LMFDB - Embedded newform 3.35.b.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,35,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 35, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 35);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 35 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.9676962128$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 789518143 x^{8} + \cdots + 50\!\cdots\!00 $ x^10 + 789518143x^8 + 211496483076151936x^6 + 21382790524640936160081920x^4 + 613809329098098496707904510361600x^2 + 5042460246515433703013776627104481280000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.10
Root			$17330.4i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.35.b.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+207965. i q^{2} +(7.87239e7 - 1.02371e8i) q^{3} -2.60695e10 q^{4} +2.95819e11i q^{5} +(2.12895e13 + 1.63718e13i) q^{6} +4.71207e13 q^{7} -1.84873e15i q^{8} +(-4.28228e15 - 1.61180e16i) q^{9} +O(q^{10})$	\(q+207965. i q^{2} +(7.87239e7 - 1.02371e8i) q^{3} -2.60695e10 q^{4} +2.95819e11i q^{5} +(2.12895e13 + 1.63718e13i) q^{6} +4.71207e13 q^{7} -1.84873e15i q^{8} +(-4.28228e15 - 1.61180e16i) q^{9} -6.15199e16 q^{10} +7.77245e17i q^{11} +(-2.05229e18 + 2.66875e18i) q^{12} -1.72495e19 q^{13} +9.79946e18i q^{14} +(3.02831e19 + 2.32880e19i) q^{15} -6.33991e19 q^{16} -6.96601e20i q^{17} +(3.35198e21 - 8.90563e20i) q^{18} -3.45404e21 q^{19} -7.71185e21i q^{20} +(3.70953e21 - 4.82378e21i) q^{21} -1.61640e23 q^{22} +2.79978e22i q^{23} +(-1.89256e23 - 1.45540e23i) q^{24} +4.94568e23 q^{25} -3.58728e24i q^{26} +(-1.98713e24 - 8.30494e23i) q^{27} -1.22841e24 q^{28} +4.47878e24i q^{29} +(-4.84309e24 + 6.29783e24i) q^{30} -3.00896e25 q^{31} -4.49458e25i q^{32} +(7.95669e25 + 6.11877e25i) q^{33} +1.44869e26 q^{34} +1.39392e25i q^{35} +(1.11637e26 + 4.20189e26i) q^{36} +9.35312e25 q^{37} -7.18319e26i q^{38} +(-1.35795e27 + 1.76584e27i) q^{39} +5.46890e26 q^{40} -2.03614e27i q^{41} +(1.00318e27 + 7.71452e26i) q^{42} -4.06643e27 q^{43} -2.02624e28i q^{44} +(4.76801e27 - 1.26678e27i) q^{45} -5.82256e27 q^{46} +1.79754e28i q^{47} +(-4.99102e27 + 6.49020e27i) q^{48} -5.18966e28 q^{49} +1.02853e29i q^{50} +(-7.13114e28 - 5.48392e28i) q^{51} +4.49685e29 q^{52} +2.88534e29i q^{53} +(1.72714e29 - 4.13253e29i) q^{54} -2.29923e29 q^{55} -8.71137e28i q^{56} +(-2.71916e29 + 3.53592e29i) q^{57} -9.31428e29 q^{58} +9.16791e29i q^{59} +(-7.89466e29 - 6.07107e29i) q^{60} -5.62818e29 q^{61} -6.25758e30i q^{62} +(-2.01784e29 - 7.59493e29i) q^{63} +8.25796e30 q^{64} -5.10271e30i q^{65} +(-1.27249e31 + 1.65471e31i) q^{66} +1.14688e31 q^{67} +1.81601e31i q^{68} +(2.86615e30 + 2.20410e30i) q^{69} -2.89886e30 q^{70} -1.71842e31i q^{71} +(-2.97979e31 + 7.91679e30i) q^{72} +4.19435e31 q^{73} +1.94512e31i q^{74} +(3.89343e31 - 5.06292e31i) q^{75} +9.00452e31 q^{76} +3.66243e31i q^{77} +(-3.67232e32 - 2.82405e32i) q^{78} -2.86486e31 q^{79} -1.87546e31i q^{80} +(-2.41453e32 + 1.38044e32i) q^{81} +4.23446e32 q^{82} +5.29892e32i q^{83} +(-9.67056e31 + 1.25754e32i) q^{84} +2.06068e32 q^{85} -8.45675e32i q^{86} +(4.58495e32 + 3.52587e32i) q^{87} +1.43692e33 q^{88} +3.88739e31i q^{89} +(2.63445e32 + 9.91579e32i) q^{90} -8.12808e32 q^{91} -7.29889e32i q^{92} +(-2.36877e33 + 3.08029e33i) q^{93} -3.73824e33 q^{94} -1.02177e33i q^{95} +(-4.60113e33 - 3.53831e33i) q^{96} +6.43166e33 q^{97} -1.07927e34i q^{98} +(1.25276e34 - 3.32838e33i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+O(q^{10}) $ 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9	$ 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+ \cdots + 25\!\cdots\!80 q^{99}+O(q^{100}) $ 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9 - 2611205560422720 * q^10 + 1839088058193784224 * q^12 + 3639874363106470052 * q^13 + 73840351311049043520 * q^15 - 458913568062658993664 * q^16 + 4458031837811233600320 * q^18 - 18128087575667617007644 * q^19 + 47155216574801503272132 * q^21 - 82944038352793331672640 * q^22 - 409540832361157949627904 * q^24 - 306157881917435527620230 * q^25 - 5188422304885629117270366 * q^27 + 1200257625823339935397952 * q^28 + 4536084230702466968226240 * q^30 - 16210124253435972809624620 * q^31 + 126080615773751026110338880 * q^33 - 95987113410493892068003584 * q^34 - 3778740843166378351675872 * q^36 + 1107877531995608327024550788 * q^37 - 1478567172848906073011055372 * q^39 + 1263325098820483891139005440 * q^40 - 1100302459230379163303563200 * q^42 - 9626706570211152095714911228 * q^43 + 6764773545409610284732206720 * q^45 - 27597232473865615892091763584 * q^46 - 8343379363160137604055750144 * q^48 + 123592722368423574378839845566 * q^49 - 154249157901217791265339790592 * q^51 + 364968511672502550561914224448 * q^52 - 627476296349871988055293152672 * q^54 + 613243149395194155294476807040 * q^55 - 200956522080425270978267102412 * q^57 + 911704545930429232428533728320 * q^58 - 5328764870697498499759490872320 * q^60 + 3721644688213000805892336114020 * q^61 - 17793115140162074693090527345068 * q^63 + 31237929890100178456062152876032 * q^64 - 56522434211150051720831749496640 * q^66 + 64610860820592975458220110976548 * q^67 - 75655347603668350171840261441152 * q^69 + 173956643092708582155719748059520 * q^70 - 251655858465803757687636471720960 * q^72 + 219744563327934154882825652170292 * q^73 - 496257346175691552817323610505790 * q^75 + 755138601297458545349651061598016 * q^76 - 1416035973322463045417779737274560 * q^78 + 1282143700776175332608732687725076 * q^79 - 1752271238163022185686811202609110 * q^81 + 2617087107433191584283809414490240 * q^82 - 3353754502177451840461431126935232 * q^84 + 3064318591304040683100089841123840 * q^85 - 1378895999771415686373632115051840 * q^87 + 2890193643030846777850875310341120 * q^88 - 3749676158586283582801263594857280 * q^90 + 3328617839789463835132355588364424 * q^91 - 913294458028957034010214182487068 * q^93 - 1912224205137436189468854646420224 * q^94 + 5756213457708614900907762734014464 * q^96 - 11994339580278056229821837667722092 * q^97 + 25463971047319347192017533065521280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			207965.i			1.58665i	0.608801	+	0.793323i	$0.291651\pi$
$2$			207965.i			1.58665i	−0.608801	+	0.793323i	$0.708349\pi$
$3$	7.87239e7	−	1.02371e8i	0.609600	−	0.792709i
$3$	7.87239e7	−	1.02371e8i	0.609600	−	0.792709i
$4$	−2.60695e10			−1.51745
$5$			2.95819e11i			0.387735i	0.981028	+	0.193868i	$0.0621033\pi$
$5$			2.95819e11i			0.387735i	−0.981028	+	0.193868i	$0.937897\pi$
$6$	2.12895e13	+	1.63718e13i	1.25775	+	0.967220i
$7$	4.71207e13			0.202556			0.101278	−	0.994858i	$-0.467707\pi$
$7$	4.71207e13			0.202556			0.101278	+	0.994858i	$0.467707\pi$
$8$		−	1.84873e15i		−	0.821003i
$9$	−4.28228e15	−	1.61180e16i	−0.256775	−	0.966471i
$10$	−6.15199e16			−0.615199
$11$			7.77245e17i			1.53774i	0.639407	+	0.768868i	$0.279180\pi$
$11$			7.77245e17i			1.53774i	−0.639407	+	0.768868i	$0.720820\pi$
$12$	−2.05229e18	+	2.66875e18i	−0.925036	+	1.20289i
$13$	−1.72495e19			−1.99406			−0.997031	−	0.0770014i	$-0.975465\pi$
$13$	−1.72495e19			−1.99406			−0.997031	+	0.0770014i	$0.975465\pi$
$14$			9.79946e18i			0.321385i
$15$	3.02831e19	+	2.32880e19i	0.307361	+	0.236364i
$16$	−6.33991e19			−0.214804
$17$		−	6.96601e20i		−	0.842078i	−0.907042	−	0.421039i	$-0.861665\pi$
$17$		−	6.96601e20i		−	0.842078i	0.907042	−	0.421039i	$-0.138335\pi$
$18$	3.35198e21	−	8.90563e20i	1.53345	−	0.407410i
$19$	−3.45404e21			−0.630255			−0.315128	−	0.949049i	$-0.602047\pi$
$19$	−3.45404e21			−0.630255			−0.315128	+	0.949049i	$0.602047\pi$
$20$		−	7.71185e21i		−	0.588368i
$21$	3.70953e21	−	4.82378e21i	0.123478	−	0.160568i
$22$	−1.61640e23			−2.43984
$23$			2.79978e22i			0.198495i	0.995063	+	0.0992477i	$0.0316436\pi$
$23$			2.79978e22i			0.198495i	−0.995063	+	0.0992477i	$0.968356\pi$
$24$	−1.89256e23	−	1.45540e23i	−0.650816	−	0.500484i
$25$	4.94568e23			0.849661
$26$		−	3.58728e24i		−	3.16387i
$27$	−1.98713e24	−	8.30494e23i	−0.922660	−	0.385614i
$28$	−1.22841e24			−0.307368
$29$			4.47878e24i			0.617154i	0.951199	+	0.308577i	$0.0998527\pi$
$29$			4.47878e24i			0.617154i	−0.951199	+	0.308577i	$0.900147\pi$
$30$	−4.84309e24	+	6.29783e24i	−0.375026	+	0.487674i
$31$	−3.00896e25			−1.33434			−0.667172	−	0.744903i	$-0.732496\pi$
$31$	−3.00896e25			−1.33434			−0.667172	+	0.744903i	$0.732496\pi$
$32$		−	4.49458e25i		−	1.16182i
$33$	7.95669e25	+	6.11877e25i	1.21898	+	0.937405i
$34$	1.44869e26			1.33608
$35$			1.39392e25i			0.0785382i
$36$	1.11637e26	+	4.20189e26i	0.389641	+	1.46657i
$37$	9.35312e25			0.204893			0.102447	−	0.994739i	$-0.467333\pi$
$37$	9.35312e25			0.204893			0.102447	+	0.994739i	$0.467333\pi$
$38$		−	7.18319e26i		−	0.999992i
$39$	−1.35795e27	+	1.76584e27i	−1.21558	+	1.58071i
$40$	5.46890e26			0.318332
$41$		−	2.03614e27i		−	0.778902i	−0.921047	−	0.389451i	$-0.872665\pi$
$41$		−	2.03614e27i		−	0.778902i	0.921047	−	0.389451i	$-0.127335\pi$
$42$	1.00318e27	+	7.71452e26i	0.254765	+	0.195916i
$43$	−4.06643e27			−0.692229			−0.346115	−	0.938192i	$-0.612499\pi$
$43$	−4.06643e27			−0.692229			−0.346115	+	0.938192i	$0.612499\pi$
$44$		−	2.02624e28i		−	2.33343i
$45$	4.76801e27	−	1.26678e27i	0.374735	−	0.0995606i
$46$	−5.82256e27			−0.314942
$47$			1.79754e28i			0.674550i	0.941406	+	0.337275i	$0.109505\pi$
$47$			1.79754e28i			0.674550i	−0.941406	+	0.337275i	$0.890495\pi$
$48$	−4.99102e27	+	6.49020e27i	−0.130945	+	0.170277i
$49$	−5.18966e28			−0.958971
$50$			1.02853e29i			1.34811i
$51$	−7.13114e28	−	5.48392e28i	−0.667523	−	0.513331i
$52$	4.49685e29			3.02588
$53$			2.88534e29i			1.40445i	0.711954	+	0.702226i	$0.247810\pi$
$53$			2.88534e29i			1.40445i	−0.711954	+	0.702226i	$0.752190\pi$
$54$	1.72714e29	−	4.13253e29i	0.611833	−	1.46394i
$55$	−2.29923e29			−0.596235
$56$		−	8.71137e28i		−	0.166299i
$57$	−2.71916e29	+	3.53592e29i	−0.384204	+	0.499609i
$58$	−9.31428e29			−0.979205
$59$			9.16791e29i			0.720752i	0.932807	+	0.360376i	$0.117352\pi$
$59$			9.16791e29i			0.720752i	−0.932807	+	0.360376i	$0.882648\pi$
$60$	−7.89466e29	−	6.07107e29i	−0.466404	−	0.358669i
$61$	−5.62818e29			−0.251050			−0.125525	−	0.992090i	$-0.540062\pi$
$61$	−5.62818e29			−0.251050			−0.125525	+	0.992090i	$0.540062\pi$
$62$		−	6.25758e30i		−	2.11713i
$63$	−2.01784e29	−	7.59493e29i	−0.0520113	−	0.195765i
$64$	8.25796e30			1.62860
$65$		−	5.10271e30i		−	0.773169i
$66$	−1.27249e31	+	1.65471e31i	−1.48733	+	1.93409i
$67$	1.14688e31			1.03812			0.519059	−	0.854739i	$-0.326283\pi$
$67$	1.14688e31			1.03812			0.519059	+	0.854739i	$0.326283\pi$
$68$			1.81601e31i			1.27781i
$69$	2.86615e30	+	2.20410e30i	0.157349	+	0.121003i
$70$	−2.89886e30			−0.124612
$71$		−	1.71842e31i		−	0.580415i	−0.956964	−	0.290207i	$-0.906276\pi$
$71$		−	1.71842e31i		−	0.580415i	0.956964	−	0.290207i	$-0.0937243\pi$
$72$	−2.97979e31	+	7.91679e30i	−0.793476	+	0.210813i
$73$	4.19435e31			0.883438			0.441719	−	0.897153i	$-0.354369\pi$
$73$	4.19435e31			0.883438			0.441719	+	0.897153i	$0.354369\pi$
$74$			1.94512e31i			0.325093i
$75$	3.89343e31	−	5.06292e31i	0.517954	−	0.673534i
$76$	9.00452e31			0.956378
$77$			3.66243e31i			0.311478i
$78$	−3.67232e32	−	2.82405e32i	−2.50803	−	1.92870i
$79$	−2.86486e31			−0.157559			−0.0787795	−	0.996892i	$-0.525102\pi$
$79$	−2.86486e31			−0.157559			−0.0787795	+	0.996892i	$0.525102\pi$
$80$		−	1.87546e31i		−	0.0832873i
$81$	−2.41453e32	+	1.38044e32i	−0.868134	+	0.496331i
$82$	4.23446e32			1.23584
$83$			5.29892e32i			1.25852i	0.777195	+	0.629260i	$0.216642\pi$
$83$			5.29892e32i			1.25852i	−0.777195	+	0.629260i	$0.783358\pi$
$84$	−9.67056e31	+	1.25754e32i	−0.187372	+	0.243653i
$85$	2.06068e32			0.326504
$86$		−	8.45675e32i		−	1.09832i
$87$	4.58495e32	+	3.52587e32i	0.489223	+	0.376217i
$88$	1.43692e33			1.26249
$89$			3.88739e31i			0.0281857i	0.999901	+	0.0140928i	$0.00448604\pi$
$89$			3.88739e31i			0.0281857i	−0.999901	+	0.0140928i	$0.995514\pi$
$90$	2.63445e32	+	9.91579e32i	0.157967	+	0.594572i
$91$	−8.12808e32			−0.403909
$92$		−	7.29889e32i		−	0.301206i
$93$	−2.36877e33	+	3.08029e33i	−0.813417	+	1.05775i
$94$	−3.73824e33			−1.07027
$95$		−	1.02177e33i		−	0.244372i
$96$	−4.60113e33	−	3.53831e33i	−0.920986	−	0.708247i
$97$	6.43166e33			1.07945			0.539727	−	0.841840i	$-0.318528\pi$
$97$	6.43166e33			1.07945			0.539727	+	0.841840i	$0.318528\pi$
$98$		−	1.07927e34i		−	1.52155i
$99$	1.25276e34	−	3.32838e33i	1.48618	−	0.394852i
$100$	−1.28931e34			−1.28931
$101$			1.21886e34i			1.02918i	0.857437	+	0.514589i	$0.172055\pi$
$101$			1.21886e34i			1.02918i	−0.857437	+	0.514589i	$0.827945\pi$
$102$	1.14046e34	−	1.48303e34i	0.814475	−	1.05912i
$103$	1.54380e33			0.0934027			0.0467013	−	0.998909i	$-0.485129\pi$
$103$	1.54380e33			0.0934027			0.0467013	+	0.998909i	$0.485129\pi$
$104$			3.18897e34i			1.63713i
$105$	1.42696e33	+	1.09735e33i	0.0622579	+	0.0478769i
$106$	−6.00049e34			−2.22837
$107$			3.86889e34i			1.22479i	0.790552	+	0.612395i	$0.209794\pi$
$107$			3.86889e34i			1.22479i	−0.790552	+	0.612395i	$0.790206\pi$
$108$	5.18035e34	+	2.16506e34i	1.40009	+	0.585148i
$109$	5.30295e34			1.22537			0.612684	−	0.790328i	$-0.290090\pi$
$109$	5.30295e34			1.22537			0.612684	+	0.790328i	$0.290090\pi$
$110$		−	4.78160e34i		−	0.946014i
$111$	7.36314e33	−	9.57484e33i	0.124903	−	0.162421i
$112$	−2.98741e33			−0.0435100
$113$		−	7.33157e34i		−	0.918044i	−0.888425	−	0.459022i	$-0.848200\pi$
$113$		−	7.33157e34i		−	0.918044i	0.888425	−	0.459022i	$-0.151800\pi$
$114$	−7.35347e34	−	5.65489e34i	−0.792702	−	0.609595i
$115$	−8.28227e33			−0.0769637
$116$		−	1.16760e35i		−	0.936498i
$117$	7.38670e34	+	2.78027e35i	0.512024	+	1.92720i
$118$	−1.90660e35			−1.14358
$119$		−	3.28244e34i		−	0.170568i
$120$	4.30533e34	−	5.59854e34i	0.194055	−	0.252345i
$121$	−3.48632e35			−1.36463
$122$		−	1.17046e35i		−	0.398328i
$123$	−2.08441e35	−	1.60293e35i	−0.617442	−	0.474819i
$124$	7.84422e35			2.02480
$125$			3.18492e35i			0.717179i
$126$	1.57948e35	−	4.19640e34i	0.310609	−	0.0825235i
$127$	6.40991e35			1.10202			0.551009	−	0.834499i	$-0.314243\pi$
$127$	6.40991e35			1.10202			0.551009	+	0.834499i	$0.314243\pi$
$128$			9.45202e35i			1.42218i
$129$	−3.20125e35	+	4.16283e35i	−0.421983	+	0.548736i
$130$	1.06119e36			1.22674
$131$		−	6.59124e35i		−	0.668891i	−0.942415	−	0.334445i	$-0.891451\pi$
$131$		−	6.59124e35i		−	0.668891i	0.942415	−	0.334445i	$-0.108549\pi$
$132$	−2.07427e36	−	1.59513e36i	−1.84973	−	1.42246i
$133$	−1.62757e35			−0.127662
$134$			2.38511e36i			1.64712i
$135$	2.45676e35	−	5.87830e35i	0.149516	−	0.357748i
$136$	−1.28783e36			−0.691349
$137$		−	1.90139e36i		−	0.901202i	−0.892726	−	0.450601i	$-0.851210\pi$
$137$		−	1.90139e36i		−	0.901202i	0.892726	−	0.450601i	$-0.148790\pi$
$138$	−4.58374e35	+	5.96058e35i	−0.191989	+	0.249657i
$139$	−9.57179e35			−0.354602			−0.177301	−	0.984157i	$-0.556737\pi$
$139$	−9.57179e35			−0.354602			−0.177301	+	0.984157i	$0.556737\pi$
$140$		−	3.63388e35i		−	0.119177i
$141$	1.84015e36	+	1.41509e36i	0.534722	+	0.411206i
$142$	3.57372e36			0.920912
$143$		−	1.34071e37i		−	3.06634i
$144$	2.71492e35	+	1.02187e36i	0.0551563	+	0.207602i
$145$	−1.32491e36			−0.239293
$146$			8.72278e36i			1.40170i
$147$	−4.08550e36	+	5.31268e36i	−0.584589	+	0.760185i
$148$	−2.43831e36			−0.310914
$149$			7.95429e36i			0.904555i	0.891877	+	0.452278i	$0.149388\pi$
$149$			7.95429e36i			0.904555i	−0.891877	+	0.452278i	$0.850612\pi$
$150$	1.05291e37	+	8.09697e36i	1.06866	+	0.821809i
$151$	4.90566e36			0.444723			0.222361	−	0.974964i	$-0.428623\pi$
$151$	4.90566e36			0.444723			0.222361	+	0.974964i	$0.428623\pi$
$152$			6.38561e36i			0.517441i
$153$	−1.12278e37	+	2.98304e36i	−0.813845	+	0.216224i
$154$	−7.61657e36			−0.494205
$155$		−	8.90107e36i		−	0.517373i
$156$	3.54010e37	−	4.60345e37i	1.84458	−	2.39864i
$157$	−2.80858e37			−1.31278			−0.656390	−	0.754422i	$-0.727917\pi$
$157$	−2.80858e37			−1.31278			−0.656390	+	0.754422i	$0.727917\pi$
$158$		−	5.95790e36i		−	0.249990i
$159$	2.95374e37	+	2.27145e37i	1.11332	+	0.856155i
$160$	1.32958e37			0.450479
$161$			1.31928e36i			0.0402065i
$162$	−2.87082e37	−	5.02137e37i	−0.787501	−	1.37742i
$163$	−5.14003e37			−1.26992			−0.634959	−	0.772545i	$-0.718983\pi$
$163$	−5.14003e37			−1.26992			−0.634959	+	0.772545i	$0.718983\pi$
$164$			5.30813e37i			1.18194i
$165$	−1.81005e37	+	2.35374e37i	−0.363465	+	0.472641i
$166$	−1.10199e38			−1.99683
$167$		−	3.68957e37i		−	0.603664i	−0.953361	−	0.301832i	$-0.902402\pi$
$167$		−	3.68957e37i		−	0.603664i	0.953361	−	0.301832i	$-0.0975982\pi$
$168$	−8.91788e36	−	6.85793e36i	−0.131827	−	0.101376i
$169$	2.22714e38			2.97628
$170$			4.28548e37i			0.518046i
$171$	1.47912e37	+	5.56723e37i	0.161833	+	0.609123i
$172$	1.06010e38			1.05042
$173$		−	1.38603e38i		−	1.24448i	−0.782826	−	0.622240i	$-0.786223\pi$
$173$		−	1.38603e38i		−	1.24448i	0.782826	−	0.622240i	$-0.213777\pi$
$174$	−7.33257e37	+	9.53508e37i	−0.596924	+	0.776224i
$175$	2.33044e37			0.172104
$176$		−	4.92766e37i		−	0.330313i
$177$	9.38524e37	+	7.21733e37i	0.571347	+	0.439371i
$178$	−8.08441e36			−0.0447207
$179$			1.76438e38i			0.887340i	0.896190	+	0.443670i	$0.146324\pi$
$179$			1.76438e38i			0.887340i	−0.896190	+	0.443670i	$0.853676\pi$
$180$	−1.24300e38	+	3.30243e37i	−0.568640	+	0.151078i
$181$	−2.46283e38			−1.02541			−0.512707	−	0.858563i	$-0.671357\pi$
$181$	−2.46283e38			−1.02541			−0.512707	+	0.858563i	$0.671357\pi$
$182$		−	1.69035e38i		−	0.640861i
$183$	−4.43072e37	+	5.76160e37i	−0.153040	+	0.199010i
$184$	5.17605e37			0.162965
$185$			2.76683e37i			0.0794443i
$186$	−6.40592e38	−	4.92621e38i	−1.67827	−	1.29060i
$187$	5.41429e38			1.29489
$188$		−	4.68609e38i		−	1.02359i
$189$	−9.36349e37	−	3.91335e37i	−0.186890	−	0.0781085i
$190$	2.12492e38			0.387732
$191$			6.03314e38i			1.00688i	0.864031	+	0.503438i	$0.167932\pi$
$191$			6.03314e38i			1.00688i	−0.864031	+	0.503438i	$0.832068\pi$
$192$	6.50099e38	−	8.45372e38i	0.992792	−	1.29100i
$193$	−4.36159e38			−0.609776			−0.304888	−	0.952388i	$-0.598619\pi$
$193$	−4.36159e38			−0.609776			−0.304888	+	0.952388i	$0.598619\pi$
$194$			1.33756e39i			1.71271i
$195$	−5.22368e38	−	4.01706e38i	−0.612898	−	0.471324i
$196$	1.35292e39			1.45519
$197$		−	5.35197e37i		−	0.0527944i	−0.999652	−	0.0263972i	$-0.991597\pi$
$197$		−	5.35197e37i		−	0.0527944i	0.999652	−	0.0263972i	$-0.00840346\pi$
$198$	6.92185e38	+	2.60531e39i	0.626490	+	2.35804i
$199$	−1.74016e39			−1.44573			−0.722863	−	0.690991i	$-0.757174\pi$
$199$	−1.74016e39			−1.44573			−0.722863	+	0.690991i	$0.757174\pi$
$200$		−	9.14325e38i		−	0.697574i
$201$	9.02869e38	−	1.17407e39i	0.632837	−	0.822925i
$202$	−2.53480e39			−1.63294
$203$			2.11043e38i			0.125008i
$204$	1.85905e39	+	1.42963e39i	1.01293	+	0.778952i
$205$	6.02329e38			0.302008
$206$			3.21057e38i			0.148197i
$207$	4.51269e38	−	1.19894e38i	0.191840	−	0.0509686i
$208$	1.09360e39			0.428333
$209$		−	2.68463e39i		−	0.969166i
$210$	−2.28210e38	+	2.96758e38i	−0.0759637	+	0.0987813i
$211$	1.47371e39			0.452493			0.226246	−	0.974070i	$-0.427355\pi$
$211$	1.47371e39			0.452493			0.226246	+	0.974070i	$0.427355\pi$
$212$		−	7.52194e39i		−	2.13118i
$213$	−1.75916e39	−	1.35281e39i	−0.460100	−	0.353821i
$214$	−8.04592e39			−1.94331
$215$		−	1.20293e39i		−	0.268402i
$216$	−1.53536e39	+	3.67367e39i	−0.316590	+	0.757507i
$217$	−1.41785e39			−0.270280
$218$			1.10283e40i			1.94423i
$219$	3.30196e39	−	4.29378e39i	0.538544	−	0.700309i
$220$	5.99399e39			0.904754
$221$			1.20160e40i			1.67916i
$222$	1.99123e39	+	1.53127e39i	0.257704	+	0.198177i
$223$	−5.53326e39			−0.663435			−0.331717	−	0.943379i	$-0.607628\pi$
$223$	−5.53326e39			−0.663435			−0.331717	+	0.943379i	$0.607628\pi$
$224$		−	2.11788e39i		−	0.235334i
$225$	−2.11788e39	−	7.97145e39i	−0.218171	−	0.821173i
$226$	1.52471e40			1.45661
$227$		−	3.63110e39i		−	0.321810i	−0.986970	−	0.160905i	$-0.948559\pi$
$227$		−	3.63110e39i		−	0.321810i	0.986970	−	0.160905i	$-0.0514412\pi$
$228$	7.08871e39	−	9.21798e39i	0.583008	−	0.758129i
$229$	8.28747e39			0.632731			0.316365	−	0.948637i	$-0.397537\pi$
$229$	8.28747e39			0.632731			0.316365	+	0.948637i	$0.397537\pi$
$230$		−	1.72242e39i		−	0.122114i
$231$	3.74925e39	+	2.88321e39i	0.246911	+	0.189877i
$232$	8.28007e39			0.506685
$233$			2.70185e40i			1.53678i	0.639983	+	0.768389i	$0.278941\pi$
$233$			2.70185e40i			1.53678i	−0.639983	+	0.768389i	$0.721059\pi$
$234$	−5.78199e40	+	1.53617e40i	−3.05779	+	0.812402i
$235$	−5.31745e39			−0.261547
$236$		−	2.39003e40i		−	1.09370i
$237$	−2.25533e39	+	2.93277e39i	−0.0960480	+	0.124898i
$238$	6.82631e39			0.270631
$239$		−	1.24963e40i		−	0.461337i	−0.973032	−	0.230668i	$-0.925909\pi$
$239$		−	1.24963e40i		−	0.461337i	0.973032	−	0.230668i	$-0.0740913\pi$
$240$	−1.91992e39	−	1.47644e39i	−0.0660226	−	0.0507720i
$241$	−2.51217e40			−0.804933			−0.402466	−	0.915435i	$-0.631847\pi$
$241$	−2.51217e40			−0.804933			−0.402466	+	0.915435i	$0.631847\pi$
$242$		−	7.25033e40i		−	2.16519i
$243$	−4.87649e39	+	3.55850e40i	−0.135769	+	0.990741i
$244$	1.46724e40			0.380955
$245$		−	1.53520e40i		−	0.371827i
$246$	3.33353e40	−	4.33484e40i	0.753369	−	0.979662i
$247$	5.95804e40			1.25677
$248$			5.56277e40i			1.09550i
$249$	5.42454e40	+	4.17152e40i	0.997640	+	0.767194i
$250$	−6.62351e40			−1.13791
$251$		−	5.06771e39i		−	0.0813502i	−0.999172	−	0.0406751i	$-0.987049\pi$
$251$		−	5.06771e39i		−	0.0813502i	0.999172	−	0.0406751i	$-0.0129509\pi$
$252$	5.26041e39	+	1.97996e40i	0.0789243	+	0.297062i
$253$	−2.17611e40			−0.305234
$254$			1.33304e41i			1.74851i
$255$	1.62224e40	−	2.10953e40i	0.199037	−	0.258822i
$256$	−5.46982e40			−0.627905
$257$			2.55087e39i			0.0274047i	0.999906	+	0.0137024i	$0.00436174\pi$
$257$			2.55087e39i			0.0274047i	−0.999906	+	0.0137024i	$0.995638\pi$
$258$	−8.65722e40	−	6.65748e40i	−0.870650	−	0.669538i
$259$	4.40726e39			0.0415023
$260$			1.33025e41i			1.17324i
$261$	7.21890e40	−	1.91794e40i	0.596462	−	0.158469i
$262$	1.37075e41			1.06129
$263$		−	1.23202e41i		−	0.894069i	−0.894517	−	0.447035i	$-0.852480\pi$
$263$		−	1.23202e41i		−	0.894069i	0.894517	−	0.447035i	$-0.147520\pi$
$264$	1.13120e41	−	1.47098e41i	0.769612	−	1.00078i
$265$	−8.53537e40			−0.544556
$266$		−	3.38477e40i		−	0.202554i
$267$	3.97955e39	+	3.06031e39i	0.0223430	+	0.0171820i
$268$	−2.98986e41			−1.57529
$269$		−	3.13267e41i		−	1.54926i	−0.632412	−	0.774632i	$-0.717935\pi$
$269$		−	3.13267e41i		−	1.54926i	0.632412	−	0.774632i	$-0.282065\pi$
$270$	1.22248e41	+	5.10919e40i	0.567620	+	0.237229i
$271$	−2.70661e41			−1.18018			−0.590090	−	0.807338i	$-0.700908\pi$
$271$	−2.70661e41			−1.18018			−0.590090	+	0.807338i	$0.700908\pi$
$272$			4.41639e40i			0.180882i
$273$	−6.39874e40	+	8.32076e40i	−0.246223	+	0.320183i
$274$	3.95423e41			1.42989
$275$			3.84400e41i			1.30656i
$276$	−7.47191e40	−	5.74597e40i	−0.238769	−	0.183615i
$277$	−1.40274e41			−0.421522			−0.210761	−	0.977538i	$-0.567594\pi$
$277$	−1.40274e41			−0.421522			−0.210761	+	0.977538i	$0.567594\pi$
$278$		−	1.99060e41i		−	0.562628i
$279$	1.28852e41	+	4.84985e41i	0.342626	+	1.28961i
$280$	2.57699e40			0.0644801
$281$		−	5.57978e41i		−	1.31404i	−0.753871	−	0.657022i	$-0.771816\pi$
$281$		−	5.57978e41i		−	1.31404i	0.753871	−	0.657022i	$-0.228184\pi$
$282$	−2.94289e41	+	3.82686e41i	−0.652438	+	0.848414i
$283$	−4.94739e41			−1.03278			−0.516389	−	0.856354i	$-0.672724\pi$
$283$	−4.94739e41			−1.03278			−0.516389	+	0.856354i	$0.672724\pi$
$284$			4.47985e41i			0.880747i
$285$	−1.04599e41	−	8.04377e40i	−0.193716	−	0.148969i
$286$	2.78820e42			4.86520
$287$		−	9.59445e40i		−	0.157771i
$288$	−7.24437e41	+	1.92470e41i	−1.12287	+	0.298326i
$289$	1.99073e41			0.290904
$290$		−	2.75534e41i		−	0.379672i
$291$	5.06326e41	−	6.58413e41i	0.658035	−	0.855692i
$292$	−1.09345e42			−1.34057
$293$			1.24478e42i			1.43993i	0.694010	+	0.719965i	$0.255842\pi$
$293$			1.24478e42i			1.43993i	−0.694010	+	0.719965i	$0.744158\pi$
$294$	−1.10485e42	−	8.49641e41i	−1.20614	−	0.927536i
$295$	−2.71204e41			−0.279461
$296$		−	1.72914e41i		−	0.168218i
$297$	6.45497e41	−	1.54448e42i	0.592973	−	1.41881i
$298$	−1.65421e42			−1.43521
$299$		−	4.82947e41i		−	0.395812i
$300$	−1.01500e42	+	1.31988e42i	−0.785967	+	1.02205i
$301$	−1.91613e41			−0.140215
$302$			1.02021e42i			0.705618i
$303$	1.24775e42	+	9.59533e41i	0.815838	+	0.627387i
$304$	2.18983e41			0.135382
$305$		−	1.66492e41i		−	0.0973411i
$306$	−6.20367e41	−	2.33499e42i	−0.343071	−	1.29128i
$307$	2.22871e42			1.16601			0.583003	−	0.812470i	$-0.301878\pi$
$307$	2.22871e42			1.16601			0.583003	+	0.812470i	$0.301878\pi$
$308$		−	9.54779e41i		−	0.472651i
$309$	1.21534e41	−	1.58040e41i	0.0569383	−	0.0740411i
$310$	1.85111e42			0.820887
$311$			1.55189e42i			0.651531i	0.945451	+	0.325765i	$0.105622\pi$
$311$			1.55189e42i			0.651531i	−0.945451	+	0.325765i	$0.894378\pi$
$312$	3.26456e42	+	2.51048e42i	1.29777	+	0.997996i
$313$	−2.29224e42			−0.862990			−0.431495	−	0.902115i	$-0.642014\pi$
$313$	−2.29224e42			−0.862990			−0.431495	+	0.902115i	$0.642014\pi$
$314$		−	5.84085e42i		−	2.08292i
$315$	2.24672e41	−	5.96915e40i	0.0759049	−	0.0201666i
$316$	7.46855e41			0.239087
$317$			4.12786e42i			1.25233i	0.779692	+	0.626163i	$0.215376\pi$
$317$			4.12786e42i			1.25233i	−0.779692	+	0.626163i	$0.784624\pi$
$318$	−4.72382e42	+	6.14273e42i	−1.35841	+	1.76645i
$319$	−3.48111e42			−0.949020
$320$			2.44286e42i			0.631464i
$321$	3.96060e42	+	3.04574e42i	0.970902	+	0.746633i
$322$	−2.74363e41			−0.0637934
$323$			2.40609e42i			0.530724i
$324$	6.29455e42	−	3.59873e42i	1.31735	−	0.753155i
$325$	−8.53103e42			−1.69428
$326$		−	1.06894e43i		−	2.01491i
$327$	4.17469e42	−	5.42865e42i	0.746985	−	0.971360i
$328$	−3.76429e42			−0.639481
$329$			8.47012e41i			0.136634i
$330$	−4.89495e42	−	3.76426e42i	−0.749914	−	0.576691i
$331$	3.56881e42			0.519335			0.259667	−	0.965698i	$-0.416387\pi$
$331$	3.56881e42			0.519335			0.259667	+	0.965698i	$0.416387\pi$
$332$		−	1.38140e43i		−	1.90974i
$333$	−4.00527e41	−	1.50754e42i	−0.0526113	−	0.198023i
$334$	7.67300e42			0.957801
$335$			3.39269e42i			0.402515i
$336$	−2.35181e41	+	3.05823e41i	−0.0265237	+	0.0344907i
$337$	4.24411e42			0.455071			0.227535	−	0.973770i	$-0.426933\pi$
$337$	4.24411e42			0.455071			0.227535	+	0.973770i	$0.426933\pi$
$338$			4.63168e43i			4.72231i
$339$	−7.50537e42	−	5.77170e42i	−0.727742	−	0.559640i
$340$	−5.37208e42			−0.495451
$341$		−	2.33870e43i		−	2.05187i
$342$	−1.15779e43	+	3.07604e42i	−0.966463	+	0.256772i
$343$	−4.99544e42			−0.396802
$344$			7.51775e42i			0.568322i
$345$	−6.52013e41	+	8.47861e41i	−0.0469171	+	0.0610098i
$346$	2.88245e43			1.97455
$347$			9.24979e42i			0.603296i	0.953419	+	0.301648i	$0.0975368\pi$
$347$			9.24979e42i			0.603296i	−0.953419	+	0.301648i	$0.902463\pi$
$348$	−1.19527e43	−	9.19177e42i	−0.742370	−	0.570889i
$349$	−9.25631e42			−0.547527			−0.273764	−	0.961797i	$-0.588269\pi$
$349$	−9.25631e42			−0.547527			−0.273764	+	0.961797i	$0.588269\pi$
$350$			4.84650e42i			0.273068i
$351$	3.42769e43	+	1.43256e43i	1.83984	+	0.768938i
$352$	3.49339e43			1.78658
$353$		−	3.35917e43i		−	1.63705i	−0.574472	−	0.818524i	$-0.694793\pi$
$353$		−	3.35917e43i		−	1.63705i	0.574472	−	0.818524i	$-0.305207\pi$
$354$	−1.50095e43	+	1.95180e43i	−0.697126	+	0.906525i
$355$	5.08342e42			0.225047
$356$		−	1.01342e42i		−	0.0427702i
$357$	−3.36025e42	−	2.58406e42i	−0.135211	−	0.103978i
$358$	−3.66929e43			−1.40789
$359$		−	1.03842e43i		−	0.379984i	−0.981786	−	0.189992i	$-0.939154\pi$
$359$		−	1.03842e43i		−	0.379984i	0.981786	−	0.189992i	$-0.0608462\pi$
$360$	−2.34194e42	−	8.81479e42i	−0.0817396	−	0.307659i
$361$	−1.81042e43			−0.602779
$362$		−	5.12183e43i		−	1.62697i
$363$	−2.74457e43	+	3.56897e43i	−0.831882	+	1.08176i
$364$	2.11895e43			0.612911
$365$			1.24077e43i			0.342540i
$366$	−1.19821e43	−	9.21435e42i	−0.315758	−	0.242821i
$367$	−1.80111e43			−0.453124			−0.226562	−	0.973997i	$-0.572749\pi$
$367$	−1.80111e43			−0.453124			−0.226562	+	0.973997i	$0.572749\pi$
$368$		−	1.77503e42i		−	0.0426377i
$369$	−3.28186e43	+	8.71933e42i	−0.752786	+	0.200002i
$370$	−5.75403e42			−0.126050
$371$			1.35959e43i			0.284480i
$372$	6.17528e43	−	8.03017e43i	1.23432	−	1.60507i
$373$	−1.30154e43			−0.248547			−0.124273	−	0.992248i	$-0.539660\pi$
$373$	−1.30154e43			−0.248547			−0.124273	+	0.992248i	$0.539660\pi$
$374$			1.12598e44i			2.05454i
$375$	3.26042e43	+	2.50729e43i	0.568514	+	0.437193i
$376$	3.32317e43			0.553807
$377$		−	7.72565e43i		−	1.23064i
$378$	8.13839e42	−	1.94728e43i	0.123930	−	0.296529i
$379$	7.64890e43			1.11361			0.556804	−	0.830644i	$-0.312027\pi$
$379$	7.64890e43			1.11361			0.556804	+	0.830644i	$0.312027\pi$
$380$			2.66371e43i			0.370822i
$381$	5.04613e43	−	6.56186e43i	0.671791	−	0.873580i
$382$	−1.25468e44			−1.59756
$383$			1.57404e44i			1.91707i	0.284981	+	0.958533i	$0.408013\pi$
$383$			1.57404e44i			1.91707i	−0.284981	+	0.958533i	$0.591987\pi$
$384$	9.67609e43	+	7.44100e43i	1.12738	+	0.866963i
$385$	−1.08342e43			−0.120771
$386$		−	9.07057e43i		−	0.967499i
$387$	1.74136e43	+	6.55428e43i	0.177747	+	0.669020i
$388$	−1.67670e44			−1.63801
$389$			1.47289e43i			0.137730i	0.997626	+	0.0688649i	$0.0219378\pi$
$389$			1.47289e43i			0.137730i	−0.997626	+	0.0688649i	$0.978062\pi$
$390$	8.35406e43	−	1.08634e44i	0.747824	−	0.972451i
$391$	1.95033e43			0.167149
$392$			9.59430e43i			0.787318i
$393$	−6.74749e43	−	5.18888e43i	−0.530236	−	0.407756i
$394$	1.11302e43			0.0837660
$395$		−	8.47480e42i		−	0.0610912i
$396$	−3.26590e44	+	8.67691e43i	−2.25520	+	0.599166i
$397$	−2.57783e43			−0.170536			−0.0852679	−	0.996358i	$-0.527175\pi$
$397$	−2.57783e43			−0.170536			−0.0852679	+	0.996358i	$0.527175\pi$
$398$		−	3.61892e44i		−	2.29386i
$399$	−1.28129e43	+	1.66615e43i	−0.0778228	+	0.101199i
$400$	−3.13552e43			−0.182511
$401$		−	5.85165e43i		−	0.326456i	−0.986588	−	0.163228i	$-0.947809\pi$
$401$		−	5.85165e43i		−	0.326456i	0.986588	−	0.163228i	$-0.0521906\pi$
$402$	2.44165e44	+	1.87765e44i	1.30569	+	1.00409i
$403$	5.19030e44			2.66077
$404$		−	3.17751e44i		−	1.56172i
$405$	−4.08359e43	−	7.14262e43i	−0.192445	−	0.336606i
$406$	−4.38896e43			−0.198344
$407$			7.26966e43i			0.315072i
$408$	−1.01383e44	+	1.31836e44i	−0.421447	+	0.548038i
$409$	−1.88883e44			−0.753175			−0.376587	−	0.926381i	$-0.622903\pi$
$409$	−1.88883e44			−0.753175			−0.376587	+	0.926381i	$0.622903\pi$
$410$			1.25263e44i			0.479180i
$411$	−1.94647e44	−	1.49685e44i	−0.714391	−	0.549373i
$412$	−4.02462e43			−0.141733
$413$			4.31998e43i			0.145993i
$414$	2.49338e43	+	9.38481e43i	0.0808691	+	0.304382i
$415$	−1.56752e44			−0.487973
$416$			7.75291e44i			2.31674i
$417$	−7.53529e43	+	9.79869e43i	−0.216166	+	0.281096i
$418$	5.58310e44			1.53772
$419$			1.49345e44i			0.394960i	0.980307	+	0.197480i	$0.0632757\pi$
$419$			1.49345e44i			0.394960i	−0.980307	+	0.197480i	$0.936724\pi$
$420$	−3.72002e43	−	2.86073e43i	−0.0944730	−	0.0726506i
$421$	−1.37366e44			−0.335030			−0.167515	−	0.985870i	$-0.553574\pi$
$421$	−1.37366e44			−0.335030			−0.167515	+	0.985870i	$0.553574\pi$
$422$			3.06481e44i			0.717946i
$423$	2.89727e44	−	7.69755e43i	0.651933	−	0.173207i
$424$	5.33422e44			1.15306
$425$		−	3.44517e44i		−	0.715481i
$426$	2.81337e44	−	3.65843e44i	0.561389	−	0.730015i
$427$	−2.65204e43			−0.0508518
$428$		−	1.00860e45i		−	1.85855i
$429$	−1.37249e45	−	1.05546e45i	−2.43072	−	1.86924i
$430$	2.50167e44			0.425859
$431$			8.60795e44i			1.40859i	0.709905	+	0.704297i	$0.248738\pi$
$431$			8.60795e44i			1.40859i	−0.709905	+	0.704297i	$0.751262\pi$
$432$	1.25982e44	+	5.26526e43i	0.198192	+	0.0828316i
$433$	4.28923e44			0.648762			0.324381	−	0.945927i	$-0.394844\pi$
$433$	4.28923e44			0.648762			0.324381	+	0.945927i	$0.394844\pi$
$434$		−	2.94862e44i		−	0.428838i
$435$	−1.04302e44	+	1.35631e44i	−0.145873	+	0.189689i
$436$	−1.38245e45			−1.85943
$437$		−	9.67055e43i		−	0.125103i
$438$	8.92955e44	+	6.86691e44i	1.11114	+	0.854479i
$439$	1.05070e44			0.125771			0.0628857	−	0.998021i	$-0.479970\pi$
$439$	1.05070e44			0.125771			0.0628857	+	0.998021i	$0.479970\pi$
$440$			4.25067e44i			0.489511i
$441$	2.22236e44	+	8.36470e44i	0.246239	+	0.926818i
$442$	−2.49890e45			−2.66423
$443$		−	4.09183e44i		−	0.419812i	−0.977722	−	0.209906i	$-0.932684\pi$
$443$		−	4.09183e44i		−	0.419812i	0.977722	−	0.209906i	$-0.0673158\pi$
$444$	−1.91954e44	+	2.49612e44i	−0.189533	+	0.246464i
$445$	−1.14996e43			−0.0109286
$446$		−	1.15072e45i		−	1.05264i
$447$	8.14285e44	+	6.26193e44i	0.717049	+	0.551417i
$448$	3.89121e44			0.329882
$449$		−	1.64896e45i		−	1.34593i	−0.739676	−	0.672963i	$-0.765021\pi$
$449$		−	1.64896e45i		−	1.34593i	0.739676	−	0.672963i	$-0.234979\pi$
$450$	1.65778e45	−	4.40444e44i	1.30291	−	0.346161i
$451$	1.58258e45			1.19775
$452$			1.91131e45i			1.39308i
$453$	3.86193e44	−	5.02195e44i	0.271103	−	0.352536i
$454$	7.55142e44			0.510598
$455$		−	2.40444e44i		−	0.156610i
$456$	6.53698e44	+	5.02700e44i	0.410180	+	0.315432i
$457$	−1.70651e45			−1.03165			−0.515827	−	0.856693i	$-0.672515\pi$
$457$	−1.70651e45			−1.03165			−0.515827	+	0.856693i	$0.672515\pi$
$458$			1.72350e45i			1.00392i
$459$	−5.78523e44	+	1.38424e45i	−0.324717	+	0.776952i
$460$	2.15915e44			0.116788
$461$		−	9.28454e43i		−	0.0483999i	−0.999707	−	0.0242000i	$-0.992296\pi$
$461$		−	9.28454e43i		−	0.0483999i	0.999707	−	0.0242000i	$-0.00770384\pi$
$462$	−5.99606e44	+	7.79713e44i	−0.301268	+	0.391761i
$463$	3.39741e45			1.64540			0.822700	−	0.568476i	$-0.192467\pi$
$463$	3.39741e45			1.64540			0.822700	+	0.568476i	$0.192467\pi$
$464$		−	2.83950e44i		−	0.132567i
$465$	−9.11208e44	−	7.00727e44i	−0.410126	−	0.315391i
$466$	−5.61891e45			−2.43832
$467$			2.42366e45i			1.01411i	0.861914	+	0.507054i	$0.169266\pi$
$467$			2.42366e45i			1.01411i	−0.861914	+	0.507054i	$0.830734\pi$
$468$	−1.92568e45	−	7.24803e45i	−0.776969	−	2.92443i
$469$	5.40418e44			0.210277
$470$		−	1.10584e45i		−	0.414982i
$471$	−2.21102e45	+	2.87515e45i	−0.800272	+	1.04065i
$472$	1.69490e45			0.591740
$473$		−	3.16061e45i		−	1.06447i
$474$	−6.09914e44	−	4.69030e44i	−0.198169	−	0.152394i
$475$	−1.70826e45			−0.535503
$476$			8.55715e44i			0.258828i
$477$	4.65059e45	−	1.23558e45i	1.35736	−	0.360628i
$478$	2.59880e45			0.731979
$479$			5.48124e45i			1.48996i	0.667086	+	0.744980i	$0.267541\pi$
$479$			5.48124e45i			1.48996i	−0.667086	+	0.744980i	$0.732459\pi$
$480$	1.04670e45	−	1.36110e45i	0.274612	−	0.357099i
$481$	−1.61336e45			−0.408569
$482$		−	5.22444e45i		−	1.27714i
$483$	1.35055e44	+	1.03859e44i	0.0318720	+	0.0245099i
$484$	9.08868e45			2.07076
$485$			1.90261e45i			0.418542i
$486$	−7.40042e45	−	1.01414e45i	−1.57195	−	0.215417i
$487$	−5.26475e45			−1.07991			−0.539953	−	0.841695i	$-0.681558\pi$
$487$	−5.26475e45			−1.07991			−0.539953	+	0.841695i	$0.681558\pi$
$488$			1.04050e45i			0.206113i
$489$	−4.04643e45	+	5.26187e45i	−0.774143	+	1.00668i
$490$	3.19267e45			0.589958
$491$		−	9.24145e45i		−	1.64951i	−0.565491	−	0.824755i	$-0.691313\pi$
$491$		−	9.24145e45i		−	1.64951i	0.565491	−	0.824755i	$-0.308687\pi$
$492$	5.43396e45	+	4.17876e45i	0.936935	+	0.720512i
$493$	3.11992e45			0.519692
$494$			1.23906e46i			1.99405i
$495$	9.84596e44	+	3.70591e45i	0.153098	+	0.576244i
$496$	1.90765e45			0.286623
$497$		−	8.09734e44i		−	0.117567i
$498$	−8.67529e45	+	1.12811e46i	−1.21727	+	1.58290i
$499$	4.27528e45			0.579769			0.289885	−	0.957062i	$-0.406383\pi$
$499$	4.27528e45			0.579769			0.289885	+	0.957062i	$0.406383\pi$
$500$		−	8.30292e45i		−	1.08828i
$501$	−3.77703e45	−	2.90457e45i	−0.478530	−	0.367994i
$502$	1.05391e45			0.129074
$503$		−	1.48668e45i		−	0.176020i	−0.996120	−	0.0880099i	$-0.971949\pi$
$503$		−	1.48668e45i		−	0.176020i	0.996120	−	0.0880099i	$-0.0280507\pi$
$504$	−1.40410e45	+	3.73045e44i	−0.160723	+	0.0427014i
$505$	−3.60561e45			−0.399048
$506$		−	4.52555e45i		−	0.484298i
$507$	1.75329e46	−	2.27994e46i	1.81434	−	2.35933i
$508$	−1.67103e46			−1.67225
$509$		−	4.13414e45i		−	0.400113i	−0.979784	−	0.200056i	$-0.935887\pi$
$509$		−	4.13414e45i		−	0.400113i	0.979784	−	0.200056i	$-0.0641125\pi$
$510$	4.38707e45	+	3.37370e45i	0.410659	+	0.315801i
$511$	1.97641e45			0.178946
$512$			4.86314e45i			0.425920i
$513$	6.86362e45	+	2.86856e45i	0.581511	+	0.243035i
$514$	−5.30492e44			−0.0434816
$515$			4.56686e44i			0.0362155i
$516$	8.34552e45	−	1.08523e46i	0.640336	−	0.832677i
$517$	−1.39712e46			−1.03728
$518$			9.16555e44i			0.0658495i
$519$	−1.41888e46	−	1.09114e46i	−0.986511	−	0.758636i
$520$	−9.43356e45			−0.634774
$521$			7.93197e45i			0.516582i	0.966067	+	0.258291i	$0.0831594\pi$
$521$			7.93197e45i			0.516582i	−0.966067	+	0.258291i	$0.916841\pi$
$522$	3.98863e45	+	1.50128e46i	0.251435	+	0.946373i
$523$	−2.90783e46			−1.77435			−0.887177	−	0.461430i	$-0.847337\pi$
$523$	−2.90783e46			−1.77435			−0.887177	+	0.461430i	$0.847337\pi$
$524$			1.71830e46i			1.01501i
$525$	1.83461e45	−	2.38568e45i	0.104915	−	0.136428i
$526$	2.56218e46			1.41857
$527$			2.09605e46i			1.12362i
$528$	−5.04447e45	−	3.87925e45i	−0.261842	−	0.201359i
$529$	1.91112e46			0.960600
$530$		−	1.77506e46i		−	0.864017i
$531$	1.47768e46	−	3.92595e45i	0.696586	−	0.185071i
$532$	4.24300e45			0.193720
$533$			3.51224e46i			1.55318i
$534$	−6.36437e44	+	8.27606e44i	−0.0272617	+	0.0354505i
$535$	−1.14449e46			−0.474895
$536$		−	2.12028e46i		−	0.852297i
$537$	1.80620e46	+	1.38899e46i	0.703402	+	0.540923i
$538$	6.51485e46			2.45813
$539$		−	4.03363e46i		−	1.47465i
$540$	−6.40465e45	+	1.53244e46i	−0.226883	+	0.542863i
$541$	−1.04019e45			−0.0357075			−0.0178537	−	0.999841i	$-0.505683\pi$
$541$	−1.04019e45			−0.0357075			−0.0178537	+	0.999841i	$0.505683\pi$
$542$		−	5.62880e46i		−	1.87253i
$543$	−1.93884e46	+	2.52122e46i	−0.625093	+	0.812855i
$544$	−3.13093e46			−0.978345
$545$			1.56871e46i			0.475119i
$546$	−1.73042e46	−	1.33071e46i	−0.508016	−	0.390669i
$547$	−1.75500e46			−0.499452			−0.249726	−	0.968317i	$-0.580341\pi$
$547$	−1.75500e46			−0.499452			−0.249726	+	0.968317i	$0.580341\pi$
$548$			4.95684e46i			1.36752i
$549$	2.41014e45	+	9.07151e45i	0.0644634	+	0.242633i
$550$	−7.99417e46			−2.07304
$551$		−	1.54699e46i		−	0.388964i
$552$	4.07479e45	−	5.29875e45i	0.0993438	−	0.129184i
$553$	−1.34994e45			−0.0319145
$554$		−	2.91720e46i		−	0.668806i
$555$	2.83242e45	+	2.17816e45i	0.0629762	+	0.0484293i
$556$	2.49532e46			0.538090
$557$			4.17096e45i			0.0872363i	0.999048	+	0.0436182i	$0.0138885\pi$
$557$			4.17096e45i			0.0872363i	−0.999048	+	0.0436182i	$0.986112\pi$
$558$	−1.00860e47	+	2.67967e46i	−2.04615	+	0.543626i
$559$	7.01438e46			1.38035
$560$		−	8.83732e44i		−	0.0168704i
$561$	4.26234e46	−	5.54264e46i	0.789368	−	1.02647i
$562$	1.16040e47			2.08492
$563$		−	2.05158e46i		−	0.357640i	−0.983882	−	0.178820i	$-0.942772\pi$
$563$		−	2.05158e46i		−	0.357640i	0.983882	−	0.178820i	$-0.0572280\pi$
$564$	−4.79717e46	−	3.68907e46i	−0.811411	−	0.623982i
$565$	2.16882e46			0.355958
$566$		−	1.02888e47i		−	1.63865i
$567$	−1.13774e46	+	6.50472e45i	−0.175846	+	0.100535i
$568$	−3.17691e46			−0.476522
$569$			1.81013e46i			0.263513i	0.991282	+	0.131756i	$0.0420617\pi$
$569$			1.81013e46i			0.263513i	−0.991282	+	0.131756i	$0.957938\pi$
$570$	1.67282e46	−	2.17530e46i	0.236362	−	0.307359i
$571$	−2.57169e46			−0.352700			−0.176350	−	0.984328i	$-0.556429\pi$
$571$	−2.57169e46			−0.352700			−0.176350	+	0.984328i	$0.556429\pi$
$572$			3.49515e47i			4.65301i
$573$	6.17615e46	+	4.74952e46i	0.798159	+	0.613792i
$574$	1.99531e46			0.250327
$575$			1.38468e46i			0.168654i
$576$	−3.53629e46	−	1.33102e47i	−0.418182	−	1.57399i
$577$	7.57994e46			0.870316			0.435158	−	0.900354i	$-0.356693\pi$
$577$	7.57994e46			0.870316			0.435158	+	0.900354i	$0.356693\pi$
$578$			4.14003e46i			0.461562i
$579$	−3.43361e46	+	4.46498e46i	−0.371720	+	0.483375i
$580$	3.45397e46			0.363113
$581$			2.49689e46i			0.254921i
$582$	1.36927e47	+	1.05298e47i	1.35768	+	1.04407i
$583$	−2.24261e47			−2.15968
$584$		−	7.75424e46i		−	0.725305i
$585$	−8.22456e46	+	2.18512e46i	−0.747245	+	0.198530i
$586$	−2.58870e47			−2.28466
$587$		−	2.23039e47i		−	1.91219i	−0.293049	−	0.956097i	$-0.594670\pi$
$587$		−	2.23039e47i		−	1.91219i	0.293049	−	0.956097i	$-0.405330\pi$
$588$	1.06507e47	−	1.38499e47i	0.887082	−	1.15354i
$589$	1.03931e47			0.840977
$590$		−	5.64009e46i		−	0.443406i
$591$	−5.47884e45	−	4.21328e45i	−0.0418506	−	0.0321835i
$592$	−5.92979e45			−0.0440119
$593$		−	7.56073e46i		−	0.545298i	−0.962114	−	0.272649i	$-0.912100\pi$
$593$		−	7.56073e46i		−	0.545298i	0.962114	−	0.272649i	$-0.0878997\pi$
$594$	3.21198e47	+	1.34241e47i	2.25115	+	0.940838i
$595$	9.71006e45			0.0661353
$596$		−	2.07365e47i		−	1.37261i
$597$	−1.36992e47	+	1.78141e47i	−0.881315	+	1.14604i
$598$	1.00436e47			0.628014
$599$			1.52602e47i			0.927478i	0.885972	+	0.463739i	$0.153492\pi$
$599$			1.52602e47i			0.927478i	−0.885972	+	0.463739i	$0.846508\pi$
$600$	−9.35999e46	−	7.19792e46i	−0.552973	−	0.425242i
$601$	−5.89346e46			−0.338458			−0.169229	−	0.985577i	$-0.554128\pi$
$601$	−5.89346e46			−0.338458			−0.169229	+	0.985577i	$0.554128\pi$
$602$		−	3.98488e46i		−	0.222472i
$603$	−4.91126e46	−	1.84854e47i	−0.266562	−	1.00331i
$604$	−1.27888e47			−0.674843
$605$		−	1.03132e47i		−	0.529117i
$606$	−1.99549e47	+	2.59489e47i	−0.995441	+	1.29445i
$607$	−3.66229e45			−0.0177642			−0.00888208	−	0.999961i	$-0.502827\pi$
$607$	−3.66229e45			−0.0177642			−0.00888208	+	0.999961i	$0.502827\pi$
$608$			1.55245e47i			0.732244i
$609$	2.16046e46	+	1.66142e46i	0.0990952	+	0.0762051i
$610$	3.46245e46			0.154446
$611$		−	3.10065e47i		−	1.34509i
$612$	2.92704e47	−	7.77664e46i	1.23496	−	0.328109i
$613$	−1.58021e47			−0.648466			−0.324233	−	0.945977i	$-0.605106\pi$
$613$	−1.58021e47			−0.648466			−0.324233	+	0.945977i	$0.605106\pi$
$614$			4.63493e47i			1.85004i
$615$	4.74177e46	−	6.16608e46i	0.184104	−	0.239404i
$616$	6.77087e46			0.255724
$617$			4.77479e47i			1.75431i	0.480206	+	0.877156i	$0.340562\pi$
$617$			4.77479e47i			1.75431i	−0.480206	+	0.877156i	$0.659438\pi$
$618$	3.28668e46	+	2.52749e46i	0.117477	+	0.0903409i
$619$	4.09248e47			1.42313			0.711567	−	0.702618i	$-0.247986\pi$
$619$	4.09248e47			1.42313			0.711567	+	0.702618i	$0.247986\pi$
$620$			2.32047e47i			0.785085i
$621$	2.32520e46	−	5.56352e46i	0.0765426	−	0.183144i
$622$	−3.22739e47			−1.03375
$623$			1.83177e45i			0.00570918i
$624$	8.60925e46	−	1.11952e47i	0.261112	−	0.339544i
$625$	1.93661e47			0.571585
$626$		−	4.76705e47i		−	1.36926i
$627$	−2.74828e47	−	2.11345e47i	−0.768267	−	0.590804i
$628$	7.32182e47			1.99207
$629$		−	6.51539e46i		−	0.172536i
$630$	1.24137e46	+	4.67239e46i	0.0319973	+	0.120434i
$631$	−1.79231e47			−0.449692			−0.224846	−	0.974394i	$-0.572188\pi$
$631$	−1.79231e47			−0.449692			−0.224846	+	0.974394i	$0.572188\pi$
$632$			5.29637e46i			0.129356i
$633$	1.16017e47	−	1.50865e47i	0.275840	−	0.358695i
$634$	−8.58450e47			−1.98700
$635$			1.89617e47i			0.427292i
$636$	−7.70025e47	−	5.92156e47i	−1.68940	−	1.29917i
$637$	8.95188e47			1.91225
$638$		−	7.23948e47i		−	1.50576i
$639$	−2.76976e47	+	7.35876e46i	−0.560954	+	0.149036i
$640$	−2.79609e47			−0.551431
$641$			6.77126e47i			1.30042i	0.759755	+	0.650209i	$0.225319\pi$
$641$			6.77126e47i			1.30042i	−0.759755	+	0.650209i	$0.774681\pi$
$642$	−6.33407e47	+	8.23666e47i	−1.18464	+	1.54048i
$643$	5.31156e47			0.967465			0.483733	−	0.875216i	$-0.339281\pi$
$643$	5.31156e47			0.967465			0.483733	+	0.875216i	$0.339281\pi$
$644$		−	3.43929e46i		−	0.0610111i
$645$	−1.23144e47	−	9.46991e46i	−0.212764	−	0.163618i
$646$	−5.00382e47			−0.842071
$647$			4.84207e47i			0.793704i	0.917883	+	0.396852i	$0.129897\pi$
$647$			4.84207e47i			0.793704i	−0.917883	+	0.396852i	$0.870103\pi$
$648$	2.55206e47	+	4.46382e47i	0.407489	+	0.712740i
$649$	−7.12570e47			−1.10833
$650$		−	1.77415e48i		−	2.68822i
$651$	−1.11618e47	+	1.45146e47i	−0.164763	+	0.214253i
$652$	1.33998e48			1.92703
$653$		−	6.49807e47i		−	0.910458i	−0.890374	−	0.455229i	$-0.849557\pi$
$653$		−	6.49807e47i		−	0.910458i	0.890374	−	0.455229i	$-0.150443\pi$
$654$	1.12897e48	+	8.68188e47i	1.54121	+	1.18520i
$655$	1.94981e47			0.259353
$656$			1.29090e47i			0.167312i
$657$	−1.79614e47	−	6.76046e47i	−0.226844	−	0.853818i
$658$	−1.76149e47			−0.216790
$659$			4.70309e47i			0.564067i	0.959404	+	0.282034i	$0.0910090\pi$
$659$			4.70309e47i			0.564067i	−0.959404	+	0.282034i	$0.908991\pi$
$660$	4.71871e47	−	6.13608e47i	0.551539	−	0.717207i
$661$	−9.07464e47			−1.03372			−0.516862	−	0.856069i	$-0.672900\pi$
$661$	−9.07464e47			−1.03372			−0.516862	+	0.856069i	$0.672900\pi$
$662$			7.42187e47i			0.824000i
$663$	1.23008e48	+	9.45946e47i	1.33108	+	1.02361i
$664$	9.79630e47			1.03325
$665$		−	4.81466e46i		−	0.0494991i
$666$	3.13515e47	−	8.32954e46i	0.314193	−	0.0834756i
$667$	−1.25396e47			−0.122502
$668$			9.61852e47i			0.916027i
$669$	−4.35600e47	+	5.66443e47i	−0.404430	+	0.525911i
$670$	−7.05560e47			−0.638649
$671$		−	4.37447e47i		−	0.386049i
$672$	−2.16808e47	−	1.66728e47i	−0.186551	−	0.143460i
$673$	2.95085e47			0.247566			0.123783	−	0.992309i	$-0.460497\pi$
$673$	2.95085e47			0.247566			0.123783	+	0.992309i	$0.460497\pi$
$674$			8.82627e47i			0.722036i
$675$	−9.82770e47	−	4.10736e47i	−0.783949	−	0.327641i
$676$	−5.80606e48			−4.51635
$677$			1.13797e47i			0.0863225i	0.999068	+	0.0431613i	$0.0137429\pi$
$677$			1.13797e47i			0.0863225i	−0.999068	+	0.0431613i	$0.986257\pi$
$678$	1.20031e48	−	1.56085e48i	0.887951	−	1.15467i
$679$	3.03065e47			0.218650
$680$		−	3.80964e47i		−	0.268060i
$681$	−3.71718e47	−	2.85855e47i	−0.255101	−	0.196175i
$682$	4.86367e48			3.25559
$683$			2.23333e48i			1.45815i	0.684435	+	0.729074i	$0.260049\pi$
$683$			2.23333e48i			1.45815i	−0.684435	+	0.729074i	$0.739951\pi$
$684$	−3.85598e47	−	1.45135e48i	−0.245574	−	0.924312i
$685$	5.62467e47			0.349428
$686$		−	1.03888e48i		−	0.629584i
$687$	6.52422e47	−	8.48393e47i	0.385713	−	0.501571i
$688$	2.57808e47			0.148694
$689$		−	4.97705e48i		−	2.80056i
$690$	−1.76325e47	−	1.35596e47i	−0.0968010	−	0.0744409i
$691$	−1.30456e48			−0.698774			−0.349387	−	0.936979i	$-0.613610\pi$
$691$	−1.30456e48			−0.698774			−0.349387	+	0.936979i	$0.613610\pi$
$692$			3.61331e48i			1.88843i
$693$	5.90312e47	−	1.56836e47i	0.301035	−	0.0799796i
$694$	−1.92363e48			−0.957218
$695$		−	2.83151e47i		−	0.137492i
$696$	6.51839e47	−	8.47635e47i	0.308876	−	0.401654i
$697$	−1.41838e48			−0.655896
$698$		−	1.92499e48i		−	0.868732i
$699$	2.76590e48	+	2.12701e48i	1.21822	+	0.936821i
$700$	−6.07535e47			−0.261159
$701$		−	2.83029e48i		−	1.18748i	−0.804658	−	0.593738i	$-0.797651\pi$
$701$		−	2.83029e48i		−	1.18748i	0.804658	−	0.593738i	$-0.202349\pi$
$702$	−2.97922e48	+	7.12839e48i	−1.22003	+	2.91918i
$703$	−3.23061e47			−0.129135
$704$			6.41845e48i			2.50435i
$705$	−4.18610e47	+	5.44350e47i	−0.159439	+	0.207331i
$706$	6.98588e48			2.59742
$707$			5.74335e47i			0.208466i
$708$	−2.44669e48	−	1.88152e48i	−0.866987	−	0.666721i
$709$	−2.37672e48			−0.822228			−0.411114	−	0.911584i	$-0.634860\pi$
$709$	−2.37672e48			−0.822228			−0.411114	+	0.911584i	$0.634860\pi$
$710$			1.05717e48i			0.357070i
$711$	1.22681e47	+	4.61759e47i	0.0404571	+	0.152276i
$712$	7.18676e46			0.0231405
$713$		−	8.42443e47i		−	0.264861i
$714$	5.37394e47	−	6.98813e47i	0.164977	−	0.214532i
$715$	3.96606e48			1.18893
$716$		−	4.59965e48i		−	1.34649i
$717$	−1.27926e48	−	9.83760e47i	−0.365706	−	0.281231i
$718$	2.15954e48			0.602900
$719$		−	1.97387e48i		−	0.538179i	−0.963115	−	0.269089i	$-0.913277\pi$
$719$		−	1.97387e48i		−	0.538179i	0.963115	−	0.269089i	$-0.0867227\pi$
$720$	−3.02288e47	+	8.03125e46i	−0.0804948	+	0.0213861i
$721$	7.27452e46			0.0189193
$722$		−	3.76504e48i		−	0.956396i
$723$	−1.97768e48	+	2.57172e48i	−0.490688	+	0.638077i
$724$	6.42049e48			1.55601
$725$			2.21506e48i			0.524372i
$726$	−7.42220e48	−	5.70774e48i	−1.71637	−	1.31990i
$727$	−1.62328e47			−0.0366697			−0.0183349	−	0.999832i	$-0.505836\pi$
$727$	−1.62328e47			−0.0366697			−0.0183349	+	0.999832i	$0.505836\pi$
$728$			1.50267e48i			0.331611i
$729$	3.25896e48	+	3.30060e48i	0.702604	+	0.711581i
$730$	−2.58036e48			−0.543490
$731$			2.83268e48i			0.582911i
$732$	1.15507e48	−	1.50202e48i	0.232231	−	0.301987i
$733$	−7.96509e48			−1.56467			−0.782335	−	0.622858i	$-0.785972\pi$
$733$	−7.96509e48			−1.56467			−0.782335	+	0.622858i	$0.785972\pi$
$734$		−	3.74568e48i		−	0.718948i
$735$	−1.57159e48	−	1.20857e48i	−0.294751	−	0.226666i
$736$	1.25838e48			0.230616
$737$			8.91406e48i			1.59635i
$738$	−1.81331e48	−	6.82511e48i	−0.317333	−	1.19441i
$739$	−5.33016e48			−0.911559			−0.455779	−	0.890093i	$-0.650639\pi$
$739$	−5.33016e48			−0.911559			−0.455779	+	0.890093i	$0.650639\pi$
$740$		−	7.21299e47i		−	0.120552i
$741$	4.69040e48	−	6.09928e48i	0.766126	−	0.996251i
$742$	−2.82747e48			−0.451370
$743$			3.48547e48i			0.543816i	0.962323	+	0.271908i	$0.0876546\pi$
$743$			3.48547e48i			0.543816i	−0.962323	+	0.271908i	$0.912345\pi$
$744$	5.69464e48	+	4.37923e48i	0.868413	+	0.667818i
$745$	−2.35303e48			−0.350728
$746$		−	2.70675e48i		−	0.394355i
$747$	8.54081e48	−	2.26915e48i	1.21632	−	0.323156i
$748$	−1.41148e49			−1.96493
$749$			1.82305e48i			0.248089i
$750$	−5.21428e48	+	6.78052e48i	−0.693670	+	0.902031i
$751$	1.41620e49			1.84181			0.920905	−	0.389788i	$-0.127452\pi$
$751$	1.41620e49			1.84181			0.920905	+	0.389788i	$0.127452\pi$
$752$		−	1.13962e48i		−	0.144896i
$753$	−5.18784e47	−	3.98950e47i	−0.0644870	−	0.0495911i
$754$	1.60666e49			1.95260
$755$			1.45119e48i			0.172435i
$756$	2.44102e48	+	1.02019e48i	0.283596	+	0.118525i
$757$	8.85054e48			1.00540			0.502701	−	0.864460i	$-0.332340\pi$
$757$	8.85054e48			1.00540			0.502701	+	0.864460i	$0.332340\pi$
$758$			1.59070e49i			1.76690i
$759$	−1.71312e48	+	2.22770e48i	−0.186071	+	0.241962i
$760$	−1.88898e48			−0.200630
$761$		−	7.49291e48i		−	0.778236i	−0.921188	−	0.389118i	$-0.872780\pi$
$761$		−	7.49291e48i		−	0.778236i	0.921188	−	0.389118i	$-0.127220\pi$
$762$	1.36464e49	+	1.04942e49i	1.38606	+	1.06589i
$763$	2.49879e48			0.248206
$764$		−	1.57281e49i		−	1.52788i
$765$	−8.82439e47	−	3.32140e48i	−0.0838378	−	0.315556i
$766$	−3.27345e49			−3.04171
$767$		−	1.58141e49i		−	1.43722i
$768$	−4.30606e48	+	5.59949e48i	−0.382771	+	0.497746i
$769$	−8.84359e48			−0.768920			−0.384460	−	0.923142i	$-0.625612\pi$
$769$	−8.84359e48			−0.768920			−0.384460	+	0.923142i	$0.625612\pi$
$770$		−	2.25313e48i		−	0.191621i
$771$	2.61134e47	+	2.00815e47i	0.0217240	+	0.0167059i
$772$	1.13704e49			0.925302
$773$			1.15976e49i			0.923245i	0.887076	+	0.461623i	$0.152733\pi$
$773$			1.15976e49i			0.923245i	−0.887076	+	0.461623i	$0.847267\pi$
$774$	−1.36306e49	+	3.62141e48i	−1.06150	+	0.282021i
$775$	−1.48814e49			−1.13374
$776$		−	1.18904e49i		−	0.886234i
$777$	3.46957e47	−	4.51174e47i	0.0252999	−	0.0328993i
$778$	−3.06310e48			−0.218529
$779$			7.03292e48i			0.490907i
$780$	1.36179e49	+	1.04723e49i	0.930039	+	0.715208i
$781$	1.33564e49			0.892525
$782$			4.05600e48i			0.265206i
$783$	3.71960e48	−	8.89990e48i	0.237983	−	0.569423i
$784$	3.29020e48			0.205991
$785$		−	8.30829e48i		−	0.509012i
$786$	1.07911e49	−	1.40324e49i	0.646964	−	0.841296i
$787$	−2.32103e49			−1.36179			−0.680895	−	0.732381i	$-0.738409\pi$
$787$	−2.32103e49			−1.36179			−0.680895	+	0.732381i	$0.738409\pi$
$788$			1.39523e48i			0.0801126i
$789$	−1.26123e49	−	9.69897e48i	−0.708737	−	0.545025i
$790$	1.76246e48			0.0969301
$791$		−	3.45469e48i		−	0.185955i
$792$	−6.15328e48	−	2.31603e49i	−0.324174	−	1.22016i
$793$	9.70831e48			0.500610
$794$		−	5.36098e48i		−	0.270580i
$795$	−6.71938e48	+	8.73770e48i	−0.331962	+	0.431674i
$796$	4.53651e49			2.19381
$797$			2.56332e49i			1.21342i	0.794923	+	0.606710i	$0.207511\pi$
$797$			2.56332e49i			1.21342i	−0.794923	+	0.606710i	$0.792489\pi$
$798$	−3.46501e48	−	2.66463e48i	−0.160567	−	0.123477i
$799$	1.25217e49			0.568024
$800$		−	2.22287e49i		−	0.987155i
$801$	6.26571e47	−	1.66469e47i	0.0272406	−	0.00723736i
$802$	1.21694e49			0.517970
$803$			3.26004e49i			1.35850i
$804$	−2.35374e49	+	3.06074e49i	−0.960295	+	1.24874i
$805$	−3.90267e47			−0.0155895
$806$			1.07940e50i			4.22169i
$807$	−3.20693e49	−	2.46616e49i	−1.22812	−	0.944432i
$808$	2.25335e49			0.844957
$809$		−	3.35758e49i		−	1.23283i	−0.787423	−	0.616413i	$-0.788585\pi$
$809$		−	3.35758e49i		−	1.23283i	0.787423	−	0.616413i	$-0.211415\pi$
$810$	1.48541e49	−	8.49243e48i	0.534075	−	0.305342i
$811$	−2.73185e49			−0.961840			−0.480920	−	0.876765i	$-0.659697\pi$
$811$	−2.73185e49			−0.961840			−0.480920	+	0.876765i	$0.659697\pi$
$812$		−	5.50180e48i		−	0.189693i
$813$	−2.13075e49	+	2.77077e49i	−0.719438	+	0.935538i
$814$	−1.51183e49			−0.499907
$815$		−	1.52052e49i		−	0.492393i
$816$	4.52108e48	+	3.47675e48i	0.143387	+	0.110266i
$817$	1.40456e49			0.436281
$818$		−	3.92810e49i		−	1.19502i
$819$	3.48067e48	+	1.31008e49i	0.103714	+	0.390367i
$820$	−1.57024e49			−0.458280
$821$		−	4.92753e49i		−	1.40863i	−0.709889	−	0.704314i	$-0.751255\pi$
$821$		−	4.92753e49i		−	1.40863i	0.709889	−	0.704314i	$-0.248745\pi$
$822$	3.11292e49	−	4.04796e49i	0.871660	−	1.13348i
$823$	5.16460e49			1.41657			0.708287	−	0.705925i	$-0.249468\pi$
$823$	5.16460e49			1.41657			0.708287	+	0.705925i	$0.249468\pi$
$824$		−	2.85408e48i		−	0.0766839i
$825$	3.93513e49	+	3.02615e49i	1.03572	+	0.796477i
$826$	−8.98405e48			−0.231639
$827$		−	7.11357e49i		−	1.79678i	−0.439202	−	0.898388i	$-0.644739\pi$
$827$		−	7.11357e49i		−	1.79678i	0.439202	−	0.898388i	$-0.355261\pi$
$828$	−1.17644e49	+	3.12559e48i	−0.291107	+	0.0773421i
$829$	1.81705e49			0.440494			0.220247	−	0.975444i	$-0.429314\pi$
$829$	1.81705e49			0.440494			0.220247	+	0.975444i	$0.429314\pi$
$830$		−	3.25989e49i		−	0.774240i
$831$	−1.10429e49	+	1.43599e49i	−0.256960	+	0.334144i
$832$	−1.42445e50			−3.24752
$833$			3.61512e49i			0.807529i
$834$	−2.03778e49	−	1.56707e49i	−0.446000	−	0.342978i
$835$	1.09144e49			0.234062
$836$			6.99871e49i			1.47066i
$837$	5.97919e49	+	2.49893e49i	1.23115	+	0.514542i
$838$	−3.10586e49			−0.626662
$839$		−	2.48853e49i		−	0.492028i	−0.969266	−	0.246014i	$-0.920879\pi$
$839$		−	2.48853e49i		−	0.492028i	0.969266	−	0.246014i	$-0.0791209\pi$
$840$	2.02870e48	−	2.63808e48i	0.0393071	−	0.0511139i
$841$	3.26067e49			0.619121
$842$		−	2.85673e49i		−	0.531573i
$843$	−5.71206e49	−	4.39262e49i	−1.04165	−	0.801042i
$844$	−3.84190e49			−0.686633
$845$			6.58831e49i			1.15401i
$846$	1.60082e49	+	6.02531e49i	0.274819	+	1.03439i
$847$	−1.64278e49			−0.276415
$848$		−	1.82928e49i		−	0.301683i
$849$	−3.89478e49	+	5.06467e49i	−0.629582	+	0.818692i
$850$	7.16473e49			1.13522
$851$			2.61867e48i			0.0406703i
$852$	4.58604e49	+	3.52671e49i	0.698176	+	0.536904i
$853$	−1.88149e49			−0.280781			−0.140391	−	0.990096i	$-0.544836\pi$
$853$	−1.88149e49			−0.280781			−0.140391	+	0.990096i	$0.544836\pi$
$854$		−	5.51531e48i		−	0.0806838i
$855$	−1.64689e49	+	4.37550e48i	−0.236179	+	0.0627486i
$856$	7.15254e49			1.00556
$857$			1.14364e50i			1.57621i	0.615538	+	0.788107i	$0.288939\pi$
$857$			1.14364e50i			1.57621i	−0.615538	+	0.788107i	$0.711061\pi$
$858$	2.19498e50	−	2.85429e50i	2.96583	−	3.85669i
$859$	1.02902e50			1.36314			0.681568	−	0.731755i	$-0.261299\pi$
$859$	1.02902e50			1.36314			0.681568	+	0.731755i	$0.261299\pi$
$860$			3.13597e49i			0.407285i
$861$	−9.82190e48	−	7.55313e48i	−0.125067	−	0.0961775i
$862$	−1.79015e50			−2.23494
$863$		−	8.75806e48i		−	0.107207i	−0.998562	−	0.0536037i	$-0.982929\pi$
$863$		−	8.75806e48i		−	0.107207i	0.998562	−	0.0536037i	$-0.0170708\pi$
$864$	−3.73272e49	+	8.93130e49i	−0.448015	+	1.07197i
$865$	4.10013e49			0.482529
$866$			8.92010e49i			1.02936i
$867$	1.56718e49	−	2.03793e49i	0.177335	−	0.230602i
$868$	3.69625e49			0.410135
$869$		−	2.22670e49i		−	0.242284i
$870$	−2.82066e49	−	2.16911e49i	−0.300970	−	0.231449i
$871$	−1.97831e50			−2.07007
$872$		−	9.80374e49i		−	1.00603i
$873$	−2.75422e49	−	1.03666e50i	−0.277176	−	1.04326i
$874$	2.01114e49			0.198494
$875$			1.50076e49i			0.145269i
$876$	−8.60804e49	+	1.11937e50i	−0.817212	+	1.06268i
$877$	−8.39113e49			−0.781317			−0.390659	−	0.920536i	$-0.627753\pi$
$877$	−8.39113e49			−0.781317			−0.390659	+	0.920536i	$0.627753\pi$
$878$			2.18509e49i			0.199555i
$879$	1.27428e50	+	9.79936e49i	1.14145	+	0.877783i
$880$	1.45769e49			0.128074
$881$			1.02201e50i			0.880770i	0.897809	+	0.440385i	$0.145158\pi$
$881$			1.02201e50i			0.880770i	−0.897809	+	0.440385i	$0.854842\pi$
$882$	−1.73956e50	+	4.62172e49i	−1.47053	+	0.390695i
$883$	5.08406e49			0.421579			0.210789	−	0.977532i	$-0.432397\pi$
$883$	5.08406e49			0.421579			0.210789	+	0.977532i	$0.432397\pi$
$884$		−	3.13251e50i		−	2.54803i
$885$	−2.13502e49	+	2.77633e49i	−0.170360	+	0.221531i
$886$	8.50958e49			0.666093
$887$		−	1.35566e50i		−	1.04100i	−0.853862	−	0.520500i	$-0.825746\pi$
$887$		−	1.35566e50i		−	1.04100i	0.853862	−	0.520500i	$-0.174254\pi$
$888$	−1.77013e49	−	1.36125e49i	−0.133348	−	0.102546i
$889$	3.02040e49			0.223221
$890$		−	2.39152e48i		−	0.0173398i
$891$	−1.07294e50	−	1.87668e50i	−0.763226	−	1.33496i
$892$	1.44249e50			1.00673
$893$		−	6.20876e49i		−	0.425138i
$894$	−1.30226e50	+	1.69343e50i	−0.874904	+	1.13770i
$895$	−5.21936e49			−0.344053
$896$			4.45386e49i			0.288072i
$897$	−4.94395e49	−	3.80195e49i	−0.313764	−	0.241287i
$898$	3.42925e50			2.13551
$899$		−	1.34765e50i		−	0.823496i
$900$	5.52120e49	+	2.07812e50i	0.331063	+	1.24609i
$901$	2.00993e50			1.18266
$902$			3.29121e50i			1.90040i
$903$	−1.50845e49	+	1.96156e49i	−0.0854753	+	0.111150i
$904$	−1.35541e50			−0.753717
$905$		−	7.28553e49i		−	0.397590i
$906$	1.04439e50	+	8.03145e49i	0.559349	+	0.430145i
$907$	6.06238e49			0.318654			0.159327	−	0.987226i	$-0.449068\pi$
$907$	6.06238e49			0.318654			0.159327	+	0.987226i	$0.449068\pi$
$908$			9.46611e49i			0.488329i
$909$	1.96456e50	−	5.21949e49i	0.994670	−	0.264267i
$910$	5.00038e49			0.248485
$911$			3.90833e50i			1.90624i	0.302587	+	0.953122i	$0.402150\pi$
$911$			3.90833e50i			1.90624i	−0.302587	+	0.953122i	$0.597850\pi$
$912$	1.72392e49	−	2.24174e49i	0.0825287	−	0.107318i
$913$	−4.11856e50			−1.93527
$914$		−	3.54895e50i		−	1.63687i
$915$	−1.70439e49	−	1.31069e49i	−0.0771632	−	0.0593392i
$916$	−2.16050e50			−0.960134
$917$		−	3.10584e49i		−	0.135488i
$918$	−2.87872e50	−	1.20312e50i	−1.23275	−	0.515211i
$919$	−2.52620e49			−0.106195			−0.0530976	−	0.998589i	$-0.516909\pi$
$919$	−2.52620e49			−0.106195			−0.0530976	+	0.998589i	$0.516909\pi$
$920$			1.53117e49i			0.0631875i
$921$	1.75453e50	−	2.28154e50i	0.710797	−	0.924303i
$922$	1.93086e49			0.0767935
$923$			2.96419e50i			1.15738i
$924$	−9.77412e49	−	7.51639e49i	−0.374675	−	0.288128i
$925$	4.62575e49			0.174090
$926$			7.06543e50i			2.61067i
$927$	−6.61099e48	−	2.48831e49i	−0.0239834	−	0.0902710i
$928$	2.01302e50			0.717023
$929$		−	4.40717e50i		−	1.54132i	−0.637247	−	0.770660i	$-0.719927\pi$
$929$		−	4.40717e50i		−	1.54132i	0.637247	−	0.770660i	$-0.280073\pi$
$930$	1.45727e50	−	1.89499e50i	0.500413	−	0.650725i
$931$	1.79253e50			0.604396
$932$		−	7.04360e50i		−	2.33198i
$933$	1.58868e50	+	1.22171e50i	0.516474	+	0.397173i
$934$	−5.04036e50			−1.60903
$935$			1.60165e50i			0.502077i
$936$	5.13998e50	−	1.36560e50i	1.58224	−	0.420374i
$937$	−3.34697e50			−1.01176			−0.505881	−	0.862603i	$-0.668833\pi$
$937$	−3.34697e50			−1.01176			−0.505881	+	0.862603i	$0.668833\pi$
$938$			1.12388e50i			0.333635i
$939$	−1.80454e50	+	2.34657e50i	−0.526079	+	0.684100i
$940$	1.38623e50			0.396883
$941$		−	3.90165e50i		−	1.09704i	−0.836136	−	0.548522i	$-0.815191\pi$
$941$		−	3.90165e50i		−	1.09704i	0.836136	−	0.548522i	$-0.184809\pi$
$942$	−5.97931e50	−	4.59815e50i	−1.65115	−	1.26975i
$943$	5.70075e49			0.154608
$944$		−	5.81237e49i		−	0.154821i
$945$	1.15764e49	−	2.76990e49i	0.0302854	−	0.0724641i
$946$	6.57296e50			1.68893
$947$			8.57852e49i			0.216503i	0.994124	+	0.108251i	$0.0345251\pi$
$947$			8.57852e49i			0.216503i	−0.994124	+	0.108251i	$0.965475\pi$
$948$	5.87954e49	−	7.64560e49i	0.145748	−	0.189526i
$949$	−7.23503e50			−1.76163
$950$		−	3.55258e50i		−	0.849654i
$951$	4.22571e50	+	3.24961e50i	0.992730	+	0.763419i
$952$	−6.06835e49			−0.140037
$953$			7.57035e50i			1.71608i	0.513586	+	0.858038i	$0.328317\pi$
$953$			7.57035e50i			1.71608i	−0.513586	+	0.858038i	$0.671683\pi$
$954$	2.56958e50	+	9.67160e50i	0.572188	+	2.15365i
$955$	−1.78471e50			−0.390401
$956$			3.25773e50i			0.700054i
$957$	−2.74046e50	+	3.56363e50i	−0.578523	+	0.752297i
$958$	−1.13990e51			−2.36404
$959$		−	8.95950e49i		−	0.182544i
$960$	2.50077e50	+	1.92311e50i	0.500567	+	0.384941i
$961$	3.96878e50			0.780475
$962$		−	3.35523e50i		−	0.648255i
$963$	6.23588e50	−	1.65676e50i	1.18372	−	0.314495i
$964$	6.54911e50			1.22144
$965$		−	1.29024e50i		−	0.236432i
$966$	−2.15989e49	+	2.80867e49i	−0.0388885	+	0.0505696i
$967$	9.49100e50			1.67904			0.839522	−	0.543326i	$-0.182835\pi$
$967$	9.49100e50			1.67904			0.839522	+	0.543326i	$0.182835\pi$
$968$			6.44529e50i			1.12037i
$969$	2.46313e50	+	1.89417e50i	0.420710	+	0.323530i
$970$	−3.95675e50			−0.664078
$971$		−	6.98988e50i		−	1.15277i	−0.817178	−	0.576385i	$-0.804463\pi$
$971$		−	6.98988e50i		−	1.15277i	0.817178	−	0.576385i	$-0.195537\pi$
$972$	1.27128e50	−	9.27683e50i	0.206022	−	1.50339i
$973$	−4.51030e49			−0.0718269
$974$		−	1.09488e51i		−	1.71343i
$975$	−6.71596e50	+	8.73326e50i	−1.03283	+	1.34307i
$976$	3.56822e49			0.0539267
$977$		−	4.61101e50i		−	0.684840i	−0.939547	−	0.342420i	$-0.888753\pi$
$977$		−	4.61101e50i		−	0.684840i	0.939547	−	0.342420i	$-0.111247\pi$
$978$	−1.09428e51	−	8.41515e50i	−1.59724	−	1.22829i
$979$	−3.02146e49			−0.0433421
$980$			4.00219e50i			0.564227i
$981$	−2.27087e50	−	8.54730e50i	−0.314643	−	1.18428i
$982$	1.92190e51			2.61719
$983$			7.69353e50i			1.02971i	0.857277	+	0.514856i	$0.172155\pi$
$983$			7.69353e50i			1.02971i	−0.857277	+	0.514856i	$0.827845\pi$
$984$	−2.96339e50	+	3.85352e50i	−0.389828	+	0.506922i
$985$	1.58321e49			0.0204702
$986$			6.48834e50i			0.824567i
$987$	8.67091e49	+	6.66801e49i	0.108311	+	0.0832923i
$988$	−1.55323e51			−1.90708
$989$		−	1.13851e50i		−	0.137404i
$990$	−7.70699e50	+	2.04761e50i	−0.914296	+	0.242912i
$991$	−6.70381e49			−0.0781753			−0.0390876	−	0.999236i	$-0.512445\pi$
$991$	−6.70381e49			−0.0781753			−0.0390876	+	0.999236i	$0.512445\pi$
$992$			1.35240e51i			1.55027i
$993$	2.80950e50	−	3.65341e50i	0.316587	−	0.411681i
$994$	1.68396e50			0.186536
$995$		−	5.14771e50i		−	0.560559i
$996$	−1.41415e51	−	1.08749e51i	−1.51386	−	1.16418i
$997$	−9.14842e50			−0.962783			−0.481391	−	0.876506i	$-0.659868\pi$
$997$	−9.14842e50			−0.962783			−0.481391	+	0.876506i	$0.659868\pi$
$998$			8.89107e50i			0.919888i
$999$	−1.85858e50	−	7.76771e49i	−0.189047	−	0.0790096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.35.b.a.2.10	yes	10
3.2	odd	2	inner	3.35.b.a.2.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.35.b.a.2.1	✓	10	3.2	odd	2	inner
3.35.b.a.2.10	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+207965. i q^{2} +(7.87239e7 - 1.02371e8i) q^{3} -2.60695e10 q^{4} +2.95819e11i q^{5} +(2.12895e13 + 1.63718e13i) q^{6} +4.71207e13 q^{7} -1.84873e15i q^{8} +(-4.28228e15 - 1.61180e16i) q^{9} +O(q^{10})\)	\(q+207965. i q^{2} +(7.87239e7 - 1.02371e8i) q^{3} -2.60695e10 q^{4} +2.95819e11i q^{5} +(2.12895e13 + 1.63718e13i) q^{6} +4.71207e13 q^{7} -1.84873e15i q^{8} +(-4.28228e15 - 1.61180e16i) q^{9} -6.15199e16 q^{10} +7.77245e17i q^{11} +(-2.05229e18 + 2.66875e18i) q^{12} -1.72495e19 q^{13} +9.79946e18i q^{14} +(3.02831e19 + 2.32880e19i) q^{15} -6.33991e19 q^{16} -6.96601e20i q^{17} +(3.35198e21 - 8.90563e20i) q^{18} -3.45404e21 q^{19} -7.71185e21i q^{20} +(3.70953e21 - 4.82378e21i) q^{21} -1.61640e23 q^{22} +2.79978e22i q^{23} +(-1.89256e23 - 1.45540e23i) q^{24} +4.94568e23 q^{25} -3.58728e24i q^{26} +(-1.98713e24 - 8.30494e23i) q^{27} -1.22841e24 q^{28} +4.47878e24i q^{29} +(-4.84309e24 + 6.29783e24i) q^{30} -3.00896e25 q^{31} -4.49458e25i q^{32} +(7.95669e25 + 6.11877e25i) q^{33} +1.44869e26 q^{34} +1.39392e25i q^{35} +(1.11637e26 + 4.20189e26i) q^{36} +9.35312e25 q^{37} -7.18319e26i q^{38} +(-1.35795e27 + 1.76584e27i) q^{39} +5.46890e26 q^{40} -2.03614e27i q^{41} +(1.00318e27 + 7.71452e26i) q^{42} -4.06643e27 q^{43} -2.02624e28i q^{44} +(4.76801e27 - 1.26678e27i) q^{45} -5.82256e27 q^{46} +1.79754e28i q^{47} +(-4.99102e27 + 6.49020e27i) q^{48} -5.18966e28 q^{49} +1.02853e29i q^{50} +(-7.13114e28 - 5.48392e28i) q^{51} +4.49685e29 q^{52} +2.88534e29i q^{53} +(1.72714e29 - 4.13253e29i) q^{54} -2.29923e29 q^{55} -8.71137e28i q^{56} +(-2.71916e29 + 3.53592e29i) q^{57} -9.31428e29 q^{58} +9.16791e29i q^{59} +(-7.89466e29 - 6.07107e29i) q^{60} -5.62818e29 q^{61} -6.25758e30i q^{62} +(-2.01784e29 - 7.59493e29i) q^{63} +8.25796e30 q^{64} -5.10271e30i q^{65} +(-1.27249e31 + 1.65471e31i) q^{66} +1.14688e31 q^{67} +1.81601e31i q^{68} +(2.86615e30 + 2.20410e30i) q^{69} -2.89886e30 q^{70} -1.71842e31i q^{71} +(-2.97979e31 + 7.91679e30i) q^{72} +4.19435e31 q^{73} +1.94512e31i q^{74} +(3.89343e31 - 5.06292e31i) q^{75} +9.00452e31 q^{76} +3.66243e31i q^{77} +(-3.67232e32 - 2.82405e32i) q^{78} -2.86486e31 q^{79} -1.87546e31i q^{80} +(-2.41453e32 + 1.38044e32i) q^{81} +4.23446e32 q^{82} +5.29892e32i q^{83} +(-9.67056e31 + 1.25754e32i) q^{84} +2.06068e32 q^{85} -8.45675e32i q^{86} +(4.58495e32 + 3.52587e32i) q^{87} +1.43692e33 q^{88} +3.88739e31i q^{89} +(2.63445e32 + 9.91579e32i) q^{90} -8.12808e32 q^{91} -7.29889e32i q^{92} +(-2.36877e33 + 3.08029e33i) q^{93} -3.73824e33 q^{94} -1.02177e33i q^{95} +(-4.60113e33 - 3.53831e33i) q^{96} +6.43166e33 q^{97} -1.07927e34i q^{98} +(1.25276e34 - 3.32838e33i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+O(q^{10}) \) 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9	\( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+ \cdots + 25\!\cdots\!80 q^{99}+O(q^{100}) \) 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9 - 2611205560422720 * q^10 + 1839088058193784224 * q^12 + 3639874363106470052 * q^13 + 73840351311049043520 * q^15 - 458913568062658993664 * q^16 + 4458031837811233600320 * q^18 - 18128087575667617007644 * q^19 + 47155216574801503272132 * q^21 - 82944038352793331672640 * q^22 - 409540832361157949627904 * q^24 - 306157881917435527620230 * q^25 - 5188422304885629117270366 * q^27 + 1200257625823339935397952 * q^28 + 4536084230702466968226240 * q^30 - 16210124253435972809624620 * q^31 + 126080615773751026110338880 * q^33 - 95987113410493892068003584 * q^34 - 3778740843166378351675872 * q^36 + 1107877531995608327024550788 * q^37 - 1478567172848906073011055372 * q^39 + 1263325098820483891139005440 * q^40 - 1100302459230379163303563200 * q^42 - 9626706570211152095714911228 * q^43 + 6764773545409610284732206720 * q^45 - 27597232473865615892091763584 * q^46 - 8343379363160137604055750144 * q^48 + 123592722368423574378839845566 * q^49 - 154249157901217791265339790592 * q^51 + 364968511672502550561914224448 * q^52 - 627476296349871988055293152672 * q^54 + 613243149395194155294476807040 * q^55 - 200956522080425270978267102412 * q^57 + 911704545930429232428533728320 * q^58 - 5328764870697498499759490872320 * q^60 + 3721644688213000805892336114020 * q^61 - 17793115140162074693090527345068 * q^63 + 31237929890100178456062152876032 * q^64 - 56522434211150051720831749496640 * q^66 + 64610860820592975458220110976548 * q^67 - 75655347603668350171840261441152 * q^69 + 173956643092708582155719748059520 * q^70 - 251655858465803757687636471720960 * q^72 + 219744563327934154882825652170292 * q^73 - 496257346175691552817323610505790 * q^75 + 755138601297458545349651061598016 * q^76 - 1416035973322463045417779737274560 * q^78 + 1282143700776175332608732687725076 * q^79 - 1752271238163022185686811202609110 * q^81 + 2617087107433191584283809414490240 * q^82 - 3353754502177451840461431126935232 * q^84 + 3064318591304040683100089841123840 * q^85 - 1378895999771415686373632115051840 * q^87 + 2890193643030846777850875310341120 * q^88 - 3749676158586283582801263594857280 * q^90 + 3328617839789463835132355588364424 * q^91 - 913294458028957034010214182487068 * q^93 - 1912224205137436189468854646420224 * q^94 + 5756213457708614900907762734014464 * q^96 - 11994339580278056229821837667722092 * q^97 + 25463971047319347192017533065521280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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