LMFDB - Embedded newform 12.15.d.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,15,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, 15, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 15 $
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:	$14.9194761782$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 9158 x^{12} + 65217 x^{11} + 61148515 x^{10} + 439019974 x^{9} + 189458968156 x^{8} + \cdots + 89\!\cdots\!84 $ x^14 - x^13 + 9158x^12 + 65217x^11 + 61148515x^10 + 439019974x^9 + 189458968156x^8 + 1788546506656x^7 + 430738312102192x^6 + 3436431888153888x^5 + 232550799864813632x^4 + 2976833070807329792x^3 + 104055634594691484928x^2 + 901843441512469175808x + 8926647999096479376384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{81}\cdot 3^{41} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.2
Root			$-9.38489 - 16.2551i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.15.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-122.841 + 35.9743i) q^{2} -1262.67i q^{3} +(13795.7 - 8838.22i) q^{4} +49804.1 q^{5} +(45423.5 + 155107. i) q^{6} +91750.3i q^{7} +(-1.37672e6 + 1.58198e6i) q^{8} -1.59432e6 q^{9} +O(q^{10})$	\(q+(-122.841 + 35.9743i) q^{2} -1262.67i q^{3} +(13795.7 - 8838.22i) q^{4} +49804.1 q^{5} +(45423.5 + 155107. i) q^{6} +91750.3i q^{7} +(-1.37672e6 + 1.58198e6i) q^{8} -1.59432e6 q^{9} +(-6.11797e6 + 1.79167e6i) q^{10} +5.97518e6i q^{11} +(-1.11597e7 - 1.74193e7i) q^{12} +2.93028e7 q^{13} +(-3.30065e6 - 1.12707e7i) q^{14} -6.28859e7i q^{15} +(1.12207e8 - 2.43859e8i) q^{16} +5.58312e8 q^{17} +(1.95848e8 - 5.73547e7i) q^{18} -1.48369e9i q^{19} +(6.87083e8 - 4.40180e8i) q^{20} +1.15850e8 q^{21} +(-2.14953e8 - 7.33996e8i) q^{22} -2.13545e9i q^{23} +(1.99752e9 + 1.73834e9i) q^{24} -3.62307e9 q^{25} +(-3.59957e9 + 1.05415e9i) q^{26} +2.01310e9i q^{27} +(8.10909e8 + 1.26576e9i) q^{28} +1.57941e10 q^{29} +(2.26228e9 + 7.72495e9i) q^{30} -3.63363e10i q^{31} +(-5.01095e9 + 3.39924e10i) q^{32} +7.54465e9 q^{33} +(-6.85835e10 + 2.00849e10i) q^{34} +4.56954e9i q^{35} +(-2.19948e10 + 1.40910e10i) q^{36} -3.90757e10 q^{37} +(5.33749e10 + 1.82258e11i) q^{38} -3.69996e10i q^{39} +(-6.85666e10 + 7.87893e10i) q^{40} +5.94097e10 q^{41} +(-1.42311e10 + 4.16762e9i) q^{42} -3.53018e11i q^{43} +(5.28100e10 + 8.24318e10i) q^{44} -7.94038e10 q^{45} +(7.68212e10 + 2.62320e11i) q^{46} -8.01986e11i q^{47} +(-3.07912e11 - 1.41680e11i) q^{48} +6.69805e11 q^{49} +(4.45060e11 - 1.30337e11i) q^{50} -7.04961e11i q^{51} +(4.04252e11 - 2.58984e11i) q^{52} +1.45434e12 q^{53} +(-7.24197e10 - 2.47290e11i) q^{54} +2.97589e11i q^{55} +(-1.45148e11 - 1.26315e11i) q^{56} -1.87341e12 q^{57} +(-1.94016e12 + 5.68182e11i) q^{58} +4.73537e12i q^{59} +(-5.55800e11 - 8.67555e11i) q^{60} -4.10839e12 q^{61} +(1.30717e12 + 4.46358e12i) q^{62} -1.46280e11i q^{63} +(-6.07304e11 - 4.35591e12i) q^{64} +1.45940e12 q^{65} +(-9.26791e11 + 2.71414e11i) q^{66} +4.11756e12i q^{67} +(7.70231e12 - 4.93449e12i) q^{68} -2.69635e12 q^{69} +(-1.64386e11 - 5.61326e11i) q^{70} +9.30799e12i q^{71} +(2.19494e12 - 2.52219e12i) q^{72} +1.43566e12 q^{73} +(4.80009e12 - 1.40572e12i) q^{74} +4.57472e12i q^{75} +(-1.31132e13 - 2.04686e13i) q^{76} -5.48225e11 q^{77} +(1.33103e12 + 4.54506e12i) q^{78} -5.55237e12i q^{79} +(5.58838e12 - 1.21452e13i) q^{80} +2.54187e12 q^{81} +(-7.29793e12 + 2.13722e12i) q^{82} -1.50733e13i q^{83} +(1.59823e12 - 1.02391e12i) q^{84} +2.78063e13 q^{85} +(1.26996e13 + 4.33649e13i) q^{86} -1.99427e13i q^{87} +(-9.45264e12 - 8.22618e12i) q^{88} -1.54757e13 q^{89} +(9.75403e12 - 2.85650e12i) q^{90} +2.68854e12i q^{91} +(-1.88736e13 - 2.94600e13i) q^{92} -4.58806e13 q^{93} +(2.88509e13 + 9.85166e13i) q^{94} -7.38941e13i q^{95} +(4.29210e13 + 6.32715e12i) q^{96} +1.27307e14 q^{97} +(-8.22793e13 + 2.40958e13i) q^{98} -9.52637e12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9}+O(q^{10}) $ 14 * q + 182 * q^2 + 9308 * q^4 - 16124 * q^5 + 56862 * q^6 + 4352816 * q^8 - 22320522 * q^9	\( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9} + 586324 q^{10} + 621108 q^{12} + 109934140 q^{13} - 200755992 q^{14} + 380631536 q^{16} - 291483380 q^{17} - 290166786 q^{18} + 5316726088 q^{20} - 1117661976 q^{21} - 9373833288 q^{22} + 2880331488 q^{24} + 12506859258 q^{25} - 45510637748 q^{26} + 83579713776 q^{28} - 12126204812 q^{29} - 44941179132 q^{30} + 67974212192 q^{32} - 34345330344 q^{33} - 57269346212 q^{34} - 14839958484 q^{36} + 119365701580 q^{37} + 102957884712 q^{38} - 491601579872 q^{40} + 189318893932 q^{41} + 240539889384 q^{42} - 997611383472 q^{44} + 25706864052 q^{45} + 1368039641184 q^{46} - 465649986384 q^{48} - 769149171250 q^{49} + 2170057449522 q^{50} - 2399333559176 q^{52} + 1251391890964 q^{53} - 90656394426 q^{54} + 2319191796096 q^{56} + 1805052294792 q^{57} - 5157502168892 q^{58} + 2354207329944 q^{60} - 7882441676660 q^{61} - 9161379391272 q^{62} + 17520900128384 q^{64} + 5858206778312 q^{65} - 6614704234440 q^{66} + 18747786717976 q^{68} - 13777261381728 q^{69} - 8213486211792 q^{70} - 6939794663568 q^{72} + 39185062250428 q^{73} - 7698562888484 q^{74} - 9224963770896 q^{76} - 41289727781472 q^{77} + 10470873014172 q^{78} - 57127847610848 q^{80} + 35586121596606 q^{81} + 107070799921084 q^{82} - 28102976768880 q^{84} - 188880254078680 q^{85} + 102443851819896 q^{86} - 83262676567680 q^{88} + 223721333984572 q^{89} - 934789838652 q^{90} - 79895035003584 q^{92} + 12688158423960 q^{93} - 52692266305296 q^{94} - 2264434006752 q^{96} + 282902280361756 q^{97} - 228639957171082 q^{98}+O(q^{100}) \) 14 * q + 182 * q^2 + 9308 * q^4 - 16124 * q^5 + 56862 * q^6 + 4352816 * q^8 - 22320522 * q^9 + 586324 * q^10 + 621108 * q^12 + 109934140 * q^13 - 200755992 * q^14 + 380631536 * q^16 - 291483380 * q^17 - 290166786 * q^18 + 5316726088 * q^20 - 1117661976 * q^21 - 9373833288 * q^22 + 2880331488 * q^24 + 12506859258 * q^25 - 45510637748 * q^26 + 83579713776 * q^28 - 12126204812 * q^29 - 44941179132 * q^30 + 67974212192 * q^32 - 34345330344 * q^33 - 57269346212 * q^34 - 14839958484 * q^36 + 119365701580 * q^37 + 102957884712 * q^38 - 491601579872 * q^40 + 189318893932 * q^41 + 240539889384 * q^42 - 997611383472 * q^44 + 25706864052 * q^45 + 1368039641184 * q^46 - 465649986384 * q^48 - 769149171250 * q^49 + 2170057449522 * q^50 - 2399333559176 * q^52 + 1251391890964 * q^53 - 90656394426 * q^54 + 2319191796096 * q^56 + 1805052294792 * q^57 - 5157502168892 * q^58 + 2354207329944 * q^60 - 7882441676660 * q^61 - 9161379391272 * q^62 + 17520900128384 * q^64 + 5858206778312 * q^65 - 6614704234440 * q^66 + 18747786717976 * q^68 - 13777261381728 * q^69 - 8213486211792 * q^70 - 6939794663568 * q^72 + 39185062250428 * q^73 - 7698562888484 * q^74 - 9224963770896 * q^76 - 41289727781472 * q^77 + 10470873014172 * q^78 - 57127847610848 * q^80 + 35586121596606 * q^81 + 107070799921084 * q^82 - 28102976768880 * q^84 - 188880254078680 * q^85 + 102443851819896 * q^86 - 83262676567680 * q^88 + 223721333984572 * q^89 - 934789838652 * q^90 - 79895035003584 * q^92 + 12688158423960 * q^93 - 52692266305296 * q^94 - 2264434006752 * q^96 + 282902280361756 * q^97 - 228639957171082 * 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 $

$2$	−122.841	+	35.9743i	−0.959693	+	0.281049i
$2$	−122.841	+	35.9743i	−0.959693	+	0.281049i
$3$		−	1262.67i		−	0.577350i
$3$		−	1262.67i		−	0.577350i
$4$	13795.7	−	8838.22i	0.842023	−	0.539442i
$5$	49804.1			0.637493			0.318746	−	0.947840i	$-0.396738\pi$
$5$	49804.1			0.637493			0.318746	+	0.947840i	$0.396738\pi$
$6$	45423.5	+	155107.i	0.162264	+	0.554079i
$7$			91750.3i			0.111409i	0.998447	+	0.0557046i	$0.0177405\pi$
$7$			91750.3i			0.111409i	−0.998447	+	0.0557046i	$0.982259\pi$
$8$	−1.37672e6	+	1.58198e6i	−0.656474	+	0.754349i
$9$	−1.59432e6			−0.333333
$10$	−6.11797e6	+	1.79167e6i	−0.611797	+	0.179167i
$11$			5.97518e6i			0.306621i	0.988178	+	0.153311i	$0.0489935\pi$
$11$			5.97518e6i			0.306621i	−0.988178	+	0.153311i	$0.951006\pi$
$12$	−1.11597e7	−	1.74193e7i	−0.311447	−	0.486142i
$13$	2.93028e7			0.466988			0.233494	−	0.972358i	$-0.424984\pi$
$13$	2.93028e7			0.466988			0.233494	+	0.972358i	$0.424984\pi$
$14$	−3.30065e6	−	1.12707e7i	−0.0313115	−	0.106919i
$15$		−	6.28859e7i		−	0.368057i
$16$	1.12207e8	−	2.43859e8i	0.418004	−	0.908445i
$17$	5.58312e8			1.36061			0.680307	−	0.732928i	$-0.261847\pi$
$17$	5.58312e8			1.36061			0.680307	+	0.732928i	$0.261847\pi$
$18$	1.95848e8	−	5.73547e7i	0.319898	−	0.0936831i
$19$		−	1.48369e9i		−	1.65985i	−0.557874	−	0.829926i	$-0.688383\pi$
$19$		−	1.48369e9i		−	1.65985i	0.557874	−	0.829926i	$-0.311617\pi$
$20$	6.87083e8	−	4.40180e8i	0.536783	−	0.343890i
$21$	1.15850e8			0.0643221
$22$	−2.14953e8	−	7.33996e8i	−0.0861757	−	0.294262i
$23$		−	2.13545e9i		−	0.627182i	−0.949558	−	0.313591i	$-0.898468\pi$
$23$		−	2.13545e9i		−	0.627182i	0.949558	−	0.313591i	$-0.101532\pi$
$24$	1.99752e9	+	1.73834e9i	0.435524	+	0.379015i
$25$	−3.62307e9			−0.593603
$26$	−3.59957e9	+	1.05415e9i	−0.448165	+	0.131247i
$27$			2.01310e9i			0.192450i
$28$	8.10909e8	+	1.26576e9i	0.0600988	+	0.0938091i
$29$	1.57941e10			0.915606			0.457803	−	0.889054i	$-0.348636\pi$
$29$	1.57941e10			0.915606			0.457803	+	0.889054i	$0.348636\pi$
$30$	2.26228e9	+	7.72495e9i	0.103442	+	0.353221i
$31$		−	3.63363e10i		−	1.32071i	−0.750952	−	0.660357i	$-0.770405\pi$
$31$		−	3.63363e10i		−	1.32071i	0.750952	−	0.660357i	$-0.229595\pi$
$32$	−5.01095e9	+	3.39924e10i	−0.145838	+	0.989309i
$33$	7.54465e9			0.177028
$34$	−6.85835e10	+	2.00849e10i	−1.30577	+	0.382399i
$35$			4.56954e9i			0.0710226i
$36$	−2.19948e10	+	1.40910e10i	−0.280674	+	0.179814i
$37$	−3.90757e10			−0.411618			−0.205809	−	0.978592i	$-0.565983\pi$
$37$	−3.90757e10			−0.411618			−0.205809	+	0.978592i	$0.565983\pi$
$38$	5.33749e10	+	1.82258e11i	0.466500	+	1.59295i
$39$		−	3.69996e10i		−	0.269615i
$40$	−6.85666e10	+	7.87893e10i	−0.418497	+	0.480892i
$41$	5.94097e10			0.305049			0.152525	−	0.988300i	$-0.451260\pi$
$41$	5.94097e10			0.305049			0.152525	+	0.988300i	$0.451260\pi$
$42$	−1.42311e10	+	4.16762e9i	−0.0617295	+	0.0180777i
$43$		−	3.53018e11i		−	1.29872i	−0.760479	−	0.649362i	$-0.775036\pi$
$43$		−	3.53018e11i		−	1.29872i	0.760479	−	0.649362i	$-0.224964\pi$
$44$	5.28100e10	+	8.24318e10i	0.165404	+	0.258182i
$45$	−7.94038e10			−0.212498
$46$	7.68212e10	+	2.62320e11i	0.176269	+	0.601903i
$47$		−	8.01986e11i		−	1.58300i	−0.611167	−	0.791502i	$-0.709300\pi$
$47$		−	8.01986e11i		−	1.58300i	0.611167	−	0.791502i	$-0.290700\pi$
$48$	−3.07912e11	−	1.41680e11i	−0.524491	−	0.241335i
$49$	6.69805e11			0.987588
$50$	4.45060e11	−	1.30337e11i	0.569677	−	0.166832i
$51$		−	7.04961e11i		−	0.785551i
$52$	4.04252e11	−	2.58984e11i	0.393214	−	0.251913i
$53$	1.45434e12			1.23804			0.619022	−	0.785374i	$-0.287529\pi$
$53$	1.45434e12			1.23804			0.619022	+	0.785374i	$0.287529\pi$
$54$	−7.24197e10	−	2.47290e11i	−0.0540880	−	0.184693i
$55$			2.97589e11i			0.195469i
$56$	−1.45148e11	−	1.26315e11i	−0.0840414	−	0.0731372i
$57$	−1.87341e12			−0.958315
$58$	−1.94016e12	+	5.68182e11i	−0.878701	+	0.257331i
$59$			4.73537e12i			1.90278i	0.307982	+	0.951392i	$0.400346\pi$
$59$			4.73537e12i			1.90278i	−0.307982	+	0.951392i	$0.599654\pi$
$60$	−5.55800e11	−	8.67555e11i	−0.198545	−	0.309912i
$61$	−4.10839e12			−1.30726			−0.653632	−	0.756813i	$-0.726755\pi$
$61$	−4.10839e12			−1.30726			−0.653632	+	0.756813i	$0.726755\pi$
$62$	1.30717e12	+	4.46358e12i	0.371186	+	1.26748i
$63$		−	1.46280e11i		−	0.0371364i
$64$	−6.07304e11	−	4.35591e12i	−0.138085	−	0.990420i
$65$	1.45940e12			0.297701
$66$	−9.26791e11	+	2.71414e11i	−0.169892	+	0.0497536i
$67$			4.11756e12i			0.679386i	0.940536	+	0.339693i	$0.110323\pi$
$67$			4.11756e12i			0.679386i	−0.940536	+	0.339693i	$0.889677\pi$
$68$	7.70231e12	−	4.93449e12i	1.14567	−	0.733972i
$69$	−2.69635e12			−0.362104
$70$	−1.64386e11	−	5.61326e11i	−0.0199608	−	0.0681599i
$71$			9.30799e12i			1.02341i	0.859163	+	0.511703i	$0.170985\pi$
$71$			9.30799e12i			1.02341i	−0.859163	+	0.511703i	$0.829015\pi$
$72$	2.19494e12	−	2.52219e12i	0.218825	−	0.251450i
$73$	1.43566e12			0.129955			0.0649773	−	0.997887i	$-0.479302\pi$
$73$	1.43566e12			0.129955			0.0649773	+	0.997887i	$0.479302\pi$
$74$	4.80009e12	−	1.40572e12i	0.395027	−	0.115685i
$75$			4.57472e12i			0.342717i
$76$	−1.31132e13	−	2.04686e13i	−0.895394	−	1.39763i
$77$	−5.48225e11			−0.0341604
$78$	1.33103e12	+	4.54506e12i	0.0757752	+	0.258748i
$79$		−	5.55237e12i		−	0.289127i	−0.989496	−	0.144563i	$-0.953822\pi$
$79$		−	5.55237e12i		−	0.289127i	0.989496	−	0.144563i	$-0.0461778\pi$
$80$	5.58838e12	−	1.21452e13i	0.266475	−	0.579127i
$81$	2.54187e12			0.111111
$82$	−7.29793e12	+	2.13722e12i	−0.292754	+	0.0857339i
$83$		−	1.50733e13i		−	0.555473i	−0.960657	−	0.277736i	$-0.910416\pi$
$83$		−	1.50733e13i		−	0.555473i	0.960657	−	0.277736i	$-0.0895842\pi$
$84$	1.59823e12	−	1.02391e12i	0.0541607	−	0.0346981i
$85$	2.78063e13			0.867381
$86$	1.26996e13	+	4.33649e13i	0.365006	+	1.24638i
$87$		−	1.99427e13i		−	0.528626i
$88$	−9.45264e12	−	8.22618e12i	−0.231299	−	0.201289i
$89$	−1.54757e13			−0.349882			−0.174941	−	0.984579i	$-0.555973\pi$
$89$	−1.54757e13			−0.349882			−0.174941	+	0.984579i	$0.555973\pi$
$90$	9.75403e12	−	2.85650e12i	0.203932	−	0.0597223i
$91$			2.68854e12i			0.0520267i
$92$	−1.88736e13	−	2.94600e13i	−0.338329	−	0.528102i
$93$	−4.58806e13			−0.762515
$94$	2.88509e13	+	9.85166e13i	0.444902	+	1.51920i
$95$		−	7.38941e13i		−	1.05814i
$96$	4.29210e13	+	6.32715e12i	0.571178	+	0.0841995i
$97$	1.27307e14			1.57562			0.787808	−	0.615921i	$-0.211216\pi$
$97$	1.27307e14			1.57562			0.787808	+	0.615921i	$0.211216\pi$
$98$	−8.22793e13	+	2.40958e13i	−0.947782	+	0.277561i
$99$		−	9.52637e12i		−	0.102207i
$100$	−4.99827e13	+	3.20215e13i	−0.499827	+	0.320215i
$101$	−1.76468e14			−1.64595			−0.822974	−	0.568079i	$-0.807687\pi$
$101$	−1.76468e14			−1.64595			−0.822974	+	0.568079i	$0.807687\pi$
$102$	2.53605e13	+	8.65980e13i	0.220778	+	0.753888i
$103$			1.01892e14i			0.828478i	0.910168	+	0.414239i	$0.135952\pi$
$103$			1.01892e14i			0.828478i	−0.910168	+	0.414239i	$0.864048\pi$
$104$	−4.03419e13	+	4.63565e13i	−0.306565	+	0.352272i
$105$	5.76980e12			0.0410049
$106$	−1.78653e14	+	5.23190e13i	−1.18814	+	0.347951i
$107$		−	1.49791e14i		−	0.932823i	−0.884568	−	0.466411i	$-0.845547\pi$
$107$		−	1.49791e14i		−	0.932823i	0.884568	−	0.466411i	$-0.154453\pi$
$108$	1.77922e13	+	2.77721e13i	0.103816	+	0.162047i
$109$	2.47325e14			1.35295			0.676476	−	0.736465i	$-0.263506\pi$
$109$	2.47325e14			1.35295			0.676476	+	0.736465i	$0.263506\pi$
$110$	−1.07055e13	−	3.65560e13i	−0.0549364	−	0.187590i
$111$			4.93395e13i			0.237648i
$112$	2.23741e13	+	1.02950e13i	0.101209	+	0.0465695i
$113$	−7.38408e13			−0.313868			−0.156934	−	0.987609i	$-0.550161\pi$
$113$	−7.38408e13			−0.313868			−0.156934	+	0.987609i	$0.550161\pi$
$114$	2.30131e14	−	6.73946e13i	0.919689	−	0.269334i
$115$		−	1.06354e14i		−	0.399824i
$116$	2.17891e14	−	1.39592e14i	0.770961	−	0.493917i
$117$	−4.67181e13			−0.155663
$118$	−1.70352e14	−	5.81696e14i	−0.534776	−	1.82609i
$119$			5.12253e13i			0.151585i
$120$	9.94845e13	+	8.65766e13i	0.277643	+	0.241619i
$121$	3.44047e14			0.905983
$122$	5.04678e14	−	1.47797e14i	1.25457	−	0.367405i
$123$		−	7.50145e13i		−	0.176120i
$124$	−3.21148e14	−	5.01285e14i	−0.712449	−	1.11207i
$125$	−4.84424e14			−1.01591
$126$	5.26231e12	+	1.79691e13i	0.0104372	+	0.0356396i
$127$			4.38541e14i			0.822970i	0.911417	+	0.411485i	$0.134990\pi$
$127$			4.38541e14i			0.822970i	−0.911417	+	0.411485i	$0.865010\pi$
$128$	2.31303e14	+	5.13237e14i	0.410876	+	0.911691i
$129$	−4.45743e14			−0.749819
$130$	−1.79274e14	+	5.25009e13i	−0.285702	+	0.0836687i
$131$			7.62113e14i			1.15112i	0.817760	+	0.575560i	$0.195216\pi$
$131$			7.62113e14i			1.15112i	−0.817760	+	0.575560i	$0.804784\pi$
$132$	1.04084e14	−	6.66813e13i	0.149061	−	0.0954963i
$133$	1.36129e14			0.184923
$134$	−1.48126e14	−	5.05805e14i	−0.190941	−	0.652002i
$135$			1.00260e14i			0.122686i
$136$	−7.68642e14	+	8.83241e14i	−0.893207	+	1.02638i
$137$	1.93920e14			0.214081			0.107041	−	0.994255i	$-0.465862\pi$
$137$	1.93920e14			0.214081			0.107041	+	0.994255i	$0.465862\pi$
$138$	3.31222e14	−	9.69995e13i	0.347509	−	0.101769i
$139$			1.18153e15i			1.17853i	0.807939	+	0.589266i	$0.200583\pi$
$139$			1.18153e15i			1.17853i	−0.807939	+	0.589266i	$0.799417\pi$
$140$	4.03866e13	+	6.30400e13i	0.0383126	+	0.0598026i
$141$	−1.01264e15			−0.913948
$142$	−3.34849e14	−	1.14340e15i	−0.287627	−	0.982155i
$143$			1.75089e14i			0.143188i
$144$	−1.78894e14	+	3.88790e14i	−0.139335	+	0.302815i
$145$	7.86611e14			0.583692
$146$	−1.76358e14	+	5.16469e13i	−0.124717	+	0.0365237i
$147$		−	8.45739e14i		−	0.570184i
$148$	−5.39077e14	+	3.45360e14i	−0.346592	+	0.222044i
$149$	8.02946e14			0.492473			0.246236	−	0.969210i	$-0.420806\pi$
$149$	8.02946e14			0.492473			0.246236	+	0.969210i	$0.420806\pi$
$150$	−1.64572e14	−	5.61962e14i	−0.0963203	−	0.328903i
$151$		−	1.36469e15i		−	0.762424i	−0.924488	−	0.381212i	$-0.875507\pi$
$151$		−	1.36469e15i		−	0.762424i	0.924488	−	0.381212i	$-0.124493\pi$
$152$	2.34718e15	+	2.04264e15i	1.25211	+	1.08965i
$153$	−8.90130e14			−0.453538
$154$	6.73443e13	−	1.97220e13i	0.0327835	−	0.00960077i
$155$		−	1.80970e15i		−	0.841946i
$156$	−3.27011e14	−	5.10435e14i	−0.145442	−	0.227022i
$157$	2.03349e15			0.864856			0.432428	−	0.901669i	$-0.357657\pi$
$157$	2.03349e15			0.864856			0.432428	+	0.901669i	$0.357657\pi$
$158$	1.99743e14	+	6.82057e14i	0.0812589	+	0.277473i
$159$		−	1.83635e15i		−	0.714785i
$160$	−2.49566e14	+	1.69296e15i	−0.0929706	+	0.630677i
$161$	1.95928e14			0.0698739
$162$	−3.12245e14	+	9.14419e13i	−0.106633	+	0.0312277i
$163$		−	3.09991e15i		−	1.01399i	−0.861948	−	0.506997i	$-0.830755\pi$
$163$		−	3.09991e15i		−	1.01399i	0.861948	−	0.506997i	$-0.169245\pi$
$164$	8.19598e14	−	5.25076e14i	0.256858	−	0.164556i
$165$	3.75755e14			0.112854
$166$	5.42253e14	+	1.85162e15i	0.156115	+	0.533084i
$167$		−	1.30654e15i		−	0.360667i	−0.983606	−	0.180333i	$-0.942282\pi$
$167$		−	1.30654e15i		−	0.360667i	0.983606	−	0.180333i	$-0.0577177\pi$
$168$	−1.59493e14	+	1.83273e14i	−0.0422258	+	0.0485213i
$169$	−3.07872e15			−0.781923
$170$	−3.41574e15	+	1.00031e15i	−0.832420	+	0.243777i
$171$			2.36549e15i			0.553284i
$172$	−3.12005e15	−	4.87012e15i	−0.700587	−	1.09356i
$173$	4.16783e14			0.0898643			0.0449322	−	0.998990i	$-0.485693\pi$
$173$	4.16783e14			0.0898643			0.0449322	+	0.998990i	$0.485693\pi$
$174$	7.17423e14	+	2.44977e15i	0.148570	+	0.507318i
$175$		−	3.32417e14i		−	0.0661329i
$176$	1.45710e15	+	6.70458e14i	0.278549	+	0.128169i
$177$	5.97918e15			1.09857
$178$	1.90105e15	−	5.56729e14i	0.335779	−	0.0983340i
$179$		−	6.91590e14i		−	0.117457i	−0.998274	−	0.0587283i	$-0.981295\pi$
$179$		−	6.91590e14i		−	0.117457i	0.998274	−	0.0587283i	$-0.0187046\pi$
$180$	−1.09543e15	+	7.01789e14i	−0.178928	+	0.114630i
$181$	1.15335e15			0.181222			0.0906108	−	0.995886i	$-0.471118\pi$
$181$	1.15335e15			0.181222			0.0906108	+	0.995886i	$0.471118\pi$
$182$	−9.67183e13	−	3.30262e14i	−0.0146221	−	0.0499297i
$183$			5.18752e15i			0.754749i
$184$	3.37824e15	+	2.93992e15i	0.473114	+	0.411729i
$185$	−1.94613e15			−0.262404
$186$	5.63600e15	−	1.65052e15i	0.731780	−	0.214304i
$187$			3.33602e15i			0.417193i
$188$	−7.08813e15	−	1.10640e16i	−0.853939	−	1.33292i
$189$	−1.84702e14			−0.0214407
$190$	2.65829e15	+	9.07720e15i	0.297390	+	1.01549i
$191$			1.02700e16i			1.10748i	0.832690	+	0.553740i	$0.186800\pi$
$191$			1.02700e16i			1.10748i	−0.832690	+	0.553740i	$0.813200\pi$
$192$	−5.50006e15	+	7.66821e14i	−0.571819	+	0.0797233i
$193$	−1.93591e16			−1.94081			−0.970405	−	0.241484i	$-0.922366\pi$
$193$	−1.93591e16			−1.94081			−0.970405	+	0.241484i	$0.922366\pi$
$194$	−1.56385e16	+	4.57978e15i	−1.51211	+	0.442826i
$195$		−	1.84273e15i		−	0.171878i
$196$	9.24043e15	−	5.91989e15i	0.831571	−	0.532747i
$197$	−5.22965e15			−0.454160			−0.227080	−	0.973876i	$-0.572918\pi$
$197$	−5.22965e15			−0.454160			−0.227080	+	0.973876i	$0.572918\pi$
$198$	3.42705e14	+	1.17023e15i	0.0287252	+	0.0980875i
$199$			1.41708e16i			1.14663i	0.819336	+	0.573313i	$0.194342\pi$
$199$			1.41708e16i			1.14663i	−0.819336	+	0.573313i	$0.805658\pi$
$200$	4.98796e15	−	5.73163e15i	0.389685	−	0.447784i
$201$	5.19910e15			0.392244
$202$	2.16774e16	−	6.34831e15i	1.57960	−	0.462592i
$203$			1.44911e15i			0.102007i
$204$	−6.23061e15	−	9.72544e15i	−0.423759	−	0.661451i
$205$	2.95885e15			0.194467
$206$	−3.66551e15	−	1.25165e16i	−0.232843	−	0.795085i
$207$			3.40459e15i			0.209061i
$208$	3.28798e15	−	7.14574e15i	0.195203	−	0.424233i
$209$	8.86534e15			0.508946
$210$	−7.08767e14	+	2.07565e14i	−0.0393521	+	0.0115244i
$211$		−	1.76498e16i		−	0.947901i	−0.880552	−	0.473950i	$-0.842828\pi$
$211$		−	1.76498e16i		−	0.947901i	0.880552	−	0.473950i	$-0.157172\pi$
$212$	2.00637e16	−	1.28538e16i	1.04246	−	0.667853i
$213$	1.17529e16			0.590863
$214$	5.38863e15	+	1.84004e16i	0.262169	+	0.895224i
$215$		−	1.75817e16i		−	0.827928i
$216$	−3.18469e15	−	2.77148e15i	−0.145175	−	0.126338i
$217$	3.33387e15			0.147140
$218$	−3.03816e16	+	8.89734e15i	−1.29842	+	0.380246i
$219$		−	1.81276e15i		−	0.0750294i
$220$	2.63015e15	+	4.10544e15i	0.105444	+	0.164589i
$221$	1.63601e16			0.635390
$222$	−1.77496e15	−	6.06090e15i	−0.0667908	−	0.228069i
$223$			2.04876e15i			0.0747064i	0.999302	+	0.0373532i	$0.0118927\pi$
$223$			2.04876e15i			0.0747064i	−0.999302	+	0.0373532i	$0.988107\pi$
$224$	−3.11881e15	−	4.59756e14i	−0.110218	−	0.0162477i
$225$	5.77634e15			0.197868
$226$	9.07066e15	−	2.65637e15i	0.301217	−	0.0882124i
$227$		−	1.15948e16i		−	0.373322i	−0.982424	−	0.186661i	$-0.940233\pi$
$227$		−	1.15948e16i		−	0.373322i	0.982424	−	0.186661i	$-0.0597667\pi$
$228$	−2.58450e16	+	1.65576e16i	−0.806923	+	0.516956i
$229$	−4.21110e16			−1.27511			−0.637555	−	0.770405i	$-0.720054\pi$
$229$	−4.21110e16			−1.27511			−0.637555	+	0.770405i	$0.720054\pi$
$230$	3.82601e15	+	1.30646e16i	0.112370	+	0.383709i
$231$			6.92224e14i			0.0197225i
$232$	−2.17441e16	+	2.49860e16i	−0.601071	+	0.690687i
$233$	6.77774e15			0.181800			0.0908999	−	0.995860i	$-0.471026\pi$
$233$	6.77774e15			0.181800			0.0908999	+	0.995860i	$0.471026\pi$
$234$	5.73888e15	−	1.68065e15i	0.149388	−	0.0437488i
$235$		−	3.99422e16i		−	1.00915i
$236$	4.18522e16	+	6.53277e16i	1.02644	+	1.60219i
$237$	−7.01078e15			−0.166928
$238$	−1.84280e15	−	6.29256e15i	−0.0426028	−	0.145475i
$239$			7.63912e16i			1.71498i	0.514504	+	0.857488i	$0.327976\pi$
$239$			7.63912e16i			1.71498i	−0.514504	+	0.857488i	$0.672024\pi$
$240$	−1.53353e16	−	7.05625e15i	−0.334359	−	0.153849i
$241$	−3.73535e16			−0.791064			−0.395532	−	0.918452i	$-0.629440\pi$
$241$	−3.73535e16			−0.791064			−0.395532	+	0.918452i	$0.629440\pi$
$242$	−4.22630e16	+	1.23769e16i	−0.869466	+	0.254626i
$243$		−	3.20953e15i		−	0.0641500i
$244$	−5.66781e16	+	3.63109e16i	−1.10075	+	0.705193i
$245$	3.33590e16			0.629580
$246$	2.69859e15	+	9.21484e15i	0.0494985	+	0.169021i
$247$		−	4.34763e16i		−	0.775130i
$248$	5.74835e16	+	5.00251e16i	0.996279	+	0.867014i
$249$	−1.90326e16			−0.320702
$250$	5.95070e16	−	1.74268e16i	0.974962	−	0.285521i
$251$		−	6.24457e16i		−	0.994917i	−0.867488	−	0.497458i	$-0.834267\pi$
$251$		−	6.24457e16i		−	0.994917i	0.867488	−	0.497458i	$-0.165733\pi$
$252$	−1.29285e15	−	2.01803e15i	−0.0200329	−	0.0312697i
$253$	1.27597e16			0.192307
$254$	−1.57762e16	−	5.38707e16i	−0.231295	−	0.789799i
$255$		−	3.51100e16i		−	0.500783i
$256$	−4.68767e16	−	5.47254e16i	−0.650545	−	0.759468i
$257$	1.12537e17			1.51972			0.759858	−	0.650089i	$-0.225268\pi$
$257$	1.12537e17			1.51972			0.759858	+	0.650089i	$0.225268\pi$
$258$	5.47554e16	−	1.60353e16i	0.719596	−	0.210736i
$259$		−	3.58521e15i		−	0.0458581i
$260$	2.01334e16	−	1.28985e16i	0.250671	−	0.160593i
$261$	−2.51809e16			−0.305202
$262$	−2.74165e16	−	9.36185e16i	−0.323521	−	1.10472i
$263$			3.30302e16i			0.379508i	0.981832	+	0.189754i	$0.0607691\pi$
$263$			3.30302e16i			0.379508i	−0.981832	+	0.189754i	$0.939231\pi$
$264$	−1.03869e16	+	1.19355e16i	−0.116214	+	0.133541i
$265$	7.24323e16			0.789243
$266$	−1.67222e16	+	4.89716e15i	−0.177469	+	0.0519724i
$267$			1.95407e16i			0.202004i
$268$	3.63919e16	+	5.68047e16i	0.366490	+	0.572058i
$269$	−1.68646e17			−1.65466			−0.827331	−	0.561714i	$-0.810142\pi$
$269$	−1.68646e17			−1.65466			−0.827331	+	0.561714i	$0.810142\pi$
$270$	−3.60680e15	−	1.23161e16i	−0.0344807	−	0.117740i
$271$			1.69197e17i			1.57619i	0.615557	+	0.788093i	$0.288931\pi$
$271$			1.69197e17i			1.57619i	−0.615557	+	0.788093i	$0.711069\pi$
$272$	6.26466e16	−	1.36149e17i	0.568742	−	1.23604i
$273$	3.39472e15			0.0300376
$274$	−2.38213e16	+	6.97614e15i	−0.205453	+	0.0601674i
$275$		−	2.16485e16i		−	0.182011i
$276$	−3.71981e16	+	2.38310e16i	−0.304900	+	0.195334i
$277$	1.49385e17			1.19384			0.596922	−	0.802299i	$-0.296390\pi$
$277$	1.49385e17			1.19384			0.596922	+	0.802299i	$0.296390\pi$
$278$	−4.25048e16	−	1.45140e17i	−0.331226	−	1.13103i
$279$			5.79318e16i			0.440238i
$280$	−7.22894e15	−	6.29100e15i	−0.0535758	−	0.0466244i
$281$	−2.17029e17			−1.56882			−0.784412	−	0.620240i	$-0.787035\pi$
$281$	−2.17029e17			−1.56882			−0.784412	+	0.620240i	$0.787035\pi$
$282$	1.24393e17	−	3.64290e16i	0.877109	−	0.256864i
$283$			9.41987e16i			0.647947i	0.946066	+	0.323974i	$0.105019\pi$
$283$			9.41987e16i			0.647947i	−0.946066	+	0.323974i	$0.894981\pi$
$284$	8.22661e16	+	1.28410e17i	0.552068	+	0.861730i
$285$	−9.33035e16			−0.610919
$286$	−6.29872e15	−	2.15081e16i	−0.0402430	−	0.137417i
$287$			5.45085e15i			0.0339853i
$288$	7.98907e15	−	5.41948e16i	0.0486126	−	0.329770i
$289$	1.43335e17			0.851269
$290$	−9.66279e16	+	2.82978e16i	−0.560166	+	0.164046i
$291$		−	1.60746e17i		−	0.909682i
$292$	1.98059e16	−	1.26887e16i	0.109425	−	0.0701030i
$293$	−8.08912e16			−0.436343			−0.218172	−	0.975910i	$-0.570009\pi$
$293$	−8.08912e16			−0.436343			−0.218172	+	0.975910i	$0.570009\pi$
$294$	3.04249e16	+	1.03891e17i	0.160250	+	0.547202i
$295$			2.35841e17i			1.21301i
$296$	5.37965e16	−	6.18172e16i	0.270217	−	0.310504i
$297$	−1.20286e16			−0.0590093
$298$	−9.86345e16	+	2.88854e16i	−0.472623	+	0.138409i
$299$		−	6.25745e16i		−	0.292886i
$300$	4.04324e16	+	6.31114e16i	0.184876	+	0.288575i
$301$	3.23895e16			0.144690
$302$	4.90939e16	+	1.67640e17i	0.214279	+	0.731693i
$303$			2.22820e17i			0.950288i
$304$	−3.61812e17	−	1.66481e17i	−1.50788	−	0.693824i
$305$	−2.04615e17			−0.833371
$306$	1.09344e17	−	3.20218e16i	0.435257	−	0.127466i
$307$		−	3.72171e17i		−	1.44802i	−0.689790	−	0.724009i	$-0.742297\pi$
$307$		−	3.72171e17i		−	1.44802i	0.689790	−	0.724009i	$-0.257703\pi$
$308$	−7.56314e15	+	4.84533e15i	−0.0287639	+	0.0184276i
$309$	1.28656e17			0.478322
$310$	6.51026e16	+	2.22305e17i	0.236628	+	0.808010i
$311$			1.62064e17i			0.575923i	0.957642	+	0.287962i	$0.0929776\pi$
$311$			1.62064e17i			0.575923i	−0.957642	+	0.287962i	$0.907022\pi$
$312$	5.85328e16	+	5.09383e16i	0.203384	+	0.176995i
$313$	2.30829e17			0.784296			0.392148	−	0.919902i	$-0.371732\pi$
$313$	2.30829e17			0.784296			0.392148	+	0.919902i	$0.371732\pi$
$314$	−2.49795e17	+	7.31533e16i	−0.829996	+	0.243067i
$315$		−	7.28532e15i		−	0.0236742i
$316$	−4.90731e16	−	7.65988e16i	−0.155967	−	0.243451i
$317$	3.13255e17			0.973831			0.486915	−	0.873449i	$-0.338122\pi$
$317$	3.13255e17			0.973831			0.486915	+	0.873449i	$0.338122\pi$
$318$	6.60614e16	+	2.25578e17i	0.200890	+	0.685974i
$319$			9.43726e16i			0.280744i
$320$	−3.02462e16	−	2.16942e17i	−0.0880281	−	0.631386i
$321$	−1.89136e17			−0.538566
$322$	−2.40679e16	+	7.04837e15i	−0.0670575	+	0.0196380i
$323$		−	8.28365e17i		−	2.25842i
$324$	3.50668e16	−	2.24656e16i	0.0935581	−	0.0599380i
$325$	−1.06166e17			−0.277205
$326$	1.11517e17	+	3.80795e17i	0.284982	+	0.973124i
$327$		−	3.12288e17i		−	0.781127i
$328$	−8.17907e16	+	9.39852e16i	−0.200257	+	0.230114i
$329$	7.35825e16			0.176361
$330$	−4.61580e16	+	1.35175e16i	−0.108305	+	0.0317175i
$331$		−	7.07732e17i		−	1.62582i	−0.582388	−	0.812911i	$-0.697882\pi$
$331$		−	7.07732e17i		−	1.62582i	0.582388	−	0.812911i	$-0.302118\pi$
$332$	−1.33222e17	−	2.07947e17i	−0.299646	−	0.467721i
$333$	6.22993e16			0.137206
$334$	4.70018e16	+	1.60496e17i	0.101365	+	0.346130i
$335$			2.05072e17i			0.433104i
$336$	1.29992e16	−	2.82510e16i	0.0268869	−	0.0584331i
$337$	2.23838e17			0.453445			0.226723	−	0.973959i	$-0.427199\pi$
$337$	2.23838e17			0.453445			0.226723	+	0.973959i	$0.427199\pi$
$338$	3.78193e17	−	1.10755e17i	0.750406	−	0.219759i
$339$			9.32362e16i			0.181212i
$340$	3.83607e17	−	2.45758e17i	0.730354	−	0.467902i
$341$	2.17116e17			0.404959
$342$	−8.50968e16	−	2.90578e17i	−0.155500	−	0.530983i
$343$			1.23682e17i			0.221436i
$344$	5.58468e17	+	4.86008e17i	0.979692	+	0.852579i
$345$	−1.34290e17			−0.230839
$346$	−5.11979e16	+	1.49935e16i	−0.0862422	+	0.0252563i
$347$			2.51806e17i			0.415681i	0.978163	+	0.207840i	$0.0666435\pi$
$347$			2.51806e17i			0.415681i	−0.978163	+	0.207840i	$0.933357\pi$
$348$	−1.76258e17	−	2.75123e17i	−0.285163	−	0.445115i
$349$	−3.52669e17			−0.559229			−0.279614	−	0.960112i	$-0.590207\pi$
$349$	−3.52669e17			−0.559229			−0.279614	+	0.960112i	$0.590207\pi$
$350$	1.19585e16	+	4.08344e16i	0.0185866	+	0.0634673i
$351$			5.89893e16i			0.0898718i
$352$	−2.03111e17	−	2.99413e16i	−0.303343	−	0.0447170i
$353$	1.36203e17			0.199417			0.0997085	−	0.995017i	$-0.468209\pi$
$353$	1.36203e17			0.199417			0.0997085	+	0.995017i	$0.468209\pi$
$354$	−7.34487e17	+	2.15097e17i	−1.05429	+	0.308753i
$355$			4.63576e17i			0.652413i
$356$	−2.13498e17	+	1.36778e17i	−0.294608	+	0.188741i
$357$	6.46804e16			0.0875176
$358$	2.48795e16	+	8.49555e16i	0.0330111	+	0.112722i
$359$			1.38140e18i			1.79745i	0.438508	+	0.898727i	$0.355507\pi$
$359$			1.38140e18i			1.79745i	−0.438508	+	0.898727i	$0.644493\pi$
$360$	1.09317e17	−	1.25616e17i	0.139499	−	0.160297i
$361$	−1.40234e18			−1.75511
$362$	−1.41678e17	+	4.14909e16i	−0.173917	+	0.0509322i
$363$		−	4.34416e17i		−	0.523070i
$364$	2.37619e16	+	3.70903e16i	0.0280654	+	0.0438077i
$365$	7.15018e16			0.0828451
$366$	−1.86618e17	−	6.37239e17i	−0.212122	−	0.724327i
$367$			1.30960e18i			1.46041i	0.683227	+	0.730206i	$0.260576\pi$
$367$			1.30960e18i			1.46041i	−0.683227	+	0.730206i	$0.739424\pi$
$368$	−5.20748e17	−	2.39612e17i	−0.569761	−	0.262165i
$369$	−9.47182e16			−0.101683
$370$	2.39064e17	−	7.00107e16i	0.251827	−	0.0737484i
$371$			1.33436e17i			0.137929i
$372$	−6.32955e17	+	4.05503e17i	−0.642055	+	0.411333i
$373$	1.08730e16			0.0108240			0.00541198	−	0.999985i	$-0.498277\pi$
$373$	1.08730e16			0.0108240			0.00541198	+	0.999985i	$0.498277\pi$
$374$	−1.20011e17	−	4.09799e17i	−0.117252	−	0.400377i
$375$			6.11665e17i			0.586536i
$376$	1.26873e18	+	1.10411e18i	1.19414	+	1.03920i
$377$	4.62811e17			0.427577
$378$	2.26889e16	−	6.64453e15i	0.0205765	−	0.00602590i
$379$		−	8.31742e17i		−	0.740482i	−0.928936	−	0.370241i	$-0.879275\pi$
$379$		−	8.31742e17i		−	0.740482i	0.928936	−	0.370241i	$-0.120725\pi$
$380$	−6.53092e17	−	1.01942e18i	−0.570807	−	0.890980i
$381$	5.53730e17			0.475142
$382$	−3.69455e17	−	1.26157e18i	−0.311256	−	1.06284i
$383$		−	3.25787e17i		−	0.269490i	−0.990880	−	0.134745i	$-0.956979\pi$
$383$		−	3.25787e17i		−	0.269490i	0.990880	−	0.134745i	$-0.0430215\pi$
$384$	6.48046e17	−	2.92058e17i	0.526365	−	0.237219i
$385$	−2.73038e16			−0.0217770
$386$	2.37808e18	−	6.96429e17i	1.86258	−	0.545463i
$387$			5.62824e17i			0.432908i
$388$	1.75629e18	−	1.12517e18i	1.32670	−	0.849954i
$389$	4.35977e17			0.323457			0.161728	−	0.986835i	$-0.448293\pi$
$389$	4.35977e17			0.323457			0.161728	+	0.986835i	$0.448293\pi$
$390$	6.62910e16	+	2.26363e17i	0.0483061	+	0.164950i
$391$		−	1.19225e18i		−	0.853353i
$392$	−9.22137e17	+	1.05962e18i	−0.648325	+	0.744986i
$393$	9.62293e17			0.664599
$394$	6.42414e17	−	1.88133e17i	0.435855	−	0.127641i
$395$		−	2.76531e17i		−	0.184316i
$396$	−8.41962e16	−	1.31423e17i	−0.0551348	−	0.0860607i
$397$	−2.60540e18			−1.67626			−0.838129	−	0.545472i	$-0.816350\pi$
$397$	−2.60540e18			−1.67626			−0.838129	+	0.545472i	$0.816350\pi$
$398$	−5.09784e17	−	1.74075e18i	−0.322258	−	1.10041i
$399$		−	1.71886e17i		−	0.106765i
$400$	−4.06534e17	+	8.83517e17i	−0.248129	+	0.539256i
$401$	1.10557e18			0.663094			0.331547	−	0.943439i	$-0.392429\pi$
$401$	1.10557e18			0.663094			0.331547	+	0.943439i	$0.392429\pi$
$402$	−6.38662e17	+	1.87034e17i	−0.376434	+	0.110240i
$403$		−	1.06475e18i		−	0.616757i
$404$	−2.43450e18	+	1.55966e18i	−1.38593	+	0.887894i
$405$	1.26595e17			0.0708325
$406$	−5.21308e16	−	1.78010e17i	−0.0286690	−	0.0978954i
$407$		−	2.33484e17i		−	0.126211i
$408$	1.11524e18	+	9.70538e17i	0.592579	+	0.515693i
$409$	−9.78324e17			−0.510999			−0.255499	−	0.966809i	$-0.582240\pi$
$409$	−9.78324e17			−0.510999			−0.255499	+	0.966809i	$0.582240\pi$
$410$	−3.63467e17	+	1.06442e17i	−0.186628	+	0.0546547i
$411$		−	2.44856e17i		−	0.123600i
$412$	9.00547e17	+	1.40568e18i	0.446916	+	0.697597i
$413$	−4.34471e17			−0.211988
$414$	−1.22478e17	−	4.18223e17i	−0.0587564	−	0.200634i
$415$		−	7.50714e17i		−	0.354110i
$416$	−1.46835e17	+	9.96071e17i	−0.0681045	+	0.461995i
$417$	1.49188e18			0.680426
$418$	−1.08903e18	+	3.18925e17i	−0.488432	+	0.143039i
$419$		−	1.41859e18i		−	0.625687i	−0.949805	−	0.312844i	$-0.898718\pi$
$419$		−	1.41859e18i		−	0.625687i	0.949805	−	0.312844i	$-0.101282\pi$
$420$	7.95984e16	−	5.09948e16i	0.0345270	−	0.0221198i
$421$	3.75609e18			1.60236			0.801182	−	0.598421i	$-0.204205\pi$
$421$	3.75609e18			1.60236			0.801182	+	0.598421i	$0.204205\pi$
$422$	6.34940e17	+	2.16812e18i	0.266407	+	0.909694i
$423$			1.27863e18i			0.527668i
$424$	−2.00223e18	+	2.30075e18i	−0.812743	+	0.933917i
$425$	−2.02280e18			−0.807664
$426$	−1.44373e18	+	4.22802e17i	−0.567048	+	0.166062i
$427$		−	3.76946e17i		−	0.145641i
$428$	−1.32389e18	−	2.06647e18i	−0.503204	−	0.785458i
$429$	2.21079e17			0.0826698
$430$	6.32491e17	+	2.15975e18i	0.232688	+	0.794557i
$431$		−	4.14482e17i		−	0.150025i	−0.997183	−	0.0750127i	$-0.976100\pi$
$431$		−	4.14482e17i		−	0.150025i	0.997183	−	0.0750127i	$-0.0238997\pi$
$432$	4.90911e17	+	2.25884e17i	0.174830	+	0.0804449i
$433$	1.37616e18			0.482229			0.241114	−	0.970497i	$-0.422487\pi$
$433$	1.37616e18			0.482229			0.241114	+	0.970497i	$0.422487\pi$
$434$	−4.09535e17	+	1.19934e17i	−0.141209	+	0.0413535i
$435$		−	9.93226e17i		−	0.336995i
$436$	3.41202e18	−	2.18591e18i	1.13922	−	0.729839i
$437$	−3.16835e18			−1.04103
$438$	6.52127e16	+	2.22681e17i	0.0210869	+	0.0720052i
$439$			4.92891e18i			1.56855i	0.620412	+	0.784276i	$0.286965\pi$
$439$			4.92891e18i			1.56855i	−0.620412	+	0.784276i	$0.713035\pi$
$440$	−4.70781e17	−	4.09698e17i	−0.147452	−	0.128320i
$441$	−1.06789e18			−0.329196
$442$	−2.00969e18	+	5.88543e17i	−0.609779	+	0.178576i
$443$		−	3.67585e18i		−	1.09782i	−0.835881	−	0.548910i	$-0.815043\pi$
$443$		−	3.67585e18i		−	1.09782i	0.835881	−	0.548910i	$-0.184957\pi$
$444$	4.36074e17	+	6.80673e17i	0.128197	+	0.200105i
$445$	−7.70755e17			−0.223047
$446$	−7.37028e16	−	2.51672e17i	−0.0209962	−	0.0716952i
$447$		−	1.01385e18i		−	0.284329i
$448$	3.99656e17	−	5.57203e16i	0.110342	−	0.0153839i
$449$	1.27078e18			0.345418			0.172709	−	0.984973i	$-0.444748\pi$
$449$	1.27078e18			0.345418			0.172709	+	0.984973i	$0.444748\pi$
$450$	−7.09570e17	+	2.07800e17i	−0.189892	+	0.0556106i
$451$			3.54983e17i			0.0935346i
$452$	−1.01869e18	+	6.52621e17i	−0.264284	+	0.169314i
$453$	−1.72315e18			−0.440186
$454$	4.17117e17	+	1.42432e18i	0.104922	+	0.358275i
$455$			1.33900e17i			0.0331666i
$456$	2.57917e18	−	2.96370e18i	0.629109	−	0.722904i
$457$	3.76445e18			0.904250			0.452125	−	0.891955i	$-0.350666\pi$
$457$	3.76445e18			0.904250			0.452125	+	0.891955i	$0.350666\pi$
$458$	5.17295e18	−	1.51491e18i	1.22371	−	0.358369i
$459$			1.12394e18i			0.261850i
$460$	−9.39981e17	−	1.46723e18i	−0.215682	−	0.336661i
$461$	−9.03282e17			−0.204135			−0.102067	−	0.994777i	$-0.532546\pi$
$461$	−9.03282e17			−0.204135			−0.102067	+	0.994777i	$0.532546\pi$
$462$	−2.49023e16	−	8.50333e16i	−0.00554300	−	0.0189276i
$463$		−	3.45649e18i		−	0.757823i	−0.925433	−	0.378912i	$-0.876298\pi$
$463$		−	3.45649e18i		−	0.757823i	0.925433	−	0.378912i	$-0.123702\pi$
$464$	1.77221e18	−	3.85153e18i	0.382727	−	0.831778i
$465$	−2.28504e18			−0.486098
$466$	−8.32583e17	+	2.43824e17i	−0.174472	+	0.0510947i
$467$			7.20839e18i			1.48806i	0.668147	+	0.744029i	$0.267088\pi$
$467$			7.20839e18i			1.48806i	−0.668147	+	0.744029i	$0.732912\pi$
$468$	−6.44509e17	+	4.12905e17i	−0.131071	+	0.0839709i
$469$	−3.77788e17			−0.0756899
$470$	1.43689e18	+	4.90653e18i	0.283622	+	0.968478i
$471$		−	2.56761e18i		−	0.499325i
$472$	−7.49128e18	−	6.51930e18i	−1.43536	−	1.24913i
$473$	2.10934e18			0.398217
$474$	8.61210e17	−	2.52208e17i	0.160199	−	0.0469149i
$475$			5.37552e18i			0.985293i
$476$	4.52741e17	+	7.06689e17i	0.0817713	+	0.127638i
$477$	−2.31869e18			−0.412681
$478$	−2.74812e18	−	9.38395e18i	−0.481993	−	1.64585i
$479$			4.68622e18i			0.809979i	0.914321	+	0.404990i	$0.132725\pi$
$479$			4.68622e18i			0.809979i	−0.914321	+	0.404990i	$0.867275\pi$
$480$	2.13764e18	+	3.15118e17i	0.364121	+	0.0536766i
$481$	−1.14503e18			−0.192221
$482$	4.58853e18	−	1.34377e18i	0.759179	−	0.222328i
$483$		−	2.47391e17i		−	0.0403417i
$484$	4.74637e18	−	3.04076e18i	0.762858	−	0.488726i
$485$	6.34041e18			1.00444
$486$	1.15460e17	+	3.94260e17i	0.0180293	+	0.0615644i
$487$		−	4.69262e18i		−	0.722292i	−0.932509	−	0.361146i	$-0.882386\pi$
$487$		−	4.69262e18i		−	0.722292i	0.932509	−	0.361146i	$-0.117614\pi$
$488$	5.65613e18	−	6.49941e18i	0.858184	−	0.986133i
$489$	−3.91415e18			−0.585430
$490$	−4.09785e18	+	1.20007e18i	−0.604204	+	0.176943i
$491$			1.25925e18i			0.183038i	0.995803	+	0.0915192i	$0.0291723\pi$
$491$			1.25925e18i			0.183038i	−0.995803	+	0.0915192i	$0.970828\pi$
$492$	−6.62995e17	−	1.03488e18i	−0.0950067	−	0.148297i
$493$	8.81804e18			1.24579
$494$	1.56403e18	+	5.34067e18i	0.217850	+	0.743887i
$495$		−	4.74452e17i		−	0.0651563i
$496$	−8.86093e18	−	4.07719e18i	−1.19980	−	0.552064i
$497$	−8.54011e17			−0.114017
$498$	2.33798e18	−	6.84684e17i	0.307776	−	0.0901332i
$499$			6.59702e18i			0.856335i	0.903699	+	0.428168i	$0.140841\pi$
$499$			6.59702e18i			0.856335i	−0.903699	+	0.428168i	$0.859159\pi$
$500$	−6.68296e18	+	4.28144e18i	−0.855419	+	0.548025i
$501$	−1.64972e18			−0.208231
$502$	2.24644e18	+	7.67088e18i	0.279621	+	0.954815i
$503$		−	3.83315e18i		−	0.470522i	−0.971932	−	0.235261i	$-0.924406\pi$
$503$		−	3.83315e18i		−	0.470522i	0.971932	−	0.235261i	$-0.0755944\pi$
$504$	2.31412e17	+	2.01387e17i	0.0280138	+	0.0243791i
$505$	−8.78883e18			−1.04928
$506$	−1.56741e18	+	4.59021e17i	−0.184556	+	0.0540479i
$507$			3.88740e18i			0.451443i
$508$	3.87592e18	+	6.04998e18i	0.443945	+	0.692959i
$509$	−1.29364e19			−1.46147			−0.730735	−	0.682661i	$-0.760822\pi$
$509$	−1.29364e19			−1.46147			−0.730735	+	0.682661i	$0.760822\pi$
$510$	1.26306e18	+	4.31294e18i	0.140745	+	0.480598i
$511$			1.31722e17i			0.0144781i
$512$	7.72708e18	+	5.03615e18i	0.837772	+	0.546021i
$513$	2.98682e18			0.319438
$514$	−1.38241e19	+	4.04843e18i	−1.45846	+	0.427115i
$515$			5.07466e18i			0.528149i
$516$	−6.14934e18	+	3.93958e18i	−0.631365	+	0.404484i
$517$	4.79201e18			0.485383
$518$	1.28975e17	+	4.40409e17i	0.0128884	+	0.0440097i
$519$		−	5.26257e17i		−	0.0518832i
$520$	−2.00919e18	+	2.30875e18i	−0.195433	+	0.224571i
$521$	−2.99173e18			−0.287117			−0.143559	−	0.989642i	$-0.545855\pi$
$521$	−2.99173e18			−0.287117			−0.143559	+	0.989642i	$0.545855\pi$
$522$	3.09324e18	−	9.05865e17i	0.292900	−	0.0857768i
$523$		−	2.98622e18i		−	0.279004i	−0.990222	−	0.139502i	$-0.955450\pi$
$523$		−	2.98622e18i		−	0.279004i	0.990222	−	0.139502i	$-0.0445502\pi$
$524$	6.73572e18	+	1.05139e19i	0.620962	+	0.969268i
$525$	−4.19732e17			−0.0381818
$526$	−1.18824e18	−	4.05746e18i	−0.106661	−	0.364212i
$527$		−	2.02870e19i		−	1.79698i
$528$	8.46564e17	−	1.83983e18i	0.0739984	−	0.160820i
$529$	7.03270e18			0.606642
$530$	−8.89763e18	+	2.60570e18i	−0.757432	+	0.221816i
$531$		−	7.54970e18i		−	0.634261i
$532$	1.87800e18	−	1.20314e18i	0.155709	−	0.0997551i
$533$	1.74087e18			0.142454
$534$	−7.02962e17	−	2.40039e18i	−0.0567731	−	0.193862i
$535$		−	7.46021e18i		−	0.594668i
$536$	−6.51392e18	−	5.66875e18i	−0.512494	−	0.445999i
$537$	−8.73247e17			−0.0678136
$538$	2.07166e19	−	6.06692e18i	1.58797	−	0.465042i
$539$			4.00221e18i			0.302815i
$540$	8.86124e17	+	1.38316e18i	0.0661818	+	0.103304i
$541$	1.14449e19			0.843784			0.421892	−	0.906646i	$-0.361366\pi$
$541$	1.14449e19			0.843784			0.421892	+	0.906646i	$0.361366\pi$
$542$	−6.08674e18	−	2.07843e19i	−0.442986	−	1.51265i
$543$		−	1.45629e18i		−	0.104628i
$544$	−2.79768e18	+	1.89784e19i	−0.198429	+	1.34607i
$545$	1.23178e19			0.862497
$546$	−4.17010e17	+	1.22123e17i	−0.0288269	+	0.00844206i
$547$		−	1.04450e18i		−	0.0712850i	−0.999365	−	0.0356425i	$-0.988652\pi$
$547$		−	1.04450e18i		−	0.0712850i	0.999365	−	0.0356425i	$-0.0113478\pi$
$548$	2.67526e18	−	1.71391e18i	0.180261	−	0.115485i
$549$	6.55010e18			0.435754
$550$	7.78789e17	+	2.65931e18i	0.0511542	+	0.174675i
$551$		−	2.34336e19i		−	1.51977i
$552$	3.71214e18	−	4.26559e18i	0.237712	−	0.273153i
$553$	5.09431e17			0.0322114
$554$	−1.83505e19	+	5.37401e18i	−1.14572	+	0.335529i
$555$			2.45731e18i			0.151499i
$556$	1.04426e19	+	1.63001e19i	0.635750	+	0.992351i
$557$	−1.13140e18			−0.0680188			−0.0340094	−	0.999422i	$-0.510828\pi$
$557$	−1.13140e18			−0.0680188			−0.0340094	+	0.999422i	$0.510828\pi$
$558$	−2.08406e18	−	7.11639e18i	−0.123729	−	0.422494i
$559$		−	1.03444e19i		−	0.606488i
$560$	1.11432e18	+	5.12735e17i	0.0645201	+	0.0296877i
$561$	4.21227e18			0.240867
$562$	2.66601e19	−	7.80749e18i	1.50559	−	0.440917i
$563$			9.10207e18i			0.507670i	0.967248	+	0.253835i	$0.0816920\pi$
$563$			9.10207e18i			0.507670i	−0.967248	+	0.253835i	$0.918308\pi$
$564$	−1.39701e19	+	8.94994e18i	−0.769565	+	0.493022i
$565$	−3.67758e18			−0.200089
$566$	−3.38873e18	−	1.15714e19i	−0.182105	−	0.621831i
$567$			2.33217e17i			0.0123788i
$568$	−1.47251e19	−	1.28145e19i	−0.772005	−	0.671839i
$569$	−1.37899e19			−0.714129			−0.357065	−	0.934080i	$-0.616222\pi$
$569$	−1.37899e19			−0.714129			−0.357065	+	0.934080i	$0.616222\pi$
$570$	1.14615e19	−	3.35653e18i	0.586295	−	0.171698i
$571$			2.18754e19i			1.10536i	0.833394	+	0.552679i	$0.186394\pi$
$571$			2.18754e19i			1.10536i	−0.833394	+	0.552679i	$0.813606\pi$
$572$	1.54748e18	+	2.41548e18i	0.0772418	+	0.120568i
$573$	1.29675e19			0.639403
$574$	−1.96091e17	−	6.69587e17i	−0.00955154	−	0.0326155i
$575$			7.73686e18i			0.372297i
$576$	9.68238e17	+	6.94474e18i	0.0460283	+	0.330140i
$577$	−3.86602e19			−1.81565			−0.907827	−	0.419344i	$-0.862260\pi$
$577$	−3.86602e19			−1.81565			−0.907827	+	0.419344i	$0.862260\pi$
$578$	−1.76074e19	+	5.15637e18i	−0.816957	+	0.239249i
$579$			2.44440e19i			1.12053i
$580$	1.08518e19	−	6.95224e18i	0.491482	−	0.314868i
$581$	1.38298e18			0.0618848
$582$	5.78273e18	+	1.97462e19i	0.255665	+	0.873016i
$583$			8.68996e18i			0.379610i
$584$	−1.97651e18	+	2.27119e18i	−0.0853118	+	0.0980312i
$585$	−2.32675e18			−0.0992337
$586$	9.93674e18	−	2.91001e18i	0.418756	−	0.122634i
$587$			2.17766e19i			0.906826i	0.891301	+	0.453413i	$0.149794\pi$
$587$			2.17766e19i			0.906826i	−0.891301	+	0.453413i	$0.850206\pi$
$588$	−7.47483e18	−	1.16676e19i	−0.307581	−	0.480108i
$589$	−5.39120e19			−2.19219
$590$	−8.48421e18	−	2.89709e19i	−0.340916	−	1.16412i
$591$			6.60330e18i			0.262210i
$592$	−4.38457e18	+	9.52896e18i	−0.172058	+	0.373933i
$593$	−3.69240e18			−0.143194			−0.0715972	−	0.997434i	$-0.522810\pi$
$593$	−3.69240e18			−0.143194			−0.0715972	+	0.997434i	$0.522810\pi$
$594$	1.47760e18	−	4.32721e17i	0.0566308	−	0.0165845i
$595$			2.55123e18i			0.0966342i
$596$	1.10772e19	−	7.09661e18i	0.414673	−	0.265661i
$597$	1.78929e19			0.662005
$598$	2.25108e18	+	7.68670e18i	0.0823155	+	0.281081i
$599$			4.44543e19i			1.60667i	0.595528	+	0.803334i	$0.296943\pi$
$599$			4.44543e19i			1.60667i	−0.595528	+	0.803334i	$0.703057\pi$
$600$	−7.23713e18	−	6.29813e18i	−0.258528	−	0.224985i
$601$	3.89796e19			1.37631			0.688154	−	0.725564i	$-0.258421\pi$
$601$	3.89796e19			1.37631			0.688154	+	0.725564i	$0.258421\pi$
$602$	−3.97875e18	+	1.16519e18i	−0.138858	+	0.0406650i
$603$		−	6.56473e18i		−	0.226462i
$604$	−1.20615e19	−	1.88269e19i	−0.411284	−	0.641978i
$605$	1.71350e19			0.577558
$606$	−8.01579e18	−	2.73714e19i	−0.267078	−	0.911985i
$607$		−	3.22063e19i		−	1.06077i	−0.847758	−	0.530384i	$-0.822048\pi$
$607$		−	3.22063e19i		−	1.06077i	0.847758	−	0.530384i	$-0.177952\pi$
$608$	5.04343e19	+	7.43472e18i	1.64210	+	0.242069i
$609$	1.82974e18			0.0588938
$610$	2.51350e19	−	7.36088e18i	0.799780	−	0.234218i
$611$		−	2.35004e19i		−	0.739243i
$612$	−1.22800e19	+	7.86717e18i	−0.381889	+	0.244657i
$613$	−3.60167e19			−1.10734			−0.553669	−	0.832737i	$-0.686773\pi$
$613$	−3.60167e19			−1.10734			−0.553669	+	0.832737i	$0.686773\pi$
$614$	1.33886e19	+	4.57178e19i	0.406964	+	1.38965i
$615$		−	3.73603e18i		−	0.112275i
$616$	7.54754e17	−	8.67283e17i	0.0224254	−	0.0257689i
$617$	5.50103e19			1.61603			0.808013	−	0.589165i	$-0.200543\pi$
$617$	5.50103e19			1.61603			0.808013	+	0.589165i	$0.200543\pi$
$618$	−1.58042e19	+	4.62831e18i	−0.459042	+	0.134432i
$619$			2.23252e19i			0.641153i	0.947223	+	0.320576i	$0.103877\pi$
$619$			2.23252e19i			0.641153i	−0.947223	+	0.320576i	$0.896123\pi$
$620$	−1.59945e19	−	2.49660e19i	−0.454181	−	0.708937i
$621$	4.29886e18			0.120701
$622$	−5.83015e18	−	1.99081e19i	−0.161863	−	0.552710i
$623$		−	1.41990e18i		−	0.0389800i
$624$	−9.02268e18	−	4.15162e18i	−0.244931	−	0.112700i
$625$	−2.01286e18			−0.0540323
$626$	−2.83552e19	+	8.30391e18i	−0.752683	+	0.220426i
$627$		−	1.11940e19i		−	0.293840i
$628$	2.80534e19	−	1.79724e19i	0.728228	−	0.466540i
$629$	−2.18164e19			−0.560053
$630$	2.62085e17	+	8.94935e17i	0.00665361	+	0.0227200i
$631$		−	3.68456e19i		−	0.925083i	−0.886598	−	0.462541i	$-0.846938\pi$
$631$		−	3.68456e19i		−	0.925083i	0.886598	−	0.462541i	$-0.153062\pi$
$632$	8.78376e18	+	7.64408e18i	0.218103	+	0.189804i
$633$	−2.22858e19			−0.547271
$634$	−3.84805e19	+	1.12691e19i	−0.934579	+	0.273695i
$635$			2.18411e19i			0.524637i
$636$	−1.62301e19	−	2.53337e19i	−0.385585	−	0.601865i
$637$	1.96271e19			0.461191
$638$	−3.39499e18	−	1.15928e19i	−0.0789030	−	0.269429i
$639$		−	1.48400e19i		−	0.341135i
$640$	1.15198e19	+	2.55613e19i	0.261930	+	0.581196i
$641$	1.84787e19			0.415590			0.207795	−	0.978172i	$-0.433371\pi$
$641$	1.84787e19			0.415590			0.207795	+	0.978172i	$0.433371\pi$
$642$	2.32336e19	−	6.80403e18i	0.516858	−	0.151363i
$643$		−	2.86386e19i		−	0.630195i	−0.949059	−	0.315097i	$-0.897963\pi$
$643$		−	2.86386e19i		−	0.630195i	0.949059	−	0.315097i	$-0.102037\pi$
$644$	2.70296e18	−	1.73165e18i	0.0588354	−	0.0376929i
$645$	−2.21998e19			−0.478004
$646$	2.97998e19	+	1.01757e20i	0.634726	+	2.16739i
$647$		−	6.92005e19i		−	1.45807i	−0.684474	−	0.729037i	$-0.739968\pi$
$647$		−	6.92005e19i		−	1.45807i	0.684474	−	0.729037i	$-0.260032\pi$
$648$	−3.49945e18	+	4.02119e18i	−0.0729415	+	0.0838166i
$649$	−2.82947e19			−0.583434
$650$	1.30415e19	−	3.81924e18i	0.266032	−	0.0779083i
$651$		−	4.20956e18i		−	0.0849512i
$652$	−2.73977e19	−	4.27654e19i	−0.546991	−	0.853806i
$653$	3.20804e19			0.633647			0.316823	−	0.948485i	$-0.397384\pi$
$653$	3.20804e19			0.633647			0.316823	+	0.948485i	$0.397384\pi$
$654$	1.12344e19	+	3.83617e19i	0.219535	+	0.749642i
$655$			3.79564e19i			0.733830i
$656$	6.66619e18	−	1.44876e19i	0.127512	−	0.277121i
$657$	−2.28891e18			−0.0433182
$658$	−9.03892e18	+	2.64708e18i	−0.169253	+	0.0495662i
$659$		−	1.74247e19i		−	0.322825i	−0.986887	−	0.161412i	$-0.948395\pi$
$659$		−	1.74247e19i		−	0.322825i	0.986887	−	0.161412i	$-0.0516049\pi$
$660$	5.18380e18	−	3.32100e18i	0.0950256	−	0.0608782i
$661$	6.85506e19			1.24337			0.621686	−	0.783267i	$-0.286448\pi$
$661$	6.85506e19			1.24337			0.621686	+	0.783267i	$0.286448\pi$
$662$	2.54602e19	+	8.69384e19i	0.456936	+	1.56029i
$663$		−	2.06573e19i		−	0.366842i
$664$	2.38458e19	+	2.07518e19i	0.419020	+	0.364653i
$665$	6.77980e18			0.117887
$666$	−7.65289e18	+	2.24117e18i	−0.131676	+	0.0385617i
$667$		−	3.37275e19i		−	0.574252i
$668$	−1.15475e19	−	1.80246e19i	−0.194559	−	0.303690i
$669$	2.58690e18			0.0431318
$670$	−7.37731e18	−	2.51911e19i	−0.121723	−	0.415647i
$671$		−	2.45484e19i		−	0.400835i
$672$	−5.80518e17	+	3.93801e18i	−0.00938060	+	0.0636344i
$673$	1.98317e18			0.0317143			0.0158572	−	0.999874i	$-0.494952\pi$
$673$	1.98317e18			0.0317143			0.0158572	+	0.999874i	$0.494952\pi$
$674$	−2.74964e19	+	8.05242e18i	−0.435168	+	0.127440i
$675$		−	7.29358e18i		−	0.114239i
$676$	−4.24731e19	+	2.72104e19i	−0.658397	+	0.421802i
$677$	−1.02414e20			−1.57123			−0.785616	−	0.618714i	$-0.787654\pi$
$677$	−1.02414e20			−1.57123			−0.785616	+	0.618714i	$0.787654\pi$
$678$	−3.35411e18	−	1.14532e19i	−0.0509295	−	0.173908i
$679$			1.16805e19i			0.175538i
$680$	−3.82816e19	+	4.39891e19i	−0.569413	+	0.654308i
$681$	−1.46404e19			−0.215538
$682$	−2.66707e19	+	7.81060e18i	−0.388637	+	0.113813i
$683$			5.52436e19i			0.796777i	0.917217	+	0.398389i	$0.130430\pi$
$683$			5.52436e19i			0.796777i	−0.917217	+	0.398389i	$0.869570\pi$
$684$	2.09067e19	+	3.26335e19i	0.298465	+	0.465877i
$685$	9.65802e18			0.136475
$686$	−4.44937e18	−	1.51932e19i	−0.0622343	−	0.212510i
$687$			5.31721e19i			0.736185i
$688$	−8.60865e19	−	3.96111e19i	−1.17982	−	0.542872i
$689$	4.26163e19			0.578151
$690$	1.64962e19	−	4.83097e18i	0.221534	−	0.0648770i
$691$			3.95588e19i			0.525892i	0.964811	+	0.262946i	$0.0846941\pi$
$691$			3.95588e19i			0.525892i	−0.964811	+	0.262946i	$0.915306\pi$
$692$	5.74981e18	−	3.68362e18i	0.0756678	−	0.0484766i
$693$	8.74047e17			0.0113868
$694$	−9.05855e18	−	3.09321e19i	−0.116827	−	0.398926i
$695$			5.88451e19i			0.751306i
$696$	3.15490e19	+	2.74556e19i	0.398768	+	0.347029i
$697$	3.31691e19			0.415054
$698$	4.33221e19	−	1.26870e19i	0.536688	−	0.157171i
$699$		−	8.55801e18i		−	0.104962i
$700$	−2.93798e18	−	4.58593e18i	−0.0356749	−	0.0556854i
$701$	−1.03081e20			−1.23923			−0.619616	−	0.784905i	$-0.712712\pi$
$701$	−1.03081e20			−1.23923			−0.619616	+	0.784905i	$0.712712\pi$
$702$	−2.12210e18	−	7.24629e18i	−0.0252584	−	0.0862494i
$703$			5.79764e19i			0.683225i
$704$	2.60274e19	−	3.62875e18i	0.303684	−	0.0423398i
$705$	−5.04336e19			−0.582635
$706$	−1.67312e19	+	4.89979e18i	−0.191379	+	0.0560460i
$707$		−	1.61910e19i		−	0.183374i
$708$	8.24870e19	−	5.28453e19i	0.925023	−	0.592617i
$709$	1.24525e20			1.38271			0.691356	−	0.722514i	$-0.257014\pi$
$709$	1.24525e20			1.38271			0.691356	+	0.722514i	$0.257014\pi$
$710$	−1.66768e19	−	5.69461e19i	−0.183360	−	0.626117i
$711$			8.85227e18i			0.0963757i
$712$	2.13058e19	−	2.44824e19i	0.229688	−	0.263933i
$713$	−7.75942e19			−0.828329
$714$	−7.94539e18	+	2.32683e18i	−0.0839900	+	0.0245967i
$715$			8.72017e18i			0.0912815i
$716$	−6.11243e18	−	9.54097e18i	−0.0633611	−	0.0989012i
$717$	9.64565e19			0.990142
$718$	−4.96949e19	−	1.69692e20i	−0.505173	−	1.72500i
$719$		−	3.12189e19i		−	0.314279i	−0.987576	−	0.157140i	$-0.949773\pi$
$719$		−	3.12189e19i		−	0.314279i	0.987576	−	0.157140i	$-0.0502273\pi$
$720$	−8.90968e18	+	1.93633e19i	−0.0888248	+	0.193042i
$721$	−9.34865e18			−0.0923001
$722$	1.72265e20	−	5.04483e19i	1.68436	−	0.493271i
$723$			4.71649e19i			0.456721i
$724$	1.59112e19	−	1.01935e19i	0.152593	−	0.0977586i
$725$	−5.72231e19			−0.543507
$726$	1.56278e19	+	5.33640e19i	0.147008	+	0.501987i
$727$			2.60624e19i			0.242814i	0.992603	+	0.121407i	$0.0387407\pi$
$727$			2.60624e19i			0.242814i	−0.992603	+	0.121407i	$0.961259\pi$
$728$	−4.25322e18	−	3.70138e18i	−0.0392463	−	0.0341542i
$729$	−4.05256e18			−0.0370370
$730$	−8.78334e18	+	2.57223e18i	−0.0795059	+	0.0232836i
$731$		−	1.97094e20i		−	1.76706i
$732$	4.58485e19	+	7.15655e19i	0.407143	+	0.635516i
$733$	5.08673e19			0.447416			0.223708	−	0.974656i	$-0.428184\pi$
$733$	5.08673e19			0.447416			0.223708	+	0.974656i	$0.428184\pi$
$734$	−4.71119e19	−	1.60872e20i	−0.410448	−	1.40155i
$735$		−	4.21213e19i		−	0.363488i
$736$	7.25889e19	+	1.07006e19i	0.620477	+	0.0914669i
$737$	−2.46032e19			−0.208314
$738$	1.16353e19	−	3.40742e18i	0.0975846	−	0.0285780i
$739$		−	4.88203e19i		−	0.405592i	−0.979221	−	0.202796i	$-0.934997\pi$
$739$		−	4.88203e19i		−	0.405592i	0.979221	−	0.202796i	$-0.0650029\pi$
$740$	−2.68482e19	+	1.72003e19i	−0.220950	+	0.141552i
$741$	−5.48961e19			−0.447521
$742$	−4.80028e18	−	1.63914e19i	−0.0387650	−	0.132370i
$743$			1.93141e20i			1.54509i	0.634963	+	0.772543i	$0.281015\pi$
$743$			1.93141e20i			1.54509i	−0.634963	+	0.772543i	$0.718985\pi$
$744$	6.31649e19	−	7.25824e19i	0.500571	−	0.575202i
$745$	3.99900e19			0.313948
$746$	−1.33564e18	+	3.91147e17i	−0.0103877	+	0.00304206i
$747$			2.40318e19i			0.185158i
$748$	2.94845e19	+	4.60227e19i	0.225052	+	0.351286i
$749$	1.37434e19			0.103925
$750$	−2.20042e19	−	7.51374e19i	−0.164846	−	0.562895i
$751$			1.53255e20i			1.13746i	0.822525	+	0.568730i	$0.192565\pi$
$751$			1.53255e20i			1.13746i	−0.822525	+	0.568730i	$0.807435\pi$
$752$	−1.95571e20	−	8.99886e19i	−1.43807	−	0.661702i
$753$	−7.88480e19			−0.574415
$754$	−5.68520e19	+	1.66493e19i	−0.410343	+	0.120170i
$755$		−	6.79674e19i		−	0.486040i
$756$	−2.54809e18	+	1.63244e18i	−0.0180536	+	0.0115660i
$757$	7.14646e19			0.501672			0.250836	−	0.968030i	$-0.419295\pi$
$757$	7.14646e19			0.501672			0.250836	+	0.968030i	$0.419295\pi$
$758$	2.99214e19	+	1.02172e20i	0.208112	+	0.710635i
$759$		−	1.61112e19i		−	0.111029i
$760$	1.16899e20	+	1.01732e20i	0.798209	+	0.694643i
$761$	1.08136e20			0.731605			0.365803	−	0.930692i	$-0.380795\pi$
$761$	1.08136e20			0.731605			0.365803	+	0.930692i	$0.380795\pi$
$762$	−6.80206e19	+	1.99201e19i	−0.455991	+	0.133538i
$763$			2.26921e19i			0.150731i
$764$	9.07683e19	+	1.41681e20i	0.597421	+	0.932522i
$765$	−4.43321e19			−0.289127
$766$	1.17200e19	+	4.00199e19i	0.0757399	+	0.258628i
$767$			1.38759e20i			0.888577i
$768$	−6.90999e19	+	5.91896e19i	−0.438479	+	0.375592i
$769$	−1.01717e20			−0.639602			−0.319801	−	0.947485i	$-0.603616\pi$
$769$	−1.01717e20			−0.639602			−0.319801	+	0.947485i	$0.603616\pi$
$770$	3.35402e18	−	9.82237e17i	0.0208993	−	0.00612042i
$771$		−	1.42096e20i		−	0.877409i
$772$	−2.67072e20	+	1.71100e20i	−1.63421	+	1.04695i
$773$	−5.42108e19			−0.328723			−0.164361	−	0.986400i	$-0.552556\pi$
$773$	−5.42108e19			−0.328723			−0.164361	+	0.986400i	$0.552556\pi$
$774$	−2.02472e19	−	6.91377e19i	−0.121669	−	0.415459i
$775$			1.31649e20i			0.783980i
$776$	−1.75267e20	+	2.01398e20i	−1.03435	+	1.18856i
$777$	−4.52691e18			−0.0264762
$778$	−5.35557e19	+	1.56840e19i	−0.310419	+	0.0909073i
$779$		−	8.81457e19i		−	0.506336i
$780$	−1.62865e19	−	2.54218e19i	−0.0927182	−	0.144725i
$781$	−5.56170e19			−0.313798
$782$	4.28902e19	+	1.46456e20i	0.239834	+	0.818957i
$783$			3.17950e19i			0.176209i
$784$	7.51569e19	−	1.63338e20i	0.412816	−	0.897170i
$785$	1.01276e20			0.551339
$786$	−1.18209e20	+	3.46178e19i	−0.637811	+	0.186785i
$787$		−	3.02717e20i		−	1.61888i	−0.587205	−	0.809439i	$-0.699772\pi$
$787$		−	3.02717e20i		−	1.61888i	0.587205	−	0.809439i	$-0.300228\pi$
$788$	−7.21467e19	+	4.62208e19i	−0.382413	+	0.244993i
$789$	4.17061e19			0.219109
$790$	9.94800e18	+	3.39692e19i	0.0518020	+	0.176887i
$791$		−	6.77491e18i		−	0.0349678i
$792$	1.50706e19	+	1.31152e19i	0.0770998	+	0.0670963i
$793$	−1.20387e20			−0.610476
$794$	3.20049e20	−	9.37275e19i	1.60869	−	0.471111i
$795$		−	9.14577e19i		−	0.455670i
$796$	1.25244e20	+	1.95496e20i	0.618539	+	0.965485i
$797$	1.80645e20			0.884337			0.442169	−	0.896932i	$-0.354209\pi$
$797$	1.80645e20			0.884337			0.442169	+	0.896932i	$0.354209\pi$
$798$	6.18347e18	+	2.11146e19i	0.0300063	+	0.102462i
$799$		−	4.47759e20i		−	2.15386i
$800$	1.81550e19	−	1.23157e20i	0.0865698	−	0.587257i
$801$	2.46733e19			0.116627
$802$	−1.35809e20	+	3.97721e19i	−0.636367	+	0.186362i
$803$			8.57833e18i			0.0398469i
$804$	7.17253e19	−	4.59508e19i	0.330278	−	0.211593i
$805$	9.75801e18			0.0445441
$806$	3.83038e19	+	1.30795e20i	0.173339	+	0.591898i
$807$			2.12943e20i			0.955320i
$808$	2.42948e20	−	2.79169e20i	1.08052	−	1.24162i
$809$	4.01451e20			1.77008			0.885039	−	0.465516i	$-0.154131\pi$
$809$	4.01451e20			1.77008			0.885039	+	0.465516i	$0.154131\pi$
$810$	−1.55511e19	+	4.55418e18i	−0.0679775	+	0.0199074i
$811$		−	1.90701e20i		−	0.826434i	−0.910633	−	0.413217i	$-0.864405\pi$
$811$		−	1.90701e20i		−	0.826434i	0.910633	−	0.413217i	$-0.135595\pi$
$812$	1.28076e19	+	1.99915e19i	0.0550269	+	0.0858922i
$813$	2.13639e20			0.910011
$814$	8.39944e18	+	2.86814e19i	0.0354715	+	0.121124i
$815$		−	1.54388e20i		−	0.646414i
$816$	−1.71911e20	−	7.91017e19i	−0.713630	−	0.328363i
$817$	−5.23770e20			−2.15569
$818$	1.20178e20	−	3.51945e19i	0.490402	−	0.143616i
$819$		−	4.28640e18i		−	0.0173422i
$820$	4.08193e19	−	2.61509e19i	0.163745	−	0.104904i
$821$	−4.09883e20			−1.63026			−0.815131	−	0.579277i	$-0.803335\pi$
$821$	−4.09883e20			−1.63026			−0.815131	+	0.579277i	$0.803335\pi$
$822$	8.80853e18	+	3.00783e19i	0.0347377	+	0.118618i
$823$			3.95028e20i			1.54465i	0.635229	+	0.772324i	$0.280906\pi$
$823$			3.95028e20i			1.54465i	−0.635229	+	0.772324i	$0.719094\pi$
$824$	−1.61192e20	−	1.40278e20i	−0.624962	−	0.543874i
$825$	−2.73348e19			−0.105084
$826$	5.33708e19	−	1.56298e19i	0.203443	−	0.0595790i
$827$			1.60435e20i			0.606402i	0.952927	+	0.303201i	$0.0980553\pi$
$827$			1.60435e20i			0.606402i	−0.952927	+	0.303201i	$0.901945\pi$
$828$	3.00905e19	+	4.69687e19i	0.112776	+	0.176034i
$829$	1.73241e20			0.643825			0.321913	−	0.946769i	$-0.395674\pi$
$829$	1.73241e20			0.643825			0.321913	+	0.946769i	$0.395674\pi$
$830$	2.70064e19	+	9.22183e19i	0.0995223	+	0.339837i
$831$		−	1.88623e20i		−	0.689266i
$832$	−1.77957e19	−	1.27640e20i	−0.0644839	−	0.462514i
$833$	3.73960e20			1.34373
$834$	−1.83263e20	+	5.36693e19i	−0.653001	+	0.191233i
$835$		−	6.50709e19i		−	0.229923i
$836$	1.22304e20	−	7.83538e19i	0.428544	−	0.274547i
$837$	7.31485e19			0.254172
$838$	5.10326e19	+	1.74260e20i	0.175849	+	0.600468i
$839$			4.45657e18i			0.0152288i	0.999971	+	0.00761442i	$0.00242377\pi$
$839$			4.45657e18i			0.0152288i	−0.999971	+	0.00761442i	$0.997576\pi$
$840$	−7.94343e18	+	9.12773e18i	−0.0269186	+	0.0309320i
$841$	−4.81047e19			−0.161665
$842$	−4.61401e20	+	1.35123e20i	−1.53778	+	0.450343i
$843$			2.74036e20i			0.905761i
$844$	−1.55993e20	−	2.43491e20i	−0.511338	−	0.798154i
$845$	−1.53333e20			−0.498470
$846$	−4.59977e19	−	1.57067e20i	−0.148301	−	0.506399i
$847$			3.15664e19i			0.100935i
$848$	1.63188e20	−	3.54655e20i	0.517507	−	1.12469i
$849$	1.18941e20			0.374093
$850$	2.48483e20	−	7.27689e19i	0.775110	−	0.226993i
$851$			8.34441e19i			0.258160i
$852$	1.62139e20	−	1.03875e20i	0.497520	−	0.318737i
$853$	−3.66073e20			−1.11410			−0.557051	−	0.830479i	$-0.688067\pi$
$853$	−3.66073e20			−1.11410			−0.557051	+	0.830479i	$0.688067\pi$
$854$	1.35604e19	+	4.63043e19i	0.0409323	+	0.139771i
$855$			1.17811e20i			0.352714i
$856$	2.36967e20	+	2.06221e20i	0.703674	+	0.612374i
$857$	4.05711e19			0.119495			0.0597477	−	0.998214i	$-0.480970\pi$
$857$	4.05711e19			0.119495			0.0597477	+	0.998214i	$0.480970\pi$
$858$	−2.71575e19	+	7.95317e18i	−0.0793377	+	0.0232343i
$859$			2.80914e19i			0.0813993i	0.999171	+	0.0406996i	$0.0129587\pi$
$859$			2.80914e19i			0.0813993i	−0.999171	+	0.0406996i	$0.987041\pi$
$860$	−1.55391e20	−	2.42552e20i	−0.446619	−	0.697134i
$861$	6.88260e18			0.0196214
$862$	1.49107e19	+	5.09153e19i	0.0421646	+	0.143978i
$863$			6.24876e20i			1.75274i	0.481635	+	0.876372i	$0.340043\pi$
$863$			6.24876e20i			1.75274i	−0.481635	+	0.876372i	$0.659957\pi$
$864$	−6.84299e19	−	1.00875e19i	−0.190393	−	0.0280665i
$865$	2.07575e19			0.0572878
$866$	−1.69048e20	+	4.95063e19i	−0.462792	+	0.135530i
$867$		−	1.80984e20i		−	0.491480i
$868$	4.59930e19	−	2.94654e19i	0.123895	−	0.0793734i
$869$	3.31764e19			0.0886525
$870$	3.57306e19	+	1.22009e20i	0.0947122	+	0.323412i
$871$			1.20656e20i			0.317265i
$872$	−3.40498e20	+	3.91264e20i	−0.888177	+	1.02060i
$873$	−2.02969e20			−0.525205
$874$	3.89202e20	−	1.13979e20i	0.999069	−	0.292581i
$875$		−	4.44460e19i		−	0.113182i
$876$	−1.60216e19	−	2.50083e19i	−0.0404740	−	0.0631764i
$877$	−1.93745e20			−0.485549			−0.242775	−	0.970083i	$-0.578058\pi$
$877$	−1.93745e20			−0.485549			−0.242775	+	0.970083i	$0.578058\pi$
$878$	−1.77314e20	−	6.05471e20i	−0.440841	−	1.50533i
$879$			1.02139e20i			0.251923i
$880$	7.25696e19	+	3.33916e19i	0.177573	+	0.0817068i
$881$	1.33978e20			0.325238			0.162619	−	0.986689i	$-0.448006\pi$
$881$	1.33978e20			0.325238			0.162619	+	0.986689i	$0.448006\pi$
$882$	1.31180e20	−	3.84164e19i	0.315927	−	0.0925203i
$883$			7.66837e20i			1.83222i	0.400923	+	0.916112i	$0.368689\pi$
$883$			7.66837e20i			1.83222i	−0.400923	+	0.916112i	$0.631311\pi$
$884$	2.25699e20	−	1.44594e20i	0.535012	−	0.342756i
$885$	2.97788e20			0.700332
$886$	1.32236e20	+	4.51544e20i	0.308542	+	1.05357i
$887$		−	3.08141e19i		−	0.0713319i	−0.999364	−	0.0356660i	$-0.988645\pi$
$887$		−	3.08141e19i		−	0.0713319i	0.999364	−	0.0356660i	$-0.0113552\pi$
$888$	−7.80544e19	−	6.79269e19i	−0.179269	−	0.156010i
$889$	−4.02362e19			−0.0916864
$890$	9.46801e19	−	2.77274e19i	0.214057	−	0.0626872i
$891$			1.51881e19i			0.0340690i
$892$	1.81074e19	+	2.82641e19i	0.0402998	+	0.0629045i
$893$	−1.18990e21			−2.62755
$894$	3.64726e19	+	1.24542e20i	0.0799106	+	0.272869i
$895$		−	3.44440e19i		−	0.0748778i
$896$	−4.70896e19	+	2.12221e19i	−0.101571	+	0.0457754i
$897$	−7.90107e19			−0.169098
$898$	−1.56103e20	+	4.57154e19i	−0.331496	+	0.0970796i
$899$		−	5.73899e20i		−	1.20925i
$900$	7.96886e19	−	5.10526e19i	0.166609	−	0.106738i
$901$	8.11978e20			1.68450
$902$	−1.27703e19	−	4.36064e19i	−0.0262878	−	0.0897645i
$903$		−	4.08970e19i		−	0.0835368i
$904$	1.01658e20	−	1.16815e20i	0.206046	−	0.236766i
$905$	5.74414e19			0.115527
$906$	2.11673e20	−	6.19892e19i	0.422443	−	0.123714i
$907$		−	1.17618e20i		−	0.232929i	−0.993195	−	0.116465i	$-0.962844\pi$
$907$		−	1.17618e20i		−	0.232929i	0.993195	−	0.116465i	$-0.0371562\pi$
$908$	−1.02478e20	−	1.59959e20i	−0.201386	−	0.314346i
$909$	2.81347e20			0.548649
$910$	−4.81697e18	−	1.64484e19i	−0.00932146	−	0.0318298i
$911$		−	1.00717e21i		−	1.93407i	−0.254635	−	0.967037i	$-0.581955\pi$
$911$		−	1.00717e21i		−	1.93407i	0.254635	−	0.967037i	$-0.418045\pi$
$912$	−2.10210e20	+	4.56847e20i	−0.400580	+	0.870577i
$913$	9.00660e19			0.170320
$914$	−4.62428e20	+	1.35424e20i	−0.867803	+	0.254139i
$915$			2.58360e20i			0.481147i
$916$	−5.80951e20	+	3.72187e20i	−1.07367	+	0.687848i
$917$	−6.99241e19			−0.128245
$918$	−4.04328e19	−	1.38065e20i	−0.0735928	−	0.251296i
$919$		−	3.05618e20i		−	0.552039i	−0.961152	−	0.276019i	$-0.910985\pi$
$919$		−	3.05618e20i		−	0.552039i	0.961152	−	0.276019i	$-0.0890154\pi$
$920$	1.68250e20	+	1.46420e20i	0.301607	+	0.262474i
$921$	−4.69927e20			−0.836014
$922$	1.10960e20	−	3.24949e19i	0.195907	−	0.0573719i
$923$			2.72750e20i			0.477918i
$924$	6.11803e18	+	9.54971e18i	0.0106392	+	0.0166068i
$925$	1.41574e20			0.244338
$926$	1.24345e20	+	4.24597e20i	0.212986	+	0.727278i
$927$		−	1.62449e20i		−	0.276159i
$928$	−7.91434e19	+	5.36879e20i	−0.133530	+	0.905817i
$929$	3.28358e20			0.549842			0.274921	−	0.961467i	$-0.411348\pi$
$929$	3.28358e20			0.549842			0.274921	+	0.961467i	$0.411348\pi$
$930$	2.80696e20	−	8.22028e19i	0.466505	−	0.136617i
$931$		−	9.93786e20i		−	1.63925i
$932$	9.35036e19	−	5.99032e19i	0.153080	−	0.0980705i
$933$	2.04633e20			0.332510
$934$	−2.59317e20	−	8.85483e20i	−0.418218	−	1.42808i
$935$			1.66147e20i			0.265958i
$936$	6.43180e19	−	7.39073e19i	0.102188	−	0.117424i
$937$	8.77510e20			1.38381			0.691903	−	0.721991i	$-0.256773\pi$
$937$	8.77510e20			1.38381			0.691903	+	0.721991i	$0.256773\pi$
$938$	4.64077e19	−	1.35906e19i	0.0726391	−	0.0212726i
$939$		−	2.91460e20i		−	0.452813i
$940$	−3.53018e20	−	5.51031e20i	−0.544380	−	0.849730i
$941$	7.64224e20			1.16975			0.584875	−	0.811123i	$-0.301143\pi$
$941$	7.64224e20			1.16975			0.584875	+	0.811123i	$0.301143\pi$
$942$	9.23681e19	+	3.15407e20i	0.140335	+	0.479199i
$943$		−	1.26866e20i		−	0.191322i
$944$	1.15476e21	+	5.31342e20i	1.72858	+	0.795372i
$945$	−9.19892e18			−0.0136683
$946$	−2.59113e20	+	7.58822e19i	−0.382166	+	0.111919i
$947$		−	4.22492e20i		−	0.618542i	−0.950974	−	0.309271i	$-0.899915\pi$
$947$		−	4.22492e20i		−	0.618542i	0.950974	−	0.309271i	$-0.100085\pi$
$948$	−9.67186e19	+	6.19628e19i	−0.140557	+	0.0900478i
$949$	4.20688e19			0.0606872
$950$	−1.93381e20	−	6.60333e20i	−0.276916	−	0.945579i
$951$		−	3.95536e20i		−	0.562242i
$952$	−8.10376e19	−	7.05232e19i	−0.114348	−	0.0995115i
$953$	−8.32275e19			−0.116578			−0.0582890	−	0.998300i	$-0.518564\pi$
$953$	−8.32275e19			−0.116578			−0.0582890	+	0.998300i	$0.518564\pi$
$954$	2.84830e20	−	8.34134e19i	0.396047	−	0.115984i
$955$			5.11487e20i			0.706010i
$956$	6.75162e20	+	1.05387e21i	0.925131	+	1.44405i
$957$	1.19161e20			0.162088
$958$	−1.68583e20	−	5.75658e20i	−0.227644	−	0.777331i
$959$			1.77922e19i			0.0238506i
$960$	−2.73926e20	+	3.81908e19i	−0.364531	+	0.0508230i
$961$	−5.63383e20			−0.744286
$962$	1.40656e20	−	4.11915e19i	0.184473	−	0.0540235i
$963$			2.38815e20i			0.310941i
$964$	−5.15317e20	+	3.30138e20i	−0.666094	+	0.426734i
$965$	−9.64160e20			−1.23725
$966$	8.89973e18	+	3.03897e19i	0.0113380	+	0.0387157i
$967$		−	3.35706e20i		−	0.424594i	−0.977205	−	0.212297i	$-0.931906\pi$
$967$		−	3.35706e20i		−	0.424594i	0.977205	−	0.212297i	$-0.0680945\pi$
$968$	−4.73658e20	+	5.44277e20i	−0.594754	+	0.683428i
$969$	−1.04595e21			−1.30390
$970$	−7.78861e20	+	2.28092e20i	−0.963957	+	0.282298i
$971$			8.76317e20i			1.07678i	0.842696	+	0.538389i	$0.180967\pi$
$971$			8.76317e20i			1.07678i	−0.842696	+	0.538389i	$0.819033\pi$
$972$	−2.83665e19	−	4.42776e19i	−0.0346052	−	0.0540158i
$973$	−1.08406e20			−0.131299
$974$	1.68814e20	+	5.76445e20i	0.203000	+	0.693179i
$975$			1.34052e20i			0.160045i
$976$	−4.60991e20	+	1.00187e21i	−0.546441	+	1.18758i
$977$	9.27757e20			1.09187			0.545937	−	0.837826i	$-0.316174\pi$
$977$	9.27757e20			1.09187			0.545937	+	0.837826i	$0.316174\pi$
$978$	4.80817e20	−	1.40809e20i	0.561833	−	0.164535i
$979$		−	9.24703e19i		−	0.107281i
$980$	4.60211e20	−	2.94835e20i	0.530121	−	0.339622i
$981$	−3.94316e20			−0.450984
$982$	−4.53007e19	−	1.54687e20i	−0.0514428	−	0.175661i
$983$			9.31863e20i			1.05070i	0.850887	+	0.525349i	$0.176065\pi$
$983$			9.31863e20i			1.05070i	−0.850887	+	0.525349i	$0.823935\pi$
$984$	1.18672e20	+	1.03274e20i	0.132856	+	0.115618i
$985$	−2.60458e20			−0.289524
$986$	−1.08321e21	+	3.17223e20i	−1.19557	+	0.350127i
$987$		−	9.29100e19i		−	0.101822i
$988$	−3.84254e20	−	5.99787e20i	−0.418138	−	0.652677i
$989$	−7.53850e20			−0.814537
$990$	1.70681e19	+	5.82821e19i	0.0183121	+	0.0625300i
$991$			3.05387e20i			0.325338i	0.986681	+	0.162669i	$0.0520102\pi$
$991$			3.05387e20i			0.325338i	−0.986681	+	0.162669i	$0.947990\pi$
$992$	1.23516e21	+	1.82079e20i	1.30659	+	0.192610i
$993$	−8.93629e20			−0.938669
$994$	1.04907e20	−	3.07225e19i	0.109421	−	0.0320443i
$995$			7.05762e20i			0.730966i
$996$	−2.62568e20	+	1.68214e20i	−0.270039	+	0.173000i
$997$	7.89264e20			0.806039			0.403020	−	0.915191i	$-0.367961\pi$
$997$	7.89264e20			0.806039			0.403020	+	0.915191i	$0.367961\pi$
$998$	−2.37323e20	−	8.10383e20i	−0.240672	−	0.821819i
$999$		−	7.86631e19i		−	0.0792160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.15.d.a.7.2	yes	14
3.2	odd	2		36.15.d.e.19.13		14
4.3	odd	2	inner	12.15.d.a.7.1	✓	14
12.11	even	2		36.15.d.e.19.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.15.d.a.7.1	✓	14	4.3	odd	2	inner
12.15.d.a.7.2	yes	14	1.1	even	1	trivial
36.15.d.e.19.13		14	3.2	odd	2
36.15.d.e.19.14		14	12.11	even	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:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-122.841 + 35.9743i) q^{2} -1262.67i q^{3} +(13795.7 - 8838.22i) q^{4} +49804.1 q^{5} +(45423.5 + 155107. i) q^{6} +91750.3i q^{7} +(-1.37672e6 + 1.58198e6i) q^{8} -1.59432e6 q^{9} +O(q^{10})\)	\(q+(-122.841 + 35.9743i) q^{2} -1262.67i q^{3} +(13795.7 - 8838.22i) q^{4} +49804.1 q^{5} +(45423.5 + 155107. i) q^{6} +91750.3i q^{7} +(-1.37672e6 + 1.58198e6i) q^{8} -1.59432e6 q^{9} +(-6.11797e6 + 1.79167e6i) q^{10} +5.97518e6i q^{11} +(-1.11597e7 - 1.74193e7i) q^{12} +2.93028e7 q^{13} +(-3.30065e6 - 1.12707e7i) q^{14} -6.28859e7i q^{15} +(1.12207e8 - 2.43859e8i) q^{16} +5.58312e8 q^{17} +(1.95848e8 - 5.73547e7i) q^{18} -1.48369e9i q^{19} +(6.87083e8 - 4.40180e8i) q^{20} +1.15850e8 q^{21} +(-2.14953e8 - 7.33996e8i) q^{22} -2.13545e9i q^{23} +(1.99752e9 + 1.73834e9i) q^{24} -3.62307e9 q^{25} +(-3.59957e9 + 1.05415e9i) q^{26} +2.01310e9i q^{27} +(8.10909e8 + 1.26576e9i) q^{28} +1.57941e10 q^{29} +(2.26228e9 + 7.72495e9i) q^{30} -3.63363e10i q^{31} +(-5.01095e9 + 3.39924e10i) q^{32} +7.54465e9 q^{33} +(-6.85835e10 + 2.00849e10i) q^{34} +4.56954e9i q^{35} +(-2.19948e10 + 1.40910e10i) q^{36} -3.90757e10 q^{37} +(5.33749e10 + 1.82258e11i) q^{38} -3.69996e10i q^{39} +(-6.85666e10 + 7.87893e10i) q^{40} +5.94097e10 q^{41} +(-1.42311e10 + 4.16762e9i) q^{42} -3.53018e11i q^{43} +(5.28100e10 + 8.24318e10i) q^{44} -7.94038e10 q^{45} +(7.68212e10 + 2.62320e11i) q^{46} -8.01986e11i q^{47} +(-3.07912e11 - 1.41680e11i) q^{48} +6.69805e11 q^{49} +(4.45060e11 - 1.30337e11i) q^{50} -7.04961e11i q^{51} +(4.04252e11 - 2.58984e11i) q^{52} +1.45434e12 q^{53} +(-7.24197e10 - 2.47290e11i) q^{54} +2.97589e11i q^{55} +(-1.45148e11 - 1.26315e11i) q^{56} -1.87341e12 q^{57} +(-1.94016e12 + 5.68182e11i) q^{58} +4.73537e12i q^{59} +(-5.55800e11 - 8.67555e11i) q^{60} -4.10839e12 q^{61} +(1.30717e12 + 4.46358e12i) q^{62} -1.46280e11i q^{63} +(-6.07304e11 - 4.35591e12i) q^{64} +1.45940e12 q^{65} +(-9.26791e11 + 2.71414e11i) q^{66} +4.11756e12i q^{67} +(7.70231e12 - 4.93449e12i) q^{68} -2.69635e12 q^{69} +(-1.64386e11 - 5.61326e11i) q^{70} +9.30799e12i q^{71} +(2.19494e12 - 2.52219e12i) q^{72} +1.43566e12 q^{73} +(4.80009e12 - 1.40572e12i) q^{74} +4.57472e12i q^{75} +(-1.31132e13 - 2.04686e13i) q^{76} -5.48225e11 q^{77} +(1.33103e12 + 4.54506e12i) q^{78} -5.55237e12i q^{79} +(5.58838e12 - 1.21452e13i) q^{80} +2.54187e12 q^{81} +(-7.29793e12 + 2.13722e12i) q^{82} -1.50733e13i q^{83} +(1.59823e12 - 1.02391e12i) q^{84} +2.78063e13 q^{85} +(1.26996e13 + 4.33649e13i) q^{86} -1.99427e13i q^{87} +(-9.45264e12 - 8.22618e12i) q^{88} -1.54757e13 q^{89} +(9.75403e12 - 2.85650e12i) q^{90} +2.68854e12i q^{91} +(-1.88736e13 - 2.94600e13i) q^{92} -4.58806e13 q^{93} +(2.88509e13 + 9.85166e13i) q^{94} -7.38941e13i q^{95} +(4.29210e13 + 6.32715e12i) q^{96} +1.27307e14 q^{97} +(-8.22793e13 + 2.40958e13i) q^{98} -9.52637e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9}+O(q^{10}) \) 14 * q + 182 * q^2 + 9308 * q^4 - 16124 * q^5 + 56862 * q^6 + 4352816 * q^8 - 22320522 * q^9	\( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9} + 586324 q^{10} + 621108 q^{12} + 109934140 q^{13} - 200755992 q^{14} + 380631536 q^{16} - 291483380 q^{17} - 290166786 q^{18} + 5316726088 q^{20} - 1117661976 q^{21} - 9373833288 q^{22} + 2880331488 q^{24} + 12506859258 q^{25} - 45510637748 q^{26} + 83579713776 q^{28} - 12126204812 q^{29} - 44941179132 q^{30} + 67974212192 q^{32} - 34345330344 q^{33} - 57269346212 q^{34} - 14839958484 q^{36} + 119365701580 q^{37} + 102957884712 q^{38} - 491601579872 q^{40} + 189318893932 q^{41} + 240539889384 q^{42} - 997611383472 q^{44} + 25706864052 q^{45} + 1368039641184 q^{46} - 465649986384 q^{48} - 769149171250 q^{49} + 2170057449522 q^{50} - 2399333559176 q^{52} + 1251391890964 q^{53} - 90656394426 q^{54} + 2319191796096 q^{56} + 1805052294792 q^{57} - 5157502168892 q^{58} + 2354207329944 q^{60} - 7882441676660 q^{61} - 9161379391272 q^{62} + 17520900128384 q^{64} + 5858206778312 q^{65} - 6614704234440 q^{66} + 18747786717976 q^{68} - 13777261381728 q^{69} - 8213486211792 q^{70} - 6939794663568 q^{72} + 39185062250428 q^{73} - 7698562888484 q^{74} - 9224963770896 q^{76} - 41289727781472 q^{77} + 10470873014172 q^{78} - 57127847610848 q^{80} + 35586121596606 q^{81} + 107070799921084 q^{82} - 28102976768880 q^{84} - 188880254078680 q^{85} + 102443851819896 q^{86} - 83262676567680 q^{88} + 223721333984572 q^{89} - 934789838652 q^{90} - 79895035003584 q^{92} + 12688158423960 q^{93} - 52692266305296 q^{94} - 2264434006752 q^{96} + 282902280361756 q^{97} - 228639957171082 q^{98}+O(q^{100}) \) 14 * q + 182 * q^2 + 9308 * q^4 - 16124 * q^5 + 56862 * q^6 + 4352816 * q^8 - 22320522 * q^9 + 586324 * q^10 + 621108 * q^12 + 109934140 * q^13 - 200755992 * q^14 + 380631536 * q^16 - 291483380 * q^17 - 290166786 * q^18 + 5316726088 * q^20 - 1117661976 * q^21 - 9373833288 * q^22 + 2880331488 * q^24 + 12506859258 * q^25 - 45510637748 * q^26 + 83579713776 * q^28 - 12126204812 * q^29 - 44941179132 * q^30 + 67974212192 * q^32 - 34345330344 * q^33 - 57269346212 * q^34 - 14839958484 * q^36 + 119365701580 * q^37 + 102957884712 * q^38 - 491601579872 * q^40 + 189318893932 * q^41 + 240539889384 * q^42 - 997611383472 * q^44 + 25706864052 * q^45 + 1368039641184 * q^46 - 465649986384 * q^48 - 769149171250 * q^49 + 2170057449522 * q^50 - 2399333559176 * q^52 + 1251391890964 * q^53 - 90656394426 * q^54 + 2319191796096 * q^56 + 1805052294792 * q^57 - 5157502168892 * q^58 + 2354207329944 * q^60 - 7882441676660 * q^61 - 9161379391272 * q^62 + 17520900128384 * q^64 + 5858206778312 * q^65 - 6614704234440 * q^66 + 18747786717976 * q^68 - 13777261381728 * q^69 - 8213486211792 * q^70 - 6939794663568 * q^72 + 39185062250428 * q^73 - 7698562888484 * q^74 - 9224963770896 * q^76 - 41289727781472 * q^77 + 10470873014172 * q^78 - 57127847610848 * q^80 + 35586121596606 * q^81 + 107070799921084 * q^82 - 28102976768880 * q^84 - 188880254078680 * q^85 + 102443851819896 * q^86 - 83262676567680 * q^88 + 223721333984572 * q^89 - 934789838652 * q^90 - 79895035003584 * q^92 + 12688158423960 * q^93 - 52692266305296 * q^94 - 2264434006752 * q^96 + 282902280361756 * q^97 - 228639957171082 * q^98

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