LMFDB - Embedded newform 1815.2.c.i.364.3

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 21x^{10} + 164x^{8} + 589x^{6} + 965x^{4} + 576x^{2} + 4 $ x^12 + 21x^10 + 164x^8 + 589x^6 + 965x^4 + 576*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.3
Root			$-1.95455i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.i.364.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95455i q^{2} -1.00000i q^{3} -1.82026 q^{4} +(-1.24280 + 1.85889i) q^{5} -1.95455 q^{6} -2.58348i q^{7} -0.351308i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.95455i q^{2} -1.00000i q^{3} -1.82026 q^{4} +(-1.24280 + 1.85889i) q^{5} -1.95455 q^{6} -2.58348i q^{7} -0.351308i q^{8} -1.00000 q^{9} +(3.63328 + 2.42911i) q^{10} +1.82026i q^{12} +6.49874i q^{13} -5.04954 q^{14} +(1.85889 + 1.24280i) q^{15} -4.32717 q^{16} +7.40085i q^{17} +1.95455i q^{18} +6.49258 q^{19} +(2.26222 - 3.38366i) q^{20} -2.58348 q^{21} +0.238335i q^{23} -0.351308 q^{24} +(-1.91091 - 4.62044i) q^{25} +12.7021 q^{26} +1.00000i q^{27} +4.70262i q^{28} -0.959152 q^{29} +(2.42911 - 3.63328i) q^{30} -2.26656 q^{31} +7.75505i q^{32} +14.4653 q^{34} +(4.80240 + 3.21075i) q^{35} +1.82026 q^{36} +9.55578i q^{37} -12.6901i q^{38} +6.49874 q^{39} +(0.653040 + 0.436604i) q^{40} -6.20447 q^{41} +5.04954i q^{42} +6.88029i q^{43} +(1.24280 - 1.85889i) q^{45} +0.465837 q^{46} +1.09789i q^{47} +4.32717i q^{48} +0.325615 q^{49} +(-9.03087 + 3.73496i) q^{50} +7.40085 q^{51} -11.8294i q^{52} -2.71078i q^{53} +1.95455 q^{54} -0.907597 q^{56} -6.49258i q^{57} +1.87471i q^{58} +1.23135 q^{59} +(-3.38366 - 2.26222i) q^{60} +1.45908 q^{61} +4.43011i q^{62} +2.58348i q^{63} +6.50329 q^{64} +(-12.0804 - 8.07662i) q^{65} -0.387707i q^{67} -13.4715i q^{68} +0.238335 q^{69} +(6.27556 - 9.38652i) q^{70} -1.12813 q^{71} +0.351308i q^{72} -7.21153i q^{73} +18.6772 q^{74} +(-4.62044 + 1.91091i) q^{75} -11.8182 q^{76} -12.7021i q^{78} +15.9707 q^{79} +(5.37780 - 8.04371i) q^{80} +1.00000 q^{81} +12.1269i q^{82} +9.40902i q^{83} +4.70262 q^{84} +(-13.7573 - 9.19776i) q^{85} +13.4479 q^{86} +0.959152i q^{87} -1.24004 q^{89} +(-3.63328 - 2.42911i) q^{90} +16.7894 q^{91} -0.433831i q^{92} +2.26656i q^{93} +2.14588 q^{94} +(-8.06896 + 12.0690i) q^{95} +7.75505 q^{96} -16.3452i q^{97} -0.636430i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9	$ 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9} + 12 q^{10} + 20 q^{14} + 22 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{25} - 24 q^{29} - 8 q^{30} + 36 q^{31} + 2 q^{34} + 24 q^{35} + 18 q^{36} - 4 q^{39} - 22 q^{40} - 12 q^{41} + 2 q^{45} - 22 q^{46} - 24 q^{49} - 58 q^{50} + 4 q^{51} - 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} + 8 q^{61} - 44 q^{64} - 14 q^{65} - 24 q^{69} - 16 q^{70} + 8 q^{74} - 12 q^{75} - 40 q^{76} - 4 q^{79} - 58 q^{80} + 12 q^{81} + 48 q^{84} - 2 q^{85} + 56 q^{86} + 32 q^{89} - 12 q^{90} + 48 q^{91} - 6 q^{94} + 62 q^{96}+O(q^{100}) $ 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9 + 12 * q^10 + 20 * q^14 + 22 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^25 - 24 * q^29 - 8 * q^30 + 36 * q^31 + 2 * q^34 + 24 * q^35 + 18 * q^36 - 4 * q^39 - 22 * q^40 - 12 * q^41 + 2 * q^45 - 22 * q^46 - 24 * q^49 - 58 * q^50 + 4 * q^51 - 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 + 8 * q^61 - 44 * q^64 - 14 * q^65 - 24 * q^69 - 16 * q^70 + 8 * q^74 - 12 * q^75 - 40 * q^76 - 4 * q^79 - 58 * q^80 + 12 * q^81 + 48 * q^84 - 2 * q^85 + 56 * q^86 + 32 * q^89 - 12 * q^90 + 48 * q^91 - 6 * q^94 + 62 * 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 $

$2$		−	1.95455i		−	1.38207i	−0.722819	−	0.691037i	$-0.757154\pi$
$2$		−	1.95455i		−	1.38207i	0.722819	−	0.691037i	$-0.242846\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.82026			−0.910131
$5$	−1.24280	+	1.85889i	−0.555796	+	0.831319i
$5$	−1.24280	+	1.85889i	−0.555796	+	0.831319i
$6$	−1.95455			−0.797941
$7$		−	2.58348i		−	0.976465i	−0.872714	−	0.488232i	$-0.837642\pi$
$7$		−	2.58348i		−	0.976465i	0.872714	−	0.488232i	$-0.162358\pi$
$8$		−	0.351308i		−	0.124206i
$9$	−1.00000			−0.333333
$10$	3.63328	+	2.42911i	1.14894	+	0.768152i
$11$		0			0
$11$		0			0
$12$			1.82026i			0.525464i
$13$			6.49874i			1.80243i	0.433376	+	0.901213i	$0.357322\pi$
$13$			6.49874i			1.80243i	−0.433376	+	0.901213i	$0.642678\pi$
$14$	−5.04954			−1.34955
$15$	1.85889	+	1.24280i	0.479962	+	0.320889i
$16$	−4.32717			−1.08179
$17$			7.40085i			1.79497i	0.441045	+	0.897485i	$0.354608\pi$
$17$			7.40085i			1.79497i	−0.441045	+	0.897485i	$0.645392\pi$
$18$			1.95455i			0.460692i
$19$	6.49258			1.48950			0.744750	−	0.667343i	$-0.232569\pi$
$19$	6.49258			1.48950			0.744750	+	0.667343i	$0.232569\pi$
$20$	2.26222	−	3.38366i	0.505847	−	0.756609i
$21$	−2.58348			−0.563762
$22$		0			0
$23$			0.238335i			0.0496962i	0.999691	+	0.0248481i	$0.00791021\pi$
$23$			0.238335i			0.0496962i	−0.999691	+	0.0248481i	$0.992090\pi$
$24$	−0.351308			−0.0717104
$25$	−1.91091	−	4.62044i	−0.382182	−	0.924087i
$26$	12.7021			2.49109
$27$			1.00000i			0.192450i
$28$			4.70262i			0.888711i
$29$	−0.959152			−0.178110			−0.0890550	−	0.996027i	$-0.528385\pi$
$29$	−0.959152			−0.178110			−0.0890550	+	0.996027i	$0.528385\pi$
$30$	2.42911	−	3.63328i	0.443493	−	0.663344i
$31$	−2.26656			−0.407087			−0.203543	−	0.979066i	$-0.565246\pi$
$31$	−2.26656			−0.407087			−0.203543	+	0.979066i	$0.565246\pi$
$32$			7.75505i			1.37091i
$33$		0			0
$34$	14.4653			2.48078
$35$	4.80240	+	3.21075i	0.811754	+	0.542715i
$36$	1.82026			0.303377
$37$			9.55578i			1.57096i	0.618887	+	0.785480i	$0.287584\pi$
$37$			9.55578i			1.57096i	−0.618887	+	0.785480i	$0.712416\pi$
$38$		−	12.6901i		−	2.05860i
$39$	6.49874			1.04063
$40$	0.653040	+	0.436604i	0.103255	+	0.0690332i
$41$	−6.20447			−0.968976			−0.484488	−	0.874798i	$-0.660994\pi$
$41$	−6.20447			−0.968976			−0.484488	+	0.874798i	$0.660994\pi$
$42$			5.04954i			0.779162i
$43$			6.88029i			1.04923i	0.851338	+	0.524617i	$0.175791\pi$
$43$			6.88029i			1.04923i	−0.851338	+	0.524617i	$0.824209\pi$
$44$		0			0
$45$	1.24280	−	1.85889i	0.185265	−	0.277106i
$46$	0.465837			0.0686839
$47$			1.09789i			0.160143i	0.996789	+	0.0800717i	$0.0255149\pi$
$47$			1.09789i			0.160143i	−0.996789	+	0.0800717i	$0.974485\pi$
$48$			4.32717i			0.624573i
$49$	0.325615			0.0465164
$50$	−9.03087	+	3.73496i	−1.27716	+	0.528204i
$51$	7.40085			1.03633
$52$		−	11.8294i		−	1.64044i
$53$		−	2.71078i		−	0.372355i	−0.982516	−	0.186177i	$-0.940390\pi$
$53$		−	2.71078i		−	0.372355i	0.982516	−	0.186177i	$-0.0596099\pi$
$54$	1.95455			0.265980
$55$		0			0
$56$	−0.907597			−0.121283
$57$		−	6.49258i		−	0.859963i
$58$			1.87471i			0.246161i
$59$	1.23135			0.160308			0.0801540	−	0.996782i	$-0.474459\pi$
$59$	1.23135			0.160308			0.0801540	+	0.996782i	$0.474459\pi$
$60$	−3.38366	−	2.26222i	−0.436828	−	0.292051i
$61$	1.45908			0.186815			0.0934077	−	0.995628i	$-0.470224\pi$
$61$	1.45908			0.186815			0.0934077	+	0.995628i	$0.470224\pi$
$62$			4.43011i			0.562625i
$63$			2.58348i			0.325488i
$64$	6.50329			0.812911
$65$	−12.0804	−	8.07662i	−1.49839	−	1.00178i
$66$		0			0
$67$		−	0.387707i		−	0.0473659i	−0.999720	−	0.0236830i	$-0.992461\pi$
$67$		−	0.387707i		−	0.0473659i	0.999720	−	0.0236830i	$-0.00753922\pi$
$68$		−	13.4715i		−	1.63366i
$69$	0.238335			0.0286921
$70$	6.27556	−	9.38652i	0.750073	−	1.12190i
$71$	−1.12813			−0.133884			−0.0669421	−	0.997757i	$-0.521324\pi$
$71$	−1.12813			−0.133884			−0.0669421	+	0.997757i	$0.521324\pi$
$72$			0.351308i			0.0414020i
$73$		−	7.21153i		−	0.844046i	−0.906585	−	0.422023i	$-0.861320\pi$
$73$		−	7.21153i		−	0.844046i	0.906585	−	0.422023i	$-0.138680\pi$
$74$	18.6772			2.17119
$75$	−4.62044	+	1.91091i	−0.533522	+	0.220653i
$76$	−11.8182			−1.35564
$77$		0			0
$78$		−	12.7021i		−	1.43823i
$79$	15.9707			1.79684			0.898421	−	0.439135i	$-0.144715\pi$
$79$	15.9707			1.79684			0.898421	+	0.439135i	$0.144715\pi$
$80$	5.37780	−	8.04371i	0.601256	−	0.899315i
$81$	1.00000			0.111111
$82$			12.1269i			1.33920i
$83$			9.40902i			1.03277i	0.856355	+	0.516387i	$0.172723\pi$
$83$			9.40902i			1.03277i	−0.856355	+	0.516387i	$0.827277\pi$
$84$	4.70262			0.513097
$85$	−13.7573	−	9.19776i	−1.49219	−	0.997637i
$86$	13.4479			1.45012
$87$			0.959152i			0.102832i
$88$		0			0
$89$	−1.24004			−0.131444			−0.0657222	−	0.997838i	$-0.520935\pi$
$89$	−1.24004			−0.131444			−0.0657222	+	0.997838i	$0.520935\pi$
$90$	−3.63328	−	2.42911i	−0.382982	−	0.256051i
$91$	16.7894			1.76001
$92$		−	0.433831i		−	0.0452300i
$93$			2.26656i			0.235032i
$94$	2.14588			0.221330
$95$	−8.06896	+	12.0690i	−0.827858	+	1.23825i
$96$	7.75505			0.791497
$97$		−	16.3452i		−	1.65960i	−0.558061	−	0.829800i	$-0.688454\pi$
$97$		−	16.3452i		−	1.65960i	0.558061	−	0.829800i	$-0.311546\pi$
$98$		−	0.636430i		−	0.0642891i
$99$		0			0
$100$	3.47835	+	8.41040i	0.347835	+	0.841040i
$101$	4.57599			0.455328			0.227664	−	0.973740i	$-0.426891\pi$
$101$	4.57599			0.455328			0.227664	+	0.973740i	$0.426891\pi$
$102$		−	14.4653i		−	1.43228i
$103$		−	9.78997i		−	0.964634i	−0.875997	−	0.482317i	$-0.839795\pi$
$103$		−	9.78997i		−	0.964634i	0.875997	−	0.482317i	$-0.160205\pi$
$104$	2.28306			0.223872
$105$	3.21075	−	4.80240i	0.313337	−	0.468666i
$106$	−5.29836			−0.514622
$107$			14.0954i			1.36265i	0.731981	+	0.681325i	$0.238596\pi$
$107$			14.0954i			1.36265i	−0.731981	+	0.681325i	$0.761404\pi$
$108$		−	1.82026i		−	0.175155i
$109$	8.23270			0.788550			0.394275	−	0.918993i	$-0.370996\pi$
$109$	8.23270			0.788550			0.394275	+	0.918993i	$0.370996\pi$
$110$		0			0
$111$	9.55578			0.906995
$112$			11.1792i			1.05633i
$113$			2.23389i			0.210146i	0.994464	+	0.105073i	$0.0335077\pi$
$113$			2.23389i			0.210146i	−0.994464	+	0.105073i	$0.966492\pi$
$114$	−12.6901			−1.18853
$115$	−0.443037	−	0.296202i	−0.0413134	−	0.0276210i
$116$	1.74591			0.162103
$117$		−	6.49874i		−	0.600809i
$118$		−	2.40673i		−	0.221558i
$119$	19.1200			1.75273
$120$	0.436604	−	0.653040i	0.0398563	−	0.0596142i
$121$		0			0
$122$		−	2.85183i		−	0.258193i
$123$			6.20447i			0.559438i
$124$	4.12574			0.370502
$125$	10.9637	+	2.19011i	0.980626	+	0.195889i
$126$	5.04954			0.449849
$127$			2.57117i			0.228154i	0.993472	+	0.114077i	$0.0363911\pi$
$127$			2.57117i			0.228154i	−0.993472	+	0.114077i	$0.963609\pi$
$128$			2.79911i			0.247409i
$129$	6.88029			0.605776
$130$	−15.7861	+	23.6118i	−1.38454	+	2.07089i
$131$	−10.8571			−0.948590			−0.474295	−	0.880366i	$-0.657297\pi$
$131$	−10.8571			−0.948590			−0.474295	+	0.880366i	$0.657297\pi$
$132$		0			0
$133$		−	16.7735i		−	1.45444i
$134$	−0.757792			−0.0654632
$135$	−1.85889	−	1.24280i	−0.159987	−	0.106963i
$136$	2.59998			0.222946
$137$			4.24754i			0.362892i	0.983401	+	0.181446i	$0.0580777\pi$
$137$			4.24754i			0.362892i	−0.983401	+	0.181446i	$0.941922\pi$
$138$		−	0.465837i		−	0.0396547i
$139$	3.96976			0.336711			0.168355	−	0.985726i	$-0.446154\pi$
$139$	3.96976			0.336711			0.168355	+	0.985726i	$0.446154\pi$
$140$	−8.74162	−	5.84440i	−0.738802	−	0.493942i
$141$	1.09789			0.0924589
$142$			2.20498i			0.185038i
$143$		0			0
$144$	4.32717			0.360598
$145$	1.19203	−	1.78295i	0.0989928	−	0.148066i
$146$	−14.0953			−1.16654
$147$		−	0.325615i		−	0.0268562i
$148$		−	17.3940i		−	1.42978i
$149$	−19.5740			−1.60356			−0.801781	−	0.597617i	$-0.796114\pi$
$149$	−19.5740			−1.60356			−0.801781	+	0.597617i	$0.796114\pi$
$150$	3.73496	+	9.03087i	0.304959	+	0.737367i
$151$	14.2646			1.16084			0.580419	−	0.814318i	$-0.302889\pi$
$151$	14.2646			1.16084			0.580419	+	0.814318i	$0.302889\pi$
$152$		−	2.28089i		−	0.185005i
$153$		−	7.40085i		−	0.598323i
$154$		0			0
$155$	2.81688	−	4.21328i	0.226257	−	0.338419i
$156$	−11.8294			−0.947111
$157$			15.1043i			1.20545i	0.797948	+	0.602727i	$0.205919\pi$
$157$			15.1043i			1.20545i	−0.797948	+	0.602727i	$0.794081\pi$
$158$		−	31.2155i		−	2.48337i
$159$	−2.71078			−0.214979
$160$	−14.4158	−	9.63796i	−1.13967	−	0.761948i
$161$	0.615734			0.0485266
$162$		−	1.95455i		−	0.153564i
$163$			2.40168i			0.188114i	0.995567	+	0.0940570i	$0.0299836\pi$
$163$			2.40168i			0.188114i	−0.995567	+	0.0940570i	$0.970016\pi$
$164$	11.2938			0.881895
$165$		0			0
$166$	18.3904			1.42737
$167$		−	11.5799i		−	0.896077i	−0.894014	−	0.448038i	$-0.852123\pi$
$167$		−	11.5799i		−	0.896077i	0.894014	−	0.448038i	$-0.147877\pi$
$168$			0.907597i			0.0700226i
$169$	−29.2336			−2.24874
$170$	−17.9775	+	26.8894i	−1.37881	+	2.06232i
$171$	−6.49258			−0.496500
$172$		−	12.5239i		−	0.954940i
$173$			6.28112i			0.477545i	0.971076	+	0.238772i	$0.0767450\pi$
$173$			6.28112i			0.477545i	−0.971076	+	0.238772i	$0.923255\pi$
$174$	1.87471			0.142121
$175$	−11.9368	+	4.93680i	−0.902339	+	0.373187i
$176$		0			0
$177$		−	1.23135i		−	0.0925538i
$178$			2.42373i			0.181666i
$179$	−15.5580			−1.16286			−0.581431	−	0.813596i	$-0.697507\pi$
$179$	−15.5580			−1.16286			−0.581431	+	0.813596i	$0.697507\pi$
$180$	−2.26222	+	3.38366i	−0.168616	+	0.252203i
$181$	3.21516			0.238981			0.119490	−	0.992835i	$-0.461874\pi$
$181$	3.21516			0.238981			0.119490	+	0.992835i	$0.461874\pi$
$182$		−	32.8157i		−	2.43246i
$183$		−	1.45908i		−	0.107858i
$184$	0.0837288			0.00617257
$185$	−17.7631	−	11.8759i	−1.30597	−	0.873133i
$186$	4.43011			0.324832
$187$		0			0
$188$		−	1.99844i		−	0.145751i
$189$	2.58348			0.187921
$190$	23.5894	+	15.7712i	1.71135	+	1.14416i
$191$	−23.4223			−1.69478			−0.847390	−	0.530972i	$-0.821827\pi$
$191$	−23.4223			−1.69478			−0.847390	+	0.530972i	$0.821827\pi$
$192$		−	6.50329i		−	0.469334i
$193$			6.58238i			0.473810i	0.971533	+	0.236905i	$0.0761330\pi$
$193$			6.58238i			0.473810i	−0.971533	+	0.236905i	$0.923867\pi$
$194$	−31.9474			−2.29369
$195$	−8.07662	+	12.0804i	−0.578379	+	0.865096i
$196$	−0.592704			−0.0423360
$197$			21.0103i			1.49693i	0.663177	+	0.748463i	$0.269208\pi$
$197$			21.0103i			1.49693i	−0.663177	+	0.748463i	$0.730792\pi$
$198$		0			0
$199$	−13.5152			−0.958069			−0.479035	−	0.877796i	$-0.659013\pi$
$199$	−13.5152			−0.958069			−0.479035	+	0.877796i	$0.659013\pi$
$200$	−1.62319	+	0.671317i	−0.114777	+	0.0474693i
$201$	−0.387707			−0.0273467
$202$		−	8.94399i		−	0.629297i
$203$			2.47795i			0.173918i
$204$	−13.4715			−0.943193
$205$	7.71090	−	11.5334i	0.538553	−	0.805528i
$206$	−19.1350			−1.33320
$207$		−	0.238335i		−	0.0165654i
$208$		−	28.1212i		−	1.94985i
$209$		0			0
$210$	−9.38652	−	6.27556i	−0.647732	−	0.433055i
$211$	2.38466			0.164167			0.0820836	−	0.996625i	$-0.473843\pi$
$211$	2.38466			0.164167			0.0820836	+	0.996625i	$0.473843\pi$
$212$			4.93434i			0.338892i
$213$			1.12813i			0.0772981i
$214$	27.5501			1.88329
$215$	−12.7897	−	8.55080i	−0.872248	−	0.583160i
$216$	0.351308			0.0239035
$217$			5.85563i			0.397506i
$218$		−	16.0912i		−	1.08983i
$219$	−7.21153			−0.487310
$220$		0			0
$221$	−48.0962			−3.23530
$222$		−	18.6772i		−	1.25353i
$223$			23.8264i			1.59553i	0.602968	+	0.797766i	$0.293985\pi$
$223$			23.8264i			1.59553i	−0.602968	+	0.797766i	$0.706015\pi$
$224$	20.0350			1.33865
$225$	1.91091	+	4.62044i	0.127394	+	0.308029i
$226$	4.36624			0.290438
$227$			21.9425i			1.45637i	0.685380	+	0.728186i	$0.259636\pi$
$227$			21.9425i			1.45637i	−0.685380	+	0.728186i	$0.740364\pi$
$228$			11.8182i			0.782679i
$229$	6.37865			0.421513			0.210757	−	0.977539i	$-0.432407\pi$
$229$	6.37865			0.421513			0.210757	+	0.977539i	$0.432407\pi$
$230$	−0.578941	+	0.865937i	−0.0381742	+	0.0570982i
$231$		0			0
$232$			0.336957i			0.0221223i
$233$			0.429662i			0.0281481i	0.999901	+	0.0140740i	$0.00448006\pi$
$233$			0.429662i			0.0281481i	−0.999901	+	0.0140740i	$0.995520\pi$
$234$	−12.7021			−0.830363
$235$	−2.04085	−	1.36445i	−0.133130	−	0.0890071i
$236$	−2.24138			−0.145901
$237$		−	15.9707i		−	1.03741i
$238$		−	37.3709i		−	2.42240i
$239$	26.9242			1.74158			0.870791	−	0.491654i	$-0.163607\pi$
$239$	26.9242			1.74158			0.870791	+	0.491654i	$0.163607\pi$
$240$	−8.04371	−	5.37780i	−0.519220	−	0.347135i
$241$	3.47499			0.223844			0.111922	−	0.993717i	$-0.464299\pi$
$241$	3.47499			0.223844			0.111922	+	0.993717i	$0.464299\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−2.65590			−0.170026
$245$	−0.404673	+	0.605280i	−0.0258536	+	0.0386699i
$246$	12.1269			0.773186
$247$			42.1936i			2.68471i
$248$			0.796261i			0.0505626i
$249$	9.40902			0.596272
$250$	4.28067	−	21.4292i	0.270733	−	1.35530i
$251$	−17.1024			−1.07949			−0.539746	−	0.841828i	$-0.681480\pi$
$251$	−17.1024			−1.07949			−0.539746	+	0.841828i	$0.681480\pi$
$252$		−	4.70262i		−	0.296237i
$253$		0			0
$254$	5.02547			0.315326
$255$	−9.19776	+	13.7573i	−0.575986	+	0.861518i
$256$	18.4776			1.15485
$257$			4.13235i			0.257769i	0.991660	+	0.128885i	$0.0411397\pi$
$257$			4.13235i			0.257769i	−0.991660	+	0.128885i	$0.958860\pi$
$258$		−	13.4479i		−	0.837227i
$259$	24.6872			1.53399
$260$	21.9895	+	14.7016i	1.36373	+	0.911752i
$261$	0.959152			0.0593700
$262$			21.2208i			1.31102i
$263$		−	19.4921i		−	1.20193i	−0.799274	−	0.600966i	$-0.794783\pi$
$263$		−	19.4921i		−	1.20193i	0.799274	−	0.600966i	$-0.205217\pi$
$264$		0			0
$265$	5.03904	+	3.36896i	0.309546	+	0.206953i
$266$	−32.7846			−2.01015
$267$			1.24004i			0.0758895i
$268$			0.705728i			0.0431092i
$269$	16.3889			0.999249			0.499625	−	0.866242i	$-0.333471\pi$
$269$	16.3889			0.999249			0.499625	+	0.866242i	$0.333471\pi$
$270$	−2.42911	+	3.63328i	−0.147831	+	0.221115i
$271$	16.0828			0.976962			0.488481	−	0.872575i	$-0.337551\pi$
$271$	16.0828			0.976962			0.488481	+	0.872575i	$0.337551\pi$
$272$		−	32.0248i		−	1.94179i
$273$		−	16.7894i		−	1.01614i
$274$	8.30203			0.501544
$275$		0			0
$276$	−0.433831			−0.0261136
$277$			17.9734i			1.07992i	0.841692	+	0.539958i	$0.181560\pi$
$277$			17.9734i			1.07992i	−0.841692	+	0.539958i	$0.818440\pi$
$278$		−	7.75909i		−	0.465359i
$279$	2.26656			0.135696
$280$	1.12796	−	1.68712i	0.0674085	−	0.100825i
$281$	−12.1589			−0.725339			−0.362669	−	0.931918i	$-0.618135\pi$
$281$	−12.1589			−0.725339			−0.362669	+	0.931918i	$0.618135\pi$
$282$		−	2.14588i		−	0.127785i
$283$			6.05689i			0.360045i	0.983663	+	0.180022i	$0.0576170\pi$
$283$			6.05689i			0.360045i	−0.983663	+	0.180022i	$0.942383\pi$
$284$	2.05349			0.121852
$285$	12.0690	+	8.06896i	0.714904	+	0.477964i
$286$		0			0
$287$			16.0292i			0.946171i
$288$		−	7.75505i		−	0.456971i
$289$	−37.7726			−2.22192
$290$	−3.48487	−	2.32988i	−0.204639	−	0.136815i
$291$	−16.3452			−0.958171
$292$			13.1269i			0.768193i
$293$		−	21.9771i		−	1.28391i	−0.766741	−	0.641957i	$-0.778123\pi$
$293$		−	21.9771i		−	1.28391i	0.766741	−	0.641957i	$-0.221877\pi$
$294$	−0.636430			−0.0371173
$295$	−1.53032	+	2.28894i	−0.0890985	+	0.133267i
$296$	3.35702			0.195123
$297$		0			0
$298$			38.2583i			2.21624i
$299$	−1.54887			−0.0895737
$300$	8.41040	−	3.47835i	0.485575	−	0.200823i
$301$	17.7751			1.02454
$302$		−	27.8809i		−	1.60437i
$303$		−	4.57599i		−	0.262884i
$304$	−28.0945			−1.61133
$305$	−1.81333	+	2.71225i	−0.103831	+	0.155303i
$306$	−14.4653			−0.826928
$307$		−	21.6041i		−	1.23301i	−0.787350	−	0.616507i	$-0.788547\pi$
$307$		−	21.6041i		−	1.23301i	0.787350	−	0.616507i	$-0.211453\pi$
$308$		0			0
$309$	−9.78997			−0.556932
$310$	−8.23507	−	5.50573i	−0.467720	−	0.312705i
$311$	26.2869			1.49060			0.745298	−	0.666732i	$-0.232307\pi$
$311$	26.2869			1.49060			0.745298	+	0.666732i	$0.232307\pi$
$312$		−	2.28306i		−	0.129253i
$313$		−	9.58638i		−	0.541854i	−0.962600	−	0.270927i	$-0.912670\pi$
$313$		−	9.58638i		−	0.541854i	0.962600	−	0.270927i	$-0.0873302\pi$
$314$	29.5221			1.66603
$315$	−4.80240	−	3.21075i	−0.270585	−	0.180905i
$316$	−29.0708			−1.63536
$317$			32.6557i			1.83413i	0.398742	+	0.917063i	$0.369447\pi$
$317$			32.6557i			1.83413i	−0.398742	+	0.917063i	$0.630553\pi$
$318$			5.29836i			0.297117i
$319$		0			0
$320$	−8.08227	+	12.0889i	−0.451813	+	0.675788i
$321$	14.0954			0.786727
$322$		−	1.20348i		−	0.0670674i
$323$			48.0506i			2.67361i
$324$	−1.82026			−0.101126
$325$	30.0270	−	12.4185i	1.66560	−	0.688854i
$326$	4.69420			0.259988
$327$		−	8.23270i		−	0.455269i
$328$			2.17968i			0.120353i
$329$	2.83638			0.156374
$330$		0			0
$331$	−2.40874			−0.132396			−0.0661982	−	0.997806i	$-0.521087\pi$
$331$	−2.40874			−0.132396			−0.0661982	+	0.997806i	$0.521087\pi$
$332$		−	17.1269i		−	0.939960i
$333$		−	9.55578i		−	0.523654i
$334$	−22.6334			−1.23844
$335$	0.720702	+	0.481841i	0.0393762	+	0.0263258i
$336$	11.1792			0.609874
$337$			26.1424i			1.42407i	0.702145	+	0.712034i	$0.252226\pi$
$337$			26.1424i			1.42407i	−0.702145	+	0.712034i	$0.747774\pi$
$338$			57.1385i			3.10793i
$339$	2.23389			0.121328
$340$	25.0419	+	16.7423i	1.35809	+	0.907980i
$341$		0			0
$342$			12.6901i			0.686200i
$343$		−	18.9256i		−	1.02189i
$344$	2.41710			0.130321
$345$	−0.296202	+	0.443037i	−0.0159470	+	0.0238523i
$346$	12.2768			0.660003
$347$			9.09766i			0.488388i	0.969726	+	0.244194i	$0.0785234\pi$
$347$			9.09766i			0.488388i	−0.969726	+	0.244194i	$0.921477\pi$
$348$		−	1.74591i		−	0.0935904i
$349$	−7.46214			−0.399439			−0.199720	−	0.979853i	$-0.564003\pi$
$349$	−7.46214			−0.399439			−0.199720	+	0.979853i	$0.564003\pi$
$350$	9.64922	+	23.3311i	0.515772	+	1.24710i
$351$	−6.49874			−0.346877
$352$		0			0
$353$		−	3.97421i		−	0.211526i	−0.994391	−	0.105763i	$-0.966272\pi$
$353$		−	3.97421i		−	0.211526i	0.994391	−	0.105763i	$-0.0337285\pi$
$354$	−2.40673			−0.127916
$355$	1.40204	−	2.09706i	0.0744123	−	0.111300i
$356$	2.25721			0.119632
$357$		−	19.1200i		−	1.01194i
$358$			30.4089i			1.60716i
$359$	−3.80057			−0.200587			−0.100293	−	0.994958i	$-0.531978\pi$
$359$	−3.80057			−0.200587			−0.100293	+	0.994958i	$0.531978\pi$
$360$	−0.653040	−	0.436604i	−0.0344183	−	0.0230111i
$361$	23.1536			1.21861
$362$		−	6.28418i		−	0.330289i
$363$		0			0
$364$	−30.5611			−1.60184
$365$	13.4054	+	8.96248i	0.701672	+	0.469117i
$366$	−2.85183			−0.149068
$367$			16.8227i			0.878136i	0.898454	+	0.439068i	$0.144691\pi$
$367$			16.8227i			0.878136i	−0.898454	+	0.439068i	$0.855309\pi$
$368$		−	1.03131i		−	0.0537610i
$369$	6.20447			0.322992
$370$	−23.2120	+	34.7188i	−1.20674	+	1.80495i
$371$	−7.00327			−0.363591
$372$		−	4.12574i		−	0.213910i
$373$			17.2215i			0.891695i	0.895109	+	0.445847i	$0.147098\pi$
$373$			17.2215i			0.891695i	−0.895109	+	0.445847i	$0.852902\pi$
$374$		0			0
$375$	2.19011	−	10.9637i	0.113097	−	0.566165i
$376$	0.385696			0.0198908
$377$		−	6.23328i		−	0.321030i
$378$		−	5.04954i		−	0.259721i
$379$	−11.8166			−0.606979			−0.303489	−	0.952835i	$-0.598152\pi$
$379$	−11.8166			−0.606979			−0.303489	+	0.952835i	$0.598152\pi$
$380$	14.6876	−	21.9687i	0.753459	−	1.12697i
$381$	2.57117			0.131725
$382$			45.7801i			2.34231i
$383$		−	23.6487i		−	1.20839i	−0.796836	−	0.604196i	$-0.793494\pi$
$383$		−	23.6487i		−	1.20839i	0.796836	−	0.604196i	$-0.206506\pi$
$384$	2.79911			0.142842
$385$		0			0
$386$	12.8656			0.654841
$387$		−	6.88029i		−	0.349745i
$388$			29.7525i			1.51045i
$389$	−15.6832			−0.795172			−0.397586	−	0.917565i	$-0.630152\pi$
$389$	−15.6832			−0.795172			−0.397586	+	0.917565i	$0.630152\pi$
$390$	23.6118	+	15.7861i	1.19563	+	0.799363i
$391$	−1.76388			−0.0892032
$392$		−	0.114391i		−	0.00577761i
$393$			10.8571i			0.547669i
$394$	41.0657			2.06886
$395$	−19.8483	+	29.6877i	−0.998677	+	1.49375i
$396$		0			0
$397$		−	31.3624i		−	1.57403i	−0.616931	−	0.787017i	$-0.711624\pi$
$397$		−	31.3624i		−	1.57403i	0.616931	−	0.787017i	$-0.288376\pi$
$398$			26.4162i			1.32412i
$399$	−16.7735			−0.839724
$400$	8.26883	+	19.9934i	0.413441	+	0.999671i
$401$	−0.688812			−0.0343976			−0.0171988	−	0.999852i	$-0.505475\pi$
$401$	−0.688812			−0.0343976			−0.0171988	+	0.999852i	$0.505475\pi$
$402$			0.757792i			0.0377952i
$403$		−	14.7298i		−	0.733744i
$404$	−8.32949			−0.414408
$405$	−1.24280	+	1.85889i	−0.0617551	+	0.0923688i
$406$	4.84328			0.240368
$407$		0			0
$408$		−	2.59998i		−	0.128718i
$409$	−0.658627			−0.0325670			−0.0162835	−	0.999867i	$-0.505183\pi$
$409$	−0.658627			−0.0325670			−0.0162835	+	0.999867i	$0.505183\pi$
$410$	−22.5426	−	15.0713i	−1.11330	−	0.744320i
$411$	4.24754			0.209516
$412$			17.8203i			0.877943i
$413$		−	3.18117i		−	0.156535i
$414$	−0.465837			−0.0228946
$415$	−17.4903	−	11.6935i	−0.858565	−	0.574012i
$416$	−50.3981			−2.47097
$417$		−	3.96976i		−	0.194400i
$418$		0			0
$419$	17.1841			0.839500			0.419750	−	0.907640i	$-0.362118\pi$
$419$	17.1841			0.839500			0.419750	+	0.907640i	$0.362118\pi$
$420$	−5.84440	+	8.74162i	−0.285177	+	0.426547i
$421$	−10.1935			−0.496803			−0.248401	−	0.968657i	$-0.579905\pi$
$421$	−10.1935			−0.496803			−0.248401	+	0.968657i	$0.579905\pi$
$422$		−	4.66094i		−	0.226891i
$423$		−	1.09789i		−	0.0533812i
$424$	−0.952319			−0.0462487
$425$	34.1952	−	14.1424i	1.65871	−	0.686005i
$426$	2.20498			0.106832
$427$		−	3.76950i		−	0.182419i
$428$		−	25.6573i		−	1.24019i
$429$		0			0
$430$	−16.7130	+	24.9980i	−0.805971	+	1.20551i
$431$	−6.36943			−0.306805			−0.153402	−	0.988164i	$-0.549023\pi$
$431$	−6.36943			−0.306805			−0.153402	+	0.988164i	$0.549023\pi$
$432$		−	4.32717i		−	0.208191i
$433$		−	20.5086i		−	0.985578i	−0.870149	−	0.492789i	$-0.835977\pi$
$433$		−	20.5086i		−	0.985578i	0.870149	−	0.492789i	$-0.164023\pi$
$434$	11.4451			0.549383
$435$	−1.78295	−	1.19203i	−0.0854861	−	0.0571535i
$436$	−14.9857			−0.717684
$437$			1.54741i			0.0740225i
$438$			14.0953i			0.673499i
$439$	−12.9144			−0.616369			−0.308185	−	0.951327i	$-0.599721\pi$
$439$	−12.9144			−0.616369			−0.308185	+	0.951327i	$0.599721\pi$
$440$		0			0
$441$	−0.325615			−0.0155055
$442$			94.0064i			4.47143i
$443$		−	21.8544i		−	1.03833i	−0.854673	−	0.519166i	$-0.826243\pi$
$443$		−	21.8544i		−	1.03833i	0.854673	−	0.519166i	$-0.173757\pi$
$444$	−17.3940			−0.825484
$445$	1.54112	−	2.30510i	0.0730563	−	0.109272i
$446$	46.5698			2.20514
$447$			19.5740i			0.925817i
$448$		−	16.8011i		−	0.793779i
$449$	−8.88057			−0.419100			−0.209550	−	0.977798i	$-0.567200\pi$
$449$	−8.88057			−0.419100			−0.209550	+	0.977798i	$0.567200\pi$
$450$	9.03087	−	3.73496i	0.425719	−	0.176068i
$451$		0			0
$452$		−	4.06626i		−	0.191261i
$453$		−	14.2646i		−	0.670211i
$454$	42.8876			2.01281
$455$	−20.8658	+	31.2095i	−0.978204	+	1.46313i
$456$	−2.28089			−0.106813
$457$			26.4643i			1.23795i	0.785412	+	0.618974i	$0.212451\pi$
$457$			26.4643i			1.23795i	−0.785412	+	0.618974i	$0.787549\pi$
$458$		−	12.4674i		−	0.582563i
$459$	−7.40085			−0.345442
$460$	0.806443	+	0.539165i	0.0376006	+	0.0251387i
$461$	32.2143			1.50037			0.750185	−	0.661228i	$-0.229964\pi$
$461$	32.2143			1.50037			0.750185	+	0.661228i	$0.229964\pi$
$462$		0			0
$463$			22.7730i			1.05835i	0.848512	+	0.529177i	$0.177499\pi$
$463$			22.7730i			1.05835i	−0.848512	+	0.529177i	$0.822501\pi$
$464$	4.15041			0.192678
$465$	−4.21328	−	2.81688i	−0.195386	−	0.130630i
$466$	0.839795			0.0389028
$467$		−	15.2557i		−	0.705947i	−0.935633	−	0.352974i	$-0.885171\pi$
$467$		−	15.2557i		−	0.705947i	0.935633	−	0.352974i	$-0.114829\pi$
$468$			11.8294i			0.546815i
$469$	−1.00163			−0.0462511
$470$	−2.66689	+	3.98894i	−0.123014	+	0.183996i
$471$	15.1043			0.695969
$472$		−	0.432582i		−	0.0199112i
$473$		0			0
$474$	−31.2155			−1.43377
$475$	−12.4067	−	29.9986i	−0.569260	−	1.37643i
$476$	−34.8034			−1.59521
$477$			2.71078i			0.124118i
$478$		−	52.6247i		−	2.40700i
$479$	18.8354			0.860609			0.430305	−	0.902684i	$-0.358406\pi$
$479$	18.8354			0.860609			0.430305	+	0.902684i	$0.358406\pi$
$480$	−9.63796	+	14.4158i	−0.439911	+	0.657986i
$481$	−62.1005			−2.83154
$482$		−	6.79203i		−	0.309369i
$483$		−	0.615734i		−	0.0280168i
$484$		0			0
$485$	30.3838	+	20.3137i	1.37966	+	0.922399i
$486$	−1.95455			−0.0886601
$487$		−	7.90508i		−	0.358213i	−0.983830	−	0.179107i	$-0.942679\pi$
$487$		−	7.90508i		−	0.358213i	0.983830	−	0.179107i	$-0.0573207\pi$
$488$		−	0.512584i		−	0.0232036i
$489$	2.40168			0.108608
$490$	1.18305	+	0.790953i	0.0534448	+	0.0357316i
$491$	12.3513			0.557407			0.278704	−	0.960377i	$-0.410095\pi$
$491$	12.3513			0.557407			0.278704	+	0.960377i	$0.410095\pi$
$492$		−	11.2938i		−	0.509162i
$493$		−	7.09854i		−	0.319702i
$494$	82.4694			3.71048
$495$		0			0
$496$	9.80781			0.440384
$497$			2.91450i			0.130733i
$498$		−	18.3904i		−	0.824093i
$499$	24.7017			1.10580			0.552901	−	0.833247i	$-0.313521\pi$
$499$	24.7017			1.10580			0.552901	+	0.833247i	$0.313521\pi$
$500$	−19.9569	−	3.98656i	−0.892498	−	0.178285i
$501$	−11.5799			−0.517350
$502$			33.4274i			1.49194i
$503$		−	16.8245i		−	0.750168i	−0.926991	−	0.375084i	$-0.877614\pi$
$503$		−	16.8245i		−	0.750168i	0.926991	−	0.375084i	$-0.122386\pi$
$504$	0.907597			0.0404276
$505$	−5.68703	+	8.50624i	−0.253069	+	0.378523i
$506$		0			0
$507$			29.2336i			1.29831i
$508$		−	4.68019i		−	0.207650i
$509$	16.4157			0.727613			0.363807	−	0.931474i	$-0.381477\pi$
$509$	16.4157			0.727613			0.363807	+	0.931474i	$0.381477\pi$
$510$	26.8894	+	17.9775i	1.19068	+	0.796056i
$511$	−18.6309			−0.824182
$512$		−	30.5171i		−	1.34868i
$513$			6.49258i			0.286654i
$514$	8.07689			0.356256
$515$	18.1984	+	12.1669i	0.801918	+	0.536140i
$516$	−12.5239			−0.551335
$517$		0			0
$518$		−	48.2523i		−	2.12009i
$519$	6.28112			0.275711
$520$	−2.83738	+	4.24394i	−0.124427	+	0.186109i
$521$	−28.7296			−1.25867			−0.629333	−	0.777136i	$-0.716672\pi$
$521$	−28.7296			−1.25867			−0.629333	+	0.777136i	$0.716672\pi$
$522$		−	1.87471i		−	0.0820538i
$523$			1.82441i			0.0797758i	0.999204	+	0.0398879i	$0.0127001\pi$
$523$			1.82441i			0.0797758i	−0.999204	+	0.0398879i	$0.987300\pi$
$524$	19.7628			0.863341
$525$	4.93680	+	11.9368i	0.215460	+	0.520965i
$526$	−38.0982			−1.66116
$527$		−	16.7745i		−	0.730709i
$528$		0			0
$529$	22.9432			0.997530
$530$	6.58479	−	9.84904i	0.286025	−	0.427815i
$531$	−1.23135			−0.0534360
$532$			30.5321i			1.32373i
$533$		−	40.3213i		−	1.74651i
$534$	2.42373			0.104885
$535$	−26.2017	−	17.5177i	−1.13280	−	0.757356i
$536$	−0.136204			−0.00588313
$537$			15.5580i			0.671379i
$538$		−	32.0329i		−	1.38104i
$539$		0			0
$540$	3.38366	+	2.26222i	0.145609	+	0.0973503i
$541$	18.6713			0.802741			0.401371	−	0.915916i	$-0.368534\pi$
$541$	18.6713			0.802741			0.401371	+	0.915916i	$0.368534\pi$
$542$		−	31.4347i		−	1.35023i
$543$		−	3.21516i		−	0.137976i
$544$	−57.3940			−2.46075
$545$	−10.2316	+	15.3036i	−0.438273	+	0.655536i
$546$	−32.8157			−1.40438
$547$		−	40.3544i		−	1.72543i	−0.505689	−	0.862716i	$-0.668762\pi$
$547$		−	40.3544i		−	1.72543i	0.505689	−	0.862716i	$-0.331238\pi$
$548$		−	7.73163i		−	0.330279i
$549$	−1.45908			−0.0622718
$550$		0			0
$551$	−6.22737			−0.265295
$552$		−	0.0837288i		−	0.00356373i
$553$		−	41.2600i		−	1.75455i
$554$	35.1298			1.49252
$555$	−11.8759	+	17.7631i	−0.504104	+	0.754002i
$556$	−7.22600			−0.306451
$557$		−	18.8650i		−	0.799336i	−0.916660	−	0.399668i	$-0.869125\pi$
$557$		−	18.8650i		−	0.799336i	0.916660	−	0.399668i	$-0.130875\pi$
$558$		−	4.43011i		−	0.187542i
$559$	−44.7132			−1.89117
$560$	−20.7808	−	13.8934i	−0.878149	−	0.587105i
$561$		0			0
$562$			23.7651i			1.00247i
$563$			17.7695i			0.748894i	0.927248	+	0.374447i	$0.122167\pi$
$563$			17.7695i			0.748894i	−0.927248	+	0.374447i	$0.877833\pi$
$564$	−1.99844			−0.0841497
$565$	−4.15254	−	2.77627i	−0.174699	−	0.116798i
$566$	11.8385			0.497608
$567$		−	2.58348i		−	0.108496i
$568$			0.396320i			0.0166292i
$569$	−9.61085			−0.402908			−0.201454	−	0.979498i	$-0.564567\pi$
$569$	−9.61085			−0.402908			−0.201454	+	0.979498i	$0.564567\pi$
$570$	15.7712	−	23.5894i	0.660582	−	0.988050i
$571$	25.7889			1.07923			0.539615	−	0.841912i	$-0.318570\pi$
$571$	25.7889			1.07923			0.539615	+	0.841912i	$0.318570\pi$
$572$		0			0
$573$			23.4223i			0.978481i
$574$	31.3298			1.30768
$575$	1.10121	−	0.455436i	0.0459236	−	0.0189930i
$576$	−6.50329			−0.270970
$577$			12.4401i			0.517888i	0.965892	+	0.258944i	$0.0833745\pi$
$577$			12.4401i			0.517888i	−0.965892	+	0.258944i	$0.916626\pi$
$578$			73.8284i			3.07086i
$579$	6.58238			0.273554
$580$	−2.16981	+	3.24544i	−0.0900964	+	0.134760i
$581$	24.3080			1.00847
$582$			31.9474i			1.32426i
$583$		0			0
$584$	−2.53347			−0.104836
$585$	12.0804	+	8.07662i	0.499464	+	0.333927i
$586$	−42.9553			−1.77447
$587$		−	24.3064i		−	1.00323i	−0.865090	−	0.501616i	$-0.832739\pi$
$587$		−	24.3064i		−	1.00323i	0.865090	−	0.501616i	$-0.167261\pi$
$588$			0.592704i			0.0244427i
$589$	−14.7159			−0.606356
$590$	4.47384	+	2.99108i	0.184185	+	0.123141i
$591$	21.0103			0.864250
$592$		−	41.3495i		−	1.69945i
$593$			0.0251833i			0.00103415i	1.00000		0.000517077i	$0.000164591\pi$
$593$			0.0251833i			0.00103415i	−1.00000		0.000517077i	$0.999835\pi$
$594$		0			0
$595$	−23.7623	+	35.5418i	−0.974158	+	1.45707i
$596$	35.6298			1.45945
$597$			13.5152i			0.553141i
$598$			3.02735i			0.123798i
$599$	0.751819			0.0307185			0.0153593	−	0.999882i	$-0.495111\pi$
$599$	0.751819			0.0307185			0.0153593	+	0.999882i	$0.495111\pi$
$600$	0.671317	+	1.62319i	0.0274064	+	0.0662666i
$601$	−9.36785			−0.382122			−0.191061	−	0.981578i	$-0.561193\pi$
$601$	−9.36785			−0.382122			−0.191061	+	0.981578i	$0.561193\pi$
$602$		−	34.7423i		−	1.41599i
$603$			0.387707i			0.0157886i
$604$	−25.9653			−1.05652
$605$		0			0
$606$	−8.94399			−0.363325
$607$			6.36218i			0.258233i	0.991629	+	0.129117i	$0.0412141\pi$
$607$			6.36218i			0.258233i	−0.991629	+	0.129117i	$0.958786\pi$
$608$			50.3503i			2.04197i
$609$	2.47795			0.100412
$610$	5.30123	+	3.54425i	0.214641	+	0.143503i
$611$	−7.13489			−0.288647
$612$			13.4715i			0.544553i
$613$			25.4560i			1.02816i	0.857743	+	0.514079i	$0.171866\pi$
$613$			25.4560i			1.02816i	−0.857743	+	0.514079i	$0.828134\pi$
$614$	−42.2264			−1.70412
$615$	−11.5334	−	7.71090i	−0.465072	−	0.310934i
$616$		0			0
$617$			36.7432i			1.47923i	0.673033	+	0.739613i	$0.264991\pi$
$617$			36.7432i			1.47923i	−0.673033	+	0.739613i	$0.735009\pi$
$618$			19.1350i			0.769721i
$619$	−28.8705			−1.16040			−0.580201	−	0.814473i	$-0.697026\pi$
$619$	−28.8705			−1.16040			−0.580201	+	0.814473i	$0.697026\pi$
$620$	−5.12746	+	7.66928i	−0.205924	+	0.308006i
$621$	−0.238335			−0.00956404
$622$		−	51.3791i		−	2.06011i
$623$			3.20363i			0.128351i
$624$	−28.1212			−1.12575
$625$	−17.6969	+	17.6585i	−0.707874	+	0.706339i
$626$	−18.7370			−0.748883
$627$		0			0
$628$		−	27.4938i		−	1.09712i
$629$	−70.7209			−2.81983
$630$	−6.27556	+	9.38652i	−0.250024	+	0.373968i
$631$	−15.7443			−0.626771			−0.313385	−	0.949626i	$-0.601463\pi$
$631$	−15.7443			−0.626771			−0.313385	+	0.949626i	$0.601463\pi$
$632$		−	5.61062i		−	0.223179i
$633$		−	2.38466i		−	0.0947819i
$634$	63.8272			2.53490
$635$	−4.77950	−	3.19544i	−0.189669	−	0.126807i
$636$	4.93434			0.195659
$637$			2.11609i			0.0838424i
$638$		0			0
$639$	1.12813			0.0446281
$640$	−5.20323	−	3.47873i	−0.205676	−	0.137509i
$641$	−2.28951			−0.0904303			−0.0452151	−	0.998977i	$-0.514397\pi$
$641$	−2.28951			−0.0904303			−0.0452151	+	0.998977i	$0.514397\pi$
$642$		−	27.5501i		−	1.08732i
$643$		−	3.38323i		−	0.133422i	−0.997772	−	0.0667109i	$-0.978749\pi$
$643$		−	3.38323i		−	0.133422i	0.997772	−	0.0667109i	$-0.0212505\pi$
$644$	−1.12080			−0.0441656
$645$	−8.55080	+	12.7897i	−0.336688	+	0.503593i
$646$	93.9173			3.69513
$647$			48.8823i			1.92176i	0.276962	+	0.960881i	$0.410672\pi$
$647$			48.8823i			1.92176i	−0.276962	+	0.960881i	$0.589328\pi$
$648$		−	0.351308i		−	0.0138007i
$649$		0			0
$650$	−24.2726	−	58.6893i	−0.952048	−	2.30198i
$651$	5.85563			0.229500
$652$		−	4.37168i		−	0.171208i
$653$			8.51472i			0.333207i	0.986024	+	0.166603i	$0.0532799\pi$
$653$			8.51472i			0.333207i	−0.986024	+	0.166603i	$0.946720\pi$
$654$	−16.0912			−0.629216
$655$	13.4932	−	20.1821i	0.527223	−	0.788581i
$656$	26.8478			1.04823
$657$			7.21153i			0.281349i
$658$		−	5.54384i		−	0.216121i
$659$	−43.5482			−1.69640			−0.848198	−	0.529679i	$-0.822312\pi$
$659$	−43.5482			−1.69640			−0.848198	+	0.529679i	$0.822312\pi$
$660$		0			0
$661$	−28.1314			−1.09419			−0.547093	−	0.837072i	$-0.684266\pi$
$661$	−28.1314			−1.09419			−0.547093	+	0.837072i	$0.684266\pi$
$662$			4.70800i			0.182982i
$663$			48.0962i			1.86790i
$664$	3.30546			0.128277
$665$	31.1800	+	20.8460i	1.20911	+	0.808374i
$666$	−18.6772			−0.723728
$667$		−	0.228599i		−	0.00885139i
$668$			21.0784i			0.815547i
$669$	23.8264			0.921180
$670$	0.941782	−	1.40865i	0.0363842	−	0.0544208i
$671$		0			0
$672$		−	20.0350i		−	0.772869i
$673$		−	26.0789i		−	1.00527i	−0.864499	−	0.502634i	$-0.832364\pi$
$673$		−	26.0789i		−	1.00527i	0.864499	−	0.502634i	$-0.167636\pi$
$674$	51.0966			1.96817
$675$	4.62044	−	1.91091i	0.177841	−	0.0735509i
$676$	53.2128			2.04665
$677$			7.81201i			0.300240i	0.988668	+	0.150120i	$0.0479660\pi$
$677$			7.81201i			0.300240i	−0.988668	+	0.150120i	$0.952034\pi$
$678$		−	4.36624i		−	0.167684i
$679$	−42.2275			−1.62054
$680$	−3.23124	+	4.83306i	−0.123912	+	0.185339i
$681$	21.9425			0.840837
$682$		0			0
$683$		−	21.1860i		−	0.810660i	−0.914170	−	0.405330i	$-0.867157\pi$
$683$		−	21.1860i		−	0.810660i	0.914170	−	0.405330i	$-0.132843\pi$
$684$	11.8182			0.451880
$685$	−7.89569	−	5.27883i	−0.301679	−	0.201694i
$686$	−36.9910			−1.41232
$687$		−	6.37865i		−	0.243361i
$688$		−	29.7722i		−	1.13505i
$689$	17.6167			0.671142
$690$	0.865937	+	0.578941i	0.0329657	+	0.0220399i
$691$	25.8352			0.982819			0.491409	−	0.870929i	$-0.336482\pi$
$691$	25.8352			0.982819			0.491409	+	0.870929i	$0.336482\pi$
$692$		−	11.4333i		−	0.434628i
$693$		0			0
$694$	17.7818			0.674989
$695$	−4.93361	+	7.37933i	−0.187142	+	0.279914i
$696$	0.336957			0.0127723
$697$		−	45.9184i		−	1.73928i
$698$			14.5851i			0.552055i
$699$	0.429662			0.0162513
$700$	21.7281	−	8.98627i	0.821246	−	0.339649i
$701$	27.4774			1.03781			0.518903	−	0.854833i	$-0.326341\pi$
$701$	27.4774			1.03781			0.518903	+	0.854833i	$0.326341\pi$
$702$			12.7021i			0.479410i
$703$			62.0417i			2.33995i
$704$		0			0
$705$	−1.36445	+	2.04085i	−0.0513883	+	0.0768628i
$706$	−7.76779			−0.292344
$707$		−	11.8220i		−	0.444612i
$708$			2.24138i			0.0842361i
$709$	26.2605			0.986234			0.493117	−	0.869963i	$-0.335858\pi$
$709$	26.2605			0.986234			0.493117	+	0.869963i	$0.335858\pi$
$710$	−4.09881	−	2.74035i	−0.153826	−	0.102843i
$711$	−15.9707			−0.598947
$712$			0.435637i			0.0163262i
$713$		−	0.540201i		−	0.0202307i
$714$	−37.3709			−1.39857
$715$		0			0
$716$	28.3197			1.05836
$717$		−	26.9242i		−	1.00550i
$718$			7.42841i			0.277226i
$719$	2.71918			0.101408			0.0507042	−	0.998714i	$-0.483853\pi$
$719$	2.71918			0.101408			0.0507042	+	0.998714i	$0.483853\pi$
$720$	−5.37780	+	8.04371i	−0.200419	+	0.299772i
$721$	−25.2922			−0.941931
$722$		−	45.2549i		−	1.68421i
$723$		−	3.47499i		−	0.129236i
$724$	−5.85243			−0.217504
$725$	1.83285	+	4.43170i	0.0680704	+	0.164589i
$726$		0			0
$727$		−	42.5803i		−	1.57921i	−0.613612	−	0.789607i	$-0.710284\pi$
$727$		−	42.5803i		−	1.57921i	0.613612	−	0.789607i	$-0.289716\pi$
$728$		−	5.89824i		−	0.218603i
$729$	−1.00000			−0.0370370
$730$	17.5176	−	26.2015i	0.648355	−	0.969763i
$731$	−50.9200			−1.88334
$732$			2.65590i			0.0981648i
$733$		−	11.8982i		−	0.439469i	−0.975560	−	0.219735i	$-0.929481\pi$
$733$		−	11.8982i		−	0.439469i	0.975560	−	0.219735i	$-0.0705192\pi$
$734$	32.8807			1.21365
$735$	0.605280	+	0.404673i	0.0223261	+	0.0149266i
$736$	−1.84830			−0.0681292
$737$		0			0
$738$		−	12.1269i		−	0.446399i
$739$	−0.988378			−0.0363581			−0.0181790	−	0.999835i	$-0.505787\pi$
$739$	−0.988378			−0.0363581			−0.0181790	+	0.999835i	$0.505787\pi$
$740$	32.3335	+	21.6172i	1.18860	+	0.794666i
$741$	42.1936			1.55002
$742$			13.6882i			0.502511i
$743$		−	37.8316i		−	1.38791i	−0.720019	−	0.693954i	$-0.755867\pi$
$743$		−	37.8316i		−	1.38791i	0.720019	−	0.693954i	$-0.244133\pi$
$744$	0.796261			0.0291924
$745$	24.3265	−	36.3858i	0.891254	−	1.33307i
$746$	33.6602			1.23239
$747$		−	9.40902i		−	0.344258i
$748$		0			0
$749$	36.4151			1.33058
$750$	−21.4292	−	4.28067i	−0.782482	−	0.156308i
$751$	24.8787			0.907838			0.453919	−	0.891043i	$-0.350026\pi$
$751$	24.8787			0.907838			0.453919	+	0.891043i	$0.350026\pi$
$752$		−	4.75075i		−	0.173242i
$753$			17.1024i			0.623244i
$754$	−12.1832			−0.443688
$755$	−17.7280	+	26.5163i	−0.645189	+	0.965027i
$756$	−4.70262			−0.171032
$757$		−	33.1405i		−	1.20451i	−0.798303	−	0.602256i	$-0.794268\pi$
$757$		−	33.1405i		−	1.20451i	0.798303	−	0.602256i	$-0.205732\pi$
$758$			23.0961i			0.838890i
$759$		0			0
$760$	4.23992	+	2.83469i	0.153798	+	0.102825i
$761$	24.6526			0.893656			0.446828	−	0.894620i	$-0.352554\pi$
$761$	24.6526			0.893656			0.446828	+	0.894620i	$0.352554\pi$
$762$		−	5.02547i		−	0.182053i
$763$		−	21.2690i		−	0.769991i
$764$	42.6347			1.54247
$765$	13.7573	+	9.19776i	0.497397	+	0.332546i
$766$	−46.2226			−1.67009
$767$			8.00221i			0.288943i
$768$		−	18.4776i		−	0.666752i
$769$	−34.6974			−1.25122			−0.625611	−	0.780135i	$-0.715150\pi$
$769$	−34.6974			−1.25122			−0.625611	+	0.780135i	$0.715150\pi$
$770$		0			0
$771$	4.13235			0.148823
$772$		−	11.9816i		−	0.431229i
$773$			21.4275i			0.770692i	0.922772	+	0.385346i	$0.125918\pi$
$773$			21.4275i			0.770692i	−0.922772	+	0.385346i	$0.874082\pi$
$774$	−13.4479			−0.483373
$775$	4.33120	+	10.4725i	0.155581	+	0.376184i
$776$	−5.74218			−0.206132
$777$		−	24.6872i		−	0.885648i
$778$			30.6537i			1.09899i
$779$	−40.2830			−1.44329
$780$	14.7016	−	21.9895i	0.526400	−	0.787351i
$781$		0			0
$782$			3.44759i			0.123286i
$783$		−	0.959152i		−	0.0342773i
$784$	−1.40899			−0.0503211
$785$	−28.0771	−	18.7716i	−1.00212	−	0.669986i
$786$	21.2208			0.756919
$787$			23.1809i			0.826311i	0.910660	+	0.413156i	$0.135573\pi$
$787$			23.1809i			0.826311i	−0.910660	+	0.413156i	$0.864427\pi$
$788$		−	38.2443i		−	1.36240i
$789$	−19.4921			−0.693936
$790$	58.0260	+	38.7945i	2.06447	+	1.38025i
$791$	5.77121			0.205200
$792$		0			0
$793$			9.48215i			0.336721i
$794$	−61.2994			−2.17543
$795$	3.36896	−	5.03904i	0.119485	−	0.178716i
$796$	24.6012			0.871968
$797$		−	4.75686i		−	0.168497i	−0.996445	−	0.0842483i	$-0.973151\pi$
$797$		−	4.75686i		−	0.168497i	0.996445	−	0.0842483i	$-0.0268489\pi$
$798$			32.7846i			1.16056i
$799$	−8.12531			−0.287453
$800$	35.8317	−	14.8192i	1.26684	−	0.523938i
$801$	1.24004			0.0438148
$802$			1.34632i			0.0475401i
$803$		0			0
$804$	0.705728			0.0248891
$805$	−0.765232	+	1.14458i	−0.0269709	+	0.0403411i
$806$	−28.7901			−1.01409
$807$		−	16.3889i		−	0.576917i
$808$		−	1.60758i		−	0.0565544i
$809$	−34.5754			−1.21561			−0.607804	−	0.794087i	$-0.707949\pi$
$809$	−34.5754			−1.21561			−0.607804	+	0.794087i	$0.707949\pi$
$810$	3.63328	+	2.42911i	0.127661	+	0.0853502i
$811$	45.9198			1.61246			0.806231	−	0.591601i	$-0.201504\pi$
$811$	45.9198			1.61246			0.806231	+	0.591601i	$0.201504\pi$
$812$		−	4.51052i		−	0.158288i
$813$		−	16.0828i		−	0.564049i
$814$		0			0
$815$	−4.46445	−	2.98480i	−0.156383	−	0.104553i
$816$	−32.0248			−1.12109
$817$			44.6708i			1.56283i
$818$			1.28732i			0.0450100i
$819$	−16.7894			−0.586669
$820$	−14.0359	+	20.9938i	−0.490153	+	0.733136i
$821$	8.62880			0.301147			0.150574	−	0.988599i	$-0.451888\pi$
$821$	8.62880			0.301147			0.150574	+	0.988599i	$0.451888\pi$
$822$		−	8.30203i		−	0.289566i
$823$			37.8023i			1.31771i	0.752272	+	0.658853i	$0.228958\pi$
$823$			37.8023i			1.31771i	−0.752272	+	0.658853i	$0.771042\pi$
$824$	−3.43929			−0.119813
$825$		0			0
$826$	−6.21775			−0.216343
$827$		−	42.9110i		−	1.49216i	−0.665856	−	0.746080i	$-0.731933\pi$
$827$		−	42.9110i		−	1.49216i	0.665856	−	0.746080i	$-0.268067\pi$
$828$			0.433831i			0.0150767i
$829$	−13.4263			−0.466314			−0.233157	−	0.972439i	$-0.574906\pi$
$829$	−13.4263			−0.466314			−0.233157	+	0.972439i	$0.574906\pi$
$830$	−22.8555	+	34.1856i	−0.793327	+	1.18660i
$831$	17.9734			0.623489
$832$			42.2632i			1.46521i
$833$			2.40983i			0.0834955i
$834$	−7.75909			−0.268675
$835$	21.5256	+	14.3914i	0.744925	+	0.498036i
$836$		0			0
$837$		−	2.26656i		−	0.0783439i
$838$		−	33.5872i		−	1.16025i
$839$	35.8411			1.23737			0.618686	−	0.785638i	$-0.287665\pi$
$839$	35.8411			1.23737			0.618686	+	0.785638i	$0.287665\pi$
$840$	−1.68712	−	1.12796i	−0.0582111	−	0.0389183i
$841$	−28.0800			−0.968277
$842$			19.9238i			0.686619i
$843$			12.1589i			0.418774i
$844$	−4.34071			−0.149414
$845$	36.3315	−	54.3420i	1.24984	−	1.86942i
$846$	−2.14588			−0.0737767
$847$		0			0
$848$			11.7300i			0.402811i
$849$	6.05689			0.207872
$850$	−27.6419	−	66.8361i	−0.948110	−	2.29246i
$851$	−2.27747			−0.0780708
$852$		−	2.05349i		−	0.0703514i
$853$		−	0.121697i		−	0.00416684i	−0.999998	−	0.00208342i	$-0.999337\pi$
$853$		−	0.121697i		−	0.00416684i	0.999998	−	0.00208342i	$-0.000663173\pi$
$854$	−7.36766			−0.252116
$855$	8.06896	−	12.0690i	0.275953	−	0.412750i
$856$	4.95181			0.169249
$857$		−	25.4338i		−	0.868801i	−0.900720	−	0.434401i	$-0.856960\pi$
$857$		−	25.4338i		−	0.868801i	0.900720	−	0.434401i	$-0.143040\pi$
$858$		0			0
$859$	−35.5202			−1.21193			−0.605967	−	0.795490i	$-0.707214\pi$
$859$	−35.5202			−1.21193			−0.605967	+	0.795490i	$0.707214\pi$
$860$	23.2805	+	15.5647i	0.793860	+	0.530752i
$861$	16.0292			0.546272
$862$			12.4494i			0.424027i
$863$			11.1259i			0.378731i	0.981907	+	0.189365i	$0.0606430\pi$
$863$			11.1259i			0.378731i	−0.981907	+	0.189365i	$0.939357\pi$
$864$	−7.75505			−0.263832
$865$	−11.6759	−	7.80616i	−0.396992	−	0.265418i
$866$	−40.0850			−1.36214
$867$			37.7726i			1.28283i
$868$		−	10.6588i		−	0.361783i
$869$		0			0
$870$	−2.32988	+	3.48487i	−0.0789905	+	0.118148i
$871$	2.51961			0.0853736
$872$		−	2.89221i		−	0.0979426i
$873$			16.3452i			0.553200i
$874$	3.02448			0.102305
$875$	5.65810	−	28.3246i	0.191279	−	0.957547i
$876$	13.1269			0.443516
$877$			25.6366i			0.865685i	0.901469	+	0.432843i	$0.142489\pi$
$877$			25.6366i			0.865685i	−0.901469	+	0.432843i	$0.857511\pi$
$878$			25.2418i			0.851869i
$879$	−21.9771			−0.741268
$880$		0			0
$881$	39.6504			1.33586			0.667928	−	0.744226i	$-0.267182\pi$
$881$	39.6504			1.33586			0.667928	+	0.744226i	$0.267182\pi$
$882$			0.636430i			0.0214297i
$883$		−	5.99439i		−	0.201727i	−0.994900	−	0.100864i	$-0.967839\pi$
$883$		−	5.99439i		−	0.201727i	0.994900	−	0.100864i	$-0.0321606\pi$
$884$	87.5477			2.94455
$885$	2.28894	+	1.53032i	0.0769417	+	0.0514410i
$886$	−42.7154			−1.43505
$887$		−	9.12613i		−	0.306426i	−0.988193	−	0.153213i	$-0.951038\pi$
$887$		−	9.12613i		−	0.306426i	0.988193	−	0.153213i	$-0.0489620\pi$
$888$		−	3.35702i		−	0.112654i
$889$	6.64256			0.222784
$890$	−4.50543	−	3.01220i	−0.151022	−	0.100969i
$891$		0			0
$892$		−	43.3702i		−	1.45214i
$893$			7.12813i			0.238534i
$894$	38.2583			1.27955
$895$	19.3355	−	28.9206i	0.646314	−	0.966709i
$896$	7.23146			0.241586
$897$			1.54887i			0.0517154i
$898$			17.3575i			0.579227i
$899$	2.17398			0.0725063
$900$	−3.47835	−	8.41040i	−0.115945	−	0.280347i
$901$	20.0621			0.668366
$902$		0			0
$903$		−	17.7751i		−	0.591519i
$904$	0.784781			0.0261014
$905$	−3.99579	+	5.97661i	−0.132825	+	0.198669i
$906$	−27.8809			−0.926281
$907$			5.84020i			0.193921i	0.995288	+	0.0969603i	$0.0309120\pi$
$907$			5.84020i			0.193921i	−0.995288	+	0.0969603i	$0.969088\pi$
$908$		−	39.9410i		−	1.32549i
$909$	−4.57599			−0.151776
$910$	61.0006	+	40.7832i	2.02215	+	1.35195i
$911$	7.77868			0.257719			0.128860	−	0.991663i	$-0.458868\pi$
$911$	7.77868			0.257719			0.128860	+	0.991663i	$0.458868\pi$
$912$			28.0945i			0.930302i
$913$		0			0
$914$	51.7258			1.71094
$915$	2.71225	+	1.81333i	0.0896643	+	0.0599470i
$916$	−11.6108			−0.383632
$917$			28.0492i			0.926265i
$918$			14.4653i			0.477427i
$919$	−27.9017			−0.920391			−0.460196	−	0.887817i	$-0.652221\pi$
$919$	−27.9017			−0.920391			−0.460196	+	0.887817i	$0.652221\pi$
$920$	−0.104058	+	0.155642i	−0.00343069	+	0.00513137i
$921$	−21.6041			−0.711881
$922$		−	62.9645i		−	2.07362i
$923$		−	7.33141i		−	0.241316i
$924$		0			0
$925$	44.1519	−	18.2602i	1.45170	−	0.600393i
$926$	44.5110			1.46272
$927$			9.78997i			0.321545i
$928$		−	7.43827i		−	0.244173i
$929$	−14.1003			−0.462617			−0.231309	−	0.972880i	$-0.574301\pi$
$929$	−14.1003			−0.462617			−0.231309	+	0.972880i	$0.574301\pi$
$930$	−5.50573	+	8.23507i	−0.180540	+	0.270039i
$931$	2.11408			0.0692862
$932$		−	0.782097i		−	0.0256184i
$933$		−	26.2869i		−	0.860596i
$934$	−29.8179			−0.975672
$935$		0			0
$936$	−2.28306			−0.0746240
$937$		−	50.8079i		−	1.65982i	−0.557897	−	0.829910i	$-0.688392\pi$
$937$		−	50.8079i		−	1.65982i	0.557897	−	0.829910i	$-0.311608\pi$
$938$			1.95774i			0.0639225i
$939$	−9.58638			−0.312840
$940$	3.71488	+	2.48366i	0.121166	+	0.0810081i
$941$	7.04108			0.229533			0.114766	−	0.993393i	$-0.463388\pi$
$941$	7.04108			0.229533			0.114766	+	0.993393i	$0.463388\pi$
$942$		−	29.5221i		−	0.961881i
$943$		−	1.47874i		−	0.0481544i
$944$	−5.32826			−0.173420
$945$	−3.21075	+	4.80240i	−0.104446	+	0.156222i
$946$		0			0
$947$		−	18.9648i		−	0.616273i	−0.951342	−	0.308137i	$-0.900295\pi$
$947$		−	18.9648i		−	0.616273i	0.951342	−	0.308137i	$-0.0997054\pi$
$948$			29.0708i			0.944176i
$949$	46.8659			1.52133
$950$	−58.6336	+	24.2496i	−1.90233	+	0.786760i
$951$	32.6557			1.05893
$952$		−	6.71699i		−	0.217699i
$953$		−	4.45198i		−	0.144214i	−0.997397	−	0.0721069i	$-0.977028\pi$
$953$		−	4.45198i		−	0.144214i	0.997397	−	0.0721069i	$-0.0229723\pi$
$954$	5.29836			0.171541
$955$	29.1092	−	43.5394i	0.941951	−	1.40890i
$956$	−49.0091			−1.58507
$957$		0			0
$958$		−	36.8146i		−	1.18943i
$959$	10.9734			0.354351
$960$	12.0889	+	8.08227i	0.390166	+	0.260854i
$961$	−25.8627			−0.834280
$962$			121.379i			3.91340i
$963$		−	14.0954i		−	0.454217i
$964$	−6.32538			−0.203727
$965$	−12.2359	−	8.18056i	−0.393887	−	0.263342i
$966$	−1.20348			−0.0387214
$967$			7.49675i			0.241079i	0.992709	+	0.120540i	$0.0384625\pi$
$967$			7.49675i			0.241079i	−0.992709	+	0.120540i	$0.961538\pi$
$968$		0			0
$969$	48.0506			1.54361
$970$	39.7042	−	59.3866i	1.27482	−	1.90679i
$971$	55.0012			1.76507			0.882537	−	0.470244i	$-0.155834\pi$
$971$	55.0012			1.76507			0.882537	+	0.470244i	$0.155834\pi$
$972$			1.82026i			0.0583849i
$973$		−	10.2558i		−	0.328786i
$974$	−15.4509			−0.495078
$975$	−12.4185	−	30.0270i	−0.397710	−	0.961634i
$976$	−6.31367			−0.202096
$977$		−	4.70635i		−	0.150569i	−0.997162	−	0.0752847i	$-0.976013\pi$
$977$		−	4.70635i		−	0.150569i	0.997162	−	0.0752847i	$-0.0239865\pi$
$978$		−	4.69420i		−	0.150104i
$979$		0			0
$980$	0.736611	−	1.10177i	0.0235302	−	0.0351947i
$981$	−8.23270			−0.262850
$982$		−	24.1413i		−	0.770379i
$983$		−	50.5723i		−	1.61301i	−0.591230	−	0.806503i	$-0.701357\pi$
$983$		−	50.5723i		−	1.61301i	0.591230	−	0.806503i	$-0.298643\pi$
$984$	2.17968			0.0694856
$985$	−39.0558	−	26.1116i	−1.24442	−	0.831985i
$986$	−13.8744			−0.441852
$987$		−	2.83638i		−	0.0902828i
$988$		−	76.8034i		−	2.44344i
$989$	−1.63981			−0.0521430
$990$		0			0
$991$	5.42430			0.172309			0.0861543	−	0.996282i	$-0.472542\pi$
$991$	5.42430			0.172309			0.0861543	+	0.996282i	$0.472542\pi$
$992$		−	17.5773i		−	0.558081i
$993$			2.40874i			0.0764391i
$994$	5.69653			0.180683
$995$	16.7967	−	25.1233i	0.532491	−	0.796461i
$996$	−17.1269			−0.542686
$997$			28.6665i			0.907876i	0.891033	+	0.453938i	$0.149981\pi$
$997$			28.6665i			0.907876i	−0.891033	+	0.453938i	$0.850019\pi$
$998$		−	48.2807i		−	1.52830i
$999$	−9.55578			−0.302332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.i.364.3	yes	12
5.2	odd	4		9075.2.a.do.1.5		6
5.3	odd	4		9075.2.a.ds.1.2		6
5.4	even	2	inner	1815.2.c.i.364.10	yes	12
11.10	odd	2		1815.2.c.h.364.10	yes	12
55.32	even	4		9075.2.a.dr.1.2		6
55.43	even	4		9075.2.a.dp.1.5		6
55.54	odd	2		1815.2.c.h.364.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.h.364.3	✓	12	55.54	odd	2
1815.2.c.h.364.10	yes	12	11.10	odd	2
1815.2.c.i.364.3	yes	12	1.1	even	1	trivial
1815.2.c.i.364.10	yes	12	5.4	even	2	inner
9075.2.a.do.1.5		6	5.2	odd	4
9075.2.a.dp.1.5		6	55.43	even	4
9075.2.a.dr.1.2		6	55.32	even	4
9075.2.a.ds.1.2		6	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.95455i q^{2} -1.00000i q^{3} -1.82026 q^{4} +(-1.24280 + 1.85889i) q^{5} -1.95455 q^{6} -2.58348i q^{7} -0.351308i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.95455i q^{2} -1.00000i q^{3} -1.82026 q^{4} +(-1.24280 + 1.85889i) q^{5} -1.95455 q^{6} -2.58348i q^{7} -0.351308i q^{8} -1.00000 q^{9} +(3.63328 + 2.42911i) q^{10} +1.82026i q^{12} +6.49874i q^{13} -5.04954 q^{14} +(1.85889 + 1.24280i) q^{15} -4.32717 q^{16} +7.40085i q^{17} +1.95455i q^{18} +6.49258 q^{19} +(2.26222 - 3.38366i) q^{20} -2.58348 q^{21} +0.238335i q^{23} -0.351308 q^{24} +(-1.91091 - 4.62044i) q^{25} +12.7021 q^{26} +1.00000i q^{27} +4.70262i q^{28} -0.959152 q^{29} +(2.42911 - 3.63328i) q^{30} -2.26656 q^{31} +7.75505i q^{32} +14.4653 q^{34} +(4.80240 + 3.21075i) q^{35} +1.82026 q^{36} +9.55578i q^{37} -12.6901i q^{38} +6.49874 q^{39} +(0.653040 + 0.436604i) q^{40} -6.20447 q^{41} +5.04954i q^{42} +6.88029i q^{43} +(1.24280 - 1.85889i) q^{45} +0.465837 q^{46} +1.09789i q^{47} +4.32717i q^{48} +0.325615 q^{49} +(-9.03087 + 3.73496i) q^{50} +7.40085 q^{51} -11.8294i q^{52} -2.71078i q^{53} +1.95455 q^{54} -0.907597 q^{56} -6.49258i q^{57} +1.87471i q^{58} +1.23135 q^{59} +(-3.38366 - 2.26222i) q^{60} +1.45908 q^{61} +4.43011i q^{62} +2.58348i q^{63} +6.50329 q^{64} +(-12.0804 - 8.07662i) q^{65} -0.387707i q^{67} -13.4715i q^{68} +0.238335 q^{69} +(6.27556 - 9.38652i) q^{70} -1.12813 q^{71} +0.351308i q^{72} -7.21153i q^{73} +18.6772 q^{74} +(-4.62044 + 1.91091i) q^{75} -11.8182 q^{76} -12.7021i q^{78} +15.9707 q^{79} +(5.37780 - 8.04371i) q^{80} +1.00000 q^{81} +12.1269i q^{82} +9.40902i q^{83} +4.70262 q^{84} +(-13.7573 - 9.19776i) q^{85} +13.4479 q^{86} +0.959152i q^{87} -1.24004 q^{89} +(-3.63328 - 2.42911i) q^{90} +16.7894 q^{91} -0.433831i q^{92} +2.26656i q^{93} +2.14588 q^{94} +(-8.06896 + 12.0690i) q^{95} +7.75505 q^{96} -16.3452i q^{97} -0.636430i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9	\( 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9} + 12 q^{10} + 20 q^{14} + 22 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{25} - 24 q^{29} - 8 q^{30} + 36 q^{31} + 2 q^{34} + 24 q^{35} + 18 q^{36} - 4 q^{39} - 22 q^{40} - 12 q^{41} + 2 q^{45} - 22 q^{46} - 24 q^{49} - 58 q^{50} + 4 q^{51} - 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} + 8 q^{61} - 44 q^{64} - 14 q^{65} - 24 q^{69} - 16 q^{70} + 8 q^{74} - 12 q^{75} - 40 q^{76} - 4 q^{79} - 58 q^{80} + 12 q^{81} + 48 q^{84} - 2 q^{85} + 56 q^{86} + 32 q^{89} - 12 q^{90} + 48 q^{91} - 6 q^{94} + 62 q^{96}+O(q^{100}) \) 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9 + 12 * q^10 + 20 * q^14 + 22 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^25 - 24 * q^29 - 8 * q^30 + 36 * q^31 + 2 * q^34 + 24 * q^35 + 18 * q^36 - 4 * q^39 - 22 * q^40 - 12 * q^41 + 2 * q^45 - 22 * q^46 - 24 * q^49 - 58 * q^50 + 4 * q^51 - 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 + 8 * q^61 - 44 * q^64 - 14 * q^65 - 24 * q^69 - 16 * q^70 + 8 * q^74 - 12 * q^75 - 40 * q^76 - 4 * q^79 - 58 * q^80 + 12 * q^81 + 48 * q^84 - 2 * q^85 + 56 * q^86 + 32 * q^89 - 12 * q^90 + 48 * q^91 - 6 * q^94 + 62 * q^96

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