LMFDB - Embedded newform 81.10.e.a.10.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not 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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.10
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.61607 - 14.8364i) q^{2} +(267.846 - 97.4881i) q^{4} +(-1174.80 - 985.775i) q^{5} +(-3599.21 - 1310.01i) q^{7} +(-6003.80 - 10398.9i) q^{8} +(-11552.0 + 20008.7i) q^{10} +(-49925.5 + 41892.5i) q^{11} +(2521.95 - 14302.7i) q^{13} +(-10020.1 + 56826.6i) q^{14} +(-26780.9 + 22471.8i) q^{16} +(163941. - 283953. i) q^{17} +(295448. + 511730. i) q^{19} +(-410767. - 149507. i) q^{20} +(752143. + 631123. i) q^{22} +(-1.32416e6 + 481955. i) q^{23} +(69247.9 + 392725. i) q^{25} -218798. q^{26} -1.09175e6 q^{28} +(364850. + 2.06917e6i) q^{29} +(3.05548e6 - 1.11211e6i) q^{31} +(-4.30610e6 - 3.61324e6i) q^{32} +(-4.64174e6 - 1.68945e6i) q^{34} +(2.93699e6 + 5.08701e6i) q^{35} +(-2.70434e6 + 4.68405e6i) q^{37} +(6.81935e6 - 5.72211e6i) q^{38} +(-3.19769e6 + 1.81350e7i) q^{40} +(1.42849e6 - 8.10140e6i) q^{41} +(-2.46362e7 + 2.06722e7i) q^{43} +(-9.28834e6 + 1.60879e7i) q^{44} +(1.06146e7 + 1.83850e7i) q^{46} +(4.90568e7 + 1.78552e7i) q^{47} +(-1.96744e7 - 1.65088e7i) q^{49} +(5.64548e6 - 2.05479e6i) q^{50} +(-718846. - 4.07678e6i) q^{52} +7.16704e7 q^{53} +9.99490e7 q^{55} +(7.98635e6 + 4.52928e7i) q^{56} +(2.97447e7 - 1.08262e7i) q^{58} +(7.22363e7 + 6.06134e7i) q^{59} +(1.25830e8 + 4.57984e7i) q^{61} +(-2.44930e7 - 4.24232e7i) q^{62} +(-5.12924e7 + 8.88411e7i) q^{64} +(-1.70620e7 + 1.43167e7i) q^{65} +(-4.82463e7 + 2.73619e8i) q^{67} +(1.62288e7 - 9.20381e7i) q^{68} +(6.77898e7 - 5.68824e7i) q^{70} +(2.00213e6 - 3.46779e6i) q^{71} +(-2.07301e8 - 3.59056e8i) q^{73} +(7.65693e7 + 2.78690e7i) q^{74} +(1.29022e8 + 1.08262e8i) q^{76} +(2.34572e8 - 8.53771e7i) q^{77} +(7.11807e7 + 4.03686e8i) q^{79} +5.36144e7 q^{80} -1.23933e8 q^{82} +(4.40096e7 + 2.49591e8i) q^{83} +(-4.72512e8 + 1.71980e8i) q^{85} +(3.71152e8 + 3.11433e8i) q^{86} +(7.35378e8 + 2.67656e8i) q^{88} +(1.50841e8 + 2.61263e8i) q^{89} +(-2.78136e7 + 4.81746e7i) q^{91} +(-3.07687e8 + 2.58180e8i) q^{92} +(1.36572e8 - 7.74540e8i) q^{94} +(1.57359e8 - 8.92426e8i) q^{95} +(-1.07337e9 + 9.00663e8i) q^{97} +(-1.93463e8 + 3.35087e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−2.61607	−	14.8364i	−0.115615	−	0.655684i	−0.986444	−	0.164099i	$-0.947528\pi$
$2$	−2.61607	−	14.8364i	−0.115615	−	0.655684i	0.870829	−	0.491586i	$-0.163583\pi$
$3$		0			0
$3$		0			0
$4$	267.846	−	97.4881i	0.523137	−	0.190406i
$5$	−1174.80	−	985.775i	−0.840619	−	0.705363i	0.117084	−	0.993122i	$-0.462645\pi$
$5$	−1174.80	−	985.775i	−0.840619	−	0.705363i	−0.957703	+	0.287759i	$0.907090\pi$
$6$		0			0
$7$	−3599.21	−	1310.01i	−0.566587	−	0.206221i	0.0428141	−	0.999083i	$-0.486368\pi$
$7$	−3599.21	−	1310.01i	−0.566587	−	0.206221i	−0.609401	+	0.792862i	$0.708590\pi$
$8$	−6003.80	−	10398.9i	−0.518229	−	0.897598i
$9$		0			0
$10$	−11552.0	+	20008.7i	−0.365308	+	0.632731i
$11$	−49925.5	+	41892.5i	−1.02815	+	0.862718i	−0.990629	−	0.136578i	$-0.956389\pi$
$11$	−49925.5	+	41892.5i	−1.02815	+	0.862718i	−0.0375177	+	0.999296i	$0.511945\pi$
$12$		0			0
$13$	2521.95	−	14302.7i	0.0244901	−	0.138890i	−0.970111	−	0.242661i	$-0.921980\pi$
$13$	2521.95	−	14302.7i	0.0244901	−	0.138890i	0.994601	+	0.103771i	$0.0330908\pi$
$14$	−10020.1	+	56826.6i	−0.0697098	+	0.395344i
$15$		0			0
$16$	−26780.9	+	22471.8i	−0.102161	+	0.0857233i
$17$	163941.	−	283953.i	0.476065	−	0.824569i	−0.523559	−	0.851989i	$-0.675396\pi$
$17$	163941.	−	283953.i	0.476065	−	0.824569i	0.999624	+	0.0274205i	$0.00872932\pi$
$18$		0			0
$19$	295448.	+	511730.i	0.520103	+	0.900845i	0.999727	+	0.0233707i	$0.00743979\pi$
$19$	295448.	+	511730.i	0.520103	+	0.900845i	−0.479624	+	0.877474i	$0.659227\pi$
$20$	−410767.	−	149507.i	−0.574065	−	0.208942i
$21$		0			0
$22$	752143.	+	631123.i	0.684540	+	0.574397i
$23$	−1.32416e6	+	481955.i	−0.986655	+	0.359113i	−0.784424	−	0.620225i	$-0.787041\pi$
$23$	−1.32416e6	+	481955.i	−0.986655	+	0.359113i	−0.202231	+	0.979338i	$0.564819\pi$
$24$		0			0
$25$	69247.9	+	392725.i	0.0354550	+	0.201075i
$26$	−218798.			−0.0938997
$27$		0			0
$28$	−1.09175e6			−0.335668
$29$	364850.	+	2.06917e6i	0.0957908	+	0.543257i	0.994502	+	0.104716i	$0.0333934\pi$
$29$	364850.	+	2.06917e6i	0.0957908	+	0.543257i	−0.898711	+	0.438541i	$0.855496\pi$
$30$		0			0
$31$	3.05548e6	−	1.11211e6i	0.594227	−	0.216281i	−0.0273605	−	0.999626i	$-0.508710\pi$
$31$	3.05548e6	−	1.11211e6i	0.594227	−	0.216281i	0.621588	+	0.783345i	$0.286488\pi$
$32$	−4.30610e6	−	3.61324e6i	−0.725954	−	0.609147i
$33$		0			0
$34$	−4.64174e6	−	1.68945e6i	−0.595697	−	0.216816i
$35$	2.93699e6	+	5.08701e6i	0.330823	+	0.573002i
$36$		0			0
$37$	−2.70434e6	+	4.68405e6i	−0.237221	+	0.410878i	−0.959916	−	0.280289i	$-0.909570\pi$
$37$	−2.70434e6	+	4.68405e6i	−0.237221	+	0.410878i	0.722695	+	0.691167i	$0.242903\pi$
$38$	6.81935e6	−	5.72211e6i	0.530538	−	0.445175i
$39$		0			0
$40$	−3.19769e6	+	1.81350e7i	−0.197500	+	1.12008i
$41$	1.42849e6	−	8.10140e6i	0.0789499	−	0.447747i	−0.919549	−	0.392975i	$-0.871446\pi$
$41$	1.42849e6	−	8.10140e6i	0.0789499	−	0.447747i	0.998499	−	0.0547716i	$-0.0174431\pi$
$42$		0			0
$43$	−2.46362e7	+	2.06722e7i	−1.09892	+	0.922101i	−0.997352	−	0.0727277i	$-0.976830\pi$
$43$	−2.46362e7	+	2.06722e7i	−1.09892	+	0.922101i	−0.101566	+	0.994829i	$0.532385\pi$
$44$	−9.28834e6	+	1.60879e7i	−0.373595	+	0.647086i
$45$		0			0
$46$	1.06146e7	+	1.83850e7i	0.349537	+	0.605416i
$47$	4.90568e7	+	1.78552e7i	1.46642	+	0.533734i	0.947127	−	0.320860i	$-0.103972\pi$
$47$	4.90568e7	+	1.78552e7i	1.46642	+	0.533734i	0.519296	+	0.854594i	$0.326194\pi$
$48$		0			0
$49$	−1.96744e7	−	1.65088e7i	−0.487551	−	0.409104i
$50$	5.64548e6	−	2.05479e6i	0.127743	−	0.0464945i
$51$		0			0
$52$	−718846.	−	4.07678e6i	−0.0136339	−	0.0773218i
$53$	7.16704e7			1.24767			0.623833	−	0.781558i	$-0.285574\pi$
$53$	7.16704e7			1.24767			0.623833	+	0.781558i	$0.285574\pi$
$54$		0			0
$55$	9.99490e7			1.47281
$56$	7.98635e6	+	4.52928e7i	0.108518	+	0.615437i
$57$		0			0
$58$	2.97447e7	−	1.08262e7i	0.345130	−	0.125617i
$59$	7.22363e7	+	6.06134e7i	0.776106	+	0.651230i	0.942265	−	0.334869i	$-0.108692\pi$
$59$	7.22363e7	+	6.06134e7i	0.776106	+	0.651230i	−0.166159	+	0.986099i	$0.553136\pi$
$60$		0			0
$61$	1.25830e8	+	4.57984e7i	1.16359	+	0.423512i	0.850379	−	0.526171i	$-0.176373\pi$
$61$	1.25830e8	+	4.57984e7i	1.16359	+	0.423512i	0.313211	+	0.949683i	$0.398595\pi$
$62$	−2.44930e7	−	4.24232e7i	−0.210514	−	0.364620i
$63$		0			0
$64$	−5.12924e7	+	8.88411e7i	−0.382158	+	0.661918i
$65$	−1.70620e7	+	1.43167e7i	−0.118555	+	0.0994795i
$66$		0			0
$67$	−4.82463e7	+	2.73619e8i	−0.292501	+	1.65886i	0.384687	+	0.923047i	$0.374309\pi$
$67$	−4.82463e7	+	2.73619e8i	−0.292501	+	1.65886i	−0.677188	+	0.735810i	$0.736802\pi$
$68$	1.62288e7	−	9.20381e7i	0.0920442	−	0.522009i
$69$		0			0
$70$	6.77898e7	−	5.68824e7i	0.337461	−	0.283163i
$71$	2.00213e6	−	3.46779e6i	0.00935040	−	0.0161954i	−0.861312	−	0.508076i	$-0.830357\pi$
$71$	2.00213e6	−	3.46779e6i	0.00935040	−	0.0161954i	0.870663	+	0.491880i	$0.163690\pi$
$72$		0			0
$73$	−2.07301e8	−	3.59056e8i	−0.854375	−	1.47982i	−0.877223	−	0.480083i	$-0.840607\pi$
$73$	−2.07301e8	−	3.59056e8i	−0.854375	−	1.47982i	0.0228478	−	0.999739i	$-0.492727\pi$
$74$	7.65693e7	+	2.78690e7i	0.296833	+	0.108038i
$75$		0			0
$76$	1.29022e8	+	1.08262e8i	0.443612	+	0.372235i
$77$	2.34572e8	−	8.53771e7i	0.760444	−	0.276779i
$78$		0			0
$79$	7.11807e7	+	4.03686e8i	0.205608	+	1.16606i	0.896480	+	0.443085i	$0.146116\pi$
$79$	7.11807e7	+	4.03686e8i	0.205608	+	1.16606i	−0.690871	+	0.722978i	$0.742773\pi$
$80$	5.36144e7			0.146344
$81$		0			0
$82$	−1.23933e8			−0.302708
$83$	4.40096e7	+	2.49591e8i	0.101788	+	0.577268i	0.992455	+	0.122611i	$0.0391269\pi$
$83$	4.40096e7	+	2.49591e8i	0.101788	+	0.577268i	−0.890667	+	0.454657i	$0.849762\pi$
$84$		0			0
$85$	−4.72512e8	+	1.71980e8i	−0.981810	+	0.357350i
$86$	3.71152e8	+	3.11433e8i	0.731659	+	0.613934i
$87$		0			0
$88$	7.35378e8	+	2.67656e8i	1.30719	+	0.475778i
$89$	1.50841e8	+	2.61263e8i	0.254837	+	0.441391i	0.964851	−	0.262796i	$-0.0846447\pi$
$89$	1.50841e8	+	2.61263e8i	0.254837	+	0.441391i	−0.710014	+	0.704188i	$0.751311\pi$
$90$		0			0
$91$	−2.78136e7	+	4.81746e7i	−0.0425178	+	0.0736431i
$92$	−3.07687e8	+	2.58180e8i	−0.447779	+	0.375731i
$93$		0			0
$94$	1.36572e8	−	7.74540e8i	0.180421	−	1.02322i
$95$	1.57359e8	−	8.92426e8i	0.198214	−	1.12413i
$96$		0			0
$97$	−1.07337e9	+	9.00663e8i	−1.23105	+	1.03297i	−0.232880	+	0.972505i	$0.574815\pi$
$97$	−1.07337e9	+	9.00663e8i	−1.23105	+	1.03297i	−0.998170	+	0.0604687i	$0.980740\pi$
$98$	−1.93463e8	+	3.35087e8i	−0.211875	+	0.366978i
$99$		0			0
$100$	5.68338e7	+	9.84390e7i	0.0568338	+	0.0984390i
$101$	4.04519e8	+	1.47233e8i	0.386806	+	0.140786i	0.528101	−	0.849182i	$-0.322904\pi$
$101$	4.04519e8	+	1.47233e8i	0.386806	+	0.140786i	−0.141295	+	0.989968i	$0.545127\pi$
$102$		0			0
$103$	−4.52437e8	−	3.79640e8i	−0.396087	−	0.332357i	0.422892	−	0.906180i	$-0.361015\pi$
$103$	−4.52437e8	−	3.79640e8i	−0.396087	−	0.332357i	−0.818979	+	0.573824i	$0.805459\pi$
$104$	−1.63873e8	+	5.96450e7i	−0.137359	+	0.0499947i
$105$		0			0
$106$	−1.87494e8	−	1.06333e9i	−0.144249	−	0.818075i
$107$	−2.37636e9			−1.75261			−0.876303	−	0.481760i	$-0.839998\pi$
$107$	−2.37636e9			−1.75261			−0.876303	+	0.481760i	$0.839998\pi$
$108$		0			0
$109$	−5.32469e8			−0.361306			−0.180653	−	0.983547i	$-0.557821\pi$
$109$	−5.32469e8			−0.361306			−0.180653	+	0.983547i	$0.557821\pi$
$110$	−2.61473e8	−	1.48289e9i	−0.170279	−	0.965698i
$111$		0			0
$112$	1.25828e8	−	4.57978e7i	0.0755609	−	0.0275019i
$113$	−2.22606e9	−	1.86789e9i	−1.28435	−	1.07770i	−0.992628	−	0.121197i	$-0.961327\pi$
$113$	−2.22606e9	−	1.86789e9i	−1.28435	−	1.07770i	−0.291724	−	0.956503i	$-0.594229\pi$
$114$		0			0
$115$	2.03072e9	+	7.39123e8i	1.08271	+	0.394073i
$116$	2.99443e8	+	5.18651e8i	0.153551	+	0.265959i
$117$		0			0
$118$	7.10313e8	−	1.23030e9i	0.337272	−	0.584173i
$119$	−9.62038e8	+	8.07245e8i	−0.439775	+	0.369015i
$120$		0			0
$121$	3.28123e8	−	1.86088e9i	0.139156	−	0.789194i
$122$	3.50306e8	−	1.98668e9i	0.143162	−	0.811912i
$123$		0			0
$124$	7.09983e8	−	5.95747e8i	0.269681	−	0.226289i
$125$	−1.19186e9	+	2.06437e9i	−0.436648	+	0.756297i
$126$		0			0
$127$	−1.13749e9	−	1.97019e9i	−0.387999	−	0.672034i	0.604181	−	0.796847i	$-0.293500\pi$
$127$	−1.13749e9	−	1.97019e9i	−0.387999	−	0.672034i	−0.992180	+	0.124813i	$0.960167\pi$
$128$	−1.25222e9	−	4.55771e8i	−0.412322	−	0.150073i
$129$		0			0
$130$	2.57045e8	+	2.15686e8i	0.0789339	+	0.0662334i
$131$	7.74815e8	−	2.82009e8i	0.229867	−	0.0836648i	−0.224519	−	0.974470i	$-0.572081\pi$
$131$	7.74815e8	−	2.82009e8i	0.229867	−	0.0836648i	0.454386	+	0.890805i	$0.349859\pi$
$132$		0			0
$133$	−3.93009e8	−	2.22886e9i	−0.108911	−	0.617663i
$134$	4.18574e9			1.12150
$135$		0			0
$136$	−3.93707e9			−0.986842
$137$	1.02609e8	+	5.81925e8i	0.0248853	+	0.141132i	0.994719	−	0.102636i	$-0.0327277\pi$
$137$	1.02609e8	+	5.81925e8i	0.0248853	+	0.141132i	−0.969834	+	0.243768i	$0.921617\pi$
$138$		0			0
$139$	6.42326e9	−	2.33788e9i	1.45945	−	0.531196i	0.514235	−	0.857649i	$-0.328076\pi$
$139$	6.42326e9	−	2.33788e9i	1.45945	−	0.531196i	0.945213	+	0.326453i	$0.105854\pi$
$140$	1.28258e9	+	1.07622e9i	0.282169	+	0.236768i
$141$		0			0
$142$	−5.66874e7	−	2.06325e7i	−0.0117001	−	0.00425849i
$143$	4.73265e8	+	8.19719e8i	0.0946438	+	0.163928i
$144$		0			0
$145$	1.61111e9	−	2.79052e9i	0.302670	−	0.524239i
$146$	−4.78480e9	+	4.01493e9i	−0.871518	+	0.731290i
$147$		0			0
$148$	−2.67708e8	+	1.51824e9i	−0.0458652	+	0.260114i
$149$	1.46402e8	−	8.30289e8i	0.0243338	−	0.138004i	−0.970221	−	0.242223i	$-0.922123\pi$
$149$	1.46402e8	−	8.30289e8i	0.0243338	−	0.138004i	0.994554	+	0.104219i	$0.0332344\pi$
$150$		0			0
$151$	−6.44433e9	+	5.40743e9i	−1.00875	+	0.846438i	−0.988172	−	0.153351i	$-0.950994\pi$
$151$	−6.44433e9	+	5.40743e9i	−1.00875	+	0.846438i	−0.0205733	+	0.999788i	$0.506549\pi$
$152$	3.54762e9	−	6.14466e9i	0.539065	−	0.933687i
$153$		0			0
$154$	−1.88035e9	−	3.25686e9i	−0.269398	−	0.466612i
$155$	−4.68587e9	−	1.70552e9i	−0.652075	−	0.237336i
$156$		0			0
$157$	−7.01092e9	−	5.88286e9i	−0.920930	−	0.772752i	0.0532367	−	0.998582i	$-0.483046\pi$
$157$	−7.01092e9	−	5.88286e9i	−0.920930	−	0.772752i	−0.974167	+	0.225830i	$0.927491\pi$
$158$	5.80305e9	−	2.11214e9i	0.740798	−	0.269628i
$159$		0			0
$160$	1.49696e9	+	8.48968e9i	0.180580	+	1.02412i
$161$	5.39730e9			0.633082
$162$		0			0
$163$	−6.76854e9			−0.751019			−0.375509	−	0.926819i	$-0.622532\pi$
$163$	−6.76854e9			−0.751019			−0.375509	+	0.926819i	$0.622532\pi$
$164$	−4.07173e8	−	2.30919e9i	−0.0439523	−	0.249266i
$165$		0			0
$166$	3.58791e9	−	1.30589e9i	0.366738	−	0.133482i
$167$	−8.24893e9	−	6.92167e9i	−0.820679	−	0.688632i	0.132452	−	0.991189i	$-0.457715\pi$
$167$	−8.24893e9	−	6.92167e9i	−0.820679	−	0.688632i	−0.953131	+	0.302558i	$0.902159\pi$
$168$		0			0
$169$	9.76676e9	+	3.55481e9i	0.921002	+	0.335217i
$170$	3.78770e9	+	6.56048e9i	0.347820	+	0.602442i
$171$		0			0
$172$	−4.58341e9	+	7.93870e9i	−0.399311	+	0.691626i
$173$	−1.15695e10	+	9.70793e9i	−0.981987	+	0.823985i	−0.984388	−	0.176012i	$-0.943680\pi$
$173$	−1.15695e10	+	9.70793e9i	−0.981987	+	0.823985i	0.00240117	+	0.999997i	$0.499236\pi$
$174$		0			0
$175$	2.65234e8	−	1.50421e9i	0.0213775	−	0.121238i
$176$	3.95649e8	−	2.24383e9i	0.0310815	−	0.176272i
$177$		0			0
$178$	3.48161e9	−	2.92142e9i	0.259950	−	0.218124i
$179$	−8.39539e9	+	1.45412e10i	−0.611227	+	1.05868i	0.379807	+	0.925066i	$0.375990\pi$
$179$	−8.39539e9	+	1.45412e10i	−0.611227	+	1.05868i	−0.991034	+	0.133610i	$0.957343\pi$
$180$		0			0
$181$	4.12115e9	+	7.13805e9i	0.285407	+	0.494340i	0.972708	−	0.232033i	$-0.0745378\pi$
$181$	4.12115e9	+	7.13805e9i	0.285407	+	0.494340i	−0.687301	+	0.726373i	$0.741204\pi$
$182$	7.87502e8	+	2.86627e8i	0.0532023	+	0.0193641i
$183$		0			0
$184$	1.29618e10	+	1.08762e10i	0.833652	+	0.699517i
$185$	7.79447e9	−	2.83695e9i	0.489231	−	0.178065i
$186$		0			0
$187$	3.71069e9	+	2.10444e10i	0.221905	+	1.25849i
$188$	1.48804e10			0.868767
$189$		0			0
$190$	−1.36521e10			−0.759990
$191$	−3.43955e9	−	1.95067e10i	−0.187005	−	1.06056i	−0.923353	−	0.383953i	$-0.874563\pi$
$191$	−3.43955e9	−	1.95067e10i	−0.187005	−	1.06056i	0.736348	−	0.676603i	$-0.236549\pi$
$192$		0			0
$193$	3.27230e10	−	1.19102e10i	1.69764	−	0.617889i	0.702084	−	0.712094i	$-0.252253\pi$
$193$	3.27230e10	−	1.19102e10i	1.69764	−	0.617889i	0.995553	+	0.0942050i	$0.0300309\pi$
$194$	1.61706e10	+	1.35688e10i	0.819633	+	0.687754i
$195$		0			0
$196$	−6.87914e9	−	2.50380e9i	−0.332952	−	0.121185i
$197$	1.37017e10	+	2.37321e10i	0.648153	+	1.12263i	0.983564	+	0.180562i	$0.0577917\pi$
$197$	1.37017e10	+	2.37321e10i	0.648153	+	1.12263i	−0.335410	+	0.942072i	$0.608875\pi$
$198$		0			0
$199$	−1.38198e10	+	2.39367e10i	−0.624690	+	1.08199i	0.363911	+	0.931434i	$0.381441\pi$
$199$	−1.38198e10	+	2.39367e10i	−0.624690	+	1.08199i	−0.988601	+	0.150560i	$0.951892\pi$
$200$	3.66815e9	−	3.07794e9i	0.162111	−	0.136027i
$201$		0			0
$202$	1.12616e9	−	6.38680e9i	0.0475905	−	0.269899i
$203$	1.39745e9	−	7.92534e9i	0.0577570	−	0.327556i
$204$		0			0
$205$	−9.66435e9	+	8.10935e9i	−0.382191	+	0.320696i
$206$	−4.44890e9	+	7.70572e9i	−0.172127	+	0.298134i
$207$		0			0
$208$	2.53867e8	+	4.39711e8i	0.00940420	+	0.0162886i
$209$	−3.61880e10	−	1.31714e10i	−1.31192	−	0.477499i
$210$		0			0
$211$	−1.54480e10	−	1.29624e10i	−0.536539	−	0.450210i	0.333813	−	0.942639i	$-0.391664\pi$
$211$	−1.54480e10	−	1.29624e10i	−0.536539	−	0.450210i	−0.870352	+	0.492430i	$0.836109\pi$
$212$	1.91967e10	−	6.98701e9i	0.652701	−	0.237564i
$213$		0			0
$214$	6.21670e9	+	3.52567e10i	0.202627	+	1.14916i
$215$	4.93207e10			1.57419
$216$		0			0
$217$	−1.24542e10			−0.381283
$218$	1.39297e9	+	7.89995e9i	0.0417723	+	0.236903i
$219$		0			0
$220$	2.67710e10	−	9.74384e9i	0.770481	−	0.280432i
$221$	−3.64784e9	−	3.06091e9i	−0.102866	−	0.0863147i
$222$		0			0
$223$	−2.58516e10	−	9.40920e9i	−0.700027	−	0.254789i	−0.0326045	−	0.999468i	$-0.510380\pi$
$223$	−2.58516e10	−	9.40920e9i	−0.700027	−	0.254789i	−0.667422	+	0.744679i	$0.732602\pi$
$224$	1.07652e10	+	1.86458e10i	0.285697	+	0.494841i
$225$		0			0
$226$	−2.18893e10	+	3.79134e10i	−0.558141	+	0.966728i
$227$	−2.29509e9	+	1.92581e9i	−0.0573699	+	0.0481391i	−0.671022	−	0.741438i	$-0.734144\pi$
$227$	−2.29509e9	+	1.92581e9i	−0.0573699	+	0.0481391i	0.613652	+	0.789577i	$0.289700\pi$
$228$		0			0
$229$	1.11920e10	−	6.34728e10i	0.268935	−	1.52521i	−0.488657	−	0.872476i	$-0.662513\pi$
$229$	1.11920e10	−	6.34728e10i	0.268935	−	1.52521i	0.757591	−	0.652729i	$-0.226376\pi$
$230$	5.65345e9	−	3.20623e10i	0.133210	−	0.755474i
$231$		0			0
$232$	1.93266e10	−	1.62169e10i	0.437985	−	0.367513i
$233$	2.95383e9	−	5.11618e9i	0.0656573	−	0.113722i	−0.831328	−	0.555782i	$-0.812419\pi$
$233$	2.95383e9	−	5.11618e9i	0.0656573	−	0.113722i	0.896985	+	0.442060i	$0.145752\pi$
$234$		0			0
$235$	−4.00308e10	−	6.93353e10i	−0.856226	−	1.48303i
$236$	2.52573e10	+	9.19291e9i	0.530009	+	0.192907i
$237$		0			0
$238$	1.44934e10	+	1.21614e10i	0.292802	+	0.245690i
$239$	−1.52704e10	+	5.55795e9i	−0.302732	+	0.110185i	−0.488920	−	0.872329i	$-0.662609\pi$
$239$	−1.52704e10	+	5.55795e9i	−0.302732	+	0.110185i	0.186188	+	0.982514i	$0.440387\pi$
$240$		0			0
$241$	−1.84235e8	−	1.04485e9i	−0.00351800	−	0.0199515i	0.982998	−	0.183615i	$-0.0587800\pi$
$241$	−1.84235e8	−	1.04485e9i	−0.00351800	−	0.0199515i	−0.986516	+	0.163663i	$0.947669\pi$
$242$	−2.84672e10			−0.533550
$243$		0			0
$244$	3.81679e10			0.689357
$245$	6.83957e9	+	3.87891e10i	0.121278	+	0.687801i
$246$		0			0
$247$	8.06422e9	−	2.93514e9i	0.137856	−	0.0501755i
$248$	−2.99092e10	−	2.50968e10i	−0.502079	−	0.421294i
$249$		0			0
$250$	3.37459e10	+	1.22825e10i	0.546375	+	0.198864i
$251$	2.74609e9	+	4.75637e9i	0.0436700	+	0.0756387i	0.887034	−	0.461704i	$-0.152762\pi$
$251$	2.74609e9	+	4.75637e9i	0.0436700	+	0.0756387i	−0.843364	+	0.537342i	$0.819428\pi$
$252$		0			0
$253$	4.59191e10	−	7.95342e10i	0.704613	−	1.22043i
$254$	−2.62549e10	+	2.20305e10i	−0.395784	+	0.332102i
$255$		0			0
$256$	−1.26067e10	+	7.14963e10i	−0.183452	+	1.04041i
$257$	1.21069e10	−	6.86616e10i	0.173115	−	0.981782i	−0.767183	−	0.641428i	$-0.778342\pi$
$257$	1.21069e10	−	6.86616e10i	0.173115	−	0.981782i	0.940298	−	0.340353i	$-0.110547\pi$
$258$		0			0
$259$	1.58696e10	−	1.33162e10i	0.219138	−	0.183878i
$260$	−3.17428e9	+	5.49802e9i	−0.0430790	+	0.0746151i
$261$		0			0
$262$	−6.21098e9	−	1.07577e10i	−0.0814338	−	0.141047i
$263$	−9.92834e10	−	3.61362e10i	−1.27960	−	0.465738i	−0.389303	−	0.921110i	$-0.627284\pi$
$263$	−9.92834e10	−	3.61362e10i	−1.27960	−	0.465738i	−0.890301	+	0.455372i	$0.849506\pi$
$264$		0			0
$265$	−8.41984e10	−	7.06509e10i	−1.04881	−	0.880058i
$266$	−3.20403e10	+	1.16617e10i	−0.392400	+	0.142822i
$267$		0			0
$268$	1.37519e10	+	7.79912e10i	0.162839	+	0.923504i
$269$	−9.78088e10			−1.13892			−0.569459	−	0.822020i	$-0.692847\pi$
$269$	−9.78088e10			−1.13892			−0.569459	+	0.822020i	$0.692847\pi$
$270$		0			0
$271$	−9.08311e10			−1.02299			−0.511496	−	0.859285i	$-0.670909\pi$
$271$	−9.08311e10			−1.02299			−0.511496	+	0.859285i	$0.670909\pi$
$272$	1.99048e9	+	1.12886e10i	0.0220494	+	0.125049i
$273$		0			0
$274$	8.36527e9	−	3.04471e9i	0.0896607	−	0.0326338i
$275$	−1.99094e10	−	1.67060e10i	−0.209924	−	0.176147i
$276$		0			0
$277$	8.23031e9	+	2.99559e9i	0.0839957	+	0.0305719i	0.383676	−	0.923468i	$-0.374658\pi$
$277$	8.23031e9	+	2.99559e9i	0.0839957	+	0.0305719i	−0.299681	+	0.954040i	$0.596880\pi$
$278$	−5.14894e10	−	8.91823e10i	−0.517031	−	0.895524i
$279$		0			0
$280$	3.52662e10	−	6.10828e10i	0.342884	−	0.593892i
$281$	−2.49252e10	+	2.09147e10i	−0.238485	+	0.200112i	−0.754195	−	0.656651i	$-0.771973\pi$
$281$	−2.49252e10	+	2.09147e10i	−0.238485	+	0.200112i	0.515710	+	0.856763i	$0.327528\pi$
$282$		0			0
$283$	−2.92267e10	+	1.65753e11i	−0.270858	+	1.53611i	0.480961	+	0.876742i	$0.340288\pi$
$283$	−2.92267e10	+	1.65753e11i	−0.270858	+	1.53611i	−0.751819	+	0.659370i	$0.770823\pi$
$284$	1.98195e8	−	1.12402e9i	0.00180784	−	0.0102528i
$285$		0			0
$286$	1.09236e10	−	9.16601e9i	0.0965427	−	0.0810089i
$287$	−1.57543e10	+	2.72873e10i	−0.137067	+	0.237406i
$288$		0			0
$289$	5.54090e9	+	9.59712e9i	0.0467240	+	0.0809284i
$290$	−4.56162e10	−	1.66029e10i	−0.378729	−	0.137846i
$291$		0			0
$292$	−9.05285e10	−	7.59624e10i	−0.728723	−	0.611471i
$293$	9.93962e9	−	3.61772e9i	0.0787890	−	0.0286768i	−0.302325	−	0.953205i	$-0.597763\pi$
$293$	9.93962e9	−	3.61772e9i	0.0787890	−	0.0286768i	0.381114	+	0.924528i	$0.375541\pi$
$294$		0			0
$295$	−2.51120e10	−	1.42417e11i	−0.193056	−	1.09487i
$296$	6.49452e10			0.491739
$297$		0			0
$298$	−1.27015e10			−0.0933004
$299$	3.55378e9	+	2.01545e10i	0.0257141	+	0.145832i
$300$		0			0
$301$	1.15751e11	−	4.21301e10i	0.812788	−	0.295831i
$302$	9.70859e10	+	8.14647e10i	0.671622	+	0.563558i
$303$		0			0
$304$	−1.94119e10	−	7.06534e9i	−0.130358	−	0.0474463i
$305$	−1.02678e11	−	1.77844e11i	−0.679406	−	1.17677i
$306$		0			0
$307$	5.06184e10	−	8.76736e10i	0.325226	−	0.563309i	−0.656332	−	0.754472i	$-0.727893\pi$
$307$	5.06184e10	−	8.76736e10i	0.325226	−	0.563309i	0.981558	+	0.191164i	$0.0612262\pi$
$308$	5.45059e10	−	4.57359e10i	0.345116	−	0.289587i
$309$		0			0
$310$	−1.30453e10	+	7.39834e10i	−0.0802279	+	0.454995i
$311$	−2.98438e10	+	1.69253e11i	−0.180898	+	1.02592i	0.750216	+	0.661192i	$0.229949\pi$
$311$	−2.98438e10	+	1.69253e11i	−0.180898	+	1.02592i	−0.931114	+	0.364729i	$0.881162\pi$
$312$		0			0
$313$	1.94522e10	−	1.63223e10i	0.114556	−	0.0961240i	−0.583710	−	0.811962i	$-0.698400\pi$
$313$	1.94522e10	−	1.63223e10i	0.114556	−	0.0961240i	0.698266	+	0.715838i	$0.253955\pi$
$314$	−6.89397e10	+	1.19407e11i	−0.400208	+	0.693181i
$315$		0			0
$316$	5.84201e10	+	1.01187e11i	0.329587	+	0.570862i
$317$	1.91039e11	+	6.95326e10i	1.06257	+	0.386742i	0.813392	−	0.581717i	$-0.197619\pi$
$317$	1.91039e11	+	6.95326e10i	1.06257	+	0.386742i	0.249174	+	0.968459i	$0.419841\pi$
$318$		0			0
$319$	−1.04898e11	−	8.80198e10i	−0.567164	−	0.475907i
$320$	1.47836e11	−	5.38078e10i	0.788142	−	0.286860i
$321$		0			0
$322$	−1.41197e10	−	8.00767e10i	−0.0731937	−	0.415102i
$323$	1.93743e11			0.990412
$324$		0			0
$325$	5.79165e9			0.0287957
$326$	1.77069e10	+	1.00421e11i	0.0868289	+	0.492431i
$327$		0			0
$328$	−9.28219e10	+	3.37844e10i	−0.442811	+	0.161170i
$329$	−1.53176e11	−	1.28530e11i	−0.720788	−	0.604813i
$330$		0			0
$331$	6.41952e10	+	2.33651e10i	0.293952	+	0.106990i	0.484787	−	0.874632i	$-0.338897\pi$
$331$	6.41952e10	+	2.33651e10i	0.293952	+	0.106990i	−0.190835	+	0.981622i	$0.561119\pi$
$332$	3.61200e10	+	6.25616e10i	0.163165	+	0.282609i
$333$		0			0
$334$	−8.11133e10	+	1.40492e11i	−0.356642	+	0.617723i
$335$	3.26406e11	−	2.73887e11i	1.41598	−	1.18815i
$336$		0			0
$337$	−1.18506e10	+	6.72081e10i	−0.0500502	+	0.283849i	−0.999553	−	0.0299110i	$-0.990478\pi$
$337$	−1.18506e10	+	6.72081e10i	−0.0500502	+	0.283849i	0.949502	+	0.313760i	$0.101589\pi$
$338$	2.71903e10	−	1.54204e11i	0.113315	−	0.642643i
$339$		0			0
$340$	−1.09794e11	+	9.21285e10i	−0.445580	+	0.373886i
$341$	−1.05958e11	+	1.83524e11i	−0.424363	+	0.735019i
$342$		0			0
$343$	1.26467e11	+	2.19047e11i	0.493349	+	0.854505i
$344$	3.62879e11	+	1.32077e11i	1.39717	+	0.508527i
$345$		0			0
$346$	1.74298e11	+	1.46253e11i	0.653806	+	0.548609i
$347$	−2.76672e11	+	1.00700e11i	−1.02443	+	0.372862i	−0.798958	−	0.601387i	$-0.794615\pi$
$347$	−2.76672e11	+	1.00700e11i	−1.02443	+	0.372862i	−0.225473	+	0.974249i	$0.572393\pi$
$348$		0			0
$349$	−2.67663e9	−	1.51799e10i	−0.00965769	−	0.0547715i	0.979598	−	0.200967i	$-0.0644083\pi$
$349$	−2.67663e9	−	1.51799e10i	−0.00965769	−	0.0547715i	−0.989256	+	0.146195i	$0.953297\pi$
$350$	−2.30111e10			−0.0819654
$351$		0			0
$352$	3.66352e11			1.27191
$353$	6.06520e9	+	3.43975e10i	0.0207902	+	0.117907i	0.993437	−	0.114383i	$-0.0364891\pi$
$353$	6.06520e9	+	3.43975e10i	0.0207902	+	0.117907i	−0.972646	+	0.232290i	$0.925378\pi$
$354$		0			0
$355$	−5.77057e9	+	2.10032e9i	−0.0192837	+	0.00701870i
$356$	6.58722e10	+	5.52733e10i	0.217359	+	0.182386i
$357$		0			0
$358$	2.37703e11	+	8.65169e10i	0.764824	+	0.278373i
$359$	−9.36376e10	−	1.62185e11i	−0.297526	−	0.515330i	0.678043	−	0.735022i	$-0.262828\pi$
$359$	−9.36376e10	−	1.62185e11i	−0.297526	−	0.515330i	−0.975569	+	0.219692i	$0.929495\pi$
$360$		0			0
$361$	−1.32348e10	+	2.29234e10i	−0.0410143	+	0.0710388i
$362$	9.51220e10	−	7.98169e10i	0.291134	−	0.244290i
$363$		0			0
$364$	−2.75333e9	+	1.56149e10i	−0.00822056	+	0.0466211i
$365$	−1.10411e11	+	6.26171e11i	−0.325607	+	1.84661i
$366$		0			0
$367$	−3.41267e11	+	2.86357e11i	−0.981966	+	0.823967i	−0.984385	−	0.176030i	$-0.943674\pi$
$367$	−3.41267e11	+	2.86357e11i	−0.981966	+	0.823967i	0.00241890	+	0.999997i	$0.499230\pi$
$368$	2.46318e10	−	4.26635e10i	0.0700133	−	0.121267i
$369$		0			0
$370$	−6.24812e10	−	1.08221e11i	−0.173317	−	0.300194i
$371$	−2.57957e11	−	9.38887e10i	−0.706911	−	0.257295i
$372$		0			0
$373$	9.16897e10	+	7.69368e10i	0.245262	+	0.205799i	0.757129	−	0.653265i	$-0.226601\pi$
$373$	9.16897e10	+	7.69368e10i	0.245262	+	0.205799i	−0.511867	+	0.859065i	$0.671046\pi$
$374$	3.02516e11	−	1.10107e11i	0.799515	−	0.291000i
$375$		0			0
$376$	−1.08853e11	−	6.17336e11i	−0.280863	−	1.59286i
$377$	3.05148e10			0.0777991
$378$		0			0
$379$	4.48236e11			1.11591			0.557957	−	0.829870i	$-0.311585\pi$
$379$	4.48236e11			1.11591			0.557957	+	0.829870i	$0.311585\pi$
$380$	−4.48529e10	−	2.54374e11i	−0.110348	−	0.625815i
$381$		0			0
$382$	−2.80412e11	+	1.02062e11i	−0.673769	+	0.245232i
$383$	3.81724e11	+	3.20305e11i	0.906474	+	0.760622i	0.971445	−	0.237265i	$-0.0762510\pi$
$383$	3.81724e11	+	3.20305e11i	0.906474	+	0.760622i	−0.0649709	+	0.997887i	$0.520695\pi$
$384$		0			0
$385$	−3.59738e11	−	1.30934e11i	−0.834474	−	0.303724i
$386$	−2.62310e11	−	4.54335e11i	−0.601412	−	1.04168i
$387$		0			0
$388$	−1.99694e11	+	3.45880e11i	−0.447324	+	0.774787i
$389$	−3.40197e11	+	2.85459e11i	−0.753281	+	0.632078i	−0.936368	−	0.351019i	$-0.885835\pi$
$389$	−3.40197e11	+	2.85459e11i	−0.753281	+	0.632078i	0.183088	+	0.983097i	$0.441391\pi$
$390$		0			0
$391$	−8.02309e10	+	4.55012e11i	−0.173599	+	0.984526i
$392$	−5.35519e10	+	3.03708e11i	−0.114548	+	0.649635i
$393$		0			0
$394$	3.16256e11	−	2.65370e11i	0.661158	−	0.554777i
$395$	3.14320e11	−	5.44419e11i	0.649659	−	1.12524i
$396$		0			0
$397$	2.97024e11	+	5.14461e11i	0.600116	+	1.03943i	0.992803	+	0.119759i	$0.0382121\pi$
$397$	2.97024e11	+	5.14461e11i	0.600116	+	1.03943i	−0.392688	+	0.919672i	$0.628455\pi$
$398$	3.91289e11	+	1.42417e11i	0.781670	+	0.284505i
$399$		0			0
$400$	−1.06798e10	−	8.96139e9i	−0.0208589	−	0.0175027i
$401$	−5.97210e11	+	2.17367e11i	−1.15339	+	0.419801i	−0.846733	−	0.532018i	$-0.821434\pi$
$401$	−5.97210e11	+	2.17367e11i	−1.15339	+	0.419801i	−0.306661	+	0.951819i	$0.599212\pi$
$402$		0			0
$403$	−8.20031e9	−	4.65063e10i	−0.0154867	−	0.0878292i
$404$	1.22702e11			0.229159
$405$		0			0
$406$	−1.21240e11			−0.221451
$407$	−6.12109e10	−	3.47145e11i	−0.110574	−	0.627098i
$408$		0			0
$409$	−2.15242e11	+	7.83418e10i	−0.380341	+	0.138433i	−0.525114	−	0.851032i	$-0.675977\pi$
$409$	−2.15242e11	+	7.83418e10i	−0.380341	+	0.138433i	0.144773	+	0.989465i	$0.453755\pi$
$410$	1.45597e11	+	1.22170e11i	0.254462	+	0.213519i
$411$		0			0
$412$	−1.58194e11	−	5.75779e10i	−0.270491	−	0.0984506i
$413$	−1.80590e11	−	3.12790e11i	−0.305434	−	0.529028i
$414$		0			0
$415$	1.94338e11	−	3.36603e11i	0.321619	−	0.557060i
$416$	−6.25388e10	+	5.24763e10i	−0.102383	+	0.0859099i
$417$		0			0
$418$	−1.00746e11	+	5.71359e11i	−0.161411	+	0.915410i
$419$	−1.75299e10	+	9.94169e10i	−0.0277854	+	0.157579i	−0.995544	−	0.0943023i	$-0.969938\pi$
$419$	−1.75299e10	+	9.94169e10i	−0.0277854	+	0.157579i	0.967758	+	0.251881i	$0.0810491\pi$
$420$		0			0
$421$	3.97866e11	−	3.33849e11i	0.617259	−	0.517942i	−0.279681	−	0.960093i	$-0.590229\pi$
$421$	3.97866e11	−	3.33849e11i	0.617259	−	0.517942i	0.896941	+	0.442151i	$0.145784\pi$
$422$	−1.51903e11	+	2.63104e11i	−0.233164	+	0.403851i
$423$		0			0
$424$	−4.30295e11	−	7.45293e11i	−0.646576	−	1.11990i
$425$	1.22868e11	+	4.47203e10i	0.182679	+	0.0664897i
$426$		0			0
$427$	−3.92893e11	−	3.29676e11i	−0.571937	−	0.479913i
$428$	−6.36498e11	+	2.31666e11i	−0.916854	+	0.333707i
$429$		0			0
$430$	−1.29026e11	−	7.31744e11i	−0.181999	−	1.03217i
$431$	1.02370e12			1.42897			0.714485	−	0.699651i	$-0.246661\pi$
$431$	1.02370e12			1.42897			0.714485	+	0.699651i	$0.246661\pi$
$432$		0			0
$433$	6.59846e10			0.0902084			0.0451042	−	0.998982i	$-0.485638\pi$
$433$	6.59846e10			0.0902084			0.0451042	+	0.998982i	$0.485638\pi$
$434$	3.25810e10	+	1.84776e11i	0.0440819	+	0.250001i
$435$		0			0
$436$	−1.42620e11	+	5.19094e10i	−0.189013	+	0.0687950i
$437$	−6.37851e11	−	5.35221e11i	−0.836667	−	0.702047i
$438$		0			0
$439$	−1.14039e12	−	4.15069e11i	−1.46543	−	0.533371i	−0.518571	−	0.855034i	$-0.673536\pi$
$439$	−1.14039e12	−	4.15069e11i	−1.46543	−	0.533371i	−0.946854	+	0.321663i	$0.895758\pi$
$440$	−6.00074e11	−	1.03936e12i	−0.763252	−	1.32199i
$441$		0			0
$442$	−3.58700e10	+	6.21286e10i	−0.0447024	+	0.0774268i
$443$	6.92069e11	−	5.80715e11i	0.853754	−	0.716384i	−0.106859	−	0.994274i	$-0.534079\pi$
$443$	6.92069e11	−	5.80715e11i	0.853754	−	0.716384i	0.960613	+	0.277890i	$0.0896350\pi$
$444$		0			0
$445$	8.03394e10	−	4.55627e11i	0.0971199	−	0.550795i
$446$	−7.19697e10	+	4.08160e11i	−0.0861276	+	0.488454i
$447$		0			0
$448$	3.00995e11	−	2.52565e11i	0.353027	−	0.296225i
$449$	−6.94965e11	+	1.20371e12i	−0.806964	+	1.39770i	0.107993	+	0.994152i	$0.465557\pi$
$449$	−6.94965e11	+	1.20371e12i	−0.806964	+	1.39770i	−0.914957	+	0.403551i	$0.867776\pi$
$450$		0			0
$451$	2.68069e11	+	4.64309e11i	0.305107	+	0.528461i
$452$	−7.78339e11	−	2.83292e11i	−0.877093	−	0.319236i
$453$		0			0
$454$	3.45763e10	+	2.90130e10i	0.0381968	+	0.0320510i
$455$	8.01648e10	−	2.91776e10i	0.0876864	−	0.0319152i
$456$		0			0
$457$	2.17240e11	+	1.23203e12i	0.232979	+	1.32129i	0.846828	+	0.531867i	$0.178510\pi$
$457$	2.17240e11	+	1.23203e12i	0.232979	+	1.32129i	−0.613848	+	0.789424i	$0.710379\pi$
$458$	−9.70990e11			−1.03115
$459$		0			0
$460$	6.15977e11			0.641438
$461$	1.92582e10	+	1.09219e11i	0.0198592	+	0.112627i	0.993126	−	0.117050i	$-0.0373439\pi$
$461$	1.92582e10	+	1.09219e11i	0.0198592	+	0.112627i	−0.973267	+	0.229678i	$0.926233\pi$
$462$		0			0
$463$	1.35017e12	−	4.91420e11i	1.36544	−	0.496980i	0.447709	−	0.894180i	$-0.352240\pi$
$463$	1.35017e12	−	4.91420e11i	1.36544	−	0.496980i	0.917732	+	0.397200i	$0.130018\pi$
$464$	−5.62691e10	−	4.72154e10i	−0.0563558	−	0.0472881i
$465$		0			0
$466$	−8.36333e10	−	3.04400e10i	−0.0821566	−	0.0299026i
$467$	−1.63841e11	−	2.83782e11i	−0.159404	−	0.276095i	0.775250	−	0.631654i	$-0.217624\pi$
$467$	−1.63841e11	−	2.83782e11i	−0.159404	−	0.276095i	−0.934654	+	0.355559i	$0.884290\pi$
$468$		0			0
$469$	5.32091e11	−	9.21608e11i	0.507818	−	0.879566i
$470$	−9.23967e11	+	7.75300e11i	−0.873406	+	0.732874i
$471$		0			0
$472$	1.96620e11	−	1.11509e12i	0.182343	−	1.03412i
$473$	3.63963e11	−	2.06414e12i	0.334336	−	1.89611i
$474$		0			0
$475$	−1.80510e11	+	1.51466e11i	−0.162697	+	0.136519i
$476$	−1.78981e11	+	3.10005e11i	−0.159800	+	0.276782i
$477$		0			0
$478$	1.22409e11	+	2.12018e11i	0.107247	+	0.185758i
$479$	1.68338e12	+	6.12699e11i	1.46107	+	0.531786i	0.945660	−	0.325157i	$-0.105417\pi$
$479$	1.68338e12	+	6.12699e11i	1.46107	+	0.531786i	0.515411	+	0.856943i	$0.327639\pi$
$480$		0			0
$481$	6.01742e10	+	5.04922e10i	0.0512575	+	0.0430102i
$482$	−1.50199e10	+	5.46678e9i	−0.0126752	+	0.00461339i
$483$		0			0
$484$	−9.35268e10	−	5.30417e11i	−0.0774697	−	0.439353i
$485$	2.14884e12			1.76347
$486$		0			0
$487$	−6.82172e11			−0.549558			−0.274779	−	0.961507i	$-0.588605\pi$
$487$	−6.82172e11			−0.549558			−0.274779	+	0.961507i	$0.588605\pi$
$488$	−2.79206e11	−	1.58346e12i	−0.222862	−	1.26391i
$489$		0			0
$490$	5.57600e11	−	2.02950e11i	0.436959	−	0.159040i
$491$	3.52157e11	+	2.95495e11i	0.273445	+	0.229448i	0.769189	−	0.639021i	$-0.220660\pi$
$491$	3.52157e11	+	2.95495e11i	0.273445	+	0.229448i	−0.495744	+	0.868469i	$0.665105\pi$
$492$		0			0
$493$	6.47362e11	+	2.35620e11i	0.493555	+	0.179639i
$494$	−6.46435e10	−	1.11966e11i	−0.0488375	−	0.0845891i
$495$		0			0
$496$	−5.68375e10	+	9.84455e10i	−0.0421665	+	0.0730346i
$497$	−1.17489e10	+	9.85852e9i	−0.00863763	+	0.00724783i
$498$		0			0
$499$	2.55340e11	−	1.44810e12i	0.184360	−	1.04556i	−0.742416	−	0.669940i	$-0.766320\pi$
$499$	2.55340e11	−	1.44810e12i	0.184360	−	1.04556i	0.926775	−	0.375616i	$-0.122569\pi$
$500$	−1.17985e11	+	6.69126e11i	−0.0844232	+	0.478788i
$501$		0			0
$502$	6.33837e10	−	5.31852e10i	0.0445462	−	0.0373787i
$503$	−1.22139e12	+	2.11552e12i	−0.850746	+	1.47354i	0.0297901	+	0.999556i	$0.490516\pi$
$503$	−1.22139e12	+	2.11552e12i	−0.850746	+	1.47354i	−0.880536	+	0.473979i	$0.842817\pi$
$504$		0			0
$505$	−3.30091e11	−	5.71734e11i	−0.225851	−	0.391186i
$506$	−1.30013e12	−	4.73209e11i	−0.881678	−	0.320905i
$507$		0			0
$508$	−4.96743e11	−	4.16816e11i	−0.330936	−	0.277689i
$509$	−3.18548e10	+	1.15942e10i	−0.0210351	+	0.00765615i	−0.352516	−	0.935806i	$-0.614674\pi$
$509$	−3.18548e10	+	1.15942e10i	−0.0210351	+	0.00765615i	0.331481	+	0.943462i	$0.392452\pi$
$510$		0			0
$511$	2.75755e11	+	1.56388e12i	0.178908	+	1.01464i
$512$	4.11448e11			0.264606
$513$		0			0
$514$	−1.05037e12			−0.663754
$515$	1.57284e11	+	8.92002e11i	0.0985263	+	0.558770i
$516$		0			0
$517$	−3.19719e12	+	1.16368e12i	−1.96816	+	0.716352i
$518$	−2.39081e11	−	2.00613e11i	−0.145902	−	0.122426i
$519$		0			0
$520$	2.51315e11	+	9.14711e10i	0.150731	+	0.0548617i
$521$	−6.11020e11	−	1.05832e12i	−0.363317	−	0.629283i	0.625188	−	0.780474i	$-0.285022\pi$
$521$	−6.11020e11	−	1.05832e12i	−0.363317	−	0.629283i	−0.988505	+	0.151191i	$0.951689\pi$
$522$		0			0
$523$	−7.53243e11	+	1.30466e12i	−0.440228	+	0.762497i	−0.997706	−	0.0676944i	$-0.978436\pi$
$523$	−7.53243e11	+	1.30466e12i	−0.440228	+	0.762497i	0.557478	+	0.830192i	$0.311769\pi$
$524$	1.80039e11	−	1.51070e11i	0.104322	−	0.0875364i
$525$		0			0
$526$	−2.76401e11	+	1.56755e12i	−0.157436	+	0.892863i
$527$	1.85132e11	−	1.04993e12i	0.104552	−	0.592945i
$528$		0			0
$529$	1.41357e11	−	1.18613e11i	0.0784814	−	0.0658537i
$530$	−8.27939e11	+	1.43403e12i	−0.455782	+	0.789437i
$531$		0			0
$532$	−3.22554e11	−	5.58679e11i	−0.174582	−	0.302385i
$533$	−1.12269e11	−	4.08626e10i	−0.0602543	−	0.0219308i
$534$		0			0
$535$	2.79174e12	+	2.34255e12i	1.47327	+	1.23622i
$536$	3.13499e12	−	1.14104e12i	1.64057	−	0.597119i
$537$		0			0
$538$	2.55874e11	+	1.45113e12i	0.131676	+	0.746771i
$539$	1.67385e12			0.854215
$540$		0			0
$541$	−3.05022e12			−1.53089			−0.765445	−	0.643501i	$-0.777481\pi$
$541$	−3.05022e12			−1.53089			−0.765445	+	0.643501i	$0.777481\pi$
$542$	2.37620e11	+	1.34761e12i	0.118273	+	0.670760i
$543$		0			0
$544$	−1.73194e12	+	6.30374e11i	−0.847885	+	0.308605i
$545$	6.25545e11	+	5.24895e11i	0.303721	+	0.254852i
$546$		0			0
$547$	2.01299e12	+	7.32668e11i	0.961388	+	0.349916i	0.774577	−	0.632480i	$-0.217963\pi$
$547$	2.01299e12	+	7.32668e11i	0.961388	+	0.349916i	0.186810	+	0.982396i	$0.440185\pi$
$548$	8.42142e10	+	1.45863e11i	0.0398908	+	0.0690929i
$549$		0			0
$550$	−1.95773e11	+	3.39089e11i	−0.0912266	+	0.158009i
$551$	−9.51063e11	+	7.98036e11i	−0.439569	+	0.368842i
$552$		0			0
$553$	2.72637e11	−	1.54620e12i	0.123971	−	0.703076i
$554$	2.29128e10	−	1.29945e11i	0.0103344	−	0.0586092i
$555$		0			0
$556$	1.49253e12	−	1.25238e12i	0.662349	−	0.555777i
$557$	3.43622e11	−	5.95170e11i	0.151263	−	0.261995i	−0.780429	−	0.625244i	$-0.784999\pi$
$557$	3.43622e11	−	5.95170e11i	0.151263	−	0.261995i	0.931692	+	0.363249i	$0.118333\pi$
$558$		0			0
$559$	2.33537e11	+	4.04497e11i	0.101158	+	0.175211i
$560$	−1.92969e11	−	7.02352e10i	−0.0829168	−	0.0301792i
$561$		0			0
$562$	3.75506e11	+	3.15087e11i	0.158783	+	0.133235i
$563$	2.32837e12	−	8.47457e11i	0.976706	−	0.355492i	0.196147	−	0.980574i	$-0.437157\pi$
$563$	2.32837e12	−	8.47457e11i	0.976706	−	0.355492i	0.780559	+	0.625082i	$0.214935\pi$
$564$		0			0
$565$	7.73862e11	+	4.38879e12i	0.319481	+	1.81187i
$566$	2.53565e12			1.03852
$567$		0			0
$568$	−4.80816e10			−0.0193826
$569$	4.83176e11	+	2.74023e12i	0.193242	+	1.09593i	0.914901	+	0.403679i	$0.132269\pi$
$569$	4.83176e11	+	2.74023e12i	0.193242	+	1.09593i	−0.721659	+	0.692248i	$0.756620\pi$
$570$		0			0
$571$	1.54335e12	−	5.61734e11i	0.607578	−	0.221140i	−0.0198650	−	0.999803i	$-0.506324\pi$
$571$	1.54335e12	−	5.61734e11i	0.607578	−	0.221140i	0.627443	+	0.778662i	$0.284101\pi$
$572$	2.06675e11	+	1.73421e11i	0.0807246	+	0.0677360i
$573$		0			0
$574$	4.46061e11	+	1.62353e11i	0.171511	+	0.0624247i
$575$	−2.80971e11	−	4.86656e11i	−0.107190	−	0.185659i
$576$		0			0
$577$	2.04659e12	−	3.54480e12i	0.768670	−	1.33138i	−0.169614	−	0.985510i	$-0.554252\pi$
$577$	2.04659e12	−	3.54480e12i	0.768670	−	1.33138i	0.938284	−	0.345865i	$-0.112414\pi$
$578$	1.27892e11	−	1.07314e11i	0.0476615	−	0.0399927i
$579$		0			0
$580$	1.59487e11	−	9.04495e11i	0.0585193	−	0.331879i
$581$	1.68566e11	−	9.55984e11i	0.0613729	−	0.348063i
$582$		0			0
$583$	−3.57818e12	+	3.00245e12i	−1.28278	+	1.07638i
$584$	−2.48919e12	+	4.31140e12i	−0.885524	+	1.53377i
$585$		0			0
$586$	−7.96769e10	−	1.38004e11i	−0.0279121	−	0.0483452i
$587$	−3.06701e12	−	1.11630e12i	−1.06621	−	0.388070i	−0.251454	−	0.967869i	$-0.580909\pi$
$587$	−3.06701e12	−	1.11630e12i	−1.06621	−	0.388070i	−0.814759	+	0.579799i	$0.803131\pi$
$588$		0			0
$589$	1.47183e12	+	1.23502e12i	0.503895	+	0.422818i
$590$	−2.04727e12	+	7.45146e11i	−0.695571	+	0.253167i
$591$		0			0
$592$	−3.28346e10	−	1.86214e11i	−0.0109871	−	0.0623111i
$593$	4.88443e12			1.62206			0.811032	−	0.585001i	$-0.198906\pi$
$593$	4.88443e12			1.62206			0.811032	+	0.585001i	$0.198906\pi$
$594$		0			0
$595$	1.92596e12			0.629973
$596$	−4.17300e10	−	2.36662e11i	−0.0135469	−	0.0768283i
$597$		0			0
$598$	2.89724e11	−	1.05451e11i	0.0926466	−	0.0337206i
$599$	−2.73777e12	−	2.29726e12i	−0.868912	−	0.729104i	0.0949567	−	0.995481i	$-0.469729\pi$
$599$	−2.73777e12	−	2.29726e12i	−0.868912	−	0.729104i	−0.963869	+	0.266378i	$0.914173\pi$
$600$		0			0
$601$	3.56881e12	+	1.29894e12i	1.11581	+	0.406120i	0.833120	−	0.553092i	$-0.186552\pi$
$601$	3.56881e12	+	1.29894e12i	1.11581	+	0.406120i	0.282686	+	0.959212i	$0.408775\pi$
$602$	−9.27874e11	−	1.60713e12i	−0.287942	−	0.498730i
$603$		0			0
$604$	−1.19893e12	+	2.07661e12i	−0.366545	+	0.634875i
$605$	−2.21988e12	+	1.86270e12i	−0.673645	+	0.565255i
$606$		0			0
$607$	5.79319e11	−	3.28548e12i	0.173208	−	0.982313i	−0.766983	−	0.641667i	$-0.778243\pi$
$607$	5.79319e11	−	3.28548e12i	0.173208	−	0.982313i	0.940192	−	0.340646i	$-0.110646\pi$
$608$	5.76781e11	−	3.27109e12i	0.171177	−	0.970791i
$609$		0			0
$610$	−2.36996e12	+	1.98863e12i	−0.693037	+	0.581527i
$611$	3.79096e11	−	6.56614e11i	0.110043	−	0.190601i
$612$		0			0
$613$	−2.77838e12	−	4.81229e12i	−0.794729	−	1.37651i	−0.923011	−	0.384774i	$-0.874279\pi$
$613$	−2.77838e12	−	4.81229e12i	−0.794729	−	1.37651i	0.128281	−	0.991738i	$-0.459054\pi$
$614$	−1.43319e12	−	5.21637e11i	−0.406954	−	0.148119i
$615$		0			0
$616$	−2.29615e12	−	1.92670e12i	−0.642521	−	0.539139i
$617$	1.62073e12	−	5.89897e11i	0.450222	−	0.163868i	−0.106950	−	0.994264i	$-0.534108\pi$
$617$	1.62073e12	−	5.89897e11i	0.450222	−	0.163868i	0.557172	+	0.830397i	$0.311886\pi$
$618$		0			0
$619$	−8.34582e11	−	4.73315e12i	−0.228487	−	1.29581i	−0.855906	−	0.517131i	$-0.827000\pi$
$619$	−8.34582e11	−	4.73315e12i	−0.228487	−	1.29581i	0.627419	−	0.778682i	$-0.284111\pi$
$620$	−1.42136e12			−0.386315
$621$		0			0
$622$	2.58918e12			0.693595
$623$	−2.00650e11	−	1.13794e12i	−0.0533634	−	0.302639i
$624$		0			0
$625$	4.16711e12	−	1.51670e12i	1.09238	−	0.397595i
$626$	−2.93053e11	−	2.45901e11i	−0.0762714	−	0.0639993i
$627$		0			0
$628$	−2.45136e12	−	8.92221e11i	−0.628910	−	0.228904i
$629$	8.86701e11	+	1.53581e12i	0.225865	+	0.391210i
$630$		0			0
$631$	−2.29459e12	+	3.97434e12i	−0.576199	+	0.998006i	0.419711	+	0.907658i	$0.362131\pi$
$631$	−2.29459e12	+	3.97434e12i	−0.576199	+	0.998006i	−0.995910	+	0.0903481i	$0.971202\pi$
$632$	3.77053e12	−	3.16385e12i	0.940104	−	0.788841i
$633$		0			0
$634$	5.31845e11	−	3.01624e12i	0.130732	−	0.741421i
$635$	−6.05840e11	+	3.43589e12i	−0.147869	+	0.838605i
$636$		0			0
$637$	−2.85738e11	+	2.39763e11i	−0.0687608	+	0.0576972i
$638$	−1.03148e12	+	1.78658e12i	−0.246472	+	0.426903i
$639$		0			0
$640$	1.02182e12	+	1.76985e12i	0.240750	+	0.416990i
$641$	3.03781e12	+	1.10567e12i	0.710721	+	0.258681i	0.671982	−	0.740568i	$-0.265443\pi$
$641$	3.03781e12	+	1.10567e12i	0.710721	+	0.258681i	0.0387398	+	0.999249i	$0.487666\pi$
$642$		0			0
$643$	3.88077e12	+	3.25636e12i	0.895301	+	0.751247i	0.969266	−	0.246014i	$-0.0791210\pi$
$643$	3.88077e12	+	3.25636e12i	0.895301	+	0.751247i	−0.0739655	+	0.997261i	$0.523565\pi$
$644$	1.44565e12	−	5.26172e11i	0.331189	−	0.120543i
$645$		0			0
$646$	−5.06846e11	−	2.87446e12i	−0.114506	−	0.649398i
$647$	7.31844e12			1.64191			0.820955	−	0.570993i	$-0.193442\pi$
$647$	7.31844e12			1.64191			0.820955	+	0.570993i	$0.193442\pi$
$648$		0			0
$649$	−6.14568e12			−1.35978
$650$	−1.51513e10	−	8.59276e10i	−0.00332921	−	0.0188809i
$651$		0			0
$652$	−1.81293e12	+	6.59852e11i	−0.392886	+	0.142999i
$653$	−2.08471e12	−	1.74928e12i	−0.448680	−	0.376487i	0.390266	−	0.920702i	$-0.372383\pi$
$653$	−2.08471e12	−	1.74928e12i	−0.448680	−	0.376487i	−0.838946	+	0.544215i	$0.816828\pi$
$654$		0			0
$655$	−1.18825e12	−	4.32488e11i	−0.252245	−	0.0918096i
$656$	1.43797e11	+	2.49064e11i	0.0303167	+	0.0525101i
$657$		0			0
$658$	−1.50620e12	+	2.60882e12i	−0.313233	+	0.542535i
$659$	−3.18784e12	+	2.67491e12i	−0.658434	+	0.552491i	−0.909617	−	0.415448i	$-0.863625\pi$
$659$	−3.18784e12	+	2.67491e12i	−0.658434	+	0.552491i	0.251183	+	0.967940i	$0.419180\pi$
$660$		0			0
$661$	−1.82179e11	+	1.03319e12i	−0.0371187	+	0.210511i	−0.997726	−	0.0673982i	$-0.978530\pi$
$661$	−1.82179e11	+	1.03319e12i	−0.0371187	+	0.210511i	0.960607	+	0.277909i	$0.0896413\pi$
$662$	1.78717e11	−	1.01355e12i	0.0361663	−	0.205109i
$663$		0			0
$664$	2.33124e12	−	1.95615e12i	0.465406	−	0.390522i
$665$	−1.73545e12	+	3.00589e12i	−0.344124	+	0.596040i
$666$		0			0
$667$	−1.48037e12	−	2.56407e12i	−0.289603	−	0.501607i
$668$	−2.88423e12	−	1.04977e12i	−0.560448	−	0.203986i
$669$		0			0
$670$	−4.91741e12	−	4.12620e12i	−0.942757	−	0.791067i
$671$	−8.20073e12	+	2.98482e12i	−1.56171	+	0.568417i
$672$		0			0
$673$	−6.25268e11	−	3.54607e12i	−0.117489	−	0.666315i	−0.985488	−	0.169748i	$-0.945705\pi$
$673$	−6.25268e11	−	3.54607e12i	−0.117489	−	0.666315i	0.867998	−	0.496567i	$-0.165406\pi$
$674$	1.02813e12			0.191902
$675$		0			0
$676$	2.96254e12			0.545638
$677$	−8.27944e11	−	4.69550e12i	−0.151479	−	0.859079i	−0.961935	−	0.273279i	$-0.911892\pi$
$677$	−8.27944e11	−	4.69550e12i	−0.151479	−	0.859079i	0.810456	−	0.585800i	$-0.199219\pi$
$678$		0			0
$679$	5.04315e12	−	1.83556e12i	0.910517	−	0.331401i
$680$	4.62527e12	+	3.88106e12i	0.829558	+	0.696082i
$681$		0			0
$682$	3.00004e12	+	1.09192e12i	0.531003	+	0.193269i
$683$	−4.45626e12	−	7.71846e12i	−0.783568	−	1.35718i	−0.929851	−	0.367937i	$-0.880064\pi$
$683$	−4.45626e12	−	7.71846e12i	−0.783568	−	1.35718i	0.146282	−	0.989243i	$-0.453269\pi$
$684$		0			0
$685$	4.53102e11	−	7.84795e11i	0.0786300	−	0.136191i
$686$	2.91904e12	−	2.44936e12i	0.503247	−	0.422274i
$687$		0			0
$688$	1.95236e11	−	1.10724e12i	0.0332210	−	0.188406i
$689$	1.80749e11	−	1.02508e12i	0.0305555	−	0.173289i
$690$		0			0
$691$	−4.69982e11	+	3.94362e11i	−0.0784206	+	0.0658027i	−0.681155	−	0.732139i	$-0.738522\pi$
$691$	−4.69982e11	+	3.94362e11i	−0.0784206	+	0.0658027i	0.602735	+	0.797942i	$0.294078\pi$
$692$	−2.15243e12	+	3.72812e12i	−0.356822	+	0.618034i
$693$		0			0
$694$	2.21783e12	+	3.84139e12i	0.362919	+	0.628595i
$695$	−9.85067e12	−	3.58535e12i	−1.60153	−	0.582908i
$696$		0			0
$697$	−2.06623e12	−	1.73377e12i	−0.331613	−	0.278256i
$698$	−2.18214e11	+	7.94232e10i	−0.0347962	+	0.0126648i
$699$		0			0
$700$	−7.56011e10	−	4.28755e11i	−0.0119011	−	0.0674945i
$701$	−4.33085e12			−0.677396			−0.338698	−	0.940895i	$-0.609986\pi$
$701$	−4.33085e12			−0.677396			−0.338698	+	0.940895i	$0.609986\pi$
$702$		0			0
$703$	−3.19596e12			−0.493517
$704$	−1.16097e12	−	6.58420e12i	−0.178133	−	1.01024i
$705$		0			0
$706$	4.94469e11	−	1.79972e11i	0.0749063	−	0.0272637i
$707$	−1.26307e12	−	1.05984e12i	−0.190126	−	0.159535i
$708$		0			0
$709$	−8.61963e12	−	3.13729e12i	−1.28109	−	0.466280i	−0.390299	−	0.920688i	$-0.627628\pi$
$709$	−8.61963e12	−	3.13729e12i	−1.28109	−	0.466280i	−0.890793	+	0.454408i	$0.849851\pi$
$710$	4.62574e10	+	8.01202e10i	0.00683154	+	0.0118326i
$711$		0			0
$712$	1.81123e12	−	3.13715e12i	0.264128	−	0.457483i
$713$	−3.50997e12	+	2.94521e12i	−0.508628	+	0.426789i
$714$		0			0
$715$	2.52066e11	−	1.42954e12i	0.0360693	−	0.204559i
$716$	−8.31077e11	+	4.71327e12i	−0.118177	+	0.670214i
$717$		0			0
$718$	−2.16129e12	+	1.81354e12i	−0.303496	+	0.254663i
$719$	−1.32786e12	+	2.29993e12i	−0.185299	+	0.320948i	−0.943677	−	0.330867i	$-0.892659\pi$
$719$	−1.32786e12	+	2.29993e12i	−0.185299	+	0.320948i	0.758378	+	0.651815i	$0.225992\pi$
$720$		0			0
$721$	1.13109e12	+	1.95910e12i	0.155879	+	0.269990i
$722$	3.74724e11	+	1.36388e11i	0.0513209	+	0.0186793i
$723$		0			0
$724$	1.79971e12	+	1.51014e12i	0.243433	+	0.204264i
$725$	−7.87349e11	+	2.86572e11i	−0.105839	+	0.0385223i
$726$		0			0
$727$	6.45108e11	+	3.65859e12i	0.0856501	+	0.485746i	0.997214	+	0.0745883i	$0.0237643\pi$
$727$	6.45108e11	+	3.65859e12i	0.0856501	+	0.485746i	−0.911564	+	0.411157i	$0.865125\pi$
$728$	6.67950e11			0.0881359
$729$		0			0
$730$	9.57900e12			1.24844
$731$	1.83107e12	+	1.03845e13i	0.237180	+	1.34511i
$732$		0			0
$733$	−5.05347e12	+	1.83931e12i	−0.646579	+	0.235336i	−0.644432	−	0.764662i	$-0.722906\pi$
$733$	−5.05347e12	+	1.83931e12i	−0.646579	+	0.235336i	−0.00214794	+	0.999998i	$0.500684\pi$
$734$	5.14129e12	+	4.31405e12i	0.653792	+	0.548597i
$735$		0			0
$736$	7.44338e12	+	2.70917e12i	0.935019	+	0.340319i
$737$	−9.05383e12	−	1.56817e13i	−1.13039	−	1.95789i
$738$		0			0
$739$	2.19535e12	−	3.80246e12i	0.270773	−	0.468992i	−0.698287	−	0.715818i	$-0.746054\pi$
$739$	2.19535e12	−	3.80246e12i	0.270773	−	0.468992i	0.969060	+	0.246826i	$0.0793875\pi$
$740$	1.81115e12	−	1.51974e12i	0.222030	−	0.186305i
$741$		0			0
$742$	−7.18142e11	+	4.07278e12i	−0.0869746	+	0.493258i
$743$	3.02652e11	−	1.71643e12i	0.0364330	−	0.206622i	−0.961157	−	0.276001i	$-0.910991\pi$
$743$	3.02652e11	−	1.71643e12i	0.0364330	−	0.206622i	0.997590	+	0.0693793i	$0.0221019\pi$
$744$		0			0
$745$	−9.90472e11	+	8.31105e11i	−0.117798	+	0.0988445i
$746$	9.01602e11	−	1.56162e12i	0.106584	−	0.184608i
$747$		0			0
$748$	3.04547e12	+	5.27491e12i	0.355711	+	0.616110i
$749$	8.55301e12	+	3.11304e12i	0.993003	+	0.361424i
$750$		0			0
$751$	2.34406e12	+	1.96690e12i	0.268899	+	0.225633i	0.767259	−	0.641337i	$-0.221620\pi$
$751$	2.34406e12	+	1.96690e12i	0.268899	+	0.225633i	−0.498360	+	0.866970i	$0.666064\pi$
$752$	−1.71503e12	+	6.24218e11i	−0.195565	+	0.0711797i
$753$		0			0
$754$	−7.98287e10	−	4.52731e11i	−0.00899473	−	0.0510116i
$755$	1.29013e13			1.44502
$756$		0			0
$757$	−1.17914e13			−1.30507			−0.652535	−	0.757758i	$-0.726295\pi$
$757$	−1.17914e13			−1.30507			−0.652535	+	0.757758i	$0.726295\pi$
$758$	−1.17262e12	−	6.65023e12i	−0.129016	−	0.731687i
$759$		0			0
$760$	−1.02250e13	+	3.72159e12i	−1.11174	+	0.404639i
$761$	−4.18195e12	−	3.50907e12i	−0.452009	−	0.379281i	0.388172	−	0.921587i	$-0.373107\pi$
$761$	−4.18195e12	−	3.50907e12i	−0.452009	−	0.379281i	−0.840181	+	0.542306i	$0.817551\pi$
$762$		0			0
$763$	1.91647e12	+	6.97538e11i	0.204711	+	0.0745088i
$764$	−2.82294e12	−	4.88948e12i	−0.299766	−	0.519209i
$765$		0			0
$766$	3.75357e12	−	6.50137e12i	0.393926	−	0.682300i
$767$	1.04911e12	−	8.80308e11i	0.109457	−	0.0918450i
$768$		0			0
$769$	−1.57900e12	+	8.95494e12i	−0.162822	+	0.923409i	0.788460	+	0.615086i	$0.210879\pi$
$769$	−1.57900e12	+	8.95494e12i	−0.162822	+	0.923409i	−0.951282	+	0.308323i	$0.900232\pi$
$770$	−1.00149e12	+	5.67976e12i	−0.102669	+	0.582266i
$771$		0			0
$772$	7.60362e12	−	6.38020e12i	0.770447	−	0.646482i
$773$	−2.65497e12	+	4.59854e12i	−0.267455	+	0.463246i	−0.968204	−	0.250162i	$-0.919516\pi$
$773$	−2.65497e12	+	4.59854e12i	−0.267455	+	0.463246i	0.700749	+	0.713408i	$0.252849\pi$
$774$		0			0
$775$	6.48337e11	+	1.12295e12i	0.0645570	+	0.111816i
$776$	1.58102e13	+	5.75444e12i	1.56516	+	0.569672i
$777$		0			0
$778$	5.12517e12	+	4.30053e12i	0.501534	+	0.420837i
$779$	4.56778e12	−	1.66253e12i	0.444413	−	0.161753i
$780$		0			0
$781$	4.53170e10	+	2.57006e11i	0.00435844	+	0.0247180i
$782$	6.96065e12			0.665609
$783$		0			0
$784$	8.97883e11			0.0848784
$785$	2.43726e12	+	1.38224e13i	0.229080	+	1.29918i
$786$		0			0
$787$	−3.51971e12	+	1.28107e12i	−0.327055	+	0.119038i	−0.500329	−	0.865835i	$-0.666788\pi$
$787$	−3.51971e12	+	1.28107e12i	−0.327055	+	0.119038i	0.173274	+	0.984874i	$0.444565\pi$
$788$	5.98356e12	+	5.02080e12i	0.552830	+	0.463879i
$789$		0			0
$790$	−8.89952e12	−	3.23916e12i	−0.812914	−	0.295877i
$791$	5.56512e12	+	9.63908e12i	0.505453	+	0.875470i
$792$		0			0
$793$	9.72376e11	−	1.68420e12i	0.0873182	−	0.151240i
$794$	6.85574e12	−	5.75265e12i	0.612156	−	0.513660i
$795$		0			0
$796$	−1.36805e12	+	7.75862e12i	−0.120780	+	0.684976i
$797$	−6.59110e11	+	3.73800e12i	−0.0578623	+	0.328153i	−0.999974	−	0.00714451i	$-0.997726\pi$
$797$	−6.59110e11	+	3.73800e12i	−0.0578623	+	0.328153i	0.942112	+	0.335298i	$0.108837\pi$
$798$		0			0
$799$	1.31125e13	−	1.10027e13i	1.13821	−	0.955075i
$800$	1.12082e12	−	1.94132e12i	0.0967457	−	0.167568i
$801$		0			0
$802$	4.78729e12	+	8.29183e12i	0.408607	+	0.707727i
$803$	2.53913e13	+	9.24169e12i	2.15509	+	0.784389i
$804$		0			0
$805$	−6.34075e12	−	5.32052e12i	−0.532181	−	0.446553i
$806$	−6.68535e11	+	2.43327e11i	−0.0557977	+	0.0203087i
$807$		0			0
$808$	−8.97594e11	−	5.09051e12i	−0.0740847	−	0.420155i
$809$	−1.37037e13			−1.12479			−0.562394	−	0.826870i	$-0.690119\pi$
$809$	−1.37037e13			−1.12479			−0.562394	+	0.826870i	$0.690119\pi$
$810$		0			0
$811$	2.17179e13			1.76289			0.881444	−	0.472289i	$-0.156572\pi$
$811$	2.17179e13			1.76289			0.881444	+	0.472289i	$0.156572\pi$
$812$	−3.98324e11	−	2.25901e12i	−0.0321539	−	0.182354i
$813$		0			0
$814$	−4.99026e12	+	1.81631e12i	−0.398394	+	0.145004i
$815$	7.95168e12	+	6.67226e12i	0.631320	+	0.529741i
$816$		0			0
$817$	−1.78573e13	−	6.49952e12i	−1.40222	−	0.510366i
$818$	1.72540e12	+	2.98849e12i	0.134741	+	0.233379i
$819$		0			0
$820$	−1.79799e12	+	3.11422e12i	−0.138876	+	0.240540i
$821$	4.62072e11	−	3.87724e11i	0.0354948	−	0.0297837i	−0.624868	−	0.780731i	$-0.714847\pi$
$821$	4.62072e11	−	3.87724e11i	0.0354948	−	0.0297837i	0.660363	+	0.750947i	$0.270403\pi$
$822$		0			0
$823$	−3.35539e12	+	1.90294e13i	−0.254943	+	1.44586i	0.541275	+	0.840846i	$0.317942\pi$
$823$	−3.35539e12	+	1.90294e13i	−0.254943	+	1.44586i	−0.796218	+	0.605010i	$0.793169\pi$
$824$	−1.23149e12	+	6.98413e12i	−0.0930590	+	0.527764i
$825$		0			0
$826$	−4.16826e12	+	3.49759e12i	−0.311562	+	0.261432i
$827$	1.29968e13	−	2.25112e13i	0.966190	−	1.67349i	0.259806	−	0.965661i	$-0.416341\pi$
$827$	1.29968e13	−	2.25112e13i	0.966190	−	1.67349i	0.706384	−	0.707829i	$-0.250325\pi$
$828$		0			0
$829$	−6.25121e12	−	1.08274e13i	−0.459694	−	0.796213i	0.539251	−	0.842145i	$-0.318708\pi$
$829$	−6.25121e12	−	1.08274e13i	−0.459694	−	0.796213i	−0.998945	+	0.0459320i	$0.985374\pi$
$830$	−5.50240e12	−	2.00271e12i	−0.402439	−	0.146476i
$831$		0			0
$832$	1.14131e12	+	9.57672e11i	0.0825749	+	0.0692886i
$833$	−7.91318e12	+	2.88016e12i	−0.569440	+	0.207259i
$834$		0			0
$835$	2.86764e12	+	1.62632e13i	0.204143	+	1.15775i
$836$	−1.09769e13			−0.777232
$837$		0			0
$838$	1.52085e12			0.106534
$839$	−2.43824e12	−	1.38280e13i	−0.169882	−	0.963451i	−0.943886	−	0.330270i	$-0.892860\pi$
$839$	−2.43824e12	−	1.38280e13i	−0.169882	−	0.963451i	0.774004	−	0.633181i	$-0.218251\pi$
$840$		0			0
$841$	9.48391e12	−	3.45186e12i	0.653741	−	0.237942i
$842$	−5.99398e12	−	5.02955e12i	−0.410971	−	0.344846i
$843$		0			0
$844$	−5.40137e12	−	1.96594e12i	−0.366406	−	0.133361i
$845$	−7.96976e12	−	1.38040e13i	−0.537762	−	0.931431i
$846$		0			0
$847$	−3.61874e12	+	6.26785e12i	−0.241592	+	0.418450i
$848$	−1.91940e12	+	1.61057e12i	−0.127463	+	0.106954i
$849$		0			0
$850$	3.42060e11	−	1.93992e12i	0.0224759	−	0.127467i
$851$	1.32347e12	−	7.50580e12i	0.0865033	−	0.490584i
$852$		0			0
$853$	−6.20170e11	+	5.20385e11i	−0.0401089	+	0.0336553i	−0.662622	−	0.748954i	$-0.730556\pi$
$853$	−6.20170e11	+	5.20385e11i	−0.0401089	+	0.0336553i	0.622513	+	0.782610i	$0.286112\pi$
$854$	−3.86339e12	+	6.69159e12i	−0.248547	+	0.430496i
$855$		0			0
$856$	1.42672e13	+	2.47115e13i	0.908251	+	1.57314i
$857$	−6.00301e12	−	2.18492e12i	−0.380150	−	0.138363i	0.144875	−	0.989450i	$-0.453722\pi$
$857$	−6.00301e12	−	2.18492e12i	−0.380150	−	0.138363i	−0.525025	+	0.851087i	$0.675944\pi$
$858$		0			0
$859$	−1.16461e13	−	9.77223e12i	−0.729812	−	0.612385i	0.200269	−	0.979741i	$-0.435819\pi$
$859$	−1.16461e13	−	9.77223e12i	−0.729812	−	0.612385i	−0.930080	+	0.367356i	$0.880263\pi$
$860$	1.32104e13	−	4.80818e12i	0.823516	−	0.299735i
$861$		0			0
$862$	−2.67805e12	−	1.51880e13i	−0.165210	−	0.936953i
$863$	−1.77505e13			−1.08933			−0.544667	−	0.838652i	$-0.683344\pi$
$863$	−1.77505e13			−1.08933			−0.544667	+	0.838652i	$0.683344\pi$
$864$		0			0
$865$	2.31616e13			1.40668
$866$	−1.72620e11	−	9.78977e11i	−0.0104294	−	0.0591483i
$867$		0			0
$868$	−3.33581e12	+	1.21414e12i	−0.199463	+	0.0725987i
$869$	−2.04651e13	−	1.71723e13i	−1.21738	−	1.02150i
$870$		0			0
$871$	3.79180e12	+	1.38010e12i	0.223236	+	0.0812512i
$872$	3.19684e12	+	5.53709e12i	0.187239	+	0.324308i
$873$		0			0
$874$	−6.27211e12	+	1.08636e13i	−0.363590	+	0.629757i
$875$	6.99411e12	−	5.86875e12i	0.403363	−	0.338462i
$876$		0			0
$877$	−7.62180e11	+	4.32254e12i	−0.0435070	+	0.246741i	−0.998803	−	0.0489099i	$-0.984425\pi$
$877$	−7.62180e11	+	4.32254e12i	−0.0435070	+	0.246741i	0.955296	+	0.295651i	$0.0955364\pi$
$878$	−3.17480e12	+	1.80052e13i	−0.180298	+	1.02252i
$879$		0			0
$880$	−2.67672e12	+	2.24604e12i	−0.150464	+	0.126254i
$881$	−1.28773e13	+	2.23041e13i	−0.720165	+	1.24736i	0.240768	+	0.970583i	$0.422601\pi$
$881$	−1.28773e13	+	2.23041e13i	−0.720165	+	1.24736i	−0.960933	+	0.276780i	$0.910733\pi$
$882$		0			0
$883$	−1.61012e13	−	2.78881e13i	−0.891322	−	1.54381i	−0.838292	−	0.545222i	$-0.816445\pi$
$883$	−1.61012e13	−	2.78881e13i	−0.891322	−	1.54381i	−0.0530302	−	0.998593i	$-0.516888\pi$
$884$	−1.27546e12	−	4.64231e11i	−0.0702478	−	0.0255681i
$885$		0			0
$886$	−1.04262e13	−	8.74865e12i	−0.568429	−	0.476968i
$887$	−1.91150e13	+	6.95730e12i	−1.03686	+	0.377385i	−0.803688	−	0.595051i	$-0.797132\pi$
$887$	−1.91150e13	+	6.95730e12i	−1.03686	+	0.377385i	−0.233169	+	0.972436i	$0.574909\pi$
$888$		0			0
$889$	1.51311e12	+	8.58125e12i	0.0812478	+	0.460779i
$890$	−6.97006e12			−0.372376
$891$		0			0
$892$	−7.84153e12			−0.414724
$893$	5.35667e12	+	3.03792e13i	0.281879	+	1.59862i
$894$		0			0
$895$	2.41973e13	−	8.80710e12i	1.26056	−	0.458806i
$896$	3.90995e12	+	3.28083e12i	0.202668	+	0.170058i
$897$		0			0
$898$	1.96769e13	+	7.16181e12i	1.00975	+	0.367519i
$899$	3.41593e12	+	5.91656e12i	0.174418	+	0.302100i
$900$		0			0
$901$	1.17497e13	−	2.03511e13i	0.593970	−	1.02879i
$902$	6.18741e12	−	5.19186e12i	0.311229	−	0.261152i
$903$		0			0
$904$	−6.05912e12	+	3.43630e13i	−0.301753	+	1.71133i
$905$	2.19497e12	−	1.24483e13i	0.108770	−	0.616867i
$906$		0			0
$907$	7.78211e12	−	6.52997e12i	0.381825	−	0.320389i	−0.431593	−	0.902068i	$-0.642048\pi$
$907$	7.78211e12	−	6.52997e12i	0.381825	−	0.320389i	0.813418	+	0.581679i	$0.197604\pi$
$908$	−4.26989e11	+	7.39566e11i	−0.0208463	+	0.0361069i
$909$		0			0
$910$	−6.42608e11	−	1.11303e12i	−0.0310642	−	0.0538047i
$911$	1.31480e13	+	4.78548e12i	0.632451	+	0.230193i	0.638298	−	0.769790i	$-0.279639\pi$
$911$	1.31480e13	+	4.78548e12i	0.632451	+	0.230193i	−0.00584676	+	0.999983i	$0.501861\pi$
$912$		0			0
$913$	−1.26532e13	−	1.06173e13i	−0.602672	−	0.505702i
$914$	1.77106e13	−	6.44615e12i	0.839414	−	0.305522i
$915$		0			0
$916$	−3.19012e12	−	1.80921e13i	−0.149719	−	0.849099i
$917$	−3.15816e12			−0.147493
$918$		0			0
$919$	−1.49823e12			−0.0692881			−0.0346440	−	0.999400i	$-0.511030\pi$
$919$	−1.49823e12			−0.0692881			−0.0346440	+	0.999400i	$0.511030\pi$
$920$	−4.50600e12	−	2.55548e13i	−0.207370	−	1.17605i
$921$		0			0
$922$	1.57004e12	−	5.71447e11i	0.0715519	−	0.0260428i
$923$	−4.45495e10	−	3.73814e10i	−0.00202039	−	0.00169531i
$924$		0			0
$925$	−2.02681e12	−	7.37699e11i	−0.0910280	−	0.0331315i
$926$	−1.08231e13	−	1.87461e13i	−0.483727	−	0.837840i
$927$		0			0
$928$	5.90533e12	−	1.02283e13i	0.261384	−	0.452730i
$929$	−1.67699e13	+	1.40716e13i	−0.738687	+	0.619832i	−0.932485	−	0.361209i	$-0.882364\pi$
$929$	−1.67699e13	+	1.40716e13i	−0.738687	+	0.619832i	0.193797	+	0.981042i	$0.437920\pi$
$930$		0			0
$931$	2.63530e12	−	1.49455e13i	0.114962	−	0.651984i
$932$	2.92405e11	−	1.65831e12i	0.0126944	−	0.0719937i
$933$		0			0
$934$	−3.78169e12	+	3.17322e12i	−0.162602	+	0.136439i
$935$	1.63857e13	−	2.83809e13i	0.701153	−	1.21443i
$936$		0			0
$937$	−8.69489e12	−	1.50600e13i	−0.368499	−	0.638258i	0.620833	−	0.783943i	$-0.286795\pi$
$937$	−8.69489e12	−	1.50600e13i	−0.368499	−	0.638258i	−0.989331	+	0.145685i	$0.953461\pi$
$938$	−1.50654e13	−	5.48335e12i	−0.635429	−	0.231277i
$939$		0			0
$940$	−1.74815e13	−	1.46687e13i	−0.730302	−	0.612796i
$941$	−1.00914e13	+	3.67298e12i	−0.419565	+	0.152709i	−0.543171	−	0.839622i	$-0.682776\pi$
$941$	−1.00914e13	+	3.67298e12i	−0.419565	+	0.152709i	0.123606	+	0.992331i	$0.460554\pi$
$942$		0			0
$943$	2.01295e12	+	1.14160e13i	0.0828955	+	0.470124i
$944$	−3.29665e12			−0.135113
$945$		0			0
$946$	−3.15766e13			−1.28190
$947$	−1.32708e12	−	7.52627e12i	−0.0536196	−	0.304092i	0.946190	−	0.323612i	$-0.104897\pi$
$947$	−1.32708e12	−	7.52627e12i	−0.0536196	−	0.304092i	−0.999809	+	0.0195201i	$0.993786\pi$
$948$		0			0
$949$	−5.65827e12	+	2.05944e12i	−0.226457	+	0.0824235i
$950$	2.71944e12	+	2.28188e12i	0.108324	+	0.0908944i
$951$		0			0
$952$	1.41703e13	+	5.15758e12i	0.559132	+	0.203507i
$953$	6.20174e12	+	1.07417e13i	0.243554	+	0.421848i	0.961724	−	0.274020i	$-0.0883534\pi$
$953$	6.20174e12	+	1.07417e13i	0.243554	+	0.421848i	−0.718170	+	0.695868i	$0.755020\pi$
$954$		0			0
$955$	−1.51884e13	+	2.63071e13i	−0.590877	+	1.02343i
$956$	−3.54827e12	+	2.97735e12i	−0.137390	+	0.115284i
$957$		0			0
$958$	4.68645e12	−	2.65782e13i	0.179763	−	1.01948i
$959$	3.93013e11	−	2.22889e12i	0.0150046	−	0.0850952i
$960$		0			0
$961$	−1.21547e13	+	1.01990e13i	−0.459716	+	0.385748i
$962$	5.91704e11	−	1.02486e12i	0.0222750	−	0.0385814i
$963$		0			0
$964$	−1.51207e11	−	2.61898e11i	−0.00563930	−	0.00976755i
$965$	−5.01837e13	−	1.82654e13i	−1.86290	−	0.678041i
$966$		0			0
$967$	2.99282e13	+	2.51128e13i	1.10068	+	0.923582i	0.997471	−	0.0710777i	$-0.0226438\pi$
$967$	2.99282e13	+	2.51128e13i	1.10068	+	0.923582i	0.103211	+	0.994659i	$0.467088\pi$
$968$	−2.13210e13	+	7.76022e12i	−0.780494	+	0.284076i
$969$		0			0
$970$	−5.62152e12	−	3.18812e13i	−0.203883	−	1.15628i
$971$	3.60297e13			1.30069			0.650345	−	0.759639i	$-0.274624\pi$
$971$	3.60297e13			1.30069			0.650345	+	0.759639i	$0.274624\pi$
$972$		0			0
$973$	−2.61813e13			−0.936448
$974$	1.78461e12	+	1.01210e13i	0.0635370	+	0.360336i
$975$		0			0
$976$	−4.39901e12	+	1.60111e12i	−0.155178	+	0.0564803i
$977$	2.48466e13	+	2.08488e13i	0.872453	+	0.732075i	0.964613	−	0.263669i	$-0.0849328\pi$
$977$	2.48466e13	+	2.08488e13i	0.872453	+	0.732075i	−0.0921604	+	0.995744i	$0.529377\pi$
$978$		0			0
$979$	−1.84758e13	−	6.72463e12i	−0.642806	−	0.233962i
$980$	5.61343e12	+	9.72275e12i	0.194407	+	0.336722i
$981$		0			0
$982$	3.46283e12	−	5.99780e12i	0.118831	−	0.205821i
$983$	−5.27198e12	+	4.42372e12i	−0.180087	+	0.151111i	−0.728375	−	0.685178i	$-0.759724\pi$
$983$	−5.27198e12	+	4.42372e12i	−0.180087	+	0.151111i	0.548288	+	0.836290i	$0.315280\pi$
$984$		0			0
$985$	7.29770e12	−	4.13873e13i	0.247015	−	1.40089i
$986$	1.80223e12	−	1.02209e13i	0.0607245	−	0.344386i
$987$		0			0
$988$	1.87383e12	−	1.57233e12i	0.0625639	−	0.0524974i
$989$	2.26592e13	−	3.92468e13i	0.753114	−	1.30443i
$990$		0			0
$991$	−2.47791e12	−	4.29187e12i	−0.0816120	−	0.141356i	0.822330	−	0.569010i	$-0.192674\pi$
$991$	−2.47791e12	−	4.29187e12i	−0.0816120	−	0.141356i	−0.903943	+	0.427654i	$0.859340\pi$
$992$	−1.71755e13	−	6.25138e12i	−0.563128	−	0.204962i
$993$		0			0
$994$	1.77001e11	+	1.48522e11i	0.00575093	+	0.00482560i
$995$	3.98317e13	−	1.44976e13i	1.28832	−	0.468912i
$996$		0			0
$997$	−3.69434e12	−	2.09517e13i	−0.118416	−	0.671568i	−0.985002	−	0.172542i	$-0.944802\pi$
$997$	−3.69434e12	−	2.09517e13i	−0.118416	−	0.671568i	0.866587	−	0.499027i	$-0.166309\pi$
$998$	−2.21527e13			−0.706870
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.10		156
3.2	odd	2		27.10.e.a.13.17	✓	156
27.2	odd	18		27.10.e.a.25.17	yes	156
27.25	even	9	inner	81.10.e.a.73.10		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.17	✓	156	3.2	odd	2
27.10.e.a.25.17	yes	156	27.2	odd	18
81.10.e.a.10.10		156	1.1	even	1	trivial
81.10.e.a.73.10		156	27.25	even	9	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.61607 - 14.8364i) q^{2} +(267.846 - 97.4881i) q^{4} +(-1174.80 - 985.775i) q^{5} +(-3599.21 - 1310.01i) q^{7} +(-6003.80 - 10398.9i) q^{8} +(-11552.0 + 20008.7i) q^{10} +(-49925.5 + 41892.5i) q^{11} +(2521.95 - 14302.7i) q^{13} +(-10020.1 + 56826.6i) q^{14} +(-26780.9 + 22471.8i) q^{16} +(163941. - 283953. i) q^{17} +(295448. + 511730. i) q^{19} +(-410767. - 149507. i) q^{20} +(752143. + 631123. i) q^{22} +(-1.32416e6 + 481955. i) q^{23} +(69247.9 + 392725. i) q^{25} -218798. q^{26} -1.09175e6 q^{28} +(364850. + 2.06917e6i) q^{29} +(3.05548e6 - 1.11211e6i) q^{31} +(-4.30610e6 - 3.61324e6i) q^{32} +(-4.64174e6 - 1.68945e6i) q^{34} +(2.93699e6 + 5.08701e6i) q^{35} +(-2.70434e6 + 4.68405e6i) q^{37} +(6.81935e6 - 5.72211e6i) q^{38} +(-3.19769e6 + 1.81350e7i) q^{40} +(1.42849e6 - 8.10140e6i) q^{41} +(-2.46362e7 + 2.06722e7i) q^{43} +(-9.28834e6 + 1.60879e7i) q^{44} +(1.06146e7 + 1.83850e7i) q^{46} +(4.90568e7 + 1.78552e7i) q^{47} +(-1.96744e7 - 1.65088e7i) q^{49} +(5.64548e6 - 2.05479e6i) q^{50} +(-718846. - 4.07678e6i) q^{52} +7.16704e7 q^{53} +9.99490e7 q^{55} +(7.98635e6 + 4.52928e7i) q^{56} +(2.97447e7 - 1.08262e7i) q^{58} +(7.22363e7 + 6.06134e7i) q^{59} +(1.25830e8 + 4.57984e7i) q^{61} +(-2.44930e7 - 4.24232e7i) q^{62} +(-5.12924e7 + 8.88411e7i) q^{64} +(-1.70620e7 + 1.43167e7i) q^{65} +(-4.82463e7 + 2.73619e8i) q^{67} +(1.62288e7 - 9.20381e7i) q^{68} +(6.77898e7 - 5.68824e7i) q^{70} +(2.00213e6 - 3.46779e6i) q^{71} +(-2.07301e8 - 3.59056e8i) q^{73} +(7.65693e7 + 2.78690e7i) q^{74} +(1.29022e8 + 1.08262e8i) q^{76} +(2.34572e8 - 8.53771e7i) q^{77} +(7.11807e7 + 4.03686e8i) q^{79} +5.36144e7 q^{80} -1.23933e8 q^{82} +(4.40096e7 + 2.49591e8i) q^{83} +(-4.72512e8 + 1.71980e8i) q^{85} +(3.71152e8 + 3.11433e8i) q^{86} +(7.35378e8 + 2.67656e8i) q^{88} +(1.50841e8 + 2.61263e8i) q^{89} +(-2.78136e7 + 4.81746e7i) q^{91} +(-3.07687e8 + 2.58180e8i) q^{92} +(1.36572e8 - 7.74540e8i) q^{94} +(1.57359e8 - 8.92426e8i) q^{95} +(-1.07337e9 + 9.00663e8i) q^{97} +(-1.93463e8 + 3.35087e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

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