LMFDB - Embedded newform 1300.2.bs.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(193,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("1300.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bs (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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1300.193
Dual form			1300.2.bs.a.357.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133975 + 0.500000i) q^{3} +(0.232051 + 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(-0.133975 + 0.500000i) q^{3} +(0.232051 + 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +(4.59808 + 1.23205i) q^{11} +(-3.00000 - 2.00000i) q^{13} +(2.86603 - 0.767949i) q^{17} +(-0.866025 - 3.23205i) q^{19} +(-0.0980762 + 0.0980762i) q^{21} +(0.133975 + 0.0358984i) q^{23} +(-2.09808 + 2.09808i) q^{27} +(-1.03590 + 0.598076i) q^{29} +(2.26795 + 2.26795i) q^{31} +(-1.23205 + 2.13397i) q^{33} +(3.23205 - 1.86603i) q^{37} +(1.40192 - 1.23205i) q^{39} +(-1.86603 + 6.96410i) q^{41} +(2.66987 + 9.96410i) q^{43} -7.46410i q^{47} +(-3.46410 - 6.00000i) q^{49} +1.53590i q^{51} +(8.46410 + 8.46410i) q^{53} +1.73205 q^{57} +(13.7942 - 3.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(0.366025 + 0.633975i) q^{63} +(6.23205 + 10.7942i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(2.86603 - 0.767949i) q^{71} -0.928203 q^{73} +(0.901924 + 0.901924i) q^{77} -11.4641i q^{79} +(3.33013 + 5.76795i) q^{81} +3.46410i q^{83} +(-0.160254 - 0.598076i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(-0.428203 - 0.866025i) q^{91} +(-1.43782 + 0.830127i) q^{93} +(-1.23205 + 2.13397i) q^{97} +(9.19615 + 9.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 6 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 6 * q^7 + 6 * q^9	$ 4 q - 4 q^{3} - 6 q^{7} + 6 q^{9} + 8 q^{11} - 12 q^{13} + 8 q^{17} + 10 q^{21} + 4 q^{23} + 2 q^{27} - 18 q^{29} + 16 q^{31} + 2 q^{33} + 6 q^{37} + 16 q^{39} - 4 q^{41} + 28 q^{43} + 20 q^{53} + 24 q^{59} + 2 q^{61} - 2 q^{63} + 18 q^{67} - 14 q^{69} + 8 q^{71} + 24 q^{73} + 14 q^{77} - 4 q^{81} + 34 q^{87} + 28 q^{89} + 26 q^{91} - 30 q^{93} + 2 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 6 * q^7 + 6 * q^9 + 8 * q^11 - 12 * q^13 + 8 * q^17 + 10 * q^21 + 4 * q^23 + 2 * q^27 - 18 * q^29 + 16 * q^31 + 2 * q^33 + 6 * q^37 + 16 * q^39 - 4 * q^41 + 28 * q^43 + 20 * q^53 + 24 * q^59 + 2 * q^61 - 2 * q^63 + 18 * q^67 - 14 * q^69 + 8 * q^71 + 24 * q^73 + 14 * q^77 - 4 * q^81 + 34 * q^87 + 28 * q^89 + 26 * q^91 - 30 * q^93 + 2 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.133975	+	0.500000i	−0.0773503	+	0.288675i	−0.993756	−	0.111576i	$-0.964410\pi$
$3$	−0.133975	+	0.500000i	−0.0773503	+	0.288675i	0.916406	+	0.400251i	$0.131077\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.232051	+	0.133975i	0.0877070	+	0.0506376i	0.543212	−	0.839596i	$-0.317208\pi$
$7$	0.232051	+	0.133975i	0.0877070	+	0.0506376i	−0.455505	+	0.890233i	$0.650541\pi$
$8$		0			0
$9$	2.36603	+	1.36603i	0.788675	+	0.455342i
$10$		0			0
$11$	4.59808	+	1.23205i	1.38637	+	0.371477i	0.873432	−	0.486947i	$-0.161889\pi$
$11$	4.59808	+	1.23205i	1.38637	+	0.371477i	0.512941	+	0.858424i	$0.328556\pi$
$12$		0			0
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.86603	−	0.767949i	0.695113	−	0.186255i	0.106073	−	0.994358i	$-0.466172\pi$
$17$	2.86603	−	0.767949i	0.695113	−	0.186255i	0.589041	+	0.808103i	$0.299506\pi$
$18$		0			0
$19$	−0.866025	−	3.23205i	−0.198680	−	0.741483i	−0.991283	−	0.131746i	$-0.957942\pi$
$19$	−0.866025	−	3.23205i	−0.198680	−	0.741483i	0.792604	−	0.609737i	$-0.208725\pi$
$20$		0			0
$21$	−0.0980762	+	0.0980762i	−0.0214020	+	0.0214020i
$22$		0			0
$23$	0.133975	+	0.0358984i	0.0279356	+	0.00748533i	0.272760	−	0.962082i	$-0.412064\pi$
$23$	0.133975	+	0.0358984i	0.0279356	+	0.00748533i	−0.244824	+	0.969567i	$0.578730\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.09808	+	2.09808i	−0.403775	+	0.403775i
$28$		0			0
$29$	−1.03590	+	0.598076i	−0.192362	+	0.111060i	−0.593088	−	0.805138i	$-0.702091\pi$
$29$	−1.03590	+	0.598076i	−0.192362	+	0.111060i	0.400726	+	0.916198i	$0.368758\pi$
$30$		0			0
$31$	2.26795	+	2.26795i	0.407336	+	0.407336i	0.880808	−	0.473473i	$-0.157000\pi$
$31$	2.26795	+	2.26795i	0.407336	+	0.407336i	−0.473473	+	0.880808i	$0.657000\pi$
$32$		0			0
$33$	−1.23205	+	2.13397i	−0.214473	+	0.371477i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.23205	−	1.86603i	0.531346	−	0.306773i	−0.210218	−	0.977654i	$-0.567418\pi$
$37$	3.23205	−	1.86603i	0.531346	−	0.306773i	0.741564	+	0.670882i	$0.234084\pi$
$38$		0			0
$39$	1.40192	−	1.23205i	0.224487	−	0.197286i
$40$		0			0
$41$	−1.86603	+	6.96410i	−0.291424	+	1.08761i	0.652592	+	0.757710i	$0.273682\pi$
$41$	−1.86603	+	6.96410i	−0.291424	+	1.08761i	−0.944016	+	0.329900i	$0.892985\pi$
$42$		0			0
$43$	2.66987	+	9.96410i	0.407152	+	1.51951i	0.800052	+	0.599930i	$0.204805\pi$
$43$	2.66987	+	9.96410i	0.407152	+	1.51951i	−0.392900	+	0.919581i	$0.628528\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	7.46410i		−	1.08875i	−0.838842	−	0.544376i	$-0.816767\pi$
$47$		−	7.46410i		−	1.08875i	0.838842	−	0.544376i	$-0.183233\pi$
$48$		0			0
$49$	−3.46410	−	6.00000i	−0.494872	−	0.857143i
$50$		0			0
$51$			1.53590i			0.215069i
$52$		0			0
$53$	8.46410	+	8.46410i	1.16263	+	1.16263i	0.983897	+	0.178737i	$0.0572011\pi$
$53$	8.46410	+	8.46410i	1.16263	+	1.16263i	0.178737	+	0.983897i	$0.442799\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.73205			0.229416
$58$		0			0
$59$	13.7942	−	3.69615i	1.79586	−	0.481198i	0.802537	−	0.596602i	$-0.203483\pi$
$59$	13.7942	−	3.69615i	1.79586	−	0.481198i	0.993319	+	0.115404i	$0.0368164\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	0.366025	+	0.633975i	0.0461149	+	0.0798733i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.23205	+	10.7942i	0.761366	+	1.31872i	0.942146	+	0.335201i	$0.108804\pi$
$67$	6.23205	+	10.7942i	0.761366	+	1.31872i	−0.180780	+	0.983524i	$0.557862\pi$
$68$		0			0
$69$	−0.0358984	+	0.0621778i	−0.00432166	+	0.00748533i
$70$		0			0
$71$	2.86603	−	0.767949i	0.340135	−	0.0911388i	−0.0847085	−	0.996406i	$-0.526996\pi$
$71$	2.86603	−	0.767949i	0.340135	−	0.0911388i	0.424843	+	0.905267i	$0.360329\pi$
$72$		0			0
$73$	−0.928203			−0.108638			−0.0543190	−	0.998524i	$-0.517299\pi$
$73$	−0.928203			−0.108638			−0.0543190	+	0.998524i	$0.517299\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.901924	+	0.901924i	0.102784	+	0.102784i
$78$		0			0
$79$		−	11.4641i		−	1.28981i	−0.764262	−	0.644906i	$-0.776896\pi$
$79$		−	11.4641i		−	1.28981i	0.764262	−	0.644906i	$-0.223104\pi$
$80$		0			0
$81$	3.33013	+	5.76795i	0.370014	+	0.640883i
$82$		0			0
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.160254	−	0.598076i	−0.0171810	−	0.0641205i
$88$		0			0
$89$	−0.794229	+	2.96410i	−0.0841881	+	0.314194i	−0.995159	−	0.0982760i	$-0.968667\pi$
$89$	−0.794229	+	2.96410i	−0.0841881	+	0.314194i	0.910971	+	0.412470i	$0.135334\pi$
$90$		0			0
$91$	−0.428203	−	0.866025i	−0.0448879	−	0.0907841i
$92$		0			0
$93$	−1.43782	+	0.830127i	−0.149095	+	0.0860802i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.23205	+	2.13397i	−0.125096	+	0.216672i	−0.921770	−	0.387736i	$-0.873257\pi$
$97$	−1.23205	+	2.13397i	−0.125096	+	0.216672i	0.796675	+	0.604408i	$0.206590\pi$
$98$		0			0
$99$	9.19615	+	9.19615i	0.924248	+	0.924248i
$100$		0			0
$101$	1.50000	−	0.866025i	0.149256	−	0.0861727i	−0.423512	−	0.905890i	$-0.639203\pi$
$101$	1.50000	−	0.866025i	0.149256	−	0.0861727i	0.572768	+	0.819718i	$0.305870\pi$
$102$		0			0
$103$	10.6603	−	10.6603i	1.05039	−	1.05039i	0.0517247	−	0.998661i	$-0.483528\pi$
$103$	10.6603	−	10.6603i	1.05039	−	1.05039i	0.998661	−	0.0517247i	$-0.0164718\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.59808	+	0.964102i	0.347839	+	0.0932032i	0.428509	−	0.903538i	$-0.359039\pi$
$107$	3.59808	+	0.964102i	0.347839	+	0.0932032i	−0.0806695	+	0.996741i	$0.525706\pi$
$108$		0			0
$109$	−11.3923	+	11.3923i	−1.09118	+	1.09118i	−0.0957826	+	0.995402i	$0.530535\pi$
$109$	−11.3923	+	11.3923i	−1.09118	+	1.09118i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$	0.500000	+	1.86603i	0.0474579	+	0.177115i
$112$		0			0
$113$	−15.5263	+	4.16025i	−1.46059	+	0.391364i	−0.899693	−	0.436522i	$-0.856210\pi$
$113$	−15.5263	+	4.16025i	−1.46059	+	0.391364i	−0.560896	+	0.827886i	$0.689543\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.36603	−	8.83013i	−0.403639	−	0.816346i
$118$		0			0
$119$	0.767949	+	0.205771i	0.0703978	+	0.0188630i
$120$		0			0
$121$	10.0981	+	5.83013i	0.918007	+	0.530012i
$122$		0			0
$123$	−3.23205	−	1.86603i	−0.291424	−	0.168254i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.20577	+	4.50000i	−0.106995	+	0.399310i	−0.998564	−	0.0535746i	$-0.982939\pi$
$127$	−1.20577	+	4.50000i	−0.106995	+	0.399310i	0.891569	+	0.452885i	$0.149605\pi$
$128$		0			0
$129$	−5.33975			−0.470138
$130$		0			0
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$		0			0
$133$	0.232051	−	0.866025i	0.0201214	−	0.0750939i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.69615	−	5.59808i	−0.828398	−	0.478276i	0.0249057	−	0.999690i	$-0.492071\pi$
$137$	−9.69615	−	5.59808i	−0.828398	−	0.478276i	−0.853304	+	0.521414i	$0.825405\pi$
$138$		0			0
$139$	5.42820	+	3.13397i	0.460414	+	0.265820i	0.712218	−	0.701958i	$-0.247691\pi$
$139$	5.42820	+	3.13397i	0.460414	+	0.265820i	−0.251804	+	0.967778i	$0.581024\pi$
$140$		0			0
$141$	3.73205	+	1.00000i	0.314295	+	0.0842152i
$142$		0			0
$143$	−11.3301	−	12.8923i	−0.947473	−	1.07811i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.46410	−	0.928203i	0.285714	−	0.0765569i
$148$		0			0
$149$	−4.25833	−	15.8923i	−0.348856	−	1.30195i	−0.888042	−	0.459762i	$-0.847935\pi$
$149$	−4.25833	−	15.8923i	−0.348856	−	1.30195i	0.539186	−	0.842187i	$-0.318732\pi$
$150$		0			0
$151$	11.1962	−	11.1962i	0.911130	−	0.911130i	−0.0852312	−	0.996361i	$-0.527163\pi$
$151$	11.1962	−	11.1962i	0.911130	−	0.911130i	0.996361	+	0.0852312i	$0.0271629\pi$
$152$		0			0
$153$	7.83013	+	2.09808i	0.633028	+	0.169619i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−13.3923	+	13.3923i	−1.06882	+	1.06882i	−0.0713726	+	0.997450i	$0.522738\pi$
$157$	−13.3923	+	13.3923i	−1.06882	+	1.06882i	−0.997450	+	0.0713726i	$0.977262\pi$
$158$		0			0
$159$	−5.36603	+	3.09808i	−0.425553	+	0.245693i
$160$		0			0
$161$	0.0262794	+	0.0262794i	0.00207111	+	0.00207111i
$162$		0			0
$163$	−4.23205	+	7.33013i	−0.331480	+	0.574140i	−0.982802	−	0.184661i	$-0.940881\pi$
$163$	−4.23205	+	7.33013i	−0.331480	+	0.574140i	0.651322	+	0.758801i	$0.274215\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.23205	−	5.33013i	0.714398	−	0.412458i	−0.0982896	−	0.995158i	$-0.531337\pi$
$167$	9.23205	−	5.33013i	0.714398	−	0.412458i	0.812687	+	0.582700i	$0.198004\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	2.36603	−	8.83013i	0.180934	−	0.675257i
$172$		0			0
$173$	−3.40192	−	12.6962i	−0.258643	−	0.965271i	−0.966027	−	0.258441i	$-0.916791\pi$
$173$	−3.40192	−	12.6962i	−0.258643	−	0.965271i	0.707384	−	0.706830i	$-0.249875\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			7.39230i			0.555640i
$178$		0			0
$179$	−0.964102	−	1.66987i	−0.0720603	−	0.124812i	0.827744	−	0.561106i	$-0.189624\pi$
$179$	−0.964102	−	1.66987i	−0.0720603	−	0.124812i	−0.899804	+	0.436294i	$0.856291\pi$
$180$		0			0
$181$			1.07180i			0.0796660i	0.999206	+	0.0398330i	$0.0126826\pi$
$181$			1.07180i			0.0796660i	−0.999206	+	0.0398330i	$0.987317\pi$
$182$		0			0
$183$	0.366025	+	0.366025i	0.0270574	+	0.0270574i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	14.1244			1.03288
$188$		0			0
$189$	−0.767949	+	0.205771i	−0.0558601	+	0.0149677i
$190$		0			0
$191$	−5.03590	+	8.72243i	−0.364385	+	0.631133i	−0.988677	−	0.150058i	$-0.952054\pi$
$191$	−5.03590	+	8.72243i	−0.364385	+	0.631133i	0.624292	+	0.781191i	$0.285387\pi$
$192$		0			0
$193$	5.16025	+	8.93782i	0.371443	+	0.643359i	0.989788	−	0.142549i	$-0.0455297\pi$
$193$	5.16025	+	8.93782i	0.371443	+	0.643359i	−0.618345	+	0.785907i	$0.712196\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.1603	−	17.5981i	−0.723888	−	1.25381i	−0.959430	−	0.281947i	$-0.909020\pi$
$197$	−10.1603	−	17.5981i	−0.723888	−	1.25381i	0.235542	−	0.971864i	$-0.424314\pi$
$198$		0			0
$199$	−1.96410	+	3.40192i	−0.139231	+	0.241156i	−0.927206	−	0.374552i	$-0.877797\pi$
$199$	−1.96410	+	3.40192i	−0.139231	+	0.241156i	0.787974	+	0.615708i	$0.211130\pi$
$200$		0			0
$201$	−6.23205	+	1.66987i	−0.439575	+	0.117784i
$202$		0			0
$203$	−0.320508			−0.0224953
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.267949	+	0.267949i	0.0186238	+	0.0186238i
$208$		0			0
$209$		−	15.9282i		−	1.10178i
$210$		0			0
$211$	−4.96410	−	8.59808i	−0.341743	−	0.591916i	0.643014	−	0.765855i	$-0.277684\pi$
$211$	−4.96410	−	8.59808i	−0.341743	−	0.591916i	−0.984756	+	0.173939i	$0.944351\pi$
$212$		0			0
$213$			1.53590i			0.105238i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.222432	+	0.830127i	0.0150997	+	0.0563527i
$218$		0			0
$219$	0.124356	−	0.464102i	0.00840318	−	0.0313611i
$220$		0			0
$221$	−10.1340	−	3.42820i	−0.681685	−	0.230606i
$222$		0			0
$223$	17.0885	−	9.86603i	1.14433	−	0.660678i	0.196829	−	0.980438i	$-0.436936\pi$
$223$	17.0885	−	9.86603i	1.14433	−	0.660678i	0.947499	+	0.319760i	$0.103602\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.232051	+	0.401924i	−0.0154018	+	0.0266766i	−0.873624	−	0.486602i	$-0.838236\pi$
$227$	−0.232051	+	0.401924i	−0.0154018	+	0.0266766i	0.858222	+	0.513279i	$0.171569\pi$
$228$		0			0
$229$	10.8564	+	10.8564i	0.717412	+	0.717412i	0.968074	−	0.250663i	$-0.0806486\pi$
$229$	10.8564	+	10.8564i	0.717412	+	0.717412i	−0.250663	+	0.968074i	$0.580649\pi$
$230$		0			0
$231$	−0.571797	+	0.330127i	−0.0376215	+	0.0217208i
$232$		0			0
$233$	11.0000	−	11.0000i	0.720634	−	0.720634i	−0.248100	−	0.968734i	$-0.579806\pi$
$233$	11.0000	−	11.0000i	0.720634	−	0.720634i	0.968734	+	0.248100i	$0.0798063\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.73205	+	1.53590i	0.372337	+	0.0997673i
$238$		0			0
$239$	−9.19615	+	9.19615i	−0.594850	+	0.594850i	−0.938937	−	0.344088i	$-0.888188\pi$
$239$	−9.19615	+	9.19615i	−0.594850	+	0.594850i	0.344088	+	0.938937i	$0.388188\pi$
$240$		0			0
$241$	−4.93782	−	18.4282i	−0.318073	−	1.18706i	−0.921094	−	0.389340i	$-0.872703\pi$
$241$	−4.93782	−	18.4282i	−0.318073	−	1.18706i	0.603021	−	0.797725i	$-0.293963\pi$
$242$		0			0
$243$	−11.9282	+	3.19615i	−0.765195	+	0.205033i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.86603	+	11.4282i	−0.245989	+	0.727159i
$248$		0			0
$249$	−1.73205	−	0.464102i	−0.109764	−	0.0294112i
$250$		0			0
$251$	−23.8923	−	13.7942i	−1.50807	−	0.870684i	−0.999956	−	0.00939359i	$-0.997010\pi$
$251$	−23.8923	−	13.7942i	−1.50807	−	0.870684i	−0.508113	−	0.861290i	$-0.669657\pi$
$252$		0			0
$253$	0.571797	+	0.330127i	0.0359486	+	0.0207549i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.52628	−	13.1603i	0.219963	−	0.820914i	−0.764397	−	0.644746i	$-0.776963\pi$
$257$	3.52628	−	13.1603i	0.219963	−	0.820914i	0.984360	−	0.176168i	$-0.0563702\pi$
$258$		0			0
$259$	1.00000			0.0621370
$260$		0			0
$261$	−3.26795			−0.202281
$262$		0			0
$263$	4.79423	−	17.8923i	0.295625	−	1.10329i	−0.645095	−	0.764102i	$-0.723182\pi$
$263$	4.79423	−	17.8923i	0.295625	−	1.10329i	0.940720	−	0.339184i	$-0.110151\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.37564	−	0.794229i	−0.0841881	−	0.0486060i
$268$		0			0
$269$	−23.4282	−	13.5263i	−1.42844	−	0.824712i	−0.431445	−	0.902139i	$-0.641996\pi$
$269$	−23.4282	−	13.5263i	−1.42844	−	0.824712i	−0.996998	+	0.0774275i	$0.975329\pi$
$270$		0			0
$271$	−19.7942	−	5.30385i	−1.20241	−	0.322186i	−0.398633	−	0.917111i	$-0.630515\pi$
$271$	−19.7942	−	5.30385i	−1.20241	−	0.322186i	−0.803781	+	0.594925i	$0.797182\pi$
$272$		0			0
$273$	0.490381	−	0.0980762i	0.0296792	−	0.00593584i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−22.9904	+	6.16025i	−1.38136	+	0.370134i	−0.871614	−	0.490192i	$-0.836927\pi$
$277$	−22.9904	+	6.16025i	−1.38136	+	0.370134i	−0.509744	+	0.860326i	$0.670260\pi$
$278$		0			0
$279$	2.26795	+	8.46410i	0.135779	+	0.506733i
$280$		0			0
$281$	−7.39230	+	7.39230i	−0.440988	+	0.440988i	−0.892344	−	0.451356i	$-0.850940\pi$
$281$	−7.39230	+	7.39230i	−0.440988	+	0.440988i	0.451356	+	0.892344i	$0.350940\pi$
$282$		0			0
$283$	12.5263	+	3.35641i	0.744610	+	0.199518i	0.611126	−	0.791533i	$-0.290717\pi$
$283$	12.5263	+	3.35641i	0.744610	+	0.199518i	0.133484	+	0.991051i	$0.457384\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.36603	+	1.36603i	−0.0806339	+	0.0806339i
$288$		0			0
$289$	−7.09808	+	4.09808i	−0.417534	+	0.241063i
$290$		0			0
$291$	−0.901924	−	0.901924i	−0.0528717	−	0.0528717i
$292$		0			0
$293$	−11.2321	+	19.4545i	−0.656183	+	1.13654i	0.325412	+	0.945572i	$0.394497\pi$
$293$	−11.2321	+	19.4545i	−0.656183	+	1.13654i	−0.981596	+	0.190971i	$0.938836\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.2321	+	7.06218i	−0.709776	+	0.409789i
$298$		0			0
$299$	−0.330127	−	0.375644i	−0.0190917	−	0.0217241i
$300$		0			0
$301$	−0.715390	+	2.66987i	−0.0412344	+	0.153889i
$302$		0			0
$303$	0.232051	+	0.866025i	0.0133310	+	0.0497519i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	30.3923i		−	1.73458i	−0.497803	−	0.867290i	$-0.665860\pi$
$307$		−	30.3923i		−	1.73458i	0.497803	−	0.867290i	$-0.334140\pi$
$308$		0			0
$309$	3.90192	+	6.75833i	0.221973	+	0.384468i
$310$		0			0
$311$		−	16.2487i		−	0.921380i	−0.887561	−	0.460690i	$-0.847602\pi$
$311$		−	16.2487i		−	0.921380i	0.887561	−	0.460690i	$-0.152398\pi$
$312$		0			0
$313$	−20.3205	−	20.3205i	−1.14858	−	1.14858i	−0.986832	−	0.161752i	$-0.948286\pi$
$313$	−20.3205	−	20.3205i	−1.14858	−	1.14858i	−0.161752	−	0.986832i	$-0.551714\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.07180			0.172529			0.0862646	−	0.996272i	$-0.472507\pi$
$317$	3.07180			0.172529			0.0862646	+	0.996272i	$0.472507\pi$
$318$		0			0
$319$	−5.50000	+	1.47372i	−0.307941	+	0.0825125i
$320$		0			0
$321$	−0.964102	+	1.66987i	−0.0538109	+	0.0932032i
$322$		0			0
$323$	−4.96410	−	8.59808i	−0.276210	−	0.478410i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.16987	−	7.22243i	−0.230595	−	0.399401i
$328$		0			0
$329$	1.00000	−	1.73205i	0.0551318	−	0.0954911i
$330$		0			0
$331$	10.3301	−	2.76795i	0.567795	−	0.152140i	0.0365099	−	0.999333i	$-0.488376\pi$
$331$	10.3301	−	2.76795i	0.567795	−	0.152140i	0.531285	+	0.847193i	$0.321709\pi$
$332$		0			0
$333$	10.1962			0.558746
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0717968	+	0.0717968i	0.00391102	+	0.00391102i	0.709060	−	0.705149i	$-0.249120\pi$
$337$	0.0717968	+	0.0717968i	0.00391102	+	0.00391102i	−0.705149	+	0.709060i	$0.749120\pi$
$338$		0			0
$339$		−	8.32051i		−	0.451908i
$340$		0			0
$341$	7.63397	+	13.2224i	0.413403	+	0.716035i
$342$		0			0
$343$		−	3.73205i		−	0.201512i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.66987	+	24.8923i	0.358058	+	1.33629i	0.876593	+	0.481233i	$0.159811\pi$
$347$	6.66987	+	24.8923i	0.358058	+	1.33629i	−0.518535	+	0.855056i	$0.673523\pi$
$348$		0			0
$349$	−5.47372	+	20.4282i	−0.293002	+	1.09350i	0.649790	+	0.760114i	$0.274857\pi$
$349$	−5.47372	+	20.4282i	−0.293002	+	1.09350i	−0.942792	+	0.333383i	$0.891810\pi$
$350$		0			0
$351$	10.4904	−	2.09808i	0.559935	−	0.111987i
$352$		0			0
$353$	13.6244	−	7.86603i	0.725151	−	0.418666i	−0.0914944	−	0.995806i	$-0.529164\pi$
$353$	13.6244	−	7.86603i	0.725151	−	0.418666i	0.816646	+	0.577139i	$0.195831\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.205771	+	0.356406i	−0.0108906	+	0.0188630i
$358$		0			0
$359$	−7.58846	−	7.58846i	−0.400503	−	0.400503i	0.477907	−	0.878410i	$-0.341396\pi$
$359$	−7.58846	−	7.58846i	−0.400503	−	0.400503i	−0.878410	+	0.477907i	$0.841396\pi$
$360$		0			0
$361$	6.75833	−	3.90192i	0.355702	−	0.205364i
$362$		0			0
$363$	−4.26795	+	4.26795i	−0.224009	+	0.224009i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−10.7942	−	2.89230i	−0.563454	−	0.150977i	−0.0341614	−	0.999416i	$-0.510876\pi$
$367$	−10.7942	−	2.89230i	−0.563454	−	0.150977i	−0.529293	+	0.848439i	$0.677543\pi$
$368$		0			0
$369$	−13.9282	+	13.9282i	−0.725073	+	0.725073i
$370$		0			0
$371$	0.830127	+	3.09808i	0.0430980	+	0.160844i
$372$		0			0
$373$	−26.9904	+	7.23205i	−1.39751	+	0.374461i	−0.877450	−	0.479669i	$-0.840757\pi$
$373$	−26.9904	+	7.23205i	−1.39751	+	0.374461i	−0.520059	+	0.854130i	$0.674090\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.30385	+	0.277568i	0.221659	+	0.0142955i
$378$		0			0
$379$	23.5263	+	6.30385i	1.20846	+	0.323807i	0.806159	−	0.591699i	$-0.201543\pi$
$379$	23.5263	+	6.30385i	1.20846	+	0.323807i	0.402305	+	0.915506i	$0.368209\pi$
$380$		0			0
$381$	−2.08846	−	1.20577i	−0.106995	−	0.0617735i
$382$		0			0
$383$	−0.696152	−	0.401924i	−0.0355717	−	0.0205373i	0.482109	−	0.876111i	$-0.339871\pi$
$383$	−0.696152	−	0.401924i	−0.0355717	−	0.0205373i	−0.517680	+	0.855574i	$0.673204\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.29423	+	27.2224i	−0.370786	+	1.38379i
$388$		0			0
$389$	−3.85641			−0.195528			−0.0977638	−	0.995210i	$-0.531169\pi$
$389$	−3.85641			−0.195528			−0.0977638	+	0.995210i	$0.531169\pi$
$390$		0			0
$391$	0.411543			0.0208126
$392$		0			0
$393$	1.85641	−	6.92820i	0.0936433	−	0.349482i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	7.37564	+	4.25833i	0.370173	+	0.213719i	0.673534	−	0.739156i	$-0.264775\pi$
$397$	7.37564	+	4.25833i	0.370173	+	0.213719i	−0.303361	+	0.952876i	$0.598109\pi$
$398$		0			0
$399$	0.401924	+	0.232051i	0.0201214	+	0.0116171i
$400$		0			0
$401$	5.86603	+	1.57180i	0.292935	+	0.0784918i	0.402294	−	0.915511i	$-0.368213\pi$
$401$	5.86603	+	1.57180i	0.292935	+	0.0784918i	−0.109359	+	0.994002i	$0.534880\pi$
$402$		0			0
$403$	−2.26795	−	11.3397i	−0.112975	−	0.564873i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	17.1603	−	4.59808i	0.850602	−	0.227918i
$408$		0			0
$409$	3.06218	+	11.4282i	0.151415	+	0.565088i	0.999386	+	0.0350453i	$0.0111575\pi$
$409$	3.06218	+	11.4282i	0.151415	+	0.565088i	−0.847971	+	0.530043i	$0.822176\pi$
$410$		0			0
$411$	4.09808	−	4.09808i	0.202143	−	0.202143i
$412$		0			0
$413$	3.69615	+	0.990381i	0.181876	+	0.0487335i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.29423	+	2.29423i	−0.112349	+	0.112349i
$418$		0			0
$419$	27.3564	−	15.7942i	1.33645	−	0.771599i	0.350169	−	0.936687i	$-0.386124\pi$
$419$	27.3564	−	15.7942i	1.33645	−	0.771599i	0.986279	+	0.165088i	$0.0527908\pi$
$420$		0			0
$421$	14.0718	+	14.0718i	0.685817	+	0.685817i	0.961305	−	0.275487i	$-0.0888392\pi$
$421$	14.0718	+	14.0718i	0.685817	+	0.685817i	−0.275487	+	0.961305i	$0.588839\pi$
$422$		0			0
$423$	10.1962	−	17.6603i	0.495754	−	0.858671i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.232051	−	0.133975i	0.0112297	−	0.00648349i
$428$		0			0
$429$	7.96410	−	3.93782i	0.384510	−	0.190120i
$430$		0			0
$431$	8.47372	−	31.6244i	0.408165	−	1.52329i	−0.389979	−	0.920824i	$-0.627518\pi$
$431$	8.47372	−	31.6244i	0.408165	−	1.52329i	0.798143	−	0.602468i	$-0.205816\pi$
$432$		0			0
$433$	−2.72243	−	10.1603i	−0.130832	−	0.488271i	0.869149	−	0.494551i	$-0.164668\pi$
$433$	−2.72243	−	10.1603i	−0.130832	−	0.488271i	−0.999980	+	0.00628046i	$0.998001\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	0.464102i		−	0.0222010i
$438$		0			0
$439$	5.96410	+	10.3301i	0.284651	+	0.493030i	0.972524	−	0.232801i	$-0.0747889\pi$
$439$	5.96410	+	10.3301i	0.284651	+	0.493030i	−0.687873	+	0.725831i	$0.741456\pi$
$440$		0			0
$441$		−	18.9282i		−	0.901343i
$442$		0			0
$443$	−27.0526	−	27.0526i	−1.28531	−	1.28531i	−0.937606	−	0.347700i	$-0.886963\pi$
$443$	−27.0526	−	27.0526i	−1.28531	−	1.28531i	−0.347700	−	0.937606i	$-0.613037\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.51666			0.402824
$448$		0			0
$449$	−23.9904	+	6.42820i	−1.13218	+	0.303366i	−0.775801	−	0.630977i	$-0.782654\pi$
$449$	−23.9904	+	6.42820i	−1.13218	+	0.303366i	−0.356375	+	0.934343i	$0.615987\pi$
$450$		0			0
$451$	−17.1603	+	29.7224i	−0.808045	+	1.39957i
$452$		0			0
$453$	4.09808	+	7.09808i	0.192544	+	0.333497i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.6962	−	25.4545i	−0.687457	−	1.19071i	−0.972658	−	0.232243i	$-0.925394\pi$
$457$	−14.6962	−	25.4545i	−0.687457	−	1.19071i	0.285201	−	0.958468i	$-0.407940\pi$
$458$		0			0
$459$	−4.40192	+	7.62436i	−0.205464	+	0.355874i
$460$		0			0
$461$	−23.9904	+	6.42820i	−1.11734	+	0.299391i	−0.769808	−	0.638276i	$-0.779648\pi$
$461$	−23.9904	+	6.42820i	−1.11734	+	0.299391i	−0.347535	+	0.937667i	$0.612981\pi$
$462$		0			0
$463$	29.8564			1.38754			0.693772	−	0.720194i	$-0.255947\pi$
$463$	29.8564			1.38754			0.693772	+	0.720194i	$0.255947\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.1244	−	20.1244i	−0.931244	−	0.931244i	0.0665397	−	0.997784i	$-0.478804\pi$
$467$	−20.1244	−	20.1244i	−0.931244	−	0.931244i	−0.997784	+	0.0665397i	$0.978804\pi$
$468$		0			0
$469$			3.33975i			0.154215i
$470$		0			0
$471$	−4.90192	−	8.49038i	−0.225869	−	0.391216i
$472$		0			0
$473$			49.1051i			2.25786i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	8.46410	+	31.5885i	0.387545	+	1.44634i
$478$		0			0
$479$	1.00962	−	3.76795i	0.0461307	−	0.172162i	−0.939017	−	0.343870i	$-0.888262\pi$
$479$	1.00962	−	3.76795i	0.0461307	−	0.172162i	0.985148	+	0.171708i	$0.0549286\pi$
$480$		0			0
$481$	−13.4282	−	0.866025i	−0.612273	−	0.0394874i
$482$		0			0
$483$	−0.0166605	+	0.00961894i	−0.000758079	+	0.000437677i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−17.1603	+	29.7224i	−0.777605	+	1.34685i	0.155713	+	0.987802i	$0.450232\pi$
$487$	−17.1603	+	29.7224i	−0.777605	+	1.34685i	−0.933318	+	0.359050i	$0.883101\pi$
$488$		0			0
$489$	−3.09808	−	3.09808i	−0.140100	−	0.140100i
$490$		0			0
$491$	−13.9641	+	8.06218i	−0.630191	+	0.363841i	−0.780826	−	0.624748i	$-0.785202\pi$
$491$	−13.9641	+	8.06218i	−0.630191	+	0.363841i	0.150635	+	0.988589i	$0.451868\pi$
$492$		0			0
$493$	−2.50962	+	2.50962i	−0.113028	+	0.113028i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.767949	+	0.205771i	0.0344472	+	0.00923011i
$498$		0			0
$499$	3.19615	−	3.19615i	0.143079	−	0.143079i	−0.631939	−	0.775018i	$-0.717741\pi$
$499$	3.19615	−	3.19615i	0.143079	−	0.143079i	0.775018	+	0.631939i	$0.217741\pi$
$500$		0			0
$501$	1.42820	+	5.33013i	0.0638074	+	0.238133i
$502$		0			0
$503$	−15.0622	+	4.03590i	−0.671589	+	0.179952i	−0.578471	−	0.815703i	$-0.696350\pi$
$503$	−15.0622	+	4.03590i	−0.671589	+	0.179952i	−0.0931187	+	0.995655i	$0.529684\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.66987	+	0.892305i	−0.296219	+	0.0396286i
$508$		0			0
$509$	8.79423	+	2.35641i	0.389797	+	0.104446i	0.448394	−	0.893836i	$-0.351996\pi$
$509$	8.79423	+	2.35641i	0.389797	+	0.104446i	−0.0585970	+	0.998282i	$0.518663\pi$
$510$		0			0
$511$	−0.215390	−	0.124356i	−0.00952831	−	0.00550117i
$512$		0			0
$513$	8.59808	+	4.96410i	0.379614	+	0.219170i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	9.19615	−	34.3205i	0.404446	−	1.50941i
$518$		0			0
$519$	6.80385			0.298656
$520$		0			0
$521$	3.85641			0.168952			0.0844761	−	0.996426i	$-0.473078\pi$
$521$	3.85641			0.168952			0.0844761	+	0.996426i	$0.473078\pi$
$522$		0			0
$523$	−9.06218	+	33.8205i	−0.396261	+	1.47887i	0.423360	+	0.905962i	$0.360851\pi$
$523$	−9.06218	+	33.8205i	−0.396261	+	1.47887i	−0.819621	+	0.572906i	$0.805816\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.24167	+	4.75833i	0.359013	+	0.207276i
$528$		0			0
$529$	−19.9019	−	11.4904i	−0.865301	−	0.499582i
$530$		0			0
$531$	37.6865	+	10.0981i	1.63546	+	0.438219i
$532$		0			0
$533$	19.5263	−	17.1603i	0.845777	−	0.743293i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.964102	−	0.258330i	0.0416041	−	0.0111478i
$538$		0			0
$539$	−8.53590	−	31.8564i	−0.367667	−	1.37215i
$540$		0			0
$541$	14.0718	−	14.0718i	0.604994	−	0.604994i	−0.336640	−	0.941634i	$-0.609290\pi$
$541$	14.0718	−	14.0718i	0.604994	−	0.604994i	0.941634	+	0.336640i	$0.109290\pi$
$542$		0			0
$543$	−0.535898	−	0.143594i	−0.0229976	−	0.00616219i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.19615	−	9.19615i	0.393199	−	0.393199i	−0.482627	−	0.875826i	$-0.660317\pi$
$547$	9.19615	−	9.19615i	0.393199	−	0.393199i	0.875826	+	0.482627i	$0.160317\pi$
$548$		0			0
$549$	2.36603	−	1.36603i	0.100980	−	0.0583005i
$550$		0			0
$551$	2.83013	+	2.83013i	0.120567	+	0.120567i
$552$		0			0
$553$	1.53590	−	2.66025i	0.0653130	−	0.113126i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.7679	−	10.2583i	0.752852	−	0.434659i	−0.0738714	−	0.997268i	$-0.523535\pi$
$557$	17.7679	−	10.2583i	0.752852	−	0.434659i	0.826724	+	0.562608i	$0.190202\pi$
$558$		0			0
$559$	11.9186	−	35.2321i	0.504102	−	1.49016i
$560$		0			0
$561$	−1.89230	+	7.06218i	−0.0798932	+	0.298165i
$562$		0			0
$563$	8.52628	+	31.8205i	0.359340	+	1.34107i	0.874934	+	0.484242i	$0.160904\pi$
$563$	8.52628	+	31.8205i	0.359340	+	1.34107i	−0.515594	+	0.856833i	$0.672429\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			1.78461i			0.0749466i
$568$		0			0
$569$	1.57180	+	2.72243i	0.0658931	+	0.114130i	0.897090	−	0.441848i	$-0.145677\pi$
$569$	1.57180	+	2.72243i	0.0658931	+	0.114130i	−0.831197	+	0.555978i	$0.812344\pi$
$570$		0			0
$571$			42.1051i			1.76204i	0.473075	+	0.881022i	$0.343144\pi$
$571$			42.1051i			1.76204i	−0.473075	+	0.881022i	$0.656856\pi$
$572$		0			0
$573$	−3.68653	−	3.68653i	−0.154007	−	0.154007i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	28.9282			1.20430			0.602148	−	0.798384i	$-0.294312\pi$
$577$	28.9282			1.20430			0.602148	+	0.798384i	$0.294312\pi$
$578$		0			0
$579$	−5.16025	+	1.38269i	−0.214453	+	0.0574625i
$580$		0			0
$581$	−0.464102	+	0.803848i	−0.0192542	+	0.0333492i
$582$		0			0
$583$	28.4904	+	49.3468i	1.17995	+	2.04374i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.1603	+	22.7942i	0.543182	+	0.940819i	0.998719	+	0.0506017i	$0.0161139\pi$
$587$	13.1603	+	22.7942i	0.543182	+	0.940819i	−0.455537	+	0.890217i	$0.650553\pi$
$588$		0			0
$589$	5.36603	−	9.29423i	0.221103	−	0.382962i
$590$		0			0
$591$	10.1603	−	2.72243i	0.417937	−	0.111986i
$592$		0			0
$593$	7.07180			0.290404			0.145202	−	0.989402i	$-0.453617\pi$
$593$	7.07180			0.290404			0.145202	+	0.989402i	$0.453617\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.43782	−	1.43782i	−0.0588461	−	0.0588461i
$598$		0			0
$599$		−	5.60770i		−	0.229124i	−0.993416	−	0.114562i	$-0.963454\pi$
$599$		−	5.60770i		−	0.229124i	0.993416	−	0.114562i	$-0.0365465\pi$
$600$		0			0
$601$	−4.57180	−	7.91858i	−0.186487	−	0.323006i	0.757589	−	0.652732i	$-0.226377\pi$
$601$	−4.57180	−	7.91858i	−0.186487	−	0.323006i	−0.944077	+	0.329726i	$0.893044\pi$
$602$		0			0
$603$			34.0526i			1.38673i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−8.93782	−	33.3564i	−0.362775	−	1.35389i	−0.870412	−	0.492324i	$-0.836148\pi$
$607$	−8.93782	−	33.3564i	−0.362775	−	1.35389i	0.507637	−	0.861571i	$-0.330519\pi$
$608$		0			0
$609$	0.0429399	−	0.160254i	0.00174001	−	0.00649382i
$610$		0			0
$611$	−14.9282	+	22.3923i	−0.603930	+	0.905896i
$612$		0			0
$613$	9.23205	−	5.33013i	0.372879	−	0.215282i	−0.301836	−	0.953360i	$-0.597600\pi$
$613$	9.23205	−	5.33013i	0.372879	−	0.215282i	0.674715	+	0.738078i	$0.264266\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.0885	−	27.8660i	0.647697	−	1.12184i	−0.335975	−	0.941871i	$-0.609066\pi$
$617$	16.0885	−	27.8660i	0.647697	−	1.12184i	0.983672	−	0.179973i	$-0.0576010\pi$
$618$		0			0
$619$	5.87564	+	5.87564i	0.236162	+	0.236162i	0.815259	−	0.579097i	$-0.196595\pi$
$619$	5.87564	+	5.87564i	0.236162	+	0.236162i	−0.579097	+	0.815259i	$0.696595\pi$
$620$		0			0
$621$	−0.356406	+	0.205771i	−0.0143021	+	0.00825732i
$622$		0			0
$623$	−0.581416	+	0.581416i	−0.0232939	+	0.0232939i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	7.96410	+	2.13397i	0.318056	+	0.0852227i
$628$		0			0
$629$	7.83013	−	7.83013i	0.312208	−	0.312208i
$630$		0			0
$631$	6.20577	+	23.1603i	0.247048	+	0.921995i	0.972343	+	0.233557i	$0.0750366\pi$
$631$	6.20577	+	23.1603i	0.247048	+	0.921995i	−0.725295	+	0.688438i	$0.758297\pi$
$632$		0			0
$633$	4.96410	−	1.33013i	0.197305	−	0.0528678i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.60770	+	24.9282i	−0.0636992	+	0.987691i
$638$		0			0
$639$	7.83013	+	2.09808i	0.309755	+	0.0829986i
$640$		0			0
$641$	40.2846	+	23.2583i	1.59115	+	0.918649i	0.993111	+	0.117179i	$0.0373852\pi$
$641$	40.2846	+	23.2583i	1.59115	+	0.918649i	0.598036	+	0.801470i	$0.295948\pi$
$642$		0			0
$643$	−35.7679	−	20.6506i	−1.41055	−	0.814382i	−0.415110	−	0.909771i	$-0.636257\pi$
$643$	−35.7679	−	20.6506i	−1.41055	−	0.814382i	−0.995440	+	0.0953896i	$0.969590\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.794229	−	2.96410i	0.0312243	−	0.116531i	−0.948555	−	0.316613i	$-0.897454\pi$
$647$	0.794229	−	2.96410i	0.0312243	−	0.116531i	0.979779	+	0.200082i	$0.0641210\pi$
$648$		0			0
$649$	67.9808			2.66848
$650$		0			0
$651$	−0.444864			−0.0174356
$652$		0			0
$653$	−0.186533	+	0.696152i	−0.00729962	+	0.0272425i	−0.969480	−	0.245172i	$-0.921156\pi$
$653$	−0.186533	+	0.696152i	−0.00729962	+	0.0272425i	0.962180	+	0.272415i	$0.0878222\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.19615	−	1.26795i	−0.0856801	−	0.0494674i
$658$		0			0
$659$	−29.2128	−	16.8660i	−1.13797	−	0.657007i	−0.192043	−	0.981387i	$-0.561511\pi$
$659$	−29.2128	−	16.8660i	−1.13797	−	0.657007i	−0.945927	+	0.324380i	$0.894845\pi$
$660$		0			0
$661$	−1.59808	−	0.428203i	−0.0621580	−	0.0166552i	0.227606	−	0.973753i	$-0.426910\pi$
$661$	−1.59808	−	0.428203i	−0.0621580	−	0.0166552i	−0.289764	+	0.957098i	$0.593577\pi$
$662$		0			0
$663$	3.07180	−	4.60770i	0.119299	−	0.178948i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.160254	+	0.0429399i	−0.00620506	+	0.00166264i
$668$		0			0
$669$	2.64359	+	9.86603i	0.102207	+	0.381443i
$670$		0			0
$671$	3.36603	−	3.36603i	0.129944	−	0.129944i
$672$		0			0
$673$	−26.9904	−	7.23205i	−1.04040	−	0.278775i	−0.302122	−	0.953269i	$-0.597695\pi$
$673$	−26.9904	−	7.23205i	−1.04040	−	0.278775i	−0.738280	+	0.674494i	$0.764362\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.3205	−	10.3205i	0.396649	−	0.396649i	−0.480400	−	0.877049i	$-0.659509\pi$
$677$	10.3205	−	10.3205i	0.396649	−	0.396649i	0.877049	+	0.480400i	$0.159509\pi$
$678$		0			0
$679$	−0.571797	+	0.330127i	−0.0219435	+	0.0126691i
$680$		0			0
$681$	−0.169873	−	0.169873i	−0.00650955	−	0.00650955i
$682$		0			0
$683$	15.2321	−	26.3827i	0.582838	−	1.00951i	−0.412303	−	0.911047i	$-0.635275\pi$
$683$	15.2321	−	26.3827i	0.582838	−	1.00951i	0.995141	−	0.0984586i	$-0.0313912\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−6.88269	+	3.97372i	−0.262591	+	0.151607i
$688$		0			0
$689$	−8.46410	−	42.3205i	−0.322457	−	1.61228i
$690$		0			0
$691$	−0.0621778	+	0.232051i	−0.00236536	+	0.00882763i	−0.967098	−	0.254403i	$-0.918121\pi$
$691$	−0.0621778	+	0.232051i	−0.00236536	+	0.00882763i	0.964733	+	0.263230i	$0.0847879\pi$
$692$		0			0
$693$	0.901924	+	3.36603i	0.0342613	+	0.127865i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			21.3923i			0.810291i
$698$		0			0
$699$	4.02628	+	6.97372i	0.152288	+	0.263770i
$700$		0			0
$701$		−	29.0718i		−	1.09803i	−0.835814	−	0.549013i	$-0.815004\pi$
$701$		−	29.0718i		−	1.09803i	0.835814	−	0.549013i	$-0.184996\pi$
$702$		0			0
$703$	−8.83013	−	8.83013i	−0.333035	−	0.333035i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.464102			0.0174543
$708$		0			0
$709$	−5.59808	+	1.50000i	−0.210240	+	0.0563337i	−0.362402	−	0.932022i	$-0.618043\pi$
$709$	−5.59808	+	1.50000i	−0.210240	+	0.0563337i	0.152162	+	0.988356i	$0.451377\pi$
$710$		0			0
$711$	15.6603	−	27.1244i	0.587305	−	1.01724i
$712$		0			0
$713$	0.222432	+	0.385263i	0.00833014	+	0.0144282i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.36603	−	5.83013i	−0.125707	−	0.217730i
$718$		0			0
$719$	−14.8923	+	25.7942i	−0.555389	+	0.961962i	0.442484	+	0.896776i	$0.354097\pi$
$719$	−14.8923	+	25.7942i	−0.555389	+	0.961962i	−0.997873	+	0.0651859i	$0.979236\pi$
$720$		0			0
$721$	3.90192	−	1.04552i	0.145315	−	0.0389371i
$722$		0			0
$723$	9.87564			0.367279
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−13.5885	−	13.5885i	−0.503968	−	0.503968i	0.408701	−	0.912669i	$-0.365982\pi$
$727$	−13.5885	−	13.5885i	−0.503968	−	0.503968i	−0.912669	+	0.408701i	$0.865982\pi$
$728$		0			0
$729$			13.5885i			0.503276i
$730$		0			0
$731$	15.3038	+	26.5070i	0.566033	+	0.980398i
$732$		0			0
$733$			38.6410i			1.42724i	0.700534	+	0.713619i	$0.252945\pi$
$733$			38.6410i			1.42724i	−0.700534	+	0.713619i	$0.747055\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.3564	+	57.3109i	0.565661	+	2.11107i
$738$		0			0
$739$	−10.7417	+	40.0885i	−0.395139	+	1.47468i	0.426405	+	0.904532i	$0.359780\pi$
$739$	−10.7417	+	40.0885i	−0.395139	+	1.47468i	−0.821544	+	0.570145i	$0.806887\pi$
$740$		0			0
$741$	−5.19615	−	3.46410i	−0.190885	−	0.127257i
$742$		0			0
$743$	−30.4808	+	17.5981i	−1.11823	+	0.645611i	−0.940949	−	0.338549i	$-0.890064\pi$
$743$	−30.4808	+	17.5981i	−1.11823	+	0.645611i	−0.177282	+	0.984160i	$0.556730\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.73205	+	8.19615i	−0.173137	+	0.299882i
$748$		0			0
$749$	0.705771	+	0.705771i	0.0257883	+	0.0257883i
$750$		0			0
$751$	31.7487	−	18.3301i	1.15853	−	0.668876i	0.207576	−	0.978219i	$-0.433442\pi$
$751$	31.7487	−	18.3301i	1.15853	−	0.668876i	0.950951	+	0.309343i	$0.100109\pi$
$752$		0			0
$753$	10.0981	−	10.0981i	0.367994	−	0.367994i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−16.0622	−	4.30385i	−0.583790	−	0.156426i	−0.0451764	−	0.998979i	$-0.514385\pi$
$757$	−16.0622	−	4.30385i	−0.583790	−	0.156426i	−0.538613	+	0.842553i	$0.681052\pi$
$758$		0			0
$759$	−0.241670	+	0.241670i	−0.00877206	+	0.00877206i
$760$		0			0
$761$	2.66987	+	9.96410i	0.0967828	+	0.361198i	0.997284	−	0.0736557i	$-0.0234666\pi$
$761$	2.66987	+	9.96410i	0.0967828	+	0.361198i	−0.900501	+	0.434854i	$0.856800\pi$
$762$		0			0
$763$	−4.16987	+	1.11731i	−0.150960	+	0.0404495i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−48.7750	−	16.5000i	−1.76116	−	0.595780i
$768$		0			0
$769$	5.33013	+	1.42820i	0.192209	+	0.0515023i	0.353639	−	0.935382i	$-0.384944\pi$
$769$	5.33013	+	1.42820i	0.192209	+	0.0515023i	−0.161430	+	0.986884i	$0.551611\pi$
$770$		0			0
$771$	6.10770	+	3.52628i	0.219963	+	0.126996i
$772$		0			0
$773$	−36.4808	−	21.0622i	−1.31212	−	0.757554i	−0.329675	−	0.944095i	$-0.606939\pi$
$773$	−36.4808	−	21.0622i	−1.31212	−	0.757554i	−0.982447	+	0.186541i	$0.940272\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.133975	+	0.500000i	−0.00480631	+	0.0179374i
$778$		0			0
$779$	24.1244			0.864345
$780$		0			0
$781$	14.1244			0.505409
$782$		0			0
$783$	0.918584	−	3.42820i	0.0328275	−	0.122514i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	38.0885	+	21.9904i	1.35771	+	0.783872i	0.989314	−	0.145798i	$-0.0465749\pi$
$787$	38.0885	+	21.9904i	1.35771	+	0.783872i	0.368392	+	0.929670i	$0.379908\pi$
$788$		0			0
$789$	8.30385	+	4.79423i	0.295625	+	0.170679i
$790$		0			0
$791$	−4.16025	−	1.11474i	−0.147922	−	0.0396355i
$792$		0			0
$793$	−3.23205	+	1.59808i	−0.114773	+	0.0567494i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	24.7224	−	6.62436i	0.875713	−	0.234647i	0.207157	−	0.978308i	$-0.433579\pi$
$797$	24.7224	−	6.62436i	0.875713	−	0.234647i	0.668557	+	0.743661i	$0.266912\pi$
$798$		0			0
$799$	−5.73205	−	21.3923i	−0.202785	−	0.756805i
$800$		0			0
$801$	−5.92820	+	5.92820i	−0.209463	+	0.209463i
$802$		0			0
$803$	−4.26795	−	1.14359i	−0.150613	−	0.0403565i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.90192	−	9.90192i	0.348564	−	0.348564i
$808$		0			0
$809$	29.8923	−	17.2583i	1.05096	−	0.606771i	0.128040	−	0.991769i	$-0.459131\pi$
$809$	29.8923	−	17.2583i	1.05096	−	0.606771i	0.922917	+	0.384998i	$0.125798\pi$
$810$		0			0
$811$	32.1244	+	32.1244i	1.12804	+	1.12804i	0.990496	+	0.137543i	$0.0439205\pi$
$811$	32.1244	+	32.1244i	1.12804	+	1.12804i	0.137543	+	0.990496i	$0.456080\pi$
$812$		0			0
$813$	5.30385	−	9.18653i	0.186014	−	0.322186i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	29.8923	−	17.2583i	1.04580	−	0.603793i
$818$		0			0
$819$	0.169873	−	2.63397i	0.00593584	−	0.0920385i
$820$		0			0
$821$	−4.40192	+	16.4282i	−0.153628	+	0.573348i	0.845591	+	0.533832i	$0.179248\pi$
$821$	−4.40192	+	16.4282i	−0.153628	+	0.573348i	−0.999219	+	0.0395165i	$0.987418\pi$
$822$		0			0
$823$	4.91858	+	18.3564i	0.171451	+	0.639864i	0.997129	+	0.0757222i	$0.0241262\pi$
$823$	4.91858	+	18.3564i	0.171451	+	0.639864i	−0.825678	+	0.564142i	$0.809207\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	24.5359i		−	0.853197i	−0.904441	−	0.426598i	$-0.859712\pi$
$827$		−	24.5359i		−	0.853197i	0.904441	−	0.426598i	$-0.140288\pi$
$828$		0			0
$829$	1.03590	+	1.79423i	0.0359782	+	0.0623161i	0.883454	−	0.468518i	$-0.155212\pi$
$829$	1.03590	+	1.79423i	0.0359782	+	0.0623161i	−0.847476	+	0.530834i	$0.821879\pi$
$830$		0			0
$831$		−	12.3205i		−	0.427394i
$832$		0			0
$833$	−14.5359	−	14.5359i	−0.503639	−	0.503639i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−9.51666			−0.328944
$838$		0			0
$839$	−25.5263	+	6.83975i	−0.881265	+	0.236134i	−0.670953	−	0.741500i	$-0.734115\pi$
$839$	−25.5263	+	6.83975i	−0.881265	+	0.236134i	−0.210312	+	0.977634i	$0.567448\pi$
$840$		0			0
$841$	−13.7846	+	23.8756i	−0.475331	+	0.823298i
$842$		0			0
$843$	−2.70577	−	4.68653i	−0.0931917	−	0.161413i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.56218	+	2.70577i	0.0536771	+	0.0929714i
$848$		0			0
$849$	−3.35641	+	5.81347i	−0.115192	+	0.199518i
$850$		0			0
$851$	0.500000	−	0.133975i	0.0171398	−	0.00459259i
$852$		0			0
$853$	55.5692			1.90265			0.951327	−	0.308184i	$-0.0997211\pi$
$853$	55.5692			1.90265			0.951327	+	0.308184i	$0.0997211\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.60770	−	8.60770i	−0.294033	−	0.294033i	0.544638	−	0.838671i	$-0.316667\pi$
$857$	−8.60770	−	8.60770i	−0.294033	−	0.294033i	−0.838671	+	0.544638i	$0.816667\pi$
$858$		0			0
$859$			46.1051i			1.57309i	0.617535	+	0.786543i	$0.288131\pi$
$859$			46.1051i			1.57309i	−0.617535	+	0.786543i	$0.711869\pi$
$860$		0			0
$861$	−0.500000	−	0.866025i	−0.0170400	−	0.0295141i
$862$		0			0
$863$			20.2487i			0.689274i	0.938736	+	0.344637i	$0.111998\pi$
$863$			20.2487i			0.689274i	−0.938736	+	0.344637i	$0.888002\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.09808	−	4.09808i	−0.0372926	−	0.139178i
$868$		0			0
$869$	14.1244	−	52.7128i	0.479136	−	1.78816i
$870$		0			0
$871$	2.89230	−	44.8468i	0.0980020	−	1.51958i
$872$		0			0
$873$	−5.83013	+	3.36603i	−0.197320	+	0.113923i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−20.5526	+	35.5981i	−0.694011	+	1.20206i	0.276502	+	0.961013i	$0.410825\pi$
$877$	−20.5526	+	35.5981i	−0.694011	+	1.20206i	−0.970513	+	0.241048i	$0.922509\pi$
$878$		0			0
$879$	−8.22243	−	8.22243i	−0.277336	−	0.277336i
$880$		0			0
$881$	−1.96410	+	1.13397i	−0.0661723	+	0.0382046i	−0.532721	−	0.846291i	$-0.678831\pi$
$881$	−1.96410	+	1.13397i	−0.0661723	+	0.0382046i	0.466549	+	0.884495i	$0.345497\pi$
$882$		0			0
$883$	16.8038	−	16.8038i	0.565494	−	0.565494i	−0.365368	−	0.930863i	$-0.619057\pi$
$883$	16.8038	−	16.8038i	0.565494	−	0.565494i	0.930863	+	0.365368i	$0.119057\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.79423	−	0.748711i	−0.0938210	−	0.0251393i	0.211603	−	0.977356i	$-0.432132\pi$
$887$	−2.79423	−	0.748711i	−0.0938210	−	0.0251393i	−0.305424	+	0.952216i	$0.598798\pi$
$888$		0			0
$889$	−0.882686	+	0.882686i	−0.0296043	+	0.0296043i
$890$		0			0
$891$	8.20577	+	30.6244i	0.274904	+	1.02595i
$892$		0			0
$893$	−24.1244	+	6.46410i	−0.807291	+	0.216313i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.232051	−	0.114737i	0.00774795	−	0.00383095i
$898$		0			0
$899$	−3.70577	−	0.992958i	−0.123594	−	0.0331170i
$900$		0			0
$901$	30.7583	+	17.7583i	1.02471	+	0.591616i
$902$		0			0
$903$	−1.23909	−	0.715390i	−0.0412344	−	0.0238067i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	3.47372	−	12.9641i	0.115343	−	0.430466i	−0.883969	−	0.467545i	$-0.845139\pi$
$907$	3.47372	−	12.9641i	0.115343	−	0.430466i	0.999312	+	0.0370789i	$0.0118053\pi$
$908$		0			0
$909$	4.73205			0.156952
$910$		0			0
$911$	−29.0718			−0.963192			−0.481596	−	0.876393i	$-0.659943\pi$
$911$	−29.0718			−0.963192			−0.481596	+	0.876393i	$0.659943\pi$
$912$		0			0
$913$	−4.26795	+	15.9282i	−0.141249	+	0.527147i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.21539	−	1.85641i	−0.106182	−	0.0613039i
$918$		0			0
$919$	−37.7487	−	21.7942i	−1.24522	−	0.718925i	−0.275064	−	0.961426i	$-0.588699\pi$
$919$	−37.7487	−	21.7942i	−1.24522	−	0.718925i	−0.970151	+	0.242501i	$0.922032\pi$
$920$		0			0
$921$	15.1962	+	4.07180i	0.500730	+	0.134170i
$922$		0			0
$923$	−10.1340	−	3.42820i	−0.333564	−	0.112841i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	39.7846	−	10.6603i	1.30670	−	0.350129i
$928$		0			0
$929$	−0.794229	−	2.96410i	−0.0260578	−	0.0972490i	0.951672	−	0.307115i	$-0.0993638\pi$
$929$	−0.794229	−	2.96410i	−0.0260578	−	0.0972490i	−0.977730	+	0.209866i	$0.932697\pi$
$930$		0			0
$931$	−16.3923	+	16.3923i	−0.537236	+	0.537236i
$932$		0			0
$933$	8.12436	+	2.17691i	0.265979	+	0.0712690i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−41.7846	+	41.7846i	−1.36504	+	1.36504i	−0.497687	+	0.867357i	$0.665817\pi$
$937$	−41.7846	+	41.7846i	−1.36504	+	1.36504i	−0.867357	+	0.497687i	$0.834183\pi$
$938$		0			0
$939$	12.8827	−	7.43782i	0.420411	−	0.242724i
$940$		0			0
$941$	−19.0000	−	19.0000i	−0.619382	−	0.619382i	0.325991	−	0.945373i	$-0.394302\pi$
$941$	−19.0000	−	19.0000i	−0.619382	−	0.619382i	−0.945373	+	0.325991i	$0.894302\pi$
$942$		0			0
$943$	−0.500000	+	0.866025i	−0.0162822	+	0.0282017i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.01666	+	1.74167i	−0.0980283	+	0.0565967i	−0.548213	−	0.836339i	$-0.684692\pi$
$947$	−3.01666	+	1.74167i	−0.0980283	+	0.0565967i	0.450184	+	0.892936i	$0.351358\pi$
$948$		0			0
$949$	2.78461	+	1.85641i	0.0903923	+	0.0602615i
$950$		0			0
$951$	−0.411543	+	1.53590i	−0.0133452	+	0.0498049i
$952$		0			0
$953$	4.99038	+	18.6244i	0.161654	+	0.603302i	0.998443	+	0.0557765i	$0.0177634\pi$
$953$	4.99038	+	18.6244i	0.161654	+	0.603302i	−0.836789	+	0.547526i	$0.815570\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	2.94744i		−	0.0952772i
$958$		0			0
$959$	−1.50000	−	2.59808i	−0.0484375	−	0.0838963i
$960$		0			0
$961$		−	20.7128i		−	0.668155i
$962$		0			0
$963$	7.19615	+	7.19615i	0.231893	+	0.231893i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	10.6410			0.342192			0.171096	−	0.985254i	$-0.445269\pi$
$967$	10.6410			0.342192			0.171096	+	0.985254i	$0.445269\pi$
$968$		0			0
$969$	4.96410	−	1.33013i	0.159470	−	0.0427298i
$970$		0			0
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	0.469897	+	0.882721i	$0.344291\pi$
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	−0.999408	+	0.0344175i	$0.989042\pi$
$972$		0			0
$973$	0.839746	+	1.45448i	0.0269210	+	0.0466286i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.375644	+	0.650635i	0.0120179	+	0.0208157i	0.871972	−	0.489556i	$-0.162841\pi$
$977$	0.375644	+	0.650635i	0.0120179	+	0.0208157i	−0.859954	+	0.510372i	$0.829508\pi$
$978$		0			0
$979$	−7.30385	+	12.6506i	−0.233432	+	0.404316i
$980$		0			0
$981$	−42.5167	+	11.3923i	−1.35745	+	0.363728i
$982$		0			0
$983$	42.9282			1.36920			0.684599	−	0.728920i	$-0.259978\pi$
$983$	42.9282			1.36920			0.684599	+	0.728920i	$0.259978\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.732051	+	0.732051i	0.0233014	+	0.0233014i
$988$		0			0
$989$			1.43078i			0.0454962i
$990$		0			0
$991$	−18.0359	−	31.2391i	−0.572929	−	0.992342i	−0.996263	−	0.0863688i	$-0.972474\pi$
$991$	−18.0359	−	31.2391i	−0.572929	−	0.992342i	0.423334	−	0.905974i	$-0.360860\pi$
$992$		0			0
$993$			5.53590i			0.175676i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.33013	−	8.69615i	−0.0737959	−	0.275410i	0.919162	−	0.393880i	$-0.128868\pi$
$997$	−2.33013	−	8.69615i	−0.0737959	−	0.275410i	−0.992958	+	0.118470i	$0.962201\pi$
$998$		0			0
$999$	−2.86603	+	10.6962i	−0.0906770	+	0.338411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bs.a.193.1		4
5.2	odd	4		1300.2.bn.b.557.1		4
5.3	odd	4		260.2.bf.a.37.1	✓	4
5.4	even	2		260.2.bk.b.193.1	yes	4
13.6	odd	12		1300.2.bn.b.1293.1		4
65.19	odd	12		260.2.bf.a.253.1	yes	4
65.32	even	12	inner	1300.2.bs.a.357.1		4
65.58	even	12		260.2.bk.b.97.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.a.37.1	✓	4	5.3	odd	4
260.2.bf.a.253.1	yes	4	65.19	odd	12
260.2.bk.b.97.1	yes	4	65.58	even	12
260.2.bk.b.193.1	yes	4	5.4	even	2
1300.2.bn.b.557.1		4	5.2	odd	4
1300.2.bn.b.1293.1		4	13.6	odd	12
1300.2.bs.a.193.1		4	1.1	even	1	trivial
1300.2.bs.a.357.1		4	65.32	even	12	inner

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.133975 + 0.500000i) q^{3} +(0.232051 + 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})\)	\(q+(-0.133975 + 0.500000i) q^{3} +(0.232051 + 0.133975i) q^{7} +(2.36603 + 1.36603i) q^{9} +(4.59808 + 1.23205i) q^{11} +(-3.00000 - 2.00000i) q^{13} +(2.86603 - 0.767949i) q^{17} +(-0.866025 - 3.23205i) q^{19} +(-0.0980762 + 0.0980762i) q^{21} +(0.133975 + 0.0358984i) q^{23} +(-2.09808 + 2.09808i) q^{27} +(-1.03590 + 0.598076i) q^{29} +(2.26795 + 2.26795i) q^{31} +(-1.23205 + 2.13397i) q^{33} +(3.23205 - 1.86603i) q^{37} +(1.40192 - 1.23205i) q^{39} +(-1.86603 + 6.96410i) q^{41} +(2.66987 + 9.96410i) q^{43} -7.46410i q^{47} +(-3.46410 - 6.00000i) q^{49} +1.53590i q^{51} +(8.46410 + 8.46410i) q^{53} +1.73205 q^{57} +(13.7942 - 3.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(0.366025 + 0.633975i) q^{63} +(6.23205 + 10.7942i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(2.86603 - 0.767949i) q^{71} -0.928203 q^{73} +(0.901924 + 0.901924i) q^{77} -11.4641i q^{79} +(3.33013 + 5.76795i) q^{81} +3.46410i q^{83} +(-0.160254 - 0.598076i) q^{87} +(-0.794229 + 2.96410i) q^{89} +(-0.428203 - 0.866025i) q^{91} +(-1.43782 + 0.830127i) q^{93} +(-1.23205 + 2.13397i) q^{97} +(9.19615 + 9.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 6 * q^7 + 6 * q^9	\( 4 q - 4 q^{3} - 6 q^{7} + 6 q^{9} + 8 q^{11} - 12 q^{13} + 8 q^{17} + 10 q^{21} + 4 q^{23} + 2 q^{27} - 18 q^{29} + 16 q^{31} + 2 q^{33} + 6 q^{37} + 16 q^{39} - 4 q^{41} + 28 q^{43} + 20 q^{53} + 24 q^{59} + 2 q^{61} - 2 q^{63} + 18 q^{67} - 14 q^{69} + 8 q^{71} + 24 q^{73} + 14 q^{77} - 4 q^{81} + 34 q^{87} + 28 q^{89} + 26 q^{91} - 30 q^{93} + 2 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 6 * q^7 + 6 * q^9 + 8 * q^11 - 12 * q^13 + 8 * q^17 + 10 * q^21 + 4 * q^23 + 2 * q^27 - 18 * q^29 + 16 * q^31 + 2 * q^33 + 6 * q^37 + 16 * q^39 - 4 * q^41 + 28 * q^43 + 20 * q^53 + 24 * q^59 + 2 * q^61 - 2 * q^63 + 18 * q^67 - 14 * q^69 + 8 * q^71 + 24 * q^73 + 14 * q^77 - 4 * q^81 + 34 * q^87 + 28 * q^89 + 26 * q^91 - 30 * q^93 + 2 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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