LMFDB - Embedded newform 1428.2.q.e.613.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1428,2,Mod(205,1428)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1428, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1428.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1428.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.4026374086$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.4
Root			$1.26359 + 0.635098i$ of defining polynomial
Character	$\chi$	$=$	1428.613
Dual form			1428.2.q.e.205.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(1.97513 + 3.42102i) q^{5} +(1.15207 + 2.38175i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(1.97513 + 3.42102i) q^{5} +(1.15207 + 2.38175i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.21154 + 2.09845i) q^{11} -0.636391 q^{13} -3.95025 q^{15} +(0.500000 - 0.866025i) q^{17} +(4.27995 + 7.41308i) q^{19} +(-2.63869 - 0.193156i) q^{21} +(-1.96363 - 3.40111i) q^{23} +(-5.30226 + 9.18378i) q^{25} +1.00000 q^{27} +6.00973 q^{29} +(1.65463 - 2.86591i) q^{31} +(-1.21154 - 2.09845i) q^{33} +(-5.87254 + 8.64551i) q^{35} +(-5.83686 - 10.1097i) q^{37} +(0.318196 - 0.551131i) q^{39} +2.99624 q^{41} -2.47146 q^{43} +(1.97513 - 3.42102i) q^{45} +(3.04541 + 5.27481i) q^{47} +(-4.34548 + 5.48788i) q^{49} +(0.500000 + 0.866025i) q^{51} +(5.86104 - 10.1516i) q^{53} -9.57179 q^{55} -8.55989 q^{57} +(4.47026 - 7.74272i) q^{59} +(-5.79076 - 10.0299i) q^{61} +(1.48662 - 2.18860i) q^{63} +(-1.25695 - 2.17711i) q^{65} +(-0.715609 + 1.23947i) q^{67} +3.92726 q^{69} -5.75021 q^{71} +(-4.35916 + 7.55029i) q^{73} +(-5.30226 - 9.18378i) q^{75} +(-6.39376 - 0.468032i) q^{77} +(6.40040 + 11.0858i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.17705 q^{83} +3.95025 q^{85} +(-3.00486 + 5.20458i) q^{87} +(-6.32050 - 10.9474i) q^{89} +(-0.733166 - 1.51573i) q^{91} +(1.65463 + 2.86591i) q^{93} +(-16.9069 + 29.2836i) q^{95} +9.25439 q^{97} +2.42308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9} - q^{11} - 20 q^{13} + 4 q^{15} + 4 q^{17} + 9 q^{19} + 5 q^{23} - 18 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - q^{33} - 18 q^{35} - 2 q^{37} + 10 q^{39} - 28 q^{43} - 2 q^{45} + 2 q^{47} + 5 q^{49} + 4 q^{51} + 15 q^{53} - 60 q^{55} - 18 q^{57} + 37 q^{59} - 19 q^{61} - 3 q^{63} + 21 q^{65} - 2 q^{67} - 10 q^{69} - 22 q^{71} + 9 q^{73} - 18 q^{75} + 13 q^{77} + 9 q^{79} - 4 q^{81} + 16 q^{83} - 4 q^{85} - 5 q^{87} - 22 q^{89} + 7 q^{91} + 24 q^{93} - 33 q^{95} + 26 q^{97} + 2 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9 - q^11 - 20 * q^13 + 4 * q^15 + 4 * q^17 + 9 * q^19 + 5 * q^23 - 18 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - q^33 - 18 * q^35 - 2 * q^37 + 10 * q^39 - 28 * q^43 - 2 * q^45 + 2 * q^47 + 5 * q^49 + 4 * q^51 + 15 * q^53 - 60 * q^55 - 18 * q^57 + 37 * q^59 - 19 * q^61 - 3 * q^63 + 21 * q^65 - 2 * q^67 - 10 * q^69 - 22 * q^71 + 9 * q^73 - 18 * q^75 + 13 * q^77 + 9 * q^79 - 4 * q^81 + 16 * q^83 - 4 * q^85 - 5 * q^87 - 22 * q^89 + 7 * q^91 + 24 * q^93 - 33 * q^95 + 26 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1428\mathbb{Z}\right)^\times$.

$n$	$409$	$715$	$953$	$1261$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	1.97513	+	3.42102i	0.883304	+	1.52993i	0.847646	+	0.530563i	$0.178019\pi$
$5$	1.97513	+	3.42102i	0.883304	+	1.52993i	0.0356582	+	0.999364i	$0.488647\pi$
$6$		0			0
$7$	1.15207	+	2.38175i	0.435441	+	0.900217i
$7$	1.15207	+	2.38175i	0.435441	+	0.900217i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.21154	+	2.09845i	−0.365293	+	0.632707i	−0.988823	−	0.149093i	$-0.952365\pi$
$11$	−1.21154	+	2.09845i	−0.365293	+	0.632707i	0.623530	+	0.781800i	$0.285698\pi$
$12$		0			0
$13$	−0.636391			−0.176503			−0.0882516	−	0.996098i	$-0.528128\pi$
$13$	−0.636391			−0.176503			−0.0882516	+	0.996098i	$0.528128\pi$
$14$		0			0
$15$	−3.95025			−1.01995
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$		0			0
$19$	4.27995	+	7.41308i	0.981887	+	1.70068i	0.655027	+	0.755605i	$0.272657\pi$
$19$	4.27995	+	7.41308i	0.981887	+	1.70068i	0.326860	+	0.945073i	$0.394009\pi$
$20$		0			0
$21$	−2.63869	−	0.193156i	−0.575810	−	0.0421501i
$22$		0			0
$23$	−1.96363	−	3.40111i	−0.409445	−	0.709180i	0.585382	−	0.810757i	$-0.300944\pi$
$23$	−1.96363	−	3.40111i	−0.409445	−	0.709180i	−0.994828	+	0.101577i	$0.967611\pi$
$24$		0			0
$25$	−5.30226	+	9.18378i	−1.06045	+	1.83676i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	6.00973			1.11598			0.557989	−	0.829848i	$-0.311573\pi$
$29$	6.00973			1.11598			0.557989	+	0.829848i	$0.311573\pi$
$30$		0			0
$31$	1.65463	−	2.86591i	0.297181	−	0.514732i	−0.678309	−	0.734777i	$-0.737287\pi$
$31$	1.65463	−	2.86591i	0.297181	−	0.514732i	0.975490	+	0.220045i	$0.0706203\pi$
$32$		0			0
$33$	−1.21154	−	2.09845i	−0.210902	−	0.365293i
$34$		0			0
$35$	−5.87254	+	8.64551i	−0.992641	+	1.46136i
$36$		0			0
$37$	−5.83686	−	10.1097i	−0.959573	−	1.66203i	−0.723538	−	0.690285i	$-0.757485\pi$
$37$	−5.83686	−	10.1097i	−0.959573	−	1.66203i	−0.236036	−	0.971744i	$-0.575848\pi$
$38$		0			0
$39$	0.318196	−	0.551131i	0.0509521	−	0.0882516i
$40$		0			0
$41$	2.99624			0.467934			0.233967	−	0.972245i	$-0.424829\pi$
$41$	2.99624			0.467934			0.233967	+	0.972245i	$0.424829\pi$
$42$		0			0
$43$	−2.47146			−0.376894			−0.188447	−	0.982083i	$-0.560345\pi$
$43$	−2.47146			−0.376894			−0.188447	+	0.982083i	$0.560345\pi$
$44$		0			0
$45$	1.97513	−	3.42102i	0.294435	−	0.509976i
$46$		0			0
$47$	3.04541	+	5.27481i	0.444219	+	0.769410i	0.997997	−	0.0632540i	$-0.0201478\pi$
$47$	3.04541	+	5.27481i	0.444219	+	0.769410i	−0.553778	+	0.832664i	$0.686814\pi$
$48$		0			0
$49$	−4.34548	+	5.48788i	−0.620783	+	0.783983i
$50$		0			0
$51$	0.500000	+	0.866025i	0.0700140	+	0.121268i
$52$		0			0
$53$	5.86104	−	10.1516i	0.805076	−	1.39443i	−0.111163	−	0.993802i	$-0.535458\pi$
$53$	5.86104	−	10.1516i	0.805076	−	1.39443i	0.916239	−	0.400631i	$-0.131209\pi$
$54$		0			0
$55$	−9.57179			−1.29066
$56$		0			0
$57$	−8.55989			−1.13379
$58$		0			0
$59$	4.47026	−	7.74272i	0.581979	−	1.00802i	−0.413266	−	0.910610i	$-0.635612\pi$
$59$	4.47026	−	7.74272i	0.581979	−	1.00802i	0.995245	−	0.0974063i	$-0.0310546\pi$
$60$		0			0
$61$	−5.79076	−	10.0299i	−0.741431	−	1.28420i	−0.951844	−	0.306583i	$-0.900814\pi$
$61$	−5.79076	−	10.0299i	−0.741431	−	1.28420i	0.210413	−	0.977613i	$-0.432519\pi$
$62$		0			0
$63$	1.48662	−	2.18860i	0.187297	−	0.275737i
$64$		0			0
$65$	−1.25695	−	2.17711i	−0.155906	−	0.270037i
$66$		0			0
$67$	−0.715609	+	1.23947i	−0.0874256	+	0.151426i	−0.906422	−	0.422373i	$-0.861197\pi$
$67$	−0.715609	+	1.23947i	−0.0874256	+	0.151426i	0.818997	+	0.573798i	$0.194531\pi$
$68$		0			0
$69$	3.92726			0.472787
$70$		0			0
$71$	−5.75021			−0.682424			−0.341212	−	0.939986i	$-0.610837\pi$
$71$	−5.75021			−0.682424			−0.341212	+	0.939986i	$0.610837\pi$
$72$		0			0
$73$	−4.35916	+	7.55029i	−0.510202	+	0.883695i	0.489729	+	0.871875i	$0.337096\pi$
$73$	−4.35916	+	7.55029i	−0.510202	+	0.883695i	−0.999930	+	0.0118201i	$0.996237\pi$
$74$		0			0
$75$	−5.30226	−	9.18378i	−0.612252	−	1.06045i
$76$		0			0
$77$	−6.39376	−	0.468032i	−0.728637	−	0.0533372i
$78$		0			0
$79$	6.40040	+	11.0858i	0.720101	+	1.24725i	0.960959	+	0.276691i	$0.0892379\pi$
$79$	6.40040	+	11.0858i	0.720101	+	1.24725i	−0.240858	+	0.970560i	$0.577429\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.17705			0.458491			0.229246	−	0.973369i	$-0.426374\pi$
$83$	4.17705			0.458491			0.229246	+	0.973369i	$0.426374\pi$
$84$		0			0
$85$	3.95025			0.428465
$86$		0			0
$87$	−3.00486	+	5.20458i	−0.322155	+	0.557989i
$88$		0			0
$89$	−6.32050	−	10.9474i	−0.669971	−	1.16042i	−0.977912	−	0.209019i	$-0.932973\pi$
$89$	−6.32050	−	10.9474i	−0.669971	−	1.16042i	0.307941	−	0.951406i	$-0.400360\pi$
$90$		0			0
$91$	−0.733166	−	1.51573i	−0.0768567	−	0.158891i
$92$		0			0
$93$	1.65463	+	2.86591i	0.171577	+	0.297181i
$94$		0			0
$95$	−16.9069	+	29.2836i	−1.73461	+	3.00443i
$96$		0			0
$97$	9.25439			0.939641			0.469820	−	0.882762i	$-0.344319\pi$
$97$	9.25439			0.939641			0.469820	+	0.882762i	$0.344319\pi$
$98$		0			0
$99$	2.42308			0.243529
$100$		0			0
$101$	−1.57504	+	2.72805i	−0.156722	+	0.271451i	−0.933685	−	0.358096i	$-0.883426\pi$
$101$	−1.57504	+	2.72805i	−0.156722	+	0.271451i	0.776963	+	0.629547i	$0.216759\pi$
$102$		0			0
$103$	5.19628	+	9.00023i	0.512005	+	0.886819i	0.999903	+	0.0139182i	$0.00443044\pi$
$103$	5.19628	+	9.00023i	0.512005	+	0.886819i	−0.487898	+	0.872901i	$0.662236\pi$
$104$		0			0
$105$	−4.55096	−	9.40852i	−0.444128	−	0.918178i
$106$		0			0
$107$	−4.39565	−	7.61348i	−0.424943	−	0.736023i	0.571472	−	0.820622i	$-0.306373\pi$
$107$	−4.39565	−	7.61348i	−0.424943	−	0.736023i	−0.996415	+	0.0845986i	$0.973039\pi$
$108$		0			0
$109$	−7.56595	+	13.1046i	−0.724687	+	1.25519i	0.234416	+	0.972136i	$0.424682\pi$
$109$	−7.56595	+	13.1046i	−0.724687	+	1.25519i	−0.959103	+	0.283058i	$0.908651\pi$
$110$		0			0
$111$	11.6737			1.10802
$112$		0			0
$113$	−12.3412			−1.16097			−0.580483	−	0.814273i	$-0.697136\pi$
$113$	−12.3412			−1.16097			−0.580483	+	0.814273i	$0.697136\pi$
$114$		0			0
$115$	7.75684	−	13.4352i	0.723329	−	1.25284i
$116$		0			0
$117$	0.318196	+	0.551131i	0.0294172	+	0.0509521i
$118$		0			0
$119$	2.63869	+	0.193156i	0.241888	+	0.0177066i
$120$		0			0
$121$	2.56434	+	4.44156i	0.233122	+	0.403778i
$122$		0			0
$123$	−1.49812	+	2.59482i	−0.135081	+	0.233967i
$124$		0			0
$125$	−22.1392			−1.98019
$126$		0			0
$127$	2.38523			0.211655			0.105828	−	0.994384i	$-0.466251\pi$
$127$	2.38523			0.211655			0.105828	+	0.994384i	$0.466251\pi$
$128$		0			0
$129$	1.23573	−	2.14035i	0.108800	−	0.188447i
$130$		0			0
$131$	4.38958	+	7.60298i	0.383520	+	0.664276i	0.991563	−	0.129628i	$-0.0413785\pi$
$131$	4.38958	+	7.60298i	0.383520	+	0.664276i	−0.608043	+	0.793904i	$0.708045\pi$
$132$		0			0
$133$	−12.7253	+	18.7341i	−1.10343	+	1.62446i
$134$		0			0
$135$	1.97513	+	3.42102i	0.169992	+	0.294435i
$136$		0			0
$137$	6.93133	−	12.0054i	0.592184	−	1.02569i	−0.401754	−	0.915748i	$-0.631599\pi$
$137$	6.93133	−	12.0054i	0.592184	−	1.02569i	0.993938	−	0.109944i	$-0.0350673\pi$
$138$		0			0
$139$	−5.85430			−0.496555			−0.248278	−	0.968689i	$-0.579865\pi$
$139$	−5.85430			−0.496555			−0.248278	+	0.968689i	$0.579865\pi$
$140$		0			0
$141$	−6.09083			−0.512940
$142$		0			0
$143$	0.771014	−	1.33544i	0.0644754	−	0.111675i
$144$		0			0
$145$	11.8700	+	20.5594i	0.985748	+	1.70737i
$146$		0			0
$147$	−2.57990	−	6.50724i	−0.212787	−	0.536708i
$148$		0			0
$149$	6.07285	+	10.5185i	0.497507	+	0.861708i	0.999996	−	0.00287600i	$-0.000915461\pi$
$149$	6.07285	+	10.5185i	0.497507	+	0.861708i	−0.502489	+	0.864584i	$0.667582\pi$
$150$		0			0
$151$	−4.81643	+	8.34230i	−0.391955	+	0.678886i	−0.992707	−	0.120549i	$-0.961535\pi$
$151$	−4.81643	+	8.34230i	−0.391955	+	0.678886i	0.600752	+	0.799435i	$0.294868\pi$
$152$		0			0
$153$	−1.00000			−0.0808452
$154$		0			0
$155$	13.0724			1.05000
$156$		0			0
$157$	5.51866	−	9.55860i	0.440437	−	0.762859i	−0.557285	−	0.830321i	$-0.688157\pi$
$157$	5.51866	−	9.55860i	0.440437	−	0.762859i	0.997722	+	0.0674621i	$0.0214902\pi$
$158$		0			0
$159$	5.86104	+	10.1516i	0.464811	+	0.805076i
$160$		0			0
$161$	5.83836	−	8.59519i	0.460127	−	0.677396i
$162$		0			0
$163$	8.24645	+	14.2833i	0.645912	+	1.11875i	0.984090	+	0.177670i	$0.0568559\pi$
$163$	8.24645	+	14.2833i	0.645912	+	1.11875i	−0.338178	+	0.941082i	$0.609811\pi$
$164$		0			0
$165$	4.78589	−	8.28941i	0.372581	−	0.645330i
$166$		0			0
$167$	−19.3222			−1.49520			−0.747599	−	0.664150i	$-0.768794\pi$
$167$	−19.3222			−1.49520			−0.747599	+	0.664150i	$0.768794\pi$
$168$		0			0
$169$	−12.5950			−0.968847
$170$		0			0
$171$	4.27995	−	7.41308i	0.327296	−	0.566893i
$172$		0			0
$173$	−4.87322	−	8.44067i	−0.370504	−	0.641732i	0.619139	−	0.785282i	$-0.287482\pi$
$173$	−4.87322	−	8.44067i	−0.370504	−	0.641732i	−0.989643	+	0.143549i	$0.954148\pi$
$174$		0			0
$175$	−27.9820	−	2.04832i	−2.11524	−	0.154839i
$176$		0			0
$177$	4.47026	+	7.74272i	0.336006	+	0.581979i
$178$		0			0
$179$	5.71859	−	9.90489i	0.427428	−	0.740326i	−0.569216	−	0.822188i	$-0.692753\pi$
$179$	5.71859	−	9.90489i	0.427428	−	0.740326i	0.996644	+	0.0818615i	$0.0260865\pi$
$180$		0			0
$181$	15.0819			1.12103			0.560516	−	0.828144i	$-0.310603\pi$
$181$	15.0819			1.12103			0.560516	+	0.828144i	$0.310603\pi$
$182$		0			0
$183$	11.5815			0.856130
$184$		0			0
$185$	23.0571	−	39.9360i	1.69519	−	2.93615i
$186$		0			0
$187$	1.21154	+	2.09845i	0.0885966	+	0.153454i
$188$		0			0
$189$	1.15207	+	2.38175i	0.0838006	+	0.173247i
$190$		0			0
$191$	0.183001	+	0.316967i	0.0132415	+	0.0229349i	0.872570	−	0.488489i	$-0.162452\pi$
$191$	0.183001	+	0.316967i	0.0132415	+	0.0229349i	−0.859329	+	0.511424i	$0.829118\pi$
$192$		0			0
$193$	8.91189	−	15.4359i	0.641492	−	1.11110i	−0.343608	−	0.939113i	$-0.611649\pi$
$193$	8.91189	−	15.4359i	0.641492	−	1.11110i	0.985100	−	0.171984i	$-0.0550176\pi$
$194$		0			0
$195$	2.51391			0.180025
$196$		0			0
$197$	27.5919			1.96584			0.982919	−	0.184037i	$-0.0589166\pi$
$197$	27.5919			1.96584			0.982919	+	0.184037i	$0.0589166\pi$
$198$		0			0
$199$	−4.62343	+	8.00802i	−0.327747	+	0.567674i	−0.982064	−	0.188546i	$-0.939623\pi$
$199$	−4.62343	+	8.00802i	−0.327747	+	0.567674i	0.654318	+	0.756220i	$0.272956\pi$
$200$		0			0
$201$	−0.715609	−	1.23947i	−0.0504752	−	0.0874256i
$202$		0			0
$203$	6.92361	+	14.3137i	0.485942	+	1.00462i
$204$		0			0
$205$	5.91795	+	10.2502i	0.413328	+	0.715905i
$206$		0			0
$207$	−1.96363	+	3.40111i	−0.136482	+	0.236393i
$208$		0			0
$209$	−20.7413			−1.43471
$210$		0			0
$211$	−19.0130			−1.30891			−0.654453	−	0.756103i	$-0.727101\pi$
$211$	−19.0130			−1.30891			−0.654453	+	0.756103i	$0.727101\pi$
$212$		0			0
$213$	2.87510	−	4.97983i	0.196999	−	0.341212i
$214$		0			0
$215$	−4.88145	−	8.45492i	−0.332912	−	0.576620i
$216$		0			0
$217$	8.73212	+	0.639204i	0.592775	+	0.0433920i
$218$		0			0
$219$	−4.35916	−	7.55029i	−0.294565	−	0.510202i
$220$		0			0
$221$	−0.318196	+	0.551131i	−0.0214042	+	0.0370731i
$222$		0			0
$223$	28.9027			1.93547			0.967734	−	0.251972i	$-0.0810791\pi$
$223$	28.9027			1.93547			0.967734	+	0.251972i	$0.0810791\pi$
$224$		0			0
$225$	10.6045			0.706967
$226$		0			0
$227$	−2.67517	+	4.63353i	−0.177557	+	0.307538i	−0.941043	−	0.338286i	$-0.890153\pi$
$227$	−2.67517	+	4.63353i	−0.177557	+	0.307538i	0.763486	+	0.645824i	$0.223486\pi$
$228$		0			0
$229$	−10.3440	−	17.9164i	−0.683552	−	1.18395i	−0.973890	−	0.227023i	$-0.927101\pi$
$229$	−10.3440	−	17.9164i	−0.683552	−	1.18395i	0.290337	−	0.956924i	$-0.406232\pi$
$230$		0			0
$231$	3.60221	−	5.30315i	0.237008	−	0.348921i
$232$		0			0
$233$	4.72085	+	8.17675i	0.309273	+	0.535677i	0.978204	−	0.207648i	$-0.0665809\pi$
$233$	4.72085	+	8.17675i	0.309273	+	0.535677i	−0.668930	+	0.743325i	$0.733248\pi$
$234$		0			0
$235$	−12.0302	+	20.8368i	−0.784761	+	1.35925i
$236$		0			0
$237$	−12.8008			−0.831501
$238$		0			0
$239$	−5.75481			−0.372248			−0.186124	−	0.982526i	$-0.559593\pi$
$239$	−5.75481			−0.372248			−0.186124	+	0.982526i	$0.559593\pi$
$240$		0			0
$241$	4.77807	−	8.27585i	0.307782	−	0.533095i	−0.670095	−	0.742276i	$-0.733746\pi$
$241$	4.77807	−	8.27585i	0.307782	−	0.533095i	0.977877	+	0.209181i	$0.0670798\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−27.3570	−	4.02672i	−1.74778	−	0.257258i
$246$		0			0
$247$	−2.72372	−	4.71762i	−0.173306	−	0.300175i
$248$		0			0
$249$	−2.08853	+	3.61743i	−0.132355	+	0.229246i
$250$		0			0
$251$	−21.8232			−1.37747			−0.688733	−	0.725015i	$-0.741833\pi$
$251$	−21.8232			−1.37747			−0.688733	+	0.725015i	$0.741833\pi$
$252$		0			0
$253$	9.51608			0.598271
$254$		0			0
$255$	−1.97513	+	3.42102i	−0.123687	+	0.214233i
$256$		0			0
$257$	3.25952	+	5.64565i	0.203323	+	0.352166i	0.949597	−	0.313473i	$-0.101492\pi$
$257$	3.25952	+	5.64565i	0.203323	+	0.352166i	−0.746274	+	0.665639i	$0.768159\pi$
$258$		0			0
$259$	17.3544	−	25.5490i	1.07835	−	1.58754i
$260$		0			0
$261$	−3.00486	−	5.20458i	−0.185996	−	0.322155i
$262$		0			0
$263$	10.8894	−	18.8610i	0.671471	−	1.16302i	−0.306016	−	0.952026i	$-0.598996\pi$
$263$	10.8894	−	18.8610i	0.671471	−	1.16302i	0.977487	−	0.210996i	$-0.0676706\pi$
$264$		0			0
$265$	46.3052			2.84451
$266$		0			0
$267$	12.6410			0.773616
$268$		0			0
$269$	11.9187	−	20.6439i	0.726699	−	1.25868i	−0.231572	−	0.972818i	$-0.574387\pi$
$269$	11.9187	−	20.6439i	0.726699	−	1.25868i	0.958271	−	0.285862i	$-0.0922798\pi$
$270$		0			0
$271$	9.49310	+	16.4425i	0.576665	+	0.998813i	0.995859	+	0.0909161i	$0.0289795\pi$
$271$	9.49310	+	16.4425i	0.576665	+	0.998813i	−0.419194	+	0.907897i	$0.637687\pi$
$272$		0			0
$273$	1.67924	+	0.122923i	0.101632	+	0.00743962i
$274$		0			0
$275$	−12.8478	−	22.2530i	−0.774751	−	1.34191i
$276$		0			0
$277$	3.39146	−	5.87419i	0.203773	−	0.352946i	−0.745968	−	0.665982i	$-0.768013\pi$
$277$	3.39146	−	5.87419i	0.203773	−	0.352946i	0.949741	+	0.313036i	$0.101346\pi$
$278$		0			0
$279$	−3.30926			−0.198120
$280$		0			0
$281$	3.20442			0.191160			0.0955799	−	0.995422i	$-0.469529\pi$
$281$	3.20442			0.191160			0.0955799	+	0.995422i	$0.469529\pi$
$282$		0			0
$283$	4.59177	−	7.95319i	0.272953	−	0.472768i	−0.696664	−	0.717398i	$-0.745333\pi$
$283$	4.59177	−	7.95319i	0.272953	−	0.472768i	0.969617	+	0.244630i	$0.0786664\pi$
$284$		0			0
$285$	−16.9069	−	29.2836i	−1.00148	−	1.73461i
$286$		0			0
$287$	3.45187	+	7.13630i	0.203757	+	0.421242i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	−4.62719	+	8.01454i	−0.271251	+	0.469820i
$292$		0			0
$293$	2.63502			0.153940			0.0769699	−	0.997033i	$-0.475475\pi$
$293$	2.63502			0.153940			0.0769699	+	0.997033i	$0.475475\pi$
$294$		0			0
$295$	35.3174			2.05626
$296$		0			0
$297$	−1.21154	+	2.09845i	−0.0703007	+	0.121764i
$298$		0			0
$299$	1.24964	+	2.16444i	0.0722684	+	0.125173i
$300$		0			0
$301$	−2.84729	−	5.88640i	−0.164115	−	0.339287i
$302$		0			0
$303$	−1.57504	−	2.72805i	−0.0904836	−	0.156722i
$304$		0			0
$305$	22.8750	−	39.6206i	1.30982	−	2.26867i
$306$		0			0
$307$	6.69074			0.381860			0.190930	−	0.981604i	$-0.438850\pi$
$307$	6.69074			0.381860			0.190930	+	0.981604i	$0.438850\pi$
$308$		0			0
$309$	−10.3926			−0.591213
$310$		0			0
$311$	−0.922818	+	1.59837i	−0.0523282	+	0.0906351i	−0.891003	−	0.453997i	$-0.849998\pi$
$311$	−0.922818	+	1.59837i	−0.0523282	+	0.0906351i	0.838675	+	0.544633i	$0.183331\pi$
$312$		0			0
$313$	7.08371	+	12.2693i	0.400395	+	0.693504i	0.993773	−	0.111419i	$-0.0355397\pi$
$313$	7.08371	+	12.2693i	0.400395	+	0.693504i	−0.593379	+	0.804923i	$0.702206\pi$
$314$		0			0
$315$	10.4235	+	0.763015i	0.587298	+	0.0429910i
$316$		0			0
$317$	4.49781	+	7.79044i	0.252622	+	0.437555i	0.964247	−	0.265005i	$-0.0853737\pi$
$317$	4.49781	+	7.79044i	0.252622	+	0.437555i	−0.711625	+	0.702560i	$0.752040\pi$
$318$		0			0
$319$	−7.28103	+	12.6111i	−0.407659	+	0.706087i
$320$		0			0
$321$	8.79129			0.490682
$322$		0			0
$323$	8.55989			0.476285
$324$		0			0
$325$	3.37431	−	5.84448i	0.187173	−	0.324193i
$326$		0			0
$327$	−7.56595	−	13.1046i	−0.418398	−	0.724687i
$328$		0			0
$329$	−9.05476	+	13.3304i	−0.499205	+	0.734926i
$330$		0			0
$331$	3.06434	+	5.30759i	0.168431	+	0.291731i	0.937868	−	0.346991i	$-0.112797\pi$
$331$	3.06434	+	5.30759i	0.168431	+	0.291731i	−0.769437	+	0.638722i	$0.779463\pi$
$332$		0			0
$333$	−5.83686	+	10.1097i	−0.319858	+	0.554010i
$334$		0			0
$335$	−5.65368			−0.308893
$336$		0			0
$337$	−10.6061			−0.577751			−0.288876	−	0.957367i	$-0.593281\pi$
$337$	−10.6061			−0.577751			−0.288876	+	0.957367i	$0.593281\pi$
$338$		0			0
$339$	6.17062	−	10.6878i	0.335142	−	0.580483i
$340$		0			0
$341$	4.00931	+	6.94433i	0.217116	+	0.376056i
$342$		0			0
$343$	−18.0770	−	4.02745i	−0.976069	−	0.217462i
$344$		0			0
$345$	7.75684	+	13.4352i	0.417614	+	0.723329i
$346$		0			0
$347$	15.2203	−	26.3624i	0.817070	−	1.41521i	−0.0907626	−	0.995873i	$-0.528930\pi$
$347$	15.2203	−	26.3624i	0.817070	−	1.41521i	0.907832	−	0.419334i	$-0.137736\pi$
$348$		0			0
$349$	−2.53743			−0.135825			−0.0679127	−	0.997691i	$-0.521634\pi$
$349$	−2.53743			−0.135825			−0.0679127	+	0.997691i	$0.521634\pi$
$350$		0			0
$351$	−0.636391			−0.0339681
$352$		0			0
$353$	10.0391	−	17.3882i	0.534327	−	0.925481i	−0.464869	−	0.885380i	$-0.653899\pi$
$353$	10.0391	−	17.3882i	0.534327	−	0.925481i	0.999196	−	0.0401015i	$-0.0127681\pi$
$354$		0			0
$355$	−11.3574	−	19.6716i	−0.602788	−	1.04406i
$356$		0			0
$357$	−1.48662	+	2.18860i	−0.0786805	+	0.115833i
$358$		0			0
$359$	11.7123	+	20.2862i	0.618150	+	1.07067i	0.989823	+	0.142303i	$0.0454508\pi$
$359$	11.7123	+	20.2862i	0.618150	+	1.07067i	−0.371673	+	0.928364i	$0.621216\pi$
$360$		0			0
$361$	−27.1359	+	47.0007i	−1.42820	+	2.47372i
$362$		0			0
$363$	−5.12867			−0.269186
$364$		0			0
$365$	−34.4396			−1.80265
$366$		0			0
$367$	−11.7732	+	20.3917i	−0.614554	+	1.06444i	0.375909	+	0.926657i	$0.377331\pi$
$367$	−11.7732	+	20.3917i	−0.614554	+	1.06444i	−0.990463	+	0.137782i	$0.956003\pi$
$368$		0			0
$369$	−1.49812	−	2.59482i	−0.0779890	−	0.135081i
$370$		0			0
$371$	30.9310	+	2.26419i	1.60586	+	0.117551i
$372$		0			0
$373$	18.3408	+	31.7671i	0.949649	+	1.64484i	0.746164	+	0.665763i	$0.231894\pi$
$373$	18.3408	+	31.7671i	0.949649	+	1.64484i	0.203486	+	0.979078i	$0.434773\pi$
$374$		0			0
$375$	11.0696	−	19.1731i	0.571633	−	0.990097i
$376$		0			0
$377$	−3.82454			−0.196974
$378$		0			0
$379$	9.70183			0.498350			0.249175	−	0.968459i	$-0.419841\pi$
$379$	9.70183			0.498350			0.249175	+	0.968459i	$0.419841\pi$
$380$		0			0
$381$	−1.19262	+	2.06567i	−0.0610996	+	0.105828i
$382$		0			0
$383$	6.37877	+	11.0484i	0.325940	+	0.564545i	0.981702	−	0.190423i	$-0.0609859\pi$
$383$	6.37877	+	11.0484i	0.325940	+	0.564545i	−0.655762	+	0.754968i	$0.727653\pi$
$384$		0			0
$385$	−11.0273	−	22.7976i	−0.562006	−	1.16187i
$386$		0			0
$387$	1.23573	+	2.14035i	0.0628157	+	0.108800i
$388$		0			0
$389$	−9.68328	+	16.7719i	−0.490962	+	0.850371i	−0.999946	−	0.0104050i	$-0.996688\pi$
$389$	−9.68328	+	16.7719i	−0.490962	+	0.850371i	0.508984	+	0.860776i	$0.330021\pi$
$390$		0			0
$391$	−3.92726			−0.198610
$392$		0			0
$393$	−8.77917			−0.442850
$394$		0			0
$395$	−25.2832	+	43.7918i	−1.27214	+	2.20340i
$396$		0			0
$397$	−0.488504	−	0.846113i	−0.0245173	−	0.0424652i	0.853506	−	0.521082i	$-0.174472\pi$
$397$	−0.488504	−	0.846113i	−0.0245173	−	0.0424652i	−0.878024	+	0.478617i	$0.841138\pi$
$398$		0			0
$399$	−9.86158	−	20.3875i	−0.493696	−	1.02065i
$400$		0			0
$401$	11.0827	+	19.1959i	0.553445	+	0.958595i	0.998023	+	0.0628549i	$0.0200205\pi$
$401$	11.0827	+	19.1959i	0.553445	+	0.958595i	−0.444577	+	0.895740i	$0.646646\pi$
$402$		0			0
$403$	−1.05299	+	1.82384i	−0.0524533	+	0.0908518i
$404$		0			0
$405$	−3.95025			−0.196290
$406$		0			0
$407$	28.2864			1.40210
$408$		0			0
$409$	5.65651	−	9.79737i	0.279697	−	0.484449i	−0.691613	−	0.722269i	$-0.743099\pi$
$409$	5.65651	−	9.79737i	0.279697	−	0.484449i	0.971309	+	0.237820i	$0.0764328\pi$
$410$		0			0
$411$	6.93133	+	12.0054i	0.341897	+	0.592184i
$412$		0			0
$413$	23.5913	+	1.72691i	1.16085	+	0.0849759i
$414$		0			0
$415$	8.25021	+	14.2898i	0.404987	+	0.701458i
$416$		0			0
$417$	2.92715	−	5.06997i	0.143343	−	0.248278i
$418$		0			0
$419$	−19.2619			−0.941006			−0.470503	−	0.882398i	$-0.655928\pi$
$419$	−19.2619			−0.941006			−0.470503	+	0.882398i	$0.655928\pi$
$420$		0			0
$421$	26.5226			1.29263			0.646316	−	0.763070i	$-0.276309\pi$
$421$	26.5226			1.29263			0.646316	+	0.763070i	$0.276309\pi$
$422$		0			0
$423$	3.04541	−	5.27481i	0.148073	−	0.256470i
$424$		0			0
$425$	5.30226	+	9.18378i	0.257197	+	0.445479i
$426$		0			0
$427$	17.2174	−	25.3473i	0.833206	−	1.22664i
$428$		0			0
$429$	0.771014	+	1.33544i	0.0372249	+	0.0644754i
$430$		0			0
$431$	9.25994	−	16.0387i	0.446035	−	0.772556i	−0.552088	−	0.833786i	$-0.686169\pi$
$431$	9.25994	−	16.0387i	0.446035	−	0.772556i	0.998124	+	0.0612296i	$0.0195022\pi$
$432$		0			0
$433$	−1.66097			−0.0798214			−0.0399107	−	0.999203i	$-0.512707\pi$
$433$	−1.66097			−0.0798214			−0.0399107	+	0.999203i	$0.512707\pi$
$434$		0			0
$435$	−23.7400			−1.13824
$436$		0			0
$437$	16.8085	−	29.1131i	0.804058	−	1.39267i
$438$		0			0
$439$	−5.53434	−	9.58575i	−0.264139	−	0.457503i	0.703198	−	0.710994i	$-0.251755\pi$
$439$	−5.53434	−	9.58575i	−0.264139	−	0.457503i	−0.967338	+	0.253491i	$0.918421\pi$
$440$		0			0
$441$	6.92538	+	1.01936i	0.329780	+	0.0485408i
$442$		0			0
$443$	3.05540	+	5.29212i	0.145167	+	0.251436i	0.929435	−	0.368986i	$-0.120295\pi$
$443$	3.05540	+	5.29212i	0.145167	+	0.251436i	−0.784268	+	0.620422i	$0.786961\pi$
$444$		0			0
$445$	24.9676	−	43.2451i	1.18358	−	2.05001i
$446$		0			0
$447$	−12.1457			−0.574472
$448$		0			0
$449$	5.73151			0.270487			0.135243	−	0.990812i	$-0.456818\pi$
$449$	5.73151			0.270487			0.135243	+	0.990812i	$0.456818\pi$
$450$		0			0
$451$	−3.63007	+	6.28746i	−0.170933	+	0.296065i
$452$		0			0
$453$	−4.81643	−	8.34230i	−0.226295	−	0.391955i
$454$		0			0
$455$	3.73723	−	5.50193i	0.175204	−	0.257934i
$456$		0			0
$457$	−3.55315	−	6.15423i	−0.166209	−	0.287883i	0.770875	−	0.636987i	$-0.219819\pi$
$457$	−3.55315	−	6.15423i	−0.166209	−	0.287883i	−0.937084	+	0.349104i	$0.886486\pi$
$458$		0			0
$459$	0.500000	−	0.866025i	0.0233380	−	0.0404226i
$460$		0			0
$461$	−19.5426			−0.910188			−0.455094	−	0.890443i	$-0.650394\pi$
$461$	−19.5426			−0.910188			−0.455094	+	0.890443i	$0.650394\pi$
$462$		0			0
$463$	−21.9206			−1.01874			−0.509368	−	0.860549i	$-0.670121\pi$
$463$	−21.9206			−1.01874			−0.509368	+	0.860549i	$0.670121\pi$
$464$		0			0
$465$	−6.53622	+	11.3211i	−0.303110	+	0.525002i
$466$		0			0
$467$	−0.961374	−	1.66515i	−0.0444871	−	0.0770539i	0.842924	−	0.538032i	$-0.180832\pi$
$467$	−0.961374	−	1.66515i	−0.0444871	−	0.0770539i	−0.887412	+	0.460978i	$0.847499\pi$
$468$		0			0
$469$	−3.77654	−	0.276448i	−0.174385	−	0.0127652i
$470$		0			0
$471$	5.51866	+	9.55860i	0.254286	+	0.440437i
$472$		0			0
$473$	2.99428	−	5.18624i	0.137677	−	0.238463i
$474$		0			0
$475$	−90.7735			−4.16497
$476$		0			0
$477$	−11.7221			−0.536718
$478$		0			0
$479$	5.62693	−	9.74613i	0.257101	−	0.445312i	−0.708363	−	0.705848i	$-0.750566\pi$
$479$	5.62693	−	9.74613i	0.257101	−	0.445312i	0.965464	+	0.260536i	$0.0838994\pi$
$480$		0			0
$481$	3.71452	+	6.43375i	0.169368	+	0.293354i
$482$		0			0
$483$	4.52447	+	9.35376i	0.205871	+	0.425611i
$484$		0			0
$485$	18.2786	+	31.6595i	0.829988	+	1.43758i
$486$		0			0
$487$	4.12007	−	7.13618i	0.186698	−	0.323371i	−0.757449	−	0.652894i	$-0.773555\pi$
$487$	4.12007	−	7.13618i	0.186698	−	0.323371i	0.944148	+	0.329523i	$0.106888\pi$
$488$		0			0
$489$	−16.4929			−0.745835
$490$		0			0
$491$	24.9659			1.12670			0.563349	−	0.826219i	$-0.309513\pi$
$491$	24.9659			1.12670			0.563349	+	0.826219i	$0.309513\pi$
$492$		0			0
$493$	3.00486	−	5.20458i	0.135332	−	0.234402i
$494$		0			0
$495$	4.78589	+	8.28941i	0.215110	+	0.372581i
$496$		0			0
$497$	−6.62463	−	13.6956i	−0.297155	−	0.614330i
$498$		0			0
$499$	−15.0819	−	26.1227i	−0.675160	−	1.16941i	−0.976422	−	0.215870i	$-0.930741\pi$
$499$	−15.0819	−	26.1227i	−0.675160	−	1.16941i	0.301262	−	0.953541i	$-0.402592\pi$
$500$		0			0
$501$	9.66111	−	16.7335i	0.431627	−	0.747599i
$502$		0			0
$503$	7.07141			0.315298			0.157649	−	0.987495i	$-0.449608\pi$
$503$	7.07141			0.315298			0.157649	+	0.987495i	$0.449608\pi$
$504$		0			0
$505$	−12.4436			−0.553733
$506$		0			0
$507$	6.29750	−	10.9076i	0.279682	−	0.484423i
$508$		0			0
$509$	−9.43984	−	16.3503i	−0.418414	−	0.724714i	0.577366	−	0.816485i	$-0.304080\pi$
$509$	−9.43984	−	16.3503i	−0.418414	−	0.724714i	−0.995780	+	0.0917714i	$0.970747\pi$
$510$		0			0
$511$	−23.0050	−	1.68400i	−1.01768	−	0.0744956i
$512$		0			0
$513$	4.27995	+	7.41308i	0.188964	+	0.327296i
$514$		0			0
$515$	−20.5266	+	35.5532i	−0.904512	+	1.56666i
$516$		0			0
$517$	−14.7586			−0.649081
$518$		0			0
$519$	9.74645			0.427822
$520$		0			0
$521$	−12.5579	+	21.7509i	−0.550170	+	0.952922i	0.448092	+	0.893987i	$0.352104\pi$
$521$	−12.5579	+	21.7509i	−0.550170	+	0.952922i	−0.998262	+	0.0589347i	$0.981230\pi$
$522$		0			0
$523$	−1.83407	−	3.17670i	−0.0801982	−	0.138907i	0.823137	−	0.567843i	$-0.192222\pi$
$523$	−1.83407	−	3.17670i	−0.0801982	−	0.138907i	−0.903335	+	0.428936i	$0.858889\pi$
$524$		0			0
$525$	15.7649	−	23.2090i	0.688037	−	1.01292i
$526$		0			0
$527$	−1.65463	−	2.86591i	−0.0720769	−	0.124841i
$528$		0			0
$529$	3.78831	−	6.56154i	0.164709	−	0.285284i
$530$		0			0
$531$	−8.94053			−0.387986
$532$		0			0
$533$	−1.90678			−0.0825918
$534$		0			0
$535$	17.3639	−	30.0752i	0.750708	−	1.30026i
$536$		0			0
$537$	5.71859	+	9.90489i	0.246775	+	0.427428i
$538$		0			0
$539$	−6.25131	−	15.7676i	−0.269263	−	0.679157i
$540$		0			0
$541$	2.99962	+	5.19550i	0.128964	+	0.223372i	0.923275	−	0.384139i	$-0.125502\pi$
$541$	2.99962	+	5.19550i	0.128964	+	0.223372i	−0.794312	+	0.607511i	$0.792168\pi$
$542$		0			0
$543$	−7.54097	+	13.0613i	−0.323614	+	0.560516i
$544$		0			0
$545$	−59.7749			−2.56047
$546$		0			0
$547$	29.4844			1.26066			0.630331	−	0.776326i	$-0.282919\pi$
$547$	29.4844			1.26066			0.630331	+	0.776326i	$0.282919\pi$
$548$		0			0
$549$	−5.79076	+	10.0299i	−0.247144	+	0.428065i
$550$		0			0
$551$	25.7213	+	44.5506i	1.09576	+	1.89792i
$552$		0			0
$553$	−19.0300	+	28.0158i	−0.809236	+	1.19135i
$554$		0			0
$555$	23.0571	+	39.9360i	0.978718	+	1.69519i
$556$		0			0
$557$	2.95308	−	5.11489i	0.125126	−	0.216725i	−0.796656	−	0.604433i	$-0.793400\pi$
$557$	2.95308	−	5.11489i	0.125126	−	0.216725i	0.921782	+	0.387708i	$0.126733\pi$
$558$		0			0
$559$	1.57282			0.0665230
$560$		0			0
$561$	−2.42308			−0.102303
$562$		0			0
$563$	7.50256	−	12.9948i	0.316195	−	0.547666i	−0.663495	−	0.748180i	$-0.730928\pi$
$563$	7.50256	−	12.9948i	0.316195	−	0.547666i	0.979691	+	0.200514i	$0.0642612\pi$
$564$		0			0
$565$	−24.3755	−	42.2196i	−1.02549	−	1.77619i
$566$		0			0
$567$	−2.63869	−	0.193156i	−0.110815	−	0.00811178i
$568$		0			0
$569$	17.5654	+	30.4241i	0.736379	+	1.27545i	0.954116	+	0.299438i	$0.0967993\pi$
$569$	17.5654	+	30.4241i	0.736379	+	1.27545i	−0.217737	+	0.976008i	$0.569867\pi$
$570$		0			0
$571$	−15.0231	+	26.0209i	−0.628699	+	1.08894i	0.359114	+	0.933294i	$0.383079\pi$
$571$	−15.0231	+	26.0209i	−0.628699	+	1.08894i	−0.987813	+	0.155645i	$0.950254\pi$
$572$		0			0
$573$	−0.366002			−0.0152900
$574$		0			0
$575$	41.6467			1.73679
$576$		0			0
$577$	4.45512	−	7.71649i	0.185469	−	0.321242i	−0.758265	−	0.651946i	$-0.773953\pi$
$577$	4.45512	−	7.71649i	0.185469	−	0.321242i	0.943734	+	0.330704i	$0.107286\pi$
$578$		0			0
$579$	8.91189	+	15.4359i	0.370366	+	0.641492i
$580$		0			0
$581$	4.81225	+	9.94870i	0.199646	+	0.412742i
$582$		0			0
$583$	14.2018	+	24.5982i	0.588178	+	1.01875i
$584$		0			0
$585$	−1.25695	+	2.17711i	−0.0519686	+	0.0900123i
$586$		0			0
$587$	27.5879			1.13868			0.569338	−	0.822104i	$-0.307200\pi$
$587$	27.5879			1.13868			0.569338	+	0.822104i	$0.307200\pi$
$588$		0			0
$589$	28.3269			1.16719
$590$		0			0
$591$	−13.7959	+	23.8953i	−0.567489	+	0.982919i
$592$		0			0
$593$	−19.4856	−	33.7500i	−0.800177	−	1.38595i	−0.919499	−	0.393092i	$-0.871406\pi$
$593$	−19.4856	−	33.7500i	−0.800177	−	1.38595i	0.119322	−	0.992856i	$-0.461928\pi$
$594$		0			0
$595$	4.55096	+	9.40852i	0.186571	+	0.385712i
$596$		0			0
$597$	−4.62343	−	8.00802i	−0.189225	−	0.327747i
$598$		0			0
$599$	5.15713	−	8.93241i	0.210715	−	0.364968i	−0.741224	−	0.671258i	$-0.765754\pi$
$599$	5.15713	−	8.93241i	0.210715	−	0.364968i	0.951938	+	0.306290i	$0.0990876\pi$
$600$		0			0
$601$	−17.5483			−0.715809			−0.357904	−	0.933758i	$-0.616509\pi$
$601$	−17.5483			−0.715809			−0.357904	+	0.933758i	$0.616509\pi$
$602$		0			0
$603$	1.43122			0.0582837
$604$		0			0
$605$	−10.1298	+	17.5453i	−0.411834	+	0.713318i
$606$		0			0
$607$	0.509821	+	0.883036i	0.0206930	+	0.0358413i	0.876186	−	0.481972i	$-0.160079\pi$
$607$	0.509821	+	0.883036i	0.0206930	+	0.0358413i	−0.855493	+	0.517814i	$0.826746\pi$
$608$		0			0
$609$	−15.8578	−	1.16081i	−0.642591	−	0.0470386i
$610$		0			0
$611$	−1.93807	−	3.35684i	−0.0784061	−	0.135803i
$612$		0			0
$613$	−13.9787	+	24.2119i	−0.564596	+	0.977909i	0.432491	+	0.901638i	$0.357635\pi$
$613$	−13.9787	+	24.2119i	−0.564596	+	0.977909i	−0.997087	+	0.0762705i	$0.975699\pi$
$614$		0			0
$615$	−11.8359			−0.477270
$616$		0			0
$617$	−43.2182			−1.73990			−0.869950	−	0.493140i	$-0.835849\pi$
$617$	−43.2182			−1.73990			−0.869950	+	0.493140i	$0.835849\pi$
$618$		0			0
$619$	−1.10818	+	1.91942i	−0.0445414	+	0.0771480i	−0.887437	−	0.460930i	$-0.847516\pi$
$619$	−1.10818	+	1.91942i	−0.0445414	+	0.0771480i	0.842895	+	0.538078i	$0.180849\pi$
$620$		0			0
$621$	−1.96363	−	3.40111i	−0.0787978	−	0.136482i
$622$		0			0
$623$	18.7924	−	27.6660i	0.752901	−	1.10842i
$624$		0			0
$625$	−17.2165	−	29.8199i	−0.688662	−	1.19280i
$626$		0			0
$627$	10.3707	−	17.9625i	0.414164	−	0.717354i
$628$		0			0
$629$	−11.6737			−0.465461
$630$		0			0
$631$	−3.63366			−0.144654			−0.0723268	−	0.997381i	$-0.523042\pi$
$631$	−3.63366			−0.144654			−0.0723268	+	0.997381i	$0.523042\pi$
$632$		0			0
$633$	9.50648	−	16.4657i	0.377849	−	0.654453i
$634$		0			0
$635$	4.71114	+	8.15993i	0.186956	+	0.323817i
$636$		0			0
$637$	2.76543	−	3.49244i	0.109570	−	0.138375i
$638$		0			0
$639$	2.87510	+	4.97983i	0.113737	+	0.196999i
$640$		0			0
$641$	23.9124	−	41.4175i	0.944484	−	1.63589i	0.187703	−	0.982226i	$-0.439896\pi$
$641$	23.9124	−	41.4175i	0.944484	−	1.63589i	0.756781	−	0.653668i	$-0.226771\pi$
$642$		0			0
$643$	−38.8354			−1.53152			−0.765760	−	0.643127i	$-0.777637\pi$
$643$	−38.8354			−1.53152			−0.765760	+	0.643127i	$0.777637\pi$
$644$		0			0
$645$	9.76290			0.384414
$646$		0			0
$647$	8.06761	−	13.9735i	0.317170	−	0.549355i	−0.662726	−	0.748862i	$-0.730601\pi$
$647$	8.06761	−	13.9735i	0.317170	−	0.549355i	0.979896	+	0.199507i	$0.0639339\pi$
$648$		0			0
$649$	10.8318	+	18.7613i	0.425186	+	0.736444i
$650$		0			0
$651$	−4.91963	+	7.24264i	−0.192815	+	0.283861i
$652$		0			0
$653$	0.290134	+	0.502527i	0.0113538	+	0.0196654i	0.871646	−	0.490135i	$-0.163053\pi$
$653$	0.290134	+	0.502527i	0.0113538	+	0.0196654i	−0.860293	+	0.509800i	$0.829719\pi$
$654$		0			0
$655$	−17.3400	+	30.0337i	−0.677529	+	1.17351i
$656$		0			0
$657$	8.71833			0.340134
$658$		0			0
$659$	1.78833			0.0696635			0.0348318	−	0.999393i	$-0.488910\pi$
$659$	1.78833			0.0696635			0.0348318	+	0.999393i	$0.488910\pi$
$660$		0			0
$661$	2.18123	−	3.77801i	0.0848401	−	0.146947i	−0.820483	−	0.571671i	$-0.806295\pi$
$661$	2.18123	−	3.77801i	0.0848401	−	0.146947i	0.905323	+	0.424724i	$0.139629\pi$
$662$		0			0
$663$	−0.318196	−	0.551131i	−0.0123577	−	0.0214042i
$664$		0			0
$665$	−89.2241	−	6.53132i	−3.45996	−	0.253274i
$666$		0			0
$667$	−11.8009	−	20.4397i	−0.456932	−	0.791430i
$668$		0			0
$669$	−14.4514	+	25.0305i	−0.558722	+	0.967734i
$670$		0			0
$671$	28.0630			1.08336
$672$		0			0
$673$	−28.2352			−1.08839			−0.544194	−	0.838959i	$-0.683165\pi$
$673$	−28.2352			−1.08839			−0.544194	+	0.838959i	$0.683165\pi$
$674$		0			0
$675$	−5.30226	+	9.18378i	−0.204084	+	0.353484i
$676$		0			0
$677$	18.1095	+	31.3666i	0.696006	+	1.20552i	0.969840	+	0.243741i	$0.0783745\pi$
$677$	18.1095	+	31.3666i	0.696006	+	1.20552i	−0.273835	+	0.961777i	$0.588292\pi$
$678$		0			0
$679$	10.6617	+	22.0417i	0.409158	+	0.845881i
$680$		0			0
$681$	−2.67517	−	4.63353i	−0.102513	−	0.177557i
$682$		0			0
$683$	8.00281	−	13.8613i	0.306219	−	0.530387i	−0.671313	−	0.741174i	$-0.734269\pi$
$683$	8.00281	−	13.8613i	0.306219	−	0.530387i	0.977532	+	0.210787i	$0.0676026\pi$
$684$		0			0
$685$	54.7610			2.09231
$686$		0			0
$687$	20.6880			0.789298
$688$		0			0
$689$	−3.72992	+	6.46041i	−0.142099	+	0.246122i
$690$		0			0
$691$	2.88054	+	4.98924i	0.109581	+	0.189800i	0.915601	−	0.402089i	$-0.131716\pi$
$691$	2.88054	+	4.98924i	0.109581	+	0.189800i	−0.806020	+	0.591889i	$0.798382\pi$
$692$		0			0
$693$	2.79155	+	5.77118i	0.106042	+	0.219229i
$694$		0			0
$695$	−11.5630	−	20.0277i	−0.438609	−	0.759693i
$696$		0			0
$697$	1.49812	−	2.59482i	0.0567453	−	0.0982858i
$698$		0			0
$699$	−9.44170			−0.357118
$700$		0			0
$701$	−23.1863			−0.875733			−0.437866	−	0.899040i	$-0.644266\pi$
$701$	−23.1863			−0.875733			−0.437866	+	0.899040i	$0.644266\pi$
$702$		0			0
$703$	49.9629	−	86.5382i	1.88438	−	3.26385i
$704$		0			0
$705$	−12.0302	−	20.8368i	−0.453082	−	0.784761i
$706$		0			0
$707$	−8.31208	−	0.608455i	−0.312608	−	0.0228833i
$708$		0			0
$709$	−24.8967	−	43.1224i	−0.935017	−	1.61950i	−0.774604	−	0.632447i	$-0.782051\pi$
$709$	−24.8967	−	43.1224i	−0.935017	−	1.61950i	−0.160413	−	0.987050i	$-0.551283\pi$
$710$		0			0
$711$	6.40040	−	11.0858i	0.240034	−	0.415750i
$712$		0			0
$713$	−12.9963			−0.486717
$714$		0			0
$715$	6.09140			0.227806
$716$		0			0
$717$	2.87740	−	4.98381i	0.107459	−	0.186124i
$718$		0			0
$719$	26.2290	+	45.4300i	0.978178	+	1.69425i	0.669020	+	0.743244i	$0.266714\pi$
$719$	26.2290	+	45.4300i	0.978178	+	1.69425i	0.309158	+	0.951011i	$0.399953\pi$
$720$		0			0
$721$	−15.4498	+	22.7451i	−0.575382	+	0.847073i
$722$		0			0
$723$	4.77807	+	8.27585i	0.177698	+	0.307782i
$724$		0			0
$725$	−31.8651	+	55.1920i	−1.18344	+	2.04978i
$726$		0			0
$727$	24.8364			0.921132			0.460566	−	0.887625i	$-0.347646\pi$
$727$	24.8364			0.921132			0.460566	+	0.887625i	$0.347646\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−1.23573	+	2.14035i	−0.0457051	+	0.0791636i
$732$		0			0
$733$	10.5861	+	18.3356i	0.391006	+	0.677241i	0.992582	−	0.121573i	$-0.0387940\pi$
$733$	10.5861	+	18.3356i	0.391006	+	0.677241i	−0.601577	+	0.798815i	$0.705461\pi$
$734$		0			0
$735$	17.1658	−	21.6785i	0.633168	−	0.799624i
$736$		0			0
$737$	−1.73398	−	3.00334i	−0.0638720	−	0.110629i
$738$		0			0
$739$	−4.78331	+	8.28493i	−0.175957	+	0.304766i	−0.940492	−	0.339816i	$-0.889635\pi$
$739$	−4.78331	+	8.28493i	−0.175957	+	0.304766i	0.764535	+	0.644582i	$0.222969\pi$
$740$		0			0
$741$	5.44744			0.200117
$742$		0			0
$743$	−44.3767			−1.62802			−0.814011	−	0.580850i	$-0.802720\pi$
$743$	−44.3767			−1.62802			−0.814011	+	0.580850i	$0.802720\pi$
$744$		0			0
$745$	−23.9893	+	41.5507i	−0.878900	+	1.52230i
$746$		0			0
$747$	−2.08853	−	3.61743i	−0.0764152	−	0.132355i
$748$		0			0
$749$	13.0693	−	19.2406i	0.477543	−	0.703035i
$750$		0			0
$751$	2.41404	+	4.18124i	0.0880895	+	0.152575i	0.906704	−	0.421769i	$-0.138591\pi$
$751$	2.41404	+	4.18124i	0.0880895	+	0.152575i	−0.818614	+	0.574344i	$0.805257\pi$
$752$		0			0
$753$	10.9116	−	18.8994i	0.397640	−	0.688733i
$754$		0			0
$755$	−38.0522			−1.38486
$756$		0			0
$757$	9.42171			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$757$	9.42171			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$758$		0			0
$759$	−4.75804	+	8.24116i	−0.172706	+	0.299135i
$760$		0			0
$761$	22.2574	+	38.5510i	0.806831	+	1.39747i	0.915048	+	0.403345i	$0.132152\pi$
$761$	22.2574	+	38.5510i	0.806831	+	1.39747i	−0.108217	+	0.994127i	$0.534514\pi$
$762$		0			0
$763$	−39.9284	−	2.92282i	−1.44551	−	0.105813i
$764$		0			0
$765$	−1.97513	−	3.42102i	−0.0714109	−	0.123687i
$766$		0			0
$767$	−2.84484	+	4.92740i	−0.102721	+	0.177918i
$768$		0			0
$769$	37.8126			1.36356			0.681779	−	0.731558i	$-0.261207\pi$
$769$	37.8126			1.36356			0.681779	+	0.731558i	$0.261207\pi$
$770$		0			0
$771$	−6.51904			−0.234777
$772$		0			0
$773$	−12.9904	+	22.5000i	−0.467232	+	0.809270i	−0.999299	−	0.0374323i	$-0.988082\pi$
$773$	−12.9904	+	22.5000i	−0.467232	+	0.809270i	0.532067	+	0.846702i	$0.321415\pi$
$774$		0			0
$775$	17.5466	+	30.3915i	0.630291	+	1.09170i
$776$		0			0
$777$	13.4489	+	27.8039i	0.482477	+	0.997459i
$778$		0			0
$779$	12.8237	+	22.2114i	0.459458	+	0.795805i
$780$		0			0
$781$	6.96661	−	12.0665i	0.249285	−	0.431774i
$782$		0			0
$783$	6.00973			0.214770
$784$		0			0
$785$	43.6002			1.55616
$786$		0			0
$787$	16.7007	−	28.9265i	0.595317	−	1.03112i	−0.398185	−	0.917305i	$-0.630360\pi$
$787$	16.7007	−	28.9265i	0.595317	−	1.03112i	0.993502	−	0.113814i	$-0.0363068\pi$
$788$		0			0
$789$	10.8894	+	18.8610i	0.387674	+	0.671471i
$790$		0			0
$791$	−14.2179	−	29.3937i	−0.505532	−	1.04512i
$792$		0			0
$793$	3.68519	+	6.38293i	0.130865	+	0.226665i
$794$		0			0
$795$	−23.1526	+	40.1015i	−0.821139	+	1.42225i
$796$		0			0
$797$	−8.76454			−0.310456			−0.155228	−	0.987879i	$-0.549611\pi$
$797$	−8.76454			−0.310456			−0.155228	+	0.987879i	$0.549611\pi$
$798$		0			0
$799$	6.09083			0.215478
$800$		0			0
$801$	−6.32050	+	10.9474i	−0.223324	+	0.386808i
$802$		0			0
$803$	−10.5626	−	18.2950i	−0.372746	−	0.645616i
$804$		0			0
$805$	40.9358	+	2.99656i	1.44280	+	0.105615i
$806$		0			0
$807$	11.9187	+	20.6439i	0.419560	+	0.726699i
$808$		0			0
$809$	−24.3328	+	42.1456i	−0.855495	+	1.48176i	0.0206894	+	0.999786i	$0.493414\pi$
$809$	−24.3328	+	42.1456i	−0.855495	+	1.48176i	−0.876185	+	0.481975i	$0.839919\pi$
$810$		0			0
$811$	−39.0617			−1.37164			−0.685821	−	0.727771i	$-0.740557\pi$
$811$	−39.0617			−1.37164			−0.685821	+	0.727771i	$0.740557\pi$
$812$		0			0
$813$	−18.9862			−0.665875
$814$		0			0
$815$	−32.5756	+	56.4225i	−1.14107	+	1.97640i
$816$		0			0
$817$	−10.5777	−	18.3211i	−0.370067	−	0.640976i
$818$		0			0
$819$	−0.946074	+	1.39280i	−0.0330585	+	0.0486685i
$820$		0			0
$821$	−2.22560	−	3.85485i	−0.0776740	−	0.134535i	0.824572	−	0.565757i	$-0.191416\pi$
$821$	−2.22560	−	3.85485i	−0.0776740	−	0.134535i	−0.902246	+	0.431222i	$0.858083\pi$
$822$		0			0
$823$	−25.5049	+	44.1758i	−0.889045	+	1.53987i	−0.0480393	+	0.998845i	$0.515297\pi$
$823$	−25.5049	+	44.1758i	−0.889045	+	1.53987i	−0.841006	+	0.541026i	$0.818036\pi$
$824$		0			0
$825$	25.6956			0.894606
$826$		0			0
$827$	−27.0947			−0.942175			−0.471088	−	0.882086i	$-0.656138\pi$
$827$	−27.0947			−0.942175			−0.471088	+	0.882086i	$0.656138\pi$
$828$		0			0
$829$	8.79061	−	15.2258i	0.305310	−	0.528813i	−0.672020	−	0.740533i	$-0.734573\pi$
$829$	8.79061	−	15.2258i	0.305310	−	0.528813i	0.977330	+	0.211720i	$0.0679065\pi$
$830$		0			0
$831$	3.39146	+	5.87419i	0.117649	+	0.203773i
$832$		0			0
$833$	2.57990	+	6.50724i	0.0893883	+	0.225462i
$834$		0			0
$835$	−38.1638	−	66.1017i	−1.32071	−	2.28754i
$836$		0			0
$837$	1.65463	−	2.86591i	0.0571924	−	0.0990602i
$838$		0			0
$839$	8.86969			0.306216			0.153108	−	0.988209i	$-0.451072\pi$
$839$	8.86969			0.306216			0.153108	+	0.988209i	$0.451072\pi$
$840$		0			0
$841$	7.11683			0.245408
$842$		0			0
$843$	−1.60221	+	2.77511i	−0.0551831	+	0.0955799i
$844$		0			0
$845$	−24.8767	−	43.0878i	−0.855786	−	1.48226i
$846$		0			0
$847$	−7.62441	+	11.2246i	−0.261978	+	0.385682i
$848$		0			0
$849$	4.59177	+	7.95319i	0.157589	+	0.272953i
$850$		0			0
$851$	−22.9229	+	39.7036i	−0.785786	+	1.36102i
$852$		0			0
$853$	15.9303			0.545442			0.272721	−	0.962093i	$-0.412076\pi$
$853$	15.9303			0.545442			0.272721	+	0.962093i	$0.412076\pi$
$854$		0			0
$855$	33.8138			1.15641
$856$		0			0
$857$	−2.12171	+	3.67490i	−0.0724761	+	0.125532i	−0.899986	−	0.435919i	$-0.856423\pi$
$857$	−2.12171	+	3.67490i	−0.0724761	+	0.125532i	0.827510	+	0.561451i	$0.189757\pi$
$858$		0			0
$859$	−6.15647	−	10.6633i	−0.210056	−	0.363828i	0.741676	−	0.670759i	$-0.234031\pi$
$859$	−6.15647	−	10.6633i	−0.210056	−	0.363828i	−0.951732	+	0.306931i	$0.900698\pi$
$860$		0			0
$861$	−7.90615	−	0.578741i	−0.269441	−	0.0197234i
$862$		0			0
$863$	1.36213	+	2.35928i	0.0463674	+	0.0803107i	0.888278	−	0.459307i	$-0.151902\pi$
$863$	1.36213	+	2.35928i	0.0463674	+	0.0803107i	−0.841910	+	0.539618i	$0.818569\pi$
$864$		0			0
$865$	19.2505	−	33.3428i	0.654536	−	1.13369i
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	−31.0174			−1.05219
$870$		0			0
$871$	0.455408	−	0.788789i	0.0154309	−	0.0267271i
$872$		0			0
$873$	−4.62719	−	8.01454i	−0.156607	−	0.271251i
$874$		0			0
$875$	−25.5059	−	52.7302i	−0.862257	−	1.78261i
$876$		0			0
$877$	−13.7860	−	23.8781i	−0.465520	−	0.806305i	0.533704	−	0.845671i	$-0.320799\pi$
$877$	−13.7860	−	23.8781i	−0.465520	−	0.806305i	−0.999225	+	0.0393661i	$0.987466\pi$
$878$		0			0
$879$	−1.31751	+	2.28200i	−0.0444386	+	0.0769699i
$880$		0			0
$881$	4.78814			0.161317			0.0806583	−	0.996742i	$-0.474298\pi$
$881$	4.78814			0.161317			0.0806583	+	0.996742i	$0.474298\pi$
$882$		0			0
$883$	−37.5632			−1.26410			−0.632051	−	0.774927i	$-0.717786\pi$
$883$	−37.5632			−1.26410			−0.632051	+	0.774927i	$0.717786\pi$
$884$		0			0
$885$	−17.6587	+	30.5857i	−0.593590	+	1.02813i
$886$		0			0
$887$	−23.3854	−	40.5048i	−0.785206	−	1.36002i	−0.928876	−	0.370392i	$-0.879223\pi$
$887$	−23.3854	−	40.5048i	−0.785206	−	1.36002i	0.143669	−	0.989626i	$-0.454110\pi$
$888$		0			0
$889$	2.74795	+	5.68103i	0.0921633	+	0.190536i
$890$		0			0
$891$	−1.21154	−	2.09845i	−0.0405881	−	0.0703007i
$892$		0			0
$893$	−26.0684	+	45.1518i	−0.872346	+	1.51095i
$894$		0			0
$895$	45.1798			1.51019
$896$		0			0
$897$	−2.49928			−0.0834484
$898$		0			0
$899$	9.94389	−	17.2233i	0.331647	−	0.574430i
$900$		0			0
$901$	−5.86104	−	10.1516i	−0.195260	−	0.338200i
$902$		0			0
$903$	6.52142	+	0.477377i	0.217019	+	0.0158861i
$904$		0			0
$905$	29.7887	+	51.5956i	0.990211	+	1.71510i
$906$		0			0
$907$	−24.0569	+	41.6678i	−0.798797	+	1.38356i	0.121603	+	0.992579i	$0.461197\pi$
$907$	−24.0569	+	41.6678i	−0.798797	+	1.38356i	−0.920400	+	0.390978i	$0.872137\pi$
$908$		0			0
$909$	3.15008			0.104481
$910$		0			0
$911$	11.4794			0.380330			0.190165	−	0.981752i	$-0.439098\pi$
$911$	11.4794			0.380330			0.190165	+	0.981752i	$0.439098\pi$
$912$		0			0
$913$	−5.06067	+	8.76534i	−0.167484	+	0.290090i
$914$		0			0
$915$	22.8750	+	39.6206i	0.756223	+	1.30982i
$916$		0			0
$917$	−13.0513	+	19.2141i	−0.430993	+	0.634504i
$918$		0			0
$919$	−7.69350	−	13.3255i	−0.253785	−	0.439569i	0.710780	−	0.703415i	$-0.248342\pi$
$919$	−7.69350	−	13.3255i	−0.253785	−	0.439569i	−0.964565	+	0.263846i	$0.915009\pi$
$920$		0			0
$921$	−3.34537	+	5.79435i	−0.110234	+	0.190930i
$922$		0			0
$923$	3.65938			0.120450
$924$		0			0
$925$	123.794			4.07032
$926$		0			0
$927$	5.19628	−	9.00023i	0.170668	−	0.295606i
$928$		0			0
$929$	−17.4325	−	30.1941i	−0.571943	−	0.990635i	−0.996366	−	0.0851708i	$-0.972856\pi$
$929$	−17.4325	−	30.1941i	−0.571943	−	0.990635i	0.424423	−	0.905464i	$-0.360477\pi$
$930$		0			0
$931$	−59.2805	−	8.72559i	−1.94284	−	0.285970i
$932$		0			0
$933$	−0.922818	−	1.59837i	−0.0302117	−	0.0523282i
$934$		0			0
$935$	−4.78589	+	8.28941i	−0.156516	+	0.271093i
$936$		0			0
$937$	−11.1099			−0.362944			−0.181472	−	0.983396i	$-0.558086\pi$
$937$	−11.1099			−0.362944			−0.181472	+	0.983396i	$0.558086\pi$
$938$		0			0
$939$	−14.1674			−0.462336
$940$		0			0
$941$	−21.6037	+	37.4188i	−0.704262	+	1.21982i	0.262696	+	0.964879i	$0.415388\pi$
$941$	−21.6037	+	37.4188i	−0.704262	+	1.21982i	−0.966957	+	0.254938i	$0.917945\pi$
$942$		0			0
$943$	−5.88351	−	10.1905i	−0.191593	−	0.331849i
$944$		0			0
$945$	−5.87254	+	8.64551i	−0.191034	+	0.281238i
$946$		0			0
$947$	−26.0761	−	45.1651i	−0.847359	−	1.46767i	−0.883556	−	0.468325i	$-0.844858\pi$
$947$	−26.0761	−	45.1651i	−0.847359	−	1.46767i	0.0361970	−	0.999345i	$-0.488476\pi$
$948$		0			0
$949$	2.77413	−	4.80494i	0.0900522	−	0.155975i
$950$		0			0
$951$	−8.99562			−0.291703
$952$		0			0
$953$	50.5711			1.63816			0.819079	−	0.573681i	$-0.194485\pi$
$953$	50.5711			1.63816			0.819079	+	0.573681i	$0.194485\pi$
$954$		0			0
$955$	−0.722900	+	1.25210i	−0.0233925	+	0.0405170i
$956$		0			0
$957$	−7.28103	−	12.6111i	−0.235362	−	0.407659i
$958$		0			0
$959$	36.5793	+	2.67765i	1.18121	+	0.0864660i
$960$		0			0
$961$	10.0244	+	17.3627i	0.323367	+	0.560089i
$962$		0			0
$963$	−4.39565	+	7.61348i	−0.141648	+	0.245341i
$964$		0			0
$965$	70.4085			2.26653
$966$		0			0
$967$	−45.7355			−1.47075			−0.735377	−	0.677658i	$-0.762995\pi$
$967$	−45.7355			−1.47075			−0.735377	+	0.677658i	$0.762995\pi$
$968$		0			0
$969$	−4.27995	+	7.41308i	−0.137492	+	0.238143i
$970$		0			0
$971$	1.09553	+	1.89752i	0.0351574	+	0.0608944i	0.883069	−	0.469244i	$-0.155473\pi$
$971$	1.09553	+	1.89752i	0.0351574	+	0.0608944i	−0.847911	+	0.530138i	$0.822140\pi$
$972$		0			0
$973$	−6.74455	−	13.9435i	−0.216220	−	0.447008i
$974$		0			0
$975$	3.37431	+	5.84448i	0.108064	+	0.187173i
$976$		0			0
$977$	0.934159	−	1.61801i	0.0298864	−	0.0517647i	−0.850695	−	0.525659i	$-0.823819\pi$
$977$	0.934159	−	1.61801i	0.0298864	−	0.0517647i	0.880582	+	0.473894i	$0.157152\pi$
$978$		0			0
$979$	30.6302			0.978944
$980$		0			0
$981$	15.1319			0.483125
$982$		0			0
$983$	14.3398	−	24.8373i	0.457370	−	0.792188i	−0.541451	−	0.840732i	$-0.682125\pi$
$983$	14.3398	−	24.8373i	0.457370	−	0.792188i	0.998821	+	0.0485444i	$0.0154582\pi$
$984$		0			0
$985$	54.4974	+	94.3923i	1.73643	+	3.00759i
$986$		0			0
$987$	−7.01704	−	14.5068i	−0.223355	−	0.461758i
$988$		0			0
$989$	4.85304	+	8.40570i	0.154318	+	0.267286i
$990$		0			0
$991$	4.16502	−	7.21403i	0.132306	−	0.229161i	−0.792259	−	0.610185i	$-0.791095\pi$
$991$	4.16502	−	7.21403i	0.132306	−	0.229161i	0.924565	+	0.381024i	$0.124428\pi$
$992$		0			0
$993$	−6.12867			−0.194488
$994$		0			0
$995$	−36.5275			−1.15800
$996$		0			0
$997$	−3.91170	+	6.77526i	−0.123885	+	0.214575i	−0.921296	−	0.388861i	$-0.872869\pi$
$997$	−3.91170	+	6.77526i	−0.123885	+	0.214575i	0.797412	+	0.603436i	$0.206202\pi$
$998$		0			0
$999$	−5.83686	−	10.1097i	−0.184670	−	0.319858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1428.2.q.e.613.4	yes	8
7.2	even	3	inner	1428.2.q.e.205.4	✓	8
7.3	odd	6		9996.2.a.z.1.4		4
7.4	even	3		9996.2.a.bd.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1428.2.q.e.205.4	✓	8	7.2	even	3	inner
1428.2.q.e.613.4	yes	8	1.1	even	1	trivial
9996.2.a.z.1.4		4	7.3	odd	6
9996.2.a.bd.1.1		4	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1428.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.97513 + 3.42102i) q^{5} +(1.15207 + 2.38175i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.97513 + 3.42102i) q^{5} +(1.15207 + 2.38175i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.21154 + 2.09845i) q^{11} -0.636391 q^{13} -3.95025 q^{15} +(0.500000 - 0.866025i) q^{17} +(4.27995 + 7.41308i) q^{19} +(-2.63869 - 0.193156i) q^{21} +(-1.96363 - 3.40111i) q^{23} +(-5.30226 + 9.18378i) q^{25} +1.00000 q^{27} +6.00973 q^{29} +(1.65463 - 2.86591i) q^{31} +(-1.21154 - 2.09845i) q^{33} +(-5.87254 + 8.64551i) q^{35} +(-5.83686 - 10.1097i) q^{37} +(0.318196 - 0.551131i) q^{39} +2.99624 q^{41} -2.47146 q^{43} +(1.97513 - 3.42102i) q^{45} +(3.04541 + 5.27481i) q^{47} +(-4.34548 + 5.48788i) q^{49} +(0.500000 + 0.866025i) q^{51} +(5.86104 - 10.1516i) q^{53} -9.57179 q^{55} -8.55989 q^{57} +(4.47026 - 7.74272i) q^{59} +(-5.79076 - 10.0299i) q^{61} +(1.48662 - 2.18860i) q^{63} +(-1.25695 - 2.17711i) q^{65} +(-0.715609 + 1.23947i) q^{67} +3.92726 q^{69} -5.75021 q^{71} +(-4.35916 + 7.55029i) q^{73} +(-5.30226 - 9.18378i) q^{75} +(-6.39376 - 0.468032i) q^{77} +(6.40040 + 11.0858i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.17705 q^{83} +3.95025 q^{85} +(-3.00486 + 5.20458i) q^{87} +(-6.32050 - 10.9474i) q^{89} +(-0.733166 - 1.51573i) q^{91} +(1.65463 + 2.86591i) q^{93} +(-16.9069 + 29.2836i) q^{95} +9.25439 q^{97} +2.42308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} - 2 q^{5} + 3 q^{7} - 4 q^{9} - q^{11} - 20 q^{13} + 4 q^{15} + 4 q^{17} + 9 q^{19} + 5 q^{23} - 18 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - q^{33} - 18 q^{35} - 2 q^{37} + 10 q^{39} - 28 q^{43} - 2 q^{45} + 2 q^{47} + 5 q^{49} + 4 q^{51} + 15 q^{53} - 60 q^{55} - 18 q^{57} + 37 q^{59} - 19 q^{61} - 3 q^{63} + 21 q^{65} - 2 q^{67} - 10 q^{69} - 22 q^{71} + 9 q^{73} - 18 q^{75} + 13 q^{77} + 9 q^{79} - 4 q^{81} + 16 q^{83} - 4 q^{85} - 5 q^{87} - 22 q^{89} + 7 q^{91} + 24 q^{93} - 33 q^{95} + 26 q^{97} + 2 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^5 + 3 * q^7 - 4 * q^9 - q^11 - 20 * q^13 + 4 * q^15 + 4 * q^17 + 9 * q^19 + 5 * q^23 - 18 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - q^33 - 18 * q^35 - 2 * q^37 + 10 * q^39 - 28 * q^43 - 2 * q^45 + 2 * q^47 + 5 * q^49 + 4 * q^51 + 15 * q^53 - 60 * q^55 - 18 * q^57 + 37 * q^59 - 19 * q^61 - 3 * q^63 + 21 * q^65 - 2 * q^67 - 10 * q^69 - 22 * q^71 + 9 * q^73 - 18 * q^75 + 13 * q^77 + 9 * q^79 - 4 * q^81 + 16 * q^83 - 4 * q^85 - 5 * q^87 - 22 * q^89 + 7 * q^91 + 24 * q^93 - 33 * q^95 + 26 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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