LMFDB - Embedded newform 675.2.k.c.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(199,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("675.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.k (of order $6$, degree $2$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Root			$-1.27588 + 0.736627i$ of defining polynomial
Character	$\chi$	$=$	675.199
Dual form			675.2.k.c.424.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27588 + 0.736627i) q^{2} +(0.0852394 - 0.147639i) q^{4} +(3.34791 - 1.93291i) q^{7} -2.69535i q^{8} +O(q^{10})$	\(q+(-1.27588 + 0.736627i) q^{2} +(0.0852394 - 0.147639i) q^{4} +(3.34791 - 1.93291i) q^{7} -2.69535i q^{8} +(0.130139 + 0.225407i) q^{11} +(-3.53235 - 2.03940i) q^{13} +(-2.84768 + 4.93232i) q^{14} +(2.15595 + 3.73421i) q^{16} -3.26028i q^{17} -4.24928 q^{19} +(-0.332082 - 0.191728i) q^{22} +(-7.53039 - 4.34768i) q^{23} +6.00912 q^{26} -0.659042i q^{28} +(-2.11105 - 3.65644i) q^{29} +(-1.32643 + 2.29744i) q^{31} +(-0.832959 - 0.480909i) q^{32} +(2.40161 + 4.15971i) q^{34} -2.27559i q^{37} +(5.42156 - 3.13014i) q^{38} +(2.82093 - 4.88599i) q^{41} +(7.85712 - 4.53631i) q^{43} +0.0443719 q^{44} +12.8105 q^{46} +(1.23745 - 0.714441i) q^{47} +(3.97232 - 6.88026i) q^{49} +(-0.602191 + 0.347675i) q^{52} +11.3816i q^{53} +(-5.20988 - 9.02378i) q^{56} +(5.38687 + 3.11011i) q^{58} +(3.56212 - 6.16977i) q^{59} +(-1.26244 - 2.18660i) q^{61} -3.90833i q^{62} -7.20679 q^{64} +(-9.77361 - 5.64280i) q^{67} +(-0.481344 - 0.277904i) q^{68} +8.38158 q^{71} -0.403568i q^{73} +(1.67626 + 2.90337i) q^{74} +(-0.362207 + 0.627360i) q^{76} +(0.871386 + 0.503095i) q^{77} +(-1.52125 - 2.63488i) q^{79} +8.31189i q^{82} +(3.96660 - 2.29012i) q^{83} +(-6.68314 + 11.5755i) q^{86} +(0.607551 - 0.350770i) q^{88} +7.17772 q^{89} -15.7680 q^{91} +(-1.28377 + 0.741187i) q^{92} +(-1.05255 + 1.82308i) q^{94} +(2.69777 - 1.55756i) q^{97} +11.7045i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.27588	+	0.736627i	−0.902180	+	0.520874i	−0.877907	−	0.478831i	$-0.841061\pi$
$2$	−1.27588	+	0.736627i	−0.902180	+	0.520874i	−0.0242735	+	0.999705i	$0.507727\pi$
$3$		0			0
$3$		0			0
$4$	0.0852394	−	0.147639i	0.0426197	−	0.0738195i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.34791	−	1.93291i	1.26539	−	0.730573i	0.291278	−	0.956639i	$-0.405920\pi$
$7$	3.34791	−	1.93291i	1.26539	−	0.730573i	0.974112	+	0.226066i	$0.0725864\pi$
$8$		−	2.69535i		−	0.952950i
$9$		0			0
$10$		0			0
$11$	0.130139	+	0.225407i	0.0392384	+	0.0679628i	0.884978	−	0.465634i	$-0.154174\pi$
$11$	0.130139	+	0.225407i	0.0392384	+	0.0679628i	−0.845739	+	0.533596i	$0.820840\pi$
$12$		0			0
$13$	−3.53235	−	2.03940i	−0.979697	−	0.565629i	−0.0775187	−	0.996991i	$-0.524700\pi$
$13$	−3.53235	−	2.03940i	−0.979697	−	0.565629i	−0.902179	+	0.431362i	$0.858033\pi$
$14$	−2.84768	+	4.93232i	−0.761073	+	1.31822i
$15$		0			0
$16$	2.15595	+	3.73421i	0.538987	+	0.933553i
$17$		−	3.26028i		−	0.790734i	−0.918523	−	0.395367i	$-0.870617\pi$
$17$		−	3.26028i		−	0.790734i	0.918523	−	0.395367i	$-0.129383\pi$
$18$		0			0
$19$	−4.24928			−0.974853			−0.487426	−	0.873164i	$-0.662064\pi$
$19$	−4.24928			−0.974853			−0.487426	+	0.873164i	$0.662064\pi$
$20$		0			0
$21$		0			0
$22$	−0.332082	−	0.191728i	−0.0708002	−	0.0408765i
$23$	−7.53039	−	4.34768i	−1.57020	−	0.906553i	−0.996144	−	0.0877339i	$-0.972037\pi$
$23$	−7.53039	−	4.34768i	−1.57020	−	0.906553i	−0.574052	−	0.818819i	$-0.694629\pi$
$24$		0			0
$25$		0			0
$26$	6.00912			1.17849
$27$		0			0
$28$		−	0.659042i		−	0.124547i
$29$	−2.11105	−	3.65644i	−0.392012	−	0.678984i	0.600703	−	0.799472i	$-0.294887\pi$
$29$	−2.11105	−	3.65644i	−0.392012	−	0.678984i	−0.992715	+	0.120488i	$0.961554\pi$
$30$		0			0
$31$	−1.32643	+	2.29744i	−0.238233	+	0.412632i	−0.960207	−	0.279288i	$-0.909902\pi$
$31$	−1.32643	+	2.29744i	−0.238233	+	0.412632i	0.721974	+	0.691920i	$0.243235\pi$
$32$	−0.832959	−	0.480909i	−0.147248	−	0.0850135i
$33$		0			0
$34$	2.40161	+	4.15971i	0.411873	+	0.713384i
$35$		0			0
$36$		0			0
$37$		−	2.27559i		−	0.374104i	−0.982350	−	0.187052i	$-0.940107\pi$
$37$		−	2.27559i		−	0.374104i	0.982350	−	0.187052i	$-0.0598933\pi$
$38$	5.42156	−	3.13014i	0.879493	−	0.507776i
$39$		0			0
$40$		0			0
$41$	2.82093	−	4.88599i	0.440555	−	0.763064i	−0.557176	−	0.830395i	$-0.688115\pi$
$41$	2.82093	−	4.88599i	0.440555	−	0.763064i	0.997731	+	0.0673308i	$0.0214483\pi$
$42$		0			0
$43$	7.85712	−	4.53631i	1.19820	−	0.691780i	0.238046	−	0.971254i	$-0.423493\pi$
$43$	7.85712	−	4.53631i	1.19820	−	0.691780i	0.960153	+	0.279474i	$0.0901599\pi$
$44$	0.0443719			0.00668931
$45$		0			0
$46$	12.8105			1.88880
$47$	1.23745	−	0.714441i	0.180500	−	0.104212i	−0.407027	−	0.913416i	$-0.633435\pi$
$47$	1.23745	−	0.714441i	0.180500	−	0.104212i	0.587528	+	0.809204i	$0.300101\pi$
$48$		0			0
$49$	3.97232	−	6.88026i	0.567474	−	0.982894i
$50$		0			0
$51$		0			0
$52$	−0.602191	+	0.347675i	−0.0835089	+	0.0482139i
$53$			11.3816i			1.56338i	0.623667	+	0.781690i	$0.285642\pi$
$53$			11.3816i			1.56338i	−0.623667	+	0.781690i	$0.714358\pi$
$54$		0			0
$55$		0			0
$56$	−5.20988	−	9.02378i	−0.696200	−	1.20585i
$57$		0			0
$58$	5.38687	+	3.11011i	0.707331	+	0.408378i
$59$	3.56212	−	6.16977i	0.463748	−	0.803235i	−0.535396	−	0.844601i	$-0.679838\pi$
$59$	3.56212	−	6.16977i	0.463748	−	0.803235i	0.999144	+	0.0413660i	$0.0131710\pi$
$60$		0			0
$61$	−1.26244	−	2.18660i	−0.161638	−	0.279966i	0.773818	−	0.633408i	$-0.218344\pi$
$61$	−1.26244	−	2.18660i	−0.161638	−	0.279966i	−0.935456	+	0.353442i	$0.885011\pi$
$62$		−	3.90833i		−	0.496358i
$63$		0			0
$64$	−7.20679			−0.900848
$65$		0			0
$66$		0			0
$67$	−9.77361	−	5.64280i	−1.19404	−	0.689377i	−0.234817	−	0.972040i	$-0.575449\pi$
$67$	−9.77361	−	5.64280i	−1.19404	−	0.689377i	−0.959219	+	0.282662i	$0.908782\pi$
$68$	−0.481344	−	0.277904i	−0.0583716	−	0.0337008i
$69$		0			0
$70$		0			0
$71$	8.38158			0.994711			0.497355	−	0.867547i	$-0.334305\pi$
$71$	8.38158			0.994711			0.497355	+	0.867547i	$0.334305\pi$
$72$		0			0
$73$		−	0.403568i		−	0.0472340i	−0.999721	−	0.0236170i	$-0.992482\pi$
$73$		−	0.403568i		−	0.0472340i	0.999721	−	0.0236170i	$-0.00751823\pi$
$74$	1.67626	+	2.90337i	0.194861	+	0.337509i
$75$		0			0
$76$	−0.362207	+	0.627360i	−0.0415480	+	0.0719632i
$77$	0.871386	+	0.503095i	0.0993036	+	0.0573330i
$78$		0			0
$79$	−1.52125	−	2.63488i	−0.171154	−	0.296447i	0.767670	−	0.640846i	$-0.221416\pi$
$79$	−1.52125	−	2.63488i	−0.171154	−	0.296447i	−0.938824	+	0.344399i	$0.888083\pi$
$80$		0			0
$81$		0			0
$82$			8.31189i			0.917895i
$83$	3.96660	−	2.29012i	0.435391	−	0.251373i	−0.266250	−	0.963904i	$-0.585785\pi$
$83$	3.96660	−	2.29012i	0.435391	−	0.251373i	0.701641	+	0.712531i	$0.252451\pi$
$84$		0			0
$85$		0			0
$86$	−6.68314	+	11.5755i	−0.720661	+	1.24822i
$87$		0			0
$88$	0.607551	−	0.350770i	0.0647652	−	0.0373922i
$89$	7.17772			0.760837			0.380419	−	0.924814i	$-0.375780\pi$
$89$	7.17772			0.760837			0.380419	+	0.924814i	$0.375780\pi$
$90$		0			0
$91$	−15.7680			−1.65293
$92$	−1.28377	+	0.741187i	−0.133843	+	0.0772741i
$93$		0			0
$94$	−1.05255	+	1.82308i	−0.108563	+	0.188036i
$95$		0			0
$96$		0			0
$97$	2.69777	−	1.55756i	0.273917	−	0.158146i	−0.356749	−	0.934200i	$-0.616115\pi$
$97$	2.69777	−	1.55756i	0.273917	−	0.158146i	0.630666	+	0.776054i	$0.282782\pi$
$98$			11.7045i			1.18233i
$99$		0			0
$100$		0			0
$101$	1.92286	+	3.33049i	0.191332	+	0.331396i	0.945692	−	0.325065i	$-0.105386\pi$
$101$	1.92286	+	3.33049i	0.191332	+	0.331396i	−0.754360	+	0.656461i	$0.772053\pi$
$102$		0			0
$103$	−3.64318	−	2.10339i	−0.358974	−	0.207254i	0.309657	−	0.950848i	$-0.399786\pi$
$103$	−3.64318	−	2.10339i	−0.358974	−	0.207254i	−0.668630	+	0.743595i	$0.733119\pi$
$104$	−5.49691	+	9.52092i	−0.539016	+	0.933603i
$105$		0			0
$106$	−8.38398	−	14.5215i	−0.814324	−	1.41045i
$107$			1.62655i			0.157245i	0.996904	+	0.0786223i	$0.0250521\pi$
$107$			1.62655i			0.157245i	−0.996904	+	0.0786223i	$0.974948\pi$
$108$		0			0
$109$	12.9021			1.23580			0.617900	−	0.786256i	$-0.287984\pi$
$109$	12.9021			1.23580			0.617900	+	0.786256i	$0.287984\pi$
$110$		0			0
$111$		0			0
$112$	14.4358	+	8.33452i	1.36406	+	0.787539i
$113$	−1.15102	−	0.664539i	−0.108278	−	0.0625146i	0.444883	−	0.895589i	$-0.353245\pi$
$113$	−1.15102	−	0.664539i	−0.108278	−	0.0625146i	−0.553161	+	0.833074i	$0.686579\pi$
$114$		0			0
$115$		0			0
$116$	−0.719778			−0.0668297
$117$		0			0
$118$			10.4958i			0.966217i
$119$	−6.30184	−	10.9151i	−0.577689	−	1.00059i
$120$		0			0
$121$	5.46613	−	9.46761i	0.496921	−	0.860692i
$122$	3.22142	+	1.85989i	0.291654	+	0.168386i
$123$		0			0
$124$	0.226128	+	0.391665i	0.0203069	+	0.0351725i
$125$		0			0
$126$		0			0
$127$		−	1.65285i		−	0.146667i	−0.997307	−	0.0733335i	$-0.976636\pi$
$127$		−	1.65285i		−	0.146667i	0.997307	−	0.0733335i	$-0.0233637\pi$
$128$	10.8609	−	6.27053i	0.959975	−	0.554242i
$129$		0			0
$130$		0			0
$131$	−6.58886	+	11.4122i	−0.575672	+	0.997092i	0.420297	+	0.907387i	$0.361926\pi$
$131$	−6.58886	+	11.4122i	−0.575672	+	0.997092i	−0.995968	+	0.0897057i	$0.971407\pi$
$132$		0			0
$133$	−14.2262	+	8.21350i	−1.23357	+	0.712201i
$134$	16.6266			1.43632
$135$		0			0
$136$	−8.78759			−0.753530
$137$	−17.5741	+	10.1464i	−1.50146	+	0.866867i	−0.501459	+	0.865181i	$0.667203\pi$
$137$	−17.5741	+	10.1464i	−1.50146	+	0.866867i	−0.999999	+	0.00168578i	$0.999463\pi$
$138$		0			0
$139$	1.53440	−	2.65766i	0.130146	−	0.225420i	−0.793587	−	0.608457i	$-0.791789\pi$
$139$	1.53440	−	2.65766i	0.130146	−	0.225420i	0.923733	+	0.383038i	$0.125122\pi$
$140$		0			0
$141$		0			0
$142$	−10.6939	+	6.17410i	−0.897409	+	0.518119i
$143$		−	1.06162i		−	0.0887774i
$144$		0			0
$145$		0			0
$146$	0.297279	+	0.514902i	0.0246030	+	0.0426136i
$147$		0			0
$148$	−0.335965	−	0.193970i	−0.0276162	−	0.0159442i
$149$	−2.03081	+	3.51747i	−0.166371	+	0.288162i	−0.937141	−	0.348951i	$-0.886538\pi$
$149$	−2.03081	+	3.51747i	−0.166371	+	0.288162i	0.770771	+	0.637113i	$0.219871\pi$
$150$		0			0
$151$	6.80994	+	11.7952i	0.554185	+	0.959876i	0.997966	+	0.0637412i	$0.0203032\pi$
$151$	6.80994	+	11.7952i	0.554185	+	0.959876i	−0.443782	+	0.896135i	$0.646363\pi$
$152$			11.4533i			0.928986i
$153$		0			0
$154$	−1.48237			−0.119453
$155$		0			0
$156$		0			0
$157$	−1.78627	−	1.03131i	−0.142560	−	0.0823071i	0.427023	−	0.904241i	$-0.359562\pi$
$157$	−1.78627	−	1.03131i	−0.142560	−	0.0823071i	−0.569584	+	0.821933i	$0.692896\pi$
$158$	3.88185	+	2.24119i	0.308823	+	0.178299i
$159$		0			0
$160$		0			0
$161$	−33.6147			−2.64921
$162$		0			0
$163$			3.50525i			0.274552i	0.990533	+	0.137276i	$0.0438347\pi$
$163$			3.50525i			0.274552i	−0.990533	+	0.137276i	$0.956165\pi$
$164$	−0.480909	−	0.832959i	−0.0375527	−	0.0650431i
$165$		0			0
$166$	−3.37393	+	5.84381i	−0.261868	+	0.453568i
$167$	17.7837	+	10.2674i	1.37615	+	0.794518i	0.991693	−	0.128626i	$-0.0410568\pi$
$167$	17.7837	+	10.2674i	1.37615	+	0.794518i	0.384453	+	0.923145i	$0.374390\pi$
$168$		0			0
$169$	1.81833	+	3.14944i	0.139871	+	0.242264i
$170$		0			0
$171$		0			0
$172$		−	1.54669i		−	0.117934i
$173$	−6.71323	+	3.87589i	−0.510397	+	0.294678i	−0.732997	−	0.680232i	$-0.761879\pi$
$173$	−6.71323	+	3.87589i	−0.510397	+	0.294678i	0.222600	+	0.974910i	$0.428546\pi$
$174$		0			0
$175$		0			0
$176$	−0.561145	+	0.971932i	−0.0422979	+	0.0732622i
$177$		0			0
$178$	−9.15788	+	5.28731i	−0.686412	+	0.396300i
$179$	−10.7632			−0.804477			−0.402238	−	0.915535i	$-0.631768\pi$
$179$	−10.7632			−0.804477			−0.402238	+	0.915535i	$0.631768\pi$
$180$		0			0
$181$	−7.84572			−0.583168			−0.291584	−	0.956545i	$-0.594182\pi$
$181$	−7.84572			−0.583168			−0.291584	+	0.956545i	$0.594182\pi$
$182$	20.1180	−	11.6151i	1.49124	−	0.860970i
$183$		0			0
$184$	−11.7185	+	20.2970i	−0.863900	+	1.49632i
$185$		0			0
$186$		0			0
$187$	0.734890	−	0.424289i	0.0537405	−	0.0310271i
$188$		−	0.243594i		−	0.0177659i
$189$		0			0
$190$		0			0
$191$	−2.86627	−	4.96453i	−0.207396	−	0.359221i	0.743497	−	0.668739i	$-0.233166\pi$
$191$	−2.86627	−	4.96453i	−0.207396	−	0.359221i	−0.950894	+	0.309518i	$0.899832\pi$
$192$		0			0
$193$	−7.34595	−	4.24119i	−0.528773	−	0.305287i	0.211744	−	0.977325i	$-0.432086\pi$
$193$	−7.34595	−	4.24119i	−0.528773	−	0.305287i	−0.740517	+	0.672038i	$0.765419\pi$
$194$	−2.29468	+	3.97450i	−0.164748	+	0.285352i
$195$		0			0
$196$	−0.677196	−	1.17294i	−0.0483712	−	0.0837813i
$197$		−	10.6266i		−	0.757110i	−0.925579	−	0.378555i	$-0.876421\pi$
$197$		−	10.6266i		−	0.757110i	0.925579	−	0.378555i	$-0.123579\pi$
$198$		0			0
$199$	18.5784			1.31699			0.658495	−	0.752585i	$-0.271193\pi$
$199$	18.5784			1.31699			0.658495	+	0.752585i	$0.271193\pi$
$200$		0			0
$201$		0			0
$202$	−4.90666	−	2.83286i	−0.345231	−	0.199319i
$203$	−14.1352	−	8.16095i	−0.992095	−	0.572786i
$204$		0			0
$205$		0			0
$206$	6.19767			0.431812
$207$		0			0
$208$		−	17.5874i		−	1.21947i
$209$	−0.552997	−	0.957820i	−0.0382516	−	0.0662538i
$210$		0			0
$211$	−5.22666	+	9.05283i	−0.359818	+	0.623223i	−0.987930	−	0.154900i	$-0.950494\pi$
$211$	−5.22666	+	9.05283i	−0.359818	+	0.623223i	0.628112	+	0.778123i	$0.283828\pi$
$212$	1.68037	+	0.970160i	0.115408	+	0.0666308i
$213$		0			0
$214$	−1.19816	−	2.07528i	−0.0819046	−	0.141863i
$215$		0			0
$216$		0			0
$217$			10.2555i			0.696187i
$218$	−16.4615	+	9.50407i	−1.11492	+	0.643697i
$219$		0			0
$220$		0			0
$221$	−6.64902	+	11.5164i	−0.447261	+	0.774680i
$222$		0			0
$223$	−3.40452	+	1.96560i	−0.227983	+	0.131626i	−0.609641	−	0.792677i	$-0.708687\pi$
$223$	−3.40452	+	1.96560i	−0.227983	+	0.131626i	0.381658	+	0.924304i	$0.375353\pi$
$224$	−3.71822			−0.248434
$225$		0			0
$226$	1.95807			0.130249
$227$	−4.18411	+	2.41570i	−0.277709	+	0.160335i	−0.632386	−	0.774654i	$-0.717924\pi$
$227$	−4.18411	+	2.41570i	−0.277709	+	0.160335i	0.354677	+	0.934989i	$0.384591\pi$
$228$		0			0
$229$	−9.42648	+	16.3271i	−0.622919	+	1.07893i	0.366020	+	0.930607i	$0.380720\pi$
$229$	−9.42648	+	16.3271i	−0.622919	+	1.07893i	−0.988939	+	0.148321i	$0.952613\pi$
$230$		0			0
$231$		0			0
$232$	−9.85539	+	5.69001i	−0.647038	+	0.373568i
$233$		−	11.9021i		−	0.779735i	−0.920871	−	0.389867i	$-0.872521\pi$
$233$		−	11.9021i		−	0.779735i	0.920871	−	0.389867i	$-0.127479\pi$
$234$		0			0
$235$		0			0
$236$	−0.607266	−	1.05181i	−0.0395296	−	0.0684673i
$237$		0			0
$238$	16.0807	+	9.28421i	1.04236	+	0.601806i
$239$	10.8147	−	18.7317i	0.699547	−	1.21165i	−0.269076	−	0.963119i	$-0.586718\pi$
$239$	10.8147	−	18.7317i	0.699547	−	1.21165i	0.968624	−	0.248533i	$-0.0799483\pi$
$240$		0			0
$241$	−1.94916	−	3.37604i	−0.125556	−	0.217470i	0.796394	−	0.604778i	$-0.206738\pi$
$241$	−1.94916	−	3.37604i	−0.125556	−	0.217470i	−0.921950	+	0.387308i	$0.873405\pi$
$242$			16.1060i			1.03533i
$243$		0			0
$244$	−0.430437			−0.0275559
$245$		0			0
$246$		0			0
$247$	15.0100	+	8.66600i	0.955061	+	0.551405i
$248$	6.19240	+	3.57518i	0.393218	+	0.227024i
$249$		0			0
$250$		0			0
$251$	30.1033			1.90010			0.950052	−	0.312092i	$-0.101030\pi$
$251$	30.1033			1.90010			0.950052	+	0.312092i	$0.101030\pi$
$252$		0			0
$253$		−	2.26321i		−	0.142287i
$254$	1.21754	+	2.10883i	0.0763950	+	0.132320i
$255$		0			0
$256$	−2.03131	+	3.51832i	−0.126957	+	0.219895i
$257$	−14.2151	−	8.20707i	−0.886711	−	0.511943i	−0.0138459	−	0.999904i	$-0.504407\pi$
$257$	−14.2151	−	8.20707i	−0.886711	−	0.511943i	−0.872865	+	0.487961i	$0.837741\pi$
$258$		0			0
$259$	−4.39851	−	7.61845i	−0.273310	−	0.473388i
$260$		0			0
$261$		0			0
$262$		−	19.4141i		−	1.19941i
$263$	22.3497	−	12.9036i	1.37814	−	0.795670i	0.386206	−	0.922413i	$-0.373786\pi$
$263$	22.3497	−	12.9036i	1.37814	−	0.795670i	0.991936	+	0.126743i	$0.0404522\pi$
$264$		0			0
$265$		0			0
$266$	12.1006	−	20.9588i	0.741934	−	1.28507i
$267$		0			0
$268$	−1.66619	+	0.961978i	−0.101779	+	0.0587621i
$269$	−12.5206			−0.763392			−0.381696	−	0.924288i	$-0.624660\pi$
$269$	−12.5206			−0.763392			−0.381696	+	0.924288i	$0.624660\pi$
$270$		0			0
$271$	19.6462			1.19342			0.596710	−	0.802457i	$-0.296474\pi$
$271$	19.6462			1.19342			0.596710	+	0.802457i	$0.296474\pi$
$272$	12.1746	−	7.02899i	0.738191	−	0.426195i
$273$		0			0
$274$	14.9483	−	25.8911i	0.903057	−	1.56414i
$275$		0			0
$276$		0			0
$277$	−18.0394	+	10.4150i	−1.08388	+	0.625779i	−0.931941	−	0.362610i	$-0.881886\pi$
$277$	−18.0394	+	10.4150i	−1.08388	+	0.625779i	−0.151941	+	0.988390i	$0.548552\pi$
$278$			4.52112i			0.271159i
$279$		0			0
$280$		0			0
$281$	2.36221	+	4.09146i	0.140917	+	0.244076i	0.927842	−	0.372973i	$-0.121661\pi$
$281$	2.36221	+	4.09146i	0.140917	+	0.244076i	−0.786925	+	0.617049i	$0.788328\pi$
$282$		0			0
$283$	20.0506	+	11.5762i	1.19189	+	0.688136i	0.958734	−	0.284304i	$-0.0917626\pi$
$283$	20.0506	+	11.5762i	1.19189	+	0.688136i	0.233152	+	0.972440i	$0.425096\pi$
$284$	0.714441	−	1.23745i	0.0423943	−	0.0734291i
$285$		0			0
$286$	0.782020	+	1.35450i	0.0462418	+	0.0800932i
$287$		−	21.8105i		−	1.28743i
$288$		0			0
$289$	6.37059			0.374740
$290$		0			0
$291$		0			0
$292$	−0.0595824	−	0.0343999i	−0.00348679	−	0.00201310i
$293$	14.6179	+	8.43963i	0.853985	+	0.493049i	0.861993	−	0.506919i	$-0.169216\pi$
$293$	14.6179	+	8.43963i	0.853985	+	0.493049i	−0.00800832	+	0.999968i	$0.502549\pi$
$294$		0			0
$295$		0			0
$296$	−6.13350			−0.356503
$297$		0			0
$298$		−	5.98380i		−	0.346632i
$299$	17.7333	+	30.7150i	1.02554	+	1.77630i
$300$		0			0
$301$	17.5366	−	30.3743i	1.01079	−	1.75074i
$302$	−17.3773	−	10.0328i	−0.999949	−	0.577321i
$303$		0			0
$304$	−9.16123	−	15.8677i	−0.525433	−	0.910076i
$305$		0			0
$306$		0			0
$307$		−	22.7177i		−	1.29657i	−0.761398	−	0.648285i	$-0.775487\pi$
$307$		−	22.7177i		−	1.29657i	0.761398	−	0.648285i	$-0.224513\pi$
$308$	0.148553	−	0.0857671i	0.00846459	−	0.00488703i
$309$		0			0
$310$		0			0
$311$	15.7968	−	27.3608i	0.895754	−	1.55149i	0.0628843	−	0.998021i	$-0.479970\pi$
$311$	15.7968	−	27.3608i	0.895754	−	1.55149i	0.832869	−	0.553470i	$-0.186697\pi$
$312$		0			0
$313$	26.4134	−	15.2498i	1.49298	−	0.861970i	0.493009	−	0.870024i	$-0.335897\pi$
$313$	26.4134	−	15.2498i	1.49298	−	0.861970i	0.999968	+	0.00805392i	$0.00256367\pi$
$314$	3.03875			0.171487
$315$		0			0
$316$	−0.518682			−0.0291781
$317$	−19.1296	+	11.0445i	−1.07443	+	0.620320i	−0.929387	−	0.369106i	$-0.879664\pi$
$317$	−19.1296	+	11.0445i	−1.07443	+	0.620320i	−0.145039	+	0.989426i	$0.546331\pi$
$318$		0			0
$319$	0.549459	−	0.951691i	0.0307638	−	0.0532845i
$320$		0			0
$321$		0			0
$322$	42.8882	−	24.7615i	2.39007	−	1.37991i
$323$			13.8538i			0.770849i
$324$		0			0
$325$		0			0
$326$	−2.58206	−	4.47226i	−0.143007	−	0.247696i
$327$		0			0
$328$	−13.1695	−	7.60339i	−0.727162	−	0.419827i
$329$	2.76191	−	4.78377i	0.152269	−	0.263738i
$330$		0			0
$331$	14.8024	+	25.6385i	0.813612	+	1.40922i	0.910321	+	0.413904i	$0.135835\pi$
$331$	14.8024	+	25.6385i	0.813612	+	1.40922i	−0.0967089	+	0.995313i	$0.530832\pi$
$332$		−	0.780834i		−	0.0428538i
$333$		0			0
$334$	−30.2531			−1.65538
$335$		0			0
$336$		0			0
$337$	−10.8522	−	6.26553i	−0.591158	−	0.341305i	0.174397	−	0.984675i	$-0.444202\pi$
$337$	−10.8522	−	6.26553i	−0.591158	−	0.341305i	−0.765555	+	0.643370i	$0.777536\pi$
$338$	−4.63992	−	2.67886i	−0.252379	−	0.145711i
$339$		0			0
$340$		0			0
$341$	−0.690479			−0.0373915
$342$		0			0
$343$		−	3.65180i		−	0.197179i
$344$	−12.2269	−	21.1777i	−0.659232	−	1.14182i
$345$		0			0
$346$	5.71017	−	9.89030i	0.306980	−	0.531706i
$347$	−14.8068	−	8.54872i	−0.794872	−	0.458919i	0.0468031	−	0.998904i	$-0.485097\pi$
$347$	−14.8068	−	8.54872i	−0.794872	−	0.458919i	−0.841675	+	0.539985i	$0.818430\pi$
$348$		0			0
$349$	−9.20231	−	15.9389i	−0.492588	−	0.853188i	0.507375	−	0.861725i	$-0.330616\pi$
$349$	−9.20231	−	15.9389i	−0.492588	−	0.853188i	−0.999964	+	0.00853709i	$0.997283\pi$
$350$		0			0
$351$		0			0
$352$		−	0.250340i		−	0.0133432i
$353$	−27.4693	+	15.8594i	−1.46204	+	0.844110i	−0.999106	−	0.0422810i	$-0.986538\pi$
$353$	−27.4693	+	15.8594i	−1.46204	+	0.844110i	−0.462936	+	0.886391i	$0.653204\pi$
$354$		0			0
$355$		0			0
$356$	0.611825	−	1.05971i	0.0324267	−	0.0561646i
$357$		0			0
$358$	13.7325	−	7.92844i	0.725783	−	0.419031i
$359$	−11.4533			−0.604483			−0.302241	−	0.953231i	$-0.597735\pi$
$359$	−11.4533			−0.604483			−0.302241	+	0.953231i	$0.597735\pi$
$360$		0			0
$361$	−0.943580			−0.0496621
$362$	10.0102	−	5.77937i	0.526122	−	0.303757i
$363$		0			0
$364$	−1.34405	+	2.32797i	−0.0704475	+	0.122019i
$365$		0			0
$366$		0			0
$367$	2.15846	−	1.24619i	0.112671	−	0.0650506i	−0.442606	−	0.896716i	$-0.645946\pi$
$367$	2.15846	−	1.24619i	0.112671	−	0.0650506i	0.555276	+	0.831666i	$0.312612\pi$
$368$		−	37.4934i		−	1.95448i
$369$		0			0
$370$		0			0
$371$	21.9996	+	38.1045i	1.14216	+	1.97829i
$372$		0			0
$373$	−13.0227	−	7.51868i	−0.674292	−	0.389303i	0.123409	−	0.992356i	$-0.460617\pi$
$373$	−13.0227	−	7.51868i	−0.674292	−	0.389303i	−0.797701	+	0.603053i	$0.793951\pi$
$374$	−0.625086	+	1.08268i	−0.0323224	+	0.0559841i
$375$		0			0
$376$	−1.92567	−	3.33536i	−0.0993088	−	0.172008i
$377$			17.2211i			0.886932i
$378$		0			0
$379$	−6.27273			−0.322208			−0.161104	−	0.986937i	$-0.551505\pi$
$379$	−6.27273			−0.322208			−0.161104	+	0.986937i	$0.551505\pi$
$380$		0			0
$381$		0			0
$382$	7.31402	+	4.22275i	0.374218	+	0.216055i
$383$	19.2161	+	11.0944i	0.981894	+	0.566897i	0.902842	−	0.429973i	$-0.141477\pi$
$383$	19.2161	+	11.0944i	0.981894	+	0.566897i	0.0790528	+	0.996870i	$0.474810\pi$
$384$		0			0
$385$		0			0
$386$	12.4967			0.636065
$387$		0			0
$388$		−	0.531061i		−	0.0269605i
$389$	15.0461	+	26.0606i	0.762869	+	1.32133i	0.941366	+	0.337387i	$0.109543\pi$
$389$	15.0461	+	26.0606i	0.762869	+	1.32133i	−0.178498	+	0.983940i	$0.557124\pi$
$390$		0			0
$391$	−14.1746	+	24.5512i	−0.716842	+	1.24161i
$392$	−18.5447	−	10.7068i	−0.936649	−	0.540774i
$393$		0			0
$394$	7.82781	+	13.5582i	0.394359	+	0.683050i
$395$		0			0
$396$		0			0
$397$			29.2313i			1.46708i	0.679648	+	0.733538i	$0.262132\pi$
$397$			29.2313i			1.46708i	−0.679648	+	0.733538i	$0.737868\pi$
$398$	−23.7038	+	13.6854i	−1.18816	+	0.685986i
$399$		0			0
$400$		0			0
$401$	12.1171	−	20.9874i	0.605098	−	1.04806i	−0.386938	−	0.922106i	$-0.626467\pi$
$401$	12.1171	−	20.9874i	0.605098	−	1.04806i	0.992036	−	0.125954i	$-0.0401993\pi$
$402$		0			0
$403$	9.37080	−	5.41024i	0.466793	−	0.269503i
$404$	0.655614			0.0326180
$405$		0			0
$406$	24.0463			1.19340
$407$	0.512934	−	0.296142i	0.0254252	−	0.0146792i
$408$		0			0
$409$	1.16995	−	2.02642i	0.0578504	−	0.100200i	−0.835650	−	0.549263i	$-0.814909\pi$
$409$	1.16995	−	2.02642i	0.0578504	−	0.100200i	0.893500	+	0.449063i	$0.148242\pi$
$410$		0			0
$411$		0			0
$412$	−0.621086	+	0.358584i	−0.0305987	+	0.0176662i
$413$		−	27.5411i		−	1.35521i
$414$		0			0
$415$		0			0
$416$	1.96153	+	3.39748i	0.0961721	+	0.166575i
$417$		0			0
$418$	1.41111	+	0.814706i	0.0690197	+	0.0398486i
$419$	−11.4212	+	19.7821i	−0.557964	+	0.966421i	0.439703	+	0.898143i	$0.355084\pi$
$419$	−11.4212	+	19.7821i	−0.557964	+	0.966421i	−0.997666	+	0.0682778i	$0.978250\pi$
$420$		0			0
$421$	−5.93792	−	10.2848i	−0.289396	−	0.501249i	0.684269	−	0.729229i	$-0.260121\pi$
$421$	−5.93792	−	10.2848i	−0.289396	−	0.501249i	−0.973666	+	0.227980i	$0.926788\pi$
$422$		−	15.4004i		−	0.749679i
$423$		0			0
$424$	30.6773			1.48982
$425$		0			0
$426$		0			0
$427$	−8.45303	−	4.88036i	−0.409071	−	0.236177i
$428$	0.240142	+	0.138646i	0.0116077	+	0.00670172i
$429$		0			0
$430$		0			0
$431$	−8.86916			−0.427212			−0.213606	−	0.976920i	$-0.568521\pi$
$431$	−8.86916			−0.427212			−0.213606	+	0.976920i	$0.568521\pi$
$432$		0			0
$433$		−	9.37059i		−	0.450322i	−0.974322	−	0.225161i	$-0.927709\pi$
$433$		−	9.37059i		−	0.450322i	0.974322	−	0.225161i	$-0.0722908\pi$
$434$	−7.55446	−	13.0847i	−0.362626	−	0.628086i
$435$		0			0
$436$	1.09977	−	1.90486i	0.0526695	−	0.0912262i
$437$	31.9988	+	18.4745i	1.53071	+	0.883756i
$438$		0			0
$439$	9.71155	+	16.8209i	0.463507	+	0.802817i	0.999133	−	0.0416380i	$-0.0132576\pi$
$439$	9.71155	+	16.8209i	0.463507	+	0.802817i	−0.535626	+	0.844455i	$0.679924\pi$
$440$		0			0
$441$		0			0
$442$		−	19.5914i		−	0.931868i
$443$	9.42172	−	5.43963i	0.447639	−	0.258445i	−0.259193	−	0.965825i	$-0.583457\pi$
$443$	9.42172	−	5.43963i	0.447639	−	0.258445i	0.706833	+	0.707381i	$0.250123\pi$
$444$		0			0
$445$		0			0
$446$	2.89583	−	5.01572i	0.137121	−	0.237501i
$447$		0			0
$448$	−24.1276	+	13.9301i	−1.13992	+	0.658136i
$449$	1.34014			0.0632451			0.0316225	−	0.999500i	$-0.489933\pi$
$449$	1.34014			0.0632451			0.0316225	+	0.999500i	$0.489933\pi$
$450$		0			0
$451$	1.46845			0.0691467
$452$	−0.196224	+	0.113290i	−0.00922959	+	0.00532871i
$453$		0			0
$454$	3.55894	−	6.16426i	0.167029	−	0.289303i
$455$		0			0
$456$		0			0
$457$	17.4169	−	10.0556i	0.814728	−	0.470383i	−0.0338671	−	0.999426i	$-0.510782\pi$
$457$	17.4169	−	10.0556i	0.814728	−	0.470383i	0.848595	+	0.529043i	$0.177449\pi$
$458$		−	27.7752i		−	1.29785i
$459$		0			0
$460$		0			0
$461$	−16.8766	−	29.2312i	−0.786024	−	1.36143i	−0.928386	−	0.371618i	$-0.878803\pi$
$461$	−16.8766	−	29.2312i	−0.786024	−	1.36143i	0.142362	−	0.989815i	$-0.454530\pi$
$462$		0			0
$463$	−4.54262	−	2.62268i	−0.211114	−	0.121886i	0.390715	−	0.920512i	$-0.372228\pi$
$463$	−4.54262	−	2.62268i	−0.211114	−	0.121886i	−0.601829	+	0.798625i	$0.705561\pi$
$464$	9.10262	−	15.7662i	0.422578	−	0.731927i
$465$		0			0
$466$	8.76744	+	15.1856i	0.406144	+	0.703462i
$467$		−	14.2120i		−	0.657652i	−0.944390	−	0.328826i	$-0.893347\pi$
$467$		−	14.2120i		−	0.657652i	0.944390	−	0.328826i	$-0.106653\pi$
$468$		0			0
$469$	−43.6282			−2.01456
$470$		0			0
$471$		0			0
$472$	−16.6297	−	9.60115i	−0.765443	−	0.441929i
$473$	2.04503	+	1.18070i	0.0940307	+	0.0542887i
$474$		0			0
$475$		0			0
$476$	−2.14866			−0.0984837
$477$		0			0
$478$			31.8657i			1.45750i
$479$	−10.2417	−	17.7391i	−0.467954	−	0.810519i	0.531376	−	0.847136i	$-0.321675\pi$
$479$	−10.2417	−	17.7391i	−0.467954	−	0.810519i	−0.999329	+	0.0366168i	$0.988342\pi$
$480$		0			0
$481$	−4.64084	+	8.03817i	−0.211604	+	0.366509i
$482$	4.97377	+	2.87161i	0.226549	+	0.130798i
$483$		0			0
$484$	−0.931859	−	1.61403i	−0.0423572	−	0.0733649i
$485$		0			0
$486$		0			0
$487$			31.3554i			1.42085i	0.703772	+	0.710425i	$0.251497\pi$
$487$			31.3554i			1.42085i	−0.703772	+	0.710425i	$0.748503\pi$
$488$	−5.89366	+	3.40271i	−0.266793	+	0.154033i
$489$		0			0
$490$		0			0
$491$	−5.19604	+	8.99980i	−0.234494	+	0.406155i	−0.959125	−	0.282981i	$-0.908677\pi$
$491$	−5.19604	+	8.99980i	−0.234494	+	0.406155i	0.724632	+	0.689136i	$0.242010\pi$
$492$		0			0
$493$	−11.9210	+	6.88260i	−0.536896	+	0.309977i
$494$	−25.5345			−1.14885
$495$		0			0
$496$	−11.4388			−0.513618
$497$	28.0607	−	16.2009i	1.25870	−	0.726709i
$498$		0			0
$499$	−1.91285	+	3.31316i	−0.0856310	+	0.148317i	−0.905660	−	0.424005i	$-0.860624\pi$
$499$	−1.91285	+	3.31316i	−0.0856310	+	0.148317i	0.820029	+	0.572322i	$0.193957\pi$
$500$		0			0
$501$		0			0
$502$	−38.4081	+	22.1749i	−1.71424	+	0.989715i
$503$			1.00236i			0.0446931i	0.999750	+	0.0223466i	$0.00711372\pi$
$503$			1.00236i			0.0446931i	−0.999750	+	0.0223466i	$0.992886\pi$
$504$		0			0
$505$		0			0
$506$	1.66714	+	2.88757i	0.0741134	+	0.128368i
$507$		0			0
$508$	−0.244026	−	0.140888i	−0.0108269	−	0.00625090i
$509$	−2.28161	+	3.95187i	−0.101131	+	0.175163i	−0.912151	−	0.409855i	$-0.865579\pi$
$509$	−2.28161	+	3.95187i	−0.101131	+	0.175163i	0.811020	+	0.585018i	$0.198913\pi$
$510$		0			0
$511$	−0.780062	−	1.35111i	−0.0345079	−	0.0597695i
$512$			19.0969i			0.843971i
$513$		0			0
$514$	24.1822			1.06663
$515$		0			0
$516$		0			0
$517$	0.322080	+	0.185953i	0.0141651	+	0.00817822i
$518$	11.2239	+	6.48013i	0.493151	+	0.284721i
$519$		0			0
$520$		0			0
$521$	−39.3708			−1.72486			−0.862432	−	0.506173i	$-0.831060\pi$
$521$	−39.3708			−1.72486			−0.862432	+	0.506173i	$0.831060\pi$
$522$		0			0
$523$			10.3998i			0.454749i	0.973807	+	0.227375i	$0.0730142\pi$
$523$			10.3998i			0.454749i	−0.973807	+	0.227375i	$0.926986\pi$
$524$	1.12326	+	1.94555i	0.0490699	+	0.0849916i
$525$		0			0
$526$	−19.0103	+	32.9268i	−0.828888	+	1.43568i
$527$	7.49029	+	4.32452i	0.326282	+	0.188379i
$528$		0			0
$529$	26.3046	+	45.5608i	1.14368	+	1.98091i
$530$		0			0
$531$		0			0
$532$			2.80046i			0.121415i
$533$	−19.9290	+	11.5060i	−0.863222	+	0.498381i
$534$		0			0
$535$		0			0
$536$	−15.2093	+	26.3433i	−0.656942	+	1.13786i
$537$		0			0
$538$	15.9747	−	9.22298i	0.688717	−	0.397631i
$539$	2.06781			0.0890670
$540$		0			0
$541$	13.7093			0.589408			0.294704	−	0.955589i	$-0.404779\pi$
$541$	13.7093			0.589408			0.294704	+	0.955589i	$0.404779\pi$
$542$	−25.0661	+	14.4719i	−1.07668	+	0.621622i
$543$		0			0
$544$	−1.56790	+	2.71568i	−0.0672230	+	0.116434i
$545$		0			0
$546$		0			0
$547$	19.7322	−	11.3924i	0.843686	−	0.487102i	−0.0148294	−	0.999890i	$-0.504721\pi$
$547$	19.7322	−	11.3924i	0.843686	−	0.487102i	0.858515	+	0.512788i	$0.171387\pi$
$548$			3.45950i			0.147783i
$549$		0			0
$550$		0			0
$551$	8.97044	+	15.5373i	0.382154	+	0.661910i
$552$		0			0
$553$	−10.1860	−	5.88089i	−0.433153	−	0.250081i
$554$	15.3440	−	26.5766i	0.651905	−	1.12913i
$555$		0			0
$556$	−0.261583	−	0.453075i	−0.0110936	−	0.0192146i
$557$			18.2341i			0.772605i	0.922372	+	0.386303i	$0.126248\pi$
$557$			18.2341i			0.772605i	−0.922372	+	0.386303i	$0.873752\pi$
$558$		0			0
$559$	−37.0054			−1.56516
$560$		0			0
$561$		0			0
$562$	−6.02776	−	3.48013i	−0.254266	−	0.146800i
$563$	−20.8809	−	12.0556i	−0.880025	−	0.508083i	−0.00935862	−	0.999956i	$-0.502979\pi$
$563$	−20.8809	−	12.0556i	−0.880025	−	0.508083i	−0.870667	+	0.491873i	$0.836312\pi$
$564$		0			0
$565$		0			0
$566$	−34.1095			−1.43373
$567$		0			0
$568$		−	22.5913i		−	0.947910i
$569$	16.0024	+	27.7170i	0.670857	+	1.16196i	0.977661	+	0.210186i	$0.0674069\pi$
$569$	16.0024	+	27.7170i	0.670857	+	1.16196i	−0.306804	+	0.951773i	$0.599260\pi$
$570$		0			0
$571$	9.89042	−	17.1307i	0.413901	−	0.716898i	−0.581411	−	0.813610i	$-0.697499\pi$
$571$	9.89042	−	17.1307i	0.413901	−	0.716898i	0.995312	+	0.0967121i	$0.0308326\pi$
$572$	−0.156737	−	0.0904921i	−0.00655350	−	0.00378367i
$573$		0			0
$574$	16.0662	+	27.8274i	0.670589	+	1.16150i
$575$		0			0
$576$		0			0
$577$		−	35.4119i		−	1.47422i	−0.675775	−	0.737108i	$-0.736191\pi$
$577$		−	35.4119i		−	1.47422i	0.675775	−	0.737108i	$-0.263809\pi$
$578$	−8.12808	+	4.69275i	−0.338084	+	0.195193i
$579$		0			0
$580$		0			0
$581$	8.85321	−	15.3342i	0.367293	−	0.636170i
$582$		0			0
$583$	−2.56549	+	1.48119i	−0.106252	+	0.0613445i
$584$	−1.08776			−0.0450117
$585$		0			0
$586$	−24.8675			−1.02726
$587$	28.0463	−	16.1925i	1.15759	−	0.668338i	0.206868	−	0.978369i	$-0.433673\pi$
$587$	28.0463	−	16.1925i	1.15759	−	0.668338i	0.950726	+	0.310031i	$0.100339\pi$
$588$		0			0
$589$	5.63636	−	9.76247i	0.232242	−	0.402255i
$590$		0			0
$591$		0			0
$592$	8.49752	−	4.90605i	0.349246	−	0.201637i
$593$			29.2504i			1.20117i	0.799561	+	0.600585i	$0.205066\pi$
$593$			29.2504i			1.20117i	−0.799561	+	0.600585i	$0.794934\pi$
$594$		0			0
$595$		0			0
$596$	0.346210	+	0.599654i	0.0141813	+	0.0245628i
$597$		0			0
$598$	−45.2510	−	26.1257i	−1.85045	−	1.06836i
$599$	−2.03081	+	3.51747i	−0.0829767	+	0.143720i	−0.904527	−	0.426416i	$-0.859776\pi$
$599$	−2.03081	+	3.51747i	−0.0829767	+	0.143720i	0.821551	+	0.570136i	$0.193109\pi$
$600$		0			0
$601$	−23.4538	−	40.6232i	−0.956700	−	1.65705i	−0.730429	−	0.682989i	$-0.760680\pi$
$601$	−23.4538	−	40.6232i	−0.956700	−	1.65705i	−0.226271	−	0.974064i	$-0.572653\pi$
$602$			51.6717i			2.10598i
$603$		0			0
$604$	2.32190			0.0944768
$605$		0			0
$606$		0			0
$607$	35.4608	+	20.4733i	1.43931	+	0.830987i	0.997802	−	0.0662702i	$-0.0211099\pi$
$607$	35.4608	+	20.4733i	1.43931	+	0.830987i	0.441509	+	0.897257i	$0.354443\pi$
$608$	3.53948	+	2.04352i	0.143545	+	0.0828756i
$609$		0			0
$610$		0			0
$611$	−5.82813			−0.235781
$612$		0			0
$613$			33.3827i			1.34831i	0.738588	+	0.674157i	$0.235493\pi$
$613$			33.3827i			1.34831i	−0.738588	+	0.674157i	$0.764507\pi$
$614$	16.7345	+	28.9850i	0.675350	+	1.16974i
$615$		0			0
$616$	1.35602	−	2.34869i	0.0546355	−	0.0946314i
$617$	1.94752	+	1.12440i	0.0784040	+	0.0452666i	0.538689	−	0.842504i	$-0.318920\pi$
$617$	1.94752	+	1.12440i	0.0784040	+	0.0452666i	−0.460285	+	0.887771i	$0.652253\pi$
$618$		0			0
$619$	−17.1467	−	29.6990i	−0.689184	−	1.19370i	−0.972102	−	0.234558i	$-0.924636\pi$
$619$	−17.1467	−	29.6990i	−0.689184	−	1.19370i	0.282918	−	0.959144i	$-0.408698\pi$
$620$		0			0
$621$		0			0
$622$			46.5454i			1.86630i
$623$	24.0303	−	13.8739i	0.962756	−	0.555847i
$624$		0			0
$625$		0			0
$626$	−22.4669	+	38.9137i	−0.897956	+	1.55531i
$627$		0			0
$628$	−0.304522	+	0.175816i	−0.0121517	+	0.00701581i
$629$	−7.41904			−0.295817
$630$		0			0
$631$	−18.7552			−0.746633			−0.373316	−	0.927704i	$-0.621779\pi$
$631$	−18.7552			−0.746633			−0.373316	+	0.927704i	$0.621779\pi$
$632$	−7.10193	+	4.10030i	−0.282499	+	0.163101i
$633$		0			0
$634$	16.2713	−	28.1828i	0.646218	−	1.11928i
$635$		0			0
$636$		0			0
$637$	−28.0632	+	16.2023i	−1.11191	+	0.641959i
$638$			1.61899i			0.0640963i
$639$		0			0
$640$		0			0
$641$	10.3175	+	17.8704i	0.407517	+	0.705840i	0.994611	−	0.103679i	$-0.0330614\pi$
$641$	10.3175	+	17.8704i	0.407517	+	0.705840i	−0.587094	+	0.809519i	$0.699728\pi$
$642$		0			0
$643$	23.5506	+	13.5970i	0.928746	+	0.536212i	0.886415	−	0.462892i	$-0.153188\pi$
$643$	23.5506	+	13.5970i	0.928746	+	0.536212i	0.0423312	+	0.999104i	$0.486522\pi$
$644$	−2.86530	+	4.96285i	−0.112909	+	0.195564i
$645$		0			0
$646$	−10.2051	−	17.6758i	−0.401515	−	0.695445i
$647$		−	16.7316i		−	0.657787i	−0.944367	−	0.328893i	$-0.893324\pi$
$647$		−	16.7316i		−	0.657787i	0.944367	−	0.328893i	$-0.106676\pi$
$648$		0			0
$649$	1.85428			0.0727869
$650$		0			0
$651$		0			0
$652$	0.517511	+	0.298785i	0.0202673	+	0.0117013i
$653$	39.6060	+	22.8666i	1.54990	+	0.894837i	0.998148	+	0.0608319i	$0.0193754\pi$
$653$	39.6060	+	22.8666i	1.54990	+	0.894837i	0.551756	+	0.834006i	$0.313958\pi$
$654$		0			0
$655$		0			0
$656$	24.3271			0.949814
$657$		0			0
$658$			8.13799i			0.317252i
$659$	−9.30543	−	16.1175i	−0.362488	−	0.627848i	0.625882	−	0.779918i	$-0.284739\pi$
$659$	−9.30543	−	16.1175i	−0.362488	−	0.627848i	−0.988370	+	0.152070i	$0.951406\pi$
$660$		0			0
$661$	−8.39799	+	14.5457i	−0.326644	+	0.565764i	−0.981844	−	0.189692i	$-0.939251\pi$
$661$	−8.39799	+	14.5457i	−0.326644	+	0.565764i	0.655200	+	0.755456i	$0.272584\pi$
$662$	−37.7720	−	21.8077i	−1.46805	−	0.847579i
$663$		0			0
$664$	−6.17267	−	10.6914i	−0.239546	−	0.414906i
$665$		0			0
$666$		0			0
$667$			36.7126i			1.42152i
$668$	3.03175	−	1.75038i	0.117302	−	0.0677243i
$669$		0			0
$670$		0			0
$671$	0.328584	−	0.569124i	0.0126848	−	0.0219708i
$672$		0			0
$673$	−43.2562	+	24.9740i	−1.66740	+	0.962676i	−0.698374	+	0.715733i	$0.746093\pi$
$673$	−43.2562	+	24.9740i	−1.66740	+	0.962676i	−0.969030	+	0.246944i	$0.920574\pi$
$674$	18.4614			0.711108
$675$		0			0
$676$	0.619973			0.0238451
$677$	−9.37998	+	5.41553i	−0.360502	+	0.208136i	−0.669301	−	0.742991i	$-0.733406\pi$
$677$	−9.37998	+	5.41553i	−0.360502	+	0.208136i	0.308799	+	0.951127i	$0.400073\pi$
$678$		0			0
$679$	6.02125	−	10.4291i	0.231074	−	0.400232i
$680$		0			0
$681$		0			0
$682$	0.880965	−	0.508625i	0.0337339	−	0.0194763i
$683$			0.429870i			0.0164485i	0.999966	+	0.00822426i	$0.00261789\pi$
$683$			0.429870i			0.0164485i	−0.999966	+	0.00822426i	$0.997382\pi$
$684$		0			0
$685$		0			0
$686$	2.69001	+	4.65924i	0.102705	+	0.177891i
$687$		0			0
$688$	33.8791	+	19.5601i	1.29163	+	0.745721i
$689$	23.2116	−	40.2037i	0.884293	−	1.53164i
$690$		0			0
$691$	−17.3518	−	30.0542i	−0.660093	−	1.14331i	−0.980591	−	0.196065i	$-0.937184\pi$
$691$	−17.3518	−	30.0542i	−0.660093	−	1.14331i	0.320498	−	0.947249i	$-0.396150\pi$
$692$			1.32151i			0.0502364i
$693$		0			0
$694$	25.1889			0.956157
$695$		0			0
$696$		0			0
$697$	−15.9297	−	9.19701i	−0.603380	−	0.348362i
$698$	23.4820	+	13.5573i	0.888807	+	0.513153i
$699$		0			0
$700$		0			0
$701$	−1.84808			−0.0698010			−0.0349005	−	0.999391i	$-0.511111\pi$
$701$	−1.84808			−0.0698010			−0.0349005	+	0.999391i	$0.511111\pi$
$702$		0			0
$703$			9.66962i			0.364696i
$704$	−0.937884	−	1.62446i	−0.0353478	−	0.0612242i
$705$		0			0
$706$	23.3649	−	40.4692i	0.879351	−	1.52308i
$707$	12.8751	+	7.43344i	0.484218	+	0.279563i
$708$		0			0
$709$	−3.15338	−	5.46181i	−0.118428	−	0.205123i	0.800717	−	0.599043i	$-0.204452\pi$
$709$	−3.15338	−	5.46181i	−0.118428	−	0.205123i	−0.919145	+	0.393920i	$0.871119\pi$
$710$		0			0
$711$		0			0
$712$		−	19.3465i		−	0.725040i
$713$	19.9770	−	11.5337i	0.748145	−	0.431942i
$714$		0			0
$715$		0			0
$716$	−0.917446	+	1.58906i	−0.0342866	+	0.0593861i
$717$		0			0
$718$	14.6130	−	8.43682i	0.545352	−	0.314859i
$719$	18.0129			0.671770			0.335885	−	0.941903i	$-0.390965\pi$
$719$	18.0129			0.671770			0.335885	+	0.941903i	$0.390965\pi$
$720$		0			0
$721$	−16.2627			−0.605655
$722$	1.20389	−	0.695067i	0.0448042	−	0.0258677i
$723$		0			0
$724$	−0.668765	+	1.15833i	−0.0248544	+	0.0430491i
$725$		0			0
$726$		0			0
$727$	22.7612	−	13.1412i	0.844165	−	0.487379i	−0.0145126	−	0.999895i	$-0.504620\pi$
$727$	22.7612	−	13.1412i	0.844165	−	0.487379i	0.858678	+	0.512516i	$0.171286\pi$
$728$			42.5002i			1.57516i
$729$		0			0
$730$		0			0
$731$	−14.7896	−	25.6164i	−0.547014	−	0.947456i
$732$		0			0
$733$	41.2777	+	23.8317i	1.52462	+	0.880243i	0.999574	+	0.0291714i	$0.00928687\pi$
$733$	41.2777	+	23.8317i	1.52462	+	0.880243i	0.525050	+	0.851071i	$0.324046\pi$
$734$	−1.83595	+	3.17997i	−0.0677663	+	0.117375i
$735$		0			0
$736$	4.18167	+	7.24287i	0.154138	+	0.266976i
$737$		−	2.93739i		−	0.108200i
$738$		0			0
$739$	10.0273			0.368859			0.184429	−	0.982846i	$-0.440956\pi$
$739$	10.0273			0.368859			0.184429	+	0.982846i	$0.440956\pi$
$740$		0			0
$741$		0			0
$742$	−56.1376	−	32.4110i	−2.06088	−	1.18985i
$743$	−7.16433	−	4.13633i	−0.262834	−	0.151747i	0.362793	−	0.931870i	$-0.381823\pi$
$743$	−7.16433	−	4.13633i	−0.262834	−	0.151747i	−0.625627	+	0.780123i	$0.715157\pi$
$744$		0			0
$745$		0			0
$746$	22.1539			0.811111
$747$		0			0
$748$		−	0.144665i		−	0.00528946i
$749$	3.14398	+	5.44554i	0.114879	+	0.198976i
$750$		0			0
$751$	2.89880	−	5.02087i	0.105779	−	0.183214i	−0.808277	−	0.588802i	$-0.799600\pi$
$751$	2.89880	−	5.02087i	0.105779	−	0.183214i	0.914056	+	0.405588i	$0.132933\pi$
$752$	5.33575	+	3.08060i	0.194575	+	0.112338i
$753$		0			0
$754$	−12.6855	−	21.9720i	−0.461980	−	0.800173i
$755$		0			0
$756$		0			0
$757$		−	25.2804i		−	0.918830i	−0.888222	−	0.459415i	$-0.848059\pi$
$757$		−	25.2804i		−	0.918830i	0.888222	−	0.459415i	$-0.151941\pi$
$758$	8.00322	−	4.62066i	0.290690	−	0.167830i
$759$		0			0
$760$		0			0
$761$	9.73190	−	16.8561i	0.352781	−	0.611035i	−0.633954	−	0.773370i	$-0.718569\pi$
$761$	9.73190	−	16.8561i	0.352781	−	0.611035i	0.986736	+	0.162335i	$0.0519027\pi$
$762$		0			0
$763$	43.1951	−	24.9387i	1.56377	−	0.902843i
$764$	−0.977278			−0.0353567
$765$		0			0
$766$	−32.6897			−1.18113
$767$	−25.1653	+	14.5292i	−0.908666	+	0.524618i
$768$		0			0
$769$	−24.6715	+	42.7324i	−0.889678	+	1.54097i	−0.0494224	+	0.998778i	$0.515738\pi$
$769$	−24.6715	+	42.7324i	−0.889678	+	1.54097i	−0.840256	+	0.542190i	$0.817595\pi$
$770$		0			0
$771$		0			0
$772$	−1.25233	+	0.723033i	−0.0450723	+	0.0260225i
$773$			20.8502i			0.749930i	0.927039	+	0.374965i	$0.122345\pi$
$773$			20.8502i			0.749930i	−0.927039	+	0.374965i	$0.877655\pi$
$774$		0			0
$775$		0			0
$776$	−4.19816	−	7.27143i	−0.150705	−	0.261029i
$777$		0			0
$778$	−38.3940	−	22.1668i	−1.37649	−	0.794717i
$779$	−11.9869	+	20.7620i	−0.429476	+	0.743875i
$780$		0			0
$781$	1.09077	+	1.88927i	0.0390308	+	0.0676034i
$782$		−	41.7657i		−	1.49354i
$783$		0			0
$784$	34.2564			1.22344
$785$		0			0
$786$		0			0
$787$	38.2682	+	22.0941i	1.36411	+	0.787571i	0.990169	−	0.139880i	$-0.0446715\pi$
$787$	38.2682	+	22.0941i	1.36411	+	0.787571i	0.373945	+	0.927451i	$0.378005\pi$
$788$	−1.56889	−	0.905801i	−0.0558895	−	0.0322678i
$789$		0			0
$790$		0			0
$791$	−5.13799			−0.182686
$792$		0			0
$793$			10.2985i			0.365709i
$794$	−21.5326	−	37.2955i	−0.764162	−	1.32357i
$795$		0			0
$796$	1.58362	−	2.74290i	0.0561297	−	0.0972196i
$797$	26.8792	+	15.5187i	0.952110	+	0.549701i	0.893736	−	0.448594i	$-0.148075\pi$
$797$	26.8792	+	15.5187i	0.952110	+	0.549701i	0.0583744	+	0.998295i	$0.481408\pi$
$798$		0			0
$799$	−2.32928	−	4.03443i	−0.0824039	−	0.142728i
$800$		0			0
$801$		0			0
$802$			35.7031i			1.26072i
$803$	0.0909671	−	0.0525199i	0.00321016	−	0.00185339i
$804$		0			0
$805$		0			0
$806$	−7.97065	+	13.8056i	−0.280754	+	0.486281i
$807$		0			0
$808$	8.97683	−	5.18278i	0.315804	−	0.182329i
$809$	14.6229			0.514114			0.257057	−	0.966396i	$-0.417247\pi$
$809$	14.6229			0.514114			0.257057	+	0.966396i	$0.417247\pi$
$810$		0			0
$811$	26.7177			0.938187			0.469093	−	0.883149i	$-0.344581\pi$
$811$	26.7177			0.938187			0.469093	+	0.883149i	$0.344581\pi$
$812$	−2.40975	+	1.39127i	−0.0845656	+	0.0488240i
$813$		0			0
$814$	−0.436293	+	0.755682i	−0.0152921	+	0.0264866i
$815$		0			0
$816$		0			0
$817$	−33.3871	+	19.2761i	−1.16807	+	0.674384i
$818$			3.44727i			0.120531i
$819$		0			0
$820$		0			0
$821$	−9.29903	−	16.1064i	−0.324538	−	0.562117i	0.656881	−	0.753995i	$-0.271876\pi$
$821$	−9.29903	−	16.1064i	−0.324538	−	0.562117i	−0.981419	+	0.191878i	$0.938542\pi$
$822$		0			0
$823$	−2.65181	−	1.53102i	−0.0924362	−	0.0533680i	0.453069	−	0.891475i	$-0.350329\pi$
$823$	−2.65181	−	1.53102i	−0.0924362	−	0.0533680i	−0.545506	+	0.838107i	$0.683662\pi$
$824$	−5.66938	+	9.81966i	−0.197502	+	0.342084i
$825$		0			0
$826$	20.2875	+	35.1390i	0.705892	+	1.22264i
$827$		−	7.27526i		−	0.252985i	−0.991968	−	0.126493i	$-0.959628\pi$
$827$		−	7.27526i		−	0.252985i	0.991968	−	0.126493i	$-0.0403720\pi$
$828$		0			0
$829$	−10.5211			−0.365411			−0.182706	−	0.983168i	$-0.558486\pi$
$829$	−10.5211			−0.365411			−0.182706	+	0.983168i	$0.558486\pi$
$830$		0			0
$831$		0			0
$832$	25.4569	+	14.6975i	0.882559	+	0.509546i
$833$	−22.4315	−	12.9509i	−0.777207	−	0.448721i
$834$		0			0
$835$		0			0
$836$	−0.188549			−0.00652109
$837$		0			0
$838$		−	33.6528i		−	1.16252i
$839$	−7.59033	−	13.1468i	−0.262047	−	0.453879i	0.704739	−	0.709467i	$-0.251064\pi$
$839$	−7.59033	−	13.1468i	−0.262047	−	0.453879i	−0.966786	+	0.255588i	$0.917731\pi$
$840$		0			0
$841$	5.58695	−	9.67689i	0.192654	−	0.333686i
$842$	15.1521	+	8.74806i	0.522176	+	0.301478i
$843$		0			0
$844$	0.891034	+	1.54332i	0.0306707	+	0.0531232i
$845$		0			0
$846$		0			0
$847$		−	42.2622i		−	1.45215i
$848$	−42.5012	+	24.5381i	−1.45950	+	0.842641i
$849$		0			0
$850$		0			0
$851$	−9.89351	+	17.1361i	−0.339145	+	0.587417i
$852$		0			0
$853$	−9.08131	+	5.24309i	−0.310938	+	0.179520i	−0.647346	−	0.762196i	$-0.724121\pi$
$853$	−9.08131	+	5.24309i	−0.310938	+	0.179520i	0.336408	+	0.941716i	$0.390788\pi$
$854$	14.3800			0.492074
$855$		0			0
$856$	4.38412			0.149846
$857$	7.65631	−	4.42038i	0.261535	−	0.150997i	−0.363500	−	0.931594i	$-0.618418\pi$
$857$	7.65631	−	4.42038i	0.261535	−	0.150997i	0.625034	+	0.780597i	$0.285085\pi$
$858$		0			0
$859$	−1.03416	+	1.79121i	−0.0352849	+	0.0611153i	−0.883129	−	0.469131i	$-0.844567\pi$
$859$	−1.03416	+	1.79121i	−0.0352849	+	0.0611153i	0.847844	+	0.530246i	$0.177901\pi$
$860$		0			0
$861$		0			0
$862$	11.3159	−	6.53326i	0.385423	−	0.222524i
$863$		−	22.4434i		−	0.763984i	−0.924166	−	0.381992i	$-0.875238\pi$
$863$		−	22.4434i		−	0.763984i	0.924166	−	0.381992i	$-0.124762\pi$
$864$		0			0
$865$		0			0
$866$	6.90263	+	11.9557i	0.234561	+	0.406271i
$867$		0			0
$868$	1.51411	+	0.874171i	0.0513922	+	0.0296713i
$869$	0.395947	−	0.685801i	0.0134316	−	0.0232642i
$870$		0			0
$871$	23.0159	+	39.8647i	0.779863	+	1.35076i
$872$		−	34.7758i		−	1.17766i
$873$		0			0
$874$	−54.4353			−1.84130
$875$		0			0
$876$		0			0
$877$	−24.1562	−	13.9466i	−0.815697	−	0.470943i	0.0332332	−	0.999448i	$-0.489420\pi$
$877$	−24.1562	−	13.9466i	−0.815697	−	0.470943i	−0.848930	+	0.528505i	$0.822753\pi$
$878$	−24.7815	−	14.3076i	−0.836334	−	0.482857i
$879$		0			0
$880$		0			0
$881$	9.22153			0.310681			0.155341	−	0.987861i	$-0.450353\pi$
$881$	9.22153			0.310681			0.155341	+	0.987861i	$0.450353\pi$
$882$		0			0
$883$		−	49.2436i		−	1.65718i	−0.559858	−	0.828589i	$-0.689144\pi$
$883$		−	49.2436i		−	1.65718i	0.559858	−	0.828589i	$-0.310856\pi$
$884$	1.13352	+	1.96331i	0.0381243	+	0.0660333i
$885$		0			0
$886$	−8.01396	+	13.8806i	−0.269234	+	0.466328i
$887$	9.32542	+	5.38403i	0.313117	+	0.180778i	0.648320	−	0.761368i	$-0.275472\pi$
$887$	9.32542	+	5.38403i	0.313117	+	0.180778i	−0.335203	+	0.942146i	$0.608805\pi$
$888$		0			0
$889$	−3.19482	−	5.53360i	−0.107151	−	0.185591i
$890$		0			0
$891$		0			0
$892$			0.670187i			0.0224395i
$893$	−5.25827	+	3.03586i	−0.175961	+	0.101591i
$894$		0			0
$895$		0			0
$896$	24.2408	−	41.9863i	0.809829	−	1.40266i
$897$		0			0
$898$	−1.70985	+	0.987183i	−0.0570585	+	0.0329427i
$899$	11.2006			0.373561
$900$		0			0
$901$	37.1071			1.23622
$902$	−1.87356	+	1.08170i	−0.0623828	+	0.0360167i
$903$		0			0
$904$	−1.79116	+	3.10239i	−0.0595733	+	0.103184i
$905$		0			0
$906$		0			0
$907$	−27.6871	+	15.9852i	−0.919336	+	0.530779i	−0.883423	−	0.468576i	$-0.844767\pi$
$907$	−27.6871	+	15.9852i	−0.919336	+	0.530779i	−0.0359130	+	0.999355i	$0.511434\pi$
$908$			0.823651i			0.0273338i
$909$		0			0
$910$		0			0
$911$	−5.04010	−	8.72970i	−0.166986	−	0.289228i	0.770373	−	0.637594i	$-0.220070\pi$
$911$	−5.04010	−	8.72970i	−0.166986	−	0.289228i	−0.937359	+	0.348366i	$0.886737\pi$
$912$		0			0
$913$	1.03242	+	0.596067i	0.0341681	+	0.0197269i
$914$	−14.8145	+	25.6595i	−0.490021	+	0.848741i
$915$		0			0
$916$	1.60702	+	2.78343i	0.0530973	+	0.0919672i
$917$			50.9428i			1.68228i
$918$		0			0
$919$	29.7976			0.982932			0.491466	−	0.870897i	$-0.336461\pi$
$919$	29.7976			0.982932			0.491466	+	0.870897i	$0.336461\pi$
$920$		0			0
$921$		0			0
$922$	43.0650	+	24.8636i	1.41827	+	0.818839i
$923$	−29.6067	−	17.0934i	−0.974516	−	0.562637i
$924$		0			0
$925$		0			0
$926$	7.72776			0.253950
$927$		0			0
$928$			4.06089i			0.133305i
$929$	6.19275	+	10.7262i	0.203178	+	0.351914i	0.949551	−	0.313614i	$-0.101540\pi$
$929$	6.19275	+	10.7262i	0.203178	+	0.351914i	−0.746373	+	0.665528i	$0.768206\pi$
$930$		0			0
$931$	−16.8795	+	29.2362i	−0.553204	+	0.958177i
$932$	−1.75722	−	1.01453i	−0.0575597	−	0.0332321i
$933$		0			0
$934$	10.4689	+	18.1327i	0.342554	+	0.593321i
$935$		0			0
$936$		0			0
$937$		−	44.4280i		−	1.45140i	−0.688012	−	0.725699i	$-0.741516\pi$
$937$		−	44.4280i		−	1.45140i	0.688012	−	0.725699i	$-0.258484\pi$
$938$	55.6641	−	32.1377i	1.81750	−	1.04933i
$939$		0			0
$940$		0			0
$941$	7.66617	−	13.2782i	0.249910	−	0.432857i	−0.713591	−	0.700563i	$-0.752932\pi$
$941$	7.66617	−	13.2782i	0.249910	−	0.432857i	0.963501	+	0.267706i	$0.0862656\pi$
$942$		0			0
$943$	−42.4854	+	24.5290i	−1.38352	+	0.798773i
$944$	30.7189			0.999816
$945$		0			0
$946$	−3.47894			−0.113110
$947$	18.7925	−	10.8498i	0.610673	−	0.352572i	−0.162556	−	0.986699i	$-0.551974\pi$
$947$	18.7925	−	10.8498i	0.610673	−	0.352572i	0.773229	+	0.634127i	$0.218640\pi$
$948$		0			0
$949$	−0.823037	+	1.42554i	−0.0267169	+	0.0462751i
$950$		0			0
$951$		0			0
$952$	−29.4200	+	16.9857i	−0.953509	+	0.550508i
$953$		−	36.9099i		−	1.19563i	−0.801634	−	0.597815i	$-0.796036\pi$
$953$		−	36.9099i		−	1.19563i	0.801634	−	0.597815i	$-0.203964\pi$
$954$		0			0
$955$		0			0
$956$	−1.84368	−	3.19336i	−0.0596290	−	0.103281i
$957$		0			0
$958$	26.1342	+	15.0886i	0.844357	+	0.487490i
$959$	−39.2243	+	67.9385i	−1.26662	+	2.19385i
$960$		0			0
$961$	11.9812	+	20.7520i	0.386490	+	0.669420i
$962$		−	13.6743i		−	0.440876i
$963$		0			0
$964$	−0.664581			−0.0214047
$965$		0			0
$966$		0			0
$967$	−18.4794	−	10.6691i	−0.594258	−	0.343095i	0.172521	−	0.985006i	$-0.444809\pi$
$967$	−18.4794	−	10.6691i	−0.594258	−	0.343095i	−0.766779	+	0.641911i	$0.778142\pi$
$968$	−25.5185	−	14.7331i	−0.820197	−	0.473541i
$969$		0			0
$970$		0			0
$971$	42.5851			1.36662			0.683311	−	0.730128i	$-0.260540\pi$
$971$	42.5851			1.36662			0.683311	+	0.730128i	$0.260540\pi$
$972$		0			0
$973$		−	11.8635i		−	0.380325i
$974$	−23.0973	−	40.0057i	−0.740085	−	1.28186i
$975$		0			0
$976$	5.44349	−	9.42840i	0.174242	−	0.301796i
$977$	−42.3826	−	24.4696i	−1.35594	−	0.782852i	−0.366865	−	0.930274i	$-0.619569\pi$
$977$	−42.3826	−	24.4696i	−1.35594	−	0.782852i	−0.989074	+	0.147423i	$0.952902\pi$
$978$		0			0
$979$	0.934101	+	1.61791i	0.0298540	+	0.0517087i
$980$		0			0
$981$		0			0
$982$		−	15.3102i		−	0.488567i
$983$	31.2712	−	18.0545i	0.997398	−	0.575848i	0.0899205	−	0.995949i	$-0.471339\pi$
$983$	31.2712	−	18.0545i	0.997398	−	0.575848i	0.907477	+	0.420101i	$0.138005\pi$
$984$		0			0
$985$		0			0
$986$	10.1398	−	17.5627i	0.322918	−	0.559310i
$987$		0			0
$988$	2.55888	−	1.47737i	0.0814088	−	0.0470014i
$989$	−78.8896			−2.50854
$990$		0			0
$991$	32.0054			1.01669			0.508343	−	0.861155i	$-0.330258\pi$
$991$	32.0054			1.01669			0.508343	+	0.861155i	$0.330258\pi$
$992$	2.20972	−	1.27578i	0.0701586	−	0.0405061i
$993$		0			0
$994$	−23.8680	+	41.3406i	−0.757048	+	1.31125i
$995$		0			0
$996$		0			0
$997$	44.8324	−	25.8840i	1.41986	−	0.819754i	0.423570	−	0.905863i	$-0.360777\pi$
$997$	44.8324	−	25.8840i	1.41986	−	0.819754i	0.996286	+	0.0861095i	$0.0274435\pi$
$998$		−	5.63624i		−	0.178412i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.k.c.199.3		16
3.2	odd	2		225.2.k.c.49.6		16
5.2	odd	4		675.2.e.c.226.2		8
5.3	odd	4		675.2.e.e.226.3		8
5.4	even	2	inner	675.2.k.c.199.6		16
9.2	odd	6		225.2.k.c.124.3		16
9.4	even	3		2025.2.b.o.649.3		8
9.5	odd	6		2025.2.b.n.649.6		8
9.7	even	3	inner	675.2.k.c.424.6		16
15.2	even	4		225.2.e.e.76.3	yes	8
15.8	even	4		225.2.e.c.76.2	✓	8
15.14	odd	2		225.2.k.c.49.3		16
45.2	even	12		225.2.e.e.151.3	yes	8
45.4	even	6		2025.2.b.o.649.6		8
45.7	odd	12		675.2.e.c.451.2		8
45.13	odd	12		2025.2.a.p.1.2		4
45.14	odd	6		2025.2.b.n.649.3		8
45.22	odd	12		2025.2.a.z.1.3		4
45.23	even	12		2025.2.a.y.1.3		4
45.29	odd	6		225.2.k.c.124.6		16
45.32	even	12		2025.2.a.q.1.2		4
45.34	even	6	inner	675.2.k.c.424.3		16
45.38	even	12		225.2.e.c.151.2	yes	8
45.43	odd	12		675.2.e.e.451.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.2	✓	8	15.8	even	4
225.2.e.c.151.2	yes	8	45.38	even	12
225.2.e.e.76.3	yes	8	15.2	even	4
225.2.e.e.151.3	yes	8	45.2	even	12
225.2.k.c.49.3		16	15.14	odd	2
225.2.k.c.49.6		16	3.2	odd	2
225.2.k.c.124.3		16	9.2	odd	6
225.2.k.c.124.6		16	45.29	odd	6
675.2.e.c.226.2		8	5.2	odd	4
675.2.e.c.451.2		8	45.7	odd	12
675.2.e.e.226.3		8	5.3	odd	4
675.2.e.e.451.3		8	45.43	odd	12
675.2.k.c.199.3		16	1.1	even	1	trivial
675.2.k.c.199.6		16	5.4	even	2	inner
675.2.k.c.424.3		16	45.34	even	6	inner
675.2.k.c.424.6		16	9.7	even	3	inner
2025.2.a.p.1.2		4	45.13	odd	12
2025.2.a.q.1.2		4	45.32	even	12
2025.2.a.y.1.3		4	45.23	even	12
2025.2.a.z.1.3		4	45.22	odd	12
2025.2.b.n.649.3		8	45.14	odd	6
2025.2.b.n.649.6		8	9.5	odd	6
2025.2.b.o.649.3		8	9.4	even	3
2025.2.b.o.649.6		8	45.4	even	6

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27588 + 0.736627i) q^{2} +(0.0852394 - 0.147639i) q^{4} +(3.34791 - 1.93291i) q^{7} -2.69535i q^{8} +O(q^{10})\)	\(q+(-1.27588 + 0.736627i) q^{2} +(0.0852394 - 0.147639i) q^{4} +(3.34791 - 1.93291i) q^{7} -2.69535i q^{8} +(0.130139 + 0.225407i) q^{11} +(-3.53235 - 2.03940i) q^{13} +(-2.84768 + 4.93232i) q^{14} +(2.15595 + 3.73421i) q^{16} -3.26028i q^{17} -4.24928 q^{19} +(-0.332082 - 0.191728i) q^{22} +(-7.53039 - 4.34768i) q^{23} +6.00912 q^{26} -0.659042i q^{28} +(-2.11105 - 3.65644i) q^{29} +(-1.32643 + 2.29744i) q^{31} +(-0.832959 - 0.480909i) q^{32} +(2.40161 + 4.15971i) q^{34} -2.27559i q^{37} +(5.42156 - 3.13014i) q^{38} +(2.82093 - 4.88599i) q^{41} +(7.85712 - 4.53631i) q^{43} +0.0443719 q^{44} +12.8105 q^{46} +(1.23745 - 0.714441i) q^{47} +(3.97232 - 6.88026i) q^{49} +(-0.602191 + 0.347675i) q^{52} +11.3816i q^{53} +(-5.20988 - 9.02378i) q^{56} +(5.38687 + 3.11011i) q^{58} +(3.56212 - 6.16977i) q^{59} +(-1.26244 - 2.18660i) q^{61} -3.90833i q^{62} -7.20679 q^{64} +(-9.77361 - 5.64280i) q^{67} +(-0.481344 - 0.277904i) q^{68} +8.38158 q^{71} -0.403568i q^{73} +(1.67626 + 2.90337i) q^{74} +(-0.362207 + 0.627360i) q^{76} +(0.871386 + 0.503095i) q^{77} +(-1.52125 - 2.63488i) q^{79} +8.31189i q^{82} +(3.96660 - 2.29012i) q^{83} +(-6.68314 + 11.5755i) q^{86} +(0.607551 - 0.350770i) q^{88} +7.17772 q^{89} -15.7680 q^{91} +(-1.28377 + 0.741187i) q^{92} +(-1.05255 + 1.82308i) q^{94} +(2.69777 - 1.55756i) q^{97} +11.7045i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74} - 22 q^{76} - 14 q^{79} - 68 q^{86} - 36 q^{89} - 68 q^{91} + 6 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Introduction

L-functions

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