LMFDB - Embedded newform 201.5.b.a.133.16

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			133.16
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.33762i q^{2} +5.19615i q^{3} +4.86032 q^{4} +44.8464i q^{5} +17.3428 q^{6} +17.0019i q^{7} -69.6237i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-3.33762i q^{2} +5.19615i q^{3} +4.86032 q^{4} +44.8464i q^{5} +17.3428 q^{6} +17.0019i q^{7} -69.6237i q^{8} -27.0000 q^{9} +149.680 q^{10} +146.473i q^{11} +25.2550i q^{12} -86.6869i q^{13} +56.7457 q^{14} -233.029 q^{15} -154.612 q^{16} +506.498 q^{17} +90.1156i q^{18} -586.978 q^{19} +217.968i q^{20} -88.3442 q^{21} +488.869 q^{22} -838.365 q^{23} +361.776 q^{24} -1386.20 q^{25} -289.328 q^{26} -140.296i q^{27} +82.6345i q^{28} -119.507 q^{29} +777.760i q^{30} +1030.04i q^{31} -597.944i q^{32} -761.094 q^{33} -1690.50i q^{34} -762.472 q^{35} -131.229 q^{36} -286.524 q^{37} +1959.11i q^{38} +450.438 q^{39} +3122.37 q^{40} +840.142i q^{41} +294.859i q^{42} +2632.23i q^{43} +711.904i q^{44} -1210.85i q^{45} +2798.14i q^{46} +2631.46 q^{47} -803.388i q^{48} +2111.94 q^{49} +4626.60i q^{50} +2631.84i q^{51} -421.326i q^{52} -3758.06i q^{53} -468.255 q^{54} -6568.77 q^{55} +1183.73 q^{56} -3050.03i q^{57} +398.870i q^{58} -533.715 q^{59} -1132.59 q^{60} +1945.31i q^{61} +3437.88 q^{62} -459.050i q^{63} -4469.50 q^{64} +3887.60 q^{65} +2540.24i q^{66} +(-4384.03 + 965.093i) q^{67} +2461.75 q^{68} -4356.27i q^{69} +2544.84i q^{70} +761.724 q^{71} +1879.84i q^{72} +4631.65 q^{73} +956.306i q^{74} -7202.90i q^{75} -2852.90 q^{76} -2490.31 q^{77} -1503.39i q^{78} +8840.14i q^{79} -6933.79i q^{80} +729.000 q^{81} +2804.07 q^{82} +9676.79 q^{83} -429.381 q^{84} +22714.6i q^{85} +8785.39 q^{86} -620.979i q^{87} +10198.0 q^{88} -11835.2 q^{89} -4041.36 q^{90} +1473.84 q^{91} -4074.72 q^{92} -5352.26 q^{93} -8782.79i q^{94} -26323.8i q^{95} +3107.01 q^{96} -4559.92i q^{97} -7048.83i q^{98} -3954.76i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.33762i		−	0.834404i	−0.908814	−	0.417202i	$-0.863011\pi$
$2$		−	3.33762i		−	0.834404i	0.908814	−	0.417202i	$-0.136989\pi$
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	4.86032			0.303770
$5$			44.8464i			1.79386i	0.442177	+	0.896928i	$0.354206\pi$
$5$			44.8464i			1.79386i	−0.442177	+	0.896928i	$0.645794\pi$
$6$	17.3428			0.481743
$7$			17.0019i			0.346977i	0.984836	+	0.173488i	$0.0555039\pi$
$7$			17.0019i			0.346977i	−0.984836	+	0.173488i	$0.944496\pi$
$8$		−	69.6237i		−	1.08787i
$9$	−27.0000			−0.333333
$10$	149.680			1.49680
$11$			146.473i			1.21052i	0.796029	+	0.605259i	$0.206930\pi$
$11$			146.473i			1.21052i	−0.796029	+	0.605259i	$0.793070\pi$
$12$			25.2550i			0.175382i
$13$		−	86.6869i		−	0.512940i	−0.966552	−	0.256470i	$-0.917440\pi$
$13$		−	86.6869i		−	0.512940i	0.966552	−	0.256470i	$-0.0825595\pi$
$14$	56.7457			0.289519
$15$	−233.029			−1.03568
$16$	−154.612			−0.603954
$17$	506.498			1.75259			0.876295	−	0.481775i	$-0.160008\pi$
$17$	506.498			1.75259			0.876295	+	0.481775i	$0.160008\pi$
$18$			90.1156i			0.278135i
$19$	−586.978			−1.62598			−0.812989	−	0.582279i	$-0.802161\pi$
$19$	−586.978			−1.62598			−0.812989	+	0.582279i	$0.802161\pi$
$20$			217.968i			0.544920i
$21$	−88.3442			−0.200327
$22$	488.869			1.01006
$23$	−838.365			−1.58481			−0.792405	−	0.609995i	$-0.791171\pi$
$23$	−838.365			−1.58481			−0.792405	+	0.609995i	$0.791171\pi$
$24$	361.776			0.628083
$25$	−1386.20			−2.21792
$26$	−289.328			−0.427999
$27$		−	140.296i		−	0.192450i
$28$			82.6345i			0.105401i
$29$	−119.507			−0.142102			−0.0710508	−	0.997473i	$-0.522635\pi$
$29$	−119.507			−0.142102			−0.0710508	+	0.997473i	$0.522635\pi$
$30$			777.760i			0.864178i
$31$			1030.04i			1.07184i	0.844268	+	0.535922i	$0.180036\pi$
$31$			1030.04i			1.07184i	−0.844268	+	0.535922i	$0.819964\pi$
$32$		−	597.944i		−	0.583930i
$33$	−761.094			−0.698892
$34$		−	1690.50i		−	1.46237i
$35$	−762.472			−0.622426
$36$	−131.229			−0.101257
$37$	−286.524			−0.209294			−0.104647	−	0.994509i	$-0.533371\pi$
$37$	−286.524			−0.209294			−0.104647	+	0.994509i	$0.533371\pi$
$38$			1959.11i			1.35672i
$39$	450.438			0.296146
$40$	3122.37			1.95148
$41$			840.142i			0.499787i	0.968273	+	0.249893i	$0.0803956\pi$
$41$			840.142i			0.499787i	−0.968273	+	0.249893i	$0.919604\pi$
$42$			294.859i			0.167154i
$43$			2632.23i			1.42360i	0.702383	+	0.711800i	$0.252120\pi$
$43$			2632.23i			1.42360i	−0.702383	+	0.711800i	$0.747880\pi$
$44$			711.904i			0.367719i
$45$		−	1210.85i		−	0.597952i
$46$			2798.14i			1.32237i
$47$	2631.46			1.19124			0.595622	−	0.803265i	$-0.296906\pi$
$47$	2631.46			1.19124			0.595622	+	0.803265i	$0.296906\pi$
$48$		−	803.388i		−	0.348693i
$49$	2111.94			0.879607
$50$			4626.60i			1.85064i
$51$			2631.84i			1.01186i
$52$		−	421.326i		−	0.155816i
$53$		−	3758.06i		−	1.33786i	−0.743323	−	0.668932i	$-0.766752\pi$
$53$		−	3758.06i		−	1.33786i	0.743323	−	0.668932i	$-0.233248\pi$
$54$	−468.255			−0.160581
$55$	−6568.77			−2.17149
$56$	1183.73			0.377466
$57$		−	3050.03i		−	0.938758i
$58$			398.870i			0.118570i
$59$	−533.715			−0.153322			−0.0766612	−	0.997057i	$-0.524426\pi$
$59$	−533.715			−0.153322			−0.0766612	+	0.997057i	$0.524426\pi$
$60$	−1132.59			−0.314610
$61$			1945.31i			0.522792i	0.965232	+	0.261396i	$0.0841829\pi$
$61$			1945.31i			0.522792i	−0.965232	+	0.261396i	$0.915817\pi$
$62$	3437.88			0.894351
$63$		−	459.050i		−	0.115659i
$64$	−4469.50			−1.09119
$65$	3887.60			0.920141
$66$			2540.24i			0.583159i
$67$	−4384.03	+	965.093i	−0.976616	+	0.214991i
$67$	−4384.03	+	965.093i	−0.976616	+	0.214991i
$68$	2461.75			0.532384
$69$		−	4356.27i		−	0.914991i
$70$			2544.84i			0.519355i
$71$	761.724			0.151106			0.0755529	−	0.997142i	$-0.475928\pi$
$71$	761.724			0.151106			0.0755529	+	0.997142i	$0.475928\pi$
$72$			1879.84i			0.362624i
$73$	4631.65			0.869141			0.434571	−	0.900638i	$-0.356900\pi$
$73$	4631.65			0.869141			0.434571	+	0.900638i	$0.356900\pi$
$74$			956.306i			0.174636i
$75$		−	7202.90i		−	1.28052i
$76$	−2852.90			−0.493923
$77$	−2490.31			−0.420021
$78$		−	1503.39i		−	0.247106i
$79$			8840.14i			1.41646i	0.705980	+	0.708231i	$0.250507\pi$
$79$			8840.14i			1.41646i	−0.705980	+	0.708231i	$0.749493\pi$
$80$		−	6933.79i		−	1.08341i
$81$	729.000			0.111111
$82$	2804.07			0.417024
$83$	9676.79			1.40467			0.702336	−	0.711845i	$-0.252140\pi$
$83$	9676.79			1.40467			0.702336	+	0.711845i	$0.252140\pi$
$84$	−429.381			−0.0608534
$85$			22714.6i			3.14389i
$86$	8785.39			1.18786
$87$		−	620.979i		−	0.0820424i
$88$	10198.0			1.31689
$89$	−11835.2			−1.49415			−0.747075	−	0.664739i	$-0.768543\pi$
$89$	−11835.2			−1.49415			−0.747075	+	0.664739i	$0.768543\pi$
$90$	−4041.36			−0.498933
$91$	1473.84			0.177978
$92$	−4074.72			−0.481418
$93$	−5352.26			−0.618829
$94$		−	8782.79i		−	0.993978i
$95$		−	26323.8i		−	2.91677i
$96$	3107.01			0.337132
$97$		−	4559.92i		−	0.484634i	−0.970197	−	0.242317i	$-0.922093\pi$
$97$		−	4559.92i		−	0.484634i	0.970197	−	0.242317i	$-0.0779074\pi$
$98$		−	7048.83i		−	0.733948i
$99$		−	3954.76i		−	0.403506i
$100$	−6737.37			−0.673737
$101$			5355.91i			0.525037i	0.964927	+	0.262519i	$0.0845531\pi$
$101$			5355.91i			0.525037i	−0.964927	+	0.262519i	$0.915447\pi$
$102$	8784.08			0.844298
$103$	−7975.31			−0.751749			−0.375875	−	0.926671i	$-0.622658\pi$
$103$	−7975.31			−0.751749			−0.375875	+	0.926671i	$0.622658\pi$
$104$	−6035.47			−0.558013
$105$		−	3961.92i		−	0.359358i
$106$	−12543.0			−1.11632
$107$	14239.7			1.24375			0.621876	−	0.783116i	$-0.286371\pi$
$107$	14239.7			1.24375			0.621876	+	0.783116i	$0.286371\pi$
$108$		−	681.884i		−	0.0584606i
$109$		−	16057.6i		−	1.35153i	−0.737116	−	0.675766i	$-0.763813\pi$
$109$		−	16057.6i		−	1.35153i	0.737116	−	0.675766i	$-0.236187\pi$
$110$			21924.0i			1.81190i
$111$		−	1488.82i		−	0.120836i
$112$		−	2628.69i		−	0.209558i
$113$			5722.40i			0.448148i	0.974572	+	0.224074i	$0.0719357\pi$
$113$			5722.40i			0.448148i	−0.974572	+	0.224074i	$0.928064\pi$
$114$	−10179.8			−0.783304
$115$		−	37597.6i		−	2.84292i
$116$	−580.845			−0.0431662
$117$			2340.55i			0.170980i
$118$			1781.34i			0.127933i
$119$			8611.41i			0.608108i
$120$			16224.3i			1.12669i
$121$	−6813.22			−0.465352
$122$	6492.70			0.436220
$123$	−4365.50			−0.288552
$124$			5006.34i			0.325594i
$125$		−	34137.0i		−	2.18477i
$126$	−1532.13			−0.0965062
$127$	−9939.81			−0.616269			−0.308135	−	0.951343i	$-0.599705\pi$
$127$	−9939.81			−0.616269			−0.308135	+	0.951343i	$0.599705\pi$
$128$			5350.37i			0.326561i
$129$	−13677.5			−0.821915
$130$		−	12975.3i		−	0.767769i
$131$	19730.4			1.14972			0.574861	−	0.818251i	$-0.305056\pi$
$131$	19730.4			1.14972			0.574861	+	0.818251i	$0.305056\pi$
$132$	−3699.16			−0.212303
$133$		−	9979.71i		−	0.564176i
$134$	3221.11	+	14632.2i	0.179389	+	0.814892i
$135$	6291.77			0.345228
$136$		−	35264.3i		−	1.90659i
$137$			23932.5i			1.27511i	0.770406	+	0.637554i	$0.220054\pi$
$137$			23932.5i			1.27511i	−0.770406	+	0.637554i	$0.779946\pi$
$138$	−14539.6			−0.763472
$139$		−	5714.23i		−	0.295752i	−0.989006	−	0.147876i	$-0.952756\pi$
$139$		−	5714.23i		−	0.295752i	0.989006	−	0.147876i	$-0.0472437\pi$
$140$	−3705.86			−0.189074
$141$			13673.5i			0.687765i
$142$		−	2542.34i		−	0.126083i
$143$	12697.3			0.620923
$144$	4174.53			0.201318
$145$		−	5359.48i		−	0.254910i
$146$		−	15458.7i		−	0.725215i
$147$			10973.9i			0.507841i
$148$	−1392.60			−0.0635773
$149$	3777.99			0.170172			0.0850859	−	0.996374i	$-0.472884\pi$
$149$	3777.99			0.170172			0.0850859	+	0.996374i	$0.472884\pi$
$150$	−24040.5			−1.06847
$151$	31590.9			1.38550			0.692752	−	0.721176i	$-0.256398\pi$
$151$	31590.9			1.38550			0.692752	+	0.721176i	$0.256398\pi$
$152$			40867.6i			1.76885i
$153$	−13675.5			−0.584197
$154$			8311.68i			0.350467i
$155$	−46193.7			−1.92273
$156$	2189.28			0.0899604
$157$	−23084.3			−0.936520			−0.468260	−	0.883591i	$-0.655119\pi$
$157$	−23084.3			−0.936520			−0.468260	+	0.883591i	$0.655119\pi$
$158$	29505.0			1.18190
$159$	19527.5			0.772416
$160$	26815.6			1.04749
$161$		−	14253.8i		−	0.549892i
$162$		−	2433.12i		−	0.0927115i
$163$	−6036.17			−0.227188			−0.113594	−	0.993527i	$-0.536236\pi$
$163$	−6036.17			−0.227188			−0.113594	+	0.993527i	$0.536236\pi$
$164$			4083.36i			0.151820i
$165$		−	34132.3i		−	1.25371i
$166$		−	32297.4i		−	1.17206i
$167$	49214.4			1.76465			0.882327	−	0.470636i	$-0.155976\pi$
$167$	49214.4			1.76465			0.882327	+	0.470636i	$0.155976\pi$
$168$			6150.86i			0.217930i
$169$	21046.4			0.736892
$170$	75812.7			2.62328
$171$	15848.4			0.541992
$172$			12793.5i			0.432447i
$173$	23255.9			0.777034			0.388517	−	0.921441i	$-0.372987\pi$
$173$	23255.9			0.777034			0.388517	+	0.921441i	$0.372987\pi$
$174$	−2072.59			−0.0684565
$175$		−	23567.9i		−	0.769565i
$176$		−	22646.4i		−	0.731096i
$177$		−	2773.27i		−	0.0885207i
$178$			39501.2i			1.24673i
$179$		−	16234.5i		−	0.506679i	−0.967377	−	0.253340i	$-0.918471\pi$
$179$		−	16234.5i		−	0.506679i	0.967377	−	0.253340i	$-0.0815290\pi$
$180$		−	5885.13i		−	0.181640i
$181$	380.951			0.0116282			0.00581409	−	0.999983i	$-0.498149\pi$
$181$	380.951			0.0116282			0.00581409	+	0.999983i	$0.498149\pi$
$182$		−	4919.11i		−	0.148506i
$183$	−10108.1			−0.301834
$184$			58370.1i			1.72407i
$185$		−	12849.5i		−	0.375443i
$186$			17863.8i			0.516354i
$187$			74188.1i			2.12154i
$188$	12789.7			0.361864
$189$	2385.29			0.0667757
$190$	−87858.8			−2.43376
$191$			67917.0i			1.86171i	0.365392	+	0.930854i	$0.380935\pi$
$191$			67917.0i			1.86171i	−0.365392	+	0.930854i	$0.619065\pi$
$192$		−	23224.2i		−	0.629997i
$193$	1883.81			0.0505734			0.0252867	−	0.999680i	$-0.491950\pi$
$193$	1883.81			0.0505734			0.0252867	+	0.999680i	$0.491950\pi$
$194$	−15219.3			−0.404381
$195$			20200.5i			0.531244i
$196$	10264.7			0.267198
$197$		−	2704.98i		−	0.0696997i	−0.999393	−	0.0348498i	$-0.988905\pi$
$197$		−	2704.98i		−	0.0696997i	0.999393	−	0.0348498i	$-0.0110953\pi$
$198$	−13199.5			−0.336687
$199$	28066.9			0.708743			0.354371	−	0.935105i	$-0.384695\pi$
$199$	28066.9			0.708743			0.354371	+	0.935105i	$0.384695\pi$
$200$			96512.3i			2.41281i
$201$	−5014.77	−	22780.1i	−0.124125	−	0.563850i
$202$	17876.0			0.438093
$203$		−	2031.85i		−	0.0493059i
$204$			12791.6i			0.307372i
$205$	−37677.3			−0.896545
$206$			26618.5i			0.627262i
$207$	22635.8			0.528270
$208$			13402.8i			0.309792i
$209$		−	85976.2i		−	1.96827i
$210$	−13223.4			−0.299850
$211$	−6877.17			−0.154470			−0.0772351	−	0.997013i	$-0.524609\pi$
$211$	−6877.17			−0.154470			−0.0772351	+	0.997013i	$0.524609\pi$
$212$		−	18265.4i		−	0.406403i
$213$			3958.04i			0.0872410i
$214$		−	47526.7i		−	1.03779i
$215$	−118046.			−2.55373
$216$	−9767.94			−0.209361
$217$	−17512.6			−0.371905
$218$	−53594.0			−1.12772
$219$			24066.8i			0.501799i
$220$	−31926.3			−0.659635
$221$		−	43906.8i		−	0.898974i
$222$	−4969.11			−0.100826
$223$	38326.8			0.770714			0.385357	−	0.922768i	$-0.374078\pi$
$223$	38326.8			0.770714			0.385357	+	0.922768i	$0.374078\pi$
$224$	10166.2			0.202610
$225$	37427.4			0.739306
$226$	19099.2			0.373936
$227$	868.163			0.0168481			0.00842403	−	0.999965i	$-0.497319\pi$
$227$	868.163			0.0168481			0.00842403	+	0.999965i	$0.497319\pi$
$228$		−	14824.1i		−	0.285167i
$229$		−	33797.2i		−	0.644480i	−0.946658	−	0.322240i	$-0.895564\pi$
$229$		−	33797.2i		−	0.644480i	0.946658	−	0.322240i	$-0.104436\pi$
$230$	−125486.			−2.37214
$231$		−	12940.0i		−	0.242499i
$232$			8320.55i			0.154588i
$233$			66765.4i			1.22982i	0.788599	+	0.614908i	$0.210807\pi$
$233$			66765.4i			1.22982i	−0.788599	+	0.614908i	$0.789193\pi$
$234$	7811.85			0.142666
$235$			118011.i			2.13692i
$236$	−2594.03			−0.0465748
$237$	−45934.7			−0.817795
$238$	28741.6			0.507407
$239$		−	97878.4i		−	1.71353i	−0.515709	−	0.856764i	$-0.672471\pi$
$239$		−	97878.4i		−	1.71353i	0.515709	−	0.856764i	$-0.327529\pi$
$240$	36029.1			0.625504
$241$	−54348.7			−0.935740			−0.467870	−	0.883797i	$-0.654978\pi$
$241$	−54348.7			−0.935740			−0.467870	+	0.883797i	$0.654978\pi$
$242$			22739.9i			0.388292i
$243$			3788.00i			0.0641500i
$244$			9454.84i			0.158809i
$245$			94712.7i			1.57789i
$246$			14570.4i			0.240769i
$247$			50883.3i			0.834029i
$248$	71715.4			1.16603
$249$			50282.1i			0.810988i
$250$	−113936.			−1.82298
$251$			89066.1i			1.41372i	0.707351	+	0.706862i	$0.249890\pi$
$251$			89066.1i			1.41372i	−0.707351	+	0.706862i	$0.750110\pi$
$252$		−	2231.13i		−	0.0351337i
$253$		−	122797.i		−	1.91844i
$254$			33175.3i			0.514218i
$255$	−118029.			−1.81513
$256$	−53654.5			−0.818703
$257$	64639.8			0.978665			0.489332	−	0.872097i	$-0.337241\pi$
$257$	64639.8			0.978665			0.489332	+	0.872097i	$0.337241\pi$
$258$			45650.2i			0.685809i
$259$		−	4871.43i		−	0.0726202i
$260$	18895.0			0.279511
$261$	3226.70			0.0473672
$262$		−	65852.4i		−	0.959333i
$263$	94229.0			1.36230			0.681151	−	0.732143i	$-0.261480\pi$
$263$	94229.0			1.36230			0.681151	+	0.732143i	$0.261480\pi$
$264$			52990.2i			0.760305i
$265$	168535.			2.39994
$266$	−33308.4			−0.470751
$267$		−	61497.3i		−	0.862648i
$268$	−21307.8	+	4690.66i	−0.296667	+	0.0653077i
$269$	115644.			1.59816			0.799079	−	0.601226i	$-0.205321\pi$
$269$	115644.			1.59816			0.799079	+	0.601226i	$0.205321\pi$
$270$		−	20999.5i		−	0.288059i
$271$		−	58543.1i		−	0.797145i	−0.917137	−	0.398572i	$-0.869506\pi$
$271$		−	58543.1i		−	0.797145i	0.917137	−	0.398572i	$-0.130494\pi$
$272$	−78310.8			−1.05848
$273$			7658.29i			0.102756i
$274$	79877.5			1.06396
$275$		−	203040.i		−	2.68483i
$276$		−	21172.9i		−	0.277947i
$277$	−56094.4			−0.731072			−0.365536	−	0.930797i	$-0.619114\pi$
$277$	−56094.4			−0.731072			−0.365536	+	0.930797i	$0.619114\pi$
$278$	−19071.9			−0.246777
$279$		−	27811.1i		−	0.357281i
$280$			53086.1i			0.677119i
$281$			56270.1i			0.712631i	0.934366	+	0.356316i	$0.115967\pi$
$281$			56270.1i			0.712631i	−0.934366	+	0.356316i	$0.884033\pi$
$282$	45636.7			0.573874
$283$	17019.9			0.212512			0.106256	−	0.994339i	$-0.466114\pi$
$283$	17019.9			0.212512			0.106256	+	0.994339i	$0.466114\pi$
$284$	3702.22			0.0459014
$285$	136783.			1.68400
$286$		−	42378.6i		−	0.518101i
$287$	−14284.0			−0.173414
$288$			16144.5i			0.194643i
$289$	173020.			2.07157
$290$	−17887.9			−0.212698
$291$	23694.1			0.279804
$292$	22511.3			0.264019
$293$	−111480.			−1.29856			−0.649278	−	0.760551i	$-0.724929\pi$
$293$	−111480.			−1.29856			−0.649278	+	0.760551i	$0.724929\pi$
$294$	36626.8			0.423745
$295$		−	23935.2i		−	0.275038i
$296$			19948.8i			0.227685i
$297$	20549.5			0.232964
$298$		−	12609.5i		−	0.141992i
$299$			72675.3i			0.812913i
$300$		−	35008.4i		−	0.388982i
$301$	−44752.9			−0.493956
$302$		−	105438.i		−	1.15607i
$303$	−27830.1			−0.303130
$304$	90753.9			0.982015
$305$	−87240.2			−0.937814
$306$			45643.4i			0.487456i
$307$	−55809.5			−0.592150			−0.296075	−	0.955165i	$-0.595678\pi$
$307$	−55809.5			−0.592150			−0.296075	+	0.955165i	$0.595678\pi$
$308$	−12103.7			−0.127590
$309$		−	41440.9i		−	0.434023i
$310$			154177.i			1.60434i
$311$		−	6768.99i		−	0.0699847i	−0.999388	−	0.0349924i	$-0.988859\pi$
$311$		−	6768.99i		−	0.0699847i	0.999388	−	0.0349924i	$-0.0111407\pi$
$312$		−	31361.2i		−	0.322169i
$313$		−	44512.6i		−	0.454354i	−0.973853	−	0.227177i	$-0.927050\pi$
$313$		−	44512.6i		−	0.454354i	0.973853	−	0.227177i	$-0.0729496\pi$
$314$			77046.5i			0.781436i
$315$	20586.7			0.207475
$316$			42965.9i			0.430279i
$317$	26745.7			0.266155			0.133078	−	0.991106i	$-0.457514\pi$
$317$	26745.7			0.266155			0.133078	+	0.991106i	$0.457514\pi$
$318$		−	65175.1i		−	0.644507i
$319$		−	17504.6i		−	0.172016i
$320$		−	200441.i		−	1.95743i
$321$			73991.7i			0.718081i
$322$	−47573.6			−0.458832
$323$	−297303.			−2.84967
$324$	3543.17			0.0337522
$325$			120165.i			1.13766i
$326$			20146.4i			0.189567i
$327$	83437.5			0.780308
$328$	58493.8			0.543703
$329$			44739.7i			0.413334i
$330$	−113921.			−1.04610
$331$		−	111222.i		−	1.01516i	−0.861605	−	0.507580i	$-0.830540\pi$
$331$		−	111222.i		−	1.01516i	0.861605	−	0.507580i	$-0.169460\pi$
$332$	47032.3			0.426698
$333$	7736.14			0.0697647
$334$		−	164259.i		−	1.47243i
$335$	−43280.9	−	196608.i	−0.385662	−	1.75191i
$336$	13659.1			0.120988
$337$			50155.6i			0.441631i	0.975316	+	0.220816i	$0.0708719\pi$
$337$			50155.6i			0.441631i	−0.975316	+	0.220816i	$0.929128\pi$
$338$		−	70244.7i		−	0.614866i
$339$	−29734.5			−0.258738
$340$			110400.i			0.955021i
$341$	−150873.			−1.29749
$342$		−	52895.9i		−	0.452241i
$343$			76728.3i			0.652180i
$344$	183266.			1.54869
$345$	195363.			1.64136
$346$		−	77619.1i		−	0.648361i
$347$		−	3646.73i		−	0.0302862i	−0.999885	−	0.0151431i	$-0.995180\pi$
$347$		−	3646.73i		−	0.0302862i	0.999885	−	0.0151431i	$-0.00482038\pi$
$348$		−	3018.16i		−	0.0249220i
$349$	−103209.			−0.847358			−0.423679	−	0.905812i	$-0.639261\pi$
$349$	−103209.			−0.847358			−0.423679	+	0.905812i	$0.639261\pi$
$350$	−78660.7			−0.642128
$351$	−12161.8			−0.0987154
$352$	87582.4			0.706857
$353$		−	205430.i		−	1.64860i	−0.566154	−	0.824300i	$-0.691569\pi$
$353$		−	205430.i		−	1.64860i	0.566154	−	0.824300i	$-0.308431\pi$
$354$	−9256.10			−0.0738621
$355$			34160.6i			0.271062i
$356$	−57522.7			−0.453878
$357$	−44746.2			−0.351091
$358$	−54184.5			−0.422775
$359$	160857.			1.24810			0.624051	−	0.781384i	$-0.285486\pi$
$359$	160857.			1.24810			0.624051	+	0.781384i	$0.285486\pi$
$360$	−84304.1			−0.650494
$361$	214222.			1.64380
$362$		−	1271.47i		−	0.00970259i
$363$		−	35402.5i		−	0.268671i
$364$	7163.33			0.0540645
$365$			207713.i			1.55911i
$366$			33737.1i			0.251852i
$367$			264246.i			1.96190i	0.194266	+	0.980949i	$0.437767\pi$
$367$			264246.i			1.96190i	−0.194266	+	0.980949i	$0.562233\pi$
$368$	129621.			0.957152
$369$		−	22683.8i		−	0.166596i
$370$	−42886.8			−0.313271
$371$	63894.0			0.464208
$372$	−26013.7			−0.187982
$373$		−	118126.i		−	0.849043i	−0.905418	−	0.424521i	$-0.860442\pi$
$373$		−	118126.i		−	0.849043i	0.905418	−	0.424521i	$-0.139558\pi$
$374$	247611.			1.77022
$375$	177381.			1.26138
$376$		−	183212.i		−	1.29592i
$377$			10359.7i			0.0728896i
$378$		−	7961.20i		−	0.0557179i
$379$			25174.1i			0.175257i	0.996153	+	0.0876284i	$0.0279288\pi$
$379$			25174.1i			0.175257i	−0.996153	+	0.0876284i	$0.972071\pi$
$380$		−	127942.i		−	0.886027i
$381$		−	51648.8i		−	0.355803i
$382$	226681.			1.55342
$383$			106852.i			0.728424i	0.931316	+	0.364212i	$0.118662\pi$
$383$			106852.i			0.728424i	−0.931316	+	0.364212i	$0.881338\pi$
$384$	−27801.4			−0.188540
$385$		−	111681.i		−	0.753457i
$386$		−	6287.43i		−	0.0421986i
$387$		−	71070.3i		−	0.474533i
$388$		−	22162.7i		−	0.147217i
$389$	35370.0			0.233741			0.116871	−	0.993147i	$-0.462714\pi$
$389$	35370.0			0.233741			0.116871	+	0.993147i	$0.462714\pi$
$390$	67421.6			0.443272
$391$	−424630.			−2.77752
$392$		−	147041.i		−	0.956899i
$393$			102522.i			0.663792i
$394$	−9028.17			−0.0581577
$395$	−396448.			−2.54093
$396$		−	19221.4i		−	0.122573i
$397$	227422.			1.44295			0.721476	−	0.692440i	$-0.243464\pi$
$397$	227422.			1.44295			0.721476	+	0.692440i	$0.243464\pi$
$398$		−	93676.6i		−	0.591378i
$399$	51856.1			0.325727
$400$	214323.			1.33952
$401$		−	302878.i		−	1.88356i	−0.336234	−	0.941779i	$-0.609153\pi$
$401$		−	302878.i		−	1.88356i	0.336234	−	0.941779i	$-0.390847\pi$
$402$	−76031.2	+	16737.4i	−0.470478	+	0.103570i
$403$	89291.2			0.549792
$404$			26031.4i			0.159491i
$405$			32693.0i			0.199317i
$406$	−6781.53			−0.0411411
$407$		−	41967.9i		−	0.253354i
$408$	183239.			1.10077
$409$		−	42002.6i		−	0.251090i	−0.992088	−	0.125545i	$-0.959932\pi$
$409$		−	42002.6i		−	0.251090i	0.992088	−	0.125545i	$-0.0400680\pi$
$410$			125752.i			0.748081i
$411$	−124357.			−0.736184
$412$	−38762.6			−0.228359
$413$		−	9074.15i		−	0.0531993i
$414$		−	75549.8i		−	0.440791i
$415$			433969.i			2.51978i
$416$	−51833.9			−0.299521
$417$	29692.0			0.170753
$418$	−286955.			−1.64234
$419$	−300221.			−1.71007			−0.855035	−	0.518571i	$-0.826464\pi$
$419$	−300221.			−1.71007			−0.855035	+	0.518571i	$0.826464\pi$
$420$		−	19256.2i		−	0.109162i
$421$	79932.0			0.450979			0.225490	−	0.974246i	$-0.427602\pi$
$421$	79932.0			0.450979			0.225490	+	0.974246i	$0.427602\pi$
$422$			22953.3i			0.128891i
$423$	−71049.3			−0.397081
$424$	−261650.			−1.45542
$425$	−702107.			−3.88710
$426$	13210.4			0.0727942
$427$	−33073.9			−0.181397
$428$	69209.6			0.377815
$429$			65976.9i			0.358490i
$430$			393993.i			2.13084i
$431$	139552.			0.751243			0.375621	−	0.926773i	$-0.377429\pi$
$431$	139552.			0.751243			0.375621	+	0.926773i	$0.377429\pi$
$432$			21691.5i			0.116231i
$433$			168451.i			0.898458i	0.893417	+	0.449229i	$0.148301\pi$
$433$			168451.i			0.898458i	−0.893417	+	0.449229i	$0.851699\pi$
$434$			58450.4i			0.310319i
$435$	27848.7			0.147172
$436$		−	78044.9i		−	0.410555i
$437$	492101.			2.57687
$438$	80325.6			0.418703
$439$	−153486.			−0.796416			−0.398208	−	0.917295i	$-0.630368\pi$
$439$	−153486.			−0.796416			−0.398208	+	0.917295i	$0.630368\pi$
$440$			457342.i			2.36230i
$441$	−57022.3			−0.293202
$442$	−146544.			−0.750107
$443$			131548.i			0.670311i	0.942163	+	0.335155i	$0.108789\pi$
$443$			131548.i			0.670311i	−0.942163	+	0.335155i	$0.891211\pi$
$444$		−	7236.14i		−	0.0367064i
$445$		−	530764.i		−	2.68029i
$446$		−	127920.i		−	0.643086i
$447$			19631.0i			0.0982488i
$448$		−	75989.8i		−	0.378616i
$449$	92475.0			0.458703			0.229351	−	0.973344i	$-0.426339\pi$
$449$	92475.0			0.458703			0.229351	+	0.973344i	$0.426339\pi$
$450$		−	124918.i		−	0.616880i
$451$	−123058.			−0.605001
$452$			27812.7i			0.136134i
$453$			164151.i			0.799921i
$454$		−	2897.60i		−	0.0140581i
$455$			66096.3i			0.319267i
$456$	−212354.			−1.02125
$457$	86650.3			0.414894			0.207447	−	0.978246i	$-0.433484\pi$
$457$	86650.3			0.414894			0.207447	+	0.978246i	$0.433484\pi$
$458$	−112802.			−0.537757
$459$		−	71059.8i		−	0.337286i
$460$		−	182737.i		−	0.863594i
$461$	−105360.			−0.495762			−0.247881	−	0.968791i	$-0.579734\pi$
$461$	−105360.			−0.495762			−0.247881	+	0.968791i	$0.579734\pi$
$462$	−43188.8			−0.202342
$463$			359909.i			1.67892i	0.543418	+	0.839462i	$0.317130\pi$
$463$			359909.i			1.67892i	−0.543418	+	0.839462i	$0.682870\pi$
$464$	18477.3			0.0858228
$465$		−	240029.i		−	1.11009i
$466$	222837.			1.02616
$467$	−346509.			−1.58884			−0.794421	−	0.607367i	$-0.792226\pi$
$467$	−346509.			−1.58884			−0.794421	+	0.607367i	$0.792226\pi$
$468$			11375.8i			0.0519387i
$469$	−16408.4	−	74536.6i	−0.0745967	−	0.338863i
$470$	393877.			1.78305
$471$		−	119949.i		−	0.540700i
$472$			37159.3i			0.166795i
$473$	−385550.			−1.72329
$474$			153312.i			0.682371i
$475$	813668.			3.60628
$476$			41854.2i			0.184725i
$477$			101468.i			0.445955i
$478$	−326681.			−1.42977
$479$	120507.			0.525219			0.262610	−	0.964902i	$-0.415417\pi$
$479$	120507.			0.525219			0.262610	+	0.964902i	$0.415417\pi$
$480$			139338.i			0.604766i
$481$			24837.8i			0.107355i
$482$			181395.i			0.780785i
$483$	74064.7			0.317480
$484$	−33114.4			−0.141360
$485$	204496.			0.869364
$486$	12642.9			0.0535270
$487$		−	153181.i		−	0.645871i	−0.946421	−	0.322935i	$-0.895330\pi$
$487$		−	153181.i		−	0.645871i	0.946421	−	0.322935i	$-0.104670\pi$
$488$	135440.			0.568731
$489$		−	31364.9i		−	0.131167i
$490$	316115.			1.31660
$491$	−253461.			−1.05135			−0.525677	−	0.850684i	$-0.676188\pi$
$491$	−253461.			−1.05135			−0.525677	+	0.850684i	$0.676188\pi$
$492$	−21217.8			−0.0876535
$493$	−60530.3			−0.249046
$494$	169829.			0.695917
$495$	177357.			0.723831
$496$		−	159257.i		−	0.647344i
$497$			12950.7i			0.0524302i
$498$	167822.			0.676692
$499$			196724.i			0.790053i	0.918670	+	0.395026i	$0.129265\pi$
$499$			196724.i			0.790053i	−0.918670	+	0.395026i	$0.870735\pi$
$500$		−	165917.i		−	0.663667i
$501$			255726.i			1.01882i
$502$	297268.			1.17962
$503$			184451.i			0.729028i	0.931198	+	0.364514i	$0.118765\pi$
$503$			184451.i			0.729028i	−0.931198	+	0.364514i	$0.881235\pi$
$504$	−31960.8			−0.125822
$505$	−240193.			−0.941841
$506$	−409851.			−1.60075
$507$			109360.i			0.425445i
$508$	−48310.7			−0.187204
$509$	−290392.			−1.12085			−0.560426	−	0.828204i	$-0.689363\pi$
$509$	−290392.			−1.12085			−0.560426	+	0.828204i	$0.689363\pi$
$510$			393934.i			1.51455i
$511$			78746.7i			0.301572i
$512$			264684.i			1.00969i
$513$			82350.7i			0.312919i
$514$		−	215743.i		−	0.816602i
$515$		−	357664.i		−	1.34853i
$516$	−66477.0			−0.249673
$517$			385436.i			1.44202i
$518$	−16259.0			−0.0605945
$519$			120841.i			0.448621i
$520$		−	270669.i		−	1.00099i
$521$			465322.i			1.71427i	0.515094	+	0.857134i	$0.327757\pi$
$521$			465322.i			1.71427i	−0.515094	+	0.857134i	$0.672243\pi$
$522$		−	10769.5i		−	0.0395234i
$523$	−251503.			−0.919473			−0.459737	−	0.888055i	$-0.652056\pi$
$523$	−251503.			−0.919473			−0.459737	+	0.888055i	$0.652056\pi$
$524$	95896.0			0.349251
$525$	122463.			0.444309
$526$		−	314500.i		−	1.13671i
$527$			521715.i			1.87850i
$528$	117674.			0.422099
$529$	423014.			1.51162
$530$		−	562507.i		−	2.00252i
$531$	14410.3			0.0511075
$532$		−	48504.6i		−	0.171380i
$533$	72829.3			0.256361
$534$	−205254.			−0.719797
$535$			638600.i			2.23111i
$536$	67193.4	+	305233.i	0.233882	+	1.06243i
$537$	84357.0			0.292531
$538$		−	385976.i		−	1.33351i
$539$			309341.i			1.06478i
$540$	30580.0			0.104870
$541$		−	453701.i		−	1.55015i	−0.631866	−	0.775077i	$-0.717711\pi$
$541$		−	453701.i		−	1.55015i	0.631866	−	0.775077i	$-0.282289\pi$
$542$	−195394.			−0.665141
$543$			1979.48i			0.00671353i
$544$		−	302858.i		−	1.02339i
$545$	720123.			2.42445
$546$	25560.4			0.0857399
$547$			3437.62i			0.0114890i	0.999984	+	0.00574452i	$0.00182855\pi$
$547$			3437.62i			0.0114890i	−0.999984	+	0.00574452i	$0.998171\pi$
$548$			116320.i			0.387340i
$549$		−	52523.4i		−	0.174264i
$550$	−677670.			−2.24023
$551$	70148.2			0.231054
$552$	−303300.			−0.995392
$553$	−150299.			−0.491479
$554$			187222.i			0.610009i
$555$	66768.2			0.216762
$556$		−	27773.0i		−	0.0898407i
$557$	−10267.4			−0.0330940			−0.0165470	−	0.999863i	$-0.505267\pi$
$557$	−10267.4			−0.0330940			−0.0165470	+	0.999863i	$0.505267\pi$
$558$	−92822.9			−0.298117
$559$	228180.			0.730221
$560$	117887.			0.375916
$561$	−385493.			−1.22487
$562$	187808.			0.594622
$563$		−	83348.5i		−	0.262955i	−0.991319	−	0.131477i	$-0.958028\pi$
$563$		−	83348.5i		−	0.262955i	0.991319	−	0.131477i	$-0.0419721\pi$
$564$			66457.4i			0.208922i
$565$	−256629.			−0.803912
$566$		−	56805.8i		−	0.177321i
$567$			12394.4i			0.0385530i
$568$		−	53034.1i		−	0.164384i
$569$	210011.			0.648660			0.324330	−	0.945944i	$-0.394861\pi$
$569$	210011.			0.648660			0.324330	+	0.945944i	$0.394861\pi$
$570$		−	456528.i		−	1.40513i
$571$	−313967.			−0.962967			−0.481483	−	0.876455i	$-0.659902\pi$
$571$	−313967.			−0.962967			−0.481483	+	0.876455i	$0.659902\pi$
$572$	61712.8			0.188618
$573$	−352907.			−1.07486
$574$			47674.4i			0.144698i
$575$	1.16214e6			3.51498
$576$	120677.			0.363729
$577$		−	33523.0i		−	0.100691i	−0.998732	−	0.0503456i	$-0.983968\pi$
$577$		−	33523.0i		−	0.100691i	0.998732	−	0.0503456i	$-0.0160323\pi$
$578$		−	577473.i		−	1.72853i
$579$			9788.55i			0.0291986i
$580$		−	26048.8i		−	0.0774339i
$581$			164523.i			0.487389i
$582$		−	79081.7i		−	0.233469i
$583$	550453.			1.61951
$584$		−	322473.i		−	0.945513i
$585$	−104965.			−0.306714
$586$			372076.i			1.08352i
$587$			147762.i			0.428832i	0.976742	+	0.214416i	$0.0687848\pi$
$587$			147762.i			0.428832i	−0.976742	+	0.214416i	$0.931215\pi$
$588$			53336.9i			0.154267i
$589$		−	604612.i		−	1.74279i
$590$	−79886.5			−0.229493
$591$	14055.5			0.0402411
$592$	44300.0			0.126404
$593$		−	101993.i		−	0.290042i	−0.989429	−	0.145021i	$-0.953675\pi$
$593$		−	101993.i		−	0.290042i	0.989429	−	0.145021i	$-0.0463249\pi$
$594$		−	68586.5i		−	0.194386i
$595$	−386191.			−1.09086
$596$	18362.2			0.0516931
$597$			145840.i			0.409193i
$598$	242562.			0.678298
$599$			107475.i			0.299540i	0.988721	+	0.149770i	$0.0478533\pi$
$599$			107475.i			0.299540i	−0.988721	+	0.149770i	$0.952147\pi$
$600$	−501493.			−1.39304
$601$	−388250.			−1.07489			−0.537443	−	0.843300i	$-0.680610\pi$
$601$	−388250.			−1.07489			−0.537443	+	0.843300i	$0.680610\pi$
$602$			149368.i			0.412159i
$603$	118369.	−	26057.5i	0.325539	−	0.0716635i
$604$	153542.			0.420875
$605$		−	305548.i		−	0.834774i
$606$			92886.2i			0.252933i
$607$	−248773.			−0.675189			−0.337595	−	0.941292i	$-0.609613\pi$
$607$	−248773.			−0.675189			−0.337595	+	0.941292i	$0.609613\pi$
$608$			350980.i			0.949456i
$609$	10557.8			0.0284668
$610$			291174.i			0.782516i
$611$		−	228113.i		−	0.611037i
$612$	−66467.1			−0.177461
$613$	222695.			0.592638			0.296319	−	0.955089i	$-0.404241\pi$
$613$	222695.			0.592638			0.296319	+	0.955089i	$0.404241\pi$
$614$			186271.i			0.494092i
$615$		−	195777.i		−	0.517621i
$616$			173384.i			0.456929i
$617$	−422064.			−1.10868			−0.554342	−	0.832289i	$-0.687030\pi$
$617$	−422064.			−1.10868			−0.554342	+	0.832289i	$0.687030\pi$
$618$	−138314.			−0.362150
$619$	−356006.			−0.929130			−0.464565	−	0.885539i	$-0.653789\pi$
$619$	−356006.			−0.929130			−0.464565	+	0.885539i	$0.653789\pi$
$620$	−224516.			−0.584069
$621$			117619.i			0.304997i
$622$	−22592.3			−0.0583955
$623$		−	201220.i		−	0.518435i
$624$	−69643.2			−0.178859
$625$	664547.			1.70124
$626$	−148566.			−0.379115
$627$	446745.			1.13638
$628$	−112197.			−0.284487
$629$	−145124.			−0.366807
$630$		−	68710.6i		−	0.173118i
$631$		−	49471.3i		−	0.124250i	−0.998068	−	0.0621248i	$-0.980212\pi$
$631$		−	49471.3i		−	0.124250i	0.998068	−	0.0621248i	$-0.0197877\pi$
$632$	615484.			1.54093
$633$		−	35734.8i		−	0.0891834i
$634$		−	89266.9i		−	0.222081i
$635$		−	445765.i		−	1.10550i
$636$	94909.7			0.234637
$637$		−	183077.i		−	0.451186i
$638$	−58423.5			−0.143531
$639$	−20566.6			−0.0503686
$640$	−239945.			−0.585803
$641$			20269.2i			0.0493311i	0.999696	+	0.0246656i	$0.00785209\pi$
$641$			20269.2i			0.0493311i	−0.999696	+	0.0246656i	$0.992148\pi$
$642$	246956.			0.599169
$643$	−343770.			−0.831469			−0.415734	−	0.909486i	$-0.636475\pi$
$643$	−343770.			−0.831469			−0.415734	+	0.909486i	$0.636475\pi$
$644$		−	69277.8i		−	0.167041i
$645$		−	613386.i		−	1.47440i
$646$			992284.i			2.37778i
$647$		−	517671.i		−	1.23664i	−0.785925	−	0.618322i	$-0.787813\pi$
$647$		−	517671.i		−	1.23664i	0.785925	−	0.618322i	$-0.212187\pi$
$648$		−	50755.7i		−	0.120875i
$649$		−	78174.7i		−	0.185599i
$650$	401065.			0.949267
$651$		−	90998.3i		−	0.214719i
$652$	−29337.7			−0.0690130
$653$		−	234767.i		−	0.550569i	−0.961363	−	0.275284i	$-0.911228\pi$
$653$		−	234767.i		−	0.550569i	0.961363	−	0.275284i	$-0.0887720\pi$
$654$		−	278482.i		−	0.651092i
$655$			884836.i			2.06244i
$656$		−	129896.i		−	0.301848i
$657$	−125055.			−0.289714
$658$	149324.			0.344887
$659$	−492518.			−1.13410			−0.567050	−	0.823684i	$-0.691915\pi$
$659$	−492518.			−1.13410			−0.567050	+	0.823684i	$0.691915\pi$
$660$		−	165894.i		−	0.380840i
$661$		−	566695.i		−	1.29702i	−0.761207	−	0.648509i	$-0.775393\pi$
$661$		−	566695.i		−	1.29702i	0.761207	−	0.648509i	$-0.224607\pi$
$662$	−371216.			−0.847053
$663$	228146.			0.519023
$664$		−	673734.i		−	1.52810i
$665$	447554.			1.01205
$666$		−	25820.2i		−	0.0582119i
$667$	100191.			0.225204
$668$	239198.			0.536049
$669$			199152.i			0.444972i
$670$	−656202.	+	144455.i	−1.46180	+	0.321798i
$671$	−284935.			−0.632849
$672$			52824.9i			0.116977i
$673$		−	680021.i		−	1.50139i	−0.660651	−	0.750693i	$-0.729720\pi$
$673$		−	680021.i		−	1.50139i	0.660651	−	0.750693i	$-0.270280\pi$
$674$	167400.			0.368499
$675$			194478.i			0.426838i
$676$	102292.			0.223846
$677$			726969.i			1.58613i	0.609138	+	0.793064i	$0.291516\pi$
$677$			726969.i			1.58613i	−0.609138	+	0.793064i	$0.708484\pi$
$678$			99242.2i			0.215892i
$679$	77527.2			0.168157
$680$	1.58148e6			3.42015
$681$			4511.11i			0.00972723i
$682$			503556.i			1.08263i
$683$		−	98955.5i		−	0.212128i	−0.994359	−	0.106064i	$-0.966175\pi$
$683$		−	98955.5i		−	0.212128i	0.994359	−	0.106064i	$-0.0338249\pi$
$684$	77028.3			0.164641
$685$	−1.07329e6			−2.28736
$686$	256090.			0.544181
$687$	175615.			0.372091
$688$		−	406975.i		−	0.859788i
$689$	−325775.			−0.686245
$690$		−	652047.i		−	1.36956i
$691$	750225.			1.57121			0.785607	−	0.618726i	$-0.212351\pi$
$691$	750225.			1.57121			0.785607	+	0.618726i	$0.212351\pi$
$692$	113031.			0.236040
$693$	67238.3			0.140007
$694$	−12171.4			−0.0252709
$695$	256262.			0.530537
$696$	−43234.9			−0.0892515
$697$			425530.i			0.875921i
$698$			344472.i			0.707039i
$699$	−346923.			−0.710034
$700$		−	114548.i		−	0.233771i
$701$		−	518930.i		−	1.05602i	−0.849238	−	0.528010i	$-0.822938\pi$
$701$		−	518930.i		−	1.05602i	0.849238	−	0.528010i	$-0.177062\pi$
$702$			40591.5i			0.0823685i
$703$	168183.			0.340307
$704$		−	654659.i		−	1.32090i
$705$	−613205.			−1.23375
$706$	−685647.			−1.37560
$707$	−91060.3			−0.182176
$708$		−	13479.0i		−	0.0268900i
$709$	−52710.0			−0.104858			−0.0524289	−	0.998625i	$-0.516696\pi$
$709$	−52710.0			−0.104858			−0.0524289	+	0.998625i	$0.516696\pi$
$710$	114015.			0.226175
$711$		−	238684.i		−	0.472154i
$712$			824009.i			1.62544i
$713$		−	863551.i		−	1.69867i
$714$			149346.i			0.292952i
$715$			569426.i			1.11385i
$716$		−	78904.9i		−	0.153914i
$717$	508591.			0.989306
$718$		−	536877.i		−	1.04142i
$719$	−722117.			−1.39685			−0.698425	−	0.715684i	$-0.746115\pi$
$719$	−722117.			−1.39685			−0.698425	+	0.715684i	$0.746115\pi$
$720$			187212.i			0.361135i
$721$		−	135595.i		−	0.260839i
$722$		−	714991.i		−	1.37160i
$723$		−	282404.i		−	0.540250i
$724$	1851.54			0.00353229
$725$	165661.			0.315170
$726$	−118160.			−0.224180
$727$		−	599281.i		−	1.13387i	−0.823764	−	0.566933i	$-0.808130\pi$
$727$		−	599281.i		−	1.13387i	0.823764	−	0.566933i	$-0.191870\pi$
$728$		−	102614.i		−	0.193617i
$729$	−19683.0			−0.0370370
$730$	693266.			1.30093
$731$			1.33322e6i			2.49499i
$732$	−49128.8			−0.0916883
$733$		−	260692.i		−	0.485199i	−0.970127	−	0.242600i	$-0.922000\pi$
$733$		−	260692.i		−	0.485199i	0.970127	−	0.242600i	$-0.0780001\pi$
$734$	881952.			1.63702
$735$	−492142.			−0.910994
$736$			501295.i			0.925418i
$737$	−141360.	−	642140.i	−0.260250	−	1.18221i
$738$	−75709.9			−0.139008
$739$			286206.i			0.524070i	0.965058	+	0.262035i	$0.0843936\pi$
$739$			286206.i			0.524070i	−0.965058	+	0.262035i	$0.915606\pi$
$740$		−	62452.9i		−	0.114048i
$741$	−264397.			−0.481527
$742$		−	213254.i		−	0.387337i
$743$	185476.			0.335977			0.167988	−	0.985789i	$-0.446273\pi$
$743$	185476.			0.335977			0.167988	+	0.985789i	$0.446273\pi$
$744$			372644.i			0.673206i
$745$			169429.i			0.305264i
$746$	−394261.			−0.708444
$747$	−261273.			−0.468224
$748$			360578.i			0.644460i
$749$			242102.i			0.431553i
$750$		−	592030.i		−	1.05250i
$751$	−37976.7			−0.0673344			−0.0336672	−	0.999433i	$-0.510719\pi$
$751$	−37976.7			−0.0673344			−0.0336672	+	0.999433i	$0.510719\pi$
$752$	−406855.			−0.719456
$753$	−462801.			−0.816214
$754$	34576.8			0.0608194
$755$			1.41674e6i			2.48539i
$756$	11593.3			0.0202845
$757$			886673.i			1.54729i	0.633620	+	0.773645i	$0.281568\pi$
$757$			886673.i			1.54729i	−0.633620	+	0.773645i	$0.718432\pi$
$758$	84021.3			0.146235
$759$	638074.			1.10761
$760$	−1.83276e6			−3.17307
$761$	−218674.			−0.377597			−0.188799	−	0.982016i	$-0.560459\pi$
$761$	−218674.			−0.377597			−0.188799	+	0.982016i	$0.560459\pi$
$762$	−172384.			−0.296884
$763$	273008.			0.468950
$764$			330098.i			0.565531i
$765$		−	613295.i		−	1.04796i
$766$	356630.			0.607800
$767$			46266.1i			0.0786453i
$768$		−	278797.i		−	0.472678i
$769$		−	458219.i		−	0.774855i	−0.921900	−	0.387428i	$-0.873364\pi$
$769$		−	458219.i		−	0.774855i	0.921900	−	0.387428i	$-0.126636\pi$
$770$	−372749.			−0.628688
$771$			335878.i			0.565032i
$772$	9155.91			0.0153627
$773$	231242.			0.386997			0.193499	−	0.981101i	$-0.438017\pi$
$773$	231242.			0.386997			0.193499	+	0.981101i	$0.438017\pi$
$774$	−237205.			−0.395952
$775$		−	1.42784e6i		−	2.37726i
$776$	−317479.			−0.527220
$777$	25312.7			0.0419273
$778$		−	118051.i		−	0.195035i
$779$		−	493144.i		−	0.812642i
$780$			98181.1i			0.161376i
$781$			111572.i			0.182916i
$782$			1.41725e6i			2.31758i
$783$			16766.4i			0.0273475i
$784$	−326531.			−0.531242
$785$		−	1.03525e6i		−	1.67998i
$786$	342179.			0.553871
$787$		−	1.02327e6i		−	1.65212i	−0.563580	−	0.826062i	$-0.690576\pi$
$787$		−	1.02327e6i		−	1.65212i	0.563580	−	0.826062i	$-0.309424\pi$
$788$		−	13147.1i		−	0.0211727i
$789$			489628.i			0.786525i
$790$			1.32319e6i			2.12016i
$791$	−97291.4			−0.155497
$792$	−275345.			−0.438962
$793$	168633.			0.268161
$794$		−	759048.i		−	1.20400i
$795$			875736.i			1.38560i
$796$	136414.			0.215295
$797$	657362.			1.03487			0.517437	−	0.855721i	$-0.326886\pi$
$797$	657362.			1.03487			0.517437	+	0.855721i	$0.326886\pi$
$798$		−	173076.i		−	0.271788i
$799$	1.33283e6			2.08776
$800$			828869.i			1.29511i
$801$	319550.			0.498050
$802$	−1.01089e6			−1.57165
$803$			678410.i			1.05211i
$804$	−24373.4	−	110719.i	−0.0377054	−	0.171281i
$805$	639229.			0.986427
$806$		−	298020.i		−	0.458749i
$807$			600905.i			0.922697i
$808$	372898.			0.571173
$809$		−	558760.i		−	0.853745i	−0.904312	−	0.426873i	$-0.859615\pi$
$809$		−	558760.i		−	0.853745i	0.904312	−	0.426873i	$-0.140385\pi$
$810$	109117.			0.166311
$811$		−	888273.i		−	1.35053i	−0.737575	−	0.675266i	$-0.764029\pi$
$811$		−	888273.i		−	1.35053i	0.737575	−	0.675266i	$-0.235971\pi$
$812$		−	9875.44i		−	0.0149777i
$813$	304199.			0.460232
$814$	−140073.			−0.211400
$815$		−	270700.i		−	0.407543i
$816$		−	406915.i		−	0.611115i
$817$		−	1.54506e6i		−	2.31474i
$818$	−140189.			−0.209511
$819$	−39793.6			−0.0593261
$820$	−183124.			−0.272344
$821$	−1.07565e6			−1.59583			−0.797913	−	0.602773i	$-0.794063\pi$
$821$	−1.07565e6			−1.59583			−0.797913	+	0.602773i	$0.794063\pi$
$822$			415056.i			0.614275i
$823$	1.01971e6			1.50548			0.752742	−	0.658316i	$-0.228731\pi$
$823$	1.01971e6			1.50548			0.752742	+	0.658316i	$0.228731\pi$
$824$			555271.i			0.817806i
$825$	1.05503e6			1.55009
$826$	−30286.0			−0.0443897
$827$	−12843.2			−0.0187786			−0.00938930	−	0.999956i	$-0.502989\pi$
$827$	−12843.2			−0.0187786			−0.00938930	+	0.999956i	$0.502989\pi$
$828$	110017.			0.160473
$829$	−339429.			−0.493902			−0.246951	−	0.969028i	$-0.579429\pi$
$829$	−339429.			−0.493902			−0.246951	+	0.969028i	$0.579429\pi$
$830$	1.44842e6			2.10251
$831$		−	291475.i		−	0.422084i
$832$			387447.i			0.559714i
$833$	1.06969e6			1.54159
$834$		−	99100.5i		−	0.142477i
$835$			2.20709e6i			3.16553i
$836$		−	417872.i		−	0.597903i
$837$	144511.			0.206276
$838$			1.00202e6i			1.42689i
$839$	888029.			1.26155			0.630773	−	0.775967i	$-0.282738\pi$
$839$	888029.			1.26155			0.630773	+	0.775967i	$0.282738\pi$
$840$	−275844.			−0.390935
$841$	−692999.			−0.979807
$842$		−	266782.i		−	0.376299i
$843$	−292388.			−0.411438
$844$	−33425.3			−0.0469234
$845$			943854.i			1.32188i
$846$			237135.i			0.331326i
$847$		−	115837.i		−	0.161466i
$848$			581042.i			0.808008i
$849$			88437.8i			0.122694i
$850$			2.34336e6i			3.24341i
$851$	240211.			0.331691
$852$			19237.3i			0.0265012i
$853$	−134033.			−0.184210			−0.0921050	−	0.995749i	$-0.529360\pi$
$853$	−134033.			−0.184210			−0.0921050	+	0.995749i	$0.529360\pi$
$854$			110388.i			0.151358i
$855$			710744.i			0.972256i
$856$		−	991422.i		−	1.35304i
$857$			1.17378e6i			1.59818i	0.601210	+	0.799091i	$0.294685\pi$
$857$			1.17378e6i			1.59818i	−0.601210	+	0.799091i	$0.705315\pi$
$858$	220206.			0.299126
$859$	603402.			0.817750			0.408875	−	0.912590i	$-0.365921\pi$
$859$	603402.			0.817750			0.408875	+	0.912590i	$0.365921\pi$
$860$	−573743.			−0.775747
$861$		−	74221.7i		−	0.100121i
$862$		−	465769.i		−	0.626840i
$863$	76716.4			0.103007			0.0515035	−	0.998673i	$-0.483599\pi$
$863$	76716.4			0.103007			0.0515035	+	0.998673i	$0.483599\pi$
$864$	−83889.2			−0.112377
$865$			1.04294e6i			1.39389i
$866$	562225.			0.749677
$867$			899036.i			1.19602i
$868$	−85117.0			−0.112974
$869$	−1.29484e6			−1.71465
$870$		−	92948.1i		−	0.122801i
$871$	83660.9	+	380038.i	0.110277	+	0.500946i
$872$	−1.11799e6			−1.47029
$873$			123118.i			0.161545i
$874$		−	1.64245e6i		−	2.15015i
$875$	580392.			0.758063
$876$			116972.i			0.152431i
$877$	−148707.			−0.193345			−0.0966723	−	0.995316i	$-0.530820\pi$
$877$	−148707.			−0.193345			−0.0966723	+	0.995316i	$0.530820\pi$
$878$			512278.i			0.664533i
$879$		−	579265.i		−	0.749721i
$880$	1.01561e6			1.31148
$881$	1.22841e6			1.58267			0.791335	−	0.611383i	$-0.209386\pi$
$881$	1.22841e6			1.58267			0.791335	+	0.611383i	$0.209386\pi$
$882$			190319.i			0.244649i
$883$		−	52489.7i		−	0.0673214i	−0.999433	−	0.0336607i	$-0.989283\pi$
$883$		−	52489.7i		−	0.0673214i	0.999433	−	0.0336607i	$-0.0107166\pi$
$884$		−	213401.i		−	0.273081i
$885$	124371.			0.158793
$886$	439056.			0.559310
$887$	−67781.7			−0.0861520			−0.0430760	−	0.999072i	$-0.513716\pi$
$887$	−67781.7			−0.0861520			−0.0430760	+	0.999072i	$0.513716\pi$
$888$	−103657.			−0.131454
$889$		−	168995.i		−	0.213831i
$890$	−1.77149e6			−2.23644
$891$			106779.i			0.134502i
$892$	186281.			0.234120
$893$	−1.54461e6			−1.93694
$894$	65520.7			0.0819791
$895$	728059.			0.908909
$896$	−90966.3			−0.113309
$897$	−377632.			−0.469336
$898$		−	308646.i		−	0.382743i
$899$		−	123098.i		−	0.152311i
$900$	181909.			0.224579
$901$		−	1.90345e6i		−	2.34473i
$902$			410719.i			0.504815i
$903$		−	232543.i		−	0.285185i
$904$	398415.			0.487527
$905$			17084.3i			0.0208593i
$906$	547873.			0.667457
$907$	−138284.			−0.168096			−0.0840478	−	0.996462i	$-0.526785\pi$
$907$	−138284.			−0.168096			−0.0840478	+	0.996462i	$0.526785\pi$
$908$	4219.55			0.00511793
$909$		−	144609.i		−	0.175012i
$910$	220604.			0.266398
$911$	482104.			0.580904			0.290452	−	0.956890i	$-0.406194\pi$
$911$	482104.			0.580904			0.290452	+	0.956890i	$0.406194\pi$
$912$			471571.i			0.566967i
$913$			1.41738e6i			1.70038i
$914$		−	289205.i		−	0.346190i
$915$		−	453313.i		−	0.541447i
$916$		−	164265.i		−	0.195774i
$917$			335453.i			0.398927i
$918$	−237170.			−0.281433
$919$			65098.5i			0.0770797i	0.999257	+	0.0385398i	$0.0122706\pi$
$919$			65098.5i			0.0770797i	−0.999257	+	0.0385398i	$0.987729\pi$
$920$	−2.61769e6			−3.09273
$921$		−	289995.i		−	0.341878i
$922$			351650.i			0.413665i
$923$		−	66031.5i		−	0.0775083i
$924$		−	62892.6i		−	0.0736641i
$925$	397178.			0.464197
$926$	1.20124e6			1.40090
$927$	215333.			0.250583
$928$			71458.7i			0.0829773i
$929$			150645.i			0.174551i	0.996184	+	0.0872756i	$0.0278161\pi$
$929$			150645.i			0.174551i	−0.996184	+	0.0872756i	$0.972184\pi$
$930$	−801126.			−0.926264
$931$	−1.23966e6			−1.43022
$932$			324502.i			0.373581i
$933$	35172.7			0.0404057
$934$			1.15651e6i			1.32574i
$935$	−3.32707e6			−3.80574
$936$	162958.			0.186004
$937$		−	35210.5i		−	0.0401045i	−0.999799	−	0.0200523i	$-0.993617\pi$
$937$		−	35210.5i		−	0.0401045i	0.999799	−	0.0200523i	$-0.00638326\pi$
$938$	−248775.	+	54764.8i	−0.282749	+	0.0622438i
$939$	231294.			0.262321
$940$			573573.i			0.649132i
$941$		−	781651.i		−	0.882742i	−0.897325	−	0.441371i	$-0.854492\pi$
$941$		−	781651.i		−	0.882742i	0.897325	−	0.441371i	$-0.145508\pi$
$942$	−400345.			−0.451162
$943$		−	704345.i		−	0.792067i
$944$	82518.9			0.0925996
$945$			106972.i			0.119786i
$946$			1.28682e6i			1.43792i
$947$	−207783.			−0.231691			−0.115845	−	0.993267i	$-0.536958\pi$
$947$	−207783.			−0.231691			−0.115845	+	0.993267i	$0.536958\pi$
$948$	−223258.			−0.248422
$949$		−	401504.i		−	0.445818i
$950$		−	2.71571e6i		−	3.00910i
$951$			138975.i			0.153665i
$952$	599559.			0.661543
$953$	780293.			0.859156			0.429578	−	0.903030i	$-0.358662\pi$
$953$	780293.			0.859156			0.429578	+	0.903030i	$0.358662\pi$
$954$	338660.			0.372106
$955$	−3.04583e6			−3.33963
$956$		−	475721.i		−	0.520518i
$957$	90956.4			0.0993137
$958$		−	402205.i		−	0.438245i
$959$	−406897.			−0.442433
$960$	1.04152e6			1.13012
$961$	−137466.			−0.148850
$962$	82899.2			0.0895777
$963$	−384472.			−0.414584
$964$	−264152.			−0.284250
$965$			84482.0i			0.0907213i
$966$		−	247199.i		−	0.264907i
$967$	361335.			0.386418			0.193209	−	0.981158i	$-0.438110\pi$
$967$	361335.			0.386418			0.193209	+	0.981158i	$0.438110\pi$
$968$			474362.i			0.506243i
$969$		−	1.54483e6i		−	1.64526i
$970$		−	682529.i		−	0.725401i
$971$	703716.			0.746378			0.373189	−	0.927755i	$-0.378264\pi$
$971$	703716.			0.746378			0.373189	+	0.927755i	$0.378264\pi$
$972$			18410.9i			0.0194869i
$973$	97152.5			0.102619
$974$	−511258.			−0.538917
$975$	−624397.			−0.656828
$976$		−	300769.i		−	0.315742i
$977$	−334405.			−0.350335			−0.175168	−	0.984539i	$-0.556047\pi$
$977$	−334405.			−0.350335			−0.175168	+	0.984539i	$0.556047\pi$
$978$	−104684.			−0.109446
$979$		−	1.73353e6i		−	1.80870i
$980$			460334.i			0.479315i
$981$			433554.i			0.450511i
$982$			845957.i			0.877254i
$983$		−	1.52269e6i		−	1.57582i	−0.615793	−	0.787908i	$-0.711164\pi$
$983$		−	1.52269e6i		−	1.57582i	0.615793	−	0.787908i	$-0.288836\pi$
$984$			303943.i			0.313907i
$985$	121308.			0.125031
$986$			202027.i			0.207805i
$987$	−232474.			−0.238638
$988$			247309.i			0.253353i
$989$		−	2.20677e6i		−	2.25613i
$990$		−	591948.i		−	0.603967i
$991$		−	241954.i		−	0.246369i	−0.992384	−	0.123184i	$-0.960689\pi$
$991$		−	241954.i		−	0.246369i	0.992384	−	0.123184i	$-0.0393106\pi$
$992$	615907.			0.625881
$993$	577926.			0.586103
$994$	43224.5			0.0437479
$995$			1.25870e6i			1.27138i
$996$			244387.i			0.246354i
$997$	−532720.			−0.535931			−0.267965	−	0.963429i	$-0.586351\pi$
$997$	−532720.			−0.535931			−0.267965	+	0.963429i	$0.586351\pi$
$998$	656589.			0.659223
$999$			40198.1i			0.0402787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.16	✓	46
67.66	odd	2	inner	201.5.b.a.133.31	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.16	✓	46	1.1	even	1	trivial
201.5.b.a.133.31	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)

\(f(q)\)	\(=\)	\(q-3.33762i q^{2} +5.19615i q^{3} +4.86032 q^{4} +44.8464i q^{5} +17.3428 q^{6} +17.0019i q^{7} -69.6237i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-3.33762i q^{2} +5.19615i q^{3} +4.86032 q^{4} +44.8464i q^{5} +17.3428 q^{6} +17.0019i q^{7} -69.6237i q^{8} -27.0000 q^{9} +149.680 q^{10} +146.473i q^{11} +25.2550i q^{12} -86.6869i q^{13} +56.7457 q^{14} -233.029 q^{15} -154.612 q^{16} +506.498 q^{17} +90.1156i q^{18} -586.978 q^{19} +217.968i q^{20} -88.3442 q^{21} +488.869 q^{22} -838.365 q^{23} +361.776 q^{24} -1386.20 q^{25} -289.328 q^{26} -140.296i q^{27} +82.6345i q^{28} -119.507 q^{29} +777.760i q^{30} +1030.04i q^{31} -597.944i q^{32} -761.094 q^{33} -1690.50i q^{34} -762.472 q^{35} -131.229 q^{36} -286.524 q^{37} +1959.11i q^{38} +450.438 q^{39} +3122.37 q^{40} +840.142i q^{41} +294.859i q^{42} +2632.23i q^{43} +711.904i q^{44} -1210.85i q^{45} +2798.14i q^{46} +2631.46 q^{47} -803.388i q^{48} +2111.94 q^{49} +4626.60i q^{50} +2631.84i q^{51} -421.326i q^{52} -3758.06i q^{53} -468.255 q^{54} -6568.77 q^{55} +1183.73 q^{56} -3050.03i q^{57} +398.870i q^{58} -533.715 q^{59} -1132.59 q^{60} +1945.31i q^{61} +3437.88 q^{62} -459.050i q^{63} -4469.50 q^{64} +3887.60 q^{65} +2540.24i q^{66} +(-4384.03 + 965.093i) q^{67} +2461.75 q^{68} -4356.27i q^{69} +2544.84i q^{70} +761.724 q^{71} +1879.84i q^{72} +4631.65 q^{73} +956.306i q^{74} -7202.90i q^{75} -2852.90 q^{76} -2490.31 q^{77} -1503.39i q^{78} +8840.14i q^{79} -6933.79i q^{80} +729.000 q^{81} +2804.07 q^{82} +9676.79 q^{83} -429.381 q^{84} +22714.6i q^{85} +8785.39 q^{86} -620.979i q^{87} +10198.0 q^{88} -11835.2 q^{89} -4041.36 q^{90} +1473.84 q^{91} -4074.72 q^{92} -5352.26 q^{93} -8782.79i q^{94} -26323.8i q^{95} +3107.01 q^{96} -4559.92i q^{97} -7048.83i q^{98} -3954.76i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 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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