LMFDB - Embedded newform 75.9.c.g.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(26,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, 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("75.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.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:	$30.5533957546$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{11}\cdot 5^{10} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.1
Root			$18.9110 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.g.26.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.5009i q^{2} +(-41.5815 - 69.5124i) q^{3} -614.301 q^{4} +(-2050.68 + 1226.69i) q^{6} -3174.27 q^{7} +10570.2i q^{8} +(-3102.96 + 5780.86i) q^{9} +O(q^{10})$	\(q-29.5009i q^{2} +(-41.5815 - 69.5124i) q^{3} -614.301 q^{4} +(-2050.68 + 1226.69i) q^{6} -3174.27 q^{7} +10570.2i q^{8} +(-3102.96 + 5780.86i) q^{9} -12996.3i q^{11} +(25543.6 + 42701.6i) q^{12} -8759.90 q^{13} +93643.7i q^{14} +154569. q^{16} -108656. i q^{17} +(170540. + 91540.0i) q^{18} -78696.7 q^{19} +(131991. + 220651. i) q^{21} -383403. q^{22} -43589.4i q^{23} +(734760. - 439524. i) q^{24} +258425. i q^{26} +(530868. - 24682.6i) q^{27} +1.94996e6 q^{28} +183211. i q^{29} +780664. q^{31} -1.85394e6i q^{32} +(-903407. + 540407. i) q^{33} -3.20544e6 q^{34} +(1.90615e6 - 3.55119e6i) q^{36} -2.20452e6 q^{37} +2.32162e6i q^{38} +(364250. + 608922. i) q^{39} -3.04685e6i q^{41} +(6.50940e6 - 3.89384e6i) q^{42} -4.84516e6 q^{43} +7.98367e6i q^{44} -1.28593e6 q^{46} +3.51057e6i q^{47} +(-6.42720e6 - 1.07444e7i) q^{48} +4.31118e6 q^{49} +(-7.55293e6 + 4.51807e6i) q^{51} +5.38121e6 q^{52} -8.64762e6i q^{53} +(-728158. - 1.56611e7i) q^{54} -3.35526e7i q^{56} +(3.27232e6 + 5.47040e6i) q^{57} +5.40489e6 q^{58} +5.16824e6i q^{59} +5.78123e6 q^{61} -2.30303e7i q^{62} +(9.84963e6 - 1.83500e7i) q^{63} -1.51233e7 q^{64} +(1.59425e7 + 2.66513e7i) q^{66} +3.67916e7 q^{67} +6.67474e7i q^{68} +(-3.03001e6 + 1.81251e6i) q^{69} -971113. i q^{71} +(-6.11048e7 - 3.27989e7i) q^{72} -9.46941e6 q^{73} +6.50352e7i q^{74} +4.83434e7 q^{76} +4.12539e7i q^{77} +(1.79637e7 - 1.07457e7i) q^{78} +5.63493e7 q^{79} +(-2.37900e7 - 3.58756e7i) q^{81} -8.98849e7 q^{82} +5.88128e7i q^{83} +(-8.10821e7 - 1.35546e8i) q^{84} +1.42936e8i q^{86} +(1.27355e7 - 7.61819e6i) q^{87} +1.37374e8 q^{88} +1.92128e7i q^{89} +2.78063e7 q^{91} +2.67770e7i q^{92} +(-3.24612e7 - 5.42658e7i) q^{93} +1.03565e8 q^{94} +(-1.28872e8 + 7.70897e7i) q^{96} +1.42760e8 q^{97} -1.27184e8i q^{98} +(7.51301e7 + 4.03271e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 3812 q^{12} + 55464 q^{13} + 280386 q^{16} + 419800 q^{18} - 231516 q^{19} + 289572 q^{21} - 1129940 q^{22} + 1136334 q^{24} + 335512 q^{27} + 3340724 q^{28} + 881620 q^{31} - 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} - 4672616 q^{37} + 1826792 q^{39} + 5392860 q^{42} - 7731336 q^{43} - 25424604 q^{46} - 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} - 21064016 q^{52} - 7979798 q^{54} + 2856304 q^{57} + 4351100 q^{58} + 22417020 q^{61} - 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} + 46646024 q^{67} + 33562632 q^{69} - 54175560 q^{72} + 129964884 q^{73} + 198922436 q^{76} - 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} - 202877560 q^{82} - 197346768 q^{84} + 168322540 q^{87} + 484775700 q^{88} + 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 + 3812 * q^12 + 55464 * q^13 + 280386 * q^16 + 419800 * q^18 - 231516 * q^19 + 289572 * q^21 - 1129940 * q^22 + 1136334 * q^24 + 335512 * q^27 + 3340724 * q^28 + 881620 * q^31 - 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 - 4672616 * q^37 + 1826792 * q^39 + 5392860 * q^42 - 7731336 * q^43 - 25424604 * q^46 - 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 - 21064016 * q^52 - 7979798 * q^54 + 2856304 * q^57 + 4351100 * q^58 + 22417020 * q^61 - 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 + 46646024 * q^67 + 33562632 * q^69 - 54175560 * q^72 + 129964884 * q^73 + 198922436 * q^76 - 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 - 202877560 * q^82 - 197346768 * q^84 + 168322540 * q^87 + 484775700 * q^88 + 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

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
$5$		0			0
$5$		0			0
$6$	−2050.68	+	1226.69i	−1.58231	+	0.946520i
$7$	−3174.27			−1.32206			−0.661031	−	0.750359i	$-0.729881\pi$
$7$	−3174.27			−1.32206			−0.661031	+	0.750359i	$0.729881\pi$
$8$			10570.2i			2.58061i
$9$	−3102.96	+	5780.86i	−0.472940	+	0.881095i
$10$		0			0
$11$		−	12996.3i		−	0.887668i	−0.896109	−	0.443834i	$-0.853618\pi$
$11$		−	12996.3i		−	0.887668i	0.896109	−	0.443834i	$-0.146382\pi$
$12$	25543.6	+	42701.6i	1.23185	+	2.05930i
$13$	−8759.90			−0.306708			−0.153354	−	0.988171i	$-0.549008\pi$
$13$	−8759.90			−0.306708			−0.153354	+	0.988171i	$0.549008\pi$
$14$			93643.7i			2.43762i
$15$		0			0
$16$	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	$0.597632\pi$
$20$		0			0
$21$	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
$25$		0			0
$26$			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	$0.0413430\pi$
$29$			183211.i			0.259036i	−0.991577	+	0.129518i	$0.958657\pi$
$30$		0			0
$31$	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
$35$		0			0
$36$	1.90615e6	−	3.55119e6i	1.13487	−	2.11429i
$37$	−2.20452e6			−1.17627			−0.588134	−	0.808763i	$-0.700137\pi$
$37$	−2.20452e6			−1.17627			−0.588134	+	0.808763i	$0.700137\pi$
$38$			2.32162e6i			1.11341i
$39$	364250.	+	608922.i	0.157449	+	0.263210i
$40$		0			0
$41$		−	3.04685e6i		−	1.07824i	−0.842228	−	0.539121i	$-0.818757\pi$
$41$		−	3.04685e6i		−	1.07824i	0.842228	−	0.539121i	$-0.181243\pi$
$42$	6.50940e6	−	3.89384e6i	2.09191	−	1.25136i
$43$	−4.84516e6			−1.41721			−0.708605	−	0.705606i	$-0.750675\pi$
$43$	−4.84516e6			−1.41721			−0.708605	+	0.705606i	$0.750675\pi$
$44$			7.98367e6i			2.13006i
$45$		0			0
$46$	−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
$50$		0			0
$51$	−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
$55$		0			0
$56$		−	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	$0.0684073\pi$
$59$			5.16824e6i			0.426515i	−0.976996	+	0.213257i	$0.931593\pi$
$60$		0			0
$61$	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
$65$		0			0
$66$	1.59425e7	+	2.66513e7i	0.840195	+	1.40457i
$67$	3.67916e7			1.82578			0.912891	−	0.408202i	$-0.133844\pi$
$67$	3.67916e7			1.82578			0.912891	+	0.408202i	$0.133844\pi$
$68$			6.67474e7i			3.12175i
$69$	−3.03001e6	+	1.81251e6i	−0.133674	+	0.0799622i
$70$		0			0
$71$		−	971113.i		−	0.0382152i	−0.999817	−	0.0191076i	$-0.993917\pi$
$71$		−	971113.i		−	0.0382152i	0.999817	−	0.0191076i	$-0.00608251\pi$
$72$	−6.11048e7	−	3.27989e7i	−2.27376	−	1.22048i
$73$	−9.46941e6			−0.333451			−0.166725	−	0.986003i	$-0.553319\pi$
$73$	−9.46941e6			−0.333451			−0.166725	+	0.986003i	$0.553319\pi$
$74$			6.50352e7i			2.16881i
$75$		0			0
$76$	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	$0.242600\pi$
$80$		0			0
$81$	−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
$85$		0			0
$86$			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	$0.0489286\pi$
$89$			1.92128e7i			0.306218i	−0.988209	+	0.153109i	$0.951071\pi$
$90$		0			0
$91$	2.78063e7			0.405487
$92$			2.67770e7i			0.373776i
$93$	−3.24612e7	−	5.42658e7i	−0.433943	−	0.725429i
$94$	1.03565e8			1.32648
$95$		0			0
$96$	−1.28872e8	+	7.70897e7i	−1.51731	+	0.907635i
$97$	1.42760e8			1.61257			0.806286	−	0.591526i	$-0.201474\pi$
$97$	1.42760e8			1.61257			0.806286	+	0.591526i	$0.201474\pi$
$98$		−	1.27184e8i		−	1.37888i
$99$	7.51301e7	+	4.03271e7i	0.782119	+	0.419814i
$100$		0			0
$101$		−	8.34775e7i		−	0.802202i	−0.916034	−	0.401101i	$-0.868628\pi$
$101$		−	8.34775e7i		−	0.802202i	0.916034	−	0.401101i	$-0.131372\pi$
$102$	1.33287e8	+	2.22818e8i	1.23137	+	2.05849i
$103$	−1.29545e8			−1.15099			−0.575494	−	0.817806i	$-0.695190\pi$
$103$	−1.29545e8			−1.15099			−0.575494	+	0.817806i	$0.695190\pi$
$104$		−	9.25938e7i		−	0.791496i
$105$		0			0
$106$	−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	$0.723136\pi$
$110$		0			0
$111$	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
$115$		0			0
$116$		−	1.12547e8i		−	0.621586i
$117$	2.71816e7	−	5.06398e7i	0.145055	−	0.270239i
$118$	1.52467e8			0.786410
$119$			3.44903e8i			1.71992i
$120$		0			0
$121$	4.54540e7			0.212046
$122$		−	1.70551e8i		−	0.769867i
$123$	−2.11794e8	+	1.26693e8i	−0.925324	+	0.553518i
$124$	−4.79563e8			−2.02842
$125$		0			0
$126$	−5.41341e8	−	2.90573e8i	−2.14778	−	1.15285i
$127$	2.17231e7			0.0835040			0.0417520	−	0.999128i	$-0.486706\pi$
$127$	2.17231e7			0.0835040			0.0417520	+	0.999128i	$0.486706\pi$
$128$		−	2.84587e7i		−	0.106017i
$129$	2.01469e8	+	3.36799e8i	0.727527	+	1.21622i
$130$		0			0
$131$			1.72425e8i			0.585485i	0.956191	+	0.292743i	$0.0945679\pi$
$131$			1.72425e8i			0.585485i	−0.956191	+	0.292743i	$0.905432\pi$
$132$	5.54964e8	−	3.31973e8i	1.82797	−	1.09347i
$133$	2.49804e8			0.798350
$134$		−	1.08538e9i		−	3.36639i
$135$		0			0
$136$	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	$0.317699\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$			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	$-0.674523\pi$
$149$		−	8.41277e8i		−	1.70685i	0.521219	−	0.853423i	$-0.325477\pi$
$150$		0			0
$151$	−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
$155$		0			0
$156$	−2.23759e8	−	3.74061e8i	−0.377817	−	0.631603i
$157$	−2.37178e8			−0.390370			−0.195185	−	0.980766i	$-0.562531\pi$
$157$	−2.37178e8			−0.390370			−0.195185	+	0.980766i	$0.562531\pi$
$158$		−	1.66235e9i		−	2.66744i
$159$	−6.01117e8	+	3.59581e8i	−0.940525	+	0.562611i
$160$		0			0
$161$			1.38365e8i			0.205931i
$162$	−1.05836e9	+	7.01826e8i	−1.53664	+	1.01899i
$163$	−6.29506e8			−0.891763			−0.445881	−	0.895092i	$-0.647110\pi$
$163$	−6.29506e8			−0.891763			−0.445881	+	0.895092i	$0.647110\pi$
$164$			1.87169e9i			2.58736i
$165$		0			0
$166$	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
$170$		0			0
$171$	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
$175$		0			0
$176$		−	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	$0.122742\pi$
$179$			7.72267e8i			0.752238i	−0.926571	+	0.376119i	$0.877258\pi$
$180$		0			0
$181$	−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
$185$		0			0
$186$	−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
$190$		0			0
$191$		−	8.93822e7i		−	0.0671611i	−0.999436	−	0.0335805i	$-0.989309\pi$
$191$		−	8.93822e7i		−	0.0671611i	0.999436	−	0.0335805i	$-0.0106910\pi$
$192$	6.28849e8	+	1.05126e9i	0.462745	+	0.773578i
$193$	−8.16090e8			−0.588178			−0.294089	−	0.955778i	$-0.595016\pi$
$193$	−8.16090e8			−0.588178			−0.294089	+	0.955778i	$0.595016\pi$
$194$		−	4.21154e9i		−	2.97327i
$195$		0			0
$196$	−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	$0.710117\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$			3.82168e9i			2.12220i
$207$	2.51985e8	+	1.35256e8i	0.137244	+	0.0736675i
$208$	−1.35401e9			−0.723381
$209$			1.02277e9i			0.536034i
$210$		0			0
$211$	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
$215$		0			0
$216$	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
$220$		0			0
$221$			9.51814e8i			0.399009i
$222$	4.52075e9	−	2.70426e9i	1.86122	−	1.11336i
$223$	4.63258e8			0.187328			0.0936642	−	0.995604i	$-0.470142\pi$
$223$	4.63258e8			0.187328			0.0936642	+	0.995604i	$0.470142\pi$
$224$			5.88491e9i			2.33748i
$225$		0			0
$226$	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	$0.768817\pi$
$230$		0			0
$231$	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
$235$		0			0
$236$		−	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	$0.102329\pi$
$239$			2.06189e9i			0.631937i	−0.948770	+	0.315968i	$0.897671\pi$
$240$		0			0
$241$	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
$245$		0			0
$246$	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
$250$		0			0
$251$			1.87286e9i			0.471856i	0.971771	+	0.235928i	$0.0758130\pi$
$251$			1.87286e9i			0.471856i	−0.971771	+	0.235928i	$0.924187\pi$
$252$	−6.05064e9	+	1.12724e10i	−1.50037	+	2.79522i
$253$	−5.66503e8			−0.138268
$254$		−	6.40851e8i		−	0.153965i
$255$		0			0
$256$	−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
$260$		0			0
$261$	−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
$265$		0			0
$266$		−	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	$-0.967835\pi$
$269$		−	1.05642e9i		−	0.201757i	0.994899	−	0.100878i	$-0.0321653\pi$
$270$		0			0
$271$	−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
$275$		0			0
$276$	1.86134e9	−	1.11343e9i	0.320766	−	0.191878i
$277$	5.81689e9			0.988034			0.494017	−	0.869452i	$-0.335528\pi$
$277$	5.81689e9			0.988034			0.494017	+	0.869452i	$0.335528\pi$
$278$		−	1.19359e10i		−	1.99837i
$279$	−2.42237e9	+	4.51291e9i	−0.399782	+	0.744800i
$280$		0			0
$281$			7.93059e9i			1.27198i	0.771698	+	0.635990i	$0.219408\pi$
$281$			7.93059e9i			1.27198i	−0.771698	+	0.635990i	$0.780592\pi$
$282$	−4.30638e9	−	7.19905e9i	−0.680951	−	1.13836i
$283$	8.19763e9			1.27803			0.639017	−	0.769193i	$-0.279341\pi$
$283$	8.19763e9			1.27803			0.639017	+	0.769193i	$0.279341\pi$
$284$			5.96556e8i			0.0917018i
$285$		0			0
$286$	3.35857e9			0.501985
$287$			9.67154e9i			1.42550i
$288$	1.07174e10	+	5.75271e9i	1.55783	+	0.836185i
$289$	−4.83032e9			−0.692444
$290$		0			0
$291$	−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
$295$		0			0
$296$		−	2.33022e10i		−	3.03549i
$297$	−3.20784e8	−	6.89934e9i	−0.0412274	−	0.886710i
$298$	−2.48184e10			−3.14709
$299$			3.81839e8i			0.0477744i
$300$		0			0
$301$	1.53798e10			1.87364
$302$			5.65026e9i			0.679267i
$303$	−5.80273e9	+	3.47112e9i	−0.688433	+	0.411812i
$304$	−1.21640e10			−1.42424
$305$		0			0
$306$	9.94635e9	−	1.85302e10i	1.13443	−	2.11346i
$307$	1.59327e10			1.79365			0.896823	−	0.442389i	$-0.145869\pi$
$307$	1.59327e10			1.79365			0.896823	+	0.442389i	$0.145869\pi$
$308$		−	2.53423e10i		−	2.81607i
$309$	5.38667e9	+	9.00498e9i	0.590862	+	0.987754i
$310$		0			0
$311$			1.47120e10i			1.57265i	0.617816	+	0.786323i	$0.288018\pi$
$311$			1.47120e10i			1.57265i	−0.617816	+	0.786323i	$0.711982\pi$
$312$	−6.43642e9	+	3.85019e9i	−0.679244	+	0.406316i
$313$	−1.09163e10			−1.13736			−0.568678	−	0.822560i	$-0.692545\pi$
$313$	−1.09163e10			−1.13736			−0.568678	+	0.822560i	$0.692545\pi$
$314$			6.99696e9i			0.719765i
$315$		0			0
$316$	−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
$320$		0			0
$321$	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
$325$		0			0
$326$			1.85710e10i			1.64424i
$327$	7.57156e9	+	1.26575e10i	0.662208	+	1.10702i
$328$	3.22058e10			2.78253
$329$		−	1.11435e10i		−	0.951126i
$330$		0			0
$331$	−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
$335$		0			0
$336$	2.04017e10	+	3.41058e10i	1.60069	+	2.67591i
$337$	−2.37856e10			−1.84414			−0.922070	−	0.387024i	$-0.873503\pi$
$337$	−2.37856e10			−1.84414			−0.922070	+	0.387024i	$0.873503\pi$
$338$			2.18010e10i			1.67036i
$339$	6.08587e8	−	3.64049e8i	0.0460812	−	0.0275652i
$340$		0			0
$341$		−	1.01458e10i		−	0.750356i
$342$	−1.34210e10	−	7.20389e9i	−0.981023	−	0.526578i
$343$	4.61417e9			0.333363
$344$		−	5.12142e10i		−	3.65727i
$345$		0			0
$346$	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	$0.408701\pi$
$350$		0			0
$351$	−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
$355$		0			0
$356$		−	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	$-0.968353\pi$
$359$		−	3.29745e9i		−	0.198518i	0.995062	−	0.0992590i	$-0.0316472\pi$
$360$		0			0
$361$	−1.07904e10			−0.635344
$362$			2.21233e10i			1.28829i
$363$	−1.89004e9	−	3.15962e9i	−0.108854	−	0.181973i
$364$	−1.70814e10			−0.973013
$365$		0			0
$366$	−1.18554e10	+	7.09178e9i	−0.660683	+	0.395213i
$367$	−1.99945e10			−1.10216			−0.551082	−	0.834451i	$-0.685785\pi$
$367$	−1.99945e10			−1.10216			−0.551082	+	0.834451i	$0.685785\pi$
$368$		−	6.73756e9i		−	0.367377i
$369$	1.76134e10	+	9.45427e9i	0.950033	+	0.509944i
$370$		0			0
$371$			2.74499e10i			1.44892i
$372$	1.99409e10	+	3.33356e10i	1.04129	+	1.74075i
$373$	8.36869e9			0.432337			0.216168	−	0.976356i	$-0.430644\pi$
$373$	8.36869e9			0.432337			0.216168	+	0.976356i	$0.430644\pi$
$374$			4.16590e10i			2.12923i
$375$		0			0
$376$	−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	$0.384576\pi$
$380$		0			0
$381$	−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
$385$		0			0
$386$			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	$-0.801747\pi$
$389$		−	2.67145e10i		−	1.16667i	0.812230	−	0.583337i	$-0.198253\pi$
$390$		0			0
$391$	−4.73624e9			−0.202641
$392$			4.55700e10i			1.92990i
$393$	1.19857e10	−	7.16970e9i	0.502451	−	0.300560i
$394$	−3.90230e10			−1.61933
$395$		0			0
$396$	−4.61525e10	−	2.47730e10i	−1.87678	−	1.00739i
$397$	7.88247e9			0.317322			0.158661	−	0.987333i	$-0.449282\pi$
$397$	7.88247e9			0.317322			0.158661	+	0.987333i	$0.449282\pi$
$398$			5.67384e10i			2.26123i
$399$	−1.03872e10	−	1.73645e10i	−0.409835	−	0.685127i
$400$		0			0
$401$		−	1.90264e10i		−	0.735834i	−0.929859	−	0.367917i	$-0.880071\pi$
$401$		−	1.90264e10i		−	0.735834i	0.929859	−	0.367917i	$-0.119929\pi$
$402$	−7.54476e10	+	4.51319e10i	−2.88896	+	1.72814i
$403$	−6.83853e9			−0.259264
$404$			5.12803e10i			1.92498i
$405$		0			0
$406$	−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	$0.527475\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$			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	$-0.788735\pi$
$419$		−	3.79749e10i		−	1.23208i	0.787713	−	0.616042i	$-0.211265\pi$
$420$		0			0
$421$	−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
$425$		0			0
$426$	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
$430$		0			0
$431$		−	1.50537e10i		−	0.436250i	−0.975921	−	0.218125i	$-0.930006\pi$
$431$		−	1.50537e10i		−	0.436250i	0.975921	−	0.218125i	$-0.0699940\pi$
$432$	8.20555e10	−	3.81516e9i	2.35599	−	0.109541i
$433$	2.72042e10			0.773899			0.386950	−	0.922101i	$-0.373529\pi$
$433$	2.72042e10			0.773899			0.386950	+	0.922101i	$0.373529\pi$
$434$			7.31042e10i			2.06055i
$435$		0			0
$436$	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	$0.655628\pi$
$440$		0			0
$441$	−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
$445$		0			0
$446$		−	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	$0.00923598\pi$
$449$			2.35824e9i			0.0580232i	−0.999579	+	0.0290116i	$0.990764\pi$
$450$		0			0
$451$	−3.95980e10			−0.957121
$452$		−	5.37825e9i		−	0.128851i
$453$	7.96404e9	+	1.33136e10i	0.189121	+	0.316157i
$454$	1.24174e11			2.92284
$455$		0			0
$456$	−5.78231e10	+	3.45891e10i	−1.33734	+	0.799981i
$457$	−2.48874e10			−0.570579			−0.285289	−	0.958441i	$-0.592090\pi$
$457$	−2.48874e10			−0.570579			−0.285289	+	0.958441i	$0.592090\pi$
$458$			1.21312e11i			2.75703i
$459$	−2.68191e9	−	5.76818e10i	−0.0604217	−	1.29954i
$460$		0			0
$461$		−	2.32674e10i		−	0.515163i	−0.966257	−	0.257581i	$-0.917074\pi$
$461$		−	2.32674e10i		−	0.515163i	0.966257	−	0.257581i	$-0.0829255\pi$
$462$	−5.06057e10	−	8.45984e10i	−1.11079	−	1.85692i
$463$	3.52388e10			0.766828			0.383414	−	0.923577i	$-0.374748\pi$
$463$	3.52388e10			0.766828			0.383414	+	0.923577i	$0.374748\pi$
$464$			2.83187e10i			0.610944i
$465$		0			0
$466$	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
$470$		0			0
$471$	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
$475$		0			0
$476$		−	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	$0.270580\pi$
$479$			7.91032e10i			1.50263i	−0.659944	+	0.751315i	$0.729420\pi$
$480$		0			0
$481$	1.93113e10			0.360771
$482$		−	5.53811e9i		−	0.102606i
$483$	9.61806e9	−	5.75341e9i	0.176725	−	0.105715i
$484$	−2.79224e10			−0.508829
$485$		0			0
$486$	9.27938e10	+	4.43862e10i	1.66331	+	0.795615i
$487$	−5.78470e10			−1.02841			−0.514203	−	0.857668i	$-0.671912\pi$
$487$	−5.78470e10			−1.02841			−0.514203	+	0.857668i	$0.671912\pi$
$488$			6.11087e10i			1.07752i
$489$	2.61758e10	+	4.37585e10i	0.457788	+	0.765292i
$490$		0			0
$491$			1.07166e11i			1.84387i	0.387339	+	0.921937i	$0.373394\pi$
$491$			1.07166e11i			1.84387i	−0.387339	+	0.921937i	$0.626606\pi$
$492$	1.30105e11	−	7.78275e10i	2.22042	−	1.32823i
$493$	1.99070e10			0.336990
$494$		−	2.03371e10i		−	0.341493i
$495$		0			0
$496$	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	$0.493709\pi$
$500$		0			0
$501$	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
$505$		0			0
$506$			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	$-0.923167\pi$
$509$		−	3.20903e10i		−	0.478082i	0.971009	−	0.239041i	$-0.0768330\pi$
$510$		0			0
$511$	3.00585e10			0.440842
$512$			1.31697e11i			1.91644i
$513$	−4.17775e10	+	1.94244e9i	−0.603216	+	0.0280464i
$514$	−7.74490e10			−1.10959
$515$		0			0
$516$	−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
$520$		0			0
$521$		−	6.76727e10i		−	0.918465i	−0.888316	−	0.459232i	$-0.848125\pi$
$521$		−	6.76727e10i		−	0.918465i	0.888316	−	0.459232i	$-0.151875\pi$
$522$	−1.67711e10	+	3.12449e10i	−0.225882	+	0.420821i
$523$	6.05025e10			0.808661			0.404330	−	0.914613i	$-0.367505\pi$
$523$	6.05025e10			0.808661			0.404330	+	0.914613i	$0.367505\pi$
$524$		−	1.05921e11i		−	1.40494i
$525$		0			0
$526$	−2.15531e11			−2.81557
$527$		−	8.48236e10i		−	1.09970i
$528$	−1.39639e11	+	8.35301e10i	−1.79668	+	1.07475i
$529$	7.64109e10			0.975737
$530$		0			0
$531$	−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
$535$		0			0
$536$			3.88894e11i			4.71164i
$537$	5.36822e10	−	3.21120e10i	0.645555	−	0.386163i
$538$	−3.11654e10			−0.372000
$539$		−	5.60296e10i		−	0.663839i
$540$		0			0
$541$	−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
$545$		0			0
$546$	−5.70217e10	+	3.41097e10i	−0.641608	+	0.383802i
$547$	−1.39645e11			−1.55983			−0.779915	−	0.625885i	$-0.784738\pi$
$547$	−1.39645e11			−1.55983			−0.779915	+	0.625885i	$0.784738\pi$
$548$		−	1.69569e11i		−	1.88029i
$549$	−1.79389e10	+	3.34205e10i	−0.197473	+	0.367895i
$550$		0			0
$551$		−	1.44181e10i		−	0.156423i
$552$	−1.91586e10	−	3.20278e10i	−0.206352	−	0.344961i
$553$	−1.78868e11			−1.91263
$554$		−	1.71603e11i		−	1.82174i
$555$		0			0
$556$	−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
$560$		0			0
$561$	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
$565$		0			0
$566$		−	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	$0.345745\pi$
$569$			1.85504e11i			1.76972i	−0.465861	+	0.884858i	$0.654255\pi$
$570$		0			0
$571$	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
$575$		0			0
$576$	4.69270e10	−	8.74257e10i	0.426317	−	0.794235i
$577$	1.80485e11			1.62831			0.814155	−	0.580648i	$-0.197201\pi$
$577$	1.80485e11			1.62831			0.814155	+	0.580648i	$0.197201\pi$
$578$			1.42499e11i			1.27673i
$579$	3.39343e10	+	5.67284e10i	0.301942	+	0.504762i
$580$		0			0
$581$		−	1.86688e11i		−	1.63837i
$582$	−2.92754e11	+	1.75122e11i	−2.55159	+	1.52633i
$583$	−1.12387e11			−0.972845
$584$		−	1.00093e11i		−	0.860507i
$585$		0			0
$586$	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
$590$		0			0
$591$	−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
$595$		0			0
$596$			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	$0.137977\pi$
$599$			1.08145e11i			0.840041i	−0.907515	+	0.420020i	$0.862023\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	1.02401e11	+	1.71185e11i	0.759301	+	1.26934i
$607$	−7.47882e10			−0.550907			−0.275453	−	0.961314i	$-0.588828\pi$
$607$	−7.47882e10			−0.550907			−0.275453	+	0.961314i	$0.588828\pi$
$608$			1.45899e11i			1.06767i
$609$	−4.04258e10	+	2.41822e10i	−0.293893	+	0.175803i
$610$		0			0
$611$		−	3.07522e10i		−	0.220654i
$612$	−3.85857e11	−	2.07114e11i	−2.75056	−	1.47640i
$613$	2.70342e11			1.91457			0.957284	−	0.289148i	$-0.0933719\pi$
$613$	2.70342e11			1.91457			0.957284	+	0.289148i	$0.0933719\pi$
$614$		−	4.70030e11i		−	3.30713i
$615$		0			0
$616$	−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	$0.605315\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$			3.22039e11i			2.09706i
$627$	7.10951e10	−	4.25282e10i	0.460013	−	0.275174i
$628$	1.45699e11			0.936736
$629$			2.39534e11i			1.53025i
$630$		0			0
$631$	−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
$635$		0			0
$636$	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
$640$		0			0
$641$		−	1.27087e11i		−	0.752780i	−0.926461	−	0.376390i	$-0.877165\pi$
$641$		−	1.27087e11i		−	0.752780i	0.926461	−	0.376390i	$-0.122835\pi$
$642$	−1.26180e11	−	2.10937e11i	−0.742764	−	1.24169i
$643$	−2.47669e11			−1.44887			−0.724433	−	0.689345i	$-0.757899\pi$
$643$	−2.47669e11			−1.44887			−0.724433	+	0.689345i	$0.757899\pi$
$644$		−	8.49975e10i		−	0.494155i
$645$		0			0
$646$	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
$650$		0			0
$651$	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
$655$		0			0
$656$		−	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	$-0.904425\pi$
$659$		−	1.11563e11i		−	0.591531i	0.955261	−	0.295765i	$-0.0955747\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	−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
$670$		0			0
$671$		−	7.51349e10i		−	0.370639i
$672$	4.09075e11	−	2.44703e11i	2.00597	−	1.19995i
$673$	5.44544e10			0.265444			0.132722	−	0.991153i	$-0.457628\pi$
$673$	5.44544e10			0.265444			0.132722	+	0.991153i	$0.457628\pi$
$674$			7.01695e11i			3.40023i
$675$		0			0
$676$	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
$680$		0			0
$681$	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
$685$		0			0
$686$		−	1.36122e11i		−	0.614656i
$687$	1.70989e11	+	2.85846e11i	0.767613	+	1.28323i
$688$	−7.48910e11			−3.34253
$689$			7.57523e10i			0.336139i
$690$		0			0
$691$	−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
$695$		0			0
$696$	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
$700$		0			0
$701$		−	4.12721e11i		−	1.70917i	−0.519316	−	0.854583i	$-0.673813\pi$
$701$		−	4.12721e11i		−	1.70917i	0.519316	−	0.854583i	$-0.326187\pi$
$702$	6.37859e9	+	1.37189e11i	0.0262649	+	0.564900i
$703$	1.73488e11			0.710311
$704$			1.96548e11i			0.800160i
$705$		0			0
$706$	−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	$0.398107\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$		−	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	$-0.888693\pi$
$719$		−	1.83117e11i		−	0.685195i	0.939482	−	0.342597i	$-0.111307\pi$
$720$		0			0
$721$	4.11210e11			1.52168
$722$			3.18326e11i			1.17145i
$723$	−7.80596e9	−	1.30494e10i	−0.0285676	−	0.0477569i
$724$	4.60676e11			1.67665
$725$		0			0
$726$	−9.32114e10	+	5.57579e10i	−0.335523	+	0.200706i
$727$	−2.59798e10			−0.0930032			−0.0465016	−	0.998918i	$-0.514807\pi$
$727$	−2.59798e10			−0.0930032			−0.0465016	+	0.998918i	$0.514807\pi$
$728$			2.93918e11i			1.04641i
$729$	2.81211e11	−	2.62064e10i	0.995686	−	0.0927891i
$730$		0			0
$731$			5.26454e11i			1.84370i
$732$	1.47673e11	+	2.46868e11i	0.514348	+	0.859844i
$733$	6.63035e10			0.229678			0.114839	−	0.993384i	$-0.463365\pi$
$733$	6.63035e10			0.229678			0.114839	+	0.993384i	$0.463365\pi$
$734$			5.89855e11i			2.03218i
$735$		0			0
$736$	−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	$0.583076\pi$
$740$		0			0
$741$	−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
$745$		0			0
$746$		−	2.46884e11i		−	0.797145i
$747$	−3.39989e11	−	1.82494e11i	−1.09190	−	0.586092i
$748$	8.67472e11			2.77108
$749$		−	3.26512e11i		−	1.03746i
$750$		0			0
$751$	−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
$755$		0			0
$756$	1.03517e12	−	4.81300e10i	3.16901	−	0.147343i
$757$	−3.97220e11			−1.20962			−0.604808	−	0.796371i	$-0.706750\pi$
$757$	−3.97220e11			−1.20962			−0.604808	+	0.796371i	$0.706750\pi$
$758$		−	4.31824e11i		−	1.30807i
$759$	2.35560e10	+	3.93790e10i	0.0709799	+	0.118658i
$760$		0			0
$761$			8.97779e10i			0.267689i	0.991002	+	0.133845i	$0.0427323\pi$
$761$			8.97779e10i			0.267689i	−0.991002	+	0.133845i	$0.957268\pi$
$762$	−4.45471e10	+	2.66475e10i	−0.132129	+	0.0790382i
$763$	5.78002e11			1.70542
$764$			5.49076e10i			0.161161i
$765$		0			0
$766$	−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	$0.710616\pi$
$770$		0			0
$771$	−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
$775$		0			0
$776$			1.50900e12i			4.16142i
$777$	−2.90976e11	−	4.86429e11i	−0.798313	−	1.33455i
$778$	−7.88102e11			−2.15112
$779$			2.39777e11i			0.651116i
$780$		0			0
$781$	−1.26209e10			−0.0339224
$782$			1.39723e11i			0.373630i
$783$	4.52213e9	+	9.72609e10i	0.0120308	+	0.258756i
$784$	6.66374e11			1.76382
$785$		0			0
$786$	−2.11512e11	−	3.53589e11i	−0.554173	−	0.926420i
$787$	−3.22875e11			−0.841658			−0.420829	−	0.907140i	$-0.638261\pi$
$787$	−3.22875e11			−0.841658			−0.420829	+	0.907140i	$0.638261\pi$
$788$			8.12583e11i			2.10748i
$789$	−5.07852e11	+	3.03791e11i	−1.31048	+	0.783912i
$790$		0			0
$791$		−	2.77910e10i		−	0.0709901i
$792$	−4.26265e11	+	7.94139e11i	−1.08338	+	2.01835i
$793$	−5.06430e10			−0.128064
$794$		−	2.32540e11i		−	0.585080i
$795$		0			0
$796$	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
$800$		0			0
$801$	−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
$805$		0			0
$806$			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	$0.0176384\pi$
$809$			4.74471e10i			0.110768i	−0.998465	+	0.0553842i	$0.982362\pi$
$810$		0			0
$811$	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
$815$		0			0
$816$	−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
$820$		0			0
$821$			8.94845e10i			0.196959i	0.995139	+	0.0984794i	$0.0313978\pi$
$821$			8.94845e10i			0.196959i	−0.995139	+	0.0984794i	$0.968602\pi$
$822$	−3.38610e11	−	5.66060e11i	−0.741674	−	1.23987i
$823$	−8.24619e11			−1.79744			−0.898719	−	0.438524i	$-0.855501\pi$
$823$	−8.24619e11			−1.79744			−0.898719	+	0.438524i	$0.855501\pi$
$824$		−	1.36931e12i		−	2.97026i
$825$		0			0
$826$	−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	$0.586935\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$		−	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	$-0.790000\pi$
$839$		−	6.07397e11i		−	1.22581i	0.790155	−	0.612907i	$-0.210000\pi$
$840$		0			0
$841$	4.66680e11			0.932900
$842$			1.73106e11i			0.344400i
$843$	5.51274e11	−	3.29766e11i	1.09158	−	0.652973i
$844$	−1.25105e12			−2.46550
$845$		0			0
$846$	−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
$850$		0			0
$851$			9.60937e10i			0.183222i
$852$	4.14681e10	−	2.48057e10i	0.0786965	−	0.0470753i
$853$	−1.34856e11			−0.254726			−0.127363	−	0.991856i	$-0.540651\pi$
$853$	−1.34856e11			−0.254726			−0.127363	+	0.991856i	$0.540651\pi$
$854$			5.41376e11i			1.01781i
$855$		0			0
$856$	−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	$0.363805\pi$
$860$		0			0
$861$	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
$865$		0			0
$866$		−	8.02548e11i		−	1.42692i
$867$	2.00852e11	+	3.35768e11i	0.355467	+	0.594241i
$868$	1.52226e12			2.68170
$869$		−	7.32335e11i		−	1.28419i
$870$		0			0
$871$	−3.22290e11			−0.559983
$872$		−	1.92472e12i		−	3.32891i
$873$	−4.42978e11	+	8.25275e11i	−0.762650	+	1.42083i
$874$	1.01198e11			0.173431
$875$		0			0
$876$	−2.41882e11	−	4.04359e11i	−0.410760	−	0.686674i
$877$	8.29492e11			1.40221			0.701106	−	0.713057i	$-0.252690\pi$
$877$	8.29492e11			1.40221			0.701106	+	0.713057i	$0.252690\pi$
$878$			1.02925e12i			1.73197i
$879$	7.09033e11	−	4.24135e11i	1.18771	−	0.710474i
$880$		0			0
$881$			1.16546e11i			0.193461i	0.995311	+	0.0967305i	$0.0308385\pi$
$881$			1.16546e11i			0.193461i	−0.995311	+	0.0967305i	$0.969161\pi$
$882$	7.35231e11	+	3.94646e11i	1.21493	+	0.652128i
$883$	4.57775e11			0.753025			0.376512	−	0.926412i	$-0.377123\pi$
$883$	4.57775e11			0.753025			0.376512	+	0.926412i	$0.377123\pi$
$884$		−	5.84700e11i		−	0.957468i
$885$		0			0
$886$	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
$890$		0			0
$891$	−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
$895$		0			0
$896$			9.03355e10i			0.140161i
$897$	2.65426e10	−	1.58774e10i	0.0409990	−	0.0245251i
$898$	6.95700e10			0.106983
$899$			1.43026e11i			0.218966i
$900$		0			0
$901$	−9.39614e11			−1.42577
$902$			1.16817e12i			1.76474i
$903$	−6.39516e11	−	1.06909e12i	−0.961835	−	1.60792i
$904$	−9.25428e10			−0.138570
$905$		0			0
$906$	3.92763e11	−	2.34946e11i	0.582932	−	0.348703i
$907$	4.83758e10			0.0714824			0.0357412	−	0.999361i	$-0.488621\pi$
$907$	4.83758e10			0.0714824			0.0357412	+	0.999361i	$0.488621\pi$
$908$		−	2.58568e12i		−	3.80393i
$909$	4.82572e11	+	2.59027e11i	0.706816	+	0.379394i
$910$		0			0
$911$			9.65899e11i			1.40236i	0.712986	+	0.701178i	$0.247342\pi$
$911$			9.65899e11i			1.40236i	−0.712986	+	0.701178i	$0.752658\pi$
$912$	5.05799e11	+	8.45552e11i	0.731137	+	1.22225i
$913$	7.64351e11			1.10004
$914$			7.34201e11i			1.05204i
$915$		0			0
$916$	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	$0.203789\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$		−	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	$0.163893\pi$
$929$			7.33571e11i			0.984870i	−0.870349	+	0.492435i	$0.836107\pi$
$930$		0			0
$931$	−3.39276e11			−0.451600
$932$		−	1.76307e12i		−	2.33671i
$933$	1.02267e12	−	6.11748e11i	1.34961	−	0.807321i
$934$	−2.59275e12			−3.40701
$935$		0			0
$936$	5.35272e11	+	2.87315e11i	0.697383	+	0.374330i
$937$	3.55464e11			0.461145			0.230573	−	0.973055i	$-0.425940\pi$
$937$	3.55464e11			0.461145			0.230573	+	0.973055i	$0.425940\pi$
$938$			3.44530e12i			4.45057i
$939$	4.53914e11	+	7.58816e11i	0.583864	+	0.976054i
$940$		0			0
$941$			6.76442e11i			0.862724i	0.902179	+	0.431362i	$0.141967\pi$
$941$			6.76442e11i			0.862724i	−0.902179	+	0.431362i	$0.858033\pi$
$942$	4.86376e11	−	2.90944e11i	0.617687	−	0.369493i
$943$	−1.32811e11			−0.167952
$944$			7.98847e11i			1.00595i
$945$		0			0
$946$	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
$950$		0			0
$951$	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
$955$		0			0
$956$		−	1.26662e12i		−	1.51640i
$957$	−9.90087e10	−	1.65514e11i	−0.118039	−	0.197328i
$958$	2.33361e12			2.77056
$959$		−	8.76212e11i		−	1.03594i
$960$		0			0
$961$	−2.43455e11			−0.285447
$962$		−	5.69701e11i		−	0.665192i
$963$	−5.94632e11	−	3.19177e11i	−0.691422	−	0.371131i
$964$	−1.15321e11			−0.133536
$965$		0			0
$966$	−1.69730e11	−	2.83741e11i	−0.194918	−	0.325847i
$967$	2.66857e11			0.305191			0.152596	−	0.988289i	$-0.451237\pi$
$967$	2.66857e11			0.305191			0.152596	+	0.988289i	$0.451237\pi$
$968$			4.80457e11i			0.547209i
$969$	5.94390e11	−	3.55557e11i	0.674181	−	0.403287i
$970$		0			0
$971$			1.52105e12i			1.71106i	0.517750	+	0.855532i	$0.326770\pi$
$971$			1.52105e12i			1.71106i	−0.517750	+	0.855532i	$0.673230\pi$
$972$	9.24261e11	−	1.93226e12i	1.03545	−	2.16471i
$973$	−1.28430e12			−1.43289
$974$			1.70654e12i			1.89618i
$975$		0			0
$976$	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
$980$		0			0
$981$	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
$985$		0			0
$986$		−	5.87272e11i		−	0.621344i
$987$	−7.74612e11	+	4.63363e11i	−0.816235	+	0.488262i
$988$	−4.23484e11			−0.444436
$989$			2.11198e11i			0.220752i
$990$		0			0
$991$	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
$995$		0			0
$996$	−2.51140e12	+	1.50229e12i	−2.55199	+	1.52657i
$997$	6.40433e11			0.648176			0.324088	−	0.946027i	$-0.394943\pi$
$997$	6.40433e11			0.648176			0.324088	+	0.946027i	$0.394943\pi$
$998$		−	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	75.9.c.g.26.1		10
3.2	odd	2	inner	75.9.c.g.26.10		10
5.2	odd	4		75.9.d.c.74.20		20
5.3	odd	4		75.9.d.c.74.1		20
5.4	even	2		15.9.c.a.11.10	yes	10
15.2	even	4		75.9.d.c.74.2		20
15.8	even	4		75.9.d.c.74.19		20
15.14	odd	2		15.9.c.a.11.1	✓	10
20.19	odd	2		240.9.l.b.161.3		10
60.59	even	2		240.9.l.b.161.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.1	✓	10	15.14	odd	2
15.9.c.a.11.10	yes	10	5.4	even	2
75.9.c.g.26.1		10	1.1	even	1	trivial
75.9.c.g.26.10		10	3.2	odd	2	inner
75.9.d.c.74.1		20	5.3	odd	4
75.9.d.c.74.2		20	15.2	even	4
75.9.d.c.74.19		20	15.8	even	4
75.9.d.c.74.20		20	5.2	odd	4
240.9.l.b.161.3		10	20.19	odd	2
240.9.l.b.161.4		10	60.59	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-29.5009i q^{2} +(-41.5815 - 69.5124i) q^{3} -614.301 q^{4} +(-2050.68 + 1226.69i) q^{6} -3174.27 q^{7} +10570.2i q^{8} +(-3102.96 + 5780.86i) q^{9} +O(q^{10})\)	\(q-29.5009i q^{2} +(-41.5815 - 69.5124i) q^{3} -614.301 q^{4} +(-2050.68 + 1226.69i) q^{6} -3174.27 q^{7} +10570.2i q^{8} +(-3102.96 + 5780.86i) q^{9} -12996.3i q^{11} +(25543.6 + 42701.6i) q^{12} -8759.90 q^{13} +93643.7i q^{14} +154569. q^{16} -108656. i q^{17} +(170540. + 91540.0i) q^{18} -78696.7 q^{19} +(131991. + 220651. i) q^{21} -383403. q^{22} -43589.4i q^{23} +(734760. - 439524. i) q^{24} +258425. i q^{26} +(530868. - 24682.6i) q^{27} +1.94996e6 q^{28} +183211. i q^{29} +780664. q^{31} -1.85394e6i q^{32} +(-903407. + 540407. i) q^{33} -3.20544e6 q^{34} +(1.90615e6 - 3.55119e6i) q^{36} -2.20452e6 q^{37} +2.32162e6i q^{38} +(364250. + 608922. i) q^{39} -3.04685e6i q^{41} +(6.50940e6 - 3.89384e6i) q^{42} -4.84516e6 q^{43} +7.98367e6i q^{44} -1.28593e6 q^{46} +3.51057e6i q^{47} +(-6.42720e6 - 1.07444e7i) q^{48} +4.31118e6 q^{49} +(-7.55293e6 + 4.51807e6i) q^{51} +5.38121e6 q^{52} -8.64762e6i q^{53} +(-728158. - 1.56611e7i) q^{54} -3.35526e7i q^{56} +(3.27232e6 + 5.47040e6i) q^{57} +5.40489e6 q^{58} +5.16824e6i q^{59} +5.78123e6 q^{61} -2.30303e7i q^{62} +(9.84963e6 - 1.83500e7i) q^{63} -1.51233e7 q^{64} +(1.59425e7 + 2.66513e7i) q^{66} +3.67916e7 q^{67} +6.67474e7i q^{68} +(-3.03001e6 + 1.81251e6i) q^{69} -971113. i q^{71} +(-6.11048e7 - 3.27989e7i) q^{72} -9.46941e6 q^{73} +6.50352e7i q^{74} +4.83434e7 q^{76} +4.12539e7i q^{77} +(1.79637e7 - 1.07457e7i) q^{78} +5.63493e7 q^{79} +(-2.37900e7 - 3.58756e7i) q^{81} -8.98849e7 q^{82} +5.88128e7i q^{83} +(-8.10821e7 - 1.35546e8i) q^{84} +1.42936e8i q^{86} +(1.27355e7 - 7.61819e6i) q^{87} +1.37374e8 q^{88} +1.92128e7i q^{89} +2.78063e7 q^{91} +2.67770e7i q^{92} +(-3.24612e7 - 5.42658e7i) q^{93} +1.03565e8 q^{94} +(-1.28872e8 + 7.70897e7i) q^{96} +1.42760e8 q^{97} -1.27184e8i q^{98} +(7.51301e7 + 4.03271e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 112 q^{3} - 786 q^{4} - 5282 q^{6} - 7156 q^{7} + 3922 q^{9}+O(q^{10}) \) 10 * q + 112 * q^3 - 786 * q^4 - 5282 * q^6 - 7156 * q^7 + 3922 * q^9	\( 10 q + 112 q^{3} - 786 q^{4} - 5282 q^{6} - 7156 q^{7} + 3922 q^{9} + 3812 q^{12} + 55464 q^{13} + 280386 q^{16} + 419800 q^{18} - 231516 q^{19} + 289572 q^{21} - 1129940 q^{22} + 1136334 q^{24} + 335512 q^{27} + 3340724 q^{28} + 881620 q^{31} - 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} - 4672616 q^{37} + 1826792 q^{39} + 5392860 q^{42} - 7731336 q^{43} - 25424604 q^{46} - 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} - 21064016 q^{52} - 7979798 q^{54} + 2856304 q^{57} + 4351100 q^{58} + 22417020 q^{61} - 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} + 46646024 q^{67} + 33562632 q^{69} - 54175560 q^{72} + 129964884 q^{73} + 198922436 q^{76} - 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} - 202877560 q^{82} - 197346768 q^{84} + 168322540 q^{87} + 484775700 q^{88} + 444288464 q^{91} - 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} + 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q + 112 * q^3 - 786 * q^4 - 5282 * q^6 - 7156 * q^7 + 3922 * q^9 + 3812 * q^12 + 55464 * q^13 + 280386 * q^16 + 419800 * q^18 - 231516 * q^19 + 289572 * q^21 - 1129940 * q^22 + 1136334 * q^24 + 335512 * q^27 + 3340724 * q^28 + 881620 * q^31 - 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 - 4672616 * q^37 + 1826792 * q^39 + 5392860 * q^42 - 7731336 * q^43 - 25424604 * q^46 - 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 - 21064016 * q^52 - 7979798 * q^54 + 2856304 * q^57 + 4351100 * q^58 + 22417020 * q^61 - 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 + 46646024 * q^67 + 33562632 * q^69 - 54175560 * q^72 + 129964884 * q^73 + 198922436 * q^76 - 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 - 202877560 * q^82 - 197346768 * q^84 + 168322540 * q^87 + 484775700 * q^88 + 444288464 * q^91 - 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 + 258825724 * q^97 - 33965200 * q^99

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