LMFDB - Embedded newform 3.33.b.a.2.6

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			2.6
Root			$5429.47i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.33.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)

$f(q)$	$=$	$q+32576.8i q^{2} +(-6.54523e6 + 4.25462e7i) q^{3} +3.23372e9 q^{4} -1.19330e11i q^{5} +(-1.38602e12 - 2.13223e11i) q^{6} -3.44644e13 q^{7} +2.45260e14i q^{8} +(-1.76734e15 - 5.56949e14i) q^{9} +O(q^{10})$	\(q+32576.8i q^{2} +(-6.54523e6 + 4.25462e7i) q^{3} +3.23372e9 q^{4} -1.19330e11i q^{5} +(-1.38602e12 - 2.13223e11i) q^{6} -3.44644e13 q^{7} +2.45260e14i q^{8} +(-1.76734e15 - 5.56949e14i) q^{9} +3.88740e15 q^{10} -2.29269e16i q^{11} +(-2.11654e16 + 1.37583e17i) q^{12} -7.69030e17 q^{13} -1.12274e18i q^{14} +(5.07705e18 + 7.81044e17i) q^{15} +5.89892e18 q^{16} -2.61771e19i q^{17} +(1.81436e19 - 5.75743e19i) q^{18} -3.34271e20 q^{19} -3.85880e20i q^{20} +(2.25578e20 - 1.46633e21i) q^{21} +7.46886e20 q^{22} -1.19887e22i q^{23} +(-1.04349e22 - 1.60529e21i) q^{24} +9.04337e21 q^{25} -2.50525e22i q^{26} +(3.52637e22 - 7.15483e22i) q^{27} -1.11448e23 q^{28} +2.90445e23i q^{29} +(-2.54439e22 + 1.65394e23i) q^{30} +3.11706e23 q^{31} +1.24555e24i q^{32} +(9.75454e23 + 1.50062e23i) q^{33} +8.52767e23 q^{34} +4.11265e24i q^{35} +(-5.71508e24 - 1.80102e24i) q^{36} -5.78500e24 q^{37} -1.08895e25i q^{38} +(5.03348e24 - 3.27193e25i) q^{39} +2.92670e25 q^{40} -3.53959e25i q^{41} +(4.77684e25 + 7.34860e24i) q^{42} -1.98562e26 q^{43} -7.41393e25i q^{44} +(-6.64609e25 + 2.10897e26i) q^{45} +3.90553e26 q^{46} +5.91452e26i q^{47} +(-3.86098e25 + 2.50977e26i) q^{48} +8.33704e25 q^{49} +2.94604e26i q^{50} +(1.11374e27 + 1.71335e26i) q^{51} -2.48683e27 q^{52} -3.37218e27i q^{53} +(2.33081e27 + 1.14878e27i) q^{54} -2.73588e27 q^{55} -8.45277e27i q^{56} +(2.18788e27 - 1.42219e28i) q^{57} -9.46178e27 q^{58} +2.27924e28i q^{59} +(1.64178e28 + 2.52568e27i) q^{60} -1.22762e28 q^{61} +1.01544e28i q^{62} +(6.09104e28 + 1.91950e28i) q^{63} -1.52405e28 q^{64} +9.17685e28i q^{65} +(-4.88854e27 + 3.17772e28i) q^{66} -2.88582e29 q^{67} -8.46495e28i q^{68} +(5.10073e29 + 7.84687e28i) q^{69} -1.33977e29 q^{70} -5.23954e29i q^{71} +(1.36598e29 - 4.33459e29i) q^{72} -2.42194e29 q^{73} -1.88457e29i q^{74} +(-5.91909e28 + 3.84761e29i) q^{75} -1.08094e30 q^{76} +7.90164e29i q^{77} +(1.06589e30 + 1.63975e29i) q^{78} -6.06341e29 q^{79} -7.03919e29i q^{80} +(2.81330e30 + 1.96864e30i) q^{81} +1.15309e30 q^{82} +9.99652e30i q^{83} +(7.29455e29 - 4.74171e30i) q^{84} -3.12372e30 q^{85} -6.46852e30i q^{86} +(-1.23574e31 - 1.90103e30i) q^{87} +5.62307e30 q^{88} -6.79334e30i q^{89} +(-6.87035e30 - 2.16508e30i) q^{90} +2.65042e31 q^{91} -3.87681e31i q^{92} +(-2.04019e30 + 1.32619e31i) q^{93} -1.92676e31 q^{94} +3.98886e31i q^{95} +(-5.29936e31 - 8.15243e30i) q^{96} +8.12346e31 q^{97} +2.71594e30i q^{98} +(-1.27691e31 + 4.05197e31i) 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 $

$2$			32576.8i			0.497082i	0.968621	+	0.248541i	$0.0799511\pi$
$2$			32576.8i			0.497082i	−0.968621	+	0.248541i	$0.920049\pi$
$3$	−6.54523e6	+	4.25462e7i	−0.152049	+	0.988373i
$3$	−6.54523e6	+	4.25462e7i	−0.152049	+	0.988373i
$4$	3.23372e9			0.752909
$5$		−	1.19330e11i		−	0.782042i	−0.920382	−	0.391021i	$-0.872122\pi$
$5$		−	1.19330e11i		−	0.782042i	0.920382	−	0.391021i	$-0.127878\pi$
$6$	−1.38602e12	−	2.13223e11i	−0.491303	−	0.0755811i
$7$	−3.44644e13			−1.03706			−0.518529	−	0.855060i	$-0.673520\pi$
$7$	−3.44644e13			−1.03706			−0.518529	+	0.855060i	$0.673520\pi$
$8$			2.45260e14i			0.871340i
$9$	−1.76734e15	−	5.56949e14i	−0.953762	−	0.300563i
$10$	3.88740e15			0.388740
$11$		−	2.29269e16i		−	0.498957i	−0.968380	−	0.249479i	$-0.919741\pi$
$11$		−	2.29269e16i		−	0.498957i	0.968380	−	0.249479i	$-0.0802592\pi$
$12$	−2.11654e16	+	1.37583e17i	−0.114479	+	0.744155i
$13$	−7.69030e17			−1.15571			−0.577856	−	0.816139i	$-0.696110\pi$
$13$	−7.69030e17			−1.15571			−0.577856	+	0.816139i	$0.696110\pi$
$14$		−	1.12274e18i		−	0.515503i
$15$	5.07705e18	+	7.81044e17i	0.772950	+	0.118909i
$16$	5.89892e18			0.319781
$17$		−	2.61771e19i		−	0.537947i	−0.963148	−	0.268973i	$-0.913316\pi$
$17$		−	2.61771e19i		−	0.537947i	0.963148	−	0.268973i	$-0.0866844\pi$
$18$	1.81436e19	−	5.75743e19i	0.149405	−	0.474098i
$19$	−3.34271e20			−1.15889			−0.579443	−	0.815013i	$-0.696730\pi$
$19$	−3.34271e20			−1.15889			−0.579443	+	0.815013i	$0.696730\pi$
$20$		−	3.85880e20i		−	0.588807i
$21$	2.25578e20	−	1.46633e21i	0.157684	−	1.02500i
$22$	7.46886e20			0.248023
$23$		−	1.19887e22i		−	1.95491i	−0.211150	−	0.977454i	$-0.567721\pi$
$23$		−	1.19887e22i		−	1.95491i	0.211150	−	0.977454i	$-0.432279\pi$
$24$	−1.04349e22	−	1.60529e21i	−0.861209	−	0.132487i
$25$	9.04337e21			0.388410
$26$		−	2.50525e22i		−	0.574484i
$27$	3.52637e22	−	7.15483e22i	0.442087	−	0.896972i
$28$	−1.11448e23			−0.780810
$29$			2.90445e23i			1.16064i	0.814389	+	0.580319i	$0.197072\pi$
$29$			2.90445e23i			1.16064i	−0.814389	+	0.580319i	$0.802928\pi$
$30$	−2.54439e22	+	1.65394e23i	−0.0591076	+	0.384220i
$31$	3.11706e23			0.428507			0.214254	−	0.976778i	$-0.431268\pi$
$31$	3.11706e23			0.428507			0.214254	+	0.976778i	$0.431268\pi$
$32$			1.24555e24i			1.03030i
$33$	9.75454e23	+	1.50062e23i	0.493156	+	0.0758661i
$34$	8.52767e23			0.267404
$35$			4.11265e24i			0.811023i
$36$	−5.71508e24	−	1.80102e24i	−0.718096	−	0.226297i
$37$	−5.78500e24			−0.468896			−0.234448	−	0.972129i	$-0.575328\pi$
$37$	−5.78500e24			−0.468896			−0.234448	+	0.972129i	$0.575328\pi$
$38$		−	1.08895e25i		−	0.576062i
$39$	5.03348e24	−	3.27193e25i	0.175725	−	1.14227i
$40$	2.92670e25			0.681425
$41$		−	3.53959e25i		−	0.555152i	−0.960704	−	0.277576i	$-0.910469\pi$
$41$		−	3.53959e25i		−	0.555152i	0.960704	−	0.277576i	$-0.0895310\pi$
$42$	4.77684e25	+	7.34860e24i	0.509509	+	0.0783819i
$43$	−1.98562e26			−1.45345			−0.726727	−	0.686927i	$-0.758959\pi$
$43$	−1.98562e26			−1.45345			−0.726727	+	0.686927i	$0.758959\pi$
$44$		−	7.41393e25i		−	0.375669i
$45$	−6.64609e25	+	2.10897e26i	−0.235053	+	0.745882i
$46$	3.90553e26			0.971750
$47$			5.91452e26i			1.04317i	0.853200	+	0.521583i	$0.174658\pi$
$47$			5.91452e26i			1.04317i	−0.853200	+	0.521583i	$0.825342\pi$
$48$	−3.86098e25	+	2.50977e26i	−0.0486225	+	0.316063i
$49$	8.33704e25			0.0754875
$50$			2.94604e26i			0.193072i
$51$	1.11374e27	+	1.71335e26i	0.531692	+	0.0817945i
$52$	−2.48683e27			−0.870146
$53$		−	3.37218e27i		−	0.869956i	−0.900441	−	0.434978i	$-0.856756\pi$
$53$		−	3.37218e27i		−	0.869956i	0.900441	−	0.434978i	$-0.143244\pi$
$54$	2.33081e27	+	1.14878e27i	0.445869	+	0.219754i
$55$	−2.73588e27			−0.390206
$56$		−	8.45277e27i		−	0.903630i
$57$	2.18788e27	−	1.42219e28i	0.176208	−	1.14541i
$58$	−9.46178e27			−0.576933
$59$			2.27924e28i			1.05720i	0.848871	+	0.528601i	$0.177283\pi$
$59$			2.27924e28i			1.05720i	−0.848871	+	0.528601i	$0.822717\pi$
$60$	1.64178e28	+	2.52568e27i	0.581961	+	0.0895277i
$61$	−1.22762e28			−0.334032			−0.167016	−	0.985954i	$-0.553413\pi$
$61$	−1.22762e28			−0.334032			−0.167016	+	0.985954i	$0.553413\pi$
$62$			1.01544e28i			0.213003i
$63$	6.09104e28	+	1.91950e28i	0.989106	+	0.311701i
$64$	−1.52405e28			−0.192362
$65$			9.17685e28i			0.903816i
$66$	−4.88854e27	+	3.17772e28i	−0.0377117	+	0.245139i
$67$	−2.88582e29			−1.75014			−0.875069	−	0.483997i	$-0.839184\pi$
$67$	−2.88582e29			−1.75014			−0.875069	+	0.483997i	$0.839184\pi$
$68$		−	8.46495e28i		−	0.405025i
$69$	5.10073e29	+	7.84687e28i	1.93218	+	0.297243i
$70$	−1.33977e29			−0.403145
$71$		−	5.23954e29i		−	1.25649i	−0.778015	−	0.628245i	$-0.783773\pi$
$71$		−	5.23954e29i		−	1.25649i	0.778015	−	0.628245i	$-0.216227\pi$
$72$	1.36598e29	−	4.33459e29i	0.261893	−	0.831051i
$73$	−2.42194e29			−0.372390			−0.186195	−	0.982513i	$-0.559616\pi$
$73$	−2.42194e29			−0.372390			−0.186195	+	0.982513i	$0.559616\pi$
$74$		−	1.88457e29i		−	0.233080i
$75$	−5.91909e28	+	3.84761e29i	−0.0590575	+	0.383893i
$76$	−1.08094e30			−0.872536
$77$			7.90164e29i			0.517447i
$78$	1.06589e30	+	1.63975e29i	0.567805	+	0.0873500i
$79$	−6.06341e29			−0.263441			−0.131720	−	0.991287i	$-0.542050\pi$
$79$	−6.06341e29			−0.263441			−0.131720	+	0.991287i	$0.542050\pi$
$80$		−	7.03919e29i		−	0.250082i
$81$	2.81330e30	+	1.96864e30i	0.819324	+	0.573331i
$82$	1.15309e30			0.275956
$83$			9.99652e30i			1.97060i	0.170820	+	0.985302i	$0.445358\pi$
$83$			9.99652e30i			1.97060i	−0.170820	+	0.985302i	$0.554642\pi$
$84$	7.29455e29	−	4.74171e30i	0.118722	−	0.771731i
$85$	−3.12372e30			−0.420697
$86$		−	6.46852e30i		−	0.722486i
$87$	−1.23574e31	−	1.90103e30i	−1.14714	−	0.176474i
$88$	5.62307e30			0.434761
$89$		−	6.79334e30i		−	0.438372i	−0.975683	−	0.219186i	$-0.929660\pi$
$89$		−	6.79334e30i		−	0.438372i	0.975683	−	0.219186i	$-0.0703402\pi$
$90$	−6.87035e30	−	2.16508e30i	−0.370765	−	0.116841i
$91$	2.65042e31			1.19854
$92$		−	3.87681e31i		−	1.47187i
$93$	−2.04019e30	+	1.32619e31i	−0.0651543	+	0.423525i
$94$	−1.92676e31			−0.518540
$95$			3.98886e31i			0.906298i
$96$	−5.29936e31	−	8.15243e30i	−1.01832	−	0.156656i
$97$	8.12346e31			1.32249			0.661246	−	0.750169i	$-0.270028\pi$
$97$	8.12346e31			1.32249			0.661246	+	0.750169i	$0.270028\pi$
$98$			2.71594e30i			0.0375235i
$99$	−1.27691e31	+	4.05197e31i	−0.149968	+	0.475886i
$100$	2.92437e31			0.292437
$101$			1.54385e32i			1.31663i	0.752742	+	0.658315i	$0.228731\pi$
$101$			1.54385e32i			1.31663i	−0.752742	+	0.658315i	$0.771269\pi$
$102$	−5.58155e30	+	3.62820e31i	−0.0406586	+	0.264295i
$103$	−1.71682e31			−0.106987			−0.0534933	−	0.998568i	$-0.517036\pi$
$103$	−1.71682e31			−0.106987			−0.0534933	+	0.998568i	$0.517036\pi$
$104$		−	1.88613e32i		−	1.00702i
$105$	−1.74978e32	−	2.69182e31i	−0.801593	−	0.123316i
$106$	1.09855e32			0.432440
$107$			1.64949e31i			0.0558738i	0.999610	+	0.0279369i	$0.00889374\pi$
$107$			1.64949e31i			0.0558738i	−0.999610	+	0.0279369i	$0.991106\pi$
$108$	1.14033e32	−	2.31367e32i	0.332852	−	0.675338i
$109$	5.26161e31			0.132524			0.0662620	−	0.997802i	$-0.478893\pi$
$109$	5.26161e31			0.132524			0.0662620	+	0.997802i	$0.478893\pi$
$110$		−	8.91261e31i		−	0.193964i
$111$	3.78642e31	−	2.46130e32i	0.0712953	−	0.463444i
$112$	−2.03303e32			−0.331631
$113$		−	4.55732e32i		−	0.644844i	−0.946596	−	0.322422i	$-0.895503\pi$
$113$		−	4.55732e32i		−	0.644844i	0.946596	−	0.322422i	$-0.104497\pi$
$114$	4.63306e32	+	7.12740e31i	0.569364	+	0.0875899i
$115$	−1.43061e33			−1.52882
$116$			9.39219e32i			0.873855i
$117$	1.35914e33	+	4.28311e32i	1.10227	+	0.347364i
$118$	−7.42503e32			−0.525516
$119$			9.02180e32i			0.557881i
$120$	−1.91559e32	+	1.24520e33i	−0.103610	+	0.673502i
$121$	1.58573e33			0.751042
$122$		−	3.99921e32i		−	0.166041i
$123$	1.50596e33	+	2.31674e32i	0.548697	+	0.0844105i
$124$	1.00797e33			0.322627
$125$		−	3.85752e33i		−	1.08580i
$126$	−6.25310e32	+	1.98427e33i	−0.154941	+	0.491667i
$127$	−7.91813e33			−1.72887			−0.864437	−	0.502741i	$-0.832325\pi$
$127$	−7.91813e33			−1.72887			−0.864437	+	0.502741i	$0.832325\pi$
$128$			4.85313e33i			0.934678i
$129$	1.29963e33	−	8.44807e33i	0.220997	−	1.43655i
$130$	−2.98952e33			−0.449271
$131$		−	4.54053e33i		−	0.603623i	−0.953368	−	0.301812i	$-0.902409\pi$
$131$		−	4.54053e33i		−	0.603623i	0.953368	−	0.301812i	$-0.0975914\pi$
$132$	3.15435e33	+	4.85259e32i	0.371301	+	0.0571203i
$133$	1.15205e34			1.20183
$134$		−	9.40108e33i		−	0.869963i
$135$	−8.53787e33	−	4.20803e33i	−0.701470	−	0.345731i
$136$	6.42022e33			0.468735
$137$			1.50643e34i			0.978179i	0.872234	+	0.489090i	$0.162671\pi$
$137$			1.50643e34i			0.978179i	−0.872234	+	0.489090i	$0.837329\pi$
$138$	−2.55626e33	+	1.66165e34i	−0.147754	+	0.960451i
$139$	−2.84433e32			−0.0146468			−0.00732340	−	0.999973i	$-0.502331\pi$
$139$	−2.84433e32			−0.0146468			−0.00732340	+	0.999973i	$0.502331\pi$
$140$			1.32992e34i			0.610626i
$141$	−2.51640e34	−	3.87119e33i	−1.03104	−	0.158613i
$142$	1.70687e34			0.624579
$143$			1.76315e34i			0.576651i
$144$	−1.04254e34	−	3.28540e33i	−0.304995	−	0.0961144i
$145$	3.46589e34			0.907668
$146$		−	7.88991e33i		−	0.185109i
$147$	−5.45679e32	+	3.54710e33i	−0.0114778	+	0.0746098i
$148$	−1.87071e34			−0.353036
$149$		−	3.94968e34i		−	0.669240i	−0.942353	−	0.334620i	$-0.891392\pi$
$149$		−	3.94968e34i		−	0.669240i	0.942353	−	0.334620i	$-0.108608\pi$
$150$	−1.25343e34	−	1.92825e33i	−0.190827	−	0.0293564i
$151$	3.66707e34			0.501982			0.250991	−	0.967989i	$-0.419244\pi$
$151$	3.66707e34			0.501982			0.250991	+	0.967989i	$0.419244\pi$
$152$		−	8.19834e34i		−	1.00978i
$153$	−1.45793e34	+	4.62639e34i	−0.161687	+	0.513073i
$154$	−2.57410e34			−0.257214
$155$		−	3.71960e34i		−	0.335111i
$156$	1.62769e34	−	1.05805e35i	0.132305	−	0.860029i
$157$	−1.58058e35			−1.15991			−0.579953	−	0.814650i	$-0.696929\pi$
$157$	−1.58058e35			−1.15991			−0.579953	+	0.814650i	$0.696929\pi$
$158$		−	1.97526e34i		−	0.130952i
$159$	1.43474e35	+	2.20717e34i	0.859841	+	0.132276i
$160$	1.48632e35			0.805737
$161$			4.13183e35i			2.02735i
$162$	−6.41319e34	+	9.16482e34i	−0.284993	+	0.407271i
$163$	−5.09520e34			−0.205191			−0.102596	−	0.994723i	$-0.532715\pi$
$163$	−5.09520e34			−0.205191			−0.102596	+	0.994723i	$0.532715\pi$
$164$		−	1.14461e35i		−	0.417979i
$165$	1.79069e34	−	1.16401e35i	0.0593305	−	0.385669i
$166$	−3.25655e35			−0.979553
$167$			3.09178e35i			0.844782i	0.906414	+	0.422391i	$0.138809\pi$
$167$			3.09178e35i			0.844782i	−0.906414	+	0.422391i	$0.861191\pi$
$168$	3.59633e35	+	5.53253e34i	0.893123	+	0.137396i
$169$	1.48628e35			0.335670
$170$		−	1.01761e35i		−	0.209121i
$171$	5.90770e35	+	1.86172e35i	1.10530	+	0.348318i
$172$	−6.42094e35			−1.09432
$173$		−	6.72781e35i		−	1.04505i	−0.852625	−	0.522524i	$-0.824991\pi$
$173$		−	6.72781e35i		−	1.04505i	0.852625	−	0.522524i	$-0.175009\pi$
$174$	6.19295e34	−	4.02563e35i	0.0877223	−	0.570224i
$175$	−3.11675e35			−0.402803
$176$		−	1.35244e35i		−	0.159557i
$177$	−9.69730e35	−	1.49181e35i	−1.04491	−	0.160747i
$178$	2.21305e35			0.217907
$179$		−	1.09444e36i		−	0.985244i	−0.870243	−	0.492622i	$-0.836039\pi$
$179$		−	1.09444e36i		−	0.985244i	0.870243	−	0.492622i	$-0.163961\pi$
$180$	−2.14916e35	+	6.81982e35i	−0.176974	+	0.561582i
$181$	3.24967e35			0.244896			0.122448	−	0.992475i	$-0.460925\pi$
$181$	3.24967e35			0.244896			0.122448	+	0.992475i	$0.460925\pi$
$182$			8.63422e35i			0.595773i
$183$	8.03508e34	−	5.22308e35i	0.0507894	−	0.330148i
$184$	2.94035e36			1.70339
$185$			6.90326e35i			0.366696i
$186$	−4.32031e35	−	6.64628e34i	−0.210527	−	0.0323871i
$187$	−6.00162e35			−0.268412
$188$			1.91259e36i			0.785410i
$189$	−1.21535e36	+	2.46587e36i	−0.458470	+	0.930211i
$190$	−1.29944e36			−0.450505
$191$		−	1.10939e36i		−	0.353632i	−0.984244	−	0.176816i	$-0.943420\pi$
$191$		−	1.10939e36i		−	0.353632i	0.984244	−	0.176816i	$-0.0565798\pi$
$192$	9.97524e34	−	6.48424e35i	0.0292485	−	0.190125i
$193$	1.94146e36			0.523855			0.261927	−	0.965088i	$-0.415642\pi$
$193$	1.94146e36			0.523855			0.261927	+	0.965088i	$0.415642\pi$
$194$			2.64636e36i			0.657388i
$195$	−3.90440e36	−	6.00646e35i	−0.893307	−	0.137425i
$196$	2.69597e35			0.0568352
$197$		−	2.96789e36i		−	0.576751i	−0.957517	−	0.288376i	$-0.906885\pi$
$197$		−	2.96789e36i		−	0.576751i	0.957517	−	0.288376i	$-0.0931152\pi$
$198$	−1.32000e36	−	4.15978e35i	−0.236555	−	0.0745465i
$199$	8.87238e36			1.46687			0.733434	−	0.679761i	$-0.237916\pi$
$199$	8.87238e36			1.46687			0.733434	+	0.679761i	$0.237916\pi$
$200$			2.21798e36i			0.338437i
$201$	1.88884e36	−	1.22781e37i	0.266108	−	1.72979i
$202$	−5.02938e36			−0.654474
$203$		−	1.00100e37i		−	1.20365i
$204$	3.60152e36	+	5.54050e35i	0.400316	+	0.0615838i
$205$	−4.22380e36			−0.434152
$206$		−	5.59285e35i		−	0.0531812i
$207$	−6.67709e36	+	2.11881e37i	−0.587573	+	1.86452i
$208$	−4.53645e36			−0.369575
$209$			7.66380e36i			0.578234i
$210$	8.76910e35	−	5.70021e36i	0.0612980	−	0.398458i
$211$	−5.02459e36			−0.325523			−0.162761	−	0.986665i	$-0.552040\pi$
$211$	−5.02459e36			−0.325523			−0.162761	+	0.986665i	$0.552040\pi$
$212$		−	1.09047e37i		−	0.654998i
$213$	2.22922e37	+	3.42940e36i	1.24188	+	0.191049i
$214$	−5.37349e35			−0.0277739
$215$			2.36945e37i			1.13666i
$216$	1.75480e37	+	8.64880e36i	0.781568	+	0.385208i
$217$	−1.07428e37			−0.444387
$218$			1.71406e36i			0.0658753i
$219$	1.58522e36	−	1.03045e37i	0.0566217	−	0.368060i
$220$	−8.84706e36			−0.293789
$221$			2.01310e37i			0.621712i
$222$	8.01813e36	+	1.23349e36i	0.230370	+	0.0354396i
$223$	−3.13856e37			−0.839176			−0.419588	−	0.907715i	$-0.637825\pi$
$223$	−3.13856e37			−0.839176			−0.419588	+	0.907715i	$0.637825\pi$
$224$		−	4.29273e37i		−	1.06848i
$225$	−1.59827e37	−	5.03670e36i	−0.370450	−	0.116742i
$226$	1.48463e37			0.320541
$227$		−	1.20256e37i		−	0.241931i	−0.992657	−	0.120966i	$-0.961401\pi$
$227$		−	1.20256e37i		−	0.241931i	0.992657	−	0.120966i	$-0.0385991\pi$
$228$	7.07498e36	−	4.59898e37i	0.132669	−	0.862391i
$229$	5.75083e37			1.00546			0.502728	−	0.864445i	$-0.332330\pi$
$229$	5.75083e37			1.00546			0.502728	+	0.864445i	$0.332330\pi$
$230$		−	4.66048e37i		−	0.759950i
$231$	−3.36185e37	−	5.17181e36i	−0.511431	−	0.0786775i
$232$	−7.12348e37			−1.01131
$233$			2.85230e37i			0.378007i	0.981976	+	0.189004i	$0.0605258\pi$
$233$			2.85230e37i			0.378007i	−0.981976	+	0.189004i	$0.939474\pi$
$234$	−1.39530e37	+	4.42763e37i	−0.172669	+	0.547921i
$235$	7.05781e37			0.815801
$236$			7.37042e37i			0.795976i
$237$	3.96864e36	−	2.57975e37i	0.0400560	−	0.260378i
$238$	−2.93901e37			−0.277313
$239$			2.92964e36i			0.0258492i	0.999916	+	0.0129246i	$0.00411415\pi$
$239$			2.92964e36i			0.0258492i	−0.999916	+	0.0129246i	$0.995886\pi$
$240$	2.99491e37	+	4.60731e36i	0.247175	+	0.0380249i
$241$	1.22457e38			0.945606			0.472803	−	0.881168i	$-0.343242\pi$
$241$	1.22457e38			0.945606			0.472803	+	0.881168i	$0.343242\pi$
$242$			5.16581e37i			0.373330i
$243$	−1.02172e38	+	1.06810e38i	−0.691243	+	0.722623i
$244$	−3.96979e37			−0.251496
$245$		−	9.94861e36i		−	0.0590344i
$246$	−7.54721e36	+	4.90594e37i	−0.0419590	+	0.272748i
$247$	2.57064e38			1.33934
$248$			7.64492e37i			0.373376i
$249$	−4.25314e38	−	6.54295e37i	−1.94769	−	0.299629i
$250$	1.25666e38			0.539730
$251$		−	1.63459e38i		−	0.658611i	−0.944223	−	0.329306i	$-0.893185\pi$
$251$		−	1.63459e38i		−	0.658611i	0.944223	−	0.329306i	$-0.106815\pi$
$252$	1.96967e38	+	6.20711e37i	0.744707	+	0.234683i
$253$	−2.74864e38			−0.975415
$254$		−	2.57947e38i		−	0.859393i
$255$	2.04455e37	−	1.32903e38i	0.0639668	−	0.415806i
$256$	−2.23557e38			−0.656974
$257$		−	2.96392e38i		−	0.818346i	−0.912457	−	0.409173i	$-0.865817\pi$
$257$		−	2.96392e38i		−	0.818346i	0.912457	−	0.409173i	$-0.134183\pi$
$258$	2.75211e38	+	4.23379e37i	0.714086	+	0.109854i
$259$	1.99377e38			0.486271
$260$			2.96754e38i			0.680491i
$261$	1.61763e38	−	5.13316e38i	0.348845	−	1.10697i
$262$	1.47916e38			0.300051
$263$			1.72040e38i			0.328351i	0.986431	+	0.164176i	$0.0524964\pi$
$263$			1.72040e38i			0.328351i	−0.986431	+	0.164176i	$0.947504\pi$
$264$	−3.68043e37	+	2.39240e38i	−0.0661052	+	0.429706i
$265$	−4.02404e38			−0.680343
$266$			3.75299e38i			0.597409i
$267$	2.89031e38	+	4.44640e37i	0.433275	+	0.0666543i
$268$	−9.33194e38			−1.31770
$269$			6.63090e38i			0.882136i	0.897474	+	0.441068i	$0.145400\pi$
$269$			6.63090e38i			0.882136i	−0.897474	+	0.441068i	$0.854600\pi$
$270$	1.37084e38	−	2.78136e38i	0.171857	−	0.348689i
$271$	5.57740e37			0.0659057			0.0329528	−	0.999457i	$-0.489509\pi$
$271$	5.57740e37			0.0659057			0.0329528	+	0.999457i	$0.489509\pi$
$272$		−	1.54417e38i		−	0.172025i
$273$	−1.73476e38	+	1.12765e39i	−0.182237	+	1.18460i
$274$	−4.90745e38			−0.486236
$275$		−	2.07337e38i		−	0.193800i
$276$	1.64943e39	+	2.53746e38i	1.45475	+	0.223797i
$277$	2.01751e39			1.67935			0.839673	−	0.543093i	$-0.182747\pi$
$277$	2.01751e39			1.67935			0.839673	+	0.543093i	$0.182747\pi$
$278$		−	9.26591e36i		−	0.00728067i
$279$	−5.50891e38	−	1.73605e38i	−0.408694	−	0.128793i
$280$	−1.00867e39			−0.706677
$281$		−	1.04715e39i		−	0.692958i	−0.938058	−	0.346479i	$-0.887377\pi$
$281$		−	1.04715e39i		−	0.692958i	0.938058	−	0.346479i	$-0.112623\pi$
$282$	1.26111e38	−	8.19764e38i	0.0788437	−	0.512511i
$283$	−1.34123e39			−0.792353			−0.396176	−	0.918174i	$-0.629663\pi$
$283$	−1.34123e39			−0.792353			−0.396176	+	0.918174i	$0.629663\pi$
$284$		−	1.69432e39i		−	0.946023i
$285$	−1.69711e39	−	2.61080e38i	−0.895760	−	0.137802i
$286$	−5.74378e38			−0.286643
$287$			1.21990e39i			0.575724i
$288$	6.93710e38	−	2.20132e39i	0.309669	−	0.982659i
$289$	1.68267e39			0.710613
$290$			1.12908e39i			0.451186i
$291$	−5.31699e38	+	3.45622e39i	−0.201084	+	1.30712i
$292$	−7.83189e38			−0.280376
$293$		−	3.88110e39i		−	1.31545i	−0.753260	−	0.657723i	$-0.771520\pi$
$293$		−	3.88110e39i		−	1.31545i	0.753260	−	0.657723i	$-0.228480\pi$
$294$	−1.15553e38	−	1.77765e37i	−0.0370872	−	0.00570542i
$295$	2.71982e39			0.826776
$296$		−	1.41883e39i		−	0.408568i
$297$	−1.64038e39	−	8.08490e38i	−0.447550	−	0.220583i
$298$	1.28668e39			0.332668
$299$			9.21966e39i			2.25931i
$300$	−1.91407e38	+	1.24421e39i	−0.0444649	+	0.289037i
$301$	6.84333e39			1.50731
$302$			1.19461e39i			0.249526i
$303$	−6.56851e39	−	1.01049e39i	−1.30132	−	0.200193i
$304$	−1.97184e39			−0.370590
$305$			1.46493e39i			0.261227i
$306$	−1.50713e39	−	4.74948e38i	−0.255040	−	0.0803717i
$307$	2.20584e38			0.0354292			0.0177146	−	0.999843i	$-0.494361\pi$
$307$	2.20584e38			0.0354292			0.0177146	+	0.999843i	$0.494361\pi$
$308$			2.55517e39i			0.389591i
$309$	1.12370e38	−	7.30443e38i	0.0162673	−	0.105743i
$310$	1.21173e39			0.166578
$311$		−	5.51616e39i		−	0.720229i	−0.932908	−	0.360115i	$-0.882738\pi$
$311$		−	5.51616e39i		−	0.720229i	0.932908	−	0.360115i	$-0.117262\pi$
$312$	8.02475e39	+	1.23451e39i	0.995310	+	0.153117i
$313$	−8.67278e39			−1.02200			−0.510998	−	0.859582i	$-0.670724\pi$
$313$	−8.67278e39			−1.02200			−0.510998	+	0.859582i	$0.670724\pi$
$314$		−	5.14903e39i		−	0.576569i
$315$	2.29054e39	−	7.26845e39i	0.243763	−	0.773523i
$316$	−1.96074e39			−0.198347
$317$		−	1.41350e40i		−	1.35940i	−0.733490	−	0.679700i	$-0.762110\pi$
$317$		−	1.41350e40i		−	1.35940i	0.733490	−	0.679700i	$-0.237890\pi$
$318$	−7.19026e38	+	4.67391e39i	−0.0657522	+	0.427412i
$319$	6.65903e39			0.579108
$320$			1.81865e39i			0.150435i
$321$	−7.01793e38	−	1.07963e38i	−0.0552241	−	0.00849557i
$322$	−1.34602e40			−1.00776
$323$			8.75025e39i			0.623419i
$324$	9.09742e39	+	6.36602e39i	0.616876	+	0.431666i
$325$	−6.95462e39			−0.448890
$326$		−	1.65985e39i		−	0.101997i
$327$	−3.44384e38	+	2.23861e39i	−0.0201502	+	0.130983i
$328$	8.68122e39			0.483726
$329$		−	2.03841e40i		−	1.08182i
$330$	3.79198e39	+	5.83351e38i	0.191709	+	0.0294922i
$331$	8.27126e39			0.398404			0.199202	−	0.979958i	$-0.436165\pi$
$331$	8.27126e39			0.398404			0.199202	+	0.979958i	$0.436165\pi$
$332$			3.23260e40i			1.48369i
$333$	1.02241e40	+	3.22195e39i	0.447215	+	0.140933i
$334$	−1.00720e40			−0.419926
$335$			3.44366e40i			1.36868i
$336$	1.33067e39	−	8.64977e39i	0.0504244	−	0.327775i
$337$	−4.31836e40			−1.56042			−0.780209	−	0.625519i	$-0.784887\pi$
$337$	−4.31836e40			−1.56042			−0.780209	+	0.625519i	$0.784887\pi$
$338$			4.84182e39i			0.166856i
$339$	1.93897e40	+	2.98287e39i	0.637346	+	0.0980481i
$340$	−1.01012e40			−0.316747
$341$		−	7.14647e39i		−	0.213807i
$342$	−6.06488e39	+	1.92454e40i	−0.173143	+	0.549426i
$343$	3.51902e40			0.958772
$344$		−	4.86994e40i		−	1.26645i
$345$	9.36369e39	−	6.08671e40i	0.232456	−	1.51104i
$346$	2.19170e40			0.519475
$347$		−	4.21051e39i		−	0.0952934i	−0.998864	−	0.0476467i	$-0.984828\pi$
$347$		−	4.21051e39i		−	0.0952934i	0.998864	−	0.0476467i	$-0.0151722\pi$
$348$	−3.99602e40	−	6.14741e39i	−0.863694	−	0.132869i
$349$	1.76986e40			0.365369			0.182685	−	0.983172i	$-0.441521\pi$
$349$	1.76986e40			0.365369			0.182685	+	0.983172i	$0.441521\pi$
$350$		−	1.01534e40i		−	0.200226i
$351$	−2.71189e40	+	5.50228e40i	−0.510926	+	1.03664i
$352$	2.85567e40			0.514074
$353$		−	3.02615e40i		−	0.520589i	−0.965529	−	0.260295i	$-0.916180\pi$
$353$		−	3.02615e40i		−	0.520589i	0.965529	−	0.260295i	$-0.0838197\pi$
$354$	4.85985e39	−	3.15907e40i	0.0799044	−	0.519406i
$355$	−6.25235e40			−0.982629
$356$		−	2.19678e40i		−	0.330055i
$357$	−3.83844e40	−	5.90498e39i	−0.551395	−	0.0848256i
$358$	3.56534e40			0.489747
$359$			9.54033e40i			1.25329i	0.779304	+	0.626646i	$0.215573\pi$
$359$			9.54033e40i			1.25329i	−0.779304	+	0.626646i	$0.784427\pi$
$360$	−5.17247e40	−	1.63002e40i	−0.649917	−	0.204811i
$361$	2.85384e40			0.343016
$362$			1.05864e40i			0.121734i
$363$	−1.03790e40	+	6.74669e40i	−0.114195	+	0.742309i
$364$	8.57071e40			0.902391
$365$			2.89011e40i			0.291225i
$366$	1.70151e40	+	2.61757e39i	0.164111	+	0.0252465i
$367$	9.31860e40			0.860386			0.430193	−	0.902737i	$-0.358445\pi$
$367$	9.31860e40			0.860386			0.430193	+	0.902737i	$0.358445\pi$
$368$		−	7.07203e40i		−	0.625143i
$369$	−1.97137e40	+	6.25567e40i	−0.166858	+	0.529483i
$370$	−2.24886e40			−0.182278
$371$			1.16220e41i			0.902194i
$372$	−6.59740e39	+	4.28853e40i	−0.0490553	+	0.318876i
$373$	−8.60796e39			−0.0613139			−0.0306569	−	0.999530i	$-0.509760\pi$
$373$	−8.60796e39			−0.0613139			−0.0306569	+	0.999530i	$0.509760\pi$
$374$		−	1.95513e40i		−	0.133423i
$375$	1.64123e41	+	2.52484e40i	1.07317	+	0.165095i
$376$	−1.45060e41			−0.908953
$377$		−	2.23361e41i		−	1.34136i
$378$	−8.03302e40	−	3.95920e40i	−0.462392	−	0.227897i
$379$	−2.58970e41			−1.42897			−0.714484	−	0.699652i	$-0.753338\pi$
$379$	−2.58970e41			−1.42897			−0.714484	+	0.699652i	$0.753338\pi$
$380$			1.28989e41i			0.682360i
$381$	5.18260e40	−	3.36887e41i	0.262874	−	1.70877i
$382$	3.61405e40			0.175784
$383$			7.99494e39i			0.0372936i	0.999826	+	0.0186468i	$0.00593581\pi$
$383$			7.99494e39i			0.0372936i	−0.999826	+	0.0186468i	$0.994064\pi$
$384$	−2.06482e41	−	3.17648e40i	−0.923811	−	0.142117i
$385$	9.42905e40			0.404665
$386$			6.32465e40i			0.260399i
$387$	3.50927e41	+	1.10589e41i	1.38625	+	0.436854i
$388$	2.62690e41			0.995717
$389$		−	2.48022e41i		−	0.902189i	−0.892476	−	0.451094i	$-0.851034\pi$
$389$		−	2.48022e41i		−	0.902189i	0.892476	−	0.451094i	$-0.148966\pi$
$390$	1.95671e40	−	1.27193e41i	0.0683114	−	0.444047i
$391$	−3.13829e41			−1.05164
$392$			2.04475e40i			0.0657753i
$393$	1.93182e41	+	2.97188e40i	0.596605	+	0.0917806i
$394$	9.66844e40			0.286693
$395$			7.23548e40i			0.206022i
$396$	−4.12918e40	+	1.31029e41i	−0.112912	+	0.358299i
$397$	−6.34349e41			−1.66602			−0.833010	−	0.553258i	$-0.813384\pi$
$397$	−6.34349e41			−1.66602			−0.833010	+	0.553258i	$0.813384\pi$
$398$			2.89034e41i			0.729154i
$399$	−7.54040e40	+	4.90152e41i	−0.182738	+	1.18786i
$400$	5.33461e40			0.124206
$401$		−	2.07013e41i		−	0.463114i	−0.972821	−	0.231557i	$-0.925618\pi$
$401$		−	2.07013e41i		−	0.463114i	0.972821	−	0.231557i	$-0.0743820\pi$
$402$	3.99980e41	+	6.15322e40i	0.859848	+	0.132277i
$403$	−2.39711e41			−0.495231
$404$			4.99239e41i			0.991303i
$405$	2.34918e41	−	3.35712e41i	0.448369	−	0.640746i
$406$	3.26095e41			0.598312
$407$			1.32632e41i			0.233959i
$408$	−4.20218e40	+	2.73156e41i	−0.0712708	+	0.463285i
$409$	2.76151e41			0.450374			0.225187	−	0.974316i	$-0.427701\pi$
$409$	2.76151e41			0.450374			0.225187	+	0.974316i	$0.427701\pi$
$410$		−	1.37598e41i		−	0.215809i
$411$	−6.40927e41	−	9.85990e40i	−0.966806	−	0.148732i
$412$	−5.55172e40			−0.0805512
$413$		−	7.85527e41i		−	1.09638i
$414$	−6.90240e41	−	2.17518e41i	−0.926818	−	0.292072i
$415$	1.19289e42			1.54110
$416$		−	9.57868e41i		−	1.19073i
$417$	1.86168e39	−	1.21015e40i	0.00222704	−	0.0144765i
$418$	−2.49662e41			−0.287430
$419$			1.00009e42i			1.10819i	0.832454	+	0.554094i	$0.186935\pi$
$419$			1.00009e42i			1.10819i	−0.832454	+	0.554094i	$0.813065\pi$
$420$	−5.65829e41	−	8.70460e40i	−0.603527	−	0.0928454i
$421$	−4.52868e41			−0.465005			−0.232503	−	0.972596i	$-0.574691\pi$
$421$	−4.52868e41			−0.465005			−0.232503	+	0.972596i	$0.574691\pi$
$422$		−	1.63685e41i		−	0.161812i
$423$	3.29409e41	−	1.04530e42i	0.313537	−	0.994933i
$424$	8.27064e41			0.758028
$425$		−	2.36729e41i		−	0.208944i
$426$	−1.11719e41	+	7.26210e41i	−0.0949670	+	0.617317i
$427$	4.23094e41			0.346410
$428$			5.33397e40i			0.0420679i
$429$	−7.50154e41	−	1.15402e41i	−0.569946	−	0.0876794i
$430$	−7.71890e41			−0.565015
$431$			4.47524e40i			0.0315631i	0.999875	+	0.0157816i	$0.00502363\pi$
$431$			4.47524e40i			0.0315631i	−0.999875	+	0.0157816i	$0.994976\pi$
$432$	2.08018e41	−	4.22058e41i	0.141371	−	0.286835i
$433$	5.96801e41			0.390862			0.195431	−	0.980717i	$-0.437389\pi$
$433$	5.96801e41			0.390862			0.195431	+	0.980717i	$0.437389\pi$
$434$		−	3.49965e41i		−	0.220897i
$435$	−2.26851e41	+	1.47461e42i	−0.138010	+	0.897114i
$436$	1.70146e41			0.0997785
$437$			4.00747e42i			2.26551i
$438$	3.35686e41	+	5.16413e40i	0.182956	+	0.0281457i
$439$	7.27745e41			0.382425			0.191213	−	0.981549i	$-0.438758\pi$
$439$	7.27745e41			0.382425			0.191213	+	0.981549i	$0.438758\pi$
$440$		−	6.71002e41i		−	0.340002i
$441$	−1.47344e41	−	4.64331e40i	−0.0719971	−	0.0226887i
$442$	−6.55803e41			−0.309042
$443$			1.23917e42i			0.563212i	0.959530	+	0.281606i	$0.0908672\pi$
$443$			1.23917e42i			0.563212i	−0.959530	+	0.281606i	$0.909133\pi$
$444$	1.22442e41	−	7.95916e41i	0.0536789	−	0.348931i
$445$	−8.10651e41			−0.342826
$446$		−	1.02244e42i		−	0.417140i
$447$	1.68044e42	+	2.58516e41i	0.661459	+	0.101758i
$448$	5.25254e41			0.199490
$449$		−	3.01079e42i		−	1.10342i	−0.834037	−	0.551708i	$-0.813976\pi$
$449$		−	3.01079e42i		−	1.10342i	0.834037	−	0.551708i	$-0.186024\pi$
$450$	1.64079e41	−	5.20665e41i	0.0580302	−	0.184144i
$451$	−8.11520e41			−0.276997
$452$		−	1.47371e42i		−	0.485509i
$453$	−2.40018e41	+	1.56020e42i	−0.0763261	+	0.496145i
$454$	3.91755e41			0.120260
$455$		−	3.16275e42i		−	0.937309i
$456$	3.48808e42	+	5.36600e41i	0.998043	+	0.153537i
$457$	−5.01707e42			−1.38609			−0.693044	−	0.720895i	$-0.743731\pi$
$457$	−5.01707e42			−1.38609			−0.693044	+	0.720895i	$0.743731\pi$
$458$			1.87344e42i			0.499794i
$459$	−1.87293e42	−	9.23103e41i	−0.482523	−	0.237819i
$460$	−4.62620e42			−1.15106
$461$		−	3.38629e42i		−	0.813785i	−0.913476	−	0.406892i	$-0.866612\pi$
$461$		−	3.38629e42i		−	0.813785i	0.913476	−	0.406892i	$-0.133388\pi$
$462$	1.68481e41	−	1.09518e42i	0.0391092	−	0.254223i
$463$	1.44371e42			0.323731			0.161865	−	0.986813i	$-0.448249\pi$
$463$	1.44371e42			0.323731			0.161865	+	0.986813i	$0.448249\pi$
$464$			1.71331e42i			0.371150i
$465$	1.58255e42	+	2.43456e41i	0.331215	+	0.0509534i
$466$	−9.29187e41			−0.187901
$467$			2.83041e42i			0.553068i	0.961004	+	0.276534i	$0.0891859\pi$
$467$			2.83041e42i			0.553068i	−0.961004	+	0.276534i	$0.910814\pi$
$468$	4.39507e42	+	1.38504e42i	0.829912	+	0.261534i
$469$	9.94582e42			1.81499
$470$			2.29921e42i			0.405520i
$471$	1.03453e42	−	6.72478e42i	0.176363	−	1.14642i
$472$	−5.59007e42			−0.921182
$473$			4.55242e42i			0.725211i
$474$	8.40400e41	+	1.29286e41i	0.129429	+	0.0199112i
$475$	−3.02293e42			−0.450122
$476$			2.91740e42i			0.420034i
$477$	−1.87814e42	+	5.95980e42i	−0.261477	+	0.829731i
$478$	−9.54382e40			−0.0128492
$479$			3.54924e42i			0.462134i	0.972938	+	0.231067i	$0.0742216\pi$
$479$			3.54924e42i			0.462134i	−0.972938	+	0.231067i	$0.925778\pi$
$480$	−9.72832e41	+	6.32374e42i	−0.122512	+	0.796368i
$481$	4.44884e42			0.541908
$482$			3.98925e42i			0.470044i
$483$	−1.75794e43	−	2.70438e42i	−2.00378	−	0.308258i
$484$	5.12782e42			0.565466
$485$		−	9.69374e42i		−	1.03425i
$486$	−3.47953e42	−	3.32843e42i	−0.359203	−	0.343605i
$487$	6.57145e42			0.656444			0.328222	−	0.944601i	$-0.393551\pi$
$487$	6.57145e42			0.656444			0.328222	+	0.944601i	$0.393551\pi$
$488$		−	3.01088e42i		−	0.291056i
$489$	3.33492e41	−	2.16781e42i	0.0311992	−	0.202806i
$490$	3.24094e41			0.0293450
$491$		−	2.24059e43i		−	1.96362i	−0.189864	−	0.981810i	$-0.560805\pi$
$491$		−	2.24059e43i		−	1.96362i	0.189864	−	0.981810i	$-0.439195\pi$
$492$	4.86986e42	+	7.49170e41i	0.413119	+	0.0635534i
$493$	7.60303e42			0.624361
$494$			8.37433e42i			0.665761i
$495$	4.83522e42	+	1.52374e42i	0.372163	+	0.117281i
$496$	1.83873e42			0.137029
$497$			1.80578e43i			1.30305i
$498$	2.13148e42	−	1.38554e43i	0.148940	−	0.968164i
$499$	−1.68499e43			−1.14022			−0.570110	−	0.821569i	$-0.693099\pi$
$499$	−1.68499e43			−1.14022			−0.570110	+	0.821569i	$0.693099\pi$
$500$		−	1.24741e43i		−	0.817505i
$501$	−1.31543e43	−	2.02364e42i	−0.834960	−	0.128449i
$502$	5.32497e42			0.327384
$503$		−	1.76336e43i		−	1.05016i	−0.851054	−	0.525078i	$-0.824036\pi$
$503$		−	1.76336e43i		−	1.05016i	0.851054	−	0.525078i	$-0.175964\pi$
$504$	−4.70776e42	+	1.49389e43i	−0.271598	+	0.861848i
$505$	1.84228e43			1.02966
$506$		−	8.95418e42i		−	0.484862i
$507$	−9.72804e41	+	6.32355e42i	−0.0510385	+	0.331768i
$508$	−2.56050e43			−1.30168
$509$			2.95377e43i			1.45510i	0.686056	+	0.727549i	$0.259341\pi$
$509$			2.95377e43i			1.45510i	−0.686056	+	0.727549i	$0.740659\pi$
$510$	4.32954e42	+	6.66048e41i	0.206690	+	0.0317968i
$511$	8.34709e42			0.386190
$512$			1.35613e43i			0.608108i
$513$	−1.17876e43	+	2.39165e43i	−0.512329	+	1.03949i
$514$	9.65551e42			0.406785
$515$			2.04869e42i			0.0836681i
$516$	4.20265e42	−	2.73187e43i	0.166390	−	1.08159i
$517$	1.35602e43			0.520495
$518$			6.49506e42i			0.241717i
$519$	2.86243e43	+	4.40351e42i	1.03290	+	0.158899i
$520$	−2.25072e43			−0.787531
$521$			2.00817e43i			0.681391i	0.940174	+	0.340696i	$0.110663\pi$
$521$			2.00817e43i			0.681391i	−0.940174	+	0.340696i	$0.889337\pi$
$522$	1.67222e43	+	5.26973e42i	0.550256	+	0.173405i
$523$	5.37535e42			0.171546			0.0857728	−	0.996315i	$-0.472664\pi$
$523$	5.37535e42			0.171546			0.0857728	+	0.996315i	$0.472664\pi$
$524$		−	1.46828e43i		−	0.454474i
$525$	2.03998e42	−	1.32606e43i	0.0612460	−	0.398119i
$526$	−5.60453e42			−0.163218
$527$		−	8.15957e42i		−	0.230514i
$528$	5.75413e42	+	8.85204e41i	0.157702	+	0.0242606i
$529$	−1.06120e44			−2.82166
$530$		−	1.31090e43i		−	0.338186i
$531$	1.26942e43	−	4.02819e43i	0.317756	−	1.00832i
$532$	3.72539e43			0.904869
$533$			2.72205e43i			0.641595i
$534$	−1.44849e42	+	9.41570e42i	−0.0331327	+	0.215374i
$535$	1.96833e42			0.0436957
$536$		−	7.07778e43i		−	1.52497i
$537$	4.65643e43	+	7.16336e42i	0.973788	+	0.149806i
$538$	−2.16013e43			−0.438495
$539$		−	1.91143e42i		−	0.0376650i
$540$	−2.76091e43	−	1.36076e43i	−0.528143	−	0.260304i
$541$	1.60260e43			0.297625			0.148813	−	0.988865i	$-0.452455\pi$
$541$	1.60260e43			0.297625			0.148813	+	0.988865i	$0.452455\pi$
$542$			1.81694e42i			0.0327606i
$543$	−2.12699e42	+	1.38261e43i	−0.0372364	+	0.242049i
$544$	3.26050e43			0.554245
$545$		−	6.27869e42i		−	0.103639i
$546$	−3.67353e43	−	5.65129e42i	−0.588846	−	0.0905869i
$547$	−2.80279e43			−0.436308			−0.218154	−	0.975914i	$-0.570003\pi$
$547$	−2.80279e43			−0.436308			−0.218154	+	0.975914i	$0.570003\pi$
$548$			4.87136e43i			0.736480i
$549$	2.16963e43	+	6.83725e42i	0.318587	+	0.100398i
$550$	6.75436e42			0.0963344
$551$		−	9.70874e43i		−	1.34505i
$552$	−1.92453e43	+	1.25101e44i	−0.258999	+	1.68358i
$553$	2.08972e43			0.273203
$554$			6.57241e43i			0.834773i
$555$	−2.93707e43	−	4.51834e42i	−0.362433	−	0.0557560i
$556$	−9.19776e41			−0.0110277
$557$			1.16007e44i			1.35145i	0.737152	+	0.675727i	$0.236170\pi$
$557$			1.16007e44i			1.35145i	−0.737152	+	0.675727i	$0.763830\pi$
$558$	5.65548e42	−	1.79463e43i	0.0640210	−	0.203155i
$559$	1.52700e44			1.67977
$560$			2.42602e43i			0.259350i
$561$	3.92819e42	−	2.55346e43i	0.0408119	−	0.265291i
$562$	3.41127e43			0.344457
$563$		−	2.75878e43i		−	0.270759i	−0.990794	−	0.135379i	$-0.956775\pi$
$563$		−	2.75878e43i		−	0.270759i	0.990794	−	0.135379i	$-0.0432253\pi$
$564$	−8.13735e43	−	1.25183e43i	−0.776278	−	0.119421i
$565$	−5.43826e43			−0.504295
$566$		−	4.36928e43i		−	0.393865i
$567$	−9.69588e43	−	6.78480e43i	−0.849685	−	0.594577i
$568$	1.28505e44			1.09483
$569$		−	1.45549e43i		−	0.120563i	−0.998181	−	0.0602814i	$-0.980800\pi$
$569$		−	1.45549e43i		−	0.120563i	0.998181	−	0.0602814i	$-0.0191998\pi$
$570$	8.50515e42	−	5.52863e43i	0.0684990	−	0.445267i
$571$	−2.49281e44			−1.95214			−0.976072	−	0.217450i	$-0.930226\pi$
$571$	−2.49281e44			−1.95214			−0.976072	+	0.217450i	$0.930226\pi$
$572$			5.70153e43i			0.434166i
$573$	4.72005e43	+	7.26123e42i	0.349520	+	0.0537696i
$574$	−3.97405e43			−0.286182
$575$		−	1.08418e44i		−	0.759305i
$576$	2.69351e43	+	8.48817e42i	0.183467	+	0.0578168i
$577$	1.65085e44			1.09369			0.546847	−	0.837233i	$-0.315828\pi$
$577$	1.65085e44			1.09369			0.546847	+	0.837233i	$0.315828\pi$
$578$			5.48160e43i			0.353233i
$579$	−1.27073e43	+	8.26017e43i	−0.0796518	+	0.517764i
$580$	1.12077e44			0.683391
$581$		−	3.44525e44i		−	2.04363i
$582$	−1.12593e44	−	1.73210e43i	−0.649744	−	0.0999554i
$583$	−7.73139e43			−0.434071
$584$		−	5.94007e43i		−	0.324479i
$585$	5.11104e43	−	1.62186e44i	0.271654	−	0.862025i
$586$	1.26434e44			0.653885
$587$			3.84776e44i			1.93642i	0.250148	+	0.968208i	$0.419521\pi$
$587$			3.84776e44i			1.93642i	−0.250148	+	0.968208i	$0.580479\pi$
$588$	−1.76457e42	+	1.14703e43i	−0.00864176	+	0.0561744i
$589$	−1.04194e44			−0.496591
$590$			8.86030e43i			0.410976i
$591$	1.26273e44	+	1.94255e43i	0.570045	+	0.0876947i
$592$	−3.41253e43			−0.149944
$593$		−	2.01475e43i		−	0.0861682i	−0.999071	−	0.0430841i	$-0.986282\pi$
$593$		−	2.01475e43i		−	0.0861682i	0.999071	−	0.0430841i	$-0.0137183\pi$
$594$	2.63380e43	−	5.34384e43i	0.109648	−	0.222469i
$595$	1.07657e44			0.436287
$596$		−	1.27722e44i		−	0.503877i
$597$	−5.80718e43	+	3.77486e44i	−0.223036	+	1.44981i
$598$	−3.00347e44			−1.12306
$599$			4.08398e44i			1.48681i	0.668843	+	0.743404i	$0.266790\pi$
$599$			4.08398e44i			1.48681i	−0.668843	+	0.743404i	$0.733210\pi$
$600$	−9.43667e43	−	1.45172e43i	−0.334502	−	0.0514591i
$601$	−3.61344e44			−1.24718			−0.623590	−	0.781751i	$-0.714327\pi$
$601$	−3.61344e44			−1.24718			−0.623590	+	0.781751i	$0.714327\pi$
$602$			2.22934e44i			0.749259i
$603$	5.10023e44	+	1.60726e44i	1.66922	+	0.526027i
$604$	1.18583e44			0.377947
$605$		−	1.89226e44i		−	0.587347i
$606$	3.29184e43	−	2.13981e44i	0.0995124	−	0.646864i
$607$	−3.35513e44			−0.987847			−0.493923	−	0.869505i	$-0.664438\pi$
$607$	−3.35513e44			−0.987847			−0.493923	+	0.869505i	$0.664438\pi$
$608$		−	4.16352e44i		−	1.19400i
$609$	4.25889e44	+	6.55180e43i	1.18965	+	0.183014i
$610$	−4.77226e43			−0.129852
$611$		−	4.54844e44i		−	1.20560i
$612$	−4.71455e43	+	1.49604e44i	−0.121736	+	0.386297i
$613$	5.40629e44			1.35998			0.679989	−	0.733222i	$-0.261984\pi$
$613$	5.40629e44			1.35998			0.679989	+	0.733222i	$0.261984\pi$
$614$			7.18594e42i			0.0176112i
$615$	2.76458e43	−	1.79707e44i	0.0660126	−	0.429104i
$616$	−1.93796e44			−0.450872
$617$			2.60746e44i			0.591091i	0.955329	+	0.295546i	$0.0955015\pi$
$617$			2.60746e44i			0.591091i	−0.955329	+	0.295546i	$0.904499\pi$
$618$	2.37955e43	+	3.66065e42i	0.0525628	+	0.00808617i
$619$	−1.43900e43			−0.0309750			−0.0154875	−	0.999880i	$-0.504930\pi$
$619$	−1.43900e43			−0.0309750			−0.0154875	+	0.999880i	$0.504930\pi$
$620$		−	1.20281e44i		−	0.252308i
$621$	−8.57770e44	−	4.22766e44i	−1.75350	−	0.864240i
$622$	1.79699e44			0.358013
$623$			2.34129e44i			0.454617i
$624$	2.96921e43	−	1.93009e44i	0.0561937	−	0.365278i
$625$	−2.49761e44			−0.460728
$626$		−	2.82531e44i		−	0.508016i
$627$	−3.26066e44	−	5.01613e43i	−0.571511	−	0.0879202i
$628$	−5.11116e44			−0.873304
$629$			1.51435e44i			0.252241i
$630$	2.36783e44	+	7.46184e43i	0.384504	+	0.121171i
$631$	6.57169e44			1.04042			0.520208	−	0.854040i	$-0.325854\pi$
$631$	6.57169e44			1.04042			0.520208	+	0.854040i	$0.325854\pi$
$632$		−	1.48711e44i		−	0.229547i
$633$	3.28871e43	−	2.13777e44i	0.0494956	−	0.321738i
$634$	4.60473e44			0.675734
$635$			9.44872e44i			1.35205i
$636$	4.63954e44	+	7.13738e43i	0.647382	+	0.0995921i
$637$	−6.41144e43			−0.0872418
$638$			2.16930e44i			0.287865i
$639$	−2.91816e44	+	9.26004e44i	−0.377655	+	1.19839i
$640$	5.79125e44			0.730958
$641$		−	1.18680e45i		−	1.46100i	−0.682914	−	0.730499i	$-0.739288\pi$
$641$		−	1.18680e45i		−	1.46100i	0.682914	−	0.730499i	$-0.260712\pi$
$642$	3.51707e42	−	2.28622e43i	0.00422300	−	0.0274509i
$643$	4.85455e44			0.568556			0.284278	−	0.958742i	$-0.408246\pi$
$643$	4.85455e44			0.568556			0.284278	+	0.958742i	$0.408246\pi$
$644$			1.33612e45i			1.52641i
$645$	−1.00811e45	−	1.55086e44i	−1.12345	−	0.172829i
$646$	−2.85055e44			−0.309891
$647$			6.54008e44i			0.693609i	0.937937	+	0.346805i	$0.112733\pi$
$647$			6.54008e44i			0.693609i	−0.937937	+	0.346805i	$0.887267\pi$
$648$	−4.82829e44	+	6.89991e44i	−0.499567	+	0.713910i
$649$	5.22560e44			0.527498
$650$		−	2.26559e44i		−	0.223135i
$651$	7.03140e43	−	4.57065e44i	0.0675687	−	0.439220i
$652$	−1.64764e44			−0.154490
$653$		−	1.22828e45i		−	1.12379i	−0.827207	−	0.561897i	$-0.810072\pi$
$653$		−	1.22828e45i		−	1.12379i	0.827207	−	0.561897i	$-0.189928\pi$
$654$	−7.29269e43	−	1.12189e43i	−0.0651094	−	0.0100163i
$655$	−5.41823e44			−0.472059
$656$		−	2.08798e44i		−	0.177527i
$657$	4.28040e44	+	1.34890e44i	0.355172	+	0.111927i
$658$	6.64048e44			0.537755
$659$		−	9.83151e44i		−	0.777058i	−0.921436	−	0.388529i	$-0.872983\pi$
$659$		−	9.83151e44i		−	0.777058i	0.921436	−	0.388529i	$-0.127017\pi$
$660$	5.79060e43	−	3.76409e44i	0.0446705	−	0.290373i
$661$	3.07694e44			0.231684			0.115842	−	0.993268i	$-0.463043\pi$
$661$	3.07694e44			0.231684			0.115842	+	0.993268i	$0.463043\pi$
$662$			2.69451e44i			0.198040i
$663$	−8.56498e44	−	1.31762e44i	−0.614483	−	0.0945309i
$664$	−2.45175e45			−1.71707
$665$		−	1.37474e45i		−	0.939883i
$666$	−1.04961e44	+	3.33067e44i	−0.0700552	+	0.222303i
$667$	3.48206e45			2.26894
$668$			9.99795e44i			0.636044i
$669$	2.05426e44	−	1.33534e45i	0.127596	−	0.829419i
$670$	−1.12183e45			−0.680348
$671$			2.81457e44i			0.166668i
$672$	1.82639e45	+	2.80969e44i	1.05605	+	0.162461i
$673$	−1.93264e45			−1.09122			−0.545608	−	0.838041i	$-0.683701\pi$
$673$	−1.93264e45			−1.09122			−0.545608	+	0.838041i	$0.683701\pi$
$674$		−	1.40678e45i		−	0.775656i
$675$	3.18903e44	−	6.47037e44i	0.171711	−	0.348393i
$676$	4.80621e44			0.252729
$677$			1.63334e45i			0.838797i	0.907802	+	0.419398i	$0.137759\pi$
$677$			1.63334e45i			0.838797i	−0.907802	+	0.419398i	$0.862241\pi$
$678$	−9.71724e43	+	6.31653e44i	−0.0487380	+	0.316814i
$679$	−2.79971e45			−1.37150
$680$		−	7.66126e44i		−	0.366570i
$681$	5.11643e44	+	7.87101e43i	0.239118	+	0.0367855i
$682$	2.32809e44			0.106280
$683$			2.16605e45i			0.965912i	0.875645	+	0.482956i	$0.160437\pi$
$683$			2.16605e45i			0.965912i	−0.875645	+	0.482956i	$0.839563\pi$
$684$	1.91038e45	+	6.02028e44i	0.832191	+	0.262252i
$685$	1.79762e45			0.764978
$686$			1.14638e45i			0.476589i
$687$	−3.76405e44	+	2.44676e45i	−0.152879	+	0.993765i
$688$	−1.17130e45			−0.464787
$689$			2.59331e45i			1.00542i
$690$	1.98286e45	+	3.05039e44i	0.751114	+	0.115550i
$691$	−2.09275e45			−0.774584			−0.387292	−	0.921957i	$-0.626589\pi$
$691$	−2.09275e45			−0.774584			−0.387292	+	0.921957i	$0.626589\pi$
$692$		−	2.17559e45i		−	0.786826i
$693$	4.40082e44	−	1.39649e45i	0.155525	−	0.493521i
$694$	1.37165e44			0.0473687
$695$			3.39414e43i			0.0114544i
$696$	4.66248e44	−	3.03077e45i	0.153769	−	0.999552i
$697$	−9.26564e44			−0.298642
$698$			5.76563e44i			0.181619i
$699$	−1.21354e45	−	1.86689e44i	−0.373612	−	0.0574758i
$700$	−1.00787e45			−0.303274
$701$			1.28379e45i			0.377578i	0.982018	+	0.188789i	$0.0604562\pi$
$701$			1.28379e45i			0.377578i	−0.982018	+	0.188789i	$0.939544\pi$
$702$	−1.79247e45	−	8.83446e44i	−0.515296	−	0.253972i
$703$	1.93376e45			0.543396
$704$			3.49417e44i			0.0959803i
$705$	−4.61950e44	+	3.00283e45i	−0.124042	+	0.806315i
$706$	9.85823e44			0.258776
$707$		−	5.32080e45i		−	1.36542i
$708$	−3.13583e45	−	4.82411e44i	−0.786721	−	0.121028i
$709$	3.46980e45			0.851068			0.425534	−	0.904942i	$-0.360086\pi$
$709$	3.46980e45			0.851068			0.425534	+	0.904942i	$0.360086\pi$
$710$		−	2.03682e45i		−	0.488448i
$711$	1.07161e45	+	3.37701e44i	0.251260	+	0.0791806i
$712$	1.66614e45			0.381972
$713$		−	3.73695e45i		−	0.837692i
$714$	1.92365e44	−	1.25044e45i	0.0421653	−	0.274089i
$715$	2.10397e45			0.450965
$716$		−	3.53911e45i		−	0.741799i
$717$	−1.24645e44	−	1.91751e43i	−0.0255487	−	0.00393036i
$718$	−3.10793e45			−0.622990
$719$			3.30156e44i			0.0647227i	0.999476	+	0.0323614i	$0.0103027\pi$
$719$			3.30156e44i			0.0647227i	−0.999476	+	0.0323614i	$0.989697\pi$
$720$	−3.92048e44	+	1.24407e45i	−0.0751655	+	0.238519i
$721$	5.91693e44			0.110951
$722$			9.29690e44i			0.170507i
$723$	−8.01508e44	+	5.21007e45i	−0.143779	+	0.934611i
$724$	1.05085e45			0.184385
$725$			2.62660e45i			0.450803i
$726$	−2.19786e45	−	3.38114e44i	−0.368989	−	0.0567646i
$727$	−7.70469e45			−1.26533			−0.632666	−	0.774425i	$-0.718039\pi$
$727$	−7.70469e45			−1.26533			−0.632666	+	0.774425i	$0.718039\pi$
$728$			6.50043e45i			1.04434i
$729$	−3.87562e45	−	5.04612e45i	−0.609118	−	0.793080i
$730$	−9.41505e44			−0.144763
$731$			5.19779e45i			0.781881i
$732$	2.59832e44	−	1.68900e45i	0.0382398	−	0.248572i
$733$	6.90519e45			0.994288			0.497144	−	0.867668i	$-0.334382\pi$
$733$	6.90519e45			0.994288			0.497144	+	0.867668i	$0.334382\pi$
$734$			3.03570e45i			0.427683i
$735$	4.23276e44	+	6.51159e43i	0.0583480	+	0.00897615i
$736$	1.49326e46			2.01414
$737$			6.61630e45i			0.873244i
$738$	−2.03790e45	−	6.42211e44i	−0.263196	−	0.0829422i
$739$	7.70771e45			0.974125			0.487062	−	0.873367i	$-0.338068\pi$
$739$	7.70771e45			0.974125			0.487062	+	0.873367i	$0.338068\pi$
$740$			2.23232e45i			0.276089i
$741$	−1.68254e45	+	1.09371e46i	−0.203646	+	1.32377i
$742$	−3.78609e45			−0.448465
$743$		−	1.53205e46i		−	1.77604i	−0.459803	−	0.888021i	$-0.652080\pi$
$743$		−	1.53205e46i		−	1.77604i	0.459803	−	0.888021i	$-0.347920\pi$
$744$	−3.25262e45	−	5.00378e44i	−0.369034	−	0.0567716i
$745$	−4.71317e45			−0.523374
$746$		−	2.80420e44i		−	0.0304781i
$747$	5.56756e45	−	1.76673e46i	0.592291	−	1.87949i
$748$	−1.94075e45			−0.202090
$749$		−	5.68486e44i		−	0.0579443i
$750$	−8.22510e44	+	5.34660e45i	−0.0820656	+	0.533454i
$751$	−1.09755e46			−1.07198			−0.535988	−	0.844226i	$-0.680061\pi$
$751$	−1.09755e46			−1.07198			−0.535988	+	0.844226i	$0.680061\pi$
$752$			3.48893e45i			0.333585i
$753$	6.95456e45	+	1.06988e45i	0.650954	+	0.100141i
$754$	7.27639e45			0.666768
$755$		−	4.37592e45i		−	0.392571i
$756$	−3.93009e45	+	7.97394e45i	−0.345186	+	0.700364i
$757$	−1.74621e46			−1.50163			−0.750816	−	0.660511i	$-0.770340\pi$
$757$	−1.74621e46			−1.50163			−0.750816	+	0.660511i	$0.770340\pi$
$758$		−	8.43642e45i		−	0.710315i
$759$	1.79905e45	−	1.16944e46i	0.148311	−	0.964074i
$760$	−9.78309e45			−0.789694
$761$			5.05977e45i			0.399923i	0.979804	+	0.199961i	$0.0640816\pi$
$761$			5.05977e45i			0.399923i	−0.979804	+	0.199961i	$0.935918\pi$
$762$	1.09747e46	+	1.68832e45i	0.849400	+	0.130670i
$763$	−1.81338e45			−0.137435
$764$		−	3.58747e45i		−	0.266253i
$765$	5.52068e45	+	1.73976e45i	0.401245	+	0.126446i
$766$	−2.60450e44			−0.0185380
$767$		−	1.75280e46i		−	1.22182i
$768$	1.46323e45	−	9.51149e45i	0.0998925	−	0.649335i
$769$	1.03873e45			0.0694514			0.0347257	−	0.999397i	$-0.488944\pi$
$769$	1.03873e45			0.0694514			0.0347257	+	0.999397i	$0.488944\pi$
$770$			3.07168e45i			0.201152i
$771$	1.26104e46	+	1.93996e45i	0.808831	+	0.124429i
$772$	6.27813e45			0.394415
$773$			3.24752e45i			0.199839i	0.994996	+	0.0999194i	$0.0318585\pi$
$773$			3.24752e45i			0.199839i	−0.994996	+	0.0999194i	$0.968142\pi$
$774$	−3.60264e45	+	1.14321e46i	−0.217153	+	0.689080i
$775$	2.81887e45			0.166436
$776$			1.99236e46i			1.15234i
$777$	−1.30497e45	+	8.48274e45i	−0.0739373	+	0.480618i
$778$	8.07978e45			0.448462
$779$			1.18318e46i			0.643357i
$780$	−1.26257e46	−	1.94232e45i	−0.672579	−	0.103468i
$781$	−1.20127e46			−0.626935
$782$		−	1.02236e46i		−	0.522750i
$783$	2.07809e46	+	1.02422e46i	1.04106	+	0.513103i
$784$	4.91796e44			0.0241395
$785$			1.88611e46i			0.907096i
$786$	−9.68144e44	+	6.29327e45i	−0.0456225	+	0.296562i
$787$	−2.75850e46			−1.27373			−0.636864	−	0.770976i	$-0.719769\pi$
$787$	−2.75850e46			−1.27373			−0.636864	+	0.770976i	$0.719769\pi$
$788$		−	9.59733e45i		−	0.434241i
$789$	−7.31967e45	−	1.12604e45i	−0.324533	−	0.0499256i
$790$	−2.35709e45			−0.102410
$791$			1.57066e46i			0.668740i
$792$	−9.93788e45	−	3.13177e45i	−0.414659	−	0.130673i
$793$	9.44080e45			0.386045
$794$		−	2.06651e46i		−	0.828149i
$795$	2.63382e45	−	1.71207e46i	0.103446	−	0.672432i
$796$	2.86908e46			1.10442
$797$		−	1.67857e46i		−	0.633294i	−0.948543	−	0.316647i	$-0.897443\pi$
$797$		−	1.67857e46i		−	0.633294i	0.948543	−	0.316647i	$-0.102557\pi$
$798$	−1.59676e46	−	2.45642e45i	−0.590463	−	0.0908357i
$799$	1.54825e46			0.561168
$800$			1.12640e46i			0.400178i
$801$	−3.78355e45	+	1.20061e46i	−0.131759	+	0.418103i
$802$	6.74383e45			0.230206
$803$			5.55278e45i			0.185807i
$804$	6.10797e45	−	3.97039e46i	0.200355	−	1.30237i
$805$	4.93053e46			1.58547
$806$		−	7.80903e45i		−	0.246171i
$807$	−2.82120e46	−	4.34007e45i	−0.871880	−	0.134128i
$808$	−3.78646e46			−1.14723
$809$		−	6.96435e45i		−	0.206873i	−0.994636	−	0.103437i	$-0.967016\pi$
$809$		−	6.96435e45i		−	0.206873i	0.994636	−	0.103437i	$-0.0329839\pi$
$810$	1.09364e46	+	7.65288e45i	0.318504	+	0.222877i
$811$	−5.91909e46			−1.69013			−0.845067	−	0.534660i	$-0.820440\pi$
$811$	−5.91909e46			−1.69013			−0.845067	+	0.534660i	$0.820440\pi$
$812$		−	3.23697e46i		−	0.906237i
$813$	−3.65053e44	+	2.37297e45i	−0.0100209	+	0.0651394i
$814$	−4.32074e45			−0.116297
$815$			6.08011e45i			0.160468i
$816$	6.56985e45	+	1.01069e45i	0.170025	+	0.0261563i
$817$	6.63735e46			1.68439
$818$			8.99611e45i			0.223873i
$819$	−4.68419e46	−	1.47615e46i	−1.14312	−	0.360237i
$820$	−1.36586e46			−0.326877
$821$			4.49542e46i			1.05507i	0.849535	+	0.527533i	$0.176883\pi$
$821$			4.49542e46i			1.05507i	−0.849535	+	0.527533i	$0.823117\pi$
$822$	3.21204e45	−	2.08793e46i	0.0739319	−	0.480582i
$823$	6.74191e46			1.52190			0.760949	−	0.648812i	$-0.224734\pi$
$823$	6.74191e46			1.52190			0.760949	+	0.648812i	$0.224734\pi$
$824$		−	4.21069e45i		−	0.0932218i
$825$	8.82139e45	+	1.35707e45i	0.191546	+	0.0294671i
$826$	2.55899e46			0.544990
$827$		−	4.31119e46i		−	0.900551i	−0.892890	−	0.450276i	$-0.851326\pi$
$827$		−	4.31119e46i		−	0.900551i	0.892890	−	0.450276i	$-0.148674\pi$
$828$	−2.15918e46	+	6.85163e46i	−0.442389	+	1.40381i
$829$	−6.45320e46			−1.29689			−0.648444	−	0.761262i	$-0.724580\pi$
$829$	−6.45320e46			−1.29689			−0.648444	+	0.761262i	$0.724580\pi$
$830$			3.88604e46i			0.766052i
$831$	−1.32051e46	+	8.58375e46i	−0.255344	+	1.65982i
$832$	1.17204e46			0.222315
$833$		−	2.18240e45i		−	0.0406082i
$834$	3.94229e44	+	6.06475e43i	0.00719602	+	0.00110702i
$835$	3.68943e46			0.660656
$836$			2.47826e46i			0.435358i
$837$	1.09919e46	−	2.23020e46i	0.189438	−	0.384359i
$838$	−3.25796e46			−0.550861
$839$			8.91849e44i			0.0147945i	0.999973	+	0.00739725i	$0.00235464\pi$
$839$			8.91849e44i			0.0147945i	−0.999973	+	0.00739725i	$0.997645\pi$
$840$	6.60198e45	−	4.29151e46i	0.107450	−	0.698460i
$841$	−2.17353e46			−0.347080
$842$		−	1.47530e46i		−	0.231146i
$843$	4.45522e46	+	6.85383e45i	0.684901	+	0.105364i
$844$	−1.62481e46			−0.245089
$845$		−	1.77358e46i		−	0.262509i
$846$	3.40524e46	+	1.07311e46i	0.494564	+	0.155854i
$847$	−5.46514e46			−0.778873
$848$		−	1.98923e46i		−	0.278196i
$849$	8.77863e45	−	5.70640e46i	0.120477	−	0.783140i
$850$	7.71188e45			0.103862
$851$			6.93546e46i			0.916647i
$852$	7.20869e46	+	1.10897e46i	0.935024	+	0.143842i
$853$	−2.65966e46			−0.338565			−0.169283	−	0.985568i	$-0.554145\pi$
$853$	−2.65966e46			−0.338565			−0.169283	+	0.985568i	$0.554145\pi$
$854$			1.37830e46i			0.172195i
$855$	2.22159e46	−	7.04967e46i	0.272400	−	0.864392i
$856$	−4.04554e45			−0.0486851
$857$		−	1.45906e47i		−	1.72338i	−0.507436	−	0.861689i	$-0.669407\pi$
$857$		−	1.45906e47i		−	1.72338i	0.507436	−	0.861689i	$-0.330593\pi$
$858$	3.75944e45	−	2.44376e46i	0.0435839	−	0.283310i
$859$	−8.28772e46			−0.943071			−0.471536	−	0.881847i	$-0.656300\pi$
$859$	−8.28772e46			−0.943071			−0.471536	+	0.881847i	$0.656300\pi$
$860$			7.66212e46i			0.855803i
$861$	−5.19022e46	−	7.98453e45i	−0.569030	−	0.0875385i
$862$	−1.45789e45			−0.0156895
$863$		−	1.45539e47i		−	1.53748i	−0.639564	−	0.768738i	$-0.720885\pi$
$863$		−	1.45539e47i		−	1.53748i	0.639564	−	0.768738i	$-0.279115\pi$
$864$	8.91172e46	+	4.39229e46i	0.924148	+	0.455482i
$865$	−8.02831e46			−0.817272
$866$			1.94419e46i			0.194290i
$867$	−1.10135e46	+	7.15912e46i	−0.108048	+	0.702351i
$868$	−3.47391e46			−0.334583
$869$			1.39015e46i			0.131446i
$870$	−4.80379e46	−	7.39006e45i	−0.445940	−	0.0686025i
$871$	2.21928e47			2.02266
$872$			1.29046e46i			0.115473i
$873$	−1.43569e47	−	4.52436e46i	−1.26134	−	0.397492i
$874$	−1.30550e47			−1.12615
$875$			1.32947e47i			1.12603i
$876$	5.12615e45	−	3.33217e46i	0.0426310	−	0.277116i
$877$	1.39827e47			1.14182			0.570911	−	0.821012i	$-0.306590\pi$
$877$	1.39827e47			1.14182			0.570911	+	0.821012i	$0.306590\pi$
$878$			2.37076e46i			0.190097i
$879$	1.65126e47	+	2.54027e46i	1.30015	+	0.200013i
$880$	−1.61387e46			−0.124780
$881$			4.31984e46i			0.327984i	0.986462	+	0.163992i	$0.0524372\pi$
$881$			4.31984e46i			0.327984i	−0.986462	+	0.163992i	$0.947563\pi$
$882$	1.51264e45	−	4.79999e45i	0.0112782	−	0.0357885i
$883$	−3.15126e46			−0.230735			−0.115368	−	0.993323i	$-0.536805\pi$
$883$	−3.15126e46			−0.230735			−0.115368	+	0.993323i	$0.536805\pi$
$884$			6.50980e46i			0.468092i
$885$	−1.78018e46	+	1.15718e47i	−0.125711	+	0.817163i
$886$	−4.03683e46			−0.279963
$887$			1.48664e47i			1.01258i	0.862364	+	0.506289i	$0.168983\pi$
$887$			1.48664e47i			1.01258i	−0.862364	+	0.506289i	$0.831017\pi$
$888$	6.03660e46	+	9.28659e45i	0.403817	+	0.0621225i
$889$	2.72894e47			1.79294
$890$		−	2.64084e46i		−	0.170413i
$891$	4.51348e46	−	6.45003e46i	0.286068	−	0.408807i
$892$	−1.01492e47			−0.631823
$893$		−	1.97705e47i		−	1.20891i
$894$	−8.42162e45	+	5.47434e46i	−0.0505819	+	0.328800i
$895$	−1.30600e47			−0.770502
$896$		−	1.67260e47i		−	0.969315i
$897$	−3.92262e47	−	6.03448e46i	−2.23304	−	0.343527i
$898$	9.80820e46			0.548489
$899$			9.05336e46i			0.497342i
$900$	−5.16836e46	−	1.62873e46i	−0.278915	−	0.0878958i
$901$	−8.82741e46			−0.467990
$902$		−	2.64367e46i		−	0.137690i
$903$	−4.47912e46	+	2.91158e47i	−0.229186	+	1.48979i
$904$	1.11773e47			0.561878
$905$		−	3.87784e46i		−	0.191519i
$906$	−5.08263e46	−	7.81902e45i	−0.246625	−	0.0379404i
$907$	2.38350e46			0.113631			0.0568157	−	0.998385i	$-0.481905\pi$
$907$	2.38350e46			0.113631			0.0568157	+	0.998385i	$0.481905\pi$
$908$		−	3.88873e46i		−	0.182152i
$909$	8.59848e46	−	2.72851e47i	0.395731	−	1.25575i
$910$	1.03032e47			0.465920
$911$		−	1.76038e47i		−	0.782190i	−0.920350	−	0.391095i	$-0.872096\pi$
$911$		−	1.76038e47i		−	0.782190i	0.920350	−	0.391095i	$-0.127904\pi$
$912$	1.29061e46	−	8.38942e46i	0.0563480	−	0.366281i
$913$	2.29190e47			0.983247
$914$		−	1.63440e47i		−	0.689000i
$915$	−6.23271e46	−	9.58828e45i	−0.258190	−	0.0397195i
$916$	1.85966e47			0.757016
$917$			1.56487e47i			0.625992i
$918$	3.00717e46	−	6.10140e46i	0.118216	−	0.239854i
$919$	−1.98683e47			−0.767561			−0.383781	−	0.923424i	$-0.625378\pi$
$919$	−1.98683e47			−0.767561			−0.383781	+	0.923424i	$0.625378\pi$
$920$		−	3.50873e47i		−	1.33212i
$921$	−1.44378e45	+	9.38503e45i	−0.00538698	+	0.0350172i
$922$	1.10315e47			0.404518
$923$			4.02936e47i			1.45214i
$924$	−1.08713e47	−	1.67242e46i	−0.385061	−	0.0592370i
$925$	−5.23159e46			−0.182124
$926$			4.70314e46i			0.160921i
$927$	3.03421e46	+	9.56183e45i	0.102040	+	0.0321562i
$928$	−3.61765e47			−1.19580
$929$			4.91494e47i			1.59686i	0.602088	+	0.798430i	$0.294336\pi$
$929$			4.91494e47i			1.59686i	−0.602088	+	0.798430i	$0.705664\pi$
$930$	−7.93102e45	+	5.15543e46i	−0.0253281	+	0.164641i
$931$	−2.78683e46			−0.0874813
$932$			9.22353e46i			0.284605i
$933$	2.34692e47	+	3.61045e46i	0.711855	+	0.109510i
$934$	−9.22056e46			−0.274921
$935$			7.16174e46i			0.209910i
$936$	−1.05048e47	+	3.33343e47i	−0.302673	+	0.960456i
$937$	1.90187e46			0.0538700			0.0269350	−	0.999637i	$-0.491425\pi$
$937$	1.90187e46			0.0538700			0.0269350	+	0.999637i	$0.491425\pi$
$938$			3.24003e47i			0.902202i
$939$	5.67653e46	−	3.68994e47i	0.155394	−	1.01011i
$940$	2.28230e47			0.614224
$941$		−	5.88799e47i		−	1.55788i	−0.627100	−	0.778939i	$-0.715758\pi$
$941$		−	5.88799e47i		−	1.55788i	0.627100	−	0.778939i	$-0.284242\pi$
$942$	2.19072e47	+	3.37016e46i	0.569865	+	0.0876670i
$943$	−4.24351e47			−1.08527
$944$			1.34450e47i			0.338073i
$945$	2.94253e47	+	1.45027e47i	0.727465	+	0.358543i
$946$	−1.48303e47			−0.360490
$947$			3.72450e47i			0.890161i	0.895491	+	0.445080i	$0.146825\pi$
$947$			3.72450e47i			0.890161i	−0.895491	+	0.445080i	$0.853175\pi$
$948$	1.28335e46	−	8.34219e46i	0.0301586	−	0.196041i
$949$	1.86255e47			0.430376
$950$		−	9.84774e46i		−	0.223748i
$951$	6.01391e47	+	9.25168e46i	1.34360	+	0.206696i
$952$	−2.21269e47			−0.486105
$953$		−	7.63371e47i		−	1.64911i	−0.565783	−	0.824554i	$-0.691426\pi$
$953$		−	7.63371e47i		−	1.64911i	0.565783	−	0.824554i	$-0.308574\pi$
$954$	−1.94151e47	−	6.11837e46i	−0.412445	−	0.129975i
$955$	−1.32384e47			−0.276555
$956$			9.47363e45i			0.0194621i
$957$	−4.35848e46	+	2.83316e47i	−0.0880531	+	0.572375i
$958$	−1.15623e47			−0.229719
$959$		−	5.19181e47i		−	1.01443i
$960$	−7.73766e46	−	1.19035e46i	−0.148686	−	0.0228736i
$961$	−4.31984e47			−0.816381
$962$			1.44929e47i			0.269373i
$963$	9.18680e45	−	2.91520e46i	0.0167936	−	0.0532903i
$964$	3.95991e47			0.711955
$965$		−	2.31675e47i		−	0.409677i
$966$	8.81000e46	−	5.72680e47i	0.153229	−	0.996043i
$967$	−1.08220e47			−0.185134			−0.0925669	−	0.995706i	$-0.529507\pi$
$967$	−1.08220e47			−0.185134			−0.0925669	+	0.995706i	$0.529507\pi$
$968$			3.88918e47i			0.654413i
$969$	−3.72290e47	−	5.72724e46i	−0.616170	−	0.0947905i
$970$	3.15791e47			0.514105
$971$		−	4.75830e47i		−	0.761982i	−0.924579	−	0.380991i	$-0.875583\pi$
$971$		−	4.75830e47i		−	0.761982i	0.924579	−	0.380991i	$-0.124417\pi$
$972$	−3.30395e47	+	3.45394e47i	−0.520443	+	0.544069i
$973$	9.80282e45			0.0151896
$974$			2.14077e47i			0.326307i
$975$	4.55196e46	−	2.95893e47i	0.0682534	−	0.443670i
$976$	−7.24166e46			−0.106817
$977$		−	3.83901e46i		−	0.0557065i	−0.999612	−	0.0278532i	$-0.991133\pi$
$977$		−	3.83901e46i		−	0.0557065i	0.999612	−	0.0278532i	$-0.00886711\pi$
$978$	7.06204e46	+	1.08641e46i	0.100811	+	0.0155086i
$979$	−1.55750e47			−0.218729
$980$		−	3.21710e46i		−	0.0444475i
$981$	−9.29905e46	−	2.93045e46i	−0.126396	−	0.0398318i
$982$	7.29911e47			0.976081
$983$		−	1.04363e47i		−	0.137306i	−0.997641	−	0.0686531i	$-0.978130\pi$
$983$		−	1.04363e47i		−	0.137306i	0.997641	−	0.0686531i	$-0.0218702\pi$
$984$	−5.68206e46	+	3.69353e47i	−0.0735503	+	0.478102i
$985$	−3.54159e47			−0.451044
$986$			2.47682e47i			0.310359i
$987$	8.67265e47	+	1.33418e47i	1.06925	+	0.164491i
$988$	8.31273e47			1.00840
$989$			2.38050e48i			2.84137i
$990$	−4.96387e46	+	1.57516e47i	−0.0582985	+	0.184996i
$991$	−6.69689e47			−0.773917			−0.386959	−	0.922097i	$-0.626474\pi$
$991$	−6.69689e47			−0.773917			−0.386959	+	0.922097i	$0.626474\pi$
$992$			3.88247e47i			0.441490i
$993$	−5.41373e46	+	3.51911e47i	−0.0605771	+	0.393772i
$994$	−5.88264e47			−0.647725
$995$		−	1.05874e48i		−	1.14715i
$996$	−1.37535e48	−	2.11581e47i	−1.46644	−	0.225594i
$997$	6.01354e47			0.630968			0.315484	−	0.948931i	$-0.397833\pi$
$997$	6.01354e47			0.630968			0.315484	+	0.948931i	$0.397833\pi$
$998$		−	5.48916e47i		−	0.566783i
$999$	−2.04001e47	+	4.13907e47i	−0.207293	+	0.420586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.33.b.a.2.6	yes	10
3.2	odd	2	inner	3.33.b.a.2.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.33.b.a.2.5	✓	10	3.2	odd	2	inner
3.33.b.a.2.6	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)

\(f(q)\)	\(=\)	\(q+32576.8i q^{2} +(-6.54523e6 + 4.25462e7i) q^{3} +3.23372e9 q^{4} -1.19330e11i q^{5} +(-1.38602e12 - 2.13223e11i) q^{6} -3.44644e13 q^{7} +2.45260e14i q^{8} +(-1.76734e15 - 5.56949e14i) q^{9} +O(q^{10})\)	\(q+32576.8i q^{2} +(-6.54523e6 + 4.25462e7i) q^{3} +3.23372e9 q^{4} -1.19330e11i q^{5} +(-1.38602e12 - 2.13223e11i) q^{6} -3.44644e13 q^{7} +2.45260e14i q^{8} +(-1.76734e15 - 5.56949e14i) q^{9} +3.88740e15 q^{10} -2.29269e16i q^{11} +(-2.11654e16 + 1.37583e17i) q^{12} -7.69030e17 q^{13} -1.12274e18i q^{14} +(5.07705e18 + 7.81044e17i) q^{15} +5.89892e18 q^{16} -2.61771e19i q^{17} +(1.81436e19 - 5.75743e19i) q^{18} -3.34271e20 q^{19} -3.85880e20i q^{20} +(2.25578e20 - 1.46633e21i) q^{21} +7.46886e20 q^{22} -1.19887e22i q^{23} +(-1.04349e22 - 1.60529e21i) q^{24} +9.04337e21 q^{25} -2.50525e22i q^{26} +(3.52637e22 - 7.15483e22i) q^{27} -1.11448e23 q^{28} +2.90445e23i q^{29} +(-2.54439e22 + 1.65394e23i) q^{30} +3.11706e23 q^{31} +1.24555e24i q^{32} +(9.75454e23 + 1.50062e23i) q^{33} +8.52767e23 q^{34} +4.11265e24i q^{35} +(-5.71508e24 - 1.80102e24i) q^{36} -5.78500e24 q^{37} -1.08895e25i q^{38} +(5.03348e24 - 3.27193e25i) q^{39} +2.92670e25 q^{40} -3.53959e25i q^{41} +(4.77684e25 + 7.34860e24i) q^{42} -1.98562e26 q^{43} -7.41393e25i q^{44} +(-6.64609e25 + 2.10897e26i) q^{45} +3.90553e26 q^{46} +5.91452e26i q^{47} +(-3.86098e25 + 2.50977e26i) q^{48} +8.33704e25 q^{49} +2.94604e26i q^{50} +(1.11374e27 + 1.71335e26i) q^{51} -2.48683e27 q^{52} -3.37218e27i q^{53} +(2.33081e27 + 1.14878e27i) q^{54} -2.73588e27 q^{55} -8.45277e27i q^{56} +(2.18788e27 - 1.42219e28i) q^{57} -9.46178e27 q^{58} +2.27924e28i q^{59} +(1.64178e28 + 2.52568e27i) q^{60} -1.22762e28 q^{61} +1.01544e28i q^{62} +(6.09104e28 + 1.91950e28i) q^{63} -1.52405e28 q^{64} +9.17685e28i q^{65} +(-4.88854e27 + 3.17772e28i) q^{66} -2.88582e29 q^{67} -8.46495e28i q^{68} +(5.10073e29 + 7.84687e28i) q^{69} -1.33977e29 q^{70} -5.23954e29i q^{71} +(1.36598e29 - 4.33459e29i) q^{72} -2.42194e29 q^{73} -1.88457e29i q^{74} +(-5.91909e28 + 3.84761e29i) q^{75} -1.08094e30 q^{76} +7.90164e29i q^{77} +(1.06589e30 + 1.63975e29i) q^{78} -6.06341e29 q^{79} -7.03919e29i q^{80} +(2.81330e30 + 1.96864e30i) q^{81} +1.15309e30 q^{82} +9.99652e30i q^{83} +(7.29455e29 - 4.74171e30i) q^{84} -3.12372e30 q^{85} -6.46852e30i q^{86} +(-1.23574e31 - 1.90103e30i) q^{87} +5.62307e30 q^{88} -6.79334e30i q^{89} +(-6.87035e30 - 2.16508e30i) q^{90} +2.65042e31 q^{91} -3.87681e31i q^{92} +(-2.04019e30 + 1.32619e31i) q^{93} -1.92676e31 q^{94} +3.98886e31i q^{95} +(-5.29936e31 - 8.15243e30i) q^{96} +8.12346e31 q^{97} +2.71594e30i q^{98} +(-1.27691e31 + 4.05197e31i) 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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