LMFDB - Embedded newform 3.37.b.b.2.3

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			2.3
Root			$-16809.5i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.37.b.b.2.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-302571. i q^{2} +(-5.37826e7 - 3.83669e8i) q^{3} -2.28297e10 q^{4} -4.03107e12i q^{5} +(-1.16087e14 + 1.62730e13i) q^{6} +4.01364e14 q^{7} -1.38849e16i q^{8} +(-1.44310e17 + 4.12694e16i) q^{9} +O(q^{10})$	\(q-302571. i q^{2} +(-5.37826e7 - 3.83669e8i) q^{3} -2.28297e10 q^{4} -4.03107e12i q^{5} +(-1.16087e14 + 1.62730e13i) q^{6} +4.01364e14 q^{7} -1.38849e16i q^{8} +(-1.44310e17 + 4.12694e16i) q^{9} -1.21969e18 q^{10} -3.25448e18i q^{11} +(1.22784e18 + 8.75906e18i) q^{12} -1.15246e20 q^{13} -1.21441e20i q^{14} +(-1.54660e21 + 2.16802e20i) q^{15} -5.77002e21 q^{16} -1.35727e22i q^{17} +(1.24869e22 + 4.36639e22i) q^{18} +1.84954e23 q^{19} +9.20283e22i q^{20} +(-2.15864e22 - 1.53991e23i) q^{21} -9.84711e23 q^{22} +3.27910e24i q^{23} +(-5.32721e24 + 7.46766e23i) q^{24} -1.69765e24 q^{25} +3.48702e25i q^{26} +(2.35951e25 + 5.31475e25i) q^{27} -9.16303e24 q^{28} +2.12751e26i q^{29} +(6.55979e25 + 4.67956e26i) q^{30} +1.84570e25 q^{31} +7.91676e26i q^{32} +(-1.24864e27 + 1.75034e26i) q^{33} -4.10669e27 q^{34} -1.61793e27i q^{35} +(3.29455e27 - 9.42170e26i) q^{36} +3.11190e28 q^{37} -5.59617e28i q^{38} +(6.19824e27 + 4.42164e28i) q^{39} -5.59711e28 q^{40} -2.06848e29i q^{41} +(-4.65932e28 + 6.53141e27i) q^{42} -1.49684e29 q^{43} +7.42989e28i q^{44} +(1.66360e29 + 5.81722e29i) q^{45} +9.92159e29 q^{46} +1.35473e29i q^{47} +(3.10326e29 + 2.21378e30i) q^{48} -2.49064e30 q^{49} +5.13659e29i q^{50} +(-5.20741e30 + 7.29973e29i) q^{51} +2.63104e30 q^{52} -1.17754e30i q^{53} +(1.60809e31 - 7.13921e30i) q^{54} -1.31191e31 q^{55} -5.57290e30i q^{56} +(-9.94730e30 - 7.09612e31i) q^{57} +6.43722e31 q^{58} +4.51532e31i q^{59} +(3.53084e31 - 4.94952e30i) q^{60} -1.40212e32 q^{61} -5.58456e30i q^{62} +(-5.79206e31 + 1.65641e31i) q^{63} -1.56974e32 q^{64} +4.64566e32i q^{65} +(5.29603e31 + 3.77803e32i) q^{66} +3.01943e32 q^{67} +3.09860e32i q^{68} +(1.25809e33 - 1.76358e32i) q^{69} -4.89538e32 q^{70} -1.78943e33i q^{71} +(5.73022e32 + 2.00372e33i) q^{72} -4.43209e33 q^{73} -9.41572e33i q^{74} +(9.13039e31 + 6.51336e32i) q^{75} -4.22245e33 q^{76} -1.30623e33i q^{77} +(1.33786e34 - 1.87541e33i) q^{78} +1.68329e34 q^{79} +2.32594e34i q^{80} +(1.91221e34 - 1.19111e34i) q^{81} -6.25861e34 q^{82} +3.28306e34i q^{83} +(4.92811e32 + 3.51557e33i) q^{84} -5.47124e34 q^{85} +4.52899e34i q^{86} +(8.16259e34 - 1.14423e34i) q^{87} -4.51882e34 q^{88} -2.03955e34i q^{89} +(1.76012e35 - 5.03358e34i) q^{90} -4.62557e34 q^{91} -7.48609e34i q^{92} +(-9.92666e32 - 7.08139e33i) q^{93} +4.09901e34 q^{94} -7.45563e35i q^{95} +(3.03742e35 - 4.25784e34i) q^{96} -9.19383e35 q^{97} +7.53595e35i q^{98} +(1.34311e35 + 4.69652e35i) 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 $

$2$		−	302571.i		−	1.15422i	−0.816668	−	0.577108i	$-0.804181\pi$
$2$		−	302571.i		−	1.15422i	0.816668	−	0.577108i	$-0.195819\pi$
$3$	−5.37826e7	−	3.83669e8i	−0.138822	−	0.990317i
$3$	−5.37826e7	−	3.83669e8i	−0.138822	−	0.990317i
$4$	−2.28297e10			−0.332216
$5$		−	4.03107e12i		−	1.05672i	−0.849020	−	0.528361i	$-0.822807\pi$
$5$		−	4.03107e12i		−	1.05672i	0.849020	−	0.528361i	$-0.177193\pi$
$6$	−1.16087e14	+	1.62730e13i	−1.14304	+	0.160231i
$7$	4.01364e14			0.246475			0.123238	−	0.992377i	$-0.460672\pi$
$7$	4.01364e14			0.246475			0.123238	+	0.992377i	$0.460672\pi$
$8$		−	1.38849e16i		−	0.770767i
$9$	−1.44310e17	+	4.12694e16i	−0.961457	+	0.274956i
$10$	−1.21969e18			−1.21969
$11$		−	3.25448e18i		−	0.585347i	−0.956212	−	0.292673i	$-0.905455\pi$
$11$		−	3.25448e18i		−	0.585347i	0.956212	−	0.292673i	$-0.0945449\pi$
$12$	1.22784e18	+	8.75906e18i	0.0461190	+	0.329000i
$13$	−1.15246e20			−1.02482			−0.512409	−	0.858742i	$-0.671247\pi$
$13$	−1.15246e20			−1.02482			−0.512409	+	0.858742i	$0.671247\pi$
$14$		−	1.21441e20i		−	0.284486i
$15$	−1.54660e21	+	2.16802e20i	−1.04649	+	0.146696i
$16$	−5.77002e21			−1.22185
$17$		−	1.35727e22i		−	0.965127i	−0.875861	−	0.482563i	$-0.839706\pi$
$17$		−	1.35727e22i		−	0.965127i	0.875861	−	0.482563i	$-0.160294\pi$
$18$	1.24869e22	+	4.36639e22i	0.317359	+	1.10973i
$19$	1.84954e23			1.77623			0.888114	−	0.459622i	$-0.152015\pi$
$19$	1.84954e23			1.77623			0.888114	+	0.459622i	$0.152015\pi$
$20$			9.20283e22i			0.351060i
$21$	−2.15864e22	−	1.53991e23i	−0.0342162	−	0.244089i
$22$	−9.84711e23			−0.675617
$23$			3.27910e24i			1.01077i	0.862893	+	0.505386i	$0.168650\pi$
$23$			3.27910e24i			1.01077i	−0.862893	+	0.505386i	$0.831350\pi$
$24$	−5.32721e24	+	7.46766e23i	−0.763304	+	0.107000i
$25$	−1.69765e24			−0.116662
$26$			3.48702e25i			1.18286i
$27$	2.35951e25	+	5.31475e25i	0.405765	+	0.913977i
$28$	−9.16303e24			−0.0818831
$29$			2.12751e26i			1.01090i	0.862857	+	0.505449i	$0.168673\pi$
$29$			2.12751e26i			1.01090i	−0.862857	+	0.505449i	$0.831327\pi$
$30$	6.55979e25	+	4.67956e26i	0.169320	+	1.20788i
$31$	1.84570e25			0.0264029			0.0132014	−	0.999913i	$-0.495798\pi$
$31$	1.84570e25			0.0264029			0.0132014	+	0.999913i	$0.495798\pi$
$32$			7.91676e26i			0.639511i
$33$	−1.24864e27	+	1.75034e26i	−0.579679	+	0.0812592i
$34$	−4.10669e27			−1.11397
$35$		−	1.61793e27i		−	0.260456i
$36$	3.29455e27	−	9.42170e26i	0.319412	−	0.0913449i
$37$	3.11190e28			1.84245			0.921224	−	0.389033i	$-0.127191\pi$
$37$	3.11190e28			1.84245			0.921224	+	0.389033i	$0.127191\pi$
$38$		−	5.59617e28i		−	2.05015i
$39$	6.19824e27	+	4.42164e28i	0.142267	+	1.01489i
$40$	−5.59711e28			−0.814487
$41$		−	2.06848e29i		−	1.92993i	−0.262382	−	0.964964i	$-0.584508\pi$
$41$		−	2.06848e29i		−	1.92993i	0.262382	−	0.964964i	$-0.415492\pi$
$42$	−4.65932e28	+	6.53141e27i	−0.281731	+	0.0394930i
$43$	−1.49684e29			−0.592573			−0.296287	−	0.955099i	$-0.595748\pi$
$43$	−1.49684e29			−0.592573			−0.296287	+	0.955099i	$0.595748\pi$
$44$			7.42989e28i			0.194462i
$45$	1.66360e29	+	5.81722e29i	0.290552	+	1.01599i
$46$	9.92159e29			1.16665
$47$			1.35473e29i			0.108166i	0.998536	+	0.0540829i	$0.0172235\pi$
$47$			1.35473e29i			0.108166i	−0.998536	+	0.0540829i	$0.982776\pi$
$48$	3.10326e29	+	2.21378e30i	0.169620	+	1.21002i
$49$	−2.49064e30			−0.939250
$50$			5.13659e29i			0.134653i
$51$	−5.20741e30	+	7.29973e29i	−0.955782	+	0.133981i
$52$	2.63104e30			0.340461
$53$		−	1.17754e30i		−	0.108146i	−0.998537	−	0.0540729i	$-0.982780\pi$
$53$		−	1.17754e30i		−	0.108146i	0.998537	−	0.0540729i	$-0.0172203\pi$
$54$	1.60809e31	−	7.13921e30i	1.05493	−	0.468341i
$55$	−1.31191e31			−0.618549
$56$		−	5.57290e30i		−	0.189975i
$57$	−9.94730e30	−	7.09612e31i	−0.246580	−	1.75903i
$58$	6.43722e31			1.16679
$59$			4.51532e31i			0.601661i	0.953678	+	0.300831i	$0.0972639\pi$
$59$			4.51532e31i			0.601661i	−0.953678	+	0.300831i	$0.902736\pi$
$60$	3.53084e31	−	4.94952e30i	0.347661	−	0.0487350i
$61$	−1.40212e32			−1.02529			−0.512645	−	0.858601i	$-0.671334\pi$
$61$	−1.40212e32			−1.02529			−0.512645	+	0.858601i	$0.671334\pi$
$62$		−	5.58456e30i		−	0.0304746i
$63$	−5.79206e31	+	1.65641e31i	−0.236975	+	0.0677699i
$64$	−1.56974e32			−0.483714
$65$			4.64566e32i			1.08295i
$66$	5.29603e31	+	3.77803e32i	0.0937907	+	0.669075i
$67$	3.01943e32			0.407923			0.203961	−	0.978979i	$-0.434618\pi$
$67$	3.01943e32			0.407923			0.203961	+	0.978979i	$0.434618\pi$
$68$			3.09860e32i			0.320631i
$69$	1.25809e33	−	1.76358e32i	1.00098	−	0.140318i
$70$	−4.89538e32			−0.300623
$71$		−	1.78943e33i		−	0.851266i	−0.904896	−	0.425633i	$-0.860051\pi$
$71$		−	1.78943e33i		−	0.851266i	0.904896	−	0.425633i	$-0.139949\pi$
$72$	5.73022e32	+	2.00372e33i	0.211927	+	0.741059i
$73$	−4.43209e33			−1.27878			−0.639392	−	0.768881i	$-0.720814\pi$
$73$	−4.43209e33			−1.27878			−0.639392	+	0.768881i	$0.720814\pi$
$74$		−	9.41572e33i		−	2.12658i
$75$	9.13039e31	+	6.51336e32i	0.0161952	+	0.115532i
$76$	−4.22245e33			−0.590092
$77$		−	1.30623e33i		−	0.144274i
$78$	1.33786e34	−	1.87541e33i	1.17141	−	0.164207i
$79$	1.68329e34			1.17185			0.585923	−	0.810367i	$-0.300732\pi$
$79$	1.68329e34			1.17185			0.585923	+	0.810367i	$0.300732\pi$
$80$			2.32594e34i			1.29115i
$81$	1.91221e34	−	1.19111e34i	0.848798	−	0.528717i
$82$	−6.25861e34			−2.22756
$83$			3.28306e34i			0.939448i	0.882813	+	0.469724i	$0.155647\pi$
$83$			3.28306e34i			0.939448i	−0.882813	+	0.469724i	$0.844353\pi$
$84$	4.92811e32	+	3.51557e33i	0.0113672	+	0.0810903i
$85$	−5.47124e34			−1.01987
$86$			4.52899e34i			0.683958i
$87$	8.16259e34	−	1.14423e34i	1.00111	−	0.140335i
$88$	−4.51882e34			−0.451166
$89$		−	2.03955e34i		−	0.166155i	−0.996543	−	0.0830775i	$-0.973525\pi$
$89$		−	2.03955e34i		−	0.166155i	0.996543	−	0.0830775i	$-0.0264749\pi$
$90$	1.76012e35	−	5.03358e34i	1.17268	−	0.335360i
$91$	−4.62557e34			−0.252592
$92$		−	7.48609e34i		−	0.335795i
$93$	−9.92666e32	−	7.08139e33i	−0.00366531	−	0.0261472i
$94$	4.09901e34			0.124847
$95$		−	7.45563e35i		−	1.87698i
$96$	3.03742e35	−	4.25784e34i	0.633319	−	0.0887783i
$97$	−9.19383e35			−1.59076			−0.795381	−	0.606110i	$-0.792729\pi$
$97$	−9.19383e35			−1.59076			−0.795381	+	0.606110i	$0.792729\pi$
$98$			7.53595e35i			1.08410i
$99$	1.34311e35	+	4.69652e35i	0.160945	+	0.562786i
$100$	3.87569e34			0.0387569
$101$		−	1.11357e36i		−	0.930966i	−0.885057	−	0.465483i	$-0.845881\pi$
$101$		−	1.11357e36i		−	0.930966i	0.885057	−	0.465483i	$-0.154119\pi$
$102$	2.20869e35	+	1.57561e36i	0.154643	+	1.10318i
$103$	7.50833e35			0.441036			0.220518	−	0.975383i	$-0.429225\pi$
$103$	7.50833e35			0.441036			0.220518	+	0.975383i	$0.429225\pi$
$104$			1.60018e36i			0.789896i
$105$	−6.20749e35	+	8.70163e34i	−0.257934	+	0.0361571i
$106$	−3.56289e35			−0.124824
$107$			1.71824e36i			0.508365i	0.967156	+	0.254183i	$0.0818064\pi$
$107$			1.71824e36i			0.508365i	−0.967156	+	0.254183i	$0.918194\pi$
$108$	−5.38671e35	−	1.21334e36i	−0.134802	−	0.303638i
$109$	4.02974e36			0.854279			0.427140	−	0.904186i	$-0.359521\pi$
$109$	4.02974e36			0.854279			0.427140	+	0.904186i	$0.359521\pi$
$110$			3.96945e36i			0.713940i
$111$	−1.67366e36	−	1.19394e37i	−0.255773	−	1.82461i
$112$	−2.31588e36			−0.301156
$113$		−	7.65975e36i		−	0.848795i	−0.905476	−	0.424398i	$-0.860486\pi$
$113$		−	7.65975e36i		−	0.848795i	0.905476	−	0.424398i	$-0.139514\pi$
$114$	−2.14708e37	+	3.00976e36i	−2.03030	+	0.284607i
$115$	1.32183e37			1.06810
$116$		−	4.85704e36i		−	0.335837i
$117$	1.66311e37	−	4.75615e36i	0.985318	−	0.281780i
$118$	1.36620e37			0.694448
$119$		−	5.44757e36i		−	0.237880i
$120$	3.01027e36	+	2.14744e37i	0.113069	+	0.806600i
$121$	2.03210e37			0.657369
$122$			4.24240e37i			1.18341i
$123$	−7.93611e37	+	1.11248e37i	−1.91124	+	0.267917i
$124$	−4.21369e35			−0.00877146
$125$		−	5.18165e37i		−	0.933443i
$126$	5.01180e36	+	1.75251e37i	0.0782211	+	0.273521i
$127$	−7.93682e37			−1.07443			−0.537217	−	0.843444i	$-0.680524\pi$
$127$	−7.93682e37			−1.07443			−0.537217	+	0.843444i	$0.680524\pi$
$128$			1.01899e38i			1.19782i
$129$	8.05037e36	+	5.74290e37i	0.0822623	+	0.586836i
$130$	1.40564e38			1.24996
$131$		−	2.07047e38i		−	1.60393i	−0.597373	−	0.801964i	$-0.703789\pi$
$131$		−	2.07047e38i		−	1.60393i	0.597373	−	0.801964i	$-0.296211\pi$
$132$	2.85062e37	−	3.99599e36i	0.192579	−	0.0269956i
$133$	7.42338e37			0.437797
$134$		−	9.13590e37i		−	0.470831i
$135$	2.14242e38	−	9.51138e37i	0.965820	−	0.428781i
$136$	−1.88455e38			−0.743888
$137$			1.60583e38i			0.555556i	0.960645	+	0.277778i	$0.0895980\pi$
$137$			1.60583e38i			0.555556i	−0.960645	+	0.277778i	$0.910402\pi$
$138$	−5.33609e37	−	3.80661e38i	−0.161957	−	1.15535i
$139$	−4.69485e38			−1.25128			−0.625641	−	0.780111i	$-0.715163\pi$
$139$	−4.69485e38			−1.25128			−0.625641	+	0.780111i	$0.715163\pi$
$140$			3.69368e37i			0.0865277i
$141$	5.19767e37	−	7.28607e36i	0.107119	−	0.0150158i
$142$	−5.41431e38			−0.982546
$143$			3.75067e38i			0.599874i
$144$	8.32668e38	−	2.38125e38i	1.17475	−	0.335955i
$145$	8.57614e38			1.06824
$146$			1.34102e39i			1.47599i
$147$	1.33953e38	+	9.55581e38i	0.130389	+	0.930155i
$148$	−7.10439e38			−0.612091
$149$		−	3.41830e38i		−	0.260890i	−0.991456	−	0.130445i	$-0.958359\pi$
$149$		−	3.41830e38i		−	0.260890i	0.991456	−	0.130445i	$-0.0416406\pi$
$150$	1.97075e38	−	2.76259e37i	0.133349	−	0.0186928i
$151$	−1.18655e39			−0.712360			−0.356180	−	0.934417i	$-0.615921\pi$
$151$	−1.18655e39			−0.712360			−0.356180	+	0.934417i	$0.615921\pi$
$152$		−	2.56807e39i		−	1.36906i
$153$	5.60136e38	+	1.95866e39i	0.265367	+	0.927928i
$154$	−3.95227e38			−0.166523
$155$		−	7.44016e37i		−	0.0279005i
$156$	−1.41504e38	−	1.00945e39i	−0.0472636	−	0.337164i
$157$	−1.95869e38			−0.0583139			−0.0291569	−	0.999575i	$-0.509282\pi$
$157$	−1.95869e38			−0.0583139			−0.0291569	+	0.999575i	$0.509282\pi$
$158$		−	5.09314e39i		−	1.35256i
$159$	−4.51785e38	+	6.33311e37i	−0.107099	+	0.0150130i
$160$	3.19131e39			0.675785
$161$			1.31611e39i			0.249130i
$162$	−3.60397e39	−	5.78578e39i	−0.610254	−	0.979697i
$163$	1.21459e39			0.184100			0.0920498	−	0.995754i	$-0.470658\pi$
$163$	1.21459e39			0.184100			0.0920498	+	0.995754i	$0.470658\pi$
$164$			4.72228e39i			0.641153i
$165$	7.05576e38	+	5.03338e39i	0.0858683	+	0.612560i
$166$	9.93358e39			1.08433
$167$		−	2.21874e39i		−	0.217375i	−0.994076	−	0.108687i	$-0.965335\pi$
$167$		−	2.21874e39i		−	0.217375i	0.994076	−	0.108687i	$-0.0346647\pi$
$168$	−2.13815e39	+	2.99725e38i	−0.188136	+	0.0263728i
$169$	6.35481e38			0.0502507
$170$			1.65544e40i			1.17715i
$171$	−2.66906e40	+	7.63295e39i	−1.70777	+	0.488385i
$172$	3.41724e39			0.196862
$173$			1.35611e40i			0.703824i	0.936033	+	0.351912i	$0.114468\pi$
$173$			1.35611e40i			0.703824i	−0.936033	+	0.351912i	$0.885532\pi$
$174$	−3.46210e39	−	2.46976e40i	−0.161977	−	1.15550i
$175$	−6.81375e38			−0.0287542
$176$			1.87784e40i			0.715205i
$177$	1.73239e40	−	2.42845e39i	0.595836	−	0.0835240i
$178$	−6.17107e39			−0.191779
$179$		−	5.52861e40i		−	1.55332i	−0.629919	−	0.776661i	$-0.716912\pi$
$179$		−	5.52861e40i		−	1.55332i	0.629919	−	0.776661i	$-0.283088\pi$
$180$	−3.79796e39	−	1.32806e40i	−0.0965262	−	0.337529i
$181$	3.79382e40			0.872694			0.436347	−	0.899778i	$-0.356272\pi$
$181$	3.79382e40			0.872694			0.436347	+	0.899778i	$0.356272\pi$
$182$			1.39956e40i			0.291546i
$183$	7.54094e39	+	5.37949e40i	0.142333	+	1.01536i
$184$	4.55299e40			0.779070
$185$		−	1.25443e41i		−	1.94695i
$186$	−2.14262e39	+	3.00352e38i	−0.0301796	+	0.00423056i
$187$	−4.41720e40			−0.564934
$188$		−	3.09280e39i		−	0.0359345i
$189$	9.47024e39	+	2.13315e40i	0.100011	+	0.225273i
$190$	−2.25586e41			−2.16644
$191$		−	4.95075e40i		−	0.432584i	−0.976329	−	0.216292i	$-0.930604\pi$
$191$		−	4.95075e40i		−	0.432584i	0.976329	−	0.216292i	$-0.0693963\pi$
$192$	8.44248e39	+	6.02262e40i	0.0671503	+	0.479031i
$193$	−8.77587e39			−0.0635709			−0.0317855	−	0.999495i	$-0.510119\pi$
$193$	−8.77587e39			−0.0635709			−0.0317855	+	0.999495i	$0.510119\pi$
$194$			2.78179e41i			1.83608i
$195$	1.78240e41	−	2.49856e40i	1.07246	−	0.150337i
$196$	5.68606e40			0.312034
$197$			1.35854e41i			0.680271i	0.940376	+	0.340135i	$0.110473\pi$
$197$			1.35854e41i			0.680271i	−0.940376	+	0.340135i	$0.889527\pi$
$198$	1.42103e41	−	4.06385e40i	0.649577	−	0.185765i
$199$	1.99122e41			0.831313			0.415657	−	0.909522i	$-0.363552\pi$
$199$	1.99122e41			0.831313			0.415657	+	0.909522i	$0.363552\pi$
$200$			2.35717e40i			0.0899189i
$201$	−1.62392e40	−	1.15846e41i	−0.0566287	−	0.403973i
$202$	−3.36935e41			−1.07454
$203$			8.53904e40i			0.249161i
$204$	1.18884e41	−	1.66651e40i	0.317526	−	0.0445107i
$205$	−8.33818e41			−2.03940
$206$		−	2.27180e41i		−	0.509051i
$207$	−1.35326e41	−	4.73205e41i	−0.277918	−	0.971813i
$208$	6.64973e41			1.25217
$209$		−	6.01929e41i		−	1.03971i
$210$	2.63286e40	+	1.87821e41i	0.0417331	+	0.297712i
$211$	4.70013e41			0.683952			0.341976	−	0.939709i	$-0.388904\pi$
$211$	4.70013e41			0.683952			0.341976	+	0.939709i	$0.388904\pi$
$212$			2.68829e40i			0.0359278i
$213$	−6.86551e41	+	9.62404e40i	−0.843024	+	0.118175i
$214$	5.19890e41			0.586764
$215$			6.03386e41i			0.626185i
$216$	7.37949e41	−	3.27616e41i	0.704464	−	0.312751i
$217$	7.40798e39			0.00650766
$218$		−	1.21928e42i		−	0.986024i
$219$	2.38369e41	+	1.70046e42i	0.177524	+	1.26640i
$220$	2.99504e41			0.205492
$221$			1.56420e42i			0.989079i
$222$	−3.61252e42	+	5.06401e41i	−2.10599	+	0.295217i
$223$	1.03823e42			0.558221			0.279111	−	0.960259i	$-0.409960\pi$
$223$	1.03823e42			0.558221			0.279111	+	0.960259i	$0.409960\pi$
$224$			3.17750e41i			0.157624i
$225$	2.44987e41	−	7.00610e40i	0.112165	−	0.0320768i
$226$	−2.31762e42			−0.979693
$227$		−	2.42318e41i		−	0.0946062i	−0.998881	−	0.0473031i	$-0.984937\pi$
$227$		−	2.42318e41i		−	0.0946062i	0.998881	−	0.0473031i	$-0.0150627\pi$
$228$	2.27094e41	+	1.62002e42i	0.0819179	+	0.584378i
$229$	3.00918e42			1.00325			0.501625	−	0.865085i	$-0.332736\pi$
$229$	3.00918e42			1.00325			0.501625	+	0.865085i	$0.332736\pi$
$230$		−	3.99947e42i		−	1.23282i
$231$	−5.01160e41	+	7.02524e40i	−0.142877	+	0.0200284i
$232$	2.95402e42			0.779167
$233$			4.01900e42i			0.981096i	0.871414	+	0.490548i	$0.163203\pi$
$233$			4.01900e42i			0.981096i	−0.871414	+	0.490548i	$0.836797\pi$
$234$	−1.43907e42	−	5.03210e42i	−0.325235	−	1.13727i
$235$	5.46100e41			0.114301
$236$		−	1.03083e42i		−	0.199882i
$237$	−9.05315e41	−	6.45826e42i	−0.162678	−	1.16050i
$238$	−1.64828e42			−0.274565
$239$			3.95230e42i			0.610503i	0.952272	+	0.305251i	$0.0987405\pi$
$239$			3.95230e42i			0.610503i	−0.952272	+	0.305251i	$0.901259\pi$
$240$	8.92390e42	−	1.25095e42i	1.27865	−	0.179241i
$241$	−2.42317e42			−0.322163			−0.161082	−	0.986941i	$-0.551498\pi$
$241$	−2.42317e42			−0.322163			−0.161082	+	0.986941i	$0.551498\pi$
$242$		−	6.14856e42i		−	0.758746i
$243$	−5.59837e42	−	6.69594e42i	−0.641429	−	0.767182i
$244$	3.20099e42			0.340618
$245$			1.00399e43i			0.992526i
$246$	3.36604e42	+	2.40124e43i	0.309234	+	2.20599i
$247$	−2.13153e43			−1.82031
$248$		−	2.56274e41i		−	0.0203505i
$249$	1.25961e43	−	1.76571e42i	0.930352	−	0.130416i
$250$	−1.56782e43			−1.07740
$251$		−	1.77576e43i		−	1.13568i	−0.823139	−	0.567840i	$-0.807779\pi$
$251$		−	1.77576e43i		−	1.13568i	0.823139	−	0.567840i	$-0.192221\pi$
$252$	1.32231e42	−	3.78153e41i	0.0787271	−	0.0225143i
$253$	1.06718e43			0.591652
$254$			2.40145e43i			1.24013i
$255$	2.94257e42	+	2.09915e43i	0.141581	+	1.01000i
$256$	2.00446e43			0.898832
$257$		−	1.54959e42i		−	0.0647769i	−0.999475	−	0.0323885i	$-0.989689\pi$
$257$		−	1.54959e42i		−	0.0647769i	0.999475	−	0.0323885i	$-0.0103114\pi$
$258$	1.73763e43	−	2.43581e42i	0.677335	−	0.0949486i
$259$	1.24901e43			0.454118
$260$		−	1.06059e43i		−	0.359773i
$261$	−8.78010e42	−	3.07020e43i	−0.277952	−	0.971934i
$262$	−6.26463e43			−1.85128
$263$		−	4.15669e43i		−	1.14695i	−0.819223	−	0.573475i	$-0.805595\pi$
$263$		−	4.15669e43i		−	1.14695i	0.819223	−	0.573475i	$-0.194405\pi$
$264$	2.43034e42	+	1.73373e43i	0.0626319	+	0.446798i
$265$	−4.74675e42			−0.114280
$266$		−	2.24610e43i		−	0.505312i
$267$	−7.82511e42	+	1.09692e42i	−0.164546	+	0.0230660i
$268$	−6.89327e42			−0.135519
$269$		−	1.00694e43i		−	0.185125i	−0.995707	−	0.0925623i	$-0.970494\pi$
$269$		−	1.00694e43i		−	0.185125i	0.995707	−	0.0925623i	$-0.0295057\pi$
$270$	−2.87787e43	−	6.48233e43i	−0.494906	−	1.11477i
$271$	7.11372e43			1.14459			0.572294	−	0.820048i	$-0.306053\pi$
$271$	7.11372e43			1.14459			0.572294	+	0.820048i	$0.306053\pi$
$272$			7.83145e43i			1.17924i
$273$	2.48775e42	+	1.77469e43i	0.0350654	+	0.250146i
$274$	4.85876e43			0.641232
$275$			5.52497e42i			0.0682875i
$276$	−2.87218e43	+	4.02621e42i	−0.332543	+	0.0466158i
$277$	9.66833e43			1.04886			0.524428	−	0.851455i	$-0.324279\pi$
$277$	9.66833e43			1.04886			0.524428	+	0.851455i	$0.324279\pi$
$278$			1.42053e44i			1.44425i
$279$	−2.66352e42	+	7.61711e41i	−0.0253852	+	0.00725963i
$280$	−2.24648e43			−0.200751
$281$			2.62074e43i			0.219640i	0.993952	+	0.109820i	$0.0350274\pi$
$281$			2.62074e43i			0.219640i	−0.993952	+	0.109820i	$0.964973\pi$
$282$	−2.20455e42	−	1.57266e43i	−0.0173315	−	0.123638i
$283$	−1.32678e44			−0.978687			−0.489344	−	0.872091i	$-0.662764\pi$
$283$	−1.32678e44			−0.978687			−0.489344	+	0.872091i	$0.662764\pi$
$284$			4.08523e43i			0.282805i
$285$	−2.86050e44	+	4.00983e43i	−1.85881	+	0.260567i
$286$	1.13484e44			0.692384
$287$		−	8.30211e43i		−	0.475680i
$288$	−3.26720e43	−	1.14246e44i	−0.175837	−	0.614862i
$289$	1.35532e43			0.0685302
$290$		−	2.59489e44i		−	1.23298i
$291$	4.94468e43	+	3.52739e44i	0.220833	+	1.57536i
$292$	1.01183e44			0.424833
$293$			4.12802e43i			0.162976i	0.996674	+	0.0814881i	$0.0259673\pi$
$293$			4.12802e43i			0.162976i	−0.996674	+	0.0814881i	$0.974033\pi$
$294$	2.89131e44	−	4.05303e43i	1.07360	−	0.150497i
$295$	1.82016e44			0.635789
$296$		−	4.32085e44i		−	1.42010i
$297$	1.72968e44	−	7.67899e43i	0.534994	−	0.237513i
$298$	−1.03428e44			−0.301124
$299$		−	3.77904e44i		−	1.03586i
$300$	−2.08444e42	−	1.48698e43i	−0.00538032	−	0.0383816i
$301$	−6.00776e43			−0.146055
$302$			3.59014e44i			0.822218i
$303$	−4.27244e44	+	5.98908e43i	−0.921952	+	0.129239i
$304$	−1.06719e45			−2.17028
$305$			5.65203e44i			1.08345i
$306$	5.92635e44	−	1.69481e44i	1.07103	−	0.306292i
$307$	4.19946e44			0.715653			0.357826	−	0.933788i	$-0.383518\pi$
$307$	4.19946e44			0.715653			0.357826	+	0.933788i	$0.383518\pi$
$308$			2.98209e43i			0.0479300i
$309$	−4.03818e43	−	2.88072e44i	−0.0612255	−	0.436765i
$310$	−2.25118e43			−0.0322032
$311$			1.24519e45i			1.68092i	0.541872	+	0.840461i	$0.317716\pi$
$311$			1.24519e45i			1.68092i	−0.541872	+	0.840461i	$0.682284\pi$
$312$	6.13941e44	−	8.60620e43i	0.782247	−	0.109655i
$313$	−6.73067e44			−0.809581			−0.404790	−	0.914410i	$-0.632656\pi$
$313$	−6.73067e44			−0.809581			−0.404790	+	0.914410i	$0.632656\pi$
$314$			5.92643e43i			0.0673068i
$315$	6.67709e43	+	2.33482e44i	0.0716139	+	0.250417i
$316$	−3.84290e44			−0.389306
$317$		−	2.19838e44i		−	0.210395i	−0.994451	−	0.105198i	$-0.966452\pi$
$317$		−	2.19838e44i		−	0.210395i	0.994451	−	0.105198i	$-0.0335475\pi$
$318$	1.91621e43	+	1.36697e44i	0.0173283	+	0.123615i
$319$	6.92393e44			0.591726
$320$			6.32775e44i			0.511152i
$321$	6.59236e44	−	9.24114e43i	0.503443	−	0.0705724i
$322$	3.98217e44			0.287550
$323$		−	2.51032e45i		−	1.71429i
$324$	−4.36552e44	+	2.71928e44i	−0.281985	+	0.175648i
$325$	1.95648e44			0.119557
$326$		−	3.67500e44i		−	0.212491i
$327$	−2.16730e44	−	1.54609e45i	−0.118593	−	0.846008i
$328$	−2.87206e45			−1.48753
$329$			5.43738e43i			0.0266602i
$330$	1.52295e45	−	2.13487e44i	0.707027	−	0.0991107i
$331$	2.56818e45			1.12907			0.564535	−	0.825409i	$-0.309055\pi$
$331$	2.56818e45			1.12907			0.564535	+	0.825409i	$0.309055\pi$
$332$		−	7.49513e44i		−	0.312100i
$333$	−4.49077e45	+	1.28426e45i	−1.77143	+	0.506592i
$334$	−6.71325e44			−0.250898
$335$		−	1.21715e45i		−	0.431061i
$336$	1.24554e44	+	8.88530e44i	0.0418071	+	0.298240i
$337$	5.21984e45			1.66081			0.830403	−	0.557164i	$-0.188110\pi$
$337$	5.21984e45			1.66081			0.830403	+	0.557164i	$0.188110\pi$
$338$		−	1.92278e44i		−	0.0580002i
$339$	−2.93881e45	+	4.11961e44i	−0.840576	+	0.117832i
$340$	1.24907e45			0.338818
$341$		−	6.00680e43i		−	0.0154548i
$342$	2.30951e45	+	8.07581e45i	0.563702	+	1.97113i
$343$	−2.06396e45			−0.477977
$344$			2.07834e45i			0.456736i
$345$	−7.10913e44	−	5.07145e45i	−0.148277	−	1.05776i
$346$	4.10319e45			0.812366
$347$			6.75600e45i			1.26987i	0.772566	+	0.634935i	$0.218973\pi$
$347$			6.75600e45i			1.26987i	−0.772566	+	0.634935i	$0.781027\pi$
$348$	−1.86350e45	+	2.61224e44i	−0.332585	+	0.0466216i
$349$	−8.04366e44			−0.136331			−0.0681657	−	0.997674i	$-0.521715\pi$
$349$	−8.04366e44			−0.136331			−0.0681657	+	0.997674i	$0.521715\pi$
$350$			2.06164e44i			0.0331886i
$351$	−2.71925e45	−	6.12505e45i	−0.415835	−	0.936660i
$352$	2.57649e45			0.374336
$353$			3.14387e45i			0.434030i	0.976168	+	0.217015i	$0.0696320\pi$
$353$			3.14387e45i			0.434030i	−0.976168	+	0.217015i	$0.930368\pi$
$354$	−7.34780e44	−	5.24171e45i	−0.0964048	−	0.687724i
$355$	−7.21334e45			−0.899552
$356$			4.65623e44i			0.0551994i
$357$	−2.09007e45	+	2.92985e44i	−0.235577	+	0.0330230i
$358$	−1.67280e46			−1.79287
$359$		−	8.72033e45i		−	0.888859i	−0.895814	−	0.444429i	$-0.853406\pi$
$359$		−	8.72033e45i		−	0.888859i	0.895814	−	0.444429i	$-0.146594\pi$
$360$	8.07716e45	−	2.30990e45i	0.783094	−	0.223948i
$361$	2.33655e46			2.15499
$362$		−	1.14790e46i		−	1.00728i
$363$	−1.09292e45	−	7.79656e45i	−0.0912574	−	0.651004i
$364$	1.05600e45			0.0839152
$365$			1.78661e46i			1.35132i
$366$	1.62768e46	−	2.28167e45i	1.17195	−	0.164283i
$367$	1.73837e46			1.19166			0.595832	−	0.803109i	$-0.296822\pi$
$367$	1.73837e46			1.19166			0.595832	+	0.803109i	$0.296822\pi$
$368$		−	1.89204e46i		−	1.23501i
$369$	8.53648e45	+	2.98501e46i	0.530645	+	1.85554i
$370$	−3.79555e46			−2.24721
$371$		−	4.72621e44i		−	0.0266553i
$372$	2.26623e43	+	1.61666e44i	0.00121767	+	0.00868653i
$373$	−2.45843e46			−1.25863			−0.629316	−	0.777150i	$-0.716665\pi$
$373$	−2.45843e46			−1.25863			−0.629316	+	0.777150i	$0.716665\pi$
$374$			1.33652e46i			0.652056i
$375$	−1.98804e46	+	2.78682e45i	−0.924405	+	0.129583i
$376$	1.88103e45			0.0833707
$377$		−	2.45187e46i		−	1.03599i
$378$	6.45429e45	−	2.86542e45i	0.260014	−	0.115435i
$379$	2.39288e44			0.00919212			0.00459606	−	0.999989i	$-0.498537\pi$
$379$	2.39288e44			0.00919212			0.00459606	+	0.999989i	$0.498537\pi$
$380$			1.70210e46i			0.623563i
$381$	4.26863e45	+	3.04511e46i	0.149155	+	1.06403i
$382$	−1.49795e46			−0.499296
$383$			3.50568e46i			1.11479i	0.830247	+	0.557396i	$0.188200\pi$
$383$			3.50568e46i			1.11479i	−0.830247	+	0.557396i	$0.811800\pi$
$384$	3.90957e46	−	5.48041e45i	1.18622	−	0.166284i
$385$	−5.26551e45			−0.152457
$386$			2.65532e45i			0.0733746i
$387$	2.16008e46	−	6.17736e45i	0.569734	−	0.162932i
$388$	2.09893e46			0.528477
$389$		−	3.85187e46i		−	0.925931i	−0.886376	−	0.462966i	$-0.846785\pi$
$389$		−	3.85187e46i		−	0.925931i	0.886376	−	0.462966i	$-0.153215\pi$
$390$	−7.55991e45	−	5.39302e46i	−0.173522	−	1.23785i
$391$	4.45061e46			0.975523
$392$			3.45823e46i			0.723943i
$393$	−7.94374e46	+	1.11355e46i	−1.58840	+	0.222661i
$394$	4.11056e46			0.785180
$395$		−	6.78546e46i		−	1.23832i
$396$	−3.06627e45	−	1.07220e46i	−0.0534684	−	0.186967i
$397$	−6.21463e46			−1.03559			−0.517793	−	0.855506i	$-0.673246\pi$
$397$	−6.21463e46			−1.03559			−0.517793	+	0.855506i	$0.673246\pi$
$398$		−	6.02487e46i		−	0.959516i
$399$	−3.99249e45	−	2.84812e46i	−0.0607759	−	0.433558i
$400$	9.79547e45			0.142543
$401$			1.07538e47i			1.49611i	0.663637	+	0.748055i	$0.269012\pi$
$401$			1.07538e47i			1.49611i	−0.663637	+	0.748055i	$0.730988\pi$
$402$	−3.50517e46	+	4.91352e45i	−0.466272	+	0.0653618i
$403$	−2.12710e45			−0.0270581
$404$			2.54226e46i			0.309282i
$405$	−4.80147e46	−	7.70825e46i	−0.558707	−	0.896944i
$406$	2.58367e46			0.287586
$407$		−	1.01276e47i		−	1.07847i
$408$	1.01356e46	+	7.23044e46i	0.103268	+	0.736685i
$409$	1.45672e47			1.42022			0.710111	−	0.704090i	$-0.248645\pi$
$409$	1.45672e47			1.42022			0.710111	+	0.704090i	$0.248645\pi$
$410$			2.52289e47i			2.35391i
$411$	6.16106e46	−	8.63654e45i	0.550177	−	0.0771235i
$412$	−1.71413e46			−0.146519
$413$			1.81229e46i			0.148295i
$414$	−1.43178e47	+	4.09459e46i	−1.12168	+	0.320777i
$415$	1.32343e47			0.992736
$416$		−	9.12377e46i		−	0.655382i
$417$	2.52501e46	+	1.80127e47i	0.173706	+	1.23917i
$418$	−1.82126e47			−1.20005
$419$		−	8.14141e46i		−	0.513863i	−0.966430	−	0.256931i	$-0.917289\pi$
$419$		−	8.14141e46i		−	0.513863i	0.966430	−	0.256931i	$-0.0827114\pi$
$420$	1.41715e46	−	1.98656e45i	0.0856899	−	0.0120120i
$421$	−5.37417e46			−0.311339			−0.155670	−	0.987809i	$-0.549754\pi$
$421$	−5.37417e46			−0.311339			−0.155670	+	0.987809i	$0.549754\pi$
$422$		−	1.42212e47i		−	0.789428i
$423$	−5.59088e45	−	1.95500e46i	−0.0297409	−	0.103997i
$424$	−1.63500e46			−0.0833552
$425$			2.30416e46i			0.112593i
$426$	2.91195e46	+	2.07730e47i	0.136399	+	0.973032i
$427$	−5.62758e46			−0.252709
$428$		−	3.92270e46i		−	0.168887i
$429$	1.43902e47	−	2.01720e46i	0.594065	−	0.0832758i
$430$	1.82567e47			0.722754
$431$		−	4.41121e47i		−	1.67481i	−0.546580	−	0.837407i	$-0.684071\pi$
$431$		−	4.41121e47i		−	1.67481i	0.546580	−	0.837407i	$-0.315929\pi$
$432$	−1.36144e47	−	3.06662e47i	−0.495784	−	1.11674i
$433$	−1.42335e47			−0.497200			−0.248600	−	0.968606i	$-0.579970\pi$
$433$	−1.42335e47			−0.497200			−0.248600	+	0.968606i	$0.579970\pi$
$434$		−	2.24144e45i		−	0.00751125i
$435$	−4.61247e46	−	3.29040e47i	−0.148295	−	1.05789i
$436$	−9.19978e46			−0.283806
$437$			6.06482e47i			1.79536i
$438$	5.14509e47	−	7.21236e46i	1.46170	−	0.204901i
$439$	−5.53626e47			−1.50958			−0.754788	−	0.655969i	$-0.772260\pi$
$439$	−5.53626e47			−1.50958			−0.754788	+	0.655969i	$0.772260\pi$
$440$			1.82157e47i			0.476757i
$441$	3.59423e47	−	1.02787e47i	0.903048	−	0.258252i
$442$	4.73281e47			1.14161
$443$			9.09125e46i			0.210551i	0.994443	+	0.105275i	$0.0335724\pi$
$443$			9.09125e46i			0.210551i	−0.994443	+	0.105275i	$0.966428\pi$
$444$	3.82092e46	+	2.72574e47i	0.0849718	+	0.606164i
$445$	−8.22156e46			−0.175580
$446$		−	3.14139e47i		−	0.644309i
$447$	−1.31150e47	+	1.83845e46i	−0.258364	+	0.0362174i
$448$	−6.30038e46			−0.119224
$449$			6.35764e47i			1.15574i	0.816127	+	0.577872i	$0.196117\pi$
$449$			6.35764e47i			1.15574i	−0.816127	+	0.577872i	$0.803883\pi$
$450$	−2.11984e46	−	7.41259e46i	−0.0370236	−	0.129463i
$451$	−6.73182e47			−1.12968
$452$			1.74870e47i			0.281984i
$453$	6.38155e46	+	4.55241e47i	0.0988914	+	0.705462i
$454$	−7.33183e46			−0.109196
$455$			1.86460e47i			0.266920i
$456$	−9.85289e47	+	1.38117e47i	−1.35580	+	0.190056i
$457$	−1.16901e47			−0.154641			−0.0773207	−	0.997006i	$-0.524637\pi$
$457$	−1.16901e47			−0.154641			−0.0773207	+	0.997006i	$0.524637\pi$
$458$		−	9.10491e47i		−	1.15797i
$459$	7.21353e47	−	3.20249e47i	0.882104	−	0.391615i
$460$	−3.01770e47			−0.354842
$461$			1.27718e48i			1.44423i	0.691773	+	0.722115i	$0.256830\pi$
$461$			1.27718e48i			1.44423i	−0.691773	+	0.722115i	$0.743170\pi$
$462$	2.12563e46	+	1.51637e47i	0.0231171	+	0.164911i
$463$	1.48188e48			1.55008			0.775040	−	0.631912i	$-0.217730\pi$
$463$	1.48188e48			1.55008			0.775040	+	0.631912i	$0.217730\pi$
$464$		−	1.22758e48i		−	1.23516i
$465$	−2.85456e46	+	4.00151e45i	−0.0276303	+	0.00387321i
$466$	1.21603e48			1.13240
$467$		−	1.88187e48i		−	1.68611i	−0.537825	−	0.843056i	$-0.680754\pi$
$467$		−	1.88187e48i		−	1.68611i	0.537825	−	0.843056i	$-0.319246\pi$
$468$	−3.79684e47	+	1.08582e47i	−0.327339	+	0.0936118i
$469$	1.21189e47			0.100543
$470$		−	1.65234e47i		−	0.131928i
$471$	1.05343e46	+	7.51489e46i	0.00809526	+	0.0577492i
$472$	6.26948e47			0.463741
$473$			4.87142e47i			0.346861i
$474$	−1.95408e48	+	2.73922e47i	−1.33947	+	0.187766i
$475$	−3.13987e47			−0.207218
$476$			1.24367e47i			0.0790276i
$477$	4.85964e46	+	1.69930e47i	0.0297353	+	0.103978i
$478$	1.19585e48			0.704653
$479$		−	2.22533e48i		−	1.26286i	−0.775433	−	0.631430i	$-0.782468\pi$
$479$		−	2.22533e48i		−	1.26286i	0.775433	−	0.631430i	$-0.217532\pi$
$480$	−1.71637e47	−	1.22441e48i	−0.0938140	−	0.669242i
$481$	−3.58635e48			−1.88817
$482$			7.33179e47i			0.371846i
$483$	5.04951e47	−	7.07838e46i	0.246718	−	0.0345848i
$484$	−4.63924e47			−0.218389
$485$			3.70610e48i			1.68099i
$486$	−2.02600e48	+	1.69391e48i	−0.885494	+	0.740349i
$487$	1.86423e48			0.785196			0.392598	−	0.919710i	$-0.371576\pi$
$487$	1.86423e48			0.785196			0.392598	+	0.919710i	$0.371576\pi$
$488$			1.94682e48i			0.790260i
$489$	−6.53237e46	−	4.66001e47i	−0.0255571	−	0.182317i
$490$	3.03780e48			1.14559
$491$		−	1.99475e48i		−	0.725140i	−0.931957	−	0.362570i	$-0.881899\pi$
$491$		−	1.99475e48i		−	0.725140i	0.931957	−	0.362570i	$-0.118101\pi$
$492$	1.81179e48	−	2.53976e47i	0.634945	−	0.0890063i
$493$	2.88759e48			0.975644
$494$			6.44938e48i			2.10103i
$495$	1.89320e48	−	5.41416e47i	0.594708	−	0.170074i
$496$	−1.06497e47			−0.0322603
$497$		−	7.18214e47i		−	0.209816i
$498$	−5.34253e47	−	3.81121e48i	−0.150529	−	1.07383i
$499$	−3.82219e48			−1.03873			−0.519364	−	0.854553i	$-0.673831\pi$
$499$	−3.82219e48			−1.03873			−0.519364	+	0.854553i	$0.673831\pi$
$500$			1.18296e48i			0.310105i
$501$	−8.51261e47	+	1.19329e47i	−0.215270	+	0.0301764i
$502$	−5.37292e48			−1.31082
$503$		−	3.60198e48i		−	0.847847i	−0.905698	−	0.423924i	$-0.860652\pi$
$503$		−	3.60198e48i		−	0.847847i	0.905698	−	0.423924i	$-0.139348\pi$
$504$	2.29990e47	+	8.04222e47i	0.0522348	+	0.182653i
$505$	−4.48890e48			−0.983773
$506$		−	3.22896e48i		−	0.682895i
$507$	−3.41778e46	−	2.43814e47i	−0.00697591	−	0.0497641i
$508$	1.81195e48			0.356944
$509$		−	9.92023e48i		−	1.88626i	−0.332423	−	0.943130i	$-0.607866\pi$
$509$		−	9.92023e48i		−	1.88626i	0.332423	−	0.943130i	$-0.392134\pi$
$510$	6.35141e48	−	8.90337e47i	1.16575	−	0.163415i
$511$	−1.77888e48			−0.315189
$512$			9.37554e47i			0.160375i
$513$	4.36402e48	+	9.82985e48i	0.720732	+	1.62343i
$514$	−4.68861e47			−0.0747666
$515$		−	3.02667e48i		−	0.466052i
$516$	−1.83788e47	−	1.31109e48i	−0.0273289	−	0.194956i
$517$	4.40893e47			0.0633146
$518$		−	3.77913e48i		−	0.524150i
$519$	5.20297e48	−	7.29350e47i	0.697010	−	0.0977065i
$520$	6.45046e48			0.834700
$521$			7.81588e48i			0.977010i	0.872561	+	0.488505i	$0.162458\pi$
$521$			7.81588e48i			0.977010i	−0.872561	+	0.488505i	$0.837542\pi$
$522$	−9.28952e48	+	2.65660e48i	−1.12182	+	0.320817i
$523$	1.26134e48			0.147164			0.0735818	−	0.997289i	$-0.476557\pi$
$523$	1.26134e48			0.147164			0.0735818	+	0.997289i	$0.476557\pi$
$524$			4.72682e48i			0.532851i
$525$	3.66461e46	+	2.61423e47i	0.00399172	+	0.0284758i
$526$	−1.25769e49			−1.32383
$527$		−	2.50511e47i		−	0.0254821i
$528$	7.20470e48	−	1.00995e48i	0.708280	−	0.0992864i
$529$	−2.27957e47			−0.0216596
$530$			1.43623e48i			0.131904i
$531$	−1.86345e48	−	6.51603e48i	−0.165430	−	0.578471i
$532$	−1.69474e48			−0.145443
$533$			2.38384e49i			1.97782i
$534$	3.31896e47	+	2.36765e48i	0.0266232	+	0.189922i
$535$	6.92636e48			0.537201
$536$		−	4.19244e48i		−	0.314413i
$537$	−2.12116e49	+	2.97343e48i	−1.53828	+	0.215636i
$538$	−3.04672e48			−0.213674
$539$			8.10573e48i			0.549787i
$540$	−4.89108e48	+	2.17142e48i	−0.320861	+	0.142448i
$541$	1.45916e49			0.925875			0.462938	−	0.886391i	$-0.346795\pi$
$541$	1.45916e49			0.925875			0.462938	+	0.886391i	$0.346795\pi$
$542$		−	2.15241e49i		−	1.32110i
$543$	−2.04041e48	−	1.45557e49i	−0.121149	−	0.864244i
$544$	1.07452e49			0.617209
$545$		−	1.62442e49i		−	0.902736i
$546$	5.36969e48	−	7.52721e47i	0.288723	−	0.0404731i
$547$	1.23830e48			0.0644247			0.0322123	−	0.999481i	$-0.489745\pi$
$547$	1.23830e48			0.0644247			0.0322123	+	0.999481i	$0.489745\pi$
$548$		−	3.66606e48i		−	0.184565i
$549$	2.02339e49	−	5.78645e48i	0.985772	−	0.281910i
$550$	1.67169e48			0.0788186
$551$			3.93491e49i			1.79559i
$552$	−2.44872e48	−	1.74684e49i	−0.108152	−	0.771526i
$553$	6.75611e48			0.288831
$554$		−	2.92536e49i		−	1.21061i
$555$	−4.81287e49	+	6.74666e48i	−1.92810	+	0.270281i
$556$	1.07182e49			0.415696
$557$		−	1.18369e49i		−	0.444471i	−0.974993	−	0.222236i	$-0.928665\pi$
$557$		−	1.18369e49i		−	0.444471i	0.974993	−	0.222236i	$-0.0713354\pi$
$558$	2.30472e47	+	8.05905e47i	0.00837919	+	0.0293000i
$559$	1.72505e49			0.607279
$560$			9.33547e48i			0.318238i
$561$	2.37568e48	+	1.69474e49i	0.0784254	+	0.559464i
$562$	7.92961e48			0.253512
$563$		−	2.35612e49i		−	0.729535i	−0.931099	−	0.364768i	$-0.881148\pi$
$563$		−	2.35612e49i		−	0.729535i	0.931099	−	0.364768i	$-0.118852\pi$
$564$	−1.18661e48	+	1.66339e47i	−0.0355865	+	0.00498850i
$565$	−3.08770e49			−0.896941
$566$			4.01446e49i			1.12962i
$567$	7.67491e48	−	4.78070e48i	0.209208	−	0.130316i
$568$	−2.48461e49			−0.656128
$569$		−	1.19704e49i		−	0.306257i	−0.988206	−	0.153129i	$-0.951065\pi$
$569$		−	1.19704e49i		−	0.306257i	0.988206	−	0.153129i	$-0.0489349\pi$
$570$	1.21326e49	+	8.65504e49i	0.300750	+	2.14547i
$571$	−2.19019e49			−0.526055			−0.263027	−	0.964788i	$-0.584721\pi$
$571$	−2.19019e49			−0.526055			−0.263027	+	0.964788i	$0.584721\pi$
$572$		−	8.56267e48i		−	0.199288i
$573$	−1.89945e49	+	2.66264e48i	−0.428395	+	0.0600522i
$574$	−2.51198e49			−0.549037
$575$		−	5.56676e48i		−	0.117918i
$576$	2.26529e49	−	6.47824e48i	0.465070	−	0.133000i
$577$	6.48145e49			1.28976			0.644878	−	0.764286i	$-0.276908\pi$
$577$	6.48145e49			1.28976			0.644878	+	0.764286i	$0.276908\pi$
$578$		−	4.10082e48i		−	0.0790987i
$579$	4.71989e47	+	3.36703e48i	0.00882506	+	0.0629554i
$580$	−1.95791e49			−0.354886
$581$			1.31770e49i			0.231551i
$582$	1.06729e50	−	1.49612e49i	1.81831	−	0.254889i
$583$	−3.83228e48			−0.0633028
$584$			6.15392e49i			0.985645i
$585$	−1.91724e49	−	6.70413e49i	−0.297763	−	1.04121i
$586$	1.24902e49			0.188110
$587$			8.48141e48i			0.123875i	0.998080	+	0.0619373i	$0.0197279\pi$
$587$			8.48141e48i			0.123875i	−0.998080	+	0.0619373i	$0.980272\pi$
$588$	−3.05811e48	−	2.18157e49i	−0.0433173	−	0.309013i
$589$	3.41370e48			0.0468975
$590$		−	5.50727e49i		−	0.733838i
$591$	5.21232e49	−	7.30660e48i	0.673684	−	0.0944367i
$592$	−1.79557e50			−2.25119
$593$		−	8.98309e49i		−	1.09255i	−0.837606	−	0.546275i	$-0.816045\pi$
$593$		−	8.98309e49i		−	1.09255i	0.837606	−	0.546275i	$-0.183955\pi$
$594$	−2.32344e49	−	5.23350e49i	−0.274142	−	0.617499i
$595$	−2.19596e49			−0.251373
$596$			7.80390e48i			0.0866720i
$597$	−1.07093e49	−	7.63971e49i	−0.115405	−	0.823264i
$598$	−1.14343e50			−1.19560
$599$			1.09973e50i			1.11584i	0.829894	+	0.557921i	$0.188401\pi$
$599$			1.09973e50i			1.11584i	−0.829894	+	0.557921i	$0.811599\pi$
$600$	9.04374e48	−	1.26775e48i	0.0890483	−	0.0124827i
$601$	1.60146e50			1.53029			0.765147	−	0.643856i	$-0.222666\pi$
$601$	1.60146e50			1.53029			0.765147	+	0.643856i	$0.222666\pi$
$602$			1.81777e49i			0.168579i
$603$	−4.35732e49	+	1.24610e49i	−0.392200	+	0.112161i
$604$	2.70885e49			0.236658
$605$		−	8.19156e49i		−	0.694656i
$606$	1.81212e49	+	1.29272e50i	0.149170	+	1.06413i
$607$	1.90465e50			1.52202			0.761008	−	0.648742i	$-0.224705\pi$
$607$	1.90465e50			1.52202			0.761008	+	0.648742i	$0.224705\pi$
$608$			1.46424e50i			1.13592i
$609$	3.27617e49	−	4.59252e48i	0.246749	−	0.0345891i
$610$	1.71014e50			1.25053
$611$		−	1.56127e49i		−	0.110850i
$612$	−1.27878e49	−	4.47158e49i	−0.0881594	−	0.308273i
$613$	−2.59144e50			−1.73481			−0.867405	−	0.497602i	$-0.834214\pi$
$613$	−2.59144e50			−1.73481			−0.867405	+	0.497602i	$0.834214\pi$
$614$		−	1.27063e50i		−	0.826018i
$615$	4.48449e49	+	3.19910e50i	0.283114	+	2.01965i
$616$	−1.81369e49			−0.111201
$617$			6.61390e49i			0.393844i	0.980419	+	0.196922i	$0.0630946\pi$
$617$			6.61390e49i			0.393844i	−0.980419	+	0.196922i	$0.936905\pi$
$618$	−8.71621e49	+	1.22183e49i	−0.504122	+	0.0706675i
$619$	−1.85446e50			−1.04180			−0.520902	−	0.853617i	$-0.674404\pi$
$619$	−1.85446e50			−1.04180			−0.520902	+	0.853617i	$0.674404\pi$
$620$			1.69857e48i			0.00926900i
$621$	−1.74276e50	+	7.73708e49i	−0.923822	+	0.410136i
$622$	3.76757e50			1.94015
$623$		−	8.18600e48i		−	0.0409531i
$624$	−3.57639e49	−	2.55130e50i	−0.173829	−	1.24005i
$625$	−2.33580e50			−1.10305
$626$			2.03651e50i			0.934432i
$627$	−2.30942e50	+	3.23733e49i	−1.02964	+	0.144335i
$628$	4.47163e48			0.0193728
$629$		−	4.22368e50i		−	1.77820i
$630$	7.06450e49	−	2.02030e49i	0.289036	−	0.0826580i
$631$	3.65828e50			1.45462			0.727308	−	0.686311i	$-0.240771\pi$
$631$	3.65828e50			1.45462			0.727308	+	0.686311i	$0.240771\pi$
$632$		−	2.33723e50i		−	0.903221i
$633$	−2.52785e49	−	1.80329e50i	−0.0949477	−	0.677329i
$634$	−6.65166e49			−0.242842
$635$			3.19939e50i			1.13538i
$636$	1.03141e49	−	1.44583e48i	0.0355799	−	0.00498758i
$637$	2.87037e50			0.962560
$638$		−	2.09498e50i		−	0.682980i
$639$	7.38489e49	+	2.58232e50i	0.234061	+	0.818456i
$640$	4.10764e50			1.26577
$641$			8.19124e49i			0.245417i	0.992443	+	0.122709i	$0.0391581\pi$
$641$			8.19124e49i			0.245417i	−0.992443	+	0.122709i	$0.960842\pi$
$642$	−2.79610e49	−	1.99466e50i	−0.0814558	−	0.581082i
$643$	−1.31465e49			−0.0372404			−0.0186202	−	0.999827i	$-0.505927\pi$
$643$	−1.31465e49			−0.0372404			−0.0186202	+	0.999827i	$0.505927\pi$
$644$		−	3.00464e49i		−	0.0827651i
$645$	2.31501e50	−	3.24516e49i	0.620122	−	0.0869284i
$646$	−7.59549e50			−1.97866
$647$		−	1.54010e50i		−	0.390187i	−0.980785	−	0.195093i	$-0.937499\pi$
$647$		−	1.54010e50i		−	0.390187i	0.980785	−	0.195093i	$-0.0625010\pi$
$648$	−1.65385e50	−	2.65508e50i	−0.407518	−	0.654226i
$649$	1.46950e50			0.352181
$650$		−	5.91973e49i		−	0.137994i
$651$	−3.98420e47	−	2.84221e48i	−0.000903407	−	0.00644465i
$652$	−2.77288e49			−0.0611609
$653$			4.90881e50i			1.05327i	0.850092	+	0.526634i	$0.176546\pi$
$653$			4.90881e50i			1.05327i	−0.850092	+	0.526634i	$0.823454\pi$
$654$	−4.67801e50	+	6.55761e49i	−0.976476	+	0.136882i
$655$	−8.34620e50			−1.69491
$656$			1.19351e51i			2.35808i
$657$	6.39593e50	−	1.82910e50i	1.22950	−	0.351609i
$658$	1.64519e49			0.0307717
$659$			4.90109e50i			0.891980i	0.895038	+	0.445990i	$0.147148\pi$
$659$			4.90109e50i			0.891980i	−0.895038	+	0.445990i	$0.852852\pi$
$660$	−1.61081e49	−	1.14911e50i	−0.0285269	−	0.203502i
$661$	6.19004e49			0.106676			0.0533381	−	0.998577i	$-0.483014\pi$
$661$	6.19004e49			0.106676			0.0533381	+	0.998577i	$0.483014\pi$
$662$		−	7.77056e50i		−	1.30319i
$663$	6.00135e50	−	8.41266e49i	0.979502	−	0.137306i
$664$	4.55849e50			0.724096
$665$		−	2.99242e50i		−	0.462629i
$666$	3.88581e50	+	1.35878e51i	0.584717	+	2.04462i
$667$	−6.97630e50			−1.02179
$668$			5.06531e49i			0.0722154i
$669$	−5.58387e49	−	3.98337e50i	−0.0774935	−	0.552816i
$670$	−3.68275e50			−0.497538
$671$			4.56316e50i			0.600150i
$672$	1.21911e50	−	1.70894e49i	0.156097	−	0.0218817i
$673$	4.01889e50			0.500997			0.250498	−	0.968117i	$-0.419406\pi$
$673$	4.01889e50			0.500997			0.250498	+	0.968117i	$0.419406\pi$
$674$		−	1.57937e51i		−	1.91693i
$675$	−4.00563e49	−	9.02259e49i	−0.0473372	−	0.106626i
$676$	−1.45079e49			−0.0166941
$677$		−	1.45928e51i		−	1.63510i	−0.575861	−	0.817548i	$-0.695333\pi$
$677$		−	1.45928e51i		−	1.63510i	0.575861	−	0.817548i	$-0.304667\pi$
$678$	1.24648e50	+	8.89199e50i	0.136003	+	0.970207i
$679$	−3.69007e50			−0.392083
$680$			7.59677e50i			0.786083i
$681$	−9.29699e49	+	1.30325e49i	−0.0936902	+	0.0131334i
$682$	−1.81748e49			−0.0178382
$683$		−	1.34938e51i		−	1.28992i	−0.764216	−	0.644960i	$-0.776874\pi$
$683$		−	1.34938e51i		−	1.28992i	0.764216	−	0.644960i	$-0.223126\pi$
$684$	6.09340e50	−	1.74258e50i	0.567348	−	0.162249i
$685$	6.47320e50			0.587069
$686$			6.24495e50i			0.551689i
$687$	−1.61841e50	−	1.15453e51i	−0.139274	−	0.993537i
$688$	8.63677e50			0.724035
$689$			1.35707e50i			0.110830i
$690$	−1.53447e51	+	2.15102e50i	−1.22089	+	0.171143i
$691$	−2.45925e51			−1.90633			−0.953165	−	0.302450i	$-0.902195\pi$
$691$	−2.45925e51			−1.90633			−0.953165	+	0.302450i	$0.902195\pi$
$692$		−	3.09596e50i		−	0.233822i
$693$	5.39074e49	+	1.88501e50i	0.0396689	+	0.138713i
$694$	2.04417e51			1.46570
$695$			1.89253e51i			1.32226i
$696$	−1.58875e50	−	1.13337e51i	−0.108166	−	0.771622i
$697$	−2.80747e51			−1.86263
$698$			2.43378e50i			0.157356i
$699$	1.54197e51	−	2.16152e50i	0.971596	−	0.136198i
$700$	1.55556e49			0.00955261
$701$			1.67963e51i			1.00529i	0.864494	+	0.502643i	$0.167639\pi$
$701$			1.67963e51i			1.00529i	−0.864494	+	0.502643i	$0.832361\pi$
$702$	−1.85326e51	+	8.22767e50i	−1.08111	+	0.479964i
$703$	5.75559e51			3.27261
$704$			5.10870e50i			0.283141i
$705$	−2.93707e49	−	2.09522e50i	−0.0158676	−	0.113195i
$706$	9.51243e50			0.500964
$707$		−	4.46948e50i		−	0.229460i
$708$	−3.95500e50	+	5.54409e49i	−0.197946	+	0.0277480i
$709$	−1.05345e51			−0.514020			−0.257010	−	0.966409i	$-0.582737\pi$
$709$	−1.05345e51			−0.514020			−0.257010	+	0.966409i	$0.582737\pi$
$710$			2.18255e51i			1.03828i
$711$	−2.42914e51	+	6.94683e50i	−1.12668	+	0.322206i
$712$	−2.83189e50			−0.128067
$713$			6.05224e49i			0.0266873i
$714$	8.86486e49	+	6.32393e50i	0.0381157	+	0.271906i
$715$	1.51192e51			0.633900
$716$			1.26217e51i			0.516039i
$717$	1.51638e51	−	2.12565e50i	0.604592	−	0.0847514i
$718$	−2.63852e51			−1.02594
$719$		−	1.24405e51i		−	0.471756i	−0.971783	−	0.235878i	$-0.924203\pi$
$719$		−	1.24405e51i		−	0.471756i	0.971783	−	0.235878i	$-0.0757966\pi$
$720$	−9.59901e50	−	3.35655e51i	−0.355011	−	1.24139i
$721$	3.01357e50			0.108704
$722$		−	7.06972e51i		−	2.48732i
$723$	1.30324e50	+	9.29694e50i	0.0447234	+	0.319044i
$724$	−8.66118e50			−0.289923
$725$		−	3.61176e50i		−	0.117933i
$726$	−2.35901e51	+	3.30685e50i	−0.751400	+	0.105331i
$727$	−2.44831e50			−0.0760759			−0.0380380	−	0.999276i	$-0.512111\pi$
$727$	−2.44831e50			−0.0760759			−0.0380380	+	0.999276i	$0.512111\pi$
$728$			6.42256e50i			0.194690i
$729$	−2.26793e51	+	2.50805e51i	−0.670709	+	0.741721i
$730$	5.40576e51			1.55972
$731$			2.03160e51i			0.571908i
$732$	−1.72158e50	−	1.22812e51i	−0.0472854	−	0.337320i
$733$	−1.42809e51			−0.382722			−0.191361	−	0.981520i	$-0.561290\pi$
$733$	−1.42809e51			−0.382722			−0.191361	+	0.981520i	$0.561290\pi$
$734$		−	5.25981e51i		−	1.37544i
$735$	3.85202e51	−	5.39974e50i	0.982916	−	0.137785i
$736$	−2.59598e51			−0.646400
$737$		−	9.82666e50i		−	0.238776i
$738$	9.03177e51	−	2.58289e51i	2.14170	−	0.612480i
$739$	−1.67560e50			−0.0387766			−0.0193883	−	0.999812i	$-0.506172\pi$
$739$	−1.67560e50			−0.0387766			−0.0193883	+	0.999812i	$0.506172\pi$
$740$			2.86383e51i			0.646810i
$741$	1.14639e51	+	8.17801e51i	0.252699	+	1.80268i
$742$	−1.43002e50			−0.0307660
$743$		−	4.58449e51i		−	0.962703i	−0.876528	−	0.481352i	$-0.840146\pi$
$743$		−	4.58449e51i		−	0.962703i	0.876528	−	0.481352i	$-0.159854\pi$
$744$	−9.83245e49	+	1.37831e49i	−0.0201534	+	0.00282510i
$745$	−1.37794e51			−0.275689
$746$			7.43849e51i			1.45273i
$747$	−1.35490e51	−	4.73776e51i	−0.258307	−	0.903239i
$748$	1.00843e51			0.187680
$749$			6.89639e50i			0.125300i
$750$	8.43212e50	+	6.01523e51i	0.149566	+	1.06696i
$751$	−7.96212e51			−1.37883			−0.689414	−	0.724368i	$-0.742132\pi$
$751$	−7.96212e51			−1.37883			−0.689414	+	0.724368i	$0.742132\pi$
$752$		−	7.81680e50i		−	0.132162i
$753$	−6.81303e51	+	9.55047e50i	−1.12468	+	0.157658i
$754$	−7.41865e51			−1.19575
$755$			4.78306e51i			0.752767i
$756$	−2.16203e50	−	4.86992e50i	−0.0332253	−	0.0748393i
$757$	4.22571e51			0.634123			0.317062	−	0.948405i	$-0.397304\pi$
$757$	4.22571e51			0.634123			0.317062	+	0.948405i	$0.397304\pi$
$758$		−	7.24017e49i		−	0.0106097i
$759$	−5.73954e50	−	4.09442e51i	−0.0821345	−	0.585923i
$760$	−1.03521e52			−1.44671
$761$			6.02868e51i			0.822808i	0.911453	+	0.411404i	$0.134961\pi$
$761$			6.02868e51i			0.822808i	−0.911453	+	0.411404i	$0.865039\pi$
$762$	9.21363e51	−	1.29156e51i	1.22812	−	0.172157i
$763$	1.61739e51			0.210559
$764$			1.13024e51i			0.143711i
$765$	7.89552e51	−	2.25795e51i	0.980562	−	0.280420i
$766$	1.06072e52			1.28671
$767$		−	5.20373e51i		−	0.616593i
$768$	−1.07805e51	−	7.69051e51i	−0.124778	−	0.890129i
$769$	1.13296e52			1.28098			0.640488	−	0.767968i	$-0.278732\pi$
$769$	1.13296e52			1.28098			0.640488	+	0.767968i	$0.278732\pi$
$770$			1.59319e51i			0.175969i
$771$	−5.94530e50	+	8.33409e49i	−0.0641497	+	0.00899248i
$772$	2.00351e50			0.0211193
$773$			1.07837e52i			1.11055i	0.831667	+	0.555274i	$0.187387\pi$
$773$			1.07837e52i			1.11055i	−0.831667	+	0.555274i	$0.812613\pi$
$774$	−1.86909e51	−	6.53577e51i	−0.188058	−	0.657596i
$775$	−3.13336e49			−0.00308020
$776$			1.27655e52i			1.22611i
$777$	−6.71747e50	−	4.79205e51i	−0.0630416	−	0.449721i
$778$	−1.16546e52			−1.06873
$779$		−	3.82573e52i		−	3.42799i
$780$	−4.06917e51	+	5.70414e50i	−0.356289	+	0.0499444i
$781$	−5.82368e51			−0.498286
$782$		−	1.34662e52i		−	1.12596i
$783$	−1.13072e52	+	5.01988e51i	−0.923937	+	0.410187i
$784$	1.43710e52			1.14762
$785$			7.89562e50i			0.0616215i
$786$	3.36928e51	+	2.40354e52i	0.256999	+	1.83335i
$787$	1.07076e52			0.798266			0.399133	−	0.916893i	$-0.369311\pi$
$787$	1.07076e52			0.798266			0.399133	+	0.916893i	$0.369311\pi$
$788$		−	3.10152e51i		−	0.225997i
$789$	−1.59479e52	+	2.23558e51i	−1.13584	+	0.159222i
$790$	−2.05308e52			−1.42928
$791$		−	3.07435e51i		−	0.209207i
$792$	6.52108e51	−	1.86489e51i	0.433777	−	0.124051i
$793$	1.61589e52			1.05074
$794$			1.88037e52i			1.19529i
$795$	2.55292e50	+	1.82118e51i	0.0158646	+	0.113174i
$796$	−4.54591e51			−0.276176
$797$			1.16807e51i			0.0693774i	0.999398	+	0.0346887i	$0.0110440\pi$
$797$			1.16807e51i			0.0693774i	−0.999398	+	0.0346887i	$0.988956\pi$
$798$	−8.61760e51	+	1.20801e51i	−0.500419	+	0.0701486i
$799$	1.83872e51			0.104394
$800$		−	1.34399e51i		−	0.0746064i
$801$	8.41709e50	+	2.94326e51i	0.0456853	+	0.159751i
$802$	3.25379e52			1.72683
$803$			1.44242e52i			0.748532i
$804$	3.70738e50	+	2.64473e51i	0.0188130	+	0.134206i
$805$	5.30534e51			0.263262
$806$			6.43600e50i			0.0312309i
$807$	−3.86333e51	+	5.41560e50i	−0.183332	+	0.0256994i
$808$	−1.54619e52			−0.717558
$809$			2.50647e52i			1.13760i	0.822476	+	0.568800i	$0.192592\pi$
$809$			2.50647e52i			1.13760i	−0.822476	+	0.568800i	$0.807408\pi$
$810$	−2.33229e52	+	1.45279e52i	−1.03527	+	0.644869i
$811$	3.84257e52			1.66820			0.834098	−	0.551617i	$-0.185989\pi$
$811$	3.84257e52			1.66820			0.834098	+	0.551617i	$0.185989\pi$
$812$		−	1.94944e51i		−	0.0827754i
$813$	−3.82594e51	−	2.72932e52i	−0.158894	−	1.13351i
$814$	−3.06433e52			−1.24479
$815$		−	4.89610e51i		−	0.194542i
$816$	3.00469e52	−	4.21195e51i	1.16782	−	0.163705i
$817$	−2.76846e52			−1.05255
$818$		−	4.40761e52i		−	1.63924i
$819$	6.67513e51	−	1.90895e51i	0.242856	−	0.0694518i
$820$	1.90358e52			0.677521
$821$			9.95155e51i			0.346508i	0.984877	+	0.173254i	$0.0554282\pi$
$821$			9.95155e51i			0.346508i	−0.984877	+	0.173254i	$0.944572\pi$
$822$	−2.61317e51	−	1.86416e52i	−0.0890173	−	0.635023i
$823$	−4.13546e52			−1.37825			−0.689123	−	0.724645i	$-0.742004\pi$
$823$	−4.13546e52			−1.37825			−0.689123	+	0.724645i	$0.742004\pi$
$824$		−	1.04253e52i		−	0.339936i
$825$	2.11976e51	−	2.97147e50i	0.0676263	−	0.00947982i
$826$	5.48345e51			0.171164
$827$			2.82281e52i			0.862150i	0.902316	+	0.431075i	$0.141866\pi$
$827$			2.82281e52i			0.862150i	−0.902316	+	0.431075i	$0.858134\pi$
$828$	3.08947e51	+	1.08031e52i	0.0923288	+	0.322852i
$829$	−5.67076e51			−0.165829			−0.0829144	−	0.996557i	$-0.526423\pi$
$829$	−5.67076e51			−0.165829			−0.0829144	+	0.996557i	$0.526423\pi$
$830$		−	4.00430e52i		−	1.14583i
$831$	−5.19988e51	−	3.70944e52i	−0.145604	−	1.03870i
$832$	1.80907e52			0.495719
$833$			3.38046e52i			0.906495i
$834$	5.45012e52	−	7.63995e51i	1.43027	−	0.200494i
$835$	−8.94389e51			−0.229705
$836$			1.37419e52i			0.345409i
$837$	4.35496e50	+	9.80945e50i	0.0107134	+	0.0241316i
$838$	−2.46335e52			−0.593109
$839$		−	3.71362e52i		−	0.875149i	−0.899182	−	0.437574i	$-0.855838\pi$
$839$		−	3.71362e52i		−	0.875149i	0.899182	−	0.437574i	$-0.144162\pi$
$840$	1.20821e51	+	8.61904e51i	0.0278687	+	0.198807i
$841$	−9.70605e50			−0.0219136
$842$			1.62607e52i			0.359353i
$843$	1.00550e52	−	1.40950e51i	0.217513	−	0.0304909i
$844$	−1.07303e52			−0.227220
$845$		−	2.56167e51i		−	0.0531010i
$846$	−5.91526e51	+	1.69164e51i	−0.120035	+	0.0343274i
$847$	8.15613e51			0.162025
$848$			6.79442e51i			0.132138i
$849$	7.13578e51	+	5.09046e52i	0.135864	+	0.969211i
$850$	6.97173e51			0.129957
$851$			1.02042e53i			1.86229i
$852$	1.56738e52	−	2.19714e51i	0.280066	−	0.0392596i
$853$	−4.36262e52			−0.763247			−0.381624	−	0.924318i	$-0.624635\pi$
$853$	−4.36262e52			−0.763247			−0.381624	+	0.924318i	$0.624635\pi$
$854$			1.70274e52i			0.291681i
$855$	3.07690e52	+	1.07592e53i	0.516087	+	1.80464i
$856$	2.38576e52			0.391831
$857$		−	1.09899e53i		−	1.76741i	−0.468045	−	0.883705i	$-0.655042\pi$
$857$		−	1.09899e53i		−	1.76741i	0.468045	−	0.883705i	$-0.344958\pi$
$858$	−6.10348e51	−	4.35404e52i	−0.0961183	−	0.685680i
$859$	8.40103e51			0.129555			0.0647777	−	0.997900i	$-0.479366\pi$
$859$	8.40103e51			0.129555			0.0647777	+	0.997900i	$0.479366\pi$
$860$		−	1.37751e52i		−	0.208029i
$861$	−3.18527e52	+	4.46509e51i	−0.471074	+	0.0660349i
$862$	−1.33470e53			−1.93310
$863$		−	5.14640e52i		−	0.729977i	−0.931012	−	0.364988i	$-0.881073\pi$
$863$		−	5.14640e52i		−	0.729977i	0.931012	−	0.364988i	$-0.118927\pi$
$864$	−4.20756e52	+	1.86797e52i	−0.584499	+	0.259491i
$865$	5.46657e52			0.743747
$866$			4.30666e52i			0.573876i
$867$	−7.28928e50	−	5.19996e51i	−0.00951352	−	0.0678667i
$868$	−1.69122e50			−0.00216195
$869$		−	5.47823e52i		−	0.685937i
$870$	−9.95580e52	+	1.39560e52i	−1.22104	+	0.171165i
$871$	−3.47977e52			−0.418046
$872$		−	5.59525e52i		−	0.658450i
$873$	1.32676e53	−	3.79424e52i	1.52945	−	0.437390i
$874$	1.83504e53			2.07224
$875$		−	2.07973e52i		−	0.230071i
$876$	−5.44191e51	−	3.88210e52i	−0.0589762	−	0.420719i
$877$	5.08694e51			0.0540087			0.0270043	−	0.999635i	$-0.491403\pi$
$877$	5.08694e51			0.0540087			0.0270043	+	0.999635i	$0.491403\pi$
$878$			1.67511e53i			1.74238i
$879$	1.58379e52	−	2.22015e51i	0.161398	−	0.0226247i
$880$	7.56972e52			0.755773
$881$		−	1.16844e53i		−	1.14298i	−0.820609	−	0.571491i	$-0.806365\pi$
$881$		−	1.16844e53i		−	1.14298i	0.820609	−	0.571491i	$-0.193635\pi$
$882$	−3.11004e52	−	1.08751e53i	−0.298079	−	1.04231i
$883$	1.03919e53			0.975894			0.487947	−	0.872873i	$-0.337746\pi$
$883$	1.03919e53			0.975894			0.487947	+	0.872873i	$0.337746\pi$
$884$		−	3.57102e52i		−	0.328588i
$885$	−9.78928e51	−	6.98339e52i	−0.0882616	−	0.629633i
$886$	2.75075e52			0.243021
$887$			1.38907e53i			1.20254i	0.799047	+	0.601269i	$0.205338\pi$
$887$			1.38907e53i			1.20254i	−0.799047	+	0.601269i	$0.794662\pi$
$888$	−1.65778e53	+	2.32386e52i	−1.40635	+	0.197141i
$889$	−3.18555e52			−0.264821
$890$			2.48761e52i			0.202657i
$891$	−3.87646e52	−	6.22324e52i	−0.309483	−	0.496841i
$892$	−2.37025e52			−0.185450
$893$			2.50562e52i			0.192127i
$894$	5.56262e51	+	3.96821e52i	0.0418027	+	0.298208i
$895$	−2.22862e53			−1.64143
$896$			4.08987e52i			0.295234i
$897$	−1.44990e53	+	2.03246e52i	−1.02583	+	0.143800i
$898$	1.92364e53			1.33398
$899$			3.92675e51i			0.0266906i
$900$	−5.59299e51	+	1.59947e51i	−0.0372631	+	0.0106564i
$901$	−1.59823e52			−0.104374
$902$			2.03685e53i			1.30389i
$903$	3.23113e51	+	2.30499e52i	0.0202756	+	0.144640i
$904$	−1.06355e53			−0.654223
$905$		−	1.52932e53i		−	0.922195i
$906$	1.37743e53	−	1.93087e52i	0.814257	−	0.114142i
$907$	3.56269e52			0.206465			0.103233	−	0.994657i	$-0.467081\pi$
$907$	3.56269e52			0.206465			0.103233	+	0.994657i	$0.467081\pi$
$908$			5.53205e51i			0.0314297i
$909$	4.59565e52	+	1.60699e53i	0.255975	+	0.895084i
$910$	5.64174e52			0.308083
$911$		−	1.82908e52i		−	0.0979269i	−0.998801	−	0.0489634i	$-0.984408\pi$
$911$		−	1.82908e52i		−	0.0979269i	0.998801	−	0.0489634i	$-0.0155918\pi$
$912$	5.73961e52	+	4.09447e53i	0.301283	+	2.14927i
$913$	1.06846e53			0.549903
$914$			3.53708e52i			0.178490i
$915$	2.16851e53	−	3.03981e52i	1.07296	−	0.150406i
$916$	−6.86988e52			−0.333296
$917$		−	8.31010e52i		−	0.395328i
$918$	−9.68980e52	−	2.18261e53i	−0.452009	−	1.01814i
$919$	−1.80411e53			−0.825245			−0.412623	−	0.910902i	$-0.635387\pi$
$919$	−1.80411e53			−0.825245			−0.412623	+	0.910902i	$0.635387\pi$
$920$		−	1.83535e53i		−	0.823260i
$921$	−2.25858e52	−	1.61120e53i	−0.0993485	−	0.708723i
$922$	3.86438e53			1.66695
$923$			2.06226e53i			0.872393i
$924$	1.14414e52	−	1.60384e51i	0.0474659	−	0.00665375i
$925$	−5.28292e52			−0.214943
$926$		−	4.48373e53i		−	1.78913i
$927$	−1.08352e53	+	3.09865e52i	−0.424037	+	0.121265i
$928$	−1.68430e53			−0.646480
$929$		−	1.51091e52i		−	0.0568793i	−0.999596	−	0.0284397i	$-0.990946\pi$
$929$		−	1.51091e52i		−	0.0568793i	0.999596	−	0.0284397i	$-0.00905385\pi$
$930$	1.21074e51	+	8.63708e51i	0.00447052	+	0.0318914i
$931$	−4.60653e53			−1.66832
$932$		−	9.17527e52i		−	0.325936i
$933$	4.77740e53	−	6.69693e52i	1.66465	−	0.233349i
$934$	−5.69400e53			−1.94614
$935$			1.78060e53i			0.596978i
$936$	−6.60387e52	−	2.30922e53i	−0.217187	−	0.759450i
$937$	−7.78835e52			−0.251265			−0.125633	−	0.992077i	$-0.540096\pi$
$937$	−7.78835e52			−0.251265			−0.125633	+	0.992077i	$0.540096\pi$
$938$		−	3.66682e52i		−	0.116048i
$939$	3.61993e52	+	2.58235e53i	0.112388	+	0.801742i
$940$	−1.24673e52			−0.0379727
$941$		−	2.83161e53i		−	0.846098i	−0.906107	−	0.423049i	$-0.860960\pi$
$941$		−	2.83161e53i		−	0.846098i	0.906107	−	0.423049i	$-0.139040\pi$
$942$	2.27379e52	−	3.18738e51i	0.0666551	−	0.00934368i
$943$	6.78273e53			1.95072
$944$		−	2.60535e53i		−	0.735139i
$945$	8.59889e52	−	3.81752e52i	0.238051	−	0.105684i
$946$	1.47395e53			0.400353
$947$			5.30934e53i			1.41495i	0.706739	+	0.707475i	$0.250166\pi$
$947$			5.30934e53i			1.41495i	−0.706739	+	0.707475i	$0.749834\pi$
$948$	2.06681e52	+	1.47440e53i	0.0540444	+	0.385537i
$949$	5.10782e53			1.31052
$950$			9.50034e52i			0.239174i
$951$	−8.43451e52	+	1.18235e52i	−0.208358	+	0.0292075i
$952$	−7.56391e52			−0.183350
$953$			6.91066e53i			1.64379i	0.569636	+	0.821897i	$0.307084\pi$
$953$			6.91066e53i			1.64379i	−0.569636	+	0.821897i	$0.692916\pi$
$954$	5.14159e52	−	1.47038e52i	0.120013	−	0.0343210i
$955$	−1.99568e53			−0.457121
$956$		−	9.02300e52i		−	0.202819i
$957$	−3.72387e52	−	2.65650e53i	−0.0821447	−	0.585996i
$958$	−6.73320e53			−1.45761
$959$			6.44520e52i			0.136931i
$960$	2.42776e53	−	3.40323e52i	0.506202	−	0.0709592i
$961$	−4.88335e53			−0.999303
$962$			1.08513e54i			2.17936i
$963$	−7.09108e52	−	2.47958e53i	−0.139778	−	0.488771i
$964$	5.53202e52			0.107028
$965$			3.53762e52i			0.0671768i
$966$	−2.14171e52	−	1.52784e53i	−0.0399184	−	0.284766i
$967$	−2.45855e51			−0.00449782			−0.00224891	−	0.999997i	$-0.500716\pi$
$967$	−2.45855e51			−0.00449782			−0.00224891	+	0.999997i	$0.500716\pi$
$968$		−	2.82156e53i		−	0.506678i
$969$	−9.63132e53	+	1.35011e53i	−1.69769	+	0.237981i
$970$	1.12136e54			1.94023
$971$		−	4.34630e53i		−	0.738199i	−0.929390	−	0.369099i	$-0.879666\pi$
$971$		−	4.34630e53i		−	0.738199i	0.929390	−	0.369099i	$-0.120334\pi$
$972$	1.27809e53	+	1.52866e53i	0.213093	+	0.254870i
$973$	−1.88434e53			−0.308410
$974$		−	5.64062e53i		−	0.906287i
$975$	−1.05224e52	−	7.50640e52i	−0.0165971	−	0.118399i
$976$	8.09023e53			1.25275
$977$		−	2.41315e52i		−	0.0366845i	−0.999832	−	0.0183422i	$-0.994161\pi$
$977$		−	2.41315e52i		−	0.0366845i	0.999832	−	0.0183422i	$-0.00583884\pi$
$978$	−1.40998e53	+	1.97651e52i	−0.210433	+	0.0294984i
$979$	−6.63766e52			−0.0972583
$980$		−	2.29209e53i		−	0.329733i
$981$	−5.81530e53	+	1.66305e53i	−0.821353	+	0.234889i
$982$	−6.03554e53			−0.836969
$983$		−	4.38130e53i		−	0.596540i	−0.954482	−	0.298270i	$-0.903590\pi$
$983$		−	4.38130e53i		−	0.596540i	0.954482	−	0.298270i	$-0.0964096\pi$
$984$	1.54467e53	+	1.10192e54i	0.206502	+	1.47312i
$985$	5.47639e53			0.718857
$986$		−	8.73702e53i		−	1.12610i
$987$	2.08616e52	−	2.92436e51i	0.0264021	−	0.00370103i
$988$	4.86622e53			0.604737
$989$		−	4.90827e53i		−	0.598956i
$990$	−1.63817e53	−	5.72829e53i	−0.196302	−	0.686422i
$991$	1.03423e54			1.21700			0.608499	−	0.793555i	$-0.291772\pi$
$991$	1.03423e54			1.21700			0.608499	+	0.793555i	$0.291772\pi$
$992$			1.46120e52i			0.0168849i
$993$	−1.38123e53	−	9.85331e53i	−0.156740	−	1.11814i
$994$	−2.17311e53			−0.242173
$995$		−	8.02677e53i		−	0.878467i
$996$	−2.87565e53	+	4.03107e52i	−0.309078	+	0.0433264i
$997$	1.08596e53			0.114631			0.0573153	−	0.998356i	$-0.481746\pi$
$997$	1.08596e53			0.114631			0.0573153	+	0.998356i	$0.481746\pi$
$998$			1.15648e54i			1.19892i
$999$	7.34258e53	+	1.65390e54i	0.747601	+	1.68396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.37.b.b.2.3	✓	10
3.2	odd	2	inner	3.37.b.b.2.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.37.b.b.2.3	✓	10	1.1	even	1	trivial
3.37.b.b.2.8	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)

\(f(q)\)	\(=\)	\(q-302571. i q^{2} +(-5.37826e7 - 3.83669e8i) q^{3} -2.28297e10 q^{4} -4.03107e12i q^{5} +(-1.16087e14 + 1.62730e13i) q^{6} +4.01364e14 q^{7} -1.38849e16i q^{8} +(-1.44310e17 + 4.12694e16i) q^{9} +O(q^{10})\)	\(q-302571. i q^{2} +(-5.37826e7 - 3.83669e8i) q^{3} -2.28297e10 q^{4} -4.03107e12i q^{5} +(-1.16087e14 + 1.62730e13i) q^{6} +4.01364e14 q^{7} -1.38849e16i q^{8} +(-1.44310e17 + 4.12694e16i) q^{9} -1.21969e18 q^{10} -3.25448e18i q^{11} +(1.22784e18 + 8.75906e18i) q^{12} -1.15246e20 q^{13} -1.21441e20i q^{14} +(-1.54660e21 + 2.16802e20i) q^{15} -5.77002e21 q^{16} -1.35727e22i q^{17} +(1.24869e22 + 4.36639e22i) q^{18} +1.84954e23 q^{19} +9.20283e22i q^{20} +(-2.15864e22 - 1.53991e23i) q^{21} -9.84711e23 q^{22} +3.27910e24i q^{23} +(-5.32721e24 + 7.46766e23i) q^{24} -1.69765e24 q^{25} +3.48702e25i q^{26} +(2.35951e25 + 5.31475e25i) q^{27} -9.16303e24 q^{28} +2.12751e26i q^{29} +(6.55979e25 + 4.67956e26i) q^{30} +1.84570e25 q^{31} +7.91676e26i q^{32} +(-1.24864e27 + 1.75034e26i) q^{33} -4.10669e27 q^{34} -1.61793e27i q^{35} +(3.29455e27 - 9.42170e26i) q^{36} +3.11190e28 q^{37} -5.59617e28i q^{38} +(6.19824e27 + 4.42164e28i) q^{39} -5.59711e28 q^{40} -2.06848e29i q^{41} +(-4.65932e28 + 6.53141e27i) q^{42} -1.49684e29 q^{43} +7.42989e28i q^{44} +(1.66360e29 + 5.81722e29i) q^{45} +9.92159e29 q^{46} +1.35473e29i q^{47} +(3.10326e29 + 2.21378e30i) q^{48} -2.49064e30 q^{49} +5.13659e29i q^{50} +(-5.20741e30 + 7.29973e29i) q^{51} +2.63104e30 q^{52} -1.17754e30i q^{53} +(1.60809e31 - 7.13921e30i) q^{54} -1.31191e31 q^{55} -5.57290e30i q^{56} +(-9.94730e30 - 7.09612e31i) q^{57} +6.43722e31 q^{58} +4.51532e31i q^{59} +(3.53084e31 - 4.94952e30i) q^{60} -1.40212e32 q^{61} -5.58456e30i q^{62} +(-5.79206e31 + 1.65641e31i) q^{63} -1.56974e32 q^{64} +4.64566e32i q^{65} +(5.29603e31 + 3.77803e32i) q^{66} +3.01943e32 q^{67} +3.09860e32i q^{68} +(1.25809e33 - 1.76358e32i) q^{69} -4.89538e32 q^{70} -1.78943e33i q^{71} +(5.73022e32 + 2.00372e33i) q^{72} -4.43209e33 q^{73} -9.41572e33i q^{74} +(9.13039e31 + 6.51336e32i) q^{75} -4.22245e33 q^{76} -1.30623e33i q^{77} +(1.33786e34 - 1.87541e33i) q^{78} +1.68329e34 q^{79} +2.32594e34i q^{80} +(1.91221e34 - 1.19111e34i) q^{81} -6.25861e34 q^{82} +3.28306e34i q^{83} +(4.92811e32 + 3.51557e33i) q^{84} -5.47124e34 q^{85} +4.52899e34i q^{86} +(8.16259e34 - 1.14423e34i) q^{87} -4.51882e34 q^{88} -2.03955e34i q^{89} +(1.76012e35 - 5.03358e34i) q^{90} -4.62557e34 q^{91} -7.48609e34i q^{92} +(-9.92666e32 - 7.08139e33i) q^{93} +4.09901e34 q^{94} -7.45563e35i q^{95} +(3.03742e35 - 4.25784e34i) q^{96} -9.19383e35 q^{97} +7.53595e35i q^{98} +(1.34311e35 + 4.69652e35i) 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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