LMFDB - Embedded newform 18.11.d.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,11,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	18.d (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:	$11.4364305481$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 63819 x^{18} - 574086 x^{17} + 1685636151 x^{16} - 13472077884 x^{15} + \cdots + 42\!\cdots\!17 $ x^20 - 10x^19 + 63819x^18 - 574086x^17 + 1685636151x^16 - 13472077884x^15 + 23849722149866x^14 - 166712339223788x^13 + 195479019402402405x^12 - 1170707468814910094x^11 + 938326637750627487341x^10 - 4680905675328128110986x^9 + 2551316542474577226379677x^8 - 10177193606819996156162676x^7 + 3644946427174260203987635170x^6 - 10899238750832113741944409252x^5 + 2446510322689300614446071763767x^4 - 4874867111497712925857039900178x^3 + 623192578601325527612865828822963x^2 - 620756959890572838693596656972206*x + 42080692026395342189225080891718217
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{46}\cdot 3^{37} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.7
Root			$0.500000 - 111.664i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.11.d.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(19.5959 + 11.3137i) q^{2} +(-120.535 + 210.998i) q^{3} +(256.000 + 443.405i) q^{4} +(-1022.89 + 590.567i) q^{5} +(-4749.17 + 2771.00i) q^{6} +(-2684.05 + 4648.92i) q^{7} +11585.2i q^{8} +(-29991.5 - 50865.5i) q^{9} -26726.0 q^{10} +(-148199. - 85562.6i) q^{11} +(-124415. + 569.593i) q^{12} +(-40805.4 - 70677.1i) q^{13} +(-105193. + 60733.2i) q^{14} +(-1314.00 - 287013. i) q^{15} +(-131072. + 227023. i) q^{16} +589227. i q^{17} +(-12233.8 - 1.33607e6i) q^{18} -2.83768e6 q^{19} +(-523721. - 302370. i) q^{20} +(-657390. - 1.12669e6i) q^{21} +(-1.93606e6 - 3.35336e6i) q^{22} +(-1.57720e6 + 910597. i) q^{23} +(-2.44446e6 - 1.39643e6i) q^{24} +(-4.18527e6 + 7.24911e6i) q^{25} -1.84664e6i q^{26} +(1.43476e7 - 197068. i) q^{27} -2.74847e6 q^{28} +(2.04067e7 + 1.17818e7i) q^{29} +(3.22143e6 - 5.63914e6i) q^{30} +(1.78311e7 + 3.08843e7i) q^{31} +(-5.13695e6 + 2.96582e6i) q^{32} +(3.59167e7 - 2.09564e7i) q^{33} +(-6.66634e6 + 1.15464e7i) q^{34} -6.34045e6i q^{35} +(1.48762e7 - 2.63199e7i) q^{36} +8.15908e7 q^{37} +(-5.56070e7 - 3.21047e7i) q^{38} +(1.98312e7 - 90791.0i) q^{39} +(-6.84186e6 - 1.18504e7i) q^{40} +(-1.05152e8 + 6.07093e7i) q^{41} +(-135130. - 2.95160e7i) q^{42} +(-9.79725e7 + 1.69693e8i) q^{43} -8.76161e7i q^{44} +(6.07175e7 + 3.43179e7i) q^{45} -4.12089e7 q^{46} +(-3.76072e8 - 2.17125e8i) q^{47} +(-3.21027e7 - 5.50203e7i) q^{48} +(1.26829e8 + 2.19675e8i) q^{49} +(-1.64029e8 + 9.47019e7i) q^{50} +(-1.24326e8 - 7.10226e7i) q^{51} +(2.08924e7 - 3.61867e7i) q^{52} -6.70997e8i q^{53} +(2.83383e8 + 1.58462e8i) q^{54} +2.02122e8 q^{55} +(-5.38588e7 - 3.10954e7i) q^{56} +(3.42041e8 - 5.98746e8i) q^{57} +(2.66592e8 + 4.61751e8i) q^{58} +(-4.59646e8 + 2.65377e8i) q^{59} +(1.26926e8 - 7.40579e7i) q^{60} +(-2.21275e8 + 3.83259e8i) q^{61} +8.06943e8i q^{62} +(3.16968e8 - 2.90234e6i) q^{63} -1.34218e8 q^{64} +(8.34791e7 + 4.81967e7i) q^{65} +(9.40916e8 - 4.30769e6i) q^{66} +(7.01885e8 + 1.21570e9i) q^{67} +(-2.61266e8 + 1.50842e8i) q^{68} +(-2.02605e6 - 4.42545e8i) q^{69} +(7.17340e7 - 1.24247e8i) q^{70} -7.13836e8i q^{71} +(5.89288e8 - 3.47459e8i) q^{72} -1.13324e9 q^{73} +(1.59885e9 + 9.23095e8i) q^{74} +(-1.02508e9 - 1.75686e9i) q^{75} +(-7.26447e8 - 1.25824e9i) q^{76} +(7.95547e8 - 4.59309e8i) q^{77} +(3.89638e8 + 2.22586e8i) q^{78} +(7.12169e8 - 1.23351e9i) q^{79} -3.09627e8i q^{80} +(-1.68781e9 + 3.05106e9i) q^{81} -2.74739e9 q^{82} +(3.74489e9 + 2.16211e9i) q^{83} +(3.31288e8 - 5.79922e8i) q^{84} +(-3.47978e8 - 6.02716e8i) q^{85} +(-3.83972e9 + 2.21686e9i) q^{86} +(-4.94567e9 + 2.88566e9i) q^{87} +(9.91263e8 - 1.71692e9i) q^{88} -5.81248e9i q^{89} +(8.01553e8 + 1.35943e9i) q^{90} +4.38096e8 q^{91} +(-8.07526e8 - 4.66225e8i) q^{92} +(-8.66581e9 + 3.96737e7i) q^{93} +(-4.91298e9 - 8.50953e9i) q^{94} +(2.90264e9 - 1.67584e9i) q^{95} +(-6.59888e6 - 1.44137e9i) q^{96} +(4.19017e9 - 7.25759e9i) q^{97} +5.73964e9i q^{98} +(9.25211e7 + 1.01044e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19}+ \cdots + 41160676842 q^{99}+O(q^{100}) $ 20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	19.5959	+	11.3137i	0.612372	+	0.353553i
$2$	19.5959	+	11.3137i	0.612372	+	0.353553i
$3$	−120.535	+	210.998i	−0.496030	+	0.868305i
$3$	−120.535	+	210.998i	−0.496030	+	0.868305i
$4$	256.000	+	443.405i	0.250000	+	0.433013i
$5$	−1022.89	+	590.567i	−0.327326	+	0.188981i	−0.654653	−	0.755929i	$-0.727185\pi$
$5$	−1022.89	+	590.567i	−0.327326	+	0.188981i	0.327328	+	0.944911i	$0.393852\pi$
$6$	−4749.17	+	2771.00i	−0.610747	+	0.356353i
$7$	−2684.05	+	4648.92i	−0.159698	+	0.276606i	−0.934760	−	0.355280i	$-0.884386\pi$
$7$	−2684.05	+	4648.92i	−0.159698	+	0.276606i	0.775061	+	0.631886i	$0.217719\pi$
$8$			11585.2i			0.353553i
$9$	−29991.5	−	50865.5i	−0.507909	−	0.861411i
$10$	−26726.0			−0.267260
$11$	−148199.	−	85562.6i	−0.920198	−	0.531277i	−0.0364997	−	0.999334i	$-0.511621\pi$
$11$	−148199.	−	85562.6i	−0.920198	−	0.531277i	−0.883698	+	0.468057i	$0.844954\pi$
$12$	−124415.	+	569.593i	−0.499995	+	0.00228907i
$13$	−40805.4	−	70677.1i	−0.109901	−	0.190354i	0.805829	−	0.592148i	$-0.201720\pi$
$13$	−40805.4	−	70677.1i	−0.109901	−	0.190354i	−0.915730	+	0.401794i	$0.868387\pi$
$14$	−105193.	+	60733.2i	−0.195590	+	0.112924i
$15$	−1314.00	−	287013.i	−0.00173037	−	0.377959i
$16$	−131072.	+	227023.i	−0.125000	+	0.216506i
$17$			589227.i			0.414990i	0.978236	+	0.207495i	$0.0665311\pi$
$17$			589227.i			0.414990i	−0.978236	+	0.207495i	$0.933469\pi$
$18$	−12233.8	−	1.33607e6i	−0.00647439	−	0.707077i
$19$	−2.83768e6			−1.14603			−0.573015	−	0.819545i	$-0.694226\pi$
$19$	−2.83768e6			−1.14603			−0.573015	+	0.819545i	$0.694226\pi$
$20$	−523721.	−	302370.i	−0.163663	−	0.0944907i
$21$	−657390.	−	1.12669e6i	−0.160963	−	0.275872i
$22$	−1.93606e6	−	3.35336e6i	−0.375669	−	0.650678i
$23$	−1.57720e6	+	910597.i	−0.245046	+	0.141477i	−0.617494	−	0.786576i	$-0.711852\pi$
$23$	−1.57720e6	+	910597.i	−0.245046	+	0.141477i	0.372448	+	0.928053i	$0.378519\pi$
$24$	−2.44446e6	−	1.39643e6i	−0.306992	−	0.175373i
$25$	−4.18527e6	+	7.24911e6i	−0.428572	+	0.742308i
$26$		−	1.84664e6i		−	0.155423i
$27$	1.43476e7	−	197068.i	0.999906	−	0.0137340i
$28$	−2.74847e6			−0.159698
$29$	2.04067e7	+	1.17818e7i	0.994908	+	0.574411i	0.906738	−	0.421695i	$-0.138565\pi$
$29$	2.04067e7	+	1.17818e7i	0.994908	+	0.574411i	0.0881706	+	0.996105i	$0.471898\pi$
$30$	3.22143e6	−	5.63914e6i	0.132569	−	0.232063i
$31$	1.78311e7	+	3.08843e7i	0.622830	+	1.07877i	0.988956	+	0.148207i	$0.0473503\pi$
$31$	1.78311e7	+	3.08843e7i	0.622830	+	1.07877i	−0.366127	+	0.930565i	$0.619316\pi$
$32$	−5.13695e6	+	2.96582e6i	−0.153093	+	0.0883883i
$33$	3.59167e7	−	2.09564e7i	0.917756	−	0.535484i
$34$	−6.66634e6	+	1.15464e7i	−0.146721	+	0.254129i
$35$		−	6.34045e6i		−	0.120720i
$36$	1.48762e7	−	2.63199e7i	0.246025	−	0.435284i
$37$	8.15908e7			1.17661			0.588305	−	0.808639i	$-0.299795\pi$
$37$	8.15908e7			1.17661			0.588305	+	0.808639i	$0.299795\pi$
$38$	−5.56070e7	−	3.21047e7i	−0.701797	−	0.405183i
$39$	1.98312e7	−	90791.0i	0.219799	−	0.00100628i
$40$	−6.84186e6	−	1.18504e7i	−0.0668150	−	0.115727i
$41$	−1.05152e8	+	6.07093e7i	−0.907604	+	0.524005i	−0.879659	−	0.475604i	$-0.842229\pi$
$41$	−1.05152e8	+	6.07093e7i	−0.907604	+	0.524005i	−0.0279444	+	0.999609i	$0.508896\pi$
$42$	−135130.	−	2.95160e7i	−0.00103396	−	0.225845i
$43$	−9.79725e7	+	1.69693e8i	−0.666441	+	1.15431i	0.312451	+	0.949934i	$0.398850\pi$
$43$	−9.79725e7	+	1.69693e8i	−0.666441	+	1.15431i	−0.978892	+	0.204376i	$0.934483\pi$
$44$		−	8.76161e7i		−	0.531277i
$45$	6.07175e7	+	3.43179e7i	0.329042	+	0.185977i
$46$	−4.12089e7			−0.200079
$47$	−3.76072e8	−	2.17125e8i	−1.63976	−	0.946718i	−0.980914	−	0.194443i	$-0.937710\pi$
$47$	−3.76072e8	−	2.17125e8i	−1.63976	−	0.946718i	−0.658850	−	0.752275i	$-0.728957\pi$
$48$	−3.21027e7	−	5.50203e7i	−0.125990	−	0.215932i
$49$	1.26829e8	+	2.19675e8i	0.448993	+	0.777678i
$50$	−1.64029e8	+	9.47019e7i	−0.524891	+	0.303046i
$51$	−1.24326e8	−	7.10226e7i	−0.360338	−	0.205848i
$52$	2.08924e7	−	3.61867e7i	0.0549504	−	0.0951769i
$53$		−	6.70997e8i		−	1.60451i	−0.596984	−	0.802253i	$-0.703634\pi$
$53$		−	6.70997e8i		−	1.60451i	0.596984	−	0.802253i	$-0.296366\pi$
$54$	2.83383e8	+	1.58462e8i	0.617170	+	0.345110i
$55$	2.02122e8			0.401606
$56$	−5.38588e7	−	3.10954e7i	−0.0977950	−	0.0564619i
$57$	3.42041e8	−	5.98746e8i	0.568465	−	0.995104i
$58$	2.66592e8	+	4.61751e8i	0.406170	+	0.703507i
$59$	−4.59646e8	+	2.65377e8i	−0.642930	+	0.371196i	−0.785742	−	0.618554i	$-0.787719\pi$
$59$	−4.59646e8	+	2.65377e8i	−0.642930	+	0.371196i	0.142812	+	0.989750i	$0.454385\pi$
$60$	1.26926e8	−	7.40579e7i	0.163228	−	0.0952390i
$61$	−2.21275e8	+	3.83259e8i	−0.261989	+	0.453778i	−0.966770	−	0.255646i	$-0.917712\pi$
$61$	−2.21275e8	+	3.83259e8i	−0.261989	+	0.453778i	0.704781	+	0.709424i	$0.251045\pi$
$62$			8.06943e8i			0.880814i
$63$	3.16968e8	−	2.90234e6i	0.319384	−	0.00292446i
$64$	−1.34218e8			−0.125000
$65$	8.34791e7	+	4.81967e7i	0.0719467	+	0.0415385i
$66$	9.40916e8	−	4.30769e6i	0.751331	−	0.00343973i
$67$	7.01885e8	+	1.21570e9i	0.519866	+	0.900435i	0.999733	+	0.0230938i	$0.00735163\pi$
$67$	7.01885e8	+	1.21570e9i	0.519866	+	0.900435i	−0.479867	+	0.877341i	$0.659315\pi$
$68$	−2.61266e8	+	1.50842e8i	−0.179696	+	0.103748i
$69$	−2.02605e6	−	4.42545e8i	−0.00129541	−	0.282952i
$70$	7.17340e7	−	1.24247e8i	0.0426810	−	0.0739257i
$71$		−	7.13836e8i		−	0.395646i	−0.980238	−	0.197823i	$-0.936613\pi$
$71$		−	7.13836e8i		−	0.395646i	0.980238	−	0.197823i	$-0.0633871\pi$
$72$	5.89288e8	−	3.47459e8i	0.304555	−	0.179573i
$73$	−1.13324e9			−0.546649			−0.273324	−	0.961922i	$-0.588123\pi$
$73$	−1.13324e9			−0.546649			−0.273324	+	0.961922i	$0.588123\pi$
$74$	1.59885e9	+	9.23095e8i	0.720524	+	0.415995i
$75$	−1.02508e9	−	1.75686e9i	−0.431966	−	0.740339i
$76$	−7.26447e8	−	1.25824e9i	−0.286508	−	0.496246i
$77$	7.95547e8	−	4.59309e8i	0.293908	−	0.169688i
$78$	3.89638e8	+	2.22586e8i	0.134955	+	0.0770946i
$79$	7.12169e8	−	1.23351e9i	0.231445	−	0.400874i	−0.726789	−	0.686861i	$-0.758988\pi$
$79$	7.12169e8	−	1.23351e9i	0.231445	−	0.400874i	0.958234	+	0.285987i	$0.0923214\pi$
$80$		−	3.09627e8i		−	0.0944907i
$81$	−1.68781e9	+	3.05106e9i	−0.484058	+	0.875036i
$82$	−2.74739e9			−0.741055
$83$	3.74489e9	+	2.16211e9i	0.950712	+	0.548894i	0.893302	−	0.449457i	$-0.148383\pi$
$83$	3.74489e9	+	2.16211e9i	0.950712	+	0.548894i	0.0574096	+	0.998351i	$0.481716\pi$
$84$	3.31288e8	−	5.79922e8i	0.0792152	−	0.138667i
$85$	−3.47978e8	−	6.02716e8i	−0.0784255	−	0.135837i
$86$	−3.83972e9	+	2.21686e9i	−0.816221	+	0.471245i
$87$	−4.94567e9	+	2.88566e9i	−0.992268	+	0.578959i
$88$	9.91263e8	−	1.71692e9i	0.187835	−	0.325339i
$89$		−	5.81248e9i		−	1.04091i	−0.853890	−	0.520453i	$-0.825763\pi$
$89$		−	5.81248e9i		−	1.04091i	0.853890	−	0.520453i	$-0.174237\pi$
$90$	8.01553e8	+	1.35943e9i	0.135744	+	0.230221i
$91$	4.38096e8			0.0702040
$92$	−8.07526e8	−	4.66225e8i	−0.122523	−	0.0707387i
$93$	−8.66581e9	+	3.96737e7i	−1.24565	+	0.00570280i
$94$	−4.91298e9	−	8.50953e9i	−0.669431	−	1.15949i
$95$	2.90264e9	−	1.67584e9i	0.375125	−	0.216578i
$96$	−6.59888e6	−	1.44137e9i	−0.000809308	−	0.176775i
$97$	4.19017e9	−	7.25759e9i	0.487947	−	0.845149i	−0.511957	−	0.859011i	$-0.671079\pi$
$97$	4.19017e9	−	7.25759e9i	0.487947	−	0.845149i	0.999904	+	0.0138619i	$0.00441251\pi$
$98$			5.73964e9i			0.634972i
$99$	9.25211e7	+	1.01044e10i	0.00972892	+	1.06251i
$100$	−4.28572e9			−0.428572
$101$	6.88287e9	+	3.97383e9i	0.654881	+	0.378096i	0.790324	−	0.612689i	$-0.209912\pi$
$101$	6.88287e9	+	3.97383e9i	0.654881	+	0.378096i	−0.135443	+	0.990785i	$0.543246\pi$
$102$	−1.63275e9	−	2.79834e9i	−0.147883	−	0.253454i
$103$	7.63491e9	+	1.32241e10i	0.658594	+	1.14072i	0.980980	+	0.194110i	$0.0621820\pi$
$103$	7.63491e9	+	1.32241e10i	0.658594	+	1.14072i	−0.322385	+	0.946608i	$0.604485\pi$
$104$	8.18811e8	−	4.72740e8i	0.0673003	−	0.0388558i
$105$	1.33782e9	+	7.64248e8i	0.104822	+	0.0598809i
$106$	7.59147e9	−	1.31488e10i	0.567279	−	0.982556i
$107$			1.04914e9i			0.0748023i	0.999300	+	0.0374012i	$0.0119079\pi$
$107$			1.04914e9i			0.0748023i	−0.999300	+	0.0374012i	$0.988092\pi$
$108$	3.76035e9	+	6.31133e9i	0.255923	+	0.429538i
$109$	1.40777e10			0.914951			0.457476	−	0.889222i	$-0.348754\pi$
$109$	1.40777e10			0.914951			0.457476	+	0.889222i	$0.348754\pi$
$110$	3.96076e9	+	2.28675e9i	0.245932	+	0.141989i
$111$	−9.83457e9	+	1.72155e10i	−0.583634	+	1.02166i
$112$	−7.03608e8	−	1.21869e9i	−0.0399246	−	0.0691515i
$113$	2.18307e10	−	1.26040e10i	1.18488	−	0.684094i	0.227745	−	0.973721i	$-0.426865\pi$
$113$	2.18307e10	−	1.26040e10i	1.18488	−	0.684094i	0.957140	+	0.289627i	$0.0935313\pi$
$114$	1.34766e10	−	7.86323e9i	0.699935	−	0.408391i
$115$	1.07554e9	−	1.86288e9i	0.0534732	−	0.0926183i
$116$			1.20646e10i			0.574411i
$117$	−2.37121e9	+	4.19530e9i	−0.108153	+	0.191352i
$118$	−1.20096e10			−0.524950
$119$	−2.73927e9	−	1.58152e9i	−0.114789	−	0.0662733i
$120$	3.32511e9	−	1.52230e7i	0.133629	−	0.000611777i
$121$	1.67321e9	+	2.89808e9i	0.0645095	+	0.111734i
$122$	−8.67217e9	+	5.00688e9i	−0.320869	+	0.185254i
$123$	−1.35077e8	−	2.95044e10i	−0.00479794	−	1.04800i
$124$	−9.12951e9	+	1.58128e10i	−0.311415	+	0.539386i
$125$		−	2.14213e10i		−	0.701932i
$126$	6.24411e9	+	3.52921e9i	0.196616	+	0.111128i
$127$	−6.34009e10			−1.91901			−0.959505	−	0.281692i	$-0.909104\pi$
$127$	−6.34009e10			−1.91901			−0.959505	+	0.281692i	$0.909104\pi$
$128$	−2.63012e9	−	1.51850e9i	−0.0765466	−	0.0441942i
$129$	−2.39959e10	−	4.11261e10i	−0.671719	−	1.15125i
$130$	1.09057e9	+	1.88892e9i	0.0293721	+	0.0508740i
$131$	−3.16551e10	+	1.82761e10i	−0.820516	+	0.473725i	−0.850595	−	0.525822i	$-0.823758\pi$
$131$	−3.16551e10	+	1.82761e10i	−0.820516	+	0.473725i	0.0300781	+	0.999548i	$0.490424\pi$
$132$	1.84868e10	+	1.05608e10i	0.461310	+	0.263529i
$133$	7.61649e9	−	1.31922e10i	0.183019	−	0.316999i
$134$			3.17637e10i			0.735202i
$135$	−1.45596e10	+	8.67477e9i	−0.324699	+	0.193459i
$136$	−6.82634e9			−0.146721
$137$	−6.23918e10	−	3.60219e10i	−1.29278	−	0.746387i	−0.313634	−	0.949544i	$-0.601546\pi$
$137$	−6.23918e10	−	3.60219e10i	−1.29278	−	0.746387i	−0.979146	+	0.203157i	$0.934880\pi$
$138$	4.96713e9	−	8.69500e9i	0.0992453	−	0.173730i
$139$	5.04283e10	+	8.73444e10i	0.971853	+	1.68330i	0.689952	+	0.723855i	$0.257631\pi$
$139$	5.04283e10	+	8.73444e10i	0.971853	+	1.68330i	0.281900	+	0.959444i	$0.409035\pi$
$140$	2.81139e9	−	1.62316e9i	0.0522734	−	0.0301801i
$141$	9.11429e10	−	5.31792e10i	1.63541	−	0.954215i
$142$	8.07613e9	−	1.39883e10i	0.139882	−	0.242283i
$143$			1.39657e10i			0.233551i
$144$	1.54787e10	−	1.41732e8i	0.249990	−	0.00228904i
$145$	−2.78318e10			−0.434212
$146$	−2.22069e10	−	1.28212e10i	−0.334752	−	0.193269i
$147$	−6.16384e10	+	2.82192e8i	−0.897976	+	0.00411110i
$148$	2.08872e10	+	3.61778e10i	0.294153	+	0.509487i
$149$	1.52528e10	−	8.80618e9i	0.207691	−	0.119910i	−0.392547	−	0.919732i	$-0.628406\pi$
$149$	1.52528e10	−	8.80618e9i	0.207691	−	0.119910i	0.600238	+	0.799822i	$0.295073\pi$
$150$	−2.10709e8	−	4.60247e10i	−0.00277477	−	0.606086i
$151$	1.02814e10	−	1.78080e10i	0.130969	−	0.226845i	−0.793081	−	0.609116i	$-0.791524\pi$
$151$	1.02814e10	−	1.78080e10i	0.130969	−	0.226845i	0.924050	+	0.382271i	$0.124858\pi$
$152$		−	3.28752e10i		−	0.405183i
$153$	2.99713e10	−	1.76718e10i	0.357477	−	0.210777i
$154$	2.07860e10			0.239975
$155$	−3.64785e10	−	2.10609e10i	−0.407736	−	0.235406i
$156$	5.11705e9	+	8.77002e9i	0.0553856	+	0.0949244i
$157$	5.54842e10	+	9.61014e10i	0.581662	+	1.00747i	0.995283	+	0.0970190i	$0.0309308\pi$
$157$	5.54842e10	+	9.61014e10i	0.581662	+	1.00747i	−0.413620	+	0.910449i	$0.635736\pi$
$158$	2.79112e10	−	1.61145e10i	0.283461	−	0.163656i
$159$	1.41579e11	+	8.08789e10i	1.39320	+	0.795883i
$160$	3.50303e9	−	6.06743e9i	0.0334075	−	0.0578635i
$161$		−	9.77636e9i		−	0.0903749i
$162$	−6.75929e10	+	4.06930e10i	−0.605796	+	0.364708i
$163$	7.01890e9			0.0610002			0.0305001	−	0.999535i	$-0.490290\pi$
$163$	7.01890e9			0.0610002			0.0305001	+	0.999535i	$0.490290\pi$
$164$	−5.38376e10	−	3.10831e10i	−0.453802	−	0.262003i
$165$	−2.43628e10	+	4.26474e10i	−0.199208	+	0.348716i
$166$	4.89231e10	+	8.47372e10i	0.388126	+	0.672255i
$167$	−3.44441e10	+	1.98863e10i	−0.265175	+	0.153099i	−0.626693	−	0.779266i	$-0.715592\pi$
$167$	−3.44441e10	+	1.98863e10i	−0.265175	+	0.153099i	0.361518	+	0.932365i	$0.382259\pi$
$168$	1.30530e10	−	7.61602e9i	0.0975354	−	0.0569091i
$169$	6.55991e10	−	1.13621e11i	0.475844	−	0.824185i
$170$		−	1.57477e10i		−	0.110910i
$171$	8.51064e10	+	1.44340e11i	0.582078	+	0.987203i
$172$	−1.00324e11			−0.666441
$173$	8.84045e10	+	5.10404e10i	0.570485	+	0.329370i	0.757343	−	0.653017i	$-0.226497\pi$
$173$	8.84045e10	+	5.10404e10i	0.570485	+	0.329370i	−0.186858	+	0.982387i	$0.559830\pi$
$174$	−1.29562e11	+	5.93161e8i	−0.812331	+	0.00371900i
$175$	−2.24670e10	−	3.89140e10i	−0.136885	−	0.237091i
$176$	3.88494e10	−	2.24297e10i	0.230049	−	0.132819i
$177$	−5.90457e8	−	1.28972e11i	−0.00339877	−	0.742384i
$178$	6.57607e10	−	1.13901e11i	0.368016	−	0.637422i
$179$			1.03170e11i			0.561419i	0.959793	+	0.280709i	$0.0905697\pi$
$179$			1.03170e11i			0.561419i	−0.959793	+	0.280709i	$0.909430\pi$
$180$	3.26961e8	+	3.57078e10i	0.00173035	+	0.188974i
$181$	−1.64562e11			−0.847103			−0.423552	−	0.905872i	$-0.639217\pi$
$181$	−1.64562e11			−0.847103			−0.423552	+	0.905872i	$0.639217\pi$
$182$	8.58488e9	+	4.95649e9i	0.0429910	+	0.0248209i
$183$	−5.41956e10	−	9.28848e10i	−0.264064	−	0.452574i
$184$	−1.05495e10	−	1.82722e10i	−0.0500198	−	0.0866368i
$185$	−8.34586e10	+	4.81849e10i	−0.385135	+	0.222358i
$186$	−1.70263e11	−	9.72651e10i	−0.764816	−	0.436910i
$187$	5.04158e10	−	8.73227e10i	0.220475	−	0.381873i
$188$		−	2.22336e11i		−	0.946718i
$189$	−3.75934e10	+	6.72295e10i	−0.155885	+	0.278773i
$190$	7.58400e10			0.306288
$191$	2.37116e11	+	1.36899e11i	0.932814	+	0.538560i	0.887700	−	0.460422i	$-0.152302\pi$
$191$	2.37116e11	+	1.36899e11i	0.932814	+	0.538560i	0.0451133	+	0.998982i	$0.485635\pi$
$192$	1.61780e10	−	2.83197e10i	0.0620037	−	0.108538i
$193$	−1.72038e11	−	2.97979e11i	−0.642448	−	1.11275i	−0.984885	−	0.173212i	$-0.944585\pi$
$193$	−1.72038e11	−	2.97979e11i	−0.642448	−	1.11275i	0.342436	−	0.939541i	$-0.388748\pi$
$194$	1.64220e11	−	9.48127e10i	0.597611	−	0.345031i
$195$	−2.02316e10	+	1.18045e10i	−0.0717558	+	0.0418674i
$196$	−6.49366e10	+	1.12474e11i	−0.224496	+	0.388839i
$197$			2.09792e11i			0.707062i	0.935423	+	0.353531i	$0.115019\pi$
$197$			2.09792e11i			0.707062i	−0.935423	+	0.353531i	$0.884981\pi$
$198$	−1.12505e11	+	1.99051e11i	−0.369696	+	0.654091i
$199$	−2.88180e11			−0.923418			−0.461709	−	0.887032i	$-0.652763\pi$
$199$	−2.88180e11			−0.923418			−0.461709	+	0.887032i	$0.652763\pi$
$200$	−8.39826e10	−	4.84874e10i	−0.262446	−	0.151523i
$201$	−3.41112e11	+	1.56168e9i	−1.03972	+	0.00476004i
$202$	8.99174e10	+	1.55742e11i	0.267354	+	0.463071i
$203$	−1.09545e11	+	6.32461e10i	−0.317771	+	0.183465i
$204$	−3.35620e8	−	7.33085e10i	−0.000949941	−	0.207493i
$205$	7.17058e10	−	1.24198e11i	0.198055	−	0.343041i
$206$			3.45517e11i			0.931393i
$207$	9.36205e10	+	5.29148e10i	0.246331	+	0.139228i
$208$	2.13938e10			0.0549504
$209$	4.20541e11	+	2.42800e11i	1.05457	+	0.608859i
$210$	1.75694e10	+	3.01119e10i	0.0430190	+	0.0737296i
$211$	−2.38481e11	−	4.13062e11i	−0.570219	−	0.987649i	−0.996543	−	0.0830783i	$-0.973525\pi$
$211$	−2.38481e11	−	4.13062e11i	−0.570219	−	0.987649i	0.426324	−	0.904571i	$-0.359808\pi$
$212$	2.97524e11	−	1.71775e11i	0.694772	−	0.401127i
$213$	1.50618e11	+	8.60424e10i	0.343542	+	0.196252i
$214$	−1.18697e10	+	2.05589e10i	−0.0264466	+	0.0458069i
$215$		−	2.31437e11i		−	0.503780i
$216$	2.28308e9	+	1.66220e11i	0.00485571	+	0.353520i
$217$	−1.91438e11			−0.397860
$218$	2.75865e11	+	1.59271e11i	0.560291	+	0.323484i
$219$	1.36596e11	−	2.39112e11i	0.271154	−	0.474658i
$220$	5.17432e10	+	8.96218e10i	0.100401	+	0.173900i
$221$	4.16448e10	−	2.40437e10i	0.0789950	−	0.0456078i
$222$	−3.87489e11	+	2.26088e11i	−0.718612	+	0.419289i
$223$	3.01038e11	−	5.21414e11i	0.545880	−	0.945492i	−0.452671	−	0.891678i	$-0.649529\pi$
$223$	3.01038e11	−	5.21414e11i	0.545880	−	0.945492i	0.998551	−	0.0538146i	$-0.0171380\pi$
$224$		−	3.18417e10i		−	0.0564619i
$225$	4.94252e11	−	4.52565e9i	0.857108	−	0.00784816i
$226$	5.70391e11			0.967454
$227$	5.51023e10	+	3.18133e10i	0.0914198	+	0.0527813i	0.545013	−	0.838428i	$-0.316525\pi$
$227$	5.51023e10	+	3.18133e10i	0.0914198	+	0.0527813i	−0.453593	+	0.891209i	$0.649858\pi$
$228$	3.53050e11	−	1.61633e9i	0.573009	−	0.00262334i
$229$	2.98929e11	+	5.17760e11i	0.474669	+	0.822151i	0.999579	−	0.0290068i	$-0.00923445\pi$
$229$	2.98929e11	+	5.17760e11i	0.474669	+	0.822151i	−0.524910	+	0.851158i	$0.675901\pi$
$230$	4.21523e10	−	2.43366e10i	0.0654910	−	0.0378113i
$231$	1.02195e9	+	2.23222e11i	0.00155371	+	0.339373i
$232$	−1.36495e11	+	2.36417e11i	−0.203085	+	0.351753i
$233$		−	7.45993e11i		−	1.08631i	−0.839631	−	0.543157i	$-0.817229\pi$
$233$		−	7.45993e11i		−	1.08631i	0.839631	−	0.543157i	$-0.182771\pi$
$234$	−9.39303e10	+	5.53836e10i	−0.133883	+	0.0789408i
$235$	5.12908e11			0.715649
$236$	−2.35339e11	−	1.35873e11i	−0.321465	−	0.185598i
$237$	1.74428e11	+	2.98948e11i	0.233278	+	0.399811i
$238$	−3.57856e10	−	6.19825e10i	−0.0468623	−	0.0811679i
$239$	−1.11610e12	+	6.44381e11i	−1.43125	+	0.826330i	−0.997216	−	0.0745688i	$-0.976242\pi$
$239$	−1.11610e12	+	6.44381e11i	−1.43125	+	0.826330i	−0.434029	+	0.900899i	$0.642909\pi$
$240$	6.53308e10	+	3.73210e10i	0.0820468	+	0.0468702i
$241$	−5.49991e11	+	9.52612e11i	−0.676504	+	1.17174i	0.299523	+	0.954089i	$0.403172\pi$
$241$	−5.49991e11	+	9.52612e11i	−0.676504	+	1.17174i	−0.976027	+	0.217650i	$0.930161\pi$
$242$			7.57208e10i			0.0912302i
$243$	−4.40328e11	−	7.23885e11i	−0.519691	−	0.854354i
$244$	−2.26585e11			−0.261989
$245$	−2.59466e11	−	1.49802e11i	−0.293934	−	0.169703i
$246$	3.31157e11	−	5.79694e11i	0.367586	−	0.643462i
$247$	1.15793e11	+	2.00559e11i	0.125950	+	0.218151i
$248$	−3.57802e11	+	2.06577e11i	−0.381404	+	0.220203i
$249$	−9.07594e11	+	5.29554e11i	−0.948189	+	0.553240i
$250$	2.42354e11	−	4.19769e11i	0.248170	−	0.429844i
$251$		−	1.01964e12i		−	1.02348i	−0.859141	−	0.511739i	$-0.829002\pi$
$251$		−	1.01964e12i		−	1.02348i	0.859141	−	0.511739i	$-0.170998\pi$
$252$	8.24307e10	+	1.39802e11i	0.0811122	+	0.137566i
$253$	3.11652e11			0.300654
$254$	−1.24240e12	−	7.17300e11i	−1.17515	−	0.678472i
$255$	1.69116e11	−	7.74242e8i	0.156849	−	0.000718085i
$256$	−3.43597e10	−	5.95128e10i	−0.0312500	−	0.0541266i
$257$	−5.43197e11	+	3.13615e11i	−0.484497	+	0.279725i	−0.722289	−	0.691592i	$-0.756910\pi$
$257$	−5.43197e11	+	3.13615e11i	−0.484497	+	0.279725i	0.237791	+	0.971316i	$0.423577\pi$
$258$	−4.93247e9	−	1.07738e12i	−0.00431485	−	0.942481i
$259$	−2.18994e11	+	3.79309e11i	−0.187903	+	0.325457i
$260$			4.93534e10i			0.0415385i
$261$	−1.27400e10	−	1.39135e12i	−0.0105188	−	1.14877i
$262$	−8.27081e11			−0.669949
$263$	−9.28282e11	−	5.35944e11i	−0.737736	−	0.425932i	0.0835094	−	0.996507i	$-0.473387\pi$
$263$	−9.28282e11	−	5.35944e11i	−0.737736	−	0.425932i	−0.821246	+	0.570575i	$0.806720\pi$
$264$	2.42784e11	+	4.16104e11i	0.189322	+	0.324476i
$265$	3.96269e11	+	6.86358e11i	0.303222	+	0.525196i
$266$	2.98504e11	−	1.72342e11i	0.224152	−	0.129414i
$267$	1.22642e12	+	7.00609e11i	0.903824	+	0.516321i
$268$	−3.59365e11	+	6.22438e11i	−0.259933	+	0.450218i
$269$			5.01748e11i			0.356225i	0.984010	+	0.178113i	$0.0569991\pi$
$269$			5.01748e11i			0.356225i	−0.984010	+	0.178113i	$0.943001\pi$
$270$	−3.83453e11	+	5.26685e9i	−0.267235	+	0.00367056i
$271$	1.53061e12			1.04717			0.523586	−	0.851973i	$-0.324594\pi$
$271$	1.53061e12			1.04717			0.523586	+	0.851973i	$0.324594\pi$
$272$	−1.33768e11	−	7.72312e10i	−0.0898481	−	0.0518738i
$273$	−5.28060e10	+	9.24374e10i	−0.0348233	+	0.0609585i
$274$	−8.15083e11	−	1.41176e12i	−0.527775	−	0.914133i
$275$	1.24050e12	−	7.16206e11i	0.788742	−	0.455380i
$276$	1.95708e11	−	1.14190e11i	0.122198	−	0.0712989i
$277$	−1.57687e12	+	2.73122e12i	−0.966934	+	1.67478i	−0.262607	+	0.964903i	$0.584582\pi$
$277$	−1.57687e12	+	2.73122e12i	−0.966934	+	1.67478i	−0.704327	+	0.709876i	$0.748751\pi$
$278$			2.28213e12i			1.37441i
$279$	1.03617e12	−	1.83325e12i	0.612926	−	1.08443i
$280$	7.34557e10			0.0426810
$281$	1.56624e12	+	9.04268e11i	0.893976	+	0.516137i	0.875241	−	0.483687i	$-0.160703\pi$
$281$	1.56624e12	+	9.04268e11i	0.893976	+	0.516137i	0.0187352	+	0.999824i	$0.494036\pi$
$282$	2.38768e12	−	1.09313e10i	1.33885	−	0.00612949i
$283$	−2.16284e11	−	3.74615e11i	−0.119150	−	0.206373i	0.800281	−	0.599625i	$-0.204683\pi$
$283$	−2.16284e11	−	3.74615e11i	−0.119150	−	0.206373i	−0.919431	+	0.393252i	$0.871350\pi$
$284$	3.16519e11	−	1.82742e11i	0.171320	−	0.0989115i
$285$	3.72871e9	+	8.14451e11i	0.00198305	+	0.433152i
$286$	−1.58004e11	+	2.73670e11i	−0.0825727	+	0.143020i
$287$		−	6.51787e11i		−	0.334731i
$288$	3.04923e11	+	1.72344e11i	0.153896	+	0.0869829i
$289$	1.66881e12			0.827783
$290$	−5.45390e11	−	3.14881e11i	−0.265899	−	0.153517i
$291$	1.02627e12	+	1.75891e12i	0.491811	+	0.842907i
$292$	−2.90110e11	−	5.02485e11i	−0.136662	−	0.236706i
$293$	7.82890e11	−	4.52001e11i	0.362545	−	0.209316i	−0.307651	−	0.951499i	$-0.599543\pi$
$293$	7.82890e11	−	4.52001e11i	0.362545	−	0.209316i	0.670197	+	0.742183i	$0.266210\pi$
$294$	−1.21105e12	−	6.91829e11i	−0.551349	−	0.314965i
$295$	3.13446e11	−	5.42904e11i	0.140298	−	0.243004i
$296$			9.45249e11i			0.415995i
$297$	−2.14315e12	−	1.19841e12i	−0.927408	−	0.518588i
$298$	3.98522e11			0.169579
$299$	1.28717e11	+	7.43146e10i	0.0538615	+	0.0310970i
$300$	5.16580e11	−	9.04279e11i	0.212585	−	0.372131i
$301$	−5.25927e11	−	9.10932e11i	−0.212859	−	0.368683i
$302$	4.02949e11	−	2.32642e11i	0.160404	−	0.0926092i
$303$	−1.66810e12	+	9.73287e11i	−0.653144	+	0.381090i
$304$	3.71941e11	−	6.44221e11i	0.143254	−	0.248123i
$305$		−	5.22710e11i		−	0.198044i
$306$	7.87249e11	−	7.20849e9i	0.293430	−	0.00268681i
$307$	1.20922e12			0.443417			0.221709	−	0.975113i	$-0.428837\pi$
$307$	1.20922e12			0.443417			0.221709	+	0.975113i	$0.428837\pi$
$308$	4.07320e11	+	2.35166e11i	0.146954	+	0.0848441i
$309$	−3.71053e12	+	1.69875e10i	−1.31717	+	0.00603027i
$310$	−4.76554e11	−	8.25415e11i	−0.166458	−	0.288313i
$311$	−3.63783e11	+	2.10030e11i	−0.125037	+	0.0721904i	−0.561214	−	0.827671i	$-0.689666\pi$
$311$	−3.63783e11	+	2.10030e11i	−0.125037	+	0.0721904i	0.436177	+	0.899861i	$0.356332\pi$
$312$	1.05184e9	+	2.29749e11i	0.000355775	+	0.0777108i
$313$	−1.50077e12	+	2.59941e12i	−0.499566	+	0.865274i	−1.00000		0.000500852i	$-0.999841\pi$
$313$	−1.50077e12	+	2.59941e12i	−0.499566	+	0.865274i	0.500434	+	0.865775i	$0.333174\pi$
$314$			2.51093e12i			0.822595i
$315$	−3.22510e11	+	1.90160e11i	−0.103990	+	0.0613148i
$316$	7.29261e11			0.231445
$317$	7.46926e11	+	4.31238e11i	0.233336	+	0.134716i	0.612110	−	0.790773i	$-0.290321\pi$
$317$	7.46926e11	+	4.31238e11i	0.233336	+	0.134716i	−0.378774	+	0.925489i	$0.623654\pi$
$318$	1.85934e12	+	3.18668e12i	0.571771	+	0.979948i
$319$	−2.01617e12	−	3.49210e12i	−0.610342	−	1.05714i
$320$	1.37290e11	−	7.92646e10i	0.0409157	−	0.0236227i
$321$	−2.21367e11	−	1.26459e11i	−0.0649513	−	0.0371042i
$322$	1.10607e11	−	1.91577e11i	0.0319523	−	0.0553431i
$323$		−	1.67204e12i		−	0.475591i
$324$	−1.78493e12	+	3.26905e10i	−0.499916	+	0.00915579i
$325$	6.83127e11			0.188402
$326$	1.37542e11	+	7.94098e10i	0.0373548	+	0.0215668i
$327$	−1.69685e12	+	2.97036e12i	−0.453843	+	0.794457i
$328$	−7.03331e11	−	1.21821e12i	−0.185264	−	0.320886i
$329$	2.01879e12	−	1.16555e12i	0.523735	−	0.302379i
$330$	−9.59911e11	+	5.60080e11i	−0.245280	+	0.143113i
$331$	3.35624e12	−	5.81318e12i	0.844720	−	1.46310i	−0.0411433	−	0.999153i	$-0.513100\pi$
$331$	3.35624e12	−	5.81318e12i	0.844720	−	1.46310i	0.885864	−	0.463945i	$-0.153567\pi$
$332$			2.21400e12i			0.548894i
$333$	−2.44703e12	−	4.15015e12i	−0.597610	−	1.01355i
$334$	−8.99952e11			−0.216514
$335$	−1.43590e12	−	8.29020e11i	−0.340331	−	0.196490i
$336$	3.41950e11	−	1.56551e9i	0.0798484	−	0.000365561i
$337$	−1.70216e12	−	2.94822e12i	−0.391606	−	0.678282i	0.601055	−	0.799208i	$-0.294747\pi$
$337$	−1.70216e12	−	2.94822e12i	−0.391606	−	0.678282i	−0.992662	+	0.120925i	$0.961414\pi$
$338$	2.57095e12	−	1.48434e12i	0.582787	−	0.336472i
$339$	2.80435e10	+	6.12547e12i	0.00626375	+	1.36817i
$340$	1.78165e11	−	3.08590e11i	0.0392127	−	0.0679185i
$341$		−	6.10270e12i		−	1.32358i
$342$	3.47157e10	+	3.79135e12i	0.00741985	+	0.810332i
$343$	−2.87802e12			−0.606211
$344$	−1.96594e12	−	1.13503e12i	−0.408110	−	0.235623i
$345$	2.63425e11	+	4.51480e11i	0.0538966	+	0.0923725i
$346$	1.15491e12	+	2.00037e12i	0.232899	+	0.403394i
$347$	−5.67434e12	+	3.27608e12i	−1.12789	+	0.651189i	−0.943404	−	0.331646i	$-0.892396\pi$
$347$	−5.67434e12	+	3.27608e12i	−1.12789	+	0.651189i	−0.184488	+	0.982835i	$0.559063\pi$
$348$	−2.54561e12	−	1.45421e12i	−0.498764	−	0.284925i
$349$	4.66578e11	−	8.08137e11i	0.0901151	−	0.156084i	−0.817444	−	0.576008i	$-0.804610\pi$
$349$	4.66578e11	−	8.08137e11i	0.0901151	−	0.156084i	0.907559	+	0.419924i	$0.137943\pi$
$350$		−	1.01674e12i		−	0.193584i
$351$	−5.99386e11	−	1.00600e12i	−0.112505	−	0.188827i
$352$	1.01505e12			0.187835
$353$	9.15046e12	+	5.28302e12i	1.66944	+	0.963849i	0.967942	+	0.251173i	$0.0808162\pi$
$353$	9.15046e12	+	5.28302e12i	1.66944	+	0.963849i	0.701493	+	0.712676i	$0.252517\pi$
$354$	1.44758e12	−	2.53400e12i	0.260391	−	0.455817i
$355$	4.21568e11	+	7.30177e11i	0.0747698	+	0.129505i
$356$	2.57728e12	−	1.48800e12i	0.450726	−	0.260227i
$357$	6.63875e11	−	3.87352e11i	0.114484	−	0.0667982i
$358$	−1.16723e12	+	2.02170e12i	−0.198492	+	0.343797i
$359$			7.18715e12i			1.20527i	0.798017	+	0.602635i	$0.205883\pi$
$359$			7.18715e12i			1.20527i	−0.798017	+	0.602635i	$0.794117\pi$
$360$	−3.97581e11	+	7.03427e11i	−0.0657526	+	0.116334i
$361$	1.92138e12			0.313385
$362$	−3.22474e12	−	1.86180e12i	−0.518743	−	0.299496i
$363$	−8.13172e11	+	3.72285e9i	−0.129018	+	0.000590667i
$364$	1.12152e11	+	1.94254e11i	0.0175510	+	0.0303992i
$365$	1.15918e12	−	6.69255e11i	0.178932	−	0.103306i
$366$	−1.11402e10	−	2.43332e12i	−0.00169624	−	0.370504i
$367$	−2.35997e12	+	4.08759e12i	−0.354467	+	0.613956i	−0.987027	−	0.160556i	$-0.948671\pi$
$367$	−2.35997e12	+	4.08759e12i	−0.354467	+	0.613956i	0.632559	+	0.774512i	$0.282004\pi$
$368$		−	4.77415e11i		−	0.0707387i
$369$	6.24166e12	+	3.52782e12i	0.912364	+	0.515673i
$370$	−2.18060e12			−0.314461
$371$	3.11941e12	+	1.80099e12i	0.443816	+	0.256237i
$372$	−2.23604e12	−	3.83231e12i	−0.313881	−	0.537955i
$373$	4.33287e12	+	7.50475e12i	0.600111	+	1.03942i	0.992804	+	0.119753i	$0.0382103\pi$
$373$	4.33287e12	+	7.50475e12i	0.600111	+	1.03942i	−0.392693	+	0.919670i	$0.628456\pi$
$374$	1.97589e12	−	1.14078e12i	0.270025	−	0.155899i
$375$	4.51985e12	+	2.58202e12i	0.609491	+	0.348179i
$376$	2.51544e12	−	4.35688e12i	0.334715	−	0.579744i
$377$		−	1.92305e12i		−	0.252513i
$378$	−1.49729e12	+	8.92103e11i	−0.194021	+	0.115599i
$379$	1.87910e12			0.240300			0.120150	−	0.992756i	$-0.461662\pi$
$379$	1.87910e12			0.240300			0.120150	+	0.992756i	$0.461662\pi$
$380$	1.48615e12	+	8.58032e11i	0.187562	+	0.108289i
$381$	7.64205e12	−	1.33775e13i	0.951886	−	1.66629i
$382$	3.09768e12	+	5.36533e12i	0.380820	+	0.659599i
$383$	−1.22961e13	+	7.09917e12i	−1.49202	+	0.861418i	−0.999958	−	0.00914306i	$-0.997090\pi$
$383$	−1.22961e13	+	7.09917e12i	−1.49202	+	0.861418i	−0.492061	+	0.870561i	$0.663756\pi$
$384$	6.37423e11	−	3.71918e11i	0.0763434	−	0.0445442i
$385$	−5.42506e11	+	9.39647e11i	−0.0641358	+	0.111087i
$386$		−	7.78556e12i		−	0.908559i
$387$	1.15699e13	−	1.05940e11i	1.33283	−	0.0122041i
$388$	4.29073e12			0.487947
$389$	1.01221e11	+	5.84402e10i	0.0113638	+	0.00656090i	0.505671	−	0.862726i	$-0.331245\pi$
$389$	1.01221e11	+	5.84402e10i	0.0113638	+	0.00656090i	−0.494307	+	0.869287i	$0.664578\pi$
$390$	−5.30010e11	+	2.42648e9i	−0.0587436	+	0.000268939i
$391$	−5.36548e11	−	9.29329e11i	−0.0587117	−	0.101692i
$392$	−2.54499e12	+	1.46935e12i	−0.274951	+	0.158743i
$393$	−4.06638e10	−	8.88208e12i	−0.00433756	−	0.947441i
$394$	−2.37352e12	+	4.11107e12i	−0.249984	+	0.432985i
$395$			1.68233e12i			0.174955i
$396$	−4.45663e12	+	2.62774e12i	−0.457647	+	0.269840i
$397$	−1.84896e13			−1.87489			−0.937443	−	0.348139i	$-0.886814\pi$
$397$	−1.84896e13			−1.87489			−0.937443	+	0.348139i	$0.886814\pi$
$398$	−5.64715e12	−	3.26038e12i	−0.565475	−	0.326477i
$399$	1.86546e12	+	3.19719e12i	0.184469	+	0.316157i
$400$	−1.09714e12	−	1.90031e12i	−0.107143	−	0.185577i
$401$	2.20354e12	−	1.27221e12i	0.212520	−	0.122698i	−0.389962	−	0.920831i	$-0.627512\pi$
$401$	2.20354e12	−	1.27221e12i	0.212520	−	0.122698i	0.602482	+	0.798133i	$0.294179\pi$
$402$	−6.70208e12	−	3.82864e12i	−0.638380	−	0.364682i
$403$	1.45521e12	−	2.52050e12i	0.136899	−	0.237116i
$404$			4.06920e12i			0.378096i
$405$	−7.54137e10	−	4.11767e12i	−0.00692110	−	0.377900i
$406$	−2.86219e12			−0.259459
$407$	−1.20917e13	−	6.98112e12i	−1.08271	−	0.625105i
$408$	8.22814e11	−	1.44034e12i	0.0727781	−	0.127399i
$409$	4.84912e12	+	8.39892e12i	0.423688	+	0.733849i	0.996297	−	0.0859795i	$-0.0274020\pi$
$409$	4.84912e12	+	8.39892e12i	0.423688	+	0.733849i	−0.572609	+	0.819829i	$0.694069\pi$
$410$	2.81028e12	−	1.62252e12i	0.242566	−	0.140046i
$411$	1.51210e13	−	8.82264e12i	1.28935	−	0.752297i
$412$	−3.90908e12	+	6.77072e12i	−0.329297	+	0.570359i
$413$		−	2.84914e12i		−	0.237118i
$414$	1.23592e12	+	2.09611e12i	0.101622	+	0.172350i
$415$	−5.10749e12			−0.414923
$416$	4.19231e11	+	2.42043e11i	0.0336501	+	0.0194279i
$417$	−2.45079e13	+	1.12202e11i	−1.94369	+	0.00889855i
$418$	5.49393e12	+	9.51576e12i	0.430528	+	0.745697i
$419$	−1.50940e13	+	8.71450e12i	−1.16878	+	0.674796i	−0.953393	−	0.301732i	$-0.902435\pi$
$419$	−1.50940e13	+	8.71450e12i	−1.16878	+	0.674796i	−0.215389	+	0.976528i	$0.569102\pi$
$420$	3.61148e9	+	7.88845e11i	0.000276337	+	0.0603595i
$421$	3.04495e12	−	5.27400e12i	0.230234	−	0.398777i	−0.727643	−	0.685956i	$-0.759384\pi$
$421$	3.04495e12	−	5.27400e12i	0.230234	−	0.398777i	0.957877	+	0.287179i	$0.0927175\pi$
$422$		−	1.07924e13i		−	0.806412i
$423$	2.34783e11	+	2.56410e13i	0.0173366	+	1.89336i
$424$	7.77366e12			0.567279
$425$	−4.27137e12	−	2.46608e12i	−0.308051	−	0.177853i
$426$	1.97804e12	+	3.39013e12i	0.140990	+	0.241640i
$427$	−1.18783e12	−	2.05738e12i	−0.0836784	−	0.144935i
$428$	−4.65195e11	+	2.68580e11i	−0.0323904	+	0.0187006i
$429$	−2.94673e12	−	1.68336e12i	−0.202794	−	0.115848i
$430$	2.61841e12	−	4.53523e12i	0.178113	−	0.308501i
$431$		−	8.56445e12i		−	0.575855i	−0.957652	−	0.287927i	$-0.907034\pi$
$431$		−	8.56445e12i		−	0.575855i	0.957652	−	0.287927i	$-0.0929662\pi$
$432$	−1.83582e12	+	3.28306e12i	−0.122015	+	0.218203i
$433$	−8.73831e12			−0.574101			−0.287050	−	0.957916i	$-0.592675\pi$
$433$	−8.73831e12			−0.574101			−0.287050	+	0.957916i	$0.592675\pi$
$434$	−3.75141e12	−	2.16588e12i	−0.243638	−	0.140665i
$435$	3.35472e12	−	5.87247e12i	0.215382	−	0.377029i
$436$	3.60388e12	+	6.24211e12i	0.228738	+	0.396186i
$437$	4.47559e12	−	2.58399e12i	0.280830	−	0.162137i
$438$	5.38196e12	−	3.14022e12i	0.333864	−	0.194800i
$439$	1.06088e13	−	1.83750e13i	0.650646	−	1.12695i	−0.332321	−	0.943166i	$-0.607832\pi$
$439$	1.06088e13	−	1.83750e13i	0.650646	−	1.12695i	0.982967	−	0.183785i	$-0.0588350\pi$
$440$			2.34163e12i			0.141989i
$441$	7.37006e12	−	1.30396e13i	0.441853	−	0.781757i
$442$	1.08809e12			0.0644992
$443$	7.51818e11	+	4.34062e11i	0.0440650	+	0.0254410i	0.521871	−	0.853025i	$-0.325234\pi$
$443$	7.51818e11	+	4.34062e11i	0.0440650	+	0.0254410i	−0.477806	+	0.878466i	$0.658568\pi$
$444$	−1.01511e13	+	4.64736e10i	−0.588299	+	0.00269334i
$445$	3.43266e12	+	5.94554e12i	0.196712	+	0.340715i
$446$	1.17982e13	−	6.81172e12i	0.668564	−	0.385996i
$447$	1.95935e10	+	4.27976e12i	0.00109793	+	0.239818i
$448$	3.60247e11	−	6.23967e11i	0.0199623	−	0.0345757i
$449$			6.58929e11i			0.0361083i	0.999837	+	0.0180541i	$0.00574712\pi$
$449$			6.58929e11i			0.0361083i	−0.999837	+	0.0180541i	$0.994253\pi$
$450$	9.73652e12	+	5.50314e12i	0.527644	+	0.298227i
$451$	2.07778e13			1.11357
$452$	1.11773e13	+	6.45324e12i	0.592442	+	0.342047i
$453$	2.51818e12	+	4.31586e12i	0.132006	+	0.226243i
$454$	7.19853e11	+	1.24682e12i	0.0373220	+	0.0646436i
$455$	−4.48125e11	+	2.58725e11i	−0.0229796	+	0.0132673i
$456$	6.93662e12	+	3.96263e12i	0.351822	+	0.200983i
$457$	−3.30422e12	+	5.72308e12i	−0.165763	+	0.287110i	−0.936926	−	0.349528i	$-0.886342\pi$
$457$	−3.30422e12	+	5.72308e12i	−0.165763	+	0.287110i	0.771163	+	0.636638i	$0.219675\pi$
$458$			1.35280e13i			0.671283i
$459$	1.16118e11	+	8.45397e12i	0.00569949	+	0.414951i
$460$	1.10135e12			0.0534732
$461$	2.31784e13	+	1.33821e13i	1.11322	+	0.642715i	0.939660	−	0.342109i	$-0.111141\pi$
$461$	2.31784e13	+	1.33821e13i	1.11322	+	0.642715i	0.173555	+	0.984824i	$0.444474\pi$
$462$	−2.50544e12	+	4.38580e12i	−0.119035	+	0.208372i
$463$	−2.51797e12	−	4.36126e12i	−0.118344	−	0.204978i	0.800768	−	0.598975i	$-0.204425\pi$
$463$	−2.51797e12	−	4.36126e12i	−0.118344	−	0.204978i	−0.919112	+	0.393997i	$0.871092\pi$
$464$	−5.34950e12	+	3.08853e12i	−0.248727	+	0.143603i
$465$	8.84076e12	−	5.15833e12i	0.406654	−	0.237271i
$466$	8.43995e12	−	1.46184e13i	0.384070	−	0.665228i
$467$			1.88333e13i			0.847893i	0.905687	+	0.423947i	$0.139356\pi$
$467$			1.88333e13i			0.847893i	−0.905687	+	0.423947i	$0.860644\pi$
$468$	−2.46724e12	+	2.25915e10i	−0.109896	+	0.00100627i
$469$	−7.53558e12			−0.332088
$470$	1.00509e13	+	5.80289e12i	0.438243	+	0.253020i
$471$	−2.69650e13	+	1.23451e11i	−1.16331	+	0.00532586i
$472$	−3.07445e12	−	5.32511e12i	−0.131237	−	0.227310i
$473$	2.90388e13	−	1.67656e13i	1.22652	−	0.708129i
$474$	3.58545e10	+	7.83159e12i	0.00149848	+	0.327309i
$475$	1.18765e13	−	2.05707e13i	0.491156	−	0.850708i
$476$		−	1.61947e12i		−	0.0662733i
$477$	−3.41306e13	+	2.01242e13i	−1.38214	+	0.814943i
$478$	−2.91614e13			−1.16861
$479$	−1.05466e13	−	6.08908e12i	−0.418249	−	0.241476i	0.276079	−	0.961135i	$-0.410965\pi$
$479$	−1.05466e13	−	6.08908e12i	−0.418249	−	0.241476i	−0.694328	+	0.719659i	$0.744298\pi$
$480$	8.57978e11	+	1.47047e12i	0.0336721	+	0.0577100i
$481$	−3.32935e12	−	5.76660e12i	−0.129310	−	0.223972i
$482$	−2.15551e13	+	1.24449e13i	−0.828544	+	0.478360i
$483$	2.06279e12	+	1.17840e12i	0.0784730	+	0.0448286i
$484$	−8.56684e11	+	1.48382e12i	−0.0322547	+	0.0558669i
$485$			9.89830e12i			0.368852i
$486$	−4.38822e11	−	1.91669e13i	−0.0161848	−	0.706922i
$487$	−3.13909e13			−1.14593			−0.572966	−	0.819579i	$-0.694207\pi$
$487$	−3.13909e13			−1.14593			−0.572966	+	0.819579i	$0.694207\pi$
$488$	−4.44015e12	−	2.56352e12i	−0.160435	−	0.0926270i
$489$	−8.46025e11	+	1.48098e12i	−0.0302579	+	0.0529668i
$490$	−3.38964e12	−	5.87103e12i	−0.119998	−	0.207842i
$491$	3.56743e13	−	2.05966e13i	1.25011	−	0.721751i	0.278979	−	0.960297i	$-0.410004\pi$
$491$	3.56743e13	−	2.05966e13i	1.25011	−	0.721751i	0.971131	+	0.238546i	$0.0766708\pi$
$492$	1.30478e13	−	7.61302e12i	0.452598	−	0.264077i
$493$	−6.94217e12	+	1.20242e13i	−0.238375	+	0.412877i
$494$			5.24019e12i			0.178120i
$495$	−6.06194e12	−	1.02810e13i	−0.203979	−	0.345948i
$496$	−9.34862e12			−0.311415
$497$	3.31856e12	+	1.91597e12i	0.109438	+	0.0631841i
$498$	−2.37764e13	+	1.08853e11i	−0.776245	+	0.00355379i
$499$	−1.21459e13	−	2.10374e13i	−0.392580	−	0.679969i	0.600209	−	0.799843i	$-0.295084\pi$
$499$	−1.21459e13	−	2.10374e13i	−0.392580	−	0.679969i	−0.992789	+	0.119875i	$0.961751\pi$
$500$	9.49829e12	−	5.48384e12i	0.303945	−	0.175483i
$501$	−4.42465e10	−	9.66465e12i	−0.00140181	−	0.306194i
$502$	1.15359e13	−	1.99808e13i	0.361854	−	0.626749i
$503$			1.14246e13i			0.354815i	0.984138	+	0.177407i	$0.0567710\pi$
$503$			1.14246e13i			0.354815i	−0.984138	+	0.177407i	$0.943229\pi$
$504$	3.36243e10	+	3.67215e12i	0.00103395	+	0.112919i
$505$	−9.38724e12			−0.285813
$506$	6.10711e12	+	3.52594e12i	0.184112	+	0.106297i
$507$	1.60668e13	+	2.75366e13i	0.479612	+	0.821998i
$508$	−1.62306e13	−	2.81123e13i	−0.479752	−	0.830956i
$509$	1.42664e13	−	8.23669e12i	0.417565	−	0.241081i	−0.276470	−	0.961023i	$-0.589165\pi$
$509$	1.42664e13	−	8.23669e12i	0.417565	−	0.241081i	0.694035	+	0.719941i	$0.255831\pi$
$510$	3.32273e12	+	1.89815e12i	0.0963041	+	0.0550149i
$511$	3.04168e12	−	5.26834e12i	0.0872989	−	0.151206i
$512$		−	1.55494e12i		−	0.0441942i
$513$	−4.07138e13	+	5.59217e11i	−1.14592	+	0.0157396i
$514$	−1.41926e13			−0.395591
$515$	−1.56194e13	−	9.01786e12i	−0.431149	−	0.248924i
$516$	1.20926e13	−	2.11682e13i	0.330575	−	0.578675i
$517$	3.71556e13	+	6.43553e13i	1.00594	+	1.74234i
$518$	−8.58278e12	+	4.95527e12i	−0.230133	+	0.132867i
$519$	−2.14253e13	+	1.25010e13i	−0.568971	+	0.331978i
$520$	−5.58370e11	+	9.67125e11i	−0.0146861	+	0.0254370i
$521$			8.79696e12i			0.229163i	0.993414	+	0.114581i	$0.0365527\pi$
$521$			8.79696e12i			0.229163i	−0.993414	+	0.114581i	$0.963447\pi$
$522$	1.54917e13	−	2.74089e13i	0.399711	−	0.707196i
$523$	4.69099e13			1.19882			0.599412	−	0.800440i	$-0.295401\pi$
$523$	4.69099e13			1.19882			0.599412	+	0.800440i	$0.295401\pi$
$524$	−1.62074e13	−	9.35736e12i	−0.410258	−	0.236863i
$525$	1.09188e13	−	4.99885e10i	0.273766	−	0.00125335i
$526$	−1.21270e13	−	2.10046e13i	−0.301180	−	0.521658i
$527$	−1.81979e13	+	1.05066e13i	−0.447680	+	0.258468i
$528$	4.99056e10	+	1.09007e13i	0.00121613	+	0.265635i
$529$	−1.90549e13	+	3.30040e13i	−0.459968	+	0.796689i
$530$			1.79331e13i			0.428821i
$531$	2.72840e13	+	1.54211e13i	0.646302	+	0.365293i
$532$	7.79929e12			0.183019
$533$	8.58150e12	+	4.95453e12i	0.199493	+	0.115177i
$534$	1.61064e13	+	2.76045e13i	0.370930	+	0.635731i
$535$	−6.19588e11	−	1.07316e12i	−0.0141363	−	0.0244847i
$536$	−1.40842e13	+	8.13150e12i	−0.318352	+	0.183801i
$537$	−2.17686e13	−	1.24356e13i	−0.487483	−	0.278481i
$538$	−5.67663e12	+	9.83222e12i	−0.125945	+	0.218142i
$539$		−	4.34074e13i		−	0.954157i
$540$	−7.57370e12	−	4.23507e12i	−0.164945	−	0.0922341i
$541$	4.49922e13			0.970846			0.485423	−	0.874279i	$-0.338666\pi$
$541$	4.49922e13			0.970846			0.485423	+	0.874279i	$0.338666\pi$
$542$	2.99937e13	+	1.73169e13i	0.641260	+	0.370231i
$543$	1.98355e13	−	3.47223e13i	0.420189	−	0.735544i
$544$	−1.74754e12	−	3.02683e12i	−0.0366803	−	0.0635322i
$545$	−1.43999e13	+	8.31380e12i	−0.299487	+	0.172909i
$546$	−2.08059e12	+	1.21396e12i	−0.0428769	+	0.0250174i
$547$	1.00724e13	−	1.74459e13i	0.205681	−	0.356251i	−0.744668	−	0.667435i	$-0.767392\pi$
$547$	1.00724e13	−	1.74459e13i	0.205681	−	0.356251i	0.950350	+	0.311184i	$0.100726\pi$
$548$		−	3.68864e13i		−	0.746387i
$549$	2.61310e13	−	2.39270e11i	0.523956	−	0.00479763i
$550$	3.24118e13			0.644005
$551$	−5.79078e13	−	3.34331e13i	−1.14020	−	0.658292i
$552$	5.12699e12	−	2.34723e10i	0.100039	−	0.000457995i
$553$	3.82300e12	+	6.62163e12i	0.0739228	+	0.128038i
$554$	−6.18004e13	+	3.56805e13i	−1.18425	+	0.683725i
$555$	−1.07210e11	−	2.34176e13i	−0.00203597	−	0.444710i
$556$	−2.58193e13	+	4.47203e13i	−0.485926	+	0.841649i
$557$			1.57733e13i			0.294202i	0.989121	+	0.147101i	$0.0469942\pi$
$557$			1.57733e13i			0.294202i	−0.989121	+	0.147101i	$0.953006\pi$
$558$	4.10455e13	−	2.42014e13i	0.758743	−	0.447373i
$559$	1.59912e13			0.292970
$560$	1.43943e12	+	8.31056e11i	0.0261367	+	0.0150900i
$561$	1.23481e13	+	2.11631e13i	0.222221	+	0.380860i
$562$	2.04612e13	+	3.54399e13i	0.364964	+	0.632137i
$563$	7.29187e13	−	4.20996e13i	1.28913	−	0.744280i	0.310631	−	0.950531i	$-0.399460\pi$
$563$	7.29187e13	−	4.20996e13i	1.28913	−	0.744280i	0.978499	+	0.206251i	$0.0661263\pi$
$564$	4.69125e13	+	2.67993e13i	0.822040	+	0.469600i
$565$	−1.48870e13	+	2.57850e13i	−0.258562	+	0.447843i
$566$		−	9.78790e12i		−	0.168503i
$567$	−9.65397e12	−	1.60357e13i	−0.164737	−	0.273635i
$568$	8.26996e12			0.139882
$569$	−7.56136e13	−	4.36555e13i	−1.26776	−	0.731944i	−0.293199	−	0.956051i	$-0.594720\pi$
$569$	−7.56136e13	−	4.36555e13i	−1.26776	−	0.731944i	−0.974564	+	0.224108i	$0.928053\pi$
$570$	−9.14139e12	+	1.60021e13i	−0.151928	+	0.265952i
$571$	1.73923e13	+	3.01243e13i	0.286534	+	0.496291i	0.972980	−	0.230890i	$-0.0741636\pi$
$571$	1.73923e13	+	3.01243e13i	0.286534	+	0.496291i	−0.686446	+	0.727181i	$0.740830\pi$
$572$	−6.19245e12	+	3.57521e12i	−0.101131	+	0.0583877i
$573$	−5.74664e13	+	3.35300e13i	−0.930338	+	0.542825i
$574$	7.37413e12	−	1.27724e13i	0.118345	−	0.204980i
$575$		−	1.52444e13i		−	0.242533i
$576$	4.02539e12	+	6.82705e12i	0.0634886	+	0.107676i
$577$	5.40383e13			0.844934			0.422467	−	0.906378i	$-0.361164\pi$
$577$	5.40383e13			0.844934			0.422467	+	0.906378i	$0.361164\pi$
$578$	3.27018e13	+	1.88804e13i	0.506911	+	0.292665i
$579$	8.36097e13	−	3.82780e11i	1.28488	−	0.00588243i
$580$	−7.12495e12	−	1.23408e13i	−0.108553	−	0.188019i
$581$	−2.01030e13	+	1.16065e13i	−0.303654	+	0.175315i
$582$	2.10956e11	+	4.60785e13i	0.00315920	+	0.690054i
$583$	−5.74123e13	+	9.94410e13i	−0.852437	+	1.47646i
$584$		−	1.31289e13i		−	0.193269i
$585$	−5.21163e10	−	5.69169e12i	−0.000760667	−	0.0830734i
$586$	2.04553e13			0.296017
$587$	1.21965e13	+	7.04166e12i	0.175003	+	0.101038i	0.584943	−	0.811075i	$-0.301117\pi$
$587$	1.21965e13	+	7.04166e12i	0.175003	+	0.101038i	−0.409940	+	0.912113i	$0.634450\pi$
$588$	−1.59046e13	−	2.72585e13i	−0.226274	−	0.387807i
$589$	−5.05990e13	−	8.76400e13i	−0.713781	−	1.23631i
$590$	1.22845e13	−	7.09247e12i	0.171830	−	0.0992058i
$591$	−4.42657e13	−	2.52873e13i	−0.613946	−	0.350724i
$592$	−1.06943e13	+	1.85230e13i	−0.147076	+	0.254744i
$593$		−	3.34770e13i		−	0.456534i	−0.973599	−	0.228267i	$-0.926694\pi$
$593$		−	3.34770e13i		−	0.456534i	0.973599	−	0.228267i	$-0.0733060\pi$
$594$	−2.84386e13	−	4.77309e13i	−0.384570	−	0.645457i
$595$	3.73597e12			0.0500977
$596$	7.80941e12	+	4.50877e12i	0.103845	+	0.0599551i
$597$	3.47358e13	−	6.08054e13i	0.458043	−	0.801808i
$598$	1.68155e12	+	2.91252e12i	0.0219889	+	0.0380858i
$599$	−9.55433e13	+	5.51620e13i	−1.23899	+	0.715329i	−0.968887	−	0.247504i	$-0.920390\pi$
$599$	−9.55433e13	+	5.51620e13i	−1.23899	+	0.715329i	−0.270099	+	0.962833i	$0.587056\pi$
$600$	2.03536e13	−	1.18757e13i	0.261749	−	0.152723i
$601$	−3.51384e13	+	6.08615e13i	−0.448136	+	0.776195i	−0.998265	−	0.0588854i	$-0.981245\pi$
$601$	−3.51384e13	+	6.08615e13i	−0.448136	+	0.776195i	0.550129	+	0.835080i	$0.314579\pi$
$602$		−	2.38007e13i		−	0.301029i
$603$	4.07866e13	−	7.21623e13i	0.511600	−	0.905157i
$604$	1.05282e13			0.130969
$605$	−3.42303e12	−	1.97629e12i	−0.0422312	−	0.0243822i
$606$	−4.36994e13	+	2.00064e11i	−0.534703	+	0.00244797i
$607$	−4.93476e13	−	8.54725e13i	−0.598856	−	1.03725i	−0.992990	−	0.118196i	$-0.962289\pi$
$607$	−4.93476e13	−	8.54725e13i	−0.598856	−	1.03725i	0.394135	−	0.919053i	$-0.371044\pi$
$608$	1.45770e13	−	8.41606e12i	0.175449	−	0.101296i
$609$	−1.40721e11	−	3.07373e13i	−0.00167986	−	0.366926i
$610$	5.91379e12	−	1.02430e13i	0.0700192	−	0.121277i
$611$			3.54395e13i			0.416180i
$612$	1.55084e13	+	8.76545e12i	0.180639	+	0.102098i
$613$	−1.04411e14			−1.20627			−0.603133	−	0.797641i	$-0.706081\pi$
$613$	−1.04411e14			−1.20627			−0.603133	+	0.797641i	$0.706081\pi$
$614$	2.36957e13	+	1.36807e13i	0.271537	+	0.156772i
$615$	1.75625e13	+	3.01000e13i	0.199623	+	0.342130i
$616$	5.32121e12	+	9.21660e12i	0.0599938	+	0.103912i
$617$	−5.15021e13	+	2.97347e13i	−0.575969	+	0.332536i	−0.759530	−	0.650473i	$-0.774571\pi$
$617$	−5.15021e13	+	2.97347e13i	−0.575969	+	0.332536i	0.183561	+	0.983008i	$0.441238\pi$
$618$	−7.29034e13	−	4.16470e13i	−0.808734	−	0.461999i
$619$	3.43722e13	−	5.95344e13i	0.378229	−	0.655111i	−0.612576	−	0.790412i	$-0.709867\pi$
$619$	3.43722e13	−	5.95344e13i	0.378229	−	0.655111i	0.990805	+	0.135301i	$0.0432000\pi$
$620$		−	2.15664e13i		−	0.235406i
$621$	−2.24495e13	+	1.33757e13i	−0.243080	+	0.144829i
$622$	−9.50488e12			−0.102093
$623$	2.70217e13	+	1.56010e13i	0.287921	+	0.166231i
$624$	−2.57871e12	+	4.51405e12i	−0.0272571	+	0.0477138i
$625$	−2.82211e13	−	4.88804e13i	−0.295920	−	0.512548i
$626$	−5.88180e13	+	3.39586e13i	−0.611841	+	0.353247i
$627$	−1.01920e14	+	5.94675e13i	−1.05178	+	0.613680i
$628$	−2.84079e13	+	4.92039e13i	−0.290831	+	0.503734i
$629$			4.80755e13i			0.488282i
$630$	−8.47129e12	+	7.75679e10i	−0.0853585	+	0.000781590i
$631$	1.67118e13			0.167061			0.0835305	−	0.996505i	$-0.473380\pi$
$631$	1.67118e13			0.167061			0.0835305	+	0.996505i	$0.473380\pi$
$632$	1.42905e13	+	8.25065e12i	0.141730	+	0.0818281i
$633$	1.15901e14	−	5.30615e11i	1.14043	−	0.00522108i
$634$	9.75780e12	+	1.69010e13i	0.0952589	+	0.164993i
$635$	6.48523e13	−	3.74425e13i	0.628141	−	0.362657i
$636$	3.82196e11	+	8.34819e13i	0.00367283	+	0.802245i
$637$	1.03506e13	−	1.79279e13i	0.0986894	−	0.170935i
$638$		−	9.12413e13i		−	0.863154i
$639$	−3.63096e13	+	2.14090e13i	−0.340814	+	0.200952i
$640$	3.58711e12			0.0334075
$641$	1.36160e14	+	7.86118e13i	1.25823	+	0.726437i	0.972729	−	0.231943i	$-0.0745084\pi$
$641$	1.36160e14	+	7.86118e13i	1.25823	+	0.726437i	0.285496	+	0.958380i	$0.407842\pi$
$642$	−2.90717e12	−	4.98255e12i	−0.0266561	−	0.0456853i
$643$	2.11630e13	+	3.66555e13i	0.192541	+	0.333491i	0.946092	−	0.323899i	$-0.104994\pi$
$643$	2.11630e13	+	3.66555e13i	0.192541	+	0.333491i	−0.753551	+	0.657390i	$0.771661\pi$
$644$	4.33489e12	−	2.50275e12i	0.0391335	−	0.0225937i
$645$	4.88329e13	+	2.78964e13i	0.437435	+	0.249890i
$646$	1.89170e13	−	3.27652e13i	0.168147	−	0.291239i
$647$			1.67068e14i			1.47357i	0.676126	+	0.736786i	$0.263658\pi$
$647$			1.67068e14i			1.47357i	−0.676126	+	0.736786i	$0.736342\pi$
$648$	−3.53473e13	−	1.95536e13i	−0.309372	−	0.171140i
$649$	9.08253e13			0.788830
$650$	1.33865e13	+	7.72870e12i	0.115372	+	0.0666101i
$651$	2.30751e13	−	4.03931e13i	0.197350	−	0.345464i
$652$	1.79684e12	+	3.11221e12i	0.0152500	+	0.0264138i
$653$	1.19596e14	−	6.90486e13i	1.00728	−	0.581552i	0.0968848	−	0.995296i	$-0.469112\pi$
$653$	1.19596e14	−	6.90486e13i	1.00728	−	0.581552i	0.910394	+	0.413743i	$0.135779\pi$
$654$	−6.68572e13	+	3.90092e13i	−0.558804	+	0.326046i
$655$	2.15865e13	−	3.73889e13i	0.179051	−	0.310125i
$656$		−	3.18291e13i		−	0.262003i
$657$	3.39876e13	+	5.76429e13i	0.277647	+	0.470889i
$658$	5.27468e13			0.427628
$659$	1.02444e14	+	5.91459e13i	0.824248	+	0.475880i	0.851879	−	0.523738i	$-0.175463\pi$
$659$	1.02444e14	+	5.91459e13i	0.824248	+	0.475880i	−0.0276309	+	0.999618i	$0.508796\pi$
$660$	−2.51469e13	+	1.15127e11i	−0.200801	+	0.000919303i
$661$	−6.62095e13	−	1.14678e14i	−0.524702	−	0.908811i	−0.999586	−	0.0287626i	$-0.990843\pi$
$661$	−6.62095e13	−	1.14678e14i	−0.524702	−	0.908811i	0.474884	−	0.880048i	$-0.342490\pi$
$662$	1.31537e14	−	7.59430e13i	1.03457	−	0.597308i
$663$	5.34965e10	+	1.16851e13i	0.000417597	+	0.0912146i
$664$	−2.50486e13	+	4.33855e13i	−0.194063	+	0.336127i
$665$			1.79922e13i			0.138349i
$666$	−9.98166e11	−	1.09011e14i	−0.00761784	−	0.831954i
$667$	−4.29140e13			−0.325064
$668$	−1.76354e13	−	1.01818e13i	−0.132587	−	0.0765494i
$669$	7.37316e13	+	1.26367e14i	0.550203	+	0.942983i
$670$	−1.87586e13	−	3.24908e13i	−0.138940	−	0.240650i
$671$	6.55853e13	−	3.78657e13i	0.482163	−	0.278377i
$672$	6.71854e12	+	3.83805e12i	0.0490262	+	0.0280068i
$673$	1.14830e14	−	1.98892e14i	0.831728	−	1.44060i	−0.0649388	−	0.997889i	$-0.520685\pi$
$673$	1.14830e14	−	1.98892e14i	0.831728	−	1.44060i	0.896667	−	0.442706i	$-0.145981\pi$
$674$		−	7.70308e13i		−	0.553815i
$675$	−5.86199e13	+	1.04832e14i	−0.418337	+	0.748124i
$676$	6.71735e13			0.475844
$677$	−1.05990e14	−	6.11935e13i	−0.745286	−	0.430291i	0.0787021	−	0.996898i	$-0.474922\pi$
$677$	−1.05990e14	−	6.11935e13i	−0.745286	−	0.430291i	−0.823988	+	0.566607i	$0.808256\pi$
$678$	−6.87522e13	+	1.20351e14i	−0.479886	+	0.840046i
$679$	2.24933e13	+	3.89595e13i	0.155849	+	0.269938i
$680$	6.98261e12	−	4.03141e12i	0.0480256	−	0.0277276i
$681$	−1.33543e13	+	7.79186e12i	−0.0911772	+	0.0531992i
$682$	6.90441e13	−	1.19588e14i	0.467956	−	0.810523i
$683$			1.16309e14i			0.782544i	0.920275	+	0.391272i	$0.127965\pi$
$683$			1.16309e14i			0.782544i	−0.920275	+	0.391272i	$0.872035\pi$
$684$	−4.22139e13	+	7.46877e13i	−0.281952	+	0.498848i
$685$	8.50934e13			0.564213
$686$	−5.63975e13	−	3.25611e13i	−0.371227	−	0.214328i
$687$	−1.45278e14	+	6.65110e11i	−0.949328	+	0.00434620i
$688$	−2.56829e13	−	4.44841e13i	−0.166610	−	0.288578i
$689$	−4.74241e13	+	2.73803e13i	−0.305424	+	0.176337i
$690$	5.41484e10	+	1.18275e13i	0.000346210	+	0.0756217i
$691$	−1.11875e14	+	1.93773e14i	−0.710136	+	1.22999i	0.254669	+	0.967028i	$0.418033\pi$
$691$	−1.11875e14	+	1.93773e14i	−0.710136	+	1.22999i	−0.964806	+	0.262964i	$0.915300\pi$
$692$			5.22654e13i			0.329370i
$693$	−4.72226e13	−	2.66905e13i	−0.295450	−	0.166990i
$694$	−1.48258e14			−0.920920
$695$	−1.03165e14	−	5.95626e13i	−0.636224	−	0.367324i
$696$	−3.34310e13	−	5.72968e13i	−0.204693	−	0.350820i
$697$	−3.57715e13	−	6.19581e13i	−0.217457	−	0.376647i
$698$	1.82861e13	−	1.05575e13i	0.110368	−	0.0637210i
$699$	1.57403e14	+	8.99185e13i	0.943252	+	0.538844i
$700$	1.15031e13	−	1.99240e13i	0.0684423	−	0.118546i
$701$		−	6.55418e12i		−	0.0387194i	−0.999813	−	0.0193597i	$-0.993837\pi$
$701$		−	6.55418e12i		−	0.0387194i	0.999813	−	0.0193597i	$-0.00616276\pi$
$702$	−3.63915e11	−	2.64948e13i	−0.00213459	−	0.155409i
$703$	−2.31529e14			−1.34843
$704$	1.98909e13	+	1.14840e13i	0.115025	+	0.0664096i
$705$	−6.18235e13	+	1.08223e14i	−0.354983	+	0.621401i
$706$	1.19541e14	+	2.07051e14i	0.681544	+	1.18047i
$707$	−3.69480e13	+	2.13319e13i	−0.209167	+	0.120763i
$708$	5.70356e13	−	3.32786e13i	0.320612	−	0.187068i
$709$	1.41468e14	−	2.45029e14i	0.789635	−	1.36769i	−0.136555	−	0.990632i	$-0.543603\pi$
$709$	1.41468e14	−	2.45029e14i	0.789635	−	1.36769i	0.926191	−	0.377056i	$-0.123063\pi$
$710$			1.90780e13i			0.105740i
$711$	−8.41022e13	+	7.70087e11i	−0.462870	+	0.00423830i
$712$	6.73390e13			0.368016
$713$	−5.62463e13	−	3.24738e13i	−0.305244	−	0.176233i
$714$	1.73916e13	−	7.96221e10i	0.0937237	−	0.000429084i
$715$	−8.24767e12	−	1.42854e13i	−0.0441368	−	0.0764472i
$716$	−4.57460e13	+	2.64114e13i	−0.243102	+	0.140355i
$717$	−1.43373e12	−	3.13166e14i	−0.00756610	−	1.65264i
$718$	−8.13133e13	+	1.40839e14i	−0.426127	+	0.738074i
$719$		−	5.36968e13i		−	0.279450i	−0.990190	−	0.139725i	$-0.955378\pi$
$719$		−	5.36968e13i		−	0.279450i	0.990190	−	0.139725i	$-0.0446218\pi$
$720$	−1.57493e13	+	9.28618e12i	−0.0813954	+	0.0479927i
$721$	−8.19700e13			−0.420706
$722$	3.76513e13	+	2.17380e13i	0.191908	+	0.110798i
$723$	−1.34706e14	−	2.30870e14i	−0.681861	−	1.16863i
$724$	−4.21278e13	−	7.29675e13i	−0.211776	−	0.366806i
$725$	−1.70815e14	+	9.86203e13i	−0.852780	+	0.492353i
$726$	−1.59770e13	−	9.12703e12i	−0.0792157	−	0.0452529i
$727$	−1.12488e14	+	1.94835e14i	−0.553903	+	0.959389i	0.444084	+	0.895985i	$0.353529\pi$
$727$	−1.12488e14	+	1.94835e14i	−0.553903	+	0.959389i	−0.997988	+	0.0634041i	$0.979804\pi$
$728$			5.07544e12i			0.0248209i
$729$	2.05813e14	−	5.65489e12i	0.999623	−	0.0274655i
$730$	3.02870e13			0.146097
$731$	−9.99879e13	−	5.77280e13i	−0.479028	−	0.276567i
$732$	2.73115e13	−	4.78091e13i	0.129954	−	0.227486i
$733$	−5.03574e12	−	8.72216e12i	−0.0237982	−	0.0412196i	0.853881	−	0.520468i	$-0.174243\pi$
$733$	−5.03574e12	−	8.72216e12i	−0.0237982	−	0.0412196i	−0.877679	+	0.479249i	$0.840909\pi$
$734$	−9.24916e13	+	5.34000e13i	−0.434132	+	0.250646i
$735$	6.28828e13	−	3.66903e13i	0.293154	−	0.171047i
$736$	5.40133e12	−	9.35538e12i	0.0250099	−	0.0433184i
$737$		−	2.40220e14i		−	1.10477i
$738$	8.23982e13	+	1.39747e14i	0.376388	+	0.638353i
$739$	1.59779e14			0.724935			0.362467	−	0.931996i	$-0.381934\pi$
$739$	1.59779e14			0.724935			0.362467	+	0.931996i	$0.381934\pi$
$740$	−4.27308e13	−	2.46706e13i	−0.192567	−	0.111179i
$741$	−5.62748e13	+	2.57636e11i	−0.251897	+	0.00115323i
$742$	4.07518e13	+	7.05842e13i	0.181187	+	0.313825i
$743$	2.90825e14	−	1.67908e14i	1.28436	−	0.741526i	0.306718	−	0.951800i	$-0.400769\pi$
$743$	2.90825e14	−	1.67908e14i	1.28436	−	0.741526i	0.977642	+	0.210275i	$0.0674358\pi$
$744$	−4.59629e11	−	1.00396e14i	−0.00201624	−	0.440402i
$745$	−1.04013e13	+	1.80156e13i	−0.0453216	+	0.0784994i
$746$			1.96083e14i			0.848685i
$747$	−2.33795e12	−	2.55331e14i	−0.0100515	−	1.09774i
$748$	5.16258e13			0.220475
$749$	−4.87737e12	−	2.81595e12i	−0.0206908	−	0.0119458i
$750$	5.93583e13	+	1.01733e14i	0.250136	+	0.428703i
$751$	1.37832e14	+	2.38731e14i	0.576964	+	0.999332i	0.995825	+	0.0912813i	$0.0290962\pi$
$751$	1.37832e14	+	2.38731e14i	0.576964	+	0.999332i	−0.418861	+	0.908051i	$0.637570\pi$
$752$	9.85849e13	−	5.69180e13i	0.409941	−	0.236679i
$753$	2.15142e14	+	1.22903e14i	0.888691	+	0.507675i
$754$	2.17568e13	−	3.76839e13i	0.0892768	−	0.154632i
$755$			2.42875e13i			0.0990030i
$756$	−3.94338e13	+	5.41636e11i	−0.159683	+	0.00219330i
$757$	−3.03919e13			−0.122258			−0.0611292	−	0.998130i	$-0.519470\pi$
$757$	−3.03919e13			−0.122258			−0.0611292	+	0.998130i	$0.519470\pi$
$758$	3.68227e13	+	2.12596e13i	0.147153	+	0.0849589i
$759$	−3.75651e13	+	6.57580e13i	−0.149134	+	0.261060i
$760$	1.94150e13	+	3.36278e13i	0.0765720	+	0.132627i
$761$	−3.28601e14	+	1.89718e14i	−1.28749	+	0.743335i	−0.978207	−	0.207634i	$-0.933424\pi$
$761$	−3.28601e14	+	1.89718e14i	−1.28749	+	0.743335i	−0.309287	+	0.950969i	$0.600090\pi$
$762$	3.01102e14	−	1.75684e14i	1.17203	−	0.683845i
$763$	−3.77852e13	+	6.54459e13i	−0.146116	+	0.253081i
$764$			1.40185e14i			0.538560i
$765$	−2.02210e13	+	3.57764e13i	−0.0771785	+	0.136549i
$766$	−3.21272e14			−1.21823
$767$	3.75121e13	+	2.16576e13i	0.141317	+	0.0815895i
$768$	1.66987e13	−	7.64495e10i	0.0624993	−	0.000286134i
$769$	2.02493e14	+	3.50729e14i	0.752972	+	1.30419i	0.946376	+	0.323067i	$0.104714\pi$
$769$	2.02493e14	+	3.50729e14i	0.752972	+	1.30419i	−0.193404	+	0.981119i	$0.561953\pi$
$770$	−2.12618e13	+	1.22755e13i	−0.0785500	+	0.0453509i
$771$	−6.97785e11	−	1.52415e14i	−0.00256124	−	0.559444i
$772$	8.80835e13	−	1.52565e14i	0.321224	−	0.556377i
$773$		−	8.97085e13i		−	0.325040i	−0.986705	−	0.162520i	$-0.948038\pi$
$773$		−	8.97085e13i		−	0.325040i	0.986705	−	0.162520i	$-0.0519621\pi$
$774$	2.27921e14	+	1.28822e14i	0.820501	+	0.463752i
$775$	−2.98512e14			−1.06771
$776$	8.40809e13	+	4.85441e13i	0.298805	+	0.172515i
$777$	−5.36370e13	−	9.19274e13i	−0.189391	−	0.324594i
$778$	1.32235e12	+	2.29038e12i	0.00463926	+	0.00803543i
$779$	2.98387e14	−	1.72274e14i	1.04014	−	0.600526i
$780$	−1.04135e13	−	5.94883e12i	−0.0360681	−	0.0206043i
$781$	−6.10777e13	+	1.05790e14i	−0.210197	+	0.364073i
$782$		−	2.42814e13i		−	0.0830309i
$783$	2.95108e14	+	1.65019e14i	1.00270	+	0.560692i
$784$	−6.64951e13			−0.224496
$785$	−1.13509e14	−	6.55343e13i	−0.380786	−	0.219847i
$786$	9.96925e13	−	1.74513e14i	0.332315	−	0.581720i
$787$	2.27598e14	+	3.94211e14i	0.753867	+	1.30574i	0.945936	+	0.324354i	$0.105147\pi$
$787$	2.27598e14	+	3.94211e14i	0.753867	+	1.30574i	−0.192069	+	0.981381i	$0.561520\pi$
$788$	−9.30228e13	+	5.37067e13i	−0.306167	+	0.176766i
$789$	2.24974e14	−	1.31266e14i	0.735779	−	0.429305i
$790$	−1.90334e13	+	3.29669e13i	−0.0618560	+	0.107138i
$791$			1.35319e14i			0.436995i
$792$	−1.17061e14	+	1.07188e12i	−0.375653	+	0.00343969i
$793$	3.61168e13			0.115171
$794$	−3.62320e14	−	2.09186e14i	−1.14813	−	0.662872i
$795$	−1.92585e14	+	8.81688e11i	−0.606438	+	0.00277638i
$796$	−7.37740e13	−	1.27780e14i	−0.230854	−	0.399852i
$797$	−1.43030e14	+	8.25783e13i	−0.444769	+	0.256788i	−0.705619	−	0.708592i	$-0.749331\pi$
$797$	−1.43030e14	+	8.25783e13i	−0.444769	+	0.256788i	0.260849	+	0.965380i	$0.415997\pi$
$798$	3.83456e11	+	8.37571e13i	0.00118495	+	0.258826i
$799$	1.27936e14	−	2.21592e14i	0.392879	−	0.680486i
$800$		−	4.96511e13i		−	0.151523i
$801$	−2.95655e14	+	1.74325e14i	−0.896648	+	0.528685i
$802$	5.75739e13			0.173522
$803$	1.67945e14	+	9.69631e13i	0.503025	+	0.290422i
$804$	−8.80172e13	−	1.50851e14i	−0.261992	−	0.449023i
$805$	5.77359e12	+	1.00002e13i	0.0170792	+	0.0295820i
$806$	5.70323e13	−	3.29276e13i	0.167666	−	0.0968022i
$807$	−1.05868e14	−	6.04784e13i	−0.309312	−	0.176698i
$808$	−4.60377e13	+	7.97397e13i	−0.133677	+	0.231536i
$809$		−	2.31662e14i		−	0.668517i	−0.942481	−	0.334259i	$-0.891514\pi$
$809$		−	2.31662e14i		−	0.668517i	0.942481	−	0.334259i	$-0.108486\pi$
$810$	4.51083e13	−	8.15427e13i	0.129369	−	0.233862i
$811$	1.29883e14			0.370210			0.185105	−	0.982719i	$-0.440737\pi$
$811$	1.29883e14			0.370210			0.185105	+	0.982719i	$0.440737\pi$
$812$	−5.60872e13	−	3.23820e13i	−0.158885	−	0.0917325i
$813$	−1.84493e14	+	3.22956e14i	−0.519429	+	0.909266i
$814$	−1.57965e14	−	2.73603e14i	−0.442016	−	0.765595i
$815$	−7.17958e12	+	4.14513e12i	−0.0199669	+	0.0115279i
$816$	3.24194e13	−	1.89158e13i	0.0896096	−	0.0522846i
$817$	2.78015e14	−	4.81536e14i	0.763762	−	1.32287i
$818$			2.19446e14i			0.599185i
$819$	−1.31391e13	−	2.22839e13i	−0.0356572	−	0.0604745i
$820$	7.34267e13			0.198055
$821$	−1.77525e14	−	1.02494e14i	−0.475931	−	0.274779i	0.242788	−	0.970079i	$-0.421938\pi$
$821$	−1.77525e14	−	1.02494e14i	−0.475931	−	0.274779i	−0.718719	+	0.695300i	$0.755271\pi$
$822$	3.96126e14	−	1.81354e12i	1.05554	−	0.00483245i
$823$	1.35137e14	+	2.34064e14i	0.357911	+	0.619920i	0.987612	−	0.156918i	$-0.0501558\pi$
$823$	1.35137e14	+	2.34064e14i	0.357911	+	0.619920i	−0.629701	+	0.776838i	$0.716822\pi$
$824$	−1.53204e14	+	8.84523e13i	−0.403305	+	0.232848i
$825$	1.59354e12	+	3.48072e14i	0.00416959	+	0.910751i
$826$	3.22344e13	−	5.58315e13i	0.0838337	−	0.145204i
$827$		−	6.14338e14i		−	1.58811i	−0.607848	−	0.794053i	$-0.707967\pi$
$827$		−	6.14338e14i		−	1.58811i	0.607848	−	0.794053i	$-0.292033\pi$
$828$	5.04142e11	+	5.50580e13i	0.00129539	+	0.141471i
$829$	2.03725e13			0.0520322			0.0260161	−	0.999662i	$-0.491718\pi$
$829$	2.03725e13			0.0520322			0.0260161	+	0.999662i	$0.491718\pi$
$830$	−1.00086e14	−	5.77847e13i	−0.254087	−	0.146697i
$831$	−3.86214e14	−	6.61925e14i	−0.974591	−	1.67033i
$832$	5.47681e12	+	9.48611e12i	0.0137376	+	0.0237942i
$833$	−1.29438e14	+	7.47313e13i	−0.322729	+	0.186328i
$834$	−4.81524e14	−	2.75077e14i	−1.19341	−	0.681747i
$835$	2.34884e13	−	4.06831e13i	0.0578657	−	0.100226i
$836$			2.48627e14i			0.608859i
$837$	2.61919e14	+	4.39601e14i	0.637587	+	1.07012i
$838$	−3.94373e14			−0.954306
$839$	4.22379e14	+	2.43861e14i	1.01600	+	0.586586i	0.912942	−	0.408089i	$-0.133805\pi$
$839$	4.22379e14	+	2.43861e14i	1.01600	+	0.586586i	0.103055	+	0.994676i	$0.467138\pi$
$840$	−8.85400e12	+	1.54990e13i	−0.0211711	+	0.0370602i
$841$	6.72691e13	+	1.16513e14i	0.159895	+	0.276947i
$842$	1.19337e14	−	6.88993e13i	0.281978	−	0.162800i
$843$	−3.79586e14	+	2.21477e14i	−0.891604	+	0.520225i
$844$	1.22102e14	−	2.11488e14i	0.285110	−	0.493825i
$845$			1.54963e14i			0.359703i
$846$	−2.85493e14	+	5.05114e14i	−0.658786	+	1.16557i
$847$	−1.79639e13			−0.0412083
$848$	1.52332e14	+	8.79490e13i	0.347386	+	0.200563i
$849$	1.05113e14	−	4.81227e11i	0.238297	−	0.00109097i
$850$	−5.58009e13	−	9.66501e13i	−0.125761	−	0.217825i
$851$	−1.28685e14	+	7.42963e13i	−0.288324	+	0.166464i
$852$	4.06596e11	+	8.88117e13i	0.000905661	+	0.197821i
$853$	−1.24459e14	+	2.15570e14i	−0.275602	+	0.477357i	−0.970287	−	0.241957i	$-0.922211\pi$
$853$	−1.24459e14	+	2.15570e14i	−0.275602	+	0.477357i	0.694685	+	0.719314i	$0.255544\pi$
$854$		−	5.37549e13i		−	0.118339i
$855$	−1.72297e14	−	9.73833e13i	−0.377092	−	0.213135i
$856$	−1.21546e13			−0.0264466
$857$	4.27952e14	+	2.47078e14i	0.925743	+	0.534478i	0.885463	−	0.464710i	$-0.153842\pi$
$857$	4.27952e14	+	2.47078e14i	0.925743	+	0.534478i	0.0402804	+	0.999188i	$0.487175\pi$
$858$	−3.86989e13	−	6.63254e13i	−0.0832266	−	0.142641i
$859$	−2.45370e14	−	4.24994e14i	−0.524633	−	0.908692i	−0.999589	−	0.0286818i	$-0.990869\pi$
$859$	−2.45370e14	−	4.24994e14i	−0.524633	−	0.908692i	0.474955	−	0.880010i	$-0.342464\pi$
$860$	1.02620e14	−	5.92480e13i	0.218143	−	0.125945i
$861$	1.37526e14	+	7.85634e13i	0.290649	+	0.166037i
$862$	9.68957e13	−	1.67828e14i	0.203595	−	0.352638i
$863$		−	7.48056e14i		−	1.56272i	−0.624083	−	0.781358i	$-0.714527\pi$
$863$		−	7.48056e14i		−	1.56272i	0.624083	−	0.781358i	$-0.285473\pi$
$864$	−7.31182e13	+	4.35646e13i	−0.151865	+	0.0904826i
$865$	−1.20571e14			−0.248979
$866$	−1.71235e14	−	9.88627e13i	−0.351563	−	0.202975i
$867$	−2.01150e14	+	3.52115e14i	−0.410605	+	0.718768i
$868$	−4.90082e13	−	8.48847e13i	−0.0994649	−	0.172278i
$869$	−2.11085e14	+	1.21870e14i	−0.425950	+	0.245922i
$870$	1.32178e14	−	7.71221e13i	0.265194	−	0.154733i
$871$	5.72814e13	−	9.92143e13i	0.114268	−	0.197917i
$872$			1.63093e14i			0.323484i
$873$	−4.94830e14	+	4.53094e12i	−0.975854	+	0.00893546i
$874$	1.16938e14			0.229297
$875$	9.95856e13	+	5.74958e13i	0.194158	+	0.112097i
$876$	1.40992e14	−	6.45487e11i	0.273321	−	0.00125132i
$877$	−2.50198e14	−	4.33356e14i	−0.482266	−	0.835309i	0.517527	−	0.855667i	$-0.326853\pi$
$877$	−2.50198e14	−	4.33356e14i	−0.482266	−	0.835309i	−0.999793	+	0.0203581i	$0.993519\pi$
$878$	4.15779e14	−	2.40050e14i	0.796875	−	0.460076i
$879$	1.00569e12	+	2.19670e14i	0.00191655	+	0.418627i
$880$	−2.64925e13	+	4.58864e13i	−0.0502007	+	0.0869502i
$881$			2.34523e14i			0.441882i	0.975287	+	0.220941i	$0.0709128\pi$
$881$			2.34523e14i			0.441882i	−0.975287	+	0.220941i	$0.929087\pi$
$882$	2.91949e14	−	1.72140e14i	0.546972	−	0.322508i
$883$	−4.70901e14			−0.877256			−0.438628	−	0.898669i	$-0.644535\pi$
$883$	−4.70901e14			−0.877256			−0.438628	+	0.898669i	$0.644535\pi$
$884$	2.13222e13	+	1.23104e13i	0.0394975	+	0.0228039i
$885$	7.67705e13	+	1.31576e14i	0.141409	+	0.242359i
$886$	9.82171e12	+	1.70117e13i	0.0179895	+	0.0311587i
$887$	2.89969e14	−	1.67414e14i	0.528121	−	0.304911i	−0.212130	−	0.977241i	$-0.568040\pi$
$887$	2.89969e14	−	1.67414e14i	0.528121	−	0.304911i	0.740251	+	0.672331i	$0.234707\pi$
$888$	−1.99446e14	−	1.13936e14i	−0.361210	−	0.206346i
$889$	1.70171e14	−	2.94746e14i	0.306463	−	0.530809i
$890$			1.55344e14i			0.278193i
$891$	5.11188e14	−	3.07751e14i	0.910315	−	0.548038i
$892$	3.08263e14			0.545880
$893$	1.06717e15	+	6.16132e14i	1.87922	+	1.08497i
$894$	−4.80360e13	+	8.40875e13i	−0.0841161	+	0.147246i
$895$	−6.09286e13	−	1.05531e14i	−0.106098	−	0.183767i
$896$	1.41188e13	−	8.15147e12i	0.0244487	−	0.0141155i
$897$	−3.11951e13	+	1.82014e13i	−0.0537186	+	0.0313432i
$898$	−7.45493e12	+	1.29123e13i	−0.0127662	+	0.0221117i
$899$			8.40331e14i			1.43104i
$900$	1.28535e14	+	2.17995e14i	0.217675	+	0.369177i
$901$	3.95370e14			0.665855
$902$	4.07160e14	+	2.35074e14i	0.681918	+	0.393705i
$903$	2.55598e14	−	1.17017e12i	0.425714	−	0.00194900i
$904$	1.46020e14	+	2.52914e14i	0.241864	+	0.418920i
$905$	1.68329e14	−	9.71848e13i	0.277278	−	0.160087i
$906$	5.17624e11	+	1.13063e14i	0.000847956	+	0.185217i
$907$	−1.51493e14	+	2.62394e14i	−0.246807	+	0.427482i	−0.962638	−	0.270791i	$-0.912715\pi$
$907$	−1.51493e14	+	2.62394e14i	−0.246807	+	0.427482i	0.715831	+	0.698273i	$0.246048\pi$
$908$			3.25768e13i			0.0527813i
$909$	−4.29700e12	−	4.69281e14i	−0.00692383	−	0.756160i
$910$	−1.17085e13			−0.0187627
$911$	1.12689e14	+	6.50609e13i	0.179593	+	0.103688i	0.587101	−	0.809513i	$-0.300269\pi$
$911$	1.12689e14	+	6.50609e13i	0.179593	+	0.103688i	−0.407509	+	0.913201i	$0.633602\pi$
$912$	9.10974e13	+	1.56130e14i	0.144388	+	0.247464i
$913$	−3.69992e14	−	6.40845e14i	−0.583229	−	1.01018i
$914$	−1.29498e14	+	7.47659e13i	−0.203017	+	0.117212i
$915$	1.10291e14	+	6.30051e13i	0.171963	+	0.0982358i
$916$	−1.53052e14	+	2.65093e14i	−0.237334	+	0.411075i
$917$		−	1.96216e14i		−	0.302613i
$918$	−9.33703e13	+	1.66977e14i	−0.143217	+	0.256120i
$919$	6.27431e14			0.957168			0.478584	−	0.878042i	$-0.341150\pi$
$919$	6.27431e14			0.957168			0.478584	+	0.878042i	$0.341150\pi$
$920$	2.15820e13	+	1.24603e13i	0.0327455	+	0.0189056i
$921$	−1.45753e14	+	2.55143e14i	−0.219948	+	0.385022i
$922$	3.02802e14	+	5.24468e14i	0.454468	+	0.787162i
$923$	−5.04518e13	+	2.91284e13i	−0.0753128	+	0.0434818i
$924$	−9.87161e13	+	5.75979e13i	−0.146564	+	0.0855159i
$925$	−3.41480e14	+	5.91460e14i	−0.504262	+	0.873408i
$926$		−	1.13951e14i		−	0.167364i
$927$	4.43665e14	−	7.84963e14i	0.648122	−	1.14670i
$928$	−1.39771e14			−0.203085
$929$	−7.26461e14	−	4.19422e14i	−1.04987	−	0.606140i	−0.127254	−	0.991870i	$-0.540616\pi$
$929$	−7.26461e14	−	4.19422e14i	−1.04987	−	0.606140i	−0.922612	+	0.385730i	$0.873950\pi$
$930$	2.31603e14	−	1.06032e12i	0.332912	−	0.00152413i
$931$	−3.59902e14	−	6.23368e14i	−0.514559	−	0.891243i
$932$	3.30777e14	−	1.90974e14i	0.470387	−	0.271578i
$933$	−4.67311e11	−	1.02074e14i	−0.000660995	−	0.144379i
$934$	−2.13074e14	+	3.69055e14i	−0.299776	+	0.519227i
$935$			1.19096e14i			0.166663i
$936$	−4.86035e13	−	2.74710e13i	−0.0676532	−	0.0382380i
$937$	1.03350e13			0.0143091			0.00715453	−	0.999974i	$-0.497723\pi$
$937$	1.03350e13			0.0143091			0.00715453	+	0.999974i	$0.497723\pi$
$938$	−1.47667e14	−	8.52554e13i	−0.203361	−	0.117411i
$939$	−3.67576e14	−	6.29981e14i	−0.503522	−	0.862978i
$940$	1.31304e14	+	2.27426e14i	0.178912	+	0.309885i
$941$	−1.17778e15	+	6.79993e14i	−1.59631	+	0.921630i	−0.604120	+	0.796893i	$0.706475\pi$
$941$	−1.17778e15	+	6.79993e14i	−1.59631	+	0.921630i	−0.992190	+	0.124737i	$0.960191\pi$
$942$	−5.29801e14	−	3.02655e14i	−0.714263	−	0.408032i
$943$	1.10563e14	−	1.91501e14i	0.148270	−	0.256811i
$944$		−	1.39134e14i		−	0.185598i
$945$	−1.24950e12	−	9.09700e13i	−0.00165797	−	0.120709i
$946$	7.58723e14			1.00145
$947$	−9.72866e14	−	5.61684e14i	−1.27733	−	0.737467i	−0.300973	−	0.953633i	$-0.597311\pi$
$947$	−9.72866e14	−	5.61684e14i	−1.27733	−	0.737467i	−0.976357	+	0.216166i	$0.930645\pi$
$948$	−8.79017e13	+	1.53873e14i	−0.114804	+	0.200965i
$949$	4.62424e13	+	8.00942e13i	0.0600771	+	0.104057i
$950$	4.65461e14	−	2.68734e14i	0.601541	−	0.347300i
$951$	−1.81021e14	+	1.05621e14i	−0.232717	+	0.135783i
$952$	1.83222e13	−	3.17351e13i	0.0234312	−	0.0405840i
$953$		−	6.09412e14i		−	0.775259i	−0.921815	−	0.387629i	$-0.873294\pi$
$953$		−	6.09412e14i		−	0.775259i	0.921815	−	0.387629i	$-0.126706\pi$
$954$	−8.96500e14	+	8.20885e12i	−1.13451	+	0.0103882i
$955$	−3.23393e14			−0.407112
$956$	−5.71444e14	−	3.29923e14i	−0.715623	−	0.413165i
$957$	9.79847e14	−	4.48592e12i	1.22067	−	0.00558846i
$958$	−1.37780e14	−	2.38642e14i	−0.170749	−	0.295747i
$959$	3.34926e14	−	1.93369e14i	0.412910	−	0.238394i
$960$	1.76362e11	+	3.85222e13i	0.000216296	+	0.0472449i
$961$	−2.26081e14	+	3.91583e14i	−0.275833	+	0.477757i
$962$		−	1.50669e14i		−	0.182873i
$963$	5.33651e13	−	3.14653e13i	0.0644356	−	0.0379927i
$964$	−5.63190e14			−0.676504
$965$	3.51953e14	+	2.03200e14i	0.420580	+	0.242822i
$966$	2.70903e13	+	4.64296e13i	0.0322054	+	0.0551962i
$967$	1.30338e14	+	2.25751e14i	0.154148	+	0.266992i	0.932748	−	0.360528i	$-0.117403\pi$
$967$	1.30338e14	+	2.25751e14i	0.154148	+	0.266992i	−0.778601	+	0.627520i	$0.784070\pi$
$968$	−3.35750e13	+	1.93845e13i	−0.0395038	+	0.0228075i
$969$	3.52797e14	+	2.01540e14i	0.412959	+	0.235908i
$970$	−1.11987e14	+	1.93966e14i	−0.130409	+	0.225875i
$971$			4.73282e14i			0.548307i	0.961686	+	0.274154i	$0.0883977\pi$
$971$			4.73282e14i			0.548307i	−0.961686	+	0.274154i	$0.911602\pi$
$972$	2.08250e14	−	3.80558e14i	0.240023	−	0.438621i
$973$	−5.41409e14			−0.620814
$974$	−6.15133e14	−	3.55147e14i	−0.701737	−	0.405148i
$975$	−8.23410e13	+	1.44139e14i	−0.0934529	+	0.163590i
$976$	−5.80059e13	−	1.00469e14i	−0.0654972	−	0.113444i
$977$	−1.27933e15	+	7.38621e14i	−1.43717	+	0.829753i	−0.997653	−	0.0684797i	$-0.978185\pi$
$977$	−1.27933e15	+	7.38621e14i	−1.43717	+	0.829753i	−0.439521	+	0.898232i	$0.644852\pi$
$978$	−3.33340e13	+	1.94494e13i	−0.0372557	+	0.0217376i
$979$	−4.97331e14	+	8.61403e14i	−0.553009	+	0.957840i
$980$		−	1.53398e14i		−	0.169703i
$981$	−4.22210e14	−	7.16067e14i	−0.464712	−	0.788149i
$982$	9.32094e14			1.02071
$983$	−8.76457e14	−	5.06022e14i	−0.954911	−	0.551318i	−0.0603078	−	0.998180i	$-0.519208\pi$
$983$	−8.76457e14	−	5.06022e14i	−0.954911	−	0.551318i	−0.894603	+	0.446862i	$0.852542\pi$
$984$	3.41815e14	−	1.56489e12i	0.370524	−	0.00169633i
$985$	−1.23896e14	−	2.14595e14i	−0.133622	−	0.231440i
$986$	−2.72076e14	+	1.57083e14i	−0.291948	+	0.168557i
$987$	2.59332e12	+	5.66451e14i	0.00276866	+	0.604751i
$988$	−5.92860e13	+	1.02686e14i	−0.0629748	+	0.109076i
$989$		−	3.56854e14i		−	0.377145i
$990$	−2.47272e12	−	2.70049e14i	−0.00260015	−	0.283966i
$991$	1.67142e15			1.74871			0.874356	−	0.485284i	$-0.161284\pi$
$991$	1.67142e15			1.74871			0.874356	+	0.485284i	$0.161284\pi$
$992$	−1.83195e14	−	1.05768e14i	−0.190702	−	0.110102i
$993$	8.22025e14	+	1.40885e15i	0.851410	+	1.45922i
$994$	4.33535e13	+	7.50905e13i	0.0446779	+	0.0773844i
$995$	2.94777e14	−	1.70190e14i	0.302258	−	0.174509i
$996$	−4.67151e14	−	2.66866e14i	−0.476607	−	0.272268i
$997$	−2.00749e14	+	3.47708e14i	−0.203788	+	0.352971i	−0.949746	−	0.313022i	$-0.898659\pi$
$997$	−2.00749e14	+	3.47708e14i	−0.203788	+	0.352971i	0.745958	+	0.665993i	$0.231992\pi$
$998$		−	5.49662e14i		−	0.555192i
$999$	1.17063e15	−	1.60790e13i	1.17650	−	0.0161596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.11.d.a.11.7	yes	20
3.2	odd	2		54.11.d.a.35.3		20
9.2	odd	6		162.11.b.c.161.16		20
9.4	even	3		54.11.d.a.17.3		20
9.5	odd	6	inner	18.11.d.a.5.7	✓	20
9.7	even	3		162.11.b.c.161.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.11.d.a.5.7	✓	20	9.5	odd	6	inner
18.11.d.a.11.7	yes	20	1.1	even	1	trivial
54.11.d.a.17.3		20	9.4	even	3
54.11.d.a.35.3		20	3.2	odd	2
162.11.b.c.161.5		20	9.7	even	3
162.11.b.c.161.16		20	9.2	odd	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(19.5959 + 11.3137i) q^{2} +(-120.535 + 210.998i) q^{3} +(256.000 + 443.405i) q^{4} +(-1022.89 + 590.567i) q^{5} +(-4749.17 + 2771.00i) q^{6} +(-2684.05 + 4648.92i) q^{7} +11585.2i q^{8} +(-29991.5 - 50865.5i) q^{9} -26726.0 q^{10} +(-148199. - 85562.6i) q^{11} +(-124415. + 569.593i) q^{12} +(-40805.4 - 70677.1i) q^{13} +(-105193. + 60733.2i) q^{14} +(-1314.00 - 287013. i) q^{15} +(-131072. + 227023. i) q^{16} +589227. i q^{17} +(-12233.8 - 1.33607e6i) q^{18} -2.83768e6 q^{19} +(-523721. - 302370. i) q^{20} +(-657390. - 1.12669e6i) q^{21} +(-1.93606e6 - 3.35336e6i) q^{22} +(-1.57720e6 + 910597. i) q^{23} +(-2.44446e6 - 1.39643e6i) q^{24} +(-4.18527e6 + 7.24911e6i) q^{25} -1.84664e6i q^{26} +(1.43476e7 - 197068. i) q^{27} -2.74847e6 q^{28} +(2.04067e7 + 1.17818e7i) q^{29} +(3.22143e6 - 5.63914e6i) q^{30} +(1.78311e7 + 3.08843e7i) q^{31} +(-5.13695e6 + 2.96582e6i) q^{32} +(3.59167e7 - 2.09564e7i) q^{33} +(-6.66634e6 + 1.15464e7i) q^{34} -6.34045e6i q^{35} +(1.48762e7 - 2.63199e7i) q^{36} +8.15908e7 q^{37} +(-5.56070e7 - 3.21047e7i) q^{38} +(1.98312e7 - 90791.0i) q^{39} +(-6.84186e6 - 1.18504e7i) q^{40} +(-1.05152e8 + 6.07093e7i) q^{41} +(-135130. - 2.95160e7i) q^{42} +(-9.79725e7 + 1.69693e8i) q^{43} -8.76161e7i q^{44} +(6.07175e7 + 3.43179e7i) q^{45} -4.12089e7 q^{46} +(-3.76072e8 - 2.17125e8i) q^{47} +(-3.21027e7 - 5.50203e7i) q^{48} +(1.26829e8 + 2.19675e8i) q^{49} +(-1.64029e8 + 9.47019e7i) q^{50} +(-1.24326e8 - 7.10226e7i) q^{51} +(2.08924e7 - 3.61867e7i) q^{52} -6.70997e8i q^{53} +(2.83383e8 + 1.58462e8i) q^{54} +2.02122e8 q^{55} +(-5.38588e7 - 3.10954e7i) q^{56} +(3.42041e8 - 5.98746e8i) q^{57} +(2.66592e8 + 4.61751e8i) q^{58} +(-4.59646e8 + 2.65377e8i) q^{59} +(1.26926e8 - 7.40579e7i) q^{60} +(-2.21275e8 + 3.83259e8i) q^{61} +8.06943e8i q^{62} +(3.16968e8 - 2.90234e6i) q^{63} -1.34218e8 q^{64} +(8.34791e7 + 4.81967e7i) q^{65} +(9.40916e8 - 4.30769e6i) q^{66} +(7.01885e8 + 1.21570e9i) q^{67} +(-2.61266e8 + 1.50842e8i) q^{68} +(-2.02605e6 - 4.42545e8i) q^{69} +(7.17340e7 - 1.24247e8i) q^{70} -7.13836e8i q^{71} +(5.89288e8 - 3.47459e8i) q^{72} -1.13324e9 q^{73} +(1.59885e9 + 9.23095e8i) q^{74} +(-1.02508e9 - 1.75686e9i) q^{75} +(-7.26447e8 - 1.25824e9i) q^{76} +(7.95547e8 - 4.59309e8i) q^{77} +(3.89638e8 + 2.22586e8i) q^{78} +(7.12169e8 - 1.23351e9i) q^{79} -3.09627e8i q^{80} +(-1.68781e9 + 3.05106e9i) q^{81} -2.74739e9 q^{82} +(3.74489e9 + 2.16211e9i) q^{83} +(3.31288e8 - 5.79922e8i) q^{84} +(-3.47978e8 - 6.02716e8i) q^{85} +(-3.83972e9 + 2.21686e9i) q^{86} +(-4.94567e9 + 2.88566e9i) q^{87} +(9.91263e8 - 1.71692e9i) q^{88} -5.81248e9i q^{89} +(8.01553e8 + 1.35943e9i) q^{90} +4.38096e8 q^{91} +(-8.07526e8 - 4.66225e8i) q^{92} +(-8.66581e9 + 3.96737e7i) q^{93} +(-4.91298e9 - 8.50953e9i) q^{94} +(2.90264e9 - 1.67584e9i) q^{95} +(-6.59888e6 - 1.44137e9i) q^{96} +(4.19017e9 - 7.25759e9i) q^{97} +5.73964e9i q^{98} +(9.25211e7 + 1.01044e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19}+ \cdots + 41160676842 q^{99}+O(q^{100}) \) 20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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