LMFDB - Embedded newform 1520.2.q.o.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.q (of order $3$, degree $2$, not 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:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			881.4
Root			$-1.02359 - 1.77290i$ of defining polynomial
Character	$\chi$	$=$	1520.881
Dual form			1520.2.q.o.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52359 + 2.63893i) q^{3} +(-0.500000 - 0.866025i) q^{5} +0.609175 q^{7} +(-3.14263 + 5.44319i) q^{9} +O(q^{10})$	\(q+(1.52359 + 2.63893i) q^{3} +(-0.500000 - 0.866025i) q^{5} +0.609175 q^{7} +(-3.14263 + 5.44319i) q^{9} -4.48517 q^{11} +(-2.21900 + 3.84342i) q^{13} +(1.52359 - 2.63893i) q^{15} +(-1.45172 - 2.51445i) q^{17} +(-3.60532 - 2.44983i) q^{19} +(0.928131 + 1.60757i) q^{21} +(-1.42363 + 2.46580i) q^{23} +(-0.500000 + 0.866025i) q^{25} -10.0107 q^{27} +(-0.558149 + 0.966742i) q^{29} +6.22908 q^{31} +(-6.83354 - 11.8360i) q^{33} +(-0.304588 - 0.527561i) q^{35} -3.77264 q^{37} -13.5233 q^{39} +(4.15184 + 7.19120i) q^{41} +(-4.99438 - 8.65053i) q^{43} +6.28525 q^{45} +(-2.94250 + 5.09656i) q^{47} -6.62891 q^{49} +(4.42363 - 7.66195i) q^{51} +(-4.22436 + 7.31681i) q^{53} +(2.24258 + 3.88427i) q^{55} +(0.971912 - 13.2467i) q^{57} +(5.11793 + 8.86451i) q^{59} +(2.49099 - 4.31453i) q^{61} +(-1.91441 + 3.31586i) q^{63} +4.43800 q^{65} +(4.23808 - 7.34057i) q^{67} -8.67608 q^{69} +(5.80995 + 10.0631i) q^{71} +(-1.86162 - 3.22443i) q^{73} -3.04717 q^{75} -2.73225 q^{77} +(4.51908 + 7.82728i) q^{79} +(-5.82432 - 10.0880i) q^{81} +2.12178 q^{83} +(-1.45172 + 2.51445i) q^{85} -3.40155 q^{87} +(-3.96608 + 6.86946i) q^{89} +(-1.35176 + 2.34131i) q^{91} +(9.49053 + 16.4381i) q^{93} +(-0.318955 + 4.34721i) q^{95} +(4.83628 + 8.37668i) q^{97} +(14.0952 - 24.4136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9	$ 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 + 4 * q^11 - 7 * q^13 + 3 * q^15 + q^17 - 5 * q^19 + 4 * q^21 + 2 * q^23 - 4 * q^25 - 24 * q^27 + q^29 - 19 * q^33 - 4 * q^35 - 4 * q^37 - 30 * q^39 + 8 * q^41 + q^43 + 2 * q^45 - 12 * q^47 - 20 * q^49 + 22 * q^51 + 5 * q^53 - 2 * q^55 + 7 * q^57 - 5 * q^59 - 3 * q^63 + 14 * q^65 + 4 * q^67 - 18 * q^69 + 20 * q^71 + 20 * q^73 - 6 * q^75 + 28 * q^77 + 17 * q^79 - 12 * q^81 - 2 * q^83 + q^85 + 32 * q^87 - 11 * q^89 + 6 * q^91 + 8 * q^93 + 4 * q^95 - q^97 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	1.52359	+	2.63893i	0.879643	+	1.52359i	0.851734	+	0.523975i	$0.175552\pi$
$3$	1.52359	+	2.63893i	0.879643	+	1.52359i	0.0279089	+	0.999610i	$0.491115\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	0.609175			0.230247			0.115123	−	0.993351i	$-0.463274\pi$
$7$	0.609175			0.230247			0.115123	+	0.993351i	$0.463274\pi$
$8$		0			0
$9$	−3.14263	+	5.44319i	−1.04754	+	1.81440i
$10$		0			0
$11$	−4.48517			−1.35233			−0.676164	−	0.736751i	$-0.736359\pi$
$11$	−4.48517			−1.35233			−0.676164	+	0.736751i	$0.736359\pi$
$12$		0			0
$13$	−2.21900	+	3.84342i	−0.615439	+	1.06597i	0.374868	+	0.927078i	$0.377688\pi$
$13$	−2.21900	+	3.84342i	−0.615439	+	1.06597i	−0.990307	+	0.138894i	$0.955645\pi$
$14$		0			0
$15$	1.52359	−	2.63893i	0.393388	−	0.681368i
$16$		0			0
$17$	−1.45172	−	2.51445i	−0.352093	−	0.609843i	0.634523	−	0.772904i	$-0.281197\pi$
$17$	−1.45172	−	2.51445i	−0.352093	−	0.609843i	−0.986616	+	0.163061i	$0.947863\pi$
$18$		0			0
$19$	−3.60532	−	2.44983i	−0.827117	−	0.562030i
$19$	−3.60532	−	2.44983i	−0.827117	−	0.562030i
$20$		0			0
$21$	0.928131	+	1.60757i	0.202535	+	0.350800i
$22$		0			0
$23$	−1.42363	+	2.46580i	−0.296847	+	0.514154i	−0.975413	−	0.220386i	$-0.929268\pi$
$23$	−1.42363	+	2.46580i	−0.296847	+	0.514154i	0.678566	+	0.734540i	$0.262602\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−10.0107			−1.92656
$28$		0			0
$29$	−0.558149	+	0.966742i	−0.103646	+	0.179519i	−0.913184	−	0.407547i	$-0.866384\pi$
$29$	−0.558149	+	0.966742i	−0.103646	+	0.179519i	0.809538	+	0.587067i	$0.199717\pi$
$30$		0			0
$31$	6.22908			1.11877			0.559387	−	0.828906i	$-0.311036\pi$
$31$	6.22908			1.11877			0.559387	+	0.828906i	$0.311036\pi$
$32$		0			0
$33$	−6.83354	−	11.8360i	−1.18957	−	2.06039i
$34$		0			0
$35$	−0.304588	−	0.527561i	−0.0514847	−	0.0891741i
$36$		0			0
$37$	−3.77264			−0.620219			−0.310109	−	0.950701i	$-0.600366\pi$
$37$	−3.77264			−0.620219			−0.310109	+	0.950701i	$0.600366\pi$
$38$		0			0
$39$	−13.5233			−2.16547
$40$		0			0
$41$	4.15184	+	7.19120i	0.648409	+	1.12308i	0.983503	+	0.180893i	$0.0578987\pi$
$41$	4.15184	+	7.19120i	0.648409	+	1.12308i	−0.335094	+	0.942185i	$0.608768\pi$
$42$		0			0
$43$	−4.99438	−	8.65053i	−0.761637	−	1.31919i	−0.942007	−	0.335594i	$-0.891063\pi$
$43$	−4.99438	−	8.65053i	−0.761637	−	1.31919i	0.180370	−	0.983599i	$-0.442270\pi$
$44$		0			0
$45$	6.28525			0.936950
$46$		0			0
$47$	−2.94250	+	5.09656i	−0.429208	+	0.743409i	−0.996803	−	0.0798983i	$-0.974540\pi$
$47$	−2.94250	+	5.09656i	−0.429208	+	0.743409i	0.567595	+	0.823308i	$0.307874\pi$
$48$		0			0
$49$	−6.62891			−0.946986
$50$		0			0
$51$	4.42363	−	7.66195i	0.619432	−	1.07289i
$52$		0			0
$53$	−4.22436	+	7.31681i	−0.580261	+	1.00504i	0.415188	+	0.909736i	$0.363716\pi$
$53$	−4.22436	+	7.31681i	−0.580261	+	1.00504i	−0.995448	+	0.0953049i	$0.969617\pi$
$54$		0			0
$55$	2.24258	+	3.88427i	0.302390	+	0.523755i
$56$		0			0
$57$	0.971912	−	13.2467i	0.128733	−	1.75457i
$58$		0			0
$59$	5.11793	+	8.86451i	0.666297	+	1.15406i	0.978932	+	0.204187i	$0.0654552\pi$
$59$	5.11793	+	8.86451i	0.666297	+	1.15406i	−0.312634	+	0.949874i	$0.601211\pi$
$60$		0			0
$61$	2.49099	−	4.31453i	0.318939	−	0.552419i	−0.661328	−	0.750097i	$-0.730007\pi$
$61$	2.49099	−	4.31453i	0.318939	−	0.552419i	0.980267	+	0.197678i	$0.0633401\pi$
$62$		0			0
$63$	−1.91441	+	3.31586i	−0.241193	+	0.417759i
$64$		0			0
$65$	4.43800			0.550466
$66$		0			0
$67$	4.23808	−	7.34057i	0.517764	−	0.896794i	−0.482023	−	0.876159i	$-0.660098\pi$
$67$	4.23808	−	7.34057i	0.517764	−	0.896794i	0.999787	−	0.0206350i	$-0.00656879\pi$
$68$		0			0
$69$	−8.67608			−1.04448
$70$		0			0
$71$	5.80995	+	10.0631i	0.689514	+	1.19427i	0.971995	+	0.235001i	$0.0755093\pi$
$71$	5.80995	+	10.0631i	0.689514	+	1.19427i	−0.282481	+	0.959273i	$0.591157\pi$
$72$		0			0
$73$	−1.86162	−	3.22443i	−0.217887	−	0.377391i	0.736275	−	0.676682i	$-0.236583\pi$
$73$	−1.86162	−	3.22443i	−0.217887	−	0.377391i	−0.954162	+	0.299292i	$0.903250\pi$
$74$		0			0
$75$	−3.04717			−0.351857
$76$		0			0
$77$	−2.73225			−0.311369
$78$		0			0
$79$	4.51908	+	7.82728i	0.508437	+	0.880638i	0.999952	+	0.00976923i	$0.00310969\pi$
$79$	4.51908	+	7.82728i	0.508437	+	0.880638i	−0.491516	+	0.870869i	$0.663557\pi$
$80$		0			0
$81$	−5.82432	−	10.0880i	−0.647146	−	1.12089i
$82$		0			0
$83$	2.12178			0.232896			0.116448	−	0.993197i	$-0.462849\pi$
$83$	2.12178			0.232896			0.116448	+	0.993197i	$0.462849\pi$
$84$		0			0
$85$	−1.45172	+	2.51445i	−0.157461	+	0.272730i
$86$		0			0
$87$	−3.40155			−0.364684
$88$		0			0
$89$	−3.96608	+	6.86946i	−0.420404	+	0.728161i	−0.995979	−	0.0895879i	$-0.971445\pi$
$89$	−3.96608	+	6.86946i	−0.420404	+	0.728161i	0.575575	+	0.817749i	$0.304778\pi$
$90$		0			0
$91$	−1.35176	+	2.34131i	−0.141703	+	0.245436i
$92$		0			0
$93$	9.49053	+	16.4381i	0.984122	+	1.70455i
$94$		0			0
$95$	−0.318955	+	4.34721i	−0.0327241	+	0.446015i
$96$		0			0
$97$	4.83628	+	8.37668i	0.491050	+	0.850523i	0.999947	−	0.0103043i	$-0.00328001\pi$
$97$	4.83628	+	8.37668i	0.491050	+	0.850523i	−0.508897	+	0.860827i	$0.669947\pi$
$98$		0			0
$99$	14.0952	−	24.4136i	1.41662	−	2.45366i
$100$		0			0
$101$	0.485632	−	0.841140i	0.0483222	−	0.0836965i	−0.840853	−	0.541264i	$-0.817946\pi$
$101$	0.485632	−	0.841140i	0.0483222	−	0.0836965i	0.889175	+	0.457568i	$0.151279\pi$
$102$		0			0
$103$	3.34143			0.329241			0.164620	−	0.986357i	$-0.447360\pi$
$103$	3.34143			0.329241			0.164620	+	0.986357i	$0.447360\pi$
$104$		0			0
$105$	0.928131	−	1.60757i	0.0905763	−	0.156883i
$106$		0			0
$107$	−9.51655			−0.920000			−0.460000	−	0.887919i	$-0.652151\pi$
$107$	−9.51655			−0.920000			−0.460000	+	0.887919i	$0.652151\pi$
$108$		0			0
$109$	−2.77178	−	4.80087i	−0.265489	−	0.459840i	0.702203	−	0.711977i	$-0.252200\pi$
$109$	−2.77178	−	4.80087i	−0.265489	−	0.459840i	−0.967692	+	0.252137i	$0.918867\pi$
$110$		0			0
$111$	−5.74795	−	9.95573i	−0.545571	−	0.944956i
$112$		0			0
$113$	1.54134			0.144997			0.0724987	−	0.997369i	$-0.476903\pi$
$113$	1.54134			0.144997			0.0724987	+	0.997369i	$0.476903\pi$
$114$		0			0
$115$	2.84726			0.265508
$116$		0			0
$117$	−13.9470	−	24.1568i	−1.28940	−	2.23330i
$118$		0			0
$119$	−0.884350	−	1.53174i	−0.0810682	−	0.140414i
$120$		0			0
$121$	9.11672			0.828793
$122$		0			0
$123$	−12.6514	+	21.9128i	−1.14074	+	1.97581i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.15274	−	1.99661i	0.102289	−	0.177171i	−0.810338	−	0.585963i	$-0.800717\pi$
$127$	1.15274	−	1.99661i	0.102289	−	0.177171i	0.912628	+	0.408792i	$0.134050\pi$
$128$		0			0
$129$	15.2187	−	26.3596i	1.33994	−	2.32084i
$130$		0			0
$131$	−6.45905	−	11.1874i	−0.564330	−	0.977448i	−0.997112	−	0.0759493i	$-0.975801\pi$
$131$	−6.45905	−	11.1874i	−0.564330	−	0.977448i	0.432782	−	0.901499i	$-0.357532\pi$
$132$		0			0
$133$	−2.19627	−	1.49238i	−0.190441	−	0.129405i
$134$		0			0
$135$	5.00536	+	8.66954i	0.430793	+	0.746155i
$136$		0			0
$137$	6.36677	−	11.0276i	0.543950	−	0.942149i	−0.454722	−	0.890633i	$-0.650261\pi$
$137$	6.36677	−	11.0276i	0.543950	−	0.942149i	0.998672	−	0.0515159i	$-0.0164053\pi$
$138$		0			0
$139$	5.30433	−	9.18738i	0.449908	−	0.779263i	−0.548472	−	0.836169i	$-0.684790\pi$
$139$	5.30433	−	9.18738i	0.449908	−	0.779263i	0.998380	+	0.0569059i	$0.0181235\pi$
$140$		0			0
$141$	−17.9326			−1.51020
$142$		0			0
$143$	9.95258	−	17.2384i	0.832276	−	1.44154i
$144$		0			0
$145$	1.11630			0.0927035
$146$		0			0
$147$	−10.0997	−	17.4932i	−0.833010	−	1.44281i
$148$		0			0
$149$	−1.88653	−	3.26757i	−0.154551	−	0.267690i	0.778344	−	0.627837i	$-0.216060\pi$
$149$	−1.88653	−	3.26757i	−0.154551	−	0.267690i	−0.932895	+	0.360147i	$0.882726\pi$
$150$		0			0
$151$	9.51562			0.774370			0.387185	−	0.922002i	$-0.373447\pi$
$151$	9.51562			0.774370			0.387185	+	0.922002i	$0.373447\pi$
$152$		0			0
$153$	18.2488			1.47533
$154$		0			0
$155$	−3.11454	−	5.39454i	−0.250166	−	0.433300i
$156$		0			0
$157$	1.72822	+	2.99336i	0.137927	+	0.238896i	0.926712	−	0.375773i	$-0.122623\pi$
$157$	1.72822	+	2.99336i	0.137927	+	0.238896i	−0.788785	+	0.614669i	$0.789290\pi$
$158$		0			0
$159$	−25.7447			−2.04169
$160$		0			0
$161$	−0.867239	+	1.50210i	−0.0683480	+	0.118382i
$162$		0			0
$163$	−6.65283			−0.521090			−0.260545	−	0.965462i	$-0.583902\pi$
$163$	−6.65283			−0.521090			−0.260545	+	0.965462i	$0.583902\pi$
$164$		0			0
$165$	−6.83354	+	11.8360i	−0.531990	+	0.921434i
$166$		0			0
$167$	−8.22775	+	14.2509i	−0.636682	+	1.10277i	0.349474	+	0.936946i	$0.386360\pi$
$167$	−8.22775	+	14.2509i	−0.636682	+	1.10277i	−0.986156	+	0.165820i	$0.946973\pi$
$168$		0			0
$169$	−3.34790	−	5.79874i	−0.257531	−	0.446057i
$170$		0			0
$171$	24.6651	−	11.9255i	1.88618	−	0.911968i
$172$		0			0
$173$	11.3912	+	19.7302i	0.866058	+	1.50006i	0.865992	+	0.500057i	$0.166688\pi$
$173$	11.3912	+	19.7302i	0.866058	+	1.50006i	6.58713e−5		1.00000i	$0.499979\pi$
$174$		0			0
$175$	−0.304588	+	0.527561i	−0.0230247	+	0.0398799i
$176$		0			0
$177$	−15.5952	+	27.0117i	−1.17221	+	2.03032i
$178$		0			0
$179$	2.32916			0.174090			0.0870449	−	0.996204i	$-0.472258\pi$
$179$	2.32916			0.174090			0.0870449	+	0.996204i	$0.472258\pi$
$180$		0			0
$181$	11.1696	−	19.3463i	0.830230	−	1.43800i	−0.0676258	−	0.997711i	$-0.521542\pi$
$181$	11.1696	−	19.3463i	0.830230	−	1.43800i	0.897856	−	0.440290i	$-0.145124\pi$
$182$		0			0
$183$	15.1810			1.12221
$184$		0			0
$185$	1.88632	+	3.26721i	0.138685	+	0.240210i
$186$		0			0
$187$	6.51119	+	11.2777i	0.476145	+	0.824708i
$188$		0			0
$189$	−6.09829			−0.443585
$190$		0			0
$191$	−2.23766			−0.161911			−0.0809556	−	0.996718i	$-0.525797\pi$
$191$	−2.23766			−0.161911			−0.0809556	+	0.996718i	$0.525797\pi$
$192$		0			0
$193$	2.27153	+	3.93441i	0.163508	+	0.283205i	0.936125	−	0.351669i	$-0.114386\pi$
$193$	2.27153	+	3.93441i	0.163508	+	0.283205i	−0.772616	+	0.634873i	$0.781052\pi$
$194$		0			0
$195$	6.76167	+	11.7115i	0.484213	+	0.838681i
$196$		0			0
$197$	−19.2236			−1.36962			−0.684812	−	0.728720i	$-0.740116\pi$
$197$	−19.2236			−1.36962			−0.684812	+	0.728720i	$0.740116\pi$
$198$		0			0
$199$	−3.07547	+	5.32687i	−0.218014	+	0.377612i	−0.954201	−	0.299167i	$-0.903291\pi$
$199$	−3.07547	+	5.32687i	−0.218014	+	0.377612i	0.736186	+	0.676779i	$0.236625\pi$
$200$		0			0
$201$	25.8283			1.82179
$202$		0			0
$203$	−0.340010	+	0.588915i	−0.0238641	+	0.0413338i
$204$		0			0
$205$	4.15184	−	7.19120i	0.289977	−	0.502255i
$206$		0			0
$207$	−8.94786	−	15.4981i	−0.621919	−	1.07720i
$208$		0			0
$209$	16.1705	+	10.9879i	1.11853	+	0.760049i
$210$		0			0
$211$	6.34661	+	10.9926i	0.436919	+	0.756765i	0.997450	−	0.0713679i	$-0.0227365\pi$
$211$	6.34661	+	10.9926i	0.436919	+	0.756765i	−0.560531	+	0.828133i	$0.689403\pi$
$212$		0			0
$213$	−17.7039	+	30.6641i	−1.21305	+	2.10107i
$214$		0			0
$215$	−4.99438	+	8.65053i	−0.340614	+	0.589961i
$216$		0			0
$217$	3.79460			0.257594
$218$		0			0
$219$	5.67269	−	9.82538i	0.383325	−	0.663938i
$220$		0			0
$221$	12.8854			0.866767
$222$		0			0
$223$	11.2688	+	19.5181i	0.754614	+	1.30703i	0.945566	+	0.325430i	$0.105509\pi$
$223$	11.2688	+	19.5181i	0.754614	+	1.30703i	−0.190952	+	0.981599i	$0.561158\pi$
$224$		0			0
$225$	−3.14263	−	5.44319i	−0.209508	−	0.362879i
$226$		0			0
$227$	−18.1124			−1.20216			−0.601080	−	0.799189i	$-0.705263\pi$
$227$	−18.1124			−1.20216			−0.601080	+	0.799189i	$0.705263\pi$
$228$		0			0
$229$	−9.41604			−0.622229			−0.311115	−	0.950372i	$-0.600702\pi$
$229$	−9.41604			−0.622229			−0.311115	+	0.950372i	$0.600702\pi$
$230$		0			0
$231$	−4.16282	−	7.21022i	−0.273894	−	0.474398i
$232$		0			0
$233$	−7.85000	−	13.5966i	−0.514271	−	0.890743i	−0.999863	−	0.0165573i	$-0.994729\pi$
$233$	−7.85000	−	13.5966i	−0.514271	−	0.890743i	0.485592	−	0.874185i	$-0.338604\pi$
$234$		0			0
$235$	5.88500			0.383895
$236$		0			0
$237$	−13.7704	+	23.8511i	−0.894485	+	1.54929i
$238$		0			0
$239$	23.4610			1.51757			0.758783	−	0.651344i	$-0.225795\pi$
$239$	23.4610			1.51757			0.758783	+	0.651344i	$0.225795\pi$
$240$		0			0
$241$	−6.58469	+	11.4050i	−0.424157	+	0.734662i	−0.996341	−	0.0854634i	$-0.972763\pi$
$241$	−6.58469	+	11.4050i	−0.424157	+	0.734662i	0.572184	+	0.820125i	$0.306096\pi$
$242$		0			0
$243$	2.73161	−	4.73128i	0.175233	−	0.303512i
$244$		0			0
$245$	3.31445	+	5.74080i	0.211753	+	0.366766i
$246$		0			0
$247$	17.4159	−	8.42058i	1.10815	−	0.535789i
$248$		0			0
$249$	3.23272	+	5.59923i	0.204865	+	0.354837i
$250$		0			0
$251$	−8.66257	+	15.0040i	−0.546776	+	0.947045i	0.451716	+	0.892162i	$0.350812\pi$
$251$	−8.66257	+	15.0040i	−0.546776	+	0.947045i	−0.998493	+	0.0548830i	$0.982521\pi$
$252$		0			0
$253$	6.38521	−	11.0595i	0.401435	−	0.695305i
$254$		0			0
$255$	−8.84726			−0.554037
$256$		0			0
$257$	2.83980	−	4.91867i	0.177142	−	0.306818i	−0.763759	−	0.645502i	$-0.776648\pi$
$257$	2.83980	−	4.91867i	0.177142	−	0.306818i	0.940900	+	0.338683i	$0.109982\pi$
$258$		0			0
$259$	−2.29820			−0.142803
$260$		0			0
$261$	−3.50811	−	6.07622i	−0.217146	−	0.376108i
$262$		0			0
$263$	2.82882	+	4.89966i	0.174433	+	0.302126i	0.939965	−	0.341272i	$-0.110858\pi$
$263$	2.82882	+	4.89966i	0.174433	+	0.302126i	−0.765532	+	0.643398i	$0.777524\pi$
$264$		0			0
$265$	8.44872			0.519001
$266$		0			0
$267$	−24.1707			−1.47922
$268$		0			0
$269$	11.9959	+	20.7775i	0.731402	+	1.26683i	0.956284	+	0.292440i	$0.0944672\pi$
$269$	11.9959	+	20.7775i	0.731402	+	1.26683i	−0.224881	+	0.974386i	$0.572199\pi$
$270$		0			0
$271$	−10.6497	−	18.4459i	−0.646926	−	1.12051i	−0.983853	−	0.178978i	$-0.942721\pi$
$271$	−10.6497	−	18.4459i	−0.646926	−	1.12051i	0.336927	−	0.941531i	$-0.390612\pi$
$272$		0			0
$273$	−8.23808			−0.498591
$274$		0			0
$275$	2.24258	−	3.88427i	0.135233	−	0.234230i
$276$		0			0
$277$	−0.821109			−0.0493357			−0.0246678	−	0.999696i	$-0.507853\pi$
$277$	−0.821109			−0.0493357			−0.0246678	+	0.999696i	$0.507853\pi$
$278$		0			0
$279$	−19.5757	+	33.9060i	−1.17196	+	2.02990i
$280$		0			0
$281$	0.293739	−	0.508772i	0.0175230	−	0.0303508i	−0.857131	−	0.515099i	$-0.827755\pi$
$281$	0.293739	−	0.508772i	0.0175230	−	0.0303508i	0.874654	+	0.484748i	$0.161089\pi$
$282$		0			0
$283$	15.4712	+	26.7969i	0.919667	+	1.59291i	0.799921	+	0.600105i	$0.204875\pi$
$283$	15.4712	+	26.7969i	0.919667	+	1.59291i	0.119746	+	0.992805i	$0.461792\pi$
$284$		0			0
$285$	−11.9579	+	5.78165i	−0.708327	+	0.342475i
$286$		0			0
$287$	2.52920	+	4.38070i	0.149294	+	0.258585i
$288$		0			0
$289$	4.28504	−	7.42191i	0.252061	−	0.436583i
$290$		0			0
$291$	−14.7370	+	25.5252i	−0.863896	+	1.49631i
$292$		0			0
$293$	3.76271			0.219820			0.109910	−	0.993942i	$-0.464944\pi$
$293$	3.76271			0.219820			0.109910	+	0.993942i	$0.464944\pi$
$294$		0			0
$295$	5.11793	−	8.86451i	0.297977	−	0.516112i
$296$		0			0
$297$	44.8998			2.60535
$298$		0			0
$299$	−6.31806	−	10.9432i	−0.365383	−	0.632861i
$300$		0			0
$301$	−3.04246	−	5.26969i	−0.175364	−	0.303740i
$302$		0			0
$303$	2.95961			0.170025
$304$		0			0
$305$	−4.98199			−0.285268
$306$		0			0
$307$	10.1709	+	17.6166i	0.580485	+	1.00543i	0.995422	+	0.0955798i	$0.0304705\pi$
$307$	10.1709	+	17.6166i	0.580485	+	1.00543i	−0.414936	+	0.909850i	$0.636196\pi$
$308$		0			0
$309$	5.09095	+	8.81779i	0.289614	+	0.501626i
$310$		0			0
$311$	7.67830			0.435397			0.217698	−	0.976016i	$-0.430145\pi$
$311$	7.67830			0.435397			0.217698	+	0.976016i	$0.430145\pi$
$312$		0			0
$313$	−11.9964	+	20.7783i	−0.678074	+	1.17446i	0.297486	+	0.954726i	$0.403852\pi$
$313$	−11.9964	+	20.7783i	−0.678074	+	1.17446i	−0.975560	+	0.219733i	$0.929481\pi$
$314$		0			0
$315$	3.82882			0.215730
$316$		0			0
$317$	−0.519518	+	0.899831i	−0.0291790	+	0.0505395i	−0.880246	−	0.474517i	$-0.842623\pi$
$317$	−0.519518	+	0.899831i	−0.0291790	+	0.0505395i	0.851067	+	0.525057i	$0.175956\pi$
$318$		0			0
$319$	2.50339	−	4.33600i	0.140163	−	0.242769i
$320$		0			0
$321$	−14.4993	−	25.1135i	−0.809271	−	1.40170i
$322$		0			0
$323$	−0.926066	+	12.6218i	−0.0515277	+	0.702298i
$324$		0			0
$325$	−2.21900	−	3.84342i	−0.123088	−	0.213194i
$326$		0			0
$327$	8.44610	−	14.6291i	0.467070	−	0.808990i
$328$		0			0
$329$	−1.79250	+	3.10470i	−0.0988236	+	0.171167i
$330$		0			0
$331$	−30.8316			−1.69466			−0.847328	−	0.531069i	$-0.821790\pi$
$331$	−30.8316			−1.69466			−0.847328	+	0.531069i	$0.821790\pi$
$332$		0			0
$333$	11.8560	−	20.5352i	0.649705	−	1.12532i
$334$		0			0
$335$	−8.47616			−0.463102
$336$		0			0
$337$	−10.3576	−	17.9400i	−0.564217	−	0.977252i	−0.997122	−	0.0758124i	$-0.975845\pi$
$337$	−10.3576	−	17.9400i	−0.564217	−	0.977252i	0.432906	−	0.901439i	$-0.357488\pi$
$338$		0			0
$339$	2.34837	+	4.06749i	0.127546	+	0.220916i
$340$		0			0
$341$	−27.9384			−1.51295
$342$		0			0
$343$	−8.30239			−0.448287
$344$		0			0
$345$	4.33804	+	7.51370i	0.233552	+	0.404524i
$346$		0			0
$347$	4.11068	+	7.11991i	0.220673	+	0.382217i	0.955013	−	0.296566i	$-0.0958413\pi$
$347$	4.11068	+	7.11991i	0.220673	+	0.382217i	−0.734340	+	0.678782i	$0.762508\pi$
$348$		0			0
$349$	11.9216			0.638150			0.319075	−	0.947730i	$-0.396628\pi$
$349$	11.9216			0.638150			0.319075	+	0.947730i	$0.396628\pi$
$350$		0			0
$351$	22.2138	−	38.4754i	1.18568	−	2.05366i
$352$		0			0
$353$	−11.7983			−0.627959			−0.313980	−	0.949430i	$-0.601662\pi$
$353$	−11.7983			−0.627959			−0.313980	+	0.949430i	$0.601662\pi$
$354$		0			0
$355$	5.80995	−	10.0631i	0.308360	−	0.534095i
$356$		0			0
$357$	2.69477	−	4.66747i	0.142622	−	0.247029i
$358$		0			0
$359$	0.0554058	+	0.0959656i	0.00292420	+	0.00506487i	0.867484	−	0.497465i	$-0.165736\pi$
$359$	0.0554058	+	0.0959656i	0.00292420	+	0.00506487i	−0.864560	+	0.502530i	$0.832403\pi$
$360$		0			0
$361$	6.99666	+	17.6648i	0.368245	+	0.929729i
$362$		0			0
$363$	13.8901	+	24.0584i	0.729042	+	1.26274i
$364$		0			0
$365$	−1.86162	+	3.22443i	−0.0974418	+	0.168774i
$366$		0			0
$367$	5.86986	−	10.1669i	0.306404	−	0.530708i	−0.671169	−	0.741305i	$-0.734207\pi$
$367$	5.86986	−	10.1669i	0.306404	−	0.530708i	0.977573	+	0.210597i	$0.0675408\pi$
$368$		0			0
$369$	−52.1908			−2.71694
$370$		0			0
$371$	−2.57338	+	4.45722i	−0.133603	+	0.231407i
$372$		0			0
$373$	14.5190			0.751763			0.375882	−	0.926668i	$-0.377340\pi$
$373$	14.5190			0.751763			0.375882	+	0.926668i	$0.377340\pi$
$374$		0			0
$375$	1.52359	+	2.63893i	0.0786776	+	0.136274i
$376$		0			0
$377$	−2.47706	−	4.29040i	−0.127575	−	0.220967i
$378$		0			0
$379$	6.59023			0.338518			0.169259	−	0.985572i	$-0.445863\pi$
$379$	6.59023			0.338518			0.169259	+	0.985572i	$0.445863\pi$
$380$		0			0
$381$	7.02522			0.359913
$382$		0			0
$383$	−1.43461	−	2.48481i	−0.0733049	−	0.126968i	0.827043	−	0.562139i	$-0.190021\pi$
$383$	−1.43461	−	2.48481i	−0.0733049	−	0.126968i	−0.900348	+	0.435171i	$0.856688\pi$
$384$		0			0
$385$	1.36613	+	2.36620i	0.0696243	+	0.120593i
$386$		0			0
$387$	62.7819			3.19138
$388$		0			0
$389$	3.16575	−	5.48323i	0.160510	−	0.278011i	−0.774542	−	0.632523i	$-0.782020\pi$
$389$	3.16575	−	5.48323i	0.160510	−	0.278011i	0.935052	+	0.354512i	$0.115353\pi$
$390$		0			0
$391$	8.26682			0.418071
$392$		0			0
$393$	19.6818	−	34.0899i	0.992817	−	1.71961i
$394$		0			0
$395$	4.51908	−	7.82728i	0.227380	−	0.393833i
$396$		0			0
$397$	15.2749	+	26.4569i	0.766626	+	1.32784i	0.939382	+	0.342871i	$0.111399\pi$
$397$	15.2749	+	26.4569i	0.766626	+	1.32784i	−0.172756	+	0.984965i	$0.555267\pi$
$398$		0			0
$399$	0.592065	−	8.06957i	0.0296403	−	0.403984i
$400$		0			0
$401$	−15.1711	−	26.2771i	−0.757609	−	1.31222i	−0.944067	−	0.329754i	$-0.893034\pi$
$401$	−15.1711	−	26.2771i	−0.757609	−	1.31222i	0.186458	−	0.982463i	$-0.440299\pi$
$402$		0			0
$403$	−13.8223	+	23.9409i	−0.688538	+	1.19258i
$404$		0			0
$405$	−5.82432	+	10.0880i	−0.289413	+	0.501277i
$406$		0			0
$407$	16.9209			0.838740
$408$		0			0
$409$	7.48628	−	12.9666i	0.370173	−	0.641158i	−0.619419	−	0.785060i	$-0.712632\pi$
$409$	7.48628	−	12.9666i	0.370173	−	0.641158i	0.989592	+	0.143903i	$0.0459652\pi$
$410$		0			0
$411$	38.8013			1.91393
$412$		0			0
$413$	3.11772	+	5.40004i	0.153413	+	0.265719i
$414$		0			0
$415$	−1.06089	−	1.83752i	−0.0520771	−	0.0902002i
$416$		0			0
$417$	32.3264			1.58303
$418$		0			0
$419$	6.17419			0.301629			0.150815	−	0.988562i	$-0.451810\pi$
$419$	6.17419			0.301629			0.150815	+	0.988562i	$0.451810\pi$
$420$		0			0
$421$	13.7714	+	23.8528i	0.671177	+	1.16251i	0.977571	+	0.210608i	$0.0675443\pi$
$421$	13.7714	+	23.8528i	0.671177	+	1.16251i	−0.306394	+	0.951905i	$0.599122\pi$
$422$		0			0
$423$	−18.4943	−	32.0331i	−0.899226	−	1.55750i
$424$		0			0
$425$	2.90343			0.140837
$426$		0			0
$427$	1.51745	−	2.62830i	0.0734347	−	0.127193i
$428$		0			0
$429$	60.6544			2.92842
$430$		0			0
$431$	−7.52941	+	13.0413i	−0.362679	+	0.628179i	−0.988401	−	0.151868i	$-0.951471\pi$
$431$	−7.52941	+	13.0413i	−0.362679	+	0.628179i	0.625722	+	0.780046i	$0.284805\pi$
$432$		0			0
$433$	0.485420	−	0.840772i	0.0233278	−	0.0404049i	−0.854126	−	0.520066i	$-0.825907\pi$
$433$	0.485420	−	0.840772i	0.0233278	−	0.0404049i	0.877454	+	0.479661i	$0.159241\pi$
$434$		0			0
$435$	1.70077	+	2.94583i	0.0815459	+	0.141242i
$436$		0			0
$437$	11.1734	−	5.40234i	0.534497	−	0.258429i
$438$		0			0
$439$	−13.7187	−	23.7616i	−0.654760	−	1.13408i	−0.981954	−	0.189120i	$-0.939436\pi$
$439$	−13.7187	−	23.7616i	−0.654760	−	1.13408i	0.327194	−	0.944957i	$-0.393897\pi$
$440$		0			0
$441$	20.8322	−	36.0824i	0.992008	−	1.71821i
$442$		0			0
$443$	−4.38272	+	7.59109i	−0.208229	+	0.360664i	−0.951157	−	0.308708i	$-0.900103\pi$
$443$	−4.38272	+	7.59109i	−0.208229	+	0.360664i	0.742928	+	0.669372i	$0.233437\pi$
$444$		0			0
$445$	7.93217			0.376021
$446$		0			0
$447$	5.74859	−	9.95686i	0.271899	−	0.470943i
$448$		0			0
$449$	−9.63397			−0.454655			−0.227327	−	0.973818i	$-0.572999\pi$
$449$	−9.63397			−0.454655			−0.227327	+	0.973818i	$0.572999\pi$
$450$		0			0
$451$	−18.6217	−	32.2538i	−0.876862	−	1.51877i
$452$		0			0
$453$	14.4979	+	25.1110i	0.681169	+	1.17982i
$454$		0			0
$455$	2.70352			0.126743
$456$		0			0
$457$	−10.6708			−0.499161			−0.249580	−	0.968354i	$-0.580293\pi$
$457$	−10.6708			−0.499161			−0.249580	+	0.968354i	$0.580293\pi$
$458$		0			0
$459$	14.5327	+	25.1714i	0.678330	+	1.17490i
$460$		0			0
$461$	−2.84340	−	4.92491i	−0.132430	−	0.229376i	0.792183	−	0.610284i	$-0.208945\pi$
$461$	−2.84340	−	4.92491i	−0.132430	−	0.229376i	−0.924613	+	0.380908i	$0.875611\pi$
$462$		0			0
$463$	−35.3550			−1.64309			−0.821543	−	0.570147i	$-0.806886\pi$
$463$	−35.3550			−1.64309			−0.821543	+	0.570147i	$0.806886\pi$
$464$		0			0
$465$	9.49053	−	16.4381i	0.440113	−	0.762298i
$466$		0			0
$467$	32.9071			1.52276			0.761380	−	0.648306i	$-0.224522\pi$
$467$	32.9071			1.52276			0.761380	+	0.648306i	$0.224522\pi$
$468$		0			0
$469$	2.58173	−	4.47169i	0.119213	−	0.206484i
$470$		0			0
$471$	−5.26617	+	9.12127i	−0.242652	+	0.420286i
$472$		0			0
$473$	22.4006	+	38.7991i	1.02998	+	1.78398i
$474$		0			0
$475$	3.92428	−	1.89738i	0.180058	−	0.0870579i
$476$		0			0
$477$	−26.5512	−	45.9880i	−1.21569	−	2.10564i
$478$		0			0
$479$	−4.52861	+	7.84378i	−0.206917	+	0.358391i	−0.950742	−	0.309984i	$-0.899676\pi$
$479$	−4.52861	+	7.84378i	−0.206917	+	0.358391i	0.743825	+	0.668375i	$0.233010\pi$
$480$		0			0
$481$	8.37149	−	14.4998i	0.381707	−	0.661136i
$482$		0			0
$483$	−5.28525			−0.240487
$484$		0			0
$485$	4.83628	−	8.37668i	0.219604	−	0.380365i
$486$		0			0
$487$	16.5206			0.748620			0.374310	−	0.927304i	$-0.377880\pi$
$487$	16.5206			0.748620			0.374310	+	0.927304i	$0.377880\pi$
$488$		0			0
$489$	−10.1362	−	17.5563i	−0.458373	−	0.793925i
$490$		0			0
$491$	−0.695625	−	1.20486i	−0.0313931	−	0.0543745i	0.849902	−	0.526941i	$-0.176661\pi$
$491$	−0.695625	−	1.20486i	−0.0313931	−	0.0543745i	−0.881295	+	0.472566i	$0.843328\pi$
$492$		0			0
$493$	3.24109			0.145972
$494$		0			0
$495$	−28.1904			−1.26706
$496$		0			0
$497$	3.53928	+	6.13021i	0.158758	+	0.274977i
$498$		0			0
$499$	−8.33255	−	14.4324i	−0.373016	−	0.646083i	0.617012	−	0.786954i	$-0.288343\pi$
$499$	−8.33255	−	14.4324i	−0.373016	−	0.646083i	−0.990028	+	0.140871i	$0.955010\pi$
$500$		0			0
$501$	−50.1427			−2.24021
$502$		0			0
$503$	7.81956	−	13.5439i	0.348657	−	0.603892i	−0.637354	−	0.770571i	$-0.719971\pi$
$503$	7.81956	−	13.5439i	0.348657	−	0.603892i	0.986011	+	0.166679i	$0.0533045\pi$
$504$		0			0
$505$	−0.971265			−0.0432207
$506$		0			0
$507$	10.2016	−	17.6697i	0.453070	−	0.784741i
$508$		0			0
$509$	9.57702	−	16.5879i	0.424494	−	0.735245i	−0.571879	−	0.820338i	$-0.693785\pi$
$509$	9.57702	−	16.5879i	0.424494	−	0.735245i	0.996373	+	0.0850929i	$0.0271187\pi$
$510$		0			0
$511$	−1.13406	−	1.96424i	−0.0501677	−	0.0868929i
$512$		0			0
$513$	36.0919	+	24.5246i	1.59349	+	1.08279i
$514$		0			0
$515$	−1.67071	−	2.89376i	−0.0736205	−	0.127514i
$516$		0			0
$517$	13.1976	−	22.8589i	0.580430	−	1.00533i
$518$		0			0
$519$	−34.7110	+	60.1212i	−1.52364	+	2.63903i
$520$		0			0
$521$	−19.2394			−0.842892			−0.421446	−	0.906853i	$-0.638477\pi$
$521$	−19.2394			−0.842892			−0.421446	+	0.906853i	$0.638477\pi$
$522$		0			0
$523$	3.31973	−	5.74993i	0.145161	−	0.251427i	−0.784272	−	0.620418i	$-0.786963\pi$
$523$	3.31973	−	5.74993i	0.145161	−	0.251427i	0.929433	+	0.368990i	$0.120296\pi$
$524$		0			0
$525$	−1.85626			−0.0810139
$526$		0			0
$527$	−9.04285	−	15.6627i	−0.393913	−	0.682277i
$528$		0			0
$529$	7.44657	+	12.8978i	0.323764	+	0.560775i
$530$		0			0
$531$	−64.3349			−2.79190
$532$		0			0
$533$	−36.8517			−1.59623
$534$		0			0
$535$	4.75828	+	8.24158i	0.205718	+	0.356314i
$536$		0			0
$537$	3.54868	+	6.14649i	0.153137	+	0.265241i
$538$		0			0
$539$	29.7317			1.28064
$540$		0			0
$541$	−20.8756	+	36.1575i	−0.897510	+	1.55453i	−0.0668435	+	0.997763i	$0.521293\pi$
$541$	−20.8756	+	36.1575i	−0.897510	+	1.55453i	−0.830667	+	0.556770i	$0.812040\pi$
$542$		0			0
$543$	68.0714			2.92122
$544$		0			0
$545$	−2.77178	+	4.80087i	−0.118730	+	0.205647i
$546$		0			0
$547$	6.10258	−	10.5700i	0.260927	−	0.451939i	−0.705561	−	0.708649i	$-0.749305\pi$
$547$	6.10258	−	10.5700i	0.260927	−	0.451939i	0.966489	+	0.256710i	$0.0826384\pi$
$548$		0			0
$549$	15.6565	+	27.1179i	0.668204	+	1.15736i
$550$		0			0
$551$	4.38066	−	2.11804i	0.186622	−	0.0902317i
$552$		0			0
$553$	2.75291	+	4.76819i	0.117066	+	0.202764i
$554$		0			0
$555$	−5.74795	+	9.95573i	−0.243987	+	0.422597i
$556$		0			0
$557$	−17.5774	+	30.4450i	−0.744779	+	1.28999i	0.205519	+	0.978653i	$0.434112\pi$
$557$	−17.5774	+	30.4450i	−0.744779	+	1.28999i	−0.950298	+	0.311342i	$0.899222\pi$
$558$		0			0
$559$	44.3301			1.87496
$560$		0			0
$561$	−19.8407	+	34.3651i	−0.837675	+	1.45090i
$562$		0			0
$563$	−17.8406			−0.751891			−0.375945	−	0.926642i	$-0.622682\pi$
$563$	−17.8406			−0.751891			−0.375945	+	0.926642i	$0.622682\pi$
$564$		0			0
$565$	−0.770672	−	1.33484i	−0.0324224	−	0.0561572i
$566$		0			0
$567$	−3.54803	−	6.14537i	−0.149003	−	0.258081i
$568$		0			0
$569$	31.6042			1.32492			0.662459	−	0.749098i	$-0.269513\pi$
$569$	31.6042			1.32492			0.662459	+	0.749098i	$0.269513\pi$
$570$		0			0
$571$	4.73053			0.197967			0.0989833	−	0.995089i	$-0.468441\pi$
$571$	4.73053			0.197967			0.0989833	+	0.995089i	$0.468441\pi$
$572$		0			0
$573$	−3.40926	−	5.90501i	−0.142424	−	0.246685i
$574$		0			0
$575$	−1.42363	−	2.46580i	−0.0593694	−	0.102831i
$576$		0			0
$577$	24.4074			1.01609			0.508047	−	0.861330i	$-0.330368\pi$
$577$	24.4074			1.01609			0.508047	+	0.861330i	$0.330368\pi$
$578$		0			0
$579$	−6.92174	+	11.9888i	−0.287658	+	0.498238i
$580$		0			0
$581$	1.29254			0.0536235
$582$		0			0
$583$	18.9470	−	32.8171i	0.784703	−	1.35915i
$584$		0			0
$585$	−13.9470	+	24.1568i	−0.576636	+	0.998763i
$586$		0			0
$587$	−14.3077	−	24.7817i	−0.590543	−	1.02285i	−0.994159	−	0.107922i	$-0.965580\pi$
$587$	−14.3077	−	24.7817i	−0.590543	−	1.02285i	0.403616	−	0.914928i	$-0.367753\pi$
$588$		0			0
$589$	−22.4578	−	15.2602i	−0.925358	−	0.628785i
$590$		0			0
$591$	−29.2888	−	50.7297i	−1.20478	−	2.08674i
$592$		0			0
$593$	−1.85756	+	3.21738i	−0.0762807	+	0.132122i	−0.901642	−	0.432482i	$-0.857638\pi$
$593$	−1.85756	+	3.21738i	−0.0762807	+	0.132122i	0.825362	+	0.564604i	$0.190971\pi$
$594$		0			0
$595$	−0.884350	+	1.53174i	−0.0362548	+	0.0627952i
$596$		0			0
$597$	−18.7430			−0.767099
$598$		0			0
$599$	3.54970	−	6.14826i	0.145037	−	0.251211i	−0.784350	−	0.620319i	$-0.787003\pi$
$599$	3.54970	−	6.14826i	0.145037	−	0.251211i	0.929387	+	0.369108i	$0.120337\pi$
$600$		0			0
$601$	−11.0596			−0.451131			−0.225566	−	0.974228i	$-0.572423\pi$
$601$	−11.0596			−0.451131			−0.225566	+	0.974228i	$0.572423\pi$
$602$		0			0
$603$	26.6374	+	46.1373i	1.08476	+	1.87886i
$604$		0			0
$605$	−4.55836	−	7.89531i	−0.185324	−	0.320990i
$606$		0			0
$607$	−27.1193			−1.10074			−0.550369	−	0.834921i	$-0.685513\pi$
$607$	−27.1193			−1.10074			−0.550369	+	0.834921i	$0.685513\pi$
$608$		0			0
$609$	−2.07214			−0.0839673
$610$		0			0
$611$	−13.0588	−	22.6185i	−0.528302	−	0.915046i
$612$		0			0
$613$	−20.9156	−	36.2268i	−0.844772	−	1.46319i	−0.885819	−	0.464031i	$-0.846403\pi$
$613$	−20.9156	−	36.2268i	−0.844772	−	1.46319i	0.0410468	−	0.999157i	$-0.486931\pi$
$614$		0			0
$615$	25.3028			1.02031
$616$		0			0
$617$	8.85262	−	15.3332i	0.356393	−	0.617291i	−0.630962	−	0.775813i	$-0.717340\pi$
$617$	8.85262	−	15.3332i	0.356393	−	0.617291i	0.987355	+	0.158523i	$0.0506731\pi$
$618$		0			0
$619$	39.8064			1.59995			0.799976	−	0.600032i	$-0.204845\pi$
$619$	39.8064			1.59995			0.799976	+	0.600032i	$0.204845\pi$
$620$		0			0
$621$	14.2515	−	24.6844i	0.571895	−	0.990551i
$622$		0			0
$623$	−2.41604	+	4.18471i	−0.0967966	+	0.167657i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−4.35919	+	59.4137i	−0.174089	+	2.37275i
$628$		0			0
$629$	5.47681	+	9.48611i	0.218375	+	0.378236i
$630$		0			0
$631$	23.0990	−	40.0087i	0.919557	−	1.59272i	0.119469	−	0.992838i	$-0.461881\pi$
$631$	23.0990	−	40.0087i	0.919557	−	1.59272i	0.800088	−	0.599882i	$-0.204786\pi$
$632$		0			0
$633$	−19.3392	+	33.4965i	−0.768664	+	1.33137i
$634$		0			0
$635$	−2.30549			−0.0914905
$636$		0			0
$637$	14.7095	−	25.4776i	0.582813	−	1.00946i
$638$		0			0
$639$	−73.0340			−2.88918
$640$		0			0
$641$	−3.30674	−	5.72744i	−0.130608	−	0.226220i	0.793303	−	0.608827i	$-0.208360\pi$
$641$	−3.30674	−	5.72744i	−0.130608	−	0.226220i	−0.923911	+	0.382607i	$0.875026\pi$
$642$		0			0
$643$	−15.3076	−	26.5135i	−0.603673	−	1.04559i	−0.992260	−	0.124180i	$-0.960370\pi$
$643$	−15.3076	−	26.5135i	−0.603673	−	1.04559i	0.388587	−	0.921412i	$-0.372963\pi$
$644$		0			0
$645$	−30.4375			−1.19847
$646$		0			0
$647$	11.8979			0.467753			0.233877	−	0.972266i	$-0.424859\pi$
$647$	11.8979			0.467753			0.233877	+	0.972266i	$0.424859\pi$
$648$		0			0
$649$	−22.9548	−	39.7588i	−0.901053	−	1.56067i
$650$		0			0
$651$	5.78140	+	10.0137i	0.226591	+	0.392467i
$652$		0			0
$653$	−1.42899			−0.0559207			−0.0279604	−	0.999609i	$-0.508901\pi$
$653$	−1.42899			−0.0559207			−0.0279604	+	0.999609i	$0.508901\pi$
$654$		0			0
$655$	−6.45905	+	11.1874i	−0.252376	+	0.437128i
$656$		0			0
$657$	23.4015			0.912981
$658$		0			0
$659$	−12.2485	+	21.2150i	−0.477134	+	0.826420i	−0.999657	−	0.0262051i	$-0.991658\pi$
$659$	−12.2485	+	21.2150i	−0.477134	+	0.826420i	0.522523	+	0.852625i	$0.324991\pi$
$660$		0			0
$661$	1.61303	−	2.79385i	0.0627396	−	0.108668i	−0.832949	−	0.553349i	$-0.813350\pi$
$661$	1.61303	−	2.79385i	0.0627396	−	0.108668i	0.895689	+	0.444681i	$0.146683\pi$
$662$		0			0
$663$	19.6320	+	34.0037i	0.762445	+	1.32059i
$664$		0			0
$665$	−0.194300	+	2.64822i	−0.00753462	+	0.102693i
$666$		0			0
$667$	−1.58919	−	2.75256i	−0.0615338	−	0.106580i
$668$		0			0
$669$	−34.3379	+	59.4750i	−1.32758	+	2.29944i
$670$		0			0
$671$	−11.1725	+	19.3514i	−0.431311	+	0.747052i
$672$		0			0
$673$	37.1424			1.43173			0.715866	−	0.698237i	$-0.246032\pi$
$673$	37.1424			1.43173			0.715866	+	0.698237i	$0.246032\pi$
$674$		0			0
$675$	5.00536	−	8.66954i	0.192656	−	0.333691i
$676$		0			0
$677$	−24.7550			−0.951412			−0.475706	−	0.879604i	$-0.657807\pi$
$677$	−24.7550			−0.951412			−0.475706	+	0.879604i	$0.657807\pi$
$678$		0			0
$679$	2.94614	+	5.10287i	0.113063	+	0.195830i
$680$		0			0
$681$	−27.5957	−	47.7972i	−1.05747	−	1.83159i
$682$		0			0
$683$	−40.1153			−1.53497			−0.767484	−	0.641068i	$-0.778492\pi$
$683$	−40.1153			−1.53497			−0.767484	+	0.641068i	$0.778492\pi$
$684$		0			0
$685$	−12.7335			−0.486524
$686$		0			0
$687$	−14.3461	−	24.8482i	−0.547340	−	0.948020i
$688$		0			0
$689$	−18.7477	−	32.4720i	−0.714230	−	1.23708i
$690$		0			0
$691$	−39.4963			−1.50251			−0.751254	−	0.660013i	$-0.770551\pi$
$691$	−39.4963			−1.50251			−0.751254	+	0.660013i	$0.770551\pi$
$692$		0			0
$693$	8.58645	−	14.8722i	0.326172	−	0.564947i
$694$		0			0
$695$	−10.6087			−0.402410
$696$		0			0
$697$	12.0546	−	20.8792i	0.456600	−	0.790855i
$698$		0			0
$699$	23.9203	−	41.4312i	0.904748	−	1.56707i
$700$		0			0
$701$	−0.0109776	−	0.0190137i	−0.000414618	−	0.000718139i	0.865818	−	0.500359i	$-0.166799\pi$
$701$	−0.0109776	−	0.0190137i	−0.000414618	−	0.000718139i	−0.866233	+	0.499641i	$0.833465\pi$
$702$		0			0
$703$	13.6016	+	9.24234i	0.512994	+	0.348581i
$704$		0			0
$705$	8.96630	+	15.5301i	0.337690	+	0.584897i
$706$		0			0
$707$	0.295835	−	0.512402i	0.0111260	−	0.0192708i
$708$		0			0
$709$	8.90087	−	15.4168i	0.334279	−	0.578989i	−0.649067	−	0.760731i	$-0.724840\pi$
$709$	8.90087	−	15.4168i	0.334279	−	0.578989i	0.983346	+	0.181743i	$0.0581738\pi$
$710$		0			0
$711$	−56.8071			−2.13043
$712$		0			0
$713$	−8.86789	+	15.3596i	−0.332105	+	0.575223i
$714$		0			0
$715$	−19.9052			−0.744410
$716$		0			0
$717$	35.7448	+	61.9118i	1.33491	+	2.31214i
$718$		0			0
$719$	9.40515	+	16.2902i	0.350753	+	0.607522i	0.986382	−	0.164473i	$-0.0525923\pi$
$719$	9.40515	+	16.2902i	0.350753	+	0.607522i	−0.635629	+	0.771995i	$0.719259\pi$
$720$		0			0
$721$	2.03552			0.0758066
$722$		0			0
$723$	−40.1294			−1.49243
$724$		0			0
$725$	−0.558149	−	0.966742i	−0.0207291	−	0.0359039i
$726$		0			0
$727$	2.50151	+	4.33274i	0.0927758	+	0.160692i	0.908678	−	0.417497i	$-0.137093\pi$
$727$	2.50151	+	4.33274i	0.0927758	+	0.160692i	−0.815902	+	0.578190i	$0.803759\pi$
$728$		0			0
$729$	−18.2986			−0.677725
$730$		0			0
$731$	−14.5009	+	25.1162i	−0.536334	+	0.928957i
$732$		0			0
$733$	−23.5259			−0.868950			−0.434475	−	0.900684i	$-0.643066\pi$
$733$	−23.5259			−0.868950			−0.434475	+	0.900684i	$0.643066\pi$
$734$		0			0
$735$	−10.0997	+	17.4932i	−0.372533	+	0.645246i
$736$		0			0
$737$	−19.0085	+	32.9237i	−0.700187	+	1.21276i
$738$		0			0
$739$	−18.6918	−	32.3752i	−0.687590	−	1.19094i	−0.972615	−	0.232421i	$-0.925335\pi$
$739$	−18.6918	−	32.3752i	−0.687590	−	1.19094i	0.285026	−	0.958520i	$-0.407998\pi$
$740$		0			0
$741$	48.7559	+	33.1299i	1.79109	+	1.21706i
$742$		0			0
$743$	5.19430	+	8.99679i	0.190560	+	0.330060i	0.945436	−	0.325808i	$-0.105636\pi$
$743$	5.19430	+	8.99679i	0.190560	+	0.330060i	−0.754876	+	0.655868i	$0.772303\pi$
$744$		0			0
$745$	−1.88653	+	3.26757i	−0.0691173	+	0.119715i
$746$		0			0
$747$	−6.66797	+	11.5493i	−0.243968	+	0.422566i
$748$		0			0
$749$	−5.79725			−0.211827
$750$		0			0
$751$	−15.6413	+	27.0915i	−0.570758	+	0.988581i	0.425731	+	0.904850i	$0.360017\pi$
$751$	−15.6413	+	27.0915i	−0.570758	+	0.988581i	−0.996488	+	0.0837314i	$0.973316\pi$
$752$		0			0
$753$	−52.7927			−1.92387
$754$		0			0
$755$	−4.75781	−	8.24077i	−0.173154	−	0.299912i
$756$		0			0
$757$	6.31205	+	10.9328i	0.229415	+	0.397359i	0.957635	−	0.287985i	$-0.0929853\pi$
$757$	6.31205	+	10.9328i	0.229415	+	0.397359i	−0.728220	+	0.685344i	$0.759652\pi$
$758$		0			0
$759$	38.9137			1.41248
$760$		0			0
$761$	11.5495			0.418668			0.209334	−	0.977844i	$-0.432870\pi$
$761$	11.5495			0.418668			0.209334	+	0.977844i	$0.432870\pi$
$762$		0			0
$763$	−1.68850	−	2.92457i	−0.0611279	−	0.105877i
$764$		0			0
$765$	−9.12440	−	15.8039i	−0.329893	−	0.571392i
$766$		0			0
$767$	−45.4267			−1.64026
$768$		0			0
$769$	13.4603	−	23.3140i	0.485392	−	0.840724i	−0.514467	−	0.857510i	$-0.672010\pi$
$769$	13.4603	−	23.3140i	0.485392	−	0.840724i	0.999859	+	0.0167864i	$0.00534353\pi$
$770$		0			0
$771$	17.3067			0.623286
$772$		0			0
$773$	−10.6666	+	18.4750i	−0.383649	+	0.664500i	−0.991581	−	0.129489i	$-0.958666\pi$
$773$	−10.6666	+	18.4750i	−0.383649	+	0.664500i	0.607932	+	0.793989i	$0.291999\pi$
$774$		0			0
$775$	−3.11454	+	5.39454i	−0.111877	+	0.193778i
$776$		0			0
$777$	−3.50151	−	6.06479i	−0.125616	−	0.217573i
$778$		0			0
$779$	2.64851	−	36.0979i	0.0948926	−	1.29334i
$780$		0			0
$781$	−26.0586	−	45.1348i	−0.932450	−	1.61505i
$782$		0			0
$783$	5.58747	−	9.67779i	0.199680	−	0.345856i
$784$		0			0
$785$	1.72822	−	2.99336i	0.0616827	−	0.106838i
$786$		0			0
$787$	−3.52489			−0.125649			−0.0628243	−	0.998025i	$-0.520011\pi$
$787$	−3.52489			−0.125649			−0.0628243	+	0.998025i	$0.520011\pi$
$788$		0			0
$789$	−8.61990	+	14.9301i	−0.306877	+	0.531526i
$790$		0			0
$791$	0.938948			0.0333852
$792$		0			0
$793$	11.0550	+	19.1479i	0.392575	+	0.679961i
$794$		0			0
$795$	12.8723	+	22.2956i	0.456535	+	0.790742i
$796$		0			0
$797$	−39.0084			−1.38175			−0.690875	−	0.722974i	$-0.742774\pi$
$797$	−39.0084			−1.38175			−0.690875	+	0.722974i	$0.742774\pi$
$798$		0			0
$799$	17.0867			0.604484
$800$		0			0
$801$	−24.9278	−	43.1763i	−0.880782	−	1.52556i
$802$		0			0
$803$	8.34969	+	14.4621i	0.294654	+	0.510356i
$804$		0			0
$805$	1.73448			0.0611323
$806$		0			0
$807$	−36.5535	+	63.3126i	−1.28675	+	2.22871i
$808$		0			0
$809$	50.7196			1.78321			0.891604	−	0.452816i	$-0.149581\pi$
$809$	50.7196			1.78321			0.891604	+	0.452816i	$0.149581\pi$
$810$		0			0
$811$	14.5188	−	25.1473i	0.509824	−	0.883041i	−0.490111	−	0.871660i	$-0.663044\pi$
$811$	14.5188	−	25.1473i	0.509824	−	0.883041i	0.999935	−	0.0113812i	$-0.00362282\pi$
$812$		0			0
$813$	32.4516	−	56.2078i	1.13813	−	1.97129i
$814$		0			0
$815$	3.32641	+	5.76152i	0.116519	+	0.201817i
$816$		0			0
$817$	−3.18597	+	43.4233i	−0.111463	+	1.51919i
$818$		0			0
$819$	−8.49614	−	14.7158i	−0.296879	−	0.514210i
$820$		0			0
$821$	−16.4939	+	28.5682i	−0.575640	+	0.997038i	0.420331	+	0.907371i	$0.361914\pi$
$821$	−16.4939	+	28.5682i	−0.575640	+	0.997038i	−0.995972	+	0.0896677i	$0.971420\pi$
$822$		0			0
$823$	−13.2767	+	22.9959i	−0.462796	+	0.801586i	−0.999099	−	0.0424397i	$-0.986487\pi$
$823$	−13.2767	+	22.9959i	−0.462796	+	0.801586i	0.536303	+	0.844025i	$0.319820\pi$
$824$		0			0
$825$	13.6671			0.475826
$826$		0			0
$827$	−16.3833	+	28.3767i	−0.569703	+	0.986754i	0.426892	+	0.904302i	$0.359608\pi$
$827$	−16.3833	+	28.3767i	−0.569703	+	0.986754i	−0.996595	+	0.0824515i	$0.973725\pi$
$828$		0			0
$829$	32.4548			1.12720			0.563601	−	0.826047i	$-0.309416\pi$
$829$	32.4548			1.12720			0.563601	+	0.826047i	$0.309416\pi$
$830$		0			0
$831$	−1.25103	−	2.16685i	−0.0433978	−	0.0751671i
$832$		0			0
$833$	9.62329	+	16.6680i	0.333427	+	0.577513i
$834$		0			0
$835$	16.4555			0.569466
$836$		0			0
$837$	−62.3576			−2.15539
$838$		0			0
$839$	−17.6049	−	30.4926i	−0.607788	−	1.05272i	−0.991604	−	0.129310i	$-0.958724\pi$
$839$	−17.6049	−	30.4926i	−0.607788	−	1.05272i	0.383816	−	0.923410i	$-0.374610\pi$
$840$		0			0
$841$	13.8769	+	24.0356i	0.478515	+	0.828813i
$842$		0			0
$843$	1.79015			0.0616560
$844$		0			0
$845$	−3.34790	+	5.79874i	−0.115171	+	0.199483i
$846$		0			0
$847$	5.55368			0.190827
$848$		0			0
$849$	−47.1434	+	81.6547i	−1.61796	+	2.80238i
$850$		0			0
$851$	5.37084	−	9.30257i	0.184110	−	0.318888i
$852$		0			0
$853$	0.894126	+	1.54867i	0.0306143	+	0.0530255i	0.880927	−	0.473253i	$-0.156920\pi$
$853$	0.894126	+	1.54867i	0.0306143	+	0.0530255i	−0.850312	+	0.526278i	$0.823587\pi$
$854$		0			0
$855$	−22.6603	−	15.3978i	−0.774967	−	0.526594i
$856$		0			0
$857$	−1.80690	−	3.12964i	−0.0617224	−	0.106906i	0.833513	−	0.552500i	$-0.186326\pi$
$857$	−1.80690	−	3.12964i	−0.0617224	−	0.106906i	−0.895235	+	0.445594i	$0.852993\pi$
$858$		0			0
$859$	−12.6824	+	21.9666i	−0.432719	+	0.749491i	−0.997106	−	0.0760192i	$-0.975779\pi$
$859$	−12.6824	+	21.9666i	−0.432719	+	0.749491i	0.564388	+	0.825510i	$0.309112\pi$
$860$		0			0
$861$	−7.70691	+	13.3488i	−0.262651	+	0.454924i
$862$		0			0
$863$	29.9878			1.02080			0.510398	−	0.859939i	$-0.329498\pi$
$863$	29.9878			1.02080			0.510398	+	0.859939i	$0.329498\pi$
$864$		0			0
$865$	11.3912	−	19.7302i	0.387313	−	0.670846i
$866$		0			0
$867$	26.1145			0.886895
$868$		0			0
$869$	−20.2688	−	35.1067i	−0.687573	−	1.19091i
$870$		0			0
$871$	18.8086	+	32.5774i	0.637305	+	1.10384i
$872$		0			0
$873$	−60.7945			−2.05758
$874$		0			0
$875$	0.609175			0.0205939
$876$		0			0
$877$	−5.32389	−	9.22125i	−0.179775	−	0.311380i	0.762028	−	0.647544i	$-0.224204\pi$
$877$	−5.32389	−	9.22125i	−0.179775	−	0.311380i	−0.941803	+	0.336164i	$0.890870\pi$
$878$		0			0
$879$	5.73281	+	9.92951i	0.193363	+	0.334914i
$880$		0			0
$881$	−31.5797			−1.06395			−0.531973	−	0.846761i	$-0.678549\pi$
$881$	−31.5797			−1.06395			−0.531973	+	0.846761i	$0.678549\pi$
$882$		0			0
$883$	8.50871	−	14.7375i	0.286341	−	0.495957i	−0.686593	−	0.727042i	$-0.740894\pi$
$883$	8.50871	−	14.7375i	0.286341	−	0.495957i	0.972933	+	0.231085i	$0.0742277\pi$
$884$		0			0
$885$	31.1904			1.04845
$886$		0			0
$887$	−6.61451	+	11.4567i	−0.222093	+	0.384677i	−0.955443	−	0.295174i	$-0.904622\pi$
$887$	−6.61451	+	11.4567i	−0.222093	+	0.384677i	0.733350	+	0.679851i	$0.237956\pi$
$888$		0			0
$889$	0.702223	−	1.21629i	0.0235518	−	0.0407929i
$890$		0			0
$891$	26.1230	+	45.2464i	0.875155	+	1.51581i
$892$		0			0
$893$	23.0943	−	11.1661i	0.772823	−	0.373659i
$894$		0			0
$895$	−1.16458	−	2.01711i	−0.0389277	−	0.0674247i
$896$		0			0
$897$	19.2522	−	33.3458i	0.642812	−	1.11338i
$898$		0			0
$899$	−3.47675	+	6.02191i	−0.115956	+	0.200842i
$900$		0			0
$901$	24.5303			0.817222
$902$		0			0
$903$	9.27088	−	16.0576i	0.308516	−	0.534365i
$904$		0			0
$905$	−22.3392			−0.742580
$906$		0			0
$907$	−7.44520	−	12.8955i	−0.247214	−	0.428187i	0.715538	−	0.698574i	$-0.246182\pi$
$907$	−7.44520	−	12.8955i	−0.247214	−	0.428187i	−0.962752	+	0.270387i	$0.912848\pi$
$908$		0			0
$909$	3.05232	+	5.28678i	0.101239	+	0.175351i
$910$		0			0
$911$	49.5480			1.64160			0.820800	−	0.571216i	$-0.193528\pi$
$911$	49.5480			1.64160			0.820800	+	0.571216i	$0.193528\pi$
$912$		0			0
$913$	−9.51655			−0.314952
$914$		0			0
$915$	−7.59049	−	13.1471i	−0.250934	−	0.434630i
$916$		0			0
$917$	−3.93469	−	6.81509i	−0.129935	−	0.225054i
$918$		0			0
$919$	−27.3835			−0.903300			−0.451650	−	0.892195i	$-0.649164\pi$
$919$	−27.3835			−0.903300			−0.451650	+	0.892195i	$0.649164\pi$
$920$		0			0
$921$	−30.9926	+	53.6807i	−1.02124	+	1.76884i
$922$		0			0
$923$	−51.5691			−1.69742
$924$		0			0
$925$	1.88632	−	3.26721i	0.0620219	−	0.107425i
$926$		0			0
$927$	−10.5009	+	18.1880i	−0.344893	+	0.597373i
$928$		0			0
$929$	−26.0947	−	45.1973i	−0.856139	−	1.48288i	−0.875584	−	0.483066i	$-0.839523\pi$
$929$	−26.0947	−	45.1973i	−0.856139	−	1.48288i	0.0194449	−	0.999811i	$-0.493810\pi$
$930$		0			0
$931$	23.8993	+	16.2397i	0.783269	+	0.532234i
$932$		0			0
$933$	11.6985	+	20.2625i	0.382993	+	0.663364i
$934$		0			0
$935$	6.51119	−	11.2777i	0.212939	−	0.368821i
$936$		0			0
$937$	−7.78988	+	13.4925i	−0.254484	+	0.440780i	−0.964755	−	0.263149i	$-0.915239\pi$
$937$	−7.78988	+	13.4925i	−0.254484	+	0.440780i	0.710271	+	0.703928i	$0.248572\pi$
$938$		0			0
$939$	−73.1099			−2.38585
$940$		0			0
$941$	29.3277	−	50.7970i	0.956055	−	1.65594i	0.224119	−	0.974562i	$-0.428050\pi$
$941$	29.3277	−	50.7970i	0.956055	−	1.65594i	0.731936	−	0.681373i	$-0.238617\pi$
$942$		0			0
$943$	−23.6427			−0.769913
$944$		0			0
$945$	3.04914	+	5.28127i	0.0991886	+	0.171800i
$946$		0			0
$947$	6.15326	+	10.6578i	0.199954	+	0.346331i	0.948513	−	0.316737i	$-0.102587\pi$
$947$	6.15326	+	10.6578i	0.199954	+	0.346331i	−0.748559	+	0.663068i	$0.769254\pi$
$948$		0			0
$949$	16.5238			0.536384
$950$		0			0
$951$	−3.16612			−0.102668
$952$		0			0
$953$	−4.13499	−	7.16201i	−0.133945	−	0.232000i	0.791249	−	0.611494i	$-0.209431\pi$
$953$	−4.13499	−	7.16201i	−0.133945	−	0.232000i	−0.925194	+	0.379494i	$0.876098\pi$
$954$		0			0
$955$	1.11883	+	1.93787i	0.0362044	+	0.0627079i
$956$		0			0
$957$	15.2565			0.493173
$958$		0			0
$959$	3.87848	−	6.71773i	0.125243	−	0.216927i
$960$		0			0
$961$	7.80138			0.251657
$962$		0			0
$963$	29.9070	−	51.8004i	0.963738	−	1.66924i
$964$		0			0
$965$	2.27153	−	3.93441i	0.0731232	−	0.126653i
$966$		0			0
$967$	7.11235	+	12.3190i	0.228718	+	0.396151i	0.957428	−	0.288671i	$-0.0932133\pi$
$967$	7.11235	+	12.3190i	0.228718	+	0.396151i	−0.728711	+	0.684822i	$0.759880\pi$
$968$		0			0
$969$	−34.7191	+	16.7866i	−1.11534	+	0.539264i
$970$		0			0
$971$	4.86930	+	8.43388i	0.156263	+	0.270656i	0.933518	−	0.358530i	$-0.116722\pi$
$971$	4.86930	+	8.43388i	0.156263	+	0.270656i	−0.777255	+	0.629186i	$0.783388\pi$
$972$		0			0
$973$	3.23127	−	5.59672i	0.103590	−	0.179423i
$974$		0			0
$975$	6.76167	−	11.7115i	0.216547	−	0.375070i
$976$		0			0
$977$	−6.35308			−0.203253			−0.101627	−	0.994823i	$-0.532405\pi$
$977$	−6.35308			−0.203253			−0.101627	+	0.994823i	$0.532405\pi$
$978$		0			0
$979$	17.7885	−	30.8107i	0.568524	−	0.984713i
$980$		0			0
$981$	34.8427			1.11244
$982$		0			0
$983$	4.94043	+	8.55708i	0.157575	+	0.272929i	0.933994	−	0.357289i	$-0.116299\pi$
$983$	4.94043	+	8.55708i	0.157575	+	0.272929i	−0.776418	+	0.630218i	$0.782966\pi$
$984$		0			0
$985$	9.61179	+	16.6481i	0.306257	+	0.530453i
$986$		0			0
$987$	−10.9241			−0.347718
$988$		0			0
$989$	28.4406			0.904358
$990$		0			0
$991$	18.6675	+	32.3331i	0.592993	+	1.02709i	0.993827	+	0.110943i	$0.0353870\pi$
$991$	18.6675	+	32.3331i	0.592993	+	1.02709i	−0.400834	+	0.916151i	$0.631280\pi$
$992$		0			0
$993$	−46.9745	−	81.3623i	−1.49069	−	2.58195i
$994$		0			0
$995$	6.15094			0.194998
$996$		0			0
$997$	21.8474	−	37.8408i	0.691914	−	1.19843i	−0.279296	−	0.960205i	$-0.590101\pi$
$997$	21.8474	−	37.8408i	0.691914	−	1.19843i	0.971210	−	0.238225i	$-0.0765656\pi$
$998$		0			0
$999$	37.7669			1.19489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.q.o.881.4		8
4.3	odd	2		95.2.e.c.26.3	yes	8
12.11	even	2		855.2.k.h.406.2		8
19.11	even	3	inner	1520.2.q.o.961.4		8
20.3	even	4		475.2.j.c.349.6		16
20.7	even	4		475.2.j.c.349.3		16
20.19	odd	2		475.2.e.e.26.2		8
76.7	odd	6		1805.2.a.o.1.2		4
76.11	odd	6		95.2.e.c.11.3	✓	8
76.31	even	6		1805.2.a.i.1.3		4
228.11	even	6		855.2.k.h.676.2		8
380.87	even	12		475.2.j.c.49.6		16
380.159	odd	6		9025.2.a.bg.1.3		4
380.163	even	12		475.2.j.c.49.3		16
380.239	odd	6		475.2.e.e.201.2		8
380.259	even	6		9025.2.a.bp.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.3	✓	8	76.11	odd	6
95.2.e.c.26.3	yes	8	4.3	odd	2
475.2.e.e.26.2		8	20.19	odd	2
475.2.e.e.201.2		8	380.239	odd	6
475.2.j.c.49.3		16	380.163	even	12
475.2.j.c.49.6		16	380.87	even	12
475.2.j.c.349.3		16	20.7	even	4
475.2.j.c.349.6		16	20.3	even	4
855.2.k.h.406.2		8	12.11	even	2
855.2.k.h.676.2		8	228.11	even	6
1520.2.q.o.881.4		8	1.1	even	1	trivial
1520.2.q.o.961.4		8	19.11	even	3	inner
1805.2.a.i.1.3		4	76.31	even	6
1805.2.a.o.1.2		4	76.7	odd	6
9025.2.a.bg.1.3		4	380.159	odd	6
9025.2.a.bp.1.2		4	380.259	even	6

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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52359 + 2.63893i) q^{3} +(-0.500000 - 0.866025i) q^{5} +0.609175 q^{7} +(-3.14263 + 5.44319i) q^{9} +O(q^{10})\)	\(q+(1.52359 + 2.63893i) q^{3} +(-0.500000 - 0.866025i) q^{5} +0.609175 q^{7} +(-3.14263 + 5.44319i) q^{9} -4.48517 q^{11} +(-2.21900 + 3.84342i) q^{13} +(1.52359 - 2.63893i) q^{15} +(-1.45172 - 2.51445i) q^{17} +(-3.60532 - 2.44983i) q^{19} +(0.928131 + 1.60757i) q^{21} +(-1.42363 + 2.46580i) q^{23} +(-0.500000 + 0.866025i) q^{25} -10.0107 q^{27} +(-0.558149 + 0.966742i) q^{29} +6.22908 q^{31} +(-6.83354 - 11.8360i) q^{33} +(-0.304588 - 0.527561i) q^{35} -3.77264 q^{37} -13.5233 q^{39} +(4.15184 + 7.19120i) q^{41} +(-4.99438 - 8.65053i) q^{43} +6.28525 q^{45} +(-2.94250 + 5.09656i) q^{47} -6.62891 q^{49} +(4.42363 - 7.66195i) q^{51} +(-4.22436 + 7.31681i) q^{53} +(2.24258 + 3.88427i) q^{55} +(0.971912 - 13.2467i) q^{57} +(5.11793 + 8.86451i) q^{59} +(2.49099 - 4.31453i) q^{61} +(-1.91441 + 3.31586i) q^{63} +4.43800 q^{65} +(4.23808 - 7.34057i) q^{67} -8.67608 q^{69} +(5.80995 + 10.0631i) q^{71} +(-1.86162 - 3.22443i) q^{73} -3.04717 q^{75} -2.73225 q^{77} +(4.51908 + 7.82728i) q^{79} +(-5.82432 - 10.0880i) q^{81} +2.12178 q^{83} +(-1.45172 + 2.51445i) q^{85} -3.40155 q^{87} +(-3.96608 + 6.86946i) q^{89} +(-1.35176 + 2.34131i) q^{91} +(9.49053 + 16.4381i) q^{93} +(-0.318955 + 4.34721i) q^{95} +(4.83628 + 8.37668i) q^{97} +(14.0952 - 24.4136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9	\( 8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 + 4 * q^11 - 7 * q^13 + 3 * q^15 + q^17 - 5 * q^19 + 4 * q^21 + 2 * q^23 - 4 * q^25 - 24 * q^27 + q^29 - 19 * q^33 - 4 * q^35 - 4 * q^37 - 30 * q^39 + 8 * q^41 + q^43 + 2 * q^45 - 12 * q^47 - 20 * q^49 + 22 * q^51 + 5 * q^53 - 2 * q^55 + 7 * q^57 - 5 * q^59 - 3 * q^63 + 14 * q^65 + 4 * q^67 - 18 * q^69 + 20 * q^71 + 20 * q^73 - 6 * q^75 + 28 * q^77 + 17 * q^79 - 12 * q^81 - 2 * q^83 + q^85 + 32 * q^87 - 11 * q^89 + 6 * q^91 + 8 * q^93 + 4 * q^95 - q^97 + 38 * q^99

Introduction

L-functions

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