LMFDB - Embedded newform 12.9.d.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,9,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	12.d (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:	$4.88854332073$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 40x^{6} - 395x^{5} + 403x^{4} + 8998x^{3} + 74584x^{2} + 217224x + 269328 $ x^8 - 3x^7 - 40x^6 - 395x^5 + 403x^4 + 8998x^3 + 74584x^2 + 217224*x + 269328
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.7
Root			$-3.64622 - 4.31154i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.9.d.a.7.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.6476 - 8.35123i) q^{2} +46.7654i q^{3} +(116.514 - 227.948i) q^{4} +904.196 q^{5} +(390.548 + 638.235i) q^{6} -888.085i q^{7} +(-313.513 - 4083.98i) q^{8} -2187.00 q^{9} +O(q^{10})$	\(q+(13.6476 - 8.35123i) q^{2} +46.7654i q^{3} +(116.514 - 227.948i) q^{4} +904.196 q^{5} +(390.548 + 638.235i) q^{6} -888.085i q^{7} +(-313.513 - 4083.98i) q^{8} -2187.00 q^{9} +(12340.1 - 7551.15i) q^{10} +14451.0i q^{11} +(10660.1 + 5448.82i) q^{12} -11609.0 q^{13} +(-7416.60 - 12120.2i) q^{14} +42285.1i q^{15} +(-38385.0 - 53118.4i) q^{16} -128520. q^{17} +(-29847.3 + 18264.1i) q^{18} +225611. i q^{19} +(105352. - 206110. i) q^{20} +41531.6 q^{21} +(120684. + 197222. i) q^{22} -441698. i q^{23} +(190989. - 14661.6i) q^{24} +426946. q^{25} +(-158435. + 96949.7i) q^{26} -102276. i q^{27} +(-202438. - 103474. i) q^{28} +115149. q^{29} +(353132. + 577090. i) q^{30} -201879. i q^{31} +(-967466. - 404376. i) q^{32} -675808. q^{33} +(-1.75398e6 + 1.07330e6i) q^{34} -803004. i q^{35} +(-254816. + 498523. i) q^{36} +2.01233e6 q^{37} +(1.88413e6 + 3.07905e6i) q^{38} -542901. i q^{39} +(-283478. - 3.69272e6i) q^{40} -2.61903e6 q^{41} +(566807. - 346840. i) q^{42} +1.75420e6i q^{43} +(3.29409e6 + 1.68375e6i) q^{44} -1.97748e6 q^{45} +(-3.68872e6 - 6.02811e6i) q^{46} +4.81199e6i q^{47} +(2.48410e6 - 1.79509e6i) q^{48} +4.97611e6 q^{49} +(5.82679e6 - 3.56553e6i) q^{50} -6.01026e6i q^{51} +(-1.35261e6 + 2.64626e6i) q^{52} +1.23892e6 q^{53} +(-854129. - 1.39582e6i) q^{54} +1.30666e7i q^{55} +(-3.62693e6 + 278427. i) q^{56} -1.05508e7 q^{57} +(1.57150e6 - 961634. i) q^{58} -1.14062e6i q^{59} +(9.63882e6 + 4.92680e6i) q^{60} -4.60247e6 q^{61} +(-1.68594e6 - 2.75517e6i) q^{62} +1.94224e6i q^{63} +(-1.65806e7 + 2.56077e6i) q^{64} -1.04968e7 q^{65} +(-9.22316e6 + 5.64383e6i) q^{66} -2.33742e7i q^{67} +(-1.49743e7 + 2.92958e7i) q^{68} +2.06561e7 q^{69} +(-6.70607e6 - 1.09591e7i) q^{70} -3.21271e7i q^{71} +(685654. + 8.93167e6i) q^{72} +4.89485e7 q^{73} +(2.74635e7 - 1.68054e7i) q^{74} +1.99663e7i q^{75} +(5.14277e7 + 2.62868e7i) q^{76} +1.28338e7 q^{77} +(-4.53389e6 - 7.40929e6i) q^{78} +4.23230e6i q^{79} +(-3.47076e7 - 4.80294e7i) q^{80} +4.78297e6 q^{81} +(-3.57434e7 + 2.18721e7i) q^{82} -1.99136e7i q^{83} +(4.83902e6 - 9.46707e6i) q^{84} -1.16207e8 q^{85} +(1.46497e7 + 2.39407e7i) q^{86} +5.38498e6i q^{87} +(5.90178e7 - 4.53060e6i) q^{88} +8.45908e6 q^{89} +(-2.69878e7 + 1.65144e7i) q^{90} +1.03098e7i q^{91} +(-1.00684e8 - 5.14639e7i) q^{92} +9.44096e6 q^{93} +(4.01860e7 + 6.56721e7i) q^{94} +2.03997e8i q^{95} +(1.89108e7 - 4.52439e7i) q^{96} -8.74596e7 q^{97} +(6.79119e7 - 4.15566e7i) q^{98} -3.16044e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9}+O(q^{10}) $ 8 * q + 6 * q^2 - 52 * q^4 - 336 * q^5 + 1134 * q^6 - 12960 * q^8 - 17496 * q^9	\( 8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9} + 36628 q^{10} - 11340 q^{12} - 2864 q^{13} + 52728 q^{14} + 99440 q^{16} - 193200 q^{17} - 13122 q^{18} + 335592 q^{20} + 121824 q^{21} - 556968 q^{22} + 221616 q^{24} - 579048 q^{25} + 21564 q^{26} - 594672 q^{28} + 2063472 q^{29} + 46980 q^{30} - 3602784 q^{32} - 920160 q^{33} + 1568476 q^{34} + 113724 q^{36} + 7470352 q^{37} + 3659400 q^{38} + 1749184 q^{40} - 8865456 q^{41} - 5288328 q^{42} + 2395920 q^{44} + 734832 q^{45} - 13649856 q^{46} + 10916208 q^{48} - 18923896 q^{49} + 14581842 q^{50} + 18592888 q^{52} + 8706672 q^{53} - 2480058 q^{54} - 45565632 q^{56} - 2325024 q^{57} - 8816444 q^{58} + 28348056 q^{60} + 13457296 q^{61} + 80783976 q^{62} + 1268864 q^{64} + 7293408 q^{65} - 51205608 q^{66} - 117288264 q^{68} - 8636544 q^{69} - 60373104 q^{70} + 28343520 q^{72} + 94738960 q^{73} + 119548428 q^{74} + 144621360 q^{76} - 56971392 q^{77} - 140630580 q^{78} - 163857888 q^{80} + 38263752 q^{81} - 188383460 q^{82} + 199712304 q^{84} - 201200416 q^{85} + 240327384 q^{86} + 156323520 q^{88} + 188992272 q^{89} - 80105436 q^{90} - 387657984 q^{92} - 54802656 q^{93} - 38749872 q^{94} + 246092256 q^{96} - 123291632 q^{97} + 691081830 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 52 * q^4 - 336 * q^5 + 1134 * q^6 - 12960 * q^8 - 17496 * q^9 + 36628 * q^10 - 11340 * q^12 - 2864 * q^13 + 52728 * q^14 + 99440 * q^16 - 193200 * q^17 - 13122 * q^18 + 335592 * q^20 + 121824 * q^21 - 556968 * q^22 + 221616 * q^24 - 579048 * q^25 + 21564 * q^26 - 594672 * q^28 + 2063472 * q^29 + 46980 * q^30 - 3602784 * q^32 - 920160 * q^33 + 1568476 * q^34 + 113724 * q^36 + 7470352 * q^37 + 3659400 * q^38 + 1749184 * q^40 - 8865456 * q^41 - 5288328 * q^42 + 2395920 * q^44 + 734832 * q^45 - 13649856 * q^46 + 10916208 * q^48 - 18923896 * q^49 + 14581842 * q^50 + 18592888 * q^52 + 8706672 * q^53 - 2480058 * q^54 - 45565632 * q^56 - 2325024 * q^57 - 8816444 * q^58 + 28348056 * q^60 + 13457296 * q^61 + 80783976 * q^62 + 1268864 * q^64 + 7293408 * q^65 - 51205608 * q^66 - 117288264 * q^68 - 8636544 * q^69 - 60373104 * q^70 + 28343520 * q^72 + 94738960 * q^73 + 119548428 * q^74 + 144621360 * q^76 - 56971392 * q^77 - 140630580 * q^78 - 163857888 * q^80 + 38263752 * q^81 - 188383460 * q^82 + 199712304 * q^84 - 201200416 * q^85 + 240327384 * q^86 + 156323520 * q^88 + 188992272 * q^89 - 80105436 * q^90 - 387657984 * q^92 - 54802656 * q^93 - 38749872 * q^94 + 246092256 * q^96 - 123291632 * q^97 + 691081830 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	13.6476	−	8.35123i	0.852975	−	0.521952i
$2$	13.6476	−	8.35123i	0.852975	−	0.521952i
$3$			46.7654i			0.577350i
$3$			46.7654i			0.577350i
$4$	116.514	−	227.948i	0.455133	−	0.890424i
$5$	904.196			1.44671			0.723357	−	0.690474i	$-0.242598\pi$
$5$	904.196			1.44671			0.723357	+	0.690474i	$0.242598\pi$
$6$	390.548	+	638.235i	0.301349	+	0.492465i
$7$		−	888.085i		−	0.369881i	−0.982750	−	0.184941i	$-0.940791\pi$
$7$		−	888.085i		−	0.369881i	0.982750	−	0.184941i	$-0.0592093\pi$
$8$	−313.513	−	4083.98i	−0.0765414	−	0.997066i
$9$	−2187.00			−0.333333
$10$	12340.1	−	7551.15i	1.23401	−	0.755115i
$11$			14451.0i			0.987026i	0.869739	+	0.493513i	$0.164287\pi$
$11$			14451.0i			0.987026i	−0.869739	+	0.493513i	$0.835713\pi$
$12$	10660.1	+	5448.82i	0.514086	+	0.262771i
$13$	−11609.0			−0.406465			−0.203232	−	0.979131i	$-0.565145\pi$
$13$	−11609.0			−0.406465			−0.203232	+	0.979131i	$0.565145\pi$
$14$	−7416.60	−	12120.2i	−0.193060	−	0.315500i
$15$			42285.1i			0.835261i
$16$	−38385.0	−	53118.4i	−0.585708	−	0.810522i
$17$	−128520.			−1.53877			−0.769385	−	0.638786i	$-0.779437\pi$
$17$	−128520.			−1.53877			−0.769385	+	0.638786i	$0.779437\pi$
$18$	−29847.3	+	18264.1i	−0.284325	+	0.173984i
$19$			225611.i			1.73120i	0.500740	+	0.865598i	$0.333061\pi$
$19$			225611.i			1.73120i	−0.500740	+	0.865598i	$0.666939\pi$
$20$	105352.	−	206110.i	0.658447	−	1.28819i
$21$	41531.6			0.213551
$22$	120684.	+	197222.i	0.515180	+	0.841908i
$23$		−	441698.i		−	1.57839i	−0.614144	−	0.789194i	$-0.710499\pi$
$23$		−	441698.i		−	1.57839i	0.614144	−	0.789194i	$-0.289501\pi$
$24$	190989.	−	14661.6i	0.575657	−	0.0441912i
$25$	426946.			1.09298
$26$	−158435.	+	96949.7i	−0.346704	+	0.212155i
$27$		−	102276.i		−	0.192450i
$28$	−202438.	−	103474.i	−0.329351	−	0.168345i
$29$	115149.			0.162805			0.0814024	−	0.996681i	$-0.474060\pi$
$29$	115149.			0.162805			0.0814024	+	0.996681i	$0.474060\pi$
$30$	353132.	+	577090.i	0.435966	+	0.712457i
$31$		−	201879.i		−	0.218597i	−0.994009	−	0.109299i	$-0.965139\pi$
$31$		−	201879.i		−	0.218597i	0.994009	−	0.109299i	$-0.0348605\pi$
$32$	−967466.	−	404376.i	−0.922648	−	0.385643i
$33$	−675808.			−0.569860
$34$	−1.75398e6	+	1.07330e6i	−1.31253	+	0.803163i
$35$		−	803004.i		−	0.535113i
$36$	−254816.	+	498523.i	−0.151711	+	0.296808i
$37$	2.01233e6			1.07372			0.536861	−	0.843671i	$-0.319610\pi$
$37$	2.01233e6			1.07372			0.536861	+	0.843671i	$0.319610\pi$
$38$	1.88413e6	+	3.07905e6i	0.903600	+	1.47667i
$39$		−	542901.i		−	0.234672i
$40$	−283478.	−	3.69272e6i	−0.110733	−	1.44247i
$41$	−2.61903e6			−0.926839			−0.463420	−	0.886139i	$-0.653378\pi$
$41$	−2.61903e6			−0.926839			−0.463420	+	0.886139i	$0.653378\pi$
$42$	566807.	−	346840.i	0.182154	−	0.111463i
$43$			1.75420e6i			0.513105i	0.966530	+	0.256552i	$0.0825866\pi$
$43$			1.75420e6i			0.513105i	−0.966530	+	0.256552i	$0.917413\pi$
$44$	3.29409e6	+	1.68375e6i	0.878871	+	0.449228i
$45$	−1.97748e6			−0.482238
$46$	−3.68872e6	−	6.02811e6i	−0.823842	−	1.34633i
$47$			4.81199e6i			0.986128i	0.869993	+	0.493064i	$0.164123\pi$
$47$			4.81199e6i			0.986128i	−0.869993	+	0.493064i	$0.835877\pi$
$48$	2.48410e6	−	1.79509e6i	0.467955	−	0.338159i
$49$	4.97611e6			0.863188
$50$	5.82679e6	−	3.56553e6i	0.932287	−	0.570484i
$51$		−	6.01026e6i		−	0.888409i
$52$	−1.35261e6	+	2.64626e6i	−0.184995	+	0.361926i
$53$	1.23892e6			0.157014			0.0785071	−	0.996914i	$-0.474985\pi$
$53$	1.23892e6			0.157014			0.0785071	+	0.996914i	$0.474985\pi$
$54$	−854129.	−	1.39582e6i	−0.100450	−	0.164155i
$55$			1.30666e7i			1.42794i
$56$	−3.62693e6	+	278427.i	−0.368796	+	0.0283112i
$57$	−1.05508e7			−0.999506
$58$	1.57150e6	−	961634.i	0.138868	−	0.0849763i
$59$		−	1.14062e6i		−	0.0941311i	−0.998892	−	0.0470655i	$-0.985013\pi$
$59$		−	1.14062e6i		−	0.0941311i	0.998892	−	0.0470655i	$-0.0149870\pi$
$60$	9.63882e6	+	4.92680e6i	0.743736	+	0.380155i
$61$	−4.60247e6			−0.332408			−0.166204	−	0.986091i	$-0.553151\pi$
$61$	−4.60247e6			−0.332408			−0.166204	+	0.986091i	$0.553151\pi$
$62$	−1.68594e6	−	2.75517e6i	−0.114097	−	0.186458i
$63$			1.94224e6i			0.123294i
$64$	−1.65806e7	+	2.56077e6i	−0.988283	+	0.152634i
$65$	−1.04968e7			−0.588038
$66$	−9.22316e6	+	5.64383e6i	−0.486076	+	0.297439i
$67$		−	2.33742e7i		−	1.15995i	−0.814635	−	0.579974i	$-0.803063\pi$
$67$		−	2.33742e7i		−	1.15995i	0.814635	−	0.579974i	$-0.196937\pi$
$68$	−1.49743e7	+	2.92958e7i	−0.700344	+	1.37016i
$69$	2.06561e7			0.911282
$70$	−6.70607e6	−	1.09591e7i	−0.279303	−	0.456438i
$71$		−	3.21271e7i		−	1.26426i	−0.774861	−	0.632132i	$-0.782180\pi$
$71$		−	3.21271e7i		−	1.26426i	0.774861	−	0.632132i	$-0.217820\pi$
$72$	685654.	+	8.93167e6i	0.0255138	+	0.332355i
$73$	4.89485e7			1.72365			0.861823	−	0.507209i	$-0.169323\pi$
$73$	4.89485e7			1.72365			0.861823	+	0.507209i	$0.169323\pi$
$74$	2.74635e7	−	1.68054e7i	0.915858	−	0.560431i
$75$			1.99663e7i			0.631034i
$76$	5.14277e7	+	2.62868e7i	1.54150	+	0.787924i
$77$	1.28338e7			0.365082
$78$	−4.53389e6	−	7.40929e6i	−0.122488	−	0.200170i
$79$			4.23230e6i			0.108660i	0.998523	+	0.0543298i	$0.0173022\pi$
$79$			4.23230e6i			0.108660i	−0.998523	+	0.0543298i	$0.982698\pi$
$80$	−3.47076e7	−	4.80294e7i	−0.847353	−	1.17259i
$81$	4.78297e6			0.111111
$82$	−3.57434e7	+	2.18721e7i	−0.790571	+	0.483765i
$83$		−	1.99136e7i		−	0.419602i	−0.977744	−	0.209801i	$-0.932718\pi$
$83$		−	1.99136e7i		−	0.419602i	0.977744	−	0.209801i	$-0.0672815\pi$
$84$	4.83902e6	−	9.46707e6i	0.0971941	−	0.190151i
$85$	−1.16207e8			−2.22616
$86$	1.46497e7	+	2.39407e7i	0.267816	+	0.437665i
$87$			5.38498e6i			0.0939954i
$88$	5.90178e7	−	4.53060e6i	0.984130	−	0.0755483i
$89$	8.45908e6			0.134823			0.0674114	−	0.997725i	$-0.478526\pi$
$89$	8.45908e6			0.134823			0.0674114	+	0.997725i	$0.478526\pi$
$90$	−2.69878e7	+	1.65144e7i	−0.411337	+	0.251705i
$91$			1.03098e7i			0.150344i
$92$	−1.00684e8	−	5.14639e7i	−1.40543	−	0.718376i
$93$	9.44096e6			0.126207
$94$	4.01860e7	+	6.56721e7i	0.514711	+	0.841142i
$95$			2.03997e8i			2.50455i
$96$	1.89108e7	−	4.52439e7i	0.222651	−	0.532691i
$97$	−8.74596e7			−0.987917			−0.493959	−	0.869485i	$-0.664451\pi$
$97$	−8.74596e7			−0.987917			−0.493959	+	0.869485i	$0.664451\pi$
$98$	6.79119e7	−	4.15566e7i	0.736278	−	0.450542i
$99$		−	3.16044e7i		−	0.329009i
$100$	4.97452e7	−	9.73217e7i	0.497452	−	0.973217i
$101$	5.47619e7			0.526251			0.263126	−	0.964762i	$-0.415247\pi$
$101$	5.47619e7			0.526251			0.263126	+	0.964762i	$0.415247\pi$
$102$	−5.01931e7	−	8.20257e7i	−0.463707	−	0.757791i
$103$		−	9.79588e6i		−	0.0870351i	−0.999053	−	0.0435175i	$-0.986144\pi$
$103$		−	9.79588e6i		−	0.0870351i	0.999053	−	0.0435175i	$-0.0138564\pi$
$104$	3.63959e6	+	4.74111e7i	0.0311114	+	0.405272i
$105$	3.75528e7			0.308947
$106$	1.69082e7	−	1.03465e7i	0.133929	−	0.0819538i
$107$		−	1.14346e8i		−	0.872340i	−0.899864	−	0.436170i	$-0.856335\pi$
$107$		−	1.14346e8i		−	0.872340i	0.899864	−	0.436170i	$-0.143665\pi$
$108$	−2.33136e7	−	1.19166e7i	−0.171362	−	0.0875903i
$109$	4.18346e7			0.296367			0.148183	−	0.988960i	$-0.452657\pi$
$109$	4.18346e7			0.296367			0.148183	+	0.988960i	$0.452657\pi$
$110$	1.09122e8	+	1.78327e8i	0.745318	+	1.21800i
$111$			9.41073e7i			0.619914i
$112$	−4.71736e7	+	3.40891e7i	−0.299797	+	0.216643i
$113$	5.24115e7			0.321449			0.160725	−	0.986999i	$-0.448617\pi$
$113$	5.24115e7			0.321449			0.160725	+	0.986999i	$0.448617\pi$
$114$	−1.43993e8	+	8.81120e7i	−0.852554	+	0.521694i
$115$		−	3.99381e8i		−	2.28348i
$116$	1.34164e7	−	2.62480e7i	0.0740978	−	0.144965i
$117$	2.53890e7			0.135488
$118$	−9.52558e6	−	1.55667e7i	−0.0491319	−	0.0802915i
$119$			1.14136e8i			0.569162i
$120$	1.72692e8	−	1.32569e7i	0.832811	−	0.0639320i
$121$	5.52626e6			0.0257804
$122$	−6.28126e7	+	3.84363e7i	−0.283536	+	0.173501i
$123$		−	1.22480e8i		−	0.535111i
$124$	−4.60181e7	−	2.35218e7i	−0.194644	−	0.0994909i
$125$	3.28415e7			0.134519
$126$	1.62201e7	+	2.65069e7i	0.0643534	+	0.105167i
$127$			3.58172e8i			1.37682i	0.725323	+	0.688409i	$0.241690\pi$
$127$			3.58172e8i			1.37682i	−0.725323	+	0.688409i	$0.758310\pi$
$128$	−2.04900e8	+	1.73417e8i	−0.763313	+	0.646029i
$129$	−8.20359e7			−0.296241
$130$	−1.43257e8	+	8.76616e7i	−0.501582	+	0.306928i
$131$		−	3.12310e8i		−	1.06048i	−0.847848	−	0.530239i	$-0.822102\pi$
$131$		−	3.12310e8i		−	1.06048i	0.847848	−	0.530239i	$-0.177898\pi$
$132$	−7.87411e7	+	1.54049e8i	−0.259362	+	0.507416i
$133$	2.00362e8			0.640337
$134$	−1.95204e8	−	3.19002e8i	−0.605437	−	0.989406i
$135$		−	9.24775e7i		−	0.278420i
$136$	4.02926e7	+	5.24872e8i	0.117779	+	1.53426i
$137$	−2.02321e8			−0.574327			−0.287163	−	0.957882i	$-0.592712\pi$
$137$	−2.02321e8			−0.574327			−0.287163	+	0.957882i	$0.592712\pi$
$138$	2.81907e8	−	1.72504e8i	0.777301	−	0.475645i
$139$			3.56101e8i			0.953924i	0.878924	+	0.476962i	$0.158262\pi$
$139$			3.56101e8i			0.953924i	−0.878924	+	0.476962i	$0.841738\pi$
$140$	−1.83043e8	−	9.35611e7i	−0.476477	−	0.243547i
$141$	−2.25034e8			−0.569341
$142$	−2.68300e8	−	4.38457e8i	−0.659885	−	1.07839i
$143$		−	1.67763e8i		−	0.401191i
$144$	8.39480e7	+	1.16170e8i	0.195236	+	0.270174i
$145$	1.04117e8			0.235532
$146$	6.68030e8	−	4.08780e8i	1.47023	−	0.899660i
$147$			2.32709e8i			0.498362i
$148$	2.34464e8	−	4.58707e8i	0.488686	−	0.956068i
$149$	−4.69207e8			−0.951961			−0.475981	−	0.879456i	$-0.657907\pi$
$149$	−4.69207e8			−0.951961			−0.475981	+	0.879456i	$0.657907\pi$
$150$	1.66743e8	+	2.72492e8i	0.329369	+	0.538256i
$151$			4.96132e8i			0.954309i	0.878819	+	0.477155i	$0.158332\pi$
$151$			4.96132e8i			0.954309i	−0.878819	+	0.477155i	$0.841668\pi$
$152$	9.21392e8	−	7.07321e7i	1.72612	−	0.132508i
$153$	2.81072e8			0.512923
$154$	1.75150e8	−	1.07178e8i	0.311406	−	0.190555i
$155$		−	1.82539e8i		−	0.316248i
$156$	−1.23753e8	−	6.32555e7i	−0.208958	−	0.106807i
$157$	9.86054e8			1.62294			0.811469	−	0.584395i	$-0.198668\pi$
$157$	9.86054e8			1.62294			0.811469	+	0.584395i	$0.198668\pi$
$158$	3.53449e7	+	5.77607e7i	0.0567150	+	0.0926839i
$159$			5.79384e7i			0.0906521i
$160$	−8.74780e8	−	3.65636e8i	−1.33481	−	0.557916i
$161$	−3.92265e8			−0.583816
$162$	6.52760e7	−	3.99437e7i	0.0947750	−	0.0579946i
$163$		−	1.41749e8i		−	0.200803i	−0.994947	−	0.100402i	$-0.967987\pi$
$163$		−	1.41749e8i		−	0.200803i	0.994947	−	0.100402i	$-0.0320128\pi$
$164$	−3.05153e8	+	5.97003e8i	−0.421835	+	0.825279i
$165$	−6.11064e8			−0.824424
$166$	−1.66303e8	−	2.71773e8i	−0.219012	−	0.357910i
$167$			6.26762e8i			0.805818i	0.915240	+	0.402909i	$0.132001\pi$
$167$			6.26762e8i			0.805818i	−0.915240	+	0.402909i	$0.867999\pi$
$168$	−1.30207e7	−	1.69615e8i	−0.0163455	−	0.212925i
$169$	−6.80961e8			−0.834787
$170$	−1.58595e9	+	9.70471e8i	−1.89886	+	1.16195i
$171$		−	4.93411e8i		−	0.577065i
$172$	3.99868e8	+	2.04389e8i	0.456880	+	0.233531i
$173$	3.25845e8			0.363770			0.181885	−	0.983320i	$-0.441780\pi$
$173$	3.25845e8			0.363770			0.181885	+	0.983320i	$0.441780\pi$
$174$	4.49712e7	+	7.34920e7i	0.0490611	+	0.0801758i
$175$		−	3.79165e8i		−	0.404274i
$176$	7.67616e8	−	5.54703e8i	0.800006	−	0.578109i
$177$	5.33415e7			0.0543466
$178$	1.15446e8	−	7.06437e7i	0.115000	−	0.0703710i
$179$			4.96016e8i			0.483152i	0.970382	+	0.241576i	$0.0776642\pi$
$179$			4.96016e8i			0.483152i	−0.970382	+	0.241576i	$0.922336\pi$
$180$	−2.30404e8	+	4.50763e8i	−0.219482	+	0.429396i
$181$	−5.63606e8			−0.525123			−0.262562	−	0.964915i	$-0.584567\pi$
$181$	−5.63606e8			−0.525123			−0.262562	+	0.964915i	$0.584567\pi$
$182$	8.60996e7	+	1.40704e8i	0.0784722	+	0.128239i
$183$		−	2.15236e8i		−	0.191916i
$184$	−1.80389e9	+	1.38478e8i	−1.57376	+	0.120812i
$185$	1.81954e9			1.55337
$186$	1.28846e8	−	7.88436e7i	0.107652	−	0.0658741i
$187$		−	1.85724e9i		−	1.51880i
$188$	1.09689e9	+	5.60664e8i	0.878072	+	0.448819i
$189$	−9.08297e7			−0.0711837
$190$	1.70362e9	+	2.78407e9i	1.30725	+	2.13631i
$191$		−	8.54684e8i		−	0.642203i	−0.947045	−	0.321101i	$-0.895947\pi$
$191$		−	8.54684e8i		−	0.642203i	0.947045	−	0.321101i	$-0.104053\pi$
$192$	−1.19755e8	−	7.75400e8i	−0.0881231	−	0.570585i
$193$	1.02603e9			0.739489			0.369745	−	0.929133i	$-0.379445\pi$
$193$	1.02603e9			0.739489			0.369745	+	0.929133i	$0.379445\pi$
$194$	−1.19361e9	+	7.30395e8i	−0.842669	+	0.515645i
$195$		−	4.90889e8i		−	0.339504i
$196$	5.79786e8	−	1.13430e9i	0.392865	−	0.768603i
$197$	8.44577e8			0.560756			0.280378	−	0.959890i	$-0.409540\pi$
$197$	8.44577e8			0.560756			0.280378	+	0.959890i	$0.409540\pi$
$198$	−2.63936e8	−	4.31325e8i	−0.171727	−	0.280636i
$199$			7.72569e8i			0.492635i	0.969189	+	0.246317i	$0.0792206\pi$
$199$			7.72569e8i			0.492635i	−0.969189	+	0.246317i	$0.920779\pi$
$200$	−1.33853e8	−	1.74364e9i	−0.0836584	−	1.08978i
$201$	1.09311e9			0.669696
$202$	7.47369e8	−	4.57329e8i	0.448879	−	0.274678i
$203$		−	1.02262e8i		−	0.0602185i
$204$	−1.37003e9	−	7.00280e8i	−0.791060	−	0.404344i
$205$	−2.36811e9			−1.34087
$206$	−8.18076e7	−	1.33690e8i	−0.0454281	−	0.0742388i
$207$			9.65993e8i			0.526129i
$208$	4.45613e8	+	6.16653e8i	0.238070	+	0.329448i
$209$	−3.26032e9			−1.70873
$210$	5.12505e8	−	3.13612e8i	0.263524	−	0.161256i
$211$			2.19966e9i			1.10975i	0.831934	+	0.554875i	$0.187234\pi$
$211$			2.19966e9i			1.10975i	−0.831934	+	0.554875i	$0.812766\pi$
$212$	1.44351e8	−	2.82409e8i	0.0714623	−	0.139809i
$213$	1.50243e9			0.729923
$214$	−9.54930e8	−	1.56055e9i	−0.455320	−	0.744085i
$215$			1.58614e9i			0.742316i
$216$	−4.17693e8	+	3.20649e7i	−0.191886	+	0.0147304i
$217$	−1.79286e8			−0.0808551
$218$	5.70942e8	−	3.49370e8i	0.252794	−	0.154689i
$219$			2.28910e9i			0.995148i
$220$	2.97851e9	+	1.52244e9i	1.27148	+	0.649904i
$221$	1.49199e9			0.625455
$222$	7.85911e8	+	1.28434e9i	0.323565	+	0.528771i
$223$		−	4.61916e9i		−	1.86786i	−0.357459	−	0.933929i	$-0.616357\pi$
$223$		−	4.61916e9i		−	1.86786i	0.357459	−	0.933929i	$-0.383643\pi$
$224$	−3.59121e8	+	8.59193e8i	−0.142642	+	0.341270i
$225$	−9.33731e8			−0.364327
$226$	7.15291e8	−	4.37700e8i	0.274188	−	0.167781i
$227$			1.24196e9i			0.467738i	0.972268	+	0.233869i	$0.0751388\pi$
$227$			1.24196e9i			0.467738i	−0.972268	+	0.233869i	$0.924861\pi$
$228$	−1.22931e9	+	2.40504e9i	−0.454908	+	0.889984i
$229$	−4.83925e9			−1.75969			−0.879845	−	0.475260i	$-0.842354\pi$
$229$	−4.83925e9			−1.75969			−0.879845	+	0.475260i	$0.842354\pi$
$230$	−3.33532e9	−	5.45060e9i	−1.19186	−	1.94775i
$231$			6.00175e8i			0.210780i
$232$	−3.61007e7	−	4.70266e8i	−0.0124613	−	0.162327i
$233$	−1.26420e9			−0.428936			−0.214468	−	0.976731i	$-0.568802\pi$
$233$	−1.26420e9			−0.428936			−0.214468	+	0.976731i	$0.568802\pi$
$234$	3.46498e8	−	2.12029e8i	0.115568	−	0.0707183i
$235$			4.35098e9i			1.42665i
$236$	−2.60003e8	−	1.32898e8i	−0.0838165	−	0.0428421i
$237$	−1.97925e8			−0.0627346
$238$	9.53178e8	+	1.55769e9i	0.297075	+	0.485481i
$239$		−	3.45214e9i		−	1.05803i	−0.848613	−	0.529014i	$-0.822562\pi$
$239$		−	3.45214e9i		−	1.05803i	0.848613	−	0.529014i	$-0.177438\pi$
$240$	2.24611e9	−	1.62311e9i	0.676997	−	0.489219i
$241$	2.81376e9			0.834101			0.417050	−	0.908883i	$-0.363064\pi$
$241$	2.81376e9			0.834101			0.417050	+	0.908883i	$0.363064\pi$
$242$	7.54201e7	−	4.61510e7i	0.0219900	−	0.0134561i
$243$			2.23677e8i			0.0641500i
$244$	−5.36252e8	+	1.04913e9i	−0.151290	+	0.295984i
$245$	4.49938e9			1.24879
$246$	−1.02286e9	−	1.67155e9i	−0.279302	−	0.456436i
$247$		−	2.61913e9i		−	0.703670i
$248$	−8.24472e8	+	6.32919e7i	−0.217956	+	0.0167317i
$249$	9.31266e8			0.242257
$250$	4.48208e8	−	2.74267e8i	0.114741	−	0.0702124i
$251$			1.02698e9i			0.258741i	0.991596	+	0.129371i	$0.0412957\pi$
$251$			1.02698e9i			0.258741i	−0.991596	+	0.129371i	$0.958704\pi$
$252$	4.42731e8	+	2.26298e8i	0.109784	+	0.0561150i
$253$	6.38299e9			1.55791
$254$	2.99117e9	+	4.88818e9i	0.718632	+	1.17439i
$255$		−	5.43446e9i		−	1.28527i
$256$	−1.34815e9	+	4.07790e9i	−0.313891	+	0.949459i
$257$	−1.80098e9			−0.412834			−0.206417	−	0.978464i	$-0.566180\pi$
$257$	−1.80098e9			−0.412834			−0.206417	+	0.978464i	$0.566180\pi$
$258$	−1.11959e9	+	6.85101e8i	−0.252686	+	0.154624i
$259$		−	1.78712e9i		−	0.397150i
$260$	−1.22303e9	+	2.39274e9i	−0.267635	+	0.523603i
$261$	−2.51830e8			−0.0542683
$262$	−2.60818e9	−	4.26229e9i	−0.553518	−	0.904561i
$263$		−	6.59493e9i		−	1.37844i	−0.724554	−	0.689219i	$-0.757954\pi$
$263$		−	6.59493e9i		−	1.37844i	0.724554	−	0.689219i	$-0.242046\pi$
$264$	2.11875e8	+	2.75999e9i	0.0436178	+	0.568188i
$265$	1.12022e9			0.227155
$266$	2.73446e9	−	1.67327e9i	0.546191	−	0.334225i
$267$			3.95592e8i			0.0778399i
$268$	−5.32812e9	−	2.72343e9i	−1.03284	−	0.527930i
$269$	−7.85945e8			−0.150101			−0.0750504	−	0.997180i	$-0.523912\pi$
$269$	−7.85945e8			−0.150101			−0.0750504	+	0.997180i	$0.523912\pi$
$270$	−7.72301e8	−	1.26210e9i	−0.145322	−	0.237486i
$271$			4.85570e9i			0.900274i	0.892959	+	0.450137i	$0.148625\pi$
$271$			4.85570e9i			0.900274i	−0.892959	+	0.450137i	$0.851375\pi$
$272$	4.93322e9	+	6.82675e9i	0.901270	+	1.24721i
$273$	−4.82142e8			−0.0868010
$274$	−2.76120e9	+	1.68963e9i	−0.489886	+	0.299771i
$275$			6.16982e9i			1.07880i
$276$	2.40673e9	−	4.70854e9i	0.414754	−	0.811427i
$277$	−5.59523e9			−0.950383			−0.475191	−	0.879882i	$-0.657621\pi$
$277$	−5.59523e9			−0.950383			−0.475191	+	0.879882i	$0.657621\pi$
$278$	2.97388e9	+	4.85992e9i	0.497902	+	0.813674i
$279$			4.41510e8i			0.0728658i
$280$	−3.27945e9	+	2.51752e8i	−0.533543	+	0.0409583i
$281$	−9.77267e9			−1.56743			−0.783715	−	0.621121i	$-0.786678\pi$
$281$	−9.77267e9			−1.56743			−0.783715	+	0.621121i	$0.786678\pi$
$282$	−3.07118e9	+	1.87931e9i	−0.485634	+	0.297169i
$283$			1.39134e9i			0.216915i	0.994101	+	0.108457i	$0.0345911\pi$
$283$			1.39134e9i			0.216915i	−0.994101	+	0.108457i	$0.965409\pi$
$284$	−7.32332e9	−	3.74325e9i	−1.12573	−	0.575408i
$285$	−9.53998e9			−1.44600
$286$	−1.40102e9	−	2.28956e9i	−0.209402	−	0.342206i
$287$			2.32592e9i			0.342821i
$288$	2.11585e9	+	8.84371e8i	0.307549	+	0.128548i
$289$	9.54152e9			1.36781
$290$	1.42095e9	−	8.69506e8i	0.200903	−	0.122936i
$291$		−	4.09008e9i		−	0.570374i
$292$	5.70319e9	−	1.11577e10i	0.784488	−	1.53478i
$293$	1.31910e10			1.78981			0.894904	−	0.446258i	$-0.147244\pi$
$293$	1.31910e10			1.78981			0.894904	+	0.446258i	$0.147244\pi$
$294$	1.94341e9	+	3.17593e9i	0.260121	+	0.425090i
$295$		−	1.03134e9i		−	0.136181i
$296$	−6.30892e8	−	8.21832e9i	−0.0821842	−	1.07057i
$297$	1.47799e9			0.189953
$298$	−6.40355e9	+	3.91845e9i	−0.811999	+	0.496878i
$299$			5.12768e9i			0.641559i
$300$	4.55129e9	+	2.32635e9i	0.561887	+	0.287204i
$301$	1.55788e9			0.189788
$302$	4.14331e9	+	6.77100e9i	0.498103	+	0.814002i
$303$			2.56096e9i			0.303831i
$304$	1.19841e10	−	8.66008e9i	1.40317	−	1.01398i
$305$	−4.16154e9			−0.480899
$306$	3.83596e9	−	2.34730e9i	0.437511	−	0.267721i
$307$			1.03003e9i			0.115957i	0.998318	+	0.0579784i	$0.0184654\pi$
$307$			1.03003e9i			0.115957i	−0.998318	+	0.0579784i	$0.981535\pi$
$308$	1.49531e9	−	2.92544e9i	0.166161	−	0.325078i
$309$	4.58108e8			0.0502497
$310$	−1.52442e9	−	2.49121e9i	−0.165066	−	0.269752i
$311$			1.03275e10i			1.10396i	0.833857	+	0.551981i	$0.186128\pi$
$311$			1.03275e10i			1.10396i	−0.833857	+	0.551981i	$0.813872\pi$
$312$	−2.21720e9	+	1.70207e8i	−0.233984	+	0.0179621i
$313$	−1.75059e9			−0.182393			−0.0911963	−	0.995833i	$-0.529069\pi$
$313$	−1.75059e9			−0.182393			−0.0911963	+	0.995833i	$0.529069\pi$
$314$	1.34573e10	−	8.23476e9i	1.38433	−	0.847096i
$315$			1.75617e9i			0.178371i
$316$	9.64746e8	+	4.93122e8i	0.0967530	+	0.0494545i
$317$	−1.25238e10			−1.24022			−0.620109	−	0.784515i	$-0.712912\pi$
$317$	−1.25238e10			−1.24022			−0.620109	+	0.784515i	$0.712912\pi$
$318$	4.83857e8	+	7.90720e8i	0.0473160	+	0.0773240i
$319$			1.66402e9i			0.160693i
$320$	−1.49922e10	+	2.31544e9i	−1.42976	+	0.220817i
$321$	5.34744e9			0.503646
$322$	−5.35348e9	+	3.27590e9i	−0.497981	+	0.304724i
$323$		−	2.89954e10i		−	2.66391i
$324$	5.57283e8	−	1.09027e9i	0.0505703	−	0.0989360i
$325$	−4.95643e9			−0.444259
$326$	−1.18378e9	−	1.93454e9i	−0.104810	−	0.171280i
$327$			1.95641e9i			0.171108i
$328$	8.21100e8	+	1.06961e10i	0.0709415	+	0.924120i
$329$	4.27346e9			0.364750
$330$	−8.33955e9	+	5.10313e9i	−0.703213	+	0.430310i
$331$			1.79988e10i			1.49945i	0.661750	+	0.749725i	$0.269814\pi$
$331$			1.79988e10i			1.49945i	−0.661750	+	0.749725i	$0.730186\pi$
$332$	−4.53927e9	−	2.32021e9i	−0.373623	−	0.190974i
$333$	−4.40096e9			−0.357907
$334$	5.23424e9	+	8.55380e9i	0.420598	+	0.687343i
$335$		−	2.11349e10i		−	1.67811i
$336$	−1.59419e9	−	2.20609e9i	−0.125079	−	0.173088i
$337$	4.52797e9			0.351062			0.175531	−	0.984474i	$-0.443836\pi$
$337$	4.52797e9			0.351062			0.175531	+	0.984474i	$0.443836\pi$
$338$	−9.29348e9	+	5.68686e9i	−0.712052	+	0.435718i
$339$			2.45104e9i			0.185589i
$340$	−1.35397e10	+	2.64892e10i	−1.01320	+	1.98223i
$341$	2.91737e9			0.215761
$342$	−4.12059e9	−	6.73388e9i	−0.301200	−	0.492222i
$343$		−	9.53884e9i		−	0.689159i
$344$	7.16414e9	−	5.49966e8i	0.511599	−	0.0392737i
$345$	1.86772e10			1.31837
$346$	4.44701e9	−	2.72121e9i	0.310287	−	0.189871i
$347$			2.28528e10i			1.57624i	0.615522	+	0.788119i	$0.288945\pi$
$347$			2.28528e10i			1.57624i	−0.615522	+	0.788119i	$0.711055\pi$
$348$	1.22750e9	+	6.27425e8i	0.0836958	+	0.0427804i
$349$	7.23857e9			0.487922			0.243961	−	0.969785i	$-0.421553\pi$
$349$	7.23857e9			0.487922			0.243961	+	0.969785i	$0.421553\pi$
$350$	−3.16649e9	−	5.17469e9i	−0.211011	−	0.344835i
$351$			1.18732e9i			0.0782242i
$352$	5.84366e9	−	1.39809e10i	0.380640	−	0.910677i
$353$	−9.02641e9			−0.581321			−0.290661	−	0.956826i	$-0.593875\pi$
$353$	−9.02641e9			−0.581321			−0.290661	+	0.956826i	$0.593875\pi$
$354$	7.27984e8	−	4.45467e8i	0.0463563	−	0.0283663i
$355$		−	2.90492e10i		−	1.82903i
$356$	9.85601e8	−	1.92823e9i	0.0613622	−	0.120049i
$357$	−5.33763e9			−0.328606
$358$	4.14234e9	+	6.76942e9i	0.252182	+	0.412116i
$359$			8.94260e9i			0.538377i	0.963088	+	0.269188i	$0.0867554\pi$
$359$			8.94260e9i			0.538377i	−0.963088	+	0.269188i	$0.913245\pi$
$360$	6.19966e8	+	8.07599e9i	0.0369112	+	0.480823i
$361$	−3.39168e10			−1.99704
$362$	−7.69187e9	+	4.70680e9i	−0.447917	+	0.274089i
$363$			2.58437e8i			0.0148843i
$364$	2.35011e9	+	1.20124e9i	0.133870	+	0.0684263i
$365$	4.42591e10			2.49362
$366$	−1.79749e9	−	2.93746e9i	−0.100171	−	0.163699i
$367$		−	9.34134e9i		−	0.514926i	−0.966288	−	0.257463i	$-0.917113\pi$
$367$		−	9.34134e9i		−	0.514926i	0.966288	−	0.257463i	$-0.0828866\pi$
$368$	−2.34622e10	+	1.69546e10i	−1.27932	+	0.924475i
$369$	5.72781e9			0.308946
$370$	2.48324e10	−	1.51954e10i	1.32499	−	0.810784i
$371$		−	1.10026e9i		−	0.0580766i
$372$	1.10000e9	−	2.15205e9i	0.0574411	−	0.112378i
$373$	−8.10234e9			−0.418577			−0.209288	−	0.977854i	$-0.567115\pi$
$373$	−8.10234e9			−0.418577			−0.209288	+	0.977854i	$0.567115\pi$
$374$	−1.55102e10	−	2.53469e10i	−0.792743	−	1.29550i
$375$			1.53585e9i			0.0776645i
$376$	1.96521e10	−	1.50862e9i	0.983235	−	0.0754796i
$377$	−1.33677e9			−0.0661744
$378$	−1.23961e9	+	7.58539e8i	−0.0607179	+	0.0371545i
$379$		−	2.76442e10i		−	1.33982i	−0.742440	−	0.669912i	$-0.766332\pi$
$379$		−	2.76442e10i		−	1.33982i	0.742440	−	0.669912i	$-0.233668\pi$
$380$	4.65007e10	+	2.37685e10i	2.23011	+	1.13990i
$381$	−1.67500e10			−0.794906
$382$	−7.13766e9	−	1.16644e10i	−0.335199	−	0.547783i
$383$			3.04532e10i			1.41526i	0.706581	+	0.707632i	$0.250237\pi$
$383$			3.04532e10i			1.41526i	−0.706581	+	0.707632i	$0.749763\pi$
$384$	−8.10991e9	−	9.58224e9i	−0.372985	−	0.440699i
$385$	1.16042e10			0.528170
$386$	1.40029e10	−	8.56863e9i	0.630766	−	0.385978i
$387$		−	3.83644e9i		−	0.171035i
$388$	−1.01903e10	+	1.99363e10i	−0.449633	+	0.879665i
$389$	−1.61385e9			−0.0704799			−0.0352399	−	0.999379i	$-0.511220\pi$
$389$	−1.61385e9			−0.0704799			−0.0352399	+	0.999379i	$0.511220\pi$
$390$	−4.09953e9	−	6.69946e9i	−0.177205	−	0.289588i
$391$			5.67668e10i			2.42877i
$392$	−1.56008e9	−	2.03223e10i	−0.0660696	−	0.860656i
$393$	1.46053e10			0.612267
$394$	1.15264e10	−	7.05325e9i	0.478311	−	0.292688i
$395$			3.82683e9i			0.157199i
$396$	−7.20418e9	−	3.68236e9i	−0.292957	−	0.149743i
$397$	−3.65388e10			−1.47093			−0.735465	−	0.677563i	$-0.763036\pi$
$397$	−3.65388e10			−1.47093			−0.735465	+	0.677563i	$0.763036\pi$
$398$	6.45190e9	+	1.05437e10i	0.257132	+	0.420205i
$399$			9.37000e9i			0.369699i
$400$	−1.63883e10	−	2.26787e10i	−0.640169	−	0.885886i
$401$	−2.62838e10			−1.01651			−0.508253	−	0.861208i	$-0.669708\pi$
$401$	−2.62838e10			−1.01651			−0.508253	+	0.861208i	$0.669708\pi$
$402$	1.49183e10	−	9.12877e9i	0.571234	−	0.349549i
$403$			2.34362e9i			0.0888521i
$404$	6.38053e9	−	1.24829e10i	0.239514	−	0.468586i
$405$	4.32474e9			0.160746
$406$	−8.54013e8	−	1.39563e9i	−0.0314312	−	0.0513649i
$407$			2.90802e10i			1.05979i
$408$	−2.45458e10	+	1.88430e9i	−0.885803	+	0.0680000i
$409$	1.69888e10			0.607114			0.303557	−	0.952813i	$-0.401826\pi$
$409$	1.69888e10			0.607114			0.303557	+	0.952813i	$0.401826\pi$
$410$	−3.23191e10	+	1.97767e10i	−1.14373	+	0.699870i
$411$		−	9.46162e9i		−	0.331588i
$412$	−2.23295e9	−	1.14136e9i	−0.0774981	−	0.0396125i
$413$	−1.01297e9			−0.0348173
$414$	8.06722e9	+	1.31835e10i	0.274614	+	0.448775i
$415$		−	1.80058e10i		−	0.607044i
$416$	1.12314e10	+	4.69442e9i	0.375024	+	0.156750i
$417$	−1.66532e10			−0.550748
$418$	−4.44955e10	+	2.72276e10i	−1.45751	+	0.891877i
$419$		−	4.79547e10i		−	1.55588i	−0.628340	−	0.777939i	$-0.716265\pi$
$419$		−	4.79547e10i		−	1.55588i	0.628340	−	0.777939i	$-0.283735\pi$
$420$	4.37542e9	−	8.56009e9i	0.140612	−	0.275094i
$421$	3.01561e9			0.0959947			0.0479973	−	0.998847i	$-0.484716\pi$
$421$	3.01561e9			0.0959947			0.0479973	+	0.998847i	$0.484716\pi$
$422$	1.83698e10	+	3.00201e10i	0.579236	+	0.946589i
$423$		−	1.05238e10i		−	0.328709i
$424$	−3.88417e8	−	5.05972e9i	−0.0120181	−	0.156554i
$425$	−5.48709e10			−1.68185
$426$	2.05046e10	−	1.25472e10i	0.622606	−	0.380985i
$427$			4.08738e9i			0.122952i
$428$	−2.60650e10	−	1.33229e10i	−0.776753	−	0.397031i
$429$	7.84548e9			0.231628
$430$	1.32462e10	+	2.16471e10i	0.387453	+	0.633177i
$431$		−	1.51705e10i		−	0.439634i	−0.975541	−	0.219817i	$-0.929454\pi$
$431$		−	1.51705e10i		−	0.439634i	0.975541	−	0.219817i	$-0.0705461\pi$
$432$	−5.43273e9	+	3.92586e9i	−0.155985	+	0.112720i
$433$	5.75689e10			1.63771			0.818853	−	0.574003i	$-0.194610\pi$
$433$	5.75689e10			1.63771			0.818853	+	0.574003i	$0.194610\pi$
$434$	−2.44682e9	+	1.49726e9i	−0.0689674	+	0.0422025i
$435$			4.86908e9i			0.135985i
$436$	4.87432e9	−	9.53614e9i	0.134886	−	0.263892i
$437$	9.96519e10			2.73250
$438$	1.91168e10	+	3.12407e10i	0.519419	+	0.848836i
$439$			5.52060e10i			1.48638i	0.669083	+	0.743188i	$0.266687\pi$
$439$			5.52060e10i			1.48638i	−0.669083	+	0.743188i	$0.733313\pi$
$440$	5.33637e10	−	4.09655e9i	1.42376	−	0.109297i
$441$	−1.08827e10			−0.287729
$442$	2.03621e10	−	1.24599e10i	0.533498	−	0.326457i
$443$		−	6.97437e10i		−	1.81088i	−0.424473	−	0.905441i	$-0.639540\pi$
$443$		−	6.97437e10i		−	1.81088i	0.424473	−	0.905441i	$-0.360460\pi$
$444$	2.14516e10	+	1.09648e10i	0.551986	+	0.282143i
$445$	7.64867e9			0.195050
$446$	−3.85757e10	−	6.30405e10i	−0.974932	−	1.59324i
$447$		−	2.19426e10i		−	0.549615i
$448$	2.27418e9	+	1.47250e10i	0.0564563	+	0.365547i
$449$	−1.47127e10			−0.361998			−0.180999	−	0.983483i	$-0.557933\pi$
$449$	−1.47127e10			−0.361998			−0.180999	+	0.983483i	$0.557933\pi$
$450$	−1.27432e10	+	7.79780e9i	−0.310762	+	0.190161i
$451$		−	3.78477e10i		−	0.914814i
$452$	6.10667e9	−	1.19471e10i	0.146302	−	0.286226i
$453$	−2.32018e10			−0.550971
$454$	1.03719e10	+	1.69497e10i	0.244137	+	0.398969i
$455$			9.32210e9i			0.217504i
$456$	3.30781e9	+	4.30892e10i	0.0765036	+	0.996574i
$457$	6.37221e10			1.46092			0.730458	−	0.682957i	$-0.239306\pi$
$457$	6.37221e10			1.46092			0.730458	+	0.682957i	$0.239306\pi$
$458$	−6.60442e10	+	4.04137e10i	−1.50097	+	0.918473i
$459$			1.31444e10i			0.296136i
$460$	−9.10384e10	−	4.65335e10i	−2.03326	−	1.03928i
$461$	−3.93282e10			−0.870763			−0.435382	−	0.900246i	$-0.643387\pi$
$461$	−3.93282e10			−0.870763			−0.435382	+	0.900246i	$0.643387\pi$
$462$	5.01220e9	+	8.19095e9i	0.110017	+	0.179790i
$463$		−	6.91241e10i		−	1.50420i	−0.659049	−	0.752100i	$-0.729041\pi$
$463$		−	6.91241e10i		−	1.50420i	0.659049	−	0.752100i	$-0.270959\pi$
$464$	−4.41999e9	−	6.11652e9i	−0.0953562	−	0.131957i
$465$	8.53648e9			0.182586
$466$	−1.72533e10	+	1.05576e10i	−0.365872	+	0.223884i
$467$			4.48917e10i			0.943840i	0.881641	+	0.471920i	$0.156439\pi$
$467$			4.48917e10i			0.943840i	−0.881641	+	0.471920i	$0.843561\pi$
$468$	2.95817e9	−	5.78737e9i	0.0616651	−	0.120642i
$469$	−2.07583e10			−0.429043
$470$	3.63361e10	+	5.93805e10i	0.744640	+	1.21689i
$471$			4.61132e10i			0.937004i
$472$	−4.65827e9	+	3.57600e8i	−0.0938549	+	0.00720492i
$473$	−2.53501e10			−0.506447
$474$	−2.70120e9	+	1.65292e9i	−0.0535111	+	0.0327444i
$475$			9.63238e10i			1.89217i
$476$	2.60172e10	+	1.32985e10i	0.506795	+	0.259044i
$477$	−2.70951e9			−0.0523380
$478$	−2.88296e10	−	4.71135e10i	−0.552240	−	0.902471i
$479$		−	7.56518e10i		−	1.43707i	−0.695492	−	0.718533i	$-0.744814\pi$
$479$		−	7.56518e10i		−	1.43707i	0.695492	−	0.718533i	$-0.255186\pi$
$480$	1.70991e10	−	4.09094e10i	0.322113	−	0.770652i
$481$	−2.33612e10			−0.436430
$482$	3.84010e10	−	2.34983e10i	0.711467	−	0.435360i
$483$		−	1.83444e10i		−	0.337066i
$484$	6.43886e8	−	1.25970e9i	0.0117335	−	0.0229555i
$485$	−7.90806e10			−1.42923
$486$	1.86798e9	+	3.05266e9i	0.0334832	+	0.0547184i
$487$			5.39416e10i			0.958977i	0.877548	+	0.479489i	$0.159178\pi$
$487$			5.39416e10i			0.958977i	−0.877548	+	0.479489i	$0.840822\pi$
$488$	1.44294e9	+	1.87964e10i	0.0254430	+	0.331433i
$489$	6.62897e9			0.115934
$490$	6.14057e10	−	3.75753e10i	1.06518	−	0.651806i
$491$			9.67425e10i			1.66453i	0.554379	+	0.832264i	$0.312956\pi$
$491$			9.67425e10i			1.66453i	−0.554379	+	0.832264i	$0.687044\pi$
$492$	−2.79191e10	−	1.42706e10i	−0.476475	−	0.243546i
$493$	−1.47989e10			−0.250519
$494$	−2.18729e10	−	3.57448e10i	−0.367282	−	0.600213i
$495$		−	2.85766e10i		−	0.475981i
$496$	−1.07235e10	+	7.74914e9i	−0.177178	+	0.128034i
$497$	−2.85316e10			−0.467628
$498$	1.27096e10	−	7.77722e9i	0.206639	−	0.126447i
$499$			1.21097e10i			0.195313i	0.995220	+	0.0976566i	$0.0311347\pi$
$499$			1.21097e10i			0.195313i	−0.995220	+	0.0976566i	$0.968865\pi$
$500$	3.82650e9	−	7.48618e9i	0.0612240	−	0.119779i
$501$	−2.93108e10			−0.465239
$502$	8.57651e9	+	1.40158e10i	0.135050	+	0.220700i
$503$			2.13349e10i			0.333286i	0.986017	+	0.166643i	$0.0532928\pi$
$503$			2.13349e10i			0.333286i	−0.986017	+	0.166643i	$0.946707\pi$
$504$	7.93209e9	−	6.08919e8i	0.122932	−	0.00943708i
$505$	4.95155e10			0.761335
$506$	8.71125e10	−	5.33058e10i	1.32886	−	0.813153i
$507$		−	3.18454e10i		−	0.481964i
$508$	8.16447e10	+	4.17320e10i	1.22595	+	0.626635i
$509$	1.22126e11			1.81944			0.909721	−	0.415221i	$-0.136296\pi$
$509$	1.22126e11			1.81944			0.909721	+	0.415221i	$0.136296\pi$
$510$	−4.53844e10	−	7.41673e10i	−0.670851	−	1.09631i
$511$		−	4.34705e10i		−	0.637545i
$512$	1.56564e10	+	6.69122e10i	0.227830	+	0.973701i
$513$	2.30746e10			0.333169
$514$	−2.45790e10	+	1.50404e10i	−0.352137	+	0.215480i
$515$		−	8.85740e9i		−	0.125915i
$516$	−9.55833e9	+	1.87000e10i	−0.134829	+	0.263780i
$517$	−6.95383e10			−0.973333
$518$	−1.49246e10	−	2.43899e10i	−0.207293	−	0.338759i
$519$			1.52383e10i			0.210023i
$520$	3.29090e9	+	4.28690e10i	0.0450092	+	0.586313i
$521$	8.66914e10			1.17659			0.588295	−	0.808646i	$-0.299799\pi$
$521$	8.66914e10			1.17659			0.588295	+	0.808646i	$0.299799\pi$
$522$	−3.43688e9	+	2.10309e9i	−0.0462895	+	0.0283254i
$523$			1.54184e10i			0.206078i	0.994677	+	0.103039i	$0.0328567\pi$
$523$			1.54184e10i			0.206078i	−0.994677	+	0.103039i	$0.967143\pi$
$524$	−7.11907e10	−	3.63885e10i	−0.944274	−	0.482658i
$525$	1.77318e10			0.233408
$526$	−5.50757e10	−	9.00049e10i	−0.719478	−	1.17577i
$527$			2.59454e10i			0.336371i
$528$	2.59409e10	+	3.58978e10i	0.333772	+	0.461884i
$529$	−1.16786e11			−1.49131
$530$	1.52884e10	−	9.35525e9i	0.193757	−	0.118564i
$531$			2.49454e9i			0.0313770i
$532$	2.33450e10	−	4.56722e10i	0.291438	−	0.570171i
$533$	3.04044e10			0.376727
$534$	3.30368e9	+	5.39888e9i	0.0406287	+	0.0663955i
$535$		−	1.03391e11i		−	1.26203i
$536$	−9.54600e10	+	7.32814e9i	−1.15654	+	0.0887840i
$537$	−2.31964e10			−0.278948
$538$	−1.07263e10	+	6.56361e9i	−0.128032	+	0.0783454i
$539$			7.19099e10i			0.851988i
$540$	−2.10801e10	−	1.07749e10i	−0.247912	−	0.126718i
$541$	1.38070e10			0.161180			0.0805899	−	0.996747i	$-0.474320\pi$
$541$	1.38070e10			0.161180			0.0805899	+	0.996747i	$0.474320\pi$
$542$	4.05511e10	+	6.62687e10i	0.469900	+	0.767912i
$543$		−	2.63572e10i		−	0.303180i
$544$	1.24338e11	+	5.19703e10i	1.41974	+	0.593416i
$545$	3.78267e10			0.428758
$546$	−6.58009e9	+	4.02648e9i	−0.0740391	+	0.0453059i
$547$		−	1.58922e11i		−	1.77514i	−0.460670	−	0.887572i	$-0.652391\pi$
$547$		−	1.58922e11i		−	1.77514i	0.460670	−	0.887572i	$-0.347609\pi$
$548$	−2.35732e10	+	4.61188e10i	−0.261395	+	0.511394i
$549$	1.00656e10			0.110803
$550$	5.15256e10	+	8.42032e10i	0.563082	+	0.920191i
$551$			2.59788e10i			0.281847i
$552$	−6.47598e9	−	8.43594e10i	−0.0697508	−	0.908609i
$553$	3.75864e9			0.0401911
$554$	−7.63614e10	+	4.67270e10i	−0.810653	+	0.496054i
$555$			8.50915e10i			0.896838i
$556$	8.11726e10	+	4.14907e10i	0.849397	+	0.434162i
$557$	−2.99226e10			−0.310870			−0.155435	−	0.987846i	$-0.549678\pi$
$557$	−2.99226e10			−0.310870			−0.155435	+	0.987846i	$0.549678\pi$
$558$	3.68715e9	+	6.02555e9i	0.0380324	+	0.0621527i
$559$		−	2.03646e10i		−	0.208559i
$560$	−4.26542e10	+	3.08233e10i	−0.433721	+	0.313420i
$561$	8.68546e10			0.876882
$562$	−1.33374e11	+	8.16138e10i	−1.33698	+	0.818123i
$563$		−	9.29383e10i		−	0.925042i	−0.886608	−	0.462521i	$-0.846945\pi$
$563$		−	9.29383e10i		−	0.925042i	0.886608	−	0.462521i	$-0.153055\pi$
$564$	−2.62197e10	+	5.12963e10i	−0.259126	+	0.506955i
$565$	4.73903e10			0.465046
$566$	1.16194e10	+	1.89885e10i	0.113219	+	0.185023i
$567$		−	4.24768e9i		−	0.0410979i
$568$	−1.31206e11	+	1.00723e10i	−1.26055	+	0.0967685i
$569$	−1.27626e11			−1.21756			−0.608778	−	0.793341i	$-0.708340\pi$
$569$	−1.27626e11			−1.21756			−0.608778	+	0.793341i	$0.708340\pi$
$570$	−1.30198e11	+	7.96706e10i	−1.23340	+	0.754742i
$571$			6.17431e10i			0.580823i	0.956902	+	0.290412i	$0.0937923\pi$
$571$			6.17431e10i			0.580823i	−0.956902	+	0.290412i	$0.906208\pi$
$572$	−3.82412e10	−	1.95467e10i	−0.357230	−	0.182595i
$573$	3.99696e10			0.370776
$574$	1.94243e10	+	3.17432e10i	0.178936	+	0.292417i
$575$		−	1.88581e11i		−	1.72515i
$576$	3.62618e10	−	5.60040e9i	0.329428	−	0.0508779i
$577$	−1.29506e11			−1.16839			−0.584194	−	0.811614i	$-0.698589\pi$
$577$	−1.29506e11			−1.16839			−0.584194	+	0.811614i	$0.698589\pi$
$578$	1.30219e11	−	7.96834e10i	1.16671	−	0.713931i
$579$			4.79828e10i			0.426944i
$580$	1.21311e10	−	2.37333e10i	0.107198	−	0.209723i
$581$	−1.76850e10			−0.155203
$582$	−3.41572e10	−	5.58198e10i	−0.297708	−	0.486515i
$583$			1.79036e10i			0.154977i
$584$	−1.53460e10	−	1.99905e11i	−0.131930	−	1.71859i
$585$	2.29566e10			0.196013
$586$	1.80025e11	−	1.10161e11i	1.52666	−	0.934194i
$587$			1.10514e11i			0.930820i	0.885095	+	0.465410i	$0.154093\pi$
$587$			1.10514e11i			0.930820i	−0.885095	+	0.465410i	$0.845907\pi$
$588$	5.30458e10	+	2.71139e10i	0.443753	+	0.226821i
$589$	4.55462e10			0.378435
$590$	−8.61300e9	−	1.40754e10i	−0.0710798	−	0.116159i
$591$			3.94969e10i			0.323753i
$592$	−7.72432e10	−	1.06892e11i	−0.628888	−	0.870275i
$593$	1.24751e11			1.00884			0.504422	−	0.863457i	$-0.331706\pi$
$593$	1.24751e11			1.00884			0.504422	+	0.863457i	$0.331706\pi$
$594$	2.01711e10	−	1.23431e10i	0.162025	−	0.0991464i
$595$			1.03202e11i			0.823415i
$596$	−5.46692e10	+	1.06955e11i	−0.433269	+	0.847649i
$597$	−3.61295e10			−0.284423
$598$	4.28224e10	+	6.99806e10i	0.334863	+	0.547234i
$599$		−	2.65710e10i		−	0.206396i	−0.994661	−	0.103198i	$-0.967092\pi$
$599$		−	2.65710e10i		−	0.206396i	0.994661	−	0.103198i	$-0.0329075\pi$
$600$	8.15420e10	−	6.25970e9i	0.629182	−	0.0483002i
$601$	−2.32310e9			−0.0178062			−0.00890308	−	0.999960i	$-0.502834\pi$
$601$	−2.32310e9			−0.0178062			−0.00890308	+	0.999960i	$0.502834\pi$
$602$	2.12613e10	−	1.30102e10i	0.161884	−	0.0990601i
$603$			5.11195e10i			0.386649i
$604$	1.13092e11	+	5.78063e10i	0.849739	+	0.434337i
$605$	4.99682e9			0.0372969
$606$	2.13872e10	+	3.49510e10i	0.158585	+	0.259160i
$607$			7.34244e10i			0.540861i	0.962739	+	0.270431i	$0.0871661\pi$
$607$			7.34244e10i			0.540861i	−0.962739	+	0.270431i	$0.912834\pi$
$608$	9.12318e10	−	2.18271e11i	0.667624	−	1.59728i
$609$	4.78232e9			0.0347672
$610$	−5.67950e10	+	3.47539e10i	−0.410195	+	0.251006i
$611$		−	5.58626e10i		−	0.400826i
$612$	3.27488e10	−	6.40700e10i	0.233448	−	0.456719i
$613$	1.67042e11			1.18300			0.591499	−	0.806306i	$-0.298536\pi$
$613$	1.67042e11			1.18300			0.591499	+	0.806306i	$0.298536\pi$
$614$	8.60201e9	+	1.40574e10i	0.0605238	+	0.0989082i
$615$		−	1.10746e11i		−	0.774152i
$616$	−4.02356e9	−	5.24129e10i	−0.0279439	−	0.364011i
$617$	5.44122e8			0.00375453			0.00187727	−	0.999998i	$-0.499402\pi$
$617$	5.44122e8			0.00375453			0.00187727	+	0.999998i	$0.499402\pi$
$618$	6.25207e9	−	3.82576e9i	0.0428618	−	0.0262279i
$619$			1.21943e11i			0.830608i	0.909683	+	0.415304i	$0.136325\pi$
$619$			1.21943e11i			0.830608i	−0.909683	+	0.415304i	$0.863675\pi$
$620$	−4.16094e10	−	2.12683e10i	−0.281595	−	0.143935i
$621$	−4.51750e10			−0.303761
$622$	8.62474e10	+	1.40946e11i	0.576215	+	0.941652i
$623$		−	7.51239e9i		−	0.0498684i
$624$	−2.88380e10	+	2.08392e10i	−0.190207	+	0.137450i
$625$	−1.37081e11			−0.898372
$626$	−2.38914e10	+	1.46196e10i	−0.155576	+	0.0952001i
$627$		−	1.52470e11i		−	0.986538i
$628$	1.14889e11	−	2.24769e11i	0.738652	−	1.44510i
$629$	−2.58624e11			−1.65221
$630$	1.46662e10	+	2.39675e10i	0.0931010	+	0.152146i
$631$		−	8.33346e10i		−	0.525664i	−0.964842	−	0.262832i	$-0.915344\pi$
$631$		−	8.33346e10i		−	0.525664i	0.964842	−	0.262832i	$-0.0846564\pi$
$632$	1.72846e10	−	1.32688e9i	0.108341	−	0.00831695i
$633$	−1.02868e11			−0.640715
$634$	−1.70920e11	+	1.04589e11i	−1.05788	+	0.647334i
$635$			3.23858e11i			1.99186i
$636$	1.32070e10	+	6.75063e9i	0.0807188	+	0.0412588i
$637$	−5.77678e10			−0.350855
$638$	1.38966e10	+	2.27099e10i	0.0838738	+	0.137067i
$639$			7.02619e10i			0.421421i
$640$	−1.85270e11	+	1.56803e11i	−1.10430	+	0.934619i
$641$	1.00359e11			0.594461			0.297230	−	0.954806i	$-0.403937\pi$
$641$	1.00359e11			0.594461			0.297230	+	0.954806i	$0.403937\pi$
$642$	7.29797e10	−	4.46577e10i	0.429597	−	0.262879i
$643$			1.93698e11i			1.13313i	0.824016	+	0.566566i	$0.191729\pi$
$643$			1.93698e11i			1.13313i	−0.824016	+	0.566566i	$0.808271\pi$
$644$	−4.57044e10	+	8.94162e10i	−0.265714	+	0.519844i
$645$	−7.41766e10			−0.428576
$646$	−2.42148e11	−	3.95718e11i	−1.39043	−	2.27225i
$647$			4.50875e10i			0.257299i	0.991690	+	0.128650i	$0.0410643\pi$
$647$			4.50875e10i			0.257299i	−0.991690	+	0.128650i	$0.958936\pi$
$648$	−1.49952e9	−	1.95336e10i	−0.00850460	−	0.110785i
$649$	1.64832e10			0.0929098
$650$	−6.76434e10	+	4.13923e10i	−0.378942	+	0.231882i
$651$		−	8.38438e9i		−	0.0466817i
$652$	−3.23116e10	−	1.65158e10i	−0.178800	−	0.0913922i
$653$	−1.52943e11			−0.841156			−0.420578	−	0.907256i	$-0.638173\pi$
$653$	−1.52943e11			−0.841156			−0.420578	+	0.907256i	$0.638173\pi$
$654$	1.63384e10	+	2.67003e10i	0.0893099	+	0.145950i
$655$		−	2.82390e11i		−	1.53421i
$656$	1.00531e11	+	1.39118e11i	0.542857	+	0.751223i
$657$	−1.07050e11			−0.574549
$658$	5.83224e10	−	3.56886e10i	0.311123	−	0.190382i
$659$		−	2.18458e11i		−	1.15831i	−0.815217	−	0.579156i	$-0.803382\pi$
$659$		−	2.18458e11i		−	1.15831i	0.815217	−	0.579156i	$-0.196618\pi$
$660$	−7.11974e10	+	1.39291e11i	−0.375222	+	0.734087i
$661$	3.70484e11			1.94073			0.970363	−	0.241654i	$-0.0776899\pi$
$661$	3.70484e11			1.94073			0.970363	+	0.241654i	$0.0776899\pi$
$662$	1.50312e11	+	2.45641e11i	0.782641	+	1.27899i
$663$			6.97734e10i			0.361107i
$664$	−8.13268e10	+	6.24318e9i	−0.418371	+	0.0321169i
$665$	1.81167e11			0.926385
$666$	−6.00626e10	+	3.67534e10i	−0.305286	+	0.186810i
$667$		−	5.08609e10i		−	0.256969i
$668$	1.42870e11	+	7.30266e10i	0.717520	+	0.366754i
$669$	2.16017e11			1.07841
$670$	−1.76502e11	−	2.88441e11i	−0.875894	−	1.43139i
$671$		−	6.65105e10i		−	0.328095i
$672$	−4.01805e10	−	1.67944e10i	−0.197033	−	0.0823546i
$673$	2.24080e11			1.09230			0.546150	−	0.837687i	$-0.316093\pi$
$673$	2.24080e11			1.09230			0.546150	+	0.837687i	$0.316093\pi$
$674$	6.17959e10	−	3.78141e10i	0.299447	−	0.183238i
$675$		−	4.36663e10i		−	0.210345i
$676$	−7.93415e10	+	1.55224e11i	−0.379939	+	0.743314i
$677$	1.16058e11			0.552483			0.276241	−	0.961088i	$-0.410911\pi$
$677$	1.16058e11			0.552483			0.276241	+	0.961088i	$0.410911\pi$
$678$	2.04692e10	+	3.34509e10i	0.0968685	+	0.158303i
$679$			7.76716e10i			0.365412i
$680$	3.64324e10	+	4.74587e11i	0.170393	+	2.21963i
$681$	−5.80806e10			−0.270049
$682$	3.98151e10	−	2.43636e10i	0.184039	−	0.112617i
$683$		−	2.91871e11i		−	1.34125i	−0.741799	−	0.670623i	$-0.766027\pi$
$683$		−	2.91871e11i		−	1.34125i	0.741799	−	0.670623i	$-0.233973\pi$
$684$	−1.12472e11	−	5.74893e10i	−0.513832	−	0.262641i
$685$	−1.82938e11			−0.830887
$686$	−7.96610e10	−	1.30182e11i	−0.359708	−	0.587835i
$687$		−	2.26309e11i		−	1.01596i
$688$	9.31804e10	−	6.73350e10i	0.415882	−	0.300530i
$689$	−1.43826e10			−0.0638207
$690$	2.54899e11	−	1.55978e11i	1.12453	−	0.688123i
$691$		−	3.60245e11i		−	1.58011i	−0.613039	−	0.790053i	$-0.710053\pi$
$691$		−	3.60245e11i		−	1.58011i	0.613039	−	0.790053i	$-0.289947\pi$
$692$	3.79655e10	−	7.42760e10i	0.165564	−	0.323910i
$693$	−2.80674e10			−0.121694
$694$	1.90849e11	+	3.11886e11i	0.822721	+	1.34449i
$695$			3.21985e11i			1.38006i
$696$	2.19922e10	−	1.68826e9i	0.0937197	−	0.00719454i
$697$	3.36596e11			1.42619
$698$	9.87890e10	−	6.04509e10i	0.416186	−	0.254672i
$699$		−	5.91209e10i		−	0.247646i
$700$	−8.64300e10	−	4.41780e10i	−0.359975	−	0.183998i
$701$	−1.34090e11			−0.555297			−0.277648	−	0.960683i	$-0.589555\pi$
$701$	−1.34090e11			−0.555297			−0.277648	+	0.960683i	$0.589555\pi$
$702$	9.91562e9	+	1.62041e10i	0.0408292	+	0.0667232i
$703$			4.54004e11i			1.85882i
$704$	−3.70058e10	−	2.39607e11i	−0.150653	−	0.975460i
$705$	−2.03475e11			−0.823674
$706$	−1.23189e11	+	7.53816e10i	−0.495853	+	0.303422i
$707$		−	4.86332e10i		−	0.194651i
$708$	6.21503e9	−	1.21591e10i	0.0247349	−	0.0483915i
$709$	−3.08644e11			−1.22144			−0.610722	−	0.791845i	$-0.709121\pi$
$709$	−3.08644e11			−1.22144			−0.610722	+	0.791845i	$0.709121\pi$
$710$	−2.42596e11	−	3.96452e11i	−0.954665	−	1.56012i
$711$		−	9.25603e9i		−	0.0362198i
$712$	−2.65204e9	−	3.45468e10i	−0.0103195	−	0.134427i
$713$	−8.91696e10			−0.345031
$714$	−7.28458e10	+	4.45757e10i	−0.280293	+	0.171516i
$715$		−	1.51690e11i		−	0.580409i
$716$	1.13066e11	+	5.77928e10i	0.430210	+	0.219898i
$717$	1.61441e11			0.610853
$718$	7.46817e10	+	1.22045e11i	0.281007	+	0.459222i
$719$			1.71505e11i			0.641743i	0.947123	+	0.320872i	$0.103976\pi$
$719$			1.71505e11i			0.641743i	−0.947123	+	0.320872i	$0.896024\pi$
$720$	7.59055e10	+	1.05040e11i	0.282451	+	0.390865i
$721$	−8.69957e9			−0.0321927
$722$	−4.62883e11	+	2.83247e11i	−1.70342	+	1.04236i
$723$			1.31586e11i			0.481568i
$724$	−6.56680e10	+	1.28473e11i	−0.239001	+	0.467582i
$725$	4.91623e10			0.177943
$726$	2.15827e9	+	3.52705e9i	0.00776890	+	0.0126960i
$727$			3.25160e11i			1.16402i	0.813182	+	0.582009i	$0.197733\pi$
$727$			3.25160e11i			1.16402i	−0.813182	+	0.582009i	$0.802267\pi$
$728$	4.21051e10	−	3.23226e9i	0.149903	−	0.0115075i
$729$	−1.04604e10			−0.0370370
$730$	6.04030e11	−	3.69618e11i	2.12700	−	1.30155i
$731$		−	2.25449e11i		−	0.789550i
$732$	−4.90627e10	−	2.50780e10i	−0.170886	−	0.0873472i
$733$	−2.93827e11			−1.01783			−0.508915	−	0.860817i	$-0.669953\pi$
$733$	−2.93827e11			−1.01783			−0.508915	+	0.860817i	$0.669953\pi$
$734$	−7.80117e10	−	1.27487e11i	−0.268767	−	0.439219i
$735$			2.10415e11i			0.720987i
$736$	−1.78612e11	+	4.27328e11i	−0.608695	+	1.45630i
$737$	3.37782e11			1.14490
$738$	7.81708e10	−	4.78342e10i	0.263524	−	0.161255i
$739$			6.13111e10i			0.205571i	0.994704	+	0.102785i	$0.0327755\pi$
$739$			6.13111e10i			0.205571i	−0.994704	+	0.102785i	$0.967225\pi$
$740$	2.12002e11	−	4.14761e11i	0.706989	−	1.38316i
$741$	1.22484e11			0.406264
$742$	−9.18855e9	−	1.50160e10i	−0.0303132	−	0.0495379i
$743$		−	1.25399e11i		−	0.411471i	−0.978608	−	0.205735i	$-0.934041\pi$
$743$		−	1.25399e11i		−	0.411471i	0.978608	−	0.205735i	$-0.0659586\pi$
$744$	−2.95987e9	−	3.85567e10i	−0.00966008	−	0.125837i
$745$	−4.24255e11			−1.37722
$746$	−1.10578e11	+	6.76645e10i	−0.357036	+	0.218477i
$747$			4.35510e10i			0.139867i
$748$	−4.23355e11	−	2.16395e11i	−1.35238	−	0.691258i
$749$	−1.01549e11			−0.322663
$750$	1.28262e10	+	2.09606e10i	0.0405371	+	0.0662459i
$751$			7.03859e10i			0.221272i	0.993861	+	0.110636i	$0.0352887\pi$
$751$			7.03859e10i			0.221272i	−0.993861	+	0.110636i	$0.964711\pi$
$752$	2.55605e11	−	1.84708e11i	0.799278	−	0.577583i
$753$	−4.80269e10			−0.149384
$754$	−1.82437e10	+	1.11636e10i	−0.0564451	+	0.0345399i
$755$			4.48600e11i			1.38061i
$756$	−1.05829e10	+	2.07045e10i	−0.0323980	+	0.0633837i
$757$	2.29777e11			0.699717			0.349859	−	0.936802i	$-0.386230\pi$
$757$	2.29777e11			0.699717			0.349859	+	0.936802i	$0.386230\pi$
$758$	−2.30863e11	−	3.77278e11i	−0.699324	−	1.14284i
$759$			2.98503e11i			0.899459i
$760$	8.33120e11	−	6.39557e10i	2.49720	−	0.191701i
$761$	−5.18557e11			−1.54617			−0.773086	−	0.634301i	$-0.781288\pi$
$761$	−5.18557e11			−1.54617			−0.773086	+	0.634301i	$0.781288\pi$
$762$	−2.28598e11	+	1.39883e11i	−0.678035	+	0.414902i
$763$		−	3.71527e10i		−	0.109621i
$764$	−1.94824e11	−	9.95826e10i	−0.571833	−	0.292287i
$765$	2.54145e11			0.742053
$766$	2.54322e11	+	4.15613e11i	0.738700	+	1.20719i
$767$			1.32415e10i			0.0382610i
$768$	−1.90704e11	−	6.30469e10i	−0.548170	−	0.181225i
$769$	−3.27159e11			−0.935521			−0.467761	−	0.883855i	$-0.654939\pi$
$769$	−3.27159e11			−0.935521			−0.467761	+	0.883855i	$0.654939\pi$
$770$	1.58370e11	−	9.69096e10i	0.450516	−	0.275679i
$771$		−	8.42234e10i		−	0.238350i
$772$	1.19547e11	−	2.33882e11i	0.336566	−	0.658459i
$773$	−4.27537e11			−1.19744			−0.598722	−	0.800957i	$-0.704325\pi$
$773$	−4.27537e11			−1.19744			−0.598722	+	0.800957i	$0.704325\pi$
$774$	−3.20390e10	−	5.23582e10i	−0.0892720	−	0.145888i
$775$		−	8.61916e10i		−	0.238923i
$776$	2.74198e10	+	3.57184e11i	0.0756165	+	0.985019i
$777$	8.35753e10			0.229295
$778$	−2.20252e10	+	1.34776e10i	−0.0601176	+	0.0367871i
$779$		−	5.90881e11i		−	1.60454i
$780$	−1.11897e11	−	5.71954e10i	−0.302302	−	0.154519i
$781$	4.64270e11			1.24786
$782$	4.74072e11	+	7.74730e11i	1.26770	+	2.07168i
$783$		−	1.17769e10i		−	0.0313318i
$784$	−1.91008e11	−	2.64323e11i	−0.505576	−	0.699633i
$785$	8.91586e11			2.34793
$786$	1.99327e11	−	1.21972e11i	0.522248	−	0.319574i
$787$		−	6.74861e11i		−	1.75920i	−0.475713	−	0.879601i	$-0.657810\pi$
$787$		−	6.74861e11i		−	1.75920i	0.475713	−	0.879601i	$-0.342190\pi$
$788$	9.84050e10	−	1.92520e11i	0.255219	−	0.499311i
$789$	3.08414e11			0.795841
$790$	3.19587e10	+	5.22270e10i	0.0820505	+	0.134087i
$791$		−	4.65459e10i		−	0.118898i
$792$	−1.29072e11	+	9.90841e9i	−0.328043	+	0.0251828i
$793$	5.34302e10			0.135112
$794$	−4.98666e11	+	3.05144e11i	−1.25467	+	0.767754i
$795$			5.23877e10i			0.131148i
$796$	1.76106e11	+	9.00151e10i	0.438654	+	0.224214i
$797$	−1.45915e11			−0.361631			−0.180816	−	0.983517i	$-0.557874\pi$
$797$	−1.45915e11			−0.361631			−0.180816	+	0.983517i	$0.557874\pi$
$798$	7.82510e10	+	1.27878e11i	0.192965	+	0.315344i
$799$		−	6.18435e11i		−	1.51742i
$800$	−4.13056e11	−	1.72647e11i	−1.00844	−	0.421501i
$801$	−1.85000e10			−0.0449409
$802$	−3.58710e11	+	2.19502e11i	−0.867054	+	0.530567i
$803$			7.07357e11i			1.70128i
$804$	1.27362e11	−	2.49172e11i	0.304801	−	0.596313i
$805$	−3.54685e11			−0.844615
$806$	1.95721e10	+	3.19849e10i	0.0463765	+	0.0757886i
$807$		−	3.67550e10i		−	0.0866607i
$808$	−1.71686e10	−	2.23647e11i	−0.0402800	−	0.524707i
$809$	8.40339e11			1.96183			0.980913	−	0.194448i	$-0.0622914\pi$
$809$	8.40339e11			1.96183			0.980913	+	0.194448i	$0.0622914\pi$
$810$	5.90224e10	−	3.61169e10i	0.137112	−	0.0839017i
$811$		−	4.58864e10i		−	0.106072i	−0.998593	−	0.0530360i	$-0.983110\pi$
$811$		−	4.58864e10i		−	0.106072i	0.998593	−	0.0530360i	$-0.0168898\pi$
$812$	−2.33105e10	−	1.19149e10i	−0.0536200	−	0.0274074i
$813$	−2.27079e11			−0.519774
$814$	2.42856e11	+	3.96875e11i	0.553160	+	0.903976i
$815$		−	1.28169e11i		−	0.290505i
$816$	−3.19255e11	+	2.30704e11i	−0.720075	+	0.520349i
$817$	−3.95768e11			−0.888284
$818$	2.31857e11	−	1.41878e11i	0.517853	−	0.316884i
$819$		−	2.25476e10i		−	0.0501146i
$820$	−2.75918e11	+	5.39808e11i	−0.610274	+	1.19394i
$821$	6.15115e11			1.35389			0.676946	−	0.736033i	$-0.263303\pi$
$821$	6.15115e11			1.35389			0.676946	+	0.736033i	$0.263303\pi$
$822$	−7.90162e10	−	1.29128e11i	−0.173073	−	0.282836i
$823$			2.81774e11i			0.614188i	0.951679	+	0.307094i	$0.0993566\pi$
$823$			2.81774e11i			0.614188i	−0.951679	+	0.307094i	$0.900643\pi$
$824$	−4.00062e10	+	3.07114e9i	−0.0867798	+	0.00666178i
$825$	−2.88534e11			−0.622846
$826$	−1.38246e10	+	8.45953e9i	−0.0296983	+	0.0181730i
$827$			3.61753e10i			0.0773375i	0.999252	+	0.0386688i	$0.0123117\pi$
$827$			3.61753e10i			0.0773375i	−0.999252	+	0.0386688i	$0.987688\pi$
$828$	2.20196e11	+	1.12552e11i	0.468478	+	0.239459i
$829$	3.05903e11			0.647687			0.323843	−	0.946111i	$-0.395025\pi$
$829$	3.05903e11			0.647687			0.323843	+	0.946111i	$0.395025\pi$
$830$	−1.50371e11	−	2.45736e11i	−0.316848	−	0.517793i
$831$		−	2.61663e11i		−	0.548704i
$832$	1.92485e11	−	2.97280e10i	0.401702	−	0.0620402i
$833$	−6.39527e11			−1.32825
$834$	−2.27276e11	+	1.39075e11i	−0.469775	+	0.287464i
$835$			5.66716e11i			1.16579i
$836$	−3.79872e11	+	7.43184e11i	−0.777701	+	1.52150i
$837$	−2.06474e10			−0.0420691
$838$	−4.00481e11	−	6.54467e11i	−0.812093	−	1.32712i
$839$			3.84879e11i			0.776741i	0.921503	+	0.388370i	$0.126962\pi$
$839$			3.84879e11i			0.776741i	−0.921503	+	0.388370i	$0.873038\pi$
$840$	−1.17733e10	−	1.53365e11i	−0.0236473	−	0.308041i
$841$	−4.86987e11			−0.973495
$842$	4.11559e10	−	2.51841e10i	0.0818810	−	0.0501046i
$843$		−	4.57023e11i		−	0.904956i
$844$	5.01409e11	+	2.56291e11i	0.988148	+	0.505084i
$845$	−6.15723e11			−1.20770
$846$	−8.78868e10	−	1.43625e11i	−0.171570	−	0.280381i
$847$		−	4.90779e9i		−	0.00953569i
$848$	−4.75558e10	−	6.58092e10i	−0.0919645	−	0.127263i
$849$	−6.50667e10			−0.125236
$850$	−7.48857e11	+	4.58240e11i	−1.43457	+	0.877843i
$851$		−	8.88840e11i		−	1.69475i
$852$	1.75055e11	−	3.42478e11i	0.332212	−	0.649941i
$853$	1.53208e11			0.289390			0.144695	−	0.989476i	$-0.453780\pi$
$853$	1.53208e11			0.289390			0.144695	+	0.989476i	$0.453780\pi$
$854$	3.41347e10	+	5.57830e10i	0.0641748	+	0.104875i
$855$		−	4.46141e11i		−	0.834848i
$856$	−4.66987e11	+	3.58490e10i	−0.869781	+	0.0667701i
$857$	1.07815e11			0.199873			0.0999365	−	0.994994i	$-0.468136\pi$
$857$	1.07815e11			0.199873			0.0999365	+	0.994994i	$0.468136\pi$
$858$	1.07072e11	−	6.55194e10i	0.197573	−	0.120899i
$859$		−	1.94089e11i		−	0.356474i	−0.983988	−	0.178237i	$-0.942961\pi$
$859$		−	1.94089e11i		−	0.356474i	0.983988	−	0.178237i	$-0.0570394\pi$
$860$	3.61559e11	+	1.84808e11i	0.660976	+	0.337852i
$861$	−1.08772e11			−0.197928
$862$	−1.26693e11	−	2.07041e11i	−0.229468	−	0.374997i
$863$			9.36925e11i			1.68913i	0.535457	+	0.844563i	$0.320139\pi$
$863$			9.36925e11i			1.68913i	−0.535457	+	0.844563i	$0.679861\pi$
$864$	−4.13579e10	+	9.89485e10i	−0.0742171	+	0.177564i
$865$	2.94628e11			0.526272
$866$	7.85677e11	−	4.80771e11i	1.39692	−	0.854804i
$867$			4.46213e11i			0.789706i
$868$	−2.08893e10	+	4.08680e10i	−0.0367998	+	0.0719953i
$869$	−6.11611e10			−0.107250
$870$	4.06628e10	+	6.64512e10i	0.0709774	+	0.115991i
$871$			2.71352e11i			0.471478i
$872$	−1.31157e10	−	1.70852e11i	−0.0226843	−	0.295498i
$873$	1.91274e11			0.329306
$874$	1.36001e12	−	8.32216e11i	2.33075	−	1.42623i
$875$		−	2.91661e10i		−	0.0497560i
$876$	5.21796e11	+	2.66712e11i	0.886103	+	0.452924i
$877$	8.90245e11			1.50491			0.752456	−	0.658643i	$-0.228869\pi$
$877$	8.90245e11			1.50491			0.752456	+	0.658643i	$0.228869\pi$
$878$	4.61038e11	+	7.53430e11i	0.775816	+	1.26784i
$879$			6.16881e11i			1.03335i
$880$	6.94075e11	−	5.01561e11i	1.15738	−	0.836359i
$881$	2.69111e11			0.446713			0.223356	−	0.974737i	$-0.428299\pi$
$881$	2.69111e11			0.446713			0.223356	+	0.974737i	$0.428299\pi$
$882$	−1.48523e11	+	9.08843e10i	−0.245426	+	0.150181i
$883$			4.13945e11i			0.680926i	0.940258	+	0.340463i	$0.110584\pi$
$883$			4.13945e11i			0.680926i	−0.940258	+	0.340463i	$0.889416\pi$
$884$	1.73837e11	−	3.40096e11i	0.284665	−	0.556920i
$885$	4.82312e10			0.0786240
$886$	−5.82446e11	−	9.51834e11i	−0.945193	−	1.54464i
$887$		−	3.61899e11i		−	0.584645i	−0.956320	−	0.292323i	$-0.905572\pi$
$887$		−	3.61899e11i		−	0.584645i	0.956320	−	0.292323i	$-0.0944281\pi$
$888$	3.84333e11	−	2.95039e10i	0.618095	−	0.0474490i
$889$	3.18087e11			0.509259
$890$	1.04386e11	−	6.38758e10i	0.166373	−	0.101807i
$891$			6.91189e10i			0.109670i
$892$	−1.05293e12	−	5.38197e11i	−1.66318	−	0.850123i
$893$	−1.08564e12			−1.70718
$894$	−1.83248e11	−	2.99464e11i	−0.286873	−	0.468808i
$895$			4.48496e11i			0.698982i
$896$	1.54009e11	+	1.81969e11i	0.238954	+	0.282335i
$897$	−2.39798e11			−0.370404
$898$	−2.00793e11	+	1.22869e11i	−0.308775	+	0.188945i
$899$		−	2.32462e10i		−	0.0355887i
$900$	−1.08793e11	+	2.12843e11i	−0.165817	+	0.324406i
$901$	−1.59225e11			−0.241608
$902$	−3.16074e11	−	5.16530e11i	−0.477489	−	0.780313i
$903$			7.28549e10i			0.109574i
$904$	−1.64317e10	−	2.14048e11i	−0.0246042	−	0.320506i
$905$	−5.09611e11			−0.759704
$906$	−3.16649e11	+	1.93763e11i	−0.469964	+	0.287580i
$907$			2.54784e11i			0.376482i	0.982123	+	0.188241i	$0.0602785\pi$
$907$			2.54784e11i			0.376482i	−0.982123	+	0.188241i	$0.939721\pi$
$908$	2.83102e11	+	1.44705e11i	0.416485	+	0.212883i
$909$	−1.19764e11			−0.175417
$910$	7.78510e10	+	1.27224e11i	0.113527	+	0.185526i
$911$		−	4.42772e11i		−	0.642845i	−0.946936	−	0.321422i	$-0.895839\pi$
$911$		−	4.42772e11i		−	0.642845i	0.946936	−	0.321422i	$-0.104161\pi$
$912$	4.04992e11	+	5.60441e11i	0.585419	+	0.810122i
$913$	2.87772e11			0.414158
$914$	8.69654e11	−	5.32158e11i	1.24613	−	0.762528i
$915$		−	1.94616e11i		−	0.277647i
$916$	−5.63840e11	+	1.10310e12i	−0.800893	+	1.56687i
$917$	−2.77358e11			−0.392251
$918$	1.09772e11	+	1.79390e11i	0.154569	+	0.252597i
$919$		−	1.21088e12i		−	1.69761i	−0.528708	−	0.848804i	$-0.677323\pi$
$919$		−	1.21088e12i		−	1.69761i	0.528708	−	0.848804i	$-0.322677\pi$
$920$	−1.63107e12	+	1.25211e11i	−2.27678	+	0.174780i
$921$	−4.81697e10			−0.0669476
$922$	−5.36735e11	+	3.28439e11i	−0.742739	+	0.454496i
$923$			3.72964e11i			0.513879i
$924$	1.36809e11	+	6.99288e10i	0.187684	+	0.0959331i
$925$	8.59156e11			1.17356
$926$	−5.77271e11	−	9.43378e11i	−0.785120	−	1.28304i
$927$			2.14236e10i			0.0290117i
$928$	−1.11403e11	−	4.65634e10i	−0.150212	−	0.0627846i
$929$	1.00636e12			1.35110			0.675552	−	0.737313i	$-0.263905\pi$
$929$	1.00636e12			1.35110			0.675552	+	0.737313i	$0.263905\pi$
$930$	1.16503e11	−	7.12901e10i	0.155741	−	0.0953010i
$931$			1.12266e12i			1.49435i
$932$	−1.47297e11	+	2.88173e11i	−0.195223	+	0.381935i
$933$	−4.82970e11			−0.637373
$934$	3.74901e11	+	6.12663e11i	0.492639	+	0.805072i
$935$		−	1.67931e12i		−	2.19728i
$936$	−7.95978e9	−	1.03688e11i	−0.0103705	−	0.135091i
$937$	−9.83820e11			−1.27631			−0.638156	−	0.769907i	$-0.720303\pi$
$937$	−9.83820e11			−1.27631			−0.638156	+	0.769907i	$0.720303\pi$
$938$	−2.83301e11	+	1.73357e11i	−0.365963	+	0.223940i
$939$		−	8.18670e10i		−	0.105304i
$940$	9.91800e11	+	5.06950e11i	1.27032	+	0.649313i
$941$	−5.99824e11			−0.765007			−0.382503	−	0.923954i	$-0.624938\pi$
$941$	−5.99824e11			−0.765007			−0.382503	+	0.923954i	$0.624938\pi$
$942$	3.85102e11	+	6.29334e11i	0.489071	+	0.799241i
$943$			1.15682e12i			1.46291i
$944$	−6.05879e10	+	4.37827e10i	−0.0762953	+	0.0551334i
$945$	−8.21279e10			−0.102982
$946$	−3.45967e11	+	2.11704e11i	−0.431987	+	0.264341i
$947$			4.79898e11i			0.596690i	0.954458	+	0.298345i	$0.0964347\pi$
$947$			4.79898e11i			0.596690i	−0.954458	+	0.298345i	$0.903565\pi$
$948$	−2.30610e10	+	4.51167e10i	−0.0285526	+	0.0558604i
$949$	−5.68245e11			−0.700601
$950$	8.04422e11	+	1.31459e12i	0.987619	+	1.61397i
$951$		−	5.85679e11i		−	0.716041i
$952$	4.66131e11	−	3.57833e10i	0.567492	−	0.0435644i
$953$	3.29855e11			0.399900			0.199950	−	0.979806i	$-0.435922\pi$
$953$	3.29855e11			0.399900			0.199950	+	0.979806i	$0.435922\pi$
$954$	−3.69783e10	+	2.26277e10i	−0.0446430	+	0.0273179i
$955$		−	7.72802e11i		−	0.929084i
$956$	−7.86911e11	−	4.02223e11i	−0.942093	−	0.481543i
$957$	−7.78185e10			−0.0927759
$958$	−6.31785e11	−	1.03246e12i	−0.750080	−	1.22578i
$959$			1.79678e11i			0.212433i
$960$	−1.08282e11	−	7.01114e11i	−0.127489	−	0.825474i
$961$	8.12136e11			0.952215
$962$	−3.18824e11	+	1.95095e11i	−0.372264	+	0.227795i
$963$			2.50075e11i			0.290780i
$964$	3.27842e11	−	6.41391e11i	0.379626	−	0.742703i
$965$	9.27735e11			1.06983
$966$	−1.53198e11	−	2.50357e11i	−0.175932	−	0.287509i
$967$		−	1.51059e12i		−	1.72759i	−0.503844	−	0.863795i	$-0.668081\pi$
$967$		−	1.51059e12i		−	1.72759i	0.503844	−	0.863795i	$-0.331919\pi$
$968$	−1.73256e9	−	2.25691e10i	−0.00197327	−	0.0257048i
$969$	1.35598e12			1.53801
$970$	−1.07926e12	+	6.60421e11i	−1.21910	+	0.745991i
$971$			2.03838e11i			0.229302i	0.993406	+	0.114651i	$0.0365750\pi$
$971$			2.03838e11i			0.229302i	−0.993406	+	0.114651i	$0.963425\pi$
$972$	5.09869e10	+	2.60615e10i	0.0571207	+	0.0291968i
$973$	3.16248e11			0.352839
$974$	4.50479e11	+	7.36174e11i	0.500540	+	0.817984i
$975$		−	2.31789e11i		−	0.256493i
$976$	1.76666e11	+	2.44476e11i	0.194694	+	0.269424i
$977$	−6.73129e11			−0.738789			−0.369394	−	0.929273i	$-0.620435\pi$
$977$	−6.73129e11			−0.738789			−0.369394	+	0.929273i	$0.620435\pi$
$978$	9.04695e10	−	5.53600e10i	0.0988887	−	0.0605119i
$979$			1.22243e11i			0.133074i
$980$	5.24240e11	−	1.02563e12i	0.568363	−	1.11195i
$981$	−9.14923e10			−0.0987890
$982$	8.07919e11	+	1.32030e12i	0.868804	+	1.41980i
$983$		−	1.18974e12i		−	1.27420i	−0.770780	−	0.637101i	$-0.780133\pi$
$983$		−	1.18974e12i		−	1.27420i	0.770780	−	0.637101i	$-0.219867\pi$
$984$	−5.00205e11	+	3.83990e10i	−0.533541	+	0.0409581i
$985$	7.63663e11			0.811254
$986$	−2.01969e11	+	1.23589e11i	−0.213687	+	0.130759i
$987$			1.99850e11i			0.210589i
$988$	−5.97026e11	−	3.05165e11i	−0.626564	−	0.320263i
$989$	7.74827e11			0.809878
$990$	−2.38650e11	−	3.90002e11i	−0.248439	−	0.406000i
$991$		−	1.02703e11i		−	0.106485i	−0.998582	−	0.0532424i	$-0.983044\pi$
$991$		−	1.02703e11i		−	0.106485i	0.998582	−	0.0532424i	$-0.0169556\pi$
$992$	−8.16352e10	+	1.95311e11i	−0.0843006	+	0.201688i
$993$	−8.41721e11			−0.865708
$994$	−3.89388e11	+	2.38274e11i	−0.398875	+	0.244079i
$995$			6.98554e11i			0.712702i
$996$	1.08506e11	−	2.12281e11i	0.110259	−	0.215711i
$997$	−6.63905e11			−0.671932			−0.335966	−	0.941874i	$-0.609063\pi$
$997$	−6.63905e11			−0.671932			−0.335966	+	0.941874i	$0.609063\pi$
$998$	1.01131e11	+	1.65269e11i	0.101944	+	0.166597i
$999$		−	2.05813e11i		−	0.206638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.9.d.a.7.7	✓	8
3.2	odd	2		36.9.d.c.19.2		8
4.3	odd	2	inner	12.9.d.a.7.8	yes	8
8.3	odd	2		192.9.g.e.127.5		8
8.5	even	2		192.9.g.e.127.1		8
12.11	even	2		36.9.d.c.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.9.d.a.7.7	✓	8	1.1	even	1	trivial
12.9.d.a.7.8	yes	8	4.3	odd	2	inner
36.9.d.c.19.1		8	12.11	even	2
36.9.d.c.19.2		8	3.2	odd	2
192.9.g.e.127.1		8	8.5	even	2
192.9.g.e.127.5		8	8.3	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(13.6476 - 8.35123i) q^{2} +46.7654i q^{3} +(116.514 - 227.948i) q^{4} +904.196 q^{5} +(390.548 + 638.235i) q^{6} -888.085i q^{7} +(-313.513 - 4083.98i) q^{8} -2187.00 q^{9} +O(q^{10})\)	\(q+(13.6476 - 8.35123i) q^{2} +46.7654i q^{3} +(116.514 - 227.948i) q^{4} +904.196 q^{5} +(390.548 + 638.235i) q^{6} -888.085i q^{7} +(-313.513 - 4083.98i) q^{8} -2187.00 q^{9} +(12340.1 - 7551.15i) q^{10} +14451.0i q^{11} +(10660.1 + 5448.82i) q^{12} -11609.0 q^{13} +(-7416.60 - 12120.2i) q^{14} +42285.1i q^{15} +(-38385.0 - 53118.4i) q^{16} -128520. q^{17} +(-29847.3 + 18264.1i) q^{18} +225611. i q^{19} +(105352. - 206110. i) q^{20} +41531.6 q^{21} +(120684. + 197222. i) q^{22} -441698. i q^{23} +(190989. - 14661.6i) q^{24} +426946. q^{25} +(-158435. + 96949.7i) q^{26} -102276. i q^{27} +(-202438. - 103474. i) q^{28} +115149. q^{29} +(353132. + 577090. i) q^{30} -201879. i q^{31} +(-967466. - 404376. i) q^{32} -675808. q^{33} +(-1.75398e6 + 1.07330e6i) q^{34} -803004. i q^{35} +(-254816. + 498523. i) q^{36} +2.01233e6 q^{37} +(1.88413e6 + 3.07905e6i) q^{38} -542901. i q^{39} +(-283478. - 3.69272e6i) q^{40} -2.61903e6 q^{41} +(566807. - 346840. i) q^{42} +1.75420e6i q^{43} +(3.29409e6 + 1.68375e6i) q^{44} -1.97748e6 q^{45} +(-3.68872e6 - 6.02811e6i) q^{46} +4.81199e6i q^{47} +(2.48410e6 - 1.79509e6i) q^{48} +4.97611e6 q^{49} +(5.82679e6 - 3.56553e6i) q^{50} -6.01026e6i q^{51} +(-1.35261e6 + 2.64626e6i) q^{52} +1.23892e6 q^{53} +(-854129. - 1.39582e6i) q^{54} +1.30666e7i q^{55} +(-3.62693e6 + 278427. i) q^{56} -1.05508e7 q^{57} +(1.57150e6 - 961634. i) q^{58} -1.14062e6i q^{59} +(9.63882e6 + 4.92680e6i) q^{60} -4.60247e6 q^{61} +(-1.68594e6 - 2.75517e6i) q^{62} +1.94224e6i q^{63} +(-1.65806e7 + 2.56077e6i) q^{64} -1.04968e7 q^{65} +(-9.22316e6 + 5.64383e6i) q^{66} -2.33742e7i q^{67} +(-1.49743e7 + 2.92958e7i) q^{68} +2.06561e7 q^{69} +(-6.70607e6 - 1.09591e7i) q^{70} -3.21271e7i q^{71} +(685654. + 8.93167e6i) q^{72} +4.89485e7 q^{73} +(2.74635e7 - 1.68054e7i) q^{74} +1.99663e7i q^{75} +(5.14277e7 + 2.62868e7i) q^{76} +1.28338e7 q^{77} +(-4.53389e6 - 7.40929e6i) q^{78} +4.23230e6i q^{79} +(-3.47076e7 - 4.80294e7i) q^{80} +4.78297e6 q^{81} +(-3.57434e7 + 2.18721e7i) q^{82} -1.99136e7i q^{83} +(4.83902e6 - 9.46707e6i) q^{84} -1.16207e8 q^{85} +(1.46497e7 + 2.39407e7i) q^{86} +5.38498e6i q^{87} +(5.90178e7 - 4.53060e6i) q^{88} +8.45908e6 q^{89} +(-2.69878e7 + 1.65144e7i) q^{90} +1.03098e7i q^{91} +(-1.00684e8 - 5.14639e7i) q^{92} +9.44096e6 q^{93} +(4.01860e7 + 6.56721e7i) q^{94} +2.03997e8i q^{95} +(1.89108e7 - 4.52439e7i) q^{96} -8.74596e7 q^{97} +(6.79119e7 - 4.15566e7i) q^{98} -3.16044e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9}+O(q^{10}) \) 8 * q + 6 * q^2 - 52 * q^4 - 336 * q^5 + 1134 * q^6 - 12960 * q^8 - 17496 * q^9	\( 8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9} + 36628 q^{10} - 11340 q^{12} - 2864 q^{13} + 52728 q^{14} + 99440 q^{16} - 193200 q^{17} - 13122 q^{18} + 335592 q^{20} + 121824 q^{21} - 556968 q^{22} + 221616 q^{24} - 579048 q^{25} + 21564 q^{26} - 594672 q^{28} + 2063472 q^{29} + 46980 q^{30} - 3602784 q^{32} - 920160 q^{33} + 1568476 q^{34} + 113724 q^{36} + 7470352 q^{37} + 3659400 q^{38} + 1749184 q^{40} - 8865456 q^{41} - 5288328 q^{42} + 2395920 q^{44} + 734832 q^{45} - 13649856 q^{46} + 10916208 q^{48} - 18923896 q^{49} + 14581842 q^{50} + 18592888 q^{52} + 8706672 q^{53} - 2480058 q^{54} - 45565632 q^{56} - 2325024 q^{57} - 8816444 q^{58} + 28348056 q^{60} + 13457296 q^{61} + 80783976 q^{62} + 1268864 q^{64} + 7293408 q^{65} - 51205608 q^{66} - 117288264 q^{68} - 8636544 q^{69} - 60373104 q^{70} + 28343520 q^{72} + 94738960 q^{73} + 119548428 q^{74} + 144621360 q^{76} - 56971392 q^{77} - 140630580 q^{78} - 163857888 q^{80} + 38263752 q^{81} - 188383460 q^{82} + 199712304 q^{84} - 201200416 q^{85} + 240327384 q^{86} + 156323520 q^{88} + 188992272 q^{89} - 80105436 q^{90} - 387657984 q^{92} - 54802656 q^{93} - 38749872 q^{94} + 246092256 q^{96} - 123291632 q^{97} + 691081830 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 52 * q^4 - 336 * q^5 + 1134 * q^6 - 12960 * q^8 - 17496 * q^9 + 36628 * q^10 - 11340 * q^12 - 2864 * q^13 + 52728 * q^14 + 99440 * q^16 - 193200 * q^17 - 13122 * q^18 + 335592 * q^20 + 121824 * q^21 - 556968 * q^22 + 221616 * q^24 - 579048 * q^25 + 21564 * q^26 - 594672 * q^28 + 2063472 * q^29 + 46980 * q^30 - 3602784 * q^32 - 920160 * q^33 + 1568476 * q^34 + 113724 * q^36 + 7470352 * q^37 + 3659400 * q^38 + 1749184 * q^40 - 8865456 * q^41 - 5288328 * q^42 + 2395920 * q^44 + 734832 * q^45 - 13649856 * q^46 + 10916208 * q^48 - 18923896 * q^49 + 14581842 * q^50 + 18592888 * q^52 + 8706672 * q^53 - 2480058 * q^54 - 45565632 * q^56 - 2325024 * q^57 - 8816444 * q^58 + 28348056 * q^60 + 13457296 * q^61 + 80783976 * q^62 + 1268864 * q^64 + 7293408 * q^65 - 51205608 * q^66 - 117288264 * q^68 - 8636544 * q^69 - 60373104 * q^70 + 28343520 * q^72 + 94738960 * q^73 + 119548428 * q^74 + 144621360 * q^76 - 56971392 * q^77 - 140630580 * q^78 - 163857888 * q^80 + 38263752 * q^81 - 188383460 * q^82 + 199712304 * q^84 - 201200416 * q^85 + 240327384 * q^86 + 156323520 * q^88 + 188992272 * q^89 - 80105436 * q^90 - 387657984 * q^92 - 54802656 * q^93 - 38749872 * q^94 + 246092256 * q^96 - 123291632 * q^97 + 691081830 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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