LMFDB - Embedded newform 84.12.b.a.55.4

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			55.4
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-44.4594 + 8.44758i) q^{2} -243.000 q^{3} +(1905.28 - 751.149i) q^{4} -11354.1i q^{5} +(10803.6 - 2052.76i) q^{6} +(-41246.7 + 16614.4i) q^{7} +(-78362.1 + 49490.6i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-44.4594 + 8.44758i) q^{2} -243.000 q^{3} +(1905.28 - 751.149i) q^{4} -11354.1i q^{5} +(10803.6 - 2052.76i) q^{6} +(-41246.7 + 16614.4i) q^{7} +(-78362.1 + 49490.6i) q^{8} +59049.0 q^{9} +(95914.4 + 504795. i) q^{10} +397197. i q^{11} +(-462982. + 182529. i) q^{12} -2.06316e6i q^{13} +(1.69345e6 - 1.08710e6i) q^{14} +2.75904e6i q^{15} +(3.06585e6 - 2.86229e6i) q^{16} -7.16448e6i q^{17} +(-2.62528e6 + 498821. i) q^{18} +1.91040e7 q^{19} +(-8.52859e6 - 2.16326e7i) q^{20} +(1.00229e7 - 4.03729e6i) q^{21} +(-3.35535e6 - 1.76591e7i) q^{22} -7.66741e6i q^{23} +(1.90420e7 - 1.20262e7i) q^{24} -8.00867e7 q^{25} +(1.74287e7 + 9.17269e7i) q^{26} -1.43489e7 q^{27} +(-6.61065e7 + 6.26374e7i) q^{28} +1.11735e8 q^{29} +(-2.33072e7 - 1.22665e8i) q^{30} +1.91846e8 q^{31} +(-1.12127e8 + 1.53155e8i) q^{32} -9.65188e7i q^{33} +(6.05225e7 + 3.18529e8i) q^{34} +(1.88641e8 + 4.68318e8i) q^{35} +(1.12505e8 - 4.43546e7i) q^{36} +6.33630e8 q^{37} +(-8.49353e8 + 1.61383e8i) q^{38} +5.01348e8i q^{39} +(5.61920e8 + 8.89728e8i) q^{40} -1.59482e8i q^{41} +(-4.11509e8 + 2.64165e8i) q^{42} -1.09522e9i q^{43} +(2.98354e8 + 7.56770e8i) q^{44} -6.70446e8i q^{45} +(6.47711e7 + 3.40889e8i) q^{46} -2.07644e9 q^{47} +(-7.45003e8 + 6.95537e8i) q^{48} +(1.42525e9 - 1.37058e9i) q^{49} +(3.56061e9 - 6.76539e8i) q^{50} +1.74097e9i q^{51} +(-1.54974e9 - 3.93089e9i) q^{52} +3.51152e9 q^{53} +(6.37944e8 - 1.21214e8i) q^{54} +4.50980e9 q^{55} +(2.40992e9 - 3.34326e9i) q^{56} -4.64228e9 q^{57} +(-4.96767e9 + 9.43891e8i) q^{58} +1.86196e9 q^{59} +(2.07245e9 + 5.25673e9i) q^{60} +9.15087e9i q^{61} +(-8.52937e9 + 1.62064e9i) q^{62} +(-2.43558e9 + 9.81062e8i) q^{63} +(3.69129e9 - 7.75637e9i) q^{64} -2.34253e10 q^{65} +(8.15350e8 + 4.29117e9i) q^{66} -4.98135e9i q^{67} +(-5.38159e9 - 1.36503e10i) q^{68} +1.86318e9i q^{69} +(-1.23430e10 - 1.92276e10i) q^{70} -1.27297e10i q^{71} +(-4.62720e9 + 2.92237e9i) q^{72} +1.29634e10i q^{73} +(-2.81708e10 + 5.35264e9i) q^{74} +1.94611e10 q^{75} +(3.63985e10 - 1.43500e10i) q^{76} +(-6.59917e9 - 1.63830e10i) q^{77} +(-4.23518e9 - 2.22896e10i) q^{78} +1.46844e10i q^{79} +(-3.24987e10 - 3.48099e10i) q^{80} +3.48678e9 q^{81} +(1.34724e9 + 7.09047e9i) q^{82} +2.39876e10 q^{83} +(1.60639e10 - 1.52209e10i) q^{84} -8.13460e10 q^{85} +(9.25196e9 + 4.86928e10i) q^{86} -2.71516e10 q^{87} +(-1.96575e10 - 3.11252e10i) q^{88} -4.95628e10i q^{89} +(5.66365e9 + 2.98076e10i) q^{90} +(3.42781e10 + 8.50985e10i) q^{91} +(-5.75937e9 - 1.46085e10i) q^{92} -4.66186e10 q^{93} +(9.23175e10 - 1.75409e10i) q^{94} -2.16908e11i q^{95} +(2.72468e10 - 3.72166e10i) q^{96} -6.05416e10i q^{97} +(-5.17878e10 + 7.29749e10i) q^{98} +2.34541e10i 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 $

$2$	−44.4594	+	8.44758i	−0.982423	+	0.186667i
$2$	−44.4594	+	8.44758i	−0.982423	+	0.186667i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	1905.28	−	751.149i	0.930311	−	0.366772i
$5$		−	11354.1i		−	1.62486i	−0.583058	−	0.812431i	$-0.698144\pi$
$5$		−	11354.1i		−	1.62486i	0.583058	−	0.812431i	$-0.301856\pi$
$6$	10803.6	−	2052.76i	0.567202	−	0.107772i
$7$	−41246.7	+	16614.4i	−0.927577	+	0.373633i
$7$	−41246.7	+	16614.4i	−0.927577	+	0.373633i
$8$	−78362.1	+	49490.6i	−0.845495	+	0.533984i
$9$	59049.0			0.333333
$10$	95914.4	+	504795.i	0.303308	+	1.59630i
$11$			397197.i			0.743611i	0.928311	+	0.371806i	$0.121261\pi$
$11$			397197.i			0.743611i	−0.928311	+	0.371806i	$0.878739\pi$
$12$	−462982.	+	182529.i	−0.537115	+	0.211756i
$13$		−	2.06316e6i		−	1.54115i	−0.637350	−	0.770574i	$-0.719969\pi$
$13$		−	2.06316e6i		−	1.54115i	0.637350	−	0.770574i	$-0.280031\pi$
$14$	1.69345e6	−	1.08710e6i	0.841528	−	0.540213i
$15$			2.75904e6i			0.938114i
$16$	3.06585e6	−	2.86229e6i	0.730957	−	0.682424i
$17$		−	7.16448e6i		−	1.22381i	−0.790929	−	0.611907i	$-0.790403\pi$
$17$		−	7.16448e6i		−	1.22381i	0.790929	−	0.611907i	$-0.209597\pi$
$18$	−2.62528e6	+	498821.i	−0.327474	+	0.0622223i
$19$	1.91040e7			1.77003			0.885014	−	0.465565i	$-0.154149\pi$
$19$	1.91040e7			1.77003			0.885014	+	0.465565i	$0.154149\pi$
$20$	−8.52859e6	−	2.16326e7i	−0.595954	−	1.51163i
$21$	1.00229e7	−	4.03729e6i	0.535537	−	0.215717i
$22$	−3.35535e6	−	1.76591e7i	−0.138808	−	0.730541i
$23$		−	7.66741e6i		−	0.248397i	−0.992257	−	0.124198i	$-0.960364\pi$
$23$		−	7.66741e6i		−	0.248397i	0.992257	−	0.124198i	$-0.0396359\pi$
$24$	1.90420e7	−	1.20262e7i	0.488147	−	0.308296i
$25$	−8.00867e7			−1.64018
$26$	1.74287e7	+	9.17269e7i	0.287682	+	1.51406i
$27$	−1.43489e7			−0.192450
$28$	−6.61065e7	+	6.26374e7i	−0.725897	+	0.687804i
$29$	1.11735e8			1.01158			0.505790	−	0.862657i	$-0.331201\pi$
$29$	1.11735e8			1.01158			0.505790	+	0.862657i	$0.331201\pi$
$30$	−2.33072e7	−	1.22665e8i	−0.175115	−	0.921625i
$31$	1.91846e8			1.20355			0.601775	−	0.798666i	$-0.294460\pi$
$31$	1.91846e8			1.20355			0.601775	+	0.798666i	$0.294460\pi$
$32$	−1.12127e8	+	1.53155e8i	−0.590723	+	0.806874i
$33$		−	9.65188e7i		−	0.429324i
$34$	6.05225e7	+	3.18529e8i	0.228446	+	1.20230i
$35$	1.88641e8	+	4.68318e8i	0.607101	+	1.50718i
$36$	1.12505e8	−	4.43546e7i	0.310104	−	0.122257i
$37$	6.33630e8			1.50219			0.751097	−	0.660192i	$-0.229525\pi$
$37$	6.33630e8			1.50219			0.751097	+	0.660192i	$0.229525\pi$
$38$	−8.49353e8	+	1.61383e8i	−1.73892	+	0.330406i
$39$			5.01348e8i			0.889783i
$40$	5.61920e8	+	8.89728e8i	0.867649	+	1.37381i
$41$		−	1.59482e8i		−	0.214981i	−0.994206	−	0.107490i	$-0.965718\pi$
$41$		−	1.59482e8i		−	0.214981i	0.994206	−	0.107490i	$-0.0342815\pi$
$42$	−4.11509e8	+	2.64165e8i	−0.485856	+	0.311892i
$43$		−	1.09522e9i		−	1.13612i	−0.822987	−	0.568061i	$-0.807694\pi$
$43$		−	1.09522e9i		−	1.13612i	0.822987	−	0.568061i	$-0.192306\pi$
$44$	2.98354e8	+	7.56770e8i	0.272736	+	0.691790i
$45$		−	6.70446e8i		−	0.541621i
$46$	6.47711e7	+	3.40889e8i	0.0463674	+	0.244031i
$47$	−2.07644e9			−1.32063			−0.660316	−	0.750988i	$-0.729578\pi$
$47$	−2.07644e9			−1.32063			−0.660316	+	0.750988i	$0.729578\pi$
$48$	−7.45003e8	+	6.95537e8i	−0.422018	+	0.393998i
$49$	1.42525e9	−	1.37058e9i	0.720797	−	0.693146i
$50$	3.56061e9	−	6.76539e8i	1.61135	−	0.306167i
$51$			1.74097e9i			0.706570i
$52$	−1.54974e9	−	3.93089e9i	−0.565250	−	1.43375i
$53$	3.51152e9			1.15339			0.576697	−	0.816958i	$-0.304341\pi$
$53$	3.51152e9			1.15339			0.576697	+	0.816958i	$0.304341\pi$
$54$	6.37944e8	−	1.21214e8i	0.189067	−	0.0359241i
$55$	4.50980e9			1.20827
$56$	2.40992e9	−	3.34326e9i	0.584748	−	0.811215i
$57$	−4.64228e9			−1.02193
$58$	−4.96767e9	+	9.43891e8i	−0.993800	+	0.188829i
$59$	1.86196e9			0.339066			0.169533	−	0.985525i	$-0.445774\pi$
$59$	1.86196e9			0.339066			0.169533	+	0.985525i	$0.445774\pi$
$60$	2.07245e9	+	5.25673e9i	0.344074	+	0.872738i
$61$			9.15087e9i			1.38723i	0.720346	+	0.693615i	$0.243983\pi$
$61$			9.15087e9i			1.38723i	−0.720346	+	0.693615i	$0.756017\pi$
$62$	−8.52937e9	+	1.62064e9i	−1.18240	+	0.224663i
$63$	−2.43558e9	+	9.81062e8i	−0.309192	+	0.124544i
$64$	3.69129e9	−	7.75637e9i	0.429723	−	0.902961i
$65$	−2.34253e10			−2.50415
$66$	8.15350e8	+	4.29117e9i	0.0801406	+	0.421778i
$67$		−	4.98135e9i		−	0.450750i	−0.974272	−	0.225375i	$-0.927639\pi$
$67$		−	4.98135e9i		−	0.450750i	0.974272	−	0.225375i	$-0.0723606\pi$
$68$	−5.38159e9	−	1.36503e10i	−0.448861	−	1.13853i
$69$			1.86318e9i			0.143412i
$70$	−1.23430e10	−	1.92276e10i	−0.877772	−	1.36737i
$71$		−	1.27297e10i		−	0.837330i	−0.908141	−	0.418665i	$-0.862498\pi$
$71$		−	1.27297e10i		−	0.837330i	0.908141	−	0.418665i	$-0.137502\pi$
$72$	−4.62720e9	+	2.92237e9i	−0.281832	+	0.177995i
$73$			1.29634e10i			0.731883i	0.930638	+	0.365941i	$0.119253\pi$
$73$			1.29634e10i			0.731883i	−0.930638	+	0.365941i	$0.880747\pi$
$74$	−2.81708e10	+	5.35264e9i	−1.47579	+	0.280410i
$75$	1.94611e10			0.946956
$76$	3.63985e10	−	1.43500e10i	1.64668	−	0.649196i
$77$	−6.59917e9	−	1.63830e10i	−0.277837	−	0.689756i
$78$	−4.23518e9	−	2.22896e10i	−0.166093	−	0.874143i
$79$			1.46844e10i			0.536916i	0.963291	+	0.268458i	$0.0865141\pi$
$79$			1.46844e10i			0.536916i	−0.963291	+	0.268458i	$0.913486\pi$
$80$	−3.24987e10	−	3.48099e10i	−1.10884	−	1.18770i
$81$	3.48678e9			0.111111
$82$	1.34724e9	+	7.09047e9i	0.0401298	+	0.211202i
$83$	2.39876e10			0.668432			0.334216	−	0.942497i	$-0.391529\pi$
$83$	2.39876e10			0.668432			0.334216	+	0.942497i	$0.391529\pi$
$84$	1.60639e10	−	1.52209e10i	0.419097	−	0.397104i
$85$	−8.13460e10			−1.98853
$86$	9.25196e9	+	4.86928e10i	0.212076	+	1.11615i
$87$	−2.71516e10			−0.584036
$88$	−1.96575e10	−	3.11252e10i	−0.397076	−	0.628719i
$89$		−	4.95628e10i		−	0.940830i	−0.882445	−	0.470415i	$-0.844104\pi$
$89$		−	4.95628e10i		−	0.940830i	0.882445	−	0.470415i	$-0.155896\pi$
$90$	5.66365e9	+	2.98076e10i	0.101103	+	0.532101i
$91$	3.42781e10	+	8.50985e10i	0.575823	+	1.42953i
$92$	−5.75937e9	−	1.46085e10i	−0.0911049	−	0.231086i
$93$	−4.66186e10			−0.694870
$94$	9.23175e10	−	1.75409e10i	1.29742	−	0.246518i
$95$		−	2.16908e11i		−	2.87605i
$96$	2.72468e10	−	3.72166e10i	0.341054	−	0.465849i
$97$		−	6.05416e10i		−	0.715829i	−0.933754	−	0.357914i	$-0.883488\pi$
$97$		−	6.05416e10i		−	0.715829i	0.933754	−	0.357914i	$-0.116512\pi$
$98$	−5.17878e10	+	7.29749e10i	−0.578741	+	0.815512i
$99$			2.34541e10i			0.247870i
$100$	−1.52587e11	+	6.01570e10i	−1.52587	+	0.601570i
$101$		−	1.14151e11i		−	1.08072i	−0.841435	−	0.540359i	$-0.818289\pi$
$101$		−	1.14151e11i		−	1.08072i	0.841435	−	0.540359i	$-0.181711\pi$
$102$	−1.47070e10	−	7.74024e10i	−0.131893	−	0.694151i
$103$	−1.36534e10			−0.116048			−0.0580238	−	0.998315i	$-0.518480\pi$
$103$	−1.36534e10			−0.116048			−0.0580238	+	0.998315i	$0.518480\pi$
$104$	1.02107e11	+	1.61674e11i	0.822948	+	1.30303i
$105$	−4.58397e10	−	1.13801e11i	−0.350510	−	0.870173i
$106$	−1.56120e11	+	2.96639e10i	−1.13312	+	0.215301i
$107$		−	2.48033e11i		−	1.70962i	−0.518942	−	0.854809i	$-0.673674\pi$
$107$		−	2.48033e11i		−	1.70962i	0.518942	−	0.854809i	$-0.326326\pi$
$108$	−2.73386e10	+	1.07782e10i	−0.179038	+	0.0705853i
$109$	−1.23442e11			−0.768452			−0.384226	−	0.923239i	$-0.625532\pi$
$109$	−1.23442e11			−0.768452			−0.384226	+	0.923239i	$0.625532\pi$
$110$	−2.00503e11	+	3.80969e10i	−1.18703	+	0.225543i
$111$	−1.53972e11			−0.867292
$112$	−7.89012e10	+	1.68997e11i	−0.423043	+	0.906110i
$113$	−1.58979e11			−0.811725			−0.405862	−	0.913934i	$-0.633029\pi$
$113$	−1.58979e11			−0.811725			−0.405862	+	0.913934i	$0.633029\pi$
$114$	2.06393e11	−	3.92160e10i	1.00396	−	0.190760i
$115$	−8.70563e10			−0.403610
$116$	2.12886e11	−	8.39296e10i	0.941084	−	0.371019i
$117$		−	1.21828e11i		−	0.513716i
$118$	−8.27816e10	+	1.57290e10i	−0.333106	+	0.0632924i
$119$	1.19033e11	+	2.95511e11i	0.457257	+	1.13518i
$120$	−1.36546e11	−	2.16204e11i	−0.500938	−	0.793171i
$121$	1.27546e11			0.447042
$122$	−7.73027e10	−	4.06842e11i	−0.258950	−	1.36285i
$123$			3.87541e10i			0.124119i
$124$	3.65520e11	−	1.44105e11i	1.11968	−	0.441428i
$125$			3.54912e11i			1.04020i
$126$	9.99966e10	−	6.41922e10i	0.280509	−	0.180071i
$127$			3.94325e10i			0.105909i	0.998597	+	0.0529546i	$0.0168638\pi$
$127$			3.94325e10i			0.105909i	−0.998597	+	0.0529546i	$0.983136\pi$
$128$	−9.85901e10	+	3.76026e11i	−0.253617	+	0.967305i
$129$			2.66138e11i			0.655940i
$130$	1.04147e12	−	1.97887e11i	2.46014	−	0.467443i
$131$	−5.85986e11			−1.32707			−0.663537	−	0.748144i	$-0.730945\pi$
$131$	−5.85986e11			−1.32707			−0.663537	+	0.748144i	$0.730945\pi$
$132$	−7.25000e10	−	1.83895e11i	−0.157464	−	0.399405i
$133$	−7.87978e11	+	3.17401e11i	−1.64184	+	0.661340i
$134$	4.20803e10	+	2.21468e11i	0.0841400	+	0.442827i
$135$			1.62918e11i			0.312705i
$136$	3.54575e11	+	5.61424e11i	0.653497	+	1.03473i
$137$	1.95352e11			0.345824			0.172912	−	0.984937i	$-0.444682\pi$
$137$	1.95352e11			0.345824			0.172912	+	0.984937i	$0.444682\pi$
$138$	−1.57394e10	−	8.28359e10i	−0.0267703	−	0.140891i
$139$	7.79814e11			1.27470			0.637352	−	0.770573i	$-0.280030\pi$
$139$	7.79814e11			1.27470			0.637352	+	0.770573i	$0.280030\pi$
$140$	7.11189e11	+	7.50577e11i	1.11759	+	1.17948i
$141$	5.04576e11			0.762468
$142$	1.07535e11	+	5.65954e11i	0.156302	+	0.822612i
$143$	8.19481e11			1.14602
$144$	1.81036e11	−	1.69016e11i	0.243652	−	0.227475i
$145$		−	1.26865e12i		−	1.64368i
$146$	−1.09509e11	−	5.76343e11i	−0.136618	−	0.719019i
$147$	−3.46336e11	+	3.33050e11i	−0.416153	+	0.400188i
$148$	1.20724e12	−	4.75950e11i	1.39751	−	0.550963i
$149$	−9.64980e11			−1.07645			−0.538225	−	0.842801i	$-0.680905\pi$
$149$	−9.64980e11			−1.07645			−0.538225	+	0.842801i	$0.680905\pi$
$150$	−8.65227e11	+	1.64399e11i	−0.930311	+	0.176765i
$151$			9.81888e9i			0.0101786i	0.999987	+	0.00508931i	$0.00161998\pi$
$151$			9.81888e9i			0.0101786i	−0.999987	+	0.00508931i	$0.998380\pi$
$152$	−1.49703e12	+	9.45470e11i	−1.49655	+	0.945166i
$153$		−	4.23055e11i		−	0.407938i
$154$	4.31793e11	+	6.72634e11i	0.401709	+	0.625770i
$155$		−	2.17824e12i		−	1.95560i
$156$	3.76587e11	+	9.55207e11i	0.326347	+	0.827775i
$157$			1.72626e12i			1.44430i	0.691735	+	0.722151i	$0.256846\pi$
$157$			1.72626e12i			1.44430i	−0.691735	+	0.722151i	$0.743154\pi$
$158$	−1.24047e11	−	6.52858e11i	−0.100224	−	0.527479i
$159$	−8.53299e11			−0.665913
$160$	1.73893e12	+	1.27309e12i	1.31106	+	0.959843i
$161$	1.27389e11	+	3.16255e11i	0.0928091	+	0.230407i
$162$	−1.55020e11	+	2.94549e10i	−0.109158	+	0.0207408i
$163$			1.43684e12i			0.978086i	0.872260	+	0.489043i	$0.162654\pi$
$163$			1.43684e12i			0.978086i	−0.872260	+	0.489043i	$0.837346\pi$
$164$	−1.19795e11	−	3.03857e11i	−0.0788490	−	0.199999i
$165$	−1.09588e12			−0.697592
$166$	−1.06647e12	+	2.02637e11i	−0.656683	+	0.124774i
$167$	−2.20423e12			−1.31315			−0.656577	−	0.754259i	$-0.727996\pi$
$167$	−2.20423e12			−1.31315			−0.656577	+	0.754259i	$0.727996\pi$
$168$	−5.85611e11	+	8.12412e11i	−0.337604	+	0.468355i
$169$	−2.46447e12			−1.37514
$170$	3.61659e12	−	6.87177e11i	1.95358	−	0.371193i
$171$	1.12807e12			0.590009
$172$	−8.22673e11	−	2.08670e12i	−0.416697	−	1.05695i
$173$		−	1.88867e12i		−	0.926624i	−0.886195	−	0.463312i	$-0.846661\pi$
$173$		−	1.88867e12i		−	0.926624i	0.886195	−	0.463312i	$-0.153339\pi$
$174$	1.20714e12	−	2.29365e11i	0.573771	−	0.109020i
$175$	3.30331e12	−	1.33059e12i	1.52139	−	0.612823i
$176$	1.13689e12	+	1.21775e12i	0.507458	+	0.543548i
$177$	−4.52456e11			−0.195760
$178$	4.18686e11	+	2.20353e12i	0.175622	+	0.924293i
$179$			1.73988e12i			0.707666i	0.935309	+	0.353833i	$0.115122\pi$
$179$			1.73988e12i			0.707666i	−0.935309	+	0.353833i	$0.884878\pi$
$180$	−5.03605e11	−	1.27739e12i	−0.198651	−	0.503876i
$181$		−	1.32775e12i		−	0.508025i	−0.967201	−	0.254013i	$-0.918250\pi$
$181$		−	1.32775e12i		−	0.508025i	0.967201	−	0.254013i	$-0.0817505\pi$
$182$	−2.24286e12	−	3.49386e12i	−0.832549	−	1.29692i
$183$		−	2.22366e12i		−	0.800918i
$184$	3.79465e11	+	6.00834e11i	0.132640	+	0.210018i
$185$		−	7.19428e12i		−	2.44086i
$186$	2.07264e12	−	3.93815e11i	0.682656	−	0.129709i
$187$	2.84571e12			0.910042
$188$	−3.95620e12	+	1.55972e12i	−1.22860	+	0.484371i
$189$	5.91845e11	−	2.38398e11i	0.178512	−	0.0719056i
$190$	1.83235e12	+	9.64362e12i	0.536864	+	2.82550i
$191$			4.26567e12i			1.21424i	0.794611	+	0.607119i	$0.207675\pi$
$191$			4.26567e12i			1.21424i	−0.794611	+	0.607119i	$0.792325\pi$
$192$	−8.96984e11	+	1.88480e12i	−0.248101	+	0.521325i
$193$	1.84890e12			0.496990			0.248495	−	0.968633i	$-0.420064\pi$
$193$	1.84890e12			0.496990			0.248495	+	0.968633i	$0.420064\pi$
$194$	5.11430e11	+	2.69164e12i	0.133622	+	0.703247i
$195$	5.69234e12			1.44577
$196$	1.68599e12	−	3.68190e12i	0.416339	−	0.909209i
$197$	−1.37742e12			−0.330753			−0.165376	−	0.986231i	$-0.552884\pi$
$197$	−1.37742e12			−0.330753			−0.165376	+	0.986231i	$0.552884\pi$
$198$	−1.98130e11	−	1.04275e12i	−0.0462692	−	0.243514i
$199$	−5.16991e12			−1.17433			−0.587167	−	0.809466i	$-0.699757\pi$
$199$	−5.16991e12			−1.17433			−0.587167	+	0.809466i	$0.699757\pi$
$200$	6.27576e12	−	3.96354e12i	1.38676	−	0.875827i
$201$			1.21047e12i			0.260240i
$202$	9.64300e11	+	5.07509e12i	0.201734	+	1.06172i
$203$	−4.60870e12	+	1.85641e12i	−0.938318	+	0.377959i
$204$	1.30773e12	+	3.31703e12i	0.259150	+	0.657330i
$205$	−1.81077e12			−0.349314
$206$	6.07023e11	−	1.15338e11i	0.114008	−	0.0216623i
$207$		−	4.52753e11i		−	0.0827989i
$208$	−5.90537e12	−	6.32535e12i	−1.05172	−	1.12651i
$209$			7.58806e12i			1.31621i
$210$	2.99935e12	+	4.67230e12i	0.506782	+	0.789450i
$211$		−	7.20518e12i		−	1.18602i	−0.805196	−	0.593009i	$-0.797940\pi$
$211$		−	7.20518e12i		−	1.18602i	0.805196	−	0.593009i	$-0.202060\pi$
$212$	6.69042e12	−	2.63767e12i	1.07302	−	0.423033i
$213$			3.09331e12i			0.483433i
$214$	2.09528e12	+	1.10274e13i	0.319129	+	1.67957i
$215$	−1.24352e13			−1.84604
$216$	1.12441e12	−	7.10136e11i	0.162716	−	0.102765i
$217$	−7.91302e12	+	3.18741e12i	−1.11638	+	0.449685i
$218$	5.48815e12	−	1.04278e12i	0.754945	−	0.143445i
$219$		−	3.15009e12i		−	0.422553i
$220$	8.59241e12	−	3.38753e12i	1.12406	−	0.443158i
$221$	−1.47815e13			−1.88608
$222$	6.84551e12	−	1.30069e12i	0.852048	−	0.161895i
$223$	5.56019e11			0.0675169			0.0337585	−	0.999430i	$-0.489252\pi$
$223$	5.56019e11			0.0675169			0.0337585	+	0.999430i	$0.489252\pi$
$224$	2.08028e12	−	8.18005e12i	0.246466	−	0.969151i
$225$	−4.72904e12			−0.546725
$226$	7.06812e12	−	1.34299e12i	0.797457	−	0.151522i
$227$	8.44433e12			0.929871			0.464936	−	0.885344i	$-0.346077\pi$
$227$	8.44433e12			0.929871			0.464936	+	0.885344i	$0.346077\pi$
$228$	−8.84482e12	+	3.48704e12i	−0.950709	+	0.374814i
$229$			1.07618e12i			0.112925i	0.998405	+	0.0564624i	$0.0179821\pi$
$229$			1.07618e12i			0.112925i	−0.998405	+	0.0564624i	$0.982018\pi$
$230$	3.87047e12	−	7.35415e11i	0.396516	−	0.0753407i
$231$	1.60360e12	+	3.98108e12i	0.160409	+	0.398231i
$232$	−8.75579e12	+	5.52983e12i	−0.855286	+	0.540167i
$233$	5.67782e12			0.541657			0.270828	−	0.962628i	$-0.412702\pi$
$233$	5.67782e12			0.541657			0.270828	+	0.962628i	$0.412702\pi$
$234$	1.02915e12	+	5.41638e12i	0.0958939	+	0.504687i
$235$			2.35761e13i			2.14585i
$236$	3.54755e12	−	1.39861e12i	0.315437	−	0.124360i
$237$		−	3.56830e12i		−	0.309989i
$238$	−7.78851e12	−	1.21327e13i	−0.661121	−	1.02987i
$239$		−	2.24357e13i		−	1.86102i	−0.366269	−	0.930509i	$-0.619365\pi$
$239$		−	2.24357e13i		−	1.86102i	0.366269	−	0.930509i	$-0.380635\pi$
$240$	7.89718e12	+	8.45881e12i	0.640192	+	0.685721i
$241$		−	2.50056e12i		−	0.198127i	−0.995081	−	0.0990633i	$-0.968415\pi$
$241$		−	2.50056e12i		−	0.198127i	0.995081	−	0.0990633i	$-0.0315846\pi$
$242$	−5.67064e12	+	1.07746e12i	−0.439185	+	0.0834481i
$243$	−8.47289e11			−0.0641500
$244$	6.87367e12	+	1.74349e13i	0.508797	+	1.29056i
$245$	−1.55616e13	−	1.61824e13i	−1.12627	−	1.17120i
$246$	−3.27378e11	−	1.72298e12i	−0.0231690	−	0.121938i
$247$		−	3.94147e13i		−	2.72788i
$248$	−1.50335e13	+	9.49459e12i	−1.01760	+	0.642676i
$249$	−5.82898e12			−0.385919
$250$	−2.99815e12	−	1.57792e13i	−0.194170	−	1.02191i
$251$	−2.81338e12			−0.178247			−0.0891236	−	0.996021i	$-0.528407\pi$
$251$	−2.81338e12			−0.178247			−0.0891236	+	0.996021i	$0.528407\pi$
$252$	−3.90352e12	+	3.69867e12i	−0.241966	+	0.229268i
$253$	3.04547e12			0.184710
$254$	−3.33109e11	−	1.75314e12i	−0.0197697	−	0.104048i
$255$	1.97671e13			1.14808
$256$	1.20674e12	−	1.75507e13i	0.0685955	−	0.997645i
$257$		−	1.86081e13i		−	1.03531i	−0.855591	−	0.517653i	$-0.826806\pi$
$257$		−	1.86081e13i		−	1.03531i	0.855591	−	0.517653i	$-0.173194\pi$
$258$	−2.24823e12	−	1.18324e13i	−0.122442	−	0.644411i
$259$	−2.61351e13	+	1.05274e13i	−1.39340	+	0.561269i
$260$	−4.46316e13	+	1.75959e13i	−2.32964	+	0.918453i
$261$	6.59784e12			0.337193
$262$	2.60526e13	−	4.95016e12i	1.30375	−	0.247721i
$263$			2.63697e13i			1.29226i	0.763229	+	0.646128i	$0.223613\pi$
$263$			2.63697e13i			1.29226i	−0.763229	+	0.646128i	$0.776387\pi$
$264$	4.77677e12	+	7.56341e12i	0.229252	+	0.362991i
$265$		−	3.98700e13i		−	1.87411i
$266$	3.23517e13	−	2.07680e13i	1.48953	−	0.956192i
$267$			1.20438e13i			0.543188i
$268$	−3.74173e12	−	9.49084e12i	−0.165322	−	0.419337i
$269$			2.19591e13i			0.950554i	0.879836	+	0.475277i	$0.157652\pi$
$269$			2.19591e13i			0.950554i	−0.879836	+	0.475277i	$0.842348\pi$
$270$	−1.37627e12	−	7.24326e12i	−0.0583716	−	0.307208i
$271$	1.22532e13			0.509234			0.254617	−	0.967042i	$-0.418051\pi$
$271$	1.22532e13			0.509234			0.254617	+	0.967042i	$0.418051\pi$
$272$	−2.05068e13	−	2.19653e13i	−0.835160	−	0.894556i
$273$	−8.32958e12	−	2.06789e13i	−0.332452	−	0.825342i
$274$	−8.68524e12	+	1.65025e12i	−0.339745	+	0.0645539i
$275$		−	3.18102e13i		−	1.21965i
$276$	1.39953e12	+	3.54988e12i	0.0525994	+	0.133418i
$277$	−1.46520e13			−0.539832			−0.269916	−	0.962884i	$-0.586996\pi$
$277$	−1.46520e13			−0.539832			−0.269916	+	0.962884i	$0.586996\pi$
$278$	−3.46700e13	+	6.58754e12i	−1.25230	+	0.237945i
$279$	1.13283e13			0.401183
$280$	−3.79596e13	−	2.73624e13i	−1.31811	−	0.950134i
$281$	−8.14758e12			−0.277424			−0.138712	−	0.990333i	$-0.544296\pi$
$281$	−8.14758e12			−0.277424			−0.138712	+	0.990333i	$0.544296\pi$
$282$	−2.24331e13	+	4.26245e12i	−0.749066	+	0.142328i
$283$	3.08539e13			1.01038			0.505189	−	0.863009i	$-0.331423\pi$
$283$	3.08539e13			1.01038			0.505189	+	0.863009i	$0.331423\pi$
$284$	−9.56188e12	−	2.42536e13i	−0.307109	−	0.778977i
$285$			5.27087e13i			1.66049i
$286$	−3.64336e13	+	6.92263e12i	−1.12587	+	0.213923i
$287$	2.64969e12	+	6.57810e12i	0.0803239	+	0.199411i
$288$	−6.62096e12	+	9.04364e12i	−0.196908	+	0.268958i
$289$	−1.70579e13			−0.497722
$290$	1.07170e13	+	5.64033e13i	0.306820	+	1.61479i
$291$			1.47116e13i			0.413284i
$292$	9.73741e12	+	2.46988e13i	0.268434	+	0.680879i
$293$			1.55829e13i			0.421576i	0.977532	+	0.210788i	$0.0676030\pi$
$293$			1.55829e13i			0.421576i	−0.977532	+	0.210788i	$0.932397\pi$
$294$	1.25844e13	−	1.77329e13i	0.334136	−	0.470836i
$295$		−	2.11408e13i		−	0.550935i
$296$	−4.96525e13	+	3.13587e13i	−1.27010	+	0.802147i
$297$		−	5.69934e12i		−	0.143108i
$298$	4.29024e13	−	8.15175e12i	1.05753	−	0.200938i
$299$	−1.58191e13			−0.382816
$300$	3.70787e13	−	1.46182e13i	0.880963	−	0.347317i
$301$	1.81964e13	+	4.51742e13i	0.424492	+	1.05384i
$302$	−8.29458e10	−	4.36542e11i	−0.00190001	−	0.00999971i
$303$			2.77387e13i			0.623953i
$304$	5.85702e13	−	5.46813e13i	1.29381	−	1.20791i
$305$	1.03900e14			2.25406
$306$	3.57380e12	+	1.88088e13i	0.0761486	+	0.400768i
$307$	−2.22956e13			−0.466615			−0.233307	−	0.972403i	$-0.574955\pi$
$307$	−2.22956e13			−0.466615			−0.233307	+	0.972403i	$0.574955\pi$
$308$	−2.48794e13	−	2.62573e13i	−0.511458	−	0.539785i
$309$	3.31778e12			0.0670002
$310$	1.84008e13	+	9.68430e13i	0.365046	+	1.92123i
$311$	−9.93403e12			−0.193617			−0.0968085	−	0.995303i	$-0.530863\pi$
$311$	−9.93403e12			−0.193617			−0.0968085	+	0.995303i	$0.530863\pi$
$312$	−2.48120e13	−	3.92867e13i	−0.475129	−	0.752307i
$313$		−	9.76805e13i		−	1.83787i	−0.394412	−	0.918934i	$-0.629052\pi$
$313$		−	9.76805e13i		−	1.83787i	0.394412	−	0.918934i	$-0.370948\pi$
$314$	−1.45827e13	−	7.67485e13i	−0.269603	−	1.41892i
$315$	1.11390e13	+	2.76537e13i	0.202367	+	0.502395i
$316$	1.10302e13	+	2.79778e13i	0.196926	+	0.499499i
$317$	2.03945e13			0.357839			0.178919	−	0.983864i	$-0.442740\pi$
$317$	2.03945e13			0.357839			0.178919	+	0.983864i	$0.442740\pi$
$318$	3.79372e13	−	7.20832e12i	0.654208	−	0.124304i
$319$			4.43808e13i			0.752222i
$320$	−8.80664e13	−	4.19112e13i	−1.46719	−	0.698241i
$321$			6.02721e13i			0.987049i
$322$	−8.33524e12	−	1.29844e13i	−0.134187	−	0.209033i
$323$		−	1.36870e14i		−	2.16619i
$324$	6.64329e12	−	2.61909e12i	0.103368	−	0.0407524i
$325$			1.65232e14i			2.52775i
$326$	−1.21378e13	−	6.38811e13i	−0.182576	−	0.960894i
$327$	2.99964e13			0.443666
$328$	7.89285e12	+	1.24973e13i	0.114796	+	0.181765i
$329$	8.56464e13	−	3.44988e13i	1.22499	−	0.493431i
$330$	4.87222e13	−	9.25754e12i	0.685331	−	0.130217i
$331$			9.48387e13i			1.31199i	0.754764	+	0.655997i	$0.227752\pi$
$331$			9.48387e13i			1.31199i	−0.754764	+	0.655997i	$0.772248\pi$
$332$	4.57030e13	−	1.80183e13i	0.621849	−	0.245162i
$333$	3.74152e13			0.500731
$334$	9.79987e13	−	1.86204e13i	1.29007	−	0.245123i
$335$	−5.65585e13			−0.732406
$336$	1.91730e13	−	4.10664e13i	0.244244	−	0.523143i
$337$	1.30535e14			1.63592			0.817962	−	0.575272i	$-0.195104\pi$
$337$	1.30535e14			1.63592			0.817962	+	0.575272i	$0.195104\pi$
$338$	1.09569e14	−	2.08188e13i	1.35097	−	0.256693i
$339$	3.86319e13			0.468649
$340$	−1.54987e14	+	6.11029e13i	−1.84995	+	0.729337i
$341$			7.62007e13i			0.894973i
$342$	−5.01535e13	+	9.52949e12i	−0.579639	+	0.110135i
$343$	−3.60157e13	+	8.02114e13i	−0.409613	+	0.912259i
$344$	5.42031e13	+	8.58237e13i	0.606670	+	0.960585i
$345$	2.11547e13			0.233024
$346$	1.59547e13	+	8.39693e13i	0.172970	+	0.910337i
$347$		−	2.65201e13i		−	0.282984i	−0.989939	−	0.141492i	$-0.954810\pi$
$347$		−	2.65201e13i		−	0.282984i	0.989939	−	0.141492i	$-0.0451900\pi$
$348$	−5.17313e13	+	2.03949e13i	−0.543335	+	0.214208i
$349$			1.27350e14i			1.31662i	0.752747	+	0.658310i	$0.228728\pi$
$349$			1.27350e14i			1.31662i	−0.752747	+	0.658310i	$0.771272\pi$
$350$	−1.35623e14	+	8.70622e13i	−1.38025	+	0.886045i
$351$			2.96041e13i			0.296594i
$352$	−6.08326e13	−	4.45363e13i	−0.600001	−	0.439268i
$353$			3.24020e13i			0.314638i	0.987548	+	0.157319i	$0.0502850\pi$
$353$			3.24020e13i			0.314638i	−0.987548	+	0.157319i	$0.949715\pi$
$354$	2.01159e13	−	3.82216e12i	0.192319	−	0.0365419i
$355$	−1.44534e14			−1.36055
$356$	−3.72291e13	−	9.44309e13i	−0.345070	−	0.875264i
$357$	−2.89251e13	−	7.18092e13i	−0.263997	−	0.655398i
$358$	−1.46978e13	−	7.73542e13i	−0.132098	−	0.695228i
$359$			1.44855e14i			1.28208i	0.767509	+	0.641038i	$0.221496\pi$
$359$			1.44855e14i			1.28208i	−0.767509	+	0.641038i	$0.778504\pi$
$360$	3.31808e13	+	5.25376e13i	0.289216	+	0.457937i
$361$	2.48473e14			2.13300
$362$	1.12163e13	+	5.90311e13i	0.0948315	+	0.499096i
$363$	−3.09938e13			−0.258100
$364$	1.29231e14	+	1.36388e14i	1.06001	+	1.11872i
$365$	1.47187e14			1.18921
$366$	1.87846e13	+	9.88627e13i	0.149505	+	0.786840i
$367$	1.79904e14			1.41052			0.705258	−	0.708951i	$-0.250831\pi$
$367$	1.79904e14			1.41052			0.705258	+	0.708951i	$0.250831\pi$
$368$	−2.19464e13	−	2.35072e13i	−0.169512	−	0.181567i
$369$		−	9.41724e12i		−	0.0716603i
$370$	6.07742e13	+	3.19853e14i	0.455628	+	2.39796i
$371$	−1.44839e14	+	5.83417e13i	−1.06986	+	0.430946i
$372$	−8.88214e13	+	3.50175e13i	−0.646445	+	0.254859i
$373$	6.09215e13			0.436890			0.218445	−	0.975849i	$-0.429902\pi$
$373$	6.09215e13			0.436890			0.218445	+	0.975849i	$0.429902\pi$
$374$	−1.26518e14	+	2.40394e13i	−0.894047	+	0.169875i
$375$		−	8.62436e13i		−	0.600558i
$376$	1.62714e14	−	1.02764e14i	1.11659	−	0.705196i
$377$		−	2.30527e14i		−	1.55900i
$378$	−2.42992e13	+	1.55987e13i	−0.161952	+	0.103964i
$379$		−	8.82292e12i		−	0.0579558i	−0.999580	−	0.0289779i	$-0.990775\pi$
$379$		−	8.82292e12i		−	0.0579558i	0.999580	−	0.0289779i	$-0.00922524\pi$
$380$	−1.62930e14	−	4.13270e14i	−1.05485	−	2.67562i
$381$		−	9.58209e12i		−	0.0611467i
$382$	−3.60346e13	−	1.89649e14i	−0.226658	−	1.19290i
$383$	−1.04306e14			−0.646717			−0.323359	−	0.946276i	$-0.604812\pi$
$383$	−1.04306e14			−0.646717			−0.323359	+	0.946276i	$0.604812\pi$
$384$	2.39574e13	−	9.13744e13i	0.146426	−	0.558474i
$385$	−1.86014e14	+	7.49275e13i	−1.12076	+	0.451447i
$386$	−8.22009e13	+	1.56187e13i	−0.488255	+	0.0927717i
$387$		−	6.46716e13i		−	0.378707i
$388$	−4.54757e13	−	1.15348e14i	−0.262546	−	0.665943i
$389$	7.33386e13			0.417455			0.208728	−	0.977974i	$-0.433068\pi$
$389$	7.33386e13			0.417455			0.208728	+	0.977974i	$0.433068\pi$
$390$	−2.53078e14	+	4.80865e13i	−1.42036	+	0.269878i
$391$	−5.49330e13			−0.303991
$392$	−4.38551e13	+	1.77938e14i	−0.239302	+	0.970945i
$393$	1.42395e14			0.766186
$394$	6.12394e13	−	1.16359e13i	0.324939	−	0.0617406i
$395$	1.66727e14			0.872414
$396$	1.76175e13	+	4.46865e13i	0.0909119	+	0.230597i
$397$		−	3.29973e14i		−	1.67931i	−0.543120	−	0.839655i	$-0.682757\pi$
$397$		−	3.29973e14i		−	1.67931i	0.543120	−	0.839655i	$-0.317243\pi$
$398$	2.29851e14	−	4.36733e13i	1.15369	−	0.219209i
$399$	1.91479e14	−	7.71285e13i	0.947915	−	0.381825i
$400$	−2.45534e14	+	2.29232e14i	−1.19890	+	1.11929i
$401$	−3.24802e14			−1.56432			−0.782159	−	0.623079i	$-0.785882\pi$
$401$	−3.24802e14			−1.56432			−0.782159	+	0.623079i	$0.785882\pi$
$402$	−1.02255e13	−	5.38166e13i	−0.0485783	−	0.255666i
$403$		−	3.95810e14i		−	1.85485i
$404$	−8.57444e13	−	2.17489e14i	−0.396377	−	1.00540i
$405$		−	3.95892e13i		−	0.180540i
$406$	1.89218e14	−	1.21467e14i	0.851273	−	0.546469i
$407$			2.51676e14i			1.11705i
$408$	−8.61616e13	−	1.36426e14i	−0.377297	−	0.597401i
$409$		−	6.26888e13i		−	0.270839i	−0.990788	−	0.135420i	$-0.956762\pi$
$409$		−	6.26888e13i		−	0.270839i	0.990788	−	0.135420i	$-0.0432383\pi$
$410$	8.05056e13	−	1.52966e13i	0.343175	−	0.0652055i
$411$	−4.74706e13			−0.199662
$412$	−2.60135e13	+	1.02557e13i	−0.107960	+	0.0425630i
$413$	−7.67996e13	+	3.09353e13i	−0.314510	+	0.126686i
$414$	3.82467e12	+	2.01291e13i	0.0154558	+	0.0813435i
$415$		−	2.72357e14i		−	1.08611i
$416$	3.15983e14	+	2.31335e14i	1.24351	+	0.910392i
$417$	−1.89495e14			−0.735951
$418$	−6.41007e13	−	3.37360e14i	−0.245693	−	1.29308i
$419$	2.11986e14			0.801916			0.400958	−	0.916096i	$-0.368677\pi$
$419$	2.11986e14			0.801916			0.400958	+	0.916096i	$0.368677\pi$
$420$	−1.72819e14	−	1.82390e14i	−0.645238	−	0.680974i
$421$	1.99202e13			0.0734078			0.0367039	−	0.999326i	$-0.488314\pi$
$421$	1.99202e13			0.0734078			0.0367039	+	0.999326i	$0.488314\pi$
$422$	6.08663e13	+	3.20338e14i	0.221390	+	1.16517i
$423$	−1.22612e14			−0.440211
$424$	−2.75170e14	+	1.73787e14i	−0.975189	+	0.615894i
$425$			5.73780e14i			2.00727i
$426$	−2.61310e13	−	1.37527e14i	−0.0902409	−	0.474935i
$427$	−1.52036e14	−	3.77443e14i	−0.518314	−	1.28676i
$428$	−1.86310e14	−	4.72572e14i	−0.627040	−	1.59048i
$429$	−1.99134e14			−0.661652
$430$	5.52861e14	−	1.05047e14i	1.81359	−	0.344595i
$431$			3.85624e14i			1.24893i	0.781052	+	0.624467i	$0.214684\pi$
$431$			3.85624e14i			1.24893i	−0.781052	+	0.624467i	$0.785316\pi$
$432$	−4.39917e13	+	4.10708e13i	−0.140673	+	0.131333i
$433$			3.68438e14i			1.16327i	0.813450	+	0.581635i	$0.197587\pi$
$433$			3.68438e14i			1.16327i	−0.813450	+	0.581635i	$0.802413\pi$
$434$	3.24882e14	−	2.08556e14i	1.01282	−	0.650174i
$435$			3.08281e14i			0.948978i
$436$	−2.35191e14	+	9.27232e13i	−0.714899	+	0.281846i
$437$		−	1.46478e14i		−	0.439669i
$438$	2.66107e13	+	1.40051e14i	0.0788766	+	0.415126i
$439$	−2.02811e14			−0.593659			−0.296829	−	0.954931i	$-0.595929\pi$
$439$	−2.02811e14			−0.593659			−0.296829	+	0.954931i	$0.595929\pi$
$440$	−3.53397e14	+	2.23193e14i	−1.02158	+	0.645194i
$441$	8.41597e13	−	8.09311e13i	0.240266	−	0.231049i
$442$	6.57176e14	−	1.24868e14i	1.85293	−	0.352069i
$443$			1.41288e14i			0.393447i	0.980459	+	0.196723i	$0.0630301\pi$
$443$			1.41288e14i			0.393447i	−0.980459	+	0.196723i	$0.936970\pi$
$444$	−2.93359e14	+	1.15656e14i	−0.806851	+	0.318098i
$445$	−5.62740e14			−1.52872
$446$	−2.47203e13	+	4.69701e12i	−0.0663302	+	0.0126032i
$447$	2.34490e14			0.621489
$448$	−2.33864e13	+	3.81253e14i	−0.0612257	+	0.998124i
$449$	−6.47787e14			−1.67524			−0.837620	−	0.546253i	$-0.816054\pi$
$449$	−6.47787e14			−1.67524			−0.837620	+	0.546253i	$0.816054\pi$
$450$	2.10250e14	−	3.99489e13i	0.537116	−	0.102056i
$451$	6.33457e13			0.159862
$452$	−3.02899e14	+	1.19417e14i	−0.755156	+	0.297718i
$453$		−	2.38599e12i		−	0.00587663i
$454$	−3.75430e14	+	7.13341e13i	−0.913527	+	0.173576i
$455$	9.66215e14	−	3.89196e14i	2.32280	−	0.935634i
$456$	3.63779e14	−	2.29749e14i	0.864033	−	0.545692i
$457$	−7.26416e13			−0.170469			−0.0852347	−	0.996361i	$-0.527164\pi$
$457$	−7.26416e13			−0.170469			−0.0852347	+	0.996361i	$0.527164\pi$
$458$	−9.09111e12	−	4.78463e13i	−0.0210793	−	0.110940i
$459$			1.02802e14i			0.235523i
$460$	−1.65866e14	+	6.53922e13i	−0.375483	+	0.148033i
$461$		−	4.87433e14i		−	1.09034i	−0.838327	−	0.545168i	$-0.816466\pi$
$461$		−	4.87433e14i		−	1.09034i	0.838327	−	0.545168i	$-0.183534\pi$
$462$	−1.04926e14	−	1.63450e14i	−0.231927	−	0.361288i
$463$			7.72684e14i			1.68774i	0.536545	+	0.843872i	$0.319729\pi$
$463$			7.72684e14i			1.68774i	−0.536545	+	0.843872i	$0.680271\pi$
$464$	3.42563e14	−	3.19818e14i	0.739421	−	0.690326i
$465$			5.29311e14i			1.12907i
$466$	−2.52432e14	+	4.79638e13i	−0.532136	+	0.101109i
$467$	−2.57657e14			−0.536783			−0.268391	−	0.963310i	$-0.586492\pi$
$467$	−2.57657e14			−0.536783			−0.268391	+	0.963310i	$0.586492\pi$
$468$	−9.15106e13	−	2.32115e14i	−0.188417	−	0.477916i
$469$	8.27619e13	+	2.05464e14i	0.168415	+	0.418105i
$470$	−1.99161e14	−	1.04818e15i	−0.400558	−	2.10813i
$471$		−	4.19481e14i		−	0.833868i
$472$	−1.45907e14	+	9.21495e13i	−0.286678	+	0.181056i
$473$	4.35018e14			0.844832
$474$	3.01435e13	+	1.58645e14i	0.0578646	+	0.304540i
$475$	−1.52998e15			−2.90316
$476$	4.48764e14	+	4.73619e14i	0.841744	+	0.888363i
$477$	2.07352e14			0.384465
$478$	1.89527e14	+	9.97477e14i	0.347391	+	1.82831i
$479$	7.07581e14			1.28213			0.641063	−	0.767488i	$-0.278494\pi$
$479$	7.07581e14			1.28213			0.641063	+	0.767488i	$0.278494\pi$
$480$	−4.22560e14	−	3.09362e14i	−0.756941	−	0.554166i
$481$		−	1.30728e15i		−	2.31511i
$482$	2.11237e13	+	1.11173e14i	0.0369837	+	0.194644i
$483$	−3.09556e13	−	7.68500e13i	−0.0535833	−	0.133026i
$484$	2.43011e14	−	9.58064e13i	0.415888	−	0.163963i
$485$	−6.87393e14			−1.16312
$486$	3.76699e13	−	7.15754e12i	0.0630225	−	0.0119747i
$487$		−	3.86387e14i		−	0.639166i	−0.947558	−	0.319583i	$-0.896457\pi$
$487$		−	3.86387e14i		−	0.639166i	0.947558	−	0.319583i	$-0.103543\pi$
$488$	−4.52882e14	−	7.17081e14i	−0.740758	−	1.17290i
$489$		−	3.49152e14i		−	0.564698i
$490$	8.28562e14	+	5.88002e14i	1.32509	+	0.940374i
$491$			4.65028e13i			0.0735413i	0.999324	+	0.0367706i	$0.0117071\pi$
$491$			4.65028e13i			0.0735413i	−0.999324	+	0.0367706i	$0.988293\pi$
$492$	2.91101e13	+	7.38373e13i	0.0455235	+	0.115470i
$493$		−	8.00524e14i		−	1.23799i
$494$	3.32959e14	+	1.75235e15i	0.509204	+	2.67993i
$495$	2.66299e14			0.402755
$496$	5.88173e14	−	5.49120e14i	0.879743	−	0.821331i
$497$	2.11496e14	+	5.25057e14i	0.312854	+	0.776688i
$498$	2.59153e14	−	4.92408e13i	0.379136	−	0.0720384i
$499$		−	9.48398e13i		−	0.137226i	−0.997643	−	0.0686132i	$-0.978143\pi$
$499$		−	9.48398e13i		−	0.137226i	0.997643	−	0.0686132i	$-0.0218574\pi$
$500$	2.66592e14	+	6.76205e14i	0.381515	+	0.967707i
$501$	5.35627e14			0.758150
$502$	1.25081e14	−	2.37662e13i	0.175114	−	0.0332729i
$503$	5.02794e14			0.696251			0.348126	−	0.937448i	$-0.386818\pi$
$503$	5.02794e14			0.696251			0.348126	+	0.937448i	$0.386818\pi$
$504$	1.42303e14	−	1.97416e14i	0.194916	−	0.270405i
$505$	−1.29608e15			−1.75602
$506$	−1.35400e14	+	2.57269e13i	−0.181464	+	0.0344793i
$507$	5.98867e14			0.793937
$508$	2.96196e13	+	7.51297e13i	0.0388445	+	0.0985284i
$509$		−	1.44549e14i		−	0.187529i	−0.995594	−	0.0937643i	$-0.970110\pi$
$509$		−	1.44549e14i		−	0.187529i	0.995594	−	0.0937643i	$-0.0298900\pi$
$510$	−8.78832e14	+	1.66984e14i	−1.12790	+	0.214308i
$511$	−2.15378e14	−	5.34695e14i	−0.273455	−	0.678877i
$512$	9.46102e13	+	7.90490e14i	0.118837	+	0.992914i
$513$	−2.74122e14			−0.340642
$514$	1.57193e14	+	8.27303e14i	0.193257	+	1.01711i
$515$			1.55022e14i			0.188561i
$516$	1.99910e14	+	5.07067e14i	0.240580	+	0.610228i
$517$		−	8.24757e14i		−	0.982037i
$518$	1.07302e15	−	6.88819e14i	1.26414	−	0.811505i
$519$			4.58948e14i			0.534987i
$520$	1.83565e15	−	1.15933e15i	2.11725	−	1.33718i
$521$		−	1.91854e14i		−	0.218959i	−0.993989	−	0.109480i	$-0.965082\pi$
$521$		−	1.91854e14i		−	0.218959i	0.993989	−	0.109480i	$-0.0349184\pi$
$522$	−2.93336e14	+	5.57358e13i	−0.331267	+	0.0629429i
$523$	−7.31321e14			−0.817238			−0.408619	−	0.912705i	$-0.633989\pi$
$523$	−7.31321e14			−0.817238			−0.408619	+	0.912705i	$0.633989\pi$
$524$	−1.11646e15	+	4.40163e14i	−1.23459	+	0.486733i
$525$	−8.02705e14	+	3.23333e14i	−0.878374	+	0.353814i
$526$	−2.22760e14	−	1.17238e15i	−0.241222	−	1.26954i
$527$		−	1.37448e15i		−	1.47292i
$528$	−2.76265e14	−	2.95913e14i	−0.292981	−	0.313817i
$529$	8.94021e14			0.938299
$530$	3.36805e14	+	1.77260e15i	0.349834	+	1.84117i
$531$	1.09947e14			0.113022
$532$	−1.26290e15	+	1.19663e15i	−1.28486	+	1.21743i
$533$	−3.29037e14			−0.331318
$534$	−1.01741e14	−	5.35459e14i	−0.101395	−	0.533641i
$535$	−2.81619e15			−2.77789
$536$	2.46530e14	+	3.90349e14i	0.240693	+	0.381106i
$537$		−	4.22792e14i		−	0.408571i
$538$	−1.85501e14	−	9.76288e14i	−0.177437	−	0.933847i
$539$	5.44388e14	+	5.66105e14i	0.515431	+	0.535993i
$540$	1.22376e14	+	3.10405e14i	0.114691	+	0.290913i
$541$	8.12662e13			0.0753920			0.0376960	−	0.999289i	$-0.487998\pi$
$541$	8.12662e13			0.0753920			0.0376960	+	0.999289i	$0.487998\pi$
$542$	−5.44769e14	+	1.03510e14i	−0.500284	+	0.0950572i
$543$			3.22644e14i			0.293308i
$544$	1.09728e15	+	8.03329e14i	0.987465	+	0.722935i
$545$			1.40157e15i			1.24863i
$546$	5.45015e14	+	8.49009e14i	0.480672	+	0.748777i
$547$		−	3.74552e14i		−	0.327025i	−0.986541	−	0.163513i	$-0.947718\pi$
$547$		−	3.74552e14i		−	0.327025i	0.986541	−	0.163513i	$-0.0522824\pi$
$548$	3.72200e14	−	1.46739e14i	0.321724	−	0.126839i
$549$			5.40350e14i			0.462410i
$550$	2.68719e14	+	1.41426e15i	0.227669	+	1.19822i
$551$	2.13459e15			1.79053
$552$	−9.22100e13	−	1.46003e14i	−0.0765796	−	0.121254i
$553$	−2.43972e14	−	6.05682e14i	−0.200609	−	0.498031i
$554$	6.51420e14	−	1.23774e14i	0.530343	−	0.100769i
$555$			1.74821e15i			1.40923i
$556$	1.48576e15	−	5.85756e14i	1.18587	−	0.467526i
$557$	−4.00192e14			−0.316275			−0.158138	−	0.987417i	$-0.550549\pi$
$557$	−4.00192e14			−0.316275			−0.158138	+	0.987417i	$0.550549\pi$
$558$	−5.03651e14	+	9.56970e13i	−0.394132	+	0.0748877i
$559$	−2.25961e15			−1.75093
$560$	1.91881e15	+	8.95849e14i	1.47230	+	0.687386i
$561$	−6.91507e14			−0.525413
$562$	3.62237e14	−	6.88273e13i	0.272548	−	0.0517859i
$563$	2.34971e15			1.75072			0.875362	−	0.483467i	$-0.160623\pi$
$563$	2.34971e15			1.75072			0.875362	+	0.483467i	$0.160623\pi$
$564$	9.61357e14	−	3.79012e14i	0.709332	−	0.279652i
$565$			1.80506e15i			1.31894i
$566$	−1.37174e15	+	2.60640e14i	−0.992619	+	0.188604i
$567$	−1.43818e14	+	5.79307e13i	−0.103064	+	0.0415147i
$568$	6.30000e14	+	9.97524e14i	0.447120	+	0.707958i
$569$	4.93075e14			0.346574			0.173287	−	0.984871i	$-0.444561\pi$
$569$	4.93075e14			0.346574			0.173287	+	0.984871i	$0.444561\pi$
$570$	−4.45261e14	−	2.34340e15i	−0.309958	−	1.63130i
$571$		−	2.22937e15i		−	1.53704i	−0.639828	−	0.768518i	$-0.720994\pi$
$571$		−	2.22937e15i		−	1.53704i	0.639828	−	0.768518i	$-0.279006\pi$
$572$	1.56134e15	−	6.15552e14i	1.06615	−	0.420326i
$573$		−	1.03656e15i		−	0.701041i
$574$	−1.73373e14	−	2.70075e14i	−0.116136	−	0.180913i
$575$			6.14058e14i			0.407414i
$576$	2.17967e14	−	4.58006e14i	0.143241	−	0.300987i
$577$			1.05015e15i			0.683573i	0.939778	+	0.341786i	$0.111032\pi$
$577$			1.05015e15i			0.683573i	−0.939778	+	0.341786i	$0.888968\pi$
$578$	7.58384e14	−	1.44098e14i	0.488974	−	0.0929083i
$579$	−4.49282e14			−0.286937
$580$	−9.52943e14	−	2.41712e15i	−0.602855	−	1.52913i
$581$	−9.89409e14	+	3.98539e14i	−0.620022	+	0.249748i
$582$	−1.24277e14	−	6.54069e14i	−0.0771464	−	0.406020i
$583$			1.39476e15i			0.857677i
$584$	−6.41564e14	−	1.01584e15i	−0.390813	−	0.618803i
$585$	−1.38324e15			−0.834718
$586$	−1.31638e14	−	6.92806e14i	−0.0786943	−	0.414166i
$587$	−1.82532e15			−1.08101			−0.540504	−	0.841341i	$-0.681766\pi$
$587$	−1.82532e15			−1.08101			−0.540504	+	0.841341i	$0.681766\pi$
$588$	−4.09696e14	+	8.94702e14i	−0.240374	+	0.524932i
$589$	3.66504e15			2.13032
$590$	1.78589e14	+	9.39907e14i	0.102841	+	0.541251i
$591$	3.34714e14			0.190960
$592$	1.94262e15	−	1.81363e15i	1.09804	−	1.02513i
$593$			1.75834e15i			0.984694i	0.870399	+	0.492347i	$0.163861\pi$
$593$			1.75834e15i			0.984694i	−0.870399	+	0.492347i	$0.836139\pi$
$594$	4.81456e13	+	2.53389e14i	0.0267135	+	0.140593i
$595$	3.35525e15	−	1.35151e15i	1.84451	−	0.742979i
$596$	−1.83855e15	+	7.24844e14i	−1.00143	+	0.394812i
$597$	1.25629e15			0.678002
$598$	7.03308e14	−	1.33633e14i	0.376088	−	0.0714591i
$599$		−	7.19558e14i		−	0.381258i	−0.981662	−	0.190629i	$-0.938947\pi$
$599$		−	7.19558e14i		−	0.381258i	0.981662	−	0.190629i	$-0.0610527\pi$
$600$	−1.52501e15	+	9.63140e14i	−0.800646	+	0.505659i
$601$			2.07875e14i			0.108142i	0.998537	+	0.0540708i	$0.0172197\pi$
$601$			2.07875e14i			0.108142i	−0.998537	+	0.0540708i	$0.982780\pi$
$602$	−1.19061e15	−	1.85470e15i	−0.613748	−	0.956078i
$603$		−	2.94143e14i		−	0.150250i
$604$	7.37544e12	+	1.87077e13i	0.00373323	+	0.00946928i
$605$		−	1.44817e15i		−	0.726382i
$606$	−2.34325e14	−	1.23325e15i	−0.116471	−	0.612986i
$607$	−1.11978e15			−0.551561			−0.275781	−	0.961221i	$-0.588936\pi$
$607$	−1.11978e15			−0.551561			−0.275781	+	0.961221i	$0.588936\pi$
$608$	−2.14207e15	+	2.92587e15i	−1.04560	+	1.42819i
$609$	1.11991e15	−	4.51107e14i	0.541738	−	0.218215i
$610$	−4.61931e15	+	8.77701e14i	−2.21444	+	0.420758i
$611$			4.28404e15i			2.03529i
$612$	−3.17778e14	−	8.06038e14i	−0.149620	−	0.379509i
$613$	8.10256e14			0.378085			0.189043	−	0.981969i	$-0.439462\pi$
$613$	8.10256e14			0.378085			0.189043	+	0.981969i	$0.439462\pi$
$614$	9.91250e14	−	1.88344e14i	0.458413	−	0.0871016i
$615$	4.40017e14			0.201677
$616$	1.32793e15	+	9.57212e14i	0.603229	+	0.434825i
$617$	−1.12596e15			−0.506939			−0.253469	−	0.967343i	$-0.581572\pi$
$617$	−1.12596e15			−0.506939			−0.253469	+	0.967343i	$0.581572\pi$
$618$	−1.47506e14	+	2.80272e13i	−0.0658225	+	0.0125067i
$619$	−3.03467e15			−1.34219			−0.671093	−	0.741374i	$-0.734175\pi$
$619$	−3.03467e15			−1.34219			−0.671093	+	0.741374i	$0.734175\pi$
$620$	−1.63618e15	−	4.15014e15i	−0.717260	−	1.81932i
$621$			1.10019e14i			0.0478040i
$622$	4.41661e14	−	8.39186e13i	0.190214	−	0.0361419i
$623$	8.23455e14	+	2.04430e15i	0.351525	+	0.872692i
$624$	1.43500e15	+	1.53706e15i	0.607209	+	0.650393i
$625$	1.19210e14			0.0500005
$626$	8.25164e14	+	4.34282e15i	0.343069	+	1.80556i
$627$		−	1.84390e15i		−	0.759916i
$628$	1.29668e15	+	3.28900e15i	0.529729	+	1.34365i
$629$		−	4.53963e15i		−	1.83841i
$630$	−7.28842e14	−	1.13537e15i	−0.292591	−	0.455789i
$631$		−	3.36157e15i		−	1.33777i	−0.743367	−	0.668883i	$-0.766773\pi$
$631$		−	3.36157e15i		−	1.33777i	0.743367	−	0.668883i	$-0.233227\pi$
$632$	−7.26739e14	−	1.15070e15i	−0.286704	−	0.453960i
$633$			1.75086e15i			0.684747i
$634$	−9.06728e14	+	1.72284e14i	−0.351549	+	0.0667967i
$635$	4.47719e14			0.172088
$636$	−1.62577e15	+	6.40955e14i	−0.619506	+	0.244238i
$637$	−2.82772e15	−	2.94052e15i	−1.06824	−	1.11086i
$638$	−3.74910e14	−	1.97314e15i	−0.140415	−	0.739001i
$639$		−	7.51675e14i		−	0.279110i
$640$	4.26943e15	+	1.11940e15i	1.57174	+	0.412093i
$641$	3.38030e15			1.23378			0.616888	−	0.787051i	$-0.288393\pi$
$641$	3.38030e15			1.23378			0.616888	+	0.787051i	$0.288393\pi$
$642$	−5.09154e14	−	2.67966e15i	−0.184249	−	0.969700i
$643$	−2.20678e15			−0.791771			−0.395886	−	0.918300i	$-0.629562\pi$
$643$	−2.20678e15			−0.791771			−0.395886	+	0.918300i	$0.629562\pi$
$644$	4.80267e14	+	5.06866e14i	0.170848	+	0.180310i
$645$	3.02175e15			1.06581
$646$	1.15622e15	+	6.08518e15i	0.404355	+	2.12811i
$647$	1.92676e15			0.668118			0.334059	−	0.942552i	$-0.391582\pi$
$647$	1.92676e15			0.668118			0.334059	+	0.942552i	$0.391582\pi$
$648$	−2.73232e14	+	1.72563e14i	−0.0939439	+	0.0593315i
$649$			7.39564e14i			0.252133i
$650$	−1.39581e15	−	7.34610e15i	−0.471848	−	2.48333i
$651$	1.92286e15	−	7.74540e14i	0.644545	−	0.259626i
$652$	1.07928e15	+	2.73758e15i	0.358734	+	0.909924i
$653$	6.48843e14			0.213854			0.106927	−	0.994267i	$-0.465899\pi$
$653$	6.48843e14			0.213854			0.106927	+	0.994267i	$0.465899\pi$
$654$	−1.33362e15	+	2.53397e14i	−0.435868	+	0.0828177i
$655$			6.65332e15i			2.15631i
$656$	−4.56484e14	−	4.88948e14i	−0.146708	−	0.157142i
$657$			7.65473e14i			0.243961i
$658$	−3.51636e15	+	2.25730e15i	−1.11135	+	0.713423i
$659$		−	2.40470e15i		−	0.753687i	−0.926277	−	0.376844i	$-0.877009\pi$
$659$		−	2.40470e15i		−	0.753687i	0.926277	−	0.376844i	$-0.122991\pi$
$660$	−2.08796e15	+	8.23170e14i	−0.648978	+	0.255857i
$661$			9.86565e14i			0.304101i	0.988373	+	0.152050i	$0.0485876\pi$
$661$			9.86565e14i			0.304101i	−0.988373	+	0.152050i	$0.951412\pi$
$662$	−8.01158e14	−	4.21647e15i	−0.244906	−	1.28893i
$663$	3.59190e15			1.08893
$664$	−1.87972e15	+	1.18716e15i	−0.565156	+	0.356932i
$665$	3.60380e15	+	8.94675e15i	1.07459	+	2.66776i
$666$	−1.66346e15	+	3.16068e14i	−0.491930	+	0.0934700i
$667$		−	8.56719e14i		−	0.251273i
$668$	−4.19966e15	+	1.65570e15i	−1.22164	+	0.481628i
$669$	−1.35113e14			−0.0389809
$670$	2.51456e15	−	4.77783e14i	0.719532	−	0.136716i
$671$	−3.63470e15			−1.03156
$672$	−5.05508e14	+	1.98775e15i	−0.142297	+	0.559540i
$673$	−1.70255e15			−0.475354			−0.237677	−	0.971344i	$-0.576386\pi$
$673$	−1.70255e15			−0.475354			−0.237677	+	0.971344i	$0.576386\pi$
$674$	−5.80352e15	+	1.10271e15i	−1.60717	+	0.305373i
$675$	1.14916e15			0.315652
$676$	−4.69550e15	+	1.85118e15i	−1.27931	+	0.504363i
$677$			1.51204e15i			0.408625i	0.978906	+	0.204313i	$0.0654959\pi$
$677$			1.51204e15i			0.408625i	−0.978906	+	0.204313i	$0.934504\pi$
$678$	−1.71755e15	+	3.26346e14i	−0.460412	+	0.0874814i
$679$	1.00586e15	+	2.49714e15i	0.267457	+	0.663986i
$680$	6.37444e15	−	4.02586e15i	1.68129	−	1.06184i
$681$	−2.05197e15			−0.536861
$682$	−6.43712e14	−	3.38784e15i	−0.167062	−	0.879242i
$683$			4.06820e15i			1.04734i	0.851920	+	0.523671i	$0.175438\pi$
$683$			4.06820e15i			1.04734i	−0.851920	+	0.523671i	$0.824562\pi$
$684$	2.14929e15	−	8.47351e14i	0.548892	−	0.216399i
$685$		−	2.21804e15i		−	0.561916i
$686$	9.23643e14	−	3.87040e15i	0.232125	−	0.972686i
$687$		−	2.61512e14i		−	0.0651972i
$688$	−3.13484e15	−	3.35778e15i	−0.775316	−	0.830455i
$689$		−	7.24483e15i		−	1.77755i
$690$	−9.40524e14	+	1.78706e14i	−0.228929	+	0.0434980i
$691$	−3.52548e15			−0.851312			−0.425656	−	0.904885i	$-0.639957\pi$
$691$	−3.52548e15			−0.851312			−0.425656	+	0.904885i	$0.639957\pi$
$692$	−1.41868e15	−	3.59845e15i	−0.339860	−	0.862048i
$693$	−3.89675e14	−	9.67403e14i	−0.0926125	−	0.229919i
$694$	2.24030e14	+	1.17907e15i	0.0528238	+	0.278010i
$695$		−	8.85406e15i		−	2.07122i
$696$	2.12766e15	−	1.34375e15i	0.493800	−	0.311866i
$697$	−1.14260e15			−0.263097
$698$	−1.07580e15	−	5.66192e15i	−0.245770	−	1.29348i
$699$	−1.37971e15			−0.312726
$700$	5.29425e15	−	5.01642e15i	1.19060	−	1.12812i
$701$	4.13613e14			0.0922880			0.0461440	−	0.998935i	$-0.485307\pi$
$701$	4.13613e14			0.0922880			0.0461440	+	0.998935i	$0.485307\pi$
$702$	−2.50083e14	−	1.31618e15i	−0.0553643	−	0.291381i
$703$	1.21049e16			2.65893
$704$	3.08081e15	+	1.46617e15i	0.671452	+	0.319547i
$705$		−	5.72899e15i		−	1.23890i
$706$	−2.73718e14	−	1.44057e15i	−0.0587325	−	0.309107i
$707$	1.89655e15	+	4.70835e15i	0.403791	+	1.00245i
$708$	−8.62054e14	+	3.39862e14i	−0.182117	+	0.0717992i
$709$	6.00979e15			1.25981			0.629904	−	0.776673i	$-0.283094\pi$
$709$	6.00979e15			1.25981			0.629904	+	0.776673i	$0.283094\pi$
$710$	6.42588e15	−	1.22096e15i	1.33663	−	0.253969i
$711$			8.67098e14i			0.178972i
$712$	2.45289e15	+	3.88385e15i	0.502388	+	0.795467i
$713$		−	1.47096e15i		−	0.298958i
$714$	1.89261e15	+	2.94825e15i	0.381698	+	0.594598i
$715$		−	9.30444e15i		−	1.86212i
$716$	1.30691e15	+	3.31496e15i	0.259552	+	0.658350i
$717$			5.45187e15i			1.07446i
$718$	−1.22367e15	−	6.44017e15i	−0.239321	−	1.25954i
$719$	−9.74670e15			−1.89168			−0.945842	−	0.324626i	$-0.894762\pi$
$719$	−9.74670e15			−1.89168			−0.945842	+	0.324626i	$0.894762\pi$
$720$	−1.91901e15	−	2.05549e15i	−0.369615	−	0.395901i
$721$	5.63158e14	−	2.26843e14i	0.107643	−	0.0433592i
$722$	−1.10470e16	+	2.09900e15i	−2.09551	+	0.398160i
$723$			6.07635e14i			0.114388i
$724$	−9.97340e14	−	2.52974e15i	−0.186329	−	0.472621i
$725$	−8.94849e15			−1.65917
$726$	1.37797e15	−	2.61823e14i	0.253564	−	0.0481788i
$727$	−5.84706e15			−1.06782			−0.533910	−	0.845541i	$-0.679278\pi$
$727$	−5.84706e15			−1.06782			−0.533910	+	0.845541i	$0.679278\pi$
$728$	−6.89768e15	−	4.97205e15i	−1.25020	−	0.901183i
$729$	2.05891e14			0.0370370
$730$	−6.54383e15	+	1.24337e15i	−1.16831	+	0.221986i
$731$	−7.84668e15			−1.39040
$732$	−1.67030e15	−	4.23669e15i	−0.293754	−	0.745102i
$733$			4.63977e15i			0.809887i	0.914342	+	0.404944i	$0.132709\pi$
$733$			4.63977e15i			0.809887i	−0.914342	+	0.404944i	$0.867291\pi$
$734$	−7.99843e15	+	1.51976e15i	−1.38572	+	0.263297i
$735$	3.78147e15	+	3.93232e15i	0.650250	+	0.676190i
$736$	1.17430e15	+	8.59721e14i	0.200425	+	0.146734i
$737$	1.97857e15			0.335182
$738$	7.95529e13	+	4.18685e14i	0.0133766	+	0.0704008i
$739$		−	5.23278e14i		−	0.0873349i	−0.999046	−	0.0436674i	$-0.986096\pi$
$739$		−	5.23278e14i		−	0.0873349i	0.999046	−	0.0436674i	$-0.0139042\pi$
$740$	−5.40397e15	−	1.37071e16i	−0.895238	−	2.27076i
$741$			9.57776e15i			1.57494i
$742$	5.94659e15	−	3.81737e15i	0.970614	−	0.623079i
$743$			2.61177e15i			0.423152i	0.977362	+	0.211576i	$0.0678596\pi$
$743$			2.61177e15i			0.423152i	−0.977362	+	0.211576i	$0.932140\pi$
$744$	3.65313e15	−	2.30719e15i	0.587509	−	0.371049i
$745$			1.09564e16i			1.74908i
$746$	−2.70853e15	+	5.14639e14i	−0.429210	+	0.0815528i
$747$	1.41644e15			0.222811
$748$	5.42186e15	−	2.13755e15i	0.846622	−	0.333778i
$749$	4.12092e15	+	1.02306e16i	0.638769	+	1.58580i
$750$	7.28550e14	+	3.83434e15i	0.112104	+	0.590002i
$751$		−	5.78081e15i		−	0.883017i	−0.897257	−	0.441508i	$-0.854444\pi$
$751$		−	5.78081e15i		−	0.883017i	0.897257	−	0.441508i	$-0.145556\pi$
$752$	−6.36608e15	+	5.94339e15i	−0.965325	+	0.901231i
$753$	6.83651e14			0.102911
$754$	1.94740e15	+	1.02491e16i	0.291013	+	1.53159i
$755$	1.11484e14			0.0165388
$756$	9.48556e14	−	8.98778e14i	0.139699	−	0.132368i
$757$	−8.50901e15			−1.24409			−0.622045	−	0.782981i	$-0.713698\pi$
$757$	−8.50901e15			−1.24409			−0.622045	+	0.782981i	$0.713698\pi$
$758$	7.45323e13	+	3.92262e14i	0.0108184	+	0.0569371i
$759$	−7.40049e14			−0.106643
$760$	1.07349e16	+	1.69974e16i	1.53576	+	2.43169i
$761$		−	5.02682e15i		−	0.713967i	−0.934111	−	0.356983i	$-0.883805\pi$
$761$		−	5.02682e15i		−	0.713967i	0.934111	−	0.356983i	$-0.116195\pi$
$762$	8.09455e13	+	4.26014e14i	0.0114141	+	0.0600719i
$763$	5.09157e15	−	2.05091e15i	0.712798	−	0.287119i
$764$	3.20415e15	+	8.12728e15i	0.445348	+	1.12962i
$765$	−4.80340e15			−0.662843
$766$	4.63737e15	−	8.81130e14i	0.635350	−	0.120721i
$767$		−	3.84152e15i		−	0.522551i
$768$	−2.93239e14	+	4.26483e15i	−0.0396036	+	0.575990i
$769$		−	6.27782e15i		−	0.841810i	−0.907105	−	0.420905i	$-0.861713\pi$
$769$		−	6.27782e15i		−	0.841810i	0.907105	−	0.420905i	$-0.138287\pi$
$770$	7.63713e15	−	4.90260e15i	1.01679	−	0.652721i
$771$			4.52176e15i			0.597734i
$772$	3.52266e15	−	1.38880e15i	0.462355	−	0.182282i
$773$		−	1.36823e16i		−	1.78308i	−0.452938	−	0.891542i	$-0.649624\pi$
$773$		−	1.36823e16i		−	1.78308i	0.452938	−	0.891542i	$-0.350376\pi$
$774$	5.46319e14	+	2.87526e15i	0.0706921	+	0.372051i
$775$	−1.53643e16			−1.97403
$776$	2.99624e15	+	4.74416e15i	0.382241	+	0.605229i
$777$	6.35084e15	−	2.55815e15i	0.804480	−	0.324049i
$778$	−3.26059e15	+	6.19534e14i	−0.410118	+	0.0779251i
$779$		−	3.04675e15i		−	0.380522i
$780$	1.08455e16	−	4.27579e15i	1.34502	−	0.530269i
$781$	5.05619e15			0.622648
$782$	2.44229e15	−	4.64051e14i	0.298648	−	0.0567452i
$783$	−1.60328e15			−0.194679
$784$	4.46626e14	−	8.28147e15i	0.0538525	−	0.998549i
$785$	1.96001e16			2.34679
$786$	−6.33078e15	+	1.20289e15i	−0.752719	+	0.143022i
$787$	−2.48331e15			−0.293204			−0.146602	−	0.989196i	$-0.546834\pi$
$787$	−2.48331e15			−0.293204			−0.146602	+	0.989196i	$0.546834\pi$
$788$	−2.62437e15	+	1.03465e15i	−0.307703	+	0.121311i
$789$		−	6.40784e15i		−	0.746085i
$790$	−7.41260e15	+	1.40844e15i	−0.857080	+	0.162851i
$791$	6.55736e15	−	2.64134e15i	0.752937	−	0.303287i
$792$	−1.16076e15	−	1.83791e15i	−0.132359	−	0.209573i
$793$	1.88797e16			2.13793
$794$	2.78748e15	+	1.46704e16i	0.313472	+	1.64979i
$795$			9.68842e15i			1.08202i
$796$	−9.85012e15	+	3.88338e15i	−1.09250	+	0.430713i
$797$			2.19572e15i			0.241856i	0.992661	+	0.120928i	$0.0385870\pi$
$797$			2.19572e15i			0.241856i	−0.992661	+	0.120928i	$0.961413\pi$
$798$	−7.86147e15	+	5.04662e15i	−0.859979	+	0.552058i
$799$			1.48766e16i			1.61621i
$800$	8.97985e15	−	1.22657e16i	0.968889	−	1.32342i
$801$		−	2.92664e15i		−	0.313610i
$802$	1.44405e16	−	2.74379e15i	1.53682	−	0.292007i
$803$	−5.14900e15			−0.544236
$804$	9.09241e14	+	2.30627e15i	0.0954488	+	0.242104i
$805$	3.59078e15	−	1.44639e15i	0.374379	−	0.150802i
$806$	3.34363e15	+	1.75975e16i	0.346239	+	1.82225i
$807$		−	5.33606e15i		−	0.548803i
$808$	5.64940e15	+	8.94511e15i	0.577085	+	0.913741i
$809$	−9.26155e14			−0.0939651			−0.0469826	−	0.998896i	$-0.514961\pi$
$809$	−9.26155e14			−0.0939651			−0.0469826	+	0.998896i	$0.514961\pi$
$810$	3.34433e14	+	1.76011e15i	0.0337009	+	0.177367i
$811$	1.21567e16			1.21675			0.608374	−	0.793650i	$-0.291822\pi$
$811$	1.21567e16			1.21675			0.608374	+	0.793650i	$0.291822\pi$
$812$	−7.38641e15	+	6.99879e15i	−0.734303	+	0.695769i
$813$	−2.97752e15			−0.294007
$814$	−2.12605e15	−	1.11894e16i	−0.208516	−	1.09741i
$815$	1.63140e16			1.58925
$816$	4.98316e15	+	5.33756e15i	0.482180	+	0.516472i
$817$		−	2.09231e16i		−	2.01097i
$818$	5.29569e14	+	2.78711e15i	0.0505568	+	0.266079i
$819$	2.02409e15	+	5.02498e15i	0.191941	+	0.476511i
$820$	−3.45001e15	+	1.36016e15i	−0.324971	+	0.128119i
$821$	−3.11132e15			−0.291110			−0.145555	−	0.989350i	$-0.546497\pi$
$821$	−3.11132e15			−0.291110			−0.145555	+	0.989350i	$0.546497\pi$
$822$	2.11051e15	−	4.01012e14i	0.196152	−	0.0372702i
$823$			9.24562e15i			0.853566i	0.904354	+	0.426783i	$0.140353\pi$
$823$			9.24562e15i			0.853566i	−0.904354	+	0.426783i	$0.859647\pi$
$824$	1.06991e15	−	6.75716e14i	0.0981177	−	0.0619676i
$825$			7.72987e15i			0.704167i
$826$	3.15314e15	−	2.02414e15i	0.285333	−	0.183168i
$827$		−	7.29656e15i		−	0.655900i	−0.944695	−	0.327950i	$-0.893642\pi$
$827$		−	7.29656e15i		−	0.655900i	0.944695	−	0.327950i	$-0.106358\pi$
$828$	−3.40085e14	−	8.62620e14i	−0.0303683	−	0.0770287i
$829$			2.21143e16i			1.96166i	0.194874	+	0.980828i	$0.437570\pi$
$829$			2.21143e16i			1.96166i	−0.194874	+	0.980828i	$0.562430\pi$
$830$	2.30076e15	+	1.21088e16i	0.202741	+	1.06702i
$831$	3.56044e15			0.311672
$832$	−1.60026e16	−	7.61573e15i	−1.39160	−	0.662267i
$833$	−9.81946e15	−	1.02112e16i	−0.848282	−	0.882122i
$834$	8.42482e15	−	1.60077e15i	0.723015	−	0.137378i
$835$			2.50270e16i			2.13370i
$836$	5.69976e15	+	1.44573e16i	0.482750	+	1.22449i
$837$	−2.75278e15			−0.231623
$838$	−9.42475e15	+	1.79076e15i	−0.787821	+	0.149691i
$839$	7.11365e15			0.590748			0.295374	−	0.955382i	$-0.404556\pi$
$839$	7.11365e15			0.590748			0.295374	+	0.955382i	$0.404556\pi$
$840$	9.22418e15	+	6.64906e15i	0.761013	+	0.548560i
$841$	2.84208e14			0.0232948
$842$	−8.85640e14	+	1.68278e14i	−0.0721175	+	0.0137028i
$843$	1.97986e15			0.160171
$844$	−5.41216e15	−	1.37279e16i	−0.434998	−	1.10336i
$845$			2.79818e16i			2.23441i
$846$	5.45125e15	−	1.03577e15i	0.432473	−	0.0821728i
$847$	−5.26087e15	+	2.11910e15i	−0.414666	+	0.167030i
$848$	1.07658e16	−	1.00510e16i	0.843081	−	0.787104i
$849$	−7.49749e15			−0.583342
$850$	−4.84705e15	−	2.55099e16i	−0.374691	−	1.97199i
$851$		−	4.85830e15i		−	0.373140i
$852$	2.32354e15	+	5.89362e15i	0.177309	+	0.449743i
$853$		−	7.34056e15i		−	0.556557i	−0.960500	−	0.278278i	$-0.910236\pi$
$853$		−	7.34056e15i		−	0.556557i	0.960500	−	0.278278i	$-0.0897638\pi$
$854$	9.94791e15	+	1.54966e16i	0.749400	+	1.16739i
$855$		−	1.28082e16i		−	0.958683i
$856$	1.22753e16	+	1.94364e16i	0.912908	+	1.44547i
$857$		−	3.44987e14i		−	0.0254922i	−0.999919	−	0.0127461i	$-0.995943\pi$
$857$		−	3.44987e14i		−	0.0254922i	0.999919	−	0.0127461i	$-0.00405732\pi$
$858$	8.85337e15	−	1.68220e15i	0.650023	−	0.123509i
$859$	3.09685e14			0.0225922			0.0112961	−	0.999936i	$-0.496404\pi$
$859$	3.09685e14			0.0225922			0.0112961	+	0.999936i	$0.496404\pi$
$860$	−2.36925e16	+	9.34068e15i	−1.71739	+	0.677076i
$861$	−6.43875e14	−	1.59848e15i	−0.0463750	−	0.115130i
$862$	−3.25759e15	−	1.71446e16i	−0.233135	−	1.22698i
$863$		−	1.23748e15i		−	0.0879994i	−0.999032	−	0.0439997i	$-0.985990\pi$
$863$		−	1.23748e15i		−	0.0879994i	0.999032	−	0.0439997i	$-0.0140101\pi$
$864$	1.60889e15	−	2.19761e15i	0.113685	−	0.155283i
$865$	−2.14441e16			−1.50564
$866$	−3.11241e15	−	1.63805e16i	−0.217144	−	1.14282i
$867$	4.14507e15			0.287360
$868$	−1.26823e16	+	1.20167e16i	−0.873653	+	0.827806i
$869$	−5.83258e15			−0.399257
$870$	−2.60423e15	−	1.37060e16i	−0.177143	−	0.932298i
$871$	−1.02773e16			−0.694672
$872$	9.67316e15	−	6.10921e15i	0.649722	−	0.410341i
$873$		−	3.57492e15i		−	0.238610i
$874$	1.23739e15	+	6.51234e15i	0.0820717	+	0.431941i
$875$	−5.89664e15	−	1.46389e16i	−0.388651	−	0.964862i
$876$	−2.36619e15	−	6.00180e15i	−0.154980	−	0.393105i
$877$	−2.61090e16			−1.69939			−0.849693	−	0.527277i	$-0.823213\pi$
$877$	−2.61090e16			−1.69939			−0.849693	+	0.527277i	$0.823213\pi$
$878$	9.01686e15	−	1.71326e15i	0.583224	−	0.110816i
$879$		−	3.78664e15i		−	0.243397i
$880$	1.38264e16	−	1.29084e16i	0.883190	−	0.824549i
$881$			5.61919e14i			0.0356702i	0.999841	+	0.0178351i	$0.00567740\pi$
$881$			5.61919e14i			0.0356702i	−0.999841	+	0.0178351i	$0.994323\pi$
$882$	−3.05802e15	+	4.30910e15i	−0.192914	+	0.271837i
$883$		−	2.72601e16i		−	1.70901i	−0.519444	−	0.854504i	$-0.673861\pi$
$883$		−	2.72601e16i		−	1.70901i	0.519444	−	0.854504i	$-0.326139\pi$
$884$	−2.81628e16	+	1.11031e16i	−1.75464	+	0.691761i
$885$			5.13722e15i			0.318083i
$886$	−1.19355e15	−	6.28160e15i	−0.0734435	−	0.386531i
$887$	−2.74818e16			−1.68060			−0.840300	−	0.542121i	$-0.817621\pi$
$887$	−2.74818e16			−1.68060			−0.840300	+	0.542121i	$0.817621\pi$
$888$	1.20656e16	−	7.62017e15i	0.733291	−	0.463120i
$889$	−6.55145e14	−	1.62646e15i	−0.0395711	−	0.0982388i
$890$	2.50191e16	−	4.75379e15i	1.50185	−	0.285361i
$891$			1.38494e15i			0.0826235i
$892$	1.05937e15	−	4.17653e14i	0.0628117	−	0.0247633i
$893$	−3.96684e16			−2.33756
$894$	−1.04253e16	+	1.98088e15i	−0.610565	+	0.116011i
$895$	1.97547e16			1.14986
$896$	−2.18092e15	−	1.71478e16i	−0.126167	−	0.992009i
$897$	3.84404e15			0.221019
$898$	2.88002e16	−	5.47223e15i	1.64579	−	0.312712i
$899$	2.14360e16			1.21749
$900$	−9.01013e15	+	3.55221e15i	−0.508624	+	0.200523i
$901$		−	2.51582e16i		−	1.41154i
$902$	−2.81631e15	+	5.35118e14i	−0.157052	+	0.0298410i
$903$	−4.42172e15	−	1.09773e16i	−0.245081	−	0.608435i
$904$	1.24579e16	−	7.86797e15i	0.686309	−	0.433448i
$905$	−1.50754e16			−0.825471
$906$	2.01558e13	+	1.06080e14i	0.00109697	+	0.00577334i
$907$		−	2.24691e16i		−	1.21547i	−0.794138	−	0.607737i	$-0.792078\pi$
$907$		−	2.24691e16i		−	1.21547i	0.794138	−	0.607737i	$-0.207922\pi$
$908$	1.60888e16	−	6.34295e15i	0.865069	−	0.341051i
$909$		−	6.74050e15i		−	0.360239i
$910$	−3.96696e16	+	2.54656e16i	−2.10732	+	1.35278i
$911$			2.40418e16i			1.26945i	0.772737	+	0.634726i	$0.218887\pi$
$911$			2.40418e16i			1.26945i	−0.772737	+	0.634726i	$0.781113\pi$
$912$	−1.42325e16	+	1.32876e16i	−0.746984	+	0.697387i
$913$			9.52779e15i			0.497053i
$914$	3.22960e15	−	6.13646e14i	0.167473	−	0.0318210i
$915$	−2.52476e16			−1.30138
$916$	8.08371e14	+	2.05042e15i	0.0414177	+	0.105055i
$917$	2.41700e16	−	9.73579e15i	1.23096	−	0.495838i
$918$	−8.68432e14	−	4.57054e15i	−0.0439644	−	0.231384i
$919$			7.71506e15i			0.388243i	0.980977	+	0.194122i	$0.0621856\pi$
$919$			7.71506e15i			0.388243i	−0.980977	+	0.194122i	$0.937814\pi$
$920$	6.82191e15	−	4.30847e15i	0.341250	−	0.215521i
$921$	5.41784e15			0.269400
$922$	4.11763e15	+	2.16710e16i	0.203530	+	1.07117i
$923$	−2.62634e16			−1.29045
$924$	6.04569e15	+	6.38052e15i	0.295291	+	0.311645i
$925$	−5.07453e16			−2.46386
$926$	−6.52731e15	−	3.43531e16i	−0.315046	−	1.65808i
$927$	−8.06220e14			−0.0386826
$928$	−1.25285e16	+	1.71128e16i	−0.597564	+	0.816218i
$929$		−	4.22250e15i		−	0.200209i	−0.994977	−	0.100104i	$-0.968082\pi$
$929$		−	4.22250e15i		−	0.200209i	0.994977	−	0.100104i	$-0.0319177\pi$
$930$	−4.47140e15	−	2.35329e16i	−0.210760	−	1.10922i
$931$	2.72280e16	−	2.61835e16i	1.27583	−	1.22689i
$932$	1.08178e16	−	4.26489e15i	0.503909	−	0.198664i
$933$	2.41397e15			0.111785
$934$	1.14553e16	−	2.17658e15i	0.527348	−	0.100200i
$935$		−	3.23104e16i		−	1.47869i
$936$	6.02932e15	+	9.54666e15i	0.274316	+	0.434344i
$937$			3.43341e15i			0.155295i	0.996981	+	0.0776477i	$0.0247409\pi$
$937$			3.43341e15i			0.155295i	−0.996981	+	0.0776477i	$0.975259\pi$
$938$	−5.41522e15	−	8.43567e15i	−0.243501	−	0.379318i
$939$			2.37364e16i			1.06109i
$940$	1.77091e16	+	4.49190e16i	0.787036	+	1.99630i
$941$		−	3.27207e16i		−	1.44570i	−0.691002	−	0.722852i	$-0.742831\pi$
$941$		−	3.27207e16i		−	1.44570i	0.691002	−	0.722852i	$-0.257169\pi$
$942$	3.54360e15	+	1.86499e16i	0.155656	+	0.819211i
$943$	−1.22281e15			−0.0534006
$944$	5.70850e15	−	5.32947e15i	0.247842	−	0.231387i
$945$	−2.70679e15	−	6.71985e15i	−0.116837	−	0.290058i
$946$	−1.93406e16	+	3.67485e15i	−0.829983	+	0.157702i
$947$			3.85597e16i			1.64516i	0.568647	+	0.822582i	$0.307467\pi$
$947$			3.85597e16i			1.64516i	−0.568647	+	0.822582i	$0.692533\pi$
$948$	−2.68033e15	−	6.79860e15i	−0.113695	−	0.288386i
$949$	2.67455e16			1.12794
$950$	6.80219e16	−	1.29246e16i	2.85213	−	0.541923i
$951$	−4.95587e15			−0.206598
$952$	−2.39527e16	−	1.72658e16i	−0.992777	−	0.715623i
$953$	−3.00224e16			−1.23718			−0.618592	−	0.785712i	$-0.712297\pi$
$953$	−3.00224e16			−1.23718			−0.618592	+	0.785712i	$0.712297\pi$
$954$	−9.21873e15	+	1.75162e15i	−0.377707	+	0.0717669i
$955$	4.84327e16			1.97297
$956$	−1.68525e16	−	4.27462e16i	−0.682569	−	1.73133i
$957$		−	1.07845e16i		−	0.434296i
$958$	−3.14586e16	+	5.97735e15i	−1.25959	+	0.239331i
$959$	−8.05763e15	+	3.24565e15i	−0.320778	+	0.129211i
$960$	2.14001e16	+	1.01844e16i	0.847080	+	0.403129i
$961$	1.13965e16			0.448532
$962$	1.10434e16	+	5.81209e16i	0.432154	+	2.27441i
$963$		−	1.46461e16i		−	0.569873i
$964$	−1.87829e15	−	4.76425e15i	−0.0726673	−	0.184319i
$965$		−	2.09925e16i		−	0.807540i
$966$	2.02546e15	+	3.15521e15i	0.0774730	+	0.120685i
$967$			3.12152e16i			1.18719i	0.804763	+	0.593596i	$0.202292\pi$
$967$			3.12152e16i			1.18719i	−0.804763	+	0.593596i	$0.797708\pi$
$968$	−9.99480e15	+	6.31235e15i	−0.377972	+	0.238713i
$969$			3.32595e16i			1.25065i
$970$	3.05611e16	−	5.80681e15i	1.14268	−	0.217117i
$971$	−4.31918e15			−0.160582			−0.0802908	−	0.996771i	$-0.525585\pi$
$971$	−4.31918e15			−0.160582			−0.0802908	+	0.996771i	$0.525585\pi$
$972$	−1.61432e15	+	6.36440e14i	−0.0596795	+	0.0235284i
$973$	−3.21647e16	+	1.29561e16i	−1.18239	+	0.476271i
$974$	3.26404e15	+	1.71785e16i	0.119311	+	0.627931i
$975$		−	4.01513e16i		−	1.45940i
$976$	2.61925e16	+	2.80552e16i	0.946679	+	1.01401i
$977$	4.13041e16			1.48448			0.742238	−	0.670137i	$-0.233765\pi$
$977$	4.13041e16			1.48448			0.742238	+	0.670137i	$0.233765\pi$
$978$	2.94949e15	+	1.55231e16i	0.105410	+	0.554773i
$979$	1.96862e16			0.699611
$980$	−4.18046e16	−	1.91429e16i	−1.47734	−	0.676494i
$981$	−7.28912e15			−0.256151
$982$	−3.92836e14	−	2.06749e15i	−0.0137277	−	0.0722486i
$983$	−4.46902e16			−1.55299			−0.776495	−	0.630124i	$-0.783004\pi$
$983$	−4.46902e16			−1.55299			−0.776495	+	0.630124i	$0.783004\pi$
$984$	−1.91796e15	−	3.03685e15i	−0.0662777	−	0.104942i
$985$			1.56394e16i			0.537427i
$986$	6.76249e15	+	3.55908e16i	0.231091	+	1.21623i
$987$	−2.08121e16	+	8.38321e15i	−0.707247	+	0.284883i
$988$	−2.96063e16	−	7.50959e16i	−1.00051	−	2.53777i
$989$	−8.39750e15			−0.282209
$990$	−1.18395e16	+	2.24958e15i	−0.395676	+	0.0751811i
$991$		−	3.62012e16i		−	1.20314i	−0.798818	−	0.601572i	$-0.794541\pi$
$991$		−	3.62012e16i		−	1.20314i	0.798818	−	0.601572i	$-0.205459\pi$
$992$	−2.15111e16	+	2.93822e16i	−0.710964	+	0.971114i
$993$		−	2.30458e16i		−	0.757480i
$994$	−1.38384e16	−	2.15571e16i	−0.452337	−	0.704637i
$995$			5.86996e16i			1.90813i
$996$	−1.11058e16	+	4.37843e15i	−0.359025	+	0.141544i
$997$		−	3.93970e16i		−	1.26660i	−0.773906	−	0.633300i	$-0.781700\pi$
$997$		−	3.93970e16i		−	1.26660i	0.773906	−	0.633300i	$-0.218300\pi$
$998$	8.01167e14	+	4.21652e15i	0.0256156	+	0.134814i
$999$	−9.09190e15			−0.289097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.4	yes	44
4.3	odd	2		84.12.b.b.55.3	yes	44
7.6	odd	2		84.12.b.b.55.4	yes	44
28.27	even	2	inner	84.12.b.a.55.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.3	✓	44	28.27	even	2	inner
84.12.b.a.55.4	yes	44	1.1	even	1	trivial
84.12.b.b.55.3	yes	44	4.3	odd	2
84.12.b.b.55.4	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)

\(f(q)\)	\(=\)	\(q+(-44.4594 + 8.44758i) q^{2} -243.000 q^{3} +(1905.28 - 751.149i) q^{4} -11354.1i q^{5} +(10803.6 - 2052.76i) q^{6} +(-41246.7 + 16614.4i) q^{7} +(-78362.1 + 49490.6i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-44.4594 + 8.44758i) q^{2} -243.000 q^{3} +(1905.28 - 751.149i) q^{4} -11354.1i q^{5} +(10803.6 - 2052.76i) q^{6} +(-41246.7 + 16614.4i) q^{7} +(-78362.1 + 49490.6i) q^{8} +59049.0 q^{9} +(95914.4 + 504795. i) q^{10} +397197. i q^{11} +(-462982. + 182529. i) q^{12} -2.06316e6i q^{13} +(1.69345e6 - 1.08710e6i) q^{14} +2.75904e6i q^{15} +(3.06585e6 - 2.86229e6i) q^{16} -7.16448e6i q^{17} +(-2.62528e6 + 498821. i) q^{18} +1.91040e7 q^{19} +(-8.52859e6 - 2.16326e7i) q^{20} +(1.00229e7 - 4.03729e6i) q^{21} +(-3.35535e6 - 1.76591e7i) q^{22} -7.66741e6i q^{23} +(1.90420e7 - 1.20262e7i) q^{24} -8.00867e7 q^{25} +(1.74287e7 + 9.17269e7i) q^{26} -1.43489e7 q^{27} +(-6.61065e7 + 6.26374e7i) q^{28} +1.11735e8 q^{29} +(-2.33072e7 - 1.22665e8i) q^{30} +1.91846e8 q^{31} +(-1.12127e8 + 1.53155e8i) q^{32} -9.65188e7i q^{33} +(6.05225e7 + 3.18529e8i) q^{34} +(1.88641e8 + 4.68318e8i) q^{35} +(1.12505e8 - 4.43546e7i) q^{36} +6.33630e8 q^{37} +(-8.49353e8 + 1.61383e8i) q^{38} +5.01348e8i q^{39} +(5.61920e8 + 8.89728e8i) q^{40} -1.59482e8i q^{41} +(-4.11509e8 + 2.64165e8i) q^{42} -1.09522e9i q^{43} +(2.98354e8 + 7.56770e8i) q^{44} -6.70446e8i q^{45} +(6.47711e7 + 3.40889e8i) q^{46} -2.07644e9 q^{47} +(-7.45003e8 + 6.95537e8i) q^{48} +(1.42525e9 - 1.37058e9i) q^{49} +(3.56061e9 - 6.76539e8i) q^{50} +1.74097e9i q^{51} +(-1.54974e9 - 3.93089e9i) q^{52} +3.51152e9 q^{53} +(6.37944e8 - 1.21214e8i) q^{54} +4.50980e9 q^{55} +(2.40992e9 - 3.34326e9i) q^{56} -4.64228e9 q^{57} +(-4.96767e9 + 9.43891e8i) q^{58} +1.86196e9 q^{59} +(2.07245e9 + 5.25673e9i) q^{60} +9.15087e9i q^{61} +(-8.52937e9 + 1.62064e9i) q^{62} +(-2.43558e9 + 9.81062e8i) q^{63} +(3.69129e9 - 7.75637e9i) q^{64} -2.34253e10 q^{65} +(8.15350e8 + 4.29117e9i) q^{66} -4.98135e9i q^{67} +(-5.38159e9 - 1.36503e10i) q^{68} +1.86318e9i q^{69} +(-1.23430e10 - 1.92276e10i) q^{70} -1.27297e10i q^{71} +(-4.62720e9 + 2.92237e9i) q^{72} +1.29634e10i q^{73} +(-2.81708e10 + 5.35264e9i) q^{74} +1.94611e10 q^{75} +(3.63985e10 - 1.43500e10i) q^{76} +(-6.59917e9 - 1.63830e10i) q^{77} +(-4.23518e9 - 2.22896e10i) q^{78} +1.46844e10i q^{79} +(-3.24987e10 - 3.48099e10i) q^{80} +3.48678e9 q^{81} +(1.34724e9 + 7.09047e9i) q^{82} +2.39876e10 q^{83} +(1.60639e10 - 1.52209e10i) q^{84} -8.13460e10 q^{85} +(9.25196e9 + 4.86928e10i) q^{86} -2.71516e10 q^{87} +(-1.96575e10 - 3.11252e10i) q^{88} -4.95628e10i q^{89} +(5.66365e9 + 2.98076e10i) q^{90} +(3.42781e10 + 8.50985e10i) q^{91} +(-5.75937e9 - 1.46085e10i) q^{92} -4.66186e10 q^{93} +(9.23175e10 - 1.75409e10i) q^{94} -2.16908e11i q^{95} +(2.72468e10 - 3.72166e10i) q^{96} -6.05416e10i q^{97} +(-5.17878e10 + 7.29749e10i) q^{98} +2.34541e10i 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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