LMFDB - Embedded newform 1900.2.i.g.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(201,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.i (of order $3$, 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:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.1
Root			$1.43632 - 2.48777i$ of defining polynomial
Character	$\chi$	$=$	1900.501
Dual form			1900.2.i.g.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43632 - 2.48777i) q^{3} +3.54568 q^{7} +(-2.62601 + 4.54838i) q^{9} +O(q^{10})$	$q+(-1.43632 - 2.48777i) q^{3} +3.54568 q^{7} +(-2.62601 + 4.54838i) q^{9} -1.81575 q^{11} +(-1.60681 + 2.78308i) q^{13} +(3.99638 + 6.92193i) q^{17} +(-0.863760 - 4.27246i) q^{19} +(-5.09271 - 8.82084i) q^{21} +(4.21480 - 7.30026i) q^{23} +6.46921 q^{27} +(4.29124 - 7.43265i) q^{29} -1.70874 q^{31} +(2.60799 + 4.51718i) q^{33} +5.50608 q^{37} +9.23155 q^{39} +(4.05694 + 7.02683i) q^{41} +(2.51363 + 4.35373i) q^{43} +(0.674543 - 1.16834i) q^{47} +5.57183 q^{49} +(11.4801 - 19.8842i) q^{51} +(1.10967 - 1.92201i) q^{53} +(-9.38828 + 8.28544i) q^{57} +(-0.960774 - 1.66411i) q^{59} +(2.83047 - 4.90251i) q^{61} +(-9.31098 + 16.1271i) q^{63} +(4.64397 - 8.04360i) q^{67} -24.2152 q^{69} +(-2.94365 - 5.09854i) q^{71} +(-1.63226 - 2.82716i) q^{73} -6.43807 q^{77} +(-2.08739 - 3.61546i) q^{79} +(-1.41381 - 2.44879i) q^{81} +6.30268 q^{83} -24.6543 q^{87} +(-2.73646 + 4.73968i) q^{89} +(-5.69723 + 9.86789i) q^{91} +(2.45429 + 4.25096i) q^{93} +(-3.99096 - 6.91255i) q^{97} +(4.76818 - 8.25873i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^9	$ 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100}) $ 20 * q - 10 * q^9 - 14 * q^19 - 8 * q^21 + 16 * q^29 + 8 * q^31 + 8 * q^39 + 26 * q^41 + 44 * q^49 + 26 * q^51 - 4 * q^59 + 2 * q^61 - 48 * q^69 - 2 * q^71 + 16 * q^79 + 26 * q^81 + 40 * q^89 - 4 * q^91 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.43632	−	2.48777i	−0.829257	−	1.43632i	−0.898622	−	0.438725i	$-0.855430\pi$
$3$	−1.43632	−	2.48777i	−0.829257	−	1.43632i	0.0693641	−	0.997591i	$-0.477903\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.54568			1.34014			0.670070	−	0.742298i	$-0.266264\pi$
$7$	3.54568			1.34014			0.670070	+	0.742298i	$0.266264\pi$
$8$		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
$13$	−1.60681	+	2.78308i	−0.445649	+	0.771887i	−0.998097	−	0.0616606i	$-0.980360\pi$
$13$	−1.60681	+	2.78308i	−0.445649	+	0.771887i	0.552448	+	0.833547i	$0.313694\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.99638	+	6.92193i	0.969264	+	1.67881i	0.697694	+	0.716396i	$0.254210\pi$
$17$	3.99638	+	6.92193i	0.969264	+	1.67881i	0.271570	+	0.962419i	$0.412457\pi$
$18$		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
$23$	4.21480	−	7.30026i	0.878848	−	1.52221i	0.0262406	−	0.999656i	$-0.491646\pi$
$23$	4.21480	−	7.30026i	0.878848	−	1.52221i	0.852607	−	0.522553i	$-0.175020\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	6.46921			1.24500
$28$		0			0
$29$	4.29124	−	7.43265i	0.796863	−	1.38021i	−0.124786	−	0.992184i	$-0.539824\pi$
$29$	4.29124	−	7.43265i	0.796863	−	1.38021i	0.921649	−	0.388024i	$-0.126842\pi$
$30$		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
$33$	2.60799	+	4.51718i	0.453994	+	0.786340i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.50608			0.905193			0.452597	−	0.891715i	$-0.350498\pi$
$37$	5.50608			0.905193			0.452597	+	0.891715i	$0.350498\pi$
$38$		0			0
$39$	9.23155			1.47823
$40$		0			0
$41$	4.05694	+	7.02683i	0.633588	+	1.09741i	0.986812	+	0.161868i	$0.0517520\pi$
$41$	4.05694	+	7.02683i	0.633588	+	1.09741i	−0.353224	+	0.935539i	$0.614915\pi$
$42$		0			0
$43$	2.51363	+	4.35373i	0.383325	+	0.663938i	0.991535	−	0.129838i	$-0.0414457\pi$
$43$	2.51363	+	4.35373i	0.383325	+	0.663938i	−0.608211	+	0.793776i	$0.708112\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.674543	−	1.16834i	0.0983922	−	0.170420i	−0.812627	−	0.582784i	$-0.801963\pi$
$47$	0.674543	−	1.16834i	0.0983922	−	0.170420i	0.911019	+	0.412364i	$0.135297\pi$
$48$		0			0
$49$	5.57183			0.795976
$50$		0			0
$51$	11.4801	−	19.8842i	1.60754	−	2.78434i
$52$		0			0
$53$	1.10967	−	1.92201i	0.152426	−	0.264009i	−0.779693	−	0.626162i	$-0.784625\pi$
$53$	1.10967	−	1.92201i	0.152426	−	0.264009i	0.932119	+	0.362153i	$0.117958\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−9.38828	+	8.28544i	−1.24351	+	1.09743i
$58$		0			0
$59$	−0.960774	−	1.66411i	−0.125082	−	0.216649i	0.796683	−	0.604398i	$-0.206586\pi$
$59$	−0.960774	−	1.66411i	−0.125082	−	0.216649i	−0.921765	+	0.387749i	$0.873253\pi$
$60$		0			0
$61$	2.83047	−	4.90251i	0.362404	−	0.627702i	−0.625952	−	0.779862i	$-0.715289\pi$
$61$	2.83047	−	4.90251i	0.362404	−	0.627702i	0.988356	+	0.152159i	$0.0486227\pi$
$62$		0			0
$63$	−9.31098	+	16.1271i	−1.17307	+	2.03182i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.64397	−	8.04360i	0.567352	−	0.982682i	−0.429475	−	0.903079i	$-0.641301\pi$
$67$	4.64397	−	8.04360i	0.567352	−	0.982682i	0.996827	−	0.0796032i	$-0.0253653\pi$
$68$		0			0
$69$	−24.2152			−2.91516
$70$		0			0
$71$	−2.94365	−	5.09854i	−0.349346	−	0.605086i	0.636787	−	0.771040i	$-0.280263\pi$
$71$	−2.94365	−	5.09854i	−0.349346	−	0.605086i	−0.986134	+	0.165954i	$0.946930\pi$
$72$		0			0
$73$	−1.63226	−	2.82716i	−0.191042	−	0.330894i	0.754554	−	0.656238i	$-0.227853\pi$
$73$	−1.63226	−	2.82716i	−0.191042	−	0.330894i	−0.945596	+	0.325344i	$0.894520\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.43807			−0.733687
$78$		0			0
$79$	−2.08739	−	3.61546i	−0.234850	−	0.406771i	0.724379	−	0.689402i	$-0.242126\pi$
$79$	−2.08739	−	3.61546i	−0.234850	−	0.406771i	−0.959229	+	0.282630i	$0.908793\pi$
$80$		0			0
$81$	−1.41381	−	2.44879i	−0.157090	−	0.272087i
$82$		0			0
$83$	6.30268			0.691809			0.345905	−	0.938270i	$-0.387572\pi$
$83$	6.30268			0.691809			0.345905	+	0.938270i	$0.387572\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−24.6543			−2.64322
$88$		0			0
$89$	−2.73646	+	4.73968i	−0.290064	+	0.502405i	−0.973825	−	0.227301i	$-0.927010\pi$
$89$	−2.73646	+	4.73968i	−0.290064	+	0.502405i	0.683761	+	0.729706i	$0.260343\pi$
$90$		0			0
$91$	−5.69723	+	9.86789i	−0.597232	+	1.03444i
$92$		0			0
$93$	2.45429	+	4.25096i	0.254499	+	0.440804i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.99096	−	6.91255i	−0.405221	−	0.701863i	0.589126	−	0.808041i	$-0.299472\pi$
$97$	−3.99096	−	6.91255i	−0.405221	−	0.701863i	−0.994347	+	0.106178i	$0.966139\pi$
$98$		0			0
$99$	4.76818	−	8.25873i	0.479220	−	0.830034i
$100$		0			0
$101$	2.46731	−	4.27351i	0.245507	−	0.425230i	−0.716767	−	0.697313i	$-0.754379\pi$
$101$	2.46731	−	4.27351i	0.245507	−	0.425230i	0.962274	+	0.272082i	$0.0877123\pi$
$102$		0			0
$103$	5.56291			0.548130			0.274065	−	0.961711i	$-0.411632\pi$
$103$	5.56291			0.548130			0.274065	+	0.961711i	$0.411632\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.12251			0.881907			0.440953	−	0.897530i	$-0.354640\pi$
$107$	9.12251			0.881907			0.440953	+	0.897530i	$0.354640\pi$
$108$		0			0
$109$	−7.57225	−	13.1155i	−0.725290	−	1.25624i	−0.958855	−	0.283898i	$-0.908372\pi$
$109$	−7.57225	−	13.1155i	−0.725290	−	1.25624i	0.233565	−	0.972341i	$-0.424961\pi$
$110$		0			0
$111$	−7.90847	−	13.6979i	−0.750638	−	1.30014i
$112$		0			0
$113$	4.46091			0.419647			0.209823	−	0.977739i	$-0.432711\pi$
$113$	4.46091			0.419647			0.209823	+	0.977739i	$0.432711\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−8.43899	−	14.6168i	−0.780185	−	1.35132i
$118$		0			0
$119$	14.1699	+	24.5429i	1.29895	+	2.24985i
$120$		0			0
$121$	−7.70304			−0.700277
$122$		0			0
$123$	11.6541	−	20.1855i	1.05082	−	1.82007i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.104025	−	0.180177i	0.00923073	−	0.0159881i	−0.861373	−	0.507973i	$-0.830395\pi$
$127$	0.104025	−	0.180177i	0.00923073	−	0.0159881i	0.870604	+	0.491985i	$0.163728\pi$
$128$		0			0
$129$	7.22073	−	12.5067i	0.635750	−	1.10115i
$130$		0			0
$131$	7.55409	+	13.0841i	0.660004	+	1.14316i	0.980614	+	0.195950i	$0.0627789\pi$
$131$	7.55409	+	13.0841i	0.660004	+	1.14316i	−0.320610	+	0.947211i	$0.603888\pi$
$132$		0			0
$133$	−3.06261	−	15.1488i	−0.265562	−	1.31356i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.63439	+	4.56291i	−0.225072	+	0.389835i	−0.956341	−	0.292253i	$-0.905595\pi$
$137$	−2.63439	+	4.56291i	−0.225072	+	0.389835i	0.731269	+	0.682089i	$0.238928\pi$
$138$		0			0
$139$	−3.38336	+	5.86016i	−0.286973	+	0.497052i	−0.973086	−	0.230443i	$-0.925982\pi$
$139$	−3.38336	+	5.86016i	−0.286973	+	0.497052i	0.686113	+	0.727495i	$0.259316\pi$
$140$		0			0
$141$	−3.87543			−0.326370
$142$		0			0
$143$	2.91757	−	5.05338i	0.243979	−	0.422585i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.00291	−	13.8614i	−0.660069	−	1.14327i
$148$		0			0
$149$	−4.83003	−	8.36586i	−0.395692	−	0.685358i	0.597498	−	0.801871i	$-0.296162\pi$
$149$	−4.83003	−	8.36586i	−0.395692	−	0.685358i	−0.993189	+	0.116513i	$0.962828\pi$
$150$		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
$153$	−41.9781			−3.39373
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.788721	+	1.36610i	0.0629468	+	0.109027i	0.895781	−	0.444495i	$-0.146617\pi$
$157$	0.788721	+	1.36610i	0.0629468	+	0.109027i	−0.832835	+	0.553522i	$0.813284\pi$
$158$		0			0
$159$	−6.37537			−0.505600
$160$		0			0
$161$	14.9443	−	25.8844i	1.17778	−	2.03997i
$162$		0			0
$163$	−16.0641			−1.25823			−0.629117	−	0.777310i	$-0.716584\pi$
$163$	−16.0641			−1.25823			−0.629117	+	0.777310i	$0.716584\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.56125	−	6.16826i	0.275578	−	0.477314i	−0.694703	−	0.719297i	$-0.744464\pi$
$167$	3.56125	−	6.16826i	0.275578	−	0.477314i	0.970281	+	0.241982i	$0.0777976\pi$
$168$		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
$173$	8.58850	+	14.8757i	0.652972	+	1.13098i	0.982398	+	0.186799i	$0.0598113\pi$
$173$	8.58850	+	14.8757i	0.652972	+	1.13098i	−0.329427	+	0.944181i	$0.606855\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.75995	+	4.78038i	−0.207451	+	0.359315i
$178$		0			0
$179$	−3.38519			−0.253021			−0.126510	−	0.991965i	$-0.540378\pi$
$179$	−3.38519			−0.253021			−0.126510	+	0.991965i	$0.540378\pi$
$180$		0			0
$181$	10.4226	−	18.0524i	0.774704	−	1.34183i	−0.160257	−	0.987075i	$-0.551232\pi$
$181$	10.4226	−	18.0524i	0.774704	−	1.34183i	0.934961	−	0.354751i	$-0.115434\pi$
$182$		0			0
$183$	−16.2618			−1.20210
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.25643	−	12.5685i	−0.530643	−	0.919101i
$188$		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
$193$	−10.0596	−	17.4238i	−0.724108	−	1.25419i	−0.959340	−	0.282252i	$-0.908918\pi$
$193$	−10.0596	−	17.4238i	−0.724108	−	1.25419i	0.235232	−	0.971939i	$-0.424415\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.983439			−0.0700671			−0.0350336	−	0.999386i	$-0.511154\pi$
$197$	−0.983439			−0.0700671			−0.0350336	+	0.999386i	$0.511154\pi$
$198$		0			0
$199$	5.84473	−	10.1234i	0.414322	−	0.717626i	−0.581035	−	0.813878i	$-0.697352\pi$
$199$	5.84473	−	10.1234i	0.414322	−	0.717626i	0.995357	+	0.0962520i	$0.0306855\pi$
$200$		0			0
$201$	−26.6809			−1.88192
$202$		0			0
$203$	15.2154	−	26.3538i	1.06791	−	1.84967i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	22.1362	+	38.3411i	1.53857	+	2.66489i
$208$		0			0
$209$	1.56837	+	7.75773i	0.108487	+	0.536613i
$210$		0			0
$211$	−5.35987	−	9.28357i	−0.368989	−	0.639107i	0.620419	−	0.784270i	$-0.286963\pi$
$211$	−5.35987	−	9.28357i	−0.368989	−	0.639107i	−0.989408	+	0.145163i	$0.953629\pi$
$212$		0			0
$213$	−8.45601	+	14.6462i	−0.579396	+	1.00354i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.05865			−0.411288
$218$		0			0
$219$	−4.68888	+	8.12139i	−0.316845	+	0.548792i
$220$		0			0
$221$	−25.6857			−1.72781
$222$		0			0
$223$	10.2936	+	17.8291i	0.689313	+	1.19393i	0.972060	+	0.234731i	$0.0754210\pi$
$223$	10.2936	+	17.8291i	0.689313	+	1.19393i	−0.282747	+	0.959195i	$0.591246\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.47441			0.496094			0.248047	−	0.968748i	$-0.420211\pi$
$227$	7.47441			0.496094			0.248047	+	0.968748i	$0.420211\pi$
$228$		0			0
$229$	−11.0863			−0.732604			−0.366302	−	0.930496i	$-0.619376\pi$
$229$	−11.0863			−0.732604			−0.366302	+	0.930496i	$0.619376\pi$
$230$		0			0
$231$	9.24711	+	16.0165i	0.608415	+	1.05381i
$232$		0			0
$233$	9.16743	+	15.8785i	0.600578	+	1.04023i	0.992734	+	0.120333i	$0.0383962\pi$
$233$	9.16743	+	15.8785i	0.600578	+	1.04023i	−0.392155	+	0.919899i	$0.628270\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.99630	+	10.3859i	−0.389501	+	0.674636i
$238$		0			0
$239$	11.8518			0.766630			0.383315	−	0.923618i	$-0.374782\pi$
$239$	11.8518			0.766630			0.383315	+	0.923618i	$0.374782\pi$
$240$		0			0
$241$	−2.34317	+	4.05850i	−0.150937	+	0.261431i	−0.931572	−	0.363556i	$-0.881562\pi$
$241$	−2.34317	+	4.05850i	−0.150937	+	0.261431i	0.780635	+	0.624987i	$0.214896\pi$
$242$		0			0
$243$	5.64247	−	9.77304i	0.361964	−	0.626941i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.2785	+	4.46112i	0.844890	+	0.283854i
$248$		0			0
$249$	−9.05264	−	15.6796i	−0.573688	−	0.993657i
$250$		0			0
$251$	0.0510129	−	0.0883569i	0.00321990	−	0.00557704i	−0.864411	−	0.502786i	$-0.832308\pi$
$251$	0.0510129	−	0.0883569i	0.00321990	−	0.00557704i	0.867631	+	0.497209i	$0.165642\pi$
$252$		0			0
$253$	−7.65304	+	13.2555i	−0.481143	+	0.833363i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.69424	−	13.3268i	0.479953	−	0.831303i	−0.519782	−	0.854299i	$-0.673987\pi$
$257$	7.69424	−	13.3268i	0.479953	−	0.831303i	0.999736	+	0.0229953i	$0.00732027\pi$
$258$		0			0
$259$	19.5228			1.21309
$260$		0			0
$261$	22.5377	+	39.0364i	1.39505	+	2.41629i
$262$		0			0
$263$	9.78416	+	16.9467i	0.603317	+	1.04498i	0.992315	+	0.123737i	$0.0394880\pi$
$263$	9.78416	+	16.9467i	0.603317	+	1.04498i	−0.388998	+	0.921239i	$0.627179\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	15.7217			0.962150
$268$		0			0
$269$	−0.585331	−	1.01382i	−0.0356883	−	0.0618139i	0.847630	−	0.530588i	$-0.178029\pi$
$269$	−0.585331	−	1.01382i	−0.0356883	−	0.0618139i	−0.883318	+	0.468775i	$0.844696\pi$
$270$		0			0
$271$	6.40442	+	11.0928i	0.389041	+	0.673838i	0.992321	−	0.123691i	$-0.0394732\pi$
$271$	6.40442	+	11.0928i	0.389041	+	0.673838i	−0.603280	+	0.797529i	$0.706140\pi$
$272$		0			0
$273$	32.7321			1.98104
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.0122			0.661656			0.330828	−	0.943691i	$-0.392672\pi$
$277$	11.0122			0.661656			0.330828	+	0.943691i	$0.392672\pi$
$278$		0			0
$279$	4.48717	−	7.77201i	0.268640	−	0.465298i
$280$		0			0
$281$	−1.93481	+	3.35119i	−0.115421	+	0.199915i	−0.917948	−	0.396701i	$-0.870155\pi$
$281$	−1.93481	+	3.35119i	−0.115421	+	0.199915i	0.802527	+	0.596616i	$0.203488\pi$
$282$		0			0
$283$	11.3099	+	19.5893i	0.672303	+	1.16446i	0.977249	+	0.212093i	$0.0680280\pi$
$283$	11.3099	+	19.5893i	0.672303	+	1.16446i	−0.304947	+	0.952369i	$0.598639\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.3846	+	24.9149i	0.849097	+	1.47068i
$288$		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
$293$	−28.4482			−1.66196			−0.830980	−	0.556303i	$-0.812219\pi$
$293$	−28.4482			−1.66196			−0.830980	+	0.556303i	$0.812219\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−11.7465			−0.681600
$298$		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
$303$	−14.1754			−0.814353
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.05802	−	12.2248i	−0.402822	−	0.697709i	0.591243	−	0.806494i	$-0.298637\pi$
$307$	−7.05802	−	12.2248i	−0.402822	−	0.697709i	−0.994065	+	0.108785i	$0.965304\pi$
$308$		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
$313$	12.4917	−	21.6363i	0.706073	−	1.22295i	−0.260229	−	0.965547i	$-0.583798\pi$
$313$	12.4917	−	21.6363i	0.706073	−	1.22295i	0.966303	−	0.257408i	$-0.0828685\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.10281	+	1.91012i	−0.0619399	+	0.107283i	−0.895332	−	0.445398i	$-0.853062\pi$
$317$	−1.10281	+	1.91012i	−0.0619399	+	0.107283i	0.833393	+	0.552681i	$0.186395\pi$
$318$		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
$323$	26.1218	−	23.0533i	1.45345	−	1.28272i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−21.7523	+	37.6761i	−1.20290	+	2.08349i
$328$		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
$333$	−14.4590	+	25.0437i	−0.792348	+	1.37239i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.20668	+	15.9464i	0.501520	+	0.868658i	0.999998	+	0.00175582i	$0.000558895\pi$
$337$	9.20668	+	15.9464i	0.501520	+	0.868658i	−0.498479	+	0.866902i	$0.666108\pi$
$338$		0			0
$339$	−6.40727	−	11.0977i	−0.347995	−	0.602745i
$340$		0			0
$341$	3.10265			0.168018
$342$		0			0
$343$	−5.06383			−0.273421
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.1677	−	22.8072i	−0.706881	−	1.22435i	−0.966009	−	0.258510i	$-0.916768\pi$
$347$	−13.1677	−	22.8072i	−0.706881	−	1.22435i	0.259128	−	0.965843i	$-0.416565\pi$
$348$		0			0
$349$	−7.40515			−0.396388			−0.198194	−	0.980163i	$-0.563508\pi$
$349$	−7.40515			−0.396388			−0.198194	+	0.980163i	$0.563508\pi$
$350$		0			0
$351$	−10.3948	+	18.0043i	−0.554833	+	0.960999i
$352$		0			0
$353$	−2.42201			−0.128910			−0.0644552	−	0.997921i	$-0.520531\pi$
$353$	−2.42201			−0.128910			−0.0644552	+	0.997921i	$0.520531\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	40.7048	−	70.5028i	2.15433	−	3.73140i
$358$		0			0
$359$	−2.28083	−	3.95051i	−0.120377	−	0.208500i	0.799539	−	0.600614i	$-0.205077\pi$
$359$	−2.28083	−	3.95051i	−0.120377	−	0.208500i	−0.919917	+	0.392114i	$0.871744\pi$
$360$		0			0
$361$	−17.5078	+	7.38076i	−0.921465	+	0.388461i
$362$		0			0
$363$	11.0640	+	19.1634i	0.580710	+	1.00582i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	5.26242	−	9.11478i	0.274696	−	0.475788i	−0.695362	−	0.718659i	$-0.744756\pi$
$367$	5.26242	−	9.11478i	0.274696	−	0.475788i	0.970058	+	0.242872i	$0.0780894\pi$
$368$		0			0
$369$	−42.6143			−2.21841
$370$		0			0
$371$	3.93455	−	6.81484i	0.204272	−	0.353809i
$372$		0			0
$373$	21.8633			1.13204			0.566019	−	0.824392i	$-0.308483\pi$
$373$	21.8633			1.13204			0.566019	+	0.824392i	$0.308483\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	13.7904	+	23.8857i	0.710243	+	1.23018i
$378$		0			0
$379$	9.33617			0.479567			0.239783	−	0.970826i	$-0.422924\pi$
$379$	9.33617			0.479567			0.239783	+	0.970826i	$0.422924\pi$
$380$		0			0
$381$	−0.597652			−0.0306186
$382$		0			0
$383$	−2.75581	−	4.77320i	−0.140815	−	0.243899i	0.786989	−	0.616968i	$-0.211639\pi$
$383$	−2.75581	−	4.77320i	−0.140815	−	0.243899i	−0.927804	+	0.373068i	$0.878306\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−26.4032			−1.34215
$388$		0			0
$389$	−8.50605	+	14.7329i	−0.431274	+	0.746988i	−0.996983	−	0.0776163i	$-0.975269\pi$
$389$	−8.50605	+	14.7329i	−0.431274	+	0.746988i	0.565709	+	0.824605i	$0.308602\pi$
$390$		0			0
$391$	67.3758			3.40734
$392$		0			0
$393$	21.7001	−	37.5857i	1.09463	−	1.89595i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	15.7110	+	27.2122i	0.788512	+	1.36574i	0.926878	+	0.375362i	$0.122482\pi$
$397$	15.7110	+	27.2122i	0.788512	+	1.36574i	−0.138366	+	0.990381i	$0.544185\pi$
$398$		0			0
$399$	−33.2878	+	29.3775i	−1.66647	+	1.47071i
$400$		0			0
$401$	13.4762	+	23.3415i	0.672971	+	1.16562i	0.977058	+	0.212976i	$0.0683155\pi$
$401$	13.4762	+	23.3415i	0.672971	+	1.16562i	−0.304087	+	0.952644i	$0.598351\pi$
$402$		0			0
$403$	2.74563	−	4.75556i	0.136769	−	0.236891i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.99767			−0.495566
$408$		0			0
$409$	17.0791	−	29.5819i	0.844509	−	1.46273i	−0.0415373	−	0.999137i	$-0.513226\pi$
$409$	17.0791	−	29.5819i	0.844509	−	1.46273i	0.886047	−	0.463596i	$-0.153441\pi$
$410$		0			0
$411$	15.1353			0.746569
$412$		0			0
$413$	−3.40660	−	5.90040i	−0.167628	−	0.290340i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	19.4383			0.951899
$418$		0			0
$419$	36.5998			1.78802			0.894009	−	0.448049i	$-0.147881\pi$
$419$	36.5998			1.78802			0.894009	+	0.448049i	$0.147881\pi$
$420$		0			0
$421$	−4.85007	−	8.40057i	−0.236378	−	0.409419i	0.723294	−	0.690540i	$-0.242627\pi$
$421$	−4.85007	−	8.40057i	−0.236378	−	0.409419i	−0.959672	+	0.281121i	$0.909294\pi$
$422$		0			0
$423$	3.54271	+	6.13615i	0.172252	+	0.298350i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	10.0359	−	17.3827i	0.485672	−	0.841209i
$428$		0			0
$429$	−16.7622			−0.809287
$430$		0			0
$431$	−14.4779	+	25.0764i	−0.697375	+	1.20789i	0.271999	+	0.962298i	$0.412315\pi$
$431$	−14.4779	+	25.0764i	−0.697375	+	1.20789i	−0.969373	+	0.245591i	$0.921018\pi$
$432$		0			0
$433$	−3.72388	+	6.44994i	−0.178958	+	0.309965i	−0.941524	−	0.336946i	$-0.890606\pi$
$433$	−3.72388	+	6.44994i	−0.178958	+	0.309965i	0.762566	+	0.646911i	$0.223939\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−34.8306	−	11.7019i	−1.66618	−	0.559779i
$438$		0			0
$439$	−5.70008	−	9.87283i	−0.272050	−	0.471204i	0.697337	−	0.716744i	$-0.254368\pi$
$439$	−5.70008	−	9.87283i	−0.272050	−	0.471204i	−0.969387	+	0.245539i	$0.921035\pi$
$440$		0			0
$441$	−14.6317	+	25.3428i	−0.696746	+	1.20680i
$442$		0			0
$443$	−3.84540	+	6.66042i	−0.182700	+	0.316446i	−0.942799	−	0.333361i	$-0.891817\pi$
$443$	−3.84540	+	6.66042i	−0.182700	+	0.316446i	0.760099	+	0.649807i	$0.225150\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.8749	+	24.0320i	−0.656260	+	1.13668i
$448$		0			0
$449$	37.0590			1.74892			0.874460	−	0.485097i	$-0.161216\pi$
$449$	37.0590			1.74892			0.874460	+	0.485097i	$0.161216\pi$
$450$		0			0
$451$	−7.36641	−	12.7590i	−0.346871	−	0.600797i
$452$		0			0
$453$	17.2726	+	29.9170i	0.811537	+	1.40562i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	22.1647			1.03682			0.518411	−	0.855131i	$-0.326524\pi$
$457$	22.1647			1.03682			0.518411	+	0.855131i	$0.326524\pi$
$458$		0			0
$459$	25.8534	+	44.7794i	1.20673	+	2.09012i
$460$		0			0
$461$	21.0779	+	36.5080i	0.981697	+	1.70035i	0.655783	+	0.754949i	$0.272339\pi$
$461$	21.0779	+	36.5080i	0.981697	+	1.70035i	0.325914	+	0.945400i	$0.394328\pi$
$462$		0			0
$463$	−5.16758			−0.240158			−0.120079	−	0.992764i	$-0.538315\pi$
$463$	−5.16758			−0.240158			−0.120079	+	0.992764i	$0.538315\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.7096			−0.588129			−0.294064	−	0.955786i	$-0.595008\pi$
$467$	−12.7096			−0.588129			−0.294064	+	0.955786i	$0.595008\pi$
$468$		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
$473$	−4.56413	−	7.90530i	−0.209859	−	0.363486i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.82803	+	10.0944i	0.266847	+	0.462193i
$478$		0			0
$479$	11.0555	−	19.1487i	0.505140	−	0.874928i	−0.494842	−	0.868983i	$-0.664774\pi$
$479$	11.0555	−	19.1487i	0.505140	−	0.874928i	0.999982	−	0.00594539i	$-0.00189249\pi$
$480$		0			0
$481$	−8.84722	+	15.3238i	−0.403399	+	0.698707i
$482$		0			0
$483$	−85.8592			−3.90673
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−28.3389			−1.28416			−0.642078	−	0.766639i	$-0.721928\pi$
$487$	−28.3389			−1.28416			−0.642078	+	0.766639i	$0.721928\pi$
$488$		0			0
$489$	23.0731	+	39.9637i	1.04340	+	1.80722i
$490$		0			0
$491$	−4.33288	−	7.50477i	−0.195540	−	0.338686i	0.751537	−	0.659691i	$-0.229313\pi$
$491$	−4.33288	−	7.50477i	−0.195540	−	0.338686i	−0.947077	+	0.321005i	$0.895979\pi$
$492$		0			0
$493$	68.5977			3.08948
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.4372	−	18.0778i	−0.468173	−	0.810900i
$498$		0			0
$499$	8.07784	+	13.9912i	0.361614	+	0.626334i	0.988227	−	0.152997i	$-0.0488925\pi$
$499$	8.07784	+	13.9912i	0.361614	+	0.626334i	−0.626613	+	0.779331i	$0.715559\pi$
$500$		0			0
$501$	−20.4603			−0.914099
$502$		0			0
$503$	12.8900	−	22.3262i	0.574737	−	0.995474i	−0.421333	−	0.906906i	$-0.638438\pi$
$503$	12.8900	−	22.3262i	0.574737	−	0.995474i	0.996070	−	0.0885682i	$-0.0282291\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.83876	−	6.64893i	0.170485	−	0.295289i
$508$		0			0
$509$	6.15335	−	10.6579i	0.272743	−	0.472404i	−0.696821	−	0.717246i	$-0.745403\pi$
$509$	6.15335	−	10.6579i	0.272743	−	0.472404i	0.969563	+	0.244842i	$0.0787359\pi$
$510$		0			0
$511$	−5.78747	−	10.0242i	−0.256023	−	0.443444i
$512$		0			0
$513$	−5.58784	−	27.6394i	−0.246709	−	1.22031i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.22480	+	2.12142i	−0.0538668	+	0.0933000i
$518$		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
$523$	−1.32368	+	2.29269i	−0.0578806	+	0.100252i	−0.893514	−	0.449036i	$-0.851768\pi$
$523$	−1.32368	+	2.29269i	−0.0578806	+	0.100252i	0.835633	+	0.549288i	$0.185101\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.82878	−	11.8278i	−0.297466	−	0.515227i
$528$		0			0
$529$	−24.0292	−	41.6197i	−1.04475	−	1.80955i
$530$		0			0
$531$	10.0920			0.437956
$532$		0			0
$533$	−26.0750			−1.12943
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.86220	+	8.42158i	0.209820	+	0.363418i
$538$		0			0
$539$	−10.1171			−0.435773
$540$		0			0
$541$	−5.06701	+	8.77631i	−0.217848	+	0.377323i	−0.954150	−	0.299330i	$-0.903237\pi$
$541$	−5.06701	+	8.77631i	−0.217848	+	0.377323i	0.736302	+	0.676653i	$0.236570\pi$
$542$		0			0
$543$	−59.8804			−2.56972
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−11.2375	+	19.4639i	−0.480480	+	0.832217i	−0.999749	−	0.0223944i	$-0.992871\pi$
$547$	−11.2375	+	19.4639i	−0.480480	+	0.832217i	0.519269	+	0.854611i	$0.326204\pi$
$548$		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
$553$	−7.40121	−	12.8193i	−0.314731	−	0.545131i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.22948	−	3.86157i	0.0944659	−	0.163620i	−0.814920	−	0.579574i	$-0.803219\pi$
$557$	2.22948	−	3.86157i	0.0944659	−	0.163620i	0.909386	+	0.415954i	$0.136552\pi$
$558$		0			0
$559$	−16.1557			−0.683313
$560$		0			0
$561$	−20.8451	+	36.1047i	−0.880079	+	1.52434i
$562$		0			0
$563$	−10.0514			−0.423616			−0.211808	−	0.977311i	$-0.567935\pi$
$563$	−10.0514			−0.423616			−0.211808	+	0.977311i	$0.567935\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−5.01291	−	8.68261i	−0.210522	−	0.364635i
$568$		0			0
$569$	−5.41442			−0.226984			−0.113492	−	0.993539i	$-0.536204\pi$
$569$	−5.41442			−0.226984			−0.113492	+	0.993539i	$0.536204\pi$
$570$		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
$573$	−6.58973	−	11.4138i	−0.275290	−	0.476816i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.40727			−0.0585855			−0.0292928	−	0.999571i	$-0.509326\pi$
$577$	−1.40727			−0.0585855			−0.0292928	+	0.999571i	$0.509326\pi$
$578$		0			0
$579$	−28.8976	+	50.0521i	−1.20094	+	2.08010i
$580$		0			0
$581$	22.3473			0.927121
$582$		0			0
$583$	−2.01489	+	3.48990i	−0.0834484	+	0.144537i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.129501	+	0.224303i	0.00534510	+	0.00925798i	0.868686	−	0.495364i	$-0.164965\pi$
$587$	0.129501	+	0.224303i	0.00534510	+	0.00925798i	−0.863340	+	0.504622i	$0.831632\pi$
$588$		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
$593$	−1.48405	+	2.57044i	−0.0609425	+	0.105555i	−0.894887	−	0.446293i	$-0.852744\pi$
$593$	−1.48405	+	2.57044i	−0.0609425	+	0.105555i	0.833944	+	0.551848i	$0.186077\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−33.5795			−1.37432
$598$		0			0
$599$	−23.7083	+	41.0640i	−0.968696	+	1.67783i	−0.269359	+	0.963040i	$0.586812\pi$
$599$	−23.7083	+	41.0640i	−0.968696	+	1.67783i	−0.699338	+	0.714791i	$0.746522\pi$
$600$		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
$603$	24.3902	+	42.2451i	0.993247	+	1.72035i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	37.6580			1.52849			0.764246	−	0.644925i	$-0.223112\pi$
$607$	37.6580			1.52849			0.764246	+	0.644925i	$0.223112\pi$
$608$		0			0
$609$	−87.4162			−3.54228
$610$		0			0
$611$	2.16772	+	3.75461i	0.0876968	+	0.151895i
$612$		0			0
$613$	−22.1526	−	38.3694i	−0.894734	−	1.54973i	−0.834133	−	0.551563i	$-0.814031\pi$
$613$	−22.1526	−	38.3694i	−0.894734	−	1.54973i	−0.0606013	−	0.998162i	$-0.519302\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.6190	−	20.1247i	0.467764	−	0.810190i	−0.531558	−	0.847022i	$-0.678393\pi$
$617$	11.6190	−	20.1247i	0.467764	−	0.810190i	0.999321	+	0.0368317i	$0.0117265\pi$
$618$		0			0
$619$	−28.8420			−1.15926			−0.579630	−	0.814880i	$-0.696803\pi$
$619$	−28.8420			−1.15926			−0.579630	+	0.814880i	$0.696803\pi$
$620$		0			0
$621$	27.2665	−	47.2269i	1.09417	−	1.89515i
$622$		0			0
$623$	−9.70259	+	16.8054i	−0.388726	+	0.673294i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	17.0468	−	15.0443i	0.680783	−	0.600812i
$628$		0			0
$629$	22.0044	+	38.1127i	0.877371	+	1.51965i
$630$		0			0
$631$	6.79323	−	11.7662i	0.270434	−	0.468406i	−0.698539	−	0.715572i	$-0.746166\pi$
$631$	6.79323	−	11.7662i	0.270434	−	0.468406i	0.968973	+	0.247166i	$0.0794994\pi$
$632$		0			0
$633$	−15.3969	+	26.6683i	−0.611973	+	1.05997i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−8.95287	+	15.5068i	−0.354726	+	0.614403i
$638$		0			0
$639$	30.9201			1.22318
$640$		0			0
$641$	3.15731	+	5.46863i	0.124706	+	0.215998i	0.921618	−	0.388098i	$-0.126868\pi$
$641$	3.15731	+	5.46863i	0.124706	+	0.215998i	−0.796912	+	0.604096i	$0.793534\pi$
$642$		0			0
$643$	−6.85067	−	11.8657i	−0.270164	−	0.467938i	0.698740	−	0.715376i	$-0.253745\pi$
$643$	−6.85067	−	11.8657i	−0.270164	−	0.467938i	−0.968904	+	0.247438i	$0.920411\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.50227			−0.334259			−0.167129	−	0.985935i	$-0.553450\pi$
$647$	−8.50227			−0.334259			−0.167129	+	0.985935i	$0.553450\pi$
$648$		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
$653$	6.89369			0.269771			0.134885	−	0.990861i	$-0.456933\pi$
$653$	6.89369			0.269771			0.134885	+	0.990861i	$0.456933\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	17.1453			0.668902
$658$		0			0
$659$	10.9585	−	18.9807i	0.426884	−	0.739384i	−0.569711	−	0.821845i	$-0.692945\pi$
$659$	10.9585	−	18.9807i	0.426884	−	0.739384i	0.996594	+	0.0824611i	$0.0262780\pi$
$660$		0			0
$661$	15.5768	−	26.9797i	0.605866	−	1.04939i	−0.386048	−	0.922479i	$-0.626160\pi$
$661$	15.5768	−	26.9797i	0.605866	−	1.04939i	0.991914	−	0.126912i	$-0.0405065\pi$
$662$		0			0
$663$	36.8928	+	63.9001i	1.43280	+	2.48168i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−36.1735	−	62.6543i	−1.40064	−	2.42598i
$668$		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
$673$	24.5193			0.945150			0.472575	−	0.881290i	$-0.343325\pi$
$673$	24.5193			0.945150			0.472575	+	0.881290i	$0.343325\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.89395			−0.303389			−0.151695	−	0.988427i	$-0.548473\pi$
$677$	−7.89395			−0.303389			−0.151695	+	0.988427i	$0.548473\pi$
$678$		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
$683$	−44.3352			−1.69644			−0.848220	−	0.529644i	$-0.822325\pi$
$683$	−44.3352			−1.69644			−0.848220	+	0.529644i	$0.822325\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	15.9234	+	27.5802i	0.607517	+	1.05225i
$688$		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
$693$	16.9064	−	29.2828i	0.642222	−	1.11236i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−32.4262	+	56.1638i	−1.22823	+	2.12735i
$698$		0			0
$699$	26.3347	−	45.6130i	0.996068	−	1.72524i
$700$		0			0
$701$	−9.27840	−	16.0707i	−0.350440	−	0.606980i	0.635886	−	0.771783i	$-0.280635\pi$
$701$	−9.27840	−	16.0707i	−0.350440	−	0.606980i	−0.986327	+	0.164802i	$0.947301\pi$
$702$		0			0
$703$	−4.75593	−	23.5245i	−0.179373	−	0.887243i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.74830	−	15.1525i	0.329014	−	0.569868i
$708$		0			0
$709$	−21.4349	+	37.1263i	−0.805003	+	1.39431i	0.111285	+	0.993788i	$0.464503\pi$
$709$	−21.4349	+	37.1263i	−0.805003	+	1.39431i	−0.916289	+	0.400518i	$0.868830\pi$
$710$		0			0
$711$	21.9260			0.822289
$712$		0			0
$713$	−7.20202	+	12.4743i	−0.269718	+	0.467165i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.0230	−	29.4846i	−0.635734	−	1.10112i
$718$		0			0
$719$	17.5024	+	30.3150i	0.652728	+	1.13056i	0.982458	+	0.186483i	$0.0597088\pi$
$719$	17.5024	+	30.3150i	0.652728	+	1.13056i	−0.329730	+	0.944075i	$0.606958\pi$
$720$		0			0
$721$	19.7243			0.734571
$722$		0			0
$723$	13.4622			0.500663
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.252064	−	0.436587i	−0.00934852	−	0.0161921i	0.861313	−	0.508074i	$-0.169642\pi$
$727$	−0.252064	−	0.436587i	−0.00934852	−	0.0161921i	−0.870662	+	0.491882i	$0.836309\pi$
$728$		0			0
$729$	−40.9003			−1.51483
$730$		0			0
$731$	−20.0908	+	34.7983i	−0.743086	+	1.28706i
$732$		0			0
$733$	26.5745			0.981553			0.490777	−	0.871285i	$-0.336713\pi$
$733$	26.5745			0.981553			0.490777	+	0.871285i	$0.336713\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.43231	+	14.6052i	−0.310608	+	0.537989i
$738$		0			0
$739$	−12.8643	−	22.2817i	−0.473222	−	0.819645i	0.526308	−	0.850294i	$-0.323576\pi$
$739$	−12.8643	−	22.2817i	−0.473222	−	0.819645i	−0.999530	+	0.0306492i	$0.990243\pi$
$740$		0			0
$741$	−7.97384	−	39.4414i	−0.292926	−	1.44892i
$742$		0			0
$743$	2.13851	+	3.70400i	0.0784542	+	0.135887i	0.902583	−	0.430516i	$-0.141668\pi$
$743$	2.13851	+	3.70400i	0.0784542	+	0.135887i	−0.824129	+	0.566402i	$0.808335\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−16.5509	+	28.6670i	−0.605565	+	1.04887i
$748$		0			0
$749$	32.3455			1.18188
$750$		0			0
$751$	−7.26869	+	12.5897i	−0.265238	+	0.459406i	−0.967626	−	0.252388i	$-0.918784\pi$
$751$	−7.26869	+	12.5897i	−0.265238	+	0.459406i	0.702388	+	0.711795i	$0.252117\pi$
$752$		0			0
$753$	−0.293082			−0.0106805
$754$		0			0
$755$		0			0
$756$		0			0
$757$	8.16844	+	14.1482i	0.296887	+	0.514224i	0.975422	−	0.220345i	$-0.0707182\pi$
$757$	8.16844	+	14.1482i	0.296887	+	0.514224i	−0.678535	+	0.734568i	$0.737385\pi$
$758$		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
$763$	−26.8488	−	46.5034i	−0.971990	−	1.68354i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.17513			0.222971
$768$		0			0
$769$	−23.1977	+	40.1796i	−0.836530	+	1.44891i	0.0562477	+	0.998417i	$0.482086\pi$
$769$	−23.1977	+	40.1796i	−0.836530	+	1.44891i	−0.892778	+	0.450496i	$0.851247\pi$
$770$		0			0
$771$	−44.2054			−1.59202
$772$		0			0
$773$	12.4954	−	21.6426i	0.449428	−	0.778431i	−0.548921	−	0.835874i	$-0.684961\pi$
$773$	12.4954	−	21.6426i	0.449428	−	0.778431i	0.998349	+	0.0574426i	$0.0182946\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−28.0409	−	48.5682i	−1.00596	−	1.74238i
$778$		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
$783$	27.7609	−	48.0834i	0.992095	−	1.71836i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−36.4986			−1.30103			−0.650517	−	0.759492i	$-0.725448\pi$
$787$	−36.4986			−1.30103			−0.650517	+	0.759492i	$0.725448\pi$
$788$		0			0
$789$	28.1063	−	48.6815i	1.00061	−	1.73311i
$790$		0			0
$791$	15.8169			0.562385
$792$		0			0
$793$	9.09604	+	15.7548i	0.323010	+	0.559470i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.9753			−0.424188			−0.212094	−	0.977249i	$-0.568028\pi$
$797$	−11.9753			−0.424188			−0.212094	+	0.977249i	$0.568028\pi$
$798$		0			0
$799$	10.7829			0.381472
$800$		0			0
$801$	−14.3719	−	24.8929i	−0.507807	−	0.879547i
$802$		0			0
$803$	2.96378	+	5.13342i	0.104590	+	0.181154i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.68144	+	2.91234i	−0.0591895	+	0.102519i
$808$		0			0
$809$	29.4153			1.03419			0.517093	−	0.855929i	$-0.327014\pi$
$809$	29.4153			1.03419			0.517093	+	0.855929i	$0.327014\pi$
$810$		0			0
$811$	−27.4062	+	47.4690i	−0.962363	+	1.66686i	−0.245825	+	0.969314i	$0.579059\pi$
$811$	−27.4062	+	47.4690i	−0.962363	+	1.66686i	−0.716538	+	0.697548i	$0.754274\pi$
$812$		0			0
$813$	18.3975	−	31.8655i	0.645230	−	1.11757i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	16.4300	−	14.5000i	0.574812	−	0.507289i
$818$		0			0
$819$	−29.9219	−	51.8263i	−1.04556	−	1.81096i
$820$		0			0
$821$	4.32200	−	7.48592i	0.150839	−	0.261260i	−0.780697	−	0.624909i	$-0.785136\pi$
$821$	4.32200	−	7.48592i	0.150839	−	0.261260i	0.931536	+	0.363649i	$0.118469\pi$
$822$		0			0
$823$	−20.3004	+	35.1614i	−0.707628	+	1.22565i	0.258106	+	0.966117i	$0.416902\pi$
$823$	−20.3004	+	35.1614i	−0.707628	+	1.22565i	−0.965735	+	0.259532i	$0.916432\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.946864	−	1.64002i	0.0329257	−	0.0570290i	−0.849093	−	0.528243i	$-0.822851\pi$
$827$	0.946864	−	1.64002i	0.0329257	−	0.0570290i	0.882019	+	0.471214i	$0.156184\pi$
$828$		0			0
$829$	−54.2488			−1.88414			−0.942070	−	0.335416i	$-0.891123\pi$
$829$	−54.2488			−1.88414			−0.942070	+	0.335416i	$0.891123\pi$
$830$		0			0
$831$	−15.8169	−	27.3957i	−0.548683	−	0.950347i
$832$		0			0
$833$	22.2671	+	38.5678i	0.771511	+	1.33630i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−11.0542			−0.382090
$838$		0			0
$839$	−19.4931	−	33.7630i	−0.672976	−	1.16563i	−0.977056	−	0.212982i	$-0.931682\pi$
$839$	−19.4931	−	33.7630i	−0.672976	−	1.16563i	0.304080	−	0.952647i	$-0.401651\pi$
$840$		0			0
$841$	−22.3295	−	38.6758i	−0.769982	−	1.33365i
$842$		0			0
$843$	11.1160			0.382855
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−27.3125			−0.938469
$848$		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
$853$	15.3058	+	26.5103i	0.524059	+	0.907697i	0.999608	+	0.0280076i	$0.00891625\pi$
$853$	15.3058	+	26.5103i	0.524059	+	0.907697i	−0.475549	+	0.879689i	$0.657750\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.73913	+	11.6725i	0.230204	+	0.398726i	0.957868	−	0.287208i	$-0.0927272\pi$
$857$	6.73913	+	11.6725i	0.230204	+	0.398726i	−0.727664	+	0.685934i	$0.759394\pi$
$858$		0			0
$859$	4.96411	−	8.59809i	0.169373	−	0.293363i	−0.768826	−	0.639458i	$-0.779159\pi$
$859$	4.96411	−	8.59809i	0.169373	−	0.293363i	0.938200	+	0.346094i	$0.112492\pi$
$860$		0			0
$861$	41.3217	−	71.5713i	1.40824	−	2.43914i
$862$		0			0
$863$	−36.8000			−1.25269			−0.626344	−	0.779547i	$-0.715449\pi$
$863$	−36.8000			−1.25269			−0.626344	+	0.779547i	$0.715449\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	134.681			4.57400
$868$		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
$873$	41.9212			1.41882
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.86520	−	4.96267i	−0.0967509	−	0.167577i	0.813587	−	0.581443i	$-0.197512\pi$
$877$	−2.86520	−	4.96267i	−0.0967509	−	0.167577i	−0.910338	+	0.413866i	$0.864178\pi$
$878$		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
$883$	−20.8368	+	36.0904i	−0.701214	+	1.21454i	0.266826	+	0.963745i	$0.414025\pi$
$883$	−20.8368	+	36.0904i	−0.701214	+	1.21454i	−0.968040	+	0.250794i	$0.919308\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	25.3951	−	43.9856i	0.852685	−	1.47689i	−0.0260915	−	0.999660i	$-0.508306\pi$
$887$	25.3951	−	43.9856i	0.852685	−	1.47689i	0.878776	−	0.477234i	$-0.158361\pi$
$888$		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
$893$	−5.57434	−	1.87279i	−0.186538	−	0.0626705i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	38.9092	−	67.3927i	1.29914	−	2.25018i
$898$		0			0
$899$	−7.33263	+	12.7005i	−0.244557	+	0.423585i
$900$		0			0
$901$	17.7387			0.590962
$902$		0			0
$903$	25.6024	−	44.3446i	0.851994	−	1.47570i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	10.0832	+	17.4646i	0.334806	+	0.579902i	0.983448	−	0.181193i	$-0.0579957\pi$
$907$	10.0832	+	17.4646i	0.334806	+	0.579902i	−0.648641	+	0.761094i	$0.724662\pi$
$908$		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
$913$	−11.4441			−0.378745
$914$		0			0
$915$		0			0
$916$		0			0
$917$	26.7844	+	46.3919i	0.884498	+	1.53200i
$918$		0			0
$919$	−33.8678			−1.11719			−0.558597	−	0.829439i	$-0.688660\pi$
$919$	−33.8678			−1.11719			−0.558597	+	0.829439i	$0.688660\pi$
$920$		0			0
$921$	−20.2751	+	35.1175i	−0.668087	+	1.15716i
$922$		0			0
$923$	18.9195			0.622744
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−14.6083	+	25.3022i	−0.479798	+	0.831035i
$928$		0			0
$929$	0.457146	+	0.791800i	0.0149985	+	0.0259781i	0.873427	−	0.486955i	$-0.161892\pi$
$929$	0.457146	+	0.791800i	0.0149985	+	0.0259781i	−0.858429	+	0.512933i	$0.828559\pi$
$930$		0			0
$931$	−4.81272	−	23.8054i	−0.157731	−	0.780191i
$932$		0			0
$933$	−23.6521	−	40.9666i	−0.774334	−	1.34119i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−25.9915	+	45.0186i	−0.849106	+	1.47069i	0.0329014	+	0.999459i	$0.489525\pi$
$937$	−25.9915	+	45.0186i	−0.849106	+	1.47069i	−0.882007	+	0.471236i	$0.843808\pi$
$938$		0			0
$939$	−71.7682			−2.34207
$940$		0			0
$941$	12.4228	−	21.5169i	0.404972	−	0.701432i	−0.589346	−	0.807880i	$-0.700615\pi$
$941$	12.4228	−	21.5169i	0.404972	−	0.701432i	0.994318	+	0.106449i	$0.0339480\pi$
$942$		0			0
$943$	68.3969			2.22731
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.8588	+	24.0042i	0.450352	+	0.780032i	0.998408	−	0.0564097i	$-0.0179653\pi$
$947$	13.8588	+	24.0042i	0.450352	+	0.780032i	−0.548056	+	0.836442i	$0.684632\pi$
$948$		0			0
$949$	10.4909			0.340550
$950$		0			0
$951$	6.33593			0.205457
$952$		0			0
$953$	−8.29103	−	14.3605i	−0.268573	−	0.465182i	0.699921	−	0.714221i	$-0.253219\pi$
$953$	−8.29103	−	14.3605i	−0.268573	−	0.465182i	−0.968494	+	0.249039i	$0.919885\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	44.7661			1.44708
$958$		0			0
$959$	−9.34072	+	16.1786i	−0.301627	+	0.522434i
$960$		0			0
$961$	−28.0802			−0.905813
$962$		0			0
$963$	−23.9558	+	41.4926i	−0.771964	+	1.33708i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.56159	+	16.5612i	0.307480	+	0.532571i	0.977810	−	0.209492i	$-0.0671809\pi$
$967$	9.56159	+	16.5612i	0.307480	+	0.532571i	−0.670330	+	0.742063i	$0.733848\pi$
$968$		0			0
$969$	−94.8704	−	31.8732i	−3.04767	−	1.02392i
$970$		0			0
$971$	7.56801	+	13.1082i	0.242869	+	0.420661i	0.961530	−	0.274699i	$-0.0885782\pi$
$971$	7.56801	+	13.1082i	0.242869	+	0.420661i	−0.718661	+	0.695360i	$0.755245\pi$
$972$		0			0
$973$	−11.9963	+	20.7782i	−0.384584	+	0.666120i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.83858			0.186793			0.0933964	−	0.995629i	$-0.470228\pi$
$977$	5.83858			0.186793			0.0933964	+	0.995629i	$0.470228\pi$
$978$		0			0
$979$	4.96873	−	8.60609i	0.158801	−	0.275052i
$980$		0			0
$981$	79.5391			2.53949
$982$		0			0
$983$	10.3479	+	17.9231i	0.330047	+	0.571657i	0.982521	−	0.186154i	$-0.0596022\pi$
$983$	10.3479	+	17.9231i	0.330047	+	0.571657i	−0.652474	+	0.757811i	$0.726269\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−13.7410			−0.437381
$988$		0			0
$989$	42.3778			1.34754
$990$		0			0
$991$	−22.9776	−	39.7984i	−0.729907	−	1.26424i	−0.956922	−	0.290345i	$-0.906230\pi$
$991$	−22.9776	−	39.7984i	−0.729907	−	1.26424i	0.227014	−	0.973891i	$-0.427104\pi$
$992$		0			0
$993$	39.5584	+	68.5171i	1.25535	+	2.17432i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−3.64870	+	6.31974i	−0.115556	+	0.200148i	−0.918002	−	0.396576i	$-0.870198\pi$
$997$	−3.64870	+	6.31974i	−0.115556	+	0.200148i	0.802446	+	0.596725i	$0.203532\pi$
$998$		0			0
$999$	35.6200			1.12697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.g.501.1		20
5.2	odd	4		380.2.r.a.349.1	yes	20
5.3	odd	4		380.2.r.a.349.10	yes	20
5.4	even	2	inner	1900.2.i.g.501.10		20
15.2	even	4		3420.2.bj.c.2629.4		20
15.8	even	4		3420.2.bj.c.2629.10		20
19.11	even	3	inner	1900.2.i.g.201.1		20
95.49	even	6	inner	1900.2.i.g.201.10		20
95.68	odd	12		380.2.r.a.49.1	✓	20
95.87	odd	12		380.2.r.a.49.10	yes	20
285.68	even	12		3420.2.bj.c.1189.4		20
285.182	even	12		3420.2.bj.c.1189.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.1	✓	20	95.68	odd	12
380.2.r.a.49.10	yes	20	95.87	odd	12
380.2.r.a.349.1	yes	20	5.2	odd	4
380.2.r.a.349.10	yes	20	5.3	odd	4
1900.2.i.g.201.1		20	19.11	even	3	inner
1900.2.i.g.201.10		20	95.49	even	6	inner
1900.2.i.g.501.1		20	1.1	even	1	trivial
1900.2.i.g.501.10		20	5.4	even	2	inner
3420.2.bj.c.1189.4		20	285.68	even	12
3420.2.bj.c.1189.10		20	285.182	even	12
3420.2.bj.c.2629.4		20	15.2	even	4
3420.2.bj.c.2629.10		20	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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43632 - 2.48777i) q^{3} +3.54568 q^{7} +(-2.62601 + 4.54838i) q^{9} +O(q^{10})\)	\(q+(-1.43632 - 2.48777i) q^{3} +3.54568 q^{7} +(-2.62601 + 4.54838i) q^{9} -1.81575 q^{11} +(-1.60681 + 2.78308i) q^{13} +(3.99638 + 6.92193i) q^{17} +(-0.863760 - 4.27246i) q^{19} +(-5.09271 - 8.82084i) q^{21} +(4.21480 - 7.30026i) q^{23} +6.46921 q^{27} +(4.29124 - 7.43265i) q^{29} -1.70874 q^{31} +(2.60799 + 4.51718i) q^{33} +5.50608 q^{37} +9.23155 q^{39} +(4.05694 + 7.02683i) q^{41} +(2.51363 + 4.35373i) q^{43} +(0.674543 - 1.16834i) q^{47} +5.57183 q^{49} +(11.4801 - 19.8842i) q^{51} +(1.10967 - 1.92201i) q^{53} +(-9.38828 + 8.28544i) q^{57} +(-0.960774 - 1.66411i) q^{59} +(2.83047 - 4.90251i) q^{61} +(-9.31098 + 16.1271i) q^{63} +(4.64397 - 8.04360i) q^{67} -24.2152 q^{69} +(-2.94365 - 5.09854i) q^{71} +(-1.63226 - 2.82716i) q^{73} -6.43807 q^{77} +(-2.08739 - 3.61546i) q^{79} +(-1.41381 - 2.44879i) q^{81} +6.30268 q^{83} -24.6543 q^{87} +(-2.73646 + 4.73968i) q^{89} +(-5.69723 + 9.86789i) q^{91} +(2.45429 + 4.25096i) q^{93} +(-3.99096 - 6.91255i) q^{97} +(4.76818 - 8.25873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^9	\( 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100}) \) 20 * q - 10 * q^9 - 14 * q^19 - 8 * q^21 + 16 * q^29 + 8 * q^31 + 8 * q^39 + 26 * q^41 + 44 * q^49 + 26 * q^51 - 4 * q^59 + 2 * q^61 - 48 * q^69 - 2 * q^71 + 16 * q^79 + 26 * q^81 + 40 * q^89 - 4 * q^91 + 20 * q^99

Introduction

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