LMFDB - Embedded newform 13.9.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,9,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 2 x^{16} + 3828 x^{15} + 1204401 x^{14} + 47082 x^{13} + 4823826 x^{12} + \cdots + 18\!\cdots\!48 $ x^18 - 2x^17 + 2x^16 + 3828x^15 + 1204401x^14 + 47082x^13 + 4823826x^12 + 3014328096x^11 + 324100560576x^10 + 1243720573056x^9 + 2594493183360x^8 + 67426704543744x^7 + 16374511738433536x^6 + 38893585626849280x^5 + 61002122197950464x^4 + 4754717719118610432x^3 + 119869629126769115136x^2 + 658222091640736579584*x + 1807198057923881730048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{2}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.1
Root			$21.6276 - 21.6276i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.9.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.6276 - 21.6276i) q^{2} -83.2917 q^{3} +679.508i q^{4} +(-706.219 - 706.219i) q^{5} +(1801.40 + 1801.40i) q^{6} +(966.123 - 966.123i) q^{7} +(9159.48 - 9159.48i) q^{8} +376.504 q^{9} +O(q^{10})$	\(q+(-21.6276 - 21.6276i) q^{2} -83.2917 q^{3} +679.508i q^{4} +(-706.219 - 706.219i) q^{5} +(1801.40 + 1801.40i) q^{6} +(966.123 - 966.123i) q^{7} +(9159.48 - 9159.48i) q^{8} +376.504 q^{9} +30547.7i q^{10} +(-431.183 + 431.183i) q^{11} -56597.4i q^{12} +(13650.7 + 25087.6i) q^{13} -41789.9 q^{14} +(58822.2 + 58822.2i) q^{15} -222241. q^{16} +5328.69i q^{17} +(-8142.89 - 8142.89i) q^{18} +(-7342.35 - 7342.35i) q^{19} +(479882. - 479882. i) q^{20} +(-80470.0 + 80470.0i) q^{21} +18650.9 q^{22} +87712.3i q^{23} +(-762908. + 762908. i) q^{24} +606866. i q^{25} +(247354. - 837818. i) q^{26} +515117. q^{27} +(656489. + 656489. i) q^{28} -787498. q^{29} -2.54437e6i q^{30} +(-398923. - 398923. i) q^{31} +(2.46173e6 + 2.46173e6i) q^{32} +(35913.9 - 35913.9i) q^{33} +(115247. - 115247. i) q^{34} -1.36459e6 q^{35} +255838. i q^{36} +(1.04786e6 - 1.04786e6i) q^{37} +317595. i q^{38} +(-1.13699e6 - 2.08959e6i) q^{39} -1.29372e7 q^{40} +(2.42006e6 + 2.42006e6i) q^{41} +3.48075e6 q^{42} +1.12816e6i q^{43} +(-292992. - 292992. i) q^{44} +(-265894. - 265894. i) q^{45} +(1.89701e6 - 1.89701e6i) q^{46} +(-5.15032e6 + 5.15032e6i) q^{47} +1.85109e7 q^{48} +3.89801e6i q^{49} +(1.31251e7 - 1.31251e7i) q^{50} -443836. i q^{51} +(-1.70473e7 + 9.27576e6i) q^{52} +1.30921e7 q^{53} +(-1.11408e7 - 1.11408e7i) q^{54} +609019. q^{55} -1.76984e7i q^{56} +(611556. + 611556. i) q^{57} +(1.70317e7 + 1.70317e7i) q^{58} +(-6.77137e6 + 6.77137e6i) q^{59} +(-3.99702e7 + 3.99702e7i) q^{60} +3.48674e6 q^{61} +1.72555e7i q^{62} +(363749. - 363749. i) q^{63} -4.95888e7i q^{64} +(8.07699e6 - 2.73577e7i) q^{65} -1.55347e6 q^{66} +(-1.71216e7 - 1.71216e7i) q^{67} -3.62089e6 q^{68} -7.30570e6i q^{69} +(2.95128e7 + 2.95128e7i) q^{70} +(1.55636e7 + 1.55636e7i) q^{71} +(3.44858e6 - 3.44858e6i) q^{72} +(3.33302e6 - 3.33302e6i) q^{73} -4.53253e7 q^{74} -5.05469e7i q^{75} +(4.98919e6 - 4.98919e6i) q^{76} +833151. i q^{77} +(-2.06025e7 + 6.97833e7i) q^{78} -4.95167e6 q^{79} +(1.56951e8 + 1.56951e8i) q^{80} -4.53752e7 q^{81} -1.04680e8i q^{82} +(-3.26970e7 - 3.26970e7i) q^{83} +(-5.46801e7 - 5.46801e7i) q^{84} +(3.76322e6 - 3.76322e6i) q^{85} +(2.43995e7 - 2.43995e7i) q^{86} +6.55921e7 q^{87} +7.89882e6i q^{88} +(-8.25743e7 + 8.25743e7i) q^{89} +1.15013e7i q^{90} +(3.74260e7 + 1.10495e7i) q^{91} -5.96012e7 q^{92} +(3.32270e7 + 3.32270e7i) q^{93} +2.22779e8 q^{94} +1.03706e7i q^{95} +(-2.05041e8 - 2.05041e8i) q^{96} +(7.02251e7 + 7.02251e7i) q^{97} +(8.43048e7 - 8.43048e7i) q^{98} +(-162342. + 162342. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20} + 279416 q^{21} - 977312 q^{22} - 986232 q^{24} + 2952238 q^{26} + 364916 q^{27} + 4497084 q^{28} - 2479024 q^{29} - 1892664 q^{31} + 947212 q^{32} + 1368644 q^{33} - 531576 q^{34} - 2918284 q^{35} - 8343978 q^{37} - 1101268 q^{39} - 12691908 q^{40} + 1140178 q^{41} + 15137212 q^{42} - 3867188 q^{44} + 6565370 q^{45} + 2006148 q^{46} - 13368572 q^{47} - 10106716 q^{48} + 37369598 q^{50} - 14821220 q^{52} + 50561348 q^{53} - 4995928 q^{54} + 76994128 q^{55} - 34755760 q^{57} + 22505716 q^{58} + 2127976 q^{59} - 161134196 q^{60} - 52016516 q^{61} - 15210112 q^{63} + 10413082 q^{65} - 51097328 q^{66} + 960292 q^{67} + 283187508 q^{68} - 166635032 q^{70} + 67412140 q^{71} + 96846900 q^{72} - 145213226 q^{73} - 233620024 q^{74} - 150533640 q^{76} + 212071160 q^{78} - 76829120 q^{79} + 524889520 q^{80} + 293280674 q^{81} - 241951556 q^{83} + 345496184 q^{84} + 260737764 q^{85} - 579480384 q^{86} - 618300656 q^{87} - 89187110 q^{89} + 232660948 q^{91} - 122690376 q^{92} + 669553400 q^{93} + 1069637380 q^{94} - 1324092400 q^{96} + 331183146 q^{97} + 588677614 q^{98} - 1125076336 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−21.6276	−	21.6276i	−1.35173	−	1.35173i	−0.883731	−	0.467996i	$-0.844976\pi$
$2$	−21.6276	−	21.6276i	−1.35173	−	1.35173i	−0.467996	−	0.883731i	$-0.655024\pi$
$3$	−83.2917			−1.02829			−0.514146	−	0.857703i	$-0.671891\pi$
$3$	−83.2917			−1.02829			−0.514146	+	0.857703i	$0.671891\pi$
$4$			679.508i			2.65433i
$5$	−706.219	−	706.219i	−1.12995	−	1.12995i	−0.990185	−	0.139766i	$-0.955365\pi$
$5$	−706.219	−	706.219i	−1.12995	−	1.12995i	−0.139766	−	0.990185i	$-0.544635\pi$
$6$	1801.40	+	1801.40i	1.38997	+	1.38997i
$7$	966.123	−	966.123i	0.402384	−	0.402384i	−0.476689	−	0.879072i	$-0.658163\pi$
$7$	966.123	−	966.123i	0.402384	−	0.402384i	0.879072	+	0.476689i	$0.158163\pi$
$8$	9159.48	−	9159.48i	2.23620	−	2.23620i
$9$	376.504			0.0573852
$10$			30547.7i			3.05477i
$11$	−431.183	+	431.183i	−0.0294504	+	0.0294504i	−0.721679	−	0.692228i	$-0.756629\pi$
$11$	−431.183	+	431.183i	−0.0294504	+	0.0294504i	0.692228	+	0.721679i	$0.256629\pi$
$12$		−	56597.4i		−	2.72943i
$13$	13650.7	+	25087.6i	0.477949	+	0.878388i
$13$	13650.7	+	25087.6i	0.477949	+	0.878388i
$14$	−41789.9			−1.08783
$15$	58822.2	+	58822.2i	1.16192	+	1.16192i
$16$	−222241.			−3.39114
$17$			5328.69i			0.0638006i	0.999491	+	0.0319003i	$0.0101559\pi$
$17$			5328.69i			0.0638006i	−0.999491	+	0.0319003i	$0.989844\pi$
$18$	−8142.89	−	8142.89i	−0.0775691	−	0.0775691i
$19$	−7342.35	−	7342.35i	−0.0563405	−	0.0563405i	0.678375	−	0.734716i	$-0.262684\pi$
$19$	−7342.35	−	7342.35i	−0.0563405	−	0.0563405i	−0.734716	+	0.678375i	$0.762684\pi$
$20$	479882.	−	479882.i	2.99926	−	2.99926i
$21$	−80470.0	+	80470.0i	−0.413768	+	0.413768i
$22$	18650.9			0.0796177
$23$			87712.3i			0.313436i	0.987643	+	0.156718i	$0.0500914\pi$
$23$			87712.3i			0.313436i	−0.987643	+	0.156718i	$0.949909\pi$
$24$	−762908.	+	762908.i	−2.29947	+	2.29947i
$25$			606866.i			1.55358i
$26$	247354.	−	837818.i	0.541284	−	1.83340i
$27$	515117.			0.969284
$28$	656489.	+	656489.i	1.06806	+	1.06806i
$29$	−787498.			−1.11342			−0.556708	−	0.830708i	$-0.687936\pi$
$29$	−787498.			−1.11342			−0.556708	+	0.830708i	$0.687936\pi$
$30$		−	2.54437e6i		−	3.14120i
$31$	−398923.	−	398923.i	−0.431959	−	0.431959i	0.457335	−	0.889294i	$-0.348804\pi$
$31$	−398923.	−	398923.i	−0.431959	−	0.431959i	−0.889294	+	0.457335i	$0.848804\pi$
$32$	2.46173e6	+	2.46173e6i	2.34769	+	2.34769i
$33$	35913.9	−	35913.9i	0.0302836	−	0.0302836i
$34$	115247.	−	115247.i	0.0862410	−	0.0862410i
$35$	−1.36459e6			−0.909347
$36$			255838.i			0.152319i
$37$	1.04786e6	−	1.04786e6i	0.559107	−	0.559107i	−0.369946	−	0.929053i	$-0.620624\pi$
$37$	1.04786e6	−	1.04786e6i	0.559107	−	0.559107i	0.929053	+	0.369946i	$0.120624\pi$
$38$			317595.i			0.152314i
$39$	−1.13699e6	−	2.08959e6i	−0.491471	−	0.903240i
$40$	−1.29372e7			−5.05359
$41$	2.42006e6	+	2.42006e6i	0.856428	+	0.856428i	0.990915	−	0.134487i	$-0.0429386\pi$
$41$	2.42006e6	+	2.42006e6i	0.856428	+	0.856428i	−0.134487	+	0.990915i	$0.542939\pi$
$42$	3.48075e6			1.11860
$43$			1.12816e6i			0.329988i	0.986295	+	0.164994i	$0.0527604\pi$
$43$			1.12816e6i			0.329988i	−0.986295	+	0.164994i	$0.947240\pi$
$44$	−292992.	−	292992.i	−0.0781709	−	0.0781709i
$45$	−265894.	−	265894.i	−0.0648424	−	0.0648424i
$46$	1.89701e6	−	1.89701e6i	0.423680	−	0.423680i
$47$	−5.15032e6	+	5.15032e6i	−1.05546	+	1.05546i	−0.0570943	+	0.998369i	$0.518184\pi$
$47$	−5.15032e6	+	5.15032e6i	−1.05546	+	1.05546i	−0.998369	+	0.0570943i	$0.981816\pi$
$48$	1.85109e7			3.48708
$49$			3.89801e6i			0.676175i
$50$	1.31251e7	−	1.31251e7i	2.10001	−	2.10001i
$51$		−	443836.i		−	0.0656057i
$52$	−1.70473e7	+	9.27576e6i	−2.33153	+	1.26863i
$53$	1.30921e7			1.65922			0.829611	−	0.558342i	$-0.188562\pi$
$53$	1.30921e7			1.65922			0.829611	+	0.558342i	$0.188562\pi$
$54$	−1.11408e7	−	1.11408e7i	−1.31021	−	1.31021i
$55$	609019.			0.0665549
$56$		−	1.76984e7i		−	1.79962i
$57$	611556.	+	611556.i	0.0579345	+	0.0579345i
$58$	1.70317e7	+	1.70317e7i	1.50503	+	1.50503i
$59$	−6.77137e6	+	6.77137e6i	−0.558816	+	0.558816i	−0.928970	−	0.370154i	$-0.879305\pi$
$59$	−6.77137e6	+	6.77137e6i	−0.558816	+	0.558816i	0.370154	+	0.928970i	$0.379305\pi$
$60$	−3.99702e7	+	3.99702e7i	−3.08412	+	3.08412i
$61$	3.48674e6			0.251826			0.125913	−	0.992041i	$-0.459814\pi$
$61$	3.48674e6			0.251826			0.125913	+	0.992041i	$0.459814\pi$
$62$			1.72555e7i			1.16778i
$63$	363749.	−	363749.i	0.0230909	−	0.0230909i
$64$		−	4.95888e7i		−	2.95573i
$65$	8.07699e6	−	2.73577e7i	0.452477	−	1.53259i
$66$	−1.55347e6			−0.0818702
$67$	−1.71216e7	−	1.71216e7i	−0.849660	−	0.849660i	0.140431	−	0.990091i	$-0.455151\pi$
$67$	−1.71216e7	−	1.71216e7i	−0.849660	−	0.849660i	−0.990091	+	0.140431i	$0.955151\pi$
$68$	−3.62089e6			−0.169348
$69$		−	7.30570e6i		−	0.322304i
$70$	2.95128e7	+	2.95128e7i	1.22919	+	1.22919i
$71$	1.55636e7	+	1.55636e7i	0.612457	+	0.612457i	0.943586	−	0.331129i	$-0.107429\pi$
$71$	1.55636e7	+	1.55636e7i	0.612457	+	0.612457i	−0.331129	+	0.943586i	$0.607429\pi$
$72$	3.44858e6	−	3.44858e6i	0.128325	−	0.128325i
$73$	3.33302e6	−	3.33302e6i	0.117367	−	0.117367i	−0.645984	−	0.763351i	$-0.723553\pi$
$73$	3.33302e6	−	3.33302e6i	0.117367	−	0.117367i	0.763351	+	0.645984i	$0.223553\pi$
$74$	−4.53253e7			−1.51152
$75$		−	5.05469e7i		−	1.59753i
$76$	4.98919e6	−	4.98919e6i	0.149546	−	0.149546i
$77$			833151.i			0.0237007i
$78$	−2.06025e7	+	6.97833e7i	−0.556599	+	1.88527i
$79$	−4.95167e6			−0.127129			−0.0635643	−	0.997978i	$-0.520247\pi$
$79$	−4.95167e6			−0.127129			−0.0635643	+	0.997978i	$0.520247\pi$
$80$	1.56951e8	+	1.56951e8i	3.83182	+	3.83182i
$81$	−4.53752e7			−1.05409
$82$		−	1.04680e8i		−	2.31531i
$83$	−3.26970e7	−	3.26970e7i	−0.688961	−	0.688961i	0.273041	−	0.962002i	$-0.411971\pi$
$83$	−3.26970e7	−	3.26970e7i	−0.688961	−	0.688961i	−0.962002	+	0.273041i	$0.911971\pi$
$84$	−5.46801e7	−	5.46801e7i	−1.09828	−	1.09828i
$85$	3.76322e6	−	3.76322e6i	0.0720915	−	0.0720915i
$86$	2.43995e7	−	2.43995e7i	0.446053	−	0.446053i
$87$	6.55921e7			1.14492
$88$			7.89882e6i			0.131714i
$89$	−8.25743e7	+	8.25743e7i	−1.31609	+	1.31609i	−0.399242	+	0.916846i	$0.630727\pi$
$89$	−8.25743e7	+	8.25743e7i	−1.31609	+	1.31609i	−0.916846	+	0.399242i	$0.869273\pi$
$90$			1.15013e7i			0.175298i
$91$	3.74260e7	+	1.10495e7i	0.545768	+	0.161130i
$92$	−5.96012e7			−0.831963
$93$	3.32270e7	+	3.32270e7i	0.444180	+	0.444180i
$94$	2.22779e8			2.85339
$95$			1.03706e7i			0.127324i
$96$	−2.05041e8	−	2.05041e8i	−2.41411	−	2.41411i
$97$	7.02251e7	+	7.02251e7i	0.793241	+	0.793241i	0.982020	−	0.188778i	$-0.0604528\pi$
$97$	7.02251e7	+	7.02251e7i	0.793241	+	0.793241i	−0.188778	+	0.982020i	$0.560453\pi$
$98$	8.43048e7	−	8.43048e7i	0.914003	−	0.914003i
$99$	−162342.	+	162342.i	−0.00169001	+	0.00169001i
$100$	−4.12371e8			−4.12371
$101$		−	1.07171e8i		−	1.02989i	−0.857222	−	0.514947i	$-0.827812\pi$
$101$		−	1.07171e8i		−	1.02989i	0.857222	−	0.514947i	$-0.172188\pi$
$102$	−9.59911e6	+	9.59911e6i	−0.0886809	+	0.0886809i
$103$			1.56166e8i			1.38751i	0.720210	+	0.693756i	$0.244045\pi$
$103$			1.56166e8i			1.38751i	−0.720210	+	0.693756i	$0.755955\pi$
$104$	3.54823e8	+	1.04756e8i	3.03304	+	0.895463i
$105$	1.13659e8			0.935075
$106$	−2.83150e8	−	2.83150e8i	−2.24281	−	2.24281i
$107$	−1.89540e8			−1.44599			−0.722996	−	0.690852i	$-0.757236\pi$
$107$	−1.89540e8			−1.44599			−0.722996	+	0.690852i	$0.757236\pi$
$108$			3.50026e8i			2.57280i
$109$	3.48339e7	+	3.48339e7i	0.246772	+	0.246772i	0.819645	−	0.572872i	$-0.194171\pi$
$109$	3.48339e7	+	3.48339e7i	0.246772	+	0.246772i	−0.572872	+	0.819645i	$0.694171\pi$
$110$	−1.31716e7	−	1.31716e7i	−0.0899640	−	0.0899640i
$111$	−8.72777e7	+	8.72777e7i	−0.574925	+	0.574925i
$112$	−2.14713e8	+	2.14713e8i	−1.36454	+	1.36454i
$113$	9.85497e7			0.604424			0.302212	−	0.953241i	$-0.402275\pi$
$113$	9.85497e7			0.604424			0.302212	+	0.953241i	$0.402275\pi$
$114$		−	2.64530e7i		−	0.156623i
$115$	6.19441e7	−	6.19441e7i	0.354167	−	0.354167i
$116$		−	5.35112e8i		−	2.95537i
$117$	5.13954e6	+	9.44560e6i	0.0274272	+	0.0504064i
$118$	2.92897e8			1.51073
$119$	5.14817e6	+	5.14817e6i	0.0256723	+	0.0256723i
$120$	1.07756e9			5.19657
$121$			2.13987e8i			0.998265i
$122$	−7.54100e7	−	7.54100e7i	−0.340400	−	0.340400i
$123$	−2.01571e8	−	2.01571e8i	−0.880659	−	0.880659i
$124$	2.71072e8	−	2.71072e8i	1.14656	−	1.14656i
$125$	1.52714e8	−	1.52714e8i	0.625515	−	0.625515i
$126$	−1.57341e7			−0.0624250
$127$			2.44685e8i			0.940575i	0.882513	+	0.470287i	$0.155850\pi$
$127$			2.44685e8i			0.940575i	−0.882513	+	0.470287i	$0.844150\pi$
$128$	−4.42287e8	+	4.42287e8i	−1.64765	+	1.64765i
$129$		−	9.39665e7i		−	0.339324i
$130$	−7.66369e8	+	4.16997e8i	−2.68327	+	1.46002i
$131$	−3.05747e8			−1.03819			−0.519095	−	0.854716i	$-0.673731\pi$
$131$	−3.05747e8			−1.03819			−0.519095	+	0.854716i	$0.673731\pi$
$132$	2.44038e7	+	2.44038e7i	0.0803826	+	0.0803826i
$133$	−1.41872e7			−0.0453410
$134$			7.40599e8i			2.29702i
$135$	−3.63786e8	−	3.63786e8i	−1.09524	−	1.09524i
$136$	4.88080e7	+	4.88080e7i	0.142671	+	0.142671i
$137$	1.87463e8	−	1.87463e8i	0.532149	−	0.532149i	−0.389062	−	0.921211i	$-0.627201\pi$
$137$	1.87463e8	−	1.87463e8i	0.532149	−	0.532149i	0.921211	+	0.389062i	$0.127201\pi$
$138$	−1.58005e8	+	1.58005e8i	−0.435667	+	0.435667i
$139$	−4.76588e8			−1.27669			−0.638343	−	0.769752i	$-0.720380\pi$
$139$	−4.76588e8			−1.27669			−0.638343	+	0.769752i	$0.720380\pi$
$140$		−	9.27250e8i		−	2.41371i
$141$	4.28979e8	−	4.28979e8i	1.08532	−	1.08532i
$142$		−	6.73206e8i		−	1.65575i
$143$	−1.67033e7	−	4.93141e6i	−0.0399446	−	0.0117931i
$144$	−8.36748e7			−0.194601
$145$	5.56147e8	+	5.56147e8i	1.25811	+	1.25811i
$146$	−1.44171e8			−0.317297
$147$		−	3.24672e8i		−	0.695305i
$148$	7.12027e8	+	7.12027e8i	1.48405	+	1.48405i
$149$	1.83994e8	+	1.83994e8i	0.373301	+	0.373301i	0.868678	−	0.495377i	$-0.164970\pi$
$149$	1.83994e8	+	1.83994e8i	0.373301	+	0.373301i	−0.495377	+	0.868678i	$0.664970\pi$
$150$	−1.09321e9	+	1.09321e9i	−2.15943	+	2.15943i
$151$	2.92294e8	−	2.92294e8i	0.562228	−	0.562228i	−0.367712	−	0.929940i	$-0.619859\pi$
$151$	2.92294e8	−	2.92294e8i	0.562228	−	0.562228i	0.929940	+	0.367712i	$0.119859\pi$
$152$	−1.34504e8			−0.251977
$153$			2.00627e6i			0.00366121i
$154$	1.80191e7	−	1.80191e7i	0.0320368	−	0.0320368i
$155$			5.63454e8i			0.976185i
$156$	1.41989e9	−	7.72593e8i	2.39750	−	1.30453i
$157$	1.69240e8			0.278551			0.139276	−	0.990254i	$-0.455523\pi$
$157$	1.69240e8			0.278551			0.139276	+	0.990254i	$0.455523\pi$
$158$	1.07093e8	+	1.07093e8i	0.171843	+	0.171843i
$159$	−1.09046e9			−1.70617
$160$		−	3.47704e9i		−	5.30554i
$161$	8.47409e7	+	8.47409e7i	0.126122	+	0.126122i
$162$	9.81358e8	+	9.81358e8i	1.42484	+	1.42484i
$163$	8.70441e8	−	8.70441e8i	1.23307	−	1.23307i	0.270296	−	0.962777i	$-0.412878\pi$
$163$	8.70441e8	−	8.70441e8i	1.23307	−	1.23307i	0.962777	−	0.270296i	$-0.0871217\pi$
$164$	−1.64445e9	+	1.64445e9i	−2.27324	+	2.27324i
$165$	−5.07262e7			−0.0684379
$166$			1.41431e9i			1.86257i
$167$	1.55595e8	−	1.55595e8i	0.200046	−	0.200046i	−0.599974	−	0.800020i	$-0.704822\pi$
$167$	1.55595e8	−	1.55595e8i	0.200046	−	0.200046i	0.800020	+	0.599974i	$0.204822\pi$
$168$			1.47413e9i			1.85054i
$169$	−4.43048e8	+	6.84927e8i	−0.543130	+	0.839648i
$170$	−1.62779e8			−0.194896
$171$	−2.76442e6	−	2.76442e6i	−0.00323311	−	0.00323311i
$172$	−7.66595e8			−0.875896
$173$		−	6.17461e7i		−	0.0689327i	−0.999406	−	0.0344663i	$-0.989027\pi$
$173$		−	6.17461e7i		−	0.0689327i	0.999406	−	0.0344663i	$-0.0109731\pi$
$174$	−1.41860e9	−	1.41860e9i	−1.54762	−	1.54762i
$175$	5.86308e8	+	5.86308e8i	0.625134	+	0.625134i
$176$	9.58267e7	−	9.58267e7i	0.0998701	−	0.0998701i
$177$	5.63999e8	−	5.63999e8i	0.574626	−	0.574626i
$178$	3.57177e9			3.55798
$179$		−	6.89754e8i		−	0.671866i	−0.941886	−	0.335933i	$-0.890948\pi$
$179$		−	6.89754e8i		−	0.671866i	0.941886	−	0.335933i	$-0.109052\pi$
$180$	1.80677e8	−	1.80677e8i	0.172113	−	0.172113i
$181$			8.50963e8i			0.792860i	0.918065	+	0.396430i	$0.129751\pi$
$181$			8.50963e8i			0.792860i	−0.918065	+	0.396430i	$0.870249\pi$
$182$	−5.70461e8	−	1.04841e9i	−0.519925	−	0.955533i
$183$	−2.90417e8			−0.258951
$184$	8.03399e8	+	8.03399e8i	0.700906	+	0.700906i
$185$	−1.48003e9			−1.26353
$186$		−	1.43724e9i		−	1.20082i
$187$	−2.29764e6	−	2.29764e6i	−0.00187895	−	0.00187895i
$188$	−3.49969e9	−	3.49969e9i	−2.80155	−	2.80155i
$189$	4.97667e8	−	4.97667e8i	0.390024	−	0.390024i
$190$	2.24292e8	−	2.24292e8i	0.172107	−	0.172107i
$191$	−6.91369e7			−0.0519489			−0.0259744	−	0.999663i	$-0.508269\pi$
$191$	−6.91369e7			−0.0519489			−0.0259744	+	0.999663i	$0.508269\pi$
$192$			4.13034e9i			3.03935i
$193$	−2.46969e8	+	2.46969e8i	−0.177997	+	0.177997i	−0.790482	−	0.612485i	$-0.790170\pi$
$193$	−2.46969e8	+	2.46969e8i	−0.177997	+	0.177997i	0.612485	+	0.790482i	$0.290170\pi$
$194$		−	3.03760e9i		−	2.14449i
$195$	−6.72746e8	+	2.27867e9i	−0.465278	+	1.57595i
$196$	−2.64873e9			−1.79479
$197$	−2.79924e8	−	2.79924e8i	−0.185855	−	0.185855i	0.608046	−	0.793902i	$-0.291954\pi$
$197$	−2.79924e8	−	2.79924e8i	−0.185855	−	0.185855i	−0.793902	+	0.608046i	$0.791954\pi$
$198$	7.02215e6			0.00456887
$199$			2.07496e8i			0.132311i	0.997809	+	0.0661557i	$0.0210734\pi$
$199$			2.07496e8i			0.132311i	−0.997809	+	0.0661557i	$0.978927\pi$
$200$	5.55858e9	+	5.55858e9i	3.47411	+	3.47411i
$201$	1.42609e9	+	1.42609e9i	0.873699	+	0.873699i
$202$	−2.31786e9	+	2.31786e9i	−1.39213	+	1.39213i
$203$	−7.60821e8	+	7.60821e8i	−0.448021	+	0.448021i
$204$	3.01590e8			0.174139
$205$		−	3.41819e9i		−	1.93544i
$206$	3.37749e9	−	3.37749e9i	1.87554	−	1.87554i
$207$			3.30240e7i			0.0179866i
$208$	−3.03375e9	−	5.57551e9i	−1.62079	−	2.97873i
$209$	6.33178e6			0.00331849
$210$	−2.45817e9	−	2.45817e9i	−1.26397	−	1.26397i
$211$	−2.54699e6			−0.00128498			−0.000642491	−	1.00000i	$-0.500205\pi$
$211$	−2.54699e6			−0.00128498			−0.000642491		1.00000i	$0.500205\pi$
$212$			8.89616e9i			4.40412i
$213$	−1.29631e9	−	1.29631e9i	−0.629785	−	0.629785i
$214$	4.09930e9	+	4.09930e9i	1.95459	+	1.95459i
$215$	7.96729e8	−	7.96729e8i	0.372870	−	0.372870i
$216$	4.71820e9	−	4.71820e9i	2.16751	−	2.16751i
$217$	−7.70818e8			−0.347626
$218$		−	1.50675e9i		−	0.667137i
$219$	−2.77613e8	+	2.77613e8i	−0.120688	+	0.120688i
$220$			4.13833e8i			0.176659i
$221$	−1.33684e8	+	7.27403e7i	−0.0560417	+	0.0304934i
$222$	3.77522e9			1.55428
$223$	−2.15016e9	−	2.15016e9i	−0.869462	−	0.869462i	0.122951	−	0.992413i	$-0.460764\pi$
$223$	−2.15016e9	−	2.15016e9i	−0.869462	−	0.869462i	−0.992413	+	0.122951i	$0.960764\pi$
$224$	4.75666e9			1.88934
$225$			2.28488e8i			0.0891523i
$226$	−2.13140e9	−	2.13140e9i	−0.817015	−	0.817015i
$227$	1.19673e9	+	1.19673e9i	0.450707	+	0.450707i	0.895589	−	0.444882i	$-0.146754\pi$
$227$	1.19673e9	+	1.19673e9i	0.450707	+	0.450707i	−0.444882	+	0.895589i	$0.646754\pi$
$228$	−4.15558e8	+	4.15558e8i	−0.153777	+	0.153777i
$229$	−1.41483e9	+	1.41483e9i	−0.514473	+	0.514473i	−0.915894	−	0.401421i	$-0.868516\pi$
$229$	−1.41483e9	+	1.41483e9i	−0.514473	+	0.514473i	0.401421	+	0.915894i	$0.368516\pi$
$230$	−2.67941e9			−0.957475
$231$		−	6.93946e7i		−	0.0243712i
$232$	−7.21308e9	+	7.21308e9i	−2.48982	+	2.48982i
$233$			4.15641e9i			1.41024i	0.709086	+	0.705122i	$0.249108\pi$
$233$			4.15641e9i			1.41024i	−0.709086	+	0.705122i	$0.750892\pi$
$234$	9.31298e7	−	3.15442e8i	0.0310617	−	0.105210i
$235$	7.27451e9			2.38524
$236$	−4.60120e9	−	4.60120e9i	−1.48328	−	1.48328i
$237$	4.12433e8			0.130725
$238$		−	2.22685e8i		−	0.0694039i
$239$	1.82691e9	+	1.82691e9i	0.559919	+	0.559919i	0.929284	−	0.369365i	$-0.120425\pi$
$239$	1.82691e9	+	1.82691e9i	0.559919	+	0.559919i	−0.369365	+	0.929284i	$0.620425\pi$
$240$	−1.30727e10	−	1.30727e10i	−3.94023	−	3.94023i
$241$	−2.91957e9	+	2.91957e9i	−0.865469	+	0.865469i	−0.991967	−	0.126498i	$-0.959626\pi$
$241$	−2.91957e9	+	2.91957e9i	−0.865469	+	0.865469i	0.126498	+	0.991967i	$0.459626\pi$
$242$	4.62803e9	−	4.62803e9i	1.34938	−	1.34938i
$243$	3.99694e8			0.114631
$244$			2.36927e9i			0.668430i
$245$	2.75285e9	−	2.75285e9i	0.764044	−	0.764044i
$246$			8.71901e9i			2.38082i
$247$	8.39740e7	−	2.84430e8i	0.0225609	−	0.0764166i
$248$	−7.30786e9			−1.93189
$249$	2.72338e9	+	2.72338e9i	0.708454	+	0.708454i
$250$	−6.60567e9			−1.69105
$251$			4.34046e9i			1.09356i	0.837278	+	0.546778i	$0.184146\pi$
$251$			4.34046e9i			1.09356i	−0.837278	+	0.546778i	$0.815854\pi$
$252$	2.47171e8	+	2.47171e8i	0.0612907	+	0.0612907i
$253$	−3.78200e7	−	3.78200e7i	−0.00923081	−	0.00923081i
$254$	5.29197e9	−	5.29197e9i	1.27140	−	1.27140i
$255$	−3.13445e8	+	3.13445e8i	−0.0741312	+	0.0741312i
$256$	6.43647e9			1.49861
$257$		−	5.42704e9i		−	1.24403i	−0.783005	−	0.622015i	$-0.786314\pi$
$257$		−	5.42704e9i		−	1.24403i	0.783005	−	0.622015i	$-0.213686\pi$
$258$	−2.03227e9	+	2.03227e9i	−0.458673	+	0.458673i
$259$		−	2.02472e9i		−	0.449951i
$260$	1.85898e10	+	5.48838e9i	4.06801	+	1.20102i
$261$	−2.96496e8			−0.0638936
$262$	6.61258e9	+	6.61258e9i	1.40335	+	1.40335i
$263$	−8.97912e9			−1.87677			−0.938385	−	0.345593i	$-0.887678\pi$
$263$	−8.97912e9			−1.87677			−0.938385	+	0.345593i	$0.887678\pi$
$264$		−	6.57906e8i		−	0.135440i
$265$	−9.24586e9	−	9.24586e9i	−1.87484	−	1.87484i
$266$	3.06836e8	+	3.06836e8i	0.0612886	+	0.0612886i
$267$	6.87775e9	−	6.87775e9i	1.35332	−	1.35332i
$268$	1.16343e10	−	1.16343e10i	2.25528	−	2.25528i
$269$	−2.61168e9			−0.498783			−0.249391	−	0.968403i	$-0.580231\pi$
$269$	−2.61168e9			−0.498783			−0.249391	+	0.968403i	$0.580231\pi$
$270$			1.57356e10i			2.96094i
$271$	5.13079e9	−	5.13079e9i	0.951277	−	0.951277i	−0.0475900	−	0.998867i	$-0.515154\pi$
$271$	5.13079e9	−	5.13079e9i	0.951277	−	0.951277i	0.998867	+	0.0475900i	$0.0151541\pi$
$272$		−	1.18426e9i		−	0.216356i
$273$	−3.11727e9	−	9.20331e8i	−0.561209	−	0.165689i
$274$	−8.10876e9			−1.43864
$275$	−2.61670e8	−	2.61670e8i	−0.0457534	−	0.0457534i
$276$	4.96429e9			0.855501
$277$			2.85168e9i			0.484375i	0.970229	+	0.242188i	$0.0778649\pi$
$277$			2.85168e9i			0.484375i	−0.970229	+	0.242188i	$0.922135\pi$
$278$	1.03075e10	+	1.03075e10i	1.72573	+	1.72573i
$279$	−1.50196e8	−	1.50196e8i	−0.0247880	−	0.0247880i
$280$	−1.24989e10	+	1.24989e10i	−2.03348	+	2.03348i
$281$	−9.40208e8	+	9.40208e8i	−0.150799	+	0.150799i	−0.778475	−	0.627676i	$-0.784006\pi$
$281$	−9.40208e8	+	9.40208e8i	−0.150799	+	0.150799i	0.627676	+	0.778475i	$0.284006\pi$
$282$	−1.85556e10			−2.93412
$283$		−	4.24340e8i		−	0.0661559i	−0.999453	−	0.0330779i	$-0.989469\pi$
$283$		−	4.24340e8i		−	0.0661559i	0.999453	−	0.0330779i	$-0.0105310\pi$
$284$	−1.05756e10	+	1.05756e10i	−1.62566	+	1.62566i
$285$		−	8.63786e8i		−	0.130926i
$286$	2.54598e8	+	4.67907e8i	0.0380531	+	0.0699352i
$287$	4.67616e9			0.689226
$288$	9.26851e8	+	9.26851e8i	0.134722	+	0.134722i
$289$	6.94736e9			0.995929
$290$		−	2.40563e10i		−	3.40123i
$291$	−5.84917e9	−	5.84917e9i	−0.815684	−	0.815684i
$292$	2.26482e9	+	2.26482e9i	0.311531	+	0.311531i
$293$	−4.76690e9	+	4.76690e9i	−0.646794	+	0.646794i	−0.952217	−	0.305423i	$-0.901202\pi$
$293$	−4.76690e9	+	4.76690e9i	−0.646794	+	0.646794i	0.305423	+	0.952217i	$0.401202\pi$
$294$	−7.02189e9	+	7.02189e9i	−0.939863	+	0.939863i
$295$	9.56415e9			1.26287
$296$		−	1.91956e10i		−	2.50055i
$297$	−2.22110e8	+	2.22110e8i	−0.0285457	+	0.0285457i
$298$		−	7.95872e9i		−	1.00920i
$299$	−2.20049e9	+	1.19733e9i	−0.275319	+	0.149806i
$300$	3.43470e10			4.24038
$301$	1.08994e9	+	1.08994e9i	0.132782	+	0.132782i
$302$	−1.26433e10			−1.51996
$303$			8.92647e9i			1.05903i
$304$	1.63177e9	+	1.63177e9i	0.191058	+	0.191058i
$305$	−2.46241e9	−	2.46241e9i	−0.284551	−	0.284551i
$306$	4.33909e7	−	4.33909e7i	0.00494895	−	0.00494895i
$307$	−2.28644e9	+	2.28644e9i	−0.257399	+	0.257399i	−0.823995	−	0.566596i	$-0.808260\pi$
$307$	−2.28644e9	+	2.28644e9i	−0.257399	+	0.257399i	0.566596	+	0.823995i	$0.308260\pi$
$308$	−5.66133e8			−0.0629094
$309$		−	1.30073e10i		−	1.42677i
$310$	1.21862e10	−	1.21862e10i	1.31953	−	1.31953i
$311$			1.65154e10i			1.76542i	0.469918	+	0.882710i	$0.344283\pi$
$311$			1.65154e10i			1.76542i	−0.469918	+	0.882710i	$0.655717\pi$
$312$	−2.95538e10	−	8.72534e9i	−3.11885	−	0.920798i
$313$	−7.14367e9			−0.744293			−0.372146	−	0.928174i	$-0.621378\pi$
$313$	−7.14367e9			−0.744293			−0.372146	+	0.928174i	$0.621378\pi$
$314$	−3.66027e9	−	3.66027e9i	−0.376525	−	0.376525i
$315$	−5.13774e8			−0.0521831
$316$		−	3.36470e9i		−	0.337441i
$317$	1.16773e10	+	1.16773e10i	1.15639	+	1.15639i	0.985246	+	0.171142i	$0.0547458\pi$
$317$	1.16773e10	+	1.16773e10i	1.15639	+	1.15639i	0.171142	+	0.985246i	$0.445254\pi$
$318$	2.35841e10	+	2.35841e10i	2.30627	+	2.30627i
$319$	3.39556e8	−	3.39556e8i	0.0327905	−	0.0327905i
$320$	−3.50206e10	+	3.50206e10i	−3.33982	+	3.33982i
$321$	1.57871e10			1.48690
$322$		−	3.66549e9i		−	0.340964i
$323$	3.91251e7	−	3.91251e7i	0.00359456	−	0.00359456i
$324$		−	3.08328e10i		−	2.79791i
$325$	−1.52248e10	+	8.28414e9i	−1.36464	+	0.742530i
$326$	−3.76511e10			−3.33356
$327$	−2.90138e9	−	2.90138e9i	−0.253754	−	0.253754i
$328$	4.43330e10			3.83029
$329$			9.95169e9i			0.849402i
$330$	1.09709e9	+	1.09709e9i	0.0925093	+	0.0925093i
$331$	−9.01779e9	−	9.01779e9i	−0.751256	−	0.751256i	0.223458	−	0.974714i	$-0.428266\pi$
$331$	−9.01779e9	−	9.01779e9i	−0.751256	−	0.751256i	−0.974714	+	0.223458i	$0.928266\pi$
$332$	2.22179e10	−	2.22179e10i	1.82873	−	1.82873i
$333$	3.94522e8	−	3.94522e8i	0.0320844	−	0.0320844i
$334$	−6.73031e9			−0.540816
$335$			2.41832e10i			1.92015i
$336$	1.78838e10	−	1.78838e10i	1.40314	−	1.40314i
$337$		−	1.63467e10i		−	1.26739i	−0.773584	−	0.633694i	$-0.781538\pi$
$337$		−	1.63467e10i		−	1.26739i	0.773584	−	0.633694i	$-0.218462\pi$
$338$	2.43954e10	−	5.23126e9i	1.86914	−	0.400811i
$339$	−8.20837e9			−0.621524
$340$	2.55714e9	+	2.55714e9i	0.191355	+	0.191355i
$341$	3.44017e8			0.0254427
$342$			1.19576e8i			0.00874055i
$343$	9.33547e9	+	9.33547e9i	0.674465	+	0.674465i
$344$	1.03334e10	+	1.03334e10i	0.737918	+	0.737918i
$345$	−5.15943e9	+	5.15943e9i	−0.364188	+	0.364188i
$346$	−1.33542e9	+	1.33542e9i	−0.0931781	+	0.0931781i
$347$	2.48764e10			1.71581			0.857906	−	0.513807i	$-0.171765\pi$
$347$	2.48764e10			1.71581			0.857906	+	0.513807i	$0.171765\pi$
$348$			4.45704e10i			3.03899i
$349$	−9.43914e9	+	9.43914e9i	−0.636254	+	0.636254i	−0.949629	−	0.313375i	$-0.898540\pi$
$349$	−9.43914e9	+	9.43914e9i	−0.636254	+	0.636254i	0.313375	+	0.949629i	$0.398540\pi$
$350$		−	2.53609e10i		−	1.69002i
$351$	7.03170e9	+	1.29231e10i	0.463268	+	0.851407i
$352$	−2.12291e9			−0.138280
$353$	4.31297e9	+	4.31297e9i	0.277765	+	0.277765i	0.832216	−	0.554451i	$-0.187072\pi$
$353$	4.31297e9	+	4.31297e9i	0.277765	+	0.277765i	−0.554451	+	0.832216i	$0.687072\pi$
$354$	−2.43959e10			−1.55347
$355$		−	2.19826e10i		−	1.38409i
$356$	−5.61099e10	−	5.61099e10i	−3.49333	−	3.49333i
$357$	−4.28800e8	−	4.28800e8i	−0.0263986	−	0.0263986i
$358$	−1.49178e10	+	1.49178e10i	−0.908179	+	0.908179i
$359$	5.34220e9	−	5.34220e9i	0.321619	−	0.321619i	−0.527769	−	0.849388i	$-0.676971\pi$
$359$	5.34220e9	−	5.34220e9i	0.321619	−	0.321619i	0.849388	+	0.527769i	$0.176971\pi$
$360$	−4.87091e9			−0.290001
$361$		−	1.68757e10i		−	0.993652i
$362$	1.84043e10	−	1.84043e10i	1.07173	−	1.07173i
$363$		−	1.78233e10i		−	1.02651i
$364$	−7.50823e9	+	2.54313e10i	−0.427693	+	1.44865i
$365$	−4.70769e9			−0.265238
$366$	6.28103e9	+	6.28103e9i	0.350031	+	0.350031i
$367$	6.12347e9			0.337546			0.168773	−	0.985655i	$-0.446019\pi$
$367$	6.12347e9			0.337546			0.168773	+	0.985655i	$0.446019\pi$
$368$		−	1.94933e10i		−	1.06290i
$369$	9.11163e8	+	9.11163e8i	0.0491463	+	0.0491463i
$370$	3.20096e10	+	3.20096e10i	1.70794	+	1.70794i
$371$	1.26485e10	−	1.26485e10i	0.667644	−	0.667644i
$372$	−2.25780e10	+	2.25780e10i	−1.17900	+	1.17900i
$373$	−3.24303e10			−1.67539			−0.837694	−	0.546139i	$-0.816097\pi$
$373$	−3.24303e10			−1.67539			−0.837694	+	0.546139i	$0.816097\pi$
$374$			9.93849e7i			0.00507965i
$375$	−1.27198e10	+	1.27198e10i	−0.643213	+	0.643213i
$376$			9.43486e10i			4.72046i
$377$	−1.07499e10	−	1.97565e10i	−0.532156	−	0.978012i
$378$	−2.15267e10			−1.05441
$379$	−1.35377e10	−	1.35377e10i	−0.656127	−	0.656127i	0.298335	−	0.954461i	$-0.403569\pi$
$379$	−1.35377e10	−	1.35377e10i	−0.656127	−	0.656127i	−0.954461	+	0.298335i	$0.903569\pi$
$380$	−7.04692e9			−0.337960
$381$		−	2.03803e10i		−	0.967186i
$382$	1.49527e9	+	1.49527e9i	0.0702207	+	0.0702207i
$383$	−2.42793e10	−	2.42793e10i	−1.12834	−	1.12834i	−0.990447	−	0.137894i	$-0.955967\pi$
$383$	−2.42793e10	−	2.42793e10i	−1.12834	−	1.12834i	−0.137894	−	0.990447i	$-0.544033\pi$
$384$	3.68388e10	−	3.68388e10i	1.69426	−	1.69426i
$385$	5.88387e8	−	5.88387e8i	0.0267806	−	0.0267806i
$386$	1.06827e10			0.481206
$387$			4.24757e8i			0.0189364i
$388$	−4.77185e10	+	4.77185e10i	−2.10552	+	2.10552i
$389$			3.75267e10i			1.63886i	0.573178	+	0.819431i	$0.305710\pi$
$389$			3.75267e10i			1.63886i	−0.573178	+	0.819431i	$0.694290\pi$
$390$	6.38322e10	−	3.47324e10i	2.75919	−	1.50133i
$391$	−4.67392e8			−0.0199974
$392$	3.57038e10	+	3.57038e10i	1.51206	+	1.51206i
$393$	2.54662e10			1.06756
$394$			1.21082e10i			0.502451i
$395$	3.49696e9	+	3.49696e9i	0.143649	+	0.143649i
$396$	−1.10313e8	−	1.10313e8i	−0.00448585	−	0.00448585i
$397$	2.65082e10	−	2.65082e10i	1.06713	−	1.06713i	0.0695533	−	0.997578i	$-0.477843\pi$
$397$	2.65082e10	−	2.65082e10i	1.06713	−	1.06713i	0.997578	−	0.0695533i	$-0.0221574\pi$
$398$	4.48764e9	−	4.48764e9i	0.178849	−	0.178849i
$399$	1.18168e9			0.0466238
$400$		−	1.34871e11i		−	5.26839i
$401$	−3.53870e9	+	3.53870e9i	−0.136857	+	0.136857i	−0.772216	−	0.635360i	$-0.780852\pi$
$401$	−3.53870e9	+	3.53870e9i	−0.136857	+	0.136857i	0.635360	+	0.772216i	$0.280852\pi$
$402$		−	6.16857e10i		−	2.36200i
$403$	4.56246e9	−	1.54536e10i	0.172973	−	0.585882i
$404$	7.28237e10			2.73368
$405$	3.20448e10	+	3.20448e10i	1.19107	+	1.19107i
$406$	3.29095e10			1.21120
$407$			9.03635e8i			0.0329318i
$408$	−4.06530e9	−	4.06530e9i	−0.146707	−	0.146707i
$409$	−7.94399e9	−	7.94399e9i	−0.283887	−	0.283887i	0.550770	−	0.834657i	$-0.314334\pi$
$409$	−7.94399e9	−	7.94399e9i	−0.283887	−	0.283887i	−0.834657	+	0.550770i	$0.814334\pi$
$410$	−7.39273e10	+	7.39273e10i	−2.61619	+	2.61619i
$411$	−1.56141e10	+	1.56141e10i	−0.547205	+	0.547205i
$412$	−1.06116e11			−3.68292
$413$			1.30840e10i			0.449717i
$414$	7.14231e8	−	7.14231e8i	0.0243129	−	0.0243129i
$415$			4.61824e10i			1.55698i
$416$	−2.81547e10	+	9.53632e10i	−0.940106	+	3.18425i
$417$	3.96958e10			1.31281
$418$	−1.36941e8	−	1.36941e8i	−0.00448570	−	0.00448570i
$419$	−2.26899e10			−0.736167			−0.368084	−	0.929793i	$-0.619986\pi$
$419$	−2.26899e10			−0.736167			−0.368084	+	0.929793i	$0.619986\pi$
$420$			7.72322e10i			2.48200i
$421$	1.46275e10	+	1.46275e10i	0.465630	+	0.465630i	0.900496	−	0.434865i	$-0.143204\pi$
$421$	1.46275e10	+	1.46275e10i	0.465630	+	0.465630i	−0.434865	+	0.900496i	$0.643204\pi$
$422$	5.50853e7	+	5.50853e7i	0.00173694	+	0.00173694i
$423$	−1.93912e9	+	1.93912e9i	−0.0605679	+	0.0605679i
$424$	1.19916e11	−	1.19916e11i	3.71035	−	3.71035i
$425$	−3.23380e9			−0.0991192
$426$			5.60724e10i			1.70259i
$427$	3.36863e9	−	3.36863e9i	0.101331	−	0.101331i
$428$		−	1.28794e11i		−	3.83814i
$429$	1.39125e9	+	4.10746e8i	0.0410747	+	0.0121267i
$430$	−3.44627e10			−1.00804
$431$	−3.07608e10	−	3.07608e10i	−0.891433	−	0.891433i	0.103225	−	0.994658i	$-0.467084\pi$
$431$	−3.07608e10	−	3.07608e10i	−0.891433	−	0.891433i	−0.994658	+	0.103225i	$0.967084\pi$
$432$	−1.14480e11			−3.28697
$433$		−	2.27162e10i		−	0.646227i	−0.946360	−	0.323113i	$-0.895270\pi$
$433$		−	2.27162e10i		−	0.646227i	0.946360	−	0.323113i	$-0.104730\pi$
$434$	1.66710e10	+	1.66710e10i	0.469896	+	0.469896i
$435$	−4.63224e10	−	4.63224e10i	−1.29370	−	1.29370i
$436$	−2.36699e10	+	2.36699e10i	−0.655015	+	0.655015i
$437$	6.44014e8	−	6.44014e8i	0.0176591	−	0.0176591i
$438$	1.20082e10			0.326274
$439$			3.91283e10i			1.05350i	0.850022	+	0.526748i	$0.176589\pi$
$439$			3.91283e10i			1.05350i	−0.850022	+	0.526748i	$0.823411\pi$
$440$	5.57830e9	−	5.57830e9i	0.148830	−	0.148830i
$441$			1.46762e9i			0.0388024i
$442$	4.46447e9	+	1.31807e9i	0.116972	+	0.0345343i
$443$	2.20125e10			0.571550			0.285775	−	0.958297i	$-0.407749\pi$
$443$	2.20125e10			0.571550			0.285775	+	0.958297i	$0.407749\pi$
$444$	−5.93059e10	−	5.93059e10i	−1.52604	−	1.52604i
$445$	1.16631e11			2.97423
$446$			9.30056e10i			2.35055i
$447$	−1.53252e10	−	1.53252e10i	−0.383863	−	0.383863i
$448$	−4.79089e10	−	4.79089e10i	−1.18934	−	1.18934i
$449$	1.45102e9	−	1.45102e9i	0.0357015	−	0.0357015i	−0.689031	−	0.724732i	$-0.741963\pi$
$449$	1.45102e9	−	1.45102e9i	0.0357015	−	0.0357015i	0.724732	+	0.689031i	$0.241963\pi$
$450$	4.94164e9	−	4.94164e9i	0.120510	−	0.120510i
$451$	−2.08698e9			−0.0504442
$452$			6.69653e10i			1.60434i
$453$	−2.43457e10	+	2.43457e10i	−0.578134	+	0.578134i
$454$		−	5.17650e10i		−	1.21846i
$455$	−1.86276e10	−	3.42343e10i	−0.434621	−	0.798760i
$456$	1.12031e10			0.259106
$457$	4.42354e10	+	4.42354e10i	1.01416	+	1.01416i	0.999898	+	0.0142587i	$0.00453885\pi$
$457$	4.42354e10	+	4.42354e10i	1.01416	+	1.01416i	0.0142587	+	0.999898i	$0.495461\pi$
$458$	6.11988e10			1.39085
$459$			2.74490e9i			0.0618409i
$460$	4.20915e10	+	4.20915e10i	0.940077	+	0.940077i
$461$	−7.59452e9	−	7.59452e9i	−0.168150	−	0.168150i	0.618016	−	0.786166i	$-0.287937\pi$
$461$	−7.59452e9	−	7.59452e9i	−0.168150	−	0.168150i	−0.786166	+	0.618016i	$0.787937\pi$
$462$	−1.50084e9	+	1.50084e9i	−0.0329432	+	0.0329432i
$463$	−5.43374e10	+	5.43374e10i	−1.18243	+	1.18243i	−0.203316	+	0.979113i	$0.565172\pi$
$463$	−5.43374e10	+	5.43374e10i	−1.18243	+	1.18243i	−0.979113	+	0.203316i	$0.934828\pi$
$464$	1.75015e11			3.77575
$465$		−	4.69311e10i		−	1.00380i
$466$	8.98932e10	−	8.98932e10i	1.90626	−	1.90626i
$467$			1.32796e10i			0.279201i	0.990208	+	0.139601i	$0.0445819\pi$
$467$			1.32796e10i			0.279201i	−0.990208	+	0.139601i	$0.955418\pi$
$468$	−6.41836e9	+	3.49236e9i	−0.133795	+	0.0728007i
$469$	−3.30831e10			−0.683778
$470$	−1.57330e11	−	1.57330e11i	−3.22420	−	3.22420i
$471$	−1.40963e10			−0.286432
$472$			1.24045e11i			2.49925i
$473$	−4.86444e8	−	4.86444e8i	−0.00971825	−	0.00971825i
$474$	−8.91994e9	−	8.91994e9i	−0.176705	−	0.176705i
$475$	4.45582e9	−	4.45582e9i	0.0875293	−	0.0875293i
$476$	−3.49822e9	+	3.49822e9i	−0.0681428	+	0.0681428i
$477$	4.92921e9			0.0952147
$478$		−	7.90233e10i		−	1.51371i
$479$	−6.72197e10	+	6.72197e10i	−1.27689	+	1.27689i	−0.334495	+	0.942397i	$0.608566\pi$
$479$	−6.72197e10	+	6.72197e10i	−1.27689	+	1.27689i	−0.942397	+	0.334495i	$0.891434\pi$
$480$			2.89608e11i			5.45565i
$481$	4.05922e10	+	1.19843e10i	0.758337	+	0.223888i
$482$	1.26287e11			2.33975
$483$	−7.05821e9	−	7.05821e9i	−0.129690	−	0.129690i
$484$	−1.45406e11			−2.64973
$485$		−	9.91886e10i		−	1.79265i
$486$	−8.64444e9	−	8.64444e9i	−0.154950	−	0.154950i
$487$	−2.47767e10	−	2.47767e10i	−0.440481	−	0.440481i	0.451692	−	0.892174i	$-0.350820\pi$
$487$	−2.47767e10	−	2.47767e10i	−0.440481	−	0.440481i	−0.892174	+	0.451692i	$0.850820\pi$
$488$	3.19368e10	−	3.19368e10i	0.563134	−	0.563134i
$489$	−7.25005e10	+	7.25005e10i	−1.26796	+	1.26796i
$490$	−1.19075e11			−2.06556
$491$			1.23003e10i			0.211636i	0.994385	+	0.105818i	$0.0337461\pi$
$491$			1.23003e10i			0.211636i	−0.994385	+	0.105818i	$0.966254\pi$
$492$	1.36969e11	−	1.36969e11i	2.33756	−	2.33756i
$493$		−	4.19633e9i		−	0.0710366i
$494$	−7.96771e9	+	4.33539e9i	−0.133791	+	0.0727982i
$495$	2.29298e8			0.00381926
$496$	8.86573e10	+	8.86573e10i	1.46483	+	1.46483i
$497$	3.00726e10			0.492885
$498$		−	1.17801e11i		−	1.91527i
$499$	3.51105e10	+	3.51105e10i	0.566284	+	0.566284i	0.931085	−	0.364801i	$-0.118863\pi$
$499$	3.51105e10	+	3.51105e10i	0.566284	+	0.566284i	−0.364801	+	0.931085i	$0.618863\pi$
$500$	1.03770e11	+	1.03770e11i	1.66032	+	1.66032i
$501$	−1.29598e10	+	1.29598e10i	−0.205706	+	0.205706i
$502$	9.38738e10	−	9.38738e10i	1.47819	−	1.47819i
$503$	9.14102e10			1.42798			0.713991	−	0.700155i	$-0.246886\pi$
$503$	9.14102e10			1.42798			0.713991	+	0.700155i	$0.246886\pi$
$504$		−	6.66351e9i		−	0.103272i
$505$	−7.56863e10	+	7.56863e10i	−1.16373	+	1.16373i
$506$			1.63591e9i			0.0249551i
$507$	3.69022e10	−	5.70487e10i	0.558497	−	0.863404i
$508$	−1.66266e11			−2.49660
$509$	−2.06174e10	−	2.06174e10i	−0.307159	−	0.307159i	0.536648	−	0.843806i	$-0.319690\pi$
$509$	−2.06174e10	−	2.06174e10i	−0.307159	−	0.307159i	−0.843806	+	0.536648i	$0.819690\pi$
$510$	1.35581e10			0.200410
$511$		−	6.44022e9i		−	0.0944533i
$512$	−2.59803e10	−	2.59803e10i	−0.378063	−	0.378063i
$513$	−3.78217e9	−	3.78217e9i	−0.0546099	−	0.0546099i
$514$	−1.17374e11	+	1.17374e11i	−1.68159	+	1.68159i
$515$	1.10287e11	−	1.10287e11i	1.56782	−	1.56782i
$516$	6.38510e10			0.900677
$517$		−	4.44146e9i		−	0.0621675i
$518$	−4.37898e10	+	4.37898e10i	−0.608211	+	0.608211i
$519$			5.14294e9i			0.0708829i
$520$	−1.76602e11	−	3.24564e11i	−2.41536	−	4.43902i
$521$	−7.52460e10			−1.02125			−0.510626	−	0.859803i	$-0.670586\pi$
$521$	−7.52460e10			−1.02125			−0.510626	+	0.859803i	$0.670586\pi$
$522$	6.41251e9	+	6.41251e9i	0.0863667	+	0.0863667i
$523$	−2.50012e10			−0.334160			−0.167080	−	0.985943i	$-0.553434\pi$
$523$	−2.50012e10			−0.334160			−0.167080	+	0.985943i	$0.553434\pi$
$524$		−	2.07758e11i		−	2.75570i
$525$	−4.88345e10	−	4.88345e10i	−0.642821	−	0.642821i
$526$	1.94197e11	+	1.94197e11i	2.53688	+	2.53688i
$527$	2.12574e9	−	2.12574e9i	0.0275592	−	0.0275592i
$528$	−7.98156e9	+	7.98156e9i	−0.102696	+	0.102696i
$529$	7.06175e10			0.901758
$530$			3.99932e11i			5.06854i
$531$	−2.54945e9	+	2.54945e9i	−0.0320677	+	0.0320677i
$532$		−	9.64033e9i		−	0.120350i
$533$	−2.76781e10	+	9.37492e10i	−0.342948	+	1.16161i
$534$	−2.97499e11			−3.65864
$535$	1.33857e11	+	1.33857e11i	1.63390	+	1.63390i
$536$	−3.13650e11			−3.80002
$537$			5.74508e10i			0.690874i
$538$	5.64845e10	+	5.64845e10i	0.674218	+	0.674218i
$539$	−1.68076e9	−	1.68076e9i	−0.0199136	−	0.0199136i
$540$	2.47195e11	−	2.47195e11i	2.90714	−	2.90714i
$541$	−1.46837e9	+	1.46837e9i	−0.0171415	+	0.0171415i	−0.715626	−	0.698484i	$-0.753858\pi$
$541$	−1.46837e9	+	1.46837e9i	−0.0171415	+	0.0171415i	0.698484	+	0.715626i	$0.253858\pi$
$542$	−2.21934e11			−2.57173
$543$		−	7.08782e10i		−	0.815292i
$544$	−1.31178e10	+	1.31178e10i	−0.149784	+	0.149784i
$545$		−	4.92008e10i		−	0.557681i
$546$	4.75146e10	+	8.73238e10i	0.534634	+	0.982567i
$547$	−2.13596e10			−0.238585			−0.119293	−	0.992859i	$-0.538063\pi$
$547$	−2.13596e10			−0.238585			−0.119293	+	0.992859i	$0.538063\pi$
$548$	1.27383e11	+	1.27383e11i	1.41250	+	1.41250i
$549$	1.31277e9			0.0144511
$550$			1.13186e10i			0.123692i
$551$	5.78209e9	+	5.78209e9i	0.0627304	+	0.0627304i
$552$	−6.69164e10	−	6.69164e10i	−0.720737	−	0.720737i
$553$	−4.78392e9	+	4.78392e9i	−0.0511545	+	0.0511545i
$554$	6.16751e10	−	6.16751e10i	0.654743	−	0.654743i
$555$	1.23274e11			1.29927
$556$		−	3.23846e11i		−	3.38874i
$557$	8.24194e10	−	8.24194e10i	0.856266	−	0.856266i	−0.134630	−	0.990896i	$-0.542985\pi$
$557$	8.24194e10	−	8.24194e10i	0.856266	−	0.856266i	0.990896	+	0.134630i	$0.0429846\pi$
$558$			6.49677e9i			0.0670133i
$559$	−2.83029e10	+	1.54002e10i	−0.289857	+	0.157717i
$560$	3.03268e11			3.08372
$561$	1.91374e8	+	1.91374e8i	0.00193211	+	0.00193211i
$562$	4.06689e10			0.407678
$563$		−	2.19548e10i		−	0.218522i	−0.994013	−	0.109261i	$-0.965151\pi$
$563$		−	2.19548e10i		−	0.218522i	0.994013	−	0.109261i	$-0.0348485\pi$
$564$	2.91495e11	+	2.91495e11i	2.88081	+	2.88081i
$565$	−6.95977e10	−	6.95977e10i	−0.682969	−	0.682969i
$566$	−9.17747e9	+	9.17747e9i	−0.0894247	+	0.0894247i
$567$	−4.38380e10	+	4.38380e10i	−0.424149	+	0.424149i
$568$	2.85108e11			2.73915
$569$		−	4.42507e9i		−	0.0422154i	−0.999777	−	0.0211077i	$-0.993281\pi$
$569$		−	4.42507e9i		−	0.0422154i	0.999777	−	0.0211077i	$-0.00671929\pi$
$570$	−1.86816e10	+	1.86816e10i	−0.176976	+	0.176976i
$571$		−	5.68177e10i		−	0.534490i	−0.963629	−	0.267245i	$-0.913887\pi$
$571$		−	5.68177e10i		−	0.534490i	0.963629	−	0.267245i	$-0.0861133\pi$
$572$	3.35094e9	−	1.13500e10i	0.0313027	−	0.106026i
$573$	5.75853e9			0.0534186
$574$	−1.01134e11	−	1.01134e11i	−0.931645	−	0.931645i
$575$	−5.32296e10			−0.486947
$576$		−	1.86704e10i		−	0.169615i
$577$	−7.62085e10	−	7.62085e10i	−0.687543	−	0.687543i	0.274145	−	0.961688i	$-0.411605\pi$
$577$	−7.62085e10	−	7.62085e10i	−0.687543	−	0.687543i	−0.961688	+	0.274145i	$0.911605\pi$
$578$	−1.50255e11	−	1.50255e11i	−1.34622	−	1.34622i
$579$	2.05704e10	−	2.05704e10i	0.183033	−	0.183033i
$580$	−3.77906e11	+	3.77906e11i	−3.33943	+	3.33943i
$581$	−6.31786e10			−0.554454
$582$			2.53007e11i			2.20516i
$583$	−5.64507e9	+	5.64507e9i	−0.0488647	+	0.0488647i
$584$		−	6.10575e10i		−	0.524913i
$585$	3.04102e9	−	1.03003e10i	0.0259655	−	0.0879481i
$586$	2.06194e11			1.74858
$587$	−6.09649e9	−	6.09649e9i	−0.0513484	−	0.0513484i	0.680966	−	0.732315i	$-0.261560\pi$
$587$	−6.09649e9	−	6.09649e9i	−0.0513484	−	0.0513484i	−0.732315	+	0.680966i	$0.761560\pi$
$588$	2.20617e11			1.84557
$589$			5.85806e9i			0.0486735i
$590$	−2.06850e11	−	2.06850e11i	−1.70705	−	1.70705i
$591$	2.33153e10	+	2.33153e10i	0.191114	+	0.191114i
$592$	−2.32877e11	+	2.32877e11i	−1.89601	+	1.89601i
$593$	−8.50831e10	+	8.50831e10i	−0.688057	+	0.688057i	−0.961802	−	0.273745i	$-0.911737\pi$
$593$	−8.50831e10	+	8.50831e10i	−0.688057	+	0.688057i	0.273745	+	0.961802i	$0.411737\pi$
$594$	9.60740e9			0.0771721
$595$		−	7.27147e9i		−	0.0580169i
$596$	−1.25026e11	+	1.25026e11i	−0.990865	+	0.990865i
$597$		−	1.72827e10i		−	0.136055i
$598$	7.34869e10	+	2.16960e10i	0.574653	+	0.169658i
$599$	9.14223e10			0.710142			0.355071	−	0.934839i	$-0.384457\pi$
$599$	9.14223e10			0.710142			0.355071	+	0.934839i	$0.384457\pi$
$600$	−4.62983e11	−	4.62983e11i	−3.57240	−	3.57240i
$601$	−3.88100e8			−0.00297472			−0.00148736	−	0.999999i	$-0.500473\pi$
$601$	−3.88100e8			−0.00297472			−0.00148736	+	0.999999i	$0.500473\pi$
$602$		−	4.71458e10i		−	0.358969i
$603$	−6.44635e9	−	6.44635e9i	−0.0487579	−	0.0487579i
$604$	1.98616e11	+	1.98616e11i	1.49234	+	1.49234i
$605$	1.51122e11	−	1.51122e11i	1.12799	−	1.12799i
$606$	1.93058e11	−	1.93058e11i	1.43152	−	1.43152i
$607$	−9.47209e10			−0.697736			−0.348868	−	0.937172i	$-0.613434\pi$
$607$	−9.47209e10			−0.697736			−0.348868	+	0.937172i	$0.613434\pi$
$608$		−	3.61497e10i		−	0.264540i
$609$	6.33700e10	−	6.33700e10i	0.460696	−	0.460696i
$610$			1.06512e11i			0.769271i
$611$	−1.99515e11	−	5.89040e10i	−1.43156	−	0.422649i
$612$	−1.36328e9			−0.00971805
$613$	−6.37233e10	−	6.37233e10i	−0.451290	−	0.451290i	0.444492	−	0.895783i	$-0.353384\pi$
$613$	−6.37233e10	−	6.37233e10i	−0.451290	−	0.451290i	−0.895783	+	0.444492i	$0.853384\pi$
$614$	9.89006e10			0.695866
$615$			2.84707e11i			1.99020i
$616$	7.63123e9	+	7.63123e9i	0.0529995	+	0.0529995i
$617$	−2.65061e10	−	2.65061e10i	−0.182896	−	0.182896i	0.609720	−	0.792617i	$-0.291282\pi$
$617$	−2.65061e10	−	2.65061e10i	−0.182896	−	0.182896i	−0.792617	+	0.609720i	$0.791282\pi$
$618$	−2.81317e11	+	2.81317e11i	−1.92860	+	1.92860i
$619$	1.76381e11	−	1.76381e11i	1.20141	−	1.20141i	0.227668	−	0.973739i	$-0.426890\pi$
$619$	1.76381e11	−	1.76381e11i	1.20141	−	1.20141i	0.973739	−	0.227668i	$-0.0731102\pi$
$620$	−3.82872e11			−2.59112
$621$			4.51821e10i			0.303809i
$622$	3.57189e11	−	3.57189e11i	2.38636	−	2.38636i
$623$			1.59554e11i			1.05914i
$624$	2.52686e11	+	4.64394e11i	1.66664	+	3.06301i
$625$	2.13584e10			0.139975
$626$	1.54501e11	+	1.54501e11i	1.00608	+	1.00608i
$627$	−5.27385e8			−0.00341238
$628$			1.15000e11i			0.739367i
$629$	5.58370e9	+	5.58370e9i	0.0356713	+	0.0356713i
$630$	1.11117e10	+	1.11117e10i	0.0705372	+	0.0705372i
$631$	−9.29590e10	+	9.29590e10i	−0.586373	+	0.586373i	−0.936647	−	0.350274i	$-0.886088\pi$
$631$	−9.29590e10	+	9.29590e10i	−0.586373	+	0.586373i	0.350274	+	0.936647i	$0.386088\pi$
$632$	−4.53547e10	+	4.53547e10i	−0.284285	+	0.284285i
$633$	2.12143e8			0.00132134
$634$		−	5.05103e11i		−	3.12624i
$635$	1.72802e11	−	1.72802e11i	1.06280	−	1.06280i
$636$		−	7.40976e11i		−	4.52872i
$637$	−9.77919e10	+	5.32106e10i	−0.593944	+	0.323177i
$638$	−1.46876e10			−0.0886476
$639$	5.85974e9	+	5.85974e9i	0.0351459	+	0.0351459i
$640$	6.24703e11			3.72352
$641$			1.24740e11i			0.738880i	0.929255	+	0.369440i	$0.120450\pi$
$641$			1.24740e11i			0.738880i	−0.929255	+	0.369440i	$0.879550\pi$
$642$	−3.41438e11	−	3.41438e11i	−2.00989	−	2.00989i
$643$	−1.21411e11	−	1.21411e11i	−0.710256	−	0.710256i	0.256333	−	0.966589i	$-0.417486\pi$
$643$	−1.21411e11	−	1.21411e11i	−0.710256	−	0.710256i	−0.966589	+	0.256333i	$0.917486\pi$
$644$	−5.75821e10	+	5.75821e10i	−0.334768	+	0.334768i
$645$	−6.63609e10	+	6.63609e10i	−0.383419	+	0.383419i
$646$	−1.69237e9			−0.00971771
$647$			3.31192e10i			0.189000i	0.995525	+	0.0945001i	$0.0301253\pi$
$647$			3.31192e10i			0.189000i	−0.995525	+	0.0945001i	$0.969875\pi$
$648$	−4.15613e11	+	4.15613e11i	−2.35716	+	2.35716i
$649$		−	5.83940e9i		−	0.0329147i
$650$	5.08443e11	+	1.50111e11i	2.84832	+	0.840927i
$651$	6.42027e10			0.357462
$652$	5.91472e11	+	5.91472e11i	3.27298	+	3.27298i
$653$	−4.14146e10			−0.227772			−0.113886	−	0.993494i	$-0.536330\pi$
$653$	−4.14146e10			−0.227772			−0.113886	+	0.993494i	$0.536330\pi$
$654$			1.25500e11i			0.686012i
$655$	2.15924e11	+	2.15924e11i	1.17310	+	1.17310i
$656$	−5.37838e11	−	5.37838e11i	−2.90426	−	2.90426i
$657$	1.25490e9	−	1.25490e9i	0.00673513	−	0.00673513i
$658$	2.15231e11	−	2.15231e11i	1.14816	−	1.14816i
$659$	−2.91147e10			−0.154373			−0.0771865	−	0.997017i	$-0.524594\pi$
$659$	−2.91147e10			−0.154373			−0.0771865	+	0.997017i	$0.524594\pi$
$660$		−	3.44689e10i		−	0.181657i
$661$	−1.10872e11	+	1.10872e11i	−0.580786	+	0.580786i	−0.935119	−	0.354333i	$-0.884708\pi$
$661$	−1.10872e11	+	1.10872e11i	−0.580786	+	0.580786i	0.354333	+	0.935119i	$0.384708\pi$
$662$			3.90067e11i			2.03099i
$663$	1.11348e10	−	6.05866e9i	0.0576272	−	0.0313561i
$664$	−5.98974e11			−3.08131
$665$	1.00193e10	+	1.00193e10i	0.0512331	+	0.0512331i
$666$	−1.70652e10			−0.0867388
$667$		−	6.90733e10i		−	0.348985i
$668$	1.05728e11	+	1.05728e11i	0.530989	+	0.530989i
$669$	1.79090e11	+	1.79090e11i	0.894061	+	0.894061i
$670$	5.23025e11	−	5.23025e11i	2.59551	−	2.59551i
$671$	−1.50342e9	+	1.50342e9i	−0.00741637	+	0.00741637i
$672$	−3.96191e11			−1.94280
$673$			1.07689e11i			0.524943i	0.964940	+	0.262472i	$0.0845376\pi$
$673$			1.07689e11i			0.524943i	−0.964940	+	0.262472i	$0.915462\pi$
$674$	−3.53540e11	+	3.53540e11i	−1.71316	+	1.71316i
$675$			3.12607e11i			1.50586i
$676$	−4.65414e11	−	3.01055e11i	−2.22870	−	1.44165i
$677$	1.69059e11			0.804793			0.402396	−	0.915466i	$-0.368177\pi$
$677$	1.69059e11			0.804793			0.402396	+	0.915466i	$0.368177\pi$
$678$	1.77528e11	+	1.77528e11i	0.840131	+	0.840131i
$679$	1.35692e11			0.638375
$680$		−	6.89383e10i		−	0.322422i
$681$	−9.96780e10	−	9.96780e10i	−0.463458	−	0.463458i
$682$	−7.44028e9	−	7.44028e9i	−0.0343916	−	0.0343916i
$683$	−5.19296e10	+	5.19296e10i	−0.238634	+	0.238634i	−0.816284	−	0.577650i	$-0.803970\pi$
$683$	−5.19296e10	+	5.19296e10i	−0.238634	+	0.238634i	0.577650	+	0.816284i	$0.303970\pi$
$684$	1.87845e9	−	1.87845e9i	0.00858173	−	0.00858173i
$685$	−2.64780e11			−1.20260
$686$		−	4.03808e11i		−	1.82339i
$687$	1.17844e11	−	1.17844e11i	0.529028	−	0.529028i
$688$		−	2.50724e11i		−	1.11903i
$689$	1.78716e11	+	3.28449e11i	0.793023	+	1.45744i
$690$	2.23172e11			0.984564
$691$	−2.33370e11	−	2.33370e11i	−1.02361	−	1.02361i	−0.999715	−	0.0238933i	$-0.992394\pi$
$691$	−2.33370e11	−	2.33370e11i	−1.02361	−	1.02361i	−0.0238933	−	0.999715i	$-0.507606\pi$
$692$	4.19570e10			0.182970
$693$			3.13685e8i			0.00136007i
$694$	−5.38017e11	−	5.38017e11i	−2.31931	−	2.31931i
$695$	3.36576e11	+	3.36576e11i	1.44259	+	1.44259i
$696$	6.00789e11	−	6.00789e11i	2.56027	−	2.56027i
$697$	−1.28958e10	+	1.28958e10i	−0.0546406	+	0.0546406i
$698$	4.08292e11			1.72008
$699$		−	3.46194e11i		−	1.45014i
$700$	−3.98401e11	+	3.98401e11i	−1.65931	+	1.65931i
$701$		−	1.62006e11i		−	0.670900i	−0.942058	−	0.335450i	$-0.891112\pi$
$701$		−	1.62006e11i		−	0.670900i	0.942058	−	0.335450i	$-0.108888\pi$
$702$	1.27416e11	−	4.31574e11i	0.524658	−	1.77708i
$703$	−1.53874e10			−0.0630007
$704$	2.13818e10	+	2.13818e10i	0.0870472	+	0.0870472i
$705$	−6.05907e11			−2.45273
$706$		−	1.86559e11i		−	0.750925i
$707$	−1.03541e11	−	1.03541e11i	−0.414413	−	0.414413i
$708$	3.83242e11	+	3.83242e11i	1.52525	+	1.52525i
$709$	7.20230e10	−	7.20230e10i	0.285027	−	0.285027i	−0.550083	−	0.835110i	$-0.685404\pi$
$709$	7.20230e10	−	7.20230e10i	0.285027	−	0.285027i	0.835110	+	0.550083i	$0.185404\pi$
$710$	−4.75431e11	+	4.75431e11i	−1.87091	+	1.87091i
$711$	−1.86432e9			−0.00729530
$712$			1.51267e12i			5.88607i
$713$	3.49905e10	−	3.49905e10i	0.135392	−	0.135392i
$714$			1.85478e10i			0.0713675i
$715$	8.31353e9	+	1.52788e10i	0.0318098	+	0.0584610i
$716$	4.68694e11			1.78335
$717$	−1.52166e11	−	1.52166e11i	−0.575760	−	0.575760i
$718$	−2.31078e11			−0.869482
$719$		−	2.25844e11i		−	0.845072i	−0.906346	−	0.422536i	$-0.861140\pi$
$719$		−	2.25844e11i		−	0.845072i	0.906346	−	0.422536i	$-0.138860\pi$
$720$	5.90928e10	+	5.90928e10i	0.219889	+	0.219889i
$721$	1.50875e11	+	1.50875e11i	0.558312	+	0.558312i
$722$	−3.64982e11	+	3.64982e11i	−1.34315	+	1.34315i
$723$	2.43176e11	−	2.43176e11i	0.889955	−	0.889955i
$724$	−5.78237e11			−2.10451
$725$		−	4.77906e11i		−	1.72978i
$726$	−3.85477e11	+	3.85477e11i	−1.38756	+	1.38756i
$727$			3.72838e11i			1.33470i	0.744746	+	0.667348i	$0.232571\pi$
$727$			3.72838e11i			1.33470i	−0.744746	+	0.667348i	$0.767429\pi$
$728$	4.44010e11	−	2.41595e11i	1.58077	−	0.860126i
$729$	2.64416e11			0.936218
$730$	1.01816e11	+	1.01816e11i	0.358530	+	0.358530i
$731$	−6.01162e9			−0.0210534
$732$		−	1.97341e11i		−	0.687341i
$733$	4.31522e10	+	4.31522e10i	0.149481	+	0.149481i	0.777886	−	0.628405i	$-0.216292\pi$
$733$	4.31522e10	+	4.31522e10i	0.149481	+	0.149481i	−0.628405	+	0.777886i	$0.716292\pi$
$734$	−1.32436e11	−	1.32436e11i	−0.456270	−	0.456270i
$735$	−2.29290e11	+	2.29290e11i	−0.785661	+	0.785661i
$736$	−2.15924e11	+	2.15924e11i	−0.735850	+	0.735850i
$737$	1.47651e10			0.0500456
$738$		−	3.94126e10i		−	0.132865i
$739$	2.19357e11	−	2.19357e11i	0.735485	−	0.735485i	−0.236216	−	0.971701i	$-0.575907\pi$
$739$	2.19357e11	−	2.19357e11i	0.735485	−	0.735485i	0.971701	+	0.236216i	$0.0759072\pi$
$740$		−	1.00569e12i		−	3.35381i
$741$	−6.99434e9	+	2.36907e10i	−0.0231992	+	0.0785786i
$742$	−5.47116e11			−1.80494
$743$	−3.11348e11	−	3.11348e11i	−1.02162	−	1.02162i	−0.999761	−	0.0218612i	$-0.993041\pi$
$743$	−3.11348e11	−	3.11348e11i	−1.02162	−	1.02162i	−0.0218612	−	0.999761i	$-0.506959\pi$
$744$	6.08684e11			1.98655
$745$		−	2.59881e11i		−	0.843624i
$746$	7.01390e11	+	7.01390e11i	2.26467	+	2.26467i
$747$	−1.23105e10	−	1.23105e10i	−0.0395362	−	0.0395362i
$748$	1.56126e9	−	1.56126e9i	0.00498735	−	0.00498735i
$749$	−1.83119e11	+	1.83119e11i	−0.581844	+	0.581844i
$750$	5.50197e11			1.73890
$751$		−	4.29225e10i		−	0.134935i	−0.997721	−	0.0674676i	$-0.978508\pi$
$751$		−	4.29225e10i		−	0.134935i	0.997721	−	0.0674676i	$-0.0214919\pi$
$752$	1.14462e12	−	1.14462e12i	3.57922	−	3.57922i
$753$		−	3.61524e11i		−	1.12449i
$754$	−1.94791e11	+	6.59780e11i	−0.602675	+	2.04133i
$755$	−4.12847e11			−1.27058
$756$	3.38169e11	+	3.38169e11i	1.03525	+	1.03525i
$757$	4.54071e10			0.138274			0.0691370	−	0.997607i	$-0.477975\pi$
$757$	4.54071e10			0.138274			0.0691370	+	0.997607i	$0.477975\pi$
$758$			5.85576e11i			1.77381i
$759$	3.15009e9	+	3.15009e9i	0.00949197	+	0.00949197i
$760$	9.49894e10	+	9.49894e10i	0.284722	+	0.284722i
$761$	3.88630e11	−	3.88630e11i	1.15877	−	1.15877i	0.174032	−	0.984740i	$-0.444321\pi$
$761$	3.88630e11	−	3.88630e11i	1.15877	−	1.15877i	0.984740	−	0.174032i	$-0.0556795\pi$
$762$	−4.40777e11	+	4.40777e11i	−1.30737	+	1.30737i
$763$	6.73077e10			0.198594
$764$		−	4.69791e10i		−	0.137889i
$765$	1.41687e9	−	1.41687e9i	0.00413698	−	0.00413698i
$766$			1.05021e12i			3.05042i
$767$	−2.62312e11	−	7.74438e10i	−0.757942	−	0.223772i
$768$	−5.36105e11			−1.54101
$769$	−3.38675e11	−	3.38675e11i	−0.968452	−	0.968452i	0.0310653	−	0.999517i	$-0.490110\pi$
$769$	−3.38675e11	−	3.38675e11i	−0.968452	−	0.968452i	−0.999517	+	0.0310653i	$0.990110\pi$
$770$	−2.54508e10			−0.0724001
$771$			4.52027e11i			1.27923i
$772$	−1.67817e11	−	1.67817e11i	−0.472462	−	0.472462i
$773$	3.10254e11	+	3.10254e11i	0.868958	+	0.868958i	0.992357	−	0.123399i	$-0.0393794\pi$
$773$	3.10254e11	+	3.10254e11i	0.868958	+	0.868958i	−0.123399	+	0.992357i	$0.539379\pi$
$774$	9.18650e9	−	9.18650e9i	0.0255968	−	0.0255968i
$775$	2.42093e11	−	2.42093e11i	0.671082	−	0.671082i
$776$	1.28645e12			3.54769
$777$			1.68642e11i			0.462681i
$778$	8.11614e11	−	8.11614e11i	2.21529	−	2.21529i
$779$		−	3.55379e10i		−	0.0965032i
$780$	−1.54838e12	−	4.57137e11i	−4.18310	−	1.23500i
$781$	−1.34215e10			−0.0360741
$782$	1.01086e10	+	1.01086e10i	0.0270310	+	0.0270310i
$783$	−4.05654e11			−1.07922
$784$		−	8.66300e11i		−	2.29300i
$785$	−1.19521e11	−	1.19521e11i	−0.314749	−	0.314749i
$786$	−5.50773e11	−	5.50773e11i	−1.44305	−	1.44305i
$787$	−9.04871e10	+	9.04871e10i	−0.235878	+	0.235878i	−0.815141	−	0.579263i	$-0.803341\pi$
$787$	−9.04871e10	+	9.04871e10i	−0.235878	+	0.235878i	0.579263	+	0.815141i	$0.303341\pi$
$788$	1.90211e11	−	1.90211e11i	0.493321	−	0.493321i
$789$	7.47886e11			1.92987
$790$		−	1.51262e11i		−	0.388348i
$791$	9.52111e10	−	9.52111e10i	0.243210	−	0.243210i
$792$			2.97394e9i			0.00755842i
$793$	4.75965e10	+	8.74742e10i	0.120360	+	0.221201i
$794$	−1.14662e12			−2.88494
$795$	7.70104e11	+	7.70104e11i	1.92788	+	1.92788i
$796$	−1.40995e11			−0.351198
$797$			5.52731e11i			1.36987i	0.728602	+	0.684937i	$0.240170\pi$
$797$			5.52731e11i			1.36987i	−0.728602	+	0.684937i	$0.759830\pi$
$798$	−2.55569e10	−	2.55569e10i	−0.0630226	−	0.0630226i
$799$	−2.74445e10	−	2.74445e10i	−0.0673392	−	0.0673392i
$800$	−1.49394e12	+	1.49394e12i	−3.64731	+	3.64731i
$801$	−3.10896e10	+	3.10896e10i	−0.0755239	+	0.0755239i
$802$	1.53067e11			0.369985
$803$			2.87428e9i			0.00691301i
$804$	−9.69038e11	+	9.69038e11i	−2.31908	+	2.31908i
$805$		−	1.19691e11i		−	0.285022i
$806$	−4.32900e11	+	2.35550e11i	−1.02576	+	0.558139i
$807$	2.17532e11			0.512895
$808$	−9.81632e11	−	9.81632e11i	−2.30305	−	2.30305i
$809$	5.92169e11			1.38246			0.691228	−	0.722637i	$-0.257070\pi$
$809$	5.92169e11			1.38246			0.691228	+	0.722637i	$0.257070\pi$
$810$		−	1.38611e12i		−	3.22001i
$811$	−1.31991e10	−	1.31991e10i	−0.0305114	−	0.0305114i	0.691686	−	0.722198i	$-0.256868\pi$
$811$	−1.31991e10	−	1.31991e10i	−0.0305114	−	0.0305114i	−0.722198	+	0.691686i	$0.756868\pi$
$812$	−5.16984e11	−	5.16984e11i	−1.18919	−	1.18919i
$813$	−4.27352e11	+	4.27352e11i	−0.978191	+	0.978191i
$814$	1.95435e10	−	1.95435e10i	0.0445148	−	0.0445148i
$815$	−1.22944e12			−2.78662
$816$			9.86386e10i			0.222478i
$817$	8.28335e9	−	8.28335e9i	0.0185917	−	0.0185917i
$818$			3.43619e11i			0.767475i
$819$	1.40910e10	+	4.16018e9i	0.0313190	+	0.00924649i
$820$	2.32269e12			5.13731
$821$	4.27080e11	+	4.27080e11i	0.940020	+	0.940020i	0.998300	−	0.0582807i	$-0.0185619\pi$
$821$	4.27080e11	+	4.27080e11i	0.940020	+	0.940020i	−0.0582807	+	0.998300i	$0.518562\pi$
$822$	6.75392e11			1.47934
$823$		−	2.42038e11i		−	0.527574i	−0.964581	−	0.263787i	$-0.915028\pi$
$823$		−	2.42038e11i		−	0.527574i	0.964581	−	0.263787i	$-0.0849716\pi$
$824$	1.43040e12	+	1.43040e12i	3.10276	+	3.10276i
$825$	2.17949e10	+	2.17949e10i	0.0470479	+	0.0470479i
$826$	2.82975e11	−	2.82975e11i	0.607894	−	0.607894i
$827$	−3.93278e11	+	3.93278e11i	−0.840771	+	0.840771i	−0.988959	−	0.148188i	$-0.952656\pi$
$827$	−3.93278e11	+	3.93278e11i	−0.840771	+	0.840771i	0.148188	+	0.988959i	$0.452656\pi$
$828$	−2.24401e10			−0.0477423
$829$			7.05049e11i			1.49280i	0.665499	+	0.746399i	$0.268219\pi$
$829$			7.05049e11i			1.49280i	−0.665499	+	0.746399i	$0.731781\pi$
$830$	9.98816e11	−	9.98816e11i	2.10462	−	2.10462i
$831$		−	2.37521e11i		−	0.498079i
$832$	1.24407e12	−	6.76922e11i	2.59627	−	1.41268i
$833$	−2.07713e10			−0.0431404
$834$	−8.58526e11	−	8.58526e11i	−1.77455	−	1.77455i
$835$	−2.19769e11			−0.452085
$836$			4.30250e9i			0.00880838i
$837$	−2.05492e11	−	2.05492e11i	−0.418691	−	0.418691i
$838$	4.90729e11	+	4.90729e11i	0.995097	+	0.995097i
$839$	5.54376e10	−	5.54376e10i	0.111881	−	0.111881i	−0.648950	−	0.760831i	$-0.724792\pi$
$839$	5.54376e10	−	5.54376e10i	0.111881	−	0.111881i	0.760831	+	0.648950i	$0.224792\pi$
$840$	1.04106e12	−	1.04106e12i	2.09102	−	2.09102i
$841$	1.19907e11			0.239697
$842$		−	6.32715e11i		−	1.25881i
$843$	7.83115e10	−	7.83115e10i	0.155066	−	0.155066i
$844$		−	1.73070e9i		−	0.00341076i
$845$	7.96598e11	−	1.70819e11i	1.56247	−	0.335051i
$846$	8.38770e10			0.163743
$847$	2.06738e11	+	2.06738e11i	0.401686	+	0.401686i
$848$	−2.90960e12			−5.62665
$849$			3.53440e10i			0.0680276i
$850$	6.99394e10	+	6.99394e10i	0.133982	+	0.133982i
$851$	9.19099e10	+	9.19099e10i	0.175244	+	0.175244i
$852$	8.80857e11	−	8.80857e11i	1.67166	−	1.67166i
$853$	9.32541e10	−	9.32541e10i	0.176146	−	0.176146i	−0.613528	−	0.789673i	$-0.710250\pi$
$853$	9.32541e10	−	9.32541e10i	0.176146	−	0.176146i	0.789673	+	0.613528i	$0.210250\pi$
$854$	−1.45711e11			−0.273943
$855$			3.90458e9i			0.00730650i
$856$	−1.73609e12	+	1.73609e12i	−3.23353	+	3.23353i
$857$		−	1.87150e11i		−	0.346949i	−0.984838	−	0.173474i	$-0.944501\pi$
$857$		−	1.87150e11i		−	0.346949i	0.984838	−	0.173474i	$-0.0554994\pi$
$858$	−2.12059e10	−	3.89728e10i	−0.0391298	−	0.0719138i
$859$	−3.60656e11			−0.662400			−0.331200	−	0.943561i	$-0.607454\pi$
$859$	−3.60656e11			−0.662400			−0.331200	+	0.943561i	$0.607454\pi$
$860$	5.41384e11	+	5.41384e11i	0.989719	+	0.989719i
$861$	−3.89485e11			−0.708726
$862$			1.33057e12i			2.40995i
$863$	−4.53196e11	−	4.53196e11i	−0.817039	−	0.817039i	0.168639	−	0.985678i	$-0.446063\pi$
$863$	−4.53196e11	−	4.53196e11i	−0.817039	−	0.817039i	−0.985678	+	0.168639i	$0.946063\pi$
$864$	1.26808e12	+	1.26808e12i	2.27557	+	2.27557i
$865$	−4.36063e10	+	4.36063e10i	−0.0778905	+	0.0778905i
$866$	−4.91299e11	+	4.91299e11i	−0.873522	+	0.873522i
$867$	−5.78657e11			−1.02411
$868$		−	5.23777e11i		−	0.922715i
$869$	2.13507e9	−	2.13507e9i	0.00374398	−	0.00374398i
$870$			2.00369e12i			3.49746i
$871$	1.95819e11	−	6.63262e11i	0.340237	−	1.15242i
$872$	6.38121e11			1.10367
$873$	2.64400e10	+	2.64400e10i	0.0455203	+	0.0455203i
$874$	−2.78570e10			−0.0477407
$875$		−	2.95080e11i		−	0.503394i
$876$	−1.88640e11	−	1.88640e11i	−0.320345	−	0.320345i
$877$	−3.62151e11	−	3.62151e11i	−0.612197	−	0.612197i	0.331321	−	0.943518i	$-0.392506\pi$
$877$	−3.62151e11	−	3.62151e11i	−0.612197	−	0.612197i	−0.943518	+	0.331321i	$0.892506\pi$
$878$	8.46252e11	−	8.46252e11i	1.42404	−	1.42404i
$879$	3.97043e11	−	3.97043e11i	0.665093	−	0.665093i
$880$	−1.35349e11			−0.225697
$881$			5.54599e11i			0.920610i	0.887761	+	0.460305i	$0.152260\pi$
$881$			5.54599e11i			0.920610i	−0.887761	+	0.460305i	$0.847740\pi$
$882$	3.17411e10	−	3.17411e10i	0.0524502	−	0.0524502i
$883$		−	1.02832e12i		−	1.69155i	−0.533539	−	0.845775i	$-0.679138\pi$
$883$		−	1.02832e12i		−	1.69155i	0.533539	−	0.845775i	$-0.320862\pi$
$884$	−4.94276e10	−	9.08395e10i	−0.0809395	−	0.148753i
$885$	−7.96614e11			−1.29860
$886$	−4.76078e11	−	4.76078e11i	−0.772580	−	0.772580i
$887$	−3.28797e11			−0.531170			−0.265585	−	0.964087i	$-0.585565\pi$
$887$	−3.28797e11			−0.531170			−0.265585	+	0.964087i	$0.585565\pi$
$888$			1.59884e12i			2.57130i
$889$	2.36396e11	+	2.36396e11i	0.378472	+	0.378472i
$890$	−2.52245e12	−	2.52245e12i	−4.02034	−	4.02034i
$891$	1.95650e10	−	1.95650e10i	0.0310434	−	0.0310434i
$892$	1.46105e12	−	1.46105e12i	2.30784	−	2.30784i
$893$	7.56309e10			0.118931
$894$			6.62896e11i			1.03776i
$895$	−4.87118e11	+	4.87118e11i	−0.759175	+	0.759175i
$896$			8.54607e11i			1.32597i
$897$	1.83283e11	−	9.97279e10i	0.283108	−	0.154045i
$898$	−6.27641e10			−0.0965174
$899$	3.14151e11	+	3.14151e11i	0.480950	+	0.480950i
$900$	−1.55259e11			−0.236640
$901$			6.97635e10i			0.105859i
$902$	4.51364e10	+	4.51364e10i	0.0681868	+	0.0681868i
$903$	−9.07832e10	−	9.07832e10i	−0.136538	−	0.136538i
$904$	9.02664e11	−	9.02664e11i	1.35161	−	1.35161i
$905$	6.00967e11	−	6.00967e11i	0.895893	−	0.895893i
$906$	1.05308e12			1.56296
$907$			1.16707e12i			1.72452i	0.506464	+	0.862261i	$0.330952\pi$
$907$			1.16707e12i			1.72452i	−0.506464	+	0.862261i	$0.669048\pi$
$908$	−8.13191e11	+	8.13191e11i	−1.19632	+	1.19632i
$909$		−	4.03504e10i		−	0.0591006i
$910$	−3.37537e11	+	1.14328e12i	−0.492216	+	1.66719i
$911$	1.42075e11			0.206273			0.103137	−	0.994667i	$-0.467112\pi$
$911$	1.42075e11			0.206273			0.103137	+	0.994667i	$0.467112\pi$
$912$	−1.35913e11	−	1.35913e11i	−0.196464	−	0.196464i
$913$	2.81967e10			0.0405803
$914$		−	1.91341e12i		−	2.74173i
$915$	2.05098e11	+	2.05098e11i	0.292602	+	0.292602i
$916$	−9.61389e11	−	9.61389e11i	−1.36558	−	1.36558i
$917$	−2.95389e11	+	2.95389e11i	−0.417751	+	0.417751i
$918$	5.93656e10	−	5.93656e10i	0.0835920	−	0.0835920i
$919$	6.85305e11			0.960775			0.480387	−	0.877056i	$-0.340496\pi$
$919$	6.85305e11			0.960775			0.480387	+	0.877056i	$0.340496\pi$
$920$		−	1.13475e12i		−	1.58398i
$921$	1.90442e11	−	1.90442e11i	0.264681	−	0.264681i
$922$			3.28503e11i			0.454586i
$923$	−1.78000e11	+	6.02906e11i	−0.245252	+	0.830698i
$924$	4.71542e10			0.0646893
$925$	6.35908e11	+	6.35908e11i	0.868616	+	0.868616i
$926$	2.35038e12			3.19664
$927$			5.87970e10i			0.0796226i
$928$	−1.93861e12	−	1.93861e12i	−2.61395	−	2.61395i
$929$	6.19559e11	+	6.19559e11i	0.831802	+	0.831802i	0.987763	−	0.155962i	$-0.0498476\pi$
$929$	6.19559e11	+	6.19559e11i	0.831802	+	0.831802i	−0.155962	+	0.987763i	$0.549848\pi$
$930$	−1.01501e12	+	1.01501e12i	−1.35687	+	1.35687i
$931$	2.86206e10	−	2.86206e10i	0.0380960	−	0.0380960i
$932$	−2.82431e12			−3.74325
$933$		−	1.37560e12i		−	1.81537i
$934$	2.87206e11	−	2.87206e11i	0.377404	−	0.377404i
$935$			3.24527e9i			0.00424624i
$936$	1.33592e11	+	3.94412e10i	0.174052	+	0.0513863i
$937$	−1.22051e11			−0.158337			−0.0791686	−	0.996861i	$-0.525227\pi$
$937$	−1.22051e11			−0.158337			−0.0791686	+	0.996861i	$0.525227\pi$
$938$	7.15510e11	+	7.15510e11i	0.924282	+	0.924282i
$939$	5.95008e11			0.765351
$940$			4.94309e12i			6.33122i
$941$	−6.18228e10	−	6.18228e10i	−0.0788479	−	0.0788479i	0.666583	−	0.745431i	$-0.267756\pi$
$941$	−6.18228e10	−	6.18228e10i	−0.0788479	−	0.0788479i	−0.745431	+	0.666583i	$0.767756\pi$
$942$	3.04870e11	+	3.04870e11i	0.387178	+	0.387178i
$943$	−2.12269e11	+	2.12269e11i	−0.268436	+	0.268436i
$944$	1.50488e12	−	1.50488e12i	1.89502	−	1.89502i
$945$	−7.02923e11			−0.881416
$946$			2.10412e10i			0.0262728i
$947$	−6.33654e11	+	6.33654e11i	−0.787866	+	0.787866i	−0.981144	−	0.193278i	$-0.938088\pi$
$947$	−6.33654e11	+	6.33654e11i	−0.787866	+	0.787866i	0.193278	+	0.981144i	$0.438088\pi$
$948$			2.80252e11i			0.346988i
$949$	1.29116e11	+	3.81196e10i	0.159189	+	0.0469984i
$950$	−1.92738e11			−0.236631
$951$	−9.72618e11	−	9.72618e11i	−1.18911	−	1.18911i
$952$	9.43091e10			0.114817
$953$		−	5.68408e11i		−	0.689110i	−0.938766	−	0.344555i	$-0.888030\pi$
$953$		−	5.68408e11i		−	0.689110i	0.938766	−	0.344555i	$-0.111970\pi$
$954$	−1.06607e11	−	1.06607e11i	−0.128704	−	0.128704i
$955$	4.88258e10	+	4.88258e10i	0.0586997	+	0.0586997i
$956$	−1.24140e12	+	1.24140e12i	−1.48621	+	1.48621i
$957$	−2.82822e10	+	2.82822e10i	−0.0337182	+	0.0337182i
$958$	2.90760e12			3.45202
$959$		−	3.62225e11i		−	0.428256i
$960$	2.91692e12	−	2.91692e12i	3.43432	−	3.43432i
$961$		−	5.34612e11i		−	0.626823i
$962$	−6.18721e11	−	1.13710e12i	−0.722428	−	1.32770i
$963$	−7.13626e10			−0.0829785
$964$	−1.98387e12	−	1.98387e12i	−2.29724	−	2.29724i
$965$	3.48828e11			0.402255
$966$			3.05305e11i			0.350610i
$967$	7.72254e11	+	7.72254e11i	0.883190	+	0.883190i	0.993858	−	0.110667i	$-0.0352988\pi$
$967$	7.72254e11	+	7.72254e11i	0.883190	+	0.883190i	−0.110667	+	0.993858i	$0.535299\pi$
$968$	1.96001e12	+	1.96001e12i	2.23232	+	2.23232i
$969$	−3.25879e9	+	3.25879e9i	−0.00369625	+	0.00369625i
$970$	−2.14521e12	+	2.14521e12i	−2.42317	+	2.42317i
$971$	−1.17024e11			−0.131643			−0.0658217	−	0.997831i	$-0.520967\pi$
$971$	−1.17024e11			−0.131643			−0.0658217	+	0.997831i	$0.520967\pi$
$972$			2.71596e11i			0.304269i
$973$	−4.60443e11	+	4.60443e11i	−0.513717	+	0.513717i
$974$			1.07172e12i			1.19082i
$975$	1.26810e12	−	6.90000e11i	1.40325	−	0.763538i
$976$	−7.74899e11			−0.853977
$977$	−1.12272e12	−	1.12272e12i	−1.23224	−	1.23224i	−0.963102	−	0.269138i	$-0.913261\pi$
$977$	−1.12272e12	−	1.12272e12i	−1.23224	−	1.23224i	−0.269138	−	0.963102i	$-0.586739\pi$
$978$	3.13603e12			3.42787
$979$		−	7.12092e10i		−	0.0775185i
$980$	1.87059e12	+	1.87059e12i	2.02802	+	2.02802i
$981$	1.31151e10	+	1.31151e10i	0.0141611	+	0.0141611i
$982$	2.66026e11	−	2.66026e11i	0.286074	−	0.286074i
$983$	−6.78634e11	+	6.78634e11i	−0.726811	+	0.726811i	−0.969983	−	0.243172i	$-0.921812\pi$
$983$	−6.78634e11	+	6.78634e11i	−0.726811	+	0.726811i	0.243172	+	0.969983i	$0.421812\pi$
$984$	−3.69257e12			−3.93866
$985$			3.95375e11i			0.420015i
$986$	−9.07568e10	+	9.07568e10i	−0.0960221	+	0.0960221i
$987$		−	8.28893e11i		−	0.873434i
$988$	1.93273e11	+	5.70610e10i	0.202835	+	0.0598842i
$989$	−9.89536e10			−0.103430
$990$	−4.95917e9	−	4.95917e9i	−0.00516260	−	0.00516260i
$991$	1.48575e12			1.54046			0.770231	−	0.637765i	$-0.220141\pi$
$991$	1.48575e12			1.54046			0.770231	+	0.637765i	$0.220141\pi$
$992$		−	1.96408e12i		−	2.02821i
$993$	7.51107e11	+	7.51107e11i	0.772511	+	0.772511i
$994$	−6.50400e11	−	6.50400e11i	−0.666246	−	0.666246i
$995$	1.46538e11	−	1.46538e11i	0.149505	−	0.149505i
$996$	−1.85056e12	+	1.85056e12i	−1.88047	+	1.88047i
$997$	1.65986e11			0.167992			0.0839962	−	0.996466i	$-0.473232\pi$
$997$	1.65986e11			0.167992			0.0839962	+	0.996466i	$0.473232\pi$
$998$		−	1.51871e12i		−	1.53092i
$999$	5.39769e11	−	5.39769e11i	0.541933	−	0.541933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.d.a.8.1	yes	18
3.2	odd	2		117.9.j.a.73.9		18
13.5	odd	4	inner	13.9.d.a.5.1	✓	18
39.5	even	4		117.9.j.a.109.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.d.a.5.1	✓	18	13.5	odd	4	inner
13.9.d.a.8.1	yes	18	1.1	even	1	trivial
117.9.j.a.73.9		18	3.2	odd	2
117.9.j.a.109.9		18	39.5	even	4

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.6276 - 21.6276i) q^{2} -83.2917 q^{3} +679.508i q^{4} +(-706.219 - 706.219i) q^{5} +(1801.40 + 1801.40i) q^{6} +(966.123 - 966.123i) q^{7} +(9159.48 - 9159.48i) q^{8} +376.504 q^{9} +O(q^{10})\)	\(q+(-21.6276 - 21.6276i) q^{2} -83.2917 q^{3} +679.508i q^{4} +(-706.219 - 706.219i) q^{5} +(1801.40 + 1801.40i) q^{6} +(966.123 - 966.123i) q^{7} +(9159.48 - 9159.48i) q^{8} +376.504 q^{9} +30547.7i q^{10} +(-431.183 + 431.183i) q^{11} -56597.4i q^{12} +(13650.7 + 25087.6i) q^{13} -41789.9 q^{14} +(58822.2 + 58822.2i) q^{15} -222241. q^{16} +5328.69i q^{17} +(-8142.89 - 8142.89i) q^{18} +(-7342.35 - 7342.35i) q^{19} +(479882. - 479882. i) q^{20} +(-80470.0 + 80470.0i) q^{21} +18650.9 q^{22} +87712.3i q^{23} +(-762908. + 762908. i) q^{24} +606866. i q^{25} +(247354. - 837818. i) q^{26} +515117. q^{27} +(656489. + 656489. i) q^{28} -787498. q^{29} -2.54437e6i q^{30} +(-398923. - 398923. i) q^{31} +(2.46173e6 + 2.46173e6i) q^{32} +(35913.9 - 35913.9i) q^{33} +(115247. - 115247. i) q^{34} -1.36459e6 q^{35} +255838. i q^{36} +(1.04786e6 - 1.04786e6i) q^{37} +317595. i q^{38} +(-1.13699e6 - 2.08959e6i) q^{39} -1.29372e7 q^{40} +(2.42006e6 + 2.42006e6i) q^{41} +3.48075e6 q^{42} +1.12816e6i q^{43} +(-292992. - 292992. i) q^{44} +(-265894. - 265894. i) q^{45} +(1.89701e6 - 1.89701e6i) q^{46} +(-5.15032e6 + 5.15032e6i) q^{47} +1.85109e7 q^{48} +3.89801e6i q^{49} +(1.31251e7 - 1.31251e7i) q^{50} -443836. i q^{51} +(-1.70473e7 + 9.27576e6i) q^{52} +1.30921e7 q^{53} +(-1.11408e7 - 1.11408e7i) q^{54} +609019. q^{55} -1.76984e7i q^{56} +(611556. + 611556. i) q^{57} +(1.70317e7 + 1.70317e7i) q^{58} +(-6.77137e6 + 6.77137e6i) q^{59} +(-3.99702e7 + 3.99702e7i) q^{60} +3.48674e6 q^{61} +1.72555e7i q^{62} +(363749. - 363749. i) q^{63} -4.95888e7i q^{64} +(8.07699e6 - 2.73577e7i) q^{65} -1.55347e6 q^{66} +(-1.71216e7 - 1.71216e7i) q^{67} -3.62089e6 q^{68} -7.30570e6i q^{69} +(2.95128e7 + 2.95128e7i) q^{70} +(1.55636e7 + 1.55636e7i) q^{71} +(3.44858e6 - 3.44858e6i) q^{72} +(3.33302e6 - 3.33302e6i) q^{73} -4.53253e7 q^{74} -5.05469e7i q^{75} +(4.98919e6 - 4.98919e6i) q^{76} +833151. i q^{77} +(-2.06025e7 + 6.97833e7i) q^{78} -4.95167e6 q^{79} +(1.56951e8 + 1.56951e8i) q^{80} -4.53752e7 q^{81} -1.04680e8i q^{82} +(-3.26970e7 - 3.26970e7i) q^{83} +(-5.46801e7 - 5.46801e7i) q^{84} +(3.76322e6 - 3.76322e6i) q^{85} +(2.43995e7 - 2.43995e7i) q^{86} +6.55921e7 q^{87} +7.89882e6i q^{88} +(-8.25743e7 + 8.25743e7i) q^{89} +1.15013e7i q^{90} +(3.74260e7 + 1.10495e7i) q^{91} -5.96012e7 q^{92} +(3.32270e7 + 3.32270e7i) q^{93} +2.22779e8 q^{94} +1.03706e7i q^{95} +(-2.05041e8 - 2.05041e8i) q^{96} +(7.02251e7 + 7.02251e7i) q^{97} +(8.43048e7 - 8.43048e7i) q^{98} +(-162342. + 162342. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20} + 279416 q^{21} - 977312 q^{22} - 986232 q^{24} + 2952238 q^{26} + 364916 q^{27} + 4497084 q^{28} - 2479024 q^{29} - 1892664 q^{31} + 947212 q^{32} + 1368644 q^{33} - 531576 q^{34} - 2918284 q^{35} - 8343978 q^{37} - 1101268 q^{39} - 12691908 q^{40} + 1140178 q^{41} + 15137212 q^{42} - 3867188 q^{44} + 6565370 q^{45} + 2006148 q^{46} - 13368572 q^{47} - 10106716 q^{48} + 37369598 q^{50} - 14821220 q^{52} + 50561348 q^{53} - 4995928 q^{54} + 76994128 q^{55} - 34755760 q^{57} + 22505716 q^{58} + 2127976 q^{59} - 161134196 q^{60} - 52016516 q^{61} - 15210112 q^{63} + 10413082 q^{65} - 51097328 q^{66} + 960292 q^{67} + 283187508 q^{68} - 166635032 q^{70} + 67412140 q^{71} + 96846900 q^{72} - 145213226 q^{73} - 233620024 q^{74} - 150533640 q^{76} + 212071160 q^{78} - 76829120 q^{79} + 524889520 q^{80} + 293280674 q^{81} - 241951556 q^{83} + 345496184 q^{84} + 260737764 q^{85} - 579480384 q^{86} - 618300656 q^{87} - 89187110 q^{89} + 232660948 q^{91} - 122690376 q^{92} + 669553400 q^{93} + 1069637380 q^{94} - 1324092400 q^{96} + 331183146 q^{97} + 588677614 q^{98} - 1125076336 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

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