LMFDB - Embedded newform 3.37.b.b.2.9

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			2.9
Root			$23576.4i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.37.b.b.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+424376. i q^{2} +(3.83451e8 + 5.53148e7i) q^{3} -1.11375e11 q^{4} -3.68903e12i q^{5} +(-2.34743e13 + 1.62727e14i) q^{6} -2.28183e15 q^{7} -1.81020e16i q^{8} +(1.43975e17 + 4.24211e16i) q^{9} +O(q^{10})$	\(q+424376. i q^{2} +(3.83451e8 + 5.53148e7i) q^{3} -1.11375e11 q^{4} -3.68903e12i q^{5} +(-2.34743e13 + 1.62727e14i) q^{6} -2.28183e15 q^{7} -1.81020e16i q^{8} +(1.43975e17 + 4.24211e16i) q^{9} +1.56554e18 q^{10} -7.84145e18i q^{11} +(-4.27069e19 - 6.16070e18i) q^{12} -7.34153e17 q^{13} -9.68352e20i q^{14} +(2.04058e20 - 1.41456e21i) q^{15} +2.84165e19 q^{16} -1.60326e22i q^{17} +(-1.80025e22 + 6.10996e22i) q^{18} +1.08973e23 q^{19} +4.10867e23i q^{20} +(-8.74970e23 - 1.26219e23i) q^{21} +3.32772e24 q^{22} -3.35294e24i q^{23} +(1.00131e24 - 6.94125e24i) q^{24} +9.42948e23 q^{25} -3.11557e23i q^{26} +(5.28610e25 + 2.42304e25i) q^{27} +2.54139e26 q^{28} +1.36652e26i q^{29} +(6.00307e26 + 8.65973e25i) q^{30} -6.89506e26 q^{31} -1.23190e27i q^{32} +(4.33748e26 - 3.00681e27i) q^{33} +6.80384e27 q^{34} +8.41774e27i q^{35} +(-1.60353e28 - 4.72465e27i) q^{36} -1.67663e28 q^{37} +4.62457e28i q^{38} +(-2.81512e26 - 4.06096e25i) q^{39} -6.67790e28 q^{40} -4.32262e28i q^{41} +(5.35642e28 - 3.71316e29i) q^{42} -2.98235e29 q^{43} +8.73342e29i q^{44} +(1.56493e29 - 5.31129e29i) q^{45} +1.42290e30 q^{46} +9.90135e29i q^{47} +(1.08963e28 + 1.57185e27i) q^{48} +2.55501e30 q^{49} +4.00164e29i q^{50} +(8.86840e29 - 6.14772e30i) q^{51} +8.17664e28 q^{52} -1.84427e31i q^{53} +(-1.02828e31 + 2.24329e31i) q^{54} -2.89274e31 q^{55} +4.13057e31i q^{56} +(4.17860e31 + 6.02784e30i) q^{57} -5.79919e31 q^{58} -9.96164e31i q^{59} +(-2.27270e31 + 1.57547e32i) q^{60} +2.76303e31 q^{61} -2.92609e32i q^{62} +(-3.28527e32 - 9.67976e31i) q^{63} +5.24742e32 q^{64} +2.70832e30i q^{65} +(1.27602e33 + 1.84072e32i) q^{66} +2.39988e31 q^{67} +1.78563e33i q^{68} +(1.85467e32 - 1.28569e33i) q^{69} -3.57228e33 q^{70} +1.79070e33i q^{71} +(7.67907e32 - 2.60624e33i) q^{72} +1.25926e33 q^{73} -7.11519e33i q^{74} +(3.61575e32 + 5.21590e31i) q^{75} -1.21369e34 q^{76} +1.78928e34i q^{77} +(1.72337e31 - 1.19467e32i) q^{78} -4.10710e33 q^{79} -1.04829e32i q^{80} +(1.89293e34 + 1.22152e34i) q^{81} +1.83442e34 q^{82} -4.33479e34i q^{83} +(9.74499e34 + 1.40576e34i) q^{84} -5.91448e34 q^{85} -1.26564e35i q^{86} +(-7.55890e33 + 5.23995e34i) q^{87} -1.41946e35 q^{88} +5.33521e34i q^{89} +(2.25398e35 + 6.64117e34i) q^{90} +1.67521e33 q^{91} +3.73434e35i q^{92} +(-2.64392e35 - 3.81399e34i) q^{93} -4.20189e35 q^{94} -4.02007e35i q^{95} +(6.81425e34 - 4.72375e35i) q^{96} -1.24213e35 q^{97} +1.08428e36i q^{98} +(3.32643e35 - 1.12897e36i) 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 $

$2$			424376.i			1.61886i	0.587213	+	0.809432i	$0.300225\pi$
$2$			424376.i			1.61886i	−0.587213	+	0.809432i	$0.699775\pi$
$3$	3.83451e8	+	5.53148e7i	0.989755	+	0.142777i
$3$	3.83451e8	+	5.53148e7i	0.989755	+	0.142777i
$4$	−1.11375e11			−1.62072
$5$		−	3.68903e12i		−	0.967058i	−0.875328	−	0.483529i	$-0.839355\pi$
$5$		−	3.68903e12i		−	0.967058i	0.875328	−	0.483529i	$-0.160645\pi$
$6$	−2.34743e13	+	1.62727e14i	−0.231137	+	1.60228i
$7$	−2.28183e15			−1.40126			−0.700629	−	0.713526i	$-0.747097\pi$
$7$	−2.28183e15			−1.40126			−0.700629	+	0.713526i	$0.747097\pi$
$8$		−	1.81020e16i		−	1.00486i
$9$	1.43975e17	+	4.24211e16i	0.959229	+	0.282629i
$10$	1.56554e18			1.56554
$11$		−	7.84145e18i		−	1.41035i	−0.709032	−	0.705176i	$-0.750868\pi$
$11$		−	7.84145e18i		−	1.41035i	0.709032	−	0.705176i	$-0.249132\pi$
$12$	−4.27069e19	−	6.16070e18i	−1.60412	−	0.231402i
$13$	−7.34153e17			−0.00652840			−0.00326420	−	0.999995i	$-0.501039\pi$
$13$	−7.34153e17			−0.00652840			−0.00326420	+	0.999995i	$0.501039\pi$
$14$		−	9.68352e20i		−	2.26845i
$15$	2.04058e20	−	1.41456e21i	0.138074	−	0.957150i
$16$	2.84165e19			0.00601742
$17$		−	1.60326e22i		−	1.14005i	−0.821628	−	0.570024i	$-0.806934\pi$
$17$		−	1.60326e22i		−	1.14005i	0.821628	−	0.570024i	$-0.193066\pi$
$18$	−1.80025e22	+	6.10996e22i	−0.457538	+	1.55286i
$19$	1.08973e23			1.04654			0.523270	−	0.852167i	$-0.324712\pi$
$19$	1.08973e23			1.04654			0.523270	+	0.852167i	$0.324712\pi$
$20$			4.10867e23i			1.56733i
$21$	−8.74970e23	−	1.26219e23i	−1.38690	−	0.200068i
$22$	3.32772e24			2.28317
$23$		−	3.35294e24i		−	1.03353i	−0.856126	−	0.516767i	$-0.827136\pi$
$23$		−	3.35294e24i		−	1.03353i	0.856126	−	0.516767i	$-0.172864\pi$
$24$	1.00131e24	−	6.94125e24i	0.143472	−	0.994569i
$25$	9.42948e23			0.0647989
$26$		−	3.11557e23i		−	0.0105686i
$27$	5.28610e25	+	2.42304e25i	0.909049	+	0.416689i
$28$	2.54139e26			2.27105
$29$			1.36652e26i			0.649312i	0.945832	+	0.324656i	$0.105248\pi$
$29$			1.36652e26i			0.649312i	−0.945832	+	0.324656i	$0.894752\pi$
$30$	6.00307e26	+	8.65973e25i	1.54950	+	0.223523i
$31$	−6.89506e26			−0.986341			−0.493171	−	0.869933i	$-0.664162\pi$
$31$	−6.89506e26			−0.986341			−0.493171	+	0.869933i	$0.664162\pi$
$32$		−	1.23190e27i		−	0.995123i
$33$	4.33748e26	−	3.00681e27i	0.201366	−	1.39590i
$34$	6.80384e27			1.84558
$35$			8.41774e27i			1.35510i
$36$	−1.60353e28	−	4.72465e27i	−1.55464	−	0.458063i
$37$	−1.67663e28			−0.992670			−0.496335	−	0.868131i	$-0.665321\pi$
$37$	−1.67663e28			−0.992670			−0.496335	+	0.868131i	$0.665321\pi$
$38$			4.62457e28i			1.69421i
$39$	−2.81512e26	−	4.06096e25i	−0.00646151	−	0.000932106i
$40$	−6.67790e28			−0.971762
$41$		−	4.32262e28i		−	0.403309i	−0.979457	−	0.201655i	$-0.935368\pi$
$41$		−	4.32262e28i		−	0.403309i	0.979457	−	0.201655i	$-0.0646318\pi$
$42$	5.35642e28	−	3.71316e29i	0.323882	−	2.24521i
$43$	−2.98235e29			−1.18067			−0.590333	−	0.807160i	$-0.701004\pi$
$43$	−2.98235e29			−1.18067			−0.590333	+	0.807160i	$0.701004\pi$
$44$			8.73342e29i			2.28579i
$45$	1.56493e29	−	5.31129e29i	0.273318	−	0.927630i
$46$	1.42290e30			1.67315
$47$			9.90135e29i			0.790556i	0.918561	+	0.395278i	$0.129352\pi$
$47$			9.90135e29i			0.790556i	−0.918561	+	0.395278i	$0.870648\pi$
$48$	1.08963e28	+	1.57185e27i	0.00595577	+	0.000859150i
$49$	2.55501e30			0.963525
$50$			4.00164e29i			0.104901i
$51$	8.86840e29	−	6.14772e30i	0.162773	−	1.12837i
$52$	8.17664e28			0.0105807
$53$		−	1.84427e31i		−	1.69378i	−0.531765	−	0.846892i	$-0.678471\pi$
$53$		−	1.84427e31i		−	1.69378i	0.531765	−	0.846892i	$-0.321529\pi$
$54$	−1.02828e31	+	2.24329e31i	−0.674564	+	1.47163i
$55$	−2.89274e31			−1.36389
$56$			4.13057e31i			1.40807i
$57$	4.17860e31	+	6.02784e30i	1.03582	+	0.149422i
$58$	−5.79919e31			−1.05115
$59$		−	9.96164e31i		−	1.32738i	−0.748008	−	0.663689i	$-0.768990\pi$
$59$		−	9.96164e31i		−	1.32738i	0.748008	−	0.663689i	$-0.231010\pi$
$60$	−2.27270e31	+	1.57547e32i	−0.223779	+	1.55127i
$61$	2.76303e31			0.202045			0.101023	−	0.994884i	$-0.467789\pi$
$61$	2.76303e31			0.202045			0.101023	+	0.994884i	$0.467789\pi$
$62$		−	2.92609e32i		−	1.59675i
$63$	−3.28527e32	−	9.67976e31i	−1.34413	−	0.396036i
$64$	5.24742e32			1.61699
$65$			2.70832e30i			0.00631334i
$66$	1.27602e33	+	1.84072e32i	2.25978	+	0.325985i
$67$	2.39988e31			0.0324222			0.0162111	−	0.999869i	$-0.494840\pi$
$67$	2.39988e31			0.0324222			0.0162111	+	0.999869i	$0.494840\pi$
$68$			1.78563e33i			1.84770i
$69$	1.85467e32	−	1.28569e33i	0.147565	−	1.02294i
$70$	−3.57228e33			−2.19372
$71$			1.79070e33i			0.851869i	0.904754	+	0.425935i	$0.140055\pi$
$71$			1.79070e33i			0.851869i	−0.904754	+	0.425935i	$0.859945\pi$
$72$	7.67907e32	−	2.60624e33i	0.284004	−	0.963895i
$73$	1.25926e33			0.363333			0.181666	−	0.983360i	$-0.441851\pi$
$73$	1.25926e33			0.363333			0.181666	+	0.983360i	$0.441851\pi$
$74$		−	7.11519e33i		−	1.60700i
$75$	3.61575e32	+	5.21590e31i	0.0641350	+	0.00925180i
$76$	−1.21369e34			−1.69615
$77$			1.78928e34i			1.97627i
$78$	1.72337e31	−	1.19467e32i	0.00150895	−	0.0104603i
$79$	−4.10710e33			−0.285922			−0.142961	−	0.989728i	$-0.545662\pi$
$79$	−4.10710e33			−0.285922			−0.142961	+	0.989728i	$0.545662\pi$
$80$		−	1.04829e32i		−	0.00581919i
$81$	1.89293e34	+	1.22152e34i	0.840242	+	0.542212i
$82$	1.83442e34			0.652903
$83$		−	4.33479e34i		−	1.24040i	−0.784443	−	0.620201i	$-0.787051\pi$
$83$		−	4.33479e34i		−	1.24040i	0.784443	−	0.620201i	$-0.212949\pi$
$84$	9.74499e34	+	1.40576e34i	2.24778	+	0.324254i
$85$	−5.91448e34			−1.10249
$86$		−	1.26564e35i		−	1.91134i
$87$	−7.55890e33	+	5.23995e34i	−0.0927069	+	0.642659i
$88$	−1.41946e35			−1.41721
$89$			5.33521e34i			0.434642i	0.976100	+	0.217321i	$0.0697318\pi$
$89$			5.33521e34i			0.434642i	−0.976100	+	0.217321i	$0.930268\pi$
$90$	2.25398e35	+	6.64117e34i	1.50171	+	0.442466i
$91$	1.67521e33			0.00914797
$92$			3.73434e35i			1.67507i
$93$	−2.64392e35	−	3.81399e34i	−0.976236	−	0.140827i
$94$	−4.20189e35			−1.27980
$95$		−	4.02007e35i		−	1.01206i
$96$	6.81425e34	−	4.72375e35i	0.142081	−	0.984928i
$97$	−1.24213e35			−0.214919			−0.107460	−	0.994209i	$-0.534272\pi$
$97$	−1.24213e35			−0.214919			−0.107460	+	0.994209i	$0.534272\pi$
$98$			1.08428e36i			1.55982i
$99$	3.32643e35	−	1.12897e36i	0.398606	−	1.35285i
$100$	−1.05021e35			−0.105021
$101$		−	4.71676e35i		−	0.394330i	−0.980370	−	0.197165i	$-0.936827\pi$
$101$		−	4.71676e35i		−	0.394330i	0.980370	−	0.197165i	$-0.0631734\pi$
$102$	2.60894e36	+	3.76353e35i	1.82668	+	0.263507i
$103$	−1.54044e36			−0.904847			−0.452424	−	0.891803i	$-0.649440\pi$
$103$	−1.54044e36			−0.904847			−0.452424	+	0.891803i	$0.649440\pi$
$104$			1.32897e34i			0.00656015i
$105$	−4.65626e35	+	3.22779e36i	−0.193477	+	1.34121i
$106$	7.82661e36			2.74201
$107$			3.09814e36i			0.916627i	0.888791	+	0.458314i	$0.151546\pi$
$107$			3.09814e36i			0.916627i	−0.888791	+	0.458314i	$0.848454\pi$
$108$	−5.88740e36	−	2.69866e36i	−1.47332	−	0.675338i
$109$	−1.74804e36			−0.370573			−0.185287	−	0.982685i	$-0.559321\pi$
$109$	−1.74804e36			−0.370573			−0.185287	+	0.982685i	$0.559321\pi$
$110$		−	1.22761e37i		−	2.20796i
$111$	−6.42904e36	−	9.27422e35i	−0.982500	−	0.141731i
$112$	−6.48415e34			−0.00843196
$113$			2.20649e36i			0.244506i	0.992499	+	0.122253i	$0.0390120\pi$
$113$			2.20649e36i			0.244506i	−0.992499	+	0.122253i	$0.960988\pi$
$114$	−2.55807e36	+	1.77330e37i	−0.241894	+	1.67685i
$115$	−1.23691e37			−0.999486
$116$		−	1.52197e37i		−	1.05235i
$117$	−1.05700e35	−	3.11436e34i	−0.00626223	−	0.00184511i
$118$	4.22748e37			2.14885
$119$			3.65836e37i			1.59750i
$120$	−2.56065e37	−	3.69387e36i	−0.961806	−	0.138745i
$121$	−3.05756e37			−0.989095
$122$			1.17256e37i			0.327084i
$123$	2.39105e36	−	1.65752e37i	0.0575833	−	0.399177i
$124$	7.67938e37			1.59859
$125$		−	5.71611e37i		−	1.02972i
$126$	4.10785e37	−	1.39419e38i	0.641129	−	2.17596i
$127$	9.04828e37			1.22489			0.612447	−	0.790511i	$-0.290185\pi$
$127$	9.04828e37			1.22489			0.612447	+	0.790511i	$0.290185\pi$
$128$			1.38032e38i			1.62256i
$129$	−1.14359e38	−	1.64968e37i	−1.16857	−	0.168572i
$130$	−1.14934e36			−0.0102204
$131$		−	1.02918e37i		−	0.0797274i	−0.999205	−	0.0398637i	$-0.987308\pi$
$131$		−	1.02918e37i		−	0.0797274i	0.999205	−	0.0398637i	$-0.0126924\pi$
$132$	−4.83088e37	+	3.34884e38i	−0.326359	+	2.26237i
$133$	−2.48659e38			−1.46647
$134$			1.01845e37i			0.0524872i
$135$	8.93867e37	−	1.95006e38i	0.402963	−	0.879103i
$136$	−2.90222e38			−1.14559
$137$		−	3.34355e36i		−	0.0115674i	−0.999983	−	0.00578372i	$-0.998159\pi$
$137$		−	3.34355e36i		−	0.0115674i	0.999983	−	0.00578372i	$-0.00184103\pi$
$138$	5.45615e38	+	7.87077e37i	1.65601	+	0.238888i
$139$	−3.57808e37			−0.0953639			−0.0476820	−	0.998863i	$-0.515183\pi$
$139$	−3.57808e37			−0.0953639			−0.0476820	+	0.998863i	$0.515183\pi$
$140$		−	9.37527e38i		−	2.19624i
$141$	−5.47691e37	+	3.79668e38i	−0.112873	+	0.782457i
$142$	−7.59930e38			−1.37906
$143$			5.75682e36i			0.00920734i
$144$	4.09126e36	+	1.20546e36i	0.00577208	+	0.00170070i
$145$	5.04115e38			0.627922
$146$			5.34400e38i			0.588187i
$147$	9.79721e38	+	1.41330e38i	0.953653	+	0.137569i
$148$	1.86734e39			1.60884
$149$			1.50133e39i			1.14584i	0.819612	+	0.572919i	$0.194189\pi$
$149$			1.50133e39i			1.14584i	−0.819612	+	0.572919i	$0.805811\pi$
$150$	−2.21350e37	+	1.53443e38i	−0.0149774	+	0.103826i
$151$	6.27675e38			0.376834			0.188417	−	0.982089i	$-0.439664\pi$
$151$	6.27675e38			0.376834			0.188417	+	0.982089i	$0.439664\pi$
$152$		−	1.97264e39i		−	1.05163i
$153$	6.80120e38	−	2.30830e39i	0.322211	−	1.09357i
$154$	−7.59328e39			−3.19931
$155$			2.54361e39i			0.953849i
$156$	3.13535e37	+	4.52290e36i	0.0104723	+	0.00151068i
$157$	1.36826e39			0.407358			0.203679	−	0.979038i	$-0.434710\pi$
$157$	1.36826e39			0.407358			0.203679	+	0.979038i	$0.434710\pi$
$158$		−	1.74295e39i		−	0.462869i
$159$	1.02015e39	−	7.07186e39i	0.241834	−	1.67643i
$160$	−4.54453e39			−0.962342
$161$			7.65083e39i			1.44825i
$162$	−5.18382e39	+	8.03313e39i	−0.877767	+	1.36024i
$163$	1.03735e40			1.57235			0.786175	−	0.618004i	$-0.212058\pi$
$163$	1.03735e40			1.57235			0.786175	+	0.618004i	$0.212058\pi$
$164$			4.81433e39i			0.653652i
$165$	−1.10922e40	−	1.60011e39i	−1.34992	−	0.194733i
$166$	1.83958e40			2.00804
$167$		−	1.58942e40i		−	1.55719i	−0.627527	−	0.778595i	$-0.715933\pi$
$167$		−	1.58942e40i		−	1.55719i	0.627527	−	0.778595i	$-0.284067\pi$
$168$	−2.28482e39	+	1.58387e40i	−0.201041	+	1.39365i
$169$	−1.26457e40			−0.999957
$170$		−	2.50996e40i		−	1.78479i
$171$	1.56895e40	+	4.62277e39i	1.00387	+	0.295782i
$172$	3.32160e40			1.91353
$173$		−	2.10599e39i		−	0.109301i	−0.998506	−	0.0546507i	$-0.982595\pi$
$173$		−	2.10599e39i		−	0.109301i	0.998506	−	0.0546507i	$-0.0174045\pi$
$174$	−2.22371e40	−	3.20781e39i	−1.04038	−	0.150080i
$175$	−2.15164e39			−0.0908000
$176$		−	2.22826e38i		−	0.00848668i
$177$	5.51026e39	−	3.81980e40i	0.189519	−	1.31378i
$178$	−2.26413e40			−0.703626
$179$			5.73503e40i			1.61132i	0.592380	+	0.805659i	$0.298188\pi$
$179$			5.73503e40i			1.61132i	−0.592380	+	0.805659i	$0.701812\pi$
$180$	−1.74294e40	+	5.91546e40i	−0.442973	+	1.50343i
$181$	1.65060e40			0.379688			0.189844	−	0.981814i	$-0.439202\pi$
$181$	1.65060e40			0.379688			0.189844	+	0.981814i	$0.439202\pi$
$182$			7.10919e38i			0.0148093i
$183$	1.05949e40	+	1.52836e39i	0.199975	+	0.0288474i
$184$	−6.06950e40			−1.03856
$185$			6.18513e40i			0.959969i
$186$	1.61856e40	−	1.12201e41i	0.227980	−	1.58039i
$187$	−1.25719e41			−1.60787
$188$		−	1.10276e41i		−	1.28127i
$189$	−1.20620e41	−	5.52895e40i	−1.27381	−	0.583889i
$190$	1.70602e41			1.63840
$191$			8.35822e40i			0.730320i	0.930945	+	0.365160i	$0.118986\pi$
$191$			8.35822e40i			0.730320i	−0.930945	+	0.365160i	$0.881014\pi$
$192$	2.01213e41	+	2.90260e40i	1.60042	+	0.230869i
$193$	2.00501e41			1.45240			0.726199	−	0.687484i	$-0.241285\pi$
$193$	2.00501e41			1.45240			0.726199	+	0.687484i	$0.241285\pi$
$194$		−	5.27130e40i		−	0.347925i
$195$	−1.49810e38	+	1.03851e39i	−0.000901401	+	0.00624866i
$196$	−2.84564e41			−1.56161
$197$			1.55876e41i			0.780524i	0.920704	+	0.390262i	$0.127616\pi$
$197$			1.55876e41i			0.780524i	−0.920704	+	0.390262i	$0.872384\pi$
$198$	4.79109e41	+	1.41165e41i	2.19008	+	0.645290i
$199$	−4.16157e41			−1.73741			−0.868704	−	0.495331i	$-0.835047\pi$
$199$	−4.16157e41			−1.73741			−0.868704	+	0.495331i	$0.835047\pi$
$200$		−	1.70693e40i		−	0.0651141i
$201$	9.20237e39	+	1.32749e39i	0.0320901	+	0.00462916i
$202$	2.00168e41			0.638366
$203$		−	3.11817e41i		−	0.909853i
$204$	−9.87719e40	+	6.84703e41i	−0.263810	+	1.82877i
$205$	−1.59463e41			−0.390023
$206$		−	6.53726e41i		−	1.46482i
$207$	1.42235e41	−	4.82740e41i	0.292106	−	0.991395i
$208$	−2.08620e37			−3.92841e−5
$209$		−	8.54509e41i		−	1.47599i
$210$	−1.36980e42	−	1.97600e41i	−2.17124	−	0.313213i
$211$	3.08375e41			0.448740			0.224370	−	0.974504i	$-0.427968\pi$
$211$	3.08375e41			0.448740			0.224370	+	0.974504i	$0.427968\pi$
$212$			2.05405e42i			2.74515i
$213$	−9.90523e40	+	6.86647e41i	−0.121627	+	0.843142i
$214$	−1.31477e42			−1.48390
$215$			1.10020e42i			1.14177i
$216$	4.38619e41	−	9.56891e41i	0.418716	−	0.913471i
$217$	1.57333e42			1.38212
$218$		−	7.41825e41i		−	0.599908i
$219$	4.82866e41	+	6.96559e40i	0.359611	+	0.0518757i
$220$	3.22179e42			2.21049
$221$			1.17704e40i			0.00744269i
$222$	3.93575e41	−	2.72833e42i	0.229443	−	1.59053i
$223$	−1.52920e42			−0.822196			−0.411098	−	0.911591i	$-0.634855\pi$
$223$	−1.52920e42			−0.822196			−0.411098	+	0.911591i	$0.634855\pi$
$224$			2.81099e42i			1.39442i
$225$	1.35761e41	+	4.00009e40i	0.0621570	+	0.0183140i
$226$	−9.36380e41			−0.395822
$227$		−	3.16945e42i		−	1.23742i	−0.785619	−	0.618711i	$-0.787655\pi$
$227$		−	3.16945e42i		−	1.23742i	0.785619	−	0.618711i	$-0.212345\pi$
$228$	−4.65392e42	−	6.71352e41i	−1.67877	−	0.242172i
$229$	3.13587e42			1.04549			0.522745	−	0.852489i	$-0.324908\pi$
$229$	3.13587e42			1.04549			0.522745	+	0.852489i	$0.324908\pi$
$230$		−	5.24914e42i		−	1.61803i
$231$	−9.89738e41	+	6.86103e42i	−0.282166	+	1.95602i
$232$	2.47368e42			0.652470
$233$			1.98672e42i			0.484987i	0.970153	+	0.242494i	$0.0779654\pi$
$233$			1.98672e42i			0.484987i	−0.970153	+	0.242494i	$0.922035\pi$
$234$	1.32166e40	−	4.48564e40i	0.00298699	−	0.0101377i
$235$	3.65264e42			0.764514
$236$			1.10948e43i			2.15131i
$237$	−1.57487e42	−	2.27183e41i	−0.282993	−	0.0408231i
$238$	−1.55252e43			−2.58614
$239$		−	5.72357e42i		−	0.884106i	−0.896989	−	0.442053i	$-0.854250\pi$
$239$		−	5.72357e42i		−	0.884106i	0.896989	−	0.442053i	$-0.145750\pi$
$240$	5.79861e39	−	4.01969e40i	0.000830848	−	0.00575957i
$241$	−1.81774e42			−0.241672			−0.120836	−	0.992673i	$-0.538557\pi$
$241$	−1.81774e42			−0.241672			−0.120836	+	0.992673i	$0.538557\pi$
$242$		−	1.29755e43i		−	1.60121i
$243$	6.58279e42	+	5.73099e42i	0.754218	+	0.656624i
$244$	−3.07733e42			−0.327459
$245$		−	9.42551e42i		−	0.931784i
$246$	7.03409e42	+	1.01470e42i	0.646214	+	0.0932196i
$247$	−8.00032e40			−0.00683223
$248$			1.24814e43i			0.991139i
$249$	2.39778e42	−	1.66218e43i	0.177101	−	1.22769i
$250$	2.42578e43			1.66698
$251$		−	9.57719e42i		−	0.612507i	−0.951950	−	0.306253i	$-0.900924\pi$
$251$		−	9.57719e42i		−	0.612507i	0.951950	−	0.306253i	$-0.0990755\pi$
$252$	3.65897e43	+	1.07808e43i	2.17846	+	0.641864i
$253$	−2.62919e43			−1.45765
$254$			3.83987e43i			1.98294i
$255$	−2.26791e43	−	3.27158e42i	−1.09120	−	0.157411i
$256$	−2.25174e43			−1.00972
$257$			3.16415e43i			1.32270i	0.750077	+	0.661350i	$0.230016\pi$
$257$			3.16415e43i			1.32270i	−0.750077	+	0.661350i	$0.769984\pi$
$258$	7.00085e42	−	4.85311e43i	0.272895	−	1.89176i
$259$	3.82577e43			1.39099
$260$		−	3.01639e41i		−	0.0102322i
$261$	−5.79694e42	+	1.96745e43i	−0.183514	+	0.622839i
$262$	4.36759e42			0.129068
$263$		−	1.63619e43i		−	0.451472i	−0.974189	−	0.225736i	$-0.927521\pi$
$263$		−	1.63619e43i		−	0.451472i	0.974189	−	0.225736i	$-0.0724787\pi$
$264$	−5.44294e43	−	7.85172e42i	−1.40269	−	0.202346i
$265$	−6.80356e43			−1.63799
$266$		−	1.05525e44i		−	2.37402i
$267$	−2.95116e42	+	2.04579e43i	−0.0620570	+	0.430189i
$268$	−2.67287e42			−0.0525474
$269$			5.32556e43i			0.979094i	0.871977	+	0.489547i	$0.162838\pi$
$269$			5.32556e43i			0.979094i	−0.871977	+	0.489547i	$0.837162\pi$
$270$	8.27557e43	+	3.79335e43i	1.42315	+	0.652342i
$271$	−2.55880e43			−0.411708			−0.205854	−	0.978583i	$-0.565997\pi$
$271$	−2.55880e43			−0.411708			−0.205854	+	0.978583i	$0.565997\pi$
$272$		−	4.55590e41i		−	0.00686015i
$273$	6.42362e41	+	9.26640e40i	0.00905425	+	0.00130612i
$274$	1.41892e42			0.0187261
$275$		−	7.39407e42i		−	0.0913893i
$276$	−2.06564e43	+	1.43194e44i	−0.239162	+	1.65791i
$277$	1.43545e44			1.55723			0.778613	−	0.627504i	$-0.215924\pi$
$277$	1.43545e44			1.55723			0.778613	+	0.627504i	$0.215924\pi$
$278$		−	1.51845e43i		−	0.154381i
$279$	−9.92717e43	−	2.92496e43i	−0.946128	−	0.278769i
$280$	1.52378e44			1.36169
$281$			8.99700e41i			0.00754022i	0.999993	+	0.00377011i	$0.00120007\pi$
$281$			8.99700e41i			0.00754022i	−0.999993	+	0.00377011i	$0.998800\pi$
$282$	−1.61122e44	−	2.32427e43i	−1.26669	−	0.182727i
$283$	1.89987e44			1.40142			0.700709	−	0.713447i	$-0.252867\pi$
$283$	1.89987e44			1.40142			0.700709	+	0.713447i	$0.252867\pi$
$284$		−	1.99440e44i		−	1.38064i
$285$	2.22369e43	−	1.54150e44i	0.144500	−	1.00170i
$286$	−2.44306e42			−0.0149054
$287$			9.86348e43i			0.565140i
$288$	5.22586e43	−	1.77363e44i	0.281250	−	0.954551i
$289$	−5.92738e43			−0.299710
$290$			2.13934e44i			1.01652i
$291$	−4.76296e43	−	6.87082e42i	−0.212718	−	0.0306856i
$292$	−1.40251e44			−0.588862
$293$			7.55971e43i			0.298461i	0.988802	+	0.149231i	$0.0476797\pi$
$293$			7.55971e43i			0.298461i	−0.988802	+	0.149231i	$0.952320\pi$
$294$	−5.99769e43	+	4.15770e44i	−0.222706	+	1.54384i
$295$	−3.67488e44			−1.28365
$296$			3.03503e44i			0.997499i
$297$	1.90001e44	−	4.14506e44i	0.587679	−	1.28208i
$298$	−6.37128e44			−1.85496
$299$			2.46157e42i			0.00674731i
$300$	−4.02704e43	−	5.80922e42i	−0.103945	−	0.0149946i
$301$	6.80522e44			1.65442
$302$			2.66370e44i			0.610043i
$303$	2.60907e43	−	1.80865e44i	0.0563013	−	0.390290i
$304$	3.09664e42			0.00629747
$305$		−	1.01929e44i		−	0.195389i
$306$	9.79584e44	+	2.88626e44i	1.77034	+	0.521615i
$307$	3.14505e44			0.535965			0.267983	−	0.963424i	$-0.413643\pi$
$307$	3.14505e44			0.535965			0.267983	+	0.963424i	$0.413643\pi$
$308$		−	1.99282e45i		−	3.20298i
$309$	−5.90684e44	−	8.52092e43i	−0.895577	−	0.129192i
$310$	−1.07945e45			−1.54415
$311$			3.59597e44i			0.485432i	0.970097	+	0.242716i	$0.0780384\pi$
$311$			3.59597e44i			0.485432i	−0.970097	+	0.242716i	$0.921962\pi$
$312$	−7.35115e41	+	5.09594e42i	−0.000936640	+	0.00649294i
$313$	5.83770e44			0.702173			0.351086	−	0.936343i	$-0.385812\pi$
$313$	5.83770e44			0.702173			0.351086	+	0.936343i	$0.385812\pi$
$314$			5.80658e44i			0.659457i
$315$	−3.57090e44	+	1.21195e45i	−0.382990	+	1.29985i
$316$	4.57429e44			0.463400
$317$			1.00111e45i			0.958113i	0.877784	+	0.479057i	$0.159021\pi$
$317$			1.00111e45i			0.958113i	−0.877784	+	0.479057i	$0.840979\pi$
$318$	3.00113e45	+	4.32928e44i	2.71391	+	0.391496i
$319$	1.07155e45			0.915758
$320$		−	1.93579e45i		−	1.56372i
$321$	−1.71373e44	+	1.18799e45i	−0.130873	+	0.907236i
$322$	−3.24682e45			−2.34451
$323$		−	1.74713e45i		−	1.19311i
$324$	−2.10825e45	−	1.36047e45i	−1.36180	−	0.878774i
$325$	−6.92268e41			−0.000423033
$326$			4.40227e45i			2.54542i
$327$	−6.70288e44	−	9.66925e43i	−0.366777	−	0.0529094i
$328$	−7.82483e44			−0.405271
$329$		−	2.25932e45i		−	1.10777i
$330$	6.79048e44	−	4.70727e45i	0.315246	−	2.18534i
$331$	−4.28276e45			−1.88287			−0.941435	−	0.337195i	$-0.890522\pi$
$331$	−4.28276e45			−1.88287			−0.941435	+	0.337195i	$0.890522\pi$
$332$			4.82788e45i			2.01035i
$333$	−2.41392e45	−	7.11242e44i	−0.952198	−	0.280557i
$334$	6.74510e45			2.52088
$335$		−	8.85324e43i		−	0.0313542i
$336$	−2.48635e43	−	3.58669e42i	−0.00834557	−	0.00120389i
$337$	2.41522e45			0.768454			0.384227	−	0.923239i	$-0.374468\pi$
$337$	2.41522e45			0.768454			0.384227	+	0.923239i	$0.374468\pi$
$338$		−	5.36652e45i		−	1.61880i
$339$	−1.22052e44	+	8.46081e44i	−0.0349099	+	0.242001i
$340$	6.58726e45			1.78683
$341$			5.40672e45i			1.39109i
$342$	−1.96179e45	+	6.65823e45i	−0.478831	+	1.62513i
$343$	2.20705e44			0.0511114
$344$			5.39867e45i			1.18641i
$345$	−4.74295e45	−	6.84194e44i	−0.989246	−	0.142704i
$346$	8.93730e44			0.176944
$347$		−	8.25781e45i		−	1.55215i	−0.630640	−	0.776076i	$-0.717207\pi$
$347$		−	8.25781e45i		−	1.55215i	0.630640	−	0.776076i	$-0.282793\pi$
$348$	8.41873e44	−	5.83600e45i	0.150252	−	1.04157i
$349$	4.21970e45			0.715194			0.357597	−	0.933876i	$-0.383596\pi$
$349$	4.21970e45			0.715194			0.357597	+	0.933876i	$0.383596\pi$
$350$		−	9.13106e44i		−	0.146993i
$351$	−3.88081e43	−	1.77888e43i	−0.00593463	−	0.00272031i
$352$	−9.65990e45			−1.40347
$353$		−	1.36665e46i		−	1.88675i	−0.331735	−	0.943373i	$-0.607634\pi$
$353$		−	1.36665e46i		−	1.88675i	0.331735	−	0.943373i	$-0.392366\pi$
$354$	1.62103e46	+	2.33842e45i	2.12683	+	0.306806i
$355$	6.60596e45			0.823807
$356$		−	5.94210e45i		−	0.704434i
$357$	−2.02362e45	+	1.40280e46i	−0.228087	+	1.58114i
$358$	−2.43381e46			−2.60850
$359$			1.37555e46i			1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$359$			1.37555e46i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$360$	−9.61452e45	−	2.83284e45i	−0.932143	−	0.274648i
$361$	1.03270e45			0.0952456
$362$			7.00474e45i			0.614664i
$363$	−1.17242e46	−	1.69128e45i	−0.978962	−	0.141220i
$364$	−1.86577e44			−0.0148263
$365$		−	4.64546e45i		−	0.351364i
$366$	−6.48601e44	+	4.49621e45i	−0.0467001	+	0.323733i
$367$	2.84960e46			1.95341			0.976707	−	0.214580i	$-0.0688381\pi$
$367$	2.84960e46			1.95341			0.976707	+	0.214580i	$0.0688381\pi$
$368$		−	9.52786e43i		−	0.00621920i
$369$	1.83370e45	−	6.22350e45i	0.113987	−	0.386866i
$370$	−2.62482e46			−1.55406
$371$			4.20830e46i			2.37343i
$372$	2.94467e46	+	4.24783e45i	1.58221	+	0.228241i
$373$	−9.28379e45			−0.475299			−0.237649	−	0.971351i	$-0.576377\pi$
$373$	−9.28379e45			−0.475299			−0.237649	+	0.971351i	$0.576377\pi$
$374$		−	5.33520e46i		−	2.60292i
$375$	3.16185e45	−	2.19185e46i	0.147021	−	1.01917i
$376$	1.79234e46			0.794402
$377$		−	1.00324e44i		−	0.00423896i
$378$	2.34635e46	−	5.11880e46i	0.945238	−	2.06213i
$379$	−2.44149e46			−0.937884			−0.468942	−	0.883229i	$-0.655365\pi$
$379$	−2.44149e46			−0.937884			−0.468942	+	0.883229i	$0.655365\pi$
$380$			4.47735e46i			1.64028i
$381$	3.46957e46	+	5.00504e45i	1.21235	+	0.174887i
$382$	−3.54702e46			−1.18229
$383$		−	4.74363e46i		−	1.50846i	−0.656613	−	0.754228i	$-0.728011\pi$
$383$		−	4.74363e46i		−	1.50846i	0.656613	−	0.754228i	$-0.271989\pi$
$384$	−7.63522e45	+	5.29286e46i	−0.231664	+	1.60594i
$385$	6.60072e46			1.91117
$386$			8.50879e46i			2.35124i
$387$	−4.29385e46	−	1.26515e46i	−1.13253	−	0.333690i
$388$	1.38342e46			0.348325
$389$			4.50416e45i			0.108273i	0.998534	+	0.0541366i	$0.0172406\pi$
$389$			4.50416e45i			0.108273i	−0.998534	+	0.0541366i	$0.982759\pi$
$390$	−4.40717e44	−	6.35757e43i	−0.0101157	−	0.00145925i
$391$	−5.37563e46			−1.17828
$392$		−	4.62508e46i		−	0.968212i
$393$	5.69289e44	−	3.94640e45i	0.0113833	−	0.0789106i
$394$	−6.61498e46			−1.26356
$395$			1.51512e46i			0.276503i
$396$	−3.70481e46	+	1.25740e47i	−0.646030	+	2.19260i
$397$	1.06014e47			1.76658			0.883292	−	0.468823i	$-0.155322\pi$
$397$	1.06014e47			1.76658			0.883292	+	0.468823i	$0.155322\pi$
$398$		−	1.76607e47i		−	2.81263i
$399$	−9.53485e46	−	1.37545e46i	−1.45145	−	0.209379i
$400$	2.67952e43			0.000389922
$401$		−	6.06638e46i		−	0.843977i	−0.906601	−	0.421989i	$-0.861332\pi$
$401$		−	6.06638e46i		−	0.843977i	0.906601	−	0.421989i	$-0.138668\pi$
$402$	−5.63354e44	+	3.90526e45i	−0.00749398	+	0.0519495i
$403$	5.06203e44			0.00643923
$404$			5.25330e46i			0.639099i
$405$	4.50621e46	−	6.98308e46i	0.524350	−	0.812563i
$406$	1.32328e47			1.47293
$407$			1.31472e47i			1.40002i
$408$	−1.11286e47	−	1.60536e46i	−1.13386	−	0.163565i
$409$	−1.18079e47			−1.15120			−0.575602	−	0.817730i	$-0.695232\pi$
$409$	−1.18079e47			−1.15120			−0.575602	+	0.817730i	$0.695232\pi$
$410$		−	6.76722e46i		−	0.631395i
$411$	1.84948e44	−	1.28209e45i	0.00165157	−	0.0114489i
$412$	1.71567e47			1.46651
$413$			2.27308e47i			1.86000i
$414$	2.04863e47	+	6.03611e46i	1.60493	+	0.472880i
$415$	−1.59912e47			−1.19954
$416$			9.04406e44i			0.00649656i
$417$	−1.37202e46	−	1.97921e45i	−0.0943869	−	0.0136158i
$418$	3.62633e47			2.38943
$419$		−	7.53107e46i		−	0.475340i	−0.971346	−	0.237670i	$-0.923616\pi$
$419$		−	7.53107e46i		−	0.475340i	0.971346	−	0.237670i	$-0.0763837\pi$
$420$	5.18591e46	−	3.59496e47i	0.313573	−	2.17374i
$421$	6.19282e46			0.358766			0.179383	−	0.983779i	$-0.442590\pi$
$421$	6.19282e46			0.358766			0.179383	+	0.983779i	$0.442590\pi$
$422$			1.30867e47i			0.726450i
$423$	−4.20026e46	+	1.42555e47i	−0.223434	+	0.758325i
$424$	−3.33850e47			−1.70202
$425$		−	1.51179e46i		−	0.0738739i
$426$	−2.91396e47	−	4.20354e46i	−1.36493	−	0.196898i
$427$	−6.30476e46			−0.283117
$428$		−	3.45056e47i		−	1.48560i
$429$	−3.18438e44	+	2.20746e45i	−0.00131460	+	0.00911301i
$430$	−4.66898e47			−1.84837
$431$		−	9.70486e46i		−	0.368467i	−0.982883	−	0.184233i	$-0.941020\pi$
$431$		−	9.70486e46i		−	0.368467i	0.982883	−	0.184233i	$-0.0589802\pi$
$432$	1.50212e45	+	6.88541e44i	0.00547013	+	0.00250739i
$433$	2.41609e47			0.843977			0.421988	−	0.906601i	$-0.361332\pi$
$433$	2.41609e47			0.843977			0.421988	+	0.906601i	$0.361332\pi$
$434$			6.67684e47i			2.23746i
$435$	1.93304e47	+	2.78850e46i	0.621489	+	0.0896529i
$436$	1.94688e47			0.600596
$437$		−	3.65381e47i		−	1.08163i
$438$	−2.95602e46	+	2.04916e47i	−0.0839796	+	0.582161i
$439$	−4.81019e47			−1.31160			−0.655800	−	0.754935i	$-0.727668\pi$
$439$	−4.81019e47			−1.31160			−0.655800	+	0.754935i	$0.727668\pi$
$440$			5.23644e47i			1.37053i
$441$	3.67858e47	+	1.08386e47i	0.924241	+	0.272320i
$442$	−4.99506e45			−0.0120487
$443$		−	2.10611e47i		−	0.487769i	−0.969804	−	0.243885i	$-0.921578\pi$
$443$		−	2.10611e47i		−	0.487769i	0.969804	−	0.243885i	$-0.0784218\pi$
$444$	7.16035e47	+	1.03292e47i	1.59236	+	0.229706i
$445$	1.96818e47			0.420324
$446$		−	6.48953e47i		−	1.33102i
$447$	−8.30458e46	+	5.75687e47i	−0.163600	+	1.13410i
$448$	−1.19737e48			−2.26582
$449$		−	1.01455e48i		−	1.84433i	−0.386798	−	0.922164i	$-0.626419\pi$
$449$		−	1.01455e48i		−	1.84433i	0.386798	−	0.922164i	$-0.373581\pi$
$450$	−1.69754e46	+	5.76137e46i	−0.0296479	+	0.100624i
$451$	−3.38956e47			−0.568808
$452$		−	2.45748e47i		−	0.396276i
$453$	2.40683e47	+	3.47197e46i	0.372973	+	0.0538033i
$454$	1.34504e48			2.00322
$455$		−	6.17991e45i		−	0.00884662i
$456$	1.09116e47	−	7.56411e47i	0.150149	−	1.04086i
$457$	1.30325e48			1.72400			0.861999	−	0.506909i	$-0.169212\pi$
$457$	1.30325e48			1.72400			0.861999	+	0.506909i	$0.169212\pi$
$458$			1.33079e48i			1.69251i
$459$	3.88476e47	−	8.47498e47i	0.475046	−	1.03636i
$460$	1.37761e48			1.61989
$461$			8.28935e47i			0.937354i	0.883369	+	0.468677i	$0.155269\pi$
$461$			8.28935e47i			0.937354i	−0.883369	+	0.468677i	$0.844731\pi$
$462$	−2.91165e48	−	4.20021e47i	−3.16653	−	0.456789i
$463$	−1.38341e48			−1.44709			−0.723543	−	0.690279i	$-0.757488\pi$
$463$	−1.38341e48			−1.44709			−0.723543	+	0.690279i	$0.757488\pi$
$464$			3.88317e45i			0.00390718i
$465$	−1.40699e47	+	9.75350e47i	−0.136188	+	0.944077i
$466$	−8.43116e47			−0.785129
$467$			3.62292e47i			0.324605i	0.986741	+	0.162302i	$0.0518920\pi$
$467$			3.62292e47i			0.324605i	−0.986741	+	0.162302i	$0.948108\pi$
$468$	1.17723e46	+	3.46862e45i	0.0101493	+	0.00299041i
$469$	−5.47611e46			−0.0454319
$470$			1.55009e48i			1.23764i
$471$	5.24663e47	+	7.56853e46i	0.403185	+	0.0581614i
$472$	−1.80326e48			−1.33384
$473$			2.33860e48i			1.66516i
$474$	9.64110e46	−	6.68337e47i	0.0660871	−	0.458127i
$475$	1.02756e47			0.0678146
$476$		−	4.07451e48i		−	2.58911i
$477$	7.82357e47	−	2.65529e48i	0.478712	−	1.62473i
$478$	2.42894e48			1.43125
$479$		−	1.80871e48i		−	1.02643i	−0.858259	−	0.513216i	$-0.828454\pi$
$479$		−	1.80871e48i		−	1.02643i	0.858259	−	0.513216i	$-0.171546\pi$
$480$	−1.74261e48	−	2.51380e47i	−0.952482	−	0.137400i
$481$	1.23090e46			0.00648054
$482$		−	7.71405e47i		−	0.391233i
$483$	−4.23204e47	+	2.93372e48i	−0.206777	+	1.43341i
$484$	3.40536e48			1.60305
$485$			4.58226e47i			0.207840i
$486$	−2.43209e48	+	2.79357e48i	−1.06299	+	1.22098i
$487$	−3.17507e48			−1.33731			−0.668655	−	0.743573i	$-0.733130\pi$
$487$	−3.17507e48			−1.33731			−0.668655	+	0.743573i	$0.733130\pi$
$488$		−	5.00164e47i		−	0.203028i
$489$	3.97774e48	+	5.73809e47i	1.55624	+	0.224496i
$490$	3.99996e48			1.50843
$491$			8.71878e47i			0.316948i	0.987363	+	0.158474i	$0.0506575\pi$
$491$			8.71878e47i			0.316948i	−0.987363	+	0.158474i	$0.949343\pi$
$492$	−2.66304e47	+	1.84606e48i	−0.0933266	+	0.646955i
$493$	2.19089e48			0.740246
$494$		−	3.39514e46i		−	0.0110604i
$495$	−4.16482e48	−	1.22713e48i	−1.30829	−	0.385475i
$496$	−1.95933e46			−0.00593523
$497$		−	4.08607e48i		−	1.19369i
$498$	7.05389e48	+	1.01756e48i	1.98747	+	0.286703i
$499$	−6.75309e48			−1.83524			−0.917620	−	0.397459i	$-0.869892\pi$
$499$	−6.75309e48			−1.83524			−0.917620	+	0.397459i	$0.869892\pi$
$500$			6.36632e48i			1.66889i
$501$	8.79183e47	−	6.09464e48i	0.222331	−	1.54124i
$502$	4.06432e48			0.991566
$503$			2.21878e48i			0.522264i	0.965303	+	0.261132i	$0.0840958\pi$
$503$			2.21878e48i			0.522264i	−0.965303	+	0.261132i	$0.915904\pi$
$504$	−1.75223e48	+	5.94700e48i	−0.397962	+	1.35067i
$505$	−1.74003e48			−0.381340
$506$		−	1.11576e49i		−	2.35973i
$507$	−4.84900e48	−	6.99493e47i	−0.989713	−	0.142771i
$508$	−1.00775e49			−1.98521
$509$			1.47051e48i			0.279606i	0.990179	+	0.139803i	$0.0446470\pi$
$509$			1.47051e48i			0.279606i	−0.990179	+	0.139803i	$0.955353\pi$
$510$	1.38838e48	−	9.62447e48i	0.254827	−	1.76650i
$511$	−2.87342e48			−0.509123
$512$		−	7.03553e46i		−	0.0120348i
$513$	5.76044e48	+	2.64047e48i	0.951356	+	0.436082i
$514$	−1.34279e49			−2.14127
$515$			5.68274e48i			0.875040i
$516$	1.27367e49	+	1.83734e48i	1.89393	+	0.273209i
$517$	7.76409e48			1.11496
$518$			1.62356e49i			2.25182i
$519$	1.16492e47	−	8.07544e47i	0.0156058	−	0.108182i
$520$	4.90260e46			0.00634405
$521$		−	1.54623e48i		−	0.193284i	−0.995319	−	0.0966419i	$-0.969190\pi$
$521$		−	1.54623e48i		−	0.193284i	0.995319	−	0.0966419i	$-0.0308101\pi$
$522$	−8.34940e48	−	2.46008e48i	−1.00829	−	0.297085i
$523$	3.66724e48			0.427867			0.213934	−	0.976848i	$-0.431372\pi$
$523$	3.66724e48			0.427867			0.213934	+	0.976848i	$0.431372\pi$
$524$			1.14625e48i			0.129216i
$525$	−8.25051e47	−	1.19018e47i	−0.0898697	−	0.0129642i
$526$	6.94360e48			0.730872
$527$			1.10546e49i			1.12448i
$528$	1.23256e46	−	8.54429e46i	0.00121170	−	0.00839974i
$529$	−7.17672e47			−0.0681905
$530$		−	2.88726e49i		−	2.65168i
$531$	4.22584e48	−	1.43423e49i	0.375155	−	1.27326i
$532$	2.76944e49			2.37674
$533$			3.17347e46i			0.00263296i
$534$	−8.68185e48	−	1.25240e48i	−0.696418	−	0.100462i
$535$	1.14291e49			0.886432
$536$		−	4.34427e47i		−	0.0325800i
$537$	−3.17232e48	+	2.19910e49i	−0.230059	+	1.59481i
$538$	−2.26004e49			−1.58502
$539$		−	2.00350e49i		−	1.35891i
$540$	−9.95545e48	+	2.17188e49i	−0.653091	+	1.42478i
$541$	−3.99340e48			−0.253391			−0.126696	−	0.991942i	$-0.540437\pi$
$541$	−3.99340e48			−0.253391			−0.126696	+	0.991942i	$0.540437\pi$
$542$		−	1.08589e49i		−	0.666500i
$543$	6.32924e48	+	9.13025e47i	0.375798	+	0.0542108i
$544$	−1.97506e49			−1.13449
$545$			6.44858e48i			0.358366i
$546$	−3.93243e46	+	2.72603e47i	−0.00211443	+	0.0146576i
$547$	7.48376e48			0.389357			0.194678	−	0.980867i	$-0.437634\pi$
$547$	7.48376e48			0.389357			0.194678	+	0.980867i	$0.437634\pi$
$548$			3.72388e47i			0.0187476i
$549$	3.97808e48	+	1.17211e48i	0.193808	+	0.0571038i
$550$	3.13786e48			0.147947
$551$			1.48915e49i			0.679530i
$552$	−2.32736e49	−	3.35733e48i	−1.02792	−	0.148283i
$553$	9.37169e48			0.400650
$554$			6.09169e49i			2.52094i
$555$	−3.42129e48	+	2.37169e49i	−0.137062	+	0.950134i
$556$	3.98510e48			0.154558
$557$		−	4.55904e49i		−	1.71190i	−0.517055	−	0.855952i	$-0.672972\pi$
$557$		−	4.55904e49i		−	1.71190i	0.517055	−	0.855952i	$-0.327028\pi$
$558$	1.24128e49	−	4.21285e49i	0.451288	−	1.53165i
$559$	2.18951e47			0.00770785
$560$			2.39202e47i			0.00815419i
$561$	−4.82070e49	−	6.95411e48i	−1.59140	−	0.229567i
$562$	−3.81811e47			−0.0122066
$563$		−	4.47479e49i		−	1.38555i	−0.721155	−	0.692774i	$-0.756388\pi$
$563$		−	4.47479e49i		−	1.38555i	0.721155	−	0.692774i	$-0.243612\pi$
$564$	6.09992e48	−	4.22856e49i	0.182936	−	1.26815i
$565$	8.13981e48			0.236452
$566$			8.06258e49i			2.26871i
$567$	−4.31934e49	−	2.78729e49i	−1.17740	−	0.759779i
$568$	3.24153e49			0.856013
$569$		−	1.68421e49i		−	0.430898i	−0.976515	−	0.215449i	$-0.930879\pi$
$569$		−	1.68421e49i		−	0.430898i	0.976515	−	0.215449i	$-0.0691215\pi$
$570$	6.54175e49	+	9.43680e48i	1.62161	+	0.233925i
$571$	6.75389e49			1.62220			0.811100	−	0.584908i	$-0.198869\pi$
$571$	6.75389e49			1.62220			0.811100	+	0.584908i	$0.198869\pi$
$572$		−	6.41167e47i		−	0.0149225i
$573$	−4.62333e48	+	3.20497e49i	−0.104273	+	0.722838i
$574$	−4.18582e49			−0.914885
$575$		−	3.16165e48i		−	0.0669718i
$576$	7.55498e49	+	2.22601e49i	1.55106	+	0.457007i
$577$	2.31892e49			0.461446			0.230723	−	0.973019i	$-0.425891\pi$
$577$	2.31892e49			0.461446			0.230723	+	0.973019i	$0.425891\pi$
$578$		−	2.51543e49i		−	0.485190i
$579$	7.68825e49	+	1.10907e49i	1.43752	+	0.207369i
$580$	−5.61459e49			−1.01769
$581$			9.89125e49i			1.73812i
$582$	2.91581e48	−	2.02129e49i	0.0496758	−	0.344361i
$583$	−1.44617e50			−2.38883
$584$		−	2.27952e49i		−	0.365100i
$585$	−1.14890e47	+	3.89930e47i	−0.00178433	+	0.00605594i
$586$	−3.20816e49			−0.483168
$587$			8.44537e49i			1.23348i	0.787166	+	0.616741i	$0.211548\pi$
$587$			8.44537e49i			1.23348i	−0.787166	+	0.616741i	$0.788452\pi$
$588$	−1.09117e50	−	1.57406e49i	−1.54561	−	0.222962i
$589$	−7.51378e49			−1.03225
$590$		−	1.55953e50i		−	2.07806i
$591$	−8.62223e48	+	5.97707e49i	−0.111441	+	0.772527i
$592$	−4.76437e47			−0.00597331
$593$		−	1.19791e50i		−	1.45693i	−0.685083	−	0.728465i	$-0.740234\pi$
$593$		−	1.19791e50i		−	1.45693i	0.685083	−	0.728465i	$-0.259766\pi$
$594$	1.75906e50	+	8.06319e49i	2.07551	+	0.951373i
$595$	1.34958e50			1.54488
$596$		−	1.67211e50i		−	1.85709i
$597$	−1.59576e50	−	2.30196e49i	−1.71961	−	0.248062i
$598$	−1.04463e48			−0.0109230
$599$		−	1.84673e49i		−	0.187379i	−0.995601	−	0.0936895i	$-0.970134\pi$
$599$		−	1.84673e49i		−	0.187379i	0.995601	−	0.0936895i	$-0.0298661\pi$
$600$	9.44183e47	−	6.54523e48i	0.00929681	−	0.0644470i
$601$	−1.81640e49			−0.173569			−0.0867844	−	0.996227i	$-0.527659\pi$
$601$	−1.81640e49			−0.173569			−0.0867844	+	0.996227i	$0.527659\pi$
$602$			2.88797e50i			2.67828i
$603$	3.45523e48	+	1.01805e48i	0.0311004	+	0.00916346i
$604$	−6.99074e49			−0.610743
$605$			1.12794e50i			0.956512i
$606$	7.67547e49	+	1.10723e49i	0.631826	+	0.0911441i
$607$	−2.81069e49			−0.224604			−0.112302	−	0.993674i	$-0.535822\pi$
$607$	−2.81069e49			−0.224604			−0.112302	+	0.993674i	$0.535822\pi$
$608$		−	1.34245e50i		−	1.04144i
$609$	1.72481e49	−	1.19567e50i	0.129906	−	0.900532i
$610$	4.32562e49			0.316309
$611$		−	7.26911e47i		−	0.00516106i
$612$	−7.57485e49	+	2.57087e50i	−0.522214	+	1.77237i
$613$	6.55578e49			0.438870			0.219435	−	0.975627i	$-0.429579\pi$
$613$	6.55578e49			0.438870			0.219435	+	0.975627i	$0.429579\pi$
$614$			1.33468e50i			0.867655i
$615$	−6.11463e49	−	8.82067e48i	−0.386027	−	0.0556864i
$616$	3.23897e50			1.98588
$617$			1.44551e50i			0.860771i	0.902645	+	0.430385i	$0.141622\pi$
$617$			1.44551e50i			0.860771i	−0.902645	+	0.430385i	$0.858378\pi$
$618$	3.61607e49	−	2.50672e50i	0.209144	−	1.44982i
$619$	2.86652e50			1.61036			0.805180	−	0.593031i	$-0.202069\pi$
$619$	2.86652e50			1.61036			0.805180	+	0.593031i	$0.202069\pi$
$620$		−	2.83295e50i		−	1.54592i
$621$	8.12429e49	−	1.77239e50i	0.430662	−	0.939532i
$622$	−1.52604e50			−0.785849
$623$		−	1.21740e50i		−	0.609046i
$624$	−7.99957e45	−	1.15398e45i	−3.88816e−5	−	5.60887e-6i
$625$	−1.97147e50			−0.931002
$626$			2.47738e50i			1.13672i
$627$	4.72670e49	−	3.27663e50i	0.210738	−	1.46087i
$628$	−1.52391e50			−0.660214
$629$			2.68807e50i			1.13169i
$630$	−5.14320e50	−	1.51540e50i	−2.10428	−	0.620008i
$631$	1.51022e50			0.600500			0.300250	−	0.953861i	$-0.402930\pi$
$631$	1.51022e50			0.600500			0.300250	+	0.953861i	$0.402930\pi$
$632$			7.43468e49i			0.287313i
$633$	1.18247e50	+	1.70577e49i	0.444143	+	0.0640699i
$634$	−4.24848e50			−1.55106
$635$		−	3.33794e50i		−	1.18454i
$636$	−1.13620e50	+	7.87630e50i	−0.391945	+	2.71703i
$637$	−1.87577e48			−0.00629027
$638$			4.54740e50i			1.48249i
$639$	−7.59635e49	+	2.57817e50i	−0.240763	+	0.817138i
$640$	5.09205e50			1.56911
$641$		−	2.02582e50i		−	0.606954i	−0.952839	−	0.303477i	$-0.901852\pi$
$641$		−	2.02582e50i		−	0.606954i	0.952839	−	0.303477i	$-0.0981476\pi$
$642$	−5.04152e50	−	7.27265e49i	−1.46869	−	0.211866i
$643$	3.57163e50			1.01174			0.505870	−	0.862610i	$-0.331172\pi$
$643$	3.57163e50			1.01174			0.505870	+	0.862610i	$0.331172\pi$
$644$		−	8.52112e50i		−	2.34720i
$645$	−6.08574e49	+	4.21873e50i	−0.163019	+	1.13007i
$646$	7.41438e50			1.93148
$647$			2.86314e50i			0.725381i	0.931910	+	0.362690i	$0.118142\pi$
$647$			2.86314e50i			0.725381i	−0.931910	+	0.362690i	$0.881858\pi$
$648$	2.21119e50	−	3.42659e50i	0.544849	−	0.844329i
$649$	−7.81137e50			−1.87207
$650$		−	2.93782e47i		−	0.000684833i
$651$	6.03297e50	+	8.70286e49i	1.36796	+	0.197335i
$652$	−1.15535e51			−2.54834
$653$		−	5.19777e50i		−	1.11527i	−0.830086	−	0.557635i	$-0.811709\pi$
$653$		−	5.19777e50i		−	1.11527i	0.830086	−	0.557635i	$-0.188291\pi$
$654$	4.10339e49	−	2.84454e50i	0.0856532	−	0.593762i
$655$	−3.79668e49			−0.0771011
$656$		−	1.22834e48i		−	0.00242688i
$657$	1.81303e50	+	5.34193e49i	0.348520	+	0.102688i
$658$	9.58799e50			1.79334
$659$			6.61615e50i			1.20411i	0.798453	+	0.602057i	$0.205652\pi$
$659$			6.61615e50i			1.20411i	−0.798453	+	0.602057i	$0.794348\pi$
$660$	1.23540e51	+	1.78213e50i	2.18784	+	0.315608i
$661$	−2.77874e50			−0.478875			−0.239437	−	0.970912i	$-0.576963\pi$
$661$	−2.77874e50			−0.478875			−0.239437	+	0.970912i	$0.576963\pi$
$662$		−	1.81750e51i		−	3.04811i
$663$	−6.51077e47	+	4.51337e48i	−0.00106265	+	0.00736643i
$664$	−7.84685e50			−1.24644
$665$			9.17310e50i			1.41816i
$666$	3.01834e50	−	1.02441e51i	0.454184	−	1.54148i
$667$	4.58187e50			0.671085
$668$			1.77022e51i			2.52377i
$669$	−5.86372e50	−	8.45872e49i	−0.813773	−	0.117391i
$670$	3.75710e49			0.0507582
$671$		−	2.16661e50i		−	0.284955i
$672$	−1.55489e50	+	1.07788e51i	−0.199092	+	1.38014i
$673$	−1.06983e51			−1.33366			−0.666828	−	0.745211i	$-0.732349\pi$
$673$	−1.06983e51			−1.33366			−0.666828	+	0.745211i	$0.732349\pi$
$674$			1.02496e51i			1.24402i
$675$	4.98451e49	+	2.28480e49i	0.0589054	+	0.0270010i
$676$	1.40841e51			1.62065
$677$		−	6.04437e50i		−	0.677259i	−0.940920	−	0.338630i	$-0.890037\pi$
$677$		−	6.04437e50i		−	0.677259i	0.940920	−	0.338630i	$-0.109963\pi$
$678$	−3.59056e50	−	5.17957e49i	−0.391767	−	0.0565144i
$679$	2.83433e50			0.301158
$680$			1.07064e51i			1.10786i
$681$	1.75317e50	−	1.21533e51i	0.176676	−	1.22474i
$682$	−2.29448e51			−2.25199
$683$		−	1.98977e51i		−	1.90209i	−0.309054	−	0.951045i	$-0.600012\pi$
$683$		−	1.98977e51i		−	1.90209i	0.309054	−	0.951045i	$-0.399988\pi$
$684$	−1.74742e51	−	5.14862e50i	−1.62700	−	0.479381i
$685$	−1.23345e49			−0.0111864
$686$			9.36617e49i			0.0827424i
$687$	1.20245e51	+	1.73460e50i	1.03478	+	0.149272i
$688$	−8.47479e48			−0.00710456
$689$			1.35397e49i			0.0110577i
$690$	2.90355e50	−	2.01279e51i	0.231018	−	1.60146i
$691$	−1.77535e51			−1.37619			−0.688097	−	0.725619i	$-0.741554\pi$
$691$	−1.77535e51			−1.37619			−0.688097	+	0.725619i	$0.741554\pi$
$692$			2.34555e50i			0.177147i
$693$	−7.59033e50	+	2.57612e51i	−0.558550	+	1.89569i
$694$	3.50441e51			2.51272
$695$			1.31997e50i			0.0922225i
$696$	9.48538e50	+	1.36831e50i	0.645785	+	0.0931578i
$697$	−6.93029e50			−0.459792
$698$			1.79074e51i			1.15780i
$699$	−1.09895e50	+	7.61811e50i	−0.0692451	+	0.480019i
$700$	2.39640e50			0.147162
$701$		−	2.09034e51i		−	1.25110i	−0.780183	−	0.625551i	$-0.784874\pi$
$701$		−	2.09034e51i		−	1.25110i	0.780183	−	0.625551i	$-0.215126\pi$
$702$	7.54914e48	−	1.64692e49i	0.00440382	−	0.00960736i
$703$	−1.82708e51			−1.03887
$704$		−	4.11474e51i		−	2.28052i
$705$	1.40061e51	+	2.02045e50i	0.756681	+	0.109155i
$706$	5.79974e51			3.05438
$707$			1.07628e51i			0.552558i
$708$	−6.13706e50	+	4.25431e51i	−0.307158	+	2.12927i
$709$	2.67147e51			1.30352			0.651761	−	0.758424i	$-0.274030\pi$
$709$	2.67147e51			1.30352			0.651761	+	0.758424i	$0.274030\pi$
$710$			2.80341e51i			1.33363i
$711$	−5.91320e50	−	1.74227e50i	−0.274265	−	0.0808098i
$712$	9.65782e50			0.436756
$713$			2.31187e51i			1.01942i
$714$	−5.95316e51	−	8.58773e50i	−2.55964	−	0.369242i
$715$	2.12371e49			0.00890403
$716$		−	6.38740e51i		−	2.61150i
$717$	3.16598e50	−	2.19471e51i	0.126230	−	0.875049i
$718$	−5.83751e51			−2.26980
$719$		−	9.98772e50i		−	0.378745i	−0.981905	−	0.189372i	$-0.939355\pi$
$719$		−	9.98772e50i		−	0.378745i	0.981905	−	0.189372i	$-0.0606453\pi$
$720$	4.44697e48	−	1.50928e49i	0.00164467	−	0.00558194i
$721$	3.51502e51			1.26792
$722$			4.38253e50i			0.154190i
$723$	−6.97016e50	−	1.00548e50i	−0.239196	−	0.0345052i
$724$	−1.83836e51			−0.615369
$725$			1.28856e50i			0.0420747i
$726$	7.17739e50	−	4.97548e51i	0.228616	−	1.58481i
$727$	−2.95088e51			−0.916921			−0.458461	−	0.888715i	$-0.651599\pi$
$727$	−2.95088e51			−0.916921			−0.458461	+	0.888715i	$0.651599\pi$
$728$		−	3.03247e49i		−	0.00919247i
$729$	2.20717e51	+	2.56168e51i	0.652740	+	0.757582i
$730$	1.97142e51			0.568811
$731$			4.78149e51i			1.34602i
$732$	−1.18001e51	−	1.70222e50i	−0.324104	−	0.0467537i
$733$	2.86424e51			0.767605			0.383803	−	0.923415i	$-0.374614\pi$
$733$	2.86424e51			0.767605			0.383803	+	0.923415i	$0.374614\pi$
$734$			1.20930e52i			3.16231i
$735$	5.21370e50	−	3.61422e51i	0.133038	−	0.922238i
$736$	−4.13049e51			−1.02849
$737$		−	1.88185e50i		−	0.0457268i
$738$	2.64110e51	+	7.78179e50i	0.626283	+	0.184529i
$739$	−5.73726e50			−0.132771			−0.0663857	−	0.997794i	$-0.521147\pi$
$739$	−5.73726e50			−0.132771			−0.0663857	+	0.997794i	$0.521147\pi$
$740$		−	6.88869e51i		−	1.55584i
$741$	−3.06773e49	−	4.42536e48i	−0.00676223	−	0.000975486i
$742$	−1.78590e52			−3.84226
$743$			6.56790e51i			1.37920i	0.724189	+	0.689601i	$0.242214\pi$
$743$			6.56790e51i			1.37920i	−0.724189	+	0.689601i	$0.757786\pi$
$744$	−6.90409e50	+	4.78603e51i	−0.141512	+	0.980985i
$745$	5.53846e51			1.10809
$746$		−	3.93982e51i		−	0.769444i
$747$	1.83887e51	−	6.24102e51i	0.350573	−	1.18983i
$748$	1.40019e52			2.60591
$749$		−	7.06942e51i		−	1.28443i
$750$	9.30167e51	+	1.34181e51i	1.64990	+	0.238007i
$751$	−8.72757e50			−0.151138			−0.0755692	−	0.997141i	$-0.524077\pi$
$751$	−8.72757e50			−0.151138			−0.0755692	+	0.997141i	$0.524077\pi$
$752$			2.81361e49i			0.00475711i
$753$	5.29760e50	−	3.67239e51i	0.0874520	−	0.606232i
$754$	4.25750e49			0.00686231
$755$		−	2.31551e51i		−	0.364420i
$756$	1.34340e52	+	6.15788e51i	2.06450	+	0.946322i
$757$	−1.51978e51			−0.228064			−0.114032	−	0.993477i	$-0.536377\pi$
$757$	−1.51978e51			−0.228064			−0.114032	+	0.993477i	$0.536377\pi$
$758$		−	1.03611e52i		−	1.51831i
$759$	−1.00817e52	−	1.45433e51i	−1.44271	−	0.208119i
$760$	−7.27713e51			−1.01699
$761$		−	6.48495e50i		−	0.0885080i	−0.999020	−	0.0442540i	$-0.985909\pi$
$761$		−	6.48495e50i		−	0.0885080i	0.999020	−	0.0442540i	$-0.0140911\pi$
$762$	−2.12402e51	+	1.47240e52i	−0.283118	+	1.96262i
$763$	3.98873e51			0.519269
$764$		−	9.30898e51i		−	1.18365i
$765$	−8.51538e51	−	2.50898e51i	−1.05754	−	0.311596i
$766$	2.01308e52			2.44199
$767$			7.31337e49i			0.00866565i
$768$	−8.63434e51	−	1.24555e51i	−0.999372	−	0.144164i
$769$	−1.21318e52			−1.37168			−0.685838	−	0.727754i	$-0.740564\pi$
$769$	−1.21318e52			−1.37168			−0.685838	+	0.727754i	$0.740564\pi$
$770$			2.80119e52i			3.09392i
$771$	−1.75025e51	+	1.21330e52i	−0.188851	+	1.30915i
$772$	−2.23309e52			−2.35393
$773$			8.56661e51i			0.882222i	0.897453	+	0.441111i	$0.145416\pi$
$773$			8.56661e51i			0.882222i	−0.897453	+	0.441111i	$0.854584\pi$
$774$	5.36897e51	−	1.82220e52i	0.540199	−	1.83341i
$775$	−6.50168e50			−0.0639138
$776$			2.24851e51i			0.215965i
$777$	1.46700e52	+	2.11622e51i	1.37674	+	0.198601i
$778$	−1.91145e51			−0.175279
$779$		−	4.71051e51i		−	0.422079i
$780$	1.66851e49	−	1.15664e50i	0.00146092	−	0.0101273i
$781$	1.40417e52			1.20144
$782$		−	2.28129e52i		−	1.90747i
$783$	−3.31114e51	+	7.22357e51i	−0.270561	+	0.590256i
$784$	7.26043e49			0.00579793
$785$		−	5.04757e51i		−	0.393939i
$786$	1.67476e51	+	2.41592e50i	0.127746	+	0.0184280i
$787$	−1.54435e52			−1.15133			−0.575666	−	0.817685i	$-0.695257\pi$
$787$	−1.54435e52			−1.15133			−0.575666	+	0.817685i	$0.695257\pi$
$788$		−	1.73607e52i		−	1.26501i
$789$	9.05057e50	−	6.27400e51i	0.0644599	−	0.446847i
$790$	−6.42981e51			−0.447621
$791$		−	5.03483e51i		−	0.342616i
$792$	−2.04367e52	−	6.02150e51i	−1.35943	−	0.400545i
$793$	−2.02849e49			−0.00131903
$794$			4.49898e52i			2.85986i
$795$	−2.60883e52	−	3.76338e51i	−1.62121	−	0.233867i
$796$	4.63496e52			2.81586
$797$			3.04943e52i			1.81121i	0.424122	+	0.905605i	$0.360583\pi$
$797$			3.04943e52i			1.81121i	−0.424122	+	0.905605i	$0.639417\pi$
$798$	5.83708e51	−	4.04636e52i	0.338956	−	2.34970i
$799$	1.58744e52			0.901272
$800$		−	1.16162e51i		−	0.0644829i
$801$	−2.26325e51	+	7.68138e51i	−0.122842	+	0.416921i
$802$	2.57442e52			1.36628
$803$		−	9.87444e51i		−	0.512428i
$804$	−1.02492e51	−	1.47849e50i	−0.0520091	−	0.00750258i
$805$	2.82242e52			1.40054
$806$			2.14820e50i			0.0104242i
$807$	−2.94583e51	+	2.04209e52i	−0.139792	+	0.969063i
$808$	−8.53830e51			−0.396248
$809$			2.61039e51i			0.118477i	0.998244	+	0.0592383i	$0.0188672\pi$
$809$			2.61039e51i			0.118477i	−0.998244	+	0.0592383i	$0.981133\pi$
$810$	2.96345e52	+	1.91233e52i	1.31543	+	0.848852i
$811$	8.22781e51			0.357198			0.178599	−	0.983922i	$-0.442844\pi$
$811$	8.22781e51			0.357198			0.178599	+	0.983922i	$0.442844\pi$
$812$			3.47287e52i			1.47462i
$813$	−9.81176e51	−	1.41540e51i	−0.407490	−	0.0587825i
$814$	−5.57934e52			−2.26643
$815$		−	3.82683e52i		−	1.52055i
$816$	2.52008e49	−	1.74696e50i	0.000979473	−	0.00678986i
$817$	−3.24997e52			−1.23561
$818$		−	5.01097e52i		−	1.86364i
$819$	2.41189e50	+	7.10643e49i	0.00877500	+	0.00258548i
$820$	1.77602e52			0.632119
$821$		−	3.51999e52i		−	1.22565i	−0.790220	−	0.612823i	$-0.790034\pi$
$821$		−	3.51999e52i		−	1.22565i	0.790220	−	0.612823i	$-0.209966\pi$
$822$	5.44087e50	+	7.84873e49i	0.0185343	+	0.00267366i
$823$	−6.41580e51			−0.213823			−0.106911	−	0.994269i	$-0.534096\pi$
$823$	−6.41580e51			−0.213823			−0.106911	+	0.994269i	$0.534096\pi$
$824$			2.78851e52i			0.909249i
$825$	4.09002e50	−	2.83527e51i	0.0130483	−	0.0904530i
$826$	−9.64638e52			−3.01109
$827$			1.85904e52i			0.567792i	0.958855	+	0.283896i	$0.0916270\pi$
$827$			1.85904e52i			0.567792i	−0.958855	+	0.283896i	$0.908373\pi$
$828$	−1.58415e52	+	5.37652e52i	−0.473423	+	1.60678i
$829$	5.08345e52			1.48654			0.743271	−	0.668991i	$-0.233274\pi$
$829$	5.08345e52			1.48654			0.743271	+	0.668991i	$0.233274\pi$
$830$		−	6.78627e52i		−	1.94189i
$831$	5.50424e52	+	7.94015e51i	1.54127	+	0.222336i
$832$	−3.85241e50			−0.0105563
$833$		−	4.09634e52i		−	1.09846i
$834$	8.39929e50	−	5.82252e51i	0.0220421	−	0.152800i
$835$	−5.86342e52			−1.50589
$836$			9.51711e52i			2.39217i
$837$	−3.64479e52	−	1.67070e52i	−0.896633	−	0.410998i
$838$	3.19600e52			0.769511
$839$			4.29155e50i			0.0101134i	0.999987	+	0.00505672i	$0.00160961\pi$
$839$			4.29155e50i			0.0101134i	−0.999987	+	0.00505672i	$0.998390\pi$
$840$	5.84296e52	+	8.42877e51i	1.34774	+	0.194418i
$841$	2.56184e52			0.578395
$842$			2.62808e52i			0.580793i
$843$	−4.97667e49	+	3.44991e50i	−0.00107657	+	0.00746297i
$844$	−3.43453e52			−0.727284
$845$			4.66503e52i			0.967017i
$846$	−6.04968e52	−	1.78249e52i	−1.22762	−	0.361709i
$847$	6.97682e52			1.38598
$848$		−	5.24075e50i		−	0.0101922i
$849$	7.28508e52	+	1.05091e52i	1.38706	+	0.200091i
$850$	6.41567e51			0.119592
$851$			5.62162e52i			1.02596i
$852$	1.10320e52	−	7.64754e52i	0.197124	−	1.36650i
$853$	−2.57721e52			−0.450887			−0.225443	−	0.974256i	$-0.572383\pi$
$853$	−2.57721e52			−0.450887			−0.225443	+	0.974256i	$0.572383\pi$
$854$		−	2.67559e52i		−	0.458329i
$855$	1.70536e52	−	5.78790e52i	0.286039	−	0.970802i
$856$	5.60826e52			0.921086
$857$		−	5.20144e52i		−	0.836505i	−0.908331	−	0.418252i	$-0.862643\pi$
$857$		−	5.20144e52i		−	0.836505i	0.908331	−	0.418252i	$-0.137357\pi$
$858$	−9.36793e50	−	1.35137e50i	−0.0147527	−	0.00212816i
$859$	−5.54657e52			−0.855357			−0.427678	−	0.903931i	$-0.640668\pi$
$859$	−5.54657e52			−0.855357			−0.427678	+	0.903931i	$0.640668\pi$
$860$		−	1.22535e53i		−	1.85050i
$861$	−5.45597e51	+	3.78217e52i	−0.0806891	+	0.559350i
$862$	4.11851e52			0.596498
$863$			2.75559e52i			0.390859i	0.980718	+	0.195430i	$0.0626101\pi$
$863$			2.75559e52i			0.390859i	−0.980718	+	0.195430i	$0.937390\pi$
$864$	2.98495e52	−	6.51196e52i	0.414657	−	0.904616i
$865$	−7.76906e51			−0.105701
$866$			1.02533e53i			1.36628i
$867$	−2.27286e52	−	3.27872e51i	−0.296640	−	0.0427918i
$868$	−1.75230e53			−2.24003
$869$			3.22056e52i			0.403251i
$870$	−1.18337e52	+	8.20333e52i	−0.145136	+	1.00611i
$871$	−1.76188e49			−0.000211665
$872$			3.16431e52i			0.372376i
$873$	−1.78836e52	−	5.26925e51i	−0.206157	−	0.0607424i
$874$	1.55059e53			1.75102
$875$			1.30432e53i			1.44291i
$876$	−5.37793e52	−	7.75793e51i	−0.582829	−	0.0840760i
$877$	4.40882e52			0.468091			0.234045	−	0.972226i	$-0.424804\pi$
$877$	4.40882e52			0.468091			0.234045	+	0.972226i	$0.424804\pi$
$878$		−	2.04133e53i		−	2.12330i
$879$	−4.18164e51	+	2.89878e52i	−0.0426135	+	0.295403i
$880$	−8.22013e50			−0.00820711
$881$			3.15747e52i			0.308868i	0.988003	+	0.154434i	$0.0493554\pi$
$881$			3.15747e52i			0.308868i	−0.988003	+	0.154434i	$0.950645\pi$
$882$	−4.59964e52	+	1.56110e53i	−0.440849	+	1.49622i
$883$	−1.34500e53			−1.26308			−0.631540	−	0.775343i	$-0.717577\pi$
$883$	−1.34500e53			−1.26308			−0.631540	+	0.775343i	$0.717577\pi$
$884$		−	1.31093e51i		−	0.0120625i
$885$	−1.40914e53	−	2.03275e52i	−1.27050	−	0.183276i
$886$	8.93783e52			0.789633
$887$		−	1.43899e53i		−	1.24575i	−0.782321	−	0.622876i	$-0.785964\pi$
$887$		−	1.43899e53i		−	1.24575i	0.782321	−	0.622876i	$-0.214036\pi$
$888$	−1.67882e52	+	1.16379e53i	−0.142420	+	0.987279i
$889$	−2.06466e53			−1.71639
$890$			8.35247e52i			0.680448i
$891$	9.57845e52	−	1.48433e53i	0.764710	−	1.18504i
$892$	1.70314e53			1.33255
$893$			1.07898e53i			0.827349i
$894$	−2.44308e53	−	3.52426e52i	−1.83595	−	0.264846i
$895$	2.11567e53			1.55824
$896$		−	3.14965e53i		−	2.27362i
$897$	−1.36161e50	+	9.43892e50i	−0.000963362	+	0.00667819i
$898$	4.30549e53			2.98572
$899$		−	9.42225e52i		−	0.640443i
$900$	−1.51204e52	−	4.45510e51i	−0.100739	−	0.0296820i
$901$	−2.95684e53			−1.93100
$902$		−	1.43845e53i		−	0.920823i
$903$	2.60947e53	+	3.76429e52i	1.63747	+	0.236213i
$904$	3.99419e52			0.245696
$905$		−	6.08911e52i		−	0.367181i
$906$	−1.47342e52	+	1.02140e53i	−0.0871002	+	0.603793i
$907$	2.72180e53			1.57734			0.788671	−	0.614816i	$-0.210770\pi$
$907$	2.72180e53			1.57734			0.788671	+	0.614816i	$0.210770\pi$
$908$			3.52997e53i			2.00552i
$909$	2.00090e52	−	6.79097e52i	0.111449	−	0.378253i
$910$	2.62260e51			0.0143215
$911$		−	9.26197e52i		−	0.495876i	−0.968776	−	0.247938i	$-0.920247\pi$
$911$		−	9.26197e52i		−	0.495876i	0.968776	−	0.247938i	$-0.0797529\pi$
$912$	1.18741e51	+	1.71290e50i	0.00623295	+	0.000899135i
$913$	−3.39910e53			−1.74940
$914$			5.53068e53i			2.79092i
$915$	5.63819e51	−	3.90848e52i	0.0278972	−	0.193388i
$916$	−3.49258e53			−1.69445
$917$			2.34841e52i			0.111719i
$918$	3.59658e53	+	1.64860e53i	1.67773	+	0.769035i
$919$	−4.91601e52			−0.224871			−0.112436	−	0.993659i	$-0.535865\pi$
$919$	−4.91601e52			−0.224871			−0.112436	+	0.993659i	$0.535865\pi$
$920$			2.23906e53i			1.00435i
$921$	1.20597e53	+	1.73968e52i	0.530474	+	0.0765236i
$922$	−3.51780e53			−1.51745
$923$		−	1.31465e51i		−	0.00556134i
$924$	1.10232e53	−	7.64148e53i	0.457313	−	3.17017i
$925$	−1.58097e52			−0.0643239
$926$		−	5.87087e53i		−	2.34264i
$927$	−2.21785e53	−	6.53472e52i	−0.867956	−	0.255736i
$928$	1.68342e53			0.646145
$929$			3.55083e53i			1.33674i	0.743829	+	0.668370i	$0.233008\pi$
$929$			3.55083e53i			1.33674i	−0.743829	+	0.668370i	$0.766992\pi$
$930$	−4.13915e53	−	5.97093e52i	−1.52833	−	0.220470i
$931$	2.78428e53			1.00837
$932$		−	2.21271e53i		−	0.786030i
$933$	−1.98910e52	+	1.37888e53i	−0.0693087	+	0.480459i
$934$	−1.53748e53			−0.525491
$935$			4.63781e53i			1.55490i
$936$	−5.63762e50	+	1.91338e51i	−0.00185409	+	0.00629269i
$937$	3.78210e53			1.22017			0.610085	−	0.792336i	$-0.291135\pi$
$937$	3.78210e53			1.22017			0.610085	+	0.792336i	$0.291135\pi$
$938$		−	2.32393e52i		−	0.0735482i
$939$	2.23848e53	+	3.22912e52i	0.694979	+	0.100254i
$940$	−4.06813e53			−1.23906
$941$		−	6.46499e53i		−	1.93177i	−0.258976	−	0.965884i	$-0.583385\pi$
$941$		−	6.46499e53i		−	1.93177i	0.258976	−	0.965884i	$-0.416615\pi$
$942$	−3.21190e52	+	2.22654e53i	−0.0941555	+	0.652701i
$943$	−1.44935e53			−0.416833
$944$		−	2.83075e51i		−	0.00798739i
$945$	−2.03965e53	+	4.44970e53i	−0.564655	+	1.23185i
$946$	−9.92443e53			−2.69566
$947$		−	2.47742e53i		−	0.660236i	−0.943940	−	0.330118i	$-0.892911\pi$
$947$		−	2.47742e53i		−	0.660236i	0.943940	−	0.330118i	$-0.107089\pi$
$948$	1.75402e53	+	2.53026e52i	0.458652	+	0.0661629i
$949$	−9.24492e50			−0.00237198
$950$			4.36072e52i			0.109783i
$951$	−5.53764e52	+	3.83879e53i	−0.136797	+	0.948297i
$952$	6.62238e53			1.60527
$953$		−	2.63848e53i		−	0.627598i	−0.949489	−	0.313799i	$-0.898398\pi$
$953$		−	2.63848e53i		−	0.627598i	0.949489	−	0.313799i	$-0.101602\pi$
$954$	1.12684e54	+	3.32013e53i	2.63021	+	0.774970i
$955$	3.08337e53			0.706262
$956$			6.37463e53i			1.43289i
$957$	4.10888e53	+	5.92727e52i	0.906376	+	0.130749i
$958$	7.67573e53			1.66165
$959$			7.62941e51i			0.0162090i
$960$	1.07078e53	−	7.42282e53i	0.223264	−	1.54770i
$961$	−1.32580e52			−0.0271305
$962$			5.22364e51i			0.0104911i
$963$	−1.31426e53	+	4.46055e53i	−0.259065	+	0.879256i
$964$	2.02451e53			0.391682
$965$		−	7.39656e53i		−	1.40455i
$966$	−1.24500e54	−	1.79597e53i	−2.32049	−	0.334743i
$967$	−4.09707e53			−0.749543			−0.374772	−	0.927117i	$-0.622279\pi$
$967$	−4.09707e53			−0.749543			−0.374772	+	0.927117i	$0.622279\pi$
$968$			5.53480e53i			0.993907i
$969$	9.66420e52	−	6.69938e53i	0.170348	−	1.18088i
$970$	−1.94460e53			−0.336464
$971$		−	5.74857e53i		−	0.976369i	−0.872740	−	0.488185i	$-0.837659\pi$
$971$		−	5.74857e53i		−	0.976369i	0.872740	−	0.488185i	$-0.162341\pi$
$972$	−7.33159e53	−	6.38290e53i	−1.22238	−	1.06420i
$973$	8.16457e52			0.133630
$974$		−	1.34742e54i		−	2.16492i
$975$	−2.65451e50	−	3.82927e49i	−0.000418699	−	6.03994e-5i
$976$	7.85155e50			0.00121579
$977$			1.05474e54i			1.60340i	0.597725	+	0.801701i	$0.296071\pi$
$977$			1.05474e54i			1.60340i	−0.597725	+	0.801701i	$0.703929\pi$
$978$	−2.43511e53	+	1.68806e54i	−0.363428	+	2.51934i
$979$	4.18358e53			0.612999
$980$			1.04977e54i			1.51016i
$981$	−2.51674e53	−	7.41537e52i	−0.355465	−	0.104735i
$982$	−3.70004e53			−0.513097
$983$		−	6.28170e53i		−	0.855290i	−0.903947	−	0.427645i	$-0.859343\pi$
$983$		−	6.28170e53i		−	0.855290i	0.903947	−	0.427645i	$-0.140657\pi$
$984$	−3.00044e53	−	4.32829e52i	−0.401119	−	0.0578634i
$985$	5.75030e53			0.754812
$986$			9.29761e53i			1.19836i
$987$	1.24974e53	−	8.66338e53i	0.158165	−	1.09642i
$988$	8.91037e51			0.0110731
$989$			9.99964e53i			1.22026i
$990$	5.20764e53	−	1.76745e54i	0.624033	−	2.11794i
$991$	−5.20787e53			−0.612822			−0.306411	−	0.951899i	$-0.599128\pi$
$991$	−5.20787e53			−0.612822			−0.306411	+	0.951899i	$0.599128\pi$
$992$			8.49404e53i			0.981531i
$993$	−1.64223e54	−	2.36900e53i	−1.86358	−	0.268831i
$994$	1.73403e54			1.93242
$995$			1.53522e54i			1.68017i
$996$	−2.67053e53	+	1.85126e54i	−0.287032	+	1.98975i
$997$	3.78042e53			0.399049			0.199525	−	0.979893i	$-0.436060\pi$
$997$	3.78042e53			0.399049			0.199525	+	0.979893i	$0.436060\pi$
$998$		−	2.86585e54i		−	2.97100i
$999$	−8.86280e53	−	4.06253e53i	−0.902386	−	0.413635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.37.b.b.2.9	yes	10
3.2	odd	2	inner	3.37.b.b.2.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.37.b.b.2.2	✓	10	3.2	odd	2	inner
3.37.b.b.2.9	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+424376. i q^{2} +(3.83451e8 + 5.53148e7i) q^{3} -1.11375e11 q^{4} -3.68903e12i q^{5} +(-2.34743e13 + 1.62727e14i) q^{6} -2.28183e15 q^{7} -1.81020e16i q^{8} +(1.43975e17 + 4.24211e16i) q^{9} +O(q^{10})\)	\(q+424376. i q^{2} +(3.83451e8 + 5.53148e7i) q^{3} -1.11375e11 q^{4} -3.68903e12i q^{5} +(-2.34743e13 + 1.62727e14i) q^{6} -2.28183e15 q^{7} -1.81020e16i q^{8} +(1.43975e17 + 4.24211e16i) q^{9} +1.56554e18 q^{10} -7.84145e18i q^{11} +(-4.27069e19 - 6.16070e18i) q^{12} -7.34153e17 q^{13} -9.68352e20i q^{14} +(2.04058e20 - 1.41456e21i) q^{15} +2.84165e19 q^{16} -1.60326e22i q^{17} +(-1.80025e22 + 6.10996e22i) q^{18} +1.08973e23 q^{19} +4.10867e23i q^{20} +(-8.74970e23 - 1.26219e23i) q^{21} +3.32772e24 q^{22} -3.35294e24i q^{23} +(1.00131e24 - 6.94125e24i) q^{24} +9.42948e23 q^{25} -3.11557e23i q^{26} +(5.28610e25 + 2.42304e25i) q^{27} +2.54139e26 q^{28} +1.36652e26i q^{29} +(6.00307e26 + 8.65973e25i) q^{30} -6.89506e26 q^{31} -1.23190e27i q^{32} +(4.33748e26 - 3.00681e27i) q^{33} +6.80384e27 q^{34} +8.41774e27i q^{35} +(-1.60353e28 - 4.72465e27i) q^{36} -1.67663e28 q^{37} +4.62457e28i q^{38} +(-2.81512e26 - 4.06096e25i) q^{39} -6.67790e28 q^{40} -4.32262e28i q^{41} +(5.35642e28 - 3.71316e29i) q^{42} -2.98235e29 q^{43} +8.73342e29i q^{44} +(1.56493e29 - 5.31129e29i) q^{45} +1.42290e30 q^{46} +9.90135e29i q^{47} +(1.08963e28 + 1.57185e27i) q^{48} +2.55501e30 q^{49} +4.00164e29i q^{50} +(8.86840e29 - 6.14772e30i) q^{51} +8.17664e28 q^{52} -1.84427e31i q^{53} +(-1.02828e31 + 2.24329e31i) q^{54} -2.89274e31 q^{55} +4.13057e31i q^{56} +(4.17860e31 + 6.02784e30i) q^{57} -5.79919e31 q^{58} -9.96164e31i q^{59} +(-2.27270e31 + 1.57547e32i) q^{60} +2.76303e31 q^{61} -2.92609e32i q^{62} +(-3.28527e32 - 9.67976e31i) q^{63} +5.24742e32 q^{64} +2.70832e30i q^{65} +(1.27602e33 + 1.84072e32i) q^{66} +2.39988e31 q^{67} +1.78563e33i q^{68} +(1.85467e32 - 1.28569e33i) q^{69} -3.57228e33 q^{70} +1.79070e33i q^{71} +(7.67907e32 - 2.60624e33i) q^{72} +1.25926e33 q^{73} -7.11519e33i q^{74} +(3.61575e32 + 5.21590e31i) q^{75} -1.21369e34 q^{76} +1.78928e34i q^{77} +(1.72337e31 - 1.19467e32i) q^{78} -4.10710e33 q^{79} -1.04829e32i q^{80} +(1.89293e34 + 1.22152e34i) q^{81} +1.83442e34 q^{82} -4.33479e34i q^{83} +(9.74499e34 + 1.40576e34i) q^{84} -5.91448e34 q^{85} -1.26564e35i q^{86} +(-7.55890e33 + 5.23995e34i) q^{87} -1.41946e35 q^{88} +5.33521e34i q^{89} +(2.25398e35 + 6.64117e34i) q^{90} +1.67521e33 q^{91} +3.73434e35i q^{92} +(-2.64392e35 - 3.81399e34i) q^{93} -4.20189e35 q^{94} -4.02007e35i q^{95} +(6.81425e34 - 4.72375e35i) q^{96} -1.24213e35 q^{97} +1.08428e36i q^{98} +(3.32643e35 - 1.12897e36i) 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

Related objects

Downloads

Learn more