LMFDB - Embedded newform 84.12.b.a.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(55,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("84.55");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.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:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.2
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-45.2221 + 1.72065i) q^{2} -243.000 q^{3} +(2042.08 - 155.623i) q^{4} -479.067i q^{5} +(10989.0 - 418.118i) q^{6} +(18444.0 + 40461.6i) q^{7} +(-92079.3 + 10551.3i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-45.2221 + 1.72065i) q^{2} -243.000 q^{3} +(2042.08 - 155.623i) q^{4} -479.067i q^{5} +(10989.0 - 418.118i) q^{6} +(18444.0 + 40461.6i) q^{7} +(-92079.3 + 10551.3i) q^{8} +59049.0 q^{9} +(824.307 + 21664.4i) q^{10} -617971. i q^{11} +(-496225. + 37816.3i) q^{12} +805412. i q^{13} +(-903698. - 1.79803e6i) q^{14} +116413. i q^{15} +(4.14587e6 - 635588. i) q^{16} -6.15701e6i q^{17} +(-2.67032e6 + 101603. i) q^{18} +3.03570e6 q^{19} +(-74553.8 - 978293. i) q^{20} +(-4.48190e6 - 9.83218e6i) q^{21} +(1.06331e6 + 2.79460e7i) q^{22} +6.78832e6i q^{23} +(2.23753e7 - 2.56396e6i) q^{24} +4.85986e7 q^{25} +(-1.38583e6 - 3.64224e7i) q^{26} -1.43489e7 q^{27} +(4.39609e7 + 7.97555e7i) q^{28} -2.53110e7 q^{29} +(-200307. - 5.26446e6i) q^{30} -2.54102e8 q^{31} +(-1.86391e8 + 3.58762e7i) q^{32} +1.50167e8i q^{33} +(1.05941e7 + 2.78433e8i) q^{34} +(1.93838e7 - 8.83593e6i) q^{35} +(1.20583e8 - 9.18937e6i) q^{36} -3.76158e8 q^{37} +(-1.37281e8 + 5.22338e6i) q^{38} -1.95715e8i q^{39} +(5.05478e6 + 4.41122e7i) q^{40} +6.88640e8i q^{41} +(2.19599e8 + 4.36920e8i) q^{42} +1.05610e9i q^{43} +(-9.61704e7 - 1.26195e9i) q^{44} -2.82884e7i q^{45} +(-1.16803e7 - 3.06982e8i) q^{46} +1.61462e9 q^{47} +(-1.00745e9 + 1.54448e8i) q^{48} +(-1.29696e9 + 1.49255e9i) q^{49} +(-2.19773e9 + 8.36212e7i) q^{50} +1.49615e9i q^{51} +(1.25340e8 + 1.64471e9i) q^{52} +2.86554e9 q^{53} +(6.48888e8 - 2.46894e7i) q^{54} -2.96050e8 q^{55} +(-2.12524e9 - 3.53107e9i) q^{56} -7.37675e8 q^{57} +(1.14462e9 - 4.35514e7i) q^{58} -5.63596e9 q^{59} +(1.81166e7 + 2.37725e8i) q^{60} -7.15254e9i q^{61} +(1.14910e10 - 4.37221e8i) q^{62} +(1.08910e9 + 2.38922e9i) q^{63} +(8.36728e9 - 1.94311e9i) q^{64} +3.85847e8 q^{65} +(-2.58385e8 - 6.79087e9i) q^{66} -3.11480e9i q^{67} +(-9.58172e8 - 1.25731e10i) q^{68} -1.64956e9i q^{69} +(-8.61375e8 + 4.32932e8i) q^{70} -1.04104e10i q^{71} +(-5.43719e9 + 6.23043e8i) q^{72} -2.84639e10i q^{73} +(1.70107e10 - 6.47236e8i) q^{74} -1.18095e10 q^{75} +(6.19914e9 - 4.72424e8i) q^{76} +(2.50041e10 - 1.13979e10i) q^{77} +(3.36757e8 + 8.85065e9i) q^{78} +4.17004e10i q^{79} +(-3.04489e8 - 1.98615e9i) q^{80} +3.48678e9 q^{81} +(-1.18491e9 - 3.11418e10i) q^{82} +3.43032e10 q^{83} +(-1.06825e10 - 1.93806e10i) q^{84} -2.94962e9 q^{85} +(-1.81718e9 - 4.77591e10i) q^{86} +6.15058e9 q^{87} +(6.52040e9 + 5.69024e10i) q^{88} -1.68359e10i q^{89} +(4.86745e7 + 1.27926e9i) q^{90} +(-3.25883e10 + 1.48550e10i) q^{91} +(1.05642e9 + 1.38623e10i) q^{92} +6.17468e10 q^{93} +(-7.30163e10 + 2.77819e9i) q^{94} -1.45430e9i q^{95} +(4.52931e10 - 8.71792e9i) q^{96} -1.64842e11i q^{97} +(5.60832e10 - 6.97280e10i) q^{98} -3.64906e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) $ 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−45.2221	+	1.72065i	−0.999277	+	0.0380213i
$2$	−45.2221	+	1.72065i	−0.999277	+	0.0380213i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	2042.08	−	155.623i	0.997109	−	0.0759877i
$5$		−	479.067i		−	0.0685585i	−0.999412	−	0.0342793i	$-0.989086\pi$
$5$		−	479.067i		−	0.0685585i	0.999412	−	0.0342793i	$-0.0109136\pi$
$6$	10989.0	−	418.118i	0.576933	−	0.0219516i
$7$	18444.0	+	40461.6i	0.414779	+	0.909922i
$7$	18444.0	+	40461.6i	0.414779	+	0.909922i
$8$	−92079.3	+	10551.3i	−0.993499	+	0.113844i
$9$	59049.0			0.333333
$10$	824.307	+	21664.4i	0.00260669	+	0.0685089i
$11$		−	617971.i		−	1.15693i	−0.815706	−	0.578467i	$-0.803651\pi$
$11$		−	617971.i		−	1.15693i	0.815706	−	0.578467i	$-0.196349\pi$
$12$	−496225.	+	37816.3i	−0.575681	+	0.0438715i
$13$			805412.i			0.601630i	0.953682	+	0.300815i	$0.0972587\pi$
$13$			805412.i			0.601630i	−0.953682	+	0.300815i	$0.902741\pi$
$14$	−903698.	−	1.79803e6i	−0.449075	−	0.893494i
$15$			116413.i			0.0395823i
$16$	4.14587e6	−	635588.i	0.988452	−	0.151536i
$17$		−	6.15701e6i		−	1.05172i	−0.850570	−	0.525861i	$-0.823743\pi$
$17$		−	6.15701e6i		−	1.05172i	0.850570	−	0.525861i	$-0.176257\pi$
$18$	−2.67032e6	+	101603.i	−0.333092	+	0.0126738i
$19$	3.03570e6			0.281264			0.140632	−	0.990062i	$-0.455087\pi$
$19$	3.03570e6			0.281264			0.140632	+	0.990062i	$0.455087\pi$
$20$	−74553.8	−	978293.i	−0.00520960	−	0.0683603i
$21$	−4.48190e6	−	9.83218e6i	−0.239473	−	0.525344i
$22$	1.06331e6	+	2.79460e7i	0.0439882	+	1.15610i
$23$			6.78832e6i			0.219917i	0.993936	+	0.109959i	$0.0350718\pi$
$23$			6.78832e6i			0.219917i	−0.993936	+	0.109959i	$0.964928\pi$
$24$	2.23753e7	−	2.56396e6i	0.573597	−	0.0657280i
$25$	4.85986e7			0.995300
$26$	−1.38583e6	−	3.64224e7i	−0.0228748	−	0.601195i
$27$	−1.43489e7			−0.192450
$28$	4.39609e7	+	7.97555e7i	0.482723	+	0.875773i
$29$	−2.53110e7			−0.229150			−0.114575	−	0.993415i	$-0.536551\pi$
$29$	−2.53110e7			−0.229150			−0.114575	+	0.993415i	$0.536551\pi$
$30$	−200307.	−	5.26446e6i	−0.00150497	−	0.0395537i
$31$	−2.54102e8			−1.59411			−0.797057	−	0.603904i	$-0.793611\pi$
$31$	−2.54102e8			−1.59411			−0.797057	+	0.603904i	$0.793611\pi$
$32$	−1.86391e8	+	3.58762e7i	−0.981975	+	0.189009i
$33$			1.50167e8i			0.667956i
$34$	1.05941e7	+	2.78433e8i	0.0399879	+	1.05096i
$35$	1.93838e7	−	8.83593e6i	0.0623829	−	0.0284366i
$36$	1.20583e8	−	9.18937e6i	0.332370	−	0.0253292i
$37$	−3.76158e8			−0.891786			−0.445893	−	0.895086i	$-0.647114\pi$
$37$	−3.76158e8			−0.891786			−0.445893	+	0.895086i	$0.647114\pi$
$38$	−1.37281e8	+	5.22338e6i	−0.281061	+	0.0106940i
$39$		−	1.95715e8i		−	0.347351i
$40$	5.05478e6	+	4.41122e7i	0.00780499	+	0.0681128i
$41$			6.88640e8i			0.928285i	0.885761	+	0.464142i	$0.153637\pi$
$41$			6.88640e8i			0.928285i	−0.885761	+	0.464142i	$0.846363\pi$
$42$	2.19599e8	+	4.36920e8i	0.259274	+	0.515859i
$43$			1.05610e9i			1.09554i	0.836629	+	0.547770i	$0.184523\pi$
$43$			1.05610e9i			1.09554i	−0.836629	+	0.547770i	$0.815477\pi$
$44$	−9.61704e7	−	1.26195e9i	−0.0879127	−	1.15359i
$45$		−	2.82884e7i		−	0.0228528i
$46$	−1.16803e7	−	3.06982e8i	−0.00836154	−	0.219758i
$47$	1.61462e9			1.02691			0.513453	−	0.858117i	$-0.328366\pi$
$47$	1.61462e9			1.02691			0.513453	+	0.858117i	$0.328366\pi$
$48$	−1.00745e9	+	1.54448e8i	−0.570683	+	0.0874893i
$49$	−1.29696e9	+	1.49255e9i	−0.655917	+	0.754833i
$50$	−2.19773e9	+	8.36212e7i	−0.994580	+	0.0378426i
$51$			1.49615e9i			0.607212i
$52$	1.25340e8	+	1.64471e9i	0.0457165	+	0.599891i
$53$	2.86554e9			0.941216			0.470608	−	0.882342i	$-0.344035\pi$
$53$	2.86554e9			0.941216			0.470608	+	0.882342i	$0.344035\pi$
$54$	6.48888e8	−	2.46894e7i	0.192311	−	0.00731721i
$55$	−2.96050e8			−0.0793177
$56$	−2.12524e9	−	3.53107e9i	−0.515672	−	0.856786i
$57$	−7.37675e8			−0.162388
$58$	1.14462e9	−	4.35514e7i	0.228985	−	0.00871261i
$59$	−5.63596e9			−1.02632			−0.513159	−	0.858293i	$-0.671525\pi$
$59$	−5.63596e9			−1.02632			−0.513159	+	0.858293i	$0.671525\pi$
$60$	1.81166e7	+	2.37725e8i	0.00300777	+	0.0394678i
$61$		−	7.15254e9i		−	1.08429i	−0.840284	−	0.542146i	$-0.817612\pi$
$61$		−	7.15254e9i		−	1.08429i	0.840284	−	0.542146i	$-0.182388\pi$
$62$	1.14910e10	−	4.37221e8i	1.59296	−	0.0606103i
$63$	1.08910e9	+	2.38922e9i	0.138260	+	0.303307i
$64$	8.36728e9	−	1.94311e9i	0.974079	−	0.226208i
$65$	3.85847e8			0.0412469
$66$	−2.58385e8	−	6.79087e9i	−0.0253966	−	0.667473i
$67$		−	3.11480e9i		−	0.281850i	−0.990020	−	0.140925i	$-0.954992\pi$
$67$		−	3.11480e9i		−	0.281850i	0.990020	−	0.140925i	$-0.0450077\pi$
$68$	−9.58172e8	−	1.25731e10i	−0.0799180	−	1.04868i
$69$		−	1.64956e9i		−	0.126969i
$70$	−8.61375e8	+	4.32932e8i	−0.0612566	+	0.0307879i
$71$		−	1.04104e10i		−	0.684772i	−0.939559	−	0.342386i	$-0.888765\pi$
$71$		−	1.04104e10i		−	0.684772i	0.939559	−	0.342386i	$-0.111235\pi$
$72$	−5.43719e9	+	6.23043e8i	−0.331166	+	0.0379481i
$73$		−	2.84639e10i		−	1.60701i	−0.595297	−	0.803506i	$-0.702966\pi$
$73$		−	2.84639e10i		−	1.60701i	0.595297	−	0.803506i	$-0.297034\pi$
$74$	1.70107e10	−	6.47236e8i	0.891141	−	0.0339069i
$75$	−1.18095e10			−0.574637
$76$	6.19914e9	−	4.72424e8i	0.280451	−	0.0213726i
$77$	2.50041e10	−	1.13979e10i	1.05272	−	0.479872i
$78$	3.36757e8	+	8.85065e9i	0.0132068	+	0.347100i
$79$			4.17004e10i			1.52472i	0.647150	+	0.762362i	$0.275961\pi$
$79$			4.17004e10i			1.52472i	−0.647150	+	0.762362i	$0.724039\pi$
$80$	−3.04489e8	−	1.98615e9i	−0.0103891	−	0.0677668i
$81$	3.48678e9			0.111111
$82$	−1.18491e9	−	3.11418e10i	−0.0352946	−	0.927614i
$83$	3.43032e10			0.955883			0.477942	−	0.878392i	$-0.341383\pi$
$83$	3.43032e10			0.955883			0.477942	+	0.878392i	$0.341383\pi$
$84$	−1.06825e10	−	1.93806e10i	−0.278700	−	0.505628i
$85$	−2.94962e9			−0.0721045
$86$	−1.81718e9	−	4.77591e10i	−0.0416539	−	1.09475i
$87$	6.15058e9			0.132300
$88$	6.52040e9	+	5.69024e10i	0.131710	+	1.14941i
$89$		−	1.68359e10i		−	0.319589i	−0.987150	−	0.159795i	$-0.948917\pi$
$89$		−	1.68359e10i		−	0.319589i	0.987150	−	0.159795i	$-0.0510832\pi$
$90$	4.86745e7	+	1.27926e9i	0.000868896	+	0.0228363i
$91$	−3.25883e10	+	1.48550e10i	−0.547437	+	0.249544i
$92$	1.05642e9	+	1.38623e10i	0.0167110	+	0.219281i
$93$	6.17468e10			0.920362
$94$	−7.30163e10	+	2.77819e9i	−1.02616	+	0.0390444i
$95$		−	1.45430e9i		−	0.0192830i
$96$	4.52931e10	−	8.71792e9i	0.566944	−	0.109124i
$97$		−	1.64842e11i		−	1.94905i	−0.224284	−	0.974524i	$-0.572004\pi$
$97$		−	1.64842e11i		−	1.94905i	0.224284	−	0.974524i	$-0.427996\pi$
$98$	5.60832e10	−	6.97280e10i	0.626743	−	0.779226i
$99$		−	3.64906e10i		−	0.385645i
$100$	9.92422e10	−	7.56305e9i	0.992422	−	0.0756305i
$101$		−	1.82562e11i		−	1.72840i	−0.503150	−	0.864199i	$-0.667826\pi$
$101$		−	1.82562e11i		−	1.72840i	0.503150	−	0.864199i	$-0.332174\pi$
$102$	−2.57436e9	−	6.76593e10i	−0.0230870	−	0.606773i
$103$	2.10558e10			0.178964			0.0894822	−	0.995988i	$-0.471479\pi$
$103$	2.10558e10			0.178964			0.0894822	+	0.995988i	$0.471479\pi$
$104$	−8.49814e9	−	7.41618e10i	−0.0684921	−	0.597719i
$105$	−4.71027e9	+	2.14713e9i	−0.0360168	+	0.0164179i
$106$	−1.29586e11	+	4.93059e9i	−0.940536	+	0.0357863i
$107$		−	5.95206e10i		−	0.410257i	−0.978735	−	0.205129i	$-0.934239\pi$
$107$		−	5.95206e10i		−	0.410257i	0.978735	−	0.205129i	$-0.0657613\pi$
$108$	−2.93016e10	+	2.23302e9i	−0.191894	+	0.0146238i
$109$	1.72861e11			1.07610			0.538049	−	0.842914i	$-0.319162\pi$
$109$	1.72861e11			1.07610			0.538049	+	0.842914i	$0.319162\pi$
$110$	1.33880e10	−	5.09398e8i	0.0792603	−	0.00301576i
$111$	9.14063e10			0.514873
$112$	1.02183e11	+	1.56026e11i	0.547875	+	0.836560i
$113$	4.09553e10			0.209112			0.104556	−	0.994519i	$-0.466658\pi$
$113$	4.09553e10			0.209112			0.104556	+	0.994519i	$0.466658\pi$
$114$	3.33592e10	−	1.26928e9i	0.162270	−	0.00617420i
$115$	3.25206e9			0.0150772
$116$	−5.16871e10	+	3.93897e9i	−0.228488	+	0.0174126i
$117$			4.75588e10i			0.200543i
$118$	2.54870e11	−	9.69752e9i	1.02558	−	0.0390220i
$119$	2.49123e11	−	1.13560e11i	0.956986	−	0.436232i
$120$	−1.22831e9	−	1.07193e10i	−0.00450621	−	0.0393249i
$121$	−9.65769e10			−0.338496
$122$	1.23070e10	+	3.23453e11i	0.0412262	+	1.08351i
$123$		−	1.67340e11i		−	0.535945i
$124$	−5.18897e11	+	3.95441e10i	−1.58950	+	0.121133i
$125$		−	4.66740e10i		−	0.136795i
$126$	−5.33625e10	−	1.06172e11i	−0.149692	−	0.297831i
$127$		−	4.58978e10i		−	0.123274i	−0.998099	−	0.0616370i	$-0.980368\pi$
$127$		−	4.58978e10i		−	0.123274i	0.998099	−	0.0616370i	$-0.0196321\pi$
$128$	−3.75042e11	+	1.02269e11i	−0.964774	+	0.263080i
$129$		−	2.56632e11i		−	0.632511i
$130$	−1.74488e10	+	6.63907e8i	−0.0412171	+	0.00156826i
$131$	−6.01350e11			−1.36187			−0.680935	−	0.732344i	$-0.738426\pi$
$131$	−6.01350e11			−1.36187			−0.680935	+	0.732344i	$0.738426\pi$
$132$	2.33694e10	+	3.06653e11i	0.0507564	+	0.666025i
$133$	5.59906e10	+	1.22829e11i	0.116662	+	0.255928i
$134$	5.35947e9	+	1.40858e11i	0.0107163	+	0.281646i
$135$			6.87409e9i			0.0131941i
$136$	6.49645e10	+	5.66934e11i	0.119732	+	1.04488i
$137$	6.29401e10			0.111420			0.0557102	−	0.998447i	$-0.482258\pi$
$137$	6.29401e10			0.111420			0.0557102	+	0.998447i	$0.482258\pi$
$138$	2.83832e9	+	7.45966e10i	0.00482754	+	0.126877i
$139$	−4.56494e11			−0.746198			−0.373099	−	0.927792i	$-0.621705\pi$
$139$	−4.56494e11			−0.746198			−0.373099	+	0.927792i	$0.621705\pi$
$140$	3.82083e10	−	2.10602e10i	0.0600417	−	0.0330947i
$141$	−3.92352e11			−0.592885
$142$	1.79126e10	+	4.70780e11i	0.0260360	+	0.684277i
$143$	4.97722e11			0.696047
$144$	2.44809e11	−	3.75308e10i	0.329484	−	0.0505120i
$145$			1.21257e10i			0.0157102i
$146$	4.89764e10	+	1.28720e12i	0.0611007	+	1.60585i
$147$	3.15162e11	−	3.62690e11i	0.378694	−	0.435803i
$148$	−7.68144e11	+	5.85387e10i	−0.889208	+	0.0677648i
$149$	7.80967e11			0.871181			0.435591	−	0.900145i	$-0.356540\pi$
$149$	7.80967e11			0.871181			0.435591	+	0.900145i	$0.356540\pi$
$150$	5.34049e11	−	2.03199e10i	0.574221	−	0.0218485i
$151$			1.59890e12i			1.65748i	0.559637	+	0.828738i	$0.310941\pi$
$151$			1.59890e12i			1.65748i	−0.559637	+	0.828738i	$0.689059\pi$
$152$	−2.79525e11	+	3.20306e10i	−0.279435	+	0.0320203i
$153$		−	3.63566e11i		−	0.350574i
$154$	−1.11113e12	+	5.58460e11i	−1.03371	+	0.519551i
$155$			1.21732e11i			0.109290i
$156$	−3.04577e10	−	3.99666e11i	−0.0263944	−	0.346347i
$157$		−	1.17727e12i		−	0.984978i	−0.870319	−	0.492489i	$-0.836087\pi$
$157$		−	1.17727e12i		−	0.984978i	0.870319	−	0.492489i	$-0.163913\pi$
$158$	−7.17518e10	−	1.88578e12i	−0.0579721	−	1.52362i
$159$	−6.96327e11			−0.543412
$160$	1.71871e10	+	8.92939e10i	0.0129582	+	0.0673228i
$161$	−2.74666e11	+	1.25204e11i	−0.200107	+	0.0912170i
$162$	−1.57680e11	+	5.99953e9i	−0.111031	+	0.00422459i
$163$			3.34549e11i			0.227734i	0.993496	+	0.113867i	$0.0363238\pi$
$163$			3.34549e11i			0.227734i	−0.993496	+	0.113867i	$0.963676\pi$
$164$	1.07168e11	+	1.40626e12i	0.0705382	+	0.925601i
$165$	7.19401e10			0.0457941
$166$	−1.55126e12	+	5.90237e10i	−0.955192	+	0.0363440i
$167$	1.18173e12			0.704008			0.352004	−	0.935998i	$-0.385500\pi$
$167$	1.18173e12			0.704008			0.352004	+	0.935998i	$0.385500\pi$
$168$	5.16433e11	+	8.58051e11i	0.297723	+	0.494666i
$169$	1.14347e12			0.638041
$170$	1.33388e11	−	5.07527e9i	0.0720524	−	0.00274151i
$171$	1.79255e11			0.0937547
$172$	1.64353e11	+	2.15664e12i	0.0832476	+	1.09237i
$173$		−	3.74576e12i		−	1.83775i	−0.394548	−	0.918875i	$-0.629099\pi$
$173$		−	3.74576e12i		−	1.83775i	0.394548	−	0.918875i	$-0.370901\pi$
$174$	−2.78142e11	+	1.05830e10i	−0.132204	+	0.00503023i
$175$	8.96355e11	+	1.96638e12i	0.412829	+	0.905645i
$176$	−3.92775e11	−	2.56203e12i	−0.175317	−	1.14357i
$177$	1.36954e12			0.592545
$178$	2.89687e10	+	7.61356e11i	0.0121512	+	0.319358i
$179$		−	3.01633e12i		−	1.22684i	−0.789758	−	0.613419i	$-0.789794\pi$
$179$		−	3.01633e12i		−	1.22684i	0.789758	−	0.613419i	$-0.210206\pi$
$180$	−4.40233e9	−	5.77672e10i	−0.00173653	−	0.0227868i
$181$		−	6.31151e11i		−	0.241491i	−0.992683	−	0.120746i	$-0.961471\pi$
$181$		−	6.31151e11i		−	0.241491i	0.992683	−	0.120746i	$-0.0385285\pi$
$182$	1.44815e12	−	7.27850e11i	0.537553	−	0.270177i
$183$			1.73807e12i			0.626016i
$184$	−7.16255e10	−	6.25064e11i	−0.0250363	−	0.218487i
$185$			1.80205e11i			0.0611395i
$186$	−2.79232e12	+	1.06245e11i	−0.919696	+	0.0349934i
$187$	−3.80486e12			−1.21677
$188$	3.29717e12	−	2.51271e11i	1.02394	−	0.0780323i
$189$	−2.64652e11	−	5.80580e11i	−0.0798242	−	0.175115i
$190$	2.50235e9	+	6.57667e10i	0.000733167	+	0.0192691i
$191$		−	3.16029e12i		−	0.899587i	−0.893133	−	0.449793i	$-0.851498\pi$
$191$		−	3.16029e12i		−	0.899587i	0.893133	−	0.449793i	$-0.148502\pi$
$192$	−2.03325e12	+	4.72176e11i	−0.562385	+	0.130601i
$193$	1.77257e12			0.476474			0.238237	−	0.971207i	$-0.423430\pi$
$193$	1.77257e12			0.476474			0.238237	+	0.971207i	$0.423430\pi$
$194$	2.83635e11	+	7.45449e12i	0.0741054	+	1.94764i
$195$	−9.37607e10			−0.0238139
$196$	−2.41622e12	+	3.24974e12i	−0.596662	+	0.802492i
$197$	−1.17677e12			−0.282572			−0.141286	−	0.989969i	$-0.545124\pi$
$197$	−1.17677e12			−0.282572			−0.141286	+	0.989969i	$0.545124\pi$
$198$	6.27875e10	+	1.65018e12i	0.0146627	+	0.385366i
$199$	−3.32981e11			−0.0756358			−0.0378179	−	0.999285i	$-0.512041\pi$
$199$	−3.32981e11			−0.0756358			−0.0378179	+	0.999285i	$0.512041\pi$
$200$	−4.47493e12	+	5.12778e11i	−0.988829	+	0.113309i
$201$			7.56895e11i			0.162726i
$202$	3.14126e11	+	8.25586e12i	0.0657160	+	1.72715i
$203$	−4.66837e11	−	1.02413e12i	−0.0950468	−	0.208509i
$204$	2.32836e11	+	3.05527e12i	0.0461407	+	0.605457i
$205$	3.29905e11			0.0636418
$206$	−9.52187e11	+	3.62296e10i	−0.178835	+	0.00680447i
$207$			4.00843e11i			0.0733057i
$208$	5.11910e11	+	3.33913e12i	0.0911686	+	0.594682i
$209$		−	1.87598e12i		−	0.325404i
$210$	2.09314e11	−	1.05203e11i	0.0353665	−	0.0177754i
$211$		−	3.77872e12i		−	0.622002i	−0.950410	−	0.311001i	$-0.899336\pi$
$211$		−	3.77872e12i		−	0.622002i	0.950410	−	0.311001i	$-0.100664\pi$
$212$	5.85166e12	−	4.45944e11i	0.938495	−	0.0715209i
$213$			2.52973e12i			0.395354i
$214$	1.02414e11	+	2.69165e12i	0.0155985	+	0.409961i
$215$	5.05943e11			0.0751086
$216$	1.32124e12	−	1.51400e11i	0.191199	−	0.0219093i
$217$	−4.68667e12	−	1.02814e13i	−0.661205	−	1.45052i
$218$	−7.81714e12	+	2.97433e11i	−1.07532	+	0.0409147i
$219$			6.91673e12i			0.927808i
$220$	−6.04557e11	+	4.60721e10i	−0.0790884	+	0.00602717i
$221$	4.95893e12			0.632748
$222$	−4.13359e12	+	1.57278e11i	−0.514501	+	0.0195762i
$223$	8.50333e12			1.03255			0.516276	−	0.856422i	$-0.327318\pi$
$223$	8.50333e12			1.03255			0.516276	+	0.856422i	$0.327318\pi$
$224$	−4.88942e12	−	6.87999e12i	−0.579286	−	0.815124i
$225$	2.86970e12			0.331767
$226$	−1.85209e12	+	7.04698e10i	−0.208961	+	0.00795072i
$227$	6.84775e12			0.754060			0.377030	−	0.926201i	$-0.376945\pi$
$227$	6.84775e12			0.754060			0.377030	+	0.926201i	$0.376945\pi$
$228$	−1.50639e12	+	1.14799e11i	−0.161918	+	0.0123395i
$229$		−	7.51129e12i		−	0.788169i	−0.919074	−	0.394085i	$-0.871062\pi$
$229$		−	7.51129e12i		−	0.788169i	0.919074	−	0.394085i	$-0.128938\pi$
$230$	−1.47065e11	+	5.59565e9i	−0.0150663	+	0.000573255i
$231$	−6.07600e12	+	2.76969e12i	−0.607788	+	0.277054i
$232$	2.33062e12	−	2.67064e11i	0.227661	−	0.0260874i
$233$	1.39492e13			1.33074			0.665369	−	0.746515i	$-0.268274\pi$
$233$	1.39492e13			1.33074			0.665369	+	0.746515i	$0.268274\pi$
$234$	−8.18320e10	−	2.15071e12i	−0.00762493	−	0.200398i
$235$		−	7.73510e11i		−	0.0704032i
$236$	−1.15091e13	+	8.77085e11i	−1.02335	+	0.0779876i
$237$		−	1.01332e13i		−	0.880300i
$238$	−1.10705e13	+	5.56408e12i	−0.939707	+	0.472303i
$239$		−	2.57628e12i		−	0.213700i	−0.994275	−	0.106850i	$-0.965923\pi$
$239$		−	2.57628e12i		−	0.213700i	0.994275	−	0.106850i	$-0.0340765\pi$
$240$	7.39909e10	+	4.82634e11i	0.00599814	+	0.0391252i
$241$		−	4.33765e12i		−	0.343685i	−0.985124	−	0.171843i	$-0.945028\pi$
$241$		−	4.33765e12i		−	0.343685i	0.985124	−	0.171843i	$-0.0549720\pi$
$242$	4.36741e12	−	1.66175e11i	0.338252	−	0.0128701i
$243$	−8.47289e11			−0.0641500
$244$	−1.11310e12	−	1.46060e13i	−0.0823928	−	1.08116i
$245$	7.15033e11	+	6.21332e11i	0.0517502	+	0.0449687i
$246$	2.87933e11	+	7.56745e12i	0.0203774	+	0.535558i
$247$			2.44499e12i			0.169217i
$248$	2.33976e13	−	2.68111e12i	1.58375	−	0.181481i
$249$	−8.33567e12			−0.551879
$250$	8.03095e10	+	2.11070e12i	0.00520112	+	0.136696i
$251$	2.49868e12			0.158309			0.0791546	−	0.996862i	$-0.474778\pi$
$251$	2.49868e12			0.158309			0.0791546	+	0.996862i	$0.474778\pi$
$252$	2.59585e12	+	4.70949e12i	0.160908	+	0.291924i
$253$	4.19499e12			0.254430
$254$	7.89741e10	+	2.07560e12i	0.00468704	+	0.123185i
$255$	7.16759e11			0.0416296
$256$	1.67842e13	−	5.27013e12i	0.954074	−	0.299572i
$257$		−	1.97217e13i		−	1.09727i	−0.836063	−	0.548634i	$-0.815148\pi$
$257$		−	1.97217e13i		−	1.09727i	0.836063	−	0.548634i	$-0.184852\pi$
$258$	4.41574e11	+	1.16055e13i	0.0240489	+	0.632053i
$259$	−6.93787e12	−	1.52200e13i	−0.369894	−	0.811456i
$260$	7.87929e11	−	6.00465e10i	0.0411276	−	0.00313426i
$261$	−1.49459e12			−0.0763835
$262$	2.71943e13	−	1.03471e12i	1.36088	−	0.0517801i
$263$			2.01705e10i			0.000988463i	1.00000		0.000494232i	$0.000157319\pi$
$263$			2.01705e10i			0.000988463i	−1.00000		0.000494232i	$0.999843\pi$
$264$	−1.58446e12	−	1.38273e13i	−0.0760429	−	0.663614i
$265$		−	1.37279e12i		−	0.0645284i
$266$	−2.74336e12	−	5.45827e12i	−0.126309	−	0.251308i
$267$			4.09113e12i			0.184515i
$268$	−4.84733e11	−	6.36066e12i	−0.0214171	−	0.281035i
$269$		−	1.36960e13i		−	0.592865i	−0.955054	−	0.296432i	$-0.904203\pi$
$269$		−	1.36960e13i		−	0.592865i	0.955054	−	0.296432i	$-0.0957969\pi$
$270$	−1.18279e10	−	3.10861e11i	−0.000501657	−	0.0131846i
$271$	−3.80787e12			−0.158253			−0.0791263	−	0.996865i	$-0.525213\pi$
$271$	−3.80787e12			−0.158253			−0.0791263	+	0.996865i	$0.525213\pi$
$272$	−3.91332e12	−	2.55262e13i	−0.159374	−	1.03958i
$273$	7.91896e12	−	3.60978e12i	0.316063	−	0.144074i
$274$	−2.84629e12	+	1.08298e11i	−0.111340	+	0.00423635i
$275$		−	3.00326e13i		−	1.15150i
$276$	−2.56709e11	−	3.36853e12i	−0.00964810	−	0.126602i
$277$	4.43508e13			1.63404			0.817021	−	0.576608i	$-0.195624\pi$
$277$	4.43508e13			1.63404			0.817021	+	0.576608i	$0.195624\pi$
$278$	2.06436e13	−	7.85467e11i	0.745658	−	0.0283714i
$279$	−1.50045e13			−0.531371
$280$	−1.69162e12	+	1.01813e12i	−0.0587400	+	0.0353537i
$281$	−1.76790e13			−0.601968			−0.300984	−	0.953629i	$-0.597315\pi$
$281$	−1.76790e13			−0.601968			−0.300984	+	0.953629i	$0.597315\pi$
$282$	1.77430e13	−	6.75100e11i	0.592456	−	0.0225423i
$283$	3.92550e13			1.28549			0.642747	−	0.766079i	$-0.277795\pi$
$283$	3.92550e13			1.28549			0.642747	+	0.766079i	$0.277795\pi$
$284$	−1.62009e12	−	2.12588e13i	−0.0520343	−	0.682793i
$285$			3.53396e11i			0.0111331i
$286$	−2.25080e13	+	8.56404e11i	−0.695543	+	0.0264646i
$287$	−2.78635e13	+	1.27013e13i	−0.844667	+	0.385033i
$288$	−1.10062e13	+	2.11845e12i	−0.327325	+	0.0630029i
$289$	−3.63693e12			−0.106120
$290$	−2.08640e10	−	5.48349e11i	−0.000597323	−	0.0156989i
$291$			4.00565e13i			1.12528i
$292$	−4.42963e12	−	5.81256e13i	−0.122113	−	1.60237i
$293$			1.66541e13i			0.450556i	0.974295	+	0.225278i	$0.0723290\pi$
$293$			1.66541e13i			0.450556i	−0.974295	+	0.225278i	$0.927671\pi$
$294$	−1.36282e13	+	1.69439e13i	−0.361850	+	0.449886i
$295$			2.70001e12i			0.0703629i
$296$	3.46364e13	−	3.96895e12i	0.885988	−	0.101525i
$297$			8.86721e12i			0.222652i
$298$	−3.53170e13	+	1.34377e12i	−0.870551	+	0.0331235i
$299$	−5.46739e12			−0.132309
$300$	−2.41159e13	+	1.83782e12i	−0.572975	+	0.0436653i
$301$	−4.27315e13	+	1.94787e13i	−0.996856	+	0.454407i
$302$	−2.75114e12	−	7.23055e13i	−0.0630195	−	1.65628i
$303$			4.43627e13i			0.997891i
$304$	1.25856e13	−	1.92945e12i	0.278016	−	0.0426216i
$305$	−3.42655e12			−0.0743374
$306$	6.25569e11	+	1.64412e13i	0.0133293	+	0.350321i
$307$	−4.82817e13			−1.01047			−0.505233	−	0.862983i	$-0.668593\pi$
$307$	−4.82817e13			−1.01047			−0.505233	+	0.862983i	$0.668593\pi$
$308$	4.92866e13	−	2.71666e13i	1.01321	−	0.558478i
$309$	−5.11656e12			−0.103325
$310$	−2.09458e11	−	5.50498e12i	−0.00415535	−	0.109211i
$311$	9.15050e13			1.78346			0.891729	−	0.452570i	$-0.149493\pi$
$311$	9.15050e13			1.78346			0.891729	+	0.452570i	$0.149493\pi$
$312$	2.06505e12	+	1.80213e13i	0.0395439	+	0.345093i
$313$			7.94015e13i			1.49395i	0.664855	+	0.746973i	$0.268493\pi$
$313$			7.94015e13i			1.49395i	−0.664855	+	0.746973i	$0.731507\pi$
$314$	2.02566e12	+	5.32385e13i	0.0374502	+	0.984266i
$315$	1.14460e12	−	5.21753e11i	0.0207943	−	0.00947888i
$316$	6.48954e12	+	8.51555e13i	0.115860	+	1.52032i
$317$	−8.50957e13			−1.49308			−0.746538	−	0.665343i	$-0.768285\pi$
$317$	−8.50957e13			−1.49308			−0.746538	+	0.665343i	$0.768285\pi$
$318$	3.14894e13	−	1.19813e12i	0.543019	−	0.0206612i
$319$			1.56415e13i			0.265112i
$320$	−9.30881e11	−	4.00849e12i	−0.0155085	−	0.0667814i
$321$			1.44635e13i			0.236862i
$322$	1.22056e13	−	6.13459e12i	0.196495	−	0.0987594i
$323$		−	1.86909e13i		−	0.295812i
$324$	7.12029e12	−	5.42623e11i	0.110790	−	0.00844308i
$325$			3.91419e13i			0.598802i
$326$	−5.75642e11	−	1.51290e13i	−0.00865875	−	0.227569i
$327$	−4.20053e13			−0.621285
$328$	−7.26605e12	−	6.34095e13i	−0.105680	−	0.922250i
$329$	2.97800e13	+	6.53300e13i	0.425939	+	0.934405i
$330$	−3.25328e12	+	1.23784e11i	−0.0457610	+	0.00174115i
$331$			3.95604e13i			0.547276i	0.961833	+	0.273638i	$0.0882271\pi$
$331$			3.95604e13i			0.547276i	−0.961833	+	0.273638i	$0.911773\pi$
$332$	7.00498e13	−	5.33836e12i	0.953120	−	0.0726354i
$333$	−2.22117e13			−0.297262
$334$	−5.34403e13	+	2.03334e12i	−0.703499	+	0.0267673i
$335$	−1.49220e12			−0.0193232
$336$	−2.48306e13	−	3.79143e13i	−0.316316	−	0.482988i
$337$	−4.49990e13			−0.563947			−0.281974	−	0.959422i	$-0.590989\pi$
$337$	−4.49990e13			−0.563947			−0.281974	+	0.959422i	$0.590989\pi$
$338$	−5.17102e13	+	1.96751e12i	−0.637580	+	0.0242592i
$339$	−9.95215e12			−0.120731
$340$	−6.02336e12	+	4.59029e11i	−0.0718961	+	0.00547906i
$341$			1.57028e14i			1.84428i
$342$	−8.10629e12	+	3.08435e11i	−0.0936869	+	0.00356468i
$343$	−8.43123e13	−	2.49485e13i	−0.958900	−	0.283744i
$344$	−1.11432e13	−	9.72450e13i	−0.124721	−	1.08842i
$345$	−7.90251e11			−0.00870482
$346$	6.44514e12	+	1.69391e14i	0.0698737	+	1.83642i
$347$		−	1.31702e14i		−	1.40534i	−0.711518	−	0.702668i	$-0.751992\pi$
$347$		−	1.31702e14i		−	1.40534i	0.711518	−	0.702668i	$-0.248008\pi$
$348$	1.25600e13	−	9.57170e11i	0.131918	−	0.0100532i
$349$			1.29885e14i			1.34283i	0.741083	+	0.671413i	$0.234312\pi$
$349$			1.29885e14i			1.34283i	−0.741083	+	0.671413i	$0.765688\pi$
$350$	−4.39185e13	−	8.73815e13i	−0.446965	−	0.889294i
$351$		−	1.15568e13i		−	0.115784i
$352$	2.21705e13	+	1.15184e14i	0.218671	+	1.13608i
$353$			1.43551e14i			1.39395i	0.717097	+	0.696974i	$0.245471\pi$
$353$			1.43551e14i			1.39395i	−0.717097	+	0.696974i	$0.754529\pi$
$354$	−6.19335e13	+	2.35650e12i	−0.592117	+	0.0225294i
$355$	−4.98728e12			−0.0469470
$356$	−2.62005e12	−	3.43803e13i	−0.0242848	−	0.318665i
$357$	−6.05369e13	+	2.75951e13i	−0.552516	+	0.251859i
$358$	5.19005e12	+	1.36405e14i	0.0466460	+	1.22595i
$359$		−	1.68359e14i		−	1.49011i	−0.667006	−	0.745053i	$-0.732424\pi$
$359$		−	1.68359e14i		−	1.49011i	0.667006	−	0.745053i	$-0.267576\pi$
$360$	2.98480e11	+	2.60478e12i	0.00260166	+	0.0227043i
$361$	−1.07275e14			−0.920891
$362$	1.08599e12	+	2.85420e13i	0.00918182	+	0.241317i
$363$	2.34682e13			0.195431
$364$	−6.42361e13	+	3.54067e13i	−0.526892	+	0.290421i
$365$	−1.36361e13			−0.110174
$366$	−2.99060e12	−	7.85991e13i	−0.0238020	−	0.625563i
$367$	1.46547e14			1.14898			0.574491	−	0.818511i	$-0.305200\pi$
$367$	1.46547e14			1.14898			0.574491	+	0.818511i	$0.305200\pi$
$368$	4.31457e12	+	2.81435e13i	0.0333254	+	0.217377i
$369$			4.06635e13i			0.309428i
$370$	−3.10069e11	−	8.14924e12i	−0.00232461	−	0.0610953i
$371$	5.28522e13	+	1.15945e14i	0.390397	+	0.856434i
$372$	1.26092e14	−	9.60922e12i	0.917701	−	0.0699362i
$373$	−1.23191e14			−0.883446			−0.441723	−	0.897152i	$-0.645633\pi$
$373$	−1.23191e14			−0.883446			−0.441723	+	0.897152i	$0.645633\pi$
$374$	1.72064e14	−	6.54683e12i	1.21589	−	0.0462634i
$375$			1.13418e13i			0.0789785i
$376$	−1.48673e14	+	1.70363e13i	−1.02023	+	0.116907i
$377$		−	2.03858e13i		−	0.137864i
$378$	1.29671e13	+	2.57997e13i	0.0864246	+	0.171953i
$379$		−	7.21254e12i		−	0.0473775i	−0.999719	−	0.0236888i	$-0.992459\pi$
$379$		−	7.21254e12i		−	0.0473775i	0.999719	−	0.0236888i	$-0.00754108\pi$
$380$	−2.26323e11	−	2.96980e12i	−0.00146527	−	0.0192273i
$381$			1.11532e13i			0.0711723i
$382$	5.43775e12	+	1.42915e14i	0.0342035	+	0.898936i
$383$	−1.36525e14			−0.846484			−0.423242	−	0.906017i	$-0.639108\pi$
$383$	−1.36525e14			−0.846484			−0.423242	+	0.906017i	$0.639108\pi$
$384$	9.11353e13	−	2.48513e13i	0.557013	−	0.151889i
$385$	−5.46035e12	−	1.19787e13i	−0.0328993	−	0.0721729i
$386$	−8.01596e13	+	3.04998e12i	−0.476130	+	0.0181162i
$387$			6.23616e13i			0.365180i
$388$	−2.56531e13	−	3.36620e14i	−0.148104	−	1.94341i
$389$	2.34420e14			1.33436			0.667178	−	0.744899i	$-0.267502\pi$
$389$	2.34420e14			1.33436			0.667178	+	0.744899i	$0.267502\pi$
$390$	4.24006e12	−	1.61329e11i	0.0237967	−	0.000905436i
$391$	4.17958e13			0.231292
$392$	1.03675e14	−	1.51118e14i	0.565719	−	0.824598i
$393$	1.46128e14			0.786276
$394$	5.32162e13	−	2.02482e12i	0.282368	−	0.0107438i
$395$	1.99773e13			0.104533
$396$	−5.67877e12	−	7.45167e13i	−0.0293042	−	0.384530i
$397$		−	1.70986e14i		−	0.870187i	−0.900385	−	0.435093i	$-0.856715\pi$
$397$		−	1.70986e14i		−	0.870187i	0.900385	−	0.435093i	$-0.143285\pi$
$398$	1.50581e13	−	5.72944e11i	0.0755811	−	0.00287578i
$399$	−1.36057e13	−	2.98475e13i	−0.0673550	−	0.147760i
$400$	2.01483e14	−	3.08887e13i	0.983806	−	0.150824i
$401$	−1.38987e14			−0.669391			−0.334695	−	0.942326i	$-0.608633\pi$
$401$	−1.38987e14			−0.669391			−0.334695	+	0.942326i	$0.608633\pi$
$402$	−1.30235e12	−	3.42284e13i	−0.00618707	−	0.162609i
$403$		−	2.04657e14i		−	0.959067i
$404$	−2.84109e13	−	3.72807e14i	−0.131337	−	1.72340i
$405$		−	1.67040e12i		−	0.00761761i
$406$	2.28735e13	+	4.55099e13i	0.102906	+	0.204745i
$407$			2.32455e14i			1.03174i
$408$	−1.57864e13	−	1.37765e14i	−0.0691276	−	0.603264i
$409$		−	1.00762e14i		−	0.435331i	−0.976023	−	0.217666i	$-0.930156\pi$
$409$		−	1.00762e14i		−	0.435331i	0.976023	−	0.217666i	$-0.0698442\pi$
$410$	−1.49190e13	+	5.67651e11i	−0.0635958	+	0.00241975i
$411$	−1.52945e13			−0.0643286
$412$	4.29976e13	−	3.27676e12i	0.178447	−	0.0135991i
$413$	−1.03950e14	−	2.28040e14i	−0.425695	−	0.933870i
$414$	−6.89711e11	−	1.81270e13i	−0.00278718	−	0.0732527i
$415$		−	1.64335e13i		−	0.0655339i
$416$	−2.88951e13	−	1.50122e14i	−0.113713	−	0.590786i
$417$	1.10928e14			0.430818
$418$	3.22790e12	+	8.48356e13i	0.0123723	+	0.325169i
$419$	−1.05522e14			−0.399177			−0.199589	−	0.979880i	$-0.563961\pi$
$419$	−1.05522e14			−0.399177			−0.199589	+	0.979880i	$0.563961\pi$
$420$	−9.28461e12	+	5.11764e12i	−0.0346651	+	0.0191073i
$421$	4.71336e14			1.73692			0.868459	−	0.495760i	$-0.165111\pi$
$421$	4.71336e14			1.73692			0.868459	+	0.495760i	$0.165111\pi$
$422$	6.50186e12	+	1.70882e14i	0.0236493	+	0.621552i
$423$	9.53415e13			0.342302
$424$	−2.63857e14	+	3.02352e13i	−0.935097	+	0.107152i
$425$		−	2.99222e14i		−	1.04678i
$426$	−4.35277e12	−	1.14400e14i	−0.0150319	−	0.395068i
$427$	2.89403e14	−	1.31922e14i	0.986621	−	0.449741i
$428$	−9.26276e12	−	1.21546e14i	−0.0311745	−	0.409071i
$429$	−1.20946e14			−0.401863
$430$	−2.28798e13	+	8.70550e11i	−0.0750543	+	0.00285573i
$431$			5.92339e14i			1.91843i	0.282680	+	0.959214i	$0.408777\pi$
$431$			5.92339e14i			1.91843i	−0.282680	+	0.959214i	$0.591223\pi$
$432$	−5.94887e13	+	9.11999e12i	−0.190228	+	0.0291631i
$433$		−	9.08413e12i		−	0.0286814i	−0.999897	−	0.0143407i	$-0.995435\pi$
$433$		−	9.08413e12i		−	0.0286814i	0.999897	−	0.0143407i	$-0.00456494\pi$
$434$	2.29632e14	+	4.56882e14i	0.715877	+	1.42433i
$435$		−	2.94654e12i		−	0.00907030i
$436$	3.52996e14	−	2.69011e13i	1.07299	−	0.0817702i
$437$			2.06073e13i			0.0618548i
$438$	−1.19013e13	−	3.12789e14i	−0.0352765	−	0.927138i
$439$	−4.78753e14			−1.40138			−0.700692	−	0.713464i	$-0.747125\pi$
$439$	−4.78753e14			−1.40138			−0.700692	+	0.713464i	$0.747125\pi$
$440$	2.72601e13	−	3.12371e12i	0.0788020	−	0.00902986i
$441$	−7.65843e13	+	8.81337e13i	−0.218639	+	0.251611i
$442$	−2.24253e14	+	8.53259e12i	−0.632290	+	0.0240579i
$443$			1.26020e14i			0.350929i	0.984486	+	0.175465i	$0.0561428\pi$
$443$			1.26020e14i			0.350929i	−0.984486	+	0.175465i	$0.943857\pi$
$444$	1.86659e14	−	1.42249e13i	0.513384	−	0.0391240i
$445$	−8.06554e12			−0.0219106
$446$	−3.84539e14	+	1.46312e13i	−1.03181	+	0.0392590i
$447$	−1.89775e14			−0.502977
$448$	2.32948e14	+	3.02715e14i	0.609859	+	0.792510i
$449$	−2.95747e14			−0.764832			−0.382416	−	0.923990i	$-0.624908\pi$
$449$	−2.95747e14			−0.764832			−0.382416	+	0.923990i	$0.624908\pi$
$450$	−1.29774e14	+	4.93775e12i	−0.331527	+	0.0126142i
$451$	4.25560e14			1.07396
$452$	8.36340e13	−	6.37358e12i	0.208507	−	0.0158899i
$453$		−	3.88532e14i		−	0.956944i
$454$	−3.09670e14	+	1.17826e13i	−0.753515	+	0.0286704i
$455$	7.11657e12	+	1.56120e13i	0.0171083	+	0.0375315i
$456$	6.79246e13	−	7.78343e12i	0.161332	−	0.0184869i
$457$	8.79287e13			0.206344			0.103172	−	0.994664i	$-0.467101\pi$
$457$	8.79287e13			0.206344			0.103172	+	0.994664i	$0.467101\pi$
$458$	1.29243e13	+	3.39677e14i	0.0299673	+	0.787600i
$459$			8.83464e13i			0.202404i
$460$	6.64096e12	−	5.06095e11i	0.0150336	−	0.00114568i
$461$		−	3.26239e14i		−	0.729760i	−0.931055	−	0.364880i	$-0.881110\pi$
$461$		−	3.26239e14i		−	0.729760i	0.931055	−	0.364880i	$-0.118890\pi$
$462$	2.70004e14	−	1.35706e14i	0.596815	−	0.299963i
$463$		−	8.05662e14i		−	1.75978i	−0.475181	−	0.879888i	$-0.657618\pi$
$463$		−	8.05662e14i		−	1.75978i	0.475181	−	0.879888i	$-0.342382\pi$
$464$	−1.04936e14	+	1.60874e13i	−0.226504	+	0.0347245i
$465$		−	2.95809e13i		−	0.0630986i
$466$	−6.30813e14	+	2.40017e13i	−1.32978	+	0.0505964i
$467$	−4.34161e14			−0.904498			−0.452249	−	0.891892i	$-0.649378\pi$
$467$	−4.34161e14			−0.904498			−0.452249	+	0.891892i	$0.649378\pi$
$468$	7.40123e12	+	9.71188e13i	0.0152388	+	0.199964i
$469$	1.26030e14	−	5.74494e13i	0.256462	−	0.116905i
$470$	1.33094e12	+	3.49797e13i	0.00267682	+	0.0703523i
$471$			2.86076e14i			0.568677i
$472$	5.18956e14	−	5.94667e13i	1.01965	−	0.116840i
$473$	6.52639e14			1.26747
$474$	1.74357e13	+	4.58245e14i	0.0334702	+	0.879664i
$475$	1.47531e14			0.279942
$476$	4.91056e14	−	2.70668e14i	0.921070	−	0.507690i
$477$	1.69207e14			0.313739
$478$	4.43288e12	+	1.16505e14i	0.00812517	+	0.213546i
$479$	1.91239e14			0.346523			0.173262	−	0.984876i	$-0.444569\pi$
$479$	1.91239e14			0.346523			0.173262	+	0.984876i	$0.444569\pi$
$480$	−4.17647e12	−	2.16984e13i	−0.00748139	−	0.0388688i
$481$		−	3.02962e14i		−	0.536525i
$482$	7.46357e12	+	1.96158e14i	0.0130674	+	0.343437i
$483$	6.67439e13	−	3.04246e13i	0.115532	−	0.0526641i
$484$	−1.97218e14	+	1.50296e13i	−0.337518	+	0.0257216i
$485$	−7.89702e13			−0.133624
$486$	3.83162e13	−	1.45789e12i	0.0641036	−	0.00243907i
$487$		−	3.73321e14i		−	0.617552i	−0.951135	−	0.308776i	$-0.900081\pi$
$487$		−	3.73321e14i		−	0.617552i	0.951135	−	0.308776i	$-0.0999193\pi$
$488$	7.54685e13	+	6.58601e14i	0.123440	+	1.07724i
$489$		−	8.12954e13i		−	0.131482i
$490$	−3.34044e13	−	2.68676e13i	−0.0534226	−	0.0429686i
$491$			7.98177e14i			1.26227i	0.775674	+	0.631133i	$0.217410\pi$
$491$			7.98177e14i			1.26227i	−0.775674	+	0.631133i	$0.782590\pi$
$492$	−2.60419e13	−	3.41721e14i	−0.0407253	−	0.534396i
$493$			1.55840e14i			0.241003i
$494$	−4.20697e12	−	1.10568e14i	−0.00643385	−	0.169095i
$495$	−1.74814e13			−0.0264392
$496$	−1.05347e15	+	1.61504e14i	−1.57570	+	0.241566i
$497$	4.21222e14	−	1.92010e14i	0.623090	−	0.284029i
$498$	3.76957e14	−	1.43428e13i	0.551480	−	0.0209832i
$499$		−	1.18142e15i		−	1.70943i	−0.519096	−	0.854716i	$-0.673731\pi$
$499$		−	1.18142e15i		−	1.70943i	0.519096	−	0.854716i	$-0.326269\pi$
$500$	−7.26353e12	−	9.53119e13i	−0.0103947	−	0.136399i
$501$	−2.87160e14			−0.406459
$502$	−1.12996e14	+	4.29936e12i	−0.158195	+	0.00601913i
$503$	−1.12155e15			−1.55309			−0.776545	−	0.630062i	$-0.783029\pi$
$503$	−1.12155e15			−1.55309			−0.776545	+	0.630062i	$0.783029\pi$
$504$	−1.25493e14	−	2.08506e14i	−0.171891	−	0.285595i
$505$	−8.74597e13			−0.118496
$506$	−1.89706e14	+	7.21810e12i	−0.254246	+	0.00967375i
$507$	−2.77864e14			−0.368373
$508$	−7.14275e12	−	9.37270e13i	−0.00936731	−	0.122918i
$509$			3.59317e14i			0.466154i	0.972458	+	0.233077i	$0.0748795\pi$
$509$			3.59317e14i			0.466154i	−0.972458	+	0.233077i	$0.925121\pi$
$510$	−3.24133e13	+	1.23329e12i	−0.0415995	+	0.00158281i
$511$	1.15170e15	−	5.24989e14i	1.46226	−	0.666554i
$512$	−7.49951e14	+	2.67206e14i	−0.941994	+	0.335631i
$513$	−4.35590e13			−0.0541293
$514$	3.39342e13	+	8.91858e14i	0.0417196	+	1.09647i
$515$		−	1.00871e13i		−	0.0122695i
$516$	−3.99378e13	−	5.24063e14i	−0.0480630	−	0.630682i
$517$		−	9.97786e14i		−	1.18806i
$518$	3.39933e14	+	6.76341e14i	0.400479	+	0.796805i
$519$			9.10220e14i			1.06103i
$520$	−3.55285e13	+	4.07118e12i	−0.0409787	+	0.00469572i
$521$		−	1.10878e15i		−	1.26543i	−0.774386	−	0.632713i	$-0.781941\pi$
$521$		−	1.10878e15i		−	1.26543i	0.774386	−	0.632713i	$-0.218059\pi$
$522$	6.75885e13	−	2.57167e12i	0.0763283	−	0.00290420i
$523$	1.37899e15			1.54100			0.770501	−	0.637439i	$-0.220006\pi$
$523$	1.37899e15			1.54100			0.770501	+	0.637439i	$0.220006\pi$
$524$	−1.22800e15	+	9.35838e13i	−1.35793	+	0.103485i
$525$	−2.17814e14	−	4.77830e14i	−0.238347	−	0.522875i
$526$	−3.47064e10	−	9.12154e11i	−3.75827e−5	−	0.000987749i
$527$			1.56451e15i			1.67656i
$528$	9.54444e13	+	6.22573e14i	0.101219	+	0.660242i
$529$	9.06729e14			0.951636
$530$	2.36209e12	+	6.20803e13i	0.00245346	+	0.0644817i
$531$	−3.32798e14			−0.342106
$532$	1.33452e14	+	2.42114e14i	0.135772	+	0.246323i
$533$	−5.54639e14			−0.558484
$534$	−7.03940e12	−	1.85009e14i	−0.00701550	−	0.184381i
$535$	−2.85144e13			−0.0281266
$536$	3.28651e13	+	2.86808e14i	0.0320870	+	0.280018i
$537$			7.32968e14i			0.708315i
$538$	2.35660e13	+	6.19361e14i	0.0225415	+	0.592436i
$539$	9.22354e14	+	8.01485e14i	0.873292	+	0.758853i
$540$	1.06977e12	+	1.40374e13i	0.00100259	+	0.0131559i
$541$	9.54173e14			0.885202			0.442601	−	0.896719i	$-0.354056\pi$
$541$	9.54173e14			0.885202			0.442601	+	0.896719i	$0.354056\pi$
$542$	1.72200e14	−	6.55201e12i	0.158138	−	0.00601698i
$543$			1.53370e14i			0.139425i
$544$	2.20890e14	+	1.14761e15i	0.198785	+	1.03277i
$545$		−	8.28121e13i		−	0.0737756i
$546$	−3.51901e14	+	1.76867e14i	−0.310356	+	0.155987i
$547$		−	1.98826e15i		−	1.73597i	−0.496588	−	0.867987i	$-0.665414\pi$
$547$		−	1.98826e15i		−	1.73597i	0.496588	−	0.867987i	$-0.334586\pi$
$548$	1.28529e14	−	9.79492e12i	0.111098	−	0.00846658i
$549$		−	4.22350e14i		−	0.361431i
$550$	5.16755e13	+	1.35814e15i	0.0437814	+	1.15066i
$551$	−7.68367e13			−0.0644518
$552$	1.74050e13	+	1.51890e14i	0.0144547	+	0.126144i
$553$	−1.68727e15	+	7.69124e14i	−1.38738	+	0.632424i
$554$	−2.00564e15	+	7.63122e13i	−1.63286	+	0.0621284i
$555$		−	4.37898e13i		−	0.0352989i
$556$	−9.32198e14	+	7.10409e13i	−0.744041	+	0.0567019i
$557$	1.11764e15			0.883281			0.441640	−	0.897192i	$-0.354397\pi$
$557$	1.11764e15			0.883281			0.441640	+	0.897192i	$0.354397\pi$
$558$	6.78534e14	−	2.58175e13i	0.530987	−	0.0202034i
$559$	−8.50595e14			−0.659110
$560$	7.47468e13	−	4.89527e13i	0.0573533	−	0.0375615i
$561$	9.24581e14			0.702504
$562$	7.99482e14	−	3.04194e13i	0.601532	−	0.0228876i
$563$	−1.17479e15			−0.875317			−0.437659	−	0.899141i	$-0.644192\pi$
$563$	−1.17479e15			−0.875317			−0.437659	+	0.899141i	$0.644192\pi$
$564$	−8.01213e14	+	6.10589e13i	−0.591171	+	0.0450520i
$565$		−	1.96204e13i		−	0.0143364i
$566$	−1.77520e15	+	6.75442e13i	−1.28456	+	0.0488762i
$567$	6.43104e13	+	1.41081e14i	0.0460865	+	0.101102i
$568$	1.09843e14	+	9.58582e14i	0.0779573	+	0.680321i
$569$	−1.75027e15			−1.23024			−0.615118	−	0.788435i	$-0.710892\pi$
$569$	−1.75027e15			−1.23024			−0.615118	+	0.788435i	$0.710892\pi$
$570$	−6.08071e11	−	1.59813e13i	−0.000423294	−	0.0111250i
$571$		−	2.54403e15i		−	1.75398i	−0.480509	−	0.876990i	$-0.659548\pi$
$571$		−	2.54403e15i		−	1.75398i	0.480509	−	0.876990i	$-0.340452\pi$
$572$	1.01639e15	−	7.74568e13i	0.694034	−	0.0528910i
$573$			7.67950e14i			0.519377i
$574$	1.23819e15	−	6.22323e14i	0.829417	−	0.416870i
$575$			3.29903e14i			0.218883i
$576$	4.94079e14	−	1.14739e14i	0.324693	−	0.0754027i
$577$		−	3.34837e14i		−	0.217955i	−0.994044	−	0.108977i	$-0.965242\pi$
$577$		−	3.34837e14i		−	0.217955i	0.994044	−	0.108977i	$-0.0347576\pi$
$578$	1.64470e14	−	6.25788e12i	0.106043	−	0.00403482i
$579$	−4.30736e14			−0.275092
$580$	1.88703e12	+	2.47616e13i	0.00119378	+	0.0156648i
$581$	6.32689e14	+	1.38796e15i	0.396480	+	0.869779i
$582$	−6.89232e13	−	1.81144e15i	−0.0427848	−	1.12447i
$583$		−	1.77082e15i		−	1.08893i
$584$	3.00331e14	+	2.62094e15i	0.182949	+	1.59656i
$585$	2.27839e13			0.0137490
$586$	−2.86558e13	−	7.53133e14i	−0.0171307	−	0.450230i
$587$	−1.69749e15			−1.00530			−0.502652	−	0.864489i	$-0.667642\pi$
$587$	−1.69749e15			−1.00530			−0.502652	+	0.864489i	$0.667642\pi$
$588$	5.87142e14	−	7.89688e14i	0.344483	−	0.463319i
$589$	−7.71378e14			−0.448367
$590$	−4.64576e12	−	1.22100e14i	−0.00267529	−	0.0703120i
$591$	2.85956e14			0.163143
$592$	−1.55950e15	+	2.39081e14i	−0.881487	+	0.135138i
$593$		−	1.60063e14i		−	0.0896376i	−0.998995	−	0.0448188i	$-0.985729\pi$
$593$		−	1.60063e14i		−	0.0896376i	0.998995	−	0.0448188i	$-0.0142711\pi$
$594$	−1.52574e13	−	4.00994e14i	−0.00846553	−	0.222491i
$595$	−5.44030e13	−	1.19347e14i	−0.0299074	−	0.0656095i
$596$	1.59480e15	−	1.21536e14i	0.868662	−	0.0661990i
$597$	8.09144e13			0.0436684
$598$	2.47247e14	−	9.40746e12i	0.132213	−	0.00503056i
$599$			2.88578e15i			1.52903i	0.644607	+	0.764514i	$0.277021\pi$
$599$			2.88578e15i			1.52903i	−0.644607	+	0.764514i	$0.722979\pi$
$600$	1.08741e15	−	1.24605e14i	0.570901	−	0.0654190i
$601$		−	1.50759e14i		−	0.0784282i	−0.999231	−	0.0392141i	$-0.987515\pi$
$601$		−	1.50759e14i		−	0.0784282i	0.999231	−	0.0392141i	$-0.0124854\pi$
$602$	1.89889e15	−	9.54396e14i	0.978859	−	0.491980i
$603$		−	1.83926e14i		−	0.0939500i
$604$	2.48825e14	+	3.26507e15i	0.125948	+	1.65268i
$605$			4.62668e13i			0.0232068i
$606$	−7.63326e13	−	2.00617e15i	−0.0379412	−	0.997170i
$607$	2.11779e15			1.04315			0.521574	−	0.853206i	$-0.325345\pi$
$607$	2.11779e15			1.04315			0.521574	+	0.853206i	$0.325345\pi$
$608$	−5.65828e14	+	1.08909e14i	−0.276194	+	0.0531613i
$609$	1.13441e14	+	2.48863e14i	0.0548753	+	0.120383i
$610$	1.54956e14	−	5.89589e12i	0.0742837	−	0.00282641i
$611$			1.30043e15i			0.617818i
$612$	−5.65791e13	−	7.42429e14i	−0.0266393	−	0.349561i
$613$	−1.19459e15			−0.557426			−0.278713	−	0.960374i	$-0.589908\pi$
$613$	−1.19459e15			−0.557426			−0.278713	+	0.960374i	$0.589908\pi$
$614$	2.18340e15	−	8.30759e13i	1.00973	−	0.0384193i
$615$	−8.01669e13			−0.0367436
$616$	−2.18210e15	+	1.31334e15i	−0.991245	+	0.596598i
$617$	−4.98737e14			−0.224545			−0.112272	−	0.993677i	$-0.535813\pi$
$617$	−4.98737e14			−0.224545			−0.112272	+	0.993677i	$0.535813\pi$
$618$	2.31382e14	−	8.80380e12i	0.103250	−	0.00392856i
$619$	2.24819e15			0.994337			0.497168	−	0.867654i	$-0.334373\pi$
$619$	2.24819e15			0.994337			0.497168	+	0.867654i	$0.334373\pi$
$620$	1.89443e13	+	2.48586e14i	0.00830470	+	0.108974i
$621$		−	9.74049e13i		−	0.0423231i
$622$	−4.13805e15	+	1.57448e14i	−1.78217	+	0.0678095i
$623$	6.81209e14	−	3.10522e14i	0.290801	−	0.132559i
$624$	−1.24394e14	−	8.11409e14i	−0.0526362	−	0.343340i
$625$	2.35062e15			0.985921
$626$	−1.36622e14	−	3.59070e15i	−0.0568018	−	1.49286i
$627$			4.55862e14i			0.187872i
$628$	−1.83209e14	−	2.40407e15i	−0.0748462	−	0.982130i
$629$			2.31601e15i			0.937911i
$630$	−5.08633e13	+	2.55642e13i	−0.0204189	+	0.0102626i
$631$			3.11509e15i			1.23968i	0.784729	+	0.619839i	$0.212802\pi$
$631$			3.11509e15i			1.23968i	−0.784729	+	0.619839i	$0.787198\pi$
$632$	−4.39993e14	−	3.83975e15i	−0.173581	−	1.51481i
$633$			9.18230e14i			0.359113i
$634$	3.84821e15	−	1.46420e14i	1.49200	−	0.0567687i
$635$	−2.19881e13			−0.00845149
$636$	−1.42195e15	+	1.08364e14i	−0.541840	+	0.0412926i
$637$	−1.20212e15	−	1.04459e15i	−0.454130	−	0.394619i
$638$	−2.69135e13	−	7.07341e14i	−0.0100799	−	0.264920i
$639$		−	6.14723e14i		−	0.228257i
$640$	4.89936e13	+	1.79671e14i	0.0180364	+	0.0661435i
$641$	−3.10799e15			−1.13439			−0.567193	−	0.823585i	$-0.691971\pi$
$641$	−3.10799e15			−1.13439			−0.567193	+	0.823585i	$0.691971\pi$
$642$	−2.48866e13	−	6.54070e14i	−0.00900582	−	0.236691i
$643$	−4.25049e15			−1.52503			−0.762515	−	0.646970i	$-0.776036\pi$
$643$	−4.25049e15			−1.52503			−0.762515	+	0.646970i	$0.776036\pi$
$644$	−5.41406e14	+	2.98421e14i	−0.192598	+	0.106159i
$645$	−1.22944e14			−0.0433640
$646$	3.21604e13	+	8.45240e14i	0.0112472	+	0.295598i
$647$	8.92140e14			0.309357			0.154678	−	0.987965i	$-0.450566\pi$
$647$	8.92140e14			0.309357			0.154678	+	0.987965i	$0.450566\pi$
$648$	−3.21061e14	+	3.67901e13i	−0.110389	+	0.0126494i
$649$			3.48286e15i			1.18738i
$650$	−6.73495e13	−	1.77008e15i	−0.0227673	−	0.598369i
$651$	1.13886e15	+	2.49838e15i	0.381747	+	0.837458i
$652$	5.20635e13	+	6.83176e14i	0.0173050	+	0.227076i
$653$	2.75032e15			0.906485			0.453242	−	0.891387i	$-0.350267\pi$
$653$	2.75032e15			0.906485			0.453242	+	0.891387i	$0.350267\pi$
$654$	1.89957e15	−	7.22763e13i	0.620836	−	0.0236221i
$655$			2.88087e14i			0.0933678i
$656$	4.37692e14	+	2.85501e15i	0.140669	+	0.917565i
$657$		−	1.68077e15i		−	0.535670i
$658$	−1.45913e15	−	2.90312e15i	−0.461159	−	0.917535i
$659$		−	2.26220e15i		−	0.709024i	−0.935051	−	0.354512i	$-0.884647\pi$
$659$		−	2.26220e15i		−	0.709024i	0.935051	−	0.354512i	$-0.115353\pi$
$660$	1.46907e14	−	1.11955e13i	0.0456617	−	0.00347979i
$661$			2.84098e15i			0.875709i	0.899046	+	0.437854i	$0.144261\pi$
$661$			2.84098e15i			0.875709i	−0.899046	+	0.437854i	$0.855739\pi$
$662$	−6.80696e13	−	1.78900e15i	−0.0208082	−	0.546880i
$663$	−1.20502e15			−0.365317
$664$	−3.15861e15	+	3.61943e14i	−0.949669	+	0.108822i
$665$	5.88435e13	−	2.68232e13i	0.0175461	−	0.00799820i
$666$	1.00446e15	−	3.82186e13i	0.297047	−	0.0113023i
$667$		−	1.71819e14i		−	0.0503941i
$668$	2.41319e15	−	1.83904e14i	0.701973	−	0.0534959i
$669$	−2.06631e15			−0.596145
$670$	6.74803e13	−	2.56755e12i	0.0193093	−	0.000734695i
$671$	−4.42006e15			−1.25445
$672$	1.18813e15	+	1.67184e15i	0.334451	+	0.470612i
$673$	−7.57562e14			−0.211512			−0.105756	−	0.994392i	$-0.533726\pi$
$673$	−7.57562e14			−0.211512			−0.105756	+	0.994392i	$0.533726\pi$
$674$	2.03495e15	−	7.74275e13i	0.563539	−	0.0214420i
$675$	−6.97337e14			−0.191546
$676$	2.33506e15	−	1.77950e14i	0.636196	−	0.0484833i
$677$		−	2.30576e15i		−	0.623126i	−0.950226	−	0.311563i	$-0.899148\pi$
$677$		−	2.30576e15i		−	0.623126i	0.950226	−	0.311563i	$-0.100852\pi$
$678$	4.50057e14	−	1.71242e13i	0.120644	−	0.00459035i
$679$	6.66976e15	−	3.04035e15i	1.77348	−	0.808424i
$680$	2.71599e14	−	3.11223e13i	0.0716357	−	0.00820868i
$681$	−1.66400e15			−0.435357
$682$	−2.70190e14	−	7.10113e15i	−0.0701221	−	1.84295i
$683$		−	1.73464e15i		−	0.446576i	−0.974753	−	0.223288i	$-0.928321\pi$
$683$		−	1.73464e15i		−	0.446576i	0.974753	−	0.223288i	$-0.0716790\pi$
$684$	3.66053e14	−	2.78962e13i	0.0934836	−	0.00712420i
$685$		−	3.01526e13i		−	0.00763882i
$686$	3.85571e15	+	9.83154e14i	0.968995	+	0.247081i
$687$			1.82524e15i			0.455050i
$688$	6.71244e14	+	4.37845e15i	0.166014	+	1.08289i
$689$			2.30794e15i			0.566264i
$690$	3.57368e13	−	1.35974e12i	0.00869853	−	0.000330969i
$691$	−4.74208e15			−1.14509			−0.572544	−	0.819874i	$-0.694044\pi$
$691$	−4.74208e15			−1.14509			−0.572544	+	0.819874i	$0.694044\pi$
$692$	−5.82926e14	−	7.64914e15i	−0.139646	−	1.83244i
$693$	1.47647e15	−	6.73034e14i	0.350907	−	0.159957i
$694$	2.26613e14	+	5.95584e15i	0.0534328	+	1.40432i
$695$			2.18692e14i			0.0511582i
$696$	−5.66341e14	+	6.48966e13i	−0.131440	+	0.0150616i
$697$	4.23997e15			0.976298
$698$	−2.23487e14	−	5.87368e15i	−0.0510560	−	1.34185i
$699$	−3.38966e15			−0.768302
$700$	2.13644e15	+	3.87601e15i	0.480454	+	0.871657i
$701$	1.09344e15			0.243975			0.121987	−	0.992532i	$-0.461073\pi$
$701$	1.09344e15			0.243975			0.121987	+	0.992532i	$0.461073\pi$
$702$	1.98852e13	+	5.22622e14i	0.00440226	+	0.115700i
$703$	−1.14190e15			−0.250827
$704$	−1.20079e15	−	5.17074e15i	−0.261708	−	1.12695i
$705$			1.87963e14i			0.0406473i
$706$	−2.47002e14	−	6.49170e15i	−0.0529998	−	1.39294i
$707$	7.38678e15	−	3.36719e15i	1.57271	−	0.716903i
$708$	2.79671e15	−	2.13132e14i	0.590832	−	0.0450262i
$709$	−3.08924e15			−0.647586			−0.323793	−	0.946128i	$-0.604958\pi$
$709$	−3.08924e15			−0.647586			−0.323793	+	0.946128i	$0.604958\pi$
$710$	2.25535e14	−	8.58136e12i	0.0469130	−	0.00178499i
$711$			2.46237e15i			0.508242i
$712$	1.77641e14	+	1.55024e15i	0.0363833	+	0.317511i
$713$		−	1.72493e15i		−	0.350573i
$714$	2.69012e15	−	1.35207e15i	0.542540	−	0.272684i
$715$		−	2.38442e14i		−	0.0477199i
$716$	−4.69410e14	−	6.15958e15i	−0.0932246	−	1.22329i
$717$			6.26037e14i			0.123380i
$718$	2.89687e14	+	7.61355e15i	0.0566558	+	1.48903i
$719$	−1.26250e15			−0.245032			−0.122516	−	0.992467i	$-0.539096\pi$
$719$	−1.26250e15			−0.245032			−0.122516	+	0.992467i	$0.539096\pi$
$720$	−1.79798e13	−	1.17280e14i	−0.00346303	−	0.0225889i
$721$	3.88354e14	+	8.51952e14i	0.0742307	+	0.162844i
$722$	4.85119e15	−	1.84582e14i	0.920225	−	0.0350135i
$723$			1.05405e15i			0.198427i
$724$	−9.82215e13	−	1.28886e15i	−0.0183504	−	0.240793i
$725$	−1.23008e15			−0.228073
$726$	−1.06128e15	+	4.03805e13i	−0.195290	+	0.00743055i
$727$	4.48259e14			0.0818634			0.0409317	−	0.999162i	$-0.486967\pi$
$727$	4.48259e14			0.0818634			0.0409317	+	0.999162i	$0.486967\pi$
$728$	2.84397e15	−	1.71169e15i	0.515469	−	0.310244i
$729$	2.05891e14			0.0370370
$730$	6.16655e14	−	2.34630e13i	0.110095	−	0.00418898i
$731$	6.50242e15			1.15220
$732$	2.70483e14	+	3.54927e15i	0.0475695	+	0.624206i
$733$		−	4.17763e15i		−	0.729219i	−0.931161	−	0.364609i	$-0.881203\pi$
$733$		−	4.17763e15i		−	0.729219i	0.931161	−	0.364609i	$-0.118797\pi$
$734$	−6.62716e15	+	2.52156e14i	−1.14815	+	0.0436858i
$735$	−1.73753e14	−	1.50984e14i	−0.0298780	−	0.0259627i
$736$	−2.43539e14	−	1.26528e15i	−0.0415662	−	0.215953i
$737$	−1.92485e15			−0.326082
$738$	−6.99677e13	−	1.83889e15i	−0.0117649	−	0.309205i
$739$		−	7.40374e14i		−	0.123568i	−0.998090	−	0.0617841i	$-0.980321\pi$
$739$		−	7.40374e14i		−	0.123568i	0.998090	−	0.0617841i	$-0.0196790\pi$
$740$	2.80440e13	+	3.67993e14i	0.00464585	+	0.0609628i
$741$		−	5.94132e14i		−	0.0976974i
$742$	−2.58959e15	−	5.15232e15i	−0.422677	−	0.840971i
$743$		−	9.28702e15i		−	1.50466i	−0.658787	−	0.752329i	$-0.728930\pi$
$743$		−	9.28702e15i		−	1.50466i	0.658787	−	0.752329i	$-0.271070\pi$
$744$	−5.68561e15	+	6.51509e14i	−0.914378	+	0.104778i
$745$		−	3.74136e14i		−	0.0597269i
$746$	5.57095e15	−	2.11968e14i	0.882807	−	0.0335898i
$747$	2.02557e15			0.318628
$748$	−7.76982e15	+	5.92123e14i	−1.21326	+	0.0924598i
$749$	2.40830e15	−	1.09780e15i	0.373302	−	0.170166i
$750$	−1.95152e13	−	5.12899e14i	−0.00300287	−	0.0789214i
$751$		−	9.18866e14i		−	0.140357i	−0.997534	−	0.0701783i	$-0.977643\pi$
$751$		−	9.18866e14i		−	0.140357i	0.997534	−	0.0701783i	$-0.0223568\pi$
$752$	6.69398e15	−	1.02623e15i	1.01505	−	0.155613i
$753$	−6.07180e14			−0.0913998
$754$	3.50768e13	+	9.21889e14i	0.00524177	+	0.137764i
$755$	7.65979e14			0.113634
$756$	−6.30791e14	−	1.14440e15i	−0.0929000	−	0.168543i
$757$	−3.02013e15			−0.441569			−0.220785	−	0.975323i	$-0.570862\pi$
$757$	−3.02013e15			−0.441569			−0.220785	+	0.975323i	$0.570862\pi$
$758$	1.24103e13	+	3.26166e14i	0.00180136	+	0.0473433i
$759$	−1.01938e15			−0.146895
$760$	1.53448e13	+	1.33911e14i	0.00219526	+	0.0191577i
$761$			5.06714e15i			0.719692i	0.933012	+	0.359846i	$0.117171\pi$
$761$			5.06714e15i			0.719692i	−0.933012	+	0.359846i	$0.882829\pi$
$762$	−1.91907e13	−	5.04370e14i	−0.00270607	−	0.0711209i
$763$	3.18826e15	+	6.99424e15i	0.446343	+	0.979165i
$764$	−4.91813e14	−	6.45356e15i	−0.0683575	−	0.896986i
$765$	−1.74172e14			−0.0240348
$766$	6.17395e15	−	2.34912e14i	0.845872	−	0.0321844i
$767$		−	4.53927e15i		−	0.617464i
$768$	−4.07857e15	+	1.28064e15i	−0.550835	+	0.172958i
$769$			1.05380e16i			1.41307i	0.707679	+	0.706534i	$0.249742\pi$
$769$			1.05380e16i			1.41307i	−0.707679	+	0.706534i	$0.750258\pi$
$770$	2.67540e14	+	5.32305e14i	0.0356196	+	0.0708699i
$771$			4.79238e15i			0.633508i
$772$	3.61974e15	−	2.75853e14i	0.475097	−	0.0362062i
$773$			7.06227e15i			0.920359i	0.887826	+	0.460180i	$0.152215\pi$
$773$			7.06227e15i			0.920359i	−0.887826	+	0.460180i	$0.847785\pi$
$774$	−1.07302e14	−	2.82012e15i	−0.0138846	−	0.364916i
$775$	−1.23490e16			−1.58662
$776$	1.73929e15	+	1.51785e16i	0.221888	+	1.93638i
$777$	1.68590e15	+	3.69845e15i	0.213558	+	0.468494i
$778$	−1.06010e16	+	4.03354e14i	−1.33339	+	0.0507340i
$779$			2.09051e15i			0.261093i
$780$	−1.91467e14	+	1.45913e13i	−0.0237450	+	0.00180956i
$781$	−6.43333e15			−0.792237
$782$	−1.89009e15	+	7.19159e13i	−0.231124	+	0.00879402i
$783$	3.63186e14			0.0441000
$784$	−4.42838e15	+	7.01225e15i	−0.533958	+	0.845511i
$785$	−5.63990e14			−0.0675286
$786$	−6.60822e15	+	2.51435e14i	−0.785707	+	0.0298953i
$787$	9.62553e15			1.13648			0.568242	−	0.822861i	$-0.307624\pi$
$787$	9.62553e15			1.13648			0.568242	+	0.822861i	$0.307624\pi$
$788$	−2.40307e15	+	1.83133e14i	−0.281755	+	0.0214720i
$789$		−	4.90144e12i		−	0.000570690i
$790$	−9.03416e14	+	3.43739e13i	−0.104457	+	0.00397448i
$791$	7.55382e14	+	1.65712e15i	0.0867353	+	0.190276i
$792$	3.85023e14	+	3.36003e15i	0.0439034	+	0.383137i
$793$	5.76074e15			0.652343
$794$	2.94207e14	+	7.73234e15i	0.0330857	+	0.869557i
$795$			3.33587e14i			0.0372555i
$796$	−6.79973e14	+	5.18194e13i	−0.0754171	+	0.00574739i
$797$			3.10132e15i			0.341607i	0.985305	+	0.170803i	$0.0546363\pi$
$797$			3.10132e15i			0.341607i	−0.985305	+	0.170803i	$0.945364\pi$
$798$	6.66636e14	+	1.32636e15i	0.0729244	+	0.145093i
$799$		−	9.94121e15i		−	1.08002i
$800$	−9.05836e15	+	1.74353e15i	−0.977360	+	0.188120i
$801$		−	9.94144e14i		−	0.106530i
$802$	6.28528e15	−	2.39148e14i	0.668907	−	0.0254511i
$803$	−1.75899e16			−1.85921
$804$	1.17790e14	+	1.54564e15i	0.0123652	+	0.162256i
$805$	5.99811e13	+	1.31584e14i	0.00625370	+	0.0137191i
$806$	3.52143e14	+	9.25502e15i	0.0364650	+	0.958373i
$807$			3.32812e15i			0.342291i
$808$	1.92627e15	+	1.68102e16i	0.196768	+	1.71716i
$809$	−1.36082e16			−1.38065			−0.690325	−	0.723499i	$-0.742533\pi$
$809$	−1.36082e16			−1.38065			−0.690325	+	0.723499i	$0.742533\pi$
$810$	2.87418e12	+	7.55392e13i	0.000289632	+	0.00761211i
$811$	5.97769e15			0.598300			0.299150	−	0.954206i	$-0.403297\pi$
$811$	5.97769e15			0.598300			0.299150	+	0.954206i	$0.403297\pi$
$812$	−1.11270e15	−	2.01869e15i	−0.110616	−	0.200684i
$813$	9.25312e14			0.0913672
$814$	−3.99973e14	−	1.05121e16i	−0.0392280	−	1.03099i
$815$	1.60271e14			0.0156131
$816$	9.50938e14	+	6.20286e15i	0.0920145	+	0.600200i
$817$			3.20600e15i			0.308136i
$818$	1.73377e14	+	4.55668e15i	0.0165519	+	0.435017i
$819$	−1.92431e15	+	8.77176e14i	−0.182479	+	0.0831812i
$820$	6.73692e14	−	5.13407e13i	0.0634578	−	0.00483600i
$821$	−2.81249e15			−0.263150			−0.131575	−	0.991306i	$-0.542003\pi$
$821$	−2.81249e15			−0.263150			−0.131575	+	0.991306i	$0.542003\pi$
$822$	6.91648e14	−	2.63164e13i	0.0642821	−	0.00244586i
$823$			3.93420e15i			0.363210i	0.983372	+	0.181605i	$0.0581292\pi$
$823$			3.93420e15i			0.363210i	−0.983372	+	0.181605i	$0.941871\pi$
$824$	−1.93880e15	+	2.22166e14i	−0.177801	+	0.0203741i
$825$			7.29791e15i			0.664817i
$826$	5.09321e15	+	1.01336e16i	0.460894	+	0.917009i
$827$			2.04668e16i			1.83980i	0.392153	+	0.919900i	$0.371730\pi$
$827$			2.04668e16i			1.83980i	−0.392153	+	0.919900i	$0.628270\pi$
$828$	6.23804e13	+	8.18554e14i	0.00557033	+	0.0730938i
$829$		−	3.72182e15i		−	0.330145i	−0.986281	−	0.165073i	$-0.947214\pi$
$829$		−	3.72182e15i		−	0.330145i	0.986281	−	0.165073i	$-0.0527858\pi$
$830$	2.82763e13	+	7.43159e14i	0.00249169	+	0.0654866i
$831$	−1.07773e16			−0.943414
$832$	1.56501e15	+	6.73910e15i	0.136094	+	0.586035i
$833$	9.18966e15	+	7.98541e15i	0.793875	+	0.689842i
$834$	−5.01640e15	+	1.90868e14i	−0.430506	+	0.0163803i
$835$		−	5.66128e14i		−	0.0482657i
$836$	−2.91945e14	−	3.83089e15i	−0.0247267	−	0.324463i
$837$	3.64609e15			0.306787
$838$	4.77193e15	−	1.81566e14i	0.398889	−	0.0151773i
$839$	9.81366e15			0.814967			0.407484	−	0.913213i	$-0.366406\pi$
$839$	9.81366e15			0.814967			0.407484	+	0.913213i	$0.366406\pi$
$840$	4.11064e14	−	2.47406e14i	0.0339136	−	0.0204115i
$841$	−1.15599e16			−0.947490
$842$	−2.13148e16	+	8.11005e14i	−1.73566	+	0.0660400i
$843$	4.29600e15			0.347546
$844$	−5.88055e14	−	7.71645e15i	−0.0472645	−	0.620203i
$845$		−	5.47800e14i		−	0.0437431i
$846$	−4.31154e15	+	1.64049e14i	−0.342055	+	0.0130148i
$847$	−1.78127e15	−	3.90766e15i	−0.140401	−	0.308005i
$848$	1.18802e16	−	1.82130e15i	0.930347	−	0.142628i
$849$	−9.53898e15			−0.742180
$850$	5.14857e14	+	1.35315e16i	0.0397999	+	1.04602i
$851$		−	2.55348e15i		−	0.196119i
$852$	3.93683e14	+	5.16590e15i	0.0300420	+	0.394211i
$853$		−	1.77580e16i		−	1.34640i	−0.739459	−	0.673202i	$-0.764919\pi$
$853$		−	1.77580e16i		−	1.34640i	0.739459	−	0.673202i	$-0.235081\pi$
$854$	−1.28604e16	+	6.46374e15i	−0.968808	+	0.486929i
$855$		−	8.58752e13i		−	0.00642768i
$856$	6.28019e14	+	5.48062e15i	0.0467054	+	0.407590i
$857$		−	1.92571e16i		−	1.42298i	−0.702699	−	0.711488i	$-0.748022\pi$
$857$		−	1.92571e16i		−	1.42298i	0.702699	−	0.711488i	$-0.251978\pi$
$858$	5.46945e15	−	2.08106e14i	0.401572	−	0.0152794i
$859$	−1.07287e16			−0.782683			−0.391342	−	0.920245i	$-0.627989\pi$
$859$	−1.07287e16			−0.782683			−0.391342	+	0.920245i	$0.627989\pi$
$860$	1.03317e15	−	7.87362e13i	0.0748915	−	0.00570733i
$861$	6.77083e15	−	3.08642e15i	0.487669	−	0.222299i
$862$	−1.01921e15	−	2.67868e16i	−0.0729412	−	1.91704i
$863$		−	1.40265e16i		−	0.997445i	−0.866762	−	0.498723i	$-0.833803\pi$
$863$		−	1.40265e16i		−	0.997445i	0.866762	−	0.498723i	$-0.166197\pi$
$864$	2.67451e15	−	5.14784e14i	0.188981	−	0.0363747i
$865$	−1.79447e15			−0.125993
$866$	1.56306e13	+	4.10804e14i	0.00109050	+	0.0286606i
$867$	8.83774e14			0.0612684
$868$	−1.11706e16	−	2.02661e16i	−0.769515	−	1.39608i
$869$	2.57697e16			1.76401
$870$	5.06996e12	+	1.33249e14i	0.000344865	+	0.00906374i
$871$	2.50869e15			0.169570
$872$	−1.59169e16	+	1.82391e15i	−1.06910	+	0.122507i
$873$		−	9.73374e15i		−	0.649683i
$874$	−3.54579e13	−	9.31905e14i	−0.00235180	−	0.0618100i
$875$	1.88850e15	−	8.60856e14i	0.124473	−	0.0567396i
$876$	1.07640e15	+	1.41245e16i	0.0705020	+	0.925126i
$877$	3.04085e16			1.97924			0.989618	−	0.143725i	$-0.0459080\pi$
$877$	3.04085e16			1.97924			0.989618	+	0.143725i	$0.0459080\pi$
$878$	2.16502e16	−	8.23767e14i	1.40037	−	0.0532825i
$879$		−	4.04694e15i		−	0.260129i
$880$	−1.22738e15	+	1.88166e14i	−0.0784017	+	0.0120195i
$881$		−	2.66651e16i		−	1.69269i	−0.532638	−	0.846343i	$-0.678799\pi$
$881$		−	2.66651e16i		−	1.69269i	0.532638	−	0.846343i	$-0.321201\pi$
$882$	3.31166e15	−	4.11737e15i	0.208914	−	0.259742i
$883$			5.38302e15i			0.337475i	0.985661	+	0.168738i	$0.0539691\pi$
$883$			5.38302e15i			0.337475i	−0.985661	+	0.168738i	$0.946031\pi$
$884$	1.01265e16	−	7.71723e14i	0.630919	−	0.0480811i
$885$		−	6.56101e14i		−	0.0406240i
$886$	−2.16837e14	−	5.69890e15i	−0.0133428	−	0.350676i
$887$	3.22721e15			0.197355			0.0986774	−	0.995119i	$-0.468539\pi$
$887$	3.22721e15			0.197355			0.0986774	+	0.995119i	$0.468539\pi$
$888$	−8.41664e15	+	9.64455e14i	−0.511525	+	0.0586153i
$889$	1.85710e15	−	8.46541e14i	0.112170	−	0.0511315i
$890$	3.64741e14	−	1.38780e13i	0.0218947	−	0.000833068i
$891$		−	2.15473e15i		−	0.128548i
$892$	1.73645e16	−	1.32331e15i	1.02957	−	0.0784613i
$893$	4.90149e15			0.288832
$894$	8.58203e15	−	3.26536e14i	0.502613	−	0.0191238i
$895$	−1.44502e15			−0.0841102
$896$	−1.10553e16	−	1.32886e16i	−0.639550	−	0.768749i
$897$	1.32858e15			0.0763885
$898$	1.33743e16	−	5.08878e14i	0.764279	−	0.0290799i
$899$	6.43159e15			0.365292
$900$	5.86015e15	−	4.46591e14i	0.330807	−	0.0252102i
$901$		−	1.76432e16i		−	0.989898i
$902$	−1.92447e16	+	7.32240e14i	−1.07319	+	0.0408336i
$903$	1.03838e16	−	4.73333e15i	0.575535	−	0.262352i
$904$	−3.77114e15	+	4.32132e14i	−0.207753	+	0.0238062i
$905$	−3.02364e14			−0.0165563
$906$	6.68527e14	+	1.75702e16i	0.0363843	+	0.956252i
$907$			1.23226e16i			0.666596i	0.942822	+	0.333298i	$0.108161\pi$
$907$			1.23226e16i			0.666596i	−0.942822	+	0.333298i	$0.891839\pi$
$908$	1.39837e16	−	1.06567e15i	0.751880	−	0.0572993i
$909$		−	1.07801e16i		−	0.576133i
$910$	−3.48689e14	−	6.93762e14i	−0.0185230	−	0.0368538i
$911$		−	3.81405e15i		−	0.201389i	−0.994917	−	0.100694i	$-0.967894\pi$
$911$		−	3.81405e15i		−	0.201389i	0.994917	−	0.100694i	$-0.0321065\pi$
$912$	−3.05830e15	+	4.68858e14i	−0.160513	+	0.0246076i
$913$		−	2.11984e16i		−	1.10589i
$914$	−3.97632e15	+	1.51294e14i	−0.206195	+	0.00784547i
$915$	8.32651e14			0.0429187
$916$	−1.16893e15	−	1.53387e16i	−0.0598912	−	0.785891i
$917$	−1.10913e16	−	2.43316e16i	−0.564875	−	1.23920i
$918$	−1.52013e14	−	3.99521e15i	−0.00769567	−	0.202258i
$919$			2.53007e16i			1.27320i	0.771193	+	0.636602i	$0.219660\pi$
$919$			2.53007e16i			1.27320i	−0.771193	+	0.636602i	$0.780340\pi$
$920$	−2.99448e14	+	3.43134e13i	−0.0149792	+	0.00171645i
$921$	1.17325e16			0.583393
$922$	5.61342e14	+	1.47532e16i	0.0277465	+	0.729233i
$923$	8.38466e15			0.411980
$924$	−1.19767e16	+	6.60148e15i	−0.584978	+	0.322438i
$925$	−1.82808e16			−0.887594
$926$	1.38626e15	+	3.64337e16i	0.0669090	+	1.75850i
$927$	1.24332e15			0.0596548
$928$	4.71775e15	−	9.08064e14i	0.225020	−	0.0433114i
$929$			9.59505e15i			0.454947i	0.973784	+	0.227473i	$0.0730465\pi$
$929$			9.59505e15i			0.454947i	−0.973784	+	0.227473i	$0.926954\pi$
$930$	5.08983e13	+	1.33771e15i	0.00239909	+	0.0630530i
$931$	−3.93719e15	+	4.53094e15i	−0.184486	+	0.212307i
$932$	2.84854e16	−	2.17082e15i	1.32689	−	0.101120i
$933$	−2.22357e16			−1.02968
$934$	1.96337e16	−	7.47039e14i	0.903844	−	0.0343902i
$935$			1.82278e15i			0.0834202i
$936$	−5.01807e14	−	4.37918e15i	−0.0228307	−	0.199240i
$937$			7.83284e15i			0.354284i	0.984185	+	0.177142i	$0.0566851\pi$
$937$			7.83284e15i			0.354284i	−0.984185	+	0.177142i	$0.943315\pi$
$938$	−5.60048e15	+	2.81484e15i	−0.251831	+	0.126572i
$939$		−	1.92946e16i		−	0.862530i
$940$	−1.20376e14	−	1.57957e15i	−0.00534978	−	0.0701997i
$941$		−	7.72736e15i		−	0.341420i	−0.985321	−	0.170710i	$-0.945394\pi$
$941$		−	7.72736e15i		−	0.341420i	0.985321	−	0.170710i	$-0.0546061\pi$
$942$	−4.92236e14	−	1.29369e16i	−0.0216219	−	0.568266i
$943$	−4.67471e15			−0.204146
$944$	−2.33660e16	+	3.58215e15i	−1.01447	+	0.155524i
$945$	−2.78137e14	+	1.26786e14i	−0.0120056	+	0.00547263i
$946$	−2.95137e16	+	1.12296e15i	−1.26655	+	0.0481908i
$947$		−	3.11271e16i		−	1.32805i	−0.747711	−	0.664024i	$-0.768847\pi$
$947$		−	3.11271e16i		−	1.32805i	0.747711	−	0.664024i	$-0.231153\pi$
$948$	−1.57696e15	−	2.06928e16i	−0.0668920	−	0.877755i
$949$	2.29252e16			0.966827
$950$	−6.67166e15	+	2.53849e14i	−0.279740	+	0.0106438i
$951$	2.06783e16			0.862028
$952$	−2.17409e16	+	1.30851e16i	−0.901101	+	0.542343i
$953$	3.64258e16			1.50106			0.750531	−	0.660835i	$-0.229798\pi$
$953$	3.64258e16			1.50106			0.750531	+	0.660835i	$0.229798\pi$
$954$	−7.65192e15	+	2.91147e14i	−0.313512	+	0.0119288i
$955$	−1.51399e15			−0.0616743
$956$	−4.00928e14	−	5.26097e15i	−0.0162386	−	0.213082i
$957$		−	3.80088e15i		−	0.153062i
$958$	−8.64825e15	+	3.29056e14i	−0.346273	+	0.0131753i
$959$	1.16087e15	+	2.54666e15i	0.0462148	+	0.101384i
$960$	2.26204e14	+	9.74062e14i	0.00895383	+	0.0385563i
$961$	3.91595e16			1.54120
$962$	5.21291e14	+	1.37006e16i	0.0203994	+	0.536137i
$963$		−	3.51463e15i		−	0.136752i
$964$	−6.75037e14	−	8.85782e15i	−0.0261158	−	0.342691i
$965$		−	8.49182e14i		−	0.0326664i
$966$	−2.96595e15	+	1.49071e15i	−0.113446	+	0.0570187i
$967$			1.27860e16i			0.486284i	0.969991	+	0.243142i	$0.0781780\pi$
$967$			1.27860e16i			0.486284i	−0.969991	+	0.243142i	$0.921822\pi$
$968$	8.89274e15	−	1.01901e15i	0.336296	−	0.0385358i
$969$			4.54188e15i			0.170787i
$970$	3.57120e15	−	1.35880e14i	0.133527	−	0.00508056i
$971$	−4.45466e16			−1.65618			−0.828092	−	0.560592i	$-0.810573\pi$
$971$	−4.45466e16			−1.65618			−0.828092	+	0.560592i	$0.810573\pi$
$972$	−1.73023e15	+	1.31857e14i	−0.0639646	+	0.00487461i
$973$	−8.41960e15	−	1.84705e16i	−0.309507	−	0.678982i
$974$	6.42355e14	+	1.68824e16i	0.0234801	+	0.617105i
$975$		−	9.51149e15i		−	0.345719i
$976$	−4.54607e15	−	2.96535e16i	−0.164309	−	1.07177i
$977$	−3.92492e16			−1.41062			−0.705311	−	0.708898i	$-0.749193\pi$
$977$	−3.92492e16			−1.41062			−0.705311	+	0.708898i	$0.749193\pi$
$978$	1.39881e14	+	3.67635e15i	0.00499913	+	0.131387i
$979$	−1.04041e16			−0.369743
$980$	1.55685e15	+	1.15753e15i	0.0550177	+	0.0409063i
$981$	1.02073e16			0.358699
$982$	−1.37338e15	−	3.60953e16i	−0.0479931	−	1.26135i
$983$	3.27689e16			1.13872			0.569361	−	0.822088i	$-0.307191\pi$
$983$	3.27689e16			1.13872			0.569361	+	0.822088i	$0.307191\pi$
$984$	1.76565e15	+	1.54085e16i	0.0610143	+	0.532461i
$985$			5.63754e14i			0.0193727i
$986$	−2.68147e14	−	7.04743e15i	−0.00916324	−	0.240828i
$987$	−7.23655e15	−	1.58752e16i	−0.245916	−	0.539479i
$988$	3.80496e14	+	4.99286e15i	0.0128584	+	0.168728i
$989$	−7.16914e15			−0.240928
$990$	7.90548e14	−	3.00794e13i	0.0264201	−	0.00100525i
$991$			3.18758e15i			0.105939i	0.998596	+	0.0529695i	$0.0168686\pi$
$991$			3.18758e15i			0.105939i	−0.998596	+	0.0529695i	$0.983131\pi$
$992$	4.73624e16	−	9.11623e15i	1.56538	−	0.301301i
$993$		−	9.61317e15i		−	0.315970i
$994$	−1.87182e16	+	9.40786e15i	−0.611840	+	0.307515i
$995$			1.59520e14i			0.00518548i
$996$	−1.70221e16	+	1.29722e15i	−0.550284	+	0.0419360i
$997$			3.91273e16i			1.25793i	0.777433	+	0.628965i	$0.216521\pi$
$997$			3.91273e16i			1.25793i	−0.777433	+	0.628965i	$0.783479\pi$
$998$	2.03281e15	+	5.34264e16i	0.0649949	+	1.70820i
$999$	5.39745e15			0.171624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.2	yes	44
4.3	odd	2		84.12.b.b.55.1	yes	44
7.6	odd	2		84.12.b.b.55.2	yes	44
28.27	even	2	inner	84.12.b.a.55.1	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.1	✓	44	28.27	even	2	inner
84.12.b.a.55.2	yes	44	1.1	even	1	trivial
84.12.b.b.55.1	yes	44	4.3	odd	2
84.12.b.b.55.2	yes	44	7.6	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-45.2221 + 1.72065i) q^{2} -243.000 q^{3} +(2042.08 - 155.623i) q^{4} -479.067i q^{5} +(10989.0 - 418.118i) q^{6} +(18444.0 + 40461.6i) q^{7} +(-92079.3 + 10551.3i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-45.2221 + 1.72065i) q^{2} -243.000 q^{3} +(2042.08 - 155.623i) q^{4} -479.067i q^{5} +(10989.0 - 418.118i) q^{6} +(18444.0 + 40461.6i) q^{7} +(-92079.3 + 10551.3i) q^{8} +59049.0 q^{9} +(824.307 + 21664.4i) q^{10} -617971. i q^{11} +(-496225. + 37816.3i) q^{12} +805412. i q^{13} +(-903698. - 1.79803e6i) q^{14} +116413. i q^{15} +(4.14587e6 - 635588. i) q^{16} -6.15701e6i q^{17} +(-2.67032e6 + 101603. i) q^{18} +3.03570e6 q^{19} +(-74553.8 - 978293. i) q^{20} +(-4.48190e6 - 9.83218e6i) q^{21} +(1.06331e6 + 2.79460e7i) q^{22} +6.78832e6i q^{23} +(2.23753e7 - 2.56396e6i) q^{24} +4.85986e7 q^{25} +(-1.38583e6 - 3.64224e7i) q^{26} -1.43489e7 q^{27} +(4.39609e7 + 7.97555e7i) q^{28} -2.53110e7 q^{29} +(-200307. - 5.26446e6i) q^{30} -2.54102e8 q^{31} +(-1.86391e8 + 3.58762e7i) q^{32} +1.50167e8i q^{33} +(1.05941e7 + 2.78433e8i) q^{34} +(1.93838e7 - 8.83593e6i) q^{35} +(1.20583e8 - 9.18937e6i) q^{36} -3.76158e8 q^{37} +(-1.37281e8 + 5.22338e6i) q^{38} -1.95715e8i q^{39} +(5.05478e6 + 4.41122e7i) q^{40} +6.88640e8i q^{41} +(2.19599e8 + 4.36920e8i) q^{42} +1.05610e9i q^{43} +(-9.61704e7 - 1.26195e9i) q^{44} -2.82884e7i q^{45} +(-1.16803e7 - 3.06982e8i) q^{46} +1.61462e9 q^{47} +(-1.00745e9 + 1.54448e8i) q^{48} +(-1.29696e9 + 1.49255e9i) q^{49} +(-2.19773e9 + 8.36212e7i) q^{50} +1.49615e9i q^{51} +(1.25340e8 + 1.64471e9i) q^{52} +2.86554e9 q^{53} +(6.48888e8 - 2.46894e7i) q^{54} -2.96050e8 q^{55} +(-2.12524e9 - 3.53107e9i) q^{56} -7.37675e8 q^{57} +(1.14462e9 - 4.35514e7i) q^{58} -5.63596e9 q^{59} +(1.81166e7 + 2.37725e8i) q^{60} -7.15254e9i q^{61} +(1.14910e10 - 4.37221e8i) q^{62} +(1.08910e9 + 2.38922e9i) q^{63} +(8.36728e9 - 1.94311e9i) q^{64} +3.85847e8 q^{65} +(-2.58385e8 - 6.79087e9i) q^{66} -3.11480e9i q^{67} +(-9.58172e8 - 1.25731e10i) q^{68} -1.64956e9i q^{69} +(-8.61375e8 + 4.32932e8i) q^{70} -1.04104e10i q^{71} +(-5.43719e9 + 6.23043e8i) q^{72} -2.84639e10i q^{73} +(1.70107e10 - 6.47236e8i) q^{74} -1.18095e10 q^{75} +(6.19914e9 - 4.72424e8i) q^{76} +(2.50041e10 - 1.13979e10i) q^{77} +(3.36757e8 + 8.85065e9i) q^{78} +4.17004e10i q^{79} +(-3.04489e8 - 1.98615e9i) q^{80} +3.48678e9 q^{81} +(-1.18491e9 - 3.11418e10i) q^{82} +3.43032e10 q^{83} +(-1.06825e10 - 1.93806e10i) q^{84} -2.94962e9 q^{85} +(-1.81718e9 - 4.77591e10i) q^{86} +6.15058e9 q^{87} +(6.52040e9 + 5.69024e10i) q^{88} -1.68359e10i q^{89} +(4.86745e7 + 1.27926e9i) q^{90} +(-3.25883e10 + 1.48550e10i) q^{91} +(1.05642e9 + 1.38623e10i) q^{92} +6.17468e10 q^{93} +(-7.30163e10 + 2.77819e9i) q^{94} -1.45430e9i q^{95} +(4.52931e10 - 8.71792e9i) q^{96} -1.64842e11i q^{97} +(5.60832e10 - 6.97280e10i) q^{98} -3.64906e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

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