LMFDB - Embedded newform 260.2.bf.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(37,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 7]))

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$-2.44766i$ of defining polynomial
Character	$\chi$	$=$	260.37
Dual form			260.2.bf.c.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.27331 - 0.877081i) q^{3} +(-1.78557 - 1.34601i) q^{5} +(-1.31216 + 2.27273i) q^{7} +(7.34722 + 4.24192i) q^{9} +O(q^{10})$	\(q+(-3.27331 - 0.877081i) q^{3} +(-1.78557 - 1.34601i) q^{5} +(-1.31216 + 2.27273i) q^{7} +(7.34722 + 4.24192i) q^{9} +(1.71196 + 0.458719i) q^{11} +(3.39379 - 1.21746i) q^{13} +(4.66416 + 5.97200i) q^{15} +(0.0972783 + 0.363048i) q^{17} +(0.462233 + 1.72508i) q^{19} +(6.28849 - 6.28849i) q^{21} +(-1.26731 + 4.72966i) q^{23} +(1.37650 + 4.80679i) q^{25} +(-13.1405 - 13.1405i) q^{27} +(-6.28709 + 3.62985i) q^{29} +(2.98238 + 2.98238i) q^{31} +(-5.20145 - 3.00306i) q^{33} +(5.40208 - 2.29193i) q^{35} +(5.10019 + 8.83378i) q^{37} +(-12.1767 + 1.00852i) q^{39} +(1.59861 - 5.96611i) q^{41} +(1.59368 - 0.427024i) q^{43} +(-7.40928 - 17.4637i) q^{45} -1.19733 q^{47} +(0.0564545 + 0.0977821i) q^{49} -1.27369i q^{51} +(5.13227 - 5.13227i) q^{53} +(-2.43938 - 3.12339i) q^{55} -6.05214i q^{57} +(2.89607 - 0.776000i) q^{59} +(-2.45432 + 4.25101i) q^{61} +(-19.2815 + 11.1322i) q^{63} +(-7.69856 - 2.39421i) q^{65} +(-6.90594 + 3.98715i) q^{67} +(8.29659 - 14.3701i) q^{69} +(4.02481 - 1.07844i) q^{71} +11.2043i q^{73} +(-0.289783 - 16.9414i) q^{75} +(-3.28892 + 3.28892i) q^{77} -2.72484i q^{79} +(18.7620 + 32.4967i) q^{81} +11.2434 q^{83} +(0.314969 - 0.779184i) q^{85} +(23.7633 - 6.36735i) q^{87} +(-1.91334 + 7.14070i) q^{89} +(-1.68623 + 9.31068i) q^{91} +(-7.14647 - 12.3780i) q^{93} +(1.49663 - 3.70242i) q^{95} +(-1.45185 - 0.838229i) q^{97} +(10.6323 + 10.6323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−3.27331	−	0.877081i	−1.88985	−	0.506383i	−0.998602	−	0.0528610i	$-0.983166\pi$
$3$	−3.27331	−	0.877081i	−1.88985	−	0.506383i	−0.891245	−	0.453522i	$-0.850167\pi$
$4$		0			0
$5$	−1.78557	−	1.34601i	−0.798530	−	0.601955i
$5$	−1.78557	−	1.34601i	−0.798530	−	0.601955i
$6$		0			0
$7$	−1.31216	+	2.27273i	−0.495951	+	0.859013i	−0.999989	−	0.00466893i	$-0.998514\pi$
$7$	−1.31216	+	2.27273i	−0.495951	+	0.859013i	0.504038	+	0.863682i	$0.331847\pi$
$8$		0			0
$9$	7.34722	+	4.24192i	2.44907	+	1.41397i
$10$		0			0
$11$	1.71196	+	0.458719i	0.516176	+	0.138309i	0.507497	−	0.861653i	$-0.330571\pi$
$11$	1.71196	+	0.458719i	0.516176	+	0.138309i	0.00867863	+	0.999962i	$0.497237\pi$
$12$		0			0
$13$	3.39379	−	1.21746i	0.941267	−	0.337664i
$13$	3.39379	−	1.21746i	0.941267	−	0.337664i
$14$		0			0
$15$	4.66416	+	5.97200i	1.20428	+	1.54196i
$16$		0			0
$17$	0.0972783	+	0.363048i	0.0235935	+	0.0880520i	0.976719	−	0.214524i	$-0.0688200\pi$
$17$	0.0972783	+	0.363048i	0.0235935	+	0.0880520i	−0.953125	+	0.302576i	$0.902153\pi$
$18$		0			0
$19$	0.462233	+	1.72508i	0.106044	+	0.395760i	0.998461	−	0.0554497i	$-0.0176592\pi$
$19$	0.462233	+	1.72508i	0.106044	+	0.395760i	−0.892418	+	0.451210i	$0.850993\pi$
$20$		0			0
$21$	6.28849	−	6.28849i	1.37226	−	1.37226i
$22$		0			0
$23$	−1.26731	+	4.72966i	−0.264252	+	0.986203i	0.698454	+	0.715655i	$0.253872\pi$
$23$	−1.26731	+	4.72966i	−0.264252	+	0.986203i	−0.962707	+	0.270548i	$0.912795\pi$
$24$		0			0
$25$	1.37650	+	4.80679i	0.275301	+	0.961358i
$26$		0			0
$27$	−13.1405	−	13.1405i	−2.52890	−	2.52890i
$28$		0			0
$29$	−6.28709	+	3.62985i	−1.16748	+	0.674047i	−0.953086	−	0.302699i	$-0.902112\pi$
$29$	−6.28709	+	3.62985i	−1.16748	+	0.674047i	−0.214398	+	0.976746i	$0.568779\pi$
$30$		0			0
$31$	2.98238	+	2.98238i	0.535651	+	0.535651i	0.922249	−	0.386597i	$-0.126350\pi$
$31$	2.98238	+	2.98238i	0.535651	+	0.535651i	−0.386597	+	0.922249i	$0.626350\pi$
$32$		0			0
$33$	−5.20145	−	3.00306i	−0.905456	−	0.522765i
$34$		0			0
$35$	5.40208	−	2.29193i	0.913119	−	0.387407i
$36$		0			0
$37$	5.10019	+	8.83378i	0.838465	+	1.45226i	0.891177	+	0.453655i	$0.149880\pi$
$37$	5.10019	+	8.83378i	0.838465	+	1.45226i	−0.0527119	+	0.998610i	$0.516786\pi$
$38$		0			0
$39$	−12.1767	+	1.00852i	−1.94984	+	0.161492i
$40$		0			0
$41$	1.59861	−	5.96611i	0.249662	−	0.931750i	−0.721321	−	0.692601i	$-0.756465\pi$
$41$	1.59861	−	5.96611i	0.249662	−	0.931750i	0.970983	−	0.239149i	$-0.0768686\pi$
$42$		0			0
$43$	1.59368	−	0.427024i	0.243033	−	0.0651205i	−0.135246	−	0.990812i	$-0.543183\pi$
$43$	1.59368	−	0.427024i	0.243033	−	0.0651205i	0.378279	+	0.925691i	$0.376516\pi$
$44$		0			0
$45$	−7.40928	−	17.4637i	−1.10451	−	2.60333i
$46$		0			0
$47$	−1.19733			−0.174649			−0.0873244	−	0.996180i	$-0.527832\pi$
$47$	−1.19733			−0.174649			−0.0873244	+	0.996180i	$0.527832\pi$
$48$		0			0
$49$	0.0564545	+	0.0977821i	0.00806493	+	0.0139689i
$50$		0			0
$51$		−	1.27369i		−	0.178352i
$52$		0			0
$53$	5.13227	−	5.13227i	0.704971	−	0.704971i	−0.260502	−	0.965473i	$-0.583888\pi$
$53$	5.13227	−	5.13227i	0.704971	−	0.704971i	0.965473	+	0.260502i	$0.0838880\pi$
$54$		0			0
$55$	−2.43938	−	3.12339i	−0.328926	−	0.421158i
$56$		0			0
$57$		−	6.05214i		−	0.801625i
$58$		0			0
$59$	2.89607	−	0.776000i	0.377036	−	0.101027i	−0.0653237	−	0.997864i	$-0.520808\pi$
$59$	2.89607	−	0.776000i	0.377036	−	0.101027i	0.442360	+	0.896838i	$0.354141\pi$
$60$		0			0
$61$	−2.45432	+	4.25101i	−0.314244	+	0.544286i	−0.979276	−	0.202528i	$-0.935084\pi$
$61$	−2.45432	+	4.25101i	−0.314244	+	0.544286i	0.665033	+	0.746814i	$0.268418\pi$
$62$		0			0
$63$	−19.2815	+	11.1322i	−2.42924	+	1.40252i
$64$		0			0
$65$	−7.69856	−	2.39421i	−0.954888	−	0.296965i
$66$		0			0
$67$	−6.90594	+	3.98715i	−0.843695	+	0.487107i	−0.858518	−	0.512783i	$-0.828615\pi$
$67$	−6.90594	+	3.98715i	−0.843695	+	0.487107i	0.0148238	+	0.999890i	$0.495281\pi$
$68$		0			0
$69$	8.29659	−	14.3701i	0.998792	−	1.72996i
$70$		0			0
$71$	4.02481	−	1.07844i	0.477657	−	0.127988i	−0.0119546	−	0.999929i	$-0.503805\pi$
$71$	4.02481	−	1.07844i	0.477657	−	0.127988i	0.489611	+	0.871941i	$0.337139\pi$
$72$		0			0
$73$			11.2043i			1.31137i	0.755037	+	0.655683i	$0.227619\pi$
$73$			11.2043i			1.31137i	−0.755037	+	0.655683i	$0.772381\pi$
$74$		0			0
$75$	−0.289783	−	16.9414i	−0.0334613	−	1.95623i
$76$		0			0
$77$	−3.28892	+	3.28892i	−0.374807	+	0.374807i
$78$		0			0
$79$		−	2.72484i		−	0.306569i	−0.988182	−	0.153284i	$-0.951015\pi$
$79$		−	2.72484i		−	0.306569i	0.988182	−	0.153284i	$-0.0489851\pi$
$80$		0			0
$81$	18.7620	+	32.4967i	2.08466	+	3.61074i
$82$		0			0
$83$	11.2434			1.23413			0.617064	−	0.786913i	$-0.288322\pi$
$83$	11.2434			1.23413			0.617064	+	0.786913i	$0.288322\pi$
$84$		0			0
$85$	0.314969	−	0.779184i	0.0341632	−	0.0845143i
$86$		0			0
$87$	23.7633	−	6.36735i	2.54769	−	0.682652i
$88$		0			0
$89$	−1.91334	+	7.14070i	−0.202814	+	0.756913i	0.787291	+	0.616582i	$0.211483\pi$
$89$	−1.91334	+	7.14070i	−0.202814	+	0.756913i	−0.990105	+	0.140330i	$0.955184\pi$
$90$		0			0
$91$	−1.68623	+	9.31068i	−0.176765	+	0.976025i
$92$		0			0
$93$	−7.14647	−	12.3780i	−0.741054	−	1.28354i
$94$		0			0
$95$	1.49663	−	3.70242i	0.153551	−	0.379860i
$96$		0			0
$97$	−1.45185	−	0.838229i	−0.147413	−	0.0851092i	0.424479	−	0.905438i	$-0.360457\pi$
$97$	−1.45185	−	0.838229i	−0.147413	−	0.0851092i	−0.571893	+	0.820329i	$0.693791\pi$
$98$		0			0
$99$	10.6323	+	10.6323i	1.06859	+	1.06859i
$100$		0			0
$101$	−12.2100	+	7.04945i	−1.21494	+	0.701447i	−0.963832	−	0.266512i	$-0.914129\pi$
$101$	−12.2100	+	7.04945i	−1.21494	+	0.701447i	−0.251110	+	0.967959i	$0.580796\pi$
$102$		0			0
$103$	8.21560	+	8.21560i	0.809508	+	0.809508i	0.984559	−	0.175052i	$-0.0560093\pi$
$103$	8.21560	+	8.21560i	0.809508	+	0.809508i	−0.175052	+	0.984559i	$0.556009\pi$
$104$		0			0
$105$	−19.6929	+	2.76414i	−1.92183	+	0.269753i
$106$		0			0
$107$	2.33402	−	8.71070i	0.225639	−	0.842095i	−0.756509	−	0.653983i	$-0.773097\pi$
$107$	2.33402	−	8.71070i	0.225639	−	0.842095i	0.982148	−	0.188112i	$-0.0602367\pi$
$108$		0			0
$109$	−8.48128	+	8.48128i	−0.812359	+	0.812359i	−0.984987	−	0.172628i	$-0.944774\pi$
$109$	−8.48128	+	8.48128i	−0.812359	+	0.812359i	0.172628	+	0.984987i	$0.444774\pi$
$110$		0			0
$111$	−8.94655	−	33.3890i	−0.849169	−	3.16914i
$112$		0			0
$113$	−0.728053	−	2.71713i	−0.0684895	−	0.255606i	0.923189	−	0.384347i	$-0.125573\pi$
$113$	−0.728053	−	2.71713i	−0.0684895	−	0.255606i	−0.991678	+	0.128740i	$0.958907\pi$
$114$		0			0
$115$	8.62905	−	6.73932i	0.804663	−	0.628445i
$116$		0			0
$117$	30.0993	+	5.45118i	2.78268	+	0.503962i
$118$		0			0
$119$	−0.952755	−	0.255290i	−0.0873389	−	0.0234024i
$120$		0			0
$121$	−6.80589	−	3.92938i	−0.618717	−	0.357217i
$122$		0			0
$123$	−10.4655	+	18.1268i	−0.943645	+	1.63444i
$124$		0			0
$125$	4.01215	−	10.4356i	0.358858	−	0.933392i
$126$		0			0
$127$	−6.39781	−	1.71429i	−0.567714	−	0.152119i	−0.0364661	−	0.999335i	$-0.511610\pi$
$127$	−6.39781	−	1.71429i	−0.567714	−	0.152119i	−0.531248	+	0.847216i	$0.678277\pi$
$128$		0			0
$129$	−5.59113			−0.492271
$130$		0			0
$131$	2.68334			0.234444			0.117222	−	0.993106i	$-0.462601\pi$
$131$	2.68334			0.234444			0.117222	+	0.993106i	$0.462601\pi$
$132$		0			0
$133$	−4.52717	−	1.21305i	−0.392555	−	0.105185i
$134$		0			0
$135$	5.77600	+	41.1506i	0.497119	+	3.54168i
$136$		0			0
$137$	1.03197	−	1.78743i	0.0881674	−	0.152710i	−0.818569	−	0.574408i	$-0.805232\pi$
$137$	1.03197	−	1.78743i	0.0881674	−	0.152710i	0.906737	+	0.421698i	$0.138566\pi$
$138$		0			0
$139$	−12.7676	−	7.37138i	−1.08293	−	0.625233i	−0.151248	−	0.988496i	$-0.548329\pi$
$139$	−12.7676	−	7.37138i	−1.08293	−	0.625233i	−0.931687	+	0.363263i	$0.881663\pi$
$140$		0			0
$141$	3.91924	+	1.05016i	0.330060	+	0.0884392i
$142$		0			0
$143$	6.36850	−	0.527460i	0.532561	−	0.0441084i
$144$		0			0
$145$	16.1119	+	1.98115i	1.33802	+	0.164525i
$146$		0			0
$147$	−0.0990304	−	0.369586i	−0.00816789	−	0.0304830i
$148$		0			0
$149$	0.823027	+	3.07158i	0.0674250	+	0.251633i	0.991409	−	0.130797i	$-0.0417537\pi$
$149$	0.823027	+	3.07158i	0.0674250	+	0.251633i	−0.923984	+	0.382431i	$0.875087\pi$
$150$		0			0
$151$	7.20288	−	7.20288i	0.586162	−	0.586162i	−0.350428	−	0.936590i	$-0.613964\pi$
$151$	7.20288	−	7.20288i	0.586162	−	0.586162i	0.936590	+	0.350428i	$0.113964\pi$
$152$		0			0
$153$	−0.825293	+	3.08004i	−0.0667210	+	0.249006i
$154$		0			0
$155$	−1.31092	−	9.33956i	−0.105296	−	0.750171i
$156$		0			0
$157$	−0.0556926	−	0.0556926i	−0.00444476	−	0.00444476i	0.704881	−	0.709326i	$-0.251000\pi$
$157$	−0.0556926	−	0.0556926i	−0.00444476	−	0.00444476i	−0.709326	+	0.704881i	$0.751000\pi$
$158$		0			0
$159$	−21.3009	+	12.2981i	−1.68927	+	0.975303i
$160$		0			0
$161$	−9.08634	−	9.08634i	−0.716104	−	0.716104i
$162$		0			0
$163$	15.4522	+	8.92131i	1.21031	+	0.698771i	0.962826	−	0.270122i	$-0.0870639\pi$
$163$	15.4522	+	8.92131i	1.21031	+	0.698771i	0.247481	+	0.968893i	$0.420397\pi$
$164$		0			0
$165$	5.24539	+	12.3634i	0.408353	+	0.962487i
$166$		0			0
$167$	−1.27427	−	2.20710i	−0.0986060	−	0.170791i	0.812502	−	0.582959i	$-0.198105\pi$
$167$	−1.27427	−	2.20710i	−0.0986060	−	0.170791i	−0.911108	+	0.412168i	$0.864772\pi$
$168$		0			0
$169$	10.0356	−	8.26363i	0.771966	−	0.635664i
$170$		0			0
$171$	−3.92151	+	14.6353i	−0.299886	+	1.11919i
$172$		0			0
$173$	−13.6460	+	3.65644i	−1.03749	+	0.277994i	−0.737071	−	0.675815i	$-0.763792\pi$
$173$	−13.6460	+	3.65644i	−1.03749	+	0.277994i	−0.300415	+	0.953809i	$0.597125\pi$
$174$		0			0
$175$	−12.7308	−	3.17887i	−0.962355	−	0.240300i
$176$		0			0
$177$	−10.1604			−0.763699
$178$		0			0
$179$	7.85350	+	13.6027i	0.586998	+	1.01671i	0.994623	+	0.103561i	$0.0330238\pi$
$179$	7.85350	+	13.6027i	0.586998	+	1.01671i	−0.407625	+	0.913149i	$0.633643\pi$
$180$		0			0
$181$		−	7.87942i		−	0.585673i	−0.956163	−	0.292836i	$-0.905401\pi$
$181$		−	7.87942i		−	0.585673i	0.956163	−	0.292836i	$-0.0945991\pi$
$182$		0			0
$183$	11.7622	−	11.7622i	0.869490	−	0.869490i
$184$		0			0
$185$	2.78365	−	22.6382i	0.204658	−	1.66440i
$186$		0			0
$187$			0.666147i			0.0487135i
$188$		0			0
$189$	47.1075	−	12.6224i	3.42656	−	0.918145i
$190$		0			0
$191$	−9.41812	+	16.3127i	−0.681471	+	1.18034i	0.293061	+	0.956094i	$0.405326\pi$
$191$	−9.41812	+	16.3127i	−0.681471	+	1.18034i	−0.974532	+	0.224249i	$0.928007\pi$
$192$		0			0
$193$	21.1878	−	12.2328i	1.52513	−	0.880533i	0.525572	−	0.850749i	$-0.323851\pi$
$193$	21.1878	−	12.2328i	1.52513	−	0.880533i	0.999556	−	0.0297844i	$-0.00948208\pi$
$194$		0			0
$195$	23.0999	+	14.5892i	1.65421	+	1.04476i
$196$		0			0
$197$	−12.2642	+	7.08076i	−0.873791	+	0.504484i	−0.868606	−	0.495503i	$-0.834984\pi$
$197$	−12.2642	+	7.08076i	−0.873791	+	0.504484i	−0.00518489	+	0.999987i	$0.501650\pi$
$198$		0			0
$199$	−1.57563	+	2.72908i	−0.111694	+	0.193459i	−0.916453	−	0.400142i	$-0.868961\pi$
$199$	−1.57563	+	2.72908i	−0.111694	+	0.193459i	0.804760	+	0.593601i	$0.202294\pi$
$200$		0			0
$201$	26.1023	−	6.99410i	1.84112	−	0.493326i
$202$		0			0
$203$		−	19.0518i		−	1.33718i
$204$		0			0
$205$	−10.8849	+	8.50114i	−0.760234	+	0.593746i
$206$		0			0
$207$	−29.3740	+	29.3740i	−2.04164	+	2.04164i
$208$		0			0
$209$			3.16530i			0.218949i
$210$		0			0
$211$	−0.323466	−	0.560259i	−0.0222683	−	0.0385698i	0.854677	−	0.519161i	$-0.173755\pi$
$211$	−0.323466	−	0.560259i	−0.0222683	−	0.0385698i	−0.876945	+	0.480591i	$0.840422\pi$
$212$		0			0
$213$	−14.1203			−0.967509
$214$		0			0
$215$	−3.42039	−	1.38263i	−0.233269	−	0.0942943i
$216$		0			0
$217$	−10.6915	+	2.86479i	−0.725788	+	0.194474i
$218$		0			0
$219$	9.82709	−	36.6752i	0.664053	−	2.47828i
$220$		0			0
$221$	0.772139	+	1.11367i	0.0519397	+	0.0749137i
$222$		0			0
$223$	6.40121	+	11.0872i	0.428657	+	0.742456i	0.996754	−	0.0805058i	$-0.0256536\pi$
$223$	6.40121	+	11.0872i	0.428657	+	0.742456i	−0.568097	+	0.822961i	$0.692320\pi$
$224$		0			0
$225$	−10.2765	+	41.1556i	−0.685102	+	2.74370i
$226$		0			0
$227$	−9.01862	−	5.20690i	−0.598587	−	0.345594i	0.169899	−	0.985462i	$-0.445656\pi$
$227$	−9.01862	−	5.20690i	−0.598587	−	0.345594i	−0.768485	+	0.639867i	$0.778989\pi$
$228$		0			0
$229$	−4.26361	−	4.26361i	−0.281747	−	0.281747i	0.552058	−	0.833806i	$-0.313843\pi$
$229$	−4.26361	−	4.26361i	−0.281747	−	0.281747i	−0.833806	+	0.552058i	$0.813843\pi$
$230$		0			0
$231$	13.6503	−	7.88100i	0.898124	−	0.518532i
$232$		0			0
$233$	−0.786053	−	0.786053i	−0.0514960	−	0.0514960i	0.680890	−	0.732386i	$-0.261593\pi$
$233$	−0.786053	−	0.786053i	−0.0514960	−	0.0514960i	−0.732386	+	0.680890i	$0.761593\pi$
$234$		0			0
$235$	2.13792	+	1.61162i	0.139462	+	0.105131i
$236$		0			0
$237$	−2.38991	+	8.91926i	−0.155241	+	0.579368i
$238$		0			0
$239$	18.7521	−	18.7521i	1.21297	−	1.21297i	0.242925	−	0.970045i	$-0.421893\pi$
$239$	18.7521	−	18.7521i	1.21297	−	1.21297i	0.970045	−	0.242925i	$-0.0781068\pi$
$240$		0			0
$241$	−2.89785	−	10.8149i	−0.186667	−	0.696652i	−0.994267	−	0.106921i	$-0.965901\pi$
$241$	−2.89785	−	10.8149i	−0.186667	−	0.696652i	0.807600	−	0.589730i	$-0.200766\pi$
$242$		0			0
$243$	−18.4823	−	68.9767i	−1.18564	−	4.42486i
$244$		0			0
$245$	0.0308125	−	0.250585i	0.00196854	−	0.0160093i
$246$		0			0
$247$	3.66894	+	5.29179i	0.233449	+	0.336709i
$248$		0			0
$249$	−36.8033	−	9.86140i	−2.33231	−	0.624941i
$250$		0			0
$251$	−24.6347	−	14.2228i	−1.55493	−	0.897737i	−0.997729	−	0.0673574i	$-0.978543\pi$
$251$	−24.6347	−	14.2228i	−1.55493	−	0.897737i	−0.557198	−	0.830380i	$-0.688123\pi$
$252$		0			0
$253$	−4.33917	+	7.51566i	−0.272801	+	0.472505i
$254$		0			0
$255$	−1.71440	+	2.27426i	−0.107360	+	0.142420i
$256$		0			0
$257$	−25.6836	−	6.88190i	−1.60210	−	0.429281i	−0.656423	−	0.754393i	$-0.727931\pi$
$257$	−25.6836	−	6.88190i	−1.60210	−	0.429281i	−0.945675	+	0.325112i	$0.894598\pi$
$258$		0			0
$259$	−26.7691			−1.66335
$260$		0			0
$261$	−61.5902			−3.81234
$262$		0			0
$263$	−10.6890	−	2.86411i	−0.659112	−	0.176609i	−0.0862670	−	0.996272i	$-0.527494\pi$
$263$	−10.6890	−	2.86411i	−0.659112	−	0.176609i	−0.572845	+	0.819663i	$0.694160\pi$
$264$		0			0
$265$	−16.0721	+	2.25592i	−0.987302	+	0.138580i
$266$		0			0
$267$	12.5259	−	21.6956i	0.766575	−	1.32775i
$268$		0			0
$269$	3.97689	+	2.29606i	0.242475	+	0.139993i	0.616314	−	0.787501i	$-0.288625\pi$
$269$	3.97689	+	2.29606i	0.242475	+	0.139993i	−0.373839	+	0.927494i	$0.621959\pi$
$270$		0			0
$271$	4.90421	+	1.31408i	0.297909	+	0.0798245i	0.404678	−	0.914459i	$-0.367384\pi$
$271$	4.90421	+	1.31408i	0.297909	+	0.0798245i	−0.106768	+	0.994284i	$0.534050\pi$
$272$		0			0
$273$	13.6858	−	28.9978i	0.828301	−	1.75503i
$274$		0			0
$275$	0.151558	+	8.86047i	0.00913931	+	0.534306i
$276$		0			0
$277$	4.33613	+	16.1826i	0.260533	+	0.972321i	0.964928	+	0.262513i	$0.0845514\pi$
$277$	4.33613	+	16.1826i	0.260533	+	0.972321i	−0.704396	+	0.709807i	$0.748782\pi$
$278$		0			0
$279$	9.26118	+	34.5632i	0.554452	+	2.06924i
$280$		0			0
$281$	18.3528	−	18.3528i	1.09483	−	1.09483i	0.0998291	−	0.995005i	$-0.468170\pi$
$281$	18.3528	−	18.3528i	1.09483	−	1.09483i	0.995005	−	0.0998291i	$-0.0318296\pi$
$282$		0			0
$283$	1.56023	−	5.82286i	0.0927461	−	0.346133i	−0.903922	−	0.427697i	$-0.859325\pi$
$283$	1.56023	−	5.82286i	0.0927461	−	0.346133i	0.996668	+	0.0815641i	$0.0259915\pi$
$284$		0			0
$285$	−8.14625	+	10.8065i	−0.482542	+	0.640122i
$286$		0			0
$287$	11.4617	+	11.4617i	0.676565	+	0.676565i
$288$		0			0
$289$	14.6001	−	8.42937i	0.858829	−	0.495845i
$290$		0			0
$291$	4.01718	+	4.01718i	0.235491	+	0.235491i
$292$		0			0
$293$	13.6280	+	7.86812i	0.796156	+	0.459661i	0.842125	−	0.539282i	$-0.181304\pi$
$293$	13.6280	+	7.86812i	0.796156	+	0.459661i	−0.0459695	+	0.998943i	$0.514638\pi$
$294$		0			0
$295$	−6.21564	−	2.51255i	−0.361888	−	0.146286i
$296$		0			0
$297$	−16.4683	−	28.5239i	−0.955586	−	1.65512i
$298$		0			0
$299$	1.45722	+	17.5944i	0.0842733	+	1.01751i
$300$		0			0
$301$	−1.12065	+	4.18232i	−0.0645932	+	0.241065i
$302$		0			0
$303$	46.1501	−	12.3659i	2.65125	−	0.710401i
$304$		0			0
$305$	10.1043	−	4.28692i	0.578569	−	0.245469i
$306$		0			0
$307$	28.0727			1.60219			0.801096	−	0.598536i	$-0.204251\pi$
$307$	28.0727			1.60219			0.801096	+	0.598536i	$0.204251\pi$
$308$		0			0
$309$	−19.6865	−	34.0980i	−1.11992	−	1.93977i
$310$		0			0
$311$			7.33583i			0.415977i	0.978131	+	0.207988i	$0.0666916\pi$
$311$			7.33583i			0.415977i	−0.978131	+	0.207988i	$0.933308\pi$
$312$		0			0
$313$	−6.41291	+	6.41291i	−0.362479	+	0.362479i	−0.864725	−	0.502246i	$-0.832507\pi$
$313$	−6.41291	+	6.41291i	−0.362479	+	0.362479i	0.502246	+	0.864725i	$0.332507\pi$
$314$		0			0
$315$	49.4125	+	6.07586i	2.78408	+	0.342336i
$316$		0			0
$317$			31.9597i			1.79503i	0.440980	+	0.897517i	$0.354631\pi$
$317$			31.9597i			1.79503i	−0.440980	+	0.897517i	$0.645369\pi$
$318$		0			0
$319$	−12.4283	+	3.33016i	−0.695853	+	0.186453i
$320$		0			0
$321$	−15.2800	+	26.4657i	−0.852845	+	1.47717i
$322$		0			0
$323$	−0.581320	+	0.335625i	−0.0323455	+	0.0186747i
$324$		0			0
$325$	10.5237	+	14.6374i	0.583748	+	0.811935i
$326$		0			0
$327$	35.2006	−	20.3231i	1.94660	−	1.12387i
$328$		0			0
$329$	1.57110	−	2.72122i	0.0866173	−	0.150026i
$330$		0			0
$331$	4.58649	−	1.22895i	0.252096	−	0.0675489i	−0.130558	−	0.991441i	$-0.541677\pi$
$331$	4.58649	−	1.22895i	0.252096	−	0.0675489i	0.382654	+	0.923892i	$0.375010\pi$
$332$		0			0
$333$			86.5383i			4.74227i
$334$		0			0
$335$	17.6978	+	2.17616i	0.966932	+	0.118896i
$336$		0			0
$337$	23.5944	−	23.5944i	1.28527	−	1.28527i	0.347645	−	0.937626i	$-0.386982\pi$
$337$	23.5944	−	23.5944i	1.28527	−	1.28527i	0.937626	−	0.347645i	$-0.113018\pi$
$338$		0			0
$339$			9.53258i			0.517738i
$340$		0			0
$341$	3.73764	+	6.47379i	0.202405	+	0.350575i
$342$		0			0
$343$	−18.6666			−1.00790
$344$		0			0
$345$	−34.1565	+	14.4915i	−1.83892	+	0.780197i
$346$		0			0
$347$	3.53586	−	0.947430i	0.189815	−	0.0508607i	−0.162659	−	0.986682i	$-0.552007\pi$
$347$	3.53586	−	0.947430i	0.189815	−	0.0508607i	0.352474	+	0.935822i	$0.385340\pi$
$348$		0			0
$349$	−0.937727	+	3.49965i	−0.0501954	+	0.187332i	−0.986471	−	0.163933i	$-0.947582\pi$
$349$	−0.937727	+	3.49965i	−0.0501954	+	0.187332i	0.936276	+	0.351265i	$0.114248\pi$
$350$		0			0
$351$	−60.5943	−	28.5980i	−3.23428	−	1.52645i
$352$		0			0
$353$	4.69419	+	8.13057i	0.249846	+	0.432747i	0.963483	−	0.267769i	$-0.0862866\pi$
$353$	4.69419	+	8.13057i	0.249846	+	0.432747i	−0.713637	+	0.700516i	$0.752953\pi$
$354$		0			0
$355$	−8.63816	−	3.49180i	−0.458466	−	0.185326i
$356$		0			0
$357$	2.89475	+	1.67129i	0.153207	+	0.0884539i
$358$		0			0
$359$	9.90682	+	9.90682i	0.522862	+	0.522862i	0.918435	−	0.395573i	$-0.129454\pi$
$359$	9.90682	+	9.90682i	0.522862	+	0.522862i	−0.395573	+	0.918435i	$0.629454\pi$
$360$		0			0
$361$	13.6922	−	7.90522i	0.720645	−	0.416064i
$362$		0			0
$363$	18.8314	+	18.8314i	0.988393	+	0.988393i
$364$		0			0
$365$	15.0811	−	20.0061i	0.789383	−	1.04716i
$366$		0			0
$367$	1.45811	−	5.44176i	0.0761130	−	0.284057i	−0.917370	−	0.398035i	$-0.869692\pi$
$367$	1.45811	−	5.44176i	0.0761130	−	0.284057i	0.993483	+	0.113977i	$0.0363591\pi$
$368$		0			0
$369$	37.0531	−	37.0531i	1.92891	−	1.92891i
$370$		0			0
$371$	4.92991	+	18.3987i	0.255948	+	0.955211i
$372$		0			0
$373$	−2.73824	−	10.2192i	−0.141780	−	0.529132i	−0.999878	−	0.0156446i	$-0.995020\pi$
$373$	−2.73824	−	10.2192i	−0.141780	−	0.529132i	0.858097	−	0.513487i	$-0.171647\pi$
$374$		0			0
$375$	−22.2859	+	30.6401i	−1.15084	+	1.58225i
$376$		0			0
$377$	−16.9178	+	19.9733i	−0.871312	+	1.02868i
$378$		0			0
$379$	−25.5928	−	6.85758i	−1.31462	−	0.352250i	−0.467657	−	0.883910i	$-0.654902\pi$
$379$	−25.5928	−	6.85758i	−1.31462	−	0.352250i	−0.846958	+	0.531660i	$0.821569\pi$
$380$		0			0
$381$	19.4385	+	11.2228i	0.995863	+	0.574962i
$382$		0			0
$383$	11.4514	−	19.8344i	0.585139	−	1.01349i	−0.409720	−	0.912212i	$-0.634373\pi$
$383$	11.4514	−	19.8344i	0.585139	−	1.01349i	0.994858	−	0.101278i	$-0.0322932\pi$
$384$		0			0
$385$	10.2995	−	1.44566i	0.524912	−	0.0736778i
$386$		0			0
$387$	13.5205	+	3.62280i	0.687285	+	0.184157i
$388$		0			0
$389$	1.00709			0.0510614			0.0255307	−	0.999674i	$-0.491872\pi$
$389$	1.00709			0.0510614			0.0255307	+	0.999674i	$0.491872\pi$
$390$		0			0
$391$	−1.84037			−0.0930717
$392$		0			0
$393$	−8.78339	−	2.35350i	−0.443063	−	0.118718i
$394$		0			0
$395$	−3.66767	+	4.86539i	−0.184541	+	0.244805i
$396$		0			0
$397$	0.282311	−	0.488978i	0.0141688	−	0.0245411i	−0.858854	−	0.512220i	$-0.828823\pi$
$397$	0.282311	−	0.488978i	0.0141688	−	0.0245411i	0.873023	+	0.487679i	$0.162156\pi$
$398$		0			0
$399$	13.7549	+	7.94139i	0.688606	+	0.397567i
$400$		0			0
$401$	2.79748	+	0.749581i	0.139699	+	0.0374323i	0.327991	−	0.944681i	$-0.393628\pi$
$401$	2.79748	+	0.749581i	0.139699	+	0.0374323i	−0.188292	+	0.982113i	$0.560295\pi$
$402$		0			0
$403$	13.7525	+	6.49061i	0.685061	+	0.323321i
$404$		0			0
$405$	10.2402	−	83.2789i	0.508837	−	4.13816i
$406$		0			0
$407$	4.67910	+	17.4626i	0.231934	+	0.865591i
$408$		0			0
$409$	7.82267	+	29.1946i	0.386806	+	1.44358i	0.835300	+	0.549795i	$0.185294\pi$
$409$	7.82267	+	29.1946i	0.386806	+	1.44358i	−0.448493	+	0.893786i	$0.648039\pi$
$410$		0			0
$411$	−4.94569	+	4.94569i	−0.243953	+	0.243953i
$412$		0			0
$413$	−2.03648	+	7.60024i	−0.100208	+	0.373983i
$414$		0			0
$415$	−20.0759	−	15.1338i	−0.985488	−	0.742889i
$416$		0			0
$417$	35.3271	+	35.3271i	1.72997	+	1.72997i
$418$		0			0
$419$	−5.06888	+	2.92652i	−0.247631	+	0.142970i	−0.618679	−	0.785644i	$-0.712332\pi$
$419$	−5.06888	+	2.92652i	−0.247631	+	0.142970i	0.371048	+	0.928614i	$0.378998\pi$
$420$		0			0
$421$	−10.2231	−	10.2231i	−0.498244	−	0.498244i	0.412647	−	0.910891i	$-0.364604\pi$
$421$	−10.2231	−	10.2231i	−0.498244	−	0.498244i	−0.910891	+	0.412647i	$0.864604\pi$
$422$		0			0
$423$	−8.79706	−	5.07899i	−0.427728	−	0.246949i
$424$		0			0
$425$	−1.61119	+	0.967333i	−0.0781542	+	0.0469225i
$426$		0			0
$427$	−6.44095	−	11.1560i	−0.311699	−	0.539879i
$428$		0			0
$429$	−21.3087	−	3.85915i	−1.02879	−	0.186322i
$430$		0			0
$431$	−9.50264	+	35.4643i	−0.457726	+	1.70826i	0.222221	+	0.974996i	$0.428669\pi$
$431$	−9.50264	+	35.4643i	−0.457726	+	1.70826i	−0.679947	+	0.733261i	$0.737997\pi$
$432$		0			0
$433$	−22.3719	+	5.99453i	−1.07513	+	0.288079i	−0.752597	−	0.658481i	$-0.771199\pi$
$433$	−22.3719	+	5.99453i	−1.07513	+	0.288079i	−0.322528	+	0.946560i	$0.604533\pi$
$434$		0			0
$435$	−51.0015	−	20.6163i	−2.44533	−	0.988477i
$436$		0			0
$437$	−8.74483			−0.418322
$438$		0			0
$439$	1.34925	+	2.33697i	0.0643962	+	0.111537i	0.896426	−	0.443193i	$-0.146155\pi$
$439$	1.34925	+	2.33697i	0.0643962	+	0.111537i	−0.832030	+	0.554731i	$0.812821\pi$
$440$		0			0
$441$			0.957902i			0.0456144i
$442$		0			0
$443$	−9.66186	+	9.66186i	−0.459049	+	0.459049i	−0.898343	−	0.439295i	$-0.855228\pi$
$443$	−9.66186	+	9.66186i	−0.459049	+	0.459049i	0.439295	+	0.898343i	$0.355228\pi$
$444$		0			0
$445$	13.0279	−	10.1748i	0.617580	−	0.482333i
$446$		0			0
$447$		−	10.7761i		−	0.509692i
$448$		0			0
$449$	1.88121	−	0.504069i	0.0887799	−	0.0237885i	−0.214156	−	0.976800i	$-0.568700\pi$
$449$	1.88121	−	0.504069i	0.0887799	−	0.0237885i	0.302936	+	0.953011i	$0.402033\pi$
$450$		0			0
$451$	5.47353	−	9.48044i	0.257739	−	0.446416i
$452$		0			0
$453$	−29.8948	+	17.2598i	−1.40458	+	0.810934i
$454$		0			0
$455$	15.5432	−	14.3552i	0.728675	−	0.672981i
$456$		0			0
$457$	11.3078	−	6.52855i	0.528956	−	0.305393i	−0.211635	−	0.977349i	$-0.567879\pi$
$457$	11.3078	−	6.52855i	0.528956	−	0.305393i	0.740591	+	0.671956i	$0.234546\pi$
$458$		0			0
$459$	3.49235	−	6.04893i	0.163009	−	0.282340i
$460$		0			0
$461$	−1.43252	+	0.383843i	−0.0667191	+	0.0178773i	−0.292024	−	0.956411i	$-0.594329\pi$
$461$	−1.43252	+	0.383843i	−0.0667191	+	0.0178773i	0.225305	+	0.974288i	$0.427662\pi$
$462$		0			0
$463$		−	27.4825i		−	1.27722i	−0.769531	−	0.638609i	$-0.779510\pi$
$463$		−	27.4825i		−	1.27722i	0.769531	−	0.638609i	$-0.220490\pi$
$464$		0			0
$465$	−3.90049	+	31.7211i	−0.180881	+	1.47103i
$466$		0			0
$467$	0.0831885	−	0.0831885i	0.00384950	−	0.00384950i	−0.705179	−	0.709029i	$-0.749134\pi$
$467$	0.0831885	−	0.0831885i	0.00384950	−	0.00384950i	0.709029	+	0.705179i	$0.249134\pi$
$468$		0			0
$469$		−	20.9271i		−	0.966326i
$470$		0			0
$471$	0.133452	+	0.231146i	0.00614916	+	0.0106507i
$472$		0			0
$473$	2.92419			0.134455
$474$		0			0
$475$	−7.65583	+	4.59644i	−0.351273	+	0.210899i
$476$		0			0
$477$	59.4786	−	15.9372i	2.72334	−	0.729716i
$478$		0			0
$479$	−6.12267	+	22.8501i	−0.279752	+	1.04405i	0.672837	+	0.739790i	$0.265075\pi$
$479$	−6.12267	+	22.8501i	−0.279752	+	1.04405i	−0.952589	+	0.304259i	$0.901591\pi$
$480$		0			0
$481$	28.0638	+	23.7707i	1.27960	+	1.08385i
$482$		0			0
$483$	21.7730	+	37.7119i	0.990704	+	1.71595i
$484$		0			0
$485$	1.46412	+	3.45093i	0.0664822	+	0.156699i
$486$		0			0
$487$	−18.5622	−	10.7169i	−0.841133	−	0.485628i	0.0165161	−	0.999864i	$-0.494743\pi$
$487$	−18.5622	−	10.7169i	−0.841133	−	0.485628i	−0.857649	+	0.514235i	$0.828076\pi$
$488$		0			0
$489$	−42.7550	−	42.7550i	−1.93345	−	1.93345i
$490$		0			0
$491$	−13.2578	+	7.65438i	−0.598315	+	0.345437i	−0.768378	−	0.639996i	$-0.778936\pi$
$491$	−13.2578	+	7.65438i	−0.598315	+	0.345437i	0.170063	+	0.985433i	$0.445603\pi$
$492$		0			0
$493$	−1.92941	−	1.92941i	−0.0868961	−	0.0868961i
$494$		0			0
$495$	−4.67349	−	33.2959i	−0.210058	−	1.49654i
$496$		0			0
$497$	−2.83019	+	10.5624i	−0.126951	+	0.473789i
$498$		0			0
$499$	8.64170	−	8.64170i	0.386856	−	0.386856i	−0.486709	−	0.873564i	$-0.661803\pi$
$499$	8.64170	−	8.64170i	0.386856	−	0.386856i	0.873564	+	0.486709i	$0.161803\pi$
$500$		0			0
$501$	2.23528	+	8.34216i	0.0998648	+	0.372700i
$502$		0			0
$503$	5.77147	+	21.5394i	0.257337	+	0.960396i	0.966775	+	0.255628i	$0.0822822\pi$
$503$	5.77147	+	21.5394i	0.257337	+	0.960396i	−0.709438	+	0.704768i	$0.751051\pi$
$504$		0			0
$505$	31.2905	+	3.84754i	1.39241	+	0.171213i
$506$		0			0
$507$	−40.0974	+	18.2474i	−1.78079	+	0.810397i
$508$		0			0
$509$	24.4129	+	6.54140i	1.08208	+	0.289943i	0.755448	−	0.655209i	$-0.227419\pi$
$509$	24.4129	+	6.54140i	1.08208	+	0.289943i	0.326633	+	0.945151i	$0.394086\pi$
$510$		0			0
$511$	−25.4644	−	14.7019i	−1.12648	−	0.650373i
$512$		0			0
$513$	16.5945	−	28.7424i	0.732663	−	1.26901i
$514$		0			0
$515$	−3.61122	−	25.7278i	−0.159129	−	1.13370i
$516$		0			0
$517$	−2.04979	−	0.549239i	−0.0901495	−	0.0241555i
$518$		0			0
$519$	47.8746			2.10146
$520$		0			0
$521$	19.3421			0.847393			0.423697	−	0.905804i	$-0.360732\pi$
$521$	19.3421			0.847393			0.423697	+	0.905804i	$0.360732\pi$
$522$		0			0
$523$	−30.0808	−	8.06014i	−1.31534	−	0.352445i	−0.468112	−	0.883669i	$-0.655066\pi$
$523$	−30.0808	−	8.06014i	−1.31534	−	0.352445i	−0.847231	+	0.531224i	$0.821732\pi$
$524$		0			0
$525$	38.8836	+	21.5713i	1.69702	+	0.941450i
$526$		0			0
$527$	−0.792625	+	1.37287i	−0.0345273	+	0.0598030i
$528$		0			0
$529$	−0.845038	−	0.487883i	−0.0367408	−	0.0212123i
$530$		0			0
$531$	24.5698	+	6.58346i	1.06624	+	0.285698i
$532$		0			0
$533$	−1.83818	−	22.1940i	−0.0796202	−	0.961327i
$534$		0			0
$535$	−15.8923	+	12.4119i	−0.687082	+	0.536614i
$536$		0			0
$537$	−13.7763	−	51.4139i	−0.594492	−	2.21867i
$538$		0			0
$539$	0.0517935	+	0.193296i	0.00223090	+	0.00832584i
$540$		0			0
$541$	10.9495	−	10.9495i	0.470757	−	0.470757i	−0.431403	−	0.902159i	$-0.641981\pi$
$541$	10.9495	−	10.9495i	0.470757	−	0.470757i	0.902159	+	0.431403i	$0.141981\pi$
$542$		0			0
$543$	−6.91089	+	25.7918i	−0.296575	+	1.10683i
$544$		0			0
$545$	26.5598	−	3.72800i	1.13770	−	0.159690i
$546$		0			0
$547$	25.2846	+	25.2846i	1.08109	+	1.08109i	0.996408	+	0.0846839i	$0.0269880\pi$
$547$	25.2846	+	25.2846i	1.08109	+	1.08109i	0.0846839	+	0.996408i	$0.473012\pi$
$548$		0			0
$549$	−36.0649	+	20.8221i	−1.53921	+	0.888664i
$550$		0			0
$551$	−9.16789	−	9.16789i	−0.390565	−	0.390565i
$552$		0			0
$553$	6.19284	+	3.57544i	0.263347	+	0.152043i
$554$		0			0
$555$	−28.9673	+	71.6605i	−1.22959	+	3.04182i
$556$		0			0
$557$	−8.46780	−	14.6667i	−0.358792	−	0.621447i	0.628967	−	0.777432i	$-0.283478\pi$
$557$	−8.46780	−	14.6667i	−0.358792	−	0.621447i	−0.987759	+	0.155985i	$0.950145\pi$
$558$		0			0
$559$	4.88870	−	3.38947i	0.206770	−	0.143359i
$560$		0			0
$561$	0.584265	−	2.18051i	0.0246677	−	0.0920610i
$562$		0			0
$563$	24.9021	−	6.67250i	1.04950	−	0.281212i	0.307454	−	0.951563i	$-0.400523\pi$
$563$	24.9021	−	6.67250i	1.04950	−	0.281212i	0.742044	+	0.670351i	$0.233856\pi$
$564$		0			0
$565$	−2.35730	+	5.83159i	−0.0991725	+	0.245337i
$566$		0			0
$567$	−98.4751			−4.13557
$568$		0			0
$569$	17.6372	+	30.5485i	0.739390	+	1.28066i	0.952770	+	0.303692i	$0.0982195\pi$
$569$	17.6372	+	30.5485i	0.739390	+	1.28066i	−0.213380	+	0.976969i	$0.568447\pi$
$570$		0			0
$571$		−	34.8260i		−	1.45742i	−0.684821	−	0.728711i	$-0.740120\pi$
$571$		−	34.8260i		−	1.45742i	0.684821	−	0.728711i	$-0.259880\pi$
$572$		0			0
$573$	45.1359	−	45.1359i	1.88558	−	1.88558i
$574$		0			0
$575$	−24.4789	+	0.418713i	−1.02084	+	0.0174615i
$576$		0			0
$577$		−	27.5561i		−	1.14717i	−0.819145	−	0.573587i	$-0.805552\pi$
$577$		−	27.5561i		−	1.14717i	0.819145	−	0.573587i	$-0.194448\pi$
$578$		0			0
$579$	−80.0833	+	21.4582i	−3.32815	+	0.891774i
$580$		0			0
$581$	−14.7532	+	25.5533i	−0.612067	+	1.06013i
$582$		0			0
$583$	11.1405	−	6.43198i	0.461393	−	0.266385i
$584$		0			0
$585$	−46.4069	−	50.2474i	−1.91869	−	2.07747i
$586$		0			0
$587$	1.20056	−	0.693144i	0.0495524	−	0.0286091i	−0.475019	−	0.879975i	$-0.657559\pi$
$587$	1.20056	−	0.693144i	0.0495524	−	0.0286091i	0.524572	+	0.851366i	$0.324226\pi$
$588$		0			0
$589$	−3.76628	+	6.52340i	−0.155187	+	0.268792i
$590$		0			0
$591$	46.3551	−	12.4208i	1.90679	−	0.510924i
$592$		0			0
$593$		−	11.7399i		−	0.482102i	−0.970512	−	0.241051i	$-0.922508\pi$
$593$		−	11.7399i		−	0.482102i	0.970512	−	0.241051i	$-0.0774921\pi$
$594$		0			0
$595$	1.35759	+	1.73826i	0.0556556	+	0.0712616i
$596$		0			0
$597$	7.55116	−	7.55116i	0.309048	−	0.309048i
$598$		0			0
$599$		−	28.5588i		−	1.16688i	−0.812155	−	0.583441i	$-0.801706\pi$
$599$		−	28.5588i		−	1.16688i	0.812155	−	0.583441i	$-0.198294\pi$
$600$		0			0
$601$	−16.1665	−	28.0013i	−0.659447	−	1.14220i	−0.980759	−	0.195222i	$-0.937457\pi$
$601$	−16.1665	−	28.0013i	−0.659447	−	1.14220i	0.321312	−	0.946973i	$-0.395876\pi$
$602$		0			0
$603$	−67.6526			−2.75503
$604$		0			0
$605$	6.86338	+	16.1770i	0.279036	+	0.657688i
$606$		0			0
$607$	12.1211	−	3.24785i	0.491982	−	0.131826i	−0.00429458	−	0.999991i	$-0.501367\pi$
$607$	12.1211	−	3.24785i	0.491982	−	0.131826i	0.496276	+	0.868165i	$0.334700\pi$
$608$		0			0
$609$	−16.7100	+	62.3626i	−0.677124	+	2.52706i
$610$		0			0
$611$	−4.06349	+	1.45771i	−0.164391	+	0.0589726i
$612$		0			0
$613$	−6.23790	−	10.8044i	−0.251946	−	0.436384i	0.712115	−	0.702063i	$-0.247737\pi$
$613$	−6.23790	−	10.8044i	−0.251946	−	0.436384i	−0.964062	+	0.265679i	$0.914404\pi$
$614$		0			0
$615$	43.0858	−	18.2800i	1.73739	−	0.737119i
$616$		0			0
$617$	−31.6876	−	18.2948i	−1.27569	−	0.736523i	−0.299641	−	0.954052i	$-0.596867\pi$
$617$	−31.6876	−	18.2948i	−1.27569	−	0.736523i	−0.976054	+	0.217530i	$0.930200\pi$
$618$		0			0
$619$	−1.93560	−	1.93560i	−0.0777985	−	0.0777985i	0.667137	−	0.744935i	$-0.267520\pi$
$619$	−1.93560	−	1.93560i	−0.0777985	−	0.0777985i	−0.744935	+	0.667137i	$0.767520\pi$
$620$		0			0
$621$	78.8034	−	45.4971i	3.16227	−	1.82574i
$622$		0			0
$623$	−13.7183	−	13.7183i	−0.549611	−	0.549611i
$624$		0			0
$625$	−21.2105	+	13.2331i	−0.848419	+	0.529326i
$626$		0			0
$627$	2.77623	−	10.3610i	0.110872	−	0.413779i
$628$		0			0
$629$	−2.71095	+	2.71095i	−0.108092	+	0.108092i
$630$		0			0
$631$	4.99996	+	18.6601i	0.199045	+	0.742848i	0.991182	+	0.132504i	$0.0423018\pi$
$631$	4.99996	+	18.6601i	0.199045	+	0.742848i	−0.792137	+	0.610343i	$0.791031\pi$
$632$		0			0
$633$	0.567411	+	2.11761i	0.0225526	+	0.0841674i
$634$		0			0
$635$	9.11628	+	11.6725i	0.361768	+	0.463209i
$636$		0			0
$637$	0.310641	+	0.263120i	0.0123080	+	0.0104252i
$638$		0			0
$639$	34.1458	+	9.14934i	1.35079	+	0.361942i
$640$		0			0
$641$	−0.725792	−	0.419036i	−0.0286671	−	0.0165509i	0.485598	−	0.874182i	$-0.338602\pi$
$641$	−0.725792	−	0.419036i	−0.0286671	−	0.0165509i	−0.514265	+	0.857631i	$0.671935\pi$
$642$		0			0
$643$	−12.6729	+	21.9500i	−0.499769	+	0.865625i	−1.00000		0.000267216i	$-0.999915\pi$
$643$	−12.6729	+	21.9500i	−0.499769	+	0.865625i	0.500231	+	0.865892i	$0.333248\pi$
$644$		0			0
$645$	9.98334	+	7.52572i	0.393094	+	0.296325i
$646$		0			0
$647$	−17.6219	−	4.72177i	−0.692787	−	0.185632i	−0.104790	−	0.994494i	$-0.533417\pi$
$647$	−17.6219	−	4.72177i	−0.692787	−	0.185632i	−0.587998	+	0.808863i	$0.700084\pi$
$648$		0			0
$649$	5.31393			0.208590
$650$		0			0
$651$	37.5093			1.47011
$652$		0			0
$653$	−28.3039	−	7.58401i	−1.10762	−	0.296785i	−0.341755	−	0.939789i	$-0.611021\pi$
$653$	−28.3039	−	7.58401i	−1.10762	−	0.296785i	−0.765863	+	0.643004i	$0.777688\pi$
$654$		0			0
$655$	−4.79128	−	3.61180i	−0.187211	−	0.141125i
$656$		0			0
$657$	−47.5278	+	82.3205i	−1.85423	+	3.21163i
$658$		0			0
$659$	25.2957	+	14.6045i	0.985380	+	0.568909i	0.903890	−	0.427765i	$-0.140699\pi$
$659$	25.2957	+	14.6045i	0.985380	+	0.568909i	0.0814899	+	0.996674i	$0.474032\pi$
$660$		0			0
$661$	9.01504	+	2.41557i	0.350645	+	0.0939549i	0.429842	−	0.902904i	$-0.358569\pi$
$661$	9.01504	+	2.41557i	0.350645	+	0.0939549i	−0.0791977	+	0.996859i	$0.525236\pi$
$662$		0			0
$663$	−1.55067	−	4.32263i	−0.0602231	−	0.167877i
$664$		0			0
$665$	6.45079	+	8.25961i	0.250151	+	0.320294i
$666$		0			0
$667$	−9.20029	−	34.3360i	−0.356237	−	1.32949i
$668$		0			0
$669$	−11.2288	−	41.9063i	−0.434129	−	1.62019i
$670$		0			0
$671$	−6.15172	+	6.15172i	−0.237485	+	0.237485i
$672$		0			0
$673$	4.13494	−	15.4318i	0.159390	−	0.594852i	−0.839299	−	0.543670i	$-0.817034\pi$
$673$	4.13494	−	15.4318i	0.159390	−	0.594852i	0.998689	−	0.0511823i	$-0.0162989\pi$
$674$		0			0
$675$	45.0758	−	81.2518i	1.73497	−	3.12738i
$676$		0			0
$677$	−5.10291	−	5.10291i	−0.196121	−	0.196121i	0.602214	−	0.798335i	$-0.294285\pi$
$677$	−5.10291	−	5.10291i	−0.196121	−	0.196121i	−0.798335	+	0.602214i	$0.794285\pi$
$678$		0			0
$679$	3.81014	−	2.19979i	0.146220	−	0.0844200i
$680$		0			0
$681$	24.9539	+	24.9539i	0.956234	+	0.956234i
$682$		0			0
$683$	−23.5179	−	13.5781i	−0.899888	−	0.519550i	−0.0227240	−	0.999742i	$-0.507234\pi$
$683$	−23.5179	−	13.5781i	−0.899888	−	0.519550i	−0.877164	+	0.480191i	$0.840567\pi$
$684$		0			0
$685$	−4.24856	+	1.80253i	−0.162329	+	0.0688711i
$686$		0			0
$687$	10.2166	+	17.6956i	0.389787	+	0.675131i
$688$		0			0
$689$	11.1695	−	23.6662i	0.425523	−	0.901610i
$690$		0			0
$691$	7.84688	−	29.2849i	0.298509	−	1.11405i	−0.639881	−	0.768474i	$-0.721016\pi$
$691$	7.84688	−	29.2849i	0.298509	−	1.11405i	0.938390	−	0.345578i	$-0.112317\pi$
$692$		0			0
$693$	−38.1157	+	10.2131i	−1.44790	+	0.387963i
$694$		0			0
$695$	12.8755	+	30.3475i	0.488394	+	1.15114i
$696$		0			0
$697$	2.32149			0.0879328
$698$		0			0
$699$	1.88356	+	3.26243i	0.0712429	+	0.123396i
$700$		0			0
$701$			21.4987i			0.811995i	0.913874	+	0.405998i	$0.133076\pi$
$701$			21.4987i			0.811995i	−0.913874	+	0.405998i	$0.866924\pi$
$702$		0			0
$703$	−12.8815	+	12.8815i	−0.485835	+	0.485835i
$704$		0			0
$705$	−5.58455	−	7.15047i	−0.210326	−	0.269302i
$706$		0			0
$707$		−	37.0001i		−	1.39153i
$708$		0			0
$709$	34.6698	−	9.28974i	1.30205	−	0.348883i	0.459825	−	0.888009i	$-0.347912\pi$
$709$	34.6698	−	9.28974i	1.30205	−	0.348883i	0.842225	+	0.539126i	$0.181245\pi$
$710$		0			0
$711$	11.5586	−	20.0200i	0.433480	−	0.750809i
$712$		0			0
$713$	−17.8852	+	10.3260i	−0.669808	+	0.386714i
$714$		0			0
$715$	−12.0814	−	7.63026i	−0.451817	−	0.285356i
$716$		0			0
$717$	−77.8284	+	44.9342i	−2.90655	+	1.67810i
$718$		0			0
$719$	12.3572	−	21.4033i	0.460845	−	0.798207i	−0.538158	−	0.842844i	$-0.680880\pi$
$719$	12.3572	−	21.4033i	0.460845	−	0.798207i	0.999003	+	0.0446370i	$0.0142131\pi$
$720$		0			0
$721$	−29.4521	+	7.89167i	−1.09685	+	0.293901i
$722$		0			0
$723$			37.9423i			1.41109i
$724$		0			0
$725$	−26.1022	−	25.2242i	−0.969410	−	0.936804i
$726$		0			0
$727$	−18.6487	+	18.6487i	−0.691643	+	0.691643i	−0.962593	−	0.270950i	$-0.912662\pi$
$727$	−18.6487	+	18.6487i	−0.691643	+	0.691643i	0.270950	+	0.962593i	$0.412662\pi$
$728$		0			0
$729$			129.421i			4.79336i
$730$		0			0
$731$	0.310060	+	0.537040i	0.0114680	+	0.0198631i
$732$		0			0
$733$	−7.50510			−0.277207			−0.138604	−	0.990348i	$-0.544261\pi$
$733$	−7.50510			−0.277207			−0.138604	+	0.990348i	$0.544261\pi$
$734$		0			0
$735$	−0.320642	+	0.793218i	−0.0118271	+	0.0292583i
$736$		0			0
$737$	−13.6517	+	3.65796i	−0.502866	+	0.134743i
$738$		0			0
$739$	8.26789	−	30.8562i	0.304139	−	1.13506i	−0.629544	−	0.776965i	$-0.716758\pi$
$739$	8.26789	−	30.8562i	0.304139	−	1.13506i	0.933684	−	0.358099i	$-0.116575\pi$
$740$		0			0
$741$	−7.36826	−	20.5396i	−0.270680	−	0.754543i
$742$		0			0
$743$	1.67158	+	2.89526i	0.0613242	+	0.106217i	0.895058	−	0.445951i	$-0.147134\pi$
$743$	1.67158	+	2.89526i	0.0613242	+	0.106217i	−0.833733	+	0.552167i	$0.813801\pi$
$744$		0			0
$745$	2.66481	−	6.59231i	0.0976311	−	0.241524i
$746$		0			0
$747$	82.6080	+	47.6937i	3.02247	+	1.74502i
$748$		0			0
$749$	16.7345	+	16.7345i	0.611464	+	0.611464i
$750$		0			0
$751$	−27.6186	+	15.9456i	−1.00782	+	0.581864i	−0.910552	−	0.413395i	$-0.864343\pi$
$751$	−27.6186	+	15.9456i	−1.00782	+	0.581864i	−0.0972656	+	0.995258i	$0.531010\pi$
$752$		0			0
$753$	68.1624	+	68.1624i	2.48397	+	2.48397i
$754$		0			0
$755$	−22.5564	+	3.16607i	−0.820911	+	0.115225i
$756$		0			0
$757$	−1.91462	+	7.14545i	−0.0695879	+	0.259706i	−0.991952	−	0.126617i	$-0.959588\pi$
$757$	−1.91462	+	7.14545i	−0.0695879	+	0.259706i	0.922364	+	0.386322i	$0.126255\pi$
$758$		0			0
$759$	20.7953	−	20.7953i	0.754821	−	0.754821i
$760$		0			0
$761$	−2.23786	−	8.35181i	−0.0811224	−	0.302753i	0.913429	−	0.406997i	$-0.133424\pi$
$761$	−2.23786	−	8.35181i	−0.0811224	−	0.302753i	−0.994552	+	0.104244i	$0.966758\pi$
$762$		0			0
$763$	−8.14686	−	30.4045i	−0.294936	−	1.10072i
$764$		0			0
$765$	5.61938	−	4.38876i	0.203169	−	0.158676i
$766$		0			0
$767$	8.88389	−	6.15944i	0.320779	−	0.222405i
$768$		0			0
$769$	−15.8736	−	4.25333i	−0.572418	−	0.153379i	−0.0390126	−	0.999239i	$-0.512421\pi$
$769$	−15.8736	−	4.25333i	−0.572418	−	0.153379i	−0.533405	+	0.845860i	$0.679088\pi$
$770$		0			0
$771$	78.0344	+	45.0532i	2.81034	+	1.62255i
$772$		0			0
$773$	20.5283	−	35.5561i	0.738352	−	1.27886i	−0.214885	−	0.976639i	$-0.568938\pi$
$773$	20.5283	−	35.5561i	0.738352	−	1.27886i	0.953237	−	0.302223i	$-0.0977288\pi$
$774$		0			0
$775$	−10.2304	+	18.4409i	−0.367487	+	0.662418i
$776$		0			0
$777$	87.6236	+	23.4787i	3.14348	+	0.842293i
$778$		0			0
$779$	11.0309			0.395225
$780$		0			0
$781$	7.38502			0.264257
$782$		0			0
$783$	130.314	+	34.9175i	4.65704	+	1.24785i
$784$		0			0
$785$	0.0244800	+	0.174406i	0.000873730	+	0.00622481i
$786$		0			0
$787$	15.1934	−	26.3157i	0.541585	−	0.938053i	−0.457228	−	0.889350i	$-0.651158\pi$
$787$	15.1934	−	26.3157i	0.541585	−	0.938053i	0.998813	−	0.0487038i	$-0.0155090\pi$
$788$		0			0
$789$	32.4764	+	18.7503i	1.15619	+	0.667527i
$790$		0			0
$791$	7.13064	+	1.91065i	0.253536	+	0.0679349i
$792$		0			0
$793$	−3.15399	+	17.4151i	−0.112001	+	0.618427i
$794$		0			0
$795$	54.5876	+	6.71222i	1.93602	+	0.238058i
$796$		0			0
$797$	−7.77181	−	29.0048i	−0.275292	−	1.02740i	−0.955646	−	0.294518i	$-0.904841\pi$
$797$	−7.77181	−	29.0048i	−0.275292	−	1.02740i	0.680354	−	0.732883i	$-0.261826\pi$
$798$		0			0
$799$	−0.116474	−	0.434689i	−0.00412057	−	0.0153782i
$800$		0			0
$801$	−44.3480	+	44.3480i	−1.56696	+	1.56696i
$802$		0			0
$803$	−5.13963	+	19.1813i	−0.181373	+	0.676895i
$804$		0			0
$805$	3.99396	+	28.4546i	0.140768	+	1.00289i
$806$		0			0
$807$	−11.0038	−	11.0038i	−0.387351	−	0.387351i
$808$		0			0
$809$	28.0361	−	16.1867i	0.985698	−	0.569093i	0.0817125	−	0.996656i	$-0.473961\pi$
$809$	28.0361	−	16.1867i	0.985698	−	0.569093i	0.903986	+	0.427563i	$0.140628\pi$
$810$		0			0
$811$	34.6643	+	34.6643i	1.21723	+	1.21723i	0.968599	+	0.248628i	$0.0799796\pi$
$811$	34.6643	+	34.6643i	1.21723	+	1.21723i	0.248628	+	0.968599i	$0.420020\pi$
$812$		0			0
$813$	−14.9004	−	8.60277i	−0.522581	−	0.301712i
$814$		0			0
$815$	−15.5827	−	36.7284i	−0.545838	−	1.28654i
$816$		0			0
$817$	1.47330	+	2.55183i	0.0515442	+	0.0892772i
$818$		0			0
$819$	−51.8842	+	61.2548i	−1.81298	+	2.14041i
$820$		0			0
$821$	5.18587	−	19.3539i	0.180988	−	0.675457i	−0.814466	−	0.580212i	$-0.802970\pi$
$821$	5.18587	−	19.3539i	0.180988	−	0.675457i	0.995454	−	0.0952454i	$-0.0303636\pi$
$822$		0			0
$823$	−45.0352	+	12.0671i	−1.56983	+	0.420634i	−0.935758	−	0.352643i	$-0.885283\pi$
$823$	−45.0352	+	12.0671i	−1.56983	+	0.420634i	−0.634069	+	0.773276i	$0.718617\pi$
$824$		0			0
$825$	7.27525	−	29.1360i	0.253292	−	1.01439i
$826$		0			0
$827$	17.0353			0.592376			0.296188	−	0.955130i	$-0.404285\pi$
$827$	17.0353			0.592376			0.296188	+	0.955130i	$0.404285\pi$
$828$		0			0
$829$	−12.2763	−	21.2632i	−0.426373	−	0.738500i	0.570174	−	0.821524i	$-0.306876\pi$
$829$	−12.2763	−	21.2632i	−0.426373	−	0.738500i	−0.996548	+	0.0830237i	$0.973542\pi$
$830$		0			0
$831$		−	56.7740i		−	1.96947i
$832$		0			0
$833$	−0.0300078	+	0.0300078i	−0.00103971	+	0.00103971i
$834$		0			0
$835$	−0.695487	+	5.65611i	−0.0240683	+	0.195738i
$836$		0			0
$837$		−	78.3801i		−	2.70921i
$838$		0			0
$839$	−16.2633	+	4.35773i	−0.561470	+	0.150446i	−0.528382	−	0.849007i	$-0.677201\pi$
$839$	−16.2633	+	4.35773i	−0.561470	+	0.150446i	−0.0330886	+	0.999452i	$0.510534\pi$
$840$		0			0
$841$	11.8517	−	20.5277i	0.408679	−	0.707852i
$842$		0			0
$843$	−76.1711	+	43.9774i	−2.62347	+	1.51466i
$844$		0			0
$845$	−29.0421	+	1.24729i	−0.999079	+	0.0429081i
$846$		0			0
$847$	17.8609	−	10.3120i	0.613707	−	0.354324i
$848$		0			0
$849$	−10.2142	+	17.6916i	−0.350552	+	0.607174i
$850$		0			0
$851$	−48.2443	+	12.9270i	−1.65379	+	0.443133i
$852$		0			0
$853$			7.14403i			0.244607i	0.992493	+	0.122303i	$0.0390281\pi$
$853$			7.14403i			0.244607i	−0.992493	+	0.122303i	$0.960972\pi$
$854$		0			0
$855$	26.7014	−	20.8539i	0.913168	−	0.713188i
$856$		0			0
$857$	14.5242	−	14.5242i	0.496138	−	0.496138i	−0.414096	−	0.910233i	$-0.635902\pi$
$857$	14.5242	−	14.5242i	0.496138	−	0.496138i	0.910233	+	0.414096i	$0.135902\pi$
$858$		0			0
$859$			23.3877i			0.797977i	0.916956	+	0.398989i	$0.130639\pi$
$859$			23.3877i			0.797977i	−0.916956	+	0.398989i	$0.869361\pi$
$860$		0			0
$861$	−27.4650	−	47.5707i	−0.936003	−	1.62121i
$862$		0			0
$863$	−37.5180			−1.27713			−0.638564	−	0.769569i	$-0.720471\pi$
$863$	−37.5180			−1.27713			−0.638564	+	0.769569i	$0.720471\pi$
$864$		0			0
$865$	29.2875	+	11.8389i	0.995804	+	0.402534i
$866$		0			0
$867$	−55.1839	+	14.7865i	−1.87414	+	0.502175i
$868$		0			0
$869$	1.24994	−	4.66483i	0.0424012	−	0.158243i
$870$		0			0
$871$	−18.5831	+	21.9393i	−0.629663	+	0.743383i
$872$		0			0
$873$	−7.11139	−	12.3173i	−0.240684	−	0.416877i
$874$		0			0
$875$	18.4528	+	22.8118i	0.623820	+	0.771180i
$876$		0			0
$877$	27.3420	+	15.7859i	0.923273	+	0.533052i	0.884678	−	0.466203i	$-0.154378\pi$
$877$	27.3420	+	15.7859i	0.923273	+	0.533052i	0.0385955	+	0.999255i	$0.487712\pi$
$878$		0			0
$879$	−37.7077	−	37.7077i	−1.27185	−	1.27185i
$880$		0			0
$881$	15.9389	−	9.20231i	0.536994	−	0.310034i	−0.206866	−	0.978369i	$-0.566326\pi$
$881$	15.9389	−	9.20231i	0.536994	−	0.310034i	0.743860	+	0.668336i	$0.232993\pi$
$882$		0			0
$883$	−25.8290	−	25.8290i	−0.869216	−	0.869216i	0.123170	−	0.992386i	$-0.460694\pi$
$883$	−25.8290	−	25.8290i	−0.869216	−	0.869216i	−0.992386	+	0.123170i	$0.960694\pi$
$884$		0			0
$885$	18.1420	+	13.6760i	0.609837	+	0.459712i
$886$		0			0
$887$	14.3914	−	53.7095i	0.483216	−	1.80339i	−0.104746	−	0.994499i	$-0.533403\pi$
$887$	14.3914	−	53.7095i	0.483216	−	1.80339i	0.587962	−	0.808889i	$-0.299930\pi$
$888$		0			0
$889$	12.2911	−	12.2911i	0.412230	−	0.412230i
$890$		0			0
$891$	17.2129	+	64.2396i	0.576655	+	2.15211i
$892$		0			0
$893$	−0.553447	−	2.06549i	−0.0185204	−	0.0691191i
$894$		0			0
$895$	4.28639	−	34.8594i	0.143278	−	1.16522i
$896$		0			0
$897$	10.6617	−	58.8699i	0.355985	−	1.96561i
$898$		0			0
$899$	−29.5761	−	7.92489i	−0.986418	−	0.264310i
$900$		0			0
$901$	2.36252	+	1.36400i	0.0787068	+	0.0454414i
$902$		0			0
$903$	7.33647	−	12.7071i	0.244143	−	0.422867i
$904$		0			0
$905$	−10.6058	+	14.0692i	−0.352548	+	0.467677i
$906$		0			0
$907$	−6.41005	−	1.71757i	−0.212842	−	0.0570309i	0.150822	−	0.988561i	$-0.451808\pi$
$907$	−6.41005	−	1.71757i	−0.212842	−	0.0570309i	−0.363665	+	0.931530i	$0.618475\pi$
$908$		0			0
$909$	−119.613			−3.96731
$910$		0			0
$911$	37.4367			1.24033			0.620167	−	0.784470i	$-0.287065\pi$
$911$	37.4367			1.24033			0.620167	+	0.784470i	$0.287065\pi$
$912$		0			0
$913$	19.2483	+	5.15757i	0.637027	+	0.170691i
$914$		0			0
$915$	−36.8344	+	5.17017i	−1.21771	+	0.170920i
$916$		0			0
$917$	−3.52097	+	6.09851i	−0.116273	+	0.201390i
$918$		0			0
$919$	−27.6405	−	15.9583i	−0.911776	−	0.526414i	−0.0307739	−	0.999526i	$-0.509797\pi$
$919$	−27.6405	−	15.9583i	−0.911776	−	0.526414i	−0.881002	+	0.473112i	$0.843131\pi$
$920$		0			0
$921$	−91.8906	−	24.6220i	−3.02790	−	0.811323i
$922$		0			0
$923$	12.3464	−	8.56007i	0.406386	−	0.281758i
$924$		0			0
$925$	−35.4417	+	36.6753i	−1.16532	+	1.20588i
$926$		0			0
$927$	25.5119	+	95.2118i	0.837921	+	3.12716i
$928$		0			0
$929$	8.48551	+	31.6684i	0.278401	+	1.03900i	0.953528	+	0.301304i	$0.0974219\pi$
$929$	8.48551	+	31.6684i	0.278401	+	1.03900i	−0.675128	+	0.737701i	$0.735911\pi$
$930$		0			0
$931$	−0.142587	+	0.142587i	−0.00467309	+	0.00467309i
$932$		0			0
$933$	6.43411	−	24.0124i	0.210643	−	0.786132i
$934$		0			0
$935$	0.896641	−	1.18945i	0.0293233	−	0.0388992i
$936$		0			0
$937$	4.85825	+	4.85825i	0.158712	+	0.158712i	0.781996	−	0.623284i	$-0.214202\pi$
$937$	4.85825	+	4.85825i	0.158712	+	0.158712i	−0.623284	+	0.781996i	$0.714202\pi$
$938$		0			0
$939$	26.6161	−	15.3668i	0.868584	−	0.501477i
$940$		0			0
$941$	33.3418	+	33.3418i	1.08691	+	1.08691i	0.995845	+	0.0910661i	$0.0290275\pi$
$941$	33.3418	+	33.3418i	1.08691	+	1.08691i	0.0910661	+	0.995845i	$0.470973\pi$
$942$		0			0
$943$	26.1917	+	15.1218i	0.852921	+	0.492434i
$944$		0			0
$945$	−101.103	−	40.8690i	−3.28890	−	1.32947i
$946$		0			0
$947$	18.4485	+	31.9537i	0.599495	+	1.03836i	0.992896	+	0.118988i	$0.0379651\pi$
$947$	18.4485	+	31.9537i	0.599495	+	1.03836i	−0.393401	+	0.919367i	$0.628702\pi$
$948$		0			0
$949$	13.6409	+	38.0250i	0.442801	+	1.23434i
$950$		0			0
$951$	28.0312	−	104.614i	0.908975	−	3.39234i
$952$		0			0
$953$	5.69846	−	1.52690i	0.184591	−	0.0494611i	−0.165339	−	0.986237i	$-0.552872\pi$
$953$	5.69846	−	1.52690i	0.184591	−	0.0494611i	0.349930	+	0.936776i	$0.386205\pi$
$954$		0			0
$955$	38.7737	−	16.4505i	1.25469	−	0.532324i
$956$		0			0
$957$	43.6026			1.40947
$958$		0			0
$959$	2.70823	+	4.69080i	0.0874535	+	0.151474i
$960$		0			0
$961$		−	13.2108i		−	0.426156i
$962$		0			0
$963$	54.0986	−	54.0986i	1.74330	−	1.74330i
$964$		0			0
$965$	−54.2976	−	6.67655i	−1.74790	−	0.214926i
$966$		0			0
$967$		−	5.23575i		−	0.168370i	−0.996450	−	0.0841851i	$-0.973171\pi$
$967$		−	5.23575i		−	0.168370i	0.996450	−	0.0841851i	$-0.0268287\pi$
$968$		0			0
$969$	2.19721	−	0.588741i	0.0705847	−	0.0189131i
$970$		0			0
$971$	−25.3905	+	43.9776i	−0.814820	+	1.41131i	0.0946379	+	0.995512i	$0.469831\pi$
$971$	−25.3905	+	43.9776i	−0.814820	+	1.41131i	−0.909457	+	0.415797i	$0.863503\pi$
$972$		0			0
$973$	33.5064	−	19.3449i	1.07417	−	0.620170i
$974$		0			0
$975$	−21.6091	−	57.1428i	−0.692044	−	1.83003i
$976$		0			0
$977$	11.8165	−	6.82225i	0.378043	−	0.218263i	−0.298924	−	0.954277i	$-0.596628\pi$
$977$	11.8165	−	6.82225i	0.378043	−	0.218263i	0.676966	+	0.736014i	$0.263294\pi$
$978$		0			0
$979$	−6.55114	+	11.3469i	−0.209375	+	0.362649i
$980$		0			0
$981$	−98.2907	+	26.3369i	−3.13818	+	0.840873i
$982$		0			0
$983$			26.5627i			0.847217i	0.905845	+	0.423609i	$0.139237\pi$
$983$			26.5627i			0.847217i	−0.905845	+	0.423609i	$0.860763\pi$
$984$		0			0
$985$	31.4294	+	3.86463i	1.00142	+	0.123137i
$986$		0			0
$987$	−7.52941	+	7.52941i	−0.239664	+	0.239664i
$988$		0			0
$989$			8.07871i			0.256888i
$990$		0			0
$991$	9.37032	+	16.2299i	0.297658	+	0.515559i	0.975600	−	0.219557i	$-0.0704611\pi$
$991$	9.37032	+	16.2299i	0.297658	+	0.515559i	−0.677942	+	0.735116i	$0.737128\pi$
$992$		0			0
$993$	−16.0909			−0.510629
$994$		0			0
$995$	6.48677	−	2.75213i	0.205644	−	0.0872484i
$996$		0			0
$997$	−8.84872	+	2.37101i	−0.280242	+	0.0750906i	−0.396202	−	0.918163i	$-0.629672\pi$
$997$	−8.84872	+	2.37101i	−0.280242	+	0.0750906i	0.115960	+	0.993254i	$0.463005\pi$
$998$		0			0
$999$	49.0614	−	183.100i	1.55223	−	5.79302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.c.37.1	✓	20
5.2	odd	4		1300.2.bs.d.193.1		20
5.3	odd	4		260.2.bk.c.193.5	yes	20
5.4	even	2		1300.2.bn.d.557.5		20
13.6	odd	12		260.2.bk.c.97.5	yes	20
65.19	odd	12		1300.2.bs.d.357.1		20
65.32	even	12		1300.2.bn.d.1293.5		20
65.58	even	12	inner	260.2.bf.c.253.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.1	✓	20	1.1	even	1	trivial
260.2.bf.c.253.1	yes	20	65.58	even	12	inner
260.2.bk.c.97.5	yes	20	13.6	odd	12
260.2.bk.c.193.5	yes	20	5.3	odd	4
1300.2.bn.d.557.5		20	5.4	even	2
1300.2.bn.d.1293.5		20	65.32	even	12
1300.2.bs.d.193.1		20	5.2	odd	4
1300.2.bs.d.357.1		20	65.19	odd	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.27331 - 0.877081i) q^{3} +(-1.78557 - 1.34601i) q^{5} +(-1.31216 + 2.27273i) q^{7} +(7.34722 + 4.24192i) q^{9} +O(q^{10})\)	\(q+(-3.27331 - 0.877081i) q^{3} +(-1.78557 - 1.34601i) q^{5} +(-1.31216 + 2.27273i) q^{7} +(7.34722 + 4.24192i) q^{9} +(1.71196 + 0.458719i) q^{11} +(3.39379 - 1.21746i) q^{13} +(4.66416 + 5.97200i) q^{15} +(0.0972783 + 0.363048i) q^{17} +(0.462233 + 1.72508i) q^{19} +(6.28849 - 6.28849i) q^{21} +(-1.26731 + 4.72966i) q^{23} +(1.37650 + 4.80679i) q^{25} +(-13.1405 - 13.1405i) q^{27} +(-6.28709 + 3.62985i) q^{29} +(2.98238 + 2.98238i) q^{31} +(-5.20145 - 3.00306i) q^{33} +(5.40208 - 2.29193i) q^{35} +(5.10019 + 8.83378i) q^{37} +(-12.1767 + 1.00852i) q^{39} +(1.59861 - 5.96611i) q^{41} +(1.59368 - 0.427024i) q^{43} +(-7.40928 - 17.4637i) q^{45} -1.19733 q^{47} +(0.0564545 + 0.0977821i) q^{49} -1.27369i q^{51} +(5.13227 - 5.13227i) q^{53} +(-2.43938 - 3.12339i) q^{55} -6.05214i q^{57} +(2.89607 - 0.776000i) q^{59} +(-2.45432 + 4.25101i) q^{61} +(-19.2815 + 11.1322i) q^{63} +(-7.69856 - 2.39421i) q^{65} +(-6.90594 + 3.98715i) q^{67} +(8.29659 - 14.3701i) q^{69} +(4.02481 - 1.07844i) q^{71} +11.2043i q^{73} +(-0.289783 - 16.9414i) q^{75} +(-3.28892 + 3.28892i) q^{77} -2.72484i q^{79} +(18.7620 + 32.4967i) q^{81} +11.2434 q^{83} +(0.314969 - 0.779184i) q^{85} +(23.7633 - 6.36735i) q^{87} +(-1.91334 + 7.14070i) q^{89} +(-1.68623 + 9.31068i) q^{91} +(-7.14647 - 12.3780i) q^{93} +(1.49663 - 3.70242i) q^{95} +(-1.45185 - 0.838229i) q^{97} +(10.6323 + 10.6323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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