LMFDB - Embedded newform 1860.2.z.e.481.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(481,1860)] 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("1860.481"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.z (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,5,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 7 x^{18} + x^{17} + 148 x^{16} + 321 x^{15} + 1813 x^{14} + 3286 x^{13} + \cdots + 102400 $ x^20 - x^19 + 7x^18 + x^17 + 148x^16 + 321x^15 + 1813x^14 + 3286x^13 + 15059x^12 + 21120x^11 + 58030x^10 + 146272x^9 + 470332x^8 + 912160x^7 + 1589880x^6 + 1843936x^5 + 2075536x^4 + 1797440x^3 + 1141760x^2 + 358400*x + 102400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			481.3
Root			$0.360597 - 1.10980i$ of defining polynomial
Character	$\chi$	$=$	1860.481
Dual form			1860.2.z.e.901.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{3} +1.00000 q^{5} +(-0.205248 + 0.631687i) q^{7} +(0.309017 + 0.951057i) q^{9} +(0.583458 - 1.79570i) q^{11} +(2.67265 + 1.94180i) q^{13} +(0.809017 + 0.587785i) q^{15} +(1.07272 + 3.30149i) q^{17} +(-6.02998 + 4.38104i) q^{19} +(-0.537345 + 0.390404i) q^{21} +(1.74693 + 5.37651i) q^{23} +1.00000 q^{25} +(-0.309017 + 0.951057i) q^{27} +(-0.525199 + 0.381579i) q^{29} +(-4.39683 - 3.41583i) q^{31} +(1.52751 - 1.10980i) q^{33} +(-0.205248 + 0.631687i) q^{35} +2.94844 q^{37} +(1.02086 + 3.14189i) q^{39} +(2.87371 - 2.08787i) q^{41} +(5.69069 - 4.13453i) q^{43} +(0.309017 + 0.951057i) q^{45} +(1.52526 + 1.10816i) q^{47} +(5.30622 + 3.85519i) q^{49} +(-1.07272 + 3.30149i) q^{51} +(-0.177229 - 0.545455i) q^{53} +(0.583458 - 1.79570i) q^{55} -7.45346 q^{57} +(5.55344 + 4.03481i) q^{59} -1.55222 q^{61} -0.664195 q^{63} +(2.67265 + 1.94180i) q^{65} +4.52257 q^{67} +(-1.74693 + 5.37651i) q^{69} +(3.44607 + 10.6059i) q^{71} +(-0.580891 + 1.78780i) q^{73} +(0.809017 + 0.587785i) q^{75} +(1.01457 + 0.737126i) q^{77} +(-1.94702 - 5.99230i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-10.5568 + 7.66999i) q^{83} +(1.07272 + 3.30149i) q^{85} -0.649182 q^{87} +(-2.75879 + 8.49070i) q^{89} +(-1.77516 + 1.28973i) q^{91} +(-1.54934 - 5.34786i) q^{93} +(-6.02998 + 4.38104i) q^{95} +(-0.319797 + 0.984235i) q^{97} +1.88811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{3} + 20 q^{5} - q^{7} - 5 q^{9} - 2 q^{11} - 10 q^{13} + 5 q^{15} + 12 q^{17} + 4 q^{19} - 4 q^{21} - 7 q^{23} + 20 q^{25} + 5 q^{27} + 3 q^{29} - 8 q^{31} - 3 q^{33} - q^{35} + 24 q^{37}+ \cdots - 2 q^{99}+O(q^{100}) $ 20 * q + 5 * q^3 + 20 * q^5 - q^7 - 5 * q^9 - 2 * q^11 - 10 * q^13 + 5 * q^15 + 12 * q^17 + 4 * q^19 - 4 * q^21 - 7 * q^23 + 20 * q^25 + 5 * q^27 + 3 * q^29 - 8 * q^31 - 3 * q^33 - q^35 + 24 * q^37 - 5 * q^39 - 10 * q^41 + 18 * q^43 - 5 * q^45 + 2 * q^47 - 16 * q^49 - 12 * q^51 - 10 * q^53 - 2 * q^55 + 26 * q^57 + 14 * q^59 - 8 * q^61 - 6 * q^63 - 10 * q^65 + 18 * q^67 + 7 * q^69 - 16 * q^71 - 36 * q^73 + 5 * q^75 + 28 * q^77 - 7 * q^79 - 5 * q^81 - 4 * q^83 + 12 * q^85 + 12 * q^87 - 38 * q^89 + 9 * q^91 + 8 * q^93 + 4 * q^95 + 19 * q^97 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.205248	+	0.631687i	−0.0775763	+	0.238755i	−0.982323	−	0.187195i	$-0.940060\pi$
$7$	−0.205248	+	0.631687i	−0.0775763	+	0.238755i	0.904746	+	0.425951i	$0.140060\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	0.583458	−	1.79570i	0.175919	−	0.541424i	−0.823755	−	0.566946i	$-0.808125\pi$
$11$	0.583458	−	1.79570i	0.175919	−	0.541424i	0.999674	+	0.0255220i	$0.00812480\pi$
$12$		0			0
$13$	2.67265	+	1.94180i	0.741261	+	0.538558i	0.893106	−	0.449847i	$-0.148521\pi$
$13$	2.67265	+	1.94180i	0.741261	+	0.538558i	−0.151845	+	0.988404i	$0.548521\pi$
$14$		0			0
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$		0			0
$17$	1.07272	+	3.30149i	0.260172	+	0.800728i	0.992766	+	0.120062i	$0.0383094\pi$
$17$	1.07272	+	3.30149i	0.260172	+	0.800728i	−0.732594	+	0.680666i	$0.761691\pi$
$18$		0			0
$19$	−6.02998	+	4.38104i	−1.38337	+	1.00508i	−0.386816	+	0.922157i	$0.626425\pi$
$19$	−6.02998	+	4.38104i	−1.38337	+	1.00508i	−0.996556	+	0.0829216i	$0.973575\pi$
$20$		0			0
$21$	−0.537345	+	0.390404i	−0.117258	+	0.0851931i
$22$		0			0
$23$	1.74693	+	5.37651i	0.364261	+	1.12108i	0.950443	+	0.310900i	$0.100630\pi$
$23$	1.74693	+	5.37651i	0.364261	+	1.12108i	−0.586182	+	0.810179i	$0.699370\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	−0.525199	+	0.381579i	−0.0975270	+	0.0708575i	−0.635480	−	0.772117i	$-0.719198\pi$
$29$	−0.525199	+	0.381579i	−0.0975270	+	0.0708575i	0.537953	+	0.842975i	$0.319198\pi$
$30$		0			0
$31$	−4.39683	−	3.41583i	−0.789694	−	0.613501i
$31$	−4.39683	−	3.41583i	−0.789694	−	0.613501i
$32$		0			0
$33$	1.52751	−	1.10980i	0.265906	−	0.193192i
$34$		0			0
$35$	−0.205248	+	0.631687i	−0.0346932	+	0.106775i
$36$		0			0
$37$	2.94844			0.484721			0.242361	−	0.970186i	$-0.422078\pi$
$37$	2.94844			0.484721			0.242361	+	0.970186i	$0.422078\pi$
$38$		0			0
$39$	1.02086	+	3.14189i	0.163469	+	0.503106i
$40$		0			0
$41$	2.87371	−	2.08787i	0.448797	−	0.326070i	−0.340323	−	0.940308i	$-0.610537\pi$
$41$	2.87371	−	2.08787i	0.448797	−	0.326070i	0.789121	+	0.614238i	$0.210537\pi$
$42$		0			0
$43$	5.69069	−	4.13453i	0.867822	−	0.630509i	−0.0621800	−	0.998065i	$-0.519805\pi$
$43$	5.69069	−	4.13453i	0.867822	−	0.630509i	0.930002	+	0.367556i	$0.119805\pi$
$44$		0			0
$45$	0.309017	+	0.951057i	0.0460655	+	0.141775i
$46$		0			0
$47$	1.52526	+	1.10816i	0.222482	+	0.161642i	0.693443	−	0.720511i	$-0.256093\pi$
$47$	1.52526	+	1.10816i	0.222482	+	0.161642i	−0.470961	+	0.882154i	$0.656093\pi$
$48$		0			0
$49$	5.30622	+	3.85519i	0.758031	+	0.550742i
$50$		0			0
$51$	−1.07272	+	3.30149i	−0.150211	+	0.462301i
$52$		0			0
$53$	−0.177229	−	0.545455i	−0.0243443	−	0.0749240i	0.938146	−	0.346239i	$-0.112541\pi$
$53$	−0.177229	−	0.545455i	−0.0243443	−	0.0749240i	−0.962491	+	0.271315i	$0.912541\pi$
$54$		0			0
$55$	0.583458	−	1.79570i	0.0786735	−	0.242132i
$56$		0			0
$57$	−7.45346			−0.987235
$58$		0			0
$59$	5.55344	+	4.03481i	0.722996	+	0.525287i	0.887340	−	0.461116i	$-0.152551\pi$
$59$	5.55344	+	4.03481i	0.722996	+	0.525287i	−0.164344	+	0.986403i	$0.552551\pi$
$60$		0			0
$61$	−1.55222			−0.198742			−0.0993709	−	0.995050i	$-0.531683\pi$
$61$	−1.55222			−0.198742			−0.0993709	+	0.995050i	$0.531683\pi$
$62$		0			0
$63$	−0.664195			−0.0836807
$64$		0			0
$65$	2.67265	+	1.94180i	0.331502	+	0.240850i
$66$		0			0
$67$	4.52257			0.552520			0.276260	−	0.961083i	$-0.410905\pi$
$67$	4.52257			0.552520			0.276260	+	0.961083i	$0.410905\pi$
$68$		0			0
$69$	−1.74693	+	5.37651i	−0.210306	+	0.647255i
$70$		0			0
$71$	3.44607	+	10.6059i	0.408973	+	1.25869i	0.917532	+	0.397662i	$0.130179\pi$
$71$	3.44607	+	10.6059i	0.408973	+	1.25869i	−0.508559	+	0.861027i	$0.669821\pi$
$72$		0			0
$73$	−0.580891	+	1.78780i	−0.0679882	+	0.209246i	−0.979278	−	0.202518i	$-0.935087\pi$
$73$	−0.580891	+	1.78780i	−0.0679882	+	0.209246i	0.911290	+	0.411765i	$0.135087\pi$
$74$		0			0
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$		0			0
$77$	1.01457	+	0.737126i	0.115621	+	0.0840033i
$78$		0			0
$79$	−1.94702	−	5.99230i	−0.219057	−	0.674187i	−0.998841	−	0.0481384i	$-0.984671\pi$
$79$	−1.94702	−	5.99230i	−0.219057	−	0.674187i	0.779784	−	0.626049i	$-0.215329\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−10.5568	+	7.66999i	−1.15876	+	0.841891i	−0.989621	−	0.143700i	$-0.954100\pi$
$83$	−10.5568	+	7.66999i	−1.15876	+	0.841891i	−0.169143	+	0.985592i	$0.554100\pi$
$84$		0			0
$85$	1.07272	+	3.30149i	0.116353	+	0.358097i
$86$		0			0
$87$	−0.649182			−0.0695996
$88$		0			0
$89$	−2.75879	+	8.49070i	−0.292432	+	0.900012i	0.691640	+	0.722242i	$0.256888\pi$
$89$	−2.75879	+	8.49070i	−0.292432	+	0.900012i	−0.984072	+	0.177770i	$0.943112\pi$
$90$		0			0
$91$	−1.77516	+	1.28973i	−0.186088	+	0.135201i
$92$		0			0
$93$	−1.54934	−	5.34786i	−0.160659	−	0.554547i
$94$		0			0
$95$	−6.02998	+	4.38104i	−0.618663	+	0.449485i
$96$		0			0
$97$	−0.319797	+	0.984235i	−0.0324705	+	0.0999339i	−0.965978	−	0.258623i	$-0.916731\pi$
$97$	−0.319797	+	0.984235i	−0.0324705	+	0.0999339i	0.933508	+	0.358557i	$0.116731\pi$
$98$		0			0
$99$	1.88811			0.189762
$100$		0			0
$101$	−2.43421	−	7.49172i	−0.242213	−	0.745454i	−0.996082	−	0.0884299i	$-0.971815\pi$
$101$	−2.43421	−	7.49172i	−0.242213	−	0.745454i	0.753870	−	0.657024i	$-0.228185\pi$
$102$		0			0
$103$	1.84762	−	1.34237i	0.182051	−	0.132268i	−0.493027	−	0.870014i	$-0.664110\pi$
$103$	1.84762	−	1.34237i	0.182051	−	0.132268i	0.675079	+	0.737746i	$0.264110\pi$
$104$		0			0
$105$	−0.537345	+	0.390404i	−0.0524395	+	0.0380995i
$106$		0			0
$107$	−6.22379	−	19.1548i	−0.601676	−	1.85177i	−0.518201	−	0.855259i	$-0.673398\pi$
$107$	−6.22379	−	19.1548i	−0.601676	−	1.85177i	−0.0834753	−	0.996510i	$-0.526602\pi$
$108$		0			0
$109$	10.1670	+	7.38678i	0.973825	+	0.707526i	0.956320	−	0.292321i	$-0.0944276\pi$
$109$	10.1670	+	7.38678i	0.973825	+	0.707526i	0.0175052	+	0.999847i	$0.494428\pi$
$110$		0			0
$111$	2.38534	+	1.73305i	0.226407	+	0.164494i
$112$		0			0
$113$	−0.896080	+	2.75785i	−0.0842961	+	0.259437i	−0.984317	−	0.176411i	$-0.943551\pi$
$113$	−0.896080	+	2.75785i	−0.0842961	+	0.259437i	0.900021	+	0.435847i	$0.143551\pi$
$114$		0			0
$115$	1.74693	+	5.37651i	0.162902	+	0.501362i
$116$		0			0
$117$	−1.02086	+	3.14189i	−0.0943788	+	0.290468i
$118$		0			0
$119$	−2.30568			−0.211361
$120$		0			0
$121$	6.01507	+	4.37021i	0.546825	+	0.397291i
$122$		0			0
$123$	3.55210			0.320282
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−2.67117	−	1.94072i	−0.237028	−	0.172211i	0.462930	−	0.886395i	$-0.346798\pi$
$127$	−2.67117	−	1.94072i	−0.237028	−	0.172211i	−0.699958	+	0.714184i	$0.746798\pi$
$128$		0			0
$129$	7.03408			0.619316
$130$		0			0
$131$	−1.95336	+	6.01181i	−0.170666	+	0.525255i	−0.999409	−	0.0343741i	$-0.989056\pi$
$131$	−1.95336	+	6.01181i	−0.170666	+	0.525255i	0.828743	+	0.559629i	$0.189056\pi$
$132$		0			0
$133$	−1.52981	−	4.70826i	−0.132651	−	0.408258i
$134$		0			0
$135$	−0.309017	+	0.951057i	−0.0265959	+	0.0818539i
$136$		0			0
$137$	2.20045	+	1.59872i	0.187997	+	0.136588i	0.677803	−	0.735244i	$-0.262932\pi$
$137$	2.20045	+	1.59872i	0.187997	+	0.136588i	−0.489806	+	0.871832i	$0.662932\pi$
$138$		0			0
$139$	−7.72228	−	5.61056i	−0.654995	−	0.475882i	0.209974	−	0.977707i	$-0.432662\pi$
$139$	−7.72228	−	5.61056i	−0.654995	−	0.475882i	−0.864969	+	0.501825i	$0.832662\pi$
$140$		0			0
$141$	0.582596	+	1.79305i	0.0490634	+	0.151002i
$142$		0			0
$143$	5.04627	−	3.66633i	0.421990	−	0.306594i
$144$		0			0
$145$	−0.525199	+	0.381579i	−0.0436154	+	0.0316884i
$146$		0			0
$147$	2.02679	+	6.23783i	0.167167	+	0.514488i
$148$		0			0
$149$	4.06265			0.332825			0.166413	−	0.986056i	$-0.446782\pi$
$149$	4.06265			0.332825			0.166413	+	0.986056i	$0.446782\pi$
$150$		0			0
$151$	5.79401	−	17.8321i	0.471510	−	1.45116i	−0.379097	−	0.925357i	$-0.623765\pi$
$151$	5.79401	−	17.8321i	0.471510	−	1.45116i	0.850607	−	0.525802i	$-0.176235\pi$
$152$		0			0
$153$	−2.80841	+	2.04043i	−0.227047	+	0.164959i
$154$		0			0
$155$	−4.39683	−	3.41583i	−0.353162	−	0.274366i
$156$		0			0
$157$	0.191894	−	0.139419i	0.0153148	−	0.0111268i	−0.580102	−	0.814544i	$-0.696987\pi$
$157$	0.191894	−	0.139419i	0.0153148	−	0.0111268i	0.595416	+	0.803417i	$0.296987\pi$
$158$		0			0
$159$	0.177229	−	0.545455i	0.0140552	−	0.0432574i
$160$		0			0
$161$	−3.75482			−0.295921
$162$		0			0
$163$	−3.75957	−	11.5708i	−0.294472	−	0.906293i	−0.983398	−	0.181461i	$-0.941917\pi$
$163$	−3.75957	−	11.5708i	−0.294472	−	0.906293i	0.688926	−	0.724832i	$-0.258083\pi$
$164$		0			0
$165$	1.52751	−	1.10980i	0.118917	−	0.0863981i
$166$		0			0
$167$	3.01644	−	2.19157i	0.233419	−	0.169589i	−0.464927	−	0.885349i	$-0.653919\pi$
$167$	3.01644	−	2.19157i	0.233419	−	0.169589i	0.698347	+	0.715760i	$0.253919\pi$
$168$		0			0
$169$	−0.644714	−	1.98423i	−0.0495934	−	0.152633i
$170$		0			0
$171$	−6.02998	−	4.38104i	−0.461124	−	0.335026i
$172$		0			0
$173$	9.15178	+	6.64916i	0.695797	+	0.505526i	0.878561	−	0.477631i	$-0.158504\pi$
$173$	9.15178	+	6.64916i	0.695797	+	0.505526i	−0.182764	+	0.983157i	$0.558504\pi$
$174$		0			0
$175$	−0.205248	+	0.631687i	−0.0155153	+	0.0477510i
$176$		0			0
$177$	2.12122	+	6.52846i	0.159441	+	0.490709i
$178$		0			0
$179$	−4.21293	+	12.9661i	−0.314889	+	0.969129i	0.660911	+	0.750464i	$0.270170\pi$
$179$	−4.21293	+	12.9661i	−0.314889	+	0.969129i	−0.975800	+	0.218665i	$0.929830\pi$
$180$		0			0
$181$	−16.8117			−1.24960			−0.624800	−	0.780785i	$-0.714820\pi$
$181$	−16.8117			−1.24960			−0.624800	+	0.780785i	$0.714820\pi$
$182$		0			0
$183$	−1.25577	−	0.912373i	−0.0928295	−	0.0674446i
$184$		0			0
$185$	2.94844			0.216774
$186$		0			0
$187$	6.55437			0.479303
$188$		0			0
$189$	−0.537345	−	0.390404i	−0.0390861	−	0.0283977i
$190$		0			0
$191$	−15.7839			−1.14208			−0.571041	−	0.820922i	$-0.693460\pi$
$191$	−15.7839			−1.14208			−0.571041	+	0.820922i	$0.693460\pi$
$192$		0			0
$193$	5.66595	−	17.4380i	0.407844	−	1.25521i	−0.510653	−	0.859787i	$-0.670596\pi$
$193$	5.66595	−	17.4380i	0.407844	−	1.25521i	0.918497	−	0.395428i	$-0.129404\pi$
$194$		0			0
$195$	1.02086	+	3.14189i	0.0731055	+	0.224996i
$196$		0			0
$197$	−5.13721	+	15.8107i	−0.366011	+	1.12647i	0.583335	+	0.812232i	$0.301748\pi$
$197$	−5.13721	+	15.8107i	−0.366011	+	1.12647i	−0.949346	+	0.314234i	$0.898252\pi$
$198$		0			0
$199$	17.1301	+	12.4458i	1.21432	+	0.882256i	0.995616	−	0.0935350i	$-0.0298167\pi$
$199$	17.1301	+	12.4458i	1.21432	+	0.882256i	0.218705	+	0.975791i	$0.429817\pi$
$200$		0			0
$201$	3.65883	+	2.65830i	0.258074	+	0.187502i
$202$		0			0
$203$	−0.133243	−	0.410080i	−0.00935182	−	0.0287819i
$204$		0			0
$205$	2.87371	−	2.08787i	0.200708	−	0.145823i
$206$		0			0
$207$	−4.57353	+	3.32286i	−0.317882	+	0.230955i
$208$		0			0
$209$	4.34879	+	13.3842i	0.300812	+	0.925804i
$210$		0			0
$211$	2.45220			0.168817			0.0844083	−	0.996431i	$-0.473100\pi$
$211$	2.45220			0.168817			0.0844083	+	0.996431i	$0.473100\pi$
$212$		0			0
$213$	−3.44607	+	10.6059i	−0.236121	+	0.726705i
$214$		0			0
$215$	5.69069	−	4.13453i	0.388102	−	0.281972i
$216$		0			0
$217$	3.06017	−	2.07633i	0.207738	−	0.140950i
$218$		0			0
$219$	−1.52079	+	1.10492i	−0.102766	+	0.0746636i
$220$		0			0
$221$	−3.54381	+	10.9067i	−0.238383	+	0.733666i
$222$		0			0
$223$	−19.6845			−1.31817			−0.659085	−	0.752068i	$-0.729056\pi$
$223$	−19.6845			−1.31817			−0.659085	+	0.752068i	$0.729056\pi$
$224$		0			0
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$		0			0
$227$	0.869076	−	0.631420i	0.0576826	−	0.0419088i	−0.558570	−	0.829457i	$-0.688650\pi$
$227$	0.869076	−	0.631420i	0.0576826	−	0.0419088i	0.616253	+	0.787548i	$0.288650\pi$
$228$		0			0
$229$	11.3611	−	8.25432i	0.750763	−	0.545461i	−0.145301	−	0.989388i	$-0.546415\pi$
$229$	11.3611	−	8.25432i	0.750763	−	0.545461i	0.896063	+	0.443927i	$0.146415\pi$
$230$		0			0
$231$	0.387530	+	1.19270i	0.0254976	+	0.0784736i
$232$		0			0
$233$	−0.844354	−	0.613459i	−0.0553155	−	0.0401891i	0.559784	−	0.828639i	$-0.310884\pi$
$233$	−0.844354	−	0.613459i	−0.0553155	−	0.0401891i	−0.615099	+	0.788450i	$0.710884\pi$
$234$		0			0
$235$	1.52526	+	1.10816i	0.0994968	+	0.0722886i
$236$		0			0
$237$	1.94702	−	5.99230i	0.126472	−	0.389242i
$238$		0			0
$239$	4.84564	+	14.9134i	0.313439	+	0.964665i	0.976392	+	0.216005i	$0.0693026\pi$
$239$	4.84564	+	14.9134i	0.313439	+	0.964665i	−0.662954	+	0.748660i	$0.730697\pi$
$240$		0			0
$241$	5.66118	−	17.4233i	0.364669	−	1.12234i	−0.585519	−	0.810658i	$-0.699109\pi$
$241$	5.66118	−	17.4233i	0.364669	−	1.12234i	0.950188	−	0.311677i	$-0.100891\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	5.30622	+	3.85519i	0.339002	+	0.246299i
$246$		0			0
$247$	−24.6231			−1.56673
$248$		0			0
$249$	−13.0490			−0.826945
$250$		0			0
$251$	−5.42867	−	3.94416i	−0.342655	−	0.248953i	0.403126	−	0.915144i	$-0.367923\pi$
$251$	−5.42867	−	3.94416i	−0.342655	−	0.248953i	−0.745781	+	0.666191i	$0.767923\pi$
$252$		0			0
$253$	10.6739			0.671059
$254$		0			0
$255$	−1.07272	+	3.30149i	−0.0671762	+	0.206747i
$256$		0			0
$257$	−3.30597	−	10.1747i	−0.206220	−	0.634681i	−0.999661	−	0.0260336i	$-0.991712\pi$
$257$	−3.30597	−	10.1747i	−0.206220	−	0.634681i	0.793441	−	0.608648i	$-0.208288\pi$
$258$		0			0
$259$	−0.605161	+	1.86249i	−0.0376029	+	0.115730i
$260$		0			0
$261$	−0.525199	−	0.381579i	−0.0325090	−	0.0236192i
$262$		0			0
$263$	8.49224	+	6.16998i	0.523654	+	0.380457i	0.817979	−	0.575248i	$-0.195095\pi$
$263$	8.49224	+	6.16998i	0.523654	+	0.380457i	−0.294324	+	0.955706i	$0.595095\pi$
$264$		0			0
$265$	−0.177229	−	0.545455i	−0.0108871	−	0.0335070i
$266$		0			0
$267$	−7.22262	+	5.24754i	−0.442017	+	0.321144i
$268$		0			0
$269$	−4.12288	+	2.99544i	−0.251376	+	0.182635i	−0.706336	−	0.707876i	$-0.749653\pi$
$269$	−4.12288	+	2.99544i	−0.251376	+	0.182635i	0.454960	+	0.890512i	$0.349653\pi$
$270$		0			0
$271$	−7.16325	−	22.0462i	−0.435137	−	1.33921i	−0.892947	−	0.450162i	$-0.851366\pi$
$271$	−7.16325	−	22.0462i	−0.435137	−	1.33921i	0.457810	−	0.889050i	$-0.348634\pi$
$272$		0			0
$273$	−2.19422			−0.132800
$274$		0			0
$275$	0.583458	−	1.79570i	0.0351839	−	0.108285i
$276$		0			0
$277$	15.8384	−	11.5072i	0.951635	−	0.691403i	0.000442011	−	1.00000i	$-0.499859\pi$
$277$	15.8384	−	11.5072i	0.951635	−	0.691403i	0.951193	+	0.308597i	$0.0998593\pi$
$278$		0			0
$279$	1.88995	−	5.23718i	0.113148	−	0.313542i
$280$		0			0
$281$	21.2418	−	15.4331i	1.26718	−	0.920660i	0.268093	−	0.963393i	$-0.413606\pi$
$281$	21.2418	−	15.4331i	1.26718	−	0.920660i	0.999087	+	0.0427327i	$0.0136064\pi$
$282$		0			0
$283$	7.39773	−	22.7679i	0.439750	−	1.35341i	−0.448391	−	0.893838i	$-0.648003\pi$
$283$	7.39773	−	22.7679i	0.439750	−	1.35341i	0.888140	−	0.459573i	$-0.151997\pi$
$284$		0			0
$285$	−7.45346			−0.441505
$286$		0			0
$287$	0.729059	+	2.24381i	0.0430350	+	0.132448i
$288$		0			0
$289$	4.00420	−	2.90922i	0.235541	−	0.171131i
$290$		0			0
$291$	−0.837240	+	0.608291i	−0.0490799	+	0.0356586i
$292$		0			0
$293$	−3.76227	−	11.5791i	−0.219794	−	0.676457i	−0.998778	−	0.0494136i	$-0.984265\pi$
$293$	−3.76227	−	11.5791i	−0.219794	−	0.676457i	0.778984	−	0.627044i	$-0.215735\pi$
$294$		0			0
$295$	5.55344	+	4.03481i	0.323334	+	0.234916i
$296$		0			0
$297$	1.52751	+	1.10980i	0.0886353	+	0.0643973i
$298$		0			0
$299$	−5.77114	+	17.7617i	−0.333753	+	1.02719i
$300$		0			0
$301$	1.44373	+	4.44333i	0.0832150	+	0.256109i
$302$		0			0
$303$	2.43421	−	7.49172i	0.139841	−	0.430388i
$304$		0			0
$305$	−1.55222			−0.0888800
$306$		0			0
$307$	−7.35073	−	5.34062i	−0.419528	−	0.304805i	0.357920	−	0.933752i	$-0.383486\pi$
$307$	−7.35073	−	5.34062i	−0.419528	−	0.304805i	−0.777448	+	0.628947i	$0.783486\pi$
$308$		0			0
$309$	2.28378			0.129920
$310$		0			0
$311$	−28.4285			−1.61203			−0.806015	−	0.591895i	$-0.798380\pi$
$311$	−28.4285			−1.61203			−0.806015	+	0.591895i	$0.798380\pi$
$312$		0			0
$313$	−19.4750	−	14.1494i	−1.10079	−	0.799773i	−0.119604	−	0.992822i	$-0.538163\pi$
$313$	−19.4750	−	14.1494i	−1.10079	−	0.799773i	−0.981189	+	0.193048i	$0.938163\pi$
$314$		0			0
$315$	−0.664195			−0.0374231
$316$		0			0
$317$	3.12205	−	9.60868i	0.175352	−	0.539677i	−0.824298	−	0.566157i	$-0.808430\pi$
$317$	3.12205	−	9.60868i	0.175352	−	0.539677i	0.999649	+	0.0264796i	$0.00842972\pi$
$318$		0			0
$319$	0.378770	+	1.16574i	0.0212071	+	0.0652687i
$320$		0			0
$321$	6.22379	−	19.1548i	0.347378	−	1.06912i
$322$		0			0
$323$	−20.9324	−	15.2083i	−1.16471	−	0.846211i
$324$		0			0
$325$	2.67265	+	1.94180i	0.148252	+	0.107712i
$326$		0			0
$327$	3.88346	+	11.9521i	0.214756	+	0.660951i
$328$		0			0
$329$	−1.01307	+	0.736037i	−0.0558522	+	0.0405790i
$330$		0			0
$331$	10.1867	−	7.40107i	0.559912	−	0.406800i	−0.271515	−	0.962434i	$-0.587525\pi$
$331$	10.1867	−	7.40107i	0.559912	−	0.406800i	0.831427	+	0.555635i	$0.187525\pi$
$332$		0			0
$333$	0.911119	+	2.80414i	0.0499290	+	0.153666i
$334$		0			0
$335$	4.52257			0.247094
$336$		0			0
$337$	2.44823	−	7.53487i	0.133363	−	0.410450i	−0.861968	−	0.506962i	$-0.830768\pi$
$337$	2.44823	−	7.53487i	0.133363	−	0.410450i	0.995332	+	0.0965115i	$0.0307684\pi$
$338$		0			0
$339$	−2.34597	+	1.70444i	−0.127415	+	0.0925727i
$340$		0			0
$341$	−8.69917	+	5.90239i	−0.471087	+	0.319632i
$342$		0			0
$343$	−7.28578	+	5.29343i	−0.393395	+	0.285818i
$344$		0			0
$345$	−1.74693	+	5.37651i	−0.0940517	+	0.289461i
$346$		0			0
$347$	18.1350			0.973539			0.486770	−	0.873530i	$-0.338175\pi$
$347$	18.1350			0.973539			0.486770	+	0.873530i	$0.338175\pi$
$348$		0			0
$349$	−2.30532	−	7.09506i	−0.123401	−	0.379790i	0.870205	−	0.492689i	$-0.163986\pi$
$349$	−2.30532	−	7.09506i	−0.123401	−	0.379790i	−0.993606	+	0.112900i	$0.963986\pi$
$350$		0			0
$351$	−2.67265	+	1.94180i	−0.142656	+	0.103645i
$352$		0			0
$353$	14.0132	−	10.1812i	0.745850	−	0.541892i	−0.148688	−	0.988884i	$-0.547505\pi$
$353$	14.0132	−	10.1812i	0.745850	−	0.541892i	0.894538	+	0.446992i	$0.147505\pi$
$354$		0			0
$355$	3.44607	+	10.6059i	0.182898	+	0.562903i
$356$		0			0
$357$	−1.86533	−	1.35524i	−0.0987239	−	0.0717271i
$358$		0			0
$359$	9.74839	+	7.08262i	0.514500	+	0.373806i	0.814528	−	0.580124i	$-0.196996\pi$
$359$	9.74839	+	7.08262i	0.514500	+	0.373806i	−0.300028	+	0.953930i	$0.596996\pi$
$360$		0			0
$361$	11.2958	−	34.7650i	0.594518	−	1.82974i
$362$		0			0
$363$	2.29755	+	7.07114i	0.120590	+	0.371139i
$364$		0			0
$365$	−0.580891	+	1.78780i	−0.0304052	+	0.0935777i
$366$		0			0
$367$	14.5235			0.758121			0.379060	−	0.925372i	$-0.376247\pi$
$367$	14.5235			0.758121			0.379060	+	0.925372i	$0.376247\pi$
$368$		0			0
$369$	2.87371	+	2.08787i	0.149599	+	0.108690i
$370$		0			0
$371$	0.380932			0.0197770
$372$		0			0
$373$	11.5775			0.599463			0.299731	−	0.954024i	$-0.403103\pi$
$373$	11.5775			0.599463			0.299731	+	0.954024i	$0.403103\pi$
$374$		0			0
$375$	0.809017	+	0.587785i	0.0417775	+	0.0303531i
$376$		0			0
$377$	−2.14463			−0.110454
$378$		0			0
$379$	2.39273	−	7.36407i	0.122906	−	0.378267i	−0.870608	−	0.491978i	$-0.836274\pi$
$379$	2.39273	−	7.36407i	0.122906	−	0.378267i	0.993514	+	0.113712i	$0.0362740\pi$
$380$		0			0
$381$	−1.02030	−	3.14015i	−0.0522714	−	0.160875i
$382$		0			0
$383$	5.04747	−	15.5345i	0.257914	−	0.793777i	−0.735328	−	0.677712i	$-0.762972\pi$
$383$	5.04747	−	15.5345i	0.257914	−	0.793777i	0.993242	−	0.116065i	$-0.0370282\pi$
$384$		0			0
$385$	1.01457	+	0.737126i	0.0517071	+	0.0375674i
$386$		0			0
$387$	5.69069	+	4.13453i	0.289274	+	0.210170i
$388$		0			0
$389$	6.49711	+	19.9961i	0.329417	+	1.01384i	0.969407	+	0.245458i	$0.0789382\pi$
$389$	6.49711	+	19.9961i	0.329417	+	1.01384i	−0.639991	+	0.768383i	$0.721062\pi$
$390$		0			0
$391$	−15.8765	+	11.5349i	−0.802909	+	0.583347i
$392$		0			0
$393$	−5.11395	+	3.71550i	−0.257965	+	0.187422i
$394$		0			0
$395$	−1.94702	−	5.99230i	−0.0979651	−	0.301506i
$396$		0			0
$397$	−23.8754			−1.19827			−0.599135	−	0.800648i	$-0.704489\pi$
$397$	−23.8754			−1.19827			−0.599135	+	0.800648i	$0.704489\pi$
$398$		0			0
$399$	1.52981	−	4.70826i	0.0765860	−	0.235708i
$400$		0			0
$401$	6.02131	−	4.37474i	0.300690	−	0.218464i	−0.427201	−	0.904156i	$-0.640500\pi$
$401$	6.02131	−	4.37474i	0.300690	−	0.218464i	0.727891	+	0.685692i	$0.240500\pi$
$402$		0			0
$403$	−5.11836	−	17.6671i	−0.254964	−	0.880060i
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$		0			0
$407$	1.72029	−	5.29452i	0.0852718	−	0.262440i
$408$		0			0
$409$	16.5277			0.817241			0.408620	−	0.912704i	$-0.366010\pi$
$409$	16.5277			0.817241			0.408620	+	0.912704i	$0.366010\pi$
$410$		0			0
$411$	0.840497	+	2.58678i	0.0414587	+	0.127597i
$412$		0			0
$413$	−3.68857	+	2.67990i	−0.181502	+	0.131869i
$414$		0			0
$415$	−10.5568	+	7.66999i	−0.518215	+	0.376505i
$416$		0			0
$417$	−2.94965	−	9.07808i	−0.144445	−	0.444556i
$418$		0			0
$419$	−1.43583	−	1.04319i	−0.0701451	−	0.0509634i	0.552160	−	0.833738i	$-0.313804\pi$
$419$	−1.43583	−	1.04319i	−0.0701451	−	0.0509634i	−0.622305	+	0.782775i	$0.713804\pi$
$420$		0			0
$421$	22.6108	+	16.4277i	1.10198	+	0.800637i	0.981382	−	0.192065i	$-0.0615183\pi$
$421$	22.6108	+	16.4277i	1.10198	+	0.800637i	0.120599	+	0.992701i	$0.461518\pi$
$422$		0			0
$423$	−0.582596	+	1.79305i	−0.0283268	+	0.0871809i
$424$		0			0
$425$	1.07272	+	3.30149i	0.0520345	+	0.160146i
$426$		0			0
$427$	0.318590	−	0.980519i	0.0154176	−	0.0474506i
$428$		0			0
$429$	6.23753			0.301151
$430$		0			0
$431$	−7.29949	−	5.30339i	−0.351604	−	0.255455i	0.397938	−	0.917413i	$-0.369726\pi$
$431$	−7.29949	−	5.30339i	−0.351604	−	0.255455i	−0.749542	+	0.661957i	$0.769726\pi$
$432$		0			0
$433$	1.98465			0.0953763			0.0476881	−	0.998862i	$-0.484815\pi$
$433$	1.98465			0.0953763			0.0476881	+	0.998862i	$0.484815\pi$
$434$		0			0
$435$	−0.649182			−0.0311259
$436$		0			0
$437$	−34.0886	−	24.7668i	−1.63068	−	1.18476i
$438$		0			0
$439$	−38.2413			−1.82516			−0.912580	−	0.408899i	$-0.865913\pi$
$439$	−38.2413			−1.82516			−0.912580	+	0.408899i	$0.865913\pi$
$440$		0			0
$441$	−2.02679	+	6.23783i	−0.0965140	+	0.297040i
$442$		0			0
$443$	−11.9741	−	36.8525i	−0.568907	−	1.75092i	−0.656047	−	0.754720i	$-0.727773\pi$
$443$	−11.9741	−	36.8525i	−0.568907	−	1.75092i	0.0871405	−	0.996196i	$-0.472227\pi$
$444$		0			0
$445$	−2.75879	+	8.49070i	−0.130779	+	0.402498i
$446$		0			0
$447$	3.28676	+	2.38797i	0.155458	+	0.112947i
$448$		0			0
$449$	−7.64594	−	5.55510i	−0.360834	−	0.262161i	0.392566	−	0.919724i	$-0.371587\pi$
$449$	−7.64594	−	5.55510i	−0.360834	−	0.262161i	−0.753400	+	0.657563i	$0.771587\pi$
$450$		0			0
$451$	−2.07250	−	6.37850i	−0.0975902	−	0.300352i
$452$		0			0
$453$	15.1689	−	11.0209i	0.712698	−	0.517805i
$454$		0			0
$455$	−1.77516	+	1.28973i	−0.0832210	+	0.0604636i
$456$		0			0
$457$	−0.526002	−	1.61887i	−0.0246053	−	0.0757275i	0.938000	−	0.346636i	$-0.112676\pi$
$457$	−0.526002	−	1.61887i	−0.0246053	−	0.0757275i	−0.962605	+	0.270908i	$0.912676\pi$
$458$		0			0
$459$	−3.47139			−0.162031
$460$		0			0
$461$	3.35682	−	10.3312i	0.156343	−	0.481173i	−0.841952	−	0.539553i	$-0.818593\pi$
$461$	3.35682	−	10.3312i	0.156343	−	0.481173i	0.998294	+	0.0583796i	$0.0185934\pi$
$462$		0			0
$463$	−4.41721	+	3.20929i	−0.205285	+	0.149148i	−0.685678	−	0.727905i	$-0.740494\pi$
$463$	−4.41721	+	3.20929i	−0.205285	+	0.149148i	0.480393	+	0.877053i	$0.340494\pi$
$464$		0			0
$465$	−1.54934	−	5.34786i	−0.0718487	−	0.248001i
$466$		0			0
$467$	13.9842	−	10.1602i	0.647114	−	0.470156i	−0.215173	−	0.976576i	$-0.569032\pi$
$467$	13.9842	−	10.1602i	0.647114	−	0.470156i	0.862287	+	0.506420i	$0.169032\pi$
$468$		0			0
$469$	−0.928246	+	2.85685i	−0.0428624	+	0.131917i
$470$		0			0
$471$	0.237194			0.0109293
$472$		0			0
$473$	−4.10409	−	12.6311i	−0.188706	−	0.580778i
$474$		0			0
$475$	−6.02998	+	4.38104i	−0.276674	+	0.201016i
$476$		0			0
$477$	0.463991	−	0.337110i	0.0212447	−	0.0154352i
$478$		0			0
$479$	8.67834	+	26.7092i	0.396523	+	1.22037i	0.927769	+	0.373156i	$0.121724\pi$
$479$	8.67834	+	26.7092i	0.396523	+	1.22037i	−0.531245	+	0.847218i	$0.678276\pi$
$480$		0			0
$481$	7.88017	+	5.72528i	0.359305	+	0.261050i
$482$		0			0
$483$	−3.03771	−	2.20703i	−0.138221	−	0.100423i
$484$		0			0
$485$	−0.319797	+	0.984235i	−0.0145212	+	0.0446918i
$486$		0			0
$487$	−10.0837	−	31.0345i	−0.456937	−	1.40631i	−0.868846	−	0.495082i	$-0.835138\pi$
$487$	−10.0837	−	31.0345i	−0.456937	−	1.40631i	0.411910	−	0.911225i	$-0.364862\pi$
$488$		0			0
$489$	3.75957	−	11.5708i	0.170014	−	0.523248i
$490$		0			0
$491$	−14.5461			−0.656455			−0.328227	−	0.944599i	$-0.606451\pi$
$491$	−14.5461			−0.656455			−0.328227	+	0.944599i	$0.606451\pi$
$492$		0			0
$493$	−1.82317	−	1.32461i	−0.0821114	−	0.0596574i
$494$		0			0
$495$	1.88811			0.0848643
$496$		0			0
$497$	−7.40691			−0.332245
$498$		0			0
$499$	−1.65022	−	1.19896i	−0.0738740	−	0.0536726i	0.550235	−	0.835010i	$-0.314538\pi$
$499$	−1.65022	−	1.19896i	−0.0738740	−	0.0536726i	−0.624109	+	0.781337i	$0.714538\pi$
$500$		0			0
$501$	3.72853			0.166578
$502$		0			0
$503$	−7.48063	+	23.0230i	−0.333545	+	1.02654i	0.633890	+	0.773423i	$0.281457\pi$
$503$	−7.48063	+	23.0230i	−0.333545	+	1.02654i	−0.967435	+	0.253121i	$0.918543\pi$
$504$		0			0
$505$	−2.43421	−	7.49172i	−0.108321	−	0.333377i
$506$		0			0
$507$	0.644714	−	1.98423i	0.0286328	−	0.0881226i
$508$		0			0
$509$	−15.4712	−	11.2405i	−0.685751	−	0.498227i	0.189510	−	0.981879i	$-0.439310\pi$
$509$	−15.4712	−	11.2405i	−0.685751	−	0.498227i	−0.875261	+	0.483652i	$0.839310\pi$
$510$		0			0
$511$	−1.01010	−	0.733883i	−0.0446843	−	0.0324651i
$512$		0			0
$513$	−2.30325	−	7.08866i	−0.101691	−	0.312972i
$514$		0			0
$515$	1.84762	−	1.34237i	0.0814158	−	0.0591521i
$516$		0			0
$517$	2.87985	−	2.09234i	0.126656	−	0.0920208i
$518$		0			0
$519$	3.49567	+	10.7586i	0.153443	+	0.472249i
$520$		0			0
$521$	0.817416			0.0358116			0.0179058	−	0.999840i	$-0.494300\pi$
$521$	0.817416			0.0358116			0.0179058	+	0.999840i	$0.494300\pi$
$522$		0			0
$523$	5.57084	−	17.1453i	0.243596	−	0.749711i	−0.752268	−	0.658857i	$-0.771040\pi$
$523$	5.57084	−	17.1453i	0.243596	−	0.749711i	0.995864	−	0.0908543i	$-0.0289598\pi$
$524$		0			0
$525$	−0.537345	+	0.390404i	−0.0234517	+	0.0170386i
$526$		0			0
$527$	6.56076	−	18.1803i	0.285791	−	0.791946i
$528$		0			0
$529$	−7.24764	+	5.26572i	−0.315115	+	0.228944i
$530$		0			0
$531$	−2.12122	+	6.52846i	−0.0920533	+	0.283311i
$532$		0			0
$533$	11.7346			0.508284
$534$		0			0
$535$	−6.22379	−	19.1548i	−0.269078	−	0.828136i
$536$		0			0
$537$	−11.0296	+	8.01347i	−0.475962	+	0.345807i
$538$		0			0
$539$	10.0187	−	7.27903i	0.431537	−	0.313530i
$540$		0			0
$541$	11.1266	+	34.2441i	0.478369	+	1.47227i	0.841360	+	0.540476i	$0.181756\pi$
$541$	11.1266	+	34.2441i	0.478369	+	1.47227i	−0.362991	+	0.931793i	$0.618244\pi$
$542$		0			0
$543$	−13.6009	−	9.88164i	−0.583671	−	0.424062i
$544$		0			0
$545$	10.1670	+	7.38678i	0.435508	+	0.316415i
$546$		0			0
$547$	−5.01656	+	15.4394i	−0.214493	+	0.660141i	0.784696	+	0.619880i	$0.212819\pi$
$547$	−5.01656	+	15.4394i	−0.214493	+	0.660141i	−0.999189	+	0.0402607i	$0.987181\pi$
$548$		0			0
$549$	−0.479663	−	1.47625i	−0.0204715	−	0.0630049i
$550$		0			0
$551$	1.49523	−	4.60183i	0.0636988	−	0.196045i
$552$		0			0
$553$	4.18488			0.177959
$554$		0			0
$555$	2.38534	+	1.73305i	0.101252	+	0.0735640i
$556$		0			0
$557$	23.0289			0.975768			0.487884	−	0.872909i	$-0.337769\pi$
$557$	23.0289			0.975768			0.487884	+	0.872909i	$0.337769\pi$
$558$		0			0
$559$	23.2377			0.982848
$560$		0			0
$561$	5.30259	+	3.85256i	0.223876	+	0.162655i
$562$		0			0
$563$	−28.1819			−1.18773			−0.593863	−	0.804566i	$-0.702398\pi$
$563$	−28.1819			−1.18773			−0.593863	+	0.804566i	$0.702398\pi$
$564$		0			0
$565$	−0.896080	+	2.75785i	−0.0376984	+	0.116024i
$566$		0			0
$567$	−0.205248	−	0.631687i	−0.00861959	−	0.0265284i
$568$		0			0
$569$	−12.1491	+	37.3912i	−0.509318	+	1.56752i	0.284070	+	0.958803i	$0.408315\pi$
$569$	−12.1491	+	37.3912i	−0.509318	+	1.56752i	−0.793388	+	0.608716i	$0.791685\pi$
$570$		0			0
$571$	−29.5894	−	21.4980i	−1.23828	−	0.899662i	−0.240796	−	0.970576i	$-0.577408\pi$
$571$	−29.5894	−	21.4980i	−1.23828	−	0.899662i	−0.997482	+	0.0709139i	$0.977408\pi$
$572$		0			0
$573$	−12.7694	−	9.27753i	−0.533450	−	0.387574i
$574$		0			0
$575$	1.74693	+	5.37651i	0.0728521	+	0.224216i
$576$		0			0
$577$	−33.1655	+	24.0961i	−1.38070	+	1.00314i	−0.383883	+	0.923382i	$0.625414\pi$
$577$	−33.1655	+	24.0961i	−1.38070	+	1.00314i	−0.996815	+	0.0797543i	$0.974586\pi$
$578$		0			0
$579$	14.8337	−	10.7773i	0.616466	−	0.447888i
$580$		0			0
$581$	−2.67827	−	8.24287i	−0.111113	−	0.341972i
$582$		0			0
$583$	−1.08288			−0.0448483
$584$		0			0
$585$	−1.02086	+	3.14189i	−0.0422075	+	0.129901i
$586$		0			0
$587$	21.9754	−	15.9661i	0.907021	−	0.658989i	−0.0332386	−	0.999447i	$-0.510582\pi$
$587$	21.9754	−	15.9661i	0.907021	−	0.658989i	0.940260	+	0.340458i	$0.110582\pi$
$588$		0			0
$589$	41.4777	+	1.33471i	1.70906	+	0.0549960i
$590$		0			0
$591$	−13.4494	+	9.77155i	−0.553234	+	0.401948i
$592$		0			0
$593$	5.35226	−	16.4726i	0.219791	−	0.676447i	−0.778988	−	0.627039i	$-0.784267\pi$
$593$	5.35226	−	16.4726i	0.219791	−	0.676447i	0.998779	−	0.0494079i	$-0.0157334\pi$
$594$		0			0
$595$	−2.30568			−0.0945236
$596$		0			0
$597$	6.54312	+	20.1376i	0.267792	+	0.824179i
$598$		0			0
$599$	−34.2509	+	24.8847i	−1.39945	+	1.01676i	−0.404700	+	0.914450i	$0.632624\pi$
$599$	−34.2509	+	24.8847i	−1.39945	+	1.01676i	−0.994752	+	0.102312i	$0.967376\pi$
$600$		0			0
$601$	−1.75529	+	1.27529i	−0.0715997	+	0.0520203i	−0.623009	−	0.782214i	$-0.714090\pi$
$601$	−1.75529	+	1.27529i	−0.0715997	+	0.0520203i	0.551410	+	0.834235i	$0.314090\pi$
$602$		0			0
$603$	1.39755	+	4.30122i	0.0569126	+	0.175159i
$604$		0			0
$605$	6.01507	+	4.37021i	0.244547	+	0.177674i
$606$		0			0
$607$	−6.61521	−	4.80623i	−0.268503	−	0.195079i	0.445384	−	0.895340i	$-0.353067\pi$
$607$	−6.61521	−	4.80623i	−0.268503	−	0.195079i	−0.713887	+	0.700261i	$0.753067\pi$
$608$		0			0
$609$	0.133243	−	0.410080i	0.00539928	−	0.0166173i
$610$		0			0
$611$	1.92465	+	5.92348i	0.0778632	+	0.239638i
$612$		0			0
$613$	11.6382	−	35.8186i	0.470061	−	1.44670i	−0.382444	−	0.923979i	$-0.624917\pi$
$613$	11.6382	−	35.8186i	0.470061	−	1.44670i	0.852505	−	0.522720i	$-0.175083\pi$
$614$		0			0
$615$	3.55210			0.143234
$616$		0			0
$617$	−25.3669	−	18.4302i	−1.02123	−	0.741970i	−0.0546989	−	0.998503i	$-0.517420\pi$
$617$	−25.3669	−	18.4302i	−1.02123	−	0.741970i	−0.966536	+	0.256533i	$0.917420\pi$
$618$		0			0
$619$	1.45141			0.0583369			0.0291685	−	0.999575i	$-0.490714\pi$
$619$	1.45141			0.0583369			0.0291685	+	0.999575i	$0.490714\pi$
$620$		0			0
$621$	−5.65319			−0.226855
$622$		0			0
$623$	−4.79723	−	3.48539i	−0.192197	−	0.139639i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−4.34879	+	13.3842i	−0.173674	+	0.534513i
$628$		0			0
$629$	3.16285	+	9.73425i	0.126111	+	0.388130i
$630$		0			0
$631$	−3.58615	+	11.0370i	−0.142762	+	0.439377i	−0.996716	−	0.0809710i	$-0.974198\pi$
$631$	−3.58615	+	11.0370i	−0.142762	+	0.439377i	0.853954	+	0.520348i	$0.174198\pi$
$632$		0			0
$633$	1.98387	+	1.44137i	0.0788519	+	0.0572892i
$634$		0			0
$635$	−2.67117	−	1.94072i	−0.106002	−	0.0770151i
$636$		0			0
$637$	6.69568	+	20.6072i	0.265293	+	0.816487i
$638$		0			0
$639$	−9.02193	+	6.55481i	−0.356902	+	0.259304i
$640$		0			0
$641$	25.5329	−	18.5507i	1.00849	−	0.732709i	0.0445960	−	0.999005i	$-0.485800\pi$
$641$	25.5329	−	18.5507i	1.00849	−	0.732709i	0.963891	+	0.266296i	$0.0857999\pi$
$642$		0			0
$643$	−10.9580	−	33.7252i	−0.432141	−	1.32999i	−0.895988	−	0.444078i	$-0.853531\pi$
$643$	−10.9580	−	33.7252i	−0.432141	−	1.32999i	0.463847	−	0.885915i	$-0.346469\pi$
$644$		0			0
$645$	7.03408			0.276966
$646$		0			0
$647$	1.32975	−	4.09256i	0.0522780	−	0.160895i	−0.921509	−	0.388357i	$-0.873043\pi$
$647$	1.32975	−	4.09256i	0.0522780	−	0.160895i	0.973787	+	0.227462i	$0.0730427\pi$
$648$		0			0
$649$	10.4855	−	7.61817i	0.411592	−	0.299039i
$650$		0			0
$651$	3.69617	+	0.118939i	0.144864	+	0.00466161i
$652$		0			0
$653$	−34.1210	+	24.7903i	−1.33526	+	0.970121i	−0.335653	+	0.941986i	$0.608957\pi$
$653$	−34.1210	+	24.7903i	−1.33526	+	0.970121i	−0.999604	+	0.0281352i	$0.991043\pi$
$654$		0			0
$655$	−1.95336	+	6.01181i	−0.0763240	+	0.234901i
$656$		0			0
$657$	−1.87980			−0.0733381
$658$		0			0
$659$	11.7166	+	36.0600i	0.456414	+	1.40470i	0.869467	+	0.493990i	$0.164462\pi$
$659$	11.7166	+	36.0600i	0.456414	+	1.40470i	−0.413054	+	0.910707i	$0.635538\pi$
$660$		0			0
$661$	24.1101	−	17.5170i	0.937774	−	0.681333i	−0.0101098	−	0.999949i	$-0.503218\pi$
$661$	24.1101	−	17.5170i	0.937774	−	0.681333i	0.947884	+	0.318616i	$0.103218\pi$
$662$		0			0
$663$	−9.27782	+	6.74073i	−0.360321	+	0.261788i
$664$		0			0
$665$	−1.52981	−	4.70826i	−0.0593233	−	0.182578i
$666$		0			0
$667$	−2.96905	−	2.15714i	−0.114962	−	0.0835249i
$668$		0			0
$669$	−15.9251	−	11.5703i	−0.615699	−	0.447332i
$670$		0			0
$671$	−0.905657	+	2.78733i	−0.0349625	+	0.107604i
$672$		0			0
$673$	9.64236	+	29.6761i	0.371686	+	1.14393i	0.945688	+	0.325077i	$0.105390\pi$
$673$	9.64236	+	29.6761i	0.371686	+	1.14393i	−0.574002	+	0.818854i	$0.694610\pi$
$674$		0			0
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$		0			0
$677$	11.0157			0.423366			0.211683	−	0.977338i	$-0.432106\pi$
$677$	11.0157			0.423366			0.211683	+	0.977338i	$0.432106\pi$
$678$		0			0
$679$	−0.556091	−	0.404024i	−0.0213408	−	0.0155050i
$680$		0			0
$681$	1.07424			0.0411648
$682$		0			0
$683$	−4.22128			−0.161523			−0.0807614	−	0.996733i	$-0.525735\pi$
$683$	−4.22128			−0.161523			−0.0807614	+	0.996733i	$0.525735\pi$
$684$		0			0
$685$	2.20045	+	1.59872i	0.0840749	+	0.0610840i
$686$		0			0
$687$	14.0431			0.535777
$688$		0			0
$689$	0.585491	−	1.80195i	0.0223054	−	0.0686490i
$690$		0			0
$691$	−11.0371	−	33.9687i	−0.419871	−	1.29223i	−0.907821	−	0.419357i	$-0.862255\pi$
$691$	−11.0371	−	33.9687i	−0.419871	−	1.29223i	0.487951	−	0.872871i	$-0.337745\pi$
$692$		0			0
$693$	−0.387530	+	1.19270i	−0.0147211	+	0.0453067i
$694$		0			0
$695$	−7.72228	−	5.61056i	−0.292923	−	0.212821i
$696$		0			0
$697$	9.97575	+	7.24781i	0.377858	+	0.274530i
$698$		0			0
$699$	−0.322515	−	0.992598i	−0.0121986	−	0.0375435i
$700$		0			0
$701$	36.9069	−	26.8145i	1.39396	−	1.01277i	0.398538	−	0.917152i	$-0.369518\pi$
$701$	36.9069	−	26.8145i	1.39396	−	1.01277i	0.995418	−	0.0956162i	$-0.0304822\pi$
$702$		0			0
$703$	−17.7791	+	12.9172i	−0.670550	+	0.487183i
$704$		0			0
$705$	0.582596	+	1.79305i	0.0219418	+	0.0675300i
$706$		0			0
$707$	5.23203			0.196771
$708$		0			0
$709$	3.77658	−	11.6231i	0.141832	−	0.436516i	−0.854758	−	0.519027i	$-0.826294\pi$
$709$	3.77658	−	11.6231i	0.141832	−	0.436516i	0.996590	+	0.0825119i	$0.0262943\pi$
$710$		0			0
$711$	5.09736	−	3.70345i	0.191166	−	0.138890i
$712$		0			0
$713$	10.6843	−	29.6068i	0.400129	−	1.10878i
$714$		0			0
$715$	5.04627	−	3.66633i	0.188720	−	0.137113i
$716$		0			0
$717$	−4.84564	+	14.9134i	−0.180964	+	0.556950i
$718$		0			0
$719$	30.0868			1.12205			0.561025	−	0.827799i	$-0.310407\pi$
$719$	30.0868			1.12205			0.561025	+	0.827799i	$0.310407\pi$
$720$		0			0
$721$	0.468741	+	1.44264i	0.0174568	+	0.0537266i
$722$		0			0
$723$	14.8212	−	10.7682i	0.551205	−	0.400474i
$724$		0			0
$725$	−0.525199	+	0.381579i	−0.0195054	+	0.0141715i
$726$		0			0
$727$	10.0742	+	31.0052i	0.373631	+	1.14992i	0.944397	+	0.328806i	$0.106646\pi$
$727$	10.0742	+	31.0052i	0.373631	+	1.14992i	−0.570766	+	0.821113i	$0.693354\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	19.7546	+	14.3525i	0.730650	+	0.530848i
$732$		0			0
$733$	4.72218	−	14.5334i	0.174418	−	0.536803i	−0.825189	−	0.564857i	$-0.808931\pi$
$733$	4.72218	−	14.5334i	0.174418	−	0.536803i	0.999606	+	0.0280544i	$0.00893118\pi$
$734$		0			0
$735$	2.02679	+	6.23783i	0.0747594	+	0.230086i
$736$		0			0
$737$	2.63873	−	8.12118i	0.0971989	−	0.299147i
$738$		0			0
$739$	−24.3610			−0.896134			−0.448067	−	0.894000i	$-0.647887\pi$
$739$	−24.3610			−0.896134			−0.448067	+	0.894000i	$0.647887\pi$
$740$		0			0
$741$	−19.9205	−	14.4731i	−0.731799	−	0.531683i
$742$		0			0
$743$	−39.7274			−1.45746			−0.728729	−	0.684802i	$-0.759889\pi$
$743$	−39.7274			−1.45746			−0.728729	+	0.684802i	$0.759889\pi$
$744$		0			0
$745$	4.06265			0.148844
$746$		0			0
$747$	−10.5568	−	7.66999i	−0.386255	−	0.280630i
$748$		0			0
$749$	13.3773			0.488795
$750$		0			0
$751$	−12.6080	+	38.8035i	−0.460074	+	1.41596i	0.405000	+	0.914317i	$0.367272\pi$
$751$	−12.6080	+	38.8035i	−0.460074	+	1.41596i	−0.865074	+	0.501645i	$0.832728\pi$
$752$		0			0
$753$	−2.07357	−	6.38178i	−0.0755650	−	0.232565i
$754$		0			0
$755$	5.79401	−	17.8321i	0.210866	−	0.648978i
$756$		0			0
$757$	16.7717	+	12.1854i	0.609579	+	0.442885i	0.849266	−	0.527965i	$-0.177045\pi$
$757$	16.7717	+	12.1854i	0.609579	+	0.442885i	−0.239687	+	0.970850i	$0.577045\pi$
$758$		0			0
$759$	8.63533	+	6.27393i	0.313443	+	0.227729i
$760$		0			0
$761$	4.40729	+	13.5642i	0.159764	+	0.491703i	0.998612	−	0.0526621i	$-0.0167706\pi$
$761$	4.40729	+	13.5642i	0.159764	+	0.491703i	−0.838848	+	0.544365i	$0.816771\pi$
$762$		0			0
$763$	−6.75289	+	4.90626i	−0.244471	+	0.177619i
$764$		0			0
$765$	−2.80841	+	2.04043i	−0.101538	+	0.0737719i
$766$		0			0
$767$	7.00764	+	21.5673i	0.253031	+	0.778750i
$768$		0			0
$769$	−25.2762			−0.911482			−0.455741	−	0.890112i	$-0.650626\pi$
$769$	−25.2762			−0.911482			−0.455741	+	0.890112i	$0.650626\pi$
$770$		0			0
$771$	3.30597	−	10.1747i	0.119061	−	0.366433i
$772$		0			0
$773$	−26.2843	+	19.0966i	−0.945380	+	0.686859i	−0.949710	−	0.313132i	$-0.898622\pi$
$773$	−26.2843	+	19.0966i	−0.945380	+	0.686859i	0.00432975	+	0.999991i	$0.498622\pi$
$774$		0			0
$775$	−4.39683	−	3.41583i	−0.157939	−	0.122700i
$776$		0			0
$777$	−1.58433	+	1.15108i	−0.0568376	+	0.0412949i
$778$		0			0
$779$	−8.18135	+	25.1796i	−0.293127	+	0.902153i
$780$		0			0
$781$	21.0557			0.753431
$782$		0			0
$783$	−0.200608	−	0.617408i	−0.00716915	−	0.0220644i
$784$		0			0
$785$	0.191894	−	0.139419i	0.00684898	−	0.00497608i
$786$		0			0
$787$	11.6400	−	8.45695i	0.414921	−	0.301458i	−0.360670	−	0.932693i	$-0.617452\pi$
$787$	11.6400	−	8.45695i	0.414921	−	0.301458i	0.775591	+	0.631236i	$0.217452\pi$
$788$		0			0
$789$	3.24375	+	9.98323i	0.115481	+	0.355412i
$790$		0			0
$791$	−1.55818	−	1.13208i	−0.0554025	−	0.0402523i
$792$		0			0
$793$	−4.14855	−	3.01410i	−0.147320	−	0.107034i
$794$		0			0
$795$	0.177229	−	0.545455i	0.00628566	−	0.0193453i
$796$		0			0
$797$	−5.02469	−	15.4644i	−0.177984	−	0.547778i	0.821773	−	0.569814i	$-0.192985\pi$
$797$	−5.02469	−	15.4644i	−0.177984	−	0.547778i	−0.999757	+	0.0220367i	$0.992985\pi$
$798$		0			0
$799$	−2.02242	+	6.22436i	−0.0715480	+	0.220202i
$800$		0			0
$801$	−8.92765			−0.315443
$802$		0			0
$803$	2.87143	+	2.08621i	0.101330	+	0.0736209i
$804$		0			0
$805$	−3.75482			−0.132340
$806$		0			0
$807$	−5.09615			−0.179393
$808$		0			0
$809$	−1.21725	−	0.884382i	−0.0427962	−	0.0310932i	0.566182	−	0.824281i	$-0.308420\pi$
$809$	−1.21725	−	0.884382i	−0.0427962	−	0.0310932i	−0.608978	+	0.793187i	$0.708420\pi$
$810$		0			0
$811$	−7.65617			−0.268845			−0.134422	−	0.990924i	$-0.542918\pi$
$811$	−7.65617			−0.268845			−0.134422	+	0.990924i	$0.542918\pi$
$812$		0			0
$813$	7.16325	−	22.0462i	0.251226	−	0.773195i
$814$		0			0
$815$	−3.75957	−	11.5708i	−0.131692	−	0.405307i
$816$		0			0
$817$	−16.2012	+	49.8622i	−0.566809	+	1.74446i
$818$		0			0
$819$	−1.77516	−	1.28973i	−0.0620292	−	0.0450669i
$820$		0			0
$821$	14.9705	+	10.8767i	0.522475	+	0.379601i	0.817536	−	0.575878i	$-0.195340\pi$
$821$	14.9705	+	10.8767i	0.522475	+	0.379601i	−0.295060	+	0.955479i	$0.595340\pi$
$822$		0			0
$823$	13.5132	+	41.5893i	0.471040	+	1.44971i	0.851225	+	0.524800i	$0.175860\pi$
$823$	13.5132	+	41.5893i	0.471040	+	1.44971i	−0.380186	+	0.924910i	$0.624140\pi$
$824$		0			0
$825$	1.52751	−	1.10980i	0.0531812	−	0.0386384i
$826$		0			0
$827$	28.1852	−	20.4778i	0.980097	−	0.712082i	0.0223665	−	0.999750i	$-0.492880\pi$
$827$	28.1852	−	20.4778i	0.980097	−	0.712082i	0.957730	+	0.287668i	$0.0928799\pi$
$828$		0			0
$829$	10.3969	+	31.9982i	0.361098	+	1.11134i	0.952389	+	0.304886i	$0.0986184\pi$
$829$	10.3969	+	31.9982i	0.361098	+	1.11134i	−0.591291	+	0.806458i	$0.701382\pi$
$830$		0			0
$831$	19.5773			0.679129
$832$		0			0
$833$	−7.03579	+	21.6539i	−0.243776	+	0.750265i
$834$		0			0
$835$	3.01644	−	2.19157i	0.104388	−	0.0758426i
$836$		0			0
$837$	4.60734	−	3.12608i	0.159253	−	0.108053i
$838$		0			0
$839$	−7.70910	+	5.60099i	−0.266148	+	0.193368i	−0.712853	−	0.701314i	$-0.752597\pi$
$839$	−7.70910	+	5.60099i	−0.266148	+	0.193368i	0.446705	+	0.894681i	$0.352597\pi$
$840$		0			0
$841$	−8.83126	+	27.1798i	−0.304526	+	0.937235i
$842$		0			0
$843$	26.2563			0.904316
$844$		0			0
$845$	−0.644714	−	1.98423i	−0.0221788	−	0.0682594i
$846$		0			0
$847$	−3.99518	+	2.90267i	−0.137276	+	0.0997369i
$848$		0			0
$849$	19.3675	−	14.0713i	0.664692	−	0.482927i
$850$		0			0
$851$	5.15073	+	15.8523i	0.176565	+	0.543411i
$852$		0			0
$853$	−34.8364	−	25.3102i	−1.19278	−	0.866603i	−0.199222	−	0.979954i	$-0.563842\pi$
$853$	−34.8364	−	25.3102i	−1.19278	−	0.866603i	−0.993555	+	0.113351i	$0.963842\pi$
$854$		0			0
$855$	−6.02998	−	4.38104i	−0.206221	−	0.149828i
$856$		0			0
$857$	9.88759	−	30.4309i	0.337753	−	1.03950i	−0.627596	−	0.778539i	$-0.715961\pi$
$857$	9.88759	−	30.4309i	0.337753	−	1.03950i	0.965350	−	0.260959i	$-0.0840389\pi$
$858$		0			0
$859$	3.54518	+	10.9110i	0.120960	+	0.372277i	0.993143	−	0.116902i	$-0.0372964\pi$
$859$	3.54518	+	10.9110i	0.120960	+	0.372277i	−0.872183	+	0.489179i	$0.837296\pi$
$860$		0			0
$861$	−0.729059	+	2.24381i	−0.0248463	+	0.0764689i
$862$		0			0
$863$	34.8618			1.18671			0.593355	−	0.804941i	$-0.297803\pi$
$863$	34.8618			1.18671			0.593355	+	0.804941i	$0.297803\pi$
$864$		0			0
$865$	9.15178	+	6.64916i	0.311170	+	0.226078i
$866$		0			0
$867$	4.94946			0.168093
$868$		0			0
$869$	−11.8964			−0.403557
$870$		0			0
$871$	12.0873	+	8.78191i	0.409561	+	0.297564i
$872$		0			0
$873$	−1.03489			−0.0350256
$874$		0			0
$875$	−0.205248	+	0.631687i	−0.00693863	+	0.0213549i
$876$		0			0
$877$	4.04346	+	12.4445i	0.136538	+	0.420220i	0.995826	−	0.0912715i	$-0.0290931\pi$
$877$	4.04346	+	12.4445i	0.136538	+	0.420220i	−0.859288	+	0.511492i	$0.829093\pi$
$878$		0			0
$879$	3.76227	−	11.5791i	0.126898	−	0.390553i
$880$		0			0
$881$	9.63571	+	7.00075i	0.324635	+	0.235861i	0.738151	−	0.674636i	$-0.235699\pi$
$881$	9.63571	+	7.00075i	0.324635	+	0.235861i	−0.413516	+	0.910497i	$0.635699\pi$
$882$		0			0
$883$	−6.22101	−	4.51983i	−0.209354	−	0.152104i	0.478168	−	0.878269i	$-0.341301\pi$
$883$	−6.22101	−	4.51983i	−0.209354	−	0.152104i	−0.687521	+	0.726164i	$0.741301\pi$
$884$		0			0
$885$	2.12122	+	6.52846i	0.0713042	+	0.219452i
$886$		0			0
$887$	30.0181	−	21.8094i	1.00791	−	0.732290i	0.0441405	−	0.999025i	$-0.485945\pi$
$887$	30.0181	−	21.8094i	1.00791	−	0.732290i	0.963770	+	0.266736i	$0.0859451\pi$
$888$		0			0
$889$	1.77418	−	1.28902i	0.0595040	−	0.0432322i
$890$		0			0
$891$	0.583458	+	1.79570i	0.0195466	+	0.0601582i
$892$		0			0
$893$	−14.0522			−0.470238
$894$		0			0
$895$	−4.21293	+	12.9661i	−0.140823	+	0.433408i
$896$		0			0
$897$	−15.1090	+	10.9774i	−0.504476	+	0.366523i
$898$		0			0
$899$	3.61262	+	0.116251i	0.120488	+	0.00387719i
$900$		0			0
$901$	1.61069	−	1.17024i	0.0536600	−	0.0389863i
$902$		0			0
$903$	−1.44373	+	4.44333i	−0.0480442	+	0.147865i
$904$		0			0
$905$	−16.8117			−0.558838
$906$		0			0
$907$	11.4718	+	35.3064i	0.380913	+	1.17233i	0.939402	+	0.342818i	$0.111382\pi$
$907$	11.4718	+	35.3064i	0.380913	+	1.17233i	−0.558488	+	0.829512i	$0.688618\pi$
$908$		0			0
$909$	6.37283	−	4.63014i	0.211374	−	0.153572i
$910$		0			0
$911$	−25.2953	+	18.3781i	−0.838071	+	0.608895i	−0.921831	−	0.387591i	$-0.873307\pi$
$911$	−25.2953	+	18.3781i	−0.838071	+	0.608895i	0.0837598	+	0.996486i	$0.473307\pi$
$912$		0			0
$913$	7.61353	+	23.4320i	0.251971	+	0.775487i
$914$		0			0
$915$	−1.25577	−	0.912373i	−0.0415146	−	0.0301621i
$916$		0			0
$917$	−3.39666	−	2.46782i	−0.112168	−	0.0814946i
$918$		0			0
$919$	0.400173	−	1.23161i	0.0132005	−	0.0406269i	−0.944239	−	0.329260i	$-0.893201\pi$
$919$	0.400173	−	1.23161i	0.0132005	−	0.0406269i	0.957440	+	0.288633i	$0.0932008\pi$
$920$		0			0
$921$	−2.80773	−	8.64130i	−0.0925179	−	0.284741i
$922$		0			0
$923$	−11.3844	+	35.0375i	−0.374721	+	1.15327i
$924$		0			0
$925$	2.94844			0.0969443
$926$		0			0
$927$	1.84762	+	1.34237i	0.0606838	+	0.0440893i
$928$		0			0
$929$	5.27050			0.172920			0.0864598	−	0.996255i	$-0.472445\pi$
$929$	5.27050			0.172920			0.0864598	+	0.996255i	$0.472445\pi$
$930$		0			0
$931$	−48.8861			−1.60218
$932$		0			0
$933$	−22.9991	−	16.7098i	−0.752957	−	0.547055i
$934$		0			0
$935$	6.55437			0.214351
$936$		0			0
$937$	−11.5102	+	35.4248i	−0.376023	+	1.15728i	0.566763	+	0.823881i	$0.308195\pi$
$937$	−11.5102	+	35.4248i	−0.376023	+	1.15728i	−0.942786	+	0.333398i	$0.891805\pi$
$938$		0			0
$939$	−7.43880	−	22.8943i	−0.242756	−	0.747126i
$940$		0			0
$941$	−7.49530	+	23.0681i	−0.244340	+	0.752000i	0.751405	+	0.659842i	$0.229377\pi$
$941$	−7.49530	+	23.0681i	−0.244340	+	0.752000i	−0.995744	+	0.0921585i	$0.970623\pi$
$942$		0			0
$943$	16.2456	+	11.8031i	0.529030	+	0.384363i
$944$		0			0
$945$	−0.537345	−	0.390404i	−0.0174798	−	0.0126998i
$946$		0			0
$947$	−0.899175	−	2.76738i	−0.0292193	−	0.0899277i	0.935383	−	0.353635i	$-0.115055\pi$
$947$	−0.899175	−	2.76738i	−0.0292193	−	0.0899277i	−0.964603	+	0.263708i	$0.915055\pi$
$948$		0			0
$949$	−5.02407	+	3.65020i	−0.163088	+	0.118490i
$950$		0			0
$951$	8.17363	−	5.93849i	0.265048	−	0.192569i
$952$		0			0
$953$	4.84799	+	14.9206i	0.157042	+	0.483325i	0.998362	−	0.0572121i	$-0.0182211\pi$
$953$	4.84799	+	14.9206i	0.157042	+	0.483325i	−0.841320	+	0.540537i	$0.818221\pi$
$954$		0			0
$955$	−15.7839			−0.510754
$956$		0			0
$957$	−0.378770	+	1.16574i	−0.0122439	+	0.0376829i
$958$		0			0
$959$	−1.46153	+	1.06186i	−0.0471952	+	0.0342893i
$960$		0			0
$961$	7.66421	+	30.0376i	0.247233	+	0.968956i
$962$		0			0
$963$	16.2941	−	11.8383i	0.525070	−	0.381485i
$964$		0			0
$965$	5.66595	−	17.4380i	0.182393	−	0.561349i
$966$		0			0
$967$	53.3802			1.71659			0.858296	−	0.513155i	$-0.171523\pi$
$967$	53.3802			1.71659			0.858296	+	0.513155i	$0.171523\pi$
$968$		0			0
$969$	−7.99546	−	24.6075i	−0.256851	−	0.790507i
$970$		0			0
$971$	25.3357	−	18.4075i	0.813063	−	0.590725i	−0.101654	−	0.994820i	$-0.532414\pi$
$971$	25.3357	−	18.4075i	0.813063	−	0.590725i	0.914717	+	0.404095i	$0.132414\pi$
$972$		0			0
$973$	5.12910	−	3.72651i	0.164431	−	0.119466i
$974$		0			0
$975$	1.02086	+	3.14189i	0.0326938	+	0.100621i
$976$		0			0
$977$	−35.6432	−	25.8963i	−1.14033	−	0.828495i	−0.153161	−	0.988201i	$-0.548945\pi$
$977$	−35.6432	−	25.8963i	−1.14033	−	0.828495i	−0.987165	+	0.159706i	$0.948945\pi$
$978$		0			0
$979$	13.6371	+	9.90793i	0.435844	+	0.316659i
$980$		0			0
$981$	−3.88346	+	11.9521i	−0.123989	+	0.381600i
$982$		0			0
$983$	12.1995	+	37.5463i	0.389105	+	1.19754i	0.933458	+	0.358686i	$0.116775\pi$
$983$	12.1995	+	37.5463i	0.389105	+	1.19754i	−0.544353	+	0.838856i	$0.683225\pi$
$984$		0			0
$985$	−5.13721	+	15.8107i	−0.163685	+	0.503771i
$986$		0			0
$987$	−1.25222			−0.0398586
$988$		0			0
$989$	32.1705	+	23.3733i	1.02296	+	0.743227i
$990$		0			0
$991$	−16.9398			−0.538111			−0.269056	−	0.963125i	$-0.586712\pi$
$991$	−16.9398			−0.538111			−0.269056	+	0.963125i	$0.586712\pi$
$992$		0			0
$993$	12.5915			0.399578
$994$		0			0
$995$	17.1301	+	12.4458i	0.543061	+	0.394557i
$996$		0			0
$997$	6.99137			0.221419			0.110710	−	0.993853i	$-0.464688\pi$
$997$	6.99137			0.221419			0.110710	+	0.993853i	$0.464688\pi$
$998$		0			0
$999$	−0.911119	+	2.80414i	−0.0288265	+	0.0887190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.z.e.481.3	✓	20
31.2	even	5	inner	1860.2.z.e.901.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.z.e.481.3	✓	20	1.1	even	1	trivial
1860.2.z.e.901.3	yes	20	31.2	even	5	inner

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:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +1.00000 q^{5} +(-0.205248 + 0.631687i) q^{7} +(0.309017 + 0.951057i) q^{9} +(0.583458 - 1.79570i) q^{11} +(2.67265 + 1.94180i) q^{13} +(0.809017 + 0.587785i) q^{15} +(1.07272 + 3.30149i) q^{17} +(-6.02998 + 4.38104i) q^{19} +(-0.537345 + 0.390404i) q^{21} +(1.74693 + 5.37651i) q^{23} +1.00000 q^{25} +(-0.309017 + 0.951057i) q^{27} +(-0.525199 + 0.381579i) q^{29} +(-4.39683 - 3.41583i) q^{31} +(1.52751 - 1.10980i) q^{33} +(-0.205248 + 0.631687i) q^{35} +2.94844 q^{37} +(1.02086 + 3.14189i) q^{39} +(2.87371 - 2.08787i) q^{41} +(5.69069 - 4.13453i) q^{43} +(0.309017 + 0.951057i) q^{45} +(1.52526 + 1.10816i) q^{47} +(5.30622 + 3.85519i) q^{49} +(-1.07272 + 3.30149i) q^{51} +(-0.177229 - 0.545455i) q^{53} +(0.583458 - 1.79570i) q^{55} -7.45346 q^{57} +(5.55344 + 4.03481i) q^{59} -1.55222 q^{61} -0.664195 q^{63} +(2.67265 + 1.94180i) q^{65} +4.52257 q^{67} +(-1.74693 + 5.37651i) q^{69} +(3.44607 + 10.6059i) q^{71} +(-0.580891 + 1.78780i) q^{73} +(0.809017 + 0.587785i) q^{75} +(1.01457 + 0.737126i) q^{77} +(-1.94702 - 5.99230i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-10.5568 + 7.66999i) q^{83} +(1.07272 + 3.30149i) q^{85} -0.649182 q^{87} +(-2.75879 + 8.49070i) q^{89} +(-1.77516 + 1.28973i) q^{91} +(-1.54934 - 5.34786i) q^{93} +(-6.02998 + 4.38104i) q^{95} +(-0.319797 + 0.984235i) q^{97} +1.88811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{3} + 20 q^{5} - q^{7} - 5 q^{9} - 2 q^{11} - 10 q^{13} + 5 q^{15} + 12 q^{17} + 4 q^{19} - 4 q^{21} - 7 q^{23} + 20 q^{25} + 5 q^{27} + 3 q^{29} - 8 q^{31} - 3 q^{33} - q^{35} + 24 q^{37}+ \cdots - 2 q^{99}+O(q^{100}) \) 20 * q + 5 * q^3 + 20 * q^5 - q^7 - 5 * q^9 - 2 * q^11 - 10 * q^13 + 5 * q^15 + 12 * q^17 + 4 * q^19 - 4 * q^21 - 7 * q^23 + 20 * q^25 + 5 * q^27 + 3 * q^29 - 8 * q^31 - 3 * q^33 - q^35 + 24 * q^37 - 5 * q^39 - 10 * q^41 + 18 * q^43 - 5 * q^45 + 2 * q^47 - 16 * q^49 - 12 * q^51 - 10 * q^53 - 2 * q^55 + 26 * q^57 + 14 * q^59 - 8 * q^61 - 6 * q^63 - 10 * q^65 + 18 * q^67 + 7 * q^69 - 16 * q^71 - 36 * q^73 + 5 * q^75 + 28 * q^77 - 7 * q^79 - 5 * q^81 - 4 * q^83 + 12 * q^85 + 12 * q^87 - 38 * q^89 + 9 * q^91 + 8 * q^93 + 4 * q^95 + 19 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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