LMFDB - Embedded newform 220.2.m.b.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(81,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("220.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Root			$1.43801 - 1.04478i$ of defining polynomial
Character	$\chi$	$=$	220.201
Dual form			220.2.m.b.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.740256 + 2.27827i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.43801 + 4.42575i) q^{7} +(-2.21550 + 1.60965i) q^{9} +O(q^{10})$	\(q+(0.740256 + 2.27827i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.43801 + 4.42575i) q^{7} +(-2.21550 + 1.60965i) q^{9} +(-3.31404 - 0.130791i) q^{11} +(4.88281 - 3.54757i) q^{13} +(0.740256 - 2.27827i) q^{15} +(2.68680 + 1.95207i) q^{17} +(0.846245 + 2.60448i) q^{19} -11.1476 q^{21} -1.97807 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.506776 + 0.368194i) q^{27} +(0.708723 - 2.18123i) q^{29} +(5.62481 - 4.08666i) q^{31} +(-2.15526 - 7.64712i) q^{33} +(3.76477 - 2.73527i) q^{35} +(-1.18571 + 3.64925i) q^{37} +(11.6969 + 8.49826i) q^{39} +(1.17216 + 3.60755i) q^{41} +7.98463 q^{43} +2.73851 q^{45} +(-3.75733 - 11.5639i) q^{47} +(-11.8563 - 8.61411i) q^{49} +(-2.45844 + 7.56629i) q^{51} +(9.30528 - 6.76068i) q^{53} +(2.60424 + 2.05376i) q^{55} +(-5.30727 + 3.85596i) q^{57} +(2.19357 - 6.75112i) q^{59} +(1.08255 + 0.786521i) q^{61} +(-3.93801 - 12.1200i) q^{63} -6.03548 q^{65} -7.18872 q^{67} +(-1.46428 - 4.50659i) q^{69} +(-5.45576 - 3.96384i) q^{71} +(-2.69357 + 8.28996i) q^{73} +(-1.93801 + 1.40805i) q^{75} +(5.34450 - 14.4791i) q^{77} +(-4.43801 + 3.22441i) q^{79} +(-3.00244 + 9.24056i) q^{81} +(6.64538 + 4.82815i) q^{83} +(-1.02626 - 3.15852i) q^{85} +5.49406 q^{87} -11.4213 q^{89} +(8.67911 + 26.7116i) q^{91} +(13.4743 + 9.78968i) q^{93} +(0.846245 - 2.60448i) q^{95} +(-5.29742 + 3.84880i) q^{97} +(7.55279 - 5.04470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} - 2 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 - 2 * q^5 - q^7 + 3 * q^9	$ 8 q + 5 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 5 q^{11} + 4 q^{13} + 5 q^{15} + 9 q^{17} - 7 q^{19} - 28 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - q^{29} + 22 q^{31} + q^{33} + 4 q^{35} + 4 q^{37} + 27 q^{39} + 24 q^{41} - 22 q^{43} + 8 q^{45} - 6 q^{47} - 27 q^{49} - 47 q^{51} - q^{53} - 5 q^{55} - 25 q^{57} - 9 q^{59} + 22 q^{61} - 21 q^{63} - 26 q^{65} - 2 q^{67} + 11 q^{69} - 22 q^{71} + 5 q^{73} - 5 q^{75} + 16 q^{77} - 25 q^{79} - 28 q^{81} + 33 q^{83} + 4 q^{85} + 14 q^{87} + 8 q^{89} + 14 q^{91} + 31 q^{93} - 7 q^{95} + 20 q^{97} + 60 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 - 2 * q^5 - q^7 + 3 * q^9 + 5 * q^11 + 4 * q^13 + 5 * q^15 + 9 * q^17 - 7 * q^19 - 28 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - q^29 + 22 * q^31 + q^33 + 4 * q^35 + 4 * q^37 + 27 * q^39 + 24 * q^41 - 22 * q^43 + 8 * q^45 - 6 * q^47 - 27 * q^49 - 47 * q^51 - q^53 - 5 * q^55 - 25 * q^57 - 9 * q^59 + 22 * q^61 - 21 * q^63 - 26 * q^65 - 2 * q^67 + 11 * q^69 - 22 * q^71 + 5 * q^73 - 5 * q^75 + 16 * q^77 - 25 * q^79 - 28 * q^81 + 33 * q^83 + 4 * q^85 + 14 * q^87 + 8 * q^89 + 14 * q^91 + 31 * q^93 - 7 * q^95 + 20 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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
$3$	0.740256	+	2.27827i	0.427387	+	1.31536i	0.900690	+	0.434462i	$0.143062\pi$
$3$	0.740256	+	2.27827i	0.427387	+	1.31536i	−0.473303	+	0.880900i	$0.656938\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−1.43801	+	4.42575i	−0.543519	+	1.67278i	0.180968	+	0.983489i	$0.442077\pi$
$7$	−1.43801	+	4.42575i	−0.543519	+	1.67278i	−0.724486	+	0.689289i	$0.757923\pi$
$8$		0			0
$9$	−2.21550	+	1.60965i	−0.738500	+	0.536551i
$10$		0			0
$11$	−3.31404	−	0.130791i	−0.999222	−	0.0394351i
$11$	−3.31404	−	0.130791i	−0.999222	−	0.0394351i
$12$		0			0
$13$	4.88281	−	3.54757i	1.35425	−	0.983918i	0.355459	−	0.934692i	$-0.384325\pi$
$13$	4.88281	−	3.54757i	1.35425	−	0.983918i	0.998788	−	0.0492260i	$-0.0156755\pi$
$14$		0			0
$15$	0.740256	−	2.27827i	0.191133	−	0.588248i
$16$		0			0
$17$	2.68680	+	1.95207i	0.651644	+	0.473447i	0.863831	−	0.503782i	$-0.168059\pi$
$17$	2.68680	+	1.95207i	0.651644	+	0.473447i	−0.212187	+	0.977229i	$0.568059\pi$
$18$		0			0
$19$	0.846245	+	2.60448i	0.194142	+	0.597508i	0.999986	+	0.00537912i	$0.00171223\pi$
$19$	0.846245	+	2.60448i	0.194142	+	0.597508i	−0.805844	+	0.592129i	$0.798288\pi$
$20$		0			0
$21$	−11.1476			−2.43260
$22$		0			0
$23$	−1.97807			−0.412457			−0.206228	−	0.978504i	$-0.566119\pi$
$23$	−1.97807			−0.412457			−0.206228	+	0.978504i	$0.566119\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	0.506776	+	0.368194i	0.0975291	+	0.0708590i
$28$		0			0
$29$	0.708723	−	2.18123i	0.131607	−	0.405043i	−0.863440	−	0.504451i	$-0.831695\pi$
$29$	0.708723	−	2.18123i	0.131607	−	0.405043i	0.995047	+	0.0994078i	$0.0316948\pi$
$30$		0			0
$31$	5.62481	−	4.08666i	1.01025	−	0.733986i	0.0459851	−	0.998942i	$-0.485357\pi$
$31$	5.62481	−	4.08666i	1.01025	−	0.733986i	0.964261	+	0.264956i	$0.0853573\pi$
$32$		0			0
$33$	−2.15526	−	7.64712i	−0.375183	−	1.33119i
$34$		0			0
$35$	3.76477	−	2.73527i	0.636363	−	0.462345i
$36$		0			0
$37$	−1.18571	+	3.64925i	−0.194930	+	0.599934i	0.805047	+	0.593211i	$0.202140\pi$
$37$	−1.18571	+	3.64925i	−0.194930	+	0.599934i	−0.999977	+	0.00672287i	$0.997860\pi$
$38$		0			0
$39$	11.6969	+	8.49826i	1.87300	+	1.36081i
$40$		0			0
$41$	1.17216	+	3.60755i	0.183061	+	0.563404i	0.999910	−	0.0134483i	$-0.00428086\pi$
$41$	1.17216	+	3.60755i	0.183061	+	0.563404i	−0.816849	+	0.576852i	$0.804281\pi$
$42$		0			0
$43$	7.98463			1.21764			0.608822	−	0.793307i	$-0.291642\pi$
$43$	7.98463			1.21764			0.608822	+	0.793307i	$0.291642\pi$
$44$		0			0
$45$	2.73851			0.408233
$46$		0			0
$47$	−3.75733	−	11.5639i	−0.548063	−	1.68676i	−0.713595	−	0.700559i	$-0.752934\pi$
$47$	−3.75733	−	11.5639i	−0.548063	−	1.68676i	0.165532	−	0.986204i	$-0.447066\pi$
$48$		0			0
$49$	−11.8563	−	8.61411i	−1.69376	−	1.23059i
$50$		0			0
$51$	−2.45844	+	7.56629i	−0.344250	+	1.05949i
$52$		0			0
$53$	9.30528	−	6.76068i	1.27818	−	0.928651i	0.278682	−	0.960383i	$-0.410102\pi$
$53$	9.30528	−	6.76068i	1.27818	−	0.928651i	0.999496	+	0.0317323i	$0.0101024\pi$
$54$		0			0
$55$	2.60424	+	2.05376i	0.351156	+	0.276929i
$56$		0			0
$57$	−5.30727	+	3.85596i	−0.702965	+	0.510734i
$58$		0			0
$59$	2.19357	−	6.75112i	0.285579	−	0.878921i	−0.700646	−	0.713509i	$-0.747105\pi$
$59$	2.19357	−	6.75112i	0.285579	−	0.878921i	0.986225	−	0.165412i	$-0.0528953\pi$
$60$		0			0
$61$	1.08255	+	0.786521i	0.138607	+	0.100704i	0.654928	−	0.755691i	$-0.272699\pi$
$61$	1.08255	+	0.786521i	0.138607	+	0.100704i	−0.516321	+	0.856395i	$0.672699\pi$
$62$		0			0
$63$	−3.93801	−	12.1200i	−0.496143	−	1.52697i
$64$		0			0
$65$	−6.03548			−0.748609
$66$		0			0
$67$	−7.18872			−0.878241			−0.439121	−	0.898428i	$-0.644710\pi$
$67$	−7.18872			−0.878241			−0.439121	+	0.898428i	$0.644710\pi$
$68$		0			0
$69$	−1.46428	−	4.50659i	−0.176279	−	0.542530i
$70$		0			0
$71$	−5.45576	−	3.96384i	−0.647479	−	0.470421i	0.214932	−	0.976629i	$-0.431047\pi$
$71$	−5.45576	−	3.96384i	−0.647479	−	0.470421i	−0.862411	+	0.506208i	$0.831047\pi$
$72$		0			0
$73$	−2.69357	+	8.28996i	−0.315259	+	0.970266i	0.660389	+	0.750924i	$0.270391\pi$
$73$	−2.69357	+	8.28996i	−0.315259	+	0.970266i	−0.975648	+	0.219343i	$0.929609\pi$
$74$		0			0
$75$	−1.93801	+	1.40805i	−0.223783	+	0.162588i
$76$		0			0
$77$	5.34450	−	14.4791i	0.609062	−	1.65004i
$78$		0			0
$79$	−4.43801	+	3.22441i	−0.499316	+	0.362774i	−0.808756	−	0.588145i	$-0.799858\pi$
$79$	−4.43801	+	3.22441i	−0.499316	+	0.362774i	0.309440	+	0.950919i	$0.399858\pi$
$80$		0			0
$81$	−3.00244	+	9.24056i	−0.333604	+	1.02673i
$82$		0			0
$83$	6.64538	+	4.82815i	0.729425	+	0.529958i	0.889382	−	0.457166i	$-0.151135\pi$
$83$	6.64538	+	4.82815i	0.729425	+	0.529958i	−0.159956	+	0.987124i	$0.551135\pi$
$84$		0			0
$85$	−1.02626	−	3.15852i	−0.111314	−	0.342589i
$86$		0			0
$87$	5.49406			0.589025
$88$		0			0
$89$	−11.4213			−1.21065			−0.605327	−	0.795977i	$-0.706958\pi$
$89$	−11.4213			−1.21065			−0.605327	+	0.795977i	$0.706958\pi$
$90$		0			0
$91$	8.67911	+	26.7116i	0.909818	+	2.80013i
$92$		0			0
$93$	13.4743	+	9.78968i	1.39722	+	1.01514i
$94$		0			0
$95$	0.846245	−	2.60448i	0.0868229	−	0.267214i
$96$		0			0
$97$	−5.29742	+	3.84880i	−0.537872	+	0.390787i	−0.823294	−	0.567615i	$-0.807866\pi$
$97$	−5.29742	+	3.84880i	−0.537872	+	0.390787i	0.285422	+	0.958402i	$0.407866\pi$
$98$		0			0
$99$	7.55279	−	5.04470i	0.759084	−	0.507011i
$100$		0			0
$101$	0.220768	−	0.160397i	0.0219672	−	0.0159601i	−0.576747	−	0.816922i	$-0.695678\pi$
$101$	0.220768	−	0.160397i	0.0219672	−	0.0159601i	0.598715	+	0.800962i	$0.295678\pi$
$102$		0			0
$103$	2.53153	−	7.79126i	0.249439	−	0.767695i	−0.745435	−	0.666578i	$-0.767758\pi$
$103$	2.53153	−	7.79126i	0.249439	−	0.767695i	0.994875	−	0.101117i	$-0.0322417\pi$
$104$		0			0
$105$	9.01858	+	6.55238i	0.880123	+	0.639447i
$106$		0			0
$107$	2.03572	+	6.26530i	0.196801	+	0.605690i	0.999951	+	0.00991335i	$0.00315557\pi$
$107$	2.03572	+	6.26530i	0.196801	+	0.605690i	−0.803150	+	0.595776i	$0.796844\pi$
$108$		0			0
$109$	3.06258			0.293342			0.146671	−	0.989185i	$-0.453144\pi$
$109$	3.06258			0.293342			0.146671	+	0.989185i	$0.453144\pi$
$110$		0			0
$111$	−9.19173			−0.872441
$112$		0			0
$113$	−1.78793	−	5.50268i	−0.168194	−	0.517649i	0.831063	−	0.556178i	$-0.187733\pi$
$113$	−1.78793	−	5.50268i	−0.168194	−	0.517649i	−0.999257	+	0.0385293i	$0.987733\pi$
$114$		0			0
$115$	1.60029	+	1.16268i	0.149228	+	0.108421i
$116$		0			0
$117$	−5.10750	+	15.7193i	−0.472188	+	1.45325i
$118$		0			0
$119$	−12.5030	+	9.08399i	−1.14615	+	0.832728i
$120$		0			0
$121$	10.9658	+	0.866898i	0.996890	+	0.0788089i
$122$		0			0
$123$	−7.35127	+	5.34101i	−0.662842	+	0.481583i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−1.41853	−	1.03062i	−0.125874	−	0.0914527i	0.523067	−	0.852292i	$-0.324788\pi$
$127$	−1.41853	−	1.03062i	−0.125874	−	0.0914527i	−0.648941	+	0.760839i	$0.724788\pi$
$128$		0			0
$129$	5.91067	+	18.1912i	0.520405	+	1.60164i
$130$		0			0
$131$	−12.7047			−1.11002			−0.555008	−	0.831845i	$-0.687285\pi$
$131$	−12.7047			−1.11002			−0.555008	+	0.831845i	$0.687285\pi$
$132$		0			0
$133$	−12.7437			−1.10502
$134$		0			0
$135$	−0.193571	−	0.595751i	−0.0166600	−	0.0512741i
$136$		0			0
$137$	1.40473	+	1.02060i	0.120015	+	0.0871957i	0.646173	−	0.763191i	$-0.276368\pi$
$137$	1.40473	+	1.02060i	0.120015	+	0.0871957i	−0.526159	+	0.850386i	$0.676368\pi$
$138$		0			0
$139$	1.99933	−	6.15331i	0.169581	−	0.521917i	−0.829763	−	0.558115i	$-0.811525\pi$
$139$	1.99933	−	6.15331i	0.169581	−	0.521917i	0.999345	+	0.0361981i	$0.0115247\pi$
$140$		0			0
$141$	23.5643	−	17.1204i	1.98447	−	1.44180i
$142$		0			0
$143$	−16.6458	+	11.1182i	−1.39199	+	0.929748i
$144$		0			0
$145$	−1.85546	+	1.34807i	−0.154088	+	0.111951i
$146$		0			0
$147$	10.8486	−	33.3885i	0.894777	−	2.75384i
$148$		0			0
$149$	−1.05849	−	0.769037i	−0.0867148	−	0.0630020i	0.543583	−	0.839355i	$-0.317067\pi$
$149$	−1.05849	−	0.769037i	−0.0867148	−	0.0630020i	−0.630298	+	0.776353i	$0.717067\pi$
$150$		0			0
$151$	−6.19819	−	19.0761i	−0.504401	−	1.55239i	−0.801775	−	0.597626i	$-0.796111\pi$
$151$	−6.19819	−	19.0761i	−0.504401	−	1.55239i	0.297374	−	0.954761i	$-0.403889\pi$
$152$		0			0
$153$	−9.09475			−0.735267
$154$		0			0
$155$	−6.95265			−0.558450
$156$		0			0
$157$	5.45768	+	16.7970i	0.435570	+	1.34055i	0.892501	+	0.451045i	$0.148948\pi$
$157$	5.45768	+	16.7970i	0.435570	+	1.34055i	−0.456932	+	0.889502i	$0.651052\pi$
$158$		0			0
$159$	22.2910	+	16.1953i	1.76779	+	1.28437i
$160$		0			0
$161$	2.84450	−	8.75446i	0.224178	−	0.689948i
$162$		0			0
$163$	−3.74110	+	2.71807i	−0.293025	+	0.212895i	−0.724579	−	0.689192i	$-0.757966\pi$
$163$	−3.74110	+	2.71807i	−0.293025	+	0.212895i	0.431553	+	0.902087i	$0.357966\pi$
$164$		0			0
$165$	−2.75122	+	7.45348i	−0.214182	+	0.580253i
$166$		0			0
$167$	−18.1445	+	13.1827i	−1.40406	+	1.02011i	−0.409909	+	0.912127i	$0.634439\pi$
$167$	−18.1445	+	13.1827i	−1.40406	+	1.02011i	−0.994153	+	0.107984i	$0.965561\pi$
$168$		0			0
$169$	7.23935	−	22.2804i	0.556873	−	1.71388i
$170$		0			0
$171$	−6.06716	−	4.40805i	−0.463967	−	0.337092i
$172$		0			0
$173$	−2.19724	−	6.76241i	−0.167053	−	0.514136i	0.832129	−	0.554583i	$-0.187122\pi$
$173$	−2.19724	−	6.76241i	−0.167053	−	0.514136i	−0.999182	+	0.0404462i	$0.987122\pi$
$174$		0			0
$175$	−4.65351			−0.351773
$176$		0			0
$177$	17.0047			1.27815
$178$		0			0
$179$	1.54508	+	4.75528i	0.115485	+	0.355427i	0.992048	−	0.125861i	$-0.0401693\pi$
$179$	1.54508	+	4.75528i	0.115485	+	0.355427i	−0.876563	+	0.481287i	$0.840169\pi$
$180$		0			0
$181$	−13.7404	−	9.98299i	−1.02132	−	0.742030i	−0.0547639	−	0.998499i	$-0.517441\pi$
$181$	−13.7404	−	9.98299i	−1.02132	−	0.742030i	−0.966552	+	0.256470i	$0.917441\pi$
$182$		0			0
$183$	−0.990544	+	3.04858i	−0.0732231	+	0.225358i
$184$		0			0
$185$	3.10424	−	2.25536i	0.228228	−	0.165818i
$186$		0			0
$187$	−8.64885	−	6.82066i	−0.632466	−	0.498776i
$188$		0			0
$189$	−2.35829	+	1.71340i	−0.171540	+	0.124631i
$190$		0			0
$191$	1.41853	−	4.36578i	0.102641	−	0.315896i	−0.886529	−	0.462674i	$-0.846890\pi$
$191$	1.41853	−	4.36578i	0.102641	−	0.315896i	0.989170	+	0.146777i	$0.0468901\pi$
$192$		0			0
$193$	7.08203	+	5.14540i	0.509776	+	0.370374i	0.812739	−	0.582629i	$-0.197976\pi$
$193$	7.08203	+	5.14540i	0.509776	+	0.370374i	−0.302963	+	0.953002i	$0.597976\pi$
$194$		0			0
$195$	−4.46780	−	13.7505i	−0.319946	−	0.984692i
$196$		0			0
$197$	13.4511			0.958352			0.479176	−	0.877719i	$-0.340936\pi$
$197$	13.4511			0.958352			0.479176	+	0.877719i	$0.340936\pi$
$198$		0			0
$199$	4.55665			0.323012			0.161506	−	0.986872i	$-0.448365\pi$
$199$	4.55665			0.323012			0.161506	+	0.986872i	$0.448365\pi$
$200$		0			0
$201$	−5.32149	−	16.3779i	−0.375349	−	1.15521i
$202$		0			0
$203$	8.63441	+	6.27327i	0.606017	+	0.440297i
$204$		0			0
$205$	1.17216	−	3.60755i	0.0818674	−	0.251962i
$206$		0			0
$207$	4.38242	−	3.18401i	0.304599	−	0.221304i
$208$		0			0
$209$	−2.46385	−	8.74203i	−0.170428	−	0.604699i
$210$		0			0
$211$	0.166677	−	0.121098i	0.0114745	−	0.00833675i	−0.582033	−	0.813165i	$-0.697743\pi$
$211$	0.166677	−	0.121098i	0.0114745	−	0.00833675i	0.593508	+	0.804828i	$0.297743\pi$
$212$		0			0
$213$	4.99205	−	15.3640i	0.342050	−	1.05272i
$214$		0			0
$215$	−6.45970	−	4.69325i	−0.440548	−	0.320077i
$216$		0			0
$217$	9.99801	+	30.7707i	0.678709	+	2.08885i
$218$		0			0
$219$	−20.8807			−1.41099
$220$		0			0
$221$	20.0442			1.34832
$222$		0			0
$223$	7.41041	+	22.8069i	0.496237	+	1.52726i	0.815019	+	0.579434i	$0.196726\pi$
$223$	7.41041	+	22.8069i	0.496237	+	1.52726i	−0.318782	+	0.947828i	$0.603274\pi$
$224$		0			0
$225$	−2.21550	−	1.60965i	−0.147700	−	0.107310i
$226$		0			0
$227$	7.23449	−	22.2655i	0.480170	−	1.47781i	−0.358686	−	0.933458i	$-0.616775\pi$
$227$	7.23449	−	22.2655i	0.480170	−	1.47781i	0.838856	−	0.544353i	$-0.183225\pi$
$228$		0			0
$229$	16.1473	−	11.7317i	1.06705	−	0.775254i	0.0916671	−	0.995790i	$-0.470780\pi$
$229$	16.1473	−	11.7317i	1.06705	−	0.775254i	0.975379	+	0.220535i	$0.0707804\pi$
$230$		0			0
$231$	36.9436	+	1.45801i	2.43071	+	0.0959299i
$232$		0			0
$233$	1.05735	−	0.768207i	0.0692690	−	0.0503269i	−0.552612	−	0.833439i	$-0.686369\pi$
$233$	1.05735	−	0.768207i	0.0692690	−	0.0503269i	0.621881	+	0.783112i	$0.286369\pi$
$234$		0			0
$235$	−3.75733	+	11.5639i	−0.245101	+	0.754344i
$236$		0			0
$237$	−10.6313	−	7.72412i	−0.690580	−	0.501736i
$238$		0			0
$239$	−3.74662	−	11.5309i	−0.242349	−	0.745872i	−0.996061	−	0.0886682i	$-0.971739\pi$
$239$	−3.74662	−	11.5309i	−0.242349	−	0.745872i	0.753713	−	0.657204i	$-0.228261\pi$
$240$		0			0
$241$	−18.3095			−1.17942			−0.589709	−	0.807616i	$-0.700758\pi$
$241$	−18.3095			−1.17942			−0.589709	+	0.807616i	$0.700758\pi$
$242$		0			0
$243$	−21.3959			−1.37255
$244$		0			0
$245$	4.52870	+	13.9379i	0.289328	+	0.890461i
$246$		0			0
$247$	13.3716	+	9.71504i	0.850815	+	0.618153i
$248$		0			0
$249$	−6.08057	+	18.7141i	−0.385340	+	1.18596i
$250$		0			0
$251$	21.6733	−	15.7466i	1.36801	−	0.993916i	0.370118	−	0.928985i	$-0.379317\pi$
$251$	21.6733	−	15.7466i	1.36801	−	0.993916i	0.997890	−	0.0649314i	$-0.0206829\pi$
$252$		0			0
$253$	6.55542	+	0.258715i	0.412136	+	0.0162653i
$254$		0			0
$255$	6.43627	−	4.67622i	0.403055	−	0.292836i
$256$		0			0
$257$	−2.22562	+	6.84976i	−0.138831	+	0.427277i	−0.996166	−	0.0874814i	$-0.972118\pi$
$257$	−2.22562	+	6.84976i	−0.138831	+	0.427277i	0.857336	+	0.514758i	$0.172118\pi$
$258$		0			0
$259$	−14.4456	−	10.4954i	−0.897608	−	0.652150i
$260$		0			0
$261$	1.94084	+	5.97330i	0.120135	+	0.369738i
$262$		0			0
$263$	11.7870			0.726816			0.363408	−	0.931630i	$-0.381613\pi$
$263$	11.7870			0.726816			0.363408	+	0.931630i	$0.381613\pi$
$264$		0			0
$265$	−11.5020			−0.706560
$266$		0			0
$267$	−8.45467	−	26.0208i	−0.517418	−	1.59245i
$268$		0			0
$269$	−11.9730	−	8.69888i	−0.730005	−	0.530380i	0.159560	−	0.987188i	$-0.448992\pi$
$269$	−11.9730	−	8.69888i	−0.730005	−	0.530380i	−0.889565	+	0.456808i	$0.848992\pi$
$270$		0			0
$271$	7.19508	−	22.1442i	0.437070	−	1.34516i	−0.453881	−	0.891063i	$-0.649961\pi$
$271$	7.19508	−	22.1442i	0.437070	−	1.34516i	0.890951	−	0.454100i	$-0.150039\pi$
$272$		0			0
$273$	−54.4315	+	39.5468i	−3.29434	+	2.39348i
$274$		0			0
$275$	−0.899706	−	3.19226i	−0.0542543	−	0.192501i
$276$		0			0
$277$	12.5293	−	9.10304i	0.752811	−	0.546949i	−0.143886	−	0.989594i	$-0.545960\pi$
$277$	12.5293	−	9.10304i	0.752811	−	0.546949i	0.896697	+	0.442645i	$0.145960\pi$
$278$		0			0
$279$	−5.88365	+	18.1080i	−0.352245	+	1.08410i
$280$		0			0
$281$	12.1529	+	8.82959i	0.724980	+	0.526729i	0.887971	−	0.459898i	$-0.152114\pi$
$281$	12.1529	+	8.82959i	0.724980	+	0.526729i	−0.162991	+	0.986628i	$0.552114\pi$
$282$		0			0
$283$	−4.47548	−	13.7741i	−0.266040	−	0.818787i	−0.991452	−	0.130472i	$-0.958351\pi$
$283$	−4.47548	−	13.7741i	−0.266040	−	0.818787i	0.725412	−	0.688315i	$-0.241649\pi$
$284$		0			0
$285$	6.56014			0.388589
$286$		0			0
$287$	−17.6517			−1.04195
$288$		0			0
$289$	−1.84500	−	5.67833i	−0.108530	−	0.334019i
$290$		0			0
$291$	−12.6901	−	9.21988i	−0.743905	−	0.540479i
$292$		0			0
$293$	−5.15326	+	15.8601i	−0.301057	+	0.926557i	0.680063	+	0.733154i	$0.261953\pi$
$293$	−5.15326	+	15.8601i	−0.301057	+	0.926557i	−0.981119	+	0.193403i	$0.938047\pi$
$294$		0			0
$295$	−5.74284	+	4.17242i	−0.334361	+	0.242928i
$296$		0			0
$297$	−1.63132	−	1.28649i	−0.0946589	−	0.0746500i
$298$		0			0
$299$	−9.65854	+	7.01734i	−0.558568	+	0.405823i
$300$		0			0
$301$	−11.4820	+	35.3380i	−0.661813	+	2.03685i
$302$		0			0
$303$	0.528853	+	0.384234i	0.0303818	+	0.0220737i
$304$		0			0
$305$	−0.413499	−	1.27262i	−0.0236769	−	0.0728699i
$306$		0			0
$307$	0.537575			0.0306810			0.0153405	−	0.999882i	$-0.495117\pi$
$307$	0.537575			0.0306810			0.0153405	+	0.999882i	$0.495117\pi$
$308$		0			0
$309$	19.6246			1.11640
$310$		0			0
$311$	3.86105	+	11.8831i	0.218940	+	0.673828i	0.998850	+	0.0479370i	$0.0152647\pi$
$311$	3.86105	+	11.8831i	0.218940	+	0.673828i	−0.779910	+	0.625891i	$0.784735\pi$
$312$		0			0
$313$	−15.2396	−	11.0722i	−0.861391	−	0.625837i	0.0668722	−	0.997762i	$-0.478698\pi$
$313$	−15.2396	−	11.0722i	−0.861391	−	0.625837i	−0.928263	+	0.371925i	$0.878698\pi$
$314$		0			0
$315$	−3.93801	+	12.1200i	−0.221882	+	0.682883i
$316$		0			0
$317$	5.71239	−	4.15030i	0.320840	−	0.233104i	−0.415694	−	0.909505i	$-0.636461\pi$
$317$	5.71239	−	4.15030i	0.320840	−	0.233104i	0.736534	+	0.676401i	$0.236461\pi$
$318$		0			0
$319$	−2.63403	+	7.13598i	−0.147477	+	0.399538i
$320$		0			0
$321$	−12.7671	+	9.27586i	−0.712591	+	0.517728i
$322$		0			0
$323$	−2.81043	+	8.64962i	−0.156377	+	0.481278i
$324$		0			0
$325$	4.88281	+	3.54757i	0.270849	+	0.196784i
$326$		0			0
$327$	2.26710	+	6.97740i	0.125371	+	0.385851i
$328$		0			0
$329$	56.5819			3.11946
$330$		0			0
$331$	7.83433			0.430614			0.215307	−	0.976546i	$-0.430925\pi$
$331$	7.83433			0.430614			0.215307	+	0.976546i	$0.430925\pi$
$332$		0			0
$333$	−3.24709	−	9.99351i	−0.177939	−	0.547641i
$334$		0			0
$335$	5.81579	+	4.22542i	0.317751	+	0.230859i
$336$		0			0
$337$	2.25876	−	6.95173i	0.123042	−	0.378685i	−0.870497	−	0.492174i	$-0.836203\pi$
$337$	2.25876	−	6.95173i	0.123042	−	0.378685i	0.993539	+	0.113489i	$0.0362025\pi$
$338$		0			0
$339$	11.2131	−	8.14678i	0.609011	−	0.442472i
$340$		0			0
$341$	−19.1754	+	12.8077i	−1.03840	+	0.693576i
$342$		0			0
$343$	28.8201	−	20.9390i	1.55614	−	1.13060i
$344$		0			0
$345$	−1.46428	+	4.50659i	−0.0788342	+	0.242627i
$346$		0			0
$347$	14.2181	+	10.3301i	0.763270	+	0.554548i	0.899912	−	0.436072i	$-0.143631\pi$
$347$	14.2181	+	10.3301i	0.763270	+	0.554548i	−0.136641	+	0.990621i	$0.543631\pi$
$348$		0			0
$349$	−6.60659	−	20.3330i	−0.353643	−	1.08840i	−0.956792	−	0.290772i	$-0.906088\pi$
$349$	−6.60659	−	20.3330i	−0.353643	−	1.08840i	0.603150	−	0.797628i	$-0.293912\pi$
$350$		0			0
$351$	3.78068			0.201798
$352$		0			0
$353$	7.59779			0.404389			0.202195	−	0.979345i	$-0.435193\pi$
$353$	7.59779			0.404389			0.202195	+	0.979345i	$0.435193\pi$
$354$		0			0
$355$	2.08391	+	6.41362i	0.110603	+	0.340400i
$356$		0			0
$357$	−29.9513	−	21.7609i	−1.58519	−	1.15171i
$358$		0			0
$359$	−10.7124	+	32.9695i	−0.565380	+	1.74006i	0.101438	+	0.994842i	$0.467656\pi$
$359$	−10.7124	+	32.9695i	−0.565380	+	1.74006i	−0.666818	+	0.745220i	$0.732344\pi$
$360$		0			0
$361$	9.30416	−	6.75987i	0.489693	−	0.355783i
$362$		0			0
$363$	6.14246	+	25.6248i	0.322395	+	1.34495i
$364$		0			0
$365$	7.05186	−	5.12348i	0.369111	−	0.268175i
$366$		0			0
$367$	−4.64462	+	14.2947i	−0.242447	+	0.746176i	0.753599	+	0.657335i	$0.228316\pi$
$367$	−4.64462	+	14.2947i	−0.242447	+	0.746176i	−0.996046	+	0.0888408i	$0.971684\pi$
$368$		0			0
$369$	−8.40383	−	6.10574i	−0.437486	−	0.317852i
$370$		0			0
$371$	16.5400	+	50.9049i	0.858713	+	2.64285i
$372$		0			0
$373$	−13.5055			−0.699286			−0.349643	−	0.936883i	$-0.613697\pi$
$373$	−13.5055			−0.699286			−0.349643	+	0.936883i	$0.613697\pi$
$374$		0			0
$375$	2.39552			0.123704
$376$		0			0
$377$	−4.27748	−	13.1647i	−0.220302	−	0.678019i
$378$		0			0
$379$	18.7641	+	13.6329i	0.963846	+	0.700275i	0.954041	−	0.299677i	$-0.0968789\pi$
$379$	18.7641	+	13.6329i	0.963846	+	0.700275i	0.00980504	+	0.999952i	$0.496879\pi$
$380$		0			0
$381$	1.29796	−	3.99471i	0.0664966	−	0.204655i
$382$		0			0
$383$	−28.4282	+	20.6543i	−1.45261	+	1.05539i	−0.467402	+	0.884045i	$0.654810\pi$
$383$	−28.4282	+	20.6543i	−1.45261	+	1.05539i	−0.985212	+	0.171341i	$0.945190\pi$
$384$		0			0
$385$	−12.8344	+	8.57240i	−0.654100	+	0.436890i
$386$		0			0
$387$	−17.6899	+	12.8525i	−0.899230	+	0.653329i
$388$		0			0
$389$	−11.0505	+	34.0101i	−0.560285	+	1.72438i	0.121278	+	0.992619i	$0.461301\pi$
$389$	−11.0505	+	34.0101i	−0.560285	+	1.72438i	−0.681562	+	0.731760i	$0.738699\pi$
$390$		0			0
$391$	−5.31467	−	3.86134i	−0.268775	−	0.195276i
$392$		0			0
$393$	−9.40473	−	28.9448i	−0.474406	−	1.46007i
$394$		0			0
$395$	5.48569			0.276015
$396$		0			0
$397$	−3.62347			−0.181857			−0.0909284	−	0.995857i	$-0.528983\pi$
$397$	−3.62347			−0.181857			−0.0909284	+	0.995857i	$0.528983\pi$
$398$		0			0
$399$	−9.43359	−	29.0336i	−0.472270	−	1.45350i
$400$		0			0
$401$	−0.851903	−	0.618944i	−0.0425420	−	0.0309086i	0.566311	−	0.824192i	$-0.308370\pi$
$401$	−0.851903	−	0.618944i	−0.0425420	−	0.0309086i	−0.608853	+	0.793283i	$0.708370\pi$
$402$		0			0
$403$	12.9671	−	39.9088i	0.645940	−	1.98800i
$404$		0			0
$405$	7.86049	−	5.71098i	0.390591	−	0.283781i
$406$		0			0
$407$	4.40680	−	11.9387i	0.218437	−	0.591780i
$408$		0			0
$409$	9.29498	−	6.75320i	0.459607	−	0.333924i	−0.333770	−	0.942655i	$-0.608321\pi$
$409$	9.29498	−	6.75320i	0.459607	−	0.333924i	0.793377	+	0.608730i	$0.208321\pi$
$410$		0			0
$411$	−1.28534	+	3.95587i	−0.0634012	+	0.195129i
$412$		0			0
$413$	26.7244	+	19.4164i	1.31502	+	0.955419i
$414$		0			0
$415$	−2.53831	−	7.81211i	−0.124601	−	0.383481i
$416$		0			0
$417$	15.4989			0.758987
$418$		0			0
$419$	9.12829			0.445946			0.222973	−	0.974825i	$-0.428424\pi$
$419$	9.12829			0.445946			0.222973	+	0.974825i	$0.428424\pi$
$420$		0			0
$421$	−7.77517	−	23.9295i	−0.378939	−	1.16625i	−0.940783	−	0.339010i	$-0.889908\pi$
$421$	−7.77517	−	23.9295i	−0.378939	−	1.16625i	0.561844	−	0.827243i	$-0.310092\pi$
$422$		0			0
$423$	26.9382	+	19.5717i	1.30978	+	0.951610i
$424$		0			0
$425$	−1.02626	+	3.15852i	−0.0497811	+	0.153211i
$426$		0			0
$427$	−5.03768	+	3.66009i	−0.243790	+	0.177124i
$428$		0			0
$429$	−37.6524	−	29.6935i	−1.81787	−	1.43361i
$430$		0			0
$431$	12.7836	−	9.28785i	0.615766	−	0.447380i	−0.235674	−	0.971832i	$-0.575730\pi$
$431$	12.7836	−	9.28785i	0.615766	−	0.447380i	0.851440	+	0.524452i	$0.175730\pi$
$432$		0			0
$433$	−0.830254	+	2.55526i	−0.0398994	+	0.122798i	−0.969022	−	0.246973i	$-0.920564\pi$
$433$	−0.830254	+	2.55526i	−0.0398994	+	0.122798i	0.929123	+	0.369771i	$0.120564\pi$
$434$		0			0
$435$	−4.44479	−	3.22933i	−0.213111	−	0.154835i
$436$		0			0
$437$	−1.67393	−	5.15184i	−0.0800751	−	0.246446i
$438$		0			0
$439$	−18.0888			−0.863333			−0.431666	−	0.902033i	$-0.642074\pi$
$439$	−18.0888			−0.863333			−0.431666	+	0.902033i	$0.642074\pi$
$440$		0			0
$441$	40.1334			1.91111
$442$		0			0
$443$	−10.1036	−	31.0956i	−0.480035	−	1.47740i	−0.839045	−	0.544063i	$-0.816885\pi$
$443$	−10.1036	−	31.0956i	−0.480035	−	1.47740i	0.359009	−	0.933334i	$-0.383115\pi$
$444$		0			0
$445$	9.24002	+	6.71326i	0.438019	+	0.318239i
$446$		0			0
$447$	0.968524	−	2.98081i	0.0458096	−	0.140987i
$448$		0			0
$449$	−7.33308	+	5.32780i	−0.346070	+	0.251434i	−0.747218	−	0.664579i	$-0.768611\pi$
$449$	−7.33308	+	5.32780i	−0.346070	+	0.251434i	0.401149	+	0.916013i	$0.368611\pi$
$450$		0			0
$451$	−3.41276	−	12.1089i	−0.160701	−	0.570185i
$452$		0			0
$453$	38.8722	−	28.2423i	1.82638	−	1.32694i
$454$		0			0
$455$	8.67911	−	26.7116i	0.406883	−	1.25226i
$456$		0			0
$457$	−12.7422	−	9.25773i	−0.596054	−	0.433058i	0.248422	−	0.968652i	$-0.420088\pi$
$457$	−12.7422	−	9.25773i	−0.596054	−	0.433058i	−0.844476	+	0.535593i	$0.820088\pi$
$458$		0			0
$459$	0.642862	+	1.97853i	0.0300062	+	0.0923497i
$460$		0			0
$461$	−33.2263			−1.54750			−0.773751	−	0.633489i	$-0.781622\pi$
$461$	−33.2263			−1.54750			−0.773751	+	0.633489i	$0.781622\pi$
$462$		0			0
$463$	6.68368			0.310617			0.155309	−	0.987866i	$-0.450363\pi$
$463$	6.68368			0.310617			0.155309	+	0.987866i	$0.450363\pi$
$464$		0			0
$465$	−5.14674	−	15.8400i	−0.238674	−	0.734564i
$466$		0			0
$467$	−17.2600	−	12.5401i	−0.798695	−	0.580286i	0.111836	−	0.993727i	$-0.464327\pi$
$467$	−17.2600	−	12.5401i	−0.798695	−	0.580286i	−0.910531	+	0.413440i	$0.864327\pi$
$468$		0			0
$469$	10.3375	−	31.8155i	0.477341	−	1.46910i
$470$		0			0
$471$	−34.2281	+	24.8682i	−1.57715	+	1.14586i
$472$		0			0
$473$	−26.4614	−	1.04432i	−1.21670	−	0.0480180i
$474$		0			0
$475$	−2.21550	+	1.60965i	−0.101654	+	0.0738560i
$476$		0			0
$477$	−9.73348	+	29.9566i	−0.445665	+	1.37162i
$478$		0			0
$479$	−31.7666	−	23.0798i	−1.45145	−	1.05454i	−0.985489	−	0.169739i	$-0.945708\pi$
$479$	−31.7666	−	23.0798i	−1.45145	−	1.05454i	−0.465964	−	0.884804i	$-0.654292\pi$
$480$		0			0
$481$	7.15636	+	22.0250i	0.326302	+	1.00425i
$482$		0			0
$483$	22.0507			1.00334
$484$		0			0
$485$	6.54798			0.297328
$486$		0			0
$487$	3.93368	+	12.1066i	0.178252	+	0.548603i	0.999767	−	0.0215836i	$-0.00687081\pi$
$487$	3.93368	+	12.1066i	0.178252	+	0.548603i	−0.821515	+	0.570187i	$0.806871\pi$
$488$		0			0
$489$	−8.96186	−	6.51117i	−0.405269	−	0.294446i
$490$		0			0
$491$	−1.67052	+	5.14133i	−0.0753895	+	0.232025i	−0.981649	−	0.190697i	$-0.938925\pi$
$491$	−1.67052	+	5.14133i	−0.0753895	+	0.232025i	0.906259	+	0.422722i	$0.138925\pi$
$492$		0			0
$493$	6.16210	−	4.47703i	0.277527	−	0.201635i
$494$		0			0
$495$	−9.07554	−	0.358173i	−0.407915	−	0.0160987i
$496$		0			0
$497$	25.3884	−	18.4458i	1.13883	−	0.827406i
$498$		0			0
$499$	−1.47238	+	4.53151i	−0.0659126	+	0.202858i	−0.978589	−	0.205826i	$-0.934012\pi$
$499$	−1.47238	+	4.53151i	−0.0659126	+	0.202858i	0.912676	+	0.408684i	$0.134012\pi$
$500$		0			0
$501$	−43.4654	−	31.5795i	−1.94189	−	1.41087i
$502$		0			0
$503$	5.06803	+	15.5978i	0.225972	+	0.695471i	0.998191	+	0.0601146i	$0.0191466\pi$
$503$	5.06803	+	15.5978i	0.225972	+	0.695471i	−0.772219	+	0.635356i	$0.780853\pi$
$504$		0			0
$505$	−0.272884			−0.0121432
$506$		0			0
$507$	56.1199			2.49237
$508$		0			0
$509$	12.6919	+	39.0615i	0.562557	+	1.73137i	0.675101	+	0.737725i	$0.264100\pi$
$509$	12.6919	+	39.0615i	0.562557	+	1.73137i	−0.112544	+	0.993647i	$0.535900\pi$
$510$		0			0
$511$	−32.8159	−	23.8422i	−1.45169	−	1.05472i
$512$		0			0
$513$	−0.530096	+	1.63147i	−0.0234043	+	0.0720311i
$514$		0			0
$515$	−6.62764	+	4.81526i	−0.292049	+	0.212186i
$516$		0			0
$517$	10.9395	+	38.8146i	0.481119	+	1.70706i
$518$		0			0
$519$	13.7801	−	10.0118i	0.604879	−	0.439470i
$520$		0			0
$521$	12.1745	−	37.4694i	0.533376	−	1.64156i	−0.213756	−	0.976887i	$-0.568570\pi$
$521$	12.1745	−	37.4694i	0.533376	−	1.64156i	0.747132	−	0.664676i	$-0.231430\pi$
$522$		0			0
$523$	13.5422	+	9.83898i	0.592159	+	0.430228i	0.843087	−	0.537777i	$-0.180736\pi$
$523$	13.5422	+	9.83898i	0.592159	+	0.430228i	−0.250928	+	0.968006i	$0.580736\pi$
$524$		0			0
$525$	−3.44479	−	10.6020i	−0.150343	−	0.462708i
$526$		0			0
$527$	23.0902			1.00582
$528$		0			0
$529$	−19.0872			−0.829880
$530$		0			0
$531$	6.00711	+	18.4880i	0.260686	+	0.802310i
$532$		0			0
$533$	18.5214	+	13.4566i	0.802253	+	0.582871i
$534$		0			0
$535$	2.03572	−	6.26530i	0.0880119	−	0.270873i
$536$		0			0
$537$	−9.69007	+	7.04025i	−0.418158	+	0.303809i
$538$		0			0
$539$	38.1657	+	30.0982i	1.64391	+	1.29642i
$540$		0			0
$541$	7.27260	−	5.28386i	0.312674	−	0.227171i	−0.420369	−	0.907353i	$-0.638099\pi$
$541$	7.27260	−	5.28386i	0.312674	−	0.227171i	0.733043	+	0.680182i	$0.238099\pi$
$542$		0			0
$543$	12.5726	−	38.6944i	0.539540	−	1.66053i
$544$		0			0
$545$	−2.47768	−	1.80014i	−0.106132	−	0.0771096i
$546$		0			0
$547$	6.47715	+	19.9346i	0.276943	+	0.852343i	0.988699	+	0.149916i	$0.0479002\pi$
$547$	6.47715	+	19.9346i	0.276943	+	0.852343i	−0.711756	+	0.702427i	$0.752100\pi$
$548$		0			0
$549$	−3.66442			−0.156394
$550$		0			0
$551$	6.28070			0.267567
$552$		0			0
$553$	−7.88850	−	24.2783i	−0.335453	−	1.03242i
$554$		0			0
$555$	7.43627	+	5.40276i	0.315652	+	0.229335i
$556$		0			0
$557$	−4.70739	+	14.4878i	−0.199458	+	0.613870i	0.800437	+	0.599417i	$0.204601\pi$
$557$	−4.70739	+	14.4878i	−0.199458	+	0.613870i	−0.999896	+	0.0144532i	$0.995399\pi$
$558$		0			0
$559$	38.9874	−	28.3260i	1.64899	−	1.19806i
$560$		0			0
$561$	9.13697	−	24.7535i	0.385763	−	1.04509i
$562$		0			0
$563$	−12.3057	+	8.94059i	−0.518622	+	0.376801i	−0.816085	−	0.577932i	$-0.803860\pi$
$563$	−12.3057	+	8.94059i	−0.518622	+	0.376801i	0.297462	+	0.954734i	$0.403860\pi$
$564$		0			0
$565$	−1.78793	+	5.50268i	−0.0752187	+	0.231499i
$566$		0			0
$567$	−36.5789	−	26.5761i	−1.53617	−	1.11609i
$568$		0			0
$569$	11.8935	+	36.6045i	0.498602	+	1.53454i	0.811267	+	0.584676i	$0.198778\pi$
$569$	11.8935	+	36.6045i	0.498602	+	1.53454i	−0.312665	+	0.949864i	$0.601222\pi$
$570$		0			0
$571$	17.3549			0.726282			0.363141	−	0.931734i	$-0.381704\pi$
$571$	17.3549			0.726282			0.363141	+	0.931734i	$0.381704\pi$
$572$		0			0
$573$	10.9965			0.459386
$574$		0			0
$575$	−0.611258	−	1.88126i	−0.0254912	−	0.0784539i
$576$		0			0
$577$	−4.02905	−	2.92728i	−0.167732	−	0.121864i	0.500753	−	0.865590i	$-0.333057\pi$
$577$	−4.02905	−	2.92728i	−0.167732	−	0.121864i	−0.668484	+	0.743726i	$0.733057\pi$
$578$		0			0
$579$	−6.48011	+	19.9437i	−0.269304	+	0.828833i
$580$		0			0
$581$	−30.9244	+	22.4679i	−1.28296	+	0.932124i
$582$		0			0
$583$	−31.7224	+	21.1882i	−1.31381	+	0.877524i
$584$		0			0
$585$	13.3716	−	9.71504i	0.552848	−	0.401667i
$586$		0			0
$587$	−12.0986	+	37.2356i	−0.499362	+	1.53688i	0.310685	+	0.950513i	$0.399442\pi$
$587$	−12.0986	+	37.2356i	−0.499362	+	1.53688i	−0.810047	+	0.586365i	$0.800558\pi$
$588$		0			0
$589$	15.4036	+	11.1914i	0.634694	+	0.461132i
$590$		0			0
$591$	9.95726	+	30.6453i	0.409587	+	1.26058i
$592$		0			0
$593$	36.2454			1.48842			0.744211	−	0.667945i	$-0.232826\pi$
$593$	36.2454			1.48842			0.744211	+	0.667945i	$0.232826\pi$
$594$		0			0
$595$	15.4546			0.633577
$596$		0			0
$597$	3.37309	+	10.3813i	0.138051	+	0.424878i
$598$		0			0
$599$	−9.75622	−	7.08831i	−0.398628	−	0.289620i	0.370354	−	0.928891i	$-0.379236\pi$
$599$	−9.75622	−	7.08831i	−0.398628	−	0.289620i	−0.768982	+	0.639270i	$0.779236\pi$
$600$		0			0
$601$	−8.60875	+	26.4950i	−0.351158	+	1.08075i	0.607045	+	0.794667i	$0.292355\pi$
$601$	−8.60875	+	26.4950i	−0.351158	+	1.08075i	−0.958204	+	0.286087i	$0.907645\pi$
$602$		0			0
$603$	15.9266	−	11.5713i	0.648581	−	0.471222i
$604$		0			0
$605$	−8.36196	−	7.14686i	−0.339962	−	0.290561i
$606$		0			0
$607$	−33.5888	+	24.4037i	−1.36333	+	0.990517i	−0.365104	+	0.930967i	$0.618966\pi$
$607$	−33.5888	+	24.4037i	−1.36333	+	0.990517i	−0.998225	+	0.0595497i	$0.981034\pi$
$608$		0			0
$609$	−7.90055	+	24.3154i	−0.320146	+	0.985309i
$610$		0			0
$611$	−59.3699	−	43.1347i	−2.40185	−	1.74505i
$612$		0			0
$613$	−13.4249	−	41.3175i	−0.542226	−	1.66880i	−0.727497	−	0.686111i	$-0.759316\pi$
$613$	−13.4249	−	41.3175i	−0.542226	−	1.66880i	0.185271	−	0.982687i	$-0.440684\pi$
$614$		0			0
$615$	9.08667			0.366410
$616$		0			0
$617$	−18.9692			−0.763672			−0.381836	−	0.924230i	$-0.624708\pi$
$617$	−18.9692			−0.763672			−0.381836	+	0.924230i	$0.624708\pi$
$618$		0			0
$619$	0.867212	+	2.66900i	0.0348562	+	0.107276i	0.966971	−	0.254887i	$-0.0820383\pi$
$619$	0.867212	+	2.66900i	0.0348562	+	0.107276i	−0.932115	+	0.362163i	$0.882038\pi$
$620$		0			0
$621$	−1.00244	−	0.728315i	−0.0402265	−	0.0292263i
$622$		0			0
$623$	16.4240	−	50.5478i	0.658013	−	2.02516i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	18.0929	−	12.0847i	0.722559	−	0.482615i
$628$		0			0
$629$	−10.3094	+	7.49020i	−0.411062	+	0.298654i
$630$		0			0
$631$	−7.30552	+	22.4841i	−0.290828	+	0.895077i	0.693763	+	0.720204i	$0.255952\pi$
$631$	−7.30552	+	22.4841i	−0.290828	+	0.895077i	−0.984591	+	0.174873i	$0.944048\pi$
$632$		0			0
$633$	0.399279	+	0.290093i	0.0158699	+	0.0115302i
$634$		0			0
$635$	0.541829	+	1.66758i	0.0215018	+	0.0661758i
$636$		0			0
$637$	−88.4511			−3.50456
$638$		0			0
$639$	18.4676			0.730568
$640$		0			0
$641$	−1.67959	−	5.16925i	−0.0663399	−	0.204173i	0.912392	−	0.409318i	$-0.134233\pi$
$641$	−1.67959	−	5.16925i	−0.0663399	−	0.204173i	−0.978732	+	0.205145i	$0.934233\pi$
$642$		0			0
$643$	−11.8081	−	8.57909i	−0.465666	−	0.338326i	0.330084	−	0.943952i	$-0.392923\pi$
$643$	−11.8081	−	8.57909i	−0.465666	−	0.338326i	−0.795750	+	0.605625i	$0.792923\pi$
$644$		0			0
$645$	5.91067	−	18.1912i	0.232732	−	0.716277i
$646$		0			0
$647$	9.26956	−	6.73473i	0.364424	−	0.264770i	−0.390471	−	0.920615i	$-0.627688\pi$
$647$	9.26956	−	6.73473i	0.364424	−	0.264770i	0.754895	+	0.655846i	$0.227688\pi$
$648$		0			0
$649$	−8.15258	+	22.0866i	−0.320017	+	0.866975i
$650$		0			0
$651$	−62.7030	+	45.5564i	−2.45752	+	1.78550i
$652$		0			0
$653$	−2.19049	+	6.74163i	−0.0857204	+	0.263820i	−0.984724	−	0.174120i	$-0.944292\pi$
$653$	−2.19049	+	6.74163i	−0.0857204	+	0.263820i	0.899004	+	0.437940i	$0.144292\pi$
$654$		0			0
$655$	10.2783	+	7.46764i	0.401607	+	0.291785i
$656$		0			0
$657$	−7.37637	−	22.7021i	−0.287779	−	0.885694i
$658$		0			0
$659$	10.2209			0.398150			0.199075	−	0.979984i	$-0.436206\pi$
$659$	10.2209			0.398150			0.199075	+	0.979984i	$0.436206\pi$
$660$		0			0
$661$	−15.7641			−0.613151			−0.306575	−	0.951846i	$-0.599183\pi$
$661$	−15.7641			−0.613151			−0.306575	+	0.951846i	$0.599183\pi$
$662$		0			0
$663$	14.8378	+	45.6662i	0.576254	+	1.77353i
$664$		0			0
$665$	10.3099	+	7.49055i	0.399799	+	0.290471i
$666$		0			0
$667$	−1.40191	+	4.31462i	−0.0542820	+	0.167063i
$668$		0			0
$669$	−46.4747	+	33.7659i	−1.79682	+	1.30546i
$670$		0			0
$671$	−3.48476	−	2.74816i	−0.134528	−	0.106091i
$672$		0			0
$673$	9.62034	−	6.98959i	0.370837	−	0.269429i	−0.386721	−	0.922197i	$-0.626392\pi$
$673$	9.62034	−	6.98959i	0.370837	−	0.269429i	0.757558	+	0.652768i	$0.226392\pi$
$674$		0			0
$675$	−0.193571	+	0.595751i	−0.00745056	+	0.0229305i
$676$		0			0
$677$	16.7178	+	12.1462i	0.642518	+	0.466816i	0.860714	−	0.509088i	$-0.170017\pi$
$677$	16.7178	+	12.1462i	0.642518	+	0.466816i	−0.218197	+	0.975905i	$0.570017\pi$
$678$		0			0
$679$	−9.41609	−	28.9797i	−0.361356	−	1.11214i
$680$		0			0
$681$	56.0822			2.14908
$682$		0			0
$683$	−22.8239			−0.873331			−0.436666	−	0.899624i	$-0.643841\pi$
$683$	−22.8239			−0.873331			−0.436666	+	0.899624i	$0.643841\pi$
$684$		0			0
$685$	−0.536561	−	1.65136i	−0.0205009	−	0.0630954i
$686$		0			0
$687$	38.6812	+	28.1036i	1.47578	+	1.07222i
$688$		0			0
$689$	21.4519	−	66.0222i	0.817253	−	2.51525i
$690$		0			0
$691$	33.1464	−	24.0823i	1.26095	−	0.916132i	0.262144	−	0.965029i	$-0.415570\pi$
$691$	33.1464	−	24.0823i	1.26095	−	0.916132i	0.998804	+	0.0488962i	$0.0155704\pi$
$692$		0			0
$693$	11.4656	+	40.6812i	0.435541	+	1.54535i
$694$		0			0
$695$	−5.23432	+	3.80296i	−0.198549	+	0.144254i
$696$		0			0
$697$	−3.89282	+	11.9809i	−0.147451	+	0.453808i
$698$		0			0
$699$	2.53289	+	1.84025i	0.0958028	+	0.0696048i
$700$		0			0
$701$	10.3083	+	31.7258i	0.389341	+	1.19827i	0.933282	+	0.359145i	$0.116932\pi$
$701$	10.3083	+	31.7258i	0.389341	+	1.19827i	−0.543941	+	0.839124i	$0.683068\pi$
$702$		0			0
$703$	−10.5078			−0.396309
$704$		0			0
$705$	−29.1270			−1.09699
$706$		0			0
$707$	0.392411	+	1.20772i	0.0147581	+	0.0454208i
$708$		0			0
$709$	12.9697	+	9.42305i	0.487088	+	0.353890i	0.804063	−	0.594544i	$-0.202667\pi$
$709$	12.9697	+	9.42305i	0.487088	+	0.353890i	−0.316975	+	0.948434i	$0.602667\pi$
$710$		0			0
$711$	4.64224	−	14.2873i	0.174098	−	0.535817i
$712$		0			0
$713$	−11.1263	+	8.08372i	−0.416682	+	0.302738i
$714$		0			0
$715$	20.0019	+	0.789389i	0.748027	+	0.0295215i
$716$		0			0
$717$	23.4971	−	17.0716i	0.877515	−	0.637552i
$718$		0			0
$719$	4.08192	−	12.5628i	0.152230	−	0.468515i	−0.845640	−	0.533754i	$-0.820781\pi$
$719$	4.08192	−	12.5628i	0.152230	−	0.468515i	0.997870	+	0.0652388i	$0.0207809\pi$
$720$		0			0
$721$	30.8418	+	22.4079i	1.14861	+	0.834513i
$722$		0			0
$723$	−13.5537	−	41.7140i	−0.504068	−	1.55136i
$724$		0			0
$725$	2.29348			0.0851776
$726$		0			0
$727$	21.9855			0.815395			0.407698	−	0.913117i	$-0.366332\pi$
$727$	21.9855			0.815395			0.407698	+	0.913117i	$0.366332\pi$
$728$		0			0
$729$	−6.83109	−	21.0239i	−0.253003	−	0.778665i
$730$		0			0
$731$	21.4531	+	15.5866i	0.793470	+	0.576490i
$732$		0			0
$733$	−10.4444	+	32.1447i	−0.385774	+	1.18729i	0.550143	+	0.835071i	$0.314573\pi$
$733$	−10.4444	+	32.1447i	−0.385774	+	1.18729i	−0.935917	+	0.352221i	$0.885427\pi$
$734$		0			0
$735$	−28.4020	+	20.6353i	−1.04762	+	0.761143i
$736$		0			0
$737$	23.8237	+	0.940223i	0.877558	+	0.0346335i
$738$		0			0
$739$	−11.9360	+	8.67203i	−0.439074	+	0.319006i	−0.785267	−	0.619158i	$-0.787474\pi$
$739$	−11.9360	+	8.67203i	−0.439074	+	0.319006i	0.346193	+	0.938163i	$0.387474\pi$
$740$		0			0
$741$	−12.2351	+	37.6558i	−0.449468	+	1.38332i
$742$		0			0
$743$	−19.6991	−	14.3122i	−0.722688	−	0.525064i	0.164554	−	0.986368i	$-0.447382\pi$
$743$	−19.6991	−	14.3122i	−0.722688	−	0.525064i	−0.887242	+	0.461304i	$0.847382\pi$
$744$		0			0
$745$	0.404307	+	1.24433i	0.0148127	+	0.0455887i
$746$		0			0
$747$	−22.4945			−0.823030
$748$		0			0
$749$	−30.6561			−1.12015
$750$		0			0
$751$	−11.6284	−	35.7884i	−0.424325	−	1.30594i	−0.903639	−	0.428295i	$-0.859114\pi$
$751$	−11.6284	−	35.7884i	−0.424325	−	1.30594i	0.479314	−	0.877644i	$-0.340886\pi$
$752$		0			0
$753$	51.9188	+	37.7212i	1.89203	+	1.37464i
$754$		0			0
$755$	−6.19819	+	19.0761i	−0.225575	+	0.694249i
$756$		0			0
$757$	35.5483	−	25.8273i	1.29202	−	0.938710i	0.292180	−	0.956363i	$-0.405619\pi$
$757$	35.5483	−	25.8273i	1.29202	−	0.938710i	0.999844	+	0.0176531i	$0.00561944\pi$
$758$		0			0
$759$	4.26326	+	15.1266i	0.154747	+	0.549059i
$760$		0			0
$761$	−33.3417	+	24.2242i	−1.20864	+	0.878126i	−0.995106	−	0.0988110i	$-0.968496\pi$
$761$	−33.3417	+	24.2242i	−1.20864	+	0.878126i	−0.213530	+	0.976937i	$0.568496\pi$
$762$		0			0
$763$	−4.40404	+	13.5542i	−0.159437	+	0.490697i
$764$		0			0
$765$	7.35781	+	5.34576i	0.266022	+	0.193276i
$766$		0			0
$767$	−13.2393	−	40.7462i	−0.478042	−	1.47126i
$768$		0			0
$769$	−21.4283			−0.772724			−0.386362	−	0.922347i	$-0.626268\pi$
$769$	−21.4283			−0.772724			−0.386362	+	0.922347i	$0.626268\pi$
$770$		0			0
$771$	−17.2532			−0.621358
$772$		0			0
$773$	1.79222	+	5.51590i	0.0644618	+	0.198393i	0.978100	−	0.208135i	$-0.0667393\pi$
$773$	1.79222	+	5.51590i	0.0644618	+	0.198393i	−0.913638	+	0.406528i	$0.866739\pi$
$774$		0			0
$775$	5.62481	+	4.08666i	0.202049	+	0.146797i
$776$		0			0
$777$	13.2178	−	40.6804i	0.474188	−	1.45940i
$778$		0			0
$779$	−8.40383	+	6.10574i	−0.301098	+	0.218761i
$780$		0			0
$781$	17.5622	+	13.8499i	0.628424	+	0.495589i
$782$		0			0
$783$	1.16228	−	0.844445i	0.0415365	−	0.0301780i
$784$		0			0
$785$	5.45768	−	16.7970i	0.194793	−	0.599511i
$786$		0			0
$787$	−20.3969	−	14.8192i	−0.727072	−	0.528248i	0.161564	−	0.986862i	$-0.448346\pi$
$787$	−20.3969	−	14.8192i	−0.727072	−	0.528248i	−0.888636	+	0.458614i	$0.848346\pi$
$788$		0			0
$789$	8.72538	+	26.8540i	0.310632	+	0.956027i
$790$		0			0
$791$	26.9246			0.957328
$792$		0			0
$793$	8.07614			0.286792
$794$		0			0
$795$	−8.51439	−	26.2046i	−0.301974	−	0.929382i
$796$		0			0
$797$	−14.9240	−	10.8429i	−0.528635	−	0.384075i	0.291212	−	0.956658i	$-0.405941\pi$
$797$	−14.9240	−	10.8429i	−0.528635	−	0.384075i	−0.819847	+	0.572583i	$0.805941\pi$
$798$		0			0
$799$	12.4783	−	38.4043i	0.441451	−	1.35865i
$800$		0			0
$801$	25.3039	−	18.3843i	0.894068	−	0.649578i
$802$		0			0
$803$	10.0109	−	27.1210i	0.353276	−	0.957079i
$804$		0			0
$805$	−7.44699	+	5.41056i	−0.262472	+	0.190697i
$806$		0			0
$807$	10.9554	−	33.7171i	0.385647	−	1.18690i
$808$		0			0
$809$	−4.21369	−	3.06142i	−0.148145	−	0.107634i	0.511244	−	0.859436i	$-0.329185\pi$
$809$	−4.21369	−	3.06142i	−0.148145	−	0.107634i	−0.659389	+	0.751802i	$0.729185\pi$
$810$		0			0
$811$	−2.40728	−	7.40885i	−0.0845310	−	0.260160i	0.899853	−	0.436193i	$-0.143673\pi$
$811$	−2.40728	−	7.40885i	−0.0845310	−	0.260160i	−0.984384	+	0.176033i	$0.943673\pi$
$812$		0			0
$813$	55.7767			1.95617
$814$		0			0
$815$	4.62425			0.161980
$816$		0			0
$817$	6.75696	+	20.7958i	0.236396	+	0.727552i
$818$		0			0
$819$	−62.2249	−	45.2091i	−2.17432	−	1.57973i
$820$		0			0
$821$	−2.95534	+	9.09561i	−0.103142	+	0.317439i	−0.989290	−	0.145964i	$-0.953372\pi$
$821$	−2.95534	+	9.09561i	−0.103142	+	0.317439i	0.886148	+	0.463403i	$0.153372\pi$
$822$		0			0
$823$	10.9118	−	7.92788i	0.380361	−	0.276348i	−0.381133	−	0.924520i	$-0.624466\pi$
$823$	10.9118	−	7.92788i	0.380361	−	0.276348i	0.761494	+	0.648172i	$0.224466\pi$
$824$		0			0
$825$	6.60683	−	4.41287i	0.230020	−	0.153636i
$826$		0			0
$827$	−15.2351	+	11.0689i	−0.529776	+	0.384905i	−0.820274	−	0.571971i	$-0.806179\pi$
$827$	−15.2351	+	11.0689i	−0.529776	+	0.384905i	0.290498	+	0.956876i	$0.406179\pi$
$828$		0			0
$829$	9.04366	−	27.8335i	0.314099	−	0.966698i	−0.662024	−	0.749482i	$-0.730302\pi$
$829$	9.04366	−	27.8335i	0.314099	−	0.966698i	0.976124	−	0.217216i	$-0.0696975\pi$
$830$		0			0
$831$	30.0141	+	21.8065i	1.04118	+	0.756459i
$832$		0			0
$833$	−15.0401	−	46.2887i	−0.521109	−	1.60381i
$834$		0			0
$835$	22.4278			0.776146
$836$		0			0
$837$	4.35521			0.150538
$838$		0			0
$839$	3.85178	+	11.8546i	0.132978	+	0.409265i	0.995270	−	0.0971469i	$-0.0309717\pi$
$839$	3.85178	+	11.8546i	0.132978	+	0.409265i	−0.862292	+	0.506412i	$0.830972\pi$
$840$		0			0
$841$	19.2060	+	13.9540i	0.662277	+	0.481173i
$842$		0			0
$843$	−11.1200	+	34.2237i	−0.382992	+	1.17873i
$844$		0			0
$845$	−18.9529	+	13.7701i	−0.651998	+	0.473704i
$846$		0			0
$847$	−19.6056	+	47.2853i	−0.673658	+	1.62474i
$848$		0			0
$849$	28.0682	−	20.3927i	0.963299	−	0.699877i
$850$		0			0
$851$	2.34543	−	7.21849i	0.0804003	−	0.247447i
$852$		0			0
$853$	−27.7985	−	20.1968i	−0.951802	−	0.691524i	−0.000569334	−	1.00000i	$-0.500181\pi$
$853$	−27.7985	−	20.1968i	−0.951802	−	0.691524i	−0.951232	+	0.308475i	$0.900181\pi$
$854$		0			0
$855$	2.31745	+	7.13238i	0.0792551	+	0.243922i
$856$		0			0
$857$	−14.9439			−0.510474			−0.255237	−	0.966879i	$-0.582153\pi$
$857$	−14.9439			−0.510474			−0.255237	+	0.966879i	$0.582153\pi$
$858$		0			0
$859$	26.2500			0.895640			0.447820	−	0.894124i	$-0.352201\pi$
$859$	26.2500			0.895640			0.447820	+	0.894124i	$0.352201\pi$
$860$		0			0
$861$	−13.0668	−	40.2154i	−0.445314	−	1.37054i
$862$		0			0
$863$	−16.2350	−	11.7954i	−0.552645	−	0.401520i	0.276115	−	0.961125i	$-0.410953\pi$
$863$	−16.2350	−	11.7954i	−0.552645	−	0.401520i	−0.828760	+	0.559604i	$0.810953\pi$
$864$		0			0
$865$	−2.19724	+	6.76241i	−0.0747084	+	0.229929i
$866$		0			0
$867$	11.5710	−	8.40684i	0.392972	−	0.285511i
$868$		0			0
$869$	15.1295	−	10.1054i	0.513233	−	0.342801i
$870$		0			0
$871$	−35.1011	+	25.5024i	−1.18936	+	0.864117i
$872$		0			0
$873$	5.54119	−	17.0540i	0.187541	−	0.577192i
$874$		0			0
$875$	3.76477	+	2.73527i	0.127273	+	0.0924689i
$876$		0			0
$877$	−11.2143	−	34.5141i	−0.378680	−	1.16546i	−0.940962	−	0.338513i	$-0.890076\pi$
$877$	−11.2143	−	34.5141i	−0.378680	−	1.16546i	0.562281	−	0.826946i	$-0.309924\pi$
$878$		0			0
$879$	−39.9484			−1.34743
$880$		0			0
$881$	26.3513			0.887796			0.443898	−	0.896077i	$-0.353595\pi$
$881$	26.3513			0.887796			0.443898	+	0.896077i	$0.353595\pi$
$882$		0			0
$883$	16.6885	+	51.3619i	0.561612	+	1.72847i	0.677808	+	0.735239i	$0.262930\pi$
$883$	16.6885	+	51.3619i	0.561612	+	1.72847i	−0.116196	+	0.993226i	$0.537070\pi$
$884$		0			0
$885$	−13.7571	−	9.99511i	−0.462439	−	0.335982i
$886$		0			0
$887$	−3.95375	+	12.1684i	−0.132754	+	0.408575i	−0.995234	−	0.0975164i	$-0.968910\pi$
$887$	−3.95375	+	12.1684i	−0.132754	+	0.408575i	0.862480	+	0.506091i	$0.168910\pi$
$888$		0			0
$889$	6.60113	−	4.79600i	0.221395	−	0.160853i
$890$		0			0
$891$	11.1588	−	30.2309i	0.373834	−	1.01277i
$892$		0			0
$893$	26.9382	−	19.5717i	0.901452	−	0.654943i
$894$		0			0
$895$	1.54508	−	4.75528i	0.0516465	−	0.158952i
$896$		0			0
$897$	−23.1372	−	16.8102i	−0.772529	−	0.561275i
$898$		0			0
$899$	−4.92750	−	15.1653i	−0.164341	−	0.505791i
$900$		0			0
$901$	38.1987			1.27258
$902$		0			0
$903$	−89.0093			−2.96204
$904$		0			0
$905$	5.24837	+	16.1528i	0.174462	+	0.536938i
$906$		0			0
$907$	−41.2677	−	29.9827i	−1.37027	−	0.995559i	−0.997716	−	0.0675488i	$-0.978482\pi$
$907$	−41.2677	−	29.9827i	−1.37027	−	0.995559i	−0.372554	−	0.928011i	$-0.621518\pi$
$908$		0			0
$909$	−0.230927	+	0.710719i	−0.00765935	+	0.0235731i
$910$		0			0
$911$	1.25100	−	0.908907i	0.0414476	−	0.0301134i	−0.566869	−	0.823808i	$-0.691845\pi$
$911$	1.25100	−	0.908907i	0.0414476	−	0.0301134i	0.608316	+	0.793695i	$0.291845\pi$
$912$		0			0
$913$	−21.3916	−	16.8699i	−0.707959	−	0.558311i
$914$		0			0
$915$	2.59328	−	1.88413i	0.0857311	−	0.0622873i
$916$		0			0
$917$	18.2696	−	56.2279i	0.603314	−	1.85681i
$918$		0			0
$919$	20.4935	+	14.8894i	0.676018	+	0.491156i	0.872034	−	0.489445i	$-0.162800\pi$
$919$	20.4935	+	14.8894i	0.676018	+	0.491156i	−0.196016	+	0.980601i	$0.562800\pi$
$920$		0			0
$921$	0.397943	+	1.22474i	0.0131127	+	0.0403567i
$922$		0			0
$923$	−40.7014			−1.33970
$924$		0			0
$925$	−3.83705			−0.126162
$926$		0			0
$927$	6.93262	+	21.3364i	0.227697	+	0.700780i
$928$		0			0
$929$	44.3317	+	32.2089i	1.45448	+	1.05674i	0.984760	+	0.173921i	$0.0556436\pi$
$929$	44.3317	+	32.2089i	1.45448	+	1.05674i	0.469716	+	0.882818i	$0.344356\pi$
$930$		0			0
$931$	12.4019	−	38.1691i	0.406456	−	1.25094i
$932$		0			0
$933$	−24.2148	+	17.5931i	−0.792756	+	0.575971i
$934$		0			0
$935$	2.98798	+	10.6017i	0.0977174	+	0.346712i
$936$		0			0
$937$	26.1416	−	18.9930i	0.854008	−	0.620473i	−0.0722402	−	0.997387i	$-0.523015\pi$
$937$	26.1416	−	18.9930i	0.854008	−	0.620473i	0.926248	+	0.376914i	$0.123015\pi$
$938$		0			0
$939$	13.9443	−	42.9161i	0.455055	−	1.40051i
$940$		0			0
$941$	−15.8392	−	11.5078i	−0.516342	−	0.375144i	0.298882	−	0.954290i	$-0.403386\pi$
$941$	−15.8392	−	11.5078i	−0.516342	−	0.375144i	−0.815224	+	0.579146i	$0.803386\pi$
$942$		0			0
$943$	−2.31862	−	7.13598i	−0.0755047	−	0.232380i
$944$		0			0
$945$	2.91501			0.0948252
$946$		0			0
$947$	−22.1674			−0.720345			−0.360172	−	0.932886i	$-0.617282\pi$
$947$	−22.1674			−0.720345			−0.360172	+	0.932886i	$0.617282\pi$
$948$		0			0
$949$	16.2570	+	50.0339i	0.527724	+	1.62417i
$950$		0			0
$951$	13.6841	+	9.94211i	0.443739	+	0.322395i
$952$		0			0
$953$	−16.2016	+	49.8633i	−0.524820	+	1.61523i	0.239852	+	0.970810i	$0.422901\pi$
$953$	−16.2016	+	49.8633i	−0.524820	+	1.61523i	−0.764672	+	0.644420i	$0.777099\pi$
$954$		0			0
$955$	−3.71375	+	2.69820i	−0.120174	+	0.0873116i
$956$		0			0
$957$	−18.2076	−	0.718577i	−0.588567	−	0.0232283i
$958$		0			0
$959$	−6.53695	+	4.74937i	−0.211089	+	0.153365i
$960$		0			0
$961$	5.35814	−	16.4907i	0.172843	−	0.531957i
$962$		0			0
$963$	−14.5951	−	10.6040i	−0.470321	−	0.341708i
$964$		0			0
$965$	−2.70510	−	8.32543i	−0.0870801	−	0.268005i
$966$		0			0
$967$	9.72125			0.312614			0.156307	−	0.987709i	$-0.450041\pi$
$967$	9.72125			0.312614			0.156307	+	0.987709i	$0.450041\pi$
$968$		0			0
$969$	−21.7866			−0.699888
$970$		0			0
$971$	−14.6007	−	44.9362i	−0.468557	−	1.44207i	−0.854453	−	0.519529i	$-0.826108\pi$
$971$	−14.6007	−	44.9362i	−0.468557	−	1.44207i	0.385896	−	0.922542i	$-0.373892\pi$
$972$		0			0
$973$	24.3580	+	17.6971i	0.780881	+	0.567343i
$974$		0			0
$975$	−4.46780	+	13.7505i	−0.143084	+	0.440368i
$976$		0			0
$977$	33.8619	−	24.6021i	1.08334	−	0.787092i	0.105077	−	0.994464i	$-0.466491\pi$
$977$	33.8619	−	24.6021i	1.08334	−	0.787092i	0.978262	+	0.207372i	$0.0664911\pi$
$978$		0			0
$979$	37.8507	+	1.49381i	1.20971	+	0.0477423i
$980$		0			0
$981$	−6.78515	+	4.92970i	−0.216633	+	0.157393i
$982$		0			0
$983$	−11.1216	+	34.2287i	−0.354723	+	1.09173i	0.601447	+	0.798913i	$0.294591\pi$
$983$	−11.1216	+	34.2287i	−0.354723	+	1.09173i	−0.956170	+	0.292813i	$0.905409\pi$
$984$		0			0
$985$	−10.8822	−	7.90636i	−0.346735	−	0.251918i
$986$		0			0
$987$	41.8851	+	128.909i	1.33322	+	4.10322i
$988$		0			0
$989$	−15.7942			−0.502226
$990$		0			0
$991$	0.548830			0.0174342			0.00871709	−	0.999962i	$-0.497225\pi$
$991$	0.548830			0.0174342			0.00871709	+	0.999962i	$0.497225\pi$
$992$		0			0
$993$	5.79941	+	17.8488i	0.184039	+	0.566413i
$994$		0			0
$995$	−3.68641	−	2.67833i	−0.116867	−	0.0849088i
$996$		0			0
$997$	−2.85845	+	8.79740i	−0.0905279	+	0.278616i	−0.986062	−	0.166376i	$-0.946794\pi$
$997$	−2.85845	+	8.79740i	−0.0905279	+	0.278616i	0.895534	+	0.444992i	$0.146794\pi$
$998$		0			0
$999$	−1.94453	+	1.41278i	−0.0615221	+	0.0446984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.m.b.201.2	yes	8
3.2	odd	2		1980.2.z.d.1081.1		8
4.3	odd	2		880.2.bo.c.641.1		8
5.2	odd	4		1100.2.cb.b.949.4		16
5.3	odd	4		1100.2.cb.b.949.1		16
5.4	even	2		1100.2.n.b.201.1		8
11.2	odd	10		2420.2.a.l.1.4		4
11.4	even	5	inner	220.2.m.b.81.2	✓	8
11.9	even	5		2420.2.a.k.1.4		4
33.26	odd	10		1980.2.z.d.1621.1		8
44.15	odd	10		880.2.bo.c.81.1		8
44.31	odd	10		9680.2.a.cp.1.1		4
44.35	even	10		9680.2.a.co.1.1		4
55.4	even	10		1100.2.n.b.301.1		8
55.37	odd	20		1100.2.cb.b.1049.1		16
55.48	odd	20		1100.2.cb.b.1049.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.b.81.2	✓	8	11.4	even	5	inner
220.2.m.b.201.2	yes	8	1.1	even	1	trivial
880.2.bo.c.81.1		8	44.15	odd	10
880.2.bo.c.641.1		8	4.3	odd	2
1100.2.n.b.201.1		8	5.4	even	2
1100.2.n.b.301.1		8	55.4	even	10
1100.2.cb.b.949.1		16	5.3	odd	4
1100.2.cb.b.949.4		16	5.2	odd	4
1100.2.cb.b.1049.1		16	55.37	odd	20
1100.2.cb.b.1049.4		16	55.48	odd	20
1980.2.z.d.1081.1		8	3.2	odd	2
1980.2.z.d.1621.1		8	33.26	odd	10
2420.2.a.k.1.4		4	11.9	even	5
2420.2.a.l.1.4		4	11.2	odd	10
9680.2.a.co.1.1		4	44.35	even	10
9680.2.a.cp.1.1		4	44.31	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.740256 + 2.27827i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.43801 + 4.42575i) q^{7} +(-2.21550 + 1.60965i) q^{9} +O(q^{10})\)	\(q+(0.740256 + 2.27827i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.43801 + 4.42575i) q^{7} +(-2.21550 + 1.60965i) q^{9} +(-3.31404 - 0.130791i) q^{11} +(4.88281 - 3.54757i) q^{13} +(0.740256 - 2.27827i) q^{15} +(2.68680 + 1.95207i) q^{17} +(0.846245 + 2.60448i) q^{19} -11.1476 q^{21} -1.97807 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.506776 + 0.368194i) q^{27} +(0.708723 - 2.18123i) q^{29} +(5.62481 - 4.08666i) q^{31} +(-2.15526 - 7.64712i) q^{33} +(3.76477 - 2.73527i) q^{35} +(-1.18571 + 3.64925i) q^{37} +(11.6969 + 8.49826i) q^{39} +(1.17216 + 3.60755i) q^{41} +7.98463 q^{43} +2.73851 q^{45} +(-3.75733 - 11.5639i) q^{47} +(-11.8563 - 8.61411i) q^{49} +(-2.45844 + 7.56629i) q^{51} +(9.30528 - 6.76068i) q^{53} +(2.60424 + 2.05376i) q^{55} +(-5.30727 + 3.85596i) q^{57} +(2.19357 - 6.75112i) q^{59} +(1.08255 + 0.786521i) q^{61} +(-3.93801 - 12.1200i) q^{63} -6.03548 q^{65} -7.18872 q^{67} +(-1.46428 - 4.50659i) q^{69} +(-5.45576 - 3.96384i) q^{71} +(-2.69357 + 8.28996i) q^{73} +(-1.93801 + 1.40805i) q^{75} +(5.34450 - 14.4791i) q^{77} +(-4.43801 + 3.22441i) q^{79} +(-3.00244 + 9.24056i) q^{81} +(6.64538 + 4.82815i) q^{83} +(-1.02626 - 3.15852i) q^{85} +5.49406 q^{87} -11.4213 q^{89} +(8.67911 + 26.7116i) q^{91} +(13.4743 + 9.78968i) q^{93} +(0.846245 - 2.60448i) q^{95} +(-5.29742 + 3.84880i) q^{97} +(7.55279 - 5.04470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} - 2 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 - 2 * q^5 - q^7 + 3 * q^9	\( 8 q + 5 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 5 q^{11} + 4 q^{13} + 5 q^{15} + 9 q^{17} - 7 q^{19} - 28 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - q^{29} + 22 q^{31} + q^{33} + 4 q^{35} + 4 q^{37} + 27 q^{39} + 24 q^{41} - 22 q^{43} + 8 q^{45} - 6 q^{47} - 27 q^{49} - 47 q^{51} - q^{53} - 5 q^{55} - 25 q^{57} - 9 q^{59} + 22 q^{61} - 21 q^{63} - 26 q^{65} - 2 q^{67} + 11 q^{69} - 22 q^{71} + 5 q^{73} - 5 q^{75} + 16 q^{77} - 25 q^{79} - 28 q^{81} + 33 q^{83} + 4 q^{85} + 14 q^{87} + 8 q^{89} + 14 q^{91} + 31 q^{93} - 7 q^{95} + 20 q^{97} + 60 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 - 2 * q^5 - q^7 + 3 * q^9 + 5 * q^11 + 4 * q^13 + 5 * q^15 + 9 * q^17 - 7 * q^19 - 28 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - q^29 + 22 * q^31 + q^33 + 4 * q^35 + 4 * q^37 + 27 * q^39 + 24 * q^41 - 22 * q^43 + 8 * q^45 - 6 * q^47 - 27 * q^49 - 47 * q^51 - q^53 - 5 * q^55 - 25 * q^57 - 9 * q^59 + 22 * q^61 - 21 * q^63 - 26 * q^65 - 2 * q^67 + 11 * q^69 - 22 * q^71 + 5 * q^73 - 5 * q^75 + 16 * q^77 - 25 * q^79 - 28 * q^81 + 33 * q^83 + 4 * q^85 + 14 * q^87 + 8 * q^89 + 14 * q^91 + 31 * q^93 - 7 * q^95 + 20 * q^97 + 60 * q^99

Introduction

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