LMFDB - Embedded newform 380.2.l.b.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(37,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("380.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.l (of order $4$, degree $2$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} + \cdots + 1370 $ x^12 - 4x^11 + 28x^10 - 64x^9 + 236x^8 - 420x^7 + 946x^6 - 1216x^5 + 1896x^4 - 1564x^3 + 2284x^2 - 1088*x + 1370
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.5
Root			$-0.585043 - 1.05342i$ of defining polynomial
Character	$\chi$	$=$	380.37
Dual form			380.2.l.b.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63846 + 1.63846i) q^{3} +(2.17009 + 0.539189i) q^{5} +(2.17009 + 2.17009i) q^{7} +2.36910i q^{9} +O(q^{10})$	\(q+(1.63846 + 1.63846i) q^{3} +(2.17009 + 0.539189i) q^{5} +(2.17009 + 2.17009i) q^{7} +2.36910i q^{9} -1.70928 q^{11} +(-4.43904 - 4.43904i) q^{13} +(2.67216 + 4.43904i) q^{15} +(-1.63090 - 1.63090i) q^{17} +(-2.80058 - 3.34017i) q^{19} +7.11120i q^{21} +(3.24846 - 3.24846i) q^{23} +(4.41855 + 2.34017i) q^{25} +(1.03370 - 1.03370i) q^{27} -3.27692 q^{29} +7.11120i q^{31} +(-2.80058 - 2.80058i) q^{33} +(3.53919 + 5.87936i) q^{35} +(0.128419 - 0.128419i) q^{37} -14.5464i q^{39} +3.83428i q^{41} +(-5.24846 + 5.24846i) q^{43} +(-1.27739 + 5.14116i) q^{45} +(0.908291 + 0.908291i) q^{47} +2.41855i q^{49} -5.34432i q^{51} +(-5.47274 - 5.47274i) q^{53} +(-3.70928 - 0.921622i) q^{55} +(0.884103 - 10.0614i) q^{57} +13.9219 q^{59} +2.63090 q^{61} +(-5.14116 + 5.14116i) q^{63} +(-7.23962 - 12.0266i) q^{65} +(7.71596 - 7.71596i) q^{67} +10.6450 q^{69} -1.51004i q^{71} +(-8.70928 + 8.70928i) q^{73} +(3.40534 + 11.0739i) q^{75} +(-3.70928 - 3.70928i) q^{77} -4.78696 q^{79} +10.4947 q^{81} +(6.46081 - 6.46081i) q^{83} +(-2.65983 - 4.41855i) q^{85} +(-5.36910 - 5.36910i) q^{87} +5.34432 q^{89} -19.2662i q^{91} +(-11.6514 + 11.6514i) q^{93} +(-4.27652 - 8.75851i) q^{95} +(-10.2597 + 10.2597i) q^{97} -4.04945i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 12 * q + 4 * q^5 + 4 * q^7	$ 12 q + 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} + 4 q^{23} - 4 q^{25} + 36 q^{35} - 28 q^{43} - 40 q^{45} + 20 q^{47} - 16 q^{55} + 24 q^{57} + 16 q^{61} + 20 q^{63} - 76 q^{73} - 16 q^{77} + 4 q^{81} + 84 q^{83} - 76 q^{85} - 80 q^{87} + 8 q^{93} - 16 q^{95}+O(q^{100}) $ 12 * q + 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 + 4 * q^23 - 4 * q^25 + 36 * q^35 - 28 * q^43 - 40 * q^45 + 20 * q^47 - 16 * q^55 + 24 * q^57 + 16 * q^61 + 20 * q^63 - 76 * q^73 - 16 * q^77 + 4 * q^81 + 84 * q^83 - 76 * q^85 - 80 * q^87 + 8 * q^93 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	1.63846	+	1.63846i	0.945965	+	0.945965i	0.998613	−	0.0526478i	$-0.0167661\pi$
$3$	1.63846	+	1.63846i	0.945965	+	0.945965i	−0.0526478	+	0.998613i	$0.516766\pi$
$4$		0			0
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$5$	2.17009	+	0.539189i	0.970492	+	0.241133i
$6$		0			0
$7$	2.17009	+	2.17009i	0.820216	+	0.820216i	0.986139	−	0.165923i	$-0.0530604\pi$
$7$	2.17009	+	2.17009i	0.820216	+	0.820216i	−0.165923	+	0.986139i	$0.553060\pi$
$8$		0			0
$9$			2.36910i			0.789701i
$10$		0			0
$11$	−1.70928			−0.515366			−0.257683	−	0.966230i	$-0.582959\pi$
$11$	−1.70928			−0.515366			−0.257683	+	0.966230i	$0.582959\pi$
$12$		0			0
$13$	−4.43904	−	4.43904i	−1.23117	−	1.23117i	−0.963516	−	0.267652i	$-0.913752\pi$
$13$	−4.43904	−	4.43904i	−1.23117	−	1.23117i	−0.267652	−	0.963516i	$-0.586248\pi$
$14$		0			0
$15$	2.67216	+	4.43904i	0.689949	+	1.14616i
$16$		0			0
$17$	−1.63090	−	1.63090i	−0.395551	−	0.395551i	0.481110	−	0.876660i	$-0.340234\pi$
$17$	−1.63090	−	1.63090i	−0.395551	−	0.395551i	−0.876660	+	0.481110i	$0.840234\pi$
$18$		0			0
$19$	−2.80058	−	3.34017i	−0.642497	−	0.766288i
$19$	−2.80058	−	3.34017i	−0.642497	−	0.766288i
$20$		0			0
$21$			7.11120i			1.55179i
$22$		0			0
$23$	3.24846	−	3.24846i	0.677352	−	0.677352i	−0.282049	−	0.959400i	$-0.591014\pi$
$23$	3.24846	−	3.24846i	0.677352	−	0.677352i	0.959400	+	0.282049i	$0.0910139\pi$
$24$		0			0
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$		0			0
$27$	1.03370	−	1.03370i	0.198936	−	0.198936i
$28$		0			0
$29$	−3.27692			−0.608509			−0.304254	−	0.952591i	$-0.598407\pi$
$29$	−3.27692			−0.608509			−0.304254	+	0.952591i	$0.598407\pi$
$30$		0			0
$31$			7.11120i			1.27721i	0.769535	+	0.638605i	$0.220488\pi$
$31$			7.11120i			1.27721i	−0.769535	+	0.638605i	$0.779512\pi$
$32$		0			0
$33$	−2.80058	−	2.80058i	−0.487518	−	0.487518i
$34$		0			0
$35$	3.53919	+	5.87936i	0.598232	+	0.993794i
$36$		0			0
$37$	0.128419	−	0.128419i	0.0211119	−	0.0211119i	−0.696472	−	0.717584i	$-0.745248\pi$
$37$	0.128419	−	0.128419i	0.0211119	−	0.0211119i	0.717584	+	0.696472i	$0.245248\pi$
$38$		0			0
$39$		−	14.5464i		−	2.32928i
$40$		0			0
$41$			3.83428i			0.598814i	0.954126	+	0.299407i	$0.0967888\pi$
$41$			3.83428i			0.598814i	−0.954126	+	0.299407i	$0.903211\pi$
$42$		0			0
$43$	−5.24846	+	5.24846i	−0.800383	+	0.800383i	−0.983155	−	0.182772i	$-0.941493\pi$
$43$	−5.24846	+	5.24846i	−0.800383	+	0.800383i	0.182772	+	0.983155i	$0.441493\pi$
$44$		0			0
$45$	−1.27739	+	5.14116i	−0.190423	+	0.766398i
$46$		0			0
$47$	0.908291	+	0.908291i	0.132488	+	0.132488i	0.770241	−	0.637753i	$-0.220136\pi$
$47$	0.908291	+	0.908291i	0.132488	+	0.132488i	−0.637753	+	0.770241i	$0.720136\pi$
$48$		0			0
$49$			2.41855i			0.345507i
$50$		0			0
$51$		−	5.34432i		−	0.748355i
$52$		0			0
$53$	−5.47274	−	5.47274i	−0.751739	−	0.751739i	0.223065	−	0.974804i	$-0.428394\pi$
$53$	−5.47274	−	5.47274i	−0.751739	−	0.751739i	−0.974804	+	0.223065i	$0.928394\pi$
$54$		0			0
$55$	−3.70928	−	0.921622i	−0.500159	−	0.124272i
$56$		0			0
$57$	0.884103	−	10.0614i	0.117102	−	1.33266i
$58$		0			0
$59$	13.9219			1.81247			0.906237	−	0.422770i	$-0.138942\pi$
$59$	13.9219			1.81247			0.906237	+	0.422770i	$0.138942\pi$
$60$		0			0
$61$	2.63090			0.336852			0.168426	−	0.985714i	$-0.446132\pi$
$61$	2.63090			0.336852			0.168426	+	0.985714i	$0.446132\pi$
$62$		0			0
$63$	−5.14116	+	5.14116i	−0.647725	+	0.647725i
$64$		0			0
$65$	−7.23962	−	12.0266i	−0.897964	−	1.49171i
$66$		0			0
$67$	7.71596	−	7.71596i	0.942654	−	0.942654i	−0.0557882	−	0.998443i	$-0.517767\pi$
$67$	7.71596	−	7.71596i	0.942654	−	0.942654i	0.998443	+	0.0557882i	$0.0177671\pi$
$68$		0			0
$69$	10.6450			1.28150
$70$		0			0
$71$		−	1.51004i		−	0.179209i	−0.995977	−	0.0896045i	$-0.971440\pi$
$71$		−	1.51004i		−	0.179209i	0.995977	−	0.0896045i	$-0.0285603\pi$
$72$		0			0
$73$	−8.70928	+	8.70928i	−1.01934	+	1.01934i	−0.0195344	+	0.999809i	$0.506218\pi$
$73$	−8.70928	+	8.70928i	−1.01934	+	1.01934i	−0.999809	+	0.0195344i	$0.993782\pi$
$74$		0			0
$75$	3.40534	+	11.0739i	0.393215	+	1.27870i
$76$		0			0
$77$	−3.70928	−	3.70928i	−0.422711	−	0.422711i
$78$		0			0
$79$	−4.78696			−0.538575			−0.269288	−	0.963060i	$-0.586788\pi$
$79$	−4.78696			−0.538575			−0.269288	+	0.963060i	$0.586788\pi$
$80$		0			0
$81$	10.4947			1.16607
$82$		0			0
$83$	6.46081	−	6.46081i	0.709166	−	0.709166i	−0.257194	−	0.966360i	$-0.582798\pi$
$83$	6.46081	−	6.46081i	0.709166	−	0.709166i	0.966360	+	0.257194i	$0.0827978\pi$
$84$		0			0
$85$	−2.65983	−	4.41855i	−0.288499	−	0.479259i
$86$		0			0
$87$	−5.36910	−	5.36910i	−0.575628	−	0.575628i
$88$		0			0
$89$	5.34432			0.566497			0.283248	−	0.959047i	$-0.408588\pi$
$89$	5.34432			0.566497			0.283248	+	0.959047i	$0.408588\pi$
$90$		0			0
$91$		−	19.2662i		−	2.01965i
$92$		0			0
$93$	−11.6514	+	11.6514i	−1.20820	+	1.20820i
$94$		0			0
$95$	−4.27652	−	8.75851i	−0.438761	−	0.898604i
$96$		0			0
$97$	−10.2597	+	10.2597i	−1.04171	+	1.04171i	−0.0426236	+	0.999091i	$0.513572\pi$
$97$	−10.2597	+	10.2597i	−1.04171	+	1.04171i	−0.999091	+	0.0426236i	$0.986428\pi$
$98$		0			0
$99$		−	4.04945i		−	0.406985i
$100$		0			0
$101$	−15.3112			−1.52353			−0.761763	−	0.647856i	$-0.775666\pi$
$101$	−15.3112			−1.52353			−0.761763	+	0.647856i	$0.775666\pi$
$102$		0			0
$103$	−13.3171	−	13.3171i	−1.31217	−	1.31217i	−0.919810	−	0.392365i	$-0.871657\pi$
$103$	−13.3171	−	13.3171i	−1.31217	−	1.31217i	−0.392365	−	0.919810i	$-0.628343\pi$
$104$		0			0
$105$	−3.83428	+	15.4319i	−0.374187	+	1.50600i
$106$		0			0
$107$	−2.67216	+	2.67216i	−0.258328	+	0.258328i	−0.824374	−	0.566046i	$-0.808472\pi$
$107$	−2.67216	+	2.67216i	−0.258328	+	0.258328i	0.566046	+	0.824374i	$0.308472\pi$
$108$		0			0
$109$	6.15852			0.589879			0.294940	−	0.955516i	$-0.404700\pi$
$109$	6.15852			0.589879			0.294940	+	0.955516i	$0.404700\pi$
$110$		0			0
$111$	0.420818			0.0399423
$112$		0			0
$113$	11.5502	+	11.5502i	1.08656	+	1.08656i	0.995881	+	0.0906745i	$0.0289023\pi$
$113$	11.5502	+	11.5502i	1.08656	+	1.08656i	0.0906745	+	0.995881i	$0.471098\pi$
$114$		0			0
$115$	8.80098	−	5.29791i	0.820696	−	0.494033i
$116$		0			0
$117$	10.5165	−	10.5165i	0.972254	−	0.972254i
$118$		0			0
$119$		−	7.07838i		−	0.648874i
$120$		0			0
$121$	−8.07838			−0.734398
$122$		0			0
$123$	−6.28231	+	6.28231i	−0.566457	+	0.566457i
$124$		0			0
$125$	8.32684	+	7.46081i	0.744775	+	0.667315i
$126$		0			0
$127$	−3.40534	+	3.40534i	−0.302175	+	0.302175i	−0.841864	−	0.539689i	$-0.818542\pi$
$127$	−3.40534	+	3.40534i	−0.302175	+	0.302175i	0.539689	+	0.841864i	$0.318542\pi$
$128$		0			0
$129$	−17.1988			−1.51427
$130$		0			0
$131$	15.5174			1.35577			0.677883	−	0.735170i	$-0.262898\pi$
$131$	15.5174			1.35577			0.677883	+	0.735170i	$0.262898\pi$
$132$		0			0
$133$	1.17096	−	13.3260i	0.101536	−	1.15551i
$134$		0			0
$135$	2.80058	−	1.68586i	0.241035	−	0.145096i
$136$		0			0
$137$	−14.1773	−	14.1773i	−1.21125	−	1.21125i	−0.970617	−	0.240629i	$-0.922646\pi$
$137$	−14.1773	−	14.1773i	−1.21125	−	1.21125i	−0.240629	−	0.970617i	$-0.577354\pi$
$138$		0			0
$139$			10.9444i			0.928293i	0.885759	+	0.464146i	$0.153639\pi$
$139$			10.9444i			0.928293i	−0.885759	+	0.464146i	$0.846361\pi$
$140$		0			0
$141$			2.97640i			0.250658i
$142$		0			0
$143$	7.58754	+	7.58754i	0.634502	+	0.634502i
$144$		0			0
$145$	−7.11120	−	1.76688i	−0.590553	−	0.146731i
$146$		0			0
$147$	−3.96270	+	3.96270i	−0.326838	+	0.326838i
$148$		0			0
$149$		−	0.532001i		−	0.0435832i	−0.999763	−	0.0217916i	$-0.993063\pi$
$149$		−	0.532001i		−	0.0435832i	0.999763	−	0.0217916i	$-0.00693703\pi$
$150$		0			0
$151$			11.8982i			0.968259i	0.874996	+	0.484129i	$0.160864\pi$
$151$			11.8982i			0.968259i	−0.874996	+	0.484129i	$0.839136\pi$
$152$		0			0
$153$	3.86376	−	3.86376i	0.312367	−	0.312367i
$154$		0			0
$155$	−3.83428	+	15.4319i	−0.307977	+	1.23952i
$156$		0			0
$157$	−5.94441	−	5.94441i	−0.474415	−	0.474415i	0.428925	−	0.903340i	$-0.358893\pi$
$157$	−5.94441	−	5.94441i	−0.474415	−	0.474415i	−0.903340	+	0.428925i	$0.858893\pi$
$158$		0			0
$159$		−	17.9337i		−	1.42224i
$160$		0			0
$161$	14.0989			1.11115
$162$		0			0
$163$	−12.0361	+	12.0361i	−0.942741	+	0.942741i	−0.998447	−	0.0557058i	$-0.982259\pi$
$163$	−12.0361	+	12.0361i	−0.942741	+	0.942741i	0.0557058	+	0.998447i	$0.482259\pi$
$164$		0			0
$165$	−4.56746	−	7.58754i	−0.355576	−	0.590689i
$166$		0			0
$167$	8.74966	−	8.74966i	0.677069	−	0.677069i	−0.282267	−	0.959336i	$-0.591086\pi$
$167$	8.74966	−	8.74966i	0.677069	−	0.677069i	0.959336	+	0.282267i	$0.0910864\pi$
$168$		0			0
$169$			26.4101i			2.03155i
$170$		0			0
$171$	7.91321	−	6.63486i	0.605138	−	0.507380i
$172$		0			0
$173$	1.16212	+	1.16212i	0.0883543	+	0.0883543i	0.749903	−	0.661548i	$-0.230100\pi$
$173$	1.16212	+	1.16212i	0.0883543	+	0.0883543i	−0.661548	+	0.749903i	$0.730100\pi$
$174$		0			0
$175$	4.51026	+	14.6670i	0.340944	+	1.10872i
$176$		0			0
$177$	22.8104	+	22.8104i	1.71454	+	1.71454i
$178$		0			0
$179$	25.5632			1.91068			0.955342	−	0.295503i	$-0.0954874\pi$
$179$	25.5632			1.91068			0.955342	+	0.295503i	$0.0954874\pi$
$180$		0			0
$181$		−	13.1077i		−	0.974286i	−0.873322	−	0.487143i	$-0.838039\pi$
$181$		−	13.1077i		−	0.974286i	0.873322	−	0.487143i	$-0.161961\pi$
$182$		0			0
$183$	4.31062	+	4.31062i	0.318650	+	0.318650i
$184$		0			0
$185$	0.347922	−	0.209438i	0.0255797	−	0.0153982i
$186$		0			0
$187$	2.78765	+	2.78765i	0.203853	+	0.203853i
$188$		0			0
$189$	4.48644			0.326340
$190$		0			0
$191$	−2.65368			−0.192014			−0.0960069	−	0.995381i	$-0.530607\pi$
$191$	−2.65368			−0.192014			−0.0960069	+	0.995381i	$0.530607\pi$
$192$		0			0
$193$	8.74966	+	8.74966i	0.629814	+	0.629814i	0.948021	−	0.318207i	$-0.103081\pi$
$193$	8.74966	+	8.74966i	0.629814	+	0.629814i	−0.318207	+	0.948021i	$0.603081\pi$
$194$		0			0
$195$	7.84324	−	31.5669i	0.561666	−	2.26055i
$196$		0			0
$197$	−4.46800	−	4.46800i	−0.318332	−	0.318332i	0.529794	−	0.848126i	$-0.322269\pi$
$197$	−4.46800	−	4.46800i	−0.318332	−	0.318332i	−0.848126	+	0.529794i	$0.822269\pi$
$198$		0			0
$199$			15.9421i			1.13011i	0.825054	+	0.565054i	$0.191145\pi$
$199$			15.9421i			1.13011i	−0.825054	+	0.565054i	$0.808855\pi$
$200$		0			0
$201$	25.2846			1.78344
$202$		0			0
$203$	−7.11120	−	7.11120i	−0.499108	−	0.499108i
$204$		0			0
$205$	−2.06740	+	8.32072i	−0.144394	+	0.581144i
$206$		0			0
$207$	7.69594	+	7.69594i	0.534905	+	0.534905i
$208$		0			0
$209$	4.78696	+	5.70928i	0.331121	+	0.394919i
$210$		0			0
$211$			16.3846i			1.12796i	0.825788	+	0.563981i	$0.190731\pi$
$211$			16.3846i			1.12796i	−0.825788	+	0.563981i	$0.809269\pi$
$212$		0			0
$213$	2.47414	−	2.47414i	0.169525	−	0.169525i
$214$		0			0
$215$	−14.2195	+	8.55971i	−0.969764	+	0.583767i
$216$		0			0
$217$	−15.4319	+	15.4319i	−1.04759	+	1.04759i
$218$		0			0
$219$	−28.5396			−1.92853
$220$		0			0
$221$			14.4792i			0.973979i
$222$		0			0
$223$	−2.19582	−	2.19582i	−0.147043	−	0.147043i	0.629753	−	0.776796i	$-0.283156\pi$
$223$	−2.19582	−	2.19582i	−0.147043	−	0.147043i	−0.776796	+	0.629753i	$0.783156\pi$
$224$		0			0
$225$	−5.54411	+	10.4680i	−0.369607	+	0.697867i
$226$		0			0
$227$	1.16212	−	1.16212i	0.0771326	−	0.0771326i	−0.667488	−	0.744621i	$-0.732630\pi$
$227$	1.16212	−	1.16212i	0.0771326	−	0.0771326i	0.744621	+	0.667488i	$0.232630\pi$
$228$		0			0
$229$		−	9.89269i		−	0.653728i	−0.945071	−	0.326864i	$-0.894008\pi$
$229$		−	9.89269i		−	0.653728i	0.945071	−	0.326864i	$-0.105992\pi$
$230$		0			0
$231$		−	12.1550i		−	0.799740i
$232$		0			0
$233$	20.8576	−	20.8576i	1.36643	−	1.36643i	0.500955	−	0.865474i	$-0.332982\pi$
$233$	20.8576	−	20.8576i	1.36643	−	1.36643i	0.865474	−	0.500955i	$-0.167018\pi$
$234$		0			0
$235$	1.48133	+	2.46081i	0.0966313	+	0.160526i
$236$		0			0
$237$	−7.84324	−	7.84324i	−0.509473	−	0.509473i
$238$		0			0
$239$		−	8.65368i		−	0.559760i	−0.960035	−	0.279880i	$-0.909705\pi$
$239$		−	8.65368i		−	0.559760i	0.960035	−	0.279880i	$-0.0902947\pi$
$240$		0			0
$241$			1.25320i			0.0807259i	0.999185	+	0.0403630i	$0.0128514\pi$
$241$			1.25320i			0.0807259i	−0.999185	+	0.0403630i	$0.987149\pi$
$242$		0			0
$243$	14.0940	+	14.0940i	0.904129	+	0.904129i
$244$		0			0
$245$	−1.30406	+	5.24846i	−0.0833131	+	0.335312i
$246$		0			0
$247$	−2.39528	+	27.2590i	−0.152408	+	1.73445i
$248$		0			0
$249$	21.1716			1.34169
$250$		0			0
$251$	1.65983			0.104767			0.0523837	−	0.998627i	$-0.483318\pi$
$251$	1.65983			0.104767			0.0523837	+	0.998627i	$0.483318\pi$
$252$		0			0
$253$	−5.55252	+	5.55252i	−0.349084	+	0.349084i
$254$		0			0
$255$	2.88160	−	11.5976i	0.180453	−	0.726272i
$256$		0			0
$257$	4.91538	−	4.91538i	0.306613	−	0.306613i	−0.536981	−	0.843594i	$-0.680435\pi$
$257$	4.91538	−	4.91538i	0.306613	−	0.306613i	0.843594	+	0.536981i	$0.180435\pi$
$258$		0			0
$259$	0.557360			0.0346327
$260$		0			0
$261$		−	7.76336i		−	0.480540i
$262$		0			0
$263$	−12.8010	+	12.8010i	−0.789342	+	0.789342i	−0.981386	−	0.192044i	$-0.938488\pi$
$263$	−12.8010	+	12.8010i	−0.789342	+	0.789342i	0.192044	+	0.981386i	$0.438488\pi$
$264$		0			0
$265$	−8.92548	−	14.8272i	−0.548288	−	0.910825i
$266$		0			0
$267$	8.75646	+	8.75646i	0.535886	+	0.535886i
$268$		0			0
$269$	−17.1988			−1.04863			−0.524315	−	0.851525i	$-0.675678\pi$
$269$	−17.1988			−1.04863			−0.524315	+	0.851525i	$0.675678\pi$
$270$		0			0
$271$	−11.2846			−0.685490			−0.342745	−	0.939429i	$-0.611357\pi$
$271$	−11.2846			−0.685490			−0.342745	+	0.939429i	$0.611357\pi$
$272$		0			0
$273$	31.5669	−	31.5669i	1.91052	−	1.91052i
$274$		0			0
$275$	−7.55252	−	4.00000i	−0.455434	−	0.241209i
$276$		0			0
$277$	−7.29072	−	7.29072i	−0.438057	−	0.438057i	0.453301	−	0.891358i	$-0.350246\pi$
$277$	−7.29072	−	7.29072i	−0.438057	−	0.438057i	−0.891358	+	0.453301i	$0.850246\pi$
$278$		0			0
$279$	−16.8472			−1.00861
$280$		0			0
$281$			25.1242i			1.49878i	0.662127	+	0.749392i	$0.269654\pi$
$281$			25.1242i			1.49878i	−0.662127	+	0.749392i	$0.730346\pi$
$282$		0			0
$283$	−4.01333	+	4.01333i	−0.238568	+	0.238568i	−0.816257	−	0.577689i	$-0.803955\pi$
$283$	−4.01333	+	4.01333i	−0.238568	+	0.238568i	0.577689	+	0.816257i	$0.303955\pi$
$284$		0			0
$285$	7.34356	−	21.3574i	0.434995	−	1.26510i
$286$		0			0
$287$	−8.32072	+	8.32072i	−0.491157	+	0.491157i
$288$		0			0
$289$		−	11.6803i		−	0.687079i
$290$		0			0
$291$	−33.6202			−1.97085
$292$		0			0
$293$	−0.824263	−	0.824263i	−0.0481539	−	0.0481539i	0.682620	−	0.730774i	$-0.260841\pi$
$293$	−0.824263	−	0.824263i	−0.0481539	−	0.0481539i	−0.730774	+	0.682620i	$0.760841\pi$
$294$		0			0
$295$	30.2117	+	7.50652i	1.75899	+	0.437047i
$296$		0			0
$297$	−1.76688	+	1.76688i	−0.102525	+	0.102525i
$298$		0			0
$299$	−28.8401			−1.66787
$300$		0			0
$301$	−22.7792			−1.31297
$302$		0			0
$303$	−25.0869	−	25.0869i	−1.44120	−	1.44120i
$304$		0			0
$305$	5.70928	+	1.41855i	0.326912	+	0.0812260i
$306$		0			0
$307$	−7.32064	+	7.32064i	−0.417811	+	0.417811i	−0.884449	−	0.466638i	$-0.845465\pi$
$307$	−7.32064	+	7.32064i	−0.417811	+	0.417811i	0.466638	+	0.884449i	$0.345465\pi$
$308$		0			0
$309$		−	43.6391i		−	2.48254i
$310$		0			0
$311$	−11.3835			−0.645498			−0.322749	−	0.946485i	$-0.604607\pi$
$311$	−11.3835			−0.645498			−0.322749	+	0.946485i	$0.604607\pi$
$312$		0			0
$313$	−5.09890	+	5.09890i	−0.288207	+	0.288207i	−0.836371	−	0.548164i	$-0.815327\pi$
$313$	−5.09890	+	5.09890i	−0.288207	+	0.288207i	0.548164	+	0.836371i	$0.315327\pi$
$314$		0			0
$315$	−13.9288	+	8.38470i	−0.784800	+	0.472424i
$316$		0			0
$317$	17.1514	−	17.1514i	0.963318	−	0.963318i	−0.0360322	−	0.999351i	$-0.511472\pi$
$317$	17.1514	−	17.1514i	0.963318	−	0.963318i	0.999351	+	0.0360322i	$0.0114719\pi$
$318$		0			0
$319$	5.60116			0.313605
$320$		0			0
$321$	−8.75646			−0.488738
$322$		0			0
$323$	−0.880022	+	10.0149i	−0.0489657	+	0.557246i
$324$		0			0
$325$	−9.22600	−	30.0022i	−0.511766	−	1.66422i
$326$		0			0
$327$	10.0905	+	10.0905i	0.558005	+	0.558005i
$328$		0			0
$329$			3.94214i			0.217337i
$330$		0			0
$331$			8.36440i			0.459749i	0.973220	+	0.229875i	$0.0738316\pi$
$331$			8.36440i			0.459749i	−0.973220	+	0.229875i	$0.926168\pi$
$332$		0			0
$333$	0.304237	+	0.304237i	0.0166721	+	0.0166721i
$334$		0			0
$335$	20.9047	−	12.5839i	1.14214	−	0.687534i
$336$		0			0
$337$	24.6579	−	24.6579i	1.34320	−	1.34320i	0.450351	−	0.892852i	$-0.351299\pi$
$337$	24.6579	−	24.6579i	1.34320	−	1.34320i	0.892852	−	0.450351i	$-0.148701\pi$
$338$		0			0
$339$			37.8492i			2.05569i
$340$		0			0
$341$		−	12.1550i		−	0.658230i
$342$		0			0
$343$	9.94214	−	9.94214i	0.536825	−	0.536825i
$344$		0			0
$345$	23.1005	+	5.73964i	1.24369	+	0.309012i
$346$		0			0
$347$	−9.68753	−	9.68753i	−0.520054	−	0.520054i	0.397534	−	0.917588i	$-0.369866\pi$
$347$	−9.68753	−	9.68753i	−0.520054	−	0.520054i	−0.917588	+	0.397534i	$0.869866\pi$
$348$		0			0
$349$		−	0.130094i		−	0.00696375i	−0.999994	−	0.00348187i	$-0.998892\pi$
$349$		−	0.130094i		−	0.00696375i	0.999994	−	0.00348187i	$-0.00110832\pi$
$350$		0			0
$351$	−9.17727			−0.489847
$352$		0			0
$353$	17.8865	−	17.8865i	0.952005	−	0.952005i	−0.0468948	−	0.998900i	$-0.514933\pi$
$353$	17.8865	−	17.8865i	0.952005	−	0.952005i	0.998900	+	0.0468948i	$0.0149326\pi$
$354$		0			0
$355$	0.814197	−	3.27692i	0.0432131	−	0.173921i
$356$		0			0
$357$	11.5976	−	11.5976i	0.613812	−	0.613812i
$358$		0			0
$359$			15.2579i			0.805282i	0.915358	+	0.402641i	$0.131908\pi$
$359$			15.2579i			0.805282i	−0.915358	+	0.402641i	$0.868092\pi$
$360$		0			0
$361$	−3.31351	+	18.7088i	−0.174395	+	0.984676i
$362$		0			0
$363$	−13.2361	−	13.2361i	−0.694715	−	0.694715i
$364$		0			0
$365$	−23.5958	+	14.2039i	−1.23506	+	0.743468i
$366$		0			0
$367$	23.2401	+	23.2401i	1.21312	+	1.21312i	0.969995	+	0.243126i	$0.0781729\pi$
$367$	23.2401	+	23.2401i	1.21312	+	1.21312i	0.243126	+	0.969995i	$0.421827\pi$
$368$		0			0
$369$	−9.08380			−0.472884
$370$		0			0
$371$		−	23.7526i		−	1.23318i
$372$		0			0
$373$	−3.70586	−	3.70586i	−0.191882	−	0.191882i	0.604627	−	0.796509i	$-0.293322\pi$
$373$	−3.70586	−	3.70586i	−0.191882	−	0.191882i	−0.796509	+	0.604627i	$0.793322\pi$
$374$		0			0
$375$	1.41896	+	25.8674i	0.0732746	+	1.33579i
$376$		0			0
$377$	14.5464	+	14.5464i	0.749177	+	0.749177i
$378$		0			0
$379$	9.57392			0.491779			0.245890	−	0.969298i	$-0.420920\pi$
$379$	9.57392			0.491779			0.245890	+	0.969298i	$0.420920\pi$
$380$		0			0
$381$	−11.1590			−0.571694
$382$		0			0
$383$	−8.01648	−	8.01648i	−0.409623	−	0.409623i	0.471984	−	0.881607i	$-0.343538\pi$
$383$	−8.01648	−	8.01648i	−0.409623	−	0.409623i	−0.881607	+	0.471984i	$0.843538\pi$
$384$		0			0
$385$	−6.04945	−	10.0494i	−0.308308	−	0.512167i
$386$		0			0
$387$	−12.4341	−	12.4341i	−0.632063	−	0.632063i
$388$		0			0
$389$			30.5692i			1.54992i	0.632011	+	0.774959i	$0.282230\pi$
$389$			30.5692i			1.54992i	−0.632011	+	0.774959i	$0.717770\pi$
$390$		0			0
$391$	−10.5958			−0.535854
$392$		0			0
$393$	25.4247	+	25.4247i	1.28251	+	1.28251i
$394$		0			0
$395$	−10.3881	−	2.58108i	−0.522683	−	0.129868i
$396$		0			0
$397$	−15.0494	−	15.0494i	−0.755310	−	0.755310i	0.220155	−	0.975465i	$-0.429344\pi$
$397$	−15.0494	−	15.0494i	−0.755310	−	0.755310i	−0.975465	+	0.220155i	$0.929344\pi$
$398$		0			0
$399$	23.7526	−	19.9155i	1.18912	−	0.997021i
$400$		0			0
$401$		−	2.06740i		−	0.103241i	−0.998667	−	0.0516205i	$-0.983561\pi$
$401$		−	2.06740i		−	0.103241i	0.998667	−	0.0516205i	$-0.0164386\pi$
$402$		0			0
$403$	31.5669	−	31.5669i	1.57246	−	1.57246i
$404$		0			0
$405$	22.7743	+	5.65860i	1.13167	+	0.281178i
$406$		0			0
$407$	−0.219503	+	0.219503i	−0.0108804	+	0.0108804i
$408$		0			0
$409$	−14.6177			−0.722800			−0.361400	−	0.932411i	$-0.617701\pi$
$409$	−14.6177			−0.722800			−0.361400	+	0.932411i	$0.617701\pi$
$410$		0			0
$411$		−	46.4578i		−	2.29159i
$412$		0			0
$413$	30.2117	+	30.2117i	1.48662	+	1.48662i
$414$		0			0
$415$	17.5041	−	10.5369i	0.859243	−	0.517237i
$416$		0			0
$417$	−17.9320	+	17.9320i	−0.878133	+	0.878133i
$418$		0			0
$419$		−	3.29299i		−	0.160873i	−0.996760	−	0.0804366i	$-0.974369\pi$
$419$		−	3.29299i		−	0.160873i	0.996760	−	0.0804366i	$-0.0256315\pi$
$420$		0			0
$421$		−	27.6306i		−	1.34663i	−0.739354	−	0.673317i	$-0.764869\pi$
$421$		−	27.6306i		−	1.34663i	0.739354	−	0.673317i	$-0.235131\pi$
$422$		0			0
$423$	−2.15183	+	2.15183i	−0.104626	+	0.104626i
$424$		0			0
$425$	−3.38962	−	11.0228i	−0.164421	−	0.534684i
$426$		0			0
$427$	5.70928	+	5.70928i	0.276291	+	0.276291i
$428$		0			0
$429$			24.8638i			1.20043i
$430$		0			0
$431$			34.3028i			1.65231i	0.563445	+	0.826154i	$0.309476\pi$
$431$			34.3028i			1.65231i	−0.563445	+	0.826154i	$0.690524\pi$
$432$		0			0
$433$	4.69588	+	4.69588i	0.225669	+	0.225669i	0.810881	−	0.585211i	$-0.198988\pi$
$433$	4.69588	+	4.69588i	0.225669	+	0.225669i	−0.585211	+	0.810881i	$0.698988\pi$
$434$		0			0
$435$	−8.75646	−	14.5464i	−0.419840	−	0.697445i
$436$		0			0
$437$	−19.9480	−	1.75285i	−0.954243	−	0.0838502i
$438$		0			0
$439$	−12.0165			−0.573517			−0.286758	−	0.958003i	$-0.592578\pi$
$439$	−12.0165			−0.573517			−0.286758	+	0.958003i	$0.592578\pi$
$440$		0			0
$441$	−5.72979			−0.272847
$442$		0			0
$443$	−16.8999	+	16.8999i	−0.802938	+	0.802938i	−0.983554	−	0.180616i	$-0.942191\pi$
$443$	−16.8999	+	16.8999i	−0.802938	+	0.802938i	0.180616	+	0.983554i	$0.442191\pi$
$444$		0			0
$445$	11.5976	+	2.88160i	0.549781	+	0.136601i
$446$		0			0
$447$	0.871662	−	0.871662i	0.0412282	−	0.0412282i
$448$		0			0
$449$	−39.6034			−1.86900			−0.934501	−	0.355961i	$-0.884154\pi$
$449$	−39.6034			−1.86900			−0.934501	+	0.355961i	$0.884154\pi$
$450$		0			0
$451$		−	6.55384i		−	0.308608i
$452$		0			0
$453$	−19.4947	+	19.4947i	−0.915939	+	0.915939i
$454$		0			0
$455$	10.3881	−	41.8093i	0.487003	−	1.96005i
$456$		0			0
$457$	−10.5174	−	10.5174i	−0.491985	−	0.491985i	0.416946	−	0.908931i	$-0.363100\pi$
$457$	−10.5174	−	10.5174i	−0.491985	−	0.491985i	−0.908931	+	0.416946i	$0.863100\pi$
$458$		0			0
$459$	−3.37172			−0.157378
$460$		0			0
$461$	25.6163			1.19307			0.596536	−	0.802586i	$-0.296543\pi$
$461$	25.6163			1.19307			0.596536	+	0.802586i	$0.296543\pi$
$462$		0			0
$463$	9.58864	−	9.58864i	0.445622	−	0.445622i	−0.448274	−	0.893896i	$-0.647961\pi$
$463$	9.58864	−	9.58864i	0.445622	−	0.445622i	0.893896	+	0.448274i	$0.147961\pi$
$464$		0			0
$465$	−31.5669	+	19.0023i	−1.46388	+	0.881209i
$466$		0			0
$467$	−9.27513	−	9.27513i	−0.429202	−	0.429202i	0.459155	−	0.888356i	$-0.348152\pi$
$467$	−9.27513	−	9.27513i	−0.429202	−	0.429202i	−0.888356	+	0.459155i	$0.848152\pi$
$468$		0			0
$469$	33.4886			1.54636
$470$		0			0
$471$		−	19.4794i		−	0.897561i
$472$		0			0
$473$	8.97107	−	8.97107i	0.412490	−	0.412490i
$474$		0			0
$475$	−4.55792	−	21.3126i	−0.209132	−	0.977887i
$476$		0			0
$477$	12.9655	−	12.9655i	0.593649	−	0.593649i
$478$		0			0
$479$			32.6719i			1.49282i	0.665487	+	0.746409i	$0.268224\pi$
$479$			32.6719i			1.49282i	−0.665487	+	0.746409i	$0.731776\pi$
$480$		0			0
$481$	−1.14011			−0.0519846
$482$		0			0
$483$	23.1005	+	23.1005i	1.05111	+	1.05111i
$484$		0			0
$485$	−27.7964	+	16.7325i	−1.26217	+	0.759785i
$486$		0			0
$487$	0.347922	−	0.347922i	0.0157658	−	0.0157658i	−0.699180	−	0.714946i	$-0.746451\pi$
$487$	0.347922	−	0.347922i	0.0157658	−	0.0157658i	0.714946	+	0.699180i	$0.246451\pi$
$488$		0			0
$489$	−39.4414			−1.78360
$490$		0			0
$491$	1.17727			0.0531297			0.0265648	−	0.999647i	$-0.491543\pi$
$491$	1.17727			0.0531297			0.0265648	+	0.999647i	$0.491543\pi$
$492$		0			0
$493$	5.34432	+	5.34432i	0.240696	+	0.240696i
$494$		0			0
$495$	2.18342	−	8.78765i	0.0981373	−	0.394976i
$496$		0			0
$497$	3.27692	−	3.27692i	0.146990	−	0.146990i
$498$		0			0
$499$		−	18.4163i		−	0.824426i	−0.911087	−	0.412213i	$-0.864756\pi$
$499$		−	18.4163i		−	0.824426i	0.911087	−	0.412213i	$-0.135244\pi$
$500$		0			0
$501$	28.6719			1.28097
$502$		0			0
$503$	10.9493	−	10.9493i	0.488206	−	0.488206i	−0.419533	−	0.907740i	$-0.637806\pi$
$503$	10.9493	−	10.9493i	0.488206	−	0.488206i	0.907740	+	0.419533i	$0.137806\pi$
$504$		0			0
$505$	−33.2267	−	8.25565i	−1.47857	−	0.367372i
$506$		0			0
$507$	−43.2720	+	43.2720i	−1.92178	+	1.92178i
$508$		0			0
$509$	−29.1406			−1.29164			−0.645818	−	0.763491i	$-0.723484\pi$
$509$	−29.1406			−1.29164			−0.645818	+	0.763491i	$0.723484\pi$
$510$		0			0
$511$	−37.7998			−1.67216
$512$		0			0
$513$	−6.34770	−	0.557778i	−0.280258	−	0.0246265i
$514$		0			0
$515$	−21.7189	−	36.0797i	−0.957047	−	1.58986i
$516$		0			0
$517$	−1.55252	−	1.55252i	−0.0682797	−	0.0682797i
$518$		0			0
$519$			3.80817i			0.167160i
$520$		0			0
$521$			36.9040i			1.61679i	0.588638	+	0.808397i	$0.299664\pi$
$521$			36.9040i			1.61679i	−0.588638	+	0.808397i	$0.700336\pi$
$522$		0			0
$523$	6.72594	+	6.72594i	0.294105	+	0.294105i	0.838699	−	0.544595i	$-0.183316\pi$
$523$	6.72594	+	6.72594i	0.294105	+	0.294105i	−0.544595	+	0.838699i	$0.683316\pi$
$524$		0			0
$525$	−16.6414	+	31.4212i	−0.726292	+	1.37133i
$526$		0			0
$527$	11.5976	−	11.5976i	0.505201	−	0.505201i
$528$		0			0
$529$			1.89496i			0.0823896i
$530$		0			0
$531$			32.9824i			1.43131i
$532$		0			0
$533$	17.0205	−	17.0205i	0.737241	−	0.737241i
$534$		0			0
$535$	−7.23962	+	4.35802i	−0.312996	+	0.188414i
$536$		0			0
$537$	41.8843	+	41.8843i	1.80744	+	1.80744i
$538$		0			0
$539$		−	4.13397i		−	0.178063i
$540$		0			0
$541$	32.5197			1.39813			0.699066	−	0.715057i	$-0.253599\pi$
$541$	32.5197			1.39813			0.699066	+	0.715057i	$0.253599\pi$
$542$		0			0
$543$	21.4764	−	21.4764i	0.921641	−	0.921641i
$544$		0			0
$545$	13.3645	+	3.32060i	0.572473	+	0.142239i
$546$		0			0
$547$	−23.2289	+	23.2289i	−0.993196	+	0.993196i	−0.999977	−	0.00678109i	$-0.997841\pi$
$547$	−23.2289	+	23.2289i	−0.993196	+	0.993196i	0.00678109	+	0.999977i	$0.497841\pi$
$548$		0			0
$549$			6.23287i			0.266012i
$550$		0			0
$551$	9.17727	+	10.9455i	0.390965	+	0.466293i
$552$		0			0
$553$	−10.3881	−	10.3881i	−0.441748	−	0.441748i
$554$		0			0
$555$	0.913212	+	0.226900i	0.0387637	+	0.00963139i
$556$		0			0
$557$	−5.14834	−	5.14834i	−0.218142	−	0.218142i	0.589573	−	0.807715i	$-0.299296\pi$
$557$	−5.14834	−	5.14834i	−0.218142	−	0.218142i	−0.807715	+	0.589573i	$0.799296\pi$
$558$		0			0
$559$	46.5963			1.97081
$560$		0			0
$561$			9.13492i			0.385676i
$562$		0			0
$563$	−11.4692	−	11.4692i	−0.483370	−	0.483370i	0.422836	−	0.906206i	$-0.361035\pi$
$563$	−11.4692	−	11.4692i	−0.483370	−	0.483370i	−0.906206	+	0.422836i	$0.861035\pi$
$564$		0			0
$565$	18.8373	+	31.2928i	0.792489	+	1.31650i
$566$		0			0
$567$	22.7743	+	22.7743i	0.956432	+	0.956432i
$568$		0			0
$569$	31.8602			1.33565			0.667825	−	0.744319i	$-0.267226\pi$
$569$	31.8602			1.33565			0.667825	+	0.744319i	$0.267226\pi$
$570$		0			0
$571$	23.5981			0.987549			0.493775	−	0.869590i	$-0.335617\pi$
$571$	23.5981			0.987549			0.493775	+	0.869590i	$0.335617\pi$
$572$		0			0
$573$	−4.34796	−	4.34796i	−0.181638	−	0.181638i
$574$		0			0
$575$	21.9555	−	6.75154i	0.915606	−	0.281559i
$576$		0			0
$577$	24.2762	+	24.2762i	1.01063	+	1.01063i	0.999943	+	0.0106873i	$0.00340195\pi$
$577$	24.2762	+	24.2762i	1.01063	+	1.01063i	0.0106873	+	0.999943i	$0.496598\pi$
$578$		0			0
$579$			28.6719i			1.19156i
$580$		0			0
$581$	28.0410			1.16334
$582$		0			0
$583$	9.35442	+	9.35442i	0.387420	+	0.387420i
$584$		0			0
$585$	28.4922	−	17.1514i	1.17801	−	0.709123i
$586$		0			0
$587$	18.7165	+	18.7165i	0.772511	+	0.772511i	0.978545	−	0.206034i	$-0.0660557\pi$
$587$	18.7165	+	18.7165i	0.772511	+	0.772511i	−0.206034	+	0.978545i	$0.566056\pi$
$588$		0			0
$589$	23.7526	−	19.9155i	0.978710	−	0.820603i
$590$		0			0
$591$		−	14.6413i		−	0.602262i
$592$		0			0
$593$	1.26794	−	1.26794i	0.0520680	−	0.0520680i	−0.680593	−	0.732661i	$-0.738278\pi$
$593$	1.26794	−	1.26794i	0.0520680	−	0.0520680i	0.732661	+	0.680593i	$0.238278\pi$
$594$		0			0
$595$	3.81658	−	15.3607i	0.156465	−	0.629727i
$596$		0			0
$597$	−26.1206	+	26.1206i	−1.06904	+	1.06904i
$598$		0			0
$599$	10.5502			0.431068			0.215534	−	0.976496i	$-0.430851\pi$
$599$	10.5502			0.431068			0.215534	+	0.976496i	$0.430851\pi$
$600$		0			0
$601$		−	38.8329i		−	1.58403i	−0.610503	−	0.792014i	$-0.709033\pi$
$601$		−	38.8329i		−	1.58403i	0.610503	−	0.792014i	$-0.290967\pi$
$602$		0			0
$603$	18.2799	+	18.2799i	0.744415	+	0.744415i
$604$		0			0
$605$	−17.5308	−	4.35577i	−0.712727	−	0.177087i
$606$		0			0
$607$	−7.97280	+	7.97280i	−0.323606	+	0.323606i	−0.850149	−	0.526543i	$-0.823488\pi$
$607$	−7.97280	+	7.97280i	−0.323606	+	0.323606i	0.526543	+	0.850149i	$0.323488\pi$
$608$		0			0
$609$		−	23.3028i		−	0.944278i
$610$		0			0
$611$		−	8.06388i		−	0.326230i
$612$		0			0
$613$	−18.1194	+	18.1194i	−0.731836	+	0.731836i	−0.970983	−	0.239147i	$-0.923132\pi$
$613$	−18.1194	+	18.1194i	−0.731836	+	0.731836i	0.239147	+	0.970983i	$0.423132\pi$
$614$		0			0
$615$	−17.0205	+	10.2458i	−0.686334	+	0.413151i
$616$		0			0
$617$	−16.2123	−	16.2123i	−0.652685	−	0.652685i	0.300954	−	0.953639i	$-0.402695\pi$
$617$	−16.2123	−	16.2123i	−0.652685	−	0.652685i	−0.953639	+	0.300954i	$0.902695\pi$
$618$		0			0
$619$			8.73433i			0.351062i	0.984474	+	0.175531i	$0.0561643\pi$
$619$			8.73433i			0.351062i	−0.984474	+	0.175531i	$0.943836\pi$
$620$		0			0
$621$		−	6.71588i		−	0.269499i
$622$		0			0
$623$	11.5976	+	11.5976i	0.464650	+	0.464650i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$		0			0
$627$	−1.51117	+	17.1977i	−0.0603505	+	0.686809i
$628$		0			0
$629$	−0.418876			−0.0167017
$630$		0			0
$631$	29.7093			1.18271			0.591354	−	0.806412i	$-0.298594\pi$
$631$	29.7093			1.18271			0.591354	+	0.806412i	$0.298594\pi$
$632$		0			0
$633$	−26.8455	+	26.8455i	−1.06701	+	1.06701i
$634$		0			0
$635$	−9.22600	+	5.55376i	−0.366123	+	0.220394i
$636$		0			0
$637$	10.7360	−	10.7360i	0.425377	−	0.425377i
$638$		0			0
$639$	3.57744			0.141521
$640$		0			0
$641$		−	40.2993i		−	1.59173i	−0.605477	−	0.795863i	$-0.707018\pi$
$641$		−	40.2993i		−	1.59173i	0.605477	−	0.795863i	$-0.292982\pi$
$642$		0			0
$643$	1.57426	−	1.57426i	0.0620828	−	0.0620828i	−0.675384	−	0.737467i	$-0.736022\pi$
$643$	1.57426	−	1.57426i	0.0620828	−	0.0620828i	0.737467	+	0.675384i	$0.236022\pi$
$644$		0			0
$645$	−37.3229	−	9.27340i	−1.46959	−	0.365140i
$646$		0			0
$647$	−5.79484	−	5.79484i	−0.227819	−	0.227819i	0.583962	−	0.811781i	$-0.301502\pi$
$647$	−5.79484	−	5.79484i	−0.227819	−	0.227819i	−0.811781	+	0.583962i	$0.801502\pi$
$648$		0			0
$649$	−23.7963			−0.934087
$650$		0			0
$651$	−50.5692			−1.98196
$652$		0			0
$653$	−21.6537	+	21.6537i	−0.847374	+	0.847374i	−0.989805	−	0.142431i	$-0.954508\pi$
$653$	−21.6537	+	21.6537i	−0.847374	+	0.847374i	0.142431	+	0.989805i	$0.454508\pi$
$654$		0			0
$655$	33.6742	+	8.36683i	1.31576	+	0.326919i
$656$		0			0
$657$	−20.6332	−	20.6332i	−0.804976	−	0.804976i
$658$		0			0
$659$	16.9420			0.659965			0.329983	−	0.943987i	$-0.392957\pi$
$659$	16.9420			0.659965			0.329983	+	0.943987i	$0.392957\pi$
$660$		0			0
$661$			27.1916i			1.05763i	0.848737	+	0.528815i	$0.177364\pi$
$661$			27.1916i			1.05763i	−0.848737	+	0.528815i	$0.822636\pi$
$662$		0			0
$663$	−23.7237	+	23.7237i	−0.921350	+	0.921350i
$664$		0			0
$665$	9.72631	−	28.2871i	0.377170	−	1.09693i
$666$		0			0
$667$	−10.6450	+	10.6450i	−0.412174	+	0.412174i
$668$		0			0
$669$		−	7.19553i		−	0.278195i
$670$		0			0
$671$	−4.49693			−0.173602
$672$		0			0
$673$	1.97632	+	1.97632i	0.0761814	+	0.0761814i	0.744171	−	0.667989i	$-0.232845\pi$
$673$	1.97632	+	1.97632i	0.0761814	+	0.0761814i	−0.667989	+	0.744171i	$0.732845\pi$
$674$		0			0
$675$	6.98650	−	2.14842i	0.268910	−	0.0826927i
$676$		0			0
$677$	21.7189	−	21.7189i	0.834723	−	0.834723i	−0.153435	−	0.988159i	$-0.549034\pi$
$677$	21.7189	−	21.7189i	0.834723	−	0.834723i	0.988159	+	0.153435i	$0.0490337\pi$
$678$		0			0
$679$	−44.5289			−1.70886
$680$		0			0
$681$	3.80817			0.145929
$682$		0			0
$683$	−22.3710	−	22.3710i	−0.856003	−	0.856003i	0.134861	−	0.990864i	$-0.456941\pi$
$683$	−22.3710	−	22.3710i	−0.856003	−	0.856003i	−0.990864	+	0.134861i	$0.956941\pi$
$684$		0			0
$685$	−23.1217	−	38.4101i	−0.883434	−	1.46758i
$686$		0			0
$687$	16.2088	−	16.2088i	0.618404	−	0.618404i
$688$		0			0
$689$			48.5874i			1.85103i
$690$		0			0
$691$	13.7093			0.521525			0.260763	−	0.965403i	$-0.416026\pi$
$691$	13.7093			0.521525			0.260763	+	0.965403i	$0.416026\pi$
$692$		0			0
$693$	8.78765	−	8.78765i	0.333815	−	0.333815i
$694$		0			0
$695$	−5.90110	+	23.7503i	−0.223842	+	0.900901i
$696$		0			0
$697$	6.25332	−	6.25332i	0.236861	−	0.236861i
$698$		0			0
$699$	68.3488			2.58519
$700$		0			0
$701$	47.8225			1.80623			0.903116	−	0.429396i	$-0.141273\pi$
$701$	47.8225			1.80623			0.903116	+	0.429396i	$0.141273\pi$
$702$		0			0
$703$	−0.788588	−	0.0692940i	−0.0297422	−	0.00261347i
$704$		0			0
$705$	−1.60484	+	6.45904i	−0.0604418	+	0.243262i
$706$		0			0
$707$	−33.2267	−	33.2267i	−1.24962	−	1.24962i
$708$		0			0
$709$			0.0143758i			0.000539896i	1.00000		0.000269948i	$8.59272e-5\pi$
$709$			0.0143758i			0.000539896i	−1.00000		0.000269948i	$0.999914\pi$
$710$		0			0
$711$		−	11.3408i		−	0.425313i
$712$		0			0
$713$	23.1005	+	23.1005i	0.865120	+	0.865120i
$714$		0			0
$715$	12.3745	+	20.5567i	0.462780	+	0.768778i
$716$		0			0
$717$	14.1787	−	14.1787i	0.529514	−	0.529514i
$718$		0			0
$719$		−	11.7237i		−	0.437218i	−0.975812	−	0.218609i	$-0.929848\pi$
$719$		−	11.7237i		−	0.437218i	0.975812	−	0.218609i	$-0.0701520\pi$
$720$		0			0
$721$		−	57.7986i		−	2.15253i
$722$		0			0
$723$	−2.05332	+	2.05332i	−0.0763639	+	0.0763639i
$724$		0			0
$725$	−14.4792	−	7.66856i	−0.537745	−	0.284803i
$726$		0			0
$727$	−3.87936	−	3.87936i	−0.143878	−	0.143878i	0.631499	−	0.775377i	$-0.282440\pi$
$727$	−3.87936	−	3.87936i	−0.143878	−	0.143878i	−0.775377	+	0.631499i	$0.782440\pi$
$728$		0			0
$729$			14.7009i			0.544476i
$730$		0			0
$731$	17.1194			0.633184
$732$		0			0
$733$	3.97948	−	3.97948i	0.146985	−	0.146985i	−0.629784	−	0.776770i	$-0.716857\pi$
$733$	3.97948	−	3.97948i	0.146985	−	0.146985i	0.776770	+	0.629784i	$0.216857\pi$
$734$		0			0
$735$	−10.7360	+	6.46276i	−0.396005	+	0.238382i
$736$		0			0
$737$	−13.1887	+	13.1887i	−0.485812	+	0.485812i
$738$		0			0
$739$		−	30.6270i		−	1.12663i	−0.826241	−	0.563317i	$-0.809525\pi$
$739$		−	30.6270i		−	1.12663i	0.826241	−	0.563317i	$-0.190475\pi$
$740$		0			0
$741$	−48.5874	+	40.7383i	−1.78490	+	1.49656i
$742$		0			0
$743$	−7.93546	−	7.93546i	−0.291124	−	0.291124i	0.546400	−	0.837524i	$-0.315998\pi$
$743$	−7.93546	−	7.93546i	−0.291124	−	0.291124i	−0.837524	+	0.546400i	$0.815998\pi$
$744$		0			0
$745$	0.286849	−	1.15449i	0.0105093	−	0.0422972i
$746$		0			0
$747$	15.3063	+	15.3063i	0.560029	+	0.560029i
$748$		0			0
$749$	−11.5976			−0.423769
$750$		0			0
$751$			7.92540i			0.289202i	0.989490	+	0.144601i	$0.0461898\pi$
$751$			7.92540i			0.289202i	−0.989490	+	0.144601i	$0.953810\pi$
$752$		0			0
$753$	2.71956	+	2.71956i	0.0991063	+	0.0991063i
$754$		0			0
$755$	−6.41536	+	25.8200i	−0.233479	+	0.939687i
$756$		0			0
$757$	2.58372	+	2.58372i	0.0939068	+	0.0939068i	0.752500	−	0.658593i	$-0.228848\pi$
$757$	2.58372	+	2.58372i	0.0939068	+	0.0939068i	−0.658593	+	0.752500i	$0.728848\pi$
$758$		0			0
$759$	−18.1952			−0.660443
$760$		0			0
$761$	−33.4680			−1.21321			−0.606607	−	0.795002i	$-0.707470\pi$
$761$	−33.4680			−1.21321			−0.606607	+	0.795002i	$0.707470\pi$
$762$		0			0
$763$	13.3645	+	13.3645i	0.483828	+	0.483828i
$764$		0			0
$765$	10.4680	−	6.30140i	0.378471	−	0.227828i
$766$		0			0
$767$	−61.7998	−	61.7998i	−2.23146	−	2.23146i
$768$		0			0
$769$		−	49.4557i		−	1.78342i	−0.452609	−	0.891709i	$-0.649506\pi$
$769$		−	49.4557i		−	1.78342i	0.452609	−	0.891709i	$-0.350494\pi$
$770$		0			0
$771$	16.1073			0.580090
$772$		0			0
$773$	−37.0698	−	37.0698i	−1.33331	−	1.33331i	−0.902394	−	0.430913i	$-0.858192\pi$
$773$	−37.0698	−	37.0698i	−1.33331	−	1.33331i	−0.430913	−	0.902394i	$-0.641808\pi$
$774$		0			0
$775$	−16.6414	+	31.4212i	−0.597778	+	1.12868i
$776$		0			0
$777$	0.913212	+	0.913212i	0.0327613	+	0.0327613i
$778$		0			0
$779$	12.8072	−	10.7382i	0.458864	−	0.384736i
$780$		0			0
$781$			2.58108i			0.0923582i
$782$		0			0
$783$	−3.38735	+	3.38735i	−0.121054	+	0.121054i
$784$		0			0
$785$	−9.69472	−	16.1050i	−0.346019	−	0.574814i
$786$		0			0
$787$	13.3981	−	13.3981i	0.477592	−	0.477592i	−0.426769	−	0.904361i	$-0.640348\pi$
$787$	13.3981	−	13.3981i	0.477592	−	0.477592i	0.904361	+	0.426769i	$0.140348\pi$
$788$		0			0
$789$	−41.9478			−1.49338
$790$		0			0
$791$			50.1300i			1.78242i
$792$		0			0
$793$	−11.6787	−	11.6787i	−0.414721	−	0.414721i
$794$		0			0
$795$	9.66967	−	38.9177i	0.342948	−	1.38027i
$796$		0			0
$797$	−5.61122	+	5.61122i	−0.198760	+	0.198760i	−0.799468	−	0.600708i	$-0.794885\pi$
$797$	−5.61122	+	5.61122i	−0.198760	+	0.198760i	0.600708	+	0.799468i	$0.294885\pi$
$798$		0			0
$799$		−	2.96266i		−	0.104811i
$800$		0			0
$801$			12.6612i			0.447363i
$802$		0			0
$803$	14.8865	−	14.8865i	0.525335	−	0.525335i
$804$		0			0
$805$	30.5958	+	7.60197i	1.07836	+	0.267934i
$806$		0			0
$807$	−28.1795	−	28.1795i	−0.991967	−	0.991967i
$808$		0			0
$809$			44.3812i			1.56036i	0.625555	+	0.780180i	$0.284873\pi$
$809$			44.3812i			1.56036i	−0.625555	+	0.780180i	$0.715127\pi$
$810$		0			0
$811$		−	19.2662i		−	0.676528i	−0.941051	−	0.338264i	$-0.890160\pi$
$811$		−	19.2662i		−	0.676528i	0.941051	−	0.338264i	$-0.109840\pi$
$812$		0			0
$813$	−18.4893	−	18.4893i	−0.648449	−	0.648449i
$814$		0			0
$815$	−32.6092	+	19.6297i	−1.14225	+	0.687598i
$816$		0			0
$817$	32.2295	+	2.83204i	1.12757	+	0.0990805i
$818$		0			0
$819$	45.6436			1.59492
$820$		0			0
$821$	−5.05172			−0.176306			−0.0881530	−	0.996107i	$-0.528096\pi$
$821$	−5.05172			−0.176306			−0.0881530	+	0.996107i	$0.528096\pi$
$822$		0			0
$823$	6.53305	−	6.53305i	0.227728	−	0.227728i	−0.584015	−	0.811743i	$-0.698519\pi$
$823$	6.53305	−	6.53305i	0.227728	−	0.227728i	0.811743	+	0.584015i	$0.198519\pi$
$824$		0			0
$825$	−5.82066	−	18.9283i	−0.202649	−	0.659000i
$826$		0			0
$827$	35.9413	−	35.9413i	1.24980	−	1.24980i	0.293992	−	0.955808i	$-0.405016\pi$
$827$	35.9413	−	35.9413i	1.24980	−	1.24980i	0.955808	−	0.293992i	$-0.0949839\pi$
$828$		0			0
$829$	−3.57744			−0.124250			−0.0621249	−	0.998068i	$-0.519788\pi$
$829$	−3.57744			−0.124250			−0.0621249	+	0.998068i	$0.519788\pi$
$830$		0			0
$831$		−	23.8911i		−	0.828774i
$832$		0			0
$833$	3.94441	−	3.94441i	0.136666	−	0.136666i
$834$		0			0
$835$	23.7052	−	14.2698i	0.820354	−	0.493827i
$836$		0			0
$837$	7.35085	+	7.35085i	0.254083	+	0.254083i
$838$		0			0
$839$	−21.0768			−0.727651			−0.363825	−	0.931467i	$-0.618529\pi$
$839$	−21.0768			−0.727651			−0.363825	+	0.931467i	$0.618529\pi$
$840$		0			0
$841$	−18.2618			−0.629717
$842$		0			0
$843$	−41.1650	+	41.1650i	−1.41780	+	1.41780i
$844$		0			0
$845$	−14.2401	+	57.3123i	−0.489873	+	1.97160i
$846$		0			0
$847$	−17.5308	−	17.5308i	−0.602365	−	0.602365i
$848$		0			0
$849$	−13.1514			−0.451354
$850$		0			0
$851$		−	0.834328i		−	0.0286004i
$852$		0			0
$853$	10.1773	−	10.1773i	0.348463	−	0.348463i	−0.511074	−	0.859537i	$-0.670752\pi$
$853$	10.1773	−	10.1773i	0.348463	−	0.348463i	0.859537	+	0.511074i	$0.170752\pi$
$854$		0			0
$855$	20.7498	−	10.1315i	0.709628	−	0.346490i
$856$		0			0
$857$	−29.2691	+	29.2691i	−0.999812	+	0.999812i	−1.00000		0.000187872i	$-0.999940\pi$
$857$	−29.2691	+	29.2691i	−0.999812	+	0.999812i	0.000187872		1.00000i	$0.499940\pi$
$858$		0			0
$859$		−	21.5318i		−	0.734656i	−0.930091	−	0.367328i	$-0.880273\pi$
$859$		−	21.5318i		−	0.734656i	0.930091	−	0.367328i	$-0.119727\pi$
$860$		0			0
$861$	−27.2663			−0.929234
$862$		0			0
$863$	−0.942616	−	0.942616i	−0.0320870	−	0.0320870i	0.690881	−	0.722968i	$-0.257223\pi$
$863$	−0.942616	−	0.942616i	−0.0320870	−	0.0320870i	−0.722968	+	0.690881i	$0.757223\pi$
$864$		0			0
$865$	1.89530	+	3.14850i	0.0644421	+	0.107052i
$866$		0			0
$867$	19.1378	−	19.1378i	0.649953	−	0.649953i
$868$		0			0
$869$	8.18223			0.277563
$870$		0			0
$871$	−68.5029			−2.32113
$872$		0			0
$873$	−24.3063	−	24.3063i	−0.822643	−	0.822643i
$874$		0			0
$875$	1.87936	+	34.2606i	0.0635340	+	1.15822i
$876$		0			0
$877$	10.8171	−	10.8171i	0.365266	−	0.365266i	−0.500481	−	0.865747i	$-0.666844\pi$
$877$	10.8171	−	10.8171i	0.365266	−	0.365266i	0.865747	+	0.500481i	$0.166844\pi$
$878$		0			0
$879$		−	2.70104i		−	0.0911039i
$880$		0			0
$881$	14.6309			0.492927			0.246464	−	0.969152i	$-0.420731\pi$
$881$	14.6309			0.492927			0.246464	+	0.969152i	$0.420731\pi$
$882$		0			0
$883$	9.87936	−	9.87936i	0.332467	−	0.332467i	−0.521056	−	0.853523i	$-0.674462\pi$
$883$	9.87936	−	9.87936i	0.332467	−	0.332467i	0.853523	+	0.521056i	$0.174462\pi$
$884$		0			0
$885$	37.2015	+	61.7998i	1.25051	+	2.07738i
$886$		0			0
$887$	30.4211	−	30.4211i	1.02144	−	1.02144i	0.0216761	−	0.999765i	$-0.493100\pi$
$887$	30.4211	−	30.4211i	1.02144	−	1.02144i	0.999765	−	0.0216761i	$-0.00690025\pi$
$888$		0			0
$889$	−14.7798			−0.495697
$890$		0			0
$891$	−17.9383			−0.600955
$892$		0			0
$893$	0.490108	−	5.57759i	0.0164008	−	0.186647i
$894$		0			0
$895$	55.4744	+	13.7834i	1.85430	+	0.460728i
$896$		0			0
$897$	−47.2534	−	47.2534i	−1.57774	−	1.57774i
$898$		0			0
$899$		−	23.3028i		−	0.777193i
$900$		0			0
$901$			17.8510i			0.594702i
$902$		0			0
$903$	−37.3229	−	37.3229i	−1.24203	−	1.24203i
$904$		0			0
$905$	7.06752	−	28.4448i	0.234932	−	0.945537i
$906$		0			0
$907$	−1.41896	+	1.41896i	−0.0471157	+	0.0471157i	−0.730272	−	0.683156i	$-0.760607\pi$
$907$	−1.41896	+	1.41896i	−0.0471157	+	0.0471157i	0.683156	+	0.730272i	$0.260607\pi$
$908$		0			0
$909$		−	36.2739i		−	1.20313i
$910$		0			0
$911$			49.4779i			1.63928i	0.572882	+	0.819638i	$0.305825\pi$
$911$			49.4779i			1.63928i	−0.572882	+	0.819638i	$0.694175\pi$
$912$		0			0
$913$	−11.0433	+	11.0433i	−0.365480	+	0.365480i
$914$		0			0
$915$	7.03018	+	11.6787i	0.232411	+	0.386085i
$916$		0			0
$917$	33.6742	+	33.6742i	1.11202	+	1.11202i
$918$		0			0
$919$			7.44521i			0.245595i	0.992432	+	0.122797i	$0.0391866\pi$
$919$			7.44521i			0.245595i	−0.992432	+	0.122797i	$0.960813\pi$
$920$		0			0
$921$	−23.9891			−0.790469
$922$		0			0
$923$	−6.70313	+	6.70313i	−0.220636	+	0.220636i
$924$		0			0
$925$	0.867947	−	0.266903i	0.0285379	−	0.00877571i
$926$		0			0
$927$	31.5496	−	31.5496i	1.03623	−	1.03623i
$928$		0			0
$929$		−	24.1133i		−	0.791131i	−0.918438	−	0.395565i	$-0.870549\pi$
$929$		−	24.1133i		−	0.791131i	0.918438	−	0.395565i	$-0.129451\pi$
$930$		0			0
$931$	8.07838	−	6.77334i	0.264758	−	0.221987i
$932$		0			0
$933$	−18.6514	−	18.6514i	−0.610619	−	0.610619i
$934$		0			0
$935$	4.54638	+	7.55252i	0.148682	+	0.246994i
$936$		0			0
$937$	4.23901	+	4.23901i	0.138482	+	0.138482i	0.772950	−	0.634467i	$-0.218780\pi$
$937$	4.23901	+	4.23901i	0.138482	+	0.138482i	−0.634467	+	0.772950i	$0.718780\pi$
$938$		0			0
$939$	−16.7087			−0.545267
$940$		0			0
$941$		−	49.5727i		−	1.61602i	−0.589167	−	0.808012i	$-0.700544\pi$
$941$		−	49.5727i		−	1.61602i	0.589167	−	0.808012i	$-0.299456\pi$
$942$		0			0
$943$	12.4555	+	12.4555i	0.405608	+	0.405608i
$944$		0			0
$945$	9.73596	+	2.41904i	0.316711	+	0.0786913i
$946$		0			0
$947$	18.8276	+	18.8276i	0.611816	+	0.611816i	0.943419	−	0.331603i	$-0.107589\pi$
$947$	18.8276	+	18.8276i	0.611816	+	0.611816i	−0.331603	+	0.943419i	$0.607589\pi$
$948$		0			0
$949$	77.3216			2.50997
$950$		0			0
$951$	56.2038			1.82253
$952$		0			0
$953$	24.4384	+	24.4384i	0.791638	+	0.791638i	0.981760	−	0.190122i	$-0.0608885\pi$
$953$	24.4384	+	24.4384i	0.791638	+	0.791638i	−0.190122	+	0.981760i	$0.560888\pi$
$954$		0			0
$955$	−5.75872	−	1.43084i	−0.186348	−	0.0463008i
$956$		0			0
$957$	9.17727	+	9.17727i	0.296659	+	0.296659i
$958$		0			0
$959$		−	61.5318i		−	1.98697i
$960$		0			0
$961$	−19.5692			−0.631263
$962$		0			0
$963$	−6.33062	−	6.33062i	−0.204001	−	0.204001i
$964$		0			0
$965$	14.2698	+	23.7052i	0.459361	+	0.763099i
$966$		0			0
$967$	21.3207	+	21.3207i	0.685627	+	0.685627i	0.961262	−	0.275635i	$-0.0888881\pi$
$967$	21.3207	+	21.3207i	0.685627	+	0.685627i	−0.275635	+	0.961262i	$0.588888\pi$
$968$		0			0
$969$	−17.8510	+	14.9672i	−0.573455	+	0.480816i
$970$		0			0
$971$			35.3940i			1.13585i	0.823082	+	0.567923i	$0.192253\pi$
$971$			35.3940i			1.13585i	−0.823082	+	0.567923i	$0.807747\pi$
$972$		0			0
$973$	−23.7503	+	23.7503i	−0.761400	+	0.761400i
$974$		0			0
$975$	34.0410	−	64.2739i	1.09019	−	2.05841i
$976$		0			0
$977$	34.3939	−	34.3939i	1.10036	−	1.10036i	0.105991	−	0.994367i	$-0.466199\pi$
$977$	34.3939	−	34.3939i	1.10036	−	1.10036i	0.994367	−	0.105991i	$-0.0338013\pi$
$978$		0			0
$979$	−9.13492			−0.291953
$980$		0			0
$981$			14.5902i			0.465828i
$982$		0			0
$983$	−18.1041	−	18.1041i	−0.577430	−	0.577430i	0.356764	−	0.934195i	$-0.383880\pi$
$983$	−18.1041	−	18.1041i	−0.577430	−	0.577430i	−0.934195	+	0.356764i	$0.883880\pi$
$984$		0			0
$985$	−7.28685	−	12.1050i	−0.232178	−	0.385699i
$986$		0			0
$987$	−6.45904	+	6.45904i	−0.205594	+	0.205594i
$988$		0			0
$989$			34.0989i			1.08428i
$990$		0			0
$991$			30.6070i			0.972263i	0.873886	+	0.486132i	$0.161592\pi$
$991$			30.6070i			0.972263i	−0.873886	+	0.486132i	$0.838408\pi$
$992$		0			0
$993$	−13.7047	+	13.7047i	−0.434907	+	0.434907i
$994$		0			0
$995$	−8.59583	+	34.5958i	−0.272506	+	1.09676i
$996$		0			0
$997$	−34.3074	−	34.3074i	−1.08653	−	1.08653i	−0.995884	−	0.0906417i	$-0.971108\pi$
$997$	−34.3074	−	34.3074i	−1.08653	−	1.08653i	−0.0906417	−	0.995884i	$-0.528892\pi$
$998$		0			0
$999$		−	0.265493i		−	0.00839983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.l.b.37.5	yes	12
3.2	odd	2		3420.2.bb.d.37.1		12
5.2	odd	4		1900.2.l.b.493.5		12
5.3	odd	4	inner	380.2.l.b.113.2	yes	12
5.4	even	2		1900.2.l.b.1557.2		12
15.8	even	4		3420.2.bb.d.2773.2		12
19.18	odd	2	inner	380.2.l.b.37.2	✓	12
57.56	even	2		3420.2.bb.d.37.2		12
95.18	even	4	inner	380.2.l.b.113.5	yes	12
95.37	even	4		1900.2.l.b.493.2		12
95.94	odd	2		1900.2.l.b.1557.5		12
285.113	odd	4		3420.2.bb.d.2773.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.l.b.37.2	✓	12	19.18	odd	2	inner
380.2.l.b.37.5	yes	12	1.1	even	1	trivial
380.2.l.b.113.2	yes	12	5.3	odd	4	inner
380.2.l.b.113.5	yes	12	95.18	even	4	inner
1900.2.l.b.493.2		12	95.37	even	4
1900.2.l.b.493.5		12	5.2	odd	4
1900.2.l.b.1557.2		12	5.4	even	2
1900.2.l.b.1557.5		12	95.94	odd	2
3420.2.bb.d.37.1		12	3.2	odd	2
3420.2.bb.d.37.2		12	57.56	even	2
3420.2.bb.d.2773.1		12	285.113	odd	4
3420.2.bb.d.2773.2		12	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63846 + 1.63846i) q^{3} +(2.17009 + 0.539189i) q^{5} +(2.17009 + 2.17009i) q^{7} +2.36910i q^{9} +O(q^{10})\)	\(q+(1.63846 + 1.63846i) q^{3} +(2.17009 + 0.539189i) q^{5} +(2.17009 + 2.17009i) q^{7} +2.36910i q^{9} -1.70928 q^{11} +(-4.43904 - 4.43904i) q^{13} +(2.67216 + 4.43904i) q^{15} +(-1.63090 - 1.63090i) q^{17} +(-2.80058 - 3.34017i) q^{19} +7.11120i q^{21} +(3.24846 - 3.24846i) q^{23} +(4.41855 + 2.34017i) q^{25} +(1.03370 - 1.03370i) q^{27} -3.27692 q^{29} +7.11120i q^{31} +(-2.80058 - 2.80058i) q^{33} +(3.53919 + 5.87936i) q^{35} +(0.128419 - 0.128419i) q^{37} -14.5464i q^{39} +3.83428i q^{41} +(-5.24846 + 5.24846i) q^{43} +(-1.27739 + 5.14116i) q^{45} +(0.908291 + 0.908291i) q^{47} +2.41855i q^{49} -5.34432i q^{51} +(-5.47274 - 5.47274i) q^{53} +(-3.70928 - 0.921622i) q^{55} +(0.884103 - 10.0614i) q^{57} +13.9219 q^{59} +2.63090 q^{61} +(-5.14116 + 5.14116i) q^{63} +(-7.23962 - 12.0266i) q^{65} +(7.71596 - 7.71596i) q^{67} +10.6450 q^{69} -1.51004i q^{71} +(-8.70928 + 8.70928i) q^{73} +(3.40534 + 11.0739i) q^{75} +(-3.70928 - 3.70928i) q^{77} -4.78696 q^{79} +10.4947 q^{81} +(6.46081 - 6.46081i) q^{83} +(-2.65983 - 4.41855i) q^{85} +(-5.36910 - 5.36910i) q^{87} +5.34432 q^{89} -19.2662i q^{91} +(-11.6514 + 11.6514i) q^{93} +(-4.27652 - 8.75851i) q^{95} +(-10.2597 + 10.2597i) q^{97} -4.04945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 12 * q + 4 * q^5 + 4 * q^7	\( 12 q + 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} + 4 q^{23} - 4 q^{25} + 36 q^{35} - 28 q^{43} - 40 q^{45} + 20 q^{47} - 16 q^{55} + 24 q^{57} + 16 q^{61} + 20 q^{63} - 76 q^{73} - 16 q^{77} + 4 q^{81} + 84 q^{83} - 76 q^{85} - 80 q^{87} + 8 q^{93} - 16 q^{95}+O(q^{100}) \) 12 * q + 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 + 4 * q^23 - 4 * q^25 + 36 * q^35 - 28 * q^43 - 40 * q^45 + 20 * q^47 - 16 * q^55 + 24 * q^57 + 16 * q^61 + 20 * q^63 - 76 * q^73 - 16 * q^77 + 4 * q^81 + 84 * q^83 - 76 * q^85 - 80 * q^87 + 8 * q^93 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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