LMFDB - Embedded newform 1815.2.c.j.364.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.6
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.j.364.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90743i q^{2} -1.00000i q^{3} -1.63829 q^{4} +(-2.10308 - 0.759628i) q^{5} -1.90743 q^{6} -4.45734i q^{7} -0.689943i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.90743i q^{2} -1.00000i q^{3} -1.63829 q^{4} +(-2.10308 - 0.759628i) q^{5} -1.90743 q^{6} -4.45734i q^{7} -0.689943i q^{8} -1.00000 q^{9} +(-1.44894 + 4.01149i) q^{10} +1.63829i q^{12} -0.534008i q^{13} -8.50206 q^{14} +(-0.759628 + 2.10308i) q^{15} -4.59259 q^{16} -4.54422i q^{17} +1.90743i q^{18} -1.92453 q^{19} +(3.44546 + 1.24449i) q^{20} -4.45734 q^{21} -5.18745i q^{23} -0.689943 q^{24} +(3.84593 + 3.19512i) q^{25} -1.01858 q^{26} +1.00000i q^{27} +7.30240i q^{28} +4.75453 q^{29} +(4.01149 + 1.44894i) q^{30} +3.49728 q^{31} +7.38016i q^{32} -8.66777 q^{34} +(-3.38592 + 9.37416i) q^{35} +1.63829 q^{36} +0.527144i q^{37} +3.67091i q^{38} -0.534008 q^{39} +(-0.524100 + 1.45101i) q^{40} +4.69578 q^{41} +8.50206i q^{42} +3.02459i q^{43} +(2.10308 + 0.759628i) q^{45} -9.89470 q^{46} -11.9878i q^{47} +4.59259i q^{48} -12.8679 q^{49} +(6.09447 - 7.33584i) q^{50} -4.54422 q^{51} +0.874857i q^{52} +5.02443i q^{53} +1.90743 q^{54} -3.07531 q^{56} +1.92453i q^{57} -9.06894i q^{58} -13.6495 q^{59} +(1.24449 - 3.44546i) q^{60} +11.6915 q^{61} -6.67082i q^{62} +4.45734i q^{63} +4.89194 q^{64} +(-0.405647 + 1.12306i) q^{65} +11.5622i q^{67} +7.44473i q^{68} -5.18745 q^{69} +(17.8805 + 6.45840i) q^{70} +3.36587 q^{71} +0.689943i q^{72} -0.650391i q^{73} +1.00549 q^{74} +(3.19512 - 3.84593i) q^{75} +3.15294 q^{76} +1.01858i q^{78} +17.7199 q^{79} +(9.65861 + 3.48866i) q^{80} +1.00000 q^{81} -8.95686i q^{82} +4.24738i q^{83} +7.30240 q^{84} +(-3.45191 + 9.55687i) q^{85} +5.76920 q^{86} -4.75453i q^{87} +8.24094 q^{89} +(1.44894 - 4.01149i) q^{90} -2.38025 q^{91} +8.49854i q^{92} -3.49728i q^{93} -22.8658 q^{94} +(4.04746 + 1.46193i) q^{95} +7.38016 q^{96} -1.13839i q^{97} +24.5445i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9} - 6 q^{10} - 12 q^{14} + 48 q^{16} + 32 q^{19} - 2 q^{20} - 16 q^{21} + 24 q^{24} + 2 q^{25} + 32 q^{26} - 8 q^{30} - 12 q^{34} + 10 q^{35} + 24 q^{36} + 36 q^{39} + 34 q^{40} + 2 q^{45} - 56 q^{46} - 24 q^{49} + 46 q^{50} - 36 q^{51} + 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} - 40 q^{61} + 12 q^{64} + 10 q^{65} - 2 q^{70} + 64 q^{71} - 136 q^{74} + 20 q^{75} - 68 q^{76} + 64 q^{79} + 76 q^{80} + 24 q^{81} + 60 q^{84} - 72 q^{86} + 20 q^{89} + 6 q^{90} - 4 q^{94} + 64 q^{95} - 56 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9 - 6 * q^10 - 12 * q^14 + 48 * q^16 + 32 * q^19 - 2 * q^20 - 16 * q^21 + 24 * q^24 + 2 * q^25 + 32 * q^26 - 8 * q^30 - 12 * q^34 + 10 * q^35 + 24 * q^36 + 36 * q^39 + 34 * q^40 + 2 * q^45 - 56 * q^46 - 24 * q^49 + 46 * q^50 - 36 * q^51 + 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 - 40 * q^61 + 12 * q^64 + 10 * q^65 - 2 * q^70 + 64 * q^71 - 136 * q^74 + 20 * q^75 - 68 * q^76 + 64 * q^79 + 76 * q^80 + 24 * q^81 + 60 * q^84 - 72 * q^86 + 20 * q^89 + 6 * q^90 - 4 * q^94 + 64 * q^95 - 56 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.90743i		−	1.34876i	−0.738386	−	0.674378i	$-0.764412\pi$
$2$		−	1.90743i		−	1.34876i	0.738386	−	0.674378i	$-0.235588\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.63829			−0.819143
$5$	−2.10308	−	0.759628i	−0.940528	−	0.339716i
$5$	−2.10308	−	0.759628i	−0.940528	−	0.339716i
$6$	−1.90743			−0.778705
$7$		−	4.45734i		−	1.68472i	−0.538919	−	0.842358i	$-0.681167\pi$
$7$		−	4.45734i		−	1.68472i	0.538919	−	0.842358i	$-0.318833\pi$
$8$		−	0.689943i		−	0.243932i
$9$	−1.00000			−0.333333
$10$	−1.44894	+	4.01149i	−0.458194	+	1.26854i
$11$		0			0
$11$		0			0
$12$			1.63829i			0.472933i
$13$		−	0.534008i		−	0.148107i	−0.997254	−	0.0740535i	$-0.976406\pi$
$13$		−	0.534008i		−	0.148107i	0.997254	−	0.0740535i	$-0.0235936\pi$
$14$	−8.50206			−2.27227
$15$	−0.759628	+	2.10308i	−0.196135	+	0.543014i
$16$	−4.59259			−1.14815
$17$		−	4.54422i		−	1.10213i	−0.834461	−	0.551067i	$-0.814221\pi$
$17$		−	4.54422i		−	1.10213i	0.834461	−	0.551067i	$-0.185779\pi$
$18$			1.90743i			0.449585i
$19$	−1.92453			−0.441518			−0.220759	−	0.975328i	$-0.570853\pi$
$19$	−1.92453			−0.441518			−0.220759	+	0.975328i	$0.570853\pi$
$20$	3.44546	+	1.24449i	0.770427	+	0.278276i
$21$	−4.45734			−0.972671
$22$		0			0
$23$		−	5.18745i		−	1.08166i	−0.841132	−	0.540830i	$-0.818110\pi$
$23$		−	5.18745i		−	1.08166i	0.841132	−	0.540830i	$-0.181890\pi$
$24$	−0.689943			−0.140834
$25$	3.84593	+	3.19512i	0.769186	+	0.639025i
$26$	−1.01858			−0.199760
$27$			1.00000i			0.192450i
$28$			7.30240i			1.38002i
$29$	4.75453			0.882895			0.441447	−	0.897287i	$-0.354465\pi$
$29$	4.75453			0.882895			0.441447	+	0.897287i	$0.354465\pi$
$30$	4.01149	+	1.44894i	0.732394	+	0.264538i
$31$	3.49728			0.628130			0.314065	−	0.949401i	$-0.398309\pi$
$31$	3.49728			0.628130			0.314065	+	0.949401i	$0.398309\pi$
$32$			7.38016i			1.30464i
$33$		0			0
$34$	−8.66777			−1.48651
$35$	−3.38592	+	9.37416i	−0.572325	+	1.58452i
$36$	1.63829			0.273048
$37$			0.527144i			0.0866620i	0.999061	+	0.0433310i	$0.0137970\pi$
$37$			0.527144i			0.0866620i	−0.999061	+	0.0433310i	$0.986203\pi$
$38$			3.67091i			0.595501i
$39$	−0.534008			−0.0855096
$40$	−0.524100	+	1.45101i	−0.0828675	+	0.229425i
$41$	4.69578			0.733357			0.366678	−	0.930348i	$-0.380495\pi$
$41$	4.69578			0.733357			0.366678	+	0.930348i	$0.380495\pi$
$42$			8.50206i			1.31190i
$43$			3.02459i			0.461246i	0.973043	+	0.230623i	$0.0740765\pi$
$43$			3.02459i			0.461246i	−0.973043	+	0.230623i	$0.925924\pi$
$44$		0			0
$45$	2.10308	+	0.759628i	0.313509	+	0.113239i
$46$	−9.89470			−1.45889
$47$		−	11.9878i		−	1.74860i	−0.485390	−	0.874298i	$-0.661323\pi$
$47$		−	11.9878i		−	1.74860i	0.485390	−	0.874298i	$-0.338677\pi$
$48$			4.59259i			0.662883i
$49$	−12.8679			−1.83827
$50$	6.09447	−	7.33584i	0.861889	−	1.03744i
$51$	−4.54422			−0.636318
$52$			0.874857i			0.121321i
$53$			5.02443i			0.690158i	0.938574	+	0.345079i	$0.112148\pi$
$53$			5.02443i			0.690158i	−0.938574	+	0.345079i	$0.887852\pi$
$54$	1.90743			0.259568
$55$		0			0
$56$	−3.07531			−0.410955
$57$			1.92453i			0.254911i
$58$		−	9.06894i		−	1.19081i
$59$	−13.6495			−1.77702			−0.888508	−	0.458861i	$-0.848258\pi$
$59$	−13.6495			−1.77702			−0.888508	+	0.458861i	$0.848258\pi$
$60$	1.24449	−	3.44546i	0.160663	−	0.444806i
$61$	11.6915			1.49695			0.748473	−	0.663165i	$-0.230787\pi$
$61$	11.6915			1.49695			0.748473	+	0.663165i	$0.230787\pi$
$62$		−	6.67082i		−	0.847195i
$63$			4.45734i			0.561572i
$64$	4.89194			0.611493
$65$	−0.405647	+	1.12306i	−0.0503143	+	0.139299i
$66$		0			0
$67$			11.5622i			1.41255i	0.707936	+	0.706276i	$0.249626\pi$
$67$			11.5622i			1.41255i	−0.707936	+	0.706276i	$0.750374\pi$
$68$			7.44473i			0.902806i
$69$	−5.18745			−0.624496
$70$	17.8805	+	6.45840i	2.13713	+	0.771926i
$71$	3.36587			0.399455			0.199728	−	0.979851i	$-0.435994\pi$
$71$	3.36587			0.399455			0.199728	+	0.979851i	$0.435994\pi$
$72$			0.689943i			0.0813105i
$73$		−	0.650391i		−	0.0761226i	−0.999275	−	0.0380613i	$-0.987882\pi$
$73$		−	0.650391i		−	0.0761226i	0.999275	−	0.0380613i	$-0.0121182\pi$
$74$	1.00549			0.116886
$75$	3.19512	−	3.84593i	0.368941	−	0.444090i
$76$	3.15294			0.361667
$77$		0			0
$78$			1.01858i			0.115332i
$79$	17.7199			1.99365			0.996823	−	0.0796525i	$-0.0253811\pi$
$79$	17.7199			1.99365			0.996823	+	0.0796525i	$0.0253811\pi$
$80$	9.65861	+	3.48866i	1.07987	+	0.390044i
$81$	1.00000			0.111111
$82$		−	8.95686i		−	0.989120i
$83$			4.24738i			0.466210i	0.972452	+	0.233105i	$0.0748886\pi$
$83$			4.24738i			0.466210i	−0.972452	+	0.233105i	$0.925111\pi$
$84$	7.30240			0.796757
$85$	−3.45191	+	9.55687i	−0.374413	+	1.03659i
$86$	5.76920			0.622109
$87$		−	4.75453i		−	0.509739i
$88$		0			0
$89$	8.24094			0.873538			0.436769	−	0.899574i	$-0.356123\pi$
$89$	8.24094			0.873538			0.436769	+	0.899574i	$0.356123\pi$
$90$	1.44894	−	4.01149i	0.152731	−	0.422848i
$91$	−2.38025			−0.249518
$92$			8.49854i			0.886034i
$93$		−	3.49728i		−	0.362651i
$94$	−22.8658			−2.35843
$95$	4.04746	+	1.46193i	0.415260	+	0.149991i
$96$	7.38016			0.753234
$97$		−	1.13839i		−	0.115586i	−0.998329	−	0.0577931i	$-0.981594\pi$
$97$		−	1.13839i		−	0.115586i	0.998329	−	0.0577931i	$-0.0184064\pi$
$98$			24.5445i			2.47937i
$99$		0			0
$100$	−6.30074	−	5.23453i	−0.630074	−	0.523453i
$101$	−1.02375			−0.101867			−0.0509333	−	0.998702i	$-0.516220\pi$
$101$	−1.02375			−0.101867			−0.0509333	+	0.998702i	$0.516220\pi$
$102$			8.66777i			0.858237i
$103$			4.79071i			0.472042i	0.971748	+	0.236021i	$0.0758435\pi$
$103$			4.79071i			0.472042i	−0.971748	+	0.236021i	$0.924157\pi$
$104$	−0.368435			−0.0361280
$105$	9.37416	+	3.38592i	0.914824	+	0.330432i
$106$	9.58374			0.930855
$107$		−	0.735971i		−	0.0711490i	−0.999367	−	0.0355745i	$-0.988674\pi$
$107$		−	0.735971i		−	0.0711490i	0.999367	−	0.0355745i	$-0.0113261\pi$
$108$		−	1.63829i		−	0.157644i
$109$	0.0433994			0.00415691			0.00207845	−	0.999998i	$-0.499338\pi$
$109$	0.0433994			0.00415691			0.00207845	+	0.999998i	$0.499338\pi$
$110$		0			0
$111$	0.527144			0.0500343
$112$			20.4707i			1.93430i
$113$		−	11.2006i		−	1.05366i	−0.849970	−	0.526831i	$-0.823380\pi$
$113$		−	11.2006i		−	1.05366i	0.849970	−	0.526831i	$-0.176620\pi$
$114$	3.67091			0.343813
$115$	−3.94053	+	10.9097i	−0.367457	+	1.01733i
$116$	−7.78929			−0.723217
$117$			0.534008i			0.0493690i
$118$			26.0355i			2.39676i
$119$	−20.2551			−1.85678
$120$	1.45101	+	0.524100i	0.132458	+	0.0478435i
$121$		0			0
$122$		−	22.3007i		−	2.01901i
$123$		−	4.69578i		−	0.423404i
$124$	−5.72955			−0.514529
$125$	−5.66121	−	9.64109i	−0.506354	−	0.862325i
$126$	8.50206			0.757423
$127$			8.17488i			0.725403i	0.931905	+	0.362702i	$0.118146\pi$
$127$			8.17488i			0.725403i	−0.931905	+	0.362702i	$0.881854\pi$
$128$			5.42927i			0.479884i
$129$	3.02459			0.266301
$130$	2.14216	+	0.773743i	0.187880	+	0.0678617i
$131$	17.7054			1.54693			0.773465	−	0.633839i	$-0.218522\pi$
$131$	17.7054			1.54693			0.773465	+	0.633839i	$0.218522\pi$
$132$		0			0
$133$			8.57830i			0.743833i
$134$	22.0542			1.90519
$135$	0.759628	−	2.10308i	0.0653784	−	0.181005i
$136$	−3.13525			−0.268845
$137$		−	5.48584i		−	0.468687i	−0.972154	−	0.234343i	$-0.924706\pi$
$137$		−	5.48584i		−	0.468687i	0.972154	−	0.234343i	$-0.0752940\pi$
$138$			9.89470i			0.842293i
$139$	−3.25952			−0.276469			−0.138235	−	0.990400i	$-0.544143\pi$
$139$	−3.25952			−0.276469			−0.138235	+	0.990400i	$0.544143\pi$
$140$	5.54710	−	15.3576i	0.468816	−	1.29795i
$141$	−11.9878			−1.00955
$142$		−	6.42016i		−	0.538768i
$143$		0			0
$144$	4.59259			0.382716
$145$	−9.99919	−	3.61168i	−0.830387	−	0.299933i
$146$	−1.24058			−0.102671
$147$			12.8679i			1.06132i
$148$		−	0.863613i		−	0.0709886i
$149$	−2.80635			−0.229905			−0.114953	−	0.993371i	$-0.536672\pi$
$149$	−2.80635			−0.229905			−0.114953	+	0.993371i	$0.536672\pi$
$150$	−7.33584	−	6.09447i	−0.598969	−	0.497612i
$151$	−14.1638			−1.15263			−0.576317	−	0.817226i	$-0.695511\pi$
$151$	−14.1638			−1.15263			−0.576317	+	0.817226i	$0.695511\pi$
$152$			1.32782i			0.107700i
$153$			4.54422i			0.367378i
$154$		0			0
$155$	−7.35508	−	2.65663i	−0.590774	−	0.213386i
$156$	0.874857			0.0700446
$157$		−	3.11084i		−	0.248272i	−0.992265	−	0.124136i	$-0.960384\pi$
$157$		−	3.11084i		−	0.248272i	0.992265	−	0.124136i	$-0.0396160\pi$
$158$		−	33.7995i		−	2.68894i
$159$	5.02443			0.398463
$160$	5.60617	−	15.5211i	0.443207	−	1.22705i
$161$	−23.1222			−1.82229
$162$		−	1.90743i		−	0.149862i
$163$			19.3745i			1.51752i	0.651368	+	0.758762i	$0.274195\pi$
$163$			19.3745i			1.51752i	−0.651368	+	0.758762i	$0.725805\pi$
$164$	−7.69303			−0.600724
$165$		0			0
$166$	8.10157			0.628804
$167$		−	4.14992i		−	0.321130i	−0.987025	−	0.160565i	$-0.948668\pi$
$167$		−	4.14992i		−	0.321130i	0.987025	−	0.160565i	$-0.0513317\pi$
$168$			3.07531i			0.237265i
$169$	12.7148			0.978064
$170$	18.2291	+	6.58428i	1.39810	+	0.504991i
$171$	1.92453			0.147173
$172$		−	4.95515i		−	0.377827i
$173$		−	10.6654i		−	0.810878i	−0.914122	−	0.405439i	$-0.867119\pi$
$173$		−	10.6654i		−	0.810878i	0.914122	−	0.405439i	$-0.132881\pi$
$174$	−9.06894			−0.687514
$175$	14.2417	−	17.1426i	1.07657	−	1.29586i
$176$		0			0
$177$			13.6495i			1.02596i
$178$		−	15.7190i		−	1.17819i
$179$	−22.6337			−1.69172			−0.845862	−	0.533402i	$-0.820913\pi$
$179$	−22.6337			−1.69172			−0.845862	+	0.533402i	$0.820913\pi$
$180$	−3.44546	−	1.24449i	−0.256809	−	0.0927587i
$181$	14.5822			1.08389			0.541944	−	0.840415i	$-0.317689\pi$
$181$	14.5822			1.08389			0.541944	+	0.840415i	$0.317689\pi$
$182$			4.54016i			0.336539i
$183$		−	11.6915i		−	0.864262i
$184$	−3.57905			−0.263851
$185$	0.400433	−	1.10863i	0.0294404	−	0.0815080i
$186$	−6.67082			−0.489128
$187$		0			0
$188$			19.6394i			1.43235i
$189$	4.45734			0.324224
$190$	2.78853	−	7.72024i	0.202301	−	0.560085i
$191$	3.96434			0.286850			0.143425	−	0.989661i	$-0.454188\pi$
$191$	3.96434			0.286850			0.143425	+	0.989661i	$0.454188\pi$
$192$		−	4.89194i		−	0.353046i
$193$		−	0.0300531i		−	0.00216327i	−0.999999	−	0.00108164i	$-0.999656\pi$
$193$		−	0.0300531i		−	0.00216327i	0.999999	−	0.00108164i	$-0.000344295\pi$
$194$	−2.17140			−0.155898
$195$	1.12306	+	0.405647i	0.0804242	+	0.0290490i
$196$	21.0812			1.50580
$197$		−	5.50562i		−	0.392259i	−0.980578	−	0.196130i	$-0.937163\pi$
$197$		−	5.50562i		−	0.392259i	0.980578	−	0.196130i	$-0.0628373\pi$
$198$		0			0
$199$	3.12623			0.221612			0.110806	−	0.993842i	$-0.464657\pi$
$199$	3.12623			0.221612			0.110806	+	0.993842i	$0.464657\pi$
$200$	2.20445	−	2.65347i	0.155878	−	0.187629i
$201$	11.5622			0.815538
$202$			1.95273i			0.137393i
$203$		−	21.1926i		−	1.48743i
$204$	7.44473			0.521235
$205$	−9.87561	−	3.56704i	−0.689743	−	0.249133i
$206$	9.13794			0.636670
$207$			5.18745i			0.360553i
$208$			2.45248i			0.170049i
$209$		0			0
$210$	6.45840	−	17.8805i	0.445672	−	1.23387i
$211$	−20.3904			−1.40373			−0.701867	−	0.712308i	$-0.747650\pi$
$211$	−20.3904			−1.40373			−0.701867	+	0.712308i	$0.747650\pi$
$212$		−	8.23145i		−	0.565338i
$213$		−	3.36587i		−	0.230626i
$214$	−1.40381			−0.0959626
$215$	2.29757	−	6.36098i	0.156693	−	0.433815i
$216$	0.689943			0.0469447
$217$		−	15.5886i		−	1.05822i
$218$		−	0.0827813i		−	0.00560666i
$219$	−0.650391			−0.0439494
$220$		0			0
$221$	−2.42665			−0.163234
$222$		−	1.00549i		−	0.0674841i
$223$			10.3019i			0.689865i	0.938627	+	0.344933i	$0.112098\pi$
$223$			10.3019i			0.689865i	−0.938627	+	0.344933i	$0.887902\pi$
$224$	32.8958			2.19795
$225$	−3.84593	−	3.19512i	−0.256395	−	0.213008i
$226$	−21.3643			−1.42113
$227$		−	6.27244i		−	0.416317i	−0.978095	−	0.208158i	$-0.933253\pi$
$227$		−	6.27244i		−	0.416317i	0.978095	−	0.208158i	$-0.0667469\pi$
$228$		−	3.15294i		−	0.208808i
$229$	−1.38111			−0.0912660			−0.0456330	−	0.998958i	$-0.514530\pi$
$229$	−1.38111			−0.0912660			−0.0456330	+	0.998958i	$0.514530\pi$
$230$	20.8094	+	7.51629i	1.37213	+	0.495610i
$231$		0			0
$232$		−	3.28036i		−	0.215366i
$233$		−	8.30444i		−	0.544042i	−0.962291	−	0.272021i	$-0.912308\pi$
$233$		−	8.30444i		−	0.544042i	0.962291	−	0.272021i	$-0.0876920\pi$
$234$	1.01858			0.0665868
$235$	−9.10624	+	25.2113i	−0.594026	+	1.64460i
$236$	22.3618			1.45563
$237$		−	17.7199i		−	1.15103i
$238$			38.6352i			2.50435i
$239$	−10.2950			−0.665931			−0.332966	−	0.942939i	$-0.608049\pi$
$239$	−10.2950			−0.665931			−0.332966	+	0.942939i	$0.608049\pi$
$240$	3.48866	−	9.65861i	0.225192	−	0.623460i
$241$	12.2340			0.788060			0.394030	−	0.919097i	$-0.371081\pi$
$241$	12.2340			0.788060			0.394030	+	0.919097i	$0.371081\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−19.1541			−1.22621
$245$	27.0622	+	9.77479i	1.72894	+	0.624488i
$246$	−8.95686			−0.571068
$247$			1.02772i			0.0653920i
$248$		−	2.41292i		−	0.153221i
$249$	4.24738			0.269167
$250$	−18.3897	+	10.7984i	−1.16307	+	0.682949i
$251$	−4.65658			−0.293921			−0.146960	−	0.989142i	$-0.546949\pi$
$251$	−4.65658			−0.293921			−0.146960	+	0.989142i	$0.546949\pi$
$252$		−	7.30240i		−	0.460008i
$253$		0			0
$254$	15.5930			0.978392
$255$	9.55687	+	3.45191i	0.598474	+	0.216167i
$256$	20.1398			1.25874
$257$		−	18.3364i		−	1.14380i	−0.820325	−	0.571898i	$-0.806207\pi$
$257$		−	18.3364i		−	1.14380i	0.820325	−	0.571898i	$-0.193793\pi$
$258$		−	5.76920i		−	0.359175i
$259$	2.34966			0.146001
$260$	0.664566	−	1.83990i	0.0412146	−	0.114106i
$261$	−4.75453			−0.294298
$262$		−	33.7719i		−	2.08643i
$263$		−	9.80198i		−	0.604416i	−0.953242	−	0.302208i	$-0.902276\pi$
$263$		−	9.80198i		−	0.604416i	0.953242	−	0.302208i	$-0.0977237\pi$
$264$		0			0
$265$	3.81669	−	10.5668i	0.234458	−	0.649113i
$266$	16.3625			1.00325
$267$		−	8.24094i		−	0.504337i
$268$		−	18.9423i		−	1.15708i
$269$	−11.9309			−0.727441			−0.363721	−	0.931508i	$-0.618494\pi$
$269$	−11.9309			−0.727441			−0.363721	+	0.931508i	$0.618494\pi$
$270$	−4.01149	−	1.44894i	−0.244131	−	0.0881795i
$271$	−30.4048			−1.84696			−0.923481	−	0.383644i	$-0.874669\pi$
$271$	−30.4048			−1.84696			−0.923481	+	0.383644i	$0.874669\pi$
$272$			20.8697i			1.26541i
$273$			2.38025i			0.144059i
$274$	−10.4638			−0.632144
$275$		0			0
$276$	8.49854			0.511552
$277$		−	22.1444i		−	1.33053i	−0.746608	−	0.665264i	$-0.768319\pi$
$277$		−	22.1444i		−	1.33053i	0.746608	−	0.665264i	$-0.231681\pi$
$278$			6.21731i			0.372890i
$279$	−3.49728			−0.209377
$280$	6.46763	+	2.33609i	0.386515	+	0.139608i
$281$	17.0323			1.01606			0.508030	−	0.861340i	$-0.330374\pi$
$281$	17.0323			1.01606			0.508030	+	0.861340i	$0.330374\pi$
$282$			22.8658i			1.36164i
$283$		−	7.92150i		−	0.470884i	−0.971888	−	0.235442i	$-0.924346\pi$
$283$		−	7.92150i		−	0.470884i	0.971888	−	0.235442i	$-0.0756538\pi$
$284$	−5.51426			−0.327211
$285$	1.46193	−	4.04746i	0.0865972	−	0.239751i
$286$		0			0
$287$		−	20.9307i		−	1.23550i
$288$		−	7.38016i		−	0.434880i
$289$	−3.64990			−0.214700
$290$	−6.88902	+	19.0727i	−0.404537	+	1.11999i
$291$	−1.13839			−0.0667337
$292$			1.06553i			0.0623553i
$293$			22.3396i			1.30509i	0.757750	+	0.652545i	$0.226299\pi$
$293$			22.3396i			1.30509i	−0.757750	+	0.652545i	$0.773701\pi$
$294$	24.5445			1.43147
$295$	28.7061	+	10.3686i	1.67133	+	0.603681i
$296$	0.363699			0.0211396
$297$		0			0
$298$			5.35291i			0.310086i
$299$	−2.77014			−0.160201
$300$	−5.23453	+	6.30074i	−0.302216	+	0.363773i
$301$	13.4816			0.777069
$302$			27.0164i			1.55462i
$303$			1.02375i			0.0588128i
$304$	8.83860			0.506928
$305$	−24.5883	−	8.88120i	−1.40792	−	0.508536i
$306$	8.66777			0.495503
$307$			9.33327i			0.532678i	0.963879	+	0.266339i	$0.0858140\pi$
$307$			9.33327i			0.532678i	−0.963879	+	0.266339i	$0.914186\pi$
$308$		0			0
$309$	4.79071			0.272534
$310$	−5.06734	+	14.0293i	−0.287806	+	0.796811i
$311$	−11.2480			−0.637815			−0.318907	−	0.947786i	$-0.603316\pi$
$311$	−11.2480			−0.637815			−0.318907	+	0.947786i	$0.603316\pi$
$312$			0.368435i			0.0208585i
$313$			10.8640i			0.614069i	0.951698	+	0.307035i	$0.0993367\pi$
$313$			10.8640i			0.614069i	−0.951698	+	0.307035i	$0.900663\pi$
$314$	−5.93371			−0.334859
$315$	3.38592	−	9.37416i	0.190775	−	0.528174i
$316$	−29.0303			−1.63308
$317$			12.6895i			0.712714i	0.934350	+	0.356357i	$0.115981\pi$
$317$			12.6895i			0.712714i	−0.934350	+	0.356357i	$0.884019\pi$
$318$		−	9.58374i		−	0.537429i
$319$		0			0
$320$	−10.2882	−	3.71606i	−0.575126	−	0.207734i
$321$	−0.735971			−0.0410779
$322$			44.1040i			2.45782i
$323$			8.74550i			0.486613i
$324$	−1.63829			−0.0910159
$325$	1.70622	−	2.05376i	0.0946441	−	0.113922i
$326$	36.9554			2.04677
$327$		−	0.0433994i		−	0.00239999i
$328$		−	3.23982i		−	0.178889i
$329$	−53.4335			−2.94588
$330$		0			0
$331$	−23.0627			−1.26764			−0.633821	−	0.773480i	$-0.718514\pi$
$331$	−23.0627			−1.26764			−0.633821	+	0.773480i	$0.718514\pi$
$332$		−	6.95842i		−	0.381893i
$333$		−	0.527144i		−	0.0288873i
$334$	−7.91568			−0.433127
$335$	8.78300	−	24.3164i	0.479867	−	1.32855i
$336$	20.4707			1.11677
$337$		−	32.3630i		−	1.76293i	−0.472254	−	0.881463i	$-0.656559\pi$
$337$		−	32.3630i		−	1.76293i	0.472254	−	0.881463i	$-0.343441\pi$
$338$		−	24.2527i		−	1.31917i
$339$	−11.2006			−0.608332
$340$	5.65522	−	15.6569i	0.306698	−	0.849114i
$341$		0			0
$342$		−	3.67091i		−	0.198500i
$343$			26.1550i			1.41224i
$344$	2.08680			0.112513
$345$	10.9097	+	3.94053i	0.587356	+	0.212151i
$346$	−20.3436			−1.09368
$347$		−	29.0843i		−	1.56133i	−0.624952	−	0.780663i	$-0.714881\pi$
$347$		−	29.0843i		−	1.56133i	0.624952	−	0.780663i	$-0.285119\pi$
$348$			7.78929i			0.417550i
$349$	14.4037			0.771012			0.385506	−	0.922705i	$-0.374027\pi$
$349$	14.4037			0.771012			0.385506	+	0.922705i	$0.374027\pi$
$350$	−32.6983	−	27.1651i	−1.74780	−	1.45204i
$351$	0.534008			0.0285032
$352$		0			0
$353$			28.9227i			1.53940i	0.638406	+	0.769700i	$0.279594\pi$
$353$			28.9227i			1.53940i	−0.638406	+	0.769700i	$0.720406\pi$
$354$	26.0355			1.38377
$355$	−7.07871	−	2.55681i	−0.375699	−	0.135701i
$356$	−13.5010			−0.715553
$357$			20.2551i			1.07201i
$358$			43.1722i			2.28172i
$359$	−23.5159			−1.24112			−0.620562	−	0.784157i	$-0.713095\pi$
$359$	−23.5159			−1.24112			−0.620562	+	0.784157i	$0.713095\pi$
$360$	0.524100	−	1.45101i	0.0276225	−	0.0764749i
$361$	−15.2962			−0.805061
$362$		−	27.8145i		−	1.46190i
$363$		0			0
$364$	3.89953			0.204391
$365$	−0.494055	+	1.36783i	−0.0258600	+	0.0715954i
$366$	−22.3007			−1.16568
$367$		−	25.3037i		−	1.32084i	−0.750895	−	0.660421i	$-0.770378\pi$
$367$		−	25.3037i		−	1.32084i	0.750895	−	0.660421i	$-0.229622\pi$
$368$			23.8239i			1.24190i
$369$	−4.69578			−0.244452
$370$	−2.11463	−	0.763798i	−0.109934	−	0.0397080i
$371$	22.3956			1.16272
$372$			5.72955i			0.297063i
$373$		−	16.2682i		−	0.842334i	−0.906983	−	0.421167i	$-0.861621\pi$
$373$		−	16.2682i		−	0.842334i	0.906983	−	0.421167i	$-0.138379\pi$
$374$		0			0
$375$	−9.64109	+	5.66121i	−0.497864	+	0.292344i
$376$	−8.27087			−0.426538
$377$		−	2.53896i		−	0.130763i
$378$		−	8.50206i		−	0.437299i
$379$	−25.0263			−1.28552			−0.642758	−	0.766069i	$-0.722210\pi$
$379$	−25.0263			−1.28552			−0.642758	+	0.766069i	$0.722210\pi$
$380$	−6.63090	−	2.39506i	−0.340158	−	0.122864i
$381$	8.17488			0.418812
$382$		−	7.56170i		−	0.386890i
$383$			13.0991i			0.669331i	0.942337	+	0.334666i	$0.108623\pi$
$383$			13.0991i			0.669331i	−0.942337	+	0.334666i	$0.891377\pi$
$384$	5.42927			0.277061
$385$		0			0
$386$	−0.0573242			−0.00291772
$387$		−	3.02459i		−	0.153749i
$388$			1.86501i			0.0946816i
$389$	−16.7136			−0.847416			−0.423708	−	0.905799i	$-0.639272\pi$
$389$	−16.7136			−0.847416			−0.423708	+	0.905799i	$0.639272\pi$
$390$	0.773743	−	2.14216i	0.0391800	−	0.108473i
$391$	−23.5729			−1.19213
$392$			8.87809i			0.448411i
$393$		−	17.7054i		−	0.893121i
$394$	−10.5016			−0.529062
$395$	−37.2665	−	13.4605i	−1.87508	−	0.677273i
$396$		0			0
$397$		−	4.22375i		−	0.211984i	−0.994367	−	0.105992i	$-0.966198\pi$
$397$		−	4.22375i		−	0.211984i	0.994367	−	0.105992i	$-0.0338018\pi$
$398$		−	5.96306i		−	0.298901i
$399$	8.57830			0.429452
$400$	−17.6628	−	14.6739i	−0.883139	−	0.733695i
$401$	−20.9464			−1.04601			−0.523005	−	0.852329i	$-0.675189\pi$
$401$	−20.9464			−1.04601			−0.523005	+	0.852329i	$0.675189\pi$
$402$		−	22.0542i		−	1.09996i
$403$		−	1.86757i		−	0.0930305i
$404$	1.67719			0.0834434
$405$	−2.10308	−	0.759628i	−0.104503	−	0.0377462i
$406$	−40.4233			−2.00618
$407$		0			0
$408$			3.13525i			0.155218i
$409$	6.86017			0.339213			0.169607	−	0.985512i	$-0.445750\pi$
$409$	6.86017			0.339213			0.169607	+	0.985512i	$0.445750\pi$
$410$	−6.80388	+	18.8370i	−0.336020	+	0.930295i
$411$	−5.48584			−0.270596
$412$		−	7.84855i		−	0.386670i
$413$			60.8405i			2.99377i
$414$	9.89470			0.486298
$415$	3.22643	−	8.93259i	0.158379	−	0.438484i
$416$	3.94106			0.193226
$417$			3.25952i			0.159620i
$418$		0			0
$419$	19.0865			0.932435			0.466217	−	0.884670i	$-0.345616\pi$
$419$	19.0865			0.932435			0.466217	+	0.884670i	$0.345616\pi$
$420$	−15.3576	−	5.54710i	−0.749372	−	0.270671i
$421$	−12.2531			−0.597180			−0.298590	−	0.954381i	$-0.596516\pi$
$421$	−12.2531			−0.597180			−0.298590	+	0.954381i	$0.596516\pi$
$422$			38.8933i			1.89329i
$423$			11.9878i			0.582865i
$424$	3.46657			0.168351
$425$	14.5193	−	17.4767i	0.704291	−	0.847746i
$426$	−6.42016			−0.311058
$427$		−	52.1131i		−	2.52193i
$428$			1.20573i			0.0582812i
$429$		0			0
$430$	−12.1331	−	4.38244i	−0.585111	−	0.211340i
$431$	−7.02245			−0.338260			−0.169130	−	0.985594i	$-0.554096\pi$
$431$	−7.02245			−0.338260			−0.169130	+	0.985594i	$0.554096\pi$
$432$		−	4.59259i		−	0.220961i
$433$		−	27.4900i		−	1.32108i	−0.750789	−	0.660542i	$-0.770326\pi$
$433$		−	27.4900i		−	1.32108i	0.750789	−	0.660542i	$-0.229674\pi$
$434$	−29.7341			−1.42728
$435$	−3.61168	+	9.99919i	−0.173167	+	0.479424i
$436$	−0.0711006			−0.00340510
$437$			9.98343i			0.477572i
$438$			1.24058i			0.0592770i
$439$	17.6992			0.844736			0.422368	−	0.906425i	$-0.361199\pi$
$439$	17.6992			0.844736			0.422368	+	0.906425i	$0.361199\pi$
$440$		0			0
$441$	12.8679			0.612755
$442$			4.62865i			0.220163i
$443$			16.5900i			0.788216i	0.919064	+	0.394108i	$0.128946\pi$
$443$			16.5900i			0.788216i	−0.919064	+	0.394108i	$0.871054\pi$
$444$	−0.863613			−0.0409853
$445$	−17.3314	−	6.26005i	−0.821587	−	0.296755i
$446$	19.6501			0.930460
$447$			2.80635i			0.132736i
$448$		−	21.8050i		−	1.03019i
$449$	26.2868			1.24055			0.620276	−	0.784383i	$-0.287020\pi$
$449$	26.2868			1.24055			0.620276	+	0.784383i	$0.287020\pi$
$450$	−6.09447	+	7.33584i	−0.287296	+	0.345815i
$451$		0			0
$452$			18.3498i			0.863100i
$453$			14.1638i			0.665473i
$454$	−11.9642			−0.561510
$455$	5.00587	+	1.80811i	0.234679	+	0.0847653i
$456$	1.32782			0.0621808
$457$			27.4515i			1.28413i	0.766652	+	0.642063i	$0.221921\pi$
$457$			27.4515i			1.28413i	−0.766652	+	0.642063i	$0.778079\pi$
$458$			2.63436i			0.123096i
$459$	4.54422			0.212106
$460$	6.45573	−	17.8731i	0.301000	−	0.833340i
$461$	16.7991			0.782410			0.391205	−	0.920304i	$-0.372058\pi$
$461$	16.7991			0.782410			0.391205	+	0.920304i	$0.372058\pi$
$462$		0			0
$463$			32.2574i			1.49913i	0.661930	+	0.749565i	$0.269737\pi$
$463$			32.2574i			1.49913i	−0.661930	+	0.749565i	$0.730263\pi$
$464$	−21.8356			−1.01369
$465$	−2.65663	+	7.35508i	−0.123198	+	0.341084i
$466$	−15.8401			−0.733780
$467$			2.29620i			0.106256i	0.998588	+	0.0531278i	$0.0169191\pi$
$467$			2.29620i			0.106256i	−0.998588	+	0.0531278i	$0.983081\pi$
$468$		−	0.874857i		−	0.0404403i
$469$	51.5368			2.37975
$470$	48.0887	+	17.3695i	2.21817	+	0.801196i
$471$	−3.11084			−0.143340
$472$			9.41739i			0.433470i
$473$		0			0
$474$	−33.7995			−1.55246
$475$	−7.40163	−	6.14912i	−0.339610	−	0.282141i
$476$	33.1837			1.52097
$477$		−	5.02443i		−	0.230053i
$478$			19.6371i			0.898179i
$479$	−0.341117			−0.0155861			−0.00779303	−	0.999970i	$-0.502481\pi$
$479$	−0.341117			−0.0155861			−0.00779303	+	0.999970i	$0.502481\pi$
$480$	−15.5211	−	5.60617i	−0.708438	−	0.255886i
$481$	0.281499			0.0128352
$482$		−	23.3355i		−	1.06290i
$483$			23.1222i			1.05210i
$484$		0			0
$485$	−0.864754	+	2.39413i	−0.0392665	+	0.108712i
$486$	−1.90743			−0.0865227
$487$			15.8553i			0.718471i	0.933247	+	0.359235i	$0.116962\pi$
$487$			15.8553i			0.718471i	−0.933247	+	0.359235i	$0.883038\pi$
$488$		−	8.06648i		−	0.365152i
$489$	19.3745			0.876143
$490$	18.6447	−	51.6192i	0.842282	−	2.33192i
$491$	30.0103			1.35435			0.677173	−	0.735824i	$-0.263205\pi$
$491$	30.0103			1.35435			0.677173	+	0.735824i	$0.263205\pi$
$492$			7.69303i			0.346828i
$493$		−	21.6056i		−	0.973068i
$494$	1.96030			0.0881978
$495$		0			0
$496$	−16.0616			−0.721186
$497$		−	15.0028i		−	0.672969i
$498$		−	8.10157i		−	0.363040i
$499$	−3.65516			−0.163627			−0.0818137	−	0.996648i	$-0.526071\pi$
$499$	−3.65516			−0.163627			−0.0818137	+	0.996648i	$0.526071\pi$
$500$	9.27469	+	15.7949i	0.414777	+	0.706368i
$501$	−4.14992			−0.185405
$502$			8.88210i			0.396427i
$503$			31.1782i			1.39017i	0.718930	+	0.695083i	$0.244632\pi$
$503$			31.1782i			1.39017i	−0.718930	+	0.695083i	$0.755368\pi$
$504$	3.07531			0.136985
$505$	2.15303	+	0.777667i	0.0958085	+	0.0346057i
$506$		0			0
$507$		−	12.7148i		−	0.564686i
$508$		−	13.3928i		−	0.594209i
$509$	14.7299			0.652893			0.326446	−	0.945216i	$-0.394149\pi$
$509$	14.7299			0.652893			0.326446	+	0.945216i	$0.394149\pi$
$510$	6.58428	−	18.2291i	0.291557	−	0.807196i
$511$	−2.89901			−0.128245
$512$		−	27.5568i		−	1.21785i
$513$		−	1.92453i		−	0.0849703i
$514$	−34.9755			−1.54270
$515$	3.63915	−	10.0753i	0.160360	−	0.443969i
$516$	−4.95515			−0.218138
$517$		0			0
$518$		−	4.48181i		−	0.196919i
$519$	−10.6654			−0.468160
$520$	0.774849	+	0.279873i	0.0339794	+	0.0122733i
$521$	−1.29570			−0.0567658			−0.0283829	−	0.999597i	$-0.509036\pi$
$521$	−1.29570			−0.0567658			−0.0283829	+	0.999597i	$0.509036\pi$
$522$			9.06894i			0.396937i
$523$		−	30.7487i		−	1.34455i	−0.740303	−	0.672274i	$-0.765318\pi$
$523$		−	30.7487i		−	1.34455i	0.740303	−	0.672274i	$-0.234682\pi$
$524$	−29.0066			−1.26716
$525$	−17.1426	−	14.2417i	−0.748165	−	0.621561i
$526$	−18.6966			−0.815210
$527$		−	15.8924i		−	0.692284i
$528$		0			0
$529$	−3.90968			−0.169986
$530$	−20.1554	−	7.28007i	−0.875495	−	0.316226i
$531$	13.6495			0.592339
$532$		−	14.0537i		−	0.609306i
$533$		−	2.50758i		−	0.108615i
$534$	−15.7190			−0.680228
$535$	−0.559064	+	1.54781i	−0.0241704	+	0.0669176i
$536$	7.97729			0.344566
$537$			22.6337i			0.976717i
$538$			22.7574i			0.981141i
$539$		0			0
$540$	−1.24449	+	3.44546i	−0.0535542	+	0.148269i
$541$	15.7550			0.677362			0.338681	−	0.940901i	$-0.390019\pi$
$541$	15.7550			0.677362			0.338681	+	0.940901i	$0.390019\pi$
$542$			57.9951i			2.49110i
$543$		−	14.5822i		−	0.625783i
$544$	33.5370			1.43789
$545$	−0.0912726	−	0.0329674i	−0.00390969	−	0.00141217i
$546$	4.54016			0.194301
$547$		−	15.3597i		−	0.656734i	−0.944550	−	0.328367i	$-0.893502\pi$
$547$		−	15.3597i		−	0.656734i	0.944550	−	0.328367i	$-0.106498\pi$
$548$			8.98738i			0.383922i
$549$	−11.6915			−0.498982
$550$		0			0
$551$	−9.15026			−0.389814
$552$			3.57905i			0.152334i
$553$		−	78.9836i		−	3.35873i
$554$	−42.2389			−1.79456
$555$	−1.10863	−	0.400433i	−0.0470587	−	0.0169974i
$556$	5.34003			0.226468
$557$			35.9189i			1.52193i	0.648791	+	0.760967i	$0.275275\pi$
$557$			35.9189i			1.52193i	−0.648791	+	0.760967i	$0.724725\pi$
$558$			6.67082i			0.282398i
$559$	1.61516			0.0683138
$560$	15.5501	−	43.0517i	0.657113	−	1.81927i
$561$		0			0
$562$		−	32.4878i		−	1.37042i
$563$		−	30.9605i		−	1.30483i	−0.757863	−	0.652414i	$-0.773756\pi$
$563$		−	30.9605i		−	1.30483i	0.757863	−	0.652414i	$-0.226244\pi$
$564$	19.6394			0.826968
$565$	−8.50827	+	23.5558i	−0.357946	+	0.990999i
$566$	−15.1097			−0.635108
$567$		−	4.45734i		−	0.187191i
$568$		−	2.32226i		−	0.0974398i
$569$	−2.33375			−0.0978360			−0.0489180	−	0.998803i	$-0.515577\pi$
$569$	−2.33375			−0.0978360			−0.0489180	+	0.998803i	$0.515577\pi$
$570$	−7.72024	−	2.78853i	−0.323365	−	0.116799i
$571$	−26.6093			−1.11357			−0.556783	−	0.830658i	$-0.687964\pi$
$571$	−26.6093			−1.11357			−0.556783	+	0.830658i	$0.687964\pi$
$572$		0			0
$573$		−	3.96434i		−	0.165613i
$574$	−39.9237			−1.66639
$575$	16.5746	−	19.9506i	0.691207	−	0.831997i
$576$	−4.89194			−0.203831
$577$		−	3.69867i		−	0.153978i	−0.997032	−	0.0769889i	$-0.975469\pi$
$577$		−	3.69867i		−	0.153978i	0.997032	−	0.0769889i	$-0.0245306\pi$
$578$			6.96192i			0.289578i
$579$	−0.0300531			−0.00124896
$580$	16.3815	+	5.91696i	0.680206	+	0.245688i
$581$	18.9320			0.785431
$582$			2.17140i			0.0900075i
$583$		0			0
$584$	−0.448733			−0.0185687
$585$	0.405647	−	1.12306i	0.0167714	−	0.0464329i
$586$	42.6111			1.76025
$587$			31.3576i			1.29427i	0.762377	+	0.647133i	$0.224032\pi$
$587$			31.3576i			1.29427i	−0.762377	+	0.647133i	$0.775968\pi$
$588$		−	21.0812i		−	0.869376i
$589$	−6.73064			−0.277331
$590$	19.7773	−	54.7548i	0.814218	−	2.25422i
$591$	−5.50562			−0.226471
$592$		−	2.42096i		−	0.0995007i
$593$		−	32.0728i		−	1.31707i	−0.752550	−	0.658535i	$-0.771176\pi$
$593$		−	32.0728i		−	1.31707i	0.752550	−	0.658535i	$-0.228824\pi$
$594$		0			0
$595$	42.5982	+	15.3863i	1.74636	+	0.630779i
$596$	4.59761			0.188325
$597$		−	3.12623i		−	0.127948i
$598$			5.28385i			0.216073i
$599$	20.3261			0.830504			0.415252	−	0.909706i	$-0.363693\pi$
$599$	20.3261			0.830504			0.415252	+	0.909706i	$0.363693\pi$
$600$	−2.65347	−	2.20445i	−0.108328	−	0.0899964i
$601$	−11.6257			−0.474222			−0.237111	−	0.971483i	$-0.576201\pi$
$601$	−11.6257			−0.474222			−0.237111	+	0.971483i	$0.576201\pi$
$602$		−	25.7153i		−	1.04808i
$603$		−	11.5622i		−	0.470851i
$604$	23.2044			0.944172
$605$		0			0
$606$	1.95273			0.0793241
$607$			25.6773i			1.04221i	0.853493	+	0.521104i	$0.174480\pi$
$607$			25.6773i			1.04221i	−0.853493	+	0.521104i	$0.825520\pi$
$608$		−	14.2034i		−	0.576022i
$609$	−21.1926			−0.858766
$610$	−16.9403	+	46.9004i	−0.685891	+	1.89894i
$611$	−6.40156			−0.258979
$612$		−	7.44473i		−	0.300935i
$613$			6.58440i			0.265941i	0.991120	+	0.132971i	$0.0424516\pi$
$613$			6.58440i			0.265941i	−0.991120	+	0.132971i	$0.957548\pi$
$614$	17.8026			0.718453
$615$	−3.56704	+	9.87561i	−0.143837	+	0.398223i
$616$		0			0
$617$			25.4721i			1.02547i	0.858548	+	0.512734i	$0.171367\pi$
$617$			25.4721i			1.02547i	−0.858548	+	0.512734i	$0.828633\pi$
$618$		−	9.13794i		−	0.367582i
$619$	1.08299			0.0435292			0.0217646	−	0.999763i	$-0.493072\pi$
$619$	1.08299			0.0435292			0.0217646	+	0.999763i	$0.493072\pi$
$620$	12.0497	+	4.35233i	0.483929	+	0.174794i
$621$	5.18745			0.208165
$622$			21.4547i			0.860256i
$623$		−	36.7327i		−	1.47166i
$624$	2.45248			0.0981777
$625$	4.58237	+	24.5764i	0.183295	+	0.983058i
$626$	20.7223			0.828230
$627$		0			0
$628$			5.09645i			0.203371i
$629$	2.39546			0.0955131
$630$	−17.8805	−	6.45840i	−0.712378	−	0.257309i
$631$	31.0566			1.23635			0.618173	−	0.786042i	$-0.287873\pi$
$631$	31.0566			1.23635			0.618173	+	0.786042i	$0.287873\pi$
$632$		−	12.2257i		−	0.486313i
$633$			20.3904i			0.810446i
$634$	24.2044			0.961278
$635$	6.20987	−	17.1925i	0.246431	−	0.682262i
$636$	−8.23145			−0.326398
$637$			6.87153i			0.272260i
$638$		0			0
$639$	−3.36587			−0.133152
$640$	4.12423	−	11.4182i	0.163024	−	0.451345i
$641$	−22.4187			−0.885485			−0.442743	−	0.896649i	$-0.645994\pi$
$641$	−22.4187			−0.885485			−0.442743	+	0.896649i	$0.645994\pi$
$642$			1.40381i			0.0554041i
$643$		−	13.8174i		−	0.544905i	−0.962169	−	0.272453i	$-0.912165\pi$
$643$		−	13.8174i		−	0.544905i	0.962169	−	0.272453i	$-0.0878348\pi$
$644$	37.8809			1.49271
$645$	−6.36098	−	2.29757i	−0.250463	−	0.0904666i
$646$	16.6814			0.656322
$647$			24.9483i			0.980819i	0.871492	+	0.490409i	$0.163153\pi$
$647$			24.9483i			0.980819i	−0.871492	+	0.490409i	$0.836847\pi$
$648$		−	0.689943i		−	0.0271035i
$649$		0			0
$650$	−3.91739	−	3.25449i	−0.153653	−	0.127652i
$651$	−15.5886			−0.610964
$652$		−	31.7409i		−	1.24307i
$653$			18.8619i			0.738125i	0.929405	+	0.369063i	$0.120321\pi$
$653$			18.8619i			0.738125i	−0.929405	+	0.369063i	$0.879679\pi$
$654$	−0.0827813			−0.00323700
$655$	−37.2360	−	13.4495i	−1.45493	−	0.525517i
$656$	−21.5658			−0.842002
$657$			0.650391i			0.0253742i
$658$			101.921i			3.97328i
$659$	2.97553			0.115910			0.0579550	−	0.998319i	$-0.481542\pi$
$659$	2.97553			0.115910			0.0579550	+	0.998319i	$0.481542\pi$
$660$		0			0
$661$	−39.0164			−1.51756			−0.758782	−	0.651345i	$-0.774205\pi$
$661$	−39.0164			−1.51756			−0.758782	+	0.651345i	$0.774205\pi$
$662$			43.9905i			1.70974i
$663$			2.42665i			0.0942431i
$664$	2.93045			0.113723
$665$	6.51632	−	18.0409i	0.252692	−	0.699596i
$666$	−1.00549			−0.0389620
$667$		−	24.6639i		−	0.954991i
$668$			6.79876i			0.263052i
$669$	10.3019			0.398294
$670$	−46.3818	−	16.7530i	−1.79188	−	0.647223i
$671$		0			0
$672$		−	32.8958i		−	1.26898i
$673$		−	15.2282i		−	0.587003i	−0.955959	−	0.293502i	$-0.905179\pi$
$673$		−	15.2282i		−	0.587003i	0.955959	−	0.293502i	$-0.0948206\pi$
$674$	−61.7302			−2.37776
$675$	−3.19512	+	3.84593i	−0.122980	+	0.148030i
$676$	−20.8305			−0.801175
$677$		−	0.829064i		−	0.0318635i	−0.999873	−	0.0159318i	$-0.994929\pi$
$677$		−	0.829064i		−	0.0318635i	0.999873	−	0.0159318i	$-0.00507145\pi$
$678$			21.3643i			0.820492i
$679$	−5.07420			−0.194730
$680$	6.59370	+	2.38162i	0.252857	+	0.0913311i
$681$	−6.27244			−0.240361
$682$		0			0
$683$			1.03468i			0.0395910i	0.999804	+	0.0197955i	$0.00630151\pi$
$683$			1.03468i			0.0395910i	−0.999804	+	0.0197955i	$0.993698\pi$
$684$	−3.15294			−0.120556
$685$	−4.16720	+	11.5372i	−0.159220	+	0.440813i
$686$	49.8889			1.90477
$687$			1.38111i			0.0526925i
$688$		−	13.8907i		−	0.529579i
$689$	2.68308			0.102217
$690$	7.51629	−	20.8094i	0.286140	−	0.792200i
$691$	19.2788			0.733399			0.366700	−	0.930339i	$-0.380488\pi$
$691$	19.2788			0.733399			0.366700	+	0.930339i	$0.380488\pi$
$692$			17.4730i			0.664225i
$693$		0			0
$694$	−55.4762			−2.10585
$695$	6.85506	+	2.47603i	0.260027	+	0.0939210i
$696$	−3.28036			−0.124342
$697$		−	21.3386i		−	0.808258i
$698$		−	27.4740i		−	1.03991i
$699$	−8.30444			−0.314103
$700$	−23.3321	+	28.0845i	−0.881869	+	1.06149i
$701$	3.29844			0.124580			0.0622902	−	0.998058i	$-0.480160\pi$
$701$	3.29844			0.124580			0.0622902	+	0.998058i	$0.480160\pi$
$702$		−	1.01858i		−	0.0384439i
$703$		−	1.01451i		−	0.0382629i
$704$		0			0
$705$	25.2113	+	9.10624i	0.949512	+	0.342961i
$706$	55.1680			2.07627
$707$			4.56319i			0.171616i
$708$		−	22.3618i		−	0.840409i
$709$	37.7593			1.41808			0.709040	−	0.705169i	$-0.249129\pi$
$709$	37.7593			1.41808			0.709040	+	0.705169i	$0.249129\pi$
$710$	−4.87693	+	13.5021i	−0.183028	+	0.506726i
$711$	−17.7199			−0.664548
$712$		−	5.68578i		−	0.213084i
$713$		−	18.1420i		−	0.679423i
$714$	38.6352			1.44589
$715$		0			0
$716$	37.0805			1.38576
$717$			10.2950i			0.384476i
$718$			44.8550i			1.67397i
$719$	29.0980			1.08517			0.542585	−	0.840001i	$-0.317446\pi$
$719$	29.0980			1.08517			0.542585	+	0.840001i	$0.317446\pi$
$720$	−9.65861	−	3.48866i	−0.359955	−	0.130015i
$721$	21.3538			0.795257
$722$			29.1764i			1.08583i
$723$		−	12.2340i		−	0.454987i
$724$	−23.8898			−0.887859
$725$	18.2856	+	15.1913i	0.679110	+	0.564192i
$726$		0			0
$727$		−	38.1331i		−	1.41428i	−0.707074	−	0.707140i	$-0.749985\pi$
$727$		−	38.1331i		−	1.41428i	0.707074	−	0.707140i	$-0.250015\pi$
$728$			1.64224i			0.0608654i
$729$	−1.00000			−0.0370370
$730$	2.60904	+	0.942376i	0.0965647	+	0.0348789i
$731$	13.7444			0.508355
$732$			19.1541i			0.707954i
$733$			40.0048i			1.47761i	0.673919	+	0.738805i	$0.264610\pi$
$733$			40.0048i			1.47761i	−0.673919	+	0.738805i	$0.735390\pi$
$734$	−48.2650			−1.78150
$735$	9.77479	−	27.0622i	0.360548	−	0.998204i
$736$	38.2842			1.41118
$737$		0			0
$738$			8.95686i			0.329707i
$739$	41.4965			1.52647			0.763236	−	0.646119i	$-0.223609\pi$
$739$	41.4965			1.52647			0.763236	+	0.646119i	$0.223609\pi$
$740$	−0.656025	+	1.81625i	−0.0241159	+	0.0667667i
$741$	1.02772			0.0377541
$742$		−	42.7180i		−	1.56823i
$743$			2.69500i			0.0988701i	0.998777	+	0.0494350i	$0.0157421\pi$
$743$			2.69500i			0.0988701i	−0.998777	+	0.0494350i	$0.984258\pi$
$744$	−2.41292			−0.0884621
$745$	5.90199	+	2.13178i	0.216232	+	0.0781024i
$746$	−31.0304			−1.13610
$747$		−	4.24738i		−	0.155403i
$748$		0			0
$749$	−3.28047			−0.119866
$750$	10.7984	+	18.3897i	0.394301	+	0.671497i
$751$	−45.6347			−1.66524			−0.832618	−	0.553848i	$-0.813159\pi$
$751$	−45.6347			−1.66524			−0.832618	+	0.553848i	$0.813159\pi$
$752$			55.0549i			2.00765i
$753$			4.65658i			0.169695i
$754$	−4.84288			−0.176367
$755$	29.7877	+	10.7592i	1.08408	+	0.391568i
$756$	−7.30240			−0.265586
$757$		−	8.99188i		−	0.326815i	−0.986559	−	0.163408i	$-0.947751\pi$
$757$		−	8.99188i		−	0.326815i	0.986559	−	0.163408i	$-0.0522486\pi$
$758$			47.7359i			1.73385i
$759$		0			0
$760$	1.00865	−	2.79252i	0.0365875	−	0.101295i
$761$	−15.0581			−0.545855			−0.272927	−	0.962035i	$-0.587992\pi$
$761$	−15.0581			−0.545855			−0.272927	+	0.962035i	$0.587992\pi$
$762$		−	15.5930i		−	0.564875i
$763$		−	0.193446i		−	0.00700321i
$764$	−6.49473			−0.234971
$765$	3.45191	−	9.55687i	0.124804	−	0.345529i
$766$	24.9856			0.902765
$767$			7.28895i			0.263189i
$768$		−	20.1398i		−	0.726734i
$769$	48.1314			1.73566			0.867831	−	0.496859i	$-0.165513\pi$
$769$	48.1314			1.73566			0.867831	+	0.496859i	$0.165513\pi$
$770$		0			0
$771$	−18.3364			−0.660371
$772$			0.0492356i			0.00177203i
$773$			28.5551i			1.02706i	0.858073	+	0.513528i	$0.171662\pi$
$773$			28.5551i			1.02706i	−0.858073	+	0.513528i	$0.828338\pi$
$774$	−5.76920			−0.207370
$775$	13.4503	+	11.1742i	0.483149	+	0.401391i
$776$	−0.785425			−0.0281951
$777$		−	2.34966i		−	0.0842936i
$778$			31.8801i			1.14296i
$779$	−9.03718			−0.323791
$780$	−1.83990	−	0.664566i	−0.0658790	−	0.0237953i
$781$		0			0
$782$			44.9637i			1.60790i
$783$			4.75453i			0.169913i
$784$	59.0968			2.11060
$785$	−2.36308	+	6.54237i	−0.0843420	+	0.233507i
$786$	−33.7719			−1.20460
$787$		−	42.7119i		−	1.52252i	−0.648450	−	0.761258i	$-0.724582\pi$
$787$		−	42.7119i		−	1.52252i	0.648450	−	0.761258i	$-0.275418\pi$
$788$			9.01978i			0.321316i
$789$	−9.80198			−0.348960
$790$	−25.6750	+	71.0832i	−0.913476	+	2.52903i
$791$	−49.9248			−1.77512
$792$		0			0
$793$		−	6.24336i		−	0.221708i
$794$	−8.05650			−0.285914
$795$	−10.5668	−	3.81669i	−0.374766	−	0.135364i
$796$	−5.12166			−0.181532
$797$			8.54872i			0.302811i	0.988472	+	0.151406i	$0.0483799\pi$
$797$			8.54872i			0.302811i	−0.988472	+	0.151406i	$0.951620\pi$
$798$		−	16.3625i		−	0.579226i
$799$	−54.4750			−1.92719
$800$	−23.5805	+	28.3836i	−0.833697	+	1.00351i
$801$	−8.24094			−0.291179
$802$			39.9537i			1.41081i
$803$		0			0
$804$	−18.9423			−0.668042
$805$	48.6280	+	17.5643i	1.71391	+	0.619060i
$806$	−3.56227			−0.125476
$807$			11.9309i			0.419989i
$808$			0.706327i			0.0248485i
$809$	−12.8182			−0.450664			−0.225332	−	0.974282i	$-0.572347\pi$
$809$	−12.8182			−0.450664			−0.225332	+	0.974282i	$0.572347\pi$
$810$	−1.44894	+	4.01149i	−0.0509104	+	0.140949i
$811$	34.0522			1.19573			0.597867	−	0.801596i	$-0.296015\pi$
$811$	34.0522			1.19573			0.597867	+	0.801596i	$0.296015\pi$
$812$			34.7195i			1.21842i
$813$			30.4048i			1.06634i
$814$		0			0
$815$	14.7174	−	40.7461i	0.515527	−	1.42727i
$816$	20.8697			0.730586
$817$		−	5.82093i		−	0.203649i
$818$		−	13.0853i		−	0.457516i
$819$	2.38025			0.0831727
$820$	16.1791	+	5.84384i	0.564998	+	0.204076i
$821$	17.3373			0.605076			0.302538	−	0.953137i	$-0.402166\pi$
$821$	17.3373			0.605076			0.302538	+	0.953137i	$0.402166\pi$
$822$			10.4638i			0.364969i
$823$		−	23.5673i		−	0.821505i	−0.911747	−	0.410752i	$-0.865266\pi$
$823$		−	23.5673i		−	0.821505i	0.911747	−	0.410752i	$-0.134734\pi$
$824$	3.30531			0.115146
$825$		0			0
$826$	116.049			4.03786
$827$		−	15.3311i		−	0.533116i	−0.963819	−	0.266558i	$-0.914114\pi$
$827$		−	15.3311i		−	0.533116i	0.963819	−	0.266558i	$-0.0858864\pi$
$828$		−	8.49854i		−	0.295345i
$829$	22.4463			0.779593			0.389797	−	0.920901i	$-0.372545\pi$
$829$	22.4463			0.779593			0.389797	+	0.920901i	$0.372545\pi$
$830$	−17.0383	−	6.15418i	−0.591408	−	0.213615i
$831$	−22.1444			−0.768181
$832$		−	2.61233i		−	0.0905664i
$833$			58.4743i			2.02602i
$834$	6.21731			0.215288
$835$	−3.15239	+	8.72763i	−0.109093	+	0.302032i
$836$		0			0
$837$			3.49728i			0.120884i
$838$		−	36.4061i		−	1.25763i
$839$	46.4511			1.60367			0.801835	−	0.597546i	$-0.203857\pi$
$839$	46.4511			1.60367			0.801835	+	0.597546i	$0.203857\pi$
$840$	2.33609	−	6.46763i	0.0806028	−	0.223155i
$841$	−6.39441			−0.220497
$842$			23.3719i			0.805451i
$843$		−	17.0323i		−	0.586622i
$844$	33.4053			1.14986
$845$	−26.7404	−	9.65854i	−0.919897	−	0.332264i
$846$	22.8658			0.786143
$847$		0			0
$848$		−	23.0751i		−	0.792403i
$849$	−7.92150			−0.271865
$850$	−33.3356	−	27.6946i	−1.14340	−	0.949917i
$851$	2.73454			0.0937387
$852$			5.51426i			0.188916i
$853$			35.6321i			1.22002i	0.792394	+	0.610009i	$0.208834\pi$
$853$			35.6321i			1.22002i	−0.792394	+	0.610009i	$0.791166\pi$
$854$	−99.4020			−3.40147
$855$	−4.04746	−	1.46193i	−0.138420	−	0.0499969i
$856$	−0.507778			−0.0173555
$857$		−	12.7176i		−	0.434424i	−0.976124	−	0.217212i	$-0.930304\pi$
$857$		−	12.7176i		−	0.434424i	0.976124	−	0.217212i	$-0.0696962\pi$
$858$		0			0
$859$	12.9964			0.443431			0.221715	−	0.975111i	$-0.428834\pi$
$859$	12.9964			0.443431			0.221715	+	0.975111i	$0.428834\pi$
$860$	−3.76407	+	10.4211i	−0.128354	+	0.355357i
$861$	−20.9307			−0.713315
$862$			13.3948i			0.456230i
$863$		−	53.1839i		−	1.81040i	−0.424985	−	0.905201i	$-0.639720\pi$
$863$		−	53.1839i		−	1.81040i	0.424985	−	0.905201i	$-0.360280\pi$
$864$	−7.38016			−0.251078
$865$	−8.10176	+	22.4303i	−0.275468	+	0.762653i
$866$	−52.4352			−1.78182
$867$			3.64990i			0.123957i
$868$			25.5385i			0.866835i
$869$		0			0
$870$	19.0727	+	6.88902i	0.646627	+	0.233560i
$871$	6.17432			0.209209
$872$		−	0.0299431i		−	0.00101400i
$873$			1.13839i			0.0385287i
$874$	19.0427			0.644129
$875$	−42.9736	+	25.2339i	−1.45277	+	0.853063i
$876$	1.06553			0.0360008
$877$			9.40681i			0.317645i	0.987307	+	0.158823i	$0.0507698\pi$
$877$			9.40681i			0.317645i	−0.987307	+	0.158823i	$0.949230\pi$
$878$		−	33.7599i		−	1.13934i
$879$	22.3396			0.753494
$880$		0			0
$881$	−26.5160			−0.893345			−0.446673	−	0.894697i	$-0.647391\pi$
$881$	−26.5160			−0.893345			−0.446673	+	0.894697i	$0.647391\pi$
$882$		−	24.5445i		−	0.826457i
$883$			11.5024i			0.387086i	0.981092	+	0.193543i	$0.0619980\pi$
$883$			11.5024i			0.387086i	−0.981092	+	0.193543i	$0.938002\pi$
$884$	3.97554			0.133712
$885$	10.3686	−	28.7061i	0.348535	−	0.964945i
$886$	31.6443			1.06311
$887$		−	32.2772i		−	1.08376i	−0.840455	−	0.541881i	$-0.817712\pi$
$887$		−	32.2772i		−	1.08376i	0.840455	−	0.541881i	$-0.182288\pi$
$888$		−	0.363699i		−	0.0122050i
$889$	36.4382			1.22210
$890$	−11.9406	+	33.0584i	−0.400250	+	1.10812i
$891$		0			0
$892$		−	16.8774i		−	0.565098i
$893$			23.0709i			0.772037i
$894$	5.35291			0.179028
$895$	47.6006	+	17.1932i	1.59111	+	0.574705i
$896$	24.2001			0.808469
$897$			2.77014i			0.0924923i
$898$		−	50.1403i		−	1.67320i
$899$	16.6279			0.554573
$900$	6.30074	+	5.23453i	0.210025	+	0.174484i
$901$	22.8321			0.760647
$902$		0			0
$903$		−	13.4816i		−	0.448641i
$904$	−7.72776			−0.257022
$905$	−30.6676	−	11.0771i	−1.01943	−	0.368214i
$906$	27.0164			0.897561
$907$			23.0090i			0.764001i	0.924162	+	0.382000i	$0.124765\pi$
$907$			23.0090i			0.764001i	−0.924162	+	0.382000i	$0.875235\pi$
$908$			10.2761i			0.341023i
$909$	1.02375			0.0339556
$910$	3.44883	−	9.54835i	0.114328	−	0.316525i
$911$	−30.1780			−0.999841			−0.499921	−	0.866071i	$-0.666637\pi$
$911$	−30.1780			−0.999841			−0.499921	+	0.866071i	$0.666637\pi$
$912$		−	8.83860i		−	0.292675i
$913$		0			0
$914$	52.3618			1.73197
$915$	−8.88120	+	24.5883i	−0.293604	+	0.812863i
$916$	2.26265			0.0747599
$917$		−	78.9191i		−	2.60614i
$918$		−	8.66777i		−	0.286079i
$919$	28.3493			0.935158			0.467579	−	0.883951i	$-0.345126\pi$
$919$	28.3493			0.935158			0.467579	+	0.883951i	$0.345126\pi$
$920$	7.52704	+	2.71874i	0.248159	+	0.0896343i
$921$	9.33327			0.307542
$922$		−	32.0430i		−	1.05528i
$923$		−	1.79740i		−	0.0591622i
$924$		0			0
$925$	−1.68429	+	2.02736i	−0.0553791	+	0.0666592i
$926$	61.5288			2.02196
$927$		−	4.79071i		−	0.157347i
$928$			35.0892i			1.15186i
$929$	31.8685			1.04557			0.522786	−	0.852464i	$-0.324893\pi$
$929$	31.8685			1.04557			0.522786	+	0.852464i	$0.324893\pi$
$930$	14.0293	+	5.06734i	0.460039	+	0.166165i
$931$	24.7646			0.811628
$932$			13.6051i			0.445648i
$933$			11.2480i			0.368242i
$934$	4.37985			0.143313
$935$		0			0
$936$	0.368435			0.0120427
$937$		−	22.2288i		−	0.726182i	−0.931754	−	0.363091i	$-0.881721\pi$
$937$		−	22.2288i		−	0.726182i	0.931754	−	0.363091i	$-0.118279\pi$
$938$		−	98.3028i		−	3.20970i
$939$	10.8640			0.354533
$940$	14.9186	−	41.3033i	0.486592	−	1.34717i
$941$	−1.43990			−0.0469393			−0.0234697	−	0.999725i	$-0.507471\pi$
$941$	−1.43990			−0.0469393			−0.0234697	+	0.999725i	$0.507471\pi$
$942$			5.93371i			0.193331i
$943$		−	24.3591i		−	0.793242i
$944$	62.6867			2.04028
$945$	−9.37416	−	3.38592i	−0.304941	−	0.110144i
$946$		0			0
$947$			22.8848i			0.743655i	0.928302	+	0.371827i	$0.121269\pi$
$947$			22.8848i			0.743655i	−0.928302	+	0.371827i	$0.878731\pi$
$948$			29.0303i			0.942860i
$949$	−0.347314			−0.0112743
$950$	−11.7290	+	14.1181i	−0.380540	+	0.458051i
$951$	12.6895			0.411486
$952$			13.9749i			0.452928i
$953$			13.9872i			0.453089i	0.974001	+	0.226544i	$0.0727428\pi$
$953$			13.9872i			0.453089i	−0.974001	+	0.226544i	$0.927257\pi$
$954$	−9.58374			−0.310285
$955$	−8.33735	−	3.01142i	−0.269790	−	0.0974474i
$956$	16.8662			0.545493
$957$		0			0
$958$			0.650657i			0.0210218i
$959$	−24.4522			−0.789604
$960$	−3.71606	+	10.2882i	−0.119935	+	0.332049i
$961$	−18.7690			−0.605452
$962$		−	0.536939i		−	0.0173116i
$963$			0.735971i			0.0237163i
$964$	−20.0428			−0.645534
$965$	−0.0228292	+	0.0632042i	−0.000734897	+	0.00203462i
$966$	44.1040			1.41902
$967$		−	34.3901i		−	1.10591i	−0.833211	−	0.552955i	$-0.813500\pi$
$967$		−	34.3901i		−	1.10591i	0.833211	−	0.552955i	$-0.186500\pi$
$968$		0			0
$969$	8.74550			0.280946
$970$	4.56664	+	1.64946i	0.146626	+	0.0529609i
$971$	40.4046			1.29665			0.648323	−	0.761365i	$-0.275471\pi$
$971$	40.4046			1.29665			0.648323	+	0.761365i	$0.275471\pi$
$972$			1.63829i			0.0525481i
$973$			14.5288i			0.465772i
$974$	30.2428			0.969042
$975$	−2.05376	−	1.70622i	−0.0657728	−	0.0546428i
$976$	−53.6944			−1.71871
$977$			48.8722i			1.56356i	0.623554	+	0.781780i	$0.285688\pi$
$977$			48.8722i			1.56356i	−0.623554	+	0.781780i	$0.714312\pi$
$978$		−	36.9554i		−	1.18170i
$979$		0			0
$980$	−44.3356	−	16.0139i	−1.41625	−	0.511545i
$981$	−0.0433994			−0.00138564
$982$		−	57.2426i		−	1.82668i
$983$		−	10.0095i		−	0.319253i	−0.987177	−	0.159626i	$-0.948971\pi$
$983$		−	10.0095i		−	0.319253i	0.987177	−	0.159626i	$-0.0510290\pi$
$984$	−3.23982			−0.103282
$985$	−4.18222	+	11.5788i	−0.133257	+	0.368931i
$986$	−41.2112			−1.31243
$987$			53.4335i			1.70081i
$988$		−	1.68369i		−	0.0535654i
$989$	15.6899			0.498911
$990$		0			0
$991$	31.6029			1.00390			0.501949	−	0.864897i	$-0.332617\pi$
$991$	31.6029			1.00390			0.501949	+	0.864897i	$0.332617\pi$
$992$			25.8105i			0.819484i
$993$			23.0627i			0.731874i
$994$	−28.6168			−0.907671
$995$	−6.57472	−	2.37477i	−0.208433	−	0.0752852i
$996$	−6.95842			−0.220486
$997$		−	53.4009i		−	1.69122i	−0.533799	−	0.845611i	$-0.679236\pi$
$997$		−	53.4009i		−	1.69122i	0.533799	−	0.845611i	$-0.320764\pi$
$998$			6.97195i			0.220693i
$999$	−0.527144			−0.0166781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.j.364.6		24
5.2	odd	4		9075.2.a.dz.1.9		12
5.3	odd	4		9075.2.a.dy.1.4		12
5.4	even	2	inner	1815.2.c.j.364.19		24
11.5	even	5		165.2.s.a.124.10	yes	48
11.9	even	5		165.2.s.a.4.3	✓	48
11.10	odd	2		1815.2.c.k.364.19		24
33.5	odd	10		495.2.ba.c.289.3		48
33.20	odd	10		495.2.ba.c.334.10		48
55.9	even	10		165.2.s.a.4.10	yes	48
55.27	odd	20		825.2.n.o.751.2		24
55.32	even	4		9075.2.a.dx.1.4		12
55.38	odd	20		825.2.n.p.751.5		24
55.42	odd	20		825.2.n.o.301.2		24
55.43	even	4		9075.2.a.ea.1.9		12
55.49	even	10		165.2.s.a.124.3	yes	48
55.53	odd	20		825.2.n.p.301.5		24
55.54	odd	2		1815.2.c.k.364.6		24
165.104	odd	10		495.2.ba.c.289.10		48
165.119	odd	10		495.2.ba.c.334.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.3	✓	48	11.9	even	5
165.2.s.a.4.10	yes	48	55.9	even	10
165.2.s.a.124.3	yes	48	55.49	even	10
165.2.s.a.124.10	yes	48	11.5	even	5
495.2.ba.c.289.3		48	33.5	odd	10
495.2.ba.c.289.10		48	165.104	odd	10
495.2.ba.c.334.3		48	165.119	odd	10
495.2.ba.c.334.10		48	33.20	odd	10
825.2.n.o.301.2		24	55.42	odd	20
825.2.n.o.751.2		24	55.27	odd	20
825.2.n.p.301.5		24	55.53	odd	20
825.2.n.p.751.5		24	55.38	odd	20
1815.2.c.j.364.6		24	1.1	even	1	trivial
1815.2.c.j.364.19		24	5.4	even	2	inner
1815.2.c.k.364.6		24	55.54	odd	2
1815.2.c.k.364.19		24	11.10	odd	2
9075.2.a.dx.1.4		12	55.32	even	4
9075.2.a.dy.1.4		12	5.3	odd	4
9075.2.a.dz.1.9		12	5.2	odd	4
9075.2.a.ea.1.9		12	55.43	even	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.90743i q^{2} -1.00000i q^{3} -1.63829 q^{4} +(-2.10308 - 0.759628i) q^{5} -1.90743 q^{6} -4.45734i q^{7} -0.689943i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.90743i q^{2} -1.00000i q^{3} -1.63829 q^{4} +(-2.10308 - 0.759628i) q^{5} -1.90743 q^{6} -4.45734i q^{7} -0.689943i q^{8} -1.00000 q^{9} +(-1.44894 + 4.01149i) q^{10} +1.63829i q^{12} -0.534008i q^{13} -8.50206 q^{14} +(-0.759628 + 2.10308i) q^{15} -4.59259 q^{16} -4.54422i q^{17} +1.90743i q^{18} -1.92453 q^{19} +(3.44546 + 1.24449i) q^{20} -4.45734 q^{21} -5.18745i q^{23} -0.689943 q^{24} +(3.84593 + 3.19512i) q^{25} -1.01858 q^{26} +1.00000i q^{27} +7.30240i q^{28} +4.75453 q^{29} +(4.01149 + 1.44894i) q^{30} +3.49728 q^{31} +7.38016i q^{32} -8.66777 q^{34} +(-3.38592 + 9.37416i) q^{35} +1.63829 q^{36} +0.527144i q^{37} +3.67091i q^{38} -0.534008 q^{39} +(-0.524100 + 1.45101i) q^{40} +4.69578 q^{41} +8.50206i q^{42} +3.02459i q^{43} +(2.10308 + 0.759628i) q^{45} -9.89470 q^{46} -11.9878i q^{47} +4.59259i q^{48} -12.8679 q^{49} +(6.09447 - 7.33584i) q^{50} -4.54422 q^{51} +0.874857i q^{52} +5.02443i q^{53} +1.90743 q^{54} -3.07531 q^{56} +1.92453i q^{57} -9.06894i q^{58} -13.6495 q^{59} +(1.24449 - 3.44546i) q^{60} +11.6915 q^{61} -6.67082i q^{62} +4.45734i q^{63} +4.89194 q^{64} +(-0.405647 + 1.12306i) q^{65} +11.5622i q^{67} +7.44473i q^{68} -5.18745 q^{69} +(17.8805 + 6.45840i) q^{70} +3.36587 q^{71} +0.689943i q^{72} -0.650391i q^{73} +1.00549 q^{74} +(3.19512 - 3.84593i) q^{75} +3.15294 q^{76} +1.01858i q^{78} +17.7199 q^{79} +(9.65861 + 3.48866i) q^{80} +1.00000 q^{81} -8.95686i q^{82} +4.24738i q^{83} +7.30240 q^{84} +(-3.45191 + 9.55687i) q^{85} +5.76920 q^{86} -4.75453i q^{87} +8.24094 q^{89} +(1.44894 - 4.01149i) q^{90} -2.38025 q^{91} +8.49854i q^{92} -3.49728i q^{93} -22.8658 q^{94} +(4.04746 + 1.46193i) q^{95} +7.38016 q^{96} -1.13839i q^{97} +24.5445i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9} - 6 q^{10} - 12 q^{14} + 48 q^{16} + 32 q^{19} - 2 q^{20} - 16 q^{21} + 24 q^{24} + 2 q^{25} + 32 q^{26} - 8 q^{30} - 12 q^{34} + 10 q^{35} + 24 q^{36} + 36 q^{39} + 34 q^{40} + 2 q^{45} - 56 q^{46} - 24 q^{49} + 46 q^{50} - 36 q^{51} + 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} - 40 q^{61} + 12 q^{64} + 10 q^{65} - 2 q^{70} + 64 q^{71} - 136 q^{74} + 20 q^{75} - 68 q^{76} + 64 q^{79} + 76 q^{80} + 24 q^{81} + 60 q^{84} - 72 q^{86} + 20 q^{89} + 6 q^{90} - 4 q^{94} + 64 q^{95} - 56 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 2 * q^5 - 8 * q^6 - 24 * q^9 - 6 * q^10 - 12 * q^14 + 48 * q^16 + 32 * q^19 - 2 * q^20 - 16 * q^21 + 24 * q^24 + 2 * q^25 + 32 * q^26 - 8 * q^30 - 12 * q^34 + 10 * q^35 + 24 * q^36 + 36 * q^39 + 34 * q^40 + 2 * q^45 - 56 * q^46 - 24 * q^49 + 46 * q^50 - 36 * q^51 + 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 - 40 * q^61 + 12 * q^64 + 10 * q^65 - 2 * q^70 + 64 * q^71 - 136 * q^74 + 20 * q^75 - 68 * q^76 + 64 * q^79 + 76 * q^80 + 24 * q^81 + 60 * q^84 - 72 * q^86 + 20 * q^89 + 6 * q^90 - 4 * q^94 + 64 * q^95 - 56 * q^96

Introduction

L-functions

Modular forms

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Database

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