LMFDB - Embedded newform 1264.2.n.i.735.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1264,2,Mod(735,1264)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1264, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1264.735");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1264 = 2^{4} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1264.n (of order $6$, 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:	$10.0930908155$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			735.13
Character	$\chi$	$=$	1264.735
Dual form			1264.2.n.i.767.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30739 - 2.26447i) q^{3} +(0.0495497 + 0.0858226i) q^{5} +(-0.841498 - 1.45752i) q^{7} +(-1.91856 - 3.32304i) q^{9} +O(q^{10})$	\(q+(1.30739 - 2.26447i) q^{3} +(0.0495497 + 0.0858226i) q^{5} +(-0.841498 - 1.45752i) q^{7} +(-1.91856 - 3.32304i) q^{9} +(-2.75282 + 1.58934i) q^{11} +(2.72282 - 4.71606i) q^{13} +0.259124 q^{15} -3.09222i q^{17} +(-1.45212 + 0.838384i) q^{19} -4.40068 q^{21} +(-5.97678 + 3.45070i) q^{23} +(2.49509 - 4.32162i) q^{25} -2.18888 q^{27} +(-1.50959 + 0.871560i) q^{29} +(-1.55839 + 0.899739i) q^{31} +8.31159i q^{33} +(0.0833919 - 0.144439i) q^{35} +(-3.60370 - 2.08059i) q^{37} +(-7.11959 - 12.3315i) q^{39} -3.90196i q^{41} +(1.98975 - 3.44636i) q^{43} +(0.190128 - 0.329311i) q^{45} +(-0.0833919 - 0.144439i) q^{47} +(2.08376 - 3.60918i) q^{49} +(-7.00224 - 4.04275i) q^{51} +(-0.426526 + 0.246255i) q^{53} +(-0.272803 - 0.157503i) q^{55} +4.38439i q^{57} +(-4.28834 + 7.42762i) q^{59} +8.99653i q^{61} +(-3.22892 + 5.59266i) q^{63} +0.539659 q^{65} -15.2758i q^{67} +18.0457i q^{69} +3.07103 q^{71} +(0.753273 + 1.30471i) q^{73} +(-6.52413 - 11.3001i) q^{75} +(4.63299 + 2.67486i) q^{77} +(6.15798 + 6.40932i) q^{79} +(2.89394 - 5.01246i) q^{81} +(5.11661 - 2.95408i) q^{83} +(0.265382 - 0.153218i) q^{85} +4.55789i q^{87} +1.59885 q^{89} -9.16498 q^{91} +4.70526i q^{93} +(-0.143905 - 0.0830833i) q^{95} +15.6098 q^{97} +(10.5629 + 6.09849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 20 q^{9}+O(q^{10}) $ 28 * q - 20 * q^9	$ 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) $ 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1264\mathbb{Z}\right)^\times$.

$n$	$159$	$161$	$949$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.30739	−	2.26447i	0.754824	−	1.30739i	−0.190637	−	0.981661i	$-0.561055\pi$
$3$	1.30739	−	2.26447i	0.754824	−	1.30739i	0.945462	−	0.325733i	$-0.105611\pi$
$4$		0			0
$5$	0.0495497	+	0.0858226i	0.0221593	+	0.0383810i	0.876892	−	0.480687i	$-0.159613\pi$
$5$	0.0495497	+	0.0858226i	0.0221593	+	0.0383810i	−0.854733	+	0.519068i	$0.826279\pi$
$6$		0			0
$7$	−0.841498	−	1.45752i	−0.318056	−	0.550890i	0.662026	−	0.749481i	$-0.269697\pi$
$7$	−0.841498	−	1.45752i	−0.318056	−	0.550890i	−0.980082	+	0.198591i	$0.936363\pi$
$8$		0			0
$9$	−1.91856	−	3.32304i	−0.639519	−	1.10768i
$10$		0			0
$11$	−2.75282	+	1.58934i	−0.830007	+	0.479205i	−0.853855	−	0.520511i	$-0.825742\pi$
$11$	−2.75282	+	1.58934i	−0.830007	+	0.479205i	0.0238482	+	0.999716i	$0.492408\pi$
$12$		0			0
$13$	2.72282	−	4.71606i	0.755174	−	1.30800i	−0.190115	−	0.981762i	$-0.560886\pi$
$13$	2.72282	−	4.71606i	0.755174	−	1.30800i	0.945288	−	0.326237i	$-0.105781\pi$
$14$		0			0
$15$	0.259124			0.0669055
$16$		0			0
$17$		−	3.09222i		−	0.749973i	−0.927030	−	0.374986i	$-0.877647\pi$
$17$		−	3.09222i		−	0.749973i	0.927030	−	0.374986i	$-0.122353\pi$
$18$		0			0
$19$	−1.45212	+	0.838384i	−0.333140	+	0.192338i	−0.657234	−	0.753686i	$-0.728274\pi$
$19$	−1.45212	+	0.838384i	−0.333140	+	0.192338i	0.324094	+	0.946025i	$0.394940\pi$
$20$		0			0
$21$	−4.40068			−0.960306
$22$		0			0
$23$	−5.97678	+	3.45070i	−1.24625	+	0.719520i	−0.970359	−	0.241670i	$-0.922305\pi$
$23$	−5.97678	+	3.45070i	−1.24625	+	0.719520i	−0.275887	+	0.961190i	$0.588972\pi$
$24$		0			0
$25$	2.49509	−	4.32162i	0.499018	−	0.864324i
$26$		0			0
$27$	−2.18888			−0.421250
$28$		0			0
$29$	−1.50959	+	0.871560i	−0.280323	+	0.161845i	−0.633570	−	0.773686i	$-0.718411\pi$
$29$	−1.50959	+	0.871560i	−0.280323	+	0.161845i	0.353247	+	0.935530i	$0.385078\pi$
$30$		0			0
$31$	−1.55839	+	0.899739i	−0.279896	+	0.161598i	−0.633376	−	0.773844i	$-0.718331\pi$
$31$	−1.55839	+	0.899739i	−0.279896	+	0.161598i	0.353480	+	0.935442i	$0.384998\pi$
$32$		0			0
$33$			8.31159i			1.44686i
$34$		0			0
$35$	0.0833919	−	0.144439i	0.0140958	−	0.0244146i
$36$		0			0
$37$	−3.60370	−	2.08059i	−0.592444	−	0.342048i	0.173619	−	0.984813i	$-0.444454\pi$
$37$	−3.60370	−	2.08059i	−0.592444	−	0.342048i	−0.766063	+	0.642765i	$0.777787\pi$
$38$		0			0
$39$	−7.11959	−	12.3315i	−1.14005	−	1.97462i
$40$		0			0
$41$		−	3.90196i		−	0.609383i	−0.952451	−	0.304692i	$-0.901447\pi$
$41$		−	3.90196i		−	0.609383i	0.952451	−	0.304692i	$-0.0985534\pi$
$42$		0			0
$43$	1.98975	−	3.44636i	0.303435	−	0.525564i	−0.673477	−	0.739208i	$-0.735200\pi$
$43$	1.98975	−	3.44636i	0.303435	−	0.525564i	0.976912	+	0.213644i	$0.0685332\pi$
$44$		0			0
$45$	0.190128	−	0.329311i	0.0283426	−	0.0490908i
$46$		0			0
$47$	−0.0833919	−	0.144439i	−0.0121640	−	0.0210686i	0.859879	−	0.510497i	$-0.170539\pi$
$47$	−0.0833919	−	0.144439i	−0.0121640	−	0.0210686i	−0.872043	+	0.489429i	$0.837205\pi$
$48$		0			0
$49$	2.08376	−	3.60918i	0.297680	−	0.515598i
$50$		0			0
$51$	−7.00224	−	4.04275i	−0.980510	−	0.566098i
$52$		0			0
$53$	−0.426526	+	0.246255i	−0.0585878	+	0.0338257i	−0.529008	−	0.848617i	$-0.677436\pi$
$53$	−0.426526	+	0.246255i	−0.0585878	+	0.0338257i	0.470420	+	0.882443i	$0.344102\pi$
$54$		0			0
$55$	−0.272803	−	0.157503i	−0.0367847	−	0.0212377i
$56$		0			0
$57$			4.38439i			0.580727i
$58$		0			0
$59$	−4.28834	+	7.42762i	−0.558294	+	0.966993i	0.439345	+	0.898318i	$0.355210\pi$
$59$	−4.28834	+	7.42762i	−0.558294	+	0.966993i	−0.997639	+	0.0686750i	$0.978123\pi$
$60$		0			0
$61$			8.99653i			1.15189i	0.817489	+	0.575944i	$0.195365\pi$
$61$			8.99653i			1.15189i	−0.817489	+	0.575944i	$0.804635\pi$
$62$		0			0
$63$	−3.22892	+	5.59266i	−0.406806	+	0.704609i
$64$		0			0
$65$	0.539659			0.0669365
$66$		0			0
$67$		−	15.2758i		−	1.86623i	−0.359576	−	0.933116i	$-0.617079\pi$
$67$		−	15.2758i		−	1.86623i	0.359576	−	0.933116i	$-0.382921\pi$
$68$		0			0
$69$			18.0457i			2.17245i
$70$		0			0
$71$	3.07103			0.364464			0.182232	−	0.983256i	$-0.441668\pi$
$71$	3.07103			0.364464			0.182232	+	0.983256i	$0.441668\pi$
$72$		0			0
$73$	0.753273	+	1.30471i	0.0881639	+	0.152704i	0.906735	−	0.421701i	$-0.138567\pi$
$73$	0.753273	+	1.30471i	0.0881639	+	0.152704i	−0.818571	+	0.574405i	$0.805233\pi$
$74$		0			0
$75$	−6.52413	−	11.3001i	−0.753342	−	1.30483i
$76$		0			0
$77$	4.63299	+	2.67486i	0.527978	+	0.304828i
$78$		0			0
$79$	6.15798	+	6.40932i	0.692826	+	0.721104i
$79$	6.15798	+	6.40932i	0.692826	+	0.721104i
$80$		0			0
$81$	2.89394	−	5.01246i	0.321549	−	0.556940i
$82$		0			0
$83$	5.11661	−	2.95408i	0.561621	−	0.324252i	−0.192175	−	0.981361i	$-0.561554\pi$
$83$	5.11661	−	2.95408i	0.561621	−	0.324252i	0.753796	+	0.657109i	$0.228221\pi$
$84$		0			0
$85$	0.265382	−	0.153218i	0.0287847	−	0.0166189i
$86$		0			0
$87$			4.55789i			0.488657i
$88$		0			0
$89$	1.59885			0.169477			0.0847386	−	0.996403i	$-0.472994\pi$
$89$	1.59885			0.169477			0.0847386	+	0.996403i	$0.472994\pi$
$90$		0			0
$91$	−9.16498			−0.960751
$92$		0			0
$93$			4.70526i			0.487912i
$94$		0			0
$95$	−0.143905	−	0.0830833i	−0.0147643	−	0.00852417i
$96$		0			0
$97$	15.6098			1.58493			0.792467	−	0.609915i	$-0.208796\pi$
$97$	15.6098			1.58493			0.792467	+	0.609915i	$0.208796\pi$
$98$		0			0
$99$	10.5629	+	6.09849i	1.06161	+	0.612921i
$100$		0			0
$101$	−18.6196			−1.85272			−0.926362	−	0.376635i	$-0.877081\pi$
$101$	−18.6196			−1.85272			−0.926362	+	0.376635i	$0.877081\pi$
$102$		0			0
$103$	−4.43582	+	7.68306i	−0.437074	+	0.757034i	−0.997462	−	0.0711956i	$-0.977319\pi$
$103$	−4.43582	+	7.68306i	−0.437074	+	0.757034i	0.560388	+	0.828230i	$0.310652\pi$
$104$		0			0
$105$	−0.218052	−	0.377677i	−0.0212797	−	0.0368575i
$106$		0			0
$107$	2.03047	−	3.51688i	0.196293	−	0.339990i	−0.751031	−	0.660267i	$-0.770443\pi$
$107$	2.03047	−	3.51688i	0.196293	−	0.339990i	0.947324	+	0.320278i	$0.103776\pi$
$108$		0			0
$109$	3.26246	+	1.88358i	0.312487	+	0.180415i	0.648039	−	0.761607i	$-0.275589\pi$
$109$	3.26246	+	1.88358i	0.312487	+	0.180415i	−0.335552	+	0.942022i	$0.608923\pi$
$110$		0			0
$111$	−9.42290	+	5.44031i	−0.894382	+	0.516372i
$112$		0			0
$113$	11.7523	+	6.78518i	1.10556	+	0.638296i	0.937676	−	0.347510i	$-0.112973\pi$
$113$	11.7523	+	6.78518i	1.10556	+	0.638296i	0.167885	+	0.985807i	$0.446306\pi$
$114$		0			0
$115$	−0.592296	−	0.341962i	−0.0552319	−	0.0318881i
$116$		0			0
$117$	−20.8955			−1.93179
$118$		0			0
$119$	−4.50696	+	2.60209i	−0.413152	+	0.238533i
$120$		0			0
$121$	−0.447983	+	0.775930i	−0.0407258	+	0.0705391i
$122$		0			0
$123$	−8.83588	−	5.10140i	−0.796704	−	0.459977i
$124$		0			0
$125$	0.990021			0.0885501
$126$		0			0
$127$	0.920895	+	1.59504i	0.0817162	+	0.141537i	0.903987	−	0.427559i	$-0.140627\pi$
$127$	0.920895	+	1.59504i	0.0817162	+	0.141537i	−0.822271	+	0.569096i	$0.807293\pi$
$128$		0			0
$129$	−5.20279	−	9.01149i	−0.458080	−	0.793417i
$130$		0			0
$131$		−	8.45401i		−	0.738630i	−0.929304	−	0.369315i	$-0.879592\pi$
$131$		−	8.45401i		−	0.738630i	0.929304	−	0.369315i	$-0.120408\pi$
$132$		0			0
$133$	2.44392	+	1.41100i	0.211914	+	0.122349i
$134$		0			0
$135$	−0.108458	−	0.187855i	−0.00933461	−	0.0161680i
$136$		0			0
$137$		−	2.36117i		−	0.201728i	−0.994900	−	0.100864i	$-0.967839\pi$
$137$		−	2.36117i		−	0.201728i	0.994900	−	0.100864i	$-0.0321607\pi$
$138$		0			0
$139$	−6.44413	−	11.1616i	−0.546584	−	0.946711i	−0.998505	−	0.0546536i	$-0.982595\pi$
$139$	−6.44413	−	11.1616i	−0.546584	−	0.946711i	0.451921	−	0.892058i	$-0.350739\pi$
$140$		0			0
$141$	−0.436104			−0.0367266
$142$		0			0
$143$			17.3099i			1.44753i
$144$		0			0
$145$	−0.149599	−	0.0863711i	−0.0124235	−	0.00717273i
$146$		0			0
$147$	−5.44860	−	9.43725i	−0.449393	−	0.778371i
$148$		0			0
$149$	13.1514	−	7.59298i	1.07741	−	0.622041i	0.147211	−	0.989105i	$-0.452970\pi$
$149$	13.1514	−	7.59298i	1.07741	−	0.622041i	0.930196	+	0.367064i	$0.119637\pi$
$150$		0			0
$151$	8.36474	−	4.82938i	0.680712	−	0.393010i	−0.119411	−	0.992845i	$-0.538101\pi$
$151$	8.36474	−	4.82938i	0.680712	−	0.393010i	0.800123	+	0.599835i	$0.204767\pi$
$152$		0			0
$153$	−10.2756	+	5.93260i	−0.830730	+	0.479622i
$154$		0			0
$155$	−0.154436	−	0.0891636i	−0.0124046	−	0.00716179i
$156$		0			0
$157$			18.5476i			1.48026i	0.672466	+	0.740128i	$0.265235\pi$
$157$			18.5476i			1.48026i	−0.672466	+	0.740128i	$0.734765\pi$
$158$		0			0
$159$			1.28781i			0.102130i
$160$		0			0
$161$	10.0589	+	5.80751i	0.792752	+	0.457696i
$162$		0			0
$163$	7.34941	−	4.24318i	0.575650	−	0.332352i	−0.183753	−	0.982972i	$-0.558825\pi$
$163$	7.34941	−	4.24318i	0.575650	−	0.332352i	0.759403	+	0.650621i	$0.225491\pi$
$164$		0			0
$165$	−0.713322	+	0.411837i	−0.0555320	+	0.0320614i
$166$		0			0
$167$	13.6389	−	7.87445i	1.05541	−	0.609343i	0.131253	−	0.991349i	$-0.458100\pi$
$167$	13.6389	−	7.87445i	1.05541	−	0.609343i	0.924160	+	0.382006i	$0.124767\pi$
$168$		0			0
$169$	−8.32746	−	14.4236i	−0.640574	−	1.10951i
$170$		0			0
$171$	5.57196	+	3.21698i	0.426099	+	0.246008i
$172$		0			0
$173$		−	19.1178i		−	1.45350i	−0.686903	−	0.726749i	$-0.741030\pi$
$173$		−	19.1178i		−	1.45350i	0.686903	−	0.726749i	$-0.258970\pi$
$174$		0			0
$175$	−8.39845			−0.634863
$176$		0			0
$177$	11.2131	+	19.4216i	0.842827	+	1.45982i
$178$		0			0
$179$			22.0965i			1.65157i	0.563987	+	0.825783i	$0.309267\pi$
$179$			22.0965i			1.65157i	−0.563987	+	0.825783i	$0.690733\pi$
$180$		0			0
$181$	−7.99597	−	13.8494i	−0.594335	−	1.02942i	−0.993640	−	0.112601i	$-0.964082\pi$
$181$	−7.99597	−	13.8494i	−0.594335	−	1.02942i	0.399305	−	0.916818i	$-0.369252\pi$
$182$		0			0
$183$	20.3724	+	11.7620i	1.50597	+	0.869472i
$184$		0			0
$185$		−	0.412371i		−	0.0303181i
$186$		0			0
$187$	4.91459	+	8.51232i	0.359390	+	0.622482i
$188$		0			0
$189$	1.84194	+	3.19033i	0.133981	+	0.232062i
$190$		0			0
$191$	−9.16785			−0.663362			−0.331681	−	0.943392i	$-0.607616\pi$
$191$	−9.16785			−0.663362			−0.331681	+	0.943392i	$0.607616\pi$
$192$		0			0
$193$	8.86877	+	5.12039i	0.638388	+	0.368574i	0.783993	−	0.620769i	$-0.213180\pi$
$193$	8.86877	+	5.12039i	0.638388	+	0.368574i	−0.145605	+	0.989343i	$0.546513\pi$
$194$		0			0
$195$	0.705547	−	1.22204i	0.0505253	−	0.0875123i
$196$		0			0
$197$	6.43248	−	3.71379i	0.458295	−	0.264597i	−0.253032	−	0.967458i	$-0.581428\pi$
$197$	6.43248	−	3.71379i	0.458295	−	0.264597i	0.711327	+	0.702861i	$0.248094\pi$
$198$		0			0
$199$	10.4831			0.743128			0.371564	−	0.928407i	$-0.378822\pi$
$199$	10.4831			0.743128			0.371564	+	0.928407i	$0.378822\pi$
$200$		0			0
$201$	−34.5916	−	19.9714i	−2.43990	−	1.40868i
$202$		0			0
$203$	2.54063	+	1.46683i	0.178317	+	0.102951i
$204$		0			0
$205$	0.334876	−	0.193341i	0.0233888	−	0.0135035i
$206$		0			0
$207$	22.9336	+	13.2407i	1.59400	+	0.920294i
$208$		0			0
$209$	2.66496	−	4.61584i	0.184339	−	0.319284i
$210$		0			0
$211$	−3.72464	−	6.45127i	−0.256415	−	0.444123i	0.708864	−	0.705345i	$-0.249208\pi$
$211$	−3.72464	−	6.45127i	−0.256415	−	0.444123i	−0.965279	+	0.261222i	$0.915875\pi$
$212$		0			0
$213$	4.01505	−	6.95426i	0.275106	−	0.476498i
$214$		0			0
$215$	0.394367			0.0268956
$216$		0			0
$217$	2.62277	+	1.51426i	0.178045	+	0.102794i
$218$		0			0
$219$	3.93930			0.266193
$220$		0			0
$221$	−14.5831	−	8.41954i	−0.980963	−	0.566360i
$222$		0			0
$223$		−	4.85505i		−	0.325118i	−0.986699	−	0.162559i	$-0.948025\pi$
$223$		−	4.85505i		−	0.325118i	0.986699	−	0.162559i	$-0.0519748\pi$
$224$		0			0
$225$	−19.1479			−1.27653
$226$		0			0
$227$	14.8764			0.987380			0.493690	−	0.869638i	$-0.335648\pi$
$227$	14.8764			0.987380			0.493690	+	0.869638i	$0.335648\pi$
$228$		0			0
$229$		−	15.4981i		−	1.02414i	−0.858943	−	0.512072i	$-0.828878\pi$
$229$		−	15.4981i		−	1.02414i	0.858943	−	0.512072i	$-0.171122\pi$
$230$		0			0
$231$	12.1143	−	6.99418i	0.797061	−	0.460183i
$232$		0			0
$233$	14.7341	−	8.50674i	0.965263	−	0.557295i	0.0674741	−	0.997721i	$-0.478506\pi$
$233$	14.7341	−	8.50674i	0.965263	−	0.557295i	0.897789	+	0.440426i	$0.145173\pi$
$234$		0			0
$235$	0.00826409	−	0.0143138i	0.000539090	−	0.000933731i
$236$		0			0
$237$	22.5646	−	5.56507i	1.46573	−	0.361490i
$238$		0			0
$239$	6.64858	+	3.83856i	0.430061	+	0.248296i	0.699373	−	0.714757i	$-0.253463\pi$
$239$	6.64858	+	3.83856i	0.430061	+	0.248296i	−0.269312	+	0.963053i	$0.586796\pi$
$240$		0			0
$241$	−1.24274	−	2.15250i	−0.0800522	−	0.138654i	0.823220	−	0.567723i	$-0.192175\pi$
$241$	−1.24274	−	2.15250i	−0.0800522	−	0.138654i	−0.903272	+	0.429068i	$0.858842\pi$
$242$		0			0
$243$	−10.8504	−	18.7934i	−0.696052	−	1.20560i
$244$		0			0
$245$	0.412999			0.0263856
$246$		0			0
$247$			9.13106i			0.580995i
$248$		0			0
$249$		−	15.4486i		−	0.979013i
$250$		0			0
$251$	14.5822			0.920418			0.460209	−	0.887811i	$-0.347774\pi$
$251$	14.5822			0.920418			0.460209	+	0.887811i	$0.347774\pi$
$252$		0			0
$253$	10.9687	−	18.9983i	0.689595	−	1.19441i
$254$		0			0
$255$		−	0.801267i		−	0.0501773i
$256$		0			0
$257$	2.16250	−	3.74555i	0.134893	−	0.233641i	−0.790664	−	0.612251i	$-0.790264\pi$
$257$	2.16250	−	3.74555i	0.134893	−	0.233641i	0.925557	+	0.378609i	$0.123598\pi$
$258$		0			0
$259$			7.00326i			0.435162i
$260$		0			0
$261$	5.79246	+	3.34428i	0.358544	+	0.207006i
$262$		0			0
$263$	−6.37736	+	3.68197i	−0.393245	+	0.227040i	−0.683565	−	0.729890i	$-0.739571\pi$
$263$	−6.37736	+	3.68197i	−0.393245	+	0.227040i	0.290320	+	0.956930i	$0.406238\pi$
$264$		0			0
$265$	−0.0422684	−	0.0244037i	−0.00259653	−	0.00149911i
$266$		0			0
$267$	2.09032	−	3.62054i	0.127926	−	0.221574i
$268$		0			0
$269$	−6.36674	−	11.0275i	−0.388187	−	0.672359i	0.604019	−	0.796970i	$-0.293565\pi$
$269$	−6.36674	−	11.0275i	−0.388187	−	0.672359i	−0.992206	+	0.124611i	$0.960232\pi$
$270$		0			0
$271$	4.54673	−	7.87517i	0.276194	−	0.478382i	−0.694241	−	0.719742i	$-0.744260\pi$
$271$	4.54673	−	7.87517i	0.276194	−	0.478382i	0.970436	+	0.241360i	$0.0775934\pi$
$272$		0			0
$273$	−11.9822	+	20.7538i	−0.725198	+	1.25608i
$274$		0			0
$275$			15.8622i			0.956527i
$276$		0			0
$277$	−1.70043	−	2.94523i	−0.102169	−	0.176962i	0.810409	−	0.585865i	$-0.199245\pi$
$277$	−1.70043	−	2.94523i	−0.102169	−	0.176962i	−0.912578	+	0.408903i	$0.865912\pi$
$278$		0			0
$279$	5.97974	+	3.45240i	0.357998	+	0.206690i
$280$		0			0
$281$	−14.1493	+	24.5073i	−0.844077	+	1.46198i	0.0423438	+	0.999103i	$0.486518\pi$
$281$	−14.1493	+	24.5073i	−0.844077	+	1.46198i	−0.886421	+	0.462881i	$0.846816\pi$
$282$		0			0
$283$			9.43354i			0.560766i	0.959888	+	0.280383i	$0.0904614\pi$
$283$			9.43354i			0.560766i	−0.959888	+	0.280383i	$0.909539\pi$
$284$		0			0
$285$	−0.376280	+	0.217245i	−0.0222889	+	0.0128685i
$286$		0			0
$287$	−5.68717	+	3.28349i	−0.335703	+	0.193818i
$288$		0			0
$289$	7.43820			0.437541
$290$		0			0
$291$	20.4081	−	35.3479i	1.19635	−	2.07213i
$292$		0			0
$293$	−3.75574	+	2.16838i	−0.219413	+	0.126678i	−0.605678	−	0.795710i	$-0.707098\pi$
$293$	−3.75574	+	2.16838i	−0.219413	+	0.126678i	0.386266	+	0.922388i	$0.373765\pi$
$294$		0			0
$295$	−0.849943			−0.0494856
$296$		0			0
$297$	6.02560	−	3.47888i	0.349641	−	0.201865i
$298$		0			0
$299$			37.5825i			2.17345i
$300$		0			0
$301$	−6.69750			−0.386037
$302$		0			0
$303$	−24.3432	+	42.1637i	−1.39848	+	2.42224i
$304$		0			0
$305$	−0.772105	+	0.445775i	−0.0442106	+	0.0255250i
$306$		0			0
$307$	−10.9448	−	18.9569i	−0.624652	−	1.08193i	−0.988608	−	0.150513i	$-0.951907\pi$
$307$	−10.9448	−	18.9569i	−0.624652	−	1.08193i	0.363956	−	0.931416i	$-0.381426\pi$
$308$		0			0
$309$	11.5987	+	20.0896i	0.659828	+	1.14286i
$310$		0			0
$311$	6.60603	+	11.4420i	0.374594	+	0.648816i	0.990266	−	0.139187i	$-0.0444488\pi$
$311$	6.60603	+	11.4420i	0.374594	+	0.648816i	−0.615672	+	0.788002i	$0.711115\pi$
$312$		0			0
$313$	−7.74976	+	13.4230i	−0.438042	+	0.758711i	−0.997538	−	0.0701216i	$-0.977661\pi$
$313$	−7.74976	+	13.4230i	−0.438042	+	0.758711i	0.559496	+	0.828833i	$0.310995\pi$
$314$		0			0
$315$	−0.639969			−0.0360582
$316$		0			0
$317$	35.3426			1.98504			0.992520	−	0.122083i	$-0.0389574\pi$
$317$	35.3426			1.98504			0.992520	+	0.122083i	$0.0389574\pi$
$318$		0			0
$319$	2.77041	−	4.79850i	0.155113	−	0.268664i
$320$		0			0
$321$	−5.30925	−	9.19590i	−0.296334	−	0.513265i
$322$		0			0
$323$	2.59246	+	4.49028i	0.144249	+	0.249846i
$324$		0			0
$325$	−13.5873	−	23.5340i	−0.753690	−	1.30543i
$326$		0			0
$327$	8.53064	−	4.92517i	0.471746	−	0.272363i
$328$		0			0
$329$	−0.140348	+	0.243090i	−0.00773765	+	0.0134020i
$330$		0			0
$331$	23.6713			1.30109			0.650545	−	0.759468i	$-0.274540\pi$
$331$	23.6713			1.30109			0.650545	+	0.759468i	$0.274540\pi$
$332$		0			0
$333$			15.9670i			0.874984i
$334$		0			0
$335$	1.31101	−	0.756909i	0.0716279	−	0.0413544i
$336$		0			0
$337$	18.6479			1.01581			0.507907	−	0.861412i	$-0.330419\pi$
$337$	18.6479			1.01581			0.507907	+	0.861412i	$0.330419\pi$
$338$		0			0
$339$	30.7297	−	17.7418i	1.66901	−	0.963603i
$340$		0			0
$341$	2.85999	−	4.95364i	0.154877	−	0.268255i
$342$		0			0
$343$	−18.7949			−1.01483
$344$		0			0
$345$	−1.54873	+	0.894158i	−0.0833807	+	0.0481399i
$346$		0			0
$347$	2.96695	−	1.71297i	0.159274	−	0.0919569i	−0.418244	−	0.908334i	$-0.637354\pi$
$347$	2.96695	−	1.71297i	0.159274	−	0.0919569i	0.577518	+	0.816378i	$0.304021\pi$
$348$		0			0
$349$			21.2930i			1.13979i	0.821718	+	0.569895i	$0.193016\pi$
$349$			21.2930i			1.13979i	−0.821718	+	0.569895i	$0.806984\pi$
$350$		0			0
$351$	−5.95992	+	10.3229i	−0.318117	+	0.550995i
$352$		0			0
$353$	1.83857	+	1.06150i	0.0978572	+	0.0564979i	0.548130	−	0.836393i	$-0.315340\pi$
$353$	1.83857	+	1.06150i	0.0978572	+	0.0564979i	−0.450273	+	0.892891i	$0.648673\pi$
$354$		0			0
$355$	0.152169	+	0.263564i	0.00807627	+	0.0139885i
$356$		0			0
$357$			13.6078i			0.720203i
$358$		0			0
$359$	0.144936	−	0.251037i	0.00764946	−	0.0132492i	−0.862175	−	0.506610i	$-0.830898\pi$
$359$	0.144936	−	0.251037i	0.00764946	−	0.0132492i	0.869825	+	0.493361i	$0.164232\pi$
$360$		0			0
$361$	−8.09423	+	14.0196i	−0.426012	+	0.737874i
$362$		0			0
$363$	1.17138	+	2.02889i	0.0614816	+	0.106489i
$364$		0			0
$365$	−0.0746489	+	0.129296i	−0.00390730	+	0.00676765i
$366$		0			0
$367$	−16.2699	−	9.39345i	−0.849283	−	0.490334i	0.0111257	−	0.999938i	$-0.496458\pi$
$367$	−16.2699	−	9.39345i	−0.849283	−	0.490334i	−0.860409	+	0.509604i	$0.829792\pi$
$368$		0			0
$369$	−12.9664	+	7.48613i	−0.675002	+	0.389712i
$370$		0			0
$371$	0.717841	+	0.414446i	0.0372684	+	0.0215169i
$372$		0			0
$373$			26.8947i			1.39256i	0.717772	+	0.696279i	$0.245162\pi$
$373$			26.8947i			1.39256i	−0.717772	+	0.696279i	$0.754838\pi$
$374$		0			0
$375$	1.29435	−	2.24187i	0.0668398	−	0.115770i
$376$		0			0
$377$			9.49239i			0.488883i
$378$		0			0
$379$	15.8676	−	27.4835i	0.815064	−	1.41173i	−0.0942185	−	0.995552i	$-0.530035\pi$
$379$	15.8676	−	27.4835i	0.815064	−	1.41173i	0.909282	−	0.416180i	$-0.136631\pi$
$380$		0			0
$381$	4.81589			0.246726
$382$		0			0
$383$			27.8864i			1.42493i	0.701708	+	0.712465i	$0.252421\pi$
$383$			27.8864i			1.42493i	−0.701708	+	0.712465i	$0.747579\pi$
$384$		0			0
$385$			0.530153i			0.0270191i
$386$		0			0
$387$	−15.2698			−0.776209
$388$		0			0
$389$	17.0473	+	29.5268i	0.864334	+	1.49707i	0.867707	+	0.497076i	$0.165593\pi$
$389$	17.0473	+	29.5268i	0.864334	+	1.49707i	−0.00337303	+	0.999994i	$0.501074\pi$
$390$		0			0
$391$	10.6703	+	18.4815i	0.539621	+	0.934650i
$392$		0			0
$393$	−19.1439	−	11.0527i	−0.965680	−	0.557536i
$394$		0			0
$395$	−0.244938	+	0.846073i	−0.0123242	+	0.0425706i
$396$		0			0
$397$	−1.68647	+	2.92105i	−0.0846413	+	0.146603i	−0.905238	−	0.424904i	$-0.860308\pi$
$397$	−1.68647	+	2.92105i	−0.0846413	+	0.146603i	0.820597	+	0.571507i	$0.193641\pi$
$398$		0			0
$399$	6.39032	−	3.68945i	0.319916	−	0.184704i
$400$		0			0
$401$	−23.2621	+	13.4304i	−1.16165	+	0.670682i	−0.951700	−	0.307029i	$-0.900665\pi$
$401$	−23.2621	+	13.4304i	−1.16165	+	0.670682i	−0.209955	+	0.977711i	$0.567332\pi$
$402$		0			0
$403$			9.79930i			0.488138i
$404$		0			0
$405$	0.573576			0.0285012
$406$		0			0
$407$	13.2271			0.655643
$408$		0			0
$409$			15.8420i			0.783339i	0.920106	+	0.391669i	$0.128102\pi$
$409$			15.8420i			0.783339i	−0.920106	+	0.391669i	$0.871898\pi$
$410$		0			0
$411$	−5.34680	−	3.08698i	−0.263738	−	0.152269i
$412$		0			0
$413$	14.4345			0.710275
$414$		0			0
$415$	0.507053	+	0.292747i	0.0248902	+	0.0143704i
$416$		0			0
$417$	−33.7001			−1.65030
$418$		0			0
$419$	−5.93906	+	10.2867i	−0.290142	+	0.502540i	−0.973843	−	0.227222i	$-0.927036\pi$
$419$	−5.93906	+	10.2867i	−0.290142	+	0.502540i	0.683701	+	0.729762i	$0.260369\pi$
$420$		0			0
$421$	−16.8653	−	29.2116i	−0.821965	−	1.42369i	−0.904217	−	0.427074i	$-0.859544\pi$
$421$	−16.8653	−	29.2116i	−0.821965	−	1.42369i	0.0822517	−	0.996612i	$-0.473789\pi$
$422$		0			0
$423$	−0.319984	+	0.554229i	−0.0155582	+	0.0269475i
$424$		0			0
$425$	−13.3634	−	7.71536i	−0.648220	−	0.374250i
$426$		0			0
$427$	13.1126	−	7.57056i	0.634563	−	0.366365i
$428$		0			0
$429$	39.1979	+	22.6309i	1.89249	+	1.09263i
$430$		0			0
$431$	22.3225	+	12.8879i	1.07524	+	0.620789i	0.929608	−	0.368550i	$-0.120146\pi$
$431$	22.3225	+	12.8879i	1.07524	+	0.620789i	0.145630	+	0.989339i	$0.453479\pi$
$432$		0			0
$433$	19.7182			0.947597			0.473798	−	0.880633i	$-0.342883\pi$
$433$	19.7182			0.947597			0.473798	+	0.880633i	$0.342883\pi$
$434$		0			0
$435$	−0.391170	+	0.225842i	−0.0187552	+	0.0108283i
$436$		0			0
$437$	5.78602	−	10.0217i	0.276783	−	0.479402i
$438$		0			0
$439$	−7.81726	−	4.51330i	−0.373098	−	0.215408i	0.301713	−	0.953399i	$-0.402441\pi$
$439$	−7.81726	−	4.51330i	−0.373098	−	0.215408i	−0.674811	+	0.737991i	$0.735775\pi$
$440$		0			0
$441$	−15.9913			−0.761490
$442$		0			0
$443$	−16.4985	−	28.5762i	−0.783866	−	1.35770i	−0.929674	−	0.368383i	$-0.879911\pi$
$443$	−16.4985	−	28.5762i	−0.783866	−	1.35770i	0.145808	−	0.989313i	$-0.453422\pi$
$444$		0			0
$445$	0.0792223	+	0.137217i	0.00375550	+	0.00650471i
$446$		0			0
$447$		−	39.7081i		−	1.87813i
$448$		0			0
$449$	32.0773	+	18.5199i	1.51382	+	0.874006i	0.999869	+	0.0161892i	$0.00515340\pi$
$449$	32.0773	+	18.5199i	1.51382	+	0.874006i	0.513955	+	0.857817i	$0.328180\pi$
$450$		0			0
$451$	6.20155	+	10.7414i	0.292019	+	0.505792i
$452$		0			0
$453$		−	25.2556i		−	1.18661i
$454$		0			0
$455$	−0.454122	−	0.786562i	−0.0212896	−	0.0368746i
$456$		0			0
$457$	18.9017			0.884185			0.442093	−	0.896969i	$-0.354236\pi$
$457$	18.9017			0.884185			0.442093	+	0.896969i	$0.354236\pi$
$458$		0			0
$459$			6.76849i			0.315926i
$460$		0			0
$461$	−5.51897	−	3.18638i	−0.257044	−	0.148404i	0.365941	−	0.930638i	$-0.380747\pi$
$461$	−5.51897	−	3.18638i	−0.257044	−	0.148404i	−0.622985	+	0.782233i	$0.714080\pi$
$462$		0			0
$463$	−17.9866	−	31.1537i	−0.835908	−	1.44784i	−0.893289	−	0.449483i	$-0.851608\pi$
$463$	−17.9866	−	31.1537i	−0.835908	−	1.44784i	0.0573805	−	0.998352i	$-0.481725\pi$
$464$		0			0
$465$	−0.403817	+	0.233144i	−0.0187266	+	0.0108118i
$466$		0			0
$467$	−20.1557	+	11.6369i	−0.932696	+	0.538492i	−0.887663	−	0.460493i	$-0.847673\pi$
$467$	−20.1557	+	11.6369i	−0.932696	+	0.538492i	−0.0450326	+	0.998986i	$0.514339\pi$
$468$		0			0
$469$	−22.2647	+	12.8545i	−1.02809	+	0.593567i
$470$		0			0
$471$	42.0004	+	24.2490i	1.93528	+	1.11733i
$472$		0			0
$473$			12.6496i			0.581629i
$474$		0			0
$475$			8.36737i			0.383921i
$476$		0			0
$477$	1.63663	+	0.944908i	0.0749361	+	0.0432644i
$478$		0			0
$479$	−3.61300	+	2.08596i	−0.165082	+	0.0953102i	−0.580265	−	0.814428i	$-0.697051\pi$
$479$	−3.61300	+	2.08596i	−0.165082	+	0.0953102i	0.415183	+	0.909738i	$0.363718\pi$
$480$		0			0
$481$	−19.6244	+	11.3302i	−0.894796	+	0.516611i
$482$		0			0
$483$	26.3019	−	15.1854i	1.19678	−	0.690960i
$484$		0			0
$485$	0.773460	+	1.33967i	0.0351210	+	0.0608314i
$486$		0			0
$487$	18.6092	+	10.7440i	0.843264	+	0.486859i	0.858372	−	0.513027i	$-0.171476\pi$
$487$	18.6092	+	10.7440i	0.843264	+	0.486859i	−0.0151083	+	0.999886i	$0.504809\pi$
$488$		0			0
$489$		−	22.1900i		−	1.00347i
$490$		0			0
$491$	−37.9677			−1.71346			−0.856728	−	0.515768i	$-0.827507\pi$
$491$	−37.9677			−1.71346			−0.856728	+	0.515768i	$0.827507\pi$
$492$		0			0
$493$	2.69505	+	4.66797i	0.121379	+	0.210235i
$494$		0			0
$495$			1.20871i			0.0543276i
$496$		0			0
$497$	−2.58426	−	4.47608i	−0.115920	−	0.200780i
$498$		0			0
$499$	−30.6347	−	17.6869i	−1.37140	−	0.791776i	−0.380292	−	0.924867i	$-0.624176\pi$
$499$	−30.6347	−	17.6869i	−1.37140	−	0.791776i	−0.991104	+	0.133091i	$0.957510\pi$
$500$		0			0
$501$		−	41.1800i		−	1.83979i
$502$		0			0
$503$	−8.31898	−	14.4089i	−0.370925	−	0.642461i	0.618783	−	0.785562i	$-0.287626\pi$
$503$	−8.31898	−	14.4089i	−0.370925	−	0.642461i	−0.989708	+	0.143101i	$0.954293\pi$
$504$		0			0
$505$	−0.922598	−	1.59799i	−0.0410551	−	0.0711094i
$506$		0			0
$507$	−43.5491			−1.93408
$508$		0			0
$509$	−20.7922	−	12.0044i	−0.921596	−	0.532084i	−0.0374525	−	0.999298i	$-0.511924\pi$
$509$	−20.7922	−	12.0044i	−0.921596	−	0.532084i	−0.884144	+	0.467214i	$0.845258\pi$
$510$		0			0
$511$	1.26775	−	2.19582i	0.0560822	−	0.0971372i
$512$		0			0
$513$	3.17852	−	1.83512i	0.140335	−	0.0810226i
$514$		0			0
$515$	−0.879173			−0.0387410
$516$		0			0
$517$	0.459126	+	0.265077i	0.0201923	+	0.0116581i
$518$		0			0
$519$	−43.2917	−	24.9945i	−1.90029	−	1.09714i
$520$		0			0
$521$	−13.1964	+	7.61893i	−0.578144	+	0.333791i	−0.760395	−	0.649461i	$-0.774995\pi$
$521$	−13.1964	+	7.61893i	−0.578144	+	0.333791i	0.182252	+	0.983252i	$0.441661\pi$
$522$		0			0
$523$	−15.3288	−	8.85009i	−0.670282	−	0.386987i	0.125902	−	0.992043i	$-0.459818\pi$
$523$	−15.3288	−	8.85009i	−0.670282	−	0.386987i	−0.796183	+	0.605055i	$0.793151\pi$
$524$		0			0
$525$	−10.9801	+	19.0181i	−0.479210	+	0.830016i
$526$		0			0
$527$	2.78219	+	4.81889i	0.121194	+	0.209914i
$528$		0			0
$529$	12.3146	−	21.3296i	0.535419	−	0.927373i
$530$		0			0
$531$	32.9097			1.42816
$532$		0			0
$533$	−18.4019	−	10.6243i	−0.797073	−	0.460190i
$534$		0			0
$535$	0.402437			0.0173989
$536$		0			0
$537$	50.0368	+	28.8888i	2.15925	+	1.24664i
$538$		0			0
$539$			13.2473i			0.570600i
$540$		0			0
$541$	21.9503			0.943718			0.471859	−	0.881674i	$-0.343583\pi$
$541$	21.9503			0.943718			0.471859	+	0.881674i	$0.343583\pi$
$542$		0			0
$543$	−41.8155			−1.79448
$544$		0			0
$545$			0.373324i			0.0159914i
$546$		0			0
$547$	−8.77251	+	5.06481i	−0.375085	+	0.216556i	−0.675678	−	0.737197i	$-0.736149\pi$
$547$	−8.77251	+	5.06481i	−0.375085	+	0.216556i	0.300592	+	0.953753i	$0.402816\pi$
$548$		0			0
$549$	29.8958	−	17.2604i	1.27592	−	0.736654i
$550$		0			0
$551$	1.46140	−	2.53123i	0.0622579	−	0.107834i
$552$		0			0
$553$	4.15976	−	14.3688i	0.176891	−	0.611023i
$554$		0			0
$555$	−0.933804	−	0.539132i	−0.0396378	−	0.0228849i
$556$		0			0
$557$	2.57758	+	4.46449i	0.109215	+	0.189167i	0.915453	−	0.402426i	$-0.131833\pi$
$557$	2.57758	+	4.46449i	0.109215	+	0.189167i	−0.806237	+	0.591592i	$0.798500\pi$
$558$		0			0
$559$	−10.8355	−	18.7676i	−0.458292	−	0.793785i
$560$		0			0
$561$	25.7012			1.08511
$562$		0			0
$563$			30.4583i			1.28366i	0.766846	+	0.641832i	$0.221825\pi$
$563$			30.4583i			1.28366i	−0.766846	+	0.641832i	$0.778175\pi$
$564$		0			0
$565$			1.34481i			0.0565768i
$566$		0			0
$567$	−9.74099			−0.409083
$568$		0			0
$569$	1.46124	−	2.53094i	0.0612584	−	0.106103i	−0.833770	−	0.552112i	$-0.813822\pi$
$569$	1.46124	−	2.53094i	0.0612584	−	0.106103i	0.895028	+	0.446010i	$0.147155\pi$
$570$		0			0
$571$		−	37.5221i		−	1.57025i	−0.619338	−	0.785125i	$-0.712599\pi$
$571$		−	37.5221i		−	1.57025i	0.619338	−	0.785125i	$-0.287401\pi$
$572$		0			0
$573$	−11.9860	+	20.7603i	−0.500722	+	0.867275i
$574$		0			0
$575$			34.4392i			1.43621i
$576$		0			0
$577$	−25.8589	−	14.9296i	−1.07652	−	0.621529i	−0.146565	−	0.989201i	$-0.546822\pi$
$577$	−25.8589	−	14.9296i	−1.07652	−	0.621529i	−0.929956	+	0.367672i	$0.880155\pi$
$578$		0			0
$579$	23.1900	−	13.3887i	0.963742	−	0.556417i
$580$		0			0
$581$	−8.61123	−	4.97170i	−0.357254	−	0.206261i
$582$		0			0
$583$	0.782766	−	1.35579i	0.0324189	−	0.0561511i
$584$		0			0
$585$	−1.03537	−	1.79331i	−0.0428072	−	0.0741442i
$586$		0			0
$587$	−13.2428	+	22.9372i	−0.546589	+	0.946720i	0.451916	+	0.892060i	$0.350741\pi$
$587$	−13.2428	+	22.9372i	−0.546589	+	0.946720i	−0.998505	+	0.0546592i	$0.982593\pi$
$588$		0			0
$589$	1.50865	−	2.61306i	0.0621630	−	0.107669i
$590$		0			0
$591$		−	19.4216i		−	0.798896i
$592$		0			0
$593$	−8.29770	−	14.3720i	−0.340746	−	0.590189i	0.643826	−	0.765172i	$-0.277346\pi$
$593$	−8.29770	−	14.3720i	−0.340746	−	0.590189i	−0.984571	+	0.174983i	$0.944013\pi$
$594$		0			0
$595$	−0.446637	−	0.257866i	−0.0183103	−	0.0105715i
$596$		0			0
$597$	13.7056	−	23.7387i	0.560931	−	0.971562i
$598$		0			0
$599$			16.7751i			0.685411i	0.939443	+	0.342705i	$0.111343\pi$
$599$			16.7751i			0.685411i	−0.939443	+	0.342705i	$0.888657\pi$
$600$		0			0
$601$	2.79534	−	1.61389i	0.114024	−	0.0658321i	−0.441903	−	0.897063i	$-0.645697\pi$
$601$	2.79534	−	1.61389i	0.114024	−	0.0658321i	0.555928	+	0.831231i	$0.312363\pi$
$602$		0			0
$603$	−50.7620	+	29.3074i	−2.06719	+	1.19349i
$604$		0			0
$605$	−0.0887897			−0.00360982
$606$		0			0
$607$	3.71191	−	6.42921i	0.150662	−	0.260954i	−0.780809	−	0.624769i	$-0.785193\pi$
$607$	3.71191	−	6.42921i	0.150662	−	0.260954i	0.931471	+	0.363816i	$0.118526\pi$
$608$		0			0
$609$	6.64320	−	3.83545i	0.269196	−	0.155420i
$610$		0			0
$611$	−0.908244			−0.0367436
$612$		0			0
$613$	−5.44694	+	3.14479i	−0.220000	+	0.127017i	−0.605950	−	0.795503i	$-0.707207\pi$
$613$	−5.44694	+	3.14479i	−0.220000	+	0.127017i	0.385950	+	0.922520i	$0.373874\pi$
$614$		0			0
$615$		−	1.01109i		−	0.0407711i
$616$		0			0
$617$	13.0162			0.524011			0.262005	−	0.965066i	$-0.415616\pi$
$617$	13.0162			0.524011			0.262005	+	0.965066i	$0.415616\pi$
$618$		0			0
$619$	−14.4398	+	25.0105i	−0.580385	+	1.00526i	0.415049	+	0.909799i	$0.363764\pi$
$619$	−14.4398	+	25.0105i	−0.580385	+	1.00526i	−0.995434	+	0.0954566i	$0.969569\pi$
$620$		0			0
$621$	13.0825	−	7.55316i	0.524981	−	0.303098i
$622$		0			0
$623$	−1.34542	−	2.33034i	−0.0539033	−	0.0933633i
$624$		0			0
$625$	−12.4264	−	21.5231i	−0.497056	−	0.860926i
$626$		0			0
$627$	−6.96830	−	12.0694i	−0.278287	−	0.482007i
$628$		0			0
$629$	−6.43365	+	11.1434i	−0.256526	+	0.444317i
$630$		0			0
$631$	38.7860			1.54405			0.772023	−	0.635594i	$-0.219245\pi$
$631$	38.7860			1.54405			0.772023	+	0.635594i	$0.219245\pi$
$632$		0			0
$633$	−19.4783			−0.774192
$634$		0			0
$635$	−0.0912602	+	0.158067i	−0.00362155	+	0.00627271i
$636$		0			0
$637$	−11.3474	−	19.6543i	−0.449601	−	0.778732i
$638$		0			0
$639$	−5.89195	−	10.2052i	−0.233082	−	0.403710i
$640$		0			0
$641$	−17.4814	−	30.2787i	−0.690474	−	1.19594i	−0.971683	−	0.236289i	$-0.924069\pi$
$641$	−17.4814	−	30.2787i	−0.690474	−	1.19594i	0.281209	−	0.959646i	$-0.409264\pi$
$642$		0			0
$643$	26.3876	−	15.2349i	1.04063	−	0.600806i	0.120615	−	0.992699i	$-0.461513\pi$
$643$	26.3876	−	15.2349i	1.04063	−	0.600806i	0.920010	+	0.391894i	$0.128180\pi$
$644$		0			0
$645$	0.515593	−	0.893033i	0.0203015	−	0.0351631i
$646$		0			0
$647$	38.3006			1.50575			0.752876	−	0.658162i	$-0.228666\pi$
$647$	38.3006			1.50575			0.752876	+	0.658162i	$0.228666\pi$
$648$		0			0
$649$		−	27.2625i		−	1.07015i
$650$		0			0
$651$	6.85799	−	3.95946i	0.268786	−	0.155184i
$652$		0			0
$653$	−21.4437			−0.839157			−0.419578	−	0.907719i	$-0.637822\pi$
$653$	−21.4437			−0.839157			−0.419578	+	0.907719i	$0.637822\pi$
$654$		0			0
$655$	0.725545	−	0.418893i	0.0283494	−	0.0163675i
$656$		0			0
$657$	2.89040	−	5.00631i	0.112765	−	0.195315i
$658$		0			0
$659$	−28.5215			−1.11104			−0.555519	−	0.831504i	$-0.687481\pi$
$659$	−28.5215			−1.11104			−0.555519	+	0.831504i	$0.687481\pi$
$660$		0			0
$661$	−4.38825	+	2.53356i	−0.170683	+	0.0985440i	−0.582908	−	0.812538i	$-0.698085\pi$
$661$	−4.38825	+	2.53356i	−0.170683	+	0.0985440i	0.412225	+	0.911082i	$0.364752\pi$
$662$		0			0
$663$	−38.1316	+	22.0153i	−1.48091	+	0.855004i
$664$		0			0
$665$			0.279658i			0.0108447i
$666$		0			0
$667$	6.01498	−	10.4183i	0.232901	−	0.403396i
$668$		0			0
$669$	−10.9941	−	6.34746i	−0.425058	−	0.245407i
$670$		0			0
$671$	−14.2986	−	24.7658i	−0.551990	−	0.956074i
$672$		0			0
$673$			39.5191i			1.52335i	0.647960	+	0.761675i	$0.275623\pi$
$673$			39.5191i			1.52335i	−0.647960	+	0.761675i	$0.724377\pi$
$674$		0			0
$675$	−5.46145	+	9.45951i	−0.210211	+	0.364097i
$676$		0			0
$677$	−16.2979	+	28.2288i	−0.626379	+	1.08492i	0.361894	+	0.932219i	$0.382130\pi$
$677$	−16.2979	+	28.2288i	−0.626379	+	1.08492i	−0.988273	+	0.152700i	$0.951203\pi$
$678$		0			0
$679$	−13.1356	−	22.7515i	−0.504098	−	0.873124i
$680$		0			0
$681$	19.4493	−	33.6871i	0.745298	−	1.29089i
$682$		0			0
$683$	−27.2640	−	15.7409i	−1.04323	−	0.602307i	−0.122481	−	0.992471i	$-0.539085\pi$
$683$	−27.2640	−	15.7409i	−1.04323	−	0.602307i	−0.920745	+	0.390164i	$0.872418\pi$
$684$		0			0
$685$	0.202642	−	0.116995i	0.00774253	−	0.00447015i
$686$		0			0
$687$	−35.0950	−	20.2621i	−1.33896	−	0.773048i
$688$		0			0
$689$			2.68203i			0.102177i
$690$		0			0
$691$	−7.23245	+	12.5270i	−0.275135	+	0.476548i	−0.970169	−	0.242429i	$-0.922056\pi$
$691$	−7.23245	+	12.5270i	−0.275135	+	0.476548i	0.695034	+	0.718977i	$0.255389\pi$
$692$		0			0
$693$		−	20.5275i		−	0.779774i
$694$		0			0
$695$	0.638609	−	1.10610i	0.0242238	−	0.0419569i
$696$		0			0
$697$	−12.0657			−0.457021
$698$		0			0
$699$		−	44.4866i		−	1.68264i
$700$		0			0
$701$		−	33.9343i		−	1.28168i	−0.767674	−	0.640840i	$-0.778586\pi$
$701$		−	33.9343i		−	1.28168i	0.767674	−	0.640840i	$-0.221414\pi$
$702$		0			0
$703$	6.97735			0.263156
$704$		0			0
$705$	−0.0216088	−	0.0374276i	−0.000813836	−	0.00140960i
$706$		0			0
$707$	15.6684	+	27.1384i	0.589270	+	1.02065i
$708$		0			0
$709$	−5.52452	−	3.18958i	−0.207478	−	0.119787i	0.392661	−	0.919683i	$-0.371555\pi$
$709$	−5.52452	−	3.18958i	−0.207478	−	0.119787i	−0.600139	+	0.799896i	$0.704888\pi$
$710$		0			0
$711$	9.48398	−	32.7598i	0.355677	−	1.22859i
$712$		0			0
$713$	6.20946	−	10.7551i	0.232546	−	0.402782i
$714$		0			0
$715$	−1.48558	+	0.857703i	−0.0555577	+	0.0320763i
$716$		0			0
$717$	17.3846	−	10.0370i	0.649241	−	0.374839i
$718$		0			0
$719$		−	13.7670i		−	0.513422i	−0.966488	−	0.256711i	$-0.917361\pi$
$719$		−	13.7670i		−	0.513422i	0.966488	−	0.256711i	$-0.0826388\pi$
$720$		0			0
$721$	14.9309			0.556056
$722$		0			0
$723$	−6.49903			−0.241701
$724$		0			0
$725$			8.69848i			0.323054i
$726$		0			0
$727$	4.87618	+	2.81527i	0.180848	+	0.104412i	0.587691	−	0.809086i	$-0.300037\pi$
$727$	4.87618	+	2.81527i	0.180848	+	0.104412i	−0.406843	+	0.913498i	$0.633370\pi$
$728$		0			0
$729$	−39.3792			−1.45849
$730$		0			0
$731$	−10.6569	−	6.15275i	−0.394159	−	0.227568i
$732$		0			0
$733$	−22.4192			−0.828073			−0.414036	−	0.910260i	$-0.635881\pi$
$733$	−22.4192			−0.828073			−0.414036	+	0.910260i	$0.635881\pi$
$734$		0			0
$735$	0.539953	−	0.935226i	0.0199165	−	0.0344963i
$736$		0			0
$737$	24.2784	+	42.0514i	0.894307	+	1.54899i
$738$		0			0
$739$	19.6121	−	33.9691i	0.721443	−	1.24958i	−0.238979	−	0.971025i	$-0.576813\pi$
$739$	19.6121	−	33.9691i	0.721443	−	1.24958i	0.960422	−	0.278551i	$-0.0898540\pi$
$740$		0			0
$741$	20.6770	+	11.9379i	0.759590	+	0.438549i
$742$		0			0
$743$	34.5941	−	19.9729i	1.26914	−	0.732736i	0.294311	−	0.955710i	$-0.404910\pi$
$743$	34.5941	−	19.9729i	1.26914	−	0.732736i	0.974824	+	0.222974i	$0.0715765\pi$
$744$		0			0
$745$	1.30330	+	0.752460i	0.0477492	+	0.0275680i
$746$		0			0
$747$	−19.6330	−	11.3351i	−0.718335	−	0.414731i
$748$		0			0
$749$	−6.83455			−0.249729
$750$		0			0
$751$	−37.7208	+	21.7781i	−1.37645	+	0.794694i	−0.991730	−	0.128340i	$-0.959035\pi$
$751$	−37.7208	+	21.7781i	−1.37645	+	0.794694i	−0.384720	+	0.923033i	$0.625702\pi$
$752$		0			0
$753$	19.0646	−	33.0209i	0.694754	−	1.20335i
$754$		0			0
$755$	0.828940	+	0.478589i	0.0301682	+	0.0174176i
$756$		0			0
$757$	−5.88714			−0.213972			−0.106986	−	0.994261i	$-0.534120\pi$
$757$	−5.88714			−0.213972			−0.106986	+	0.994261i	$0.534120\pi$
$758$		0			0
$759$	−28.6808	−	49.6765i	−1.04105	−	1.80314i
$760$		0			0
$761$	20.0676	+	34.7582i	0.727451	+	1.25998i	0.957957	+	0.286911i	$0.0926285\pi$
$761$	20.0676	+	34.7582i	0.727451	+	1.25998i	−0.230506	+	0.973071i	$0.574038\pi$
$762$		0			0
$763$		−	6.34012i		−	0.229528i
$764$		0			0
$765$	−1.01830	−	0.587917i	−0.0368168	−	0.0212562i
$766$		0			0
$767$	23.3527	+	40.4481i	0.843217	+	1.46050i
$768$		0			0
$769$		−	8.51771i		−	0.307157i	−0.988136	−	0.153578i	$-0.950920\pi$
$769$		−	8.51771i		−	0.307157i	0.988136	−	0.153578i	$-0.0490797\pi$
$770$		0			0
$771$	−5.65447	−	9.79383i	−0.203641	−	0.352716i
$772$		0			0
$773$	−47.0317			−1.69161			−0.845807	−	0.533489i	$-0.820881\pi$
$773$	−47.0317			−1.69161			−0.845807	+	0.533489i	$0.820881\pi$
$774$		0			0
$775$			8.97972i			0.322561i
$776$		0			0
$777$	15.8587	+	9.15602i	0.568928	+	0.328471i
$778$		0			0
$779$	3.27134	+	5.66612i	0.117208	+	0.203010i
$780$		0			0
$781$	−8.45400	+	4.88092i	−0.302508	+	0.174653i
$782$		0			0
$783$	3.30430	−	1.90774i	0.118086	−	0.0681771i
$784$		0			0
$785$	−1.59180	+	0.919026i	−0.0568138	+	0.0328014i
$786$		0			0
$787$	31.5081	+	18.1912i	1.12314	+	0.648446i	0.942201	−	0.335048i	$-0.108753\pi$
$787$	31.5081	+	18.1912i	1.12314	+	0.648446i	0.180941	+	0.983494i	$0.442086\pi$
$788$		0			0
$789$			19.2551i			0.685501i
$790$		0			0
$791$		−	22.8389i		−	0.812056i
$792$		0			0
$793$	42.4281	+	24.4959i	1.50667	+	0.869875i
$794$		0			0
$795$	−0.110523	+	0.0638105i	−0.00391985	+	0.00226312i
$796$		0			0
$797$	−35.1409	+	20.2886i	−1.24475	+	0.718659i	−0.970058	−	0.242873i	$-0.921910\pi$
$797$	−35.1409	+	20.2886i	−1.24475	+	0.718659i	−0.274695	+	0.961531i	$0.588577\pi$
$798$		0			0
$799$	−0.446637	+	0.257866i	−0.0158009	+	0.00912264i
$800$		0			0
$801$	−3.06748	−	5.31303i	−0.108384	−	0.187727i
$802$		0			0
$803$	−4.14725	−	2.39442i	−0.146353	−	0.0844971i
$804$		0			0
$805$			1.15104i			0.0405689i
$806$		0			0
$807$	−33.2953			−1.17205
$808$		0			0
$809$	−9.61331	−	16.6507i	−0.337986	−	0.585409i	0.646068	−	0.763280i	$-0.276412\pi$
$809$	−9.61331	−	16.6507i	−0.337986	−	0.585409i	−0.984054	+	0.177871i	$0.943079\pi$
$810$		0			0
$811$			35.3395i			1.24094i	0.784231	+	0.620469i	$0.213058\pi$
$811$			35.3395i			1.24094i	−0.784231	+	0.620469i	$0.786942\pi$
$812$		0			0
$813$	−11.8887	−	20.5919i	−0.416956	−	0.722189i
$814$		0			0
$815$	0.728322	+	0.420497i	0.0255120	+	0.0147294i
$816$		0			0
$817$			6.67271i			0.233449i
$818$		0			0
$819$	17.5835	+	30.4556i	0.614418	+	1.06420i
$820$		0			0
$821$	19.9370	+	34.5319i	0.695805	+	1.20517i	0.969908	+	0.243470i	$0.0782858\pi$
$821$	19.9370	+	34.5319i	0.695805	+	1.20517i	−0.274103	+	0.961700i	$0.588381\pi$
$822$		0			0
$823$	−54.0505			−1.88408			−0.942042	−	0.335496i	$-0.891096\pi$
$823$	−54.0505			−1.88408			−0.942042	+	0.335496i	$0.891096\pi$
$824$		0			0
$825$	35.9195	+	20.7381i	1.25056	+	0.722010i
$826$		0			0
$827$	−18.9320	+	32.7912i	−0.658331	+	1.14026i	0.322716	+	0.946496i	$0.395404\pi$
$827$	−18.9320	+	32.7912i	−0.658331	+	1.14026i	−0.981048	+	0.193767i	$0.937929\pi$
$828$		0			0
$829$	−13.4943	+	7.79092i	−0.468675	+	0.270590i	−0.715685	−	0.698423i	$-0.753885\pi$
$829$	−13.4943	+	7.79092i	−0.468675	+	0.270590i	0.247010	+	0.969013i	$0.420552\pi$
$830$		0			0
$831$	−8.89254			−0.308479
$832$		0			0
$833$	−11.1604	−	6.44345i	−0.386684	−	0.223252i
$834$		0			0
$835$	1.35161	+	0.780353i	0.0467744	+	0.0270052i
$836$		0			0
$837$	3.41114	−	1.96942i	0.117906	−	0.0680732i
$838$		0			0
$839$	31.9920	+	18.4706i	1.10449	+	0.637676i	0.937396	−	0.348265i	$-0.113229\pi$
$839$	31.9920	+	18.4706i	1.10449	+	0.637676i	0.167092	+	0.985941i	$0.446562\pi$
$840$		0			0
$841$	−12.9808	+	22.4833i	−0.447613	+	0.775288i
$842$		0			0
$843$	36.9974	+	64.0814i	1.27426	+	2.20708i
$844$		0			0
$845$	0.825247	−	1.42937i	0.0283893	−	0.0491718i
$846$		0			0
$847$	1.50791			0.0518123
$848$		0			0
$849$	21.3620	+	12.3333i	0.733142	+	0.423279i
$850$		0			0
$851$	28.7180			0.984441
$852$		0			0
$853$	46.1008	+	26.6163i	1.57846	+	0.911325i	0.995074	+	0.0991313i	$0.0316064\pi$
$853$	46.1008	+	26.6163i	1.57846	+	0.911325i	0.583387	+	0.812194i	$0.301727\pi$
$854$		0			0
$855$			0.637601i			0.0218055i
$856$		0			0
$857$	5.06794			0.173117			0.0865587	−	0.996247i	$-0.472413\pi$
$857$	5.06794			0.173117			0.0865587	+	0.996247i	$0.472413\pi$
$858$		0			0
$859$	−26.5062			−0.904378			−0.452189	−	0.891922i	$-0.649357\pi$
$859$	−26.5062			−0.904378			−0.452189	+	0.891922i	$0.649357\pi$
$860$		0			0
$861$			17.1712i			0.585195i
$862$		0			0
$863$	−28.6539	+	16.5433i	−0.975390	+	0.563142i	−0.900875	−	0.434078i	$-0.857074\pi$
$863$	−28.6539	+	16.5433i	−0.975390	+	0.563142i	−0.0745148	+	0.997220i	$0.523741\pi$
$864$		0			0
$865$	1.64074	−	0.947280i	0.0557867	−	0.0322085i
$866$		0			0
$867$	9.72465	−	16.8436i	0.330267	−	0.572038i
$868$		0			0
$869$	−27.1384	−	7.85657i	−0.920607	−	0.266516i
$870$		0			0
$871$	−72.0414	−	41.5931i	−2.44103	−	1.40933i
$872$		0			0
$873$	−29.9483	−	51.8720i	−1.01360	−	1.75560i
$874$		0			0
$875$	−0.833100	−	1.44297i	−0.0281639	−	0.0487813i
$876$		0			0
$877$	19.1240			0.645772			0.322886	−	0.946438i	$-0.395347\pi$
$877$	19.1240			0.645772			0.322886	+	0.946438i	$0.395347\pi$
$878$		0			0
$879$			11.3397i			0.382478i
$880$		0			0
$881$		−	44.2459i		−	1.49068i	−0.666683	−	0.745341i	$-0.732287\pi$
$881$		−	44.2459i		−	1.49068i	0.666683	−	0.745341i	$-0.267713\pi$
$882$		0			0
$883$	17.7633			0.597783			0.298892	−	0.954287i	$-0.403383\pi$
$883$	17.7633			0.597783			0.298892	+	0.954287i	$0.403383\pi$
$884$		0			0
$885$	−1.11121	+	1.92467i	−0.0373529	+	0.0646972i
$886$		0			0
$887$		−	10.4773i		−	0.351794i	−0.984409	−	0.175897i	$-0.943717\pi$
$887$		−	10.4773i		−	0.351794i	0.984409	−	0.175897i	$-0.0562826\pi$
$888$		0			0
$889$	1.54986	−	2.68444i	0.0519807	−	0.0900332i
$890$		0			0
$891$			18.3979i			0.616352i
$892$		0			0
$893$	0.242191	+	0.139829i	0.00810460	+	0.00467919i
$894$		0			0
$895$	−1.89638	+	1.09487i	−0.0633888	+	0.0365976i
$896$		0			0
$897$	85.1045	+	49.1351i	2.84156	+	1.64057i
$898$		0			0
$899$	1.56835	−	2.71647i	0.0523075	−	0.0905993i
$900$		0			0
$901$	0.761473	+	1.31891i	0.0253683	+	0.0439393i
$902$		0			0
$903$	−8.75626	+	15.1663i	−0.291390	+	0.504703i
$904$		0			0
$905$	0.792395	−	1.37247i	0.0263401	−	0.0456224i
$906$		0			0
$907$		−	1.63680i		−	0.0543492i	−0.999631	−	0.0271746i	$-0.991349\pi$
$907$		−	1.63680i		−	0.0543492i	0.999631	−	0.0271746i	$-0.00865100\pi$
$908$		0			0
$909$	35.7229	+	61.8738i	1.18485	+	2.05222i
$910$		0			0
$911$	5.59797	+	3.23199i	0.185469	+	0.107081i	0.589860	−	0.807506i	$-0.299183\pi$
$911$	5.59797	+	3.23199i	0.185469	+	0.107081i	−0.404391	+	0.914586i	$0.632516\pi$
$912$		0			0
$913$	−9.39007	+	16.2641i	−0.310766	+	0.538263i
$914$		0			0
$915$			2.33122i			0.0770676i
$916$		0			0
$917$	−12.3219	+	7.11403i	−0.406904	+	0.234926i
$918$		0			0
$919$	−5.18496	+	2.99354i	−0.171036	+	0.0987476i	−0.583074	−	0.812419i	$-0.698150\pi$
$919$	−5.18496	+	2.99354i	−0.171036	+	0.0987476i	0.412038	+	0.911167i	$0.364817\pi$
$920$		0			0
$921$	−57.2366			−1.88601
$922$		0			0
$923$	8.36185	−	14.4832i	0.275234	−	0.476719i
$924$		0			0
$925$	−17.9831	+	10.3825i	−0.591280	+	0.341376i
$926$		0			0
$927$	34.0415			1.11807
$928$		0			0
$929$	5.59740	−	3.23166i	0.183645	−	0.106027i	−0.405359	−	0.914158i	$-0.632854\pi$
$929$	5.59740	−	3.23166i	0.183645	−	0.106027i	0.589004	+	0.808130i	$0.299520\pi$
$930$		0			0
$931$			6.98797i			0.229022i
$932$		0			0
$933$	34.5468			1.13101
$934$		0			0
$935$	−0.487033	+	0.843566i	−0.0159277	+	0.0275875i
$936$		0			0
$937$	−37.6328	+	21.7273i	−1.22941	+	0.709800i	−0.966906	−	0.255131i	$-0.917881\pi$
$937$	−37.6328	+	21.7273i	−1.22941	+	0.709800i	−0.262503	+	0.964931i	$0.584548\pi$
$938$		0			0
$939$	20.2640	+	35.0982i	0.661290	+	1.14539i
$940$		0			0
$941$	−9.26401	−	16.0457i	−0.301998	−	0.523076i	0.674590	−	0.738192i	$-0.264320\pi$
$941$	−9.26401	−	16.0457i	−0.301998	−	0.523076i	−0.976588	+	0.215116i	$0.930987\pi$
$942$		0			0
$943$	13.4645	+	23.3212i	0.438464	+	0.759441i
$944$		0			0
$945$	−0.182535	+	0.316160i	−0.00593786	+	0.0102847i
$946$		0			0
$947$	10.0590			0.326875			0.163437	−	0.986554i	$-0.447742\pi$
$947$	10.0590			0.326875			0.163437	+	0.986554i	$0.447742\pi$
$948$		0			0
$949$	8.20410			0.266316
$950$		0			0
$951$	46.2067	−	80.0324i	1.49836	−	2.59523i
$952$		0			0
$953$	23.7502	+	41.1365i	0.769343	+	1.33254i	0.937920	+	0.346852i	$0.112750\pi$
$953$	23.7502	+	41.1365i	0.769343	+	1.33254i	−0.168577	+	0.985689i	$0.553917\pi$
$954$		0			0
$955$	−0.454264	−	0.786808i	−0.0146996	−	0.0254605i
$956$		0			0
$957$	−7.24405	−	12.5471i	−0.234167	−	0.405589i
$958$		0			0
$959$	−3.44144	+	1.98692i	−0.111130	+	0.0641609i
$960$		0			0
$961$	−13.8809	+	24.0425i	−0.447772	+	0.775564i
$962$		0			0
$963$	−15.5823			−0.502133
$964$		0			0
$965$			1.01485i			0.0326693i
$966$		0			0
$967$	−12.4098	+	7.16478i	−0.399071	+	0.230404i	−0.686083	−	0.727523i	$-0.740671\pi$
$967$	−12.4098	+	7.16478i	−0.399071	+	0.230404i	0.287012	+	0.957927i	$0.407338\pi$
$968$		0			0
$969$	13.5575			0.435529
$970$		0			0
$971$	10.7437	−	6.20290i	0.344783	−	0.199061i	−0.317602	−	0.948224i	$-0.602878\pi$
$971$	10.7437	−	6.20290i	0.344783	−	0.199061i	0.662385	+	0.749164i	$0.269544\pi$
$972$		0			0
$973$	−10.8454	+	18.7849i	−0.347689	+	0.602215i
$974$		0			0
$975$	−71.0560			−2.27561
$976$		0			0
$977$	−10.0483	+	5.80138i	−0.321473	+	0.185603i	−0.652049	−	0.758177i	$-0.726090\pi$
$977$	−10.0483	+	5.80138i	−0.321473	+	0.185603i	0.330576	+	0.943779i	$0.392757\pi$
$978$		0			0
$979$	−4.40134	+	2.54111i	−0.140667	+	0.0812143i
$980$		0			0
$981$		−	14.4551i		−	0.461514i
$982$		0			0
$983$	25.6653	−	44.4536i	0.818595	−	1.41785i	−0.0881222	−	0.996110i	$-0.528087\pi$
$983$	25.6653	−	44.4536i	0.818595	−	1.41785i	0.906717	−	0.421739i	$-0.138580\pi$
$984$		0			0
$985$	0.637455	+	0.368035i	0.0203110	+	0.0117266i
$986$		0			0
$987$	0.366981	+	0.635629i	0.0116811	+	0.0202323i
$988$		0			0
$989$			27.4642i			0.873310i
$990$		0			0
$991$	0.0511537	−	0.0886008i	0.00162495	−	0.00281450i	−0.865212	−	0.501407i	$-0.832816\pi$
$991$	0.0511537	−	0.0886008i	0.00162495	−	0.00281450i	0.866837	+	0.498592i	$0.166149\pi$
$992$		0			0
$993$	30.9477	−	53.6029i	0.982095	−	1.70104i
$994$		0			0
$995$	0.519435	+	0.899688i	0.0164672	+	0.0285220i
$996$		0			0
$997$	−16.6641	+	28.8630i	−0.527756	+	0.914100i	0.471721	+	0.881748i	$0.343633\pi$
$997$	−16.6641	+	28.8630i	−0.527756	+	0.914100i	−0.999477	+	0.0323520i	$0.989700\pi$
$998$		0			0
$999$	7.88806	+	4.55417i	0.249567	+	0.144088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1264.2.n.i.735.13	yes	28
4.3	odd	2	inner	1264.2.n.i.735.2	✓	28
79.56	odd	6	inner	1264.2.n.i.767.2	yes	28
316.135	even	6	inner	1264.2.n.i.767.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1264.2.n.i.735.2	✓	28	4.3	odd	2	inner
1264.2.n.i.735.13	yes	28	1.1	even	1	trivial
1264.2.n.i.767.2	yes	28	79.56	odd	6	inner
1264.2.n.i.767.13	yes	28	316.135	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1264 = 2^{4} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1264.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30739 - 2.26447i) q^{3} +(0.0495497 + 0.0858226i) q^{5} +(-0.841498 - 1.45752i) q^{7} +(-1.91856 - 3.32304i) q^{9} +O(q^{10})\)	\(q+(1.30739 - 2.26447i) q^{3} +(0.0495497 + 0.0858226i) q^{5} +(-0.841498 - 1.45752i) q^{7} +(-1.91856 - 3.32304i) q^{9} +(-2.75282 + 1.58934i) q^{11} +(2.72282 - 4.71606i) q^{13} +0.259124 q^{15} -3.09222i q^{17} +(-1.45212 + 0.838384i) q^{19} -4.40068 q^{21} +(-5.97678 + 3.45070i) q^{23} +(2.49509 - 4.32162i) q^{25} -2.18888 q^{27} +(-1.50959 + 0.871560i) q^{29} +(-1.55839 + 0.899739i) q^{31} +8.31159i q^{33} +(0.0833919 - 0.144439i) q^{35} +(-3.60370 - 2.08059i) q^{37} +(-7.11959 - 12.3315i) q^{39} -3.90196i q^{41} +(1.98975 - 3.44636i) q^{43} +(0.190128 - 0.329311i) q^{45} +(-0.0833919 - 0.144439i) q^{47} +(2.08376 - 3.60918i) q^{49} +(-7.00224 - 4.04275i) q^{51} +(-0.426526 + 0.246255i) q^{53} +(-0.272803 - 0.157503i) q^{55} +4.38439i q^{57} +(-4.28834 + 7.42762i) q^{59} +8.99653i q^{61} +(-3.22892 + 5.59266i) q^{63} +0.539659 q^{65} -15.2758i q^{67} +18.0457i q^{69} +3.07103 q^{71} +(0.753273 + 1.30471i) q^{73} +(-6.52413 - 11.3001i) q^{75} +(4.63299 + 2.67486i) q^{77} +(6.15798 + 6.40932i) q^{79} +(2.89394 - 5.01246i) q^{81} +(5.11661 - 2.95408i) q^{83} +(0.265382 - 0.153218i) q^{85} +4.55789i q^{87} +1.59885 q^{89} -9.16498 q^{91} +4.70526i q^{93} +(-0.143905 - 0.0830833i) q^{95} +15.6098 q^{97} +(10.5629 + 6.09849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 20 q^{9}+O(q^{10}) \) 28 * q - 20 * q^9	\( 28 q - 20 q^{9} - 8 q^{13} + 32 q^{21} - 14 q^{25} + 30 q^{37} - 6 q^{45} - 12 q^{49} - 18 q^{53} - 48 q^{65} + 22 q^{73} - 66 q^{77} - 14 q^{81} + 60 q^{89} - 16 q^{97}+O(q^{100}) \) 28 * q - 20 * q^9 - 8 * q^13 + 32 * q^21 - 14 * q^25 + 30 * q^37 - 6 * q^45 - 12 * q^49 - 18 * q^53 - 48 * q^65 + 22 * q^73 - 66 * q^77 - 14 * q^81 + 60 * q^89 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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