LMFDB - Embedded newform 276.2.i.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 18 x^{18} - 58 x^{17} + 169 x^{16} - 363 x^{15} + 800 x^{14} - 1682 x^{13} + \cdots + 529 $ x^20 - 4x^19 + 18x^18 - 58x^17 + 169x^16 - 363x^15 + 800x^14 - 1682x^13 + 2817x^12 - 3731x^11 + 5829x^10 - 8312x^9 + 7737x^8 + 4348x^7 - 12995x^6 - 2574x^5 + 24401x^4 + 22582x^3 + 9558x^2 + 2829*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.1
Root			$-0.0489501 - 0.340455i$ of defining polynomial
Character	$\chi$	$=$	276.73
Dual form			276.2.i.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{3} +(-3.55432 - 2.28422i) q^{5} +(0.00534053 + 0.0371442i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{3} +(-3.55432 - 2.28422i) q^{5} +(0.00534053 + 0.0371442i) q^{7} +(0.841254 - 0.540641i) q^{9} +(2.38440 - 5.22111i) q^{11} +(0.217316 - 1.51146i) q^{13} +(-4.05388 - 1.19033i) q^{15} +(-3.33853 - 3.85287i) q^{17} +(-0.384947 + 0.444253i) q^{19} +(0.0155889 + 0.0341350i) q^{21} +(2.33840 + 4.18711i) q^{23} +(5.33844 + 11.6896i) q^{25} +(0.654861 - 0.755750i) q^{27} +(2.90795 + 3.35595i) q^{29} +(-6.02205 - 1.76823i) q^{31} +(0.816859 - 5.68138i) q^{33} +(0.0658637 - 0.144221i) q^{35} +(-0.00692866 + 0.00445278i) q^{37} +(-0.217316 - 1.51146i) q^{39} +(7.48861 + 4.81264i) q^{41} +(5.23143 - 1.53609i) q^{43} -4.22503 q^{45} -8.73269 q^{47} +(6.71510 - 1.97173i) q^{49} +(-4.28877 - 2.75623i) q^{51} +(0.0960784 + 0.668240i) q^{53} +(-20.4011 + 13.1110i) q^{55} +(-0.244194 + 0.534710i) q^{57} +(1.44116 - 10.0235i) q^{59} +(14.1607 + 4.15796i) q^{61} +(0.0245744 + 0.0283604i) q^{63} +(-4.22493 + 4.87583i) q^{65} +(1.71948 + 3.76513i) q^{67} +(3.42332 + 3.35870i) q^{69} +(0.566009 + 1.23939i) q^{71} +(1.23154 - 1.42128i) q^{73} +(8.41552 + 9.71203i) q^{75} +(0.206668 + 0.0606832i) q^{77} +(0.122878 - 0.854635i) q^{79} +(0.415415 - 0.909632i) q^{81} +(4.29089 - 2.75759i) q^{83} +(3.06539 + 21.3203i) q^{85} +(3.73564 + 2.40075i) q^{87} +(-11.5826 + 3.40094i) q^{89} +0.0573027 q^{91} -6.27628 q^{93} +(2.38300 - 0.699711i) q^{95} +(3.28427 + 2.11067i) q^{97} +(-0.816859 - 5.68138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$		0			0
$5$	−3.55432	−	2.28422i	−1.58954	−	1.02154i	−0.971995	−	0.235000i	$-0.924491\pi$
$5$	−3.55432	−	2.28422i	−1.58954	−	1.02154i	−0.617545	−	0.786536i	$-0.711872\pi$
$6$		0			0
$7$	0.00534053	+	0.0371442i	0.00201853	+	0.0140392i	0.990806	−	0.135292i	$-0.0431971\pi$
$7$	0.00534053	+	0.0371442i	0.00201853	+	0.0140392i	−0.988787	+	0.149331i	$0.952288\pi$
$8$		0			0
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$		0			0
$11$	2.38440	−	5.22111i	0.718924	−	1.57422i	−0.0964828	−	0.995335i	$-0.530759\pi$
$11$	2.38440	−	5.22111i	0.718924	−	1.57422i	0.815407	−	0.578889i	$-0.196513\pi$
$12$		0			0
$13$	0.217316	−	1.51146i	0.0602725	−	0.419205i	−0.937238	−	0.348690i	$-0.886627\pi$
$13$	0.217316	−	1.51146i	0.0602725	−	0.419205i	0.997511	−	0.0705148i	$-0.0224642\pi$
$14$		0			0
$15$	−4.05388	−	1.19033i	−1.04671	−	0.307341i
$16$		0			0
$17$	−3.33853	−	3.85287i	−0.809712	−	0.934457i	0.189160	−	0.981946i	$-0.439424\pi$
$17$	−3.33853	−	3.85287i	−0.809712	−	0.934457i	−0.998872	+	0.0474891i	$0.984878\pi$
$18$		0			0
$19$	−0.384947	+	0.444253i	−0.0883130	+	0.101919i	−0.798186	−	0.602411i	$-0.794207\pi$
$19$	−0.384947	+	0.444253i	−0.0883130	+	0.101919i	0.709873	+	0.704330i	$0.248752\pi$
$20$		0			0
$21$	0.0155889	+	0.0341350i	0.00340179	+	0.00744887i
$22$		0			0
$23$	2.33840	+	4.18711i	0.487590	+	0.873073i
$23$	2.33840	+	4.18711i	0.487590	+	0.873073i
$24$		0			0
$25$	5.33844	+	11.6896i	1.06769	+	2.33791i
$26$		0			0
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$		0			0
$29$	2.90795	+	3.35595i	0.539993	+	0.623185i	0.958522	−	0.285019i	$-0.0919998\pi$
$29$	2.90795	+	3.35595i	0.539993	+	0.623185i	−0.418529	+	0.908203i	$0.637454\pi$
$30$		0			0
$31$	−6.02205	−	1.76823i	−1.08159	−	0.317584i	−0.308076	−	0.951362i	$-0.599685\pi$
$31$	−6.02205	−	1.76823i	−1.08159	−	0.317584i	−0.773515	+	0.633778i	$0.781503\pi$
$32$		0			0
$33$	0.816859	−	5.68138i	0.142197	−	0.989001i
$34$		0			0
$35$	0.0658637	−	0.144221i	0.0111330	−	0.0243779i
$36$		0			0
$37$	−0.00692866	+	0.00445278i	−0.00113907	+	0.000732033i	−0.541210	−	0.840887i	$-0.682034\pi$
$37$	−0.00692866	+	0.00445278i	−0.00113907	+	0.000732033i	0.540071	+	0.841619i	$0.318397\pi$
$38$		0			0
$39$	−0.217316	−	1.51146i	−0.0347984	−	0.242028i
$40$		0			0
$41$	7.48861	+	4.81264i	1.16952	+	0.751608i	0.973432	−	0.228978i	$-0.0735383\pi$
$41$	7.48861	+	4.81264i	1.16952	+	0.751608i	0.196093	+	0.980585i	$0.437175\pi$
$42$		0			0
$43$	5.23143	−	1.53609i	0.797786	−	0.234251i	0.142661	−	0.989772i	$-0.454434\pi$
$43$	5.23143	−	1.53609i	0.797786	−	0.234251i	0.655125	+	0.755521i	$0.272616\pi$
$44$		0			0
$45$	−4.22503			−0.629830
$46$		0			0
$47$	−8.73269			−1.27379			−0.636897	−	0.770949i	$-0.719782\pi$
$47$	−8.73269			−1.27379			−0.636897	+	0.770949i	$0.719782\pi$
$48$		0			0
$49$	6.71510	−	1.97173i	0.959300	−	0.281676i
$50$		0			0
$51$	−4.28877	−	2.75623i	−0.600548	−	0.385949i
$52$		0			0
$53$	0.0960784	+	0.668240i	0.0131974	+	0.0917898i	0.995356	−	0.0962669i	$-0.0306902\pi$
$53$	0.0960784	+	0.668240i	0.0131974	+	0.0917898i	−0.982158	+	0.188057i	$0.939781\pi$
$54$		0			0
$55$	−20.4011	+	13.1110i	−2.75088	+	1.76789i
$56$		0			0
$57$	−0.244194	+	0.534710i	−0.0323443	+	0.0708240i
$58$		0			0
$59$	1.44116	−	10.0235i	0.187623	−	1.30495i	−0.650518	−	0.759491i	$-0.725448\pi$
$59$	1.44116	−	10.0235i	0.187623	−	1.30495i	0.838141	−	0.545454i	$-0.183643\pi$
$60$		0			0
$61$	14.1607	+	4.15796i	1.81309	+	0.532372i	0.998841	−	0.0481407i	$-0.0153296\pi$
$61$	14.1607	+	4.15796i	1.81309	+	0.532372i	0.814251	+	0.580513i	$0.197148\pi$
$62$		0			0
$63$	0.0245744	+	0.0283604i	0.00309609	+	0.00357308i
$64$		0			0
$65$	−4.22493	+	4.87583i	−0.524038	+	0.604772i
$66$		0			0
$67$	1.71948	+	3.76513i	0.210068	+	0.459984i	0.985110	−	0.171925i	$-0.0549988\pi$
$67$	1.71948	+	3.76513i	0.210068	+	0.459984i	−0.775042	+	0.631909i	$0.782272\pi$
$68$		0			0
$69$	3.42332	+	3.35870i	0.412120	+	0.404340i
$70$		0			0
$71$	0.566009	+	1.23939i	0.0671729	+	0.147088i	0.940241	−	0.340511i	$-0.110600\pi$
$71$	0.566009	+	1.23939i	0.0671729	+	0.147088i	−0.873068	+	0.487599i	$0.837873\pi$
$72$		0			0
$73$	1.23154	−	1.42128i	0.144141	−	0.166348i	−0.679088	−	0.734057i	$-0.737625\pi$
$73$	1.23154	−	1.42128i	0.144141	−	0.166348i	0.823229	+	0.567709i	$0.192170\pi$
$74$		0			0
$75$	8.41552	+	9.71203i	0.971741	+	1.12145i
$76$		0			0
$77$	0.206668	+	0.0606832i	0.0235520	+	0.00691549i
$78$		0			0
$79$	0.122878	−	0.854635i	0.0138248	−	0.0961539i	−0.981741	−	0.190224i	$-0.939079\pi$
$79$	0.122878	−	0.854635i	0.0138248	−	0.0961539i	0.995566	+	0.0940699i	$0.0299877\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$		0			0
$83$	4.29089	−	2.75759i	0.470986	−	0.302684i	−0.283533	−	0.958962i	$-0.591507\pi$
$83$	4.29089	−	2.75759i	0.470986	−	0.302684i	0.754519	+	0.656278i	$0.227870\pi$
$84$		0			0
$85$	3.06539	+	21.3203i	0.332488	+	2.31251i
$86$		0			0
$87$	3.73564	+	2.40075i	0.400502	+	0.257387i
$88$		0			0
$89$	−11.5826	+	3.40094i	−1.22775	+	0.360499i	−0.830399	−	0.557169i	$-0.811888\pi$
$89$	−11.5826	+	3.40094i	−1.22775	+	0.360499i	−0.397348	+	0.917668i	$0.630070\pi$
$90$		0			0
$91$	0.0573027			0.00600696
$92$		0			0
$93$	−6.27628			−0.650820
$94$		0			0
$95$	2.38300	−	0.699711i	0.244490	−	0.0717889i
$96$		0			0
$97$	3.28427	+	2.11067i	0.333467	+	0.214306i	0.696649	−	0.717412i	$-0.254673\pi$
$97$	3.28427	+	2.11067i	0.333467	+	0.214306i	−0.363182	+	0.931718i	$0.618310\pi$
$98$		0			0
$99$	−0.816859	−	5.68138i	−0.0820974	−	0.571000i
$100$		0			0
$101$	−2.28458	+	1.46821i	−0.227324	+	0.146092i	−0.649345	−	0.760494i	$-0.724957\pi$
$101$	−2.28458	+	1.46821i	−0.227324	+	0.146092i	0.422021	+	0.906586i	$0.361321\pi$
$102$		0			0
$103$	4.87794	−	10.6812i	0.480638	−	1.05245i	−0.501650	−	0.865071i	$-0.667273\pi$
$103$	4.87794	−	10.6812i	0.480638	−	1.05245i	0.982288	−	0.187380i	$-0.0599994\pi$
$104$		0			0
$105$	0.0225639	−	0.156935i	0.00220201	−	0.0153153i
$106$		0			0
$107$	−11.4148	−	3.35169i	−1.10351	−	0.324020i	−0.321265	−	0.946989i	$-0.604108\pi$
$107$	−11.4148	−	3.35169i	−1.10351	−	0.324020i	−0.782246	+	0.622969i	$0.785926\pi$
$108$		0			0
$109$	−8.61771	−	9.94537i	−0.825427	−	0.952593i	0.174056	−	0.984736i	$-0.444312\pi$
$109$	−8.61771	−	9.94537i	−0.825427	−	0.952593i	−0.999483	+	0.0321423i	$0.989767\pi$
$110$		0			0
$111$	−0.00539351	+	0.00622444i	−0.000511929	+	0.000590798i
$112$		0			0
$113$	3.95060	+	8.65061i	0.371641	+	0.813781i	0.999375	+	0.0353529i	$0.0112555\pi$
$113$	3.95060	+	8.65061i	0.371641	+	0.813781i	−0.627733	+	0.778428i	$0.716017\pi$
$114$		0			0
$115$	1.25287	−	20.2238i	0.116831	−	1.88587i
$116$		0			0
$117$	−0.634341	−	1.38901i	−0.0586449	−	0.128414i
$118$		0			0
$119$	0.125282	−	0.144583i	0.0114846	−	0.0132539i
$120$		0			0
$121$	−14.3711	−	16.5852i	−1.30647	−	1.50774i
$122$		0			0
$123$	8.54115	+	2.50791i	0.770129	+	0.226130i
$124$		0			0
$125$	4.72060	−	32.8325i	0.422223	−	2.93663i
$126$		0			0
$127$	−0.621104	+	1.36003i	−0.0551140	+	0.120683i	−0.935185	−	0.354159i	$-0.884767\pi$
$127$	−0.621104	+	1.36003i	−0.0551140	+	0.120683i	0.880071	+	0.474841i	$0.157495\pi$
$128$		0			0
$129$	4.58675	−	2.94773i	0.403841	−	0.259533i
$130$		0			0
$131$	2.49193	+	17.3318i	0.217721	+	1.51428i	0.746421	+	0.665474i	$0.231771\pi$
$131$	2.49193	+	17.3318i	0.217721	+	1.51428i	−0.528700	+	0.848809i	$0.677320\pi$
$132$		0			0
$133$	−0.0185573	−	0.0119260i	−0.00160912	−	0.00103412i
$134$		0			0
$135$	−4.05388	+	1.19033i	−0.348903	+	0.102447i
$136$		0			0
$137$	8.99900			0.768836			0.384418	−	0.923159i	$-0.374402\pi$
$137$	8.99900			0.768836			0.384418	+	0.923159i	$0.374402\pi$
$138$		0			0
$139$	−2.09248			−0.177482			−0.0887409	−	0.996055i	$-0.528284\pi$
$139$	−2.09248			−0.177482			−0.0887409	+	0.996055i	$0.528284\pi$
$140$		0			0
$141$	−8.37895	+	2.46028i	−0.705635	+	0.207193i
$142$		0			0
$143$	−7.37335	−	4.73856i	−0.616590	−	0.396259i
$144$		0			0
$145$	−2.67004	−	18.5705i	−0.221735	−	1.54220i
$146$		0			0
$147$	5.88759	−	3.78372i	0.485600	−	0.312076i
$148$		0			0
$149$	1.00136	−	2.19267i	0.0820345	−	0.179631i	−0.864170	−	0.503200i	$-0.832156\pi$
$149$	1.00136	−	2.19267i	0.0820345	−	0.179631i	0.946204	+	0.323570i	$0.104883\pi$
$150$		0			0
$151$	2.98956	−	20.7929i	0.243287	−	1.69210i	−0.392113	−	0.919917i	$-0.628256\pi$
$151$	2.98956	−	20.7929i	0.243287	−	1.69210i	0.635400	−	0.772183i	$-0.280835\pi$
$152$		0			0
$153$	−4.89156	−	1.43629i	−0.395460	−	0.116117i
$154$		0			0
$155$	17.3652	+	20.0406i	1.39481	+	1.60970i
$156$		0			0
$157$	−10.4682	+	12.0809i	−0.835450	+	0.964161i	−0.999752	−	0.0222495i	$-0.992917\pi$
$157$	−10.4682	+	12.0809i	−0.835450	+	0.964161i	0.164303	+	0.986410i	$0.447463\pi$
$158$		0			0
$159$	0.280451	+	0.614103i	0.0222412	+	0.0487015i
$160$		0			0
$161$	−0.143039	+	0.109219i	−0.0112730	+	0.00860770i
$162$		0			0
$163$	−1.81090	−	3.96533i	−0.141841	−	0.310588i	0.825357	−	0.564611i	$-0.190974\pi$
$163$	−1.81090	−	3.96533i	−0.141841	−	0.310588i	−0.967198	+	0.254022i	$0.918246\pi$
$164$		0			0
$165$	−15.8809	+	18.3276i	−1.23633	+	1.42680i
$166$		0			0
$167$	7.78975	+	8.98985i	0.602789	+	0.695656i	0.972344	−	0.233553i	$-0.0750353\pi$
$167$	7.78975	+	8.98985i	0.602789	+	0.695656i	−0.369555	+	0.929209i	$0.620490\pi$
$168$		0			0
$169$	10.2361	+	3.00559i	0.787393	+	0.231200i
$170$		0			0
$171$	−0.0836571	+	0.581848i	−0.00639741	+	0.0444950i
$172$		0			0
$173$	9.65287	−	21.1368i	0.733894	−	1.60700i	−0.0594510	−	0.998231i	$-0.518935\pi$
$173$	9.65287	−	21.1368i	0.733894	−	1.60700i	0.793345	−	0.608772i	$-0.208338\pi$
$174$		0			0
$175$	−0.405689	+	0.260721i	−0.0306672	+	0.0197086i
$176$		0			0
$177$	−1.44116	−	10.0235i	−0.108324	−	0.753411i
$178$		0			0
$179$	11.3188	+	7.27416i	0.846008	+	0.543696i	0.890327	−	0.455321i	$-0.150476\pi$
$179$	11.3188	+	7.27416i	0.846008	+	0.543696i	−0.0443193	+	0.999017i	$0.514112\pi$
$180$		0			0
$181$	19.1340	−	5.61826i	1.42222	−	0.417602i	0.521968	−	0.852965i	$-0.325198\pi$
$181$	19.1340	−	5.61826i	1.42222	−	0.417602i	0.900255	+	0.435363i	$0.143380\pi$
$182$		0			0
$183$	14.7585			1.09098
$184$		0			0
$185$	0.0347978			0.00255839
$186$		0			0
$187$	−28.0766	+	8.24404i	−2.05317	+	0.602864i
$188$		0			0
$189$	0.0315690	+	0.0202882i	0.00229631	+	0.00147575i
$190$		0			0
$191$	−0.115167	−	0.801007i	−0.00833322	−	0.0579588i	0.985231	−	0.171233i	$-0.0547752\pi$
$191$	−0.115167	−	0.801007i	−0.00833322	−	0.0579588i	−0.993564	+	0.113274i	$0.963866\pi$
$192$		0			0
$193$	−8.17839	+	5.25593i	−0.588693	+	0.378330i	−0.800814	−	0.598913i	$-0.795599\pi$
$193$	−8.17839	+	5.25593i	−0.588693	+	0.378330i	0.212121	+	0.977243i	$0.431963\pi$
$194$		0			0
$195$	−2.68011	+	5.86862i	−0.191927	+	0.420261i
$196$		0			0
$197$	−3.83692	+	26.6864i	−0.273369	+	1.90132i	0.138975	+	0.990296i	$0.455619\pi$
$197$	−3.83692	+	26.6864i	−0.273369	+	1.90132i	−0.412344	+	0.911028i	$0.635290\pi$
$198$		0			0
$199$	−11.9702	−	3.51476i	−0.848543	−	0.249155i	−0.171579	−	0.985170i	$-0.554887\pi$
$199$	−11.9702	−	3.51476i	−0.848543	−	0.249155i	−0.676965	+	0.736016i	$0.736705\pi$
$200$		0			0
$201$	2.71059	+	3.12818i	0.191190	+	0.220645i
$202$		0			0
$203$	−0.109124	+	0.125936i	−0.00765902	+	0.00883898i
$204$		0			0
$205$	−15.6238	−	34.2113i	−1.09121	−	2.38942i
$206$		0			0
$207$	4.23091	+	2.25819i	0.294069	+	0.156955i
$208$		0			0
$209$	1.40162	+	3.06913i	0.0969524	+	0.212296i
$210$		0			0
$211$	6.50485	−	7.50700i	0.447812	−	0.516803i	−0.486295	−	0.873795i	$-0.661652\pi$
$211$	6.50485	−	7.50700i	0.447812	−	0.516803i	0.934108	+	0.356992i	$0.116198\pi$
$212$		0			0
$213$	0.892257	+	1.02972i	0.0611364	+	0.0705552i
$214$		0			0
$215$	−22.1029	−	6.49001i	−1.50741	−	0.442615i
$216$		0			0
$217$	0.0335187	−	0.233128i	0.00227540	−	0.0158257i
$218$		0			0
$219$	0.781237	−	1.71067i	0.0527911	−	0.115596i
$220$		0			0
$221$	−6.54898	+	4.20877i	−0.440532	+	0.283113i
$222$		0			0
$223$	1.08296	+	7.53216i	0.0725204	+	0.504391i	0.993414	+	0.114577i	$0.0365514\pi$
$223$	1.08296	+	7.53216i	0.0725204	+	0.504391i	−0.920894	+	0.389813i	$0.872540\pi$
$224$		0			0
$225$	10.8108	+	6.94770i	0.720722	+	0.463180i
$226$		0			0
$227$	−21.3660	+	6.27364i	−1.41811	+	0.416396i	−0.898864	−	0.438227i	$-0.855607\pi$
$227$	−21.3660	+	6.27364i	−1.41811	+	0.416396i	−0.519250	+	0.854623i	$0.673788\pi$
$228$		0			0
$229$	13.4548			0.889116			0.444558	−	0.895750i	$-0.353361\pi$
$229$	13.4548			0.889116			0.444558	+	0.895750i	$0.353361\pi$
$230$		0			0
$231$	0.215393			0.0141718
$232$		0			0
$233$	−1.90785	+	0.560196i	−0.124988	+	0.0366997i	−0.343628	−	0.939106i	$-0.611656\pi$
$233$	−1.90785	+	0.560196i	−0.124988	+	0.0366997i	0.218641	+	0.975805i	$0.429838\pi$
$234$		0			0
$235$	31.0388	+	19.9474i	2.02475	+	1.30122i
$236$		0			0
$237$	−0.122878	−	0.854635i	−0.00798178	−	0.0555145i
$238$		0			0
$239$	9.88793	−	6.35458i	0.639597	−	0.411044i	−0.180255	−	0.983620i	$-0.557692\pi$
$239$	9.88793	−	6.35458i	0.639597	−	0.411044i	0.819852	+	0.572576i	$0.194056\pi$
$240$		0			0
$241$	−10.2655	+	22.4784i	−0.661260	+	1.44796i	0.220083	+	0.975481i	$0.429367\pi$
$241$	−10.2655	+	22.4784i	−0.661260	+	1.44796i	−0.881343	+	0.472477i	$0.843360\pi$
$242$		0			0
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$		0			0
$245$	−28.3715	−	8.33062i	−1.81259	−	0.532224i
$246$		0			0
$247$	0.587817	+	0.678377i	0.0374019	+	0.0431641i
$248$		0			0
$249$	3.34017	−	3.85477i	0.211675	−	0.244286i
$250$		0			0
$251$	−6.94313	−	15.2033i	−0.438246	−	0.959625i	−0.991917	−	0.126890i	$-0.959501\pi$
$251$	−6.94313	−	15.2033i	−0.438246	−	0.959625i	0.553671	−	0.832736i	$-0.313227\pi$
$252$		0			0
$253$	27.4370	−	2.22529i	1.72495	−	0.139903i
$254$		0			0
$255$	8.94783	+	19.5930i	0.560335	+	1.22696i
$256$		0			0
$257$	−11.2225	+	12.9514i	−0.700038	+	0.807887i	−0.988758	−	0.149527i	$-0.952225\pi$
$257$	−11.2225	+	12.9514i	−0.700038	+	0.807887i	0.288719	+	0.957414i	$0.406771\pi$
$258$		0			0
$259$	−0.000202398	0	0.000233580i	−1.25764e−5	0	1.45139e-5i
$260$		0			0
$261$	4.26069	+	1.25105i	0.263730	+	0.0774381i
$262$		0			0
$263$	−2.99294	+	20.8164i	−0.184553	+	1.28359i	0.661279	+	0.750140i	$0.270014\pi$
$263$	−2.99294	+	20.8164i	−0.184553	+	1.28359i	−0.845831	+	0.533451i	$0.820895\pi$
$264$		0			0
$265$	1.18492	−	2.59460i	0.0727888	−	0.159385i
$266$		0			0
$267$	−10.1552	+	6.52636i	−0.621489	+	0.399407i
$268$		0			0
$269$	0.160782	+	1.11826i	0.00980305	+	0.0681817i	0.994136	−	0.108140i	$-0.0344893\pi$
$269$	0.160782	+	1.11826i	0.00980305	+	0.0681817i	−0.984333	+	0.176321i	$0.943580\pi$
$270$		0			0
$271$	3.05285	+	1.96195i	0.185448	+	0.119180i	0.630071	−	0.776538i	$-0.283026\pi$
$271$	3.05285	+	1.96195i	0.185448	+	0.119180i	−0.444623	+	0.895718i	$0.646662\pi$
$272$		0			0
$273$	0.0549816	−	0.0161440i	0.00332764	−	0.000977082i
$274$		0			0
$275$	73.7614			4.44798
$276$		0			0
$277$	−13.0572			−0.784532			−0.392266	−	0.919852i	$-0.628309\pi$
$277$	−13.0572			−0.784532			−0.392266	+	0.919852i	$0.628309\pi$
$278$		0			0
$279$	−6.02205	+	1.76823i	−0.360531	+	0.105861i
$280$		0			0
$281$	11.5955	+	7.45197i	0.691729	+	0.444547i	0.838700	−	0.544594i	$-0.183316\pi$
$281$	11.5955	+	7.45197i	0.691729	+	0.444547i	−0.146971	+	0.989141i	$0.546952\pi$
$282$		0			0
$283$	0.270849	+	1.88380i	0.0161003	+	0.111980i	0.996287	−	0.0860969i	$-0.0274395\pi$
$283$	0.270849	+	1.88380i	0.0161003	+	0.111980i	−0.980186	+	0.198077i	$0.936530\pi$
$284$		0			0
$285$	2.08934	−	1.34274i	0.123762	−	0.0795368i
$286$		0			0
$287$	−0.138769	+	0.303861i	−0.00819125	+	0.0179363i
$288$		0			0
$289$	−1.27946	+	8.89883i	−0.0752623	+	0.523461i
$290$		0			0
$291$	3.74588	+	1.09989i	0.219587	+	0.0644766i
$292$		0			0
$293$	6.42196	+	7.41134i	0.375175	+	0.432975i	0.911667	−	0.410931i	$-0.134796\pi$
$293$	6.42196	+	7.41134i	0.375175	+	0.432975i	−0.536492	+	0.843906i	$0.680251\pi$
$294$		0			0
$295$	−28.0182	+	32.3347i	−1.63128	+	1.88260i
$296$		0			0
$297$	−2.38440	−	5.22111i	−0.138357	−	0.302959i
$298$		0			0
$299$	6.83684	−	2.62448i	0.395384	−	0.151778i
$300$		0			0
$301$	0.0849954	+	0.186114i	0.00489905	+	0.0107274i
$302$		0			0
$303$	−1.77839	+	2.05238i	−0.102166	+	0.117906i
$304$		0			0
$305$	−40.8340	−	47.1249i	−2.33815	−	2.69836i
$306$		0			0
$307$	−14.5835	−	4.28210i	−0.832325	−	0.244393i	−0.162309	−	0.986740i	$-0.551894\pi$
$307$	−14.5835	−	4.28210i	−0.832325	−	0.244393i	−0.670015	+	0.742347i	$0.733712\pi$
$308$		0			0
$309$	1.67111	−	11.6228i	0.0950661	−	0.661199i
$310$		0			0
$311$	−5.63469	+	12.3382i	−0.319514	+	0.699638i	−0.999434	−	0.0336488i	$-0.989287\pi$
$311$	−5.63469	+	12.3382i	−0.319514	+	0.699638i	0.679920	+	0.733286i	$0.262015\pi$
$312$		0			0
$313$	−16.6839	+	10.7221i	−0.943032	+	0.606050i	−0.919253	−	0.393667i	$-0.871206\pi$
$313$	−16.6839	+	10.7221i	−0.943032	+	0.606050i	−0.0237793	+	0.999717i	$0.507570\pi$
$314$		0			0
$315$	−0.0225639	−	0.156935i	−0.00127133	−	0.00884231i
$316$		0			0
$317$	13.8134	+	8.87730i	0.775835	+	0.498599i	0.867649	−	0.497177i	$-0.165630\pi$
$317$	13.8134	+	8.87730i	0.775835	+	0.498599i	−0.0918137	+	0.995776i	$0.529266\pi$
$318$		0			0
$319$	24.4555	−	7.18078i	1.36925	−	0.402047i
$320$		0			0
$321$	−11.8967			−0.664010
$322$		0			0
$323$	2.99680			0.166747
$324$		0			0
$325$	18.8285	−	5.52854i	1.04442	−	0.306668i
$326$		0			0
$327$	−11.0706	−	7.11462i	−0.612204	−	0.393439i
$328$		0			0
$329$	−0.0466372	−	0.324369i	−0.00257119	−	0.0178830i
$330$		0			0
$331$	14.7956	−	9.50854i	0.813239	−	0.522637i	−0.0666726	−	0.997775i	$-0.521238\pi$
$331$	14.7956	−	9.50854i	0.813239	−	0.522637i	0.879911	+	0.475138i	$0.157602\pi$
$332$		0			0
$333$	−0.00342141	+	0.00749184i	−0.000187492	+	0.000410550i
$334$		0			0
$335$	2.48882	−	17.3101i	0.135979	−	0.945754i
$336$		0			0
$337$	−23.6134	−	6.93352i	−1.28630	−	0.377693i	−0.434082	−	0.900873i	$-0.642927\pi$
$337$	−23.6134	−	6.93352i	−1.28630	−	0.377693i	−0.852222	+	0.523181i	$0.824745\pi$
$338$		0			0
$339$	6.22774	+	7.18719i	0.338244	+	0.390355i
$340$		0			0
$341$	−23.5911	+	27.2256i	−1.27753	+	1.47435i
$342$		0			0
$343$	0.218223	+	0.477842i	0.0117829	+	0.0258011i
$344$		0			0
$345$	−4.49557	−	19.7575i	−0.242033	−	1.06371i
$346$		0			0
$347$	−4.79714	−	10.5043i	−0.257524	−	0.563899i	0.736070	−	0.676905i	$-0.236679\pi$
$347$	−4.79714	−	10.5043i	−0.257524	−	0.563899i	−0.993594	+	0.113006i	$0.963952\pi$
$348$		0			0
$349$	13.8352	−	15.9667i	0.740581	−	0.854676i	−0.253039	−	0.967456i	$-0.581430\pi$
$349$	13.8352	−	15.9667i	0.740581	−	0.854676i	0.993620	+	0.112780i	$0.0359757\pi$
$350$		0			0
$351$	−0.999977	−	1.15403i	−0.0533748	−	0.0615978i
$352$		0			0
$353$	10.1918	+	2.99259i	0.542457	+	0.159280i	0.541470	−	0.840720i	$-0.317868\pi$
$353$	10.1918	+	2.99259i	0.542457	+	0.159280i	0.000986444		1.00000i	$0.499686\pi$
$354$		0			0
$355$	0.819258	−	5.69807i	0.0434817	−	0.302422i
$356$		0			0
$357$	0.0794736	−	0.174023i	0.00420619	−	0.00921027i
$358$		0			0
$359$	14.8822	−	9.56421i	0.785452	−	0.504780i	−0.0853867	−	0.996348i	$-0.527213\pi$
$359$	14.8822	−	9.56421i	0.785452	−	0.504780i	0.870839	+	0.491568i	$0.163576\pi$
$360$		0			0
$361$	2.65481	+	18.4646i	0.139727	+	0.971820i
$362$		0			0
$363$	−18.4616	−	11.8645i	−0.968982	−	0.622727i
$364$		0			0
$365$	−7.62380	+	2.23855i	−0.399048	+	0.117171i
$366$		0			0
$367$	−3.11851			−0.162785			−0.0813925	−	0.996682i	$-0.525937\pi$
$367$	−3.11851			−0.162785			−0.0813925	+	0.996682i	$0.525937\pi$
$368$		0			0
$369$	8.90173			0.463405
$370$		0			0
$371$	−0.0243081	+	0.00713752i	−0.00126202	+	0.000370561i
$372$		0			0
$373$	−2.17283	−	1.39639i	−0.112505	−	0.0723026i	0.483178	−	0.875522i	$-0.339482\pi$
$373$	−2.17283	−	1.39639i	−0.112505	−	0.0723026i	−0.595683	+	0.803219i	$0.703119\pi$
$374$		0			0
$375$	−4.72060	−	32.8325i	−0.243771	−	1.69546i
$376$		0			0
$377$	5.70434	−	3.66596i	0.293789	−	0.188806i
$378$		0			0
$379$	−9.37077	+	20.5191i	−0.481344	+	1.05400i	0.500748	+	0.865593i	$0.333059\pi$
$379$	−9.37077	+	20.5191i	−0.481344	+	1.05400i	−0.982092	+	0.188403i	$0.939669\pi$
$380$		0			0
$381$	−0.212781	+	1.47992i	−0.0109011	+	0.0758187i
$382$		0			0
$383$	−7.22285	−	2.12082i	−0.369071	−	0.108369i	0.0919377	−	0.995765i	$-0.470694\pi$
$383$	−7.22285	−	2.12082i	−0.369071	−	0.108369i	−0.461008	+	0.887396i	$0.652512\pi$
$384$		0			0
$385$	−0.595950	−	0.687763i	−0.0303724	−	0.0350517i
$386$		0			0
$387$	3.57049	−	4.12056i	0.181498	−	0.209460i
$388$		0			0
$389$	6.40504	+	14.0251i	0.324748	+	0.711100i	0.999640	−	0.0268169i	$-0.00853711\pi$
$389$	6.40504	+	14.0251i	0.324748	+	0.711100i	−0.674892	+	0.737916i	$0.735810\pi$
$390$		0			0
$391$	8.32556	−	22.9883i	0.421042	−	1.16257i
$392$		0			0
$393$	7.27391	+	15.9276i	0.366920	+	0.803443i
$394$		0			0
$395$	−2.38892	+	2.75697i	−0.120200	+	0.138718i
$396$		0			0
$397$	3.89907	+	4.49976i	0.195689	+	0.225837i	0.845111	−	0.534592i	$-0.179535\pi$
$397$	3.89907	+	4.49976i	0.195689	+	0.225837i	−0.649422	+	0.760428i	$0.724989\pi$
$398$		0			0
$399$	−0.0211655	−	0.00621475i	−0.00105960	−	0.000311127i
$400$		0			0
$401$	−1.34800	+	9.37552i	−0.0673157	+	0.468191i	0.928083	+	0.372373i	$0.121456\pi$
$401$	−1.34800	+	9.37552i	−0.0673157	+	0.468191i	−0.995399	+	0.0958180i	$0.969453\pi$
$402$		0			0
$403$	−3.98130	+	8.71784i	−0.198323	+	0.434267i
$404$		0			0
$405$	−3.55432	+	2.28422i	−0.176616	+	0.113504i
$406$		0			0
$407$	0.00672775	+	0.0467925i	0.000333482	+	0.00231942i
$408$		0			0
$409$	4.78063	+	3.07232i	0.236387	+	0.151917i	0.653472	−	0.756951i	$-0.273312\pi$
$409$	4.78063	+	3.07232i	0.236387	+	0.151917i	−0.417085	+	0.908868i	$0.636948\pi$
$410$		0			0
$411$	8.63447	−	2.53531i	0.425907	−	0.125058i
$412$		0			0
$413$	0.380011			0.0186991
$414$		0			0
$415$	−21.5501			−1.05785
$416$		0			0
$417$	−2.00772	+	0.589520i	−0.0983185	+	0.0288689i
$418$		0			0
$419$	11.4503	+	7.35866i	0.559383	+	0.359494i	0.789577	−	0.613651i	$-0.210300\pi$
$419$	11.4503	+	7.35866i	0.559383	+	0.359494i	−0.230194	+	0.973145i	$0.573936\pi$
$420$		0			0
$421$	2.11448	+	14.7065i	0.103053	+	0.716751i	0.974193	+	0.225716i	$0.0724722\pi$
$421$	2.11448	+	14.7065i	0.103053	+	0.716751i	−0.871140	+	0.491035i	$0.836619\pi$
$422$		0			0
$423$	−7.34640	+	4.72125i	−0.357194	+	0.229555i
$424$		0			0
$425$	27.2158	−	59.5942i	1.32016	−	2.89074i
$426$		0			0
$427$	−0.0788184	+	0.548194i	−0.00381429	+	0.0265290i
$428$		0			0
$429$	−8.40968	−	2.46931i	−0.406023	−	0.119219i
$430$		0			0
$431$	−17.9810	−	20.7512i	−0.866113	−	0.999548i	−0.999963	−	0.00854665i	$-0.997279\pi$
$431$	−17.9810	−	20.7512i	−0.866113	−	0.999548i	0.133850	−	0.991002i	$-0.457266\pi$
$432$		0			0
$433$	8.46837	−	9.77302i	0.406964	−	0.469661i	−0.514858	−	0.857276i	$-0.672155\pi$
$433$	8.46837	−	9.77302i	0.406964	−	0.469661i	0.921822	+	0.387614i	$0.126701\pi$
$434$		0			0
$435$	−7.79381	−	17.0661i	−0.373684	−	0.818255i
$436$		0			0
$437$	−2.76030	−	0.572976i	−0.132043	−	0.0274092i
$438$		0			0
$439$	8.29923	+	18.1728i	0.396100	+	0.867339i	0.997651	+	0.0685042i	$0.0218226\pi$
$439$	8.29923	+	18.1728i	0.396100	+	0.867339i	−0.601550	+	0.798835i	$0.705450\pi$
$440$		0			0
$441$	4.58310	−	5.28918i	0.218243	−	0.251866i
$442$		0			0
$443$	−6.69197	−	7.72295i	−0.317945	−	0.366928i	0.574170	−	0.818736i	$-0.305325\pi$
$443$	−6.69197	−	7.72295i	−0.317945	−	0.366928i	−0.892115	+	0.451808i	$0.850779\pi$
$444$		0			0
$445$	48.9366	+	14.3691i	2.31982	+	0.681160i
$446$		0			0
$447$	0.343050	−	2.38597i	0.0162257	−	0.112852i
$448$		0			0
$449$	5.43898	−	11.9097i	0.256681	−	0.562054i	−0.736792	−	0.676120i	$-0.763660\pi$
$449$	5.43898	−	11.9097i	0.256681	−	0.562054i	0.993473	+	0.114066i	$0.0363875\pi$
$450$		0			0
$451$	42.9831	−	27.6236i	2.02400	−	1.30074i
$452$		0			0
$453$	−2.98956	−	20.7929i	−0.140462	−	0.976934i
$454$		0			0
$455$	−0.203672	−	0.130892i	−0.00954830	−	0.00613632i
$456$		0			0
$457$	−33.6710	+	9.88671i	−1.57506	+	0.462481i	−0.948470	−	0.316866i	$-0.897370\pi$
$457$	−33.6710	+	9.88671i	−1.57506	+	0.462481i	−0.626594	+	0.779346i	$0.715551\pi$
$458$		0			0
$459$	−5.09807			−0.237958
$460$		0			0
$461$	−25.4568			−1.18564			−0.592821	−	0.805334i	$-0.701986\pi$
$461$	−25.4568			−1.18564			−0.592821	+	0.805334i	$0.701986\pi$
$462$		0			0
$463$	−11.3043	+	3.31926i	−0.525358	+	0.154259i	−0.533648	−	0.845707i	$-0.679179\pi$
$463$	−11.3043	+	3.31926i	−0.525358	+	0.154259i	0.00829034	+	0.999966i	$0.497361\pi$
$464$		0			0
$465$	22.3079	+	14.3364i	1.03450	+	0.664836i
$466$		0			0
$467$	−4.42599	−	30.7835i	−0.204810	−	1.42449i	−0.789759	−	0.613418i	$-0.789794\pi$
$467$	−4.42599	−	30.7835i	−0.204810	−	1.42449i	0.584948	−	0.811071i	$-0.301115\pi$
$468$		0			0
$469$	−0.130670	+	0.0839765i	−0.00603378	+	0.00387767i
$470$		0			0
$471$	−6.64054	+	14.5408i	−0.305980	+	0.670003i
$472$		0			0
$473$	4.45375	−	30.9765i	0.204784	−	1.42430i
$474$		0			0
$475$	−7.24814	−	2.12825i	−0.332567	−	0.0976506i
$476$		0			0
$477$	0.442104	+	0.510215i	0.0202426	+	0.0233611i
$478$		0			0
$479$	3.97977	−	4.59290i	0.181840	−	0.209855i	−0.657510	−	0.753446i	$-0.728390\pi$
$479$	3.97977	−	4.59290i	0.181840	−	0.209855i	0.839350	+	0.543591i	$0.182936\pi$
$480$		0			0
$481$	0.00522451	+	0.0114401i	0.000238217	+	0.000521623i
$482$		0			0
$483$	−0.106474	+	0.145094i	−0.00484473	+	0.00660200i
$484$		0			0
$485$	−6.85210	−	15.0040i	−0.311138	−	0.681296i
$486$		0			0
$487$	−25.6501	+	29.6018i	−1.16232	+	1.34138i	−0.232834	+	0.972516i	$0.574800\pi$
$487$	−25.6501	+	29.6018i	−1.16232	+	1.34138i	−0.929482	+	0.368868i	$0.879745\pi$
$488$		0			0
$489$	−2.85471	−	3.29451i	−0.129094	−	0.148983i
$490$		0			0
$491$	−36.4474	−	10.7019i	−1.64485	−	0.482970i	−0.677309	−	0.735699i	$-0.736854\pi$
$491$	−36.4474	−	10.7019i	−1.64485	−	0.482970i	−0.967537	+	0.252728i	$0.918672\pi$
$492$		0			0
$493$	3.22177	−	22.4079i	0.145101	−	1.00920i
$494$		0			0
$495$	−10.0742	+	22.0593i	−0.452800	+	0.991493i
$496$		0			0
$497$	−0.0430133	+	0.0276430i	−0.00192941	+	0.00123996i
$498$		0			0
$499$	−3.81768	−	26.5525i	−0.170903	−	1.18865i	−0.876983	−	0.480522i	$-0.840447\pi$
$499$	−3.81768	−	26.5525i	−0.170903	−	1.18865i	0.706080	−	0.708132i	$-0.250462\pi$
$500$		0			0
$501$	10.0069	+	6.43107i	0.447077	+	0.287319i
$502$		0			0
$503$	−30.4701	+	8.94682i	−1.35859	+	0.398919i	−0.878267	−	0.478171i	$-0.841300\pi$
$503$	−30.4701	+	8.94682i	−1.35859	+	0.398919i	−0.480326	+	0.877090i	$0.659482\pi$
$504$		0			0
$505$	11.4738			0.510579
$506$		0			0
$507$	10.6683			0.473794
$508$		0			0
$509$	17.3532	−	5.09535i	0.769166	−	0.225848i	0.126472	−	0.991970i	$-0.459635\pi$
$509$	17.3532	−	5.09535i	0.769166	−	0.225848i	0.642694	+	0.766123i	$0.277816\pi$
$510$		0			0
$511$	0.0593693	+	0.0381543i	0.00262634	+	0.00168785i
$512$		0			0
$513$	0.0836571	+	0.581848i	0.00369355	+	0.0256892i
$514$		0			0
$515$	−41.7360	+	26.8221i	−1.83911	+	1.18192i
$516$		0			0
$517$	−20.8222	+	45.5943i	−0.915760	+	2.00524i
$518$		0			0
$519$	3.30692	−	23.0002i	0.145158	−	1.00960i
$520$		0			0
$521$	17.9989	+	5.28496i	0.788547	+	0.231538i	0.651121	−	0.758974i	$-0.274299\pi$
$521$	17.9989	+	5.28496i	0.788547	+	0.231538i	0.137426	+	0.990512i	$0.456117\pi$
$522$		0			0
$523$	4.87343	+	5.62424i	0.213100	+	0.245931i	0.852229	−	0.523169i	$-0.175250\pi$
$523$	4.87343	+	5.62424i	0.213100	+	0.245931i	−0.639129	+	0.769100i	$0.720705\pi$
$524$		0			0
$525$	−0.315803	+	0.364456i	−0.0137828	+	0.0159061i
$526$		0			0
$527$	13.2920	+	29.1054i	0.579009	+	1.26785i
$528$		0			0
$529$	−12.0638	+	19.5823i	−0.524512	+	0.851403i
$530$		0			0
$531$	−4.20672	−	9.21143i	−0.182556	−	0.399742i
$532$		0			0
$533$	8.90152	−	10.2729i	0.385568	−	0.444969i
$534$		0			0
$535$	32.9159	+	37.9870i	1.42308	+	1.64232i
$536$		0			0
$537$	12.9097	+	3.79063i	0.557094	+	0.163578i
$538$		0			0
$539$	5.71686	−	39.7617i	0.246243	−	1.71266i
$540$		0			0
$541$	3.13255	−	6.85932i	0.134679	−	0.294905i	−0.830262	−	0.557373i	$-0.811809\pi$
$541$	3.13255	−	6.85932i	0.134679	−	0.294905i	0.964941	+	0.262468i	$0.0845365\pi$
$542$		0			0
$543$	16.7761	−	10.7814i	0.719933	−	0.462673i
$544$		0			0
$545$	7.91266	+	55.0338i	0.338941	+	2.35739i
$546$		0			0
$547$	25.4444	+	16.3521i	1.08792	+	0.699167i	0.956375	−	0.292143i	$-0.0943682\pi$
$547$	25.4444	+	16.3521i	1.08792	+	0.699167i	0.131550	+	0.991310i	$0.458005\pi$
$548$		0			0
$549$	14.1607	−	4.15796i	0.604364	−	0.177457i
$550$		0			0
$551$	−2.61030			−0.111202
$552$		0			0
$553$	0.0324010			0.00137783
$554$		0			0
$555$	0.0333883	−	0.00980368i	0.00141725	−	0.000416143i
$556$		0			0
$557$	−6.64422	−	4.26998i	−0.281525	−	0.180925i	0.392256	−	0.919856i	$-0.371695\pi$
$557$	−6.64422	−	4.26998i	−0.281525	−	0.180925i	−0.673781	+	0.738931i	$0.735331\pi$
$558$		0			0
$559$	−1.18487	−	8.24093i	−0.0501145	−	0.348554i
$560$		0			0
$561$	−24.6167	+	15.8202i	−1.03932	+	0.667929i
$562$		0			0
$563$	−6.81369	+	14.9199i	−0.287163	+	0.628799i	−0.997152	−	0.0754135i	$-0.975972\pi$
$563$	−6.81369	+	14.9199i	−0.287163	+	0.628799i	0.709990	+	0.704212i	$0.248700\pi$
$564$		0			0
$565$	5.71822	−	39.7711i	0.240567	−	1.67318i
$566$		0			0
$567$	0.0360061	+	0.0105724i	0.00151211	+	0.000443997i
$568$		0			0
$569$	16.9329	+	19.5417i	0.709866	+	0.819229i	0.990050	−	0.140717i	$-0.0449409\pi$
$569$	16.9329	+	19.5417i	0.709866	+	0.819229i	−0.280184	+	0.959946i	$0.590395\pi$
$570$		0			0
$571$	4.71980	−	5.44694i	0.197518	−	0.227947i	−0.648347	−	0.761345i	$-0.724539\pi$
$571$	4.71980	−	5.44694i	0.197518	−	0.227947i	0.845865	+	0.533397i	$0.179085\pi$
$572$		0			0
$573$	−0.336172	−	0.736114i	−0.0140438	−	0.0307516i
$574$		0			0
$575$	−36.4620	+	49.6875i	−1.52057	+	2.07211i
$576$		0			0
$577$	12.6556	+	27.7118i	0.526857	+	1.15366i	0.966777	+	0.255620i	$0.0822796\pi$
$577$	12.6556	+	27.7118i	0.526857	+	1.15366i	−0.439920	+	0.898037i	$0.644993\pi$
$578$		0			0
$579$	−6.36634	+	7.34714i	−0.264576	+	0.305337i
$580$		0			0
$581$	0.125344	+	0.144655i	0.00520015	+	0.00600129i
$582$		0			0
$583$	3.71804	+	1.09172i	0.153986	+	0.0452142i
$584$		0			0
$585$	−0.918165	+	6.38598i	−0.0379614	+	0.264028i
$586$		0			0
$587$	9.65038	−	21.1314i	0.398314	−	0.872186i	−0.599125	−	0.800656i	$-0.704485\pi$
$587$	9.65038	−	21.1314i	0.398314	−	0.872186i	0.997438	−	0.0715300i	$-0.0227882\pi$
$588$		0			0
$589$	3.10371	−	1.99464i	0.127886	−	0.0821875i
$590$		0			0
$591$	3.83692	+	26.6864i	0.157830	+	1.09773i
$592$		0			0
$593$	26.0894	+	16.7667i	1.07136	+	0.688524i	0.952547	−	0.304392i	$-0.0984533\pi$
$593$	26.0894	+	16.7667i	1.07136	+	0.688524i	0.118818	+	0.992916i	$0.462090\pi$
$594$		0			0
$595$	−0.775554	+	0.227723i	−0.0317946	+	0.00933574i
$596$		0			0
$597$	−12.4755			−0.510589
$598$		0			0
$599$	8.93668			0.365143			0.182571	−	0.983193i	$-0.441558\pi$
$599$	8.93668			0.365143			0.182571	+	0.983193i	$0.441558\pi$
$600$		0			0
$601$	8.20105	−	2.40804i	0.334528	−	0.0982262i	−0.110155	−	0.993914i	$-0.535135\pi$
$601$	8.20105	−	2.40804i	0.334528	−	0.0982262i	0.444683	+	0.895688i	$0.353316\pi$
$602$		0			0
$603$	3.48210	+	2.23781i	0.141802	+	0.0911306i
$604$		0			0
$605$	13.1954	+	91.7759i	0.536469	+	3.73122i
$606$		0			0
$607$	−3.24163	+	2.08327i	−0.131574	+	0.0845574i	−0.604772	−	0.796399i	$-0.706736\pi$
$607$	−3.24163	+	2.08327i	−0.131574	+	0.0845574i	0.473198	+	0.880956i	$0.343099\pi$
$608$		0			0
$609$	−0.0692237	+	0.151579i	−0.00280508	+	0.00614228i
$610$		0			0
$611$	−1.89775	+	13.1991i	−0.0767747	+	0.533980i
$612$		0			0
$613$	−11.5221	−	3.38318i	−0.465372	−	0.136645i	0.0406368	−	0.999174i	$-0.487061\pi$
$613$	−11.5221	−	3.38318i	−0.465372	−	0.136645i	−0.506008	+	0.862529i	$0.668880\pi$
$614$		0			0
$615$	−24.6293	−	28.4238i	−0.993151	−	1.14616i
$616$		0			0
$617$	25.1286	−	29.0000i	1.01164	−	1.16750i	0.0258252	−	0.999666i	$-0.491779\pi$
$617$	25.1286	−	29.0000i	1.01164	−	1.16750i	0.985816	−	0.167830i	$-0.0536759\pi$
$618$		0			0
$619$	10.4296	+	22.8375i	0.419199	+	0.917918i	0.994957	+	0.100298i	$0.0319796\pi$
$619$	10.4296	+	22.8375i	0.419199	+	0.917918i	−0.575758	+	0.817620i	$0.695293\pi$
$620$		0			0
$621$	4.69573	+	0.974729i	0.188433	+	0.0391145i
$622$		0			0
$623$	−0.188182	−	0.412062i	−0.00753937	−	0.0165089i
$624$		0			0
$625$	−49.6976	+	57.3541i	−1.98790	+	2.29416i
$626$		0			0
$627$	2.20952	+	2.54992i	0.0882398	+	0.101834i
$628$		0			0
$629$	0.0402875	+	0.0118295i	0.00160637	+	0.000471672i
$630$		0			0
$631$	1.91761	−	13.3373i	0.0763390	−	0.530949i	−0.915387	−	0.402575i	$-0.868115\pi$
$631$	1.91761	−	13.3373i	0.0763390	−	0.530949i	0.991726	−	0.128374i	$-0.0409758\pi$
$632$		0			0
$633$	4.12639	−	9.03554i	0.164009	−	0.359130i
$634$		0			0
$635$	5.31421	−	3.41523i	0.210888	−	0.135529i
$636$		0			0
$637$	−1.52090	−	10.5781i	−0.0602604	−	0.419120i
$638$		0			0
$639$	1.14622	+	0.736631i	0.0453438	+	0.0291407i
$640$		0			0
$641$	1.42282	−	0.417776i	0.0561978	−	0.0165012i	−0.253513	−	0.967332i	$-0.581586\pi$
$641$	1.42282	−	0.417776i	0.0561978	−	0.0165012i	0.309711	+	0.950831i	$0.399768\pi$
$642$		0			0
$643$	−43.7615			−1.72578			−0.862892	−	0.505388i	$-0.831349\pi$
$643$	−43.7615			−1.72578			−0.862892	+	0.505388i	$0.831349\pi$
$644$		0			0
$645$	−23.0361			−0.907044
$646$		0			0
$647$	26.9324	−	7.90807i	1.05882	−	0.310898i	0.294446	−	0.955668i	$-0.404865\pi$
$647$	26.9324	−	7.90807i	1.05882	−	0.310898i	0.764377	+	0.644770i	$0.223047\pi$
$648$		0			0
$649$	−48.8974	−	31.4244i	−1.91939	−	1.23352i
$650$		0			0
$651$	−0.0335187	−	0.233128i	−0.00131370	−	0.00913699i
$652$		0			0
$653$	2.74109	−	1.76159i	0.107267	−	0.0689363i	−0.485907	−	0.874010i	$-0.661511\pi$
$653$	2.74109	−	1.76159i	0.107267	−	0.0689363i	0.593174	+	0.805074i	$0.297874\pi$
$654$		0			0
$655$	30.7325	−	67.2947i	1.20082	−	2.62942i
$656$		0			0
$657$	0.267640	−	1.86147i	0.0104416	−	0.0726231i
$658$		0			0
$659$	−20.9066	−	6.13872i	−0.814404	−	0.239131i	−0.152099	−	0.988365i	$-0.548603\pi$
$659$	−20.9066	−	6.13872i	−0.814404	−	0.239131i	−0.662305	+	0.749235i	$0.730421\pi$
$660$		0			0
$661$	−30.1734	−	34.8220i	−1.17361	−	1.35442i	−0.922283	−	0.386516i	$-0.873678\pi$
$661$	−30.1734	−	34.8220i	−1.17361	−	1.35442i	−0.251328	−	0.967902i	$-0.580867\pi$
$662$		0			0
$663$	−5.09795	+	5.88335i	−0.197988	+	0.228490i
$664$		0			0
$665$	0.0387167	+	0.0847778i	0.00150137	+	0.00328754i
$666$		0			0
$667$	−7.25179	+	20.0235i	−0.280791	+	0.775311i
$668$		0			0
$669$	3.16115	+	6.92195i	0.122217	+	0.267618i
$670$		0			0
$671$	55.4739	−	64.0203i	2.14155	−	2.47148i
$672$		0			0
$673$	17.2222	+	19.8755i	0.663868	+	0.766145i	0.983404	−	0.181430i	$-0.0580725\pi$
$673$	17.2222	+	19.8755i	0.663868	+	0.766145i	−0.319536	+	0.947574i	$0.603527\pi$
$674$		0			0
$675$	12.3303	+	3.62051i	0.474594	+	0.139353i
$676$		0			0
$677$	−2.01977	+	14.0478i	−0.0776261	+	0.539902i	0.913486	+	0.406871i	$0.133380\pi$
$677$	−2.01977	+	14.0478i	−0.0776261	+	0.539902i	−0.991112	+	0.133031i	$0.957529\pi$
$678$		0			0
$679$	−0.0608595	+	0.133264i	−0.00233557	+	0.00511419i
$680$		0			0
$681$	−18.7331	+	12.0390i	−0.717853	+	0.461336i
$682$		0			0
$683$	2.93021	+	20.3800i	0.112121	+	0.779820i	0.965850	+	0.259102i	$0.0834267\pi$
$683$	2.93021	+	20.3800i	0.112121	+	0.779820i	−0.853729	+	0.520718i	$0.825664\pi$
$684$		0			0
$685$	−31.9853	−	20.5557i	−1.22210	−	0.785393i
$686$		0			0
$687$	12.9097	−	3.79064i	0.492538	−	0.144622i
$688$		0			0
$689$	1.03090			0.0392741
$690$		0			0
$691$	17.8924			0.680661			0.340330	−	0.940306i	$-0.389461\pi$
$691$	17.8924			0.680661			0.340330	+	0.940306i	$0.389461\pi$
$692$		0			0
$693$	0.206668	−	0.0606832i	0.00785067	−	0.00230516i
$694$		0			0
$695$	7.43734	+	4.77969i	0.282115	+	0.181304i
$696$		0			0
$697$	−6.45848	−	44.9197i	−0.244632	−	1.70146i
$698$		0			0
$699$	−1.67275	+	1.07501i	−0.0632690	+	0.0406605i
$700$		0			0
$701$	2.41494	−	5.28797i	0.0912109	−	0.199724i	−0.858528	−	0.512766i	$-0.828621\pi$
$701$	2.41494	−	5.28797i	0.0912109	−	0.199724i	0.949739	+	0.313042i	$0.101348\pi$
$702$		0			0
$703$	0.000689009	−	0.00479216i	2.59865e−5	−	0.000180740i
$704$		0			0
$705$	35.4013	+	10.3948i	1.33329	+	0.391489i
$706$		0			0
$707$	−0.0667364	−	0.0770179i	−0.00250988	−	0.00289656i
$708$		0			0
$709$	28.5761	−	32.9786i	1.07320	−	1.23854i	0.103398	−	0.994640i	$-0.467028\pi$
$709$	28.5761	−	32.9786i	1.07320	−	1.23854i	0.969801	−	0.243898i	$-0.0784262\pi$
$710$		0			0
$711$	−0.358679	−	0.785397i	−0.0134515	−	0.0294547i
$712$		0			0
$713$	−6.67817	−	29.3498i	−0.250099	−	1.09916i
$714$		0			0
$715$	15.3833	+	33.6847i	0.575303	+	1.25974i
$716$		0			0
$717$	7.69710	−	8.88293i	0.287454	−	0.331739i
$718$		0			0
$719$	−21.1227	−	24.3769i	−0.787744	−	0.909106i	0.209899	−	0.977723i	$-0.432687\pi$
$719$	−21.1227	−	24.3769i	−0.787744	−	0.909106i	−0.997643	+	0.0686176i	$0.978141\pi$
$720$		0			0
$721$	0.422796	+	0.124144i	0.0157457	+	0.00462337i
$722$		0			0
$723$	−3.51681	+	24.4600i	−0.130792	+	0.909676i
$724$		0			0
$725$	−23.7057	+	51.9082i	−0.880406	+	1.92782i
$726$		0			0
$727$	30.9518	−	19.8915i	1.14794	−	0.737736i	0.178711	−	0.983902i	$-0.442807\pi$
$727$	30.9518	−	19.8915i	1.14794	−	0.737736i	0.969228	+	0.246166i	$0.0791708\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$		0			0
$731$	−23.3836	−	15.0277i	−0.864874	−	0.555821i
$732$		0			0
$733$	2.88297	−	0.846518i	0.106485	−	0.0312668i	−0.228056	−	0.973648i	$-0.573237\pi$
$733$	2.88297	−	0.846518i	0.106485	−	0.0312668i	0.334541	+	0.942381i	$0.391419\pi$
$734$		0			0
$735$	−29.5692			−1.09068
$736$		0			0
$737$	23.7581			0.875140
$738$		0			0
$739$	−33.9875	+	9.97964i	−1.25025	+	0.367107i	−0.838858	−	0.544351i	$-0.816776\pi$
$739$	−33.9875	+	9.97964i	−1.25025	+	0.367107i	−0.411394	+	0.911458i	$0.634958\pi$
$740$		0			0
$741$	0.755127	+	0.485291i	0.0277403	+	0.0178276i
$742$		0			0
$743$	3.78614	+	26.3332i	0.138900	+	0.966072i	0.933408	+	0.358818i	$0.116820\pi$
$743$	3.78614	+	26.3332i	0.138900	+	0.966072i	−0.794507	+	0.607254i	$0.792271\pi$
$744$		0			0
$745$	−8.56770	+	5.50612i	−0.313896	+	0.201729i
$746$		0			0
$747$	2.11886	−	4.63966i	0.0775251	−	0.169756i
$748$		0			0
$749$	0.0635348	−	0.441894i	0.00232151	−	0.0161465i
$750$		0			0
$751$	21.2958	+	6.25302i	0.777096	+	0.228176i	0.646147	−	0.763213i	$-0.276379\pi$
$751$	21.2958	+	6.25302i	0.777096	+	0.228176i	0.130949	+	0.991389i	$0.458198\pi$
$752$		0			0
$753$	−10.9452	−	12.6314i	−0.398864	−	0.460313i
$754$		0			0
$755$	−58.1214	+	67.0757i	−2.11525	+	2.44113i
$756$		0			0
$757$	8.62026	+	18.8757i	0.313309	+	0.686050i	0.999129	−	0.0417203i	$-0.0132839\pi$
$757$	8.62026	+	18.8757i	0.313309	+	0.686050i	−0.685821	+	0.727771i	$0.740557\pi$
$758$		0			0
$759$	25.6987	−	9.86506i	0.932804	−	0.358079i
$760$		0			0
$761$	4.52559	+	9.90966i	0.164053	+	0.359225i	0.973749	−	0.227624i	$-0.0730956\pi$
$761$	4.52559	+	9.90966i	0.164053	+	0.359225i	−0.809697	+	0.586849i	$0.800368\pi$
$762$		0			0
$763$	0.323390	−	0.373212i	0.0117075	−	0.0135112i
$764$		0			0
$765$	14.1054	+	16.2785i	0.509981	+	0.588549i
$766$		0			0
$767$	−14.8369	−	4.35652i	−0.535731	−	0.157305i
$768$		0			0
$769$	0.861237	−	5.99003i	0.0310570	−	0.216006i	−0.968383	−	0.249468i	$-0.919744\pi$
$769$	0.861237	−	5.99003i	0.0310570	−	0.216006i	0.999440	+	0.0334620i	$0.0106533\pi$
$770$		0			0
$771$	−7.11904	+	15.5885i	−0.256386	+	0.561407i
$772$		0			0
$773$	30.5411	−	19.6276i	1.09849	−	0.705955i	0.139732	−	0.990189i	$-0.455376\pi$
$773$	30.5411	−	19.6276i	1.09849	−	0.705955i	0.958755	+	0.284235i	$0.0917394\pi$
$774$		0			0
$775$	−11.4785	−	79.8347i	−0.412320	−	2.86775i
$776$		0			0
$777$	−0.000260006	0	0.000167096i	−9.32768e−6	0	5.99453e-6i
$778$		0			0
$779$	−5.02075	+	1.47422i	−0.179887	+	0.0528196i
$780$		0			0
$781$	7.82056			0.279842
$782$		0			0
$783$	4.44056			0.158693
$784$		0			0
$785$	64.8026	−	19.0278i	2.31291	−	0.679130i
$786$		0			0
$787$	−40.7452	−	26.1853i	−1.45241	−	0.933406i	−0.999116	−	0.0420449i	$-0.986613\pi$
$787$	−40.7452	−	26.1853i	−1.45241	−	0.933406i	−0.453293	−	0.891362i	$-0.649751\pi$
$788$		0			0
$789$	2.99294	+	20.8164i	0.106551	+	0.741082i
$790$		0			0
$791$	−0.300222	+	0.192941i	−0.0106747	+	0.00686019i
$792$		0			0
$793$	9.36194	−	20.4998i	0.332452	−	0.727969i
$794$		0			0
$795$	0.405934	−	2.82333i	0.0143970	−	0.100133i
$796$		0			0
$797$	−34.0346	−	9.99346i	−1.20557	−	0.353987i	−0.383589	−	0.923504i	$-0.625312\pi$
$797$	−34.0346	−	9.99346i	−1.20557	−	0.353987i	−0.821979	+	0.569517i	$0.807130\pi$
$798$		0			0
$799$	29.1543	+	33.6459i	1.03141	+	1.19031i
$800$		0			0
$801$	−7.90517	+	9.12306i	−0.279316	+	0.322347i
$802$		0			0
$803$	−4.48414	−	9.81890i	−0.158242	−	0.346502i
$804$		0			0
$805$	0.757887	−	0.0614687i	0.0267120	−	0.00216649i
$806$		0			0
$807$	0.469320	+	1.02767i	0.0165209	+	0.0361756i
$808$		0			0
$809$	13.2591	−	15.3018i	0.466165	−	0.537983i	−0.473176	−	0.880968i	$-0.656893\pi$
$809$	13.2591	−	15.3018i	0.466165	−	0.537983i	0.939341	+	0.342985i	$0.111438\pi$
$810$		0			0
$811$	−12.6681	−	14.6197i	−0.444837	−	0.513369i	0.488406	−	0.872617i	$-0.337579\pi$
$811$	−12.6681	−	14.6197i	−0.444837	−	0.513369i	−0.933242	+	0.359248i	$0.883033\pi$
$812$		0			0
$813$	3.48194	+	1.02239i	0.122117	+	0.0358567i
$814$		0			0
$815$	−2.62116	+	18.2305i	−0.0918151	+	0.638588i
$816$		0			0
$817$	−1.33141	+	2.91539i	−0.0465803	+	0.101997i
$818$		0			0
$819$	0.0482061	−	0.0309802i	0.00168446	−	0.00108254i
$820$		0			0
$821$	0.730959	+	5.08393i	0.0255106	+	0.177430i	0.998593	−	0.0530269i	$-0.0168869\pi$
$821$	0.730959	+	5.08393i	0.0255106	+	0.177430i	−0.973082	+	0.230457i	$0.925978\pi$
$822$		0			0
$823$	23.1957	+	14.9070i	0.808553	+	0.519625i	0.878396	−	0.477933i	$-0.158614\pi$
$823$	23.1957	+	14.9070i	0.808553	+	0.519625i	−0.0698438	+	0.997558i	$0.522250\pi$
$824$		0			0
$825$	70.7736	−	20.7810i	2.46402	−	0.723501i
$826$		0			0
$827$	−35.3359			−1.22875			−0.614375	−	0.789014i	$-0.710592\pi$
$827$	−35.3359			−1.22875			−0.614375	+	0.789014i	$0.710592\pi$
$828$		0			0
$829$	6.60816			0.229511			0.114756	−	0.993394i	$-0.463392\pi$
$829$	6.60816			0.229511			0.114756	+	0.993394i	$0.463392\pi$
$830$		0			0
$831$	−12.5283	+	3.67864i	−0.434602	+	0.127611i
$832$		0			0
$833$	−30.0154	−	19.2897i	−1.03997	−	0.668348i
$834$		0			0
$835$	−7.15244	−	49.7463i	−0.247521	−	1.72154i
$836$		0			0
$837$	−5.27994	+	3.39321i	−0.182502	+	0.117287i
$838$		0			0
$839$	3.33479	−	7.30217i	0.115130	−	0.252099i	−0.843291	−	0.537457i	$-0.819385\pi$
$839$	3.33479	−	7.30217i	0.115130	−	0.252099i	0.958421	+	0.285358i	$0.0921124\pi$
$840$		0			0
$841$	1.32088	−	9.18695i	0.0455477	−	0.316791i
$842$		0			0
$843$	13.2252	+	3.88328i	0.455502	+	0.133747i
$844$		0			0
$845$	−29.5170	−	34.0644i	−1.01541	−	1.17185i
$846$		0			0
$847$	0.539294	−	0.622379i	0.0185304	−	0.0213852i
$848$		0			0
$849$	0.790606	+	1.73118i	0.0271335	+	0.0594141i
$850$		0			0
$851$	−0.0348463	−	0.0185987i	−0.00119451	−	0.000637555i
$852$		0			0
$853$	−12.4865	−	27.3417i	−0.427531	−	0.936163i	−0.993721	−	0.111888i	$-0.964310\pi$
$853$	−12.4865	−	27.3417i	−0.427531	−	0.936163i	0.566190	−	0.824275i	$-0.308417\pi$
$854$		0			0
$855$	1.62641	−	1.87698i	0.0556222	−	0.0641914i
$856$		0			0
$857$	−1.77477	−	2.04820i	−0.0606251	−	0.0699650i	0.724627	−	0.689141i	$-0.242012\pi$
$857$	−1.77477	−	2.04820i	−0.0606251	−	0.0699650i	−0.785252	+	0.619176i	$0.787467\pi$
$858$		0			0
$859$	4.43327	+	1.30173i	0.151261	+	0.0444143i	0.356487	−	0.934300i	$-0.383975\pi$
$859$	4.43327	+	1.30173i	0.151261	+	0.0444143i	−0.205225	+	0.978715i	$0.565793\pi$
$860$		0			0
$861$	−0.0475400	+	0.330648i	−0.00162016	+	0.0112684i
$862$		0			0
$863$	20.8303	−	45.6120i	0.709072	−	1.55265i	−0.119541	−	0.992829i	$-0.538142\pi$
$863$	20.8303	−	45.6120i	0.709072	−	1.55265i	0.828613	−	0.559821i	$-0.189130\pi$
$864$		0			0
$865$	−82.5906	+	53.0778i	−2.80816	+	1.80470i
$866$		0			0
$867$	1.27946	+	8.89883i	0.0434527	+	0.302220i
$868$		0			0
$869$	−4.16915	−	2.67935i	−0.141429	−	0.0908907i
$870$		0			0
$871$	6.06453	−	1.78071i	0.205489	−	0.0603369i
$872$		0			0
$873$	3.90402			0.132131
$874$		0			0
$875$	1.24475			0.0420802
$876$		0			0
$877$	23.3342	−	6.85154i	0.787940	−	0.231360i	0.137082	−	0.990560i	$-0.456228\pi$
$877$	23.3342	−	6.85154i	0.787940	−	0.231360i	0.650858	+	0.759200i	$0.274409\pi$
$878$		0			0
$879$	8.24984	+	5.30185i	0.278260	+	0.178827i
$880$		0			0
$881$	2.29090	+	15.9336i	0.0771825	+	0.536816i	0.991326	+	0.131426i	$0.0419554\pi$
$881$	2.29090	+	15.9336i	0.0771825	+	0.536816i	−0.914143	+	0.405391i	$0.867135\pi$
$882$		0			0
$883$	30.0753	−	19.3282i	1.01212	−	0.650447i	0.0741757	−	0.997245i	$-0.476367\pi$
$883$	30.0753	−	19.3282i	1.01212	−	0.650447i	0.937940	+	0.346798i	$0.112731\pi$
$884$		0			0
$885$	−17.7735	+	38.9186i	−0.597450	+	1.30823i
$886$		0			0
$887$	3.16113	−	21.9861i	0.106140	−	0.738223i	−0.865354	−	0.501161i	$-0.832907\pi$
$887$	3.16113	−	21.9861i	0.106140	−	0.738223i	0.971495	−	0.237062i	$-0.0761844\pi$
$888$		0			0
$889$	−0.0538342	−	0.0158071i	−0.00180554	−	0.000530155i
$890$		0			0
$891$	−3.75877	−	4.33785i	−0.125924	−	0.145324i
$892$		0			0
$893$	3.36162	−	3.87952i	0.112492	−	0.129823i
$894$		0			0
$895$	−23.6149	−	51.7094i	−0.789359	−	1.72845i
$896$		0			0
$897$	5.82049	−	4.44433i	0.194341	−	0.148392i
$898$		0			0
$899$	−11.5777	−	25.3516i	−0.386138	−	0.845524i
$900$		0			0
$901$	2.25388	−	2.60111i	0.0750876	−	0.0866557i
$902$		0			0
$903$	0.133987	+	0.154629i	0.00445880	+	0.00514573i
$904$		0			0
$905$	−80.8419	−	23.7373i	−2.68728	−	0.789055i
$906$		0			0
$907$	−2.81163	+	19.5553i	−0.0933585	+	0.649323i	0.888383	+	0.459103i	$0.151829\pi$
$907$	−2.81163	+	19.5553i	−0.0933585	+	0.649323i	−0.981742	+	0.190220i	$0.939080\pi$
$908$		0			0
$909$	−1.12814	+	2.47027i	−0.0374179	+	0.0819337i
$910$		0			0
$911$	−21.8132	+	14.0185i	−0.722703	+	0.464453i	−0.849576	−	0.527466i	$-0.823142\pi$
$911$	−21.8132	+	14.0185i	−0.722703	+	0.464453i	0.126873	+	0.991919i	$0.459506\pi$
$912$		0			0
$913$	−4.16646	−	28.9784i	−0.137890	−	0.959044i
$914$		0			0
$915$	−52.4565	−	33.7118i	−1.73416	−	1.11448i
$916$		0			0
$917$	−0.630467	+	0.185122i	−0.0208198	+	0.00611326i
$918$		0			0
$919$	−10.0034			−0.329981			−0.164991	−	0.986295i	$-0.552759\pi$
$919$	−10.0034			−0.329981			−0.164991	+	0.986295i	$0.552759\pi$
$920$		0			0
$921$	−15.1992			−0.500830
$922$		0			0
$923$	1.99629	−	0.586164i	0.0657087	−	0.0192938i
$924$		0			0
$925$	−0.0890393	−	0.0572221i	−0.00292759	−	0.00188145i
$926$		0			0
$927$	−1.67111	−	11.6228i	−0.0548864	−	0.381743i
$928$		0			0
$929$	3.71575	−	2.38796i	0.121910	−	0.0783466i	−0.478265	−	0.878216i	$-0.658734\pi$
$929$	3.71575	−	2.38796i	0.121910	−	0.0783466i	0.600175	+	0.799869i	$0.295098\pi$
$930$		0			0
$931$	−1.70901	+	3.74222i	−0.0560106	+	0.122646i
$932$		0			0
$933$	−1.93036	+	13.4259i	−0.0631971	+	0.439545i
$934$		0			0
$935$	118.624	+	34.8313i	3.87944	+	1.13910i
$936$		0			0
$937$	9.99623	+	11.5363i	0.326562	+	0.376873i	0.895162	−	0.445741i	$-0.147060\pi$
$937$	9.99623	+	11.5363i	0.326562	+	0.376873i	−0.568599	+	0.822615i	$0.692514\pi$
$938$		0			0
$939$	−12.9874	+	14.9882i	−0.423826	+	0.489122i
$940$		0			0
$941$	16.5301	+	36.1958i	0.538865	+	1.17995i	0.961791	+	0.273786i	$0.0882760\pi$
$941$	16.5301	+	36.1958i	0.538865	+	1.17995i	−0.422925	+	0.906165i	$0.638997\pi$
$942$		0			0
$943$	−2.63968	+	42.6095i	−0.0859598	+	1.38756i
$944$		0			0
$945$	−0.0658637	−	0.144221i	−0.00214255	−	0.00469152i
$946$		0			0
$947$	14.6012	−	16.8506i	0.474474	−	0.547573i	−0.467176	−	0.884164i	$-0.654729\pi$
$947$	14.6012	−	16.8506i	0.474474	−	0.547573i	0.941651	+	0.336592i	$0.109274\pi$
$948$		0			0
$949$	−1.88057	−	2.17030i	−0.0610460	−	0.0704508i
$950$		0			0
$951$	15.7548	+	4.62604i	0.510886	+	0.150010i
$952$		0			0
$953$	−3.19403	+	22.2150i	−0.103465	+	0.719614i	0.870377	+	0.492386i	$0.163875\pi$
$953$	−3.19403	+	22.2150i	−0.103465	+	0.719614i	−0.973842	+	0.227227i	$0.927034\pi$
$954$		0			0
$955$	−1.42034	+	3.11010i	−0.0459610	+	0.100641i
$956$		0			0
$957$	21.4418	−	13.7798i	0.693116	−	0.445438i
$958$		0			0
$959$	0.0480594	+	0.334261i	0.00155192	+	0.0107938i
$960$		0			0
$961$	7.05955	+	4.53690i	0.227727	+	0.146351i
$962$		0			0
$963$	−11.4148	+	3.35169i	−0.367837	+	0.108007i
$964$		0			0
$965$	41.0743			1.32223
$966$		0			0
$967$	5.99490			0.192783			0.0963916	−	0.995343i	$-0.469270\pi$
$967$	5.99490			0.192783			0.0963916	+	0.995343i	$0.469270\pi$
$968$		0			0
$969$	2.87541	−	0.844297i	0.0923716	−	0.0271227i
$970$		0			0
$971$	39.7962	+	25.5754i	1.27712	+	0.820755i	0.990530	−	0.137298i	$-0.0438420\pi$
$971$	39.7962	+	25.5754i	1.27712	+	0.820755i	0.286590	+	0.958053i	$0.407478\pi$
$972$		0			0
$973$	−0.0111750	−	0.0777236i	−0.000358253	−	0.00249170i
$974$		0			0
$975$	16.5082	−	10.6092i	0.528686	−	0.339766i
$976$		0			0
$977$	15.3564	−	33.6259i	0.491296	−	1.07579i	−0.487905	−	0.872897i	$-0.662239\pi$
$977$	15.3564	−	33.6259i	0.491296	−	1.07579i	0.979201	−	0.202892i	$-0.0650340\pi$
$978$		0			0
$979$	−9.86074	+	68.5830i	−0.315151	+	2.19192i
$980$		0			0
$981$	−12.6265	−	3.70749i	−0.403135	−	0.118371i
$982$		0			0
$983$	17.8919	+	20.6483i	0.570663	+	0.658580i	0.965571	−	0.260141i	$-0.0837690\pi$
$983$	17.8919	+	20.6483i	0.570663	+	0.658580i	−0.394908	+	0.918721i	$0.629224\pi$
$984$		0			0
$985$	74.5952	−	86.0875i	2.37680	−	2.74297i
$986$		0			0
$987$	−0.136133	−	0.298091i	−0.00433317	−	0.00948833i
$988$		0			0
$989$	18.6649	+	18.3126i	0.593510	+	0.582306i
$990$		0			0
$991$	10.0261	+	21.9541i	0.318489	+	0.697394i	0.999388	−	0.0349835i	$-0.0111379\pi$
$991$	10.0261	+	21.9541i	0.318489	+	0.697394i	−0.680899	+	0.732378i	$0.738411\pi$
$992$		0			0
$993$	11.5174	−	13.2918i	0.365493	−	0.421802i
$994$		0			0
$995$	34.5173	+	39.8351i	1.09427	+	1.26286i
$996$		0			0
$997$	−28.9734	−	8.50736i	−0.917598	−	0.269431i	−0.211362	−	0.977408i	$-0.567790\pi$
$997$	−28.9734	−	8.50736i	−0.917598	−	0.269431i	−0.706236	+	0.707977i	$0.749608\pi$
$998$		0			0
$999$	−0.00117212	+	0.00815229i	−3.70843e−5	+	0.000257927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.73.1	✓	20
3.2	odd	2		828.2.q.b.73.2		20
23.6	even	11	inner	276.2.i.b.121.1	yes	20
23.11	odd	22		6348.2.a.q.1.10		10
23.12	even	11		6348.2.a.r.1.1		10
69.29	odd	22		828.2.q.b.397.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.73.1	✓	20	1.1	even	1	trivial
276.2.i.b.121.1	yes	20	23.6	even	11	inner
828.2.q.b.73.2		20	3.2	odd	2
828.2.q.b.397.2		20	69.29	odd	22
6348.2.a.q.1.10		10	23.11	odd	22
6348.2.a.r.1.1		10	23.12	even	11

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{3} +(-3.55432 - 2.28422i) q^{5} +(0.00534053 + 0.0371442i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{3} +(-3.55432 - 2.28422i) q^{5} +(0.00534053 + 0.0371442i) q^{7} +(0.841254 - 0.540641i) q^{9} +(2.38440 - 5.22111i) q^{11} +(0.217316 - 1.51146i) q^{13} +(-4.05388 - 1.19033i) q^{15} +(-3.33853 - 3.85287i) q^{17} +(-0.384947 + 0.444253i) q^{19} +(0.0155889 + 0.0341350i) q^{21} +(2.33840 + 4.18711i) q^{23} +(5.33844 + 11.6896i) q^{25} +(0.654861 - 0.755750i) q^{27} +(2.90795 + 3.35595i) q^{29} +(-6.02205 - 1.76823i) q^{31} +(0.816859 - 5.68138i) q^{33} +(0.0658637 - 0.144221i) q^{35} +(-0.00692866 + 0.00445278i) q^{37} +(-0.217316 - 1.51146i) q^{39} +(7.48861 + 4.81264i) q^{41} +(5.23143 - 1.53609i) q^{43} -4.22503 q^{45} -8.73269 q^{47} +(6.71510 - 1.97173i) q^{49} +(-4.28877 - 2.75623i) q^{51} +(0.0960784 + 0.668240i) q^{53} +(-20.4011 + 13.1110i) q^{55} +(-0.244194 + 0.534710i) q^{57} +(1.44116 - 10.0235i) q^{59} +(14.1607 + 4.15796i) q^{61} +(0.0245744 + 0.0283604i) q^{63} +(-4.22493 + 4.87583i) q^{65} +(1.71948 + 3.76513i) q^{67} +(3.42332 + 3.35870i) q^{69} +(0.566009 + 1.23939i) q^{71} +(1.23154 - 1.42128i) q^{73} +(8.41552 + 9.71203i) q^{75} +(0.206668 + 0.0606832i) q^{77} +(0.122878 - 0.854635i) q^{79} +(0.415415 - 0.909632i) q^{81} +(4.29089 - 2.75759i) q^{83} +(3.06539 + 21.3203i) q^{85} +(3.73564 + 2.40075i) q^{87} +(-11.5826 + 3.40094i) q^{89} +0.0573027 q^{91} -6.27628 q^{93} +(2.38300 - 0.699711i) q^{95} +(3.28427 + 2.11067i) q^{97} +(-0.816859 - 5.68138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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