LMFDB - Embedded newform 15.9.c.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,9,Mod(11,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("15.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	15.c (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:	$6.11067915092$
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} - 4 x^{9} - 433 x^{8} - 2220 x^{7} + 49747 x^{6} + 744964 x^{5} + 4580249 x^{4} + 16418988 x^{3} + \cdots + 53656344 $ x^10 - 4x^9 - 433x^8 - 2220x^7 + 49747x^6 + 744964x^5 + 4580249x^4 + 16418988x^3 + 38943804x^2 + 57910464*x + 53656344
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{10}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.7
Root			$-1.94191 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.9.c.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.27106i q^{2} +(70.4414 + 39.9876i) q^{3} +187.590 q^{4} -279.508i q^{5} +(-330.740 + 582.625i) q^{6} +860.291 q^{7} +3668.96i q^{8} +(3362.98 + 5633.57i) q^{9} +O(q^{10})$	\(q+8.27106i q^{2} +(70.4414 + 39.9876i) q^{3} +187.590 q^{4} -279.508i q^{5} +(-330.740 + 582.625i) q^{6} +860.291 q^{7} +3668.96i q^{8} +(3362.98 + 5633.57i) q^{9} +2311.83 q^{10} +8660.22i q^{11} +(13214.1 + 7501.26i) q^{12} -18472.1 q^{13} +7115.52i q^{14} +(11176.9 - 19689.0i) q^{15} +17676.8 q^{16} -110116. i q^{17} +(-46595.6 + 27815.4i) q^{18} -71227.1 q^{19} -52432.9i q^{20} +(60600.1 + 34401.0i) q^{21} -71629.2 q^{22} -369004. i q^{23} +(-146713. + 258446. i) q^{24} -78125.0 q^{25} -152783. i q^{26} +(11620.0 + 531314. i) q^{27} +161382. q^{28} -306317. i q^{29} +(162849. + 92444.7i) q^{30} +1.39489e6 q^{31} +1.08546e6i q^{32} +(-346302. + 610038. i) q^{33} +910773. q^{34} -240459. i q^{35} +(630860. + 1.05680e6i) q^{36} -3.68589e6 q^{37} -589123. i q^{38} +(-1.30120e6 - 738653. i) q^{39} +1.02550e6 q^{40} -5.05129e6i q^{41} +(-284533. + 501227. i) q^{42} -1.42558e6 q^{43} +1.62457e6i q^{44} +(1.57463e6 - 939981. i) q^{45} +3.05206e6 q^{46} -779661. i q^{47} +(1.24518e6 + 706852. i) q^{48} -5.02470e6 q^{49} -646177. i q^{50} +(4.40326e6 - 7.75670e6i) q^{51} -3.46516e6 q^{52} +7.55943e6i q^{53} +(-4.39453e6 + 96109.4i) q^{54} +2.42060e6 q^{55} +3.15637e6i q^{56} +(-5.01733e6 - 2.84820e6i) q^{57} +2.53356e6 q^{58} +2.08194e7i q^{59} +(2.09667e6 - 3.69344e6i) q^{60} +2.03126e7 q^{61} +1.15372e7i q^{62} +(2.89314e6 + 4.84651e6i) q^{63} -4.45264e6 q^{64} +5.16310e6i q^{65} +(-5.04566e6 - 2.86428e6i) q^{66} -1.37810e6 q^{67} -2.06565e7i q^{68} +(1.47556e7 - 2.59932e7i) q^{69} +1.98885e6 q^{70} -4.19202e6i q^{71} +(-2.06693e7 + 1.23386e7i) q^{72} -2.57861e7 q^{73} -3.04862e7i q^{74} +(-5.50323e6 - 3.12403e6i) q^{75} -1.33615e7 q^{76} +7.45030e6i q^{77} +(6.10945e6 - 1.07623e7i) q^{78} +1.07664e7 q^{79} -4.94081e6i q^{80} +(-2.04275e7 + 3.78911e7i) q^{81} +4.17795e7 q^{82} -1.63457e7i q^{83} +(1.13679e7 + 6.45327e6i) q^{84} -3.07783e7 q^{85} -1.17910e7i q^{86} +(1.22489e7 - 2.15774e7i) q^{87} -3.17740e7 q^{88} +5.98434e7i q^{89} +(7.77464e6 + 1.30239e7i) q^{90} -1.58913e7 q^{91} -6.92213e7i q^{92} +(9.82577e7 + 5.57782e7i) q^{93} +6.44862e6 q^{94} +1.99086e7i q^{95} +(-4.34049e7 + 7.64612e7i) q^{96} +1.07731e8 q^{97} -4.15596e7i q^{98} +(-4.87879e7 + 2.91241e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9}+O(q^{10}) $ 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} - 8750 q^{10} - 3812 q^{12} - 55464 q^{13} - 21250 q^{15} + 280386 q^{16} - 419800 q^{18} - 231516 q^{19} + 289572 q^{21} + 1129940 q^{22} + 1136334 q^{24} - 781250 q^{25} - 335512 q^{27} - 3340724 q^{28} - 965000 q^{30} + 881620 q^{31} + 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} + 4672616 q^{37} + 1826792 q^{39} + 2913750 q^{40} - 5392860 q^{42} + 7731336 q^{43} - 2142500 q^{45} - 25424604 q^{46} + 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} + 21064016 q^{52} - 7979798 q^{54} - 4377500 q^{55} - 2856304 q^{57} - 4351100 q^{58} + 23016250 q^{60} + 22417020 q^{61} + 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} - 46646024 q^{67} + 33562632 q^{69} - 62992500 q^{70} + 54175560 q^{72} - 129964884 q^{73} + 8750000 q^{75} + 198922436 q^{76} + 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} + 202877560 q^{82} - 197346768 q^{84} - 110682500 q^{85} - 168322540 q^{87} - 484775700 q^{88} + 171878750 q^{90} + 444288464 q^{91} + 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} - 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9 - 8750 * q^10 - 3812 * q^12 - 55464 * q^13 - 21250 * q^15 + 280386 * q^16 - 419800 * q^18 - 231516 * q^19 + 289572 * q^21 + 1129940 * q^22 + 1136334 * q^24 - 781250 * q^25 - 335512 * q^27 - 3340724 * q^28 - 965000 * q^30 + 881620 * q^31 + 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 + 4672616 * q^37 + 1826792 * q^39 + 2913750 * q^40 - 5392860 * q^42 + 7731336 * q^43 - 2142500 * q^45 - 25424604 * q^46 + 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 + 21064016 * q^52 - 7979798 * q^54 - 4377500 * q^55 - 2856304 * q^57 - 4351100 * q^58 + 23016250 * q^60 + 22417020 * q^61 + 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 - 46646024 * q^67 + 33562632 * q^69 - 62992500 * q^70 + 54175560 * q^72 - 129964884 * q^73 + 8750000 * q^75 + 198922436 * q^76 + 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 + 202877560 * q^82 - 197346768 * q^84 - 110682500 * q^85 - 168322540 * q^87 - 484775700 * q^88 + 171878750 * q^90 + 444288464 * q^91 + 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 - 258825724 * q^97 - 33965200 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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 $

$2$			8.27106i			0.516941i	0.966019	+	0.258471i	$0.0832185\pi$
$2$			8.27106i			0.516941i	−0.966019	+	0.258471i	$0.916781\pi$
$3$	70.4414	+	39.9876i	0.869647	+	0.493674i
$3$	70.4414	+	39.9876i	0.869647	+	0.493674i
$4$	187.590			0.732772
$5$		−	279.508i		−	0.447214i
$5$		−	279.508i		−	0.447214i
$6$	−330.740	+	582.625i	−0.255201	+	0.449556i
$7$	860.291			0.358305			0.179153	−	0.983821i	$-0.442664\pi$
$7$	860.291			0.358305			0.179153	+	0.983821i	$0.442664\pi$
$8$			3668.96i			0.895741i
$9$	3362.98	+	5633.57i	0.512571	+	0.858645i
$10$	2311.83			0.231183
$11$			8660.22i			0.591505i	0.955265	+	0.295752i	$0.0955703\pi$
$11$			8660.22i			0.591505i	−0.955265	+	0.295752i	$0.904430\pi$
$12$	13214.1	+	7501.26i	0.637253	+	0.361751i
$13$	−18472.1			−0.646758			−0.323379	−	0.946270i	$-0.604819\pi$
$13$	−18472.1			−0.646758			−0.323379	+	0.946270i	$0.604819\pi$
$14$			7115.52i			0.185223i
$15$	11176.9	−	19689.0i	0.220778	−	0.388918i
$16$	17676.8			0.269726
$17$		−	110116.i		−	1.31842i	−0.751960	−	0.659209i	$-0.770891\pi$
$17$		−	110116.i		−	1.31842i	0.751960	−	0.659209i	$-0.229109\pi$
$18$	−46595.6	+	27815.4i	−0.443869	+	0.264969i
$19$	−71227.1			−0.546551			−0.273275	−	0.961936i	$-0.588107\pi$
$19$	−71227.1			−0.546551			−0.273275	+	0.961936i	$0.588107\pi$
$20$		−	52432.9i		−	0.327705i
$21$	60600.1	+	34401.0i	0.311599	+	0.176886i
$22$	−71629.2			−0.305773
$23$		−	369004.i		−	1.31862i	−0.751871	−	0.659311i	$-0.770848\pi$
$23$		−	369004.i		−	1.31862i	0.751871	−	0.659311i	$-0.229152\pi$
$24$	−146713.	+	258446.i	−0.442204	+	0.778978i
$25$	−78125.0			−0.200000
$26$		−	152783.i		−	0.334336i
$27$	11620.0	+	531314.i	0.0218650	+	0.999761i
$28$	161382.			0.262556
$29$		−	306317.i		−	0.433090i	−0.976273	−	0.216545i	$-0.930521\pi$
$29$		−	306317.i		−	0.433090i	0.976273	−	0.216545i	$-0.0694788\pi$
$30$	162849.	+	92444.7i	0.201048	+	0.114129i
$31$	1.39489e6			1.51040			0.755200	−	0.655494i	$-0.227540\pi$
$31$	1.39489e6			1.51040			0.755200	+	0.655494i	$0.227540\pi$
$32$			1.08546e6i			1.03517i
$33$	−346302.	+	610038.i	−0.292011	+	0.514400i
$34$	910773.			0.681545
$35$		−	240459.i		−	0.160239i
$36$	630860.	+	1.05680e6i	0.375598	+	0.629191i
$37$	−3.68589e6			−1.96669			−0.983345	−	0.181751i	$-0.941823\pi$
$37$	−3.68589e6			−1.96669			−0.983345	+	0.181751i	$0.941823\pi$
$38$		−	589123.i		−	0.282535i
$39$	−1.30120e6	−	738653.i	−0.562451	−	0.319288i
$40$	1.02550e6			0.400588
$41$		−	5.05129e6i		−	1.78758i	−0.448481	−	0.893792i	$-0.648035\pi$
$41$		−	5.05129e6i		−	1.78758i	0.448481	−	0.893792i	$-0.351965\pi$
$42$	−284533.	+	501227.i	−0.0914397	+	0.161078i
$43$	−1.42558e6			−0.416981			−0.208491	−	0.978024i	$-0.566855\pi$
$43$	−1.42558e6			−0.416981			−0.208491	+	0.978024i	$0.566855\pi$
$44$			1.62457e6i			0.433438i
$45$	1.57463e6	−	939981.i	0.383998	−	0.229229i
$46$	3.05206e6			0.681650
$47$		−	779661.i		−	0.159777i	−0.996804	−	0.0798885i	$-0.974544\pi$
$47$		−	779661.i		−	0.159777i	0.996804	−	0.0798885i	$-0.0254564\pi$
$48$	1.24518e6	+	706852.i	0.234566	+	0.133157i
$49$	−5.02470e6			−0.871617
$50$		−	646177.i		−	0.103388i
$51$	4.40326e6	−	7.75670e6i	0.650869	−	1.14656i
$52$	−3.46516e6			−0.473926
$53$			7.55943e6i			0.958044i	0.877803	+	0.479022i	$0.159009\pi$
$53$			7.55943e6i			0.958044i	−0.877803	+	0.479022i	$0.840991\pi$
$54$	−4.39453e6	+	96109.4i	−0.516818	+	0.0113029i
$55$	2.42060e6			0.264529
$56$			3.15637e6i			0.320949i
$57$	−5.01733e6	−	2.84820e6i	−0.475306	−	0.269818i
$58$	2.53356e6			0.223882
$59$			2.08194e7i			1.71814i	0.511856	+	0.859071i	$0.328958\pi$
$59$			2.08194e7i			1.71814i	−0.511856	+	0.859071i	$0.671042\pi$
$60$	2.09667e6	−	3.69344e6i	0.161780	−	0.284988i
$61$	2.03126e7			1.46706			0.733528	−	0.679659i	$-0.237872\pi$
$61$	2.03126e7			1.46706			0.733528	+	0.679659i	$0.237872\pi$
$62$			1.15372e7i			0.780788i
$63$	2.89314e6	+	4.84651e6i	0.183657	+	0.307657i
$64$	−4.45264e6			−0.265398
$65$			5.16310e6i			0.289239i
$66$	−5.04566e6	−	2.86428e6i	−0.265915	−	0.150952i
$67$	−1.37810e6			−0.0683884			−0.0341942	−	0.999415i	$-0.510886\pi$
$67$	−1.37810e6			−0.0683884			−0.0341942	+	0.999415i	$0.510886\pi$
$68$		−	2.06565e7i		−	0.966100i
$69$	1.47556e7	−	2.59932e7i	0.650969	−	1.14673i
$70$	1.98885e6			0.0828341
$71$		−	4.19202e6i		−	0.164964i	−0.996593	−	0.0824821i	$-0.973715\pi$
$71$		−	4.19202e6i		−	0.164964i	0.996593	−	0.0824821i	$-0.0262847\pi$
$72$	−2.06693e7	+	1.23386e7i	−0.769123	+	0.459131i
$73$	−2.57861e7			−0.908018			−0.454009	−	0.890997i	$-0.650007\pi$
$73$	−2.57861e7			−0.908018			−0.454009	+	0.890997i	$0.650007\pi$
$74$		−	3.04862e7i		−	1.01666i
$75$	−5.50323e6	−	3.12403e6i	−0.173929	−	0.0987349i
$76$	−1.33615e7			−0.400497
$77$			7.45030e6i			0.211939i
$78$	6.10945e6	−	1.07623e7i	0.165053	−	0.290754i
$79$	1.07664e7			0.276416			0.138208	−	0.990403i	$-0.455866\pi$
$79$	1.07664e7			0.276416			0.138208	+	0.990403i	$0.455866\pi$
$80$		−	4.94081e6i		−	0.120625i
$81$	−2.04275e7	+	3.78911e7i	−0.474542	+	0.880233i
$82$	4.17795e7			0.924076
$83$		−	1.63457e7i		−	0.344422i	−0.985060	−	0.172211i	$-0.944909\pi$
$83$		−	1.63457e7i		−	0.344422i	0.985060	−	0.172211i	$-0.0550911\pi$
$84$	1.13679e7	+	6.45327e6i	0.228331	+	0.129617i
$85$	−3.07783e7			−0.589615
$86$		−	1.17910e7i		−	0.215555i
$87$	1.22489e7	−	2.15774e7i	0.213806	−	0.376636i
$88$	−3.17740e7			−0.529835
$89$			5.98434e7i			0.953798i	0.878958	+	0.476899i	$0.158239\pi$
$89$			5.98434e7i			0.953798i	−0.878958	+	0.476899i	$0.841761\pi$
$90$	7.77464e6	+	1.30239e7i	0.118498	+	0.198504i
$91$	−1.58913e7			−0.231737
$92$		−	6.92213e7i		−	0.966248i
$93$	9.82577e7	+	5.57782e7i	1.31351	+	0.745646i
$94$	6.44862e6			0.0825954
$95$			1.99086e7i			0.244425i
$96$	−4.34049e7	+	7.64612e7i	−0.511039	+	0.900236i
$97$	1.07731e8			1.21690			0.608449	−	0.793593i	$-0.291792\pi$
$97$	1.07731e8			1.21690			0.608449	+	0.793593i	$0.291792\pi$
$98$		−	4.15596e7i		−	0.450575i
$99$	−4.87879e7	+	2.91241e7i	−0.507892	+	0.303188i
$100$	−1.46554e7			−0.146554
$101$			7.89183e7i			0.758390i	0.925317	+	0.379195i	$0.123799\pi$
$101$			7.89183e7i			0.758390i	−0.925317	+	0.379195i	$0.876201\pi$
$102$	6.41561e7	+	3.64196e7i	0.592703	+	0.336461i
$103$	−9.16877e6			−0.0814634			−0.0407317	−	0.999170i	$-0.512969\pi$
$103$	−9.16877e6			−0.0814634			−0.0407317	+	0.999170i	$0.512969\pi$
$104$		−	6.77731e7i		−	0.579328i
$105$	9.61537e6	−	1.69382e7i	0.0791059	−	0.139351i
$106$	−6.25245e7			−0.495252
$107$		−	1.58104e8i		−	1.20617i	−0.797678	−	0.603084i	$-0.793938\pi$
$107$		−	1.58104e8i		−	1.20617i	0.797678	−	0.603084i	$-0.206062\pi$
$108$	2.17978e6	+	9.96690e7i	0.0160221	+	0.732597i
$109$	6.69807e7			0.474508			0.237254	−	0.971448i	$-0.423753\pi$
$109$	6.69807e7			0.474508			0.237254	+	0.971448i	$0.423753\pi$
$110$			2.00210e7i			0.136746i
$111$	−2.59639e8	−	1.47390e8i	−1.71032	−	0.970904i
$112$	1.52072e7			0.0966443
$113$			5.15107e7i			0.315925i	0.987445	+	0.157962i	$0.0504924\pi$
$113$			5.15107e7i			0.315925i	−0.987445	+	0.157962i	$0.949508\pi$
$114$	2.35576e7	−	4.14987e7i	0.139480	−	0.245705i
$115$	−1.03140e8			−0.589705
$116$		−	5.74618e7i		−	0.317356i
$117$	−6.21211e7	−	1.04064e8i	−0.331509	−	0.555335i
$118$	−1.72198e8			−0.888179
$119$		−	9.47314e7i		−	0.472396i
$120$	7.22380e7	+	4.10075e7i	0.348370	+	0.197760i
$121$	1.39360e8			0.650122
$122$			1.68007e8i			0.758382i
$123$	2.01989e8	−	3.55820e8i	0.882485	−	1.55457i
$124$	2.61666e8			1.10678
$125$			2.18366e7i			0.0894427i
$126$	−4.00857e7	+	2.39293e7i	−0.159041	+	0.0949398i
$127$	−1.00091e8			−0.384751			−0.192376	−	0.981321i	$-0.561619\pi$
$127$	−1.00091e8			−0.384751			−0.192376	+	0.981321i	$0.561619\pi$
$128$			2.41049e8i			0.897979i
$129$	−1.00420e8	−	5.70054e7i	−0.362627	−	0.205853i
$130$	−4.27043e7			−0.149520
$131$			2.06368e8i			0.700741i	0.936611	+	0.350371i	$0.113944\pi$
$131$			2.06368e8i			0.700741i	−0.936611	+	0.350371i	$0.886056\pi$
$132$	−6.49626e7	+	1.14437e8i	−0.213977	+	0.376938i
$133$	−6.12760e7			−0.195832
$134$		−	1.13984e7i		−	0.0353528i
$135$	1.48507e8	−	3.24788e6i	0.447107	−	0.00977833i
$136$	4.04009e8			1.18096
$137$			5.13588e8i			1.45792i	0.684558	+	0.728958i	$0.259995\pi$
$137$			5.13588e8i			1.45792i	−0.684558	+	0.728958i	$0.740005\pi$
$138$	2.14991e8	+	1.22044e8i	0.592794	+	0.336513i
$139$	−4.42986e8			−1.18667			−0.593337	−	0.804955i	$-0.702190\pi$
$139$	−4.42986e8			−1.18667			−0.593337	+	0.804955i	$0.702190\pi$
$140$		−	4.51075e7i		−	0.117419i
$141$	3.11768e7	−	5.49204e7i	0.0788778	−	0.138950i
$142$	3.46724e7			0.0852768
$143$		−	1.59972e8i		−	0.382560i
$144$	5.94466e7	+	9.95833e7i	0.138254	+	0.231599i
$145$	−8.56181e7			−0.193684
$146$		−	2.13279e8i		−	0.469392i
$147$	−3.53947e8	−	2.00926e8i	−0.757999	−	0.430295i
$148$	−6.91435e8			−1.44113
$149$			6.58947e8i			1.33692i	0.743748	+	0.668460i	$0.233046\pi$
$149$			6.58947e8i			1.33692i	−0.743748	+	0.668460i	$0.766954\pi$
$150$	2.58391e7	−	4.55176e7i	0.0510401	−	0.0899113i
$151$	9.73120e8			1.87180			0.935898	−	0.352270i	$-0.114590\pi$
$151$	9.73120e8			1.87180			0.935898	+	0.352270i	$0.114590\pi$
$152$		−	2.61329e8i		−	0.489568i
$153$	6.20344e8	−	3.70317e8i	1.13205	−	0.675783i
$154$	−6.16219e7			−0.109560
$155$		−	3.89883e8i		−	0.675471i
$156$	−2.44091e8	−	1.38564e8i	−0.412148	−	0.233965i
$157$	1.40153e8			0.230677			0.115338	−	0.993326i	$-0.463205\pi$
$157$	1.40153e8			0.230677			0.115338	+	0.993326i	$0.463205\pi$
$158$			8.90496e7i			0.142891i
$159$	−3.02284e8	+	5.32497e8i	−0.472962	+	0.833160i
$160$	3.03395e8			0.462944
$161$		−	3.17451e8i		−	0.472469i
$162$	−3.13400e8	−	1.68957e8i	−0.455029	−	0.245310i
$163$	−7.69236e8			−1.08970			−0.544852	−	0.838532i	$-0.683414\pi$
$163$	−7.69236e8			−1.08970			−0.544852	+	0.838532i	$0.683414\pi$
$164$		−	9.47569e8i		−	1.30989i
$165$	1.70511e8	+	9.67942e7i	0.230047	+	0.130591i
$166$	1.35196e8			0.178046
$167$		−	1.29661e8i		−	0.166703i	−0.996520	−	0.0833513i	$-0.973438\pi$
$167$		−	1.29661e8i		−	0.166703i	0.996520	−	0.0833513i	$-0.0265623\pi$
$168$	−1.26216e8	+	2.22339e8i	−0.158444	+	0.279112i
$169$	−4.74514e8			−0.581704
$170$		−	2.54569e8i		−	0.304796i
$171$	−2.39535e8	−	4.01263e8i	−0.280146	−	0.469293i
$172$	−2.67423e8			−0.305552
$173$			1.60800e8i			0.179516i	0.995964	+	0.0897578i	$0.0286093\pi$
$173$			1.60800e8i			0.179516i	−0.995964	+	0.0897578i	$0.971391\pi$
$174$	1.78468e8	+	1.01311e8i	0.194698	+	0.110525i
$175$	−6.72102e7			−0.0716610
$176$			1.53085e8i			0.159544i
$177$	−8.32517e8	+	1.46654e9i	−0.848203	+	1.49418i
$178$	−4.94968e8			−0.493057
$179$		−	6.02527e8i		−	0.586900i	−0.955974	−	0.293450i	$-0.905197\pi$
$179$		−	6.02527e8i		−	0.586900i	0.955974	−	0.293450i	$-0.0948034\pi$
$180$	2.95384e8	−	1.76331e8i	0.281383	−	0.167972i
$181$	1.13516e9			1.05765			0.528824	−	0.848732i	$-0.322633\pi$
$181$	1.13516e9			1.05765			0.528824	+	0.848732i	$0.322633\pi$
$182$		−	1.31438e8i		−	0.119794i
$183$	1.43085e9	+	8.12254e8i	1.27582	+	0.724248i
$184$	1.35386e9			1.18114
$185$			1.03024e9i			0.879530i
$186$	−4.61345e8	+	8.12695e8i	−0.385455	+	0.679010i
$187$	9.53625e8			0.779850
$188$		−	1.46256e8i		−	0.117080i
$189$	9.99655e6	+	4.57084e8i	0.00783435	+	0.358220i
$190$	−1.64665e8			−0.126353
$191$		−	7.00191e8i		−	0.526118i	−0.964780	−	0.263059i	$-0.915269\pi$
$191$		−	7.00191e8i		−	0.526118i	0.964780	−	0.263059i	$-0.0847314\pi$
$192$	−3.13650e8	−	1.78050e8i	−0.230802	−	0.131020i
$193$	1.04738e9			0.754872			0.377436	−	0.926036i	$-0.376806\pi$
$193$	1.04738e9			0.754872			0.377436	+	0.926036i	$0.376806\pi$
$194$			8.91051e8i			0.629065i
$195$	−2.06460e8	+	3.63696e8i	−0.142790	+	0.251536i
$196$	−9.42581e8			−0.638697
$197$		−	2.30634e8i		−	0.153129i	−0.997065	−	0.0765646i	$-0.975605\pi$
$197$		−	2.30634e8i		−	0.153129i	0.997065	−	0.0765646i	$-0.0243951\pi$
$198$	−2.40887e8	−	4.03528e8i	−0.156730	−	0.262550i
$199$	−1.31166e9			−0.836389			−0.418195	−	0.908357i	$-0.637337\pi$
$199$	−1.31166e9			−0.836389			−0.418195	+	0.908357i	$0.637337\pi$
$200$		−	2.86637e8i		−	0.179148i
$201$	−9.70755e7	−	5.51070e7i	−0.0594737	−	0.0337616i
$202$	−6.52738e8			−0.392043
$203$		−	2.63521e8i		−	0.155178i
$204$	8.26006e8	−	1.45508e9i	0.476939	−	0.840166i
$205$	−1.41188e9			−0.799432
$206$		−	7.58355e7i		−	0.0421118i
$207$	2.07881e9	−	1.24095e9i	1.13223	−	0.675887i
$208$	−3.26526e8			−0.174447
$209$		−	6.16842e8i		−	0.323287i
$210$	1.40097e8	+	7.95293e7i	0.0720364	+	0.0408931i
$211$	−2.00097e9			−1.00951			−0.504756	−	0.863262i	$-0.668417\pi$
$211$	−2.00097e9			−1.00951			−0.504756	+	0.863262i	$0.668417\pi$
$212$			1.41807e9i			0.702027i
$213$	1.67629e8	−	2.95292e8i	0.0814386	−	0.143461i
$214$	1.30769e9			0.623518
$215$			3.98461e8i			0.186480i
$216$	−1.94937e9	+	4.26331e7i	−0.895527	+	0.0195854i
$217$	1.20001e9			0.541184
$218$			5.54001e8i			0.245293i
$219$	−1.81641e9	−	1.03113e9i	−0.789655	−	0.448265i
$220$	4.54080e8			0.193839
$221$			2.03406e9i			0.852697i
$222$	1.21907e9	−	2.14749e9i	0.501900	−	0.884138i
$223$	−6.09667e8			−0.246532			−0.123266	−	0.992374i	$-0.539337\pi$
$223$	−6.09667e8			−0.246532			−0.123266	+	0.992374i	$0.539337\pi$
$224$			9.33810e8i			0.370908i
$225$	−2.62733e8	−	4.40123e8i	−0.102514	−	0.171729i
$226$	−4.26048e8			−0.163314
$227$		−	3.91198e9i		−	1.47331i	−0.676270	−	0.736654i	$-0.736405\pi$
$227$		−	3.91198e9i		−	1.47331i	0.676270	−	0.736654i	$-0.263595\pi$
$228$	−9.41199e8	−	5.34293e8i	−0.348291	−	0.197715i
$229$	5.02295e8			0.182649			0.0913244	−	0.995821i	$-0.470890\pi$
$229$	5.02295e8			0.182649			0.0913244	+	0.995821i	$0.470890\pi$
$230$		−	8.53076e8i		−	0.304843i
$231$	−2.97920e8	+	5.24810e8i	−0.104629	+	0.184312i
$232$	1.12386e9			0.387937
$233$		−	3.16835e9i		−	1.07500i	−0.843263	−	0.537502i	$-0.819368\pi$
$233$		−	3.16835e9i		−	1.07500i	0.843263	−	0.537502i	$-0.180632\pi$
$234$	8.60716e8	−	5.13808e8i	0.287076	−	0.171371i
$235$	−2.17922e8			−0.0714545
$236$			3.90549e9i			1.25901i
$237$	7.58401e8	+	4.30523e8i	0.240384	+	0.136459i
$238$	7.83530e8			0.244201
$239$			4.48748e9i			1.37534i	0.726022	+	0.687672i	$0.241367\pi$
$239$			4.48748e9i			1.37534i	−0.726022	+	0.687672i	$0.758633\pi$
$240$	1.97571e8	−	3.48037e8i	0.0595496	−	0.104901i
$241$	−1.29718e9			−0.384532			−0.192266	−	0.981343i	$-0.561584\pi$
$241$	−1.29718e9			−0.384532			−0.192266	+	0.981343i	$0.561584\pi$
$242$			1.15265e9i			0.336075i
$243$	−2.95412e9	+	1.85226e9i	−0.847232	+	0.531223i
$244$	3.81044e9			1.07502
$245$			1.40445e9i			0.389799i
$246$	2.94301e9	+	1.67066e9i	0.803620	+	0.456193i
$247$	1.31571e9			0.353486
$248$			5.11778e9i			1.35293i
$249$	6.53625e8	−	1.15141e9i	0.170032	−	0.299525i
$250$	−1.80612e8			−0.0462366
$251$		−	2.67142e9i		−	0.673050i	−0.941675	−	0.336525i	$-0.890748\pi$
$251$		−	2.67142e9i		−	0.673050i	0.941675	−	0.336525i	$-0.109252\pi$
$252$	5.42723e8	+	9.09154e8i	0.134579	+	0.225442i
$253$	3.19566e9			0.779970
$254$		−	8.27858e8i		−	0.198894i
$255$	−2.16806e9	−	1.23075e9i	−0.512756	−	0.291078i
$256$	−3.13361e9			−0.729600
$257$			3.44128e9i			0.788838i	0.918931	+	0.394419i	$0.129054\pi$
$257$			3.44128e9i			0.788838i	−0.918931	+	0.394419i	$0.870946\pi$
$258$	4.71495e8	−	8.30576e8i	0.106414	−	0.187457i
$259$	−3.17094e9			−0.704675
$260$			9.68543e8i			0.211946i
$261$	1.72565e9	−	1.03014e9i	0.371871	−	0.221990i
$262$	−1.70688e9			−0.362242
$263$		−	5.78459e9i		−	1.20906i	−0.796581	−	0.604532i	$-0.793360\pi$
$263$		−	5.78459e9i		−	1.20906i	0.796581	−	0.604532i	$-0.206640\pi$
$264$	−2.23820e9	−	1.27057e9i	−0.460769	−	0.261566i
$265$	2.11292e9			0.428450
$266$		−	5.06817e8i		−	0.101234i
$267$	−2.39300e9	+	4.21545e9i	−0.470865	+	0.829467i
$268$	−2.58518e8			−0.0501131
$269$		−	7.11504e9i		−	1.35884i	−0.733749	−	0.679420i	$-0.762231\pi$
$269$		−	7.11504e9i		−	1.35884i	0.733749	−	0.679420i	$-0.237769\pi$
$270$	2.68634e7	+	1.22831e9i	0.00505482	+	0.231128i
$271$	1.82473e9			0.338314			0.169157	−	0.985589i	$-0.445895\pi$
$271$	1.82473e9			0.338314			0.169157	+	0.985589i	$0.445895\pi$
$272$		−	1.94649e9i		−	0.355612i
$273$	−1.11941e9	−	6.35457e8i	−0.201529	−	0.114402i
$274$	−4.24792e9			−0.753657
$275$		−	6.76579e8i		−	0.118301i
$276$	2.76800e9	−	4.87605e9i	0.477012	−	0.840295i
$277$	−8.53355e9			−1.44947			−0.724737	−	0.689025i	$-0.758039\pi$
$277$	−8.53355e9			−1.44947			−0.724737	+	0.689025i	$0.758039\pi$
$278$		−	3.66397e9i		−	0.613440i
$279$	4.69097e9	+	7.85819e9i	0.774187	+	1.29690i
$280$	8.82232e8			0.143533
$281$		−	5.59999e9i		−	0.898177i	−0.893487	−	0.449088i	$-0.851749\pi$
$281$		−	5.59999e9i		−	0.898177i	0.893487	−	0.449088i	$-0.148251\pi$
$282$	4.54250e8	+	2.57865e8i	0.0718288	+	0.0407752i
$283$	1.05463e10			1.64420			0.822099	−	0.569344i	$-0.192803\pi$
$283$	1.05463e10			1.64420			0.822099	+	0.569344i	$0.192803\pi$
$284$		−	7.86379e8i		−	0.120881i
$285$	−7.96096e8	+	1.40239e9i	−0.120666	+	0.212563i
$286$	1.32314e9			0.197761
$287$		−	4.34558e9i		−	0.640501i
$288$	−6.11500e9	+	3.65037e9i	−0.888847	+	0.530600i
$289$	−5.14969e9			−0.738227
$290$		−	7.08152e8i		−	0.100123i
$291$	7.58873e9	+	4.30791e9i	1.05827	+	0.600752i
$292$	−4.83721e9			−0.665370
$293$			7.76813e9i			1.05401i	0.849861	+	0.527006i	$0.176686\pi$
$293$			7.76813e9i			1.05401i	−0.849861	+	0.527006i	$0.823314\pi$
$294$	1.66187e9	−	2.92752e9i	0.222437	−	0.391841i
$295$	5.81919e9			0.768377
$296$		−	1.35234e10i		−	1.76164i
$297$	−4.60129e9	+	1.00631e8i	−0.591363	+	0.0129333i
$298$	−5.45019e9			−0.691109
$299$			6.81627e9i			0.852829i
$300$	−1.03235e9	−	5.86036e8i	−0.127451	−	0.0723501i
$301$	−1.22641e9			−0.149407
$302$			8.04874e9i			0.967609i
$303$	−3.15576e9	+	5.55912e9i	−0.374398	+	0.659531i
$304$	−1.25906e9			−0.147419
$305$		−	5.67755e9i		−	0.656088i
$306$	3.06291e9	+	5.13090e9i	0.349340	+	0.585205i
$307$	4.13874e9			0.465924			0.232962	−	0.972486i	$-0.425158\pi$
$307$	4.13874e9			0.465924			0.232962	+	0.972486i	$0.425158\pi$
$308$			1.39760e9i			0.155303i
$309$	−6.45861e8	−	3.66637e8i	−0.0708444	−	0.0402164i
$310$	3.22474e9			0.349179
$311$			1.50911e10i			1.61316i	0.591124	+	0.806581i	$0.298685\pi$
$311$			1.50911e10i			1.61316i	−0.591124	+	0.806581i	$0.701315\pi$
$312$	2.71009e9	−	4.77403e9i	0.285999	−	0.503810i
$313$	2.10030e9			0.218829			0.109414	−	0.993996i	$-0.465102\pi$
$313$	2.10030e9			0.218829			0.109414	+	0.993996i	$0.465102\pi$
$314$			1.15921e9i			0.119246i
$315$	1.35464e9	−	8.08657e8i	0.137588	−	0.0821339i
$316$	2.01967e9			0.202550
$317$			2.98247e9i			0.295351i	0.989036	+	0.147676i	$0.0471791\pi$
$317$			2.98247e9i			0.295351i	−0.989036	+	0.147676i	$0.952821\pi$
$318$	−4.40431e9	−	2.50021e9i	−0.430695	−	0.244493i
$319$	2.65277e9			0.256175
$320$			1.24455e9i			0.118690i
$321$	6.32221e9	−	1.11371e10i	0.595454	−	1.04894i
$322$	2.62566e9			0.244239
$323$			7.84321e9i			0.720583i
$324$	−3.83198e9	+	7.10798e9i	−0.347731	+	0.645010i
$325$	1.44313e9			0.129352
$326$		−	6.36239e9i		−	0.563313i
$327$	4.71821e9	+	2.67840e9i	0.412655	+	0.234253i
$328$	1.85330e10			1.60121
$329$		−	6.70735e8i		−	0.0572490i
$330$	−8.00591e8	+	1.41030e9i	−0.0675079	+	0.118921i
$331$	−7.32884e9			−0.610553			−0.305277	−	0.952264i	$-0.598749\pi$
$331$	−7.32884e9			−0.610553			−0.305277	+	0.952264i	$0.598749\pi$
$332$		−	3.06628e9i		−	0.252383i
$333$	−1.23956e10	−	2.07647e10i	−1.00807	−	1.68869i
$334$	1.07243e9			0.0861754
$335$			3.85191e8i			0.0305842i
$336$	1.07121e9	+	6.08098e8i	0.0840464	+	0.0477108i
$337$	−1.13784e10			−0.882191			−0.441095	−	0.897460i	$-0.645410\pi$
$337$	−1.13784e10			−0.882191			−0.441095	+	0.897460i	$0.645410\pi$
$338$		−	3.92473e9i		−	0.300707i
$339$	−2.05979e9	+	3.62848e9i	−0.155964	+	0.274743i
$340$	−5.77368e9			−0.432053
$341$			1.20800e10i			0.893408i
$342$	3.31887e9	−	1.98121e9i	0.242597	−	0.144819i
$343$	−9.28211e9			−0.670610
$344$		−	5.23038e9i		−	0.373507i
$345$	−7.26531e9	−	4.12432e9i	−0.512835	−	0.291122i
$346$	−1.32999e9			−0.0927990
$347$		−	3.88679e9i		−	0.268086i	−0.990976	−	0.134043i	$-0.957204\pi$
$347$		−	3.88679e9i		−	0.268086i	0.990976	−	0.134043i	$-0.0427960\pi$
$348$	2.29776e9	−	4.04769e9i	0.156671	−	0.275988i
$349$	4.13731e9			0.278879			0.139440	−	0.990231i	$-0.455470\pi$
$349$	4.13731e9			0.278879			0.139440	+	0.990231i	$0.455470\pi$
$350$		−	5.55900e8i		−	0.0370445i
$351$	−2.14645e8	−	9.81446e9i	−0.0141414	−	0.646603i
$352$	−9.40031e9			−0.612310
$353$		−	4.18048e9i		−	0.269232i	−0.990898	−	0.134616i	$-0.957020\pi$
$353$		−	4.18048e9i		−	0.269232i	0.990898	−	0.134616i	$-0.0429801\pi$
$354$	−1.21299e10	−	6.88580e9i	−0.772402	−	0.438471i
$355$	−1.17170e9			−0.0737742
$356$			1.12260e10i			0.698916i
$357$	3.78809e9	−	6.67302e9i	0.233210	−	0.410818i
$358$	4.98353e9			0.303393
$359$		−	1.48870e10i		−	0.896249i	−0.893971	−	0.448124i	$-0.852092\pi$
$359$		−	1.48870e10i		−	0.896249i	0.893971	−	0.448124i	$-0.147908\pi$
$360$	3.44875e9	+	5.77725e9i	0.205330	+	0.343962i
$361$	−1.19103e10			−0.701282
$362$			9.38894e9i			0.546742i
$363$	9.81668e9	+	5.57266e9i	0.565377	+	0.320949i
$364$	−2.98105e9			−0.169810
$365$			7.20744e9i			0.406078i
$366$	−6.71820e9	+	1.18346e10i	−0.374394	+	0.659525i
$367$	1.50821e10			0.831374			0.415687	−	0.909508i	$-0.363541\pi$
$367$	1.50821e10			0.831374			0.415687	+	0.909508i	$0.363541\pi$
$368$		−	6.52280e9i		−	0.355667i
$369$	2.84568e10	−	1.69874e10i	1.53490	−	0.916265i
$370$	−8.52116e9			−0.454665
$371$			6.50331e9i			0.343272i
$372$	1.84321e10	+	1.04634e10i	0.962506	+	0.546388i
$373$	−6.56465e9			−0.339138			−0.169569	−	0.985518i	$-0.554238\pi$
$373$	−6.56465e9			−0.339138			−0.169569	+	0.985518i	$0.554238\pi$
$374$			7.88749e9i			0.403137i
$375$	−8.73194e8	+	1.53820e9i	−0.0441556	+	0.0777836i
$376$	2.86054e9			0.143119
$377$			5.65829e9i			0.280105i
$378$	−3.78057e9	+	8.26820e7i	−0.185178	+	0.00404990i
$379$	2.75446e10			1.33499			0.667497	−	0.744612i	$-0.267366\pi$
$379$	2.75446e10			1.33499			0.667497	+	0.744612i	$0.267366\pi$
$380$			3.73464e9i			0.179108i
$381$	−7.05055e9	−	4.00240e9i	−0.334598	−	0.189942i
$382$	5.79132e9			0.271972
$383$			1.76457e10i			0.820058i	0.912073	+	0.410029i	$0.134481\pi$
$383$			1.76457e10i			0.820058i	−0.912073	+	0.410029i	$0.865519\pi$
$384$	−9.63899e9	+	1.69798e10i	−0.443309	+	0.780924i
$385$	2.08242e9			0.0947821
$386$			8.66290e9i			0.390224i
$387$	−4.79418e9	−	8.03108e9i	−0.213733	−	0.358039i
$388$	2.02092e10			0.891709
$389$			1.70171e9i			0.0743167i	0.999309	+	0.0371583i	$0.0118306\pi$
$389$			1.70171e9i			0.0743167i	−0.999309	+	0.0371583i	$0.988169\pi$
$390$	−3.00815e9	−	1.70764e9i	−0.130029	−	0.0738140i
$391$	−4.06331e10			−1.73849
$392$		−	1.84354e10i		−	0.780744i
$393$	−8.25218e9	+	1.45369e10i	−0.345938	+	0.609397i
$394$	1.90759e9			0.0791588
$395$		−	3.00930e9i		−	0.123617i
$396$	−9.15211e9	+	5.46338e9i	−0.372169	+	0.222168i
$397$	3.12255e10			1.25703			0.628517	−	0.777796i	$-0.283662\pi$
$397$	3.12255e10			1.25703			0.628517	+	0.777796i	$0.283662\pi$
$398$		−	1.08488e10i		−	0.432364i
$399$	−4.31637e9	−	2.45028e9i	−0.170305	−	0.0966773i
$400$	−1.38100e9			−0.0539452
$401$		−	1.81268e10i		−	0.701041i	−0.936555	−	0.350521i	$-0.886005\pi$
$401$		−	1.81268e10i		−	0.701041i	0.936555	−	0.350521i	$-0.113995\pi$
$402$	4.55794e8	−	8.02917e8i	0.0174528	−	0.0307444i
$403$	−2.57664e10			−0.976863
$404$			1.48043e10i			0.555726i
$405$	1.05909e10	+	5.70965e9i	0.393652	+	0.212221i
$406$	2.17960e9			0.0802182
$407$		−	3.19206e10i		−	1.16331i
$408$	2.84590e10	+	1.61554e10i	1.02702	+	0.583011i
$409$	−1.54793e10			−0.553171			−0.276585	−	0.960989i	$-0.589203\pi$
$409$	−1.54793e10			−0.553171			−0.276585	+	0.960989i	$0.589203\pi$
$410$		−	1.16777e10i		−	0.413260i
$411$	−2.05372e10	+	3.61778e10i	−0.719736	+	1.26787i
$412$	−1.71997e9			−0.0596941
$413$			1.79107e10i			0.615620i
$414$	1.02640e10	+	1.71940e10i	0.349394	+	0.585295i
$415$	−4.56876e9			−0.154030
$416$		−	2.00506e10i		−	0.669507i
$417$	−3.12046e10	−	1.77140e10i	−1.03199	−	0.585830i
$418$	5.10194e9			0.167121
$419$		−	3.93876e10i		−	1.27792i	−0.769240	−	0.638960i	$-0.779365\pi$
$419$		−	3.93876e10i		−	1.27792i	0.769240	−	0.638960i	$-0.220635\pi$
$420$	1.80374e9	−	3.17744e9i	0.0579665	−	0.102113i
$421$	4.76055e10			1.51540			0.757702	−	0.652601i	$-0.226322\pi$
$421$	4.76055e10			1.51540			0.757702	+	0.652601i	$0.226322\pi$
$422$		−	1.65502e10i		−	0.521858i
$423$	4.39227e9	−	2.62198e9i	0.137192	−	0.0818971i
$424$	−2.77352e10			−0.858159
$425$			8.60278e9i			0.263684i
$426$	2.44237e9	+	1.38647e9i	0.0741607	+	0.0420990i
$427$	1.74748e10			0.525654
$428$		−	2.96587e10i		−	0.883846i
$429$	6.39690e9	−	1.12686e10i	0.188860	−	0.332692i
$430$	−3.29569e9			−0.0963991
$431$		−	3.36447e10i		−	0.975007i	−0.873121	−	0.487503i	$-0.837908\pi$
$431$		−	3.36447e10i		−	0.975007i	0.873121	−	0.487503i	$-0.162092\pi$
$432$	2.05403e8	+	9.39192e9i	0.00589756	+	0.269662i
$433$	−4.21393e10			−1.19877			−0.599384	−	0.800461i	$-0.704588\pi$
$433$	−4.21393e10			−1.19877			−0.599384	+	0.800461i	$0.704588\pi$
$434$			9.92533e9i			0.279760i
$435$	−6.03106e9	−	3.42366e9i	−0.168437	−	0.0956168i
$436$	1.25649e10			0.347706
$437$			2.62831e10i			0.720694i
$438$	8.52850e9	−	1.50236e10i	0.231727	−	0.408205i
$439$	−1.50964e10			−0.406458			−0.203229	−	0.979131i	$-0.565144\pi$
$439$	−1.50964e10			−0.406458			−0.203229	+	0.979131i	$0.565144\pi$
$440$			8.88109e9i			0.236949i
$441$	−1.68980e10	−	2.83070e10i	−0.446766	−	0.748410i
$442$	−1.68238e10			−0.440794
$443$		−	2.67455e10i		−	0.694442i	−0.937783	−	0.347221i	$-0.887125\pi$
$443$		−	2.67455e10i		−	0.694442i	0.937783	−	0.347221i	$-0.112875\pi$
$444$	−4.87056e10	−	2.76488e10i	−1.25328	−	0.711451i
$445$	1.67267e10			0.426551
$446$		−	5.04259e9i		−	0.127443i
$447$	−2.63497e10	+	4.64172e10i	−0.660003	+	1.16265i
$448$	−3.83056e9			−0.0950934
$449$			7.24234e10i			1.78194i	0.454061	+	0.890970i	$0.349975\pi$
$449$			7.24234e10i			1.78194i	−0.454061	+	0.890970i	$0.650025\pi$
$450$	3.64028e9	−	2.17308e9i	0.0887738	−	0.0529938i
$451$	4.37452e10			1.05736
$452$			9.66286e9i			0.231501i
$453$	6.85479e10	+	3.89128e10i	1.62780	+	0.924058i
$454$	3.23562e10			0.761613
$455$			4.44176e9i			0.103636i
$456$	1.04499e10	−	1.84084e10i	0.241687	−	0.425751i
$457$	1.17186e10			0.268665			0.134332	−	0.990936i	$-0.457111\pi$
$457$	1.17186e10			0.268665			0.134332	+	0.990936i	$0.457111\pi$
$458$			4.15451e9i			0.0944187i
$459$	5.85060e10	−	1.27954e9i	1.31810	−	0.0288272i
$460$	−1.93480e10			−0.432119
$461$			8.60209e10i			1.90458i	0.305189	+	0.952292i	$0.401280\pi$
$461$			8.60209e10i			1.90458i	−0.305189	+	0.952292i	$0.598720\pi$
$462$	−4.34073e9	−	2.46411e9i	−0.0952786	−	0.0540870i
$463$	−3.65148e10			−0.794594			−0.397297	−	0.917690i	$-0.630052\pi$
$463$	−3.65148e10			−0.794594			−0.397297	+	0.917690i	$0.630052\pi$
$464$		−	5.41469e9i		−	0.116816i
$465$	1.55905e10	−	2.74639e10i	0.333463	−	0.587422i
$466$	2.62056e10			0.555714
$467$			8.61531e10i			1.81135i	0.423969	+	0.905677i	$0.360637\pi$
$467$			8.61531e10i			1.81135i	−0.423969	+	0.905677i	$0.639363\pi$
$468$	−1.16533e10	−	1.95212e10i	−0.242921	−	0.406934i
$469$	−1.18557e9			−0.0245039
$470$		−	1.80245e9i		−	0.0369378i
$471$	9.87257e9	+	5.60438e9i	0.200607	+	0.113879i
$472$	−7.63853e10			−1.53901
$473$		−	1.23458e10i		−	0.246646i
$474$	−3.56088e9	+	6.27278e9i	−0.0705415	+	0.124264i
$475$	5.56461e9			0.109310
$476$		−	1.77706e10i		−	0.346159i
$477$	−4.25865e10	+	2.54222e10i	−0.822619	+	0.491066i
$478$	−3.71162e10			−0.710972
$479$		−	4.44469e10i		−	0.844306i	−0.906525	−	0.422153i	$-0.861275\pi$
$479$		−	4.44469e10i		−	0.844306i	0.906525	−	0.422153i	$-0.138725\pi$
$480$	2.13716e10	+	1.21320e10i	0.402598	+	0.228543i
$481$	6.80860e10			1.27197
$482$		−	1.07291e10i		−	0.198781i
$483$	1.26941e10	−	2.23617e10i	0.233246	−	0.410881i
$484$	2.61424e10			0.476391
$485$		−	3.01118e10i		−	0.544214i
$486$	−1.53202e10	−	2.44337e10i	−0.274611	−	0.437969i
$487$	4.69494e9			0.0834668			0.0417334	−	0.999129i	$-0.486712\pi$
$487$	4.69494e9			0.0834668			0.0417334	+	0.999129i	$0.486712\pi$
$488$			7.45262e10i			1.31410i
$489$	−5.41860e10	−	3.07599e10i	−0.947658	−	0.537959i
$490$	−1.16163e10			−0.201503
$491$		−	5.52069e10i		−	0.949876i	−0.880019	−	0.474938i	$-0.842470\pi$
$491$		−	5.52069e10i		−	0.949876i	0.880019	−	0.474938i	$-0.157530\pi$
$492$	3.78910e10	−	6.67481e10i	0.646660	−	1.13914i
$493$	−3.37302e10			−0.570994
$494$			1.08823e10i			0.182732i
$495$	8.14044e9	+	1.36366e10i	0.135590	+	0.227136i
$496$	2.46571e10			0.407394
$497$		−	3.60635e9i		−	0.0591075i
$498$	9.52341e9	+	5.40617e9i	0.154837	+	0.0878967i
$499$	−1.49484e10			−0.241097			−0.120548	−	0.992707i	$-0.538465\pi$
$499$	−1.49484e10			−0.241097			−0.120548	+	0.992707i	$0.538465\pi$
$500$			4.09632e9i			0.0655411i
$501$	5.18482e9	−	9.13347e9i	0.0822968	−	0.144972i
$502$	2.20955e10			0.347927
$503$		−	4.72327e10i		−	0.737854i	−0.929458	−	0.368927i	$-0.879725\pi$
$503$		−	4.72327e10i		−	0.737854i	0.929458	−	0.368927i	$-0.120275\pi$
$504$	−1.77816e10	+	1.06148e10i	−0.275581	+	0.164509i
$505$	2.20583e10			0.339162
$506$			2.64315e10i			0.403199i
$507$	−3.34254e10	−	1.89747e10i	−0.505877	−	0.287172i
$508$	−1.87760e10			−0.281935
$509$			5.95408e10i			0.887041i	0.896264	+	0.443520i	$0.146271\pi$
$509$			5.95408e10i			0.887041i	−0.896264	+	0.443520i	$0.853729\pi$
$510$	1.01796e10	−	1.79322e10i	0.150470	−	0.265065i
$511$	−2.21836e10			−0.325348
$512$			3.57904e10i			0.520818i
$513$	−8.27656e8	−	3.78439e10i	−0.0119503	−	0.546420i
$514$	−2.84630e10			−0.407783
$515$			2.56275e9i			0.0364315i
$516$	−1.88377e10	−	1.06936e10i	−0.265722	−	0.150843i
$517$	6.75204e9			0.0945089
$518$		−	2.62270e10i		−	0.364276i
$519$	−6.43002e9	+	1.13270e10i	−0.0886222	+	0.156115i
$520$	−1.89432e10			−0.259083
$521$		−	5.61267e10i		−	0.761761i	−0.924624	−	0.380880i	$-0.875621\pi$
$521$		−	5.61267e10i		−	0.761761i	0.924624	−	0.380880i	$-0.124379\pi$
$522$	8.52032e9	+	1.42730e10i	0.114756	+	0.192235i
$523$	3.49100e10			0.466599			0.233299	−	0.972405i	$-0.425048\pi$
$523$	3.49100e10			0.466599			0.233299	+	0.972405i	$0.425048\pi$
$524$			3.87125e10i			0.513483i
$525$	−4.73438e9	−	2.68758e9i	−0.0623198	−	0.0353772i
$526$	4.78447e10			0.625015
$527$		−	1.53599e11i		−	1.99134i
$528$	−6.12149e9	+	1.07835e10i	−0.0787629	+	0.138747i
$529$	−5.78531e10			−0.738762
$530$			1.74761e10i			0.221484i
$531$	−1.17287e11	+	7.00151e10i	−1.47527	+	0.880671i
$532$	−1.14947e10			−0.143500
$533$			9.33076e10i			1.15613i
$534$	−3.48663e10	−	1.97926e10i	−0.428786	−	0.243410i
$535$	−4.41914e10			−0.539415
$536$		−	5.05620e9i		−	0.0612583i
$537$	2.40936e10	−	4.24428e10i	0.289738	−	0.510396i
$538$	5.88489e10			0.702441
$539$		−	4.35150e10i		−	0.515566i
$540$	2.78583e10	−	6.09268e8i	0.327627	−	0.00716528i
$541$	−3.13461e10			−0.365927			−0.182963	−	0.983120i	$-0.558569\pi$
$541$	−3.13461e10			−0.365927			−0.182963	+	0.983120i	$0.558569\pi$
$542$			1.50924e10i			0.174889i
$543$	7.99619e10	+	4.53922e10i	0.919780	+	0.522133i
$544$	1.19526e11			1.36479
$545$		−	1.87217e10i		−	0.212206i
$546$	5.25590e9	−	9.25869e9i	0.0591394	−	0.104179i
$547$	5.00255e10			0.558781			0.279391	−	0.960178i	$-0.409868\pi$
$547$	5.00255e10			0.558781			0.279391	+	0.960178i	$0.409868\pi$
$548$			9.63437e10i			1.06832i
$549$	6.83110e10	+	1.14433e11i	0.751971	+	1.25968i
$550$	5.59603e9			0.0611546
$551$			2.18180e10i			0.236706i
$552$	9.53678e10	+	5.41377e10i	1.02718	+	0.583100i
$553$	9.26224e9			0.0990412
$554$		−	7.05815e10i		−	0.749293i
$555$	−4.11968e10	+	7.25714e10i	−0.434201	+	0.764881i
$556$	−8.30996e10			−0.869560
$557$			6.39723e10i			0.664617i	0.943171	+	0.332309i	$0.107828\pi$
$557$			6.39723e10i			0.664617i	−0.943171	+	0.332309i	$0.892172\pi$
$558$	−6.49955e10	+	3.87993e10i	−0.670420	+	0.400209i
$559$	2.63333e10			0.269686
$560$		−	4.25053e9i		−	0.0432206i
$561$	6.71747e10	+	3.81332e10i	0.678194	+	0.384992i
$562$	4.63178e10			0.464305
$563$		−	1.47936e11i		−	1.47245i	−0.676736	−	0.736225i	$-0.736606\pi$
$563$		−	1.47936e11i		−	1.47245i	0.676736	−	0.736225i	$-0.263394\pi$
$564$	5.84844e9	−	1.03025e10i	0.0577995	−	0.101818i
$565$	1.43977e10			0.141286
$566$			8.72290e10i			0.849954i
$567$	−1.75736e10	+	3.25974e10i	−0.170031	+	0.315392i
$568$	1.53803e10			0.147765
$569$		−	1.24543e11i		−	1.18815i	−0.804410	−	0.594075i	$-0.797518\pi$
$569$		−	1.24543e11i		−	1.18815i	0.804410	−	0.594075i	$-0.202482\pi$
$570$	−1.15992e10	−	6.58456e9i	−0.109883	−	0.0623774i
$571$	−1.25257e11			−1.17830			−0.589151	−	0.808023i	$-0.700538\pi$
$571$	−1.25257e11			−1.17830			−0.589151	+	0.808023i	$0.700538\pi$
$572$		−	3.00091e10i		−	0.280329i
$573$	2.79990e10	−	4.93224e10i	0.259731	−	0.457537i
$574$	3.59425e10			0.331101
$575$			2.88285e10i			0.263724i
$576$	−1.49741e10	−	2.50842e10i	−0.136035	−	0.227883i
$577$	1.59567e10			0.143959			0.0719797	−	0.997406i	$-0.477068\pi$
$577$	1.59567e10			0.143959			0.0719797	+	0.997406i	$0.477068\pi$
$578$		−	4.25934e10i		−	0.381620i
$579$	7.37786e10	+	4.18820e10i	0.656472	+	0.372661i
$580$	−1.60611e10			−0.141926
$581$		−	1.40620e10i		−	0.123408i
$582$	−3.56310e10	+	6.27669e10i	−0.310553	+	0.547065i
$583$	−6.54663e10			−0.566687
$584$		−	9.46081e10i		−	0.813349i
$585$	−2.90866e10	+	1.73634e10i	−0.248353	+	0.148256i
$586$	−6.42506e10			−0.544863
$587$		−	8.97851e10i		−	0.756226i	−0.925759	−	0.378113i	$-0.876573\pi$
$587$		−	8.97851e10i		−	0.756226i	0.925759	−	0.378113i	$-0.123427\pi$
$588$	−6.63967e10	−	3.76916e10i	−0.555440	−	0.315308i
$589$	−9.93536e10			−0.825510
$590$			4.81309e10i			0.397206i
$591$	9.22250e9	−	1.62462e10i	0.0755960	−	0.133168i
$592$	−6.51547e10			−0.530467
$593$			4.22870e10i			0.341970i	0.985274	+	0.170985i	$0.0546950\pi$
$593$			4.22870e10i			0.341970i	−0.985274	+	0.170985i	$0.945305\pi$
$594$	−8.32328e8	−	3.80576e10i	−0.00668573	−	0.305700i
$595$	−2.64782e10			−0.211262
$596$			1.23612e11i			0.979657i
$597$	−9.23951e10	−	5.24501e10i	−0.727363	−	0.412904i
$598$	−5.63777e10			−0.440862
$599$		−	7.21992e10i		−	0.560822i	−0.959880	−	0.280411i	$-0.909529\pi$
$599$		−	7.21992e10i		−	0.560822i	0.959880	−	0.280411i	$-0.0904707\pi$
$600$	1.14619e10	−	2.01911e10i	0.0884409	−	0.155796i
$601$	−6.40453e10			−0.490896			−0.245448	−	0.969410i	$-0.578935\pi$
$601$	−6.40453e10			−0.490896			−0.245448	+	0.969410i	$0.578935\pi$
$602$		−	1.01437e10i		−	0.0772344i
$603$	−4.63453e9	−	7.76363e9i	−0.0350539	−	0.0587213i
$604$	1.82547e11			1.37160
$605$		−	3.89522e10i		−	0.290744i
$606$	−4.59798e10	−	2.61015e10i	−0.340939	−	0.193542i
$607$	2.21809e11			1.63390			0.816949	−	0.576711i	$-0.195664\pi$
$607$	2.21809e11			1.63390			0.816949	+	0.576711i	$0.195664\pi$
$608$		−	7.73140e10i		−	0.565775i
$609$	1.05376e10	−	1.85628e10i	0.0766076	−	0.134950i
$610$	4.69594e10			0.339159
$611$			1.44019e10i			0.103337i
$612$	1.16370e11	−	6.94675e10i	0.829536	−	0.495195i
$613$	1.52452e11			1.07967			0.539835	−	0.841771i	$-0.318487\pi$
$613$	1.52452e11			1.07967			0.539835	+	0.841771i	$0.318487\pi$
$614$			3.42318e10i			0.240855i
$615$	−9.94546e10	−	5.64576e10i	−0.695224	−	0.394659i
$616$	−2.73348e10			−0.189843
$617$		−	8.38162e9i		−	0.0578345i	−0.999582	−	0.0289173i	$-0.990794\pi$
$617$		−	8.38162e9i		−	0.0578345i	0.999582	−	0.0289173i	$-0.00920593\pi$
$618$	3.03248e9	−	5.34196e9i	0.0207895	−	0.0366224i
$619$	−1.86669e11			−1.27148			−0.635741	−	0.771902i	$-0.719305\pi$
$619$	−1.86669e11			−1.27148			−0.635741	+	0.771902i	$0.719305\pi$
$620$		−	7.31379e10i		−	0.494966i
$621$	1.96057e11	−	4.28782e9i	1.31831	−	0.0288317i
$622$	−1.24819e11			−0.833910
$623$			5.14827e10i			0.341751i
$624$	−2.30010e10	−	1.30570e10i	−0.151708	−	0.0861203i
$625$	6.10352e9			0.0400000
$626$			1.73717e10i			0.113122i
$627$	2.46660e10	−	4.34512e10i	0.159599	−	0.281146i
$628$	2.62912e10			0.169033
$629$			4.05874e11i			2.59292i
$630$	6.68845e9	+	1.12043e10i	0.0424584	+	0.0711251i
$631$	1.95553e10			0.123352			0.0616761	−	0.998096i	$-0.480355\pi$
$631$	1.95553e10			0.123352			0.0616761	+	0.998096i	$0.480355\pi$
$632$			3.95015e10i			0.247597i
$633$	−1.40951e11	−	8.00142e10i	−0.877919	−	0.498370i
$634$	−2.46682e10			−0.152679
$635$			2.79763e10i			0.172066i
$636$	−5.67052e10	+	9.98908e10i	−0.346573	+	0.610516i
$637$	9.28165e10			0.563725
$638$			2.19412e10i			0.132427i
$639$	2.36160e10	−	1.40977e10i	0.141646	−	0.0845559i
$640$	6.73753e10			0.401588
$641$		−	1.22798e11i		−	0.727373i	−0.931521	−	0.363687i	$-0.881518\pi$
$641$		−	1.22798e11i		−	0.727373i	0.931521	−	0.363687i	$-0.118482\pi$
$642$	9.21154e10	+	5.22914e10i	0.542241	+	0.307815i
$643$	2.19260e11			1.28267			0.641337	−	0.767259i	$-0.278380\pi$
$643$	2.19260e11			1.28267			0.641337	+	0.767259i	$0.278380\pi$
$644$		−	5.95505e10i		−	0.346212i
$645$	−1.59335e10	+	2.80681e10i	−0.0920603	+	0.162172i
$646$	−6.48717e10			−0.372499
$647$			2.09093e11i			1.19322i	0.802530	+	0.596611i	$0.203487\pi$
$647$			2.09093e11i			1.19322i	−0.802530	+	0.596611i	$0.796513\pi$
$648$	−1.39021e11	−	7.49474e10i	−0.788461	−	0.425066i
$649$	−1.80300e11			−1.01629
$650$			1.19362e10i			0.0668672i
$651$	8.45302e10	+	4.79855e10i	0.470639	+	0.267169i
$652$	−1.44301e11			−0.798505
$653$			1.89323e11i			1.04124i	0.853788	+	0.520621i	$0.174300\pi$
$653$			1.89323e11i			1.04124i	−0.853788	+	0.520621i	$0.825700\pi$
$654$	−2.21532e10	+	3.90246e10i	−0.121095	+	0.213318i
$655$	5.76817e10			0.313381
$656$		−	8.92905e10i		−	0.482158i
$657$	−8.67182e10	−	1.45268e11i	−0.465424	−	0.779665i
$658$	5.54769e9			0.0295943
$659$			1.58406e11i			0.839904i	0.907546	+	0.419952i	$0.137953\pi$
$659$			1.58406e11i			0.839904i	−0.907546	+	0.419952i	$0.862047\pi$
$660$	3.19860e10	+	1.81576e10i	0.168572	+	0.0956935i
$661$	3.37961e11			1.77036			0.885178	−	0.465252i	$-0.154036\pi$
$661$	3.37961e11			1.77036			0.885178	+	0.465252i	$0.154036\pi$
$662$		−	6.06173e10i		−	0.315620i
$663$	−8.13373e10	+	1.43282e11i	−0.420955	+	0.741546i
$664$	5.99716e10			0.308513
$665$			1.71272e10i			0.0875787i
$666$	1.71746e11	−	1.02525e11i	0.872952	−	0.521112i
$667$	−1.13032e11			−0.571082
$668$		−	2.43230e10i		−	0.122155i
$669$	−4.29458e10	−	2.43791e10i	−0.214396	−	0.121707i
$670$	−3.18594e9			−0.0158102
$671$			1.75912e11i			0.867771i
$672$	−3.73408e10	+	6.57789e10i	−0.183108	+	0.322559i
$673$	3.10614e10			0.151412			0.0757061	−	0.997130i	$-0.475879\pi$
$673$	3.10614e10			0.151412			0.0757061	+	0.997130i	$0.475879\pi$
$674$		−	9.41116e10i		−	0.456041i
$675$	−9.07810e8	−	4.15089e10i	−0.00437300	−	0.199952i
$676$	−8.90139e10			−0.426256
$677$			5.35620e10i			0.254978i	0.991840	+	0.127489i	$0.0406917\pi$
$677$			5.35620e10i			0.254978i	−0.991840	+	0.127489i	$0.959308\pi$
$678$	−3.00114e10	−	1.70366e10i	−0.142026	−	0.0806242i
$679$	9.26801e10			0.436021
$680$		−	1.12924e11i		−	0.528142i
$681$	1.56431e11	−	2.75565e11i	0.727334	−	1.28126i
$682$	−9.99145e10			−0.461840
$683$			1.38214e10i			0.0635139i	0.999496	+	0.0317570i	$0.0101103\pi$
$683$			1.38214e10i			0.0635139i	−0.999496	+	0.0317570i	$0.989890\pi$
$684$	−4.49343e10	−	7.52727e10i	−0.205283	−	0.343885i
$685$	1.43552e11			0.652000
$686$		−	7.67729e10i		−	0.346666i
$687$	3.53823e10	+	2.00856e10i	0.158840	+	0.0901690i
$688$	−2.51996e10			−0.112471
$689$		−	1.39638e11i		−	0.619622i
$690$	3.41125e10	−	6.00918e10i	0.150493	−	0.265106i
$691$	−2.88658e11			−1.26611			−0.633054	−	0.774107i	$-0.718199\pi$
$691$	−2.88658e11			−1.26611			−0.633054	+	0.774107i	$0.718199\pi$
$692$			3.01644e10i			0.131544i
$693$	−4.19718e10	+	2.50552e10i	−0.181980	+	0.108634i
$694$	3.21479e10			0.138584
$695$			1.23818e11i			0.530696i
$696$	7.91664e10	+	4.49406e10i	0.337368	+	0.191514i
$697$	−5.56226e11			−2.35678
$698$			3.42199e10i			0.144164i
$699$	1.26695e11	−	2.23183e11i	0.530702	−	0.934873i
$700$	−1.26079e10			−0.0525112
$701$		−	4.28713e11i		−	1.77539i	−0.460429	−	0.887696i	$-0.652305\pi$
$701$		−	4.28713e11i		−	1.77539i	0.460429	−	0.887696i	$-0.347695\pi$
$702$	8.11760e10	−	1.77534e9i	0.334256	−	0.00731026i
$703$	2.62535e11			1.07490
$704$		−	3.85608e10i		−	0.156984i
$705$	−1.53507e10	−	8.71418e9i	−0.0621402	−	0.0352752i
$706$	3.45770e10			0.139177
$707$			6.78927e10i			0.271735i
$708$	−1.56171e11	+	2.75108e11i	−0.621539	+	1.09489i
$709$	−1.93857e11			−0.767179			−0.383589	−	0.923504i	$-0.625312\pi$
$709$	−1.93857e11			−0.767179			−0.383589	+	0.923504i	$0.625312\pi$
$710$		−	9.69124e9i		−	0.0381370i
$711$	3.62072e10	+	6.06533e10i	0.141683	+	0.237343i
$712$	−2.19563e11			−0.854356
$713$		−	5.14719e11i		−	1.99165i
$714$	5.51929e10	+	3.13315e10i	0.212369	+	0.120556i
$715$	−4.47135e10			−0.171086
$716$		−	1.13028e11i		−	0.430064i
$717$	−1.79444e11	+	3.16105e11i	−0.678972	+	1.19606i
$718$	1.23131e11			0.463308
$719$			9.46617e10i			0.354208i	0.984192	+	0.177104i	$0.0566730\pi$
$719$			9.46617e10i			0.354208i	−0.984192	+	0.177104i	$0.943327\pi$
$720$	2.78344e10	−	1.66158e10i	0.103574	−	0.0618290i
$721$	−7.88781e9			−0.0291887
$722$		−	9.85105e10i		−	0.362522i
$723$	−9.13753e10	−	5.18712e10i	−0.334407	−	0.189834i
$724$	2.12943e11			0.775014
$725$			2.39310e10i			0.0866181i
$726$	−4.60918e10	+	8.11943e10i	−0.165912	+	0.292267i
$727$	3.90262e11			1.39707			0.698536	−	0.715575i	$-0.253835\pi$
$727$	3.90262e11			1.39707			0.698536	+	0.715575i	$0.253835\pi$
$728$		−	5.83046e10i		−	0.207576i
$729$	−2.82159e11	+	1.23477e10i	−0.999044	+	0.0437196i
$730$	−5.96132e10			−0.209919
$731$			1.56978e11i			0.549756i
$732$	2.68413e11	+	1.52370e11i	0.934886	+	0.530709i
$733$	−2.42553e11			−0.840215			−0.420108	−	0.907474i	$-0.638008\pi$
$733$	−2.42553e11			−0.840215			−0.420108	+	0.907474i	$0.638008\pi$
$734$			1.24745e11i			0.429771i
$735$	−5.61605e10	+	9.89312e10i	−0.192434	+	0.338988i
$736$	4.00539e11			1.36500
$737$		−	1.19347e10i		−	0.0404520i
$738$	1.40504e11	+	2.35368e11i	0.473655	+	0.793453i
$739$	4.33550e9			0.0145365			0.00726827	−	0.999974i	$-0.497686\pi$
$739$	4.33550e9			0.0145365			0.00726827	+	0.999974i	$0.497686\pi$
$740$			1.93262e11i			0.644495i
$741$	9.26804e10	+	5.26121e10i	0.307408	+	0.174507i
$742$	−5.37892e10			−0.177452
$743$			1.85138e11i			0.607493i	0.952753	+	0.303746i	$0.0982376\pi$
$743$			1.85138e11i			0.607493i	−0.952753	+	0.303746i	$0.901762\pi$
$744$	−2.04648e11	+	3.60503e11i	−0.667906	+	1.17657i
$745$	1.84181e11			0.597889
$746$		−	5.42966e10i		−	0.175314i
$747$	9.20845e10	−	5.49702e10i	0.295736	−	0.176541i
$748$	1.78890e11			0.571452
$749$		−	1.36015e11i		−	0.432176i
$750$	−1.27225e10	−	7.22224e9i	−0.0402095	−	0.0228258i
$751$	−1.76039e11			−0.553414			−0.276707	−	0.960954i	$-0.589243\pi$
$751$	−1.76039e11			−0.553414			−0.276707	+	0.960954i	$0.589243\pi$
$752$		−	1.37819e10i		−	0.0430961i
$753$	1.06824e11	−	1.88178e11i	0.332267	−	0.585315i
$754$	−4.68001e10			−0.144798
$755$		−	2.71995e11i		−	0.837093i
$756$	1.87525e9	+	8.57443e10i	0.00574079	+	0.262493i
$757$	1.04686e11			0.318789			0.159395	−	0.987215i	$-0.449046\pi$
$757$	1.04686e11			0.318789			0.159395	+	0.987215i	$0.449046\pi$
$758$			2.27823e11i			0.690114i
$759$	2.25107e11	+	1.27787e11i	0.678299	+	0.385051i
$760$	−7.30437e10			−0.218942
$761$			1.31591e11i			0.392362i	0.980568	+	0.196181i	$0.0628541\pi$
$761$			1.31591e11i			0.392362i	−0.980568	+	0.196181i	$0.937146\pi$
$762$	3.31041e10	−	5.83155e10i	0.0981887	−	0.172967i
$763$	5.76229e10			0.170019
$764$		−	1.31349e11i		−	0.385524i
$765$	−1.03507e11	−	1.73391e11i	−0.302219	−	0.506269i
$766$	−1.45949e11			−0.423922
$767$		−	3.84576e11i		−	1.11122i
$768$	−2.20736e11	−	1.25306e11i	−0.634494	−	0.360185i
$769$	−2.25269e9			−0.00644165			−0.00322082	−	0.999995i	$-0.501025\pi$
$769$	−2.25269e9			−0.00644165			−0.00322082	+	0.999995i	$0.501025\pi$
$770$			1.72239e10i			0.0489968i
$771$	−1.37609e11	+	2.42409e11i	−0.389429	+	0.686010i
$772$	1.96477e11			0.553149
$773$		−	1.83457e11i		−	0.513825i	−0.966435	−	0.256913i	$-0.917295\pi$
$773$		−	1.83457e11i		−	0.513825i	0.966435	−	0.256913i	$-0.0827052\pi$
$774$	6.64256e10	−	3.96530e10i	0.185085	−	0.110487i
$775$	−1.08975e11			−0.302080
$776$			3.95261e11i			1.09003i
$777$	−2.23365e11	−	1.26798e11i	−0.612818	−	0.347880i
$778$	−1.40749e10			−0.0384174
$779$			3.59788e11i			0.977006i
$780$	−3.87297e10	+	6.82255e10i	−0.104632	+	0.184318i
$781$	3.63038e10			0.0975771
$782$		−	3.36079e11i		−	0.898699i
$783$	1.62750e11	−	3.55939e9i	0.432987	−	0.00946952i
$784$	−8.88205e10			−0.235098
$785$		−	3.91739e10i		−	0.103162i
$786$	−1.20235e11	−	6.82542e10i	−0.315023	−	0.178830i
$787$	5.90552e11			1.53943			0.769714	−	0.638389i	$-0.220399\pi$
$787$	5.90552e11			1.53943			0.769714	+	0.638389i	$0.220399\pi$
$788$		−	4.32645e10i		−	0.112209i
$789$	2.31312e11	−	4.07474e11i	0.596884	−	1.05146i
$790$	2.48901e10			0.0639026
$791$			4.43141e10i			0.113197i
$792$	−1.06855e11	−	1.79001e11i	−0.271578	−	0.454940i
$793$	−3.75216e11			−0.948830
$794$			2.58268e11i			0.649813i
$795$	1.48837e11	+	8.44908e10i	0.372600	+	0.211515i
$796$	−2.46053e11			−0.612882
$797$			5.88219e11i			1.45783i	0.684606	+	0.728914i	$0.259974\pi$
$797$			5.88219e11i			1.45783i	−0.684606	+	0.728914i	$0.740026\pi$
$798$	2.02664e10	−	3.57009e10i	0.0499765	−	0.0880375i
$799$	−8.58529e10			−0.210653
$800$		−	8.48014e10i		−	0.207035i
$801$	−3.37132e11	+	2.01252e11i	−0.818973	+	0.488889i
$802$	1.49928e11			0.362397
$803$		−	2.23313e11i		−	0.537097i
$804$	−1.82103e10	−	1.03375e10i	−0.0435807	−	0.0247395i
$805$	−8.87302e10			−0.211294
$806$		−	2.13116e11i		−	0.504981i
$807$	2.84514e11	−	5.01194e11i	0.670825	−	1.18171i
$808$	−2.89548e11			−0.679321
$809$		−	5.05936e11i		−	1.18114i	−0.806987	−	0.590570i	$-0.798903\pi$
$809$		−	5.05936e11i		−	1.18114i	0.806987	−	0.590570i	$-0.201097\pi$
$810$	−4.72248e10	+	8.75980e10i	−0.109706	+	0.203495i
$811$	−5.19700e11			−1.20135			−0.600674	−	0.799494i	$-0.705101\pi$
$811$	−5.19700e11			−1.20135			−0.600674	+	0.799494i	$0.705101\pi$
$812$		−	4.94338e10i		−	0.113710i
$813$	1.28536e11	+	7.29664e10i	0.294214	+	0.167017i
$814$	2.64017e11			0.601361
$815$			2.15008e11i			0.487331i
$816$	7.78355e10	−	1.37113e11i	0.175556	−	0.309257i
$817$	1.01540e11			0.227902
$818$		−	1.28030e11i		−	0.285957i
$819$	−5.34422e10	−	8.95249e10i	−0.118782	−	0.198979i
$820$	−2.64854e11			−0.585801
$821$			1.31370e11i			0.289150i	0.989494	+	0.144575i	$0.0461815\pi$
$821$			1.31370e11i			0.289150i	−0.989494	+	0.144575i	$0.953819\pi$
$822$	−2.99229e11	−	1.69864e11i	−0.655415	−	0.372061i
$823$	−5.04661e11			−1.10002			−0.550010	−	0.835158i	$-0.685376\pi$
$823$	−5.04661e11			−1.10002			−0.550010	+	0.835158i	$0.685376\pi$
$824$		−	3.36398e10i		−	0.0729701i
$825$	2.70548e10	−	4.76592e10i	0.0584021	−	0.102880i
$826$	−1.48140e11			−0.318239
$827$		−	1.62367e10i		−	0.0347117i	−0.999849	−	0.0173559i	$-0.994475\pi$
$827$		−	1.62367e10i		−	0.0347117i	0.999849	−	0.0173559i	$-0.00552482\pi$
$828$	3.89963e11	−	2.32790e11i	0.829664	−	0.495271i
$829$	3.49989e11			0.741031			0.370515	−	0.928826i	$-0.379181\pi$
$829$	3.49989e11			0.741031			0.370515	+	0.928826i	$0.379181\pi$
$830$		−	3.77885e10i		−	0.0796246i
$831$	−6.01115e11	−	3.41236e11i	−1.26053	−	0.715569i
$832$	8.22494e10			0.171648
$833$			5.53298e11i			1.14916i
$834$	1.46513e11	−	2.58095e11i	0.302840	−	0.533476i
$835$	−3.62412e10			−0.0745516
$836$		−	1.15713e11i		−	0.236896i
$837$	1.62085e10	+	7.41122e11i	0.0330249	+	1.51004i
$838$	3.25777e11			0.660609
$839$		−	5.47730e11i		−	1.10540i	−0.833381	−	0.552699i	$-0.813598\pi$
$839$		−	5.47730e11i		−	1.10540i	0.833381	−	0.552699i	$-0.186402\pi$
$840$	6.21456e10	+	3.52784e10i	0.124823	+	0.0708584i
$841$	4.06417e11			0.812433
$842$			3.93748e11i			0.783375i
$843$	2.23930e11	−	3.94471e11i	0.443407	−	0.781097i
$844$	−3.75362e11			−0.739742
$845$			1.32631e11i			0.260146i
$846$	2.16866e10	+	3.63288e10i	0.0423360	+	0.0709201i
$847$	1.19890e11			0.232942
$848$			1.33626e11i			0.258409i
$849$	7.42896e11	+	4.21721e11i	1.42987	+	0.811699i
$850$	−7.11541e10			−0.136309
$851$			1.36011e12i			2.59332i
$852$	3.14454e10	−	5.53936e10i	0.0596759	−	0.105124i
$853$	2.92272e11			0.552067			0.276033	−	0.961148i	$-0.410980\pi$
$853$	2.92272e11			0.552067			0.276033	+	0.961148i	$0.410980\pi$
$854$			1.44535e11i			0.271732i
$855$	−1.12156e11	+	6.69521e10i	−0.209874	+	0.125285i
$856$	5.80077e11			1.08041
$857$		−	2.42186e11i		−	0.448979i	−0.974476	−	0.224490i	$-0.927929\pi$
$857$		−	2.42186e11i		−	0.448979i	0.974476	−	0.224490i	$-0.0720715\pi$
$858$	9.32037e10	+	5.29091e10i	0.171982	+	0.0976296i
$859$	2.79708e11			0.513727			0.256864	−	0.966448i	$-0.417311\pi$
$859$	2.79708e11			0.513727			0.256864	+	0.966448i	$0.417311\pi$
$860$			7.47471e10i			0.136647i
$861$	1.73769e11	−	3.06108e11i	0.316199	−	0.557010i
$862$	2.78277e11			0.504021
$863$			7.52248e11i			1.35618i	0.734978	+	0.678091i	$0.237193\pi$
$863$			7.52248e11i			1.35618i	−0.734978	+	0.678091i	$0.762807\pi$
$864$	−5.76719e11	+	1.26130e10i	−1.03493	+	0.0226341i
$865$	4.49450e10			0.0802818
$866$		−	3.48536e11i		−	0.619693i
$867$	−3.62751e11	−	2.05924e11i	−0.641997	−	0.364444i
$868$	2.25109e11			0.396564
$869$			9.32395e10i			0.163501i
$870$	2.83173e10	−	4.98832e10i	0.0494282	−	0.0870718i
$871$	2.54564e10			0.0442307
$872$			2.45749e11i			0.425037i
$873$	3.62298e11	+	6.06911e11i	0.623747	+	1.04488i
$874$	−2.17389e11			−0.372556
$875$			1.87858e10i			0.0320478i
$876$	−3.40740e11	−	1.93428e11i	−0.578637	−	0.328476i
$877$	−9.81199e11			−1.65866			−0.829332	−	0.558756i	$-0.811279\pi$
$877$	−9.81199e11			−1.65866			−0.829332	+	0.558756i	$0.811279\pi$
$878$		−	1.24863e11i		−	0.210115i
$879$	−3.10629e11	+	5.47198e11i	−0.520339	+	0.916619i
$880$	4.27885e10			0.0713503
$881$		−	5.64513e11i		−	0.937067i	−0.883446	−	0.468533i	$-0.844783\pi$
$881$		−	5.64513e11i		−	0.937067i	0.883446	−	0.468533i	$-0.155217\pi$
$882$	2.34129e11	−	1.39764e11i	0.386884	−	0.230952i
$883$	−8.27626e11			−1.36142			−0.680708	−	0.732555i	$-0.738328\pi$
$883$	−8.27626e11			−1.36142			−0.680708	+	0.732555i	$0.738328\pi$
$884$			3.81569e11i			0.624833i
$885$	4.09912e11	+	2.32695e11i	0.668217	+	0.379328i
$886$	2.21214e11			0.358986
$887$		−	7.27364e11i		−	1.17505i	−0.809205	−	0.587526i	$-0.800102\pi$
$887$		−	7.27364e11i		−	1.17505i	0.809205	−	0.587526i	$-0.199898\pi$
$888$	5.40768e11	−	9.52605e11i	0.869679	−	1.53201i
$889$	−8.61073e10			−0.137858
$890$			1.38348e11i			0.220502i
$891$	−3.28146e11	−	1.76906e11i	−0.520662	−	0.280693i
$892$	−1.14367e11			−0.180652
$893$			5.55330e10i			0.0873263i
$894$	−3.83919e11	−	2.17940e11i	−0.601021	−	0.341183i
$895$	−1.68411e11			−0.262470
$896$			2.07372e11i			0.321750i
$897$	−2.72566e11	+	4.80147e11i	−0.421020	+	0.741660i
$898$	−5.99018e11			−0.921159
$899$		−	4.27277e11i		−	0.654139i
$900$	−4.92859e10	−	8.25624e10i	−0.0751195	−	0.125838i
$901$	8.32411e11			1.26310
$902$			3.61820e11i			0.546595i
$903$	−8.63900e10	−	4.90412e10i	−0.129931	−	0.0737582i
$904$	−1.88990e11			−0.282987
$905$		−	3.17285e11i		−	0.472994i
$906$	−3.21850e11	+	5.66964e11i	−0.477684	+	0.841478i
$907$	1.16923e12			1.72771			0.863853	−	0.503743i	$-0.168044\pi$
$907$	1.16923e12			1.72771			0.863853	+	0.503743i	$0.168044\pi$
$908$		−	7.33847e11i		−	1.07960i
$909$	−4.44592e11	+	2.65401e11i	−0.651187	+	0.388729i
$910$	−3.67381e10			−0.0535736
$911$		−	1.19802e12i		−	1.73936i	−0.493614	−	0.869681i	$-0.664324\pi$
$911$		−	1.19802e12i		−	1.73936i	0.493614	−	0.869681i	$-0.335676\pi$
$912$	−8.86903e10	−	5.03470e10i	−0.128203	−	0.0727770i
$913$	1.41557e11			0.203727
$914$			9.69253e10i			0.138884i
$915$	2.27032e11	−	3.99935e11i	0.323894	−	0.570565i
$916$	9.42252e10			0.133840
$917$			1.77537e11i			0.251079i
$918$	1.05831e10	+	4.83906e11i	0.0149020	+	0.681382i
$919$	9.42803e11			1.32178			0.660890	−	0.750483i	$-0.270179\pi$
$919$	9.42803e11			1.32178			0.660890	+	0.750483i	$0.270179\pi$
$920$		−	3.78415e11i		−	0.528223i
$921$	2.91539e11	+	1.65498e11i	0.405189	+	0.230015i
$922$	−7.11484e11			−0.984558
$923$			7.74352e10i			0.106692i
$924$	−5.58867e10	+	9.84489e10i	−0.0766691	+	0.135059i
$925$	2.87960e11			0.393338
$926$		−	3.02016e11i		−	0.410758i
$927$	−3.08344e10	−	5.16529e10i	−0.0417558	−	0.0699481i
$928$	3.32494e11			0.448324
$929$		−	5.40213e11i		−	0.725274i	−0.931930	−	0.362637i	$-0.881876\pi$
$929$		−	5.40213e11i		−	0.725274i	0.931930	−	0.362637i	$-0.118124\pi$
$930$	2.27155e11	+	1.28950e11i	0.303662	+	0.172381i
$931$	3.57895e11			0.476383
$932$		−	5.94350e11i		−	0.787732i
$933$	−6.03455e11	+	1.06303e12i	−0.796377	+	1.40288i
$934$	−7.12577e11			−0.936363
$935$		−	2.66546e11i		−	0.348760i
$936$	3.81805e11	−	2.27920e11i	0.497437	−	0.296947i
$937$	−8.00616e11			−1.03864			−0.519321	−	0.854579i	$-0.673815\pi$
$937$	−8.00616e11			−1.03864			−0.519321	+	0.854579i	$0.673815\pi$
$938$		−	9.80591e9i		−	0.0126671i
$939$	1.47948e11	+	8.39862e10i	0.190304	+	0.108030i
$940$	−4.08799e10			−0.0523598
$941$		−	4.51353e11i		−	0.575649i	−0.957683	−	0.287825i	$-0.907068\pi$
$941$		−	4.51353e11i		−	0.575649i	0.957683	−	0.287825i	$-0.0929321\pi$
$942$	−4.63542e10	+	8.16566e10i	−0.0588688	+	0.103702i
$943$	−1.86395e12			−2.35715
$944$			3.68019e11i			0.463428i
$945$	1.27759e11	−	2.79412e9i	0.160201	−	0.00350363i
$946$	1.02113e11			0.127502
$947$		−	3.43776e11i		−	0.427441i	−0.976895	−	0.213720i	$-0.931442\pi$
$947$		−	3.43776e11i		−	0.427441i	0.976895	−	0.213720i	$-0.0685581\pi$
$948$	1.42268e11	+	8.07617e10i	0.176147	+	0.0999935i
$949$	4.76323e11			0.587268
$950$			4.60253e10i			0.0565069i
$951$	−1.19262e11	+	2.10089e11i	−0.145807	+	0.256851i
$952$	3.47566e11			0.423145
$953$		−	7.01344e11i		−	0.850275i	−0.905129	−	0.425138i	$-0.860226\pi$
$953$		−	7.01344e11i		−	0.850275i	0.905129	−	0.425138i	$-0.139774\pi$
$954$	−2.10269e11	−	3.52236e11i	−0.253852	−	0.425246i
$955$	−1.95709e11			−0.235287
$956$			8.41805e11i			1.00781i
$957$	1.86865e11	+	1.06078e11i	0.222782	+	0.126467i
$958$	3.67623e11			0.436456
$959$			4.41835e11i			0.522379i
$960$	−4.97666e10	+	8.76678e10i	−0.0585940	+	0.103218i
$961$	1.09282e12			1.28131
$962$			5.63143e11i			0.657535i
$963$	8.90690e11	−	5.31701e11i	1.03567	−	0.618247i
$964$	−2.43338e11			−0.281774
$965$		−	2.92750e11i		−	0.337589i
$966$	1.84955e11	+	1.04994e11i	0.212401	+	0.120574i
$967$	−1.29211e12			−1.47773			−0.738863	−	0.673855i	$-0.764637\pi$
$967$	−1.29211e12			−1.47773			−0.738863	+	0.673855i	$0.764637\pi$
$968$			5.11304e11i			0.582341i
$969$	−3.13631e11	+	5.52487e11i	−0.355733	+	0.626653i
$970$	2.49056e11			0.281326
$971$			3.10599e11i			0.349400i	0.984622	+	0.174700i	$0.0558955\pi$
$971$			3.10599e11i			0.349400i	−0.984622	+	0.174700i	$0.944104\pi$
$972$	−5.54161e11	+	3.47465e11i	−0.620828	+	0.389265i
$973$	−3.81097e11			−0.425191
$974$			3.88321e10i			0.0431475i
$975$	1.01656e11	+	5.77073e10i	0.112490	+	0.0638576i
$976$	3.59062e11			0.395704
$977$			1.06003e12i			1.16343i	0.813392	+	0.581716i	$0.197618\pi$
$977$			1.06003e12i			1.16343i	−0.813392	+	0.581716i	$0.802382\pi$
$978$	2.54417e11	−	4.48176e11i	0.278093	−	0.489884i
$979$	−5.18257e11			−0.564176
$980$			2.63460e11i			0.285634i
$981$	2.25255e11	+	3.77340e11i	0.243219	+	0.407434i
$982$	4.56619e11			0.491030
$983$		−	1.23511e11i		−	0.132279i	−0.997810	−	0.0661395i	$-0.978932\pi$
$983$		−	1.23511e11i		−	0.132279i	0.997810	−	0.0661395i	$-0.0210682\pi$
$984$	1.30549e12	+	7.41089e11i	1.39249	+	0.790478i
$985$	−6.44641e10			−0.0684815
$986$		−	2.78985e11i		−	0.295170i
$987$	2.68211e10	−	4.72475e10i	0.0282623	−	0.0497864i
$988$	2.46813e11			0.259025
$989$			5.26044e11i			0.549840i
$990$	−1.12789e11	+	6.73301e10i	−0.117416	+	0.0700920i
$991$	−1.19256e11			−0.123648			−0.0618238	−	0.998087i	$-0.519692\pi$
$991$	−1.19256e11			−0.123648			−0.0618238	+	0.998087i	$0.519692\pi$
$992$			1.51409e12i			1.56353i
$993$	−5.16254e11	−	2.93063e11i	−0.530966	−	0.301414i
$994$	2.98284e10			0.0305551
$995$			3.66620e11i			0.374045i
$996$	1.22613e11	−	2.15993e11i	0.124595	−	0.219484i
$997$	2.68628e11			0.271876			0.135938	−	0.990717i	$-0.456595\pi$
$997$	2.68628e11			0.271876			0.135938	+	0.990717i	$0.456595\pi$
$998$		−	1.23639e11i		−	0.124633i
$999$	−4.28299e10	−	1.95837e12i	−0.0430017	−	1.96622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.9.c.a.11.7	yes	10
3.2	odd	2	inner	15.9.c.a.11.4	✓	10
4.3	odd	2		240.9.l.b.161.1		10
5.2	odd	4		75.9.d.c.74.7		20
5.3	odd	4		75.9.d.c.74.14		20
5.4	even	2		75.9.c.g.26.4		10
12.11	even	2		240.9.l.b.161.2		10
15.2	even	4		75.9.d.c.74.13		20
15.8	even	4		75.9.d.c.74.8		20
15.14	odd	2		75.9.c.g.26.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.4	✓	10	3.2	odd	2	inner
15.9.c.a.11.7	yes	10	1.1	even	1	trivial
75.9.c.g.26.4		10	5.4	even	2
75.9.c.g.26.7		10	15.14	odd	2
75.9.d.c.74.7		20	5.2	odd	4
75.9.d.c.74.8		20	15.8	even	4
75.9.d.c.74.13		20	15.2	even	4
75.9.d.c.74.14		20	5.3	odd	4
240.9.l.b.161.1		10	4.3	odd	2
240.9.l.b.161.2		10	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+8.27106i q^{2} +(70.4414 + 39.9876i) q^{3} +187.590 q^{4} -279.508i q^{5} +(-330.740 + 582.625i) q^{6} +860.291 q^{7} +3668.96i q^{8} +(3362.98 + 5633.57i) q^{9} +O(q^{10})\)	\(q+8.27106i q^{2} +(70.4414 + 39.9876i) q^{3} +187.590 q^{4} -279.508i q^{5} +(-330.740 + 582.625i) q^{6} +860.291 q^{7} +3668.96i q^{8} +(3362.98 + 5633.57i) q^{9} +2311.83 q^{10} +8660.22i q^{11} +(13214.1 + 7501.26i) q^{12} -18472.1 q^{13} +7115.52i q^{14} +(11176.9 - 19689.0i) q^{15} +17676.8 q^{16} -110116. i q^{17} +(-46595.6 + 27815.4i) q^{18} -71227.1 q^{19} -52432.9i q^{20} +(60600.1 + 34401.0i) q^{21} -71629.2 q^{22} -369004. i q^{23} +(-146713. + 258446. i) q^{24} -78125.0 q^{25} -152783. i q^{26} +(11620.0 + 531314. i) q^{27} +161382. q^{28} -306317. i q^{29} +(162849. + 92444.7i) q^{30} +1.39489e6 q^{31} +1.08546e6i q^{32} +(-346302. + 610038. i) q^{33} +910773. q^{34} -240459. i q^{35} +(630860. + 1.05680e6i) q^{36} -3.68589e6 q^{37} -589123. i q^{38} +(-1.30120e6 - 738653. i) q^{39} +1.02550e6 q^{40} -5.05129e6i q^{41} +(-284533. + 501227. i) q^{42} -1.42558e6 q^{43} +1.62457e6i q^{44} +(1.57463e6 - 939981. i) q^{45} +3.05206e6 q^{46} -779661. i q^{47} +(1.24518e6 + 706852. i) q^{48} -5.02470e6 q^{49} -646177. i q^{50} +(4.40326e6 - 7.75670e6i) q^{51} -3.46516e6 q^{52} +7.55943e6i q^{53} +(-4.39453e6 + 96109.4i) q^{54} +2.42060e6 q^{55} +3.15637e6i q^{56} +(-5.01733e6 - 2.84820e6i) q^{57} +2.53356e6 q^{58} +2.08194e7i q^{59} +(2.09667e6 - 3.69344e6i) q^{60} +2.03126e7 q^{61} +1.15372e7i q^{62} +(2.89314e6 + 4.84651e6i) q^{63} -4.45264e6 q^{64} +5.16310e6i q^{65} +(-5.04566e6 - 2.86428e6i) q^{66} -1.37810e6 q^{67} -2.06565e7i q^{68} +(1.47556e7 - 2.59932e7i) q^{69} +1.98885e6 q^{70} -4.19202e6i q^{71} +(-2.06693e7 + 1.23386e7i) q^{72} -2.57861e7 q^{73} -3.04862e7i q^{74} +(-5.50323e6 - 3.12403e6i) q^{75} -1.33615e7 q^{76} +7.45030e6i q^{77} +(6.10945e6 - 1.07623e7i) q^{78} +1.07664e7 q^{79} -4.94081e6i q^{80} +(-2.04275e7 + 3.78911e7i) q^{81} +4.17795e7 q^{82} -1.63457e7i q^{83} +(1.13679e7 + 6.45327e6i) q^{84} -3.07783e7 q^{85} -1.17910e7i q^{86} +(1.22489e7 - 2.15774e7i) q^{87} -3.17740e7 q^{88} +5.98434e7i q^{89} +(7.77464e6 + 1.30239e7i) q^{90} -1.58913e7 q^{91} -6.92213e7i q^{92} +(9.82577e7 + 5.57782e7i) q^{93} +6.44862e6 q^{94} +1.99086e7i q^{95} +(-4.34049e7 + 7.64612e7i) q^{96} +1.07731e8 q^{97} -4.15596e7i q^{98} +(-4.87879e7 + 2.91241e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9}+O(q^{10}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9	\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} - 8750 q^{10} - 3812 q^{12} - 55464 q^{13} - 21250 q^{15} + 280386 q^{16} - 419800 q^{18} - 231516 q^{19} + 289572 q^{21} + 1129940 q^{22} + 1136334 q^{24} - 781250 q^{25} - 335512 q^{27} - 3340724 q^{28} - 965000 q^{30} + 881620 q^{31} + 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} + 4672616 q^{37} + 1826792 q^{39} + 2913750 q^{40} - 5392860 q^{42} + 7731336 q^{43} - 2142500 q^{45} - 25424604 q^{46} + 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} + 21064016 q^{52} - 7979798 q^{54} - 4377500 q^{55} - 2856304 q^{57} - 4351100 q^{58} + 23016250 q^{60} + 22417020 q^{61} + 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} - 46646024 q^{67} + 33562632 q^{69} - 62992500 q^{70} + 54175560 q^{72} - 129964884 q^{73} + 8750000 q^{75} + 198922436 q^{76} + 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} + 202877560 q^{82} - 197346768 q^{84} - 110682500 q^{85} - 168322540 q^{87} - 484775700 q^{88} + 171878750 q^{90} + 444288464 q^{91} + 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} - 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q - 112 * q^3 - 786 * q^4 - 5282 * q^6 + 7156 * q^7 + 3922 * q^9 - 8750 * q^10 - 3812 * q^12 - 55464 * q^13 - 21250 * q^15 + 280386 * q^16 - 419800 * q^18 - 231516 * q^19 + 289572 * q^21 + 1129940 * q^22 + 1136334 * q^24 - 781250 * q^25 - 335512 * q^27 - 3340724 * q^28 - 965000 * q^30 + 881620 * q^31 + 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 + 4672616 * q^37 + 1826792 * q^39 + 2913750 * q^40 - 5392860 * q^42 + 7731336 * q^43 - 2142500 * q^45 - 25424604 * q^46 + 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 + 21064016 * q^52 - 7979798 * q^54 - 4377500 * q^55 - 2856304 * q^57 - 4351100 * q^58 + 23016250 * q^60 + 22417020 * q^61 + 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 - 46646024 * q^67 + 33562632 * q^69 - 62992500 * q^70 + 54175560 * q^72 - 129964884 * q^73 + 8750000 * q^75 + 198922436 * q^76 + 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 + 202877560 * q^82 - 197346768 * q^84 - 110682500 * q^85 - 168322540 * q^87 - 484775700 * q^88 + 171878750 * q^90 + 444288464 * q^91 + 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 - 258825724 * q^97 - 33965200 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more