LMFDB - Embedded newform 1452.2.i.p.1213.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1452,2,Mod(493,1452)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1452.493"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1452, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1452 = 2^{2} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1452.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1,0,8,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5942783735$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1213.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	1452.1213
Dual form			1452.2.i.p.565.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{3} +(3.11803 + 2.26538i) q^{5} +(0.0729490 - 0.224514i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-5.04508 + 3.66547i) q^{13} +(1.19098 - 3.66547i) q^{15} +(1.92705 + 1.40008i) q^{17} +(1.57295 + 4.84104i) q^{19} -0.236068 q^{21} -0.236068 q^{23} +(3.04508 + 9.37181i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-1.38197 + 4.25325i) q^{29} +(5.16312 - 3.75123i) q^{31} +(0.736068 - 0.534785i) q^{35} +(-1.16312 + 3.57971i) q^{37} +(5.04508 + 3.66547i) q^{39} +(-2.92705 - 9.00854i) q^{41} -9.47214 q^{43} -3.85410 q^{45} +(1.11803 + 3.44095i) q^{47} +(5.61803 + 4.08174i) q^{49} +(0.736068 - 2.26538i) q^{51} +(-5.30902 + 3.85723i) q^{53} +(4.11803 - 2.99193i) q^{57} +(0.663119 - 2.04087i) q^{59} +(-2.11803 - 1.53884i) q^{61} +(0.0729490 + 0.224514i) q^{63} -24.0344 q^{65} -0.145898 q^{67} +(0.0729490 + 0.224514i) q^{69} +(1.11803 + 0.812299i) q^{71} +(-1.00000 + 3.07768i) q^{73} +(7.97214 - 5.79210i) q^{75} +(11.5172 - 8.36775i) q^{79} +(0.309017 - 0.951057i) q^{81} +(12.5172 + 9.09429i) q^{83} +(2.83688 + 8.73102i) q^{85} +4.47214 q^{87} +1.00000 q^{89} +(0.454915 + 1.40008i) q^{91} +(-5.16312 - 3.75123i) q^{93} +(-6.06231 + 18.6579i) q^{95} +(4.11803 - 2.99193i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + 8 q^{5} + 7 q^{7} - q^{9} - 9 q^{13} + 7 q^{15} + q^{17} + 13 q^{19} + 8 q^{21} + 8 q^{23} + q^{25} + q^{27} - 10 q^{29} + 5 q^{31} - 6 q^{35} + 11 q^{37} + 9 q^{39} - 5 q^{41} - 20 q^{43}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q + q^3 + 8 * q^5 + 7 * q^7 - q^9 - 9 * q^13 + 7 * q^15 + q^17 + 13 * q^19 + 8 * q^21 + 8 * q^23 + q^25 + q^27 - 10 * q^29 + 5 * q^31 - 6 * q^35 + 11 * q^37 + 9 * q^39 - 5 * q^41 - 20 * q^43 - 2 * q^45 + 18 * q^49 - 6 * q^51 - 19 * q^53 + 12 * q^57 - 13 * q^59 - 4 * q^61 + 7 * q^63 - 38 * q^65 - 14 * q^67 + 7 * q^69 - 4 * q^73 + 14 * q^75 + 17 * q^79 - q^81 + 21 * q^83 + 27 * q^85 + 4 * q^89 + 13 * q^91 - 5 * q^93 + 16 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	3.11803	+	2.26538i	1.39443	+	1.01311i	0.995363	+	0.0961876i	$0.0306649\pi$
$5$	3.11803	+	2.26538i	1.39443	+	1.01311i	0.399064	+	0.916923i	$0.369335\pi$
$6$		0			0
$7$	0.0729490	−	0.224514i	0.0275721	−	0.0848583i	−0.936324	−	0.351138i	$-0.885795\pi$
$7$	0.0729490	−	0.224514i	0.0275721	−	0.0848583i	0.963896	+	0.266280i	$0.0857946\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−5.04508	+	3.66547i	−1.39925	+	1.01662i	−0.404478	+	0.914548i	$0.632547\pi$
$13$	−5.04508	+	3.66547i	−1.39925	+	1.01662i	−0.994777	+	0.102070i	$0.967453\pi$
$14$		0			0
$15$	1.19098	−	3.66547i	0.307510	−	0.946420i
$16$		0			0
$17$	1.92705	+	1.40008i	0.467379	+	0.339570i	0.796419	−	0.604746i	$-0.206725\pi$
$17$	1.92705	+	1.40008i	0.467379	+	0.339570i	−0.329040	+	0.944316i	$0.606725\pi$
$18$		0			0
$19$	1.57295	+	4.84104i	0.360859	+	1.11061i	0.952534	+	0.304434i	$0.0984671\pi$
$19$	1.57295	+	4.84104i	0.360859	+	1.11061i	−0.591674	+	0.806177i	$0.701533\pi$
$20$		0			0
$21$	−0.236068			−0.0515143
$22$		0			0
$23$	−0.236068			−0.0492236			−0.0246118	−	0.999697i	$-0.507835\pi$
$23$	−0.236068			−0.0492236			−0.0246118	+	0.999697i	$0.507835\pi$
$24$		0			0
$25$	3.04508	+	9.37181i	0.609017	+	1.87436i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−1.38197	+	4.25325i	−0.256625	+	0.789809i	0.736881	+	0.676023i	$0.236298\pi$
$29$	−1.38197	+	4.25325i	−0.256625	+	0.789809i	−0.993505	+	0.113787i	$0.963702\pi$
$30$		0			0
$31$	5.16312	−	3.75123i	0.927324	−	0.673740i	−0.0180125	−	0.999838i	$-0.505734\pi$
$31$	5.16312	−	3.75123i	0.927324	−	0.673740i	0.945336	+	0.326098i	$0.105734\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.736068	−	0.534785i	0.124418	−	0.0903951i
$36$		0			0
$37$	−1.16312	+	3.57971i	−0.191216	+	0.588501i	0.808784	+	0.588105i	$0.200126\pi$
$37$	−1.16312	+	3.57971i	−0.191216	+	0.588501i	−1.00000		0.000395703i	$0.999874\pi$
$38$		0			0
$39$	5.04508	+	3.66547i	0.807860	+	0.586945i
$40$		0			0
$41$	−2.92705	−	9.00854i	−0.457129	−	1.40690i	−0.868618	−	0.495482i	$-0.834991\pi$
$41$	−2.92705	−	9.00854i	−0.457129	−	1.40690i	0.411489	−	0.911415i	$-0.365009\pi$
$42$		0			0
$43$	−9.47214			−1.44449			−0.722244	−	0.691639i	$-0.756889\pi$
$43$	−9.47214			−1.44449			−0.722244	+	0.691639i	$0.756889\pi$
$44$		0			0
$45$	−3.85410			−0.574536
$46$		0			0
$47$	1.11803	+	3.44095i	0.163082	+	0.501915i	0.998890	−	0.0471073i	$-0.0150003\pi$
$47$	1.11803	+	3.44095i	0.163082	+	0.501915i	−0.835808	+	0.549022i	$0.815000\pi$
$48$		0			0
$49$	5.61803	+	4.08174i	0.802576	+	0.583106i
$50$		0			0
$51$	0.736068	−	2.26538i	0.103070	−	0.317217i
$52$		0			0
$53$	−5.30902	+	3.85723i	−0.729250	+	0.529831i	−0.889326	−	0.457274i	$-0.848826\pi$
$53$	−5.30902	+	3.85723i	−0.729250	+	0.529831i	0.160076	+	0.987105i	$0.448826\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	4.11803	−	2.99193i	0.545447	−	0.396290i
$58$		0			0
$59$	0.663119	−	2.04087i	0.0863307	−	0.265699i	−0.898567	−	0.438837i	$-0.855391\pi$
$59$	0.663119	−	2.04087i	0.0863307	−	0.265699i	0.984898	+	0.173138i	$0.0553907\pi$
$60$		0			0
$61$	−2.11803	−	1.53884i	−0.271186	−	0.197028i	0.443878	−	0.896087i	$-0.353602\pi$
$61$	−2.11803	−	1.53884i	−0.271186	−	0.197028i	−0.715064	+	0.699059i	$0.753602\pi$
$62$		0			0
$63$	0.0729490	+	0.224514i	0.00919071	+	0.0282861i
$64$		0			0
$65$	−24.0344			−2.98111
$66$		0			0
$67$	−0.145898			−0.0178243			−0.00891214	−	0.999960i	$-0.502837\pi$
$67$	−0.145898			−0.0178243			−0.00891214	+	0.999960i	$0.502837\pi$
$68$		0			0
$69$	0.0729490	+	0.224514i	0.00878203	+	0.0270283i
$70$		0			0
$71$	1.11803	+	0.812299i	0.132686	+	0.0964022i	0.652149	−	0.758091i	$-0.273868\pi$
$71$	1.11803	+	0.812299i	0.132686	+	0.0964022i	−0.519462	+	0.854493i	$0.673868\pi$
$72$		0			0
$73$	−1.00000	+	3.07768i	−0.117041	+	0.360216i	−0.992367	−	0.123317i	$-0.960647\pi$
$73$	−1.00000	+	3.07768i	−0.117041	+	0.360216i	0.875326	+	0.483533i	$0.160647\pi$
$74$		0			0
$75$	7.97214	−	5.79210i	0.920543	−	0.668814i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	11.5172	−	8.36775i	1.29579	−	0.941446i	0.295884	−	0.955224i	$-0.404386\pi$
$79$	11.5172	−	8.36775i	1.29579	−	0.941446i	0.999905	+	0.0137785i	$0.00438597\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	12.5172	+	9.09429i	1.37394	+	0.998228i	0.997417	+	0.0718223i	$0.0228815\pi$
$83$	12.5172	+	9.09429i	1.37394	+	0.998228i	0.376526	+	0.926406i	$0.377119\pi$
$84$		0			0
$85$	2.83688	+	8.73102i	0.307703	+	0.947012i
$86$		0			0
$87$	4.47214			0.479463
$88$		0			0
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	0.454915	+	1.40008i	0.0476881	+	0.146769i
$92$		0			0
$93$	−5.16312	−	3.75123i	−0.535390	−	0.388984i
$94$		0			0
$95$	−6.06231	+	18.6579i	−0.621979	+	1.91426i
$96$		0			0
$97$	4.11803	−	2.99193i	0.418123	−	0.303784i	−0.358759	−	0.933430i	$-0.616800\pi$
$97$	4.11803	−	2.99193i	0.418123	−	0.303784i	0.776882	+	0.629646i	$0.216800\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.80902	+	3.49396i	−0.478515	+	0.347662i	−0.800751	−	0.598998i	$-0.795566\pi$
$101$	−4.80902	+	3.49396i	−0.478515	+	0.347662i	0.322235	+	0.946660i	$0.395566\pi$
$102$		0			0
$103$	3.85410	−	11.8617i	0.379756	−	1.16877i	−0.560458	−	0.828183i	$-0.689375\pi$
$103$	3.85410	−	11.8617i	0.379756	−	1.16877i	0.940214	−	0.340586i	$-0.110625\pi$
$104$		0			0
$105$	−0.736068	−	0.534785i	−0.0718329	−	0.0521896i
$106$		0			0
$107$	−2.01722	−	6.20837i	−0.195012	−	0.600186i	−0.999976	−	0.00686237i	$-0.997816\pi$
$107$	−2.01722	−	6.20837i	−0.195012	−	0.600186i	0.804964	−	0.593323i	$-0.202184\pi$
$108$		0			0
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$		0			0
$111$	3.76393			0.357257
$112$		0			0
$113$	3.78115	+	11.6372i	0.355701	+	1.09473i	0.955602	+	0.294661i	$0.0952066\pi$
$113$	3.78115	+	11.6372i	0.355701	+	1.09473i	−0.599901	+	0.800074i	$0.704793\pi$
$114$		0			0
$115$	−0.736068	−	0.534785i	−0.0686387	−	0.0498689i
$116$		0			0
$117$	1.92705	−	5.93085i	0.178156	−	0.548308i
$118$		0			0
$119$	0.454915	−	0.330515i	0.0417020	−	0.0302983i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−7.66312	+	5.56758i	−0.690960	+	0.502012i
$124$		0			0
$125$	−5.78115	+	17.7926i	−0.517082	+	1.59141i
$126$		0			0
$127$	12.7082	+	9.23305i	1.12767	+	0.819301i	0.985354	−	0.170520i	$-0.0545449\pi$
$127$	12.7082	+	9.23305i	1.12767	+	0.819301i	0.142317	+	0.989821i	$0.454545\pi$
$128$		0			0
$129$	2.92705	+	9.00854i	0.257712	+	0.793157i
$130$		0			0
$131$	8.56231			0.748092			0.374046	−	0.927410i	$-0.377970\pi$
$131$	8.56231			0.748092			0.374046	+	0.927410i	$0.377970\pi$
$132$		0			0
$133$	1.20163			0.104194
$134$		0			0
$135$	1.19098	+	3.66547i	0.102503	+	0.315473i
$136$		0			0
$137$	16.9894	+	12.3435i	1.45150	+	1.05458i	0.985478	+	0.169802i	$0.0543127\pi$
$137$	16.9894	+	12.3435i	1.45150	+	1.05458i	0.466020	+	0.884774i	$0.345687\pi$
$138$		0			0
$139$	−1.17376	+	3.61247i	−0.0995572	+	0.306406i	−0.988415	−	0.151779i	$-0.951500\pi$
$139$	−1.17376	+	3.61247i	−0.0995572	+	0.306406i	0.888857	+	0.458184i	$0.151500\pi$
$140$		0			0
$141$	2.92705	−	2.12663i	0.246502	−	0.179094i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−13.9443	+	10.1311i	−1.15801	+	0.841343i
$146$		0			0
$147$	2.14590	−	6.60440i	0.176991	−	0.544721i
$148$		0			0
$149$	−13.6631	−	9.92684i	−1.11933	−	0.813238i	−0.135219	−	0.990816i	$-0.543174\pi$
$149$	−13.6631	−	9.92684i	−1.11933	−	0.813238i	−0.984107	+	0.177577i	$0.943174\pi$
$150$		0			0
$151$	−1.38197	−	4.25325i	−0.112463	−	0.346125i	0.878947	−	0.476920i	$-0.158247\pi$
$151$	−1.38197	−	4.25325i	−0.112463	−	0.346125i	−0.991409	+	0.130795i	$0.958247\pi$
$152$		0			0
$153$	−2.38197			−0.192571
$154$		0			0
$155$	24.5967			1.97566
$156$		0			0
$157$	−5.32624	−	16.3925i	−0.425080	−	1.30826i	−0.902918	−	0.429814i	$-0.858579\pi$
$157$	−5.32624	−	16.3925i	−0.425080	−	1.30826i	0.477838	−	0.878448i	$-0.341421\pi$
$158$		0			0
$159$	5.30902	+	3.85723i	0.421032	+	0.305898i
$160$		0			0
$161$	−0.0172209	+	0.0530006i	−0.00135720	+	0.00417703i
$162$		0			0
$163$	3.92705	−	2.85317i	0.307590	−	0.223477i	−0.423271	−	0.906003i	$-0.639118\pi$
$163$	3.92705	−	2.85317i	0.307590	−	0.223477i	0.730862	+	0.682525i	$0.239118\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.500000	+	0.363271i	−0.0386912	+	0.0281108i	−0.606963	−	0.794730i	$-0.707612\pi$
$167$	−0.500000	+	0.363271i	−0.0386912	+	0.0281108i	0.568272	+	0.822841i	$0.307612\pi$
$168$		0			0
$169$	8.00000	−	24.6215i	0.615385	−	1.89396i
$170$		0			0
$171$	−4.11803	−	2.99193i	−0.314914	−	0.228798i
$172$		0			0
$173$	−1.71885	−	5.29007i	−0.130682	−	0.402196i	0.864212	−	0.503128i	$-0.167818\pi$
$173$	−1.71885	−	5.29007i	−0.130682	−	0.402196i	−0.994893	+	0.100932i	$0.967818\pi$
$174$		0			0
$175$	2.32624			0.175847
$176$		0			0
$177$	−2.14590			−0.161296
$178$		0			0
$179$	−5.54508	−	17.0660i	−0.414459	−	1.27557i	−0.912734	−	0.408555i	$-0.866033\pi$
$179$	−5.54508	−	17.0660i	−0.414459	−	1.27557i	0.498275	−	0.867019i	$-0.333967\pi$
$180$		0			0
$181$	−4.80902	−	3.49396i	−0.357451	−	0.259704i	0.394537	−	0.918880i	$-0.370905\pi$
$181$	−4.80902	−	3.49396i	−0.357451	−	0.259704i	−0.751988	+	0.659176i	$0.770905\pi$
$182$		0			0
$183$	−0.809017	+	2.48990i	−0.0598043	+	0.184059i
$184$		0			0
$185$	−11.7361	+	8.52675i	−0.862853	+	0.626899i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.190983	−	0.138757i	0.0138920	−	0.0100931i
$190$		0			0
$191$	−6.69098	+	20.5927i	−0.484143	+	1.49004i	0.349076	+	0.937094i	$0.386495\pi$
$191$	−6.69098	+	20.5927i	−0.484143	+	1.49004i	−0.833219	+	0.552943i	$0.813505\pi$
$192$		0			0
$193$	12.3992	+	9.00854i	0.892513	+	0.648449i	0.936532	−	0.350582i	$-0.114016\pi$
$193$	12.3992	+	9.00854i	0.892513	+	0.648449i	−0.0440190	+	0.999031i	$0.514016\pi$
$194$		0			0
$195$	7.42705	+	22.8581i	0.531862	+	1.63690i
$196$		0			0
$197$	5.90983			0.421058			0.210529	−	0.977588i	$-0.432481\pi$
$197$	5.90983			0.421058			0.210529	+	0.977588i	$0.432481\pi$
$198$		0			0
$199$	−10.4164			−0.738400			−0.369200	−	0.929350i	$-0.620368\pi$
$199$	−10.4164			−0.738400			−0.369200	+	0.929350i	$0.620368\pi$
$200$		0			0
$201$	0.0450850	+	0.138757i	0.00318005	+	0.00978718i
$202$		0			0
$203$	0.854102	+	0.620541i	0.0599462	+	0.0435535i
$204$		0			0
$205$	11.2812	−	34.7198i	0.787910	−	2.42494i
$206$		0			0
$207$	0.190983	−	0.138757i	0.0132742	−	0.00964430i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	15.1631	−	11.0167i	1.04387	−	0.758418i	0.0728345	−	0.997344i	$-0.476796\pi$
$211$	15.1631	−	11.0167i	1.04387	−	0.758418i	0.971038	+	0.238927i	$0.0767955\pi$
$212$		0			0
$213$	0.427051	−	1.31433i	0.0292611	−	0.0900563i
$214$		0			0
$215$	−29.5344	−	21.4580i	−2.01423	−	1.46343i
$216$		0			0
$217$	−0.465558	−	1.43284i	−0.0316041	−	0.0972676i
$218$		0			0
$219$	3.23607			0.218673
$220$		0			0
$221$	−14.8541			−0.999195
$222$		0			0
$223$	−2.30902	−	7.10642i	−0.154623	−	0.475881i	0.843499	−	0.537130i	$-0.180492\pi$
$223$	−2.30902	−	7.10642i	−0.154623	−	0.475881i	−0.998123	+	0.0612489i	$0.980492\pi$
$224$		0			0
$225$	−7.97214	−	5.79210i	−0.531476	−	0.386140i
$226$		0			0
$227$	−3.92705	+	12.0862i	−0.260648	+	0.802191i	0.732017	+	0.681287i	$0.238579\pi$
$227$	−3.92705	+	12.0862i	−0.260648	+	0.802191i	−0.992664	+	0.120904i	$0.961421\pi$
$228$		0			0
$229$	−8.85410	+	6.43288i	−0.585096	+	0.425097i	−0.840558	−	0.541722i	$-0.817772\pi$
$229$	−8.85410	+	6.43288i	−0.585096	+	0.425097i	0.255462	+	0.966819i	$0.417772\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.972136	−	0.706298i	0.0636867	−	0.0462711i	−0.555486	−	0.831526i	$-0.687468\pi$
$233$	0.972136	−	0.706298i	0.0636867	−	0.0462711i	0.619173	+	0.785255i	$0.287468\pi$
$234$		0			0
$235$	−4.30902	+	13.2618i	−0.281089	+	0.865104i
$236$		0			0
$237$	−11.5172	−	8.36775i	−0.748124	−	0.543544i
$238$		0			0
$239$	−5.40983	−	16.6497i	−0.349933	−	1.07698i	−0.958890	−	0.283779i	$-0.908412\pi$
$239$	−5.40983	−	16.6497i	−0.349933	−	1.07698i	0.608957	−	0.793203i	$-0.291588\pi$
$240$		0			0
$241$	23.7082			1.52718			0.763590	−	0.645702i	$-0.223435\pi$
$241$	23.7082			1.52718			0.763590	+	0.645702i	$0.223435\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	8.27051	+	25.4540i	0.528383	+	1.62620i
$246$		0			0
$247$	−25.6803	−	18.6579i	−1.63400	−	1.18717i
$248$		0			0
$249$	4.78115	−	14.7149i	0.302993	−	0.932517i
$250$		0			0
$251$	−19.4894	+	14.1598i	−1.23016	+	0.893762i	−0.996902	−	0.0786539i	$-0.974938\pi$
$251$	−19.4894	+	14.1598i	−1.23016	+	0.893762i	−0.233255	+	0.972416i	$0.574938\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	7.42705	−	5.39607i	0.465100	−	0.337915i
$256$		0			0
$257$	−0.864745	+	2.66141i	−0.0539413	+	0.166014i	−0.974398	−	0.224831i	$-0.927817\pi$
$257$	−0.864745	+	2.66141i	−0.0539413	+	0.166014i	0.920457	+	0.390845i	$0.127817\pi$
$258$		0			0
$259$	0.718847	+	0.522273i	0.0446670	+	0.0324525i
$260$		0			0
$261$	−1.38197	−	4.25325i	−0.0855415	−	0.263270i
$262$		0			0
$263$	−23.8541			−1.47091			−0.735453	−	0.677575i	$-0.763031\pi$
$263$	−23.8541			−1.47091			−0.735453	+	0.677575i	$0.763031\pi$
$264$		0			0
$265$	−25.2918			−1.55366
$266$		0			0
$267$	−0.309017	−	0.951057i	−0.0189115	−	0.0582037i
$268$		0			0
$269$	−23.0344	−	16.7355i	−1.40443	−	1.02038i	−0.994102	−	0.108445i	$-0.965413\pi$
$269$	−23.0344	−	16.7355i	−1.40443	−	1.02038i	−0.410332	−	0.911936i	$-0.634587\pi$
$270$		0			0
$271$	0.753289	−	2.31838i	0.0457590	−	0.140832i	−0.925567	−	0.378585i	$-0.876411\pi$
$271$	0.753289	−	2.31838i	0.0457590	−	0.140832i	0.971326	+	0.237753i	$0.0764109\pi$
$272$		0			0
$273$	1.19098	−	0.865300i	0.0720816	−	0.0523703i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.07295	−	1.50609i	0.124551	−	0.0904919i	−0.523765	−	0.851862i	$-0.675473\pi$
$277$	2.07295	−	1.50609i	0.124551	−	0.0904919i	0.648317	+	0.761371i	$0.275473\pi$
$278$		0			0
$279$	−1.97214	+	6.06961i	−0.118069	+	0.363378i
$280$		0			0
$281$	13.8541	+	10.0656i	0.826466	+	0.600463i	0.918557	−	0.395288i	$-0.129355\pi$
$281$	13.8541	+	10.0656i	0.826466	+	0.600463i	−0.0920910	+	0.995751i	$0.529355\pi$
$282$		0			0
$283$	−7.18034	−	22.0988i	−0.426827	−	1.31364i	−0.901234	−	0.433333i	$-0.857338\pi$
$283$	−7.18034	−	22.0988i	−0.426827	−	1.31364i	0.474407	−	0.880306i	$-0.342662\pi$
$284$		0			0
$285$	19.6180			1.16207
$286$		0			0
$287$	−2.23607			−0.131991
$288$		0			0
$289$	−3.50000	−	10.7719i	−0.205882	−	0.633641i
$290$		0			0
$291$	−4.11803	−	2.99193i	−0.241403	−	0.175390i
$292$		0			0
$293$	1.54508	−	4.75528i	0.0902648	−	0.277807i	−0.895726	−	0.444607i	$-0.853343\pi$
$293$	1.54508	−	4.75528i	0.0902648	−	0.277807i	0.985991	+	0.166800i	$0.0533435\pi$
$294$		0			0
$295$	6.69098	−	4.86128i	0.389564	−	0.283035i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.19098	−	0.865300i	0.0688763	−	0.0500416i
$300$		0			0
$301$	−0.690983	+	2.12663i	−0.0398276	+	0.122577i
$302$		0			0
$303$	4.80902	+	3.49396i	0.276271	+	0.200722i
$304$		0			0
$305$	−3.11803	−	9.59632i	−0.178538	−	0.549484i
$306$		0			0
$307$	0.673762			0.0384536			0.0192268	−	0.999815i	$-0.493880\pi$
$307$	0.673762			0.0384536			0.0192268	+	0.999815i	$0.493880\pi$
$308$		0			0
$309$	−12.4721			−0.709515
$310$		0			0
$311$	−9.01722	−	27.7522i	−0.511320	−	1.57368i	−0.789880	−	0.613261i	$-0.789857\pi$
$311$	−9.01722	−	27.7522i	−0.511320	−	1.57368i	0.278560	−	0.960419i	$-0.410143\pi$
$312$		0			0
$313$	0.809017	+	0.587785i	0.0457283	+	0.0332236i	0.610415	−	0.792082i	$-0.291003\pi$
$313$	0.809017	+	0.587785i	0.0457283	+	0.0332236i	−0.564686	+	0.825306i	$0.691003\pi$
$314$		0			0
$315$	−0.281153	+	0.865300i	−0.0158412	+	0.0487541i
$316$		0			0
$317$	−6.89919	+	5.01255i	−0.387497	+	0.281533i	−0.764429	−	0.644708i	$-0.776979\pi$
$317$	−6.89919	+	5.01255i	−0.387497	+	0.281533i	0.376932	+	0.926241i	$0.376979\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−5.28115	+	3.83698i	−0.294765	+	0.214159i
$322$		0			0
$323$	−3.74671	+	11.5312i	−0.208473	+	0.641613i
$324$		0			0
$325$	−49.7148	−	36.1199i	−2.75768	−	2.00357i
$326$		0			0
$327$	−2.47214	−	7.60845i	−0.136709	−	0.420748i
$328$		0			0
$329$	0.854102			0.0470882
$330$		0			0
$331$	11.9443			0.656517			0.328258	−	0.944588i	$-0.393538\pi$
$331$	11.9443			0.656517			0.328258	+	0.944588i	$0.393538\pi$
$332$		0			0
$333$	−1.16312	−	3.57971i	−0.0637385	−	0.196167i
$334$		0			0
$335$	−0.454915	−	0.330515i	−0.0248547	−	0.0180580i
$336$		0			0
$337$	5.43769	−	16.7355i	0.296210	−	0.911641i	−0.686602	−	0.727033i	$-0.740899\pi$
$337$	5.43769	−	16.7355i	0.296210	−	0.911641i	0.982812	−	0.184608i	$-0.0591014\pi$
$338$		0			0
$339$	9.89919	−	7.19218i	0.537650	−	0.390626i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	2.66312	−	1.93487i	0.143795	−	0.104473i
$344$		0			0
$345$	−0.281153	+	0.865300i	−0.0151368	+	0.0465862i
$346$		0			0
$347$	−6.47214	−	4.70228i	−0.347442	−	0.252432i	0.400353	−	0.916361i	$-0.368888\pi$
$347$	−6.47214	−	4.70228i	−0.347442	−	0.252432i	−0.747795	+	0.663929i	$0.768888\pi$
$348$		0			0
$349$	8.72542	+	26.8541i	0.467061	+	1.43747i	0.856372	+	0.516360i	$0.172713\pi$
$349$	8.72542	+	26.8541i	0.467061	+	1.43747i	−0.389310	+	0.921107i	$0.627287\pi$
$350$		0			0
$351$	−6.23607			−0.332857
$352$		0			0
$353$	−10.4721			−0.557376			−0.278688	−	0.960382i	$-0.589899\pi$
$353$	−10.4721			−0.557376			−0.278688	+	0.960382i	$0.589899\pi$
$354$		0			0
$355$	1.64590	+	5.06555i	0.0873552	+	0.268852i
$356$		0			0
$357$	−0.454915	−	0.330515i	−0.0240767	−	0.0174927i
$358$		0			0
$359$	7.18034	−	22.0988i	0.378964	−	1.16633i	−0.561801	−	0.827272i	$-0.689891\pi$
$359$	7.18034	−	22.0988i	0.378964	−	1.16633i	0.940765	−	0.339059i	$-0.110109\pi$
$360$		0			0
$361$	−5.59017	+	4.06150i	−0.294219	+	0.213763i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.0902	+	7.33094i	−0.528144	+	0.383719i
$366$		0			0
$367$	−1.66312	+	5.11855i	−0.0868141	+	0.267186i	−0.985034	−	0.172360i	$-0.944861\pi$
$367$	−1.66312	+	5.11855i	−0.0868141	+	0.267186i	0.898220	+	0.439546i	$0.144861\pi$
$368$		0			0
$369$	7.66312	+	5.56758i	0.398926	+	0.289837i
$370$		0			0
$371$	0.478714	+	1.47333i	0.0248536	+	0.0764915i
$372$		0			0
$373$	13.9443			0.722007			0.361004	−	0.932564i	$-0.382434\pi$
$373$	13.9443			0.722007			0.361004	+	0.932564i	$0.382434\pi$
$374$		0			0
$375$	18.7082			0.966087
$376$		0			0
$377$	−8.61803	−	26.5236i	−0.443851	−	1.36603i
$378$		0			0
$379$	10.2812	+	7.46969i	0.528107	+	0.383692i	0.819649	−	0.572866i	$-0.194168\pi$
$379$	10.2812	+	7.46969i	0.528107	+	0.383692i	−0.291542	+	0.956558i	$0.594168\pi$
$380$		0			0
$381$	4.85410	−	14.9394i	0.248683	−	0.765368i
$382$		0			0
$383$	−8.28115	+	6.01661i	−0.423147	+	0.307434i	−0.778903	−	0.627145i	$-0.784224\pi$
$383$	−8.28115	+	6.01661i	−0.423147	+	0.307434i	0.355756	+	0.934579i	$0.384224\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.66312	−	5.56758i	0.389538	−	0.283016i
$388$		0			0
$389$	4.97214	−	15.3027i	0.252097	−	0.775876i	−0.742290	−	0.670078i	$-0.766261\pi$
$389$	4.97214	−	15.3027i	0.252097	−	0.775876i	0.994388	−	0.105797i	$-0.0337395\pi$
$390$		0			0
$391$	−0.454915	−	0.330515i	−0.0230060	−	0.0167149i
$392$		0			0
$393$	−2.64590	−	8.14324i	−0.133468	−	0.410772i
$394$		0			0
$395$	54.8673			2.76067
$396$		0			0
$397$	27.1803			1.36414			0.682071	−	0.731286i	$-0.261079\pi$
$397$	27.1803			1.36414			0.682071	+	0.731286i	$0.261079\pi$
$398$		0			0
$399$	−0.371323	−	1.14281i	−0.0185894	−	0.0572123i
$400$		0			0
$401$	2.30902	+	1.67760i	0.115307	+	0.0837753i	0.643944	−	0.765072i	$-0.277297\pi$
$401$	2.30902	+	1.67760i	0.115307	+	0.0837753i	−0.528637	+	0.848848i	$0.677297\pi$
$402$		0			0
$403$	−12.2984	+	37.8505i	−0.612626	+	1.88547i
$404$		0			0
$405$	3.11803	−	2.26538i	0.154936	−	0.112568i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	8.00000	−	5.81234i	0.395575	−	0.287402i	−0.372161	−	0.928168i	$-0.621383\pi$
$409$	8.00000	−	5.81234i	0.395575	−	0.287402i	0.767736	+	0.640766i	$0.221383\pi$
$410$		0			0
$411$	6.48936	−	19.9722i	0.320096	−	0.985155i
$412$		0			0
$413$	−0.409830	−	0.297759i	−0.0201664	−	0.0146518i
$414$		0			0
$415$	18.4271	+	56.7126i	0.904548	+	2.78391i
$416$		0			0
$417$	3.79837			0.186007
$418$		0			0
$419$	17.8541			0.872230			0.436115	−	0.899891i	$-0.356354\pi$
$419$	17.8541			0.872230			0.436115	+	0.899891i	$0.356354\pi$
$420$		0			0
$421$	−2.86475	−	8.81678i	−0.139619	−	0.429704i	0.856661	−	0.515880i	$-0.172535\pi$
$421$	−2.86475	−	8.81678i	−0.139619	−	0.429704i	−0.996280	+	0.0861767i	$0.972535\pi$
$422$		0			0
$423$	−2.92705	−	2.12663i	−0.142318	−	0.103400i
$424$		0			0
$425$	−7.25329	+	22.3233i	−0.351836	+	1.08284i
$426$		0			0
$427$	−0.500000	+	0.363271i	−0.0241967	+	0.0175799i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.7812	−	7.83297i	0.519310	−	0.377301i	−0.297034	−	0.954867i	$-0.595997\pi$
$431$	10.7812	−	7.83297i	0.519310	−	0.377301i	0.816344	+	0.577566i	$0.195997\pi$
$432$		0			0
$433$	−4.61803	+	14.2128i	−0.221929	+	0.683026i	0.776660	+	0.629920i	$0.216912\pi$
$433$	−4.61803	+	14.2128i	−0.221929	+	0.683026i	−0.998589	+	0.0531062i	$0.983088\pi$
$434$		0			0
$435$	13.9443	+	10.1311i	0.668577	+	0.485749i
$436$		0			0
$437$	−0.371323	−	1.14281i	−0.0177628	−	0.0546682i
$438$		0			0
$439$	19.3607			0.924035			0.462017	−	0.886871i	$-0.347126\pi$
$439$	19.3607			0.924035			0.462017	+	0.886871i	$0.347126\pi$
$440$		0			0
$441$	−6.94427			−0.330680
$442$		0			0
$443$	0.0557281	+	0.171513i	0.00264772	+	0.00814885i	0.952372	−	0.304940i	$-0.0986363\pi$
$443$	0.0557281	+	0.171513i	0.00264772	+	0.00814885i	−0.949724	+	0.313089i	$0.898636\pi$
$444$		0			0
$445$	3.11803	+	2.26538i	0.147809	+	0.107390i
$446$		0			0
$447$	−5.21885	+	16.0620i	−0.246843	+	0.759705i
$448$		0			0
$449$	6.09017	−	4.42477i	0.287413	−	0.208818i	−0.434731	−	0.900560i	$-0.643157\pi$
$449$	6.09017	−	4.42477i	0.287413	−	0.208818i	0.722144	+	0.691742i	$0.243157\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−3.61803	+	2.62866i	−0.169990	+	0.123505i
$454$		0			0
$455$	−1.75329	+	5.39607i	−0.0821955	+	0.252972i
$456$		0			0
$457$	0.927051	+	0.673542i	0.0433656	+	0.0315070i	0.609257	−	0.792973i	$-0.291468\pi$
$457$	0.927051	+	0.673542i	0.0433656	+	0.0315070i	−0.565891	+	0.824480i	$0.691468\pi$
$458$		0			0
$459$	0.736068	+	2.26538i	0.0343567	+	0.105739i
$460$		0			0
$461$	−19.5623			−0.911107			−0.455554	−	0.890208i	$-0.650559\pi$
$461$	−19.5623			−0.911107			−0.455554	+	0.890208i	$0.650559\pi$
$462$		0			0
$463$	21.2148			0.985935			0.492967	−	0.870048i	$-0.335912\pi$
$463$	21.2148			0.985935			0.492967	+	0.870048i	$0.335912\pi$
$464$		0			0
$465$	−7.60081	−	23.3929i	−0.352479	−	1.08482i
$466$		0			0
$467$	−16.0451	−	11.6574i	−0.742478	−	0.539442i	0.151008	−	0.988533i	$-0.451748\pi$
$467$	−16.0451	−	11.6574i	−0.742478	−	0.539442i	−0.893486	+	0.449091i	$0.851748\pi$
$468$		0			0
$469$	−0.0106431	+	0.0327561i	−0.000491454	+	0.00151254i
$470$		0			0
$471$	−13.9443	+	10.1311i	−0.642518	+	0.466817i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−40.5795	+	29.4828i	−1.86192	+	1.35276i
$476$		0			0
$477$	2.02786	−	6.24112i	0.0928495	−	0.285761i
$478$		0			0
$479$	10.7812	+	7.83297i	0.492603	+	0.357897i	0.806185	−	0.591664i	$-0.201529\pi$
$479$	10.7812	+	7.83297i	0.492603	+	0.357897i	−0.313581	+	0.949561i	$0.601529\pi$
$480$		0			0
$481$	−7.25329	−	22.3233i	−0.330722	−	1.01786i
$482$		0			0
$483$	0.0557281			0.00253572
$484$		0			0
$485$	19.6180			0.890809
$486$		0			0
$487$	11.0729	+	34.0790i	0.501763	+	1.54427i	0.806145	+	0.591718i	$0.201550\pi$
$487$	11.0729	+	34.0790i	0.501763	+	1.54427i	−0.304382	+	0.952550i	$0.598450\pi$
$488$		0			0
$489$	−3.92705	−	2.85317i	−0.177587	−	0.129025i
$490$		0			0
$491$	1.59017	−	4.89404i	0.0717634	−	0.220865i	−0.908742	−	0.417359i	$-0.862956\pi$
$491$	1.59017	−	4.89404i	0.0717634	−	0.220865i	0.980505	+	0.196494i	$0.0629557\pi$
$492$		0			0
$493$	−8.61803	+	6.26137i	−0.388137	+	0.281998i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.263932	−	0.191758i	0.0118390	−	0.00860151i
$498$		0			0
$499$	4.71885	−	14.5231i	0.211245	−	0.650144i	−0.788154	−	0.615478i	$-0.788963\pi$
$499$	4.71885	−	14.5231i	0.211245	−	0.650144i	0.999399	−	0.0346664i	$-0.0110369\pi$
$500$		0			0
$501$	0.500000	+	0.363271i	0.0223384	+	0.0162298i
$502$		0			0
$503$	−5.32624	−	16.3925i	−0.237485	−	0.730904i	−0.996782	−	0.0801599i	$-0.974457\pi$
$503$	−5.32624	−	16.3925i	−0.237485	−	0.730904i	0.759297	−	0.650744i	$-0.225543\pi$
$504$		0			0
$505$	−22.9098			−1.01947
$506$		0			0
$507$	−25.8885			−1.14975
$508$		0			0
$509$	3.93769	+	12.1190i	0.174535	+	0.537164i	0.999612	−	0.0278565i	$-0.00886816\pi$
$509$	3.93769	+	12.1190i	0.174535	+	0.537164i	−0.825077	+	0.565021i	$0.808868\pi$
$510$		0			0
$511$	0.618034	+	0.449028i	0.0273402	+	0.0198638i
$512$		0			0
$513$	−1.57295	+	4.84104i	−0.0694474	+	0.213737i
$514$		0			0
$515$	38.8885	−	28.2542i	1.71363	−	1.24503i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−4.50000	+	3.26944i	−0.197528	+	0.143513i
$520$		0			0
$521$	4.58359	−	14.1068i	0.200811	−	0.618032i	−0.799049	−	0.601266i	$-0.794663\pi$
$521$	4.58359	−	14.1068i	0.200811	−	0.618032i	0.999859	−	0.0167657i	$-0.00533695\pi$
$522$		0			0
$523$	−17.6353	−	12.8128i	−0.771136	−	0.560263i	0.131170	−	0.991360i	$-0.458127\pi$
$523$	−17.6353	−	12.8128i	−0.771136	−	0.560263i	−0.902306	+	0.431097i	$0.858127\pi$
$524$		0			0
$525$	−0.718847	−	2.21238i	−0.0313731	−	0.0965563i
$526$		0			0
$527$	15.2016			0.662193
$528$		0			0
$529$	−22.9443			−0.997577
$530$		0			0
$531$	0.663119	+	2.04087i	0.0287769	+	0.0885662i
$532$		0			0
$533$	47.7877	+	34.7198i	2.06992	+	1.50388i
$534$		0			0
$535$	7.77458	−	23.9277i	0.336124	−	1.03448i
$536$		0			0
$537$	−14.5172	+	10.5474i	−0.626464	+	0.455153i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5.11803	+	3.71847i	−0.220041	+	0.159869i	−0.692345	−	0.721566i	$-0.743423\pi$
$541$	−5.11803	+	3.71847i	−0.220041	+	0.159869i	0.472304	+	0.881436i	$0.343423\pi$
$542$		0			0
$543$	−1.83688	+	5.65334i	−0.0788281	+	0.242608i
$544$		0			0
$545$	24.9443	+	18.1231i	1.06850	+	0.776307i
$546$		0			0
$547$	−4.11803	−	12.6740i	−0.176074	−	0.541901i	0.823606	−	0.567162i	$-0.191959\pi$
$547$	−4.11803	−	12.6740i	−0.176074	−	0.541901i	−0.999681	+	0.0252603i	$0.991959\pi$
$548$		0			0
$549$	2.61803			0.111735
$550$		0			0
$551$	−22.7639			−0.969776
$552$		0			0
$553$	−1.03851	−	3.19620i	−0.0441618	−	0.135916i
$554$		0			0
$555$	11.7361	+	8.52675i	0.498168	+	0.361940i
$556$		0			0
$557$	−1.57295	+	4.84104i	−0.0666480	+	0.205121i	−0.978834	−	0.204654i	$-0.934393\pi$
$557$	−1.57295	+	4.84104i	−0.0666480	+	0.205121i	0.912186	+	0.409776i	$0.134393\pi$
$558$		0			0
$559$	47.7877	−	34.7198i	2.02121	−	1.46849i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	32.9336	−	23.9277i	1.38799	−	1.00843i	0.391904	−	0.920006i	$-0.371816\pi$
$563$	32.9336	−	23.9277i	1.38799	−	1.00843i	0.996083	−	0.0884255i	$-0.0281835\pi$
$564$		0			0
$565$	−14.5729	+	44.8509i	−0.613089	+	1.88689i
$566$		0			0
$567$	−0.190983	−	0.138757i	−0.00802053	−	0.00582726i
$568$		0			0
$569$	−1.50658	−	4.63677i	−0.0631590	−	0.194383i	0.914498	−	0.404591i	$-0.132586\pi$
$569$	−1.50658	−	4.63677i	−0.0631590	−	0.194383i	−0.977657	+	0.210207i	$0.932586\pi$
$570$		0			0
$571$	−24.3262			−1.01802			−0.509011	−	0.860760i	$-0.669989\pi$
$571$	−24.3262			−1.01802			−0.509011	+	0.860760i	$0.669989\pi$
$572$		0			0
$573$	21.6525			0.904545
$574$		0			0
$575$	−0.718847	−	2.21238i	−0.0299780	−	0.0922628i
$576$		0			0
$577$	−23.6525	−	17.1845i	−0.984665	−	0.715401i	−0.0259190	−	0.999664i	$-0.508251\pi$
$577$	−23.6525	−	17.1845i	−0.984665	−	0.715401i	−0.958746	+	0.284263i	$0.908251\pi$
$578$		0			0
$579$	4.73607	−	14.5761i	0.196824	−	0.605763i
$580$		0			0
$581$	2.95492	−	2.14687i	0.122591	−	0.0890672i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	19.4443	−	14.1271i	0.803922	−	0.584083i
$586$		0			0
$587$	7.96149	−	24.5030i	0.328606	−	1.01135i	−0.641181	−	0.767390i	$-0.721555\pi$
$587$	7.96149	−	24.5030i	0.328606	−	1.01135i	0.969787	−	0.243955i	$-0.0784450\pi$
$588$		0			0
$589$	26.2812	+	19.0944i	1.08290	+	0.786770i
$590$		0			0
$591$	−1.82624	−	5.62058i	−0.0751214	−	0.231200i
$592$		0			0
$593$	−19.4508			−0.798751			−0.399375	−	0.916788i	$-0.630773\pi$
$593$	−19.4508			−0.798751			−0.399375	+	0.916788i	$0.630773\pi$
$594$		0			0
$595$	2.16718			0.0888459
$596$		0			0
$597$	3.21885	+	9.90659i	0.131739	+	0.405450i
$598$		0			0
$599$	−32.8885	−	23.8949i	−1.34379	−	0.976320i	−0.999295	−	0.0375317i	$-0.988050\pi$
$599$	−32.8885	−	23.8949i	−1.34379	−	0.976320i	−0.344494	−	0.938789i	$-0.611950\pi$
$600$		0			0
$601$	−6.16312	+	18.9681i	−0.251399	+	0.773726i	0.743119	+	0.669159i	$0.233346\pi$
$601$	−6.16312	+	18.9681i	−0.251399	+	0.773726i	−0.994518	+	0.104567i	$0.966654\pi$
$602$		0			0
$603$	0.118034	−	0.0857567i	0.00480672	−	0.00349228i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	7.01722	−	5.09831i	0.284820	−	0.206934i	−0.436197	−	0.899851i	$-0.643675\pi$
$607$	7.01722	−	5.09831i	0.284820	−	0.206934i	0.721017	+	0.692917i	$0.243675\pi$
$608$		0			0
$609$	0.326238	−	1.00406i	0.0132198	−	0.0406864i
$610$		0			0
$611$	−18.2533	−	13.2618i	−0.738449	−	0.536515i
$612$		0			0
$613$	−5.29180	−	16.2865i	−0.213734	−	0.657804i	−0.999241	−	0.0389523i	$-0.987598\pi$
$613$	−5.29180	−	16.2865i	−0.213734	−	0.657804i	0.785507	−	0.618852i	$-0.212402\pi$
$614$		0			0
$615$	−36.5066			−1.47209
$616$		0			0
$617$	−7.00000			−0.281809			−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000			−0.281809			−0.140905	+	0.990023i	$0.545001\pi$
$618$		0			0
$619$	−2.30902	−	7.10642i	−0.0928072	−	0.285631i	0.893869	−	0.448329i	$-0.147981\pi$
$619$	−2.30902	−	7.10642i	−0.0928072	−	0.285631i	−0.986676	+	0.162697i	$0.947981\pi$
$620$		0			0
$621$	−0.190983	−	0.138757i	−0.00766388	−	0.00556814i
$622$		0			0
$623$	0.0729490	−	0.224514i	0.00292264	−	0.00899496i
$624$		0			0
$625$	−18.4721	+	13.4208i	−0.738885	+	0.536832i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.25329	+	5.26982i	−0.289208	+	0.210122i
$630$		0			0
$631$	2.38854	−	7.35118i	0.0950864	−	0.292646i	−0.892190	−	0.451661i	$-0.850832\pi$
$631$	2.38854	−	7.35118i	0.0950864	−	0.292646i	0.987276	+	0.159015i	$0.0508318\pi$
$632$		0			0
$633$	−15.1631	−	11.0167i	−0.602680	−	0.437873i
$634$		0			0
$635$	18.7082	+	57.5779i	0.742412	+	2.28491i
$636$		0			0
$637$	−43.3050			−1.71580
$638$		0			0
$639$	−1.38197			−0.0546697
$640$		0			0
$641$	7.71885	+	23.7562i	0.304876	+	0.938312i	0.979723	+	0.200355i	$0.0642095\pi$
$641$	7.71885	+	23.7562i	0.304876	+	0.938312i	−0.674847	+	0.737957i	$0.735791\pi$
$642$		0			0
$643$	32.4894	+	23.6049i	1.28126	+	0.930886i	0.999590	−	0.0286264i	$-0.00911333\pi$
$643$	32.4894	+	23.6049i	1.28126	+	0.930886i	0.281665	+	0.959513i	$0.409113\pi$
$644$		0			0
$645$	−11.2812	+	34.7198i	−0.444195	+	1.36709i
$646$		0			0
$647$	−28.8713	+	20.9762i	−1.13505	+	0.824661i	−0.986422	−	0.164232i	$-0.947485\pi$
$647$	−28.8713	+	20.9762i	−1.13505	+	0.824661i	−0.148627	+	0.988893i	$0.547485\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−1.21885	+	0.885544i	−0.0477704	+	0.0347072i
$652$		0			0
$653$	−6.53444	+	20.1109i	−0.255712	+	0.787002i	0.737976	+	0.674827i	$0.235782\pi$
$653$	−6.53444	+	20.1109i	−0.255712	+	0.787002i	−0.993688	+	0.112175i	$0.964218\pi$
$654$		0			0
$655$	26.6976	+	19.3969i	1.04316	+	0.757900i
$656$		0			0
$657$	−1.00000	−	3.07768i	−0.0390137	−	0.120072i
$658$		0			0
$659$	−9.70820			−0.378178			−0.189089	−	0.981960i	$-0.560553\pi$
$659$	−9.70820			−0.378178			−0.189089	+	0.981960i	$0.560553\pi$
$660$		0			0
$661$	−13.3262			−0.518331			−0.259165	−	0.965833i	$-0.583447\pi$
$661$	−13.3262			−0.518331			−0.259165	+	0.965833i	$0.583447\pi$
$662$		0			0
$663$	4.59017	+	14.1271i	0.178267	+	0.548651i
$664$		0			0
$665$	3.74671	+	2.72214i	0.145291	+	0.105560i
$666$		0			0
$667$	0.326238	−	1.00406i	0.0126320	−	0.0388772i
$668$		0			0
$669$	−6.04508	+	4.39201i	−0.233716	+	0.169805i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	28.6976	−	20.8500i	1.10621	−	0.803708i	0.124147	−	0.992264i	$-0.460381\pi$
$673$	28.6976	−	20.8500i	1.10621	−	0.803708i	0.982063	+	0.188555i	$0.0603805\pi$
$674$		0			0
$675$	−3.04508	+	9.37181i	−0.117205	+	0.360721i
$676$		0			0
$677$	2.00000	+	1.45309i	0.0768662	+	0.0558466i	0.625555	−	0.780180i	$-0.284873\pi$
$677$	2.00000	+	1.45309i	0.0768662	+	0.0558466i	−0.548688	+	0.836027i	$0.684873\pi$
$678$		0			0
$679$	−0.371323	−	1.14281i	−0.0142501	−	0.0438572i
$680$		0			0
$681$	12.7082			0.486979
$682$		0			0
$683$	−37.6525			−1.44073			−0.720366	−	0.693594i	$-0.756026\pi$
$683$	−37.6525			−1.44073			−0.720366	+	0.693594i	$0.756026\pi$
$684$		0			0
$685$	25.0106	+	76.9748i	0.955608	+	2.94106i
$686$		0			0
$687$	8.85410	+	6.43288i	0.337805	+	0.245430i
$688$		0			0
$689$	12.6459	−	38.9201i	0.481770	−	1.48274i
$690$		0			0
$691$	−26.3262	+	19.1271i	−1.00150	+	0.727630i	−0.962409	−	0.271605i	$-0.912445\pi$
$691$	−26.3262	+	19.1271i	−1.00150	+	0.727630i	−0.0390886	+	0.999236i	$0.512445\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.8435	+	8.60478i	−0.449248	+	0.326398i
$696$		0			0
$697$	6.97214	−	21.4580i	0.264088	−	0.812781i
$698$		0			0
$699$	−0.972136	−	0.706298i	−0.0367696	−	0.0267146i
$700$		0			0
$701$	8.80902	+	27.1114i	0.332712	+	1.02398i	0.967838	+	0.251574i	$0.0809481\pi$
$701$	8.80902	+	27.1114i	0.332712	+	1.02398i	−0.635126	+	0.772408i	$0.719052\pi$
$702$		0			0
$703$	−19.1591			−0.722597
$704$		0			0
$705$	13.9443			0.525172
$706$		0			0
$707$	0.433629	+	1.33457i	0.0163083	+	0.0501918i
$708$		0			0
$709$	−13.5451	−	9.84108i	−0.508696	−	0.369590i	0.303632	−	0.952789i	$-0.401801\pi$
$709$	−13.5451	−	9.84108i	−0.508696	−	0.369590i	−0.812329	+	0.583200i	$0.801801\pi$
$710$		0			0
$711$	−4.39919	+	13.5393i	−0.164982	+	0.507764i
$712$		0			0
$713$	−1.21885	+	0.885544i	−0.0456462	+	0.0331639i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−14.1631	+	10.2901i	−0.528931	+	0.384291i
$718$		0			0
$719$	5.89261	−	18.1356i	0.219757	−	0.676343i	−0.779024	−	0.626994i	$-0.784285\pi$
$719$	5.89261	−	18.1356i	0.219757	−	0.676343i	0.998782	−	0.0493495i	$-0.0157148\pi$
$720$		0			0
$721$	−2.38197	−	1.73060i	−0.0887090	−	0.0644509i
$722$		0			0
$723$	−7.32624	−	22.5478i	−0.272466	−	0.838563i
$724$		0			0
$725$	−44.0689			−1.63668
$726$		0			0
$727$	−8.85410			−0.328380			−0.164190	−	0.986429i	$-0.552501\pi$
$727$	−8.85410			−0.328380			−0.164190	+	0.986429i	$0.552501\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−18.2533	−	13.2618i	−0.675122	−	0.490505i
$732$		0			0
$733$	−13.7639	+	42.3610i	−0.508382	+	1.56464i	0.286626	+	0.958042i	$0.407466\pi$
$733$	−13.7639	+	42.3610i	−0.508382	+	1.56464i	−0.795009	+	0.606598i	$0.792534\pi$
$734$		0			0
$735$	21.6525	−	15.7314i	0.798664	−	0.580263i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−10.3713	+	7.53521i	−0.381515	+	0.277187i	−0.761970	−	0.647613i	$-0.775768\pi$
$739$	−10.3713	+	7.53521i	−0.381515	+	0.277187i	0.380455	+	0.924800i	$0.375768\pi$
$740$		0			0
$741$	−9.80902	+	30.1891i	−0.360343	+	1.10902i
$742$		0			0
$743$	9.28115	+	6.74315i	0.340492	+	0.247382i	0.744870	−	0.667210i	$-0.232512\pi$
$743$	9.28115	+	6.74315i	0.340492	+	0.247382i	−0.404377	+	0.914592i	$0.632512\pi$
$744$		0			0
$745$	−20.1140	−	61.9044i	−0.736919	−	2.26800i
$746$		0			0
$747$	−15.4721			−0.566096
$748$		0			0
$749$	−1.54102			−0.0563076
$750$		0			0
$751$	−12.8647	−	39.5936i	−0.469441	−	1.44479i	−0.853310	−	0.521404i	$-0.825409\pi$
$751$	−12.8647	−	39.5936i	−0.469441	−	1.44479i	0.383869	−	0.923388i	$-0.374591\pi$
$752$		0			0
$753$	19.4894	+	14.1598i	0.710232	+	0.516013i
$754$		0			0
$755$	5.32624	−	16.3925i	0.193842	−	0.596583i
$756$		0			0
$757$	8.42705	−	6.12261i	0.306286	−	0.222530i	−0.424015	−	0.905655i	$-0.639380\pi$
$757$	8.42705	−	6.12261i	0.306286	−	0.222530i	0.730301	+	0.683125i	$0.239380\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.6631	+	17.1923i	−0.857787	+	0.623219i	−0.927282	−	0.374363i	$-0.877861\pi$
$761$	−23.6631	+	17.1923i	−0.857787	+	0.623219i	0.0694947	+	0.997582i	$0.477861\pi$
$762$		0			0
$763$	0.583592	−	1.79611i	0.0211275	−	0.0650236i
$764$		0			0
$765$	−7.42705	−	5.39607i	−0.268526	−	0.195095i
$766$		0			0
$767$	4.13525	+	12.7270i	0.149315	+	0.459546i
$768$		0			0
$769$	33.5623			1.21029			0.605144	−	0.796116i	$-0.293116\pi$
$769$	33.5623			1.21029			0.605144	+	0.796116i	$0.293116\pi$
$770$		0			0
$771$	2.79837			0.100781
$772$		0			0
$773$	9.07295	+	27.9237i	0.326331	+	1.00434i	0.970836	+	0.239744i	$0.0770636\pi$
$773$	9.07295	+	27.9237i	0.326331	+	1.00434i	−0.644505	+	0.764600i	$0.722936\pi$
$774$		0			0
$775$	50.8779	+	36.9650i	1.82759	+	1.32782i
$776$		0			0
$777$	0.274575	−	0.845055i	0.00985033	−	0.0303162i
$778$		0			0
$779$	39.0066	−	28.3399i	1.39756	−	1.01538i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−3.61803	+	2.62866i	−0.129298	+	0.0939405i
$784$		0			0
$785$	20.5279	−	63.1783i	0.732671	−	2.25493i
$786$		0			0
$787$	36.2148	+	26.3116i	1.29092	+	0.937907i	0.999823	−	0.0187879i	$-0.00598074\pi$
$787$	36.2148	+	26.3116i	1.29092	+	0.937907i	0.291094	+	0.956694i	$0.405981\pi$
$788$		0			0
$789$	7.37132	+	22.6866i	0.262426	+	0.807664i
$790$		0			0
$791$	2.88854			0.102705
$792$		0			0
$793$	16.3262			0.579762
$794$		0			0
$795$	7.81559	+	24.0539i	0.277191	+	0.853105i
$796$		0			0
$797$	39.6525	+	28.8092i	1.40456	+	1.02047i	0.994085	+	0.108604i	$0.0346380\pi$
$797$	39.6525	+	28.8092i	1.40456	+	1.02047i	0.410478	+	0.911871i	$0.365362\pi$
$798$		0			0
$799$	−2.66312	+	8.19624i	−0.0942144	+	0.289962i
$800$		0			0
$801$	−0.809017	+	0.587785i	−0.0285852	+	0.0207684i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−0.173762	+	0.126246i	−0.00612431	+	0.00444957i
$806$		0			0
$807$	−8.79837	+	27.0786i	−0.309717	+	0.953212i
$808$		0			0
$809$	28.5344	+	20.7315i	1.00322	+	0.728880i	0.962776	−	0.270302i	$-0.0871234\pi$
$809$	28.5344	+	20.7315i	1.00322	+	0.728880i	0.0404419	+	0.999182i	$0.487123\pi$
$810$		0			0
$811$	0.680340	+	2.09387i	0.0238900	+	0.0735258i	0.962291	−	0.272023i	$-0.0876927\pi$
$811$	0.680340	+	2.09387i	0.0238900	+	0.0735258i	−0.938401	+	0.345549i	$0.887693\pi$
$812$		0			0
$813$	−2.43769			−0.0854937
$814$		0			0
$815$	18.7082			0.655320
$816$		0			0
$817$	−14.8992	−	45.8550i	−0.521257	−	1.60426i
$818$		0			0
$819$	−1.19098	−	0.865300i	−0.0416163	−	0.0302360i
$820$		0			0
$821$	−8.45492	+	26.0216i	−0.295079	+	0.908158i	0.688116	+	0.725600i	$0.258438\pi$
$821$	−8.45492	+	26.0216i	−0.295079	+	0.908158i	−0.983195	+	0.182558i	$0.941562\pi$
$822$		0			0
$823$	−18.7533	+	13.6251i	−0.653699	+	0.474940i	−0.864529	−	0.502583i	$-0.832383\pi$
$823$	−18.7533	+	13.6251i	−0.653699	+	0.474940i	0.210831	+	0.977523i	$0.432383\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−33.2705	+	24.1724i	−1.15693	+	0.840558i	−0.989387	−	0.145307i	$-0.953583\pi$
$827$	−33.2705	+	24.1724i	−1.15693	+	0.840558i	−0.167542	+	0.985865i	$0.553583\pi$
$828$		0			0
$829$	1.46556	−	4.51052i	0.0509009	−	0.156657i	−0.922375	−	0.386296i	$-0.873754\pi$
$829$	1.46556	−	4.51052i	0.0509009	−	0.156657i	0.973276	+	0.229639i	$0.0737544\pi$
$830$		0			0
$831$	−2.07295	−	1.50609i	−0.0719098	−	0.0522455i
$832$		0			0
$833$	5.11146	+	15.7314i	0.177101	+	0.545062i
$834$		0			0
$835$	−2.38197			−0.0824313
$836$		0			0
$837$	6.38197			0.220593
$838$		0			0
$839$	11.6910	+	35.9811i	0.403618	+	1.24221i	0.922044	+	0.387085i	$0.126518\pi$
$839$	11.6910	+	35.9811i	0.403618	+	1.24221i	−0.518427	+	0.855122i	$0.673482\pi$
$840$		0			0
$841$	7.28115	+	5.29007i	0.251074	+	0.182416i
$842$		0			0
$843$	5.29180	−	16.2865i	0.182259	−	0.560936i
$844$		0			0
$845$	80.7214	−	58.6475i	2.77690	−	2.01754i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−18.7984	+	13.6578i	−0.645159	+	0.468735i
$850$		0			0
$851$	0.274575	−	0.845055i	0.00941231	−	0.0289681i
$852$		0			0
$853$	8.60739	+	6.25364i	0.294711	+	0.214120i	0.725309	−	0.688424i	$-0.241697\pi$
$853$	8.60739	+	6.25364i	0.294711	+	0.214120i	−0.430597	+	0.902544i	$0.641697\pi$
$854$		0			0
$855$	−6.06231	−	18.6579i	−0.207326	−	0.638085i
$856$		0			0
$857$	50.1935			1.71458			0.857289	−	0.514836i	$-0.172147\pi$
$857$	50.1935			1.71458			0.857289	+	0.514836i	$0.172147\pi$
$858$		0			0
$859$	8.81966			0.300923			0.150461	−	0.988616i	$-0.451924\pi$
$859$	8.81966			0.300923			0.150461	+	0.988616i	$0.451924\pi$
$860$		0			0
$861$	0.690983	+	2.12663i	0.0235486	+	0.0724753i
$862$		0			0
$863$	11.6180	+	8.44100i	0.395482	+	0.287335i	0.767698	−	0.640811i	$-0.221402\pi$
$863$	11.6180	+	8.44100i	0.395482	+	0.287335i	−0.372216	+	0.928146i	$0.621402\pi$
$864$		0			0
$865$	6.62461	−	20.3885i	0.225244	−	0.693228i
$866$		0			0
$867$	−9.16312	+	6.65740i	−0.311196	+	0.226097i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	0.736068	−	0.534785i	0.0249407	−	0.0181205i
$872$		0			0
$873$	−1.57295	+	4.84104i	−0.0532363	+	0.163844i
$874$		0			0
$875$	3.57295	+	2.59590i	0.120788	+	0.0877574i
$876$		0			0
$877$	−0.274575	−	0.845055i	−0.00927174	−	0.0285355i	0.946314	−	0.323250i	$-0.104775\pi$
$877$	−0.274575	−	0.845055i	−0.00927174	−	0.0285355i	−0.955585	+	0.294714i	$0.904775\pi$
$878$		0			0
$879$	−5.00000			−0.168646
$880$		0			0
$881$	40.5623			1.36658			0.683289	−	0.730148i	$-0.260549\pi$
$881$	40.5623			1.36658			0.683289	+	0.730148i	$0.260549\pi$
$882$		0			0
$883$	4.61803	+	14.2128i	0.155409	+	0.478300i	0.998202	−	0.0599376i	$-0.0190902\pi$
$883$	4.61803	+	14.2128i	0.155409	+	0.478300i	−0.842793	+	0.538238i	$0.819090\pi$
$884$		0			0
$885$	−6.69098	−	4.86128i	−0.224915	−	0.163410i
$886$		0			0
$887$	10.2877	−	31.6624i	0.345428	−	1.06312i	−0.615926	−	0.787804i	$-0.711218\pi$
$887$	10.2877	−	31.6624i	0.345428	−	1.06312i	0.961354	−	0.275315i	$-0.0887820\pi$
$888$		0			0
$889$	3.00000	−	2.17963i	0.100617	−	0.0731024i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−14.8992	+	10.8249i	−0.498582	+	0.362241i
$894$		0			0
$895$	21.3713	−	65.7742i	0.714365	−	2.19859i
$896$		0			0
$897$	−1.19098	−	0.865300i	−0.0397658	−	0.0288915i
$898$		0			0
$899$	8.81966	+	27.1441i	0.294152	+	0.905307i
$900$		0			0
$901$	−15.6312			−0.520750
$902$		0			0
$903$	2.23607			0.0744117
$904$		0			0
$905$	−7.07953	−	21.7885i	−0.235331	−	0.724276i
$906$		0			0
$907$	34.6803	+	25.1967i	1.15154	+	0.836644i	0.988685	−	0.150006i	$-0.0479292\pi$
$907$	34.6803	+	25.1967i	1.15154	+	0.836644i	0.162857	+	0.986650i	$0.447929\pi$
$908$		0			0
$909$	1.83688	−	5.65334i	0.0609255	−	0.187509i
$910$		0			0
$911$	−20.6631	+	15.0126i	−0.684600	+	0.497391i	−0.874880	−	0.484339i	$-0.839060\pi$
$911$	−20.6631	+	15.0126i	−0.684600	+	0.497391i	0.190281	+	0.981730i	$0.439060\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−8.16312	+	5.93085i	−0.269864	+	0.196068i
$916$		0			0
$917$	0.624612	−	1.92236i	0.0206265	−	0.0634818i
$918$		0			0
$919$	−12.8090	−	9.30630i	−0.422530	−	0.306986i	0.356125	−	0.934438i	$-0.384098\pi$
$919$	−12.8090	−	9.30630i	−0.422530	−	0.306986i	−0.778655	+	0.627452i	$0.784098\pi$
$920$		0			0
$921$	−0.208204	−	0.640786i	−0.00686055	−	0.0211146i
$922$		0			0
$923$	−8.61803			−0.283666
$924$		0			0
$925$	−37.0902			−1.21952
$926$		0			0
$927$	3.85410	+	11.8617i	0.126585	+	0.389590i
$928$		0			0
$929$	−15.8435	−	11.5109i	−0.519807	−	0.377662i	0.296724	−	0.954963i	$-0.404106\pi$
$929$	−15.8435	−	11.5109i	−0.519807	−	0.377662i	−0.816531	+	0.577301i	$0.804106\pi$
$930$		0			0
$931$	−10.9230	+	33.6175i	−0.357986	+	1.10177i
$932$		0			0
$933$	−23.6074	+	17.1518i	−0.772871	+	0.561524i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	15.9894	−	11.6169i	0.522350	−	0.379509i	−0.295139	−	0.955454i	$-0.595366\pi$
$937$	15.9894	−	11.6169i	0.522350	−	0.379509i	0.817488	+	0.575945i	$0.195366\pi$
$938$		0			0
$939$	0.309017	−	0.951057i	0.0100844	−	0.0310366i
$940$		0			0
$941$	−2.07295	−	1.50609i	−0.0675762	−	0.0490970i	0.553484	−	0.832860i	$-0.313298\pi$
$941$	−2.07295	−	1.50609i	−0.0675762	−	0.0490970i	−0.621061	+	0.783763i	$0.713298\pi$
$942$		0			0
$943$	0.690983	+	2.12663i	0.0225015	+	0.0692525i
$944$		0			0
$945$	0.909830			0.0295968
$946$		0			0
$947$	−2.79837			−0.0909349			−0.0454675	−	0.998966i	$-0.514478\pi$
$947$	−2.79837			−0.0909349			−0.0454675	+	0.998966i	$0.514478\pi$
$948$		0			0
$949$	−6.23607	−	19.1926i	−0.202431	−	0.623020i
$950$		0			0
$951$	6.89919	+	5.01255i	0.223721	+	0.162543i
$952$		0			0
$953$	−10.7426	+	33.0625i	−0.347988	+	1.07100i	0.611976	+	0.790876i	$0.290375\pi$
$953$	−10.7426	+	33.0625i	−0.347988	+	1.07100i	−0.959964	+	0.280122i	$0.909625\pi$
$954$		0			0
$955$	−67.5132	+	49.0512i	−2.18467	+	1.58726i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.01064	−	2.91390i	0.129510	−	0.0940948i
$960$		0			0
$961$	3.00658	−	9.25330i	0.0969864	−	0.298493i
$962$		0			0
$963$	5.28115	+	3.83698i	0.170183	+	0.123645i
$964$		0			0
$965$	18.2533	+	56.1778i	0.587594	+	1.80843i
$966$		0			0
$967$	−14.7295			−0.473668			−0.236834	−	0.971550i	$-0.576110\pi$
$967$	−14.7295			−0.473668			−0.236834	+	0.971550i	$0.576110\pi$
$968$		0			0
$969$	12.1246			0.389499
$970$		0			0
$971$	0.729490	+	2.24514i	0.0234105	+	0.0720500i	0.962079	−	0.272770i	$-0.0879399\pi$
$971$	0.729490	+	2.24514i	0.0234105	+	0.0720500i	−0.938669	+	0.344820i	$0.887940\pi$
$972$		0			0
$973$	0.725425	+	0.527052i	0.0232561	+	0.0168965i
$974$		0			0
$975$	−18.9894	+	58.4432i	−0.608146	+	1.87168i
$976$		0			0
$977$	26.6074	−	19.3314i	0.851246	−	0.618466i	−0.0742434	−	0.997240i	$-0.523654\pi$
$977$	26.6074	−	19.3314i	0.851246	−	0.618466i	0.925489	+	0.378774i	$0.123654\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−6.47214	+	4.70228i	−0.206639	+	0.150132i
$982$		0			0
$983$	−11.3820	+	35.0301i	−0.363028	+	1.11729i	0.588178	+	0.808731i	$0.299845\pi$
$983$	−11.3820	+	35.0301i	−0.363028	+	1.11729i	−0.951207	+	0.308555i	$0.900155\pi$
$984$		0			0
$985$	18.4271	+	13.3880i	0.587135	+	0.426578i
$986$		0			0
$987$	−0.263932	−	0.812299i	−0.00840105	−	0.0258558i
$988$		0			0
$989$	2.23607			0.0711028
$990$		0			0
$991$	43.2705			1.37453			0.687267	−	0.726405i	$-0.258810\pi$
$991$	43.2705			1.37453			0.687267	+	0.726405i	$0.258810\pi$
$992$		0			0
$993$	−3.69098	−	11.3597i	−0.117130	−	0.360488i
$994$		0			0
$995$	−32.4787	−	23.5972i	−1.02964	−	0.748080i
$996$		0			0
$997$	−9.04508	+	27.8379i	−0.286461	+	0.881635i	0.699496	+	0.714636i	$0.253408\pi$
$997$	−9.04508	+	27.8379i	−0.286461	+	0.881635i	−0.985957	+	0.166999i	$0.946592\pi$
$998$		0			0
$999$	−3.04508	+	2.21238i	−0.0963422	+	0.0699967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.p.1213.1		4
11.2	odd	10		1452.2.a.j.1.1		2
11.3	even	5		1452.2.i.j.1237.1		4
11.4	even	5	inner	1452.2.i.p.565.1		4
11.5	even	5		1452.2.i.j.493.1		4
11.6	odd	10		132.2.i.b.97.1	yes	4
11.7	odd	10		1452.2.i.o.565.1		4
11.8	odd	10		132.2.i.b.49.1	✓	4
11.9	even	5		1452.2.a.i.1.1		2
11.10	odd	2		1452.2.i.o.1213.1		4
33.2	even	10		4356.2.a.v.1.2		2
33.8	even	10		396.2.j.c.181.1		4
33.17	even	10		396.2.j.c.361.1		4
33.20	odd	10		4356.2.a.s.1.2		2
44.19	even	10		528.2.y.a.49.1		4
44.31	odd	10		5808.2.a.cf.1.1		2
44.35	even	10		5808.2.a.cc.1.1		2
44.39	even	10		528.2.y.a.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.b.49.1	✓	4	11.8	odd	10
132.2.i.b.97.1	yes	4	11.6	odd	10
396.2.j.c.181.1		4	33.8	even	10
396.2.j.c.361.1		4	33.17	even	10
528.2.y.a.49.1		4	44.19	even	10
528.2.y.a.97.1		4	44.39	even	10
1452.2.a.i.1.1		2	11.9	even	5
1452.2.a.j.1.1		2	11.2	odd	10
1452.2.i.j.493.1		4	11.5	even	5
1452.2.i.j.1237.1		4	11.3	even	5
1452.2.i.o.565.1		4	11.7	odd	10
1452.2.i.o.1213.1		4	11.10	odd	2
1452.2.i.p.565.1		4	11.4	even	5	inner
1452.2.i.p.1213.1		4	1.1	even	1	trivial
4356.2.a.s.1.2		2	33.20	odd	10
4356.2.a.v.1.2		2	33.2	even	10
5808.2.a.cc.1.1		2	44.35	even	10
5808.2.a.cf.1.1		2	44.31	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(3.11803 + 2.26538i) q^{5} +(0.0729490 - 0.224514i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-5.04508 + 3.66547i) q^{13} +(1.19098 - 3.66547i) q^{15} +(1.92705 + 1.40008i) q^{17} +(1.57295 + 4.84104i) q^{19} -0.236068 q^{21} -0.236068 q^{23} +(3.04508 + 9.37181i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-1.38197 + 4.25325i) q^{29} +(5.16312 - 3.75123i) q^{31} +(0.736068 - 0.534785i) q^{35} +(-1.16312 + 3.57971i) q^{37} +(5.04508 + 3.66547i) q^{39} +(-2.92705 - 9.00854i) q^{41} -9.47214 q^{43} -3.85410 q^{45} +(1.11803 + 3.44095i) q^{47} +(5.61803 + 4.08174i) q^{49} +(0.736068 - 2.26538i) q^{51} +(-5.30902 + 3.85723i) q^{53} +(4.11803 - 2.99193i) q^{57} +(0.663119 - 2.04087i) q^{59} +(-2.11803 - 1.53884i) q^{61} +(0.0729490 + 0.224514i) q^{63} -24.0344 q^{65} -0.145898 q^{67} +(0.0729490 + 0.224514i) q^{69} +(1.11803 + 0.812299i) q^{71} +(-1.00000 + 3.07768i) q^{73} +(7.97214 - 5.79210i) q^{75} +(11.5172 - 8.36775i) q^{79} +(0.309017 - 0.951057i) q^{81} +(12.5172 + 9.09429i) q^{83} +(2.83688 + 8.73102i) q^{85} +4.47214 q^{87} +1.00000 q^{89} +(0.454915 + 1.40008i) q^{91} +(-5.16312 - 3.75123i) q^{93} +(-6.06231 + 18.6579i) q^{95} +(4.11803 - 2.99193i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + 8 q^{5} + 7 q^{7} - q^{9} - 9 q^{13} + 7 q^{15} + q^{17} + 13 q^{19} + 8 q^{21} + 8 q^{23} + q^{25} + q^{27} - 10 q^{29} + 5 q^{31} - 6 q^{35} + 11 q^{37} + 9 q^{39} - 5 q^{41} - 20 q^{43}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q + q^3 + 8 * q^5 + 7 * q^7 - q^9 - 9 * q^13 + 7 * q^15 + q^17 + 13 * q^19 + 8 * q^21 + 8 * q^23 + q^25 + q^27 - 10 * q^29 + 5 * q^31 - 6 * q^35 + 11 * q^37 + 9 * q^39 - 5 * q^41 - 20 * q^43 - 2 * q^45 + 18 * q^49 - 6 * q^51 - 19 * q^53 + 12 * q^57 - 13 * q^59 - 4 * q^61 + 7 * q^63 - 38 * q^65 - 14 * q^67 + 7 * q^69 - 4 * q^73 + 14 * q^75 + 17 * q^79 - q^81 + 21 * q^83 + 27 * q^85 + 4 * q^89 + 13 * q^91 - 5 * q^93 + 16 * q^95 + 12 * q^97

Introduction

L-functions

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