LMFDB - Embedded newform 550.3.d.a.351.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,3,Mod(351,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("550.351");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	550.d (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:	$14.9864145398$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			351.2
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	550.351
Dual form			550.3.d.a.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.00000 q^{3} -2.00000 q^{4} -1.41421i q^{6} -8.48528i q^{7} -2.82843i q^{8} -8.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.00000 q^{3} -2.00000 q^{4} -1.41421i q^{6} -8.48528i q^{7} -2.82843i q^{8} -8.00000 q^{9} +(7.00000 - 8.48528i) q^{11} +2.00000 q^{12} +8.48528i q^{13} +12.0000 q^{14} +4.00000 q^{16} +25.4558i q^{17} -11.3137i q^{18} +25.4558i q^{19} +8.48528i q^{21} +(12.0000 + 9.89949i) q^{22} -17.0000 q^{23} +2.82843i q^{24} -12.0000 q^{26} +17.0000 q^{27} +16.9706i q^{28} +33.9411i q^{29} +17.0000 q^{31} +5.65685i q^{32} +(-7.00000 + 8.48528i) q^{33} -36.0000 q^{34} +16.0000 q^{36} -47.0000 q^{37} -36.0000 q^{38} -8.48528i q^{39} -8.48528i q^{41} -12.0000 q^{42} +16.9706i q^{43} +(-14.0000 + 16.9706i) q^{44} -24.0416i q^{46} +58.0000 q^{47} -4.00000 q^{48} -23.0000 q^{49} -25.4558i q^{51} -16.9706i q^{52} -2.00000 q^{53} +24.0416i q^{54} -24.0000 q^{56} -25.4558i q^{57} -48.0000 q^{58} -55.0000 q^{59} +84.8528i q^{61} +24.0416i q^{62} +67.8823i q^{63} -8.00000 q^{64} +(-12.0000 - 9.89949i) q^{66} -89.0000 q^{67} -50.9117i q^{68} +17.0000 q^{69} -7.00000 q^{71} +22.6274i q^{72} +127.279i q^{73} -66.4680i q^{74} -50.9117i q^{76} +(-72.0000 - 59.3970i) q^{77} +12.0000 q^{78} +33.9411i q^{79} +55.0000 q^{81} +12.0000 q^{82} -33.9411i q^{83} -16.9706i q^{84} -24.0000 q^{86} -33.9411i q^{87} +(-24.0000 - 19.7990i) q^{88} -97.0000 q^{89} +72.0000 q^{91} +34.0000 q^{92} -17.0000 q^{93} +82.0244i q^{94} -5.65685i q^{96} +121.000 q^{97} -32.5269i q^{98} +(-56.0000 + 67.8823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{4} - 16 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 4 * q^4 - 16 * q^9	$ 2 q - 2 q^{3} - 4 q^{4} - 16 q^{9} + 14 q^{11} + 4 q^{12} + 24 q^{14} + 8 q^{16} + 24 q^{22} - 34 q^{23} - 24 q^{26} + 34 q^{27} + 34 q^{31} - 14 q^{33} - 72 q^{34} + 32 q^{36} - 94 q^{37} - 72 q^{38} - 24 q^{42} - 28 q^{44} + 116 q^{47} - 8 q^{48} - 46 q^{49} - 4 q^{53} - 48 q^{56} - 96 q^{58} - 110 q^{59} - 16 q^{64} - 24 q^{66} - 178 q^{67} + 34 q^{69} - 14 q^{71} - 144 q^{77} + 24 q^{78} + 110 q^{81} + 24 q^{82} - 48 q^{86} - 48 q^{88} - 194 q^{89} + 144 q^{91} + 68 q^{92} - 34 q^{93} + 242 q^{97} - 112 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^4 - 16 * q^9 + 14 * q^11 + 4 * q^12 + 24 * q^14 + 8 * q^16 + 24 * q^22 - 34 * q^23 - 24 * q^26 + 34 * q^27 + 34 * q^31 - 14 * q^33 - 72 * q^34 + 32 * q^36 - 94 * q^37 - 72 * q^38 - 24 * q^42 - 28 * q^44 + 116 * q^47 - 8 * q^48 - 46 * q^49 - 4 * q^53 - 48 * q^56 - 96 * q^58 - 110 * q^59 - 16 * q^64 - 24 * q^66 - 178 * q^67 + 34 * q^69 - 14 * q^71 - 144 * q^77 + 24 * q^78 + 110 * q^81 + 24 * q^82 - 48 * q^86 - 48 * q^88 - 194 * q^89 + 144 * q^91 + 68 * q^92 - 34 * q^93 + 242 * q^97 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.00000			−0.333333			−0.166667	−	0.986013i	$-0.553300\pi$
$3$	−1.00000			−0.333333			−0.166667	+	0.986013i	$0.553300\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	1.41421i		−	0.235702i
$7$		−	8.48528i		−	1.21218i	−0.795395	−	0.606092i	$-0.792737\pi$
$7$		−	8.48528i		−	1.21218i	0.795395	−	0.606092i	$-0.207263\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−8.00000			−0.888889
$10$		0			0
$11$	7.00000	−	8.48528i	0.636364	−	0.771389i
$11$	7.00000	−	8.48528i	0.636364	−	0.771389i
$12$	2.00000			0.166667
$13$			8.48528i			0.652714i	0.945247	+	0.326357i	$0.105821\pi$
$13$			8.48528i			0.652714i	−0.945247	+	0.326357i	$0.894179\pi$
$14$	12.0000			0.857143
$15$		0			0
$16$	4.00000			0.250000
$17$			25.4558i			1.49740i	0.662908	+	0.748701i	$0.269322\pi$
$17$			25.4558i			1.49740i	−0.662908	+	0.748701i	$0.730678\pi$
$18$		−	11.3137i		−	0.628539i
$19$			25.4558i			1.33978i	0.742460	+	0.669891i	$0.233659\pi$
$19$			25.4558i			1.33978i	−0.742460	+	0.669891i	$0.766341\pi$
$20$		0			0
$21$			8.48528i			0.404061i
$22$	12.0000	+	9.89949i	0.545455	+	0.449977i
$23$	−17.0000			−0.739130			−0.369565	−	0.929205i	$-0.620493\pi$
$23$	−17.0000			−0.739130			−0.369565	+	0.929205i	$0.620493\pi$
$24$			2.82843i			0.117851i
$25$		0			0
$26$	−12.0000			−0.461538
$27$	17.0000			0.629630
$28$			16.9706i			0.606092i
$29$			33.9411i			1.17038i	0.810895	+	0.585192i	$0.198981\pi$
$29$			33.9411i			1.17038i	−0.810895	+	0.585192i	$0.801019\pi$
$30$		0			0
$31$	17.0000			0.548387			0.274194	−	0.961675i	$-0.411589\pi$
$31$	17.0000			0.548387			0.274194	+	0.961675i	$0.411589\pi$
$32$			5.65685i			0.176777i
$33$	−7.00000	+	8.48528i	−0.212121	+	0.257130i
$34$	−36.0000			−1.05882
$35$		0			0
$36$	16.0000			0.444444
$37$	−47.0000			−1.27027			−0.635135	−	0.772401i	$-0.719056\pi$
$37$	−47.0000			−1.27027			−0.635135	+	0.772401i	$0.719056\pi$
$38$	−36.0000			−0.947368
$39$		−	8.48528i		−	0.217571i
$40$		0			0
$41$		−	8.48528i		−	0.206958i	−0.994632	−	0.103479i	$-0.967003\pi$
$41$		−	8.48528i		−	0.206958i	0.994632	−	0.103479i	$-0.0329975\pi$
$42$	−12.0000			−0.285714
$43$			16.9706i			0.394664i	0.980337	+	0.197332i	$0.0632277\pi$
$43$			16.9706i			0.394664i	−0.980337	+	0.197332i	$0.936772\pi$
$44$	−14.0000	+	16.9706i	−0.318182	+	0.385695i
$45$		0			0
$46$		−	24.0416i		−	0.522644i
$47$	58.0000			1.23404			0.617021	−	0.786946i	$-0.288339\pi$
$47$	58.0000			1.23404			0.617021	+	0.786946i	$0.288339\pi$
$48$	−4.00000			−0.0833333
$49$	−23.0000			−0.469388
$50$		0			0
$51$		−	25.4558i		−	0.499134i
$52$		−	16.9706i		−	0.326357i
$53$	−2.00000			−0.0377358			−0.0188679	−	0.999822i	$-0.506006\pi$
$53$	−2.00000			−0.0377358			−0.0188679	+	0.999822i	$0.506006\pi$
$54$			24.0416i			0.445215i
$55$		0			0
$56$	−24.0000			−0.428571
$57$		−	25.4558i		−	0.446594i
$58$	−48.0000			−0.827586
$59$	−55.0000			−0.932203			−0.466102	−	0.884731i	$-0.654342\pi$
$59$	−55.0000			−0.932203			−0.466102	+	0.884731i	$0.654342\pi$
$60$		0			0
$61$			84.8528i			1.39103i	0.718512	+	0.695515i	$0.244824\pi$
$61$			84.8528i			1.39103i	−0.718512	+	0.695515i	$0.755176\pi$
$62$			24.0416i			0.387768i
$63$			67.8823i			1.07750i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−12.0000	−	9.89949i	−0.181818	−	0.149992i
$67$	−89.0000			−1.32836			−0.664179	−	0.747573i	$-0.731219\pi$
$67$	−89.0000			−1.32836			−0.664179	+	0.747573i	$0.731219\pi$
$68$		−	50.9117i		−	0.748701i
$69$	17.0000			0.246377
$70$		0			0
$71$	−7.00000			−0.0985915			−0.0492958	−	0.998784i	$-0.515698\pi$
$71$	−7.00000			−0.0985915			−0.0492958	+	0.998784i	$0.515698\pi$
$72$			22.6274i			0.314270i
$73$			127.279i			1.74355i	0.489906	+	0.871775i	$0.337031\pi$
$73$			127.279i			1.74355i	−0.489906	+	0.871775i	$0.662969\pi$
$74$		−	66.4680i		−	0.898217i
$75$		0			0
$76$		−	50.9117i		−	0.669891i
$77$	−72.0000	−	59.3970i	−0.935065	−	0.771389i
$78$	12.0000			0.153846
$79$			33.9411i			0.429634i	0.976654	+	0.214817i	$0.0689156\pi$
$79$			33.9411i			0.429634i	−0.976654	+	0.214817i	$0.931084\pi$
$80$		0			0
$81$	55.0000			0.679012
$82$	12.0000			0.146341
$83$		−	33.9411i		−	0.408929i	−0.978874	−	0.204465i	$-0.934455\pi$
$83$		−	33.9411i		−	0.408929i	0.978874	−	0.204465i	$-0.0655453\pi$
$84$		−	16.9706i		−	0.202031i
$85$		0			0
$86$	−24.0000			−0.279070
$87$		−	33.9411i		−	0.390128i
$88$	−24.0000	−	19.7990i	−0.272727	−	0.224989i
$89$	−97.0000			−1.08989			−0.544944	−	0.838473i	$-0.683449\pi$
$89$	−97.0000			−1.08989			−0.544944	+	0.838473i	$0.683449\pi$
$90$		0			0
$91$	72.0000			0.791209
$92$	34.0000			0.369565
$93$	−17.0000			−0.182796
$94$			82.0244i			0.872600i
$95$		0			0
$96$		−	5.65685i		−	0.0589256i
$97$	121.000			1.24742			0.623711	−	0.781655i	$-0.285624\pi$
$97$	121.000			1.24742			0.623711	+	0.781655i	$0.285624\pi$
$98$		−	32.5269i		−	0.331907i
$99$	−56.0000	+	67.8823i	−0.565657	+	0.685679i
$100$		0			0
$101$			8.48528i			0.0840127i	0.999117	+	0.0420063i	$0.0133750\pi$
$101$			8.48528i			0.0840127i	−0.999117	+	0.0420063i	$0.986625\pi$
$102$	36.0000			0.352941
$103$	82.0000			0.796117			0.398058	−	0.917360i	$-0.369684\pi$
$103$	82.0000			0.796117			0.398058	+	0.917360i	$0.369684\pi$
$104$	24.0000			0.230769
$105$		0			0
$106$		−	2.82843i		−	0.0266833i
$107$			76.3675i			0.713715i	0.934159	+	0.356858i	$0.116152\pi$
$107$			76.3675i			0.713715i	−0.934159	+	0.356858i	$0.883848\pi$
$108$	−34.0000			−0.314815
$109$		−	152.735i		−	1.40124i	−0.713535	−	0.700620i	$-0.752907\pi$
$109$		−	152.735i		−	1.40124i	0.713535	−	0.700620i	$-0.247093\pi$
$110$		0			0
$111$	47.0000			0.423423
$112$		−	33.9411i		−	0.303046i
$113$	1.00000			0.00884956			0.00442478	−	0.999990i	$-0.498592\pi$
$113$	1.00000			0.00884956			0.00442478	+	0.999990i	$0.498592\pi$
$114$	36.0000			0.315789
$115$		0			0
$116$		−	67.8823i		−	0.585192i
$117$		−	67.8823i		−	0.580190i
$118$		−	77.7817i		−	0.659167i
$119$	216.000			1.81513
$120$		0			0
$121$	−23.0000	−	118.794i	−0.190083	−	0.981768i
$122$	−120.000			−0.983607
$123$			8.48528i			0.0689860i
$124$	−34.0000			−0.274194
$125$		0			0
$126$	−96.0000			−0.761905
$127$		−	25.4558i		−	0.200440i	−0.994965	−	0.100220i	$-0.968045\pi$
$127$		−	25.4558i		−	0.200440i	0.994965	−	0.100220i	$-0.0319546\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	16.9706i		−	0.131555i
$130$		0			0
$131$			93.3381i			0.712505i	0.934390	+	0.356252i	$0.115946\pi$
$131$			93.3381i			0.712505i	−0.934390	+	0.356252i	$0.884054\pi$
$132$	14.0000	−	16.9706i	0.106061	−	0.128565i
$133$	216.000			1.62406
$134$		−	125.865i		−	0.939291i
$135$		0			0
$136$	72.0000			0.529412
$137$	−167.000			−1.21898			−0.609489	−	0.792794i	$-0.708625\pi$
$137$	−167.000			−1.21898			−0.609489	+	0.792794i	$0.708625\pi$
$138$			24.0416i			0.174215i
$139$			93.3381i			0.671497i	0.941952	+	0.335749i	$0.108989\pi$
$139$			93.3381i			0.671497i	−0.941952	+	0.335749i	$0.891011\pi$
$140$		0			0
$141$	−58.0000			−0.411348
$142$		−	9.89949i		−	0.0697148i
$143$	72.0000	+	59.3970i	0.503497	+	0.415363i
$144$	−32.0000			−0.222222
$145$		0			0
$146$	−180.000			−1.23288
$147$	23.0000			0.156463
$148$	94.0000			0.635135
$149$		−	161.220i		−	1.08202i	−0.841018	−	0.541008i	$-0.818043\pi$
$149$		−	161.220i		−	1.08202i	0.841018	−	0.541008i	$-0.181957\pi$
$150$		0			0
$151$			288.500i			1.91059i	0.295649	+	0.955297i	$0.404464\pi$
$151$			288.500i			1.91059i	−0.295649	+	0.955297i	$0.595536\pi$
$152$	72.0000			0.473684
$153$		−	203.647i		−	1.33102i
$154$	84.0000	−	101.823i	0.545455	−	0.661191i
$155$		0			0
$156$			16.9706i			0.108786i
$157$	1.00000			0.00636943			0.00318471	−	0.999995i	$-0.498986\pi$
$157$	1.00000			0.00636943			0.00318471	+	0.999995i	$0.498986\pi$
$158$	−48.0000			−0.303797
$159$	2.00000			0.0125786
$160$		0			0
$161$			144.250i			0.895961i
$162$			77.7817i			0.480134i
$163$	−110.000			−0.674847			−0.337423	−	0.941353i	$-0.609555\pi$
$163$	−110.000			−0.674847			−0.337423	+	0.941353i	$0.609555\pi$
$164$			16.9706i			0.103479i
$165$		0			0
$166$	48.0000			0.289157
$167$			110.309i			0.660531i	0.943888	+	0.330265i	$0.107138\pi$
$167$			110.309i			0.660531i	−0.943888	+	0.330265i	$0.892862\pi$
$168$	24.0000			0.142857
$169$	97.0000			0.573964
$170$		0			0
$171$		−	203.647i		−	1.19092i
$172$		−	33.9411i		−	0.197332i
$173$			16.9706i			0.0980957i	0.998796	+	0.0490479i	$0.0156187\pi$
$173$			16.9706i			0.0980957i	−0.998796	+	0.0490479i	$0.984381\pi$
$174$	48.0000			0.275862
$175$		0			0
$176$	28.0000	−	33.9411i	0.159091	−	0.192847i
$177$	55.0000			0.310734
$178$		−	137.179i		−	0.770667i
$179$	209.000			1.16760			0.583799	−	0.811898i	$-0.301566\pi$
$179$	209.000			1.16760			0.583799	+	0.811898i	$0.301566\pi$
$180$		0			0
$181$	119.000			0.657459			0.328729	−	0.944424i	$-0.393380\pi$
$181$	119.000			0.657459			0.328729	+	0.944424i	$0.393380\pi$
$182$			101.823i			0.559469i
$183$		−	84.8528i		−	0.463677i
$184$			48.0833i			0.261322i
$185$		0			0
$186$		−	24.0416i		−	0.129256i
$187$	216.000	+	178.191i	1.15508	+	0.952893i
$188$	−116.000			−0.617021
$189$		−	144.250i		−	0.763226i
$190$		0			0
$191$	−319.000			−1.67016			−0.835079	−	0.550131i	$-0.814578\pi$
$191$	−319.000			−1.67016			−0.835079	+	0.550131i	$0.814578\pi$
$192$	8.00000			0.0416667
$193$		−	16.9706i		−	0.0879304i	−0.999033	−	0.0439652i	$-0.986001\pi$
$193$		−	16.9706i		−	0.0879304i	0.999033	−	0.0439652i	$-0.0139991\pi$
$194$			171.120i			0.882061i
$195$		0			0
$196$	46.0000			0.234694
$197$		−	101.823i		−	0.516870i	−0.966029	−	0.258435i	$-0.916793\pi$
$197$		−	101.823i		−	0.516870i	0.966029	−	0.258435i	$-0.0832068\pi$
$198$	−96.0000	−	79.1960i	−0.484848	−	0.399980i
$199$	182.000			0.914573			0.457286	−	0.889319i	$-0.348821\pi$
$199$	182.000			0.914573			0.457286	+	0.889319i	$0.348821\pi$
$200$		0			0
$201$	89.0000			0.442786
$202$	−12.0000			−0.0594059
$203$	288.000			1.41872
$204$			50.9117i			0.249567i
$205$		0			0
$206$			115.966i			0.562939i
$207$	136.000			0.657005
$208$			33.9411i			0.163178i
$209$	216.000	+	178.191i	1.03349	+	0.852588i
$210$		0			0
$211$			118.794i			0.563004i	0.959561	+	0.281502i	$0.0908327\pi$
$211$			118.794i			0.563004i	−0.959561	+	0.281502i	$0.909167\pi$
$212$	4.00000			0.0188679
$213$	7.00000			0.0328638
$214$	−108.000			−0.504673
$215$		0			0
$216$		−	48.0833i		−	0.222608i
$217$		−	144.250i		−	0.664746i
$218$	216.000			0.990826
$219$		−	127.279i		−	0.581184i
$220$		0			0
$221$	−216.000			−0.977376
$222$			66.4680i			0.299406i
$223$	31.0000			0.139013			0.0695067	−	0.997581i	$-0.477857\pi$
$223$	31.0000			0.139013			0.0695067	+	0.997581i	$0.477857\pi$
$224$	48.0000			0.214286
$225$		0			0
$226$			1.41421i			0.00625758i
$227$			93.3381i			0.411181i	0.978638	+	0.205591i	$0.0659115\pi$
$227$			93.3381i			0.411181i	−0.978638	+	0.205591i	$0.934089\pi$
$228$			50.9117i			0.223297i
$229$	−73.0000			−0.318777			−0.159389	−	0.987216i	$-0.550952\pi$
$229$	−73.0000			−0.318777			−0.159389	+	0.987216i	$0.550952\pi$
$230$		0			0
$231$	72.0000	+	59.3970i	0.311688	+	0.257130i
$232$	96.0000			0.413793
$233$		−	203.647i		−	0.874020i	−0.899457	−	0.437010i	$-0.856037\pi$
$233$		−	203.647i		−	0.874020i	0.899457	−	0.437010i	$-0.143963\pi$
$234$	96.0000			0.410256
$235$		0			0
$236$	110.000			0.466102
$237$		−	33.9411i		−	0.143211i
$238$			305.470i			1.28349i
$239$		−	288.500i		−	1.20711i	−0.797321	−	0.603556i	$-0.793750\pi$
$239$		−	288.500i		−	1.20711i	0.797321	−	0.603556i	$-0.206250\pi$
$240$		0			0
$241$		−	118.794i		−	0.492921i	−0.969153	−	0.246460i	$-0.920732\pi$
$241$		−	118.794i		−	0.492921i	0.969153	−	0.246460i	$-0.0792675\pi$
$242$	168.000	−	32.5269i	0.694215	−	0.134409i
$243$	−208.000			−0.855967
$244$		−	169.706i		−	0.695515i
$245$		0			0
$246$	−12.0000			−0.0487805
$247$	−216.000			−0.874494
$248$		−	48.0833i		−	0.193884i
$249$			33.9411i			0.136310i
$250$		0			0
$251$	65.0000			0.258964			0.129482	−	0.991582i	$-0.458669\pi$
$251$	65.0000			0.258964			0.129482	+	0.991582i	$0.458669\pi$
$252$		−	135.765i		−	0.538748i
$253$	−119.000	+	144.250i	−0.470356	+	0.570157i
$254$	36.0000			0.141732
$255$		0			0
$256$	16.0000			0.0625000
$257$	−170.000			−0.661479			−0.330739	−	0.943722i	$-0.607298\pi$
$257$	−170.000			−0.661479			−0.330739	+	0.943722i	$0.607298\pi$
$258$	24.0000			0.0930233
$259$			398.808i			1.53980i
$260$		0			0
$261$		−	271.529i		−	1.04034i
$262$	−132.000			−0.503817
$263$		−	313.955i		−	1.19375i	−0.802335	−	0.596873i	$-0.796409\pi$
$263$		−	313.955i		−	1.19375i	0.802335	−	0.596873i	$-0.203591\pi$
$264$	24.0000	+	19.7990i	0.0909091	+	0.0749962i
$265$		0			0
$266$			305.470i			1.14838i
$267$	97.0000			0.363296
$268$	178.000			0.664179
$269$	−430.000			−1.59851			−0.799257	−	0.600990i	$-0.794773\pi$
$269$	−430.000			−1.59851			−0.799257	+	0.600990i	$0.794773\pi$
$270$		0			0
$271$		−	381.838i		−	1.40900i	−0.709706	−	0.704498i	$-0.751172\pi$
$271$		−	381.838i		−	1.40900i	0.709706	−	0.704498i	$-0.248828\pi$
$272$			101.823i			0.374351i
$273$	−72.0000			−0.263736
$274$		−	236.174i		−	0.861948i
$275$		0			0
$276$	−34.0000			−0.123188
$277$		−	84.8528i		−	0.306328i	−0.988201	−	0.153164i	$-0.951054\pi$
$277$		−	84.8528i		−	0.306328i	0.988201	−	0.153164i	$-0.0489463\pi$
$278$	−132.000			−0.474820
$279$	−136.000			−0.487455
$280$		0			0
$281$			135.765i			0.483148i	0.970382	+	0.241574i	$0.0776636\pi$
$281$			135.765i			0.483148i	−0.970382	+	0.241574i	$0.922336\pi$
$282$		−	82.0244i		−	0.290867i
$283$		−	67.8823i		−	0.239867i	−0.992782	−	0.119933i	$-0.961732\pi$
$283$		−	67.8823i		−	0.239867i	0.992782	−	0.119933i	$-0.0382681\pi$
$284$	14.0000			0.0492958
$285$		0			0
$286$	−84.0000	+	101.823i	−0.293706	+	0.356026i
$287$	−72.0000			−0.250871
$288$		−	45.2548i		−	0.157135i
$289$	−359.000			−1.24221
$290$		0			0
$291$	−121.000			−0.415808
$292$		−	254.558i		−	0.871775i
$293$			517.602i			1.76656i	0.468846	+	0.883280i	$0.344670\pi$
$293$			517.602i			1.76656i	−0.468846	+	0.883280i	$0.655330\pi$
$294$			32.5269i			0.110636i
$295$		0			0
$296$			132.936i			0.449108i
$297$	119.000	−	144.250i	0.400673	−	0.485690i
$298$	228.000			0.765101
$299$		−	144.250i		−	0.482441i
$300$		0			0
$301$	144.000			0.478405
$302$	−408.000			−1.35099
$303$		−	8.48528i		−	0.0280042i
$304$			101.823i			0.334945i
$305$		0			0
$306$	288.000			0.941176
$307$			25.4558i			0.0829181i	0.999140	+	0.0414590i	$0.0132006\pi$
$307$			25.4558i			0.0829181i	−0.999140	+	0.0414590i	$0.986799\pi$
$308$	144.000	+	118.794i	0.467532	+	0.385695i
$309$	−82.0000			−0.265372
$310$		0			0
$311$	−154.000			−0.495177			−0.247588	−	0.968865i	$-0.579638\pi$
$311$	−154.000			−0.495177			−0.247588	+	0.968865i	$0.579638\pi$
$312$	−24.0000			−0.0769231
$313$	−95.0000			−0.303514			−0.151757	−	0.988418i	$-0.548493\pi$
$313$	−95.0000			−0.303514			−0.151757	+	0.988418i	$0.548493\pi$
$314$			1.41421i			0.00450386i
$315$		0			0
$316$		−	67.8823i		−	0.214817i
$317$	−23.0000			−0.0725552			−0.0362776	−	0.999342i	$-0.511550\pi$
$317$	−23.0000			−0.0725552			−0.0362776	+	0.999342i	$0.511550\pi$
$318$			2.82843i			0.00889442i
$319$	288.000	+	237.588i	0.902821	+	0.744790i
$320$		0			0
$321$		−	76.3675i		−	0.237905i
$322$	−204.000			−0.633540
$323$	−648.000			−2.00619
$324$	−110.000			−0.339506
$325$		0			0
$326$		−	155.563i		−	0.477189i
$327$			152.735i			0.467080i
$328$	−24.0000			−0.0731707
$329$		−	492.146i		−	1.49589i
$330$		0			0
$331$	185.000			0.558912			0.279456	−	0.960158i	$-0.409846\pi$
$331$	185.000			0.558912			0.279456	+	0.960158i	$0.409846\pi$
$332$			67.8823i			0.204465i
$333$	376.000			1.12913
$334$	−156.000			−0.467066
$335$		0			0
$336$			33.9411i			0.101015i
$337$			8.48528i			0.0251789i	0.999921	+	0.0125894i	$0.00400745\pi$
$337$			8.48528i			0.0251789i	−0.999921	+	0.0125894i	$0.995993\pi$
$338$			137.179i			0.405854i
$339$	−1.00000			−0.00294985
$340$		0			0
$341$	119.000	−	144.250i	0.348974	−	0.423020i
$342$	288.000			0.842105
$343$		−	220.617i		−	0.643199i
$344$	48.0000			0.139535
$345$		0			0
$346$	−24.0000			−0.0693642
$347$			212.132i			0.611332i	0.952139	+	0.305666i	$0.0988790\pi$
$347$			212.132i			0.611332i	−0.952139	+	0.305666i	$0.901121\pi$
$348$			67.8823i			0.195064i
$349$			263.044i			0.753707i	0.926273	+	0.376853i	$0.122994\pi$
$349$			263.044i			0.753707i	−0.926273	+	0.376853i	$0.877006\pi$
$350$		0			0
$351$			144.250i			0.410968i
$352$	48.0000	+	39.5980i	0.136364	+	0.112494i
$353$	−167.000			−0.473088			−0.236544	−	0.971621i	$-0.576015\pi$
$353$	−167.000			−0.473088			−0.236544	+	0.971621i	$0.576015\pi$
$354$			77.7817i			0.219722i
$355$		0			0
$356$	194.000			0.544944
$357$	−216.000			−0.605042
$358$			295.571i			0.825616i
$359$			636.396i			1.77269i	0.463024	+	0.886346i	$0.346764\pi$
$359$			636.396i			1.77269i	−0.463024	+	0.886346i	$0.653236\pi$
$360$		0			0
$361$	−287.000			−0.795014
$362$			168.291i			0.464893i
$363$	23.0000	+	118.794i	0.0633609	+	0.327256i
$364$	−144.000			−0.395604
$365$		0			0
$366$	120.000			0.327869
$367$	607.000			1.65395			0.826975	−	0.562238i	$-0.190060\pi$
$367$	607.000			1.65395			0.826975	+	0.562238i	$0.190060\pi$
$368$	−68.0000			−0.184783
$369$			67.8823i			0.183963i
$370$		0			0
$371$			16.9706i			0.0457428i
$372$	34.0000			0.0913978
$373$		−	347.897i		−	0.932698i	−0.884601	−	0.466349i	$-0.845569\pi$
$373$		−	347.897i		−	0.932698i	0.884601	−	0.466349i	$-0.154431\pi$
$374$	−252.000	+	305.470i	−0.673797	+	0.816765i
$375$		0			0
$376$		−	164.049i		−	0.436300i
$377$	−288.000			−0.763926
$378$	204.000			0.539683
$379$	−295.000			−0.778364			−0.389182	−	0.921161i	$-0.627242\pi$
$379$	−295.000			−0.778364			−0.389182	+	0.921161i	$0.627242\pi$
$380$		0			0
$381$			25.4558i			0.0668132i
$382$		−	451.134i		−	1.18098i
$383$	−377.000			−0.984334			−0.492167	−	0.870501i	$-0.663795\pi$
$383$	−377.000			−0.984334			−0.492167	+	0.870501i	$0.663795\pi$
$384$			11.3137i			0.0294628i
$385$		0			0
$386$	24.0000			0.0621762
$387$		−	135.765i		−	0.350813i
$388$	−242.000			−0.623711
$389$	−121.000			−0.311054			−0.155527	−	0.987832i	$-0.549708\pi$
$389$	−121.000			−0.311054			−0.155527	+	0.987832i	$0.549708\pi$
$390$		0			0
$391$		−	432.749i		−	1.10678i
$392$			65.0538i			0.165954i
$393$		−	93.3381i		−	0.237502i
$394$	144.000			0.365482
$395$		0			0
$396$	112.000	−	135.765i	0.282828	−	0.342840i
$397$	−578.000			−1.45592			−0.727960	−	0.685620i	$-0.759531\pi$
$397$	−578.000			−1.45592			−0.727960	+	0.685620i	$0.759531\pi$
$398$			257.387i			0.646701i
$399$	−216.000			−0.541353
$400$		0			0
$401$	−550.000			−1.37157			−0.685786	−	0.727804i	$-0.740541\pi$
$401$	−550.000			−1.37157			−0.685786	+	0.727804i	$0.740541\pi$
$402$			125.865i			0.313097i
$403$			144.250i			0.357940i
$404$		−	16.9706i		−	0.0420063i
$405$		0			0
$406$			407.294i			1.00319i
$407$	−329.000	+	398.808i	−0.808354	+	0.979873i
$408$	−72.0000			−0.176471
$409$		−	593.970i		−	1.45225i	−0.687563	−	0.726124i	$-0.741320\pi$
$409$		−	593.970i		−	1.45225i	0.687563	−	0.726124i	$-0.258680\pi$
$410$		0			0
$411$	167.000			0.406326
$412$	−164.000			−0.398058
$413$			466.690i			1.13000i
$414$			192.333i			0.464573i
$415$		0			0
$416$	−48.0000			−0.115385
$417$		−	93.3381i		−	0.223832i
$418$	−252.000	+	305.470i	−0.602871	+	0.730790i
$419$	−370.000			−0.883055			−0.441527	−	0.897248i	$-0.645563\pi$
$419$	−370.000			−0.883055			−0.441527	+	0.897248i	$0.645563\pi$
$420$		0			0
$421$	338.000			0.802850			0.401425	−	0.915892i	$-0.368515\pi$
$421$	338.000			0.802850			0.401425	+	0.915892i	$0.368515\pi$
$422$	−168.000			−0.398104
$423$	−464.000			−1.09693
$424$			5.65685i			0.0133416i
$425$		0			0
$426$			9.89949i			0.0232383i
$427$	720.000			1.68618
$428$		−	152.735i		−	0.356858i
$429$	−72.0000	−	59.3970i	−0.167832	−	0.138454i
$430$		0			0
$431$		−	229.103i		−	0.531561i	−0.964034	−	0.265780i	$-0.914370\pi$
$431$		−	229.103i		−	0.531561i	0.964034	−	0.265780i	$-0.0856296\pi$
$432$	68.0000			0.157407
$433$	25.0000			0.0577367			0.0288684	−	0.999583i	$-0.490810\pi$
$433$	25.0000			0.0577367			0.0288684	+	0.999583i	$0.490810\pi$
$434$	204.000			0.470046
$435$		0			0
$436$			305.470i			0.700620i
$437$		−	432.749i		−	0.990273i
$438$	180.000			0.410959
$439$		−	373.352i		−	0.850461i	−0.905085	−	0.425231i	$-0.860193\pi$
$439$		−	373.352i		−	0.850461i	0.905085	−	0.425231i	$-0.139807\pi$
$440$		0			0
$441$	184.000			0.417234
$442$		−	305.470i		−	0.691109i
$443$	−257.000			−0.580135			−0.290068	−	0.957006i	$-0.593678\pi$
$443$	−257.000			−0.580135			−0.290068	+	0.957006i	$0.593678\pi$
$444$	−94.0000			−0.211712
$445$		0			0
$446$			43.8406i			0.0982974i
$447$			161.220i			0.360672i
$448$			67.8823i			0.151523i
$449$	47.0000			0.104677			0.0523385	−	0.998629i	$-0.483333\pi$
$449$	47.0000			0.104677			0.0523385	+	0.998629i	$0.483333\pi$
$450$		0			0
$451$	−72.0000	−	59.3970i	−0.159645	−	0.131701i
$452$	−2.00000			−0.00442478
$453$		−	288.500i		−	0.636864i
$454$	−132.000			−0.290749
$455$		0			0
$456$	−72.0000			−0.157895
$457$			271.529i			0.594155i	0.954853	+	0.297078i	$0.0960120\pi$
$457$			271.529i			0.594155i	−0.954853	+	0.297078i	$0.903988\pi$
$458$		−	103.238i		−	0.225410i
$459$			432.749i			0.942809i
$460$		0			0
$461$			492.146i			1.06756i	0.845623	+	0.533781i	$0.179229\pi$
$461$			492.146i			1.06756i	−0.845623	+	0.533781i	$0.820771\pi$
$462$	−84.0000	+	101.823i	−0.181818	+	0.220397i
$463$	631.000			1.36285			0.681425	−	0.731887i	$-0.261360\pi$
$463$	631.000			1.36285			0.681425	+	0.731887i	$0.261360\pi$
$464$			135.765i			0.292596i
$465$		0			0
$466$	288.000			0.618026
$467$	367.000			0.785867			0.392934	−	0.919567i	$-0.371460\pi$
$467$	367.000			0.785867			0.392934	+	0.919567i	$0.371460\pi$
$468$			135.765i			0.290095i
$469$			755.190i			1.61021i
$470$		0			0
$471$	−1.00000			−0.00212314
$472$			155.563i			0.329584i
$473$	144.000	+	118.794i	0.304440	+	0.251150i
$474$	48.0000			0.101266
$475$		0			0
$476$	−432.000			−0.907563
$477$	16.0000			0.0335430
$478$	408.000			0.853556
$479$			466.690i			0.974302i	0.873318	+	0.487151i	$0.161964\pi$
$479$			466.690i			0.974302i	−0.873318	+	0.487151i	$0.838036\pi$
$480$		0			0
$481$		−	398.808i		−	0.829123i
$482$	168.000			0.348548
$483$		−	144.250i		−	0.298654i
$484$	46.0000	+	237.588i	0.0950413	+	0.490884i
$485$		0			0
$486$		−	294.156i		−	0.605260i
$487$	511.000			1.04928			0.524641	−	0.851324i	$-0.324200\pi$
$487$	511.000			1.04928			0.524641	+	0.851324i	$0.324200\pi$
$488$	240.000			0.491803
$489$	110.000			0.224949
$490$		0			0
$491$		−	33.9411i		−	0.0691265i	−0.999403	−	0.0345633i	$-0.988996\pi$
$491$		−	33.9411i		−	0.0691265i	0.999403	−	0.0345633i	$-0.0110040\pi$
$492$		−	16.9706i		−	0.0344930i
$493$	−864.000			−1.75254
$494$		−	305.470i		−	0.618361i
$495$		0			0
$496$	68.0000			0.137097
$497$			59.3970i			0.119511i
$498$	−48.0000			−0.0963855
$499$	494.000			0.989980			0.494990	−	0.868899i	$-0.335172\pi$
$499$	494.000			0.989980			0.494990	+	0.868899i	$0.335172\pi$
$500$		0			0
$501$		−	110.309i		−	0.220177i
$502$			91.9239i			0.183115i
$503$		−	661.852i		−	1.31581i	−0.753101	−	0.657905i	$-0.771443\pi$
$503$		−	661.852i		−	1.31581i	0.753101	−	0.657905i	$-0.228557\pi$
$504$	192.000			0.380952
$505$		0			0
$506$	−204.000	−	168.291i	−0.403162	−	0.332592i
$507$	−97.0000			−0.191321
$508$			50.9117i			0.100220i
$509$	503.000			0.988212			0.494106	−	0.869402i	$-0.335495\pi$
$509$	503.000			0.988212			0.494106	+	0.869402i	$0.335495\pi$
$510$		0			0
$511$	1080.00			2.11350
$512$			22.6274i			0.0441942i
$513$			432.749i			0.843566i
$514$		−	240.416i		−	0.467736i
$515$		0			0
$516$			33.9411i			0.0657774i
$517$	406.000	−	492.146i	0.785300	−	0.951927i
$518$	−564.000			−1.08880
$519$		−	16.9706i		−	0.0326986i
$520$		0			0
$521$	−745.000			−1.42994			−0.714971	−	0.699154i	$-0.753560\pi$
$521$	−745.000			−1.42994			−0.714971	+	0.699154i	$0.753560\pi$
$522$	384.000			0.735632
$523$			330.926i			0.632746i	0.948635	+	0.316373i	$0.102465\pi$
$523$			330.926i			0.632746i	−0.948635	+	0.316373i	$0.897535\pi$
$524$		−	186.676i		−	0.356252i
$525$		0			0
$526$	444.000			0.844106
$527$			432.749i			0.821156i
$528$	−28.0000	+	33.9411i	−0.0530303	+	0.0642824i
$529$	−240.000			−0.453686
$530$		0			0
$531$	440.000			0.828625
$532$	−432.000			−0.812030
$533$	72.0000			0.135084
$534$			137.179i			0.256889i
$535$		0			0
$536$			251.730i			0.469646i
$537$	−209.000			−0.389199
$538$		−	608.112i		−	1.13032i
$539$	−161.000	+	195.161i	−0.298701	+	0.362081i
$540$		0			0
$541$			687.308i			1.27044i	0.772331	+	0.635220i	$0.219090\pi$
$541$			687.308i			1.27044i	−0.772331	+	0.635220i	$0.780910\pi$
$542$	540.000			0.996310
$543$	−119.000			−0.219153
$544$	−144.000			−0.264706
$545$		0			0
$546$		−	101.823i		−	0.186490i
$547$			831.558i			1.52021i	0.649797	+	0.760107i	$0.274854\pi$
$547$			831.558i			1.52021i	−0.649797	+	0.760107i	$0.725146\pi$
$548$	334.000			0.609489
$549$		−	678.823i		−	1.23647i
$550$		0			0
$551$	−864.000			−1.56806
$552$		−	48.0833i		−	0.0871074i
$553$	288.000			0.520796
$554$	120.000			0.216606
$555$		0			0
$556$		−	186.676i		−	0.335749i
$557$			636.396i			1.14254i	0.820761	+	0.571271i	$0.193550\pi$
$557$			636.396i			1.14254i	−0.820761	+	0.571271i	$0.806450\pi$
$558$		−	192.333i		−	0.344683i
$559$	−144.000			−0.257603
$560$		0			0
$561$	−216.000	−	178.191i	−0.385027	−	0.317631i
$562$	−192.000			−0.341637
$563$		−	780.646i		−	1.38658i	−0.720658	−	0.693291i	$-0.756160\pi$
$563$		−	780.646i		−	1.38658i	0.720658	−	0.693291i	$-0.243840\pi$
$564$	116.000			0.205674
$565$		0			0
$566$	96.0000			0.169611
$567$		−	466.690i		−	0.823087i
$568$			19.7990i			0.0348574i
$569$		−	576.999i		−	1.01406i	−0.861929	−	0.507029i	$-0.830744\pi$
$569$		−	576.999i		−	1.01406i	0.861929	−	0.507029i	$-0.169256\pi$
$570$		0			0
$571$			627.911i			1.09967i	0.835274	+	0.549834i	$0.185309\pi$
$571$			627.911i			1.09967i	−0.835274	+	0.549834i	$0.814691\pi$
$572$	−144.000	−	118.794i	−0.251748	−	0.207682i
$573$	319.000			0.556719
$574$		−	101.823i		−	0.177393i
$575$		0			0
$576$	64.0000			0.111111
$577$	385.000			0.667244			0.333622	−	0.942707i	$-0.391729\pi$
$577$	385.000			0.667244			0.333622	+	0.942707i	$0.391729\pi$
$578$		−	507.703i		−	0.878378i
$579$			16.9706i			0.0293101i
$580$		0			0
$581$	−288.000			−0.495697
$582$		−	171.120i		−	0.294020i
$583$	−14.0000	+	16.9706i	−0.0240137	+	0.0291090i
$584$	360.000			0.616438
$585$		0			0
$586$	−732.000			−1.24915
$587$	−806.000			−1.37308			−0.686542	−	0.727090i	$-0.740872\pi$
$587$	−806.000			−1.37308			−0.686542	+	0.727090i	$0.740872\pi$
$588$	−46.0000			−0.0782313
$589$			432.749i			0.734719i
$590$		0			0
$591$			101.823i			0.172290i
$592$	−188.000			−0.317568
$593$		−	152.735i		−	0.257563i	−0.991673	−	0.128782i	$-0.958893\pi$
$593$		−	152.735i		−	0.257563i	0.991673	−	0.128782i	$-0.0411066\pi$
$594$	204.000	+	168.291i	0.343434	+	0.283319i
$595$		0			0
$596$			322.441i			0.541008i
$597$	−182.000			−0.304858
$598$	204.000			0.341137
$599$	998.000			1.66611			0.833055	−	0.553190i	$-0.186590\pi$
$599$	998.000			1.66611			0.833055	+	0.553190i	$0.186590\pi$
$600$		0			0
$601$		−	755.190i		−	1.25656i	−0.777989	−	0.628278i	$-0.783760\pi$
$601$		−	755.190i		−	1.25656i	0.777989	−	0.628278i	$-0.216240\pi$
$602$			203.647i			0.338284i
$603$	712.000			1.18076
$604$		−	576.999i		−	0.955297i
$605$		0			0
$606$	12.0000			0.0198020
$607$		−	373.352i		−	0.615078i	−0.951535	−	0.307539i	$-0.900495\pi$
$607$		−	373.352i		−	0.615078i	0.951535	−	0.307539i	$-0.0995055\pi$
$608$	−144.000			−0.236842
$609$	−288.000			−0.472906
$610$		0			0
$611$			492.146i			0.805477i
$612$			407.294i			0.665512i
$613$			356.382i			0.581373i	0.956818	+	0.290687i	$0.0938837\pi$
$613$			356.382i			0.581373i	−0.956818	+	0.290687i	$0.906116\pi$
$614$	−36.0000			−0.0586319
$615$		0			0
$616$	−168.000	+	203.647i	−0.272727	+	0.330595i
$617$	−314.000			−0.508914			−0.254457	−	0.967084i	$-0.581897\pi$
$617$	−314.000			−0.508914			−0.254457	+	0.967084i	$0.581897\pi$
$618$		−	115.966i		−	0.187646i
$619$	1193.00			1.92730			0.963651	−	0.267164i	$-0.0860866\pi$
$619$	1193.00			1.92730			0.963651	+	0.267164i	$0.0860866\pi$
$620$		0			0
$621$	−289.000			−0.465378
$622$		−	217.789i		−	0.350143i
$623$			823.072i			1.32114i
$624$		−	33.9411i		−	0.0543928i
$625$		0			0
$626$		−	134.350i		−	0.214617i
$627$	−216.000	−	178.191i	−0.344498	−	0.284196i
$628$	−2.00000			−0.00318471
$629$		−	1196.42i		−	1.90211i
$630$		0			0
$631$	−439.000			−0.695721			−0.347861	−	0.937546i	$-0.613092\pi$
$631$	−439.000			−0.695721			−0.347861	+	0.937546i	$0.613092\pi$
$632$	96.0000			0.151899
$633$		−	118.794i		−	0.187668i
$634$		−	32.5269i		−	0.0513043i
$635$		0			0
$636$	−4.00000			−0.00628931
$637$		−	195.161i		−	0.306376i
$638$	−336.000	+	407.294i	−0.526646	+	0.638391i
$639$	56.0000			0.0876369
$640$		0			0
$641$	671.000			1.04680			0.523401	−	0.852087i	$-0.324663\pi$
$641$	671.000			1.04680			0.523401	+	0.852087i	$0.324663\pi$
$642$	108.000			0.168224
$643$	487.000			0.757387			0.378694	−	0.925522i	$-0.376373\pi$
$643$	487.000			0.757387			0.378694	+	0.925522i	$0.376373\pi$
$644$		−	288.500i		−	0.447981i
$645$		0			0
$646$		−	916.410i		−	1.41859i
$647$	−569.000			−0.879444			−0.439722	−	0.898134i	$-0.644923\pi$
$647$	−569.000			−0.879444			−0.439722	+	0.898134i	$0.644923\pi$
$648$		−	155.563i		−	0.240067i
$649$	−385.000	+	466.690i	−0.593220	+	0.719092i
$650$		0			0
$651$			144.250i			0.221582i
$652$	220.000			0.337423
$653$	1081.00			1.65544			0.827718	−	0.561144i	$-0.189639\pi$
$653$	1081.00			1.65544			0.827718	+	0.561144i	$0.189639\pi$
$654$	−216.000			−0.330275
$655$		0			0
$656$		−	33.9411i		−	0.0517395i
$657$		−	1018.23i		−	1.54982i
$658$	696.000			1.05775
$659$		−	780.646i		−	1.18459i	−0.805721	−	0.592296i	$-0.798222\pi$
$659$		−	780.646i		−	1.18459i	0.805721	−	0.592296i	$-0.201778\pi$
$660$		0			0
$661$	1007.00			1.52345			0.761725	−	0.647901i	$-0.224353\pi$
$661$	1007.00			1.52345			0.761725	+	0.647901i	$0.224353\pi$
$662$			261.630i			0.395211i
$663$	216.000			0.325792
$664$	−96.0000			−0.144578
$665$		0			0
$666$			531.744i			0.798415i
$667$		−	576.999i		−	0.865066i
$668$		−	220.617i		−	0.330265i
$669$	−31.0000			−0.0463378
$670$		0			0
$671$	720.000	+	593.970i	1.07303	+	0.885201i
$672$	−48.0000			−0.0714286
$673$		−	644.881i		−	0.958219i	−0.877755	−	0.479109i	$-0.840960\pi$
$673$		−	644.881i		−	0.958219i	0.877755	−	0.479109i	$-0.159040\pi$
$674$	−12.0000			−0.0178042
$675$		0			0
$676$	−194.000			−0.286982
$677$		−	873.984i		−	1.29097i	−0.763775	−	0.645483i	$-0.776656\pi$
$677$		−	873.984i		−	1.29097i	0.763775	−	0.645483i	$-0.223344\pi$
$678$		−	1.41421i		−	0.00208586i
$679$		−	1026.72i		−	1.51210i
$680$		0			0
$681$		−	93.3381i		−	0.137060i
$682$	204.000	+	168.291i	0.299120	+	0.246762i
$683$	610.000			0.893119			0.446559	−	0.894754i	$-0.352649\pi$
$683$	610.000			0.893119			0.446559	+	0.894754i	$0.352649\pi$
$684$			407.294i			0.595458i
$685$		0			0
$686$	312.000			0.454810
$687$	73.0000			0.106259
$688$			67.8823i			0.0986661i
$689$		−	16.9706i		−	0.0246307i
$690$		0			0
$691$	−1255.00			−1.81621			−0.908104	−	0.418744i	$-0.862470\pi$
$691$	−1255.00			−1.81621			−0.908104	+	0.418744i	$0.862470\pi$
$692$		−	33.9411i		−	0.0490479i
$693$	576.000	+	475.176i	0.831169	+	0.685679i
$694$	−300.000			−0.432277
$695$		0			0
$696$	−96.0000			−0.137931
$697$	216.000			0.309900
$698$	−372.000			−0.532951
$699$			203.647i			0.291340i
$700$		0			0
$701$			76.3675i			0.108941i	0.998515	+	0.0544704i	$0.0173471\pi$
$701$			76.3675i			0.108941i	−0.998515	+	0.0544704i	$0.982653\pi$
$702$	−204.000			−0.290598
$703$		−	1196.42i		−	1.70188i
$704$	−56.0000	+	67.8823i	−0.0795455	+	0.0964237i
$705$		0			0
$706$		−	236.174i		−	0.334524i
$707$	72.0000			0.101839
$708$	−110.000			−0.155367
$709$	455.000			0.641749			0.320874	−	0.947122i	$-0.396023\pi$
$709$	455.000			0.641749			0.320874	+	0.947122i	$0.396023\pi$
$710$		0			0
$711$		−	271.529i		−	0.381897i
$712$			274.357i			0.385333i
$713$	−289.000			−0.405330
$714$		−	305.470i		−	0.427829i
$715$		0			0
$716$	−418.000			−0.583799
$717$			288.500i			0.402370i
$718$	−900.000			−1.25348
$719$	−223.000			−0.310153			−0.155076	−	0.987902i	$-0.549562\pi$
$719$	−223.000			−0.310153			−0.155076	+	0.987902i	$0.549562\pi$
$720$		0			0
$721$		−	695.793i		−	0.965039i
$722$		−	405.879i		−	0.562160i
$723$			118.794i			0.164307i
$724$	−238.000			−0.328729
$725$		0			0
$726$	−168.000	+	32.5269i	−0.231405	+	0.0448029i
$727$	535.000			0.735901			0.367950	−	0.929845i	$-0.380060\pi$
$727$	535.000			0.735901			0.367950	+	0.929845i	$0.380060\pi$
$728$		−	203.647i		−	0.279735i
$729$	−287.000			−0.393690
$730$		0			0
$731$	−432.000			−0.590971
$732$			169.706i			0.231838i
$733$		−	627.911i		−	0.856631i	−0.903629	−	0.428316i	$-0.859107\pi$
$733$		−	627.911i		−	0.856631i	0.903629	−	0.428316i	$-0.140893\pi$
$734$			858.428i			1.16952i
$735$		0			0
$736$		−	96.1665i		−	0.130661i
$737$	−623.000	+	755.190i	−0.845319	+	1.02468i
$738$	−96.0000			−0.130081
$739$		−	865.499i		−	1.17118i	−0.810609	−	0.585588i	$-0.800864\pi$
$739$		−	865.499i		−	1.17118i	0.810609	−	0.585588i	$-0.199136\pi$
$740$		0			0
$741$	216.000			0.291498
$742$	−24.0000			−0.0323450
$743$			1154.00i			1.55316i	0.630018	+	0.776580i	$0.283047\pi$
$743$			1154.00i			1.55316i	−0.630018	+	0.776580i	$0.716953\pi$
$744$			48.0833i			0.0646280i
$745$		0			0
$746$	492.000			0.659517
$747$			271.529i			0.363493i
$748$	−432.000	−	356.382i	−0.577540	−	0.476446i
$749$	648.000			0.865154
$750$		0			0
$751$	−55.0000			−0.0732357			−0.0366178	−	0.999329i	$-0.511658\pi$
$751$	−55.0000			−0.0732357			−0.0366178	+	0.999329i	$0.511658\pi$
$752$	232.000			0.308511
$753$	−65.0000			−0.0863214
$754$		−	407.294i		−	0.540177i
$755$		0			0
$756$			288.500i			0.381613i
$757$	−2.00000			−0.00264201			−0.00132100	−	0.999999i	$-0.500420\pi$
$757$	−2.00000			−0.00264201			−0.00132100	+	0.999999i	$0.500420\pi$
$758$		−	417.193i		−	0.550387i
$759$	119.000	−	144.250i	0.156785	−	0.190052i
$760$		0			0
$761$			1264.31i			1.66138i	0.556738	+	0.830688i	$0.312053\pi$
$761$			1264.31i			1.66138i	−0.556738	+	0.830688i	$0.687947\pi$
$762$	−36.0000			−0.0472441
$763$	−1296.00			−1.69856
$764$	638.000			0.835079
$765$		0			0
$766$		−	533.159i		−	0.696029i
$767$		−	466.690i		−	0.608462i
$768$	−16.0000			−0.0208333
$769$			602.455i			0.783426i	0.920087	+	0.391713i	$0.128117\pi$
$769$			602.455i			0.783426i	−0.920087	+	0.391713i	$0.871883\pi$
$770$		0			0
$771$	170.000			0.220493
$772$			33.9411i			0.0439652i
$773$	1222.00			1.58085			0.790427	−	0.612556i	$-0.209859\pi$
$773$	1222.00			1.58085			0.790427	+	0.612556i	$0.209859\pi$
$774$	192.000			0.248062
$775$		0			0
$776$		−	342.240i		−	0.441031i
$777$		−	398.808i		−	0.513267i
$778$		−	171.120i		−	0.219948i
$779$	216.000			0.277279
$780$		0			0
$781$	−49.0000	+	59.3970i	−0.0627401	+	0.0760525i
$782$	612.000			0.782609
$783$			576.999i			0.736908i
$784$	−92.0000			−0.117347
$785$		0			0
$786$	132.000			0.167939
$787$			899.440i			1.14287i	0.820647	+	0.571436i	$0.193613\pi$
$787$			899.440i			1.14287i	−0.820647	+	0.571436i	$0.806387\pi$
$788$			203.647i			0.258435i
$789$			313.955i			0.397916i
$790$		0			0
$791$		−	8.48528i		−	0.0107273i
$792$	192.000	+	158.392i	0.242424	+	0.199990i
$793$	−720.000			−0.907945
$794$		−	817.415i		−	1.02949i
$795$		0			0
$796$	−364.000			−0.457286
$797$	289.000			0.362610			0.181305	−	0.983427i	$-0.441968\pi$
$797$	289.000			0.362610			0.181305	+	0.983427i	$0.441968\pi$
$798$		−	305.470i		−	0.382795i
$799$			1476.44i			1.84786i
$800$		0			0
$801$	776.000			0.968789
$802$		−	777.817i		−	0.969847i
$803$	1080.00	+	890.955i	1.34496	+	1.10953i
$804$	−178.000			−0.221393
$805$		0			0
$806$	−204.000			−0.253102
$807$	430.000			0.532838
$808$	24.0000			0.0297030
$809$			229.103i			0.283192i	0.989925	+	0.141596i	$0.0452234\pi$
$809$			229.103i			0.283192i	−0.989925	+	0.141596i	$0.954777\pi$
$810$		0			0
$811$			763.675i			0.941647i	0.882228	+	0.470823i	$0.156043\pi$
$811$			763.675i			0.941647i	−0.882228	+	0.470823i	$0.843957\pi$
$812$	−576.000			−0.709360
$813$			381.838i			0.469665i
$814$	−564.000	−	465.276i	−0.692875	−	0.571592i
$815$		0			0
$816$		−	101.823i		−	0.124784i
$817$	−432.000			−0.528764
$818$	840.000			1.02689
$819$	−576.000			−0.703297
$820$		0			0
$821$			593.970i			0.723471i	0.932281	+	0.361736i	$0.117816\pi$
$821$			593.970i			0.723471i	−0.932281	+	0.361736i	$0.882184\pi$
$822$			236.174i			0.287316i
$823$	−305.000			−0.370595			−0.185298	−	0.982682i	$-0.559325\pi$
$823$	−305.000			−0.370595			−0.185298	+	0.982682i	$0.559325\pi$
$824$		−	231.931i		−	0.281470i
$825$		0			0
$826$	−660.000			−0.799031
$827$		−	585.484i		−	0.707962i	−0.935253	−	0.353981i	$-0.884828\pi$
$827$		−	585.484i		−	0.707962i	0.935253	−	0.353981i	$-0.115172\pi$
$828$	−272.000			−0.328502
$829$	119.000			0.143546			0.0717732	−	0.997421i	$-0.477134\pi$
$829$	119.000			0.143546			0.0717732	+	0.997421i	$0.477134\pi$
$830$		0			0
$831$			84.8528i			0.102109i
$832$		−	67.8823i		−	0.0815892i
$833$		−	585.484i		−	0.702862i
$834$	132.000			0.158273
$835$		0			0
$836$	−432.000	−	356.382i	−0.516746	−	0.426294i
$837$	289.000			0.345281
$838$		−	523.259i		−	0.624414i
$839$	−1615.00			−1.92491			−0.962455	−	0.271440i	$-0.912500\pi$
$839$	−1615.00			−1.92491			−0.962455	+	0.271440i	$0.912500\pi$
$840$		0			0
$841$	−311.000			−0.369798
$842$			478.004i			0.567701i
$843$		−	135.765i		−	0.161049i
$844$		−	237.588i		−	0.281502i
$845$		0			0
$846$		−	656.195i		−	0.775644i
$847$	−1008.00	+	195.161i	−1.19008	+	0.230415i
$848$	−8.00000			−0.00943396
$849$			67.8823i			0.0799555i
$850$		0			0
$851$	799.000			0.938895
$852$	−14.0000			−0.0164319
$853$			1086.12i			1.27329i	0.771157	+	0.636645i	$0.219678\pi$
$853$			1086.12i			1.27329i	−0.771157	+	0.636645i	$0.780322\pi$
$854$			1018.23i			1.19231i
$855$		0			0
$856$	216.000			0.252336
$857$		−	1001.26i		−	1.16834i	−0.811633	−	0.584168i	$-0.801421\pi$
$857$		−	1001.26i		−	1.16834i	0.811633	−	0.584168i	$-0.198579\pi$
$858$	84.0000	−	101.823i	0.0979021	−	0.118675i
$859$	593.000			0.690338			0.345169	−	0.938541i	$-0.387822\pi$
$859$	593.000			0.690338			0.345169	+	0.938541i	$0.387822\pi$
$860$		0			0
$861$	72.0000			0.0836237
$862$	324.000			0.375870
$863$	−1190.00			−1.37891			−0.689455	−	0.724328i	$-0.742150\pi$
$863$	−1190.00			−1.37891			−0.689455	+	0.724328i	$0.742150\pi$
$864$			96.1665i			0.111304i
$865$		0			0
$866$			35.3553i			0.0408260i
$867$	359.000			0.414072
$868$			288.500i			0.332373i
$869$	288.000	+	237.588i	0.331415	+	0.273404i
$870$		0			0
$871$		−	755.190i		−	0.867038i
$872$	−432.000			−0.495413
$873$	−968.000			−1.10882
$874$	612.000			0.700229
$875$		0			0
$876$			254.558i			0.290592i
$877$			924.896i			1.05461i	0.849675	+	0.527307i	$0.176798\pi$
$877$			924.896i			1.05461i	−0.849675	+	0.527307i	$0.823202\pi$
$878$	528.000			0.601367
$879$		−	517.602i		−	0.588853i
$880$		0			0
$881$	263.000			0.298524			0.149262	−	0.988798i	$-0.452310\pi$
$881$	263.000			0.298524			0.149262	+	0.988798i	$0.452310\pi$
$882$			260.215i			0.295029i
$883$	394.000			0.446206			0.223103	−	0.974795i	$-0.428381\pi$
$883$	394.000			0.446206			0.223103	+	0.974795i	$0.428381\pi$
$884$	432.000			0.488688
$885$		0			0
$886$		−	363.453i		−	0.410218i
$887$		−	16.9706i		−	0.0191325i	−0.999954	−	0.00956627i	$-0.996955\pi$
$887$		−	16.9706i		−	0.0191325i	0.999954	−	0.00956627i	$-0.00304508\pi$
$888$		−	132.936i		−	0.149703i
$889$	−216.000			−0.242970
$890$		0			0
$891$	385.000	−	466.690i	0.432099	−	0.523783i
$892$	−62.0000			−0.0695067
$893$			1476.44i			1.65335i
$894$	−228.000			−0.255034
$895$		0			0
$896$	−96.0000			−0.107143
$897$			144.250i			0.160814i
$898$			66.4680i			0.0740179i
$899$			576.999i			0.641823i
$900$		0			0
$901$		−	50.9117i		−	0.0565058i
$902$	84.0000	−	101.823i	0.0931264	−	0.112886i
$903$	−144.000			−0.159468
$904$		−	2.82843i		−	0.00312879i
$905$		0			0
$906$	408.000			0.450331
$907$	418.000			0.460860			0.230430	−	0.973089i	$-0.425987\pi$
$907$	418.000			0.460860			0.230430	+	0.973089i	$0.425987\pi$
$908$		−	186.676i		−	0.205591i
$909$		−	67.8823i		−	0.0746779i
$910$		0			0
$911$	−490.000			−0.537870			−0.268935	−	0.963158i	$-0.586672\pi$
$911$	−490.000			−0.537870			−0.268935	+	0.963158i	$0.586672\pi$
$912$		−	101.823i		−	0.111648i
$913$	−288.000	−	237.588i	−0.315444	−	0.260228i
$914$	−384.000			−0.420131
$915$		0			0
$916$	146.000			0.159389
$917$	792.000			0.863686
$918$	−612.000			−0.666667
$919$			610.940i			0.664788i	0.943141	+	0.332394i	$0.107856\pi$
$919$			610.940i			0.664788i	−0.943141	+	0.332394i	$0.892144\pi$
$920$		0			0
$921$		−	25.4558i		−	0.0276394i
$922$	−696.000			−0.754881
$923$		−	59.3970i		−	0.0643521i
$924$	−144.000	−	118.794i	−0.155844	−	0.128565i
$925$		0			0
$926$			892.369i			0.963681i
$927$	−656.000			−0.707659
$928$	−192.000			−0.206897
$929$	−742.000			−0.798708			−0.399354	−	0.916797i	$-0.630766\pi$
$929$	−742.000			−0.798708			−0.399354	+	0.916797i	$0.630766\pi$
$930$		0			0
$931$		−	585.484i		−	0.628877i
$932$			407.294i			0.437010i
$933$	154.000			0.165059
$934$			519.016i			0.555692i
$935$		0			0
$936$	−192.000			−0.205128
$937$			1196.42i			1.27687i	0.769677	+	0.638434i	$0.220417\pi$
$937$			1196.42i			1.27687i	−0.769677	+	0.638434i	$0.779583\pi$
$938$	−1068.00			−1.13859
$939$	95.0000			0.101171
$940$		0			0
$941$		−	135.765i		−	0.144277i	−0.997395	−	0.0721384i	$-0.977018\pi$
$941$		−	135.765i		−	0.144277i	0.997395	−	0.0721384i	$-0.0229823\pi$
$942$		−	1.41421i		−	0.00150129i
$943$			144.250i			0.152969i
$944$	−220.000			−0.233051
$945$		0			0
$946$	−168.000	+	203.647i	−0.177590	+	0.215271i
$947$	−113.000			−0.119324			−0.0596621	−	0.998219i	$-0.519002\pi$
$947$	−113.000			−0.119324			−0.0596621	+	0.998219i	$0.519002\pi$
$948$			67.8823i			0.0716057i
$949$	−1080.00			−1.13804
$950$		0			0
$951$	23.0000			0.0241851
$952$		−	610.940i		−	0.641744i
$953$		−	25.4558i		−	0.0267113i	−0.999911	−	0.0133556i	$-0.995749\pi$
$953$		−	25.4558i		−	0.0267113i	0.999911	−	0.0133556i	$-0.00425136\pi$
$954$			22.6274i			0.0237185i
$955$		0			0
$956$			576.999i			0.603556i
$957$	−288.000	−	237.588i	−0.300940	−	0.248263i
$958$	−660.000			−0.688935
$959$			1417.04i			1.47762i
$960$		0			0
$961$	−672.000			−0.699272
$962$	564.000			0.586279
$963$		−	610.940i		−	0.634414i
$964$			237.588i			0.246460i
$965$		0			0
$966$	204.000			0.211180
$967$			339.411i			0.350994i	0.984480	+	0.175497i	$0.0561532\pi$
$967$			339.411i			0.350994i	−0.984480	+	0.175497i	$0.943847\pi$
$968$	−336.000	+	65.0538i	−0.347107	+	0.0672044i
$969$	648.000			0.668731
$970$		0			0
$971$	569.000			0.585994			0.292997	−	0.956113i	$-0.405347\pi$
$971$	569.000			0.585994			0.292997	+	0.956113i	$0.405347\pi$
$972$	416.000			0.427984
$973$	792.000			0.813977
$974$			722.663i			0.741954i
$975$		0			0
$976$			339.411i			0.347757i
$977$	649.000			0.664278			0.332139	−	0.943230i	$-0.392230\pi$
$977$	649.000			0.664278			0.332139	+	0.943230i	$0.392230\pi$
$978$			155.563i			0.159063i
$979$	−679.000	+	823.072i	−0.693565	+	0.840728i
$980$		0			0
$981$			1221.88i			1.24555i
$982$	48.0000			0.0488798
$983$	175.000			0.178026			0.0890132	−	0.996030i	$-0.471629\pi$
$983$	175.000			0.178026			0.0890132	+	0.996030i	$0.471629\pi$
$984$	24.0000			0.0243902
$985$		0			0
$986$		−	1221.88i		−	1.23923i
$987$			492.146i			0.498628i
$988$	432.000			0.437247
$989$		−	288.500i		−	0.291708i
$990$		0			0
$991$	1334.00			1.34612			0.673058	−	0.739590i	$-0.264981\pi$
$991$	1334.00			1.34612			0.673058	+	0.739590i	$0.264981\pi$
$992$			96.1665i			0.0969421i
$993$	−185.000			−0.186304
$994$	−84.0000			−0.0845070
$995$		0			0
$996$		−	67.8823i		−	0.0681549i
$997$			1111.57i			1.11492i	0.830205	+	0.557458i	$0.188223\pi$
$997$			1111.57i			1.11492i	−0.830205	+	0.557458i	$0.811777\pi$
$998$			698.621i			0.700022i
$999$	−799.000			−0.799800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.3.d.a.351.2		2
5.2	odd	4		550.3.c.a.549.2		4
5.3	odd	4		550.3.c.a.549.3		4
5.4	even	2		22.3.b.a.21.1	✓	2
11.10	odd	2	inner	550.3.d.a.351.1		2
15.14	odd	2		198.3.d.b.109.2		2
20.19	odd	2		176.3.h.c.65.1		2
35.34	odd	2		1078.3.d.a.197.1		2
40.19	odd	2		704.3.h.e.65.1		2
40.29	even	2		704.3.h.d.65.2		2
55.4	even	10		242.3.d.b.215.2		8
55.9	even	10		242.3.d.b.161.1		8
55.14	even	10		242.3.d.b.233.1		8
55.19	odd	10		242.3.d.b.233.2		8
55.24	odd	10		242.3.d.b.161.2		8
55.29	odd	10		242.3.d.b.215.1		8
55.32	even	4		550.3.c.a.549.4		4
55.39	odd	10		242.3.d.b.239.1		8
55.43	even	4		550.3.c.a.549.1		4
55.49	even	10		242.3.d.b.239.2		8
55.54	odd	2		22.3.b.a.21.2	yes	2
60.59	even	2		1584.3.j.d.1297.1		2
165.164	even	2		198.3.d.b.109.1		2
220.219	even	2		176.3.h.c.65.2		2
385.384	even	2		1078.3.d.a.197.2		2
440.109	odd	2		704.3.h.d.65.1		2
440.219	even	2		704.3.h.e.65.2		2
660.659	odd	2		1584.3.j.d.1297.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.3.b.a.21.1	✓	2	5.4	even	2
22.3.b.a.21.2	yes	2	55.54	odd	2
176.3.h.c.65.1		2	20.19	odd	2
176.3.h.c.65.2		2	220.219	even	2
198.3.d.b.109.1		2	165.164	even	2
198.3.d.b.109.2		2	15.14	odd	2
242.3.d.b.161.1		8	55.9	even	10
242.3.d.b.161.2		8	55.24	odd	10
242.3.d.b.215.1		8	55.29	odd	10
242.3.d.b.215.2		8	55.4	even	10
242.3.d.b.233.1		8	55.14	even	10
242.3.d.b.233.2		8	55.19	odd	10
242.3.d.b.239.1		8	55.39	odd	10
242.3.d.b.239.2		8	55.49	even	10
550.3.c.a.549.1		4	55.43	even	4
550.3.c.a.549.2		4	5.2	odd	4
550.3.c.a.549.3		4	5.3	odd	4
550.3.c.a.549.4		4	55.32	even	4
550.3.d.a.351.1		2	11.10	odd	2	inner
550.3.d.a.351.2		2	1.1	even	1	trivial
704.3.h.d.65.1		2	440.109	odd	2
704.3.h.d.65.2		2	40.29	even	2
704.3.h.e.65.1		2	40.19	odd	2
704.3.h.e.65.2		2	440.219	even	2
1078.3.d.a.197.1		2	35.34	odd	2
1078.3.d.a.197.2		2	385.384	even	2
1584.3.j.d.1297.1		2	60.59	even	2
1584.3.j.d.1297.2		2	660.659	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	550.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.00000 q^{3} -2.00000 q^{4} -1.41421i q^{6} -8.48528i q^{7} -2.82843i q^{8} -8.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.00000 q^{3} -2.00000 q^{4} -1.41421i q^{6} -8.48528i q^{7} -2.82843i q^{8} -8.00000 q^{9} +(7.00000 - 8.48528i) q^{11} +2.00000 q^{12} +8.48528i q^{13} +12.0000 q^{14} +4.00000 q^{16} +25.4558i q^{17} -11.3137i q^{18} +25.4558i q^{19} +8.48528i q^{21} +(12.0000 + 9.89949i) q^{22} -17.0000 q^{23} +2.82843i q^{24} -12.0000 q^{26} +17.0000 q^{27} +16.9706i q^{28} +33.9411i q^{29} +17.0000 q^{31} +5.65685i q^{32} +(-7.00000 + 8.48528i) q^{33} -36.0000 q^{34} +16.0000 q^{36} -47.0000 q^{37} -36.0000 q^{38} -8.48528i q^{39} -8.48528i q^{41} -12.0000 q^{42} +16.9706i q^{43} +(-14.0000 + 16.9706i) q^{44} -24.0416i q^{46} +58.0000 q^{47} -4.00000 q^{48} -23.0000 q^{49} -25.4558i q^{51} -16.9706i q^{52} -2.00000 q^{53} +24.0416i q^{54} -24.0000 q^{56} -25.4558i q^{57} -48.0000 q^{58} -55.0000 q^{59} +84.8528i q^{61} +24.0416i q^{62} +67.8823i q^{63} -8.00000 q^{64} +(-12.0000 - 9.89949i) q^{66} -89.0000 q^{67} -50.9117i q^{68} +17.0000 q^{69} -7.00000 q^{71} +22.6274i q^{72} +127.279i q^{73} -66.4680i q^{74} -50.9117i q^{76} +(-72.0000 - 59.3970i) q^{77} +12.0000 q^{78} +33.9411i q^{79} +55.0000 q^{81} +12.0000 q^{82} -33.9411i q^{83} -16.9706i q^{84} -24.0000 q^{86} -33.9411i q^{87} +(-24.0000 - 19.7990i) q^{88} -97.0000 q^{89} +72.0000 q^{91} +34.0000 q^{92} -17.0000 q^{93} +82.0244i q^{94} -5.65685i q^{96} +121.000 q^{97} -32.5269i q^{98} +(-56.0000 + 67.8823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{4} - 16 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 4 * q^4 - 16 * q^9	\( 2 q - 2 q^{3} - 4 q^{4} - 16 q^{9} + 14 q^{11} + 4 q^{12} + 24 q^{14} + 8 q^{16} + 24 q^{22} - 34 q^{23} - 24 q^{26} + 34 q^{27} + 34 q^{31} - 14 q^{33} - 72 q^{34} + 32 q^{36} - 94 q^{37} - 72 q^{38} - 24 q^{42} - 28 q^{44} + 116 q^{47} - 8 q^{48} - 46 q^{49} - 4 q^{53} - 48 q^{56} - 96 q^{58} - 110 q^{59} - 16 q^{64} - 24 q^{66} - 178 q^{67} + 34 q^{69} - 14 q^{71} - 144 q^{77} + 24 q^{78} + 110 q^{81} + 24 q^{82} - 48 q^{86} - 48 q^{88} - 194 q^{89} + 144 q^{91} + 68 q^{92} - 34 q^{93} + 242 q^{97} - 112 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^4 - 16 * q^9 + 14 * q^11 + 4 * q^12 + 24 * q^14 + 8 * q^16 + 24 * q^22 - 34 * q^23 - 24 * q^26 + 34 * q^27 + 34 * q^31 - 14 * q^33 - 72 * q^34 + 32 * q^36 - 94 * q^37 - 72 * q^38 - 24 * q^42 - 28 * q^44 + 116 * q^47 - 8 * q^48 - 46 * q^49 - 4 * q^53 - 48 * q^56 - 96 * q^58 - 110 * q^59 - 16 * q^64 - 24 * q^66 - 178 * q^67 + 34 * q^69 - 14 * q^71 - 144 * q^77 + 24 * q^78 + 110 * q^81 + 24 * q^82 - 48 * q^86 - 48 * q^88 - 194 * q^89 + 144 * q^91 + 68 * q^92 - 34 * q^93 + 242 * q^97 - 112 * q^99

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