LMFDB - Embedded newform 3.37.b.b.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,37,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, 37, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 37);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 37 $
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:	$24.6273775978$
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} + 1732091138 x^{8} + \cdots + 87\!\cdots\!00 $ x^10 + 1732091138x^8 + 1041970113139590528x^6 + 259633704442571812012752896x^4 + 25957407434307800681948964695572480x^2 + 871827272021197959834823668999764154777600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{71}\cdot 5^{4}\cdot 7^{2}\cdot 13 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.1
Root			$-26735.5i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.37.b.b.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-481239. i q^{2} +(-3.00483e8 + 2.44550e8i) q^{3} -1.62872e11 q^{4} -1.10872e12i q^{5} +(1.17687e14 + 1.44604e14i) q^{6} +2.90621e15 q^{7} +4.53097e16i q^{8} +(3.04857e16 - 1.46966e17i) q^{9} +O(q^{10})$	\(q-481239. i q^{2} +(-3.00483e8 + 2.44550e8i) q^{3} -1.62872e11 q^{4} -1.10872e12i q^{5} +(1.17687e14 + 1.44604e14i) q^{6} +2.90621e15 q^{7} +4.53097e16i q^{8} +(3.04857e16 - 1.46966e17i) q^{9} -5.33560e17 q^{10} +4.36755e18i q^{11} +(4.89402e19 - 3.98302e19i) q^{12} +4.74813e19 q^{13} -1.39858e21i q^{14} +(2.71137e20 + 3.33152e20i) q^{15} +1.06123e22 q^{16} +5.47148e21i q^{17} +(-7.07258e22 - 1.46709e22i) q^{18} -3.53105e22 q^{19} +1.80579e23i q^{20} +(-8.73269e23 + 7.10713e23i) q^{21} +2.10184e24 q^{22} -3.93423e24i q^{23} +(-1.10805e25 - 1.36148e25i) q^{24} +1.33227e25 q^{25} -2.28498e25i q^{26} +(2.67801e25 + 5.16161e25i) q^{27} -4.73340e26 q^{28} -8.94976e25i q^{29} +(1.60326e26 - 1.30482e26i) q^{30} -2.09423e26 q^{31} -1.99341e27i q^{32} +(-1.06808e27 - 1.31238e27i) q^{33} +2.63309e27 q^{34} -3.22218e27i q^{35} +(-4.96525e27 + 2.39366e28i) q^{36} +1.24419e28 q^{37} +1.69928e28i q^{38} +(-1.42673e28 + 1.16115e28i) q^{39} +5.02358e28 q^{40} -1.88686e29i q^{41} +(3.42023e29 + 4.20251e29i) q^{42} -3.88685e28 q^{43} -7.11350e29i q^{44} +(-1.62944e29 - 3.38001e28i) q^{45} -1.89330e30 q^{46} +3.19458e28i q^{47} +(-3.18883e30 + 2.59524e30i) q^{48} +5.79435e30 q^{49} -6.41138e30i q^{50} +(-1.33805e30 - 1.64409e30i) q^{51} -7.73335e30 q^{52} -7.64301e30i q^{53} +(2.48397e31 - 1.28876e31i) q^{54} +4.84239e30 q^{55} +1.31680e32i q^{56} +(1.06102e31 - 8.63518e30i) q^{57} -4.30697e31 q^{58} -7.04173e31i q^{59} +(-4.41605e31 - 5.42610e31i) q^{60} +2.17887e32 q^{61} +1.00783e32i q^{62} +(8.85979e31 - 4.27115e32i) q^{63} -2.30034e32 q^{64} -5.26435e31i q^{65} +(-6.31566e32 + 5.14003e32i) q^{66} -9.44351e32 q^{67} -8.91148e32i q^{68} +(9.62114e32 + 1.18217e33i) q^{69} -1.55064e33 q^{70} -7.27970e32i q^{71} +(6.65898e33 + 1.38130e33i) q^{72} +4.28526e32 q^{73} -5.98752e33i q^{74} +(-4.00323e33 + 3.25805e33i) q^{75} +5.75108e33 q^{76} +1.26930e34i q^{77} +(5.58792e33 + 6.86599e33i) q^{78} +6.42143e32 q^{79} -1.17661e34i q^{80} +(-2.06696e34 - 8.96072e33i) q^{81} -9.08031e34 q^{82} +4.10739e34i q^{83} +(1.42231e35 - 1.15755e35i) q^{84} +6.06634e33 q^{85} +1.87051e34i q^{86} +(2.18866e34 + 2.68925e34i) q^{87} -1.97892e35 q^{88} -1.85710e35i q^{89} +(-1.62659e34 + 7.84152e34i) q^{90} +1.37991e35 q^{91} +6.40774e35i q^{92} +(6.29281e34 - 5.12143e34i) q^{93} +1.53735e34 q^{94} +3.91495e34i q^{95} +(4.87488e35 + 5.98987e35i) q^{96} +3.60798e35 q^{97} -2.78847e36i q^{98} +(6.41882e35 + 1.33148e35i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 552156750 q^{3} - 435200290064 q^{4} + 77238909590832 q^{6} - 12\!\cdots\!00 q^{7}+ \cdots + 69\!\cdots\!78 q^{9}+O(q^{10}) $ 10 * q - 552156750 * q^3 - 435200290064 * q^4 + 77238909590832 * q^6 - 1227392913852700 * q^7 + 69328040174658378 * q^9	$ 10 q - 552156750 q^{3} - 435200290064 q^{4} + 77238909590832 q^{6} - 12\!\cdots\!00 q^{7}+ \cdots + 29\!\cdots\!20 q^{99}+O(q^{100}) $ 10 * q - 552156750 * q^3 - 435200290064 * q^4 + 77238909590832 * q^6 - 1227392913852700 * q^7 + 69328040174658378 * q^9 + 976353968400999840 * q^10 - 13909669295912917200 * q^12 + 146442021383468630900 * q^13 + 7346306914204243680 * q^15 + 8190375794092103561344 * q^16 - 116380061882656121268000 * q^18 + 251867201240528510816036 * q^19 - 3316093374315604451804172 * q^21 + 6375713195756021276887200 * q^22 - 18479722715707703137259904 * q^24 - 7272407101172449985508950 * q^25 + 37081479963629919172136850 * q^27 - 581040957055587380082052000 * q^28 + 832077359475776822335514400 * q^30 - 2837400895897932038626257820 * q^31 - 1833168501223628340439879200 * q^33 + 11044532239488942328340194176 * q^34 - 32262827456884310986989469968 * q^36 + 46026416879684258821119845300 * q^37 + 57128063394219587707605260868 * q^39 + 14850499435375431475622142720 * q^40 + 551003488989169331884355647200 * q^42 - 543751838871943644621511222300 * q^43 - 75992211973807694886478996800 * q^45 - 887182867438274648036289139776 * q^46 - 6175798579441788000263903318400 * q^48 + 4160815567016241405173969776926 * q^49 - 2349347159740543712848217109888 * q^51 - 1307858224937756917383112717600 * q^52 + 35390782846752825865826083751568 * q^54 - 30568574550133842572339360395200 * q^55 + 140759907582972539349070577896500 * q^57 - 112605799975805654976196455444000 * q^58 + 19469866547367779716225803605760 * q^60 + 250499227169556248885727488200820 * q^61 - 434037118158370938102741493062300 * q^63 - 628754572186817852398452012827648 * q^64 + 1808913396822349027193824888380960 * q^66 - 3266640518886976176082778405004700 * q^67 + 5226032060124551681525948207907648 * q^69 - 11529100185846942980259125797809600 * q^70 + 19879821238248816464160255047788800 * q^72 - 4353366099339985469471204489853100 * q^73 + 15739280815644629096708517058487250 * q^75 - 32093648191079013144382153537026976 * q^76 + 66756441224105756984056960627624800 * q^78 - 62441157931070689325228267195149084 * q^79 + 102373232392301630415794998228710090 * q^81 - 295731520386077266321378186874491200 * q^82 + 492063662513568202891754719135343328 * q^84 - 416995278796335191384264774379644160 * q^85 + 502161755301600073278417594406864800 * q^87 - 1043368725545479380062123692743456000 * q^88 + 1148239664725140620121403824942828960 * q^90 - 198812949993474284590473149470475384 * q^91 + 709190784760155706508652430361622900 * q^93 - 1775468098694354855547362712124166784 * q^94 + 2402404280227868861578148783194622976 * q^96 - 502412071359393103768239713429459500 * q^97 + 2995711137935834844910948248309577920 * 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 $

$2$		−	481239.i		−	1.83578i	−0.396833	−	0.917891i	$-0.629891\pi$
$2$		−	481239.i		−	1.83578i	0.396833	−	0.917891i	$-0.370109\pi$
$3$	−3.00483e8	+	2.44550e8i	−0.775600	+	0.631225i
$3$	−3.00483e8	+	2.44550e8i	−0.775600	+	0.631225i
$4$	−1.62872e11			−2.37009
$5$		−	1.10872e12i		−	0.290644i	−0.989384	−	0.145322i	$-0.953578\pi$
$5$		−	1.10872e12i		−	0.290644i	0.989384	−	0.145322i	$-0.0464219\pi$
$6$	1.17687e14	+	1.44604e14i	1.15879	+	1.42383i
$7$	2.90621e15			1.78469			0.892345	−	0.451354i	$-0.149059\pi$
$7$	2.90621e15			1.78469			0.892345	+	0.451354i	$0.149059\pi$
$8$			4.53097e16i			2.51519i
$9$	3.04857e16	−	1.46966e17i	0.203110	−	0.979156i
$10$	−5.33560e17			−0.533560
$11$			4.36755e18i			0.785542i	0.919636	+	0.392771i	$0.128484\pi$
$11$			4.36755e18i			0.785542i	−0.919636	+	0.392771i	$0.871516\pi$
$12$	4.89402e19	−	3.98302e19i	1.83824	−	1.49606i
$13$	4.74813e19			0.422223			0.211112	−	0.977462i	$-0.432292\pi$
$13$	4.74813e19			0.422223			0.211112	+	0.977462i	$0.432292\pi$
$14$		−	1.39858e21i		−	3.27630i
$15$	2.71137e20	+	3.33152e20i	0.183462	+	0.225424i
$16$	1.06123e22			2.24725
$17$			5.47148e21i			0.389067i	0.980896	+	0.194533i	$0.0623193\pi$
$17$			5.47148e21i			0.389067i	−0.980896	+	0.194533i	$0.937681\pi$
$18$	−7.07258e22	−	1.46709e22i	−1.79752	−	0.372865i
$19$	−3.53105e22			−0.339109			−0.169555	−	0.985521i	$-0.554233\pi$
$19$	−3.53105e22			−0.339109			−0.169555	+	0.985521i	$0.554233\pi$
$20$			1.80579e23i			0.688854i
$21$	−8.73269e23	+	7.10713e23i	−1.38421	+	1.12654i
$22$	2.10184e24			1.44208
$23$		−	3.93423e24i		−	1.21271i	−0.795192	−	0.606357i	$-0.792630\pi$
$23$		−	3.93423e24i		−	1.21271i	0.795192	−	0.606357i	$-0.207370\pi$
$24$	−1.10805e25	−	1.36148e25i	−1.58765	−	1.95078i
$25$	1.33227e25			0.915526
$26$		−	2.28498e25i		−	0.775109i
$27$	2.67801e25	+	5.16161e25i	0.460536	+	0.887641i
$28$	−4.73340e26			−4.22988
$29$		−	8.94976e25i		−	0.425253i	−0.977134	−	0.212627i	$-0.931798\pi$
$29$		−	8.94976e25i		−	0.425253i	0.977134	−	0.212627i	$-0.0682018\pi$
$30$	1.60326e26	−	1.30482e26i	0.413829	−	0.336796i
$31$	−2.09423e26			−0.299581			−0.149790	−	0.988718i	$-0.547860\pi$
$31$	−2.09423e26			−0.299581			−0.149790	+	0.988718i	$0.547860\pi$
$32$		−	1.99341e27i		−	1.61026i
$33$	−1.06808e27	−	1.31238e27i	−0.495854	−	0.609266i
$34$	2.63309e27			0.714242
$35$		−	3.22218e27i		−	0.518710i
$36$	−4.96525e27	+	2.39366e28i	−0.481389	+	2.32069i
$37$	1.24419e28			0.736640			0.368320	−	0.929699i	$-0.379933\pi$
$37$	1.24419e28			0.736640			0.368320	+	0.929699i	$0.379933\pi$
$38$			1.69928e28i			0.622530i
$39$	−1.42673e28	+	1.16115e28i	−0.327476	+	0.266518i
$40$	5.02358e28			0.731026
$41$		−	1.88686e29i		−	1.76048i	−0.474532	−	0.880238i	$-0.657383\pi$
$41$		−	1.88686e29i		−	1.76048i	0.474532	−	0.880238i	$-0.342617\pi$
$42$	3.42023e29	+	4.20251e29i	2.06808	+	2.54110i
$43$	−3.88685e28			−0.153874			−0.0769371	−	0.997036i	$-0.524514\pi$
$43$	−3.88685e28			−0.153874			−0.0769371	+	0.997036i	$0.524514\pi$
$44$		−	7.11350e29i		−	1.86181i
$45$	−1.62944e29	−	3.38001e28i	−0.284586	−	0.0590327i
$46$	−1.89330e30			−2.22628
$47$			3.19458e28i			0.0255066i	0.999919	+	0.0127533i	$0.00405960\pi$
$47$			3.19458e28i			0.0255066i	−0.999919	+	0.0127533i	$0.995940\pi$
$48$	−3.18883e30	+	2.59524e30i	−1.74296	+	1.41852i
$49$	5.79435e30			2.18512
$50$		−	6.41138e30i		−	1.68071i
$51$	−1.33805e30	−	1.64409e30i	−0.245589	−	0.301760i
$52$	−7.73335e30			−1.00071
$53$		−	7.64301e30i		−	0.701938i	−0.936387	−	0.350969i	$-0.885852\pi$
$53$		−	7.64301e30i		−	0.701938i	0.936387	−	0.350969i	$-0.114148\pi$
$54$	2.48397e31	−	1.28876e31i	1.62951	−	0.845443i
$55$	4.84239e30			0.228314
$56$			1.31680e32i			4.48884i
$57$	1.06102e31	−	8.63518e30i	0.263013	−	0.214054i
$58$	−4.30697e31			−0.780672
$59$		−	7.04173e31i		−	0.938303i	−0.883118	−	0.469151i	$-0.844560\pi$
$59$		−	7.04173e31i		−	0.938303i	0.883118	−	0.469151i	$-0.155440\pi$
$60$	−4.41605e31	−	5.42610e31i	−0.434822	−	0.534275i
$61$	2.17887e32			1.59329			0.796645	−	0.604447i	$-0.206606\pi$
$61$	2.17887e32			1.59329			0.796645	+	0.604447i	$0.206606\pi$
$62$			1.00783e32i			0.549965i
$63$	8.85979e31	−	4.27115e32i	0.362488	−	1.74749i
$64$	−2.30034e32			−0.708846
$65$		−	5.26435e31i		−	0.122717i
$66$	−6.31566e32	+	5.14003e32i	−1.11848	+	0.910280i
$67$	−9.44351e32			−1.27581			−0.637906	−	0.770114i	$-0.720199\pi$
$67$	−9.44351e32			−1.27581			−0.637906	+	0.770114i	$0.720199\pi$
$68$		−	8.91148e32i		−	0.922124i
$69$	9.62114e32	+	1.18217e33i	0.765496	+	0.940581i
$70$	−1.55064e33			−0.952239
$71$		−	7.27970e32i		−	0.346309i	−0.984895	−	0.173154i	$-0.944604\pi$
$71$		−	7.27970e32i		−	0.346309i	0.984895	−	0.173154i	$-0.0553960\pi$
$72$	6.65898e33	+	1.38130e33i	2.46276	+	0.510860i
$73$	4.28526e32			0.123642			0.0618210	−	0.998087i	$-0.480309\pi$
$73$	4.28526e32			0.123642			0.0618210	+	0.998087i	$0.480309\pi$
$74$		−	5.98752e33i		−	1.35231i
$75$	−4.00323e33	+	3.25805e33i	−0.710082	+	0.577903i
$76$	5.75108e33			0.803721
$77$			1.26930e34i			1.40195i
$78$	5.58792e33	+	6.86599e33i	0.489268	+	0.601175i
$79$	6.42143e32			0.0447038			0.0223519	−	0.999750i	$-0.492885\pi$
$79$	6.42143e32			0.0447038			0.0223519	+	0.999750i	$0.492885\pi$
$80$		−	1.17661e34i		−	0.653150i
$81$	−2.06696e34	−	8.96072e33i	−0.917493	−	0.397752i
$82$	−9.08031e34			−3.23185
$83$			4.10739e34i			1.17533i	0.809104	+	0.587665i	$0.199953\pi$
$83$			4.10739e34i			1.17533i	−0.809104	+	0.587665i	$0.800047\pi$
$84$	1.42231e35	−	1.15755e35i	3.28070	−	2.67001i
$85$	6.06634e33			0.113080
$86$			1.87051e34i			0.282479i
$87$	2.18866e34	+	2.68925e34i	0.268430	+	0.329826i
$88$	−1.97892e35			−1.97579
$89$		−	1.85710e35i		−	1.51292i	−0.654043	−	0.756458i	$-0.726928\pi$
$89$		−	1.85710e35i		−	1.51292i	0.654043	−	0.756458i	$-0.273072\pi$
$90$	−1.62659e34	+	7.84152e34i	−0.108371	+	0.522438i
$91$	1.37991e35			0.753538
$92$			6.40774e35i			2.87425i
$93$	6.29281e34	−	5.12143e34i	0.232355	−	0.189103i
$94$	1.53735e34			0.0468245
$95$			3.91495e34i			0.0985602i
$96$	4.87488e35	+	5.98987e35i	1.01644	+	1.24892i
$97$	3.60798e35			0.624271			0.312135	−	0.950038i	$-0.398956\pi$
$97$	3.60798e35			0.624271			0.312135	+	0.950038i	$0.398956\pi$
$98$		−	2.78847e36i		−	4.01140i
$99$	6.41882e35	+	1.33148e35i	0.769169	+	0.159551i
$100$	−2.16988e36			−2.16988
$101$			5.31989e35i			0.444752i	0.974961	+	0.222376i	$0.0713812\pi$
$101$			5.31989e35i			0.444752i	−0.974961	+	0.222376i	$0.928619\pi$
$102$	−7.91199e35	+	6.43921e35i	−0.553965	+	0.450847i
$103$	4.54208e35			0.266799			0.133400	−	0.991062i	$-0.457411\pi$
$103$	4.54208e35			0.266799			0.133400	+	0.991062i	$0.457411\pi$
$104$			2.15136e36i			1.06197i
$105$	7.87983e35	+	9.68211e35i	0.327423	+	0.402312i
$106$	−3.67811e36			−1.28860
$107$		−	1.82385e35i		−	0.0539612i	−0.999636	−	0.0269806i	$-0.991411\pi$
$107$		−	1.82385e35i		−	0.0539612i	0.999636	−	0.0269806i	$-0.00858923\pi$
$108$	−4.36171e36	−	8.40679e36i	−1.09151	−	2.10379i
$109$	3.88230e36			0.823023			0.411511	−	0.911405i	$-0.365001\pi$
$109$	3.88230e36			0.823023			0.411511	+	0.911405i	$0.365001\pi$
$110$		−	2.33035e36i		−	0.419134i
$111$	−3.73858e36	+	3.04266e36i	−0.571338	+	0.464986i
$112$	3.08417e37			4.01064
$113$			1.41668e37i			1.56985i	0.619588	+	0.784927i	$0.287300\pi$
$113$			1.41668e37i			1.56985i	−0.619588	+	0.784927i	$0.712700\pi$
$114$	−4.15559e36	−	5.10606e36i	−0.392957	−	0.482834i
$115$	−4.36196e36			−0.352469
$116$			1.45766e37i			1.00789i
$117$	1.44750e36	−	6.97814e36i	0.0857576	−	0.413422i
$118$	−3.38875e37			−1.72252
$119$			1.59013e37i			0.694364i
$120$	−1.50950e37	+	1.22851e37i	−0.566984	+	0.461442i
$121$	1.18372e37			0.382923
$122$		−	1.04856e38i		−	2.92493i
$123$	4.61431e37	+	5.66970e37i	1.11126	+	1.36542i
$124$	3.41091e37			0.710035
$125$		−	3.09051e37i		−	0.556737i
$126$	−2.05544e38	−	4.26368e37i	−3.20801	−	0.665449i
$127$	9.30260e37			1.25932			0.629662	−	0.776870i	$-0.283194\pi$
$127$	9.30260e37			1.25932			0.629662	+	0.776870i	$0.283194\pi$
$128$		−	2.62850e37i		−	0.308978i
$129$	1.16793e37	−	9.50528e36i	0.119345	−	0.0971293i
$130$	−2.53341e37			−0.225281
$131$		−	3.31927e37i		−	0.257134i	−0.991701	−	0.128567i	$-0.958962\pi$
$131$		−	3.31927e37i		−	0.257134i	0.991701	−	0.128567i	$-0.0410377\pi$
$132$	1.73960e38	+	2.13749e38i	1.17522	+	1.44402i
$133$	−1.02620e38			−0.605205
$134$			4.54459e38i			2.34211i
$135$	5.72278e37	−	2.96916e37i	0.257988	−	0.133852i
$136$	−2.47911e38			−0.978577
$137$		−	3.19904e38i		−	1.10675i	−0.832933	−	0.553374i	$-0.813340\pi$
$137$		−	3.19904e38i		−	1.10675i	0.832933	−	0.553374i	$-0.186660\pi$
$138$	5.68906e38	−	4.63007e38i	1.72670	−	1.40528i
$139$	2.46081e38			0.655861			0.327931	−	0.944702i	$-0.393649\pi$
$139$	2.46081e38			0.655861			0.327931	+	0.944702i	$0.393649\pi$
$140$			5.24801e38i			1.22939i
$141$	−7.81232e36	−	9.59916e36i	−0.0161004	−	0.0197829i
$142$	−3.50328e38			−0.635747
$143$			2.07377e38i			0.331674i
$144$	3.23524e38	−	1.55965e39i	0.456438	−	2.20041i
$145$	−9.92278e37			−0.123597
$146$		−	2.06223e38i		−	0.226980i
$147$	−1.74110e39	+	1.41701e39i	−1.69478	+	1.37930i
$148$	−2.02643e39			−1.74590
$149$		−	7.31711e38i		−	0.558453i	−0.960225	−	0.279226i	$-0.909922\pi$
$149$		−	7.31711e38i		−	0.558453i	0.960225	−	0.279226i	$-0.0900780\pi$
$150$	1.56790e39	+	1.92651e39i	1.06090	+	1.30355i
$151$	−1.58015e39			−0.948666			−0.474333	−	0.880345i	$-0.657311\pi$
$151$	−1.58015e39			−0.948666			−0.474333	+	0.880345i	$0.657311\pi$
$152$		−	1.59991e39i		−	0.852925i
$153$	8.04122e38	+	1.66802e38i	0.380957	+	0.0790232i
$154$	6.10839e39			2.57367
$155$			2.32192e38i			0.0870715i
$156$	2.32374e39	−	1.89119e39i	0.776149	−	0.631672i
$157$	−2.89411e39			−0.861631			−0.430815	−	0.902440i	$-0.641774\pi$
$157$	−2.89411e39			−0.861631			−0.430815	+	0.902440i	$0.641774\pi$
$158$		−	3.09024e38i		−	0.0820664i
$159$	1.86909e39	+	2.29660e39i	0.443081	+	0.544423i
$160$	−2.21014e39			−0.468015
$161$		−	1.14337e40i		−	2.16432i
$162$	−4.31225e39	+	9.94704e39i	−0.730186	+	1.68432i
$163$	2.01343e39			0.305183			0.152592	−	0.988289i	$-0.451238\pi$
$163$	2.01343e39			0.305183			0.152592	+	0.988289i	$0.451238\pi$
$164$			3.07316e40i			4.17249i
$165$	−1.45506e39	+	1.18421e39i	−0.177080	+	0.144117i
$166$	1.97664e40			2.15765
$167$		−	1.05538e40i		−	1.03398i	−0.855992	−	0.516990i	$-0.827053\pi$
$167$		−	1.05538e40i		−	1.03398i	0.855992	−	0.516990i	$-0.172947\pi$
$168$	−3.22022e40	−	3.95675e40i	−2.83347	−	3.48154i
$169$	−1.03917e40			−0.821728
$170$		−	2.91936e39i		−	0.207590i
$171$	−1.07647e39	+	5.18945e39i	−0.0688764	+	0.332041i
$172$	6.33058e39			0.364696
$173$		−	2.80866e40i		−	1.45770i	−0.684672	−	0.728851i	$-0.740055\pi$
$173$		−	2.80866e40i		−	1.45770i	0.684672	−	0.728851i	$-0.259945\pi$
$174$	1.29417e40	−	1.05327e40i	0.605489	−	0.492779i
$175$	3.87185e40			1.63393
$176$			4.63499e40i			1.76531i
$177$	1.72205e40	+	2.11592e40i	0.592280	+	0.727747i
$178$	−8.93708e40			−2.77738
$179$			4.29449e40i			1.20658i	0.797521	+	0.603291i	$0.206144\pi$
$179$			4.29449e40i			1.20658i	−0.797521	+	0.603291i	$0.793856\pi$
$180$	2.65390e40	+	5.50507e39i	0.674496	+	0.139913i
$181$	−1.80786e40			−0.415864			−0.207932	−	0.978143i	$-0.566673\pi$
$181$	−1.80786e40			−0.415864			−0.207932	+	0.978143i	$0.566673\pi$
$182$		−	6.64065e40i		−	1.38333i
$183$	−6.54715e40	+	5.32843e40i	−1.23576	+	1.00573i
$184$	1.78259e41			3.05021
$185$		−	1.37946e40i		−	0.214100i
$186$	−2.46463e40	−	3.02835e40i	−0.347152	−	0.426553i
$187$	−2.38970e40			−0.305628
$188$		−	5.20306e39i		−	0.0604529i
$189$	7.78286e40	+	1.50007e41i	0.821914	+	1.58416i
$190$	1.88403e40			0.180935
$191$		−	1.69559e41i		−	1.48156i	−0.671747	−	0.740781i	$-0.734456\pi$
$191$		−	1.69559e41i		−	1.48156i	0.671747	−	0.740781i	$-0.265544\pi$
$192$	6.91213e40	−	5.62546e40i	0.549781	−	0.447442i
$193$	1.42268e40			0.103057			0.0515284	−	0.998672i	$-0.483591\pi$
$193$	1.42268e40			0.103057			0.0515284	+	0.998672i	$0.483591\pi$
$194$		−	1.73630e41i		−	1.14602i
$195$	1.28739e40	+	1.58185e40i	0.0774619	+	0.0951791i
$196$	−9.43735e41			−5.17894
$197$			3.21854e41i			1.61164i	0.592162	+	0.805819i	$0.298274\pi$
$197$			3.21854e41i			1.61164i	−0.592162	+	0.805819i	$0.701726\pi$
$198$	6.40759e40	−	3.08899e41i	0.292901	−	1.41203i
$199$	2.25830e41			0.942814			0.471407	−	0.881916i	$-0.343746\pi$
$199$	2.25830e41			0.942814			0.471407	+	0.881916i	$0.343746\pi$
$200$			6.03645e41i			2.30272i
$201$	2.83762e41	−	2.30941e41i	0.989520	−	0.805325i
$202$	2.56014e41			0.816467
$203$		−	2.60099e41i		−	0.758945i
$204$	2.17930e41	+	2.67775e41i	0.582068	+	0.715199i
$205$	−2.09200e41			−0.511673
$206$		−	2.18583e41i		−	0.489785i
$207$	−5.78198e41	−	1.19938e41i	−1.18744	−	0.246314i
$208$	5.03887e41			0.948840
$209$		−	1.54221e41i		−	0.266385i
$210$	4.65941e41	−	3.79208e41i	0.738556	−	0.601077i
$211$	1.08242e42			1.57512			0.787559	−	0.616240i	$-0.211345\pi$
$211$	1.08242e42			1.57512			0.787559	+	0.616240i	$0.211345\pi$
$212$			1.24483e42i			1.66366i
$213$	1.78025e41	+	2.18743e41i	0.218599	+	0.268597i
$214$	−8.77709e40			−0.0990609
$215$			4.30943e40i			0.0447227i
$216$	−2.33871e42	+	1.21339e42i	−2.23259	+	1.15834i
$217$	−6.08628e41			−0.534659
$218$		−	1.86831e42i		−	1.51089i
$219$	−1.28765e41	+	1.04796e41i	−0.0958966	+	0.0780459i
$220$	−7.88688e41			−0.541124
$221$			2.59793e41i			0.164273i
$222$	1.46425e42	+	1.79915e42i	0.853612	+	1.04885i
$223$	−2.27690e42			−1.22421			−0.612105	−	0.790776i	$-0.709677\pi$
$223$	−2.27690e42			−1.22421			−0.612105	+	0.790776i	$0.709677\pi$
$224$		−	5.79328e42i		−	2.87382i
$225$	4.06150e41	−	1.95798e42i	0.185952	−	0.896443i
$226$	6.81761e42			2.88191
$227$			6.95886e41i			0.271689i	0.990730	+	0.135845i	$0.0433748\pi$
$227$			6.95886e41i			0.271689i	−0.990730	+	0.135845i	$0.956625\pi$
$228$	−1.72810e42	+	1.40642e42i	−0.623365	+	0.507329i
$229$	−3.39107e42			−1.13057			−0.565286	−	0.824895i	$-0.691234\pi$
$229$	−3.39107e42			−1.13057			−0.565286	+	0.824895i	$0.691234\pi$
$230$			2.09915e42i			0.647055i
$231$	−3.10408e42	−	3.81404e42i	−0.884946	−	1.08735i
$232$	4.05511e42			1.06959
$233$			6.53021e42i			1.59412i	0.603901	+	0.797059i	$0.293612\pi$
$233$			6.53021e42i			1.59412i	−0.603901	+	0.797059i	$0.706388\pi$
$234$	−3.35815e42	−	6.96593e41i	−0.758953	−	0.157432i
$235$	3.54189e40			0.00741334
$236$			1.14690e43i			2.22386i
$237$	−1.92953e41	+	1.57036e41i	−0.0346722	+	0.0282182i
$238$	7.65232e42			1.27470
$239$		−	2.39059e42i		−	0.369269i	−0.982807	−	0.184635i	$-0.940890\pi$
$239$		−	2.39059e42i		−	0.369269i	0.982807	−	0.184635i	$-0.0591102\pi$
$240$	2.87740e42	+	3.53552e42i	0.412285	+	0.506583i
$241$	7.26334e42			0.965671			0.482836	−	0.875711i	$-0.339607\pi$
$241$	7.26334e42			0.965671			0.482836	+	0.875711i	$0.339607\pi$
$242$		−	5.69651e42i		−	0.702963i
$243$	8.40222e42	−	2.36221e42i	0.962678	−	0.270648i
$244$	−3.54877e43			−3.77625
$245$		−	6.42431e42i		−	0.635093i
$246$	2.72848e43	−	2.22058e43i	2.50662	−	2.04002i
$247$	−1.67659e42			−0.143180
$248$		−	9.48889e42i		−	0.753503i
$249$	−1.00446e43	−	1.23420e43i	−0.741898	−	0.911586i
$250$	−1.48727e43			−1.02205
$251$			2.77723e43i			1.77617i	0.459676	+	0.888087i	$0.347966\pi$
$251$			2.77723e43i			1.77617i	−0.459676	+	0.888087i	$0.652034\pi$
$252$	−1.44301e43	+	6.95649e43i	−0.859130	+	4.14171i
$253$	1.71829e43			0.952638
$254$		−	4.47677e43i		−	2.31184i
$255$	−1.82283e42	+	1.48352e42i	−0.0877049	+	0.0713790i
$256$	−2.84572e43			−1.27606
$257$		−	1.53513e43i		−	0.641726i	−0.947126	−	0.320863i	$-0.896027\pi$
$257$		−	1.53513e43i		−	0.641726i	0.947126	−	0.320863i	$-0.103973\pi$
$258$	−4.57431e42	−	5.62055e42i	−0.178308	−	0.219091i
$259$	3.61588e43			1.31467
$260$			8.57412e42i			0.290850i
$261$	−1.31531e43	−	2.72839e42i	−0.416389	−	0.0863730i
$262$	−1.59736e43			−0.472042
$263$			2.71249e42i			0.0748454i	0.999300	+	0.0374227i	$0.0119148\pi$
$263$			2.71249e42i			0.0748454i	−0.999300	+	0.0374227i	$0.988085\pi$
$264$	5.94633e43	−	4.83945e43i	1.53242	−	1.24717i
$265$	−8.47396e42			−0.204014
$266$			4.93848e43i			1.11102i
$267$	4.54152e43	+	5.58027e43i	0.954990	+	1.17342i
$268$	1.53808e44			3.02380
$269$		−	1.53247e43i		−	0.281741i	−0.990028	−	0.140870i	$-0.955010\pi$
$269$		−	1.53247e43i		−	0.281741i	0.990028	−	0.140870i	$-0.0449901\pi$
$270$	−1.42888e43	−	2.75403e43i	−0.245723	−	0.473609i
$271$	−1.01038e44			−1.62569			−0.812845	−	0.582480i	$-0.802082\pi$
$271$	−1.01038e44			−1.62569			−0.812845	+	0.582480i	$0.802082\pi$
$272$			5.80651e43i			0.874330i
$273$	−4.14639e43	+	3.37456e43i	−0.584443	+	0.475652i
$274$	−1.53950e44			−2.03175
$275$			5.81874e43i			0.719184i
$276$	−1.56701e44	−	1.92542e44i	−1.81430	−	2.22926i
$277$	7.15778e43			0.776502			0.388251	−	0.921554i	$-0.373079\pi$
$277$	7.15778e43			0.776502			0.388251	+	0.921554i	$0.373079\pi$
$278$		−	1.18424e44i		−	1.20402i
$279$	−6.38440e42	+	3.07781e43i	−0.0608478	+	0.293336i
$280$	1.45996e44			1.30466
$281$			1.46146e44i			1.22482i	0.790540	+	0.612410i	$0.209800\pi$
$281$			1.46146e44i			1.22482i	−0.790540	+	0.612410i	$0.790200\pi$
$282$	−4.61949e42	+	3.75959e42i	−0.0363170	+	0.0295568i
$283$	4.68747e43			0.345767			0.172883	−	0.984942i	$-0.444692\pi$
$283$	4.68747e43			0.345767			0.172883	+	0.984942i	$0.444692\pi$
$284$			1.18566e44i			0.820784i
$285$	−9.57400e42	−	1.17638e43i	−0.0622137	−	0.0764433i
$286$	9.97978e43			0.608881
$287$		−	5.48362e44i		−	3.14190i
$288$	−2.92964e44	−	6.07705e43i	−1.57670	−	0.327060i
$289$	1.67833e44			0.848627
$290$			4.77523e43i			0.226898i
$291$	−1.08414e44	+	8.82330e43i	−0.484184	+	0.394055i
$292$	−6.97947e43			−0.293043
$293$		−	2.65359e44i		−	1.04765i	−0.851825	−	0.523826i	$-0.824504\pi$
$293$		−	2.65359e44i		−	1.04765i	0.851825	−	0.523826i	$-0.175496\pi$
$294$	6.81918e44	+	8.37888e44i	2.53210	+	3.11124i
$295$	−7.80731e43			−0.272712
$296$			5.63738e44i			1.85279i
$297$	−2.25436e44	+	1.16963e44i	−0.697280	+	0.361771i
$298$	−3.52128e44			−1.02520
$299$		−	1.86802e44i		−	0.512036i
$300$	6.52013e44	−	5.30644e44i	1.68296	−	1.36968i
$301$	−1.12960e44			−0.274618
$302$			7.60430e44i			1.74154i
$303$	−1.30098e44	−	1.59854e44i	−0.280739	−	0.344949i
$304$	−3.74727e44			−0.762063
$305$		−	2.41576e44i		−	0.463081i
$306$	8.02715e43	−	3.86975e44i	0.145069	−	0.699354i
$307$	5.89591e44			1.00475			0.502377	−	0.864649i	$-0.332459\pi$
$307$	5.89591e44			1.00475			0.502377	+	0.864649i	$0.332459\pi$
$308$		−	2.06733e45i		−	3.32275i
$309$	−1.36482e44	+	1.11076e44i	−0.206930	+	0.168411i
$310$	1.11740e44			0.159844
$311$			8.11743e44i			1.09580i	0.836544	+	0.547900i	$0.184573\pi$
$311$			8.11743e44i			1.09580i	−0.836544	+	0.547900i	$0.815427\pi$
$312$	−5.26114e44	−	6.46448e44i	−0.670343	−	0.823665i
$313$	−7.36195e44			−0.885512			−0.442756	−	0.896642i	$-0.645999\pi$
$313$	−7.36195e44			−0.885512			−0.442756	+	0.896642i	$0.645999\pi$
$314$			1.39276e45i			1.58177i
$315$	−4.73551e44	−	9.82303e43i	−0.507898	−	0.105355i
$316$	−1.04587e44			−0.105952
$317$			1.28944e45i			1.23406i	0.786941	+	0.617028i	$0.211664\pi$
$317$			1.28944e45i			1.23406i	−0.786941	+	0.617028i	$0.788336\pi$
$318$	1.10521e45	−	8.99481e44i	0.999441	−	0.813400i
$319$	3.90885e44			0.334054
$320$			2.55043e44i			0.206022i
$321$	4.46022e43	+	5.48037e43i	0.0340617	+	0.0418523i
$322$	−5.50235e45			−3.97322
$323$		−	1.93201e44i		−	0.131936i
$324$	3.36650e45	+	1.45945e45i	2.17454	+	0.942710i
$325$	6.32577e44			0.386556
$326$		−	9.68943e44i		−	0.560250i
$327$	−1.16657e45	+	9.49414e44i	−0.638336	+	0.519513i
$328$	8.54930e45			4.42793
$329$			9.28412e43i			0.0455213i
$330$	5.69886e44	+	7.00231e44i	0.264568	+	0.325080i
$331$	1.67336e45			0.735672			0.367836	−	0.929891i	$-0.380099\pi$
$331$	1.67336e45			0.735672			0.367836	+	0.929891i	$0.380099\pi$
$332$		−	6.68977e45i		−	2.78564i
$333$	3.79299e44	−	1.82854e45i	0.149619	−	0.721285i
$334$	−5.07890e45			−1.89816
$335$			1.04702e45i			0.370808i
$336$	−9.26741e45	+	7.54232e45i	−3.11065	+	2.53162i
$337$	3.63622e45			1.15694			0.578471	−	0.815703i	$-0.303650\pi$
$337$	3.63622e45			1.15694			0.578471	+	0.815703i	$0.303650\pi$
$338$			5.00091e45i			1.50851i
$339$	−3.46448e45	−	4.25688e45i	−0.990932	−	1.21758i
$340$	−9.88034e44			−0.268010
$341$		−	9.14666e44i		−	0.235333i
$342$	2.49737e45	+	5.18037e44i	0.609554	+	0.126442i
$343$	9.13312e45			2.11507
$344$		−	1.76112e45i		−	0.387023i
$345$	1.31070e45	−	1.06672e45i	0.273375	−	0.222487i
$346$	−1.35164e46			−2.67602
$347$			7.40140e45i			1.39118i	0.718439	+	0.695590i	$0.244857\pi$
$347$			7.40140e45i			1.39118i	−0.718439	+	0.695590i	$0.755143\pi$
$348$	−3.56470e45	−	4.38003e45i	−0.636205	−	0.781719i
$349$	−4.50106e45			−0.762882			−0.381441	−	0.924393i	$-0.624572\pi$
$349$	−4.50106e45			−0.762882			−0.381441	+	0.924393i	$0.624572\pi$
$350$		−	1.86328e46i		−	2.99954i
$351$	1.27155e45	+	2.45080e45i	0.194449	+	0.374783i
$352$	8.70633e45			1.26493
$353$		−	4.96312e45i		−	0.685189i	−0.939483	−	0.342594i	$-0.888694\pi$
$353$		−	4.96312e45i		−	0.685189i	0.939483	−	0.342594i	$-0.111306\pi$
$354$	1.01826e46	−	8.28718e45i	1.33598	−	1.08730i
$355$	−8.07116e44			−0.100653
$356$			3.02468e46i			3.58575i
$357$	−3.88865e45	−	4.77807e45i	−0.438300	−	0.538548i
$358$	2.06668e46			2.21502
$359$			1.49811e46i			1.52702i	0.645797	+	0.763509i	$0.276525\pi$
$359$			1.49811e46i			1.52702i	−0.645797	+	0.763509i	$0.723475\pi$
$360$	1.53147e45	−	7.38295e45i	0.148479	−	0.715789i
$361$	−9.59567e45			−0.885005
$362$			8.70015e45i			0.763435i
$363$	−3.55687e45	+	2.89478e45i	−0.296995	+	0.241711i
$364$	−2.24748e46			−1.78595
$365$		−	4.75116e44i		−	0.0359358i
$366$	2.56425e46	+	3.15074e46i	1.84629	+	2.26858i
$367$	6.60727e45			0.452932			0.226466	−	0.974019i	$-0.427283\pi$
$367$	6.60727e45			0.452932			0.226466	+	0.974019i	$0.427283\pi$
$368$		−	4.17513e46i		−	2.72527i
$369$	−2.77304e46	−	5.75222e45i	−1.72378	−	0.357570i
$370$	−6.63849e45			−0.393041
$371$		−	2.22122e46i		−	1.25274i
$372$	−1.02492e46	+	8.34136e45i	−0.550703	+	0.448192i
$373$	1.54911e46			0.793089			0.396545	−	0.918015i	$-0.370209\pi$
$373$	1.54911e46			0.793089			0.396545	+	0.918015i	$0.370209\pi$
$374$			1.15002e46i			0.561067i
$375$	7.55783e45	+	9.28647e45i	0.351426	+	0.431805i
$376$	−1.44745e45			−0.0641539
$377$		−	4.24946e45i		−	0.179552i
$378$	7.21894e46	−	3.74541e46i	2.90818	−	1.50885i
$379$	−1.24977e46			−0.480092			−0.240046	−	0.970761i	$-0.577163\pi$
$379$	−1.24977e46			−0.480092			−0.240046	+	0.970761i	$0.577163\pi$
$380$		−	6.37635e45i		−	0.233597i
$381$	−2.79527e46	+	2.27495e46i	−0.976731	+	0.794916i
$382$	−8.15983e46			−2.71982
$383$		−	2.71713e46i		−	0.864036i	−0.901865	−	0.432018i	$-0.857802\pi$
$383$		−	2.71713e46i		−	0.864036i	0.901865	−	0.432018i	$-0.142198\pi$
$384$	6.42798e45	+	7.89819e45i	0.195035	+	0.239644i
$385$	1.40730e46			0.407469
$386$		−	6.84650e45i		−	0.189190i
$387$	−1.18493e45	+	5.71235e45i	−0.0312533	+	0.150667i
$388$	−5.87637e46			−1.47958
$389$		−	5.98118e46i		−	1.43779i	−0.695121	−	0.718893i	$-0.744649\pi$
$389$		−	5.98118e46i		−	1.43779i	0.695121	−	0.718893i	$-0.255351\pi$
$390$	7.61247e45	−	6.19544e45i	0.174728	−	0.142203i
$391$	2.15260e46			0.471827
$392$			2.62540e47i			5.49599i
$393$	8.11726e45	+	9.97385e45i	0.162309	+	0.199433i
$394$	1.54889e47			2.95861
$395$		−	7.11958e44i		−	0.0129929i
$396$	−1.04544e47	−	2.16860e46i	−1.82300	−	0.378151i
$397$	5.85443e46			0.975564			0.487782	−	0.872966i	$-0.337806\pi$
$397$	5.85443e46			0.975564			0.487782	+	0.872966i	$0.337806\pi$
$398$		−	1.08678e47i		−	1.73080i
$399$	3.08356e46	−	2.50957e46i	0.469397	−	0.382021i
$400$	1.41384e47			2.05741
$401$			6.98513e46i			0.971798i	0.874015	+	0.485899i	$0.161508\pi$
$401$			6.98513e46i			0.971798i	−0.874015	+	0.485899i	$0.838492\pi$
$402$	−1.11138e47	−	1.36557e47i	−1.47840	−	1.81654i
$403$	−9.94368e45			−0.126490
$404$		−	8.66458e46i		−	1.05410i
$405$	−9.93493e45	+	2.29169e46i	−0.115604	+	0.266664i
$406$	−1.25170e47			−1.39326
$407$			5.43406e46i			0.578662i
$408$	7.44930e46	−	6.06265e46i	0.758984	−	0.617703i
$409$	−8.93586e46			−0.871198			−0.435599	−	0.900141i	$-0.643463\pi$
$409$	−8.93586e46			−0.871198			−0.435599	+	0.900141i	$0.643463\pi$
$410$			1.00675e47i			0.939319i
$411$	7.82323e46	+	9.61256e46i	0.698607	+	0.858393i
$412$	−7.39776e46			−0.632340
$413$		−	2.04648e47i		−	1.67458i
$414$	−5.77187e46	+	2.78251e47i	−0.452179	+	2.17987i
$415$	4.55394e46			0.341603
$416$		−	9.46497e46i		−	0.679891i
$417$	−7.39433e46	+	6.01791e46i	−0.508686	+	0.413996i
$418$	−7.42170e46			−0.489024
$419$			2.16424e47i			1.36601i	0.730414	+	0.683005i	$0.239327\pi$
$419$			2.16424e47i			1.36601i	−0.730414	+	0.683005i	$0.760673\pi$
$420$	−1.28340e47	−	1.57694e47i	−0.776023	−	0.953516i
$421$	−2.44931e47			−1.41895			−0.709474	−	0.704732i	$-0.751067\pi$
$421$	−2.44931e47			−1.41895			−0.709474	+	0.704732i	$0.751067\pi$
$422$		−	5.20904e47i		−	2.89157i
$423$	4.69494e45	+	9.73888e44i	0.0249749	+	0.00518063i
$424$	3.46302e47			1.76551
$425$			7.28946e46i			0.356201i
$426$	1.05268e47	−	8.56725e46i	0.493085	−	0.401300i
$427$	6.33227e47			2.84353
$428$			2.97054e46i			0.127893i
$429$	−5.07139e46	−	6.23133e46i	−0.209361	−	0.257246i
$430$	2.07387e46			0.0821011
$431$			3.49151e46i			0.132563i	0.997801	+	0.0662815i	$0.0211135\pi$
$431$			3.49151e46i			0.132563i	−0.997801	+	0.0662815i	$0.978886\pi$
$432$	2.84199e47	+	5.47767e47i	1.03494	+	1.99475i
$433$	−1.41911e47			−0.495718			−0.247859	−	0.968796i	$-0.579727\pi$
$433$	−1.41911e47			−0.495718			−0.247859	+	0.968796i	$0.579727\pi$
$434$			2.92896e47i			0.981517i
$435$	2.98163e46	−	2.42661e46i	0.0958621	−	0.0780178i
$436$	−6.32316e47			−1.95064
$437$			1.38920e47i			0.411243i
$438$	5.04319e46	+	6.19667e46i	0.143275	+	0.176045i
$439$	−5.77505e47			−1.57469			−0.787344	−	0.616514i	$-0.788544\pi$
$439$	−5.77505e47			−1.57469			−0.787344	+	0.616514i	$0.788544\pi$
$440$			2.19407e47i			0.574252i
$441$	1.76645e47	−	8.51573e47i	0.443819	−	2.13957i
$442$	1.25022e47			0.301569
$443$			3.83260e47i			0.887620i	0.896121	+	0.443810i	$0.146373\pi$
$443$			3.83260e47i			0.887620i	−0.896121	+	0.443810i	$0.853627\pi$
$444$	6.08908e47	−	4.95562e47i	1.35412	−	1.10206i
$445$	−2.05900e47			−0.439720
$446$			1.09573e48i			2.24738i
$447$	1.78940e47	+	2.19867e47i	0.352509	+	0.433136i
$448$	−6.68527e47			−1.26507
$449$		−	8.13689e47i		−	1.47919i	−0.673052	−	0.739596i	$-0.735017\pi$
$449$		−	8.13689e47i		−	1.47919i	0.673052	−	0.739596i	$-0.264983\pi$
$450$	−9.42255e47	−	1.95455e47i	−1.64567	−	0.341368i
$451$	8.24095e47			1.38293
$452$		−	2.30737e48i		−	3.72070i
$453$	4.74809e47	−	3.86425e47i	0.735785	−	0.598822i
$454$	3.34887e47			0.498762
$455$		−	1.52993e47i		−	0.219012i
$456$	3.91257e47	+	4.80746e47i	0.538387	+	0.661528i
$457$	−1.31620e48			−1.74113			−0.870565	−	0.492054i	$-0.836246\pi$
$457$	−1.31620e48			−1.74113			−0.870565	+	0.492054i	$0.836246\pi$
$458$			1.63192e48i			2.07548i
$459$	−2.82416e47	+	1.46526e47i	−0.345352	+	0.179179i
$460$	7.10439e47			0.835384
$461$		−	2.37887e47i		−	0.269001i	−0.990914	−	0.134500i	$-0.957057\pi$
$461$		−	2.37887e47i		−	0.269001i	0.990914	−	0.134500i	$-0.0429429\pi$
$462$	−1.83547e48	+	1.49380e48i	−1.99614	+	1.62457i
$463$	2.45381e47			0.256675			0.128337	−	0.991731i	$-0.459036\pi$
$463$	2.45381e47			0.256675			0.128337	+	0.991731i	$0.459036\pi$
$464$		−	9.49778e47i		−	0.955649i
$465$	−5.67824e46	−	6.97697e46i	−0.0549617	−	0.0675326i
$466$	3.14259e48			2.92645
$467$			1.66258e48i			1.48963i	0.667271	+	0.744815i	$0.267462\pi$
$467$			1.66258e48i			1.48963i	−0.667271	+	0.744815i	$0.732538\pi$
$468$	−2.35756e47	+	1.13654e48i	−0.203254	+	0.979849i
$469$	−2.74449e48			−2.27693
$470$		−	1.70450e46i		−	0.0136093i
$471$	8.69631e47	−	7.07753e47i	0.668281	−	0.543883i
$472$	3.19058e48			2.36001
$473$		−	1.69760e47i		−	0.120875i
$474$	7.55718e46	+	9.28567e46i	0.0518024	+	0.0636507i
$475$	−4.70430e47			−0.310463
$476$		−	2.58987e48i		−	1.64571i
$477$	−1.12326e48	−	2.33002e47i	−0.687307	−	0.142570i
$478$	−1.15045e48			−0.677898
$479$			1.23312e48i			0.699790i	0.936789	+	0.349895i	$0.113783\pi$
$479$			1.23312e48i			0.699790i	−0.936789	+	0.349895i	$0.886217\pi$
$480$	6.64109e47	−	5.40488e47i	0.362992	−	0.295423i
$481$	5.90757e47			0.311026
$482$		−	3.49540e48i		−	1.77276i
$483$	2.79611e48	+	3.43564e48i	1.36617	+	1.67865i
$484$	−1.92794e48			−0.907564
$485$		−	4.00024e47i		−	0.181441i
$486$	−1.13679e48	−	4.04348e48i	−0.496851	−	1.76727i
$487$	3.47839e48			1.46507			0.732534	−	0.680731i	$-0.238338\pi$
$487$	3.47839e48			1.46507			0.732534	+	0.680731i	$0.238338\pi$
$488$			9.87240e48i			4.00743i
$489$	−6.05003e47	+	4.92384e47i	−0.236700	+	0.192639i
$490$	−3.09163e48			−1.16589
$491$		−	1.84723e48i		−	0.671513i	−0.941949	−	0.335756i	$-0.891008\pi$
$491$		−	1.84723e48i		−	0.671513i	0.941949	−	0.335756i	$-0.108992\pi$
$492$	−7.51539e48	−	9.23432e48i	−2.63378	−	3.23618i
$493$	4.89684e47			0.165452
$494$			8.06840e47i			0.262847i
$495$	1.47624e47	−	7.11667e47i	0.0463727	−	0.223555i
$496$	−2.22247e48			−0.673233
$497$		−	2.11564e48i		−	0.618054i
$498$	−5.93946e48	+	4.83385e48i	−1.67347	+	1.36196i
$499$	−3.04891e48			−0.828581			−0.414290	−	0.910145i	$-0.635970\pi$
$499$	−3.04891e48			−0.828581			−0.414290	+	0.910145i	$0.635970\pi$
$500$			5.03356e48i			1.31952i
$501$	2.58092e48	+	3.17124e48i	0.652674	+	0.801954i
$502$	1.33651e49			3.26067
$503$		−	1.71874e48i		−	0.404563i	−0.979327	−	0.202282i	$-0.935164\pi$
$503$		−	1.71874e48i		−	0.404563i	0.979327	−	0.202282i	$-0.0648356\pi$
$504$	1.93524e49	+	4.01434e48i	4.39527	+	0.911726i
$505$	5.89827e47			0.129265
$506$		−	8.26910e48i		−	1.74884i
$507$	3.12255e48	−	2.54130e48i	0.637332	−	0.518695i
$508$	−1.51513e49			−2.98471
$509$		−	4.50425e48i		−	0.856450i	−0.903672	−	0.428225i	$-0.859139\pi$
$509$		−	4.50425e48i		−	0.856450i	0.903672	−	0.428225i	$-0.140861\pi$
$510$	7.13928e47	+	8.77219e47i	0.131036	+	0.161007i
$511$	1.24539e48			0.220663
$512$			1.18884e49i			2.03359i
$513$	−9.45618e47	−	1.82259e48i	−0.156172	−	0.301007i
$514$	−7.38765e48			−1.17807
$515$		−	5.03590e47i		−	0.0775438i
$516$	−1.90223e48	+	1.54814e48i	−0.282858	+	0.230205i
$517$	−1.39525e47			−0.0200365
$518$		−	1.74010e49i		−	2.41345i
$519$	6.86856e48	+	8.43954e48i	0.920138	+	1.13059i
$520$	2.38526e48			0.308656
$521$			7.22252e48i			0.902838i	0.892312	+	0.451419i	$0.149082\pi$
$521$			7.22252e48i			0.902838i	−0.892312	+	0.451419i	$0.850918\pi$
$522$	−1.31301e48	+	6.32979e48i	−0.158562	+	0.764399i
$523$	−1.78836e47			−0.0208653			−0.0104326	−	0.999946i	$-0.503321\pi$
$523$	−1.78836e47			−0.0208653			−0.0104326	+	0.999946i	$0.503321\pi$
$524$			5.40615e48i			0.609431i
$525$	−1.16343e49	+	9.46859e48i	−1.26728	+	1.03138i
$526$	1.30536e48			0.137400
$527$		−	1.14585e48i		−	0.116557i
$528$	−1.13348e49	−	1.39274e49i	−1.11431	−	1.36917i
$529$	−4.95364e48			−0.470676
$530$			4.07800e48i			0.374526i
$531$	−1.03489e49	−	2.14672e48i	−0.918745	−	0.190578i
$532$	1.67139e49			1.43439
$533$		−	8.95905e48i		−	0.743314i
$534$	2.68544e49	−	2.18556e49i	2.15414	−	1.75315i
$535$	−2.02214e47			−0.0156835
$536$		−	4.27882e49i		−	3.20891i
$537$	−1.05022e49	−	1.29042e49i	−0.761625	−	0.935825i
$538$	−7.37482e48			−0.517214
$539$			2.53071e49i			1.71650i
$540$	−9.32078e48	+	4.83592e48i	−0.611455	+	0.317242i
$541$	−6.67122e48			−0.423306			−0.211653	−	0.977345i	$-0.567885\pi$
$541$	−6.67122e48			−0.423306			−0.211653	+	0.977345i	$0.567885\pi$
$542$			4.86234e49i			2.98441i
$543$	5.43233e48	−	4.42112e48i	0.322544	−	0.262504i
$544$	1.09069e49			0.626501
$545$		−	4.30438e48i		−	0.239207i
$546$	1.62397e49	+	1.99540e49i	0.873193	+	1.07291i
$547$	8.07158e48			0.419940			0.209970	−	0.977708i	$-0.432663\pi$
$547$	8.07158e48			0.419940			0.209970	+	0.977708i	$0.432663\pi$
$548$			5.21032e49i			2.62310i
$549$	6.64244e48	−	3.20220e49i	0.323613	−	1.56008i
$550$	2.80020e49			1.32027
$551$			3.16021e48i			0.144207i
$552$	−5.35637e49	+	4.35930e49i	−2.36574	+	1.92537i
$553$	1.86621e48			0.0797824
$554$		−	3.44460e49i		−	1.42549i
$555$	3.37346e48	+	4.14504e48i	0.135145	+	0.166056i
$556$	−4.00796e49			−1.55445
$557$		−	3.43656e49i		−	1.29042i	−0.764006	−	0.645209i	$-0.776770\pi$
$557$		−	3.43656e49i		−	1.29042i	0.764006	−	0.645209i	$-0.223230\pi$
$558$	1.48116e49	+	3.07242e48i	0.538502	+	0.111703i
$559$	−1.84553e48			−0.0649692
$560$		−	3.41948e49i		−	1.16567i
$561$	7.18064e48	−	5.84399e48i	0.237045	−	0.192920i
$562$	7.03310e49			2.24850
$563$			2.81114e48i			0.0870425i	0.999053	+	0.0435213i	$0.0138576\pi$
$563$			2.81114e48i			0.0870425i	−0.999053	+	0.0435213i	$0.986142\pi$
$564$	1.27240e48	+	1.56343e48i	0.0381594	+	0.0468873i
$565$	1.57070e49			0.456270
$566$		−	2.25580e49i		−	0.634752i
$567$	−6.00704e49	−	2.60418e49i	−1.63744	−	0.709864i
$568$	3.29841e49			0.871033
$569$			4.06322e49i			1.03956i	0.854300	+	0.519780i	$0.173986\pi$
$569$			4.06322e49i			1.03956i	−0.854300	+	0.519780i	$0.826014\pi$
$570$	−5.66119e48	+	4.60738e48i	−0.140333	+	0.114211i
$571$	3.23928e49			0.778034			0.389017	−	0.921231i	$-0.372815\pi$
$571$	3.23928e49			0.778034			0.389017	+	0.921231i	$0.372815\pi$
$572$		−	3.37758e49i		−	0.786099i
$573$	4.14655e49	+	5.09496e49i	0.935199	+	1.14910i
$574$	−2.63893e50			−5.76785
$575$		−	5.24144e49i		−	1.11027i
$576$	−7.01273e48	+	3.38072e49i	−0.143974	+	0.694071i
$577$	2.22776e49			0.443306			0.221653	−	0.975126i	$-0.428855\pi$
$577$	2.22776e49			0.443306			0.221653	+	0.975126i	$0.428855\pi$
$578$		−	8.07679e49i		−	1.55789i
$579$	−4.27492e48	+	3.47916e48i	−0.0799308	+	0.0650520i
$580$	1.61614e49			0.292937
$581$			1.19369e50i			2.09760i
$582$	4.24612e49	+	5.21729e49i	0.723400	+	0.888856i
$583$	3.33812e49			0.551402
$584$			1.94164e49i			0.310983i
$585$	−7.73680e48	−	1.60487e48i	−0.120159	−	0.0249250i
$586$	−1.27701e50			−1.92326
$587$			1.08044e50i			1.57802i	0.614378	+	0.789012i	$0.289407\pi$
$587$			1.08044e50i			1.57802i	−0.614378	+	0.789012i	$0.710593\pi$
$588$	2.83576e50	−	2.30790e50i	4.01678	−	3.26908i
$589$	7.39484e48			0.101591
$590$			3.75718e49i			0.500640i
$591$	−7.87093e49	−	9.67118e49i	−1.01731	−	1.24999i
$592$	1.32037e50			1.65541
$593$		−	2.99675e49i		−	0.364473i	−0.983255	−	0.182237i	$-0.941666\pi$
$593$		−	2.99675e49i		−	0.364473i	0.983255	−	0.182237i	$-0.0583337\pi$
$594$	5.62873e49	+	1.08489e50i	0.664132	+	1.28005i
$595$	1.76301e49			0.201813
$596$			1.19175e50i			1.32359i
$597$	−6.78581e49	+	5.52266e49i	−0.731246	+	0.595128i
$598$	−8.98965e49			−0.939986
$599$		−	1.36972e50i		−	1.38979i	−0.719113	−	0.694893i	$-0.755452\pi$
$599$		−	1.36972e50i		−	1.38979i	0.719113	−	0.694893i	$-0.244548\pi$
$600$	−1.47621e50	−	1.81385e50i	−1.45354	−	1.78599i
$601$	1.02608e50			0.980486			0.490243	−	0.871586i	$-0.336908\pi$
$601$	1.02608e50			0.980486			0.490243	+	0.871586i	$0.336908\pi$
$602$			5.43609e49i			0.504138i
$603$	−2.87892e49	+	1.38788e50i	−0.259130	+	1.24922i
$604$	2.57362e50			2.24843
$605$		−	1.31241e49i		−	0.111294i
$606$	−7.69278e49	+	6.26081e49i	−0.633252	+	0.515375i
$607$	−1.38851e50			−1.10957			−0.554784	−	0.831994i	$-0.687199\pi$
$607$	−1.38851e50			−1.10957			−0.554784	+	0.831994i	$0.687199\pi$
$608$			7.03885e49i			0.546056i
$609$	6.36071e49	+	7.81554e49i	0.479065	+	0.588637i
$610$	−1.16256e50			−0.850116
$611$			1.51683e48i			0.0107695i
$612$	−1.30969e50	−	2.71673e49i	−0.902904	−	0.187292i
$613$	3.70097e47			0.00247758			0.00123879	−	0.999999i	$-0.499606\pi$
$613$	3.70097e47			0.00247758			0.00123879	+	0.999999i	$0.499606\pi$
$614$		−	2.83734e50i		−	1.84451i
$615$	6.28611e49	−	5.11598e49i	0.396853	−	0.322981i
$616$	−5.75117e50			−3.52617
$617$			1.34587e49i			0.0801441i	0.999197	+	0.0400721i	$0.0127587\pi$
$617$			1.34587e49i			0.0801441i	−0.999197	+	0.0400721i	$0.987241\pi$
$618$	5.34543e49	+	6.56804e49i	0.309165	+	0.379877i
$619$	4.35337e49			0.244565			0.122282	−	0.992495i	$-0.460979\pi$
$619$	4.35337e49			0.244565			0.122282	+	0.992495i	$0.460979\pi$
$620$		−	3.78174e49i		−	0.206368i
$621$	2.03069e50	−	1.05359e50i	1.07645	−	0.558499i
$622$	3.90642e50			2.01165
$623$		−	5.39712e50i		−	2.70009i
$624$	−1.51410e50	+	1.23225e50i	−0.735920	+	0.598932i
$625$	1.59605e50			0.753713
$626$			3.54286e50i			1.62561i
$627$	3.77146e49	+	4.63407e49i	0.168149	+	0.206608i
$628$	4.71368e50			2.04215
$629$			6.80755e49i			0.286602i
$630$	−4.72723e49	+	2.27891e50i	−0.193409	+	0.932390i
$631$	−4.47383e50			−1.77890			−0.889448	−	0.457036i	$-0.848911\pi$
$631$	−4.47383e50			−1.77890			−0.889448	+	0.457036i	$0.848911\pi$
$632$			2.90953e49i			0.112439i
$633$	−3.25250e50	+	2.64706e50i	−1.22166	+	0.994254i
$634$	6.20530e50			2.26546
$635$		−	1.03140e50i		−	0.366015i
$636$	−3.04422e50	−	3.74050e50i	−1.05014	−	1.29033i
$637$	2.75123e50			0.922608
$638$		−	1.88109e50i		−	0.613251i
$639$	−1.06987e50	−	2.21927e49i	−0.339090	−	0.0703387i
$640$	−2.91427e49			−0.0898029
$641$			1.45609e50i			0.436259i	0.975920	+	0.218130i	$0.0699956\pi$
$641$			1.45609e50i			0.436259i	−0.975920	+	0.218130i	$0.930004\pi$
$642$	2.63737e49	−	2.14643e49i	0.0768316	−	0.0625297i
$643$	−5.51358e50			−1.56184			−0.780919	−	0.624632i	$-0.785249\pi$
$643$	−5.51358e50			−1.56184			−0.780919	+	0.624632i	$0.785249\pi$
$644$			1.86223e51i			5.12964i
$645$	−1.05387e49	−	1.29491e49i	−0.0282301	−	0.0346869i
$646$	−9.29758e49			−0.242206
$647$		−	8.48602e49i		−	0.214994i	−0.994205	−	0.107497i	$-0.965716\pi$
$647$		−	8.48602e49i		−	0.214994i	0.994205	−	0.107497i	$-0.0342837\pi$
$648$	4.06007e50	−	9.36535e50i	1.00042	−	2.30767i
$649$	3.07551e50			0.737077
$650$		−	3.04421e50i		−	0.709633i
$651$	1.82883e50	−	1.48840e50i	0.414681	−	0.337490i
$652$	−3.27931e50			−0.723312
$653$			4.89873e49i			0.105111i	0.998618	+	0.0525553i	$0.0167366\pi$
$653$			4.89873e49i			0.105111i	−0.998618	+	0.0525553i	$0.983263\pi$
$654$	4.56895e50	+	5.61397e50i	0.953712	+	1.17185i
$655$	−3.68014e49			−0.0747345
$656$		−	2.00240e51i		−	3.95623i
$657$	1.30639e49	−	6.29788e49i	0.0251129	−	0.121065i
$658$	4.46788e49			0.0835671
$659$			4.39614e50i			0.800082i	0.916497	+	0.400041i	$0.131004\pi$
$659$			4.39614e50i			0.800082i	−0.916497	+	0.400041i	$0.868996\pi$
$660$	2.36988e50	−	1.92873e50i	0.419696	−	0.341571i
$661$	−3.85512e50			−0.664373			−0.332186	−	0.943214i	$-0.607786\pi$
$661$	−3.85512e50			−0.664373			−0.332186	+	0.943214i	$0.607786\pi$
$662$		−	8.05284e50i		−	1.35053i
$663$	−6.35322e49	−	7.80634e49i	−0.103693	−	0.127410i
$664$	−1.86104e51			−2.95618
$665$			1.13777e50i			0.175899i
$666$	−8.79962e50	−	1.82534e50i	−1.32412	−	0.274667i
$667$	−3.52104e50			−0.515710
$668$			1.71891e51i			2.45063i
$669$	6.84169e50	−	5.56814e50i	0.949497	−	0.772752i
$670$	5.03868e50			0.680722
$671$			9.51634e50i			1.25160i
$672$	1.41674e51	+	1.74078e51i	1.81403	+	2.22894i
$673$	−2.05581e50			−0.256278			−0.128139	−	0.991756i	$-0.540900\pi$
$673$	−2.05581e50			−0.256278			−0.128139	+	0.991756i	$0.540900\pi$
$674$		−	1.74989e51i		−	2.12389i
$675$	3.56781e50	+	6.87663e50i	0.421633	+	0.812658i
$676$	1.69252e51			1.94757
$677$			3.35181e50i			0.375563i	0.982211	+	0.187782i	$0.0601297\pi$
$677$			3.35181e50i			0.375563i	−0.982211	+	0.187782i	$0.939870\pi$
$678$	−2.04858e51	+	1.66724e51i	−2.23521	+	1.81913i
$679$	1.04856e51			1.11413
$680$			2.74864e50i			0.284418i
$681$	−1.70179e50	−	2.09102e50i	−0.171497	−	0.210722i
$682$	−4.40173e50			−0.432021
$683$		−	2.97706e50i		−	0.284587i	−0.989825	−	0.142294i	$-0.954552\pi$
$683$		−	2.97706e50i		−	0.284587i	0.989825	−	0.142294i	$-0.0454477\pi$
$684$	1.75326e50	−	8.45214e50i	0.163243	−	0.786968i
$685$	−3.54684e50			−0.321670
$686$		−	4.39522e51i		−	3.88281i
$687$	1.01896e51	−	8.29285e50i	0.876872	−	0.713646i
$688$	−4.12486e50			−0.345794
$689$		−	3.62900e50i		−	0.296374i
$690$	−5.13345e50	−	6.30758e50i	−0.408438	−	0.501856i
$691$	2.30735e50			0.178858			0.0894292	−	0.995993i	$-0.471496\pi$
$691$	2.30735e50			0.178858			0.0894292	+	0.995993i	$0.471496\pi$
$692$			4.57450e51i			3.45489i
$693$	1.86545e51	+	3.86956e50i	1.37273	+	0.284750i
$694$	3.56184e51			2.55390
$695$		−	2.72835e50i		−	0.190622i
$696$	−1.21849e51	+	9.91674e50i	−0.829576	+	0.675154i
$697$	1.03239e51			0.684943
$698$			2.16609e51i			1.40048i
$699$	−1.59696e51	−	1.96222e51i	−1.00625	−	1.23640i
$700$	−6.30614e51			−3.87257
$701$			6.87937e50i			0.411741i	0.978579	+	0.205871i	$0.0660026\pi$
$701$			6.87937e50i			0.411741i	−0.978579	+	0.205871i	$0.933997\pi$
$702$	1.17942e51	−	6.11920e50i	0.688019	−	0.356966i
$703$	−4.39330e50			−0.249801
$704$		−	1.00468e51i		−	0.556829i
$705$	−1.06428e49	+	8.66168e48i	−0.00574978	+	0.00467949i
$706$	−2.38845e51			−1.25786
$707$			1.54607e51i			0.793744i
$708$	−2.80473e51	−	3.44623e51i	−1.40376	−	1.72483i
$709$	−3.24219e51			−1.58200			−0.790999	−	0.611818i	$-0.790439\pi$
$709$	−3.24219e51			−1.58200			−0.790999	+	0.611818i	$0.790439\pi$
$710$			3.88416e50i			0.184776i
$711$	1.95762e49	−	9.43733e49i	0.00907977	−	0.0437720i
$712$	8.41445e51			3.80527
$713$			8.23918e50i			0.363306i
$714$	−2.29939e51	+	1.87137e51i	−0.988657	+	0.804623i
$715$	2.29923e50			0.0963993
$716$		−	6.99450e51i		−	2.85971i
$717$	5.84618e50	+	7.18333e50i	0.233092	+	0.286405i
$718$	7.20950e51			2.80327
$719$		−	2.21538e51i		−	0.840095i	−0.907502	−	0.420047i	$-0.862013\pi$
$719$		−	2.21538e51i		−	0.840095i	0.907502	−	0.420047i	$-0.137987\pi$
$720$	−1.72922e51	−	3.58698e50i	−0.639536	−	0.132661i
$721$	1.32003e51			0.476154
$722$			4.61781e51i			1.62468i
$723$	−2.18251e51	+	1.77625e51i	−0.748974	+	0.609556i
$724$	2.94450e51			0.985636
$725$		−	1.19235e51i		−	0.389330i
$726$	1.39308e51	+	1.71171e51i	0.443728	+	0.545218i
$727$	−2.90436e51			−0.902467			−0.451233	−	0.892406i	$-0.649016\pi$
$727$	−2.90436e51			−0.902467			−0.451233	+	0.892406i	$0.649016\pi$
$728$			6.25231e51i			1.89529i
$729$	−1.94705e51	+	2.76456e51i	−0.575813	+	0.817581i
$730$	−2.28644e50			−0.0659703
$731$		−	2.12668e50i		−	0.0598673i
$732$	1.06634e52	−	8.67849e51i	2.92886	−	2.38366i
$733$	−4.35575e51			−1.16732			−0.583662	−	0.811997i	$-0.698381\pi$
$733$	−4.35575e51			−1.16732			−0.583662	+	0.811997i	$0.698381\pi$
$734$		−	3.17968e51i		−	0.831484i
$735$	1.57106e51	+	1.93040e51i	0.400887	+	0.492578i
$736$	−7.84254e51			−1.95279
$737$		−	4.12450e51i		−	1.00220i
$738$	−2.76819e51	+	1.33450e52i	−0.656420	+	3.16448i
$739$	3.05824e51			0.707737			0.353868	−	0.935295i	$-0.384866\pi$
$739$	3.05824e51			0.707737			0.353868	+	0.935295i	$0.384866\pi$
$740$			2.24674e51i			0.507438i
$741$	5.03787e50	−	4.10009e50i	0.111050	−	0.0903787i
$742$	−1.06894e52			−2.29976
$743$		−	1.31930e51i		−	0.277042i	−0.990359	−	0.138521i	$-0.955765\pi$
$743$		−	1.31930e51i		−	0.277042i	0.990359	−	0.138521i	$-0.0442349\pi$
$744$	2.32050e51	+	2.85125e51i	0.475630	+	0.584417i
$745$	−8.11263e50			−0.162311
$746$		−	7.45490e51i		−	1.45594i
$747$	6.03647e51	+	1.25216e51i	1.15083	+	0.238721i
$748$	3.89214e51			0.724368
$749$		−	5.30050e50i		−	0.0963040i
$750$	4.46901e51	−	3.63712e51i	0.792700	−	0.645142i
$751$	6.64229e51			1.15027			0.575134	−	0.818059i	$-0.304950\pi$
$751$	6.64229e51			1.15027			0.575134	+	0.818059i	$0.304950\pi$
$752$			3.39019e50i			0.0573196i
$753$	−6.79171e51	−	8.34512e51i	−1.12117	−	1.37760i
$754$	−2.04501e51			−0.329618
$755$			1.75195e51i			0.275725i
$756$	−1.26761e52	−	2.44319e52i	−1.94801	−	3.75462i
$757$	−5.14116e51			−0.771498			−0.385749	−	0.922604i	$-0.626057\pi$
$757$	−5.14116e51			−0.771498			−0.385749	+	0.922604i	$0.626057\pi$
$758$			6.01439e51i			0.881344i
$759$	−5.16319e51	+	4.20208e51i	−0.738866	+	0.601329i
$760$	−1.77385e51			−0.247898
$761$		−	9.26714e51i		−	1.26480i	−0.774642	−	0.632400i	$-0.782070\pi$
$761$		−	9.26714e51i		−	1.26480i	0.774642	−	0.632400i	$-0.217930\pi$
$762$	1.09479e52	+	1.34519e52i	1.45929	+	1.79306i
$763$	1.12828e52			1.46884
$764$			2.76163e52i			3.51144i
$765$	1.84937e50	−	8.91546e50i	0.0229677	−	0.110723i
$766$	−1.30759e52			−1.58618
$767$		−	3.34350e51i		−	0.396173i
$768$	8.55090e51	−	6.95918e51i	0.989714	−	0.805483i
$769$	1.00774e52			1.13939			0.569697	−	0.821855i	$-0.307061\pi$
$769$	1.00774e52			1.13939			0.569697	+	0.821855i	$0.307061\pi$
$770$		−	6.77249e51i		−	0.748024i
$771$	3.75416e51	+	4.61281e51i	0.405073	+	0.497722i
$772$	−2.31715e51			−0.244254
$773$			4.54674e50i			0.0468241i	0.999726	+	0.0234120i	$0.00745296\pi$
$773$			4.54674e50i			0.0468241i	−0.999726	+	0.0234120i	$0.992547\pi$
$774$	2.74901e51	+	5.70236e50i	0.276591	+	0.0573743i
$775$	−2.79007e51			−0.274274
$776$			1.63476e52i			1.57016i
$777$	−1.08651e52	+	8.84261e51i	−1.01966	+	0.829855i
$778$	−2.87838e52			−2.63946
$779$			6.66260e51i			0.596994i
$780$	−2.09680e51	−	2.57638e51i	−0.183592	−	0.225583i
$781$	3.17945e51			0.272040
$782$		−	1.03592e52i		−	0.866171i
$783$	4.61952e51	−	2.39675e51i	0.377472	−	0.195844i
$784$	6.14915e52			4.91051
$785$			3.20876e51i			0.250428i
$786$	4.79981e51	−	3.90634e51i	0.366115	−	0.297965i
$787$	−4.40152e51			−0.328139			−0.164069	−	0.986449i	$-0.552462\pi$
$787$	−4.40152e51			−0.328139			−0.164069	+	0.986449i	$0.552462\pi$
$788$		−	5.24209e52i		−	3.81973i
$789$	−6.63339e50	−	8.15059e50i	−0.0472443	−	0.0580501i
$790$	−3.42622e50			−0.0238521
$791$			4.11717e52i			2.80170i
$792$	−6.03288e51	+	2.90834e52i	−0.401302	+	1.93461i
$793$	1.03456e52			0.672724
$794$		−	2.81738e52i		−	1.79092i
$795$	2.54628e51	−	2.07230e51i	0.158233	−	0.128779i
$796$	−3.67813e52			−2.23456
$797$		−	8.55189e51i		−	0.507940i	−0.967212	−	0.253970i	$-0.918264\pi$
$797$		−	8.55189e51i		−	0.507940i	0.967212	−	0.253970i	$-0.0817364\pi$
$798$	−1.20770e52	−	1.48393e52i	−0.701306	−	0.861710i
$799$	−1.74791e50			−0.00992375
$800$		−	2.65575e52i		−	1.47424i
$801$	−2.72930e52	−	5.66149e51i	−1.48138	−	0.307288i
$802$	3.36152e52			1.78401
$803$			1.87161e51i			0.0971260i
$804$	−4.62167e52	+	3.76137e52i	−2.34525	+	1.90870i
$805$	−1.26768e52			−0.629047
$806$			4.78528e51i			0.232208i
$807$	3.74764e51	+	4.60480e51i	0.177842	+	0.218518i
$808$	−2.41042e52			−1.11864
$809$			8.76393e51i			0.397764i	0.980023	+	0.198882i	$0.0637310\pi$
$809$			8.76393e51i			0.397764i	−0.980023	+	0.198882i	$0.936269\pi$
$810$	1.10285e52	+	4.78108e51i	0.489537	+	0.212225i
$811$	4.45476e51			0.193397			0.0966983	−	0.995314i	$-0.469172\pi$
$811$	4.45476e51			0.193397			0.0966983	+	0.995314i	$0.469172\pi$
$812$			4.23628e52i			1.79877i
$813$	3.03602e52	−	2.47088e52i	1.26088	−	1.02618i
$814$	2.61508e52			1.06230
$815$		−	2.23234e51i		−	0.0886998i
$816$	−1.41998e52	−	1.74476e52i	−0.551899	−	0.678130i
$817$	1.37247e51			0.0521802
$818$			4.30029e52i			1.59933i
$819$	4.20674e51	−	2.02800e52i	0.153051	−	0.737831i
$820$	3.40727e52			1.21271
$821$		−	2.03198e52i		−	0.707525i	−0.935335	−	0.353763i	$-0.884902\pi$
$821$		−	2.03198e52i		−	0.707525i	0.935335	−	0.353763i	$-0.115098\pi$
$822$	4.62594e52	−	3.76484e52i	1.57582	−	1.28249i
$823$	3.57553e52			1.19164			0.595818	−	0.803119i	$-0.296828\pi$
$823$	3.57553e52			1.19164			0.595818	+	0.803119i	$0.296828\pi$
$824$			2.05800e52i			0.671052i
$825$	−1.42297e52	−	1.74843e52i	−0.453967	−	0.557799i
$826$	−9.84844e52			−3.07416
$827$		−	4.91418e52i		−	1.50090i	−0.660927	−	0.750450i	$-0.729837\pi$
$827$		−	4.91418e52i		−	1.50090i	0.660927	−	0.750450i	$-0.270163\pi$
$828$	9.41720e52	+	1.95344e52i	2.81433	+	0.583787i
$829$	−4.50516e52			−1.31743			−0.658717	−	0.752391i	$-0.728901\pi$
$829$	−4.50516e52			−1.31743			−0.658717	+	0.752391i	$0.728901\pi$
$830$		−	2.19154e52i		−	0.627109i
$831$	−2.15079e52	+	1.75043e52i	−0.602255	+	0.490148i
$832$	−1.09223e52			−0.299291
$833$			3.17037e52i			0.850157i
$834$	2.89605e52	+	3.55844e52i	0.760007	+	0.933836i
$835$	−1.17012e52			−0.300520
$836$			2.51182e52i			0.631357i
$837$	−5.60836e51	−	1.08096e52i	−0.137968	−	0.265920i
$838$	1.04152e53			2.50769
$839$			2.12502e52i			0.500780i	0.968145	+	0.250390i	$0.0805588\pi$
$839$			2.12502e52i			0.500780i	−0.968145	+	0.250390i	$0.919441\pi$
$840$	−4.38693e52	+	3.57032e52i	−1.01189	+	0.823532i
$841$	3.62824e52			0.819160
$842$			1.17870e53i			2.60488i
$843$	−3.57399e52	−	4.39143e52i	−0.773137	−	0.949970i
$844$	−1.76296e53			−3.73318
$845$			1.15215e52i			0.238831i
$846$	4.68673e50	−	2.25939e51i	0.00951050	−	0.0458484i
$847$	3.44014e52			0.683399
$848$		−	8.11101e52i		−	1.57743i
$849$	−1.40851e52	+	1.14632e52i	−0.268176	+	0.218257i
$850$	3.50797e52			0.653907
$851$		−	4.89492e52i		−	0.893334i
$852$	−2.89952e52	−	3.56270e52i	−0.518099	−	0.636600i
$853$	−8.39514e50			−0.0146874			−0.00734371	−	0.999973i	$-0.502338\pi$
$853$	−8.39514e50			−0.0146874			−0.00734371	+	0.999973i	$0.502338\pi$
$854$		−	3.04734e53i		−	5.22010i
$855$	5.75365e51	+	1.19350e51i	0.0965058	+	0.0200185i
$856$	8.26381e51			0.135723
$857$			6.11107e52i			0.982794i	0.870936	+	0.491397i	$0.163514\pi$
$857$			6.11107e52i			0.982794i	−0.870936	+	0.491397i	$0.836486\pi$
$858$	−2.99876e52	+	2.44055e52i	−0.472248	+	0.384341i
$859$	−9.41279e52			−1.45158			−0.725791	−	0.687915i	$-0.758526\pi$
$859$	−9.41279e52			−1.45158			−0.725791	+	0.687915i	$0.758526\pi$
$860$		−	7.01884e51i		−	0.105997i
$861$	1.34102e53	+	1.64774e53i	1.98325	+	2.43686i
$862$	1.68025e52			0.243357
$863$		−	3.23780e52i		−	0.459256i	−0.973278	−	0.229628i	$-0.926249\pi$
$863$		−	3.23780e52i		−	0.459256i	0.973278	−	0.229628i	$-0.0737510\pi$
$864$	1.02892e53	−	5.33837e52i	1.42934	−	0.741585i
$865$	−3.11402e52			−0.423673
$866$			6.82932e52i			0.910029i
$867$	−5.04311e52	+	4.10435e52i	−0.658195	+	0.535675i
$868$	9.91283e52			1.26719
$869$			2.80459e51i			0.0351167i
$870$	−1.16778e52	−	1.43488e52i	−0.143224	−	0.175982i
$871$	−4.48390e52			−0.538678
$872$			1.75906e53i			2.07006i
$873$	1.09992e52	−	5.30251e52i	0.126795	−	0.611258i
$874$	6.68536e52			0.754952
$875$		−	8.98169e52i		−	0.993603i
$876$	2.09721e52	−	1.70683e52i	0.227284	−	0.184976i
$877$	−8.68144e52			−0.921720			−0.460860	−	0.887473i	$-0.652459\pi$
$877$	−8.68144e52			−0.921720			−0.460860	+	0.887473i	$0.652459\pi$
$878$			2.77918e53i			2.89078i
$879$	6.48935e52	+	7.97360e52i	0.661304	+	0.812559i
$880$	5.13891e52			0.513077
$881$		−	8.66949e52i		−	0.848061i	−0.905648	−	0.424030i	$-0.860615\pi$
$881$		−	8.66949e52i		−	0.848061i	0.905648	−	0.424030i	$-0.139385\pi$
$882$	−4.09810e53	−	8.50083e52i	−3.92779	−	0.814755i
$883$	−8.21886e52			−0.771825			−0.385913	−	0.922535i	$-0.626113\pi$
$883$	−8.21886e52			−0.771825			−0.385913	+	0.922535i	$0.626113\pi$
$884$		−	4.23129e52i		−	0.389342i
$885$	2.34596e52	−	1.90927e52i	0.211516	−	0.172143i
$886$	1.84440e53			1.62948
$887$			1.02042e53i			0.883391i	0.897165	+	0.441695i	$0.145623\pi$
$887$			1.02042e53i			0.883391i	−0.897165	+	0.441695i	$0.854377\pi$
$888$	−1.37862e53	−	1.69394e53i	−1.16953	−	1.43702i
$889$	2.70353e53			2.24750
$890$			9.90872e52i			0.807231i
$891$	3.91364e52	−	9.02757e52i	0.312451	−	0.720730i
$892$	3.70842e53			2.90149
$893$		−	1.12802e51i		−	0.00864951i
$894$	1.05808e53	−	8.61127e52i	0.795143	−	0.647130i
$895$	4.76139e52			0.350686
$896$		−	7.63898e52i		−	0.551431i
$897$	4.56824e52	+	5.61309e52i	0.323210	+	0.397135i
$898$	−3.91579e53			−2.71547
$899$			1.87429e52i			0.127398i
$900$	−6.61503e52	+	3.18899e53i	−0.440724	+	2.12465i
$901$	4.18186e52			0.273101
$902$		−	3.96587e53i		−	2.53875i
$903$	3.39427e52	−	2.76244e52i	0.212993	−	0.173346i
$904$	−6.41892e53			−3.94848
$905$			2.00442e52i			0.120869i
$906$	−1.85963e53	−	2.28496e53i	−1.09931	−	1.35074i
$907$	1.49493e53			0.866345			0.433172	−	0.901311i	$-0.357394\pi$
$907$	1.49493e53			0.866345			0.433172	+	0.901311i	$0.357394\pi$
$908$		−	1.13340e53i		−	0.643929i
$909$	7.81843e52	+	1.62180e52i	0.435481	+	0.0903334i
$910$	−7.36263e52			−0.402057
$911$		−	2.17995e52i		−	0.116712i	−0.998296	−	0.0583561i	$-0.981414\pi$
$911$		−	2.17995e52i		−	0.116712i	0.998296	−	0.0583561i	$-0.0185859\pi$
$912$	1.12599e53	−	9.16394e52i	0.591056	−	0.481033i
$913$	−1.79392e53			−0.923272
$914$			6.33408e53i			3.19633i
$915$	5.90774e52	+	7.25896e52i	0.292308	+	0.359166i
$916$	5.52309e53			2.67956
$917$		−	9.64651e52i		−	0.458904i
$918$	7.05143e52	+	1.35910e53i	0.328934	+	0.633990i
$919$	−3.79287e53			−1.73496			−0.867479	−	0.497474i	$-0.834261\pi$
$919$	−3.79287e53			−1.73496			−0.867479	+	0.497474i	$0.834261\pi$
$920$		−	1.97639e53i		−	0.886526i
$921$	−1.77162e53	+	1.44184e53i	−0.779287	+	0.634226i
$922$	−1.14480e53			−0.493827
$923$		−	3.45650e52i		−	0.146220i
$924$	5.05566e53	+	6.21199e53i	2.09740	+	2.57713i
$925$	1.65759e53			0.674413
$926$		−	1.18087e53i		−	0.471199i
$927$	1.38468e52	−	6.67532e52i	0.0541896	−	0.261238i
$928$	−1.78406e53			−0.684770
$929$		−	1.09245e53i		−	0.411262i	−0.978630	−	0.205631i	$-0.934075\pi$
$929$		−	1.09245e53i		−	0.411262i	0.978630	−	0.205631i	$-0.0659246\pi$
$930$	−3.35759e52	+	2.73259e52i	−0.123975	+	0.100898i
$931$	−2.04602e53			−0.740994
$932$		−	1.06359e54i		−	3.77821i
$933$	−1.98511e53	−	2.43915e53i	−0.691697	−	0.849903i
$934$	8.00098e53			2.73463
$935$			2.64951e52i			0.0888292i
$936$	3.16177e53	+	6.55857e52i	1.03984	+	0.215697i
$937$	4.12250e53			1.32999			0.664994	−	0.746849i	$-0.268434\pi$
$937$	4.12250e53			1.32999			0.664994	+	0.746849i	$0.268434\pi$
$938$			1.32075e54i			4.17995i
$939$	2.21214e53	−	1.80036e53i	0.686803	−	0.558958i
$940$	−5.76873e51			−0.0175703
$941$			6.31442e53i			1.88678i	0.331691	+	0.943388i	$0.392381\pi$
$941$			6.31442e53i			1.88678i	−0.331691	+	0.943388i	$0.607619\pi$
$942$	−3.40598e53	−	4.18501e53i	−0.998450	−	1.22682i
$943$	−7.42334e53			−2.13495
$944$		−	7.47291e53i		−	2.10860i
$945$	1.66316e53	−	8.62901e52i	0.460429	−	0.238885i
$946$	−8.16953e52			−0.221900
$947$			2.09561e53i			0.558485i	0.960221	+	0.279242i	$0.0900833\pi$
$947$			2.09561e53i			0.558485i	−0.960221	+	0.279242i	$0.909917\pi$
$948$	3.14266e52	−	2.55767e52i	0.0821764	−	0.0668797i
$949$	2.03470e52			0.0522045
$950$			2.26389e53i			0.569943i
$951$	−3.15333e53	−	3.87456e53i	−0.778968	−	0.957134i
$952$	−7.20482e53			−1.74646
$953$			3.21520e53i			0.764779i	0.924001	+	0.382389i	$0.124899\pi$
$953$			3.21520e53i			0.764779i	−0.924001	+	0.382389i	$0.875101\pi$
$954$	−1.12130e53	+	5.40558e53i	−0.261728	+	1.26174i
$955$	−1.87993e53			−0.430608
$956$			3.89359e53i			0.875203i
$957$	−1.17454e53	+	9.55908e52i	−0.259092	+	0.210863i
$958$	5.93428e53			1.28466
$959$		−	9.29708e53i		−	1.97520i
$960$	−6.23707e52	−	7.66362e52i	−0.130046	−	0.159791i
$961$	−4.44818e53			−0.910251
$962$		−	2.84295e53i		−	0.570976i
$963$	−2.68044e52	−	5.56013e51i	−0.0528364	−	0.0109600i
$964$	−1.18299e54			−2.28873
$965$		−	1.57736e52i		−	0.0299529i
$966$	1.65336e54	−	1.34560e54i	3.08163	−	2.50799i
$967$	6.29599e53			1.15183			0.575914	−	0.817511i	$-0.304646\pi$
$967$	6.29599e53			1.15183			0.575914	+	0.817511i	$0.304646\pi$
$968$			5.36339e53i			0.963125i
$969$	4.72472e52	+	5.80536e52i	0.0832814	+	0.102330i
$970$	−1.92507e53			−0.333086
$971$			8.34790e53i			1.41785i	0.705282	+	0.708927i	$0.250820\pi$
$971$			8.34790e53i			1.41785i	−0.705282	+	0.708927i	$0.749180\pi$
$972$	−1.36848e54	+	3.84736e53i	−2.28164	+	0.641461i
$973$	7.15165e53			1.17051
$974$		−	1.67394e54i		−	2.68954i
$975$	−1.90079e53	+	1.54696e53i	−0.299813	+	0.244004i
$976$	2.31229e54			3.58052
$977$		−	1.77356e53i		−	0.269614i	−0.990872	−	0.134807i	$-0.956959\pi$
$977$		−	1.77356e53i		−	0.269614i	0.990872	−	0.134807i	$-0.0430415\pi$
$978$	2.36955e53	+	2.91151e53i	0.353644	+	0.434529i
$979$	8.11097e53			1.18846
$980$			1.04634e54i			1.50523i
$981$	1.18354e53	−	5.70566e53i	0.167164	−	0.805868i
$982$	−8.88959e53			−1.23275
$983$		−	8.19512e53i		−	1.11581i	−0.829903	−	0.557907i	$-0.811605\pi$
$983$		−	8.19512e53i		−	1.11581i	0.829903	−	0.557907i	$-0.188395\pi$
$984$	−2.56892e54	+	2.09073e54i	−3.43430	+	2.79502i
$985$	3.56847e53			0.468413
$986$		−	2.35655e53i		−	0.303733i
$987$	−2.27043e52	−	2.78972e52i	−0.0287342	−	0.0353063i
$988$	2.73069e53			0.339349
$989$			1.52918e53i			0.186605i
$990$	−3.42482e53	−	7.10423e52i	−0.410397	−	0.0851301i
$991$	1.00354e54			1.18089			0.590447	−	0.807077i	$-0.298952\pi$
$991$	1.00354e54			1.18089			0.590447	+	0.807077i	$0.298952\pi$
$992$			4.17466e53i			0.482405i
$993$	−5.02815e53	+	4.09218e53i	−0.570587	+	0.464375i
$994$	−1.01813e54			−1.13461
$995$		−	2.50382e53i		−	0.274024i
$996$	1.63598e54	+	2.01016e54i	1.75837	+	2.16054i
$997$	−1.37211e54			−1.44836			−0.724180	−	0.689611i	$-0.757782\pi$
$997$	−1.37211e54			−1.44836			−0.724180	+	0.689611i	$0.757782\pi$
$998$			1.46726e54i			1.52109i
$999$	3.33194e53	+	6.42202e53i	0.339249	+	0.653872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.37.b.b.2.1	✓	10
3.2	odd	2	inner	3.37.b.b.2.10	yes	10

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

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:	\( k \)	\(=\)	\( 37 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-481239. i q^{2} +(-3.00483e8 + 2.44550e8i) q^{3} -1.62872e11 q^{4} -1.10872e12i q^{5} +(1.17687e14 + 1.44604e14i) q^{6} +2.90621e15 q^{7} +4.53097e16i q^{8} +(3.04857e16 - 1.46966e17i) q^{9} +O(q^{10})\)	\(q-481239. i q^{2} +(-3.00483e8 + 2.44550e8i) q^{3} -1.62872e11 q^{4} -1.10872e12i q^{5} +(1.17687e14 + 1.44604e14i) q^{6} +2.90621e15 q^{7} +4.53097e16i q^{8} +(3.04857e16 - 1.46966e17i) q^{9} -5.33560e17 q^{10} +4.36755e18i q^{11} +(4.89402e19 - 3.98302e19i) q^{12} +4.74813e19 q^{13} -1.39858e21i q^{14} +(2.71137e20 + 3.33152e20i) q^{15} +1.06123e22 q^{16} +5.47148e21i q^{17} +(-7.07258e22 - 1.46709e22i) q^{18} -3.53105e22 q^{19} +1.80579e23i q^{20} +(-8.73269e23 + 7.10713e23i) q^{21} +2.10184e24 q^{22} -3.93423e24i q^{23} +(-1.10805e25 - 1.36148e25i) q^{24} +1.33227e25 q^{25} -2.28498e25i q^{26} +(2.67801e25 + 5.16161e25i) q^{27} -4.73340e26 q^{28} -8.94976e25i q^{29} +(1.60326e26 - 1.30482e26i) q^{30} -2.09423e26 q^{31} -1.99341e27i q^{32} +(-1.06808e27 - 1.31238e27i) q^{33} +2.63309e27 q^{34} -3.22218e27i q^{35} +(-4.96525e27 + 2.39366e28i) q^{36} +1.24419e28 q^{37} +1.69928e28i q^{38} +(-1.42673e28 + 1.16115e28i) q^{39} +5.02358e28 q^{40} -1.88686e29i q^{41} +(3.42023e29 + 4.20251e29i) q^{42} -3.88685e28 q^{43} -7.11350e29i q^{44} +(-1.62944e29 - 3.38001e28i) q^{45} -1.89330e30 q^{46} +3.19458e28i q^{47} +(-3.18883e30 + 2.59524e30i) q^{48} +5.79435e30 q^{49} -6.41138e30i q^{50} +(-1.33805e30 - 1.64409e30i) q^{51} -7.73335e30 q^{52} -7.64301e30i q^{53} +(2.48397e31 - 1.28876e31i) q^{54} +4.84239e30 q^{55} +1.31680e32i q^{56} +(1.06102e31 - 8.63518e30i) q^{57} -4.30697e31 q^{58} -7.04173e31i q^{59} +(-4.41605e31 - 5.42610e31i) q^{60} +2.17887e32 q^{61} +1.00783e32i q^{62} +(8.85979e31 - 4.27115e32i) q^{63} -2.30034e32 q^{64} -5.26435e31i q^{65} +(-6.31566e32 + 5.14003e32i) q^{66} -9.44351e32 q^{67} -8.91148e32i q^{68} +(9.62114e32 + 1.18217e33i) q^{69} -1.55064e33 q^{70} -7.27970e32i q^{71} +(6.65898e33 + 1.38130e33i) q^{72} +4.28526e32 q^{73} -5.98752e33i q^{74} +(-4.00323e33 + 3.25805e33i) q^{75} +5.75108e33 q^{76} +1.26930e34i q^{77} +(5.58792e33 + 6.86599e33i) q^{78} +6.42143e32 q^{79} -1.17661e34i q^{80} +(-2.06696e34 - 8.96072e33i) q^{81} -9.08031e34 q^{82} +4.10739e34i q^{83} +(1.42231e35 - 1.15755e35i) q^{84} +6.06634e33 q^{85} +1.87051e34i q^{86} +(2.18866e34 + 2.68925e34i) q^{87} -1.97892e35 q^{88} -1.85710e35i q^{89} +(-1.62659e34 + 7.84152e34i) q^{90} +1.37991e35 q^{91} +6.40774e35i q^{92} +(6.29281e34 - 5.12143e34i) q^{93} +1.53735e34 q^{94} +3.91495e34i q^{95} +(4.87488e35 + 5.98987e35i) q^{96} +3.60798e35 q^{97} -2.78847e36i q^{98} +(6.41882e35 + 1.33148e35i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 552156750 q^{3} - 435200290064 q^{4} + 77238909590832 q^{6} - 12\!\cdots\!00 q^{7}+ \cdots + 69\!\cdots\!78 q^{9}+O(q^{10}) \) 10 * q - 552156750 * q^3 - 435200290064 * q^4 + 77238909590832 * q^6 - 1227392913852700 * q^7 + 69328040174658378 * q^9	\( 10 q - 552156750 q^{3} - 435200290064 q^{4} + 77238909590832 q^{6} - 12\!\cdots\!00 q^{7}+ \cdots + 29\!\cdots\!20 q^{99}+O(q^{100}) \) 10 * q - 552156750 * q^3 - 435200290064 * q^4 + 77238909590832 * q^6 - 1227392913852700 * q^7 + 69328040174658378 * q^9 + 976353968400999840 * q^10 - 13909669295912917200 * q^12 + 146442021383468630900 * q^13 + 7346306914204243680 * q^15 + 8190375794092103561344 * q^16 - 116380061882656121268000 * q^18 + 251867201240528510816036 * q^19 - 3316093374315604451804172 * q^21 + 6375713195756021276887200 * q^22 - 18479722715707703137259904 * q^24 - 7272407101172449985508950 * q^25 + 37081479963629919172136850 * q^27 - 581040957055587380082052000 * q^28 + 832077359475776822335514400 * q^30 - 2837400895897932038626257820 * q^31 - 1833168501223628340439879200 * q^33 + 11044532239488942328340194176 * q^34 - 32262827456884310986989469968 * q^36 + 46026416879684258821119845300 * q^37 + 57128063394219587707605260868 * q^39 + 14850499435375431475622142720 * q^40 + 551003488989169331884355647200 * q^42 - 543751838871943644621511222300 * q^43 - 75992211973807694886478996800 * q^45 - 887182867438274648036289139776 * q^46 - 6175798579441788000263903318400 * q^48 + 4160815567016241405173969776926 * q^49 - 2349347159740543712848217109888 * q^51 - 1307858224937756917383112717600 * q^52 + 35390782846752825865826083751568 * q^54 - 30568574550133842572339360395200 * q^55 + 140759907582972539349070577896500 * q^57 - 112605799975805654976196455444000 * q^58 + 19469866547367779716225803605760 * q^60 + 250499227169556248885727488200820 * q^61 - 434037118158370938102741493062300 * q^63 - 628754572186817852398452012827648 * q^64 + 1808913396822349027193824888380960 * q^66 - 3266640518886976176082778405004700 * q^67 + 5226032060124551681525948207907648 * q^69 - 11529100185846942980259125797809600 * q^70 + 19879821238248816464160255047788800 * q^72 - 4353366099339985469471204489853100 * q^73 + 15739280815644629096708517058487250 * q^75 - 32093648191079013144382153537026976 * q^76 + 66756441224105756984056960627624800 * q^78 - 62441157931070689325228267195149084 * q^79 + 102373232392301630415794998228710090 * q^81 - 295731520386077266321378186874491200 * q^82 + 492063662513568202891754719135343328 * q^84 - 416995278796335191384264774379644160 * q^85 + 502161755301600073278417594406864800 * q^87 - 1043368725545479380062123692743456000 * q^88 + 1148239664725140620121403824942828960 * q^90 - 198812949993474284590473149470475384 * q^91 + 709190784760155706508652430361622900 * q^93 - 1775468098694354855547362712124166784 * q^94 + 2402404280227868861578148783194622976 * q^96 - 502412071359393103768239713429459500 * q^97 + 2995711137935834844910948248309577920 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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