LMFDB - Embedded newform 180.2.r.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(49,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("180.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 10x^{8} - 6x^{6} + 90x^{4} - 324x^{2} + 729 $ x^12 - 4x^10 + 10x^8 - 6x^6 + 90x^4 - 324*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$0.690466 + 1.58848i$ of defining polynomial
Character	$\chi$	$=$	180.49
Dual form			180.2.r.a.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690466 + 1.58848i) q^{3} +(1.99531 + 1.00932i) q^{5} +(-1.11574 + 0.644175i) q^{7} +(-2.04651 + 2.19358i) q^{9} +O(q^{10})$	\(q+(0.690466 + 1.58848i) q^{3} +(1.99531 + 1.00932i) q^{5} +(-1.11574 + 0.644175i) q^{7} +(-2.04651 + 2.19358i) q^{9} +(-2.54651 - 4.41069i) q^{11} +(3.09128 + 1.78475i) q^{13} +(-0.225579 + 3.86641i) q^{15} +0.895796i q^{17} +5.34015 q^{19} +(-1.79364 - 1.32755i) q^{21} +(-4.38690 - 2.53278i) q^{23} +(2.96256 + 4.02781i) q^{25} +(-4.89749 - 1.73625i) q^{27} +(-1.50000 - 2.59808i) q^{29} +(3.29939 - 5.71471i) q^{31} +(5.24800 - 7.09051i) q^{33} +(-2.87644 + 0.159193i) q^{35} -7.24970i q^{37} +(-0.700613 + 6.14274i) q^{39} +(3.92295 - 6.79475i) q^{41} +(-9.46557 + 5.46495i) q^{43} +(-6.29745 + 2.31130i) q^{45} +(2.57145 - 1.48463i) q^{47} +(-2.67008 + 4.62471i) q^{49} +(-1.42295 + 0.618517i) q^{51} -4.78369i q^{53} +(-0.629311 - 11.3710i) q^{55} +(3.68719 + 8.48271i) q^{57} +(-2.87644 + 4.98213i) q^{59} +(-2.17008 - 3.75868i) q^{61} +(0.870338 - 3.76578i) q^{63} +(4.36670 + 6.68123i) q^{65} +(7.39417 + 4.26903i) q^{67} +(0.994253 - 8.71728i) q^{69} -5.34015 q^{71} +9.34600i q^{73} +(-4.35253 + 7.48702i) q^{75} +(5.68251 + 3.28080i) q^{77} +(-0.370689 - 0.642053i) q^{79} +(-0.623563 - 8.97837i) q^{81} +(-7.97824 + 4.60624i) q^{83} +(-0.904142 + 1.78739i) q^{85} +(3.09128 - 4.17660i) q^{87} +9.24713 q^{89} -4.59877 q^{91} +(11.3558 + 1.29519i) q^{93} +(10.6553 + 5.38991i) q^{95} +(-2.99543 + 1.72941i) q^{97} +(14.8867 + 3.44057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{5} + 8 q^{9}+O(q^{10}) $ 12 * q + q^5 + 8 * q^9	$ 12 q + q^{5} + 8 q^{9} + 2 q^{11} - 5 q^{15} + 10 q^{21} - 3 q^{25} - 18 q^{29} + 6 q^{31} - 34 q^{35} - 42 q^{39} + 14 q^{41} - 31 q^{45} + 16 q^{51} - 6 q^{55} - 34 q^{59} + 6 q^{61} + 15 q^{65} + 14 q^{69} + 41 q^{75} - 6 q^{79} - 8 q^{81} - 12 q^{85} + 112 q^{89} + 12 q^{91} + 36 q^{95} + 82 q^{99}+O(q^{100}) $ 12 * q + q^5 + 8 * q^9 + 2 * q^11 - 5 * q^15 + 10 * q^21 - 3 * q^25 - 18 * q^29 + 6 * q^31 - 34 * q^35 - 42 * q^39 + 14 * q^41 - 31 * q^45 + 16 * q^51 - 6 * q^55 - 34 * q^59 + 6 * q^61 + 15 * q^65 + 14 * q^69 + 41 * q^75 - 6 * q^79 - 8 * q^81 - 12 * q^85 + 112 * q^89 + 12 * q^91 + 36 * q^95 + 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.690466	+	1.58848i	0.398641	+	0.917107i
$3$	0.690466	+	1.58848i	0.398641	+	0.917107i
$4$		0			0
$5$	1.99531	+	1.00932i	0.892332	+	0.451380i
$5$	1.99531	+	1.00932i	0.892332	+	0.451380i
$6$		0			0
$7$	−1.11574	+	0.644175i	−0.421712	+	0.243475i	−0.695809	−	0.718227i	$-0.744954\pi$
$7$	−1.11574	+	0.644175i	−0.421712	+	0.243475i	0.274098	+	0.961702i	$0.411621\pi$
$8$		0			0
$9$	−2.04651	+	2.19358i	−0.682171	+	0.731192i
$10$		0			0
$11$	−2.54651	−	4.41069i	−0.767803	−	1.32987i	−0.938752	−	0.344594i	$-0.888017\pi$
$11$	−2.54651	−	4.41069i	−0.767803	−	1.32987i	0.170949	−	0.985280i	$-0.445317\pi$
$12$		0			0
$13$	3.09128	+	1.78475i	0.857368	+	0.495002i	0.863130	−	0.504982i	$-0.168501\pi$
$13$	3.09128	+	1.78475i	0.857368	+	0.495002i	−0.00576215	+	0.999983i	$0.501834\pi$
$14$		0			0
$15$	−0.225579	+	3.86641i	−0.0582443	+	0.998302i
$16$		0			0
$17$			0.895796i			0.217262i	0.994082	+	0.108631i	$0.0346468\pi$
$17$			0.895796i			0.217262i	−0.994082	+	0.108631i	$0.965353\pi$
$18$		0			0
$19$	5.34015			1.22512			0.612558	−	0.790426i	$-0.290141\pi$
$19$	5.34015			1.22512			0.612558	+	0.790426i	$0.290141\pi$
$20$		0			0
$21$	−1.79364	−	1.32755i	−0.391404	−	0.289696i
$22$		0			0
$23$	−4.38690	−	2.53278i	−0.914732	−	0.528121i	−0.0327812	−	0.999463i	$-0.510436\pi$
$23$	−4.38690	−	2.53278i	−0.914732	−	0.528121i	−0.881951	+	0.471342i	$0.843770\pi$
$24$		0			0
$25$	2.96256	+	4.02781i	0.592512	+	0.805562i
$26$		0			0
$27$	−4.89749	−	1.73625i	−0.942523	−	0.334141i
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	3.29939	−	5.71471i	0.592587	−	1.02639i	−0.401295	−	0.915949i	$-0.631440\pi$
$31$	3.29939	−	5.71471i	0.592587	−	1.02639i	0.993882	−	0.110443i	$-0.0352269\pi$
$32$		0			0
$33$	5.24800	−	7.09051i	0.913559	−	1.23430i
$34$		0			0
$35$	−2.87644	+	0.159193i	−0.486207	+	0.0269085i
$36$		0			0
$37$		−	7.24970i		−	1.19184i	−0.803043	−	0.595922i	$-0.796787\pi$
$37$		−	7.24970i		−	1.19184i	0.803043	−	0.595922i	$-0.203213\pi$
$38$		0			0
$39$	−0.700613	+	6.14274i	−0.112188	+	0.983626i
$40$		0			0
$41$	3.92295	−	6.79475i	0.612662	−	1.06116i	−0.378128	−	0.925753i	$-0.623432\pi$
$41$	3.92295	−	6.79475i	0.612662	−	1.06116i	0.990790	−	0.135408i	$-0.0432346\pi$
$42$		0			0
$43$	−9.46557	+	5.46495i	−1.44349	+	0.833397i	−0.998080	−	0.0619325i	$-0.980274\pi$
$43$	−9.46557	+	5.46495i	−1.44349	+	0.833397i	−0.445405	+	0.895329i	$0.646940\pi$
$44$		0			0
$45$	−6.29745	+	2.31130i	−0.938769	+	0.344548i
$46$		0			0
$47$	2.57145	−	1.48463i	0.375085	−	0.216555i	−0.300593	−	0.953753i	$-0.597185\pi$
$47$	2.57145	−	1.48463i	0.375085	−	0.216555i	0.675677	+	0.737197i	$0.263851\pi$
$48$		0			0
$49$	−2.67008	+	4.62471i	−0.381440	+	0.660673i
$50$		0			0
$51$	−1.42295	+	0.618517i	−0.199253	+	0.0866096i
$52$		0			0
$53$		−	4.78369i		−	0.657090i	−0.944488	−	0.328545i	$-0.893442\pi$
$53$		−	4.78369i		−	0.657090i	0.944488	−	0.328545i	$-0.106558\pi$
$54$		0			0
$55$	−0.629311	−	11.3710i	−0.0848562	−	1.53326i
$56$		0			0
$57$	3.68719	+	8.48271i	0.488381	+	1.12356i
$58$		0			0
$59$	−2.87644	+	4.98213i	−0.374480	+	0.648619i	−0.990249	−	0.139308i	$-0.955512\pi$
$59$	−2.87644	+	4.98213i	−0.374480	+	0.648619i	0.615769	+	0.787927i	$0.288845\pi$
$60$		0			0
$61$	−2.17008	−	3.75868i	−0.277850	−	0.481250i	0.693000	−	0.720937i	$-0.256288\pi$
$61$	−2.17008	−	3.75868i	−0.277850	−	0.481250i	−0.970850	+	0.239687i	$0.922955\pi$
$62$		0			0
$63$	0.870338	−	3.76578i	0.109652	−	0.474444i
$64$		0			0
$65$	4.36670	+	6.68123i	0.541623	+	0.828704i
$66$		0			0
$67$	7.39417	+	4.26903i	0.903342	+	0.521544i	0.878283	−	0.478141i	$-0.158689\pi$
$67$	7.39417	+	4.26903i	0.903342	+	0.521544i	0.0250587	+	0.999686i	$0.492023\pi$
$68$		0			0
$69$	0.994253	−	8.71728i	0.119694	−	1.04944i
$70$		0			0
$71$	−5.34015			−0.633760			−0.316880	−	0.948466i	$-0.602635\pi$
$71$	−5.34015			−0.633760			−0.316880	+	0.948466i	$0.602635\pi$
$72$		0			0
$73$			9.34600i			1.09387i	0.837176	+	0.546933i	$0.184205\pi$
$73$			9.34600i			1.09387i	−0.837176	+	0.546933i	$0.815795\pi$
$74$		0			0
$75$	−4.35253	+	7.48702i	−0.502587	+	0.864527i
$76$		0			0
$77$	5.68251	+	3.28080i	0.647583	+	0.373882i
$78$		0			0
$79$	−0.370689	−	0.642053i	−0.0417058	−	0.0722366i	0.844419	−	0.535683i	$-0.179946\pi$
$79$	−0.370689	−	0.642053i	−0.0417058	−	0.0722366i	−0.886125	+	0.463447i	$0.846613\pi$
$80$		0			0
$81$	−0.623563	−	8.97837i	−0.0692848	−	0.997597i
$82$		0			0
$83$	−7.97824	+	4.60624i	−0.875725	+	0.505600i	−0.869247	−	0.494379i	$-0.835396\pi$
$83$	−7.97824	+	4.60624i	−0.875725	+	0.505600i	−0.00647856	+	0.999979i	$0.502062\pi$
$84$		0			0
$85$	−0.904142	+	1.78739i	−0.0980680	+	0.193870i
$86$		0			0
$87$	3.09128	−	4.17660i	0.331420	−	0.447778i
$88$		0			0
$89$	9.24713			0.980193			0.490097	−	0.871668i	$-0.336961\pi$
$89$	9.24713			0.980193			0.490097	+	0.871668i	$0.336961\pi$
$90$		0			0
$91$	−4.59877			−0.482083
$92$		0			0
$93$	11.3558	+	1.29519i	1.17754	+	0.134305i
$94$		0			0
$95$	10.6553	+	5.38991i	1.09321	+	0.552993i
$96$		0			0
$97$	−2.99543	+	1.72941i	−0.304139	+	0.175595i	−0.644301	−	0.764772i	$-0.722852\pi$
$97$	−2.99543	+	1.72941i	−0.304139	+	0.175595i	0.340162	+	0.940367i	$0.389518\pi$
$98$		0			0
$99$	14.8867	+	3.44057i	1.49617	+	0.345790i
$100$		0			0
$101$	8.21659	+	14.2316i	0.817581	+	1.41609i	0.907459	+	0.420140i	$0.138019\pi$
$101$	8.21659	+	14.2316i	0.817581	+	1.41609i	−0.0898782	+	0.995953i	$0.528648\pi$
$102$		0			0
$103$	13.7368	+	7.93096i	1.35353	+	0.781461i	0.988742	−	0.149630i	$-0.0478082\pi$
$103$	13.7368	+	7.93096i	1.35353	+	0.781461i	0.364788	+	0.931091i	$0.381142\pi$
$104$		0			0
$105$	−2.23896	−	4.45923i	−0.218500	−	0.435177i
$106$		0			0
$107$			9.53086i			0.921383i	0.887560	+	0.460691i	$0.152399\pi$
$107$			9.53086i			0.921383i	−0.887560	+	0.460691i	$0.847601\pi$
$108$		0			0
$109$	−16.2791			−1.55925			−0.779627	−	0.626245i	$-0.784591\pi$
$109$	−16.2791			−1.55925			−0.779627	+	0.626245i	$0.784591\pi$
$110$		0			0
$111$	11.5160	−	5.00567i	1.09305	−	0.475117i
$112$		0			0
$113$	−15.7440	−	9.08980i	−1.48107	−	0.855096i	−0.481300	−	0.876556i	$-0.659835\pi$
$113$	−15.7440	−	9.08980i	−1.48107	−	0.855096i	−0.999770	+	0.0214594i	$0.993169\pi$
$114$		0			0
$115$	−6.19687	−	9.48146i	−0.577861	−	0.884151i
$116$		0			0
$117$	−10.2413	+	3.12845i	−0.946813	+	0.289225i
$118$		0			0
$119$	−0.577049	−	0.999479i	−0.0528980	−	0.0916221i
$120$		0			0
$121$	−7.46946	+	12.9375i	−0.679042	+	1.17614i
$122$		0			0
$123$	13.5020	+	1.53997i	1.21743	+	0.138855i
$124$		0			0
$125$	1.84590	+	11.0269i	0.165102	+	0.986276i
$126$		0			0
$127$		−	11.9969i		−	1.06455i	−0.846571	−	0.532275i	$-0.821337\pi$
$127$		−	11.9969i		−	1.06455i	0.846571	−	0.532275i	$-0.178663\pi$
$128$		0			0
$129$	−15.2166	−	11.2625i	−1.33975	−	0.991605i
$130$		0			0
$131$	−4.96946	+	8.60736i	−0.434184	+	0.752029i	−0.997229	−	0.0743976i	$-0.976297\pi$
$131$	−4.96946	+	8.60736i	−0.434184	+	0.752029i	0.563045	+	0.826427i	$0.309630\pi$
$132$		0			0
$133$	−5.95824	+	3.43999i	−0.516645	+	0.298285i
$134$		0			0
$135$	−8.01961	−	8.40748i	−0.690219	−	0.723601i
$136$		0			0
$137$	4.90673	−	2.83290i	0.419210	−	0.242031i	−0.275529	−	0.961293i	$-0.588853\pi$
$137$	4.90673	−	2.83290i	0.419210	−	0.242031i	0.694739	+	0.719261i	$0.255520\pi$
$138$		0			0
$139$	3.96946	−	6.87531i	0.336686	−	0.583157i	−0.647122	−	0.762387i	$-0.724027\pi$
$139$	3.96946	−	6.87531i	0.336686	−	0.583157i	0.983807	+	0.179230i	$0.0573607\pi$
$140$		0			0
$141$	4.13379	+	3.05960i	0.348128	+	0.257665i
$142$		0			0
$143$		−	18.1796i		−	1.52025i
$144$		0			0
$145$	−0.370689	−	6.69795i	−0.0307841	−	0.556235i
$146$		0			0
$147$	−9.18984	−	1.04815i	−0.757965	−	0.0864500i
$148$		0			0
$149$	−7.41720	+	12.8470i	−0.607641	+	1.05247i	0.383987	+	0.923338i	$0.374551\pi$
$149$	−7.41720	+	12.8470i	−0.607641	+	1.05247i	−0.991628	+	0.129127i	$0.958783\pi$
$150$		0			0
$151$	0.299387	+	0.518554i	0.0243638	+	0.0421993i	0.877950	−	0.478752i	$-0.158911\pi$
$151$	0.299387	+	0.518554i	0.0243638	+	0.0421993i	−0.853586	+	0.520951i	$0.825577\pi$
$152$		0			0
$153$	−1.96500	−	1.83326i	−0.158861	−	0.148210i
$154$		0			0
$155$	12.3513	−	8.07251i	0.992077	−	0.648400i
$156$		0			0
$157$	−15.5523	−	8.97911i	−1.24121	−	0.716611i	−0.271867	−	0.962335i	$-0.587641\pi$
$157$	−15.5523	−	8.97911i	−1.24121	−	0.716611i	−0.969340	+	0.245724i	$0.920974\pi$
$158$		0			0
$159$	7.59877	−	3.30297i	0.602622	−	0.261943i
$160$		0			0
$161$	6.52621			0.514337
$162$		0			0
$163$			4.67300i			0.366018i	0.983111	+	0.183009i	$0.0585837\pi$
$163$			4.67300i			0.366018i	−0.983111	+	0.183009i	$0.941416\pi$
$164$		0			0
$165$	17.6280	−	8.85090i	1.37234	−	0.689042i
$166$		0			0
$167$	−5.16268	−	2.98068i	−0.399500	−	0.230652i	0.286768	−	0.958000i	$-0.407419\pi$
$167$	−5.16268	−	2.98068i	−0.399500	−	0.230652i	−0.686268	+	0.727348i	$0.740752\pi$
$168$		0			0
$169$	−0.129311	−	0.223972i	−0.00994696	−	0.0172286i
$170$		0			0
$171$	−10.9287	+	11.7140i	−0.835738	+	0.895795i
$172$		0			0
$173$	−8.49807	+	4.90636i	−0.646096	+	0.373024i	−0.786959	−	0.617005i	$-0.788346\pi$
$173$	−8.49807	+	4.90636i	−0.646096	+	0.373024i	0.140863	+	0.990029i	$0.455012\pi$
$174$		0			0
$175$	−5.90007	−	2.58560i	−0.446003	−	0.195453i
$176$		0			0
$177$	−9.90008	−	1.12916i	−0.744136	−	0.0848727i
$178$		0			0
$179$	16.3516			1.22218			0.611090	−	0.791561i	$-0.290731\pi$
$179$	16.3516			1.22218			0.611090	+	0.791561i	$0.290731\pi$
$180$		0			0
$181$	2.93893			0.218449			0.109224	−	0.994017i	$-0.465163\pi$
$181$	2.93893			0.218449			0.109224	+	0.994017i	$0.465163\pi$
$182$		0			0
$183$	4.47222	−	6.04236i	0.330596	−	0.446664i
$184$		0			0
$185$	7.31725	−	14.4654i	0.537975	−	1.06352i
$186$		0			0
$187$	3.95108	−	2.28116i	0.288932	−	0.166815i
$188$		0			0
$189$	6.58280	−	1.21763i	0.478828	−	0.0885699i
$190$		0			0
$191$	2.29939	+	3.98266i	0.166378	+	0.288175i	0.937144	−	0.348944i	$-0.113460\pi$
$191$	2.29939	+	3.98266i	0.166378	+	0.288175i	−0.770766	+	0.637118i	$0.780126\pi$
$192$		0			0
$193$	−1.37169	−	0.791947i	−0.0987366	−	0.0570056i	0.449819	−	0.893120i	$-0.351489\pi$
$193$	−1.37169	−	0.791947i	−0.0987366	−	0.0570056i	−0.548555	+	0.836114i	$0.684822\pi$
$194$		0			0
$195$	−7.59792	+	11.5496i	−0.544098	+	0.827081i
$196$		0			0
$197$		−	13.0775i		−	0.931735i	−0.884855	−	0.465867i	$-0.845742\pi$
$197$		−	13.0775i		−	0.931735i	0.884855	−	0.465867i	$-0.154258\pi$
$198$		0			0
$199$	5.34015			0.378553			0.189277	−	0.981924i	$-0.439386\pi$
$199$	5.34015			0.378553			0.189277	+	0.981924i	$0.439386\pi$
$200$		0			0
$201$	−1.67582	+	14.6931i	−0.118204	+	1.03637i
$202$		0			0
$203$	3.34723	+	1.93253i	0.234930	+	0.135637i
$204$		0			0
$205$	14.6856	−	9.59816i	1.02569	−	0.670365i
$206$		0			0
$207$	14.5337	−	4.43964i	1.01016	−	0.308576i
$208$		0			0
$209$	−13.5988	−	23.5538i	−0.940647	−	1.62925i
$210$		0			0
$211$	−2.29939	+	3.98266i	−0.158296	+	0.274177i	−0.934254	−	0.356607i	$-0.883933\pi$
$211$	−2.29939	+	3.98266i	−0.158296	+	0.274177i	0.775958	+	0.630784i	$0.217267\pi$
$212$		0			0
$213$	−3.68719	−	8.48271i	−0.252642	−	0.581226i
$214$		0			0
$215$	−24.4026	+	1.35053i	−1.66425	+	0.0921055i
$216$		0			0
$217$			8.50153i			0.577122i
$218$		0			0
$219$	−14.8459	+	6.45309i	−1.00319	+	0.436060i
$220$		0			0
$221$	−1.59877	+	2.76916i	−0.107545	+	0.186274i
$222$		0			0
$223$	−7.39417	+	4.26903i	−0.495150	+	0.285875i	−0.726709	−	0.686946i	$-0.758951\pi$
$223$	−7.39417	+	4.26903i	−0.495150	+	0.285875i	0.231558	+	0.972821i	$0.425618\pi$
$224$		0			0
$225$	−14.8982	−	1.74436i	−0.993215	−	0.116291i
$226$		0			0
$227$	−14.9682	+	8.64190i	−0.993475	+	0.573583i	−0.906311	−	0.422611i	$-0.861114\pi$
$227$	−14.9682	+	8.64190i	−0.993475	+	0.573583i	−0.0871638	+	0.996194i	$0.527780\pi$
$228$		0			0
$229$	7.84015	−	13.5795i	0.518092	−	0.897362i	−0.481687	−	0.876343i	$-0.659976\pi$
$229$	7.84015	−	13.5795i	0.518092	−	0.897362i	0.999779	−	0.0210183i	$-0.00669083\pi$
$230$		0			0
$231$	−1.28789	+	11.2918i	−0.0847371	+	0.742947i
$232$		0			0
$233$			15.7649i			1.03279i	0.856349	+	0.516397i	$0.172727\pi$
$233$			15.7649i			1.03279i	−0.856349	+	0.516397i	$0.827273\pi$
$234$		0			0
$235$	6.62931	−	0.366890i	0.432449	−	0.0239333i
$236$		0			0
$237$	0.763938	−	1.03215i	0.0496231	−	0.0670452i
$238$		0			0
$239$	−0.783409	+	1.35690i	−0.0506745	+	0.0877709i	−0.890250	−	0.455472i	$-0.849470\pi$
$239$	−0.783409	+	1.35690i	−0.0506745	+	0.0877709i	0.839575	+	0.543243i	$0.182804\pi$
$240$		0			0
$241$	10.5102	+	18.2043i	0.677023	+	1.17264i	0.975873	+	0.218339i	$0.0700638\pi$
$241$	10.5102	+	18.2043i	0.677023	+	1.17264i	−0.298850	+	0.954300i	$0.596603\pi$
$242$		0			0
$243$	13.8314	−	7.18978i	0.887284	−	0.461224i
$244$		0			0
$245$	−9.99544	+	6.53279i	−0.638585	+	0.417365i
$246$		0			0
$247$	16.5079	+	9.53086i	1.05037	+	0.606434i
$248$		0			0
$249$	−12.8256	−	9.49279i	−0.812789	−	0.601581i
$250$		0			0
$251$	−9.85740			−0.622193			−0.311097	−	0.950378i	$-0.600696\pi$
$251$	−9.85740			−0.622193			−0.311097	+	0.950378i	$0.600696\pi$
$252$		0			0
$253$			25.7990i			1.62197i
$254$		0			0
$255$	−3.46351	−	0.202073i	−0.216894	−	0.0126543i
$256$		0			0
$257$	22.4385	+	12.9548i	1.39967	+	0.808101i	0.994358	−	0.106076i	$-0.0338287\pi$
$257$	22.4385	+	12.9548i	1.39967	+	0.808101i	0.405314	+	0.914177i	$0.367162\pi$
$258$		0			0
$259$	4.67008	+	8.08881i	0.290184	+	0.502614i
$260$		0			0
$261$	8.76885	+	2.02663i	0.542778	+	0.125445i
$262$		0			0
$263$	17.0080	−	9.81956i	1.04876	−	0.605500i	0.126456	−	0.991972i	$-0.459640\pi$
$263$	17.0080	−	9.81956i	1.04876	−	0.605500i	0.922301	+	0.386472i	$0.126306\pi$
$264$		0			0
$265$	4.82826	−	9.54496i	0.296597	−	0.586342i
$266$		0			0
$267$	6.38483	+	14.6888i	0.390745	+	0.898942i
$268$		0			0
$269$	−0.279082			−0.0170160			−0.00850798	−	0.999964i	$-0.502708\pi$
$269$	−0.279082			−0.0170160			−0.00850798	+	0.999964i	$0.502708\pi$
$270$		0			0
$271$	9.34015			0.567374			0.283687	−	0.958917i	$-0.408442\pi$
$271$	9.34015			0.567374			0.283687	+	0.958917i	$0.408442\pi$
$272$		0			0
$273$	−3.17530	−	7.30504i	−0.192178	−	0.442121i
$274$		0			0
$275$	10.2212	−	23.3238i	0.616363	−	1.40648i
$276$		0			0
$277$	15.6481	−	9.03445i	0.940205	−	0.542828i	0.0501806	−	0.998740i	$-0.484020\pi$
$277$	15.6481	−	9.03445i	0.940205	−	0.542828i	0.890025	+	0.455912i	$0.150687\pi$
$278$		0			0
$279$	5.78341	+	18.9327i	0.346244	+	1.13347i
$280$		0			0
$281$	−3.51023	−	6.07990i	−0.209403	−	0.362696i	0.742124	−	0.670263i	$-0.233819\pi$
$281$	−3.51023	−	6.07990i	−0.209403	−	0.362696i	−0.951527	+	0.307567i	$0.900485\pi$
$282$		0			0
$283$	−15.9041	−	9.18223i	−0.945400	−	0.545827i	−0.0537507	−	0.998554i	$-0.517118\pi$
$283$	−15.9041	−	9.18223i	−0.945400	−	0.545827i	−0.891649	+	0.452728i	$0.850451\pi$
$284$		0			0
$285$	−1.20463	+	20.6472i	−0.0713560	+	1.22304i
$286$		0			0
$287$			10.1083i			0.596672i
$288$		0			0
$289$	16.1975			0.952797
$290$		0			0
$291$	−4.81537	−	3.56406i	−0.282282	−	0.208929i
$292$		0			0
$293$	−9.27385	−	5.35426i	−0.541784	−	0.312799i	0.204018	−	0.978967i	$-0.434600\pi$
$293$	−9.27385	−	5.35426i	−0.541784	−	0.312799i	−0.745802	+	0.666168i	$0.767933\pi$
$294$		0			0
$295$	−10.7679	+	7.03769i	−0.626934	+	0.409750i
$296$		0			0
$297$	4.81348	+	26.0227i	0.279306	+	1.50999i
$298$		0			0
$299$	−9.04077	−	15.6591i	−0.522841	−	0.905587i
$300$		0			0
$301$	7.04077	−	12.1950i	0.405823	−	0.702906i
$302$		0			0
$303$	−16.9332	+	22.8783i	−0.972787	+	1.31432i
$304$		0			0
$305$	−0.536283	−	9.69005i	−0.0307075	−	0.554851i
$306$		0			0
$307$			14.3145i			0.816974i	0.912764	+	0.408487i	$0.133944\pi$
$307$			14.3145i			0.816974i	−0.912764	+	0.408487i	$0.866056\pi$
$308$		0			0
$309$	−3.11333	+	27.2967i	−0.177111	+	1.55285i
$310$		0			0
$311$	12.2383	−	21.1974i	0.693971	−	1.20199i	−0.276555	−	0.960998i	$-0.589193\pi$
$311$	12.2383	−	21.1974i	0.693971	−	1.20199i	0.970526	−	0.240995i	$-0.0774739\pi$
$312$		0			0
$313$	27.6931	−	15.9886i	1.56531	−	0.903730i	0.568601	−	0.822613i	$-0.307485\pi$
$313$	27.6931	−	15.9886i	1.56531	−	0.903730i	0.996705	−	0.0811165i	$-0.0258486\pi$
$314$		0			0
$315$	5.53747	−	6.63548i	0.312001	−	0.373867i
$316$		0			0
$317$	22.7023	−	13.1072i	1.27509	−	0.736174i	0.299149	−	0.954206i	$-0.403297\pi$
$317$	22.7023	−	13.1072i	1.27509	−	0.736174i	0.975941	+	0.218033i	$0.0699639\pi$
$318$		0			0
$319$	−7.63954	+	13.2321i	−0.427732	+	0.740854i
$320$		0			0
$321$	−15.1395	+	6.58073i	−0.845007	+	0.367301i
$322$		0			0
$323$			4.78369i			0.266172i
$324$		0			0
$325$	1.96946	+	17.7385i	0.109246	+	0.983957i
$326$		0			0
$327$	−11.2402	−	25.8589i	−0.621582	−	1.43000i
$328$		0			0
$329$	−1.91272	+	3.31293i	−0.105452	+	0.182648i
$330$		0			0
$331$	1.37069	+	2.37410i	0.0753399	+	0.130493i	0.901234	−	0.433333i	$-0.142662\pi$
$331$	1.37069	+	2.37410i	0.0753399	+	0.130493i	−0.825894	+	0.563825i	$0.809329\pi$
$332$		0			0
$333$	15.9028	+	14.8366i	0.871467	+	0.813041i
$334$		0			0
$335$	10.4449	+	15.9811i	0.570665	+	0.873141i
$336$		0			0
$337$	−28.3008	−	16.3395i	−1.54165	−	0.890069i	−0.998735	−	0.0502783i	$-0.983989\pi$
$337$	−28.3008	−	16.3395i	−1.54165	−	0.890069i	−0.542910	−	0.839791i	$-0.682677\pi$
$338$		0			0
$339$	3.56824	−	31.2852i	0.193800	−	1.69918i
$340$		0			0
$341$	−33.6077			−1.81996
$342$		0			0
$343$		−	15.8984i		−	0.858435i
$344$		0			0
$345$	10.7823	−	16.3902i	0.580502	−	0.882419i
$346$		0			0
$347$	−11.3769	−	6.56844i	−0.610743	−	0.352612i	0.162513	−	0.986706i	$-0.448040\pi$
$347$	−11.3769	−	6.56844i	−0.610743	−	0.352612i	−0.773256	+	0.634094i	$0.781373\pi$
$348$		0			0
$349$	−7.09877	−	12.2954i	−0.379989	−	0.658160i	0.611071	−	0.791575i	$-0.290739\pi$
$349$	−7.09877	−	12.2954i	−0.379989	−	0.658160i	−0.991060	+	0.133416i	$0.957405\pi$
$350$		0			0
$351$	−12.0408	−	14.1081i	−0.642689	−	0.753032i
$352$		0			0
$353$	−4.41853	+	2.55104i	−0.235174	+	0.135778i	−0.612957	−	0.790116i	$-0.710020\pi$
$353$	−4.41853	+	2.55104i	−0.235174	+	0.135778i	0.377782	+	0.925894i	$0.376687\pi$
$354$		0			0
$355$	−10.6553	−	5.38991i	−0.565524	−	0.286067i
$356$		0			0
$357$	1.18922	−	1.60674i	0.0629400	−	0.0850375i
$358$		0			0
$359$	12.8229			0.676767			0.338384	−	0.941008i	$-0.390120\pi$
$359$	12.8229			0.676767			0.338384	+	0.941008i	$0.390120\pi$
$360$		0			0
$361$	9.51724			0.500907
$362$		0			0
$363$	−25.7083	−	2.93217i	−1.34934	−	0.153899i
$364$		0			0
$365$	−9.43308	+	18.6482i	−0.493750	+	0.976092i
$366$		0			0
$367$	−5.00259	+	2.88825i	−0.261133	+	0.150765i	−0.624851	−	0.780744i	$-0.714840\pi$
$367$	−5.00259	+	2.88825i	−0.261133	+	0.150765i	0.363718	+	0.931509i	$0.381507\pi$
$368$		0			0
$369$	6.87644	+	22.5108i	0.357973	+	1.17187i
$370$		0			0
$371$	3.08153	+	5.33737i	0.159985	+	0.277103i
$372$		0			0
$373$	−11.0893	−	6.40241i	−0.574182	−	0.331504i	0.184636	−	0.982807i	$-0.440889\pi$
$373$	−11.0893	−	6.40241i	−0.574182	−	0.331504i	−0.758818	+	0.651303i	$0.774223\pi$
$374$		0			0
$375$	−16.2414	+	10.5459i	−0.838705	+	0.544587i
$376$		0			0
$377$		−	10.7085i		−	0.551517i
$378$		0			0
$379$	7.19755			0.369713			0.184857	−	0.982765i	$-0.440818\pi$
$379$	7.19755			0.369713			0.184857	+	0.982765i	$0.440818\pi$
$380$		0			0
$381$	19.0567	−	8.28343i	0.976307	−	0.424373i
$382$		0			0
$383$	2.09118	+	1.20734i	0.106854	+	0.0616923i	0.552475	−	0.833530i	$-0.313684\pi$
$383$	2.09118	+	1.20734i	0.106854	+	0.0616923i	−0.445620	+	0.895222i	$0.647017\pi$
$384$		0			0
$385$	8.02704	+	12.2817i	0.409096	+	0.625933i
$386$		0			0
$387$	7.38363	−	31.9475i	0.375331	−	1.62398i
$388$		0			0
$389$	−5.32418	−	9.22174i	−0.269946	−	0.467561i	0.698901	−	0.715218i	$-0.253673\pi$
$389$	−5.32418	−	9.22174i	−0.269946	−	0.467561i	−0.968848	+	0.247657i	$0.920339\pi$
$390$		0			0
$391$	2.26885	−	3.92977i	0.114741	−	0.198737i
$392$		0			0
$393$	−17.1038	−	1.95078i	−0.862775	−	0.0984041i
$394$		0			0
$395$	−0.0916071	−	1.65524i	−0.00460925	−	0.0832842i
$396$		0			0
$397$			10.3068i			0.517284i	0.965973	+	0.258642i	$0.0832749\pi$
$397$			10.3068i			0.517284i	−0.965973	+	0.258642i	$0.916725\pi$
$398$		0			0
$399$	−9.57831	−	7.08933i	−0.479515	−	0.354910i
$400$		0			0
$401$	8.87644	−	15.3744i	0.443268	−	0.767763i	−0.554662	−	0.832076i	$-0.687152\pi$
$401$	8.87644	−	15.3744i	0.443268	−	0.767763i	0.997930	+	0.0643131i	$0.0204856\pi$
$402$		0			0
$403$	20.3987	−	11.7772i	1.01613	−	0.586663i
$404$		0			0
$405$	7.81782	−	18.5440i	0.388470	−	0.921461i
$406$		0			0
$407$	−31.9762	+	18.4615i	−1.58500	+	0.915101i
$408$		0			0
$409$	−11.5682	+	20.0368i	−0.572013	+	0.990755i	0.424347	+	0.905500i	$0.360504\pi$
$409$	−11.5682	+	20.0368i	−0.572013	+	0.990755i	−0.996359	+	0.0852550i	$0.972829\pi$
$410$		0			0
$411$	7.88793	+	5.83821i	0.389083	+	0.287977i
$412$		0			0
$413$		−	7.41172i		−	0.364707i
$414$		0			0
$415$	−20.5682	+	1.13832i	−1.00966	+	0.0558780i
$416$		0			0
$417$	13.6621	+	1.55823i	0.669034	+	0.0763069i
$418$		0			0
$419$	−14.1338	+	24.4804i	−0.690481	+	1.19595i	0.281199	+	0.959649i	$0.409268\pi$
$419$	−14.1338	+	24.4804i	−0.690481	+	1.19595i	−0.971680	+	0.236299i	$0.924066\pi$
$420$		0			0
$421$	−17.5682	−	30.4291i	−0.856224	−	1.48302i	−0.875505	−	0.483209i	$-0.839471\pi$
$421$	−17.5682	−	30.4291i	−0.856224	−	1.48302i	0.0192816	−	0.999814i	$-0.493862\pi$
$422$		0			0
$423$	−2.00586	+	8.67898i	−0.0975284	+	0.421987i
$424$		0			0
$425$	−3.60809	+	2.65385i	−0.175018	+	0.128731i
$426$		0			0
$427$	4.84250	+	2.79582i	0.234345	+	0.135299i
$428$		0			0
$429$	28.8779	−	12.5524i	1.39424	−	0.606035i
$430$		0			0
$431$	36.8894			1.77690			0.888449	−	0.458976i	$-0.151784\pi$
$431$	36.8894			1.77690			0.888449	+	0.458976i	$0.151784\pi$
$432$		0			0
$433$		−	11.8120i		−	0.567649i	−0.958876	−	0.283825i	$-0.908397\pi$
$433$		−	11.8120i		−	0.567649i	0.958876	−	0.283825i	$-0.0916033\pi$
$434$		0			0
$435$	10.3836	−	5.21354i	0.497855	−	0.249970i
$436$		0			0
$437$	−23.4267	−	13.5254i	−1.12065	−	0.647009i
$438$		0			0
$439$	−0.370689	−	0.642053i	−0.0176920	−	0.0306435i	0.857044	−	0.515244i	$-0.172299\pi$
$439$	−0.370689	−	0.642053i	−0.0176920	−	0.0306435i	−0.874736	+	0.484600i	$0.838965\pi$
$440$		0			0
$441$	−4.68031	−	15.3216i	−0.222872	−	0.729598i
$442$		0			0
$443$	4.65078	−	2.68513i	0.220965	−	0.127574i	−0.385432	−	0.922736i	$-0.625947\pi$
$443$	4.65078	−	2.68513i	0.220965	−	0.127574i	0.606397	+	0.795162i	$0.292614\pi$
$444$		0			0
$445$	18.4509	+	9.33328i	0.874658	+	0.442440i
$446$		0			0
$447$	−25.5284	−	2.91165i	−1.20745	−	0.137717i
$448$		0			0
$449$	21.1975			1.00037			0.500187	−	0.865917i	$-0.333265\pi$
$449$	21.1975			1.00037			0.500187	+	0.865917i	$0.333265\pi$
$450$		0			0
$451$	−39.9594			−1.88161
$452$		0			0
$453$	−0.616994	+	0.833614i	−0.0289889	+	0.0391666i
$454$		0			0
$455$	−9.17600	−	4.64162i	−0.430178	−	0.217603i
$456$		0			0
$457$	−0.859796	+	0.496403i	−0.0402195	+	0.0232208i	−0.519975	−	0.854182i	$-0.674059\pi$
$457$	−0.859796	+	0.496403i	−0.0402195	+	0.0232208i	0.479755	+	0.877402i	$0.340725\pi$
$458$		0			0
$459$	1.55532	−	4.38715i	0.0725963	−	0.204775i
$460$		0			0
$461$	5.15985	+	8.93712i	0.240318	+	0.416243i	0.960805	−	0.277226i	$-0.0894149\pi$
$461$	5.15985	+	8.93712i	0.240318	+	0.416243i	−0.720487	+	0.693469i	$0.756082\pi$
$462$		0			0
$463$	−11.3136	−	6.53192i	−0.525789	−	0.303564i	0.213511	−	0.976941i	$-0.431510\pi$
$463$	−11.3136	−	6.53192i	−0.525789	−	0.303564i	−0.739300	+	0.673376i	$0.764843\pi$
$464$		0			0
$465$	21.3511	+	14.0459i	0.990134	+	0.651363i
$466$		0			0
$467$		−	19.3938i		−	0.897437i	−0.893673	−	0.448718i	$-0.851881\pi$
$467$		−	19.3938i		−	0.897437i	0.893673	−	0.448718i	$-0.148119\pi$
$468$		0			0
$469$	−11.0000			−0.507933
$470$		0			0
$471$	3.52479	−	30.9042i	0.162414	−	1.42399i
$472$		0			0
$473$	48.2084	+	27.8331i	2.21662	+	1.27977i
$474$		0			0
$475$	15.8205	+	21.5091i	0.725895	+	0.986906i
$476$		0			0
$477$	10.4934	+	9.78988i	0.480459	+	0.448248i
$478$		0			0
$479$	5.95797	+	10.3195i	0.272227	+	0.471510i	0.969432	−	0.245361i	$-0.0789066\pi$
$479$	5.95797	+	10.3195i	0.272227	+	0.471510i	−0.697205	+	0.716872i	$0.745573\pi$
$480$		0			0
$481$	12.9389	−	22.4109i	0.589964	−	1.02185i
$482$		0			0
$483$	4.50612	+	10.3667i	0.205036	+	0.471702i
$484$		0			0
$485$	−7.72234	+	0.427383i	−0.350653	+	0.0194064i
$486$		0			0
$487$			18.8027i			0.852031i	0.904716	+	0.426016i	$0.140083\pi$
$487$			18.8027i			0.852031i	−0.904716	+	0.426016i	$0.859917\pi$
$488$		0			0
$489$	−7.42295	+	3.22655i	−0.335677	+	0.145910i
$490$		0			0
$491$	−4.96946	+	8.60736i	−0.224269	+	0.388445i	−0.956100	−	0.293041i	$-0.905333\pi$
$491$	−4.96946	+	8.60736i	−0.224269	+	0.388445i	0.731831	+	0.681486i	$0.238666\pi$
$492$		0			0
$493$	2.32735	−	1.34369i	0.104818	−	0.0605169i
$494$		0			0
$495$	26.2310	+	21.8904i	1.17899	+	0.983899i
$496$		0			0
$497$	5.95824	−	3.43999i	0.267264	−	0.154305i
$498$		0			0
$499$	−4.96946	+	8.60736i	−0.222464	+	0.385319i	−0.955556	−	0.294811i	$-0.904743\pi$
$499$	−4.96946	+	8.60736i	−0.222464	+	0.385319i	0.733092	+	0.680130i	$0.238077\pi$
$500$		0			0
$501$	1.17008	−	10.2589i	0.0522752	−	0.458332i
$502$		0			0
$503$			36.0636i			1.60800i	0.594630	+	0.803999i	$0.297298\pi$
$503$			36.0636i			1.60800i	−0.594630	+	0.803999i	$0.702702\pi$
$504$		0			0
$505$	2.03054	+	36.6896i	0.0903577	+	1.63266i
$506$		0			0
$507$	0.266490	−	0.360052i	0.0118353	−	0.0159905i
$508$		0			0
$509$	−20.4389	+	35.4013i	−0.905940	+	1.56913i	−0.0862886	+	0.996270i	$0.527501\pi$
$509$	−20.4389	+	35.4013i	−0.905940	+	1.56913i	−0.819651	+	0.572863i	$0.805833\pi$
$510$		0			0
$511$	−6.02046	−	10.4277i	−0.266330	−	0.461296i
$512$		0			0
$513$	−26.1534	−	9.27183i	−1.15470	−	0.409361i
$514$		0			0
$515$	19.4044	+	29.6896i	0.855062	+	1.30828i
$516$		0			0
$517$	−13.0965	−	7.56125i	−0.575982	−	0.332543i
$518$		0			0
$519$	−13.6613	−	10.1113i	−0.599663	−	0.443837i
$520$		0			0
$521$	−17.9504			−0.786422			−0.393211	−	0.919448i	$-0.628636\pi$
$521$	−17.9504			−0.786422			−0.393211	+	0.919448i	$0.628636\pi$
$522$		0			0
$523$		−	20.9732i		−	0.917092i	−0.888671	−	0.458546i	$-0.848370\pi$
$523$		−	20.9732i		−	0.917092i	0.888671	−	0.458546i	$-0.151630\pi$
$524$		0			0
$525$	0.0333611	−	11.1574i	0.00145600	−	0.486948i
$526$		0			0
$527$	5.11921	+	2.95558i	0.222996	+	0.128747i
$528$		0			0
$529$	1.32992	+	2.30349i	0.0578227	+	0.100152i
$530$		0			0
$531$	−5.04203	−	16.5057i	−0.218805	−	0.716286i
$532$		0			0
$533$	24.2539	−	14.0030i	1.05055	−	0.606537i
$534$		0			0
$535$	−9.61966	+	19.0171i	−0.415894	+	0.822179i
$536$		0			0
$537$	11.2903	+	25.9742i	0.487210	+	1.12087i
$538$		0			0
$539$	27.1975			1.17148
$540$		0			0
$541$	−13.6192			−0.585537			−0.292768	−	0.956183i	$-0.594576\pi$
$541$	−13.6192			−0.585537			−0.292768	+	0.956183i	$0.594576\pi$
$542$		0			0
$543$	2.02923	+	4.66842i	0.0870826	+	0.200341i
$544$		0			0
$545$	−32.4819	−	16.4308i	−1.39137	−	0.703816i
$546$		0			0
$547$	7.61849	−	4.39854i	0.325743	−	0.188068i	−0.328206	−	0.944606i	$-0.606444\pi$
$547$	7.61849	−	4.39854i	0.325743	−	0.188068i	0.653950	+	0.756538i	$0.273111\pi$
$548$		0			0
$549$	12.6861	+	2.93197i	0.541428	+	0.125133i
$550$		0			0
$551$	−8.01023	−	13.8741i	−0.341247	−	0.591058i
$552$		0			0
$553$	0.827189	+	0.477578i	0.0351757	+	0.0203087i
$554$		0			0
$555$	28.0303	+	1.63538i	1.18982	+	0.0694181i
$556$		0			0
$557$			33.9308i			1.43770i	0.695168	+	0.718848i	$0.255330\pi$
$557$			33.9308i			1.43770i	−0.695168	+	0.718848i	$0.744670\pi$
$558$		0			0
$559$	−39.0143			−1.65013
$560$		0			0
$561$	6.35165	+	4.70113i	0.268167	+	0.198482i
$562$		0			0
$563$	28.8928	+	16.6813i	1.21769	+	0.703033i	0.964423	−	0.264364i	$-0.0851621\pi$
$563$	28.8928	+	16.6813i	1.21769	+	0.703033i	0.253265	+	0.967397i	$0.418495\pi$
$564$		0			0
$565$	−22.2397	−	34.0277i	−0.935632	−	1.43156i
$566$		0			0
$567$	6.47938	+	9.61588i	0.272108	+	0.403829i
$568$		0			0
$569$	3.81537	+	6.60841i	0.159948	+	0.277039i	0.934850	−	0.355043i	$-0.115534\pi$
$569$	3.81537	+	6.60841i	0.159948	+	0.277039i	−0.774901	+	0.632082i	$0.782201\pi$
$570$		0			0
$571$	−13.2485	+	22.9472i	−0.554434	+	0.960309i	0.443513	+	0.896268i	$0.353732\pi$
$571$	−13.2485	+	22.9472i	−0.554434	+	0.960309i	−0.997947	+	0.0640406i	$0.979601\pi$
$572$		0			0
$573$	−4.73871	+	6.40241i	−0.197962	+	0.267465i
$574$		0			0
$575$	−2.79490	−	25.1731i	−0.116556	−	1.04979i
$576$		0			0
$577$		−	9.93709i		−	0.413686i	−0.978374	−	0.206843i	$-0.933681\pi$
$577$		−	9.93709i		−	0.413686i	0.978374	−	0.206843i	$-0.0663190\pi$
$578$		0			0
$579$	0.310882	−	2.72571i	0.0129198	−	0.113277i
$580$		0			0
$581$	5.93445	−	10.2788i	0.246202	−	0.426435i
$582$		0			0
$583$	−21.0994	+	12.1817i	−0.873847	+	0.504516i
$584$		0			0
$585$	−23.5923	−	4.09453i	−0.975422	−	0.169288i
$586$		0			0
$587$	20.3671	−	11.7589i	0.840638	−	0.485343i	−0.0168427	−	0.999858i	$-0.505361\pi$
$587$	20.3671	−	11.7589i	0.840638	−	0.485343i	0.857481	+	0.514515i	$0.172028\pi$
$588$		0			0
$589$	17.6192	−	30.5174i	0.725988	−	1.25745i
$590$		0			0
$591$	20.7733	−	9.02958i	0.854501	−	0.371427i
$592$		0			0
$593$			11.6637i			0.478970i	0.970900	+	0.239485i	$0.0769786\pi$
$593$			11.6637i			0.478970i	−0.970900	+	0.239485i	$0.923021\pi$
$594$		0			0
$595$	−0.142604	−	2.57670i	−0.00584620	−	0.105634i
$596$		0			0
$597$	3.68719	+	8.48271i	0.150907	+	0.347174i
$598$		0			0
$599$	1.03054	−	1.78494i	0.0421065	−	0.0729307i	−0.844204	−	0.536022i	$-0.819926\pi$
$599$	1.03054	−	1.78494i	0.0421065	−	0.0729307i	0.886311	+	0.463091i	$0.153260\pi$
$600$		0			0
$601$	6.96946	+	12.0715i	0.284290	+	0.492405i	0.972437	−	0.233166i	$-0.0749087\pi$
$601$	6.96946	+	12.0715i	0.284290	+	0.492405i	−0.688146	+	0.725572i	$0.741575\pi$
$602$		0			0
$603$	−24.4967	+	7.48306i	−0.997583	+	0.304734i
$604$		0			0
$605$	−27.9620	+	18.2753i	−1.13682	+	0.742997i
$606$		0			0
$607$	40.9219	+	23.6263i	1.66097	+	0.958961i	0.972253	+	0.233930i	$0.0751588\pi$
$607$	40.9219	+	23.6263i	1.66097	+	0.958961i	0.688716	+	0.725031i	$0.258175\pi$
$608$		0			0
$609$	−0.758621	+	6.65134i	−0.0307409	+	0.269526i
$610$		0			0
$611$	10.5988			0.428781
$612$		0			0
$613$		−	31.4648i		−	1.27085i	−0.772162	−	0.635426i	$-0.780825\pi$
$613$		−	31.4648i		−	1.27085i	0.772162	−	0.635426i	$-0.219175\pi$
$614$		0			0
$615$	25.3863	+	16.7005i	1.02368	+	0.673429i
$616$		0			0
$617$	−18.2720	−	10.5493i	−0.735602	−	0.424700i	0.0848661	−	0.996392i	$-0.472954\pi$
$617$	−18.2720	−	10.5493i	−0.735602	−	0.424700i	−0.820468	+	0.571692i	$0.806287\pi$
$618$		0			0
$619$	−1.95923	−	3.39349i	−0.0787482	−	0.136396i	0.823962	−	0.566645i	$-0.191759\pi$
$619$	−1.95923	−	3.39349i	−0.0787482	−	0.136396i	−0.902710	+	0.430249i	$0.858426\pi$
$620$		0			0
$621$	17.0873	+	20.0210i	0.685689	+	0.803415i
$622$		0			0
$623$	−10.3174	+	5.95677i	−0.413359	+	0.238653i
$624$		0			0
$625$	−7.44649	+	23.8652i	−0.297860	+	0.954610i
$626$		0			0
$627$	28.0251	−	37.8644i	1.11922	−	1.51216i
$628$		0			0
$629$	6.49425			0.258943
$630$		0			0
$631$	44.5582			1.77383			0.886916	−	0.461930i	$-0.152843\pi$
$631$	44.5582			1.77383			0.886916	+	0.461930i	$0.152843\pi$
$632$		0			0
$633$	−7.91400	−	0.902634i	−0.314553	−	0.0358765i
$634$		0			0
$635$	12.1086	−	23.9375i	0.480517	−	0.949932i
$636$		0			0
$637$	−16.5079	+	9.53086i	−0.654068	+	0.377626i
$638$		0			0
$639$	10.9287	−	11.7140i	0.432333	−	0.463400i
$640$		0			0
$641$	7.66433	+	13.2750i	0.302723	+	0.524331i	0.976752	−	0.214374i	$-0.0687710\pi$
$641$	7.66433	+	13.2750i	0.302723	+	0.524331i	−0.674029	+	0.738705i	$0.735438\pi$
$642$		0			0
$643$	−4.65078	−	2.68513i	−0.183409	−	0.105891i	0.405484	−	0.914102i	$-0.367103\pi$
$643$	−4.65078	−	2.68513i	−0.183409	−	0.105891i	−0.588893	+	0.808211i	$0.700436\pi$
$644$		0			0
$645$	−18.9945	−	37.8305i	−0.747907	−	1.48958i
$646$		0			0
$647$			2.65087i			0.104216i	0.998641	+	0.0521082i	$0.0165941\pi$
$647$			2.65087i			0.104216i	−0.998641	+	0.0521082i	$0.983406\pi$
$648$		0			0
$649$	29.2995			1.15011
$650$		0			0
$651$	−13.5045	+	5.87002i	−0.529282	+	0.230064i
$652$		0			0
$653$	−6.68262	−	3.85821i	−0.261511	−	0.150984i	0.363513	−	0.931589i	$-0.381577\pi$
$653$	−6.68262	−	3.85821i	−0.261511	−	0.150984i	−0.625024	+	0.780606i	$0.714911\pi$
$654$		0			0
$655$	−18.6032	+	12.1586i	−0.726887	+	0.475077i
$656$		0			0
$657$	−20.5012	−	19.1267i	−0.799827	−	0.746204i
$658$		0			0
$659$	−5.87644	−	10.1783i	−0.228913	−	0.396490i	0.728573	−	0.684968i	$-0.240184\pi$
$659$	−5.87644	−	10.1783i	−0.228913	−	0.396490i	−0.957486	+	0.288478i	$0.906851\pi$
$660$		0			0
$661$	−5.03054	+	8.71314i	−0.195665	+	0.338902i	−0.947118	−	0.320884i	$-0.896020\pi$
$661$	−5.03054	+	8.71314i	−0.195665	+	0.338902i	0.751453	+	0.659786i	$0.229353\pi$
$662$		0			0
$663$	−5.50264	−	0.627606i	−0.213705	−	0.0243742i
$664$		0			0
$665$	−15.3606	+	0.850113i	−0.595659	+	0.0329660i
$666$		0			0
$667$			15.1967i			0.588417i
$668$		0			0
$669$	−11.8867	−	8.79785i	−0.459565	−	0.340144i
$670$		0			0
$671$	−11.0523	+	19.1431i	−0.426668	+	0.739010i
$672$		0			0
$673$	27.8848	−	16.0993i	1.07488	−	0.620582i	0.145369	−	0.989377i	$-0.453563\pi$
$673$	27.8848	−	16.0993i	1.07488	−	0.620582i	0.929511	+	0.368795i	$0.120230\pi$
$674$		0			0
$675$	−7.51584	−	24.8699i	−0.289285	−	0.957243i
$676$		0			0
$677$	−1.57928	+	0.911799i	−0.0606967	+	0.0350433i	−0.530041	−	0.847972i	$-0.677824\pi$
$677$	−1.57928	+	0.911799i	−0.0606967	+	0.0350433i	0.469345	+	0.883015i	$0.344490\pi$
$678$		0			0
$679$	2.22809	−	3.85916i	0.0855061	−	0.148101i
$680$		0			0
$681$	−24.0625	−	17.8097i	−0.922077	−	0.682470i
$682$		0			0
$683$		−	36.5909i		−	1.40011i	−0.714089	−	0.700055i	$-0.753159\pi$
$683$		−	36.5909i		−	1.40011i	0.714089	−	0.700055i	$-0.246841\pi$
$684$		0			0
$685$	12.6498	−	0.700085i	0.483323	−	0.0267489i
$686$		0			0
$687$	26.9841	+	3.07769i	1.02951	+	0.117421i
$688$		0			0
$689$	8.53770	−	14.7877i	0.325261	−	0.563368i
$690$		0			0
$691$	−3.69038	−	6.39193i	−0.140389	−	0.243160i	0.787254	−	0.616628i	$-0.211502\pi$
$691$	−3.69038	−	6.39193i	−0.140389	−	0.243160i	−0.927643	+	0.373468i	$0.878169\pi$
$692$		0			0
$693$	−18.8260	+	5.75083i	−0.715142	+	0.218456i
$694$		0			0
$695$	14.8597	−	9.71197i	0.563661	−	0.368396i
$696$		0			0
$697$	6.08671	+	3.51416i	0.230551	+	0.133108i
$698$		0			0
$699$	−25.0422	+	10.8851i	−0.947182	+	0.411714i
$700$		0			0
$701$	−31.1045			−1.17480			−0.587401	−	0.809296i	$-0.699849\pi$
$701$	−31.1045			−1.17480			−0.587401	+	0.809296i	$0.699849\pi$
$702$		0			0
$703$		−	38.7145i		−	1.46015i
$704$		0			0
$705$	5.16011	+	10.2772i	0.194341	+	0.387061i
$706$		0			0
$707$	−18.3352	−	10.5858i	−0.689567	−	0.398122i
$708$		0			0
$709$	13.0377	+	22.5820i	0.489641	+	0.848083i	0.999929	−	0.0119203i	$-0.00379443\pi$
$709$	13.0377	+	22.5820i	0.489641	+	0.848083i	−0.510288	+	0.860004i	$0.670461\pi$
$710$		0			0
$711$	2.16701	+	0.500834i	0.0812694	+	0.0187828i
$712$		0			0
$713$	−28.9482	+	16.7132i	−1.08412	+	0.625915i
$714$		0			0
$715$	18.3490	−	36.2740i	0.686213	−	1.35657i
$716$		0			0
$717$	−2.69633	−	0.307531i	−0.100696	−	0.0114849i
$718$		0			0
$719$	−43.0524			−1.60558			−0.802792	−	0.596259i	$-0.796653\pi$
$719$	−43.0524			−1.60558			−0.802792	+	0.596259i	$0.796653\pi$
$720$		0			0
$721$	−20.4357			−0.761066
$722$		0			0
$723$	−21.6601	+	29.2647i	−0.805547	+	1.08836i
$724$		0			0
$725$	6.02072	−	13.7387i	0.223604	−	0.510241i
$726$		0			0
$727$	−12.3690	+	7.14127i	−0.458742	+	0.264855i	−0.711515	−	0.702671i	$-0.751991\pi$
$727$	−12.3690	+	7.14127i	−0.458742	+	0.264855i	0.252773	+	0.967526i	$0.418657\pi$
$728$		0			0
$729$	20.9709	+	17.0065i	0.776699	+	0.629871i
$730$		0			0
$731$	−4.89548	−	8.47922i	−0.181066	−	0.313615i
$732$		0			0
$733$	−3.05868	−	1.76593i	−0.112975	−	0.0652260i	0.442448	−	0.896794i	$-0.354110\pi$
$733$	−3.05868	−	1.76593i	−0.112975	−	0.0652260i	−0.555423	+	0.831568i	$0.687444\pi$
$734$		0			0
$735$	−17.2787	−	11.3668i	−0.637334	−	0.419272i
$736$		0			0
$737$		−	43.4845i		−	1.60177i
$738$		0			0
$739$	−13.3606			−0.491478			−0.245739	−	0.969336i	$-0.579031\pi$
$739$	−13.3606			−0.491478			−0.245739	+	0.969336i	$0.579031\pi$
$740$		0			0
$741$	−3.74138	+	32.8032i	−0.137443	+	1.20506i
$742$		0			0
$743$	18.3273	+	10.5813i	0.672363	+	0.388189i	0.796971	−	0.604017i	$-0.206434\pi$
$743$	18.3273	+	10.5813i	0.672363	+	0.388189i	−0.124608	+	0.992206i	$0.539767\pi$
$744$		0			0
$745$	−27.7663	+	18.1474i	−1.01728	+	0.664871i
$746$		0			0
$747$	6.22343	−	26.9276i	0.227703	−	0.985229i
$748$		0			0
$749$	−6.13954	−	10.6340i	−0.224334	−	0.388558i
$750$		0			0
$751$	−4.04077	+	6.99881i	−0.147450	+	0.255390i	−0.930284	−	0.366840i	$-0.880440\pi$
$751$	−4.04077	+	6.99881i	−0.147450	+	0.255390i	0.782835	+	0.622230i	$0.213773\pi$
$752$		0			0
$753$	−6.80620	−	15.6582i	−0.248032	−	0.570618i
$754$		0			0
$755$	0.0739865	+	1.33686i	0.00269264	+	0.0486532i
$756$		0			0
$757$		−	26.3114i		−	0.956305i	−0.878277	−	0.478152i	$-0.841307\pi$
$757$		−	26.3114i		−	0.956305i	0.878277	−	0.478152i	$-0.158693\pi$
$758$		0			0
$759$	−40.9811	+	17.8133i	−1.48752	+	0.646583i
$760$		0			0
$761$	13.5815	−	23.5239i	0.492330	−	0.852741i	−0.507631	−	0.861575i	$-0.669479\pi$
$761$	13.5815	−	23.5239i	0.492330	−	0.852741i	0.999961	+	0.00883382i	$0.00281193\pi$
$762$		0			0
$763$	18.1633	−	10.4866i	0.657555	−	0.379640i
$764$		0			0
$765$	−2.07045	−	5.64123i	−0.0748572	−	0.203959i
$766$		0			0
$767$	−17.7838	+	10.2675i	−0.642135	+	0.370737i
$768$		0			0
$769$	1.41847	−	2.45686i	0.0511512	−	0.0885965i	−0.839316	−	0.543644i	$-0.817044\pi$
$769$	1.41847	−	2.45686i	0.0511512	−	0.0885965i	0.890467	+	0.455047i	$0.150378\pi$
$770$		0			0
$771$	−5.08548	+	44.5878i	−0.183149	+	1.60579i
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$	32.7924	−	3.64085i	1.17794	−	0.130783i
$776$		0			0
$777$	−9.62435	+	13.0034i	−0.345272	+	0.466493i
$778$		0			0
$779$	20.9492	−	36.2850i	0.750582	−	1.30005i
$780$		0			0
$781$	13.5988	+	23.5538i	0.486602	+	0.842820i
$782$		0			0
$783$	2.83534	+	15.3284i	0.101327	+	0.547794i
$784$		0			0
$785$	−21.9689	−	33.6133i	−0.784104	−	1.19971i
$786$		0			0
$787$	−3.28300	−	1.89544i	−0.117026	−	0.0675652i	0.440344	−	0.897829i	$-0.354856\pi$
$787$	−3.28300	−	1.89544i	−0.117026	−	0.0675652i	−0.557371	+	0.830264i	$0.688190\pi$
$788$		0			0
$789$	27.3416	+	20.2367i	0.973386	+	0.720446i
$790$		0			0
$791$	23.4217			0.832779
$792$		0			0
$793$		−	15.4922i		−	0.550144i
$794$		0			0
$795$	18.4957	+	1.07910i	0.655975	+	0.0382718i
$796$		0			0
$797$	38.1706	+	22.0378i	1.35207	+	0.780619i	0.988540	−	0.150962i	$-0.0482372\pi$
$797$	38.1706	+	22.0378i	1.35207	+	0.780619i	0.363533	+	0.931581i	$0.381571\pi$
$798$		0			0
$799$	1.32992	+	2.30349i	0.0470493	+	0.0814918i
$800$		0			0
$801$	−18.9244	+	20.2843i	−0.668660	+	0.716710i
$802$		0			0
$803$	41.2223	−	23.7997i	1.45470	−	0.839874i
$804$		0			0
$805$	13.0218	+	6.58701i	0.458959	+	0.232162i
$806$		0			0
$807$	−0.192697	−	0.443316i	−0.00678325	−	0.0156055i
$808$		0			0
$809$	1.48276			0.0521310			0.0260655	−	0.999660i	$-0.491702\pi$
$809$	1.48276			0.0521310			0.0260655	+	0.999660i	$0.491702\pi$
$810$		0			0
$811$	51.2385			1.79923			0.899613	−	0.436688i	$-0.143849\pi$
$811$	51.2385			1.79923			0.899613	+	0.436688i	$0.143849\pi$
$812$		0			0
$813$	6.44906	+	14.8366i	0.226178	+	0.520343i
$814$		0			0
$815$	−4.71654	+	9.32411i	−0.165213	+	0.326609i
$816$		0			0
$817$	−50.5476	+	29.1837i	−1.76844	+	1.02101i
$818$		0			0
$819$	9.41146	−	10.0878i	0.328863	−	0.352495i
$820$		0			0
$821$	11.3561	+	19.6694i	0.396332	+	0.686467i	0.993270	−	0.115820i	$-0.0369497\pi$
$821$	11.3561	+	19.6694i	0.396332	+	0.686467i	−0.596938	+	0.802287i	$0.703616\pi$
$822$		0			0
$823$	11.3452	+	6.55018i	0.395470	+	0.228325i	0.684528	−	0.728987i	$-0.260008\pi$
$823$	11.3452	+	6.55018i	0.395470	+	0.228325i	−0.289057	+	0.957312i	$0.593342\pi$
$824$		0			0
$825$	44.1067	+	0.131881i	1.53560	+	0.00459151i
$826$		0			0
$827$			34.8631i			1.21231i	0.795346	+	0.606155i	$0.207289\pi$
$827$			34.8631i			1.21231i	−0.795346	+	0.606155i	$0.792711\pi$
$828$		0			0
$829$	25.5988			0.889082			0.444541	−	0.895758i	$-0.353367\pi$
$829$	25.5988			0.889082			0.444541	+	0.895758i	$0.353367\pi$
$830$		0			0
$831$	25.1555	+	18.6187i	0.872635	+	0.645876i
$832$		0			0
$833$	−4.14280	−	2.39184i	−0.143539	−	0.0828725i
$834$		0			0
$835$	−7.29273	−	11.1582i	−0.252375	−	0.386144i
$836$		0			0
$837$	−26.0809	+	22.2592i	−0.901487	+	0.769390i
$838$		0			0
$839$	−20.1657	−	34.9281i	−0.696199	−	1.20585i	−0.969775	−	0.244002i	$-0.921540\pi$
$839$	−20.1657	−	34.9281i	−0.696199	−	1.20585i	0.273576	−	0.961850i	$-0.411794\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	7.23408	−	9.77388i	0.249155	−	0.336630i
$844$		0			0
$845$	−0.0319560	−	0.577411i	−0.00109932	−	0.0198635i
$846$		0			0
$847$		−	19.2466i		−	0.661320i
$848$		0			0
$849$	3.60452	−	31.6033i	0.123707	−	1.08462i
$850$		0			0
$851$	−18.3619	+	31.8037i	−0.629437	+	1.09022i
$852$		0			0
$853$	−34.8994	+	20.1492i	−1.19493	+	0.689896i	−0.959422	−	0.281976i	$-0.909010\pi$
$853$	−34.8994	+	20.1492i	−1.19493	+	0.689896i	−0.235513	+	0.971871i	$0.575677\pi$
$854$		0			0
$855$	−33.6294	+	12.3427i	−1.15010	+	0.422111i
$856$		0			0
$857$	19.0873	−	11.0201i	0.652010	−	0.376438i	−0.137216	−	0.990541i	$-0.543815\pi$
$857$	19.0873	−	11.0201i	0.652010	−	0.376438i	0.789226	+	0.614103i	$0.210482\pi$
$858$		0			0
$859$	14.6395	−	25.3564i	0.499495	−	0.865150i	−0.500505	−	0.865734i	$-0.666852\pi$
$859$	14.6395	−	25.3564i	0.499495	−	0.865150i	1.00000		0.000583373i	$0.000185693\pi$
$860$		0			0
$861$	−16.0567	+	6.97941i	−0.547212	+	0.237858i
$862$		0			0
$863$			46.1491i			1.57093i	0.618904	+	0.785466i	$0.287577\pi$
$863$			46.1491i			1.57093i	−0.618904	+	0.785466i	$0.712423\pi$
$864$		0			0
$865$	−21.9084	+	1.21249i	−0.744908	+	0.0412259i
$866$		0			0
$867$	11.1839	+	25.7294i	0.379824	+	0.873817i
$868$		0			0
$869$	−1.88793	+	3.26999i	−0.0640437	+	0.110927i
$870$		0			0
$871$	15.2383	+	26.3935i	0.516331	+	0.894311i
$872$		0			0
$873$	2.33659	−	10.1100i	0.0790814	−	0.342170i
$874$		0			0
$875$	−9.16281	−	11.1141i	−0.309760	−	0.375726i
$876$		0			0
$877$	23.9337	+	13.8181i	0.808184	+	0.466606i	0.846325	−	0.532667i	$-0.178810\pi$
$877$	23.9337	+	13.8181i	0.808184	+	0.466606i	−0.0381405	+	0.999272i	$0.512143\pi$
$878$		0			0
$879$	2.10184	−	18.4282i	0.0708932	−	0.621569i
$880$		0			0
$881$	4.79632			0.161592			0.0807961	−	0.996731i	$-0.474254\pi$
$881$	4.79632			0.161592			0.0807961	+	0.996731i	$0.474254\pi$
$882$		0			0
$883$			21.7126i			0.730687i	0.930873	+	0.365343i	$0.119048\pi$
$883$			21.7126i			0.730687i	−0.930873	+	0.365343i	$0.880952\pi$
$884$		0			0
$885$	−18.6141	−	12.2453i	−0.625706	−	0.411623i
$886$		0			0
$887$	−19.0873	−	11.0201i	−0.640889	−	0.370018i	0.144068	−	0.989568i	$-0.453982\pi$
$887$	−19.0873	−	11.0201i	−0.640889	−	0.370018i	−0.784957	+	0.619550i	$0.787315\pi$
$888$		0			0
$889$	7.72809	+	13.3854i	0.259192	+	0.448933i
$890$		0			0
$891$	−38.0129	+	25.6139i	−1.27348	+	0.858098i
$892$		0			0
$893$	13.7319	−	7.92814i	0.459522	−	0.265305i
$894$		0			0
$895$	32.6267	+	16.5040i	1.09059	+	0.551668i
$896$		0			0
$897$	18.6317	−	25.1731i	0.622095	−	0.840505i
$898$		0			0
$899$	−19.7963			−0.660244
$900$		0			0
$901$	4.28521			0.142761
$902$		0			0
$903$	24.2328	+	2.76388i	0.806418	+	0.0919763i
$904$		0			0
$905$	5.86409	+	2.96631i	0.194929	+	0.0986035i
$906$		0			0
$907$	34.0357	−	19.6505i	1.13014	−	0.652486i	0.186169	−	0.982518i	$-0.440393\pi$
$907$	34.0357	−	19.6505i	1.13014	−	0.652486i	0.943970	+	0.330032i	$0.107060\pi$
$908$		0			0
$909$	−48.0334	−	11.1013i	−1.59317	−	0.368208i
$910$		0			0
$911$	−7.96946	−	13.8035i	−0.264040	−	0.457331i	0.703272	−	0.710921i	$-0.251722\pi$
$911$	−7.96946	−	13.8035i	−0.264040	−	0.457331i	−0.967312	+	0.253590i	$0.918388\pi$
$912$		0			0
$913$	40.6334	+	23.4597i	1.34477	+	0.776402i
$914$		0			0
$915$	15.0221	−	7.54252i	0.496616	−	0.249348i
$916$		0			0
$917$		−	12.8048i		−	0.422852i
$918$		0			0
$919$	6.16307			0.203301			0.101650	−	0.994820i	$-0.467588\pi$
$919$	6.16307			0.203301			0.101650	+	0.994820i	$0.467588\pi$
$920$		0			0
$921$	−22.7383	+	9.88371i	−0.749253	+	0.325679i
$922$		0			0
$923$	−16.5079	−	9.53086i	−0.543365	−	0.313712i
$924$		0			0
$925$	29.2004	−	21.4777i	0.960104	−	0.706181i
$926$		0			0
$927$	−45.5098	+	13.9020i	−1.49474	+	0.456601i
$928$		0			0
$929$	−5.05100	−	8.74858i	−0.165718	−	0.287032i	0.771192	−	0.636602i	$-0.219661\pi$
$929$	−5.05100	−	8.74858i	−0.165718	−	0.287032i	−0.936910	+	0.349571i	$0.886327\pi$
$930$		0			0
$931$	−14.2586	+	24.6967i	−0.467307	+	0.809400i
$932$		0			0
$933$	42.1217	+	4.80420i	1.37900	+	0.157283i
$934$		0			0
$935$	10.1861	−	0.563734i	0.333120	−	0.0184361i
$936$		0			0
$937$		−	5.00506i		−	0.163508i	−0.996653	−	0.0817541i	$-0.973948\pi$
$937$		−	5.00506i		−	0.163508i	0.996653	−	0.0817541i	$-0.0260522\pi$
$938$		0			0
$939$	44.5187	+	32.9502i	1.45281	+	1.07529i
$940$		0			0
$941$	4.99425	−	8.65030i	0.162808	−	0.281992i	−0.773067	−	0.634325i	$-0.781278\pi$
$941$	4.99425	−	8.65030i	0.162808	−	0.281992i	0.935875	+	0.352333i	$0.114612\pi$
$942$		0			0
$943$	−34.4192	+	19.8719i	−1.12084	+	0.647119i
$944$		0			0
$945$	14.3637	+	4.21456i	0.467252	+	0.137100i
$946$		0			0
$947$	−41.2421	+	23.8111i	−1.34019	+	0.773758i	−0.986835	−	0.161732i	$-0.948292\pi$
$947$	−41.2421	+	23.8111i	−1.34019	+	0.773758i	−0.353354	+	0.935490i	$0.614959\pi$
$948$		0			0
$949$	−16.6803	+	28.8911i	−0.541466	+	0.937846i
$950$		0			0
$951$	36.4957	+	27.0121i	1.18345	+	0.875926i
$952$		0			0
$953$			34.2355i			1.10900i	0.832184	+	0.554499i	$0.187090\pi$
$953$			34.2355i			1.10900i	−0.832184	+	0.554499i	$0.812910\pi$
$954$		0			0
$955$	0.568239	+	10.2675i	0.0183878	+	0.332247i
$956$		0			0
$957$	−26.2937	−	2.99893i	−0.849954	−	0.0969418i
$958$		0			0
$959$	−3.64977	+	6.32159i	−0.117857	+	0.204135i
$960$		0			0
$961$	−6.27191	−	10.8633i	−0.202320	−	0.350428i
$962$		0			0
$963$	−20.9067	−	19.5050i	−0.673708	−	0.628541i
$964$		0			0
$965$	−1.93763	−	2.96466i	−0.0623746	−	0.0954356i
$966$		0			0
$967$	−3.21877	−	1.85836i	−0.103509	−	0.0597607i	0.447352	−	0.894358i	$-0.352367\pi$
$967$	−3.21877	−	1.85836i	−0.103509	−	0.0597607i	−0.550861	+	0.834597i	$0.685700\pi$
$968$		0			0
$969$	−7.59877	+	3.30297i	−0.244108	+	0.106107i
$970$		0			0
$971$	−45.0959			−1.44720			−0.723598	−	0.690222i	$-0.757513\pi$
$971$	−45.0959			−1.44720			−0.723598	+	0.690222i	$0.757513\pi$
$972$		0			0
$973$			10.2281i			0.327898i
$974$		0			0
$975$	−26.8174	+	15.3763i	−0.858844	+	0.492436i
$976$		0			0
$977$	−5.70620	−	3.29448i	−0.182558	−	0.105400i	0.405936	−	0.913901i	$-0.366946\pi$
$977$	−5.70620	−	3.29448i	−0.182558	−	0.105400i	−0.588494	+	0.808502i	$0.700279\pi$
$978$		0			0
$979$	−23.5479	−	40.7862i	−0.752595	−	1.30353i
$980$		0			0
$981$	33.3154	−	35.7094i	1.06368	−	1.14011i
$982$		0			0
$983$	10.5932	−	6.11596i	0.337869	−	0.195069i	−0.321460	−	0.946923i	$-0.604174\pi$
$983$	10.5932	−	6.11596i	0.337869	−	0.195069i	0.659329	+	0.751854i	$0.270840\pi$
$984$		0			0
$985$	13.1994	−	26.0938i	0.420567	−	0.831417i
$986$		0			0
$987$	−6.58318	−	0.750846i	−0.209545	−	0.0238997i
$988$		0			0
$989$	55.3660			1.76054
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		0			0
$993$	−2.82479	+	3.81655i	−0.0896421	+	0.121114i
$994$		0			0
$995$	10.6553	+	5.38991i	0.337795	+	0.170872i
$996$		0			0
$997$	−2.80371	+	1.61872i	−0.0887944	+	0.0512655i	−0.543740	−	0.839254i	$-0.682992\pi$
$997$	−2.80371	+	1.61872i	−0.0887944	+	0.0512655i	0.454945	+	0.890519i	$0.349659\pi$
$998$		0			0
$999$	−12.5873	+	35.5054i	−0.398244	+	1.12334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.r.a.49.4	yes	12
3.2	odd	2		540.2.r.a.469.1		12
4.3	odd	2		720.2.by.e.49.3		12
5.2	odd	4		900.2.i.f.301.6		12
5.3	odd	4		900.2.i.f.301.1		12
5.4	even	2	inner	180.2.r.a.49.3	✓	12
9.2	odd	6		540.2.r.a.289.5		12
9.4	even	3		1620.2.d.c.649.3		6
9.5	odd	6		1620.2.d.d.649.4		6
9.7	even	3	inner	180.2.r.a.169.3	yes	12
12.11	even	2		2160.2.by.e.1009.1		12
15.2	even	4		2700.2.i.f.901.3		12
15.8	even	4		2700.2.i.f.901.4		12
15.14	odd	2		540.2.r.a.469.5		12
20.19	odd	2		720.2.by.e.49.4		12
36.7	odd	6		720.2.by.e.529.4		12
36.11	even	6		2160.2.by.e.289.5		12
45.2	even	12		2700.2.i.f.1801.3		12
45.4	even	6		1620.2.d.c.649.4		6
45.7	odd	12		900.2.i.f.601.6		12
45.13	odd	12		8100.2.a.bc.1.3		6
45.14	odd	6		1620.2.d.d.649.3		6
45.22	odd	12		8100.2.a.bc.1.4		6
45.23	even	12		8100.2.a.bd.1.3		6
45.29	odd	6		540.2.r.a.289.1		12
45.32	even	12		8100.2.a.bd.1.4		6
45.34	even	6	inner	180.2.r.a.169.4	yes	12
45.38	even	12		2700.2.i.f.1801.4		12
45.43	odd	12		900.2.i.f.601.1		12
60.59	even	2		2160.2.by.e.1009.5		12
180.79	odd	6		720.2.by.e.529.3		12
180.119	even	6		2160.2.by.e.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.r.a.49.3	✓	12	5.4	even	2	inner
180.2.r.a.49.4	yes	12	1.1	even	1	trivial
180.2.r.a.169.3	yes	12	9.7	even	3	inner
180.2.r.a.169.4	yes	12	45.34	even	6	inner
540.2.r.a.289.1		12	45.29	odd	6
540.2.r.a.289.5		12	9.2	odd	6
540.2.r.a.469.1		12	3.2	odd	2
540.2.r.a.469.5		12	15.14	odd	2
720.2.by.e.49.3		12	4.3	odd	2
720.2.by.e.49.4		12	20.19	odd	2
720.2.by.e.529.3		12	180.79	odd	6
720.2.by.e.529.4		12	36.7	odd	6
900.2.i.f.301.1		12	5.3	odd	4
900.2.i.f.301.6		12	5.2	odd	4
900.2.i.f.601.1		12	45.43	odd	12
900.2.i.f.601.6		12	45.7	odd	12
1620.2.d.c.649.3		6	9.4	even	3
1620.2.d.c.649.4		6	45.4	even	6
1620.2.d.d.649.3		6	45.14	odd	6
1620.2.d.d.649.4		6	9.5	odd	6
2160.2.by.e.289.1		12	180.119	even	6
2160.2.by.e.289.5		12	36.11	even	6
2160.2.by.e.1009.1		12	12.11	even	2
2160.2.by.e.1009.5		12	60.59	even	2
2700.2.i.f.901.3		12	15.2	even	4
2700.2.i.f.901.4		12	15.8	even	4
2700.2.i.f.1801.3		12	45.2	even	12
2700.2.i.f.1801.4		12	45.38	even	12
8100.2.a.bc.1.3		6	45.13	odd	12
8100.2.a.bc.1.4		6	45.22	odd	12
8100.2.a.bd.1.3		6	45.23	even	12
8100.2.a.bd.1.4		6	45.32	even	12

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.690466 + 1.58848i) q^{3} +(1.99531 + 1.00932i) q^{5} +(-1.11574 + 0.644175i) q^{7} +(-2.04651 + 2.19358i) q^{9} +O(q^{10})\)	\(q+(0.690466 + 1.58848i) q^{3} +(1.99531 + 1.00932i) q^{5} +(-1.11574 + 0.644175i) q^{7} +(-2.04651 + 2.19358i) q^{9} +(-2.54651 - 4.41069i) q^{11} +(3.09128 + 1.78475i) q^{13} +(-0.225579 + 3.86641i) q^{15} +0.895796i q^{17} +5.34015 q^{19} +(-1.79364 - 1.32755i) q^{21} +(-4.38690 - 2.53278i) q^{23} +(2.96256 + 4.02781i) q^{25} +(-4.89749 - 1.73625i) q^{27} +(-1.50000 - 2.59808i) q^{29} +(3.29939 - 5.71471i) q^{31} +(5.24800 - 7.09051i) q^{33} +(-2.87644 + 0.159193i) q^{35} -7.24970i q^{37} +(-0.700613 + 6.14274i) q^{39} +(3.92295 - 6.79475i) q^{41} +(-9.46557 + 5.46495i) q^{43} +(-6.29745 + 2.31130i) q^{45} +(2.57145 - 1.48463i) q^{47} +(-2.67008 + 4.62471i) q^{49} +(-1.42295 + 0.618517i) q^{51} -4.78369i q^{53} +(-0.629311 - 11.3710i) q^{55} +(3.68719 + 8.48271i) q^{57} +(-2.87644 + 4.98213i) q^{59} +(-2.17008 - 3.75868i) q^{61} +(0.870338 - 3.76578i) q^{63} +(4.36670 + 6.68123i) q^{65} +(7.39417 + 4.26903i) q^{67} +(0.994253 - 8.71728i) q^{69} -5.34015 q^{71} +9.34600i q^{73} +(-4.35253 + 7.48702i) q^{75} +(5.68251 + 3.28080i) q^{77} +(-0.370689 - 0.642053i) q^{79} +(-0.623563 - 8.97837i) q^{81} +(-7.97824 + 4.60624i) q^{83} +(-0.904142 + 1.78739i) q^{85} +(3.09128 - 4.17660i) q^{87} +9.24713 q^{89} -4.59877 q^{91} +(11.3558 + 1.29519i) q^{93} +(10.6553 + 5.38991i) q^{95} +(-2.99543 + 1.72941i) q^{97} +(14.8867 + 3.44057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{5} + 8 q^{9}+O(q^{10}) \) 12 * q + q^5 + 8 * q^9	\( 12 q + q^{5} + 8 q^{9} + 2 q^{11} - 5 q^{15} + 10 q^{21} - 3 q^{25} - 18 q^{29} + 6 q^{31} - 34 q^{35} - 42 q^{39} + 14 q^{41} - 31 q^{45} + 16 q^{51} - 6 q^{55} - 34 q^{59} + 6 q^{61} + 15 q^{65} + 14 q^{69} + 41 q^{75} - 6 q^{79} - 8 q^{81} - 12 q^{85} + 112 q^{89} + 12 q^{91} + 36 q^{95} + 82 q^{99}+O(q^{100}) \) 12 * q + q^5 + 8 * q^9 + 2 * q^11 - 5 * q^15 + 10 * q^21 - 3 * q^25 - 18 * q^29 + 6 * q^31 - 34 * q^35 - 42 * q^39 + 14 * q^41 - 31 * q^45 + 16 * q^51 - 6 * q^55 - 34 * q^59 + 6 * q^61 + 15 * q^65 + 14 * q^69 + 41 * q^75 - 6 * q^79 - 8 * q^81 - 12 * q^85 + 112 * q^89 + 12 * q^91 + 36 * q^95 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more