LMFDB - Embedded newform 21.9.f.b.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,9,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, degree $2$, 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:	$8.55495081128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 1331 x^{10} + 1482 x^{9} + 1359381 x^{8} + 1222227 x^{7} + 474169529 x^{6} + \cdots + 556282980265104 $ x^12 - 3x^11 + 1331x^10 + 1482x^9 + 1359381x^8 + 1222227x^7 + 474169529x^6 + 1911324162x^5 + 121870629463x^4 + 259296590901x^3 + 9508380016437x^2 - 12075311354004*x + 556282980265104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Root			$-14.8255 - 25.6786i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.9.f.b.10.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.3255 - 26.5446i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-341.745 - 591.919i) q^{4} +(563.914 + 325.576i) q^{5} -1433.41i q^{6} +(-1071.89 - 2148.45i) q^{7} -13103.0 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})$	\(q+(15.3255 - 26.5446i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-341.745 - 591.919i) q^{4} +(563.914 + 325.576i) q^{5} -1433.41i q^{6} +(-1071.89 - 2148.45i) q^{7} -13103.0 q^{8} +(1093.50 - 1894.00i) q^{9} +(17284.6 - 9979.26i) q^{10} +(12256.7 + 21229.2i) q^{11} +(-27681.3 - 15981.8i) q^{12} +1952.42i q^{13} +(-73457.2 - 4473.33i) q^{14} +30451.4 q^{15} +(-113324. + 196283. i) q^{16} +(54853.7 - 31669.8i) q^{17} +(-33517.0 - 58053.1i) q^{18} +(-19861.3 - 11467.0i) q^{19} -445055. i q^{20} +(-93648.1 - 61948.7i) q^{21} +751363. q^{22} +(65128.8 - 112806. i) q^{23} +(-530672. + 306383. i) q^{24} +(16687.1 + 28902.8i) q^{25} +(51826.1 + 29921.8i) q^{26} -102276. i q^{27} +(-905398. + 1.36869e6i) q^{28} +415506. q^{29} +(466684. - 808320. i) q^{30} +(950531. - 548789. i) q^{31} +(1.79632e6 + 3.11132e6i) q^{32} +(992793. + 573190. i) q^{33} -1.94143e6i q^{34} +(95031.5 - 1.56053e6i) q^{35} -1.49479e6 q^{36} +(-636959. + 1.10325e6i) q^{37} +(-608772. + 351475. i) q^{38} +(45652.7 + 79072.9i) q^{39} +(-7.38897e6 - 4.26602e6i) q^{40} +4.21678e6i q^{41} +(-3.07961e6 + 1.53646e6i) q^{42} -1.04779e6 q^{43} +(8.37733e6 - 1.45100e7i) q^{44} +(1.23328e6 - 712035. i) q^{45} +(-1.99627e6 - 3.45764e6i) q^{46} +(-1.94584e6 - 1.12343e6i) q^{47} +1.05993e7i q^{48} +(-3.46691e6 + 4.60581e6i) q^{49} +1.02295e6 q^{50} +(1.48105e6 - 2.56525e6i) q^{51} +(1.15567e6 - 667228. i) q^{52} +(1.65326e6 + 2.86353e6i) q^{53} +(-2.71487e6 - 1.56743e6i) q^{54} +1.59620e7i q^{55} +(1.40450e7 + 2.81512e7i) q^{56} -1.07251e6 q^{57} +(6.36785e6 - 1.10294e7i) q^{58} +(-1.48113e7 + 8.55134e6i) q^{59} +(-1.04066e7 - 1.80247e7i) q^{60} +(2.44056e6 + 1.40906e6i) q^{61} -3.36420e7i q^{62} +(-5.24128e6 - 319179. i) q^{63} +5.20964e7 q^{64} +(-635660. + 1.10100e6i) q^{65} +(3.04302e7 - 1.75689e7i) q^{66} +(1.33511e7 + 2.31248e7i) q^{67} +(-3.74919e7 - 2.16460e7i) q^{68} -6.09154e6i q^{69} +(-3.99671e7 - 2.64385e7i) q^{70} +1.07071e7 q^{71} +(-1.43281e7 + 2.48171e7i) q^{72} +(-2.55681e7 + 1.47617e7i) q^{73} +(1.95235e7 + 3.38157e7i) q^{74} +(1.35165e6 + 780377. i) q^{75} +1.56751e7i q^{76} +(3.24722e7 - 4.90884e7i) q^{77} +2.79861e6 q^{78} +(-1.28884e7 + 2.23234e7i) q^{79} +(-1.27810e8 + 7.37912e7i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(1.11933e8 + 6.46245e7i) q^{82} -8.30488e7i q^{83} +(-4.66489e6 + 7.66027e7i) q^{84} +4.12437e7 q^{85} +(-1.60580e7 + 2.78132e7i) q^{86} +(1.68280e7 - 9.71565e6i) q^{87} +(-1.60600e8 - 2.78167e8i) q^{88} +(3.82648e7 + 2.20922e7i) q^{89} -4.36493e7i q^{90} +(4.19468e6 - 2.09277e6i) q^{91} -8.90296e7 q^{92} +(2.56643e7 - 4.44519e7i) q^{93} +(-5.96423e7 + 3.44345e7i) q^{94} +(-7.46673e6 - 1.29328e7i) q^{95} +(1.45502e8 + 8.40056e7i) q^{96} +3.44602e7i q^{97} +(6.91272e7 + 1.62614e8i) q^{98} +5.36108e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	15.3255	−	26.5446i	0.957846	−	1.65904i	0.230131	−	0.973160i	$-0.426085\pi$
$2$	15.3255	−	26.5446i	0.957846	−	1.65904i	0.727716	−	0.685879i	$-0.240582\pi$
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$4$	−341.745	−	591.919i	−1.33494	−	2.31218i
$5$	563.914	+	325.576i	0.902263	+	0.520922i	0.877934	−	0.478782i	$-0.158922\pi$
$5$	563.914	+	325.576i	0.902263	+	0.520922i	0.0243292	+	0.999704i	$0.492255\pi$
$6$		−	1433.41i		−	1.10603i
$7$	−1071.89	−	2148.45i	−0.446435	−	0.894816i
$7$	−1071.89	−	2148.45i	−0.446435	−	0.894816i
$8$	−13103.0			−3.19898
$9$	1093.50	−	1894.00i	0.166667	−	0.288675i
$10$	17284.6	−	9979.26i	1.72846	−	0.997926i
$11$	12256.7	+	21229.2i	0.837150	+	1.44999i	0.892268	+	0.451506i	$0.149113\pi$
$11$	12256.7	+	21229.2i	0.837150	+	1.44999i	−0.0551184	+	0.998480i	$0.517554\pi$
$12$	−27681.3	−	15981.8i	−1.33494	−	0.770728i
$13$			1952.42i			0.0683595i	0.999416	+	0.0341798i	$0.0108819\pi$
$13$			1952.42i			0.0683595i	−0.999416	+	0.0341798i	$0.989118\pi$
$14$	−73457.2	−	4473.33i	−1.91215	−	0.116444i
$15$	30451.4			0.601509
$16$	−113324.	+	196283.i	−1.72919	+	2.99504i
$17$	54853.7	−	31669.8i	0.656766	−	0.379184i	−0.134278	−	0.990944i	$-0.542871\pi$
$17$	54853.7	−	31669.8i	0.656766	−	0.379184i	0.791044	+	0.611760i	$0.209538\pi$
$18$	−33517.0	−	58053.1i	−0.319282	−	0.553013i
$19$	−19861.3	−	11467.0i	−0.152403	−	0.0879901i	0.421859	−	0.906661i	$-0.361378\pi$
$19$	−19861.3	−	11467.0i	−0.152403	−	0.0879901i	−0.574262	+	0.818671i	$0.694711\pi$
$20$		−	445055.i		−	2.78160i
$21$	−93648.1	−	61948.7i	−0.481528	−	0.318534i
$22$	751363.			3.20744
$23$	65128.8	−	112806.i	0.232735	−	0.403109i	−0.725877	−	0.687824i	$-0.758566\pi$
$23$	65128.8	−	112806.i	0.232735	−	0.403109i	0.958612	+	0.284716i	$0.0918992\pi$
$24$	−530672.	+	306383.i	−1.59949	+	0.923465i
$25$	16687.1	+	28902.8i	0.0427189	+	0.0739913i
$26$	51826.1	+	29921.8i	0.113411	+	0.0654779i
$27$		−	102276.i		−	0.192450i
$28$	−905398.	+	1.36869e6i	−1.47302	+	2.22676i
$29$	415506.			0.587469			0.293735	−	0.955887i	$-0.405102\pi$
$29$	415506.			0.587469			0.293735	+	0.955887i	$0.405102\pi$
$30$	466684.	−	808320.i	0.576153	−	0.997926i
$31$	950531.	−	548789.i	1.02925	−	0.594236i	0.112478	−	0.993654i	$-0.464121\pi$
$31$	950531.	−	548789.i	1.02925	−	0.594236i	0.916769	+	0.399418i	$0.130788\pi$
$32$	1.79632e6	+	3.11132e6i	1.71310	+	2.96718i
$33$	992793.	+	573190.i	0.837150	+	0.483329i
$34$		−	1.94143e6i		−	1.45280i
$35$	95031.5	−	1.56053e6i	0.0633280	−	1.03992i
$36$	−1.49479e6			−0.889960
$37$	−636959.	+	1.10325e6i	−0.339864	+	0.588661i	−0.984407	−	0.175907i	$-0.943714\pi$
$37$	−636959.	+	1.10325e6i	−0.339864	+	0.588661i	0.644543	+	0.764568i	$0.277048\pi$
$38$	−608772.	+	351475.i	−0.291958	+	0.168562i
$39$	45652.7	+	79072.9i	0.0197337	+	0.0341798i
$40$	−7.38897e6	−	4.26602e6i	−2.88632	−	1.66642i
$41$			4.21678e6i			1.49226i	0.665798	+	0.746132i	$0.268091\pi$
$41$			4.21678e6i			1.49226i	−0.665798	+	0.746132i	$0.731909\pi$
$42$	−3.07961e6	+	1.53646e6i	−0.989690	+	0.493768i
$43$	−1.04779e6			−0.306479			−0.153240	−	0.988189i	$-0.548971\pi$
$43$	−1.04779e6			−0.306479			−0.153240	+	0.988189i	$0.548971\pi$
$44$	8.37733e6	−	1.45100e7i	2.23509	−	3.87129i
$45$	1.23328e6	−	712035.i	0.300754	−	0.173641i
$46$	−1.99627e6	−	3.45764e6i	−0.445849	−	0.772232i
$47$	−1.94584e6	−	1.12343e6i	−0.398765	−	0.230227i	0.287186	−	0.957875i	$-0.407280\pi$
$47$	−1.94584e6	−	1.12343e6i	−0.398765	−	0.230227i	−0.685951	+	0.727648i	$0.740614\pi$
$48$			1.05993e7i			1.99669i
$49$	−3.46691e6	+	4.60581e6i	−0.601392	+	0.798954i
$50$	1.02295e6			0.163672
$51$	1.48105e6	−	2.56525e6i	0.218922	−	0.379184i
$52$	1.15567e6	−	667228.i	0.158060	−	0.0912558i
$53$	1.65326e6	+	2.86353e6i	0.209526	+	0.362909i	0.951565	−	0.307447i	$-0.0994747\pi$
$53$	1.65326e6	+	2.86353e6i	0.209526	+	0.362909i	−0.742040	+	0.670356i	$0.766141\pi$
$54$	−2.71487e6	−	1.56743e6i	−0.319282	−	0.184338i
$55$			1.59620e7i			1.74436i
$56$	1.40450e7	+	2.81512e7i	1.42813	+	2.86250i
$57$	−1.07251e6			−0.101602
$58$	6.36785e6	−	1.10294e7i	0.562706	−	0.974635i
$59$	−1.48113e7	+	8.55134e6i	−1.22232	+	0.705709i	−0.965413	−	0.260725i	$-0.916038\pi$
$59$	−1.48113e7	+	8.55134e6i	−1.22232	+	0.705709i	−0.256912	+	0.966435i	$0.582705\pi$
$60$	−1.04066e7	−	1.80247e7i	−0.802978	−	1.39080i
$61$	2.44056e6	+	1.40906e6i	0.176267	+	0.101768i	0.585538	−	0.810645i	$-0.300883\pi$
$61$	2.44056e6	+	1.40906e6i	0.176267	+	0.101768i	−0.409271	+	0.912413i	$0.634217\pi$
$62$		−	3.36420e7i		−	2.27675i
$63$	−5.24128e6	−	319179.i	−0.332717	−	0.0202615i
$64$	5.20964e7			3.10519
$65$	−635660.	+	1.10100e6i	−0.0356100	+	0.0616783i
$66$	3.04302e7	−	1.75689e7i	1.60372	−	0.925909i
$67$	1.33511e7	+	2.31248e7i	0.662550	+	1.14757i	0.979943	+	0.199276i	$0.0638591\pi$
$67$	1.33511e7	+	2.31248e7i	0.662550	+	1.14757i	−0.317393	+	0.948294i	$0.602808\pi$
$68$	−3.74919e7	−	2.16460e7i	−1.75348	−	1.01237i
$69$		−	6.09154e6i		−	0.268739i
$70$	−3.99671e7	−	2.64385e7i	−1.66460	−	1.10114i
$71$	1.07071e7			0.421347			0.210674	−	0.977556i	$-0.432434\pi$
$71$	1.07071e7			0.421347			0.210674	+	0.977556i	$0.432434\pi$
$72$	−1.43281e7	+	2.48171e7i	−0.533163	+	0.923465i
$73$	−2.55681e7	+	1.47617e7i	−0.900340	+	0.519812i	−0.877310	−	0.479923i	$-0.840665\pi$
$73$	−2.55681e7	+	1.47617e7i	−0.900340	+	0.519812i	−0.0230295	+	0.999735i	$0.507331\pi$
$74$	1.95235e7	+	3.38157e7i	0.651075	+	1.12769i
$75$	1.35165e6	+	780377.i	0.0427189	+	0.0246638i
$76$			1.56751e7i			0.469846i
$77$	3.24722e7	−	4.90884e7i	0.923738	−	1.39642i
$78$	2.79861e6			0.0756074
$79$	−1.28884e7	+	2.23234e7i	−0.330896	+	0.573129i	−0.982688	−	0.185269i	$-0.940684\pi$
$79$	−1.28884e7	+	2.23234e7i	−0.330896	+	0.573129i	0.651791	+	0.758398i	$0.274018\pi$
$80$	−1.27810e8	+	7.37912e7i	−3.12036	+	1.80154i
$81$	−2.39148e6	−	4.14217e6i	−0.0555556	−	0.0962250i
$82$	1.11933e8	+	6.46245e7i	2.47572	+	1.42936i
$83$		−	8.30488e7i		−	1.74993i	−0.484185	−	0.874966i	$-0.660884\pi$
$83$		−	8.30488e7i		−	1.74993i	0.484185	−	0.874966i	$-0.339116\pi$
$84$	−4.66489e6	+	7.66027e7i	−0.0936966	+	1.53861i
$85$	4.12437e7			0.790100
$86$	−1.60580e7	+	2.78132e7i	−0.293560	+	0.508461i
$87$	1.68280e7	−	9.71565e6i	0.293735	−	0.169588i
$88$	−1.60600e8	−	2.78167e8i	−2.67802	−	4.63847i
$89$	3.82648e7	+	2.20922e7i	0.609874	+	0.352111i	0.772916	−	0.634508i	$-0.218797\pi$
$89$	3.82648e7	+	2.20922e7i	0.609874	+	0.352111i	−0.163042	+	0.986619i	$0.552131\pi$
$90$		−	4.36493e7i		−	0.665284i
$91$	4.19468e6	−	2.09277e6i	0.0611692	−	0.0305180i
$92$	−8.90296e7			−1.24275
$93$	2.56643e7	−	4.44519e7i	0.343082	−	0.594236i
$94$	−5.96423e7	+	3.44345e7i	−0.763911	+	0.441044i
$95$	−7.46673e6	−	1.29328e7i	−0.0916719	−	0.158780i
$96$	1.45502e8	+	8.40056e7i	1.71310	+	0.989061i
$97$			3.44602e7i			0.389252i	0.980878	+	0.194626i	$0.0623493\pi$
$97$			3.44602e7i			0.389252i	−0.980878	+	0.194626i	$0.937651\pi$
$98$	6.91272e7	+	1.62614e8i	0.749454	+	1.76301i
$99$	5.36108e7			0.558100
$100$	1.14054e7	−	1.97548e7i	0.114054	−	0.197548i
$101$	2.88103e7	−	1.66336e7i	0.276861	−	0.159846i	−0.355140	−	0.934813i	$-0.615567\pi$
$101$	2.88103e7	−	1.66336e7i	0.276861	−	0.159846i	0.632002	+	0.774967i	$0.282234\pi$
$102$	−4.53958e7	−	7.86278e7i	−0.419387	−	0.726400i
$103$	−1.60995e8	−	9.29506e7i	−1.43042	−	0.825854i	−0.433269	−	0.901265i	$-0.642640\pi$
$103$	−1.60995e8	−	9.29506e7i	−1.43042	−	0.825854i	−0.997153	+	0.0754108i	$0.975973\pi$
$104$		−	2.55825e7i		−	0.218680i
$105$	−3.26405e7	−	6.54234e7i	−0.268534	−	0.538240i
$106$	1.01348e8			0.802774
$107$	383824.	−	664802.i	0.00292817	−	0.00507174i	−0.864558	−	0.502534i	$-0.832401\pi$
$107$	383824.	−	664802.i	0.00292817	−	0.00507174i	0.867486	+	0.497462i	$0.165735\pi$
$108$	−6.05390e7	+	3.49522e7i	−0.444980	+	0.256909i
$109$	2.21977e7	+	3.84475e7i	0.157254	+	0.272372i	0.933877	−	0.357593i	$-0.116403\pi$
$109$	2.21977e7	+	3.84475e7i	0.157254	+	0.272372i	−0.776624	+	0.629965i	$0.783069\pi$
$110$	4.23704e8	+	2.44626e8i	2.89396	+	1.67083i
$111$			5.95753e7i			0.392441i
$112$	5.43176e8	+	3.30778e7i	3.45198	+	0.210216i
$113$	−2.61458e8			−1.60357			−0.801784	−	0.597613i	$-0.796116\pi$
$113$	−2.61458e8			−1.60357			−0.801784	+	0.597613i	$0.796116\pi$
$114$	−1.64368e7	+	2.84694e7i	−0.0973193	+	0.168562i
$115$	7.34541e7	−	4.24087e7i	0.419976	−	0.242473i
$116$	−1.41997e8	−	2.45946e8i	−0.784236	−	1.35834i
$117$	3.69787e6	+	2.13497e6i	0.0197337	+	0.0113933i
$118$			5.24215e8i			2.70385i
$119$	−1.26838e8	−	8.39042e7i	−0.632503	−	0.418404i
$120$	−3.99004e8			−1.92421
$121$	−1.93274e8	+	3.34761e8i	−0.901639	+	1.56168i
$122$	7.48059e7	−	4.31892e7i	0.337673	−	0.194956i
$123$	9.85997e7	+	1.70780e8i	0.430780	+	0.746132i
$124$	−6.49678e8	−	3.75091e8i	−2.74796	−	1.58654i
$125$		−	2.32625e8i		−	0.952831i
$126$	−8.87979e7	+	1.34236e8i	−0.352306	+	0.532583i
$127$	2.92944e8			1.12608			0.563040	−	0.826429i	$-0.309632\pi$
$127$	2.92944e8			1.12608			0.563040	+	0.826429i	$0.309632\pi$
$128$	3.38548e8	−	5.86382e8i	1.26119	−	2.18444i
$129$	−4.24356e7	+	2.45002e7i	−0.153240	+	0.0884730i
$130$	1.94837e7	+	3.37467e7i	0.0682177	+	0.118157i
$131$	8.65228e6	+	4.99539e6i	0.0293796	+	0.0169623i	0.514618	−	0.857420i	$-0.327934\pi$
$131$	8.65228e6	+	4.99539e6i	0.0293796	+	0.0169623i	−0.485238	+	0.874382i	$0.661267\pi$
$132$		−	7.83538e8i		−	2.58086i
$133$	−3.34706e6	+	5.49625e7i	−0.0106969	+	0.175655i
$134$	8.18453e8			2.53848
$135$	3.32986e7	−	5.76748e7i	0.100251	−	0.173641i
$136$	−7.18748e8	+	4.14970e8i	−2.10098	+	1.21300i
$137$	−1.62696e8	−	2.81798e8i	−0.461843	−	0.799936i	0.537210	−	0.843449i	$-0.319478\pi$
$137$	−1.62696e8	−	2.81798e8i	−0.461843	−	0.799936i	−0.999053	+	0.0435130i	$0.986145\pi$
$138$	−1.61698e8	−	9.33562e7i	−0.445849	−	0.257411i
$139$		−	6.56035e8i		−	1.75739i	−0.477384	−	0.878695i	$-0.658415\pi$
$139$		−	6.56035e8i		−	1.75739i	0.477384	−	0.878695i	$-0.341585\pi$
$140$	−9.56181e8	+	4.77050e8i	−2.48902	+	1.24180i
$141$	−1.05076e8			−0.265843
$142$	1.64093e8	−	2.84217e8i	0.403586	−	0.699031i
$143$	−4.14483e7	+	2.39302e7i	−0.0991203	+	0.0572272i
$144$	2.47840e8	+	4.29271e8i	0.576396	+	0.998347i
$145$	2.34310e8	+	1.35279e8i	0.530052	+	0.306026i
$146$			9.04926e8i			1.99160i
$147$	−3.27136e7	+	2.67601e8i	−0.0700581	+	0.573084i
$148$	8.70710e8			1.81479
$149$	−4.44661e8	+	7.70175e8i	−0.902160	+	1.56259i	−0.0774758	+	0.996994i	$0.524686\pi$
$149$	−4.44661e8	+	7.70175e8i	−0.902160	+	1.56259i	−0.824684	+	0.565593i	$0.808647\pi$
$150$	4.14296e7	−	2.39194e7i	0.0818362	−	0.0472482i
$151$	1.57670e8	+	2.73093e8i	0.303279	+	0.525294i	0.976877	−	0.213804i	$-0.0685853\pi$
$151$	1.57670e8	+	2.73093e8i	0.303279	+	0.525294i	−0.673598	+	0.739098i	$0.735252\pi$
$152$	2.60243e8	+	1.50252e8i	0.487534	+	0.281478i
$153$		−	1.38524e8i		−	0.252789i
$154$	−8.05378e8	−	1.61427e9i	−1.43191	−	2.87007i
$155$	7.14691e8			1.23820
$156$	3.12031e7	−	5.40454e7i	0.0526866	−	0.0912558i
$157$	−4.07436e8	+	2.35233e8i	−0.670596	+	0.387169i	−0.796302	−	0.604899i	$-0.793214\pi$
$157$	−4.07436e8	+	2.35233e8i	−0.670596	+	0.387169i	0.125707	+	0.992067i	$0.459880\pi$
$158$	3.95045e8	+	6.84238e8i	0.633896	+	1.09794i
$159$	1.33914e8	+	7.73152e7i	0.209526	+	0.120970i
$160$			2.33936e9i			3.56957i
$161$	−3.12170e8	−	1.90103e7i	−0.464609	−	0.0282934i
$162$	−1.46603e8			−0.212855
$163$	6.57963e8	−	1.13963e9i	0.932076	−	1.61440i	0.152308	−	0.988333i	$-0.451329\pi$
$163$	6.57963e8	−	1.13963e9i	0.932076	−	1.61440i	0.779767	−	0.626069i	$-0.215337\pi$
$164$	2.49599e9	−	1.44106e9i	3.45039	−	1.99208i
$165$	3.73234e8	+	6.46460e8i	0.503553	+	0.872179i
$166$	−2.20450e9	−	1.27277e9i	−2.90320	−	1.67617i
$167$		−	8.84736e8i		−	1.13749i	−0.822514	−	0.568745i	$-0.807429\pi$
$167$		−	8.84736e8i		−	1.13749i	0.822514	−	0.568745i	$-0.192571\pi$
$168$	1.22707e9	+	8.11714e8i	1.54040	+	1.01898i
$169$	8.11919e8			0.995327
$170$	6.32083e8	−	1.09480e9i	0.756795	−	1.31081i
$171$	−4.34368e7	+	2.50782e7i	−0.0508011	+	0.0293300i
$172$	3.58077e8	+	6.20208e8i	0.409132	+	0.708637i
$173$	−1.81737e8	−	1.04926e8i	−0.202889	−	0.117138i	0.395113	−	0.918632i	$-0.370705\pi$
$173$	−1.81737e8	−	1.04926e8i	−0.202889	−	0.117138i	−0.598003	+	0.801494i	$0.704039\pi$
$174$		−	5.95590e8i		−	0.649756i
$175$	4.42097e7	−	6.68320e7i	0.0471374	−	0.0712578i
$176$	−5.55592e9			−5.79035
$177$	−3.99906e8	+	6.92658e8i	−0.407442	+	0.705709i
$178$	1.17286e9	−	6.77151e8i	1.16833	−	0.674536i
$179$	3.71272e8	+	6.43062e8i	0.361643	+	0.626384i	0.988231	−	0.152966i	$-0.0488826\pi$
$179$	3.71272e8	+	6.43062e8i	0.361643	+	0.626384i	−0.626588	+	0.779350i	$0.715549\pi$
$180$	−8.42934e8	−	4.86668e8i	−0.802978	−	0.463599i
$181$		−	5.39407e8i		−	0.502577i	−0.967912	−	0.251288i	$-0.919146\pi$
$181$		−	5.39407e8i		−	0.502577i	0.967912	−	0.251288i	$-0.0808542\pi$
$182$	8.73381e6	−	1.43419e8i	0.00796009	−	0.130714i
$183$	1.31790e8			0.117511
$184$	−8.53382e8	+	1.47810e9i	−0.744513	+	1.28953i
$185$	−7.18381e8	+	4.14757e8i	−0.613293	+	0.354085i
$186$	−7.86640e8	−	1.36250e9i	−0.657240	−	1.13837i
$187$	1.34465e9	+	7.76335e8i	1.09962	+	0.634867i
$188$			1.53571e9i			1.22936i
$189$	−2.19735e8	+	1.09628e8i	−0.172207	+	0.0859164i
$190$	−4.57727e8			−0.351230
$191$	−2.56904e8	+	4.44971e8i	−0.193036	+	0.334348i	−0.946255	−	0.323422i	$-0.895167\pi$
$191$	−2.56904e8	+	4.44971e8i	−0.193036	+	0.334348i	0.753219	+	0.657770i	$0.228500\pi$
$192$	2.10990e9	−	1.21815e9i	1.55259	−	0.896391i
$193$	−2.20212e8	−	3.81419e8i	−0.158713	−	0.274899i	0.775692	−	0.631112i	$-0.217401\pi$
$193$	−2.20212e8	−	3.81419e8i	−0.158713	−	0.274899i	−0.934405	+	0.356213i	$0.884068\pi$
$194$	9.14732e8	+	5.28121e8i	0.645784	+	0.372843i
$195$			5.94538e7i			0.0411188i
$196$	3.91106e9	+	4.78118e8i	2.65015	+	0.323975i
$197$	−2.91630e8			−0.193628			−0.0968139	−	0.995303i	$-0.530865\pi$
$197$	−2.91630e8			−0.193628			−0.0968139	+	0.995303i	$0.530865\pi$
$198$	8.21615e8	−	1.42308e9i	0.534574	−	0.925909i
$199$	−1.65949e9	+	9.58107e8i	−1.05819	+	0.610944i	−0.924930	−	0.380137i	$-0.875877\pi$
$199$	−1.65949e9	+	9.58107e8i	−1.05819	+	0.610944i	−0.133256	+	0.991082i	$0.542543\pi$
$200$	−2.18651e8	−	3.78714e8i	−0.136657	−	0.236696i
$201$	1.08144e9	+	6.24370e8i	0.662550	+	0.382523i
$202$		−	1.01968e9i		−	0.612432i
$203$	−4.45376e8	−	8.92696e8i	−0.262267	−	0.525677i
$204$	−2.02456e9			−1.16899
$205$	−1.37288e9	+	2.37790e9i	−0.777353	+	1.34641i
$206$	−4.93468e9	+	2.84904e9i	−2.74025	+	1.58208i
$207$	−1.42437e8	−	2.46707e8i	−0.0775783	−	0.134370i
$208$	−3.83226e8	−	2.21256e8i	−0.204740	−	0.118206i
$209$		−	5.62188e8i		−	0.294643i
$210$	−2.23687e9	−	1.36219e8i	−1.15017	−	0.0700424i
$211$	1.33850e9			0.675288			0.337644	−	0.941274i	$-0.390370\pi$
$211$	1.33850e9			0.675288			0.337644	+	0.941274i	$0.390370\pi$
$212$	1.12998e9	−	1.95719e9i	0.559408	−	0.968923i
$213$	4.33639e8	−	2.50362e8i	0.210674	−	0.121632i
$214$	−1.17646e7	−	2.03769e7i	−0.00560948	−	0.00971590i
$215$	−5.90865e8	−	3.41136e8i	−0.276525	−	0.159652i
$216$			1.34012e9i			0.615643i
$217$	−2.19791e9	−	1.45393e9i	−0.991223	−	0.655699i
$218$	1.36076e9			0.602500
$219$	−6.90338e8	+	1.19570e9i	−0.300113	+	0.519812i
$220$	9.44819e9	−	5.45491e9i	4.03327	−	2.32861i
$221$	6.18327e7	+	1.07097e8i	0.0259208	+	0.0448962i
$222$	1.58140e9	+	9.13024e8i	0.651075	+	0.375898i
$223$		−	8.72131e8i		−	0.352665i	−0.984331	−	0.176333i	$-0.943577\pi$
$223$		−	8.72131e8i		−	0.352665i	0.984331	−	0.176333i	$-0.0564234\pi$
$224$	4.75907e9	−	7.19430e9i	1.89030	−	2.85757i
$225$	7.29892e7			0.0284792
$226$	−4.00698e9	+	6.94029e9i	−1.53597	+	2.66038i
$227$	1.55927e9	−	9.00246e8i	0.587244	−	0.339045i	−0.176763	−	0.984253i	$-0.556563\pi$
$227$	1.55927e9	−	9.00246e8i	0.587244	−	0.339045i	0.764007	+	0.645208i	$0.223229\pi$
$228$	3.66525e8	+	6.34840e8i	0.135633	+	0.234923i
$229$	1.10855e9	+	6.40020e8i	0.403099	+	0.232730i	0.687820	−	0.725881i	$-0.258568\pi$
$229$	1.10855e9	+	6.40020e8i	0.403099	+	0.232730i	−0.284721	+	0.958610i	$0.591901\pi$
$230$		−	2.59975e9i		−	0.929009i
$231$	1.67307e8	−	2.74737e9i	0.0587578	−	0.964870i
$232$	−5.44438e9			−1.87930
$233$	−6.63524e8	+	1.14926e9i	−0.225130	+	0.389936i	−0.956358	−	0.292196i	$-0.905614\pi$
$233$	−6.63524e8	+	1.14926e9i	−0.225130	+	0.389936i	0.731229	+	0.682132i	$0.238947\pi$
$234$	1.13344e8	−	6.54391e7i	0.0378037	−	0.0218260i
$235$	−7.31527e8	−	1.26704e9i	−0.239860	−	0.415450i
$236$	1.01234e10	+	5.84474e9i	3.26346	+	1.88416i
$237$			1.20547e9i			0.382086i
$238$	−4.17107e9	+	2.08100e9i	−1.29999	+	0.648580i
$239$	2.12392e9			0.650949			0.325474	−	0.945551i	$-0.394476\pi$
$239$	2.12392e9			0.650949			0.325474	+	0.945551i	$0.394476\pi$
$240$	−3.45087e9	+	5.97709e9i	−1.04012	+	1.80154i
$241$	−2.15256e9	+	1.24278e9i	−0.638097	+	0.368406i	−0.783881	−	0.620911i	$-0.786763\pi$
$241$	−2.15256e9	+	1.24278e9i	−0.638097	+	0.368406i	0.145784	+	0.989316i	$0.453430\pi$
$242$	5.92407e9	+	1.02608e10i	1.72726	+	2.99171i
$243$	−1.93710e8	−	1.11839e8i	−0.0555556	−	0.0320750i
$244$		−	1.92615e9i		−	0.543415i
$245$	−3.45458e9	+	1.46854e9i	−0.958806	+	0.407588i
$246$	6.04438e9			1.65048
$247$	2.23883e7	−	3.87776e7i	0.00601496	−	0.0104182i
$248$	−1.24548e10	+	7.19079e9i	−3.29253	+	1.90095i
$249$	−1.94190e9	−	3.36348e9i	−0.505162	−	0.874966i
$250$	−6.17493e9	−	3.56510e9i	−1.58078	−	0.912665i
$251$		−	6.32961e9i		−	1.59471i	−0.603509	−	0.797356i	$-0.706231\pi$
$251$		−	6.32961e9i		−	1.59471i	0.603509	−	0.797356i	$-0.293769\pi$
$252$	1.60225e9	+	3.21149e9i	0.397309	+	0.796350i
$253$	3.19306e9			0.779336
$254$	4.48952e9	−	7.77608e9i	1.07861	−	1.86821i
$255$	1.67037e9	−	9.64389e8i	0.395050	−	0.228082i
$256$	−3.70852e9	−	6.42334e9i	−0.863457	−	1.49555i
$257$	−1.83363e9	−	1.05865e9i	−0.420320	−	0.242672i	0.274894	−	0.961475i	$-0.411357\pi$
$257$	−1.83363e9	−	1.05865e9i	−0.420320	−	0.242672i	−0.695214	+	0.718803i	$0.744691\pi$
$258$			1.50192e9i			0.338974i
$259$	3.05302e9	+	1.85920e8i	0.678471	+	0.0413169i
$260$	8.68933e8			0.190149
$261$	4.54356e8	−	7.86967e8i	0.0979116	−	0.169588i
$262$	2.65202e8	−	1.53114e8i	0.0562822	−	0.0324945i
$263$	−1.69730e9	−	2.93982e9i	−0.354762	−	0.614465i	0.632315	−	0.774711i	$-0.282105\pi$
$263$	−1.69730e9	−	2.93982e9i	−0.354762	−	0.614465i	−0.987077	+	0.160246i	$0.948771\pi$
$264$	−1.30086e10	−	7.51050e9i	−2.67802	−	1.54616i
$265$			2.15305e9i			0.436586i
$266$	1.40766e9	+	9.31176e8i	0.281172	+	0.185997i
$267$	2.06630e9			0.406583
$268$	9.12535e9	−	1.58056e10i	1.76893	−	3.06387i
$269$	4.14244e9	−	2.39164e9i	0.791129	−	0.456759i	−0.0492306	−	0.998787i	$-0.515677\pi$
$269$	4.14244e9	−	2.39164e9i	0.791129	−	0.456759i	0.840360	+	0.542029i	$0.182344\pi$
$270$	−1.02064e9	−	1.76780e9i	−0.192051	−	0.332642i
$271$	6.27801e9	+	3.62461e9i	1.16398	+	0.672023i	0.952254	−	0.305306i	$-0.0987589\pi$
$271$	6.27801e9	+	3.62461e9i	1.16398	+	0.672023i	0.211724	+	0.977329i	$0.432092\pi$
$272$			1.43558e10i			2.62272i
$273$	1.20950e8	−	1.82840e8i	0.0217748	−	0.0329171i
$274$	−9.97361e9			−1.76950
$275$	−4.09057e8	+	7.08507e8i	−0.0715242	+	0.123884i
$276$	−3.60570e9	+	2.08175e9i	−0.621374	+	0.358750i
$277$	−1.27124e9	−	2.20185e9i	−0.215928	−	0.373998i	0.737631	−	0.675204i	$-0.235944\pi$
$277$	−1.27124e9	−	2.20185e9i	−0.215928	−	0.373998i	−0.953559	+	0.301206i	$0.902611\pi$
$278$	−1.74142e10	−	1.00541e10i	−2.91558	−	1.68331i
$279$		−	2.40040e9i		−	0.396157i
$280$	−1.24520e9	+	2.04476e10i	−0.202585	+	3.32667i
$281$	1.71771e9			0.275501			0.137751	−	0.990467i	$-0.456013\pi$
$281$	1.71771e9			0.275501			0.137751	+	0.990467i	$0.456013\pi$
$282$	−1.61034e9	+	2.78919e9i	−0.254637	+	0.441044i
$283$	−4.21678e9	+	2.43456e9i	−0.657408	+	0.379555i	−0.791289	−	0.611443i	$-0.790589\pi$
$283$	−4.21678e9	+	2.43456e9i	−0.657408	+	0.379555i	0.133881	+	0.990997i	$0.457256\pi$
$284$	−3.65911e9	−	6.33776e9i	−0.562473	−	0.974232i
$285$	−6.04805e8	−	3.49184e8i	−0.0916719	−	0.0529268i
$286$			1.46697e9i			0.219259i
$287$	9.05956e9	−	4.51992e9i	1.33530	−	0.666198i
$288$	7.85710e9			1.14207
$289$	−1.48192e9	+	2.56677e9i	−0.212439	+	0.367956i
$290$	7.18185e9	−	4.14644e9i	1.01542	−	0.586251i
$291$	8.05771e8	+	1.39564e9i	0.112367	+	0.194626i
$292$	1.74755e10	+	1.00895e10i	2.40380	+	1.38783i
$293$			9.70891e9i			1.31735i	0.752429	+	0.658673i	$0.228882\pi$
$293$			9.70891e9i			1.31735i	−0.752429	+	0.658673i	$0.771118\pi$
$294$	6.60201e9	+	4.96950e9i	0.883663	+	0.665156i
$295$	−1.11364e10			−1.47048
$296$	8.34608e9	−	1.44558e10i	1.08722	−	1.88311i
$297$	2.17124e9	−	1.25357e9i	0.279050	−	0.161110i
$298$	1.36293e10	+	2.36067e10i	1.72826	+	2.99344i
$299$	2.20245e8	+	1.27158e8i	0.0275563	+	0.0159096i
$300$		−	1.06676e9i		−	0.131698i
$301$	1.12312e9	+	2.25113e9i	0.136823	+	0.274243i
$302$	9.66553e9			1.16198
$303$	7.77878e8	−	1.34733e9i	0.0922872	−	0.159846i
$304$	4.50154e9	−	2.59896e9i	0.527068	−	0.304303i
$305$	9.17512e8	+	1.58918e9i	0.106026	+	0.183642i
$306$	−3.67706e9	−	2.12295e9i	−0.419387	−	0.242133i
$307$		−	1.10736e10i		−	1.24663i	−0.781973	−	0.623313i	$-0.785786\pi$
$307$		−	1.10736e10i		−	1.24663i	0.781973	−	0.623313i	$-0.214214\pi$
$308$	−4.01535e10	−	2.44524e9i	−4.46191	−	0.271718i
$309$	−8.69374e9			−0.953614
$310$	1.09530e10	−	1.89712e10i	1.18601	−	2.05422i
$311$	8.59683e8	−	4.96338e8i	0.0918961	−	0.0530562i	−0.453348	−	0.891334i	$-0.649770\pi$
$311$	8.59683e8	−	4.96338e8i	0.0918961	−	0.0530562i	0.545244	+	0.838278i	$0.316437\pi$
$312$	−5.98188e8	−	1.03609e9i	−0.0631276	−	0.109340i
$313$	−1.11896e10	−	6.46029e9i	−1.16583	−	0.673092i	−0.213136	−	0.977023i	$-0.568368\pi$
$313$	−1.11896e10	−	6.46029e9i	−1.16583	−	0.673092i	−0.952694	+	0.303930i	$0.901701\pi$
$314$			1.44203e10i			1.48339i
$315$	−2.85171e9	−	1.88642e9i	−0.289644	−	0.191601i
$316$	1.76182e10			1.76691
$317$	−7.63421e9	+	1.32228e10i	−0.756009	+	1.30945i	0.188861	+	0.982004i	$0.439520\pi$
$317$	−7.63421e9	+	1.32228e10i	−0.756009	+	1.30945i	−0.944871	+	0.327443i	$0.893813\pi$
$318$	4.10461e9	−	2.36980e9i	0.401387	−	0.231741i
$319$	5.09274e9	+	8.82088e9i	0.491800	+	0.851822i
$320$	2.93779e10	+	1.69613e10i	2.80170	+	1.61756i
$321$		−	3.58993e7i		−	0.00338116i
$322$	−5.28880e9	+	7.99509e9i	−0.491964	+	0.743704i
$323$	−1.45263e9			−0.133458
$324$	−1.63455e9	+	2.83113e9i	−0.148327	+	0.256909i
$325$	−5.64304e7	+	3.25801e7i	−0.00505801	+	0.00292024i
$326$	−2.01673e10	−	3.49308e10i	−1.78557	−	3.09270i
$327$	1.79801e9	+	1.03808e9i	0.157254	+	0.0907905i
$328$		−	5.52525e10i		−	4.77372i
$329$	−3.27916e8	+	5.38476e9i	−0.0279885	+	0.459602i
$330$	2.28800e10			1.92930
$331$	−4.64280e9	+	8.04157e9i	−0.386784	+	0.669929i	−0.992015	−	0.126121i	$-0.959747\pi$
$331$	−4.64280e9	+	8.04157e9i	−0.386784	+	0.669929i	0.605231	+	0.796050i	$0.293081\pi$
$332$	−4.91582e10	+	2.83815e10i	−4.04616	+	2.33605i
$333$	1.39303e9	+	2.41280e9i	0.113288	+	0.196220i
$334$	−2.34850e10	−	1.35591e10i	−1.88714	−	1.08954i
$335$			1.73872e10i			1.38055i
$336$	2.27721e10	−	1.13613e10i	1.78667	−	0.891393i
$337$	−5.30639e9			−0.411415			−0.205707	−	0.978614i	$-0.565949\pi$
$337$	−5.30639e9			−0.411415			−0.205707	+	0.978614i	$0.565949\pi$
$338$	1.24431e10	−	2.15521e10i	0.953370	−	1.65129i
$339$	−1.05890e10	+	6.11358e9i	−0.801784	+	0.462910i
$340$	−1.40948e10	−	2.44129e10i	−1.05474	−	1.82686i
$341$	2.33008e10	+	1.34527e10i	1.72327	+	0.994929i
$342$			1.53735e9i			0.112375i
$343$	1.36115e10	+	2.51157e9i	0.983399	+	0.181455i
$344$	1.37292e10			0.980420
$345$	1.98326e9	−	3.43511e9i	0.139992	−	0.242473i
$346$	−5.57044e9	+	3.21610e9i	−0.388674	+	0.224401i
$347$	−1.52387e9	−	2.63941e9i	−0.105106	−	0.182049i	0.808675	−	0.588255i	$-0.200185\pi$
$347$	−1.52387e9	−	2.63941e9i	−0.105106	−	0.182049i	−0.913782	+	0.406206i	$0.866852\pi$
$348$	−1.15017e10	−	6.64054e9i	−0.784236	−	0.452779i
$349$		−	5.11150e9i		−	0.344545i	−0.985049	−	0.172273i	$-0.944889\pi$
$349$		−	5.11150e9i		−	0.344545i	0.985049	−	0.172273i	$-0.0551110\pi$
$350$	−1.09649e9	−	2.19777e9i	−0.0730690	−	0.146457i
$351$	1.99685e8			0.0131558
$352$	−4.40339e10	+	7.62690e10i	−2.86825	+	4.96795i
$353$	1.20174e10	−	6.93828e9i	0.773951	−	0.446841i	−0.0603313	−	0.998178i	$-0.519216\pi$
$353$	1.20174e10	−	6.93828e9i	0.773951	−	0.446841i	0.834282	+	0.551338i	$0.185882\pi$
$354$	1.22576e10	+	2.12307e10i	0.780533	+	1.35192i
$355$	6.03791e9	+	3.48599e9i	0.380166	+	0.219489i
$356$		−	3.01996e10i		−	1.88019i
$357$	−7.09885e9	−	4.32300e8i	−0.437034	−	0.0266141i
$358$	2.27598e10			1.38559
$359$	−2.10394e9	+	3.64414e9i	−0.126665	+	0.219390i	−0.922383	−	0.386278i	$-0.873761\pi$
$359$	−2.10394e9	+	3.64414e9i	−0.126665	+	0.219390i	0.795718	+	0.605668i	$0.207094\pi$
$360$	−1.61597e10	+	9.32979e9i	−0.962106	+	0.555472i
$361$	−8.22880e9	−	1.42527e10i	−0.484515	−	0.839205i
$362$	−1.43184e10	−	8.26671e9i	−0.833794	−	0.481391i
$363$			1.80771e10i			1.04112i
$364$	−2.67226e9	−	1.76771e9i	−0.152221	−	0.100695i
$365$	−1.92243e10			−1.08312
$366$	2.01976e9	−	3.49833e9i	0.112558	−	0.194956i
$367$	8.93366e9	−	5.15785e9i	0.492454	−	0.284318i	−0.233138	−	0.972444i	$-0.574899\pi$
$367$	8.93366e9	−	5.15785e9i	0.492454	−	0.284318i	0.725592	+	0.688125i	$0.241566\pi$
$368$	1.47613e10	+	2.55673e10i	0.804884	+	1.39410i
$369$	7.98658e9	+	4.61105e9i	0.430780	+	0.248711i
$370$			2.54255e10i			1.35664i
$371$	4.38005e9	−	6.62133e9i	0.231197	−	0.349502i
$372$	−3.50826e10			−1.83198
$373$	1.38521e10	−	2.39926e10i	0.715617	−	1.23949i	−0.247104	−	0.968989i	$-0.579479\pi$
$373$	1.38521e10	−	2.39926e10i	0.715617	−	1.23949i	0.962721	−	0.270496i	$-0.0871878\pi$
$374$	4.12150e10	−	2.37955e10i	2.10654	−	1.21621i
$375$	−5.43939e9	−	9.42130e9i	−0.275059	−	0.476415i
$376$	2.54964e10	+	1.47204e10i	1.27564	+	0.736490i
$377$			8.11241e8i			0.0401591i
$378$	−4.57514e8	+	7.51290e9i	−0.0224098	+	0.367994i
$379$	−3.05523e10			−1.48077			−0.740384	−	0.672184i	$-0.765356\pi$
$379$	−3.05523e10			−1.48077			−0.740384	+	0.672184i	$0.765356\pi$
$380$	−5.10343e9	+	8.83940e9i	−0.244753	+	0.423924i
$381$	1.18642e10	−	6.84981e9i	0.563040	−	0.325071i
$382$	7.87439e9	+	1.36388e10i	0.369797	+	0.640508i
$383$	2.37675e10	+	1.37221e10i	1.10456	+	0.637716i	0.937414	−	0.348217i	$-0.113213\pi$
$383$	2.37675e10	+	1.37221e10i	1.10456	+	0.637716i	0.167142	+	0.985933i	$0.446546\pi$
$384$		−	3.16646e10i		−	1.45630i
$385$	3.42935e10	−	1.71095e10i	1.56088	−	0.778742i
$386$	−1.34995e10			−0.608090
$387$	−1.14576e9	+	1.98452e9i	−0.0510799	+	0.0884730i
$388$	2.03976e10	−	1.17766e10i	0.900021	−	0.519627i
$389$	−2.10395e10	−	3.64415e10i	−0.918834	−	1.59147i	−0.801189	−	0.598411i	$-0.795799\pi$
$389$	−2.10395e10	−	3.64415e10i	−0.918834	−	1.59147i	−0.117645	−	0.993056i	$-0.537534\pi$
$390$	1.57818e9	+	9.11161e8i	0.0682177	+	0.0393855i
$391$		−	8.25046e9i		−	0.352997i
$392$	4.54269e10	−	6.03499e10i	1.92384	−	2.55583i
$393$	4.67223e8			0.0195864
$394$	−4.46939e9	+	7.74121e9i	−0.185466	+	0.321236i
$395$	−1.45360e10	+	8.39234e9i	−0.597111	+	0.344742i
$396$	−1.83212e10	−	3.17333e10i	−0.745029	−	1.29043i
$397$	1.37015e9	+	7.91056e8i	0.0551576	+	0.0318453i	0.527325	−	0.849664i	$-0.323195\pi$
$397$	1.37015e9	+	7.91056e8i	0.0551576	+	0.0318453i	−0.472168	+	0.881509i	$0.656528\pi$
$398$			5.87340e10i			2.34076i
$399$	1.14961e9	+	2.30424e9i	0.0453587	+	0.0909153i
$400$	−7.56418e9			−0.295476
$401$	−4.99836e9	+	8.65742e9i	−0.193308	+	0.334820i	−0.946345	−	0.323159i	$-0.895255\pi$
$401$	−4.99836e9	+	8.65742e9i	−0.193308	+	0.334820i	0.753036	+	0.657979i	$0.228588\pi$
$402$	3.31473e10	−	1.91376e10i	1.26924	−	0.732797i
$403$	1.07147e9	+	1.85583e9i	0.0406217	+	0.0703588i
$404$	−1.96915e10	−	1.13689e10i	−0.739187	−	0.426770i
$405$		−	3.11444e9i		−	0.115760i
$406$	−3.05219e10	−	1.85870e9i	−1.12333	−	0.0684076i
$407$	−3.12281e10			−1.13807
$408$	−1.94062e10	+	3.36125e10i	−0.700326	+	1.21300i
$409$	−8.95606e9	+	5.17078e9i	−0.320054	+	0.184783i	−0.651417	−	0.758720i	$-0.725825\pi$
$409$	−8.95606e9	+	5.17078e9i	−0.320054	+	0.184783i	0.331363	+	0.943504i	$0.392492\pi$
$410$	4.20804e10	+	7.28853e10i	1.48917	+	2.57932i
$411$	−1.31784e10	−	7.60854e9i	−0.461843	−	0.266645i
$412$			1.27061e11i			4.40986i
$413$	3.42483e10	+	2.26554e10i	1.17717	+	0.778703i
$414$	−8.73167e9			−0.297232
$415$	2.70387e10	−	4.68324e10i	0.911577	−	1.57890i
$416$	−6.07459e9	+	3.50716e9i	−0.202835	+	0.117107i
$417$	−1.53399e10	−	2.65694e10i	−0.507315	−	0.878695i
$418$	−1.49231e10	−	8.61584e9i	−0.488825	−	0.282223i
$419$		−	8.96187e9i		−	0.290765i	−0.989376	−	0.145383i	$-0.953559\pi$
$419$		−	8.96187e9i		−	0.290765i	0.989376	−	0.145383i	$-0.0464413\pi$
$420$	−2.75706e10	+	4.16786e10i	−0.886032	+	1.33942i
$421$	3.47886e10			1.10741			0.553705	−	0.832713i	$-0.313214\pi$
$421$	3.47886e10			1.10741			0.553705	+	0.832713i	$0.313214\pi$
$422$	2.05133e10	−	3.55300e10i	0.646822	−	1.12033i
$423$	−4.25556e9	+	2.45695e9i	−0.132922	+	0.0767423i
$424$	−2.16626e10	−	3.75208e10i	−0.670267	−	1.16094i
$425$	1.83069e9	+	1.05695e9i	0.0561126	+	0.0323966i
$426$		−	1.53477e10i		−	0.466021i
$427$	4.11287e8	−	6.75379e9i	0.0123718	−	0.203159i
$428$	−5.24678e8			−0.0156357
$429$	−1.11910e9	+	1.93835e9i	−0.0330401	+	0.0572272i
$430$	−1.81107e10	+	1.04562e10i	−0.529737	+	0.305844i
$431$	1.19627e9	+	2.07199e9i	0.0346672	+	0.0600453i	0.882838	−	0.469677i	$-0.155630\pi$
$431$	1.19627e9	+	2.07199e9i	0.0346672	+	0.0600453i	−0.848171	+	0.529722i	$0.822296\pi$
$432$	2.00750e10	+	1.15903e10i	0.576396	+	0.332782i
$433$			2.52121e10i			0.717228i	0.933486	+	0.358614i	$0.116751\pi$
$433$			2.52121e10i			0.717228i	−0.933486	+	0.358614i	$0.883249\pi$
$434$	−7.22782e10	+	3.60605e10i	−2.03727	+	1.01642i
$435$	1.26527e10			0.353368
$436$	1.51719e10	−	2.62784e10i	0.419849	−	0.727199i
$437$	−2.58709e9	+	1.49366e9i	−0.0709391	+	0.0409567i
$438$	2.11596e10	+	3.66495e10i	0.574925	+	0.995799i
$439$	−3.05195e10	−	1.76205e10i	−0.821712	−	0.474416i	0.0292943	−	0.999571i	$-0.490674\pi$
$439$	−3.05195e10	−	1.76205e10i	−0.821712	−	0.474416i	−0.851007	+	0.525155i	$0.824007\pi$
$440$		−	2.09150e11i		−	5.58016i
$441$	4.93233e9	+	1.16028e10i	0.130406	+	0.306766i
$442$	3.79048e9			0.0993127
$443$	1.43650e10	−	2.48809e10i	0.372984	−	0.646027i	−0.617039	−	0.786932i	$-0.711668\pi$
$443$	1.43650e10	−	2.48809e10i	0.372984	−	0.646027i	0.990023	+	0.140905i	$0.0450013\pi$
$444$	3.52637e10	−	2.03595e10i	0.907395	−	0.523885i
$445$	1.43854e10	+	2.49162e10i	0.366844	+	0.635393i
$446$	−2.31504e10	−	1.33659e10i	−0.585085	−	0.337799i
$447$			4.15894e10i			1.04172i
$448$	−5.58416e10	−	1.11927e11i	−1.38626	−	2.77857i
$449$	−8.45964e9			−0.208145			−0.104073	−	0.994570i	$-0.533187\pi$
$449$	−8.45964e9			−0.208145			−0.104073	+	0.994570i	$0.533187\pi$
$450$	1.11860e9	−	1.93747e9i	0.0272787	−	0.0472482i
$451$	−8.95191e10	+	5.16839e10i	−2.16376	+	1.24925i
$452$	8.93517e10	+	1.54762e11i	2.14067	+	3.70774i
$453$	1.27713e10	+	7.37351e9i	0.303279	+	0.175098i
$454$		−	5.51870e10i		−	1.29901i
$455$	3.04680e9	+	1.85541e8i	0.0710882	+	0.00432907i
$456$	1.40531e10			0.325023
$457$	−3.08251e10	+	5.33906e10i	−0.706707	+	1.22405i	0.259364	+	0.965780i	$0.416487\pi$
$457$	−3.08251e10	+	5.33906e10i	−0.706707	+	1.22405i	−0.966072	+	0.258274i	$0.916846\pi$
$458$	3.39782e10	−	1.96173e10i	0.772215	−	0.445838i
$459$	−3.23906e9	−	5.61021e9i	−0.0729740	−	0.126395i
$460$	−5.02051e10	−	2.89859e10i	−1.12129	−	0.647374i
$461$		−	3.84216e10i		−	0.850690i	−0.905031	−	0.425345i	$-0.860153\pi$
$461$		−	3.84216e10i		−	0.850690i	0.905031	−	0.425345i	$-0.139847\pi$
$462$	−7.03637e10	−	4.65460e10i	−1.54448	−	1.02168i
$463$	−7.81565e10			−1.70075			−0.850376	−	0.526175i	$-0.823626\pi$
$463$	−7.81565e10			−1.70075			−0.850376	+	0.526175i	$0.823626\pi$
$464$	−4.70868e10	+	8.15568e10i	−1.01584	+	1.75949i
$465$	2.89450e10	−	1.67114e10i	0.619101	−	0.357438i
$466$	2.03377e10	+	3.52260e10i	0.431279	+	0.746998i
$467$	−3.69764e10	−	2.13483e10i	−0.777422	−	0.448845i	0.0580935	−	0.998311i	$-0.481498\pi$
$467$	−3.69764e10	−	2.13483e10i	−0.777422	−	0.448845i	−0.835516	+	0.549466i	$0.814831\pi$
$468$		−	2.91845e9i		−	0.0608372i
$469$	3.53717e10	−	5.34715e10i	0.731079	−	1.10518i
$470$	−4.48442e10			−0.918998
$471$	−1.10008e10	+	1.90539e10i	−0.223532	+	0.387169i
$472$	1.94073e11	−	1.12048e11i	3.91019	−	2.25755i
$473$	−1.28425e10	−	2.22438e10i	−0.256569	−	0.444391i
$474$	3.19986e10	+	1.84744e10i	0.633896	+	0.365980i
$475$		−	7.65399e8i		−	0.0150353i
$476$	−6.31818e9	+	1.03752e11i	−0.123073	+	2.02101i
$477$	7.23135e9			0.139684
$478$	3.25502e10	−	5.63787e10i	0.623509	−	1.07995i
$479$	5.38490e9	−	3.10897e9i	0.102290	−	0.0590574i	−0.447982	−	0.894043i	$-0.647857\pi$
$479$	5.38490e9	−	3.10897e9i	0.102290	−	0.0590574i	0.550273	+	0.834985i	$0.314524\pi$
$480$	5.47004e10	+	9.47439e10i	1.03045	+	1.78479i
$481$	−2.15400e9	−	1.24361e9i	−0.0402406	−	0.0232329i
$482$			7.61851e10i			1.41150i
$483$	−1.30874e10	+	6.52946e9i	−0.240472	+	0.119974i
$484$	2.64202e11			4.81454
$485$	−1.12194e10	+	1.94326e10i	−0.202770	+	0.351207i
$486$	−5.93743e9	+	3.42798e9i	−0.106427	+	0.0614459i
$487$	3.41554e10	+	5.91590e10i	0.607217	+	1.05173i	0.991697	+	0.128598i	$0.0410476\pi$
$487$	3.41554e10	+	5.91590e10i	0.607217	+	1.05173i	−0.384480	+	0.923134i	$0.625619\pi$
$488$	−3.19787e10	−	1.84629e10i	−0.563873	−	0.325552i
$489$		−	6.15398e10i		−	1.07627i
$490$	−1.39615e10	+	1.14207e11i	−0.242185	+	1.98110i
$491$	7.04766e10			1.21260			0.606302	−	0.795234i	$-0.292652\pi$
$491$	7.04766e10			1.21260			0.606302	+	0.795234i	$0.292652\pi$
$492$	6.73918e10	−	1.16726e11i	1.15013	−	1.99208i
$493$	2.27921e10	−	1.31590e10i	0.385830	−	0.222759i
$494$	−6.86225e8	−	1.18858e9i	−0.0115228	−	0.0199581i
$495$	3.02319e10	+	1.74544e10i	0.503553	+	0.290726i
$496$			2.48764e11i			4.11018i
$497$	−1.14769e10	−	2.30038e10i	−0.188104	−	0.377028i
$498$	−1.19043e11			−1.93547
$499$	−5.59329e10	+	9.68787e10i	−0.902123	+	1.56252i	−0.0773887	+	0.997001i	$0.524658\pi$
$499$	−5.59329e10	+	9.68787e10i	−0.902123	+	1.56252i	−0.824734	+	0.565521i	$0.808675\pi$
$500$	−1.37695e11	+	7.94982e10i	−2.20312	+	1.27197i
$501$	−2.06875e10	−	3.58318e10i	−0.328365	−	0.568745i
$502$	−1.68017e11	−	9.70047e10i	−2.64569	−	1.52749i
$503$			8.32236e10i			1.30009i	0.759894	+	0.650047i	$0.225251\pi$
$503$			8.32236e10i			1.30009i	−0.759894	+	0.650047i	$0.774749\pi$
$504$	6.86765e10	+	4.18220e9i	1.06435	+	0.0648161i
$505$	2.16621e10			0.333069
$506$	4.89353e10	−	8.47585e10i	0.746484	−	1.29295i
$507$	3.28827e10	−	1.89848e10i	0.497663	−	0.287326i
$508$	−1.00112e11	−	1.73399e11i	−1.50325	−	2.60370i
$509$	2.87844e9	+	1.66187e9i	0.0428832	+	0.0247586i	0.521288	−	0.853381i	$-0.325452\pi$
$509$	2.87844e9	+	1.66187e9i	0.0428832	+	0.0247586i	−0.478405	+	0.878139i	$0.658785\pi$
$510$		−	5.91192e10i		−	0.873871i
$511$	5.91210e10	+	3.91089e10i	0.867079	+	0.573577i
$512$	−5.40038e10			−0.785858
$513$	−1.17279e9	+	2.03134e9i	−0.0169337	+	0.0293300i
$514$	−5.62029e10	+	3.24488e10i	−0.805204	+	0.464885i
$515$	−6.05250e10	−	1.04832e11i	−0.860411	−	1.49027i
$516$	2.90043e10	+	1.67456e10i	0.409132	+	0.236212i
$517$		−	5.50784e10i		−	0.770938i
$518$	5.17244e10	−	7.81920e10i	0.718417	−	1.08603i
$519$	−9.81381e9			−0.135260
$520$	8.32905e9	−	1.44263e10i	0.113915	−	0.197307i
$521$	6.56163e10	−	3.78836e10i	0.890555	−	0.514162i	0.0164311	−	0.999865i	$-0.494770\pi$
$521$	6.56163e10	−	3.78836e10i	0.890555	−	0.514162i	0.874124	+	0.485703i	$0.161436\pi$
$522$	−1.39265e10	−	2.41214e10i	−0.187569	−	0.324878i
$523$	1.17918e11	+	6.80799e10i	1.57606	+	0.909939i	0.995401	+	0.0957932i	$0.0305388\pi$
$523$	1.17918e11	+	6.80799e10i	1.57606	+	0.909939i	0.580660	+	0.814146i	$0.302795\pi$
$524$		−	6.82859e9i		−	0.0905746i
$525$	2.27782e8	−	3.74044e9i	0.00299835	−	0.0492363i
$526$	−1.04048e11			−1.35923
$527$	3.47601e10	−	6.02063e10i	0.450649	−	0.780547i
$528$	−2.25015e11	+	1.29912e11i	−2.89518	+	1.67153i
$529$	3.06720e10	+	5.31254e10i	0.391669	+	0.678391i
$530$	5.71518e10	+	3.29966e10i	0.724313	+	0.418182i
$531$			3.74035e10i			0.470473i
$532$	3.36772e10	−	1.68019e10i	0.420426	−	0.209755i
$533$	−8.23291e9			−0.102010
$534$	3.16672e10	−	5.48492e10i	0.389444	−	0.674536i
$535$	4.32887e8	−	2.49928e8i	0.00528396	−	0.00305070i
$536$	−1.74940e11	−	3.03005e11i	−2.11948	−	3.67105i
$537$	3.00730e10	+	1.73627e10i	0.361643	+	0.208795i
$538$		−	1.46613e11i		−	1.75002i
$539$	−1.40271e11	−	1.71478e10i	−1.66193	−	0.203167i
$540$	−4.55184e10			−0.535318
$541$	2.43620e10	−	4.21963e10i	0.284397	−	0.492590i	−0.688066	−	0.725648i	$-0.741540\pi$
$541$	2.43620e10	−	4.21963e10i	0.284397	−	0.492590i	0.972463	+	0.233059i	$0.0748734\pi$
$542$	1.92428e11	−	1.11098e11i	2.22982	−	1.28739i
$543$	−1.26128e10	−	2.18460e10i	−0.145081	−	0.251288i
$544$	1.97070e11	+	1.13778e11i	2.25022	+	1.29916i
$545$			2.89081e10i			0.327668i
$546$	−2.99980e9	−	6.01269e9i	−0.0337537	−	0.0676547i
$547$	2.02062e10			0.225702			0.112851	−	0.993612i	$-0.464002\pi$
$547$	2.02062e10			0.225702			0.112851	+	0.993612i	$0.464002\pi$
$548$	−1.11201e11	+	1.92606e11i	−1.23307	+	2.13573i
$549$	5.33751e9	−	3.08161e9i	0.0587556	−	0.0339226i
$550$	1.25380e10	+	2.17165e10i	0.137018	+	0.237323i
$551$	−8.25251e9	−	4.76459e9i	−0.0895323	−	0.0516915i
$552$			7.98175e10i			0.859690i
$553$	6.17759e10	+	3.76197e9i	0.660569	+	0.0402268i
$554$	−7.79297e10			−0.827302
$555$	−1.93963e10	+	3.35954e10i	−0.204431	+	0.354085i
$556$	−3.88320e11	+	2.24197e11i	−4.06341	+	2.34601i
$557$	4.78354e10	+	8.28533e10i	0.496968	+	0.860774i	0.999994	−	0.00349724i	$-0.00111321\pi$
$557$	4.78354e10	+	8.28533e10i	0.496968	+	0.860774i	−0.503026	+	0.864271i	$0.667780\pi$
$558$	−6.37178e10	−	3.67875e10i	−0.657240	−	0.379458i
$559$		−	2.04573e9i		−	0.0209508i
$560$	2.95535e11	+	1.95498e11i	3.00509	+	1.98788i
$561$	7.26112e10			0.733082
$562$	2.63248e10	−	4.55958e10i	0.263888	−	0.457067i
$563$	9.59103e10	−	5.53738e10i	0.954622	−	0.551151i	0.0601086	−	0.998192i	$-0.480855\pi$
$563$	9.59103e10	−	5.53738e10i	0.954622	−	0.551151i	0.894514	+	0.447040i	$0.147522\pi$
$564$	3.59090e10	+	6.21962e10i	0.354885	+	0.614678i
$565$	−1.47440e11	−	8.51244e10i	−1.44684	−	0.835334i
$566$			1.49244e11i			1.45422i
$567$	−6.33586e9	+	9.57794e9i	−0.0613018	+	0.0926702i
$568$	−1.40296e11			−1.34788
$569$	−5.65007e10	+	9.78621e10i	−0.539020	+	0.933610i	0.459937	+	0.887951i	$0.347872\pi$
$569$	−5.65007e10	+	9.78621e10i	−0.539020	+	0.933610i	−0.998957	+	0.0456583i	$0.985461\pi$
$570$	−1.85379e10	+	1.07029e10i	−0.175615	+	0.101391i
$571$	4.26220e10	+	7.38235e10i	0.400950	+	0.694465i	0.993841	−	0.110818i	$-0.0353469\pi$
$571$	4.26220e10	+	7.38235e10i	0.400950	+	0.694465i	−0.592891	+	0.805283i	$0.702014\pi$
$572$	2.83295e10	+	1.63560e10i	0.264639	+	0.152790i
$573$			2.40284e10i			0.222898i
$574$	1.88631e10	−	3.09753e11i	0.173766	−	2.85343i
$575$	4.34723e9			0.0397687
$576$	5.69674e10	−	9.86705e10i	0.517531	−	0.896391i
$577$	−1.17478e11	+	6.78259e10i	−1.05987	+	0.611917i	−0.925397	−	0.379000i	$-0.876268\pi$
$577$	−1.17478e11	+	6.78259e10i	−1.05987	+	0.611917i	−0.134474	+	0.990917i	$0.542935\pi$
$578$	4.54226e10	+	7.86743e10i	0.406968	+	0.704890i
$579$	−1.78372e10	−	1.02983e10i	−0.158713	−	0.0916329i
$580$		−	1.84923e11i		−	1.63410i
$581$	−1.78427e11	+	8.90191e10i	−1.56587	+	0.781230i
$582$	4.93955e10			0.430522
$583$	−4.05270e10	+	7.01948e10i	−0.350809	+	0.607618i
$584$	3.35019e11	−	1.93423e11i	2.88017	−	1.66286i
$585$	1.39019e9	+	2.40788e9i	0.0118700	+	0.0205594i
$586$	2.57719e11	+	1.48794e11i	2.18553	+	1.26181i
$587$		−	2.26995e11i		−	1.91190i	−0.293533	−	0.955949i	$-0.594831\pi$
$587$		−	2.26995e11i		−	1.91190i	0.293533	−	0.955949i	$-0.405169\pi$
$588$	1.69578e11	−	7.20874e10i	1.41860	−	0.603045i
$589$	−2.51718e10			−0.209147
$590$	−1.70672e11	+	2.95613e11i	−1.40849	+	2.43958i
$591$	−1.18110e10	+	6.81910e9i	−0.0968139	+	0.0558955i
$592$	−1.44366e11	−	2.50049e11i	−1.17538	−	2.03581i
$593$	1.63632e11	+	9.44731e10i	1.32327	+	0.763993i	0.984250	−	0.176784i	$-0.0565696\pi$
$593$	1.63632e11	+	9.44731e10i	1.32327	+	0.763993i	0.339025	+	0.940777i	$0.389903\pi$
$594$		−	7.68463e10i		−	0.617273i
$595$	−4.42087e10	−	8.86103e10i	−0.352728	−	0.706995i
$596$	6.07841e11			4.81732
$597$	−4.48062e10	+	7.76066e10i	−0.352729	+	0.610944i
$598$	6.75075e9	−	3.89754e9i	0.0527894	−	0.0304780i
$599$	−7.05625e10	−	1.22218e11i	−0.548109	−	0.949352i	−0.998404	−	0.0564726i	$-0.982015\pi$
$599$	−7.05625e10	−	1.22218e11i	−0.548109	−	0.949352i	0.450295	−	0.892880i	$-0.351319\pi$
$600$	−1.77107e10	−	1.02253e10i	−0.136657	−	0.0788987i
$601$		−	1.91655e11i		−	1.46900i	−0.678609	−	0.734499i	$-0.737417\pi$
$601$		−	1.91655e11i		−	1.46900i	0.678609	−	0.734499i	$-0.262583\pi$
$602$	7.69679e10	+	4.68712e9i	0.586035	+	0.0356878i
$603$	5.83978e10			0.441700
$604$	1.07766e11	−	1.86656e11i	0.809718	−	1.40247i
$605$	−2.17980e11	+	1.25851e11i	−1.62703	+	0.939367i
$606$	−2.38428e10	−	4.12970e10i	−0.176794	−	0.306216i
$607$	1.14122e11	+	6.58882e10i	0.840647	+	0.485348i	0.857484	−	0.514510i	$-0.172026\pi$
$607$	1.14122e11	+	6.58882e10i	0.840647	+	0.485348i	−0.0168370	+	0.999858i	$0.505360\pi$
$608$		−	8.23933e10i		−	0.602945i
$609$	−3.89114e10	−	2.57401e10i	−0.282883	−	0.187129i
$610$	5.62455e10			0.406227
$611$	2.19341e9	−	3.79910e9i	0.0157382	−	0.0272594i
$612$	−8.19948e10	+	4.73397e10i	−0.584495	+	0.337458i
$613$	5.01797e10	+	8.69138e10i	0.355374	+	0.615527i	0.987182	−	0.159599i	$-0.0510200\pi$
$613$	5.01797e10	+	8.69138e10i	0.355374	+	0.615527i	−0.631808	+	0.775125i	$0.717687\pi$
$614$	−2.93945e11	−	1.69709e11i	−2.06820	−	1.19408i
$615$			1.28407e11i			0.897610i
$616$	−4.25484e11	+	6.43205e11i	−2.95502	+	4.46711i
$617$	−6.91461e10			−0.477120			−0.238560	−	0.971128i	$-0.576675\pi$
$617$	−6.91461e10			−0.477120			−0.238560	+	0.971128i	$0.576675\pi$
$618$	−1.33236e11	+	2.30772e11i	−0.913416	+	1.58208i
$619$	−1.07988e11	+	6.23470e10i	−0.735553	+	0.424671i	−0.820450	−	0.571718i	$-0.806277\pi$
$619$	−1.07988e11	+	6.23470e10i	−0.735553	+	0.424671i	0.0848975	+	0.996390i	$0.472944\pi$
$620$	−2.44242e11	−	4.23039e11i	−1.65292	−	2.86295i
$621$	−1.15374e10	−	6.66110e9i	−0.0775783	−	0.0447899i
$622$		−	3.04266e10i		−	0.203279i
$623$	6.44844e9	−	1.05891e11i	0.0428058	−	0.702919i
$624$	−2.06942e10			−0.136493
$625$	8.22554e10	−	1.42471e11i	0.539069	−	0.933695i
$626$	−3.42972e11	+	1.98015e11i	−2.23337	+	1.28944i
$627$	−1.31455e10	−	2.27686e10i	−0.0850562	−	0.147322i
$628$	2.78478e11	+	1.60779e11i	1.79041	+	1.03369i
$629$			8.06895e10i			0.515483i
$630$	−9.37785e10	+	4.67872e10i	−0.595307	+	0.297006i
$631$	1.45583e11			0.918318			0.459159	−	0.888354i	$-0.348151\pi$
$631$	1.45583e11			0.918318			0.459159	+	0.888354i	$0.348151\pi$
$632$	1.68877e11	−	2.92504e11i	1.05853	−	1.83343i
$633$	5.42093e10	−	3.12978e10i	0.337644	−	0.194939i
$634$	2.33997e11	+	4.05295e11i	1.44828	+	2.50850i
$635$	1.65195e11	+	9.53755e10i	1.01602	+	0.586600i
$636$		−	1.05688e11i		−	0.645949i
$637$	−8.99246e9	−	6.76885e9i	−0.0546161	−	0.0411109i
$638$	3.12196e11			1.88428
$639$	1.17083e10	−	2.02793e10i	0.0702245	−	0.121632i
$640$	3.81824e11	−	2.20446e11i	2.27585	−	1.31396i
$641$	8.63926e10	+	1.49636e11i	0.511734	+	0.886349i	0.999907	+	0.0136028i	$0.00433004\pi$
$641$	8.63926e10	+	1.49636e11i	0.511734	+	0.886349i	−0.488173	+	0.872747i	$0.662337\pi$
$642$	−9.52934e8	−	5.50176e8i	−0.00560948	−	0.00323863i
$643$		−	3.33550e11i		−	1.95127i	−0.219401	−	0.975635i	$-0.570410\pi$
$643$		−	3.33550e11i		−	1.95127i	0.219401	−	0.975635i	$-0.429590\pi$
$644$	9.54299e10	+	1.91276e11i	0.554806	+	1.11203i
$645$	−3.19067e10			−0.184350
$646$	−2.22623e10	+	3.85594e10i	−0.127832	+	0.221411i
$647$	2.23139e11	−	1.28829e11i	1.27338	−	0.735187i	0.297758	−	0.954641i	$-0.403761\pi$
$647$	2.23139e11	−	1.28829e11i	1.27338	−	0.735187i	0.975623	+	0.219455i	$0.0704279\pi$
$648$	3.13356e10	+	5.42749e10i	0.177721	+	0.307822i
$649$	−3.63077e11	−	2.09622e11i	−2.04654	−	1.18157i
$650$			1.99723e9i			0.0111886i
$651$	−1.23012e11	−	7.49109e9i	−0.684896	−	0.0417082i
$652$	−8.99421e11			−4.97706
$653$	−4.34196e10	+	7.52050e10i	−0.238799	+	0.413613i	−0.960370	−	0.278728i	$-0.910087\pi$
$653$	−4.34196e10	+	7.52050e10i	−0.238799	+	0.413613i	0.721571	+	0.692341i	$0.243421\pi$
$654$	5.51110e10	−	3.18183e10i	0.301250	−	0.173927i
$655$	3.25276e9	+	5.63395e9i	0.0176721	+	0.0306089i
$656$	−8.27683e11	−	4.77863e11i	−4.46939	−	2.58040i
$657$			6.45678e10i			0.346541i
$658$	1.37911e11	+	9.12287e10i	0.735690	+	0.486663i
$659$	−1.52693e11			−0.809612			−0.404806	−	0.914403i	$-0.632661\pi$
$659$	−1.52693e11			−0.809612			−0.404806	+	0.914403i	$0.632661\pi$
$660$	2.55101e11	−	4.41848e11i	1.34442	−	2.32861i
$661$	1.33616e11	−	7.71432e10i	0.699927	−	0.404103i	−0.107393	−	0.994217i	$-0.534250\pi$
$661$	1.33616e11	−	7.71432e10i	0.699927	−	0.404103i	0.807320	+	0.590114i	$0.200917\pi$
$662$	1.42307e11	+	2.46483e11i	0.740958	+	1.28338i
$663$	5.00845e9	+	2.89163e9i	0.0259208	+	0.0149654i
$664$			1.08819e12i			5.59799i
$665$	−1.97819e10	+	2.99044e10i	−0.101154	+	0.152915i
$666$	8.53958e10			0.434050
$667$	2.70614e10	−	4.68717e10i	0.136725	−	0.236814i
$668$	−5.23692e11	+	3.02354e11i	−2.63009	+	1.51848i
$669$	−2.03928e10	−	3.53213e10i	−0.101806	−	0.176333i
$670$	4.61537e11	+	2.66469e11i	2.29038	+	1.32235i
$671$			6.90817e10i			0.340779i
$672$	2.45202e10	−	4.02649e11i	0.120239	−	1.97446i
$673$	2.36882e11			1.15471			0.577354	−	0.816494i	$-0.304085\pi$
$673$	2.36882e11			1.15471			0.577354	+	0.816494i	$0.304085\pi$
$674$	−8.13233e10	+	1.40856e11i	−0.394072	+	0.682553i
$675$	2.95606e9	−	1.70668e9i	0.0142396	−	0.00822125i
$676$	−2.77469e11	−	4.80590e11i	−1.32870	−	2.30138i
$677$	−1.56754e11	−	9.05022e10i	−0.746217	−	0.430829i	0.0781082	−	0.996945i	$-0.475112\pi$
$677$	−1.56754e11	−	9.05022e10i	−0.746217	−	0.430829i	−0.824325	+	0.566116i	$0.808445\pi$
$678$			3.74776e11i			1.77359i
$679$	7.40361e10	−	3.69375e10i	0.348309	−	0.173775i
$680$	−5.40417e11			−2.52751
$681$	4.21003e10	−	7.29199e10i	0.195748	−	0.339045i
$682$	7.14194e11	−	4.12340e11i	3.30125	−	1.90598i
$683$	5.76235e10	+	9.98069e10i	0.264799	+	0.458646i	0.967511	−	0.252829i	$-0.0813609\pi$
$683$	5.76235e10	+	9.98069e10i	0.264799	+	0.458646i	−0.702712	+	0.711475i	$0.748028\pi$
$684$	2.96886e10	+	1.71407e10i	0.135633	+	0.0783076i
$685$		−	2.11880e11i		−	0.962336i
$686$	2.75273e11	−	3.22821e11i	1.24299	−	1.45769i
$687$	5.98615e10			0.268733
$688$	1.18740e11	−	2.05664e11i	0.529960	−	0.917918i
$689$	−5.59080e9	+	3.22785e9i	−0.0248083	+	0.0143231i
$690$	−6.07891e10	−	1.05290e11i	−0.268182	−	0.464504i
$691$	−2.41583e11	−	1.39478e11i	−1.05963	−	0.611778i	−0.134301	−	0.990941i	$-0.542879\pi$
$691$	−2.41583e11	−	1.39478e11i	−1.05963	−	0.611778i	−0.925330	+	0.379163i	$0.876212\pi$
$692$			1.43432e11i			0.625490i
$693$	−5.74649e10	−	1.15180e11i	−0.249155	−	0.499397i
$694$	−9.34162e10			−0.402703
$695$	2.13589e11	−	3.69948e11i	0.915462	−	1.58563i
$696$	−2.20497e11	+	1.27304e11i	−0.939650	+	0.542507i
$697$	1.33545e11	+	2.31306e11i	0.565843	+	0.980068i
$698$	−1.35683e11	−	7.83365e10i	−0.571614	−	0.330022i
$699$			6.20599e10i			0.259957i
$700$	−5.46676e10	−	3.32910e9i	−0.227687	−	0.0138655i
$701$	2.31657e11			0.959340			0.479670	−	0.877449i	$-0.340756\pi$
$701$	2.31657e11			0.959340			0.479670	+	0.877449i	$0.340756\pi$
$702$	3.06028e9	−	5.30056e9i	0.0126012	−	0.0218260i
$703$	2.53017e10	−	1.46080e10i	0.103593	−	0.0598093i
$704$	6.38531e11	+	1.10597e12i	2.59951	+	4.50248i
$705$	−5.92536e10	−	3.42101e10i	−0.239860	−	0.138483i
$706$		−	4.25331e11i		−	1.71202i
$707$	−6.66181e10	−	4.40682e10i	−0.266633	−	0.176379i
$708$	5.46663e11			2.17564
$709$	6.11339e10	−	1.05887e11i	0.241934	−	0.419042i	−0.719331	−	0.694668i	$-0.755551\pi$
$709$	6.11339e10	−	1.05887e11i	0.241934	−	0.419042i	0.961265	+	0.275625i	$0.0888848\pi$
$710$	1.85068e11	−	1.06849e11i	0.728281	−	0.420473i
$711$	2.81870e10	+	4.88214e10i	0.110299	+	0.191043i
$712$	−5.01384e11	−	2.89474e11i	−1.95097	−	1.12639i
$713$		−	1.42968e11i		−	0.553198i
$714$	−1.20269e11	+	1.81811e11i	−0.462765	+	0.699564i
$715$	−3.11644e10			−0.119243
$716$	2.53760e11	−	4.39526e11i	0.965543	−	1.67237i
$717$	8.60188e10	−	4.96630e10i	0.325474	−	0.187913i
$718$	6.44882e10	+	1.11697e11i	0.242651	+	0.420284i
$719$	2.21520e11	+	1.27895e11i	0.828890	+	0.478560i	0.853472	−	0.521138i	$-0.174492\pi$
$719$	2.21520e11	+	1.27895e11i	0.828890	+	0.478560i	−0.0245824	+	0.999698i	$0.507826\pi$
$720$			3.22763e11i			1.20103i
$721$	−2.71311e10	+	4.45523e11i	−0.100398	+	1.64865i
$722$	−5.04443e11			−1.85637
$723$	−5.81191e10	+	1.00665e11i	−0.212699	+	0.368406i
$724$	−3.19285e11	+	1.84339e11i	−1.16205	+	0.670910i
$725$	6.93357e9	+	1.20093e10i	0.0250960	+	0.0434676i
$726$	4.79850e11	+	2.77041e11i	1.72726	+	0.997236i
$727$			4.63666e11i			1.65984i	0.557879	+	0.829922i	$0.311615\pi$
$727$			4.63666e11i			1.65984i	−0.557879	+	0.829922i	$0.688385\pi$
$728$	−5.49629e10	+	2.74216e10i	−0.195679	+	0.0976265i
$729$	−1.04604e10			−0.0370370
$730$	−2.94622e11	+	5.10301e11i	−1.03747	+	1.79695i
$731$	−5.74753e10	+	3.31834e10i	−0.201285	+	0.116212i
$732$	−4.50386e10	−	7.80092e10i	−0.156870	−	0.271707i
$733$	1.22278e11	+	7.05971e10i	0.423576	+	0.244552i	0.696606	−	0.717454i	$-0.254693\pi$
$733$	1.22278e11	+	7.05971e10i	0.423576	+	0.244552i	−0.273030	+	0.962006i	$0.588026\pi$
$734$		−	3.16188e11i		−	1.08933i
$735$	−1.05572e11	+	1.40253e11i	−0.361743	+	0.480578i
$736$	4.67968e11			1.59480
$737$	−3.27282e11	+	5.66869e11i	−1.10931	+	1.92138i
$738$	2.44797e11	−	1.41334e11i	0.825241	−	0.476453i
$739$	−1.67804e11	−	2.90645e11i	−0.562633	−	0.974509i	−0.997266	−	0.0739008i	$-0.976455\pi$
$739$	−1.67804e11	−	2.90645e11i	−0.562633	−	0.974509i	0.434633	−	0.900608i	$-0.356878\pi$
$740$	4.91006e11	+	2.83482e11i	1.63742	+	0.945364i
$741$		−	2.09399e9i		−	0.00694548i
$742$	−1.08634e11	−	2.17742e11i	−0.358386	−	0.718335i
$743$	4.56688e11			1.49853			0.749263	−	0.662273i	$-0.230408\pi$
$743$	4.56688e11			1.49853			0.749263	+	0.662273i	$0.230408\pi$
$744$	−3.36280e11	+	5.82454e11i	−1.09751	+	1.90095i
$745$	−5.01501e11	+	2.89542e11i	−1.62797	+	0.939910i
$746$	−4.24582e11	−	7.35398e11i	−1.37090	−	2.37447i
$747$	−1.57294e11	−	9.08139e10i	−0.505162	−	0.291655i
$748$		−	1.06123e12i		−	3.39004i
$749$	−1.83971e9	−	1.12033e8i	−0.00584552	−	0.000355975i
$750$	−3.33446e11			−1.05386
$751$	3.18491e10	−	5.51643e10i	0.100124	−	0.173420i	−0.811612	−	0.584197i	$-0.801409\pi$
$751$	3.18491e10	−	5.51643e10i	0.100124	−	0.173420i	0.911736	+	0.410778i	$0.134743\pi$
$752$	4.41022e11	−	2.54624e11i	1.37908	−	0.796211i
$753$	−1.48003e11	−	2.56349e11i	−0.460354	−	0.797356i
$754$	2.15341e10	+	1.24327e10i	0.0666256	+	0.0384663i
$755$			2.05335e11i			0.631938i
$756$	1.39984e11	+	9.26004e10i	0.428541	+	0.283482i
$757$	8.33797e10			0.253908			0.126954	−	0.991909i	$-0.459480\pi$
$757$	8.33797e10			0.253908			0.126954	+	0.991909i	$0.459480\pi$
$758$	−4.68230e11	+	8.10999e11i	−1.41835	+	2.45665i
$759$	1.29319e11	−	7.46623e10i	0.389668	−	0.224975i
$760$	9.78366e10	+	1.69458e11i	0.293256	+	0.507934i
$761$	−2.45433e10	−	1.41701e10i	−0.0731802	−	0.0422506i	0.462963	−	0.886377i	$-0.346786\pi$
$761$	−2.45433e10	−	1.41701e10i	−0.0731802	−	0.0422506i	−0.536144	+	0.844127i	$0.680119\pi$
$762$		−	4.19908e11i		−	1.24547i
$763$	5.88092e10	−	8.89021e10i	0.173519	−	0.262309i
$764$	3.51182e11			1.03076
$765$	4.51000e10	−	7.81155e10i	0.131683	−	0.228082i
$766$	7.28498e11	−	4.20599e11i	2.11599	−	1.22167i
$767$	−1.66958e10	−	2.89179e10i	−0.0482420	−	0.0835575i
$768$	−3.00390e11	−	1.73430e11i	−0.863457	−	0.498517i
$769$		−	4.43772e10i		−	0.126898i	−0.997985	−	0.0634490i	$-0.979790\pi$
$769$		−	4.43772e10i		−	0.126898i	0.997985	−	0.0634490i	$-0.0202100\pi$
$770$	7.14032e10	−	1.17252e12i	0.203121	−	3.33547i
$771$	−9.90163e10			−0.280213
$772$	−1.50513e11	+	2.60695e11i	−0.423744	+	0.733946i
$773$	−8.28240e10	+	4.78185e10i	−0.231973	+	0.133930i	−0.611482	−	0.791258i	$-0.709426\pi$
$773$	−8.28240e10	+	4.78185e10i	−0.231973	+	0.133930i	0.379509	+	0.925188i	$0.376093\pi$
$774$	3.51188e10	+	6.08276e10i	0.0978534	+	0.169487i
$775$	3.17231e10	+	1.83154e10i	0.0879365	+	0.0507702i
$776$		−	4.51532e11i		−	1.24521i
$777$	1.27995e11	−	6.38581e10i	0.351163	−	0.175199i
$778$	−1.28977e12			−3.52041
$779$	4.83536e10	−	8.37510e10i	0.131304	−	0.227426i
$780$	3.51918e10	−	2.03180e10i	0.0950743	−	0.0548912i
$781$	1.31234e11	+	2.27304e11i	0.352731	+	0.610947i
$782$	−2.19005e11	−	1.26443e11i	−0.585636	−	0.338117i
$783$		−	4.24962e10i		−	0.113059i
$784$	−5.11158e11	−	1.20244e12i	−1.35298	−	3.18274i
$785$	−3.06345e11			−0.806738
$786$	7.16045e9	−	1.24023e10i	0.0187607	−	0.0324945i
$787$	−3.13558e11	+	1.81033e11i	−0.817370	+	0.471909i	−0.849509	−	0.527574i	$-0.823102\pi$
$787$	−3.13558e11	+	1.81033e11i	−0.817370	+	0.471909i	0.0321384	+	0.999483i	$0.489768\pi$
$788$	9.96630e10	+	1.72621e11i	0.258481	+	0.447703i
$789$	−1.37482e11	−	7.93751e10i	−0.354762	−	0.204822i
$790$			5.14468e11i			1.32084i
$791$	2.80254e11	+	5.61730e11i	0.715888	+	1.43490i
$792$	−7.02463e11			−1.78535
$793$	−2.75107e9	+	4.76499e9i	−0.00695679	+	0.0120495i
$794$	4.19965e10	−	2.42467e10i	0.105665	−	0.0610058i
$795$	5.03440e10	+	8.71983e10i	0.126031	+	0.218293i
$796$	1.13424e12	+	6.54855e11i	2.82523	+	1.63115i
$797$			5.21156e11i			1.29162i	0.763499	+	0.645809i	$0.223480\pi$
$797$			5.21156e11i			1.29162i	−0.763499	+	0.645809i	$0.776520\pi$
$798$	7.87838e10	+	4.79770e9i	0.194279	+	0.0118310i
$799$	−1.42316e11			−0.349193
$800$	−5.99506e10	+	1.03837e11i	−0.146364	+	0.253509i
$801$	8.36852e10	−	4.83157e10i	0.203291	−	0.117370i
$802$	1.53205e11	+	2.65359e11i	0.370319	+	0.641412i
$803$	−6.26761e11	−	3.61861e11i	−1.50744	−	0.870320i
$804$		−	8.53501e11i		−	2.04258i
$805$	−1.69848e11	−	1.12355e11i	−0.404461	−	0.267553i
$806$	6.56831e10			0.155637
$807$	1.11846e11	−	1.93723e11i	0.263710	−	0.456759i
$808$	−3.77502e11	+	2.17951e11i	−0.885673	+	0.511343i
$809$	5.19542e10	+	8.99874e10i	0.121291	+	0.210081i	0.920277	−	0.391268i	$-0.127963\pi$
$809$	5.19542e10	+	8.99874e10i	0.121291	+	0.210081i	−0.798986	+	0.601349i	$0.794630\pi$
$810$	−8.26716e10	−	4.77305e10i	−0.192051	−	0.110881i
$811$			5.38192e11i			1.24410i	0.782979	+	0.622048i	$0.213699\pi$
$811$			5.38192e11i			1.24410i	−0.782979	+	0.622048i	$0.786301\pi$
$812$	−3.76198e11	+	5.68700e11i	−0.865352	+	1.30816i
$813$	3.39013e11			0.775985
$814$	−4.78588e11	+	8.28938e11i	−1.09009	+	1.88810i
$815$	7.42070e11	−	4.28434e11i	1.68195	−	0.971077i
$816$	3.35677e11	+	5.81410e11i	0.757114	+	1.31136i
$817$	2.08106e10	+	1.20150e10i	0.0467085	+	0.0269672i
$818$			3.16980e11i			0.707977i
$819$	6.23170e8	−	1.02332e10i	0.00138507	−	0.0227444i
$820$	1.87670e12			4.15088
$821$	1.90782e11	−	3.30444e11i	0.419919	−	0.727320i	−0.576012	−	0.817441i	$-0.695392\pi$
$821$	1.90782e11	−	3.30444e11i	0.419919	−	0.727320i	0.995931	+	0.0901206i	$0.0287253\pi$
$822$	−4.03931e11	+	2.33210e11i	−0.884749	+	0.510810i
$823$	2.35041e11	+	4.07103e11i	0.512324	+	0.887371i	0.999898	+	0.0142896i	$0.00454867\pi$
$823$	2.35041e11	+	4.07103e11i	0.512324	+	0.887371i	−0.487574	+	0.873082i	$0.662118\pi$
$824$	2.10952e12	+	1.21793e12i	4.57588	+	2.64189i
$825$			3.82594e10i			0.0825890i
$826$	1.12625e12	−	5.61901e11i	2.41944	−	1.20709i
$827$	−5.75326e11			−1.22996			−0.614981	−	0.788542i	$-0.710836\pi$
$827$	−5.75326e11			−1.22996			−0.614981	+	0.788542i	$0.710836\pi$
$828$	−9.73539e10	+	1.68622e11i	−0.207125	+	0.358750i
$829$	−4.87574e11	+	2.81501e11i	−1.03234	+	0.596022i	−0.917654	−	0.397380i	$-0.869919\pi$
$829$	−4.87574e11	+	2.81501e11i	−1.03234	+	0.596022i	−0.114686	+	0.993402i	$0.536586\pi$
$830$	−8.28766e11	−	1.43546e12i	−1.74630	−	3.02468i
$831$	−1.02970e11	−	5.94500e10i	−0.215928	−	0.124666i
$832$			1.01714e11i			0.212269i
$833$	−4.43077e10	+	3.62442e11i	−0.0920236	+	0.752764i
$834$	−9.40367e11			−1.94372
$835$	2.88049e11	−	4.98915e11i	0.592543	−	1.02632i
$836$	−3.32770e11	+	1.92125e11i	−0.681270	+	0.393331i
$837$	−5.61279e10	−	9.72164e10i	−0.114361	−	0.198079i
$838$	−2.37889e11	−	1.37345e11i	−0.482391	−	0.278508i
$839$		−	7.63569e11i		−	1.54099i	−0.637444	−	0.770496i	$-0.720008\pi$
$839$		−	7.63569e11i		−	1.54099i	0.637444	−	0.770496i	$-0.279992\pi$
$840$	4.27689e11	+	8.57243e11i	0.859034	+	1.72182i
$841$	−3.27601e11			−0.654880
$842$	5.33154e11	−	9.23450e11i	1.06073	−	1.83724i
$843$	6.95671e10	−	4.01646e10i	0.137751	−	0.0795303i
$844$	−4.57426e11	−	7.92284e11i	−0.901469	−	1.56139i
$845$	4.57853e11	+	2.64341e11i	0.898047	+	0.518487i
$846$			1.50616e11i			0.294029i
$847$	9.26387e11	+	5.64143e10i	1.79994	+	0.109611i
$848$	−7.49415e11			−1.44924
$849$	−1.13853e11	+	1.97199e11i	−0.219136	+	0.379555i
$850$	5.61128e10	−	3.23967e10i	0.107494	−	0.0620620i
$851$	8.29688e10	+	1.43706e11i	0.158196	+	0.274004i
$852$	−2.96388e11	−	1.71119e11i	−0.562473	−	0.324744i
$853$			2.88270e11i			0.544508i	0.962225	+	0.272254i	$0.0877690\pi$
$853$			2.88270e11i			0.544508i	−0.962225	+	0.272254i	$0.912231\pi$
$854$	−1.72974e11	−	1.14423e11i	−0.325198	−	0.215120i
$855$	−3.26595e10			−0.0611146
$856$	−5.02924e9	+	8.71090e9i	−0.00936715	+	0.0162244i
$857$	4.04582e11	−	2.33585e11i	0.750037	−	0.433034i	−0.0756701	−	0.997133i	$-0.524110\pi$
$857$	4.04582e11	−	2.33585e11i	0.750037	−	0.433034i	0.825707	+	0.564099i	$0.190776\pi$
$858$	3.43018e10	+	5.94124e10i	0.0632947	+	0.109630i
$859$	−7.74712e11	−	4.47280e11i	−1.42288	−	0.821499i	−0.426334	−	0.904566i	$-0.640195\pi$
$859$	−7.74712e11	−	4.47280e11i	−1.42288	−	0.821499i	−0.996544	+	0.0830664i	$0.973529\pi$
$860$			4.66326e11i			0.852502i
$861$	2.61224e11	−	3.94894e11i	0.475336	−	0.718568i
$862$	7.33337e10			0.132823
$863$	5.16717e11	−	8.94980e11i	0.931557	−	1.61350i	0.150896	−	0.988550i	$-0.451784\pi$
$863$	5.16717e11	−	8.94980e11i	0.931557	−	1.61350i	0.780661	−	0.624954i	$-0.214882\pi$
$864$	3.18213e11	−	1.83720e11i	0.571035	−	0.329687i
$865$	−6.83228e10	−	1.18339e11i	−0.122040	−	0.211379i
$866$	6.69245e11	+	3.86389e11i	1.18991	+	0.686994i
$867$			1.38606e11i			0.245304i
$868$	−1.09484e11	+	1.79786e12i	−0.192874	+	3.16721i
$869$	−6.31879e11			−1.10804
$870$	1.93910e11	−	3.35862e11i	0.338472	−	0.586251i
$871$	−4.51493e10	+	2.60670e10i	−0.0784474	+	0.0452916i
$872$	−2.90856e11	−	5.03777e11i	−0.503051	−	0.871310i
$873$	6.52675e10	+	3.76822e10i	0.112367	+	0.0648753i
$874$			9.15644e10i			0.156921i
$875$	−4.99783e11	+	2.49348e11i	−0.852608	+	0.425376i
$876$	9.43677e11			1.60253
$877$	3.43223e11	−	5.94479e11i	0.580200	−	1.00494i	−0.415255	−	0.909705i	$-0.636308\pi$
$877$	3.43223e11	−	5.94479e11i	0.580200	−	1.00494i	0.995455	−	0.0952306i	$-0.0303589\pi$
$878$	−9.35457e11	+	5.40086e11i	−1.57415	+	0.908835i
$879$	2.27020e11	+	3.93211e11i	0.380285	+	0.658673i
$880$	−3.13306e12	−	1.80887e12i	−5.22442	−	3.01632i
$881$		−	8.06663e10i		−	0.133902i	−0.997756	−	0.0669512i	$-0.978673\pi$
$881$		−	8.06663e10i		−	0.133902i	0.997756	−	0.0669512i	$-0.0213272\pi$
$882$	3.83582e11	+	4.68919e10i	0.633846	+	0.0774861i
$883$	4.94869e10			0.0814043			0.0407021	−	0.999171i	$-0.487041\pi$
$883$	4.94869e10			0.0814043			0.0407021	+	0.999171i	$0.487041\pi$
$884$	4.22619e10	−	7.31998e10i	0.0692055	−	0.119867i
$885$	−4.51026e11	+	2.60400e11i	−0.735239	+	0.424490i
$886$	−4.40302e11	−	7.62626e11i	−0.714522	−	1.23759i
$887$	1.39887e11	+	8.07636e10i	0.225986	+	0.130473i	0.608719	−	0.793386i	$-0.291684\pi$
$887$	1.39887e11	+	8.07636e10i	0.225986	+	0.130473i	−0.382733	+	0.923859i	$0.625017\pi$
$888$		−	7.80615e11i		−	1.25541i
$889$	−3.14003e11	−	6.29376e11i	−0.502721	−	1.00764i
$890$	8.81856e11			1.40552
$891$	5.86235e10	−	1.01539e11i	0.0930166	−	0.161110i
$892$	−5.16231e11	+	2.98046e11i	−0.815426	+	0.470787i
$893$	2.57647e10	+	4.46258e10i	0.0405154	+	0.0701747i
$894$	1.10398e12	+	6.37381e11i	1.72826	+	0.997812i
$895$			4.83509e11i			0.753551i
$896$	−1.62270e12	−	9.88178e10i	−2.51771	−	0.153322i
$897$	1.18932e10			0.0183709
$898$	−1.29649e11	+	2.24558e11i	−0.199371	+	0.345321i
$899$	3.94951e11	−	2.28025e11i	0.604651	−	0.349095i
$900$	−2.49437e10	−	4.32037e10i	−0.0380181	−	0.0658492i
$901$	1.81375e11	+	1.04717e11i	0.275218	+	0.158897i
$902$			3.16833e12i			4.78635i
$903$	9.81238e10	+	6.49094e10i	0.147579	+	0.0976240i
$904$	3.42588e12			5.12978
$905$	1.75618e11	−	3.04179e11i	0.261803	−	0.453456i
$906$	3.91454e11	−	2.26006e11i	0.580989	−	0.335434i
$907$	−3.85048e11	−	6.66922e11i	−0.568965	−	0.985476i	−0.996669	−	0.0815567i	$-0.974011\pi$
$907$	−3.85048e11	−	6.66922e11i	−0.568965	−	0.985476i	0.427704	−	0.903919i	$-0.359323\pi$
$908$	−1.06575e12	−	6.15308e11i	−1.56787	−	0.905210i
$909$		−	7.27556e10i		−	0.106564i
$910$	5.16189e10	−	7.80325e10i	0.0752737	−	0.113792i
$911$	−7.35040e11			−1.06718			−0.533589	−	0.845744i	$-0.679157\pi$
$911$	−7.35040e11			−1.06718			−0.533589	+	0.845744i	$0.679157\pi$
$912$	1.21541e11	−	2.10516e11i	0.175689	−	0.304303i
$913$	1.76306e12	−	1.01790e12i	2.53738	−	1.46495i
$914$	9.44823e11	+	1.63648e12i	1.35383	+	2.34491i
$915$	7.43185e10	+	4.29078e10i	0.106026	+	0.0612141i
$916$		−	8.74893e11i		−	1.24272i
$917$	1.45809e9	−	2.39435e10i	0.00206209	−	0.0338619i
$918$	−1.98561e11			−0.279591
$919$	−2.71903e11	+	4.70949e11i	−0.381199	+	0.660255i	−0.991234	−	0.132119i	$-0.957822\pi$
$919$	−2.71903e11	+	4.70949e11i	−0.381199	+	0.660255i	0.610035	+	0.792374i	$0.291155\pi$
$920$	−9.62469e11	+	5.55682e11i	−1.34349	+	0.775666i
$921$	−2.58931e11	−	4.48481e11i	−0.359870	−	0.623313i
$922$	−1.01989e12	−	5.88832e11i	−1.41133	−	0.814831i
$923$			2.09048e10i			0.0288031i
$924$	−1.68339e12	+	8.39865e11i	−2.30939	+	1.15218i
$925$	−4.25159e10			−0.0580744
$926$	−1.19779e12	+	2.07463e12i	−1.62906	+	2.82161i
$927$	−3.52096e11	+	2.03283e11i	−0.476807	+	0.275285i
$928$	7.46382e11	+	1.29277e12i	1.00640	+	1.74313i
$929$	−2.54149e11	−	1.46733e11i	−0.341214	−	0.197000i	0.319595	−	0.947554i	$-0.396453\pi$
$929$	−2.54149e11	−	1.46733e11i	−0.341214	−	0.197000i	−0.660809	+	0.750554i	$0.729786\pi$
$930$		−	1.02444e12i		−	1.36948i
$931$	1.21672e11	−	5.17227e10i	0.161954	−	0.0688466i
$932$	9.07022e11			1.20214
$933$	2.32114e10	−	4.02034e10i	0.0306320	−	0.0530562i
$934$	−1.13337e12	+	6.54350e11i	−1.48930	+	0.859849i
$935$	5.05512e11	+	8.75573e11i	0.661432	+	1.14563i
$936$	−4.84532e10	−	2.79745e10i	−0.0631276	−	0.0364467i
$937$		−	5.72665e11i		−	0.742920i	−0.928449	−	0.371460i	$-0.878857\pi$
$937$		−	5.72665e11i		−	0.742920i	0.928449	−	0.371460i	$-0.121143\pi$
$938$	−8.77291e11	−	1.75841e12i	−1.13327	−	2.27148i
$939$	−6.04236e11			−0.777220
$940$	−4.99990e11	+	8.66009e11i	−0.640398	+	1.10920i
$941$	−1.60432e11	+	9.26254e10i	−0.204613	+	0.118133i	−0.598805	−	0.800895i	$-0.704358\pi$
$941$	−1.60432e11	+	9.26254e10i	−0.204613	+	0.118133i	0.394193	+	0.919028i	$0.371024\pi$
$942$	3.37186e11	+	5.84023e11i	0.428219	+	0.741696i
$943$	4.75680e11	+	2.74634e11i	0.601545	+	0.347302i
$944$		−	3.87629e12i		−	4.88122i
$945$	−1.59604e11	−	9.71943e9i	−0.200132	−	0.0121875i
$946$	−7.87272e11			−0.983016
$947$	2.86748e10	−	4.96663e10i	0.0356534	−	0.0617535i	−0.847648	−	0.530559i	$-0.821982\pi$
$947$	2.86748e10	−	4.96663e10i	0.0356534	−	0.0617535i	0.883302	+	0.468805i	$0.155315\pi$
$948$	7.13538e11	−	4.11961e11i	0.883453	−	0.510062i
$949$	−2.88210e10	−	4.99195e10i	−0.0355341	−	0.0615468i
$950$	−2.03172e10	−	1.17302e10i	−0.0249442	−	0.0144016i
$951$			7.14034e11i			0.872965i
$952$	1.66196e12	+	1.09940e12i	2.02336	+	1.33846i
$953$	6.64050e11			0.805062			0.402531	−	0.915406i	$-0.368131\pi$
$953$	6.64050e11			0.805062			0.402531	+	0.915406i	$0.368131\pi$
$954$	1.10824e11	−	1.91953e11i	0.133796	−	0.231741i
$955$	−2.89744e11	+	1.67284e11i	−0.348338	+	0.201113i
$956$	−7.25838e11	−	1.25719e12i	−0.868977	−	1.50511i
$957$	4.12512e11	+	2.38164e11i	0.491800	+	0.283941i
$958$		−	1.90587e11i		−	0.226272i
$959$	−4.31037e11	+	6.51601e11i	−0.509613	+	0.770384i
$960$	1.58641e12			1.86780
$961$	1.75894e11	−	3.04657e11i	0.206233	−	0.357205i
$962$	−6.60223e10	+	3.81180e10i	−0.0770886	+	0.0445071i
$963$	−8.39422e8	−	1.45392e9i	−0.000976057	−	0.00169058i
$964$	1.47125e12	+	8.49427e11i	1.70364	+	0.983598i
$965$		−	2.86783e11i		−	0.330708i
$966$	−2.72495e10	+	4.47467e11i	−0.0312932	+	0.513870i
$967$	1.49408e11			0.170871			0.0854357	−	0.996344i	$-0.472772\pi$
$967$	1.49408e11			0.170871			0.0854357	+	0.996344i	$0.472772\pi$
$968$	2.53247e12	−	4.38637e12i	2.88432	−	4.99579i
$969$	−5.88313e10	+	3.39663e10i	−0.0667288	+	0.0385259i
$970$	3.43887e11	+	5.95630e11i	0.388444	+	0.672805i
$971$	−1.29764e12	−	7.49193e11i	−1.45975	−	0.842785i	−0.460748	−	0.887531i	$-0.652419\pi$
$971$	−1.29764e12	−	7.49193e11i	−1.45975	−	0.842785i	−0.998998	+	0.0447457i	$0.985752\pi$
$972$			1.52881e11i			0.171273i
$973$	−1.40946e12	+	7.03197e11i	−1.57254	+	0.784559i
$974$	2.09380e12			2.32648
$975$	−1.52362e9	+	2.63899e9i	−0.00168600	+	0.00292024i
$976$	−5.53149e11	+	3.19361e11i	−0.609597	+	0.351951i
$977$	−5.45071e11	−	9.44092e11i	−0.598240	−	1.03618i	−0.993081	−	0.117432i	$-0.962534\pi$
$977$	−5.45071e11	−	9.44092e11i	−0.598240	−	1.03618i	0.394841	−	0.918749i	$-0.370800\pi$
$978$	−1.63355e12	−	9.43131e11i	−1.78557	−	1.03090i
$979$			1.08311e12i			1.17908i
$980$	2.04984e12	+	1.54297e12i	2.22237	+	1.67283i
$981$	9.70926e10			0.104836
$982$	1.08009e12	−	1.87078e12i	1.16149	−	2.01176i
$983$	−1.07564e12	+	6.21022e11i	−1.15200	+	0.665110i	−0.949375	−	0.314146i	$-0.898282\pi$
$983$	−1.07564e12	+	6.21022e11i	−1.15200	+	0.665110i	−0.202629	+	0.979256i	$0.564948\pi$
$984$	−1.29195e12	−	2.23773e12i	−1.37805	−	2.38686i
$985$	−1.64454e11	−	9.49478e10i	−0.174703	−	0.100865i
$986$		−	8.06675e11i		−	0.853475i
$987$	1.12629e11	+	2.25750e11i	0.118682	+	0.237881i
$988$	−3.06043e10			−0.0321184
$989$	−6.82414e10	+	1.18198e11i	−0.0713285	+	0.123545i
$990$	9.26641e11	−	5.34997e11i	0.964652	−	0.556942i
$991$	−4.36830e11	−	7.56612e11i	−0.452916	−	0.784474i	0.545649	−	0.838014i	$-0.316283\pi$
$991$	−4.36830e11	−	7.56612e11i	−0.452916	−	0.784474i	−0.998566	+	0.0535393i	$0.982950\pi$
$992$	3.41492e12	+	1.97160e12i	3.52641	+	2.03598i
$993$			4.34245e11i			0.446619i
$994$	−7.86516e11	−	4.78966e10i	−0.805679	−	0.0490635i
$995$	−1.24775e12			−1.27302
$996$	−1.32727e12	+	2.29890e12i	−1.34872	+	2.33605i
$997$	9.27060e11	−	5.35238e11i	0.938268	−	0.541709i	0.0488512	−	0.998806i	$-0.484444\pi$
$997$	9.27060e11	−	5.35238e11i	0.938268	−	0.541709i	0.889417	+	0.457097i	$0.151111\pi$
$998$	1.71441e12	+	2.96944e12i	1.72819	+	2.99331i
$999$	1.12835e11	+	6.51456e10i	0.113288	+	0.0654068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.9.f.b.19.6	yes	12
3.2	odd	2		63.9.m.d.19.1		12
7.2	even	3		147.9.d.b.97.2		12
7.3	odd	6	inner	21.9.f.b.10.6	✓	12
7.5	odd	6		147.9.d.b.97.1		12
21.17	even	6		63.9.m.d.10.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.9.f.b.10.6	✓	12	7.3	odd	6	inner
21.9.f.b.19.6	yes	12	1.1	even	1	trivial
63.9.m.d.10.1		12	21.17	even	6
63.9.m.d.19.1		12	3.2	odd	2
147.9.d.b.97.1		12	7.5	odd	6
147.9.d.b.97.2		12	7.2	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(15.3255 - 26.5446i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-341.745 - 591.919i) q^{4} +(563.914 + 325.576i) q^{5} -1433.41i q^{6} +(-1071.89 - 2148.45i) q^{7} -13103.0 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\)	\(q+(15.3255 - 26.5446i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-341.745 - 591.919i) q^{4} +(563.914 + 325.576i) q^{5} -1433.41i q^{6} +(-1071.89 - 2148.45i) q^{7} -13103.0 q^{8} +(1093.50 - 1894.00i) q^{9} +(17284.6 - 9979.26i) q^{10} +(12256.7 + 21229.2i) q^{11} +(-27681.3 - 15981.8i) q^{12} +1952.42i q^{13} +(-73457.2 - 4473.33i) q^{14} +30451.4 q^{15} +(-113324. + 196283. i) q^{16} +(54853.7 - 31669.8i) q^{17} +(-33517.0 - 58053.1i) q^{18} +(-19861.3 - 11467.0i) q^{19} -445055. i q^{20} +(-93648.1 - 61948.7i) q^{21} +751363. q^{22} +(65128.8 - 112806. i) q^{23} +(-530672. + 306383. i) q^{24} +(16687.1 + 28902.8i) q^{25} +(51826.1 + 29921.8i) q^{26} -102276. i q^{27} +(-905398. + 1.36869e6i) q^{28} +415506. q^{29} +(466684. - 808320. i) q^{30} +(950531. - 548789. i) q^{31} +(1.79632e6 + 3.11132e6i) q^{32} +(992793. + 573190. i) q^{33} -1.94143e6i q^{34} +(95031.5 - 1.56053e6i) q^{35} -1.49479e6 q^{36} +(-636959. + 1.10325e6i) q^{37} +(-608772. + 351475. i) q^{38} +(45652.7 + 79072.9i) q^{39} +(-7.38897e6 - 4.26602e6i) q^{40} +4.21678e6i q^{41} +(-3.07961e6 + 1.53646e6i) q^{42} -1.04779e6 q^{43} +(8.37733e6 - 1.45100e7i) q^{44} +(1.23328e6 - 712035. i) q^{45} +(-1.99627e6 - 3.45764e6i) q^{46} +(-1.94584e6 - 1.12343e6i) q^{47} +1.05993e7i q^{48} +(-3.46691e6 + 4.60581e6i) q^{49} +1.02295e6 q^{50} +(1.48105e6 - 2.56525e6i) q^{51} +(1.15567e6 - 667228. i) q^{52} +(1.65326e6 + 2.86353e6i) q^{53} +(-2.71487e6 - 1.56743e6i) q^{54} +1.59620e7i q^{55} +(1.40450e7 + 2.81512e7i) q^{56} -1.07251e6 q^{57} +(6.36785e6 - 1.10294e7i) q^{58} +(-1.48113e7 + 8.55134e6i) q^{59} +(-1.04066e7 - 1.80247e7i) q^{60} +(2.44056e6 + 1.40906e6i) q^{61} -3.36420e7i q^{62} +(-5.24128e6 - 319179. i) q^{63} +5.20964e7 q^{64} +(-635660. + 1.10100e6i) q^{65} +(3.04302e7 - 1.75689e7i) q^{66} +(1.33511e7 + 2.31248e7i) q^{67} +(-3.74919e7 - 2.16460e7i) q^{68} -6.09154e6i q^{69} +(-3.99671e7 - 2.64385e7i) q^{70} +1.07071e7 q^{71} +(-1.43281e7 + 2.48171e7i) q^{72} +(-2.55681e7 + 1.47617e7i) q^{73} +(1.95235e7 + 3.38157e7i) q^{74} +(1.35165e6 + 780377. i) q^{75} +1.56751e7i q^{76} +(3.24722e7 - 4.90884e7i) q^{77} +2.79861e6 q^{78} +(-1.28884e7 + 2.23234e7i) q^{79} +(-1.27810e8 + 7.37912e7i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(1.11933e8 + 6.46245e7i) q^{82} -8.30488e7i q^{83} +(-4.66489e6 + 7.66027e7i) q^{84} +4.12437e7 q^{85} +(-1.60580e7 + 2.78132e7i) q^{86} +(1.68280e7 - 9.71565e6i) q^{87} +(-1.60600e8 - 2.78167e8i) q^{88} +(3.82648e7 + 2.20922e7i) q^{89} -4.36493e7i q^{90} +(4.19468e6 - 2.09277e6i) q^{91} -8.90296e7 q^{92} +(2.56643e7 - 4.44519e7i) q^{93} +(-5.96423e7 + 3.44345e7i) q^{94} +(-7.46673e6 - 1.29328e7i) q^{95} +(1.45502e8 + 8.40056e7i) q^{96} +3.44602e7i q^{97} +(6.91272e7 + 1.62614e8i) q^{98} +5.36108e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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