LMFDB - Embedded newform 1815.2.c.j.364.17

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			364.17
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.j.364.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.803366i q^{2} +1.00000i q^{3} +1.35460 q^{4} +(2.13623 - 0.660705i) q^{5} -0.803366 q^{6} -0.508505i q^{7} +2.69497i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.803366i q^{2} +1.00000i q^{3} +1.35460 q^{4} +(2.13623 - 0.660705i) q^{5} -0.803366 q^{6} -0.508505i q^{7} +2.69497i q^{8} -1.00000 q^{9} +(0.530788 + 1.71617i) q^{10} +1.35460i q^{12} +5.13798i q^{13} +0.408516 q^{14} +(0.660705 + 2.13623i) q^{15} +0.544158 q^{16} +3.34542i q^{17} -0.803366i q^{18} +1.17303 q^{19} +(2.89374 - 0.894993i) q^{20} +0.508505 q^{21} -2.91459i q^{23} -2.69497 q^{24} +(4.12694 - 2.82283i) q^{25} -4.12768 q^{26} -1.00000i q^{27} -0.688823i q^{28} +0.392594 q^{29} +(-1.71617 + 0.530788i) q^{30} -6.35529 q^{31} +5.82710i q^{32} -2.68759 q^{34} +(-0.335972 - 1.08628i) q^{35} -1.35460 q^{36} +4.45218i q^{37} +0.942375i q^{38} -5.13798 q^{39} +(1.78058 + 5.75708i) q^{40} -2.79867 q^{41} +0.408516i q^{42} +3.05350i q^{43} +(-2.13623 + 0.660705i) q^{45} +2.34148 q^{46} -11.4923i q^{47} +0.544158i q^{48} +6.74142 q^{49} +(2.26777 + 3.31544i) q^{50} -3.34542 q^{51} +6.95993i q^{52} +9.80747i q^{53} +0.803366 q^{54} +1.37041 q^{56} +1.17303i q^{57} +0.315396i q^{58} +3.02854 q^{59} +(0.894993 + 2.89374i) q^{60} +1.05512 q^{61} -5.10562i q^{62} +0.508505i q^{63} -3.59298 q^{64} +(3.39469 + 10.9759i) q^{65} +5.31327i q^{67} +4.53171i q^{68} +2.91459 q^{69} +(0.872682 - 0.269908i) q^{70} +4.09976 q^{71} -2.69497i q^{72} -13.1083i q^{73} -3.57673 q^{74} +(2.82283 + 4.12694i) q^{75} +1.58900 q^{76} -4.12768i q^{78} +16.1403 q^{79} +(1.16245 - 0.359528i) q^{80} +1.00000 q^{81} -2.24836i q^{82} -15.3587i q^{83} +0.688823 q^{84} +(2.21033 + 7.14657i) q^{85} -2.45308 q^{86} +0.392594i q^{87} +9.84603 q^{89} +(-0.530788 - 1.71617i) q^{90} +2.61269 q^{91} -3.94812i q^{92} -6.35529i q^{93} +9.23252 q^{94} +(2.50587 - 0.775030i) q^{95} -5.82710 q^{96} +15.1692i q^{97} +5.41583i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.803366i			0.568065i	0.958815	+	0.284033i	$0.0916724\pi$
$2$			0.803366i			0.568065i	−0.958815	+	0.284033i	$0.908328\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.35460			0.677302
$5$	2.13623	−	0.660705i	0.955350	−	0.295476i
$5$	2.13623	−	0.660705i	0.955350	−	0.295476i
$6$	−0.803366			−0.327973
$7$		−	0.508505i		−	0.192197i	−0.995372	−	0.0960984i	$-0.969364\pi$
$7$		−	0.508505i		−	0.192197i	0.995372	−	0.0960984i	$-0.0306364\pi$
$8$			2.69497i			0.952817i
$9$	−1.00000			−0.333333
$10$	0.530788	+	1.71617i	0.167850	+	0.542701i
$11$		0			0
$11$		0			0
$12$			1.35460i			0.391040i
$13$			5.13798i			1.42502i	0.701662	+	0.712509i	$0.252441\pi$
$13$			5.13798i			1.42502i	−0.701662	+	0.712509i	$0.747559\pi$
$14$	0.408516			0.109180
$15$	0.660705	+	2.13623i	0.170593	+	0.551572i
$16$	0.544158			0.136040
$17$			3.34542i			0.811383i	0.914010	+	0.405691i	$0.132969\pi$
$17$			3.34542i			0.811383i	−0.914010	+	0.405691i	$0.867031\pi$
$18$		−	0.803366i		−	0.189355i
$19$	1.17303			0.269113			0.134556	−	0.990906i	$-0.457039\pi$
$19$	1.17303			0.269113			0.134556	+	0.990906i	$0.457039\pi$
$20$	2.89374	−	0.894993i	0.647060	−	0.200127i
$21$	0.508505			0.110965
$22$		0			0
$23$		−	2.91459i		−	0.607734i	−0.952714	−	0.303867i	$-0.901722\pi$
$23$		−	2.91459i		−	0.607734i	0.952714	−	0.303867i	$-0.0982779\pi$
$24$	−2.69497			−0.550109
$25$	4.12694	−	2.82283i	0.825388	−	0.564567i
$26$	−4.12768			−0.809504
$27$		−	1.00000i		−	0.192450i
$28$		−	0.688823i		−	0.130175i
$29$	0.392594			0.0729028			0.0364514	−	0.999335i	$-0.488395\pi$
$29$	0.392594			0.0729028			0.0364514	+	0.999335i	$0.488395\pi$
$30$	−1.71617	+	0.530788i	−0.313329	+	0.0969081i
$31$	−6.35529			−1.14144			−0.570722	−	0.821143i	$-0.693337\pi$
$31$	−6.35529			−1.14144			−0.570722	+	0.821143i	$0.693337\pi$
$32$			5.82710i			1.03010i
$33$		0			0
$34$	−2.68759			−0.460918
$35$	−0.335972	−	1.08628i	−0.0567896	−	0.183615i
$36$	−1.35460			−0.225767
$37$			4.45218i			0.731934i	0.930628	+	0.365967i	$0.119262\pi$
$37$			4.45218i			0.731934i	−0.930628	+	0.365967i	$0.880738\pi$
$38$			0.942375i			0.152873i
$39$	−5.13798			−0.822735
$40$	1.78058	+	5.75708i	0.281535	+	0.910274i
$41$	−2.79867			−0.437079			−0.218540	−	0.975828i	$-0.570129\pi$
$41$	−2.79867			−0.437079			−0.218540	+	0.975828i	$0.570129\pi$
$42$			0.408516i			0.0630353i
$43$			3.05350i			0.465654i	0.972518	+	0.232827i	$0.0747976\pi$
$43$			3.05350i			0.465654i	−0.972518	+	0.232827i	$0.925202\pi$
$44$		0			0
$45$	−2.13623	+	0.660705i	−0.318450	+	0.0984921i
$46$	2.34148			0.345233
$47$		−	11.4923i		−	1.67633i	−0.545421	−	0.838163i	$-0.683630\pi$
$47$		−	11.4923i		−	1.67633i	0.545421	−	0.838163i	$-0.316370\pi$
$48$			0.544158i			0.0785425i
$49$	6.74142			0.963060
$50$	2.26777	+	3.31544i	0.320711	+	0.468874i
$51$	−3.34542			−0.468452
$52$			6.95993i			0.965168i
$53$			9.80747i			1.34716i	0.739114	+	0.673580i	$0.235244\pi$
$53$			9.80747i			1.34716i	−0.739114	+	0.673580i	$0.764756\pi$
$54$	0.803366			0.109324
$55$		0			0
$56$	1.37041			0.183128
$57$			1.17303i			0.155372i
$58$			0.315396i			0.0414136i
$59$	3.02854			0.394282			0.197141	−	0.980375i	$-0.436834\pi$
$59$	3.02854			0.394282			0.197141	+	0.980375i	$0.436834\pi$
$60$	0.894993	+	2.89374i	0.115543	+	0.373580i
$61$	1.05512			0.135095			0.0675473	−	0.997716i	$-0.478483\pi$
$61$	1.05512			0.135095			0.0675473	+	0.997716i	$0.478483\pi$
$62$		−	5.10562i		−	0.648415i
$63$			0.508505i			0.0640656i
$64$	−3.59298			−0.449122
$65$	3.39469	+	10.9759i	0.421059	+	1.36139i
$66$		0			0
$67$			5.31327i			0.649120i	0.945865	+	0.324560i	$0.105216\pi$
$67$			5.31327i			0.649120i	−0.945865	+	0.324560i	$0.894784\pi$
$68$			4.53171i			0.549551i
$69$	2.91459			0.350876
$70$	0.872682	−	0.269908i	0.104305	−	0.0322602i
$71$	4.09976			0.486552			0.243276	−	0.969957i	$-0.421778\pi$
$71$	4.09976			0.486552			0.243276	+	0.969957i	$0.421778\pi$
$72$		−	2.69497i		−	0.317606i
$73$		−	13.1083i		−	1.53422i	−0.641518	−	0.767108i	$-0.721695\pi$
$73$		−	13.1083i		−	1.53422i	0.641518	−	0.767108i	$-0.278305\pi$
$74$	−3.57673			−0.415787
$75$	2.82283	+	4.12694i	0.325953	+	0.476538i
$76$	1.58900			0.182270
$77$		0			0
$78$		−	4.12768i		−	0.467367i
$79$	16.1403			1.81593			0.907963	−	0.419051i	$-0.137637\pi$
$79$	16.1403			1.81593			0.907963	+	0.419051i	$0.137637\pi$
$80$	1.16245	−	0.359528i	0.129965	−	0.0401965i
$81$	1.00000			0.111111
$82$		−	2.24836i		−	0.248290i
$83$		−	15.3587i		−	1.68584i	−0.538039	−	0.842920i	$-0.680835\pi$
$83$		−	15.3587i		−	1.68584i	0.538039	−	0.842920i	$-0.319165\pi$
$84$	0.688823			0.0751567
$85$	2.21033	+	7.14657i	0.239744	+	0.775154i
$86$	−2.45308			−0.264522
$87$			0.392594i			0.0420905i
$88$		0			0
$89$	9.84603			1.04368			0.521838	−	0.853044i	$-0.325246\pi$
$89$	9.84603			1.04368			0.521838	+	0.853044i	$0.325246\pi$
$90$	−0.530788	−	1.71617i	−0.0559499	−	0.180900i
$91$	2.61269			0.273884
$92$		−	3.94812i		−	0.411620i
$93$		−	6.35529i		−	0.659013i
$94$	9.23252			0.952262
$95$	2.50587	−	0.775030i	0.257097	−	0.0795164i
$96$	−5.82710			−0.594726
$97$			15.1692i			1.54020i	0.637926	+	0.770098i	$0.279793\pi$
$97$			15.1692i			1.54020i	−0.637926	+	0.770098i	$0.720207\pi$
$98$			5.41583i			0.547081i
$99$		0			0
$100$	5.59037	−	3.82382i	0.559037	−	0.382382i
$101$	−16.5472			−1.64650			−0.823252	−	0.567677i	$-0.807842\pi$
$101$	−16.5472			−1.64650			−0.823252	+	0.567677i	$0.807842\pi$
$102$		−	2.68759i		−	0.266111i
$103$			14.3340i			1.41237i	0.708025	+	0.706187i	$0.249586\pi$
$103$			14.3340i			1.41237i	−0.708025	+	0.706187i	$0.750414\pi$
$104$	−13.8467			−1.35778
$105$	1.08628	−	0.335972i	0.106010	−	0.0327875i
$106$	−7.87899			−0.765275
$107$		−	6.87095i		−	0.664239i	−0.943237	−	0.332120i	$-0.892236\pi$
$107$		−	6.87095i		−	0.664239i	0.943237	−	0.332120i	$-0.107764\pi$
$108$		−	1.35460i		−	0.130347i
$109$	−16.9516			−1.62367			−0.811833	−	0.583890i	$-0.801530\pi$
$109$	−16.9516			−1.62367			−0.811833	+	0.583890i	$0.801530\pi$
$110$		0			0
$111$	−4.45218			−0.422583
$112$		−	0.276707i		−	0.0261464i
$113$		−	4.50913i		−	0.424184i	−0.977250	−	0.212092i	$-0.931972\pi$
$113$		−	4.50913i		−	0.424184i	0.977250	−	0.212092i	$-0.0680276\pi$
$114$	−0.942375			−0.0882615
$115$	−1.92569	−	6.22623i	−0.179571	−	0.580599i
$116$	0.531809			0.0493772
$117$		−	5.13798i		−	0.475006i
$118$			2.43303i			0.223978i
$119$	1.70116			0.155945
$120$	−5.75708	+	1.78058i	−0.525547	+	0.162544i
$121$		0			0
$122$			0.847649i			0.0767425i
$123$		−	2.79867i		−	0.252348i
$124$	−8.60890			−0.773102
$125$	6.95102	−	8.75690i	0.621718	−	0.783241i
$126$	−0.408516			−0.0363935
$127$			10.6946i			0.948990i	0.880258	+	0.474495i	$0.157369\pi$
$127$			10.6946i			0.948990i	−0.880258	+	0.474495i	$0.842631\pi$
$128$			8.76773i			0.774966i
$129$	−3.05350			−0.268846
$130$	−8.81766	+	2.72718i	−0.773360	+	0.239189i
$131$	−7.00557			−0.612079			−0.306040	−	0.952019i	$-0.599004\pi$
$131$	−7.00557			−0.612079			−0.306040	+	0.952019i	$0.599004\pi$
$132$		0			0
$133$		−	0.596494i		−	0.0517226i
$134$	−4.26850			−0.368742
$135$	−0.660705	−	2.13623i	−0.0568644	−	0.183857i
$136$	−9.01581			−0.773099
$137$		−	11.0079i		−	0.940465i	−0.882542	−	0.470233i	$-0.844170\pi$
$137$		−	11.0079i		−	0.940465i	0.882542	−	0.470233i	$-0.155830\pi$
$138$			2.34148i			0.199320i
$139$	14.2028			1.20467			0.602334	−	0.798244i	$-0.294237\pi$
$139$	14.2028			1.20467			0.602334	+	0.798244i	$0.294237\pi$
$140$	−0.455109	−	1.47148i	−0.0384637	−	0.124363i
$141$	11.4923			0.967827
$142$			3.29361i			0.276393i
$143$		0			0
$144$	−0.544158			−0.0453465
$145$	0.838670	−	0.259389i	0.0696477	−	0.0215411i
$146$	10.5308			0.871535
$147$			6.74142i			0.556023i
$148$			6.03094i			0.495741i
$149$	−13.0575			−1.06971			−0.534854	−	0.844944i	$-0.679633\pi$
$149$	−13.0575			−1.06971			−0.534854	+	0.844944i	$0.679633\pi$
$150$	−3.31544	+	2.26777i	−0.270705	+	0.185162i
$151$	18.3513			1.49340			0.746702	−	0.665158i	$-0.231636\pi$
$151$	18.3513			1.49340			0.746702	+	0.665158i	$0.231636\pi$
$152$			3.16130i			0.256415i
$153$		−	3.34542i		−	0.270461i
$154$		0			0
$155$	−13.5763	+	4.19897i	−1.09048	+	0.337270i
$156$	−6.95993			−0.557240
$157$		−	10.9402i		−	0.873127i	−0.899673	−	0.436563i	$-0.856195\pi$
$157$		−	10.9402i		−	0.873127i	0.899673	−	0.436563i	$-0.143805\pi$
$158$			12.9666i			1.03156i
$159$	−9.80747			−0.777783
$160$	3.85000	+	12.4480i	0.304369	+	0.984103i
$161$	−1.48208			−0.116805
$162$			0.803366i			0.0631184i
$163$		−	23.0823i		−	1.80795i	−0.427589	−	0.903973i	$-0.640637\pi$
$163$		−	23.0823i		−	1.80795i	0.427589	−	0.903973i	$-0.359363\pi$
$164$	−3.79109			−0.296035
$165$		0			0
$166$	12.3387			0.957667
$167$			4.17425i			0.323013i	0.986872	+	0.161507i	$0.0516353\pi$
$167$			4.17425i			0.323013i	−0.986872	+	0.161507i	$0.948365\pi$
$168$			1.37041i			0.105729i
$169$	−13.3988			−1.03068
$170$	−5.74131	+	1.77571i	−0.440338	+	0.136190i
$171$	−1.17303			−0.0897042
$172$			4.13628i			0.315388i
$173$		−	3.71693i		−	0.282593i	−0.989967	−	0.141297i	$-0.954873\pi$
$173$		−	3.71693i		−	0.282593i	0.989967	−	0.141297i	$-0.0451271\pi$
$174$	−0.315396			−0.0239101
$175$	−1.43542	−	2.09857i	−0.108508	−	0.158637i
$176$		0			0
$177$			3.02854i			0.227639i
$178$			7.90996i			0.592876i
$179$	−17.8921			−1.33732			−0.668661	−	0.743568i	$-0.733132\pi$
$179$	−17.8921			−1.33732			−0.668661	+	0.743568i	$0.733132\pi$
$180$	−2.89374	+	0.894993i	−0.215687	+	0.0667089i
$181$	15.1181			1.12372			0.561859	−	0.827233i	$-0.310086\pi$
$181$	15.1181			1.12372			0.561859	+	0.827233i	$0.310086\pi$
$182$			2.09894i			0.155584i
$183$			1.05512i			0.0779969i
$184$	7.85475			0.579060
$185$	2.94158	+	9.51088i	0.216269	+	0.699254i
$186$	5.10562			0.374362
$187$		0			0
$188$		−	15.5675i		−	1.13538i
$189$	−0.508505			−0.0369883
$190$	0.622632	+	2.01313i	0.0451705	+	0.146048i
$191$	0.745573			0.0539478			0.0269739	−	0.999636i	$-0.491413\pi$
$191$	0.745573			0.0539478			0.0269739	+	0.999636i	$0.491413\pi$
$192$		−	3.59298i		−	0.259301i
$193$		−	8.87896i		−	0.639121i	−0.947566	−	0.319561i	$-0.896465\pi$
$193$		−	8.87896i		−	0.639121i	0.947566	−	0.319561i	$-0.103535\pi$
$194$	−12.1864			−0.874931
$195$	−10.9759	+	3.39469i	−0.786000	+	0.243099i
$196$	9.13196			0.652283
$197$			1.05280i			0.0750089i	0.999296	+	0.0375044i	$0.0119408\pi$
$197$			1.05280i			0.0750089i	−0.999296	+	0.0375044i	$0.988059\pi$
$198$		0			0
$199$	2.28171			0.161746			0.0808730	−	0.996724i	$-0.474229\pi$
$199$	2.28171			0.161746			0.0808730	+	0.996724i	$0.474229\pi$
$200$	7.60746	+	11.1220i	0.537929	+	0.786443i
$201$	−5.31327			−0.374769
$202$		−	13.2934i		−	0.935321i
$203$		−	0.199636i		−	0.0140117i
$204$	−4.53171			−0.317283
$205$	−5.97860	+	1.84910i	−0.417564	+	0.129147i
$206$	−11.5155			−0.802321
$207$			2.91459i			0.202578i
$208$			2.79587i			0.193859i
$209$		0			0
$210$	0.269908	+	0.872682i	0.0186254	+	0.0602208i
$211$	−9.56919			−0.658771			−0.329385	−	0.944196i	$-0.606841\pi$
$211$	−9.56919			−0.658771			−0.329385	+	0.944196i	$0.606841\pi$
$212$			13.2852i			0.912434i
$213$			4.09976i			0.280911i
$214$	5.51988			0.377331
$215$	2.01746	+	6.52297i	0.137590	+	0.444863i
$216$	2.69497			0.183370
$217$			3.23170i			0.219382i
$218$		−	13.6183i		−	0.922348i
$219$	13.1083			0.885780
$220$		0			0
$221$	−17.1887			−1.15624
$222$		−	3.57673i		−	0.240054i
$223$			8.81925i			0.590581i	0.955408	+	0.295290i	$0.0954164\pi$
$223$			8.81925i			0.590581i	−0.955408	+	0.295290i	$0.904584\pi$
$224$	2.96311			0.197981
$225$	−4.12694	+	2.82283i	−0.275129	+	0.188189i
$226$	3.62248			0.240964
$227$		−	5.38764i		−	0.357590i	−0.983886	−	0.178795i	$-0.942780\pi$
$227$		−	5.38764i		−	0.357590i	0.983886	−	0.178795i	$-0.0572199\pi$
$228$			1.58900i			0.105234i
$229$	−24.3817			−1.61119			−0.805595	−	0.592466i	$-0.798154\pi$
$229$	−24.3817			−1.61119			−0.805595	+	0.592466i	$0.798154\pi$
$230$	5.00194	−	1.54703i	0.329818	−	0.102008i
$231$		0			0
$232$			1.05803i			0.0694631i
$233$		−	4.61992i		−	0.302661i	−0.988483	−	0.151331i	$-0.951644\pi$
$233$		−	4.61992i		−	0.302661i	0.988483	−	0.151331i	$-0.0483558\pi$
$234$	4.12768			0.269835
$235$	−7.59302	−	24.5502i	−0.495314	−	1.60148i
$236$	4.10247			0.267048
$237$			16.1403i			1.04843i
$238$			1.36665i			0.0885870i
$239$	−4.81862			−0.311691			−0.155845	−	0.987781i	$-0.549810\pi$
$239$	−4.81862			−0.311691			−0.155845	+	0.987781i	$0.549810\pi$
$240$	0.359528	+	1.16245i	0.0232074	+	0.0750356i
$241$	0.424606			0.0273513			0.0136757	−	0.999906i	$-0.495647\pi$
$241$	0.424606			0.0273513			0.0136757	+	0.999906i	$0.495647\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	1.42927			0.0914998
$245$	14.4012	−	4.45409i	0.920060	−	0.284561i
$246$	2.24836			0.143350
$247$			6.02703i			0.383490i
$248$		−	17.1273i		−	1.08759i
$249$	15.3587			0.973320
$250$	7.03499	+	5.58421i	0.444932	+	0.353176i
$251$	15.3627			0.969688			0.484844	−	0.874601i	$-0.338876\pi$
$251$	15.3627			0.969688			0.484844	+	0.874601i	$0.338876\pi$
$252$			0.688823i			0.0433918i
$253$		0			0
$254$	−8.59165			−0.539088
$255$	−7.14657	+	2.21033i	−0.447536	+	0.138416i
$256$	−14.2297			−0.889353
$257$		−	7.41474i		−	0.462519i	−0.972892	−	0.231259i	$-0.925715\pi$
$257$		−	7.41474i		−	0.462519i	0.972892	−	0.231259i	$-0.0742846\pi$
$258$		−	2.45308i		−	0.152722i
$259$	2.26396			0.140676
$260$	4.59846	+	14.8680i	0.285184	+	0.922073i
$261$	−0.392594			−0.0243009
$262$		−	5.62803i		−	0.347701i
$263$		−	30.6870i		−	1.89224i	−0.323815	−	0.946120i	$-0.604966\pi$
$263$		−	30.6870i		−	1.89224i	0.323815	−	0.946120i	$-0.395034\pi$
$264$		0			0
$265$	6.47985	+	20.9510i	0.398054	+	1.28701i
$266$	0.479203			0.0293818
$267$			9.84603i			0.602567i
$268$			7.19738i			0.439650i
$269$	−18.2413			−1.11219			−0.556095	−	0.831119i	$-0.687701\pi$
$269$	−18.2413			−1.11219			−0.556095	+	0.831119i	$0.687701\pi$
$270$	1.71617	−	0.530788i	0.104443	−	0.0323027i
$271$	13.7411			0.834714			0.417357	−	0.908743i	$-0.362956\pi$
$271$	13.7411			0.834714			0.417357	+	0.908743i	$0.362956\pi$
$272$			1.82044i			0.110380i
$273$			2.61269i			0.158127i
$274$	8.84334			0.534246
$275$		0			0
$276$	3.94812			0.237649
$277$			1.37752i			0.0827674i	0.999143	+	0.0413837i	$0.0131766\pi$
$277$			1.37752i			0.0827674i	−0.999143	+	0.0413837i	$0.986823\pi$
$278$			11.4101i			0.684330i
$279$	6.35529			0.380481
$280$	2.92750	−	0.905435i	0.174952	−	0.0541101i
$281$	−19.3025			−1.15149			−0.575746	−	0.817629i	$-0.695288\pi$
$281$	−19.3025			−1.15149			−0.575746	+	0.817629i	$0.695288\pi$
$282$			9.23252i			0.549789i
$283$		−	2.19620i		−	0.130551i	−0.997867	−	0.0652754i	$-0.979207\pi$
$283$		−	2.19620i		−	0.130551i	0.997867	−	0.0652754i	$-0.0207926\pi$
$284$	5.55355			0.329543
$285$	0.775030	+	2.50587i	0.0459088	+	0.148435i
$286$		0			0
$287$			1.42314i			0.0840053i
$288$		−	5.82710i		−	0.343365i
$289$	5.80819			0.341658
$290$	0.208384	+	0.673758i	0.0122367	+	0.0395645i
$291$	−15.1692			−0.889232
$292$		−	17.7566i		−	1.03913i
$293$		−	27.3180i		−	1.59594i	−0.602700	−	0.797968i	$-0.705909\pi$
$293$		−	27.3180i		−	1.59594i	0.602700	−	0.797968i	$-0.294091\pi$
$294$	−5.41583			−0.315857
$295$	6.46965	−	2.00097i	0.376678	−	0.116501i
$296$	−11.9985			−0.697400
$297$		0			0
$298$		−	10.4899i		−	0.607664i
$299$	14.9751			0.866033
$300$	3.82382	+	5.59037i	0.220768	+	0.322760i
$301$	1.55272			0.0894973
$302$			14.7428i			0.848351i
$303$		−	16.5472i		−	0.950609i
$304$	0.638317			0.0366100
$305$	2.25398	−	0.697124i	0.129063	−	0.0399172i
$306$	2.68759			0.153639
$307$		−	26.9287i		−	1.53690i	−0.639908	−	0.768451i	$-0.721028\pi$
$307$		−	26.9287i		−	1.53690i	0.639908	−	0.768451i	$-0.278972\pi$
$308$		0			0
$309$	−14.3340			−0.815434
$310$	−3.37331	−	10.9068i	−0.191591	−	0.619463i
$311$	11.9344			0.676740			0.338370	−	0.941013i	$-0.390124\pi$
$311$	11.9344			0.676740			0.338370	+	0.941013i	$0.390124\pi$
$312$		−	13.8467i		−	0.783916i
$313$			14.9612i			0.845658i	0.906209	+	0.422829i	$0.138963\pi$
$313$			14.9612i			0.845658i	−0.906209	+	0.422829i	$0.861037\pi$
$314$	8.78902			0.495993
$315$	0.335972	+	1.08628i	0.0189299	+	0.0612051i
$316$	21.8637			1.22993
$317$		−	9.78534i		−	0.549600i	−0.961501	−	0.274800i	$-0.911388\pi$
$317$		−	9.78534i		−	0.549600i	0.961501	−	0.274800i	$-0.0886116\pi$
$318$		−	7.87899i		−	0.441832i
$319$		0			0
$320$	−7.67542	+	2.37390i	−0.429069	+	0.132705i
$321$	6.87095			0.383499
$322$		−	1.19066i		−	0.0663527i
$323$			3.92429i			0.218353i
$324$	1.35460			0.0752558
$325$	14.5037	+	21.2041i	0.804518	+	1.17619i
$326$	18.5435			1.02703
$327$		−	16.9516i		−	0.937424i
$328$		−	7.54235i		−	0.416456i
$329$	−5.84390			−0.322184
$330$		0			0
$331$	5.14693			0.282901			0.141450	−	0.989945i	$-0.454823\pi$
$331$	5.14693			0.282901			0.141450	+	0.989945i	$0.454823\pi$
$332$		−	20.8050i		−	1.14182i
$333$		−	4.45218i		−	0.243978i
$334$	−3.35345			−0.183492
$335$	3.51051	+	11.3504i	0.191799	+	0.620136i
$336$	0.276707			0.0150956
$337$			29.3514i			1.59887i	0.600750	+	0.799437i	$0.294869\pi$
$337$			29.3514i			1.59887i	−0.600750	+	0.799437i	$0.705131\pi$
$338$		−	10.7642i		−	0.585493i
$339$	4.50913			0.244902
$340$	2.99413	+	9.68077i	0.162379	+	0.525014i
$341$		0			0
$342$		−	0.942375i		−	0.0509578i
$343$		−	6.98758i		−	0.377294i
$344$	−8.22910			−0.443683
$345$	6.22623	−	1.92569i	0.335209	−	0.103675i
$346$	2.98606			0.160531
$347$			7.33591i			0.393812i	0.980422	+	0.196906i	$0.0630894\pi$
$347$			7.33591i			0.393812i	−0.980422	+	0.196906i	$0.936911\pi$
$348$			0.531809i			0.0285080i
$349$	28.5268			1.52701			0.763503	−	0.645804i	$-0.223478\pi$
$349$	28.5268			1.52701			0.763503	+	0.645804i	$0.223478\pi$
$350$	1.68592	−	1.15317i	0.0901161	−	0.0616396i
$351$	5.13798			0.274245
$352$		0			0
$353$		−	16.1818i		−	0.861271i	−0.902526	−	0.430636i	$-0.858289\pi$
$353$		−	16.1818i		−	0.861271i	0.902526	−	0.430636i	$-0.141711\pi$
$354$	−2.43303			−0.129314
$355$	8.75802	−	2.70873i	0.464828	−	0.143765i
$356$	13.3375			0.706884
$357$			1.70116i			0.0900350i
$358$		−	14.3739i		−	0.759686i
$359$	−16.9324			−0.893659			−0.446829	−	0.894619i	$-0.647447\pi$
$359$	−16.9324			−0.893659			−0.446829	+	0.894619i	$0.647447\pi$
$360$	−1.78058	−	5.75708i	−0.0938449	−	0.303425i
$361$	−17.6240			−0.927578
$362$			12.1453i			0.638345i
$363$		0			0
$364$	3.53916			0.185502
$365$	−8.66075	−	28.0024i	−0.453324	−	1.46571i
$366$	−0.847649			−0.0443073
$367$			4.02281i			0.209989i	0.994473	+	0.104994i	$0.0334825\pi$
$367$			4.02281i			0.209989i	−0.994473	+	0.104994i	$0.966518\pi$
$368$		−	1.58600i		−	0.0826759i
$369$	2.79867			0.145693
$370$	−7.64071	+	2.36316i	−0.397222	+	0.122855i
$371$	4.98715			0.258920
$372$		−	8.60890i		−	0.446351i
$373$		−	36.2624i		−	1.87760i	−0.344469	−	0.938798i	$-0.611941\pi$
$373$		−	36.2624i		−	1.87760i	0.344469	−	0.938798i	$-0.388059\pi$
$374$		0			0
$375$	8.75690	+	6.95102i	0.452204	+	0.358949i
$376$	30.9715			1.59723
$377$			2.01714i			0.103888i
$378$		−	0.408516i		−	0.0210118i
$379$	19.8668			1.02049			0.510243	−	0.860030i	$-0.329555\pi$
$379$	19.8668			1.02049			0.510243	+	0.860030i	$0.329555\pi$
$380$	3.39446	−	1.04986i	0.174132	−	0.0538566i
$381$	−10.6946			−0.547899
$382$			0.598968i			0.0306459i
$383$		−	24.4491i		−	1.24929i	−0.780908	−	0.624646i	$-0.785243\pi$
$383$		−	24.4491i		−	1.24929i	0.780908	−	0.624646i	$-0.214757\pi$
$384$	−8.76773			−0.447427
$385$		0			0
$386$	7.13305			0.363063
$387$		−	3.05350i		−	0.155218i
$388$			20.5482i			1.04318i
$389$	12.0876			0.612866			0.306433	−	0.951892i	$-0.400865\pi$
$389$	12.0876			0.612866			0.306433	+	0.951892i	$0.400865\pi$
$390$	−2.72718	−	8.81766i	−0.138096	−	0.446499i
$391$	9.75052			0.493105
$392$			18.1680i			0.917620i
$393$		−	7.00557i		−	0.353384i
$394$	−0.845783			−0.0426099
$395$	34.4794	−	10.6640i	1.73484	−	0.536563i
$396$		0			0
$397$			22.7158i			1.14007i	0.821619	+	0.570037i	$0.193071\pi$
$397$			22.7158i			1.14007i	−0.821619	+	0.570037i	$0.806929\pi$
$398$			1.83305i			0.0918823i
$399$	0.596494			0.0298620
$400$	2.24571	−	1.53607i	0.112285	−	0.0768034i
$401$	−2.35795			−0.117750			−0.0588751	−	0.998265i	$-0.518751\pi$
$401$	−2.35795			−0.117750			−0.0588751	+	0.998265i	$0.518751\pi$
$402$		−	4.26850i		−	0.212893i
$403$		−	32.6533i		−	1.62658i
$404$	−22.4148			−1.11518
$405$	2.13623	−	0.660705i	0.106150	−	0.0328307i
$406$	0.160381			0.00795956
$407$		0			0
$408$		−	9.01581i		−	0.446349i
$409$	2.74377			0.135671			0.0678353	−	0.997697i	$-0.478391\pi$
$409$	2.74377			0.135671			0.0678353	+	0.997697i	$0.478391\pi$
$410$	−1.48550	−	4.80300i	−0.0733637	−	0.237203i
$411$	11.0079			0.542978
$412$			19.4169i			0.956603i
$413$		−	1.54003i		−	0.0757799i
$414$	−2.34148			−0.115078
$415$	−10.1476	−	32.8097i	−0.498126	−	1.61057i
$416$	−29.9395			−1.46791
$417$			14.2028i			0.695516i
$418$		0			0
$419$	13.9861			0.683266			0.341633	−	0.939833i	$-0.389020\pi$
$419$	13.9861			0.683266			0.341633	+	0.939833i	$0.389020\pi$
$420$	1.47148	−	0.455109i	0.0718010	−	0.0222070i
$421$	−17.7744			−0.866273			−0.433137	−	0.901328i	$-0.642593\pi$
$421$	−17.7744			−0.866273			−0.433137	+	0.901328i	$0.642593\pi$
$422$		−	7.68756i		−	0.374225i
$423$			11.4923i			0.558775i
$424$	−26.4309			−1.28360
$425$	9.44355	+	13.8063i	0.458079	+	0.669705i
$426$	−3.29361			−0.159576
$427$		−	0.536535i		−	0.0259647i
$428$		−	9.30741i		−	0.449891i
$429$		0			0
$430$	−5.24033	+	1.62076i	−0.252711	+	0.0781600i
$431$	7.11619			0.342775			0.171387	−	0.985204i	$-0.445175\pi$
$431$	7.11619			0.342775			0.171387	+	0.985204i	$0.445175\pi$
$432$		−	0.544158i		−	0.0261808i
$433$		−	11.3817i		−	0.546970i	−0.961876	−	0.273485i	$-0.911824\pi$
$433$		−	11.3817i		−	0.546970i	0.961876	−	0.273485i	$-0.0881764\pi$
$434$	−2.59623			−0.124623
$435$	0.259389	+	0.838670i	0.0124367	+	0.0402111i
$436$	−22.9626			−1.09971
$437$		−	3.41892i		−	0.163549i
$438$			10.5308i			0.503181i
$439$	16.1917			0.772788			0.386394	−	0.922334i	$-0.373721\pi$
$439$	16.1917			0.772788			0.386394	+	0.922334i	$0.373721\pi$
$440$		0			0
$441$	−6.74142			−0.321020
$442$		−	13.8088i		−	0.656817i
$443$			23.7522i			1.12850i	0.825604	+	0.564250i	$0.190834\pi$
$443$			23.7522i			1.12850i	−0.825604	+	0.564250i	$0.809166\pi$
$444$	−6.03094			−0.286216
$445$	21.0334	−	6.50532i	0.997077	−	0.308382i
$446$	−7.08508			−0.335488
$447$		−	13.0575i		−	0.617596i
$448$			1.82705i			0.0863199i
$449$	20.6589			0.974954			0.487477	−	0.873136i	$-0.337917\pi$
$449$	20.6589			0.974954			0.487477	+	0.873136i	$0.337917\pi$
$450$	−2.26777	−	3.31544i	−0.106904	−	0.156291i
$451$		0			0
$452$		−	6.10809i		−	0.287300i
$453$			18.3513i			0.862218i
$454$	4.32824			0.203135
$455$	5.58130	−	1.72622i	0.261655	−	0.0809263i
$456$	−3.16130			−0.148041
$457$			7.72035i			0.361143i	0.983562	+	0.180571i	$0.0577947\pi$
$457$			7.72035i			0.361143i	−0.983562	+	0.180571i	$0.942205\pi$
$458$		−	19.5874i		−	0.915261i
$459$	3.34542			0.156151
$460$	−2.60854	−	8.43408i	−0.121624	−	0.393241i
$461$	41.3034			1.92369			0.961845	−	0.273595i	$-0.0882128\pi$
$461$	41.3034			1.92369			0.961845	+	0.273595i	$0.0882128\pi$
$462$		0			0
$463$		−	19.5424i		−	0.908214i	−0.890947	−	0.454107i	$-0.849958\pi$
$463$		−	19.5424i		−	0.908214i	0.890947	−	0.454107i	$-0.150042\pi$
$464$	0.213633			0.00991767
$465$	−4.19897	−	13.5763i	−0.194723	−	0.629588i
$466$	3.71149			0.171931
$467$		−	21.3613i		−	0.988483i	−0.869325	−	0.494242i	$-0.835446\pi$
$467$		−	21.3613i		−	0.988483i	0.869325	−	0.494242i	$-0.164554\pi$
$468$		−	6.95993i		−	0.321723i
$469$	2.70183			0.124759
$470$	19.7228	−	6.09997i	0.909744	−	0.281371i
$471$	10.9402			0.504100
$472$			8.16184i			0.375679i
$473$		0			0
$474$	−12.9666			−0.595574
$475$	4.84104	−	3.31128i	0.222122	−	0.151932i
$476$	2.30440			0.105622
$477$		−	9.80747i		−	0.449053i
$478$		−	3.87111i		−	0.177061i
$479$	15.4162			0.704383			0.352191	−	0.935928i	$-0.385437\pi$
$479$	15.4162			0.704383			0.352191	+	0.935928i	$0.385437\pi$
$480$	−12.4480	+	3.85000i	−0.568172	+	0.175728i
$481$	−22.8752			−1.04302
$482$			0.341114i			0.0155373i
$483$		−	1.48208i		−	0.0674372i
$484$		0			0
$485$	10.0223	+	32.4048i	0.455091	+	1.47143i
$486$	−0.803366			−0.0364414
$487$			25.1124i			1.13795i	0.822354	+	0.568976i	$0.192660\pi$
$487$			25.1124i			1.13795i	−0.822354	+	0.568976i	$0.807340\pi$
$488$			2.84353i			0.128720i
$489$	23.0823			1.04382
$490$	3.57826	+	11.5694i	0.161649	+	0.522654i
$491$	1.10386			0.0498165			0.0249083	−	0.999690i	$-0.492071\pi$
$491$	1.10386			0.0498165			0.0249083	+	0.999690i	$0.492071\pi$
$492$		−	3.79109i		−	0.170916i
$493$			1.31339i			0.0591521i
$494$	−4.84190			−0.217848
$495$		0			0
$496$	−3.45829			−0.155282
$497$		−	2.08475i		−	0.0935138i
$498$			12.3387i			0.552909i
$499$	−2.29718			−0.102836			−0.0514179	−	0.998677i	$-0.516374\pi$
$499$	−2.29718			−0.102836			−0.0514179	+	0.998677i	$0.516374\pi$
$500$	9.41588	−	11.8621i	0.421091	−	0.530491i
$501$	−4.17425			−0.186492
$502$			12.3419i			0.550846i
$503$		−	6.85667i		−	0.305724i	−0.988248	−	0.152862i	$-0.951151\pi$
$503$		−	6.85667i		−	0.305724i	0.988248	−	0.152862i	$-0.0488490\pi$
$504$	−1.37041			−0.0610428
$505$	−35.3485	+	10.9328i	−1.57299	+	0.486503i
$506$		0			0
$507$		−	13.3988i		−	0.595063i
$508$			14.4869i			0.642752i
$509$	−25.8834			−1.14726			−0.573630	−	0.819114i	$-0.694465\pi$
$509$	−25.8834			−1.14726			−0.573630	+	0.819114i	$0.694465\pi$
$510$	−1.77571	−	5.74131i	−0.0786296	−	0.254229i
$511$	−6.66566			−0.294871
$512$			6.10385i			0.269755i
$513$		−	1.17303i		−	0.0517907i
$514$	5.95675			0.262741
$515$	9.47057	+	30.6208i	0.417323	+	1.34931i
$516$	−4.13628			−0.182090
$517$		0			0
$518$			1.81879i			0.0799129i
$519$	3.71693			0.163155
$520$	−29.5797	+	9.14859i	−1.29716	+	0.401192i
$521$	−28.7809			−1.26091			−0.630456	−	0.776225i	$-0.717132\pi$
$521$	−28.7809			−1.26091			−0.630456	+	0.776225i	$0.717132\pi$
$522$		−	0.315396i		−	0.0138045i
$523$		−	29.9930i		−	1.31150i	−0.754976	−	0.655752i	$-0.772352\pi$
$523$		−	29.9930i		−	1.31150i	0.754976	−	0.655752i	$-0.227648\pi$
$524$	−9.48977			−0.414563
$525$	2.09857	−	1.43542i	0.0915891	−	0.0626471i
$526$	24.6529			1.07492
$527$		−	21.2611i		−	0.926148i
$528$		0			0
$529$	14.5052			0.630659
$530$	−16.8313	+	5.20569i	−0.731105	+	0.226121i
$531$	−3.02854			−0.131427
$532$		−	0.808013i		−	0.0350318i
$533$		−	14.3795i		−	0.622846i
$534$	−7.90996			−0.342297
$535$	−4.53967	−	14.6779i	−0.196267	−	0.634581i
$536$	−14.3191			−0.618492
$537$		−	17.8921i		−	0.772103i
$538$		−	14.6544i		−	0.631796i
$539$		0			0
$540$	−0.894993	−	2.89374i	−0.0385144	−	0.124527i
$541$	2.65449			0.114126			0.0570628	−	0.998371i	$-0.481826\pi$
$541$	2.65449			0.114126			0.0570628	+	0.998371i	$0.481826\pi$
$542$			11.0392i			0.474172i
$543$			15.1181i			0.648779i
$544$	−19.4941			−0.835802
$545$	−36.2124	+	11.2000i	−1.55117	+	0.479755i
$546$	−2.09894			−0.0898265
$547$			3.36255i			0.143772i	0.997413	+	0.0718861i	$0.0229018\pi$
$547$			3.36255i			0.143772i	−0.997413	+	0.0718861i	$0.977098\pi$
$548$		−	14.9113i		−	0.636979i
$549$	−1.05512			−0.0450315
$550$		0			0
$551$	0.460526			0.0196191
$552$			7.85475i			0.334320i
$553$		−	8.20743i		−	0.349015i
$554$	−1.10666			−0.0470173
$555$	−9.51088	+	2.94158i	−0.403714	+	0.124863i
$556$	19.2392			0.815924
$557$			24.5074i			1.03841i	0.854649	+	0.519206i	$0.173772\pi$
$557$			24.5074i			1.03841i	−0.854649	+	0.519206i	$0.826228\pi$
$558$			5.10562i			0.216138i
$559$	−15.6888			−0.663566
$560$	−0.182822	−	0.591110i	−0.00772564	−	0.0249790i
$561$		0			0
$562$		−	15.5070i		−	0.654123i
$563$			8.01826i			0.337929i	0.985622	+	0.168965i	$0.0540424\pi$
$563$			8.01826i			0.337929i	−0.985622	+	0.168965i	$0.945958\pi$
$564$	15.5675			0.655511
$565$	−2.97921	−	9.63253i	−0.125336	−	0.405244i
$566$	1.76435			0.0741613
$567$		−	0.508505i		−	0.0213552i
$568$			11.0487i			0.463595i
$569$	−9.51091			−0.398718			−0.199359	−	0.979927i	$-0.563886\pi$
$569$	−9.51091			−0.398718			−0.199359	+	0.979927i	$0.563886\pi$
$570$	−2.01313	+	0.622632i	−0.0843207	+	0.0260792i
$571$	−11.6232			−0.486415			−0.243208	−	0.969974i	$-0.578200\pi$
$571$	−11.6232			−0.486415			−0.243208	+	0.969974i	$0.578200\pi$
$572$		0			0
$573$			0.745573i			0.0311468i
$574$	−1.14330			−0.0477205
$575$	−8.22740	−	12.0283i	−0.343106	−	0.501616i
$576$	3.59298			0.149707
$577$			9.73590i			0.405311i	0.979250	+	0.202655i	$0.0649571\pi$
$577$			9.73590i			0.405311i	−0.979250	+	0.202655i	$0.935043\pi$
$578$			4.66610i			0.194084i
$579$	8.87896			0.368997
$580$	1.13607	−	0.351369i	0.0471725	−	0.0145898i
$581$	−7.80999			−0.324013
$582$		−	12.1864i		−	0.505142i
$583$		0			0
$584$	35.3266			1.46183
$585$	−3.39469	−	10.9759i	−0.140353	−	0.453797i
$586$	21.9463			0.906595
$587$			6.35480i			0.262291i	0.991363	+	0.131145i	$0.0418655\pi$
$587$			6.35480i			0.262291i	−0.991363	+	0.131145i	$0.958135\pi$
$588$			9.13196i			0.376596i
$589$	−7.45497			−0.307177
$590$	1.60751	+	5.19750i	0.0661802	+	0.213978i
$591$	−1.05280			−0.0433064
$592$			2.42269i			0.0995721i
$593$		−	4.58134i		−	0.188133i	−0.995566	−	0.0940666i	$-0.970013\pi$
$593$		−	4.58134i		−	0.188133i	0.995566	−	0.0940666i	$-0.0299867\pi$
$594$		0			0
$595$	3.63407	−	1.12397i	0.148982	−	0.0460781i
$596$	−17.6877			−0.724516
$597$			2.28171i			0.0933841i
$598$			12.0305i			0.491963i
$599$	9.26327			0.378487			0.189244	−	0.981930i	$-0.439396\pi$
$599$	9.26327			0.378487			0.189244	+	0.981930i	$0.439396\pi$
$600$	−11.1220	+	7.60746i	−0.454053	+	0.310573i
$601$	−10.4939			−0.428054			−0.214027	−	0.976828i	$-0.568658\pi$
$601$	−10.4939			−0.428054			−0.214027	+	0.976828i	$0.568658\pi$
$602$			1.24740i			0.0508403i
$603$		−	5.31327i		−	0.216373i
$604$	24.8587			1.01149
$605$		0			0
$606$	13.2934			0.540008
$607$			20.8000i			0.844244i	0.906539	+	0.422122i	$0.138715\pi$
$607$			20.8000i			0.844244i	−0.906539	+	0.422122i	$0.861285\pi$
$608$			6.83539i			0.277212i
$609$	0.199636			0.00808966
$610$	0.560046	+	1.81077i	0.0226756	+	0.0733160i
$611$	59.0472			2.38879
$612$		−	4.53171i		−	0.183184i
$613$		−	24.7575i		−	0.999945i	−0.866041	−	0.499973i	$-0.833343\pi$
$613$		−	24.7575i		−	0.999945i	0.866041	−	0.499973i	$-0.166657\pi$
$614$	21.6336			0.873061
$615$	−1.84910	−	5.97860i	−0.0745628	−	0.241080i
$616$		0			0
$617$			28.2943i			1.13909i	0.821962	+	0.569543i	$0.192880\pi$
$617$			28.2943i			1.13909i	−0.821962	+	0.569543i	$0.807120\pi$
$618$		−	11.5155i		−	0.463220i
$619$	26.6041			1.06931			0.534654	−	0.845071i	$-0.320442\pi$
$619$	26.6041			1.06931			0.534654	+	0.845071i	$0.320442\pi$
$620$	−18.3906	+	5.68794i	−0.738583	+	0.228433i
$621$	−2.91459			−0.116959
$622$			9.58772i			0.384432i
$623$		−	5.00675i		−	0.200591i
$624$	−2.79587			−0.111925
$625$	9.06323	−	23.2993i	0.362529	−	0.931972i
$626$	−12.0193			−0.480389
$627$		0			0
$628$		−	14.8197i		−	0.591370i
$629$	−14.8944			−0.593879
$630$	−0.872682	+	0.269908i	−0.0347685	+	0.0107534i
$631$	16.4724			0.655757			0.327879	−	0.944720i	$-0.393666\pi$
$631$	16.4724			0.655757			0.327879	+	0.944720i	$0.393666\pi$
$632$			43.4977i			1.73024i
$633$		−	9.56919i		−	0.380341i
$634$	7.86121			0.312208
$635$	7.06596	+	22.8460i	0.280404	+	0.906617i
$636$	−13.2852			−0.526794
$637$			34.6373i			1.37238i
$638$		0			0
$639$	−4.09976			−0.162184
$640$	5.79289	+	18.7299i	0.228984	+	0.740363i
$641$	7.15197			0.282486			0.141243	−	0.989975i	$-0.454890\pi$
$641$	7.15197			0.282486			0.141243	+	0.989975i	$0.454890\pi$
$642$			5.51988i			0.217852i
$643$		−	17.7623i		−	0.700477i	−0.936661	−	0.350238i	$-0.886101\pi$
$643$		−	17.7623i		−	0.700477i	0.936661	−	0.350238i	$-0.113899\pi$
$644$	−2.00764			−0.0791120
$645$	−6.52297	+	2.01746i	−0.256842	+	0.0794375i
$646$	−3.15264			−0.124039
$647$			1.43164i			0.0562836i	0.999604	+	0.0281418i	$0.00895899\pi$
$647$			1.43164i			0.0562836i	−0.999604	+	0.0281418i	$0.991041\pi$
$648$			2.69497i			0.105869i
$649$		0			0
$650$	−17.0347	+	11.6517i	−0.668154	+	0.457019i
$651$	−3.23170			−0.126660
$652$		−	31.2674i		−	1.22453i
$653$			29.2874i			1.14611i	0.819518	+	0.573053i	$0.194241\pi$
$653$			29.2874i			1.14611i	−0.819518	+	0.573053i	$0.805759\pi$
$654$	13.6183			0.532518
$655$	−14.9655	+	4.62861i	−0.584750	+	0.180855i
$656$	−1.52292			−0.0594601
$657$			13.1083i			0.511405i
$658$		−	4.69479i		−	0.183022i
$659$	−21.2056			−0.826054			−0.413027	−	0.910719i	$-0.635529\pi$
$659$	−21.2056			−0.826054			−0.413027	+	0.910719i	$0.635529\pi$
$660$		0			0
$661$	−16.5453			−0.643537			−0.321768	−	0.946818i	$-0.604277\pi$
$661$	−16.5453			−0.643537			−0.321768	+	0.946818i	$0.604277\pi$
$662$			4.13486i			0.160706i
$663$		−	17.1887i		−	0.667553i
$664$	41.3914			1.60630
$665$	−0.394107	−	1.27425i	−0.0152828	−	0.0494132i
$666$	3.57673			0.138596
$667$		−	1.14425i		−	0.0443056i
$668$			5.65445i			0.218777i
$669$	−8.81925			−0.340972
$670$	−9.11849	+	2.82022i	−0.352278	+	0.108955i
$671$		0			0
$672$			2.96311i			0.114305i
$673$		−	18.9533i		−	0.730597i	−0.930890	−	0.365299i	$-0.880967\pi$
$673$		−	18.9533i		−	0.730597i	0.930890	−	0.365299i	$-0.119033\pi$
$674$	−23.5799			−0.908265
$675$	−2.82283	−	4.12694i	−0.108651	−	0.158846i
$676$	−18.1501			−0.698081
$677$			33.0448i			1.27002i	0.772506	+	0.635008i	$0.219003\pi$
$677$			33.0448i			1.27002i	−0.772506	+	0.635008i	$0.780997\pi$
$678$			3.62248i			0.139121i
$679$	7.71360			0.296021
$680$	−19.2598	+	5.95679i	−0.738580	+	0.228432i
$681$	5.38764			0.206455
$682$		0			0
$683$			26.1102i			0.999079i	0.866291	+	0.499540i	$0.166497\pi$
$683$			26.1102i			0.999079i	−0.866291	+	0.499540i	$0.833503\pi$
$684$	−1.58900			−0.0607568
$685$	−7.27295	−	23.5153i	−0.277885	−	0.898474i
$686$	5.61358			0.214328
$687$		−	24.3817i		−	0.930221i
$688$			1.66159i			0.0633474i
$689$	−50.3906			−1.91973
$690$	1.54703	+	5.00194i	0.0588944	+	0.190421i
$691$	−23.8340			−0.906690			−0.453345	−	0.891335i	$-0.649769\pi$
$691$	−23.8340			−0.906690			−0.453345	+	0.891335i	$0.649769\pi$
$692$		−	5.03497i		−	0.191401i
$693$		0			0
$694$	−5.89342			−0.223711
$695$	30.3405	−	9.38388i	1.15088	−	0.355951i
$696$	−1.05803			−0.0401045
$697$		−	9.36272i		−	0.354638i
$698$			22.9175i			0.867439i
$699$	4.61992			0.174741
$700$	−1.94443	−	2.84273i	−0.0734926	−	0.107445i
$701$	16.3561			0.617761			0.308880	−	0.951101i	$-0.400046\pi$
$701$	16.3561			0.617761			0.308880	+	0.951101i	$0.400046\pi$
$702$			4.12768i			0.155789i
$703$			5.22256i			0.196973i
$704$		0			0
$705$	24.5502	−	7.59302i	0.924613	−	0.285970i
$706$	12.9999			0.489258
$707$			8.41431i			0.316453i
$708$			4.10247i			0.154180i
$709$	−15.0833			−0.566464			−0.283232	−	0.959051i	$-0.591407\pi$
$709$	−15.0833			−0.566464			−0.283232	+	0.959051i	$0.591407\pi$
$710$	2.17610	+	7.03590i	0.0816677	+	0.264052i
$711$	−16.1403			−0.605309
$712$			26.5348i			0.994433i
$713$			18.5231i			0.693695i
$714$	−1.36665			−0.0511458
$715$		0			0
$716$	−24.2368			−0.905770
$717$		−	4.81862i		−	0.179955i
$718$		−	13.6029i		−	0.507657i
$719$	−22.6232			−0.843702			−0.421851	−	0.906665i	$-0.638619\pi$
$719$	−22.6232			−0.843702			−0.421851	+	0.906665i	$0.638619\pi$
$720$	−1.16245	+	0.359528i	−0.0433218	+	0.0133988i
$721$	7.28893			0.271454
$722$		−	14.1585i		−	0.526925i
$723$			0.424606i			0.0157913i
$724$	20.4790			0.761096
$725$	1.62021	−	1.10823i	0.0601731	−	0.0411585i
$726$		0			0
$727$		−	20.2062i		−	0.749408i	−0.927144	−	0.374704i	$-0.877744\pi$
$727$		−	20.2062i		−	0.749408i	0.927144	−	0.374704i	$-0.122256\pi$
$728$			7.04113i			0.260961i
$729$	−1.00000			−0.0370370
$730$	22.4962	−	6.95775i	0.832621	−	0.257518i
$731$	−10.2152			−0.377824
$732$			1.42927i			0.0528274i
$733$			1.50517i			0.0555947i	0.999614	+	0.0277974i	$0.00884932\pi$
$733$			1.50517i			0.0555947i	−0.999614	+	0.0277974i	$0.991151\pi$
$734$	−3.23178			−0.119287
$735$	4.45409	+	14.4012i	0.164292	+	0.531197i
$736$	16.9836			0.626025
$737$		0			0
$738$			2.24836i			0.0827632i
$739$	−38.7837			−1.42668			−0.713340	−	0.700818i	$-0.752818\pi$
$739$	−38.7837			−1.42668			−0.713340	+	0.700818i	$0.752818\pi$
$740$	3.98468	+	12.8835i	0.146480	+	0.473606i
$741$	−6.02703			−0.221408
$742$			4.00651i			0.147083i
$743$		−	26.8606i		−	0.985419i	−0.870194	−	0.492710i	$-0.836007\pi$
$743$		−	26.8606i		−	0.985419i	0.870194	−	0.492710i	$-0.163993\pi$
$744$	17.1273			0.627919
$745$	−27.8937	+	8.62713i	−1.02195	+	0.316073i
$746$	29.1320			1.06660
$747$			15.3587i			0.561947i
$748$		0			0
$749$	−3.49391			−0.127665
$750$	−5.58421	+	7.03499i	−0.203907	+	0.256882i
$751$	26.0025			0.948845			0.474423	−	0.880297i	$-0.342657\pi$
$751$	26.0025			0.948845			0.474423	+	0.880297i	$0.342657\pi$
$752$		−	6.25364i		−	0.228047i
$753$			15.3627i			0.559850i
$754$	−1.62050			−0.0590151
$755$	39.2025	−	12.1248i	1.42672	−	0.441266i
$756$	−0.688823			−0.0250522
$757$			29.5909i			1.07550i	0.843105	+	0.537749i	$0.180725\pi$
$757$			29.5909i			1.07550i	−0.843105	+	0.537749i	$0.819275\pi$
$758$			15.9603i			0.579703i
$759$		0			0
$760$	2.08868	+	6.75325i	0.0757645	+	0.244966i
$761$	33.0705			1.19880			0.599401	−	0.800449i	$-0.295405\pi$
$761$	33.0705			1.19880			0.599401	+	0.800449i	$0.295405\pi$
$762$		−	8.59165i		−	0.311243i
$763$			8.61996i			0.312063i
$764$	1.00996			0.0365389
$765$	−2.21033	−	7.14657i	−0.0799148	−	0.258385i
$766$	19.6416			0.709679
$767$			15.5606i			0.561860i
$768$		−	14.2297i		−	0.513468i
$769$	−3.37489			−0.121702			−0.0608508	−	0.998147i	$-0.519381\pi$
$769$	−3.37489			−0.121702			−0.0608508	+	0.998147i	$0.519381\pi$
$770$		0			0
$771$	7.41474			0.267035
$772$		−	12.0275i		−	0.432878i
$773$		−	23.1887i		−	0.834041i	−0.908897	−	0.417020i	$-0.863074\pi$
$773$		−	23.1887i		−	0.834041i	0.908897	−	0.417020i	$-0.136926\pi$
$774$	2.45308			0.0881740
$775$	−26.2279	+	17.9399i	−0.942134	+	0.644421i
$776$	−40.8805			−1.46752
$777$			2.26396i			0.0812190i
$778$			9.71076i			0.348148i
$779$	−3.28294			−0.117623
$780$	−14.8680	+	4.59846i	−0.532359	+	0.164651i
$781$		0			0
$782$			7.83323i			0.280116i
$783$		−	0.392594i		−	0.0140302i
$784$	3.66840			0.131014
$785$	−7.22828	−	23.3709i	−0.257988	−	0.834142i
$786$	5.62803			0.200745
$787$		−	41.0681i		−	1.46392i	−0.681348	−	0.731959i	$-0.738606\pi$
$787$		−	41.0681i		−	1.46392i	0.681348	−	0.731959i	$-0.261394\pi$
$788$			1.42613i			0.0508036i
$789$	30.6870			1.09249
$790$	8.56707	+	27.6995i	0.304803	+	0.985505i
$791$	−2.29292			−0.0815267
$792$		0			0
$793$			5.42119i			0.192512i
$794$	−18.2491			−0.647637
$795$	−20.9510	+	6.47985i	−0.743055	+	0.229816i
$796$	3.09081			0.109551
$797$		−	48.2620i		−	1.70953i	−0.519016	−	0.854765i	$-0.673701\pi$
$797$		−	48.2620i		−	1.70953i	0.519016	−	0.854765i	$-0.326299\pi$
$798$			0.479203i			0.0169636i
$799$	38.4465			1.36014
$800$	16.4489	+	24.0481i	0.581558	+	0.850229i
$801$	−9.84603			−0.347892
$802$		−	1.89429i		−	0.0668898i
$803$		0			0
$804$	−7.19738			−0.253832
$805$	−3.16607	+	0.979221i	−0.111589	+	0.0345130i
$806$	26.2326			0.924003
$807$		−	18.2413i		−	0.642123i
$808$		−	44.5941i		−	1.56882i
$809$	43.8433			1.54145			0.770724	−	0.637170i	$-0.219895\pi$
$809$	43.8433			1.54145			0.770724	+	0.637170i	$0.219895\pi$
$810$	0.530788	+	1.71617i	0.0186500	+	0.0603001i
$811$	−41.3933			−1.45351			−0.726757	−	0.686895i	$-0.758973\pi$
$811$	−41.3933			−1.45351			−0.726757	+	0.686895i	$0.758973\pi$
$812$		−	0.270428i		−	0.00949015i
$813$			13.7411i			0.481922i
$814$		0			0
$815$	−15.2506	−	49.3091i	−0.534205	−	1.72722i
$816$	−1.82044			−0.0637280
$817$			3.58186i			0.125313i
$818$			2.20425i			0.0770698i
$819$	−2.61269			−0.0912947
$820$	−8.09864	+	2.50479i	−0.282817	+	0.0874712i
$821$	42.9590			1.49928			0.749639	−	0.661847i	$-0.230227\pi$
$821$	42.9590			1.49928			0.749639	+	0.661847i	$0.230227\pi$
$822$			8.84334i			0.308447i
$823$		−	14.0263i		−	0.488925i	−0.969659	−	0.244462i	$-0.921389\pi$
$823$		−	14.0263i		−	0.488925i	0.969659	−	0.244462i	$-0.0786115\pi$
$824$	−38.6298			−1.34573
$825$		0			0
$826$	1.23721			0.0430479
$827$			30.9045i			1.07465i	0.843374	+	0.537327i	$0.180566\pi$
$827$			30.9045i			1.07465i	−0.843374	+	0.537327i	$0.819434\pi$
$828$			3.94812i			0.137207i
$829$	−36.9798			−1.28436			−0.642181	−	0.766553i	$-0.721970\pi$
$829$	−36.9798			−1.28436			−0.642181	+	0.766553i	$0.721970\pi$
$830$	26.3582	−	8.15223i	0.914907	−	0.282968i
$831$	−1.37752			−0.0477858
$832$		−	18.4606i		−	0.640008i
$833$			22.5529i			0.781410i
$834$	−11.4101			−0.395098
$835$	2.75795	+	8.91715i	0.0954427	+	0.308591i
$836$		0			0
$837$			6.35529i			0.219671i
$838$			11.2360i			0.388140i
$839$	−2.20030			−0.0759626			−0.0379813	−	0.999278i	$-0.512093\pi$
$839$	−2.20030			−0.0759626			−0.0379813	+	0.999278i	$0.512093\pi$
$840$	0.905435	+	2.92750i	0.0312405	+	0.101008i
$841$	−28.8459			−0.994685
$842$		−	14.2794i		−	0.492100i
$843$		−	19.3025i		−	0.664814i
$844$	−12.9625			−0.446186
$845$	−28.6229	+	8.85267i	−0.984659	+	0.304541i
$846$	−9.23252			−0.317421
$847$		0			0
$848$			5.33682i			0.183267i
$849$	2.19620			0.0753735
$850$	−11.0915	+	7.58662i	−0.380436	+	0.260219i
$851$	12.9763			0.444822
$852$			5.55355i			0.190262i
$853$			33.1729i			1.13582i	0.823092	+	0.567909i	$0.192247\pi$
$853$			33.1729i			1.13582i	−0.823092	+	0.567909i	$0.807753\pi$
$854$	0.431034			0.0147497
$855$	−2.50587	+	0.775030i	−0.0856989	+	0.0265055i
$856$	18.5170			0.632899
$857$			28.5419i			0.974972i	0.873131	+	0.487486i	$0.162086\pi$
$857$			28.5419i			0.974972i	−0.873131	+	0.487486i	$0.837914\pi$
$858$		0			0
$859$	−53.6600			−1.83085			−0.915427	−	0.402484i	$-0.868147\pi$
$859$	−53.6600			−1.83085			−0.915427	+	0.402484i	$0.868147\pi$
$860$	2.73286	+	8.83604i	0.0931898	+	0.301306i
$861$	−1.42314			−0.0485005
$862$			5.71690i			0.194719i
$863$			19.0942i			0.649974i	0.945719	+	0.324987i	$0.105360\pi$
$863$			19.0942i			0.649974i	−0.945719	+	0.324987i	$0.894640\pi$
$864$	5.82710			0.198242
$865$	−2.45580	−	7.94021i	−0.0834996	−	0.269975i
$866$	9.14368			0.310715
$867$			5.80819i			0.197257i
$868$			4.37767i			0.148588i
$869$		0			0
$870$	−0.673758	+	0.208384i	−0.0228425	+	0.00706488i
$871$	−27.2995			−0.925008
$872$		−	45.6840i		−	1.54706i
$873$		−	15.1692i		−	0.513398i
$874$	2.74664			0.0929065
$875$	−4.45293	−	3.53463i	−0.150536	−	0.119492i
$876$	17.7566			0.599940
$877$		−	13.8148i		−	0.466494i	−0.972418	−	0.233247i	$-0.925065\pi$
$877$		−	13.8148i		−	0.466494i	0.972418	−	0.233247i	$-0.0749351\pi$
$878$			13.0079i			0.438994i
$879$	27.3180			0.921414
$880$		0			0
$881$	−14.7416			−0.496658			−0.248329	−	0.968676i	$-0.579881\pi$
$881$	−14.7416			−0.496658			−0.248329	+	0.968676i	$0.579881\pi$
$882$		−	5.41583i		−	0.182360i
$883$		−	0.165486i		−	0.00556904i	−0.999996	−	0.00278452i	$-0.999114\pi$
$883$		−	0.165486i		−	0.00556904i	0.999996	−	0.00278452i	$-0.000886342\pi$
$884$	−23.2838			−0.783120
$885$	2.00097	+	6.46965i	0.0672619	+	0.217475i
$886$	−19.0817			−0.641061
$887$		−	13.8749i		−	0.465874i	−0.972492	−	0.232937i	$-0.925166\pi$
$887$		−	13.8749i		−	0.465874i	0.972492	−	0.232937i	$-0.0748336\pi$
$888$		−	11.9985i		−	0.402644i
$889$	5.43824			0.182393
$890$	5.22615	+	16.8975i	0.175181	+	0.566405i
$891$		0			0
$892$			11.9466i			0.400001i
$893$		−	13.4809i		−	0.451120i
$894$	10.4899			0.350835
$895$	−38.2217	+	11.8214i	−1.27761	+	0.395147i
$896$	4.45844			0.148946
$897$			14.9751i			0.500004i
$898$			16.5967i			0.553838i
$899$	−2.49505			−0.0832145
$900$	−5.59037	+	3.82382i	−0.186346	+	0.127461i
$901$	−32.8101			−1.09306
$902$		0			0
$903$			1.55272i			0.0516713i
$904$	12.1520			0.404169
$905$	32.2957	−	9.98859i	1.07354	−	0.332032i
$906$	−14.7428			−0.489796
$907$		−	9.10404i		−	0.302295i	−0.988511	−	0.151147i	$-0.951703\pi$
$907$		−	9.10404i		−	0.302295i	0.988511	−	0.151147i	$-0.0482968\pi$
$908$		−	7.29811i		−	0.242196i
$909$	16.5472			0.548834
$910$	1.38678	+	4.48382i	0.0459714	+	0.148637i
$911$	−45.2779			−1.50012			−0.750062	−	0.661367i	$-0.769977\pi$
$911$	−45.2779			−1.50012			−0.750062	+	0.661367i	$0.769977\pi$
$912$			0.638317i			0.0211368i
$913$		0			0
$914$	−6.20227			−0.205153
$915$	0.697124	+	2.25398i	0.0230462	+	0.0745143i
$916$	−33.0276			−1.09126
$917$			3.56237i			0.117640i
$918$			2.68759i			0.0887038i
$919$	14.8633			0.490296			0.245148	−	0.969486i	$-0.421163\pi$
$919$	14.8633			0.490296			0.245148	+	0.969486i	$0.421163\pi$
$920$	16.7795	−	5.18967i	0.553205	−	0.171098i
$921$	26.9287			0.887331
$922$			33.1817i			1.09278i
$923$			21.0645i			0.693346i
$924$		0			0
$925$	12.5678	+	18.3739i	0.413226	+	0.604130i
$926$	15.6997			0.515925
$927$		−	14.3340i		−	0.470791i
$928$			2.28769i			0.0750969i
$929$	−3.29372			−0.108063			−0.0540317	−	0.998539i	$-0.517207\pi$
$929$	−3.29372			−0.108063			−0.0540317	+	0.998539i	$0.517207\pi$
$930$	10.9068	−	3.37331i	0.357647	−	0.110615i
$931$	7.90792			0.259172
$932$		−	6.25816i		−	0.204993i
$933$			11.9344i			0.390716i
$934$	17.1609			0.561523
$935$		0			0
$936$	13.8467			0.452594
$937$		−	0.798303i		−	0.0260794i	−0.999915	−	0.0130397i	$-0.995849\pi$
$937$		−	0.798303i		−	0.0260794i	0.999915	−	0.0130397i	$-0.00415079\pi$
$938$			2.17055i			0.0708711i
$939$	−14.9612			−0.488241
$940$	−10.2855	−	33.2558i	−0.335477	−	1.08468i
$941$	−25.2852			−0.824275			−0.412138	−	0.911122i	$-0.635218\pi$
$941$	−25.2852			−0.824275			−0.412138	+	0.911122i	$0.635218\pi$
$942$			8.78902i			0.286362i
$943$			8.15699i			0.265628i
$944$	1.64801			0.0536380
$945$	−1.08628	+	0.335972i	−0.0353368	+	0.0109292i
$946$		0			0
$947$		−	49.6668i		−	1.61396i	−0.590582	−	0.806978i	$-0.701102\pi$
$947$		−	49.6668i		−	1.61396i	0.590582	−	0.806978i	$-0.298898\pi$
$948$			21.8637i			0.710100i
$949$	67.3504			2.18629
$950$	2.66017	+	3.88912i	0.0863072	+	0.126180i
$951$	9.78534			0.317311
$952$			4.58458i			0.148587i
$953$			27.7742i			0.899694i	0.893106	+	0.449847i	$0.148521\pi$
$953$			27.7742i			0.899694i	−0.893106	+	0.449847i	$0.851479\pi$
$954$	7.87899			0.255092
$955$	1.59271	−	0.492604i	0.0515390	−	0.0159403i
$956$	−6.52732			−0.211109
$957$		0			0
$958$			12.3848i			0.400135i
$959$	−5.59756			−0.180754
$960$	−2.37390	−	7.67542i	−0.0766173	−	0.247723i
$961$	9.38972			0.302894
$962$		−	18.3772i		−	0.592504i
$963$			6.87095i			0.221413i
$964$	0.575173			0.0185251
$965$	−5.86637	−	18.9675i	−0.188845	−	0.610585i
$966$	1.19066			0.0383087
$967$			11.0951i			0.356793i	0.983959	+	0.178396i	$0.0570909\pi$
$967$			11.0951i			0.356793i	−0.983959	+	0.178396i	$0.942909\pi$
$968$		0			0
$969$	−3.92429			−0.126066
$970$	−26.0329	+	8.05161i	−0.835866	+	0.258521i
$971$	−31.9217			−1.02442			−0.512208	−	0.858861i	$-0.671172\pi$
$971$	−31.9217			−1.02442			−0.512208	+	0.858861i	$0.671172\pi$
$972$			1.35460i			0.0434489i
$973$		−	7.22221i		−	0.231534i
$974$	−20.1745			−0.646431
$975$	−21.2041	+	14.5037i	−0.679075	+	0.464489i
$976$	0.574154			0.0183782
$977$			10.4056i			0.332904i	0.986050	+	0.166452i	$0.0532311\pi$
$977$			10.4056i			0.332904i	−0.986050	+	0.166452i	$0.946769\pi$
$978$			18.5435i			0.592957i
$979$		0			0
$980$	19.5079	−	6.03353i	0.623158	−	0.192734i
$981$	16.9516			0.541222
$982$			0.886804i			0.0282991i
$983$			41.4334i			1.32152i	0.750597	+	0.660760i	$0.229766\pi$
$983$			41.4334i			1.32152i	−0.750597	+	0.660760i	$0.770234\pi$
$984$	7.54235			0.240441
$985$	0.695590	+	2.24902i	0.0221633	+	0.0716597i
$986$	−1.05513			−0.0336022
$987$		−	5.84390i		−	0.186013i
$988$			8.16423i			0.259739i
$989$	8.89970			0.282994
$990$		0			0
$991$	−2.17000			−0.0689322			−0.0344661	−	0.999406i	$-0.510973\pi$
$991$	−2.17000			−0.0689322			−0.0344661	+	0.999406i	$0.510973\pi$
$992$		−	37.0329i		−	1.17580i
$993$			5.14693i			0.163333i
$994$	1.67482			0.0531219
$995$	4.87425	−	1.50754i	0.154524	−	0.0477921i
$996$	20.8050			0.659231
$997$		−	0.808994i		−	0.0256211i	−0.999918	−	0.0128105i	$-0.995922\pi$
$997$		−	0.808994i		−	0.0256211i	0.999918	−	0.0128105i	$-0.00407783\pi$
$998$		−	1.84547i		−	0.0584174i
$999$	4.45218			0.140861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.j.364.17		24
5.2	odd	4		9075.2.a.dy.1.5		12
5.3	odd	4		9075.2.a.dz.1.8		12
5.4	even	2	inner	1815.2.c.j.364.8		24
11.5	even	5		165.2.s.a.124.4	yes	48
11.9	even	5		165.2.s.a.4.9	yes	48
11.10	odd	2		1815.2.c.k.364.8		24
33.5	odd	10		495.2.ba.c.289.9		48
33.20	odd	10		495.2.ba.c.334.4		48
55.9	even	10		165.2.s.a.4.4	✓	48
55.27	odd	20		825.2.n.p.751.4		24
55.32	even	4		9075.2.a.ea.1.8		12
55.38	odd	20		825.2.n.o.751.3		24
55.42	odd	20		825.2.n.p.301.4		24
55.43	even	4		9075.2.a.dx.1.5		12
55.49	even	10		165.2.s.a.124.9	yes	48
55.53	odd	20		825.2.n.o.301.3		24
55.54	odd	2		1815.2.c.k.364.17		24
165.104	odd	10		495.2.ba.c.289.4		48
165.119	odd	10		495.2.ba.c.334.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.4	✓	48	55.9	even	10
165.2.s.a.4.9	yes	48	11.9	even	5
165.2.s.a.124.4	yes	48	11.5	even	5
165.2.s.a.124.9	yes	48	55.49	even	10
495.2.ba.c.289.4		48	165.104	odd	10
495.2.ba.c.289.9		48	33.5	odd	10
495.2.ba.c.334.4		48	33.20	odd	10
495.2.ba.c.334.9		48	165.119	odd	10
825.2.n.o.301.3		24	55.53	odd	20
825.2.n.o.751.3		24	55.38	odd	20
825.2.n.p.301.4		24	55.42	odd	20
825.2.n.p.751.4		24	55.27	odd	20
1815.2.c.j.364.8		24	5.4	even	2	inner
1815.2.c.j.364.17		24	1.1	even	1	trivial
1815.2.c.k.364.8		24	11.10	odd	2
1815.2.c.k.364.17		24	55.54	odd	2
9075.2.a.dx.1.5		12	55.43	even	4
9075.2.a.dy.1.5		12	5.2	odd	4
9075.2.a.dz.1.8		12	5.3	odd	4
9075.2.a.ea.1.8		12	55.32	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)

\(f(q)\)	\(=\)	\(q+0.803366i q^{2} +1.00000i q^{3} +1.35460 q^{4} +(2.13623 - 0.660705i) q^{5} -0.803366 q^{6} -0.508505i q^{7} +2.69497i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.803366i q^{2} +1.00000i q^{3} +1.35460 q^{4} +(2.13623 - 0.660705i) q^{5} -0.803366 q^{6} -0.508505i q^{7} +2.69497i q^{8} -1.00000 q^{9} +(0.530788 + 1.71617i) q^{10} +1.35460i q^{12} +5.13798i q^{13} +0.408516 q^{14} +(0.660705 + 2.13623i) q^{15} +0.544158 q^{16} +3.34542i q^{17} -0.803366i q^{18} +1.17303 q^{19} +(2.89374 - 0.894993i) q^{20} +0.508505 q^{21} -2.91459i q^{23} -2.69497 q^{24} +(4.12694 - 2.82283i) q^{25} -4.12768 q^{26} -1.00000i q^{27} -0.688823i q^{28} +0.392594 q^{29} +(-1.71617 + 0.530788i) q^{30} -6.35529 q^{31} +5.82710i q^{32} -2.68759 q^{34} +(-0.335972 - 1.08628i) q^{35} -1.35460 q^{36} +4.45218i q^{37} +0.942375i q^{38} -5.13798 q^{39} +(1.78058 + 5.75708i) q^{40} -2.79867 q^{41} +0.408516i q^{42} +3.05350i q^{43} +(-2.13623 + 0.660705i) q^{45} +2.34148 q^{46} -11.4923i q^{47} +0.544158i q^{48} +6.74142 q^{49} +(2.26777 + 3.31544i) q^{50} -3.34542 q^{51} +6.95993i q^{52} +9.80747i q^{53} +0.803366 q^{54} +1.37041 q^{56} +1.17303i q^{57} +0.315396i q^{58} +3.02854 q^{59} +(0.894993 + 2.89374i) q^{60} +1.05512 q^{61} -5.10562i q^{62} +0.508505i q^{63} -3.59298 q^{64} +(3.39469 + 10.9759i) q^{65} +5.31327i q^{67} +4.53171i q^{68} +2.91459 q^{69} +(0.872682 - 0.269908i) q^{70} +4.09976 q^{71} -2.69497i q^{72} -13.1083i q^{73} -3.57673 q^{74} +(2.82283 + 4.12694i) q^{75} +1.58900 q^{76} -4.12768i q^{78} +16.1403 q^{79} +(1.16245 - 0.359528i) q^{80} +1.00000 q^{81} -2.24836i q^{82} -15.3587i q^{83} +0.688823 q^{84} +(2.21033 + 7.14657i) q^{85} -2.45308 q^{86} +0.392594i q^{87} +9.84603 q^{89} +(-0.530788 - 1.71617i) q^{90} +2.61269 q^{91} -3.94812i q^{92} -6.35529i q^{93} +9.23252 q^{94} +(2.50587 - 0.775030i) q^{95} -5.82710 q^{96} +15.1692i q^{97} +5.41583i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} - 8 q^{6} - 24 q^{9}+O(q^{10}) \) 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

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