LMFDB - Embedded newform 260.2.bf.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$4$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.37
Dual form			260.2.bf.a.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.133975i) q^{3} +(2.00000 - 1.00000i) q^{5} +(0.133975 - 0.232051i) q^{7} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.133975i) q^{3} +(2.00000 - 1.00000i) q^{5} +(0.133975 - 0.232051i) q^{7} +(-2.36603 - 1.36603i) q^{9} +(4.59808 + 1.23205i) q^{11} +(2.00000 - 3.00000i) q^{13} +(-1.13397 + 0.232051i) q^{15} +(-0.767949 - 2.86603i) q^{17} +(0.866025 + 3.23205i) q^{19} +(-0.0980762 + 0.0980762i) q^{21} +(-0.0358984 + 0.133975i) q^{23} +(3.00000 - 4.00000i) q^{25} +(2.09808 + 2.09808i) q^{27} +(1.03590 - 0.598076i) q^{29} +(2.26795 + 2.26795i) q^{31} +(-2.13397 - 1.23205i) q^{33} +(0.0358984 - 0.598076i) q^{35} +(-1.86603 - 3.23205i) q^{37} +(-1.40192 + 1.23205i) q^{39} +(-1.86603 + 6.96410i) q^{41} +(-9.96410 + 2.66987i) q^{43} +(-6.09808 - 0.366025i) q^{45} -7.46410 q^{47} +(3.46410 + 6.00000i) q^{49} +1.53590i q^{51} +(-8.46410 + 8.46410i) q^{53} +(10.4282 - 2.13397i) q^{55} -1.73205i q^{57} +(-13.7942 + 3.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-0.633975 + 0.366025i) q^{63} +(1.00000 - 8.00000i) q^{65} +(10.7942 - 6.23205i) q^{67} +(0.0358984 - 0.0621778i) q^{69} +(2.86603 - 0.767949i) q^{71} -0.928203i q^{73} +(-2.03590 + 1.59808i) q^{75} +(0.901924 - 0.901924i) q^{77} +11.4641i q^{79} +(3.33013 + 5.76795i) q^{81} -3.46410 q^{83} +(-4.40192 - 4.96410i) q^{85} +(-0.598076 + 0.160254i) q^{87} +(0.794229 - 2.96410i) q^{89} +(-0.428203 - 0.866025i) q^{91} +(-0.830127 - 1.43782i) q^{93} +(4.96410 + 5.59808i) q^{95} +(2.13397 + 1.23205i) q^{97} +(-9.19615 - 9.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9	$ 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 10 q^{17} + 10 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} + 18 q^{29} + 16 q^{31} - 12 q^{33} + 14 q^{35} - 4 q^{37} - 16 q^{39} - 4 q^{41} - 26 q^{43} - 14 q^{45} - 16 q^{47} - 20 q^{53} + 14 q^{55} - 24 q^{59} + 2 q^{61} - 6 q^{63} + 4 q^{65} + 12 q^{67} + 14 q^{69} + 8 q^{71} - 22 q^{75} + 14 q^{77} - 4 q^{81} - 28 q^{85} + 8 q^{87} - 28 q^{89} + 26 q^{91} + 14 q^{93} + 6 q^{95} + 12 q^{97} - 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 10 * q^17 + 10 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 + 18 * q^29 + 16 * q^31 - 12 * q^33 + 14 * q^35 - 4 * q^37 - 16 * q^39 - 4 * q^41 - 26 * q^43 - 14 * q^45 - 16 * q^47 - 20 * q^53 + 14 * q^55 - 24 * q^59 + 2 * q^61 - 6 * q^63 + 4 * q^65 + 12 * q^67 + 14 * q^69 + 8 * q^71 - 22 * q^75 + 14 * q^77 - 4 * q^81 - 28 * q^85 + 8 * q^87 - 28 * q^89 + 26 * q^91 + 14 * q^93 + 6 * q^95 + 12 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.133975i	−0.288675	−	0.0773503i	0.111576	−	0.993756i	$-0.464410\pi$
$3$	−0.500000	−	0.133975i	−0.288675	−	0.0773503i	−0.400251	+	0.916406i	$0.631077\pi$
$4$		0			0
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$		0			0
$7$	0.133975	−	0.232051i	0.0506376	−	0.0877070i	−0.839596	−	0.543212i	$-0.817208\pi$
$7$	0.133975	−	0.232051i	0.0506376	−	0.0877070i	0.890233	+	0.455505i	$0.150541\pi$
$8$		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
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$		0			0
$15$	−1.13397	+	0.232051i	−0.292791	+	0.0599153i
$16$		0			0
$17$	−0.767949	−	2.86603i	−0.186255	−	0.695113i	−0.994358	−	0.106073i	$-0.966172\pi$
$17$	−0.767949	−	2.86603i	−0.186255	−	0.695113i	0.808103	−	0.589041i	$-0.200494\pi$
$18$		0			0
$19$	0.866025	+	3.23205i	0.198680	+	0.741483i	0.991283	+	0.131746i	$0.0420584\pi$
$19$	0.866025	+	3.23205i	0.198680	+	0.741483i	−0.792604	+	0.609737i	$0.791275\pi$
$20$		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	$-0.921270\pi$
$23$	−0.0358984	+	0.133975i	−0.00748533	+	0.0279356i	0.962082	+	0.272760i	$0.0879364\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$	2.09808	+	2.09808i	0.403775	+	0.403775i
$28$		0			0
$29$	1.03590	−	0.598076i	0.192362	−	0.111060i	−0.400726	−	0.916198i	$-0.631242\pi$
$29$	1.03590	−	0.598076i	0.192362	−	0.111060i	0.593088	+	0.805138i	$0.297909\pi$
$30$		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
$33$	−2.13397	−	1.23205i	−0.371477	−	0.214473i
$34$		0			0
$35$	0.0358984	−	0.598076i	0.00606793	−	0.101093i
$36$		0			0
$37$	−1.86603	−	3.23205i	−0.306773	−	0.531346i	0.670882	−	0.741564i	$-0.265916\pi$
$37$	−1.86603	−	3.23205i	−0.306773	−	0.531346i	−0.977654	+	0.210218i	$0.932582\pi$
$38$		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
$43$	−9.96410	+	2.66987i	−1.51951	+	0.407152i	−0.919581	−	0.392900i	$-0.871472\pi$
$43$	−9.96410	+	2.66987i	−1.51951	+	0.407152i	−0.599930	+	0.800052i	$0.704805\pi$
$44$		0			0
$45$	−6.09808	−	0.366025i	−0.909048	−	0.0545638i
$46$		0			0
$47$	−7.46410			−1.08875			−0.544376	−	0.838842i	$-0.683233\pi$
$47$	−7.46410			−1.08875			−0.544376	+	0.838842i	$0.683233\pi$
$48$		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	−0.178737	+	0.983897i	$0.557201\pi$
$53$	−8.46410	+	8.46410i	−1.16263	+	1.16263i	−0.983897	+	0.178737i	$0.942799\pi$
$54$		0			0
$55$	10.4282	−	2.13397i	1.40614	−	0.287745i
$56$		0			0
$57$		−	1.73205i		−	0.229416i
$58$		0			0
$59$	−13.7942	+	3.69615i	−1.79586	+	0.481198i	−0.993319	−	0.115404i	$-0.963184\pi$
$59$	−13.7942	+	3.69615i	−1.79586	+	0.481198i	−0.802537	+	0.596602i	$0.796517\pi$
$60$		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
$63$	−0.633975	+	0.366025i	−0.0798733	+	0.0461149i
$64$		0			0
$65$	1.00000	−	8.00000i	0.124035	−	0.992278i
$66$		0			0
$67$	10.7942	−	6.23205i	1.31872	−	0.761366i	0.335201	−	0.942146i	$-0.391196\pi$
$67$	10.7942	−	6.23205i	1.31872	−	0.761366i	0.983524	+	0.180780i	$0.0578623\pi$
$68$		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
$73$		−	0.928203i		−	0.108638i	−0.998524	−	0.0543190i	$-0.982701\pi$
$73$		−	0.928203i		−	0.108638i	0.998524	−	0.0543190i	$-0.0172988\pi$
$74$		0			0
$75$	−2.03590	+	1.59808i	−0.235085	+	0.184530i
$76$		0			0
$77$	0.901924	−	0.901924i	0.102784	−	0.102784i
$78$		0			0
$79$			11.4641i			1.28981i	0.764262	+	0.644906i	$0.223104\pi$
$79$			11.4641i			1.28981i	−0.764262	+	0.644906i	$0.776896\pi$
$80$		0			0
$81$	3.33013	+	5.76795i	0.370014	+	0.640883i
$82$		0			0
$83$	−3.46410			−0.380235			−0.190117	−	0.981761i	$-0.560887\pi$
$83$	−3.46410			−0.380235			−0.190117	+	0.981761i	$0.560887\pi$
$84$		0			0
$85$	−4.40192	−	4.96410i	−0.477456	−	0.538432i
$86$		0			0
$87$	−0.598076	+	0.160254i	−0.0641205	+	0.0171810i
$88$		0			0
$89$	0.794229	−	2.96410i	0.0841881	−	0.314194i	−0.910971	−	0.412470i	$-0.864666\pi$
$89$	0.794229	−	2.96410i	0.0841881	−	0.314194i	0.995159	+	0.0982760i	$0.0313328\pi$
$90$		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
$95$	4.96410	+	5.59808i	0.509306	+	0.574351i
$96$		0			0
$97$	2.13397	+	1.23205i	0.216672	+	0.125096i	0.604408	−	0.796675i	$-0.293410\pi$
$97$	2.13397	+	1.23205i	0.216672	+	0.125096i	−0.387736	+	0.921770i	$0.626743\pi$
$98$		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	0.998661	+	0.0517247i	$0.0164718\pi$
$103$	10.6603	+	10.6603i	1.05039	+	1.05039i	0.0517247	+	0.998661i	$0.483528\pi$
$104$		0			0
$105$	−0.0980762	+	0.294229i	−0.00957126	+	0.0287138i
$106$		0			0
$107$	0.964102	−	3.59808i	0.0932032	−	0.347839i	−0.903538	−	0.428509i	$-0.859039\pi$
$107$	0.964102	−	3.59808i	0.0932032	−	0.347839i	0.996741	+	0.0806695i	$0.0257058\pi$
$108$		0			0
$109$	11.3923	−	11.3923i	1.09118	−	1.09118i	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	11.3923	−	11.3923i	1.09118	−	1.09118i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		0			0
$111$	0.500000	+	1.86603i	0.0474579	+	0.177115i
$112$		0			0
$113$	−4.16025	−	15.5263i	−0.391364	−	1.46059i	−0.827886	−	0.560896i	$-0.810457\pi$
$113$	−4.16025	−	15.5263i	−0.391364	−	1.46059i	0.436522	−	0.899693i	$-0.356210\pi$
$114$		0			0
$115$	0.0621778	+	0.303848i	0.00579811	+	0.0283339i
$116$		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
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$	4.50000	+	1.20577i	0.399310	+	0.106995i	0.452885	−	0.891569i	$-0.350395\pi$
$127$	4.50000	+	1.20577i	0.399310	+	0.106995i	−0.0535746	+	0.998564i	$0.517061\pi$
$128$		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
$135$	6.29423	+	2.09808i	0.541721	+	0.180574i
$136$		0			0
$137$	−5.59808	+	9.69615i	−0.478276	+	0.828398i	−0.999690	−	0.0249057i	$-0.992071\pi$
$137$	−5.59808	+	9.69615i	−0.478276	+	0.828398i	0.521414	+	0.853304i	$0.325405\pi$
$138$		0			0
$139$	−5.42820	−	3.13397i	−0.460414	−	0.265820i	0.251804	−	0.967778i	$-0.418976\pi$
$139$	−5.42820	−	3.13397i	−0.460414	−	0.265820i	−0.712218	+	0.701958i	$0.752309\pi$
$140$		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
$145$	1.47372	−	2.23205i	0.122386	−	0.185362i
$146$		0			0
$147$	−0.928203	−	3.46410i	−0.0765569	−	0.285714i
$148$		0			0
$149$	4.25833	+	15.8923i	0.348856	+	1.30195i	0.888042	+	0.459762i	$0.152065\pi$
$149$	4.25833	+	15.8923i	0.348856	+	1.30195i	−0.539186	+	0.842187i	$0.681268\pi$
$150$		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
$153$	−2.09808	+	7.83013i	−0.169619	+	0.633028i
$154$		0			0
$155$	6.80385	+	2.26795i	0.546498	+	0.182166i
$156$		0			0
$157$	13.3923	+	13.3923i	1.06882	+	1.06882i	0.997450	+	0.0713726i	$0.0227379\pi$
$157$	13.3923	+	13.3923i	1.06882	+	1.06882i	0.0713726	+	0.997450i	$0.477262\pi$
$158$		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	$-0.440881\pi$
$163$	−7.33013	−	4.23205i	−0.574140	−	0.331480i	−0.758801	+	0.651322i	$0.774215\pi$
$164$		0			0
$165$	−5.50000	−	0.330127i	−0.428174	−	0.0257004i
$166$		0			0
$167$	−5.33013	−	9.23205i	−0.412458	−	0.714398i	0.582700	−	0.812687i	$-0.301996\pi$
$167$	−5.33013	−	9.23205i	−0.412458	−	0.714398i	−0.995158	+	0.0982896i	$0.968663\pi$
$168$		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	$-0.416791\pi$
$173$	12.6962	−	3.40192i	0.965271	−	0.258643i	0.706830	+	0.707384i	$0.250125\pi$
$174$		0			0
$175$	−0.526279	−	1.23205i	−0.0397830	−	0.0931343i
$176$		0			0
$177$	7.39230			0.555640
$178$		0			0
$179$	0.964102	+	1.66987i	0.0720603	+	0.124812i	0.899804	−	0.436294i	$-0.143709\pi$
$179$	0.964102	+	1.66987i	0.0720603	+	0.124812i	−0.827744	+	0.561106i	$0.810376\pi$
$180$		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
$185$	−6.96410	−	4.59808i	−0.512011	−	0.338057i
$186$		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	−0.988677	−	0.150058i	$-0.952054\pi$
$191$	−5.03590	+	8.72243i	−0.364385	+	0.631133i	0.624292	+	0.781191i	$0.285387\pi$
$192$		0			0
$193$	−8.93782	+	5.16025i	−0.643359	+	0.371443i	−0.785907	−	0.618345i	$-0.787804\pi$
$193$	−8.93782	+	5.16025i	−0.643359	+	0.371443i	0.142549	+	0.989788i	$0.454470\pi$
$194$		0			0
$195$	−1.57180	+	3.86603i	−0.112559	+	0.276852i
$196$		0			0
$197$	−17.5981	+	10.1603i	−1.25381	+	0.723888i	−0.971864	−	0.235542i	$-0.924314\pi$
$197$	−17.5981	+	10.1603i	−1.25381	+	0.723888i	−0.281947	+	0.959430i	$0.590980\pi$
$198$		0			0
$199$	1.96410	−	3.40192i	0.139231	−	0.241156i	−0.787974	−	0.615708i	$-0.788870\pi$
$199$	1.96410	−	3.40192i	0.139231	−	0.241156i	0.927206	+	0.374552i	$0.122203\pi$
$200$		0			0
$201$	−6.23205	+	1.66987i	−0.439575	+	0.117784i
$202$		0			0
$203$		−	0.320508i		−	0.0224953i
$204$		0			0
$205$	3.23205	+	15.7942i	0.225736	+	1.10312i
$206$		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
$213$	−1.53590			−0.105238
$214$		0			0
$215$	−17.2583	+	15.3038i	−1.17701	+	1.04371i
$216$		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	0.980438	+	0.196829i	$0.0630644\pi$
$223$	9.86603	+	17.0885i	0.660678	+	1.14433i	−0.319760	+	0.947499i	$0.603602\pi$
$224$		0			0
$225$	−12.5622	+	5.36603i	−0.837479	+	0.357735i
$226$		0			0
$227$	0.401924	+	0.232051i	0.0266766	+	0.0154018i	0.513279	−	0.858222i	$-0.328431\pi$
$227$	0.401924	+	0.232051i	0.0266766	+	0.0154018i	−0.486602	+	0.873624i	$0.661764\pi$
$228$		0			0
$229$	−10.8564	−	10.8564i	−0.717412	−	0.717412i	0.250663	−	0.968074i	$-0.419351\pi$
$229$	−10.8564	−	10.8564i	−0.717412	−	0.717412i	−0.968074	+	0.250663i	$0.919351\pi$
$230$		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	$-0.0798063\pi$
$233$	11.0000	+	11.0000i	0.720634	+	0.720634i	−0.248100	+	0.968734i	$0.579806\pi$
$234$		0			0
$235$	−14.9282	+	7.46410i	−0.973809	+	0.486904i
$236$		0			0
$237$	1.53590	−	5.73205i	0.0997673	−	0.372337i
$238$		0			0
$239$	9.19615	−	9.19615i	0.594850	−	0.594850i	−0.344088	−	0.938937i	$-0.611812\pi$
$239$	9.19615	−	9.19615i	0.594850	−	0.594850i	0.938937	+	0.344088i	$0.111812\pi$
$240$		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
$243$	−3.19615	−	11.9282i	−0.205033	−	0.765195i
$244$		0			0
$245$	12.9282	+	8.53590i	0.825953	+	0.545339i
$246$		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	−0.999956	−	0.00939359i	$-0.997010\pi$
$251$	−23.8923	−	13.7942i	−1.50807	−	0.870684i	−0.508113	−	0.861290i	$-0.669657\pi$
$252$		0			0
$253$	−0.330127	+	0.571797i	−0.0207549	+	0.0359486i
$254$		0			0
$255$	1.53590	+	3.07180i	0.0961817	+	0.192363i
$256$		0			0
$257$	−13.1603	−	3.52628i	−0.820914	−	0.219963i	−0.176168	−	0.984360i	$-0.556370\pi$
$257$	−13.1603	−	3.52628i	−0.820914	−	0.219963i	−0.644746	+	0.764397i	$0.723037\pi$
$258$		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	$-0.223182\pi$
$263$	17.8923	+	4.79423i	1.10329	+	0.295625i	0.339184	+	0.940720i	$0.389849\pi$
$264$		0			0
$265$	−8.46410	+	25.3923i	−0.519946	+	1.55984i
$266$		0			0
$267$	−0.794229	+	1.37564i	−0.0486060	+	0.0841881i
$268$		0			0
$269$	23.4282	+	13.5263i	1.42844	+	0.824712i	0.996998	−	0.0774275i	$-0.0246706\pi$
$269$	23.4282	+	13.5263i	1.42844	+	0.824712i	0.431445	+	0.902139i	$0.358004\pi$
$270$		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
$273$	0.0980762	+	0.490381i	0.00593584	+	0.0296792i
$274$		0			0
$275$	18.7224	−	14.6962i	1.12901	−	0.886211i
$276$		0			0
$277$	6.16025	+	22.9904i	0.370134	+	1.38136i	0.860326	+	0.509744i	$0.170260\pi$
$277$	6.16025	+	22.9904i	0.370134	+	1.38136i	−0.490192	+	0.871614i	$0.663073\pi$
$278$		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
$283$	−3.35641	+	12.5263i	−0.199518	+	0.744610i	0.791533	+	0.611126i	$0.209283\pi$
$283$	−3.35641	+	12.5263i	−0.199518	+	0.744610i	−0.991051	+	0.133484i	$0.957384\pi$
$284$		0			0
$285$	−1.73205	−	3.46410i	−0.102598	−	0.205196i
$286$		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	$-0.561164\pi$
$293$	−19.4545	−	11.2321i	−1.13654	−	0.656183i	−0.945572	+	0.325412i	$0.894497\pi$
$294$		0			0
$295$	−23.8923	+	21.1865i	−1.39106	+	1.23353i
$296$		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
$305$	0.133975	−	2.23205i	0.00767136	−	0.127807i
$306$		0			0
$307$	−30.3923			−1.73458			−0.867290	−	0.497803i	$-0.834140\pi$
$307$	−30.3923			−1.73458			−0.867290	+	0.497803i	$0.834140\pi$
$308$		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	0.161752	−	0.986832i	$-0.448286\pi$
$313$	20.3205	−	20.3205i	1.14858	−	1.14858i	0.986832	−	0.161752i	$-0.0517143\pi$
$314$		0			0
$315$	−0.901924	+	1.36603i	−0.0508176	+	0.0769668i
$316$		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
$325$	−6.00000	−	17.0000i	−0.332820	−	0.942990i
$326$		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	0.0365099	−	0.999333i	$-0.488376\pi$
$331$	10.3301	−	2.76795i	0.567795	−	0.152140i	0.531285	+	0.847193i	$0.321709\pi$
$332$		0			0
$333$			10.1962i			0.558746i
$334$		0			0
$335$	15.3564	−	23.2583i	0.839010	−	1.27074i
$336$		0			0
$337$	0.0717968	−	0.0717968i	0.00391102	−	0.00391102i	−0.705149	−	0.709060i	$-0.749120\pi$
$337$	0.0717968	−	0.0717968i	0.00391102	−	0.00391102i	0.709060	+	0.705149i	$0.249120\pi$
$338$		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
$345$	0.00961894	−	0.160254i	0.000517866	−	0.00862779i
$346$		0			0
$347$	24.8923	−	6.66987i	1.33629	−	0.358058i	0.481233	−	0.876593i	$-0.340189\pi$
$347$	24.8923	−	6.66987i	1.33629	−	0.358058i	0.855056	+	0.518535i	$0.173523\pi$
$348$		0			0
$349$	5.47372	−	20.4282i	0.293002	−	1.09350i	−0.649790	−	0.760114i	$-0.725143\pi$
$349$	5.47372	−	20.4282i	0.293002	−	1.09350i	0.942792	−	0.333383i	$-0.108190\pi$
$350$		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	$-0.0291644\pi$
$353$	7.86603	+	13.6244i	0.418666	+	0.725151i	−0.577139	+	0.816646i	$0.695831\pi$
$354$		0			0
$355$	4.96410	−	4.40192i	0.263467	−	0.233630i
$356$		0			0
$357$	0.356406	+	0.205771i	0.0188630	+	0.0108906i
$358$		0			0
$359$	7.58846	+	7.58846i	0.400503	+	0.400503i	0.878410	−	0.477907i	$-0.158604\pi$
$359$	7.58846	+	7.58846i	0.400503	+	0.400503i	−0.477907	+	0.878410i	$0.658604\pi$
$360$		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
$365$	−0.928203	−	1.85641i	−0.0485844	−	0.0971688i
$366$		0			0
$367$	−2.89230	+	10.7942i	−0.150977	+	0.563454i	0.848439	+	0.529293i	$0.177543\pi$
$367$	−2.89230	+	10.7942i	−0.150977	+	0.563454i	−0.999416	+	0.0341614i	$0.989124\pi$
$368$		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	−0.854130	−	0.520059i	$-0.825910\pi$
$373$	−7.23205	−	26.9904i	−0.374461	−	1.39751i	0.479669	−	0.877450i	$-0.340757\pi$
$374$		0			0
$375$	−2.47372	+	5.23205i	−0.127742	+	0.270182i
$376$		0			0
$377$	0.277568	−	4.30385i	0.0142955	−	0.221659i
$378$		0			0
$379$	−23.5263	−	6.30385i	−1.20846	−	0.323807i	−0.402305	−	0.915506i	$-0.631791\pi$
$379$	−23.5263	−	6.30385i	−1.20846	−	0.323807i	−0.806159	+	0.591699i	$0.798457\pi$
$380$		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	$-0.826796\pi$
$383$	0.401924	−	0.696152i	0.0205373	−	0.0355717i	0.876111	+	0.482109i	$0.160129\pi$
$384$		0			0
$385$	0.901924	−	2.70577i	0.0459663	−	0.137899i
$386$		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
$395$	11.4641	+	22.9282i	0.576822	+	1.15364i
$396$		0			0
$397$	4.25833	−	7.37564i	0.213719	−	0.370173i	−0.739156	−	0.673534i	$-0.764775\pi$
$397$	4.25833	−	7.37564i	0.213719	−	0.370173i	0.952876	+	0.303361i	$0.0981088\pi$
$398$		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
$403$	11.3397	−	2.26795i	0.564873	−	0.112975i
$404$		0			0
$405$	12.4282	+	8.20577i	0.617562	+	0.407748i
$406$		0			0
$407$	−4.59808	−	17.1603i	−0.227918	−	0.850602i
$408$		0			0
$409$	−3.06218	−	11.4282i	−0.151415	−	0.565088i	−0.999386	−	0.0350453i	$-0.988842\pi$
$409$	−3.06218	−	11.4282i	−0.151415	−	0.565088i	0.847971	−	0.530043i	$-0.177824\pi$
$410$		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
$415$	−6.92820	+	3.46410i	−0.340092	+	0.170046i
$416$		0			0
$417$	2.29423	+	2.29423i	0.112349	+	0.112349i
$418$		0			0
$419$	−27.3564	+	15.7942i	−1.33645	+	0.771599i	−0.986279	−	0.165088i	$-0.947209\pi$
$419$	−27.3564	+	15.7942i	−1.33645	+	0.771599i	−0.350169	+	0.936687i	$0.613876\pi$
$420$		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
$423$	17.6603	+	10.1962i	0.858671	+	0.495754i
$424$		0			0
$425$	−13.7679	−	5.52628i	−0.667844	−	0.268064i
$426$		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	−0.389979	−	0.920824i	$-0.627518\pi$
$431$	8.47372	−	31.6244i	0.408165	−	1.52329i	0.798143	−	0.602468i	$-0.205816\pi$
$432$		0			0
$433$	10.1603	−	2.72243i	0.488271	−	0.130832i	−0.00628046	−	0.999980i	$-0.501999\pi$
$433$	10.1603	−	2.72243i	0.488271	−	0.130832i	0.494551	+	0.869149i	$0.335332\pi$
$434$		0			0
$435$	−1.03590	+	0.918584i	−0.0496675	+	0.0440427i
$436$		0			0
$437$	−0.464102			−0.0222010
$438$		0			0
$439$	−5.96410	−	10.3301i	−0.284651	−	0.493030i	0.687873	−	0.725831i	$-0.258544\pi$
$439$	−5.96410	−	10.3301i	−0.284651	−	0.493030i	−0.972524	+	0.232801i	$0.925211\pi$
$440$		0			0
$441$		−	18.9282i		−	0.901343i
$442$		0			0
$443$	27.0526	−	27.0526i	1.28531	−	1.28531i	0.347700	−	0.937606i	$-0.386963\pi$
$443$	27.0526	−	27.0526i	1.28531	−	1.28531i	0.937606	−	0.347700i	$-0.113037\pi$
$444$		0			0
$445$	−1.37564	−	6.72243i	−0.0652118	−	0.318674i
$446$		0			0
$447$		−	8.51666i		−	0.402824i
$448$		0			0
$449$	23.9904	−	6.42820i	1.13218	−	0.303366i	0.356375	−	0.934343i	$-0.384013\pi$
$449$	23.9904	−	6.42820i	1.13218	−	0.303366i	0.775801	+	0.630977i	$0.217346\pi$
$450$		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
$455$	−1.72243	−	1.30385i	−0.0807489	−	0.0611253i
$456$		0			0
$457$	−25.4545	+	14.6962i	−1.19071	+	0.687457i	−0.958468	−	0.285201i	$-0.907940\pi$
$457$	−25.4545	+	14.6962i	−1.19071	+	0.687457i	−0.232243	+	0.972658i	$0.574606\pi$
$458$		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
$463$			29.8564i			1.38754i	0.720194	+	0.693772i	$0.244053\pi$
$463$			29.8564i			1.38754i	−0.720194	+	0.693772i	$0.755947\pi$
$464$		0			0
$465$	−3.09808	−	2.04552i	−0.143670	−	0.0948586i
$466$		0			0
$467$	−20.1244	+	20.1244i	−0.931244	+	0.931244i	−0.997784	−	0.0665397i	$-0.978804\pi$
$467$	−20.1244	+	20.1244i	−0.931244	+	0.931244i	0.0665397	+	0.997784i	$0.478804\pi$
$468$		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
$475$	15.5263	+	6.23205i	0.712395	+	0.285946i
$476$		0			0
$477$	31.5885	−	8.46410i	1.44634	−	0.387545i
$478$		0			0
$479$	−1.00962	+	3.76795i	−0.0461307	+	0.172162i	−0.985148	−	0.171708i	$-0.945071\pi$
$479$	−1.00962	+	3.76795i	−0.0461307	+	0.172162i	0.939017	+	0.343870i	$0.111738\pi$
$480$		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
$485$	5.50000	+	0.330127i	0.249742	+	0.0149903i
$486$		0			0
$487$	29.7224	+	17.1603i	1.34685	+	0.777605i	0.987802	−	0.155713i	$-0.0497675\pi$
$487$	29.7224	+	17.1603i	1.34685	+	0.777605i	0.359050	+	0.933318i	$0.383101\pi$
$488$		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
$495$	−27.5885	−	9.19615i	−1.24001	−	0.413336i
$496$		0			0
$497$	0.205771	−	0.767949i	0.00923011	−	0.0344472i
$498$		0			0
$499$	−3.19615	+	3.19615i	−0.143079	+	0.143079i	−0.775018	−	0.631939i	$-0.782259\pi$
$499$	−3.19615	+	3.19615i	−0.143079	+	0.143079i	0.631939	+	0.775018i	$0.282259\pi$
$500$		0			0
$501$	1.42820	+	5.33013i	0.0638074	+	0.238133i
$502$		0			0
$503$	−4.03590	−	15.0622i	−0.179952	−	0.671589i	−0.995655	−	0.0931187i	$-0.970316\pi$
$503$	−4.03590	−	15.0622i	−0.179952	−	0.671589i	0.815703	−	0.578471i	$-0.196350\pi$
$504$		0			0
$505$	2.13397	−	3.23205i	0.0949606	−	0.143824i
$506$		0			0
$507$	0.892305	+	6.66987i	0.0396286	+	0.296219i
$508$		0			0
$509$	−8.79423	−	2.35641i	−0.389797	−	0.104446i	0.0585970	−	0.998282i	$-0.481337\pi$
$509$	−8.79423	−	2.35641i	−0.389797	−	0.104446i	−0.448394	+	0.893836i	$0.648004\pi$
$510$		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
$515$	31.9808	+	10.6603i	1.40924	+	0.469747i
$516$		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	$-0.694184\pi$
$523$	−33.8205	−	9.06218i	−1.47887	−	0.396261i	−0.905962	+	0.423360i	$0.860851\pi$
$524$		0			0
$525$	0.0980762	+	0.686533i	0.00428040	+	0.0299628i
$526$		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
$535$	−1.66987	−	8.16025i	−0.0721949	−	0.352799i
$536$		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	−0.336640	−	0.941634i	$-0.609290\pi$
$541$	14.0718	−	14.0718i	0.604994	−	0.604994i	0.941634	+	0.336640i	$0.109290\pi$
$542$		0			0
$543$	0.143594	−	0.535898i	0.00616219	−	0.0229976i
$544$		0			0
$545$	11.3923	−	34.1769i	0.487993	−	1.46398i
$546$		0			0
$547$	−9.19615	−	9.19615i	−0.393199	−	0.393199i	0.482627	−	0.875826i	$-0.339683\pi$
$547$	−9.19615	−	9.19615i	−0.393199	−	0.393199i	−0.875826	+	0.482627i	$0.839683\pi$
$548$		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
$555$	2.86603	+	3.23205i	0.121656	+	0.137193i
$556$		0			0
$557$	−10.2583	−	17.7679i	−0.434659	−	0.752852i	0.562608	−	0.826724i	$-0.309798\pi$
$557$	−10.2583	−	17.7679i	−0.434659	−	0.752852i	−0.997268	+	0.0738714i	$0.976465\pi$
$558$		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	$-0.827571\pi$
$563$	−31.8205	+	8.52628i	−1.34107	+	0.359340i	−0.484242	+	0.874934i	$0.660904\pi$
$564$		0			0
$565$	−23.8468	−	26.8923i	−1.00324	−	1.13137i
$566$		0			0
$567$	1.78461			0.0749466
$568$		0			0
$569$	−1.57180	−	2.72243i	−0.0658931	−	0.114130i	0.831197	−	0.555978i	$-0.187656\pi$
$569$	−1.57180	−	2.72243i	−0.0658931	−	0.114130i	−0.897090	+	0.441848i	$0.854323\pi$
$570$		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
$575$	0.428203	+	0.545517i	0.0178573	+	0.0227496i
$576$		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
$585$	−13.2942	+	17.5622i	−0.549649	+	0.726107i
$586$		0			0
$587$	22.7942	−	13.1603i	0.940819	−	0.543182i	0.0506017	−	0.998719i	$-0.483886\pi$
$587$	22.7942	−	13.1603i	0.940819	−	0.543182i	0.890217	+	0.455537i	$0.150553\pi$
$588$		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
$595$	−1.74167	+	0.356406i	−0.0714015	+	0.0146112i
$596$		0			0
$597$	−1.43782	+	1.43782i	−0.0588461	+	0.0588461i
$598$		0			0
$599$			5.60770i			0.229124i	0.993416	+	0.114562i	$0.0365465\pi$
$599$			5.60770i			0.229124i	−0.993416	+	0.114562i	$0.963454\pi$
$600$		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
$603$	−34.0526			−1.38673
$604$		0			0
$605$	26.0263	+	1.56218i	1.05812	+	0.0635116i
$606$		0			0
$607$	−33.3564	+	8.93782i	−1.35389	+	0.362775i	−0.861571	−	0.507637i	$-0.830519\pi$
$607$	−33.3564	+	8.93782i	−1.35389	+	0.362775i	−0.492324	+	0.870412i	$0.663852\pi$
$608$		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	$-0.0975997\pi$
$613$	5.33013	+	9.23205i	0.215282	+	0.372879i	−0.738078	+	0.674715i	$0.764266\pi$
$614$		0			0
$615$	0.500000	−	8.33013i	0.0201619	−	0.335903i
$616$		0			0
$617$	−27.8660	−	16.0885i	−1.12184	−	0.647697i	−0.179973	−	0.983672i	$-0.557601\pi$
$617$	−27.8660	−	16.0885i	−1.12184	−	0.647697i	−0.941871	+	0.335975i	$0.890934\pi$
$618$		0			0
$619$	−5.87564	−	5.87564i	−0.236162	−	0.236162i	0.579097	−	0.815259i	$-0.303405\pi$
$619$	−5.87564	−	5.87564i	−0.236162	−	0.236162i	−0.815259	+	0.579097i	$0.803405\pi$
$620$		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
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		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	0.972343	+	0.233557i	$0.0750366\pi$
$631$	6.20577	+	23.1603i	0.247048	+	0.921995i	−0.725295	+	0.688438i	$0.758297\pi$
$632$		0			0
$633$	1.33013	+	4.96410i	0.0528678	+	0.197305i
$634$		0			0
$635$	10.2058	−	2.08846i	0.405004	−	0.0828779i
$636$		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	0.993111	+	0.117179i	$0.0373852\pi$
$641$	40.2846	+	23.2583i	1.59115	+	0.918649i	0.598036	+	0.801470i	$0.295948\pi$
$642$		0			0
$643$	20.6506	−	35.7679i	0.814382	−	1.41055i	−0.0953896	−	0.995440i	$-0.530410\pi$
$643$	20.6506	−	35.7679i	0.814382	−	1.41055i	0.909771	−	0.415110i	$-0.136257\pi$
$644$		0			0
$645$	10.6795	−	5.33975i	0.420505	−	0.210252i
$646$		0			0
$647$	−2.96410	−	0.794229i	−0.116531	−	0.0312243i	0.200082	−	0.979779i	$-0.435879\pi$
$647$	−2.96410	−	0.794229i	−0.116531	−	0.0312243i	−0.316613	+	0.948555i	$0.602546\pi$
$648$		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	$-0.421156\pi$
$653$	−0.696152	−	0.186533i	−0.0272425	−	0.00729962i	−0.272415	+	0.962180i	$0.587822\pi$
$654$		0			0
$655$	−27.7128	+	13.8564i	−1.08283	+	0.541415i
$656$		0			0
$657$	−1.26795	+	2.19615i	−0.0494674	+	0.0856801i
$658$		0			0
$659$	29.2128	+	16.8660i	1.13797	+	0.657007i	0.945927	−	0.324380i	$-0.105155\pi$
$659$	29.2128	+	16.8660i	1.13797	+	0.657007i	0.192043	+	0.981387i	$0.438489\pi$
$660$		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
$663$	4.60770	+	3.07180i	0.178948	+	0.119299i
$664$		0			0
$665$	1.96410	−	0.401924i	0.0761646	−	0.0155859i
$666$		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	−0.674494	−	0.738280i	$-0.735638\pi$
$673$	7.23205	−	26.9904i	0.278775	−	1.04040i	0.953269	−	0.302122i	$-0.0976952\pi$
$674$		0			0
$675$	14.6865	−	2.09808i	0.565285	−	0.0807550i
$676$		0			0
$677$	−10.3205	−	10.3205i	−0.396649	−	0.396649i	0.480400	−	0.877049i	$-0.340491\pi$
$677$	−10.3205	−	10.3205i	−0.396649	−	0.396649i	−0.877049	+	0.480400i	$0.840491\pi$
$678$		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	$-0.135275\pi$
$683$	26.3827	+	15.2321i	1.00951	+	0.582838i	0.0984586	+	0.995141i	$0.468609\pi$
$684$		0			0
$685$	−1.50000	+	24.9904i	−0.0573121	+	0.954833i
$686$		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	−0.967098	−	0.254403i	$-0.918121\pi$
$691$	−0.0621778	+	0.232051i	−0.00236536	+	0.00882763i	0.964733	+	0.263230i	$0.0847879\pi$
$692$		0			0
$693$	−3.36603	+	0.901924i	−0.127865	+	0.0342613i
$694$		0			0
$695$	−13.9904	−	0.839746i	−0.530685	−	0.0318534i
$696$		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	$-0.815004\pi$
$701$		−	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
$705$	8.46410	−	1.73205i	0.318777	−	0.0652328i
$706$		0			0
$707$		−	0.464102i		−	0.0174543i
$708$		0			0
$709$	5.59808	−	1.50000i	0.210240	−	0.0563337i	−0.152162	−	0.988356i	$-0.548623\pi$
$709$	5.59808	−	1.50000i	0.210240	−	0.0563337i	0.362402	+	0.932022i	$0.381957\pi$
$710$		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
$715$	14.4545	−	35.5526i	0.540567	−	1.32959i
$716$		0			0
$717$	−5.83013	+	3.36603i	−0.217730	+	0.125707i
$718$		0			0
$719$	14.8923	−	25.7942i	0.555389	−	0.961962i	−0.442484	−	0.896776i	$-0.645903\pi$
$719$	14.8923	−	25.7942i	0.555389	−	0.961962i	0.997873	−	0.0651859i	$-0.0207641\pi$
$720$		0			0
$721$	3.90192	−	1.04552i	0.145315	−	0.0389371i
$722$		0			0
$723$			9.87564i			0.367279i
$724$		0			0
$725$	0.715390	−	5.93782i	0.0265689	−	0.220525i
$726$		0			0
$727$	−13.5885	+	13.5885i	−0.503968	+	0.503968i	−0.912669	−	0.408701i	$-0.865982\pi$
$727$	−13.5885	+	13.5885i	−0.503968	+	0.503968i	0.408701	+	0.912669i	$0.365982\pi$
$728$		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	$-0.752945\pi$
$733$	−38.6410			−1.42724			−0.713619	+	0.700534i	$0.752945\pi$
$734$		0			0
$735$	−5.32051	−	6.00000i	−0.196250	−	0.221313i
$736$		0			0
$737$	57.3109	−	15.3564i	2.11107	−	0.565661i
$738$		0			0
$739$	10.7417	−	40.0885i	0.395139	−	1.47468i	−0.426405	−	0.904532i	$-0.640220\pi$
$739$	10.7417	−	40.0885i	0.395139	−	1.47468i	0.821544	−	0.570145i	$-0.193113\pi$
$740$		0			0
$741$	−5.19615	−	3.46410i	−0.190885	−	0.127257i
$742$		0			0
$743$	−17.5981	−	30.4808i	−0.645611	−	1.11823i	−0.984160	−	0.177282i	$-0.943270\pi$
$743$	−17.5981	−	30.4808i	−0.645611	−	1.11823i	0.338549	−	0.940949i	$-0.390064\pi$
$744$		0			0
$745$	24.4090	+	27.5263i	0.894275	+	1.00848i
$746$		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	0.207576	−	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
$755$	11.1962	−	33.5885i	0.407470	−	1.22241i
$756$		0			0
$757$	−4.30385	+	16.0622i	−0.156426	+	0.583790i	0.842553	+	0.538613i	$0.181052\pi$
$757$	−4.30385	+	16.0622i	−0.156426	+	0.583790i	−0.998979	+	0.0451764i	$0.985615\pi$
$758$		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
$763$	−1.11731	−	4.16987i	−0.0404495	−	0.150960i
$764$		0			0
$765$	3.63397	+	17.7583i	0.131387	+	0.642054i
$766$		0			0
$767$	−16.5000	+	48.7750i	−0.595780	+	1.76116i
$768$		0			0
$769$	−5.33013	−	1.42820i	−0.192209	−	0.0515023i	0.161430	−	0.986884i	$-0.448389\pi$
$769$	−5.33013	−	1.42820i	−0.192209	−	0.0515023i	−0.353639	+	0.935382i	$0.615056\pi$
$770$		0			0
$771$	6.10770	+	3.52628i	0.219963	+	0.126996i
$772$		0			0
$773$	21.0622	−	36.4808i	0.757554	−	1.31212i	−0.186541	−	0.982447i	$-0.559728\pi$
$773$	21.0622	−	36.4808i	0.757554	−	1.31212i	0.944095	−	0.329675i	$-0.106939\pi$
$774$		0			0
$775$	15.8756	−	2.26795i	0.570270	−	0.0814671i
$776$		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
$785$	40.1769	+	13.3923i	1.43398	+	0.477992i
$786$		0			0
$787$	21.9904	−	38.0885i	0.783872	−	1.35771i	−0.145798	−	0.989314i	$-0.546575\pi$
$787$	21.9904	−	38.0885i	0.783872	−	1.35771i	0.929670	−	0.368392i	$-0.120092\pi$
$788$		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
$795$	7.63397	−	11.5622i	0.270749	−	0.410068i
$796$		0			0
$797$	−6.62436	−	24.7224i	−0.234647	−	0.875713i	−0.978308	−	0.207157i	$-0.933579\pi$
$797$	−6.62436	−	24.7224i	−0.234647	−	0.875713i	0.743661	−	0.668557i	$-0.233088\pi$
$798$		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
$805$	0.0788383	+	0.0262794i	0.00277869	+	0.000926229i
$806$		0			0
$807$	−9.90192	−	9.90192i	−0.348564	−	0.348564i
$808$		0			0
$809$	−29.8923	+	17.2583i	−1.05096	+	0.606771i	−0.922917	−	0.384998i	$-0.874202\pi$
$809$	−29.8923	+	17.2583i	−1.05096	+	0.606771i	−0.128040	+	0.991769i	$0.540869\pi$
$810$		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
$813$	9.18653	+	5.30385i	0.322186	+	0.186014i
$814$		0			0
$815$	−18.8923	−	1.13397i	−0.661769	−	0.0397214i
$816$		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	0.845591	+	0.533832i	$0.179248\pi$
$821$	−4.40192	+	16.4282i	−0.153628	+	0.573348i	−0.999219	+	0.0395165i	$0.987418\pi$
$822$		0			0
$823$	−18.3564	+	4.91858i	−0.639864	+	0.171451i	−0.564142	−	0.825678i	$-0.690793\pi$
$823$	−18.3564	+	4.91858i	−0.639864	+	0.171451i	−0.0757222	+	0.997129i	$0.524126\pi$
$824$		0			0
$825$	−11.3301	+	4.83975i	−0.394464	+	0.168498i
$826$		0			0
$827$	−24.5359			−0.853197			−0.426598	−	0.904441i	$-0.640288\pi$
$827$	−24.5359			−0.853197			−0.426598	+	0.904441i	$0.640288\pi$
$828$		0			0
$829$	−1.03590	−	1.79423i	−0.0359782	−	0.0623161i	0.847476	−	0.530834i	$-0.178121\pi$
$829$	−1.03590	−	1.79423i	−0.0359782	−	0.0623161i	−0.883454	+	0.468518i	$0.844788\pi$
$830$		0			0
$831$		−	12.3205i		−	0.427394i
$832$		0			0
$833$	14.5359	−	14.5359i	0.503639	−	0.503639i
$834$		0			0
$835$	−19.8923	−	13.1340i	−0.688402	−	0.454520i
$836$		0			0
$837$			9.51666i			0.328944i
$838$		0			0
$839$	25.5263	−	6.83975i	0.881265	−	0.236134i	0.210312	−	0.977634i	$-0.432552\pi$
$839$	25.5263	−	6.83975i	0.881265	−	0.236134i	0.670953	+	0.741500i	$0.265885\pi$
$840$		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
$845$	−22.0000	−	19.0000i	−0.756823	−	0.653620i
$846$		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
$855$	−4.09808	−	20.0263i	−0.140151	−	0.684884i
$856$		0			0
$857$	−8.60770	+	8.60770i	−0.294033	+	0.294033i	−0.838671	−	0.544638i	$-0.816667\pi$
$857$	−8.60770	+	8.60770i	−0.294033	+	0.294033i	0.544638	+	0.838671i	$0.316667\pi$
$858$		0			0
$859$		−	46.1051i		−	1.57309i	−0.617535	−	0.786543i	$-0.711869\pi$
$859$		−	46.1051i		−	1.57309i	0.617535	−	0.786543i	$-0.288131\pi$
$860$		0			0
$861$	−0.500000	−	0.866025i	−0.0170400	−	0.0295141i
$862$		0			0
$863$	−20.2487			−0.689274			−0.344637	−	0.938736i	$-0.611998\pi$
$863$	−20.2487			−0.689274			−0.344637	+	0.938736i	$0.611998\pi$
$864$		0			0
$865$	21.9904	−	19.5000i	0.747695	−	0.663020i
$866$		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
$875$	−2.28461	−	1.93782i	−0.0772339	−	0.0655103i
$876$		0			0
$877$	35.5981	+	20.5526i	1.20206	+	0.694011i	0.961013	−	0.276502i	$-0.0891754\pi$
$877$	35.5981	+	20.5526i	1.20206	+	0.694011i	0.241048	+	0.970513i	$0.422509\pi$
$878$		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	0.930863	−	0.365368i	$-0.119057\pi$
$883$	16.8038	+	16.8038i	0.565494	+	0.565494i	−0.365368	+	0.930863i	$0.619057\pi$
$884$		0			0
$885$	14.7846	−	7.39230i	0.496979	−	0.248490i
$886$		0			0
$887$	−0.748711	+	2.79423i	−0.0251393	+	0.0938210i	−0.977356	−	0.211603i	$-0.932132\pi$
$887$	−0.748711	+	2.79423i	−0.0251393	+	0.0938210i	0.952216	+	0.305424i	$0.0987982\pi$
$888$		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
$895$	3.59808	+	2.37564i	0.120270	+	0.0794090i
$896$		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
$905$	1.07180	+	2.14359i	0.0356277	+	0.0712555i
$906$		0			0
$907$	−12.9641	−	3.47372i	−0.430466	−	0.115343i	0.0370789	−	0.999312i	$-0.488195\pi$
$907$	−12.9641	−	3.47372i	−0.430466	−	0.115343i	−0.467545	+	0.883969i	$0.654861\pi$
$908$		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
$915$	−0.366025	+	1.09808i	−0.0121004	+	0.0363013i
$916$		0			0
$917$	−1.85641	+	3.21539i	−0.0613039	+	0.106182i
$918$		0			0
$919$	37.7487	+	21.7942i	1.24522	+	0.718925i	0.970151	−	0.242501i	$-0.0779677\pi$
$919$	37.7487	+	21.7942i	1.24522	+	0.718925i	0.275064	+	0.961426i	$0.411301\pi$
$920$		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
$925$	−18.5263	−	2.23205i	−0.609140	−	0.0733894i
$926$		0			0
$927$	−10.6603	−	39.7846i	−0.350129	−	1.30670i
$928$		0			0
$929$	0.794229	+	2.96410i	0.0260578	+	0.0972490i	0.977730	−	0.209866i	$-0.0673029\pi$
$929$	0.794229	+	2.96410i	0.0260578	+	0.0972490i	−0.951672	+	0.307115i	$0.900636\pi$
$930$		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
$935$	−14.1244	−	28.2487i	−0.461916	−	0.923832i
$936$		0			0
$937$	41.7846	+	41.7846i	1.36504	+	1.36504i	0.867357	+	0.497687i	$0.165817\pi$
$937$	41.7846	+	41.7846i	1.36504	+	1.36504i	0.497687	+	0.867357i	$0.334183\pi$
$938$		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
$943$	−0.866025	−	0.500000i	−0.0282017	−	0.0162822i
$944$		0			0
$945$	1.33013	−	1.17949i	0.0432690	−	0.0383689i
$946$		0			0
$947$	1.74167	+	3.01666i	0.0565967	+	0.0980283i	0.892936	−	0.450184i	$-0.148642\pi$
$947$	1.74167	+	3.01666i	0.0565967	+	0.0980283i	−0.836339	+	0.548213i	$0.815308\pi$
$948$		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	$-0.684430\pi$
$953$	−18.6244	+	4.99038i	−0.603302	+	0.161654i	−0.0557765	+	0.998443i	$0.517763\pi$
$954$		0			0
$955$	−1.34936	+	22.4808i	−0.0436644	+	0.727460i
$956$		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
$965$	−12.7154	+	19.2583i	−0.409323	+	0.619948i
$966$		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	0.469897	+	0.882721i	$0.344291\pi$
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	−0.999408	+	0.0344175i	$0.989042\pi$
$972$		0			0
$973$	−1.45448	+	0.839746i	−0.0466286	+	0.0269210i
$974$		0			0
$975$	0.722432	+	9.30385i	0.0231363	+	0.297962i
$976$		0			0
$977$	0.650635	−	0.375644i	0.0208157	−	0.0120179i	−0.489556	−	0.871972i	$-0.662841\pi$
$977$	0.650635	−	0.375644i	0.0208157	−	0.0120179i	0.510372	+	0.859954i	$0.329508\pi$
$978$		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
$985$	−25.0359	+	37.9186i	−0.797710	+	1.20819i
$986$		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
$993$	−5.53590			−0.175676
$994$		0			0
$995$	0.526279	−	8.76795i	0.0166842	−	0.277963i
$996$		0			0
$997$	−8.69615	+	2.33013i	−0.275410	+	0.0737959i	−0.393880	−	0.919162i	$-0.628868\pi$
$997$	−8.69615	+	2.33013i	−0.275410	+	0.0737959i	0.118470	+	0.992958i	$0.462201\pi$
$998$		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	260.2.bf.a.37.1	✓	4
5.2	odd	4		1300.2.bs.a.193.1		4
5.3	odd	4		260.2.bk.b.193.1	yes	4
5.4	even	2		1300.2.bn.b.557.1		4
13.6	odd	12		260.2.bk.b.97.1	yes	4
65.19	odd	12		1300.2.bs.a.357.1		4
65.32	even	12		1300.2.bn.b.1293.1		4
65.58	even	12	inner	260.2.bf.a.253.1	yes	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.133975i) q^{3} +(2.00000 - 1.00000i) q^{5} +(0.133975 - 0.232051i) q^{7} +(-2.36603 - 1.36603i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.133975i) q^{3} +(2.00000 - 1.00000i) q^{5} +(0.133975 - 0.232051i) q^{7} +(-2.36603 - 1.36603i) q^{9} +(4.59808 + 1.23205i) q^{11} +(2.00000 - 3.00000i) q^{13} +(-1.13397 + 0.232051i) q^{15} +(-0.767949 - 2.86603i) q^{17} +(0.866025 + 3.23205i) q^{19} +(-0.0980762 + 0.0980762i) q^{21} +(-0.0358984 + 0.133975i) q^{23} +(3.00000 - 4.00000i) q^{25} +(2.09808 + 2.09808i) q^{27} +(1.03590 - 0.598076i) q^{29} +(2.26795 + 2.26795i) q^{31} +(-2.13397 - 1.23205i) q^{33} +(0.0358984 - 0.598076i) q^{35} +(-1.86603 - 3.23205i) q^{37} +(-1.40192 + 1.23205i) q^{39} +(-1.86603 + 6.96410i) q^{41} +(-9.96410 + 2.66987i) q^{43} +(-6.09808 - 0.366025i) q^{45} -7.46410 q^{47} +(3.46410 + 6.00000i) q^{49} +1.53590i q^{51} +(-8.46410 + 8.46410i) q^{53} +(10.4282 - 2.13397i) q^{55} -1.73205i q^{57} +(-13.7942 + 3.69615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-0.633975 + 0.366025i) q^{63} +(1.00000 - 8.00000i) q^{65} +(10.7942 - 6.23205i) q^{67} +(0.0358984 - 0.0621778i) q^{69} +(2.86603 - 0.767949i) q^{71} -0.928203i q^{73} +(-2.03590 + 1.59808i) q^{75} +(0.901924 - 0.901924i) q^{77} +11.4641i q^{79} +(3.33013 + 5.76795i) q^{81} -3.46410 q^{83} +(-4.40192 - 4.96410i) q^{85} +(-0.598076 + 0.160254i) q^{87} +(0.794229 - 2.96410i) q^{89} +(-0.428203 - 0.866025i) q^{91} +(-0.830127 - 1.43782i) q^{93} +(4.96410 + 5.59808i) q^{95} +(2.13397 + 1.23205i) q^{97} +(-9.19615 - 9.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9	\( 4 q - 2 q^{3} + 8 q^{5} + 4 q^{7} - 6 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 10 q^{17} + 10 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} + 18 q^{29} + 16 q^{31} - 12 q^{33} + 14 q^{35} - 4 q^{37} - 16 q^{39} - 4 q^{41} - 26 q^{43} - 14 q^{45} - 16 q^{47} - 20 q^{53} + 14 q^{55} - 24 q^{59} + 2 q^{61} - 6 q^{63} + 4 q^{65} + 12 q^{67} + 14 q^{69} + 8 q^{71} - 22 q^{75} + 14 q^{77} - 4 q^{81} - 28 q^{85} + 8 q^{87} - 28 q^{89} + 26 q^{91} + 14 q^{93} + 6 q^{95} + 12 q^{97} - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 8 * q^5 + 4 * q^7 - 6 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 10 * q^17 + 10 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 + 18 * q^29 + 16 * q^31 - 12 * q^33 + 14 * q^35 - 4 * q^37 - 16 * q^39 - 4 * q^41 - 26 * q^43 - 14 * q^45 - 16 * q^47 - 20 * q^53 + 14 * q^55 - 24 * q^59 + 2 * q^61 - 6 * q^63 + 4 * q^65 + 12 * q^67 + 14 * q^69 + 8 * q^71 - 22 * q^75 + 14 * q^77 - 4 * q^81 - 28 * q^85 + 8 * q^87 - 28 * q^89 + 26 * q^91 + 14 * q^93 + 6 * q^95 + 12 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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Database

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