LMFDB - Embedded newform 952.2.q.e.681.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(137,952)] 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("952.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 17 x^{12} - 18 x^{11} + 102 x^{10} - 59 x^{9} + 462 x^{8} - 28 x^{7} + 1148 x^{6} + \cdots + 361 $ x^14 - 3x^13 + 17x^12 - 18x^11 + 102x^10 - 59x^9 + 462x^8 - 28x^7 + 1148x^6 - x^5 + 1982x^4 + 198x^3 + 1563x^2 - 532x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			681.4
Root			$0.237215 + 0.410869i$ of defining polynomial
Character	$\chi$	$=$	952.681
Dual form			952.2.q.e.137.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.237215 + 0.410869i) q^{3} +(-0.817607 + 1.41614i) q^{5} +(2.62656 + 0.318109i) q^{7} +(1.38746 - 2.40315i) q^{9} +(0.120552 + 0.208801i) q^{11} +1.90325 q^{13} -0.775795 q^{15} +(-0.500000 - 0.866025i) q^{17} +(2.55706 - 4.42896i) q^{19} +(0.492358 + 1.15463i) q^{21} +(-1.83206 + 3.17323i) q^{23} +(1.16304 + 2.01444i) q^{25} +2.73980 q^{27} +2.50385 q^{29} +(1.20792 + 2.09217i) q^{31} +(-0.0571933 + 0.0990617i) q^{33} +(-2.59798 + 3.45948i) q^{35} +(-1.67756 + 2.90562i) q^{37} +(0.451479 + 0.781985i) q^{39} -9.52792 q^{41} +9.54468 q^{43} +(2.26879 + 3.92966i) q^{45} +(4.31973 - 7.48198i) q^{47} +(6.79761 + 1.67106i) q^{49} +(0.237215 - 0.410869i) q^{51} +(5.80792 + 10.0596i) q^{53} -0.394255 q^{55} +2.42629 q^{57} +(1.03546 + 1.79348i) q^{59} +(-5.33802 + 9.24572i) q^{61} +(4.40870 - 5.87064i) q^{63} +(-1.55611 + 2.69526i) q^{65} +(6.28311 + 10.8827i) q^{67} -1.73837 q^{69} +0.576299 q^{71} +(-7.77213 - 13.4617i) q^{73} +(-0.551780 + 0.955711i) q^{75} +(0.250214 + 0.586777i) q^{77} +(4.23303 - 7.33183i) q^{79} +(-3.51245 - 6.08375i) q^{81} +1.02923 q^{83} +1.63521 q^{85} +(0.593951 + 1.02875i) q^{87} +(-5.71344 + 9.89597i) q^{89} +(4.99899 + 0.605440i) q^{91} +(-0.573072 + 0.992590i) q^{93} +(4.18134 + 7.24229i) q^{95} -3.69602 q^{97} +0.669041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 4 q^{9} + 12 q^{11} + 4 q^{13} - 12 q^{15} - 7 q^{17} + 3 q^{19} + 18 q^{21} + 18 q^{23} - 15 q^{25} - 36 q^{27} + 10 q^{29} + 10 q^{31} - 21 q^{33} + 19 q^{35} - 11 q^{37}+ \cdots - 40 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 4 * q^9 + 12 * q^11 + 4 * q^13 - 12 * q^15 - 7 * q^17 + 3 * q^19 + 18 * q^21 + 18 * q^23 - 15 * q^25 - 36 * q^27 + 10 * q^29 + 10 * q^31 - 21 * q^33 + 19 * q^35 - 11 * q^37 + 12 * q^39 - 30 * q^43 - 13 * q^45 - 15 * q^47 + 20 * q^49 + 3 * q^51 - 8 * q^53 - 18 * q^55 - 6 * q^57 - 9 * q^59 + 4 * q^61 + 41 * q^63 + 38 * q^65 + 30 * q^67 - 56 * q^69 - 54 * q^71 + 5 * q^73 + 2 * q^75 + 27 * q^77 - 3 * q^79 + 17 * q^81 - 24 * q^83 + 4 * q^85 - 19 * q^87 - 32 * q^89 - 11 * q^91 + 9 * q^93 + 42 * q^95 - 78 * q^97 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.237215	+	0.410869i	0.136956	+	0.237215i	0.926343	−	0.376681i	$-0.122935\pi$
$3$	0.237215	+	0.410869i	0.136956	+	0.237215i	−0.789387	+	0.613896i	$0.789601\pi$
$4$		0			0
$5$	−0.817607	+	1.41614i	−0.365645	+	0.633316i	−0.988879	−	0.148719i	$-0.952485\pi$
$5$	−0.817607	+	1.41614i	−0.365645	+	0.633316i	0.623234	+	0.782035i	$0.285818\pi$
$6$		0			0
$7$	2.62656	+	0.318109i	0.992746	+	0.120234i
$7$	2.62656	+	0.318109i	0.992746	+	0.120234i
$8$		0			0
$9$	1.38746	−	2.40315i	0.462486	−	0.801049i
$10$		0			0
$11$	0.120552	+	0.208801i	0.0363477	+	0.0629560i	0.883627	−	0.468192i	$-0.155094\pi$
$11$	0.120552	+	0.208801i	0.0363477	+	0.0629560i	−0.847279	+	0.531148i	$0.821761\pi$
$12$		0			0
$13$	1.90325			0.527866			0.263933	−	0.964541i	$-0.414980\pi$
$13$	1.90325			0.527866			0.263933	+	0.964541i	$0.414980\pi$
$14$		0			0
$15$	−0.775795			−0.200310
$16$		0			0
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$		0			0
$19$	2.55706	−	4.42896i	0.586630	−	1.01607i	−0.408041	−	0.912964i	$-0.633788\pi$
$19$	2.55706	−	4.42896i	0.586630	−	1.01607i	0.994670	−	0.103108i	$-0.0328789\pi$
$20$		0			0
$21$	0.492358	+	1.15463i	0.107441	+	0.251961i
$22$		0			0
$23$	−1.83206	+	3.17323i	−0.382012	+	0.661663i	−0.991350	−	0.131247i	$-0.958102\pi$
$23$	−1.83206	+	3.17323i	−0.382012	+	0.661663i	0.609338	+	0.792910i	$0.291435\pi$
$24$		0			0
$25$	1.16304	+	2.01444i	0.232607	+	0.402888i
$26$		0			0
$27$	2.73980			0.527274
$28$		0			0
$29$	2.50385			0.464953			0.232477	−	0.972602i	$-0.425317\pi$
$29$	2.50385			0.464953			0.232477	+	0.972602i	$0.425317\pi$
$30$		0			0
$31$	1.20792	+	2.09217i	0.216948	+	0.375765i	0.953873	−	0.300209i	$-0.0970564\pi$
$31$	1.20792	+	2.09217i	0.216948	+	0.375765i	−0.736925	+	0.675974i	$0.763723\pi$
$32$		0			0
$33$	−0.0571933	+	0.0990617i	−0.00995608	+	0.0172444i
$34$		0			0
$35$	−2.59798	+	3.45948i	−0.439139	+	0.584759i
$36$		0			0
$37$	−1.67756	+	2.90562i	−0.275789	+	0.477681i	−0.970334	−	0.241768i	$-0.922273\pi$
$37$	−1.67756	+	2.90562i	−0.275789	+	0.477681i	0.694545	+	0.719450i	$0.255606\pi$
$38$		0			0
$39$	0.451479	+	0.781985i	0.0722945	+	0.125218i
$40$		0			0
$41$	−9.52792			−1.48801			−0.744006	−	0.668173i	$-0.767076\pi$
$41$	−9.52792			−1.48801			−0.744006	+	0.668173i	$0.767076\pi$
$42$		0			0
$43$	9.54468			1.45555			0.727775	−	0.685816i	$-0.240555\pi$
$43$	9.54468			1.45555			0.727775	+	0.685816i	$0.240555\pi$
$44$		0			0
$45$	2.26879	+	3.92966i	0.338211	+	0.585799i
$46$		0			0
$47$	4.31973	−	7.48198i	0.630097	−	1.09136i	−0.357435	−	0.933938i	$-0.616349\pi$
$47$	4.31973	−	7.48198i	0.630097	−	1.09136i	0.987532	−	0.157421i	$-0.0503181\pi$
$48$		0			0
$49$	6.79761	+	1.67106i	0.971088	+	0.238723i
$50$		0			0
$51$	0.237215	−	0.410869i	0.0332168	−	0.0575331i
$52$		0			0
$53$	5.80792	+	10.0596i	0.797779	+	1.38179i	0.921059	+	0.389423i	$0.127325\pi$
$53$	5.80792	+	10.0596i	0.797779	+	1.38179i	−0.123280	+	0.992372i	$0.539341\pi$
$54$		0			0
$55$	−0.394255			−0.0531614
$56$		0			0
$57$	2.42629			0.321370
$58$		0			0
$59$	1.03546	+	1.79348i	0.134806	+	0.233491i	0.925523	−	0.378691i	$-0.123626\pi$
$59$	1.03546	+	1.79348i	0.134806	+	0.233491i	−0.790717	+	0.612181i	$0.790292\pi$
$60$		0			0
$61$	−5.33802	+	9.24572i	−0.683463	+	1.18379i	0.290454	+	0.956889i	$0.406194\pi$
$61$	−5.33802	+	9.24572i	−0.683463	+	1.18379i	−0.973917	+	0.226904i	$0.927140\pi$
$62$		0			0
$63$	4.40870	−	5.87064i	0.555444	−	0.739632i
$64$		0			0
$65$	−1.55611	+	2.69526i	−0.193012	+	0.334306i
$66$		0			0
$67$	6.28311	+	10.8827i	0.767604	+	1.32953i	0.938859	+	0.344303i	$0.111885\pi$
$67$	6.28311	+	10.8827i	0.767604	+	1.32953i	−0.171254	+	0.985227i	$0.554782\pi$
$68$		0			0
$69$	−1.73837			−0.209275
$70$		0			0
$71$	0.576299			0.0683942			0.0341971	−	0.999415i	$-0.489113\pi$
$71$	0.576299			0.0683942			0.0341971	+	0.999415i	$0.489113\pi$
$72$		0			0
$73$	−7.77213	−	13.4617i	−0.909659	−	1.57558i	−0.814538	−	0.580111i	$-0.803009\pi$
$73$	−7.77213	−	13.4617i	−0.909659	−	1.57558i	−0.0951216	−	0.995466i	$-0.530324\pi$
$74$		0			0
$75$	−0.551780	+	0.955711i	−0.0637141	+	0.110356i
$76$		0			0
$77$	0.250214	+	0.586777i	0.0285145	+	0.0668695i
$78$		0			0
$79$	4.23303	−	7.33183i	0.476253	−	0.824895i	−0.523377	−	0.852102i	$-0.675328\pi$
$79$	4.23303	−	7.33183i	0.476253	−	0.824895i	0.999630	+	0.0272066i	$0.00866120\pi$
$80$		0			0
$81$	−3.51245	−	6.08375i	−0.390273	−	0.675972i
$82$		0			0
$83$	1.02923			0.112972			0.0564862	−	0.998403i	$-0.482010\pi$
$83$	1.02923			0.112972			0.0564862	+	0.998403i	$0.482010\pi$
$84$		0			0
$85$	1.63521			0.177364
$86$		0			0
$87$	0.593951	+	1.02875i	0.0636782	+	0.110294i
$88$		0			0
$89$	−5.71344	+	9.89597i	−0.605624	+	1.04897i	0.386329	+	0.922361i	$0.373743\pi$
$89$	−5.71344	+	9.89597i	−0.605624	+	1.04897i	−0.991953	+	0.126610i	$0.959590\pi$
$90$		0			0
$91$	4.99899	+	0.605440i	0.524037	+	0.0634674i
$92$		0			0
$93$	−0.573072	+	0.992590i	−0.0594248	+	0.102927i
$94$		0			0
$95$	4.18134	+	7.24229i	0.428996	+	0.743044i
$96$		0			0
$97$	−3.69602			−0.375274			−0.187637	−	0.982238i	$-0.560083\pi$
$97$	−3.69602			−0.375274			−0.187637	+	0.982238i	$0.560083\pi$
$98$		0			0
$99$	0.669041			0.0672411
$100$		0			0
$101$	−4.34060	−	7.51814i	−0.431906	−	0.748083i	0.565132	−	0.825001i	$-0.308825\pi$
$101$	−4.34060	−	7.51814i	−0.431906	−	0.748083i	−0.997037	+	0.0769181i	$0.975492\pi$
$102$		0			0
$103$	7.05600	−	12.2213i	0.695248	−	1.20421i	−0.274849	−	0.961487i	$-0.588628\pi$
$103$	7.05600	−	12.2213i	0.695248	−	1.20421i	0.970097	−	0.242718i	$-0.0780389\pi$
$104$		0			0
$105$	−2.03767	−	0.246787i	−0.198856	−	0.0240840i
$106$		0			0
$107$	6.92645	−	11.9970i	0.669605	−	1.15979i	−0.308410	−	0.951254i	$-0.599797\pi$
$107$	6.92645	−	11.9970i	0.669605	−	1.15979i	0.978015	−	0.208536i	$-0.0668699\pi$
$108$		0			0
$109$	3.13370	+	5.42772i	0.300154	+	0.519882i	0.976171	−	0.217005i	$-0.0696287\pi$
$109$	3.13370	+	5.42772i	0.300154	+	0.519882i	−0.676017	+	0.736886i	$0.736295\pi$
$110$		0			0
$111$	−1.59177			−0.151084
$112$		0			0
$113$	−14.5983			−1.37329			−0.686644	−	0.726993i	$-0.740917\pi$
$113$	−14.5983			−1.37329			−0.686644	+	0.726993i	$0.740917\pi$
$114$		0			0
$115$	−2.99582	−	5.18891i	−0.279361	−	0.483868i
$116$		0			0
$117$	2.64068	−	4.57378i	0.244131	−	0.422847i
$118$		0			0
$119$	−1.03779	−	2.43372i	−0.0951339	−	0.223099i
$120$		0			0
$121$	5.47093	−	9.47594i	0.497358	−	0.861449i
$122$		0			0
$123$	−2.26017	−	3.91472i	−0.203792	−	0.352979i
$124$		0			0
$125$	−11.9797			−1.07150
$126$		0			0
$127$	−14.9323			−1.32502			−0.662512	−	0.749052i	$-0.730510\pi$
$127$	−14.9323			−1.32502			−0.662512	+	0.749052i	$0.730510\pi$
$128$		0			0
$129$	2.26414	+	3.92161i	0.199347	+	0.345278i
$130$		0			0
$131$	−4.61868	+	7.99979i	−0.403536	+	0.698945i	−0.994150	−	0.108010i	$-0.965552\pi$
$131$	−4.61868	+	7.99979i	−0.403536	+	0.698945i	0.590614	+	0.806954i	$0.298886\pi$
$132$		0			0
$133$	8.12515	−	10.8195i	0.704540	−	0.938169i
$134$		0			0
$135$	−2.24008	+	3.87993i	−0.192795	+	0.333931i
$136$		0			0
$137$	0.100997	+	0.174931i	0.00862872	+	0.0149454i	0.870308	−	0.492509i	$-0.163920\pi$
$137$	0.100997	+	0.174931i	0.00862872	+	0.0149454i	−0.861679	+	0.507454i	$0.830587\pi$
$138$		0			0
$139$	−8.80733			−0.747028			−0.373514	−	0.927625i	$-0.621847\pi$
$139$	−8.80733			−0.747028			−0.373514	+	0.927625i	$0.621847\pi$
$140$		0			0
$141$	4.09882			0.345183
$142$		0			0
$143$	0.229439	+	0.397401i	0.0191867	+	0.0332323i
$144$		0			0
$145$	−2.04716	+	3.54579i	−0.170008	+	0.294462i
$146$		0			0
$147$	0.925910	+	3.18933i	0.0763677	+	0.263051i
$148$		0			0
$149$	2.45347	−	4.24953i	0.200996	−	0.348135i	−0.747854	−	0.663864i	$-0.768916\pi$
$149$	2.45347	−	4.24953i	0.200996	−	0.348135i	0.948850	+	0.315728i	$0.102249\pi$
$150$		0			0
$151$	1.51957	+	2.63197i	0.123661	+	0.214186i	0.921209	−	0.389069i	$-0.127203\pi$
$151$	1.51957	+	2.63197i	0.123661	+	0.214186i	−0.797548	+	0.603255i	$0.793870\pi$
$152$		0			0
$153$	−2.77492			−0.224339
$154$		0			0
$155$	−3.95040			−0.317304
$156$		0			0
$157$	9.95417	+	17.2411i	0.794429	+	1.37599i	0.923201	+	0.384317i	$0.125563\pi$
$157$	9.95417	+	17.2411i	0.794429	+	1.37599i	−0.128772	+	0.991674i	$0.541104\pi$
$158$		0			0
$159$	−2.75545	+	4.77259i	−0.218522	+	0.378491i
$160$		0			0
$161$	−5.82145	+	7.75187i	−0.458795	+	0.610933i
$162$		0			0
$163$	−2.77077	+	4.79912i	−0.217024	+	0.375896i	−0.953897	−	0.300135i	$-0.902968\pi$
$163$	−2.77077	+	4.79912i	−0.217024	+	0.375896i	0.736873	+	0.676031i	$0.236302\pi$
$164$		0			0
$165$	−0.0935233	−	0.161987i	−0.00728078	−	0.0126107i
$166$		0			0
$167$	3.42008			0.264654			0.132327	−	0.991206i	$-0.457755\pi$
$167$	3.42008			0.264654			0.132327	+	0.991206i	$0.457755\pi$
$168$		0			0
$169$	−9.37765			−0.721358
$170$		0			0
$171$	−7.09562	−	12.2900i	−0.542616	−	0.939838i
$172$		0			0
$173$	−5.67678	+	9.83247i	−0.431598	+	0.747549i	−0.997011	−	0.0772587i	$-0.975383\pi$
$173$	−5.67678	+	9.83247i	−0.431598	+	0.747549i	0.565414	+	0.824808i	$0.308717\pi$
$174$		0			0
$175$	2.41397	+	5.66101i	0.182479	+	0.427932i
$176$		0			0
$177$	−0.491256	+	0.850880i	−0.0369250	+	0.0639560i
$178$		0			0
$179$	−7.38337	−	12.7884i	−0.551859	−	0.955847i	−0.998141	−	0.0609548i	$-0.980585\pi$
$179$	−7.38337	−	12.7884i	−0.551859	−	0.955847i	0.446282	−	0.894892i	$-0.352748\pi$
$180$		0			0
$181$	4.00555			0.297730			0.148865	−	0.988858i	$-0.452438\pi$
$181$	4.00555			0.297730			0.148865	+	0.988858i	$0.452438\pi$
$182$		0			0
$183$	−5.06504			−0.374418
$184$		0			0
$185$	−2.74317	−	4.75132i	−0.201682	−	0.349324i
$186$		0			0
$187$	0.120552	−	0.208801i	0.00881560	−	0.0152691i
$188$		0			0
$189$	7.19623	+	0.871553i	0.523449	+	0.0633962i
$190$		0			0
$191$	10.8124	−	18.7276i	0.782357	−	1.35508i	−0.148209	−	0.988956i	$-0.547351\pi$
$191$	10.8124	−	18.7276i	0.782357	−	1.35508i	0.930565	−	0.366126i	$-0.119316\pi$
$192$		0			0
$193$	−7.76416	−	13.4479i	−0.558877	−	0.968002i	−0.997591	−	0.0693758i	$-0.977899\pi$
$193$	−7.76416	−	13.4479i	−0.558877	−	0.968002i	0.438714	−	0.898627i	$-0.355434\pi$
$194$		0			0
$195$	−1.47653			−0.105737
$196$		0			0
$197$	0.389479			0.0277492			0.0138746	−	0.999904i	$-0.495583\pi$
$197$	0.389479			0.0277492			0.0138746	+	0.999904i	$0.495583\pi$
$198$		0			0
$199$	−1.53439	−	2.65763i	−0.108770	−	0.188395i	0.806502	−	0.591231i	$-0.201358\pi$
$199$	−1.53439	−	2.65763i	−0.108770	−	0.188395i	−0.915272	+	0.402836i	$0.868024\pi$
$200$		0			0
$201$	−2.98090	+	5.16307i	−0.210256	+	0.364175i
$202$		0			0
$203$	6.57650	+	0.796497i	0.461580	+	0.0559031i
$204$		0			0
$205$	7.79010	−	13.4928i	0.544084	−	0.942381i
$206$		0			0
$207$	5.08382	+	8.80544i	0.353350	+	0.612020i
$208$		0			0
$209$	1.23303			0.0852904
$210$		0			0
$211$	−16.8747			−1.16170			−0.580850	−	0.814010i	$-0.697280\pi$
$211$	−16.8747			−1.16170			−0.580850	+	0.814010i	$0.697280\pi$
$212$		0			0
$213$	0.136707	+	0.236783i	0.00936701	+	0.0162241i
$214$		0			0
$215$	−7.80380	+	13.5166i	−0.532214	+	0.921822i
$216$		0			0
$217$	2.50712	+	5.87946i	0.170195	+	0.399124i
$218$		0			0
$219$	3.68734	−	6.38665i	0.249167	−	0.431570i
$220$		0			0
$221$	−0.951624	−	1.64826i	−0.0640131	−	0.110874i
$222$		0			0
$223$	−4.32590			−0.289683			−0.144842	−	0.989455i	$-0.546267\pi$
$223$	−4.32590			−0.289683			−0.144842	+	0.989455i	$0.546267\pi$
$224$		0			0
$225$	6.45466			0.430311
$226$		0			0
$227$	−12.0610	−	20.8902i	−0.800514	−	1.38653i	−0.919278	−	0.393609i	$-0.871226\pi$
$227$	−12.0610	−	20.8902i	−0.800514	−	1.38653i	0.118763	−	0.992923i	$-0.462107\pi$
$228$		0			0
$229$	0.204077	−	0.353472i	0.0134858	−	0.0233581i	−0.859204	−	0.511634i	$-0.829041\pi$
$229$	0.204077	−	0.353472i	0.0134858	−	0.0233581i	0.872690	+	0.488275i	$0.162374\pi$
$230$		0			0
$231$	−0.181734	+	0.241998i	−0.0119572	+	0.0159223i
$232$		0			0
$233$	0.787341	−	1.36371i	0.0515804	−	0.0893399i	−0.839082	−	0.544004i	$-0.816907\pi$
$233$	0.787341	−	1.36371i	0.0515804	−	0.0893399i	0.890663	+	0.454664i	$0.150241\pi$
$234$		0			0
$235$	7.06368	+	12.2346i	0.460784	+	0.798101i
$236$		0			0
$237$	4.01656			0.260903
$238$		0			0
$239$	−7.31831			−0.473382			−0.236691	−	0.971585i	$-0.576063\pi$
$239$	−7.31831			−0.473382			−0.236691	+	0.971585i	$0.576063\pi$
$240$		0			0
$241$	−6.53210	−	11.3139i	−0.420770	−	0.728795i	0.575245	−	0.817981i	$-0.304907\pi$
$241$	−6.53210	−	11.3139i	−0.420770	−	0.728795i	−0.996015	+	0.0891863i	$0.971573\pi$
$242$		0			0
$243$	5.77611	−	10.0045i	0.370537	−	0.641790i
$244$		0			0
$245$	−7.92423	+	8.26008i	−0.506261	+	0.527717i
$246$		0			0
$247$	4.86672	−	8.42940i	0.309662	−	0.536350i
$248$		0			0
$249$	0.244149	+	0.422878i	0.0154723	+	0.0267988i
$250$		0			0
$251$	−10.1335			−0.639619			−0.319810	−	0.947482i	$-0.603619\pi$
$251$	−10.1335			−0.639619			−0.319810	+	0.947482i	$0.603619\pi$
$252$		0			0
$253$	−0.883432			−0.0555409
$254$		0			0
$255$	0.387898	+	0.671859i	0.0242911	+	0.0420734i
$256$		0			0
$257$	−7.17544	+	12.4282i	−0.447591	+	0.775251i	−0.998229	−	0.0594936i	$-0.981051\pi$
$257$	−7.17544	+	12.4282i	−0.447591	+	0.775251i	0.550637	+	0.834745i	$0.314385\pi$
$258$		0			0
$259$	−5.33052	+	7.09814i	−0.331222	+	0.441057i
$260$		0			0
$261$	3.47398	−	6.01712i	0.215034	−	0.372450i
$262$		0			0
$263$	8.82134	+	15.2790i	0.543947	+	0.942144i	0.998672	+	0.0515119i	$0.0164040\pi$
$263$	8.82134	+	15.2790i	0.543947	+	0.942144i	−0.454726	+	0.890632i	$0.650263\pi$
$264$		0			0
$265$	−18.9944			−1.16682
$266$		0			0
$267$	−5.42126			−0.331776
$268$		0			0
$269$	−4.50383	−	7.80086i	−0.274603	−	0.475627i	0.695432	−	0.718592i	$-0.255213\pi$
$269$	−4.50383	−	7.80086i	−0.274603	−	0.475627i	−0.970035	+	0.242966i	$0.921880\pi$
$270$		0			0
$271$	9.75978	−	16.9044i	0.592864	−	1.02687i	−0.400980	−	0.916087i	$-0.631330\pi$
$271$	9.75978	−	16.9044i	0.592864	−	1.02687i	0.993844	−	0.110785i	$-0.0353364\pi$
$272$		0			0
$273$	0.937080	+	2.19755i	0.0567147	+	0.133002i
$274$		0			0
$275$	−0.280412	+	0.485687i	−0.0169095	+	0.0292881i
$276$		0			0
$277$	−13.1338	−	22.7483i	−0.789131	−	1.36681i	−0.926500	−	0.376294i	$-0.877198\pi$
$277$	−13.1338	−	22.7483i	−0.789131	−	1.36681i	0.137370	−	0.990520i	$-0.456135\pi$
$278$		0			0
$279$	6.70373			0.401342
$280$		0			0
$281$	−0.117643			−0.00701798			−0.00350899	−	0.999994i	$-0.501117\pi$
$281$	−0.117643			−0.00701798			−0.00350899	+	0.999994i	$0.501117\pi$
$282$		0			0
$283$	1.43448	+	2.48459i	0.0852708	+	0.147693i	0.905507	−	0.424332i	$-0.139491\pi$
$283$	1.43448	+	2.48459i	0.0852708	+	0.147693i	−0.820236	+	0.572026i	$0.806158\pi$
$284$		0			0
$285$	−1.98375	+	3.43596i	−0.117507	+	0.203529i
$286$		0			0
$287$	−25.0256	−	3.03092i	−1.47722	−	0.178909i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	−0.876751	−	1.51858i	−0.0513961	−	0.0890206i
$292$		0			0
$293$	−17.8039			−1.04011			−0.520057	−	0.854132i	$-0.674089\pi$
$293$	−17.8039			−1.04011			−0.520057	+	0.854132i	$0.674089\pi$
$294$		0			0
$295$	−3.38641			−0.197164
$296$		0			0
$297$	0.330287	+	0.572073i	0.0191652	+	0.0331950i
$298$		0			0
$299$	−3.48687	+	6.03943i	−0.201651	+	0.349270i
$300$		0			0
$301$	25.0696	+	3.03625i	1.44499	+	0.175006i
$302$		0			0
$303$	2.05931	−	3.56683i	0.118304	−	0.204909i
$304$		0			0
$305$	−8.72881	−	15.1187i	−0.499810	−	0.865697i
$306$		0			0
$307$	−21.8210			−1.24539			−0.622695	−	0.782465i	$-0.713962\pi$
$307$	−21.8210			−1.24539			−0.622695	+	0.782465i	$0.713962\pi$
$308$		0			0
$309$	6.69516			0.380874
$310$		0			0
$311$	−2.97172	−	5.14716i	−0.168511	−	0.291869i	0.769386	−	0.638784i	$-0.220562\pi$
$311$	−2.97172	−	5.14716i	−0.168511	−	0.291869i	−0.937896	+	0.346916i	$0.887229\pi$
$312$		0			0
$313$	6.43219	−	11.1409i	0.363569	−	0.629720i	−0.624976	−	0.780644i	$-0.714891\pi$
$313$	6.43219	−	11.1409i	0.363569	−	0.629720i	0.988545	+	0.150923i	$0.0482247\pi$
$314$		0			0
$315$	4.70905	+	11.0432i	0.265325	+	0.622214i
$316$		0			0
$317$	1.65872	−	2.87299i	0.0931629	−	0.161363i	−0.815677	−	0.578507i	$-0.803636\pi$
$317$	1.65872	−	2.87299i	0.0931629	−	0.161363i	0.908840	+	0.417144i	$0.136969\pi$
$318$		0			0
$319$	0.301843	+	0.522807i	0.0169000	+	0.0292716i
$320$		0			0
$321$	6.57223			0.366826
$322$		0			0
$323$	−5.11412			−0.284557
$324$		0			0
$325$	2.21355	+	3.83398i	0.122785	+	0.212671i
$326$		0			0
$327$	−1.48672	+	2.57508i	−0.0822159	+	0.142402i
$328$		0			0
$329$	13.7261	−	18.2777i	0.756744	−	1.00768i
$330$		0			0
$331$	−3.72252	+	6.44760i	−0.204608	+	0.354392i	−0.950008	−	0.312226i	$-0.898925\pi$
$331$	−3.72252	+	6.44760i	−0.204608	+	0.354392i	0.745399	+	0.666618i	$0.232259\pi$
$332$		0			0
$333$	4.65509	+	8.06286i	0.255098	+	0.441842i
$334$		0			0
$335$	−20.5485			−1.12268
$336$		0			0
$337$	−4.05359			−0.220813			−0.110407	−	0.993887i	$-0.535215\pi$
$337$	−4.05359			−0.220813			−0.110407	+	0.993887i	$0.535215\pi$
$338$		0			0
$339$	−3.46293	−	5.99797i	−0.188080	−	0.325765i
$340$		0			0
$341$	−0.291232	+	0.504429i	−0.0157711	+	0.0273164i
$342$		0			0
$343$	17.3227	+	6.55152i	0.935340	+	0.353749i
$344$		0			0
$345$	1.42131	−	2.46177i	0.0765205	−	0.132537i
$346$		0			0
$347$	17.6541	+	30.5778i	0.947722	+	1.64150i	0.750206	+	0.661204i	$0.229954\pi$
$347$	17.6541	+	30.5778i	0.947722	+	1.64150i	0.197516	+	0.980300i	$0.436713\pi$
$348$		0			0
$349$	−1.80670			−0.0967104			−0.0483552	−	0.998830i	$-0.515398\pi$
$349$	−1.80670			−0.0967104			−0.0483552	+	0.998830i	$0.515398\pi$
$350$		0			0
$351$	5.21451			0.278330
$352$		0			0
$353$	0.225328	+	0.390280i	0.0119930	+	0.0207725i	0.871960	−	0.489578i	$-0.162849\pi$
$353$	0.225328	+	0.390280i	0.0119930	+	0.0207725i	−0.859967	+	0.510350i	$0.829516\pi$
$354$		0			0
$355$	−0.471187	+	0.816119i	−0.0250080	+	0.0433151i
$356$		0			0
$357$	0.753760	−	1.00371i	0.0398932	−	0.0531220i
$358$		0			0
$359$	−18.1137	+	31.3739i	−0.956007	+	1.65585i	−0.223960	+	0.974598i	$0.571899\pi$
$359$	−18.1137	+	31.3739i	−0.956007	+	1.65585i	−0.732047	+	0.681254i	$0.761435\pi$
$360$		0			0
$361$	−3.57710	−	6.19572i	−0.188269	−	0.326091i
$362$		0			0
$363$	5.19116			0.272465
$364$		0			0
$365$	25.4182			1.33045
$366$		0			0
$367$	9.63081	+	16.6811i	0.502724	+	0.870744i	0.999995	+	0.00314852i	$0.00100221\pi$
$367$	9.63081	+	16.6811i	0.502724	+	0.870744i	−0.497271	+	0.867595i	$0.665664\pi$
$368$		0			0
$369$	−13.2196	+	22.8970i	−0.688184	+	1.19197i
$370$		0			0
$371$	12.0548	+	28.2697i	0.625854	+	1.46769i
$372$		0			0
$373$	11.2166	−	19.4277i	0.580774	−	1.00593i	−0.414613	−	0.909998i	$-0.636083\pi$
$373$	11.2166	−	19.4277i	0.580774	−	1.00593i	0.995388	−	0.0959331i	$-0.0305835\pi$
$374$		0			0
$375$	−2.84177	−	4.92209i	−0.146748	−	0.254175i
$376$		0			0
$377$	4.76544			0.245433
$378$		0			0
$379$	1.03798			0.0533176			0.0266588	−	0.999645i	$-0.491513\pi$
$379$	1.03798			0.0533176			0.0266588	+	0.999645i	$0.491513\pi$
$380$		0			0
$381$	−3.54216	−	6.13520i	−0.181470	−	0.314316i
$382$		0			0
$383$	11.5778	−	20.0534i	0.591600	−	1.02468i	−0.402417	−	0.915456i	$-0.631830\pi$
$383$	11.5778	−	20.0534i	0.591600	−	1.02468i	0.994017	−	0.109225i	$-0.0348368\pi$
$384$		0			0
$385$	−1.03553	−	0.125416i	−0.0527757	−	0.00639180i
$386$		0			0
$387$	13.2428	−	22.9373i	0.673171	−	1.16597i
$388$		0			0
$389$	18.3216	+	31.7339i	0.928940	+	1.60897i	0.785099	+	0.619370i	$0.212612\pi$
$389$	18.3216	+	31.7339i	0.928940	+	1.60897i	0.143840	+	0.989601i	$0.454055\pi$
$390$		0			0
$391$	3.66413			0.185303
$392$		0			0
$393$	−4.38248			−0.221067
$394$		0			0
$395$	6.92192	+	11.9891i	0.348279	+	0.603238i
$396$		0			0
$397$	8.58159	−	14.8638i	0.430698	−	0.745991i	−0.566236	−	0.824243i	$-0.691601\pi$
$397$	8.58159	−	14.8638i	0.430698	−	0.745991i	0.996934	+	0.0782528i	$0.0249341\pi$
$398$		0			0
$399$	6.37280	+	0.771825i	0.319039	+	0.0386396i
$400$		0			0
$401$	−1.97898	+	3.42770i	−0.0988256	+	0.171171i	−0.911199	−	0.411967i	$-0.864842\pi$
$401$	−1.97898	+	3.42770i	−0.0988256	+	0.171171i	0.812373	+	0.583138i	$0.198175\pi$
$402$		0			0
$403$	2.29896	+	3.98192i	0.114520	+	0.198354i
$404$		0			0
$405$	11.4872			0.570805
$406$		0			0
$407$	−0.808931			−0.0400972
$408$		0			0
$409$	−3.03370	−	5.25452i	−0.150007	−	0.259819i	0.781223	−	0.624252i	$-0.214596\pi$
$409$	−3.03370	−	5.25452i	−0.150007	−	0.259819i	−0.931230	+	0.364433i	$0.881263\pi$
$410$		0			0
$411$	−0.0479159	+	0.0829927i	−0.00236351	+	0.00409373i
$412$		0			0
$413$	2.14919	+	5.04006i	0.105754	+	0.248005i
$414$		0			0
$415$	−0.841505	+	1.45753i	−0.0413078	+	0.0715473i
$416$		0			0
$417$	−2.08923	−	3.61866i	−0.102310	−	0.177206i
$418$		0			0
$419$	5.33057			0.260415			0.130208	−	0.991487i	$-0.458436\pi$
$419$	5.33057			0.260415			0.130208	+	0.991487i	$0.458436\pi$
$420$		0			0
$421$	17.1834			0.837466			0.418733	−	0.908109i	$-0.362474\pi$
$421$	17.1834			0.837466			0.418733	+	0.908109i	$0.362474\pi$
$422$		0			0
$423$	−11.9869	−	20.7619i	−0.582822	−	1.00948i
$424$		0			0
$425$	1.16304	−	2.01444i	0.0564156	−	0.0977146i
$426$		0			0
$427$	−16.9618	+	22.5864i	−0.820837	+	1.09303i
$428$		0			0
$429$	−0.108853	+	0.188539i	−0.00525547	+	0.00910275i
$430$		0			0
$431$	−2.81008	−	4.86720i	−0.135357	−	0.234445i	0.790377	−	0.612621i	$-0.209885\pi$
$431$	−2.81008	−	4.86720i	−0.135357	−	0.234445i	−0.925734	+	0.378176i	$0.876551\pi$
$432$		0			0
$433$	−6.15198			−0.295645			−0.147823	−	0.989014i	$-0.547227\pi$
$433$	−6.15198			−0.295645			−0.147823	+	0.989014i	$0.547227\pi$
$434$		0			0
$435$	−1.94247			−0.0931345
$436$		0			0
$437$	9.36939	+	16.2283i	0.448199	+	0.776303i
$438$		0			0
$439$	−19.3334	+	33.4864i	−0.922731	+	1.59822i	−0.127562	+	0.991831i	$0.540715\pi$
$439$	−19.3334	+	33.4864i	−0.922731	+	1.59822i	−0.795170	+	0.606387i	$0.792618\pi$
$440$		0			0
$441$	13.4472	−	14.0171i	0.640343	−	0.667483i
$442$		0			0
$443$	17.4494	−	30.2232i	0.829045	−	1.43595i	−0.0697441	−	0.997565i	$-0.522218\pi$
$443$	17.4494	−	30.2232i	0.829045	−	1.43595i	0.898789	−	0.438382i	$-0.144448\pi$
$444$		0			0
$445$	−9.34270	−	16.1820i	−0.442887	−	0.767102i
$446$		0			0
$447$	2.32800			0.110111
$448$		0			0
$449$	13.1959			0.622752			0.311376	−	0.950287i	$-0.399210\pi$
$449$	13.1959			0.622752			0.311376	+	0.950287i	$0.399210\pi$
$450$		0			0
$451$	−1.14861	−	1.98944i	−0.0540857	−	0.0936792i
$452$		0			0
$453$	−0.720928	+	1.24868i	−0.0338722	+	0.0586683i
$454$		0			0
$455$	−4.94460	+	6.58424i	−0.231806	+	0.308674i
$456$		0			0
$457$	10.8853	−	18.8539i	0.509193	−	0.881948i	−0.490751	−	0.871300i	$-0.663277\pi$
$457$	10.8853	−	18.8539i	0.509193	−	0.881948i	0.999943	−	0.0106475i	$-0.00338927\pi$
$458$		0			0
$459$	−1.36990	−	2.37273i	−0.0639414	−	0.110750i
$460$		0			0
$461$	20.9376			0.975159			0.487579	−	0.873079i	$-0.337880\pi$
$461$	20.9376			0.975159			0.487579	+	0.873079i	$0.337880\pi$
$462$		0			0
$463$	12.4193			0.577175			0.288588	−	0.957453i	$-0.406814\pi$
$463$	12.4193			0.577175			0.288588	+	0.957453i	$0.406814\pi$
$464$		0			0
$465$	−0.937096	−	1.62310i	−0.0434568	−	0.0752693i
$466$		0			0
$467$	−4.71506	+	8.16672i	−0.218187	+	0.377911i	−0.954254	−	0.298998i	$-0.903348\pi$
$467$	−4.71506	+	8.16672i	−0.218187	+	0.377911i	0.736067	+	0.676909i	$0.236681\pi$
$468$		0			0
$469$	13.0411	+	30.5827i	0.602181	+	1.41218i
$470$		0			0
$471$	−4.72256	+	8.17971i	−0.217604	+	0.376901i
$472$		0			0
$473$	1.15063	+	1.99294i	0.0529058	+	0.0916355i
$474$		0			0
$475$	11.8958			0.545817
$476$		0			0
$477$	32.2330			1.47585
$478$		0			0
$479$	−0.259657	−	0.449739i	−0.0118640	−	0.0205491i	0.860032	−	0.510239i	$-0.170443\pi$
$479$	−0.259657	−	0.449739i	−0.0118640	−	0.0205491i	−0.871896	+	0.489690i	$0.837110\pi$
$480$		0			0
$481$	−3.19282	+	5.53012i	−0.145580	+	0.252152i
$482$		0			0
$483$	−4.56594	−	0.552992i	−0.207757	−	0.0251620i
$484$		0			0
$485$	3.02189	−	5.23407i	0.137217	−	0.237667i
$486$		0			0
$487$	18.7952	+	32.5542i	0.851691	+	1.47517i	0.879681	+	0.475565i	$0.157756\pi$
$487$	18.7952	+	32.5542i	0.851691	+	1.47517i	−0.0279894	+	0.999608i	$0.508910\pi$
$488$		0			0
$489$	−2.62908			−0.118891
$490$		0			0
$491$	−27.0798			−1.22210			−0.611048	−	0.791593i	$-0.709252\pi$
$491$	−27.0798			−1.22210			−0.611048	+	0.791593i	$0.709252\pi$
$492$		0			0
$493$	−1.25192	−	2.16840i	−0.0563838	−	0.0976597i
$494$		0			0
$495$	−0.547013	+	0.947453i	−0.0245864	+	0.0425849i
$496$		0			0
$497$	1.51368	+	0.183326i	0.0678980	+	0.00822329i
$498$		0			0
$499$	14.0361	−	24.3112i	0.628342	−	1.08832i	−0.359543	−	0.933129i	$-0.617067\pi$
$499$	14.0361	−	24.3112i	0.628342	−	1.08832i	0.987884	−	0.155191i	$-0.0495994\pi$
$500$		0			0
$501$	0.811295	+	1.40520i	0.0362460	+	0.0627799i
$502$		0			0
$503$	−33.5454			−1.49572			−0.747858	−	0.663858i	$-0.768918\pi$
$503$	−33.5454			−1.49572			−0.747858	+	0.663858i	$0.768918\pi$
$504$		0			0
$505$	14.1956			0.631697
$506$		0			0
$507$	−2.22452	−	3.85298i	−0.0987944	−	0.171117i
$508$		0			0
$509$	−5.54900	+	9.61116i	−0.245955	+	0.426007i	−0.962400	−	0.271637i	$-0.912435\pi$
$509$	−5.54900	+	9.61116i	−0.245955	+	0.426007i	0.716445	+	0.697644i	$0.245768\pi$
$510$		0			0
$511$	−16.1317	−	37.8304i	−0.713623	−	1.67352i
$512$		0			0
$513$	7.00582	−	12.1344i	0.309314	−	0.535748i
$514$		0			0
$515$	11.5381	+	19.9845i	0.508428	+	0.880623i
$516$		0			0
$517$	2.08300			0.0916102
$518$		0			0
$519$	−5.38647			−0.236440
$520$		0			0
$521$	17.4319	+	30.1929i	0.763704	+	1.32277i	0.940929	+	0.338604i	$0.109955\pi$
$521$	17.4319	+	30.1929i	0.763704	+	1.32277i	−0.177225	+	0.984170i	$0.556712\pi$
$522$		0			0
$523$	−11.9368	+	20.6752i	−0.521961	+	0.904063i	0.477712	+	0.878516i	$0.341466\pi$
$523$	−11.9368	+	20.6752i	−0.521961	+	0.904063i	−0.999674	+	0.0255470i	$0.991867\pi$
$524$		0			0
$525$	−1.75330	+	2.33470i	−0.0765204	+	0.101895i
$526$		0			0
$527$	1.20792	−	2.09217i	0.0526177	−	0.0911365i
$528$		0			0
$529$	4.78709	+	8.29148i	0.208134	+	0.360499i
$530$		0			0
$531$	5.74665			0.249383
$532$		0			0
$533$	−18.1340			−0.785470
$534$		0			0
$535$	11.3262	+	19.6176i	0.489675	+	0.848143i
$536$		0			0
$537$	3.50289	−	6.06719i	0.151161	−	0.261818i
$538$		0			0
$539$	0.470542	+	1.62080i	0.0202677	+	0.0698128i
$540$		0			0
$541$	−8.72549	+	15.1130i	−0.375138	+	0.649758i	−0.990348	−	0.138605i	$-0.955738\pi$
$541$	−8.72549	+	15.1130i	−0.375138	+	0.649758i	0.615210	+	0.788364i	$0.289071\pi$
$542$		0			0
$543$	0.950177	+	1.64576i	0.0407760	+	0.0706261i
$544$		0			0
$545$	−10.2485			−0.438999
$546$		0			0
$547$	17.0311			0.728198			0.364099	−	0.931360i	$-0.381377\pi$
$547$	17.0311			0.728198			0.364099	+	0.931360i	$0.381377\pi$
$548$		0			0
$549$	14.8126	+	25.6561i	0.632185	+	1.09498i
$550$		0			0
$551$	6.40249	−	11.0894i	0.272755	−	0.472426i
$552$		0			0
$553$	13.4506	−	17.9109i	0.571979	−	0.761649i
$554$		0			0
$555$	1.30144	−	2.25417i	0.0552433	−	0.0956841i
$556$		0			0
$557$	−0.877019	−	1.51904i	−0.0371605	−	0.0643639i	0.846847	−	0.531837i	$-0.178498\pi$
$557$	−0.877019	−	1.51904i	−0.0371605	−	0.0643639i	−0.884007	+	0.467473i	$0.845165\pi$
$558$		0			0
$559$	18.1659			0.768335
$560$		0			0
$561$	0.114387			0.00482941
$562$		0			0
$563$	−18.3305	−	31.7494i	−0.772539	−	1.33808i	−0.936167	−	0.351554i	$-0.885653\pi$
$563$	−18.3305	−	31.7494i	−0.772539	−	1.33808i	0.163629	−	0.986522i	$-0.447680\pi$
$564$		0			0
$565$	11.9356	−	20.6731i	0.502136	−	0.869726i
$566$		0			0
$567$	−7.29037	−	17.0967i	−0.306167	−	0.717992i
$568$		0			0
$569$	−20.8523	+	36.1172i	−0.874173	+	1.51411i	−0.0165316	+	0.999863i	$0.505262\pi$
$569$	−20.8523	+	36.1172i	−0.874173	+	1.51411i	−0.857641	+	0.514248i	$0.828071\pi$
$570$		0			0
$571$	4.53790	+	7.85987i	0.189905	+	0.328925i	0.945218	−	0.326439i	$-0.105849\pi$
$571$	4.53790	+	7.85987i	0.189905	+	0.328925i	−0.755313	+	0.655364i	$0.772515\pi$
$572$		0			0
$573$	10.2594			0.428595
$574$		0			0
$575$	−8.52303			−0.355435
$576$		0			0
$577$	−22.7712	−	39.4409i	−0.947977	−	1.64194i	−0.749677	−	0.661803i	$-0.769791\pi$
$577$	−22.7712	−	39.4409i	−0.947977	−	1.64194i	−0.198300	−	0.980141i	$-0.563542\pi$
$578$		0			0
$579$	3.68355	−	6.38010i	0.153083	−	0.265148i
$580$		0			0
$581$	2.70333	+	0.327407i	0.112153	+	0.0135831i
$582$		0			0
$583$	−1.40031	+	2.42540i	−0.0579948	+	0.100450i
$584$		0			0
$585$	4.31807	+	7.47912i	0.178530	+	0.309224i
$586$		0			0
$587$	−14.6764			−0.605759			−0.302879	−	0.953029i	$-0.597948\pi$
$587$	−14.6764			−0.605759			−0.302879	+	0.953029i	$0.597948\pi$
$588$		0			0
$589$	12.3549			0.509073
$590$		0			0
$591$	0.0923903	+	0.160025i	0.00380043	+	0.00658254i
$592$		0			0
$593$	11.2216	−	19.4364i	0.460817	−	0.798158i	−0.538185	−	0.842827i	$-0.680890\pi$
$593$	11.2216	−	19.4364i	0.460817	−	0.798158i	0.999002	+	0.0446688i	$0.0142232\pi$
$594$		0			0
$595$	4.29499	+	0.520176i	0.176077	+	0.0213251i
$596$		0			0
$597$	0.727959	−	1.26086i	0.0297934	−	0.0516037i
$598$		0			0
$599$	9.54172	+	16.5267i	0.389864	+	0.675264i	0.992431	−	0.122804i	$-0.0391887\pi$
$599$	9.54172	+	16.5267i	0.389864	+	0.675264i	−0.602567	+	0.798068i	$0.705855\pi$
$600$		0			0
$601$	−13.1280			−0.535503			−0.267751	−	0.963488i	$-0.586281\pi$
$601$	−13.1280			−0.535503			−0.267751	+	0.963488i	$0.586281\pi$
$602$		0			0
$603$	34.8702			1.42002
$604$		0			0
$605$	8.94615	+	15.4952i	0.363713	+	0.629969i
$606$		0			0
$607$	6.93698	−	12.0152i	0.281563	−	0.487682i	−0.690207	−	0.723612i	$-0.742480\pi$
$607$	6.93698	−	12.0152i	0.281563	−	0.487682i	0.971770	+	0.235930i	$0.0758138\pi$
$608$		0			0
$609$	1.23279	+	2.89102i	0.0499552	+	0.117150i
$610$		0			0
$611$	8.22151	−	14.2401i	0.332607	−	0.576092i
$612$		0			0
$613$	−22.0584	−	38.2063i	−0.890931	−	1.54314i	−0.838761	−	0.544500i	$-0.816719\pi$
$613$	−22.0584	−	38.2063i	−0.890931	−	1.54314i	−0.0521706	−	0.998638i	$-0.516614\pi$
$614$		0			0
$615$	7.39172			0.298063
$616$		0			0
$617$	−35.7861			−1.44069			−0.720347	−	0.693614i	$-0.756018\pi$
$617$	−35.7861			−1.44069			−0.720347	+	0.693614i	$0.756018\pi$
$618$		0			0
$619$	6.83536	+	11.8392i	0.274736	+	0.475857i	0.970069	−	0.242831i	$-0.0780761\pi$
$619$	6.83536	+	11.8392i	0.274736	+	0.475857i	−0.695332	+	0.718688i	$0.744743\pi$
$620$		0			0
$621$	−5.01948	+	8.69399i	−0.201425	+	0.348878i
$622$		0			0
$623$	−18.1547	+	24.1748i	−0.727352	+	0.968545i
$624$		0			0
$625$	3.97951	−	6.89271i	0.159180	−	0.275708i
$626$		0			0
$627$	0.292493	+	0.506613i	0.0116811	+	0.0202322i
$628$		0			0
$629$	3.35512			0.133778
$630$		0			0
$631$	−11.5439			−0.459557			−0.229779	−	0.973243i	$-0.573800\pi$
$631$	−11.5439			−0.459557			−0.229779	+	0.973243i	$0.573800\pi$
$632$		0			0
$633$	−4.00293	−	6.93328i	−0.159102	−	0.275573i
$634$		0			0
$635$	12.2087	−	21.1461i	0.484488	−	0.839158i
$636$		0			0
$637$	12.9375	+	3.18045i	0.512604	+	0.126014i
$638$		0			0
$639$	0.799591	−	1.38493i	0.0316313	−	0.0547871i
$640$		0			0
$641$	−7.05438	−	12.2185i	−0.278631	−	0.482604i	0.692414	−	0.721501i	$-0.256547\pi$
$641$	−7.05438	−	12.2185i	−0.278631	−	0.482604i	−0.971045	+	0.238897i	$0.923214\pi$
$642$		0			0
$643$	31.8841			1.25738			0.628692	−	0.777654i	$-0.283590\pi$
$643$	31.8841			1.25738			0.628692	+	0.777654i	$0.283590\pi$
$644$		0			0
$645$	−7.40472			−0.291560
$646$		0			0
$647$	1.34019	+	2.32128i	0.0526884	+	0.0912589i	0.891167	−	0.453676i	$-0.149888\pi$
$647$	1.34019	+	2.32128i	0.0526884	+	0.0912589i	−0.838478	+	0.544935i	$0.816554\pi$
$648$		0			0
$649$	−0.249654	+	0.432413i	−0.00979976	+	0.0169737i
$650$		0			0
$651$	−1.82096	+	2.42480i	−0.0713690	+	0.0950352i
$652$		0			0
$653$	−1.94055	+	3.36114i	−0.0759398	+	0.131532i	−0.901495	−	0.432790i	$-0.857529\pi$
$653$	−1.94055	+	3.36114i	−0.0759398	+	0.131532i	0.825555	+	0.564322i	$0.190862\pi$
$654$		0			0
$655$	−7.55253	−	13.0814i	−0.295102	−	0.511131i
$656$		0			0
$657$	−43.1340			−1.68282
$658$		0			0
$659$	−18.8524			−0.734383			−0.367192	−	0.930145i	$-0.619681\pi$
$659$	−18.8524			−0.734383			−0.367192	+	0.930145i	$0.619681\pi$
$660$		0			0
$661$	10.2000	+	17.6669i	0.396734	+	0.687164i	0.993321	−	0.115385i	$-0.0368101\pi$
$661$	10.2000	+	17.6669i	0.396734	+	0.687164i	−0.596586	+	0.802549i	$0.703477\pi$
$662$		0			0
$663$	0.451479	−	0.781985i	0.0175340	−	0.0303698i
$664$		0			0
$665$	8.67869	+	20.3524i	0.336545	+	0.789233i
$666$		0			0
$667$	−4.58721	+	7.94528i	−0.177617	+	0.307642i
$668$		0			0
$669$	−1.02617	−	1.77738i	−0.0396740	−	0.0687173i
$670$		0			0
$671$	−2.57403			−0.0993692
$672$		0			0
$673$	51.4240			1.98225			0.991125	−	0.132931i	$-0.0424389\pi$
$673$	51.4240			1.98225			0.991125	+	0.132931i	$0.0424389\pi$
$674$		0			0
$675$	3.18648	+	5.51915i	0.122648	+	0.212432i
$676$		0			0
$677$	−12.2023	+	21.1349i	−0.468971	+	0.812281i	−0.999371	−	0.0354664i	$-0.988708\pi$
$677$	−12.2023	+	21.1349i	−0.468971	+	0.812281i	0.530400	+	0.847747i	$0.322042\pi$
$678$		0			0
$679$	−9.70780	−	1.17574i	−0.372551	−	0.0451206i
$680$		0			0
$681$	5.72209	−	9.91095i	0.219271	−	0.379788i
$682$		0			0
$683$	11.5015	+	19.9211i	0.440091	+	0.762260i	0.997696	−	0.0678467i	$-0.0216129\pi$
$683$	11.5015	+	19.9211i	0.440091	+	0.762260i	−0.557605	+	0.830107i	$0.688280\pi$
$684$		0			0
$685$	−0.330302			−0.0126202
$686$		0			0
$687$	0.193641			0.00738785
$688$		0			0
$689$	11.0539	+	19.1459i	0.421121	+	0.729402i
$690$		0			0
$691$	4.25661	−	7.37267i	0.161929	−	0.280469i	−0.773631	−	0.633636i	$-0.781562\pi$
$691$	4.25661	−	7.37267i	0.161929	−	0.280469i	0.935560	+	0.353166i	$0.114895\pi$
$692$		0			0
$693$	1.75727	+	0.212828i	0.0667533	+	0.00808466i
$694$		0			0
$695$	7.20093	−	12.4724i	0.273147	−	0.473104i
$696$		0			0
$697$	4.76396	+	8.25142i	0.180448	+	0.312545i
$698$		0			0
$699$	0.747077			0.0282570
$700$		0			0
$701$	−28.3455			−1.07060			−0.535298	−	0.844663i	$-0.679801\pi$
$701$	−28.3455			−1.07060			−0.535298	+	0.844663i	$0.679801\pi$
$702$		0			0
$703$	8.57925	+	14.8597i	0.323573	+	0.560444i
$704$		0			0
$705$	−3.35122	+	5.80449i	−0.126214	+	0.218610i
$706$		0			0
$707$	−9.00925	−	21.1276i	−0.338828	−	0.794585i
$708$		0			0
$709$	−11.1436	+	19.3013i	−0.418506	+	0.724874i	−0.995789	−	0.0916701i	$-0.970779\pi$
$709$	−11.1436	+	19.3013i	−0.418506	+	0.724874i	0.577283	+	0.816544i	$0.304113\pi$
$710$		0			0
$711$	−11.7463	−	20.3452i	−0.440521	−	0.763005i
$712$		0			0
$713$	−8.85191			−0.331507
$714$		0			0
$715$	−0.750365			−0.0280621
$716$		0			0
$717$	−1.73601	−	3.00686i	−0.0648326	−	0.112293i
$718$		0			0
$719$	9.56097	−	16.5601i	0.356564	−	0.617587i	−0.630820	−	0.775929i	$-0.717281\pi$
$719$	9.56097	−	16.5601i	0.356564	−	0.617587i	0.987384	+	0.158342i	$0.0506148\pi$
$720$		0			0
$721$	22.4207	−	29.8555i	0.834991	−	1.11188i
$722$		0			0
$723$	3.09903	−	5.36768i	0.115254	−	0.199626i
$724$		0			0
$725$	2.91207	+	5.04385i	0.108151	+	0.187324i
$726$		0			0
$727$	−8.01996			−0.297444			−0.148722	−	0.988879i	$-0.547516\pi$
$727$	−8.01996			−0.297444			−0.148722	+	0.988879i	$0.547516\pi$
$728$		0			0
$729$	−15.5940			−0.577555
$730$		0			0
$731$	−4.77234	−	8.26593i	−0.176511	−	0.305727i
$732$		0			0
$733$	−18.1380	+	31.4159i	−0.669941	+	1.16037i	0.307979	+	0.951393i	$0.400347\pi$
$733$	−18.1380	+	31.4159i	−0.669941	+	1.16037i	−0.977920	+	0.208979i	$0.932986\pi$
$734$		0			0
$735$	−5.27356	−	1.29640i	−0.194518	−	0.0478185i
$736$		0			0
$737$	−1.51488	+	2.62384i	−0.0558012	+	0.0966506i
$738$		0			0
$739$	18.2500	+	31.6099i	0.671336	+	1.16279i	0.977525	+	0.210817i	$0.0676126\pi$
$739$	18.2500	+	31.6099i	0.671336	+	1.16279i	−0.306189	+	0.951971i	$0.599054\pi$
$740$		0			0
$741$	4.61784			0.169640
$742$		0			0
$743$	5.06824			0.185936			0.0929678	−	0.995669i	$-0.470365\pi$
$743$	5.06824			0.185936			0.0929678	+	0.995669i	$0.470365\pi$
$744$		0			0
$745$	4.01195	+	6.94890i	0.146986	+	0.254588i
$746$		0			0
$747$	1.42801	−	2.47339i	0.0522482	−	0.0904965i
$748$		0			0
$749$	22.0091	−	29.3073i	0.804193	−	1.07087i
$750$		0			0
$751$	−12.6068	+	21.8356i	−0.460029	+	0.796794i	−0.998962	−	0.0455548i	$-0.985494\pi$
$751$	−12.6068	+	21.8356i	−0.460029	+	0.796794i	0.538933	+	0.842349i	$0.318828\pi$
$752$		0			0
$753$	−2.40381	−	4.16353i	−0.0875999	−	0.151727i
$754$		0			0
$755$	−4.96963			−0.180863
$756$		0			0
$757$	−7.28908			−0.264926			−0.132463	−	0.991188i	$-0.542289\pi$
$757$	−7.28908			−0.264926			−0.132463	+	0.991188i	$0.542289\pi$
$758$		0			0
$759$	−0.209563	−	0.362975i	−0.00760667	−	0.0131751i
$760$		0			0
$761$	−2.65844	+	4.60455i	−0.0963683	+	0.166915i	−0.910179	−	0.414215i	$-0.864056\pi$
$761$	−2.65844	+	4.60455i	−0.0963683	+	0.166915i	0.813811	+	0.581130i	$0.197389\pi$
$762$		0			0
$763$	6.50423	+	15.2531i	0.235469	+	0.552199i
$764$		0			0
$765$	2.26879	−	3.92966i	0.0820283	−	0.142077i
$766$		0			0
$767$	1.97074	+	3.41343i	0.0711595	+	0.123252i
$768$		0			0
$769$	−32.0489			−1.15571			−0.577857	−	0.816138i	$-0.696111\pi$
$769$	−32.0489			−1.15571			−0.577857	+	0.816138i	$0.696111\pi$
$770$		0			0
$771$	−6.80849			−0.245202
$772$		0			0
$773$	−2.85261	−	4.94087i	−0.102601	−	0.177711i	0.810154	−	0.586217i	$-0.199383\pi$
$773$	−2.85261	−	4.94087i	−0.102601	−	0.177711i	−0.912756	+	0.408506i	$0.866050\pi$
$774$		0			0
$775$	−2.80970	+	4.86655i	−0.100927	+	0.174812i
$776$		0			0
$777$	−4.18088	−	0.506357i	−0.149988	−	0.0181655i
$778$		0			0
$779$	−24.3635	+	42.1987i	−0.872911	+	1.51193i
$780$		0			0
$781$	0.0694738	+	0.120332i	0.00248597	+	0.00430582i
$782$		0			0
$783$	6.86003			0.245158
$784$		0			0
$785$	−32.5544			−1.16192
$786$		0			0
$787$	−19.8183	−	34.3263i	−0.706446	−	1.22360i	−0.966167	−	0.257917i	$-0.916964\pi$
$787$	−19.8183	−	34.3263i	−0.706446	−	1.22360i	0.259721	−	0.965684i	$-0.416370\pi$
$788$		0			0
$789$	−4.18511	+	7.24882i	−0.148994	+	0.258065i
$790$		0			0
$791$	−38.3432	−	4.64384i	−1.36333	−	0.165116i
$792$		0			0
$793$	−10.1596	+	17.5969i	−0.360777	+	0.624884i
$794$		0			0
$795$	−4.50576	−	7.80420i	−0.159803	−	0.276787i
$796$		0			0
$797$	−30.9698			−1.09701			−0.548503	−	0.836148i	$-0.684802\pi$
$797$	−30.9698			−1.09701			−0.548503	+	0.836148i	$0.684802\pi$
$798$		0			0
$799$	−8.63945			−0.305642
$800$		0			0
$801$	15.8543	+	27.4605i	0.560185	+	0.970269i
$802$		0			0
$803$	1.87389	−	3.24566i	0.0661280	−	0.114537i
$804$		0			0
$805$	−6.21805	−	14.5820i	−0.219157	−	0.513946i
$806$		0			0
$807$	2.13675	−	3.70096i	0.0752172	−	0.130280i
$808$		0			0
$809$	19.9944	+	34.6314i	0.702967	+	1.21757i	0.967420	+	0.253176i	$0.0814751\pi$
$809$	19.9944	+	34.6314i	0.702967	+	1.21757i	−0.264453	+	0.964398i	$0.585192\pi$
$810$		0			0
$811$	−8.21437			−0.288446			−0.144223	−	0.989545i	$-0.546068\pi$
$811$	−8.21437			−0.288446			−0.144223	+	0.989545i	$0.546068\pi$
$812$		0			0
$813$	9.26067			0.324786
$814$		0			0
$815$	−4.53081	−	7.84759i	−0.158707	−	0.274889i
$816$		0			0
$817$	24.4063	−	42.2729i	0.853868	−	1.47894i
$818$		0			0
$819$	8.39085	−	11.1733i	0.293200	−	0.390426i
$820$		0			0
$821$	24.6670	−	42.7246i	0.860886	−	1.49110i	−0.0101897	−	0.999948i	$-0.503244\pi$
$821$	24.6670	−	42.7246i	0.860886	−	1.49110i	0.871075	−	0.491150i	$-0.163423\pi$
$822$		0			0
$823$	−0.988862	−	1.71276i	−0.0344696	−	0.0597031i	0.848276	−	0.529554i	$-0.177641\pi$
$823$	−0.988862	−	1.71276i	−0.0344696	−	0.0597031i	−0.882746	+	0.469851i	$0.844308\pi$
$824$		0			0
$825$	−0.266072			−0.00926343
$826$		0			0
$827$	−9.58007			−0.333132			−0.166566	−	0.986030i	$-0.553268\pi$
$827$	−9.58007			−0.333132			−0.166566	+	0.986030i	$0.553268\pi$
$828$		0			0
$829$	−5.97750	−	10.3533i	−0.207607	−	0.359586i	0.743353	−	0.668899i	$-0.233234\pi$
$829$	−5.97750	−	10.3533i	−0.207607	−	0.359586i	−0.950960	+	0.309313i	$0.899901\pi$
$830$		0			0
$831$	6.23105	−	10.7925i	0.216153	−	0.374388i
$832$		0			0
$833$	−1.95162	−	6.72244i	−0.0676198	−	0.232919i
$834$		0			0
$835$	−2.79628	+	4.84330i	−0.0967694	+	0.167609i
$836$		0			0
$837$	3.30944	+	5.73212i	0.114391	+	0.198131i
$838$		0			0
$839$	34.7915			1.20114			0.600569	−	0.799573i	$-0.294941\pi$
$839$	34.7915			1.20114			0.600569	+	0.799573i	$0.294941\pi$
$840$		0			0
$841$	−22.7307			−0.783819
$842$		0			0
$843$	−0.0279066	−	0.0483357i	−0.000961156	−	0.00166477i
$844$		0			0
$845$	7.66723	−	13.2800i	0.263761	−	0.456847i
$846$		0			0
$847$	17.3841	−	23.1487i	0.597325	−	0.795400i
$848$		0			0
$849$	−0.680559	+	1.17876i	−0.0233567	+	0.0404550i
$850$		0			0
$851$	−6.14680	−	10.6466i	−0.210710	−	0.364960i
$852$		0			0
$853$	−54.9715			−1.88219			−0.941095	−	0.338143i	$-0.890201\pi$
$853$	−54.9715			−1.88219			−0.941095	+	0.338143i	$0.890201\pi$
$854$		0			0
$855$	23.2057			0.793619
$856$		0			0
$857$	−12.2786	−	21.2672i	−0.419429	−	0.726473i	0.576453	−	0.817130i	$-0.304436\pi$
$857$	−12.2786	−	21.2672i	−0.419429	−	0.726473i	−0.995882	+	0.0906577i	$0.971103\pi$
$858$		0			0
$859$	−16.6168	+	28.7812i	−0.566959	+	0.982002i	0.429905	+	0.902874i	$0.358547\pi$
$859$	−16.6168	+	28.7812i	−0.566959	+	0.982002i	−0.996864	+	0.0791280i	$0.974786\pi$
$860$		0			0
$861$	−4.69115	−	11.0012i	−0.159874	−	0.374921i
$862$		0			0
$863$	−4.68623	+	8.11679i	−0.159521	+	0.276299i	−0.934696	−	0.355448i	$-0.884328\pi$
$863$	−4.68623	+	8.11679i	−0.159521	+	0.276299i	0.775175	+	0.631747i	$0.217662\pi$
$864$		0			0
$865$	−9.28275	−	16.0782i	−0.315623	−	0.546675i
$866$		0			0
$867$	−0.474430			−0.0161125
$868$		0			0
$869$	2.04119			0.0692428
$870$		0			0
$871$	11.9583	+	20.7124i	0.405192	+	0.701813i
$872$		0			0
$873$	−5.12807	+	8.88207i	−0.173559	+	0.300613i
$874$		0			0
$875$	−31.4654	−	3.81085i	−1.06372	−	0.128830i
$876$		0			0
$877$	−16.0433	+	27.7877i	−0.541742	+	0.938325i	0.457062	+	0.889435i	$0.348902\pi$
$877$	−16.0433	+	27.7877i	−0.541742	+	0.938325i	−0.998804	+	0.0488901i	$0.984432\pi$
$878$		0			0
$879$	−4.22335	−	7.31506i	−0.142450	−	0.246731i
$880$		0			0
$881$	−4.55055			−0.153312			−0.0766559	−	0.997058i	$-0.524424\pi$
$881$	−4.55055			−0.153312			−0.0766559	+	0.997058i	$0.524424\pi$
$882$		0			0
$883$	−20.7818			−0.699362			−0.349681	−	0.936869i	$-0.613710\pi$
$883$	−20.7818			−0.699362			−0.349681	+	0.936869i	$0.613710\pi$
$884$		0			0
$885$	−0.803308	−	1.39137i	−0.0270029	−	0.0467704i
$886$		0			0
$887$	7.48267	−	12.9604i	0.251243	−	0.435166i	−0.712625	−	0.701545i	$-0.752494\pi$
$887$	7.48267	−	12.9604i	0.251243	−	0.435166i	0.963868	+	0.266379i	$0.0858272\pi$
$888$		0			0
$889$	−39.2204	−	4.75008i	−1.31541	−	0.159313i
$890$		0			0
$891$	0.846863	−	1.46681i	0.0283710	−	0.0491400i
$892$		0			0
$893$	−22.0916	−	38.2638i	−0.739267	−	1.28045i
$894$		0			0
$895$	24.1468			0.807138
$896$		0			0
$897$	−3.30855			−0.110469
$898$		0			0
$899$	3.02444	+	5.23848i	0.100871	+	0.174713i
$900$		0			0
$901$	5.80792	−	10.0596i	0.193490	−	0.335134i
$902$		0			0
$903$	4.69940	+	11.0206i	0.156386	+	0.366742i
$904$		0			0
$905$	−3.27497	+	5.67241i	−0.108864	+	0.188557i
$906$		0			0
$907$	−21.0412	−	36.4444i	−0.698661	−	1.21012i	−0.968931	−	0.247331i	$-0.920446\pi$
$907$	−21.0412	−	36.4444i	−0.698661	−	1.21012i	0.270270	−	0.962784i	$-0.412887\pi$
$908$		0			0
$909$	−24.0896			−0.799001
$910$		0			0
$911$	4.98375			0.165119			0.0825594	−	0.996586i	$-0.473691\pi$
$911$	4.98375			0.165119			0.0825594	+	0.996586i	$0.473691\pi$
$912$		0			0
$913$	0.124075	+	0.214904i	0.00410628	+	0.00711229i
$914$		0			0
$915$	4.14121	−	7.17279i	0.136904	−	0.237125i
$916$		0			0
$917$	−14.6760	+	19.5427i	−0.484645	+	0.645356i
$918$		0			0
$919$	−9.00977	+	15.6054i	−0.297205	+	0.514774i	−0.975495	−	0.220020i	$-0.929388\pi$
$919$	−9.00977	+	15.6054i	−0.297205	+	0.514774i	0.678291	+	0.734794i	$0.262721\pi$
$920$		0			0
$921$	−5.17627	−	8.96557i	−0.170564	−	0.295425i
$922$		0			0
$923$	1.09684			0.0361029
$924$		0			0
$925$	−7.80426			−0.256603
$926$		0			0
$927$	−19.5798	−	33.9132i	−0.643085	−	1.11386i
$928$		0			0
$929$	−15.5991	+	27.0185i	−0.511791	+	0.886448i	0.488115	+	0.872779i	$0.337685\pi$
$929$	−15.5991	+	27.0185i	−0.511791	+	0.886448i	−0.999907	+	0.0136692i	$0.995649\pi$
$930$		0			0
$931$	24.7830	−	25.8333i	0.812229	−	0.846653i
$932$		0			0
$933$	1.40987	−	2.44197i	0.0461571	−	0.0799465i
$934$		0			0
$935$	0.197128	+	0.341435i	0.00644676	+	0.0111661i
$936$		0			0
$937$	58.5957			1.91424			0.957119	−	0.289695i	$-0.0935540\pi$
$937$	58.5957			1.91424			0.957119	+	0.289695i	$0.0935540\pi$
$938$		0			0
$939$	6.10326			0.199172
$940$		0			0
$941$	−16.6352	−	28.8131i	−0.542293	−	0.939279i	−0.998772	−	0.0495450i	$-0.984223\pi$
$941$	−16.6352	−	28.8131i	−0.542293	−	0.939279i	0.456479	−	0.889734i	$-0.349110\pi$
$942$		0			0
$943$	17.4557	−	30.2342i	0.568437	−	0.984563i
$944$		0			0
$945$	−7.11793	+	9.47826i	−0.231546	+	0.308328i
$946$		0			0
$947$	23.9844	−	41.5422i	0.779388	−	1.34994i	−0.152907	−	0.988241i	$-0.548864\pi$
$947$	23.9844	−	41.5422i	0.779388	−	1.34994i	0.932295	−	0.361699i	$-0.117803\pi$
$948$		0			0
$949$	−14.7923	−	25.6210i	−0.480178	−	0.831693i
$950$		0			0
$951$	1.57389			0.0510370
$952$		0			0
$953$	−4.51078			−0.146119			−0.0730593	−	0.997328i	$-0.523276\pi$
$953$	−4.51078			−0.146119			−0.0730593	+	0.997328i	$0.523276\pi$
$954$		0			0
$955$	17.6806	+	30.6236i	0.572130	+	0.990958i
$956$		0			0
$957$	−0.143203	+	0.248036i	−0.00462911	+	0.00801785i
$958$		0			0
$959$	0.209626	+	0.491595i	0.00676918	+	0.0158744i
$960$		0			0
$961$	12.5819	−	21.7925i	0.405867	−	0.702982i
$962$		0			0
$963$	−19.2203	−	33.2905i	−0.619366	−	1.07277i
$964$		0			0
$965$	25.3921			0.817402
$966$		0			0
$967$	−12.4644			−0.400830			−0.200415	−	0.979711i	$-0.564229\pi$
$967$	−12.4644			−0.400830			−0.200415	+	0.979711i	$0.564229\pi$
$968$		0			0
$969$	−1.21315	−	2.10123i	−0.0389719	−	0.0675013i
$970$		0			0
$971$	0.603282	−	1.04492i	0.0193602	−	0.0335329i	−0.856183	−	0.516673i	$-0.827170\pi$
$971$	0.603282	−	1.04492i	0.0193602	−	0.0335329i	0.875543	+	0.483140i	$0.160504\pi$
$972$		0			0
$973$	−23.1330	−	2.80169i	−0.741608	−	0.0898180i
$974$		0			0
$975$	−1.05017	+	1.81895i	−0.0336325	+	0.0582532i
$976$		0			0
$977$	6.01455	+	10.4175i	0.192422	+	0.333286i	0.946053	−	0.324013i	$-0.105032\pi$
$977$	6.01455	+	10.4175i	0.192422	+	0.333286i	−0.753630	+	0.657299i	$0.771699\pi$
$978$		0			0
$979$	−2.75506			−0.0880520
$980$		0			0
$981$	17.3915			0.555268
$982$		0			0
$983$	4.05275	+	7.01958i	0.129263	+	0.223890i	0.923391	−	0.383860i	$-0.125406\pi$
$983$	4.05275	+	7.01958i	0.129263	+	0.223890i	−0.794128	+	0.607750i	$0.792072\pi$
$984$		0			0
$985$	−0.318441	+	0.551556i	−0.0101464	+	0.0175740i
$986$		0			0
$987$	10.7658	+	1.30387i	0.342679	+	0.0415027i
$988$		0			0
$989$	−17.4864	+	30.2874i	−0.556037	+	0.963084i
$990$		0			0
$991$	−8.42522	−	14.5929i	−0.267636	−	0.463559i	0.700615	−	0.713540i	$-0.252909\pi$
$991$	−8.42522	−	14.5929i	−0.267636	−	0.463559i	−0.968251	+	0.249981i	$0.919576\pi$
$992$		0			0
$993$	−3.53216			−0.112090
$994$		0			0
$995$	5.01810			0.159084
$996$		0			0
$997$	8.08907	+	14.0107i	0.256184	+	0.443723i	0.965216	−	0.261453i	$-0.0842015\pi$
$997$	8.08907	+	14.0107i	0.256184	+	0.443723i	−0.709033	+	0.705176i	$0.750868\pi$
$998$		0			0
$999$	−4.59618	+	7.96081i	−0.145417	+	0.251869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.q.e.681.4	yes	14
7.2	even	3		6664.2.a.v.1.4		7
7.4	even	3	inner	952.2.q.e.137.4	✓	14
7.5	odd	6		6664.2.a.y.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.q.e.137.4	✓	14	7.4	even	3	inner
952.2.q.e.681.4	yes	14	1.1	even	1	trivial
6664.2.a.v.1.4		7	7.2	even	3
6664.2.a.y.1.4		7	7.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.237215 + 0.410869i) q^{3} +(-0.817607 + 1.41614i) q^{5} +(2.62656 + 0.318109i) q^{7} +(1.38746 - 2.40315i) q^{9} +(0.120552 + 0.208801i) q^{11} +1.90325 q^{13} -0.775795 q^{15} +(-0.500000 - 0.866025i) q^{17} +(2.55706 - 4.42896i) q^{19} +(0.492358 + 1.15463i) q^{21} +(-1.83206 + 3.17323i) q^{23} +(1.16304 + 2.01444i) q^{25} +2.73980 q^{27} +2.50385 q^{29} +(1.20792 + 2.09217i) q^{31} +(-0.0571933 + 0.0990617i) q^{33} +(-2.59798 + 3.45948i) q^{35} +(-1.67756 + 2.90562i) q^{37} +(0.451479 + 0.781985i) q^{39} -9.52792 q^{41} +9.54468 q^{43} +(2.26879 + 3.92966i) q^{45} +(4.31973 - 7.48198i) q^{47} +(6.79761 + 1.67106i) q^{49} +(0.237215 - 0.410869i) q^{51} +(5.80792 + 10.0596i) q^{53} -0.394255 q^{55} +2.42629 q^{57} +(1.03546 + 1.79348i) q^{59} +(-5.33802 + 9.24572i) q^{61} +(4.40870 - 5.87064i) q^{63} +(-1.55611 + 2.69526i) q^{65} +(6.28311 + 10.8827i) q^{67} -1.73837 q^{69} +0.576299 q^{71} +(-7.77213 - 13.4617i) q^{73} +(-0.551780 + 0.955711i) q^{75} +(0.250214 + 0.586777i) q^{77} +(4.23303 - 7.33183i) q^{79} +(-3.51245 - 6.08375i) q^{81} +1.02923 q^{83} +1.63521 q^{85} +(0.593951 + 1.02875i) q^{87} +(-5.71344 + 9.89597i) q^{89} +(4.99899 + 0.605440i) q^{91} +(-0.573072 + 0.992590i) q^{93} +(4.18134 + 7.24229i) q^{95} -3.69602 q^{97} +0.669041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 4 q^{9} + 12 q^{11} + 4 q^{13} - 12 q^{15} - 7 q^{17} + 3 q^{19} + 18 q^{21} + 18 q^{23} - 15 q^{25} - 36 q^{27} + 10 q^{29} + 10 q^{31} - 21 q^{33} + 19 q^{35} - 11 q^{37}+ \cdots - 40 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 4 * q^9 + 12 * q^11 + 4 * q^13 - 12 * q^15 - 7 * q^17 + 3 * q^19 + 18 * q^21 + 18 * q^23 - 15 * q^25 - 36 * q^27 + 10 * q^29 + 10 * q^31 - 21 * q^33 + 19 * q^35 - 11 * q^37 + 12 * q^39 - 30 * q^43 - 13 * q^45 - 15 * q^47 + 20 * q^49 + 3 * q^51 - 8 * q^53 - 18 * q^55 - 6 * q^57 - 9 * q^59 + 4 * q^61 + 41 * q^63 + 38 * q^65 + 30 * q^67 - 56 * q^69 - 54 * q^71 + 5 * q^73 + 2 * q^75 + 27 * q^77 - 3 * q^79 + 17 * q^81 - 24 * q^83 + 4 * q^85 - 19 * q^87 - 32 * q^89 - 11 * q^91 + 9 * q^93 + 42 * q^95 - 78 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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