LMFDB - Embedded newform 91.10.k.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(4,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("91.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.k (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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$164$
Relative dimension:	$82$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	91.4
Dual form			91.10.k.a.23.80

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.9063i q^{2} +(-3.86494 - 6.69428i) q^{3} -1328.95 q^{4} +(1575.27 - 909.485i) q^{5} +(-287.227 + 165.831i) q^{6} +(-4344.78 - 4634.27i) q^{7} +35052.4i q^{8} +(9811.62 - 16994.2i) q^{9} +O(q^{10})$	\(q-42.9063i q^{2} +(-3.86494 - 6.69428i) q^{3} -1328.95 q^{4} +(1575.27 - 909.485i) q^{5} +(-287.227 + 165.831i) q^{6} +(-4344.78 - 4634.27i) q^{7} +35052.4i q^{8} +(9811.62 - 16994.2i) q^{9} +(-39022.6 - 67589.2i) q^{10} +(23355.4 - 13484.2i) q^{11} +(5136.33 + 8896.38i) q^{12} +(-21210.2 - 100770. i) q^{13} +(-198839. + 186419. i) q^{14} +(-12176.7 - 7030.22i) q^{15} +823547. q^{16} -593824. q^{17} +(-729160. - 420981. i) q^{18} +(-449200. - 259346. i) q^{19} +(-2.09346e6 + 1.20866e6i) q^{20} +(-14230.8 + 46996.4i) q^{21} +(-578559. - 1.00209e6i) q^{22} +1.80702e6 q^{23} +(234651. - 135476. i) q^{24} +(677762. - 1.17392e6i) q^{25} +(-4.32368e6 + 910050. i) q^{26} -303833. q^{27} +(5.77401e6 + 6.15872e6i) q^{28} +(1.13858e6 - 1.97207e6i) q^{29} +(-301641. + 522457. i) q^{30} +(-2.87313e6 - 1.65880e6i) q^{31} -1.73885e7i q^{32} +(-180535. - 104232. i) q^{33} +2.54788e7i q^{34} +(-1.10590e7 - 3.34873e6i) q^{35} +(-1.30392e7 + 2.25845e7i) q^{36} +1.50250e7i q^{37} +(-1.11276e7 + 1.92735e7i) q^{38} +(-592608. + 531458. i) q^{39} +(3.18797e7 + 5.52172e7i) q^{40} +(-1.32457e7 - 7.64743e6i) q^{41} +(2.01644e6 + 610589. i) q^{42} +(1.12094e7 + 1.94153e7i) q^{43} +(-3.10382e7 + 1.79199e7i) q^{44} -3.56941e7i q^{45} -7.75328e7i q^{46} +(3.29827e7 - 1.90425e7i) q^{47} +(-3.18296e6 - 5.51306e6i) q^{48} +(-2.59931e6 + 4.02698e7i) q^{49} +(-5.03685e7 - 2.90803e7i) q^{50} +(2.29510e6 + 3.97522e6i) q^{51} +(2.81873e7 + 1.33919e8i) q^{52} +(1.05115e7 - 1.82064e7i) q^{53} +1.30364e7i q^{54} +(2.45274e7 - 4.24827e7i) q^{55} +(1.62442e8 - 1.52295e8i) q^{56} +4.00943e6i q^{57} +(-8.46144e7 - 4.88522e7i) q^{58} -1.86955e6i q^{59} +(1.61822e7 + 9.34282e6i) q^{60} +(3.74771e7 - 6.49123e7i) q^{61} +(-7.11730e7 + 1.23275e8i) q^{62} +(-1.21385e8 + 2.83666e7i) q^{63} -3.24422e8 q^{64} +(-1.25061e8 - 1.39450e8i) q^{65} +(-4.47220e6 + 7.74607e6i) q^{66} +(1.47227e8 - 8.50016e7i) q^{67} +7.89164e8 q^{68} +(-6.98405e6 - 1.20967e7i) q^{69} +(-1.43682e8 + 4.74502e8i) q^{70} +(5.78058e6 - 3.33742e6i) q^{71} +(5.95689e8 + 3.43921e8i) q^{72} +(-1.34676e7 - 7.77552e6i) q^{73} +6.44666e8 q^{74} -1.04781e7 q^{75} +(5.96965e8 + 3.44658e8i) q^{76} +(-1.63964e8 - 4.96490e7i) q^{77} +(2.28029e7 + 2.54266e7i) q^{78} +(2.98414e8 + 5.16868e8i) q^{79} +(1.29731e9 - 7.49004e8i) q^{80} +(-1.91948e8 - 3.32464e8i) q^{81} +(-3.28123e8 + 5.68326e8i) q^{82} -2.71423e8i q^{83} +(1.89120e7 - 6.24560e7i) q^{84} +(-9.35435e8 + 5.40074e8i) q^{85} +(8.33041e8 - 4.80956e8i) q^{86} -1.76021e7 q^{87} +(4.72655e8 + 8.18663e8i) q^{88} -6.72024e7i q^{89} -1.53150e9 q^{90} +(-3.74843e8 + 5.36118e8i) q^{91} -2.40145e9 q^{92} +2.56447e7i q^{93} +(-8.17046e8 - 1.41516e9i) q^{94} -9.43484e8 q^{95} +(-1.16404e8 + 6.72057e7i) q^{96} +(-2.44831e7 + 1.41353e7i) q^{97} +(1.72783e9 + 1.11527e8i) q^{98} -5.29209e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 164 q - 161 q^{3} - 40962 q^{4} - 6 q^{6} - 2055 q^{7} - 510909 q^{9}+O(q^{10}) $ 164 * q - 161 * q^3 - 40962 * q^4 - 6 * q^6 - 2055 * q^7 - 510909 * q^9	\( 164 q - 161 q^{3} - 40962 q^{4} - 6 q^{6} - 2055 q^{7} - 510909 q^{9} + 41025 q^{10} - 85389 q^{11} + 43064 q^{12} - 232462 q^{13} + 82708 q^{14} + 338445 q^{15} + 9425286 q^{16} - 1277590 q^{17} + 1176873 q^{18} - 1344159 q^{19} + 571062 q^{20} - 1367523 q^{21} - 1417332 q^{22} - 2148066 q^{23} + 62118 q^{24} + 29660776 q^{25} + 3184908 q^{26} + 7350574 q^{27} + 4828755 q^{28} + 996812 q^{29} - 9177016 q^{30} - 21474090 q^{31} - 15796239 q^{33} + 10592613 q^{35} + 131881331 q^{36} - 8950274 q^{38} - 35258971 q^{39} - 7901342 q^{40} + 24649770 q^{41} - 51088299 q^{42} + 15892214 q^{43} - 1176612 q^{44} - 69222114 q^{47} - 15455476 q^{48} - 57160671 q^{49} + 309166224 q^{50} + 52823362 q^{51} + 177629625 q^{52} - 155327528 q^{53} - 77925569 q^{55} - 92078463 q^{56} - 597924735 q^{58} - 290928939 q^{60} - 468761537 q^{61} + 238770500 q^{62} - 358980429 q^{63} - 2035250696 q^{64} - 542245158 q^{65} - 154929237 q^{66} - 353402973 q^{67} + 1196053594 q^{68} + 127053056 q^{69} - 1180478502 q^{70} - 269829840 q^{71} - 485282307 q^{72} - 35353098 q^{73} + 920062914 q^{74} - 1606576144 q^{75} + 1140965370 q^{76} - 1032378781 q^{77} - 835494667 q^{78} - 683323974 q^{79} - 432598794 q^{80} - 1724339502 q^{81} - 324994534 q^{82} + 3803919051 q^{84} - 196261605 q^{85} + 572477022 q^{86} + 3699935866 q^{87} + 37403221 q^{88} - 9086462948 q^{90} + 2603275581 q^{91} - 2683122798 q^{92} - 2561821264 q^{94} - 397964902 q^{95} + 392112 q^{96} + 6155159124 q^{97} + 2492693148 q^{98}+O(q^{100}) \) 164 * q - 161 * q^3 - 40962 * q^4 - 6 * q^6 - 2055 * q^7 - 510909 * q^9 + 41025 * q^10 - 85389 * q^11 + 43064 * q^12 - 232462 * q^13 + 82708 * q^14 + 338445 * q^15 + 9425286 * q^16 - 1277590 * q^17 + 1176873 * q^18 - 1344159 * q^19 + 571062 * q^20 - 1367523 * q^21 - 1417332 * q^22 - 2148066 * q^23 + 62118 * q^24 + 29660776 * q^25 + 3184908 * q^26 + 7350574 * q^27 + 4828755 * q^28 + 996812 * q^29 - 9177016 * q^30 - 21474090 * q^31 - 15796239 * q^33 + 10592613 * q^35 + 131881331 * q^36 - 8950274 * q^38 - 35258971 * q^39 - 7901342 * q^40 + 24649770 * q^41 - 51088299 * q^42 + 15892214 * q^43 - 1176612 * q^44 - 69222114 * q^47 - 15455476 * q^48 - 57160671 * q^49 + 309166224 * q^50 + 52823362 * q^51 + 177629625 * q^52 - 155327528 * q^53 - 77925569 * q^55 - 92078463 * q^56 - 597924735 * q^58 - 290928939 * q^60 - 468761537 * q^61 + 238770500 * q^62 - 358980429 * q^63 - 2035250696 * q^64 - 542245158 * q^65 - 154929237 * q^66 - 353402973 * q^67 + 1196053594 * q^68 + 127053056 * q^69 - 1180478502 * q^70 - 269829840 * q^71 - 485282307 * q^72 - 35353098 * q^73 + 920062914 * q^74 - 1606576144 * q^75 + 1140965370 * q^76 - 1032378781 * q^77 - 835494667 * q^78 - 683323974 * q^79 - 432598794 * q^80 - 1724339502 * q^81 - 324994534 * q^82 + 3803919051 * q^84 - 196261605 * q^85 + 572477022 * q^86 + 3699935866 * q^87 + 37403221 * q^88 - 9086462948 * q^90 + 2603275581 * q^91 - 2683122798 * q^92 - 2561821264 * q^94 - 397964902 * q^95 + 392112 * q^96 + 6155159124 * q^97 + 2492693148 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	42.9063i		−	1.89621i	−0.317958	−	0.948105i	$-0.602997\pi$
$2$		−	42.9063i		−	1.89621i	0.317958	−	0.948105i	$-0.397003\pi$
$3$	−3.86494	−	6.69428i	−0.0275485	−	0.0477154i	0.851922	−	0.523668i	$-0.175437\pi$
$3$	−3.86494	−	6.69428i	−0.0275485	−	0.0477154i	−0.879471	+	0.475953i	$0.842103\pi$
$4$	−1328.95			−2.59561
$5$	1575.27	−	909.485i	1.12717	−	0.650774i	0.183951	−	0.982935i	$-0.441111\pi$
$5$	1575.27	−	909.485i	1.12717	−	0.650774i	0.943223	+	0.332161i	$0.107778\pi$
$6$	−287.227	+	165.831i	−0.0904783	+	0.0522377i
$7$	−4344.78	−	4634.27i	−0.683954	−	0.729525i
$7$	−4344.78	−	4634.27i	−0.683954	−	0.729525i
$8$			35052.4i			3.02561i
$9$	9811.62	−	16994.2i	0.498482	−	0.863396i
$10$	−39022.6	−	67589.2i	−1.23400	−	2.13736i
$11$	23355.4	−	13484.2i	0.480972	−	0.277689i	−0.239849	−	0.970810i	$-0.577098\pi$
$11$	23355.4	−	13484.2i	0.480972	−	0.277689i	0.720822	+	0.693121i	$0.243765\pi$
$12$	5136.33	+	8896.38i	0.0715051	+	0.123851i
$13$	−21210.2	−	100770.i	−0.205968	−	0.978559i
$13$	−21210.2	−	100770.i	−0.205968	−	0.978559i
$14$	−198839.	+	186419.i	−1.38333	+	1.29692i
$15$	−12176.7	−	7030.22i	−0.0621039	−	0.0358557i
$16$	823547.			3.14158
$17$	−593824.			−1.72440			−0.862199	−	0.506570i	$-0.830913\pi$
$17$	−593824.			−1.72440			−0.862199	+	0.506570i	$0.830913\pi$
$18$	−729160.	−	420981.i	−1.63718	−	0.945227i
$19$	−449200.	−	259346.i	−0.790767	−	0.456549i	0.0494656	−	0.998776i	$-0.484248\pi$
$19$	−449200.	−	259346.i	−0.790767	−	0.456549i	−0.840232	+	0.542226i	$0.817582\pi$
$20$	−2.09346e6	+	1.20866e6i	−2.92571	+	1.68916i
$21$	−14230.8	+	46996.4i	−0.0159677	+	0.0527324i
$22$	−578559.	−	1.00209e6i	−0.526557	−	0.912024i
$23$	1.80702e6			1.34645			0.673223	−	0.739440i	$-0.264909\pi$
$23$	1.80702e6			1.34645			0.673223	+	0.739440i	$0.264909\pi$
$24$	234651.	−	135476.i	0.144368	−	0.0833510i
$25$	677762.	−	1.17392e6i	0.347014	−	0.601046i
$26$	−4.32368e6	+	910050.i	−1.85555	+	0.390558i
$27$	−303833.			−0.110027
$28$	5.77401e6	+	6.15872e6i	1.77528	+	1.89356i
$29$	1.13858e6	−	1.97207e6i	0.298931	−	0.517764i	−0.676960	−	0.736019i	$-0.736703\pi$
$29$	1.13858e6	−	1.97207e6i	0.298931	−	0.517764i	0.975892	+	0.218255i	$0.0700365\pi$
$30$	−301641.	+	522457.i	−0.0679899	+	0.117762i
$31$	−2.87313e6	−	1.65880e6i	−0.558763	−	0.322602i	0.193886	−	0.981024i	$-0.437891\pi$
$31$	−2.87313e6	−	1.65880e6i	−0.558763	−	0.322602i	−0.752649	+	0.658422i	$0.771224\pi$
$32$		−	1.73885e7i		−	2.93149i
$33$	−180535.	−	104232.i	−0.0265001	−	0.0152998i
$34$			2.54788e7i			3.26982i
$35$	−1.10590e7	−	3.34873e6i	−1.24569	−	0.377202i
$36$	−1.30392e7	+	2.25845e7i	−1.29387	+	2.24104i
$37$			1.50250e7i			1.31797i	0.752156	+	0.658985i	$0.229014\pi$
$37$			1.50250e7i			1.31797i	−0.752156	+	0.658985i	$0.770986\pi$
$38$	−1.11276e7	+	1.92735e7i	−0.865713	+	1.49946i
$39$	−592608.	+	531458.i	−0.0410182	+	0.0367856i
$40$	3.18797e7	+	5.52172e7i	1.96899	+	3.41039i
$41$	−1.32457e7	−	7.64743e6i	−0.732064	−	0.422657i	0.0871131	−	0.996198i	$-0.472236\pi$
$41$	−1.32457e7	−	7.64743e6i	−0.732064	−	0.422657i	−0.819177	+	0.573541i	$0.805569\pi$
$42$	2.01644e6	+	610589.i	0.0999917	+	0.0302780i
$43$	1.12094e7	+	1.94153e7i	0.500007	+	0.866038i	1.00000		8.28016e-6i	$2.63566e-6\pi$
$43$	1.12094e7	+	1.94153e7i	0.500007	+	0.866038i	−0.499993	+	0.866030i	$0.666664\pi$
$44$	−3.10382e7	+	1.79199e7i	−1.24842	+	0.720773i
$45$		−	3.56941e7i		−	1.29760i
$46$		−	7.75328e7i		−	2.55314i
$47$	3.29827e7	−	1.90425e7i	0.985928	−	0.569226i	0.0818736	−	0.996643i	$-0.473910\pi$
$47$	3.29827e7	−	1.90425e7i	0.985928	−	0.569226i	0.904055	+	0.427417i	$0.140576\pi$
$48$	−3.18296e6	−	5.51306e6i	−0.0865459	−	0.149902i
$49$	−2.59931e6	+	4.02698e7i	−0.0644132	+	0.997923i
$50$	−5.03685e7	−	2.90803e7i	−1.13971	−	0.658012i
$51$	2.29510e6	+	3.97522e6i	0.0475045	+	0.0822803i
$52$	2.81873e7	+	1.33919e8i	0.534612	+	2.53996i
$53$	1.05115e7	−	1.82064e7i	0.182987	−	0.316944i	−0.759909	−	0.650029i	$-0.774757\pi$
$53$	1.05115e7	−	1.82064e7i	0.182987	−	0.316944i	0.942897	+	0.333086i	$0.108090\pi$
$54$			1.30364e7i			0.208634i
$55$	2.45274e7	−	4.24827e7i	0.361426	−	0.626009i
$56$	1.62442e8	−	1.52295e8i	2.20726	−	2.06938i
$57$			4.00943e6i			0.0503090i
$58$	−8.46144e7	−	4.88522e7i	−0.981789	−	0.566836i
$59$		−	1.86955e6i		−	0.0200865i	−0.999950	−	0.0100432i	$-0.996803\pi$
$59$		−	1.86955e6i		−	0.0200865i	0.999950	−	0.0100432i	$-0.00319691\pi$
$60$	1.61822e7	+	9.34282e6i	0.161197	+	0.0930674i
$61$	3.74771e7	−	6.49123e7i	0.346563	−	0.600265i	−0.639073	−	0.769146i	$-0.720682\pi$
$61$	3.74771e7	−	6.49123e7i	0.346563	−	0.600265i	0.985636	+	0.168881i	$0.0540154\pi$
$62$	−7.11730e7	+	1.23275e8i	−0.611720	+	1.05953i
$63$	−1.21385e8	+	2.83666e7i	−0.970808	+	0.226868i
$64$	−3.24422e8			−2.41713
$65$	−1.25061e8	−	1.39450e8i	−0.868982	−	0.968968i
$66$	−4.47220e6	+	7.74607e6i	−0.0290117	+	0.0502497i
$67$	1.47227e8	−	8.50016e7i	0.892588	−	0.515336i	0.0177999	−	0.999842i	$-0.494334\pi$
$67$	1.47227e8	−	8.50016e7i	0.892588	−	0.515336i	0.874788	+	0.484506i	$0.161000\pi$
$68$	7.89164e8			4.47587
$69$	−6.98405e6	−	1.20967e7i	−0.0370925	−	0.0642461i
$70$	−1.43682e8	+	4.74502e8i	−0.715254	+	2.36209i
$71$	5.78058e6	−	3.33742e6i	0.0269966	−	0.0155865i	−0.486441	−	0.873713i	$-0.661705\pi$
$71$	5.78058e6	−	3.33742e6i	0.0269966	−	0.0155865i	0.513438	+	0.858127i	$0.328372\pi$
$72$	5.95689e8	+	3.43921e8i	2.61230	+	1.50821i
$73$	−1.34676e7	−	7.77552e6i	−0.0555057	−	0.0320462i	0.471990	−	0.881604i	$-0.343536\pi$
$73$	−1.34676e7	−	7.77552e6i	−0.0555057	−	0.0320462i	−0.527496	+	0.849557i	$0.676869\pi$
$74$	6.44666e8			2.49915
$75$	−1.04781e7			−0.0382389
$76$	5.96965e8	+	3.44658e8i	2.05252	+	1.18502i
$77$	−1.63964e8	−	4.96490e7i	−0.531544	−	0.160954i
$78$	2.28029e7	+	2.54266e7i	0.0697533	+	0.0777791i
$79$	2.98414e8	+	5.16868e8i	0.861979	+	1.49299i	0.870015	+	0.493025i	$0.164109\pi$
$79$	2.98414e8	+	5.16868e8i	0.861979	+	1.49299i	−0.00803596	+	0.999968i	$0.502558\pi$
$80$	1.29731e9	−	7.49004e8i	3.54111	−	2.04446i
$81$	−1.91948e8	−	3.32464e8i	−0.495451	−	0.858146i
$82$	−3.28123e8	+	5.68326e8i	−0.801446	+	1.38815i
$83$		−	2.71423e8i		−	0.627763i	−0.949462	−	0.313881i	$-0.898371\pi$
$83$		−	2.71423e8i		−	0.627763i	0.949462	−	0.313881i	$-0.101629\pi$
$84$	1.89120e7	−	6.24560e7i	0.0414458	−	0.136873i
$85$	−9.35435e8	+	5.40074e8i	−1.94370	+	1.12219i
$86$	8.33041e8	−	4.80956e8i	1.64219	−	0.948118i
$87$	−1.76021e7			−0.0329404
$88$	4.72655e8	+	8.18663e8i	0.840180	+	1.45523i
$89$		−	6.72024e7i		−	0.113535i	−0.998387	−	0.0567675i	$-0.981921\pi$
$89$		−	6.72024e7i		−	0.113535i	0.998387	−	0.0567675i	$-0.0180794\pi$
$90$	−1.53150e9			−2.46052
$91$	−3.74843e8	+	5.36118e8i	−0.573011	+	0.819548i
$92$	−2.40145e9			−3.49485
$93$			2.56447e7i			0.0355487i
$94$	−8.17046e8	−	1.41516e9i	−1.07937	−	1.86953i
$95$	−9.43484e8			−1.18844
$96$	−1.16404e8	+	6.72057e7i	−0.139877	+	0.0807581i
$97$	−2.44831e7	+	1.41353e7i	−0.0280798	+	0.0162119i	−0.513974	−	0.857806i	$-0.671827\pi$
$97$	−2.44831e7	+	1.41353e7i	−0.0280798	+	0.0162119i	0.485894	+	0.874018i	$0.338494\pi$
$98$	1.72783e9	+	1.11527e8i	1.89227	+	0.122141i
$99$		−	5.29209e8i		−	0.553693i
$100$	−9.00714e8	+	1.56008e9i	−0.900714	+	1.56008i
$101$	1.01802e9	+	1.76326e9i	0.973440	+	1.68605i	0.684990	+	0.728552i	$0.259806\pi$
$101$	1.01802e9	+	1.76326e9i	0.973440	+	1.68605i	0.288449	+	0.957495i	$0.406860\pi$
$102$	1.70562e8	−	9.84742e7i	0.156021	−	0.0900786i
$103$	−7.43975e8	−	1.28860e9i	−0.651315	−	1.12811i	−0.982804	−	0.184651i	$-0.940884\pi$
$103$	−7.43975e8	−	1.28860e9i	−0.651315	−	1.12811i	0.331489	−	0.943459i	$-0.392449\pi$
$104$	3.53224e9	−	7.43468e8i	2.96074	−	0.623178i
$105$	2.03252e7	+	8.69749e7i	0.0163186	+	0.0698300i
$106$	−7.81169e8	−	4.51008e8i	−0.600992	−	0.346983i
$107$	−2.19291e9			−1.61731			−0.808655	−	0.588283i	$-0.799804\pi$
$107$	−2.19291e9			−1.61731			−0.808655	+	0.588283i	$0.799804\pi$
$108$	4.03780e8			0.285586
$109$	1.20480e9	+	6.95594e8i	0.817518	+	0.471994i	0.849560	−	0.527492i	$-0.176868\pi$
$109$	1.20480e9	+	6.95594e8i	0.817518	+	0.471994i	−0.0320417	+	0.999487i	$0.510201\pi$
$110$	−1.82278e9	−	1.05238e9i	−1.18704	−	0.685340i
$111$	1.00581e8	−	5.80706e7i	0.0628874	−	0.0363081i
$112$	−3.57814e9	−	3.81654e9i	−2.14870	−	2.29186i
$113$	4.22823e8	+	7.32351e8i	0.243953	+	0.422539i	0.961837	−	0.273624i	$-0.0882225\pi$
$113$	4.22823e8	+	7.32351e8i	0.243953	+	0.422539i	−0.717884	+	0.696163i	$0.754889\pi$
$114$	1.72030e8			0.0953964
$115$	2.84656e9	−	1.64346e9i	1.51768	−	0.876232i
$116$	−1.51311e9	+	2.62079e9i	−0.775909	+	1.34391i
$117$	−1.92062e9	−	6.28269e8i	−0.947555	−	0.309962i
$118$	−8.02156e7			−0.0380881
$119$	2.58004e9	+	2.75194e9i	1.17941	+	1.25799i
$120$	2.46426e8	−	4.26823e8i	0.108485	−	0.187902i
$121$	−8.15325e8	+	1.41218e9i	−0.345777	+	0.598904i
$122$	−2.78515e9	−	1.60801e9i	−1.13823	−	0.657156i
$123$			1.18228e8i			0.0465742i
$124$	3.81825e9	+	2.20447e9i	1.45033	+	0.837348i
$125$			1.08702e9i			0.398237i
$126$	1.21710e9	+	5.20819e9i	0.430190	+	1.84086i
$127$	−1.86007e9	+	3.22173e9i	−0.634471	+	1.09894i	0.352156	+	0.935941i	$0.385449\pi$
$127$	−1.86007e9	+	3.22173e9i	−0.634471	+	1.09894i	−0.986627	+	0.162994i	$0.947885\pi$
$128$			5.01683e9i			1.65190i
$129$	8.66478e7	−	1.50078e8i	0.0275489	−	0.0477161i
$130$	−5.98330e9	+	5.36590e9i	−1.83737	+	1.64777i
$131$	−1.48877e9	−	2.57862e9i	−0.441679	−	0.765010i	0.556136	−	0.831092i	$-0.312283\pi$
$131$	−1.48877e9	−	2.57862e9i	−0.441679	−	0.765010i	−0.997814	+	0.0660818i	$0.978950\pi$
$132$	2.39922e8	+	1.38519e8i	0.0687839	+	0.0397124i
$133$	7.49799e8	+	3.20851e9i	0.207784	+	0.889143i
$134$	−3.64711e9	−	6.31697e9i	−0.977185	−	1.69253i
$135$	−4.78620e8	+	2.76331e8i	−0.124019	+	0.0716025i
$136$		−	2.08150e10i		−	5.21736i
$137$			5.19659e9i			1.26030i	0.776472	+	0.630152i	$0.217008\pi$
$137$			5.19659e9i			1.26030i	−0.776472	+	0.630152i	$0.782992\pi$
$138$	−5.19026e8	+	2.99660e8i	−0.121824	+	0.0703352i
$139$	−8.90671e8	−	1.54269e9i	−0.202372	−	0.350519i	0.746920	−	0.664914i	$-0.231532\pi$
$139$	−8.90671e8	−	1.54269e9i	−0.202372	−	0.350519i	−0.949292	+	0.314395i	$0.898198\pi$
$140$	1.46969e10	+	4.45030e9i	3.23333	+	0.979069i
$141$	−2.54952e8	−	1.47197e8i	−0.0543217	−	0.0313626i
$142$	−1.43196e8	−	2.48024e8i	−0.0295553	−	0.0511912i
$143$	−1.85418e9	−	2.06752e9i	−0.370800	−	0.413464i
$144$	8.08034e9	−	1.39956e10i	1.56602	−	2.71243i
$145$		−	4.14207e9i		−	0.778147i
$146$	−3.33619e8	+	5.77845e8i	−0.0607663	+	0.105250i
$147$	2.79624e8	−	1.38240e8i	0.0493908	−	0.0244178i
$148$		−	1.99675e10i		−	3.42094i
$149$	8.06072e7	+	4.65386e7i	0.0133979	+	0.00773526i	0.506684	−	0.862132i	$-0.330871\pi$
$149$	8.06072e7	+	4.65386e7i	0.0133979	+	0.00773526i	−0.493286	+	0.869867i	$0.664204\pi$
$150$			4.49575e8i			0.0725089i
$151$	5.09221e8	+	2.93999e8i	0.0797095	+	0.0460203i	0.539325	−	0.842098i	$-0.318679\pi$
$151$	5.09221e8	+	2.93999e8i	0.0797095	+	0.0460203i	−0.459616	+	0.888118i	$0.652013\pi$
$152$	9.09070e9	−	1.57455e10i	1.38134	−	2.39255i
$153$	−5.82638e9	+	1.00916e10i	−0.859582	+	1.48884i
$154$	−2.13026e9	+	7.03508e9i	−0.305203	+	1.00792i
$155$	−6.03462e9			−0.839764
$156$	7.87548e8	−	7.06282e8i	0.106467	−	0.0954812i
$157$	−3.01795e9	+	5.22725e9i	−0.396428	+	0.686633i	−0.993282	−	0.115717i	$-0.963084\pi$
$157$	−3.01795e9	+	5.22725e9i	−0.396428	+	0.686633i	0.596855	+	0.802349i	$0.296417\pi$
$158$	2.21769e10	−	1.28038e10i	2.83103	−	1.63449i
$159$	−1.62505e8			−0.0201641
$160$	−1.58146e10	−	2.73917e10i	−1.90774	−	3.30430i
$161$	−7.85113e9	−	8.37424e9i	−0.920907	−	0.982266i
$162$	−1.42648e10	+	8.23578e9i	−1.62723	+	0.939479i
$163$	−8.46777e9	−	4.88887e9i	−0.939560	−	0.542455i	−0.0497379	−	0.998762i	$-0.515839\pi$
$163$	−8.46777e9	−	4.88887e9i	−0.939560	−	0.542455i	−0.889822	+	0.456307i	$0.849172\pi$
$164$	1.76030e10	+	1.01631e10i	1.90015	+	1.09705i
$165$	−3.79188e8			−0.0398270
$166$	−1.16458e10			−1.19037
$167$	1.04248e7	+	6.01877e6i	0.00103716	+	0.000598802i	0.500518	−	0.865726i	$-0.333143\pi$
$167$	1.04248e7	+	6.01877e6i	0.00103716	+	0.000598802i	−0.499481	+	0.866325i	$0.666476\pi$
$168$	−1.64734e9	−	4.98822e8i	−0.159548	−	0.0483119i
$169$	−9.70476e9	+	4.27470e9i	−0.915155	+	0.403103i
$170$	2.31726e10	+	4.01361e10i	2.12791	+	3.68566i
$171$	−8.81476e9	+	5.08920e9i	−0.788366	+	0.455163i
$172$	−1.48968e10	−	2.58021e10i	−1.29782	−	2.24790i
$173$	1.04859e10	−	1.81621e10i	0.890016	−	1.54155i	0.0501614	−	0.998741i	$-0.484026\pi$
$173$	1.04859e10	−	1.81621e10i	0.890016	−	1.54155i	0.839855	−	0.542812i	$-0.182640\pi$
$174$			7.55244e8i			0.0624619i
$175$	−8.38499e9	+	1.95949e9i	−0.675820	+	0.157933i
$176$	1.92343e10	−	1.11049e10i	1.51101	−	0.872384i
$177$	−1.25153e7	+	7.22572e6i	−0.000958433	+	0.000553352i
$178$	−2.88341e9			−0.215286
$179$	−1.19623e10	−	2.07193e10i	−0.870916	−	1.50847i	−0.861051	−	0.508519i	$-0.830193\pi$
$179$	−1.19623e10	−	2.07193e10i	−0.870916	−	1.50847i	−0.00986494	−	0.999951i	$-0.503140\pi$
$180$			4.74358e10i			3.36806i
$181$	1.98654e10			1.37576			0.687880	−	0.725824i	$-0.258542\pi$
$181$	1.98654e10			1.37576			0.687880	+	0.725824i	$0.258542\pi$
$182$	2.30029e10	+	1.60831e10i	1.55403	+	1.08655i
$183$	−5.79388e8			−0.0381891
$184$			6.33406e10i			4.07382i
$185$	1.36650e10	+	2.36684e10i	0.857701	+	1.48558i
$186$	1.10032e9			0.0674079
$187$	−1.38690e10	+	8.00726e9i	−0.829387	+	0.478847i
$188$	−4.38324e10	+	2.53066e10i	−2.55909	+	1.47749i
$189$	1.32009e9	+	1.40804e9i	0.0752532	+	0.0802672i
$190$			4.04814e10i			2.25354i
$191$	1.18703e10	−	2.05600e10i	0.645377	−	1.11783i	−0.338838	−	0.940845i	$-0.610034\pi$
$191$	1.18703e10	−	2.05600e10i	0.645377	−	1.11783i	0.984214	−	0.176980i	$-0.0566329\pi$
$192$	1.25387e9	+	2.17177e9i	0.0665883	+	0.115334i
$193$	2.83316e10	−	1.63573e10i	1.46982	−	0.848600i	0.470392	−	0.882458i	$-0.344113\pi$
$193$	2.83316e10	−	1.63573e10i	1.46982	−	0.848600i	0.999427	+	0.0338576i	$0.0107793\pi$
$194$	6.06495e8	+	1.05048e9i	0.0307411	+	0.0532452i
$195$	−4.50166e8	+	1.37616e9i	−0.0222955	+	0.0681574i
$196$	3.45435e9	−	5.35167e10i	0.167192	−	2.59022i
$197$	3.29436e9	+	1.90200e9i	0.155838	+	0.0899730i	0.575891	−	0.817526i	$-0.304655\pi$
$197$	3.29436e9	+	1.90200e9i	0.155838	+	0.0899730i	−0.420053	+	0.907499i	$0.637989\pi$
$198$	−2.27064e10			−1.04992
$199$	−3.48638e10			−1.57593			−0.787963	−	0.615723i	$-0.788864\pi$
$199$	−3.48638e10			−1.57593			−0.787963	+	0.615723i	$0.788864\pi$
$200$	4.11487e10	+	2.37572e10i	1.81853	+	1.04993i
$201$	−1.13805e9	−	6.57053e8i	−0.0491789	−	0.0283934i
$202$	7.56549e10	−	4.36794e10i	3.19710	−	1.84585i
$203$	−1.40860e10	+	3.29176e9i	−0.582177	+	0.136049i
$204$	−3.05007e9	−	5.28288e9i	−0.123303	−	0.213568i
$205$	−2.78209e10			−1.10022
$206$	−5.52892e10	+	3.19212e10i	−2.13913	+	1.23503i
$207$	1.77298e10	−	3.07090e10i	0.671179	−	1.16252i
$208$	−1.74676e10	−	8.29890e10i	−0.647065	−	3.07422i
$209$	−1.39883e10			−0.507116
$210$	3.73177e9	−	8.72079e8i	0.132412	−	0.0309435i
$211$	−1.11652e10	+	1.93388e10i	−0.387790	+	0.671673i	−0.992152	−	0.125038i	$-0.960095\pi$
$211$	−1.11652e10	+	1.93388e10i	−0.387790	+	0.671673i	0.604362	+	0.796710i	$0.293428\pi$
$212$	−1.39692e10	+	2.41954e10i	−0.474964	+	0.822662i
$213$	−4.46833e7	−	2.57979e7i	−0.00148743	−	0.000858768i
$214$			9.40896e10i			3.06676i
$215$	3.53159e10	+	2.03896e10i	1.12719	+	0.650784i
$216$		−	1.06501e10i		−	0.332898i
$217$	4.79579e9	+	2.05220e10i	0.146822	+	0.628276i
$218$	2.98454e10	−	5.16937e10i	0.895000	−	1.55019i
$219$			1.20208e8i			0.00353130i
$220$	−3.25958e10	+	5.64575e10i	−0.938122	+	1.62487i
$221$	1.25951e10	+	5.98397e10i	0.355170	+	1.68743i
$222$	−2.49160e9	−	4.31557e9i	−0.0688477	−	0.119248i
$223$	3.65686e9	+	2.11129e9i	0.0990231	+	0.0571710i	0.548694	−	0.836023i	$-0.315125\pi$
$223$	3.65686e9	+	2.11129e9i	0.0990231	+	0.0571710i	−0.449671	+	0.893194i	$0.648459\pi$
$224$	−8.05832e10	+	7.55495e10i	−2.13859	+	2.00500i
$225$	−1.32999e10	−	2.30361e10i	−0.345961	−	0.599222i
$226$	3.14225e10	−	1.81418e10i	0.801222	−	0.462586i
$227$		−	1.89137e10i		−	0.472782i	−0.971658	−	0.236391i	$-0.924035\pi$
$227$		−	1.89137e10i		−	0.472782i	0.971658	−	0.236391i	$-0.0759646\pi$
$228$		−	5.32834e9i		−	0.130583i
$229$	−3.26779e10	+	1.88666e10i	−0.785225	+	0.453350i	−0.838279	−	0.545242i	$-0.816438\pi$
$229$	−3.26779e10	+	1.88666e10i	−0.785225	+	0.453350i	0.0530541	+	0.998592i	$0.483104\pi$
$230$	−7.05149e10	−	1.22135e11i	−1.66152	−	2.87784i
$231$	3.01346e8	+	1.28951e9i	0.00696324	+	0.0297969i
$232$	6.91260e10	+	3.99099e10i	1.56655	+	0.904450i
$233$	−4.11238e10	−	7.12285e10i	−0.914096	−	1.58326i	−0.808220	−	0.588881i	$-0.799569\pi$
$233$	−4.11238e10	−	7.12285e10i	−0.914096	−	1.58326i	−0.105876	−	0.994379i	$-0.533765\pi$
$234$	−2.69567e10	+	8.24067e10i	−0.587754	+	1.79676i
$235$	3.46378e10	−	5.99945e10i	0.740875	−	1.28323i
$236$			2.48455e9i			0.0521366i
$237$	2.30671e9	−	3.99533e9i	0.0474924	−	0.0822593i
$238$	1.18076e11	−	1.10700e11i	2.38542	−	2.23641i
$239$		−	7.09407e10i		−	1.40639i	−0.710998	−	0.703194i	$-0.751757\pi$
$239$		−	7.09407e10i		−	1.40639i	0.710998	−	0.703194i	$-0.248243\pi$
$240$	−1.00281e10	−	5.78972e9i	−0.195104	−	0.112644i
$241$		−	9.29571e9i		−	0.177503i	−0.996054	−	0.0887515i	$-0.971712\pi$
$241$		−	9.29571e9i		−	0.177503i	0.996054	−	0.0887515i	$-0.0282877\pi$
$242$	6.05916e10	+	3.49826e10i	1.13565	+	0.655666i
$243$	−4.47391e9	+	7.74904e9i	−0.0823112	+	0.142567i
$244$	−4.98053e10	+	8.62654e10i	−0.899542	+	1.55805i
$245$	3.25302e10	+	6.58000e10i	0.576818	+	1.16675i
$246$	5.07271e9			0.0883145
$247$	−1.66067e10	+	5.07667e10i	−0.283888	+	0.867846i
$248$	5.81450e10	−	1.00710e11i	0.976067	−	1.69060i
$249$	−1.81698e9	+	1.04904e9i	−0.0299539	+	0.0172939i
$250$	4.66399e10			0.755140
$251$	−1.82778e10	−	3.16580e10i	−0.290664	−	0.503445i	0.683303	−	0.730135i	$-0.260543\pi$
$251$	−1.82778e10	−	3.16580e10i	−0.290664	−	0.503445i	−0.973967	+	0.226690i	$0.927210\pi$
$252$	1.61315e11	−	3.76978e10i	2.51984	−	0.588862i
$253$	4.22037e10	−	2.43663e10i	0.647603	−	0.373894i
$254$	1.38233e11	+	7.98086e10i	2.08381	+	1.20309i
$255$	7.23081e9	+	4.17471e9i	0.107092	+	0.0618295i
$256$	4.91495e10			0.715220
$257$	−3.93693e9			−0.0562935			−0.0281468	−	0.999604i	$-0.508961\pi$
$257$	−3.93693e9			−0.0562935			−0.0281468	+	0.999604i	$0.508961\pi$
$258$	−6.43931e9	−	3.71774e9i	−0.0904796	−	0.0522384i
$259$	6.96297e10	−	6.52802e10i	0.961492	−	0.901431i
$260$	1.66200e11	+	1.85323e11i	2.25554	+	2.51506i
$261$	−2.23426e10	−	3.86985e10i	−0.298024	−	0.516192i
$262$	−1.10639e11	+	6.38776e10i	−1.45062	+	0.837515i
$263$	−8.01565e9	−	1.38835e10i	−0.103309	−	0.178936i	0.809737	−	0.586793i	$-0.199610\pi$
$263$	−8.01565e9	−	1.38835e10i	−0.103309	−	0.178936i	−0.913046	+	0.407857i	$0.866276\pi$
$264$	3.65357e9	−	6.32817e9i	0.0462914	−	0.0801790i
$265$		−	3.82400e10i		−	0.476334i
$266$	1.37666e11	−	3.21711e10i	1.68600	−	0.394002i
$267$	−4.49872e8	+	2.59734e8i	−0.00541736	+	0.00312772i
$268$	−1.95658e11	+	1.12963e11i	−2.31681	+	1.33761i
$269$	−5.68829e10			−0.662363			−0.331182	−	0.943567i	$-0.607447\pi$
$269$	−5.68829e10			−0.662363			−0.331182	+	0.943567i	$0.607447\pi$
$270$	1.18564e10	+	2.05358e10i	0.135773	+	0.235166i
$271$		−	5.86294e10i		−	0.660318i	−0.943925	−	0.330159i	$-0.892898\pi$
$271$		−	5.86294e10i		−	0.660318i	0.943925	−	0.330159i	$-0.107102\pi$
$272$	−4.89042e11			−5.41734
$273$	5.03767e9	+	4.37234e8i	0.0548906	+	0.00476411i
$274$	2.22966e11			2.38980
$275$		−	3.65564e10i		−	0.385449i
$276$	9.28147e9	+	1.60760e10i	0.0962778	+	0.166758i
$277$	1.56130e10			0.159341			0.0796704	−	0.996821i	$-0.474613\pi$
$277$	1.56130e10			0.159341			0.0796704	+	0.996821i	$0.474613\pi$
$278$	−6.61911e10	+	3.82154e10i	−0.664657	+	0.383740i
$279$	−5.63801e10	+	3.25511e10i	−0.557066	+	0.321622i
$280$	1.17381e11	−	3.87646e11i	1.14127	−	3.76898i
$281$		−	4.69470e10i		−	0.449189i	−0.974452	−	0.224595i	$-0.927894\pi$
$281$		−	4.69470e10i		−	0.449189i	0.974452	−	0.224595i	$-0.0721058\pi$
$282$	−6.31567e9	+	1.09391e10i	−0.0594701	+	0.103005i
$283$	2.65504e10	+	4.59866e10i	0.246055	+	0.426180i	0.962428	−	0.271538i	$-0.0875323\pi$
$283$	2.65504e10	+	4.59866e10i	0.246055	+	0.426180i	−0.716373	+	0.697718i	$0.754199\pi$
$284$	−7.68212e9	+	4.43527e9i	−0.0700726	+	0.0404565i
$285$	3.64651e9	+	6.31594e9i	0.0327398	+	0.0567070i
$286$	−8.87098e10	+	7.95561e10i	−0.784015	+	0.703115i
$287$	2.21096e10	+	9.46108e10i	0.192359	+	0.823137i
$288$	−2.95505e11	−	1.70610e11i	−2.53104	−	1.46129i
$289$	2.34039e11			1.97355
$290$	−1.77721e11			−1.47553
$291$	1.89252e8	+	1.09265e8i	0.00154711	+	0.000893225i
$292$	1.78978e10	+	1.03333e10i	0.144071	+	0.0831795i
$293$	−2.03064e10	+	1.17239e10i	−0.160964	+	0.0929324i	−0.578318	−	0.815811i	$-0.696291\pi$
$293$	−2.03064e10	+	1.17239e10i	−0.160964	+	0.0929324i	0.417354	+	0.908744i	$0.362957\pi$
$294$	−5.93137e9	−	1.19976e10i	−0.0463012	−	0.0936552i
$295$	−1.70033e9	−	2.94506e9i	−0.0130718	−	0.0226409i
$296$	−5.26661e11			−3.98767
$297$	−7.09613e9	+	4.09696e9i	−0.0529198	+	0.0305532i
$298$	1.99680e9	−	3.45856e9i	0.0146677	−	0.0254052i
$299$	−3.83273e10	−	1.82094e11i	−0.277324	−	1.31758i
$300$	1.39248e10			0.0992532
$301$	4.12733e10	−	1.36303e11i	0.289814	−	0.957098i
$302$	1.26144e10	−	2.18488e10i	0.0872641	−	0.151146i
$303$	7.86916e9	−	1.36298e10i	0.0536336	−	0.0928961i
$304$	−3.69937e11	−	2.13583e11i	−2.48426	−	1.43429i
$305$		−	1.36340e11i		−	0.902137i
$306$	4.32993e11	+	2.49988e11i	2.82315	+	1.62995i
$307$		−	2.01694e11i		−	1.29590i	−0.761684	−	0.647949i	$-0.775627\pi$
$307$		−	2.01694e11i		−	1.29590i	0.761684	−	0.647949i	$-0.224373\pi$
$308$	2.17900e11	+	6.59812e10i	1.37968	+	0.417775i
$309$	−5.75085e9	+	9.96076e9i	−0.0358855	+	0.0621554i
$310$			2.58923e11i			1.59237i
$311$	1.10888e11	−	1.92064e11i	0.672146	−	1.16419i	−0.305148	−	0.952305i	$-0.598706\pi$
$311$	1.10888e11	−	1.92064e11i	0.672146	−	1.16419i	0.977294	−	0.211887i	$-0.0679608\pi$
$312$	−1.86289e10	−	2.07723e10i	−0.111299	−	0.124105i
$313$	2.47968e10	+	4.29494e10i	0.146032	+	0.252934i	0.929757	−	0.368173i	$-0.120017\pi$
$313$	2.47968e10	+	4.29494e10i	0.146032	+	0.252934i	−0.783726	+	0.621107i	$0.786683\pi$
$314$	2.24282e11	+	1.29489e11i	1.30200	+	0.751710i
$315$	−1.65416e11	+	1.55083e11i	−0.946630	+	0.887497i
$316$	−3.96578e11	−	6.86893e11i	−2.23736	−	3.87523i
$317$	−1.77683e11	+	1.02585e11i	−0.988278	+	0.570583i	−0.904759	−	0.425924i	$-0.859949\pi$
$317$	−1.77683e11	+	1.02585e11i	−0.988278	+	0.570583i	−0.0835190	+	0.996506i	$0.526616\pi$
$318$			6.97248e9i			0.0382354i
$319$		−	6.14114e10i		−	0.332040i
$320$	−5.11054e11	+	2.95057e11i	−2.72453	+	1.57301i
$321$	8.47547e9	+	1.46799e10i	0.0445544	+	0.0771706i
$322$	−3.59308e11	+	3.36863e11i	−1.86258	+	1.74623i
$323$	2.66746e11	+	1.54006e11i	1.36360	+	0.787273i
$324$	2.55090e11	+	4.41828e11i	1.28600	+	2.22741i
$325$	−1.32671e11	−	4.33992e10i	−0.659633	−	0.215778i
$326$	−2.09763e11	+	3.63321e11i	−1.02861	+	1.78160i
$327$		−	1.07537e10i		−	0.0520109i
$328$	2.68061e11	−	4.64295e11i	1.27880	−	2.21494i
$329$	−2.31551e11	−	7.01148e10i	−1.08959	−	0.329935i
$330$			1.62696e10i			0.0755203i
$331$	3.57484e10	+	2.06393e10i	0.163693	+	0.0945082i	0.579609	−	0.814895i	$-0.303205\pi$
$331$	3.57484e10	+	2.06393e10i	0.163693	+	0.0945082i	−0.415916	+	0.909403i	$0.636539\pi$
$332$			3.60709e11i			1.62943i
$333$	2.55338e11	+	1.47419e11i	1.13793	+	0.656985i
$334$	2.58243e8	−	4.47290e8i	0.00113545	−	0.00196667i
$335$	1.54615e11	−	2.67802e11i	0.670735	−	1.16175i
$336$	−1.17197e10	+	3.87038e10i	−0.0501637	+	0.165663i
$337$	−2.77285e11			−1.17109			−0.585547	−	0.810638i	$-0.699120\pi$
$337$	−2.77285e11			−1.17109			−0.585547	+	0.810638i	$0.699120\pi$
$338$	1.83412e11	+	4.16395e11i	0.764368	+	1.73532i
$339$	3.26838e9	−	5.66099e9i	0.0134411	−	0.0232806i
$340$	1.24315e12	−	7.17732e11i	5.04508	−	2.91278i
$341$	−8.94706e10			−0.358332
$342$	2.18359e11	+	3.78209e11i	0.863085	+	1.49491i
$343$	1.97915e11	−	1.62918e11i	0.772066	−	0.635543i
$344$	−6.80555e11	+	3.92918e11i	−2.62029	+	1.51283i
$345$	−2.20036e10	−	1.27038e10i	−0.0836195	−	0.0482777i
$346$	−7.79269e11	−	4.49911e11i	−2.92311	−	1.68766i
$347$	−4.82096e11			−1.78505			−0.892527	−	0.450994i	$-0.851069\pi$
$347$	−4.82096e11			−1.78505			−0.892527	+	0.450994i	$0.851069\pi$
$348$	2.33924e10			0.0855005
$349$	2.52331e10	+	1.45683e10i	0.0910451	+	0.0525649i	0.544831	−	0.838546i	$-0.316594\pi$
$349$	2.52331e10	+	1.45683e10i	0.0910451	+	0.0525649i	−0.453786	+	0.891111i	$0.649927\pi$
$350$	8.40745e10	+	3.59769e11i	0.299473	+	1.28150i
$351$	6.44435e9	+	3.06173e10i	0.0226619	+	0.107668i
$352$	−2.34471e11	−	4.06116e11i	−0.814043	−	1.40996i
$353$	4.00094e11	−	2.30994e11i	1.37144	−	0.791799i	0.380328	−	0.924852i	$-0.375811\pi$
$353$	4.00094e11	−	2.30994e11i	1.37144	−	0.791799i	0.991109	+	0.133052i	$0.0424778\pi$
$354$	3.10029e8	+	5.36986e8i	0.00104927	+	0.00181739i
$355$	6.07067e9	−	1.05147e10i	0.0202866	−	0.0351374i
$356$			8.93088e10i			0.294693i
$357$	8.45056e9	−	2.79076e10i	0.0275346	−	0.0909317i
$358$	−8.88990e11	+	5.13258e11i	−2.86038	+	1.65144i
$359$	−3.68509e11	+	2.12759e11i	−1.17091	+	0.676025i	−0.953894	−	0.300143i	$-0.902966\pi$
$359$	−3.68509e11	+	2.12759e11i	−1.17091	+	0.676025i	−0.217016	+	0.976168i	$0.569632\pi$
$360$	1.25116e12			3.92603
$361$	−2.68235e10	−	4.64596e10i	−0.0831252	−	0.143977i
$362$		−	8.52349e11i		−	2.60873i
$363$	1.26047e10			0.0381025
$364$	4.98148e11	−	7.12476e11i	1.48731	−	2.12723i
$365$	−2.82869e10			−0.0834194
$366$			2.48594e10i			0.0724146i
$367$	1.00992e11	+	1.74924e11i	0.290597	+	0.503328i	0.973951	−	0.226759i	$-0.0728129\pi$
$367$	1.00992e11	+	1.74924e11i	0.290597	+	0.503328i	−0.683354	+	0.730087i	$0.739480\pi$
$368$	1.48817e12			4.22997
$369$	−2.59924e11	+	1.50067e11i	−0.729841	+	0.421374i
$370$	1.01553e12	−	5.86314e11i	2.81697	−	1.62638i
$371$	−1.30043e11	+	3.03898e10i	−0.356373	+	0.0832810i
$372$		−	3.40806e10i		−	0.0922707i
$373$	1.35345e11	−	2.34425e11i	0.362037	−	0.627067i	−0.626259	−	0.779615i	$-0.715415\pi$
$373$	1.35345e11	−	2.34425e11i	0.362037	−	0.627067i	0.988296	+	0.152548i	$0.0487479\pi$
$374$	3.43562e11	+	5.95067e11i	0.907994	+	1.57269i
$375$	7.27679e9	−	4.20126e9i	0.0190020	−	0.0109708i
$376$	6.67488e11	+	1.15612e12i	1.72226	+	2.98304i
$377$	−2.22876e11	−	7.29066e10i	−0.568233	−	0.185879i
$378$	6.04140e10	−	5.66402e10i	0.152203	−	0.142696i
$379$	3.25909e11	+	1.88163e11i	0.811371	+	0.468445i	0.847432	−	0.530904i	$-0.178148\pi$
$379$	3.25909e11	+	1.88163e11i	0.811371	+	0.468445i	−0.0360609	+	0.999350i	$0.511481\pi$
$380$	1.25385e12			3.08473
$381$	2.87562e10			0.0699148
$382$	−8.82156e11	−	5.09313e11i	−2.11963	−	1.22377i
$383$	−3.73692e11	−	2.15751e11i	−0.887399	−	0.512340i	−0.0143082	−	0.999898i	$-0.504555\pi$
$383$	−3.73692e11	−	2.15751e11i	−0.887399	−	0.512340i	−0.873091	+	0.487558i	$0.837888\pi$
$384$	3.35841e10	−	1.93898e10i	0.0788211	−	0.0455074i
$385$	−3.03443e11	+	7.09116e10i	−0.703888	+	0.164492i
$386$	−7.01831e11	−	1.21561e12i	−1.60912	−	2.78708i
$387$	4.39932e11			0.996979
$388$	3.25369e10	−	1.87852e10i	0.0728842	−	0.0420797i
$389$	8.54522e10	−	1.48008e11i	0.189213	−	0.327726i	−0.755775	−	0.654831i	$-0.772740\pi$
$389$	8.54522e10	−	1.48008e11i	0.189213	−	0.327726i	0.944988	+	0.327105i	$0.106073\pi$
$390$	5.90459e10	+	1.93150e10i	0.129241	+	0.0422770i
$391$	−1.07305e12			−2.32181
$392$	−1.41155e12	−	9.11120e10i	−3.01933	−	0.194889i
$393$	−1.15080e10	+	1.99325e10i	−0.0243351	+	0.0421497i
$394$	8.16078e10	−	1.41349e11i	0.170608	−	0.295501i
$395$	9.40167e11	+	5.42805e11i	1.94320	+	1.12191i
$396$			7.03294e11i			1.43717i
$397$	6.06010e11	+	3.49880e11i	1.22440	+	0.706907i	0.965853	−	0.259092i	$-0.0834233\pi$
$397$	6.06010e11	+	3.49880e11i	1.22440	+	0.706907i	0.258546	+	0.965999i	$0.416757\pi$
$398$			1.49588e12i			2.98828i
$399$	1.85808e10	−	1.74201e10i	0.0367016	−	0.0344090i
$400$	5.58169e11	−	9.66778e11i	1.09017	−	1.88824i
$401$			2.52813e11i			0.488258i	0.969743	+	0.244129i	$0.0785020\pi$
$401$			2.52813e11i			0.488258i	−0.969743	+	0.244129i	$0.921498\pi$
$402$	−2.81917e10	+	4.88295e10i	−0.0538399	+	0.0932535i
$403$	−1.06218e11	+	3.24709e11i	−0.200598	+	0.613227i
$404$	−1.35290e12	−	2.34329e12i	−2.52667	−	4.37632i
$405$	−6.04741e11	−	3.49147e11i	−1.11692	−	0.644854i
$406$	1.41237e11	+	6.04378e11i	0.257978	+	1.10393i
$407$	2.02600e11	+	3.50914e11i	0.365986	+	0.633907i
$408$	−1.39341e11	+	8.04487e10i	−0.248948	+	0.143730i
$409$		−	9.40590e11i		−	1.66206i	−0.556231	−	0.831028i	$-0.687753\pi$
$409$		−	9.40590e11i		−	1.66206i	0.556231	−	0.831028i	$-0.312247\pi$
$410$			1.19369e12i			2.08624i
$411$	3.47874e10	−	2.00845e10i	0.0601359	−	0.0347195i
$412$	9.88708e11	+	1.71249e12i	1.69056	+	2.92813i
$413$	−8.66401e9	+	8.12280e9i	−0.0146536	+	0.0137382i
$414$	−1.31761e12	−	7.60723e11i	−2.20437	−	1.27270i
$415$	−2.46855e11	−	4.27566e11i	−0.408532	−	0.707598i
$416$	−1.75225e12	+	3.68814e11i	−2.86863	+	0.603792i
$417$	−6.88479e9	+	1.19248e10i	−0.0111501	+	0.0193125i
$418$			6.00187e11i			0.961598i
$419$	−2.20634e11	+	3.82149e11i	−0.349711	+	0.605717i	−0.986198	−	0.165570i	$-0.947054\pi$
$419$	−2.20634e11	+	3.82149e11i	−0.349711	+	0.605717i	0.636487	+	0.771287i	$0.280387\pi$
$420$	−2.70112e10	−	1.15585e11i	−0.0423567	−	0.181251i
$421$			6.69943e11i			1.03937i	0.854359	+	0.519683i	$0.173950\pi$
$421$			6.69943e11i			1.03937i	−0.854359	+	0.519683i	$0.826050\pi$
$422$	8.29755e11	+	4.79059e11i	1.27363	+	0.735332i
$423$		−	7.47353e11i		−	1.13500i
$424$	6.38178e11	+	3.68452e11i	0.958948	+	0.553649i
$425$	−4.02472e11	+	6.97101e11i	−0.598391	+	1.03644i
$426$	−1.10689e9	+	1.91719e9i	−0.00162840	+	0.00282048i
$427$	−4.63651e11	+	1.08351e11i	−0.674941	+	0.157727i
$428$	2.91427e12			4.19791
$429$	−6.67427e9	+	2.04033e10i	−0.00951363	+	0.0290832i
$430$	8.74845e11	−	1.51528e12i	1.23402	−	2.13739i
$431$	5.81472e11	−	3.35713e11i	0.811673	−	0.468620i	−0.0358633	−	0.999357i	$-0.511418\pi$
$431$	5.81472e11	−	3.35713e11i	0.811673	−	0.468620i	0.847537	+	0.530737i	$0.178085\pi$
$432$	−2.50221e11			−0.345658
$433$	2.66228e11	+	4.61120e11i	0.363964	+	0.630403i	0.988609	−	0.150505i	$-0.0480899\pi$
$433$	2.66228e11	+	4.61120e11i	0.363964	+	0.630403i	−0.624646	+	0.780908i	$0.714757\pi$
$434$	8.80523e11	−	2.05770e11i	1.19134	−	0.278405i
$435$	−2.77282e10	+	1.60089e10i	−0.0371296	+	0.0214368i
$436$	−1.60113e12	−	9.24412e11i	−2.12196	−	1.22511i
$437$	−8.11715e11	−	4.68644e11i	−1.06472	−	0.614719i
$438$	5.15768e9			0.00669608
$439$	−1.09355e12			−1.40523			−0.702613	−	0.711572i	$-0.747984\pi$
$439$	−1.09355e12			−1.40523			−0.702613	+	0.711572i	$0.747984\pi$
$440$	1.48912e12	+	8.59745e11i	1.89406	+	1.09354i
$441$	6.58851e11	+	4.39285e11i	0.829495	+	0.553061i
$442$	2.56750e12	−	5.40410e11i	3.19971	−	0.673477i
$443$	1.16337e11	+	2.01501e11i	0.143516	+	0.248577i	0.928818	−	0.370536i	$-0.120826\pi$
$443$	1.16337e11	+	2.01501e11i	0.143516	+	0.248577i	−0.785302	+	0.619112i	$0.787492\pi$
$444$	−1.33668e11	+	7.71731e10i	−0.163231	+	0.0942416i
$445$	−6.11195e10	−	1.05862e11i	−0.0738856	−	0.127974i
$446$	9.05877e10	−	1.56902e11i	0.108408	−	0.187769i
$447$		−	7.19476e8i		−	0.000852379i
$448$	1.40954e12	+	1.50346e12i	1.65321	+	1.76336i
$449$	−1.33924e12	+	7.73210e11i	−1.55507	+	0.897819i	−0.557352	+	0.830277i	$0.688182\pi$
$449$	−1.33924e12	+	7.73210e11i	−1.55507	+	0.897819i	−0.997716	+	0.0675424i	$0.978484\pi$
$450$	−9.88394e11	+	5.70650e11i	−1.13625	+	0.656014i
$451$	−4.12479e11			−0.469470
$452$	−5.61912e11	−	9.73260e11i	−0.633206	−	1.09675i
$453$		−	4.54516e9i		−	0.00507116i
$454$	−8.11518e11			−0.896493
$455$	−1.02888e11	+	1.18545e12i	−0.112542	+	1.29667i
$456$	−1.40540e11			−0.152215
$457$		−	9.30283e11i		−	0.997682i	−0.866694	−	0.498841i	$-0.833759\pi$
$457$		−	9.30283e11i		−	0.997682i	0.866694	−	0.498841i	$-0.166241\pi$
$458$	8.09495e11	+	1.40209e12i	0.859646	+	1.48895i
$459$	1.80423e11			0.189730
$460$	−3.78294e12	+	2.18408e12i	−3.93930	+	2.27436i
$461$	4.13263e11	−	2.38598e11i	0.426160	−	0.246043i	−0.271550	−	0.962424i	$-0.587536\pi$
$461$	4.13263e11	−	2.38598e11i	0.426160	−	0.246043i	0.697709	+	0.716381i	$0.254203\pi$
$462$	5.53281e10	−	1.29296e10i	0.0565011	−	0.0132038i
$463$			1.52431e11i			0.154156i	0.997025	+	0.0770779i	$0.0245590\pi$
$463$			1.52431e11i			0.154156i	−0.997025	+	0.0770779i	$0.975441\pi$
$464$	9.37672e11	−	1.62410e12i	0.939118	−	1.62660i
$465$	2.33235e10	+	4.03974e10i	0.0231342	+	0.0400696i
$466$	−3.05615e12	+	1.76447e12i	−3.00219	+	1.73332i
$467$	6.85545e11	+	1.18740e12i	0.666975	+	1.15524i	0.978746	+	0.205078i	$0.0657448\pi$
$467$	6.85545e11	+	1.18740e12i	0.666975	+	1.15524i	−0.311770	+	0.950158i	$0.600922\pi$
$468$	2.55241e12	+	8.34939e11i	2.45948	+	0.804542i
$469$	−1.03359e12	−	3.12976e11i	−0.986440	−	0.298699i
$470$	−2.57414e12	−	1.48618e12i	−2.43328	−	1.40485i
$471$	4.66569e10			0.0436839
$472$	6.55323e10			0.0607738
$473$	5.23602e11	+	3.02302e11i	0.480979	+	0.277693i
$474$	−1.71425e11	−	9.89722e10i	−0.155981	−	0.0900556i
$475$	−6.08902e11	+	3.51549e11i	−0.548815	+	0.316858i
$476$	−3.42875e12	−	3.65720e12i	−3.06129	−	3.26526i
$477$	−2.06269e11	−	3.57268e11i	−0.182432	−	0.315981i
$478$	−3.04381e12			−2.66681
$479$	−1.23270e11	+	7.11700e10i	−0.106991	+	0.0617713i	−0.552541	−	0.833486i	$-0.686342\pi$
$479$	−1.23270e11	+	7.11700e10i	−0.106991	+	0.0617713i	0.445550	+	0.895257i	$0.353008\pi$
$480$	−1.22245e11	+	2.11735e11i	−0.105111	+	0.182057i
$481$	1.51407e12	−	3.18682e11i	1.28971	−	0.271459i
$482$	−3.98845e11			−0.336583
$483$	−2.57153e10	+	8.49237e10i	−0.0214996	+	0.0710013i
$484$	1.08353e12	−	1.87673e12i	0.897503	−	1.55452i
$485$	−2.57117e10	+	4.45340e10i	−0.0211005	+	0.0365472i
$486$	3.32483e11	+	1.91959e11i	0.270337	+	0.156079i
$487$			9.14183e11i			0.736466i	0.929733	+	0.368233i	$0.120037\pi$
$487$			9.14183e11i			0.736466i	−0.929733	+	0.368233i	$0.879963\pi$
$488$	2.27533e12	+	1.31366e12i	1.81617	+	1.04856i
$489$			7.55808e10i			0.0597753i
$490$	2.82324e12	−	1.39575e12i	2.21241	−	1.09377i
$491$	3.71960e11	−	6.44253e11i	0.288821	−	0.500253i	−0.684707	−	0.728818i	$-0.740070\pi$
$491$	3.71960e11	−	6.44253e11i	0.288821	−	0.500253i	0.973529	+	0.228565i	$0.0734033\pi$
$492$		−	1.57119e11i		−	0.120889i
$493$	−6.76114e11	+	1.17106e12i	−0.515477	+	0.892832i
$494$	2.17821e12	+	7.12533e11i	1.64562	+	0.538311i
$495$	−4.81308e11	−	8.33649e11i	−0.360329	−	0.624108i
$496$	−2.36616e12	−	1.36610e12i	−1.75540	−	1.01348i
$497$	−4.05819e10	−	1.22884e10i	−0.0298352	−	0.00903424i
$498$	4.50103e10	+	7.79601e10i	0.0327929	+	0.0567989i
$499$	6.21947e11	−	3.59082e11i	0.449057	−	0.259263i	−0.258375	−	0.966045i	$-0.583187\pi$
$499$	6.21947e11	−	3.59082e11i	0.449057	−	0.259263i	0.707432	+	0.706782i	$0.249854\pi$
$500$		−	1.44459e12i		−	1.03367i
$501$		−	9.30489e7i		−	6.59844e-5i
$502$	−1.35833e12	+	7.84232e11i	−0.954637	+	0.551160i
$503$	−6.83356e11	−	1.18361e12i	−0.475982	−	0.824425i	0.523639	−	0.851940i	$-0.324574\pi$
$503$	−6.83356e11	−	1.18361e12i	−0.475982	−	0.824425i	−0.999621	+	0.0275147i	$0.991241\pi$
$504$	−9.94317e11	−	4.25485e12i	−0.686416	−	2.93729i
$505$	3.20731e12	+	1.85174e12i	2.19447	+	1.26698i
$506$	−1.04547e12	−	1.81081e12i	−0.708981	−	1.22799i
$507$	6.61244e10	+	4.84449e10i	0.0444453	+	0.0325621i
$508$	2.47194e12	−	4.28152e12i	1.64684	−	2.85241i
$509$		−	7.38864e11i		−	0.487904i	−0.969787	−	0.243952i	$-0.921556\pi$
$509$		−	7.38864e11i		−	0.487904i	0.969787	−	0.243952i	$-0.0784439\pi$
$510$	1.79121e11	−	3.10248e11i	0.117242	−	0.203068i
$511$	2.24800e10	+	9.61955e10i	0.0145848	+	0.0624109i
$512$			4.59791e11i			0.295696i
$513$	1.36482e11	+	7.87978e10i	0.0870054	+	0.0502326i
$514$			1.68919e11i			0.106744i
$515$	−2.34393e12	−	1.35327e12i	−1.46829	−	0.847718i
$516$	−1.15151e11	+	1.99447e11i	−0.0715062	+	0.123852i
$517$	5.13548e11	−	8.89492e11i	0.316136	−	0.547564i
$518$	−2.80093e12	−	2.98755e12i	−1.70930	−	1.82319i
$519$	−1.62110e11			−0.0980743
$520$	4.88807e12	−	4.38368e12i	2.93172	−	2.62920i
$521$	−5.79708e11	+	1.00408e12i	−0.344699	+	0.597036i	−0.985299	−	0.170839i	$-0.945352\pi$
$521$	−5.79708e11	+	1.00408e12i	−0.344699	+	0.597036i	0.640600	+	0.767875i	$0.278686\pi$
$522$	−1.66041e12	+	9.58638e11i	−0.978809	+	0.565116i
$523$	1.13419e12			0.662868			0.331434	−	0.943478i	$-0.392468\pi$
$523$	1.13419e12			0.662868			0.331434	+	0.943478i	$0.392468\pi$
$524$	1.97850e12	+	3.42687e12i	1.14643	+	1.98567i
$525$	4.55249e10	+	4.85581e10i	0.0261536	+	0.0278962i
$526$	−5.95690e11	+	3.43922e11i	−0.339301	+	0.195895i
$527$	1.70613e12	+	9.85036e11i	0.963529	+	0.556294i
$528$	−1.48679e11	−	8.58397e10i	−0.0832523	−	0.0480657i
$529$	1.46419e12			0.812916
$530$	−1.64074e12			−0.903229
$531$	−3.17716e10	−	1.83433e10i	−0.0173426	−	0.0100127i
$532$	−9.96447e11	−	4.26396e12i	−0.539327	−	2.30787i
$533$	−4.89689e11	+	1.49698e12i	−0.262813	+	0.803421i
$534$	1.11442e10	+	1.93023e10i	0.00593081	+	0.0102725i
$535$	−3.45443e12	+	1.99442e12i	−1.82299	+	1.05250i
$536$	2.97951e12	+	5.16067e12i	1.55921	+	2.70063i
$537$	−9.24673e10	+	1.60158e11i	−0.0479848	+	0.0831121i
$538$			2.44064e12i			1.25598i
$539$	4.82300e11	+	9.75566e11i	0.246132	+	0.497860i
$540$	6.36063e11	−	3.67231e11i	0.321906	−	0.185852i
$541$	2.89396e12	−	1.67083e12i	1.45246	−	0.838580i	0.453842	−	0.891082i	$-0.350053\pi$
$541$	2.89396e12	−	1.67083e12i	1.45246	−	0.838580i	0.998621	+	0.0525027i	$0.0167198\pi$
$542$	−2.51557e12			−1.25210
$543$	−7.67785e10	−	1.32984e11i	−0.0379001	−	0.0656449i
$544$			1.03257e13i			5.05505i
$545$	2.53053e12			1.22865
$546$	1.87601e10	−	2.16148e11i	0.00903375	−	0.104084i
$547$	−2.30812e11			−0.110234			−0.0551169	−	0.998480i	$-0.517553\pi$
$547$	−2.30812e11			−0.110234			−0.0551169	+	0.998480i	$0.517553\pi$
$548$		−	6.90602e12i		−	3.27126i
$549$	−7.35423e11	−	1.27379e12i	−0.345511	−	0.598442i
$550$	−1.56850e12			−0.730892
$551$	−1.02290e12	+	5.90570e11i	−0.472770	+	0.272954i
$552$	4.24020e11	−	2.44808e11i	0.194384	−	0.112228i
$553$	1.09876e12	−	3.62861e12i	0.499621	−	1.64997i
$554$		−	6.69896e11i		−	0.302144i
$555$	1.05629e11	−	1.82954e11i	0.0472567	−	0.0818510i
$556$	1.18366e12	+	2.05016e12i	0.525279	+	0.909811i
$557$	2.67988e12	−	1.54723e12i	1.17969	−	0.681094i	0.223747	−	0.974647i	$-0.428171\pi$
$557$	2.67988e12	−	1.54723e12i	1.17969	−	0.681094i	0.955943	+	0.293553i	$0.0948378\pi$
$558$	1.39665e12	+	2.41906e12i	0.609863	+	1.05631i
$559$	1.71873e12	−	1.54138e12i	0.744484	−	0.667662i
$560$	−9.10763e12	−	2.75784e12i	−3.91344	−	1.18501i
$561$	1.07206e11	+	6.18953e10i	0.0456967	+	0.0263830i
$562$	−2.01432e12			−0.851757
$563$	4.76368e12			1.99827			0.999137	−	0.0415278i	$-0.0132225\pi$
$563$	4.76368e12			1.99827			0.999137	+	0.0415278i	$0.0132225\pi$
$564$	3.38820e11	+	1.95618e11i	0.140998	+	0.0814052i
$565$	1.33212e12	+	7.69102e11i	0.549955	+	0.317516i
$566$	1.97312e12	−	1.13918e12i	0.808126	−	0.466572i
$567$	−7.06753e11	+	2.33402e12i	−0.287173	+	0.948377i
$568$	1.16985e11	+	2.02623e11i	0.0471587	+	0.0816812i
$569$	−2.28391e12			−0.913428			−0.456714	−	0.889614i	$-0.650974\pi$
$569$	−2.28391e12			−0.913428			−0.456714	+	0.889614i	$0.650974\pi$
$570$	2.70994e11	−	1.56458e11i	0.107528	−	0.0620815i
$571$	−9.09311e11	+	1.57497e12i	−0.357973	+	0.620027i	−0.987622	−	0.156852i	$-0.949865\pi$
$571$	−9.09311e11	+	1.57497e12i	−0.357973	+	0.620027i	0.629649	+	0.776880i	$0.283199\pi$
$572$	2.46412e12	+	2.74764e12i	0.962453	+	1.07319i
$573$	−1.83513e11			−0.0711166
$574$	4.05940e12	−	9.48642e11i	1.56084	−	0.364753i
$575$	1.22473e12	−	2.12130e12i	0.467236	−	0.809276i
$576$	−3.18311e12	+	5.51330e12i	−1.20490	+	2.08694i
$577$	−3.91714e11	−	2.26156e11i	−0.147122	−	0.0849410i	0.424632	−	0.905366i	$-0.360404\pi$
$577$	−3.91714e11	−	2.26156e11i	−0.147122	−	0.0849410i	−0.571754	+	0.820425i	$0.693737\pi$
$578$		−	1.00418e13i		−	3.74226i
$579$	−2.19000e11	−	1.26440e11i	−0.0809825	−	0.0467553i
$580$			5.50462e12i			2.01977i
$581$	−1.25785e12	+	1.17928e12i	−0.457969	+	0.429361i
$582$	4.68814e9	−	8.12010e9i	0.00169374	−	0.00293365i
$583$		−	5.66956e11i		−	0.203255i
$584$	2.72551e11	−	4.72072e11i	0.0969594	−	0.167939i
$585$	−3.59690e12	+	7.57078e11i	−1.26978	+	0.267263i
$586$	5.03029e11	+	8.71272e11i	0.176219	+	0.305221i
$587$	3.06466e12	+	1.76938e12i	1.06539	+	0.615106i	0.926920	−	0.375260i	$-0.122447\pi$
$587$	3.06466e12	+	1.76938e12i	1.06539	+	0.615106i	0.138475	+	0.990366i	$0.455780\pi$
$588$	−3.71606e11	+	1.83715e11i	−0.128199	+	0.0633790i
$589$	8.60406e11	+	1.49027e12i	0.294567	+	0.510205i
$590$	−1.26362e11	+	7.29549e10i	−0.0429320	+	0.0247868i
$591$		−	2.94045e10i		−	0.00991448i
$592$			1.23738e13i			4.14051i
$593$	1.83471e12	−	1.05927e12i	0.609285	−	0.351771i	−0.163401	−	0.986560i	$-0.552246\pi$
$593$	1.83471e12	−	1.05927e12i	0.609285	−	0.351771i	0.772685	+	0.634789i	$0.218913\pi$
$594$	1.75785e11	+	3.04469e11i	0.0579353	+	0.100347i
$595$	6.56711e12	+	1.98856e12i	2.14807	+	0.650446i
$596$	−1.07123e11	−	6.18476e10i	−0.0347756	−	0.0200777i
$597$	1.34747e11	+	2.33388e11i	0.0434143	+	0.0751958i
$598$	−7.81299e12	+	1.64448e12i	−2.49840	+	0.525865i
$599$	−2.48588e11	+	4.30568e11i	−0.0788969	+	0.136653i	−0.902774	−	0.430115i	$-0.858473\pi$
$599$	−2.48588e11	+	4.30568e11i	−0.0788969	+	0.136653i	0.823877	+	0.566768i	$0.191806\pi$
$600$		−	3.67281e11i		−	0.115696i
$601$	−1.00222e11	+	1.73590e11i	−0.0313349	+	0.0542736i	−0.881268	−	0.472618i	$-0.843309\pi$
$601$	−1.00222e11	+	1.73590e11i	−0.0313349	+	0.0542736i	0.849933	+	0.526891i	$0.176642\pi$
$602$	−5.84826e12	−	1.77088e12i	−1.81486	−	0.549548i
$603$		−	3.33601e12i		−	1.02754i
$604$	−6.76731e11	−	3.90711e11i	−0.206895	−	0.119451i
$605$			2.96610e12i			0.900092i
$606$	−5.84804e11	−	3.37637e11i	−0.176150	−	0.101700i
$607$	1.41415e11	−	2.44938e11i	0.0422810	−	0.0732329i	−0.844110	−	0.536169i	$-0.819871\pi$
$607$	1.41415e11	−	2.44938e11i	0.0422810	−	0.0732329i	0.886391	+	0.462936i	$0.153204\pi$
$608$	−4.50964e12	+	7.81093e12i	−1.33837	+	2.31812i
$609$	7.64775e10	+	8.15731e10i	0.0225297	+	0.0240309i
$610$	−5.84983e12			−1.71064
$611$	−2.61849e12	−	2.91977e12i	−0.760090	−	0.847547i
$612$	7.74298e12	−	1.34112e13i	2.23114	−	3.86445i
$613$	−1.93346e12	+	1.11628e12i	−0.553048	+	0.319302i	−0.750350	−	0.661040i	$-0.770115\pi$
$613$	−1.93346e12	+	1.11628e12i	−0.553048	+	0.319302i	0.197303	+	0.980343i	$0.436782\pi$
$614$	−8.65395e12			−2.45729
$615$	1.07526e11	+	1.86241e11i	0.0303093	+	0.0524973i
$616$	1.74032e12	−	5.74733e12i	0.486985	−	1.60825i
$617$	−3.94432e12	+	2.27725e12i	−1.09569	+	0.632598i	−0.935086	−	0.354421i	$-0.884678\pi$
$617$	−3.94432e12	+	2.27725e12i	−1.09569	+	0.632598i	−0.160606	+	0.987019i	$0.551345\pi$
$618$	4.27379e11	+	2.46748e11i	0.117860	+	0.0680464i
$619$	−4.57406e12	−	2.64084e12i	−1.25226	−	0.722992i	−0.280701	−	0.959795i	$-0.590567\pi$
$619$	−4.57406e12	−	2.64084e12i	−1.25226	−	0.722992i	−0.971558	+	0.236803i	$0.923900\pi$
$620$	8.01972e12			2.17970
$621$	−5.49034e11			−0.148145
$622$	−8.24077e12	−	4.75781e12i	−2.20755	−	1.27453i
$623$	−3.11434e11	+	2.91980e11i	−0.0828266	+	0.0776527i
$624$	−4.88040e11	+	4.37681e11i	−0.128862	+	0.115565i
$625$	2.31238e12	+	4.00516e12i	0.606176	+	1.04993i
$626$	1.84280e12	−	1.06394e12i	0.479616	−	0.276906i
$627$	5.40641e10	+	9.36417e10i	0.0139703	+	0.0241972i
$628$	4.01072e12	−	6.94676e12i	1.02897	−	1.78223i
$629$		−	8.92218e12i		−	2.27271i
$630$	6.65405e12	+	7.09739e12i	1.68288	+	1.79501i
$631$	3.97648e11	−	2.29582e11i	0.0998544	−	0.0576509i	−0.449241	−	0.893410i	$-0.648306\pi$
$631$	3.97648e11	−	2.29582e11i	0.0998544	−	0.0576509i	0.549096	+	0.835760i	$0.314972\pi$
$632$	−1.81175e13	+	1.04601e13i	−4.51721	+	2.60802i
$633$	1.72612e11			0.0427321
$634$	4.40156e12	+	7.62372e12i	1.08194	+	1.87398i
$635$			6.76681e12i			1.65159i
$636$	2.15961e11			0.0523382
$637$	4.11313e12	−	5.92197e11i	0.989794	−	0.142508i
$638$	−2.63494e12			−0.629618
$639$		−	1.30982e11i		−	0.0310784i
$640$	4.56273e12	+	7.90288e12i	1.07502	+	1.86198i
$641$	−6.86475e12			−1.60607			−0.803033	−	0.595935i	$-0.796782\pi$
$641$	−6.86475e12			−1.60607			−0.803033	+	0.595935i	$0.796782\pi$
$642$	6.29862e11	−	3.63651e11i	0.146332	−	0.0844846i
$643$	−1.07301e12	+	6.19501e11i	−0.247545	+	0.142920i	−0.618639	−	0.785675i	$-0.712316\pi$
$643$	−1.07301e12	+	6.19501e11i	−0.247545	+	0.142920i	0.371095	+	0.928595i	$0.378982\pi$
$644$	1.04338e13	+	1.11290e13i	2.39032	+	2.54958i
$645$		−	3.15219e11i		−	0.0717124i
$646$	6.60782e12	−	1.14451e13i	1.49283	−	2.58567i
$647$	1.51721e12	+	2.62789e12i	0.340391	+	0.589574i	0.984505	−	0.175355i	$-0.0561074\pi$
$647$	1.51721e12	+	2.62789e12i	0.340391	+	0.589574i	−0.644115	+	0.764929i	$0.722774\pi$
$648$	1.16537e13	−	6.72824e12i	2.59642	−	1.49904i
$649$	−2.52095e10	−	4.36641e10i	−0.00557780	−	0.00966103i
$650$	−1.86210e12	+	5.69244e12i	−0.409160	+	1.25080i
$651$	1.18844e11	−	1.11421e11i	0.0259337	−	0.0243137i
$652$	1.12533e13	+	6.49707e12i	2.43873	+	1.40800i
$653$	4.35457e12			0.937207			0.468604	−	0.883409i	$-0.344757\pi$
$653$	4.35457e12			0.937207			0.468604	+	0.883409i	$0.344757\pi$
$654$	−4.61403e11			−0.0986236
$655$	−4.69044e12	−	2.70802e12i	−0.995697	−	0.574866i
$656$	−1.09085e13	−	6.29802e12i	−2.29984	−	1.32781i
$657$	−2.64278e11	+	1.52581e11i	−0.0553372	+	0.0319489i
$658$	−3.00837e12	+	9.93500e12i	−0.625625	+	2.06610i
$659$	1.98975e12	+	3.44635e12i	0.410973	+	0.711827i	0.994996	−	0.0999102i	$-0.0318556\pi$
$659$	1.98975e12	+	3.44635e12i	0.410973	+	0.711827i	−0.584023	+	0.811737i	$0.698522\pi$
$660$	5.03923e11			0.103375
$661$	3.85307e12	−	2.22457e12i	0.785056	−	0.453252i	−0.0531635	−	0.998586i	$-0.516930\pi$
$661$	3.85307e12	−	2.22457e12i	0.785056	−	0.453252i	0.838219	+	0.545334i	$0.183597\pi$
$662$	8.85557e11	−	1.53383e12i	0.179207	−	0.310396i
$663$	3.51905e11	−	3.15592e11i	0.0707317	−	0.0634331i
$664$	9.51405e12			1.89937
$665$	4.09923e12	+	4.37236e12i	0.812840	+	0.866998i
$666$	6.32522e12	−	1.09556e13i	1.24578	−	2.15775i
$667$	2.05744e12	−	3.56358e12i	0.402495	−	0.697141i
$668$	−1.38541e10	−	7.99866e9i	−0.00269205	−	0.00155426i
$669$		−	3.26401e10i		−	0.00629990i
$670$	−1.14904e13	−	6.63397e12i	−2.20292	−	1.27185i
$671$		−	2.02140e12i		−	0.384947i
$672$	8.17199e11	+	2.47452e11i	0.154585	+	0.0468090i
$673$	−4.83248e11	+	8.37010e11i	−0.0908034	+	0.157276i	−0.907849	−	0.419296i	$-0.862277\pi$
$673$	−4.83248e11	+	8.37010e11i	−0.0908034	+	0.157276i	0.817046	+	0.576573i	$0.195610\pi$
$674$			1.18973e13i			2.22064i
$675$	−2.05927e11	+	3.56675e11i	−0.0381808	+	0.0661311i
$676$	1.28972e13	−	5.68088e12i	2.37539	−	1.04630i
$677$	4.35992e11	+	7.55160e11i	0.0797681	+	0.138162i	0.903150	−	0.429325i	$-0.141249\pi$
$677$	4.35992e11	+	7.55160e11i	0.0797681	+	0.138162i	−0.823382	+	0.567488i	$0.807915\pi$
$678$	−2.42892e11	−	1.40234e11i	−0.0441449	−	0.0254871i
$679$	1.71881e11	+	5.20464e10i	0.0310323	+	0.00939673i
$680$	−1.89309e13	−	3.27893e13i	−3.39532	−	5.88087i
$681$	−1.26614e11	+	7.31005e10i	−0.0225590	+	0.0130244i
$682$			3.83886e12i			0.679473i
$683$		−	4.12129e12i		−	0.724669i	−0.932048	−	0.362335i	$-0.881980\pi$
$683$		−	4.12129e12i		−	0.724669i	0.932048	−	0.362335i	$-0.118020\pi$
$684$	1.17144e13	−	6.76331e12i	2.04629	−	1.18143i
$685$	4.72621e12	+	8.18604e12i	0.820174	+	1.42058i
$686$	−6.99020e12	−	8.49179e12i	−1.20512	−	1.46400i
$687$	2.52596e11	+	1.45837e11i	0.0432635	+	0.0249782i
$688$	9.23151e12	+	1.59894e13i	1.57081	+	2.72073i
$689$	−2.05761e12	−	6.73081e11i	−0.347837	−	0.113784i
$690$	−5.45072e11	+	9.44093e11i	−0.0915447	+	0.158560i
$691$		−	8.82978e12i		−	1.47332i	−0.676261	−	0.736662i	$-0.736401\pi$
$691$		−	8.82978e12i		−	1.47332i	0.676261	−	0.736662i	$-0.263599\pi$
$692$	−1.39352e13	+	2.41366e13i	−2.31013	+	4.00127i
$693$	−2.45250e12	+	2.29930e12i	−0.403933	+	0.378701i
$694$			2.06850e13i			3.38484i
$695$	−2.80610e12	−	1.62010e12i	−0.456217	−	0.263397i
$696$		−	6.16998e11i		−	0.0996649i
$697$	7.86564e12	+	4.54123e12i	1.26237	+	0.728829i
$698$	6.25074e11	−	1.08266e12i	0.0996741	−	0.172641i
$699$	−3.17882e11	+	5.50589e11i	−0.0503639	+	0.0872328i
$700$	1.11433e13	−	2.60407e12i	1.75417	−	0.409932i
$701$	6.80754e10			0.0106478			0.00532389	−	0.999986i	$-0.498305\pi$
$701$	6.80754e10			0.0106478			0.00532389	+	0.999986i	$0.498305\pi$
$702$	1.31368e12	−	2.76503e11i	0.204160	−	0.0429718i
$703$	3.89666e12	−	6.74921e12i	0.601718	−	1.04221i
$704$	−7.57700e12	+	4.37458e12i	−1.16257	+	0.671212i
$705$	−5.35493e11			−0.0816400
$706$	−9.91112e12	−	1.71666e13i	−1.50142	−	2.60053i
$707$	3.74835e12	−	1.23787e13i	0.564225	−	1.86333i
$708$	1.66322e10	−	9.60263e9i	0.00248772	−	0.00143629i
$709$	8.39643e12	+	4.84768e12i	1.24792	+	0.720486i	0.970694	−	0.240319i	$-0.0772520\pi$
$709$	8.39643e12	+	4.84768e12i	1.24792	+	0.720486i	0.277225	+	0.960805i	$0.410585\pi$
$710$	−4.51147e11	−	2.60470e11i	−0.0666278	−	0.0384676i
$711$	1.17117e13			1.71873
$712$	2.35561e12			0.343513
$713$	−5.19181e12	−	2.99749e12i	−0.752343	−	0.434366i
$714$	−1.19741e12	−	3.62583e11i	−0.172426	−	0.0522113i
$715$	−4.80122e12	−	1.57057e12i	−0.687028	−	0.224739i
$716$	1.58973e13	+	2.75350e13i	2.26056	+	3.91540i
$717$	−4.74897e11	+	2.74182e11i	−0.0671063	+	0.0387439i
$718$	9.12870e12	+	1.58114e13i	1.28189	+	2.22029i
$719$	2.94104e12	−	5.09404e12i	0.410413	−	0.710857i	−0.584522	−	0.811378i	$-0.698718\pi$
$719$	2.94104e12	−	5.09404e12i	0.410413	−	0.710857i	0.994935	+	0.100521i	$0.0320511\pi$
$720$		−	2.93958e13i		−	4.07651i
$721$	−2.73932e12	+	9.04648e12i	−0.377515	+	1.24673i
$722$	−1.99341e12	+	1.15090e12i	−0.273011	+	0.157623i
$723$	−6.22281e10	+	3.59274e10i	−0.00846962	+	0.00488994i
$724$	−2.64001e13			−3.57094
$725$	−1.54337e12	−	2.67319e12i	−0.207467	−	0.359343i
$726$		−	5.40823e11i		−	0.0722504i
$727$	3.89214e12			0.516753			0.258377	−	0.966044i	$-0.416812\pi$
$727$	3.89214e12			0.516753			0.258377	+	0.966044i	$0.416812\pi$
$728$	−1.87923e13	−	1.31391e13i	−2.47963	−	1.73371i
$729$	−7.48706e12			−0.981832
$730$			1.21369e12i			0.158181i
$731$	−6.65644e12	−	1.15293e13i	−0.862211	−	1.49339i
$732$	7.69980e11			0.0991241
$733$	−6.05449e12	+	3.49556e12i	−0.774658	+	0.447249i	−0.834534	−	0.550957i	$-0.814263\pi$
$733$	−6.05449e12	+	3.49556e12i	−0.774658	+	0.447249i	0.0598760	+	0.998206i	$0.480929\pi$
$734$	7.50533e12	−	4.33320e12i	0.954415	−	0.551032i
$735$	3.14756e11	−	4.72079e11i	0.0397815	−	0.0596653i
$736$		−	3.14215e13i		−	3.94709i
$737$	2.29236e12	−	3.97049e12i	0.286207	−	0.495724i
$738$	6.43884e12	+	1.11524e13i	0.799013	+	1.38393i
$739$	−4.48175e12	+	2.58754e12i	−0.552774	+	0.319144i	−0.750240	−	0.661165i	$-0.770062\pi$
$739$	−4.48175e12	+	2.58754e12i	−0.552774	+	0.319144i	0.197466	+	0.980310i	$0.436729\pi$
$740$	−1.81601e13	−	3.14542e13i	−2.22626	−	3.85599i
$741$	4.04031e11	−	8.50406e10i	0.0492303	−	0.0103620i
$742$	1.30392e12	+	5.57968e12i	0.157918	+	0.675759i
$743$	−1.74319e12	−	1.00643e12i	−0.209843	−	0.121153i	0.391395	−	0.920223i	$-0.371993\pi$
$743$	−1.74319e12	−	1.00643e12i	−0.209843	−	0.121153i	−0.601239	+	0.799070i	$0.705326\pi$
$744$	−8.98909e11			−0.107557
$745$	1.69304e11			0.0201356
$746$	−1.00583e13	−	5.80717e12i	−1.18905	−	0.686499i
$747$	−4.61263e12	−	2.66310e12i	−0.542008	−	0.312929i
$748$	1.84312e13	−	1.06413e13i	2.15277	−	1.24290i
$749$	9.52771e12	+	1.01625e13i	1.10617	+	1.17987i
$750$	−1.80261e11	−	3.12220e11i	−0.0208030	−	0.0360318i
$751$	−1.62849e13			−1.86813			−0.934064	−	0.357106i	$-0.883763\pi$
$751$	−1.62849e13			−1.86813			−0.934064	+	0.357106i	$0.883763\pi$
$752$	2.71628e13	−	1.56824e13i	3.09738	−	1.78827i
$753$	−1.41285e11	+	2.44713e11i	−0.0160147	+	0.0277383i
$754$	−3.12815e12	+	9.56277e12i	−0.352466	+	1.07749i
$755$	1.06955e12			0.119795
$756$	−1.75434e12	−	1.87122e12i	−0.195328	−	0.208342i
$757$	−3.31753e12	+	5.74613e12i	−0.367184	+	0.635981i	−0.989124	−	0.147084i	$-0.953011\pi$
$757$	−3.31753e12	+	5.74613e12i	−0.367184	+	0.635981i	0.621940	+	0.783065i	$0.286345\pi$
$758$	8.07340e12	−	1.39835e13i	0.888270	−	1.53853i
$759$	−3.26230e11	−	1.88349e11i	−0.0356809	−	0.0206004i
$760$		−	3.30714e13i		−	3.59577i
$761$	−2.44802e12	−	1.41336e12i	−0.264596	−	0.152765i	0.361833	−	0.932243i	$-0.382151\pi$
$761$	−2.44802e12	−	1.41336e12i	−0.264596	−	0.152765i	−0.626429	+	0.779478i	$0.715484\pi$
$762$		−	1.23382e12i		−	0.132573i
$763$	−2.01104e12	−	8.60560e12i	−0.214813	−	0.919222i
$764$	−1.57751e13	+	2.73233e13i	−1.67515	+	2.90144i
$765$			2.11960e13i			2.23757i
$766$	−9.25708e12	+	1.60337e13i	−0.971504	+	1.68269i
$767$	−1.88395e11	+	3.96535e10i	−0.0196558	+	0.00413716i
$768$	−1.89960e11	−	3.29021e11i	−0.0197032	−	0.0341270i
$769$	−1.15632e13	−	6.67602e12i	−1.19237	−	0.688413i	−0.233523	−	0.972351i	$-0.575026\pi$
$769$	−1.15632e13	−	6.67602e12i	−1.19237	−	0.688413i	−0.958843	+	0.283938i	$0.908359\pi$
$770$	3.04256e12	+	1.30196e13i	0.311911	+	1.33472i
$771$	1.52160e10	+	2.63549e10i	0.00155080	+	0.00268607i
$772$	−3.76514e13	+	2.17380e13i	−3.81508	+	2.20264i
$773$			6.54939e12i			0.659771i	0.944021	+	0.329886i	$0.107010\pi$
$773$			6.54939e12i			0.659771i	−0.944021	+	0.329886i	$0.892990\pi$
$774$		−	1.88758e13i		−	1.89048i
$775$	−3.89460e12	+	2.24855e12i	−0.387797	+	0.223895i
$776$	−4.95478e11	−	8.58193e11i	−0.0490508	−	0.0849586i
$777$	−7.06119e11	−	2.13816e11i	−0.0694998	−	0.0210449i
$778$	−6.35046e12	−	3.66644e12i	−0.621437	−	0.358787i
$779$	3.96666e12	+	6.87045e12i	0.385928	+	0.668446i
$780$	5.98250e11	−	1.82885e12i	0.0578705	−	0.176910i
$781$	9.00051e10	−	1.55893e11i	0.00865641	−	0.0149933i
$782$			4.60408e13i			4.40263i
$783$	−3.45937e11	+	5.99181e11i	−0.0328904	+	0.0569679i
$784$	−2.14065e12	+	3.31641e13i	−0.202360	+	3.13506i
$785$			1.09791e13i			1.03194i
$786$	8.55229e11	+	4.93767e11i	0.0799247	+	0.0461445i
$787$			4.50829e12i			0.418915i	0.977818	+	0.209457i	$0.0671697\pi$
$787$			4.50829e12i			0.418915i	−0.977818	+	0.209457i	$0.932830\pi$
$788$	−4.37805e12	−	2.52767e12i	−0.404494	−	0.233535i
$789$	−6.19601e10	+	1.07318e11i	−0.00569201	+	0.00985885i
$790$	2.32898e13	−	4.03391e13i	2.12737	−	3.68472i
$791$	1.55684e12	−	5.14139e12i	0.141400	−	0.466967i
$792$	1.85501e13			1.67526
$793$	−7.33612e12	−	2.39978e12i	−0.658775	−	0.215497i
$794$	1.50121e13	−	2.60017e13i	1.34044	−	2.32172i
$795$	−2.55989e11	+	1.47796e11i	−0.0227285	+	0.0131223i
$796$	4.63323e13			4.09049
$797$	8.63400e12	+	1.49545e13i	0.757966	+	1.31283i	0.943886	+	0.330270i	$0.107140\pi$
$797$	8.63400e12	+	1.49545e13i	0.757966	+	1.31283i	−0.185921	+	0.982565i	$0.559527\pi$
$798$	−7.47432e11	−	7.97232e11i	−0.0652467	−	0.0695940i
$799$	−1.95859e13	+	1.13079e13i	−1.70013	+	0.981572i
$800$	−2.04127e13	−	1.17853e13i	−1.76196	−	1.01727i
$801$	−1.14205e12	−	6.59365e11i	−0.0980257	−	0.0565952i
$802$	1.08473e13			0.925840
$803$	−4.19388e11			−0.0355956
$804$	1.51241e12	+	8.73192e11i	0.127649	+	0.0736983i
$805$	−1.99839e13	−	6.05123e12i	−1.67726	−	0.507882i
$806$	1.39321e13	+	4.55743e12i	1.16281	+	0.380375i
$807$	2.19849e11	+	3.80790e11i	0.0182471	+	0.0316049i
$808$	−6.18065e13	+	3.56840e13i	−5.10132	+	2.94525i
$809$	−1.06057e12	−	1.83695e12i	−0.0870501	−	0.150775i	0.819213	−	0.573490i	$-0.194411\pi$
$809$	−1.06057e12	−	1.83695e12i	−0.0870501	−	0.150775i	−0.906263	+	0.422714i	$0.861077\pi$
$810$	−1.49806e13	+	2.59472e13i	−1.22278	+	2.11791i
$811$			7.05598e12i			0.572748i	0.958118	+	0.286374i	$0.0924499\pi$
$811$			7.05598e12i			0.572748i	−0.958118	+	0.286374i	$0.907550\pi$
$812$	1.87196e13	−	4.37459e12i	1.51111	−	0.353131i
$813$	−3.92481e11	+	2.26599e11i	−0.0315073	+	0.0181908i
$814$	1.50564e13	−	8.69283e12i	1.20202	−	0.693987i
$815$	−1.77854e13			−1.41206
$816$	1.89012e12	+	3.27379e12i	0.149240	+	0.258490i
$817$		−	1.16285e13i		−	0.913112i
$818$	−4.03573e13			−3.15161
$819$	5.43310e12	+	1.16304e13i	0.421959	+	0.903265i
$820$	3.69726e13			2.85574
$821$		−	1.96379e12i		−	0.150852i	−0.997151	−	0.0754258i	$-0.975968\pi$
$821$		−	1.96379e12i		−	0.150852i	0.997151	−	0.0754258i	$-0.0240316\pi$
$822$	−8.61753e11	−	1.49260e12i	−0.0658354	−	0.114030i
$823$	3.87494e12			0.294419			0.147209	−	0.989105i	$-0.452971\pi$
$823$	3.87494e12			0.294419			0.147209	+	0.989105i	$0.452971\pi$
$824$	4.51687e13	−	2.60781e13i	3.41322	−	1.97063i
$825$	−2.44719e11	+	1.41289e11i	−0.0183918	+	0.0106185i
$826$	3.48520e11	+	3.71741e11i	0.0260505	+	0.0277863i
$827$		−	1.22015e13i		−	0.907066i	−0.891239	−	0.453533i	$-0.850163\pi$
$827$		−	1.22015e13i		−	0.907066i	0.891239	−	0.453533i	$-0.149837\pi$
$828$	−2.35621e13	+	4.08108e13i	−1.74212	+	3.01744i
$829$	−7.71339e12	−	1.33600e13i	−0.567218	−	0.982450i	−0.996840	−	0.0794408i	$-0.974687\pi$
$829$	−7.71339e12	−	1.33600e13i	−0.567218	−	0.982450i	0.429622	−	0.903009i	$-0.358647\pi$
$830$	−1.83453e13	+	1.05917e13i	−1.34175	+	0.774662i
$831$	−6.03433e10	−	1.04518e11i	−0.00438960	−	0.00760300i
$832$	6.88105e12	+	3.26921e13i	0.497851	+	2.36531i
$833$	1.54353e12	−	2.39132e13i	0.111074	−	1.72082i
$834$	5.11650e11	+	2.95401e11i	0.0366206	+	0.0211429i
$835$	2.18959e10			0.00155874
$836$	1.85898e13			1.31627
$837$	8.72951e11	+	5.03998e11i	0.0614788	+	0.0354948i
$838$	1.63966e13	+	9.46659e12i	1.14857	+	0.663125i
$839$	−2.43138e12	+	1.40376e12i	−0.169404	+	0.0978055i	−0.582305	−	0.812971i	$-0.697849\pi$
$839$	−2.43138e12	+	1.40376e12i	−0.169404	+	0.0978055i	0.412901	+	0.910776i	$0.364516\pi$
$840$	−3.04868e12	+	7.12447e11i	−0.211278	+	0.0493737i
$841$	4.66086e12	+	8.07284e12i	0.321280	+	0.556474i
$842$	2.87448e13			1.97086
$843$	−3.14276e11	+	1.81448e11i	−0.0214332	+	0.0123745i
$844$	1.48381e13	−	2.57003e13i	1.00655	−	1.74340i
$845$	−1.13999e13	+	1.55602e13i	−0.769210	+	1.04993i
$846$	−3.20662e13			−2.15219
$847$	1.00868e13	−	2.35720e12i	0.673411	−	0.157370i
$848$	8.65668e12	−	1.49938e13i	0.574870	−	0.995705i
$849$	2.05232e11	−	3.55472e11i	0.0135569	−	0.0234812i
$850$	2.99100e13	+	1.72686e13i	1.96531	+	1.13467i
$851$			2.71505e13i			1.77457i
$852$	5.93819e10	+	3.42842e10i	0.00386079	+	0.00222903i
$853$			1.78401e13i			1.15379i	0.816818	+	0.576896i	$0.195736\pi$
$853$			1.78401e13i			1.15379i	−0.816818	+	0.576896i	$0.804264\pi$
$854$	4.64893e12	+	1.98936e13i	0.299084	+	1.27983i
$855$	−9.25711e12	+	1.60338e13i	−0.592417	+	1.02610i
$856$		−	7.68668e13i		−	4.89335i
$857$	1.27430e13	−	2.20715e13i	0.806972	−	1.39772i	−0.107980	−	0.994153i	$-0.534438\pi$
$857$	1.27430e13	−	2.20715e13i	0.806972	−	1.39772i	0.914952	−	0.403564i	$-0.132229\pi$
$858$	8.75429e11	+	2.86369e11i	0.0551478	+	0.0180398i
$859$	−3.42455e12	−	5.93149e12i	−0.214602	−	0.371702i	0.738547	−	0.674202i	$-0.235512\pi$
$859$	−3.42455e12	−	5.93149e12i	−0.214602	−	0.371702i	−0.953149	+	0.302500i	$0.902179\pi$
$860$	−4.69332e13	−	2.70969e13i	−2.92575	−	1.68918i
$861$	5.47898e11	−	5.13673e11i	0.0339771	−	0.0318546i
$862$	−1.44042e13	−	2.49488e13i	−0.888601	−	1.53910i
$863$	1.29584e13	−	7.48152e12i	0.795246	−	0.459136i	−0.0465598	−	0.998916i	$-0.514826\pi$
$863$	1.29584e13	−	7.48152e12i	0.795246	−	0.459136i	0.841806	+	0.539780i	$0.181492\pi$
$864$			5.28321e12i			0.322542i
$865$		−	3.81470e13i		−	2.31680i
$866$	1.97850e13	−	1.14229e13i	1.19538	−	0.690151i
$867$	−9.04548e11	−	1.56672e12i	−0.0543683	−	0.0941686i
$868$	−6.37337e12	−	2.72727e13i	−0.381093	−	1.63076i
$869$	1.39391e13	+	8.04776e12i	0.829176	+	0.478725i
$870$	6.86882e11	+	1.18972e12i	0.0406486	+	0.0704055i
$871$	−1.16883e13	−	1.30332e13i	−0.688131	−	0.767307i
$872$	−2.43823e13	+	4.22313e13i	−1.42807	+	2.47349i
$873$			5.54762e11i			0.0323253i
$874$	−2.01078e13	+	3.48277e13i	−1.16564	+	2.01894i
$875$	5.03753e12	−	4.72285e12i	0.290523	−	0.272376i
$876$		−	1.59751e11i		−	0.00916588i
$877$	−2.29989e12	−	1.32784e12i	−0.131283	−	0.0757964i	0.432920	−	0.901432i	$-0.357483\pi$
$877$	−2.29989e12	−	1.32784e12i	−0.131283	−	0.0757964i	−0.564203	+	0.825636i	$0.690817\pi$
$878$			4.69200e13i			2.66460i
$879$	1.56966e11	+	9.06243e10i	0.00886861	+	0.00512029i
$880$	2.01995e13	−	3.49865e13i	1.13545	−	1.96666i
$881$	6.48728e12	−	1.12363e13i	0.362803	−	0.628394i	−0.625618	−	0.780130i	$-0.715153\pi$
$881$	6.48728e12	−	1.12363e13i	0.362803	−	0.628394i	0.988421	+	0.151736i	$0.0484863\pi$
$882$	1.88481e13	−	2.82689e13i	1.04872	−	1.57290i
$883$	1.96551e13			1.08806			0.544029	−	0.839066i	$-0.316898\pi$
$883$	1.96551e13			1.08806			0.544029	+	0.839066i	$0.316898\pi$
$884$	−1.67383e13	−	7.95242e13i	−0.921884	−	4.37990i
$885$	−1.31434e10	+	2.27650e10i	−0.000720214	+	0.00124745i
$886$	8.64567e12	−	4.99158e12i	0.471354	−	0.272136i
$887$	−3.96000e12			−0.214802			−0.107401	−	0.994216i	$-0.534253\pi$
$887$	−3.96000e12			−0.214802			−0.107401	+	0.994216i	$0.534253\pi$
$888$	2.03552e12	+	3.52562e12i	0.109854	+	0.190273i
$889$	2.30119e13	−	5.37767e12i	1.23565	−	0.288759i
$890$	−4.54216e12	+	2.62242e12i	−0.242665	+	0.140103i
$891$	−8.96603e12	−	5.17654e12i	−0.476596	−	0.275163i
$892$	−4.85979e12	−	2.80580e12i	−0.257025	−	0.148394i
$893$	−1.97544e13			−1.03952
$894$	−3.08701e10			−0.00161629
$895$	−3.76878e13	−	2.17591e13i	−1.96335	−	1.13354i
$896$	2.32493e13	−	2.17970e13i	1.20510	−	1.12983i
$897$	−1.07086e12	+	9.60358e11i	−0.0552288	+	0.0495298i
$898$	3.31756e13	+	5.74618e13i	1.70245	+	2.94873i
$899$	−6.54255e12	+	3.77735e12i	−0.334063	+	0.192871i
$900$	1.76749e13	+	3.06139e13i	0.897980	+	1.55535i
$901$	−6.24195e12	+	1.08114e13i	−0.315543	+	0.546537i
$902$			1.76980e13i			0.890213i
$903$	−1.07197e12	+	2.50509e11i	−0.0536522	+	0.0125380i
$904$	−2.56707e13	+	1.48210e13i	−1.27844	+	0.738107i
$905$	3.12934e13	−	1.80672e13i	1.55072	−	0.895309i
$906$	−1.95016e11			−0.00961598
$907$	6.65261e12	+	1.15227e13i	0.326407	+	0.565354i	0.981796	−	0.189938i	$-0.0608287\pi$
$907$	6.65261e12	+	1.15227e13i	0.326407	+	0.565354i	−0.655389	+	0.755291i	$0.727495\pi$
$908$			2.51354e13i			1.22716i
$909$	3.99536e13			1.94097
$910$	5.08632e13	+	4.41456e12i	2.45877	+	0.213403i
$911$	1.14914e13			0.552764			0.276382	−	0.961048i	$-0.410864\pi$
$911$	1.14914e13			0.552764			0.276382	+	0.961048i	$0.410864\pi$
$912$			3.30195e12i			0.158050i
$913$	−3.65994e12	−	6.33919e12i	−0.174323	−	0.301936i
$914$	−3.99150e13			−1.89181
$915$	−9.12695e11	+	5.26945e11i	−0.0430458	+	0.0248525i
$916$	4.34273e13	−	2.50728e13i	2.03814	−	1.17672i
$917$	−5.48165e12	+	1.81029e13i	−0.256006	+	0.845447i
$918$		−	7.74130e12i		−	0.359767i
$919$	6.19263e12	−	1.07260e13i	0.286388	−	0.496039i	−0.686556	−	0.727076i	$-0.740879\pi$
$919$	6.19263e12	−	1.07260e13i	0.286388	−	0.496039i	0.972945	+	0.231037i	$0.0742119\pi$
$920$	5.76073e13	+	9.97788e13i	2.65114	+	4.59191i
$921$	−1.35020e12	+	7.79537e11i	−0.0618342	+	0.0357000i
$922$	−1.02373e13	−	1.77316e13i	−0.466550	−	0.808088i
$923$	−4.58920e11	−	5.11723e11i	−0.0208127	−	0.0232074i
$924$	−4.00474e11	−	1.71370e12i	−0.0180739	−	0.0773411i
$925$	1.76381e13	+	1.01834e13i	0.792161	+	0.457355i
$926$	6.54027e12			0.292312
$927$	−2.91984e13			−1.29868
$928$	−3.42915e13	−	1.97982e13i	−1.51782	−	0.876314i
$929$	−1.83170e13	−	1.05754e13i	−0.806835	−	0.465826i	0.0390206	−	0.999238i	$-0.487576\pi$
$929$	−1.83170e13	−	1.05754e13i	−0.806835	−	0.465826i	−0.845856	+	0.533412i	$0.820910\pi$
$930$	1.73330e12	−	1.00072e12i	0.0759804	−	0.0438673i
$931$	1.16114e13	−	1.74151e13i	0.506537	−	0.759717i
$932$	5.46516e13	+	9.46593e13i	2.37264	+	4.10953i
$933$	−1.71431e12			−0.0740665
$934$	5.09469e13	−	2.94142e13i	2.19057	−	1.26473i
$935$	−1.45650e13	+	2.52273e13i	−0.623243	+	1.07949i
$936$	2.20223e13	−	6.73223e13i	0.937826	−	2.86693i
$937$	−3.12033e13			−1.32243			−0.661214	−	0.750198i	$-0.729958\pi$
$937$	−3.12033e13			−1.32243			−0.661214	+	0.750198i	$0.729958\pi$
$938$	−1.34287e13	+	4.43476e13i	−0.566396	+	1.87050i
$939$	1.91677e11	−	3.31994e11i	0.00804589	−	0.0139359i
$940$	−4.60320e13	+	7.97298e13i	−1.92302	+	3.33077i
$941$	8.98983e11	+	5.19028e11i	0.0373765	+	0.0215793i	0.518572	−	0.855034i	$-0.326464\pi$
$941$	8.98983e11	+	5.19028e11i	0.0373765	+	0.0215793i	−0.481195	+	0.876613i	$0.659797\pi$
$942$		−	2.00187e12i		−	0.0828339i
$943$	−2.39354e13	−	1.38191e13i	−0.985684	−	0.569085i
$944$		−	1.53966e12i		−	0.0631033i
$945$	3.36010e12	+	1.01745e12i	0.137059	+	0.0415023i
$946$	1.29707e13	−	2.24658e13i	0.526565	−	0.912037i
$947$		−	1.36907e13i		−	0.553161i	−0.960991	−	0.276580i	$-0.910799\pi$
$947$		−	1.36907e13i		−	0.553161i	0.960991	−	0.276580i	$-0.0892012\pi$
$948$	−3.06550e12	+	5.30961e12i	−0.123272	+	0.213513i
$949$	−4.97891e11	+	1.52205e12i	−0.0199267	+	0.0609161i
$950$	1.50837e13	+	2.61257e13i	0.600830	+	1.04067i
$951$	1.37347e12	+	7.92973e11i	0.0544511	+	0.0314374i
$952$	−9.64622e13	+	9.04366e13i	−3.80619	+	3.56844i
$953$	1.40761e13	+	2.43804e13i	0.552793	+	0.957466i	0.998072	+	0.0620739i	$0.0197714\pi$
$953$	1.40761e13	+	2.43804e13i	0.552793	+	0.957466i	−0.445278	+	0.895392i	$0.646895\pi$
$954$	−1.53291e13	+	8.85024e12i	−0.599167	+	0.345929i
$955$		−	4.31836e13i		−	1.67998i
$956$			9.42769e13i			3.65044i
$957$	−4.11105e11	+	2.37352e11i	−0.0158434	+	0.00914720i
$958$	3.05364e12	+	5.28906e12i	0.117131	+	0.202877i
$959$	2.40824e13	−	2.25780e13i	0.919424	−	0.861991i
$960$	3.95039e12	+	2.28076e12i	0.150113	+	0.0866680i
$961$	−7.71657e12	−	1.33655e13i	−0.291856	−	0.505510i
$962$	−1.36735e13	−	6.49631e13i	−0.514744	−	2.44556i
$963$	−2.15160e13	+	3.72668e13i	−0.806200	+	1.39638i
$964$			1.23536e13i			0.460729i
$965$	2.97534e13	−	5.15344e13i	1.10449	−	1.91304i
$966$	3.64376e12	+	1.10335e12i	0.134633	+	0.0407677i
$967$			2.77117e13i			1.01917i	0.860422	+	0.509583i	$0.170200\pi$
$967$			2.77117e13i			1.01917i	−0.860422	+	0.509583i	$0.829800\pi$
$968$	−4.95005e13	−	2.85791e13i	−1.81205	−	1.04619i
$969$		−	2.38089e12i		−	0.0867527i
$970$	1.91079e12	+	1.10320e12i	0.0693012	+	0.0400111i
$971$	−5.57980e12	+	9.66449e12i	−0.201434	+	0.348893i	−0.948991	−	0.315304i	$-0.897893\pi$
$971$	−5.57980e12	+	9.66449e12i	−0.201434	+	0.348893i	0.747557	+	0.664198i	$0.231227\pi$
$972$	5.94561e12	−	1.02981e13i	0.213648	−	0.370049i
$973$	−3.27946e12	+	1.08303e13i	−0.117299	+	0.387374i
$974$	3.92242e13			1.39649
$975$	2.22241e11	+	1.05588e12i	0.00787597	+	0.0374190i
$976$	3.08642e13	−	5.34583e13i	1.08876	−	1.88578i
$977$	3.58317e13	−	2.06875e13i	1.25818	−	0.726410i	0.285459	−	0.958391i	$-0.407854\pi$
$977$	3.58317e13	−	2.06875e13i	1.25818	−	0.726410i	0.972720	+	0.231981i	$0.0745207\pi$
$978$	3.24290e12			0.113346
$979$	−9.06173e11	−	1.56954e12i	−0.0315275	−	0.0546072i
$980$	−4.32310e13	−	8.74451e13i	−1.49719	−	3.02843i
$981$	2.36422e13	−	1.36498e13i	0.815036	−	0.470562i
$982$	−2.76425e13	−	1.59594e13i	−0.948585	−	0.547666i
$983$	5.16023e12	+	2.97926e12i	0.176270	+	0.101770i	0.585539	−	0.810644i	$-0.300883\pi$
$983$	5.16023e12	+	2.97926e12i	0.176270	+	0.101770i	−0.409269	+	0.912414i	$0.634216\pi$
$984$	−4.14416e12			−0.140916
$985$	6.91936e12			0.234208
$986$	5.02461e13	+	2.90096e13i	1.69300	+	0.977452i
$987$	4.25563e11	+	1.82106e12i	0.0142737	+	0.0610796i
$988$	2.20695e13	−	6.74666e13i	0.736863	−	2.25259i
$989$	2.02558e13	+	3.50840e13i	0.673232	+	1.16607i
$990$	−3.57688e13	+	2.06511e13i	−1.18344	+	0.683259i
$991$	−1.58431e13	−	2.74410e13i	−0.521805	−	0.903793i	−0.999678	−	0.0253642i	$-0.991925\pi$
$991$	−1.58431e13	−	2.74410e13i	−0.521805	−	0.903793i	0.477873	−	0.878429i	$-0.341408\pi$
$992$	−2.88441e13	+	4.99595e13i	−0.945703	+	1.63801i
$993$		−	3.19079e11i		−	0.0104142i
$994$	−5.27250e11	+	1.74122e12i	−0.0171308	+	0.0565737i
$995$	−5.49200e13	+	3.17081e13i	−1.77634	+	1.02557i
$996$	2.41469e12	−	1.39412e12i	0.0777488	−	0.0448883i
$997$	−1.71401e13			−0.549395			−0.274698	−	0.961531i	$-0.588578\pi$
$997$	−1.71401e13			−0.549395			−0.274698	+	0.961531i	$0.588578\pi$
$998$	−1.54069e13	−	2.66855e13i	−0.491617	−	0.851506i
$999$		−	4.56508e12i		−	0.145012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.k.a.4.3	✓	164
7.2	even	3		91.10.u.a.30.3	yes	164
13.10	even	6		91.10.u.a.88.3	yes	164
91.23	even	6	inner	91.10.k.a.23.80	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.k.a.4.3	✓	164	1.1	even	1	trivial
91.10.k.a.23.80	yes	164	91.23	even	6	inner
91.10.u.a.30.3	yes	164	7.2	even	3
91.10.u.a.88.3	yes	164	13.10	even	6

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-42.9063i q^{2} +(-3.86494 - 6.69428i) q^{3} -1328.95 q^{4} +(1575.27 - 909.485i) q^{5} +(-287.227 + 165.831i) q^{6} +(-4344.78 - 4634.27i) q^{7} +35052.4i q^{8} +(9811.62 - 16994.2i) q^{9} +O(q^{10})\)	\(q-42.9063i q^{2} +(-3.86494 - 6.69428i) q^{3} -1328.95 q^{4} +(1575.27 - 909.485i) q^{5} +(-287.227 + 165.831i) q^{6} +(-4344.78 - 4634.27i) q^{7} +35052.4i q^{8} +(9811.62 - 16994.2i) q^{9} +(-39022.6 - 67589.2i) q^{10} +(23355.4 - 13484.2i) q^{11} +(5136.33 + 8896.38i) q^{12} +(-21210.2 - 100770. i) q^{13} +(-198839. + 186419. i) q^{14} +(-12176.7 - 7030.22i) q^{15} +823547. q^{16} -593824. q^{17} +(-729160. - 420981. i) q^{18} +(-449200. - 259346. i) q^{19} +(-2.09346e6 + 1.20866e6i) q^{20} +(-14230.8 + 46996.4i) q^{21} +(-578559. - 1.00209e6i) q^{22} +1.80702e6 q^{23} +(234651. - 135476. i) q^{24} +(677762. - 1.17392e6i) q^{25} +(-4.32368e6 + 910050. i) q^{26} -303833. q^{27} +(5.77401e6 + 6.15872e6i) q^{28} +(1.13858e6 - 1.97207e6i) q^{29} +(-301641. + 522457. i) q^{30} +(-2.87313e6 - 1.65880e6i) q^{31} -1.73885e7i q^{32} +(-180535. - 104232. i) q^{33} +2.54788e7i q^{34} +(-1.10590e7 - 3.34873e6i) q^{35} +(-1.30392e7 + 2.25845e7i) q^{36} +1.50250e7i q^{37} +(-1.11276e7 + 1.92735e7i) q^{38} +(-592608. + 531458. i) q^{39} +(3.18797e7 + 5.52172e7i) q^{40} +(-1.32457e7 - 7.64743e6i) q^{41} +(2.01644e6 + 610589. i) q^{42} +(1.12094e7 + 1.94153e7i) q^{43} +(-3.10382e7 + 1.79199e7i) q^{44} -3.56941e7i q^{45} -7.75328e7i q^{46} +(3.29827e7 - 1.90425e7i) q^{47} +(-3.18296e6 - 5.51306e6i) q^{48} +(-2.59931e6 + 4.02698e7i) q^{49} +(-5.03685e7 - 2.90803e7i) q^{50} +(2.29510e6 + 3.97522e6i) q^{51} +(2.81873e7 + 1.33919e8i) q^{52} +(1.05115e7 - 1.82064e7i) q^{53} +1.30364e7i q^{54} +(2.45274e7 - 4.24827e7i) q^{55} +(1.62442e8 - 1.52295e8i) q^{56} +4.00943e6i q^{57} +(-8.46144e7 - 4.88522e7i) q^{58} -1.86955e6i q^{59} +(1.61822e7 + 9.34282e6i) q^{60} +(3.74771e7 - 6.49123e7i) q^{61} +(-7.11730e7 + 1.23275e8i) q^{62} +(-1.21385e8 + 2.83666e7i) q^{63} -3.24422e8 q^{64} +(-1.25061e8 - 1.39450e8i) q^{65} +(-4.47220e6 + 7.74607e6i) q^{66} +(1.47227e8 - 8.50016e7i) q^{67} +7.89164e8 q^{68} +(-6.98405e6 - 1.20967e7i) q^{69} +(-1.43682e8 + 4.74502e8i) q^{70} +(5.78058e6 - 3.33742e6i) q^{71} +(5.95689e8 + 3.43921e8i) q^{72} +(-1.34676e7 - 7.77552e6i) q^{73} +6.44666e8 q^{74} -1.04781e7 q^{75} +(5.96965e8 + 3.44658e8i) q^{76} +(-1.63964e8 - 4.96490e7i) q^{77} +(2.28029e7 + 2.54266e7i) q^{78} +(2.98414e8 + 5.16868e8i) q^{79} +(1.29731e9 - 7.49004e8i) q^{80} +(-1.91948e8 - 3.32464e8i) q^{81} +(-3.28123e8 + 5.68326e8i) q^{82} -2.71423e8i q^{83} +(1.89120e7 - 6.24560e7i) q^{84} +(-9.35435e8 + 5.40074e8i) q^{85} +(8.33041e8 - 4.80956e8i) q^{86} -1.76021e7 q^{87} +(4.72655e8 + 8.18663e8i) q^{88} -6.72024e7i q^{89} -1.53150e9 q^{90} +(-3.74843e8 + 5.36118e8i) q^{91} -2.40145e9 q^{92} +2.56447e7i q^{93} +(-8.17046e8 - 1.41516e9i) q^{94} -9.43484e8 q^{95} +(-1.16404e8 + 6.72057e7i) q^{96} +(-2.44831e7 + 1.41353e7i) q^{97} +(1.72783e9 + 1.11527e8i) q^{98} -5.29209e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 164 q - 161 q^{3} - 40962 q^{4} - 6 q^{6} - 2055 q^{7} - 510909 q^{9}+O(q^{10}) \) 164 * q - 161 * q^3 - 40962 * q^4 - 6 * q^6 - 2055 * q^7 - 510909 * q^9	\( 164 q - 161 q^{3} - 40962 q^{4} - 6 q^{6} - 2055 q^{7} - 510909 q^{9} + 41025 q^{10} - 85389 q^{11} + 43064 q^{12} - 232462 q^{13} + 82708 q^{14} + 338445 q^{15} + 9425286 q^{16} - 1277590 q^{17} + 1176873 q^{18} - 1344159 q^{19} + 571062 q^{20} - 1367523 q^{21} - 1417332 q^{22} - 2148066 q^{23} + 62118 q^{24} + 29660776 q^{25} + 3184908 q^{26} + 7350574 q^{27} + 4828755 q^{28} + 996812 q^{29} - 9177016 q^{30} - 21474090 q^{31} - 15796239 q^{33} + 10592613 q^{35} + 131881331 q^{36} - 8950274 q^{38} - 35258971 q^{39} - 7901342 q^{40} + 24649770 q^{41} - 51088299 q^{42} + 15892214 q^{43} - 1176612 q^{44} - 69222114 q^{47} - 15455476 q^{48} - 57160671 q^{49} + 309166224 q^{50} + 52823362 q^{51} + 177629625 q^{52} - 155327528 q^{53} - 77925569 q^{55} - 92078463 q^{56} - 597924735 q^{58} - 290928939 q^{60} - 468761537 q^{61} + 238770500 q^{62} - 358980429 q^{63} - 2035250696 q^{64} - 542245158 q^{65} - 154929237 q^{66} - 353402973 q^{67} + 1196053594 q^{68} + 127053056 q^{69} - 1180478502 q^{70} - 269829840 q^{71} - 485282307 q^{72} - 35353098 q^{73} + 920062914 q^{74} - 1606576144 q^{75} + 1140965370 q^{76} - 1032378781 q^{77} - 835494667 q^{78} - 683323974 q^{79} - 432598794 q^{80} - 1724339502 q^{81} - 324994534 q^{82} + 3803919051 q^{84} - 196261605 q^{85} + 572477022 q^{86} + 3699935866 q^{87} + 37403221 q^{88} - 9086462948 q^{90} + 2603275581 q^{91} - 2683122798 q^{92} - 2561821264 q^{94} - 397964902 q^{95} + 392112 q^{96} + 6155159124 q^{97} + 2492693148 q^{98}+O(q^{100}) \) 164 * q - 161 * q^3 - 40962 * q^4 - 6 * q^6 - 2055 * q^7 - 510909 * q^9 + 41025 * q^10 - 85389 * q^11 + 43064 * q^12 - 232462 * q^13 + 82708 * q^14 + 338445 * q^15 + 9425286 * q^16 - 1277590 * q^17 + 1176873 * q^18 - 1344159 * q^19 + 571062 * q^20 - 1367523 * q^21 - 1417332 * q^22 - 2148066 * q^23 + 62118 * q^24 + 29660776 * q^25 + 3184908 * q^26 + 7350574 * q^27 + 4828755 * q^28 + 996812 * q^29 - 9177016 * q^30 - 21474090 * q^31 - 15796239 * q^33 + 10592613 * q^35 + 131881331 * q^36 - 8950274 * q^38 - 35258971 * q^39 - 7901342 * q^40 + 24649770 * q^41 - 51088299 * q^42 + 15892214 * q^43 - 1176612 * q^44 - 69222114 * q^47 - 15455476 * q^48 - 57160671 * q^49 + 309166224 * q^50 + 52823362 * q^51 + 177629625 * q^52 - 155327528 * q^53 - 77925569 * q^55 - 92078463 * q^56 - 597924735 * q^58 - 290928939 * q^60 - 468761537 * q^61 + 238770500 * q^62 - 358980429 * q^63 - 2035250696 * q^64 - 542245158 * q^65 - 154929237 * q^66 - 353402973 * q^67 + 1196053594 * q^68 + 127053056 * q^69 - 1180478502 * q^70 - 269829840 * q^71 - 485282307 * q^72 - 35353098 * q^73 + 920062914 * q^74 - 1606576144 * q^75 + 1140965370 * q^76 - 1032378781 * q^77 - 835494667 * q^78 - 683323974 * q^79 - 432598794 * q^80 - 1724339502 * q^81 - 324994534 * q^82 + 3803919051 * q^84 - 196261605 * q^85 + 572477022 * q^86 + 3699935866 * q^87 + 37403221 * q^88 - 9086462948 * q^90 + 2603275581 * q^91 - 2683122798 * q^92 - 2561821264 * q^94 - 397964902 * q^95 + 392112 * q^96 + 6155159124 * q^97 + 2492693148 * q^98

Introduction

L-functions

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