LMFDB - Embedded newform 201.5.b.a.133.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,5,Mod(133,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("201.133");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	201.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.7773625799$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			133.7
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.76041i q^{2} +5.19615i q^{3} -17.1823 q^{4} -16.3188i q^{5} +29.9320 q^{6} +86.3035i q^{7} +6.81074i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-5.76041i q^{2} +5.19615i q^{3} -17.1823 q^{4} -16.3188i q^{5} +29.9320 q^{6} +86.3035i q^{7} +6.81074i q^{8} -27.0000 q^{9} -94.0028 q^{10} +86.2419i q^{11} -89.2820i q^{12} -311.642i q^{13} +497.143 q^{14} +84.7948 q^{15} -235.685 q^{16} +434.776 q^{17} +155.531i q^{18} +485.813 q^{19} +280.395i q^{20} -448.446 q^{21} +496.789 q^{22} -180.572 q^{23} -35.3896 q^{24} +358.698 q^{25} -1795.19 q^{26} -140.296i q^{27} -1482.89i q^{28} +1188.97 q^{29} -488.453i q^{30} -1419.01i q^{31} +1466.61i q^{32} -448.126 q^{33} -2504.49i q^{34} +1408.37 q^{35} +463.923 q^{36} -1090.53 q^{37} -2798.48i q^{38} +1619.34 q^{39} +111.143 q^{40} -814.136i q^{41} +2583.23i q^{42} -919.690i q^{43} -1481.84i q^{44} +440.607i q^{45} +1040.17i q^{46} +2948.78 q^{47} -1224.65i q^{48} -5047.29 q^{49} -2066.25i q^{50} +2259.16i q^{51} +5354.74i q^{52} +1775.08i q^{53} -808.163 q^{54} +1407.36 q^{55} -587.790 q^{56} +2524.36i q^{57} -6848.94i q^{58} -2868.35 q^{59} -1456.97 q^{60} -2313.22i q^{61} -8174.07 q^{62} -2330.19i q^{63} +4677.34 q^{64} -5085.61 q^{65} +2581.39i q^{66} +(4472.85 + 380.480i) q^{67} -7470.47 q^{68} -938.281i q^{69} -8112.77i q^{70} +6048.31 q^{71} -183.890i q^{72} -5038.51 q^{73} +6281.88i q^{74} +1863.85i q^{75} -8347.41 q^{76} -7442.98 q^{77} -9328.06i q^{78} +5514.48i q^{79} +3846.08i q^{80} +729.000 q^{81} -4689.76 q^{82} -2712.87 q^{83} +7705.35 q^{84} -7095.01i q^{85} -5297.79 q^{86} +6178.06i q^{87} -587.371 q^{88} +7757.28 q^{89} +2538.08 q^{90} +26895.8 q^{91} +3102.65 q^{92} +7373.39 q^{93} -16986.2i q^{94} -7927.87i q^{95} -7620.74 q^{96} -695.839i q^{97} +29074.4i q^{98} -2328.53i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) $ 46 * q - 396 * q^4 - 1242 * q^9	$ 46 q - 396 q^{4} - 1242 q^{9} + 396 q^{10} + 792 q^{14} - 252 q^{15} + 3396 q^{16} + 462 q^{17} - 590 q^{19} - 936 q^{21} + 3184 q^{22} - 1446 q^{23} - 1404 q^{24} - 6278 q^{25} + 2700 q^{26} - 1014 q^{29} + 540 q^{33} + 9924 q^{35} + 10692 q^{36} - 386 q^{37} + 4968 q^{39} - 9988 q^{40} - 2754 q^{47} - 19062 q^{49} - 2320 q^{55} - 3396 q^{56} - 7098 q^{59} + 72 q^{60} - 21180 q^{62} - 75644 q^{64} + 18396 q^{65} + 8574 q^{67} + 9084 q^{68} - 23040 q^{71} - 22338 q^{73} + 28016 q^{76} + 45084 q^{77} + 33534 q^{81} + 17564 q^{82} + 35856 q^{83} + 40176 q^{84} + 31764 q^{86} - 19448 q^{88} - 14538 q^{89} - 10692 q^{90} + 13792 q^{91} - 67692 q^{92} + 22464 q^{93} + 22464 q^{96}+O(q^{100}) $ 46 * q - 396 * q^4 - 1242 * q^9 + 396 * q^10 + 792 * q^14 - 252 * q^15 + 3396 * q^16 + 462 * q^17 - 590 * q^19 - 936 * q^21 + 3184 * q^22 - 1446 * q^23 - 1404 * q^24 - 6278 * q^25 + 2700 * q^26 - 1014 * q^29 + 540 * q^33 + 9924 * q^35 + 10692 * q^36 - 386 * q^37 + 4968 * q^39 - 9988 * q^40 - 2754 * q^47 - 19062 * q^49 - 2320 * q^55 - 3396 * q^56 - 7098 * q^59 + 72 * q^60 - 21180 * q^62 - 75644 * q^64 + 18396 * q^65 + 8574 * q^67 + 9084 * q^68 - 23040 * q^71 - 22338 * q^73 + 28016 * q^76 + 45084 * q^77 + 33534 * q^81 + 17564 * q^82 + 35856 * q^83 + 40176 * q^84 + 31764 * q^86 - 19448 * q^88 - 14538 * q^89 - 10692 * q^90 + 13792 * q^91 - 67692 * q^92 + 22464 * q^93 + 22464 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	5.76041i		−	1.44010i	−0.693921	−	0.720051i	$-0.744118\pi$
$2$		−	5.76041i		−	1.44010i	0.693921	−	0.720051i	$-0.255882\pi$
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	−17.1823			−1.07390
$5$		−	16.3188i		−	0.652751i	−0.945240	−	0.326375i	$-0.894173\pi$
$5$		−	16.3188i		−	0.652751i	0.945240	−	0.326375i	$-0.105827\pi$
$6$	29.9320			0.831444
$7$			86.3035i			1.76130i	0.473772	+	0.880648i	$0.342892\pi$
$7$			86.3035i			1.76130i	−0.473772	+	0.880648i	$0.657108\pi$
$8$			6.81074i			0.106418i
$9$	−27.0000			−0.333333
$10$	−94.0028			−0.940028
$11$			86.2419i			0.712743i	0.934344	+	0.356372i	$0.115986\pi$
$11$			86.2419i			0.712743i	−0.934344	+	0.356372i	$0.884014\pi$
$12$		−	89.2820i		−	0.620014i
$13$		−	311.642i		−	1.84403i	−0.387148	−	0.922017i	$-0.626540\pi$
$13$		−	311.642i		−	1.84403i	0.387148	−	0.922017i	$-0.373460\pi$
$14$	497.143			2.53645
$15$	84.7948			0.376866
$16$	−235.685			−0.920643
$17$	434.776			1.50442			0.752208	−	0.658926i	$-0.228989\pi$
$17$	434.776			1.50442			0.752208	+	0.658926i	$0.228989\pi$
$18$			155.531i			0.480034i
$19$	485.813			1.34574			0.672872	−	0.739759i	$-0.265061\pi$
$19$	485.813			1.34574			0.672872	+	0.739759i	$0.265061\pi$
$20$			280.395i			0.700986i
$21$	−448.446			−1.01688
$22$	496.789			1.02642
$23$	−180.572			−0.341346			−0.170673	−	0.985328i	$-0.554594\pi$
$23$	−180.572			−0.341346			−0.170673	+	0.985328i	$0.554594\pi$
$24$	−35.3896			−0.0614403
$25$	358.698			0.573917
$26$	−1795.19			−2.65560
$27$		−	140.296i		−	0.192450i
$28$		−	1482.89i		−	1.89145i
$29$	1188.97			1.41375			0.706877	−	0.707336i	$-0.250103\pi$
$29$	1188.97			1.41375			0.706877	+	0.707336i	$0.250103\pi$
$30$		−	488.453i		−	0.542725i
$31$		−	1419.01i		−	1.47660i	−0.674475	−	0.738298i	$-0.735630\pi$
$31$		−	1419.01i		−	1.47660i	0.674475	−	0.738298i	$-0.264370\pi$
$32$			1466.61i			1.43224i
$33$	−448.126			−0.411502
$34$		−	2504.49i		−	2.16651i
$35$	1408.37			1.14969
$36$	463.923			0.357965
$37$	−1090.53			−0.796586			−0.398293	−	0.917258i	$-0.630397\pi$
$37$	−1090.53			−0.796586			−0.398293	+	0.917258i	$0.630397\pi$
$38$		−	2798.48i		−	1.93801i
$39$	1619.34			1.06465
$40$	111.143			0.0694643
$41$		−	814.136i		−	0.484317i	−0.970237	−	0.242158i	$-0.922145\pi$
$41$		−	814.136i		−	0.484317i	0.970237	−	0.242158i	$-0.0778553\pi$
$42$			2583.23i			1.46442i
$43$		−	919.690i		−	0.497399i	−0.968581	−	0.248699i	$-0.919997\pi$
$43$		−	919.690i		−	0.497399i	0.968581	−	0.248699i	$-0.0800031\pi$
$44$		−	1481.84i		−	0.765412i
$45$			440.607i			0.217584i
$46$			1040.17i			0.491574i
$47$	2948.78			1.33489			0.667447	−	0.744657i	$-0.267387\pi$
$47$	2948.78			1.33489			0.667447	+	0.744657i	$0.267387\pi$
$48$		−	1224.65i		−	0.531534i
$49$	−5047.29			−2.10216
$50$		−	2066.25i		−	0.826499i
$51$			2259.16i			0.868575i
$52$			5354.74i			1.98030i
$53$			1775.08i			0.631926i	0.948772	+	0.315963i	$0.102328\pi$
$53$			1775.08i			0.631926i	−0.948772	+	0.315963i	$0.897672\pi$
$54$	−808.163			−0.277148
$55$	1407.36			0.465244
$56$	−587.790			−0.187433
$57$			2524.36i			0.776965i
$58$		−	6848.94i		−	2.03595i
$59$	−2868.35			−0.824002			−0.412001	−	0.911183i	$-0.635170\pi$
$59$	−2868.35			−0.824002			−0.412001	+	0.911183i	$0.635170\pi$
$60$	−1456.97			−0.404715
$61$		−	2313.22i		−	0.621667i	−0.950464	−	0.310833i	$-0.899392\pi$
$61$		−	2313.22i		−	0.621667i	0.950464	−	0.310833i	$-0.100608\pi$
$62$	−8174.07			−2.12645
$63$		−	2330.19i		−	0.587098i
$64$	4677.34			1.14193
$65$	−5085.61			−1.20370
$66$			2581.39i			0.592606i
$67$	4472.85	+	380.480i	0.996402	+	0.0847582i
$67$	4472.85	+	380.480i	0.996402	+	0.0847582i
$68$	−7470.47			−1.61559
$69$		−	938.281i		−	0.197076i
$70$		−	8112.77i		−	1.65567i
$71$	6048.31			1.19982			0.599912	−	0.800066i	$-0.295202\pi$
$71$	6048.31			1.19982			0.599912	+	0.800066i	$0.295202\pi$
$72$		−	183.890i		−	0.0354726i
$73$	−5038.51			−0.945490			−0.472745	−	0.881199i	$-0.656737\pi$
$73$	−5038.51			−0.945490			−0.472745	+	0.881199i	$0.656737\pi$
$74$			6281.88i			1.14717i
$75$			1863.85i			0.331351i
$76$	−8347.41			−1.44519
$77$	−7442.98			−1.25535
$78$		−	9328.06i		−	1.53321i
$79$			5514.48i			0.883589i	0.897116	+	0.441794i	$0.145658\pi$
$79$			5514.48i			0.883589i	−0.897116	+	0.441794i	$0.854342\pi$
$80$			3846.08i			0.600951i
$81$	729.000			0.111111
$82$	−4689.76			−0.697466
$83$	−2712.87			−0.393798			−0.196899	−	0.980424i	$-0.563087\pi$
$83$	−2712.87			−0.393798			−0.196899	+	0.980424i	$0.563087\pi$
$84$	7705.35			1.09203
$85$		−	7095.01i		−	0.982009i
$86$	−5297.79			−0.716305
$87$			6178.06i			0.816232i
$88$	−587.371			−0.0758485
$89$	7757.28			0.979331			0.489666	−	0.871910i	$-0.337119\pi$
$89$	7757.28			0.979331			0.489666	+	0.871910i	$0.337119\pi$
$90$	2538.08			0.313343
$91$	26895.8			3.24789
$92$	3102.65			0.366571
$93$	7373.39			0.852513
$94$		−	16986.2i		−	1.92239i
$95$		−	7927.87i		−	0.878435i
$96$	−7620.74			−0.826904
$97$		−	695.839i		−	0.0739547i	−0.999316	−	0.0369773i	$-0.988227\pi$
$97$		−	695.839i		−	0.0739547i	0.999316	−	0.0369773i	$-0.0117729\pi$
$98$			29074.4i			3.02733i
$99$		−	2328.53i		−	0.237581i
$100$	−6163.27			−0.616327
$101$			2771.39i			0.271678i	0.990731	+	0.135839i	$0.0433730\pi$
$101$			2771.39i			0.271678i	−0.990731	+	0.135839i	$0.956627\pi$
$102$	13013.7			1.25084
$103$	18022.5			1.69880			0.849398	−	0.527752i	$-0.176965\pi$
$103$	18022.5			1.69880			0.849398	+	0.527752i	$0.176965\pi$
$104$	2122.51			0.196238
$105$			7318.08i			0.663772i
$106$	10225.2			0.910038
$107$	10558.3			0.922207			0.461104	−	0.887346i	$-0.347454\pi$
$107$	10558.3			0.922207			0.461104	+	0.887346i	$0.347454\pi$
$108$			2410.61i			0.206671i
$109$			18717.8i			1.57544i	0.616032	+	0.787721i	$0.288739\pi$
$109$			18717.8i			1.57544i	−0.616032	+	0.787721i	$0.711261\pi$
$110$		−	8106.98i		−	0.669999i
$111$		−	5666.54i		−	0.459909i
$112$		−	20340.4i		−	1.62152i
$113$			4387.09i			0.343574i	0.985134	+	0.171787i	$0.0549540\pi$
$113$			4387.09i			0.343574i	−0.985134	+	0.171787i	$0.945046\pi$
$114$	14541.4			1.11891
$115$			2946.72i			0.222814i
$116$	−20429.2			−1.51823
$117$			8414.33i			0.614678i
$118$			16522.9i			1.18665i
$119$			37522.7i			2.64972i
$120$			577.515i			0.0401052i
$121$	7203.33			0.491997
$122$	−13325.1			−0.895264
$123$	4230.38			0.279620
$124$			24381.9i			1.58571i
$125$		−	16052.7i		−	1.02738i
$126$	−13422.9			−0.845482
$127$	−3707.89			−0.229890			−0.114945	−	0.993372i	$-0.536669\pi$
$127$	−3707.89			−0.229890			−0.114945	+	0.993372i	$0.536669\pi$
$128$		−	3477.58i		−	0.212254i
$129$	4778.85			0.287173
$130$			29295.2i			1.73344i
$131$	−27487.9			−1.60176			−0.800882	−	0.598822i	$-0.795636\pi$
$131$	−27487.9			−1.60176			−0.800882	+	0.598822i	$0.795636\pi$
$132$	7699.85			0.441911
$133$			41927.4i			2.37025i
$134$	2191.72	−	25765.4i	0.122061	−	1.43492i
$135$	−2289.46			−0.125622
$136$			2961.15i			0.160097i
$137$		−	20627.7i		−	1.09903i	−0.835484	−	0.549515i	$-0.814813\pi$
$137$		−	20627.7i		−	1.09903i	0.835484	−	0.549515i	$-0.185187\pi$
$138$	−5404.89			−0.283810
$139$		−	36008.5i		−	1.86370i	−0.362844	−	0.931850i	$-0.618194\pi$
$139$		−	36008.5i		−	1.86370i	0.362844	−	0.931850i	$-0.381806\pi$
$140$	−24199.0			−1.23464
$141$			15322.3i			0.770702i
$142$		−	34840.7i		−	1.72787i
$143$	26876.6			1.31432
$144$	6363.49			0.306881
$145$		−	19402.5i		−	0.922829i
$146$			29023.9i			1.36160i
$147$		−	26226.5i		−	1.21368i
$148$	18737.8			0.855450
$149$	16264.7			0.732613			0.366307	−	0.930494i	$-0.380622\pi$
$149$	16264.7			0.732613			0.366307	+	0.930494i	$0.380622\pi$
$150$	10736.5			0.477179
$151$	13924.1			0.610681			0.305341	−	0.952243i	$-0.401230\pi$
$151$	13924.1			0.610681			0.305341	+	0.952243i	$0.401230\pi$
$152$			3308.75i			0.143211i
$153$	−11739.0			−0.501472
$154$			42874.6i			1.80783i
$155$	−23156.5			−0.963849
$156$	−27824.0			−1.14333
$157$	−2277.32			−0.0923900			−0.0461950	−	0.998932i	$-0.514710\pi$
$157$	−2277.32			−0.0923900			−0.0461950	+	0.998932i	$0.514710\pi$
$158$	31765.7			1.27246
$159$	−9223.58			−0.364843
$160$	23933.3			0.934895
$161$		−	15584.0i		−	0.601212i
$162$		−	4199.34i		−	0.160011i
$163$	−39405.3			−1.48313			−0.741565	−	0.670881i	$-0.765916\pi$
$163$	−39405.3			−1.48313			−0.741565	+	0.670881i	$0.765916\pi$
$164$			13988.8i			0.520106i
$165$			7312.87i			0.268608i
$166$			15627.3i			0.567109i
$167$	22796.2			0.817389			0.408695	−	0.912671i	$-0.365984\pi$
$167$	22796.2			0.817389			0.408695	+	0.912671i	$0.365984\pi$
$168$		−	3054.25i		−	0.108215i
$169$	−68559.7			−2.40046
$170$	−40870.2			−1.41419
$171$	−13117.0			−0.448581
$172$			15802.4i			0.534155i
$173$	−46042.3			−1.53839			−0.769193	−	0.639017i	$-0.779341\pi$
$173$	−46042.3			−1.53839			−0.769193	+	0.639017i	$0.779341\pi$
$174$	35588.1			1.17546
$175$			30956.9i			1.01084i
$176$		−	20325.9i		−	0.656182i
$177$		−	14904.4i		−	0.475738i
$178$		−	44685.1i		−	1.41034i
$179$		−	6788.00i		−	0.211854i	−0.994374	−	0.105927i	$-0.966219\pi$
$179$		−	6788.00i		−	0.211854i	0.994374	−	0.105927i	$-0.0337809\pi$
$180$		−	7570.65i		−	0.233662i
$181$	−35436.0			−1.08165			−0.540826	−	0.841135i	$-0.681888\pi$
$181$	−35436.0			−1.08165			−0.540826	+	0.841135i	$0.681888\pi$
$182$		−	154931.i		−	4.67729i
$183$	12019.9			0.358920
$184$		−	1229.83i		−	0.0363253i
$185$			17796.0i			0.519972i
$186$		−	42473.7i		−	1.22771i
$187$			37495.9i			1.07226i
$188$	−50667.0			−1.43354
$189$	12108.0			0.338961
$190$	−45667.8			−1.26504
$191$			63644.1i			1.74458i	0.488988	+	0.872291i	$0.337366\pi$
$191$			63644.1i			1.74458i	−0.488988	+	0.872291i	$0.662634\pi$
$192$			24304.2i			0.659292i
$193$	21912.7			0.588276			0.294138	−	0.955763i	$-0.404967\pi$
$193$	21912.7			0.588276			0.294138	+	0.955763i	$0.404967\pi$
$194$	−4008.32			−0.106502
$195$		−	26425.6i		−	0.694954i
$196$	86724.2			2.25750
$197$			35731.9i			0.920712i	0.887734	+	0.460356i	$0.152278\pi$
$197$			35731.9i			0.920712i	−0.887734	+	0.460356i	$0.847722\pi$
$198$	−13413.3			−0.342141
$199$	−17606.5			−0.444597			−0.222299	−	0.974979i	$-0.571356\pi$
$199$	−17606.5			−0.444597			−0.222299	+	0.974979i	$0.571356\pi$
$200$			2443.00i			0.0610749i
$201$	−1977.03	+	23241.6i	−0.0489352	+	0.575273i
$202$	15964.3			0.391245
$203$			102612.i			2.49004i
$204$		−	38817.7i		−	0.932759i
$205$	−13285.7			−0.316138
$206$		−	103817.i		−	2.44644i
$207$	4875.45			0.113782
$208$			73449.2i			1.69770i
$209$			41897.5i			0.959169i
$210$	42155.2			0.955900
$211$	−36603.2			−0.822155			−0.411077	−	0.911600i	$-0.634847\pi$
$211$	−36603.2			−0.822155			−0.411077	+	0.911600i	$0.634847\pi$
$212$		−	30500.0i		−	0.678623i
$213$			31427.9i			0.692718i
$214$		−	60820.4i		−	1.32807i
$215$	−15008.2			−0.324677
$216$	955.520			0.0204801
$217$	122465.			2.60072
$218$	107822.			2.26880
$219$		−	26180.9i		−	0.545879i
$220$	−24181.8			−0.499623
$221$		−	135494.i		−	2.77420i
$222$	−32641.6			−0.662316
$223$	38562.5			0.775453			0.387726	−	0.921775i	$-0.373261\pi$
$223$	38562.5			0.775453			0.387726	+	0.921775i	$0.373261\pi$
$224$	−126574.			−2.52260
$225$	−9684.84			−0.191306
$226$	25271.5			0.494781
$227$	−18509.8			−0.359211			−0.179606	−	0.983739i	$-0.557482\pi$
$227$	−18509.8			−0.359211			−0.179606	+	0.983739i	$0.557482\pi$
$228$		−	43374.4i		−	0.834380i
$229$		−	1515.16i		−	0.0288926i	−0.999896	−	0.0144463i	$-0.995401\pi$
$229$		−	1515.16i		−	0.0288926i	0.999896	−	0.0144463i	$-0.00459857\pi$
$230$	16974.3			0.320875
$231$		−	38674.8i		−	0.724777i
$232$			8097.74i			0.150449i
$233$			59203.3i			1.09052i	0.838266	+	0.545261i	$0.183569\pi$
$233$			59203.3i			1.09052i	−0.838266	+	0.545261i	$0.816431\pi$
$234$	48470.0			0.885200
$235$		−	48120.5i		−	0.871353i
$236$	49285.0			0.884893
$237$	−28654.1			−0.510140
$238$	216146.			3.81587
$239$			6305.02i			0.110380i	0.998476	+	0.0551901i	$0.0175765\pi$
$239$			6305.02i			0.110380i	−0.998476	+	0.0551901i	$0.982424\pi$
$240$	−19984.8			−0.346959
$241$	−105494.			−1.81632			−0.908160	−	0.418624i	$-0.862513\pi$
$241$	−105494.			−1.81632			−0.908160	+	0.418624i	$0.862513\pi$
$242$		−	41494.1i		−	0.708527i
$243$			3788.00i			0.0641500i
$244$			39746.6i			0.667606i
$245$			82365.5i			1.37219i
$246$		−	24368.7i		−	0.402682i
$247$		−	151400.i		−	2.48160i
$248$	9664.50			0.157136
$249$		−	14096.5i		−	0.227359i
$250$	−92470.4			−1.47953
$251$		−	52199.7i		−	0.828554i	−0.910151	−	0.414277i	$-0.864035\pi$
$251$		−	52199.7i		−	0.828554i	0.910151	−	0.414277i	$-0.135965\pi$
$252$			40038.2i			0.630483i
$253$		−	15572.9i		−	0.243292i
$254$			21359.0i			0.331065i
$255$	36866.8			0.566963
$256$	54805.1			0.836260
$257$	24835.1			0.376010			0.188005	−	0.982168i	$-0.439798\pi$
$257$	24835.1			0.376010			0.188005	+	0.982168i	$0.439798\pi$
$258$		−	27528.1i		−	0.413559i
$259$		−	94116.2i		−	1.40302i
$260$	87382.7			1.29264
$261$	−32102.1			−0.471252
$262$			158341.i			2.30671i
$263$	33240.7			0.480572			0.240286	−	0.970702i	$-0.422759\pi$
$263$	33240.7			0.480572			0.240286	+	0.970702i	$0.422759\pi$
$264$		−	3052.07i		−	0.0437912i
$265$	28967.1			0.412490
$266$	241519.			3.41340
$267$			40308.0i			0.565417i
$268$	−76853.9	−	6537.53i	−1.07003	−	0.0910215i
$269$	87123.6			1.20401			0.602006	−	0.798491i	$-0.294368\pi$
$269$	87123.6			1.20401			0.602006	+	0.798491i	$0.294368\pi$
$270$			13188.2i			0.180908i
$271$			14034.5i			0.191099i	0.995425	+	0.0955495i	$0.0304608\pi$
$271$			14034.5i			0.191099i	−0.995425	+	0.0955495i	$0.969539\pi$
$272$	−102470.			−1.38503
$273$			139755.i			1.87517i
$274$	−118824.			−1.58272
$275$			30934.8i			0.409055i
$276$			16121.9i			0.211640i
$277$	−61727.7			−0.804490			−0.402245	−	0.915532i	$-0.631770\pi$
$277$	−61727.7			−0.804490			−0.402245	+	0.915532i	$0.631770\pi$
$278$	−207424.			−2.68392
$279$			38313.2i			0.492199i
$280$			9592.01i			0.122347i
$281$		−	68067.2i		−	0.862036i	−0.902343	−	0.431018i	$-0.858155\pi$
$281$		−	68067.2i		−	0.862036i	0.902343	−	0.431018i	$-0.141845\pi$
$282$	88262.9			1.10989
$283$	−72721.5			−0.908009			−0.454005	−	0.890999i	$-0.650005\pi$
$283$	−72721.5			−0.908009			−0.454005	+	0.890999i	$0.650005\pi$
$284$	−103924.			−1.28849
$285$	41194.4			0.507165
$286$		−	154820.i		−	1.89276i
$287$	70262.8			0.853024
$288$		−	39598.5i		−	0.477413i
$289$	105509.			1.26327
$290$	−111766.			−1.32897
$291$	3615.69			0.0426977
$292$	86573.5			1.01536
$293$	−42836.4			−0.498973			−0.249487	−	0.968378i	$-0.580262\pi$
$293$	−42836.4			−0.498973			−0.249487	+	0.968378i	$0.580262\pi$
$294$	−151075.			−1.74783
$295$			46808.0i			0.537868i
$296$		−	7427.28i		−	0.0847709i
$297$	12099.4			0.137167
$298$		−	93691.6i		−	1.05504i
$299$			56273.9i			0.629455i
$300$		−	32025.3i		−	0.355836i
$301$	79372.5			0.876066
$302$		−	80208.8i		−	0.879443i
$303$	−14400.6			−0.156854
$304$	−114499.			−1.23895
$305$	−37748.9			−0.405793
$306$			67621.2i			0.722171i
$307$	−89613.9			−0.950821			−0.475410	−	0.879764i	$-0.657700\pi$
$307$	−89613.9			−0.950821			−0.475410	+	0.879764i	$0.657700\pi$
$308$	127888.			1.34812
$309$			93647.8i			0.980801i
$310$			133391.i			1.38804i
$311$		−	107275.i		−	1.10912i	−0.832145	−	0.554559i	$-0.812887\pi$
$311$		−	107275.i		−	1.10912i	0.832145	−	0.554559i	$-0.187113\pi$
$312$			11028.9i			0.113298i
$313$		−	46104.9i		−	0.470607i	−0.971922	−	0.235304i	$-0.924392\pi$
$313$		−	46104.9i		−	0.470607i	0.971922	−	0.235304i	$-0.0756084\pi$
$314$			13118.3i			0.133051i
$315$	−38025.9			−0.383229
$316$		−	94751.6i		−	0.948883i
$317$	−181612.			−1.80729			−0.903643	−	0.428287i	$-0.859117\pi$
$317$	−181612.			−1.80729			−0.903643	+	0.428287i	$0.859117\pi$
$318$			53131.6i			0.525411i
$319$			102539.i			1.00764i
$320$		−	76328.4i		−	0.745394i
$321$			54862.8i			0.532437i
$322$	−89770.3			−0.865807
$323$	211220.			2.02456
$324$	−12525.9			−0.119322
$325$		−	111785.i		−	1.05832i
$326$			226991.i			2.13586i
$327$	−97260.7			−0.909582
$328$	5544.87			0.0515399
$329$			254490.i			2.35114i
$330$	42125.1			0.386824
$331$			181566.i			1.65722i	0.559828	+	0.828609i	$0.310867\pi$
$331$			181566.i			1.65722i	−0.559828	+	0.828609i	$0.689133\pi$
$332$	46613.5			0.422898
$333$	29444.2			0.265529
$334$		−	131315.i		−	1.17712i
$335$	6208.96	−	72991.3i	0.0553260	−	0.650402i
$336$	105692.			0.936188
$337$		−	24181.1i		−	0.212920i	−0.994317	−	0.106460i	$-0.966048\pi$
$337$		−	24181.1i		−	0.212920i	0.994317	−	0.106460i	$-0.0339516\pi$
$338$			394932.i			3.45692i
$339$	−22796.0			−0.198362
$340$			121909.i			1.05458i
$341$	122378.			1.05243
$342$			75559.1i			0.646003i
$343$		−	228384.i		−	1.94123i
$344$	6263.77			0.0529321
$345$	−15311.6			−0.128642
$346$			265223.i			2.21543i
$347$		−	13343.4i		−	0.110818i	−0.998464	−	0.0554088i	$-0.982354\pi$
$347$		−	13343.4i		−	0.110818i	0.998464	−	0.0554088i	$-0.0176462\pi$
$348$		−	106153.i		−	0.876548i
$349$	−86655.7			−0.711453			−0.355726	−	0.934590i	$-0.615766\pi$
$349$	−86655.7			−0.711453			−0.355726	+	0.934590i	$0.615766\pi$
$350$	178324.			1.45571
$351$	−43722.1			−0.354885
$352$	−126483.			−1.02082
$353$		−	51063.5i		−	0.409790i	−0.978784	−	0.204895i	$-0.934315\pi$
$353$		−	51063.5i		−	0.409790i	0.978784	−	0.204895i	$-0.0656852\pi$
$354$	−85855.4			−0.685111
$355$		−	98700.9i		−	0.783185i
$356$	−133288.			−1.05170
$357$	−194974.			−1.52982
$358$	−39101.7			−0.305091
$359$	150507.			1.16780			0.583899	−	0.811826i	$-0.301526\pi$
$359$	150507.			1.16780			0.583899	+	0.811826i	$0.301526\pi$
$360$	−3000.86			−0.0231548
$361$	105694.			0.811025
$362$			204126.i			1.55769i
$363$			37429.6i			0.284055i
$364$	−462132.			−3.48790
$365$			82222.3i			0.617169i
$366$		−	69239.3i		−	0.516881i
$367$		−	38461.0i		−	0.285554i	−0.989755	−	0.142777i	$-0.954397\pi$
$367$		−	38461.0i		−	0.285554i	0.989755	−	0.142777i	$-0.0456032\pi$
$368$	42558.1			0.314258
$369$			21981.7i			0.161439i
$370$	102512.			0.748813
$371$	−153195.			−1.11301
$372$	−126692.			−0.915510
$373$		−	90240.9i		−	0.648613i	−0.945952	−	0.324306i	$-0.894869\pi$
$373$		−	90240.9i		−	0.648613i	0.945952	−	0.324306i	$-0.105131\pi$
$374$	215992.			1.54417
$375$	83412.5			0.593155
$376$			20083.4i			0.142056i
$377$		−	370532.i		−	2.60701i
$378$		−	69747.3i		−	0.488139i
$379$		−	12401.5i		−	0.0863364i	−0.999068	−	0.0431682i	$-0.986255\pi$
$379$		−	12401.5i		−	0.0863364i	0.999068	−	0.0431682i	$-0.0137451\pi$
$380$			136219.i			0.943348i
$381$		−	19266.8i		−	0.132727i
$382$	366616.			2.51238
$383$			143756.i			0.980002i	0.871722	+	0.490001i	$0.163004\pi$
$383$			143756.i			0.980002i	−0.871722	+	0.490001i	$0.836996\pi$
$384$	18070.0			0.122545
$385$			121460.i			0.819431i
$386$		−	126226.i		−	0.847178i
$387$			24831.6i			0.165800i
$388$			11956.1i			0.0794196i
$389$	214877.			1.42001			0.710005	−	0.704197i	$-0.248693\pi$
$389$	214877.			1.42001			0.710005	+	0.704197i	$0.248693\pi$
$390$	−152222.			−1.00080
$391$	−78508.5			−0.513527
$392$		−	34375.7i		−	0.223707i
$393$		−	142831.i		−	0.924779i
$394$	205830.			1.32592
$395$	89989.5			0.576763
$396$			40009.6i			0.255137i
$397$	3085.76			0.0195786			0.00978929	−	0.999952i	$-0.496884\pi$
$397$	3085.76			0.0195786			0.00978929	+	0.999952i	$0.496884\pi$
$398$			101421.i			0.640266i
$399$	−217861.			−1.36846
$400$	−84539.6			−0.528373
$401$			227380.i			1.41404i	0.707192	+	0.707022i	$0.249962\pi$
$401$			227380.i			1.41404i	−0.707192	+	0.707022i	$0.750038\pi$
$402$	133881.	+	11388.5i	0.828452	+	0.0704717i
$403$	−442223.			−2.72289
$404$		−	47618.9i		−	0.291754i
$405$		−	11896.4i		−	0.0725279i
$406$	591087.			3.58591
$407$		−	94049.0i		−	0.567761i
$408$	−15386.6			−0.0924318
$409$		−	98253.2i		−	0.587354i	−0.955905	−	0.293677i	$-0.905121\pi$
$409$		−	98253.2i		−	0.587354i	0.955905	−	0.293677i	$-0.0948791\pi$
$410$			76531.1i			0.455271i
$411$	107185.			0.634525
$412$	−309669.			−1.82433
$413$		−	247549.i		−	1.45131i
$414$		−	28084.6i		−	0.163858i
$415$			44270.7i			0.257052i
$416$	457058.			2.64110
$417$	187106.			1.07601
$418$	241347.			1.38130
$419$	92893.9			0.529126			0.264563	−	0.964368i	$-0.414772\pi$
$419$	92893.9			0.529126			0.264563	+	0.964368i	$0.414772\pi$
$420$		−	125742.i		−	0.712822i
$421$	−216621.			−1.22218			−0.611092	−	0.791560i	$-0.709269\pi$
$421$	−216621.			−1.22218			−0.611092	+	0.791560i	$0.709269\pi$
$422$			210849.i			1.18399i
$423$	−79617.1			−0.444965
$424$	−12089.6			−0.0672481
$425$	155953.			0.863409
$426$	181038.			0.997585
$427$	199639.			1.09494
$428$	−181417.			−0.990354
$429$			139655.i			0.758825i
$430$			86453.5i			0.467569i
$431$	−18306.9			−0.0985509			−0.0492755	−	0.998785i	$-0.515691\pi$
$431$	−18306.9			−0.0985509			−0.0492755	+	0.998785i	$0.515691\pi$
$432$			33065.7i			0.177178i
$433$		−	33621.4i		−	0.179325i	−0.995972	−	0.0896623i	$-0.971421\pi$
$433$		−	33621.4i		−	0.179325i	0.995972	−	0.0896623i	$-0.0285788\pi$
$434$		−	705451.i		−	3.74531i
$435$	100818.			0.532796
$436$		−	321616.i		−	1.69186i
$437$	−87724.4			−0.459365
$438$	−150813.			−0.786122
$439$	240262.			1.24668			0.623341	−	0.781950i	$-0.285775\pi$
$439$	240262.			1.24668			0.623341	+	0.781950i	$0.285775\pi$
$440$			9585.17i			0.0495102i
$441$	136277.			0.700720
$442$	−780504.			−3.99513
$443$		−	3573.43i		−	0.0182087i	−0.999959	−	0.00910434i	$-0.997102\pi$
$443$		−	3573.43i		−	0.0182087i	0.999959	−	0.00910434i	$-0.00289804\pi$
$444$			97364.4i			0.493894i
$445$		−	126589.i		−	0.639259i
$446$		−	222136.i		−	1.11673i
$447$			84514.1i			0.422974i
$448$			403670.i			2.01127i
$449$	102462.			0.508242			0.254121	−	0.967172i	$-0.418214\pi$
$449$	102462.			0.508242			0.254121	+	0.967172i	$0.418214\pi$
$450$			55788.7i			0.275500i
$451$	70212.7			0.345193
$452$		−	75380.5i		−	0.368962i
$453$			72351.9i			0.352577i
$454$			106624.i			0.517301i
$455$		−	438906.i		−	2.12006i
$456$	−17192.7			−0.0826829
$457$	−118522.			−0.567502			−0.283751	−	0.958898i	$-0.591579\pi$
$457$	−118522.			−0.567502			−0.283751	+	0.958898i	$0.591579\pi$
$458$	−8727.94			−0.0416084
$459$		−	60997.4i		−	0.289525i
$460$		−	50631.5i		−	0.239279i
$461$	238754.			1.12344			0.561718	−	0.827329i	$-0.310141\pi$
$461$	238754.			1.12344			0.561718	+	0.827329i	$0.310141\pi$
$462$	−222783.			−1.04375
$463$		−	107037.i		−	0.499313i	−0.968334	−	0.249657i	$-0.919682\pi$
$463$		−	107037.i		−	0.499313i	0.968334	−	0.249657i	$-0.0803178\pi$
$464$	−280221.			−1.30156
$465$		−	120325.i		−	0.556479i
$466$	341036.			1.57046
$467$	−431716.			−1.97954			−0.989771	−	0.142668i	$-0.954432\pi$
$467$	−431716.			−1.97954			−0.989771	+	0.142668i	$0.954432\pi$
$468$		−	144578.i		−	0.660101i
$469$	−32836.7	+	386022.i	−0.149284	+	1.75496i
$470$	−277194.			−1.25484
$471$		−	11833.3i		−	0.0533414i
$472$		−	19535.6i		−	0.0876885i
$473$	79315.9			0.354518
$474$			165059.i			0.734654i
$475$	174260.			0.772344
$476$		−	644727.i		−	2.84552i
$477$		−	47927.1i		−	0.210642i
$478$	36319.5			0.158959
$479$	122200.			0.532599			0.266300	−	0.963890i	$-0.414199\pi$
$479$	122200.			0.532599			0.266300	+	0.963890i	$0.414199\pi$
$480$			124361.i			0.539762i
$481$			339854.i			1.46893i
$482$			607687.i			2.61569i
$483$	80976.9			0.347110
$484$	−123770.			−0.528354
$485$	−11355.2			−0.0482740
$486$	21820.4			0.0923826
$487$		−	181229.i		−	0.764133i	−0.924135	−	0.382066i	$-0.875213\pi$
$487$		−	181229.i		−	0.764133i	0.924135	−	0.382066i	$-0.124787\pi$
$488$	15754.7			0.0661564
$489$		−	204756.i		−	0.856285i
$490$	474459.			1.97609
$491$	115960.			0.480999			0.240499	−	0.970649i	$-0.422689\pi$
$491$	115960.			0.480999			0.240499	+	0.970649i	$0.422689\pi$
$492$	−72687.7			−0.300283
$493$	516935.			2.12688
$494$	−872125.			−3.57376
$495$	−37998.8			−0.155081
$496$			334439.i			1.35942i
$497$			521990.i			2.11324i
$498$	−81201.6			−0.327421
$499$			193834.i			0.778446i	0.921143	+	0.389223i	$0.127257\pi$
$499$			193834.i			0.778446i	−0.921143	+	0.389223i	$0.872743\pi$
$500$			275823.i			1.10329i
$501$			118452.i			0.471920i
$502$	−300692.			−1.19320
$503$			283738.i			1.12145i	0.828001	+	0.560726i	$0.189478\pi$
$503$			283738.i			1.12145i	−0.828001	+	0.560726i	$0.810522\pi$
$504$	15870.3			0.0624777
$505$	45225.7			0.177338
$506$	−89706.3			−0.350366
$507$		−	356247.i		−	1.38591i
$508$	63710.2			0.246877
$509$	183450.			0.708082			0.354041	−	0.935230i	$-0.384807\pi$
$509$	183450.			0.708082			0.354041	+	0.935230i	$0.384807\pi$
$510$		−	212368.i		−	0.816485i
$511$		−	434841.i		−	1.66529i
$512$		−	371341.i		−	1.41655i
$513$		−	68157.7i		−	0.258988i
$514$		−	143060.i		−	0.541493i
$515$		−	294105.i		−	1.10889i
$516$	−82111.8			−0.308394
$517$			254309.i			0.951437i
$518$	−542148.			−2.02050
$519$		−	239243.i		−	0.888187i
$520$		−	34636.8i		−	0.128095i
$521$			43722.8i			0.161077i	0.996752	+	0.0805384i	$0.0256640\pi$
$521$			43722.8i			0.161077i	−0.996752	+	0.0805384i	$0.974336\pi$
$522$			184921.i			0.678651i
$523$	−48943.2			−0.178932			−0.0894662	−	0.995990i	$-0.528516\pi$
$523$	−48943.2			−0.178932			−0.0894662	+	0.995990i	$0.528516\pi$
$524$	472306.			1.72013
$525$	−160857.			−0.583607
$526$		−	191480.i		−	0.692074i
$527$		−	616951.i		−	2.22141i
$528$	105616.			0.378847
$529$	−247235.			−0.883483
$530$		−	166862.i		−	0.594028i
$531$	77445.5			0.274667
$532$		−	720410.i		−	2.54540i
$533$	−253719.			−0.893097
$534$	232191.			0.814259
$535$		−	172299.i		−	0.601971i
$536$	−2591.35	+	30463.4i	−0.00901978	+	0.106035i
$537$	35271.5			0.122314
$538$		−	501868.i		−	1.73390i
$539$		−	435288.i		−	1.49830i
$540$	39338.3			0.134905
$541$			156811.i			0.535773i	0.963450	+	0.267886i	$0.0863252\pi$
$541$			156811.i			0.535773i	−0.963450	+	0.267886i	$0.913675\pi$
$542$	80844.5			0.275202
$543$		−	184131.i		−	0.624492i
$544$			637648.i			2.15468i
$545$	305452.			1.02837
$546$	805044.			2.70044
$547$			349846.i			1.16924i	0.811309	+	0.584618i	$0.198755\pi$
$547$			349846.i			1.16924i	−0.811309	+	0.584618i	$0.801245\pi$
$548$			354432.i			1.18024i
$549$			62457.0i			0.207222i
$550$	178197.			0.589081
$551$	577616.			1.90255
$552$	6390.39			0.0209724
$553$	−475919.			−1.55626
$554$			355577.i			1.15855i
$555$	−92470.9			−0.300206
$556$			618711.i			2.00142i
$557$	−478942.			−1.54373			−0.771867	−	0.635785i	$-0.780677\pi$
$557$	−478942.			−1.54373			−0.771867	+	0.635785i	$0.780677\pi$
$558$	220700.			0.708817
$559$	−286614.			−0.917221
$560$	−331930.			−1.05845
$561$	−194835.			−0.619071
$562$	−392095.			−1.24142
$563$			159087.i			0.501902i	0.968000	+	0.250951i	$0.0807434\pi$
$563$			159087.i			0.501902i	−0.968000	+	0.250951i	$0.919257\pi$
$564$		−	263273.i		−	0.827653i
$565$	71591.9			0.224268
$566$			418906.i			1.30763i
$567$			62915.2i			0.195699i
$568$			41193.4i			0.127682i
$569$	−252587.			−0.780166			−0.390083	−	0.920780i	$-0.627554\pi$
$569$	−252587.			−0.780166			−0.390083	+	0.920780i	$0.627554\pi$
$570$		−	237297.i		−	0.730369i
$571$	−98898.1			−0.303330			−0.151665	−	0.988432i	$-0.548464\pi$
$571$	−98898.1			−0.303330			−0.151665	+	0.988432i	$0.548464\pi$
$572$	−461803.			−1.41145
$573$	−330704.			−1.00723
$574$		−	404742.i		−	1.22844i
$575$	−64770.9			−0.195904
$576$	−126288.			−0.380643
$577$		−	413596.i		−	1.24229i	−0.783694	−	0.621147i	$-0.786667\pi$
$577$		−	413596.i		−	1.24229i	0.783694	−	0.621147i	$-0.213333\pi$
$578$		−	607777.i		−	1.81924i
$579$			113862.i			0.339641i
$580$			333380.i			0.991023i
$581$		−	234130.i		−	0.693594i
$582$		−	20827.8i		−	0.0614891i
$583$	−153086.			−0.450401
$584$		−	34316.0i		−	0.100617i
$585$	137312.			0.401232
$586$			246755.i			0.718573i
$587$			64740.5i			0.187888i	0.995577	+	0.0939442i	$0.0299475\pi$
$587$			64740.5i			0.187888i	−0.995577	+	0.0939442i	$0.970052\pi$
$588$			450632.i			1.30337i
$589$		−	689373.i		−	1.98712i
$590$	269633.			0.774585
$591$	−185668.			−0.531573
$592$	257020.			0.733371
$593$			128726.i			0.366065i	0.983107	+	0.183032i	$0.0585913\pi$
$593$			128726.i			0.366065i	−0.983107	+	0.183032i	$0.941409\pi$
$594$		−	69697.6i		−	0.197535i
$595$	612324.			1.72961
$596$	−279466.			−0.786750
$597$		−	91486.1i		−	0.256688i
$598$	324161.			0.906480
$599$			598963.i			1.66935i	0.550745	+	0.834673i	$0.314344\pi$
$599$			598963.i			1.66935i	−0.550745	+	0.834673i	$0.685656\pi$
$600$	−12694.2			−0.0352616
$601$	190324.			0.526921			0.263460	−	0.964670i	$-0.415136\pi$
$601$	190324.			0.526921			0.263460	+	0.964670i	$0.415136\pi$
$602$		−	457218.i		−	1.26163i
$603$	−120767.	−	10272.9i	−0.332134	−	0.0282527i
$604$	−239249.			−0.655808
$605$		−	117549.i		−	0.321152i
$606$			82953.2i			0.225885i
$607$	−358286.			−0.972418			−0.486209	−	0.873843i	$-0.661621\pi$
$607$	−358286.			−0.972418			−0.486209	+	0.873843i	$0.661621\pi$
$608$			712500.i			1.92743i
$609$	−533188.			−1.43762
$610$			217449.i			0.584384i
$611$		−	918964.i		−	2.46159i
$612$	201703.			0.538529
$613$	−8353.72			−0.0222310			−0.0111155	−	0.999938i	$-0.503538\pi$
$613$	−8353.72			−0.0222310			−0.0111155	+	0.999938i	$0.503538\pi$
$614$			516213.i			1.36928i
$615$		−	69034.5i		−	0.182522i
$616$		−	50692.1i		−	0.133592i
$617$	104298.			0.273973			0.136986	−	0.990573i	$-0.456258\pi$
$617$	104298.			0.273973			0.136986	+	0.990573i	$0.456258\pi$
$618$	539450.			1.41245
$619$	236148.			0.616316			0.308158	−	0.951335i	$-0.400287\pi$
$619$	236148.			0.616316			0.308158	+	0.951335i	$0.400287\pi$
$620$	397882.			1.03507
$621$			25333.6i			0.0656922i
$622$	−617948.			−1.59724
$623$			669480.i			1.72489i
$624$	−381653.			−0.980167
$625$	−37774.7			−0.0967032
$626$	−265583.			−0.677723
$627$	−217706.			−0.553777
$628$	39129.7			0.0992173
$629$	−474135.			−1.19840
$630$			219045.i			0.551889i
$631$			129164.i			0.324401i	0.986758	+	0.162201i	$0.0518592\pi$
$631$			129164.i			0.324401i	−0.986758	+	0.162201i	$0.948141\pi$
$632$	−37557.7			−0.0940295
$633$		−	190196.i		−	0.474671i
$634$			1.04616e6i			2.60268i
$635$			60508.2i			0.150061i
$636$	158483.			0.391803
$637$			1.57295e6i			3.87646i
$638$	590666.			1.45111
$639$	−163304.			−0.399941
$640$	−56749.8			−0.138549
$641$			175966.i			0.428264i	0.976805	+	0.214132i	$0.0686923\pi$
$641$			175966.i			0.428264i	−0.976805	+	0.214132i	$0.931308\pi$
$642$	316032.			0.766763
$643$	198080.			0.479091			0.239545	−	0.970885i	$-0.423002\pi$
$643$	198080.			0.479091			0.239545	+	0.970885i	$0.423002\pi$
$644$			267770.i			0.645639i
$645$		−	77985.0i		−	0.187453i
$646$		−	1.21671e6i		−	2.91557i
$647$		−	175858.i		−	0.420100i	−0.977691	−	0.210050i	$-0.932637\pi$
$647$		−	175858.i		−	0.420100i	0.977691	−	0.210050i	$-0.0673627\pi$
$648$			4965.03i			0.0118242i
$649$		−	247372.i		−	0.587302i
$650$	−643929.			−1.52409
$651$			636349.i			1.50153i
$652$	677075.			1.59273
$653$			540589.i			1.26777i	0.773427	+	0.633886i	$0.218541\pi$
$653$			540589.i			1.26777i	−0.773427	+	0.633886i	$0.781459\pi$
$654$			560262.i			1.30989i
$655$			448568.i			1.04555i
$656$			191879.i			0.445883i
$657$	136040.			0.315163
$658$	1.46597e6			3.38589
$659$	−205492.			−0.473178			−0.236589	−	0.971610i	$-0.576029\pi$
$659$	−205492.			−0.473178			−0.236589	+	0.971610i	$0.576029\pi$
$660$		−	125652.i		−	0.288458i
$661$		−	11851.9i		−	0.0271259i	−0.999908	−	0.0135629i	$-0.995683\pi$
$661$		−	11851.9i		−	0.0271259i	0.999908	−	0.0135629i	$-0.00431735\pi$
$662$	1.04590e6			2.38656
$663$	704050.			1.60168
$664$		−	18476.7i		−	0.0419071i
$665$	684203.			1.54718
$666$		−	169611.i		−	0.382388i
$667$	−214695.			−0.482580
$668$	−391691.			−0.877791
$669$			200377.i			0.447708i
$670$	−420460.	−	35766.2i	−0.936645	−	0.0796751i
$671$	199497.			0.443089
$672$		−	657696.i		−	1.45642i
$673$			137469.i			0.303511i	0.988418	+	0.151755i	$0.0484926\pi$
$673$			137469.i			0.303511i	−0.988418	+	0.151755i	$0.951507\pi$
$674$	−139293.			−0.306627
$675$		−	50323.9i		−	0.110450i
$676$	1.17802e6			2.57785
$677$		−	335816.i		−	0.732696i	−0.930478	−	0.366348i	$-0.880608\pi$
$677$		−	335816.i		−	0.732696i	0.930478	−	0.366348i	$-0.119392\pi$
$678$			131314.i			0.285662i
$679$	60053.3			0.130256
$680$	48322.3			0.104503
$681$		−	96179.7i		−	0.207391i
$682$		−	704948.i		−	1.51561i
$683$		−	749968.i		−	1.60769i	−0.594841	−	0.803843i	$-0.702785\pi$
$683$		−	749968.i		−	1.60769i	0.594841	−	0.803843i	$-0.297215\pi$
$684$	225380.			0.481729
$685$	−336618.			−0.717392
$686$	−1.31558e6			−2.79557
$687$	7873.00			0.0166812
$688$			216757.i			0.457927i
$689$	553189.			1.16529
$690$			88201.1i			0.185257i
$691$	780098.			1.63378			0.816889	−	0.576795i	$-0.195697\pi$
$691$	780098.			1.63378			0.816889	+	0.576795i	$0.195697\pi$
$692$	791115.			1.65207
$693$	200960.			0.418450
$694$	−76863.7			−0.159589
$695$	−587615.			−1.21653
$696$	−42077.1			−0.0868615
$697$		−	353967.i		−	0.728614i
$698$			499172.i			1.02457i
$699$	−307630.			−0.629613
$700$		−	531911.i		−	1.08553i
$701$		−	133811.i		−	0.272304i	−0.990688	−	0.136152i	$-0.956526\pi$
$701$		−	133811.i		−	0.272304i	0.990688	−	0.136152i	$-0.0434736\pi$
$702$			251858.i			0.511070i
$703$	−529792.			−1.07200
$704$			403382.i			0.813901i
$705$	250041.			0.503076
$706$	−294147.			−0.590139
$707$	−239181.			−0.478506
$708$			256092.i			0.510893i
$709$	−317818.			−0.632246			−0.316123	−	0.948718i	$-0.602381\pi$
$709$	−317818.			−0.632246			−0.316123	+	0.948718i	$0.602381\pi$
$710$	−568558.			−1.12787
$711$		−	148891.i		−	0.294530i
$712$			52832.8i			0.104218i
$713$			256234.i			0.504031i
$714$			1.12313e6i			2.20309i
$715$		−	438593.i		−	0.857925i
$716$			116634.i			0.227509i
$717$	−32761.9			−0.0637280
$718$		−	866982.i		−	1.68175i
$719$	500267.			0.967708			0.483854	−	0.875149i	$-0.339237\pi$
$719$	500267.			0.967708			0.483854	+	0.875149i	$0.339237\pi$
$720$		−	103844.i		−	0.200317i
$721$			1.55541e6i			2.99208i
$722$		−	608838.i		−	1.16796i
$723$		−	548161.i		−	1.04865i
$724$	608873.			1.16158
$725$	426480.			0.811377
$726$	215610.			0.409068
$727$			468574.i			0.886563i	0.896382	+	0.443282i	$0.146186\pi$
$727$			468574.i			0.886563i	−0.896382	+	0.443282i	$0.853814\pi$
$728$			183180.i			0.345633i
$729$	−19683.0			−0.0370370
$730$	473635.			0.888787
$731$		−	399859.i		−	0.748295i
$732$	−206529.			−0.385442
$733$		−	432833.i		−	0.805587i	−0.915291	−	0.402793i	$-0.868039\pi$
$733$		−	432833.i		−	0.805587i	0.915291	−	0.402793i	$-0.131961\pi$
$734$	−221551.			−0.411228
$735$	−427984.			−0.792232
$736$		−	264830.i		−	0.488890i
$737$	−32813.3	+	385747.i	−0.0604108	+	0.710178i
$738$	126623.			0.232489
$739$		−	503169.i		−	0.921351i	−0.887569	−	0.460675i	$-0.847607\pi$
$739$		−	503169.i		−	0.921351i	0.887569	−	0.460675i	$-0.152393\pi$
$740$		−	305777.i		−	0.558396i
$741$	786696.			1.43275
$742$			882469.i			1.60285i
$743$	17048.3			0.0308819			0.0154409	−	0.999881i	$-0.495085\pi$
$743$	17048.3			0.0308819			0.0154409	+	0.999881i	$0.495085\pi$
$744$			50218.2i			0.0907225i
$745$		−	265421.i		−	0.478214i
$746$	−519824.			−0.934069
$747$	73247.6			0.131266
$748$		−	644268.i		−	1.15150i
$749$			911222.i			1.62428i
$750$		−	480490.i		−	0.854205i
$751$	−902747.			−1.60061			−0.800307	−	0.599591i	$-0.795330\pi$
$751$	−902747.			−1.60061			−0.800307	+	0.599591i	$0.795330\pi$
$752$	−694983.			−1.22896
$753$	271238.			0.478366
$754$	−2.13442e6			−3.75437
$755$		−	227225.i		−	0.398622i
$756$	−208044.			−0.364009
$757$		−	653413.i		−	1.14024i	−0.821562	−	0.570119i	$-0.806897\pi$
$757$		−	653413.i		−	1.14024i	0.821562	−	0.570119i	$-0.193103\pi$
$758$	−71437.5			−0.124333
$759$	80919.2			0.140465
$760$	53994.7			0.0934811
$761$	−324.671			−0.000560627			−0.000280314	−	1.00000i	$-0.500089\pi$
$761$	−324.671			−0.000560627			−0.000280314		1.00000i	$0.500089\pi$
$762$	−110984.			−0.191140
$763$	−1.61541e6			−2.77482
$764$		−	1.09355e6i		−	1.87350i
$765$			191565.i			0.327336i
$766$	828091.			1.41130
$767$			893898.i			1.51949i
$768$			284776.i			0.482815i
$769$			536234.i			0.906780i	0.891312	+	0.453390i	$0.149786\pi$
$769$			536234.i			0.906780i	−0.891312	+	0.453390i	$0.850214\pi$
$770$	699661.			1.18007
$771$			129047.i			0.217089i
$772$	−376511.			−0.631747
$773$	−356958.			−0.597390			−0.298695	−	0.954349i	$-0.596551\pi$
$773$	−356958.			−0.597390			−0.298695	+	0.954349i	$0.596551\pi$
$774$	143040.			0.238768
$775$		−	508995.i		−	0.847443i
$776$	4739.18			0.00787009
$777$	489042.			0.810035
$778$		−	1.23778e6i		−	2.04496i
$779$		−	395518.i		−	0.651766i
$780$			454054.i			0.746308i
$781$			521618.i			0.855166i
$782$			452241.i			0.739532i
$783$		−	166808.i		−	0.272077i
$784$	1.18957e6			1.93534
$785$			37163.1i			0.0603077i
$786$	−822766.			−1.33178
$787$		−	319376.i		−	0.515647i	−0.966192	−	0.257824i	$-0.916995\pi$
$787$		−	319376.i		−	0.515647i	0.966192	−	0.257824i	$-0.0830053\pi$
$788$		−	613958.i		−	0.988749i
$789$			172724.i			0.277459i
$790$		−	518376.i		−	0.830598i
$791$	−378621.			−0.605135
$792$	15859.0			0.0252828
$793$	−720897.			−1.14638
$794$		−	17775.3i		−	0.0281952i
$795$			150518.i			0.238151i
$796$	302521.			0.477451
$797$	342526.			0.539234			0.269617	−	0.962968i	$-0.413103\pi$
$797$	342526.			0.539234			0.269617	+	0.962968i	$0.413103\pi$
$798$			1.25497e6i			1.97073i
$799$	1.28206e6			2.00824
$800$			526071.i			0.821986i
$801$	−209447.			−0.326444
$802$	1.30980e6			2.03637
$803$		−	434531.i		−	0.673891i
$804$	33970.0	−	399345.i	0.0525513	−	0.617783i
$805$	−254312.			−0.392441
$806$			2.54738e6i			3.92125i
$807$			452707.i			0.695137i
$808$	−18875.2			−0.0289114
$809$		−	111456.i		−	0.170297i	−0.996368	−	0.0851485i	$-0.972864\pi$
$809$		−	111456.i		−	0.170297i	0.996368	−	0.0851485i	$-0.0271365\pi$
$810$	−68528.0			−0.104448
$811$			738825.i			1.12331i	0.827371	+	0.561655i	$0.189835\pi$
$811$			738825.i			1.12331i	−0.827371	+	0.561655i	$0.810165\pi$
$812$		−	1.76311e6i		−	2.67404i
$813$	−72925.4			−0.110331
$814$	−541761.			−0.817634
$815$			643046.i			0.968114i
$816$		−	532450.i		−	0.799648i
$817$		−	446798.i		−	0.669371i
$818$	−565979.			−0.845851
$819$	−726186.			−1.08263
$820$	228279.			0.339499
$821$	−455433.			−0.675676			−0.337838	−	0.941204i	$-0.609696\pi$
$821$	−455433.			−0.675676			−0.337838	+	0.941204i	$0.609696\pi$
$822$		−	617427.i		−	0.913781i
$823$	−555561.			−0.820223			−0.410111	−	0.912035i	$-0.634510\pi$
$823$	−555561.			−0.820223			−0.410111	+	0.912035i	$0.634510\pi$
$824$			122747.i			0.180782i
$825$	−160742.			−0.236168
$826$	−1.42598e6			−2.09004
$827$	−544518.			−0.796161			−0.398081	−	0.917350i	$-0.630324\pi$
$827$	−544518.			−0.796161			−0.398081	+	0.917350i	$0.630324\pi$
$828$	−83771.6			−0.122190
$829$	1.18036e6			1.71753			0.858766	−	0.512368i	$-0.171232\pi$
$829$	1.18036e6			1.71753			0.858766	+	0.512368i	$0.171232\pi$
$830$	255018.			0.370181
$831$		−	320747.i		−	0.464473i
$832$		−	1.45765e6i		−	2.10575i
$833$	−2.19444e6			−3.16252
$834$		−	1.07781e6i		−	1.54956i
$835$		−	372005.i		−	0.533551i
$836$		−	719896.i		−	1.03005i
$837$	−199081.			−0.284171
$838$		−	535107.i		−	0.761996i
$839$	673909.			0.957365			0.478682	−	0.877988i	$-0.341115\pi$
$839$	673909.			0.957365			0.478682	+	0.877988i	$0.341115\pi$
$840$	−49841.5			−0.0706371
$841$	706363.			0.998702
$842$			1.24783e6i			1.76007i
$843$	353688.			0.497696
$844$	628928.			0.882909
$845$			1.11881e6i			1.56691i
$846$			458627.i			0.640795i
$847$			621672.i			0.866552i
$848$		−	418359.i		−	0.581778i
$849$		−	377872.i		−	0.524239i
$850$		−	898355.i		−	1.24340i
$851$	196919.			0.271912
$852$		−	540005.i		−	0.743907i
$853$	1.11206e6			1.52837			0.764186	−	0.644996i	$-0.223141\pi$
$853$	1.11206e6			1.52837			0.764186	+	0.644996i	$0.223141\pi$
$854$		−	1.15000e6i		−	1.57682i
$855$			214053.i			0.292812i
$856$			71910.1i			0.0981392i
$857$			794509.i			1.08178i	0.841095	+	0.540888i	$0.181912\pi$
$857$			794509.i			1.08178i	−0.841095	+	0.540888i	$0.818088\pi$
$858$	804470.			1.09279
$859$	155891.			0.211268			0.105634	−	0.994405i	$-0.466313\pi$
$859$	155891.			0.211268			0.105634	+	0.994405i	$0.466313\pi$
$860$	257876.			0.348670
$861$			365096.i			0.492494i
$862$			105455.i			0.141923i
$863$	−1.41522e6			−1.90021			−0.950106	−	0.311927i	$-0.899026\pi$
$863$	−1.41522e6			−1.90021			−0.950106	+	0.311927i	$0.899026\pi$
$864$	205760.			0.275635
$865$			751354.i			1.00418i
$866$	−193673.			−0.258246
$867$			548243.i			0.729348i
$868$	−2.10424e6			−2.79290
$869$	−475579.			−0.629772
$870$		−	580755.i		−	0.767281i
$871$	118573.	−	1.39393e6i	0.156297	−	1.83740i
$872$	−127482.			−0.167655
$873$			18787.7i			0.0246516i
$874$			505329.i			0.661532i
$875$	1.38541e6			1.80951
$876$			449849.i			0.586217i
$877$	1.36528e6			1.77510			0.887550	−	0.460712i	$-0.152406\pi$
$877$	1.36528e6			1.77510			0.887550	+	0.460712i	$0.152406\pi$
$878$		−	1.38401e6i		−	1.79535i
$879$		−	222584.i		−	0.288082i
$880$	−331694.			−0.428323
$881$	1.21115e6			1.56044			0.780221	−	0.625505i	$-0.215107\pi$
$881$	1.21115e6			1.56044			0.780221	+	0.625505i	$0.215107\pi$
$882$		−	785010.i		−	1.00911i
$883$			633428.i			0.812411i	0.913782	+	0.406205i	$0.133148\pi$
$883$			633428.i			0.812411i	−0.913782	+	0.406205i	$0.866852\pi$
$884$			2.32811e6i			2.97920i
$885$	−243221.			−0.310538
$886$	−20584.4			−0.0262224
$887$	−1.19266e6			−1.51590			−0.757948	−	0.652315i	$-0.773798\pi$
$887$	−1.19266e6			−1.51590			−0.757948	+	0.652315i	$0.773798\pi$
$888$	38593.3			0.0489425
$889$		−	320004.i		−	0.404903i
$890$	−729206.			−0.920599
$891$			62870.4i			0.0791937i
$892$	−662593.			−0.832755
$893$	1.43256e6			1.79643
$894$	486836.			0.609127
$895$	−110772.			−0.138288
$896$	300127.			0.373843
$897$	−292408.			−0.363416
$898$		−	590224.i		−	0.731921i
$899$		−	1.68716e6i		−	2.08754i
$900$	166408.			0.205442
$901$			771762.i			0.950679i
$902$		−	404454.i		−	0.497114i
$903$			412431.i			0.505797i
$904$	−29879.3			−0.0365623
$905$			578272.i			0.706049i
$906$	416777.			0.507747
$907$	−371239.			−0.451272			−0.225636	−	0.974212i	$-0.572446\pi$
$907$	−371239.			−0.451272			−0.225636	+	0.974212i	$0.572446\pi$
$908$	318041.			0.385755
$909$		−	74827.5i		−	0.0905594i
$910$	−2.52828e6			−3.05311
$911$	1.46041e6			1.75969			0.879846	−	0.475259i	$-0.157646\pi$
$911$	1.46041e6			1.75969			0.879846	+	0.475259i	$0.157646\pi$
$912$		−	594953.i		−	0.715308i
$913$		−	233963.i		−	0.280677i
$914$			682737.i			0.817262i
$915$		−	196149.i		−	0.234285i
$916$			26034.0i			0.0310277i
$917$		−	2.37230e6i		−	2.82118i
$918$	−351370.			−0.416946
$919$			779236.i			0.922652i	0.887231	+	0.461326i	$0.152626\pi$
$919$			779236.i			0.922652i	−0.887231	+	0.461326i	$0.847374\pi$
$920$	−20069.3			−0.0237114
$921$		−	465648.i		−	0.548957i
$922$		−	1.37532e6i		−	1.61786i
$923$		−	1.88491e6i		−	2.21252i
$924$			664524.i			0.778335i
$925$	−391169.			−0.457174
$926$	−616579.			−0.719063
$927$	−486608.			−0.566265
$928$			1.74375e6i			2.02483i
$929$		−	1.43683e6i		−	1.66485i	−0.554137	−	0.832425i	$-0.686952\pi$
$929$		−	1.43683e6i		−	1.66485i	0.554137	−	0.832425i	$-0.313048\pi$
$930$	−693119.			−0.801386
$931$	−2.45204e6			−2.82897
$932$		−	1.01725e6i		−	1.17111i
$933$	557417.			0.640349
$934$			2.48686e6i			2.85074i
$935$	611887.			0.699920
$936$	−57307.8			−0.0654127
$937$		−	456967.i		−	0.520482i	−0.965544	−	0.260241i	$-0.916198\pi$
$937$		−	456967.i		−	0.520482i	0.965544	−	0.260241i	$-0.0838020\pi$
$938$	2.22365e6	+	189153.i	2.52732	+	0.214985i
$939$	239568.			0.271705
$940$			826822.i			0.935743i
$941$			697846.i			0.788099i	0.919089	+	0.394049i	$0.128926\pi$
$941$			697846.i			0.788099i	−0.919089	+	0.394049i	$0.871074\pi$
$942$	−68164.7			−0.0768171
$943$			147010.i			0.165320i
$944$	676027.			0.758612
$945$		−	197588.i		−	0.221257i
$946$		−	456892.i		−	0.510542i
$947$	−687201.			−0.766274			−0.383137	−	0.923692i	$-0.625156\pi$
$947$	−687201.			−0.766274			−0.383137	+	0.923692i	$0.625156\pi$
$948$	492344.			0.547838
$949$			1.57021e6i			1.74352i
$950$		−	1.00381e6i		−	1.11226i
$951$		−	943685.i		−	1.04344i
$952$	−255557.			−0.281977
$953$	294960.			0.324772			0.162386	−	0.986727i	$-0.448081\pi$
$953$	294960.			0.324772			0.162386	+	0.986727i	$0.448081\pi$
$954$	−276080.			−0.303346
$955$	1.03859e6			1.13878
$956$		−	108335.i		−	0.118537i
$957$	−532807.			−0.581763
$958$		−	703923.i		−	0.766998i
$959$	1.78024e6			1.93572
$960$	396614.			0.430353
$961$	−1.09007e6			−1.18034
$962$	1.95770e6			2.11541
$963$	−285075.			−0.307402
$964$	1.81263e6			1.95054
$965$		−	357588.i		−	0.383998i
$966$		−	466460.i		−	0.499874i
$967$	1.01094e6			1.08111			0.540556	−	0.841308i	$-0.318214\pi$
$967$	1.01094e6			1.08111			0.540556	+	0.841308i	$0.318214\pi$
$968$			49060.0i			0.0523572i
$969$			1.09753e6i			1.16888i
$970$			65410.9i			0.0695195i
$971$	461934.			0.489938			0.244969	−	0.969531i	$-0.421222\pi$
$971$	461934.			0.489938			0.244969	+	0.969531i	$0.421222\pi$
$972$		−	65086.6i		−	0.0688905i
$973$	3.10766e6			3.28252
$974$	−1.04395e6			−1.10043
$975$	580853.			0.611023
$976$			545191.i			0.572334i
$977$	−836119.			−0.875949			−0.437974	−	0.898987i	$-0.644304\pi$
$977$	−836119.			−0.875949			−0.437974	+	0.898987i	$0.644304\pi$
$978$	−1.17948e6			−1.23314
$979$			669003.i			0.698012i
$980$		−	1.41523e6i		−	1.47359i
$981$		−	505382.i		−	0.525148i
$982$		−	667976.i		−	0.692688i
$983$		−	1.06049e6i		−	1.09749i	−0.835991	−	0.548743i	$-0.815106\pi$
$983$		−	1.06049e6i		−	1.09749i	0.835991	−	0.548743i	$-0.184894\pi$
$984$			28812.0i			0.0297566i
$985$	583101.			0.600995
$986$		−	2.97776e6i		−	3.06292i
$987$	−1.32237e6			−1.35743
$988$			2.60140e6i			2.66498i
$989$			166071.i			0.169785i
$990$			218889.i			0.223333i
$991$			691702.i			0.704323i	0.935939	+	0.352161i	$0.114553\pi$
$991$			691702.i			0.704323i	−0.935939	+	0.352161i	$0.885447\pi$
$992$	2.08114e6			2.11484
$993$	−943447.			−0.956795
$994$	3.00688e6			3.04329
$995$			287316.i			0.290211i
$996$			242211.i			0.244160i
$997$	−764270.			−0.768876			−0.384438	−	0.923151i	$-0.625605\pi$
$997$	−764270.			−0.768876			−0.384438	+	0.923151i	$0.625605\pi$
$998$	1.11656e6			1.12104
$999$			152997.i			0.153303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.7	✓	46
67.66	odd	2	inner	201.5.b.a.133.40	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.7	✓	46	1.1	even	1	trivial
201.5.b.a.133.40	yes	46	67.66	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	201.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.76041i q^{2} +5.19615i q^{3} -17.1823 q^{4} -16.3188i q^{5} +29.9320 q^{6} +86.3035i q^{7} +6.81074i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-5.76041i q^{2} +5.19615i q^{3} -17.1823 q^{4} -16.3188i q^{5} +29.9320 q^{6} +86.3035i q^{7} +6.81074i q^{8} -27.0000 q^{9} -94.0028 q^{10} +86.2419i q^{11} -89.2820i q^{12} -311.642i q^{13} +497.143 q^{14} +84.7948 q^{15} -235.685 q^{16} +434.776 q^{17} +155.531i q^{18} +485.813 q^{19} +280.395i q^{20} -448.446 q^{21} +496.789 q^{22} -180.572 q^{23} -35.3896 q^{24} +358.698 q^{25} -1795.19 q^{26} -140.296i q^{27} -1482.89i q^{28} +1188.97 q^{29} -488.453i q^{30} -1419.01i q^{31} +1466.61i q^{32} -448.126 q^{33} -2504.49i q^{34} +1408.37 q^{35} +463.923 q^{36} -1090.53 q^{37} -2798.48i q^{38} +1619.34 q^{39} +111.143 q^{40} -814.136i q^{41} +2583.23i q^{42} -919.690i q^{43} -1481.84i q^{44} +440.607i q^{45} +1040.17i q^{46} +2948.78 q^{47} -1224.65i q^{48} -5047.29 q^{49} -2066.25i q^{50} +2259.16i q^{51} +5354.74i q^{52} +1775.08i q^{53} -808.163 q^{54} +1407.36 q^{55} -587.790 q^{56} +2524.36i q^{57} -6848.94i q^{58} -2868.35 q^{59} -1456.97 q^{60} -2313.22i q^{61} -8174.07 q^{62} -2330.19i q^{63} +4677.34 q^{64} -5085.61 q^{65} +2581.39i q^{66} +(4472.85 + 380.480i) q^{67} -7470.47 q^{68} -938.281i q^{69} -8112.77i q^{70} +6048.31 q^{71} -183.890i q^{72} -5038.51 q^{73} +6281.88i q^{74} +1863.85i q^{75} -8347.41 q^{76} -7442.98 q^{77} -9328.06i q^{78} +5514.48i q^{79} +3846.08i q^{80} +729.000 q^{81} -4689.76 q^{82} -2712.87 q^{83} +7705.35 q^{84} -7095.01i q^{85} -5297.79 q^{86} +6178.06i q^{87} -587.371 q^{88} +7757.28 q^{89} +2538.08 q^{90} +26895.8 q^{91} +3102.65 q^{92} +7373.39 q^{93} -16986.2i q^{94} -7927.87i q^{95} -7620.74 q^{96} -695.839i q^{97} +29074.4i q^{98} -2328.53i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 46 * q - 396 * q^4 - 1242 * q^9	\( 46 q - 396 q^{4} - 1242 q^{9} + 396 q^{10} + 792 q^{14} - 252 q^{15} + 3396 q^{16} + 462 q^{17} - 590 q^{19} - 936 q^{21} + 3184 q^{22} - 1446 q^{23} - 1404 q^{24} - 6278 q^{25} + 2700 q^{26} - 1014 q^{29} + 540 q^{33} + 9924 q^{35} + 10692 q^{36} - 386 q^{37} + 4968 q^{39} - 9988 q^{40} - 2754 q^{47} - 19062 q^{49} - 2320 q^{55} - 3396 q^{56} - 7098 q^{59} + 72 q^{60} - 21180 q^{62} - 75644 q^{64} + 18396 q^{65} + 8574 q^{67} + 9084 q^{68} - 23040 q^{71} - 22338 q^{73} + 28016 q^{76} + 45084 q^{77} + 33534 q^{81} + 17564 q^{82} + 35856 q^{83} + 40176 q^{84} + 31764 q^{86} - 19448 q^{88} - 14538 q^{89} - 10692 q^{90} + 13792 q^{91} - 67692 q^{92} + 22464 q^{93} + 22464 q^{96}+O(q^{100}) \) 46 * q - 396 * q^4 - 1242 * q^9 + 396 * q^10 + 792 * q^14 - 252 * q^15 + 3396 * q^16 + 462 * q^17 - 590 * q^19 - 936 * q^21 + 3184 * q^22 - 1446 * q^23 - 1404 * q^24 - 6278 * q^25 + 2700 * q^26 - 1014 * q^29 + 540 * q^33 + 9924 * q^35 + 10692 * q^36 - 386 * q^37 + 4968 * q^39 - 9988 * q^40 - 2754 * q^47 - 19062 * q^49 - 2320 * q^55 - 3396 * q^56 - 7098 * q^59 + 72 * q^60 - 21180 * q^62 - 75644 * q^64 + 18396 * q^65 + 8574 * q^67 + 9084 * q^68 - 23040 * q^71 - 22338 * q^73 + 28016 * q^76 + 45084 * q^77 + 33534 * q^81 + 17564 * q^82 + 35856 * q^83 + 40176 * q^84 + 31764 * q^86 - 19448 * q^88 - 14538 * q^89 - 10692 * q^90 + 13792 * q^91 - 67692 * q^92 + 22464 * q^93 + 22464 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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