LMFDB - Embedded newform 276.2.i.b.265.2

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			265.2
Root			$-1.25953 - 1.45357i$ of defining polynomial
Character	$\chi$	$=$	276.265
Dual form			276.2.i.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{3} +(1.44496 - 0.424279i) q^{5} +(2.15021 + 2.48148i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{3} +(1.44496 - 0.424279i) q^{5} +(2.15021 + 2.48148i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(0.328901 + 0.211372i) q^{11} +(1.81146 - 2.09054i) q^{13} +(-0.214321 - 1.49063i) q^{15} +(-1.32520 - 2.90178i) q^{17} +(0.211006 - 0.462038i) q^{19} +(2.76223 - 1.77518i) q^{21} +(4.28800 - 2.14781i) q^{23} +(-2.29837 + 1.47707i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-2.62381 - 5.74533i) q^{29} +(1.36281 + 9.47855i) q^{31} +(0.256028 - 0.295472i) q^{33} +(4.15981 + 2.67335i) q^{35} +(-1.14473 - 0.336124i) q^{37} +(-1.81146 - 2.09054i) q^{39} +(-3.11518 + 0.914700i) q^{41} +(-1.13550 + 7.89759i) q^{43} -1.50596 q^{45} -11.8320 q^{47} +(-0.538112 + 3.74265i) q^{49} +(-3.06084 + 0.898745i) q^{51} +(0.458430 + 0.529056i) q^{53} +(0.564930 + 0.165878i) q^{55} +(-0.427306 - 0.274613i) q^{57} +(0.00941384 - 0.0108641i) q^{59} +(-0.106098 - 0.737928i) q^{61} +(-1.36400 - 2.98674i) q^{63} +(1.73052 - 3.78931i) q^{65} +(3.41571 - 2.19514i) q^{67} +(-1.51570 - 4.55002i) q^{69} +(-8.47217 + 5.44473i) q^{71} +(-3.48245 + 7.62550i) q^{73} +(1.13495 + 2.48519i) q^{75} +(0.182693 + 1.27066i) q^{77} +(-0.0674484 + 0.0778396i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-5.87497 - 1.72505i) q^{83} +(-3.14603 - 3.63071i) q^{85} +(-6.06026 + 1.77945i) q^{87} +(-0.0197428 + 0.137314i) q^{89} +9.08266 q^{91} +9.57602 q^{93} +(0.108862 - 0.757151i) q^{95} +(-6.64725 + 1.95181i) q^{97} +(-0.256028 - 0.295472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$	$1$

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
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$		0			0
$5$	1.44496	−	0.424279i	0.646206	−	0.189743i	0.0578246	−	0.998327i	$-0.481584\pi$
$5$	1.44496	−	0.424279i	0.646206	−	0.189743i	0.588381	+	0.808584i	$0.299765\pi$
$6$		0			0
$7$	2.15021	+	2.48148i	0.812704	+	0.937910i	0.999006	−	0.0445824i	$-0.0141957\pi$
$7$	2.15021	+	2.48148i	0.812704	+	0.937910i	−0.186302	+	0.982493i	$0.559650\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	0.328901	+	0.211372i	0.0991675	+	0.0637311i	0.589285	−	0.807925i	$-0.299410\pi$
$11$	0.328901	+	0.211372i	0.0991675	+	0.0637311i	−0.490117	+	0.871657i	$0.663046\pi$
$12$		0			0
$13$	1.81146	−	2.09054i	0.502410	−	0.579811i	−0.446729	−	0.894669i	$-0.647411\pi$
$13$	1.81146	−	2.09054i	0.502410	−	0.579811i	0.949139	+	0.314858i	$0.101957\pi$
$14$		0			0
$15$	−0.214321	−	1.49063i	−0.0553374	−	0.384880i
$16$		0			0
$17$	−1.32520	−	2.90178i	−0.321408	−	0.703786i	0.678105	−	0.734965i	$-0.262801\pi$
$17$	−1.32520	−	2.90178i	−0.321408	−	0.703786i	−0.999514	+	0.0311785i	$0.990074\pi$
$18$		0			0
$19$	0.211006	−	0.462038i	0.0484080	−	0.105999i	−0.883883	−	0.467709i	$-0.845080\pi$
$19$	0.211006	−	0.462038i	0.0484080	−	0.105999i	0.932291	+	0.361710i	$0.117807\pi$
$20$		0			0
$21$	2.76223	−	1.77518i	0.602767	−	0.387375i
$22$		0			0
$23$	4.28800	−	2.14781i	0.894109	−	0.447848i
$23$	4.28800	−	2.14781i	0.894109	−	0.447848i
$24$		0			0
$25$	−2.29837	+	1.47707i	−0.459674	+	0.295415i
$26$		0			0
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$		0			0
$29$	−2.62381	−	5.74533i	−0.487228	−	1.06688i	−0.980412	−	0.196956i	$-0.936894\pi$
$29$	−2.62381	−	5.74533i	−0.487228	−	1.06688i	0.493184	−	0.869925i	$-0.335833\pi$
$30$		0			0
$31$	1.36281	+	9.47855i	0.244768	+	1.70240i	0.627564	+	0.778565i	$0.284052\pi$
$31$	1.36281	+	9.47855i	0.244768	+	1.70240i	−0.382796	+	0.923833i	$0.625039\pi$
$32$		0			0
$33$	0.256028	−	0.295472i	0.0445688	−	0.0514351i
$34$		0			0
$35$	4.15981	+	2.67335i	0.703136	+	0.451878i
$36$		0			0
$37$	−1.14473	−	0.336124i	−0.188193	−	0.0552585i	0.186278	−	0.982497i	$-0.440358\pi$
$37$	−1.14473	−	0.336124i	−0.188193	−	0.0552585i	−0.374471	+	0.927239i	$0.622176\pi$
$38$		0			0
$39$	−1.81146	−	2.09054i	−0.290066	−	0.334754i
$40$		0			0
$41$	−3.11518	+	0.914700i	−0.486510	+	0.142852i	−0.515783	−	0.856719i	$-0.672499\pi$
$41$	−3.11518	+	0.914700i	−0.486510	+	0.142852i	0.0292731	+	0.999571i	$0.490681\pi$
$42$		0			0
$43$	−1.13550	+	7.89759i	−0.173162	+	1.20437i	0.698988	+	0.715133i	$0.253634\pi$
$43$	−1.13550	+	7.89759i	−0.173162	+	1.20437i	−0.872151	+	0.489237i	$0.837275\pi$
$44$		0			0
$45$	−1.50596			−0.224496
$46$		0			0
$47$	−11.8320			−1.72588			−0.862939	−	0.505309i	$-0.831379\pi$
$47$	−11.8320			−1.72588			−0.862939	+	0.505309i	$0.831379\pi$
$48$		0			0
$49$	−0.538112	+	3.74265i	−0.0768732	+	0.534665i
$50$		0			0
$51$	−3.06084	+	0.898745i	−0.428604	+	0.125849i
$52$		0			0
$53$	0.458430	+	0.529056i	0.0629702	+	0.0726715i	0.786361	−	0.617768i	$-0.211963\pi$
$53$	0.458430	+	0.529056i	0.0629702	+	0.0726715i	−0.723390	+	0.690439i	$0.757417\pi$
$54$		0			0
$55$	0.564930	+	0.165878i	0.0761751	+	0.0223670i
$56$		0			0
$57$	−0.427306	−	0.274613i	−0.0565980	−	0.0363733i
$58$		0			0
$59$	0.00941384	−	0.0108641i	0.00122558	−	0.00141439i	−0.755136	−	0.655568i	$-0.772429\pi$
$59$	0.00941384	−	0.0108641i	0.00122558	−	0.00141439i	0.756362	+	0.654153i	$0.226975\pi$
$60$		0			0
$61$	−0.106098	−	0.737928i	−0.0135845	−	0.0944820i	0.981901	−	0.189394i	$-0.0606522\pi$
$61$	−0.106098	−	0.737928i	−0.0135845	−	0.0944820i	−0.995486	+	0.0949116i	$0.969743\pi$
$62$		0			0
$63$	−1.36400	−	2.98674i	−0.171848	−	0.376294i
$64$		0			0
$65$	1.73052	−	3.78931i	0.214645	−	0.470006i
$66$		0			0
$67$	3.41571	−	2.19514i	0.417295	−	0.268179i	−0.315101	−	0.949058i	$-0.602038\pi$
$67$	3.41571	−	2.19514i	0.417295	−	0.268179i	0.732396	+	0.680879i	$0.238402\pi$
$68$		0			0
$69$	−1.51570	−	4.55002i	−0.182469	−	0.547758i
$70$		0			0
$71$	−8.47217	+	5.44473i	−1.00546	+	0.646171i	−0.936215	−	0.351429i	$-0.885696\pi$
$71$	−8.47217	+	5.44473i	−1.00546	+	0.646171i	−0.0692466	+	0.997600i	$0.522060\pi$
$72$		0			0
$73$	−3.48245	+	7.62550i	−0.407590	+	0.892497i	0.588854	+	0.808239i	$0.299579\pi$
$73$	−3.48245	+	7.62550i	−0.407590	+	0.892497i	−0.996444	+	0.0842580i	$0.973148\pi$
$74$		0			0
$75$	1.13495	+	2.48519i	0.131052	+	0.286964i
$76$		0			0
$77$	0.182693	+	1.27066i	0.0208198	+	0.144805i
$78$		0			0
$79$	−0.0674484	+	0.0778396i	−0.00758854	+	0.00875764i	−0.759531	−	0.650471i	$-0.774572\pi$
$79$	−0.0674484	+	0.0778396i	−0.00758854	+	0.00875764i	0.751943	+	0.659229i	$0.229117\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	−5.87497	−	1.72505i	−0.644862	−	0.189349i	−0.0570821	−	0.998369i	$-0.518180\pi$
$83$	−5.87497	−	1.72505i	−0.644862	−	0.189349i	−0.587780	+	0.809021i	$0.699998\pi$
$84$		0			0
$85$	−3.14603	−	3.63071i	−0.341235	−	0.393806i
$86$		0			0
$87$	−6.06026	+	1.77945i	−0.649728	+	0.190777i
$88$		0			0
$89$	−0.0197428	+	0.137314i	−0.00209274	+	0.0145553i	−0.990841	−	0.135033i	$-0.956886\pi$
$89$	−0.0197428	+	0.137314i	−0.00209274	+	0.0145553i	0.988748	+	0.149589i	$0.0477949\pi$
$90$		0			0
$91$	9.08266			0.952121
$92$		0			0
$93$	9.57602			0.992987
$94$		0			0
$95$	0.108862	−	0.757151i	0.0111690	−	0.0776821i
$96$		0			0
$97$	−6.64725	+	1.95181i	−0.674925	+	0.198176i	−0.601195	−	0.799102i	$-0.705309\pi$
$97$	−6.64725	+	1.95181i	−0.674925	+	0.198176i	−0.0737303	+	0.997278i	$0.523490\pi$
$98$		0			0
$99$	−0.256028	−	0.295472i	−0.0257318	−	0.0296961i
$100$		0			0
$101$	12.9471	+	3.80160i	1.28828	+	0.378273i	0.852948	−	0.521996i	$-0.174812\pi$
$101$	12.9471	+	3.80160i	1.28828	+	0.378273i	0.435333	+	0.900270i	$0.356631\pi$
$102$		0			0
$103$	−12.0172	−	7.72296i	−1.18409	−	0.760965i	−0.207952	−	0.978139i	$-0.566680\pi$
$103$	−12.0172	−	7.72296i	−1.18409	−	0.760965i	−0.976133	+	0.217174i	$0.930316\pi$
$104$		0			0
$105$	3.23814	−	3.73701i	0.316010	−	0.364695i
$106$		0			0
$107$	2.20028	+	15.3033i	0.212710	+	1.47943i	0.764055	+	0.645151i	$0.223205\pi$
$107$	2.20028	+	15.3033i	0.212710	+	1.47943i	−0.551346	+	0.834277i	$0.685886\pi$
$108$		0			0
$109$	−5.79032	−	12.6790i	−0.554612	−	1.21443i	−0.954595	−	0.297908i	$-0.903711\pi$
$109$	−5.79032	−	12.6790i	−0.554612	−	1.21443i	0.399983	−	0.916523i	$-0.369016\pi$
$110$		0			0
$111$	−0.495616	+	1.08525i	−0.0470418	+	0.103007i
$112$		0			0
$113$	14.4039	−	9.25684i	1.35501	−	0.870810i	0.357011	−	0.934100i	$-0.383796\pi$
$113$	14.4039	−	9.25684i	1.35501	−	0.870810i	0.997995	+	0.0632901i	$0.0201593\pi$
$114$		0			0
$115$	5.28472	−	4.92280i	0.492803	−	0.459053i
$116$		0			0
$117$	−2.32706	+	1.49551i	−0.215137	+	0.138260i
$118$		0			0
$119$	4.35125	−	9.52791i	0.398878	−	0.873422i
$120$		0			0
$121$	−4.50607	−	9.86691i	−0.409642	−	0.896992i
$122$		0			0
$123$	0.462053	+	3.21365i	0.0416619	+	0.289765i
$124$		0			0
$125$	−7.62534	+	8.80011i	−0.682031	+	0.787106i
$126$		0			0
$127$	10.7953	+	6.93770i	0.957925	+	0.615621i	0.923423	−	0.383784i	$-0.125379\pi$
$127$	10.7953	+	6.93770i	0.957925	+	0.615621i	0.0345021	+	0.999405i	$0.489015\pi$
$128$		0			0
$129$	7.65560	+	2.24789i	0.674038	+	0.197915i
$130$		0			0
$131$	−3.96105	−	4.57129i	−0.346078	−	0.399396i	0.555849	−	0.831283i	$-0.312393\pi$
$131$	−3.96105	−	4.57129i	−0.346078	−	0.399396i	−0.901927	+	0.431888i	$0.857848\pi$
$132$		0			0
$133$	1.60024	−	0.469874i	0.138759	−	0.0407432i
$134$		0			0
$135$	−0.214321	+	1.49063i	−0.0184458	+	0.128293i
$136$		0			0
$137$	9.86419			0.842754			0.421377	−	0.906885i	$-0.361547\pi$
$137$	9.86419			0.842754			0.421377	+	0.906885i	$0.361547\pi$
$138$		0			0
$139$	18.2084			1.54441			0.772206	−	0.635372i	$-0.219153\pi$
$139$	18.2084			1.54441			0.772206	+	0.635372i	$0.219153\pi$
$140$		0			0
$141$	−1.68387	+	11.7116i	−0.141808	+	0.986293i
$142$		0			0
$143$	1.03767	−	0.304689i	0.0867747	−	0.0254793i
$144$		0			0
$145$	−6.22892	−	7.18855i	−0.517283	−	0.596977i
$146$		0			0
$147$	3.62798	+	1.06527i	0.299231	+	0.0878620i
$148$		0			0
$149$	−12.1600	−	7.81474i	−0.996184	−	0.640209i	−0.0624020	−	0.998051i	$-0.519876\pi$
$149$	−12.1600	−	7.81474i	−0.996184	−	0.640209i	−0.933782	+	0.357843i	$0.883512\pi$
$150$		0			0
$151$	6.74579	−	7.78506i	0.548965	−	0.633539i	−0.411677	−	0.911330i	$-0.635057\pi$
$151$	6.74579	−	7.78506i	0.548965	−	0.633539i	0.960642	+	0.277791i	$0.0896022\pi$
$152$		0			0
$153$	0.453993	+	3.15759i	0.0367032	+	0.255276i
$154$		0			0
$155$	5.99075	+	13.1179i	0.481189	+	1.05366i
$156$		0			0
$157$	−3.47719	+	7.61399i	−0.277510	+	0.607663i	−0.996145	−	0.0877252i	$-0.972040\pi$
$157$	−3.47719	+	7.61399i	−0.277510	+	0.607663i	0.718634	+	0.695388i	$0.244768\pi$
$158$		0			0
$159$	0.588913	−	0.378471i	0.0467038	−	0.0300147i
$160$		0			0
$161$	14.5498	+	6.02233i	1.14669	+	0.474626i
$162$		0			0
$163$	8.24257	−	5.29718i	0.645608	−	0.414907i	−0.176451	−	0.984309i	$-0.556462\pi$
$163$	8.24257	−	5.29718i	0.645608	−	0.414907i	0.822059	+	0.569402i	$0.192825\pi$
$164$		0			0
$165$	0.244588	−	0.535573i	0.0190411	−	0.0416943i
$166$		0			0
$167$	−4.78092	−	10.4688i	−0.369959	−	0.810097i	−0.999452	−	0.0330912i	$-0.989465\pi$
$167$	−4.78092	−	10.4688i	−0.369959	−	0.810097i	0.629493	−	0.777006i	$-0.283262\pi$
$168$		0			0
$169$	0.761134	+	5.29381i	0.0585488	+	0.407216i
$170$		0			0
$171$	−0.332629	+	0.383875i	−0.0254368	+	0.0293556i
$172$		0			0
$173$	11.7180	+	7.53070i	0.890903	+	0.572548i	0.904079	−	0.427365i	$-0.140558\pi$
$173$	11.7180	+	7.53070i	0.890903	+	0.572548i	−0.0131765	+	0.999913i	$0.504194\pi$
$174$		0			0
$175$	−8.60730	−	2.52733i	−0.650651	−	0.191048i
$176$		0			0
$177$	−0.00941384	−	0.0108641i	−0.000707587	−	0.000816599i
$178$		0			0
$179$	10.3570	−	3.04108i	0.774115	−	0.227301i	0.129265	−	0.991610i	$-0.458738\pi$
$179$	10.3570	−	3.04108i	0.774115	−	0.227301i	0.644850	+	0.764309i	$0.276920\pi$
$180$		0			0
$181$	3.05999	−	21.2827i	0.227448	−	1.58193i	−0.481355	−	0.876526i	$-0.659855\pi$
$181$	3.05999	−	21.2827i	0.227448	−	1.58193i	0.708803	−	0.705407i	$-0.249236\pi$
$182$		0			0
$183$	−0.745517			−0.0551102
$184$		0			0
$185$	−1.79671			−0.132096
$186$		0			0
$187$	0.177496	−	1.23451i	0.0129798	−	0.0902764i
$188$		0			0
$189$	−3.15046	+	0.925059i	−0.229162	+	0.0672881i
$190$		0			0
$191$	−16.2405	−	18.7426i	−1.17512	−	1.35616i	−0.921271	−	0.388921i	$-0.872848\pi$
$191$	−16.2405	−	18.7426i	−1.17512	−	1.35616i	−0.253852	−	0.967243i	$-0.581698\pi$
$192$		0			0
$193$	3.15091	+	0.925190i	0.226807	+	0.0665966i	0.393161	−	0.919469i	$-0.371381\pi$
$193$	3.15091	+	0.925190i	0.226807	+	0.0665966i	−0.166354	+	0.986066i	$0.553200\pi$
$194$		0			0
$195$	−3.50446	−	2.25218i	−0.250960	−	0.161282i
$196$		0			0
$197$	−17.9364	+	20.6997i	−1.27792	+	1.47480i	−0.473425	+	0.880834i	$0.656982\pi$
$197$	−17.9364	+	20.6997i	−1.27792	+	1.47480i	−0.804493	+	0.593962i	$0.797563\pi$
$198$		0			0
$199$	−1.68521	−	11.7209i	−0.119461	−	0.830872i	−0.958151	−	0.286262i	$-0.907587\pi$
$199$	−1.68521	−	11.7209i	−0.119461	−	0.830872i	0.838690	−	0.544609i	$-0.183322\pi$
$200$		0			0
$201$	−1.68669	−	3.69334i	−0.118970	−	0.260508i
$202$		0			0
$203$	8.61517	−	18.8646i	0.604667	−	1.32404i
$204$		0			0
$205$	−4.11323	+	2.64341i	−0.287280	+	0.184624i
$206$		0			0
$207$	−4.71941	+	0.852736i	−0.328022	+	0.0592692i
$208$		0			0
$209$	0.167062	−	0.107364i	0.0115559	−	0.00742653i
$210$		0			0
$211$	5.20435	−	11.3959i	0.358282	−	0.784529i	−0.641565	−	0.767068i	$-0.721715\pi$
$211$	5.20435	−	11.3959i	0.358282	−	0.784529i	0.999848	−	0.0174604i	$-0.00555810\pi$
$212$		0			0
$213$	4.18360	+	9.16080i	0.286655	+	0.627688i
$214$		0			0
$215$	1.71002	+	11.8935i	0.116623	+	0.811128i
$216$		0			0
$217$	−20.5905	+	23.7627i	−1.39777	+	1.61312i
$218$		0			0
$219$	7.05228	+	4.53223i	0.476549	+	0.306259i
$220$		0			0
$221$	−8.46685	−	2.48609i	−0.569542	−	0.167233i
$222$		0			0
$223$	−10.0283	−	11.5732i	−0.671542	−	0.775000i	0.313075	−	0.949728i	$-0.398641\pi$
$223$	−10.0283	−	11.5732i	−0.671542	−	0.775000i	−0.984617	+	0.174728i	$0.944095\pi$
$224$		0			0
$225$	2.62141	−	0.769715i	0.174761	−	0.0513143i
$226$		0			0
$227$	−2.34043	+	16.2781i	−0.155340	+	1.08041i	0.751742	+	0.659457i	$0.229214\pi$
$227$	−2.34043	+	16.2781i	−0.155340	+	1.08041i	−0.907082	+	0.420955i	$0.861695\pi$
$228$		0			0
$229$	6.90633			0.456383			0.228192	−	0.973616i	$-0.426719\pi$
$229$	6.90633			0.456383			0.228192	+	0.973616i	$0.426719\pi$
$230$		0			0
$231$	1.28372			0.0844627
$232$		0			0
$233$	−3.54266	+	24.6397i	−0.232087	+	1.61420i	0.456962	+	0.889486i	$0.348938\pi$
$233$	−3.54266	+	24.6397i	−0.232087	+	1.61420i	−0.689049	+	0.724715i	$0.741971\pi$
$234$		0			0
$235$	−17.0968	+	5.02007i	−1.11527	+	0.327473i
$236$		0			0
$237$	0.0674484	+	0.0778396i	0.00438124	+	0.00505622i
$238$		0			0
$239$	−8.07576	−	2.37126i	−0.522377	−	0.153384i	0.00990473	−	0.999951i	$-0.496847\pi$
$239$	−8.07576	−	2.37126i	−0.522377	−	0.153384i	−0.532282	+	0.846567i	$0.678665\pi$
$240$		0			0
$241$	−18.0679	−	11.6115i	−1.16386	−	0.747965i	−0.191506	−	0.981491i	$-0.561337\pi$
$241$	−18.0679	−	11.6115i	−1.16386	−	0.747965i	−0.972351	+	0.233526i	$0.924974\pi$
$242$		0			0
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$		0			0
$245$	0.810377	+	5.63630i	0.0517731	+	0.360090i
$246$		0			0
$247$	−0.583680	−	1.27808i	−0.0371386	−	0.0813223i
$248$		0			0
$249$	−2.54358	+	5.56967i	−0.161193	+	0.352964i
$250$		0			0
$251$	8.05342	−	5.17562i	0.508327	−	0.326682i	−0.261212	−	0.965281i	$-0.584122\pi$
$251$	8.05342	−	5.17562i	0.508327	−	0.326682i	0.769539	+	0.638599i	$0.220486\pi$
$252$		0			0
$253$	1.86431	+	0.199947i	0.117208	+	0.0125705i
$254$		0			0
$255$	−4.04148	+	2.59730i	−0.253087	+	0.162649i
$256$		0			0
$257$	0.262094	−	0.573906i	0.0163490	−	0.0357993i	−0.901281	−	0.433234i	$-0.857372\pi$
$257$	0.262094	−	0.573906i	0.0163490	−	0.0357993i	0.917630	+	0.397435i	$0.130100\pi$
$258$		0			0
$259$	−1.62734	−	3.56337i	−0.101118	−	0.221417i
$260$		0			0
$261$	0.898876	+	6.25182i	0.0556390	+	0.386978i
$262$		0			0
$263$	−14.6001	+	16.8494i	−0.900279	+	1.03898i	0.0987583	+	0.995111i	$0.468513\pi$
$263$	−14.6001	+	16.8494i	−0.900279	+	1.03898i	−0.999037	+	0.0438661i	$0.986033\pi$
$264$		0			0
$265$	0.886880	+	0.569963i	0.0544806	+	0.0350126i
$266$		0			0
$267$	0.133107	+	0.0390838i	0.00814602	+	0.00239189i
$268$		0			0
$269$	16.5601	+	19.1113i	1.00968	+	1.16524i	0.986208	+	0.165513i	$0.0529280\pi$
$269$	16.5601	+	19.1113i	1.00968	+	1.16524i	0.0234765	+	0.999724i	$0.492526\pi$
$270$		0			0
$271$	−10.3862	+	3.04968i	−0.630920	+	0.185255i	−0.581530	−	0.813525i	$-0.697546\pi$
$271$	−10.3862	+	3.04968i	−0.630920	+	0.185255i	−0.0493894	+	0.998780i	$0.515728\pi$
$272$		0			0
$273$	1.29260	−	8.99021i	0.0782315	−	0.544112i
$274$		0			0
$275$	−1.06815			−0.0644118
$276$		0			0
$277$	24.7512			1.48716			0.743579	−	0.668648i	$-0.233127\pi$
$277$	24.7512			1.48716			0.743579	+	0.668648i	$0.233127\pi$
$278$		0			0
$279$	1.36281	−	9.47855i	0.0815893	−	0.567466i
$280$		0			0
$281$	1.83015	−	0.537379i	0.109177	−	0.0320573i	−0.226688	−	0.973968i	$-0.572790\pi$
$281$	1.83015	−	0.537379i	0.109177	−	0.0320573i	0.335865	+	0.941910i	$0.390971\pi$
$282$		0			0
$283$	−0.612778	−	0.707183i	−0.0364259	−	0.0420377i	0.737244	−	0.675626i	$-0.236127\pi$
$283$	−0.612778	−	0.707183i	−0.0364259	−	0.0420377i	−0.773670	+	0.633589i	$0.781581\pi$
$284$		0			0
$285$	−0.733952	−	0.215508i	−0.0434756	−	0.0127656i
$286$		0			0
$287$	−8.96811	−	5.76346i	−0.529371	−	0.340206i
$288$		0			0
$289$	4.46844	−	5.15685i	0.262849	−	0.303344i
$290$		0			0
$291$	0.985939	+	6.85736i	0.0577968	+	0.401985i
$292$		0			0
$293$	−9.72189	−	21.2880i	−0.567959	−	1.24366i	−0.947877	−	0.318637i	$-0.896775\pi$
$293$	−9.72189	−	21.2880i	−0.567959	−	1.24366i	0.379918	−	0.925020i	$-0.375952\pi$
$294$		0			0
$295$	0.00899319	−	0.0196924i	0.000523604	−	0.00114653i
$296$		0			0
$297$	−0.328901	+	0.211372i	−0.0190848	+	0.0122651i
$298$		0			0
$299$	3.27748	−	12.8549i	0.189541	−	0.743418i
$300$		0			0
$301$	−22.0392	+	14.1638i	−1.27032	+	0.816386i
$302$		0			0
$303$	5.60546	−	12.2743i	0.322026	−	0.705138i
$304$		0			0
$305$	−0.466395	−	1.02126i	−0.0267057	−	0.0584773i
$306$		0			0
$307$	4.03311	+	28.0509i	0.230182	+	1.60095i	0.697317	+	0.716763i	$0.254377\pi$
$307$	4.03311	+	28.0509i	0.230182	+	1.60095i	−0.467135	+	0.884186i	$0.654714\pi$
$308$		0			0
$309$	−9.35457	+	10.7957i	−0.532163	+	0.614148i
$310$		0			0
$311$	15.2879	+	9.82491i	0.866895	+	0.557119i	0.896801	−	0.442433i	$-0.145885\pi$
$311$	15.2879	+	9.82491i	0.866895	+	0.557119i	−0.0299068	+	0.999553i	$0.509521\pi$
$312$		0			0
$313$	−4.34349	−	1.27536i	−0.245509	−	0.0720878i	0.156663	−	0.987652i	$-0.449926\pi$
$313$	−4.34349	−	1.27536i	−0.245509	−	0.0720878i	−0.402172	+	0.915564i	$0.631744\pi$
$314$		0			0
$315$	−3.23814	−	3.73701i	−0.182448	−	0.210557i
$316$		0			0
$317$	2.61228	−	0.767034i	0.146720	−	0.0430809i	−0.207548	−	0.978225i	$-0.566548\pi$
$317$	2.61228	−	0.767034i	0.146720	−	0.0430809i	0.354268	+	0.935144i	$0.384730\pi$
$318$		0			0
$319$	0.351430	−	2.44425i	0.0196763	−	0.136852i
$320$		0			0
$321$	15.4607			0.862931
$322$		0			0
$323$	−1.62036			−0.0901592
$324$		0			0
$325$	−1.07553	+	7.48050i	−0.0596598	+	0.414943i
$326$		0			0
$327$	−13.3740	+	3.92697i	−0.739585	+	0.217162i
$328$		0			0
$329$	−25.4414	−	29.3609i	−1.40263	−	1.61872i
$330$		0			0
$331$	−3.10768	−	0.912498i	−0.170814	−	0.0501554i	0.195207	−	0.980762i	$-0.437462\pi$
$331$	−3.10768	−	0.912498i	−0.170814	−	0.0501554i	−0.366021	+	0.930607i	$0.619280\pi$
$332$		0			0
$333$	1.00367	+	0.645018i	0.0550006	+	0.0353468i
$334$		0			0
$335$	4.00421	−	4.62110i	0.218773	−	0.252478i
$336$		0			0
$337$	3.86999	+	26.9164i	0.210812	+	1.46623i	0.770454	+	0.637495i	$0.220030\pi$
$337$	3.86999	+	26.9164i	0.210812	+	1.46623i	−0.559642	+	0.828734i	$0.689061\pi$
$338$		0			0
$339$	−7.11272	−	15.5747i	−0.386310	−	0.845901i
$340$		0			0
$341$	−1.55527	+	3.40557i	−0.0842226	+	0.184422i
$342$		0			0
$343$	8.89122	−	5.71404i	0.480081	−	0.308529i
$344$		0			0
$345$	−4.12060	−	5.93152i	−0.221846	−	0.319342i
$346$		0			0
$347$	−0.0398716	+	0.0256239i	−0.00214042	+	0.00137557i	−0.541711	−	0.840565i	$-0.682223\pi$
$347$	−0.0398716	+	0.0256239i	−0.00214042	+	0.00137557i	0.539570	+	0.841941i	$0.318587\pi$
$348$		0			0
$349$	8.03839	−	17.6016i	0.430285	−	0.942193i	−0.562995	−	0.826460i	$-0.690351\pi$
$349$	8.03839	−	17.6016i	0.430285	−	0.942193i	0.993280	−	0.115733i	$-0.0369217\pi$
$350$		0			0
$351$	1.14911	+	2.51621i	0.0613351	+	0.134305i
$352$		0			0
$353$	−1.12743	−	7.84147i	−0.0600072	−	0.417359i	−0.997578	−	0.0695635i	$-0.977839\pi$
$353$	−1.12743	−	7.84147i	−0.0600072	−	0.417359i	0.937570	−	0.347796i	$-0.113070\pi$
$354$		0			0
$355$	−9.93186	+	11.4620i	−0.527128	+	0.608339i
$356$		0			0
$357$	−8.81168	−	5.66292i	−0.466364	−	0.299714i
$358$		0			0
$359$	−0.224316	−	0.0658652i	−0.0118390	−	0.00347623i	0.275808	−	0.961213i	$-0.411055\pi$
$359$	−0.224316	−	0.0658652i	−0.0118390	−	0.00347623i	−0.287647	+	0.957737i	$0.592873\pi$
$360$		0			0
$361$	12.2734	+	14.1643i	0.645968	+	0.745487i
$362$		0			0
$363$	−10.4078	+	3.05599i	−0.546266	+	0.160398i
$364$		0			0
$365$	−1.79666	+	12.4961i	−0.0940417	+	0.654074i
$366$		0			0
$367$	15.0127			0.783656			0.391828	−	0.920039i	$-0.371843\pi$
$367$	15.0127			0.783656			0.391828	+	0.920039i	$0.371843\pi$
$368$		0			0
$369$	3.24670			0.169016
$370$		0			0
$371$	−0.327120	+	2.27517i	−0.0169832	+	0.118121i
$372$		0			0
$373$	31.2913	−	9.18796i	1.62020	−	0.475735i	0.659130	−	0.752029i	$-0.270925\pi$
$373$	31.2913	−	9.18796i	1.62020	−	0.475735i	0.961073	+	0.276294i	$0.0891065\pi$
$374$		0			0
$375$	7.62534	+	8.80011i	0.393771	+	0.454436i
$376$		0			0
$377$	−16.7638	−	4.92229i	−0.863378	−	0.253511i
$378$		0			0
$379$	26.6773	+	17.1445i	1.37032	+	0.880653i	0.998857	−	0.0477939i	$-0.0152191\pi$
$379$	26.6773	+	17.1445i	1.37032	+	0.880653i	0.371465	+	0.928447i	$0.378855\pi$
$380$		0			0
$381$	8.40341	−	9.69805i	0.430520	−	0.496846i
$382$		0			0
$383$	−4.32236	−	30.0627i	−0.220862	−	1.53613i	−0.734789	−	0.678296i	$-0.762719\pi$
$383$	−4.32236	−	30.0627i	−0.220862	−	1.53613i	0.513926	−	0.857834i	$-0.328190\pi$
$384$		0			0
$385$	0.803096	+	1.75853i	0.0409296	+	0.0896232i
$386$		0			0
$387$	3.31451	−	7.25777i	0.168486	−	0.368933i
$388$		0			0
$389$	23.6796	−	15.2179i	1.20060	−	0.771580i	0.221541	−	0.975151i	$-0.428891\pi$
$389$	23.6796	−	15.2179i	1.20060	−	0.771580i	0.979060	+	0.203571i	$0.0652549\pi$
$390$		0			0
$391$	−11.9149	−	9.59657i	−0.602564	−	0.485320i
$392$		0			0
$393$	−5.08848	+	3.27017i	−0.256680	+	0.164958i
$394$		0			0
$395$	−0.0644346	+	0.141092i	−0.00324205	+	0.00709911i
$396$		0			0
$397$	−5.10599	−	11.1806i	−0.256262	−	0.561136i	0.737150	−	0.675729i	$-0.236171\pi$
$397$	−5.10599	−	11.1806i	−0.256262	−	0.561136i	−0.993413	+	0.114593i	$0.963444\pi$
$398$		0			0
$399$	−0.237353	−	1.65082i	−0.0118825	−	0.0826446i
$400$		0			0
$401$	22.7838	−	26.2939i	1.13777	−	1.31305i	0.194544	−	0.980894i	$-0.437677\pi$
$401$	22.7838	−	26.2939i	1.13777	−	1.31305i	0.943223	−	0.332160i	$-0.107777\pi$
$402$		0			0
$403$	22.2840	+	14.3210i	1.11004	+	0.713382i
$404$		0			0
$405$	1.44496	+	0.424279i	0.0718007	+	0.0210826i
$406$		0			0
$407$	−0.305457	−	0.352517i	−0.0151410	−	0.0174736i
$408$		0			0
$409$	1.66662	−	0.489365i	0.0824092	−	0.0241975i	−0.240268	−	0.970707i	$-0.577235\pi$
$409$	1.66662	−	0.489365i	0.0824092	−	0.0241975i	0.322677	+	0.946509i	$0.395417\pi$
$410$		0			0
$411$	1.40382	−	9.76378i	0.0692453	−	0.481612i
$412$		0			0
$413$	0.0472009			0.00232260
$414$		0			0
$415$	−9.22100			−0.452641
$416$		0			0
$417$	2.59132	−	18.0230i	0.126897	−	0.882591i
$418$		0			0
$419$	13.6381	−	4.00451i	0.666265	−	0.195633i	0.0689256	−	0.997622i	$-0.478043\pi$
$419$	13.6381	−	4.00451i	0.666265	−	0.195633i	0.597339	+	0.801989i	$0.296225\pi$
$420$		0			0
$421$	1.12300	+	1.29602i	0.0547319	+	0.0631640i	0.782455	−	0.622707i	$-0.213967\pi$
$421$	1.12300	+	1.29602i	0.0547319	+	0.0631640i	−0.727723	+	0.685871i	$0.759422\pi$
$422$		0			0
$423$	11.3527	+	3.33346i	0.551989	+	0.162079i
$424$		0			0
$425$	7.33195	+	4.71196i	0.355652	+	0.228563i
$426$		0			0
$427$	1.60302	−	1.84998i	0.0775755	−	0.0895269i
$428$		0			0
$429$	−0.153911	−	1.07047i	−0.00743089	−	0.0516830i
$430$		0			0
$431$	16.4157	+	35.9454i	0.790718	+	1.73143i	0.674585	+	0.738197i	$0.264323\pi$
$431$	16.4157	+	35.9454i	0.790718	+	1.73143i	0.116133	+	0.993234i	$0.462950\pi$
$432$		0			0
$433$	−2.32839	+	5.09846i	−0.111895	+	0.245017i	−0.957292	−	0.289122i	$-0.906637\pi$
$433$	−2.32839	+	5.09846i	−0.111895	+	0.245017i	0.845397	+	0.534139i	$0.179364\pi$
$434$		0			0
$435$	−8.00185	+	5.14248i	−0.383659	+	0.246563i
$436$		0			0
$437$	−0.0875758	−	2.43442i	−0.00418932	−	0.116454i
$438$		0			0
$439$	−4.57472	+	2.93999i	−0.218339	+	0.140318i	−0.645239	−	0.763981i	$-0.723242\pi$
$439$	−4.57472	+	2.93999i	−0.218339	+	0.140318i	0.426899	+	0.904299i	$0.359606\pi$
$440$		0			0
$441$	1.57074	−	3.43945i	0.0747973	−	0.163783i
$442$		0			0
$443$	−12.3621	−	27.0692i	−0.587340	−	1.28610i	−0.937036	−	0.349232i	$-0.886442\pi$
$443$	−12.3621	−	27.0692i	−0.587340	−	1.28610i	0.349696	−	0.936863i	$-0.386285\pi$
$444$		0			0
$445$	0.0297320	+	0.206790i	0.00140943	+	0.00980281i
$446$		0			0
$447$	−9.46574	+	10.9241i	−0.447714	+	0.516690i
$448$		0			0
$449$	27.0618	+	17.3916i	1.27713	+	0.820759i	0.990530	−	0.137293i	$-0.0438403\pi$
$449$	27.0618	+	17.3916i	1.27713	+	0.820759i	0.286595	+	0.958052i	$0.407477\pi$
$450$		0			0
$451$	−1.21793	−	0.357617i	−0.0573501	−	0.0168395i
$452$		0			0
$453$	−6.74579	−	7.78506i	−0.316945	−	0.365774i
$454$		0			0
$455$	13.1241	−	3.85358i	0.615266	−	0.180658i
$456$		0			0
$457$	−4.89309	+	34.0322i	−0.228889	+	1.59196i	0.473913	+	0.880572i	$0.342841\pi$
$457$	−4.89309	+	34.0322i	−0.228889	+	1.59196i	−0.702802	+	0.711386i	$0.748068\pi$
$458$		0			0
$459$	3.19006			0.148899
$460$		0			0
$461$	0.317693			0.0147964			0.00739822	−	0.999973i	$-0.497645\pi$
$461$	0.317693			0.0147964			0.00739822	+	0.999973i	$0.497645\pi$
$462$		0			0
$463$	1.01410	−	7.05321i	0.0471292	−	0.327791i	−0.952594	−	0.304246i	$-0.901596\pi$
$463$	1.01410	−	7.05321i	0.0471292	−	0.327791i	0.999723	−	0.0235450i	$-0.00749529\pi$
$464$		0			0
$465$	13.8370	−	4.06290i	0.641674	−	0.188413i
$466$		0			0
$467$	−16.8907	−	19.4929i	−0.781608	−	0.902024i	0.215616	−	0.976478i	$-0.430824\pi$
$467$	−16.8907	−	19.4929i	−0.781608	−	0.902024i	−0.997224	+	0.0744544i	$0.976278\pi$
$468$		0			0
$469$	12.7917	+	3.75598i	0.590665	+	0.173435i
$470$		0			0
$471$	7.04164	+	4.52539i	0.324462	+	0.208519i
$472$		0			0
$473$	−2.04280	+	2.35751i	−0.0939279	+	0.108399i
$474$		0			0
$475$	0.197494	+	1.37360i	0.00906167	+	0.0630253i
$476$		0			0
$477$	−0.290808	−	0.636780i	−0.0133152	−	0.0291562i
$478$		0			0
$479$	1.43537	−	3.14301i	0.0655835	−	0.143608i	−0.874002	−	0.485923i	$-0.838484\pi$
$479$	1.43537	−	3.14301i	0.0655835	−	0.143608i	0.939585	+	0.342315i	$0.111211\pi$
$480$		0			0
$481$	−2.77633	+	1.78424i	−0.126590	+	0.0813542i
$482$		0			0
$483$	8.03169	−	13.5447i	0.365455	−	0.616304i
$484$		0			0
$485$	−8.77689	+	5.64057i	−0.398538	+	0.256125i
$486$		0			0
$487$	−1.29318	+	2.83166i	−0.0585995	+	0.128315i	−0.936666	−	0.350223i	$-0.886106\pi$
$487$	−1.29318	+	2.83166i	−0.0585995	+	0.128315i	0.878067	+	0.478538i	$0.158833\pi$
$488$		0			0
$489$	−4.07022	−	8.91254i	−0.184062	−	0.403039i
$490$		0			0
$491$	5.76001	+	40.0618i	0.259946	+	1.80796i	0.533165	+	0.846011i	$0.321002\pi$
$491$	5.76001	+	40.0618i	0.259946	+	1.80796i	−0.273220	+	0.961952i	$0.588089\pi$
$492$		0			0
$493$	−13.1947	+	15.2274i	−0.594257	+	0.685809i
$494$		0			0
$495$	−0.495313	−	0.318318i	−0.0222627	−	0.0143073i
$496$		0			0
$497$	−31.7279	−	9.31616i	−1.42319	−	0.417887i
$498$		0			0
$499$	2.48625	+	2.86928i	0.111300	+	0.128447i	0.808666	−	0.588269i	$-0.200190\pi$
$499$	2.48625	+	2.86928i	0.111300	+	0.128447i	−0.697366	+	0.716715i	$0.745645\pi$
$500$		0			0
$501$	−11.0426	+	3.24240i	−0.493347	+	0.144860i
$502$		0			0
$503$	−4.27463	+	29.7307i	−0.190596	+	1.32563i	0.639838	+	0.768510i	$0.279001\pi$
$503$	−4.27463	+	29.7307i	−0.190596	+	1.32563i	−0.830434	+	0.557117i	$0.811908\pi$
$504$		0			0
$505$	20.3209			0.904269
$506$		0			0
$507$	5.34824			0.237524
$508$		0			0
$509$	−1.12688	+	7.83759i	−0.0499479	+	0.347395i	0.949488	+	0.313804i	$0.101603\pi$
$509$	−1.12688	+	7.83759i	−0.0499479	+	0.347395i	−0.999436	+	0.0335911i	$0.989306\pi$
$510$		0			0
$511$	−26.4105	+	7.75483i	−1.16833	+	0.343053i
$512$		0			0
$513$	0.332629	+	0.383875i	0.0146860	+	0.0169485i
$514$		0			0
$515$	−20.6410	−	6.06074i	−0.909551	−	0.267068i
$516$		0			0
$517$	−3.89157	−	2.50096i	−0.171151	−	0.109992i
$518$		0			0
$519$	9.12169	−	10.5270i	0.400398	−	0.462084i
$520$		0			0
$521$	−3.64792	−	25.3718i	−0.159818	−	1.11156i	−0.898967	−	0.438017i	$-0.855681\pi$
$521$	−3.64792	−	25.3718i	−0.159818	−	1.11156i	0.739148	−	0.673543i	$-0.235228\pi$
$522$		0			0
$523$	−12.1840	−	26.6793i	−0.532770	−	1.16660i	−0.964375	−	0.264540i	$-0.914780\pi$
$523$	−12.1840	−	26.6793i	−0.532770	−	1.16660i	0.431605	−	0.902063i	$-0.357948\pi$
$524$		0			0
$525$	−3.72656	+	8.16002i	−0.162640	+	0.356132i
$526$		0			0
$527$	25.6987	−	16.5156i	1.11945	−	0.719429i
$528$		0			0
$529$	13.7739	−	18.4196i	0.598863	−	0.800851i
$530$		0			0
$531$	−0.0120933	+	0.00777189i	−0.000524804	+	0.000337271i
$532$		0			0
$533$	−3.73082	+	8.16936i	−0.161600	+	0.353854i
$534$		0			0
$535$	9.67219	+	21.1791i	0.418165	+	0.915655i
$536$		0			0
$537$	−1.53617	−	10.6843i	−0.0662908	−	0.461063i
$538$		0			0
$539$	−0.968078	+	1.11722i	−0.0416981	+	0.0481222i
$540$		0			0
$541$	−18.5738	−	11.9366i	−0.798549	−	0.513196i	0.0765930	−	0.997062i	$-0.475596\pi$
$541$	−18.5738	−	11.9366i	−0.798549	−	0.513196i	−0.875142	+	0.483866i	$0.839232\pi$
$542$		0			0
$543$	−20.6306	−	6.05769i	−0.885344	−	0.259961i
$544$		0			0
$545$	−13.7462	−	15.8640i	−0.588823	−	0.679538i
$546$		0			0
$547$	−9.46581	+	2.77941i	−0.404729	+	0.118839i	−0.477760	−	0.878491i	$-0.658551\pi$
$547$	−9.46581	+	2.77941i	−0.404729	+	0.118839i	0.0730307	+	0.997330i	$0.476733\pi$
$548$		0			0
$549$	−0.106098	+	0.737928i	−0.00452816	+	0.0314940i
$550$		0			0
$551$	−3.20820			−0.136674
$552$		0			0
$553$	−0.338185			−0.0143811
$554$		0			0
$555$	−0.255698	+	1.77842i	−0.0108538	+	0.0754896i
$556$		0			0
$557$	−12.2554	+	3.59852i	−0.519280	+	0.152474i	−0.530861	−	0.847459i	$-0.678131\pi$
$557$	−12.2554	+	3.59852i	−0.519280	+	0.152474i	0.0115818	+	0.999933i	$0.496313\pi$
$558$		0			0
$559$	14.4533	+	16.6800i	0.611309	+	0.705489i
$560$		0			0
$561$	−1.19669	−	0.351379i	−0.0505241	−	0.0148352i
$562$		0			0
$563$	19.4865	+	12.5232i	0.821259	+	0.527791i	0.882489	−	0.470332i	$-0.155866\pi$
$563$	19.4865	+	12.5232i	0.821259	+	0.527791i	−0.0612301	+	0.998124i	$0.519502\pi$
$564$		0			0
$565$	16.8856	−	19.4870i	0.710383	−	0.819826i
$566$		0			0
$567$	0.467286	+	3.25004i	0.0196242	+	0.136489i
$568$		0			0
$569$	−6.10488	−	13.3678i	−0.255930	−	0.560408i	0.737434	−	0.675419i	$-0.236037\pi$
$569$	−6.10488	−	13.3678i	−0.255930	−	0.560408i	−0.993364	+	0.115011i	$0.963310\pi$
$570$		0			0
$571$	−6.70164	+	14.6745i	−0.280455	+	0.614110i	−0.996468	−	0.0839768i	$-0.973238\pi$
$571$	−6.70164	+	14.6745i	−0.280455	+	0.614110i	0.716013	+	0.698087i	$0.245965\pi$
$572$		0			0
$573$	−20.8631	+	13.4079i	−0.871567	+	0.560122i
$574$		0			0
$575$	−6.68294	+	11.2701i	−0.278698	+	0.469997i
$576$		0			0
$577$	−22.3809	+	14.3833i	−0.931728	+	0.598785i	−0.916038	−	0.401091i	$-0.868631\pi$
$577$	−22.3809	+	14.3833i	−0.931728	+	0.598785i	−0.0156903	+	0.999877i	$0.504995\pi$
$578$		0			0
$579$	1.36419	−	2.98717i	0.0566940	−	0.124142i
$580$		0			0
$581$	−8.35177	−	18.2878i	−0.346490	−	0.758707i
$582$		0			0
$583$	0.0389505	+	0.270907i	0.00161316	+	0.0112198i
$584$		0			0
$585$	−2.72800	+	3.14827i	−0.112789	+	0.130165i
$586$		0			0
$587$	−8.04712	−	5.17157i	−0.332140	−	0.213453i	0.363932	−	0.931426i	$-0.381434\pi$
$587$	−8.04712	−	5.17157i	−0.332140	−	0.213453i	−0.696072	+	0.717972i	$0.745070\pi$
$588$		0			0
$589$	4.66701	+	1.37036i	0.192301	+	0.0564646i
$590$		0			0
$591$	17.9364	+	20.6997i	0.737806	+	0.851474i
$592$		0			0
$593$	21.3592	−	6.27163i	0.877118	−	0.257545i	0.187978	−	0.982173i	$-0.439807\pi$
$593$	21.3592	−	6.27163i	0.877118	−	0.257545i	0.689140	+	0.724628i	$0.257989\pi$
$594$		0			0
$595$	2.24490	−	15.6136i	0.0920317	−	0.640095i
$596$		0			0
$597$	−11.8414			−0.484637
$598$		0			0
$599$	−8.47121			−0.346124			−0.173062	−	0.984911i	$-0.555366\pi$
$599$	−8.47121			−0.346124			−0.173062	+	0.984911i	$0.555366\pi$
$600$		0			0
$601$	4.25186	−	29.5723i	0.173437	−	1.20628i	−0.698118	−	0.715983i	$-0.745979\pi$
$601$	4.25186	−	29.5723i	0.173437	−	1.20628i	0.871555	−	0.490298i	$-0.163112\pi$
$602$		0			0
$603$	−3.89579	+	1.14391i	−0.158649	+	0.0465835i
$604$		0			0
$605$	−10.6974	−	12.3455i	−0.434911	−	0.501915i
$606$		0			0
$607$	31.7159	+	9.31262i	1.28731	+	0.377988i	0.852590	−	0.522580i	$-0.175030\pi$
$607$	31.7159	+	9.31262i	1.28731	+	0.377988i	0.434717	+	0.900567i	$0.356848\pi$
$608$		0			0
$609$	−17.4465	−	11.2122i	−0.706969	−	0.454341i
$610$		0			0
$611$	−21.4333	+	24.7353i	−0.867097	+	1.00068i
$612$		0			0
$613$	1.06961	+	7.43927i	0.0432010	+	0.300469i	0.999954	+	0.00956857i	$0.00304582\pi$
$613$	1.06961	+	7.43927i	0.0432010	+	0.300469i	−0.956753	+	0.290901i	$0.906045\pi$
$614$		0			0
$615$	2.03113	+	4.44756i	0.0819031	+	0.179343i
$616$		0			0
$617$	−12.7773	+	27.9784i	−0.514395	+	1.12637i	0.457123	+	0.889403i	$0.348880\pi$
$617$	−12.7773	+	27.9784i	−0.514395	+	1.12637i	−0.971518	+	0.236965i	$0.923847\pi$
$618$		0			0
$619$	−36.0484	+	23.1669i	−1.44891	+	0.931156i	−0.449627	+	0.893217i	$0.648443\pi$
$619$	−36.0484	+	23.1669i	−1.44891	+	0.931156i	−0.999280	+	0.0379391i	$0.987921\pi$
$620$		0			0
$621$	0.172414	+	4.79273i	0.00691873	+	0.192326i
$622$		0			0
$623$	−0.383194	+	0.246264i	−0.0153523	+	0.00986635i
$624$		0			0
$625$	−1.60988	+	3.52515i	−0.0643954	+	0.141006i
$626$		0			0
$627$	−0.0824960	−	0.180641i	−0.00329457	−	0.00721411i
$628$		0			0
$629$	0.541642	+	3.76720i	0.0215967	+	0.150208i
$630$		0			0
$631$	−14.8768	+	17.1687i	−0.592235	+	0.683476i	−0.970189	−	0.242348i	$-0.922082\pi$
$631$	−14.8768	+	17.1687i	−0.592235	+	0.683476i	0.377954	+	0.925824i	$0.376628\pi$
$632$		0			0
$633$	−10.5393	−	6.77319i	−0.418899	−	0.269210i
$634$		0			0
$635$	18.5422	+	5.44450i	0.735827	+	0.216058i
$636$		0			0
$637$	6.84940	+	7.90462i	0.271383	+	0.313193i
$638$		0			0
$639$	9.66294	−	2.83730i	0.382260	−	0.112242i
$640$		0			0
$641$	−2.75712	+	19.1762i	−0.108900	+	0.757413i	0.860060	+	0.510193i	$0.170426\pi$
$641$	−2.75712	+	19.1762i	−0.108900	+	0.757413i	−0.968959	+	0.247220i	$0.920483\pi$
$642$		0			0
$643$	−21.9932			−0.867327			−0.433663	−	0.901075i	$-0.642779\pi$
$643$	−21.9932			−0.867327			−0.433663	+	0.901075i	$0.642779\pi$
$644$		0			0
$645$	12.0158			0.473120
$646$		0			0
$647$	−3.99373	+	27.7770i	−0.157010	+	1.09203i	0.747096	+	0.664717i	$0.231448\pi$
$647$	−3.99373	+	27.7770i	−0.157010	+	1.09203i	−0.904105	+	0.427310i	$0.859461\pi$
$648$		0			0
$649$	0.00539260	−	0.00158341i	0.000211678	−	6.21543e-5i
$650$		0			0
$651$	20.5905	+	23.7627i	0.807004	+	0.931333i
$652$		0			0
$653$	−38.8533	−	11.4084i	−1.52045	−	0.446444i	−0.588337	−	0.808616i	$-0.700217\pi$
$653$	−38.8533	−	11.4084i	−1.52045	−	0.446444i	−0.932111	+	0.362172i	$0.882035\pi$
$654$		0			0
$655$	−7.66306	−	4.92475i	−0.299420	−	0.192426i
$656$		0			0
$657$	5.48974	−	6.33550i	0.214175	−	0.247171i
$658$		0			0
$659$	−0.480569	−	3.34243i	−0.0187203	−	0.130203i	0.978318	−	0.207108i	$-0.0664052\pi$
$659$	−0.480569	−	3.34243i	−0.0187203	−	0.130203i	−0.997038	+	0.0769054i	$0.975496\pi$
$660$		0			0
$661$	−16.5685	−	36.2799i	−0.644438	−	1.41112i	−0.896339	−	0.443370i	$-0.853783\pi$
$661$	−16.5685	−	36.2799i	−0.644438	−	1.41112i	0.251900	−	0.967753i	$-0.418944\pi$
$662$		0			0
$663$	−3.66574	+	8.02686i	−0.142366	+	0.311737i
$664$		0			0
$665$	2.11293	−	1.35790i	0.0819359	−	0.0526570i
$666$		0			0
$667$	−23.5907	−	19.0006i	−0.913437	−	0.735704i
$668$		0			0
$669$	−12.8826	+	8.27914i	−0.498070	+	0.320090i
$670$		0			0
$671$	0.121082	−	0.265132i	0.00467430	−	0.0102353i
$672$		0			0
$673$	18.0967	+	39.6263i	0.697577	+	1.52748i	0.842885	+	0.538094i	$0.180856\pi$
$673$	18.0967	+	39.6263i	0.697577	+	1.52748i	−0.145307	+	0.989387i	$0.546417\pi$
$674$		0			0
$675$	−0.388815	−	2.70427i	−0.0149655	−	0.104087i
$676$		0			0
$677$	33.4680	−	38.6242i	1.28628	−	1.48445i	0.500797	−	0.865565i	$-0.333040\pi$
$677$	33.4680	−	38.6242i	1.28628	−	1.48445i	0.785484	−	0.618882i	$-0.212414\pi$
$678$		0			0
$679$	−19.1364	−	12.2982i	−0.734386	−	0.471961i
$680$		0			0
$681$	15.7793	+	4.63322i	0.604664	+	0.177545i
$682$		0			0
$683$	−24.7190	−	28.5273i	−0.945848	−	1.09157i	−0.995684	−	0.0928089i	$-0.970415\pi$
$683$	−24.7190	−	28.5273i	−0.945848	−	1.09157i	0.0498364	−	0.998757i	$-0.484130\pi$
$684$		0			0
$685$	14.2534	−	4.18516i	0.544593	−	0.159907i
$686$		0			0
$687$	0.982873	−	6.83603i	0.0374990	−	0.260811i
$688$		0			0
$689$	1.93644			0.0737726
$690$		0			0
$691$	−15.1130			−0.574927			−0.287463	−	0.957792i	$-0.592812\pi$
$691$	−15.1130			−0.574927			−0.287463	+	0.957792i	$0.592812\pi$
$692$		0			0
$693$	0.182693	−	1.27066i	0.00693992	−	0.0482682i
$694$		0			0
$695$	26.3103	−	7.72541i	0.998008	−	0.293042i
$696$		0			0
$697$	6.78251	+	7.82743i	0.256906	+	0.296485i
$698$		0			0
$699$	23.8847	+	7.01319i	0.903404	+	0.265263i
$700$		0			0
$701$	−1.23408	−	0.793094i	−0.0466105	−	0.0299547i	0.517128	−	0.855908i	$-0.327001\pi$
$701$	−1.23408	−	0.793094i	−0.0466105	−	0.0299547i	−0.563739	+	0.825953i	$0.690637\pi$
$702$		0			0
$703$	−0.396847	+	0.457986i	−0.0149674	+	0.0172733i
$704$		0			0
$705$	2.53585	+	17.6372i	0.0955055	+	0.664256i
$706$		0			0
$707$	18.4053	+	40.3021i	0.692204	+	1.51572i
$708$		0			0
$709$	11.5643	−	25.3222i	0.434306	−	0.950996i	−0.558303	−	0.829637i	$-0.688547\pi$
$709$	11.5643	−	25.3222i	0.434306	−	0.950996i	0.992609	−	0.121359i	$-0.0387254\pi$
$710$		0			0
$711$	0.0866462	−	0.0556841i	0.00324949	−	0.00208832i
$712$		0			0
$713$	26.2018	+	37.7170i	0.981266	+	1.41251i
$714$		0			0
$715$	1.37013	−	0.880526i	0.0512398	−	0.0329298i
$716$		0			0
$717$	−3.49642	+	7.65609i	−0.130576	+	0.285922i
$718$		0			0
$719$	−7.10840	−	15.5652i	−0.265099	−	0.580485i	0.729535	−	0.683943i	$-0.239736\pi$
$719$	−7.10840	−	15.5652i	−0.265099	−	0.580485i	−0.994634	+	0.103458i	$0.967009\pi$
$720$		0			0
$721$	−6.67509	−	46.4263i	−0.248593	−	1.72901i
$722$		0			0
$723$	−14.0647	+	16.2315i	−0.523071	+	0.603656i
$724$		0			0
$725$	14.5168	+	9.32935i	0.539139	+	0.346483i
$726$		0			0
$727$	8.49114	+	2.49322i	0.314919	+	0.0924686i	0.435373	−	0.900250i	$-0.356617\pi$
$727$	8.49114	+	2.49322i	0.314919	+	0.0924686i	−0.120453	+	0.992719i	$0.538435\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	24.4219	−	7.17090i	0.903275	−	0.265225i
$732$		0			0
$733$	4.01056	−	27.8940i	0.148133	−	1.03029i	−0.771139	−	0.636667i	$-0.780313\pi$
$733$	4.01056	−	27.8940i	0.148133	−	1.03029i	0.919272	−	0.393623i	$-0.128778\pi$
$734$		0			0
$735$	5.69425			0.210036
$736$		0			0
$737$	1.58742			0.0584734
$738$		0			0
$739$	−3.14937	+	21.9043i	−0.115851	+	0.805763i	0.846194	+	0.532874i	$0.178888\pi$
$739$	−3.14937	+	21.9043i	−0.115851	+	0.805763i	−0.962046	+	0.272889i	$0.912021\pi$
$740$		0			0
$741$	−1.34814	+	0.395849i	−0.0495251	+	0.0145419i
$742$		0			0
$743$	−4.35206	−	5.02254i	−0.159662	−	0.184259i	0.670282	−	0.742106i	$-0.266173\pi$
$743$	−4.35206	−	5.02254i	−0.159662	−	0.184259i	−0.829944	+	0.557847i	$0.811628\pi$
$744$		0			0
$745$	−20.8863	−	6.13277i	−0.765215	−	0.224687i
$746$		0			0
$747$	5.15099	+	3.31034i	0.188465	+	0.121119i
$748$		0			0
$749$	−33.2437	+	38.3653i	−1.21470	+	1.40184i
$750$		0			0
$751$	−2.48809	−	17.3050i	−0.0907917	−	0.631470i	−0.983510	−	0.180855i	$-0.942114\pi$
$751$	−2.48809	−	17.3050i	−0.0907917	−	0.631470i	0.892718	−	0.450615i	$-0.148795\pi$
$752$		0			0
$753$	−3.97682	−	8.70802i	−0.144923	−	0.317338i
$754$		0			0
$755$	6.44437	−	14.1112i	0.234535	−	0.513559i
$756$		0			0
$757$	31.2051	−	20.0543i	1.13417	−	0.728886i	0.167743	−	0.985831i	$-0.446352\pi$
$757$	31.2051	−	20.0543i	1.13417	−	0.728886i	0.966426	+	0.256945i	$0.0827158\pi$
$758$		0			0
$759$	0.463231	−	1.81688i	0.0168142	−	0.0659487i
$760$		0			0
$761$	0.415863	−	0.267259i	0.0150750	−	0.00968813i	−0.533082	−	0.846064i	$-0.678966\pi$
$761$	0.415863	−	0.267259i	0.0150750	−	0.00968813i	0.548157	+	0.836376i	$0.315330\pi$
$762$		0			0
$763$	19.0123	−	41.6311i	0.688292	−	1.50715i
$764$		0			0
$765$	1.99570	+	4.36998i	0.0721548	+	0.157997i
$766$		0			0
$767$	−0.00565911	−	0.0393600i	−0.000204339	−	0.00142121i
$768$		0			0
$769$	21.1293	−	24.3845i	0.761941	−	0.879326i	−0.233728	−	0.972302i	$-0.575092\pi$
$769$	21.1293	−	24.3845i	0.761941	−	0.879326i	0.995668	+	0.0929756i	$0.0296379\pi$
$770$		0			0
$771$	−0.530765	−	0.341102i	−0.0191150	−	0.0122845i
$772$		0			0
$773$	28.0333	+	8.23131i	1.00829	+	0.296060i	0.743852	−	0.668344i	$-0.232997\pi$
$773$	28.0333	+	8.23131i	1.00829	+	0.296060i	0.264434	+	0.964404i	$0.414815\pi$
$774$		0			0
$775$	−17.1328	−	19.7722i	−0.615427	−	0.710240i
$776$		0			0
$777$	−3.75869	+	1.10365i	−0.134842	+	0.0395933i
$778$		0			0
$779$	−0.234695	+	1.63234i	−0.00840882	+	0.0584846i
$780$		0			0
$781$	−3.93737			−0.140890
$782$		0			0
$783$	6.31611			0.225719
$784$		0			0
$785$	−1.79395	+	12.4772i	−0.0640289	+	0.445331i
$786$		0			0
$787$	−37.5446	+	11.0241i	−1.33832	+	0.392966i	−0.871070	−	0.491158i	$-0.836574\pi$
$787$	−37.5446	+	11.0241i	−1.33832	+	0.392966i	−0.467251	+	0.884125i	$0.654755\pi$
$788$		0			0
$789$	14.6001	+	16.8494i	0.519776	+	0.599854i
$790$		0			0
$791$	53.9421	+	15.8388i	1.91796	+	0.563164i
$792$		0			0
$793$	−1.73486	−	1.11493i	−0.0616067	−	0.0395922i
$794$		0			0
$795$	0.690378	−	0.796739i	0.0244852	−	0.0282574i
$796$		0			0
$797$	−4.43729	−	30.8620i	−0.157177	−	1.09319i	−0.903804	−	0.427946i	$-0.859237\pi$
$797$	−4.43729	−	30.8620i	−0.157177	−	1.09319i	0.746627	−	0.665243i	$-0.231672\pi$
$798$		0			0
$799$	15.6798	+	34.3340i	0.554711	+	1.21465i
$800$		0			0
$801$	0.0576291	−	0.126190i	0.00203622	−	0.00445871i
$802$		0			0
$803$	−2.75720	+	1.77194i	−0.0972995	+	0.0625306i
$804$		0			0
$805$	23.5791	+	2.52885i	0.831053	+	0.0891301i
$806$		0			0
$807$	21.2735	−	13.6717i	0.748864	−	0.481266i
$808$		0			0
$809$	−8.48331	+	18.5758i	−0.298257	+	0.653092i	−0.998127	−	0.0611785i	$-0.980514\pi$
$809$	−8.48331	+	18.5758i	−0.298257	+	0.653092i	0.699870	+	0.714271i	$0.253241\pi$
$810$		0			0
$811$	−13.5379	−	29.6438i	−0.475379	−	1.04093i	−0.983708	−	0.179771i	$-0.942464\pi$
$811$	−13.5379	−	29.6438i	−0.475379	−	1.04093i	0.508330	−	0.861162i	$-0.330263\pi$
$812$		0			0
$813$	1.54052	+	10.7145i	0.0540284	+	0.375775i
$814$		0			0
$815$	9.66270	−	11.1514i	0.338470	−	0.390615i
$816$		0			0
$817$	3.40939	+	2.19108i	0.119279	+	0.0766562i
$818$		0			0
$819$	−8.71475	−	2.55888i	−0.304518	−	0.0894145i
$820$		0			0
$821$	18.8720	+	21.7795i	0.658639	+	0.760110i	0.982554	−	0.185976i	$-0.0595448\pi$
$821$	18.8720	+	21.7795i	0.658639	+	0.760110i	−0.323915	+	0.946086i	$0.604999\pi$
$822$		0			0
$823$	2.37272	−	0.696694i	0.0827079	−	0.0242852i	−0.240117	−	0.970744i	$-0.577186\pi$
$823$	2.37272	−	0.696694i	0.0827079	−	0.0242852i	0.322825	+	0.946459i	$0.395368\pi$
$824$		0			0
$825$	−0.152013	+	1.05728i	−0.00529243	+	0.0368096i
$826$		0			0
$827$	−12.3320			−0.428827			−0.214414	−	0.976743i	$-0.568784\pi$
$827$	−12.3320			−0.428827			−0.214414	+	0.976743i	$0.568784\pi$
$828$		0			0
$829$	14.1559			0.491654			0.245827	−	0.969314i	$-0.420940\pi$
$829$	14.1559			0.491654			0.245827	+	0.969314i	$0.420940\pi$
$830$		0			0
$831$	3.52247	−	24.4993i	0.122193	−	0.849871i
$832$		0			0
$833$	11.5735	−	3.39828i	0.400997	−	0.117743i
$834$		0			0
$835$	−11.3499	−	13.0985i	−0.392780	−	0.453292i
$836$		0			0
$837$	−9.18813	−	2.69788i	−0.317588	−	0.0932523i
$838$		0			0
$839$	−23.2315	−	14.9300i	−0.802040	−	0.515440i	0.0742411	−	0.997240i	$-0.476347\pi$
$839$	−23.2315	−	14.9300i	−0.802040	−	0.515440i	−0.876281	+	0.481801i	$0.839983\pi$
$840$		0			0
$841$	−7.13353	+	8.23254i	−0.245984	+	0.283881i
$842$		0			0
$843$	−0.271453	−	1.88799i	−0.00934932	−	0.0650260i
$844$		0			0
$845$	3.34586	+	7.32641i	0.115101	+	0.252036i
$846$		0			0
$847$	14.7955	−	32.3977i	0.508380	−	1.11320i
$848$		0			0
$849$	−0.787193	+	0.505898i	−0.0270164	+	0.0173624i
$850$		0			0
$851$	−5.63055	+	1.01737i	−0.193013	+	0.0348749i
$852$		0			0
$853$	8.55768	−	5.49969i	0.293009	−	0.188306i	−0.385875	−	0.922551i	$-0.626100\pi$
$853$	8.55768	−	5.49969i	0.293009	−	0.188306i	0.678884	+	0.734246i	$0.262464\pi$
$854$		0			0
$855$	−0.317766	+	0.695811i	−0.0108674	+	0.0237963i
$856$		0			0
$857$	6.62846	+	14.5143i	0.226424	+	0.495799i	0.988413	−	0.151791i	$-0.0485041\pi$
$857$	6.62846	+	14.5143i	0.226424	+	0.495799i	−0.761989	+	0.647590i	$0.775777\pi$
$858$		0			0
$859$	−4.24672	−	29.5366i	−0.144896	−	1.00777i	−0.924413	−	0.381393i	$-0.875444\pi$
$859$	−4.24672	−	29.5366i	−0.144896	−	1.00777i	0.779517	−	0.626381i	$-0.215465\pi$
$860$		0			0
$861$	−6.98109	+	8.05661i	−0.237915	+	0.274568i
$862$		0			0
$863$	−6.70374	−	4.30823i	−0.228198	−	0.146654i	0.421546	−	0.906807i	$-0.361488\pi$
$863$	−6.70374	−	4.30823i	−0.228198	−	0.146654i	−0.649744	+	0.760153i	$0.725124\pi$
$864$		0			0
$865$	20.1272	+	5.90987i	0.684344	+	0.200941i
$866$		0			0
$867$	−4.46844	−	5.15685i	−0.151756	−	0.175136i
$868$		0			0
$869$	−0.0386370	+	0.0113448i	−0.00131067	+	0.000384847i
$870$		0			0
$871$	1.59840	−	11.1171i	0.0541596	−	0.376688i
$872$		0			0
$873$	6.92787			0.234473
$874$		0			0
$875$	−38.2334			−1.29252
$876$		0			0
$877$	0.912139	−	6.34406i	0.0308007	−	0.214224i	−0.968609	−	0.248591i	$-0.920032\pi$
$877$	0.912139	−	6.34406i	0.0308007	−	0.214224i	0.999409	+	0.0343672i	$0.0109416\pi$
$878$		0			0
$879$	−22.4549	+	6.59334i	−0.757384	+	0.222388i
$880$		0			0
$881$	−18.5964	−	21.4613i	−0.626527	−	0.723051i	0.350405	−	0.936598i	$-0.386044\pi$
$881$	−18.5964	−	21.4613i	−0.626527	−	0.723051i	−0.976933	+	0.213547i	$0.931498\pi$
$882$		0			0
$883$	35.0175	+	10.2821i	1.17843	+	0.346019i	0.811570	−	0.584255i	$-0.198613\pi$
$883$	35.0175	+	10.2821i	1.17843	+	0.346019i	0.366864	+	0.930275i	$0.380431\pi$
$884$		0			0
$885$	−0.0182120	−	0.0117042i	−0.000612191	−	0.000393431i
$886$		0			0
$887$	−0.236303	+	0.272708i	−0.00793428	+	0.00915665i	−0.759703	−	0.650270i	$-0.774656\pi$
$887$	−0.236303	+	0.272708i	−0.00793428	+	0.00915665i	0.751769	+	0.659427i	$0.229201\pi$
$888$		0			0
$889$	5.99638	+	41.7057i	0.201112	+	1.39877i
$890$		0			0
$891$	0.162413	+	0.355635i	0.00544104	+	0.0119142i
$892$		0			0
$893$	−2.49662	+	5.46684i	−0.0835463	+	0.182941i
$894$		0			0
$895$	13.6751	−	8.78847i	0.457109	−	0.293766i
$896$		0			0
$897$	−12.2576	−	5.07356i	−0.409270	−	0.169401i
$898$		0			0
$899$	50.8817	−	32.6997i	1.69700	−	1.09060i
$900$		0			0
$901$	0.927696	−	2.03137i	0.0309060	−	0.0676748i
$902$		0			0
$903$	10.8831	+	23.8306i	0.362166	+	0.793034i
$904$		0			0
$905$	−4.60823	−	32.0510i	−0.153183	−	1.06541i
$906$		0			0
$907$	15.5811	−	17.9816i	0.517364	−	0.597069i	−0.435605	−	0.900138i	$-0.643466\pi$
$907$	15.5811	−	17.9816i	0.517364	−	0.597069i	0.952969	+	0.303068i	$0.0980111\pi$
$908$		0			0
$909$	−11.3516	−	7.29522i	−0.376508	−	0.241967i
$910$		0			0
$911$	33.1829	+	9.74337i	1.09940	+	0.322812i	0.780613	−	0.625015i	$-0.214907\pi$
$911$	33.1829	+	9.74337i	1.09940	+	0.322812i	0.318784	+	0.947827i	$0.396725\pi$
$912$		0			0
$913$	−1.56766	−	1.80918i	−0.0518819	−	0.0598750i
$914$		0			0
$915$	−1.07724	+	0.316307i	−0.0356125	+	0.0104568i
$916$		0			0
$917$	2.82646	−	19.6585i	0.0933381	−	0.649181i
$918$		0			0
$919$	−48.9646			−1.61519			−0.807596	−	0.589736i	$-0.799232\pi$
$919$	−48.9646			−1.61519			−0.807596	+	0.589736i	$0.799232\pi$
$920$		0			0
$921$	28.3393			0.933813
$922$		0			0
$923$	−3.96459	+	27.5743i	−0.130496	+	0.907620i
$924$		0			0
$925$	3.12750	−	0.918318i	0.102832	−	0.0301941i
$926$		0			0
$927$	9.35457	+	10.7957i	0.307244	+	0.354579i
$928$		0			0
$929$	−29.5713	−	8.68291i	−0.970202	−	0.284877i	−0.242028	−	0.970269i	$-0.577813\pi$
$929$	−29.5713	−	8.68291i	−0.970202	−	0.284877i	−0.728174	+	0.685392i	$0.759631\pi$
$930$		0			0
$931$	1.61570	+	1.03835i	0.0529525	+	0.0340305i
$932$		0			0
$933$	11.9006	−	13.7340i	0.389608	−	0.449631i
$934$		0			0
$935$	−0.267302	−	1.85913i	−0.00874172	−	0.0608000i
$936$		0			0
$937$	9.85242	+	21.5738i	0.321864	+	0.704785i	0.999532	−	0.0305834i	$-0.00973651\pi$
$937$	9.85242	+	21.5738i	0.321864	+	0.704785i	−0.677668	+	0.735368i	$0.737009\pi$
$938$		0			0
$939$	−1.88053	+	4.11778i	−0.0613686	+	0.134379i
$940$		0			0
$941$	−14.7565	+	9.48345i	−0.481049	+	0.309152i	−0.758597	−	0.651560i	$-0.774115\pi$
$941$	−14.7565	+	9.48345i	−0.481049	+	0.309152i	0.277548	+	0.960712i	$0.410478\pi$
$942$		0			0
$943$	−11.3933	+	10.6130i	−0.371017	+	0.345608i
$944$		0			0
$945$	−4.15981	+	2.67335i	−0.135319	+	0.0869640i
$946$		0			0
$947$	−10.2389	+	22.4200i	−0.332719	+	0.728553i	−0.999866	−	0.0163733i	$-0.994788\pi$
$947$	−10.2389	+	22.4200i	−0.332719	+	0.728553i	0.667147	+	0.744926i	$0.267515\pi$
$948$		0			0
$949$	9.63309	+	21.0935i	0.312703	+	0.684724i
$950$		0			0
$951$	−0.387461	−	2.69485i	−0.0125643	−	0.0873865i
$952$		0			0
$953$	5.50666	−	6.35502i	0.178378	−	0.205859i	−0.659518	−	0.751688i	$-0.729240\pi$
$953$	5.50666	−	6.35502i	0.178378	−	0.205859i	0.837897	+	0.545829i	$0.183785\pi$
$954$		0			0
$955$	−31.4190	−	20.1917i	−1.01669	−	0.653390i
$956$		0			0
$957$	−2.36935	−	0.695705i	−0.0765903	−	0.0224890i
$958$		0			0
$959$	21.2101	+	24.4778i	0.684910	+	0.790428i
$960$		0			0
$961$	−58.2414	+	17.1012i	−1.87876	+	0.551652i
$962$		0			0
$963$	2.20028	−	15.3033i	0.0709032	−	0.493142i
$964$		0			0
$965$	4.94547			0.159200
$966$		0			0
$967$	29.6971			0.954993			0.477497	−	0.878634i	$-0.341544\pi$
$967$	29.6971			0.954993			0.477497	+	0.878634i	$0.341544\pi$
$968$		0			0
$969$	−0.230601	+	1.60387i	−0.00740798	+	0.0515236i
$970$		0			0
$971$	−10.9824	+	3.22472i	−0.352442	+	0.103486i	−0.453161	−	0.891429i	$-0.649704\pi$
$971$	−10.9824	+	3.22472i	−0.352442	+	0.103486i	0.100719	+	0.994915i	$0.467886\pi$
$972$		0			0
$973$	39.1518	+	45.1836i	1.25515	+	1.44852i
$974$		0			0
$975$	7.25129	+	2.12917i	0.232227	+	0.0681881i
$976$		0			0
$977$	18.7384	+	12.0424i	0.599494	+	0.385271i	0.804904	−	0.593405i	$-0.202217\pi$
$977$	18.7384	+	12.0424i	0.599494	+	0.385271i	−0.205410	+	0.978676i	$0.565853\pi$
$978$		0			0
$979$	−0.0355179	+	0.0409898i	−0.00113516	+	0.00131004i
$980$		0			0
$981$	1.98367	+	13.7968i	0.0633339	+	0.440497i
$982$		0			0
$983$	9.90292	+	21.6844i	0.315854	+	0.691624i	0.999262	−	0.0384128i	$-0.0122302\pi$
$983$	9.90292	+	21.6844i	0.315854	+	0.691624i	−0.683408	+	0.730037i	$0.739503\pi$
$984$		0			0
$985$	−17.1350	+	37.5204i	−0.545966	+	1.19550i
$986$		0			0
$987$	−32.6827	+	21.0039i	−1.04030	+	0.668562i
$988$		0			0
$989$	12.0935	+	36.3037i	0.384549	+	1.15439i
$990$		0			0
$991$	19.7037	−	12.6628i	0.625909	−	0.402247i	−0.188884	−	0.981999i	$-0.560487\pi$
$991$	19.7037	−	12.6628i	0.625909	−	0.402247i	0.814793	+	0.579752i	$0.196851\pi$
$992$		0			0
$993$	−1.34548	+	2.94619i	−0.0426975	+	0.0934945i
$994$		0			0
$995$	−7.40798	−	16.2212i	−0.234849	−	0.514247i
$996$		0			0
$997$	−3.05617	−	21.2561i	−0.0967898	−	0.673188i	−0.979228	−	0.202760i	$-0.935009\pi$
$997$	−3.05617	−	21.2561i	−0.0967898	−	0.673188i	0.882439	−	0.470428i	$-0.155900\pi$
$998$		0			0
$999$	0.781289	−	0.901656i	0.0247189	−	0.0285271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.265.2	yes	20
3.2	odd	2		828.2.q.b.541.1		20
23.2	even	11	inner	276.2.i.b.25.2	✓	20
23.5	odd	22		6348.2.a.q.1.8		10
23.18	even	11		6348.2.a.r.1.3		10
69.2	odd	22		828.2.q.b.577.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.25.2	✓	20	23.2	even	11	inner
276.2.i.b.265.2	yes	20	1.1	even	1	trivial
828.2.q.b.541.1		20	3.2	odd	2
828.2.q.b.577.1		20	69.2	odd	22
6348.2.a.q.1.8		10	23.5	odd	22
6348.2.a.r.1.3		10	23.18	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)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{3} +(1.44496 - 0.424279i) q^{5} +(2.15021 + 2.48148i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{3} +(1.44496 - 0.424279i) q^{5} +(2.15021 + 2.48148i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(0.328901 + 0.211372i) q^{11} +(1.81146 - 2.09054i) q^{13} +(-0.214321 - 1.49063i) q^{15} +(-1.32520 - 2.90178i) q^{17} +(0.211006 - 0.462038i) q^{19} +(2.76223 - 1.77518i) q^{21} +(4.28800 - 2.14781i) q^{23} +(-2.29837 + 1.47707i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-2.62381 - 5.74533i) q^{29} +(1.36281 + 9.47855i) q^{31} +(0.256028 - 0.295472i) q^{33} +(4.15981 + 2.67335i) q^{35} +(-1.14473 - 0.336124i) q^{37} +(-1.81146 - 2.09054i) q^{39} +(-3.11518 + 0.914700i) q^{41} +(-1.13550 + 7.89759i) q^{43} -1.50596 q^{45} -11.8320 q^{47} +(-0.538112 + 3.74265i) q^{49} +(-3.06084 + 0.898745i) q^{51} +(0.458430 + 0.529056i) q^{53} +(0.564930 + 0.165878i) q^{55} +(-0.427306 - 0.274613i) q^{57} +(0.00941384 - 0.0108641i) q^{59} +(-0.106098 - 0.737928i) q^{61} +(-1.36400 - 2.98674i) q^{63} +(1.73052 - 3.78931i) q^{65} +(3.41571 - 2.19514i) q^{67} +(-1.51570 - 4.55002i) q^{69} +(-8.47217 + 5.44473i) q^{71} +(-3.48245 + 7.62550i) q^{73} +(1.13495 + 2.48519i) q^{75} +(0.182693 + 1.27066i) q^{77} +(-0.0674484 + 0.0778396i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-5.87497 - 1.72505i) q^{83} +(-3.14603 - 3.63071i) q^{85} +(-6.06026 + 1.77945i) q^{87} +(-0.0197428 + 0.137314i) q^{89} +9.08266 q^{91} +9.57602 q^{93} +(0.108862 - 0.757151i) q^{95} +(-6.64725 + 1.95181i) q^{97} +(-0.256028 - 0.295472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more