LMFDB - Embedded newform 5.27.c.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,27,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 27, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 27);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 27 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.4146460365$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	5.3
Dual form			5.27.c.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8964.00 + 8964.00i) q^{2} +(-84346.8 - 84346.8i) q^{3} -9.35978e7i q^{4} +(-6.90551e8 + 1.00661e9i) q^{5} +1.51217e9 q^{6} +(-8.97185e10 + 8.97185e10i) q^{7} +(2.37446e11 + 2.37446e11i) q^{8} -2.52764e12i q^{9} +O(q^{10})$	\(q+(-8964.00 + 8964.00i) q^{2} +(-84346.8 - 84346.8i) q^{3} -9.35978e7i q^{4} +(-6.90551e8 + 1.00661e9i) q^{5} +1.51217e9 q^{6} +(-8.97185e10 + 8.97185e10i) q^{7} +(2.37446e11 + 2.37446e11i) q^{8} -2.52764e12i q^{9} +(-2.83311e12 - 1.52133e13i) q^{10} -9.83010e12 q^{11} +(-7.89467e12 + 7.89467e12i) q^{12} +(-2.69524e14 - 2.69524e14i) q^{13} -1.60847e15i q^{14} +(1.43150e14 - 2.66582e13i) q^{15} +2.02430e15 q^{16} +(-8.05943e15 + 8.05943e15i) q^{17} +(2.26577e16 + 2.26577e16i) q^{18} +1.22289e15i q^{19} +(9.42160e16 + 6.46340e16i) q^{20} +1.51349e16 q^{21} +(8.81170e16 - 8.81170e16i) q^{22} +(2.54183e17 + 2.54183e17i) q^{23} -4.00557e16i q^{24} +(-5.36394e17 - 1.39023e18i) q^{25} +4.83203e18 q^{26} +(-4.27596e17 + 4.27596e17i) q^{27} +(8.39745e18 + 8.39745e18i) q^{28} +9.37717e18i q^{29} +(-1.04423e18 + 1.52216e18i) q^{30} +3.37841e19 q^{31} +(-3.40806e19 + 3.40806e19i) q^{32} +(8.29138e17 + 8.29138e17i) q^{33} -1.44489e20i q^{34} +(-2.83559e19 - 1.52266e20i) q^{35} -2.36581e20 q^{36} +(-1.40139e20 + 1.40139e20i) q^{37} +(-1.09619e19 - 1.09619e19i) q^{38} +4.54670e19i q^{39} +(-4.02984e20 + 7.50460e19i) q^{40} +5.50191e20 q^{41} +(-1.35670e20 + 1.35670e20i) q^{42} +(-2.83578e20 - 2.83578e20i) q^{43} +9.20075e20i q^{44} +(2.54433e21 + 1.74546e21i) q^{45} -4.55700e21 q^{46} +(6.66549e21 - 6.66549e21i) q^{47} +(-1.70743e20 - 1.70743e20i) q^{48} -6.71135e21i q^{49} +(1.72702e22 + 7.65375e21i) q^{50} +1.35957e21 q^{51} +(-2.52269e22 + 2.52269e22i) q^{52} +(3.12389e22 + 3.12389e22i) q^{53} -7.66595e21i q^{54} +(6.78819e21 - 9.89503e21i) q^{55} -4.26067e22 q^{56} +(1.03147e20 - 1.03147e20i) q^{57} +(-8.40570e22 - 8.40570e22i) q^{58} -2.03375e23i q^{59} +(-2.49515e21 - 1.33985e22i) q^{60} -1.20939e23 q^{61} +(-3.02841e23 + 3.02841e23i) q^{62} +(2.26776e23 + 2.26776e23i) q^{63} -4.75148e23i q^{64} +(4.57425e23 - 8.51843e22i) q^{65} -1.48648e22 q^{66} +(-3.15073e23 + 3.15073e23i) q^{67} +(7.54345e23 + 7.54345e23i) q^{68} -4.28791e22i q^{69} +(1.61910e24 + 1.11073e24i) q^{70} -1.27673e24 q^{71} +(6.00178e23 - 6.00178e23i) q^{72} +(-9.38292e23 - 9.38292e23i) q^{73} -2.51242e24i q^{74} +(-7.20180e22 + 1.62504e23i) q^{75} +1.14459e23 q^{76} +(8.81942e23 - 8.81942e23i) q^{77} +(-4.07566e23 - 4.07566e23i) q^{78} +2.70121e24i q^{79} +(-1.39788e24 + 2.03767e24i) q^{80} -6.35278e24 q^{81} +(-4.93192e24 + 4.93192e24i) q^{82} +(3.59611e24 + 3.59611e24i) q^{83} -1.41660e24i q^{84} +(-2.54722e24 - 1.36781e25i) q^{85} +5.08398e24 q^{86} +(7.90935e23 - 7.90935e23i) q^{87} +(-2.33412e24 - 2.33412e24i) q^{88} -1.92808e25i q^{89} +(-3.84537e25 + 7.16108e24i) q^{90} +4.83626e25 q^{91} +(2.37910e25 - 2.37910e25i) q^{92} +(-2.84958e24 - 2.84958e24i) q^{93} +1.19499e26i q^{94} +(-1.23096e24 - 8.44465e23i) q^{95} +5.74918e24 q^{96} +(7.59970e25 - 7.59970e25i) q^{97} +(6.01606e25 + 6.01606e25i) q^{98} +2.48469e25i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8}+O(q^{10}) $ 24 * q + 8190 * q^2 + 1867680 * q^3 - 140947920 * q^5 - 3382472712 * q^6 - 99234643200 * q^7 - 2004366809340 * q^8	$ 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8} - 1486502924970 q^{10} - 60046450487712 q^{11} + 474303804173880 q^{12} - 175933888149240 q^{13} + 81\!\cdots\!60 q^{15}+ \cdots + 37\!\cdots\!90 q^{98}+O(q^{100}) $ 24 * q + 8190 * q^2 + 1867680 * q^3 - 140947920 * q^5 - 3382472712 * q^6 - 99234643200 * q^7 - 2004366809340 * q^8 - 1486502924970 * q^10 - 60046450487712 * q^11 + 474303804173880 * q^12 - 175933888149240 * q^13 + 8120813383152960 * q^15 - 33177982875701256 * q^16 + 13120603958605320 * q^17 + 30866287060816530 * q^18 - 155387715501860460 * q^20 + 711072085237596768 * q^21 - 1230085358274609120 * q^22 - 95943648493582560 * q^23 - 2199572636699820600 * q^25 + 5610652365807815508 * q^26 - 4182554138103802080 * q^27 + 9022697066815419960 * q^28 - 73497992102613921840 * q^30 + 136536207174201936768 * q^31 - 313156508993493901560 * q^32 + 310679334418782310560 * q^33 - 294265004156402368320 * q^35 + 1280456324930471178684 * q^36 - 813771390050070972840 * q^37 - 241574669977239410760 * q^38 - 634199087129857022100 * q^40 - 1209719584341877336992 * q^41 + 3329982079791874237920 * q^42 - 2155184970418473088800 * q^43 + 8900452148996849486760 * q^45 - 9558960779134484923272 * q^46 + 14032272766974133560480 * q^47 - 23339469323152065294960 * q^48 - 5039825198339566324350 * q^50 - 34517174933375733238272 * q^51 + 89834235163276703786700 * q^52 - 76996005973852456719720 * q^53 + 61786508697335020764960 * q^55 + 140965426896397798196880 * q^56 - 373196499625490096640960 * q^57 + 527990314981987315382160 * q^58 - 985009875968846023801320 * q^60 + 711008904295257078187488 * q^61 - 106522048356410497848120 * q^62 + 129194443701484657698720 * q^63 + 810043281159028896596760 * q^65 - 243183023298774209168544 * q^66 + 475247161241828436325920 * q^67 - 1328735440043135338553820 * q^68 - 1284031520218999793566920 * q^70 - 5316544531031301273526272 * q^71 + 6424730229084419392336260 * q^72 + 368145928043753098041240 * q^73 - 1071958391540662870531200 * q^75 - 193843537989214188398640 * q^76 + 10746086757941471790823200 * q^77 - 2877347849192885454991800 * q^78 - 155629044348497668149120 * q^80 - 13389238123125713812551096 * q^81 - 11578218915296284645122720 * q^82 + 25615096518304734510222720 * q^83 - 60208098774533809021022520 * q^85 + 56773655020233836832486168 * q^86 - 25953487917103015108688640 * q^87 + 117068604801345686184349920 * q^88 - 128643549677224721883790890 * q^90 - 19525332839000266679349312 * q^91 + 18999183544674712785412920 * q^92 + 207592489093568143530468960 * q^93 - 172205668812635374982450400 * q^95 - 605527074895544071145393952 * q^96 + 347025186458821372557867480 * q^97 + 372096096878694378037335390 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−8964.00	+	8964.00i	−1.09424	+	1.09424i	−0.0991676	+	0.995071i	$0.531618\pi$
$2$	−8964.00	+	8964.00i	−1.09424	+	1.09424i	−0.995071	+	0.0991676i	$0.968382\pi$
$3$	−84346.8	−	84346.8i	−0.0529045	−	0.0529045i	0.680160	−	0.733064i	$-0.261910\pi$
$3$	−84346.8	−	84346.8i	−0.0529045	−	0.0529045i	−0.733064	+	0.680160i	$0.761910\pi$
$4$		−	9.35978e7i		−	1.39472i
$5$	−6.90551e8	+	1.00661e9i	−0.565700	+	0.824611i
$5$	−6.90551e8	+	1.00661e9i	−0.565700	+	0.824611i
$6$	1.51217e9			0.115780
$7$	−8.97185e10	+	8.97185e10i	−0.925993	+	0.925993i	−0.997444	−	0.0714511i	$-0.977237\pi$
$7$	−8.97185e10	+	8.97185e10i	−0.925993	+	0.925993i	0.0714511	+	0.997444i	$0.477237\pi$
$8$	2.37446e11	+	2.37446e11i	0.431912	+	0.431912i
$9$		−	2.52764e12i		−	0.994402i
$10$	−2.83311e12	−	1.52133e13i	−0.283311	−	1.52133i
$11$	−9.83010e12			−0.284743			−0.142371	−	0.989813i	$-0.545473\pi$
$11$	−9.83010e12			−0.284743			−0.142371	+	0.989813i	$0.545473\pi$
$12$	−7.89467e12	+	7.89467e12i	−0.0737867	+	0.0737867i
$13$	−2.69524e14	−	2.69524e14i	−0.889886	−	0.889886i	0.104626	−	0.994512i	$-0.466635\pi$
$13$	−2.69524e14	−	2.69524e14i	−0.889886	−	0.889886i	−0.994512	+	0.104626i	$0.966635\pi$
$14$		−	1.60847e15i		−	2.02651i
$15$	1.43150e14	−	2.66582e13i	0.0735537	−	0.0136976i
$16$	2.02430e15			0.449485
$17$	−8.05943e15	+	8.05943e15i	−0.813708	+	0.813708i	−0.985188	−	0.171480i	$-0.945145\pi$
$17$	−8.05943e15	+	8.05943e15i	−0.813708	+	0.813708i	0.171480	+	0.985188i	$0.445145\pi$
$18$	2.26577e16	+	2.26577e16i	1.08811	+	1.08811i
$19$			1.22289e15i			0.0290796i	0.999894	+	0.0145398i	$0.00462833\pi$
$19$			1.22289e15i			0.0290796i	−0.999894	+	0.0145398i	$0.995372\pi$
$20$	9.42160e16	+	6.46340e16i	1.15010	+	0.788990i
$21$	1.51349e16			0.0979783
$22$	8.81170e16	−	8.81170e16i	0.311577	−	0.311577i
$23$	2.54183e17	+	2.54183e17i	0.504296	+	0.504296i	0.912770	−	0.408474i	$-0.133939\pi$
$23$	2.54183e17	+	2.54183e17i	0.504296	+	0.504296i	−0.408474	+	0.912770i	$0.633939\pi$
$24$		−	4.00557e16i		−	0.0457002i
$25$	−5.36394e17	−	1.39023e18i	−0.359968	−	0.932965i
$26$	4.83203e18			1.94749
$27$	−4.27596e17	+	4.27596e17i	−0.105513	+	0.105513i
$28$	8.39745e18	+	8.39745e18i	1.29150	+	1.29150i
$29$			9.37717e18i			0.913898i	0.889493	+	0.456949i	$0.151058\pi$
$29$			9.37717e18i			0.913898i	−0.889493	+	0.456949i	$0.848942\pi$
$30$	−1.04423e18	+	1.52216e18i	−0.0654968	+	0.0954737i
$31$	3.37841e19			1.38360			0.691800	−	0.722090i	$-0.256818\pi$
$31$	3.37841e19			1.38360			0.691800	+	0.722090i	$0.256818\pi$
$32$	−3.40806e19	+	3.40806e19i	−0.923756	+	0.923756i
$33$	8.29138e17	+	8.29138e17i	0.0150642	+	0.0150642i
$34$		−	1.44489e20i		−	1.78078i
$35$	−2.83559e19	−	1.52266e20i	−0.239750	−	1.28742i
$36$	−2.36581e20			−1.38691
$37$	−1.40139e20	+	1.40139e20i	−0.575358	+	0.575358i	−0.933621	−	0.358263i	$-0.883369\pi$
$37$	−1.40139e20	+	1.40139e20i	−0.575358	+	0.575358i	0.358263	+	0.933621i	$0.383369\pi$
$38$	−1.09619e19	−	1.09619e19i	−0.0318201	−	0.0318201i
$39$			4.54670e19i			0.0941579i
$40$	−4.02984e20	+	7.50460e19i	−0.600493	+	0.111827i
$41$	5.50191e20			0.594735			0.297368	−	0.954763i	$-0.403891\pi$
$41$	5.50191e20			0.594735			0.297368	+	0.954763i	$0.403891\pi$
$42$	−1.35670e20	+	1.35670e20i	−0.107212	+	0.107212i
$43$	−2.83578e20	−	2.83578e20i	−0.165037	−	0.165037i	0.619757	−	0.784794i	$-0.287231\pi$
$43$	−2.83578e20	−	2.83578e20i	−0.165037	−	0.165037i	−0.784794	+	0.619757i	$0.787231\pi$
$44$			9.20075e20i			0.397135i
$45$	2.54433e21	+	1.74546e21i	0.819995	+	0.562533i
$46$	−4.55700e21			−1.10364
$47$	6.66549e21	−	6.66549e21i	1.22056	−	1.22056i	0.253129	−	0.967432i	$-0.418540\pi$
$47$	6.66549e21	−	6.66549e21i	1.22056	−	1.22056i	0.967432	−	0.253129i	$-0.0814598\pi$
$48$	−1.70743e20	−	1.70743e20i	−0.0237798	−	0.0237798i
$49$		−	6.71135e21i		−	0.714926i
$50$	1.72702e22	+	7.65375e21i	1.41478	+	0.626995i
$51$	1.35957e21			0.0860975
$52$	−2.52269e22	+	2.52269e22i	−1.24114	+	1.24114i
$53$	3.12389e22	+	3.12389e22i	1.19980	+	1.19980i	0.974226	+	0.225576i	$0.0724265\pi$
$53$	3.12389e22	+	3.12389e22i	1.19980	+	1.19980i	0.225576	+	0.974226i	$0.427574\pi$
$54$		−	7.66595e21i		−	0.230912i
$55$	6.78819e21	−	9.89503e21i	0.161079	−	0.234802i
$56$	−4.26067e22			−0.799896
$57$	1.03147e20	−	1.03147e20i	0.00153844	−	0.00153844i
$58$	−8.40570e22	−	8.40570e22i	−1.00002	−	1.00002i
$59$		−	2.03375e23i		−	1.93741i	−0.248214	−	0.968705i	$-0.579844\pi$
$59$		−	2.03375e23i		−	1.93741i	0.248214	−	0.968705i	$-0.420156\pi$
$60$	−2.49515e21	−	1.33985e22i	−0.0191042	−	0.102586i
$61$	−1.20939e23			−0.746927			−0.373464	−	0.927645i	$-0.621830\pi$
$61$	−1.20939e23			−0.746927			−0.373464	+	0.927645i	$0.621830\pi$
$62$	−3.02841e23	+	3.02841e23i	−1.51399	+	1.51399i
$63$	2.26776e23	+	2.26776e23i	0.920810	+	0.920810i
$64$		−	4.75148e23i		−	1.57213i
$65$	4.57425e23	−	8.51843e22i	1.23722	−	0.230402i
$66$	−1.48648e22			−0.0329676
$67$	−3.15073e23	+	3.15073e23i	−0.574698	+	0.574698i	−0.933438	−	0.358740i	$-0.883206\pi$
$67$	−3.15073e23	+	3.15073e23i	−0.574698	+	0.574698i	0.358740	+	0.933438i	$0.383206\pi$
$68$	7.54345e23	+	7.54345e23i	1.13489	+	1.13489i
$69$		−	4.28791e22i		−	0.0533590i
$70$	1.61910e24	+	1.11073e24i	1.67109	+	1.14640i
$71$	−1.27673e24			−1.09583			−0.547914	−	0.836535i	$-0.684578\pi$
$71$	−1.27673e24			−1.09583			−0.547914	+	0.836535i	$0.684578\pi$
$72$	6.00178e23	−	6.00178e23i	0.429495	−	0.429495i
$73$	−9.38292e23	−	9.38292e23i	−0.561230	−	0.561230i	0.368427	−	0.929657i	$-0.379897\pi$
$73$	−9.38292e23	−	9.38292e23i	−0.561230	−	0.561230i	−0.929657	+	0.368427i	$0.879897\pi$
$74$		−	2.51242e24i		−	1.25916i
$75$	−7.20180e22	+	1.62504e23i	−0.0303141	+	0.0684019i
$76$	1.14459e23			0.0405578
$77$	8.81942e23	−	8.81942e23i	0.263670	−	0.263670i
$78$	−4.07566e23	−	4.07566e23i	−0.103031	−	0.103031i
$79$			2.70121e24i			0.578637i	0.957233	+	0.289319i	$0.0934287\pi$
$79$			2.70121e24i			0.578637i	−0.957233	+	0.289319i	$0.906571\pi$
$80$	−1.39788e24	+	2.03767e24i	−0.254273	+	0.370650i
$81$	−6.35278e24			−0.983238
$82$	−4.93192e24	+	4.93192e24i	−0.650782	+	0.650782i
$83$	3.59611e24	+	3.59611e24i	0.405338	+	0.405338i	0.880109	−	0.474771i	$-0.157469\pi$
$83$	3.59611e24	+	3.59611e24i	0.405338	+	0.405338i	−0.474771	+	0.880109i	$0.657469\pi$
$84$		−	1.41660e24i		−	0.136652i
$85$	−2.54722e24	−	1.36781e25i	−0.210678	−	1.13131i
$86$	5.08398e24			0.361180
$87$	7.90935e23	−	7.90935e23i	0.0483493	−	0.0483493i
$88$	−2.33412e24	−	2.33412e24i	−0.122984	−	0.122984i
$89$		−	1.92808e25i		−	0.877114i	−0.898703	−	0.438557i	$-0.855490\pi$
$89$		−	1.92808e25i		−	0.877114i	0.898703	−	0.438557i	$-0.144510\pi$
$90$	−3.84537e25	+	7.16108e24i	−1.51282	+	0.281725i
$91$	4.83626e25			1.64806
$92$	2.37910e25	−	2.37910e25i	0.703349	−	0.703349i
$93$	−2.84958e24	−	2.84958e24i	−0.0731986	−	0.0731986i
$94$			1.19499e26i			2.67117i
$95$	−1.23096e24	−	8.44465e23i	−0.0239794	−	0.0164503i
$96$	5.74918e24			0.0977416
$97$	7.59970e25	−	7.59970e25i	1.12918	−	1.12918i	0.138872	−	0.990310i	$-0.455652\pi$
$97$	7.59970e25	−	7.59970e25i	1.12918	−	1.12918i	0.990310	−	0.138872i	$-0.0443476\pi$
$98$	6.01606e25	+	6.01606e25i	0.782300	+	0.782300i
$99$			2.48469e25i			0.283149i
$100$	−1.30122e26	+	5.02053e25i	−1.30122	+	0.502053i
$101$	7.94753e25			0.698319			0.349160	−	0.937063i	$-0.386467\pi$
$101$	7.94753e25			0.698319			0.349160	+	0.937063i	$0.386467\pi$
$102$	−1.21872e25	+	1.21872e25i	−0.0942112	+	0.0942112i
$103$	−1.31492e26	−	1.31492e26i	−0.895396	−	0.895396i	0.0996284	−	0.995025i	$-0.468235\pi$
$103$	−1.31492e26	−	1.31492e26i	−0.895396	−	0.895396i	−0.995025	+	0.0996284i	$0.968235\pi$
$104$		−	1.27995e26i		−	0.768706i
$105$	−1.04515e25	+	1.52349e25i	−0.0554263	+	0.0807941i
$106$	−5.60051e26			−2.62574
$107$	2.17748e26	−	2.17748e26i	0.903577	−	0.903577i	−0.0921667	−	0.995744i	$-0.529379\pi$
$107$	2.17748e26	−	2.17748e26i	0.903577	−	0.903577i	0.995744	+	0.0921667i	$0.0293793\pi$
$108$	4.00221e25	+	4.00221e25i	0.147160	+	0.147160i
$109$		−	3.29008e26i		−	1.07315i	−0.843852	−	0.536577i	$-0.819717\pi$
$109$		−	3.29008e26i		−	1.07315i	0.843852	−	0.536577i	$-0.180283\pi$
$110$	2.78498e25	+	1.49548e26i	0.0806709	+	0.433188i
$111$	2.36406e25			0.0608780
$112$	−1.81617e26	+	1.81617e26i	−0.416220	+	0.416220i
$113$	3.52291e26	+	3.52291e26i	0.719253	+	0.719253i	0.968452	−	0.249199i	$-0.0801675\pi$
$113$	3.52291e26	+	3.52291e26i	0.719253	+	0.719253i	−0.249199	+	0.968452i	$0.580167\pi$
$114$			1.84921e24i			0.00336685i
$115$	−4.31389e26	+	8.03358e25i	−0.701128	+	0.130568i
$116$	8.77682e26			1.27463
$117$	−6.81259e26	+	6.81259e26i	−0.884904	+	0.884904i
$118$	1.82305e27	+	1.82305e27i	2.11999	+	2.11999i
$119$		−	1.44616e27i		−	1.50698i
$120$	4.03203e25	+	2.76605e25i	0.0376849	+	0.0258526i
$121$	−1.09519e27			−0.918921
$122$	1.08410e27	−	1.08410e27i	0.817316	−	0.817316i
$123$	−4.64069e25	−	4.64069e25i	−0.0314642	−	0.0314642i
$124$		−	3.16212e27i		−	1.92973i
$125$	1.76982e27	+	4.20085e26i	0.972967	+	0.230944i
$126$	−4.06564e27			−2.01517
$127$	6.25503e25	−	6.25503e25i	0.0279757	−	0.0279757i	−0.692981	−	0.720956i	$-0.743703\pi$
$127$	6.25503e25	−	6.25503e25i	0.0279757	−	0.0279757i	0.720956	+	0.692981i	$0.243703\pi$
$128$	1.97212e27	+	1.97212e27i	0.796533	+	0.796533i
$129$			4.78377e25i			0.0174624i
$130$	−3.33677e27	+	4.86395e27i	−1.10170	+	1.60593i
$131$	3.29287e26			0.0984119			0.0492059	−	0.998789i	$-0.484331\pi$
$131$	3.29287e26			0.0984119			0.0492059	+	0.998789i	$0.484331\pi$
$132$	7.76054e25	−	7.76054e25i	0.0210102	−	0.0210102i
$133$	−1.09716e26	−	1.09716e26i	−0.0269275	−	0.0269275i
$134$		−	5.64864e27i		−	1.25771i
$135$	−1.35144e26	−	7.25698e26i	−0.0273185	−	0.146696i
$136$	−3.82737e27			−0.702901
$137$	4.19917e27	−	4.19917e27i	0.701126	−	0.701126i	−0.263526	−	0.964652i	$-0.584886\pi$
$137$	4.19917e27	−	4.19917e27i	0.701126	−	0.701126i	0.964652	+	0.263526i	$0.0848856\pi$
$138$	3.84368e26	+	3.84368e26i	0.0583875	+	0.0583875i
$139$			9.48817e27i			1.31217i	0.754687	+	0.656085i	$0.227789\pi$
$139$			9.48817e27i			1.31217i	−0.754687	+	0.656085i	$0.772211\pi$
$140$	−1.42518e28	+	2.65405e27i	−1.79558	+	0.334384i
$141$	−1.12443e27			−0.129146
$142$	1.14447e28	−	1.14447e28i	1.19910	−	1.19910i
$143$	2.64945e27	+	2.64945e27i	0.253389	+	0.253389i
$144$		−	5.11669e27i		−	0.446969i
$145$	−9.43912e27	−	6.47542e27i	−0.753611	−	0.516992i
$146$	1.68217e28			1.22824
$147$	−5.66081e26	+	5.66081e26i	−0.0378228	+	0.0378228i
$148$	1.31167e28	+	1.31167e28i	0.802460	+	0.802460i
$149$			2.65633e27i			0.148888i	0.997225	+	0.0744441i	$0.0237182\pi$
$149$			2.65633e27i			0.148888i	−0.997225	+	0.0744441i	$0.976282\pi$
$150$	−8.11119e26	−	2.10226e27i	−0.0416772	−	0.108019i
$151$	1.36487e28			0.643269			0.321634	−	0.946864i	$-0.395768\pi$
$151$	1.36487e28			0.643269			0.321634	+	0.946864i	$0.395768\pi$
$152$	−2.90370e26	+	2.90370e26i	−0.0125599	+	0.0125599i
$153$	2.03713e28	+	2.03713e28i	0.809153	+	0.809153i
$154$			1.58115e28i			0.577036i
$155$	−2.33297e28	+	3.40073e28i	−0.782702	+	1.14093i
$156$	4.25561e27			0.131323
$157$	−8.68963e27	+	8.68963e27i	−0.246778	+	0.246778i	−0.819647	−	0.572869i	$-0.805830\pi$
$157$	−8.68963e27	+	8.68963e27i	−0.246778	+	0.246778i	0.572869	+	0.819647i	$0.305830\pi$
$158$	−2.42137e28	−	2.42137e28i	−0.633167	−	0.633167i
$159$		−	5.26980e27i		−	0.126950i
$160$	−1.07713e28	−	5.78401e28i	−0.239171	−	1.28431i
$161$	−4.56099e28			−0.933949
$162$	5.69463e28	−	5.69463e28i	1.07590	−	1.07590i
$163$	−4.92408e28	−	4.92408e28i	−0.858788	−	0.858788i	0.132407	−	0.991195i	$-0.457729\pi$
$163$	−4.92408e28	−	4.92408e28i	−0.858788	−	0.858788i	−0.991195	+	0.132407i	$0.957729\pi$
$164$		−	5.14967e28i		−	0.829486i
$165$	−1.40718e27	+	2.62053e26i	−0.0209439	+	0.00390029i
$166$	−6.44710e28			−0.887073
$167$	−6.09628e28	+	6.09628e28i	−0.775802	+	0.775802i	−0.979114	−	0.203312i	$-0.934830\pi$
$167$	−6.09628e28	+	6.09628e28i	−0.775802	+	0.775802i	0.203312	+	0.979114i	$0.434830\pi$
$168$	3.59374e27	+	3.59374e27i	0.0423181	+	0.0423181i
$169$			5.35533e28i			0.583793i
$170$	1.45444e29	+	9.97774e28i	1.46845	+	1.00739i
$171$	3.09101e27			0.0289169
$172$	−2.65422e28	+	2.65422e28i	−0.230180	+	0.230180i
$173$	−2.12399e28	−	2.12399e28i	−0.170826	−	0.170826i	0.616516	−	0.787342i	$-0.288543\pi$
$173$	−2.12399e28	−	2.12399e28i	−0.170826	−	0.170826i	−0.787342	+	0.616516i	$0.788543\pi$
$174$			1.41799e28i			0.105811i
$175$	1.72854e29	+	7.66046e28i	1.19725	+	0.530591i
$176$	−1.98991e28			−0.127988
$177$	−1.71540e28	+	1.71540e28i	−0.102498	+	0.102498i
$178$	1.72833e29	+	1.72833e29i	0.959772	+	0.959772i
$179$		−	2.77609e29i		−	1.43332i	−0.697421	−	0.716662i	$-0.745669\pi$
$179$		−	2.77609e29i		−	1.43332i	0.697421	−	0.716662i	$-0.254331\pi$
$180$	1.63371e29	−	2.38144e29i	0.784573	−	1.14366i
$181$	2.40334e29			1.07397			0.536986	−	0.843591i	$-0.319563\pi$
$181$	2.40334e29			1.07397			0.536986	+	0.843591i	$0.319563\pi$
$182$	−4.33523e29	+	4.33523e29i	−1.80337	+	1.80337i
$183$	1.02008e28	+	1.02008e28i	0.0395158	+	0.0395158i
$184$			1.20710e29i			0.435623i
$185$	−4.42917e28	−	2.37839e29i	−0.148967	−	0.799926i
$186$	5.10873e28			0.160193
$187$	7.92250e28	−	7.92250e28i	0.231697	−	0.231697i
$188$	−6.23875e29	−	6.23875e29i	−1.70234	−	1.70234i
$189$		−	7.67267e28i		−	0.195408i
$190$	1.86041e28	−	3.46457e27i	0.0442398	−	0.00823859i
$191$	3.18701e29			0.707865			0.353932	−	0.935271i	$-0.384844\pi$
$191$	3.18701e29			0.707865			0.353932	+	0.935271i	$0.384844\pi$
$192$	−4.00772e28	+	4.00772e28i	−0.0831729	+	0.0831729i
$193$	−4.50231e28	−	4.50231e28i	−0.0873355	−	0.0873355i	0.662089	−	0.749425i	$-0.269670\pi$
$193$	−4.50231e28	−	4.50231e28i	−0.0873355	−	0.0873355i	−0.749425	+	0.662089i	$0.769670\pi$
$194$			1.36247e30i			2.47119i
$195$	−4.57674e28	−	3.13973e28i	−0.0776437	−	0.0532651i
$196$	−6.28168e29			−0.997118
$197$	4.50941e29	−	4.50941e29i	0.669976	−	0.669976i	−0.287734	−	0.957710i	$-0.592902\pi$
$197$	4.50941e29	−	4.50941e29i	0.669976	−	0.669976i	0.957710	+	0.287734i	$0.0929020\pi$
$198$	−2.22728e29	−	2.22728e29i	−0.309832	−	0.309832i
$199$			3.91154e29i			0.509633i	0.966989	+	0.254816i	$0.0820150\pi$
$199$			3.91154e29i			0.509633i	−0.966989	+	0.254816i	$0.917985\pi$
$200$	2.02739e29	−	4.57469e29i	0.247484	−	0.558434i
$201$	5.31509e28			0.0608081
$202$	−7.12416e29	+	7.12416e29i	−0.764128	+	0.764128i
$203$	−8.41306e29	−	8.41306e29i	−0.846264	−	0.846264i
$204$		−	1.27253e29i		−	0.120082i
$205$	−3.79935e29	+	5.53826e29i	−0.336441	+	0.490425i
$206$	2.35739e30			1.95955
$207$	6.42483e29	−	6.42483e29i	0.501473	−	0.501473i
$208$	−5.45598e29	−	5.45598e29i	−0.399990	−	0.399990i
$209$		−	1.20211e28i		−	0.00828022i
$210$	−4.28790e28	−	2.30253e29i	−0.0277584	−	0.149058i
$211$	−9.64793e29			−0.587168			−0.293584	−	0.955933i	$-0.594848\pi$
$211$	−9.64793e29			−0.587168			−0.293584	+	0.955933i	$0.594848\pi$
$212$	2.92389e30	−	2.92389e30i	1.67338	−	1.67338i
$213$	1.07689e29	+	1.07689e29i	0.0579742	+	0.0579742i
$214$			3.90379e30i			1.97746i
$215$	4.81276e29	−	8.96260e28i	0.229453	−	0.0427301i
$216$	−2.03062e29			−0.0911446
$217$	−3.03106e30	+	3.03106e30i	−1.28120	+	1.28120i
$218$	2.94923e30	+	2.94923e30i	1.17429	+	1.17429i
$219$			1.58284e29i			0.0593832i
$220$	−9.26153e29	−	6.35359e29i	−0.327482	−	0.224659i
$221$	4.34442e30			1.44821
$222$	−2.11915e29	+	2.11915e29i	−0.0666150	+	0.0666150i
$223$	1.53799e29	+	1.53799e29i	0.0456026	+	0.0456026i	0.729540	−	0.683938i	$-0.239734\pi$
$223$	1.53799e29	+	1.53799e29i	0.0456026	+	0.0456026i	−0.683938	+	0.729540i	$0.739734\pi$
$224$		−	6.11532e30i		−	1.71078i
$225$	−3.51399e30	+	1.35581e30i	−0.927742	+	0.357953i
$226$	−6.31587e30			−1.57407
$227$	−1.71810e30	+	1.71810e30i	−0.404309	+	0.404309i	−0.879748	−	0.475440i	$-0.842289\pi$
$227$	−1.71810e30	+	1.71810e30i	−0.404309	+	0.404309i	0.475440	+	0.879748i	$0.342289\pi$
$228$	−9.65428e27	−	9.65428e27i	−0.00214569	−	0.00214569i
$229$		−	6.62235e30i		−	1.39043i	−0.718800	−	0.695217i	$-0.755308\pi$
$229$		−	6.62235e30i		−	1.39043i	0.718800	−	0.695217i	$-0.244692\pi$
$230$	3.14684e30	−	4.58710e30i	0.624328	−	0.910074i
$231$	−1.48778e29			−0.0278986
$232$	−2.22658e30	+	2.22658e30i	−0.394724	+	0.394724i
$233$	−2.40704e30	−	2.40704e30i	−0.403511	−	0.403511i	0.475957	−	0.879468i	$-0.342102\pi$
$233$	−2.40704e30	−	2.40704e30i	−0.403511	−	0.403511i	−0.879468	+	0.475957i	$0.842102\pi$
$234$		−	1.22136e31i		−	1.93659i
$235$	2.10666e30	+	1.13124e31i	0.316018	+	1.69696i
$236$	−1.90355e31			−2.70214
$237$	2.27839e29	−	2.27839e29i	0.0306125	−	0.0306125i
$238$	1.29634e31	+	1.29634e31i	1.64899	+	1.64899i
$239$		−	2.78542e29i		−	0.0335520i	−0.999859	−	0.0167760i	$-0.994660\pi$
$239$		−	2.78542e29i		−	0.0335520i	0.999859	−	0.0167760i	$-0.00534022\pi$
$240$	2.89778e29	−	5.39641e28i	0.0330613	−	0.00615686i
$241$	8.49659e30			0.918381			0.459190	−	0.888338i	$-0.348140\pi$
$241$	8.49659e30			0.918381			0.459190	+	0.888338i	$0.348140\pi$
$242$	9.81726e30	−	9.81726e30i	1.00552	−	1.00552i
$243$	1.62273e30	+	1.62273e30i	0.157530	+	0.157530i
$244$			1.13196e31i			1.04175i
$245$	6.75569e30	+	4.63453e30i	0.589536	+	0.404433i
$246$	8.31983e29			0.0688586
$247$	3.29597e29	−	3.29597e29i	0.0258776	−	0.0258776i
$248$	8.02191e30	+	8.02191e30i	0.597594	+	0.597594i
$249$		−	6.06640e29i		−	0.0428884i
$250$	−1.96303e31	+	1.20990e31i	−1.31737	+	0.811950i
$251$	−1.21653e30			−0.0775111			−0.0387555	−	0.999249i	$-0.512339\pi$
$251$	−1.21653e30			−0.0775111			−0.0387555	+	0.999249i	$0.512339\pi$
$252$	2.12257e31	−	2.12257e31i	1.28427	−	1.28427i
$253$	−2.49865e30	−	2.49865e30i	−0.143595	−	0.143595i
$254$			1.12140e30i			0.0612242i
$255$	−9.38856e29	+	1.36856e30i	−0.0487053	+	0.0709970i
$256$	−3.46951e30			−0.171060
$257$	−1.59515e31	+	1.59515e31i	−0.747603	+	0.747603i	−0.974028	−	0.226425i	$-0.927296\pi$
$257$	−1.59515e31	+	1.59515e31i	−0.747603	+	0.747603i	0.226425	+	0.974028i	$0.427296\pi$
$258$	−4.28818e29	−	4.28818e29i	−0.0191081	−	0.0191081i
$259$		−	2.51462e31i		−	1.06555i
$260$	−7.97306e30	−	4.28139e31i	−0.321345	−	1.72557i
$261$	2.37021e31			0.908783
$262$	−2.95173e30	+	2.95173e30i	−0.107686	+	0.107686i
$263$	−2.07498e31	−	2.07498e31i	−0.720427	−	0.720427i	0.248265	−	0.968692i	$-0.420140\pi$
$263$	−2.07498e31	−	2.07498e31i	−0.720427	−	0.720427i	−0.968692	+	0.248265i	$0.920140\pi$
$264$			3.93751e29i			0.0130128i
$265$	−5.30173e31	+	9.87319e30i	−1.66810	+	0.310643i
$266$	1.96698e30			0.0589303
$267$	−1.62628e30	+	1.62628e30i	−0.0464032	+	0.0464032i
$268$	2.94902e31	+	2.94902e31i	0.801539	+	0.801539i
$269$			4.94553e31i			1.28066i	0.768101	+	0.640329i	$0.221202\pi$
$269$			4.94553e31i			1.28066i	−0.768101	+	0.640329i	$0.778798\pi$
$270$	7.71659e30	+	5.29373e30i	0.190413	+	0.130627i
$271$	−6.61593e30			−0.155593			−0.0777965	−	0.996969i	$-0.524788\pi$
$271$	−6.61593e30			−0.155593			−0.0777965	+	0.996969i	$0.524788\pi$
$272$	−1.63147e31	+	1.63147e31i	−0.365749	+	0.365749i
$273$	−4.07924e30	−	4.07924e30i	−0.0871895	−	0.0871895i
$274$			7.52827e31i			1.53440i
$275$	5.27280e30	+	1.36661e31i	0.102498	+	0.265655i
$276$	−4.01339e30			−0.0744206
$277$	6.26247e31	−	6.26247e31i	1.10792	−	1.10792i	0.114497	−	0.993424i	$-0.463474\pi$
$277$	6.26247e31	−	6.26247e31i	1.10792	−	1.10792i	0.993424	−	0.114497i	$-0.0365257\pi$
$278$	−8.50519e31	−	8.50519e31i	−1.43583	−	1.43583i
$279$		−	8.53939e31i		−	1.37585i
$280$	2.94221e31	−	4.28881e31i	0.452501	−	0.659603i
$281$	1.04830e32			1.53923			0.769616	−	0.638507i	$-0.220448\pi$
$281$	1.04830e32			1.53923			0.769616	+	0.638507i	$0.220448\pi$
$282$	1.00793e31	−	1.00793e31i	0.141317	−	0.141317i
$283$	−1.67783e31	−	1.67783e31i	−0.224659	−	0.224659i	0.585798	−	0.810457i	$-0.300781\pi$
$283$	−1.67783e31	−	1.67783e31i	−0.224659	−	0.224659i	−0.810457	+	0.585798i	$0.800781\pi$
$284$			1.19500e32i			1.52837i
$285$	3.25999e28	+	1.75056e29i	0.000398321	+	0.00213891i
$286$	−4.74993e31			−0.554535
$287$	−4.93624e31	+	4.93624e31i	−0.550721	+	0.550721i
$288$	8.61433e31	+	8.61433e31i	0.918585	+	0.918585i
$289$		−	3.18082e31i		−	0.324240i
$290$	1.42658e32	−	2.65666e31i	1.39034	−	0.258918i
$291$	−1.28202e31			−0.119478
$292$	−8.78220e31	+	8.78220e31i	−0.782756	+	0.782756i
$293$	−8.11379e31	−	8.11379e31i	−0.691743	−	0.691743i	0.270872	−	0.962615i	$-0.412688\pi$
$293$	−8.11379e31	−	8.11379e31i	−0.691743	−	0.691743i	−0.962615	+	0.270872i	$0.912688\pi$
$294$		−	1.01487e31i		−	0.0827743i
$295$	2.04719e32	+	1.40441e32i	1.59761	+	1.09599i
$296$	−6.65512e31			−0.497008
$297$	4.20332e30	−	4.20332e30i	0.0300440	−	0.0300440i
$298$	−2.38113e31	−	2.38113e31i	−0.162919	−	0.162919i
$299$		−	1.37017e32i		−	0.897531i
$300$	1.52100e31	+	6.74072e30i	0.0954012	+	0.0422795i
$301$	5.08843e31			0.305647
$302$	−1.22347e32	+	1.22347e32i	−0.703889	+	0.703889i
$303$	−6.70348e30	−	6.70348e30i	−0.0369442	−	0.0369442i
$304$			2.47549e30i			0.0130709i
$305$	8.35145e31	−	1.21738e32i	0.422536	−	0.615925i
$306$	−3.65217e32			−1.77081
$307$	−1.90717e32	+	1.90717e32i	−0.886318	+	0.886318i	−0.994167	−	0.107849i	$-0.965604\pi$
$307$	−1.90717e32	+	1.90717e32i	−0.886318	+	0.886318i	0.107849	+	0.994167i	$0.465604\pi$
$308$	−8.25478e31	−	8.25478e31i	−0.367744	−	0.367744i
$309$			2.21819e31i			0.0947409i
$310$	−9.57141e31	−	5.13968e32i	−0.391989	−	2.10491i
$311$	2.95453e32			1.16039			0.580195	−	0.814478i	$-0.302977\pi$
$311$	2.95453e32			1.16039			0.580195	+	0.814478i	$0.302977\pi$
$312$	−1.07960e31	+	1.07960e31i	−0.0406680	+	0.0406680i
$313$	−4.09862e31	−	4.09862e31i	−0.148102	−	0.148102i	0.629168	−	0.777270i	$-0.283396\pi$
$313$	−4.09862e31	−	4.09862e31i	−0.148102	−	0.148102i	−0.777270	+	0.629168i	$0.783396\pi$
$314$		−	1.55788e32i		−	0.540067i
$315$	−3.84874e32	+	7.16735e31i	−1.28021	+	0.238408i
$316$	2.52827e32			0.807034
$317$	−5.56585e31	+	5.56585e31i	−0.170514	+	0.170514i	−0.787205	−	0.616691i	$-0.788473\pi$
$317$	−5.56585e31	+	5.56585e31i	−0.170514	+	0.170514i	0.616691	+	0.787205i	$0.288473\pi$
$318$	4.72385e31	+	4.72385e31i	0.138913	+	0.138913i
$319$		−	9.21785e31i		−	0.260226i
$320$	4.78287e32	+	3.28114e32i	1.29640	+	0.889355i
$321$	−3.67327e31			−0.0956065
$322$	4.08847e32	−	4.08847e32i	1.02196	−	1.02196i
$323$	−9.85576e30	−	9.85576e30i	−0.0236623	−	0.0236623i
$324$			5.94606e32i			1.37134i
$325$	−2.30128e32	+	5.19271e32i	−0.509902	+	1.15056i
$326$	8.82788e32			1.87944
$327$	−2.77508e31	+	2.77508e31i	−0.0567746	+	0.0567746i
$328$	1.30641e32	+	1.30641e32i	0.256874	+	0.256874i
$329$			1.19604e33i			2.26046i
$330$	1.02649e31	−	1.49630e31i	0.0186498	−	0.0271855i
$331$	−1.08201e33			−1.89002			−0.945011	−	0.327039i	$-0.893949\pi$
$331$	−1.08201e33			−1.89002			−0.945011	+	0.327039i	$0.893949\pi$
$332$	3.36588e32	−	3.36588e32i	0.565331	−	0.565331i
$333$	3.54222e32	+	3.54222e32i	0.572137	+	0.572137i
$334$		−	1.09294e33i		−	1.69783i
$335$	−9.95803e31	−	5.34729e32i	−0.148796	−	0.799008i
$336$	3.06377e31			0.0440398
$337$	9.36294e32	−	9.36294e32i	1.29486	−	1.29486i	0.363120	−	0.931742i	$-0.381711\pi$
$337$	9.36294e32	−	9.36294e32i	1.29486	−	1.29486i	0.931742	−	0.363120i	$-0.118289\pi$
$338$	−4.80052e32	−	4.80052e32i	−0.638809	−	0.638809i
$339$		−	5.94292e31i		−	0.0761034i
$340$	−1.28024e33	+	2.38414e32i	−1.57785	+	0.293836i
$341$	−3.32101e32			−0.393970
$342$	−2.77078e31	+	2.77078e31i	−0.0316419	+	0.0316419i
$343$	−2.40098e32	−	2.40098e32i	−0.263976	−	0.263976i
$344$		−	1.34669e32i		−	0.142563i
$345$	4.31624e31	+	2.96102e31i	0.0440004	+	0.0301852i
$346$	3.80790e32			0.373849
$347$	−4.22093e32	+	4.22093e32i	−0.399140	+	0.399140i	−0.877930	−	0.478790i	$-0.841076\pi$
$347$	−4.22093e32	+	4.22093e32i	−0.399140	+	0.399140i	0.478790	+	0.877930i	$0.341076\pi$
$348$	−7.40297e31	−	7.40297e31i	−0.0674335	−	0.0674335i
$349$		−	2.85347e31i		−	0.0250405i	−0.999922	−	0.0125203i	$-0.996015\pi$
$349$		−	2.85347e31i		−	0.0250405i	0.999922	−	0.0125203i	$-0.00398543\pi$
$350$	−2.23614e33	+	8.62776e32i	−1.89067	+	0.729480i
$351$	2.30495e32			0.187789
$352$	3.35015e32	−	3.35015e32i	0.263033	−	0.263033i
$353$	8.87104e32	+	8.87104e32i	0.671279	+	0.671279i	0.958011	−	0.286732i	$-0.0925688\pi$
$353$	8.87104e32	+	8.87104e32i	0.671279	+	0.671279i	−0.286732	+	0.958011i	$0.592569\pi$
$354$		−	3.07538e32i		−	0.224314i
$355$	8.81651e32	−	1.28517e33i	0.619909	−	0.903632i
$356$	−1.80464e33			−1.22332
$357$	−1.21979e32	+	1.21979e32i	−0.0797257	+	0.0797257i
$358$	2.48849e33	+	2.48849e33i	1.56840	+	1.56840i
$359$		−	3.07101e32i		−	0.186661i	−0.995635	−	0.0933305i	$-0.970249\pi$
$359$		−	3.07101e32i		−	0.186661i	0.995635	−	0.0933305i	$-0.0297513\pi$
$360$	1.89689e32	+	1.01860e33i	0.111201	+	0.597131i
$361$	1.76696e33			0.999154
$362$	−2.15435e33	+	2.15435e33i	−1.17518	+	1.17518i
$363$	9.23755e31	+	9.23755e31i	0.0486151	+	0.0486151i
$364$		−	4.52663e33i		−	2.29857i
$365$	1.59243e33	−	2.96551e32i	0.780284	−	0.145309i
$366$	−1.82880e32			−0.0864794
$367$	1.14835e33	−	1.14835e33i	0.524101	−	0.524101i	−0.394707	−	0.918807i	$-0.629154\pi$
$367$	1.14835e33	−	1.14835e33i	0.524101	−	0.524101i	0.918807	+	0.394707i	$0.129154\pi$
$368$	5.14543e32	+	5.14543e32i	0.226673	+	0.226673i
$369$		−	1.39068e33i		−	0.591406i
$370$	2.52902e33	+	1.73495e33i	1.03831	+	0.712304i
$371$	−5.60542e33			−2.22202
$372$	−2.66714e32	+	2.66714e32i	−0.102091	+	0.102091i
$373$	−6.01167e32	−	6.01167e32i	−0.222218	−	0.222218i	0.587214	−	0.809432i	$-0.300225\pi$
$373$	−6.01167e32	−	6.01167e32i	−0.222218	−	0.222218i	−0.809432	+	0.587214i	$0.800225\pi$
$374$			1.42035e33i			0.507065i
$375$	−1.13846e32	−	1.84711e32i	−0.0392563	−	0.0636923i
$376$	3.16539e33			1.05435
$377$	2.52738e33	−	2.52738e33i	0.813265	−	0.813265i
$378$	6.87778e32	+	6.87778e32i	0.213823	+	0.213823i
$379$			3.08824e32i			0.0927687i	0.998924	+	0.0463844i	$0.0147699\pi$
$379$			3.08824e32i			0.0927687i	−0.998924	+	0.0463844i	$0.985230\pi$
$380$	−7.90401e31	+	1.15215e32i	−0.0229435	+	0.0334444i
$381$	−1.05518e31			−0.00296008
$382$	−2.85684e33	+	2.85684e33i	−0.774573	+	0.774573i
$383$	1.84392e33	+	1.84392e33i	0.483234	+	0.483234i	0.906163	−	0.422929i	$-0.138998\pi$
$383$	1.84392e33	+	1.84392e33i	0.483234	+	0.483234i	−0.422929	+	0.906163i	$0.638998\pi$
$384$		−	3.32684e32i		−	0.0842803i
$385$	2.78742e32	+	1.49679e33i	0.0682672	+	0.366583i
$386$	8.07175e32			0.191132
$387$	−7.16781e32	+	7.16781e32i	−0.164113	+	0.164113i
$388$	−7.11315e33	−	7.11315e33i	−1.57489	−	1.57489i
$389$			2.44569e33i			0.523669i	0.965113	+	0.261834i	$0.0843274\pi$
$389$			2.44569e33i			0.523669i	−0.965113	+	0.261834i	$0.915673\pi$
$390$	6.91704e32	−	1.28813e32i	0.143245	−	0.0266760i
$391$	−4.09715e33			−0.820699
$392$	1.59359e33	−	1.59359e33i	0.308786	−	0.308786i
$393$	−2.77743e31	−	2.77743e31i	−0.00520643	−	0.00520643i
$394$			8.08448e33i			1.46623i
$395$	−2.71905e33	−	1.86532e33i	−0.477151	−	0.327335i
$396$	2.32562e33			0.394912
$397$	−4.48928e31	+	4.48928e31i	−0.00737735	+	0.00737735i	−0.710786	−	0.703408i	$-0.751660\pi$
$397$	−4.48928e31	+	4.48928e31i	−0.00737735	+	0.00737735i	0.703408	+	0.710786i	$0.251660\pi$
$398$	−3.50630e33	−	3.50630e33i	−0.557660	−	0.557660i
$399$			1.85083e31i			0.00284918i
$400$	−1.08582e33	−	2.81423e33i	−0.161800	−	0.419353i
$401$	−2.32372e31			−0.00335202			−0.00167601	−	0.999999i	$-0.500533\pi$
$401$	−2.32372e31			−0.00335202			−0.00167601	+	0.999999i	$0.500533\pi$
$402$	−4.76445e32	+	4.76445e32i	−0.0665386	+	0.0665386i
$403$	−9.10563e33	−	9.10563e33i	−1.23125	−	1.23125i
$404$		−	7.43870e33i		−	0.973957i
$405$	4.38692e33	−	6.39475e33i	0.556217	−	0.810789i
$406$	1.50829e34			1.85203
$407$	1.37758e33	−	1.37758e33i	0.163829	−	0.163829i
$408$	3.22826e32	+	3.22826e32i	0.0371866	+	0.0371866i
$409$			1.02905e34i			1.14825i	0.818769	+	0.574123i	$0.194657\pi$
$409$			1.02905e34i			1.14825i	−0.818769	+	0.574123i	$0.805343\pi$
$410$	−1.55875e33	−	8.37024e33i	−0.168495	−	0.904789i
$411$	−7.08373e32			−0.0741854
$412$	−1.23074e34	+	1.23074e34i	−1.24882	+	1.24882i
$413$	1.82465e34	+	1.82465e34i	1.79403	+	1.79403i
$414$			1.15184e34i			1.09746i
$415$	−6.10316e33	+	1.13657e33i	−0.563546	+	0.104947i
$416$	1.83711e34			1.64407
$417$	8.00297e32	−	8.00297e32i	0.0694196	−	0.0694196i
$418$	1.07757e32	+	1.07757e32i	0.00906054	+	0.00906054i
$419$			1.34539e34i			1.09665i	0.836267	+	0.548323i	$0.184733\pi$
$419$			1.34539e34i			1.09665i	−0.836267	+	0.548323i	$0.815267\pi$
$420$	1.42595e33	+	9.78233e32i	0.112685	+	0.0773039i
$421$	3.02346e33			0.231652			0.115826	−	0.993269i	$-0.463048\pi$
$421$	3.02346e33			0.231652			0.115826	+	0.993269i	$0.463048\pi$
$422$	8.64840e33	−	8.64840e33i	0.642501	−	0.642501i
$423$	−1.68479e34	−	1.68479e34i	−1.21373	−	1.21373i
$424$			1.48351e34i			1.03642i
$425$	1.55275e34	+	6.88140e33i	1.05207	+	0.466252i
$426$	−1.93064e33			−0.126875
$427$	1.08505e34	−	1.08505e34i	0.691649	−	0.691649i
$428$	−2.03807e34	−	2.03807e34i	−1.26023	−	1.26023i
$429$		−	4.46945e32i		−	0.0268108i
$430$	−3.51075e33	+	5.11756e33i	−0.204320	+	0.297833i
$431$	−1.60367e34			−0.905548			−0.452774	−	0.891625i	$-0.649565\pi$
$431$	−1.60367e34			−0.905548			−0.452774	+	0.891625i	$0.649565\pi$
$432$	−8.65583e32	+	8.65583e32i	−0.0474264	+	0.0474264i
$433$	5.55564e33	+	5.55564e33i	0.295387	+	0.295387i	0.839204	−	0.543817i	$-0.183021\pi$
$433$	5.55564e33	+	5.55564e33i	0.295387	+	0.295387i	−0.543817	+	0.839204i	$0.683021\pi$
$434$		−	5.43408e34i		−	2.80388i
$435$	2.49978e32	+	1.34234e33i	0.0125182	+	0.0672206i
$436$	−3.07944e34			−1.49674
$437$	−3.10837e32	+	3.10837e32i	−0.0146647	+	0.0146647i
$438$	−1.41886e33	−	1.41886e33i	−0.0649793	−	0.0649793i
$439$		−	4.57273e33i		−	0.203300i	−0.994820	−	0.101650i	$-0.967588\pi$
$439$		−	4.57273e33i		−	0.203300i	0.994820	−	0.101650i	$-0.0324121\pi$
$440$	3.96137e33	−	7.37709e32i	0.170986	−	0.0318420i
$441$	−1.69639e34			−0.710924
$442$	−3.89434e34	+	3.89434e34i	−1.58469	+	1.58469i
$443$	1.70975e33	+	1.70975e33i	0.0675593	+	0.0675593i	0.740079	−	0.672520i	$-0.234788\pi$
$443$	1.70975e33	+	1.70975e33i	0.0675593	+	0.0675593i	−0.672520	+	0.740079i	$0.734788\pi$
$444$		−	2.21271e33i		−	0.0849074i
$445$	1.94082e34	+	1.33144e34i	0.723278	+	0.496183i
$446$	−2.75730e33			−0.0998002
$447$	2.24053e32	−	2.24053e32i	0.00787685	−	0.00787685i
$448$	4.26296e34	+	4.26296e34i	1.45578	+	1.45578i
$449$		−	1.11957e34i		−	0.371405i	−0.982606	−	0.185703i	$-0.940544\pi$
$449$		−	1.11957e34i		−	0.371405i	0.982606	−	0.185703i	$-0.0594561\pi$
$450$	1.93459e34	−	4.36528e34i	0.623485	−	1.40686i
$451$	−5.40844e33			−0.169347
$452$	3.29736e34	−	3.29736e34i	1.00315	−	1.00315i
$453$	−1.15123e33	−	1.15123e33i	−0.0340318	−	0.0340318i
$454$		−	3.08022e34i		−	0.884820i
$455$	−3.33969e34	+	4.86821e34i	−0.932305	+	1.35901i
$456$	4.89835e31			0.00132895
$457$	−3.37862e34	+	3.37862e34i	−0.890900	+	0.890900i	−0.994608	−	0.103707i	$-0.966929\pi$
$457$	−3.37862e34	+	3.37862e34i	−0.890900	+	0.890900i	0.103707	+	0.994608i	$0.466929\pi$
$458$	5.93627e34	+	5.93627e34i	1.52147	+	1.52147i
$459$		−	6.89237e33i		−	0.171713i
$460$	7.51925e33	+	4.03771e34i	0.182105	+	0.977874i
$461$	4.11229e34			0.968214			0.484107	−	0.875009i	$-0.339145\pi$
$461$	4.11229e34			0.968214			0.484107	+	0.875009i	$0.339145\pi$
$462$	1.33365e33	−	1.33365e33i	0.0305278	−	0.0305278i
$463$	−6.06259e34	−	6.06259e34i	−1.34929	−	1.34929i	−0.886432	−	0.462859i	$-0.846824\pi$
$463$	−6.06259e34	−	6.06259e34i	−1.34929	−	1.34929i	−0.462859	−	0.886432i	$-0.653176\pi$
$464$			1.89822e34i			0.410783i
$465$	4.83619e33	−	9.00623e32i	0.101769	−	0.0189520i
$466$	4.31533e34			0.883075
$467$	1.18106e34	−	1.18106e34i	0.235045	−	0.235045i	−0.579750	−	0.814795i	$-0.696850\pi$
$467$	1.18106e34	−	1.18106e34i	0.235045	−	0.235045i	0.814795	+	0.579750i	$0.196850\pi$
$468$	6.37644e34	+	6.37644e34i	1.23419	+	1.23419i
$469$		−	5.65359e34i		−	1.06433i
$470$	−1.20288e35	−	8.25201e34i	−2.20268	−	1.51108i
$471$	1.46589e33			0.0261113
$472$	4.82907e34	−	4.82907e34i	0.836792	−	0.836792i
$473$	2.78760e33	+	2.78760e33i	0.0469932	+	0.0469932i
$474$			4.08469e33i			0.0669947i
$475$	1.70009e33	−	6.55948e32i	0.0271303	−	0.0104677i
$476$	−1.35357e35			−2.10180
$477$	7.89606e34	−	7.89606e34i	1.19309	−	1.19309i
$478$	2.49685e33	+	2.49685e33i	0.0367139	+	0.0367139i
$479$			2.39443e34i			0.342642i	0.985215	+	0.171321i	$0.0548035\pi$
$479$			2.39443e34i			0.342642i	−0.985215	+	0.171321i	$0.945197\pi$
$480$	−3.97010e33	+	5.78715e33i	−0.0552924	+	0.0805989i
$481$	7.55419e34			1.02401
$482$	−7.61634e34	+	7.61634e34i	−1.00493	+	1.00493i
$483$	3.84705e33	+	3.84705e33i	0.0494101	+	0.0494101i
$484$			1.02507e35i			1.28163i
$485$	2.40192e34	+	1.28979e35i	0.292359	+	1.56991i
$486$	−2.90923e34			−0.344752
$487$	3.55738e34	−	3.55738e34i	0.410444	−	0.410444i	−0.471449	−	0.881893i	$-0.656269\pi$
$487$	3.55738e34	−	3.55738e34i	0.410444	−	0.410444i	0.881893	+	0.471449i	$0.156269\pi$
$488$	−2.87165e34	−	2.87165e34i	−0.322607	−	0.322607i
$489$			8.30660e33i			0.0908674i
$490$	−1.02102e35	+	1.90140e34i	−1.08764	+	0.202547i
$491$	−7.77826e34			−0.806906			−0.403453	−	0.915000i	$-0.632190\pi$
$491$	−7.77826e34			−0.806906			−0.403453	+	0.915000i	$0.632190\pi$
$492$	−4.34358e33	+	4.34358e33i	−0.0438835	+	0.0438835i
$493$	−7.55747e34	−	7.55747e34i	−0.743646	−	0.743646i
$494$			5.90902e33i			0.0566324i
$495$	−2.50111e34	−	1.71581e34i	−0.233488	−	0.160177i
$496$	6.83891e34			0.621907
$497$	1.14547e35	−	1.14547e35i	1.01473	−	1.01473i
$498$	5.43792e33	+	5.43792e33i	0.0469301	+	0.0469301i
$499$		−	9.60514e34i		−	0.807600i	−0.914847	−	0.403800i	$-0.867689\pi$
$499$		−	9.60514e34i		−	0.807600i	0.914847	−	0.403800i	$-0.132311\pi$
$500$	3.93190e34	−	1.65651e35i	0.322101	−	1.35701i
$501$	1.02840e34			0.0820868
$502$	1.09050e34	−	1.09050e34i	0.0848156	−	0.0848156i
$503$	−5.67041e34	−	5.67041e34i	−0.429765	−	0.429765i	0.458784	−	0.888548i	$-0.348285\pi$
$503$	−5.67041e34	−	5.67041e34i	−0.429765	−	0.429765i	−0.888548	+	0.458784i	$0.848285\pi$
$504$			1.07694e35i			0.795418i
$505$	−5.48817e34	+	8.00002e34i	−0.395039	+	0.575842i
$506$	4.47958e34			0.314254
$507$	4.51705e33	−	4.51705e33i	0.0308853	−	0.0308853i
$508$	−5.85457e33	−	5.85457e33i	−0.0390181	−	0.0390181i
$509$			2.56612e35i			1.66704i	0.552492	+	0.833518i	$0.313677\pi$
$509$			2.56612e35i			1.66704i	−0.552492	+	0.833518i	$0.686323\pi$
$510$	−3.85183e33	−	2.06836e34i	−0.0243924	−	0.130983i
$511$	1.68364e35			1.03939
$512$	−1.01246e35	+	1.01246e35i	−0.609352	+	0.609352i
$513$	−5.22902e32	−	5.22902e32i	−0.00306827	−	0.00306827i
$514$		−	2.85979e35i		−	1.63611i
$515$	2.23163e35	−	4.15586e34i	1.24488	−	0.231829i
$516$	4.47751e33			0.0243551
$517$	−6.55224e34	+	6.55224e34i	−0.347546	+	0.347546i
$518$	2.25411e35	+	2.25411e35i	1.16597	+	1.16597i
$519$			3.58304e33i			0.0180749i
$520$	1.28841e35	+	8.83872e34i	0.633883	+	0.434856i
$521$	−3.63605e34			−0.174478			−0.0872388	−	0.996187i	$-0.527804\pi$
$521$	−3.63605e34			−0.174478			−0.0872388	+	0.996187i	$0.527804\pi$
$522$	−2.12466e35	+	2.12466e35i	−0.994425	+	0.994425i
$523$	3.70335e34	+	3.70335e34i	0.169072	+	0.169072i	0.786571	−	0.617499i	$-0.211854\pi$
$523$	3.70335e34	+	3.70335e34i	0.169072	+	0.169072i	−0.617499	+	0.786571i	$0.711854\pi$
$524$		−	3.08205e34i		−	0.137257i
$525$	−8.11829e33	−	2.10410e34i	−0.0352691	−	0.0914103i
$526$	3.72003e35			1.57664
$527$	−2.72281e35	+	2.72281e35i	−1.12585	+	1.12585i
$528$	1.67842e33	+	1.67842e33i	0.00677112	+	0.00677112i
$529$		−	1.24834e35i		−	0.491372i
$530$	3.86744e35	−	5.63751e35i	1.48538	−	2.16521i
$531$	−5.14058e35			−1.92657
$532$	−1.02691e34	+	1.02691e34i	−0.0375563	+	0.0375563i
$533$	−1.48290e35	−	1.48290e35i	−0.529246	−	0.529246i
$534$		−	2.91559e34i		−	0.101552i
$535$	6.88202e34	+	3.69553e35i	0.233947	+	1.25625i
$536$	−1.49626e35			−0.496438
$537$	−2.34154e34	+	2.34154e34i	−0.0758292	+	0.0758292i
$538$	−4.43317e35	−	4.43317e35i	−1.40134	−	1.40134i
$539$			6.59733e34i			0.203570i
$540$	−6.79237e34	+	1.26491e34i	−0.204599	+	0.0381015i
$541$	−4.27082e35			−1.25588			−0.627939	−	0.778263i	$-0.716101\pi$
$541$	−4.27082e35			−1.25588			−0.627939	+	0.778263i	$0.716101\pi$
$542$	5.93052e34	−	5.93052e34i	0.170256	−	0.170256i
$543$	−2.02714e34	−	2.02714e34i	−0.0568179	−	0.0568179i
$544$		−	5.49340e35i		−	1.50333i
$545$	3.31181e35	+	2.27197e35i	0.884934	+	0.607082i
$546$	7.31325e34			0.190812
$547$	2.55888e35	−	2.55888e35i	0.651951	−	0.651951i	−0.301511	−	0.953463i	$-0.597491\pi$
$547$	2.55888e35	−	2.55888e35i	0.651951	−	0.651951i	0.953463	+	0.301511i	$0.0974911\pi$
$548$	−3.93033e35	−	3.93033e35i	−0.977871	−	0.977871i
$549$			3.05690e35i			0.742746i
$550$	−1.69768e35	−	7.52371e34i	−0.402848	−	0.178532i
$551$	−1.14672e34			−0.0265758
$552$	1.01815e34	−	1.01815e34i	0.0230464	−	0.0230464i
$553$	−2.42349e35	−	2.42349e35i	−0.535814	−	0.535814i
$554$			1.12274e36i			2.42466i
$555$	−1.63251e34	+	2.37968e34i	−0.0344387	+	0.0502007i
$556$	8.88071e35			1.83010
$557$	3.97433e35	−	3.97433e35i	0.800104	−	0.800104i	−0.183008	−	0.983111i	$-0.558583\pi$
$557$	3.97433e35	−	3.97433e35i	0.800104	−	0.800104i	0.983111	+	0.183008i	$0.0585834\pi$
$558$	7.65471e35	+	7.65471e35i	1.50551	+	1.50551i
$559$			1.52862e35i			0.293729i
$560$	−5.74009e34	−	3.08233e35i	−0.107764	−	0.578675i
$561$	−1.33648e34			−0.0245157
$562$	−9.39698e35	+	9.39698e35i	−1.68429	+	1.68429i
$563$	4.73022e35	+	4.73022e35i	0.828462	+	0.828462i	0.987304	−	0.158842i	$-0.0507761\pi$
$563$	4.73022e35	+	4.73022e35i	0.828462	+	0.828462i	−0.158842	+	0.987304i	$0.550776\pi$
$564$			1.05244e35i			0.180122i
$565$	−5.97893e35	+	1.11343e35i	−0.999985	+	0.186223i
$566$	3.00801e35			0.491660
$567$	5.69962e35	−	5.69962e35i	0.910472	−	0.910472i
$568$	−3.03156e35	−	3.03156e35i	−0.473302	−	0.473302i
$569$			2.84905e35i			0.434751i	0.976088	+	0.217375i	$0.0697496\pi$
$569$			2.84905e35i			0.434751i	−0.976088	+	0.217375i	$0.930250\pi$
$570$	−1.86143e33	−	1.27697e33i	−0.00277634	−	0.00190462i
$571$	9.43778e35			1.37594			0.687972	−	0.725737i	$-0.258501\pi$
$571$	9.43778e35			1.37594			0.687972	+	0.725737i	$0.258501\pi$
$572$	2.47983e35	−	2.47983e35i	0.353405	−	0.353405i
$573$	−2.68815e34	−	2.68815e34i	−0.0374492	−	0.0374492i
$574$		−	8.84969e35i		−	1.20524i
$575$	2.17030e35	−	4.89715e35i	0.288960	−	0.652020i
$576$	−1.20100e36			−1.56333
$577$	5.34296e35	−	5.34296e35i	0.679981	−	0.679981i	−0.280015	−	0.959996i	$-0.590339\pi$
$577$	5.34296e35	−	5.34296e35i	0.679981	−	0.679981i	0.959996	+	0.280015i	$0.0903395\pi$
$578$	2.85128e35	+	2.85128e35i	0.354796	+	0.354796i
$579$			7.59512e33i			0.00924088i
$580$	−6.06085e35	+	8.83480e35i	−0.721057	+	1.05107i
$581$	−6.45275e35			−0.750680
$582$	1.14920e35	−	1.14920e35i	0.130737	−	0.130737i
$583$	−3.07082e35	−	3.07082e35i	−0.341635	−	0.341635i
$584$		−	4.45588e35i		−	0.484805i
$585$	−2.15315e35	−	1.15620e36i	−0.229112	−	1.23029i
$586$	1.45464e36			1.51386
$587$	−2.83557e35	+	2.83557e35i	−0.288633	+	0.288633i	−0.836539	−	0.547907i	$-0.815425\pi$
$587$	−2.83557e35	+	2.83557e35i	−0.288633	+	0.288633i	0.547907	+	0.836539i	$0.315425\pi$
$588$	5.29839e34	+	5.29839e34i	0.0527520	+	0.0527520i
$589$			4.13141e34i			0.0402346i
$590$	−3.09401e36	+	5.76184e35i	−2.94744	+	0.548890i
$591$	−7.60709e34			−0.0708894
$592$	−2.83684e35	+	2.83684e35i	−0.258614	+	0.258614i
$593$	−4.24891e35	−	4.24891e35i	−0.378936	−	0.378936i	0.491782	−	0.870718i	$-0.336346\pi$
$593$	−4.24891e35	−	4.24891e35i	−0.378936	−	0.378936i	−0.870718	+	0.491782i	$0.836346\pi$
$594$			7.53570e34i			0.0657506i
$595$	1.45571e36	+	9.98648e35i	1.24267	+	0.852495i
$596$	2.48626e35			0.207657
$597$	3.29926e34	−	3.29926e34i	0.0269619	−	0.0269619i
$598$	1.22822e36	+	1.22822e36i	0.982113	+	0.982113i
$599$			6.56146e35i			0.513395i	0.966492	+	0.256698i	$0.0826345\pi$
$599$			6.56146e35i			0.513395i	−0.966492	+	0.256698i	$0.917366\pi$
$600$	−5.56865e34	+	2.14856e34i	−0.0426367	+	0.0164506i
$601$	−2.21403e36			−1.65888			−0.829441	−	0.558594i	$-0.811341\pi$
$601$	−2.21403e36			−1.65888			−0.829441	+	0.558594i	$0.811341\pi$
$602$	−4.56127e35	+	4.56127e35i	−0.334450	+	0.334450i
$603$	7.96391e35	+	7.96391e35i	0.571480	+	0.571480i
$604$		−	1.27749e36i		−	0.897177i
$605$	7.56283e35	−	1.10242e36i	0.519834	−	0.757753i
$606$	1.20180e35			0.0808516
$607$	1.40817e36	−	1.40817e36i	0.927262	−	0.927262i	−0.0702659	−	0.997528i	$-0.522385\pi$
$607$	1.40817e36	−	1.40817e36i	0.927262	−	0.927262i	0.997528	+	0.0702659i	$0.0223848\pi$
$608$	−4.16767e34	−	4.16767e34i	−0.0268625	−	0.0268625i
$609$			1.41923e35i			0.0895423i
$610$	3.42634e35	+	1.83988e36i	0.211613	+	1.13632i
$611$	−3.59302e36			−2.17232
$612$	1.90671e36	−	1.90671e36i	1.12854	−	1.12854i
$613$	−5.66636e34	−	5.66636e34i	−0.0328335	−	0.0328335i	0.690499	−	0.723333i	$-0.257391\pi$
$613$	−5.66636e34	−	5.66636e34i	−0.0328335	−	0.0328335i	−0.723333	+	0.690499i	$0.757391\pi$
$614$		−	3.41917e36i		−	1.93969i
$615$	7.87598e34	−	1.46671e34i	0.0437450	−	0.00814644i
$616$	4.18828e35			0.227765
$617$	−3.02814e35	+	3.02814e35i	−0.161239	+	0.161239i	−0.783115	−	0.621877i	$-0.786371\pi$
$617$	−3.02814e35	+	3.02814e35i	−0.161239	+	0.161239i	0.621877	+	0.783115i	$0.286371\pi$
$618$	−1.98838e35	−	1.98838e35i	−0.103669	−	0.103669i
$619$		−	3.50224e35i		−	0.178800i	−0.995996	−	0.0894001i	$-0.971505\pi$
$619$		−	3.50224e35i		−	0.178800i	0.995996	−	0.0894001i	$-0.0284950\pi$
$620$	3.18300e36	+	2.18360e36i	1.59127	+	1.09165i
$621$	−2.17376e35			−0.106419
$622$	−2.64844e36	+	2.64844e36i	−1.26974	+	1.26974i
$623$	1.72985e36	+	1.72985e36i	0.812201	+	0.812201i
$624$			9.20389e34i			0.0423225i
$625$	−1.64501e36	+	1.49142e36i	−0.740846	+	0.671675i
$626$	7.34800e35			0.324118
$627$	−1.01394e33	+	1.01394e33i	−0.000438061	+	0.000438061i
$628$	8.13330e35	+	8.13330e35i	0.344185	+	0.344185i
$629$		−	2.25889e36i		−	0.936346i
$630$	2.80753e36	−	4.09250e36i	1.13998	−	1.66173i
$631$	3.41731e36			1.35926			0.679630	−	0.733555i	$-0.262140\pi$
$631$	3.41731e36			1.35926			0.679630	+	0.733555i	$0.262140\pi$
$632$	−6.41393e35	+	6.41393e35i	−0.249921	+	0.249921i
$633$	8.13772e34	+	8.13772e34i	0.0310638	+	0.0310638i
$634$		−	9.97845e35i		−	0.373167i
$635$	1.97693e34	+	1.06158e35i	0.00724324	+	0.0388949i
$636$	−4.93242e35			−0.177059
$637$	−1.80887e36	+	1.80887e36i	−0.636203	+	0.636203i
$638$	8.26288e35	+	8.26288e35i	0.284749	+	0.284749i
$639$			3.22712e36i			1.08969i
$640$	−3.34700e36	+	6.23297e35i	−1.10743	+	0.206232i
$641$	−6.27166e35			−0.203343			−0.101671	−	0.994818i	$-0.532419\pi$
$641$	−6.27166e35			−0.203343			−0.101671	+	0.994818i	$0.532419\pi$
$642$	3.29272e35	−	3.29272e35i	0.104616	−	0.104616i
$643$	−1.40071e36	−	1.40071e36i	−0.436119	−	0.436119i	0.454584	−	0.890704i	$-0.349788\pi$
$643$	−1.40071e36	−	1.40071e36i	−0.436119	−	0.436119i	−0.890704	+	0.454584i	$0.849788\pi$
$644$			4.26899e36i			1.30259i
$645$	−4.81537e34	−	3.30344e34i	−0.0143997	−	0.00987849i
$646$	1.76694e35			0.0517844
$647$	2.66811e36	−	2.66811e36i	0.766387	−	0.766387i	−0.211081	−	0.977468i	$-0.567699\pi$
$647$	2.66811e36	−	2.66811e36i	0.766387	−	0.766387i	0.977468	+	0.211081i	$0.0676985\pi$
$648$	−1.50845e36	−	1.50845e36i	−0.424673	−	0.424673i
$649$			1.99920e36i			0.551664i
$650$	−2.59187e36	−	6.71761e36i	−0.701035	−	1.81694i
$651$	5.11321e35			0.135563
$652$	−4.60882e36	+	4.60882e36i	−1.19776	+	1.19776i
$653$	−6.58518e35	−	6.58518e35i	−0.167763	−	0.167763i	0.618232	−	0.785995i	$-0.287849\pi$
$653$	−6.58518e35	−	6.58518e35i	−0.167763	−	0.167763i	−0.785995	+	0.618232i	$0.787849\pi$
$654$		−	4.97516e35i		−	0.124250i
$655$	−2.27389e35	+	3.31462e35i	−0.0556715	+	0.0811515i
$656$	1.11375e36			0.267324
$657$	−2.37166e36	+	2.37166e36i	−0.558088	+	0.558088i
$658$	−1.07213e37	−	1.07213e37i	−2.47349	−	2.47349i
$659$		−	3.01706e36i		−	0.682453i	−0.939981	−	0.341227i	$-0.889158\pi$
$659$		−	3.01706e36i		−	0.682453i	0.939981	−	0.341227i	$-0.110842\pi$
$660$	2.45275e34	+	1.31709e35i	0.00543980	+	0.0292108i
$661$	6.13427e36			1.33396			0.666981	−	0.745074i	$-0.267586\pi$
$661$	6.13427e36			1.33396			0.666981	+	0.745074i	$0.267586\pi$
$662$	9.69913e36	−	9.69913e36i	2.06813	−	2.06813i
$663$	−3.66438e35	−	3.66438e35i	−0.0766170	−	0.0766170i
$664$			1.70777e36i			0.350141i
$665$	1.86204e35	−	3.46761e34i	0.0374377	−	0.00697186i
$666$	−6.35048e36			−1.25211
$667$	−2.38352e36	+	2.38352e36i	−0.460875	+	0.460875i
$668$	5.70598e36	+	5.70598e36i	1.08202	+	1.08202i
$669$		−	2.59449e34i		−	0.00482516i
$670$	5.68595e36	+	3.90067e36i	1.03712	+	0.711487i
$671$	1.18884e36			0.212682
$672$	−5.15808e35	+	5.15808e35i	−0.0905081	+	0.0905081i
$673$	−3.25937e36	−	3.25937e36i	−0.560967	−	0.560967i	0.368615	−	0.929582i	$-0.379832\pi$
$673$	−3.25937e36	−	3.25937e36i	−0.560967	−	0.560967i	−0.929582	+	0.368615i	$0.879832\pi$
$674$			1.67859e37i			2.83378i
$675$	8.23816e35	+	3.65095e35i	0.136421	+	0.0604585i
$676$	5.01247e36			0.814225
$677$	6.85098e35	−	6.85098e35i	0.109169	−	0.109169i	−0.650412	−	0.759581i	$-0.725404\pi$
$677$	6.85098e35	−	6.85098e35i	0.109169	−	0.109169i	0.759581	+	0.650412i	$0.225404\pi$
$678$	5.32724e35	+	5.32724e35i	0.0832752	+	0.0832752i
$679$			1.36367e37i			2.09123i
$680$	2.64299e36	−	3.85265e36i	0.397631	−	0.579620i
$681$	2.89833e35			0.0427795
$682$	2.97695e36	−	2.97695e36i	0.431097	−	0.431097i
$683$	−1.14607e35	−	1.14607e35i	−0.0162832	−	0.0162832i	0.698918	−	0.715202i	$-0.253665\pi$
$683$	−1.14607e35	−	1.14607e35i	−0.0162832	−	0.0162832i	−0.715202	+	0.698918i	$0.753665\pi$
$684$		−	2.89312e35i		−	0.0403308i
$685$	1.32717e36	+	7.12665e36i	0.181530	+	0.974783i
$686$	4.30448e36			0.577706
$687$	−5.58574e35	+	5.58574e35i	−0.0735602	+	0.0735602i
$688$	−5.74046e35	−	5.74046e35i	−0.0741817	−	0.0741817i
$689$		−	1.68393e37i		−	2.13537i
$690$	−6.52334e35	+	1.21481e35i	−0.0811767	+	0.0151172i
$691$	9.17260e36			1.12015			0.560077	−	0.828441i	$-0.310772\pi$
$691$	9.17260e36			1.12015			0.560077	+	0.828441i	$0.310772\pi$
$692$	−1.98801e36	+	1.98801e36i	−0.238254	+	0.238254i
$693$	−2.22923e36	−	2.22923e36i	−0.262194	−	0.262194i
$694$		−	7.56728e36i		−	0.873508i
$695$	−9.55084e36	−	6.55207e36i	−1.08203	−	0.742294i
$696$	3.75609e35			0.0417653
$697$	−4.43423e36	+	4.43423e36i	−0.483941	+	0.483941i
$698$	2.55785e35	+	2.55785e35i	0.0274003	+	0.0274003i
$699$			4.06052e35i			0.0426951i
$700$	7.17001e36	−	1.61787e37i	0.740023	−	1.66982i
$701$	−1.56278e37			−1.58330			−0.791652	−	0.610972i	$-0.790779\pi$
$701$	−1.56278e37			−1.58330			−0.791652	+	0.610972i	$0.790779\pi$
$702$	−2.06616e36	+	2.06616e36i	−0.205486	+	0.205486i
$703$	−1.71374e35	−	1.71374e35i	−0.0167312	−	0.0167312i
$704$			4.67075e36i			0.447654i
$705$	7.76473e35	−	1.13185e36i	0.0730580	−	0.106496i
$706$	−1.59040e37			−1.46908
$707$	−7.13040e36	+	7.13040e36i	−0.646639	+	0.646639i
$708$	1.60558e36	+	1.60558e36i	0.142955	+	0.142955i
$709$		−	1.30662e37i		−	1.14222i	−0.820875	−	0.571108i	$-0.806514\pi$
$709$		−	1.30662e37i		−	1.14222i	0.820875	−	0.571108i	$-0.193486\pi$
$710$	3.61713e36	+	1.94234e37i	0.310460	+	1.66712i
$711$	6.82768e36			0.575398
$712$	4.57817e36	−	4.57817e36i	0.378836	−	0.378836i
$713$	8.58736e36	+	8.58736e36i	0.697743	+	0.697743i
$714$		−	2.18684e36i		−	0.174478i
$715$	−4.49653e36	+	8.37370e35i	−0.352289	+	0.0656053i
$716$	−2.59836e37			−1.99908
$717$	−2.34942e34	+	2.34942e34i	−0.00177505	+	0.00177505i
$718$	2.75286e36	+	2.75286e36i	0.204252	+	0.204252i
$719$		−	2.21512e37i		−	1.61407i	−0.590506	−	0.807033i	$-0.701072\pi$
$719$		−	2.21512e37i		−	1.61407i	0.590506	−	0.807033i	$-0.298928\pi$
$720$	5.15049e36	+	3.53334e36i	0.368575	+	0.252850i
$721$	2.35945e37			1.65826
$722$	−1.58390e37	+	1.58390e37i	−1.09331	+	1.09331i
$723$	−7.16660e35	−	7.16660e35i	−0.0485865	−	0.0485865i
$724$		−	2.24947e37i		−	1.49789i
$725$	1.30364e37	−	5.02986e36i	0.852635	−	0.328974i
$726$	−1.65611e36			−0.106393
$727$	−9.58321e34	+	9.58321e34i	−0.00604733	+	0.00604733i	−0.710124	−	0.704077i	$-0.751361\pi$
$727$	−9.58321e34	+	9.58321e34i	−0.00604733	+	0.00604733i	0.704077	+	0.710124i	$0.251361\pi$
$728$	1.14835e37	+	1.14835e37i	0.711816	+	0.711816i
$729$			1.58742e37i			0.966570i
$730$	−1.16162e37	+	1.69328e37i	−0.694814	+	1.01282i
$731$	4.57095e36			0.268584
$732$	9.54773e35	−	9.54773e35i	0.0551133	−	0.0551133i
$733$	1.42443e37	+	1.42443e37i	0.807771	+	0.807771i	0.984296	−	0.176525i	$-0.0564858\pi$
$733$	1.42443e37	+	1.42443e37i	0.807771	+	0.807771i	−0.176525	+	0.984296i	$0.556486\pi$
$734$			2.05876e37i			1.14698i
$735$	−1.78913e35	−	9.60729e35i	−0.00979276	−	0.0525854i
$736$	−1.73254e37			−0.931692
$737$	3.09720e36	−	3.09720e36i	0.163641	−	0.163641i
$738$	1.24661e37	+	1.24661e37i	0.647139	+	0.647139i
$739$		−	3.72231e37i		−	1.89861i	−0.314362	−	0.949303i	$-0.601790\pi$
$739$		−	3.72231e37i		−	1.89861i	0.314362	−	0.949303i	$-0.398210\pi$
$740$	−2.22612e37	+	4.14560e36i	−1.11567	+	0.207766i
$741$	−5.56010e34			−0.00273808
$742$	5.02470e37	−	5.02470e37i	2.43142	−	2.43142i
$743$	−2.34225e37	−	2.34225e37i	−1.11372	−	1.11372i	−0.992642	−	0.121082i	$-0.961363\pi$
$743$	−2.34225e37	−	2.34225e37i	−1.11372	−	1.11372i	−0.121082	−	0.992642i	$-0.538637\pi$
$744$		−	1.35325e36i		−	0.0632308i
$745$	−2.67387e36	−	1.83433e36i	−0.122775	−	0.0842260i
$746$	1.07777e37			0.486320
$747$	9.08965e36	−	9.08965e36i	0.403069	−	0.403069i
$748$	−7.41528e36	−	7.41528e36i	−0.323152	−	0.323152i
$749$			3.90721e37i			1.67341i
$750$	2.67626e36	+	6.35240e35i	0.112650	+	0.0267388i
$751$	−1.24516e37			−0.515115			−0.257558	−	0.966263i	$-0.582918\pi$
$751$	−1.24516e37			−0.515115			−0.257558	+	0.966263i	$0.582918\pi$
$752$	1.34929e37	−	1.34929e37i	0.548624	−	0.548624i
$753$	1.02610e35	+	1.02610e35i	0.00410068	+	0.00410068i
$754$			4.53108e37i			1.77981i
$755$	−9.42516e36	+	1.37389e37i	−0.363897	+	0.530447i
$756$	−7.18144e36			−0.272539
$757$	3.91841e36	−	3.91841e36i	0.146172	−	0.146172i	−0.630234	−	0.776406i	$-0.717041\pi$
$757$	3.91841e36	−	3.91841e36i	0.146172	−	0.146172i	0.776406	+	0.630234i	$0.217041\pi$
$758$	−2.76830e36	−	2.76830e36i	−0.101511	−	0.101511i
$759$			4.21506e35i			0.0151936i
$760$	−9.17726e34	−	4.92803e35i	−0.00325190	−	0.0174621i
$761$	4.63473e37			1.61445			0.807223	−	0.590247i	$-0.200970\pi$
$761$	4.63473e37			1.61445			0.807223	+	0.590247i	$0.200970\pi$
$762$	9.45867e34	−	9.45867e34i	0.00323903	−	0.00323903i
$763$	2.95181e37	+	2.95181e37i	0.993732	+	0.993732i
$764$		−	2.98297e37i		−	0.987270i
$765$	−3.45733e37	+	6.43844e36i	−1.12497	+	0.209499i
$766$	−3.30577e37			−1.05755
$767$	−5.48145e37	+	5.48145e37i	−1.72407	+	1.72407i
$768$	2.92642e35	+	2.92642e35i	0.00904985	+	0.00904985i
$769$		−	3.88888e36i		−	0.118245i	−0.998251	−	0.0591224i	$-0.981170\pi$
$769$		−	3.88888e36i		−	0.118245i	0.998251	−	0.0591224i	$-0.0188302\pi$
$770$	−1.59159e37	−	1.09186e37i	−0.475830	−	0.326429i
$771$	2.69092e36			0.0791031
$772$	−4.21407e36	+	4.21407e36i	−0.121808	+	0.121808i
$773$	−7.78554e36	−	7.78554e36i	−0.221287	−	0.221287i	0.587753	−	0.809040i	$-0.300012\pi$
$773$	−7.78554e36	−	7.78554e36i	−0.221287	−	0.221287i	−0.809040	+	0.587753i	$0.800012\pi$
$774$		−	1.28505e37i		−	0.359158i
$775$	−1.81216e37	−	4.69675e37i	−0.498051	−	1.29085i
$776$	3.60904e37			0.975416
$777$	−2.12100e36	+	2.12100e36i	−0.0563726	+	0.0563726i
$778$	−2.19232e37	−	2.19232e37i	−0.573018	−	0.573018i
$779$			6.72821e35i			0.0172947i
$780$	−2.93872e36	+	4.28372e36i	−0.0742896	+	0.108291i
$781$	1.25504e37			0.312029
$782$	3.67268e37	−	3.67268e37i	0.898040	−	0.898040i
$783$	−4.00965e36	−	4.00965e36i	−0.0964280	−	0.0964280i
$784$		−	1.35858e37i		−	0.321348i
$785$	−2.74640e36	−	1.47477e37i	−0.0638936	−	0.343098i
$786$	4.97938e35			0.0113941
$787$	−1.85666e37	+	1.85666e37i	−0.417888	+	0.417888i	−0.884475	−	0.466587i	$-0.845483\pi$
$787$	−1.85666e37	+	1.85666e37i	−0.417888	+	0.417888i	0.466587	+	0.884475i	$0.345483\pi$
$788$	−4.22071e37	−	4.22071e37i	−0.934425	−	0.934425i
$789$			3.50037e36i			0.0762276i
$790$	4.10944e37	−	7.65283e36i	0.880299	−	0.163934i
$791$	−6.32140e37			−1.33205
$792$	−5.89981e36	+	5.89981e36i	−0.122296	+	0.122296i
$793$	3.25960e37	+	3.25960e37i	0.664680	+	0.664680i
$794$		−	8.04839e35i		−	0.0161452i
$795$	5.30462e36	+	3.63907e36i	0.104684	+	0.0718154i
$796$	3.66111e37			0.710793
$797$	4.55035e36	−	4.55035e36i	0.0869133	−	0.0869133i	−0.662313	−	0.749227i	$-0.730425\pi$
$797$	4.55035e36	−	4.55035e36i	0.0869133	−	0.0869133i	0.749227	+	0.662313i	$0.230425\pi$
$798$	−1.65909e35	−	1.65909e35i	−0.00311768	−	0.00311768i
$799$			1.07440e38i			1.98636i
$800$	6.56603e37	+	2.90991e37i	1.19435	+	0.529309i
$801$	−4.87350e37			−0.872204
$802$	2.08298e35	−	2.08298e35i	0.00366791	−	0.00366791i
$803$	9.22350e36	+	9.22350e36i	0.159806	+	0.159806i
$804$		−	4.97480e36i		−	0.0848100i
$805$	3.14960e37	−	4.59112e37i	0.528334	−	0.770145i
$806$	1.63246e38			2.69455
$807$	4.17139e36	−	4.17139e36i	0.0677525	−	0.0677525i
$808$	1.88711e37	+	1.88711e37i	0.301613	+	0.301613i
$809$			3.55257e36i			0.0558743i	0.999610	+	0.0279372i	$0.00889383\pi$
$809$			3.55257e36i			0.0558743i	−0.999610	+	0.0279372i	$0.991106\pi$
$810$	1.79981e37	+	9.66469e37i	0.278562	+	1.49583i
$811$	−8.50898e37			−1.29600			−0.648002	−	0.761639i	$-0.724395\pi$
$811$	−8.50898e37			−1.29600			−0.648002	+	0.761639i	$0.724395\pi$
$812$	−7.87444e37	+	7.87444e37i	−1.18030	+	1.18030i
$813$	5.58032e35	+	5.58032e35i	0.00823156	+	0.00823156i
$814$			2.46973e37i			0.358536i
$815$	8.35693e37	−	1.55628e37i	1.19398	−	0.222350i
$816$	2.75219e36			0.0386995
$817$	3.46783e35	−	3.46783e35i	0.00479923	−	0.00479923i
$818$	−9.22443e37	−	9.22443e37i	−1.25645	−	1.25645i
$819$		−	1.22243e38i		−	1.63883i
$820$	5.18368e37	+	3.55611e37i	0.684004	+	0.469240i
$821$	1.21680e38			1.58037			0.790185	−	0.612868i	$-0.209984\pi$
$821$	1.21680e38			1.58037			0.790185	+	0.612868i	$0.209984\pi$
$822$	6.34986e36	−	6.34986e36i	0.0811765	−	0.0811765i
$823$	2.49097e37	+	2.49097e37i	0.313452	+	0.313452i	0.846245	−	0.532794i	$-0.178858\pi$
$823$	2.49097e37	+	2.49097e37i	0.313452	+	0.313452i	−0.532794	+	0.846245i	$0.678858\pi$
$824$		−	6.24446e37i		−	0.773466i
$825$	7.07944e35	−	1.59743e36i	0.00863172	−	0.0194770i
$826$	−3.27124e38			−3.92619
$827$	3.02704e37	−	3.02704e37i	0.357640	−	0.357640i	−0.505302	−	0.862942i	$-0.668619\pi$
$827$	3.02704e37	−	3.02704e37i	0.357640	−	0.357640i	0.862942	+	0.505302i	$0.168619\pi$
$828$	−6.01350e37	−	6.01350e37i	−0.699412	−	0.699412i
$829$			2.53344e37i			0.290069i	0.989427	+	0.145035i	$0.0463294\pi$
$829$			2.53344e37i			0.290069i	−0.989427	+	0.145035i	$0.953671\pi$
$830$	4.45205e37	−	6.48969e37i	0.501817	−	0.731490i
$831$	−1.05644e37			−0.117228
$832$	−1.28064e38	+	1.28064e38i	−1.39902	+	1.39902i
$833$	5.40897e37	+	5.40897e37i	0.581741	+	0.581741i
$834$			1.43477e37i			0.151923i
$835$	−1.92676e37	−	1.03464e38i	−0.200864	−	1.07861i
$836$	−1.12515e36			−0.0115486
$837$	−1.44460e37	+	1.44460e37i	−0.145987	+	0.145987i
$838$	−1.20601e38	−	1.20601e38i	−1.19999	−	1.19999i
$839$		−	1.15547e38i		−	1.13202i	−0.824399	−	0.566009i	$-0.808487\pi$
$839$		−	1.15547e38i		−	1.13202i	0.824399	−	0.566009i	$-0.191513\pi$
$840$	−6.09914e36	+	1.13582e36i	−0.0588353	+	0.0109566i
$841$	1.73491e37			0.164790
$842$	−2.71023e37	+	2.71023e37i	−0.253483	+	0.253483i
$843$	−8.84209e36	−	8.84209e36i	−0.0814323	−	0.0814323i
$844$			9.03024e37i			0.818932i
$845$	−5.39070e37	−	3.69813e37i	−0.481403	−	0.330252i
$846$	3.02050e38			2.65622
$847$	9.82586e37	−	9.82586e37i	0.850915	−	0.850915i
$848$	6.32369e37	+	6.32369e37i	0.539293	+	0.539293i
$849$			2.83038e36i			0.0237709i
$850$	−2.00873e38	+	7.75033e37i	−1.66140	+	0.641024i
$851$	−7.12422e37			−0.580301
$852$	1.00794e37	−	1.00794e37i	0.0808575	−	0.0808575i
$853$	8.06083e37	+	8.06083e37i	0.636858	+	0.636858i	0.949779	−	0.312921i	$-0.101308\pi$
$853$	8.06083e37	+	8.06083e37i	0.636858	+	0.636858i	−0.312921	+	0.949779i	$0.601308\pi$
$854$			1.94527e38i			1.51366i
$855$	−2.13450e36	+	3.11143e36i	−0.0163583	+	0.0238452i
$856$	1.03407e38			0.780532
$857$	−6.92117e37	+	6.92117e37i	−0.514552	+	0.514552i	−0.915918	−	0.401366i	$-0.868536\pi$
$857$	−6.92117e37	+	6.92117e37i	−0.514552	+	0.514552i	0.401366	+	0.915918i	$0.368536\pi$
$858$	4.00642e36	+	4.00642e36i	0.0293374	+	0.0293374i
$859$			1.81048e38i			1.30582i	0.757436	+	0.652909i	$0.226452\pi$
$859$			1.81048e38i			1.30582i	−0.757436	+	0.652909i	$0.773548\pi$
$860$	−8.38879e36	−	4.50463e37i	−0.0595963	−	0.320022i
$861$	8.32712e36			0.0582712
$862$	1.43753e38	−	1.43753e38i	0.990885	−	0.990885i
$863$	−8.05209e37	−	8.05209e37i	−0.546724	−	0.546724i	0.378768	−	0.925492i	$-0.376348\pi$
$863$	−8.05209e37	−	8.05209e37i	−0.546724	−	0.546724i	−0.925492	+	0.378768i	$0.876348\pi$
$864$		−	2.91455e37i		−	0.194936i
$865$	3.60475e37	−	6.71298e36i	0.237501	−	0.0442289i
$866$	−9.96016e37			−0.646448
$867$	−2.68292e36	+	2.68292e36i	−0.0171537	+	0.0171537i
$868$	2.83700e38	+	2.83700e38i	1.78691	+	1.78691i
$869$		−	2.65532e37i		−	0.164763i
$870$	−1.42735e37	−	9.79193e36i	−0.0872532	−	0.0598574i
$871$	1.69840e38			1.02283
$872$	7.81217e37	−	7.81217e37i	0.463508	−	0.463508i
$873$	−1.92093e38	−	1.92093e38i	−1.12286	−	1.12286i
$874$		−	5.57269e36i		−	0.0320934i
$875$	−1.96475e38	+	1.21096e38i	−1.11481	+	0.687108i
$876$	1.48150e37			0.0828226
$877$	1.19542e38	−	1.19542e38i	0.658455	−	0.658455i	−0.296559	−	0.955014i	$-0.595839\pi$
$877$	1.19542e38	−	1.19542e38i	0.658455	−	0.658455i	0.955014	+	0.296559i	$0.0958392\pi$
$878$	4.09900e37	+	4.09900e37i	0.222458	+	0.222458i
$879$			1.36875e37i			0.0731926i
$880$	1.37413e37	−	2.00305e37i	0.0724025	−	0.105540i
$881$	−6.33187e37			−0.328735			−0.164367	−	0.986399i	$-0.552558\pi$
$881$	−6.33187e37			−0.328735			−0.164367	+	0.986399i	$0.552558\pi$
$882$	1.52064e38	−	1.52064e38i	0.777920	−	0.777920i
$883$	−3.05685e37	−	3.05685e37i	−0.154094	−	0.154094i	0.625850	−	0.779944i	$-0.284752\pi$
$883$	−3.05685e37	−	3.05685e37i	−0.154094	−	0.154094i	−0.779944	+	0.625850i	$0.784752\pi$
$884$		−	4.06628e38i		−	2.01985i
$885$	−5.42161e36	−	2.91131e37i	−0.0265379	−	0.142504i
$886$	−3.06525e37			−0.147852
$887$	−1.07750e38	+	1.07750e38i	−0.512167	+	0.512167i	−0.915190	−	0.403023i	$-0.867959\pi$
$887$	−1.07750e38	+	1.07750e38i	−0.512167	+	0.512167i	0.403023	+	0.915190i	$0.367959\pi$
$888$	5.61338e36	+	5.61338e36i	0.0262940	+	0.0262940i
$889$			1.12238e37i			0.0518106i
$890$	−2.93326e38	+	5.46248e37i	−1.33438	+	0.248496i
$891$	6.24485e37			0.279970
$892$	1.43952e37	−	1.43952e37i	0.0636027	−	0.0636027i
$893$	8.15113e36	+	8.15113e36i	0.0354935	+	0.0354935i
$894$			4.01682e36i			0.0172383i
$895$	2.79443e38	+	1.91703e38i	1.18194	+	0.810831i
$896$	−3.53872e38			−1.47517
$897$	−1.15570e37	+	1.15570e37i	−0.0474834	+	0.0474834i
$898$	1.00358e38	+	1.00358e38i	0.406406	+	0.406406i
$899$			3.16799e38i			1.26447i
$900$	1.26901e38	+	3.28901e38i	0.499242	+	1.29394i
$901$	−5.03536e38			−1.95258
$902$	4.84812e37	−	4.84812e37i	0.185306	−	0.185306i
$903$	−4.29193e36	−	4.29193e36i	−0.0161701	−	0.0161701i
$904$			1.67300e38i			0.621309i
$905$	−1.65963e38	+	2.41921e38i	−0.607546	+	0.885610i
$906$	2.06392e37			0.0744778
$907$	1.17592e38	−	1.17592e38i	0.418294	−	0.418294i	−0.466321	−	0.884615i	$-0.654421\pi$
$907$	1.17592e38	−	1.17592e38i	0.418294	−	0.418294i	0.884615	+	0.466321i	$0.154421\pi$
$908$	1.60811e38	+	1.60811e38i	0.563896	+	0.563896i
$909$		−	2.00885e38i		−	0.694410i
$910$	−1.37017e38	−	7.35756e38i	−0.466913	−	2.50724i
$911$	4.02801e38			1.35317			0.676585	−	0.736365i	$-0.263459\pi$
$911$	4.02801e38			1.35317			0.676585	+	0.736365i	$0.263459\pi$
$912$	2.08799e35	−	2.08799e35i	0.000691507	−	0.000691507i
$913$	−3.53501e37	−	3.53501e37i	−0.115417	−	0.115417i
$914$		−	6.05720e38i		−	1.94971i
$915$	−1.73124e37	+	3.22401e36i	−0.0549392	+	0.0102311i
$916$	−6.19837e38			−1.93926
$917$	−2.95431e37	+	2.95431e37i	−0.0911287	+	0.0911287i
$918$	6.17832e37	+	6.17832e37i	0.187895	+	0.187895i
$919$		−	4.81218e38i		−	1.44291i	−0.692460	−	0.721456i	$-0.743473\pi$
$919$		−	4.81218e38i		−	1.44291i	0.692460	−	0.721456i	$-0.256527\pi$
$920$	−1.21507e38	−	8.33564e37i	−0.359220	−	0.246432i
$921$	3.21727e37			0.0937804
$922$	−3.68625e38	+	3.68625e38i	−1.05946	+	1.05946i
$923$	3.44111e38	+	3.44111e38i	0.975161	+	0.975161i
$924$			1.39253e37i			0.0389107i
$925$	2.69995e38	+	1.19655e38i	0.743899	+	0.329678i
$926$	1.08690e39			2.95289
$927$	−3.32364e38	+	3.32364e38i	−0.890384	+	0.890384i
$928$	−3.19579e38	−	3.19579e38i	−0.844219	−	0.844219i
$929$		−	3.71177e38i		−	0.966889i	−0.875375	−	0.483444i	$-0.839386\pi$
$929$		−	3.71177e38i		−	0.966889i	0.875375	−	0.483444i	$-0.160614\pi$
$930$	−3.52784e37	+	5.14248e37i	−0.0906214	+	0.132097i
$931$	8.20722e36			0.0207898
$932$	−2.25293e38	+	2.25293e38i	−0.562783	+	0.562783i
$933$	−2.49205e37	−	2.49205e37i	−0.0613898	−	0.0613898i
$934$			2.11740e38i			0.514391i
$935$	2.50394e37	+	1.34457e38i	0.0599892	+	0.322132i
$936$	−3.23525e38			−0.764402
$937$	−1.66704e37	+	1.66704e37i	−0.0388446	+	0.0388446i	−0.726262	−	0.687418i	$-0.758744\pi$
$937$	−1.66704e37	+	1.66704e37i	−0.0388446	+	0.0388446i	0.687418	+	0.726262i	$0.258744\pi$
$938$	5.06787e38	+	5.06787e38i	1.16463	+	1.16463i
$939$			6.91410e36i			0.0156705i
$940$	1.05881e39	−	1.97178e38i	2.36678	−	0.440755i
$941$	−3.76950e38			−0.831034			−0.415517	−	0.909585i	$-0.636399\pi$
$941$	−3.76950e38			−0.831034			−0.415517	+	0.909585i	$0.636399\pi$
$942$	−1.31402e37	+	1.31402e37i	−0.0285720	+	0.0285720i
$943$	1.39850e38	+	1.39850e38i	0.299922	+	0.299922i
$944$		−	4.11692e38i		−	0.870836i
$945$	7.72335e37	+	5.29837e37i	0.161136	+	0.110542i
$946$	−4.99760e37			−0.102844
$947$	5.14523e38	−	5.14523e38i	1.04437	−	1.04437i	0.0454024	−	0.998969i	$-0.485543\pi$
$947$	5.14523e38	−	5.14523e38i	1.04437	−	1.04437i	0.998969	−	0.0454024i	$-0.0144570\pi$
$948$	−2.13252e37	−	2.13252e37i	−0.0426957	−	0.0426957i
$949$			5.05785e38i			0.998861i
$950$	−9.35966e36	+	2.11195e37i	−0.0182328	+	0.0411412i
$951$	9.38923e36			0.0180419
$952$	3.43386e38	−	3.43386e38i	0.650881	−	0.650881i
$953$	−3.88881e38	−	3.88881e38i	−0.727125	−	0.727125i	0.242921	−	0.970046i	$-0.421894\pi$
$953$	−3.88881e38	−	3.88881e38i	−0.727125	−	0.727125i	−0.970046	+	0.242921i	$0.921894\pi$
$954$			1.41561e39i			2.61104i
$955$	−2.20080e38	+	3.20807e38i	−0.400439	+	0.583713i
$956$	−2.60709e37			−0.0467955
$957$	−7.77497e36	+	7.77497e36i	−0.0137671	+	0.0137671i
$958$	−2.14637e38	−	2.14637e38i	−0.374932	−	0.374932i
$959$			7.53487e38i			1.29848i
$960$	−1.26666e37	−	6.80174e37i	−0.0215344	−	0.115636i
$961$	5.45149e38			0.914347
$962$	−6.77158e38	+	6.77158e38i	−1.12051	+	1.12051i
$963$	−5.50388e38	−	5.50388e38i	−0.898519	−	0.898519i
$964$		−	7.95261e38i		−	1.28088i
$965$	7.64114e37	−	1.42298e37i	0.121424	−	0.0226122i
$966$	−6.89700e37			−0.108133
$967$	3.28550e38	−	3.28550e38i	0.508227	−	0.508227i	−0.405755	−	0.913982i	$-0.632991\pi$
$967$	3.28550e38	−	3.28550e38i	0.508227	−	0.508227i	0.913982	+	0.405755i	$0.132991\pi$
$968$	−2.60048e38	−	2.60048e38i	−0.396894	−	0.396894i
$969$			1.66260e36i			0.00250369i
$970$	−1.37147e39	−	9.40859e38i	−2.03777	−	1.39795i
$971$	4.07409e38			0.597284			0.298642	−	0.954365i	$-0.403466\pi$
$971$	4.07409e38			0.597284			0.298642	+	0.954365i	$0.403466\pi$
$972$	1.51884e38	−	1.51884e38i	0.219710	−	0.219710i
$973$	−8.51265e38	−	8.51265e38i	−1.21506	−	1.21506i
$974$			6.37767e38i			0.898247i
$975$	6.32094e37	−	2.43882e37i	0.0878460	−	0.0338938i
$976$	−2.44817e38			−0.335732
$977$	−3.81179e37	+	3.81179e37i	−0.0515822	+	0.0515822i	−0.732427	−	0.680845i	$-0.761613\pi$
$977$	−3.81179e37	+	3.81179e37i	−0.0515822	+	0.0515822i	0.680845	+	0.732427i	$0.261613\pi$
$978$	−7.44604e37	−	7.44604e37i	−0.0994306	−	0.0994306i
$979$			1.89533e38i			0.249752i
$980$	4.33782e38	−	6.32317e38i	0.564069	−	0.822235i
$981$	−8.31612e38			−1.06715
$982$	6.97243e38	−	6.97243e38i	0.882948	−	0.882948i
$983$	−9.88158e38	−	9.88158e38i	−1.23490	−	1.23490i	−0.962060	−	0.272837i	$-0.912038\pi$
$983$	−9.88158e38	−	9.88158e38i	−1.23490	−	1.23490i	−0.272837	−	0.962060i	$-0.587962\pi$
$984$		−	2.20383e37i		−	0.0271795i
$985$	1.42522e38	+	7.65318e38i	0.173465	+	0.931475i
$986$	1.35490e39			1.62745
$987$	1.00882e38	−	1.00882e38i	0.119589	−	0.119589i
$988$	−3.08496e37	−	3.08496e37i	−0.0360918	−	0.0360918i
$989$		−	1.44161e38i		−	0.166455i
$990$	3.78004e38	−	7.03941e37i	0.430764	−	0.0802193i
$991$	1.01547e39			1.14211			0.571056	−	0.820911i	$-0.306534\pi$
$991$	1.01547e39			1.14211			0.571056	+	0.820911i	$0.306534\pi$
$992$	−1.15138e39	+	1.15138e39i	−1.27811	+	1.27811i
$993$	9.12640e37	+	9.12640e37i	0.0999906	+	0.0999906i
$994$			2.05360e39i			2.22071i
$995$	−3.93738e38	−	2.70112e38i	−0.420249	−	0.288299i
$996$	−5.67802e37			−0.0598171
$997$	−2.28478e38	+	2.28478e38i	−0.237579	+	0.237579i	−0.815847	−	0.578268i	$-0.803729\pi$
$997$	−2.28478e38	+	2.28478e38i	−0.237579	+	0.237579i	0.578268	+	0.815847i	$0.303729\pi$
$998$	8.61005e38	+	8.61005e38i	0.883707	+	0.883707i
$999$		−	1.19846e38i		−	0.121415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.27.c.a.3.3	yes	24
5.2	odd	4	inner	5.27.c.a.2.3	✓	24
5.3	odd	4		25.27.c.b.7.10		24
5.4	even	2		25.27.c.b.18.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.27.c.a.2.3	✓	24	5.2	odd	4	inner
5.27.c.a.3.3	yes	24	1.1	even	1	trivial
25.27.c.b.7.10		24	5.3	odd	4
25.27.c.b.18.10		24	5.4	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 27 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8964.00 + 8964.00i) q^{2} +(-84346.8 - 84346.8i) q^{3} -9.35978e7i q^{4} +(-6.90551e8 + 1.00661e9i) q^{5} +1.51217e9 q^{6} +(-8.97185e10 + 8.97185e10i) q^{7} +(2.37446e11 + 2.37446e11i) q^{8} -2.52764e12i q^{9} +O(q^{10})\)	\(q+(-8964.00 + 8964.00i) q^{2} +(-84346.8 - 84346.8i) q^{3} -9.35978e7i q^{4} +(-6.90551e8 + 1.00661e9i) q^{5} +1.51217e9 q^{6} +(-8.97185e10 + 8.97185e10i) q^{7} +(2.37446e11 + 2.37446e11i) q^{8} -2.52764e12i q^{9} +(-2.83311e12 - 1.52133e13i) q^{10} -9.83010e12 q^{11} +(-7.89467e12 + 7.89467e12i) q^{12} +(-2.69524e14 - 2.69524e14i) q^{13} -1.60847e15i q^{14} +(1.43150e14 - 2.66582e13i) q^{15} +2.02430e15 q^{16} +(-8.05943e15 + 8.05943e15i) q^{17} +(2.26577e16 + 2.26577e16i) q^{18} +1.22289e15i q^{19} +(9.42160e16 + 6.46340e16i) q^{20} +1.51349e16 q^{21} +(8.81170e16 - 8.81170e16i) q^{22} +(2.54183e17 + 2.54183e17i) q^{23} -4.00557e16i q^{24} +(-5.36394e17 - 1.39023e18i) q^{25} +4.83203e18 q^{26} +(-4.27596e17 + 4.27596e17i) q^{27} +(8.39745e18 + 8.39745e18i) q^{28} +9.37717e18i q^{29} +(-1.04423e18 + 1.52216e18i) q^{30} +3.37841e19 q^{31} +(-3.40806e19 + 3.40806e19i) q^{32} +(8.29138e17 + 8.29138e17i) q^{33} -1.44489e20i q^{34} +(-2.83559e19 - 1.52266e20i) q^{35} -2.36581e20 q^{36} +(-1.40139e20 + 1.40139e20i) q^{37} +(-1.09619e19 - 1.09619e19i) q^{38} +4.54670e19i q^{39} +(-4.02984e20 + 7.50460e19i) q^{40} +5.50191e20 q^{41} +(-1.35670e20 + 1.35670e20i) q^{42} +(-2.83578e20 - 2.83578e20i) q^{43} +9.20075e20i q^{44} +(2.54433e21 + 1.74546e21i) q^{45} -4.55700e21 q^{46} +(6.66549e21 - 6.66549e21i) q^{47} +(-1.70743e20 - 1.70743e20i) q^{48} -6.71135e21i q^{49} +(1.72702e22 + 7.65375e21i) q^{50} +1.35957e21 q^{51} +(-2.52269e22 + 2.52269e22i) q^{52} +(3.12389e22 + 3.12389e22i) q^{53} -7.66595e21i q^{54} +(6.78819e21 - 9.89503e21i) q^{55} -4.26067e22 q^{56} +(1.03147e20 - 1.03147e20i) q^{57} +(-8.40570e22 - 8.40570e22i) q^{58} -2.03375e23i q^{59} +(-2.49515e21 - 1.33985e22i) q^{60} -1.20939e23 q^{61} +(-3.02841e23 + 3.02841e23i) q^{62} +(2.26776e23 + 2.26776e23i) q^{63} -4.75148e23i q^{64} +(4.57425e23 - 8.51843e22i) q^{65} -1.48648e22 q^{66} +(-3.15073e23 + 3.15073e23i) q^{67} +(7.54345e23 + 7.54345e23i) q^{68} -4.28791e22i q^{69} +(1.61910e24 + 1.11073e24i) q^{70} -1.27673e24 q^{71} +(6.00178e23 - 6.00178e23i) q^{72} +(-9.38292e23 - 9.38292e23i) q^{73} -2.51242e24i q^{74} +(-7.20180e22 + 1.62504e23i) q^{75} +1.14459e23 q^{76} +(8.81942e23 - 8.81942e23i) q^{77} +(-4.07566e23 - 4.07566e23i) q^{78} +2.70121e24i q^{79} +(-1.39788e24 + 2.03767e24i) q^{80} -6.35278e24 q^{81} +(-4.93192e24 + 4.93192e24i) q^{82} +(3.59611e24 + 3.59611e24i) q^{83} -1.41660e24i q^{84} +(-2.54722e24 - 1.36781e25i) q^{85} +5.08398e24 q^{86} +(7.90935e23 - 7.90935e23i) q^{87} +(-2.33412e24 - 2.33412e24i) q^{88} -1.92808e25i q^{89} +(-3.84537e25 + 7.16108e24i) q^{90} +4.83626e25 q^{91} +(2.37910e25 - 2.37910e25i) q^{92} +(-2.84958e24 - 2.84958e24i) q^{93} +1.19499e26i q^{94} +(-1.23096e24 - 8.44465e23i) q^{95} +5.74918e24 q^{96} +(7.59970e25 - 7.59970e25i) q^{97} +(6.01606e25 + 6.01606e25i) q^{98} +2.48469e25i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8}+O(q^{10}) \) 24 * q + 8190 * q^2 + 1867680 * q^3 - 140947920 * q^5 - 3382472712 * q^6 - 99234643200 * q^7 - 2004366809340 * q^8	\( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8} - 1486502924970 q^{10} - 60046450487712 q^{11} + 474303804173880 q^{12} - 175933888149240 q^{13} + 81\!\cdots\!60 q^{15}+ \cdots + 37\!\cdots\!90 q^{98}+O(q^{100}) \) 24 * q + 8190 * q^2 + 1867680 * q^3 - 140947920 * q^5 - 3382472712 * q^6 - 99234643200 * q^7 - 2004366809340 * q^8 - 1486502924970 * q^10 - 60046450487712 * q^11 + 474303804173880 * q^12 - 175933888149240 * q^13 + 8120813383152960 * q^15 - 33177982875701256 * q^16 + 13120603958605320 * q^17 + 30866287060816530 * q^18 - 155387715501860460 * q^20 + 711072085237596768 * q^21 - 1230085358274609120 * q^22 - 95943648493582560 * q^23 - 2199572636699820600 * q^25 + 5610652365807815508 * q^26 - 4182554138103802080 * q^27 + 9022697066815419960 * q^28 - 73497992102613921840 * q^30 + 136536207174201936768 * q^31 - 313156508993493901560 * q^32 + 310679334418782310560 * q^33 - 294265004156402368320 * q^35 + 1280456324930471178684 * q^36 - 813771390050070972840 * q^37 - 241574669977239410760 * q^38 - 634199087129857022100 * q^40 - 1209719584341877336992 * q^41 + 3329982079791874237920 * q^42 - 2155184970418473088800 * q^43 + 8900452148996849486760 * q^45 - 9558960779134484923272 * q^46 + 14032272766974133560480 * q^47 - 23339469323152065294960 * q^48 - 5039825198339566324350 * q^50 - 34517174933375733238272 * q^51 + 89834235163276703786700 * q^52 - 76996005973852456719720 * q^53 + 61786508697335020764960 * q^55 + 140965426896397798196880 * q^56 - 373196499625490096640960 * q^57 + 527990314981987315382160 * q^58 - 985009875968846023801320 * q^60 + 711008904295257078187488 * q^61 - 106522048356410497848120 * q^62 + 129194443701484657698720 * q^63 + 810043281159028896596760 * q^65 - 243183023298774209168544 * q^66 + 475247161241828436325920 * q^67 - 1328735440043135338553820 * q^68 - 1284031520218999793566920 * q^70 - 5316544531031301273526272 * q^71 + 6424730229084419392336260 * q^72 + 368145928043753098041240 * q^73 - 1071958391540662870531200 * q^75 - 193843537989214188398640 * q^76 + 10746086757941471790823200 * q^77 - 2877347849192885454991800 * q^78 - 155629044348497668149120 * q^80 - 13389238123125713812551096 * q^81 - 11578218915296284645122720 * q^82 + 25615096518304734510222720 * q^83 - 60208098774533809021022520 * q^85 + 56773655020233836832486168 * q^86 - 25953487917103015108688640 * q^87 + 117068604801345686184349920 * q^88 - 128643549677224721883790890 * q^90 - 19525332839000266679349312 * q^91 + 18999183544674712785412920 * q^92 + 207592489093568143530468960 * q^93 - 172205668812635374982450400 * q^95 - 605527074895544071145393952 * q^96 + 347025186458821372557867480 * q^97 + 372096096878694378037335390 * q^98

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