LMFDB - Embedded newform 1045.2.b.d.419.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.4
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.d.419.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.06343i q^{2} -3.28666i q^{3} -2.25776 q^{4} +(0.951609 - 2.02347i) q^{5} -6.78181 q^{6} +3.51972i q^{7} +0.531875i q^{8} -7.80213 q^{9} +O(q^{10})$	\(q-2.06343i q^{2} -3.28666i q^{3} -2.25776 q^{4} +(0.951609 - 2.02347i) q^{5} -6.78181 q^{6} +3.51972i q^{7} +0.531875i q^{8} -7.80213 q^{9} +(-4.17530 - 1.96358i) q^{10} -1.00000 q^{11} +7.42049i q^{12} -6.22938i q^{13} +7.26272 q^{14} +(-6.65046 - 3.12762i) q^{15} -3.41803 q^{16} -0.355073i q^{17} +16.0992i q^{18} +1.00000 q^{19} +(-2.14851 + 4.56852i) q^{20} +11.5681 q^{21} +2.06343i q^{22} +2.52714i q^{23} +1.74809 q^{24} +(-3.18888 - 3.85111i) q^{25} -12.8539 q^{26} +15.7829i q^{27} -7.94670i q^{28} +10.2445 q^{29} +(-6.45363 + 13.7228i) q^{30} +3.86688 q^{31} +8.11664i q^{32} +3.28666i q^{33} -0.732669 q^{34} +(7.12207 + 3.34940i) q^{35} +17.6153 q^{36} -1.98749i q^{37} -2.06343i q^{38} -20.4739 q^{39} +(1.07623 + 0.506137i) q^{40} -3.07818 q^{41} -23.8701i q^{42} +1.96877i q^{43} +2.25776 q^{44} +(-7.42458 + 15.7874i) q^{45} +5.21459 q^{46} +5.25337i q^{47} +11.2339i q^{48} -5.38846 q^{49} +(-7.94651 + 6.58004i) q^{50} -1.16700 q^{51} +14.0645i q^{52} -6.40350i q^{53} +32.5671 q^{54} +(-0.951609 + 2.02347i) q^{55} -1.87205 q^{56} -3.28666i q^{57} -21.1388i q^{58} -3.13558 q^{59} +(15.0152 + 7.06141i) q^{60} +6.01417 q^{61} -7.97906i q^{62} -27.4613i q^{63} +9.91209 q^{64} +(-12.6050 - 5.92794i) q^{65} +6.78181 q^{66} -5.90311i q^{67} +0.801669i q^{68} +8.30585 q^{69} +(6.91127 - 14.6959i) q^{70} +7.16983 q^{71} -4.14976i q^{72} -16.2081i q^{73} -4.10106 q^{74} +(-12.6573 + 10.4808i) q^{75} -2.25776 q^{76} -3.51972i q^{77} +42.2465i q^{78} -6.41286 q^{79} +(-3.25263 + 6.91630i) q^{80} +28.4668 q^{81} +6.35163i q^{82} +5.77215i q^{83} -26.1181 q^{84} +(-0.718479 - 0.337890i) q^{85} +4.06243 q^{86} -33.6701i q^{87} -0.531875i q^{88} -12.1514 q^{89} +(32.5762 + 15.3201i) q^{90} +21.9257 q^{91} -5.70568i q^{92} -12.7091i q^{93} +10.8400 q^{94} +(0.951609 - 2.02347i) q^{95} +26.6766 q^{96} +0.839854i q^{97} +11.1187i q^{98} +7.80213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	2.06343i		−	1.45907i	−0.683944	−	0.729534i	$-0.739737\pi$
$2$		−	2.06343i		−	1.45907i	0.683944	−	0.729534i	$-0.260263\pi$
$3$		−	3.28666i		−	1.89755i	−0.315948	−	0.948777i	$-0.602322\pi$
$3$		−	3.28666i		−	1.89755i	0.315948	−	0.948777i	$-0.397678\pi$
$4$	−2.25776			−1.12888
$5$	0.951609	−	2.02347i	0.425573	−	0.904924i
$5$	0.951609	−	2.02347i	0.425573	−	0.904924i
$6$	−6.78181			−2.76866
$7$			3.51972i			1.33033i	0.746696	+	0.665165i	$0.231639\pi$
$7$			3.51972i			1.33033i	−0.746696	+	0.665165i	$0.768361\pi$
$8$			0.531875i			0.188046i
$9$	−7.80213			−2.60071
$10$	−4.17530	−	1.96358i	−1.32035	−	0.620940i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			7.42049i			2.14211i
$13$		−	6.22938i		−	1.72772i	−0.503732	−	0.863860i	$-0.668040\pi$
$13$		−	6.22938i		−	1.72772i	0.503732	−	0.863860i	$-0.331960\pi$
$14$	7.26272			1.94104
$15$	−6.65046	−	3.12762i	−1.71714	−	0.807547i
$16$	−3.41803			−0.854509
$17$		−	0.355073i		−	0.0861178i	−0.999073	−	0.0430589i	$-0.986290\pi$
$17$		−	0.355073i		−	0.0861178i	0.999073	−	0.0430589i	$-0.0137103\pi$
$18$			16.0992i			3.79461i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−2.14851	+	4.56852i	−0.480421	+	1.02155i
$21$	11.5681			2.52437
$22$			2.06343i			0.439926i
$23$			2.52714i			0.526945i	0.964667	+	0.263473i	$0.0848679\pi$
$23$			2.52714i			0.526945i	−0.964667	+	0.263473i	$0.915132\pi$
$24$	1.74809			0.356828
$25$	−3.18888	−	3.85111i	−0.637776	−	0.770222i
$26$	−12.8539			−2.52086
$27$			15.7829i			3.03743i
$28$		−	7.94670i		−	1.50179i
$29$	10.2445			1.90235			0.951175	−	0.308653i	$-0.0998782\pi$
$29$	10.2445			1.90235			0.951175	+	0.308653i	$0.0998782\pi$
$30$	−6.45363	+	13.7228i	−1.17827	+	2.50543i
$31$	3.86688			0.694513			0.347256	−	0.937770i	$-0.387113\pi$
$31$	3.86688			0.694513			0.347256	+	0.937770i	$0.387113\pi$
$32$			8.11664i			1.43483i
$33$			3.28666i			0.572134i
$34$	−0.732669			−0.125652
$35$	7.12207	+	3.34940i	1.20385	+	0.566152i
$36$	17.6153			2.93589
$37$		−	1.98749i		−	0.326742i	−0.986565	−	0.163371i	$-0.947763\pi$
$37$		−	1.98749i		−	0.326742i	0.986565	−	0.163371i	$-0.0522368\pi$
$38$		−	2.06343i		−	0.334733i
$39$	−20.4739			−3.27844
$40$	1.07623	+	0.506137i	0.170168	+	0.0800274i
$41$	−3.07818			−0.480731			−0.240366	−	0.970682i	$-0.577267\pi$
$41$	−3.07818			−0.480731			−0.240366	+	0.970682i	$0.577267\pi$
$42$		−	23.8701i		−	3.68323i
$43$			1.96877i			0.300235i	0.988668	+	0.150118i	$0.0479652\pi$
$43$			1.96877i			0.300235i	−0.988668	+	0.150118i	$0.952035\pi$
$44$	2.25776			0.340370
$45$	−7.42458	+	15.7874i	−1.10679	+	2.35344i
$46$	5.21459			0.768849
$47$			5.25337i			0.766283i	0.923690	+	0.383141i	$0.125158\pi$
$47$			5.25337i			0.766283i	−0.923690	+	0.383141i	$0.874842\pi$
$48$			11.2339i			1.62148i
$49$	−5.38846			−0.769780
$50$	−7.94651	+	6.58004i	−1.12381	+	0.930559i
$51$	−1.16700			−0.163413
$52$			14.0645i			1.95039i
$53$		−	6.40350i		−	0.879589i	−0.898099	−	0.439794i	$-0.855051\pi$
$53$		−	6.40350i		−	0.879589i	0.898099	−	0.439794i	$-0.144949\pi$
$54$	32.5671			4.43182
$55$	−0.951609	+	2.02347i	−0.128315	+	0.272845i
$56$	−1.87205			−0.250164
$57$		−	3.28666i		−	0.435329i
$58$		−	21.1388i		−	2.77566i
$59$	−3.13558			−0.408218			−0.204109	−	0.978948i	$-0.565430\pi$
$59$	−3.13558			−0.408218			−0.204109	+	0.978948i	$0.565430\pi$
$60$	15.0152	+	7.06141i	1.93845	+	0.911624i
$61$	6.01417			0.770035			0.385018	−	0.922909i	$-0.374195\pi$
$61$	6.01417			0.770035			0.385018	+	0.922909i	$0.374195\pi$
$62$		−	7.97906i		−	1.01334i
$63$		−	27.4613i		−	3.45980i
$64$	9.91209			1.23901
$65$	−12.6050	−	5.92794i	−1.56346	−	0.735271i
$66$	6.78181			0.834783
$67$		−	5.90311i		−	0.721180i	−0.932724	−	0.360590i	$-0.882575\pi$
$67$		−	5.90311i		−	0.721180i	0.932724	−	0.360590i	$-0.117425\pi$
$68$			0.801669i			0.0972167i
$69$	8.30585			0.999907
$70$	6.91127	−	14.6959i	0.826055	−	1.75650i
$71$	7.16983			0.850903			0.425451	−	0.904981i	$-0.360115\pi$
$71$	7.16983			0.850903			0.425451	+	0.904981i	$0.360115\pi$
$72$		−	4.14976i		−	0.489054i
$73$		−	16.2081i		−	1.89701i	−0.316759	−	0.948506i	$-0.602595\pi$
$73$		−	16.2081i		−	1.89701i	0.316759	−	0.948506i	$-0.397405\pi$
$74$	−4.10106			−0.476739
$75$	−12.6573	+	10.4808i	−1.46154	+	1.21021i
$76$	−2.25776			−0.258983
$77$		−	3.51972i		−	0.401110i
$78$			42.2465i			4.78347i
$79$	−6.41286			−0.721503			−0.360752	−	0.932662i	$-0.617480\pi$
$79$	−6.41286			−0.721503			−0.360752	+	0.932662i	$0.617480\pi$
$80$	−3.25263	+	6.91630i	−0.363655	+	0.773266i
$81$	28.4668			3.16298
$82$			6.35163i			0.701420i
$83$			5.77215i			0.633575i	0.948496	+	0.316788i	$0.102604\pi$
$83$			5.77215i			0.633575i	−0.948496	+	0.316788i	$0.897396\pi$
$84$	−26.1181			−2.84972
$85$	−0.718479	−	0.337890i	−0.0779300	−	0.0366494i
$86$	4.06243			0.438063
$87$		−	33.6701i		−	3.60981i
$88$		−	0.531875i		−	0.0566981i
$89$	−12.1514			−1.28805			−0.644025	−	0.765004i	$-0.722737\pi$
$89$	−12.1514			−1.28805			−0.644025	+	0.765004i	$0.722737\pi$
$90$	32.5762	+	15.3201i	3.43384	+	1.61488i
$91$	21.9257			2.29844
$92$		−	5.70568i		−	0.594858i
$93$		−	12.7091i		−	1.31787i
$94$	10.8400			1.11806
$95$	0.951609	−	2.02347i	0.0976331	−	0.207604i
$96$	26.6766			2.72267
$97$			0.839854i			0.0852742i	0.999091	+	0.0426371i	$0.0135759\pi$
$97$			0.839854i			0.0852742i	−0.999091	+	0.0426371i	$0.986424\pi$
$98$			11.1187i			1.12316i
$99$	7.80213			0.784143
$100$	7.19973	+	8.69489i	0.719973	+	0.869489i
$101$	−17.6163			−1.75289			−0.876445	−	0.481502i	$-0.840091\pi$
$101$	−17.6163			−1.75289			−0.876445	+	0.481502i	$0.840091\pi$
$102$			2.40803i			0.238431i
$103$			0.639148i			0.0629771i	0.999504	+	0.0314885i	$0.0100248\pi$
$103$			0.639148i			0.0629771i	−0.999504	+	0.0314885i	$0.989975\pi$
$104$	3.31326			0.324891
$105$	11.0083	−	23.4078i	1.07430	−	2.28437i
$106$	−13.2132			−1.28338
$107$		−	5.05501i		−	0.488686i	−0.969689	−	0.244343i	$-0.921428\pi$
$107$		−	5.05501i		−	0.488686i	0.969689	−	0.244343i	$-0.0785723\pi$
$108$		−	35.6341i		−	3.42890i
$109$	−3.88408			−0.372027			−0.186014	−	0.982547i	$-0.559557\pi$
$109$	−3.88408			−0.372027			−0.186014	+	0.982547i	$0.559557\pi$
$110$	4.17530	+	1.96358i	0.398099	+	0.187220i
$111$	−6.53221			−0.620010
$112$		−	12.0305i		−	1.13678i
$113$			8.02383i			0.754818i	0.926047	+	0.377409i	$0.123185\pi$
$113$			8.02383i			0.754818i	−0.926047	+	0.377409i	$0.876815\pi$
$114$	−6.78181			−0.635174
$115$	5.11360	+	2.40485i	0.476846	+	0.224253i
$116$	−23.1296			−2.14753
$117$			48.6024i			4.49330i
$118$			6.47006i			0.595618i
$119$	1.24976			0.114565
$120$	1.66350	−	3.53722i	0.151856	−	0.322902i
$121$	1.00000			0.0909091
$122$		−	12.4098i		−	1.12353i
$123$			10.1169i			0.912213i
$124$	−8.73050			−0.784022
$125$	−10.8272	+	2.78786i	−0.968413	+	0.249353i
$126$	−56.6647			−5.04809
$127$		−	20.5239i		−	1.82120i	−0.413290	−	0.910599i	$-0.635621\pi$
$127$		−	20.5239i		−	1.82120i	0.413290	−	0.910599i	$-0.364379\pi$
$128$		−	4.21966i		−	0.372969i
$129$	6.47068			0.569712
$130$	−12.2319	+	26.0096i	−1.07281	+	2.28119i
$131$	−7.19630			−0.628743			−0.314372	−	0.949300i	$-0.601794\pi$
$131$	−7.19630			−0.628743			−0.314372	+	0.949300i	$0.601794\pi$
$132$		−	7.42049i		−	0.645871i
$133$			3.51972i			0.305199i
$134$	−12.1807			−1.05225
$135$	31.9364	+	15.0192i	2.74864	+	1.29265i
$136$	0.188854			0.0161941
$137$			18.7800i			1.60449i	0.596998	+	0.802243i	$0.296360\pi$
$137$			18.7800i			1.60449i	−0.596998	+	0.802243i	$0.703640\pi$
$138$		−	17.1386i		−	1.45893i
$139$	−5.86435			−0.497408			−0.248704	−	0.968580i	$-0.580005\pi$
$139$	−5.86435			−0.497408			−0.248704	+	0.968580i	$0.580005\pi$
$140$	−16.0799	−	7.56216i	−1.35900	−	0.639119i
$141$	17.2660			1.45406
$142$		−	14.7945i		−	1.24153i
$143$			6.22938i			0.520927i
$144$	26.6679			2.22233
$145$	9.74873	−	20.7294i	0.809588	−	1.72148i
$146$	−33.4443			−2.76787
$147$			17.7100i			1.46070i
$148$			4.48729i			0.368853i
$149$	14.5237			1.18983			0.594915	−	0.803789i	$-0.297186\pi$
$149$	14.5237			1.18983			0.594915	+	0.803789i	$0.297186\pi$
$150$	21.6264	+	26.1175i	1.76578	+	2.13248i
$151$	4.28673			0.348849			0.174425	−	0.984671i	$-0.444193\pi$
$151$	4.28673			0.348849			0.174425	+	0.984671i	$0.444193\pi$
$152$			0.531875i			0.0431408i
$153$			2.77032i			0.223967i
$154$	−7.26272			−0.585247
$155$	3.67976	−	7.82453i	0.295566	−	0.628481i
$156$	46.2251			3.70097
$157$		−	1.35491i		−	0.108134i	−0.998537	−	0.0540670i	$-0.982782\pi$
$157$		−	1.35491i		−	0.108134i	0.998537	−	0.0540670i	$-0.0172185\pi$
$158$			13.2325i			1.05272i
$159$	−21.0461			−1.66907
$160$	16.4238	+	7.72387i	1.29842	+	0.610626i
$161$	−8.89484			−0.701012
$162$		−	58.7394i		−	4.61500i
$163$			3.79536i			0.297276i	0.988892	+	0.148638i	$0.0474888\pi$
$163$			3.79536i			0.297276i	−0.988892	+	0.148638i	$0.952511\pi$
$164$	6.94980			0.542688
$165$	6.65046	+	3.12762i	0.517738	+	0.243485i
$166$	11.9104			0.924430
$167$		−	19.6538i		−	1.52086i	−0.649422	−	0.760428i	$-0.724989\pi$
$167$		−	19.6538i		−	1.52086i	0.649422	−	0.760428i	$-0.275011\pi$
$168$			6.15280i			0.474699i
$169$	−25.8052			−1.98502
$170$	−0.697215	+	1.48254i	−0.0534739	+	0.113705i
$171$	−7.80213			−0.596643
$172$		−	4.44502i		−	0.338930i
$173$			10.5685i			0.803505i	0.915748	+	0.401752i	$0.131599\pi$
$173$			10.5685i			0.803505i	−0.915748	+	0.401752i	$0.868401\pi$
$174$	−69.4760			−5.26696
$175$	13.5548	−	11.2240i	1.02465	−	0.848453i
$176$	3.41803			0.257644
$177$			10.3056i			0.774615i
$178$			25.0737i			1.87935i
$179$	18.4947			1.38236			0.691178	−	0.722685i	$-0.257092\pi$
$179$	18.4947			1.38236			0.691178	+	0.722685i	$0.257092\pi$
$180$	16.7629	−	35.6442i	1.24943	−	2.65676i
$181$	2.43171			0.180748			0.0903738	−	0.995908i	$-0.471194\pi$
$181$	2.43171			0.180748			0.0903738	+	0.995908i	$0.471194\pi$
$182$		−	45.2423i		−	3.35358i
$183$		−	19.7665i		−	1.46118i
$184$	−1.34412			−0.0990901
$185$	−4.02164	−	1.89132i	−0.295677	−	0.139052i
$186$	−26.2244			−1.92287
$187$			0.355073i			0.0259655i
$188$		−	11.8609i		−	0.865042i
$189$	−55.5516			−4.04079
$190$	−4.17530	−	1.96358i	−0.302908	−	0.142453i
$191$	26.3774			1.90860			0.954302	−	0.298845i	$-0.0966013\pi$
$191$	26.3774			1.90860			0.954302	+	0.298845i	$0.0966013\pi$
$192$		−	32.5777i		−	2.35109i
$193$			15.0639i			1.08432i	0.840274	+	0.542162i	$0.182394\pi$
$193$			15.0639i			1.08432i	−0.840274	+	0.542162i	$0.817606\pi$
$194$	1.73298			0.124421
$195$	−19.4831	+	41.4283i	−1.39522	+	2.96674i
$196$	12.1659			0.868991
$197$		−	13.6955i		−	0.975763i	−0.872910	−	0.487882i	$-0.837770\pi$
$197$		−	13.6955i		−	0.975763i	0.872910	−	0.487882i	$-0.162230\pi$
$198$		−	16.0992i		−	1.14412i
$199$	−2.24023			−0.158806			−0.0794029	−	0.996843i	$-0.525301\pi$
$199$	−2.24023			−0.158806			−0.0794029	+	0.996843i	$0.525301\pi$
$200$	2.04831	−	1.69609i	0.144837	−	0.119931i
$201$	−19.4015			−1.36848
$202$			36.3501i			2.55759i
$203$			36.0577i			2.53075i
$204$	2.63481			0.184474
$205$	−2.92923	+	6.22862i	−0.204586	+	0.435025i
$206$	1.31884			0.0918879
$207$		−	19.7171i		−	1.37043i
$208$			21.2923i			1.47635i
$209$	−1.00000			−0.0691714
$210$	−48.3005	−	22.7150i	−3.33305	−	1.56748i
$211$	16.0597			1.10559			0.552797	−	0.833316i	$-0.313560\pi$
$211$	16.0597			1.10559			0.552797	+	0.833316i	$0.313560\pi$
$212$			14.4576i			0.992951i
$213$		−	23.5648i		−	1.61463i
$214$	−10.4307			−0.713027
$215$	3.98376	+	1.87350i	0.271690	+	0.127772i
$216$	−8.39456			−0.571177
$217$			13.6104i			0.923932i
$218$			8.01454i			0.542813i
$219$	−53.2704			−3.59968
$220$	2.14851	−	4.56852i	0.144852	−	0.308009i
$221$	−2.21188			−0.148787
$222$			13.4788i			0.904638i
$223$		−	21.5262i		−	1.44150i	−0.693194	−	0.720751i	$-0.743797\pi$
$223$		−	21.5262i		−	1.44150i	0.693194	−	0.720751i	$-0.256203\pi$
$224$	−28.5683			−1.90880
$225$	24.8800	+	30.0468i	1.65867	+	2.00312i
$226$	16.5566			1.10133
$227$			1.30868i			0.0868602i	0.999056	+	0.0434301i	$0.0138286\pi$
$227$			1.30868i			0.0868602i	−0.999056	+	0.0434301i	$0.986171\pi$
$228$			7.42049i			0.491434i
$229$	17.7805			1.17497			0.587483	−	0.809237i	$-0.300119\pi$
$229$	17.7805			1.17497			0.587483	+	0.809237i	$0.300119\pi$
$230$	4.96225	−	10.5516i	0.327201	−	0.695750i
$231$	−11.5681			−0.761127
$232$			5.44878i			0.357730i
$233$		−	12.8674i		−	0.842968i	−0.906836	−	0.421484i	$-0.861509\pi$
$233$		−	12.8674i		−	0.842968i	0.906836	−	0.421484i	$-0.138491\pi$
$234$	100.288			6.55603
$235$	10.6300	+	4.99916i	0.693428	+	0.326109i
$236$	7.07939			0.460829
$237$			21.0769i			1.36909i
$238$		−	2.57879i		−	0.167158i
$239$	−11.1342			−0.720212			−0.360106	−	0.932911i	$-0.617260\pi$
$239$	−11.1342			−0.720212			−0.360106	+	0.932911i	$0.617260\pi$
$240$	22.7315	+	10.6903i	1.46731	+	0.690056i
$241$	−20.1958			−1.30092			−0.650462	−	0.759539i	$-0.725425\pi$
$241$	−20.1958			−1.30092			−0.650462	+	0.759539i	$0.725425\pi$
$242$		−	2.06343i		−	0.132643i
$243$		−	46.2118i		−	2.96449i
$244$	−13.5786			−0.869278
$245$	−5.12771	+	10.9034i	−0.327598	+	0.696593i
$246$	20.8756			1.33098
$247$		−	6.22938i		−	0.396366i
$248$			2.05670i			0.130601i
$249$	18.9711			1.20224
$250$	5.75256	+	22.3412i	0.363824	+	1.41298i
$251$	1.58219			0.0998671			0.0499336	−	0.998753i	$-0.484099\pi$
$251$	1.58219			0.0998671			0.0499336	+	0.998753i	$0.484099\pi$
$252$			62.0012i			3.90571i
$253$		−	2.52714i		−	0.158880i
$254$	−42.3497			−2.65725
$255$	−1.11053	+	2.36140i	−0.0695441	+	0.147876i
$256$	11.1172			0.694824
$257$			16.8357i			1.05018i	0.851047	+	0.525090i	$0.175968\pi$
$257$			16.8357i			1.05018i	−0.851047	+	0.525090i	$0.824032\pi$
$258$		−	13.3518i		−	0.831249i
$259$	6.99543			0.434675
$260$	28.4591	+	13.3839i	1.76496	+	0.830033i
$261$	−79.9286			−4.94746
$262$			14.8491i			0.917380i
$263$		−	8.41800i		−	0.519076i	−0.965733	−	0.259538i	$-0.916430\pi$
$263$		−	8.41800i		−	0.519076i	0.965733	−	0.259538i	$-0.0835703\pi$
$264$	−1.74809			−0.107588
$265$	−12.9573	−	6.09363i	−0.795961	−	0.374329i
$266$	7.26272			0.445306
$267$			39.9377i			2.44415i
$268$			13.3278i			0.814126i
$269$	−22.2801			−1.35844			−0.679222	−	0.733933i	$-0.737683\pi$
$269$	−22.2801			−1.35844			−0.679222	+	0.733933i	$0.737683\pi$
$270$	30.9911	−	65.8986i	1.88606	−	4.01046i
$271$	−11.0913			−0.673749			−0.336875	−	0.941550i	$-0.609370\pi$
$271$	−11.0913			−0.673749			−0.336875	+	0.941550i	$0.609370\pi$
$272$			1.21365i			0.0735884i
$273$		−	72.0624i		−	4.36141i
$274$	38.7513			2.34105
$275$	3.18888	+	3.85111i	0.192297	+	0.232231i
$276$	−18.7526			−1.12878
$277$		−	8.68181i		−	0.521639i	−0.965388	−	0.260820i	$-0.916007\pi$
$277$		−	8.68181i		−	0.521639i	0.965388	−	0.260820i	$-0.0839928\pi$
$278$			12.1007i			0.725752i
$279$	−30.1699			−1.80622
$280$	−1.78146	+	3.78805i	−0.106463	+	0.226379i
$281$	28.4596			1.69776			0.848879	−	0.528588i	$-0.177278\pi$
$281$	28.4596			1.69776			0.848879	+	0.528588i	$0.177278\pi$
$282$		−	35.6273i		−	2.12158i
$283$			0.278130i			0.0165331i	0.999966	+	0.00826656i	$0.00263136\pi$
$283$			0.278130i			0.0165331i	−0.999966	+	0.00826656i	$0.997369\pi$
$284$	−16.1878			−0.960568
$285$	−6.65046	−	3.12762i	−0.393939	−	0.185264i
$286$	12.8539			0.760069
$287$		−	10.8344i		−	0.639532i
$288$		−	63.3271i		−	3.73158i
$289$	16.8739			0.992584
$290$	−42.7737	−	20.1159i	−2.51176	−	1.18124i
$291$	2.76031			0.161812
$292$			36.5940i			2.14150i
$293$			17.3974i			1.01637i	0.861248	+	0.508184i	$0.169683\pi$
$293$			17.3974i			1.01637i	−0.861248	+	0.508184i	$0.830317\pi$
$294$	36.5435			2.13126
$295$	−2.98385	+	6.34476i	−0.173726	+	0.369406i
$296$	1.05710			0.0614426
$297$		−	15.7829i		−	0.915820i
$298$		−	29.9687i		−	1.73604i
$299$	15.7425			0.910414
$300$	28.5771	−	23.6631i	1.64990	−	1.36619i
$301$	−6.92954			−0.399412
$302$		−	8.84539i		−	0.508995i
$303$			57.8989i			3.32620i
$304$	−3.41803			−0.196038
$305$	5.72314	−	12.1695i	0.327706	−	0.696823i
$306$	5.71638			0.326783
$307$		−	15.7895i		−	0.901152i	−0.892738	−	0.450576i	$-0.851219\pi$
$307$		−	15.7895i		−	0.901152i	0.892738	−	0.450576i	$-0.148781\pi$
$308$			7.94670i			0.452805i
$309$	2.10066			0.119502
$310$	−16.1454	−	7.59295i	−0.916997	−	0.431250i
$311$	2.19777			0.124624			0.0623121	−	0.998057i	$-0.480153\pi$
$311$	2.19777			0.124624			0.0623121	+	0.998057i	$0.480153\pi$
$312$		−	10.8895i		−	0.616499i
$313$		−	7.28572i		−	0.411813i	−0.978572	−	0.205907i	$-0.933986\pi$
$313$		−	7.28572i		−	0.411813i	0.978572	−	0.205907i	$-0.0660143\pi$
$314$	−2.79578			−0.157775
$315$	−55.5672	−	26.1325i	−3.13086	−	1.47240i
$316$	14.4787			0.814491
$317$		−	33.6008i		−	1.88721i	−0.331075	−	0.943605i	$-0.607411\pi$
$317$		−	33.6008i		−	1.88721i	0.331075	−	0.943605i	$-0.392589\pi$
$318$			43.4273i			2.43528i
$319$	−10.2445			−0.573580
$320$	9.43244	−	20.0568i	0.527289	−	1.12121i
$321$	−16.6141			−0.927308
$322$			18.3539i			1.02282i
$323$		−	0.355073i		−	0.0197568i
$324$	−64.2712			−3.57062
$325$	−23.9900	+	19.8648i	−1.33073	+	1.10190i
$326$	7.83148			0.433745
$327$			12.7656i			0.705942i
$328$		−	1.63721i		−	0.0903997i
$329$	−18.4904			−1.01941
$330$	6.45363	−	13.7228i	0.355261	−	0.755415i
$331$	−21.3551			−1.17378			−0.586892	−	0.809665i	$-0.699649\pi$
$331$	−21.3551			−1.17378			−0.586892	+	0.809665i	$0.699649\pi$
$332$		−	13.0321i		−	0.715231i
$333$			15.5067i			0.849761i
$334$	−40.5543			−2.21903
$335$	−11.9448	−	5.61746i	−0.652613	−	0.306914i
$336$	−39.5403			−2.15710
$337$		−	18.9060i		−	1.02988i	−0.857227	−	0.514938i	$-0.827815\pi$
$337$		−	18.9060i		−	1.02988i	0.857227	−	0.514938i	$-0.172185\pi$
$338$			53.2474i			2.89628i
$339$	26.3716			1.43231
$340$	1.62216	+	0.762876i	0.0879737	+	0.0413728i
$341$	−3.86688			−0.209403
$342$			16.0992i			0.870544i
$343$			5.67217i			0.306268i
$344$	−1.04714			−0.0564581
$345$	7.90392	−	16.8067i	0.425533	−	0.904840i
$346$	21.8073			1.17237
$347$			29.2091i			1.56803i	0.620743	+	0.784014i	$0.286831\pi$
$347$			29.2091i			1.56803i	−0.620743	+	0.784014i	$0.713169\pi$
$348$			76.0190i			4.07505i
$349$	26.1324			1.39883			0.699417	−	0.714714i	$-0.253443\pi$
$349$	26.1324			1.39883			0.699417	+	0.714714i	$0.253443\pi$
$350$	−23.1599	−	27.9695i	−1.23795	−	1.49503i
$351$	98.3181			5.24783
$352$		−	8.11664i		−	0.432618i
$353$			1.73200i			0.0921850i	0.998937	+	0.0460925i	$0.0146769\pi$
$353$			1.73200i			0.0921850i	−0.998937	+	0.0460925i	$0.985323\pi$
$354$	21.2649			1.13022
$355$	6.82288	−	14.5080i	0.362121	−	0.770002i
$356$	27.4351			1.45406
$357$		−	4.10753i		−	0.217393i
$358$		−	38.1625i		−	2.01695i
$359$	9.14154			0.482472			0.241236	−	0.970467i	$-0.422447\pi$
$359$	9.14154			0.482472			0.241236	+	0.970467i	$0.422447\pi$
$360$	−8.39692	−	3.94895i	−0.442557	−	0.208128i
$361$	1.00000			0.0526316
$362$		−	5.01767i		−	0.263723i
$363$		−	3.28666i		−	0.172505i
$364$	−49.5031			−2.59467
$365$	−32.7966	−	15.4238i	−1.71665	−	0.807316i
$366$	−40.7869			−2.13197
$367$			31.5882i			1.64889i	0.565943	+	0.824445i	$0.308512\pi$
$367$			31.5882i			1.64889i	−0.565943	+	0.824445i	$0.691488\pi$
$368$		−	8.63785i		−	0.450279i
$369$	24.0164			1.25024
$370$	−3.90261	+	8.29839i	−0.202887	+	0.431413i
$371$	22.5386			1.17014
$372$			28.6942i			1.48772i
$373$		−	19.9396i		−	1.03243i	−0.856458	−	0.516217i	$-0.827340\pi$
$373$		−	19.9396i		−	1.03243i	0.856458	−	0.516217i	$-0.172660\pi$
$374$	0.732669			0.0378854
$375$	9.16273	+	35.5853i	0.473161	+	1.83761i
$376$	−2.79414			−0.144097
$377$		−	63.8167i		−	3.28673i
$378$			114.627i			5.89579i
$379$	14.9551			0.768190			0.384095	−	0.923294i	$-0.374514\pi$
$379$	14.9551			0.768190			0.384095	+	0.923294i	$0.374514\pi$
$380$	−2.14851	+	4.56852i	−0.110216	+	0.234360i
$381$	−67.4549			−3.45582
$382$		−	54.4281i		−	2.78478i
$383$			18.1544i			0.927645i	0.885928	+	0.463822i	$0.153522\pi$
$383$			18.1544i			0.927645i	−0.885928	+	0.463822i	$0.846478\pi$
$384$	−13.8686			−0.707729
$385$	−7.12207	−	3.34940i	−0.362974	−	0.170701i
$386$	31.0834			1.58210
$387$		−	15.3606i		−	0.780824i
$388$		−	1.89619i		−	0.0962645i
$389$	17.7257			0.898730			0.449365	−	0.893348i	$-0.351650\pi$
$389$	17.7257			0.898730			0.449365	+	0.893348i	$0.351650\pi$
$390$	85.4846	+	40.2021i	4.32868	+	2.03571i
$391$	0.897318			0.0453793
$392$		−	2.86599i		−	0.144754i
$393$			23.6518i			1.19307i
$394$	−28.2597			−1.42371
$395$	−6.10254	+	12.9762i	−0.307052	+	0.652906i
$396$	−17.6153			−0.885204
$397$		−	8.73977i		−	0.438636i	−0.975653	−	0.219318i	$-0.929617\pi$
$397$		−	8.73977i		−	0.438636i	0.975653	−	0.219318i	$-0.0703833\pi$
$398$			4.62257i			0.231709i
$399$	11.5681			0.579131
$400$	10.8997	+	13.1632i	0.544985	+	0.658161i
$401$	9.03579			0.451226			0.225613	−	0.974217i	$-0.427562\pi$
$401$	9.03579			0.451226			0.225613	+	0.974217i	$0.427562\pi$
$402$			40.0338i			1.99670i
$403$		−	24.0883i		−	1.19992i
$404$	39.7735			1.97880
$405$	27.0893	−	57.6018i	1.34608	−	2.86225i
$406$	74.4027			3.69254
$407$			1.98749i			0.0985164i
$408$		−	0.620700i		−	0.0307292i
$409$	5.75990			0.284809			0.142404	−	0.989809i	$-0.454517\pi$
$409$	5.75990			0.284809			0.142404	+	0.989809i	$0.454517\pi$
$410$	12.8523	+	6.04427i	0.634732	+	0.298505i
$411$	61.7235			3.04460
$412$		−	1.44304i		−	0.0710936i
$413$		−	11.0364i		−	0.543065i
$414$	−40.6849			−1.99955
$415$	11.6798	+	5.49283i	0.573338	+	0.269632i
$416$	50.5617			2.47899
$417$			19.2741i			0.943858i
$418$			2.06343i			0.100926i
$419$	32.7890			1.60185			0.800924	−	0.598766i	$-0.204342\pi$
$419$	32.7890			1.60185			0.800924	+	0.598766i	$0.204342\pi$
$420$	−24.8542	+	52.8492i	−1.21276	+	2.57878i
$421$	17.6138			0.858444			0.429222	−	0.903199i	$-0.358788\pi$
$421$	17.6138			0.858444			0.429222	+	0.903199i	$0.358788\pi$
$422$		−	33.1381i		−	1.61314i
$423$		−	40.9875i		−	1.99288i
$424$	3.40586			0.165403
$425$	−1.36742	+	1.13228i	−0.0663298	+	0.0549238i
$426$	−48.6244			−2.35586
$427$			21.1682i			1.02440i
$428$			11.4130i			0.551669i
$429$	20.4739			0.988487
$430$	3.86585	−	8.22022i	0.186428	−	0.396414i
$431$	32.6689			1.57360			0.786802	−	0.617205i	$-0.211735\pi$
$431$	32.6689			1.57360			0.786802	+	0.617205i	$0.211735\pi$
$432$		−	53.9467i		−	2.59551i
$433$			12.7466i			0.612562i	0.951941	+	0.306281i	$0.0990846\pi$
$433$			12.7466i			0.612562i	−0.951941	+	0.306281i	$0.900915\pi$
$434$	28.0841			1.34808
$435$	−68.1304	−	32.0407i	−3.26660	−	1.53624i
$436$	8.76933			0.419975
$437$			2.52714i			0.120890i
$438$			109.920i			5.25218i
$439$	−9.92889			−0.473880			−0.236940	−	0.971524i	$-0.576145\pi$
$439$	−9.92889			−0.473880			−0.236940	+	0.971524i	$0.576145\pi$
$440$	−1.07623	−	0.506137i	−0.0513075	−	0.0241292i
$441$	42.0415			2.00197
$442$			4.56408i			0.217091i
$443$			9.75569i			0.463507i	0.972775	+	0.231753i	$0.0744462\pi$
$443$			9.75569i			0.463507i	−0.972775	+	0.231753i	$0.925554\pi$
$444$	14.7482			0.699918
$445$	−11.5634	+	24.5881i	−0.548159	+	1.16559i
$446$	−44.4179			−2.10325
$447$		−	47.7345i		−	2.25776i
$448$			34.8878i			1.64829i
$449$	−25.3232			−1.19508			−0.597538	−	0.801841i	$-0.703854\pi$
$449$	−25.3232			−1.19508			−0.597538	+	0.801841i	$0.703854\pi$
$450$	61.9997	−	51.3383i	2.92269	−	2.42011i
$451$	3.07818			0.144946
$452$		−	18.1159i		−	0.852100i
$453$		−	14.0890i		−	0.661960i
$454$	2.70038			0.126735
$455$	20.8647	−	44.3661i	0.978153	−	2.07991i
$456$	1.74809			0.0818619
$457$		−	0.839797i		−	0.0392840i	−0.999807	−	0.0196420i	$-0.993747\pi$
$457$		−	0.839797i		−	0.0392840i	0.999807	−	0.0196420i	$-0.00625265\pi$
$458$		−	36.6888i		−	1.71436i
$459$	5.60409			0.261577
$460$	−11.5453	−	5.42958i	−0.538302	−	0.253155i
$461$	5.26000			0.244983			0.122491	−	0.992470i	$-0.460912\pi$
$461$	5.26000			0.244983			0.122491	+	0.992470i	$0.460912\pi$
$462$			23.8701i			1.11054i
$463$			11.5714i			0.537767i	0.963173	+	0.268884i	$0.0866547\pi$
$463$			11.5714i			0.537767i	−0.963173	+	0.268884i	$0.913345\pi$
$464$	−35.0159			−1.62557
$465$	−25.7166	−	12.0941i	−1.19258	−	0.560851i
$466$	−26.5509			−1.22995
$467$		−	13.2634i		−	0.613758i	−0.951749	−	0.306879i	$-0.900715\pi$
$467$		−	13.2634i		−	0.613758i	0.951749	−	0.306879i	$-0.0992847\pi$
$468$		−	109.733i		−	5.07240i
$469$	20.7773			0.959408
$470$	10.3154	−	21.9344i	0.475815	−	1.01176i
$471$	−4.45314			−0.205190
$472$		−	1.66774i		−	0.0767638i
$473$		−	1.96877i		−	0.0905243i
$474$	43.4908			1.99760
$475$	−3.18888	−	3.85111i	−0.146316	−	0.176701i
$476$	−2.82166			−0.129330
$477$			49.9609i			2.28755i
$478$			22.9747i			1.05084i
$479$	22.8275			1.04301			0.521507	−	0.853247i	$-0.325370\pi$
$479$	22.8275			1.04301			0.521507	+	0.853247i	$0.325370\pi$
$480$	25.3857	−	53.9794i	1.15869	−	2.46381i
$481$	−12.3809			−0.564519
$482$			41.6726i			1.89814i
$483$			29.2343i			1.33021i
$484$	−2.25776			−0.102626
$485$	1.69942	+	0.799213i	0.0771667	+	0.0362904i
$486$	−95.3550			−4.32539
$487$			10.2612i			0.464977i	0.972599	+	0.232489i	$0.0746869\pi$
$487$			10.2612i			0.464977i	−0.972599	+	0.232489i	$0.925313\pi$
$488$			3.19879i			0.144802i
$489$	12.4741			0.564096
$490$	22.4985	+	10.5807i	1.01638	+	0.477987i
$491$	−31.4381			−1.41878			−0.709391	−	0.704816i	$-0.751030\pi$
$491$	−31.4381			−1.41878			−0.709391	+	0.704816i	$0.751030\pi$
$492$		−	22.8416i		−	1.02978i
$493$		−	3.63753i		−	0.163826i
$494$	−12.8539			−0.578326
$495$	7.42458	−	15.7874i	0.333710	−	0.709590i
$496$	−13.2171			−0.593467
$497$			25.2358i			1.13198i
$498$		−	39.1456i		−	1.75415i
$499$	−14.8767			−0.665972			−0.332986	−	0.942932i	$-0.608056\pi$
$499$	−14.8767			−0.665972			−0.332986	+	0.942932i	$0.608056\pi$
$500$	24.4452	−	6.29431i	1.09322	−	0.281490i
$501$	−64.5953			−2.88590
$502$		−	3.26475i		−	0.145713i
$503$		−	4.59574i		−	0.204914i	−0.994737	−	0.102457i	$-0.967330\pi$
$503$		−	4.59574i		−	0.204914i	0.994737	−	0.102457i	$-0.0326704\pi$
$504$	14.6060			0.650603
$505$	−16.7639	+	35.6462i	−0.745982	+	1.58623i
$506$	−5.21459			−0.231817
$507$			84.8130i			3.76668i
$508$			46.3380i			2.05592i
$509$	5.13160			0.227454			0.113727	−	0.993512i	$-0.463721\pi$
$509$	5.13160			0.227454			0.113727	+	0.993512i	$0.463721\pi$
$510$	4.87259	+	2.29151i	0.215762	+	0.101470i
$511$	57.0480			2.52365
$512$		−	31.3789i		−	1.38676i
$513$			15.7829i			0.696834i
$514$	34.7393			1.53229
$515$	1.29330	+	0.608219i	0.0569895	+	0.0268013i
$516$	−14.6093			−0.643137
$517$		−	5.25337i		−	0.231043i
$518$		−	14.4346i		−	0.634221i
$519$	34.7349			1.52469
$520$	3.15293	−	6.70428i	0.138265	−	0.294002i
$521$	−44.6143			−1.95459			−0.977294	−	0.211887i	$-0.932039\pi$
$521$	−44.6143			−1.95459			−0.977294	+	0.211887i	$0.932039\pi$
$522$			164.927i			7.21868i
$523$		−	31.5350i		−	1.37893i	−0.724319	−	0.689465i	$-0.757846\pi$
$523$		−	31.5350i		−	1.37893i	0.724319	−	0.689465i	$-0.242154\pi$
$524$	16.2475			0.709776
$525$	−36.8894	−	44.5502i	−1.60998	−	1.94433i
$526$	−17.3700			−0.757368
$527$		−	1.37302i		−	0.0598099i
$528$		−	11.2339i		−	0.488893i
$529$	16.6136			0.722329
$530$	−12.5738	+	26.7366i	−0.546171	+	1.16136i
$531$	24.4642			1.06166
$532$		−	7.94670i		−	0.344533i
$533$			19.1752i			0.830569i
$534$	82.4087			3.56618
$535$	−10.2287	−	4.81039i	−0.442224	−	0.207971i
$536$	3.13972			0.135615
$537$		−	60.7856i		−	2.62309i
$538$			45.9736i			1.98206i
$539$	5.38846			0.232098
$540$	−72.1047	−	33.9098i	−3.10289	−	1.45924i
$541$	−20.7044			−0.890151			−0.445076	−	0.895493i	$-0.646823\pi$
$541$	−20.7044			−0.890151			−0.445076	+	0.895493i	$0.646823\pi$
$542$			22.8862i			0.983046i
$543$		−	7.99220i		−	0.342978i
$544$	2.88200			0.123565
$545$	−3.69613	+	7.85933i	−0.158325	+	0.336657i
$546$	−148.696			−6.36360
$547$			9.33120i			0.398973i	0.979901	+	0.199487i	$0.0639274\pi$
$547$			9.33120i			0.398973i	−0.979901	+	0.199487i	$0.936073\pi$
$548$		−	42.4008i		−	1.81127i
$549$	−46.9233			−2.00264
$550$	7.94651	−	6.58004i	0.338840	−	0.280574i
$551$	10.2445			0.436429
$552$			4.41768i			0.188029i
$553$		−	22.5715i		−	0.959838i
$554$	−17.9143			−0.761107
$555$	−6.21612	+	13.2178i	−0.263859	+	0.561062i
$556$	13.2403			0.561514
$557$			11.2336i			0.475983i	0.971267	+	0.237992i	$0.0764891\pi$
$557$			11.2336i			0.475983i	−0.971267	+	0.237992i	$0.923511\pi$
$558$			62.2536i			2.63541i
$559$	12.2642			0.518722
$560$	−24.3435	−	11.4484i	−1.02870	−	0.483782i
$561$	1.16700			0.0492709
$562$		−	58.7245i		−	2.47714i
$563$		−	9.07342i		−	0.382399i	−0.981551	−	0.191199i	$-0.938762\pi$
$563$		−	9.07342i		−	0.382399i	0.981551	−	0.191199i	$-0.0612377\pi$
$564$	−38.9826			−1.64146
$565$	16.2360	+	7.63555i	0.683053	+	0.321230i
$566$	0.573903			0.0241229
$567$			100.195i			4.20781i
$568$			3.81346i			0.160009i
$569$	−13.2415			−0.555114			−0.277557	−	0.960709i	$-0.589525\pi$
$569$	−13.2415			−0.555114			−0.277557	+	0.960709i	$0.589525\pi$
$570$	−6.45363	+	13.7228i	−0.270313	+	0.574785i
$571$	−7.30573			−0.305735			−0.152868	−	0.988247i	$-0.548851\pi$
$571$	−7.30573			−0.305735			−0.152868	+	0.988247i	$0.548851\pi$
$572$		−	14.0645i		−	0.588065i
$573$		−	86.6936i		−	3.62168i
$574$	−22.3560			−0.933121
$575$	9.73230	−	8.05875i	0.405865	−	0.336073i
$576$	−77.3354			−3.22231
$577$		−	6.46508i		−	0.269145i	−0.990904	−	0.134572i	$-0.957034\pi$
$577$		−	6.46508i		−	0.269145i	0.990904	−	0.134572i	$-0.0429661\pi$
$578$		−	34.8182i		−	1.44825i
$579$	49.5100			2.05756
$580$	−22.0103	+	46.8020i	−0.913928	+	1.94335i
$581$	−20.3164			−0.842865
$582$		−	5.69572i		−	0.236095i
$583$			6.40350i			0.265206i
$584$	8.62068			0.356726
$585$	98.3457	+	46.2505i	4.06609	+	1.91222i
$586$	35.8984			1.48295
$587$		−	14.4506i		−	0.596438i	−0.954497	−	0.298219i	$-0.903607\pi$
$587$		−	14.4506i		−	0.596438i	0.954497	−	0.298219i	$-0.0963926\pi$
$588$		−	39.9851i		−	1.64896i
$589$	3.86688			0.159332
$590$	13.0920	+	6.15697i	0.538989	+	0.253479i
$591$	−45.0124			−1.85156
$592$			6.79332i			0.279204i
$593$		−	14.8419i		−	0.609483i	−0.952435	−	0.304741i	$-0.901430\pi$
$593$		−	14.8419i		−	0.609483i	0.952435	−	0.304741i	$-0.0985701\pi$
$594$	−32.5671			−1.33624
$595$	1.18928	−	2.52885i	0.0487558	−	0.103673i
$596$	−32.7911			−1.34318
$597$			7.36288i			0.301343i
$598$		−	32.4837i		−	1.32836i
$599$	27.5835			1.12703			0.563515	−	0.826106i	$-0.309449\pi$
$599$	27.5835			1.12703			0.563515	+	0.826106i	$0.309449\pi$
$600$	−5.57446	−	6.73210i	−0.227576	−	0.274837i
$601$	36.2287			1.47780			0.738899	−	0.673816i	$-0.235346\pi$
$601$	36.2287			1.47780			0.738899	+	0.673816i	$0.235346\pi$
$602$			14.2986i			0.582769i
$603$			46.0568i			1.87558i
$604$	−9.67842			−0.393809
$605$	0.951609	−	2.02347i	0.0386884	−	0.0822658i
$606$	119.471			4.85316
$607$			22.3694i			0.907947i	0.891015	+	0.453973i	$0.149994\pi$
$607$			22.3694i			0.907947i	−0.891015	+	0.453973i	$0.850006\pi$
$608$			8.11664i			0.329173i
$609$	118.509			4.80224
$610$	−25.1110	−	11.8093i	−1.01671	−	0.478145i
$611$	32.7253			1.32392
$612$		−	6.25473i		−	0.252832i
$613$			16.0661i			0.648904i	0.945902	+	0.324452i	$0.105180\pi$
$613$			16.0661i			0.648904i	−0.945902	+	0.324452i	$0.894820\pi$
$614$	−32.5805			−1.31484
$615$	20.4713	+	9.62737i	0.825484	+	0.388213i
$616$	1.87205			0.0754272
$617$		−	36.4273i		−	1.46651i	−0.679955	−	0.733254i	$-0.738001\pi$
$617$		−	36.4273i		−	1.46651i	0.679955	−	0.733254i	$-0.261999\pi$
$618$		−	4.33457i		−	0.174362i
$619$	8.38132			0.336874			0.168437	−	0.985712i	$-0.446128\pi$
$619$	8.38132			0.336874			0.168437	+	0.985712i	$0.446128\pi$
$620$	−8.30803	+	17.6659i	−0.333658	+	0.709481i
$621$	−39.8857			−1.60056
$622$		−	4.53496i		−	0.181835i
$623$		−	42.7697i		−	1.71353i
$624$	69.9804			2.80146
$625$	−4.66210	+	24.5615i	−0.186484	+	0.982458i
$626$	−15.0336			−0.600864
$627$			3.28666i			0.131257i
$628$			3.05908i			0.122070i
$629$	−0.705705			−0.0281383
$630$	−53.9226	+	114.659i	−2.14833	+	4.56814i
$631$	41.1776			1.63925			0.819626	−	0.572898i	$-0.194181\pi$
$631$	41.1776			1.63925			0.819626	+	0.572898i	$0.194181\pi$
$632$		−	3.41084i		−	0.135676i
$633$		−	52.7827i		−	2.09792i
$634$	−69.3331			−2.75357
$635$	−41.5295	−	19.5307i	−1.64805	−	0.775052i
$636$	47.5171			1.88418
$637$			33.5668i			1.32997i
$638$			21.1388i			0.836892i
$639$	−55.9399			−2.21295
$640$	−8.53837	−	4.01547i	−0.337509	−	0.158725i
$641$	21.5315			0.850443			0.425221	−	0.905089i	$-0.360196\pi$
$641$	21.5315			0.850443			0.425221	+	0.905089i	$0.360196\pi$
$642$			34.2821i			1.35301i
$643$			5.42094i			0.213781i	0.994271	+	0.106891i	$0.0340894\pi$
$643$			5.42094i			0.213781i	−0.994271	+	0.106891i	$0.965911\pi$
$644$	20.0824			0.791359
$645$	6.15756	−	13.0932i	0.242454	−	0.515546i
$646$	−0.732669			−0.0288265
$647$			7.53314i			0.296158i	0.988976	+	0.148079i	$0.0473090\pi$
$647$			7.53314i			0.296158i	−0.988976	+	0.148079i	$0.952691\pi$
$648$			15.1408i			0.594786i
$649$	3.13558			0.123082
$650$	40.9896	+	49.5019i	1.60775	+	1.94162i
$651$	44.7326			1.75321
$652$		−	8.56902i		−	0.335589i
$653$		−	24.6142i		−	0.963229i	−0.876383	−	0.481614i	$-0.840051\pi$
$653$		−	24.6142i		−	0.963229i	0.876383	−	0.481614i	$-0.159949\pi$
$654$	26.3411			1.03002
$655$	−6.84806	+	14.5615i	−0.267576	+	0.568965i
$656$	10.5213			0.410789
$657$			126.457i			4.93358i
$658$			38.1538i			1.48739i
$659$	36.9944			1.44110			0.720550	−	0.693403i	$-0.243890\pi$
$659$	36.9944			1.44110			0.720550	+	0.693403i	$0.243890\pi$
$660$	−15.0152	−	7.06141i	−0.584464	−	0.274865i
$661$	8.41944			0.327478			0.163739	−	0.986504i	$-0.447644\pi$
$661$	8.41944			0.327478			0.163739	+	0.986504i	$0.447644\pi$
$662$			44.0649i			1.71263i
$663$			7.26971i			0.282332i
$664$	−3.07006			−0.119141
$665$	7.12207	+	3.34940i	0.276182	+	0.129884i
$666$	31.9970			1.23986
$667$			25.8892i			1.00243i
$668$			44.3736i			1.71687i
$669$	−70.7493			−2.73533
$670$	−11.5913	+	24.6473i	−0.447809	+	0.952207i
$671$	−6.01417			−0.232174
$672$			93.8944i			3.62205i
$673$		−	34.2157i		−	1.31892i	−0.751741	−	0.659459i	$-0.770785\pi$
$673$		−	34.2157i		−	1.31892i	0.751741	−	0.659459i	$-0.229215\pi$
$674$	−39.0113			−1.50266
$675$	60.7819	−	50.3299i	2.33950	−	1.93720i
$676$	58.2621			2.24085
$677$			46.1777i			1.77475i	0.461045	+	0.887377i	$0.347475\pi$
$677$			46.1777i			1.77475i	−0.461045	+	0.887377i	$0.652525\pi$
$678$		−	54.4160i		−	2.08984i
$679$	−2.95605			−0.113443
$680$	0.179716	−	0.382141i	0.00689178	−	0.0146545i
$681$	4.30119			0.164822
$682$			7.97906i			0.305534i
$683$			30.8246i			1.17947i	0.807597	+	0.589735i	$0.200768\pi$
$683$			30.8246i			1.17947i	−0.807597	+	0.589735i	$0.799232\pi$
$684$	17.6153			0.673540
$685$	38.0009	+	17.8712i	1.45194	+	0.682825i
$686$	11.7041			0.446866
$687$		−	58.4383i		−	2.22956i
$688$		−	6.72933i		−	0.256553i
$689$	−39.8899			−1.51968
$690$	−34.6794	−	16.3092i	−1.32022	−	0.620882i
$691$	12.8941			0.490516			0.245258	−	0.969458i	$-0.421127\pi$
$691$	12.8941			0.490516			0.245258	+	0.969458i	$0.421127\pi$
$692$		−	23.8611i		−	0.907061i
$693$			27.4613i			1.04317i
$694$	60.2711			2.28786
$695$	−5.58057	+	11.8664i	−0.211683	+	0.450117i
$696$	17.9083			0.678811
$697$			1.09298i			0.0413995i
$698$		−	53.9225i		−	2.04099i
$699$	−42.2906			−1.59958
$700$	−30.6036	+	25.3411i	−1.15671	+	0.957802i
$701$	−10.2320			−0.386457			−0.193229	−	0.981154i	$-0.561896\pi$
$701$	−10.2320			−0.386457			−0.193229	+	0.981154i	$0.561896\pi$
$702$		−	202.873i		−	7.65694i
$703$		−	1.98749i		−	0.0749598i
$704$	−9.91209			−0.373576
$705$	16.4305	−	34.9373i	0.618809	−	1.31582i
$706$	3.57387			0.134504
$707$		−	62.0046i		−	2.33192i
$708$		−	23.2676i		−	0.874448i
$709$	−10.9462			−0.411094			−0.205547	−	0.978647i	$-0.565897\pi$
$709$	−10.9462			−0.411094			−0.205547	+	0.978647i	$0.565897\pi$
$710$	−29.9362	−	14.0786i	−1.12349	−	0.528359i
$711$	50.0340			1.87642
$712$		−	6.46305i		−	0.242213i
$713$			9.77215i			0.365970i
$714$	−8.47561			−0.317192
$715$	12.6050	+	5.92794i	0.471400	+	0.221692i
$716$	−41.7565			−1.56052
$717$			36.5944i			1.36664i
$718$		−	18.8630i		−	0.703959i
$719$	−49.5704			−1.84866			−0.924332	−	0.381588i	$-0.875377\pi$
$719$	−49.5704			−1.84866			−0.924332	+	0.381588i	$0.875377\pi$
$720$	25.3775	−	53.9618i	0.945762	−	2.01104i
$721$	−2.24962			−0.0837804
$722$		−	2.06343i		−	0.0767931i
$723$			66.3766i			2.46857i
$724$	−5.49022			−0.204042
$725$	−32.6684	−	39.4526i	−1.21327	−	1.46523i
$726$	−6.78181			−0.251696
$727$			9.28812i			0.344477i	0.985055	+	0.172239i	$0.0551000\pi$
$727$			9.28812i			0.344477i	−0.985055	+	0.172239i	$0.944900\pi$
$728$			11.6617i			0.432213i
$729$	−66.4820			−2.46230
$730$	−31.8259	+	67.6736i	−1.17793	+	2.50471i
$731$	0.699057			0.0258556
$732$			44.6281i			1.64950i
$733$			19.8384i			0.732746i	0.930468	+	0.366373i	$0.119401\pi$
$733$			19.8384i			0.732746i	−0.930468	+	0.366373i	$0.880599\pi$
$734$	65.1801			2.40584
$735$	35.8358	+	16.8530i	1.32182	+	0.621634i
$736$	−20.5119			−0.756078
$737$			5.90311i			0.217444i
$738$		−	49.5562i		−	1.82419i
$739$	14.9719			0.550750			0.275375	−	0.961337i	$-0.411198\pi$
$739$	14.9719			0.550750			0.275375	+	0.961337i	$0.411198\pi$
$740$	9.07990	+	4.27015i	0.333784	+	0.156974i
$741$	−20.4739			−0.752126
$742$		−	46.5069i		−	1.70732i
$743$		−	14.0663i		−	0.516044i	−0.966139	−	0.258022i	$-0.916929\pi$
$743$		−	14.0663i		−	0.516044i	0.966139	−	0.258022i	$-0.0830707\pi$
$744$	6.75967			0.247821
$745$	13.8209	−	29.3883i	0.506359	−	1.07671i
$746$	−41.1441			−1.50639
$747$		−	45.0350i		−	1.64774i
$748$		−	0.801669i		−	0.0293119i
$749$	17.7922			0.650114
$750$	73.4278	−	18.9067i	2.68121	−	0.690375i
$751$	−20.3882			−0.743975			−0.371988	−	0.928238i	$-0.621324\pi$
$751$	−20.3882			−0.743975			−0.371988	+	0.928238i	$0.621324\pi$
$752$		−	17.9562i		−	0.654795i
$753$		−	5.20013i		−	0.189503i
$754$	−131.682			−4.79556
$755$	4.07929	−	8.67408i	0.148461	−	0.315682i
$756$	125.422			4.56157
$757$			35.6405i			1.29537i	0.761906	+	0.647687i	$0.224264\pi$
$757$			35.6405i			1.29537i	−0.761906	+	0.647687i	$0.775736\pi$
$758$		−	30.8588i		−	1.12084i
$759$	−8.30585			−0.301483
$760$	1.07623	+	0.506137i	0.0390391	+	0.0183595i
$761$	−34.5369			−1.25196			−0.625981	−	0.779839i	$-0.715301\pi$
$761$	−34.5369			−1.25196			−0.625981	+	0.779839i	$0.715301\pi$
$762$			139.189i			5.04228i
$763$		−	13.6709i		−	0.494920i
$764$	−59.5539			−2.15459
$765$	5.60567	+	2.63626i	0.202673	+	0.0953143i
$766$	37.4603			1.35350
$767$			19.5327i			0.705286i
$768$		−	36.5384i		−	1.31846i
$769$	37.2223			1.34227			0.671135	−	0.741335i	$-0.265807\pi$
$769$	37.2223			1.34227			0.671135	+	0.741335i	$0.265807\pi$
$770$	−6.91127	+	14.6959i	−0.249065	+	0.529604i
$771$	55.3331			1.99277
$772$		−	34.0107i		−	1.22407i
$773$			5.08375i			0.182850i	0.995812	+	0.0914250i	$0.0291422\pi$
$773$			5.08375i			0.182850i	−0.995812	+	0.0914250i	$0.970858\pi$
$774$	−31.6956			−1.13928
$775$	−12.3310	−	14.8918i	−0.442943	−	0.534929i
$776$	−0.446697			−0.0160355
$777$		−	22.9916i		−	0.824819i
$778$		−	36.5759i		−	1.31131i
$779$	−3.07818			−0.110287
$780$	43.9882	−	93.5352i	1.57503	−	3.34910i
$781$	−7.16983			−0.256557
$782$		−	1.85156i		−	0.0662116i
$783$			161.688i			5.77825i
$784$	18.4180			0.657784
$785$	−2.74163	−	1.28935i	−0.0978531	−	0.0460189i
$786$	48.8039			1.74078
$787$			18.1020i			0.645268i	0.946524	+	0.322634i	$0.104568\pi$
$787$			18.1020i			0.645268i	−0.946524	+	0.322634i	$0.895432\pi$
$788$			30.9212i			1.10152i
$789$	−27.6671			−0.984975
$790$	26.7756	+	12.5922i	0.952634	+	0.448010i
$791$	−28.2417			−1.00416
$792$			4.14976i			0.147455i
$793$		−	37.4646i		−	1.33041i
$794$	−18.0339			−0.640001
$795$	−20.0277	+	42.5862i	−0.710309	+	1.51038i
$796$	5.05791			0.179273
$797$			15.9705i			0.565706i	0.959163	+	0.282853i	$0.0912808\pi$
$797$			15.9705i			0.565706i	−0.959163	+	0.282853i	$0.908719\pi$
$798$		−	23.8701i		−	0.844992i
$799$	1.86533			0.0659906
$800$	31.2581	−	25.8830i	1.10514	−	0.915102i
$801$	94.8071			3.34984
$802$		−	18.6448i		−	0.658370i
$803$			16.2081i			0.571971i
$804$	43.8040			1.54485
$805$	−8.46441	+	17.9985i	−0.298331	+	0.634362i
$806$	−49.7046			−1.75077
$807$			73.2272i			2.57772i
$808$		−	9.36969i		−	0.329625i
$809$	23.8474			0.838430			0.419215	−	0.907887i	$-0.362305\pi$
$809$	23.8474			0.838430			0.419215	+	0.907887i	$0.362305\pi$
$810$	−118.857	−	55.8969i	−4.17623	−	1.96402i
$811$	−14.8937			−0.522989			−0.261495	−	0.965205i	$-0.584215\pi$
$811$	−14.8937			−0.522989			−0.261495	+	0.965205i	$0.584215\pi$
$812$		−	81.4097i		−	2.85692i
$813$			36.4534i			1.27847i
$814$	4.10106			0.143742
$815$	7.67981	+	3.61170i	0.269012	+	0.126512i
$816$	3.98885			0.139638
$817$			1.96877i			0.0688786i
$818$		−	11.8852i		−	0.415555i
$819$	−171.067			−5.97757
$820$	6.61350	−	14.0627i	0.230953	−	0.491092i
$821$	27.9298			0.974756			0.487378	−	0.873191i	$-0.337953\pi$
$821$	27.9298			0.974756			0.487378	+	0.873191i	$0.337953\pi$
$822$		−	127.362i		−	4.44228i
$823$		−	5.81039i		−	0.202537i	−0.994859	−	0.101269i	$-0.967710\pi$
$823$		−	5.81039i		−	0.202537i	0.994859	−	0.101269i	$-0.0322902\pi$
$824$	−0.339947			−0.0118426
$825$	12.6573	−	10.4808i	0.440670	−	0.364893i
$826$	−22.7728			−0.792369
$827$			4.88459i			0.169854i	0.996387	+	0.0849270i	$0.0270657\pi$
$827$			4.88459i			0.169854i	−0.996387	+	0.0849270i	$0.972934\pi$
$828$			44.5164i			1.54705i
$829$	−14.1082			−0.489999			−0.244999	−	0.969523i	$-0.578788\pi$
$829$	−14.1082			−0.489999			−0.244999	+	0.969523i	$0.578788\pi$
$830$	11.3341	−	24.1005i	0.393412	−	0.836539i
$831$	−28.5341			−0.989838
$832$		−	61.7462i		−	2.14066i
$833$			1.91330i			0.0662918i
$834$	39.7709			1.37715
$835$	−39.7689	−	18.7027i	−1.37626	−	0.647235i
$836$	2.25776			0.0780863
$837$			61.0308i			2.10953i
$838$		−	67.6580i		−	2.33721i
$839$	−8.66407			−0.299117			−0.149559	−	0.988753i	$-0.547785\pi$
$839$	−8.66407			−0.299117			−0.149559	+	0.988753i	$0.547785\pi$
$840$	12.4500	+	5.85507i	0.429567	+	0.202019i
$841$	75.9491			2.61893
$842$		−	36.3449i		−	1.25253i
$843$		−	93.5370i		−	3.22159i
$844$	−36.2589			−1.24808
$845$	−24.5565	+	52.2162i	−0.844769	+	1.79629i
$846$	−84.5749			−2.90775
$847$			3.51972i			0.120939i
$848$			21.8874i			0.751616i
$849$	0.914118			0.0313725
$850$	2.33639	+	2.82159i	0.0801376	+	0.0967797i
$851$	5.02268			0.172175
$852$			53.2037i			1.82273i
$853$		−	34.3954i		−	1.17768i	−0.808251	−	0.588838i	$-0.799585\pi$
$853$		−	34.3954i		−	1.17768i	0.808251	−	0.588838i	$-0.200415\pi$
$854$	43.6792			1.49467
$855$	−7.42458	+	15.7874i	−0.253915	+	0.539917i
$856$	2.68863			0.0918956
$857$			15.7773i			0.538941i	0.963009	+	0.269470i	$0.0868486\pi$
$857$			15.7773i			0.538941i	−0.963009	+	0.269470i	$0.913151\pi$
$858$		−	42.2465i		−	1.44227i
$859$	−50.5565			−1.72497			−0.862484	−	0.506085i	$-0.831092\pi$
$859$	−50.5565			−1.72497			−0.862484	+	0.506085i	$0.831092\pi$
$860$	−8.99438	−	4.22992i	−0.306706	−	0.144239i
$861$	−35.6088			−1.21355
$862$		−	67.4101i		−	2.29600i
$863$		−	6.98665i		−	0.237828i	−0.992905	−	0.118914i	$-0.962059\pi$
$863$		−	6.98665i		−	0.237828i	0.992905	−	0.118914i	$-0.0379413\pi$
$864$	−128.105			−4.35820
$865$	21.3850	+	10.0570i	0.727111	+	0.341950i
$866$	26.3017			0.893769
$867$		−	55.4588i		−	1.88348i
$868$		−	30.7290i		−	1.04301i
$869$	6.41286			0.217541
$870$	−66.1140	+	140.583i	−2.24147	+	4.76620i
$871$	−36.7728			−1.24600
$872$		−	2.06585i		−	0.0699584i
$873$		−	6.55264i		−	0.221773i
$874$	5.21459			0.176386
$875$	−9.81248	−	38.1087i	−0.331723	−	1.28831i
$876$	120.272			4.06361
$877$		−	48.2962i		−	1.63085i	−0.578864	−	0.815424i	$-0.696504\pi$
$877$		−	48.2962i		−	1.63085i	0.578864	−	0.815424i	$-0.303496\pi$
$878$			20.4876i			0.691424i
$879$	57.1794			1.92861
$880$	3.25263	−	6.91630i	0.109646	−	0.233148i
$881$	40.4926			1.36423			0.682115	−	0.731245i	$-0.261060\pi$
$881$	40.4926			1.36423			0.682115	+	0.731245i	$0.261060\pi$
$882$		−	86.7498i		−	2.92102i
$883$			24.3138i			0.818225i	0.912484	+	0.409112i	$0.134162\pi$
$883$			24.3138i			0.818225i	−0.912484	+	0.409112i	$0.865838\pi$
$884$	4.99391			0.167963
$885$	20.8531	+	9.80689i	0.700968	+	0.329655i
$886$	20.1302			0.676288
$887$		−	45.5238i		−	1.52854i	−0.644896	−	0.764270i	$-0.723099\pi$
$887$		−	45.5238i		−	1.52854i	0.644896	−	0.764270i	$-0.276901\pi$
$888$		−	3.47432i		−	0.116591i
$889$	72.2384			2.42280
$890$	50.7360	+	23.8604i	1.70067	+	0.799802i
$891$	−28.4668			−0.953673
$892$			48.6011i			1.62728i
$893$			5.25337i			0.175797i
$894$	−98.4970			−3.29423
$895$	17.5997	−	37.4234i	0.588293	−	1.25093i
$896$	14.8521			0.496172
$897$		−	51.7403i		−	1.72756i
$898$			52.2528i			1.74370i
$899$	39.6141			1.32121
$900$	−56.1732	−	67.8386i	−1.87244	−	2.26129i
$901$	−2.27371			−0.0757482
$902$		−	6.35163i		−	0.211486i
$903$			22.7750i			0.757905i
$904$	−4.26768			−0.141941
$905$	2.31404	−	4.92050i	0.0769212	−	0.163563i
$906$	−29.0718			−0.965845
$907$		−	51.3222i		−	1.70413i	−0.523439	−	0.852063i	$-0.675351\pi$
$907$		−	51.3222i		−	1.70413i	0.523439	−	0.852063i	$-0.324649\pi$
$908$		−	2.95469i		−	0.0980549i
$909$	137.445			4.55876
$910$	−91.5465	−	43.0530i	−3.03474	−	1.42719i
$911$	−38.1272			−1.26321			−0.631605	−	0.775290i	$-0.717604\pi$
$911$	−38.1272			−1.26321			−0.631605	+	0.775290i	$0.717604\pi$
$912$			11.2339i			0.371992i
$913$		−	5.77215i		−	0.191030i
$914$	−1.73287			−0.0573181
$915$	−39.9970	−	18.8100i	−1.32226	−	0.621839i
$916$	−40.1440			−1.32640
$917$		−	25.3290i		−	0.836437i
$918$		−	11.5637i		−	0.381658i
$919$	35.2877			1.16403			0.582016	−	0.813177i	$-0.302264\pi$
$919$	35.2877			1.16403			0.582016	+	0.813177i	$0.302264\pi$
$920$	−1.27908	+	2.71980i	−0.0421700	+	0.0896690i
$921$	−51.8946			−1.70998
$922$		−	10.8537i		−	0.357447i
$923$		−	44.6636i		−	1.47012i
$924$	26.1181			0.859222
$925$	−7.65406	+	6.33788i	−0.251664	+	0.208388i
$926$	23.8768			0.784639
$927$		−	4.98671i		−	0.163785i
$928$			83.1506i			2.72955i
$929$	12.5507			0.411775			0.205888	−	0.978576i	$-0.433992\pi$
$929$	12.5507			0.411775			0.205888	+	0.978576i	$0.433992\pi$
$930$	−24.9554	+	53.0644i	−0.818321	+	1.74005i
$931$	−5.38846			−0.176600
$932$			29.0514i			0.951611i
$933$		−	7.22332i		−	0.236481i
$934$	−27.3682			−0.895515
$935$	0.718479	+	0.337890i	0.0234968	+	0.0110502i
$936$	−25.8504			−0.844948
$937$		−	38.3760i		−	1.25369i	−0.779145	−	0.626844i	$-0.784346\pi$
$937$		−	38.3760i		−	1.25369i	0.779145	−	0.626844i	$-0.215654\pi$
$938$		−	42.8727i		−	1.39984i
$939$	−23.9457			−0.781438
$940$	−24.0001	−	11.2869i	−0.782798	−	0.368138i
$941$	−4.06046			−0.132367			−0.0661837	−	0.997807i	$-0.521082\pi$
$941$	−4.06046			−0.132367			−0.0661837	+	0.997807i	$0.521082\pi$
$942$			9.18877i			0.299386i
$943$		−	7.77900i		−	0.253319i
$944$	10.7175			0.348826
$945$	−52.8635	+	112.407i	−1.71965	+	3.65661i
$946$	−4.06243			−0.132081
$947$			20.9272i			0.680043i	0.940418	+	0.340021i	$0.110434\pi$
$947$			20.9272i			0.680043i	−0.940418	+	0.340021i	$0.889566\pi$
$948$		−	47.5866i		−	1.54554i
$949$	−100.966			−3.27751
$950$	−7.94651	+	6.58004i	−0.257819	+	0.213485i
$951$	−110.434			−3.58108
$952$			0.664715i			0.0215435i
$953$		−	7.53124i		−	0.243961i	−0.992533	−	0.121980i	$-0.961076\pi$
$953$		−	7.53124i		−	0.243961i	0.992533	−	0.121980i	$-0.0389245\pi$
$954$	103.091			3.33770
$955$	25.1010	−	53.3740i	0.812249	−	1.72714i
$956$	25.1384			0.813034
$957$			33.6701i			1.08840i
$958$		−	47.1030i		−	1.52183i
$959$	−66.1005			−2.13450
$960$	−65.9200	−	31.0012i	−2.12756	−	1.00056i
$961$	−16.0472			−0.517652
$962$			25.5471i			0.823672i
$963$			39.4398i			1.27093i
$964$	45.5972			1.46859
$965$	30.4814	+	14.3350i	0.981232	+	0.461459i
$966$	60.3231			1.94086
$967$		−	44.2364i		−	1.42255i	−0.702916	−	0.711273i	$-0.748119\pi$
$967$		−	44.2364i		−	1.42255i	0.702916	−	0.711273i	$-0.251881\pi$
$968$			0.531875i			0.0170951i
$969$	−1.16700			−0.0374895
$970$	1.64912	−	3.50664i	0.0529502	−	0.112592i
$971$	−18.9432			−0.607915			−0.303958	−	0.952686i	$-0.598308\pi$
$971$	−18.9432			−0.607915			−0.303958	+	0.952686i	$0.598308\pi$
$972$			104.335i			3.34655i
$973$		−	20.6409i		−	0.661717i
$974$	21.1732			0.678434
$975$	65.2887	+	78.8471i	2.09091	+	2.52513i
$976$	−20.5566			−0.658002
$977$		−	11.2237i		−	0.359078i	−0.983751	−	0.179539i	$-0.942539\pi$
$977$		−	11.2237i		−	0.359078i	0.983751	−	0.179539i	$-0.0574606\pi$
$978$		−	25.7394i		−	0.823055i
$979$	12.1514			0.388362
$980$	11.5772	−	24.6173i	0.369819	−	0.786371i
$981$	30.3041			0.967535
$982$			64.8704i			2.07010i
$983$			10.8822i			0.347089i	0.984826	+	0.173545i	$0.0555221\pi$
$983$			10.8822i			0.347089i	−0.984826	+	0.173545i	$0.944478\pi$
$984$	−5.38095			−0.171538
$985$	−27.7124	−	13.0328i	−0.882992	−	0.415258i
$986$	−7.50580			−0.239033
$987$			60.7717i			1.93438i
$988$			14.0645i			0.447450i
$989$	−4.97537			−0.158207
$990$	−32.5762	−	15.3201i	−1.03534	−	0.486906i
$991$	−32.5993			−1.03555			−0.517776	−	0.855517i	$-0.673240\pi$
$991$	−32.5993			−1.03555			−0.517776	+	0.855517i	$0.673240\pi$
$992$			31.3861i			0.996510i
$993$			70.1870i			2.22732i
$994$	52.0725			1.65164
$995$	−2.13183	+	4.53305i	−0.0675834	+	0.143707i
$996$	−42.8322			−1.35719
$997$			5.39629i			0.170902i	0.996342	+	0.0854511i	$0.0272331\pi$
$997$			5.39629i			0.170902i	−0.996342	+	0.0854511i	$0.972767\pi$
$998$			30.6971i			0.971699i
$999$	31.3685			0.992456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.d.419.4	✓	22
5.2	odd	4		5225.2.a.bb.1.19		22
5.3	odd	4		5225.2.a.bb.1.4		22
5.4	even	2	inner	1045.2.b.d.419.19	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.d.419.4	✓	22	1.1	even	1	trivial
1045.2.b.d.419.19	yes	22	5.4	even	2	inner
5225.2.a.bb.1.4		22	5.3	odd	4
5225.2.a.bb.1.19		22	5.2	odd	4

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.06343i q^{2} -3.28666i q^{3} -2.25776 q^{4} +(0.951609 - 2.02347i) q^{5} -6.78181 q^{6} +3.51972i q^{7} +0.531875i q^{8} -7.80213 q^{9} +O(q^{10})\)	\(q-2.06343i q^{2} -3.28666i q^{3} -2.25776 q^{4} +(0.951609 - 2.02347i) q^{5} -6.78181 q^{6} +3.51972i q^{7} +0.531875i q^{8} -7.80213 q^{9} +(-4.17530 - 1.96358i) q^{10} -1.00000 q^{11} +7.42049i q^{12} -6.22938i q^{13} +7.26272 q^{14} +(-6.65046 - 3.12762i) q^{15} -3.41803 q^{16} -0.355073i q^{17} +16.0992i q^{18} +1.00000 q^{19} +(-2.14851 + 4.56852i) q^{20} +11.5681 q^{21} +2.06343i q^{22} +2.52714i q^{23} +1.74809 q^{24} +(-3.18888 - 3.85111i) q^{25} -12.8539 q^{26} +15.7829i q^{27} -7.94670i q^{28} +10.2445 q^{29} +(-6.45363 + 13.7228i) q^{30} +3.86688 q^{31} +8.11664i q^{32} +3.28666i q^{33} -0.732669 q^{34} +(7.12207 + 3.34940i) q^{35} +17.6153 q^{36} -1.98749i q^{37} -2.06343i q^{38} -20.4739 q^{39} +(1.07623 + 0.506137i) q^{40} -3.07818 q^{41} -23.8701i q^{42} +1.96877i q^{43} +2.25776 q^{44} +(-7.42458 + 15.7874i) q^{45} +5.21459 q^{46} +5.25337i q^{47} +11.2339i q^{48} -5.38846 q^{49} +(-7.94651 + 6.58004i) q^{50} -1.16700 q^{51} +14.0645i q^{52} -6.40350i q^{53} +32.5671 q^{54} +(-0.951609 + 2.02347i) q^{55} -1.87205 q^{56} -3.28666i q^{57} -21.1388i q^{58} -3.13558 q^{59} +(15.0152 + 7.06141i) q^{60} +6.01417 q^{61} -7.97906i q^{62} -27.4613i q^{63} +9.91209 q^{64} +(-12.6050 - 5.92794i) q^{65} +6.78181 q^{66} -5.90311i q^{67} +0.801669i q^{68} +8.30585 q^{69} +(6.91127 - 14.6959i) q^{70} +7.16983 q^{71} -4.14976i q^{72} -16.2081i q^{73} -4.10106 q^{74} +(-12.6573 + 10.4808i) q^{75} -2.25776 q^{76} -3.51972i q^{77} +42.2465i q^{78} -6.41286 q^{79} +(-3.25263 + 6.91630i) q^{80} +28.4668 q^{81} +6.35163i q^{82} +5.77215i q^{83} -26.1181 q^{84} +(-0.718479 - 0.337890i) q^{85} +4.06243 q^{86} -33.6701i q^{87} -0.531875i q^{88} -12.1514 q^{89} +(32.5762 + 15.3201i) q^{90} +21.9257 q^{91} -5.70568i q^{92} -12.7091i q^{93} +10.8400 q^{94} +(0.951609 - 2.02347i) q^{95} +26.6766 q^{96} +0.839854i q^{97} +11.1187i q^{98} +7.80213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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