5.29730e37i	−0.674166	+	0.0556483i
$274$	1.01332e38			0.100401
$275$		−	2.00409e39i		−	1.87325i
$276$	3.23275e36	+	3.91640e37i	0.00285119	+	0.0345415i
$277$	−6.47922e38			−0.539320			−0.269660	−	0.962956i	$-0.586911\pi$
$277$	−6.47922e38			−0.539320			−0.269660	+	0.962956i	$0.586911\pi$
$278$			1.44486e39i			1.13530i
$279$	1.09502e39	−	1.82015e38i	0.812374	−	0.135033i
$280$	−2.77861e39			−1.94670
$281$		−	2.12114e39i		−	1.40368i	−0.712335	−	0.701840i	$-0.752362\pi$
$281$		−	2.12114e39i		−	1.40368i	0.712335	−	0.701840i	$-0.247638\pi$
$282$	−9.82519e38	+	8.11010e37i	−0.614264	+	0.0507038i
$283$	1.94227e39			1.14743			0.573716	−	0.819054i	$-0.305501\pi$
$283$	1.94227e39			1.14743			0.573716	+	0.819054i	$0.305501\pi$
$284$		−	5.51656e38i		−	0.308017i
$285$	1.86081e38	+	2.25432e39i	0.0982164	+	1.18987i
$286$	−1.61448e39			−0.805708
$287$			6.78340e38i			0.320138i
$288$	1.31801e38	+	7.92931e38i	0.0588355	+	0.353961i
$289$	2.02851e38			0.0856668
$290$		−	8.25488e38i		−	0.329870i
$291$	−3.51949e39	+	2.90513e38i	−1.33104	+	0.109869i
$292$	−8.22393e38			−0.294411
$293$			3.43320e39i			1.16364i	0.813319	+	0.581818i	$0.197658\pi$
$293$			3.43320e39i			1.16364i	−0.813319	+	0.581818i	$0.802342\pi$
$294$	−1.26795e38	−	1.53610e39i	−0.0406955	−	0.493016i
$295$	5.94751e39			1.80794
$296$		−	1.52512e39i		−	0.439174i
$297$	−1.46805e39	−	5.82039e39i	−0.400532	−	1.58800i
$298$	8.50820e38			0.219977
$299$		−	4.23092e38i		−	0.103680i
$300$	8.92171e38	−	7.36433e37i	0.207257	−	0.0171078i
$301$	3.10864e39			0.684710
$302$			1.70807e39i			0.356775i
$303$	2.61876e38	+	3.17257e39i	0.0518817	+	0.628535i
$304$	3.40642e39			0.640208
$305$			4.34545e39i			0.774885i
$306$	5.04200e39	−	8.38083e38i	0.853217	−	0.141822i
$307$	6.82077e39			1.09552			0.547759	−	0.836636i	$-0.315481\pi$
$307$	6.82077e39			1.09552			0.547759	+	0.836636i	$0.315481\pi$
$308$			2.42893e39i			0.370342i
$309$	−1.16440e40	+	9.61145e38i	−1.68565	+	0.139140i
$310$	−7.93377e39			−1.09067
$311$		−	1.29849e40i		−	1.69540i	−0.530477	−	0.847699i	$-0.677987\pi$
$311$		−	1.29849e40i		−	1.69540i	0.530477	−	0.847699i	$-0.322013\pi$
$312$	−3.85629e38	−	4.67180e39i	−0.0478295	−	0.579443i
$313$	−1.25320e40			−1.47676			−0.738379	−	0.674386i	$-0.764408\pi$
$313$	−1.25320e40			−1.47676			−0.738379	+	0.674386i	$0.764408\pi$
$314$			7.33352e39i			0.821179i
$315$	2.80582e39	+	1.68801e40i	0.298600	+	1.79641i
$316$	7.86595e38			0.0795716
$317$			1.74328e39i			0.167656i	0.996480	+	0.0838278i	$0.0267146\pi$
$317$			1.74328e39i			0.167656i	−0.996480	+	0.0838278i	$0.973285\pi$
$318$	3.01551e39	−	2.48912e38i	0.275758	−	0.0227621i
$319$	−4.69048e39			−0.407912
$320$		−	1.96424e40i		−	1.62478i
$321$	−1.66016e39	−	2.01125e40i	−0.130638	−	1.58265i
$322$	2.86442e39			0.214458
$323$			1.09439e40i			0.779709i
$324$	2.53715e39	−	8.67417e38i	0.172038	−	0.0588177i
$325$	−9.63821e39			−0.622103
$326$			9.01875e39i			0.554198i
$327$	2.53856e40	−	2.09542e39i	1.48533	−	0.122605i
$328$	−4.93813e39			−0.275157
$329$		−	1.59687e40i		−	0.847492i
$330$	3.52935e39	+	4.27572e40i	0.178431	+	2.16165i
$331$	−9.71402e39			−0.467898			−0.233949	−	0.972249i	$-0.575165\pi$
$331$	−9.71402e39			−0.467898			−0.233949	+	0.972249i	$0.575165\pi$
$332$			1.38817e39i			0.0637139i
$333$	−9.26512e39	+	1.54005e39i	−0.405269	+	0.0673639i
$334$	1.72333e40			0.718499
$335$			8.03518e39i			0.319359i
$336$	2.56818e40	−	2.11988e39i	0.973190	−	0.0803309i
$337$	2.11020e40			0.762508			0.381254	−	0.924470i	$-0.375492\pi$
$337$	2.11020e40			0.762508			0.381254	+	0.924470i	$0.375492\pi$
$338$		−	1.84833e40i		−	0.636961i
$339$	−3.73127e39	−	4.52034e40i	−0.122648	−	1.48585i
$340$	8.11779e39			0.254551
$341$			4.50802e40i			1.34870i
$342$	−4.23633e39	−	2.54862e40i	−0.120941	−	0.727592i
$343$	−2.06837e40			−0.563538
$344$			2.26300e40i			0.588505i
$345$	−1.12049e40	+	9.24900e38i	−0.278166	+	0.0229609i
$346$	−3.65812e40			−0.867041
$347$		−	6.27866e39i		−	0.142100i	−0.997473	−	0.0710502i	$-0.977365\pi$
$347$		−	6.27866e39i		−	0.142100i	0.997473	−	0.0710502i	$-0.0226351\pi$
$348$	−1.72358e38	−	2.08808e39i	−0.00372533	−	0.0451315i
$349$	−4.78424e40			−0.987658			−0.493829	−	0.869559i	$-0.664403\pi$
$349$	−4.78424e40			−0.987658			−0.493829	+	0.869559i	$0.664403\pi$
$350$		−	6.52527e40i		−	1.28680i
$351$	−2.79918e40	+	7.06023e39i	−0.527372	+	0.133016i
$352$	−3.26436e40			−0.587646
$353$			3.60680e40i			0.620478i	0.950659	+	0.310239i	$0.100409\pi$
$353$			3.60680e40i			0.620478i	−0.950659	+	0.310239i	$0.899591\pi$
$354$	−6.77008e40	+	5.58829e39i	−1.11312	+	0.0918812i
$355$	1.57831e41			2.48049
$356$			8.03072e38i			0.0120658i
$357$	6.81061e39	+	8.25089e40i	0.0978350	+	1.18525i
$358$	8.07397e40			1.10907
$359$			1.54924e40i			0.203520i	0.994809	+	0.101760i	$0.0324474\pi$
$359$			1.54924e40i			0.203520i	−0.994809	+	0.101760i	$0.967553\pi$
$360$	−1.22882e41	+	2.04256e40i	−1.54401	+	0.256646i
$361$	−2.78792e40			−0.335093
$362$			2.52506e40i			0.290358i
$363$	1.52369e41	−	1.25772e40i	1.67645	−	0.138381i
$364$	1.16814e40			0.122990
$365$		−	2.35290e41i		−	2.37092i
$366$	−4.08299e39	−	4.94644e40i	−0.0393805	−	0.477085i
$367$	7.66738e40			0.707929			0.353965	−	0.935259i	$-0.384833\pi$
$367$	7.66738e40			0.707929			0.353965	+	0.935259i	$0.384833\pi$
$368$			1.69313e40i			0.149667i
$369$	4.98647e39	+	2.99992e40i	0.0422058	+	0.253914i
$370$	6.71286e40			0.544102
$371$			4.90106e40i			0.380459i
$372$	−2.00686e40	+	1.65654e39i	−0.149221	+	0.0123173i
$373$	−2.08328e41			−1.48391			−0.741954	−	0.670451i	$-0.766101\pi$
$373$	−2.08328e41			−1.48391			−0.741954	+	0.670451i	$0.766101\pi$
$374$			2.07570e41i			1.41651i
$375$	2.64901e39	+	3.20921e40i	0.0173214	+	0.209845i
$376$	1.16248e41			0.728416
$377$			2.25577e40i			0.135467i
$378$	−4.77993e40	−	1.89510e41i	−0.275139	−	1.09085i
$379$	2.15705e41			1.19023			0.595117	−	0.803639i	$-0.297106\pi$
$379$	2.15705e41			1.19023			0.595117	+	0.803639i	$0.297106\pi$
$380$		−	4.10337e40i		−	0.217072i
$381$	−6.62358e39	+	5.46737e38i	−0.0335965	+	0.00277318i
$382$	−2.81040e41			−1.36695
$383$			9.70993e40i			0.452935i	0.974019	+	0.226467i	$0.0727177\pi$
$383$			9.70993e40i			0.452935i	−0.974019	+	0.226467i	$0.927282\pi$
$384$	1.18585e40	+	1.43662e41i	0.0530553	+	0.642752i
$385$	−6.94925e41			−2.98240
$386$		−	1.93387e40i		−	0.0796213i
$387$	1.37478e41	−	2.28516e40i	0.543071	−	0.0902695i
$388$	6.40625e40			0.242827
$389$		−	3.87011e41i		−	1.40776i	−0.710317	−	0.703881i	$-0.751449\pi$
$389$		−	3.87011e41i		−	1.40776i	0.710317	−	0.703881i	$-0.248551\pi$
$390$	2.05631e41	−	1.69735e40i	0.717883	−	0.0592569i
$391$	−5.43959e40			−0.182280
$392$			1.81745e41i			0.584635i
$393$	−2.25546e40	−	2.73243e41i	−0.0696552	−	0.843856i
$394$	3.55193e41			1.05323
$395$			2.25048e41i			0.640797i
$396$	1.78550e40	+	1.07418e41i	0.0488245	+	0.293734i
$397$	−1.83712e41			−0.482490			−0.241245	−	0.970464i	$-0.577556\pi$
$397$	−1.83712e41			−0.482490			−0.241245	+	0.970464i	$0.577556\pi$
$398$		−	4.24877e41i		−	1.07185i
$399$	4.17065e41	−	3.44262e40i	1.01074	−	0.0834300i
$400$	3.85703e41			0.898035
$401$			7.65867e41i			1.71334i	0.515865	+	0.856670i	$0.327471\pi$
$401$			7.65867e41i			1.71334i	−0.515865	+	0.856670i	$0.672529\pi$
$402$	−7.54986e39	−	9.14648e40i	−0.0162301	−	0.196624i
$403$	2.16803e41			0.447903
$404$		−	5.77478e40i		−	0.114666i
$405$	2.48171e41	+	7.25886e41i	0.473664	+	1.38544i
$406$	−1.52721e41			−0.280208
$407$		−	3.81429e41i		−	0.672827i
$408$	−6.00642e41	+	4.95793e40i	−1.01872	+	0.0840888i
$409$	−3.59886e41			−0.586938			−0.293469	−	0.955969i	$-0.594810\pi$
$409$	−3.59886e41			−0.586938			−0.293469	+	0.955969i	$0.594810\pi$
$410$		−	2.17353e41i		−	0.340898i
$411$	6.05332e39	+	7.33345e40i	0.00913112	+	0.110621i
$412$	2.11948e41			0.307520
$413$		−	1.10033e42i		−	1.53575i
$414$	1.26677e41	−	2.10563e40i	0.170096	−	0.0282734i
$415$	−3.97161e41			−0.513095
$416$			1.56992e41i			0.195157i
$417$	−1.04565e42	+	8.63119e40i	−1.25086	+	0.103251i
$418$	1.04922e42			1.20795
$419$			9.52365e40i			0.105531i	0.998607	+	0.0527654i	$0.0168035\pi$
$419$			9.52365e40i			0.105531i	−0.998607	+	0.0527654i	$0.983196\pi$
$420$	−2.55360e40	−	3.09363e41i	−0.0272374	−	0.329974i
$421$	−2.89754e41			−0.297520			−0.148760	−	0.988873i	$-0.547528\pi$
$421$	−2.89754e41			−0.297520			−0.148760	+	0.988873i	$0.547528\pi$
$422$			6.75301e41i			0.667572i
$423$	−1.17386e41	−	7.06206e41i	−0.111730	−	0.672180i
$424$	−3.56784e41			−0.327003
$425$			1.23916e42i			1.09372i
$426$	−1.79659e42	+	1.48298e41i	−1.52720	+	0.126061i
$427$	8.03937e41			0.658227
$428$			3.66091e41i			0.288728i
$429$	−9.64448e40	−	1.16841e42i	−0.0732761	−	0.887723i
$430$	−9.96068e41			−0.729111
$431$		−	9.54246e40i		−	0.0673014i	−0.999434	−	0.0336507i	$-0.989287\pi$
$431$		−	9.54246e40i		−	0.0673014i	0.999434	−	0.0336507i	$-0.0107134\pi$
$432$	1.12018e42	−	2.82537e41i	0.761286	−	0.192015i
$433$	2.84667e42			1.86436			0.932181	−	0.361991i	$-0.117903\pi$
$433$	2.84667e42			1.86436			0.932181	+	0.361991i	$0.117903\pi$
$434$			1.46780e42i			0.926470i
$435$	5.97407e41	−	4.93123e40i	0.363448	−	0.0300004i
$436$	−4.62074e41			−0.270974
$437$			2.74960e41i			0.155441i
$438$	2.21078e41	+	2.67831e42i	0.120493	+	1.45974i
$439$	9.80139e41			0.515057			0.257528	−	0.966271i	$-0.417092\pi$
$439$	9.80139e41			0.515057			0.257528	+	0.966271i	$0.417092\pi$
$440$		−	5.05886e42i		−	2.56336i
$441$	1.10410e42	−	1.83524e41i	0.539500	−	0.0896759i
$442$	9.98261e41			0.470422
$443$		−	6.27228e41i		−	0.285079i	−0.989789	−	0.142540i	$-0.954473\pi$
$443$		−	6.27228e41i		−	0.285079i	0.989789	−	0.142540i	$-0.0455268\pi$
$444$	1.69803e41	−	1.40162e40i	0.0744418	−	0.00614472i
$445$	−2.29762e41			−0.0971667
$446$			3.39647e41i			0.138570i
$447$	5.08256e40	+	6.15740e41i	0.0200061	+	0.242369i
$448$	−3.63397e42			−1.38017
$449$			1.71719e42i			0.629327i	0.949203	+	0.314664i	$0.101892\pi$
$449$			1.71719e42i			0.629327i	−0.949203	+	0.314664i	$0.898108\pi$
$450$	−4.79672e41	−	2.88576e42i	−0.169646	−	1.02061i
$451$	−1.23502e42			−0.421549
$452$			8.22802e41i			0.271069i
$453$	−1.23613e42	+	1.02035e41i	−0.393092	+	0.0324473i
$454$	−3.67267e42			−1.12743
$455$			3.34208e42i			0.990453i
$456$	2.50613e41	+	3.03612e42i	0.0717078	+	0.868723i
$457$	6.30033e41			0.174062			0.0870310	−	0.996206i	$-0.472262\pi$
$457$	6.30033e41			0.174062			0.0870310	+	0.996206i	$0.472262\pi$
$458$		−	2.01540e42i		−	0.537666i
$459$	9.07717e41	+	3.59884e42i	0.233855	+	0.927170i
$460$	2.03955e41			0.0507468
$461$		−	5.19464e42i		−	1.24836i	−0.781279	−	0.624181i	$-0.785433\pi$
$461$		−	5.19464e42i		−	1.24836i	0.781279	−	0.624181i	$-0.214567\pi$
$462$	7.91036e42	−	6.52952e41i	1.83622	−	0.151569i
$463$	−6.60695e42			−1.48151			−0.740756	−	0.671774i	$-0.765533\pi$
$463$	−6.60695e42			−1.48151			−0.740756	+	0.671774i	$0.765533\pi$
$464$		−	9.02718e41i		−	0.195553i
$465$	−4.73941e41	−	5.74169e42i	−0.0991922	−	1.20169i
$466$	−2.09306e42			−0.423261
$467$		−	6.72550e41i		−	0.131418i	−0.997839	−	0.0657090i	$-0.979069\pi$
$467$		−	6.72550e41i		−	0.131418i	0.997839	−	0.0657090i	$-0.0209309\pi$
$468$	5.16601e41	−	8.58696e40i	0.0975487	−	0.0162146i
$469$	1.48656e42			0.271280
$470$			5.11668e42i			0.902449i
$471$	−5.30728e42	+	4.38084e41i	−0.904769	+	0.0746832i
$472$	8.01009e42			1.31997
$473$			5.65972e42i			0.901606i
$474$	−2.11455e41	−	2.56173e42i	−0.0325660	−	0.394529i
$475$	6.26370e42			0.932681
$476$		−	1.50184e42i		−	0.216229i
$477$	3.60277e41	+	2.16747e42i	0.0501583	+	0.301758i
$478$	5.69689e42			0.766993
$479$		−	1.28463e43i		−	1.67267i	−0.548219	−	0.836335i	$-0.684694\pi$
$479$		−	1.28463e43i		−	1.67267i	0.548219	−	0.836335i	$-0.315306\pi$
$480$	4.15769e42	−	3.43192e41i	0.523591	−	0.0432192i
$481$	−1.83439e42			−0.223445
$482$			1.05607e43i			1.24434i
$483$	1.71113e41	+	2.07299e42i	0.0195042	+	0.236289i
$484$	−2.77346e42			−0.305841
$485$			1.83285e43i			1.95551i
$486$	−3.50698e42	−	8.02961e42i	−0.362037	−	0.828923i
$487$	4.56018e42			0.455532			0.227766	−	0.973716i	$-0.426858\pi$
$487$	4.56018e42			0.455532			0.227766	+	0.973716i	$0.426858\pi$
$488$			5.85244e42i			0.565744i
$489$	−6.52689e42	+	5.38755e41i	−0.610611	+	0.0504022i
$490$	−7.99955e42			−0.724317
$491$		−	2.10358e43i		−	1.84355i	−0.387719	−	0.921777i	$-0.626737\pi$
$491$		−	2.10358e43i		−	1.84355i	0.387719	−	0.921777i	$-0.373263\pi$
$492$	−4.53824e40	−	5.49798e41i	−0.00384987	−	0.0466403i
$493$	2.90019e42			0.238164
$494$		−	5.04600e42i		−	0.401158i
$495$	−3.07326e43	+	5.10839e42i	−2.36547	+	0.393189i
$496$	−8.67604e42			−0.646569
$497$		−	2.91997e43i		−	2.10706i
$498$	4.52090e42	−	3.73173e41i	0.315904	−	0.0260760i
$499$	1.55751e43			1.05396			0.526979	−	0.849879i	$-0.323325\pi$
$499$	1.55751e43			1.05396			0.526979	+	0.849879i	$0.323325\pi$
$500$		−	5.84148e41i		−	0.0382827i
$501$	1.02947e42	+	1.24718e43i	0.0653448	+	0.791636i
$502$	−3.33451e42			−0.205009
$503$			1.84255e43i			1.09731i	0.836047	+	0.548657i	$0.184861\pi$
$503$			1.84255e43i			1.09731i	−0.836047	+	0.548657i	$0.815139\pi$
$504$	3.77887e42	+	2.27341e43i	0.218008	+	1.31156i
$505$	1.65219e43			0.923415
$506$			5.21509e42i			0.282393i
$507$	1.33764e43	−	1.10414e42i	0.701799	−	0.0579292i
$508$	1.20564e41			0.00612912
$509$			4.83669e42i			0.238267i	0.992878	+	0.119133i	$0.0380116\pi$
$509$			4.83669e42i			0.238267i	−0.992878	+	0.119133i	$0.961988\pi$
$510$	−2.18225e42	−	2.64374e43i	−0.104179	−	1.26211i
$511$	−4.35301e43			−2.01398
$512$		−	2.49995e43i		−	1.12102i
$513$	1.81914e43	−	4.58832e42i	0.790656	−	0.199423i
$514$	3.97747e43			1.67570
$515$			6.06389e43i			2.47649i
$516$	−2.51957e42	+	2.07975e41i	−0.0997540	+	0.00823409i
$517$	2.90733e43			1.11595
$518$		−	1.24192e43i		−	0.462188i
$519$	−2.18526e42	−	2.64739e43i	−0.0788542	−	0.955300i
$520$	−2.43294e43			−0.851291
$521$		−	3.83455e42i		−	0.130110i	−0.997882	−	0.0650551i	$-0.979278\pi$
$521$		−	3.83455e42i		−	0.130110i	0.997882	−	0.0650551i	$-0.0207223\pi$
$522$	−6.75398e42	+	1.12265e42i	−0.222245	+	0.0369416i
$523$	−5.75426e41			−0.0183638			−0.00918191	−	0.999958i	$-0.502923\pi$
$523$	−5.75426e41			−0.0183638			−0.00918191	+	0.999958i	$0.502923\pi$
$524$			4.97363e42i			0.153948i
$525$	4.72235e43	−	3.89802e42i	1.41778	−	0.117029i
$526$	−5.88655e43			−1.71431
$527$		−	2.78738e43i		−	0.787456i
$528$	3.85954e42	+	4.67574e43i	0.105777	+	1.28147i
$529$	3.62422e43			0.963661
$530$		−	1.57039e43i		−	0.405130i
$531$	−8.08851e42	−	4.86614e43i	−0.202468	−	1.21807i
$532$	−7.59151e42			−0.184392
$533$			5.93951e42i			0.139996i
$534$	2.61539e42	−	2.15884e41i	0.0598241	−	0.00493811i
$535$	−1.04740e44			−2.32515
$536$			1.08218e43i			0.233164i
$537$	4.82316e42	+	5.84315e43i	0.100866	+	1.22196i
$538$	−4.66077e43			−0.946109
$539$			4.54540e43i			0.895678i
$540$	−3.40344e42	−	1.34937e43i	−0.0651056	−	0.258125i
$541$	1.75852e43			0.326580			0.163290	−	0.986578i	$-0.447789\pi$
$541$	1.75852e43			0.326580			0.163290	+	0.986578i	$0.447789\pi$
$542$			6.66895e43i			1.20246i
$543$	−1.82739e43	+	1.50840e42i	−0.319914	+	0.0264070i
$544$	2.01840e43			0.343104
$545$		−	1.32201e44i		−	2.18218i
$546$	−3.14022e42	−	3.80430e43i	−0.0503359	−	0.609807i
$547$	2.24132e43			0.348904			0.174452	−	0.984666i	$-0.444185\pi$
$547$	2.24132e43			0.348904			0.174452	+	0.984666i	$0.444185\pi$
$548$		−	1.33485e42i		−	0.0201810i
$549$	3.55536e43	−	5.90974e42i	0.522067	−	0.0867782i
$550$	1.18802e44			1.69442
$551$		−	1.46599e43i		−	0.203097i
$552$	−1.50908e43	+	1.24565e42i	−0.203089	+	0.0167638i
$553$	4.16353e43			0.544326
$554$		−	3.84086e43i		−	0.487834i
$555$	4.01008e42	+	4.85811e43i	0.0494840	+	0.599487i
$556$	1.90331e43			0.228199
$557$			1.14851e44i			1.33799i	0.743269	+	0.668993i	$0.233274\pi$
$557$			1.14851e44i			1.33799i	−0.743269	+	0.668993i	$0.766726\pi$
$558$	1.07898e43	+	6.49126e43i	0.122142	+	0.734821i
$559$	2.72191e43			0.299423
$560$		−	1.33744e44i		−	1.42977i
$561$	−1.50219e44	+	1.23997e43i	−1.56070	+	0.128826i
$562$	1.25740e44			1.26968
$563$		−	9.61039e43i		−	0.943206i	−0.881811	−	0.471603i	$-0.843676\pi$
$563$		−	9.61039e43i		−	0.943206i	0.881811	−	0.471603i	$-0.156324\pi$
$564$	1.06834e42	+	1.29427e43i	0.0101916	+	0.123469i
$565$	−2.35407e44			−2.18295
$566$			1.15137e44i			1.03789i
$567$	1.34294e44	−	4.59133e43i	1.17687	−	0.402355i
$568$	2.12566e44			1.81101
$569$			1.70961e44i			1.41612i	0.706153	+	0.708059i	$0.250429\pi$
$569$			1.70961e44i			1.41612i	−0.706153	+	0.708059i	$0.749571\pi$
$570$	−1.33636e44	+	1.10308e43i	−1.07628	+	0.0888402i
$571$	−1.93974e44			−1.51903			−0.759515	−	0.650490i	$-0.774563\pi$
$571$	−1.93974e44			−1.51903			−0.759515	+	0.650490i	$0.774563\pi$
$572$			2.12676e43i			0.161950i
$573$	−1.67885e43	−	2.03389e44i	−0.124319	−	1.50610i
$574$	−4.02118e43			−0.289576
$575$			3.11332e43i			0.218041i
$576$	−1.60710e44	+	2.67133e43i	−1.09467	+	0.181957i
$577$	2.40795e44			1.59527			0.797635	−	0.603141i	$-0.206084\pi$
$577$	2.40795e44			1.59527			0.797635	+	0.603141i	$0.206084\pi$
$578$			1.20250e43i			0.0774887i
$579$	1.39954e43	−	1.15524e42i	0.0877262	−	0.00724126i
$580$	−1.08741e43			−0.0663051
$581$			7.34775e43i			0.435849i
$582$	−1.72215e43	−	2.08634e44i	−0.0993809	−	1.20398i
$583$	−8.92309e43			−0.500978
$584$		−	3.16887e44i		−	1.73101i
$585$	2.45676e43	+	1.47801e44i	0.130578	+	0.785569i
$586$	−2.03519e44			−1.05255
$587$		−	1.34332e44i		−	0.676037i	−0.941139	−	0.338019i	$-0.890243\pi$
$587$		−	1.34332e44i		−	0.676037i	0.941139	−	0.338019i	$-0.109757\pi$
$588$	−2.02350e43	+	1.67027e42i	−0.0990981	+	0.00817995i
$589$	−1.40896e44			−0.671513
$590$			3.52566e44i			1.63534i
$591$	2.12182e43	+	2.57054e44i	0.0957877	+	1.16045i
$592$	7.34090e43			0.322554
$593$		−	1.34856e44i		−	0.576761i	−0.957516	−	0.288380i	$-0.906883\pi$
$593$		−	1.34856e44i		−	0.576761i	0.957516	−	0.288380i	$-0.0931168\pi$
$594$	3.45031e44	−	8.70254e43i	1.43640	−	0.362296i
$595$	4.29683e44			1.74131
$596$		−	1.12078e43i		−	0.0442162i
$597$	3.07485e44	−	2.53810e43i	1.18096	−	0.0974809i
$598$	2.50807e43			0.0937824
$599$			1.91321e44i			0.696518i	0.937398	+	0.348259i	$0.113227\pi$
$599$			1.91321e44i			0.696518i	−0.937398	+	0.348259i	$0.886773\pi$
$600$	2.83765e43	+	3.43774e44i	0.100586	+	1.21858i
$601$	−4.52647e44			−1.56231			−0.781156	−	0.624336i	$-0.785370\pi$
$601$	−4.52647e44			−1.56231			−0.781156	+	0.624336i	$0.785370\pi$
$602$			1.84279e44i			0.619344i
$603$	6.57423e43	−	1.09277e43i	0.215163	−	0.0357645i
$604$	2.25004e43			0.0717131
$605$		−	7.93496e44i		−	2.46297i
$606$	−1.88069e44	+	1.55239e43i	−0.568532	+	0.0469289i
$607$	4.02988e44			1.18651			0.593257	−	0.805013i	$-0.297842\pi$
$607$	4.02988e44			1.18651			0.593257	+	0.805013i	$0.297842\pi$
$608$		−	1.02026e44i		−	0.292586i
$609$	−9.12311e42	−	1.10524e44i	−0.0254839	−	0.308732i
$610$	−2.57597e44			−0.700911
$611$		−	1.39821e44i		−	0.370607i
$612$	−1.10400e43	−	6.64181e43i	−0.0285068	−	0.171500i
$613$	−2.12847e44			−0.535426			−0.267713	−	0.963499i	$-0.586268\pi$
$613$	−2.12847e44			−0.535426			−0.267713	+	0.963499i	$0.586268\pi$
$614$			4.04333e44i			0.990935i
$615$	1.57299e44	−	1.29841e43i	0.375599	−	0.0310034i
$616$	−9.35923e44			−2.17745
$617$			5.63491e44i			1.27739i	0.769459	+	0.638697i	$0.220526\pi$
$617$			5.63491e44i			1.27739i	−0.769459	+	0.638697i	$0.779474\pi$
$618$	−5.69764e43	−	6.90255e44i	−0.125858	−	1.52473i
$619$	−2.56791e44			−0.552752			−0.276376	−	0.961050i	$-0.589133\pi$
$619$	−2.56791e44			−0.552752			−0.276376	+	0.961050i	$0.589133\pi$
$620$			1.04511e44i			0.219228i
$621$	2.28059e43	+	9.04188e43i	0.0466209	+	0.184839i
$622$	7.69739e44			1.53355
$623$			4.25074e43i			0.0825384i
$624$	2.24869e44	−	1.85616e43i	0.425575	−	0.0351286i
$625$	−4.52932e44			−0.835513
$626$		−	7.42890e44i		−	1.33578i
$627$	6.26778e43	+	7.59326e44i	0.109858	+	1.33091i
$628$	9.66043e43			0.165060
$629$			2.35844e44i			0.392838i
$630$	−1.00065e45	+	1.66328e44i	−1.62492	+	0.270095i
$631$	1.12891e45			1.78727			0.893633	−	0.448798i	$-0.148148\pi$
$631$	1.12891e45			1.78727			0.893633	+	0.448798i	$0.148148\pi$
$632$			3.03093e44i			0.467846i
$633$	−4.88717e44	+	4.03406e43i	−0.735526	+	0.0607132i
$634$	−1.03341e44			−0.151650
$635$			3.44938e43i			0.0493584i
$636$	−3.27892e42	−	3.97233e43i	−0.00457527	−	0.0554283i
$637$	2.18600e44			0.297454
$638$		−	2.78050e44i		−	0.368971i
$639$	−2.14647e44	−	1.29134e45i	−0.277786	−	1.67119i
$640$	7.48153e44			0.944302
$641$			9.04167e44i			1.11306i	0.830826	+	0.556532i	$0.187868\pi$
$641$			9.04167e44i			1.11306i	−0.830826	+	0.556532i	$0.812132\pi$
$642$	1.19226e45	−	9.84138e43i	1.43156	−	0.118167i
$643$	2.79423e44			0.327255			0.163628	−	0.986522i	$-0.447680\pi$
$643$	2.79423e44			0.327255			0.163628	+	0.986522i	$0.447680\pi$
$644$		−	3.77330e43i		−	0.0431069i
$645$	−5.95023e43	−	7.20856e44i	−0.0663099	−	0.803329i
$646$	−6.48752e44			−0.705275
$647$		−	9.56214e44i		−	1.01411i	−0.861913	−	0.507057i	$-0.830733\pi$
$647$		−	9.56214e44i		−	1.01411i	0.861913	−	0.507057i	$-0.169267\pi$
$648$	3.34236e44	+	9.77622e44i	0.345822	+	1.01151i
$649$	2.00331e45			2.02224
$650$		−	5.71350e44i		−	0.562715i
$651$	−1.06225e45	+	8.76823e43i	−1.02078	+	0.0842590i
$652$	1.18804e44			0.111396
$653$			1.09206e45i			0.999158i	0.866268	+	0.499579i	$0.166512\pi$
$653$			1.09206e45i			0.999158i	−0.866268	+	0.499579i	$0.833488\pi$
$654$	1.24216e44	+	1.50485e45i	0.110901	+	1.34353i
$655$	−1.42297e45			−1.23975
$656$		−	2.37688e44i		−	0.202091i
$657$	−1.92509e45	+	3.19990e44i	−1.59737	+	0.265516i
$658$	9.46619e44			0.766586
$659$			5.16445e43i			0.0408185i	0.999792	+	0.0204093i	$0.00649692\pi$
$659$			5.16445e43i			0.0408185i	−0.999792	+	0.0204093i	$0.993503\pi$
$660$	5.63240e44	−	4.64920e43i	0.434501	−	0.0358654i
$661$	−2.03767e45			−1.53430			−0.767151	−	0.641467i	$-0.778326\pi$
$661$	−2.03767e45			−1.53430			−0.767151	+	0.641467i	$0.778326\pi$
$662$		−	5.75844e44i		−	0.423230i
$663$	5.96333e43	+	7.22444e44i	0.0427831	+	0.518308i
$664$	−5.34896e44			−0.374610
$665$		−	2.17196e45i		−	1.48493i
$666$	−9.12937e43	−	5.49233e44i	−0.0609331	−	0.366580i
$667$	7.28657e43			0.0474799
$668$		−	2.27015e44i		−	0.144421i
$669$	−2.45803e44	+	2.02895e43i	−0.152675	+	0.0126024i
$670$	−4.76323e44			−0.288871
$671$			1.46368e45i			0.866735i
$672$	−6.34927e43	−	7.69199e44i	−0.0367126	−	0.444765i
$673$	−1.43440e45			−0.809896			−0.404948	−	0.914340i	$-0.632710\pi$
$673$	−1.43440e45			−0.809896			−0.404948	+	0.914340i	$0.632710\pi$
$674$			1.25092e45i			0.689716i
$675$	2.05978e45	−	5.19527e44i	1.10907	−	0.279736i
$676$	−2.43480e44			−0.128032
$677$		−	1.05793e45i		−	0.543298i	−0.962396	−	0.271649i	$-0.912431\pi$
$677$		−	1.05793e45i		−	0.543298i	0.962396	−	0.271649i	$-0.0875689\pi$
$678$	2.67964e45	−	2.21188e44i	1.34401	−	0.110940i
$679$	3.39090e45			1.66111
$680$			3.12797e45i			1.49665i
$681$	−2.19395e44	−	2.65792e45i	−0.102535	−	1.24219i
$682$	−2.67234e45			−1.21995
$683$		−	1.03612e44i		−	0.0462040i	−0.999733	−	0.0231020i	$-0.992646\pi$
$683$		−	1.03612e44i		−	0.0462040i	0.999733	−	0.0231020i	$-0.00735425\pi$
$684$	−3.35730e44	+	5.58051e43i	−0.146249	+	0.0243095i
$685$	3.81905e44			0.162520
$686$		−	1.22612e45i		−	0.509740i
$687$	1.45855e45	−	1.20394e44i	0.592397	−	0.0488987i
$688$	−1.08926e45			−0.432231
$689$			4.29135e44i			0.166374i
$690$	−5.48277e43	−	6.64225e44i	−0.0207690	−	0.251611i
$691$	7.58228e44			0.280641			0.140321	−	0.990106i	$-0.455187\pi$
$691$	7.58228e44			0.280641			0.140321	+	0.990106i	$0.455187\pi$
$692$			4.81883e44i			0.174279i
$693$	9.45086e44	+	5.68574e45i	0.333995	+	2.00935i
$694$	3.72197e44			0.128535
$695$			5.44544e45i			1.83771i
$696$	8.04586e44	−	6.64137e43i	0.265353	−	0.0219033i
$697$	7.63629e44			0.246126
$698$		−	2.83608e45i		−	0.893372i
$699$	−1.25034e44	−	1.51475e45i	−0.0384940	−	0.466345i
$700$	−8.59573e44			−0.258651
$701$		−	3.48232e45i		−	1.02419i	−0.858929	−	0.512094i	$-0.828870\pi$
$701$		−	3.48232e45i		−	1.02419i	0.858929	−	0.512094i	$-0.171130\pi$
$702$	−4.18528e44	−	1.65934e45i	−0.120318	−	0.477027i
$703$	1.19214e45			0.334998
$704$		−	6.61617e45i		−	1.81737i
$705$	−3.70295e45	+	3.05656e44i	−0.994311	+	0.0820743i
$706$	−2.13810e45			−0.561244
$707$		−	3.05665e45i		−	0.784396i
$708$	7.36144e43	+	8.91821e44i	0.0184685	+	0.223741i
$709$	−1.31377e45			−0.322241			−0.161121	−	0.986935i	$-0.551511\pi$
$709$	−1.31377e45			−0.322241			−0.161121	+	0.986935i	$0.551511\pi$
$710$			9.35614e45i			2.24369i
$711$	1.84129e45	−	3.06061e44i	0.431727	−	0.0717619i
$712$	−3.09442e44			−0.0709414
$713$		−	7.00313e44i		−	0.156986i
$714$	−4.89110e45	+	4.03730e44i	−1.07210	+	0.0884953i
$715$	−6.08473e45			−1.30420
$716$		−	1.06358e45i		−	0.222927i
$717$	3.40316e44	+	4.12285e45i	0.0697551	+	0.845067i
$718$	−9.18384e44			−0.184091
$719$			9.88190e44i			0.193722i	0.995298	+	0.0968608i	$0.0308802\pi$
$719$			9.88190e44i			0.193722i	−0.995298	+	0.0968608i	$0.969120\pi$
$720$	−9.83149e44	−	5.91473e45i	−0.188495	−	1.13401i
$721$	1.12186e46			2.10365
$722$		−	1.65267e45i		−	0.303104i
$723$	−7.64280e45	+	6.30867e44i	−1.37101	+	0.113168i
$724$	3.32625e44			0.0583631
$725$		−	1.65991e45i		−	0.284890i
$726$	7.45570e44	+	9.03240e45i	0.125171	+	1.51641i
$727$	3.69569e45			0.606938			0.303469	−	0.952841i	$-0.401855\pi$
$727$	3.69569e45			0.606938			0.303469	+	0.952841i	$0.401855\pi$
$728$			4.50110e45i			0.723130i
$729$	5.60155e45	−	3.01768e45i	0.880375	−	0.474278i
$730$	1.39479e46			2.14458
$731$		−	3.49949e45i		−	0.526414i
$732$	−6.51594e44	+	5.37852e43i	−0.0958959	+	0.00791562i
$733$	1.24024e45			0.178583			0.0892917	−	0.996006i	$-0.471540\pi$
$733$	1.24024e45			0.178583			0.0892917	+	0.996006i	$0.471540\pi$
$734$			4.54519e45i			0.640347i
$735$	−4.77871e44	−	5.78929e45i	−0.0658739	−	0.798047i
$736$	5.07113e44			0.0684005
$737$			2.70650e45i			0.357214i
$738$	−1.77834e45	+	2.95596e44i	−0.229675	+	0.0381766i
$739$	−9.81413e45			−1.24034			−0.620170	−	0.784467i	$-0.712936\pi$
$739$	−9.81413e45			−1.24034			−0.620170	+	0.784467i	$0.712936\pi$
$740$		−	8.84284e44i		−	0.109366i
$741$	3.65180e45	−	3.01434e44i	0.441993	−	0.0364839i
$742$	−2.90533e45			−0.344139
$743$		−	8.13009e45i		−	0.942485i	−0.882004	−	0.471243i	$-0.843806\pi$
$743$		−	8.13009e45i		−	0.942485i	0.882004	−	0.471243i	$-0.156194\pi$
$744$	−6.38303e44	−	7.73289e45i	−0.0724202	−	0.877354i
$745$	3.20660e45			0.356078
$746$		−	1.23496e46i		−	1.34225i
$747$	5.40132e44	+	3.24950e45i	0.0574607	+	0.345690i
$748$	2.73432e45			0.284724
$749$			1.93776e46i			1.97511i
$750$	−1.90241e45	+	1.57032e44i	−0.189812	+	0.0156678i
$751$	−5.01101e45			−0.489425			−0.244713	−	0.969596i	$-0.578694\pi$
$751$	−5.01101e45			−0.489425			−0.244713	+	0.969596i	$0.578694\pi$
$752$			5.59538e45i			0.534989i
$753$	−1.99194e44	−	2.41319e45i	−0.0186448	−	0.225877i
$754$	−1.33721e45			−0.122535
$755$			6.43743e45i			0.577513i
$756$	−2.49642e45	+	6.29659e44i	−0.219265	+	0.0553040i
$757$	−1.55189e46			−1.33452			−0.667261	−	0.744824i	$-0.732533\pi$
$757$	−1.55189e46			−1.33452			−0.667261	+	0.744824i	$0.732533\pi$
$758$			1.27869e46i			1.07661i
$759$	−3.77417e45	+	3.11535e44i	−0.311138	+	0.0256826i
$760$	1.58112e46			1.27629
$761$		−	1.16745e46i		−	0.922753i	−0.887204	−	0.461376i	$-0.847356\pi$
$761$		−	1.16745e46i		−	0.922753i	0.887204	−	0.461376i	$-0.152644\pi$
$762$	−3.24104e43	−	3.92644e44i	−0.00250844	−	0.0303892i
$763$	−2.44580e46			−1.85366
$764$			3.70213e45i			0.274763i
$765$	1.90025e46	−	3.15860e45i	1.38111	−	0.229568i
$766$	−5.75601e45			−0.409696
$767$		−	9.63442e45i		−	0.671583i
$768$	7.68345e45	−	6.34222e44i	0.524538	−	0.0432974i
$769$	−1.55774e46			−1.04153			−0.520766	−	0.853700i	$-0.674354\pi$
$769$	−1.55774e46			−1.04153			−0.520766	+	0.853700i	$0.674354\pi$
$770$		−	4.11949e46i		−	2.69769i
$771$	2.37603e45	+	2.87851e46i	0.152399	+	1.84628i
$772$	−2.54748e44			−0.0160042
$773$		−	1.57517e46i		−	0.969295i	−0.874709	−	0.484648i	$-0.838948\pi$
$773$		−	1.57517e46i		−	0.969295i	0.874709	−	0.484648i	$-0.161052\pi$
$774$	1.35463e45	+	8.14963e45i	0.0816520	+	0.491227i
$775$	−1.59534e46			−0.941948
$776$			2.46848e46i			1.42772i
$777$	8.98783e45	−	7.41890e44i	0.509235	−	0.0420343i
$778$	2.29419e46			1.27337
$779$		−	3.85998e45i		−	0.209887i
$780$	−2.23592e44	−	2.70877e45i	−0.0119109	−	0.144297i
$781$	5.31622e46			2.77451
$782$		−	3.22457e45i		−	0.164878i
$783$	−1.21593e45	−	4.82080e45i	−0.0609143	−	0.241508i
$784$	−8.74797e45			−0.429389
$785$			2.76388e46i			1.32925i
$786$	1.61978e46	−	1.33703e45i	0.763298	−	0.0630056i
$787$	7.81929e45			0.361054			0.180527	−	0.983570i	$-0.442220\pi$
$787$	7.81929e45			0.361054			0.180527	+	0.983570i	$0.442220\pi$
$788$		−	4.67895e45i		−	0.211704i
$789$	−3.51646e45	−	4.26011e46i	−0.155910	−	1.88881i
$790$	−1.33407e46			−0.579624
$791$			4.35518e46i			1.85431i
$792$	−4.13906e46	+	6.87996e45i	−1.72703	+	0.287067i
$793$	7.03923e45			0.287842
$794$		−	1.08904e46i		−	0.436429i
$795$	1.13650e46	−	9.38110e44i	0.446370	−	0.0368451i
$796$	−5.59690e45			−0.215446
$797$			2.82457e46i			1.06566i	0.846222	+	0.532830i	$0.178872\pi$
$797$			2.82457e46i			1.06566i	−0.846222	+	0.532830i	$0.821128\pi$
$798$	2.04077e45	+	2.47235e46i	0.0754655	+	0.914246i
$799$	−1.79765e46			−0.651563
$800$		−	1.15522e46i		−	0.410418i
$801$	3.12472e44	+	1.87987e45i	0.0108816	+	0.0654646i
$802$	−4.54003e46			−1.54978
$803$		−	7.92528e46i		−	2.65195i
$804$	−1.20486e45	+	9.94543e43i	−0.0395222	+	0.00326232i
$805$	1.07955e46			0.347144
$806$			1.28520e46i			0.405144i
$807$	−2.78421e45	−	3.37301e46i	−0.0860451	−	1.04242i
$808$	2.22516e46			0.674185
$809$			1.24511e46i			0.369855i	0.982752	+	0.184928i	$0.0592050\pi$
$809$			1.24511e46i			0.369855i	−0.982752	+	0.184928i	$0.940795\pi$
$810$	−4.30303e46	+	1.47115e46i	−1.25318	+	0.428446i
$811$	4.76809e46			1.36148			0.680739	−	0.732526i	$-0.261659\pi$
$811$	4.76809e46			1.36148			0.680739	+	0.732526i	$0.261659\pi$
$812$			2.01179e45i			0.0563230i
$813$	−4.82634e46	+	3.98385e45i	−1.32486	+	0.109359i
$814$	2.26110e46			0.608596
$815$			3.39902e46i			0.897081i
$816$	−2.38641e45	−	2.89108e46i	−0.0617594	−	0.748201i
$817$	−1.76892e46			−0.448906
$818$		−	2.13339e46i		−	0.530907i
$819$	2.73442e46	−	4.54517e45i	0.667303	−	0.110919i
$820$	−2.86319e45			−0.0685218
$821$		−	4.02966e46i		−	0.945754i	−0.881129	−	0.472877i	$-0.843216\pi$
$821$		−	4.02966e46i		−	0.945754i	0.881129	−	0.472877i	$-0.156784\pi$
$822$	−4.34724e45	+	3.58838e44i	−0.100061	+	0.00825943i
$823$	−2.14512e46			−0.484232			−0.242116	−	0.970247i	$-0.577841\pi$
$823$	−2.14512e46			−0.484232			−0.242116	+	0.970247i	$0.577841\pi$
$824$			8.16683e46i			1.80808i
$825$	7.09690e45	+	8.59772e46i	0.154101	+	1.86690i
$826$	6.52271e46			1.38914
$827$			7.70894e45i			0.161030i	0.996753	+	0.0805150i	$0.0256565\pi$
$827$			7.70894e45i			0.161030i	−0.996753	+	0.0805150i	$0.974344\pi$
$828$	−2.77375e44	−	1.66872e45i	−0.00568305	−	0.0341899i
$829$	−4.57067e45			−0.0918559			−0.0459280	−	0.998945i	$-0.514624\pi$
$829$	−4.57067e45			−0.0918559			−0.0459280	+	0.998945i	$0.514624\pi$
$830$		−	2.35436e46i		−	0.464112i
$831$	2.77964e46	−	2.29442e45i	0.537492	−	0.0443667i
$832$	−3.18189e46			−0.603548
$833$		−	2.81049e46i		−	0.522952i
$834$	−5.11654e45	−	6.19857e46i	−0.0933941	−	1.13145i
$835$	6.49496e46			1.16304
$836$		−	1.38214e46i		−	0.242802i
$837$	−4.63328e46	+	1.16863e46i	−0.798512	+	0.201405i
$838$	−5.64558e45			−0.0954563
$839$			9.50352e45i			0.157650i	0.996888	+	0.0788248i	$0.0251168\pi$
$839$			9.50352e45i			0.157650i	−0.996888	+	0.0788248i	$0.974883\pi$
$840$	1.19205e47	−	9.83963e45i	1.94010	−	0.160144i
$841$	5.87384e46			0.937963
$842$		−	1.71765e46i		−	0.269117i
$843$	7.51138e45	+	9.09986e46i	0.115472	+	1.39892i
$844$	8.89573e45			0.134185
$845$		−	6.96606e46i		−	1.03105i
$846$	4.18637e46	−	6.95859e45i	0.608011	−	0.101064i
$847$	−1.46802e47			−2.09217
$848$		−	1.71732e46i		−	0.240169i
$849$	−8.33251e46	+	6.87798e45i	−1.14354	+	0.0943926i
$850$	−7.34571e46			−0.989306
$851$			5.92543e45i			0.0783154i
$852$	1.95352e45	+	2.36665e46i	0.0253387	+	0.306973i
$853$	−1.58700e46			−0.202019			−0.101009	−	0.994885i	$-0.532207\pi$
$853$	−1.58700e46			−0.202019			−0.101009	+	0.994885i	$0.532207\pi$
$854$			4.76571e46i			0.595390i
$855$	−1.59660e46	−	9.60534e46i	−0.195767	−	1.17776i
$856$	−1.41063e47			−1.69760
$857$			2.79317e45i			0.0329917i	0.999864	+	0.0164959i	$0.00525103\pi$
$857$			2.79317e45i			0.0329917i	−0.999864	+	0.0164959i	$0.994749\pi$
$858$	6.92627e46	−	5.71722e45i	0.802977	−	0.0662808i
$859$	8.48408e46			0.965415			0.482708	−	0.875782i	$-0.339653\pi$
$859$	8.48408e46			0.965415			0.482708	+	0.875782i	$0.339653\pi$
$860$			1.31212e46i			0.146554i
$861$	−2.40214e45	−	2.91013e46i	−0.0263359	−	0.319053i
$862$	5.65673e45			0.0608765
$863$			7.27198e46i			0.768209i	0.923290	+	0.384105i	$0.125490\pi$
$863$			7.27198e46i			0.768209i	−0.923290	+	0.384105i	$0.874510\pi$
$864$	−8.46231e45	−	3.35506e46i	−0.0877544	−	0.347921i
$865$	−1.37868e47			−1.40348
$866$			1.68749e47i			1.68638i
$867$	−8.70249e45	+	7.18338e44i	−0.0853765	+	0.00704731i
$868$	1.93353e46			0.186224
$869$			7.58030e46i			0.716754i
$870$	2.92322e45	+	3.54141e46i	0.0271365	+	0.328752i
$871$	1.30163e46			0.118630
$872$		−	1.78048e47i		−	1.59321i
$873$	1.49960e47	−	2.49265e46i	1.31749	−	0.218994i
$874$	−1.62995e46			−0.140602
$875$		−	3.09196e46i		−	0.261881i
$876$	3.52813e46	−	2.91226e45i	0.293413	−	0.0242195i
$877$	1.07360e47			0.876692			0.438346	−	0.898806i	$-0.355564\pi$
$877$	1.07360e47			0.876692			0.438346	+	0.898806i	$0.355564\pi$
$878$			5.81023e46i			0.465887i
$879$	−1.21576e46	−	1.47287e47i	−0.0957255	−	1.15969i
$880$	2.43500e47			1.88268
$881$		−	2.03751e47i		−	1.54698i	−0.633807	−	0.773491i	$-0.718509\pi$
$881$		−	2.03751e47i		−	1.54698i	0.633807	−	0.773491i	$-0.281491\pi$
$882$	1.08793e46	+	6.54508e46i	0.0811151	+	0.487997i
$883$	−1.03103e47			−0.754916			−0.377458	−	0.926027i	$-0.623202\pi$
$883$	−1.03103e47			−0.754916			−0.377458	+	0.926027i	$0.623202\pi$
$884$		−	1.31501e46i		−	0.0945566i
$885$	−2.55153e47	+	2.10613e46i	−1.80181	+	0.148728i
$886$	3.71818e46			0.257864
$887$			3.59512e46i			0.244870i	0.992477	+	0.122435i	$0.0390703\pi$
$887$			3.59512e46i			0.244870i	−0.992477	+	0.122435i	$0.960930\pi$
$888$	5.40076e45	+	6.54289e46i	0.0361283	+	0.437685i
$889$	6.38157e45			0.0419275
$890$		−	1.36202e46i		−	0.0878908i
$891$	8.35917e46	+	2.44501e47i	0.529810	+	1.54966i
$892$	4.47416e45			0.0278531
$893$			9.08673e46i			0.555628i
$894$	−3.65009e46	+	3.01293e45i	−0.219232	+	0.0180962i
$895$	3.04295e47			1.79525
$896$		−	1.38413e47i		−	0.802139i
$897$	1.49825e45	+	1.81510e46i	0.00852916	+	0.103329i
$898$	−1.01794e47			−0.569249
$899$			3.73382e46i			0.205115i
$900$	−3.80141e46	+	6.31872e45i	−0.205147	+	0.0340996i
$901$	5.51728e46			0.292502
$902$		−	7.32113e46i		−	0.381306i
$903$	−1.33363e47	+	1.10083e46i	−0.682389	+	0.0563270i
$904$	−3.17045e47			−1.59377
$905$			9.51652e46i			0.470003i
$906$	−6.04862e45	−	7.32776e46i	−0.0293498	−	0.355566i
$907$	2.13320e47			1.01699			0.508493	−	0.861066i	$-0.330203\pi$
$907$	2.13320e47			1.01699			0.508493	+	0.861066i	$0.330203\pi$
$908$			4.83800e46i			0.226617i
$909$	−2.24694e46	−	1.35179e47i	−0.103412	−	0.622136i
$910$	−1.98117e47			−0.895901
$911$		−	1.32953e47i		−	0.590752i	−0.955381	−	0.295376i	$-0.904555\pi$
$911$		−	1.32953e47i		−	0.590752i	0.955381	−	0.295376i	$-0.0954450\pi$
$912$	−1.46138e47	+	1.20628e46i	−0.638038	+	0.0526661i
$913$	−1.33776e47			−0.573914
$914$			3.73481e46i			0.157445i
$915$	−1.53881e46	−	1.86423e47i	−0.0637453	−	0.772259i
$916$	−2.65488e46			−0.108073
$917$			2.63259e47i			1.05311i
$918$	−2.13338e47	+	5.38092e46i	−0.838659	+	0.211531i
$919$	1.69273e47			0.653941			0.326970	−	0.945035i	$-0.393972\pi$
$919$	1.69273e47			0.653941			0.326970	+	0.945035i	$0.393972\pi$
$920$			7.85885e46i			0.298369i
$921$	−2.92617e47	+	2.41537e46i	−1.09180	+	0.0901218i
$922$	3.07937e47			1.12919
$923$		−	2.55671e47i		−	0.921413i
$924$	−8.60133e45	−	1.04203e47i	−0.0304659	−	0.369087i
$925$	1.34984e47			0.469909
$926$		−	3.91658e47i		−	1.34008i
$927$	4.96136e47	−	8.24679e46i	1.66849	−	0.277338i
$928$	−2.70374e46			−0.0893712
$929$			6.31549e46i			0.205190i	0.994723	+	0.102595i	$0.0327145\pi$
$929$			6.31549e46i			0.205190i	−0.994723	+	0.102595i	$0.967285\pi$
$930$	3.40365e47	−	2.80951e46i	1.08697	−	0.0897229i
$931$	−1.42064e47			−0.445954
$932$			2.75719e46i			0.0850770i
$933$	4.59821e46	+	5.57062e47i	0.139471	+	1.68965i
$934$	3.98686e46			0.118872
$935$			7.82299e47i			2.29291i
$936$	3.30876e46	+	1.99058e47i	0.0953347	+	0.573544i
$937$	−1.50838e47			−0.427245			−0.213623	−	0.976916i	$-0.568526\pi$
$937$	−1.50838e47			−0.427245			−0.213623	+	0.976916i	$0.568526\pi$
$938$			8.81229e46i			0.245382i
$939$	5.37631e47	−	4.43782e46i	1.47175	−	0.121484i
$940$	6.74019e46			0.181396
$941$		−	2.33487e47i		−	0.617771i	−0.951099	−	0.308886i	$-0.900044\pi$
$941$		−	2.33487e47i		−	0.617771i	0.951099	−	0.308886i	$-0.0999561\pi$
$942$	−2.59695e46	−	3.14614e47i	−0.0675536	−	0.818396i
$943$	1.91857e46			0.0490672
$944$			3.85552e47i			0.969462i
$945$	−1.80148e47	−	7.14234e47i	−0.445369	−	1.76576i
$946$	−3.35506e47			−0.815535
$947$		−	4.86775e47i		−	1.16340i	−0.813404	−	0.581699i	$-0.802388\pi$
$947$		−	4.86775e47i		−	1.16340i	0.813404	−	0.581699i	$-0.197612\pi$
$948$	−3.37456e46	+	2.78549e45i	−0.0793019	+	0.00654589i
$949$	−3.81148e47			−0.880712
$950$			3.71310e47i			0.843643i
$951$	−6.17329e45	−	7.47880e46i	−0.0137920	−	0.167087i
$952$	5.78696e47			1.27133
$953$		−	5.83414e47i		−	1.26035i	−0.776454	−	0.630174i	$-0.782983\pi$
$953$		−	5.83414e47i		−	1.26035i	0.776454	−	0.630174i	$-0.217017\pi$
$954$	−1.28487e47	+	2.13571e46i	−0.272950	+	0.0453699i
$955$	−1.05919e48			−2.21269
$956$		−	7.50450e46i		−	0.154168i
$957$	2.01225e47	−	1.66099e46i	0.406529	−	0.0335565i
$958$	7.61525e47			1.51299
$959$		−	7.06550e46i		−	0.138053i
$960$	6.95577e46	+	8.42675e47i	0.133661	+	1.61927i
$961$	−1.70287e47			−0.321815
$962$		−	1.08742e47i		−	0.202114i
$963$	1.42445e47	+	8.56962e47i	0.260390	+	1.56654i
$964$	1.39116e47			0.250118
$965$		−	7.28842e46i		−	0.128883i
$966$	−1.22886e47	+	1.01435e46i	−0.213731	+	0.0176422i
$967$	−1.13419e48			−1.94026			−0.970132	−	0.242577i	$-0.922007\pi$
$967$	−1.13419e48			−1.94026			−0.970132	+	0.242577i	$0.922007\pi$
$968$		−	1.06868e48i		−	1.79821i
$969$	−3.87546e46	−	4.69503e47i	−0.0641421	−	0.777066i
$970$	−1.08651e48			−1.76883
$971$			1.97882e47i			0.316883i	0.987368	+	0.158441i	$0.0506469\pi$
$971$			1.97882e47i			0.316883i	−0.987368	+	0.158441i	$0.949353\pi$
$972$	−1.05774e47	+	4.61975e46i	−0.166617	+	0.0727709i
$973$	1.00744e48			1.56104
$974$			2.70326e47i			0.412045i
$975$	4.13487e47	−	3.41308e46i	0.619995	−	0.0511768i
$976$	−2.81697e47			−0.415513
$977$			1.16434e48i			1.68953i	0.535137	+	0.844766i	$0.320260\pi$
$977$			1.16434e48i			1.68953i	−0.535137	+	0.844766i	$0.679740\pi$
$978$	−3.19372e46	−	3.86912e47i	−0.0455906	−	0.552319i
$979$	−7.73909e46			−0.108684
$980$			1.05378e47i			0.145590i
$981$	−1.08164e48	+	1.79791e47i	−1.47021	+	0.244379i
$982$	1.24700e48			1.66756
$983$		−	1.47807e47i		−	0.194464i	−0.995262	−	0.0972318i	$-0.969001\pi$
$983$		−	1.47807e47i		−	0.194464i	0.995262	−	0.0972318i	$-0.0309988\pi$
$984$	2.11850e47	−	1.74869e46i	0.274225	−	0.0226356i
$985$	1.33866e48			1.70487
$986$			1.71922e47i			0.215428i
$987$	5.65484e46	+	6.85071e47i	0.0697182	+	0.844619i
$988$	−6.64709e46			−0.0806344
$989$		−	8.79228e46i		−	0.104945i
$990$	−3.02824e47	−	1.82182e48i	−0.355653	−	2.13965i
$991$	−3.85924e47			−0.445988			−0.222994	−	0.974820i	$-0.571583\pi$
$991$	−3.85924e47			−0.445988			−0.222994	+	0.974820i	$0.571583\pi$
$992$			2.59857e47i			0.295493i
$993$	4.16739e47	−	3.43993e46i	0.466312	−	0.0384912i
$994$	1.73095e48			1.90591
$995$		−	1.60129e48i		−	1.73501i
$996$	−4.91580e45	−	5.95538e46i	−0.00524137	−	0.0634980i
$997$	6.94320e47			0.728513			0.364257	−	0.931299i	$-0.381323\pi$
$997$	6.94320e47			0.728513			0.364257	+	0.931299i	$0.381323\pi$
$998$			9.23288e47i			0.953342i
$999$	3.92027e47	−	9.88791e46i	0.398354	−	0.100475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.33.b.a.2.8	yes	10
3.2	odd	2	inner	3.33.b.a.2.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.33.b.a.2.3	✓	10	3.2	odd	2	inner
3.33.b.a.2.8	yes	10	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+59279.7i q^{2} +(-4.29008e7 + 3.54120e6i) q^{3} +7.80890e8 q^{4} +2.23415e11i q^{5} +(-2.09921e11 - 2.54315e12i) q^{6} +4.13333e13 q^{7} +3.00895e14i q^{8} +(1.82794e15 - 3.03841e14i) q^{9} +O(q^{10})\)	\(q+59279.7i q^{2} +(-4.29008e7 + 3.54120e6i) q^{3} +7.80890e8 q^{4} +2.23415e11i q^{5} +(-2.09921e11 - 2.54315e12i) q^{6} +4.13333e13 q^{7} +3.00895e14i q^{8} +(1.82794e15 - 3.03841e14i) q^{9} -1.32440e16 q^{10} +7.52532e16i q^{11} +(-3.35008e16 + 2.76529e15i) q^{12} +3.61912e17 q^{13} +2.45022e18i q^{14} +(-7.91159e17 - 9.58470e18i) q^{15} -1.44831e19 q^{16} -4.65302e19i q^{17} +(1.80116e19 + 1.08360e20i) q^{18} -2.35200e20 q^{19} +1.74463e20i q^{20} +(-1.77323e21 + 1.46370e20i) q^{21} -4.46098e21 q^{22} -1.16904e21i q^{23} +(-1.06553e21 - 1.29086e22i) q^{24} -2.66313e22 q^{25} +2.14540e22i q^{26} +(-7.73442e22 + 1.95081e22i) q^{27} +3.22768e22 q^{28} +6.23293e22i q^{29} +(5.68178e23 - 4.68996e22i) q^{30} +5.99047e23 q^{31} +4.33784e23i q^{32} +(-2.66487e23 - 3.22842e24i) q^{33} +2.75829e24 q^{34} +9.23449e24i q^{35} +(1.42742e24 - 2.37266e23i) q^{36} -5.06861e24 q^{37} -1.39426e25i q^{38} +(-1.55263e25 + 1.28160e24i) q^{39} -6.72246e25 q^{40} +1.64115e25i q^{41} +(-8.67674e24 - 1.05117e26i) q^{42} +7.52091e25 q^{43} +5.87645e25i q^{44} +(6.78827e25 + 4.08390e26i) q^{45} +6.93006e25 q^{46} -3.86340e26i q^{47} +(6.21335e26 - 5.12874e25i) q^{48} +6.04014e26 q^{49} -1.57870e27i q^{50} +(1.64773e26 + 1.99618e27i) q^{51} +2.82614e26 q^{52} +1.18574e27i q^{53} +(-1.15643e27 - 4.58493e27i) q^{54} -1.68127e28 q^{55} +1.24370e28i q^{56} +(1.00903e28 - 8.32892e26i) q^{57} -3.69486e27 q^{58} -2.66209e28i q^{59} +(-6.17808e26 - 7.48460e27i) q^{60} +1.94501e28 q^{61} +3.55113e28i q^{62} +(7.55548e28 - 1.25587e28i) q^{63} -8.79188e28 q^{64} +8.08568e28i q^{65} +(1.91380e29 - 1.57972e28i) q^{66} +3.59652e28 q^{67} -3.63350e28i q^{68} +(4.13982e27 + 5.01530e28i) q^{69} -5.47418e29 q^{70} -7.06445e29i q^{71} +(9.14242e28 + 5.50018e29i) q^{72} -1.05315e30 q^{73} -3.00466e29i q^{74} +(1.14251e30 - 9.43069e28i) q^{75} -1.83666e29 q^{76} +3.11046e30i q^{77} +(-7.59731e28 - 9.20396e29i) q^{78} +1.00731e30 q^{79} -3.23574e30i q^{80} +(3.24905e30 - 1.11081e30i) q^{81} -9.72866e29 q^{82} +1.77768e30i q^{83} +(-1.38470e30 + 1.14299e29i) q^{84} +1.03956e31 q^{85} +4.45837e30i q^{86} +(-2.20720e29 - 2.67398e30i) q^{87} -2.26433e31 q^{88} +1.02841e30i q^{89} +(-2.42092e31 + 4.02406e30i) q^{90} +1.49590e31 q^{91} -9.12895e29i q^{92} +(-2.56996e31 + 2.12135e30i) q^{93} +2.29021e31 q^{94} -5.25474e31i q^{95} +(-1.53612e30 - 1.86097e31i) q^{96} +8.20379e31 q^{97} +3.58058e31i q^{98} +(2.28650e31 + 1.37558e32i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9}+O(q^{10}) \) 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9	\( 10 q - 21387150 q^{3} - 25792034864 q^{4} - 2424530788848 q^{6} - 5568062418940 q^{7} - 790123604155542 q^{9} - 70\!\cdots\!40 q^{10}+ \cdots - 33\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q - 21387150 * q^3 - 25792034864 * q^4 - 2424530788848 * q^6 - 5568062418940 * q^7 - 790123604155542 * q^9 - 7003812786596640 * q^10 - 279007424380502640 * q^12 + 567697557679805780 * q^13 - 20342205597863242080 * q^15 + 93452609752238437504 * q^16 - 546532439317269948000 * q^18 + 571007688520350419876 * q^19 - 202809296674597359852 * q^21 - 7726803521259943913760 * q^22 + 40966888307328818303616 * q^24 - 68909708350780834128950 * q^25 - 72967926462080465281230 * q^27 + 205937256056975756717600 * q^28 - 1107420825536697507876000 * q^30 + 2337947500037502285593540 * q^31 + 2522449071689961111334560 * q^33 - 6060358314194999366692224 * q^34 + 19880961335883894024618192 * q^36 - 35307903416851790686359340 * q^37 - 31624005377757923978634972 * q^39 + 103824872020641394026996480 * q^40 - 141365101025586253616004960 * q^42 + 20133134465218107006792740 * q^43 + 324508325822765233105320000 * q^45 - 1081312096716791246752963776 * q^46 + 3981901930430244196770990720 * q^48 - 2767041101974767237639509154 * q^49 + 1958591008210563208705802112 * q^51 - 5054272042223836449280397920 * q^52 + 8609682620485865645134310448 * q^54 - 11870374622399979665591304000 * q^55 + 40568829971233106153298510900 * q^57 - 126691224865576416891245282400 * q^58 + 279833341447916827662753642240 * q^60 - 196667345182223458343232398380 * q^61 + 349775312774222889759843110340 * q^63 - 738816306154787409411488427008 * q^64 + 939413077861687418842822458720 * q^66 - 442550741350999501345614861340 * q^67 + 1096443581430237499419700598208 * q^69 - 3084260511067452830890360584000 * q^70 + 5478956649034785201935062114560 * q^72 - 4530286149796751043896742263020 * q^73 + 5689646867484953837977805651250 * q^75 - 10804853453030293252172855440096 * q^76 + 9245617327241370897996048982560 * q^78 - 2115110787448996851533482223164 * q^79 - 454653247801524309158818752630 * q^81 + 6754240700896495824250705604160 * q^82 - 10589261014798101343390846457952 * q^84 + 8783873758902640422771709896960 * q^85 - 12893796544943502316879779198240 * q^87 + 15416255855088684041150976480000 * q^88 - 76437416541013126109366518121760 * q^90 + 59544256621898576615810233543816 * q^91 - 105131728169400940473110940107820 * q^93 + 301803894289991891760064059517056 * q^94 - 522680019947351351608967407401984 * q^96 + 390148965222370670128665882607700 * q^97 - 333895893109019690643343683610560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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