LMFDB - Embedded newform 260.2.bk.c.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.2
Root			$-1.86950i$ of defining polynomial
Character	$\chi$	$=$	260.33
Dual form			260.2.bk.c.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41732 + 0.647720i) q^{3} +(-2.18528 - 0.473860i) q^{5} +(3.34088 - 1.92886i) q^{7} +(2.82584 - 1.63150i) q^{9} +O(q^{10})$	\(q+(-2.41732 + 0.647720i) q^{3} +(-2.18528 - 0.473860i) q^{5} +(3.34088 - 1.92886i) q^{7} +(2.82584 - 1.63150i) q^{9} +(1.17419 + 4.38214i) q^{11} +(2.93090 - 2.09996i) q^{13} +(5.58946 - 0.269977i) q^{15} +(1.34075 - 5.00375i) q^{17} +(6.75335 + 1.80956i) q^{19} +(-6.82663 + 6.82663i) q^{21} +(0.490083 + 1.82902i) q^{23} +(4.55091 + 2.07104i) q^{25} +(-0.465395 + 0.465395i) q^{27} +(-1.71600 - 0.990731i) q^{29} +(-2.74684 - 2.74684i) q^{31} +(-5.67679 - 9.83250i) q^{33} +(-8.21477 + 2.63199i) q^{35} +(-10.2855 - 5.93836i) q^{37} +(-5.72474 + 6.97469i) q^{39} +(7.04912 - 1.88880i) q^{41} +(5.07520 + 1.35990i) q^{43} +(-6.94835 + 2.22623i) q^{45} +2.88429i q^{47} +(3.94098 - 6.82598i) q^{49} +12.9641i q^{51} +(3.37298 + 3.37298i) q^{53} +(-0.489416 - 10.1326i) q^{55} -17.4971 q^{57} +(-1.22940 + 4.58817i) q^{59} +(1.59692 + 2.76595i) q^{61} +(6.29385 - 10.9013i) q^{63} +(-7.39992 + 3.20018i) q^{65} +(-1.60567 + 2.78111i) q^{67} +(-2.36938 - 4.10389i) q^{69} +(1.70510 - 6.36353i) q^{71} +3.35146 q^{73} +(-12.3425 - 2.05865i) q^{75} +(12.3753 + 12.3753i) q^{77} +0.191160i q^{79} +(-4.07093 + 7.05105i) q^{81} -7.50696i q^{83} +(-5.30100 + 10.2993i) q^{85} +(4.78983 + 1.28343i) q^{87} +(10.5771 - 2.83413i) q^{89} +(5.74124 - 12.6690i) q^{91} +(8.41918 + 4.86082i) q^{93} +(-13.9005 - 7.15454i) q^{95} +(3.13619 + 5.43203i) q^{97} +(10.4675 + 10.4675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−2.41732	+	0.647720i	−1.39564	+	0.373961i	−0.876778	−	0.480895i	$-0.840312\pi$
$3$	−2.41732	+	0.647720i	−1.39564	+	0.373961i	−0.518864	+	0.854857i	$0.673645\pi$
$4$		0			0
$5$	−2.18528	−	0.473860i	−0.977288	−	0.211917i
$5$	−2.18528	−	0.473860i	−0.977288	−	0.211917i
$6$		0			0
$7$	3.34088	−	1.92886i	1.26273	−	0.729040i	0.289131	−	0.957290i	$-0.406634\pi$
$7$	3.34088	−	1.92886i	1.26273	−	0.729040i	0.973603	+	0.228250i	$0.0733003\pi$
$8$		0			0
$9$	2.82584	−	1.63150i	0.941945	−	0.543832i
$10$		0			0
$11$	1.17419	+	4.38214i	0.354032	+	1.32126i	0.881699	+	0.471813i	$0.156400\pi$
$11$	1.17419	+	4.38214i	0.354032	+	1.32126i	−0.527667	+	0.849451i	$0.676933\pi$
$12$		0			0
$13$	2.93090	−	2.09996i	0.812885	−	0.582425i
$13$	2.93090	−	2.09996i	0.812885	−	0.582425i
$14$		0			0
$15$	5.58946	−	0.269977i	1.44319	−	0.0697078i
$16$		0			0
$17$	1.34075	−	5.00375i	0.325180	−	1.21359i	−0.588951	−	0.808169i	$-0.700459\pi$
$17$	1.34075	−	5.00375i	0.325180	−	1.21359i	0.914131	−	0.405419i	$-0.132875\pi$
$18$		0			0
$19$	6.75335	+	1.80956i	1.54933	+	0.415141i	0.929265	−	0.369413i	$-0.120441\pi$
$19$	6.75335	+	1.80956i	1.54933	+	0.415141i	0.620061	+	0.784554i	$0.287108\pi$
$20$		0			0
$21$	−6.82663	+	6.82663i	−1.48969	+	1.48969i
$22$		0			0
$23$	0.490083	+	1.82902i	0.102189	+	0.381376i	0.998011	−	0.0630374i	$-0.0200788\pi$
$23$	0.490083	+	1.82902i	0.102189	+	0.381376i	−0.895822	+	0.444414i	$0.853412\pi$
$24$		0			0
$25$	4.55091	+	2.07104i	0.910183	+	0.414207i
$26$		0			0
$27$	−0.465395	+	0.465395i	−0.0895652	+	0.0895652i
$28$		0			0
$29$	−1.71600	−	0.990731i	−0.318652	−	0.183974i	0.332139	−	0.943230i	$-0.392230\pi$
$29$	−1.71600	−	0.990731i	−0.318652	−	0.183974i	−0.650792	+	0.759256i	$0.725563\pi$
$30$		0			0
$31$	−2.74684	−	2.74684i	−0.493347	−	0.493347i	0.416012	−	0.909359i	$-0.363427\pi$
$31$	−2.74684	−	2.74684i	−0.493347	−	0.493347i	−0.909359	+	0.416012i	$0.863427\pi$
$32$		0			0
$33$	−5.67679	−	9.83250i	−0.988203	−	1.71162i
$34$		0			0
$35$	−8.21477	+	2.63199i	−1.38855	+	0.444887i
$36$		0			0
$37$	−10.2855	−	5.93836i	−1.69093	−	0.976260i	−0.953767	−	0.300548i	$-0.902830\pi$
$37$	−10.2855	−	5.93836i	−1.69093	−	0.976260i	−0.737165	−	0.675712i	$-0.763836\pi$
$38$		0			0
$39$	−5.72474	+	6.97469i	−0.916692	+	1.11684i
$40$		0			0
$41$	7.04912	−	1.88880i	1.10089	−	0.294982i	0.337761	−	0.941232i	$-0.390330\pi$
$41$	7.04912	−	1.88880i	1.10089	−	0.294982i	0.763126	+	0.646250i	$0.223664\pi$
$42$		0			0
$43$	5.07520	+	1.35990i	0.773961	+	0.207382i	0.624121	−	0.781328i	$-0.285457\pi$
$43$	5.07520	+	1.35990i	0.773961	+	0.207382i	0.149841	+	0.988710i	$0.452124\pi$
$44$		0			0
$45$	−6.94835	+	2.22623i	−1.03580	+	0.331867i
$46$		0			0
$47$			2.88429i			0.420717i	0.977624	+	0.210358i	$0.0674631\pi$
$47$			2.88429i			0.420717i	−0.977624	+	0.210358i	$0.932537\pi$
$48$		0			0
$49$	3.94098	−	6.82598i	0.562997	−	0.975140i
$50$		0			0
$51$			12.9641i			1.81534i
$52$		0			0
$53$	3.37298	+	3.37298i	0.463315	+	0.463315i	0.899740	−	0.436425i	$-0.143756\pi$
$53$	3.37298	+	3.37298i	0.463315	+	0.463315i	−0.436425	+	0.899740i	$0.643756\pi$
$54$		0			0
$55$	−0.489416	−	10.1326i	−0.0659928	−	1.36628i
$56$		0			0
$57$	−17.4971			−2.31755
$58$		0			0
$59$	−1.22940	+	4.58817i	−0.160054	+	0.597329i	0.838565	+	0.544801i	$0.183395\pi$
$59$	−1.22940	+	4.58817i	−0.160054	+	0.597329i	−0.998619	+	0.0525286i	$0.983272\pi$
$60$		0			0
$61$	1.59692	+	2.76595i	0.204465	+	0.354144i	0.949962	−	0.312365i	$-0.101121\pi$
$61$	1.59692	+	2.76595i	0.204465	+	0.354144i	−0.745497	+	0.666509i	$0.767788\pi$
$62$		0			0
$63$	6.29385	−	10.9013i	0.792950	−	1.37343i
$64$		0			0
$65$	−7.39992	+	3.20018i	−0.917848	+	0.396933i
$66$		0			0
$67$	−1.60567	+	2.78111i	−0.196164	+	0.339767i	−0.947282	−	0.320402i	$-0.896182\pi$
$67$	−1.60567	+	2.78111i	−0.196164	+	0.339767i	0.751117	+	0.660169i	$0.229515\pi$
$68$		0			0
$69$	−2.36938	−	4.10389i	−0.285240	−	0.494050i
$70$		0			0
$71$	1.70510	−	6.36353i	0.202358	−	0.755212i	−0.787880	−	0.615829i	$-0.788821\pi$
$71$	1.70510	−	6.36353i	0.202358	−	0.755212i	0.990239	−	0.139383i	$-0.0445120\pi$
$72$		0			0
$73$	3.35146			0.392259			0.196129	−	0.980578i	$-0.437163\pi$
$73$	3.35146			0.392259			0.196129	+	0.980578i	$0.437163\pi$
$74$		0			0
$75$	−12.3425	−	2.05865i	−1.42519	−	0.237712i
$76$		0			0
$77$	12.3753	+	12.3753i	1.41030	+	1.41030i
$78$		0			0
$79$			0.191160i			0.0215072i	0.999942	+	0.0107536i	$0.00342304\pi$
$79$			0.191160i			0.0215072i	−0.999942	+	0.0107536i	$0.996577\pi$
$80$		0			0
$81$	−4.07093	+	7.05105i	−0.452325	+	0.783450i
$82$		0			0
$83$		−	7.50696i		−	0.823996i	−0.911185	−	0.411998i	$-0.864831\pi$
$83$		−	7.50696i		−	0.823996i	0.911185	−	0.411998i	$-0.135169\pi$
$84$		0			0
$85$	−5.30100	+	10.2993i	−0.574974	+	1.11711i
$86$		0			0
$87$	4.78983	+	1.28343i	0.513524	+	0.137598i
$88$		0			0
$89$	10.5771	−	2.83413i	1.12117	−	0.300418i	0.349816	−	0.936819i	$-0.386244\pi$
$89$	10.5771	−	2.83413i	1.12117	−	0.300418i	0.771358	+	0.636401i	$0.219578\pi$
$90$		0			0
$91$	5.74124	−	12.6690i	0.601846	−	1.32807i
$92$		0			0
$93$	8.41918	+	4.86082i	0.873029	+	0.504043i
$94$		0			0
$95$	−13.9005	−	7.15454i	−1.42616	−	0.734040i
$96$		0			0
$97$	3.13619	+	5.43203i	0.318431	+	0.551539i	0.980161	−	0.198203i	$-0.0635106\pi$
$97$	3.13619	+	5.43203i	0.318431	+	0.551539i	−0.661730	+	0.749743i	$0.730177\pi$
$98$		0			0
$99$	10.4675	+	10.4675i	1.05202	+	1.05202i
$100$		0			0
$101$	−5.84851	−	3.37664i	−0.581949	−	0.335988i	0.179959	−	0.983674i	$-0.442404\pi$
$101$	−5.84851	−	3.37664i	−0.581949	−	0.335988i	−0.761907	+	0.647686i	$0.775737\pi$
$102$		0			0
$103$	−7.17259	+	7.17259i	−0.706736	+	0.706736i	−0.965847	−	0.259111i	$-0.916570\pi$
$103$	−7.17259	+	7.17259i	−0.706736	+	0.706736i	0.259111	+	0.965847i	$0.416570\pi$
$104$		0			0
$105$	18.1530	−	11.6832i	1.77155	−	1.14017i
$106$		0			0
$107$	−0.595458	−	2.22228i	−0.0575651	−	0.214836i	0.931152	−	0.364632i	$-0.118805\pi$
$107$	−0.595458	−	2.22228i	−0.0575651	−	0.214836i	−0.988717	+	0.149796i	$0.952138\pi$
$108$		0			0
$109$	1.63415	−	1.63415i	0.156523	−	0.156523i	−0.624501	−	0.781024i	$-0.714698\pi$
$109$	1.63415	−	1.63415i	0.156523	−	0.156523i	0.781024	+	0.624501i	$0.214698\pi$
$110$		0			0
$111$	28.7099	+	7.69279i	2.72502	+	0.730167i
$112$		0			0
$113$	−2.65149	+	9.89551i	−0.249432	+	0.930891i	0.721672	+	0.692235i	$0.243374\pi$
$113$	−2.65149	+	9.89551i	−0.249432	+	0.930891i	−0.971104	+	0.238657i	$0.923293\pi$
$114$		0			0
$115$	−0.204272	−	4.22915i	−0.0190485	−	0.394370i
$116$		0			0
$117$	4.85615	−	10.7159i	0.448951	−	0.990685i
$118$		0			0
$119$	−5.17224	−	19.3031i	−0.474138	−	1.76951i
$120$		0			0
$121$	−8.29812	+	4.79092i	−0.754375	+	0.435538i
$122$		0			0
$123$	−15.8166	+	9.13170i	−1.42613	+	0.823378i
$124$		0			0
$125$	−8.96365	−	6.68229i	−0.801733	−	0.597683i
$126$		0			0
$127$	6.33875	−	1.69846i	0.562473	−	0.150714i	0.0336308	−	0.999434i	$-0.489293\pi$
$127$	6.33875	−	1.69846i	0.562473	−	0.150714i	0.528842	+	0.848720i	$0.322626\pi$
$128$		0			0
$129$	−13.1492			−1.15773
$130$		0			0
$131$	−9.05372			−0.791027			−0.395514	−	0.918460i	$-0.629433\pi$
$131$	−9.05372			−0.791027			−0.395514	+	0.918460i	$0.629433\pi$
$132$		0			0
$133$	26.0525	−	6.98075i	2.25904	−	0.605308i
$134$		0			0
$135$	1.23755	−	0.796486i	0.106511	−	0.0685506i
$136$		0			0
$137$	−2.92353	+	1.68790i	−0.249774	+	0.144207i	−0.619661	−	0.784870i	$-0.712730\pi$
$137$	−2.92353	+	1.68790i	−0.249774	+	0.144207i	0.369887	+	0.929077i	$0.379396\pi$
$138$		0			0
$139$	8.53706	−	4.92888i	0.724104	−	0.418062i	−0.0921571	−	0.995744i	$-0.529376\pi$
$139$	8.53706	−	4.92888i	0.724104	−	0.418062i	0.816261	+	0.577683i	$0.196043\pi$
$140$		0			0
$141$	−1.86821	−	6.97226i	−0.157332	−	0.587170i
$142$		0			0
$143$	12.6438	+	10.3778i	1.05732	+	0.867838i
$144$		0			0
$145$	3.28047	+	2.97817i	0.272428	+	0.247323i
$146$		0			0
$147$	−5.10530	+	19.0533i	−0.421078	+	1.57149i
$148$		0			0
$149$	2.20843	+	0.591746i	0.180921	+	0.0484777i	0.348142	−	0.937442i	$-0.386813\pi$
$149$	2.20843	+	0.591746i	0.180921	+	0.0484777i	−0.167221	+	0.985919i	$0.553479\pi$
$150$		0			0
$151$	−13.2429	+	13.2429i	−1.07769	+	1.07769i	−0.0809746	+	0.996716i	$0.525803\pi$
$151$	−13.2429	+	13.2429i	−1.07769	+	1.07769i	−0.996716	+	0.0809746i	$0.974197\pi$
$152$		0			0
$153$	−4.37486	−	16.3272i	−0.353687	−	1.31998i
$154$		0			0
$155$	4.70100	+	7.30424i	0.377593	+	0.586690i
$156$		0			0
$157$	−1.52992	+	1.52992i	−0.122101	+	0.122101i	−0.765517	−	0.643416i	$-0.777517\pi$
$157$	−1.52992	+	1.52992i	−0.122101	+	0.122101i	0.643416	+	0.765517i	$0.277517\pi$
$158$		0			0
$159$	−10.3383	−	5.96884i	−0.819884	−	0.473360i
$160$		0			0
$161$	5.16522	+	5.16522i	0.407076	+	0.407076i
$162$		0			0
$163$	−7.70822	−	13.3510i	−0.603755	−	1.04573i	−0.992247	−	0.124282i	$-0.960337\pi$
$163$	−7.70822	−	13.3510i	−0.603755	−	1.04573i	0.388492	−	0.921452i	$-0.372996\pi$
$164$		0			0
$165$	7.74617	+	24.1768i	0.603038	+	1.88216i
$166$		0			0
$167$	−12.1902	−	7.03801i	−0.943306	−	0.544618i	−0.0523106	−	0.998631i	$-0.516659\pi$
$167$	−12.1902	−	7.03801i	−0.943306	−	0.544618i	−0.890995	+	0.454013i	$0.849992\pi$
$168$		0			0
$169$	4.18031	−	12.3095i	0.321562	−	0.946888i
$170$		0			0
$171$	22.0362	−	5.90457i	1.68515	−	0.451534i
$172$		0			0
$173$	−10.2249	−	2.73977i	−0.777388	−	0.208301i	−0.151755	−	0.988418i	$-0.548493\pi$
$173$	−10.2249	−	2.73977i	−0.777388	−	0.208301i	−0.625633	+	0.780118i	$0.715159\pi$
$174$		0			0
$175$	19.1988	−	1.85898i	1.45129	−	0.140526i
$176$		0			0
$177$		−	11.8874i		−	0.893512i
$178$		0			0
$179$	−7.94948	+	13.7689i	−0.594172	+	1.02914i	0.399491	+	0.916737i	$0.369187\pi$
$179$	−7.94948	+	13.7689i	−0.594172	+	1.02914i	−0.993663	+	0.112399i	$0.964146\pi$
$180$		0			0
$181$		−	18.0258i		−	1.33985i	−0.742430	−	0.669923i	$-0.766327\pi$
$181$		−	18.0258i		−	1.33985i	0.742430	−	0.669923i	$-0.233673\pi$
$182$		0			0
$183$	−5.65184	−	5.65184i	−0.417796	−	0.417796i
$184$		0			0
$185$	19.6628	+	17.8509i	1.44564	+	1.31242i
$186$		0			0
$187$	23.5014			1.71859
$188$		0			0
$189$	−0.657147	+	2.45251i	−0.0478004	+	0.178394i
$190$		0			0
$191$	7.25135	+	12.5597i	0.524689	+	0.908788i	0.999587	+	0.0287469i	$0.00915169\pi$
$191$	7.25135	+	12.5597i	0.524689	+	0.908788i	−0.474898	+	0.880041i	$0.657515\pi$
$192$		0			0
$193$	−0.660752	+	1.14446i	−0.0475620	+	0.0823798i	−0.888826	−	0.458244i	$-0.848478\pi$
$193$	−0.660752	+	1.14446i	−0.0475620	+	0.0823798i	0.841264	+	0.540624i	$0.181812\pi$
$194$		0			0
$195$	15.8152	−	12.5289i	1.13255	−	0.897216i
$196$		0			0
$197$	6.96097	−	12.0568i	0.495949	−	0.859009i	−0.504040	−	0.863680i	$-0.668154\pi$
$197$	6.96097	−	12.0568i	0.495949	−	0.859009i	0.999989	+	0.00467150i	$0.00148699\pi$
$198$		0			0
$199$	6.73532	+	11.6659i	0.477454	+	0.826975i	0.999666	−	0.0258407i	$-0.00822625\pi$
$199$	6.73532	+	11.6659i	0.477454	+	0.826975i	−0.522212	+	0.852816i	$0.674893\pi$
$200$		0			0
$201$	2.08005	−	7.76287i	0.146716	−	0.547550i
$202$		0			0
$203$	−7.64391			−0.536498
$204$		0			0
$205$	−16.2993	+	0.787275i	−1.13839	+	0.0549857i
$206$		0			0
$207$	4.36893	+	4.36893i	0.303661	+	0.303661i
$208$		0			0
$209$			31.7189i			2.19404i
$210$		0			0
$211$	−9.02243	+	15.6273i	−0.621129	+	1.07583i	0.368146	+	0.929768i	$0.379993\pi$
$211$	−9.02243	+	15.6273i	−0.621129	+	1.07583i	−0.989276	+	0.146060i	$0.953341\pi$
$212$		0			0
$213$			16.4871i			1.12968i
$214$		0			0
$215$	−10.4464	−	5.37670i	−0.712435	−	0.366688i
$216$		0			0
$217$	−14.4751	−	3.87860i	−0.982635	−	0.263296i
$218$		0			0
$219$	−8.10156	+	2.17081i	−0.547453	+	0.146690i
$220$		0			0
$221$	−6.57809	−	17.4810i	−0.442490	−	1.17590i
$222$		0			0
$223$	−3.73310	−	2.15531i	−0.249987	−	0.144330i	0.369771	−	0.929123i	$-0.379436\pi$
$223$	−3.73310	−	2.15531i	−0.249987	−	0.144330i	−0.619758	+	0.784793i	$0.712769\pi$
$224$		0			0
$225$	16.2390	−	1.57239i	1.08260	−	0.104826i
$226$		0			0
$227$	−10.6548	−	18.4546i	−0.707182	−	1.22488i	−0.965898	−	0.258922i	$-0.916633\pi$
$227$	−10.6548	−	18.4546i	−0.707182	−	1.22488i	0.258716	−	0.965953i	$-0.416701\pi$
$228$		0			0
$229$	−1.68567	−	1.68567i	−0.111392	−	0.111392i	0.649214	−	0.760606i	$-0.275098\pi$
$229$	−1.68567	−	1.68567i	−0.111392	−	0.111392i	−0.760606	+	0.649214i	$0.775098\pi$
$230$		0			0
$231$	−37.9310	−	21.8995i	−2.49567	−	1.44088i
$232$		0			0
$233$	−19.8733	+	19.8733i	−1.30195	+	1.30195i	−0.374867	+	0.927079i	$0.622312\pi$
$233$	−19.8733	+	19.8733i	−1.30195	+	1.30195i	−0.927079	+	0.374867i	$0.877688\pi$
$234$		0			0
$235$	1.36675	−	6.30298i	0.0891569	−	0.411161i
$236$		0			0
$237$	−0.123818	−	0.462096i	−0.00804286	−	0.0300164i
$238$		0			0
$239$	0.515620	−	0.515620i	0.0333527	−	0.0333527i	−0.690234	−	0.723586i	$-0.742492\pi$
$239$	0.515620	−	0.515620i	0.0333527	−	0.0333527i	0.723586	+	0.690234i	$0.242492\pi$
$240$		0			0
$241$	−13.9645	−	3.74178i	−0.899533	−	0.241029i	−0.220717	−	0.975338i	$-0.570840\pi$
$241$	−13.9645	−	3.74178i	−0.899533	−	0.241029i	−0.678816	+	0.734309i	$0.737506\pi$
$242$		0			0
$243$	5.78468	−	21.5887i	0.371087	−	1.38492i
$244$		0			0
$245$	−11.8467	+	13.0492i	−0.756859	+	0.833684i
$246$		0			0
$247$	23.5934	−	8.87817i	1.50121	−	0.564905i
$248$		0			0
$249$	4.86241	+	18.1467i	0.308143	+	1.15000i
$250$		0			0
$251$	−12.3324	+	7.12014i	−0.778417	+	0.449419i	−0.835869	−	0.548929i	$-0.815036\pi$
$251$	−12.3324	+	7.12014i	−0.778417	+	0.449419i	0.0574522	+	0.998348i	$0.481702\pi$
$252$		0			0
$253$	−7.43955	+	4.29522i	−0.467720	+	0.270038i
$254$		0			0
$255$	6.14318	−	28.3303i	0.384701	−	1.77411i
$256$		0			0
$257$	−9.08035	+	2.43307i	−0.566417	+	0.151771i	−0.530653	−	0.847589i	$-0.678053\pi$
$257$	−9.08035	+	2.43307i	−0.566417	+	0.151771i	−0.0357640	+	0.999360i	$0.511386\pi$
$258$		0			0
$259$	−45.8170			−2.84693
$260$		0			0
$261$	−6.46550			−0.400204
$262$		0			0
$263$	−19.2807	+	5.16623i	−1.18890	+	0.318564i	−0.798449	−	0.602062i	$-0.794346\pi$
$263$	−19.2807	+	5.16623i	−1.18890	+	0.318564i	−0.390446	+	0.920626i	$0.627679\pi$
$264$		0			0
$265$	−5.77260	−	8.96924i	−0.354608	−	0.550976i
$266$		0			0
$267$	−23.7326	+	13.7020i	−1.45241	+	0.838551i
$268$		0			0
$269$	18.8136	−	10.8620i	1.14708	−	0.662270i	0.198909	−	0.980018i	$-0.436260\pi$
$269$	18.8136	−	10.8620i	1.14708	−	0.662270i	0.948175	+	0.317748i	$0.102927\pi$
$270$		0			0
$271$	−1.58261	−	5.90638i	−0.0961367	−	0.358787i	0.901053	−	0.433710i	$-0.142796\pi$
$271$	−1.58261	−	5.90638i	−0.0961367	−	0.358787i	−0.997189	+	0.0749226i	$0.976129\pi$
$272$		0			0
$273$	−5.67248	+	34.3438i	−0.343314	+	2.07858i
$274$		0			0
$275$	−3.73193	+	22.3745i	−0.225044	+	1.34923i
$276$		0			0
$277$	−5.11654	+	19.0952i	−0.307423	+	1.14732i	0.623416	+	0.781891i	$0.285744\pi$
$277$	−5.11654	+	19.0952i	−0.307423	+	1.14732i	−0.930839	+	0.365429i	$0.880922\pi$
$278$		0			0
$279$	−12.2436	−	3.28066i	−0.733004	−	0.196408i
$280$		0			0
$281$	14.1598	−	14.1598i	0.844700	−	0.844700i	−0.144766	−	0.989466i	$-0.546243\pi$
$281$	14.1598	−	14.1598i	0.844700	−	0.844700i	0.989466	+	0.144766i	$0.0462429\pi$
$282$		0			0
$283$	8.46917	+	31.6074i	0.503440	+	1.87886i	0.476400	+	0.879229i	$0.341941\pi$
$283$	8.46917	+	31.6074i	0.503440	+	1.87886i	0.0270400	+	0.999634i	$0.491392\pi$
$284$		0			0
$285$	38.2362	+	8.29119i	2.26491	+	0.491128i
$286$		0			0
$287$	19.9070	−	19.9070i	1.17507	−	1.17507i
$288$		0			0
$289$	−8.51750	−	4.91758i	−0.501029	−	0.289269i
$290$		0			0
$291$	−11.0996	−	11.0996i	−0.650671	−	0.650671i
$292$		0			0
$293$	−6.02783	−	10.4405i	−0.352150	−	0.609941i	0.634476	−	0.772943i	$-0.281216\pi$
$293$	−6.02783	−	10.4405i	−0.352150	−	0.609941i	−0.986626	+	0.163001i	$0.947883\pi$
$294$		0			0
$295$	4.86073	−	9.44389i	0.283003	−	0.549845i
$296$		0			0
$297$	−2.58588	−	1.49296i	−0.150048	−	0.0866304i
$298$		0			0
$299$	5.27725	+	4.33150i	0.305191	+	0.250497i
$300$		0			0
$301$	19.5787	−	5.24609i	1.12850	−	0.302380i
$302$		0			0
$303$	16.3249	+	4.37423i	0.937839	+	0.251293i
$304$		0			0
$305$	−2.17905	−	6.80110i	−0.124772	−	0.389430i
$306$		0			0
$307$			25.5219i			1.45661i	0.685252	+	0.728306i	$0.259692\pi$
$307$			25.5219i			1.45661i	−0.685252	+	0.728306i	$0.740308\pi$
$308$		0			0
$309$	12.6926	−	21.9843i	0.722059	−	1.25064i
$310$		0			0
$311$		−	18.9993i		−	1.07735i	−0.842513	−	0.538676i	$-0.818925\pi$
$311$		−	18.9993i		−	1.07735i	0.842513	−	0.538676i	$-0.181075\pi$
$312$		0			0
$313$	16.2567	+	16.2567i	0.918883	+	0.918883i	0.996948	−	0.0780653i	$-0.0248743\pi$
$313$	16.2567	+	16.2567i	0.918883	+	0.918883i	−0.0780653	+	0.996948i	$0.524874\pi$
$314$		0			0
$315$	−18.9195	+	20.8399i	−1.06599	+	1.17420i
$316$		0			0
$317$	20.9422			1.17623			0.588115	−	0.808777i	$-0.299870\pi$
$317$	20.9422			1.17623			0.588115	+	0.808777i	$0.299870\pi$
$318$		0			0
$319$	2.32661	−	8.68303i	0.130265	−	0.486157i
$320$		0			0
$321$	2.87883	+	4.98628i	0.160681	+	0.278307i
$322$		0			0
$323$	18.1091	−	31.3660i	1.00762	−	1.74525i
$324$		0			0
$325$	17.6874	−	3.48675i	0.981118	−	0.193410i
$326$		0			0
$327$	−2.89179	+	5.00873i	−0.159916	+	0.276983i
$328$		0			0
$329$	5.56338	+	9.63606i	0.306719	+	0.531253i
$330$		0			0
$331$	2.54739	−	9.50699i	0.140017	−	0.522551i	−0.859910	−	0.510446i	$-0.829480\pi$
$331$	2.54739	−	9.50699i	0.140017	−	0.522551i	0.999927	−	0.0121049i	$-0.00385320\pi$
$332$		0			0
$333$	−38.7537			−2.12369
$334$		0			0
$335$	4.82671	−	5.31664i	0.263711	−	0.290479i
$336$		0			0
$337$	−8.77242	−	8.77242i	−0.477864	−	0.477864i	0.426584	−	0.904448i	$-0.359717\pi$
$337$	−8.77242	−	8.77242i	−0.477864	−	0.477864i	−0.904448	+	0.426584i	$0.859717\pi$
$338$		0			0
$339$		−	25.6381i		−	1.39247i
$340$		0			0
$341$	8.81171	−	15.2623i	0.477181	−	0.826502i
$342$		0			0
$343$		−	3.40236i		−	0.183710i
$344$		0			0
$345$	3.23309	+	10.0909i	0.174064	+	0.543276i
$346$		0			0
$347$	1.16045	+	0.310942i	0.0622963	+	0.0166922i	0.289833	−	0.957077i	$-0.406400\pi$
$347$	1.16045	+	0.310942i	0.0622963	+	0.0166922i	−0.227536	+	0.973770i	$0.573067\pi$
$348$		0			0
$349$	−18.3696	+	4.92212i	−0.983303	+	0.263475i	−0.714435	−	0.699702i	$-0.753316\pi$
$349$	−18.3696	+	4.92212i	−0.983303	+	0.263475i	−0.268868	+	0.963177i	$0.586650\pi$
$350$		0			0
$351$	−0.386712	+	2.34133i	−0.0206412	+	0.124971i
$352$		0			0
$353$	−8.40342	−	4.85172i	−0.447269	−	0.258231i	0.259407	−	0.965768i	$-0.416473\pi$
$353$	−8.40342	−	4.85172i	−0.447269	−	0.258231i	−0.706676	+	0.707537i	$0.749806\pi$
$354$		0			0
$355$	−6.74155	+	13.0981i	−0.357804	+	0.695176i
$356$		0			0
$357$	25.0059	+	43.3116i	1.32345	+	2.29229i
$358$		0			0
$359$	24.3084	+	24.3084i	1.28295	+	1.28295i	0.938981	+	0.343969i	$0.111772\pi$
$359$	24.3084	+	24.3084i	1.28295	+	1.28295i	0.343969	+	0.938981i	$0.388228\pi$
$360$		0			0
$361$	25.8788	+	14.9411i	1.36204	+	0.786376i
$362$		0			0
$363$	16.9561	−	16.9561i	0.889963	−	0.889963i
$364$		0			0
$365$	−7.32389	−	1.58812i	−0.383350	−	0.0831262i
$366$		0			0
$367$	1.97860	+	7.38424i	0.103282	+	0.385454i	0.998145	−	0.0608877i	$-0.0193931\pi$
$367$	1.97860	+	7.38424i	0.103282	+	0.385454i	−0.894862	+	0.446342i	$0.852726\pi$
$368$		0			0
$369$	16.8381	−	16.8381i	0.876554	−	0.876554i
$370$		0			0
$371$	17.7747	+	4.76273i	0.922818	+	0.247268i
$372$		0			0
$373$	−1.11739	+	4.17016i	−0.0578563	+	0.215923i	−0.988802	−	0.149236i	$-0.952319\pi$
$373$	−1.11739	+	4.17016i	−0.0578563	+	0.215923i	0.930945	+	0.365159i	$0.118985\pi$
$374$		0			0
$375$	25.9963	+	10.3473i	1.34244	+	0.534334i
$376$		0			0
$377$	−7.10990	+	0.699798i	−0.366179	+	0.0360414i
$378$		0			0
$379$	−3.78500	−	14.1258i	−0.194422	−	0.725594i	−0.992416	−	0.122928i	$-0.960772\pi$
$379$	−3.78500	−	14.1258i	−0.194422	−	0.725594i	0.797993	−	0.602666i	$-0.205895\pi$
$380$		0			0
$381$	−14.2227	+	8.21147i	−0.728650	+	0.420686i
$382$		0			0
$383$	2.93423	−	1.69408i	0.149932	−	0.0865635i	−0.423157	−	0.906056i	$-0.639078\pi$
$383$	2.93423	−	1.69408i	0.149932	−	0.0865635i	0.573089	+	0.819493i	$0.305745\pi$
$384$		0			0
$385$	−21.1794	−	32.9078i	−1.07940	−	1.67714i
$386$		0			0
$387$	16.5604	−	4.43734i	0.841810	−	0.225562i
$388$		0			0
$389$	22.8218			1.15711			0.578555	−	0.815643i	$-0.303617\pi$
$389$	22.8218			1.15711			0.578555	+	0.815643i	$0.303617\pi$
$390$		0			0
$391$	9.80902			0.496064
$392$		0			0
$393$	21.8858	−	5.86427i	1.10399	−	0.295814i
$394$		0			0
$395$	0.0905832	−	0.417739i	0.00455774	−	0.0210187i
$396$		0			0
$397$	−8.77734	+	5.06760i	−0.440522	+	0.254335i	−0.703819	−	0.710379i	$-0.748523\pi$
$397$	−8.77734	+	5.06760i	−0.440522	+	0.254335i	0.263297	+	0.964715i	$0.415190\pi$
$398$		0			0
$399$	−58.4558	+	33.7495i	−2.92645	+	1.68959i
$400$		0			0
$401$	8.05785	+	30.0723i	0.402390	+	1.50174i	0.808819	+	0.588057i	$0.200107\pi$
$401$	8.05785	+	30.0723i	0.402390	+	1.50174i	−0.406430	+	0.913682i	$0.633226\pi$
$402$		0			0
$403$	−13.8190	−	2.28244i	−0.688372	−	0.113697i
$404$		0			0
$405$	12.2373	−	13.4795i	0.608078	−	0.669801i
$406$		0			0
$407$	13.9455	−	52.0454i	0.691254	−	2.57979i
$408$		0			0
$409$	−16.1424	−	4.32535i	−0.798192	−	0.213875i	−0.163402	−	0.986560i	$-0.552247\pi$
$409$	−16.1424	−	4.32535i	−0.798192	−	0.213875i	−0.634790	+	0.772685i	$0.718913\pi$
$410$		0			0
$411$	5.97383	−	5.97383i	0.294667	−	0.294667i
$412$		0			0
$413$	4.74267	+	17.6999i	0.233371	+	0.870954i
$414$		0			0
$415$	−3.55725	+	16.4048i	−0.174619	+	0.805281i
$416$		0			0
$417$	−17.4443	+	17.4443i	−0.854252	+	0.854252i
$418$		0			0
$419$	3.80652	+	2.19769i	0.185960	+	0.107364i	0.590090	−	0.807337i	$-0.299092\pi$
$419$	3.80652	+	2.19769i	0.185960	+	0.107364i	−0.404130	+	0.914702i	$0.632426\pi$
$420$		0			0
$421$	−14.0586	−	14.0586i	−0.685175	−	0.685175i	0.275987	−	0.961161i	$-0.410995\pi$
$421$	−14.0586	−	14.0586i	−0.685175	−	0.685175i	−0.961161	+	0.275987i	$0.910995\pi$
$422$		0			0
$423$	4.70571	+	8.15053i	0.228799	+	0.396292i
$424$		0			0
$425$	16.4646	−	19.9949i	0.798650	−	0.969895i
$426$		0			0
$427$	10.6703	+	6.16047i	0.516370	+	0.298126i
$428$		0			0
$429$	−37.2860	−	16.8970i	−1.80018	−	0.815794i
$430$		0			0
$431$	−1.45418	+	0.389648i	−0.0700456	+	0.0187687i	−0.293672	−	0.955906i	$-0.594877\pi$
$431$	−1.45418	+	0.389648i	−0.0700456	+	0.0187687i	0.223626	+	0.974675i	$0.428211\pi$
$432$		0			0
$433$	−14.3146	−	3.83559i	−0.687917	−	0.184327i	−0.102105	−	0.994774i	$-0.532558\pi$
$433$	−14.3146	−	3.83559i	−0.687917	−	0.184327i	−0.585812	+	0.810447i	$0.699224\pi$
$434$		0			0
$435$	−9.85897	−	5.07437i	−0.472701	−	0.243297i
$436$		0			0
$437$			13.2388i			0.633299i
$438$		0			0
$439$	3.62582	−	6.28011i	0.173051	−	0.299733i	−0.766434	−	0.642323i	$-0.777971\pi$
$439$	3.62582	−	6.28011i	0.173051	−	0.299733i	0.939485	+	0.342590i	$0.111304\pi$
$440$		0			0
$441$		−	25.7188i		−	1.22470i
$442$		0			0
$443$	12.2198	+	12.2198i	0.580581	+	0.580581i	0.935063	−	0.354482i	$-0.115343\pi$
$443$	12.2198	+	12.2198i	0.580581	+	0.580581i	−0.354482	+	0.935063i	$0.615343\pi$
$444$		0			0
$445$	−24.4570	+	1.18130i	−1.15937	+	0.0559990i
$446$		0			0
$447$	−5.72177			−0.270630
$448$		0			0
$449$	9.84620	−	36.7465i	0.464671	−	1.73417i	−0.193308	−	0.981138i	$-0.561922\pi$
$449$	9.84620	−	36.7465i	0.464671	−	1.73417i	0.657979	−	0.753037i	$-0.271412\pi$
$450$		0			0
$451$	16.5540	+	28.6724i	0.779497	+	1.35013i
$452$		0			0
$453$	23.4347	−	40.5900i	1.10106	−	1.90709i
$454$		0			0
$455$	−18.5496	+	24.9648i	−0.869617	+	1.17037i
$456$		0			0
$457$	−6.35050	+	10.9994i	−0.297064	+	0.514530i	−0.975463	−	0.220164i	$-0.929341\pi$
$457$	−6.35050	+	10.9994i	−0.297064	+	0.514530i	0.678399	+	0.734694i	$0.262674\pi$
$458$		0			0
$459$	1.70474	+	2.95270i	0.0795705	+	0.137820i
$460$		0			0
$461$	7.37555	−	27.5259i	0.343513	−	1.28201i	−0.550826	−	0.834620i	$-0.685687\pi$
$461$	7.37555	−	27.5259i	0.343513	−	1.28201i	0.894339	−	0.447389i	$-0.147646\pi$
$462$		0			0
$463$	11.9895			0.557201			0.278601	−	0.960407i	$-0.410129\pi$
$463$	11.9895			0.557201			0.278601	+	0.960407i	$0.410129\pi$
$464$		0			0
$465$	−16.0949	−	14.6118i	−0.746385	−	0.677605i
$466$		0			0
$467$	−2.12252	−	2.12252i	−0.0982186	−	0.0982186i	0.656290	−	0.754509i	$-0.272125\pi$
$467$	−2.12252	−	2.12252i	−0.0982186	−	0.0982186i	−0.754509	+	0.656290i	$0.772125\pi$
$468$		0			0
$469$			12.3885i			0.572046i
$470$		0			0
$471$	2.70736	−	4.68928i	0.124748	−	0.216071i
$472$		0			0
$473$			23.8370i			1.09603i
$474$		0			0
$475$	26.9863	+	22.2216i	1.23822	+	1.01960i
$476$		0			0
$477$	15.0345	+	4.02848i	0.688383	+	0.184452i
$478$		0			0
$479$	−36.2773	+	9.72046i	−1.65755	+	0.444139i	−0.961713	−	0.274060i	$-0.911633\pi$
$479$	−36.2773	+	9.72046i	−1.65755	+	0.444139i	−0.695837	+	0.718199i	$0.744967\pi$
$480$		0			0
$481$	−42.6162	+	4.19453i	−1.94313	+	0.191254i
$482$		0			0
$483$	−15.8316	−	9.14039i	−0.720364	−	0.415902i
$484$		0			0
$485$	−4.27943	−	13.3566i	−0.194319	−	0.606494i
$486$		0			0
$487$	−1.64663	−	2.85205i	−0.0746160	−	0.129239i	0.826303	−	0.563225i	$-0.190440\pi$
$487$	−1.64663	−	2.85205i	−0.0746160	−	0.129239i	−0.900919	+	0.433987i	$0.857106\pi$
$488$		0			0
$489$	27.2810	+	27.2810i	1.23369	+	1.23369i
$490$		0			0
$491$	17.1647	+	9.91005i	0.774633	+	0.447234i	0.834525	−	0.550971i	$-0.185742\pi$
$491$	17.1647	+	9.91005i	0.774633	+	0.447234i	−0.0598922	+	0.998205i	$0.519076\pi$
$492$		0			0
$493$	−7.25810	+	7.25810i	−0.326888	+	0.326888i
$494$		0			0
$495$	−17.9143	−	27.8346i	−0.805189	−	1.25107i
$496$		0			0
$497$	−6.57780	−	24.5487i	−0.295055	−	1.10116i
$498$		0			0
$499$	6.58653	−	6.58653i	0.294854	−	0.294854i	−0.544141	−	0.838994i	$-0.683144\pi$
$499$	6.58653	−	6.58653i	0.294854	−	0.294854i	0.838994	+	0.544141i	$0.183144\pi$
$500$		0			0
$501$	34.0263	+	9.11732i	1.52018	+	0.407332i
$502$		0			0
$503$	0.767145	−	2.86302i	0.0342053	−	0.127656i	−0.946712	−	0.322081i	$-0.895618\pi$
$503$	0.767145	−	2.86302i	0.0342053	−	0.127656i	0.980917	+	0.194425i	$0.0622842\pi$
$504$		0			0
$505$	11.1806	+	10.1503i	0.497530	+	0.451682i
$506$		0			0
$507$	−2.13203	+	32.4638i	−0.0946867	+	1.44177i
$508$		0			0
$509$	5.86672	+	21.8949i	0.260038	+	0.970475i	0.965218	+	0.261446i	$0.0841995\pi$
$509$	5.86672	+	21.8949i	0.260038	+	0.970475i	−0.705180	+	0.709028i	$0.749134\pi$
$510$		0			0
$511$	11.1968	−	6.46449i	0.495318	−	0.285972i
$512$		0			0
$513$	−3.98513	+	2.30082i	−0.175948	+	0.101584i
$514$		0			0
$515$	19.0729	−	12.2753i	0.840454	−	0.540915i
$516$		0			0
$517$	−12.6393	+	3.38670i	−0.555878	+	0.148947i
$518$		0			0
$519$	26.4916			1.16285
$520$		0			0
$521$	−31.4316			−1.37704			−0.688521	−	0.725216i	$-0.741740\pi$
$521$	−31.4316			−1.37704			−0.688521	+	0.725216i	$0.741740\pi$
$522$		0			0
$523$	32.5167	−	8.71283i	1.42186	−	0.380985i	0.535715	−	0.844399i	$-0.320042\pi$
$523$	32.5167	−	8.71283i	1.42186	−	0.380985i	0.886142	+	0.463414i	$0.153376\pi$
$524$		0			0
$525$	−45.2056	+	16.9292i	−1.97293	+	0.738850i
$526$		0			0
$527$	−17.4273	+	10.0617i	−0.759147	+	0.438294i
$528$		0			0
$529$	16.8135	−	9.70726i	0.731020	−	0.422055i
$530$		0			0
$531$	4.01152	+	14.9712i	0.174085	+	0.649694i
$532$		0			0
$533$	16.6938	−	20.3388i	0.723089	−	0.880970i
$534$		0			0
$535$	0.248194	+	5.13847i	0.0107304	+	0.222155i
$536$		0			0
$537$	10.2981	−	38.4329i	0.444395	−	1.65850i
$538$		0			0
$539$	34.5398	+	9.25492i	1.48774	+	0.398638i
$540$		0			0
$541$	−2.00796	+	2.00796i	−0.0863288	+	0.0863288i	−0.748953	−	0.662624i	$-0.769443\pi$
$541$	−2.00796	+	2.00796i	−0.0863288	+	0.0863288i	0.662624	+	0.748953i	$0.269443\pi$
$542$		0			0
$543$	11.6757	+	43.5742i	0.501051	+	1.86995i
$544$		0			0
$545$	−4.34543	+	2.79671i	−0.186138	+	0.119798i
$546$		0			0
$547$	−9.19675	+	9.19675i	−0.393224	+	0.393224i	−0.875835	−	0.482611i	$-0.839689\pi$
$547$	−9.19675	+	9.19675i	−0.393224	+	0.393224i	0.482611	+	0.875835i	$0.339689\pi$
$548$		0			0
$549$	9.02528	+	5.21075i	0.385190	+	0.222389i
$550$		0			0
$551$	−9.79595	−	9.79595i	−0.417321	−	0.417321i
$552$		0			0
$553$	0.368721	+	0.638643i	0.0156796	+	0.0271579i
$554$		0			0
$555$	−59.0938	−	30.4154i	−2.50839	−	1.29106i
$556$		0			0
$557$	−17.3556	−	10.0203i	−0.735381	−	0.424572i	0.0850066	−	0.996380i	$-0.472909\pi$
$557$	−17.3556	−	10.0203i	−0.735381	−	0.424572i	−0.820387	+	0.571808i	$0.806242\pi$
$558$		0			0
$559$	17.7306	−	6.67202i	0.749926	−	0.282197i
$560$		0			0
$561$	−56.8105	+	15.2223i	−2.39854	+	0.642688i
$562$		0			0
$563$	−31.9878	−	8.57109i	−1.34812	−	0.361229i	−0.488682	−	0.872462i	$-0.662522\pi$
$563$	−31.9878	−	8.57109i	−1.34812	−	0.361229i	−0.859442	+	0.511234i	$0.829189\pi$
$564$		0			0
$565$	10.4834	−	20.3680i	0.441038	−	0.856890i
$566$		0			0
$567$			31.4089i			1.31905i
$568$		0			0
$569$	18.5265	−	32.0889i	0.776672	−	1.34524i	−0.157178	−	0.987570i	$-0.550240\pi$
$569$	18.5265	−	32.0889i	0.776672	−	1.34524i	0.933850	−	0.357665i	$-0.116427\pi$
$570$		0			0
$571$			24.2209i			1.01361i	0.862060	+	0.506807i	$0.169174\pi$
$571$			24.2209i			1.01361i	−0.862060	+	0.506807i	$0.830826\pi$
$572$		0			0
$573$	−25.6640	−	25.6640i	−1.07213	−	1.07213i
$574$		0			0
$575$	−1.55763	+	9.33867i	−0.0649577	+	0.389449i
$576$		0			0
$577$	−2.85093			−0.118686			−0.0593429	−	0.998238i	$-0.518901\pi$
$577$	−2.85093			−0.118686			−0.0593429	+	0.998238i	$0.518901\pi$
$578$		0			0
$579$	0.855965	−	3.19450i	0.0355727	−	0.132759i
$580$		0			0
$581$	−14.4799	−	25.0798i	−0.600726	−	1.04049i
$582$		0			0
$583$	−10.8204	+	18.7414i	−0.448133	+	0.776189i
$584$		0			0
$585$	−15.6899	+	21.1161i	−0.648697	+	0.873044i
$586$		0			0
$587$	1.91874	−	3.32335i	0.0791947	−	0.137169i	−0.823708	−	0.567014i	$-0.808098\pi$
$587$	1.91874	−	3.32335i	0.0791947	−	0.137169i	0.902903	+	0.429845i	$0.141432\pi$
$588$		0			0
$589$	−13.5798	−	23.5209i	−0.559547	−	0.969164i
$590$		0			0
$591$	−9.01752	+	33.6539i	−0.370931	+	1.38433i
$592$		0			0
$593$	−16.4597			−0.675919			−0.337960	−	0.941161i	$-0.609737\pi$
$593$	−16.4597			−0.675919			−0.337960	+	0.941161i	$0.609737\pi$
$594$		0			0
$595$	2.15585	+	44.6335i	0.0883811	+	1.82980i
$596$		0			0
$597$	−23.8377	−	23.8377i	−0.975612	−	0.975612i
$598$		0			0
$599$			37.2957i			1.52386i	0.647659	+	0.761931i	$0.275748\pi$
$599$			37.2957i			1.52386i	−0.647659	+	0.761931i	$0.724252\pi$
$600$		0			0
$601$	−0.218654	+	0.378720i	−0.00891908	+	0.0154483i	−0.870450	−	0.492256i	$-0.836172\pi$
$601$	−0.218654	+	0.378720i	−0.00891908	+	0.0154483i	0.861531	+	0.507704i	$0.169506\pi$
$602$		0			0
$603$			10.4786i			0.426722i
$604$		0			0
$605$	20.4040	−	6.53737i	0.829539	−	0.265782i
$606$		0			0
$607$	−31.2280	−	8.36751i	−1.26750	−	0.339627i	−0.438430	−	0.898765i	$-0.644465\pi$
$607$	−31.2280	−	8.36751i	−1.26750	−	0.339627i	−0.829074	+	0.559139i	$0.811132\pi$
$608$		0			0
$609$	18.4778	−	4.95111i	0.748759	−	0.200629i
$610$		0			0
$611$	6.05690	+	8.45355i	0.245036	+	0.341994i
$612$		0			0
$613$	−25.2582	−	14.5828i	−1.02017	−	0.588996i	−0.106017	−	0.994364i	$-0.533810\pi$
$613$	−25.2582	−	14.5828i	−1.02017	−	0.588996i	−0.914153	+	0.405369i	$0.867143\pi$
$614$		0			0
$615$	38.8908	−	12.4605i	1.56823	−	0.502456i
$616$		0			0
$617$	20.3229	+	35.2002i	0.818168	+	1.41711i	0.907031	+	0.421064i	$0.138343\pi$
$617$	20.3229	+	35.2002i	0.818168	+	1.41711i	−0.0888631	+	0.996044i	$0.528323\pi$
$618$		0			0
$619$	−14.2874	−	14.2874i	−0.574260	−	0.574260i	0.359056	−	0.933316i	$-0.383099\pi$
$619$	−14.2874	−	14.2874i	−0.574260	−	0.574260i	−0.933316	+	0.359056i	$0.883099\pi$
$620$		0			0
$621$	−1.07930	−	0.623132i	−0.0433107	−	0.0250054i
$622$		0			0
$623$	29.8703	−	29.8703i	1.19673	−	1.19673i
$624$		0			0
$625$	16.4216	+	18.8502i	0.656865	+	0.754008i
$626$		0			0
$627$	−20.5450	−	76.6748i	−0.820486	−	3.06210i
$628$		0			0
$629$	−43.5044	+	43.5044i	−1.73464	+	1.73464i
$630$		0			0
$631$	−30.8788	−	8.27394i	−1.22926	−	0.329380i	−0.414971	−	0.909834i	$-0.636208\pi$
$631$	−30.8788	−	8.27394i	−1.22926	−	0.329380i	−0.814293	+	0.580454i	$0.802875\pi$
$632$		0			0
$633$	11.6880	−	43.6202i	0.464557	−	1.73375i
$634$		0			0
$635$	−14.6568	+	0.707939i	−0.581637	+	0.0280937i
$636$		0			0
$637$	−2.78369	−	28.2822i	−0.110294	−	1.12058i
$638$		0			0
$639$	−5.56374	−	20.7641i	−0.220098	−	0.821417i
$640$		0			0
$641$	30.7120	−	17.7316i	1.21305	−	0.700354i	0.249627	−	0.968342i	$-0.419692\pi$
$641$	30.7120	−	17.7316i	1.21305	−	0.700354i	0.963422	+	0.267988i	$0.0863587\pi$
$642$		0			0
$643$	−25.3268	+	14.6224i	−0.998790	+	0.576652i	−0.907890	−	0.419208i	$-0.862308\pi$
$643$	−25.3268	+	14.6224i	−0.998790	+	0.576652i	−0.0909000	+	0.995860i	$0.528974\pi$
$644$		0			0
$645$	28.7348	+	6.23090i	1.13143	+	0.245342i
$646$		0			0
$647$	21.0890	−	5.65079i	0.829095	−	0.222155i	0.180776	−	0.983524i	$-0.442139\pi$
$647$	21.0890	−	5.65079i	0.829095	−	0.222155i	0.648319	+	0.761369i	$0.275472\pi$
$648$		0			0
$649$	−21.5496			−0.845894
$650$		0			0
$651$	37.5033			1.46987
$652$		0			0
$653$	−9.64542	+	2.58448i	−0.377454	+	0.101139i	−0.442558	−	0.896740i	$-0.645929\pi$
$653$	−9.64542	+	2.58448i	−0.377454	+	0.101139i	0.0651035	+	0.997879i	$0.479262\pi$
$654$		0			0
$655$	19.7849	+	4.29020i	0.773061	+	0.167632i
$656$		0			0
$657$	9.47068	−	5.46790i	0.369486	−	0.213323i
$658$		0			0
$659$	−17.9408	+	10.3581i	−0.698873	+	0.403494i	−0.806927	−	0.590651i	$-0.798871\pi$
$659$	−17.9408	+	10.3581i	−0.698873	+	0.403494i	0.108055	+	0.994145i	$0.465538\pi$
$660$		0			0
$661$	11.9997	+	44.7834i	0.466734	+	1.74187i	0.651077	+	0.759012i	$0.274318\pi$
$661$	11.9997	+	44.7834i	0.466734	+	1.74187i	−0.184343	+	0.982862i	$0.559016\pi$
$662$		0			0
$663$	27.2242	+	37.9965i	1.05730	+	1.47566i
$664$		0			0
$665$	−60.2400	+	2.90966i	−2.33601	+	0.112832i
$666$		0			0
$667$	0.971081	−	3.62412i	0.0376004	−	0.140327i
$668$		0			0
$669$	10.4201	+	2.79207i	0.402866	+	0.107948i
$670$		0			0
$671$	−10.2457	+	10.2457i	−0.395530	+	0.395530i
$672$		0			0
$673$	4.44409	+	16.5856i	0.171307	+	0.639327i	0.997151	+	0.0754282i	$0.0240324\pi$
$673$	4.44409	+	16.5856i	0.171307	+	0.639327i	−0.825844	+	0.563898i	$0.809301\pi$
$674$		0			0
$675$	−3.08182	+	1.15412i	−0.118619	+	0.0444221i
$676$		0			0
$677$	16.9842	−	16.9842i	0.652756	−	0.652756i	−0.300900	−	0.953656i	$-0.597287\pi$
$677$	16.9842	−	16.9842i	0.652756	−	0.652756i	0.953656	+	0.300900i	$0.0972870\pi$
$678$		0			0
$679$	20.9552	+	12.0985i	0.804188	+	0.464298i
$680$		0			0
$681$	37.7095	+	37.7095i	1.44503	+	1.44503i
$682$		0			0
$683$	−18.7675	−	32.5062i	−0.718117	−	1.24382i	−0.961745	−	0.273946i	$-0.911671\pi$
$683$	−18.7675	−	32.5062i	−0.718117	−	1.24382i	0.243628	−	0.969869i	$-0.421662\pi$
$684$		0			0
$685$	7.18856	−	2.30319i	0.274661	−	0.0880005i
$686$		0			0
$687$	5.16665	+	2.98297i	0.197120	+	0.113807i
$688$		0			0
$689$	16.9690	+	2.80273i	0.646468	+	0.106775i
$690$		0			0
$691$	−29.8582	+	8.00047i	−1.13586	+	0.304352i	−0.777284	−	0.629149i	$-0.783403\pi$
$691$	−29.8582	+	8.00047i	−1.13586	+	0.304352i	−0.358573	+	0.933502i	$0.616737\pi$
$692$		0			0
$693$	55.1610	+	14.7803i	2.09539	+	0.561459i
$694$		0			0
$695$	−20.9915	+	6.72561i	−0.796253	+	0.255117i
$696$		0			0
$697$		−	37.8044i		−	1.43195i
$698$		0			0
$699$	35.1679	−	60.9126i	1.33017	−	2.30393i
$700$		0			0
$701$			38.2090i			1.44313i	0.692345	+	0.721566i	$0.256577\pi$
$701$			38.2090i			1.44313i	−0.692345	+	0.721566i	$0.743423\pi$
$702$		0			0
$703$	−58.7161	−	58.7161i	−2.21452	−	2.21452i
$704$		0			0
$705$	0.778692	+	16.1216i	0.0293272	+	0.607175i
$706$		0			0
$707$	−26.0522			−0.979795
$708$		0			0
$709$	−9.62682	+	35.9278i	−0.361543	+	1.34930i	0.510505	+	0.859875i	$0.329458\pi$
$709$	−9.62682	+	35.9278i	−0.361543	+	1.34930i	−0.872048	+	0.489421i	$0.837208\pi$
$710$		0			0
$711$	0.311877	+	0.540187i	0.0116963	+	0.0202586i
$712$		0			0
$713$	3.67783	−	6.37019i	0.137736	−	0.238566i
$714$		0			0
$715$	−22.7125	−	28.6699i	−0.849400	−	1.07219i
$716$		0			0
$717$	−0.912443	+	1.58040i	−0.0340758	+	0.0590210i
$718$		0			0
$719$	22.5751	+	39.1012i	0.841908	+	1.45823i	0.888280	+	0.459303i	$0.151901\pi$
$719$	22.5751	+	39.1012i	0.841908	+	1.45823i	−0.0463715	+	0.998924i	$0.514766\pi$
$720$		0			0
$721$	−10.1279	+	37.7977i	−0.377181	+	1.40766i
$722$		0			0
$723$	36.1803			1.34556
$724$		0			0
$725$	−5.75751	−	8.06262i	−0.213829	−	0.299438i
$726$		0			0
$727$	2.21203	+	2.21203i	0.0820398	+	0.0820398i	0.746936	−	0.664896i	$-0.231524\pi$
$727$	2.21203	+	2.21203i	0.0820398	+	0.0820398i	−0.664896	+	0.746936i	$0.731524\pi$
$728$		0			0
$729$			31.5082i			1.16697i
$730$		0			0
$731$	13.6092	−	23.5718i	0.503354	−	0.871834i
$732$		0			0
$733$		−	17.9002i		−	0.661161i	−0.943778	−	0.330580i	$-0.892756\pi$
$733$		−	17.9002i		−	0.661161i	0.943778	−	0.330580i	$-0.107244\pi$
$734$		0			0
$735$	20.1851	−	39.2175i	0.744539	−	1.44656i
$736$		0			0
$737$	−14.0726	−	3.77073i	−0.518370	−	0.138897i
$738$		0			0
$739$	−15.0511	+	4.03294i	−0.553665	+	0.148354i	−0.524794	−	0.851229i	$-0.675858\pi$
$739$	−15.0511	+	4.03294i	−0.553665	+	0.148354i	−0.0288707	+	0.999583i	$0.509191\pi$
$740$		0			0
$741$	−51.2823	+	36.7433i	−1.88390	+	1.34980i
$742$		0			0
$743$	3.81686	+	2.20366i	0.140027	+	0.0808446i	0.568377	−	0.822768i	$-0.307572\pi$
$743$	3.81686	+	2.20366i	0.140027	+	0.0808446i	−0.428350	+	0.903613i	$0.640905\pi$
$744$		0			0
$745$	−4.54563	−	2.33962i	−0.166539	−	0.0857170i
$746$		0			0
$747$	−12.2476	−	21.2134i	−0.448116	−	0.776159i
$748$		0			0
$749$	−6.27581	−	6.27581i	−0.229313	−	0.229313i
$750$		0			0
$751$	−37.2400	−	21.5005i	−1.35891	−	0.784565i	−0.369429	−	0.929259i	$-0.620447\pi$
$751$	−37.2400	−	21.5005i	−1.35891	−	0.784565i	−0.989476	+	0.144694i	$0.953780\pi$
$752$		0			0
$753$	25.1996	−	25.1996i	0.918326	−	0.918326i
$754$		0			0
$755$	35.2147	−	22.6642i	1.28159	−	0.824833i
$756$		0			0
$757$	7.50026	+	27.9914i	0.272602	+	1.01736i	0.957432	+	0.288660i	$0.0932098\pi$
$757$	7.50026	+	27.9914i	0.272602	+	1.01736i	−0.684830	+	0.728703i	$0.740124\pi$
$758$		0			0
$759$	15.2017	−	15.2017i	0.551786	−	0.551786i
$760$		0			0
$761$	9.09438	+	2.43683i	0.329671	+	0.0883350i	0.419858	−	0.907590i	$-0.362080\pi$
$761$	9.09438	+	2.43683i	0.329671	+	0.0883350i	−0.0901872	+	0.995925i	$0.528747\pi$
$762$		0			0
$763$	2.30745	−	8.61152i	0.0835353	−	0.311758i
$764$		0			0
$765$	1.82349	+	37.7526i	0.0659285	+	1.36495i
$766$		0			0
$767$	6.03176	+	16.0292i	0.217794	+	0.578779i
$768$		0			0
$769$	3.95609	+	14.7643i	0.142660	+	0.532416i	0.999848	+	0.0174122i	$0.00554276\pi$
$769$	3.95609	+	14.7643i	0.142660	+	0.532416i	−0.857188	+	0.515004i	$0.827791\pi$
$770$		0			0
$771$	20.3742	−	11.7630i	0.733759	−	0.423636i
$772$		0			0
$773$	14.8233	−	8.55826i	0.533158	−	0.307819i	−0.209143	−	0.977885i	$-0.567067\pi$
$773$	14.8233	−	8.55826i	0.533158	−	0.307819i	0.742302	+	0.670066i	$0.233734\pi$
$774$		0			0
$775$	−6.81182	−	18.1894i	−0.244688	−	0.653384i
$776$		0			0
$777$	110.754	−	29.6766i	3.97329	−	1.06464i
$778$		0			0
$779$	51.0231			1.82809
$780$		0			0
$781$	29.8880			1.06948
$782$		0			0
$783$	1.25970	−	0.337534i	0.0450179	−	0.0120625i
$784$		0			0
$785$	4.06828	−	2.61834i	0.145203	−	0.0934527i
$786$		0			0
$787$	12.5805	−	7.26333i	0.448445	−	0.258910i	−0.258728	−	0.965950i	$-0.583303\pi$
$787$	12.5805	−	7.26333i	0.448445	−	0.258910i	0.707173	+	0.707040i	$0.249970\pi$
$788$		0			0
$789$	43.2613	−	24.9769i	1.54014	−	0.889202i
$790$		0			0
$791$	10.2287	+	38.1741i	0.363691	+	1.35731i
$792$		0			0
$793$	10.4888	+	4.75324i	0.372469	+	0.168793i
$794$		0			0
$795$	19.7638	+	17.9425i	0.700949	+	0.636356i
$796$		0			0
$797$	−12.4168	+	46.3403i	−0.439827	+	1.64146i	0.289418	+	0.957203i	$0.406538\pi$
$797$	−12.4168	+	46.3403i	−0.439827	+	1.64146i	−0.729244	+	0.684253i	$0.760128\pi$
$798$		0			0
$799$	14.4323	+	3.86712i	0.510577	+	0.136809i
$800$		0			0
$801$	25.2654	−	25.2654i	0.892708	−	0.892708i
$802$		0			0
$803$	3.93525	+	14.6866i	0.138872	+	0.518277i
$804$		0			0
$805$	−8.83987	−	13.7351i	−0.311564	−	0.484097i
$806$		0			0
$807$	−38.4430	+	38.4430i	−1.35326	+	1.35326i
$808$		0			0
$809$	−39.5328	−	22.8242i	−1.38990	−	0.802458i	−0.396594	−	0.917994i	$-0.629808\pi$
$809$	−39.5328	−	22.8242i	−1.38990	−	0.802458i	−0.993303	+	0.115536i	$0.963141\pi$
$810$		0			0
$811$	35.2035	+	35.2035i	1.23616	+	1.23616i	0.961557	+	0.274606i	$0.0885475\pi$
$811$	35.2035	+	35.2035i	1.23616	+	1.23616i	0.274606	+	0.961557i	$0.411452\pi$
$812$		0			0
$813$	7.65136	+	13.2525i	0.268345	+	0.464787i
$814$		0			0
$815$	10.5181	+	32.8284i	0.368433	+	1.14993i
$816$		0			0
$817$	31.8138	+	18.3677i	1.11303	+	0.642606i
$818$		0			0
$819$	−4.44563	−	45.1673i	−0.155343	−	1.57827i
$820$		0			0
$821$	47.3788	−	12.6951i	1.65353	−	0.443062i	0.692933	−	0.721002i	$-0.256318\pi$
$821$	47.3788	−	12.6951i	1.65353	−	0.443062i	0.960599	+	0.277940i	$0.0896515\pi$
$822$		0			0
$823$	32.3492	+	8.66794i	1.12762	+	0.302145i	0.773964	−	0.633230i	$-0.218271\pi$
$823$	32.3492	+	8.66794i	1.12762	+	0.302145i	0.353658	+	0.935375i	$0.384938\pi$
$824$		0			0
$825$	−5.47114	−	56.5037i	−0.190481	−	1.96721i
$826$		0			0
$827$			0.102239i			0.00355520i	0.999998	+	0.00177760i	$0.000565828\pi$
$827$			0.102239i			0.00355520i	−0.999998	+	0.00177760i	$0.999434\pi$
$828$		0			0
$829$	−21.0347	+	36.4332i	−0.730567	+	1.26538i	0.226075	+	0.974110i	$0.427411\pi$
$829$	−21.0347	+	36.4332i	−0.730567	+	1.26538i	−0.956641	+	0.291268i	$0.905923\pi$
$830$		0			0
$831$		−	49.4734i		−	1.71621i
$832$		0			0
$833$	−28.8716	−	28.8716i	−1.00034	−	1.00034i
$834$		0			0
$835$	23.3040	+	21.1565i	0.806467	+	0.732150i
$836$		0			0
$837$	2.55673			0.0883735
$838$		0			0
$839$	1.59501	−	5.95267i	0.0550660	−	0.205509i	−0.932912	−	0.360105i	$-0.882741\pi$
$839$	1.59501	−	5.95267i	0.0550660	−	0.205509i	0.987978	+	0.154596i	$0.0494076\pi$
$840$		0			0
$841$	−12.5369	−	21.7146i	−0.432307	−	0.748778i
$842$		0			0
$843$	−25.0571	+	43.4002i	−0.863014	+	1.49478i
$844$		0			0
$845$	−14.9682	+	24.9189i	−0.514921	+	0.857238i
$846$		0			0
$847$	−18.4820	+	32.0118i	−0.635049	+	1.09994i
$848$		0			0
$849$	−40.9454	−	70.9196i	−1.40524	−	2.43395i
$850$		0			0
$851$	5.82058	−	21.7227i	0.199527	−	0.744645i
$852$		0			0
$853$	−44.1436			−1.51145			−0.755724	−	0.654890i	$-0.772715\pi$
$853$	−44.1436			−1.51145			−0.755724	+	0.654890i	$0.772715\pi$
$854$		0			0
$855$	−50.9531	+	2.46109i	−1.74256	+	0.0841676i
$856$		0			0
$857$	−24.9216	−	24.9216i	−0.851305	−	0.851305i	0.138989	−	0.990294i	$-0.455615\pi$
$857$	−24.9216	−	24.9216i	−0.851305	−	0.851305i	−0.990294	+	0.138989i	$0.955615\pi$
$858$		0			0
$859$		−	38.2383i		−	1.30467i	−0.757929	−	0.652337i	$-0.773789\pi$
$859$		−	38.2383i		−	1.30467i	0.757929	−	0.652337i	$-0.226211\pi$
$860$		0			0
$861$	−35.2275	+	61.0158i	−1.20055	+	2.07941i
$862$		0			0
$863$		−	0.948734i		−	0.0322953i	−0.999870	−	0.0161476i	$-0.994860\pi$
$863$		−	0.948734i		−	0.0322953i	0.999870	−	0.0161476i	$-0.00514018\pi$
$864$		0			0
$865$	21.0461	+	10.8324i	0.715590	+	0.368311i
$866$		0			0
$867$	23.7748	+	6.37043i	0.807433	+	0.216351i
$868$		0			0
$869$	−0.837690	+	0.224458i	−0.0284167	+	0.00761423i
$870$		0			0
$871$	1.13416	+	11.5230i	0.0384296	+	0.390442i
$872$		0			0
$873$	17.7247	+	10.2334i	0.599890	+	0.346347i
$874$		0			0
$875$	−42.8356	−	5.03514i	−1.44811	−	0.170219i
$876$		0			0
$877$	−20.8949	−	36.1910i	−0.705569	−	1.22208i	−0.966486	−	0.256721i	$-0.917358\pi$
$877$	−20.8949	−	36.1910i	−0.705569	−	1.22208i	0.260916	−	0.965361i	$-0.415975\pi$
$878$		0			0
$879$	21.3338	+	21.3338i	0.719570	+	0.719570i
$880$		0			0
$881$	27.5194	+	15.8883i	0.927151	+	0.535291i	0.885910	−	0.463858i	$-0.153535\pi$
$881$	27.5194	+	15.8883i	0.927151	+	0.535291i	0.0412419	+	0.999149i	$0.486869\pi$
$882$		0			0
$883$	10.2531	−	10.2531i	0.345043	−	0.345043i	−0.513217	−	0.858259i	$-0.671546\pi$
$883$	10.2531	−	10.2531i	0.345043	−	0.345043i	0.858259	+	0.513217i	$0.171546\pi$
$884$		0			0
$885$	−5.63297	+	25.9773i	−0.189350	+	0.873218i
$886$		0			0
$887$	−2.69367	−	10.0529i	−0.0904447	−	0.337544i	0.905845	−	0.423610i	$-0.139237\pi$
$887$	−2.69367	−	10.0529i	−0.0904447	−	0.337544i	−0.996289	+	0.0860657i	$0.972571\pi$
$888$		0			0
$889$	17.9009	−	17.9009i	0.600377	−	0.600377i
$890$		0			0
$891$	−35.6787	−	9.56008i	−1.19528	−	0.320275i
$892$		0			0
$893$	−5.21928	+	19.4786i	−0.174657	+	0.651827i
$894$		0			0
$895$	23.8964	−	26.3220i	0.798768	−	0.879847i
$896$		0			0
$897$	−15.5624	−	7.05246i	−0.519614	−	0.235475i
$898$		0			0
$899$	1.99219	+	7.43494i	0.0664432	+	0.247969i
$900$		0			0
$901$	21.3999	−	12.3552i	0.712934	−	0.411613i
$902$		0			0
$903$	−43.9300	+	25.3630i	−1.46190	+	0.844028i
$904$		0			0
$905$	−8.54170	+	39.3914i	−0.283936	+	1.30942i
$906$		0			0
$907$	−11.1887	+	2.99801i	−0.371516	+	0.0995473i	−0.439746	−	0.898122i	$-0.644931\pi$
$907$	−11.1887	+	2.99801i	−0.371516	+	0.0995473i	0.0682301	+	0.997670i	$0.478265\pi$
$908$		0			0
$909$	−22.0359			−0.730885
$910$		0			0
$911$	−16.9445			−0.561397			−0.280699	−	0.959796i	$-0.590566\pi$
$911$	−16.9445			−0.561397			−0.280699	+	0.959796i	$0.590566\pi$
$912$		0			0
$913$	32.8965	−	8.81460i	1.08872	−	0.291721i
$914$		0			0
$915$	9.67268	+	15.0291i	0.319769	+	0.496845i
$916$		0			0
$917$	−30.2474	+	17.4633i	−0.998857	+	0.576690i
$918$		0			0
$919$	−2.13979	+	1.23541i	−0.0705851	+	0.0407523i	−0.534877	−	0.844930i	$-0.679642\pi$
$919$	−2.13979	+	1.23541i	−0.0705851	+	0.0407523i	0.464292	+	0.885682i	$0.346309\pi$
$920$		0			0
$921$	−16.5310	−	61.6947i	−0.544717	−	2.03291i
$922$		0			0
$923$	−8.36569	−	22.2315i	−0.275360	−	0.731758i
$924$		0			0
$925$	−34.5100	−	48.3267i	−1.13468	−	1.58897i
$926$		0			0
$927$	−8.56650	+	31.9706i	−0.281361	+	1.05005i
$928$		0			0
$929$	6.19975	+	1.66122i	0.203407	+	0.0545028i	0.359084	−	0.933305i	$-0.383089\pi$
$929$	6.19975	+	1.66122i	0.203407	+	0.0545028i	−0.155677	+	0.987808i	$0.549756\pi$
$930$		0			0
$931$	38.9668	−	38.9668i	1.27709	−	1.27709i
$932$		0			0
$933$	12.3062	+	45.9275i	0.402888	+	1.50360i
$934$		0			0
$935$	−51.3572	−	11.1364i	−1.67956	−	0.364199i
$936$		0			0
$937$	−29.9242	+	29.9242i	−0.977581	+	0.977581i	−0.999754	−	0.0221727i	$-0.992942\pi$
$937$	−29.9242	+	29.9242i	−0.977581	+	0.977581i	0.0221727	+	0.999754i	$0.492942\pi$
$938$		0			0
$939$	−49.8275	−	28.7679i	−1.62606	−	0.938805i
$940$		0			0
$941$	−10.0049	−	10.0049i	−0.326150	−	0.326150i	0.524970	−	0.851121i	$-0.324076\pi$
$941$	−10.0049	−	10.0049i	−0.326150	−	0.326150i	−0.851121	+	0.524970i	$0.824076\pi$
$942$		0			0
$943$	6.90931	+	11.9673i	0.224998	+	0.389708i
$944$		0			0
$945$	2.59820	−	5.04802i	0.0845194	−	0.164212i
$946$		0			0
$947$	−8.33687	−	4.81329i	−0.270912	−	0.156411i	0.358390	−	0.933572i	$-0.383326\pi$
$947$	−8.33687	−	4.81329i	−0.270912	−	0.156411i	−0.629302	+	0.777161i	$0.716659\pi$
$948$		0			0
$949$	9.82279	−	7.03794i	0.318861	−	0.228461i
$950$		0			0
$951$	−50.6241	+	13.5647i	−1.64160	+	0.439865i
$952$		0			0
$953$	7.91919	+	2.12194i	0.256528	+	0.0687364i	0.384791	−	0.923004i	$-0.374274\pi$
$953$	7.91919	+	2.12194i	0.256528	+	0.0687364i	−0.128263	+	0.991740i	$0.540940\pi$
$954$		0			0
$955$	−9.89469	−	30.8826i	−0.320185	−	0.999338i
$956$		0			0
$957$			22.4967i			0.727215i
$958$		0			0
$959$	−6.51143	+	11.2781i	−0.210265	+	0.364190i
$960$		0			0
$961$		−	15.9097i		−	0.513218i
$962$		0			0
$963$	−5.30831	−	5.30831i	−0.171058	−	0.171058i
$964$		0			0
$965$	1.98624	−	2.18786i	0.0639394	−	0.0704296i
$966$		0			0
$967$	53.8159			1.73060			0.865301	−	0.501252i	$-0.167127\pi$
$967$	53.8159			1.73060			0.865301	+	0.501252i	$0.167127\pi$
$968$		0			0
$969$	−23.4593	+	87.5513i	−0.753621	+	2.81255i
$970$		0			0
$971$	−28.7496	−	49.7958i	−0.922619	−	1.59802i	−0.795347	−	0.606154i	$-0.792711\pi$
$971$	−28.7496	−	49.7958i	−0.922619	−	1.59802i	−0.127272	−	0.991868i	$-0.540622\pi$
$972$		0			0
$973$	19.0142	−	32.9336i	0.609567	−	1.05580i
$974$		0			0
$975$	−40.4976	+	19.8851i	−1.29696	+	0.636832i
$976$		0			0
$977$	−3.46271	+	5.99759i	−0.110782	+	0.191880i	−0.916086	−	0.400982i	$-0.868669\pi$
$977$	−3.46271	+	5.99759i	−0.110782	+	0.191880i	0.805304	+	0.592862i	$0.202002\pi$
$978$		0			0
$979$	24.8391	+	43.0226i	0.793862	+	1.37501i
$980$		0			0
$981$	1.95172	−	7.28393i	0.0623138	−	0.232558i
$982$		0			0
$983$	−33.9827			−1.08388			−0.541941	−	0.840417i	$-0.682310\pi$
$983$	−33.9827			−1.08388			−0.541941	+	0.840417i	$0.682310\pi$
$984$		0			0
$985$	−20.9249	+	23.0489i	−0.666723	+	0.734399i
$986$		0			0
$987$	−19.6900	−	19.6900i	−0.626738	−	0.626738i
$988$		0			0
$989$			9.94909i			0.316363i
$990$		0			0
$991$	−7.93170	+	13.7381i	−0.251959	+	0.436405i	−0.964065	−	0.265666i	$-0.914408\pi$
$991$	−7.93170	+	13.7381i	−0.251959	+	0.436405i	0.712106	+	0.702072i	$0.247741\pi$
$992$		0			0
$993$			24.6315i			0.781656i
$994$		0			0
$995$	−9.19056	−	28.6849i	−0.291360	−	0.909373i
$996$		0			0
$997$	19.5993	+	5.25161i	0.620715	+	0.166320i	0.555453	−	0.831548i	$-0.312545\pi$
$997$	19.5993	+	5.25161i	0.620715	+	0.166320i	0.0652620	+	0.997868i	$0.479212\pi$
$998$		0			0
$999$	7.55051	−	2.02315i	0.238888	−	0.0640098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bk.c.33.2	yes	20
5.2	odd	4		260.2.bf.c.137.4	yes	20
5.3	odd	4		1300.2.bn.d.657.2		20
5.4	even	2		1300.2.bs.d.293.4		20
13.2	odd	12		260.2.bf.c.93.4	✓	20
65.2	even	12	inner	260.2.bk.c.197.2	yes	20
65.28	even	12		1300.2.bs.d.457.4		20
65.54	odd	12		1300.2.bn.d.93.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.4	✓	20	13.2	odd	12
260.2.bf.c.137.4	yes	20	5.2	odd	4
260.2.bk.c.33.2	yes	20	1.1	even	1	trivial
260.2.bk.c.197.2	yes	20	65.2	even	12	inner
1300.2.bn.d.93.2		20	65.54	odd	12
1300.2.bn.d.657.2		20	5.3	odd	4
1300.2.bs.d.293.4		20	5.4	even	2
1300.2.bs.d.457.4		20	65.28	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.41732 + 0.647720i) q^{3} +(-2.18528 - 0.473860i) q^{5} +(3.34088 - 1.92886i) q^{7} +(2.82584 - 1.63150i) q^{9} +O(q^{10})\)	\(q+(-2.41732 + 0.647720i) q^{3} +(-2.18528 - 0.473860i) q^{5} +(3.34088 - 1.92886i) q^{7} +(2.82584 - 1.63150i) q^{9} +(1.17419 + 4.38214i) q^{11} +(2.93090 - 2.09996i) q^{13} +(5.58946 - 0.269977i) q^{15} +(1.34075 - 5.00375i) q^{17} +(6.75335 + 1.80956i) q^{19} +(-6.82663 + 6.82663i) q^{21} +(0.490083 + 1.82902i) q^{23} +(4.55091 + 2.07104i) q^{25} +(-0.465395 + 0.465395i) q^{27} +(-1.71600 - 0.990731i) q^{29} +(-2.74684 - 2.74684i) q^{31} +(-5.67679 - 9.83250i) q^{33} +(-8.21477 + 2.63199i) q^{35} +(-10.2855 - 5.93836i) q^{37} +(-5.72474 + 6.97469i) q^{39} +(7.04912 - 1.88880i) q^{41} +(5.07520 + 1.35990i) q^{43} +(-6.94835 + 2.22623i) q^{45} +2.88429i q^{47} +(3.94098 - 6.82598i) q^{49} +12.9641i q^{51} +(3.37298 + 3.37298i) q^{53} +(-0.489416 - 10.1326i) q^{55} -17.4971 q^{57} +(-1.22940 + 4.58817i) q^{59} +(1.59692 + 2.76595i) q^{61} +(6.29385 - 10.9013i) q^{63} +(-7.39992 + 3.20018i) q^{65} +(-1.60567 + 2.78111i) q^{67} +(-2.36938 - 4.10389i) q^{69} +(1.70510 - 6.36353i) q^{71} +3.35146 q^{73} +(-12.3425 - 2.05865i) q^{75} +(12.3753 + 12.3753i) q^{77} +0.191160i q^{79} +(-4.07093 + 7.05105i) q^{81} -7.50696i q^{83} +(-5.30100 + 10.2993i) q^{85} +(4.78983 + 1.28343i) q^{87} +(10.5771 - 2.83413i) q^{89} +(5.74124 - 12.6690i) q^{91} +(8.41918 + 4.86082i) q^{93} +(-13.9005 - 7.15454i) q^{95} +(3.13619 + 5.43203i) q^{97} +(10.4675 + 10.4675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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