LMFDB - Embedded newform 352.2.m.f.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(97,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("352.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.m (of order $5$, degree $4$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			257.2
Root			$0.198931 - 0.144532i$ of defining polynomial
Character	$\chi$	$=$	352.257
Dual form			352.2.m.f.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385002 + 1.18491i) q^{3} +(3.03889 - 2.20788i) q^{5} +(-1.04575 - 3.21850i) q^{7} +(1.17126 + 0.850967i) q^{9} +O(q^{10})$	\(q+(-0.385002 + 1.18491i) q^{3} +(3.03889 - 2.20788i) q^{5} +(-1.04575 - 3.21850i) q^{7} +(1.17126 + 0.850967i) q^{9} +(-1.01050 - 3.15894i) q^{11} +(-3.68264 - 2.67560i) q^{13} +(1.44617 + 4.45086i) q^{15} +(0.239899 - 0.174297i) q^{17} +(-0.887292 + 2.73080i) q^{19} +4.21626 q^{21} +8.74861 q^{23} +(2.81501 - 8.66371i) q^{25} +(-4.48310 + 3.25717i) q^{27} +(1.21337 + 3.73437i) q^{29} +(4.68224 + 3.40185i) q^{31} +(4.13212 + 0.0188365i) q^{33} +(-10.2840 - 7.47175i) q^{35} +(0.784212 + 2.41356i) q^{37} +(4.58818 - 3.33351i) q^{39} +(-2.23328 + 6.87333i) q^{41} +4.03696 q^{43} +5.43814 q^{45} +(-1.57228 + 4.83898i) q^{47} +(-3.60201 + 2.61701i) q^{49} +(0.114165 + 0.351364i) q^{51} +(-9.78533 - 7.10946i) q^{53} +(-10.0454 - 7.36858i) q^{55} +(-2.89416 - 2.10273i) q^{57} +(0.216456 + 0.666183i) q^{59} +(-2.27279 + 1.65128i) q^{61} +(1.51399 - 4.65958i) q^{63} -17.0985 q^{65} -5.78333 q^{67} +(-3.36823 + 10.3664i) q^{69} +(-1.94537 + 1.41339i) q^{71} +(1.89804 + 5.84158i) q^{73} +(9.18197 + 6.67109i) q^{75} +(-9.11029 + 6.55577i) q^{77} +(-0.502385 - 0.365004i) q^{79} +(-0.791319 - 2.43543i) q^{81} +(8.76835 - 6.37058i) q^{83} +(0.344199 - 1.05934i) q^{85} -4.89206 q^{87} -2.37592 q^{89} +(-4.76027 + 14.6506i) q^{91} +(-5.83357 + 4.23834i) q^{93} +(3.33291 + 10.2576i) q^{95} +(8.00482 + 5.81585i) q^{97} +(1.50459 - 4.55983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{7} - q^{9}+O(q^{10}) $ 12 * q + 6 * q^7 - q^9	$ 12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43} + 28 q^{45} - 24 q^{47} - 5 q^{49} + 17 q^{51} - 14 q^{53} - 46 q^{55} - 37 q^{57} + 31 q^{59} - 14 q^{61} + 58 q^{63} - 52 q^{65} - 62 q^{67} - 18 q^{69} + 6 q^{71} - 8 q^{73} + 53 q^{75} - 46 q^{77} - 4 q^{79} - 22 q^{81} + 41 q^{83} - 36 q^{85} - 76 q^{87} - 2 q^{89} - 22 q^{91} + 8 q^{93} + 16 q^{95} + 3 q^{97} - 65 q^{99}+O(q^{100}) $ 12 * q + 6 * q^7 - q^9 - 11 * q^11 - 2 * q^13 + 4 * q^15 + 12 * q^17 + 5 * q^19 + 24 * q^21 - 12 * q^23 + 13 * q^25 + 3 * q^27 + 16 * q^31 - 7 * q^33 - 28 * q^35 - 4 * q^37 + 46 * q^39 - 4 * q^41 - 22 * q^43 + 28 * q^45 - 24 * q^47 - 5 * q^49 + 17 * q^51 - 14 * q^53 - 46 * q^55 - 37 * q^57 + 31 * q^59 - 14 * q^61 + 58 * q^63 - 52 * q^65 - 62 * q^67 - 18 * q^69 + 6 * q^71 - 8 * q^73 + 53 * q^75 - 46 * q^77 - 4 * q^79 - 22 * q^81 + 41 * q^83 - 36 * q^85 - 76 * q^87 - 2 * q^89 - 22 * q^91 + 8 * q^93 + 16 * q^95 + 3 * q^97 - 65 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.385002	+	1.18491i	−0.222281	+	0.684111i	0.776275	+	0.630394i	$0.217107\pi$
$3$	−0.385002	+	1.18491i	−0.222281	+	0.684111i	−0.998556	+	0.0537165i	$0.982893\pi$
$4$		0			0
$5$	3.03889	−	2.20788i	1.35903	−	0.987394i	0.360526	−	0.932749i	$-0.382597\pi$
$5$	3.03889	−	2.20788i	1.35903	−	0.987394i	0.998506	−	0.0546447i	$-0.0174026\pi$
$6$		0			0
$7$	−1.04575	−	3.21850i	−0.395258	−	1.21648i	−0.928761	−	0.370680i	$-0.879125\pi$
$7$	−1.04575	−	3.21850i	−0.395258	−	1.21648i	0.533503	−	0.845798i	$-0.320875\pi$
$8$		0			0
$9$	1.17126	+	0.850967i	0.390418	+	0.283656i
$10$		0			0
$11$	−1.01050	−	3.15894i	−0.304678	−	0.952455i
$11$	−1.01050	−	3.15894i	−0.304678	−	0.952455i
$12$		0			0
$13$	−3.68264	−	2.67560i	−1.02138	−	0.742077i	−0.0548156	−	0.998496i	$-0.517457\pi$
$13$	−3.68264	−	2.67560i	−1.02138	−	0.742077i	−0.966566	+	0.256420i	$0.917457\pi$
$14$		0			0
$15$	1.44617	+	4.45086i	0.373400	+	1.14921i
$16$		0			0
$17$	0.239899	−	0.174297i	0.0581840	−	0.0422732i	−0.558313	−	0.829630i	$-0.688551\pi$
$17$	0.239899	−	0.174297i	0.0581840	−	0.0422732i	0.616497	+	0.787357i	$0.288551\pi$
$18$		0			0
$19$	−0.887292	+	2.73080i	−0.203559	+	0.626489i	0.796211	+	0.605019i	$0.206835\pi$
$19$	−0.887292	+	2.73080i	−0.203559	+	0.626489i	−0.999769	+	0.0214698i	$0.993165\pi$
$20$		0			0
$21$	4.21626			0.920064
$22$		0			0
$23$	8.74861			1.82421			0.912106	−	0.409956i	$-0.134456\pi$
$23$	8.74861			1.82421			0.912106	+	0.409956i	$0.134456\pi$
$24$		0			0
$25$	2.81501	−	8.66371i	0.563002	−	1.73274i
$26$		0			0
$27$	−4.48310	+	3.25717i	−0.862774	+	0.626842i
$28$		0			0
$29$	1.21337	+	3.73437i	0.225317	+	0.693456i	0.998259	+	0.0589789i	$0.0187845\pi$
$29$	1.21337	+	3.73437i	0.225317	+	0.693456i	−0.772942	+	0.634477i	$0.781216\pi$
$30$		0			0
$31$	4.68224	+	3.40185i	0.840955	+	0.610990i	0.922637	−	0.385669i	$-0.126029\pi$
$31$	4.68224	+	3.40185i	0.840955	+	0.610990i	−0.0816822	+	0.996658i	$0.526029\pi$
$32$		0			0
$33$	4.13212	+	0.0188365i	0.719309	+	0.00327901i
$34$		0			0
$35$	−10.2840	−	7.47175i	−1.73831	−	1.26296i
$36$		0			0
$37$	0.784212	+	2.41356i	0.128924	+	0.396786i	0.994596	−	0.103826i	$-0.0331084\pi$
$37$	0.784212	+	2.41356i	0.128924	+	0.396786i	−0.865672	+	0.500612i	$0.833108\pi$
$38$		0			0
$39$	4.58818	−	3.33351i	0.734696	−	0.533788i
$40$		0			0
$41$	−2.23328	+	6.87333i	−0.348780	+	1.07343i	0.610749	+	0.791824i	$0.290868\pi$
$41$	−2.23328	+	6.87333i	−0.348780	+	1.07343i	−0.959529	+	0.281610i	$0.909132\pi$
$42$		0			0
$43$	4.03696			0.615631			0.307815	−	0.951446i	$-0.400402\pi$
$43$	4.03696			0.615631			0.307815	+	0.951446i	$0.400402\pi$
$44$		0			0
$45$	5.43814			0.810671
$46$		0			0
$47$	−1.57228	+	4.83898i	−0.229341	+	0.705838i	0.768481	+	0.639872i	$0.221013\pi$
$47$	−1.57228	+	4.83898i	−0.229341	+	0.705838i	−0.997822	+	0.0659657i	$0.978987\pi$
$48$		0			0
$49$	−3.60201	+	2.61701i	−0.514573	+	0.373859i
$50$		0			0
$51$	0.114165	+	0.351364i	0.0159863	+	0.0492008i
$52$		0			0
$53$	−9.78533	−	7.10946i	−1.34412	−	0.976559i	−0.999282	−	0.0378969i	$-0.987934\pi$
$53$	−9.78533	−	7.10946i	−1.34412	−	0.976559i	−0.344837	−	0.938663i	$-0.612066\pi$
$54$		0			0
$55$	−10.0454	−	7.36858i	−1.35452	−	0.993579i
$56$		0			0
$57$	−2.89416	−	2.10273i	−0.383341	−	0.278513i
$58$		0			0
$59$	0.216456	+	0.666183i	0.0281802	+	0.0867296i	0.964157	−	0.265331i	$-0.0854812\pi$
$59$	0.216456	+	0.666183i	0.0281802	+	0.0867296i	−0.935977	+	0.352060i	$0.885481\pi$
$60$		0			0
$61$	−2.27279	+	1.65128i	−0.291001	+	0.211425i	−0.723702	−	0.690113i	$-0.757561\pi$
$61$	−2.27279	+	1.65128i	−0.291001	+	0.211425i	0.432700	+	0.901538i	$0.357561\pi$
$62$		0			0
$63$	1.51399	−	4.65958i	0.190745	−	0.587052i
$64$		0			0
$65$	−17.0985			−2.12081
$66$		0			0
$67$	−5.78333			−0.706546			−0.353273	−	0.935520i	$-0.614931\pi$
$67$	−5.78333			−0.706546			−0.353273	+	0.935520i	$0.614931\pi$
$68$		0			0
$69$	−3.36823	+	10.3664i	−0.405488	+	1.24796i
$70$		0			0
$71$	−1.94537	+	1.41339i	−0.230873	+	0.167739i	−0.697207	−	0.716870i	$-0.745574\pi$
$71$	−1.94537	+	1.41339i	−0.230873	+	0.167739i	0.466335	+	0.884608i	$0.345574\pi$
$72$		0			0
$73$	1.89804	+	5.84158i	0.222149	+	0.683705i	0.998568	+	0.0534883i	$0.0170340\pi$
$73$	1.89804	+	5.84158i	0.222149	+	0.683705i	−0.776419	+	0.630217i	$0.782966\pi$
$74$		0			0
$75$	9.18197	+	6.67109i	1.06024	+	0.770312i
$76$		0			0
$77$	−9.11029	+	6.55577i	−1.03821	+	0.747100i
$78$		0			0
$79$	−0.502385	−	0.365004i	−0.0565227	−	0.0410661i	0.559165	−	0.829056i	$-0.311122\pi$
$79$	−0.502385	−	0.365004i	−0.0565227	−	0.0410661i	−0.615688	+	0.787990i	$0.711122\pi$
$80$		0			0
$81$	−0.791319	−	2.43543i	−0.0879244	−	0.270603i
$82$		0			0
$83$	8.76835	−	6.37058i	0.962452	−	0.699262i	0.00873296	−	0.999962i	$-0.497220\pi$
$83$	8.76835	−	6.37058i	0.962452	−	0.699262i	0.953719	+	0.300700i	$0.0972202\pi$
$84$		0			0
$85$	0.344199	−	1.05934i	0.0373336	−	0.114901i
$86$		0			0
$87$	−4.89206			−0.524484
$88$		0			0
$89$	−2.37592			−0.251847			−0.125923	−	0.992040i	$-0.540189\pi$
$89$	−2.37592			−0.251847			−0.125923	+	0.992040i	$0.540189\pi$
$90$		0			0
$91$	−4.76027	+	14.6506i	−0.499011	+	1.53580i
$92$		0			0
$93$	−5.83357	+	4.23834i	−0.604913	+	0.439495i
$94$		0			0
$95$	3.33291	+	10.2576i	0.341949	+	1.05241i
$96$		0			0
$97$	8.00482	+	5.81585i	0.812767	+	0.590510i	0.914631	−	0.404289i	$-0.132481\pi$
$97$	8.00482	+	5.81585i	0.812767	+	0.590510i	−0.101865	+	0.994798i	$0.532481\pi$
$98$		0			0
$99$	1.50459	−	4.55983i	0.151217	−	0.458280i
$100$		0			0
$101$	0.598544	+	0.434868i	0.0595574	+	0.0432710i	0.617166	−	0.786833i	$-0.288281\pi$
$101$	0.598544	+	0.434868i	0.0595574	+	0.0432710i	−0.557608	+	0.830104i	$0.688281\pi$
$102$		0			0
$103$	−2.97788	−	9.16498i	−0.293419	−	0.903052i	−0.983748	−	0.179556i	$-0.942534\pi$
$103$	−2.97788	−	9.16498i	−0.293419	−	0.903052i	0.690328	−	0.723496i	$-0.257466\pi$
$104$		0			0
$105$	12.8127	−	9.30900i	1.25040	−	0.908466i
$106$		0			0
$107$	−1.63863	+	5.04319i	−0.158413	+	0.487544i	−0.998491	−	0.0549217i	$-0.982509\pi$
$107$	−1.63863	+	5.04319i	−0.158413	+	0.487544i	0.840078	+	0.542466i	$0.182509\pi$
$108$		0			0
$109$	16.9513			1.62364			0.811819	−	0.583910i	$-0.198478\pi$
$109$	16.9513			1.62364			0.811819	+	0.583910i	$0.198478\pi$
$110$		0			0
$111$	−3.16178			−0.300103
$112$		0			0
$113$	−0.641648	+	1.97479i	−0.0603611	+	0.185772i	−0.976690	−	0.214653i	$-0.931138\pi$
$113$	−0.641648	+	1.97479i	−0.0603611	+	0.185772i	0.916329	+	0.400426i	$0.131138\pi$
$114$		0			0
$115$	26.5860	−	19.3159i	2.47916	−	1.80122i
$116$		0			0
$117$	−2.03647	−	6.26761i	−0.188272	−	0.579441i
$118$		0			0
$119$	−0.811849	−	0.589843i	−0.0744220	−	0.0540708i
$120$		0			0
$121$	−8.95776	+	6.38424i	−0.814342	+	0.580385i
$122$		0			0
$123$	−7.28449	−	5.29249i	−0.656821	−	0.477208i
$124$		0			0
$125$	−4.77019	−	14.6811i	−0.426658	−	1.31312i
$126$		0			0
$127$	8.11140	−	5.89328i	0.719770	−	0.522944i	−0.166541	−	0.986035i	$-0.553260\pi$
$127$	8.11140	−	5.89328i	0.719770	−	0.522944i	0.886311	+	0.463091i	$0.153260\pi$
$128$		0			0
$129$	−1.55424	+	4.78345i	−0.136843	+	0.421159i
$130$		0			0
$131$	−18.7775			−1.64060			−0.820301	−	0.571932i	$-0.806194\pi$
$131$	−18.7775			−1.64060			−0.820301	+	0.571932i	$0.806194\pi$
$132$		0			0
$133$	9.71697			0.842568
$134$		0			0
$135$	−6.43221	+	19.7963i	−0.553597	+	1.70380i
$136$		0			0
$137$	−2.85494	+	2.07424i	−0.243914	+	0.177214i	−0.703025	−	0.711165i	$-0.748168\pi$
$137$	−2.85494	+	2.07424i	−0.243914	+	0.177214i	0.459111	+	0.888379i	$0.348168\pi$
$138$		0			0
$139$	4.94201	+	15.2099i	0.419175	+	1.29009i	0.908462	+	0.417967i	$0.137257\pi$
$139$	4.94201	+	15.2099i	0.419175	+	1.29009i	−0.489287	+	0.872123i	$0.662743\pi$
$140$		0			0
$141$	−5.12845	−	3.72604i	−0.431893	−	0.313789i
$142$		0			0
$143$	−4.73072	+	14.3369i	−0.395602	+	1.19891i
$144$		0			0
$145$	11.9323	+	8.66936i	0.990928	+	0.719951i
$146$		0			0
$147$	−1.71416	−	5.27563i	−0.141381	−	0.435127i
$148$		0			0
$149$	−16.1917	+	11.7639i	−1.32647	+	0.963740i	−0.326647	+	0.945146i	$0.605919\pi$
$149$	−16.1917	+	11.7639i	−1.32647	+	0.963740i	−0.999827	+	0.0185937i	$0.994081\pi$
$150$		0			0
$151$	1.15986	−	3.56967i	0.0943879	−	0.290496i	−0.892706	−	0.450640i	$-0.851196\pi$
$151$	1.15986	−	3.56967i	0.0943879	−	0.290496i	0.987094	+	0.160144i	$0.0511958\pi$
$152$		0			0
$153$	0.429303			0.0347071
$154$		0			0
$155$	21.7397			1.74617
$156$		0			0
$157$	3.08141	−	9.48362i	0.245924	−	0.756875i	−0.749560	−	0.661937i	$-0.769735\pi$
$157$	3.08141	−	9.48362i	0.245924	−	0.756875i	0.995483	−	0.0949381i	$-0.0302653\pi$
$158$		0			0
$159$	12.1915	−	8.85762i	0.966847	−	0.702455i
$160$		0			0
$161$	−9.14889	−	28.1574i	−0.721033	−	2.21911i
$162$		0			0
$163$	0.627037	+	0.455569i	0.0491133	+	0.0356829i	0.612071	−	0.790803i	$-0.290337\pi$
$163$	0.627037	+	0.455569i	0.0491133	+	0.0356829i	−0.562958	+	0.826486i	$0.690337\pi$
$164$		0			0
$165$	12.5986	−	9.06598i	0.980801	−	0.705785i
$166$		0			0
$167$	−10.6330	−	7.72530i	−0.822803	−	0.597801i	0.0947109	−	0.995505i	$-0.469807\pi$
$167$	−10.6330	−	7.72530i	−0.822803	−	0.597801i	−0.917514	+	0.397703i	$0.869807\pi$
$168$		0			0
$169$	2.38582	+	7.34279i	0.183524	+	0.564830i
$170$		0			0
$171$	−3.36307	+	2.44341i	−0.257180	+	0.186852i
$172$		0			0
$173$	3.72617	−	11.4680i	0.283295	−	0.871893i	−0.703609	−	0.710587i	$-0.748429\pi$
$173$	3.72617	−	11.4680i	0.283295	−	0.871893i	0.986904	−	0.161306i	$-0.0515705\pi$
$174$		0			0
$175$	−30.8280			−2.33037
$176$		0			0
$177$	−0.872706			−0.0655966
$178$		0			0
$179$	−1.44794	+	4.45632i	−0.108224	+	0.333081i	−0.990474	−	0.137702i	$-0.956028\pi$
$179$	−1.44794	+	4.45632i	−0.108224	+	0.333081i	0.882249	+	0.470783i	$0.156028\pi$
$180$		0			0
$181$	10.2750	−	7.46519i	0.763731	−	0.554883i	−0.136321	−	0.990665i	$-0.543528\pi$
$181$	10.2750	−	7.46519i	0.763731	−	0.554883i	0.900053	+	0.435781i	$0.143528\pi$
$182$		0			0
$183$	−1.08160	−	3.32881i	−0.0799539	−	0.246073i
$184$		0			0
$185$	7.71198	+	5.60308i	0.566996	+	0.411947i
$186$		0			0
$187$	−0.793011	−	0.581698i	−0.0579907	−	0.0425380i
$188$		0			0
$189$	15.1714	+	11.0227i	1.10356	+	0.801781i
$190$		0			0
$191$	−6.41165	−	19.7330i	−0.463931	−	1.42783i	−0.860322	−	0.509751i	$-0.829738\pi$
$191$	−6.41165	−	19.7330i	−0.463931	−	1.42783i	0.396391	−	0.918082i	$-0.370262\pi$
$192$		0			0
$193$	18.0737	−	13.1313i	1.30097	−	0.945213i	0.301009	−	0.953621i	$-0.402677\pi$
$193$	18.0737	−	13.1313i	1.30097	−	0.945213i	0.999965	+	0.00840857i	$0.00267656\pi$
$194$		0			0
$195$	6.58297	−	20.2603i	0.471416	−	1.45087i
$196$		0			0
$197$	−4.46864			−0.318378			−0.159189	−	0.987248i	$-0.550888\pi$
$197$	−4.46864			−0.318378			−0.159189	+	0.987248i	$0.550888\pi$
$198$		0			0
$199$	−17.2749			−1.22458			−0.612291	−	0.790632i	$-0.709752\pi$
$199$	−17.2749			−1.22458			−0.612291	+	0.790632i	$0.709752\pi$
$200$		0			0
$201$	2.22659	−	6.85275i	0.157052	−	0.483356i
$202$		0			0
$203$	10.7502	−	7.81047i	0.754515	−	0.548187i
$204$		0			0
$205$	8.38881	+	25.8181i	0.585900	+	1.80321i
$206$		0			0
$207$	10.2469	+	7.44478i	0.712206	+	0.517448i
$208$		0			0
$209$	9.52304	+	0.0434113i	0.658723	+	0.00300282i
$210$		0			0
$211$	12.1114	+	8.79946i	0.833784	+	0.605780i	0.920627	−	0.390442i	$-0.127678\pi$
$211$	12.1114	+	8.79946i	0.833784	+	0.605780i	−0.0868431	+	0.996222i	$0.527678\pi$
$212$		0			0
$213$	−0.925778	−	2.84925i	−0.0634333	−	0.195227i
$214$		0			0
$215$	12.2679	−	8.91312i	0.836661	−	0.607870i
$216$		0			0
$217$	6.05237	−	18.6273i	0.410861	−	1.26450i
$218$		0			0
$219$	−7.65252			−0.517110
$220$		0			0
$221$	−1.34981			−0.0907980
$222$		0			0
$223$	−8.11417	+	24.9728i	−0.543365	+	1.67230i	0.181482	+	0.983394i	$0.441911\pi$
$223$	−8.11417	+	24.9728i	−0.543365	+	1.67230i	−0.724847	+	0.688910i	$0.758089\pi$
$224$		0			0
$225$	10.6696	−	7.75194i	0.711309	−	0.516796i
$226$		0			0
$227$	6.11096	+	18.8076i	0.405599	+	1.24830i	0.920394	+	0.390992i	$0.127868\pi$
$227$	6.11096	+	18.8076i	0.405599	+	1.24830i	−0.514795	+	0.857313i	$0.672132\pi$
$228$		0			0
$229$	9.15903	+	6.65442i	0.605246	+	0.439737i	0.847737	−	0.530417i	$-0.177965\pi$
$229$	9.15903	+	6.65442i	0.605246	+	0.439737i	−0.242491	+	0.970154i	$0.577965\pi$
$230$		0			0
$231$	−4.26055	−	13.3189i	−0.280324	−	0.876320i
$232$		0			0
$233$	−20.9749	−	15.2392i	−1.37411	−	0.998352i	−0.997403	−	0.0720214i	$-0.977055\pi$
$233$	−20.9749	−	15.2392i	−1.37411	−	0.998352i	−0.376711	−	0.926331i	$-0.622945\pi$
$234$		0			0
$235$	5.90591	+	18.1765i	0.385259	+	1.18571i
$236$		0			0
$237$	0.625918	−	0.454756i	0.0406577	−	0.0295396i
$238$		0			0
$239$	−2.22331	+	6.84265i	−0.143814	+	0.442614i	−0.996857	−	0.0792274i	$-0.974755\pi$
$239$	−2.22331	+	6.84265i	−0.143814	+	0.442614i	0.853043	+	0.521841i	$0.174755\pi$
$240$		0			0
$241$	5.62893			0.362591			0.181296	−	0.983429i	$-0.441971\pi$
$241$	5.62893			0.362591			0.181296	+	0.983429i	$0.441971\pi$
$242$		0			0
$243$	−13.4338			−0.861780
$244$		0			0
$245$	−5.16805	+	15.9056i	−0.330174	+	1.01617i
$246$		0			0
$247$	10.5741	−	7.68254i	0.672814	−	0.488828i
$248$		0			0
$249$	4.17276	+	12.8424i	0.264438	+	0.813856i
$250$		0			0
$251$	9.26628	+	6.73235i	0.584883	+	0.424942i	0.840481	−	0.541841i	$-0.182273\pi$
$251$	9.26628	+	6.73235i	0.584883	+	0.424942i	−0.255598	+	0.966783i	$0.582273\pi$
$252$		0			0
$253$	−8.84050	−	27.6363i	−0.555798	−	1.73748i
$254$		0			0
$255$	1.12270	+	0.815693i	0.0703065	+	0.0510807i
$256$		0			0
$257$	9.25759	+	28.4919i	0.577472	+	1.77728i	0.627602	+	0.778534i	$0.284037\pi$
$257$	9.25759	+	28.4919i	0.577472	+	1.77728i	−0.0501297	+	0.998743i	$0.515963\pi$
$258$		0			0
$259$	6.94794	−	5.04797i	0.431724	−	0.313666i
$260$		0			0
$261$	−1.75666	+	5.40644i	−0.108735	+	0.334650i
$262$		0			0
$263$	19.9162			1.22808			0.614042	−	0.789273i	$-0.289542\pi$
$263$	19.9162			1.22808			0.614042	+	0.789273i	$0.289542\pi$
$264$		0			0
$265$	−45.4334			−2.79095
$266$		0			0
$267$	0.914732	−	2.81526i	0.0559807	−	0.172291i
$268$		0			0
$269$	−8.16816	+	5.93451i	−0.498021	+	0.361834i	−0.808261	−	0.588825i	$-0.799591\pi$
$269$	−8.16816	+	5.93451i	−0.498021	+	0.361834i	0.310239	+	0.950658i	$0.399591\pi$
$270$		0			0
$271$	4.42081	+	13.6058i	0.268545	+	0.826496i	0.990855	+	0.134928i	$0.0430802\pi$
$271$	4.42081	+	13.6058i	0.268545	+	0.826496i	−0.722311	+	0.691569i	$0.756920\pi$
$272$		0			0
$273$	−15.5270	−	11.2810i	−0.939736	−	0.682758i
$274$		0			0
$275$	−30.2127	−	0.137726i	−1.82189	−	0.00830520i
$276$		0			0
$277$	−9.29180	−	6.75089i	−0.558290	−	0.405622i	0.272543	−	0.962144i	$-0.412135\pi$
$277$	−9.29180	−	6.75089i	−0.558290	−	0.405622i	−0.830833	+	0.556522i	$0.812135\pi$
$278$		0			0
$279$	2.58924	+	7.96886i	0.155014	+	0.477083i
$280$		0			0
$281$	−12.1855	+	8.85327i	−0.726925	+	0.528142i	−0.888589	−	0.458704i	$-0.848314\pi$
$281$	−12.1855	+	8.85327i	−0.726925	+	0.528142i	0.161664	+	0.986846i	$0.448314\pi$
$282$		0			0
$283$	4.57017	−	14.0655i	0.271669	−	0.836110i	−0.718413	−	0.695617i	$-0.755131\pi$
$283$	4.57017	−	14.0655i	0.271669	−	0.836110i	0.990082	−	0.140493i	$-0.0448688\pi$
$284$		0			0
$285$	−13.4376			−0.795974
$286$		0			0
$287$	24.4573			1.44367
$288$		0			0
$289$	−5.22612	+	16.0843i	−0.307419	+	0.946137i
$290$		0			0
$291$	−9.97315	+	7.24592i	−0.584637	+	0.424763i
$292$		0			0
$293$	−0.904696	−	2.78437i	−0.0528529	−	0.162665i	0.921146	−	0.389217i	$-0.127254\pi$
$293$	−0.904696	−	2.78437i	−0.0528529	−	0.162665i	−0.973999	+	0.226553i	$0.927254\pi$
$294$		0			0
$295$	2.12864	+	1.54655i	0.123934	+	0.0900434i
$296$		0			0
$297$	14.8194	+	10.8705i	0.859907	+	0.630768i
$298$		0			0
$299$	−32.2180	−	23.4077i	−1.86321	−	1.35370i
$300$		0			0
$301$	−4.22166	−	12.9929i	−0.243333	−	0.748901i
$302$		0			0
$303$	−0.745722	+	0.541799i	−0.0428406	+	0.0311255i
$304$		0			0
$305$	−3.26093	+	10.0361i	−0.186720	+	0.574666i
$306$		0			0
$307$	−3.20827			−0.183105			−0.0915527	−	0.995800i	$-0.529183\pi$
$307$	−3.20827			−0.183105			−0.0915527	+	0.995800i	$0.529183\pi$
$308$		0			0
$309$	12.0062			0.683009
$310$		0			0
$311$	6.16756	−	18.9818i	0.349730	−	1.07636i	−0.609272	−	0.792961i	$-0.708538\pi$
$311$	6.16756	−	18.9818i	0.349730	−	1.07636i	0.959002	−	0.283398i	$-0.0914617\pi$
$312$		0			0
$313$	0.864755	−	0.628281i	0.0488788	−	0.0355126i	−0.563078	−	0.826404i	$-0.690383\pi$
$313$	0.864755	−	0.628281i	0.0488788	−	0.0355126i	0.611956	+	0.790891i	$0.290383\pi$
$314$		0			0
$315$	−5.68696	−	17.5027i	−0.320424	−	0.986163i
$316$		0			0
$317$	8.73600	+	6.34707i	0.490662	+	0.356487i	0.805439	−	0.592679i	$-0.201930\pi$
$317$	8.73600	+	6.34707i	0.490662	+	0.356487i	−0.314777	+	0.949166i	$0.601930\pi$
$318$		0			0
$319$	10.5705	−	7.60656i	0.591836	−	0.425886i
$320$		0			0
$321$	−5.34487	−	3.88328i	−0.298322	−	0.216743i
$322$		0			0
$323$	0.263110	+	0.809768i	0.0146398	+	0.0450567i
$324$		0			0
$325$	−33.5473	+	24.3735i	−1.86087	+	1.35200i
$326$		0			0
$327$	−6.52627	+	20.0858i	−0.360904	+	1.11075i
$328$		0			0
$329$	17.2185			0.949285
$330$		0			0
$331$	−5.24230			−0.288143			−0.144071	−	0.989567i	$-0.546019\pi$
$331$	−5.24230			−0.288143			−0.144071	+	0.989567i	$0.546019\pi$
$332$		0			0
$333$	−1.13534	+	3.49423i	−0.0622165	+	0.191483i
$334$		0			0
$335$	−17.5749	+	12.7689i	−0.960218	+	0.697639i
$336$		0			0
$337$	−10.1253	−	31.1624i	−0.551559	−	1.69752i	−0.704862	−	0.709344i	$-0.748991\pi$
$337$	−10.1253	−	31.1624i	−0.551559	−	1.69752i	0.153303	−	0.988179i	$-0.451009\pi$
$338$		0			0
$339$	−2.09292	−	1.52059i	−0.113672	−	0.0825874i
$340$		0			0
$341$	6.01480	−	18.2285i	0.325719	−	0.987127i
$342$		0			0
$343$	−6.97506	−	5.06768i	−0.376618	−	0.273629i
$344$		0			0
$345$	12.6520	+	38.9388i	0.681160	+	2.09640i
$346$		0			0
$347$	10.6495	−	7.73735i	0.571698	−	0.415363i	−0.264024	−	0.964516i	$-0.585050\pi$
$347$	10.6495	−	7.73735i	0.571698	−	0.415363i	0.835721	+	0.549154i	$0.185050\pi$
$348$		0			0
$349$	−3.39895	+	10.4609i	−0.181942	+	0.559959i	−0.999882	−	0.0153436i	$-0.995116\pi$
$349$	−3.39895	+	10.4609i	−0.181942	+	0.559959i	0.817941	+	0.575303i	$0.195116\pi$
$350$		0			0
$351$	25.2245			1.34639
$352$		0			0
$353$	−9.43370			−0.502105			−0.251053	−	0.967973i	$-0.580777\pi$
$353$	−9.43370			−0.502105			−0.251053	+	0.967973i	$0.580777\pi$
$354$		0			0
$355$	−2.79115	+	8.59027i	−0.148139	+	0.455924i
$356$		0			0
$357$	1.01148	−	0.734881i	0.0535330	−	0.0388940i
$358$		0			0
$359$	−1.93707	−	5.96168i	−0.102235	−	0.314645i	0.886837	−	0.462083i	$-0.152898\pi$
$359$	−1.93707	−	5.96168i	−0.102235	−	0.314645i	−0.989071	+	0.147437i	$0.952898\pi$
$360$		0			0
$361$	8.70133	+	6.32188i	0.457965	+	0.332731i
$362$		0			0
$363$	−4.11602	−	13.0721i	−0.216035	−	0.686109i
$364$		0			0
$365$	18.6654	+	13.5612i	0.976994	+	0.709828i
$366$		0			0
$367$	−2.24200	−	6.90018i	−0.117032	−	0.360186i	0.875334	−	0.483519i	$-0.160642\pi$
$367$	−2.24200	−	6.90018i	−0.117032	−	0.360186i	−0.992365	+	0.123333i	$0.960642\pi$
$368$		0			0
$369$	−8.46472	+	6.14998i	−0.440656	+	0.320155i
$370$		0			0
$371$	−12.6487	+	38.9288i	−0.656690	+	2.02108i
$372$		0			0
$373$	−8.24993			−0.427165			−0.213583	−	0.976925i	$-0.568513\pi$
$373$	−8.24993			−0.427165			−0.213583	+	0.976925i	$0.568513\pi$
$374$		0			0
$375$	19.2324			0.993157
$376$		0			0
$377$	5.52326	−	16.9989i	0.284463	−	0.875486i
$378$		0			0
$379$	−25.8510	+	18.7819i	−1.32788	+	0.964759i	−0.328079	+	0.944650i	$0.606401\pi$
$379$	−25.8510	+	18.7819i	−1.32788	+	0.964759i	−0.999798	+	0.0201088i	$0.993599\pi$
$380$		0			0
$381$	3.86012	+	11.8802i	0.197760	+	0.608643i
$382$		0			0
$383$	4.34134	+	3.15417i	0.221832	+	0.161170i	0.693151	−	0.720792i	$-0.256222\pi$
$383$	4.34134	+	3.15417i	0.221832	+	0.161170i	−0.471319	+	0.881963i	$0.656222\pi$
$384$		0			0
$385$	−13.2108	+	40.0367i	−0.673284	+	2.04046i
$386$		0			0
$387$	4.72831	+	3.43532i	0.240354	+	0.174627i
$388$		0			0
$389$	−5.02852	−	15.4762i	−0.254956	−	0.784673i	−0.993838	−	0.110839i	$-0.964646\pi$
$389$	−5.02852	−	15.4762i	−0.254956	−	0.784673i	0.738882	−	0.673834i	$-0.235354\pi$
$390$		0			0
$391$	2.09878	−	1.52485i	0.106140	−	0.0771152i
$392$		0			0
$393$	7.22939	−	22.2498i	0.364675	−	1.12235i
$394$		0			0
$395$	−2.33258			−0.117365
$396$		0			0
$397$	−16.7112			−0.838709			−0.419355	−	0.907822i	$-0.637744\pi$
$397$	−16.7112			−0.838709			−0.419355	+	0.907822i	$0.637744\pi$
$398$		0			0
$399$	−3.74105	+	11.5138i	−0.187287	+	0.576410i
$400$		0			0
$401$	−1.17469	+	0.853462i	−0.0586612	+	0.0426199i	−0.616729	−	0.787175i	$-0.711543\pi$
$401$	−1.17469	+	0.853462i	−0.0586612	+	0.0426199i	0.558068	+	0.829795i	$0.311543\pi$
$402$		0			0
$403$	−8.14105	−	25.0556i	−0.405534	−	1.24811i
$404$		0			0
$405$	−7.78187	−	5.65386i	−0.386684	−	0.280943i
$406$		0			0
$407$	6.83183	−	4.91619i	0.338641	−	0.243686i
$408$		0			0
$409$	2.22515	+	1.61667i	0.110027	+	0.0799392i	0.641438	−	0.767175i	$-0.278338\pi$
$409$	2.22515	+	1.61667i	0.110027	+	0.0799392i	−0.531411	+	0.847114i	$0.678338\pi$
$410$		0			0
$411$	−1.35863	−	4.18145i	−0.0670165	−	0.206256i
$412$		0			0
$413$	1.91775	−	1.39333i	0.0943663	−	0.0685611i
$414$		0			0
$415$	12.5805	−	38.7190i	0.617555	−	1.90064i
$416$		0			0
$417$	−19.9251			−0.975739
$418$		0			0
$419$	29.0769			1.42050			0.710249	−	0.703951i	$-0.248582\pi$
$419$	29.0769			1.42050			0.710249	+	0.703951i	$0.248582\pi$
$420$		0			0
$421$	7.20468	−	22.1737i	0.351135	−	1.08068i	−0.607082	−	0.794639i	$-0.707660\pi$
$421$	7.20468	−	22.1737i	0.351135	−	1.08068i	0.958217	−	0.286042i	$-0.0923398\pi$
$422$		0			0
$423$	−5.95935	+	4.32972i	−0.289754	+	0.210518i
$424$		0			0
$425$	−0.834739	−	2.56906i	−0.0404908	−	0.124618i
$426$		0			0
$427$	7.69142	+	5.58814i	0.372214	+	0.270429i
$428$		0			0
$429$	−15.1667	−	11.1252i	−0.732255	−	0.537132i
$430$		0			0
$431$	−16.4067	−	11.9202i	−0.790282	−	0.574174i	0.117765	−	0.993041i	$-0.462427\pi$
$431$	−16.4067	−	11.9202i	−0.790282	−	0.574174i	−0.908047	+	0.418868i	$0.862427\pi$
$432$		0			0
$433$	−11.2547	−	34.6384i	−0.540866	−	1.66461i	−0.730621	−	0.682783i	$-0.760769\pi$
$433$	−11.2547	−	34.6384i	−0.540866	−	1.66461i	0.189755	−	0.981831i	$-0.439231\pi$
$434$		0			0
$435$	−14.8664	+	10.8011i	−0.712791	+	0.517873i
$436$		0			0
$437$	−7.76257	+	23.8907i	−0.371334	+	1.14285i
$438$		0			0
$439$	0.374597			0.0178785			0.00893926	−	0.999960i	$-0.497155\pi$
$439$	0.374597			0.0178785			0.00893926	+	0.999960i	$0.497155\pi$
$440$		0			0
$441$	−6.44587			−0.306946
$442$		0			0
$443$	−3.03925	+	9.35386i	−0.144399	+	0.444415i	−0.996933	−	0.0782566i	$-0.975065\pi$
$443$	−3.03925	+	9.35386i	−0.144399	+	0.444415i	0.852534	+	0.522672i	$0.175065\pi$
$444$		0			0
$445$	−7.22014	+	5.24574i	−0.342267	+	0.248672i
$446$		0			0
$447$	−7.70544	−	23.7149i	−0.364455	−	1.12168i
$448$		0			0
$449$	14.0447	+	10.2041i	0.662811	+	0.481561i	0.867611	−	0.497243i	$-0.165654\pi$
$449$	14.0447	+	10.2041i	0.662811	+	0.481561i	−0.204800	+	0.978804i	$0.565654\pi$
$450$		0			0
$451$	23.9692	+	0.109265i	1.12866	+	0.00514507i
$452$		0			0
$453$	3.78321	+	2.74866i	0.177751	+	0.129144i
$454$		0			0
$455$	17.8808	+	55.0316i	0.838267	+	2.57992i
$456$		0			0
$457$	33.2966	−	24.1914i	1.55755	−	1.13163i	0.619567	−	0.784944i	$-0.287308\pi$
$457$	33.2966	−	24.1914i	1.55755	−	1.13163i	0.937983	−	0.346682i	$-0.112692\pi$
$458$		0			0
$459$	−0.507778	+	1.56278i	−0.0237011	+	0.0729443i
$460$		0			0
$461$	24.0893			1.12195			0.560975	−	0.827833i	$-0.310426\pi$
$461$	24.0893			1.12195			0.560975	+	0.827833i	$0.310426\pi$
$462$		0			0
$463$	−18.6542			−0.866932			−0.433466	−	0.901170i	$-0.642710\pi$
$463$	−18.6542			−0.866932			−0.433466	+	0.901170i	$0.642710\pi$
$464$		0			0
$465$	−8.36982	+	25.7596i	−0.388141	+	1.19457i
$466$		0			0
$467$	−11.1634	+	8.11068i	−0.516580	+	0.375318i	−0.815314	−	0.579019i	$-0.803436\pi$
$467$	−11.1634	+	8.11068i	−0.516580	+	0.375318i	0.298734	+	0.954336i	$0.403436\pi$
$468$		0			0
$469$	6.04794	+	18.6136i	0.279268	+	0.859498i
$470$		0			0
$471$	10.0509	+	7.30242i	0.463122	+	0.336478i
$472$		0			0
$473$	−4.07936	−	12.7525i	−0.187569	−	0.586361i
$474$		0			0
$475$	21.1612	+	15.3745i	0.970940	+	0.705429i
$476$		0			0
$477$	−5.41121	−	16.6540i	−0.247762	−	0.762534i
$478$		0			0
$479$	−5.94317	+	4.31796i	−0.271550	+	0.197293i	−0.715224	−	0.698896i	$-0.753675\pi$
$479$	−5.94317	+	4.31796i	−0.271550	+	0.197293i	0.443673	+	0.896189i	$0.353675\pi$
$480$		0			0
$481$	3.56973	−	10.9865i	0.162766	−	0.500942i
$482$		0			0
$483$	36.8864			1.67839
$484$		0			0
$485$	37.1664			1.68764
$486$		0			0
$487$	3.40472	−	10.4787i	0.154283	−	0.474833i	−0.843805	−	0.536650i	$-0.819690\pi$
$487$	3.40472	−	10.4787i	0.154283	−	0.474833i	0.998088	+	0.0618170i	$0.0196895\pi$
$488$		0			0
$489$	−0.781221	+	0.567590i	−0.0353280	+	0.0256673i
$490$		0			0
$491$	−9.83538	−	30.2702i	−0.443864	−	1.36607i	−0.883724	−	0.468008i	$-0.844972\pi$
$491$	−9.83538	−	30.2702i	−0.443864	−	1.36607i	0.439860	−	0.898066i	$-0.355028\pi$
$492$		0			0
$493$	0.941975	+	0.684385i	0.0424244	+	0.0308232i
$494$		0			0
$495$	−5.49527	−	17.1788i	−0.246994	−	0.772128i
$496$		0			0
$497$	6.58337	+	4.78310i	0.295305	+	0.214551i
$498$		0			0
$499$	−6.78029	−	20.8676i	−0.303528	−	0.934162i	−0.980223	−	0.197898i	$-0.936588\pi$
$499$	−6.78029	−	20.8676i	−0.303528	−	0.934162i	0.676695	−	0.736264i	$-0.263412\pi$
$500$		0			0
$501$	13.2475	−	9.62489i	0.591856	−	0.430008i
$502$		0			0
$503$	−11.4228	+	35.1557i	−0.509317	+	1.56752i	0.284074	+	0.958802i	$0.408314\pi$
$503$	−11.4228	+	35.1557i	−0.509317	+	1.56752i	−0.793390	+	0.608713i	$0.791686\pi$
$504$		0			0
$505$	2.77904			0.123666
$506$		0			0
$507$	−9.61913			−0.427200
$508$		0			0
$509$	−6.18315	+	19.0298i	−0.274063	+	0.843480i	0.715403	+	0.698713i	$0.246243\pi$
$509$	−6.18315	+	19.0298i	−0.274063	+	0.843480i	−0.989466	+	0.144767i	$0.953757\pi$
$510$		0			0
$511$	16.8162	−	12.2177i	0.743906	−	0.540479i
$512$		0			0
$513$	−4.91686	−	15.1325i	−0.217085	−	0.668117i
$514$		0			0
$515$	−29.2846	−	21.2765i	−1.29043	−	0.937555i
$516$		0			0
$517$	16.8748	+	0.0769248i	0.742154	+	0.00338315i
$518$		0			0
$519$	12.1540	+	8.83037i	0.533500	+	0.387610i
$520$		0			0
$521$	0.173952	+	0.535370i	0.00762099	+	0.0234550i	0.954795	−	0.297266i	$-0.0960748\pi$
$521$	0.173952	+	0.535370i	0.00762099	+	0.0234550i	−0.947174	+	0.320721i	$0.896075\pi$
$522$		0			0
$523$	−9.23048	+	6.70633i	−0.403621	+	0.293247i	−0.771014	−	0.636818i	$-0.780250\pi$
$523$	−9.23048	+	6.70633i	−0.403621	+	0.293247i	0.367394	+	0.930066i	$0.380250\pi$
$524$		0			0
$525$	11.8688	−	36.5285i	0.517998	−	1.59423i
$526$		0			0
$527$	1.71619			0.0747586
$528$		0			0
$529$	53.5382			2.32775
$530$		0			0
$531$	−0.313374	+	0.964467i	−0.0135993	+	0.0418543i
$532$		0			0
$533$	26.6146	−	19.3367i	1.15281	−	0.837564i
$534$		0			0
$535$	6.15515	+	18.9436i	0.266110	+	0.819003i
$536$		0			0
$537$	−4.72289	−	3.43138i	−0.203808	−	0.148075i
$538$		0			0
$539$	11.9068	+	8.73402i	0.512863	+	0.376201i
$540$		0			0
$541$	15.7454	+	11.4397i	0.676949	+	0.491832i	0.872344	−	0.488893i	$-0.162599\pi$
$541$	15.7454	+	11.4397i	0.676949	+	0.491832i	−0.195395	+	0.980725i	$0.562599\pi$
$542$		0			0
$543$	4.88973	+	15.0491i	0.209839	+	0.645817i
$544$		0			0
$545$	51.5130	−	37.4264i	2.20657	−	1.60317i
$546$		0			0
$547$	−2.08944	+	6.43062i	−0.0893379	+	0.274954i	−0.985737	−	0.168295i	$-0.946174\pi$
$547$	−2.08944	+	6.43062i	−0.0893379	+	0.274954i	0.896399	+	0.443248i	$0.146174\pi$
$548$		0			0
$549$	−4.06720			−0.173584
$550$		0			0
$551$	−11.2745			−0.480308
$552$		0			0
$553$	−0.649394	+	1.99863i	−0.0276150	+	0.0849903i
$554$		0			0
$555$	−9.60830	+	6.98084i	−0.407850	+	0.296320i
$556$		0			0
$557$	−6.21042	−	19.1137i	−0.263144	−	0.809874i	−0.992115	−	0.125330i	$-0.960001\pi$
$557$	−6.21042	−	19.1137i	−0.263144	−	0.809874i	0.728971	−	0.684545i	$-0.239999\pi$
$558$		0			0
$559$	−14.8667	−	10.8013i	−0.628793	−	0.456845i
$560$		0			0
$561$	0.994573	−	0.715695i	0.0419909	−	0.0302167i
$562$		0			0
$563$	9.78196	+	7.10701i	0.412261	+	0.299525i	0.774516	−	0.632554i	$-0.217993\pi$
$563$	9.78196	+	7.10701i	0.412261	+	0.299525i	−0.362256	+	0.932079i	$0.617993\pi$
$564$		0			0
$565$	2.41020	+	7.41784i	0.101398	+	0.312071i
$566$		0			0
$567$	−7.01090	+	5.09372i	−0.294430	+	0.213916i
$568$		0			0
$569$	−5.27050	+	16.2209i	−0.220951	+	0.680017i	0.777726	+	0.628603i	$0.216373\pi$
$569$	−5.27050	+	16.2209i	−0.220951	+	0.680017i	−0.998677	+	0.0514142i	$0.983627\pi$
$570$		0			0
$571$	−9.40036			−0.393393			−0.196696	−	0.980464i	$-0.563021\pi$
$571$	−9.40036			−0.393393			−0.196696	+	0.980464i	$0.563021\pi$
$572$		0			0
$573$	25.8505			1.07992
$574$		0			0
$575$	24.6274	−	75.7954i	1.02703	−	3.16089i
$576$		0			0
$577$	−28.7669	+	20.9004i	−1.19758	+	0.870095i	−0.994045	−	0.108971i	$-0.965244\pi$
$577$	−28.7669	+	20.9004i	−1.19758	+	0.870095i	−0.203539	+	0.979067i	$0.565244\pi$
$578$		0			0
$579$	8.60107	+	26.4714i	0.357448	+	1.10011i
$580$		0			0
$581$	−29.6732	−	21.5589i	−1.23105	−	0.894413i
$582$		0			0
$583$	−12.5702	+	38.0954i	−0.520605	+	1.57775i
$584$		0			0
$585$	−20.0267	−	14.5503i	−0.828004	−	0.601580i
$586$		0			0
$587$	−11.1482	−	34.3107i	−0.460136	−	1.41615i	−0.864998	−	0.501775i	$-0.832680\pi$
$587$	−11.1482	−	34.3107i	−0.460136	−	1.41615i	0.404862	−	0.914378i	$-0.367320\pi$
$588$		0			0
$589$	−13.4443	+	9.76784i	−0.553962	+	0.402477i
$590$		0			0
$591$	1.72044	−	5.29496i	0.0707693	−	0.217806i
$592$		0			0
$593$	−6.57566			−0.270030			−0.135015	−	0.990844i	$-0.543108\pi$
$593$	−6.57566			−0.270030			−0.135015	+	0.990844i	$0.543108\pi$
$594$		0			0
$595$	−3.76942			−0.154531
$596$		0			0
$597$	6.65086	−	20.4692i	0.272201	−	0.837750i
$598$		0			0
$599$	−7.87951	+	5.72480i	−0.321948	+	0.233909i	−0.737006	−	0.675886i	$-0.763761\pi$
$599$	−7.87951	+	5.72480i	−0.321948	+	0.233909i	0.415058	+	0.909795i	$0.363761\pi$
$600$		0			0
$601$	−1.49359	−	4.59680i	−0.0609248	−	0.187507i	0.915962	−	0.401266i	$-0.131430\pi$
$601$	−1.49359	−	4.59680i	−0.0609248	−	0.187507i	−0.976887	+	0.213758i	$0.931430\pi$
$602$		0			0
$603$	−6.77375	−	4.92142i	−0.275849	−	0.200416i
$604$		0			0
$605$	−13.1260	+	39.1786i	−0.533648	+	1.59284i
$606$		0			0
$607$	−4.77369	−	3.46829i	−0.193758	−	0.140774i	0.486677	−	0.873582i	$-0.338209\pi$
$607$	−4.77369	−	3.46829i	−0.193758	−	0.140774i	−0.680435	+	0.732809i	$0.738209\pi$
$608$		0			0
$609$	5.11589	+	15.7451i	0.207306	+	0.638024i
$610$		0			0
$611$	18.7373	−	13.6135i	0.758030	−	0.550741i
$612$		0			0
$613$	−3.76108	+	11.5754i	−0.151908	+	0.467526i	−0.997835	−	0.0657741i	$-0.979048\pi$
$613$	−3.76108	+	11.5754i	−0.151908	+	0.467526i	0.845926	+	0.533300i	$0.179048\pi$
$614$		0			0
$615$	−33.8219			−1.36383
$616$		0			0
$617$	−16.5622			−0.666770			−0.333385	−	0.942791i	$-0.608191\pi$
$617$	−16.5622			−0.666770			−0.333385	+	0.942791i	$0.608191\pi$
$618$		0			0
$619$	7.98261	−	24.5679i	0.320848	−	0.987469i	−0.652432	−	0.757847i	$-0.726251\pi$
$619$	7.98261	−	24.5679i	0.320848	−	0.987469i	0.973280	−	0.229621i	$-0.0737488\pi$
$620$		0			0
$621$	−39.2209	+	28.4957i	−1.57388	+	1.14349i
$622$		0			0
$623$	2.48462	+	7.64688i	0.0995443	+	0.306366i
$624$		0			0
$625$	−10.0612	−	7.30992i	−0.402450	−	0.292397i
$626$		0			0
$627$	−3.71783	+	11.2673i	−0.148476	+	0.449972i
$628$		0			0
$629$	0.608807	+	0.442324i	0.0242747	+	0.0176366i
$630$		0			0
$631$	−9.16147	−	28.1961i	−0.364712	−	1.12247i	−0.950161	−	0.311760i	$-0.899082\pi$
$631$	−9.16147	−	28.1961i	−0.364712	−	1.12247i	0.585449	−	0.810709i	$-0.300918\pi$
$632$		0			0
$633$	−15.0895	+	10.9632i	−0.599755	+	0.435747i
$634$		0			0
$635$	11.6380	−	35.8180i	0.461839	−	1.42139i
$636$		0			0
$637$	20.2670			0.803007
$638$		0			0
$639$	−3.48127			−0.137717
$640$		0			0
$641$	14.3296	−	44.1019i	0.565984	−	1.74192i	−0.0990245	−	0.995085i	$-0.531572\pi$
$641$	14.3296	−	44.1019i	0.565984	−	1.74192i	0.665009	−	0.746836i	$-0.268428\pi$
$642$		0			0
$643$	19.9036	−	14.4608i	0.784920	−	0.570277i	−0.121532	−	0.992588i	$-0.538781\pi$
$643$	19.9036	−	14.4608i	0.784920	−	0.570277i	0.906451	+	0.422310i	$0.138781\pi$
$644$		0			0
$645$	5.83814	+	17.9679i	0.229876	+	0.707487i
$646$		0			0
$647$	−30.5692	−	22.2098i	−1.20180	−	0.873157i	−0.207337	−	0.978270i	$-0.566480\pi$
$647$	−30.5692	−	22.2098i	−1.20180	−	0.873157i	−0.994460	+	0.105112i	$0.966480\pi$
$648$		0			0
$649$	1.88570	−	1.35695i	0.0740202	−	0.0532650i
$650$		0			0
$651$	19.7416	+	14.3431i	0.773732	+	0.562149i
$652$		0			0
$653$	−6.43293	−	19.7985i	−0.251740	−	0.774776i	−0.994455	−	0.105168i	$-0.966462\pi$
$653$	−6.43293	−	19.7985i	−0.251740	−	0.774776i	0.742715	−	0.669608i	$-0.233538\pi$
$654$		0			0
$655$	−57.0628	+	41.4586i	−2.22963	+	1.61992i
$656$		0			0
$657$	−2.74790	+	8.45715i	−0.107206	+	0.329945i
$658$		0			0
$659$	29.7663			1.15953			0.579766	−	0.814783i	$-0.303144\pi$
$659$	29.7663			1.15953			0.579766	+	0.814783i	$0.303144\pi$
$660$		0			0
$661$	−16.5979			−0.645583			−0.322791	−	0.946470i	$-0.604621\pi$
$661$	−16.5979			−0.645583			−0.322791	+	0.946470i	$0.604621\pi$
$662$		0			0
$663$	0.519679	−	1.59941i	0.0201827	−	0.0621159i
$664$		0			0
$665$	29.5288	−	21.4539i	1.14508	−	0.831947i
$666$		0			0
$667$	10.6153	+	32.6706i	0.411027	+	1.26501i
$668$		0			0
$669$	−26.4667	−	19.2292i	−1.02326	−	0.743443i
$670$		0			0
$671$	7.51295	+	5.51098i	0.290034	+	0.212749i
$672$		0			0
$673$	1.16332	+	0.845202i	0.0448427	+	0.0325801i	0.609981	−	0.792416i	$-0.291177\pi$
$673$	1.16332	+	0.845202i	0.0448427	+	0.0325801i	−0.565138	+	0.824996i	$0.691177\pi$
$674$		0			0
$675$	15.5992	+	48.0093i	0.600412	+	1.84788i
$676$		0			0
$677$	−8.40719	+	6.10818i	−0.323114	+	0.234756i	−0.737503	−	0.675344i	$-0.763995\pi$
$677$	−8.40719	+	6.10818i	−0.323114	+	0.234756i	0.414389	+	0.910100i	$0.363995\pi$
$678$		0			0
$679$	10.3472	−	31.8455i	0.397090	−	1.22212i
$680$		0			0
$681$	−24.6381			−0.944136
$682$		0			0
$683$	−13.5452			−0.518291			−0.259146	−	0.965838i	$-0.583441\pi$
$683$	−13.5452			−0.518291			−0.259146	+	0.965838i	$0.583441\pi$
$684$		0			0
$685$	−4.09618	+	12.6067i	−0.156507	+	0.481679i
$686$		0			0
$687$	−11.4112	+	8.29070i	−0.435363	+	0.316310i
$688$		0			0
$689$	17.0138	+	52.3632i	0.648175	+	1.99488i
$690$		0			0
$691$	21.3382	+	15.5031i	0.811745	+	0.589767i	0.914336	−	0.404956i	$-0.132713\pi$
$691$	21.3382	+	15.5031i	0.811745	+	0.589767i	−0.102591	+	0.994724i	$0.532713\pi$
$692$		0			0
$693$	−16.2492	−	0.0740729i	−0.617257	−	0.00281380i
$694$		0			0
$695$	48.5999	+	35.3099i	1.84350	+	1.33938i
$696$		0			0
$697$	0.662238	+	2.03816i	0.0250840	+	0.0772007i
$698$		0			0
$699$	26.1325	−	18.9864i	0.988423	−	0.718131i
$700$		0			0
$701$	5.93693	−	18.2720i	0.224235	−	0.690123i	−0.774134	−	0.633022i	$-0.781814\pi$
$701$	5.93693	−	18.2720i	0.224235	−	0.690123i	0.998368	−	0.0571011i	$-0.0181857\pi$
$702$		0			0
$703$	−7.28678			−0.274826
$704$		0			0
$705$	−23.8114			−0.896790
$706$		0			0
$707$	0.773692	−	2.38118i	0.0290977	−	0.0895534i
$708$		0			0
$709$	13.8321	−	10.0496i	0.519475	−	0.377420i	−0.296931	−	0.954899i	$-0.595963\pi$
$709$	13.8321	−	10.0496i	0.519475	−	0.377420i	0.816406	+	0.577478i	$0.195963\pi$
$710$		0			0
$711$	−0.277815	−	0.855026i	−0.0104189	−	0.0320660i
$712$		0			0
$713$	40.9631	+	29.7614i	1.53408	+	1.11457i
$714$		0			0
$715$	17.2781	+	54.0132i	0.646165	+	2.01998i
$716$		0			0
$717$	−7.25197	−	5.26887i	−0.270830	−	0.196769i
$718$		0			0
$719$	−1.77316	−	5.45721i	−0.0661276	−	0.203520i	0.912533	−	0.409003i	$-0.134123\pi$
$719$	−1.77316	−	5.45721i	−0.0661276	−	0.203520i	−0.978661	+	0.205483i	$0.934123\pi$
$720$		0			0
$721$	−26.3833	+	19.1686i	−0.982566	+	0.713876i
$722$		0			0
$723$	−2.16715	+	6.66980i	−0.0805972	+	0.248053i
$724$		0			0
$725$	35.7692			1.32843
$726$		0			0
$727$	−36.6245			−1.35833			−0.679164	−	0.733986i	$-0.737658\pi$
$727$	−36.6245			−1.35833			−0.679164	+	0.733986i	$0.737658\pi$
$728$		0			0
$729$	7.54601	−	23.2242i	0.279482	−	0.860157i
$730$		0			0
$731$	0.968462	−	0.703629i	0.0358199	−	0.0260246i
$732$		0			0
$733$	−7.89938	−	24.3118i	−0.291770	−	0.897976i	−0.984287	−	0.176575i	$-0.943498\pi$
$733$	−7.89938	−	24.3118i	−0.291770	−	0.897976i	0.692517	−	0.721401i	$-0.256502\pi$
$734$		0			0
$735$	−16.8571	−	12.2474i	−0.621783	−	0.451752i
$736$		0			0
$737$	5.84408	+	18.2692i	0.215269	+	0.672954i
$738$		0			0
$739$	39.3637	+	28.5994i	1.44802	+	1.05205i	0.986290	+	0.165024i	$0.0527702\pi$
$739$	39.3637	+	28.5994i	1.44802	+	1.05205i	0.461728	+	0.887022i	$0.347230\pi$
$740$		0			0
$741$	5.03210	+	15.4872i	0.184859	+	0.568936i
$742$		0			0
$743$	−38.4101	+	27.9065i	−1.40913	+	1.02379i	−0.415680	+	0.909511i	$0.636456\pi$
$743$	−38.4101	+	27.9065i	−1.40913	+	1.02379i	−0.993448	+	0.114281i	$0.963544\pi$
$744$		0			0
$745$	−23.2313	+	71.4986i	−0.851129	+	2.61951i
$746$		0			0
$747$	15.6911			0.574109
$748$		0			0
$749$	17.9451			0.655700
$750$		0			0
$751$	2.58144	−	7.94484i	0.0941979	−	0.289911i	−0.892846	−	0.450362i	$-0.851295\pi$
$751$	2.58144	−	7.94484i	0.0941979	−	0.289911i	0.987044	+	0.160451i	$0.0512948\pi$
$752$		0			0
$753$	−11.5448	+	8.38778i	−0.420716	+	0.305668i
$754$		0			0
$755$	−4.35674	−	13.4087i	−0.158558	−	0.487991i
$756$		0			0
$757$	2.86603	+	2.08229i	0.104168	+	0.0756823i	0.638650	−	0.769498i	$-0.279493\pi$
$757$	2.86603	+	2.08229i	0.104168	+	0.0756823i	−0.534482	+	0.845180i	$0.679493\pi$
$758$		0			0
$759$	36.1503	+	0.164793i	1.31217	+	0.00598160i
$760$		0			0
$761$	−2.77625	−	2.01706i	−0.100639	−	0.0731185i	0.536328	−	0.844010i	$-0.319811\pi$
$761$	−2.77625	−	2.01706i	−0.100639	−	0.0731185i	−0.636967	+	0.770891i	$0.719811\pi$
$762$		0			0
$763$	−17.7269	−	54.5576i	−0.641755	−	1.97512i
$764$		0			0
$765$	1.30460	−	0.947851i	0.0471681	−	0.0342696i
$766$		0			0
$767$	0.985307	−	3.03246i	0.0355774	−	0.109496i
$768$		0			0
$769$	−34.2558			−1.23530			−0.617648	−	0.786455i	$-0.711914\pi$
$769$	−34.2558			−1.23530			−0.617648	+	0.786455i	$0.711914\pi$
$770$		0			0
$771$	−37.3247			−1.34422
$772$		0			0
$773$	−8.73080	+	26.8706i	−0.314025	+	0.966469i	0.662129	+	0.749390i	$0.269653\pi$
$773$	−8.73080	+	26.8706i	−0.314025	+	0.966469i	−0.976154	+	0.217079i	$0.930347\pi$
$774$		0			0
$775$	42.6532	−	30.9893i	1.53215	−	1.11317i
$776$		0			0
$777$	3.30645	+	10.1762i	0.118618	+	0.365069i
$778$		0			0
$779$	−16.7881	−	12.1973i	−0.601498	−	0.437014i
$780$		0			0
$781$	6.43061	+	4.71705i	0.230105	+	0.168789i
$782$		0			0
$783$	−17.6031	−	12.7894i	−0.629085	−	0.457057i
$784$		0			0
$785$	−11.5746	−	35.6230i	−0.413116	−	1.27144i
$786$		0			0
$787$	−32.8646	+	23.8775i	−1.17150	+	0.851141i	−0.991187	−	0.132469i	$-0.957710\pi$
$787$	−32.8646	+	23.8775i	−1.17150	+	0.851141i	−0.180308	+	0.983610i	$0.557710\pi$
$788$		0			0
$789$	−7.66777	+	23.5990i	−0.272980	+	0.840146i
$790$		0			0
$791$	7.02686			0.249846
$792$		0			0
$793$	12.7880			0.454116
$794$		0			0
$795$	17.4919	−	53.8346i	0.620375	−	1.90932i
$796$		0			0
$797$	17.4308	−	12.6642i	0.617432	−	0.448591i	−0.234592	−	0.972094i	$-0.575375\pi$
$797$	17.4308	−	12.6642i	0.617432	−	0.448591i	0.852024	+	0.523503i	$0.175375\pi$
$798$		0			0
$799$	0.466230	+	1.43491i	0.0164940	+	0.0507634i
$800$		0			0
$801$	−2.78280	−	2.02182i	−0.0983255	−	0.0714377i
$802$		0			0
$803$	16.5352	−	11.8987i	0.583515	−	0.419897i
$804$		0			0
$805$	−89.9706	−	65.3674i	−3.17105	−	2.30390i
$806$		0			0
$807$	−3.88713	−	11.9634i	−0.136834	−	0.421131i
$808$		0			0
$809$	−32.1992	+	23.3941i	−1.13206	+	0.822491i	−0.985994	−	0.166783i	$-0.946662\pi$
$809$	−32.1992	+	23.3941i	−1.13206	+	0.822491i	−0.146068	+	0.989274i	$0.546662\pi$
$810$		0			0
$811$	3.68040	−	11.3271i	0.129236	−	0.397749i	−0.865413	−	0.501060i	$-0.832944\pi$
$811$	3.68040	−	11.3271i	0.129236	−	0.397749i	0.994649	+	0.103311i	$0.0329437\pi$
$812$		0			0
$813$	−17.8238			−0.625107
$814$		0			0
$815$	2.91134			0.101980
$816$		0			0
$817$	−3.58196	+	11.0241i	−0.125317	+	0.385686i
$818$		0			0
$819$	−18.0427	+	13.1088i	−0.630461	+	0.458057i
$820$		0			0
$821$	8.28925	+	25.5117i	0.289297	+	0.890364i	0.985078	+	0.172110i	$0.0550584\pi$
$821$	8.28925	+	25.5117i	0.289297	+	0.890364i	−0.695781	+	0.718254i	$0.744942\pi$
$822$		0			0
$823$	−10.4787	−	7.61322i	−0.365264	−	0.265380i	0.389980	−	0.920823i	$-0.372482\pi$
$823$	−10.4787	−	7.61322i	−0.365264	−	0.265380i	−0.755245	+	0.655443i	$0.772482\pi$
$824$		0			0
$825$	11.7951	−	35.7464i	0.410654	−	1.24453i
$826$		0			0
$827$	21.2851	+	15.4645i	0.740156	+	0.537755i	0.892760	−	0.450533i	$-0.148766\pi$
$827$	21.2851	+	15.4645i	0.740156	+	0.537755i	−0.152604	+	0.988287i	$0.548766\pi$
$828$		0			0
$829$	6.50852	+	20.0312i	0.226050	+	0.695711i	0.998183	+	0.0602502i	$0.0191899\pi$
$829$	6.50852	+	20.0312i	0.226050	+	0.695711i	−0.772133	+	0.635461i	$0.780810\pi$
$830$		0			0
$831$	11.5766	−	8.41088i	0.401587	−	0.291770i
$832$		0			0
$833$	−0.407981	+	1.25564i	−0.0141357	+	0.0435052i
$834$		0			0
$835$	−49.3689			−1.70848
$836$		0			0
$837$	−32.0713			−1.10855
$838$		0			0
$839$	−9.48444	+	29.1901i	−0.327439	+	1.00775i	0.642889	+	0.765960i	$0.277736\pi$
$839$	−9.48444	+	29.1901i	−0.327439	+	1.00775i	−0.970328	+	0.241794i	$0.922264\pi$
$840$		0			0
$841$	10.9882	−	7.98341i	0.378904	−	0.275290i
$842$		0			0
$843$	−5.79893	−	17.8473i	−0.199726	−	0.614693i
$844$		0			0
$845$	23.4622	+	17.0463i	0.807125	+	0.586411i
$846$		0			0
$847$	29.9153	+	22.1542i	1.02790	+	0.761228i
$848$		0			0
$849$	14.9069	+	10.8305i	0.511605	+	0.371703i
$850$		0			0
$851$	6.86077	+	21.1153i	0.235184	+	0.723822i
$852$		0			0
$853$	−17.8246	+	12.9503i	−0.610302	+	0.443410i	−0.849521	−	0.527555i	$-0.823109\pi$
$853$	−17.8246	+	12.9503i	−0.610302	+	0.443410i	0.239219	+	0.970966i	$0.423109\pi$
$854$		0			0
$855$	−4.82522	+	14.8505i	−0.165019	+	0.507876i
$856$		0			0
$857$	−39.9495			−1.36465			−0.682324	−	0.731050i	$-0.739031\pi$
$857$	−39.9495			−1.36465			−0.682324	+	0.731050i	$0.739031\pi$
$858$		0			0
$859$	−6.09897			−0.208094			−0.104047	−	0.994572i	$-0.533179\pi$
$859$	−6.09897			−0.208094			−0.104047	+	0.994572i	$0.533179\pi$
$860$		0			0
$861$	−9.41610	+	28.9798i	−0.320900	+	0.987628i
$862$		0			0
$863$	−16.8480	+	12.2408i	−0.573512	+	0.416681i	−0.836379	−	0.548151i	$-0.815332\pi$
$863$	−16.8480	+	12.2408i	−0.573512	+	0.416681i	0.262867	+	0.964832i	$0.415332\pi$
$864$		0			0
$865$	−13.9965	−	43.0767i	−0.475895	−	1.46465i
$866$		0			0
$867$	−17.0465	−	12.3850i	−0.578929	−	0.420617i
$868$		0			0
$869$	−0.645363	+	1.95584i	−0.0218924	+	0.0663473i
$870$		0			0
$871$	21.2979	+	15.4739i	0.721653	+	0.524312i
$872$		0			0
$873$	4.42660	+	13.6237i	0.149818	+	0.461092i
$874$		0			0
$875$	−42.2627	+	30.7057i	−1.42874	+	1.03804i
$876$		0			0
$877$	−5.26901	+	16.2163i	−0.177922	+	0.547587i	−0.999755	−	0.0221413i	$-0.992952\pi$
$877$	−5.26901	+	16.2163i	−0.177922	+	0.547587i	0.821833	+	0.569728i	$0.192952\pi$
$878$		0			0
$879$	3.64755			0.123029
$880$		0			0
$881$	8.15303			0.274683			0.137341	−	0.990524i	$-0.456144\pi$
$881$	8.15303			0.274683			0.137341	+	0.990524i	$0.456144\pi$
$882$		0			0
$883$	12.0784	−	37.1735i	0.406471	−	1.25099i	−0.513190	−	0.858275i	$-0.671536\pi$
$883$	12.0784	−	37.1735i	0.406471	−	1.25099i	0.919661	−	0.392713i	$-0.128464\pi$
$884$		0			0
$885$	−2.65205	+	1.92683i	−0.0891478	+	0.0647697i
$886$		0			0
$887$	−3.78462	−	11.6479i	−0.127075	−	0.391097i	0.867198	−	0.497963i	$-0.165918\pi$
$887$	−3.78462	−	11.6479i	−0.127075	−	0.391097i	−0.994273	+	0.106866i	$0.965918\pi$
$888$		0			0
$889$	−27.4500	−	19.9436i	−0.920644	−	0.668887i
$890$		0			0
$891$	−6.89374	+	4.96074i	−0.230949	+	0.166191i
$892$		0			0
$893$	−11.8192	−	8.58718i	−0.395516	−	0.287359i
$894$		0			0
$895$	5.43887	+	16.7391i	0.181801	+	0.559527i
$896$		0			0
$897$	40.1402	−	29.1635i	1.34024	−	0.973742i
$898$		0			0
$899$	−7.02247	+	21.6129i	−0.234212	+	0.720832i
$900$		0			0
$901$	−3.58664			−0.119488
$902$		0			0
$903$	17.0209			0.566419
$904$		0			0
$905$	14.7422	−	45.3717i	0.490046	−	1.50821i
$906$		0			0
$907$	26.1820	−	19.0223i	0.869358	−	0.631626i	−0.0610567	−	0.998134i	$-0.519447\pi$
$907$	26.1820	−	19.0223i	0.869358	−	0.631626i	0.930415	+	0.366509i	$0.119447\pi$
$908$		0			0
$909$	0.330990	+	1.01868i	0.0109782	+	0.0337876i
$910$		0			0
$911$	−6.10557	−	4.43596i	−0.202287	−	0.146970i	0.482030	−	0.876155i	$-0.339900\pi$
$911$	−6.10557	−	4.43596i	−0.202287	−	0.146970i	−0.684317	+	0.729185i	$0.739900\pi$
$912$		0			0
$913$	−28.9847	−	21.2612i	−0.959254	−	0.703642i
$914$		0			0
$915$	−10.6365	−	7.72784i	−0.351631	−	0.255475i
$916$		0			0
$917$	19.6367	+	60.4355i	0.648460	+	1.99576i
$918$		0			0
$919$	36.9770	−	26.8654i	1.21976	−	0.886207i	0.223679	−	0.974663i	$-0.428193\pi$
$919$	36.9770	−	26.8654i	1.21976	−	0.886207i	0.996080	+	0.0884556i	$0.0281931\pi$
$920$		0			0
$921$	1.23519	−	3.80152i	0.0407009	−	0.125264i
$922$		0			0
$923$	10.9458			0.360284
$924$		0			0
$925$	23.1179			0.760113
$926$		0			0
$927$	4.31123	−	13.2686i	0.141599	−	0.435798i
$928$		0			0
$929$	−21.2649	+	15.4498i	−0.697677	+	0.506892i	−0.879175	−	0.476499i	$-0.841906\pi$
$929$	−21.2649	+	15.4498i	−0.697677	+	0.506892i	0.181498	+	0.983391i	$0.441906\pi$
$930$		0			0
$931$	−3.95051	−	12.1584i	−0.129473	−	0.398477i
$932$		0			0
$933$	20.1173	+	14.6161i	0.658610	+	0.478508i
$934$		0			0
$935$	−3.69419	−	0.0168402i	−0.120813	−	0.000550732i
$936$		0			0
$937$	8.19687	+	5.95537i	0.267780	+	0.194554i	0.713570	−	0.700584i	$-0.247077\pi$
$937$	8.19687	+	5.95537i	0.267780	+	0.194554i	−0.445790	+	0.895138i	$0.647077\pi$
$938$		0			0
$939$	0.411527	+	1.26655i	0.0134297	+	0.0413323i
$940$		0			0
$941$	21.8106	−	15.8463i	0.711005	−	0.516575i	−0.172493	−	0.985011i	$-0.555182\pi$
$941$	21.8106	−	15.8463i	0.711005	−	0.516575i	0.883498	+	0.468436i	$0.155182\pi$
$942$		0			0
$943$	−19.5381	+	60.1321i	−0.636248	+	1.95817i
$944$		0			0
$945$	70.4409			2.29144
$946$		0			0
$947$	17.3567			0.564018			0.282009	−	0.959412i	$-0.408999\pi$
$947$	17.3567			0.564018			0.282009	+	0.959412i	$0.408999\pi$
$948$		0			0
$949$	8.63989	−	26.5908i	0.280463	−	0.863175i
$950$		0			0
$951$	−10.8841	+	7.90777i	−0.352942	+	0.256427i
$952$		0			0
$953$	12.1745	+	37.4692i	0.394370	+	1.21375i	0.929451	+	0.368946i	$0.120281\pi$
$953$	12.1745	+	37.4692i	0.394370	+	1.21375i	−0.535081	+	0.844801i	$0.679719\pi$
$954$		0			0
$955$	−63.0525	−	45.8103i	−2.04033	−	1.48239i
$956$		0			0
$957$	4.94345	+	15.4537i	0.159799	+	0.499548i
$958$		0			0
$959$	9.66149	+	7.01948i	0.311986	+	0.226671i
$960$		0			0
$961$	0.771284	+	2.37377i	0.0248801	+	0.0765732i
$962$		0			0
$963$	−6.21085	+	4.51244i	−0.200142	+	0.145411i
$964$		0			0
$965$	25.9316	−	79.8092i	0.834767	−	2.56915i
$966$		0			0
$967$	54.6439			1.75723			0.878615	−	0.477532i	$-0.158468\pi$
$967$	54.6439			1.75723			0.878615	+	0.477532i	$0.158468\pi$
$968$		0			0
$969$	−1.06080			−0.0340779
$970$		0			0
$971$	−6.92370	+	21.3089i	−0.222192	+	0.683837i	0.776373	+	0.630274i	$0.217058\pi$
$971$	−6.92370	+	21.3089i	−0.222192	+	0.683837i	−0.998565	+	0.0535623i	$0.982942\pi$
$972$		0			0
$973$	43.7850	−	31.8117i	1.40368	−	1.01984i
$974$		0			0
$975$	−15.9648	−	49.1345i	−0.511282	−	1.57356i
$976$		0			0
$977$	−2.36147	−	1.71571i	−0.0755502	−	0.0548905i	0.549369	−	0.835580i	$-0.314868\pi$
$977$	−2.36147	−	1.71571i	−0.0755502	−	0.0548905i	−0.624919	+	0.780689i	$0.714868\pi$
$978$		0			0
$979$	2.40087	+	7.50537i	0.0767322	+	0.239873i
$980$		0			0
$981$	19.8543	+	14.4250i	0.633898	+	0.460554i
$982$		0			0
$983$	−6.03120	−	18.5621i	−0.192365	−	0.592040i	−0.999997	−	0.00235284i	$-0.999251\pi$
$983$	−6.03120	−	18.5621i	−0.192365	−	0.592040i	0.807632	−	0.589687i	$-0.200749\pi$
$984$		0			0
$985$	−13.5797	+	9.86623i	−0.432685	+	0.314364i
$986$		0			0
$987$	−6.62915	+	20.4024i	−0.211008	+	0.649416i
$988$		0			0
$989$	35.3178			1.12304
$990$		0			0
$991$	3.24921			0.103214			0.0516072	−	0.998667i	$-0.483566\pi$
$991$	3.24921			0.103214			0.0516072	+	0.998667i	$0.483566\pi$
$992$		0			0
$993$	2.01830	−	6.21167i	0.0640487	−	0.197122i
$994$		0			0
$995$	−52.4963	+	38.1408i	−1.66425	+	1.20915i
$996$		0			0
$997$	3.79619	+	11.6835i	0.120226	+	0.370019i	0.993001	−	0.118104i	$-0.0376817\pi$
$997$	3.79619	+	11.6835i	0.120226	+	0.370019i	−0.872775	+	0.488123i	$0.837682\pi$
$998$		0			0
$999$	−11.3771	−	8.26592i	−0.359954	−	0.261522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.f.257.2	yes	12
4.3	odd	2		352.2.m.e.257.2	✓	12
8.3	odd	2		704.2.m.m.257.2		12
8.5	even	2		704.2.m.n.257.2		12
11.3	even	5	inner	352.2.m.f.289.2	yes	12
11.5	even	5		3872.2.a.bn.1.3		6
11.6	odd	10		3872.2.a.bo.1.3		6
44.3	odd	10		352.2.m.e.289.2	yes	12
44.27	odd	10		3872.2.a.bq.1.4		6
44.39	even	10		3872.2.a.bp.1.4		6
88.3	odd	10		704.2.m.m.641.2		12
88.5	even	10		7744.2.a.dv.1.4		6
88.27	odd	10		7744.2.a.du.1.3		6
88.61	odd	10		7744.2.a.dw.1.4		6
88.69	even	10		704.2.m.n.641.2		12
88.83	even	10		7744.2.a.dt.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.e.257.2	✓	12	4.3	odd	2
352.2.m.e.289.2	yes	12	44.3	odd	10
352.2.m.f.257.2	yes	12	1.1	even	1	trivial
352.2.m.f.289.2	yes	12	11.3	even	5	inner
704.2.m.m.257.2		12	8.3	odd	2
704.2.m.m.641.2		12	88.3	odd	10
704.2.m.n.257.2		12	8.5	even	2
704.2.m.n.641.2		12	88.69	even	10
3872.2.a.bn.1.3		6	11.5	even	5
3872.2.a.bo.1.3		6	11.6	odd	10
3872.2.a.bp.1.4		6	44.39	even	10
3872.2.a.bq.1.4		6	44.27	odd	10
7744.2.a.dt.1.3		6	88.83	even	10
7744.2.a.du.1.3		6	88.27	odd	10
7744.2.a.dv.1.4		6	88.5	even	10
7744.2.a.dw.1.4		6	88.61	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.385002 + 1.18491i) q^{3} +(3.03889 - 2.20788i) q^{5} +(-1.04575 - 3.21850i) q^{7} +(1.17126 + 0.850967i) q^{9} +O(q^{10})\)	\(q+(-0.385002 + 1.18491i) q^{3} +(3.03889 - 2.20788i) q^{5} +(-1.04575 - 3.21850i) q^{7} +(1.17126 + 0.850967i) q^{9} +(-1.01050 - 3.15894i) q^{11} +(-3.68264 - 2.67560i) q^{13} +(1.44617 + 4.45086i) q^{15} +(0.239899 - 0.174297i) q^{17} +(-0.887292 + 2.73080i) q^{19} +4.21626 q^{21} +8.74861 q^{23} +(2.81501 - 8.66371i) q^{25} +(-4.48310 + 3.25717i) q^{27} +(1.21337 + 3.73437i) q^{29} +(4.68224 + 3.40185i) q^{31} +(4.13212 + 0.0188365i) q^{33} +(-10.2840 - 7.47175i) q^{35} +(0.784212 + 2.41356i) q^{37} +(4.58818 - 3.33351i) q^{39} +(-2.23328 + 6.87333i) q^{41} +4.03696 q^{43} +5.43814 q^{45} +(-1.57228 + 4.83898i) q^{47} +(-3.60201 + 2.61701i) q^{49} +(0.114165 + 0.351364i) q^{51} +(-9.78533 - 7.10946i) q^{53} +(-10.0454 - 7.36858i) q^{55} +(-2.89416 - 2.10273i) q^{57} +(0.216456 + 0.666183i) q^{59} +(-2.27279 + 1.65128i) q^{61} +(1.51399 - 4.65958i) q^{63} -17.0985 q^{65} -5.78333 q^{67} +(-3.36823 + 10.3664i) q^{69} +(-1.94537 + 1.41339i) q^{71} +(1.89804 + 5.84158i) q^{73} +(9.18197 + 6.67109i) q^{75} +(-9.11029 + 6.55577i) q^{77} +(-0.502385 - 0.365004i) q^{79} +(-0.791319 - 2.43543i) q^{81} +(8.76835 - 6.37058i) q^{83} +(0.344199 - 1.05934i) q^{85} -4.89206 q^{87} -2.37592 q^{89} +(-4.76027 + 14.6506i) q^{91} +(-5.83357 + 4.23834i) q^{93} +(3.33291 + 10.2576i) q^{95} +(8.00482 + 5.81585i) q^{97} +(1.50459 - 4.55983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{7} - q^{9}+O(q^{10}) \) 12 * q + 6 * q^7 - q^9	\( 12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43} + 28 q^{45} - 24 q^{47} - 5 q^{49} + 17 q^{51} - 14 q^{53} - 46 q^{55} - 37 q^{57} + 31 q^{59} - 14 q^{61} + 58 q^{63} - 52 q^{65} - 62 q^{67} - 18 q^{69} + 6 q^{71} - 8 q^{73} + 53 q^{75} - 46 q^{77} - 4 q^{79} - 22 q^{81} + 41 q^{83} - 36 q^{85} - 76 q^{87} - 2 q^{89} - 22 q^{91} + 8 q^{93} + 16 q^{95} + 3 q^{97} - 65 q^{99}+O(q^{100}) \) 12 * q + 6 * q^7 - q^9 - 11 * q^11 - 2 * q^13 + 4 * q^15 + 12 * q^17 + 5 * q^19 + 24 * q^21 - 12 * q^23 + 13 * q^25 + 3 * q^27 + 16 * q^31 - 7 * q^33 - 28 * q^35 - 4 * q^37 + 46 * q^39 - 4 * q^41 - 22 * q^43 + 28 * q^45 - 24 * q^47 - 5 * q^49 + 17 * q^51 - 14 * q^53 - 46 * q^55 - 37 * q^57 + 31 * q^59 - 14 * q^61 + 58 * q^63 - 52 * q^65 - 62 * q^67 - 18 * q^69 + 6 * q^71 - 8 * q^73 + 53 * q^75 - 46 * q^77 - 4 * q^79 - 22 * q^81 + 41 * q^83 - 36 * q^85 - 76 * q^87 - 2 * q^89 - 22 * q^91 + 8 * q^93 + 16 * q^95 + 3 * q^97 - 65 * q^99

Introduction

L-functions

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Database

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