LMFDB - Embedded newform 380.2.r.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(49,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("380.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.r (of order $6$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-2.48777 + 1.43632i$ of defining polynomial
Character	$\chi$	$=$	380.49
Dual form			380.2.r.a.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.48777 - 1.43632i) q^{3} +(1.38776 + 1.75332i) q^{5} -3.54568i q^{7} +(2.62601 + 4.54838i) q^{9} -1.81575 q^{11} +(2.78308 - 1.60681i) q^{13} +(-0.934123 - 6.35512i) q^{15} +(-6.92193 - 3.99638i) q^{17} +(0.863760 - 4.27246i) q^{19} +(-5.09271 + 8.82084i) q^{21} +(-7.30026 + 4.21480i) q^{23} +(-1.14823 + 4.86637i) q^{25} -6.46921i q^{27} +(-4.29124 - 7.43265i) q^{29} -1.70874 q^{31} +(4.51718 + 2.60799i) q^{33} +(6.21669 - 4.92056i) q^{35} -5.50608i q^{37} -9.23155 q^{39} +(4.05694 - 7.02683i) q^{41} +(4.35373 + 2.51363i) q^{43} +(-4.33047 + 10.9163i) q^{45} +(1.16834 - 0.674543i) q^{47} -5.57183 q^{49} +(11.4801 + 19.8842i) q^{51} +(-1.92201 + 1.10967i) q^{53} +(-2.51983 - 3.18359i) q^{55} +(-8.28544 + 9.38828i) q^{57} +(0.960774 - 1.66411i) q^{59} +(2.83047 + 4.90251i) q^{61} +(16.1271 - 9.31098i) q^{63} +(6.67950 + 2.64974i) q^{65} +(8.04360 - 4.64397i) q^{67} +24.2152 q^{69} +(-2.94365 + 5.09854i) q^{71} +(-2.82716 - 1.63226i) q^{73} +(9.84618 - 10.4572i) q^{75} +6.43807i q^{77} +(2.08739 - 3.61546i) q^{79} +(-1.41381 + 2.44879i) q^{81} +6.30268i q^{83} +(-2.59909 - 17.6824i) q^{85} +24.6543i q^{87} +(2.73646 + 4.73968i) q^{89} +(-5.69723 - 9.86789i) q^{91} +(4.25096 + 2.45429i) q^{93} +(8.68966 - 4.41472i) q^{95} +(6.91255 + 3.99096i) q^{97} +(-4.76818 - 8.25873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65}+ \cdots - 20 q^{99}+O(q^{100}) $ 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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
$3$	−2.48777	−	1.43632i	−1.43632	−	0.829257i	−0.438725	−	0.898622i	$-0.644570\pi$
$3$	−2.48777	−	1.43632i	−1.43632	−	0.829257i	−0.997591	+	0.0693641i	$0.977903\pi$
$4$		0			0
$5$	1.38776	+	1.75332i	0.620626	+	0.784106i
$5$	1.38776	+	1.75332i	0.620626	+	0.784106i
$6$		0			0
$7$		−	3.54568i		−	1.34014i	−0.742298	−	0.670070i	$-0.766264\pi$
$7$		−	3.54568i		−	1.34014i	0.742298	−	0.670070i	$-0.233736\pi$
$8$		0			0
$9$	2.62601	+	4.54838i	0.875336	+	1.51613i
$10$		0			0
$11$	−1.81575			−0.547470			−0.273735	−	0.961805i	$-0.588259\pi$
$11$	−1.81575			−0.547470			−0.273735	+	0.961805i	$0.588259\pi$
$12$		0			0
$13$	2.78308	−	1.60681i	0.771887	−	0.445649i	−0.0616606	−	0.998097i	$-0.519640\pi$
$13$	2.78308	−	1.60681i	0.771887	−	0.445649i	0.833547	+	0.552448i	$0.186306\pi$
$14$		0			0
$15$	−0.934123	−	6.35512i	−0.241190	−	1.64088i
$16$		0			0
$17$	−6.92193	−	3.99638i	−1.67881	−	0.969264i	−0.962419	−	0.271570i	$-0.912457\pi$
$17$	−6.92193	−	3.99638i	−1.67881	−	0.969264i	−0.716396	−	0.697694i	$-0.754210\pi$
$18$		0			0
$19$	0.863760	−	4.27246i	0.198160	−	0.980170i
$19$	0.863760	−	4.27246i	0.198160	−	0.980170i
$20$		0			0
$21$	−5.09271	+	8.82084i	−1.11132	+	1.92486i
$22$		0			0
$23$	−7.30026	+	4.21480i	−1.52221	+	0.878848i	−0.522553	+	0.852607i	$0.675020\pi$
$23$	−7.30026	+	4.21480i	−1.52221	+	0.878848i	−0.999656	+	0.0262406i	$0.991646\pi$
$24$		0			0
$25$	−1.14823	+	4.86637i	−0.229646	+	0.973274i
$26$		0			0
$27$		−	6.46921i		−	1.24500i
$28$		0			0
$29$	−4.29124	−	7.43265i	−0.796863	−	1.38021i	−0.921649	−	0.388024i	$-0.873158\pi$
$29$	−4.29124	−	7.43265i	−0.796863	−	1.38021i	0.124786	−	0.992184i	$-0.460176\pi$
$30$		0			0
$31$	−1.70874			−0.306899			−0.153450	−	0.988156i	$-0.549038\pi$
$31$	−1.70874			−0.306899			−0.153450	+	0.988156i	$0.549038\pi$
$32$		0			0
$33$	4.51718	+	2.60799i	0.786340	+	0.453994i
$34$		0			0
$35$	6.21669	−	4.92056i	1.05081	−	0.831726i
$36$		0			0
$37$		−	5.50608i		−	0.905193i	−0.891715	−	0.452597i	$-0.850498\pi$
$37$		−	5.50608i		−	0.905193i	0.891715	−	0.452597i	$-0.149502\pi$
$38$		0			0
$39$	−9.23155			−1.47823
$40$		0			0
$41$	4.05694	−	7.02683i	0.633588	−	1.09741i	−0.353224	−	0.935539i	$-0.614915\pi$
$41$	4.05694	−	7.02683i	0.633588	−	1.09741i	0.986812	−	0.161868i	$-0.0517520\pi$
$42$		0			0
$43$	4.35373	+	2.51363i	0.663938	+	0.383325i	0.793776	−	0.608211i	$-0.208112\pi$
$43$	4.35373	+	2.51363i	0.663938	+	0.383325i	−0.129838	+	0.991535i	$0.541446\pi$
$44$		0			0
$45$	−4.33047	+	10.9163i	−0.645548	+	1.62730i
$46$		0			0
$47$	1.16834	−	0.674543i	0.170420	−	0.0983922i	−0.412364	−	0.911019i	$-0.635297\pi$
$47$	1.16834	−	0.674543i	0.170420	−	0.0983922i	0.582784	+	0.812627i	$0.301963\pi$
$48$		0			0
$49$	−5.57183			−0.795976
$50$		0			0
$51$	11.4801	+	19.8842i	1.60754	+	2.78434i
$52$		0			0
$53$	−1.92201	+	1.10967i	−0.264009	+	0.152426i	−0.626162	−	0.779693i	$-0.715375\pi$
$53$	−1.92201	+	1.10967i	−0.264009	+	0.152426i	0.362153	+	0.932119i	$0.382042\pi$
$54$		0			0
$55$	−2.51983	−	3.18359i	−0.339774	−	0.429275i
$56$		0			0
$57$	−8.28544	+	9.38828i	−1.09743	+	1.24351i
$58$		0			0
$59$	0.960774	−	1.66411i	0.125082	−	0.216649i	−0.796683	−	0.604398i	$-0.793414\pi$
$59$	0.960774	−	1.66411i	0.125082	−	0.216649i	0.921765	+	0.387749i	$0.126747\pi$
$60$		0			0
$61$	2.83047	+	4.90251i	0.362404	+	0.627702i	0.988356	−	0.152159i	$-0.0486227\pi$
$61$	2.83047	+	4.90251i	0.362404	+	0.627702i	−0.625952	+	0.779862i	$0.715289\pi$
$62$		0			0
$63$	16.1271	−	9.31098i	2.03182	−	1.17307i
$64$		0			0
$65$	6.67950	+	2.64974i	0.828489	+	0.328660i
$66$		0			0
$67$	8.04360	−	4.64397i	0.982682	−	0.567352i	0.0796032	−	0.996827i	$-0.474635\pi$
$67$	8.04360	−	4.64397i	0.982682	−	0.567352i	0.903079	+	0.429475i	$0.141301\pi$
$68$		0			0
$69$	24.2152			2.91516
$70$		0			0
$71$	−2.94365	+	5.09854i	−0.349346	+	0.605086i	−0.986134	−	0.165954i	$-0.946930\pi$
$71$	−2.94365	+	5.09854i	−0.349346	+	0.605086i	0.636787	+	0.771040i	$0.280263\pi$
$72$		0			0
$73$	−2.82716	−	1.63226i	−0.330894	−	0.191042i	0.325344	−	0.945596i	$-0.394520\pi$
$73$	−2.82716	−	1.63226i	−0.330894	−	0.191042i	−0.656238	+	0.754554i	$0.727853\pi$
$74$		0			0
$75$	9.84618	−	10.4572i	1.13694	−	1.20749i
$76$		0			0
$77$			6.43807i			0.733687i
$78$		0			0
$79$	2.08739	−	3.61546i	0.234850	−	0.406771i	−0.724379	−	0.689402i	$-0.757874\pi$
$79$	2.08739	−	3.61546i	0.234850	−	0.406771i	0.959229	+	0.282630i	$0.0912069\pi$
$80$		0			0
$81$	−1.41381	+	2.44879i	−0.157090	+	0.272087i
$82$		0			0
$83$			6.30268i			0.691809i	0.938270	+	0.345905i	$0.112428\pi$
$83$			6.30268i			0.691809i	−0.938270	+	0.345905i	$0.887572\pi$
$84$		0			0
$85$	−2.59909	−	17.6824i	−0.281910	−	1.91792i
$86$		0			0
$87$			24.6543i			2.64322i
$88$		0			0
$89$	2.73646	+	4.73968i	0.290064	+	0.502405i	0.973825	−	0.227301i	$-0.0729901\pi$
$89$	2.73646	+	4.73968i	0.290064	+	0.502405i	−0.683761	+	0.729706i	$0.739657\pi$
$90$		0			0
$91$	−5.69723	−	9.86789i	−0.597232	−	1.03444i
$92$		0			0
$93$	4.25096	+	2.45429i	0.440804	+	0.254499i
$94$		0			0
$95$	8.68966	−	4.41472i	0.891541	−	0.452941i
$96$		0			0
$97$	6.91255	+	3.99096i	0.701863	+	0.405221i	0.808041	−	0.589126i	$-0.200528\pi$
$97$	6.91255	+	3.99096i	0.701863	+	0.405221i	−0.106178	+	0.994347i	$0.533861\pi$
$98$		0			0
$99$	−4.76818	−	8.25873i	−0.479220	−	0.830034i
$100$		0			0
$101$	2.46731	+	4.27351i	0.245507	+	0.425230i	0.962274	−	0.272082i	$-0.0877123\pi$
$101$	2.46731	+	4.27351i	0.245507	+	0.425230i	−0.716767	+	0.697313i	$0.754379\pi$
$102$		0			0
$103$			5.56291i			0.548130i	0.961711	+	0.274065i	$0.0883684\pi$
$103$			5.56291i			0.548130i	−0.961711	+	0.274065i	$0.911632\pi$
$104$		0			0
$105$	−22.5332	+	3.31210i	−2.19901	+	0.323228i
$106$		0			0
$107$		−	9.12251i		−	0.881907i	−0.897530	−	0.440953i	$-0.854640\pi$
$107$		−	9.12251i		−	0.881907i	0.897530	−	0.440953i	$-0.145360\pi$
$108$		0			0
$109$	7.57225	−	13.1155i	0.725290	−	1.25624i	−0.233565	−	0.972341i	$-0.575039\pi$
$109$	7.57225	−	13.1155i	0.725290	−	1.25624i	0.958855	−	0.283898i	$-0.0916276\pi$
$110$		0			0
$111$	−7.90847	+	13.6979i	−0.750638	+	1.30014i
$112$		0			0
$113$			4.46091i			0.419647i	0.977739	+	0.209823i	$0.0672889\pi$
$113$			4.46091i			0.419647i	−0.977739	+	0.209823i	$0.932711\pi$
$114$		0			0
$115$	−17.5209	−	6.95050i	−1.63383	−	0.648138i
$116$		0			0
$117$	14.6168	+	8.43899i	1.35132	+	0.780185i
$118$		0			0
$119$	−14.1699	+	24.5429i	−1.29895	+	2.24985i
$120$		0			0
$121$	−7.70304			−0.700277
$122$		0			0
$123$	−20.1855	+	11.6541i	−1.82007	+	1.05082i
$124$		0			0
$125$	−10.1258	+	4.74016i	−0.905675	+	0.423973i
$126$		0			0
$127$	0.180177	−	0.104025i	0.0159881	−	0.00923073i	−0.491985	−	0.870604i	$-0.663728\pi$
$127$	0.180177	−	0.104025i	0.0159881	−	0.00923073i	0.507973	+	0.861373i	$0.330395\pi$
$128$		0			0
$129$	−7.22073	−	12.5067i	−0.635750	−	1.10115i
$130$		0			0
$131$	7.55409	−	13.0841i	0.660004	−	1.14316i	−0.320610	−	0.947211i	$-0.603888\pi$
$131$	7.55409	−	13.0841i	0.660004	−	1.14316i	0.980614	−	0.195950i	$-0.0627789\pi$
$132$		0			0
$133$	−15.1488	−	3.06261i	−1.31356	−	0.265562i
$134$		0			0
$135$	11.3426	−	8.97773i	0.976213	−	0.772680i
$136$		0			0
$137$	−4.56291	+	2.63439i	−0.389835	+	0.225072i	−0.682089	−	0.731269i	$-0.738928\pi$
$137$	−4.56291	+	2.63439i	−0.389835	+	0.225072i	0.292253	+	0.956341i	$0.405595\pi$
$138$		0			0
$139$	3.38336	+	5.86016i	0.286973	+	0.497052i	0.973086	−	0.230443i	$-0.0740176\pi$
$139$	3.38336	+	5.86016i	0.286973	+	0.497052i	−0.686113	+	0.727495i	$0.740684\pi$
$140$		0			0
$141$	−3.87543			−0.326370
$142$		0			0
$143$	−5.05338	+	2.91757i	−0.422585	+	0.243979i
$144$		0			0
$145$	7.07655	−	17.8386i	0.587675	−	1.48142i
$146$		0			0
$147$	13.8614	+	8.00291i	1.14327	+	0.660069i
$148$		0			0
$149$	4.83003	−	8.36586i	0.395692	−	0.685358i	−0.597498	−	0.801871i	$-0.703838\pi$
$149$	4.83003	−	8.36586i	0.395692	−	0.685358i	0.993189	+	0.116513i	$0.0371716\pi$
$150$		0			0
$151$	−12.0256			−0.978631			−0.489316	−	0.872107i	$-0.662753\pi$
$151$	−12.0256			−0.978631			−0.489316	+	0.872107i	$0.662753\pi$
$152$		0			0
$153$		−	41.9781i		−	3.39373i
$154$		0			0
$155$	−2.37133	−	2.99597i	−0.190470	−	0.240642i
$156$		0			0
$157$	−1.36610	−	0.788721i	−0.109027	−	0.0629468i	0.444495	−	0.895781i	$-0.353383\pi$
$157$	−1.36610	−	0.788721i	−0.109027	−	0.0629468i	−0.553522	+	0.832835i	$0.686716\pi$
$158$		0			0
$159$	6.37537			0.505600
$160$		0			0
$161$	14.9443	+	25.8844i	1.17778	+	2.03997i
$162$		0			0
$163$		−	16.0641i		−	1.25823i	−0.777310	−	0.629117i	$-0.783416\pi$
$163$		−	16.0641i		−	1.25823i	0.777310	−	0.629117i	$-0.216584\pi$
$164$		0			0
$165$	1.69614	+	11.5393i	0.132044	+	0.898335i
$166$		0			0
$167$	6.16826	−	3.56125i	0.477314	−	0.275578i	−0.241982	−	0.970281i	$-0.577798\pi$
$167$	6.16826	−	3.56125i	0.477314	−	0.275578i	0.719297	+	0.694703i	$0.244464\pi$
$168$		0			0
$169$	−1.33632	+	2.31458i	−0.102794	+	0.178044i
$170$		0			0
$171$	21.7010	−	7.29081i	1.65952	−	0.557542i
$172$		0			0
$173$	14.8757	+	8.58850i	1.13098	+	0.652972i	0.944181	−	0.329427i	$-0.106855\pi$
$173$	14.8757	+	8.58850i	1.13098	+	0.652972i	0.186799	+	0.982398i	$0.440189\pi$
$174$		0			0
$175$	17.2546	+	4.07125i	1.30432	+	0.307758i
$176$		0			0
$177$	−4.78038	+	2.75995i	−0.359315	+	0.207451i
$178$		0			0
$179$	3.38519			0.253021			0.126510	−	0.991965i	$-0.459622\pi$
$179$	3.38519			0.253021			0.126510	+	0.991965i	$0.459622\pi$
$180$		0			0
$181$	10.4226	+	18.0524i	0.774704	+	1.34183i	0.934961	+	0.354751i	$0.115434\pi$
$181$	10.4226	+	18.0524i	0.774704	+	1.34183i	−0.160257	+	0.987075i	$0.551232\pi$
$182$		0			0
$183$		−	16.2618i		−	1.20210i
$184$		0			0
$185$	9.65389	−	7.64113i	0.709768	−	0.561787i
$186$		0			0
$187$	12.5685	+	7.25643i	0.919101	+	0.530643i
$188$		0			0
$189$	−22.9377			−1.66847
$190$		0			0
$191$	4.58794			0.331972			0.165986	−	0.986128i	$-0.446919\pi$
$191$	4.58794			0.331972			0.165986	+	0.986128i	$0.446919\pi$
$192$		0			0
$193$	−17.4238	−	10.0596i	−1.25419	−	0.724108i	−0.282252	−	0.959340i	$-0.591082\pi$
$193$	−17.4238	−	10.0596i	−1.25419	−	0.724108i	−0.971939	+	0.235232i	$0.924415\pi$
$194$		0			0
$195$	−12.8112	−	16.1858i	−0.917429	−	1.15909i
$196$		0			0
$197$			0.983439i			0.0700671i	0.999386	+	0.0350336i	$0.0111538\pi$
$197$			0.983439i			0.0700671i	−0.999386	+	0.0350336i	$0.988846\pi$
$198$		0			0
$199$	−5.84473	−	10.1234i	−0.414322	−	0.717626i	0.581035	−	0.813878i	$-0.302648\pi$
$199$	−5.84473	−	10.1234i	−0.414322	−	0.717626i	−0.995357	+	0.0962520i	$0.969315\pi$
$200$		0			0
$201$	−26.6809			−1.88192
$202$		0			0
$203$	−26.3538	+	15.2154i	−1.84967	+	1.06791i
$204$		0			0
$205$	17.9503	−	2.63848i	1.25371	−	0.184279i
$206$		0			0
$207$	−38.3411	−	22.1362i	−2.66489	−	1.53857i
$208$		0			0
$209$	−1.56837	+	7.75773i	−0.108487	+	0.536613i
$210$		0			0
$211$	−5.35987	+	9.28357i	−0.368989	+	0.639107i	−0.989408	−	0.145163i	$-0.953629\pi$
$211$	−5.35987	+	9.28357i	−0.368989	+	0.639107i	0.620419	+	0.784270i	$0.286963\pi$
$212$		0			0
$213$	14.6462	−	8.45601i	1.00354	−	0.579396i
$214$		0			0
$215$	1.63476	+	11.1218i	0.111490	+	0.758499i
$216$		0			0
$217$			6.05865i			0.411288i
$218$		0			0
$219$	4.68888	+	8.12139i	0.316845	+	0.548792i
$220$		0			0
$221$	−25.6857			−1.72781
$222$		0			0
$223$	17.8291	+	10.2936i	1.19393	+	0.689313i	0.959195	−	0.282747i	$-0.0912456\pi$
$223$	17.8291	+	10.2936i	1.19393	+	0.689313i	0.234731	+	0.972060i	$0.424579\pi$
$224$		0			0
$225$	−25.1494	+	7.55655i	−1.67662	+	0.503770i
$226$		0			0
$227$		−	7.47441i		−	0.496094i	−0.968748	−	0.248047i	$-0.920211\pi$
$227$		−	7.47441i		−	0.496094i	0.968748	−	0.248047i	$-0.0797887\pi$
$228$		0			0
$229$	11.0863			0.732604			0.366302	−	0.930496i	$-0.380624\pi$
$229$	11.0863			0.732604			0.366302	+	0.930496i	$0.380624\pi$
$230$		0			0
$231$	9.24711	−	16.0165i	0.608415	−	1.05381i
$232$		0			0
$233$	15.8785	+	9.16743i	1.04023	+	0.600578i	0.919899	−	0.392155i	$-0.128270\pi$
$233$	15.8785	+	9.16743i	1.04023	+	0.600578i	0.120333	+	0.992734i	$0.461604\pi$
$234$		0			0
$235$	2.80407	+	1.11237i	0.182917	+	0.0725628i
$236$		0			0
$237$	−10.3859	+	5.99630i	−0.674636	+	0.389501i
$238$		0			0
$239$	−11.8518			−0.766630			−0.383315	−	0.923618i	$-0.625218\pi$
$239$	−11.8518			−0.766630			−0.383315	+	0.923618i	$0.625218\pi$
$240$		0			0
$241$	−2.34317	−	4.05850i	−0.150937	−	0.261431i	0.780635	−	0.624987i	$-0.214896\pi$
$241$	−2.34317	−	4.05850i	−0.150937	−	0.261431i	−0.931572	+	0.363556i	$0.881562\pi$
$242$		0			0
$243$	−9.77304	+	5.64247i	−0.626941	+	0.361964i
$244$		0			0
$245$	−7.73238	−	9.76918i	−0.494004	−	0.624130i
$246$		0			0
$247$	−4.46112	−	13.2785i	−0.283854	−	0.844890i
$248$		0			0
$249$	9.05264	−	15.6796i	0.573688	−	0.993657i
$250$		0			0
$251$	0.0510129	+	0.0883569i	0.00321990	+	0.00557704i	0.867631	−	0.497209i	$-0.165642\pi$
$251$	0.0510129	+	0.0883569i	0.00321990	+	0.00557704i	−0.864411	+	0.502786i	$0.832308\pi$
$252$		0			0
$253$	13.2555	−	7.65304i	0.833363	−	0.481143i
$254$		0			0
$255$	−18.9315	+	47.7228i	−1.18554	+	2.98852i
$256$		0			0
$257$	13.3268	−	7.69424i	0.831303	−	0.479953i	−0.0229953	−	0.999736i	$-0.507320\pi$
$257$	13.3268	−	7.69424i	0.831303	−	0.479953i	0.854299	+	0.519782i	$0.173987\pi$
$258$		0			0
$259$	−19.5228			−1.21309
$260$		0			0
$261$	22.5377	−	39.0364i	1.39505	−	2.41629i
$262$		0			0
$263$	16.9467	+	9.78416i	1.04498	+	0.603317i	0.921239	−	0.388998i	$-0.127179\pi$
$263$	16.9467	+	9.78416i	1.04498	+	0.603317i	0.123737	+	0.992315i	$0.460512\pi$
$264$		0			0
$265$	−4.61291	−	1.82993i	−0.283369	−	0.112412i
$266$		0			0
$267$		−	15.7217i		−	0.962150i
$268$		0			0
$269$	0.585331	−	1.01382i	0.0356883	−	0.0618139i	−0.847630	−	0.530588i	$-0.821971\pi$
$269$	0.585331	−	1.01382i	0.0356883	−	0.0618139i	0.883318	+	0.468775i	$0.155304\pi$
$270$		0			0
$271$	6.40442	−	11.0928i	0.389041	−	0.673838i	−0.603280	−	0.797529i	$-0.706140\pi$
$271$	6.40442	−	11.0928i	0.389041	−	0.673838i	0.992321	+	0.123691i	$0.0394732\pi$
$272$		0			0
$273$			32.7321i			1.98104i
$274$		0			0
$275$	2.08490	−	8.83613i	0.125724	−	0.532838i
$276$		0			0
$277$		−	11.0122i		−	0.661656i	−0.943691	−	0.330828i	$-0.892672\pi$
$277$		−	11.0122i		−	0.661656i	0.943691	−	0.330828i	$-0.107328\pi$
$278$		0			0
$279$	−4.48717	−	7.77201i	−0.268640	−	0.465298i
$280$		0			0
$281$	−1.93481	−	3.35119i	−0.115421	−	0.199915i	0.802527	−	0.596616i	$-0.203488\pi$
$281$	−1.93481	−	3.35119i	−0.115421	−	0.199915i	−0.917948	+	0.396701i	$0.870155\pi$
$282$		0			0
$283$	19.5893	+	11.3099i	1.16446	+	0.672303i	0.952369	−	0.304947i	$-0.0986387\pi$
$283$	19.5893	+	11.3099i	1.16446	+	0.672303i	0.212093	+	0.977249i	$0.431972\pi$
$284$		0			0
$285$	−27.9588	−	1.49829i	−1.65614	−	0.0887510i
$286$		0			0
$287$	−24.9149	−	14.3846i	−1.47068	−	0.849097i
$288$		0			0
$289$	23.4421	+	40.6029i	1.37895	+	2.38840i
$290$		0			0
$291$	−11.4646	−	19.8572i	−0.672065	−	1.16405i
$292$		0			0
$293$		−	28.4482i		−	1.66196i	−0.556303	−	0.830980i	$-0.687781\pi$
$293$		−	28.4482i		−	1.66196i	0.556303	−	0.830980i	$-0.312219\pi$
$294$		0			0
$295$	4.25104	−	0.624850i	0.247505	−	0.0363801i
$296$		0			0
$297$			11.7465i			0.681600i
$298$		0			0
$299$	−13.5448	+	23.4603i	−0.783315	+	1.35674i
$300$		0			0
$301$	8.91251	−	15.4369i	0.513709	−	0.889770i
$302$		0			0
$303$		−	14.1754i		−	0.814353i
$304$		0			0
$305$	−4.66763	+	11.7662i	−0.267268	+	0.673732i
$306$		0			0
$307$	12.2248	+	7.05802i	0.697709	+	0.402822i	0.806494	−	0.591243i	$-0.201363\pi$
$307$	12.2248	+	7.05802i	0.697709	+	0.402822i	−0.108785	+	0.994065i	$0.534696\pi$
$308$		0			0
$309$	7.99010	−	13.8393i	0.454541	−	0.787288i
$310$		0			0
$311$	16.4672			0.933768			0.466884	−	0.884319i	$-0.345377\pi$
$311$	16.4672			0.933768			0.466884	+	0.884319i	$0.345377\pi$
$312$		0			0
$313$	−21.6363	+	12.4917i	−1.22295	+	0.706073i	−0.965547	−	0.260229i	$-0.916202\pi$
$313$	−21.6363	+	12.4917i	−1.22295	+	0.706073i	−0.257408	+	0.966303i	$0.582868\pi$
$314$		0			0
$315$	38.7056	+	15.3544i	2.18082	+	0.865124i
$316$		0			0
$317$	−1.91012	+	1.10281i	−0.107283	+	0.0619399i	−0.552681	−	0.833393i	$-0.686395\pi$
$317$	−1.91012	+	1.10281i	−0.107283	+	0.0619399i	0.445398	+	0.895332i	$0.353062\pi$
$318$		0			0
$319$	7.79183	+	13.4958i	0.436259	+	0.755622i
$320$		0			0
$321$	−13.1028	+	22.6947i	−0.731328	+	1.26670i
$322$		0			0
$323$	−23.0533	+	26.1218i	−1.28272	+	1.45345i
$324$		0			0
$325$	4.62373	+	15.3885i	0.256478	+	0.853599i
$326$		0			0
$327$	−37.6761	+	21.7523i	−2.08349	+	1.20290i
$328$		0			0
$329$	−2.39171	−	4.14257i	−0.131859	−	0.228387i
$330$		0			0
$331$	−27.5415			−1.51382			−0.756910	−	0.653519i	$-0.773292\pi$
$331$	−27.5415			−1.51382			−0.756910	+	0.653519i	$0.773292\pi$
$332$		0			0
$333$	25.0437	−	14.4590i	1.37239	−	0.792348i
$334$		0			0
$335$	19.3050	+	7.65823i	1.05474	+	0.418414i
$336$		0			0
$337$	−15.9464	−	9.20668i	−0.868658	−	0.501520i	−0.00175582	−	0.999998i	$-0.500559\pi$
$337$	−15.9464	−	9.20668i	−0.868658	−	0.501520i	−0.866902	+	0.498479i	$0.833892\pi$
$338$		0			0
$339$	6.40727	−	11.0977i	0.347995	−	0.602745i
$340$		0			0
$341$	3.10265			0.168018
$342$		0			0
$343$		−	5.06383i		−	0.273421i
$344$		0			0
$345$	33.6049	+	42.4568i	1.80923	+	2.28580i
$346$		0			0
$347$	22.8072	+	13.1677i	1.22435	+	0.706881i	0.965843	−	0.259128i	$-0.0834351\pi$
$347$	22.8072	+	13.1677i	1.22435	+	0.706881i	0.258510	+	0.966009i	$0.416768\pi$
$348$		0			0
$349$	7.40515			0.396388			0.198194	−	0.980163i	$-0.436492\pi$
$349$	7.40515			0.396388			0.198194	+	0.980163i	$0.436492\pi$
$350$		0			0
$351$	−10.3948	−	18.0043i	−0.554833	−	0.960999i
$352$		0			0
$353$		−	2.42201i		−	0.128910i	−0.997921	−	0.0644552i	$-0.979469\pi$
$353$		−	2.42201i		−	0.128910i	0.997921	−	0.0644552i	$-0.0205309\pi$
$354$		0			0
$355$	−13.0244	+	1.91443i	−0.691265	+	0.101607i
$356$		0			0
$357$	70.5028	−	40.7048i	3.73140	−	2.15433i
$358$		0			0
$359$	2.28083	−	3.95051i	0.120377	−	0.208500i	−0.799539	−	0.600614i	$-0.794923\pi$
$359$	2.28083	−	3.95051i	0.120377	−	0.208500i	0.919917	+	0.392114i	$0.128256\pi$
$360$		0			0
$361$	−17.5078	−	7.38076i	−0.921465	−	0.388461i
$362$		0			0
$363$	19.1634	+	11.0640i	1.00582	+	0.580710i
$364$		0			0
$365$	−1.06156	−	7.22209i	−0.0555645	−	0.378021i
$366$		0			0
$367$	9.11478	−	5.26242i	0.475788	−	0.274696i	−0.242872	−	0.970058i	$-0.578089\pi$
$367$	9.11478	−	5.26242i	0.475788	−	0.274696i	0.718659	+	0.695362i	$0.244756\pi$
$368$		0			0
$369$	42.6143			2.21841
$370$		0			0
$371$	3.93455	+	6.81484i	0.204272	+	0.353809i
$372$		0			0
$373$			21.8633i			1.13204i	0.824392	+	0.566019i	$0.191517\pi$
$373$			21.8633i			1.13204i	−0.824392	+	0.566019i	$0.808483\pi$
$374$		0			0
$375$	31.9989	+	2.75134i	1.65242	+	0.142079i
$376$		0			0
$377$	−23.8857	−	13.7904i	−1.23018	−	0.710243i
$378$		0			0
$379$	−9.33617			−0.479567			−0.239783	−	0.970826i	$-0.577076\pi$
$379$	−9.33617			−0.479567			−0.239783	+	0.970826i	$0.577076\pi$
$380$		0			0
$381$	−0.597652			−0.0306186
$382$		0			0
$383$	−4.77320	−	2.75581i	−0.243899	−	0.140815i	0.373068	−	0.927804i	$-0.378306\pi$
$383$	−4.77320	−	2.75581i	−0.243899	−	0.140815i	−0.616968	+	0.786989i	$0.711639\pi$
$384$		0			0
$385$	−11.2880	+	8.93452i	−0.575288	+	0.455345i
$386$		0			0
$387$			26.4032i			1.34215i
$388$		0			0
$389$	8.50605	+	14.7329i	0.431274	+	0.746988i	0.996983	−	0.0776163i	$-0.0247309\pi$
$389$	8.50605	+	14.7329i	0.431274	+	0.746988i	−0.565709	+	0.824605i	$0.691398\pi$
$390$		0			0
$391$	67.3758			3.40734
$392$		0			0
$393$	−37.5857	+	21.7001i	−1.89595	+	1.09463i
$394$		0			0
$395$	9.23585	−	1.35755i	0.464706	−	0.0683060i
$396$		0			0
$397$	−27.2122	−	15.7110i	−1.36574	−	0.788512i	−0.375362	−	0.926878i	$-0.622482\pi$
$397$	−27.2122	−	15.7110i	−1.36574	−	0.788512i	−0.990381	+	0.138366i	$0.955815\pi$
$398$		0			0
$399$	33.2878	+	29.3775i	1.66647	+	1.47071i
$400$		0			0
$401$	13.4762	−	23.3415i	0.672971	−	1.16562i	−0.304087	−	0.952644i	$-0.598351\pi$
$401$	13.4762	−	23.3415i	0.672971	−	1.16562i	0.977058	−	0.212976i	$-0.0683155\pi$
$402$		0			0
$403$	−4.75556	+	2.74563i	−0.236891	+	0.136769i
$404$		0			0
$405$	−6.25553	+	0.919485i	−0.310840	+	0.0456896i
$406$		0			0
$407$			9.99767i			0.495566i
$408$		0			0
$409$	−17.0791	−	29.5819i	−0.844509	−	1.46273i	−0.886047	−	0.463596i	$-0.846559\pi$
$409$	−17.0791	−	29.5819i	−0.844509	−	1.46273i	0.0415373	−	0.999137i	$-0.486774\pi$
$410$		0			0
$411$	15.1353			0.746569
$412$		0			0
$413$	−5.90040	−	3.40660i	−0.290340	−	0.167628i
$414$		0			0
$415$	−11.0506	+	8.74663i	−0.542452	+	0.429355i
$416$		0			0
$417$		−	19.4383i		−	0.951899i
$418$		0			0
$419$	−36.5998			−1.78802			−0.894009	−	0.448049i	$-0.852119\pi$
$419$	−36.5998			−1.78802			−0.894009	+	0.448049i	$0.852119\pi$
$420$		0			0
$421$	−4.85007	+	8.40057i	−0.236378	+	0.409419i	−0.959672	−	0.281121i	$-0.909294\pi$
$421$	−4.85007	+	8.40057i	−0.236378	+	0.409419i	0.723294	+	0.690540i	$0.242627\pi$
$422$		0			0
$423$	6.13615	+	3.54271i	0.298350	+	0.172252i
$424$		0			0
$425$	27.3958	−	29.0959i	1.32889	−	1.41136i
$426$		0			0
$427$	17.3827	−	10.0359i	0.841209	−	0.485672i
$428$		0			0
$429$	16.7622			0.809287
$430$		0			0
$431$	−14.4779	−	25.0764i	−0.697375	−	1.20789i	−0.969373	−	0.245591i	$-0.921018\pi$
$431$	−14.4779	−	25.0764i	−0.697375	−	1.20789i	0.271999	−	0.962298i	$-0.412315\pi$
$432$		0			0
$433$	6.44994	−	3.72388i	0.309965	−	0.178958i	−0.336946	−	0.941524i	$-0.609394\pi$
$433$	6.44994	−	3.72388i	0.309965	−	0.178958i	0.646911	+	0.762566i	$0.276061\pi$
$434$		0			0
$435$	−43.2268	+	34.2143i	−2.07257	+	1.64045i
$436$		0			0
$437$	11.7019	+	34.8306i	0.559779	+	1.66618i
$438$		0			0
$439$	5.70008	−	9.87283i	0.272050	−	0.471204i	−0.697337	−	0.716744i	$-0.745632\pi$
$439$	5.70008	−	9.87283i	0.272050	−	0.471204i	0.969387	+	0.245539i	$0.0789650\pi$
$440$		0			0
$441$	−14.6317	−	25.3428i	−0.696746	−	1.20680i
$442$		0			0
$443$	6.66042	−	3.84540i	0.316446	−	0.182700i	−0.333361	−	0.942799i	$-0.608183\pi$
$443$	6.66042	−	3.84540i	0.316446	−	0.182700i	0.649807	+	0.760099i	$0.274850\pi$
$444$		0			0
$445$	−4.51260	+	11.3754i	−0.213918	+	0.539247i
$446$		0			0
$447$	−24.0320	+	13.8749i	−1.13668	+	0.656260i
$448$		0			0
$449$	−37.0590			−1.74892			−0.874460	−	0.485097i	$-0.838784\pi$
$449$	−37.0590			−1.74892			−0.874460	+	0.485097i	$0.838784\pi$
$450$		0			0
$451$	−7.36641	+	12.7590i	−0.346871	+	0.600797i
$452$		0			0
$453$	29.9170	+	17.2726i	1.40562	+	0.811537i
$454$		0			0
$455$	9.39512	−	23.6833i	0.440450	−	1.11029i
$456$		0			0
$457$		−	22.1647i		−	1.03682i	−0.855131	−	0.518411i	$-0.826524\pi$
$457$		−	22.1647i		−	1.03682i	0.855131	−	0.518411i	$-0.173476\pi$
$458$		0			0
$459$	−25.8534	+	44.7794i	−1.20673	+	2.09012i
$460$		0			0
$461$	21.0779	−	36.5080i	0.981697	−	1.70035i	0.325914	−	0.945400i	$-0.394328\pi$
$461$	21.0779	−	36.5080i	0.981697	−	1.70035i	0.655783	−	0.754949i	$-0.272339\pi$
$462$		0			0
$463$		−	5.16758i		−	0.240158i	−0.992764	−	0.120079i	$-0.961685\pi$
$463$		−	5.16758i		−	0.240158i	0.992764	−	0.120079i	$-0.0383148\pi$
$464$		0			0
$465$	1.59618	+	10.8593i	0.0740209	+	0.503586i
$466$		0			0
$467$			12.7096i			0.588129i	0.955786	+	0.294064i	$0.0950080\pi$
$467$			12.7096i			0.588129i	−0.955786	+	0.294064i	$0.904992\pi$
$468$		0			0
$469$	−16.4660	−	28.5200i	−0.760331	−	1.31693i
$470$		0			0
$471$	2.26570	+	3.92431i	0.104398	+	0.180823i
$472$		0			0
$473$	−7.90530	−	4.56413i	−0.363486	−	0.209859i
$474$		0			0
$475$	19.7996	+	9.10914i	0.908467	+	0.417956i
$476$		0			0
$477$	−10.0944	−	5.82803i	−0.462193	−	0.266847i
$478$		0			0
$479$	−11.0555	−	19.1487i	−0.505140	−	0.874928i	−0.999982	−	0.00594539i	$-0.998108\pi$
$479$	−11.0555	−	19.1487i	−0.505140	−	0.874928i	0.494842	−	0.868983i	$-0.335226\pi$
$480$		0			0
$481$	−8.84722	−	15.3238i	−0.403399	−	0.698707i
$482$		0			0
$483$		−	85.8592i		−	3.90673i
$484$		0			0
$485$	2.59556	+	17.6584i	0.117858	+	0.801826i
$486$		0			0
$487$			28.3389i			1.28416i	0.766639	+	0.642078i	$0.221928\pi$
$487$			28.3389i			1.28416i	−0.766639	+	0.642078i	$0.778072\pi$
$488$		0			0
$489$	−23.0731	+	39.9637i	−1.04340	+	1.80722i
$490$		0			0
$491$	−4.33288	+	7.50477i	−0.195540	+	0.338686i	−0.947077	−	0.321005i	$-0.895979\pi$
$491$	−4.33288	+	7.50477i	−0.195540	+	0.338686i	0.751537	+	0.659691i	$0.229313\pi$
$492$		0			0
$493$			68.5977i			3.08948i
$494$		0			0
$495$	7.86305	−	19.8213i	0.353418	−	0.890900i
$496$		0			0
$497$	18.0778	+	10.4372i	0.810900	+	0.468173i
$498$		0			0
$499$	−8.07784	+	13.9912i	−0.361614	+	0.626334i	−0.988227	−	0.152997i	$-0.951107\pi$
$499$	−8.07784	+	13.9912i	−0.361614	+	0.626334i	0.626613	+	0.779331i	$0.284441\pi$
$500$		0			0
$501$	−20.4603			−0.914099
$502$		0			0
$503$	−22.3262	+	12.8900i	−0.995474	+	0.574737i	−0.906906	−	0.421333i	$-0.861562\pi$
$503$	−22.3262	+	12.8900i	−0.995474	+	0.574737i	−0.0885682	+	0.996070i	$0.528229\pi$
$504$		0			0
$505$	−4.06877	+	10.2566i	−0.181058	+	0.456413i
$506$		0			0
$507$	6.64893	−	3.83876i	0.295289	−	0.170485i
$508$		0			0
$509$	−6.15335	−	10.6579i	−0.272743	−	0.472404i	0.696821	−	0.717246i	$-0.254597\pi$
$509$	−6.15335	−	10.6579i	−0.272743	−	0.472404i	−0.969563	+	0.244842i	$0.921264\pi$
$510$		0			0
$511$	−5.78747	+	10.0242i	−0.256023	+	0.443444i
$512$		0			0
$513$	−27.6394	−	5.58784i	−1.22031	−	0.246709i
$514$		0			0
$515$	−9.75354	+	7.72000i	−0.429792	+	0.340184i
$516$		0			0
$517$	−2.12142	+	1.22480i	−0.0933000	+	0.0538668i
$518$		0			0
$519$	−24.6716	−	42.7325i	−1.08296	−	1.87575i
$520$		0			0
$521$	17.0934			0.748875			0.374438	−	0.927252i	$-0.377836\pi$
$521$	17.0934			0.748875			0.374438	+	0.927252i	$0.377836\pi$
$522$		0			0
$523$	2.29269	−	1.32368i	0.100252	−	0.0578806i	−0.449036	−	0.893514i	$-0.648232\pi$
$523$	2.29269	−	1.32368i	0.100252	−	0.0578806i	0.549288	+	0.835633i	$0.314899\pi$
$524$		0			0
$525$	−37.0779	−	34.9114i	−1.61821	−	1.52366i
$526$		0			0
$527$	11.8278	+	6.82878i	0.515227	+	0.297466i
$528$		0			0
$529$	24.0292	−	41.6197i	1.04475	−	1.80955i
$530$		0			0
$531$	10.0920			0.437956
$532$		0			0
$533$		−	26.0750i		−	1.12943i
$534$		0			0
$535$	15.9946	−	12.6599i	0.691509	−	0.547335i
$536$		0			0
$537$	−8.42158	−	4.86220i	−0.363418	−	0.209820i
$538$		0			0
$539$	10.1171			0.435773
$540$		0			0
$541$	−5.06701	−	8.77631i	−0.217848	−	0.377323i	0.736302	−	0.676653i	$-0.236570\pi$
$541$	−5.06701	−	8.77631i	−0.217848	−	0.377323i	−0.954150	+	0.299330i	$0.903237\pi$
$542$		0			0
$543$		−	59.8804i		−	2.56972i
$544$		0			0
$545$	33.5041	−	4.92469i	1.43516	−	0.210951i
$546$		0			0
$547$	−19.4639	+	11.2375i	−0.832217	+	0.480480i	−0.854611	−	0.519269i	$-0.826204\pi$
$547$	−19.4639	+	11.2375i	−0.832217	+	0.480480i	0.0223944	+	0.999749i	$0.492871\pi$
$548$		0			0
$549$	−14.8656	+	25.7481i	−0.634450	+	1.09890i
$550$		0			0
$551$	−35.4623	+	11.9141i	−1.51074	+	0.507559i
$552$		0			0
$553$	−12.8193	−	7.40121i	−0.545131	−	0.314731i
$554$		0			0
$555$	−34.9918	+	5.14335i	−1.48532	+	0.218323i
$556$		0			0
$557$	3.86157	−	2.22948i	0.163620	−	0.0944659i	−0.415954	−	0.909386i	$-0.636552\pi$
$557$	3.86157	−	2.22948i	0.163620	−	0.0944659i	0.579574	+	0.814920i	$0.303219\pi$
$558$		0			0
$559$	16.1557			0.683313
$560$		0			0
$561$	−20.8451	−	36.1047i	−0.880079	−	1.52434i
$562$		0			0
$563$		−	10.0514i		−	0.423616i	−0.977311	−	0.211808i	$-0.932065\pi$
$563$		−	10.0514i		−	0.423616i	0.977311	−	0.211808i	$-0.0679352\pi$
$564$		0			0
$565$	−7.82137	+	6.19068i	−0.329048	+	0.260444i
$566$		0			0
$567$	8.68261	+	5.01291i	0.364635	+	0.210522i
$568$		0			0
$569$	5.41442			0.226984			0.113492	−	0.993539i	$-0.463796\pi$
$569$	5.41442			0.226984			0.113492	+	0.993539i	$0.463796\pi$
$570$		0			0
$571$	−24.0418			−1.00612			−0.503059	−	0.864252i	$-0.667792\pi$
$571$	−24.0418			−1.00612			−0.503059	+	0.864252i	$0.667792\pi$
$572$		0			0
$573$	−11.4138	−	6.58973i	−0.476816	−	0.275290i
$574$		0			0
$575$	−12.1284	−	40.3653i	−0.505791	−	1.68335i
$576$		0			0
$577$			1.40727i			0.0585855i	0.999571	+	0.0292928i	$0.00932551\pi$
$577$			1.40727i			0.0585855i	−0.999571	+	0.0292928i	$0.990674\pi$
$578$		0			0
$579$	28.8976	+	50.0521i	1.20094	+	2.08010i
$580$		0			0
$581$	22.3473			0.927121
$582$		0			0
$583$	3.48990	−	2.01489i	0.144537	−	0.0834484i
$584$		0			0
$585$	5.48839	+	37.3391i	0.226917	+	1.54378i
$586$		0			0
$587$	−0.224303	−	0.129501i	−0.00925798	−	0.00534510i	0.495364	−	0.868686i	$-0.335035\pi$
$587$	−0.224303	−	0.129501i	−0.00925798	−	0.00534510i	−0.504622	+	0.863340i	$0.668368\pi$
$588$		0			0
$589$	−1.47594	+	7.30054i	−0.0608152	+	0.300813i
$590$		0			0
$591$	1.41253	−	2.44657i	0.0581037	−	0.100639i
$592$		0			0
$593$	2.57044	−	1.48405i	0.105555	−	0.0609425i	−0.446293	−	0.894887i	$-0.647256\pi$
$593$	2.57044	−	1.48405i	0.105555	−	0.0609425i	0.551848	+	0.833944i	$0.313923\pi$
$594$		0			0
$595$	−62.6959	+	9.21552i	−2.57028	+	0.377800i
$596$		0			0
$597$			33.5795i			1.37432i
$598$		0			0
$599$	23.7083	+	41.0640i	0.968696	+	1.67783i	0.699338	+	0.714791i	$0.253478\pi$
$599$	23.7083	+	41.0640i	0.968696	+	1.67783i	0.269359	+	0.963040i	$0.413188\pi$
$600$		0			0
$601$	−22.2047			−0.905747			−0.452874	−	0.891575i	$-0.649601\pi$
$601$	−22.2047			−0.905747			−0.452874	+	0.891575i	$0.649601\pi$
$602$		0			0
$603$	42.2451	+	24.3902i	1.72035	+	0.993247i
$604$		0			0
$605$	−10.6900	−	13.5059i	−0.434610	−	0.549091i
$606$		0			0
$607$		−	37.6580i		−	1.52849i	−0.644925	−	0.764246i	$-0.723112\pi$
$607$		−	37.6580i		−	1.52849i	0.644925	−	0.764246i	$-0.276888\pi$
$608$		0			0
$609$	87.4162			3.54228
$610$		0			0
$611$	2.16772	−	3.75461i	0.0876968	−	0.151895i
$612$		0			0
$613$	−38.3694	−	22.1526i	−1.54973	−	0.894734i	−0.998162	−	0.0606013i	$-0.980698\pi$
$613$	−38.3694	−	22.1526i	−1.54973	−	0.894734i	−0.551563	−	0.834133i	$-0.685969\pi$
$614$		0			0
$615$	−48.4460	−	19.2184i	−1.95353	−	0.774962i
$616$		0			0
$617$	20.1247	−	11.6190i	0.810190	−	0.467764i	−0.0368317	−	0.999321i	$-0.511727\pi$
$617$	20.1247	−	11.6190i	0.810190	−	0.467764i	0.847022	+	0.531558i	$0.178393\pi$
$618$		0			0
$619$	28.8420			1.15926			0.579630	−	0.814880i	$-0.303197\pi$
$619$	28.8420			1.15926			0.579630	+	0.814880i	$0.303197\pi$
$620$		0			0
$621$	27.2665	+	47.2269i	1.09417	+	1.89515i
$622$		0			0
$623$	16.8054	−	9.70259i	0.673294	−	0.388726i
$624$		0			0
$625$	−22.3631	−	11.1754i	−0.894526	−	0.447017i
$626$		0			0
$627$	15.0443	−	17.0468i	0.600812	−	0.680783i
$628$		0			0
$629$	−22.0044	+	38.1127i	−0.877371	+	1.51965i
$630$		0			0
$631$	6.79323	+	11.7662i	0.270434	+	0.468406i	0.968973	−	0.247166i	$-0.0794994\pi$
$631$	6.79323	+	11.7662i	0.270434	+	0.468406i	−0.698539	+	0.715572i	$0.746166\pi$
$632$		0			0
$633$	26.6683	−	15.3969i	1.05997	−	0.611973i
$634$		0			0
$635$	0.432431	+	0.171544i	0.0171605	+	0.00680753i
$636$		0			0
$637$	−15.5068	+	8.95287i	−0.614403	+	0.354726i
$638$		0			0
$639$	−30.9201			−1.22318
$640$		0			0
$641$	3.15731	−	5.46863i	0.124706	−	0.215998i	−0.796912	−	0.604096i	$-0.793534\pi$
$641$	3.15731	−	5.46863i	0.124706	−	0.215998i	0.921618	+	0.388098i	$0.126868\pi$
$642$		0			0
$643$	−11.8657	−	6.85067i	−0.467938	−	0.270164i	0.247438	−	0.968904i	$-0.420411\pi$
$643$	−11.8657	−	6.85067i	−0.467938	−	0.270164i	−0.715376	+	0.698740i	$0.753745\pi$
$644$		0			0
$645$	11.9075	−	30.0165i	0.468856	−	1.18190i
$646$		0			0
$647$			8.50227i			0.334259i	0.985935	+	0.167129i	$0.0534497\pi$
$647$			8.50227i			0.334259i	−0.985935	+	0.167129i	$0.946550\pi$
$648$		0			0
$649$	−1.74453	+	3.02161i	−0.0684787	+	0.118609i
$650$		0			0
$651$	8.70214	−	15.0725i	0.341064	−	0.590740i
$652$		0			0
$653$			6.89369i			0.269771i	0.990861	+	0.134885i	$0.0430667\pi$
$653$			6.89369i			0.269771i	−0.990861	+	0.134885i	$0.956933\pi$
$654$		0			0
$655$	33.4238	−	4.91288i	1.30598	−	0.191962i
$656$		0			0
$657$		−	17.1453i		−	0.668902i
$658$		0			0
$659$	−10.9585	−	18.9807i	−0.426884	−	0.739384i	0.569711	−	0.821845i	$-0.307055\pi$
$659$	−10.9585	−	18.9807i	−0.426884	−	0.739384i	−0.996594	+	0.0824611i	$0.973722\pi$
$660$		0			0
$661$	15.5768	+	26.9797i	0.605866	+	1.04939i	0.991914	+	0.126912i	$0.0405065\pi$
$661$	15.5768	+	26.9797i	0.605866	+	1.04939i	−0.386048	+	0.922479i	$0.626160\pi$
$662$		0			0
$663$	63.9001	+	36.8928i	2.48168	+	1.43280i
$664$		0			0
$665$	−15.6532	−	30.8107i	−0.607004	−	1.19479i
$666$		0			0
$667$	62.6543	+	36.1735i	2.42598	+	1.40064i
$668$		0			0
$669$	−29.5699	−	51.2165i	−1.14324	−	1.98014i
$670$		0			0
$671$	−5.13943	−	8.90175i	−0.198405	−	0.343648i
$672$		0			0
$673$			24.5193i			0.945150i	0.881290	+	0.472575i	$0.156675\pi$
$673$			24.5193i			0.945150i	−0.881290	+	0.472575i	$0.843325\pi$
$674$		0			0
$675$	31.4816	+	7.42814i	1.21173	+	0.285909i
$676$		0			0
$677$			7.89395i			0.303389i	0.988427	+	0.151695i	$0.0484730\pi$
$677$			7.89395i			0.303389i	−0.988427	+	0.151695i	$0.951527\pi$
$678$		0			0
$679$	14.1507	−	24.5097i	0.543053	−	0.940595i
$680$		0			0
$681$	−10.7356	+	18.5946i	−0.411390	+	0.712548i
$682$		0			0
$683$		−	44.3352i		−	1.69644i	−0.529644	−	0.848220i	$-0.677675\pi$
$683$		−	44.3352i		−	1.69644i	0.529644	−	0.848220i	$-0.322325\pi$
$684$		0			0
$685$	−10.9512	−	4.34430i	−0.418422	−	0.165987i
$686$		0			0
$687$	−27.5802	−	15.9234i	−1.05225	−	0.607517i
$688$		0			0
$689$	−3.56607	+	6.17662i	−0.135857	+	0.235311i
$690$		0			0
$691$	44.2501			1.68335			0.841676	−	0.539982i	$-0.181569\pi$
$691$	44.2501			1.68335			0.841676	+	0.539982i	$0.181569\pi$
$692$		0			0
$693$	−29.2828	+	16.9064i	−1.11236	+	0.642222i
$694$		0			0
$695$	−5.57940	+	14.0646i	−0.211639	+	0.533501i
$696$		0			0
$697$	−56.1638	+	32.4262i	−2.12735	+	1.22823i
$698$		0			0
$699$	−26.3347	−	45.6130i	−0.996068	−	1.72524i
$700$		0			0
$701$	−9.27840	+	16.0707i	−0.350440	+	0.606980i	−0.986327	−	0.164802i	$-0.947301\pi$
$701$	−9.27840	+	16.0707i	−0.350440	+	0.606980i	0.635886	+	0.771783i	$0.280635\pi$
$702$		0			0
$703$	−23.5245	−	4.75593i	−0.887243	−	0.179373i
$704$		0			0
$705$	−5.37817	−	6.79485i	−0.202554	−	0.255909i
$706$		0			0
$707$	15.1525	−	8.74830i	0.569868	−	0.329014i
$708$		0			0
$709$	21.4349	+	37.1263i	0.805003	+	1.39431i	0.916289	+	0.400518i	$0.131170\pi$
$709$	21.4349	+	37.1263i	0.805003	+	1.39431i	−0.111285	+	0.993788i	$0.535497\pi$
$710$		0			0
$711$	21.9260			0.822289
$712$		0			0
$713$	12.4743	−	7.20202i	0.467165	−	0.269718i
$714$		0			0
$715$	−12.1283	−	4.81127i	−0.453573	−	0.179931i
$716$		0			0
$717$	29.4846	+	17.0230i	1.10112	+	0.635734i
$718$		0			0
$719$	−17.5024	+	30.3150i	−0.652728	+	1.13056i	0.329730	+	0.944075i	$0.393042\pi$
$719$	−17.5024	+	30.3150i	−0.652728	+	1.13056i	−0.982458	+	0.186483i	$0.940291\pi$
$720$		0			0
$721$	19.7243			0.734571
$722$		0			0
$723$			13.4622i			0.500663i
$724$		0			0
$725$	41.0973	−	12.3484i	1.52632	−	0.458608i
$726$		0			0
$727$	0.436587	+	0.252064i	0.0161921	+	0.00934852i	0.508074	−	0.861313i	$-0.330358\pi$
$727$	0.436587	+	0.252064i	0.0161921	+	0.00934852i	−0.491882	+	0.870662i	$0.663691\pi$
$728$		0			0
$729$	40.9003			1.51483
$730$		0			0
$731$	−20.0908	−	34.7983i	−0.743086	−	1.28706i
$732$		0			0
$733$			26.5745i			0.981553i	0.871285	+	0.490777i	$0.163287\pi$
$733$			26.5745i			0.981553i	−0.871285	+	0.490777i	$0.836713\pi$
$734$		0			0
$735$	5.20477	+	35.4096i	0.191981	+	1.30610i
$736$		0			0
$737$	−14.6052	+	8.43231i	−0.537989	+	0.310608i
$738$		0			0
$739$	12.8643	−	22.2817i	0.473222	−	0.819645i	−0.526308	−	0.850294i	$-0.676424\pi$
$739$	12.8643	−	22.2817i	0.473222	−	0.819645i	0.999530	+	0.0306492i	$0.00975746\pi$
$740$		0			0
$741$	−7.97384	+	39.4414i	−0.292926	+	1.44892i
$742$		0			0
$743$	3.70400	+	2.13851i	0.135887	+	0.0784542i	0.566402	−	0.824129i	$-0.308335\pi$
$743$	3.70400	+	2.13851i	0.135887	+	0.0784542i	−0.430516	+	0.902583i	$0.641668\pi$
$744$		0			0
$745$	21.3709	−	3.14126i	0.782970	−	0.115087i
$746$		0			0
$747$	−28.6670	+	16.5509i	−1.04887	+	0.605565i
$748$		0			0
$749$	−32.3455			−1.18188
$750$		0			0
$751$	−7.26869	−	12.5897i	−0.265238	−	0.459406i	0.702388	−	0.711795i	$-0.252117\pi$
$751$	−7.26869	−	12.5897i	−0.265238	−	0.459406i	−0.967626	+	0.252388i	$0.918784\pi$
$752$		0			0
$753$		−	0.293082i		−	0.0106805i
$754$		0			0
$755$	−16.6887	−	21.0847i	−0.607364	−	0.767351i
$756$		0			0
$757$	−14.1482	−	8.16844i	−0.514224	−	0.296887i	0.220345	−	0.975422i	$-0.429282\pi$
$757$	−14.1482	−	8.16844i	−0.514224	−	0.296887i	−0.734568	+	0.678535i	$0.762615\pi$
$758$		0			0
$759$	−43.9687			−1.59596
$760$		0			0
$761$	−21.9812			−0.796819			−0.398409	−	0.917208i	$-0.630438\pi$
$761$	−21.9812			−0.796819			−0.398409	+	0.917208i	$0.630438\pi$
$762$		0			0
$763$	−46.5034	−	26.8488i	−1.68354	−	0.971990i
$764$		0			0
$765$	73.6008	−	58.2556i	2.66104	−	2.10624i
$766$		0			0
$767$		−	6.17513i		−	0.222971i
$768$		0			0
$769$	23.1977	+	40.1796i	0.836530	+	1.44891i	0.892778	+	0.450496i	$0.148753\pi$
$769$	23.1977	+	40.1796i	0.836530	+	1.44891i	−0.0562477	+	0.998417i	$0.517914\pi$
$770$		0			0
$771$	−44.2054			−1.59202
$772$		0			0
$773$	−21.6426	+	12.4954i	−0.778431	+	0.449428i	−0.835874	−	0.548921i	$-0.815039\pi$
$773$	−21.6426	+	12.4954i	−0.778431	+	0.449428i	0.0574426	+	0.998349i	$0.481705\pi$
$774$		0			0
$775$	1.96203	−	8.31538i	0.0704781	−	0.298697i
$776$		0			0
$777$	48.5682	+	28.0409i	1.74238	+	1.00596i
$778$		0			0
$779$	−26.5176	−	23.4026i	−0.950093	−	0.838486i
$780$		0			0
$781$	5.34493	−	9.25769i	0.191257	−	0.331266i
$782$		0			0
$783$	−48.0834	+	27.7609i	−1.71836	+	0.992095i
$784$		0			0
$785$	−0.512953	−	3.48977i	−0.0183081	−	0.124555i
$786$		0			0
$787$			36.4986i			1.30103i	0.759492	+	0.650517i	$0.225448\pi$
$787$			36.4986i			1.30103i	−0.759492	+	0.650517i	$0.774552\pi$
$788$		0			0
$789$	−28.1063	−	48.6815i	−1.00061	−	1.73311i
$790$		0			0
$791$	15.8169			0.562385
$792$		0			0
$793$	15.7548	+	9.09604i	0.559470	+	0.323010i
$794$		0			0
$795$	8.84751	+	11.1780i	0.313789	+	0.396444i
$796$		0			0
$797$			11.9753i			0.424188i	0.977249	+	0.212094i	$0.0680283\pi$
$797$			11.9753i			0.424188i	−0.977249	+	0.212094i	$0.931972\pi$
$798$		0			0
$799$	−10.7829			−0.381472
$800$		0			0
$801$	−14.3719	+	24.8929i	−0.507807	+	0.879547i
$802$		0			0
$803$	5.13342	+	2.96378i	0.181154	+	0.104590i
$804$		0			0
$805$	−24.6442	+	62.1235i	−0.868595	+	2.18956i
$806$		0			0
$807$	−2.91234	+	1.68144i	−0.102519	+	0.0591895i
$808$		0			0
$809$	−29.4153			−1.03419			−0.517093	−	0.855929i	$-0.672986\pi$
$809$	−29.4153			−1.03419			−0.517093	+	0.855929i	$0.672986\pi$
$810$		0			0
$811$	−27.4062	−	47.4690i	−0.962363	−	1.66686i	−0.716538	−	0.697548i	$-0.754274\pi$
$811$	−27.4062	−	47.4690i	−0.962363	−	1.66686i	−0.245825	−	0.969314i	$-0.579059\pi$
$812$		0			0
$813$	−31.8655	+	18.3975i	−1.11757	+	0.645230i
$814$		0			0
$815$	28.1654	−	22.2931i	0.986590	−	0.780894i
$816$		0			0
$817$	14.5000	−	16.4300i	0.507289	−	0.574812i
$818$		0			0
$819$	29.9219	−	51.8263i	1.04556	−	1.81096i
$820$		0			0
$821$	4.32200	+	7.48592i	0.150839	+	0.261260i	0.931536	−	0.363649i	$-0.118469\pi$
$821$	4.32200	+	7.48592i	0.150839	+	0.261260i	−0.780697	+	0.624909i	$0.785136\pi$
$822$		0			0
$823$	35.1614	−	20.3004i	1.22565	−	0.707628i	0.259532	−	0.965735i	$-0.416432\pi$
$823$	35.1614	−	20.3004i	1.22565	−	0.707628i	0.966117	+	0.258106i	$0.0830985\pi$
$824$		0			0
$825$	−17.8782	+	18.9877i	−0.622440	+	0.661067i
$826$		0			0
$827$	1.64002	−	0.946864i	0.0570290	−	0.0329257i	−0.471214	−	0.882019i	$-0.656184\pi$
$827$	1.64002	−	0.946864i	0.0570290	−	0.0329257i	0.528243	+	0.849093i	$0.322851\pi$
$828$		0			0
$829$	54.2488			1.88414			0.942070	−	0.335416i	$-0.108877\pi$
$829$	54.2488			1.88414			0.942070	+	0.335416i	$0.108877\pi$
$830$		0			0
$831$	−15.8169	+	27.3957i	−0.548683	+	0.950347i
$832$		0			0
$833$	38.5678	+	22.2671i	1.33630	+	0.771511i
$834$		0			0
$835$	14.8041	+	5.87274i	0.512316	+	0.203235i
$836$		0			0
$837$			11.0542i			0.382090i
$838$		0			0
$839$	19.4931	−	33.7630i	0.672976	−	1.16563i	−0.304080	−	0.952647i	$-0.598349\pi$
$839$	19.4931	−	33.7630i	0.672976	−	1.16563i	0.977056	−	0.212982i	$-0.0683177\pi$
$840$		0			0
$841$	−22.3295	+	38.6758i	−0.769982	+	1.33365i
$842$		0			0
$843$			11.1160i			0.382855i
$844$		0			0
$845$	−5.91268	+	0.869090i	−0.203402	+	0.0298976i
$846$		0			0
$847$			27.3125i			0.938469i
$848$		0			0
$849$	−32.4891	−	56.2728i	−1.11502	−	1.93128i
$850$		0			0
$851$	23.2070	+	40.1958i	0.795527	+	1.37789i
$852$		0			0
$853$	26.5103	+	15.3058i	0.907697	+	0.524059i	0.879689	−	0.475549i	$-0.157750\pi$
$853$	26.5103	+	15.3058i	0.907697	+	0.524059i	0.0280076	+	0.999608i	$0.491084\pi$
$854$		0			0
$855$	42.8989	+	27.9308i	1.46711	+	0.955213i
$856$		0			0
$857$	−11.6725	−	6.73913i	−0.398726	−	0.230204i	0.287208	−	0.957868i	$-0.407273\pi$
$857$	−11.6725	−	6.73913i	−0.398726	−	0.230204i	−0.685934	+	0.727664i	$0.740606\pi$
$858$		0			0
$859$	−4.96411	−	8.59809i	−0.169373	−	0.293363i	0.768826	−	0.639458i	$-0.220841\pi$
$859$	−4.96411	−	8.59809i	−0.169373	−	0.293363i	−0.938200	+	0.346094i	$0.887508\pi$
$860$		0			0
$861$	41.3217	+	71.5713i	1.40824	+	2.43914i
$862$		0			0
$863$		−	36.8000i		−	1.25269i	−0.779547	−	0.626344i	$-0.784551\pi$
$863$		−	36.8000i		−	1.25269i	0.779547	−	0.626344i	$-0.215449\pi$
$864$		0			0
$865$	5.58562	+	38.0006i	0.189917	+	1.29206i
$866$		0			0
$867$		−	134.681i		−	4.57400i
$868$		0			0
$869$	−3.79018	+	6.56479i	−0.128573	+	0.222695i
$870$		0			0
$871$	14.9240	−	25.8491i	0.505679	−	0.875862i
$872$		0			0
$873$			41.9212i			1.41882i
$874$		0			0
$875$	16.8071	+	35.9027i	0.568183	+	1.21373i
$876$		0			0
$877$	4.96267	+	2.86520i	0.167577	+	0.0967509i	0.581443	−	0.813587i	$-0.302488\pi$
$877$	4.96267	+	2.86520i	0.167577	+	0.0967509i	−0.413866	+	0.910338i	$0.635822\pi$
$878$		0			0
$879$	−40.8605	+	70.7725i	−1.37819	+	2.38710i
$880$		0			0
$881$	21.5926			0.727474			0.363737	−	0.931502i	$-0.381501\pi$
$881$	21.5926			0.727474			0.363737	+	0.931502i	$0.381501\pi$
$882$		0			0
$883$	36.0904	−	20.8368i	1.21454	−	0.701214i	0.250794	−	0.968040i	$-0.419308\pi$
$883$	36.0904	−	20.8368i	1.21454	−	0.701214i	0.963745	+	0.266826i	$0.0859749\pi$
$884$		0			0
$885$	−11.4731	−	4.55135i	−0.385664	−	0.152992i
$886$		0			0
$887$	43.9856	−	25.3951i	1.47689	−	0.852685i	0.477234	−	0.878776i	$-0.341639\pi$
$887$	43.9856	−	25.3951i	1.47689	−	0.852685i	0.999660	+	0.0260915i	$0.00830612\pi$
$888$		0			0
$889$	−0.368839	−	0.638849i	−0.0123705	−	0.0214263i
$890$		0			0
$891$	2.56713	−	4.44639i	0.0860019	−	0.148960i
$892$		0			0
$893$	−1.87279	−	5.57434i	−0.0626705	−	0.186538i
$894$		0			0
$895$	4.69784	+	5.93531i	0.157031	+	0.198395i
$896$		0			0
$897$	67.3927	−	38.9092i	2.25018	−	1.29914i
$898$		0			0
$899$	7.33263	+	12.7005i	0.244557	+	0.423585i
$900$		0			0
$901$	17.7387			0.590962
$902$		0			0
$903$	−44.3446	+	25.6024i	−1.47570	+	0.851994i
$904$		0			0
$905$	−17.1875	+	43.3265i	−0.571333	+	1.44022i
$906$		0			0
$907$	−17.4646	−	10.0832i	−0.579902	−	0.334806i	0.181193	−	0.983448i	$-0.442004\pi$
$907$	−17.4646	−	10.0832i	−0.579902	−	0.334806i	−0.761094	+	0.648641i	$0.775338\pi$
$908$		0			0
$909$	−12.9584	+	22.4445i	−0.429802	+	0.744439i
$910$		0			0
$911$	47.2962			1.56699			0.783496	−	0.621397i	$-0.213434\pi$
$911$	47.2962			1.56699			0.783496	+	0.621397i	$0.213434\pi$
$912$		0			0
$913$		−	11.4441i		−	0.378745i
$914$		0			0
$915$	28.5120	−	22.5675i	0.942578	−	0.746058i
$916$		0			0
$917$	−46.3919	−	26.7844i	−1.53200	−	0.884498i
$918$		0			0
$919$	33.8678			1.11719			0.558597	−	0.829439i	$-0.311340\pi$
$919$	33.8678			1.11719			0.558597	+	0.829439i	$0.311340\pi$
$920$		0			0
$921$	−20.2751	−	35.1175i	−0.668087	−	1.15716i
$922$		0			0
$923$			18.9195i			0.622744i
$924$		0			0
$925$	26.7946	+	6.32224i	0.881001	+	0.207874i
$926$		0			0
$927$	−25.3022	+	14.6083i	−0.831035	+	0.479798i
$928$		0			0
$929$	−0.457146	+	0.791800i	−0.0149985	+	0.0259781i	−0.873427	−	0.486955i	$-0.838108\pi$
$929$	−0.457146	+	0.791800i	−0.0149985	+	0.0259781i	0.858429	+	0.512933i	$0.171441\pi$
$930$		0			0
$931$	−4.81272	+	23.8054i	−0.157731	+	0.780191i
$932$		0			0
$933$	−40.9666	−	23.6521i	−1.34119	−	0.774334i
$934$		0			0
$935$	4.71930	+	32.1068i	0.154337	+	1.05000i
$936$		0			0
$937$	−45.0186	+	25.9915i	−1.47069	+	0.849106i	−0.999459	−	0.0329014i	$-0.989525\pi$
$937$	−45.0186	+	25.9915i	−1.47069	+	0.849106i	−0.471236	+	0.882007i	$0.656192\pi$
$938$		0			0
$939$	71.7682			2.34207
$940$		0			0
$941$	12.4228	+	21.5169i	0.404972	+	0.701432i	0.994318	−	0.106449i	$-0.0339480\pi$
$941$	12.4228	+	21.5169i	0.404972	+	0.701432i	−0.589346	+	0.807880i	$0.700615\pi$
$942$		0			0
$943$			68.3969i			2.22731i
$944$		0			0
$945$	−31.8321	−	40.2171i	−1.03550	−	1.30826i
$946$		0			0
$947$	−24.0042	−	13.8588i	−0.780032	−	0.450352i	0.0564097	−	0.998408i	$-0.482035\pi$
$947$	−24.0042	−	13.8588i	−0.780032	−	0.450352i	−0.836442	+	0.548056i	$0.815368\pi$
$948$		0			0
$949$	−10.4909			−0.340550
$950$		0			0
$951$	6.33593			0.205457
$952$		0			0
$953$	−14.3605	−	8.29103i	−0.465182	−	0.268573i	0.249039	−	0.968494i	$-0.419885\pi$
$953$	−14.3605	−	8.29103i	−0.465182	−	0.268573i	−0.714221	+	0.699921i	$0.753219\pi$
$954$		0			0
$955$	6.36697	+	8.04411i	0.206030	+	0.260301i
$956$		0			0
$957$		−	44.7661i		−	1.44708i
$958$		0			0
$959$	9.34072	+	16.1786i	0.301627	+	0.522434i
$960$		0			0
$961$	−28.0802			−0.905813
$962$		0			0
$963$	41.4926	−	23.9558i	1.33708	−	0.771964i
$964$		0			0
$965$	−6.54238	−	44.5098i	−0.210607	−	1.43282i
$966$		0			0
$967$	−16.5612	−	9.56159i	−0.532571	−	0.307480i	0.209492	−	0.977810i	$-0.432819\pi$
$967$	−16.5612	−	9.56159i	−0.532571	−	0.307480i	−0.742063	+	0.670330i	$0.766152\pi$
$968$		0			0
$969$	94.8704	−	31.8732i	3.04767	−	1.02392i
$970$		0			0
$971$	7.56801	−	13.1082i	0.242869	−	0.420661i	−0.718661	−	0.695360i	$-0.755245\pi$
$971$	7.56801	−	13.1082i	0.242869	−	0.420661i	0.961530	+	0.274699i	$0.0885782\pi$
$972$		0			0
$973$	20.7782	−	11.9963i	0.666120	−	0.384584i
$974$		0			0
$975$	10.5999	−	44.9241i	0.339470	−	1.43872i
$976$		0			0
$977$		−	5.83858i		−	0.186793i	−0.995629	−	0.0933964i	$-0.970228\pi$
$977$		−	5.83858i		−	0.186793i	0.995629	−	0.0933964i	$-0.0297724\pi$
$978$		0			0
$979$	−4.96873	−	8.60609i	−0.158801	−	0.275052i
$980$		0			0
$981$	79.5391			2.53949
$982$		0			0
$983$	17.9231	+	10.3479i	0.571657	+	0.330047i	0.757811	−	0.652474i	$-0.226269\pi$
$983$	17.9231	+	10.3479i	0.571657	+	0.330047i	−0.186154	+	0.982521i	$0.559602\pi$
$984$		0			0
$985$	−1.72428	+	1.36478i	−0.0549401	+	0.0434855i
$986$		0			0
$987$			13.7410i			0.437381i
$988$		0			0
$989$	−42.3778			−1.34754
$990$		0			0
$991$	−22.9776	+	39.7984i	−0.729907	+	1.26424i	0.227014	+	0.973891i	$0.427104\pi$
$991$	−22.9776	+	39.7984i	−0.729907	+	1.26424i	−0.956922	+	0.290345i	$0.906230\pi$
$992$		0			0
$993$	68.5171	+	39.5584i	2.17432	+	1.25535i
$994$		0			0
$995$	9.63836	−	24.2965i	0.305556	−	0.770250i
$996$		0			0
$997$	−6.31974	+	3.64870i	−0.200148	+	0.115556i	−0.596725	−	0.802446i	$-0.703532\pi$
$997$	−6.31974	+	3.64870i	−0.200148	+	0.115556i	0.396576	+	0.918002i	$0.370198\pi$
$998$		0			0
$999$	−35.6200			−1.12697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.r.a.49.1	✓	20
3.2	odd	2		3420.2.bj.c.1189.4		20
5.2	odd	4		1900.2.i.g.201.1		20
5.3	odd	4		1900.2.i.g.201.10		20
5.4	even	2	inner	380.2.r.a.49.10	yes	20
15.14	odd	2		3420.2.bj.c.1189.10		20
19.7	even	3	inner	380.2.r.a.349.10	yes	20
57.26	odd	6		3420.2.bj.c.2629.10		20
95.7	odd	12		1900.2.i.g.501.1		20
95.64	even	6	inner	380.2.r.a.349.1	yes	20
95.83	odd	12		1900.2.i.g.501.10		20
285.254	odd	6		3420.2.bj.c.2629.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.1	✓	20	1.1	even	1	trivial
380.2.r.a.49.10	yes	20	5.4	even	2	inner
380.2.r.a.349.1	yes	20	95.64	even	6	inner
380.2.r.a.349.10	yes	20	19.7	even	3	inner
1900.2.i.g.201.1		20	5.2	odd	4
1900.2.i.g.201.10		20	5.3	odd	4
1900.2.i.g.501.1		20	95.7	odd	12
1900.2.i.g.501.10		20	95.83	odd	12
3420.2.bj.c.1189.4		20	3.2	odd	2
3420.2.bj.c.1189.10		20	15.14	odd	2
3420.2.bj.c.2629.4		20	285.254	odd	6
3420.2.bj.c.2629.10		20	57.26	odd	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48777 - 1.43632i) q^{3} +(1.38776 + 1.75332i) q^{5} -3.54568i q^{7} +(2.62601 + 4.54838i) q^{9} -1.81575 q^{11} +(2.78308 - 1.60681i) q^{13} +(-0.934123 - 6.35512i) q^{15} +(-6.92193 - 3.99638i) q^{17} +(0.863760 - 4.27246i) q^{19} +(-5.09271 + 8.82084i) q^{21} +(-7.30026 + 4.21480i) q^{23} +(-1.14823 + 4.86637i) q^{25} -6.46921i q^{27} +(-4.29124 - 7.43265i) q^{29} -1.70874 q^{31} +(4.51718 + 2.60799i) q^{33} +(6.21669 - 4.92056i) q^{35} -5.50608i q^{37} -9.23155 q^{39} +(4.05694 - 7.02683i) q^{41} +(4.35373 + 2.51363i) q^{43} +(-4.33047 + 10.9163i) q^{45} +(1.16834 - 0.674543i) q^{47} -5.57183 q^{49} +(11.4801 + 19.8842i) q^{51} +(-1.92201 + 1.10967i) q^{53} +(-2.51983 - 3.18359i) q^{55} +(-8.28544 + 9.38828i) q^{57} +(0.960774 - 1.66411i) q^{59} +(2.83047 + 4.90251i) q^{61} +(16.1271 - 9.31098i) q^{63} +(6.67950 + 2.64974i) q^{65} +(8.04360 - 4.64397i) q^{67} +24.2152 q^{69} +(-2.94365 + 5.09854i) q^{71} +(-2.82716 - 1.63226i) q^{73} +(9.84618 - 10.4572i) q^{75} +6.43807i q^{77} +(2.08739 - 3.61546i) q^{79} +(-1.41381 + 2.44879i) q^{81} +6.30268i q^{83} +(-2.59909 - 17.6824i) q^{85} +24.6543i q^{87} +(2.73646 + 4.73968i) q^{89} +(-5.69723 - 9.86789i) q^{91} +(4.25096 + 2.45429i) q^{93} +(8.68966 - 4.41472i) q^{95} +(6.91255 + 3.99096i) q^{97} +(-4.76818 - 8.25873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65}+ \cdots - 20 q^{99}+O(q^{100}) \) 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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