LMFDB - Embedded newform 1300.2.bn.b.1293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(93,1300)]

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, 1]))

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

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

chi := DirichletCharacter("1300.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bn (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			1293.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1300.1293
Dual form			1300.2.bn.b.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.500000	−	0.133975i	0.288675	−	0.0773503i	−0.111576	−	0.993756i	$-0.535590\pi$
$3$	0.500000	−	0.133975i	0.288675	−	0.0773503i	0.400251	+	0.916406i	$0.368923\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.133975	−	0.232051i	−0.0506376	−	0.0877070i	0.839596	−	0.543212i	$-0.182792\pi$
$7$	−0.133975	−	0.232051i	−0.0506376	−	0.0877070i	−0.890233	+	0.455505i	$0.849459\pi$
$8$		0			0
$9$	−2.36603	+	1.36603i	−0.788675	+	0.455342i
$10$		0			0
$11$	4.59808	−	1.23205i	1.38637	−	0.371477i	0.512941	−	0.858424i	$-0.328556\pi$
$11$	4.59808	−	1.23205i	1.38637	−	0.371477i	0.873432	+	0.486947i	$0.161889\pi$
$12$		0			0
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.767949	−	2.86603i	0.186255	−	0.695113i	−0.808103	−	0.589041i	$-0.799506\pi$
$17$	0.767949	−	2.86603i	0.186255	−	0.695113i	0.994358	−	0.106073i	$-0.0338276\pi$
$18$		0			0
$19$	0.866025	−	3.23205i	0.198680	−	0.741483i	−0.792604	−	0.609737i	$-0.791275\pi$
$19$	0.866025	−	3.23205i	0.198680	−	0.741483i	0.991283	−	0.131746i	$-0.0420584\pi$
$20$		0			0
$21$	−0.0980762	−	0.0980762i	−0.0214020	−	0.0214020i
$22$		0			0
$23$	0.0358984	+	0.133975i	0.00748533	+	0.0279356i	0.969567	−	0.244824i	$-0.0787302\pi$
$23$	0.0358984	+	0.133975i	0.00748533	+	0.0279356i	−0.962082	+	0.272760i	$0.912064\pi$
$24$		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	$-0.297909\pi$
$29$	1.03590	+	0.598076i	0.192362	+	0.111060i	−0.400726	+	0.916198i	$0.631242\pi$
$30$		0			0
$31$	2.26795	−	2.26795i	0.407336	−	0.407336i	−0.473473	−	0.880808i	$-0.657000\pi$
$31$	2.26795	−	2.26795i	0.407336	−	0.407336i	0.880808	+	0.473473i	$0.157000\pi$
$32$		0			0
$33$	2.13397	−	1.23205i	0.371477	−	0.214473i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.86603	−	3.23205i	0.306773	−	0.531346i	−0.670882	−	0.741564i	$-0.734084\pi$
$37$	1.86603	−	3.23205i	0.306773	−	0.531346i	0.977654	+	0.210218i	$0.0674175\pi$
$38$		0			0
$39$	−1.40192	−	1.23205i	−0.224487	−	0.197286i
$40$		0			0
$41$	−1.86603	−	6.96410i	−0.291424	−	1.08761i	−0.944016	−	0.329900i	$-0.892985\pi$
$41$	−1.86603	−	6.96410i	−0.291424	−	1.08761i	0.652592	−	0.757710i	$-0.273682\pi$
$42$		0			0
$43$	9.96410	+	2.66987i	1.51951	+	0.407152i	0.919581	−	0.392900i	$-0.128528\pi$
$43$	9.96410	+	2.66987i	1.51951	+	0.407152i	0.599930	+	0.800052i	$0.295195\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.46410			1.08875			0.544376	−	0.838842i	$-0.316767\pi$
$47$	7.46410			1.08875			0.544376	+	0.838842i	$0.316767\pi$
$48$		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
$57$		−	1.73205i		−	0.229416i
$58$		0			0
$59$	−13.7942	−	3.69615i	−1.79586	−	0.481198i	−0.802537	−	0.596602i	$-0.796517\pi$
$59$	−13.7942	−	3.69615i	−1.79586	−	0.481198i	−0.993319	+	0.115404i	$0.963184\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	0.633975	+	0.366025i	0.0798733	+	0.0461149i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−10.7942	−	6.23205i	−1.31872	−	0.761366i	−0.335201	−	0.942146i	$-0.608804\pi$
$67$	−10.7942	−	6.23205i	−1.31872	−	0.761366i	−0.983524	+	0.180780i	$0.942138\pi$
$68$		0			0
$69$	0.0358984	+	0.0621778i	0.00432166	+	0.00748533i
$70$		0			0
$71$	2.86603	+	0.767949i	0.340135	+	0.0911388i	0.424843	−	0.905267i	$-0.360329\pi$
$71$	2.86603	+	0.767949i	0.340135	+	0.0911388i	−0.0847085	+	0.996406i	$0.526996\pi$
$72$		0			0
$73$		−	0.928203i		−	0.108638i	−0.998524	−	0.0543190i	$-0.982701\pi$
$73$		−	0.928203i		−	0.108638i	0.998524	−	0.0543190i	$-0.0172988\pi$
$74$		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
$83$	3.46410			0.380235			0.190117	−	0.981761i	$-0.439113\pi$
$83$	3.46410			0.380235			0.190117	+	0.981761i	$0.439113\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.598076	+	0.160254i	0.0641205	+	0.0171810i
$88$		0			0
$89$	0.794229	+	2.96410i	0.0841881	+	0.314194i	0.995159	−	0.0982760i	$-0.0313328\pi$
$89$	0.794229	+	2.96410i	0.0841881	+	0.314194i	−0.910971	+	0.412470i	$0.864666\pi$
$90$		0			0
$91$	−0.428203	+	0.866025i	−0.0448879	+	0.0907841i
$92$		0			0
$93$	0.830127	−	1.43782i	0.0860802	−	0.149095i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.13397	+	1.23205i	−0.216672	+	0.125096i	−0.604408	−	0.796675i	$-0.706590\pi$
$97$	−2.13397	+	1.23205i	−0.216672	+	0.125096i	0.387736	+	0.921770i	$0.373257\pi$
$98$		0			0
$99$	−9.19615	+	9.19615i	−0.924248	+	0.924248i
$100$		0			0
$101$	1.50000	+	0.866025i	0.149256	+	0.0861727i	0.572768	−	0.819718i	$-0.305870\pi$
$101$	1.50000	+	0.866025i	0.149256	+	0.0861727i	−0.423512	+	0.905890i	$0.639203\pi$
$102$		0			0
$103$	−10.6603	+	10.6603i	−1.05039	+	1.05039i	−0.0517247	+	0.998661i	$0.516472\pi$
$103$	−10.6603	+	10.6603i	−1.05039	+	1.05039i	−0.998661	+	0.0517247i	$0.983528\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.964102	−	3.59808i	−0.0932032	−	0.347839i	0.903538	−	0.428509i	$-0.140961\pi$
$107$	−0.964102	−	3.59808i	−0.0932032	−	0.347839i	−0.996741	+	0.0806695i	$0.974294\pi$
$108$		0			0
$109$	11.3923	+	11.3923i	1.09118	+	1.09118i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$	11.3923	+	11.3923i	1.09118	+	1.09118i	0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	0.500000	−	1.86603i	0.0474579	−	0.177115i
$112$		0			0
$113$	4.16025	−	15.5263i	0.391364	−	1.46059i	−0.436522	−	0.899693i	$-0.643790\pi$
$113$	4.16025	−	15.5263i	0.391364	−	1.46059i	0.827886	−	0.560896i	$-0.189543\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	8.83013	+	4.36603i	0.816346	+	0.403639i
$118$		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
$123$	−1.86603	−	3.23205i	−0.168254	−	0.291424i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.50000	+	1.20577i	−0.399310	+	0.106995i	−0.452885	−	0.891569i	$-0.649605\pi$
$127$	−4.50000	+	1.20577i	−0.399310	+	0.106995i	0.0535746	+	0.998564i	$0.482939\pi$
$128$		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
$133$	−0.866025	+	0.232051i	−0.0750939	+	0.0201214i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.59808	+	9.69615i	0.478276	+	0.828398i	0.999690	−	0.0249057i	$-0.00792855\pi$
$137$	5.59808	+	9.69615i	0.478276	+	0.828398i	−0.521414	+	0.853304i	$0.674595\pi$
$138$		0			0
$139$	−5.42820	+	3.13397i	−0.460414	+	0.265820i	−0.712218	−	0.701958i	$-0.752309\pi$
$139$	−5.42820	+	3.13397i	−0.460414	+	0.265820i	0.251804	+	0.967778i	$0.418976\pi$
$140$		0			0
$141$	3.73205	−	1.00000i	0.314295	−	0.0842152i
$142$		0			0
$143$	−12.8923	−	11.3301i	−1.07811	−	0.947473i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.928203	−	3.46410i	0.0765569	−	0.285714i
$148$		0			0
$149$	4.25833	−	15.8923i	0.348856	−	1.30195i	−0.539186	−	0.842187i	$-0.681268\pi$
$149$	4.25833	−	15.8923i	0.348856	−	1.30195i	0.888042	−	0.459762i	$-0.152065\pi$
$150$		0			0
$151$	11.1962	+	11.1962i	0.911130	+	0.911130i	0.996361	−	0.0852312i	$-0.0271629\pi$
$151$	11.1962	+	11.1962i	0.911130	+	0.911130i	−0.0852312	+	0.996361i	$0.527163\pi$
$152$		0			0
$153$	2.09808	+	7.83013i	0.169619	+	0.633028i
$154$		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
$163$	7.33013	−	4.23205i	0.574140	−	0.331480i	−0.184661	−	0.982802i	$-0.559119\pi$
$163$	7.33013	−	4.23205i	0.574140	−	0.331480i	0.758801	+	0.651322i	$0.225785\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.33013	−	9.23205i	0.412458	−	0.714398i	−0.582700	−	0.812687i	$-0.698004\pi$
$167$	5.33013	−	9.23205i	0.412458	−	0.714398i	0.995158	+	0.0982896i	$0.0313372\pi$
$168$		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
$173$	−12.6962	−	3.40192i	−0.965271	−	0.258643i	−0.258441	−	0.966027i	$-0.583209\pi$
$173$	−12.6962	−	3.40192i	−0.965271	−	0.258643i	−0.706830	+	0.707384i	$0.749875\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.39230			−0.555640
$178$		0			0
$179$	0.964102	−	1.66987i	0.0720603	−	0.124812i	−0.827744	−	0.561106i	$-0.810376\pi$
$179$	0.964102	−	1.66987i	0.0720603	−	0.124812i	0.899804	+	0.436294i	$0.143709\pi$
$180$		0			0
$181$		−	1.07180i		−	0.0796660i	−0.999206	−	0.0398330i	$-0.987317\pi$
$181$		−	1.07180i		−	0.0796660i	0.999206	−	0.0398330i	$-0.0126826\pi$
$182$		0			0
$183$	0.366025	+	0.366025i	0.0270574	+	0.0270574i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	14.1244i		−	1.03288i
$188$		0			0
$189$	0.767949	+	0.205771i	0.0558601	+	0.0149677i
$190$		0			0
$191$	−5.03590	−	8.72243i	−0.364385	−	0.631133i	0.624292	−	0.781191i	$-0.285387\pi$
$191$	−5.03590	−	8.72243i	−0.364385	−	0.631133i	−0.988677	+	0.150058i	$0.952054\pi$
$192$		0			0
$193$	8.93782	+	5.16025i	0.643359	+	0.371443i	0.785907	−	0.618345i	$-0.212196\pi$
$193$	8.93782	+	5.16025i	0.643359	+	0.371443i	−0.142549	+	0.989788i	$0.545530\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.5981	+	10.1603i	1.25381	+	0.723888i	0.971864	−	0.235542i	$-0.0756865\pi$
$197$	17.5981	+	10.1603i	1.25381	+	0.723888i	0.281947	+	0.959430i	$0.409020\pi$
$198$		0			0
$199$	1.96410	+	3.40192i	0.139231	+	0.241156i	0.927206	−	0.374552i	$-0.122203\pi$
$199$	1.96410	+	3.40192i	0.139231	+	0.241156i	−0.787974	+	0.615708i	$0.788870\pi$
$200$		0			0
$201$	−6.23205	−	1.66987i	−0.439575	−	0.117784i
$202$		0			0
$203$		−	0.320508i		−	0.0224953i
$204$		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	−0.984756	−	0.173939i	$-0.944351\pi$
$211$	−4.96410	+	8.59808i	−0.341743	+	0.591916i	0.643014	+	0.765855i	$0.277684\pi$
$212$		0			0
$213$	1.53590			0.105238
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.830127	−	0.222432i	−0.0563527	−	0.0150997i
$218$		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
$223$	−9.86603	+	17.0885i	−0.660678	+	1.14433i	0.319760	+	0.947499i	$0.396398\pi$
$223$	−9.86603	+	17.0885i	−0.660678	+	1.14433i	−0.980438	+	0.196829i	$0.936936\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.401924	+	0.232051i	−0.0266766	+	0.0154018i	−0.513279	−	0.858222i	$-0.671569\pi$
$227$	−0.401924	+	0.232051i	−0.0266766	+	0.0154018i	0.486602	+	0.873624i	$0.338236\pi$
$228$		0			0
$229$	−10.8564	+	10.8564i	−0.717412	+	0.717412i	−0.968074	−	0.250663i	$-0.919351\pi$
$229$	−10.8564	+	10.8564i	−0.717412	+	0.717412i	0.250663	+	0.968074i	$0.419351\pi$
$230$		0			0
$231$	−0.571797	−	0.330127i	−0.0376215	−	0.0217208i
$232$		0			0
$233$	−11.0000	+	11.0000i	−0.720634	+	0.720634i	−0.968734	−	0.248100i	$-0.920194\pi$
$233$	−11.0000	+	11.0000i	−0.720634	+	0.720634i	0.248100	+	0.968734i	$0.420194\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.53590	−	5.73205i	−0.0997673	−	0.372337i
$238$		0			0
$239$	9.19615	+	9.19615i	0.594850	+	0.594850i	0.938937	−	0.344088i	$-0.111812\pi$
$239$	9.19615	+	9.19615i	0.594850	+	0.594850i	−0.344088	+	0.938937i	$0.611812\pi$
$240$		0			0
$241$	−4.93782	+	18.4282i	−0.318073	+	1.18706i	0.603021	+	0.797725i	$0.293963\pi$
$241$	−4.93782	+	18.4282i	−0.318073	+	1.18706i	−0.921094	+	0.389340i	$0.872703\pi$
$242$		0			0
$243$	3.19615	−	11.9282i	0.205033	−	0.765195i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−11.4282	+	3.86603i	−0.727159	+	0.245989i
$248$		0			0
$249$	1.73205	−	0.464102i	0.109764	−	0.0294112i
$250$		0			0
$251$	−23.8923	+	13.7942i	−1.50807	+	0.870684i	−0.508113	+	0.861290i	$0.669657\pi$
$251$	−23.8923	+	13.7942i	−1.50807	+	0.870684i	−0.999956	+	0.00939359i	$0.997010\pi$
$252$		0			0
$253$	0.330127	+	0.571797i	0.0207549	+	0.0359486i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.1603	−	3.52628i	0.820914	−	0.219963i	0.176168	−	0.984360i	$-0.443630\pi$
$257$	13.1603	−	3.52628i	0.820914	−	0.219963i	0.644746	+	0.764397i	$0.276963\pi$
$258$		0			0
$259$	−1.00000			−0.0621370
$260$		0			0
$261$	−3.26795			−0.202281
$262$		0			0
$263$	−17.8923	+	4.79423i	−1.10329	+	0.295625i	−0.764102	−	0.645095i	$-0.776818\pi$
$263$	−17.8923	+	4.79423i	−1.10329	+	0.295625i	−0.339184	+	0.940720i	$0.610151\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.794229	+	1.37564i	0.0486060	+	0.0841881i
$268$		0			0
$269$	23.4282	−	13.5263i	1.42844	−	0.824712i	0.431445	−	0.902139i	$-0.358004\pi$
$269$	23.4282	−	13.5263i	1.42844	−	0.824712i	0.996998	+	0.0774275i	$0.0246706\pi$
$270$		0			0
$271$	−19.7942	+	5.30385i	−1.20241	+	0.322186i	−0.803781	−	0.594925i	$-0.797182\pi$
$271$	−19.7942	+	5.30385i	−1.20241	+	0.322186i	−0.398633	+	0.917111i	$0.630515\pi$
$272$		0			0
$273$	−0.0980762	+	0.490381i	−0.00593584	+	0.0296792i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.16025	+	22.9904i	−0.370134	+	1.38136i	0.490192	+	0.871614i	$0.336927\pi$
$277$	−6.16025	+	22.9904i	−0.370134	+	1.38136i	−0.860326	+	0.509744i	$0.829740\pi$
$278$		0			0
$279$	−2.26795	+	8.46410i	−0.135779	+	0.506733i
$280$		0			0
$281$	−7.39230	−	7.39230i	−0.440988	−	0.440988i	0.451356	−	0.892344i	$-0.350940\pi$
$281$	−7.39230	−	7.39230i	−0.440988	−	0.440988i	−0.892344	+	0.451356i	$0.850940\pi$
$282$		0			0
$283$	3.35641	+	12.5263i	0.199518	+	0.744610i	0.991051	+	0.133484i	$0.0426165\pi$
$283$	3.35641	+	12.5263i	0.199518	+	0.744610i	−0.791533	+	0.611126i	$0.790717\pi$
$284$		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
$293$	19.4545	−	11.2321i	1.13654	−	0.656183i	0.190971	−	0.981596i	$-0.438836\pi$
$293$	19.4545	−	11.2321i	1.13654	−	0.656183i	0.945572	+	0.325412i	$0.105503\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−7.06218	+	12.2321i	−0.409789	+	0.709776i
$298$		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
$303$	0.866025	+	0.232051i	0.0497519	+	0.0133310i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	30.3923			1.73458			0.867290	−	0.497803i	$-0.165860\pi$
$307$	30.3923			1.73458			0.867290	+	0.497803i	$0.165860\pi$
$308$		0			0
$309$	−3.90192	+	6.75833i	−0.221973	+	0.384468i
$310$		0			0
$311$			16.2487i			0.921380i	0.887561	+	0.460690i	$0.152398\pi$
$311$			16.2487i			0.921380i	−0.887561	+	0.460690i	$0.847602\pi$
$312$		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
$317$		−	3.07180i		−	0.172529i	−0.996272	−	0.0862646i	$-0.972507\pi$
$317$		−	3.07180i		−	0.172529i	0.996272	−	0.0862646i	$-0.0274931\pi$
$318$		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
$323$	−8.59808	−	4.96410i	−0.478410	−	0.276210i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	7.22243	+	4.16987i	0.399401	+	0.230595i
$328$		0			0
$329$	−1.00000	−	1.73205i	−0.0551318	−	0.0954911i
$330$		0			0
$331$	10.3301	+	2.76795i	0.567795	+	0.152140i	0.531285	−	0.847193i	$-0.321709\pi$
$331$	10.3301	+	2.76795i	0.567795	+	0.152140i	0.0365099	+	0.999333i	$0.488376\pi$
$332$		0			0
$333$			10.1962i			0.558746i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0717968	−	0.0717968i	−0.00391102	−	0.00391102i	0.705149	−	0.709060i	$-0.250880\pi$
$337$	−0.0717968	−	0.0717968i	−0.00391102	−	0.00391102i	−0.709060	+	0.705149i	$0.750880\pi$
$338$		0			0
$339$		−	8.32051i		−	0.451908i
$340$		0			0
$341$	7.63397	−	13.2224i	0.413403	−	0.716035i
$342$		0			0
$343$	−3.73205			−0.201512
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−24.8923	−	6.66987i	−1.33629	−	0.358058i	−0.481233	−	0.876593i	$-0.659811\pi$
$347$	−24.8923	−	6.66987i	−1.33629	−	0.358058i	−0.855056	+	0.518535i	$0.826477\pi$
$348$		0			0
$349$	5.47372	+	20.4282i	0.293002	+	1.09350i	0.942792	+	0.333383i	$0.108190\pi$
$349$	5.47372	+	20.4282i	0.293002	+	1.09350i	−0.649790	+	0.760114i	$0.725143\pi$
$350$		0			0
$351$	10.4904	+	2.09808i	0.559935	+	0.111987i
$352$		0			0
$353$	−7.86603	+	13.6244i	−0.418666	+	0.725151i	−0.995806	−	0.0914944i	$-0.970836\pi$
$353$	−7.86603	+	13.6244i	−0.418666	+	0.725151i	0.577139	+	0.816646i	$0.304169\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.356406	+	0.205771i	−0.0188630	+	0.0108906i
$358$		0			0
$359$	7.58846	−	7.58846i	0.400503	−	0.400503i	−0.477907	−	0.878410i	$-0.658604\pi$
$359$	7.58846	−	7.58846i	0.400503	−	0.400503i	0.878410	+	0.477907i	$0.158604\pi$
$360$		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
$367$	2.89230	+	10.7942i	0.150977	+	0.563454i	0.999416	+	0.0341614i	$0.0108760\pi$
$367$	2.89230	+	10.7942i	0.150977	+	0.563454i	−0.848439	+	0.529293i	$0.822457\pi$
$368$		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
$373$	7.23205	−	26.9904i	0.374461	−	1.39751i	−0.479669	−	0.877450i	$-0.659243\pi$
$373$	7.23205	−	26.9904i	0.374461	−	1.39751i	0.854130	−	0.520059i	$-0.174090\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.277568	−	4.30385i	−0.0142955	−	0.221659i
$378$		0			0
$379$	−23.5263	+	6.30385i	−1.20846	+	0.323807i	−0.806159	−	0.591699i	$-0.798457\pi$
$379$	−23.5263	+	6.30385i	−1.20846	+	0.323807i	−0.402305	+	0.915506i	$0.631791\pi$
$380$		0			0
$381$	−2.08846	+	1.20577i	−0.106995	+	0.0617735i
$382$		0			0
$383$	−0.401924	−	0.696152i	−0.0205373	−	0.0355717i	0.855574	−	0.517680i	$-0.173204\pi$
$383$	−0.401924	−	0.696152i	−0.0205373	−	0.0355717i	−0.876111	+	0.482109i	$0.839871\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−27.2224	+	7.29423i	−1.38379	+	0.370786i
$388$		0			0
$389$	3.85641			0.195528			0.0977638	−	0.995210i	$-0.468831\pi$
$389$	3.85641			0.195528			0.0977638	+	0.995210i	$0.468831\pi$
$390$		0			0
$391$	0.411543			0.0208126
$392$		0			0
$393$	−6.92820	+	1.85641i	−0.349482	+	0.0936433i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.25833	−	7.37564i	−0.213719	−	0.370173i	0.739156	−	0.673534i	$-0.235225\pi$
$397$	−4.25833	−	7.37564i	−0.213719	−	0.370173i	−0.952876	+	0.303361i	$0.901891\pi$
$398$		0			0
$399$	−0.401924	+	0.232051i	−0.0201214	+	0.0116171i
$400$		0			0
$401$	5.86603	−	1.57180i	0.292935	−	0.0784918i	−0.109359	−	0.994002i	$-0.534880\pi$
$401$	5.86603	−	1.57180i	0.292935	−	0.0784918i	0.402294	+	0.915511i	$0.368213\pi$
$402$		0			0
$403$	−11.3397	−	2.26795i	−0.564873	−	0.112975i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.59808	−	17.1603i	0.227918	−	0.850602i
$408$		0			0
$409$	−3.06218	+	11.4282i	−0.151415	+	0.565088i	0.847971	+	0.530043i	$0.177824\pi$
$409$	−3.06218	+	11.4282i	−0.151415	+	0.565088i	−0.999386	+	0.0350453i	$0.988842\pi$
$410$		0			0
$411$	4.09808	+	4.09808i	0.202143	+	0.202143i
$412$		0			0
$413$	0.990381	+	3.69615i	0.0487335	+	0.181876i
$414$		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	$-0.613876\pi$
$419$	−27.3564	−	15.7942i	−1.33645	−	0.771599i	−0.986279	+	0.165088i	$0.947209\pi$
$420$		0			0
$421$	14.0718	−	14.0718i	0.685817	−	0.685817i	−0.275487	−	0.961305i	$-0.588839\pi$
$421$	14.0718	−	14.0718i	0.685817	−	0.685817i	0.961305	+	0.275487i	$0.0888392\pi$
$422$		0			0
$423$	−17.6603	+	10.1962i	−0.858671	+	0.495754i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.133975	−	0.232051i	0.00648349	−	0.0112297i
$428$		0			0
$429$	−7.96410	−	3.93782i	−0.384510	−	0.190120i
$430$		0			0
$431$	8.47372	+	31.6244i	0.408165	+	1.52329i	0.798143	+	0.602468i	$0.205816\pi$
$431$	8.47372	+	31.6244i	0.408165	+	1.52329i	−0.389979	+	0.920824i	$0.627518\pi$
$432$		0			0
$433$	−10.1603	−	2.72243i	−0.488271	−	0.130832i	0.00628046	−	0.999980i	$-0.498001\pi$
$433$	−10.1603	−	2.72243i	−0.488271	−	0.130832i	−0.494551	+	0.869149i	$0.664668\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.464102			0.0222010
$438$		0			0
$439$	−5.96410	+	10.3301i	−0.284651	+	0.493030i	−0.972524	−	0.232801i	$-0.925211\pi$
$439$	−5.96410	+	10.3301i	−0.284651	+	0.493030i	0.687873	+	0.725831i	$0.258544\pi$
$440$		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
$447$		−	8.51666i		−	0.402824i
$448$		0			0
$449$	23.9904	+	6.42820i	1.13218	+	0.303366i	0.775801	−	0.630977i	$-0.217346\pi$
$449$	23.9904	+	6.42820i	1.13218	+	0.303366i	0.356375	+	0.934343i	$0.384013\pi$
$450$		0			0
$451$	−17.1603	−	29.7224i	−0.808045	−	1.39957i
$452$		0			0
$453$	7.09808	+	4.09808i	0.333497	+	0.192544i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	25.4545	+	14.6962i	1.19071	+	0.687457i	0.958468	−	0.285201i	$-0.0920603\pi$
$457$	25.4545	+	14.6962i	1.19071	+	0.687457i	0.232243	+	0.972658i	$0.425394\pi$
$458$		0			0
$459$	4.40192	+	7.62436i	0.205464	+	0.355874i
$460$		0			0
$461$	−23.9904	−	6.42820i	−1.11734	−	0.299391i	−0.347535	−	0.937667i	$-0.612981\pi$
$461$	−23.9904	−	6.42820i	−1.11734	−	0.299391i	−0.769808	+	0.638276i	$0.779648\pi$
$462$		0			0
$463$			29.8564i			1.38754i	0.720194	+	0.693772i	$0.244053\pi$
$463$			29.8564i			1.38754i	−0.720194	+	0.693772i	$0.755947\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.1244	+	20.1244i	0.931244	+	0.931244i	0.997784	−	0.0665397i	$-0.0211959\pi$
$467$	20.1244	+	20.1244i	0.931244	+	0.931244i	−0.0665397	+	0.997784i	$0.521196\pi$
$468$		0			0
$469$			3.33975i			0.154215i
$470$		0			0
$471$	−4.90192	+	8.49038i	−0.225869	+	0.391216i
$472$		0			0
$473$	49.1051			2.25786
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−31.5885	−	8.46410i	−1.44634	−	0.387545i
$478$		0			0
$479$	−1.00962	−	3.76795i	−0.0461307	−	0.172162i	0.939017	−	0.343870i	$-0.111738\pi$
$479$	−1.00962	−	3.76795i	−0.0461307	−	0.172162i	−0.985148	+	0.171708i	$0.945071\pi$
$480$		0			0
$481$	−13.4282	+	0.866025i	−0.612273	+	0.0394874i
$482$		0			0
$483$	0.00961894	−	0.0166605i	0.000437677	−	0.000758079i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−29.7224	+	17.1603i	−1.34685	+	0.777605i	−0.987802	−	0.155713i	$-0.950232\pi$
$487$	−29.7224	+	17.1603i	−1.34685	+	0.777605i	−0.359050	+	0.933318i	$0.616899\pi$
$488$		0			0
$489$	3.09808	−	3.09808i	0.140100	−	0.140100i
$490$		0			0
$491$	−13.9641	−	8.06218i	−0.630191	−	0.363841i	0.150635	−	0.988589i	$-0.451868\pi$
$491$	−13.9641	−	8.06218i	−0.630191	−	0.363841i	−0.780826	+	0.624748i	$0.785202\pi$
$492$		0			0
$493$	2.50962	−	2.50962i	0.113028	−	0.113028i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.205771	−	0.767949i	−0.00923011	−	0.0344472i
$498$		0			0
$499$	−3.19615	−	3.19615i	−0.143079	−	0.143079i	0.631939	−	0.775018i	$-0.282259\pi$
$499$	−3.19615	−	3.19615i	−0.143079	−	0.143079i	−0.775018	+	0.631939i	$0.782259\pi$
$500$		0			0
$501$	1.42820	−	5.33013i	0.0638074	−	0.238133i
$502$		0			0
$503$	4.03590	−	15.0622i	0.179952	−	0.671589i	−0.815703	−	0.578471i	$-0.803650\pi$
$503$	4.03590	−	15.0622i	0.179952	−	0.671589i	0.995655	−	0.0931187i	$-0.0296836\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.892305	+	6.66987i	−0.0396286	+	0.296219i
$508$		0			0
$509$	−8.79423	+	2.35641i	−0.389797	+	0.104446i	−0.448394	−	0.893836i	$-0.648004\pi$
$509$	−8.79423	+	2.35641i	−0.389797	+	0.104446i	0.0585970	+	0.998282i	$0.481337\pi$
$510$		0			0
$511$	−0.215390	+	0.124356i	−0.00952831	+	0.00550117i
$512$		0			0
$513$	4.96410	+	8.59808i	0.219170	+	0.379614i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	34.3205	−	9.19615i	1.50941	−	0.404446i
$518$		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
$523$	33.8205	−	9.06218i	1.47887	−	0.396261i	0.572906	−	0.819621i	$-0.305816\pi$
$523$	33.8205	−	9.06218i	1.47887	−	0.396261i	0.905962	+	0.423360i	$0.139149\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.75833	−	8.24167i	−0.207276	−	0.359013i
$528$		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
$533$	−17.1603	+	19.5263i	−0.743293	+	0.845777i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.258330	−	0.964102i	0.0111478	−	0.0416041i
$538$		0			0
$539$	8.53590	−	31.8564i	0.367667	−	1.37215i
$540$		0			0
$541$	14.0718	+	14.0718i	0.604994	+	0.604994i	0.941634	−	0.336640i	$-0.109290\pi$
$541$	14.0718	+	14.0718i	0.604994	+	0.604994i	−0.336640	+	0.941634i	$0.609290\pi$
$542$		0			0
$543$	−0.143594	−	0.535898i	−0.00616219	−	0.0229976i
$544$		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
$553$	−2.66025	+	1.53590i	−0.113126	+	0.0653130i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.2583	−	17.7679i	0.434659	−	0.752852i	−0.562608	−	0.826724i	$-0.690202\pi$
$557$	10.2583	−	17.7679i	0.434659	−	0.752852i	0.997268	+	0.0738714i	$0.0235354\pi$
$558$		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
$563$	31.8205	+	8.52628i	1.34107	+	0.359340i	0.856833	−	0.515594i	$-0.172429\pi$
$563$	31.8205	+	8.52628i	1.34107	+	0.359340i	0.484242	+	0.874934i	$0.339096\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.78461			−0.0749466
$568$		0			0
$569$	−1.57180	+	2.72243i	−0.0658931	+	0.114130i	−0.897090	−	0.441848i	$-0.854323\pi$
$569$	−1.57180	+	2.72243i	−0.0658931	+	0.114130i	0.831197	+	0.555978i	$0.187656\pi$
$570$		0			0
$571$		−	42.1051i		−	1.76204i	−0.473075	−	0.881022i	$-0.656856\pi$
$571$		−	42.1051i		−	1.76204i	0.473075	−	0.881022i	$-0.343144\pi$
$572$		0			0
$573$	−3.68653	−	3.68653i	−0.154007	−	0.154007i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	28.9282i		−	1.20430i	−0.798384	−	0.602148i	$-0.794312\pi$
$577$		−	28.9282i		−	1.20430i	0.798384	−	0.602148i	$-0.205688\pi$
$578$		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
$583$	49.3468	+	28.4904i	2.04374	+	1.17995i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.7942	−	13.1603i	−0.940819	−	0.543182i	−0.0506017	−	0.998719i	$-0.516114\pi$
$587$	−22.7942	−	13.1603i	−0.940819	−	0.543182i	−0.890217	+	0.455537i	$0.849447\pi$
$588$		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
$593$			7.07180i			0.290404i	0.989402	+	0.145202i	$0.0463832\pi$
$593$			7.07180i			0.290404i	−0.989402	+	0.145202i	$0.953617\pi$
$594$		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	−0.944077	−	0.329726i	$-0.893044\pi$
$601$	−4.57180	+	7.91858i	−0.186487	+	0.323006i	0.757589	+	0.652732i	$0.226377\pi$
$602$		0			0
$603$	34.0526			1.38673
$604$		0			0
$605$		0			0
$606$		0			0
$607$	33.3564	+	8.93782i	1.35389	+	0.362775i	0.861571	−	0.507637i	$-0.169481\pi$
$607$	33.3564	+	8.93782i	1.35389	+	0.362775i	0.492324	+	0.870412i	$0.336148\pi$
$608$		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
$613$	−5.33013	+	9.23205i	−0.215282	+	0.372879i	−0.953360	−	0.301836i	$-0.902400\pi$
$613$	−5.33013	+	9.23205i	−0.215282	+	0.372879i	0.738078	+	0.674715i	$0.235734\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.8660	−	16.0885i	1.12184	−	0.647697i	0.179973	−	0.983672i	$-0.442399\pi$
$617$	27.8660	−	16.0885i	1.12184	−	0.647697i	0.941871	+	0.335975i	$0.109066\pi$
$618$		0			0
$619$	−5.87564	+	5.87564i	−0.236162	+	0.236162i	−0.815259	−	0.579097i	$-0.803405\pi$
$619$	−5.87564	+	5.87564i	−0.236162	+	0.236162i	0.579097	+	0.815259i	$0.303405\pi$
$620$		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
$627$	−2.13397	−	7.96410i	−0.0852227	−	0.318056i
$628$		0			0
$629$	−7.83013	−	7.83013i	−0.312208	−	0.312208i
$630$		0			0
$631$	6.20577	−	23.1603i	0.247048	−	0.921995i	−0.725295	−	0.688438i	$-0.758297\pi$
$631$	6.20577	−	23.1603i	0.247048	−	0.921995i	0.972343	−	0.233557i	$-0.0750366\pi$
$632$		0			0
$633$	−1.33013	+	4.96410i	−0.0528678	+	0.197305i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−24.9282	+	1.60770i	−0.987691	+	0.0636992i
$638$		0			0
$639$	−7.83013	+	2.09808i	−0.309755	+	0.0829986i
$640$		0			0
$641$	40.2846	−	23.2583i	1.59115	−	0.918649i	0.598036	−	0.801470i	$-0.295948\pi$
$641$	40.2846	−	23.2583i	1.59115	−	0.918649i	0.993111	−	0.117179i	$-0.0373852\pi$
$642$		0			0
$643$	−20.6506	−	35.7679i	−0.814382	−	1.41055i	−0.909771	−	0.415110i	$-0.863743\pi$
$643$	−20.6506	−	35.7679i	−0.814382	−	1.41055i	0.0953896	−	0.995440i	$-0.469590\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.96410	−	0.794229i	0.116531	−	0.0312243i	−0.200082	−	0.979779i	$-0.564121\pi$
$647$	2.96410	−	0.794229i	0.116531	−	0.0312243i	0.316613	+	0.948555i	$0.397454\pi$
$648$		0			0
$649$	−67.9808			−2.66848
$650$		0			0
$651$	−0.444864			−0.0174356
$652$		0			0
$653$	0.696152	−	0.186533i	0.0272425	−	0.00729962i	−0.245172	−	0.969480i	$-0.578844\pi$
$653$	0.696152	−	0.186533i	0.0272425	−	0.00729962i	0.272415	+	0.962180i	$0.412178\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.26795	+	2.19615i	0.0494674	+	0.0856801i
$658$		0			0
$659$	29.2128	−	16.8660i	1.13797	−	0.657007i	0.192043	−	0.981387i	$-0.438489\pi$
$659$	29.2128	−	16.8660i	1.13797	−	0.657007i	0.945927	+	0.324380i	$0.105155\pi$
$660$		0			0
$661$	−1.59808	+	0.428203i	−0.0621580	+	0.0166552i	−0.289764	−	0.957098i	$-0.593577\pi$
$661$	−1.59808	+	0.428203i	−0.0621580	+	0.0166552i	0.227606	+	0.973753i	$0.426910\pi$
$662$		0			0
$663$	−4.60770	+	3.07180i	−0.178948	+	0.119299i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.0429399	+	0.160254i	−0.00166264	+	0.00620506i
$668$		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
$673$	−7.23205	−	26.9904i	−0.278775	−	1.04040i	−0.953269	−	0.302122i	$-0.902305\pi$
$673$	−7.23205	−	26.9904i	−0.278775	−	1.04040i	0.674494	−	0.738280i	$-0.264362\pi$
$674$		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
$683$	−26.3827	+	15.2321i	−1.00951	+	0.582838i	−0.911047	−	0.412303i	$-0.864725\pi$
$683$	−26.3827	+	15.2321i	−1.00951	+	0.582838i	−0.0984586	+	0.995141i	$0.531391\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.97372	+	6.88269i	−0.151607	+	0.262591i
$688$		0			0
$689$	8.46410	−	42.3205i	0.322457	−	1.61228i
$690$		0			0
$691$	−0.0621778	−	0.232051i	−0.00236536	−	0.00882763i	0.964733	−	0.263230i	$-0.0847879\pi$
$691$	−0.0621778	−	0.232051i	−0.00236536	−	0.00882763i	−0.967098	+	0.254403i	$0.918121\pi$
$692$		0			0
$693$	3.36603	+	0.901924i	0.127865	+	0.0342613i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−21.3923			−0.810291
$698$		0			0
$699$	−4.02628	+	6.97372i	−0.152288	+	0.263770i
$700$		0			0
$701$			29.0718i			1.09803i	0.835814	+	0.549013i	$0.184996\pi$
$701$			29.0718i			1.09803i	−0.835814	+	0.549013i	$0.815004\pi$
$702$		0			0
$703$	−8.83013	−	8.83013i	−0.333035	−	0.333035i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	0.464102i		−	0.0174543i
$708$		0			0
$709$	5.59808	+	1.50000i	0.210240	+	0.0563337i	0.362402	−	0.932022i	$-0.381957\pi$
$709$	5.59808	+	1.50000i	0.210240	+	0.0563337i	−0.152162	+	0.988356i	$0.548623\pi$
$710$		0			0
$711$	15.6603	+	27.1244i	0.587305	+	1.01724i
$712$		0			0
$713$	0.385263	+	0.222432i	0.0144282	+	0.00833014i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.83013	+	3.36603i	0.217730	+	0.125707i
$718$		0			0
$719$	14.8923	+	25.7942i	0.555389	+	0.961962i	0.997873	+	0.0651859i	$0.0207641\pi$
$719$	14.8923	+	25.7942i	0.555389	+	0.961962i	−0.442484	+	0.896776i	$0.645903\pi$
$720$		0			0
$721$	3.90192	+	1.04552i	0.145315	+	0.0389371i
$722$		0			0
$723$			9.87564i			0.367279i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	13.5885	+	13.5885i	0.503968	+	0.503968i	0.912669	−	0.408701i	$-0.134018\pi$
$727$	13.5885	+	13.5885i	0.503968	+	0.503968i	−0.408701	+	0.912669i	$0.634018\pi$
$728$		0			0
$729$			13.5885i			0.503276i
$730$		0			0
$731$	15.3038	−	26.5070i	0.566033	−	0.980398i
$732$		0			0
$733$	38.6410			1.42724			0.713619	−	0.700534i	$-0.247055\pi$
$733$	38.6410			1.42724			0.713619	+	0.700534i	$0.247055\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−57.3109	−	15.3564i	−2.11107	−	0.565661i
$738$		0			0
$739$	10.7417	+	40.0885i	0.395139	+	1.47468i	0.821544	+	0.570145i	$0.193113\pi$
$739$	10.7417	+	40.0885i	0.395139	+	1.47468i	−0.426405	+	0.904532i	$0.640220\pi$
$740$		0			0
$741$	−5.19615	+	3.46410i	−0.190885	+	0.127257i
$742$		0			0
$743$	17.5981	−	30.4808i	0.645611	−	1.11823i	−0.338549	−	0.940949i	$-0.609936\pi$
$743$	17.5981	−	30.4808i	0.645611	−	1.11823i	0.984160	−	0.177282i	$-0.0567305\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−8.19615	+	4.73205i	−0.299882	+	0.173137i
$748$		0			0
$749$	−0.705771	+	0.705771i	−0.0257883	+	0.0257883i
$750$		0			0
$751$	31.7487	+	18.3301i	1.15853	+	0.668876i	0.950951	−	0.309343i	$-0.100109\pi$
$751$	31.7487	+	18.3301i	1.15853	+	0.668876i	0.207576	+	0.978219i	$0.433442\pi$
$752$		0			0
$753$	−10.0981	+	10.0981i	−0.367994	+	0.367994i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	4.30385	+	16.0622i	0.156426	+	0.583790i	0.998979	+	0.0451764i	$0.0143850\pi$
$757$	4.30385	+	16.0622i	0.156426	+	0.583790i	−0.842553	+	0.538613i	$0.818948\pi$
$758$		0			0
$759$	0.241670	+	0.241670i	0.00877206	+	0.00877206i
$760$		0			0
$761$	2.66987	−	9.96410i	0.0967828	−	0.361198i	−0.900501	−	0.434854i	$-0.856800\pi$
$761$	2.66987	−	9.96410i	0.0967828	−	0.361198i	0.997284	+	0.0736557i	$0.0234666\pi$
$762$		0			0
$763$	1.11731	−	4.16987i	0.0404495	−	0.150960i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	16.5000	+	48.7750i	0.595780	+	1.76116i
$768$		0			0
$769$	−5.33013	+	1.42820i	−0.192209	+	0.0515023i	−0.353639	−	0.935382i	$-0.615056\pi$
$769$	−5.33013	+	1.42820i	−0.192209	+	0.0515023i	0.161430	+	0.986884i	$0.448389\pi$
$770$		0			0
$771$	6.10770	−	3.52628i	0.219963	−	0.126996i
$772$		0			0
$773$	−21.0622	−	36.4808i	−0.757554	−	1.31212i	−0.944095	−	0.329675i	$-0.893061\pi$
$773$	−21.0622	−	36.4808i	−0.757554	−	1.31212i	0.186541	−	0.982447i	$-0.440272\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.500000	+	0.133975i	−0.0179374	+	0.00480631i
$778$		0			0
$779$	−24.1244			−0.864345
$780$		0			0
$781$	14.1244			0.505409
$782$		0			0
$783$	−3.42820	+	0.918584i	−0.122514	+	0.0328275i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−21.9904	−	38.0885i	−0.783872	−	1.35771i	−0.929670	−	0.368392i	$-0.879908\pi$
$787$	−21.9904	−	38.0885i	−0.783872	−	1.35771i	0.145798	−	0.989314i	$-0.453425\pi$
$788$		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
$793$	1.59808	−	3.23205i	0.0567494	−	0.114773i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.62436	−	24.7224i	0.234647	−	0.875713i	−0.743661	−	0.668557i	$-0.766912\pi$
$797$	6.62436	−	24.7224i	0.234647	−	0.875713i	0.978308	−	0.207157i	$-0.0664210\pi$
$798$		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
$803$	−1.14359	−	4.26795i	−0.0403565	−	0.150613i
$804$		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	$-0.540869\pi$
$809$	−29.8923	−	17.2583i	−1.05096	−	0.606771i	−0.922917	+	0.384998i	$0.874202\pi$
$810$		0			0
$811$	32.1244	−	32.1244i	1.12804	−	1.12804i	0.137543	−	0.990496i	$-0.456080\pi$
$811$	32.1244	−	32.1244i	1.12804	−	1.12804i	0.990496	−	0.137543i	$-0.0439205\pi$
$812$		0			0
$813$	−9.18653	+	5.30385i	−0.322186	+	0.186014i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	17.2583	−	29.8923i	0.603793	−	1.04580i
$818$		0			0
$819$	−0.169873	−	2.63397i	−0.00593584	−	0.0920385i
$820$		0			0
$821$	−4.40192	−	16.4282i	−0.153628	−	0.573348i	−0.999219	−	0.0395165i	$-0.987418\pi$
$821$	−4.40192	−	16.4282i	−0.153628	−	0.573348i	0.845591	−	0.533832i	$-0.179248\pi$
$822$		0			0
$823$	18.3564	+	4.91858i	0.639864	+	0.171451i	0.564142	−	0.825678i	$-0.309207\pi$
$823$	18.3564	+	4.91858i	0.639864	+	0.171451i	0.0757222	+	0.997129i	$0.475874\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	24.5359			0.853197			0.426598	−	0.904441i	$-0.359712\pi$
$827$	24.5359			0.853197			0.426598	+	0.904441i	$0.359712\pi$
$828$		0			0
$829$	−1.03590	+	1.79423i	−0.0359782	+	0.0623161i	−0.883454	−	0.468518i	$-0.844788\pi$
$829$	−1.03590	+	1.79423i	−0.0359782	+	0.0623161i	0.847476	+	0.530834i	$0.178121\pi$
$830$		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
$837$			9.51666i			0.328944i
$838$		0			0
$839$	25.5263	+	6.83975i	0.881265	+	0.236134i	0.670953	−	0.741500i	$-0.265885\pi$
$839$	25.5263	+	6.83975i	0.881265	+	0.236134i	0.210312	+	0.977634i	$0.432552\pi$
$840$		0			0
$841$	−13.7846	−	23.8756i	−0.475331	−	0.823298i
$842$		0			0
$843$	−4.68653	−	2.70577i	−0.161413	−	0.0931917i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.70577	−	1.56218i	−0.0929714	−	0.0536771i
$848$		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
$853$			55.5692i			1.90265i	0.308184	+	0.951327i	$0.400279\pi$
$853$			55.5692i			1.90265i	−0.308184	+	0.951327i	$0.599721\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.60770	+	8.60770i	0.294033	+	0.294033i	0.838671	−	0.544638i	$-0.183333\pi$
$857$	8.60770	+	8.60770i	0.294033	+	0.294033i	−0.544638	+	0.838671i	$0.683333\pi$
$858$		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
$863$	20.2487			0.689274			0.344637	−	0.938736i	$-0.388002\pi$
$863$	20.2487			0.689274			0.344637	+	0.938736i	$0.388002\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.09808	+	1.09808i	0.139178	+	0.0372926i
$868$		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
$873$	3.36603	−	5.83013i	0.113923	−	0.197320i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−35.5981	+	20.5526i	−1.20206	+	0.694011i	−0.961013	−	0.276502i	$-0.910825\pi$
$877$	−35.5981	+	20.5526i	−1.20206	+	0.694011i	−0.241048	+	0.970513i	$0.577491\pi$
$878$		0			0
$879$	8.22243	−	8.22243i	0.277336	−	0.277336i
$880$		0			0
$881$	−1.96410	−	1.13397i	−0.0661723	−	0.0382046i	0.466549	−	0.884495i	$-0.345497\pi$
$881$	−1.96410	−	1.13397i	−0.0661723	−	0.0382046i	−0.532721	+	0.846291i	$0.678831\pi$
$882$		0			0
$883$	−16.8038	+	16.8038i	−0.565494	+	0.565494i	−0.930863	−	0.365368i	$-0.880943\pi$
$883$	−16.8038	+	16.8038i	−0.565494	+	0.565494i	0.365368	+	0.930863i	$0.380943\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.748711	+	2.79423i	0.0251393	+	0.0938210i	0.977356	−	0.211603i	$-0.0678684\pi$
$887$	0.748711	+	2.79423i	0.0251393	+	0.0938210i	−0.952216	+	0.305424i	$0.901202\pi$
$888$		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
$893$	6.46410	−	24.1244i	0.216313	−	0.807291i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.114737	−	0.232051i	0.00383095	−	0.00774795i
$898$		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
$903$	−0.715390	−	1.23909i	−0.0238067	−	0.0412344i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	12.9641	−	3.47372i	0.430466	−	0.115343i	−0.0370789	−	0.999312i	$-0.511805\pi$
$907$	12.9641	−	3.47372i	0.430466	−	0.115343i	0.467545	+	0.883969i	$0.345139\pi$
$908$		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
$913$	15.9282	−	4.26795i	0.527147	−	0.141249i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.85641	+	3.21539i	0.0613039	+	0.106182i
$918$		0			0
$919$	37.7487	−	21.7942i	1.24522	−	0.718925i	0.275064	−	0.961426i	$-0.411301\pi$
$919$	37.7487	−	21.7942i	1.24522	−	0.718925i	0.970151	+	0.242501i	$0.0779677\pi$
$920$		0			0
$921$	15.1962	−	4.07180i	0.500730	−	0.134170i
$922$		0			0
$923$	−3.42820	−	10.1340i	−0.112841	−	0.333564i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	10.6603	−	39.7846i	0.350129	−	1.30670i
$928$		0			0
$929$	0.794229	−	2.96410i	0.0260578	−	0.0972490i	−0.951672	−	0.307115i	$-0.900636\pi$
$929$	0.794229	−	2.96410i	0.0260578	−	0.0972490i	0.977730	+	0.209866i	$0.0673029\pi$
$930$		0			0
$931$	−16.3923	−	16.3923i	−0.537236	−	0.537236i
$932$		0			0
$933$	2.17691	+	8.12436i	0.0712690	+	0.265979i
$934$		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	−0.945373	−	0.325991i	$-0.894302\pi$
$941$	−19.0000	+	19.0000i	−0.619382	+	0.619382i	0.325991	+	0.945373i	$0.394302\pi$
$942$		0			0
$943$	0.866025	−	0.500000i	0.0282017	−	0.0162822i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.74167	+	3.01666i	−0.0565967	+	0.0980283i	−0.892936	−	0.450184i	$-0.851358\pi$
$947$	−1.74167	+	3.01666i	−0.0565967	+	0.0980283i	0.836339	+	0.548213i	$0.184692\pi$
$948$		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
$953$	18.6244	+	4.99038i	0.603302	+	0.161654i	0.547526	−	0.836789i	$-0.315570\pi$
$953$	18.6244	+	4.99038i	0.603302	+	0.161654i	0.0557765	+	0.998443i	$0.482237\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.94744			0.0952772
$958$		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
$967$		−	10.6410i		−	0.342192i	−0.985254	−	0.171096i	$-0.945269\pi$
$967$		−	10.6410i		−	0.342192i	0.985254	−	0.171096i	$-0.0547308\pi$
$968$		0			0
$969$	−4.96410	−	1.33013i	−0.159470	−	0.0427298i
$970$		0			0
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$		0			0
$973$	1.45448	+	0.839746i	0.0466286	+	0.0269210i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.650635	−	0.375644i	−0.0208157	−	0.0120179i	0.489556	−	0.871972i	$-0.337159\pi$
$977$	−0.650635	−	0.375644i	−0.0208157	−	0.0120179i	−0.510372	+	0.859954i	$0.670492\pi$
$978$		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
$983$			42.9282i			1.36920i	0.728920	+	0.684599i	$0.240022\pi$
$983$			42.9282i			1.36920i	−0.728920	+	0.684599i	$0.759978\pi$
$984$		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	0.423334	+	0.905974i	$0.360860\pi$
$991$	−18.0359	+	31.2391i	−0.572929	+	0.992342i	−0.996263	+	0.0863688i	$0.972474\pi$
$992$		0			0
$993$	5.53590			0.175676
$994$		0			0
$995$		0			0
$996$		0			0
$997$	8.69615	+	2.33013i	0.275410	+	0.0737959i	0.393880	−	0.919162i	$-0.371132\pi$
$997$	8.69615	+	2.33013i	0.275410	+	0.0737959i	−0.118470	+	0.992958i	$0.537799\pi$
$998$		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.bn.b.1293.1		4
5.2	odd	4		1300.2.bs.a.357.1		4
5.3	odd	4		260.2.bk.b.97.1	yes	4
5.4	even	2		260.2.bf.a.253.1	yes	4
13.11	odd	12		1300.2.bs.a.193.1		4
65.24	odd	12		260.2.bk.b.193.1	yes	4
65.37	even	12	inner	1300.2.bn.b.557.1		4
65.63	even	12		260.2.bf.a.37.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.a.37.1	✓	4	65.63	even	12
260.2.bf.a.253.1	yes	4	5.4	even	2
260.2.bk.b.97.1	yes	4	5.3	odd	4
260.2.bk.b.193.1	yes	4	65.24	odd	12
1300.2.bn.b.557.1		4	65.37	even	12	inner
1300.2.bn.b.1293.1		4	1.1	even	1	trivial
1300.2.bs.a.193.1		4	13.11	odd	12
1300.2.bs.a.357.1		4	5.2	odd	4

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.bn (of order \(12\), degree \(4\), minimal)

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

Introduction

L-functions

Modular forms

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