LMFDB - Embedded newform 8.18.b.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,18,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.6577669876$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} + \cdots + 12\!\cdots\!00 $ x^16 - 7x^15 + 4022x^14 - 1102776x^13 - 373411968x^12 + 2100004864x^11 - 3763915816960x^10 + 7317489121656832x^9 - 1108241988138827776x^8 + 163121042717484777472x^7 + 5699397839986467274752x^6 + 1127435088957285706235904x^5 - 217909345031306501735579648x^4 - 78950720850572326734309359616x^3 + 13720647095471028734661620662272x^2 - 5242030267748791654842336509165568*x + 1286374137827816254118965326485913600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{14}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.7
Root			$1.16697 + 180.787i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.18.b.a.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(18.3339 - 361.574i) q^{2} -13786.7i q^{3} +(-130400. - 13258.2i) q^{4} -96356.3i q^{5} +(-4.98490e6 - 252764. i) q^{6} -1.47728e7 q^{7} +(-7.18455e6 + 4.69061e7i) q^{8} -6.09318e7 q^{9} +O(q^{10})$	\(q+(18.3339 - 361.574i) q^{2} -13786.7i q^{3} +(-130400. - 13258.2i) q^{4} -96356.3i q^{5} +(-4.98490e6 - 252764. i) q^{6} -1.47728e7 q^{7} +(-7.18455e6 + 4.69061e7i) q^{8} -6.09318e7 q^{9} +(-3.48399e7 - 1.76659e6i) q^{10} -6.68721e8i q^{11} +(-1.82786e8 + 1.79778e9i) q^{12} +1.72473e8i q^{13} +(-2.70845e8 + 5.34148e9i) q^{14} -1.32843e9 q^{15} +(1.68283e10 + 3.45772e9i) q^{16} +1.92991e10 q^{17} +(-1.11712e9 + 2.20314e10i) q^{18} +1.11328e11i q^{19} +(-1.27751e9 + 1.25648e10i) q^{20} +2.03668e11i q^{21} +(-2.41792e11 - 1.22603e10i) q^{22} -5.92040e11 q^{23} +(6.46678e11 + 9.90509e10i) q^{24} +7.53655e11 q^{25} +(6.23619e10 + 3.16212e9i) q^{26} -9.40365e11i q^{27} +(1.92638e12 + 1.95861e11i) q^{28} -2.95085e12i q^{29} +(-2.43554e10 + 4.80326e11i) q^{30} -7.53978e12 q^{31} +(1.55875e12 - 6.02129e12i) q^{32} -9.21942e12 q^{33} +(3.53828e11 - 6.97805e12i) q^{34} +1.42346e12i q^{35} +(7.94549e12 + 8.07844e11i) q^{36} +2.20235e13i q^{37} +(4.02534e13 + 2.04108e12i) q^{38} +2.37783e12 q^{39} +(4.51970e12 + 6.92276e11i) q^{40} -8.98214e13 q^{41} +(7.36412e13 + 3.73404e12i) q^{42} +1.45802e13i q^{43} +(-8.86600e12 + 8.72010e13i) q^{44} +5.87116e12i q^{45} +(-1.08544e13 + 2.14066e14i) q^{46} -7.43032e13 q^{47} +(4.76704e13 - 2.32006e14i) q^{48} -1.43935e13 q^{49} +(1.38175e13 - 2.72502e14i) q^{50} -2.66070e14i q^{51} +(2.28668e12 - 2.24905e13i) q^{52} +2.84157e14i q^{53} +(-3.40012e14 - 1.72406e13i) q^{54} -6.44354e13 q^{55} +(1.06136e14 - 6.92937e14i) q^{56} +1.53484e15 q^{57} +(-1.06695e15 - 5.41007e13i) q^{58} -1.09328e15i q^{59} +(1.73227e14 + 1.76125e13i) q^{60} +4.14860e14i q^{61} +(-1.38234e14 + 2.72619e15i) q^{62} +9.00136e14 q^{63} +(-2.14856e15 - 6.73998e14i) q^{64} +1.66189e13 q^{65} +(-1.69028e14 + 3.33351e15i) q^{66} -2.20200e15i q^{67} +(-2.51660e15 - 2.55870e14i) q^{68} +8.16225e15i q^{69} +(5.14685e14 + 2.60976e13i) q^{70} +6.67796e15 q^{71} +(4.37768e14 - 2.85807e15i) q^{72} -1.64289e15 q^{73} +(7.96311e15 + 4.03777e14i) q^{74} -1.03904e16i q^{75} +(1.47601e15 - 1.45172e16i) q^{76} +9.87891e15i q^{77} +(4.35950e13 - 8.59762e14i) q^{78} -1.46317e16 q^{79} +(3.33173e14 - 1.62151e15i) q^{80} -2.08332e16 q^{81} +(-1.64678e15 + 3.24771e16i) q^{82} -3.05535e16i q^{83} +(2.70027e15 - 2.65583e16i) q^{84} -1.85959e15i q^{85} +(5.27183e15 + 2.67313e14i) q^{86} -4.06824e16 q^{87} +(3.13671e16 + 4.80446e15i) q^{88} +4.48498e16 q^{89} +(2.12286e15 + 1.07642e14i) q^{90} -2.54792e15i q^{91} +(7.72018e16 + 7.84936e15i) q^{92} +1.03948e17i q^{93} +(-1.36227e15 + 2.68661e16i) q^{94} +1.07272e16 q^{95} +(-8.30135e16 - 2.14900e16i) q^{96} -3.26514e16 q^{97} +(-2.63889e14 + 5.20431e15i) q^{98} +4.07464e16i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9}+O(q^{10}) $ 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9	$ 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9} + 131002712 q^{10} - 2795125400 q^{12} + 16363788528 q^{14} - 9993282176 q^{15} + 26500434192 q^{16} - 7489125600 q^{17} - 113450563870 q^{18} - 209445719856 q^{20} + 223126527100 q^{22} + 746845345920 q^{23} - 1099415493232 q^{24} - 1809682431664 q^{25} + 2467726531080 q^{26} + 3220542267040 q^{28} - 1188624268048 q^{30} - 318979758592 q^{31} + 1455647316000 q^{32} + 5633526177600 q^{33} - 4461251980292 q^{34} - 33088278002484 q^{36} + 24076283913900 q^{38} - 18457706051456 q^{39} + 60626292962592 q^{40} + 7482251536032 q^{41} - 51630378688160 q^{42} + 193654716236040 q^{44} - 195097141003568 q^{46} - 376698804821760 q^{47} - 329350060416480 q^{48} + 127691292101520 q^{49} + 474997408872102 q^{50} - 272251877663120 q^{52} + 735354219382520 q^{54} + 22\!\cdots\!52 q^{55}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9 + 131002712 * q^10 - 2795125400 * q^12 + 16363788528 * q^14 - 9993282176 * q^15 + 26500434192 * q^16 - 7489125600 * q^17 - 113450563870 * q^18 - 209445719856 * q^20 + 223126527100 * q^22 + 746845345920 * q^23 - 1099415493232 * q^24 - 1809682431664 * q^25 + 2467726531080 * q^26 + 3220542267040 * q^28 - 1188624268048 * q^30 - 318979758592 * q^31 + 1455647316000 * q^32 + 5633526177600 * q^33 - 4461251980292 * q^34 - 33088278002484 * q^36 + 24076283913900 * q^38 - 18457706051456 * q^39 + 60626292962592 * q^40 + 7482251536032 * q^41 - 51630378688160 * q^42 + 193654716236040 * q^44 - 195097141003568 * q^46 - 376698804821760 * q^47 - 329350060416480 * q^48 + 127691292101520 * q^49 + 474997408872102 * q^50 - 272251877663120 * q^52 + 735354219382520 * q^54 + 2209036687713152 * q^55 - 162767516076480 * q^56 - 190521298294720 * q^57 - 623262610679960 * q^58 - 1973616194963808 * q^60 + 695695648144320 * q^62 - 8131096607338880 * q^63 + 1111931745501248 * q^64 + 2385987975356160 * q^65 + 3598826202828312 * q^66 + 5981109959771880 * q^68 - 10044559836180288 * q^70 + 9025926285576576 * q^71 - 19918679666289160 * q^72 + 11332002046118560 * q^73 + 11098735408189464 * q^74 + 5959440926938280 * q^76 + 4184252259031760 * q^78 - 45299671392008448 * q^79 + 1337342539452480 * q^80 + 20101901999290832 * q^81 + 15639739637081420 * q^82 + 19796542864700224 * q^84 - 14252032276026564 * q^86 + 25965768920837760 * q^87 - 66964872768837680 * q^88 - 69879174608766048 * q^89 + 136151511125051240 * q^90 + 57336249810701280 * q^92 - 192318922166254176 * q^94 + 93790444358203776 * q^95 - 342799224184788928 * q^96 + 95593398602180640 * q^97 + 339641261743253790 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	18.3339	−	361.574i	0.0506408	−	0.998717i
$2$	18.3339	−	361.574i	0.0506408	−	0.998717i
$3$		−	13786.7i		−	1.21319i	−0.795011	−	0.606594i	$-0.792535\pi$
$3$		−	13786.7i		−	1.21319i	0.795011	−	0.606594i	$-0.207465\pi$
$4$	−130400.	−	13258.2i	−0.994871	−	0.101152i
$5$		−	96356.3i		−	0.110315i	−0.998478	−	0.0551575i	$-0.982434\pi$
$5$		−	96356.3i		−	0.110315i	0.998478	−	0.0551575i	$-0.0175661\pi$
$6$	−4.98490e6	−	252764.i	−1.21163	−	0.0614369i
$7$	−1.47728e7			−0.968570			−0.484285	−	0.874910i	$-0.660920\pi$
$7$	−1.47728e7			−0.968570			−0.484285	+	0.874910i	$0.660920\pi$
$8$	−7.18455e6	+	4.69061e7i	−0.151403	+	0.988472i
$9$	−6.09318e7			−0.471827
$10$	−3.48399e7	−	1.76659e6i	−0.110174	−	0.00558645i
$11$		−	6.68721e8i		−	0.940604i	−0.882505	−	0.470302i	$-0.844145\pi$
$11$		−	6.68721e8i		−	0.940604i	0.882505	−	0.470302i	$-0.155855\pi$
$12$	−1.82786e8	+	1.79778e9i	−0.122716	+	1.20697i
$13$			1.72473e8i			0.0586413i	0.999570	+	0.0293206i	$0.00933439\pi$
$13$			1.72473e8i			0.0586413i	−0.999570	+	0.0293206i	$0.990666\pi$
$14$	−2.70845e8	+	5.34148e9i	−0.0490492	+	0.967327i
$15$	−1.32843e9			−0.133833
$16$	1.68283e10	+	3.45772e9i	0.979537	+	0.201266i
$17$	1.92991e10			0.670998			0.335499	−	0.942041i	$-0.391095\pi$
$17$	1.92991e10			0.670998			0.335499	+	0.942041i	$0.391095\pi$
$18$	−1.11712e9	+	2.20314e10i	−0.0238937	+	0.471222i
$19$			1.11328e11i			1.50383i	0.659259	+	0.751916i	$0.270870\pi$
$19$			1.11328e11i			1.50383i	−0.659259	+	0.751916i	$0.729130\pi$
$20$	−1.27751e9	+	1.25648e10i	−0.0111586	+	0.109749i
$21$			2.03668e11i			1.17506i
$22$	−2.41792e11	−	1.22603e10i	−0.939397	−	0.0476330i
$23$	−5.92040e11			−1.57639			−0.788196	−	0.615424i	$-0.788985\pi$
$23$	−5.92040e11			−1.57639			−0.788196	+	0.615424i	$0.788985\pi$
$24$	6.46678e11	+	9.90509e10i	1.19920	+	0.183680i
$25$	7.53655e11			0.987831
$26$	6.23619e10	+	3.16212e9i	0.0585660	+	0.00296964i
$27$		−	9.40365e11i		−	0.640774i
$28$	1.92638e12	+	1.95861e11i	0.963602	+	0.0979725i
$29$		−	2.95085e12i		−	1.09538i	−0.836682	−	0.547689i	$-0.815508\pi$
$29$		−	2.95085e12i		−	1.09538i	0.836682	−	0.547689i	$-0.184492\pi$
$30$	−2.43554e10	+	4.80326e11i	−0.00677742	+	0.133661i
$31$	−7.53978e12			−1.58776			−0.793879	−	0.608075i	$-0.791942\pi$
$31$	−7.53978e12			−1.58776			−0.793879	+	0.608075i	$0.791942\pi$
$32$	1.55875e12	−	6.02129e12i	0.250612	−	0.968088i
$33$	−9.21942e12			−1.14113
$34$	3.53828e11	−	6.97805e12i	0.0339799	−	0.670137i
$35$			1.42346e12i			0.106848i
$36$	7.94549e12	+	8.07844e11i	0.469407	+	0.0477261i
$37$			2.20235e13i			1.03079i	0.856952	+	0.515396i	$0.172355\pi$
$37$			2.20235e13i			1.03079i	−0.856952	+	0.515396i	$0.827645\pi$
$38$	4.02534e13	+	2.04108e12i	1.50190	+	0.0761553i
$39$	2.37783e12			0.0711430
$40$	4.51970e12	+	6.92276e11i	0.109043	+	0.0167020i
$41$	−8.98214e13			−1.75678			−0.878389	−	0.477946i	$-0.841382\pi$
$41$	−8.98214e13			−1.75678			−0.878389	+	0.477946i	$0.841382\pi$
$42$	7.36412e13	+	3.73404e12i	1.17355	+	0.0595059i
$43$			1.45802e13i			0.190231i	0.995466	+	0.0951157i	$0.0303221\pi$
$43$			1.45802e13i			0.190231i	−0.995466	+	0.0951157i	$0.969678\pi$
$44$	−8.86600e12	+	8.72010e13i	−0.0951437	+	0.935780i
$45$			5.87116e12i			0.0520496i
$46$	−1.08544e13	+	2.14066e14i	−0.0798298	+	1.57437i
$47$	−7.43032e13			−0.455172			−0.227586	−	0.973758i	$-0.573083\pi$
$47$	−7.43032e13			−0.455172			−0.227586	+	0.973758i	$0.573083\pi$
$48$	4.76704e13	−	2.32006e14i	0.244173	−	1.18836i
$49$	−1.43935e13			−0.0618727
$50$	1.38175e13	−	2.72502e14i	0.0500246	−	0.986563i
$51$		−	2.66070e14i		−	0.814047i
$52$	2.28668e12	−	2.24905e13i	0.00593167	−	0.0583405i
$53$			2.84157e14i			0.626922i	0.949601	+	0.313461i	$0.101488\pi$
$53$			2.84157e14i			0.626922i	−0.949601	+	0.313461i	$0.898512\pi$
$54$	−3.40012e14	−	1.72406e13i	−0.639951	−	0.0324493i
$55$	−6.44354e13			−0.103763
$56$	1.06136e14	−	6.92937e14i	0.146644	−	0.957404i
$57$	1.53484e15			1.82443
$58$	−1.06695e15	−	5.41007e13i	−1.09397	−	0.0554709i
$59$		−	1.09328e15i		−	0.969373i	−0.874688	−	0.484687i	$-0.838934\pi$
$59$		−	1.09328e15i		−	0.969373i	0.874688	−	0.484687i	$-0.161066\pi$
$60$	1.73227e14	+	1.76125e13i	0.133147	+	0.0135374i
$61$			4.14860e14i			0.277075i	0.990357	+	0.138538i	$0.0442402\pi$
$61$			4.14860e14i			0.277075i	−0.990357	+	0.138538i	$0.955760\pi$
$62$	−1.38234e14	+	2.72619e15i	−0.0804054	+	1.58572i
$63$	9.00136e14			0.456997
$64$	−2.14856e15	−	6.73998e14i	−0.954154	−	0.299315i
$65$	1.66189e13			0.00646902
$66$	−1.69028e14	+	3.33351e15i	−0.0577878	+	1.13967i
$67$		−	2.20200e15i		−	0.662492i	−0.943544	−	0.331246i	$-0.892531\pi$
$67$		−	2.20200e15i		−	0.662492i	0.943544	−	0.331246i	$-0.107469\pi$
$68$	−2.51660e15	−	2.55870e14i	−0.667556	−	0.0678726i
$69$			8.16225e15i			1.91246i
$70$	5.14685e14	+	2.60976e13i	0.106711	+	0.00541086i
$71$	6.67796e15			1.22729			0.613646	−	0.789581i	$-0.289702\pi$
$71$	6.67796e15			1.22729			0.613646	+	0.789581i	$0.289702\pi$
$72$	4.37768e14	−	2.85807e15i	0.0714360	−	0.466388i
$73$	−1.64289e15			−0.238432			−0.119216	−	0.992868i	$-0.538038\pi$
$73$	−1.64289e15			−0.238432			−0.119216	+	0.992868i	$0.538038\pi$
$74$	7.96311e15	+	4.03777e14i	1.02947	+	0.0522001i
$75$		−	1.03904e16i		−	1.19842i
$76$	1.47601e15	−	1.45172e16i	0.152115	−	1.49612i
$77$			9.87891e15i			0.911041i
$78$	4.35950e13	−	8.59762e14i	0.00360274	−	0.0710517i
$79$	−1.46317e16			−1.08509			−0.542543	−	0.840028i	$-0.682539\pi$
$79$	−1.46317e16			−1.08509			−0.542543	+	0.840028i	$0.682539\pi$
$80$	3.33173e14	−	1.62151e15i	0.0222027	−	0.108058i
$81$	−2.08332e16			−1.24921
$82$	−1.64678e15	+	3.24771e16i	−0.0889647	+	1.75452i
$83$		−	3.05535e16i		−	1.48901i	−0.667618	−	0.744504i	$-0.732686\pi$
$83$		−	3.05535e16i		−	1.48901i	0.667618	−	0.744504i	$-0.267314\pi$
$84$	2.70027e15	−	2.65583e16i	0.118859	−	1.16903i
$85$		−	1.85959e15i		−	0.0740211i
$86$	5.27183e15	+	2.67313e14i	0.189987	+	0.00963348i
$87$	−4.06824e16			−1.32890
$88$	3.13671e16	+	4.80446e15i	0.929761	+	0.142410i
$89$	4.48498e16			1.20766			0.603831	−	0.797112i	$-0.293640\pi$
$89$	4.48498e16			1.20766			0.603831	+	0.797112i	$0.293640\pi$
$90$	2.12286e15	+	1.07642e14i	0.0519828	+	0.00263584i
$91$		−	2.54792e15i		−	0.0567982i
$92$	7.72018e16	+	7.84936e15i	1.56831	+	0.159455i
$93$			1.03948e17i			1.92625i
$94$	−1.36227e15	+	2.68661e16i	−0.0230503	+	0.454588i
$95$	1.07272e16			0.165895
$96$	−8.30135e16	−	2.14900e16i	−1.17447	−	0.304040i
$97$	−3.26514e16			−0.423002			−0.211501	−	0.977378i	$-0.567835\pi$
$97$	−3.26514e16			−0.423002			−0.211501	+	0.977378i	$0.567835\pi$
$98$	−2.63889e14	+	5.20431e15i	−0.00313328	+	0.0617933i
$99$			4.07464e16i			0.443802i
$100$	−9.82764e16	−	9.99208e15i	−0.982764	−	0.0999208i
$101$		−	4.25294e16i		−	0.390803i	−0.980723	−	0.195402i	$-0.937399\pi$
$101$		−	4.25294e16i		−	0.390803i	0.980723	−	0.195402i	$-0.0626010\pi$
$102$	−9.62040e16	−	4.87811e15i	−0.813002	−	0.0412240i
$103$	1.23310e17			0.959140			0.479570	−	0.877504i	$-0.340793\pi$
$103$	1.23310e17			0.959140			0.479570	+	0.877504i	$0.340793\pi$
$104$	−8.09005e15	−	1.23914e15i	−0.0579653	−	0.00887847i
$105$	1.96247e16			0.129627
$106$	1.02744e17	+	5.20972e15i	0.626117	+	0.0317478i
$107$		−	6.12850e16i		−	0.344820i	−0.985025	−	0.172410i	$-0.944845\pi$
$107$		−	6.12850e16i		−	0.344820i	0.985025	−	0.172410i	$-0.0551554\pi$
$108$	−1.24675e16	+	1.22623e17i	−0.0648153	+	0.637487i
$109$		−	3.63163e17i		−	1.74573i	−0.487962	−	0.872865i	$-0.662260\pi$
$109$		−	3.63163e17i		−	1.74573i	0.487962	−	0.872865i	$-0.337740\pi$
$110$	−1.18136e15	+	2.32982e16i	−0.00525464	+	0.103630i
$111$	3.03630e17			1.25054
$112$	−2.48602e17	−	5.10804e16i	−0.948750	−	0.194940i
$113$	6.33950e16			0.224330			0.112165	−	0.993690i	$-0.464221\pi$
$113$	6.33950e16			0.224330			0.112165	+	0.993690i	$0.464221\pi$
$114$	2.81397e16	−	5.54959e17i	0.0923907	−	1.82209i
$115$			5.70467e16i			0.173900i
$116$	−3.91228e16	+	3.84790e17i	−0.110799	+	1.08976i
$117$		−	1.05091e16i		−	0.0276685i
$118$	−3.95303e17	−	2.00442e16i	−0.968130	−	0.0490899i
$119$	−2.85102e17			−0.649908
$120$	9.54418e15	−	6.23115e16i	0.0202627	−	0.132290i
$121$	5.82597e16			0.115264
$122$	1.50002e17	+	7.60601e15i	0.276720	+	0.0140313i
$123$			1.23834e18i			2.13130i
$124$	9.83186e17	+	9.99636e16i	1.57961	+	0.160604i
$125$		−	1.46133e17i		−	0.219288i
$126$	1.65030e16	−	3.25466e17i	0.0231427	−	0.456411i
$127$	−8.96529e17			−1.17553			−0.587764	−	0.809033i	$-0.699991\pi$
$127$	−8.96529e17			−1.17553			−0.587764	+	0.809033i	$0.699991\pi$
$128$	−2.83092e17	+	7.64508e17i	−0.347250	+	0.937772i
$129$	2.01013e17			0.230787
$130$	3.04690e14	−	6.00896e15i	0.000327596	−	0.00646072i
$131$			7.31204e17i			0.736601i	0.929707	+	0.368301i	$0.120060\pi$
$131$			7.31204e17i			0.736601i	−0.929707	+	0.368301i	$0.879940\pi$
$132$	1.20221e18	+	1.22233e17i	1.13528	+	0.115427i
$133$		−	1.64463e18i		−	1.45657i
$134$	−7.96185e17	−	4.03713e16i	−0.661642	−	0.0335492i
$135$	−9.06101e16			−0.0706870
$136$	−1.38655e17	+	9.05245e17i	−0.101591	+	0.663262i
$137$	−1.67484e18			−1.15305			−0.576524	−	0.817080i	$-0.695591\pi$
$137$	−1.67484e18			−1.15305			−0.576524	+	0.817080i	$0.695591\pi$
$138$	2.95126e18	+	1.49646e17i	1.91001	+	0.0968486i
$139$		−	1.51826e18i		−	0.924105i	−0.886853	−	0.462053i	$-0.847113\pi$
$139$		−	1.51826e18i		−	0.924105i	0.886853	−	0.462053i	$-0.152887\pi$
$140$	1.88724e16	−	1.85618e17i	0.0108078	−	0.106300i
$141$			1.02439e18i			0.552209i
$142$	1.22433e17	−	2.41458e18i	0.0621511	−	1.22572i
$143$	1.15336e17			0.0551582
$144$	−1.02538e18	−	2.10685e17i	−0.462172	−	0.0949626i
$145$	−2.84333e17			−0.120837
$146$	−3.01206e16	+	5.94026e17i	−0.0120744	+	0.238126i
$147$			1.98438e17i			0.0750632i
$148$	2.91990e17	−	2.87185e18i	0.104266	−	1.02550i
$149$		−	9.25567e17i		−	0.312122i	−0.987747	−	0.156061i	$-0.950120\pi$
$149$		−	9.25567e17i		−	0.312122i	0.987747	−	0.156061i	$-0.0498796\pi$
$150$	−3.75689e18	−	1.90497e17i	−1.19689	−	0.0606892i
$151$	2.49950e18			0.752574			0.376287	−	0.926503i	$-0.377201\pi$
$151$	2.49950e18			0.752574			0.376287	+	0.926503i	$0.377201\pi$
$152$	−5.22197e18	−	7.99842e17i	−1.48650	−	0.227685i
$153$	−1.17593e18			−0.316595
$154$	3.57196e18	+	1.81119e17i	0.909872	+	0.0461359i
$155$			7.26505e17i			0.175154i
$156$	−3.10069e17	−	3.15257e16i	−0.0707781	−	0.00719623i
$157$			5.60339e18i			1.21145i	0.795676	+	0.605723i	$0.207116\pi$
$157$			5.60339e18i			1.21145i	−0.795676	+	0.605723i	$0.792884\pi$
$158$	−2.68257e17	+	5.29044e18i	−0.0549497	+	1.08369i
$159$	3.91757e18			0.760574
$160$	−5.80189e17	−	1.50195e17i	−0.106795	−	0.0276463i
$161$	8.74611e18			1.52685
$162$	−3.81955e17	+	7.53276e18i	−0.0632608	+	1.24760i
$163$		−	9.07691e18i		−	1.42673i	−0.700790	−	0.713367i	$-0.747169\pi$
$163$		−	9.07691e18i		−	1.42673i	0.700790	−	0.713367i	$-0.252831\pi$
$164$	1.17127e19	+	1.19087e18i	1.74777	+	0.177701i
$165$			8.88349e17i			0.125884i
$166$	−1.10474e19	−	5.60166e17i	−1.48710	−	0.0754046i
$167$	−3.89443e18			−0.498143			−0.249071	−	0.968485i	$-0.580125\pi$
$167$	−3.89443e18			−0.498143			−0.249071	+	0.968485i	$0.580125\pi$
$168$	−9.55328e18	−	1.46326e18i	−1.16151	−	0.177907i
$169$	8.62067e18			0.996561
$170$	−6.72379e17	−	3.40936e16i	−0.0739262	−	0.00374849i
$171$		−	6.78342e18i		−	0.709548i
$172$	1.93307e17	−	1.90126e18i	0.0192422	−	0.189256i
$173$			1.88076e19i			1.78214i	0.453868	+	0.891069i	$0.350044\pi$
$173$			1.88076e19i			1.78214i	−0.453868	+	0.891069i	$0.649956\pi$
$174$	−7.45868e17	+	1.47097e19i	−0.0672966	+	1.32720i
$175$	−1.11336e19			−0.956783
$176$	2.31225e18	−	1.12534e19i	0.189311	−	0.921356i
$177$	−1.50727e19			−1.17603
$178$	8.22273e17	−	1.62165e19i	0.0611570	−	1.20611i
$179$			3.45942e18i			0.245331i	0.992448	+	0.122665i	$0.0391442\pi$
$179$			3.45942e18i			0.245331i	−0.992448	+	0.122665i	$0.960856\pi$
$180$	7.78408e16	−	7.65598e17i	0.00526491	−	0.0517827i
$181$		−	1.78211e19i		−	1.14992i	−0.818182	−	0.574959i	$-0.805018\pi$
$181$		−	1.78211e19i		−	1.14992i	0.818182	−	0.574959i	$-0.194982\pi$
$182$	−9.21263e17	−	4.67135e16i	−0.0567253	−	0.00287631i
$183$	5.71953e18			0.336144
$184$	4.25354e18	−	2.77703e19i	0.238671	−	1.55822i
$185$	2.12210e18			0.113712
$186$	3.75851e19	+	1.90578e18i	1.92378	+	0.0975469i
$187$		−	1.29057e19i		−	0.631143i
$188$	9.68911e18	+	9.85123e17i	0.452837	+	0.0460414i
$189$			1.38919e19i			0.620634i
$190$	1.96671e17	−	3.87866e18i	0.00840107	−	0.165682i
$191$	6.12664e18			0.250287			0.125144	−	0.992139i	$-0.460061\pi$
$191$	6.12664e18			0.250287			0.125144	+	0.992139i	$0.460061\pi$
$192$	−9.29218e18	+	2.96215e19i	−0.363126	+	1.15757i
$193$	−3.57527e19			−1.33682			−0.668408	−	0.743795i	$-0.733024\pi$
$193$	−3.57527e19			−1.33682			−0.668408	+	0.743795i	$0.733024\pi$
$194$	−5.98630e17	+	1.18059e19i	−0.0214212	+	0.422459i
$195$		−	2.29119e17i		−	0.00784814i
$196$	1.87690e18	+	1.90831e17i	0.0615553	+	0.00625853i
$197$		−	1.53763e19i		−	0.482936i	−0.970409	−	0.241468i	$-0.922371\pi$
$197$		−	1.53763e19i		−	0.482936i	0.970409	−	0.241468i	$-0.0776290\pi$
$198$	1.47328e19	+	7.47041e17i	0.443233	+	0.0224745i
$199$	−2.52712e19			−0.728407			−0.364204	−	0.931319i	$-0.618659\pi$
$199$	−2.52712e19			−0.728407			−0.364204	+	0.931319i	$0.618659\pi$
$200$	−5.41467e18	+	3.53510e19i	−0.149561	+	0.976443i
$201$	−3.03582e19			−0.803728
$202$	−1.53775e19	−	7.79732e17i	−0.390302	−	0.0197906i
$203$			4.35925e19i			1.06095i
$204$	−3.52760e18	+	3.46955e19i	−0.0823422	+	0.809871i
$205$			8.65485e18i			0.193799i
$206$	2.26076e18	−	4.45857e19i	0.0485716	−	0.957909i
$207$	3.60741e19			0.743784
$208$	−5.96365e17	+	2.90244e18i	−0.0118025	+	0.0574413i
$209$	7.44474e19			1.41451
$210$	3.59798e17	−	7.09579e18i	0.00656440	−	0.129460i
$211$			7.63891e19i			1.33854i	0.743020	+	0.669269i	$0.233393\pi$
$211$			7.63891e19i			1.33854i	−0.743020	+	0.669269i	$0.766607\pi$
$212$	3.76740e18	−	3.70540e19i	0.0634142	−	0.623706i
$213$		−	9.20667e19i		−	1.48894i
$214$	−2.21591e19	−	1.12360e18i	−0.344377	−	0.0174620i
$215$	1.40490e18			0.0209854
$216$	4.41089e19	+	6.75610e18i	0.633387	+	0.0970151i
$217$	1.11384e20			1.53785
$218$	−1.31311e20	−	6.65822e18i	−1.74349	−	0.0884052i
$219$			2.26500e19i			0.289263i
$220$	8.40236e18	+	8.54295e17i	0.103231	+	0.0104958i
$221$			3.32858e18i			0.0393482i
$222$	5.56673e18	−	1.09785e20i	0.0633286	−	1.24894i
$223$	−5.35584e19			−0.586457			−0.293229	−	0.956042i	$-0.594730\pi$
$223$	−5.35584e19			−0.586457			−0.293229	+	0.956042i	$0.594730\pi$
$224$	−2.30272e19	+	8.89516e19i	−0.242735	+	0.937660i
$225$	−4.59216e19			−0.466085
$226$	1.16228e18	−	2.29220e19i	0.0113603	−	0.224043i
$227$		−	8.47585e19i		−	0.797928i	−0.916967	−	0.398964i	$-0.869370\pi$
$227$		−	8.47585e19i		−	0.797928i	0.916967	−	0.398964i	$-0.130630\pi$
$228$	−2.00143e20	−	2.03492e19i	−1.81507	−	0.184544i
$229$		−	2.17239e20i		−	1.89817i	−0.315016	−	0.949086i	$-0.602010\pi$
$229$		−	2.17239e20i		−	1.89817i	0.315016	−	0.949086i	$-0.397990\pi$
$230$	2.06266e19	+	1.04589e18i	0.173677	+	0.00880643i
$231$	1.36197e20			1.10526
$232$	1.38413e20	+	2.12005e19i	1.08275	+	0.165844i
$233$	−4.79641e19			−0.361736			−0.180868	−	0.983507i	$-0.557891\pi$
$233$	−4.79641e19			−0.361736			−0.180868	+	0.983507i	$0.557891\pi$
$234$	−3.79982e18	−	1.92673e17i	−0.0276330	−	0.00140116i
$235$			7.15957e18i			0.0502123i
$236$	−1.44949e19	+	1.42564e20i	−0.0980538	+	0.964401i
$237$			2.01722e20i			1.31641i
$238$	−5.22705e18	+	1.03086e20i	−0.0329119	+	0.649074i
$239$	−6.27917e18			−0.0381523			−0.0190761	−	0.999818i	$-0.506072\pi$
$239$	−6.27917e18			−0.0381523			−0.0190761	+	0.999818i	$0.506072\pi$
$240$	−2.23552e19	−	4.59334e18i	−0.131094	−	0.0269360i
$241$	1.50770e19			0.0853436			0.0426718	−	0.999089i	$-0.486413\pi$
$241$	1.50770e19			0.0853436			0.0426718	+	0.999089i	$0.486413\pi$
$242$	1.06813e18	−	2.10652e19i	0.00583705	−	0.115116i
$243$			1.65782e20i			0.874749i
$244$	5.50027e18	−	5.40976e19i	0.0280266	−	0.275654i
$245$			1.38690e18i			0.00682549i
$246$	4.47751e20	+	2.27036e19i	2.12857	+	0.107931i
$247$	−1.92011e19			−0.0881866
$248$	5.41699e19	−	3.53662e20i	0.240391	−	1.56945i
$249$	−4.21231e20			−1.80645
$250$	−5.28380e19	−	2.67920e18i	−0.219006	−	0.0111049i
$251$		−	6.51149e18i		−	0.0260888i	−0.999915	−	0.0130444i	$-0.995848\pi$
$251$		−	6.51149e18i		−	0.0260888i	0.999915	−	0.0130444i	$-0.00415227\pi$
$252$	−1.17378e20	−	1.19342e19i	−0.454653	−	0.0462261i
$253$			3.95909e20i			1.48276i
$254$	−1.64369e19	+	3.24162e20i	−0.0595297	+	1.17402i
$255$	−2.56375e19			−0.0898016
$256$	2.71236e20	+	1.16375e20i	0.918984	+	0.394294i
$257$	2.25404e20			0.738805			0.369402	−	0.929269i	$-0.379562\pi$
$257$	2.25404e20			0.738805			0.369402	+	0.929269i	$0.379562\pi$
$258$	3.68535e18	−	7.26810e19i	0.0116872	−	0.230491i
$259$		−	3.25349e20i		−	0.998394i
$260$	−2.16710e18	−	2.20336e17i	−0.00643584	−	0.000654352i
$261$			1.79801e20i			0.516829i
$262$	2.64384e20	+	1.34059e19i	0.735656	+	0.0373021i
$263$	−4.46257e20			−1.20216			−0.601079	−	0.799190i	$-0.705262\pi$
$263$	−4.46257e20			−1.20216			−0.601079	+	0.799190i	$0.705262\pi$
$264$	6.62374e19	−	4.32447e20i	0.172771	−	1.12798i
$265$	2.73803e19			0.0691589
$266$	−5.94657e20	−	3.01526e19i	−1.45470	−	0.0737617i
$267$		−	6.18329e20i		−	1.46512i
$268$	−2.91944e19	+	2.87140e20i	−0.0670122	+	0.659094i
$269$		−	4.92825e20i		−	1.09597i	−0.836489	−	0.547984i	$-0.815395\pi$
$269$		−	4.92825e20i		−	1.09597i	0.836489	−	0.547984i	$-0.184605\pi$
$270$	−1.66124e18	+	3.27623e19i	−0.00357965	+	0.0705963i
$271$	−3.92364e20			−0.819313			−0.409657	−	0.912240i	$-0.634351\pi$
$271$	−3.92364e20			−0.819313			−0.409657	+	0.912240i	$0.634351\pi$
$272$	3.24771e20	+	6.67308e19i	0.657267	+	0.135049i
$273$	−3.51273e19			−0.0689069
$274$	−3.07064e19	+	6.05578e20i	−0.0583914	+	1.15157i
$275$		−	5.03985e20i		−	0.929158i
$276$	1.08216e20	−	1.06436e21i	0.193449	−	1.90265i
$277$			7.33443e20i			1.27142i	0.771929	+	0.635709i	$0.219292\pi$
$277$			7.33443e20i			1.27142i	−0.771929	+	0.635709i	$0.780708\pi$
$278$	−5.48965e20	−	2.78358e19i	−0.922919	−	0.0467975i
$279$	4.59413e20			0.749147
$280$	−6.67688e19	−	1.02269e19i	−0.105616	−	0.0161771i
$281$	1.18919e21			1.82493			0.912467	−	0.409149i	$-0.134174\pi$
$281$	1.18919e21			1.82493			0.912467	+	0.409149i	$0.134174\pi$
$282$	3.70394e20	+	1.87811e19i	0.551501	+	0.0279643i
$283$			6.56438e20i			0.948438i	0.880407	+	0.474219i	$0.157269\pi$
$283$			6.56438e20i			0.948438i	−0.880407	+	0.474219i	$0.842731\pi$
$284$	−8.70804e20	−	8.85374e19i	−1.22100	−	0.124143i
$285$		−	1.47892e20i		−	0.201262i
$286$	2.11457e18	−	4.17027e19i	0.00279326	−	0.0550875i
$287$	1.32692e21			1.70156
$288$	−9.49776e19	+	3.66888e20i	−0.118246	+	0.456770i
$289$	−4.54785e20			−0.549762
$290$	−5.21294e18	+	1.02807e20i	−0.00611927	+	0.120682i
$291$			4.50154e20i			0.513181i
$292$	2.14232e20	+	2.17817e19i	0.237209	+	0.0241178i
$293$			6.98093e20i			0.750825i	0.926858	+	0.375412i	$0.122499\pi$
$293$			6.98093e20i			0.750825i	−0.926858	+	0.375412i	$0.877501\pi$
$294$	7.17500e19	+	3.63815e18i	0.0749669	+	0.00380126i
$295$	−1.05345e20			−0.106936
$296$	−1.03303e21	−	1.58229e20i	−1.01891	−	0.156065i
$297$	−6.28842e20			−0.602714
$298$	−3.34661e20	−	1.69693e19i	−0.311722	−	0.0158061i
$299$		−	1.02111e20i		−	0.0924417i
$300$	−1.37757e20	+	1.35490e21i	−0.121223	+	1.19228i
$301$		−	2.15391e20i		−	0.184252i
$302$	4.58257e19	−	9.03755e20i	0.0381110	−	0.751608i
$303$	−5.86339e20			−0.474118
$304$	−3.84941e20	+	1.87346e21i	−0.302670	+	1.47306i
$305$	3.99743e19			0.0305656
$306$	−2.15594e19	+	4.25185e20i	−0.0160326	+	0.316189i
$307$			3.85295e20i			0.278687i	0.990244	+	0.139344i	$0.0444992\pi$
$307$			3.85295e20i			0.278687i	−0.990244	+	0.139344i	$0.955501\pi$
$308$	1.30976e20	−	1.28821e21i	0.0921533	−	0.906368i
$309$		−	1.70003e21i		−	1.16362i
$310$	2.62686e20	+	1.33197e19i	0.174929	+	0.00886993i
$311$	2.10525e21			1.36408			0.682041	−	0.731313i	$-0.261092\pi$
$311$	2.10525e21			1.36408			0.682041	+	0.731313i	$0.261092\pi$
$312$	−1.70836e19	+	1.11535e20i	−0.0107713	+	0.0703228i
$313$	−2.88772e20			−0.177186			−0.0885928	−	0.996068i	$-0.528237\pi$
$313$	−2.88772e20			−0.177186			−0.0885928	+	0.996068i	$0.528237\pi$
$314$	2.02604e21	+	1.02732e20i	1.20989	+	0.0613486i
$315$		−	8.67338e19i		−	0.0504137i
$316$	1.90797e21	+	1.93989e20i	1.07952	+	0.109758i
$317$		−	2.62929e21i		−	1.44822i	−0.689683	−	0.724111i	$-0.742250\pi$
$317$		−	2.62929e21i		−	1.44822i	0.689683	−	0.724111i	$-0.257750\pi$
$318$	7.18246e19	−	1.41649e21i	0.0385161	−	0.759598i
$319$	−1.97329e21			−1.03032
$320$	−6.49439e19	+	2.07028e20i	−0.0330190	+	0.105258i
$321$	−8.44915e20			−0.418331
$322$	1.60351e20	−	3.16237e21i	0.0773208	−	1.52489i
$323$			2.14853e21i			1.00907i
$324$	2.71665e21	+	2.76210e20i	1.24280	+	0.126359i
$325$			1.29985e20i			0.0579277i
$326$	−3.28197e21	−	1.66415e20i	−1.42490	−	0.0722510i
$327$	−5.00681e21			−2.11790
$328$	6.45326e20	−	4.21317e21i	0.265982	−	1.73653i
$329$	1.09767e21			0.440866
$330$	3.21204e20	+	1.62869e19i	0.125722	+	0.00637487i
$331$			3.08298e21i			1.17607i	0.808836	+	0.588035i	$0.200098\pi$
$331$			3.08298e21i			1.17607i	−0.808836	+	0.588035i	$0.799902\pi$
$332$	−4.05083e20	+	3.98417e21i	−0.150616	+	1.48137i
$333$		−	1.34193e21i		−	0.486355i
$334$	−7.14002e19	+	1.40812e21i	−0.0252264	+	0.497503i
$335$	−2.12176e20			−0.0730829
$336$	−7.04228e20	+	3.42739e21i	−0.236499	+	1.15101i
$337$	−1.59524e21			−0.522363			−0.261181	−	0.965290i	$-0.584112\pi$
$337$	−1.59524e21			−0.522363			−0.261181	+	0.965290i	$0.584112\pi$
$338$	1.58051e20	−	3.11701e21i	0.0504667	−	0.995283i
$339$		−	8.74005e20i		−	0.272155i
$340$	−2.46547e19	+	2.42490e20i	−0.00748737	+	0.0736415i
$341$			5.04201e21i			1.49345i
$342$	−2.45271e21	−	1.24367e20i	−0.708638	−	0.0359321i
$343$	3.64925e21			1.02850
$344$	−6.83902e20	−	1.04752e20i	−0.188039	−	0.0288016i
$345$	7.86484e20			0.210973
$346$	6.80034e21	+	3.44817e20i	1.77985	+	0.0902490i
$347$		−	1.54612e21i		−	0.394859i	−0.980317	−	0.197430i	$-0.936741\pi$
$347$		−	1.54612e21i		−	0.394859i	0.980317	−	0.197430i	$-0.0632594\pi$
$348$	5.30497e21	+	5.39373e20i	1.32208	+	0.134421i
$349$		−	5.41385e21i		−	1.31671i	−0.752708	−	0.658355i	$-0.771253\pi$
$349$		−	5.41385e21i		−	1.31671i	0.752708	−	0.658355i	$-0.228747\pi$
$350$	−2.04123e20	+	4.02563e21i	−0.0484523	+	0.955555i
$351$	1.62188e20			0.0375758
$352$	−4.02656e21	−	1.04237e21i	−0.910587	−	0.235727i
$353$	3.93297e21			0.868232			0.434116	−	0.900857i	$-0.357061\pi$
$353$	3.93297e21			0.868232			0.434116	+	0.900857i	$0.357061\pi$
$354$	−2.76343e20	+	5.44991e21i	−0.0595553	+	1.17452i
$355$		−	6.43463e20i		−	0.135389i
$356$	−5.84840e21	−	5.94626e20i	−1.20147	−	0.122157i
$357$			3.93061e21i			0.788461i
$358$	1.25084e21	+	6.34247e19i	0.245016	+	0.0124238i
$359$	7.90394e21			1.51196			0.755981	−	0.654593i	$-0.227160\pi$
$359$	7.90394e21			1.51196			0.755981	+	0.654593i	$0.227160\pi$
$360$	−2.75393e20	−	4.21816e19i	−0.0514496	−	0.00788047i
$361$	−6.91355e21			−1.26151
$362$	−6.44365e21	−	3.26731e20i	−1.14844	−	0.0582328i
$363$		−	8.03207e20i		−	0.139837i
$364$	−3.37808e19	+	3.32248e20i	−0.00574523	+	0.0565069i
$365$			1.58303e20i			0.0263026i
$366$	1.04861e20	−	2.06803e21i	0.0170226	−	0.335713i
$367$	5.10700e20			0.0810036			0.0405018	−	0.999179i	$-0.487104\pi$
$367$	5.10700e20			0.0810036			0.0405018	+	0.999179i	$0.487104\pi$
$368$	−9.96303e21	−	2.04711e21i	−1.54413	−	0.317274i
$369$	5.47298e21			0.828896
$370$	3.89064e19	−	7.67296e20i	0.00575846	−	0.113566i
$371$		−	4.19781e21i		−	0.607217i
$372$	1.37816e21	−	1.35548e22i	0.194844	−	1.91637i
$373$			3.13000e21i			0.432533i	0.976334	+	0.216266i	$0.0693880\pi$
$373$			3.13000e21i			0.432533i	−0.976334	+	0.216266i	$0.930612\pi$
$374$	−4.66637e21	−	2.36612e20i	−0.630333	−	0.0319616i
$375$	−2.01469e21			−0.266037
$376$	5.33835e20	−	3.48527e21i	0.0689144	−	0.449925i
$377$	5.08943e20			0.0642344
$378$	5.02294e21	+	2.54693e20i	0.619838	+	0.0314294i
$379$		−	1.31559e22i		−	1.58741i	−0.608305	−	0.793704i	$-0.708150\pi$
$379$		−	1.31559e22i		−	1.58741i	0.608305	−	0.793704i	$-0.291850\pi$
$380$	−1.39882e21	−	1.42222e20i	−0.165044	−	0.0167806i
$381$			1.23601e22i			1.42614i
$382$	1.12325e20	−	2.21524e21i	0.0126748	−	0.249966i
$383$	3.30408e21			0.364637			0.182319	−	0.983239i	$-0.441640\pi$
$383$	3.30408e21			0.364637			0.182319	+	0.983239i	$0.441640\pi$
$384$	1.05400e22	+	3.90289e21i	1.13769	+	0.421280i
$385$	9.51895e20			0.100502
$386$	−6.55488e20	+	1.29273e22i	−0.0676975	+	1.33510i
$387$		−	8.88400e20i		−	0.0897564i
$388$	4.25774e21	+	4.32898e20i	0.420833	+	0.0427874i
$389$		−	7.70023e20i		−	0.0744615i	−0.999307	−	0.0372308i	$-0.988146\pi$
$389$		−	7.70023e20i		−	0.0744615i	0.999307	−	0.0372308i	$-0.0118537\pi$
$390$	−8.28435e19	−	4.20065e18i	−0.00783807	−	0.000397436i
$391$	−1.14258e22			−1.05776
$392$	1.03411e20	−	6.75142e20i	0.00936771	−	0.0611594i
$393$	1.00809e22			0.893637
$394$	−5.55969e21	−	2.81909e20i	−0.482317	−	0.0244563i
$395$			1.40986e21i			0.119701i
$396$	5.40222e20	−	5.31331e21i	0.0448914	−	0.441526i
$397$		−	5.29693e21i		−	0.430829i	−0.976523	−	0.215415i	$-0.930890\pi$
$397$		−	5.29693e21i		−	0.430829i	0.976523	−	0.215415i	$-0.0691103\pi$
$398$	−4.63320e20	+	9.13740e21i	−0.0368871	+	0.727472i
$399$	−2.26740e22			−1.76709
$400$	1.26827e22	+	2.60593e21i	0.967616	+	0.198817i
$401$	−4.56356e21			−0.340861			−0.170430	−	0.985370i	$-0.554516\pi$
$401$	−4.56356e21			−0.340861			−0.170430	+	0.985370i	$0.554516\pi$
$402$	−5.56585e20	+	1.09767e22i	−0.0407015	+	0.802697i
$403$		−	1.30041e21i		−	0.0931082i
$404$	−5.63862e20	+	5.54583e21i	−0.0395304	+	0.388799i
$405$			2.00741e21i			0.137806i
$406$	1.57619e22	+	7.99222e20i	1.05959	+	0.0537274i
$407$	1.47275e22			0.969567
$408$	1.24803e22	+	1.91159e21i	0.804662	+	0.123249i
$409$	−1.58699e22			−1.00214			−0.501069	−	0.865407i	$-0.667060\pi$
$409$	−1.58699e22			−1.00214			−0.501069	+	0.865407i	$0.667060\pi$
$410$	3.12937e21	+	1.58678e20i	0.193551	+	0.00981415i
$411$			2.30904e22i			1.39887i
$412$	−1.60796e22	−	1.63486e21i	−0.954220	−	0.0970186i
$413$			1.61509e22i			0.938906i
$414$	6.61380e20	−	1.30434e22i	0.0376659	−	0.742830i
$415$	−2.94402e21			−0.164260
$416$	1.03851e21	+	2.68843e20i	0.0567699	+	0.0146962i
$417$	−2.09318e22			−1.12111
$418$	1.36491e21	−	2.69182e22i	0.0716320	−	1.41270i
$419$		−	2.63907e21i		−	0.135716i	−0.997695	−	0.0678581i	$-0.978383\pi$
$419$		−	2.63907e21i		−	0.135716i	0.997695	−	0.0678581i	$-0.0216165\pi$
$420$	−2.55906e21	−	2.60187e20i	−0.128962	−	0.0131120i
$421$		−	1.44643e22i		−	0.714329i	−0.934041	−	0.357165i	$-0.883743\pi$
$421$		−	1.44643e22i		−	0.714329i	0.934041	−	0.357165i	$-0.116257\pi$
$422$	2.76203e22	+	1.40051e21i	1.33682	+	0.0677847i
$423$	4.52743e21			0.214762
$424$	−1.33287e22	−	2.04154e21i	−0.619695	−	0.0949178i
$425$	1.45449e22			0.662832
$426$	−3.32890e22	−	1.68795e21i	−1.48703	−	0.0754010i
$427$		−	6.12866e21i		−	0.268367i
$428$	−8.12526e20	+	7.99155e21i	−0.0348791	+	0.343051i
$429$		−	1.59010e21i		−	0.0669174i
$430$	2.57573e19	−	5.07974e20i	0.00106272	−	0.0209585i
$431$	1.52835e22			0.618253			0.309127	−	0.951021i	$-0.399963\pi$
$431$	1.52835e22			0.618253			0.309127	+	0.951021i	$0.399963\pi$
$432$	3.25152e21	−	1.58248e22i	0.128966	−	0.627661i
$433$	−2.10323e21			−0.0817975			−0.0408988	−	0.999163i	$-0.513022\pi$
$433$	−2.10323e21			−0.0817975			−0.0408988	+	0.999163i	$0.513022\pi$
$434$	2.04211e21	−	4.02736e22i	0.0778782	−	1.53588i
$435$			3.92000e21i			0.146598i
$436$	−4.81488e21	+	4.73564e22i	−0.176584	+	1.73678i
$437$		−	6.59107e22i		−	2.37063i
$438$	8.18964e21	+	4.15263e20i	0.288891	+	0.0146485i
$439$	3.28337e22			1.13598			0.567991	−	0.823035i	$-0.307721\pi$
$439$	3.28337e22			1.13598			0.567991	+	0.823035i	$0.307721\pi$
$440$	4.62939e20	−	3.02241e21i	0.0157100	−	0.102567i
$441$	8.77020e20			0.0291932
$442$	1.20353e21	+	6.10260e19i	0.0392977	+	0.00199262i
$443$			9.12162e21i			0.292173i	0.989272	+	0.146087i	$0.0466678\pi$
$443$			9.12162e21i			0.292173i	−0.989272	+	0.146087i	$0.953332\pi$
$444$	−3.95933e22	−	4.02557e21i	−1.24413	−	0.126495i
$445$		−	4.32156e21i		−	0.133223i
$446$	−9.81937e20	+	1.93653e22i	−0.0296987	+	0.585705i
$447$	−1.27605e22			−0.378663
$448$	3.17404e22	+	9.95687e21i	0.924165	+	0.289908i
$449$	2.31577e22			0.661610			0.330805	−	0.943699i	$-0.392680\pi$
$449$	2.31577e22			0.661610			0.330805	+	0.943699i	$0.392680\pi$
$450$	−8.41923e20	+	1.66040e22i	−0.0236029	+	0.465487i
$451$			6.00654e22i			1.65243i
$452$	−8.26669e21	−	8.40501e20i	−0.223180	−	0.0226914i
$453$		−	3.44598e22i		−	0.913014i
$454$	−3.06465e22	−	1.55396e21i	−0.796904	−	0.0404077i
$455$	−2.45508e20			−0.00626570
$456$	−1.10271e22	+	7.19935e22i	−0.276224	+	1.80340i
$457$	3.81496e22			0.937999			0.468999	−	0.883198i	$-0.344615\pi$
$457$	3.81496e22			0.937999			0.468999	+	0.883198i	$0.344615\pi$
$458$	−7.85479e22	−	3.98284e21i	−1.89574	−	0.0961250i
$459$		−	1.81482e22i		−	0.429958i
$460$	7.56335e20	−	7.43888e21i	0.0175903	−	0.173008i
$461$			6.60861e22i			1.50887i	0.656373	+	0.754436i	$0.272090\pi$
$461$			6.60861e22i			1.50887i	−0.656373	+	0.754436i	$0.727910\pi$
$462$	2.49703e21	−	4.92454e22i	0.0559715	−	1.10385i
$463$	−6.02518e22			−1.32596			−0.662981	−	0.748636i	$-0.730709\pi$
$463$	−6.02518e22			−1.32596			−0.662981	+	0.748636i	$0.730709\pi$
$464$	1.02032e22	−	4.96578e22i	0.220462	−	1.07296i
$465$	1.00161e22			0.212494
$466$	−8.79372e20	+	1.73426e22i	−0.0183186	+	0.361271i
$467$		−	3.05437e21i		−	0.0624782i	−0.999512	−	0.0312391i	$-0.990055\pi$
$467$		−	3.05437e21i		−	0.0624782i	0.999512	−	0.0312391i	$-0.00994534\pi$
$468$	−1.39331e20	+	1.37039e21i	−0.00279872	+	0.0275266i
$469$			3.25298e22i			0.641670i
$470$	2.58872e21	+	1.31263e20i	0.0501479	+	0.00254279i
$471$	7.72520e22			1.46971
$472$	5.12817e22	+	7.85475e21i	0.958199	+	0.146766i
$473$	9.75010e21			0.178933
$474$	7.29375e22	+	3.69836e21i	1.31473	+	0.0666643i
$475$			8.39030e22i			1.48553i
$476$	3.71773e22	+	3.77993e21i	0.646575	+	0.0657393i
$477$		−	1.73142e22i		−	0.295799i
$478$	−1.15122e20	+	2.27039e21i	−0.00193206	+	0.0381033i
$479$	−8.21420e22			−1.35430			−0.677148	−	0.735847i	$-0.736784\pi$
$479$	−8.21420e22			−1.35430			−0.677148	+	0.735847i	$0.736784\pi$
$480$	−2.07069e21	+	7.99887e21i	−0.0335402	+	0.129562i
$481$	−3.79846e21			−0.0604469
$482$	2.76421e20	−	5.45146e21i	0.00432187	−	0.0852341i
$483$		−	1.20580e23i		−	1.85235i
$484$	−7.59705e21	−	7.72416e20i	−0.114673	−	0.0116591i
$485$			3.14617e21i			0.0466635i
$486$	5.99424e22	+	3.03943e21i	0.873627	+	0.0442980i
$487$	4.20663e22			0.602473			0.301237	−	0.953549i	$-0.402601\pi$
$487$	4.20663e22			0.602473			0.301237	+	0.953549i	$0.402601\pi$
$488$	−1.94594e22	−	2.98058e21i	−0.273881	−	0.0419500i
$489$	−1.25140e23			−1.73090
$490$	5.01467e20	+	2.54274e19i	0.00681673	+	0.000345648i
$491$		−	8.80209e22i		−	1.17596i	−0.808875	−	0.587980i	$-0.799923\pi$
$491$		−	8.80209e22i		−	1.17596i	0.808875	−	0.587980i	$-0.200077\pi$
$492$	1.64181e22	−	1.61479e23i	0.215585	−	2.12037i
$493$		−	5.69487e22i		−	0.734996i
$494$	−3.52032e20	+	6.94263e21i	−0.00446584	+	0.0880735i
$495$	3.92617e21			0.0489581
$496$	−1.26882e23	−	2.60705e22i	−1.55527	−	0.319562i
$497$	−9.86525e22			−1.18872
$498$	−7.72281e21	+	1.52306e23i	−0.0914800	+	1.80413i
$499$			2.77007e22i			0.322579i	0.986907	+	0.161290i	$0.0515654\pi$
$499$			2.77007e22i			0.322579i	−0.986907	+	0.161290i	$0.948435\pi$
$500$	−1.93746e21	+	1.90558e22i	−0.0221813	+	0.218163i
$501$			5.36912e22i			0.604341i
$502$	−2.35439e21	−	1.19381e20i	−0.0260553	−	0.00132116i
$503$	−1.28825e23			−1.40176			−0.700878	−	0.713281i	$-0.747208\pi$
$503$	−1.28825e23			−1.40176			−0.700878	+	0.713281i	$0.747208\pi$
$504$	−6.46707e21	+	4.22219e22i	−0.0691908	+	0.451729i
$505$	−4.09798e21			−0.0431115
$506$	1.43151e23	+	7.25858e21i	1.48086	+	0.0750883i
$507$		−	1.18850e23i		−	1.20902i
$508$	1.16907e23	+	1.18863e22i	1.16950	+	0.118907i
$509$			1.41955e23i			1.39653i	0.715839	+	0.698265i	$0.246044\pi$
$509$			1.41955e23i			1.39653i	−0.715839	+	0.698265i	$0.753956\pi$
$510$	−4.70036e20	+	9.26986e21i	−0.00454763	+	0.0896864i
$511$	2.42702e22			0.230938
$512$	4.70511e22	−	9.59384e22i	0.440327	−	0.897838i
$513$	1.04689e23			0.963615
$514$	4.13254e21	−	8.15002e22i	0.0374137	−	0.737857i
$515$		−	1.18817e22i		−	0.105808i
$516$	−2.62120e22	−	2.66506e21i	−0.229603	−	0.0233445i
$517$			4.96881e22i			0.428137i
$518$	−1.17638e23	−	5.96493e21i	−0.997112	−	0.0505595i
$519$	2.59294e23			2.16207
$520$	−1.19399e20	+	7.79527e20i	−0.000979429	+	0.00639444i
$521$	−1.60040e22			−0.129154			−0.0645772	−	0.997913i	$-0.520570\pi$
$521$	−1.60040e22			−0.129154			−0.0645772	+	0.997913i	$0.520570\pi$
$522$	6.50113e22	+	3.29645e21i	0.516166	+	0.0261727i
$523$			4.32799e22i			0.338082i	0.985609	+	0.169041i	$0.0540670\pi$
$523$			4.32799e22i			0.338082i	−0.985609	+	0.169041i	$0.945933\pi$
$524$	9.69442e21	−	9.53488e22i	0.0745085	−	0.732823i
$525$			1.53496e23i			1.16076i
$526$	−8.18165e21	+	1.61355e23i	−0.0608783	+	1.20062i
$527$	−1.45511e23			−1.06538
$528$	−1.55147e23	−	3.18782e22i	−1.11778	−	0.229671i
$529$	2.09461e23			1.48501
$530$	5.01989e20	−	9.90001e21i	0.00350227	−	0.0690702i
$531$			6.66158e22i			0.457376i
$532$	−2.18048e22	+	2.14460e23i	−0.147334	+	1.44909i
$533$		−	1.54918e22i		−	0.103020i
$534$	−2.23572e23	−	1.13364e22i	−1.46324	−	0.0741950i
$535$	−5.90519e21			−0.0380388
$536$	1.03287e23	+	1.58204e22i	0.654855	+	0.100303i
$537$	4.76938e22			0.297633
$538$	−1.78193e23	−	9.03542e21i	−1.09456	−	0.0555007i
$539$			9.62521e21i			0.0581977i
$540$	1.18155e22	+	1.20132e21i	0.0703244	+	0.00715011i
$541$		−	2.24293e23i		−	1.31413i	−0.753833	−	0.657066i	$-0.771797\pi$
$541$		−	2.24293e23i		−	1.31413i	0.753833	−	0.657066i	$-0.228203\pi$
$542$	−7.19358e21	+	1.41869e23i	−0.0414907	+	0.818262i
$543$	−2.45693e23			−1.39507
$544$	3.00825e22	−	1.16205e23i	0.168160	−	0.649584i
$545$	−3.49931e22			−0.192580
$546$	−6.44023e20	+	1.27011e22i	−0.00348950	+	0.0688185i
$547$		−	7.07789e22i		−	0.377582i	−0.982017	−	0.188791i	$-0.939543\pi$
$547$		−	7.07789e22i		−	0.377582i	0.982017	−	0.188791i	$-0.0604569\pi$
$548$	2.18398e23	+	2.22053e22i	1.14714	+	0.116633i
$549$		−	2.52781e22i		−	0.130732i
$550$	−1.82228e23	−	9.24002e21i	−0.927965	−	0.0470533i
$551$	3.28512e23			1.64726
$552$	−3.82859e23	−	5.86421e22i	−1.89041	−	0.289552i
$553$	2.16152e23			1.05098
$554$	2.65194e23	+	1.34469e22i	1.26979	+	0.0643857i
$555$		−	2.92566e22i		−	0.137954i
$556$	−2.01294e22	+	1.97981e23i	−0.0934748	+	0.919365i
$557$		−	2.94239e23i		−	1.34565i	−0.739803	−	0.672823i	$-0.765081\pi$
$557$		−	2.94239e23i		−	1.34565i	0.739803	−	0.672823i	$-0.234919\pi$
$558$	8.42284e21	−	1.66112e23i	0.0379374	−	0.748186i
$559$	−2.51470e21			−0.0111554
$560$	−4.92191e21	+	2.39544e22i	−0.0215048	+	0.104661i
$561$	−1.77926e23			−0.765696
$562$	2.18025e22	−	4.29980e23i	0.0924162	−	1.82259i
$563$		−	9.39183e22i		−	0.392129i	−0.980591	−	0.196064i	$-0.937184\pi$
$563$		−	9.39183e22i		−	0.392129i	0.980591	−	0.196064i	$-0.0628162\pi$
$564$	1.35816e22	−	1.33580e23i	0.0558569	−	0.549377i
$565$		−	6.10850e21i		−	0.0247470i
$566$	2.37351e23	+	1.20351e22i	0.947221	+	0.0480297i
$567$	3.07766e23			1.20994
$568$	−4.79781e22	+	3.13237e23i	−0.185816	+	1.21314i
$569$	−7.54187e22			−0.287756			−0.143878	−	0.989595i	$-0.545957\pi$
$569$	−7.54187e22			−0.287756			−0.143878	+	0.989595i	$0.545957\pi$
$570$	−5.34738e22	−	2.71144e21i	−0.201004	−	0.0101921i
$571$			3.40566e23i			1.26123i	0.776095	+	0.630616i	$0.217198\pi$
$571$			3.40566e23i			1.26123i	−0.776095	+	0.630616i	$0.782802\pi$
$572$	−1.50398e22	−	1.52915e21i	−0.0548753	−	0.00557935i
$573$		−	8.44659e22i		−	0.303646i
$574$	2.43276e22	−	4.79779e23i	0.0861685	−	1.69938i
$575$	−4.46194e23			−1.55721
$576$	1.30916e23	+	4.10679e22i	0.450196	+	0.141225i
$577$	−4.78683e23			−1.62201			−0.811006	−	0.585038i	$-0.801079\pi$
$577$	−4.78683e23			−1.62201			−0.811006	+	0.585038i	$0.801079\pi$
$578$	−8.33801e21	+	1.64439e23i	−0.0278404	+	0.549057i
$579$			4.92910e23i			1.62181i
$580$	3.70769e22	+	3.76973e21i	0.120217	+	0.0122228i
$581$			4.51362e23i			1.44221i
$582$	1.62764e23	+	8.25310e21i	0.512523	+	0.0259879i
$583$	1.90022e23			0.589685
$584$	1.18034e22	−	7.70615e22i	0.0360993	−	0.235683i
$585$	−1.01262e21			−0.00305226
$586$	2.52412e23	+	1.27988e22i	0.749861	+	0.0380224i
$587$			1.81919e22i			0.0532666i	0.999645	+	0.0266333i	$0.00847865\pi$
$587$			1.81919e22i			0.0532666i	−0.999645	+	0.0266333i	$0.991521\pi$
$588$	2.63092e21	−	2.58762e22i	0.00759277	−	0.0746782i
$589$		−	8.39390e23i		−	2.38772i
$590$	−1.93139e21	+	3.80900e22i	−0.00541535	+	0.106799i
$591$	−2.11988e23			−0.585893
$592$	−7.61510e22	+	3.70618e23i	−0.207463	+	1.00970i
$593$	−9.82089e22			−0.263746			−0.131873	−	0.991267i	$-0.542099\pi$
$593$	−9.82089e22			−0.263746			−0.131873	+	0.991267i	$0.542099\pi$
$594$	−1.15291e22	+	2.27373e23i	−0.0305220	+	0.601941i
$595$			2.74714e22i			0.0716946i
$596$	−1.22713e22	+	1.20694e23i	−0.0315717	+	0.310521i
$597$			3.48405e23i			0.883695i
$598$	−3.69207e22	−	1.87210e21i	−0.0923231	−	0.00468132i
$599$	2.49917e22			0.0616124			0.0308062	−	0.999525i	$-0.490193\pi$
$599$	2.49917e22			0.0616124			0.0308062	+	0.999525i	$0.490193\pi$
$600$	4.87372e23	+	7.46502e22i	1.18461	+	0.181445i
$601$	−1.67913e23			−0.402394			−0.201197	−	0.979551i	$-0.564483\pi$
$601$	−1.67913e23			−0.402394			−0.201197	+	0.979551i	$0.564483\pi$
$602$	−7.78800e22	−	3.94897e21i	−0.184016	−	0.00933070i
$603$			1.34172e23i			0.312582i
$604$	−3.25934e23	−	3.31388e22i	−0.748714	−	0.0761242i
$605$		−	5.61369e21i		−	0.0127153i
$606$	−1.07499e22	+	2.12005e23i	−0.0240097	+	0.473510i
$607$	−3.57610e23			−0.787600			−0.393800	−	0.919196i	$-0.628840\pi$
$607$	−3.57610e23			−0.787600			−0.393800	+	0.919196i	$0.628840\pi$
$608$	6.70339e23	+	1.73533e23i	1.45584	+	0.376878i
$609$	6.00994e23			1.28713
$610$	7.32887e20	−	1.44537e22i	0.00154787	−	0.0305263i
$611$		−	1.28153e22i		−	0.0266919i
$612$	1.53341e23	+	1.55906e22i	0.314971	+	0.0320241i
$613$		−	5.01122e23i		−	1.01515i	−0.861608	−	0.507575i	$-0.830542\pi$
$613$		−	5.01122e23i		−	1.01515i	0.861608	−	0.507575i	$-0.169458\pi$
$614$	1.39313e23	+	7.06397e21i	0.278330	+	0.0141129i
$615$	1.19322e23			0.235115
$616$	−4.63381e23	−	7.09755e22i	−0.900538	−	0.137934i
$617$	−1.62324e23			−0.311141			−0.155571	−	0.987825i	$-0.549722\pi$
$617$	−1.62324e23			−0.311141			−0.155571	+	0.987825i	$0.549722\pi$
$618$	−6.14688e23	−	3.11683e22i	−1.16212	−	0.0589266i
$619$		−	3.38341e23i		−	0.630934i	−0.948937	−	0.315467i	$-0.897839\pi$
$619$		−	3.38341e23i		−	0.630934i	0.948937	−	0.315467i	$-0.102161\pi$
$620$	9.63212e21	−	9.47361e22i	0.0177171	−	0.174255i
$621$			5.56734e23i			1.01011i
$622$	3.85976e22	−	7.61205e23i	0.0690783	−	1.36233i
$623$	−6.62559e23			−1.16970
$624$	4.00149e22	+	8.22188e21i	0.0696871	+	0.0143186i
$625$	5.60912e23			0.963640
$626$	−5.29433e21	+	1.04413e23i	−0.00897283	+	0.176958i
$627$		−	1.02638e24i		−	1.71607i
$628$	7.42906e22	−	7.30681e23i	0.122540	−	1.20523i
$629$			4.25033e23i			0.691659i
$630$	−3.13607e22	−	1.59017e21i	−0.0503490	−	0.00255299i
$631$	1.07823e24			1.70789			0.853947	−	0.520359i	$-0.174202\pi$
$631$	1.07823e24			1.70789			0.853947	+	0.520359i	$0.174202\pi$
$632$	1.05122e23	−	6.86316e23i	0.164285	−	1.07258i
$633$	1.05315e24			1.62390
$634$	−9.50684e23	−	4.82053e22i	−1.44636	−	0.0733392i
$635$			8.63862e22i			0.129678i
$636$	−5.10851e23	−	5.19398e22i	−0.756673	−	0.0769334i
$637$		−	2.48249e21i		−	0.00362829i
$638$	−3.61783e22	+	7.13492e23i	−0.0521761	+	1.02900i
$639$	−4.06900e23			−0.579069
$640$	7.36652e22	+	2.72777e22i	0.103450	+	0.0383070i
$641$	−8.18063e23			−1.13369			−0.566844	−	0.823825i	$-0.691836\pi$
$641$	−8.18063e23			−1.13369			−0.566844	+	0.823825i	$0.691836\pi$
$642$	−1.54906e22	+	3.05500e23i	−0.0211847	+	0.417795i
$643$			1.03008e24i			1.39020i	0.718913	+	0.695100i	$0.244640\pi$
$643$			1.03008e24i			1.39020i	−0.718913	+	0.695100i	$0.755360\pi$
$644$	−1.14049e24	−	1.15957e23i	−1.51901	−	0.154443i
$645$		−	1.93688e22i		−	0.0254593i
$646$	7.76853e23	+	3.93910e22i	1.00777	+	0.0511000i
$647$	1.16066e24			1.48600			0.742998	−	0.669293i	$-0.233403\pi$
$647$	1.16066e24			1.48600			0.742998	+	0.669293i	$0.233403\pi$
$648$	1.49677e23	−	9.77206e23i	0.189134	−	1.23481i
$649$	−7.31102e23			−0.911797
$650$	4.69994e22	+	2.38314e21i	0.0578533	+	0.00293350i
$651$		−	1.53561e24i		−	1.86571i
$652$	−1.20343e23	+	1.18363e24i	−0.144317	+	1.41942i
$653$			1.25728e24i			1.48823i	0.668054	+	0.744113i	$0.267128\pi$
$653$			1.25728e24i			1.48823i	−0.668054	+	0.744113i	$0.732872\pi$
$654$	−9.17946e22	+	1.81033e24i	−0.107252	+	2.11518i
$655$	7.04561e22			0.0812582
$656$	−1.51154e24	−	3.10577e23i	−1.72083	−	0.353579i
$657$	1.00104e23			0.112499
$658$	2.01246e22	−	3.96889e23i	0.0223258	−	0.440300i
$659$		−	1.29456e24i		−	1.41774i	−0.705338	−	0.708871i	$-0.749205\pi$
$659$		−	1.29456e24i		−	1.41774i	0.705338	−	0.708871i	$-0.250795\pi$
$660$	1.17779e22	−	1.15840e23i	0.0127334	−	0.125238i
$661$		−	8.22393e23i		−	0.877742i	−0.898550	−	0.438871i	$-0.855378\pi$
$661$		−	8.22393e23i		−	0.877742i	0.898550	−	0.438871i	$-0.144622\pi$
$662$	1.11473e24	+	5.65232e22i	1.17456	+	0.0595572i
$663$	4.58900e22			0.0477367
$664$	1.43314e24	+	2.19513e23i	1.47184	+	0.225440i
$665$	−1.58471e23			−0.160681
$666$	−4.85207e23	−	2.46029e22i	−0.485731	−	0.0246294i
$667$			1.74702e24i			1.72675i
$668$	5.07832e23	+	5.16329e22i	0.495588	+	0.0503880i
$669$			7.38391e23i			0.711483i
$670$	−3.89003e21	+	7.67174e22i	−0.00370098	+	0.0729891i
$671$	2.77425e23			0.260618
$672$	1.22635e24	+	3.17468e23i	1.13756	+	0.294484i
$673$	1.06449e24			0.975016			0.487508	−	0.873118i	$-0.337906\pi$
$673$	1.06449e24			0.975016			0.487508	+	0.873118i	$0.337906\pi$
$674$	−2.92470e22	+	5.76798e23i	−0.0264529	+	0.521692i
$675$		−	7.08711e23i		−	0.632976i
$676$	−1.12413e24	−	1.14294e23i	−0.991450	−	0.100804i
$677$			1.14609e24i			0.998198i	0.866545	+	0.499099i	$0.166336\pi$
$677$			1.14609e24i			0.998198i	−0.866545	+	0.499099i	$0.833664\pi$
$678$	−3.16018e23	−	1.60240e22i	−0.271806	−	0.0137822i
$679$	4.82355e23			0.409707
$680$	8.72260e22	+	1.33603e22i	0.0731678	+	0.0112070i
$681$	−1.16854e24			−0.968037
$682$	1.82306e24	+	9.24399e22i	1.49154	+	0.0756297i
$683$		−	1.21554e24i		−	0.982186i	−0.871107	−	0.491093i	$-0.836598\pi$
$683$		−	1.21554e24i		−	0.982186i	0.871107	−	0.491093i	$-0.163402\pi$
$684$	−8.99357e22	+	8.84556e23i	−0.0717720	+	0.705909i
$685$			1.61381e23i			0.127199i
$686$	6.69051e22	−	1.31947e24i	0.0520840	−	1.02718i
$687$	−2.99500e24			−2.30284
$688$	−5.04143e22	+	2.45361e23i	−0.0382871	+	0.186339i
$689$	−4.90095e22			−0.0367635
$690$	1.44194e22	−	2.84372e23i	0.0106839	−	0.210703i
$691$			1.76793e24i			1.29390i	0.762531	+	0.646952i	$0.223957\pi$
$691$			1.76793e24i			1.29390i	−0.762531	+	0.646952i	$0.776043\pi$
$692$	2.49354e23	−	2.45251e24i	0.180266	−	1.77300i
$693$		−	6.01940e23i		−	0.429854i
$694$	−5.59037e23	−	2.83465e22i	−0.394353	−	0.0199960i
$695$	−1.46294e23			−0.101943
$696$	2.92284e23	−	1.90825e24i	0.201200	−	1.31358i
$697$	−1.73347e24			−1.17879
$698$	−1.95751e24	−	9.92571e22i	−1.31502	−	0.0666792i
$699$			6.61265e23i			0.438854i
$700$	1.45182e24	+	1.47611e23i	0.951875	+	0.0967802i
$701$		−	1.00329e24i		−	0.649868i	−0.945737	−	0.324934i	$-0.894658\pi$
$701$		−	1.00329e24i		−	0.649868i	0.945737	−	0.324934i	$-0.105342\pi$
$702$	2.97354e21	−	5.86430e22i	0.00190287	−	0.0375276i
$703$	−2.45183e24			−1.55014
$704$	−4.50717e23	+	1.43679e24i	−0.281537	+	0.897481i
$705$	9.87066e22			0.0609170
$706$	7.21069e22	−	1.42206e24i	0.0439680	−	0.867118i
$707$			6.28281e23i			0.378520i
$708$	1.96548e24	+	1.99837e23i	1.17000	+	0.118958i
$709$		−	2.79760e24i		−	1.64548i	−0.568418	−	0.822740i	$-0.692444\pi$
$709$		−	2.79760e24i		−	1.64548i	0.568418	−	0.822740i	$-0.307556\pi$
$710$	−2.32660e23	−	1.17972e22i	−0.135215	−	0.00685620i
$711$	8.91536e23			0.511973
$712$	−3.22225e23	+	2.10373e24i	−0.182844	+	1.19374i
$713$	4.46385e24			2.50293
$714$	1.42121e24	+	7.20636e22i	0.787449	+	0.0399283i
$715$		−	1.11134e22i		−	0.00608479i
$716$	4.58655e22	−	4.51107e23i	0.0248156	−	0.244072i
$717$			8.65688e22i			0.0462859i
$718$	1.44910e23	−	2.85786e24i	0.0765670	−	1.51002i
$719$	1.18105e24			0.616699			0.308349	−	0.951273i	$-0.400223\pi$
$719$	1.18105e24			0.616699			0.308349	+	0.951273i	$0.400223\pi$
$720$	−2.03008e22	+	9.88017e22i	−0.0104758	+	0.0509845i
$721$	−1.82164e24			−0.928994
$722$	−1.26753e23	+	2.49976e24i	−0.0638838	+	1.25989i
$723$		−	2.07862e23i		−	0.103538i
$724$	−2.36275e23	+	2.32387e24i	−0.116316	+	1.14402i
$725$		−	2.22392e24i		−	1.08205i
$726$	−2.90419e23	−	1.47259e22i	−0.139657	−	0.00708145i
$727$	2.11470e24			1.00509			0.502547	−	0.864550i	$-0.332396\pi$
$727$	2.11470e24			1.00509			0.502547	+	0.864550i	$0.332396\pi$
$728$	1.19513e23	+	1.83057e22i	0.0561434	+	0.00859942i
$729$	−4.04830e23			−0.187970
$730$	5.72381e22	+	2.90231e21i	0.0262689	+	0.00133199i
$731$			2.81385e23i			0.127645i
$732$	−7.45825e23	−	7.58304e22i	−0.334420	−	0.0340016i
$733$			1.52276e24i			0.674912i	0.941341	+	0.337456i	$0.109566\pi$
$733$			1.52276e24i			0.674912i	−0.941341	+	0.337456i	$0.890434\pi$
$734$	9.36314e21	−	1.84656e23i	0.00410209	−	0.0808996i
$735$	1.91207e22			0.00828061
$736$	−9.22843e23	+	3.56484e24i	−0.395063	+	1.52609i
$737$	−1.47252e24			−0.623143
$738$	1.00341e23	−	1.97889e24i	0.0419760	−	0.827832i
$739$			2.35464e24i			0.973750i	0.873472	+	0.486875i	$0.161863\pi$
$739$			2.35464e24i			0.973750i	−0.873472	+	0.486875i	$0.838137\pi$
$740$	−2.76721e23	−	2.81351e22i	−0.113129	−	0.0115021i
$741$			2.64719e23i			0.106987i
$742$	−1.51782e24	−	7.69623e22i	−0.606438	−	0.0307500i
$743$	1.71431e24			0.677150			0.338575	−	0.940939i	$-0.390055\pi$
$743$	1.71431e24			0.677150			0.338575	+	0.940939i	$0.390055\pi$
$744$	−4.87581e24	−	7.46822e23i	−1.90405	−	0.291640i
$745$	−8.91841e22			−0.0344318
$746$	1.13173e24	+	5.73852e22i	0.431978	+	0.0219038i
$747$			1.86168e24i			0.702554i
$748$	−1.71106e23	+	1.68290e24i	−0.0638412	+	0.627906i
$749$			9.05354e23i			0.333982i
$750$	−3.69372e22	+	7.28460e23i	−0.0134724	+	0.265696i
$751$	−3.84431e23			−0.138637			−0.0693184	−	0.997595i	$-0.522082\pi$
$751$	−3.84431e23			−0.138637			−0.0693184	+	0.997595i	$0.522082\pi$
$752$	−1.25040e24	−	2.56920e23i	−0.445858	−	0.0916106i
$753$	−8.97716e22			−0.0316506
$754$	9.33093e21	−	1.84021e23i	0.00325288	−	0.0641520i
$755$		−	2.40843e23i		−	0.0830203i
$756$	1.84181e23	−	1.81150e24i	0.0627782	−	0.617451i
$757$		−	1.62822e24i		−	0.548781i	−0.961618	−	0.274390i	$-0.911524\pi$
$757$		−	1.62822e24i		−	0.548781i	0.961618	−	0.274390i	$-0.0884760\pi$
$758$	−4.75685e24	−	2.41200e23i	−1.58537	−	0.0803876i
$759$	5.45827e24			1.79887
$760$	−7.70698e22	+	5.03169e23i	−0.0251170	+	0.163983i
$761$	2.88866e24			0.930950			0.465475	−	0.885061i	$-0.345884\pi$
$761$	2.88866e24			0.930950			0.465475	+	0.885061i	$0.345884\pi$
$762$	4.46911e24	+	2.26610e23i	1.42431	+	0.0722207i
$763$			5.36496e24i			1.69086i
$764$	−7.98912e23	−	8.12280e22i	−0.249004	−	0.0253170i
$765$			1.13308e23i			0.0349252i
$766$	6.05768e22	−	1.19467e24i	0.0184655	−	0.364169i
$767$	1.88562e23			0.0568453
$768$	1.60443e24	−	3.73944e24i	0.478354	−	1.11490i
$769$	3.36233e24			0.991440			0.495720	−	0.868482i	$-0.334904\pi$
$769$	3.36233e24			0.991440			0.495720	+	0.868482i	$0.334904\pi$
$770$	1.74520e22	−	3.44181e23i	0.00508948	−	0.100373i
$771$		−	3.10757e24i		−	0.896310i
$772$	4.66214e24	+	4.74015e23i	1.32996	+	0.135221i
$773$		−	7.95637e23i		−	0.224486i	−0.993681	−	0.112243i	$-0.964197\pi$
$773$		−	7.95637e23i		−	0.224486i	0.993681	−	0.112243i	$-0.0358035\pi$
$774$	−3.21222e23	−	1.62879e22i	−0.0896412	−	0.00454534i
$775$	−5.68239e24			−1.56844
$776$	2.34586e23	−	1.53155e24i	0.0640438	−	0.418126i
$777$	−4.48548e24			−1.21124
$778$	−2.78420e23	−	1.41175e22i	−0.0743660	−	0.00377079i
$779$		−	9.99964e24i		−	2.64190i
$780$	−3.03769e21	+	2.98770e22i	−0.000793853	+	0.00780789i
$781$		−	4.46569e24i		−	1.15440i
$782$	−2.09480e23	+	4.13128e24i	−0.0535656	+	1.05640i
$783$	−2.77488e24			−0.701890
$784$	−2.42218e23	−	4.97686e22i	−0.0606065	−	0.0124529i
$785$	5.39922e23			0.133641
$786$	1.84822e23	−	3.64498e24i	0.0452545	−	0.892490i
$787$		−	1.65941e24i		−	0.401947i	−0.979597	−	0.200973i	$-0.935590\pi$
$787$		−	1.65941e24i		−	0.401947i	0.979597	−	0.200973i	$-0.0644104\pi$
$788$	−2.03862e23	+	2.00507e24i	−0.0488498	+	0.480459i
$789$			6.15240e24i			1.45844i
$790$	5.09767e23	+	2.58482e22i	0.119548	+	0.00606178i
$791$	−9.36524e23			−0.217280
$792$	−1.91125e24	−	2.92744e23i	−0.438686	−	0.0671930i
$793$	−7.15522e22			−0.0162480
$794$	−1.91523e24	−	9.71137e22i	−0.430276	−	0.0218176i
$795$		−	3.77483e23i		−	0.0839028i
$796$	3.29535e24	+	3.35049e23i	0.724671	+	0.0736796i
$797$			4.56354e24i			0.992902i	0.868065	+	0.496451i	$0.165364\pi$
$797$			4.56354e24i			0.992902i	−0.868065	+	0.496451i	$0.834636\pi$
$798$	−4.15704e23	+	8.19833e24i	−0.0894869	+	1.76482i
$799$	−1.43398e24			−0.305419
$800$	1.17476e24	−	4.53797e24i	0.247562	−	0.956307i
$801$	−2.73278e24			−0.569807
$802$	−8.36681e22	+	1.65007e24i	−0.0172615	+	0.340423i
$803$			1.09863e24i			0.224270i
$804$	3.95870e24	+	4.02494e23i	0.799606	+	0.0812985i
$805$		−	8.42743e23i		−	0.168434i
$806$	−4.70195e23	−	2.38417e22i	−0.0929887	−	0.00471508i
$807$	−6.79440e24			−1.32962
$808$	1.99489e24	+	3.05555e23i	0.386298	+	0.0591688i
$809$	4.31106e24			0.826080			0.413040	−	0.910713i	$-0.364467\pi$
$809$	4.31106e24			0.826080			0.413040	+	0.910713i	$0.364467\pi$
$810$	7.25829e23	+	3.68038e22i	0.137629	+	0.00697863i
$811$		−	3.06428e24i		−	0.574978i	−0.957784	−	0.287489i	$-0.907180\pi$
$811$		−	3.06428e24i		−	0.574978i	0.957784	−	0.287489i	$-0.0928204\pi$
$812$	5.77956e23	−	5.68445e24i	0.107317	−	1.05551i
$813$			5.40939e24i			0.993982i
$814$	2.70014e23	−	5.32510e24i	0.0490997	−	0.968323i
$815$	−8.74617e23			−0.157390
$816$	9.19995e23	−	4.47751e24i	0.163840	−	0.797389i
$817$	−1.62319e24			−0.286076
$818$	−2.90959e23	+	5.73816e24i	−0.0507491	+	1.00085i
$819$			1.55250e23i			0.0267989i
$820$	1.14747e23	−	1.12859e24i	0.0196031	−	0.192805i
$821$			6.52742e24i			1.10363i	0.833965	+	0.551817i	$0.186065\pi$
$821$			6.52742e24i			1.10363i	−0.833965	+	0.551817i	$0.813935\pi$
$822$	8.34889e24	+	4.23338e23i	1.39707	+	0.0708397i
$823$	2.74865e24			0.455219			0.227610	−	0.973752i	$-0.426909\pi$
$823$	2.74865e24			0.455219			0.227610	+	0.973752i	$0.426909\pi$
$824$	−8.85927e23	+	5.78399e24i	−0.145217	+	0.948083i
$825$	−6.94826e24			−1.12724
$826$	5.83976e24	+	2.96110e23i	0.937701	+	0.0475470i
$827$			1.09366e25i			1.73814i	0.494690	+	0.869069i	$0.335282\pi$
$827$			1.09366e25i			1.73814i	−0.494690	+	0.869069i	$0.664718\pi$
$828$	−4.70405e24	−	4.78276e23i	−0.739970	−	0.0752351i
$829$		−	4.30001e24i		−	0.669509i	−0.942305	−	0.334754i	$-0.891347\pi$
$829$		−	4.30001e24i		−	0.669509i	0.942305	−	0.334754i	$-0.108653\pi$
$830$	−5.39755e22	+	1.06448e24i	−0.00831826	+	0.164049i
$831$	1.01117e25			1.54247
$832$	1.16247e23	−	3.70570e23i	0.0175522	−	0.0559528i
$833$	−2.77781e23			−0.0415164
$834$	−3.83762e23	+	7.56839e24i	−0.0567741	+	1.11968i
$835$			3.75253e23i			0.0549526i
$836$	−9.70792e24	−	9.87035e23i	−1.40725	−	0.143080i
$837$			7.09015e24i			1.01739i
$838$	−9.54220e23	−	4.83846e22i	−0.135542	−	0.00687278i
$839$	4.56684e24			0.642154			0.321077	−	0.947053i	$-0.395955\pi$
$839$	4.56684e24			0.642154			0.321077	+	0.947053i	$0.395955\pi$
$840$	−1.40995e23	+	9.20518e23i	−0.0196259	+	0.128132i
$841$	−1.45037e24			−0.199854
$842$	−5.22990e24	−	2.65187e23i	−0.713413	−	0.0361742i
$843$		−	1.63950e25i		−	2.21399i
$844$	1.01278e24	−	9.96112e24i	0.135395	−	1.33167i
$845$		−	8.30655e23i		−	0.109936i
$846$	8.30056e22	−	1.63700e24i	0.0108757	−	0.214487i
$847$	−8.60662e23			−0.111641
$848$	−9.82535e23	+	4.78188e24i	−0.126178	+	0.614093i
$849$	9.05009e24			1.15063
$850$	2.66664e23	−	5.25904e24i	0.0335664	−	0.661981i
$851$		−	1.30388e25i		−	1.62493i
$852$	−1.22064e24	+	1.20055e25i	−0.150608	+	1.48130i
$853$		−	5.04765e24i		−	0.616627i	−0.951285	−	0.308314i	$-0.900235\pi$
$853$		−	5.04765e24i		−	0.616627i	0.951285	−	0.308314i	$-0.0997647\pi$
$854$	−2.21596e24	−	1.12362e23i	−0.268022	−	0.0135903i
$855$	−6.53625e23			−0.0782739
$856$	2.87464e24	+	4.40305e23i	0.340845	+	0.0522068i
$857$	−3.32276e24			−0.390088			−0.195044	−	0.980795i	$-0.562485\pi$
$857$	−3.32276e24			−0.390088			−0.195044	+	0.980795i	$0.562485\pi$
$858$	−5.74941e23	−	2.91529e22i	−0.0668315	−	0.00338875i
$859$			1.10498e25i			1.27178i	0.771780	+	0.635889i	$0.219367\pi$
$859$			1.10498e25i			1.27178i	−0.771780	+	0.635889i	$0.780633\pi$
$860$	−1.83198e23	−	1.86263e22i	−0.0208778	−	0.00212271i
$861$		−	1.82938e25i		−	2.06432i
$862$	2.80207e23	−	5.52612e24i	0.0313089	−	0.617460i
$863$	2.29368e23			0.0253770			0.0126885	−	0.999919i	$-0.495961\pi$
$863$	2.29368e23			0.0253770			0.0126885	+	0.999919i	$0.495961\pi$
$864$	−5.66221e24	−	1.46580e24i	−0.620325	−	0.160586i
$865$	1.81223e24			0.196597
$866$	−3.85605e22	+	7.60474e23i	−0.00414229	+	0.0816926i
$867$			6.26997e24i			0.666965i
$868$	−1.45245e25	−	1.47675e24i	−1.52997	−	0.155557i
$869$			9.78452e24i			1.02064i
$870$	1.41737e24	+	7.18691e22i	0.146410	+	0.00742383i
$871$	3.79786e23			0.0388494
$872$	1.70346e25	+	2.60917e24i	1.72560	+	0.264309i
$873$	1.98951e24			0.199584
$874$	−2.38316e25	−	1.20840e24i	−2.36759	−	0.120051i
$875$			2.15881e24i			0.212395i
$876$	3.00297e23	−	2.95355e24i	0.0292594	−	0.287779i
$877$		−	1.16909e25i		−	1.12811i	−0.825738	−	0.564054i	$-0.809241\pi$
$877$		−	1.16909e25i		−	1.12811i	0.825738	−	0.564054i	$-0.190759\pi$
$878$	6.01971e23	−	1.18718e25i	0.0575270	−	1.13452i
$879$	9.62437e24			0.910892
$880$	−1.08434e24	−	2.22800e23i	−0.101639	−	0.0208839i
$881$	6.35170e24			0.589651			0.294825	−	0.955551i	$-0.404738\pi$
$881$	6.35170e24			0.589651			0.294825	+	0.955551i	$0.404738\pi$
$882$	1.60792e22	−	3.17108e23i	0.00147837	−	0.0291557i
$883$			5.61888e24i			0.511663i	0.966721	+	0.255831i	$0.0823492\pi$
$883$			5.61888e24i			0.511663i	−0.966721	+	0.255831i	$0.917651\pi$
$884$	4.41308e22	−	4.34046e23i	0.00398013	−	0.0391463i
$885$			1.45235e24i			0.129734i
$886$	3.29814e24	+	1.67235e23i	0.291798	+	0.0147959i
$887$	−1.44844e25			−1.26926			−0.634630	−	0.772816i	$-0.718847\pi$
$887$	−1.44844e25			−1.26926			−0.634630	+	0.772816i	$0.718847\pi$
$888$	−2.18144e24	+	1.42421e25i	−0.189336	+	1.23613i
$889$	1.32443e25			1.13858
$890$	−1.56256e24	−	7.92312e22i	−0.133052	−	0.00674654i
$891$			1.39316e25i			1.17501i
$892$	6.98400e24	+	7.10086e23i	0.583449	+	0.0593211i
$893$		−	8.27203e24i		−	0.684502i
$894$	−2.33950e23	+	4.61386e24i	−0.0191758	+	0.378177i
$895$	3.33336e23			0.0270637
$896$	4.18207e24	−	1.12940e25i	0.336336	−	0.908298i
$897$	−1.40777e24			−0.112149
$898$	4.24572e23	−	8.37323e24i	0.0335045	−	0.660761i
$899$			2.22488e25i			1.73920i
$900$	5.98816e24	+	6.08835e23i	0.463695	+	0.0471453i
$901$			5.48397e24i			0.420663i
$902$	2.17181e25	+	1.10124e24i	1.65031	+	0.0836806i
$903$	−2.96953e24			−0.223533
$904$	−4.55464e23	+	2.97361e24i	−0.0339643	+	0.221744i
$905$	−1.71717e24			−0.126853
$906$	−1.24598e25	−	6.31783e23i	−0.911843	−	0.0462358i
$907$		−	1.33655e25i		−	0.969000i	−0.874791	−	0.484500i	$-0.839001\pi$
$907$		−	1.33655e25i		−	0.969000i	0.874791	−	0.484500i	$-0.160999\pi$
$908$	−1.12374e24	+	1.10525e25i	−0.0807117	+	0.793835i
$909$			2.59140e24i			0.184391i
$910$	−4.50113e21	+	8.87694e22i	−0.000317300	+	0.00625766i
$911$	−6.62275e23			−0.0462522			−0.0231261	−	0.999733i	$-0.507362\pi$
$911$	−6.62275e23			−0.0462522			−0.0231261	+	0.999733i	$0.507362\pi$
$912$	2.58288e25	+	5.30706e24i	1.78710	+	0.367196i
$913$	−2.04317e25			−1.40057
$914$	6.99433e23	−	1.37939e25i	0.0475010	−	0.936795i
$915$		−	5.51112e23i		−	0.0370818i
$916$	−2.88019e24	+	2.83279e25i	−0.192003	+	1.88844i
$917$		−	1.08020e25i		−	0.713450i
$918$	−6.56192e24	−	3.32728e23i	−0.429406	−	0.0217734i
$919$	−1.15477e25			−0.748708			−0.374354	−	0.927286i	$-0.622136\pi$
$919$	−1.15477e25			−0.748708			−0.374354	+	0.927286i	$0.622136\pi$
$920$	−2.67584e24	−	4.09855e23i	−0.171895	−	0.0263290i
$921$	5.31193e24			0.338100
$922$	2.38950e25	+	1.21162e24i	1.50694	+	0.0764106i
$923$			1.15177e24i			0.0719700i
$924$	−1.77601e25	−	1.80572e24i	−1.09960	−	0.111799i
$925$			1.65981e25i			1.01825i
$926$	−1.10465e24	+	2.17855e25i	−0.0671479	+	1.32426i
$927$	−7.51350e24			−0.452548
$928$	−1.77679e25	−	4.59964e24i	−1.06042	−	0.274515i
$929$	−2.55502e25			−1.51099			−0.755494	−	0.655155i	$-0.772603\pi$
$929$	−2.55502e25			−1.51099			−0.755494	+	0.655155i	$0.772603\pi$
$930$	1.83634e23	−	3.62156e24i	0.0107609	−	0.212222i
$931$		−	1.60240e24i		−	0.0930460i
$932$	6.25451e24	+	6.35916e23i	0.359880	+	0.0365902i
$933$		−	2.90244e25i		−	1.65489i
$934$	−1.10438e24	−	5.59987e22i	−0.0623981	−	0.00316395i
$935$	−1.24354e24			−0.0696246
$936$	4.92942e23	+	7.55032e22i	0.0273496	+	0.00418910i
$937$	−1.85797e25			−1.02153			−0.510765	−	0.859720i	$-0.670638\pi$
$937$	−1.85797e25			−1.02153			−0.510765	+	0.859720i	$0.670638\pi$
$938$	1.17619e25	+	5.96399e23i	0.640847	+	0.0324947i
$939$			3.98120e24i			0.214960i
$940$	9.49228e22	−	9.33607e23i	0.00507906	−	0.0499548i
$941$		−	2.94823e24i		−	0.156333i	−0.996940	−	0.0781664i	$-0.975093\pi$
$941$		−	2.94823e24i		−	0.156333i	0.996940	−	0.0781664i	$-0.0249066\pi$
$942$	1.41633e24	−	2.79323e25i	0.0744274	−	1.46783i
$943$	5.31778e25			2.76937
$944$	3.78027e24	−	1.83981e25i	0.195102	−	0.949537i
$945$	1.33857e24			0.0684653
$946$	1.78758e23	−	3.52538e24i	0.00906129	−	0.178703i
$947$		−	2.14283e25i		−	1.07650i	−0.842786	−	0.538249i	$-0.819086\pi$
$947$		−	2.14283e25i		−	1.07650i	0.842786	−	0.538249i	$-0.180914\pi$
$948$	2.67446e24	−	2.63045e25i	0.133158	−	1.30966i
$949$		−	2.83355e23i		−	0.0139819i
$950$	3.03371e25	+	1.53827e24i	1.48362	+	0.0752285i
$951$	−3.62492e25			−1.75697
$952$	2.04833e24	−	1.33730e25i	0.0983980	−	0.642416i
$953$	−1.03026e24			−0.0490520			−0.0245260	−	0.999699i	$-0.507808\pi$
$953$	−1.03026e24			−0.0490520			−0.0245260	+	0.999699i	$0.507808\pi$
$954$	−6.26036e24	−	3.17437e23i	−0.295419	−	0.0149795i
$955$		−	5.90340e23i		−	0.0276105i
$956$	8.18802e23	+	8.32502e22i	0.0379566	+	0.00385917i
$957$			2.72051e25i			1.24997i
$958$	−1.50599e24	+	2.97004e25i	−0.0685826	+	1.35256i
$959$	2.47421e25			1.11681
$960$	2.85422e24	+	8.95360e23i	0.127697	+	0.0400583i
$961$	3.42982e25			1.52098
$962$	−6.96407e22	+	1.37342e24i	−0.00306108	+	0.0603694i
$963$			3.73421e24i			0.162695i
$964$	−1.96604e24	−	1.99894e23i	−0.0849059	−	0.00863265i
$965$			3.44500e24i			0.147471i
$966$	−4.35985e25	−	2.21070e24i	−1.84998	−	0.0938047i
$967$	−2.08697e25			−0.877790			−0.438895	−	0.898538i	$-0.644630\pi$
$967$	−2.08697e25			−0.877790			−0.438895	+	0.898538i	$0.644630\pi$
$968$	−4.18570e23	+	2.73274e24i	−0.0174513	+	0.113935i
$969$	2.96211e25			1.22419
$970$	1.13757e24	+	5.76817e22i	0.0466036	+	0.00236308i
$971$		−	4.19124e24i		−	0.170208i	−0.996372	−	0.0851038i	$-0.972878\pi$
$971$		−	4.19124e24i		−	0.170208i	0.996372	−	0.0851038i	$-0.0271222\pi$
$972$	2.19796e24	−	2.16179e25i	0.0884824	−	0.870263i
$973$			2.24291e25i			0.895060i
$974$	7.71240e23	−	1.52101e25i	0.0305097	−	0.601700i
$975$	1.79206e24			0.0702772
$976$	−1.43447e24	+	6.98139e24i	−0.0557657	+	0.271405i
$977$	−2.32588e25			−0.896362			−0.448181	−	0.893943i	$-0.647928\pi$
$977$	−2.32588e25			−0.896362			−0.448181	+	0.893943i	$0.647928\pi$
$978$	−2.29431e24	+	4.52475e25i	−0.0876541	+	1.72868i
$979$		−	2.99920e25i		−	1.13593i
$980$	1.83878e22	−	1.80852e23i	0.000690410	−	0.00679048i
$981$			2.21282e25i			0.823682i
$982$	−3.18261e25	−	1.61377e24i	−1.17445	−	0.0595516i
$983$	−8.66584e24			−0.317034			−0.158517	−	0.987356i	$-0.550671\pi$
$983$	−8.66584e24			−0.317034			−0.158517	+	0.987356i	$0.550671\pi$
$984$	−5.80856e25	−	8.89689e24i	−2.10673	−	0.322686i
$985$	−1.48161e24			−0.0532752
$986$	−2.05912e25	−	1.04409e24i	−0.734053	−	0.0372208i
$987$		−	1.51332e25i		−	0.534853i
$988$	2.50382e24	+	2.54572e23i	0.0877343	+	0.00892023i
$989$		−	8.63208e24i		−	0.299879i
$990$	7.19821e22	−	1.41960e24i	0.00247928	−	0.0488953i
$991$	6.64102e24			0.226782			0.113391	−	0.993550i	$-0.463829\pi$
$991$	6.64102e24			0.226782			0.113391	+	0.993550i	$0.463829\pi$
$992$	−1.17526e25	+	4.53992e25i	−0.397912	+	1.53709i
$993$	4.25040e25			1.42679
$994$	−1.80869e24	+	3.56702e25i	−0.0601976	+	1.18719i
$995$			2.43503e24i			0.0803543i
$996$	5.49283e25	+	5.58474e24i	1.79718	+	0.182725i
$997$			1.58692e25i			0.514808i	0.966304	+	0.257404i	$0.0828671\pi$
$997$			1.58692e25i			0.514808i	−0.966304	+	0.257404i	$0.917133\pi$
$998$	1.00159e25	+	5.07864e23i	0.322166	+	0.0163357i
$999$	2.07101e25			0.660504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.18.b.a.5.7	✓	16
3.2	odd	2		72.18.d.b.37.10		16
4.3	odd	2		32.18.b.a.17.13		16
8.3	odd	2		32.18.b.a.17.4		16
8.5	even	2	inner	8.18.b.a.5.8	yes	16
24.5	odd	2		72.18.d.b.37.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.7	✓	16	1.1	even	1	trivial
8.18.b.a.5.8	yes	16	8.5	even	2	inner
32.18.b.a.17.4		16	8.3	odd	2
32.18.b.a.17.13		16	4.3	odd	2
72.18.d.b.37.9		16	24.5	odd	2
72.18.d.b.37.10		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(18.3339 - 361.574i) q^{2} -13786.7i q^{3} +(-130400. - 13258.2i) q^{4} -96356.3i q^{5} +(-4.98490e6 - 252764. i) q^{6} -1.47728e7 q^{7} +(-7.18455e6 + 4.69061e7i) q^{8} -6.09318e7 q^{9} +O(q^{10})\)	\(q+(18.3339 - 361.574i) q^{2} -13786.7i q^{3} +(-130400. - 13258.2i) q^{4} -96356.3i q^{5} +(-4.98490e6 - 252764. i) q^{6} -1.47728e7 q^{7} +(-7.18455e6 + 4.69061e7i) q^{8} -6.09318e7 q^{9} +(-3.48399e7 - 1.76659e6i) q^{10} -6.68721e8i q^{11} +(-1.82786e8 + 1.79778e9i) q^{12} +1.72473e8i q^{13} +(-2.70845e8 + 5.34148e9i) q^{14} -1.32843e9 q^{15} +(1.68283e10 + 3.45772e9i) q^{16} +1.92991e10 q^{17} +(-1.11712e9 + 2.20314e10i) q^{18} +1.11328e11i q^{19} +(-1.27751e9 + 1.25648e10i) q^{20} +2.03668e11i q^{21} +(-2.41792e11 - 1.22603e10i) q^{22} -5.92040e11 q^{23} +(6.46678e11 + 9.90509e10i) q^{24} +7.53655e11 q^{25} +(6.23619e10 + 3.16212e9i) q^{26} -9.40365e11i q^{27} +(1.92638e12 + 1.95861e11i) q^{28} -2.95085e12i q^{29} +(-2.43554e10 + 4.80326e11i) q^{30} -7.53978e12 q^{31} +(1.55875e12 - 6.02129e12i) q^{32} -9.21942e12 q^{33} +(3.53828e11 - 6.97805e12i) q^{34} +1.42346e12i q^{35} +(7.94549e12 + 8.07844e11i) q^{36} +2.20235e13i q^{37} +(4.02534e13 + 2.04108e12i) q^{38} +2.37783e12 q^{39} +(4.51970e12 + 6.92276e11i) q^{40} -8.98214e13 q^{41} +(7.36412e13 + 3.73404e12i) q^{42} +1.45802e13i q^{43} +(-8.86600e12 + 8.72010e13i) q^{44} +5.87116e12i q^{45} +(-1.08544e13 + 2.14066e14i) q^{46} -7.43032e13 q^{47} +(4.76704e13 - 2.32006e14i) q^{48} -1.43935e13 q^{49} +(1.38175e13 - 2.72502e14i) q^{50} -2.66070e14i q^{51} +(2.28668e12 - 2.24905e13i) q^{52} +2.84157e14i q^{53} +(-3.40012e14 - 1.72406e13i) q^{54} -6.44354e13 q^{55} +(1.06136e14 - 6.92937e14i) q^{56} +1.53484e15 q^{57} +(-1.06695e15 - 5.41007e13i) q^{58} -1.09328e15i q^{59} +(1.73227e14 + 1.76125e13i) q^{60} +4.14860e14i q^{61} +(-1.38234e14 + 2.72619e15i) q^{62} +9.00136e14 q^{63} +(-2.14856e15 - 6.73998e14i) q^{64} +1.66189e13 q^{65} +(-1.69028e14 + 3.33351e15i) q^{66} -2.20200e15i q^{67} +(-2.51660e15 - 2.55870e14i) q^{68} +8.16225e15i q^{69} +(5.14685e14 + 2.60976e13i) q^{70} +6.67796e15 q^{71} +(4.37768e14 - 2.85807e15i) q^{72} -1.64289e15 q^{73} +(7.96311e15 + 4.03777e14i) q^{74} -1.03904e16i q^{75} +(1.47601e15 - 1.45172e16i) q^{76} +9.87891e15i q^{77} +(4.35950e13 - 8.59762e14i) q^{78} -1.46317e16 q^{79} +(3.33173e14 - 1.62151e15i) q^{80} -2.08332e16 q^{81} +(-1.64678e15 + 3.24771e16i) q^{82} -3.05535e16i q^{83} +(2.70027e15 - 2.65583e16i) q^{84} -1.85959e15i q^{85} +(5.27183e15 + 2.67313e14i) q^{86} -4.06824e16 q^{87} +(3.13671e16 + 4.80446e15i) q^{88} +4.48498e16 q^{89} +(2.12286e15 + 1.07642e14i) q^{90} -2.54792e15i q^{91} +(7.72018e16 + 7.84936e15i) q^{92} +1.03948e17i q^{93} +(-1.36227e15 + 2.68661e16i) q^{94} +1.07272e16 q^{95} +(-8.30135e16 - 2.14900e16i) q^{96} -3.26514e16 q^{97} +(-2.63889e14 + 5.20431e15i) q^{98} +4.07464e16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9}+O(q^{10}) \) 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9	\( 16 q + 270 q^{2} - 27436 q^{4} + 5839948 q^{6} + 11529600 q^{7} + 24334920 q^{8} - 602654096 q^{9} + 131002712 q^{10} - 2795125400 q^{12} + 16363788528 q^{14} - 9993282176 q^{15} + 26500434192 q^{16} - 7489125600 q^{17} - 113450563870 q^{18} - 209445719856 q^{20} + 223126527100 q^{22} + 746845345920 q^{23} - 1099415493232 q^{24} - 1809682431664 q^{25} + 2467726531080 q^{26} + 3220542267040 q^{28} - 1188624268048 q^{30} - 318979758592 q^{31} + 1455647316000 q^{32} + 5633526177600 q^{33} - 4461251980292 q^{34} - 33088278002484 q^{36} + 24076283913900 q^{38} - 18457706051456 q^{39} + 60626292962592 q^{40} + 7482251536032 q^{41} - 51630378688160 q^{42} + 193654716236040 q^{44} - 195097141003568 q^{46} - 376698804821760 q^{47} - 329350060416480 q^{48} + 127691292101520 q^{49} + 474997408872102 q^{50} - 272251877663120 q^{52} + 735354219382520 q^{54} + 22\!\cdots\!52 q^{55}+ \cdots + 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q + 270 * q^2 - 27436 * q^4 + 5839948 * q^6 + 11529600 * q^7 + 24334920 * q^8 - 602654096 * q^9 + 131002712 * q^10 - 2795125400 * q^12 + 16363788528 * q^14 - 9993282176 * q^15 + 26500434192 * q^16 - 7489125600 * q^17 - 113450563870 * q^18 - 209445719856 * q^20 + 223126527100 * q^22 + 746845345920 * q^23 - 1099415493232 * q^24 - 1809682431664 * q^25 + 2467726531080 * q^26 + 3220542267040 * q^28 - 1188624268048 * q^30 - 318979758592 * q^31 + 1455647316000 * q^32 + 5633526177600 * q^33 - 4461251980292 * q^34 - 33088278002484 * q^36 + 24076283913900 * q^38 - 18457706051456 * q^39 + 60626292962592 * q^40 + 7482251536032 * q^41 - 51630378688160 * q^42 + 193654716236040 * q^44 - 195097141003568 * q^46 - 376698804821760 * q^47 - 329350060416480 * q^48 + 127691292101520 * q^49 + 474997408872102 * q^50 - 272251877663120 * q^52 + 735354219382520 * q^54 + 2209036687713152 * q^55 - 162767516076480 * q^56 - 190521298294720 * q^57 - 623262610679960 * q^58 - 1973616194963808 * q^60 + 695695648144320 * q^62 - 8131096607338880 * q^63 + 1111931745501248 * q^64 + 2385987975356160 * q^65 + 3598826202828312 * q^66 + 5981109959771880 * q^68 - 10044559836180288 * q^70 + 9025926285576576 * q^71 - 19918679666289160 * q^72 + 11332002046118560 * q^73 + 11098735408189464 * q^74 + 5959440926938280 * q^76 + 4184252259031760 * q^78 - 45299671392008448 * q^79 + 1337342539452480 * q^80 + 20101901999290832 * q^81 + 15639739637081420 * q^82 + 19796542864700224 * q^84 - 14252032276026564 * q^86 + 25965768920837760 * q^87 - 66964872768837680 * q^88 - 69879174608766048 * q^89 + 136151511125051240 * q^90 + 57336249810701280 * q^92 - 192318922166254176 * q^94 + 93790444358203776 * q^95 - 342799224184788928 * q^96 + 95593398602180640 * q^97 + 339641261743253790 * q^98

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