LMFDB - Embedded newform 15.9.c.a.11.1

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			11.1
Root			$18.9110 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.9.c.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.5009i q^{2} +(41.5815 - 69.5124i) q^{3} -614.301 q^{4} -279.508i q^{5} +(-2050.68 - 1226.69i) q^{6} +3174.27 q^{7} +10570.2i q^{8} +(-3102.96 - 5780.86i) q^{9} +O(q^{10})$	\(q-29.5009i q^{2} +(41.5815 - 69.5124i) q^{3} -614.301 q^{4} -279.508i q^{5} +(-2050.68 - 1226.69i) q^{6} +3174.27 q^{7} +10570.2i q^{8} +(-3102.96 - 5780.86i) q^{9} -8245.74 q^{10} +12996.3i q^{11} +(-25543.6 + 42701.6i) q^{12} +8759.90 q^{13} -93643.7i q^{14} +(-19429.3 - 11622.4i) q^{15} +154569. q^{16} -108656. i q^{17} +(-170540. + 91540.0i) q^{18} -78696.7 q^{19} +171702. i q^{20} +(131991. - 220651. i) q^{21} +383403. q^{22} -43589.4i q^{23} +(734760. + 439524. i) q^{24} -78125.0 q^{25} -258425. i q^{26} +(-530868. - 24682.6i) q^{27} -1.94996e6 q^{28} -183211. i q^{29} +(-342870. + 573182. i) q^{30} +780664. q^{31} -1.85394e6i q^{32} +(903407. + 540407. i) q^{33} -3.20544e6 q^{34} -887235. i q^{35} +(1.90615e6 + 3.55119e6i) q^{36} +2.20452e6 q^{37} +2.32162e6i q^{38} +(364250. - 608922. i) q^{39} +2.95446e6 q^{40} +3.04685e6i q^{41} +(-6.50940e6 - 3.89384e6i) q^{42} +4.84516e6 q^{43} -7.98367e6i q^{44} +(-1.61580e6 + 867303. i) q^{45} -1.28593e6 q^{46} +3.51057e6i q^{47} +(6.42720e6 - 1.07444e7i) q^{48} +4.31118e6 q^{49} +2.30476e6i q^{50} +(-7.55293e6 - 4.51807e6i) q^{51} -5.38121e6 q^{52} -8.64762e6i q^{53} +(-728158. + 1.56611e7i) q^{54} +3.63259e6 q^{55} +3.35526e7i q^{56} +(-3.27232e6 + 5.47040e6i) q^{57} -5.40489e6 q^{58} -5.16824e6i q^{59} +(1.19355e7 + 7.13964e6i) q^{60} +5.78123e6 q^{61} -2.30303e7i q^{62} +(-9.84963e6 - 1.83500e7i) q^{63} -1.51233e7 q^{64} -2.44847e6i q^{65} +(1.59425e7 - 2.66513e7i) q^{66} -3.67916e7 q^{67} +6.67474e7i q^{68} +(-3.03001e6 - 1.81251e6i) q^{69} -2.61742e7 q^{70} +971113. i q^{71} +(6.11048e7 - 3.27989e7i) q^{72} +9.46941e6 q^{73} -6.50352e7i q^{74} +(-3.24855e6 + 5.43066e6i) q^{75} +4.83434e7 q^{76} +4.12539e7i q^{77} +(-1.79637e7 - 1.07457e7i) q^{78} +5.63493e7 q^{79} -4.32033e7i q^{80} +(-2.37900e7 + 3.58756e7i) q^{81} +8.98849e7 q^{82} +5.88128e7i q^{83} +(-8.10821e7 + 1.35546e8i) q^{84} -3.03702e7 q^{85} -1.42936e8i q^{86} +(-1.27355e7 - 7.61819e6i) q^{87} -1.37374e8 q^{88} -1.92128e7i q^{89} +(2.55862e7 + 4.76675e7i) q^{90} +2.78063e7 q^{91} +2.67770e7i q^{92} +(3.24612e7 - 5.42658e7i) q^{93} +1.03565e8 q^{94} +2.19964e7i q^{95} +(-1.28872e8 - 7.70897e7i) q^{96} -1.42760e8 q^{97} -1.27184e8i q^{98} +(7.51301e7 - 4.03271e7i) 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 $

$2$		−	29.5009i		−	1.84380i	−0.387423	−	0.921902i	$-0.626635\pi$
$2$		−	29.5009i		−	1.84380i	0.387423	−	0.921902i	$-0.373365\pi$
$3$	41.5815	−	69.5124i	0.513352	−	0.858178i
$3$	41.5815	−	69.5124i	0.513352	−	0.858178i
$4$	−614.301			−2.39961
$5$		−	279.508i		−	0.447214i
$5$		−	279.508i		−	0.447214i
$6$	−2050.68	−	1226.69i	−1.58231	−	0.946520i
$7$	3174.27			1.32206			0.661031	−	0.750359i	$-0.270119\pi$
$7$	3174.27			1.32206			0.661031	+	0.750359i	$0.270119\pi$
$8$			10570.2i			2.58061i
$9$	−3102.96	−	5780.86i	−0.472940	−	0.881095i
$10$	−8245.74			−0.824574
$11$			12996.3i			0.887668i	0.896109	+	0.443834i	$0.146382\pi$
$11$			12996.3i			0.887668i	−0.896109	+	0.443834i	$0.853618\pi$
$12$	−25543.6	+	42701.6i	−1.23185	+	2.05930i
$13$	8759.90			0.306708			0.153354	−	0.988171i	$-0.450992\pi$
$13$	8759.90			0.306708			0.153354	+	0.988171i	$0.450992\pi$
$14$		−	93643.7i		−	2.43762i
$15$	−19429.3	−	11622.4i	−0.383789	−	0.229578i
$16$	154569.			2.35853
$17$		−	108656.i		−	1.30094i	−0.759532	−	0.650470i	$-0.774572\pi$
$17$		−	108656.i		−	1.30094i	0.759532	−	0.650470i	$-0.225428\pi$
$18$	−170540.	+	91540.0i	−1.62457	+	0.872009i
$19$	−78696.7			−0.603868			−0.301934	−	0.953329i	$-0.597632\pi$
$19$	−78696.7			−0.603868			−0.301934	+	0.953329i	$0.597632\pi$
$20$			171702.i			1.07314i
$21$	131991.	−	220651.i	0.678683	−	1.13456i
$22$	383403.			1.63669
$23$		−	43589.4i		−	0.155765i	−0.996963	−	0.0778825i	$-0.975184\pi$
$23$		−	43589.4i		−	0.155765i	0.996963	−	0.0778825i	$-0.0248159\pi$
$24$	734760.	+	439524.i	2.21463	+	1.32476i
$25$	−78125.0			−0.200000
$26$		−	258425.i		−	0.565510i
$27$	−530868.	−	24682.6i	−0.998921	−	0.0464447i
$28$	−1.94996e6			−3.17244
$29$		−	183211.i		−	0.259036i	−0.991577	−	0.129518i	$-0.958657\pi$
$29$		−	183211.i		−	0.259036i	0.991577	−	0.129518i	$-0.0413430\pi$
$30$	−342870.	+	573182.i	−0.423297	+	0.707632i
$31$	780664.			0.845312			0.422656	−	0.906290i	$-0.361098\pi$
$31$	780664.			0.845312			0.422656	+	0.906290i	$0.361098\pi$
$32$		−	1.85394e6i		−	1.76806i
$33$	903407.	+	540407.i	0.761777	+	0.455686i
$34$	−3.20544e6			−2.39868
$35$		−	887235.i		−	0.591244i
$36$	1.90615e6	+	3.55119e6i	1.13487	+	2.11429i
$37$	2.20452e6			1.17627			0.588134	−	0.808763i	$-0.299863\pi$
$37$	2.20452e6			1.17627			0.588134	+	0.808763i	$0.299863\pi$
$38$			2.32162e6i			1.11341i
$39$	364250.	−	608922.i	0.157449	−	0.263210i
$40$	2.95446e6			1.15409
$41$			3.04685e6i			1.07824i	0.842228	+	0.539121i	$0.181243\pi$
$41$			3.04685e6i			1.07824i	−0.842228	+	0.539121i	$0.818757\pi$
$42$	−6.50940e6	−	3.89384e6i	−2.09191	−	1.25136i
$43$	4.84516e6			1.41721			0.708605	−	0.705606i	$-0.249325\pi$
$43$	4.84516e6			1.41721			0.708605	+	0.705606i	$0.249325\pi$
$44$		−	7.98367e6i		−	2.13006i
$45$	−1.61580e6	+	867303.i	−0.394038	+	0.211505i
$46$	−1.28593e6			−0.287200
$47$			3.51057e6i			0.719426i	0.933063	+	0.359713i	$0.117125\pi$
$47$			3.51057e6i			0.719426i	−0.933063	+	0.359713i	$0.882875\pi$
$48$	6.42720e6	−	1.07444e7i	1.21076	−	2.02404i
$49$	4.31118e6			0.747846
$50$			2.30476e6i			0.368761i
$51$	−7.55293e6	−	4.51807e6i	−1.11644	−	0.667840i
$52$	−5.38121e6			−0.735982
$53$		−	8.64762e6i		−	1.09596i	−0.836493	−	0.547978i	$-0.815398\pi$
$53$		−	8.64762e6i		−	1.09596i	0.836493	−	0.547978i	$-0.184602\pi$
$54$	−728158.	+	1.56611e7i	−0.0856349	+	1.84181i
$55$	3.63259e6			0.396977
$56$			3.35526e7i			3.41173i
$57$	−3.27232e6	+	5.47040e6i	−0.309997	+	0.518226i
$58$	−5.40489e6			−0.477611
$59$		−	5.16824e6i		−	0.426515i	−0.976996	−	0.213257i	$-0.931593\pi$
$59$		−	5.16824e6i		−	0.426515i	0.976996	−	0.213257i	$-0.0684073\pi$
$60$	1.19355e7	+	7.13964e6i	0.920945	+	0.550898i
$61$	5.78123e6			0.417543			0.208771	−	0.977964i	$-0.433054\pi$
$61$	5.78123e6			0.417543			0.208771	+	0.977964i	$0.433054\pi$
$62$		−	2.30303e7i		−	1.55859i
$63$	−9.84963e6	−	1.83500e7i	−0.625256	−	1.16486i
$64$	−1.51233e7			−0.901419
$65$		−	2.44847e6i		−	0.137164i
$66$	1.59425e7	−	2.66513e7i	0.840195	−	1.40457i
$67$	−3.67916e7			−1.82578			−0.912891	−	0.408202i	$-0.866156\pi$
$67$	−3.67916e7			−1.82578			−0.912891	+	0.408202i	$0.866156\pi$
$68$			6.67474e7i			3.12175i
$69$	−3.03001e6	−	1.81251e6i	−0.133674	−	0.0799622i
$70$	−2.61742e7			−1.09014
$71$			971113.i			0.0382152i	0.999817	+	0.0191076i	$0.00608251\pi$
$71$			971113.i			0.0382152i	−0.999817	+	0.0191076i	$0.993917\pi$
$72$	6.11048e7	−	3.27989e7i	2.27376	−	1.22048i
$73$	9.46941e6			0.333451			0.166725	−	0.986003i	$-0.446681\pi$
$73$	9.46941e6			0.333451			0.166725	+	0.986003i	$0.446681\pi$
$74$		−	6.50352e7i		−	2.16881i
$75$	−3.24855e6	+	5.43066e6i	−0.102670	+	0.171636i
$76$	4.83434e7			1.44905
$77$			4.12539e7i			1.17355i
$78$	−1.79637e7	−	1.07457e7i	−0.485309	−	0.290306i
$79$	5.63493e7			1.44671			0.723353	−	0.690479i	$-0.242600\pi$
$79$	5.63493e7			1.44671			0.723353	+	0.690479i	$0.242600\pi$
$80$		−	4.32033e7i		−	1.05477i
$81$	−2.37900e7	+	3.58756e7i	−0.552656	+	0.833410i
$82$	8.98849e7			1.98807
$83$			5.88128e7i			1.23925i	0.784897	+	0.619626i	$0.212716\pi$
$83$			5.88128e7i			1.23925i	−0.784897	+	0.619626i	$0.787284\pi$
$84$	−8.10821e7	+	1.35546e8i	−1.62858	+	2.72252i
$85$	−3.03702e7			−0.581798
$86$		−	1.42936e8i		−	2.61306i
$87$	−1.27355e7	−	7.61819e6i	−0.222299	−	0.132977i
$88$	−1.37374e8			−2.29073
$89$		−	1.92128e7i		−	0.306218i	−0.988209	−	0.153109i	$-0.951071\pi$
$89$		−	1.92128e7i		−	0.306218i	0.988209	−	0.153109i	$-0.0489286\pi$
$90$	2.55862e7	+	4.76675e7i	0.389974	+	0.726528i
$91$	2.78063e7			0.405487
$92$			2.67770e7i			0.373776i
$93$	3.24612e7	−	5.42658e7i	0.433943	−	0.725429i
$94$	1.03565e8			1.32648
$95$			2.19964e7i			0.270058i
$96$	−1.28872e8	−	7.70897e7i	−1.51731	−	0.907635i
$97$	−1.42760e8			−1.61257			−0.806286	−	0.591526i	$-0.798526\pi$
$97$	−1.42760e8			−1.61257			−0.806286	+	0.591526i	$0.798526\pi$
$98$		−	1.27184e8i		−	1.37888i
$99$	7.51301e7	−	4.03271e7i	0.782119	−	0.419814i
$100$	4.79923e7			0.479923
$101$			8.34775e7i			0.802202i	0.916034	+	0.401101i	$0.131372\pi$
$101$			8.34775e7i			0.802202i	−0.916034	+	0.401101i	$0.868628\pi$
$102$	−1.33287e8	+	2.22818e8i	−1.23137	+	2.05849i
$103$	1.29545e8			1.15099			0.575494	−	0.817806i	$-0.304810\pi$
$103$	1.29545e8			1.15099			0.575494	+	0.817806i	$0.304810\pi$
$104$			9.25938e7i			0.791496i
$105$	−6.16739e7	−	3.68926e7i	−0.507393	−	0.303516i
$106$	−2.55112e8			−2.02073
$107$			1.02862e8i			0.784731i	0.919809	+	0.392365i	$0.128343\pi$
$107$			1.02862e8i			0.784731i	−0.919809	+	0.392365i	$0.871657\pi$
$108$	3.26112e8	+	1.51626e7i	2.39702	+	0.111449i
$109$	−1.82090e8			−1.28997			−0.644984	−	0.764196i	$-0.723136\pi$
$109$	−1.82090e8			−1.28997			−0.644984	+	0.764196i	$0.723136\pi$
$110$		−	1.07164e8i		−	0.731948i
$111$	9.16671e7	−	1.53241e8i	0.603840	−	1.00945i
$112$	4.90643e8			3.11812
$113$			8.75507e6i			0.0536965i	0.999640	+	0.0268483i	$0.00854709\pi$
$113$			8.75507e6i			0.0536965i	−0.999640	+	0.0268483i	$0.991453\pi$
$114$	1.61381e8	+	9.65364e7i	0.955508	+	0.571573i
$115$	−1.21836e7			−0.0696602
$116$			1.12547e8i			0.621586i
$117$	−2.71816e7	−	5.06398e7i	−0.145055	−	0.270239i
$118$	−1.52467e8			−0.786410
$119$		−	3.44903e8i		−	1.71992i
$120$	1.22851e8	−	2.05372e8i	0.592452	−	0.990411i
$121$	4.54540e7			0.212046
$122$		−	1.70551e8i		−	0.769867i
$123$	2.11794e8	+	1.26693e8i	0.925324	+	0.553518i
$124$	−4.79563e8			−2.02842
$125$			2.18366e7i			0.0894427i
$126$	−5.41341e8	+	2.90573e8i	−2.14778	+	1.15285i
$127$	−2.17231e7			−0.0835040			−0.0417520	−	0.999128i	$-0.513294\pi$
$127$	−2.17231e7			−0.0835040			−0.0417520	+	0.999128i	$0.513294\pi$
$128$		−	2.84587e7i		−	0.106017i
$129$	2.01469e8	−	3.36799e8i	0.727527	−	1.21622i
$130$	−7.22319e7			−0.252904
$131$		−	1.72425e8i		−	0.585485i	−0.956191	−	0.292743i	$-0.905432\pi$
$131$		−	1.72425e8i		−	0.585485i	0.956191	−	0.292743i	$-0.0945679\pi$
$132$	−5.54964e8	−	3.31973e8i	−1.82797	−	1.09347i
$133$	−2.49804e8			−0.798350
$134$			1.08538e9i			3.36639i
$135$	−6.89900e6	+	1.48382e8i	−0.0207707	+	0.446731i
$136$	1.14851e9			3.35722
$137$			2.76036e8i			0.783580i	0.920055	+	0.391790i	$0.128144\pi$
$137$			2.76036e8i			0.783580i	−0.920055	+	0.391790i	$0.871856\pi$
$138$	−5.34707e7	+	8.93879e7i	−0.147435	+	0.246469i
$139$	4.04596e8			1.08383			0.541916	−	0.840433i	$-0.317699\pi$
$139$	4.04596e8			1.08383			0.541916	+	0.840433i	$0.317699\pi$
$140$			5.45030e8i			1.41876i
$141$	2.44028e8	+	1.45975e8i	0.617396	+	0.369319i
$142$	2.86487e7			0.0704614
$143$			1.13847e8i			0.272255i
$144$	−4.79620e8	−	8.93540e8i	−1.11544	−	2.07809i
$145$	−5.12091e7			−0.115844
$146$		−	2.79356e8i		−	0.614818i
$147$	1.79265e8	−	2.99681e8i	0.383908	−	0.641785i
$148$	−1.35424e9			−2.82259
$149$			8.41277e8i			1.70685i	0.521219	+	0.853423i	$0.325477\pi$
$149$			8.41277e8i			1.70685i	−0.521219	+	0.853423i	$0.674523\pi$
$150$	1.60209e8	+	9.58352e7i	0.316463	+	0.189304i
$151$	−1.91529e8			−0.368405			−0.184203	−	0.982888i	$-0.558970\pi$
$151$	−1.91529e8			−0.368405			−0.184203	+	0.982888i	$0.558970\pi$
$152$		−	8.31839e8i		−	1.55835i
$153$	−6.28124e8	+	3.37154e8i	−1.14625	+	0.615266i
$154$	1.21703e9			2.16380
$155$		−	2.18202e8i		−	0.378035i
$156$	−2.23759e8	+	3.74061e8i	−0.377817	+	0.631603i
$157$	2.37178e8			0.390370			0.195185	−	0.980766i	$-0.437469\pi$
$157$	2.37178e8			0.390370			0.195185	+	0.980766i	$0.437469\pi$
$158$		−	1.66235e9i		−	2.66744i
$159$	−6.01117e8	−	3.59581e8i	−0.940525	−	0.562611i
$160$	−5.18193e8			−0.790699
$161$		−	1.38365e8i		−	0.205931i
$162$	1.05836e9	+	7.01826e8i	1.53664	+	1.01899i
$163$	6.29506e8			0.891763			0.445881	−	0.895092i	$-0.352890\pi$
$163$	6.29506e8			0.891763			0.445881	+	0.895092i	$0.352890\pi$
$164$		−	1.87169e9i		−	2.58736i
$165$	1.51048e8	−	2.52510e8i	0.203789	−	0.340677i
$166$	1.73503e9			2.28494
$167$			3.79259e7i			0.0487607i	0.999703	+	0.0243803i	$0.00776127\pi$
$167$			3.79259e7i			0.0487607i	−0.999703	+	0.0243803i	$0.992239\pi$
$168$	2.33233e9	+	1.39517e9i	2.92787	+	1.75142i
$169$	−7.38995e8			−0.905930
$170$			8.95948e8i			1.07272i
$171$	2.44193e8	+	4.54935e8i	0.285593	+	0.532065i
$172$	−2.97638e9			−3.40075
$173$			1.49961e9i			1.67415i	0.547085	+	0.837077i	$0.315737\pi$
$173$			1.49961e9i			1.67415i	−0.547085	+	0.837077i	$0.684263\pi$
$174$	−2.24743e8	+	3.75707e8i	−0.245183	+	0.409876i
$175$	−2.47990e8			−0.264412
$176$			2.00883e9i			2.09359i
$177$	−3.59257e8	−	2.14903e8i	−0.366026	−	0.218952i
$178$	−5.66795e8			−0.564606
$179$		−	7.72267e8i		−	0.752238i	−0.926571	−	0.376119i	$-0.877258\pi$
$179$		−	7.72267e8i		−	0.752238i	0.926571	−	0.376119i	$-0.122742\pi$
$180$	9.92588e8	−	5.32785e8i	0.945538	−	0.507531i
$181$	−7.49920e8			−0.698716			−0.349358	−	0.936989i	$-0.613600\pi$
$181$	−7.49920e8			−0.698716			−0.349358	+	0.936989i	$0.613600\pi$
$182$		−	8.20309e8i		−	0.747639i
$183$	2.40392e8	−	4.01867e8i	0.214346	−	0.358326i
$184$	4.60749e8			0.401969
$185$		−	6.16181e8i		−	0.526043i
$186$	−1.60089e9	−	9.57632e8i	−1.33755	−	0.800105i
$187$	1.41213e9			1.15480
$188$		−	2.15655e9i		−	1.72635i
$189$	−1.68512e9	−	7.83492e7i	−1.32063	−	0.0614027i
$190$	6.48912e8			0.497934
$191$			8.93822e7i			0.0671611i	0.999436	+	0.0335805i	$0.0106910\pi$
$191$			8.93822e7i			0.0671611i	−0.999436	+	0.0335805i	$0.989309\pi$
$192$	−6.28849e8	+	1.05126e9i	−0.462745	+	0.773578i
$193$	8.16090e8			0.588178			0.294089	−	0.955778i	$-0.404984\pi$
$193$	8.16090e8			0.588178			0.294089	+	0.955778i	$0.404984\pi$
$194$			4.21154e9i			2.97327i
$195$	−1.70199e8	−	1.01811e8i	−0.117711	−	0.0704135i
$196$	−2.64837e9			−1.79454
$197$		−	1.32278e9i		−	0.878256i	−0.898424	−	0.439128i	$-0.855287\pi$
$197$		−	1.32278e9i		−	0.878256i	0.898424	−	0.439128i	$-0.144713\pi$
$198$	−1.18968e9	−	2.21640e9i	−0.774054	−	1.44207i
$199$	−1.92328e9			−1.22639			−0.613197	−	0.789930i	$-0.710117\pi$
$199$	−1.92328e9			−1.22639			−0.613197	+	0.789930i	$0.710117\pi$
$200$		−	8.25796e8i		−	0.516123i
$201$	−1.52985e9	+	2.55747e9i	−0.937269	+	1.56685i
$202$	2.46266e9			1.47910
$203$		−	5.81562e8i		−	0.342461i
$204$	4.63977e9	+	2.77546e9i	2.67902	+	1.60256i
$205$	8.51622e8			0.482205
$206$		−	3.82168e9i		−	2.12220i
$207$	−2.51985e8	+	1.35256e8i	−0.137244	+	0.0736675i
$208$	1.35401e9			0.723381
$209$		−	1.02277e9i		−	0.536034i
$210$	−1.08836e9	+	1.81943e9i	−0.559624	+	0.935533i
$211$	2.03655e9			1.02746			0.513729	−	0.857952i	$-0.328264\pi$
$211$	2.03655e9			1.02746			0.513729	+	0.857952i	$0.328264\pi$
$212$			5.31224e9i			2.62987i
$213$	6.75045e7	+	4.03803e7i	0.0327955	+	0.0196179i
$214$	3.03452e9			1.44689
$215$		−	1.35426e9i		−	0.633795i
$216$	2.60900e8	−	5.61137e9i	0.119856	−	2.57783i
$217$	2.47804e9			1.11755
$218$			5.37180e9i			2.37845i
$219$	3.93752e8	−	6.58242e8i	0.171177	−	0.286160i
$220$	−2.23150e9			−0.952592
$221$		−	9.51814e8i		−	0.399009i
$222$	−4.52075e9	−	2.70426e9i	−1.86122	−	1.11336i
$223$	−4.63258e8			−0.187328			−0.0936642	−	0.995604i	$-0.529858\pi$
$223$	−4.63258e8			−0.187328			−0.0936642	+	0.995604i	$0.529858\pi$
$224$		−	5.88491e9i		−	2.33748i
$225$	2.42419e8	+	4.51630e8i	0.0945880	+	0.176219i
$226$	2.58282e8			0.0990059
$227$			4.20915e9i			1.58522i	0.609726	+	0.792612i	$0.291279\pi$
$227$			4.20915e9i			1.58522i	−0.609726	+	0.792612i	$0.708721\pi$
$228$	2.01019e9	−	3.36047e9i	0.743872	−	1.24354i
$229$	−4.11215e9			−1.49530			−0.747648	−	0.664095i	$-0.768817\pi$
$229$	−4.11215e9			−1.49530			−0.747648	+	0.664095i	$0.768817\pi$
$230$			3.59427e8i			0.128440i
$231$	2.86766e9	+	1.71540e9i	1.00712	+	0.602445i
$232$	1.93658e9			0.668471
$233$			2.87004e9i			0.973788i	0.873461	+	0.486894i	$0.161870\pi$
$233$			2.87004e9i			0.973788i	−0.873461	+	0.486894i	$0.838130\pi$
$234$	−1.49392e9	+	8.01881e8i	−0.498268	+	0.267452i
$235$	9.81234e8			0.321737
$236$			3.17485e9i			1.02347i
$237$	2.34309e9	−	3.91698e9i	0.742669	−	1.24153i
$238$	−1.01749e10			−3.17120
$239$		−	2.06189e9i		−	0.631937i	−0.948770	−	0.315968i	$-0.897671\pi$
$239$		−	2.06189e9i		−	0.631937i	0.948770	−	0.315968i	$-0.102329\pi$
$240$	−3.00316e9	−	1.79646e9i	−0.905178	−	0.541467i
$241$	1.87727e8			0.0556491			0.0278246	−	0.999613i	$-0.491142\pi$
$241$	1.87727e8			0.0556491			0.0278246	+	0.999613i	$0.491142\pi$
$242$		−	1.34093e9i		−	0.390971i
$243$	1.50457e9	+	3.14546e9i	0.431507	+	0.902109i
$244$	−3.55142e9			−1.00194
$245$		−	1.20501e9i		−	0.334447i
$246$	3.73755e9	−	6.24812e9i	1.02058	−	1.70612i
$247$	−6.89375e8			−0.185211
$248$			8.25177e9i			2.18142i
$249$	4.08822e9	+	2.44552e9i	1.06350	+	0.636172i
$250$	6.44199e8			0.164915
$251$		−	1.87286e9i		−	0.471856i	−0.971771	−	0.235928i	$-0.924187\pi$
$251$		−	1.87286e9i		−	0.471856i	0.971771	−	0.235928i	$-0.0758130\pi$
$252$	6.05064e9	+	1.12724e10i	1.50037	+	2.79522i
$253$	5.66503e8			0.138268
$254$			6.40851e8i			0.153965i
$255$	−1.26284e9	+	2.11111e9i	−0.298667	+	0.499286i
$256$	−4.71112e9			−1.09689
$257$		−	2.62531e9i		−	0.601795i	−0.953656	−	0.300898i	$-0.902714\pi$
$257$		−	2.62531e9i		−	0.601795i	0.953656	−	0.300898i	$-0.0972862\pi$
$258$	−9.93585e9	−	5.94351e9i	−2.24247	−	1.34142i
$259$	6.99773e9			1.55510
$260$			1.50410e9i			0.329141i
$261$	−1.05912e9	+	5.68497e8i	−0.228235	+	0.122508i
$262$	−5.08670e9			−1.07952
$263$		−	7.30592e9i		−	1.52705i	−0.645781	−	0.763523i	$-0.723468\pi$
$263$		−	7.30592e9i		−	1.52705i	0.645781	−	0.763523i	$-0.276532\pi$
$264$	−5.71221e9	+	9.54919e9i	−1.17595	+	1.96585i
$265$	−2.41708e9			−0.490126
$266$			7.36945e9i			1.47200i
$267$	−1.33553e9	−	7.98898e8i	−0.262790	−	0.157198i
$268$	2.26011e10			4.38117
$269$			1.05642e9i			0.201757i	0.994899	+	0.100878i	$0.0321653\pi$
$269$			1.05642e9i			0.201757i	−0.994899	+	0.100878i	$0.967835\pi$
$270$	4.37740e9	+	2.03526e8i	0.823684	+	0.0382971i
$271$	−5.55499e9			−1.02993			−0.514963	−	0.857212i	$-0.672194\pi$
$271$	−5.55499e9			−1.02993			−0.514963	+	0.857212i	$0.672194\pi$
$272$		−	1.67948e10i		−	3.06831i
$273$	1.15623e9	−	1.93288e9i	0.208158	−	0.347980i
$274$	8.14330e9			1.44477
$275$		−	1.01534e9i		−	0.177534i
$276$	1.86134e9	+	1.11343e9i	0.320766	+	0.191878i
$277$	−5.81689e9			−0.988034			−0.494017	−	0.869452i	$-0.664472\pi$
$277$	−5.81689e9			−0.988034			−0.494017	+	0.869452i	$0.664472\pi$
$278$		−	1.19359e10i		−	1.99837i
$279$	−2.42237e9	−	4.51291e9i	−0.399782	−	0.744800i
$280$	9.37825e9			1.52577
$281$		−	7.93059e9i		−	1.27198i	−0.771698	−	0.635990i	$-0.780592\pi$
$281$		−	7.93059e9i		−	1.27198i	0.771698	−	0.635990i	$-0.219408\pi$
$282$	4.30638e9	−	7.19905e9i	0.680951	−	1.13836i
$283$	−8.19763e9			−1.27803			−0.639017	−	0.769193i	$-0.720659\pi$
$283$	−8.19763e9			−1.27803			−0.639017	+	0.769193i	$0.720659\pi$
$284$		−	5.96556e8i		−	0.0917018i
$285$	1.52902e9	+	9.14642e8i	0.231758	+	0.138635i
$286$	3.35857e9			0.501985
$287$			9.67154e9i			1.42550i
$288$	−1.07174e10	+	5.75271e9i	−1.55783	+	0.836185i
$289$	−4.83032e9			−0.692444
$290$			1.51071e9i			0.213594i
$291$	−5.93617e9	+	9.92359e9i	−0.827817	+	1.38387i
$292$	−5.81707e9			−0.800153
$293$			1.02001e10i			1.38399i	0.721902	+	0.691995i	$0.243268\pi$
$293$			1.02001e10i			1.38399i	−0.721902	+	0.691995i	$0.756732\pi$
$294$	−8.84085e9	−	5.28849e9i	−1.18333	−	0.707851i
$295$	−1.44457e9			−0.190743
$296$			2.33022e10i			3.03549i
$297$	3.20784e8	−	6.89934e9i	0.0412274	−	0.886710i
$298$	2.48184e10			3.14709
$299$		−	3.81839e8i		−	0.0477744i
$300$	1.99559e9	−	3.33606e9i	0.246369	−	0.411859i
$301$	1.53798e10			1.87364
$302$			5.65026e9i			0.679267i
$303$	5.80273e9	+	3.47112e9i	0.688433	+	0.411812i
$304$	−1.21640e10			−1.42424
$305$		−	1.61590e9i		−	0.186731i
$306$	9.94635e9	+	1.85302e10i	1.13443	+	2.11346i
$307$	−1.59327e10			−1.79365			−0.896823	−	0.442389i	$-0.854131\pi$
$307$	−1.59327e10			−1.79365			−0.896823	+	0.442389i	$0.854131\pi$
$308$		−	2.53423e10i		−	2.81607i
$309$	5.38667e9	−	9.00498e9i	0.590862	−	0.987754i
$310$	−6.43715e9			−0.697023
$311$		−	1.47120e10i		−	1.57265i	−0.617816	−	0.786323i	$-0.711982\pi$
$311$		−	1.47120e10i		−	1.57265i	0.617816	−	0.786323i	$-0.288018\pi$
$312$	6.43642e9	+	3.85019e9i	0.679244	+	0.406316i
$313$	1.09163e10			1.13736			0.568678	−	0.822560i	$-0.307455\pi$
$313$	1.09163e10			1.13736			0.568678	+	0.822560i	$0.307455\pi$
$314$		−	6.99696e9i		−	0.719765i
$315$	−5.12898e9	+	2.75305e9i	−0.520942	+	0.279623i
$316$	−3.46154e10			−3.47153
$317$			1.31319e10i			1.30044i	0.759746	+	0.650220i	$0.225323\pi$
$317$			1.31319e10i			1.30044i	−0.759746	+	0.650220i	$0.774677\pi$
$318$	−1.06079e10	+	1.77335e10i	−1.03734	+	1.73414i
$319$	2.38108e9			0.229938
$320$			4.22709e9i			0.403127i
$321$	7.15020e9	+	4.27716e9i	0.673439	+	0.402843i
$322$	−4.08188e9			−0.379696
$323$			8.55085e9i			0.785596i
$324$	1.46142e10	−	2.20384e10i	1.32616	−	1.99986i
$325$	−6.84367e8			−0.0613417
$326$		−	1.85710e10i		−	1.64424i
$327$	−7.57156e9	+	1.26575e10i	−0.662208	+	1.10702i
$328$	−3.22058e10			−2.78253
$329$			1.11435e10i			0.951126i
$330$	−7.44927e9	−	4.45606e9i	−0.628142	−	0.375747i
$331$	−5.11274e9			−0.425934			−0.212967	−	0.977059i	$-0.568313\pi$
$331$	−5.11274e9			−0.425934			−0.212967	+	0.977059i	$0.568313\pi$
$332$		−	3.61288e10i		−	2.97372i
$333$	−6.84053e9	−	1.27440e10i	−0.556305	−	1.03640i
$334$	1.11885e9			0.0899052
$335$			1.02836e10i			0.816515i
$336$	2.04017e10	−	3.41058e10i	1.60069	−	2.67591i
$337$	2.37856e10			1.84414			0.922070	−	0.387024i	$-0.126497\pi$
$337$	2.37856e10			1.84414			0.922070	+	0.387024i	$0.126497\pi$
$338$			2.18010e10i			1.67036i
$339$	6.08587e8	+	3.64049e8i	0.0460812	+	0.0275652i
$340$	1.86565e10			1.39609
$341$			1.01458e10i			0.750356i
$342$	1.34210e10	−	7.20389e9i	0.981023	−	0.526578i
$343$	−4.61417e9			−0.333363
$344$			5.12142e10i			3.65727i
$345$	−5.06613e8	+	8.46913e8i	−0.0357602	+	0.0597809i
$346$	4.42399e10			3.08681
$347$		−	3.67752e9i		−	0.253652i	−0.991925	−	0.126826i	$-0.959521\pi$
$347$		−	3.67752e9i		−	0.253652i	0.991925	−	0.126826i	$-0.0404789\pi$
$348$	7.82340e9	+	4.67986e9i	0.533432	+	0.319092i
$349$	8.39415e9			0.565816			0.282908	−	0.959147i	$-0.408701\pi$
$349$	8.39415e9			0.565816			0.282908	+	0.959147i	$0.408701\pi$
$350$			7.31591e9i			0.487524i
$351$	−4.65034e9	−	2.16217e8i	−0.306377	−	0.0142450i
$352$	2.40945e10			1.56945
$353$		−	2.53478e10i		−	1.63246i	−0.577729	−	0.816229i	$-0.696061\pi$
$353$		−	2.53478e10i		−	1.63246i	0.577729	−	0.816229i	$-0.303939\pi$
$354$	−6.33982e9	+	1.05984e10i	−0.403705	+	0.674880i
$355$	2.71434e8			0.0170904
$356$			1.18025e10i			0.734805i
$357$	−2.39750e10	−	1.43416e10i	−1.47600	−	0.882925i
$358$	−2.27825e10			−1.38698
$359$			3.29745e9i			0.198518i	0.995062	+	0.0992590i	$0.0316472\pi$
$359$			3.29745e9i			0.198518i	−0.995062	+	0.0992590i	$0.968353\pi$
$360$	−9.16756e9	−	1.70793e10i	−0.545813	−	1.01686i
$361$	−1.07904e10			−0.635344
$362$			2.21233e10i			1.28829i
$363$	1.89004e9	−	3.15962e9i	0.108854	−	0.181973i
$364$	−1.70814e10			−0.973013
$365$		−	2.64678e9i		−	0.149124i
$366$	−1.18554e10	−	7.09178e9i	−0.660683	−	0.395213i
$367$	1.99945e10			1.10216			0.551082	−	0.834451i	$-0.314215\pi$
$367$	1.99945e10			1.10216			0.551082	+	0.834451i	$0.314215\pi$
$368$		−	6.73756e9i		−	0.367377i
$369$	1.76134e10	−	9.45427e9i	0.950033	−	0.509944i
$370$	−1.81779e10			−0.969921
$371$		−	2.74499e10i		−	1.44892i
$372$	−1.99409e10	+	3.33356e10i	−1.04129	+	1.74075i
$373$	−8.36869e9			−0.432337			−0.216168	−	0.976356i	$-0.569356\pi$
$373$	−8.36869e9			−0.432337			−0.216168	+	0.976356i	$0.569356\pi$
$374$		−	4.16590e10i		−	2.12923i
$375$	1.51792e9	+	9.07998e8i	0.0767578	+	0.0459156i
$376$	−3.71074e10			−1.85656
$377$		−	1.60491e9i		−	0.0794485i
$378$	−2.31137e9	+	4.97124e10i	−0.113215	+	2.43499i
$379$	1.46377e10			0.709440			0.354720	−	0.934973i	$-0.384576\pi$
$379$	1.46377e10			0.709440			0.354720	+	0.934973i	$0.384576\pi$
$380$		−	1.35124e10i		−	0.648035i
$381$	−9.03280e8	+	1.51003e9i	−0.0428669	+	0.0716613i
$382$	2.63685e9			0.123832
$383$		−	9.54053e9i		−	0.443381i	−0.975117	−	0.221691i	$-0.928842\pi$
$383$		−	9.54053e9i		−	0.443381i	0.975117	−	0.221691i	$-0.0711575\pi$
$384$	−1.97823e9	−	1.18335e9i	−0.0909814	−	0.0544239i
$385$	1.15308e10			0.524828
$386$		−	2.40754e10i		−	1.08449i
$387$	−1.50343e10	−	2.80092e10i	−0.670255	−	1.24870i
$388$	8.76975e10			3.86955
$389$			2.67145e10i			1.16667i	0.812230	+	0.583337i	$0.198253\pi$
$389$			2.67145e10i			1.16667i	−0.812230	+	0.583337i	$0.801747\pi$
$390$	−3.00351e9	+	5.02101e9i	−0.129829	+	0.217037i
$391$	−4.73624e9			−0.202641
$392$			4.55700e10i			1.92990i
$393$	−1.19857e10	−	7.16970e9i	−0.502451	−	0.300560i
$394$	−3.90230e10			−1.61933
$395$		−	1.57501e10i		−	0.646986i
$396$	−4.61525e10	+	2.47730e10i	−1.87678	+	1.00739i
$397$	−7.88247e9			−0.317322			−0.158661	−	0.987333i	$-0.550718\pi$
$397$	−7.88247e9			−0.317322			−0.158661	+	0.987333i	$0.550718\pi$
$398$			5.67384e10i			2.26123i
$399$	−1.03872e10	+	1.73645e10i	−0.409835	+	0.685127i
$400$	−1.20757e10			−0.471706
$401$			1.90264e10i			0.735834i	0.929859	+	0.367917i	$0.119929\pi$
$401$			1.90264e10i			0.735834i	−0.929859	+	0.367917i	$0.880071\pi$
$402$	7.54476e10	+	4.51319e10i	2.88896	+	1.72814i
$403$	6.83853e9			0.259264
$404$		−	5.12803e10i		−	1.92498i
$405$	1.00275e10	+	6.64951e9i	0.372712	+	0.247155i
$406$	−1.71566e10			−0.631432
$407$			2.86507e10i			1.04414i
$408$	4.77569e10	−	7.98359e10i	1.72344	−	2.88110i
$409$	−4.82473e9			−0.172417			−0.0862084	−	0.996277i	$-0.527475\pi$
$409$	−4.82473e9			−0.172417			−0.0862084	+	0.996277i	$0.527475\pi$
$410$		−	2.51236e10i		−	0.889091i
$411$	1.91879e10	+	1.14780e10i	0.672451	+	0.402252i
$412$	−7.95795e10			−2.76193
$413$		−	1.64054e10i		−	0.563879i
$414$	3.99018e9	+	7.43376e9i	0.135828	+	0.253051i
$415$	1.64387e10			0.554210
$416$		−	1.62403e10i		−	0.542278i
$417$	1.68237e10	−	2.81244e10i	0.556387	−	0.930121i
$418$	−3.01726e10			−0.988342
$419$			3.79749e10i			1.23208i	0.787713	+	0.616042i	$0.211265\pi$
$419$			3.79749e10i			1.23208i	−0.787713	+	0.616042i	$0.788735\pi$
$420$	3.78863e10	+	2.26631e10i	1.21755	+	0.728321i
$421$	−5.86781e9			−0.186787			−0.0933937	−	0.995629i	$-0.529772\pi$
$421$	−5.86781e9			−0.186787			−0.0933937	+	0.995629i	$0.529772\pi$
$422$		−	6.00799e10i		−	1.89443i
$423$	2.02941e10	−	1.08932e10i	0.633883	−	0.340245i
$424$	9.14070e10			2.82824
$425$			8.48873e9i			0.260188i
$426$	1.19125e9	−	1.99144e9i	0.0361715	−	0.0604684i
$427$	1.83512e10			0.552017
$428$		−	6.31884e10i		−	1.88305i
$429$	7.91376e9	+	4.73391e9i	0.233643	+	0.139763i
$430$	−3.99519e10			−1.16859
$431$			1.50537e10i			0.436250i	0.975921	+	0.218125i	$0.0699940\pi$
$431$			1.50537e10i			0.436250i	−0.975921	+	0.218125i	$0.930006\pi$
$432$	−8.20555e10	−	3.81516e9i	−2.35599	−	0.109541i
$433$	−2.72042e10			−0.773899			−0.386950	−	0.922101i	$-0.626471\pi$
$433$	−2.72042e10			−0.773899			−0.386950	+	0.922101i	$0.626471\pi$
$434$		−	7.31042e10i		−	2.06055i
$435$	−2.12935e9	+	3.55967e9i	−0.0594689	+	0.0994151i
$436$	1.11858e11			3.09543
$437$			3.43034e9i			0.0940615i
$438$	−1.94187e10	−	1.16160e10i	−0.527623	−	0.315618i
$439$	−3.48887e10			−0.939348			−0.469674	−	0.882840i	$-0.655628\pi$
$439$	−3.48887e10			−0.939348			−0.469674	+	0.882840i	$0.655628\pi$
$440$			3.83972e10i			1.02444i
$441$	−1.33774e10	−	2.49224e10i	−0.353686	−	0.658923i
$442$	−2.80793e10			−0.735695
$443$			1.32254e10i			0.343395i	0.985150	+	0.171698i	$0.0549252\pi$
$443$			1.32254e10i			0.343395i	−0.985150	+	0.171698i	$0.945075\pi$
$444$	−5.63112e10	+	9.41363e10i	−1.44898	+	2.42229i
$445$	−5.37015e9			−0.136945
$446$			1.36665e10i			0.345397i
$447$	5.84793e10	+	3.49816e10i	1.46478	+	0.876212i
$448$	−4.80054e10			−1.19173
$449$		−	2.35824e9i		−	0.0580232i	−0.999579	−	0.0290116i	$-0.990764\pi$
$449$		−	2.35824e9i		−	0.0580232i	0.999579	−	0.0290116i	$-0.00923598\pi$
$450$	1.33235e10	−	7.15156e9i	0.324913	−	0.174402i
$451$	−3.95980e10			−0.957121
$452$		−	5.37825e9i		−	0.128851i
$453$	−7.96404e9	+	1.33136e10i	−0.189121	+	0.316157i
$454$	1.24174e11			2.92284
$455$		−	7.77209e9i		−	0.181339i
$456$	−5.78231e10	−	3.45891e10i	−1.33734	−	0.799981i
$457$	2.48874e10			0.570579			0.285289	−	0.958441i	$-0.407910\pi$
$457$	2.48874e10			0.570579			0.285289	+	0.958441i	$0.407910\pi$
$458$			1.21312e11i			2.75703i
$459$	−2.68191e9	+	5.76818e10i	−0.0604217	+	1.29954i
$460$	7.48441e9			0.167158
$461$			2.32674e10i			0.515163i	0.966257	+	0.257581i	$0.0829255\pi$
$461$			2.32674e10i			0.515163i	−0.966257	+	0.257581i	$0.917074\pi$
$462$	5.06057e10	−	8.45984e10i	1.11079	−	1.85692i
$463$	−3.52388e10			−0.766828			−0.383414	−	0.923577i	$-0.625252\pi$
$463$	−3.52388e10			−0.766828			−0.383414	+	0.923577i	$0.625252\pi$
$464$		−	2.83187e10i		−	0.610944i
$465$	−1.51678e10	−	9.07317e9i	−0.324422	−	0.194065i
$466$	8.46687e10			1.79547
$467$		−	8.78873e10i		−	1.84781i	−0.382616	−	0.923907i	$-0.624977\pi$
$467$		−	8.78873e10i		−	1.84781i	0.382616	−	0.923907i	$-0.375023\pi$
$468$	1.66977e10	+	3.11081e10i	0.348075	+	0.648469i
$469$	−1.16786e11			−2.41380
$470$		−	2.89473e10i		−	0.593220i
$471$	9.86222e9	−	1.64868e10i	0.200397	−	0.335007i
$472$	5.46292e10			1.10067
$473$			6.29693e10i			1.25801i
$474$	−1.15554e11	−	6.91231e10i	−2.28914	−	1.36934i
$475$	6.14818e9			0.120774
$476$			2.11874e11i			4.12715i
$477$	−4.99907e10	+	2.68332e10i	−0.965641	+	0.518321i
$478$	−6.08275e10			−1.16517
$479$		−	7.91032e10i		−	1.50263i	−0.659944	−	0.751315i	$-0.729420\pi$
$479$		−	7.91032e10i		−	1.50263i	0.659944	−	0.751315i	$-0.270580\pi$
$480$	−2.15472e10	+	3.60208e10i	−0.405907	+	0.678561i
$481$	1.93113e10			0.360771
$482$		−	5.53811e9i		−	0.102606i
$483$	−9.61806e9	−	5.75341e9i	−0.176725	−	0.105715i
$484$	−2.79224e10			−0.508829
$485$			3.99026e10i			0.721164i
$486$	9.27938e10	−	4.43862e10i	1.66331	−	0.795615i
$487$	5.78470e10			1.02841			0.514203	−	0.857668i	$-0.328088\pi$
$487$	5.78470e10			1.02841			0.514203	+	0.857668i	$0.328088\pi$
$488$			6.11087e10i			1.07752i
$489$	2.61758e10	−	4.37585e10i	0.457788	−	0.765292i
$490$	−3.55489e10			−0.616655
$491$		−	1.07166e11i		−	1.84387i	−0.387339	−	0.921937i	$-0.626606\pi$
$491$		−	1.07166e11i		−	1.84387i	0.387339	−	0.921937i	$-0.373394\pi$
$492$	−1.30105e11	−	7.78275e10i	−2.22042	−	1.32823i
$493$	−1.99070e10			−0.336990
$494$			2.03371e10i			0.341493i
$495$	−1.12718e10	−	2.09995e10i	−0.187746	−	0.349774i
$496$	1.20666e11			1.99370
$497$			3.08257e9i			0.0505229i
$498$	7.21451e10	−	1.20606e11i	1.17298	−	1.96088i
$499$	2.45077e9			0.0395276			0.0197638	−	0.999805i	$-0.493709\pi$
$499$	2.45077e9			0.0395276			0.0197638	+	0.999805i	$0.493709\pi$
$500$		−	1.34142e10i		−	0.214628i
$501$	2.63632e9	+	1.57701e9i	0.0418454	+	0.0250314i
$502$	−5.52509e10			−0.870010
$503$		−	4.84386e10i		−	0.756694i	−0.925664	−	0.378347i	$-0.876493\pi$
$503$		−	4.84386e10i		−	0.756694i	0.925664	−	0.378347i	$-0.123507\pi$
$504$	1.93963e11	−	1.04112e11i	3.00606	−	1.61354i
$505$	2.33327e10			0.358756
$506$		−	1.67123e10i		−	0.254938i
$507$	−3.07285e10	+	5.13693e10i	−0.465061	+	0.777449i
$508$	1.33445e10			0.200377
$509$			3.20903e10i			0.478082i	0.971009	+	0.239041i	$0.0768330\pi$
$509$			3.20903e10i			0.478082i	−0.971009	+	0.239041i	$0.923167\pi$
$510$	6.22795e10	+	3.72548e10i	0.920586	+	0.550683i
$511$	3.00585e10			0.440842
$512$			1.31697e11i			1.91644i
$513$	4.17775e10	+	1.94244e9i	0.603216	+	0.0280464i
$514$	−7.74490e10			−1.10959
$515$		−	3.62089e10i		−	0.514738i
$516$	−1.23763e11	+	2.06896e11i	−1.74578	+	2.91845i
$517$	−4.56246e10			−0.638611
$518$		−	2.06439e11i		−	2.86730i
$519$	1.04242e11	+	6.23562e10i	1.43672	+	0.859430i
$520$	2.58808e10			0.353968
$521$			6.76727e10i			0.918465i	0.888316	+	0.459232i	$0.151875\pi$
$521$			6.76727e10i			0.918465i	−0.888316	+	0.459232i	$0.848125\pi$
$522$	1.67711e10	+	3.12449e10i	0.225882	+	0.420821i
$523$	−6.05025e10			−0.808661			−0.404330	−	0.914613i	$-0.632495\pi$
$523$	−6.05025e10			−0.808661			−0.404330	+	0.914613i	$0.632495\pi$
$524$			1.05921e11i			1.40494i
$525$	−1.03118e10	+	1.72384e10i	−0.135737	+	0.226913i
$526$	−2.15531e11			−2.81557
$527$		−	8.48236e10i		−	1.09970i
$528$	1.39639e11	+	8.35301e10i	1.79668	+	1.07475i
$529$	7.64109e10			0.975737
$530$			7.13060e10i			0.903697i
$531$	−2.98769e10	+	1.60368e10i	−0.375800	+	0.201716i
$532$	1.53455e11			1.91573
$533$			2.66901e10i			0.330706i
$534$	−2.35682e10	+	3.93993e10i	−0.289842	+	0.484533i
$535$	2.87509e10			0.350942
$536$		−	3.88894e11i		−	4.71164i
$537$	−5.36822e10	−	3.21120e10i	−0.645555	−	0.386163i
$538$	3.11654e10			0.372000
$539$			5.60296e10i			0.663839i
$540$	4.23806e9	−	9.11512e10i	0.0498416	−	1.07198i
$541$	−2.66748e10			−0.311396			−0.155698	−	0.987805i	$-0.549763\pi$
$541$	−2.66748e10			−0.311396			−0.155698	+	0.987805i	$0.549763\pi$
$542$			1.63877e11i			1.89898i
$543$	−3.11828e10	+	5.21287e10i	−0.358687	+	0.599622i
$544$	−2.01442e11			−2.30014
$545$			5.08956e10i			0.576892i
$546$	−5.70217e10	−	3.41097e10i	−0.641608	−	0.383802i
$547$	1.39645e11			1.55983			0.779915	−	0.625885i	$-0.215262\pi$
$547$	1.39645e11			1.55983			0.779915	+	0.625885i	$0.215262\pi$
$548$		−	1.69569e11i		−	1.88029i
$549$	−1.79389e10	−	3.34205e10i	−0.197473	−	0.367895i
$550$	−2.99534e10			−0.327337
$551$			1.44181e10i			0.156423i
$552$	1.91586e10	−	3.20278e10i	0.206352	−	0.344961i
$553$	1.78868e11			1.91263
$554$			1.71603e11i			1.82174i
$555$	−4.28323e10	−	2.56217e10i	−0.451439	−	0.270045i
$556$	−2.48544e11			−2.60078
$557$		−	1.88635e10i		−	0.195975i	−0.995188	−	0.0979876i	$-0.968759\pi$
$557$		−	1.88635e10i		−	0.195975i	0.995188	−	0.0979876i	$-0.0312405\pi$
$558$	−1.33135e11	+	7.14619e10i	−1.37327	+	0.737120i
$559$	4.24431e10			0.434670
$560$		−	1.37139e11i		−	1.39447i
$561$	5.87184e10	−	9.81605e10i	0.592820	−	0.991026i
$562$	−2.33959e11			−2.34528
$563$		−	3.06642e10i		−	0.305210i	−0.988287	−	0.152605i	$-0.951234\pi$
$563$		−	3.06642e10i		−	0.305210i	0.988287	−	0.152605i	$-0.0487662\pi$
$564$	−1.49907e11	−	8.96725e10i	−1.48151	−	0.886222i
$565$	2.44712e9			0.0240138
$566$			2.41837e11i			2.35644i
$567$	−7.55159e10	+	1.13879e11i	−0.730645	+	1.10182i
$568$	−1.02649e10			−0.0986187
$569$		−	1.85504e11i		−	1.76972i	−0.465861	−	0.884858i	$-0.654255\pi$
$569$		−	1.85504e11i		−	1.76972i	0.465861	−	0.884858i	$-0.345745\pi$
$570$	2.69827e10	−	4.51075e10i	0.255615	−	0.427316i
$571$	8.50195e10			0.799786			0.399893	−	0.916562i	$-0.369047\pi$
$571$	8.50195e10			0.799786			0.399893	+	0.916562i	$0.369047\pi$
$572$		−	6.99361e10i		−	0.653307i
$573$	6.21317e9	+	3.71664e9i	0.0576362	+	0.0344772i
$574$	2.85319e11			2.62835
$575$			3.40542e9i			0.0311530i
$576$	4.69270e10	+	8.74257e10i	0.426317	+	0.794235i
$577$	−1.80485e11			−1.62831			−0.814155	−	0.580648i	$-0.802799\pi$
$577$	−1.80485e11			−1.62831			−0.814155	+	0.580648i	$0.802799\pi$
$578$			1.42499e11i			1.27673i
$579$	3.39343e10	−	5.67284e10i	0.301942	−	0.504762i
$580$	3.14578e10			0.277982
$581$			1.86688e11i			1.63837i
$582$	2.92754e11	+	1.75122e11i	2.55159	+	1.52633i
$583$	1.12387e11			0.972845
$584$			1.00093e11i			0.860507i
$585$	−1.41542e10	+	7.59749e9i	−0.120855	+	0.0648704i
$586$	3.00911e11			2.55181
$587$			3.34184e10i			0.281471i	0.990047	+	0.140736i	$0.0449467\pi$
$587$			3.34184e10i			0.281471i	−0.990047	+	0.140736i	$0.955053\pi$
$588$	−1.10123e11	+	1.84094e11i	−0.921231	+	1.54004i
$589$	−6.14356e10			−0.510457
$590$			4.26159e10i			0.351693i
$591$	−9.19494e10	−	5.50030e10i	−0.753701	−	0.450854i
$592$	3.40749e11			2.77427
$593$		−	1.21264e11i		−	0.980647i	−0.871541	−	0.490323i	$-0.836879\pi$
$593$		−	1.21264e11i		−	0.980647i	0.871541	−	0.490323i	$-0.163121\pi$
$594$	−2.03536e11	−	9.46339e9i	−1.63492	−	0.0760153i
$595$	−9.64032e10			−0.769173
$596$		−	5.16798e11i		−	4.09577i
$597$	−7.99728e10	+	1.33692e11i	−0.629571	+	1.05246i
$598$	−1.12646e10			−0.0880867
$599$		−	1.08145e11i		−	0.840041i	−0.907515	−	0.420020i	$-0.862023\pi$
$599$		−	1.08145e11i		−	0.840041i	0.907515	−	0.420020i	$-0.137977\pi$
$600$	−5.74031e10	−	3.43378e10i	−0.442925	−	0.264952i
$601$	1.99467e11			1.52888			0.764440	−	0.644695i	$-0.223016\pi$
$601$	1.99467e11			1.52888			0.764440	+	0.644695i	$0.223016\pi$
$602$		−	4.53718e11i		−	3.45462i
$603$	1.14163e11	+	2.12687e11i	0.863486	+	1.60869i
$604$	1.17656e11			0.884030
$605$		−	1.27048e10i		−	0.0948299i
$606$	1.02401e11	−	1.71185e11i	0.759301	−	1.26934i
$607$	7.47882e10			0.550907			0.275453	−	0.961314i	$-0.411172\pi$
$607$	7.47882e10			0.550907			0.275453	+	0.961314i	$0.411172\pi$
$608$			1.45899e11i			1.06767i
$609$	−4.04258e10	−	2.41822e10i	−0.293893	−	0.175803i
$610$	−4.76705e10			−0.344295
$611$			3.07522e10i			0.220654i
$612$	3.85857e11	−	2.07114e11i	2.75056	−	1.47640i
$613$	−2.70342e11			−1.91457			−0.957284	−	0.289148i	$-0.906628\pi$
$613$	−2.70342e11			−1.91457			−0.957284	+	0.289148i	$0.906628\pi$
$614$			4.70030e11i			3.30713i
$615$	3.54117e10	−	5.91983e10i	0.247541	−	0.413818i
$616$	−4.36062e11			−3.02848
$617$			7.48975e10i			0.516805i	0.966037	+	0.258403i	$0.0831961\pi$
$617$			7.48975e10i			0.516805i	−0.966037	+	0.258403i	$0.916804\pi$
$618$	−2.65655e11	−	1.58911e11i	−1.82122	−	1.08943i
$619$	−9.53847e10			−0.649705			−0.324852	−	0.945765i	$-0.605315\pi$
$619$	−9.53847e10			−0.649705			−0.324852	+	0.945765i	$0.605315\pi$
$620$			1.34042e11i			0.907138i
$621$	−1.07590e9	+	2.31402e10i	−0.00723446	+	0.155597i
$622$	−4.34018e11			−2.89965
$623$		−	6.09867e10i		−	0.404839i
$624$	5.63016e10	−	9.41203e10i	0.371349	−	0.620790i
$625$	6.10352e9			0.0400000
$626$		−	3.22039e11i		−	2.09706i
$627$	−7.10951e10	−	4.25282e10i	−0.460013	−	0.275174i
$628$	−1.45699e11			−0.936736
$629$		−	2.39534e11i		−	1.53025i
$630$	8.12175e10	+	1.51309e11i	0.515570	+	0.960515i
$631$	−2.63469e11			−1.66193			−0.830965	−	0.556325i	$-0.812211\pi$
$631$	−2.63469e11			−1.66193			−0.830965	+	0.556325i	$0.812211\pi$
$632$			5.95623e11i			3.73339i
$633$	8.46826e10	−	1.41565e11i	0.527448	−	0.881743i
$634$	3.87402e11			2.39776
$635$			6.07180e9i			0.0373441i
$636$	3.69267e11	+	2.20891e11i	2.25690	+	1.35005i
$637$	3.77655e10			0.229371
$638$		−	7.02438e10i		−	0.423960i
$639$	5.61387e9	−	3.01332e9i	0.0336712	−	0.0180735i
$640$	−7.95445e9			−0.0474122
$641$			1.27087e11i			0.752780i	0.926461	+	0.376390i	$0.122835\pi$
$641$			1.27087e11i			0.752780i	−0.926461	+	0.376390i	$0.877165\pi$
$642$	1.26180e11	−	2.10937e11i	0.742764	−	1.24169i
$643$	2.47669e11			1.44887			0.724433	−	0.689345i	$-0.242101\pi$
$643$	2.47669e11			1.44887			0.724433	+	0.689345i	$0.242101\pi$
$644$			8.49975e10i			0.494155i
$645$	−9.41381e10	−	5.63123e10i	−0.543909	−	0.325360i
$646$	2.52257e11			1.44848
$647$			1.34645e11i			0.768374i	0.923255	+	0.384187i	$0.125518\pi$
$647$			1.34645e11i			0.768374i	−0.923255	+	0.384187i	$0.874482\pi$
$648$	−3.79211e11	−	2.51465e11i	−2.15071	−	1.42619i
$649$	6.71682e10			0.378603
$650$			2.01894e10i			0.113102i
$651$	1.03040e11	−	1.72254e11i	0.573699	−	0.959061i
$652$	−3.86706e11			−2.13989
$653$			1.95881e11i			1.07731i	0.842527	+	0.538655i	$0.181067\pi$
$653$			1.95881e11i			1.07731i	−0.842527	+	0.538655i	$0.818933\pi$
$654$	3.73407e11	+	2.23368e11i	2.04113	+	1.22098i
$655$	−4.81943e10			−0.261837
$656$			4.70948e11i			2.54307i
$657$	−2.93832e10	−	5.47414e10i	−0.157702	−	0.293802i
$658$	3.28743e11			1.75369
$659$			1.11563e11i			0.591531i	0.955261	+	0.295765i	$0.0955747\pi$
$659$			1.11563e11i			0.591531i	−0.955261	+	0.295765i	$0.904425\pi$
$660$	−9.27892e10	+	1.55117e11i	−0.489015	+	0.817493i
$661$	−2.12263e11			−1.11191			−0.555953	−	0.831214i	$-0.687647\pi$
$661$	−2.12263e11			−1.11191			−0.555953	+	0.831214i	$0.687647\pi$
$662$			1.50830e11i			0.785338i
$663$	−6.61629e10	−	3.95778e10i	−0.342421	−	0.204832i
$664$	−6.21663e11			−3.19803
$665$			6.98224e10i			0.357033i
$666$	−3.75959e11	+	2.01801e11i	−1.91093	+	1.02572i
$667$	−7.98607e9			−0.0403487
$668$		−	2.32979e10i		−	0.117007i
$669$	−1.92630e10	+	3.22022e10i	−0.0961654	+	0.160761i
$670$	3.03374e11			1.50549
$671$			7.51349e10i			0.370639i
$672$	−4.09075e11	−	2.44703e11i	−2.00597	−	1.19995i
$673$	−5.44544e10			−0.265444			−0.132722	−	0.991153i	$-0.542372\pi$
$673$	−5.44544e10			−0.265444			−0.132722	+	0.991153i	$0.542372\pi$
$674$		−	7.01695e11i		−	3.40023i
$675$	4.14740e10	+	1.92833e9i	0.199784	+	0.00928894i
$676$	4.53965e11			2.17388
$677$		−	3.73397e11i		−	1.77753i	−0.458367	−	0.888763i	$-0.651565\pi$
$677$		−	3.73397e11i		−	1.77753i	0.458367	−	0.888763i	$-0.348435\pi$
$678$	1.07398e10	−	1.79538e10i	0.0508248	−	0.0849647i
$679$	−4.53158e11			−2.13192
$680$		−	3.21019e11i		−	1.50140i
$681$	2.92588e11	+	1.75023e11i	1.36041	+	0.813778i
$682$	2.99309e11			1.38351
$683$			3.36543e11i			1.54653i	0.634085	+	0.773263i	$0.281377\pi$
$683$			3.36543e11i			1.54653i	−0.634085	+	0.773263i	$0.718623\pi$
$684$	−1.50008e11	−	2.79467e11i	−0.685313	−	1.27675i
$685$	7.71544e10			0.350428
$686$			1.36122e11i			0.614656i
$687$	−1.70989e11	+	2.85846e11i	−0.767613	+	1.28323i
$688$	7.48910e11			3.34253
$689$		−	7.57523e10i		−	0.336139i
$690$	2.49847e10	+	1.49455e10i	0.110224	+	0.0659348i
$691$	−1.37252e11			−0.602013			−0.301007	−	0.953622i	$-0.597323\pi$
$691$	−1.37252e11			−0.602013			−0.301007	+	0.953622i	$0.597323\pi$
$692$		−	9.21215e11i		−	4.01732i
$693$	2.38483e11	−	1.28009e11i	1.03401	−	0.555019i
$694$	−1.08490e11			−0.467684
$695$		−	1.13088e11i		−	0.484705i
$696$	8.05258e10	−	1.34616e11i	0.343161	−	0.573668i
$697$	3.31058e11			1.40273
$698$		−	2.47635e11i		−	1.04325i
$699$	1.99504e11	+	1.19341e11i	0.835684	+	0.499896i
$700$	1.52340e11			0.634487
$701$			4.12721e11i			1.70917i	0.519316	+	0.854583i	$0.326187\pi$
$701$			4.12721e11i			1.70917i	−0.519316	+	0.854583i	$0.673813\pi$
$702$	−6.37859e9	+	1.37189e11i	−0.0262649	+	0.564900i
$703$	−1.73488e11			−0.710311
$704$		−	1.96548e11i		−	0.800160i
$705$	4.08012e10	−	6.82080e10i	0.165164	−	0.276108i
$706$	−7.47783e11			−3.00993
$707$			2.64980e11i			1.06056i
$708$	2.20692e11	+	1.32015e11i	0.878321	+	0.525401i
$709$	1.59025e11			0.629333			0.314667	−	0.949202i	$-0.398107\pi$
$709$	1.59025e11			0.629333			0.314667	+	0.949202i	$0.398107\pi$
$710$		−	8.00755e9i		−	0.0315113i
$711$	−1.74850e11	−	3.25747e11i	−0.684205	−	1.27468i
$712$	2.03083e11			0.790231
$713$		−	3.40287e10i		−	0.131670i
$714$	−4.23089e11	+	7.07284e11i	−1.62794	+	2.72145i
$715$	3.18211e10			0.121756
$716$			4.74405e11i			1.80508i
$717$	−1.43327e11	−	8.57364e10i	−0.542314	−	0.324406i
$718$	9.72775e10			0.366028
$719$			1.83117e11i			0.685195i	0.939482	+	0.342597i	$0.111307\pi$
$719$			1.83117e11i			0.685195i	−0.939482	+	0.342597i	$0.888693\pi$
$720$	−2.49752e11	+	1.34058e11i	−0.929350	+	0.498842i
$721$	4.11210e11			1.52168
$722$			3.18326e11i			1.17145i
$723$	7.80596e9	−	1.30494e10i	0.0285676	−	0.0477569i
$724$	4.60676e11			1.67665
$725$			1.43134e10i			0.0518072i
$726$	−9.32114e10	−	5.57579e10i	−0.335523	−	0.200706i
$727$	2.59798e10			0.0930032			0.0465016	−	0.998918i	$-0.485193\pi$
$727$	2.59798e10			0.0930032			0.0465016	+	0.998918i	$0.485193\pi$
$728$			2.93918e11i			1.04641i
$729$	2.81211e11	+	2.62064e10i	0.995686	+	0.0927891i
$730$	−7.80823e10			−0.274955
$731$		−	5.26454e11i		−	1.84370i
$732$	−1.47673e11	+	2.46868e11i	−0.514348	+	0.859844i
$733$	−6.63035e10			−0.229678			−0.114839	−	0.993384i	$-0.536635\pi$
$733$	−6.63035e10			−0.229678			−0.114839	+	0.993384i	$0.536635\pi$
$734$		−	5.89855e11i		−	2.03218i
$735$	−8.37634e10	−	5.01062e10i	−0.287015	−	0.171689i
$736$	−8.08123e10			−0.275401
$737$		−	4.78156e11i		−	1.62069i
$738$	−2.78909e11	−	5.19612e11i	−0.940237	−	1.75168i
$739$	−1.53919e11			−0.516078			−0.258039	−	0.966135i	$-0.583076\pi$
$739$	−1.53919e11			−0.516078			−0.258039	+	0.966135i	$0.583076\pi$
$740$			3.78521e11i			1.26230i
$741$	−2.86652e10	+	4.79201e10i	−0.0950785	+	0.158944i
$742$	−8.09795e11			−2.67153
$743$		−	3.56107e9i		−	0.0116849i	−0.999983	−	0.00584246i	$-0.998140\pi$
$743$		−	3.56107e9i		−	0.0116849i	0.999983	−	0.00584246i	$-0.00185972\pi$
$744$	5.73600e11	+	3.43121e11i	1.87205	+	1.11984i
$745$	2.35144e11			0.763324
$746$			2.46884e11i			0.797145i
$747$	3.39989e11	−	1.82494e11i	1.09190	−	0.586092i
$748$	−8.67472e11			−2.77108
$749$			3.26512e11i			1.03746i
$750$	2.67867e10	−	4.47798e10i	0.0846593	−	0.141526i
$751$	−3.54316e10			−0.111386			−0.0556931	−	0.998448i	$-0.517737\pi$
$751$	−3.54316e10			−0.111386			−0.0556931	+	0.998448i	$0.517737\pi$
$752$			5.42624e11i			1.69679i
$753$	−1.30187e11	−	7.78761e10i	−0.404937	−	0.242228i
$754$	−4.73463e10			−0.146487
$755$			5.35339e10i			0.164756i
$756$	1.03517e12	+	4.81300e10i	3.16901	+	0.147343i
$757$	3.97220e11			1.20962			0.604808	−	0.796371i	$-0.293250\pi$
$757$	3.97220e11			1.20962			0.604808	+	0.796371i	$0.293250\pi$
$758$		−	4.31824e11i		−	1.30807i
$759$	2.35560e10	−	3.93790e10i	0.0709799	−	0.118658i
$760$	−2.32506e11			−0.696915
$761$		−	8.97779e10i		−	0.267689i	−0.991002	−	0.133845i	$-0.957268\pi$
$761$		−	8.97779e10i		−	0.267689i	0.991002	−	0.133845i	$-0.0427323\pi$
$762$	4.45471e10	+	2.66475e10i	0.132129	+	0.0790382i
$763$	−5.78002e11			−1.70542
$764$		−	5.49076e10i		−	0.161161i
$765$	9.42375e10	+	1.75566e11i	0.275155	+	0.512619i
$766$	−2.81454e11			−0.817508
$767$		−	4.52732e10i		−	0.130816i
$768$	−1.95895e11	+	3.27482e11i	−0.563092	+	0.941330i
$769$	−4.29746e11			−1.22887			−0.614436	−	0.788967i	$-0.710616\pi$
$769$	−4.29746e11			−1.22887			−0.614436	+	0.788967i	$0.710616\pi$
$770$		−	3.40169e11i		−	0.967680i
$771$	−1.82492e11	−	1.09164e11i	−0.516448	−	0.308933i
$772$	−5.01325e11			−1.41140
$773$			1.11151e11i			0.311312i	0.987811	+	0.155656i	$0.0497491\pi$
$773$			1.11151e11i			0.311312i	−0.987811	+	0.155656i	$0.950251\pi$
$774$	−8.26295e11	+	4.43526e11i	−2.30235	+	1.23582i
$775$	−6.09894e10			−0.169062
$776$		−	1.50900e12i		−	4.16142i
$777$	2.90976e11	−	4.86429e11i	0.798313	−	1.33455i
$778$	7.88102e11			2.15112
$779$		−	2.39777e11i		−	0.651116i
$780$	1.04553e11	+	6.25425e10i	0.282462	+	0.168965i
$781$	−1.26209e10			−0.0339224
$782$			1.39723e11i			0.373630i
$783$	−4.52213e9	+	9.72609e10i	−0.0120308	+	0.258756i
$784$	6.66374e11			1.76382
$785$		−	6.62933e10i		−	0.174579i
$786$	−2.11512e11	+	3.53589e11i	−0.554173	+	0.926420i
$787$	3.22875e11			0.841658			0.420829	−	0.907140i	$-0.361739\pi$
$787$	3.22875e11			0.841658			0.420829	+	0.907140i	$0.361739\pi$
$788$			8.12583e11i			2.10748i
$789$	−5.07852e11	−	3.03791e11i	−1.31048	−	0.783912i
$790$	−4.64642e11			−1.19292
$791$			2.77910e10i			0.0709901i
$792$	4.26265e11	+	7.94139e11i	1.08338	+	2.01835i
$793$	5.06430e10			0.128064
$794$			2.32540e11i			0.585080i
$795$	−1.00506e11	+	1.68017e11i	−0.251607	+	0.420616i
$796$	1.18147e12			2.94287
$797$			4.82426e10i			0.119563i	0.998211	+	0.0597815i	$0.0190404\pi$
$797$			4.82426e10i			0.119563i	−0.998211	+	0.0597815i	$0.980960\pi$
$798$	5.12268e11	+	3.06433e11i	1.26324	+	0.755655i
$799$	3.81444e11			0.935930
$800$			1.44839e11i			0.353611i
$801$	−1.11067e11	+	5.96166e10i	−0.269807	+	0.144823i
$802$	5.61296e11			1.35673
$803$			1.23068e11i			0.295993i
$804$	9.39787e11	−	1.57106e12i	2.24908	−	3.75983i
$805$	−3.86741e10			−0.0920951
$806$		−	2.01743e11i		−	0.478033i
$807$	7.34345e10	+	4.39276e10i	0.173143	+	0.103572i
$808$	−8.82373e11			−2.07017
$809$		−	4.74471e10i		−	0.110768i	−0.998465	−	0.0553842i	$-0.982362\pi$
$809$		−	4.74471e10i		−	0.110768i	0.998465	−	0.0553842i	$-0.0176384\pi$
$810$	1.96166e11	−	2.95821e11i	0.455706	−	0.687208i
$811$	1.83507e11			0.424199			0.212100	−	0.977248i	$-0.431970\pi$
$811$	1.83507e11			0.424199			0.212100	+	0.977248i	$0.431970\pi$
$812$			3.57254e11i			0.821775i
$813$	−2.30985e11	+	3.86141e11i	−0.528715	+	0.883861i
$814$	8.45219e11			1.92518
$815$		−	1.75952e11i		−	0.398809i
$816$	−1.16745e12	−	6.98352e11i	−2.63315	−	1.57512i
$817$	−3.81298e11			−0.855807
$818$			1.42334e11i			0.317903i
$819$	−8.62817e10	−	1.60744e11i	−0.191771	−	0.357273i
$820$	−5.23152e11			−1.15710
$821$		−	8.94845e10i		−	0.196959i	−0.995139	−	0.0984794i	$-0.968602\pi$
$821$		−	8.94845e10i		−	0.196959i	0.995139	−	0.0984794i	$-0.0313978\pi$
$822$	3.38610e11	−	5.66060e11i	0.741674	−	1.23987i
$823$	8.24619e11			1.79744			0.898719	−	0.438524i	$-0.144499\pi$
$823$	8.24619e11			1.79744			0.898719	+	0.438524i	$0.144499\pi$
$824$			1.36931e12i			2.97026i
$825$	−7.05787e10	−	4.22193e10i	−0.152355	−	0.0911372i
$826$	−4.83973e11			−1.03968
$827$			8.26757e11i			1.76749i	0.467973	+	0.883743i	$0.344985\pi$
$827$			8.26757e11i			1.76749i	−0.467973	+	0.883743i	$0.655015\pi$
$828$	1.54794e11	−	8.30880e10i	0.329332	−	0.176774i
$829$	−2.54789e11			−0.539465			−0.269732	−	0.962935i	$-0.586935\pi$
$829$	−2.54789e11			−0.539465			−0.269732	+	0.962935i	$0.586935\pi$
$830$		−	4.84955e11i		−	1.02185i
$831$	−2.41875e11	+	4.04346e11i	−0.507209	+	0.847909i
$832$	−1.32479e11			−0.276473
$833$		−	4.68435e11i		−	0.972903i
$834$	−8.29695e11	−	4.96314e11i	−1.71496	−	1.02587i
$835$	1.06006e10			0.0218064
$836$			6.28288e11i			1.28627i
$837$	−4.14429e11	−	1.92688e10i	−0.844400	−	0.0392603i
$838$	1.12029e12			2.27172
$839$			6.07397e11i			1.22581i	0.790155	+	0.612907i	$0.210000\pi$
$839$			6.07397e11i			1.22581i	−0.790155	+	0.612907i	$0.790000\pi$
$840$	3.89961e11	−	6.51905e11i	0.783257	−	1.30938i
$841$	4.66680e11			0.932900
$842$			1.73106e11i			0.344400i
$843$	−5.51274e11	−	3.29766e11i	−1.09158	−	0.652973i
$844$	−1.25105e12			−2.46550
$845$			2.06555e11i			0.405144i
$846$	−3.21358e11	−	5.98694e11i	−0.627346	−	1.16876i
$847$	1.44283e11			0.280338
$848$		−	1.33665e12i		−	2.58485i
$849$	−3.40870e11	+	5.69837e11i	−0.656081	+	1.09678i
$850$	2.50425e11			0.479736
$851$		−	9.60937e10i		−	0.183222i
$852$	−4.14681e10	−	2.48057e10i	−0.0786965	−	0.0470753i
$853$	1.34856e11			0.254726			0.127363	−	0.991856i	$-0.459349\pi$
$853$	1.34856e11			0.254726			0.127363	+	0.991856i	$0.459349\pi$
$854$		−	5.41376e11i		−	1.01781i
$855$	1.27158e11	−	6.82539e10i	0.237947	−	0.127721i
$856$	−1.08727e12			−2.02509
$857$		−	7.33386e11i		−	1.35959i	−0.733400	−	0.679797i	$-0.762068\pi$
$857$		−	7.33386e11i		−	1.35959i	0.733400	−	0.679797i	$-0.237932\pi$
$858$	1.39655e11	−	2.33463e11i	0.257695	−	0.430793i
$859$	4.51837e11			0.829868			0.414934	−	0.909852i	$-0.363805\pi$
$859$	4.51837e11			0.829868			0.414934	+	0.909852i	$0.363805\pi$
$860$			8.31925e11i			1.52086i
$861$	6.72292e11	+	4.02157e11i	1.22334	+	0.731784i
$862$	4.44098e11			0.804359
$863$		−	6.73082e11i		−	1.21346i	−0.794909	−	0.606729i	$-0.792481\pi$
$863$		−	6.73082e11i		−	1.21346i	0.794909	−	0.606729i	$-0.207519\pi$
$864$	−4.57601e10	+	9.84198e11i	−0.0821168	+	1.76615i
$865$	4.19155e11			0.748704
$866$			8.02548e11i			1.42692i
$867$	−2.00852e11	+	3.35768e11i	−0.355467	+	0.594241i
$868$	−1.52226e12			−2.68170
$869$			7.32335e11i			1.28419i
$870$	1.05013e11	+	6.28177e10i	0.183302	+	0.109649i
$871$	−3.22290e11			−0.559983
$872$		−	1.92472e12i		−	3.32891i
$873$	4.42978e11	+	8.25275e11i	0.762650	+	1.42083i
$874$	1.01198e11			0.173431
$875$			6.93153e10i			0.118249i
$876$	−2.41882e11	+	4.04359e11i	−0.410760	+	0.686674i
$877$	−8.29492e11			−1.40221			−0.701106	−	0.713057i	$-0.747310\pi$
$877$	−8.29492e11			−1.40221			−0.701106	+	0.713057i	$0.747310\pi$
$878$			1.02925e12i			1.73197i
$879$	7.09033e11	+	4.24135e11i	1.18771	+	0.710474i
$880$	5.61484e11			0.936283
$881$		−	1.16546e11i		−	0.193461i	−0.995311	−	0.0967305i	$-0.969161\pi$
$881$		−	1.16546e11i		−	0.193461i	0.995311	−	0.0967305i	$-0.0308385\pi$
$882$	−7.35231e11	+	3.94646e11i	−1.21493	+	0.652128i
$883$	−4.57775e11			−0.753025			−0.376512	−	0.926412i	$-0.622877\pi$
$883$	−4.57775e11			−0.753025			−0.376512	+	0.926412i	$0.622877\pi$
$884$			5.84700e11i			0.957468i
$885$	−6.00672e10	+	1.00415e11i	−0.0979184	+	0.163692i
$886$	3.90161e11			0.633153
$887$			8.01818e11i			1.29533i	0.761924	+	0.647667i	$0.224255\pi$
$887$			8.01818e11i			1.29533i	−0.761924	+	0.647667i	$0.775745\pi$
$888$	1.61979e12	+	9.68939e11i	2.60500	+	1.55828i
$889$	−6.89550e10			−0.110397
$890$			1.58424e11i			0.252500i
$891$	−4.66251e11	−	3.09183e11i	−0.739791	−	0.490575i
$892$	2.84580e11			0.449516
$893$		−	2.76270e11i		−	0.434438i
$894$	1.03199e12	−	1.72519e12i	1.61556	−	2.70076i
$895$	−2.15855e11			−0.336411
$896$		−	9.03355e10i		−	0.140161i
$897$	−2.65426e10	−	1.58774e10i	−0.0409990	−	0.0245251i
$898$	−6.95700e10			−0.106983
$899$		−	1.43026e11i		−	0.218966i
$900$	−1.48918e11	−	2.77437e11i	−0.226975	−	0.422857i
$901$	−9.39614e11			−1.42577
$902$			1.16817e12i			1.76474i
$903$	6.39516e11	−	1.06909e12i	0.961835	−	1.60792i
$904$	−9.25428e10			−0.138570
$905$			2.09609e11i			0.312475i
$906$	3.92763e11	+	2.34946e11i	0.582932	+	0.348703i
$907$	−4.83758e10			−0.0714824			−0.0357412	−	0.999361i	$-0.511379\pi$
$907$	−4.83758e10			−0.0714824			−0.0357412	+	0.999361i	$0.511379\pi$
$908$		−	2.58568e12i		−	3.80393i
$909$	4.82572e11	−	2.59027e11i	0.706816	−	0.379394i
$910$	−2.29283e11			−0.334354
$911$		−	9.65899e11i		−	1.40236i	−0.712986	−	0.701178i	$-0.752658\pi$
$911$		−	9.65899e11i		−	1.40236i	0.712986	−	0.701178i	$-0.247342\pi$
$912$	−5.05799e11	+	8.45552e11i	−0.731137	+	1.22225i
$913$	−7.64351e11			−1.10004
$914$		−	7.34201e11i		−	1.05204i
$915$	−1.12325e11	−	6.71917e10i	−0.160248	−	0.0958586i
$916$	2.52610e12			3.58813
$917$		−	5.47324e11i		−	0.774047i
$918$	1.70166e12	+	7.91186e10i	2.39609	+	0.111406i
$919$	1.14405e12			1.60392			0.801962	−	0.597375i	$-0.203789\pi$
$919$	1.14405e12			1.60392			0.801962	+	0.597375i	$0.203789\pi$
$920$		−	1.28783e11i		−	0.179766i
$921$	−6.62507e11	+	1.10752e12i	−0.920772	+	1.53927i
$922$	6.86409e11			0.949859
$923$			8.50685e9i			0.0117209i
$924$	−1.76161e12	−	1.05377e12i	−2.41669	−	1.44563i
$925$	−1.72228e11			−0.235254
$926$			1.03958e12i			1.41388i
$927$	−4.01972e11	−	7.48881e11i	−0.544349	−	1.01413i
$928$	−3.39663e11			−0.457990
$929$		−	7.33571e11i		−	0.984870i	−0.870349	−	0.492435i	$-0.836107\pi$
$929$		−	7.33571e11i		−	0.984870i	0.870349	−	0.492435i	$-0.163893\pi$
$930$	−2.67666e11	+	4.47462e11i	−0.357818	+	0.598170i
$931$	−3.39276e11			−0.451600
$932$		−	1.76307e12i		−	2.33671i
$933$	−1.02267e12	−	6.11748e11i	−1.34961	−	0.807321i
$934$	−2.59275e12			−3.40701
$935$		−	3.94702e11i		−	0.516443i
$936$	5.35272e11	−	2.87315e11i	0.697383	−	0.374330i
$937$	−3.55464e11			−0.461145			−0.230573	−	0.973055i	$-0.574060\pi$
$937$	−3.55464e11			−0.461145			−0.230573	+	0.973055i	$0.574060\pi$
$938$			3.44530e12i			4.45057i
$939$	4.53914e11	−	7.58816e11i	0.583864	−	0.976054i
$940$	−6.02773e11			−0.772045
$941$		−	6.76442e11i		−	0.862724i	−0.902179	−	0.431362i	$-0.858033\pi$
$941$		−	6.76442e11i		−	0.862724i	0.902179	−	0.431362i	$-0.141967\pi$
$942$	−4.86376e11	−	2.90944e11i	−0.617687	−	0.369493i
$943$	1.32811e11			0.167952
$944$		−	7.98847e11i		−	1.00595i
$945$	−2.18993e10	+	4.71004e11i	−0.0274601	+	0.590606i
$946$	1.85765e12			2.31953
$947$			1.02862e12i			1.27896i	0.768809	+	0.639479i	$0.220850\pi$
$947$			1.02862e12i			1.27896i	−0.768809	+	0.639479i	$0.779150\pi$
$948$	−1.43936e12	+	2.40620e12i	−1.78212	+	2.97919i
$949$	8.29511e10			0.102272
$950$		−	1.81377e11i		−	0.222683i
$951$	9.12830e11	+	5.46044e11i	1.11601	+	0.667583i
$952$	3.64569e12			4.43845
$953$		−	1.23011e11i		−	0.149132i	−0.997216	−	0.0745661i	$-0.976243\pi$
$953$		−	1.23011e11i		−	0.149132i	0.997216	−	0.0745661i	$-0.0237572\pi$
$954$	7.91603e11	+	1.47477e12i	0.955683	+	1.78045i
$955$	2.49831e10			0.0300353
$956$			1.26662e12i			1.51640i
$957$	9.90087e10	−	1.65514e11i	0.118039	−	0.197328i
$958$	−2.33361e12			−2.77056
$959$			8.76212e11i			1.03594i
$960$	2.93835e11	+	1.75769e11i	0.345955	+	0.206946i
$961$	−2.43455e11			−0.285447
$962$		−	5.69701e11i		−	0.665192i
$963$	5.94632e11	−	3.19177e11i	0.691422	−	0.371131i
$964$	−1.15321e11			−0.133536
$965$		−	2.28104e11i		−	0.263041i
$966$	−1.69730e11	+	2.83741e11i	−0.194918	+	0.325847i
$967$	−2.66857e11			−0.305191			−0.152596	−	0.988289i	$-0.548763\pi$
$967$	−2.66857e11			−0.305191			−0.152596	+	0.988289i	$0.548763\pi$
$968$			4.80457e11i			0.547209i
$969$	5.94390e11	+	3.55557e11i	0.674181	+	0.403287i
$970$	1.17716e12			1.32969
$971$		−	1.52105e12i		−	1.71106i	−0.517750	−	0.855532i	$-0.673230\pi$
$971$		−	1.52105e12i		−	1.71106i	0.517750	−	0.855532i	$-0.326770\pi$
$972$	−9.24261e11	−	1.93226e12i	−1.03545	−	2.16471i
$973$	1.28430e12			1.43289
$974$		−	1.70654e12i		−	1.89618i
$975$	−2.84570e10	+	4.75720e10i	−0.0314899	+	0.0526421i
$976$	8.93597e11			0.984788
$977$			1.09651e12i			1.20347i	0.798696	+	0.601735i	$0.205524\pi$
$977$			1.09651e12i			1.20347i	−0.798696	+	0.601735i	$0.794476\pi$
$978$	−1.29091e12	−	7.72209e11i	−1.41105	−	0.844072i
$979$	2.49696e11			0.271820
$980$			7.40241e11i			0.802543i
$981$	5.65017e11	+	1.05264e12i	0.610078	+	1.13658i
$982$	−3.16149e12			−3.39974
$983$		−	4.45708e11i		−	0.477349i	−0.971100	−	0.238675i	$-0.923287\pi$
$983$		−	4.45708e11i		−	0.477349i	0.971100	−	0.238675i	$-0.0767129\pi$
$984$	−1.33917e12	+	2.23871e12i	−1.42841	+	2.38790i
$985$	−3.69727e11			−0.392768
$986$			5.87272e11i			0.621344i
$987$	7.74612e11	+	4.63363e11i	0.816235	+	0.488262i
$988$	4.23484e11			0.444436
$989$		−	2.11198e11i		−	0.220752i
$990$	−6.19503e11	+	3.32527e11i	−0.644915	+	0.346167i
$991$	5.99867e11			0.621957			0.310979	−	0.950417i	$-0.399343\pi$
$991$	5.99867e11			0.621957			0.310979	+	0.950417i	$0.399343\pi$
$992$		−	1.44731e12i		−	1.49456i
$993$	−2.12595e11	+	3.55399e11i	−0.218654	+	0.365527i
$994$	9.09386e10			0.0931543
$995$			5.37573e11i			0.548460i
$996$	−2.51140e12	−	1.50229e12i	−2.55199	−	1.52657i
$997$	−6.40433e11			−0.648176			−0.324088	−	0.946027i	$-0.605057\pi$
$997$	−6.40433e11			−0.648176			−0.324088	+	0.946027i	$0.605057\pi$
$998$		−	7.22998e10i		−	0.0728811i
$999$	−1.17031e12	−	5.44132e10i	−1.17500	−	0.0546314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.9.c.a.11.1	✓	10
3.2	odd	2	inner	15.9.c.a.11.10	yes	10
4.3	odd	2		240.9.l.b.161.4		10
5.2	odd	4		75.9.d.c.74.19		20
5.3	odd	4		75.9.d.c.74.2		20
5.4	even	2		75.9.c.g.26.10		10
12.11	even	2		240.9.l.b.161.3		10
15.2	even	4		75.9.d.c.74.1		20
15.8	even	4		75.9.d.c.74.20		20
15.14	odd	2		75.9.c.g.26.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.1	✓	10	1.1	even	1	trivial
15.9.c.a.11.10	yes	10	3.2	odd	2	inner
75.9.c.g.26.1		10	15.14	odd	2
75.9.c.g.26.10		10	5.4	even	2
75.9.d.c.74.1		20	15.2	even	4
75.9.d.c.74.2		20	5.3	odd	4
75.9.d.c.74.19		20	5.2	odd	4
75.9.d.c.74.20		20	15.8	even	4
240.9.l.b.161.3		10	12.11	even	2
240.9.l.b.161.4		10	4.3	odd	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)

\(f(q)\)	\(=\)	\(q-29.5009i q^{2} +(41.5815 - 69.5124i) q^{3} -614.301 q^{4} -279.508i q^{5} +(-2050.68 - 1226.69i) q^{6} +3174.27 q^{7} +10570.2i q^{8} +(-3102.96 - 5780.86i) q^{9} +O(q^{10})\)	\(q-29.5009i q^{2} +(41.5815 - 69.5124i) q^{3} -614.301 q^{4} -279.508i q^{5} +(-2050.68 - 1226.69i) q^{6} +3174.27 q^{7} +10570.2i q^{8} +(-3102.96 - 5780.86i) q^{9} -8245.74 q^{10} +12996.3i q^{11} +(-25543.6 + 42701.6i) q^{12} +8759.90 q^{13} -93643.7i q^{14} +(-19429.3 - 11622.4i) q^{15} +154569. q^{16} -108656. i q^{17} +(-170540. + 91540.0i) q^{18} -78696.7 q^{19} +171702. i q^{20} +(131991. - 220651. i) q^{21} +383403. q^{22} -43589.4i q^{23} +(734760. + 439524. i) q^{24} -78125.0 q^{25} -258425. i q^{26} +(-530868. - 24682.6i) q^{27} -1.94996e6 q^{28} -183211. i q^{29} +(-342870. + 573182. i) q^{30} +780664. q^{31} -1.85394e6i q^{32} +(903407. + 540407. i) q^{33} -3.20544e6 q^{34} -887235. i q^{35} +(1.90615e6 + 3.55119e6i) q^{36} +2.20452e6 q^{37} +2.32162e6i q^{38} +(364250. - 608922. i) q^{39} +2.95446e6 q^{40} +3.04685e6i q^{41} +(-6.50940e6 - 3.89384e6i) q^{42} +4.84516e6 q^{43} -7.98367e6i q^{44} +(-1.61580e6 + 867303. i) q^{45} -1.28593e6 q^{46} +3.51057e6i q^{47} +(6.42720e6 - 1.07444e7i) q^{48} +4.31118e6 q^{49} +2.30476e6i q^{50} +(-7.55293e6 - 4.51807e6i) q^{51} -5.38121e6 q^{52} -8.64762e6i q^{53} +(-728158. + 1.56611e7i) q^{54} +3.63259e6 q^{55} +3.35526e7i q^{56} +(-3.27232e6 + 5.47040e6i) q^{57} -5.40489e6 q^{58} -5.16824e6i q^{59} +(1.19355e7 + 7.13964e6i) q^{60} +5.78123e6 q^{61} -2.30303e7i q^{62} +(-9.84963e6 - 1.83500e7i) q^{63} -1.51233e7 q^{64} -2.44847e6i q^{65} +(1.59425e7 - 2.66513e7i) q^{66} -3.67916e7 q^{67} +6.67474e7i q^{68} +(-3.03001e6 - 1.81251e6i) q^{69} -2.61742e7 q^{70} +971113. i q^{71} +(6.11048e7 - 3.27989e7i) q^{72} +9.46941e6 q^{73} -6.50352e7i q^{74} +(-3.24855e6 + 5.43066e6i) q^{75} +4.83434e7 q^{76} +4.12539e7i q^{77} +(-1.79637e7 - 1.07457e7i) q^{78} +5.63493e7 q^{79} -4.32033e7i q^{80} +(-2.37900e7 + 3.58756e7i) q^{81} +8.98849e7 q^{82} +5.88128e7i q^{83} +(-8.10821e7 + 1.35546e8i) q^{84} -3.03702e7 q^{85} -1.42936e8i q^{86} +(-1.27355e7 - 7.61819e6i) q^{87} -1.37374e8 q^{88} -1.92128e7i q^{89} +(2.55862e7 + 4.76675e7i) q^{90} +2.78063e7 q^{91} +2.67770e7i q^{92} +(3.24612e7 - 5.42658e7i) q^{93} +1.03565e8 q^{94} +2.19964e7i q^{95} +(-1.28872e8 - 7.70897e7i) q^{96} -1.42760e8 q^{97} -1.27184e8i q^{98} +(7.51301e7 - 4.03271e7i) 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

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