LMFDB - Embedded newform 1920.2.bl.a.289.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.19
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.a.1249.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-2.18678 - 0.466917i) q^{5} +1.00010 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-2.18678 - 0.466917i) q^{5} +1.00010 q^{7} -1.00000i q^{9} +(1.89490 - 1.89490i) q^{11} +(-2.65915 + 2.65915i) q^{13} +(-1.87644 + 1.21612i) q^{15} +1.73836i q^{17} +(-5.33902 - 5.33902i) q^{19} +(0.707179 - 0.707179i) q^{21} +0.160230 q^{23} +(4.56398 + 2.04209i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-2.70291 - 2.70291i) q^{29} -4.64288 q^{31} -2.67980i q^{33} +(-2.18700 - 0.466965i) q^{35} +(-5.35773 - 5.35773i) q^{37} +3.76061i q^{39} -9.89786i q^{41} +(7.23165 + 7.23165i) q^{43} +(-0.466917 + 2.18678i) q^{45} +4.79583i q^{47} -5.99980 q^{49} +(1.22921 + 1.22921i) q^{51} +(-3.44618 - 3.44618i) q^{53} +(-5.02849 + 3.25896i) q^{55} -7.55051 q^{57} +(-0.101729 + 0.101729i) q^{59} +(6.01811 + 6.01811i) q^{61} -1.00010i q^{63} +(7.05657 - 4.57336i) q^{65} +(-9.04430 + 9.04430i) q^{67} +(0.113300 - 0.113300i) q^{69} -4.60679i q^{71} -12.1920 q^{73} +(4.67119 - 1.78325i) q^{75} +(1.89509 - 1.89509i) q^{77} -5.73529 q^{79} -1.00000 q^{81} +(-2.04924 + 2.04924i) q^{83} +(0.811670 - 3.80140i) q^{85} -3.82249 q^{87} -15.0386i q^{89} +(-2.65942 + 2.65942i) q^{91} +(-3.28301 + 3.28301i) q^{93} +(9.18235 + 14.1681i) q^{95} +3.84735i q^{97} +(-1.89490 - 1.89490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) $ 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−2.18678	−	0.466917i	−0.977956	−	0.208812i
$5$	−2.18678	−	0.466917i	−0.977956	−	0.208812i
$6$		0			0
$7$	1.00010			0.378003			0.189001	−	0.981977i	$-0.439475\pi$
$7$	1.00010			0.378003			0.189001	+	0.981977i	$0.439475\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.89490	−	1.89490i	0.571334	−	0.571334i	−0.361167	−	0.932501i	$-0.617622\pi$
$11$	1.89490	−	1.89490i	0.571334	−	0.571334i	0.932501	+	0.361167i	$0.117622\pi$
$12$		0			0
$13$	−2.65915	+	2.65915i	−0.737515	+	0.737515i	−0.972097	−	0.234581i	$-0.924628\pi$
$13$	−2.65915	+	2.65915i	−0.737515	+	0.737515i	0.234581	+	0.972097i	$0.424628\pi$
$14$		0			0
$15$	−1.87644	+	1.21612i	−0.484496	+	0.314002i
$16$		0			0
$17$			1.73836i			0.421614i	0.977528	+	0.210807i	$0.0676092\pi$
$17$			1.73836i			0.421614i	−0.977528	+	0.210807i	$0.932391\pi$
$18$		0			0
$19$	−5.33902	−	5.33902i	−1.22485	−	1.22485i	−0.965886	−	0.258968i	$-0.916617\pi$
$19$	−5.33902	−	5.33902i	−1.22485	−	1.22485i	−0.258968	−	0.965886i	$-0.583383\pi$
$20$		0			0
$21$	0.707179	−	0.707179i	0.154319	−	0.154319i
$22$		0			0
$23$	0.160230			0.0334103			0.0167051	−	0.999860i	$-0.494682\pi$
$23$	0.160230			0.0334103			0.0167051	+	0.999860i	$0.494682\pi$
$24$		0			0
$25$	4.56398	+	2.04209i	0.912795	+	0.408417i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	−2.70291	−	2.70291i	−0.501918	−	0.501918i	0.410116	−	0.912034i	$-0.365488\pi$
$29$	−2.70291	−	2.70291i	−0.501918	−	0.501918i	−0.912034	+	0.410116i	$0.865488\pi$
$30$		0			0
$31$	−4.64288			−0.833885			−0.416943	−	0.908933i	$-0.636898\pi$
$31$	−4.64288			−0.833885			−0.416943	+	0.908933i	$0.636898\pi$
$32$		0			0
$33$		−	2.67980i		−	0.466493i
$34$		0			0
$35$	−2.18700	−	0.466965i	−0.369670	−	0.0789314i
$36$		0			0
$37$	−5.35773	−	5.35773i	−0.880806	−	0.880806i	0.112811	−	0.993616i	$-0.464015\pi$
$37$	−5.35773	−	5.35773i	−0.880806	−	0.880806i	−0.993616	+	0.112811i	$0.964015\pi$
$38$		0			0
$39$			3.76061i			0.602179i
$40$		0			0
$41$		−	9.89786i		−	1.54579i	−0.634536	−	0.772893i	$-0.718809\pi$
$41$		−	9.89786i		−	1.54579i	0.634536	−	0.772893i	$-0.281191\pi$
$42$		0			0
$43$	7.23165	+	7.23165i	1.10282	+	1.10282i	0.994069	+	0.108747i	$0.0346838\pi$
$43$	7.23165	+	7.23165i	1.10282	+	1.10282i	0.108747	+	0.994069i	$0.465316\pi$
$44$		0			0
$45$	−0.466917	+	2.18678i	−0.0696039	+	0.325985i
$46$		0			0
$47$			4.79583i			0.699544i	0.936835	+	0.349772i	$0.113741\pi$
$47$			4.79583i			0.699544i	−0.936835	+	0.349772i	$0.886259\pi$
$48$		0			0
$49$	−5.99980			−0.857114
$50$		0			0
$51$	1.22921	+	1.22921i	0.172123	+	0.172123i
$52$		0			0
$53$	−3.44618	−	3.44618i	−0.473369	−	0.473369i	0.429634	−	0.903003i	$-0.358643\pi$
$53$	−3.44618	−	3.44618i	−0.473369	−	0.473369i	−0.903003	+	0.429634i	$0.858643\pi$
$54$		0			0
$55$	−5.02849	+	3.25896i	−0.678041	+	0.439438i
$56$		0			0
$57$	−7.55051			−1.00009
$58$		0			0
$59$	−0.101729	+	0.101729i	−0.0132440	+	0.0132440i	−0.713698	−	0.700454i	$-0.752981\pi$
$59$	−0.101729	+	0.101729i	−0.0132440	+	0.0132440i	0.700454	+	0.713698i	$0.252981\pi$
$60$		0			0
$61$	6.01811	+	6.01811i	0.770540	+	0.770540i	0.978201	−	0.207661i	$-0.0665850\pi$
$61$	6.01811	+	6.01811i	0.770540	+	0.770540i	−0.207661	+	0.978201i	$0.566585\pi$
$62$		0			0
$63$		−	1.00010i		−	0.126001i
$64$		0			0
$65$	7.05657	−	4.57336i	0.875259	−	0.567256i
$66$		0			0
$67$	−9.04430	+	9.04430i	−1.10494	+	1.10494i	−0.111131	+	0.993806i	$0.535447\pi$
$67$	−9.04430	+	9.04430i	−1.10494	+	1.10494i	−0.993806	+	0.111131i	$0.964553\pi$
$68$		0			0
$69$	0.113300	−	0.113300i	0.0136397	−	0.0136397i
$70$		0			0
$71$		−	4.60679i		−	0.546726i	−0.961911	−	0.273363i	$-0.911864\pi$
$71$		−	4.60679i		−	0.546726i	0.961911	−	0.273363i	$-0.0881360\pi$
$72$		0			0
$73$	−12.1920			−1.42697			−0.713485	−	0.700671i	$-0.752884\pi$
$73$	−12.1920			−1.42697			−0.713485	+	0.700671i	$0.752884\pi$
$74$		0			0
$75$	4.67119	−	1.78325i	0.539383	−	0.205912i
$76$		0			0
$77$	1.89509	−	1.89509i	0.215966	−	0.215966i
$78$		0			0
$79$	−5.73529			−0.645271			−0.322635	−	0.946523i	$-0.604569\pi$
$79$	−5.73529			−0.645271			−0.322635	+	0.946523i	$0.604569\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.04924	+	2.04924i	−0.224934	+	0.224934i	−0.810572	−	0.585639i	$-0.800844\pi$
$83$	−2.04924	+	2.04924i	−0.224934	+	0.224934i	0.585639	+	0.810572i	$0.300844\pi$
$84$		0			0
$85$	0.811670	−	3.80140i	0.0880380	−	0.412320i
$86$		0			0
$87$	−3.82249			−0.409814
$88$		0			0
$89$		−	15.0386i		−	1.59409i	−0.603922	−	0.797044i	$-0.706396\pi$
$89$		−	15.0386i		−	1.59409i	0.603922	−	0.797044i	$-0.293604\pi$
$90$		0			0
$91$	−2.65942	+	2.65942i	−0.278783	+	0.278783i
$92$		0			0
$93$	−3.28301	+	3.28301i	−0.340432	+	0.340432i
$94$		0			0
$95$	9.18235	+	14.1681i	0.942089	+	1.45362i
$96$		0			0
$97$			3.84735i			0.390639i	0.980740	+	0.195320i	$0.0625744\pi$
$97$			3.84735i			0.390639i	−0.980740	+	0.195320i	$0.937426\pi$
$98$		0			0
$99$	−1.89490	−	1.89490i	−0.190445	−	0.190445i
$100$		0			0
$101$	−5.60917	+	5.60917i	−0.558133	+	0.558133i	−0.928776	−	0.370642i	$-0.879138\pi$
$101$	−5.60917	+	5.60917i	−0.558133	+	0.558133i	0.370642	+	0.928776i	$0.379138\pi$
$102$		0			0
$103$	−14.9978			−1.47778			−0.738888	−	0.673828i	$-0.764649\pi$
$103$	−14.9978			−1.47778			−0.738888	+	0.673828i	$0.764649\pi$
$104$		0			0
$105$	−1.87663	+	1.21625i	−0.183141	+	0.118694i
$106$		0			0
$107$	1.22436	+	1.22436i	0.118363	+	0.118363i	0.763807	−	0.645444i	$-0.223328\pi$
$107$	1.22436	+	1.22436i	0.118363	+	0.118363i	−0.645444	+	0.763807i	$0.723328\pi$
$108$		0			0
$109$	−5.31222	−	5.31222i	−0.508819	−	0.508819i	0.405345	−	0.914164i	$-0.367151\pi$
$109$	−5.31222	−	5.31222i	−0.508819	−	0.508819i	−0.914164	+	0.405345i	$0.867151\pi$
$110$		0			0
$111$	−7.57698			−0.719175
$112$		0			0
$113$		−	10.5478i		−	0.992249i	−0.868251	−	0.496125i	$-0.834756\pi$
$113$		−	10.5478i		−	0.992249i	0.868251	−	0.496125i	$-0.165244\pi$
$114$		0			0
$115$	−0.350387	−	0.0748141i	−0.0326738	−	0.00697645i
$116$		0			0
$117$	2.65915	+	2.65915i	0.245838	+	0.245838i
$118$		0			0
$119$			1.73854i			0.159371i
$120$		0			0
$121$			3.81870i			0.347154i
$122$		0			0
$123$	−6.99885	−	6.99885i	−0.631065	−	0.631065i
$124$		0			0
$125$	−9.02691	−	6.59658i	−0.807391	−	0.590016i
$126$		0			0
$127$		−	5.78563i		−	0.513391i	−0.966492	−	0.256696i	$-0.917366\pi$
$127$		−	5.78563i		−	0.513391i	0.966492	−	0.256696i	$-0.0826338\pi$
$128$		0			0
$129$	10.2271			0.900446
$130$		0			0
$131$	1.01902	+	1.01902i	0.0890321	+	0.0890321i	0.750220	−	0.661188i	$-0.229947\pi$
$131$	1.01902	+	1.01902i	0.0890321	+	0.0890321i	−0.661188	+	0.750220i	$0.729947\pi$
$132$		0			0
$133$	−5.33956	−	5.33956i	−0.462998	−	0.462998i
$134$		0			0
$135$	1.21612	+	1.87644i	0.104667	+	0.161499i
$136$		0			0
$137$	−11.1576			−0.953260			−0.476630	−	0.879104i	$-0.658142\pi$
$137$	−11.1576			−0.953260			−0.476630	+	0.879104i	$0.658142\pi$
$138$		0			0
$139$	−15.9657	+	15.9657i	−1.35419	+	1.35419i	−0.473277	+	0.880914i	$0.656929\pi$
$139$	−15.9657	+	15.9657i	−1.35419	+	1.35419i	−0.880914	+	0.473277i	$0.843071\pi$
$140$		0			0
$141$	3.39117	+	3.39117i	0.285588	+	0.285588i
$142$		0			0
$143$			10.0777i			0.842736i
$144$		0			0
$145$	4.64862	+	7.17270i	0.386047	+	0.595660i
$146$		0			0
$147$	−4.24250	+	4.24250i	−0.349915	+	0.349915i
$148$		0			0
$149$	14.5202	−	14.5202i	1.18954	−	1.18954i	0.212342	−	0.977195i	$-0.431891\pi$
$149$	14.5202	−	14.5202i	1.18954	−	1.18954i	0.977195	−	0.212342i	$-0.0681090\pi$
$150$		0			0
$151$		−	14.7230i		−	1.19814i	−0.800695	−	0.599072i	$-0.795536\pi$
$151$		−	14.7230i		−	1.19814i	0.800695	−	0.599072i	$-0.204464\pi$
$152$		0			0
$153$	1.73836			0.140538
$154$		0			0
$155$	10.1529	+	2.16784i	0.815503	+	0.174125i
$156$		0			0
$157$	9.44726	−	9.44726i	0.753974	−	0.753974i	−0.221245	−	0.975218i	$-0.571012\pi$
$157$	9.44726	−	9.44726i	0.753974	−	0.753974i	0.975218	+	0.221245i	$0.0710119\pi$
$158$		0			0
$159$	−4.87364			−0.386505
$160$		0			0
$161$	0.160246			0.0126292
$162$		0			0
$163$	7.66138	−	7.66138i	0.600086	−	0.600086i	−0.340250	−	0.940335i	$-0.610512\pi$
$163$	7.66138	−	7.66138i	0.600086	−	0.600086i	0.940335	+	0.340250i	$0.110512\pi$
$164$		0			0
$165$	−1.25124	+	5.86011i	−0.0974091	+	0.456209i
$166$		0			0
$167$	14.4195			1.11581			0.557906	−	0.829904i	$-0.311605\pi$
$167$	14.4195			1.11581			0.557906	+	0.829904i	$0.311605\pi$
$168$		0			0
$169$		−	1.14216i		−	0.0878581i
$170$		0			0
$171$	−5.33902	+	5.33902i	−0.408285	+	0.408285i
$172$		0			0
$173$	−0.942572	+	0.942572i	−0.0716624	+	0.0716624i	−0.742030	−	0.670367i	$-0.766137\pi$
$173$	−0.942572	+	0.942572i	−0.0716624	+	0.0716624i	0.670367	+	0.742030i	$0.266137\pi$
$174$		0			0
$175$	4.56444	+	2.04229i	0.345039	+	0.154383i
$176$		0			0
$177$			0.143867i			0.0108137i
$178$		0			0
$179$	3.23789	+	3.23789i	0.242011	+	0.242011i	0.817682	−	0.575671i	$-0.195259\pi$
$179$	3.23789	+	3.23789i	0.242011	+	0.242011i	−0.575671	+	0.817682i	$0.695259\pi$
$180$		0			0
$181$	13.0914	−	13.0914i	0.973076	−	0.973076i	−0.0265713	−	0.999647i	$-0.508459\pi$
$181$	13.0914	−	13.0914i	0.973076	−	0.973076i	0.999647	+	0.0265713i	$0.00845891\pi$
$182$		0			0
$183$	8.51089			0.629143
$184$		0			0
$185$	9.21454	+	14.2178i	0.677467	+	1.04531i
$186$		0			0
$187$	3.29402	+	3.29402i	0.240883	+	0.240883i
$188$		0			0
$189$	−0.707179	−	0.707179i	−0.0514397	−	0.0514397i
$190$		0			0
$191$	9.80663			0.709583			0.354791	−	0.934946i	$-0.384552\pi$
$191$	9.80663			0.709583			0.354791	+	0.934946i	$0.384552\pi$
$192$		0			0
$193$			6.82164i			0.491033i	0.969392	+	0.245516i	$0.0789575\pi$
$193$			6.82164i			0.491033i	−0.969392	+	0.245516i	$0.921043\pi$
$194$		0			0
$195$	1.75589	−	8.22360i	0.125742	−	0.588904i
$196$		0			0
$197$	15.5142	+	15.5142i	1.10534	+	1.10534i	0.993755	+	0.111587i	$0.0355933\pi$
$197$	15.5142	+	15.5142i	1.10534	+	1.10534i	0.111587	+	0.993755i	$0.464407\pi$
$198$		0			0
$199$			7.92050i			0.561469i	0.959785	+	0.280735i	$0.0905781\pi$
$199$			7.92050i			0.561469i	−0.959785	+	0.280735i	$0.909422\pi$
$200$		0			0
$201$			12.7906i			0.902177i
$202$		0			0
$203$	−2.70319	−	2.70319i	−0.189726	−	0.189726i
$204$		0			0
$205$	−4.62148	+	21.6444i	−0.322778	+	1.51171i
$206$		0			0
$207$		−	0.160230i		−	0.0111368i
$208$		0			0
$209$	−20.2338			−1.39960
$210$		0			0
$211$	10.2008	+	10.2008i	0.702253	+	0.702253i	0.964894	−	0.262641i	$-0.0845935\pi$
$211$	10.2008	+	10.2008i	0.702253	+	0.702253i	−0.262641	+	0.964894i	$0.584594\pi$
$212$		0			0
$213$	−3.25750	−	3.25750i	−0.223200	−	0.223200i
$214$		0			0
$215$	−12.4374	−	19.1906i	−0.848225	−	1.30879i
$216$		0			0
$217$	−4.64335			−0.315211
$218$		0			0
$219$	−8.62107	+	8.62107i	−0.582558	+	0.582558i
$220$		0			0
$221$	−4.62256	−	4.62256i	−0.310947	−	0.310947i
$222$		0			0
$223$		−	13.8689i		−	0.928732i	−0.885643	−	0.464366i	$-0.846282\pi$
$223$		−	13.8689i		−	0.928732i	0.885643	−	0.464366i	$-0.153718\pi$
$224$		0			0
$225$	2.04209	−	4.56398i	0.136139	−	0.304265i
$226$		0			0
$227$	−17.9180	+	17.9180i	−1.18926	+	1.18926i	−0.211987	+	0.977273i	$0.567993\pi$
$227$	−17.9180	+	17.9180i	−1.18926	+	1.18926i	−0.977273	+	0.211987i	$0.932007\pi$
$228$		0			0
$229$	2.04384	−	2.04384i	0.135061	−	0.135061i	−0.636344	−	0.771405i	$-0.719554\pi$
$229$	2.04384	−	2.04384i	0.135061	−	0.135061i	0.771405	+	0.636344i	$0.219554\pi$
$230$		0			0
$231$		−	2.68007i		−	0.176336i
$232$		0			0
$233$	11.1084			0.727733			0.363867	−	0.931451i	$-0.381456\pi$
$233$	11.1084			0.727733			0.363867	+	0.931451i	$0.381456\pi$
$234$		0			0
$235$	2.23926	−	10.4874i	0.146073	−	0.684123i
$236$		0			0
$237$	−4.05546	+	4.05546i	−0.263431	+	0.263431i
$238$		0			0
$239$	−19.1106			−1.23616			−0.618080	−	0.786115i	$-0.712089\pi$
$239$	−19.1106			−1.23616			−0.618080	+	0.786115i	$0.712089\pi$
$240$		0			0
$241$	−5.95102			−0.383339			−0.191669	−	0.981460i	$-0.561390\pi$
$241$	−5.95102			−0.383339			−0.191669	+	0.981460i	$0.561390\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	13.1202	+	2.80141i	0.838220	+	0.178975i
$246$		0			0
$247$	28.3945			1.80670
$248$		0			0
$249$			2.89807i			0.183658i
$250$		0			0
$251$	20.8714	−	20.8714i	1.31739	−	1.31739i	0.401552	−	0.915836i	$-0.368471\pi$
$251$	20.8714	−	20.8714i	1.31739	−	1.31739i	0.915836	−	0.401552i	$-0.131529\pi$
$252$		0			0
$253$	0.303620	−	0.303620i	0.0190884	−	0.0190884i
$254$		0			0
$255$	−2.11406	−	3.26194i	−0.132388	−	0.204270i
$256$		0			0
$257$			9.30565i			0.580470i	0.956955	+	0.290235i	$0.0937335\pi$
$257$			9.30565i			0.580470i	−0.956955	+	0.290235i	$0.906266\pi$
$258$		0			0
$259$	−5.35828	−	5.35828i	−0.332947	−	0.332947i
$260$		0			0
$261$	−2.70291	+	2.70291i	−0.167306	+	0.167306i
$262$		0			0
$263$	20.0922			1.23894			0.619469	−	0.785021i	$-0.287348\pi$
$263$	20.0922			1.23894			0.619469	+	0.785021i	$0.287348\pi$
$264$		0			0
$265$	5.92695	+	9.14511i	0.364089	+	0.561780i
$266$		0			0
$267$	−10.6339	−	10.6339i	−0.650783	−	0.650783i
$268$		0			0
$269$	−21.1446	−	21.1446i	−1.28921	−	1.28921i	−0.935268	−	0.353941i	$-0.884841\pi$
$269$	−21.1446	−	21.1446i	−1.28921	−	1.28921i	−0.353941	−	0.935268i	$-0.615159\pi$
$270$		0			0
$271$	21.4729			1.30438			0.652192	−	0.758053i	$-0.273849\pi$
$271$	21.4729			1.30438			0.652192	+	0.758053i	$0.273849\pi$
$272$		0			0
$273$			3.76099i			0.227625i
$274$		0			0
$275$	12.5178	−	4.77873i	0.754854	−	0.288169i
$276$		0			0
$277$	−4.23508	−	4.23508i	−0.254461	−	0.254461i	0.568336	−	0.822797i	$-0.307588\pi$
$277$	−4.23508	−	4.23508i	−0.254461	−	0.254461i	−0.822797	+	0.568336i	$0.807588\pi$
$278$		0			0
$279$			4.64288i			0.277962i
$280$		0			0
$281$		−	13.5822i		−	0.810248i	−0.914262	−	0.405124i	$-0.867228\pi$
$281$		−	13.5822i		−	0.810248i	0.914262	−	0.405124i	$-0.132772\pi$
$282$		0			0
$283$	−15.9090	−	15.9090i	−0.945692	−	0.945692i	0.0529078	−	0.998599i	$-0.483151\pi$
$283$	−15.9090	−	15.9090i	−0.945692	−	0.945692i	−0.998599	+	0.0529078i	$0.983151\pi$
$284$		0			0
$285$	16.5113	+	3.52546i	0.978043	+	0.208830i
$286$		0			0
$287$		−	9.89887i		−	0.584312i
$288$		0			0
$289$	13.9781			0.822241
$290$		0			0
$291$	2.72049	+	2.72049i	0.159478	+	0.159478i
$292$		0			0
$293$	−6.55813	−	6.55813i	−0.383130	−	0.383130i	0.489098	−	0.872229i	$-0.337326\pi$
$293$	−6.55813	−	6.55813i	−0.383130	−	0.383130i	−0.872229	+	0.489098i	$0.837326\pi$
$294$		0			0
$295$	0.269958	−	0.174960i	0.0157176	−	0.0101866i
$296$		0			0
$297$	−2.67980			−0.155498
$298$		0			0
$299$	−0.426076	+	0.426076i	−0.0246406	+	0.0246406i
$300$		0			0
$301$	7.23238	+	7.23238i	0.416868	+	0.416868i
$302$		0			0
$303$			7.93257i			0.455714i
$304$		0			0
$305$	−10.3503	−	15.9702i	−0.592656	−	0.914452i
$306$		0			0
$307$	6.02585	−	6.02585i	0.343913	−	0.343913i	−0.513923	−	0.857836i	$-0.671808\pi$
$307$	6.02585	−	6.02585i	0.343913	−	0.343913i	0.857836	+	0.513923i	$0.171808\pi$
$308$		0			0
$309$	−10.6050	+	10.6050i	−0.603300	+	0.603300i
$310$		0			0
$311$			21.1776i			1.20087i	0.799673	+	0.600436i	$0.205006\pi$
$311$			21.1776i			1.20087i	−0.799673	+	0.600436i	$0.794994\pi$
$312$		0			0
$313$	4.30438			0.243298			0.121649	−	0.992573i	$-0.461182\pi$
$313$	4.30438			0.243298			0.121649	+	0.992573i	$0.461182\pi$
$314$		0			0
$315$	−0.466965	+	2.18700i	−0.0263105	+	0.123223i
$316$		0			0
$317$	23.4323	−	23.4323i	1.31609	−	1.31609i	0.399242	−	0.916845i	$-0.369273\pi$
$317$	23.4323	−	23.4323i	1.31609	−	1.31609i	0.916845	−	0.399242i	$-0.130727\pi$
$318$		0			0
$319$	−10.2435			−0.573526
$320$		0			0
$321$	1.73151			0.0966432
$322$		0			0
$323$	9.28113	−	9.28113i	0.516416	−	0.516416i
$324$		0			0
$325$	−17.5665	+	6.70608i	−0.974415	+	0.371987i
$326$		0			0
$327$	−7.51262			−0.415449
$328$		0			0
$329$			4.79632i			0.264430i
$330$		0			0
$331$	−5.03806	+	5.03806i	−0.276917	+	0.276917i	−0.831877	−	0.554960i	$-0.812733\pi$
$331$	−5.03806	+	5.03806i	−0.276917	+	0.276917i	0.554960	+	0.831877i	$0.312733\pi$
$332$		0			0
$333$	−5.35773	+	5.35773i	−0.293602	+	0.293602i
$334$		0			0
$335$	24.0008	−	15.5549i	1.31130	−	0.849856i
$336$		0			0
$337$		−	11.5659i		−	0.630037i	−0.949086	−	0.315018i	$-0.897989\pi$
$337$		−	11.5659i		−	0.630037i	0.949086	−	0.315018i	$-0.102011\pi$
$338$		0			0
$339$	−7.45839	−	7.45839i	−0.405084	−	0.405084i
$340$		0			0
$341$	−8.79779	+	8.79779i	−0.476427	+	0.476427i
$342$		0			0
$343$	−13.0011			−0.701994
$344$		0			0
$345$	−0.300663	+	0.194860i	−0.0161871	+	0.0104909i
$346$		0			0
$347$	1.64106	+	1.64106i	0.0880968	+	0.0880968i	0.749782	−	0.661685i	$-0.230158\pi$
$347$	1.64106	+	1.64106i	0.0880968	+	0.0880968i	−0.661685	+	0.749782i	$0.730158\pi$
$348$		0			0
$349$	−13.8252	−	13.8252i	−0.740045	−	0.740045i	0.232542	−	0.972586i	$-0.425296\pi$
$349$	−13.8252	−	13.8252i	−0.740045	−	0.740045i	−0.972586	+	0.232542i	$0.925296\pi$
$350$		0			0
$351$	3.76061			0.200726
$352$		0			0
$353$			3.70491i			0.197193i	0.995128	+	0.0985964i	$0.0314353\pi$
$353$			3.70491i			0.197193i	−0.995128	+	0.0985964i	$0.968565\pi$
$354$		0			0
$355$	−2.15099	+	10.0740i	−0.114163	+	0.534674i
$356$		0			0
$357$	1.22933	+	1.22933i	0.0650631	+	0.0650631i
$358$		0			0
$359$		−	12.9673i		−	0.684387i	−0.939630	−	0.342194i	$-0.888830\pi$
$359$		−	12.9673i		−	0.684387i	0.939630	−	0.342194i	$-0.111170\pi$
$360$		0			0
$361$			38.0102i			2.00054i
$362$		0			0
$363$	2.70023	+	2.70023i	0.141725	+	0.141725i
$364$		0			0
$365$	26.6612	+	5.69267i	1.39551	+	0.297968i
$366$		0			0
$367$		−	3.12457i		−	0.163101i	−0.996669	−	0.0815507i	$-0.974013\pi$
$367$		−	3.12457i		−	0.163101i	0.996669	−	0.0815507i	$-0.0259873\pi$
$368$		0			0
$369$	−9.89786			−0.515262
$370$		0			0
$371$	−3.44653	−	3.44653i	−0.178935	−	0.178935i
$372$		0			0
$373$	21.1651	+	21.1651i	1.09589	+	1.09589i	0.994886	+	0.101002i	$0.0322050\pi$
$373$	21.1651	+	21.1651i	1.09589	+	1.09589i	0.101002	+	0.994886i	$0.467795\pi$
$374$		0			0
$375$	−11.0475	+	1.71850i	−0.570489	+	0.0887429i
$376$		0			0
$377$	14.3749			0.740344
$378$		0			0
$379$	−2.37189	+	2.37189i	−0.121836	+	0.121836i	−0.765396	−	0.643560i	$-0.777457\pi$
$379$	−2.37189	+	2.37189i	−0.121836	+	0.121836i	0.643560	+	0.765396i	$0.277457\pi$
$380$		0			0
$381$	−4.09106	−	4.09106i	−0.209591	−	0.209591i
$382$		0			0
$383$			3.48238i			0.177942i	0.996034	+	0.0889708i	$0.0283578\pi$
$383$			3.48238i			0.177942i	−0.996034	+	0.0889708i	$0.971642\pi$
$384$		0			0
$385$	−5.02900	+	3.25929i	−0.256301	+	0.166109i
$386$		0			0
$387$	7.23165	−	7.23165i	0.367605	−	0.367605i
$388$		0			0
$389$	−5.90261	+	5.90261i	−0.299274	+	0.299274i	−0.840730	−	0.541455i	$-0.817874\pi$
$389$	−5.90261	+	5.90261i	−0.299274	+	0.299274i	0.541455	+	0.840730i	$0.317874\pi$
$390$		0			0
$391$			0.278537i			0.0140862i
$392$		0			0
$393$	1.44111			0.0726944
$394$		0			0
$395$	12.5418	+	2.67791i	0.631046	+	0.134740i
$396$		0			0
$397$	9.12810	−	9.12810i	0.458126	−	0.458126i	−0.439914	−	0.898040i	$-0.644991\pi$
$397$	9.12810	−	9.12810i	0.458126	−	0.458126i	0.898040	+	0.439914i	$0.144991\pi$
$398$		0			0
$399$	−7.55128			−0.378037
$400$		0			0
$401$	−0.825205			−0.0412088			−0.0206044	−	0.999788i	$-0.506559\pi$
$401$	−0.825205			−0.0412088			−0.0206044	+	0.999788i	$0.506559\pi$
$402$		0			0
$403$	12.3461	−	12.3461i	0.615003	−	0.615003i
$404$		0			0
$405$	2.18678	+	0.466917i	0.108662	+	0.0232013i
$406$		0			0
$407$	−20.3047			−1.00647
$408$		0			0
$409$		−	35.3312i		−	1.74702i	−0.486809	−	0.873508i	$-0.661839\pi$
$409$		−	35.3312i		−	1.74702i	0.486809	−	0.873508i	$-0.338161\pi$
$410$		0			0
$411$	−7.88963	+	7.88963i	−0.389167	+	0.389167i
$412$		0			0
$413$	−0.101740	+	0.101740i	−0.00500628	+	0.00500628i
$414$		0			0
$415$	5.43806	−	3.52441i	0.266944	−	0.173006i
$416$		0			0
$417$			22.5789i			1.10569i
$418$		0			0
$419$	11.7984	+	11.7984i	0.576392	+	0.576392i	0.933907	−	0.357516i	$-0.116376\pi$
$419$	11.7984	+	11.7984i	0.576392	+	0.576392i	−0.357516	+	0.933907i	$0.616376\pi$
$420$		0			0
$421$	−24.9466	+	24.9466i	−1.21582	+	1.21582i	−0.246739	+	0.969082i	$0.579359\pi$
$421$	−24.9466	+	24.9466i	−1.21582	+	1.21582i	−0.969082	+	0.246739i	$0.920641\pi$
$422$		0			0
$423$	4.79583			0.233181
$424$		0			0
$425$	−3.54988	+	7.93383i	−0.172195	+	0.384847i
$426$		0			0
$427$	6.01872	+	6.01872i	0.291266	+	0.291266i
$428$		0			0
$429$	7.12598	+	7.12598i	0.344045	+	0.344045i
$430$		0			0
$431$	10.8925			0.524672			0.262336	−	0.964977i	$-0.415507\pi$
$431$	10.8925			0.524672			0.262336	+	0.964977i	$0.415507\pi$
$432$		0			0
$433$		−	3.09561i		−	0.148765i	−0.997230	−	0.0743827i	$-0.976301\pi$
$433$		−	3.09561i		−	0.148765i	0.997230	−	0.0743827i	$-0.0236986\pi$
$434$		0			0
$435$	8.35894	+	1.78479i	0.400780	+	0.0855740i
$436$		0			0
$437$	−0.855471	−	0.855471i	−0.0409227	−	0.0409227i
$438$		0			0
$439$			26.4374i			1.26179i	0.775869	+	0.630894i	$0.217312\pi$
$439$			26.4374i			1.26179i	−0.775869	+	0.630894i	$0.782688\pi$
$440$		0			0
$441$			5.99980i			0.285705i
$442$		0			0
$443$	18.8131	+	18.8131i	0.893840	+	0.893840i	0.994882	−	0.101042i	$-0.0322178\pi$
$443$	18.8131	+	18.8131i	0.893840	+	0.893840i	−0.101042	+	0.994882i	$0.532218\pi$
$444$		0			0
$445$	−7.02178	+	32.8860i	−0.332864	+	1.55895i
$446$		0			0
$447$		−	20.5346i		−	0.971253i
$448$		0			0
$449$	−16.9583			−0.800310			−0.400155	−	0.916447i	$-0.631044\pi$
$449$	−16.9583			−0.800310			−0.400155	+	0.916447i	$0.631044\pi$
$450$		0			0
$451$	−18.7555	−	18.7555i	−0.883161	−	0.883161i
$452$		0			0
$453$	−10.4108	−	10.4108i	−0.489140	−	0.489140i
$454$		0			0
$455$	7.05728	−	4.57383i	0.330851	−	0.214424i
$456$		0			0
$457$	5.71266			0.267227			0.133614	−	0.991034i	$-0.457342\pi$
$457$	5.71266			0.267227			0.133614	+	0.991034i	$0.457342\pi$
$458$		0			0
$459$	1.22921	−	1.22921i	0.0573744	−	0.0573744i
$460$		0			0
$461$	23.4428	+	23.4428i	1.09184	+	1.09184i	0.995332	+	0.0965077i	$0.0307672\pi$
$461$	23.4428	+	23.4428i	1.09184	+	1.09184i	0.0965077	+	0.995332i	$0.469233\pi$
$462$		0			0
$463$		−	16.7093i		−	0.776547i	−0.921544	−	0.388273i	$-0.873072\pi$
$463$		−	16.7093i		−	0.776547i	0.921544	−	0.388273i	$-0.126928\pi$
$464$		0			0
$465$	8.71210	−	5.64631i	0.404014	−	0.261841i
$466$		0			0
$467$	14.3258	−	14.3258i	0.662918	−	0.662918i	−0.293149	−	0.956067i	$-0.594703\pi$
$467$	14.3258	−	14.3258i	0.662918	−	0.662918i	0.956067	+	0.293149i	$0.0947032\pi$
$468$		0			0
$469$	−9.04522	+	9.04522i	−0.417669	+	0.417669i
$470$		0			0
$471$		−	13.3604i		−	0.615617i
$472$		0			0
$473$	27.4065			1.26015
$474$		0			0
$475$	−13.4644	−	35.2699i	−0.617790	−	1.61829i
$476$		0			0
$477$	−3.44618	+	3.44618i	−0.157790	+	0.157790i
$478$		0			0
$479$	11.2464			0.513860			0.256930	−	0.966430i	$-0.417289\pi$
$479$	11.2464			0.513860			0.256930	+	0.966430i	$0.417289\pi$
$480$		0			0
$481$	28.4940			1.29922
$482$		0			0
$483$	0.113311	−	0.113311i	0.00515584	−	0.00515584i
$484$		0			0
$485$	1.79639	−	8.41330i	0.0815701	−	0.382028i
$486$		0			0
$487$	6.82860			0.309434			0.154717	−	0.987959i	$-0.450553\pi$
$487$	6.82860			0.309434			0.154717	+	0.987959i	$0.450553\pi$
$488$		0			0
$489$		−	10.8348i		−	0.489968i
$490$		0			0
$491$	26.3274	−	26.3274i	1.18814	−	1.18814i	0.210560	−	0.977581i	$-0.432471\pi$
$491$	26.3274	−	26.3274i	1.18814	−	1.18814i	0.977581	−	0.210560i	$-0.0675287\pi$
$492$		0			0
$493$	4.69863	−	4.69863i	0.211616	−	0.211616i
$494$		0			0
$495$	3.25896	+	5.02849i	0.146479	+	0.226014i
$496$		0			0
$497$		−	4.60726i		−	0.206664i
$498$		0			0
$499$	16.9896	+	16.9896i	0.760558	+	0.760558i	0.976423	−	0.215865i	$-0.0692573\pi$
$499$	16.9896	+	16.9896i	0.760558	+	0.760558i	−0.215865	+	0.976423i	$0.569257\pi$
$500$		0			0
$501$	10.1961	−	10.1961i	0.455528	−	0.455528i
$502$		0			0
$503$	−12.7938			−0.570447			−0.285223	−	0.958461i	$-0.592068\pi$
$503$	−12.7938			−0.570447			−0.285223	+	0.958461i	$0.592068\pi$
$504$		0			0
$505$	14.8850	−	9.64698i	0.662375	−	0.429285i
$506$		0			0
$507$	−0.807626	−	0.807626i	−0.0358679	−	0.0358679i
$508$		0			0
$509$	−15.4048	−	15.4048i	−0.682807	−	0.682807i	0.277825	−	0.960632i	$-0.410387\pi$
$509$	−15.4048	−	15.4048i	−0.682807	−	0.682807i	−0.960632	+	0.277825i	$0.910387\pi$
$510$		0			0
$511$	−12.1933			−0.539398
$512$		0			0
$513$			7.55051i			0.333363i
$514$		0			0
$515$	32.7968	+	7.00273i	1.44520	+	0.308577i
$516$		0			0
$517$	9.08763	+	9.08763i	0.399674	+	0.399674i
$518$		0			0
$519$			1.33300i			0.0585121i
$520$		0			0
$521$			2.66408i			0.116715i	0.998296	+	0.0583577i	$0.0185864\pi$
$521$			2.66408i			0.116715i	−0.998296	+	0.0583577i	$0.981414\pi$
$522$		0			0
$523$	10.1050	+	10.1050i	0.441861	+	0.441861i	0.892637	−	0.450776i	$-0.148853\pi$
$523$	10.1050	+	10.1050i	0.441861	+	0.441861i	−0.450776	+	0.892637i	$0.648853\pi$
$524$		0			0
$525$	4.67167	−	1.78343i	0.203888	−	0.0778351i
$526$		0			0
$527$		−	8.07099i		−	0.351578i
$528$		0			0
$529$	−22.9743			−0.998884
$530$		0			0
$531$	0.101729	+	0.101729i	0.00441468	+	0.00441468i
$532$		0			0
$533$	26.3199	+	26.3199i	1.14004	+	1.14004i
$534$		0			0
$535$	−2.10573	−	3.24907i	−0.0910385	−	0.140470i
$536$		0			0
$537$	4.57907			0.197601
$538$		0			0
$539$	−11.3690	+	11.3690i	−0.489699	+	0.489699i
$540$		0			0
$541$	−14.4482	−	14.4482i	−0.621177	−	0.621177i	0.324656	−	0.945832i	$-0.394752\pi$
$541$	−14.4482	−	14.4482i	−0.621177	−	0.621177i	−0.945832	+	0.324656i	$0.894752\pi$
$542$		0			0
$543$		−	18.5140i		−	0.794513i
$544$		0			0
$545$	9.13627	+	14.0970i	0.391355	+	0.603850i
$546$		0			0
$547$	18.9410	−	18.9410i	0.809860	−	0.809860i	−0.174753	−	0.984612i	$-0.555913\pi$
$547$	18.9410	−	18.9410i	0.809860	−	0.809860i	0.984612	+	0.174753i	$0.0559125\pi$
$548$		0			0
$549$	6.01811	−	6.01811i	0.256847	−	0.256847i
$550$		0			0
$551$			28.8618i			1.22955i
$552$		0			0
$553$	−5.73588			−0.243914
$554$		0			0
$555$	16.5691	+	3.53782i	0.703321	+	0.150172i
$556$		0			0
$557$	−29.6116	+	29.6116i	−1.25468	+	1.25468i	−0.301086	+	0.953597i	$0.597349\pi$
$557$	−29.6116	+	29.6116i	−1.25468	+	1.25468i	−0.953597	+	0.301086i	$0.902651\pi$
$558$		0			0
$559$	−38.4601			−1.62669
$560$		0			0
$561$	4.65845			0.196680
$562$		0			0
$563$	−4.19738	+	4.19738i	−0.176898	+	0.176898i	−0.790002	−	0.613104i	$-0.789921\pi$
$563$	−4.19738	+	4.19738i	−0.176898	+	0.176898i	0.613104	+	0.790002i	$0.289921\pi$
$564$		0			0
$565$	−4.92493	+	23.0656i	−0.207193	+	0.970376i
$566$		0			0
$567$	−1.00010			−0.0420003
$568$		0			0
$569$		−	41.7953i		−	1.75215i	−0.482173	−	0.876076i	$-0.660152\pi$
$569$		−	41.7953i		−	1.75215i	0.482173	−	0.876076i	$-0.339848\pi$
$570$		0			0
$571$	10.7600	−	10.7600i	0.450290	−	0.450290i	−0.445160	−	0.895451i	$-0.646853\pi$
$571$	10.7600	−	10.7600i	0.450290	−	0.450290i	0.895451	+	0.445160i	$0.146853\pi$
$572$		0			0
$573$	6.93433	−	6.93433i	0.289686	−	0.289686i
$574$		0			0
$575$	0.731286	+	0.327204i	0.0304967	+	0.0136453i
$576$		0			0
$577$		−	10.6682i		−	0.444124i	−0.975032	−	0.222062i	$-0.928721\pi$
$577$		−	10.6682i		−	0.444124i	0.975032	−	0.222062i	$-0.0712788\pi$
$578$		0			0
$579$	4.82363	+	4.82363i	0.200463	+	0.200463i
$580$		0			0
$581$	−2.04945	+	2.04945i	−0.0850256	+	0.0850256i
$582$		0			0
$583$	−13.0604			−0.540904
$584$		0			0
$585$	−4.57336	−	7.05657i	−0.189085	−	0.291753i
$586$		0			0
$587$	−17.6711	−	17.6711i	−0.729365	−	0.729365i	0.241128	−	0.970493i	$-0.422482\pi$
$587$	−17.6711	−	17.6711i	−0.729365	−	0.729365i	−0.970493	+	0.241128i	$0.922482\pi$
$588$		0			0
$589$	24.7884	+	24.7884i	1.02139	+	1.02139i
$590$		0			0
$591$	21.9404			0.902507
$592$		0			0
$593$			4.79734i			0.197003i	0.995137	+	0.0985016i	$0.0314050\pi$
$593$			4.79734i			0.197003i	−0.995137	+	0.0985016i	$0.968595\pi$
$594$		0			0
$595$	0.811752	−	3.80179i	0.0332786	−	0.155858i
$596$		0			0
$597$	5.60064	+	5.60064i	0.229219	+	0.229219i
$598$		0			0
$599$			1.03944i			0.0424705i	0.999775	+	0.0212353i	$0.00675991\pi$
$599$			1.03944i			0.0424705i	−0.999775	+	0.0212353i	$0.993240\pi$
$600$		0			0
$601$			6.22752i			0.254026i	0.991901	+	0.127013i	$0.0405390\pi$
$601$			6.22752i			0.254026i	−0.991901	+	0.127013i	$0.959461\pi$
$602$		0			0
$603$	9.04430	+	9.04430i	0.368312	+	0.368312i
$604$		0			0
$605$	1.78301	−	8.35063i	0.0724898	−	0.339501i
$606$		0			0
$607$			25.3718i			1.02981i	0.857247	+	0.514905i	$0.172173\pi$
$607$			25.3718i			1.02981i	−0.857247	+	0.514905i	$0.827827\pi$
$608$		0			0
$609$	−3.82288			−0.154911
$610$		0			0
$611$	−12.7528	−	12.7528i	−0.515925	−	0.515925i
$612$		0			0
$613$	17.1175	+	17.1175i	0.691369	+	0.691369i	0.962533	−	0.271164i	$-0.0874086\pi$
$613$	17.1175	+	17.1175i	0.691369	+	0.691369i	−0.271164	+	0.962533i	$0.587409\pi$
$614$		0			0
$615$	12.0370	+	18.5728i	0.485380	+	0.748927i
$616$		0			0
$617$	8.28793			0.333659			0.166830	−	0.985986i	$-0.446647\pi$
$617$	8.28793			0.333659			0.166830	+	0.985986i	$0.446647\pi$
$618$		0			0
$619$	−2.23506	+	2.23506i	−0.0898348	+	0.0898348i	−0.750596	−	0.660761i	$-0.770234\pi$
$619$	−2.23506	+	2.23506i	−0.0898348	+	0.0898348i	0.660761	+	0.750596i	$0.270234\pi$
$620$		0			0
$621$	−0.113300	−	0.113300i	−0.00454656	−	0.00454656i
$622$		0			0
$623$		−	15.0401i		−	0.602570i
$624$		0			0
$625$	16.6598	+	18.6401i	0.666391	+	0.745603i
$626$		0			0
$627$	−14.3075	+	14.3075i	−0.571385	+	0.571385i
$628$		0			0
$629$	9.31367	−	9.31367i	0.371360	−	0.371360i
$630$		0			0
$631$			17.2372i			0.686201i	0.939299	+	0.343100i	$0.111477\pi$
$631$			17.2372i			0.686201i	−0.939299	+	0.343100i	$0.888523\pi$
$632$		0			0
$633$	14.4261			0.573387
$634$		0			0
$635$	−2.70141	+	12.6519i	−0.107202	+	0.502074i
$636$		0			0
$637$	15.9544	−	15.9544i	0.632135	−	0.632135i
$638$		0			0
$639$	−4.60679			−0.182242
$640$		0			0
$641$	24.8101			0.979941			0.489971	−	0.871739i	$-0.337007\pi$
$641$	24.8101			0.979941			0.489971	+	0.871739i	$0.337007\pi$
$642$		0			0
$643$	−20.7142	+	20.7142i	−0.816887	+	0.816887i	−0.985656	−	0.168769i	$-0.946021\pi$
$643$	−20.7142	+	20.7142i	−0.816887	+	0.816887i	0.168769	+	0.985656i	$0.446021\pi$
$644$		0			0
$645$	−22.3644	−	4.77521i	−0.880596	−	0.188024i
$646$		0			0
$647$	−14.3607			−0.564577			−0.282289	−	0.959330i	$-0.591094\pi$
$647$	−14.3607			−0.564577			−0.282289	+	0.959330i	$0.591094\pi$
$648$		0			0
$649$			0.385534i			0.0151335i
$650$		0			0
$651$	−3.28334	+	3.28334i	−0.128684	+	0.128684i
$652$		0			0
$653$	8.23394	−	8.23394i	0.322219	−	0.322219i	−0.527399	−	0.849618i	$-0.676833\pi$
$653$	8.23394	−	8.23394i	0.322219	−	0.322219i	0.849618	+	0.527399i	$0.176833\pi$
$654$		0			0
$655$	−1.75257	−	2.70416i	−0.0684785	−	0.105660i
$656$		0			0
$657$			12.1920i			0.475656i
$658$		0			0
$659$	−32.8934	−	32.8934i	−1.28134	−	1.28134i	−0.939904	−	0.341440i	$-0.889085\pi$
$659$	−32.8934	−	32.8934i	−1.28134	−	1.28134i	−0.341440	−	0.939904i	$-0.610915\pi$
$660$		0			0
$661$	15.8937	−	15.8937i	0.618193	−	0.618193i	−0.326875	−	0.945068i	$-0.605996\pi$
$661$	15.8937	−	15.8937i	0.618193	−	0.618193i	0.945068	+	0.326875i	$0.105996\pi$
$662$		0			0
$663$	−6.53729			−0.253887
$664$		0			0
$665$	9.18328	+	14.1695i	0.356113	+	0.549471i
$666$		0			0
$667$	−0.433087	−	0.433087i	−0.0167692	−	0.0167692i
$668$		0			0
$669$	−9.80681	−	9.80681i	−0.379153	−	0.379153i
$670$		0			0
$671$	22.8075			0.880472
$672$		0			0
$673$			1.87365i			0.0722238i	0.999348	+	0.0361119i	$0.0114973\pi$
$673$			1.87365i			0.0722238i	−0.999348	+	0.0361119i	$0.988503\pi$
$674$		0			0
$675$	−1.78325	−	4.67119i	−0.0686372	−	0.179794i
$676$		0			0
$677$	−27.7045	−	27.7045i	−1.06477	−	1.06477i	−0.997752	−	0.0670200i	$-0.978651\pi$
$677$	−27.7045	−	27.7045i	−1.06477	−	1.06477i	−0.0670200	−	0.997752i	$-0.521349\pi$
$678$		0			0
$679$			3.84774i			0.147663i
$680$		0			0
$681$			25.3399i			0.971026i
$682$		0			0
$683$	−15.9666	−	15.9666i	−0.610945	−	0.610945i	0.332247	−	0.943192i	$-0.392193\pi$
$683$	−15.9666	−	15.9666i	−0.610945	−	0.610945i	−0.943192	+	0.332247i	$0.892193\pi$
$684$		0			0
$685$	24.3992	+	5.20968i	0.932246	+	0.199052i
$686$		0			0
$687$		−	2.89043i		−	0.110277i
$688$		0			0
$689$	18.3278			0.698235
$690$		0			0
$691$	8.47128	+	8.47128i	0.322263	+	0.322263i	0.849635	−	0.527372i	$-0.176823\pi$
$691$	8.47128	+	8.47128i	0.322263	+	0.322263i	−0.527372	+	0.849635i	$0.676823\pi$
$692$		0			0
$693$	−1.89509	−	1.89509i	−0.0719887	−	0.0719887i
$694$		0			0
$695$	42.3680	−	27.4587i	1.60711	−	1.04157i
$696$		0			0
$697$	17.2061			0.651726
$698$		0			0
$699$	7.85480	−	7.85480i	0.297096	−	0.297096i
$700$		0			0
$701$	−12.7252	−	12.7252i	−0.480624	−	0.480624i	0.424707	−	0.905331i	$-0.360377\pi$
$701$	−12.7252	−	12.7252i	−0.480624	−	0.480624i	−0.905331	+	0.424707i	$0.860377\pi$
$702$		0			0
$703$			57.2100i			2.15772i
$704$		0			0
$705$	−5.83233	−	8.99912i	−0.219658	−	0.338926i
$706$		0			0
$707$	−5.60974	+	5.60974i	−0.210976	+	0.210976i
$708$		0			0
$709$	5.12731	−	5.12731i	0.192560	−	0.192560i	−0.604241	−	0.796801i	$-0.706524\pi$
$709$	5.12731	−	5.12731i	0.192560	−	0.192560i	0.796801	+	0.604241i	$0.206524\pi$
$710$		0			0
$711$			5.73529i			0.215090i
$712$		0			0
$713$	−0.743928			−0.0278603
$714$		0			0
$715$	4.70543	−	22.0376i	0.175973	−	0.824158i
$716$		0			0
$717$	−13.5132	+	13.5132i	−0.504660	+	0.504660i
$718$		0			0
$719$	7.22269			0.269361			0.134681	−	0.990889i	$-0.456999\pi$
$719$	7.22269			0.269361			0.134681	+	0.990889i	$0.456999\pi$
$720$		0			0
$721$	−14.9993			−0.558604
$722$		0			0
$723$	−4.20801	+	4.20801i	−0.156497	+	0.156497i
$724$		0			0
$725$	−6.81645	−	17.8556i	−0.253156	−	0.663140i
$726$		0			0
$727$	50.4488			1.87104			0.935522	−	0.353268i	$-0.114930\pi$
$727$	50.4488			1.87104			0.935522	+	0.353268i	$0.114930\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−12.5712	+	12.5712i	−0.464963	+	0.464963i
$732$		0			0
$733$	−9.19912	+	9.19912i	−0.339777	+	0.339777i	−0.856283	−	0.516506i	$-0.827232\pi$
$733$	−9.19912	+	9.19912i	−0.339777	+	0.339777i	0.516506	+	0.856283i	$0.327232\pi$
$734$		0			0
$735$	11.2583	−	7.29650i	0.415268	−	0.269135i
$736$		0			0
$737$			34.2761i			1.26258i
$738$		0			0
$739$	−5.53064	−	5.53064i	−0.203448	−	0.203448i	0.598028	−	0.801476i	$-0.295951\pi$
$739$	−5.53064	−	5.53064i	−0.203448	−	0.203448i	−0.801476	+	0.598028i	$0.795951\pi$
$740$		0			0
$741$	20.0779	−	20.0779i	0.737581	−	0.737581i
$742$		0			0
$743$	7.49683			0.275032			0.137516	−	0.990500i	$-0.456088\pi$
$743$	7.49683			0.275032			0.137516	+	0.990500i	$0.456088\pi$
$744$		0			0
$745$	−38.5320	+	24.9726i	−1.41170	+	0.914926i
$746$		0			0
$747$	2.04924	+	2.04924i	0.0749779	+	0.0749779i
$748$		0			0
$749$	1.22448	+	1.22448i	0.0447417	+	0.0447417i
$750$		0			0
$751$	8.92232			0.325580			0.162790	−	0.986661i	$-0.447951\pi$
$751$	8.92232			0.325580			0.162790	+	0.986661i	$0.447951\pi$
$752$		0			0
$753$		−	29.5166i		−	1.07564i
$754$		0			0
$755$	−6.87444	+	32.1960i	−0.250186	+	1.17173i
$756$		0			0
$757$	−7.26524	−	7.26524i	−0.264060	−	0.264060i	0.562641	−	0.826701i	$-0.309785\pi$
$757$	−7.26524	−	7.26524i	−0.264060	−	0.264060i	−0.826701	+	0.562641i	$0.809785\pi$
$758$		0			0
$759$		−	0.429384i		−	0.0155856i
$760$		0			0
$761$		−	21.6817i		−	0.785963i	−0.919546	−	0.392981i	$-0.871444\pi$
$761$		−	21.6817i		−	0.785963i	0.919546	−	0.392981i	$-0.128556\pi$
$762$		0			0
$763$	−5.31276	−	5.31276i	−0.192335	−	0.192335i
$764$		0			0
$765$	−3.80140	−	0.811670i	−0.137440	−	0.0293460i
$766$		0			0
$767$		−	0.541027i		−	0.0195354i
$768$		0			0
$769$	0.339883			0.0122565			0.00612824	−	0.999981i	$-0.498049\pi$
$769$	0.339883			0.0122565			0.00612824	+	0.999981i	$0.498049\pi$
$770$		0			0
$771$	6.58009	+	6.58009i	0.236976	+	0.236976i
$772$		0			0
$773$	−30.8536	−	30.8536i	−1.10973	−	1.10973i	−0.993186	−	0.116541i	$-0.962819\pi$
$773$	−30.8536	−	30.8536i	−1.10973	−	1.10973i	−0.116541	−	0.993186i	$-0.537181\pi$
$774$		0			0
$775$	−21.1900	−	9.48115i	−0.761167	−	0.340573i
$776$		0			0
$777$	−7.57775			−0.271850
$778$		0			0
$779$	−52.8449	+	52.8449i	−1.89336	+	1.89336i
$780$		0			0
$781$	−8.72942	−	8.72942i	−0.312363	−	0.312363i
$782$		0			0
$783$			3.82249i			0.136605i
$784$		0			0
$785$	−25.0701	+	16.2480i	−0.894791	+	0.579914i
$786$		0			0
$787$	9.03797	−	9.03797i	0.322169	−	0.322169i	−0.527430	−	0.849599i	$-0.676844\pi$
$787$	9.03797	−	9.03797i	0.322169	−	0.322169i	0.849599	+	0.527430i	$0.176844\pi$
$788$		0			0
$789$	14.2073	−	14.2073i	0.505795	−	0.505795i
$790$		0			0
$791$		−	10.5488i		−	0.375073i
$792$		0			0
$793$	−32.0061			−1.13657
$794$		0			0
$795$	10.6576	+	2.27558i	0.377984	+	0.0807067i
$796$		0			0
$797$	−26.5763	+	26.5763i	−0.941380	+	0.941380i	−0.998374	−	0.0569944i	$-0.981848\pi$
$797$	−26.5763	+	26.5763i	−0.941380	+	0.941380i	0.0569944	+	0.998374i	$0.481848\pi$
$798$		0			0
$799$	−8.33689			−0.294938
$800$		0			0
$801$	−15.0386			−0.531362
$802$		0			0
$803$	−23.1027	+	23.1027i	−0.815277	+	0.815277i
$804$		0			0
$805$	−0.350423	−	0.0748217i	−0.0123508	−	0.00263712i
$806$		0			0
$807$	−29.9030			−1.05263
$808$		0			0
$809$			40.1166i			1.41043i	0.708996	+	0.705213i	$0.249148\pi$
$809$			40.1166i			1.41043i	−0.708996	+	0.705213i	$0.750852\pi$
$810$		0			0
$811$	4.55343	−	4.55343i	0.159893	−	0.159893i	−0.622627	−	0.782519i	$-0.713934\pi$
$811$	4.55343	−	4.55343i	0.159893	−	0.159893i	0.782519	+	0.622627i	$0.213934\pi$
$812$		0			0
$813$	15.1836	−	15.1836i	0.532513	−	0.532513i
$814$		0			0
$815$	−20.3309	+	13.1765i	−0.712162	+	0.461552i
$816$		0			0
$817$		−	77.2198i		−	2.70158i
$818$		0			0
$819$	2.65942	+	2.65942i	0.0929276	+	0.0929276i
$820$		0			0
$821$	−15.8058	+	15.8058i	−0.551627	+	0.551627i	−0.926910	−	0.375283i	$-0.877545\pi$
$821$	−15.8058	+	15.8058i	−0.551627	+	0.551627i	0.375283	+	0.926910i	$0.377545\pi$
$822$		0			0
$823$	−3.03903			−0.105934			−0.0529669	−	0.998596i	$-0.516868\pi$
$823$	−3.03903			−0.105934			−0.0529669	+	0.998596i	$0.516868\pi$
$824$		0			0
$825$	5.47237	−	12.2305i	0.190524	−	0.425812i
$826$		0			0
$827$	−1.52610	−	1.52610i	−0.0530678	−	0.0530678i	0.680075	−	0.733143i	$-0.261947\pi$
$827$	−1.52610	−	1.52610i	−0.0530678	−	0.0530678i	−0.733143	+	0.680075i	$0.761947\pi$
$828$		0			0
$829$	−28.7055	−	28.7055i	−0.996984	−	0.996984i	0.00301145	−	0.999995i	$-0.499041\pi$
$829$	−28.7055	−	28.7055i	−0.996984	−	0.996984i	−0.999995	+	0.00301145i	$0.999041\pi$
$830$		0			0
$831$	−5.98931			−0.207767
$832$		0			0
$833$		−	10.4298i		−	0.361371i
$834$		0			0
$835$	−31.5321	−	6.73270i	−1.09121	−	0.232995i
$836$		0			0
$837$	3.28301	+	3.28301i	0.113477	+	0.113477i
$838$		0			0
$839$			11.9438i			0.412346i	0.978516	+	0.206173i	$0.0661010\pi$
$839$			11.9438i			0.412346i	−0.978516	+	0.206173i	$0.933899\pi$
$840$		0			0
$841$		−	14.3885i		−	0.496157i
$842$		0			0
$843$	−9.60409	−	9.60409i	−0.330782	−	0.330782i
$844$		0			0
$845$	−0.533292	+	2.49764i	−0.0183458	+	0.0859213i
$846$		0			0
$847$			3.81908i			0.131225i
$848$		0			0
$849$	−22.4987			−0.772154
$850$		0			0
$851$	−0.858469	−	0.858469i	−0.0294280	−	0.0294280i
$852$		0			0
$853$	3.53433	+	3.53433i	0.121013	+	0.121013i	0.765020	−	0.644007i	$-0.222729\pi$
$853$	3.53433	+	3.53433i	0.121013	+	0.121013i	−0.644007	+	0.765020i	$0.722729\pi$
$854$		0			0
$855$	14.1681	−	9.18235i	0.484539	−	0.314030i
$856$		0			0
$857$	−56.1606			−1.91841			−0.959205	−	0.282710i	$-0.908767\pi$
$857$	−56.1606			−1.91841			−0.959205	+	0.282710i	$0.908767\pi$
$858$		0			0
$859$	4.66448	−	4.66448i	0.159150	−	0.159150i	−0.623040	−	0.782190i	$-0.714103\pi$
$859$	4.66448	−	4.66448i	0.159150	−	0.159150i	0.782190	+	0.623040i	$0.214103\pi$
$860$		0			0
$861$	−6.99956	−	6.99956i	−0.238544	−	0.238544i
$862$		0			0
$863$			12.5882i			0.428507i	0.976778	+	0.214253i	$0.0687319\pi$
$863$			12.5882i			0.428507i	−0.976778	+	0.214253i	$0.931268\pi$
$864$		0			0
$865$	2.50130	−	1.62109i	0.0850467	−	0.0551188i
$866$		0			0
$867$	9.88401	−	9.88401i	0.335679	−	0.335679i
$868$		0			0
$869$	−10.8678	+	10.8678i	−0.368665	+	0.368665i
$870$		0			0
$871$		−	48.1003i		−	1.62982i
$872$		0			0
$873$	3.84735			0.130213
$874$		0			0
$875$	−9.02783	−	6.59725i	−0.305196	−	0.223028i
$876$		0			0
$877$	−23.7329	+	23.7329i	−0.801403	+	0.801403i	−0.983315	−	0.181912i	$-0.941772\pi$
$877$	−23.7329	+	23.7329i	−0.801403	+	0.801403i	0.181912	+	0.983315i	$0.441772\pi$
$878$		0			0
$879$	−9.27460			−0.312825
$880$		0			0
$881$	−3.75776			−0.126602			−0.0633011	−	0.997994i	$-0.520163\pi$
$881$	−3.75776			−0.126602			−0.0633011	+	0.997994i	$0.520163\pi$
$882$		0			0
$883$	−17.1877	+	17.1877i	−0.578413	+	0.578413i	−0.934466	−	0.356053i	$-0.884122\pi$
$883$	−17.1877	+	17.1877i	−0.578413	+	0.578413i	0.356053	+	0.934466i	$0.384122\pi$
$884$		0			0
$885$	0.0671740	−	0.314605i	0.00225803	−	0.0105753i
$886$		0			0
$887$	−49.8359			−1.67333			−0.836663	−	0.547718i	$-0.815497\pi$
$887$	−49.8359			−1.67333			−0.836663	+	0.547718i	$0.815497\pi$
$888$		0			0
$889$		−	5.78621i		−	0.194063i
$890$		0			0
$891$	−1.89490	+	1.89490i	−0.0634816	+	0.0634816i
$892$		0			0
$893$	25.6050	−	25.6050i	0.856840	−	0.856840i
$894$		0			0
$895$	−5.56871	−	8.59236i	−0.186142	−	0.287211i
$896$		0			0
$897$			0.602562i			0.0201190i
$898$		0			0
$899$	12.5493	+	12.5493i	0.418542	+	0.418542i
$900$		0			0
$901$	5.99070	−	5.99070i	0.199579	−	0.199579i
$902$		0			0
$903$	10.2281			0.340371
$904$		0			0
$905$	−34.7405	+	22.5153i	−1.15481	+	0.748435i
$906$		0			0
$907$	25.1326	+	25.1326i	0.834515	+	0.834515i	0.988131	−	0.153616i	$-0.0490919\pi$
$907$	25.1326	+	25.1326i	0.834515	+	0.834515i	−0.153616	+	0.988131i	$0.549092\pi$
$908$		0			0
$909$	5.60917	+	5.60917i	0.186044	+	0.186044i
$910$		0			0
$911$	−49.4774			−1.63926			−0.819629	−	0.572894i	$-0.805821\pi$
$911$	−49.4774			−1.63926			−0.819629	+	0.572894i	$0.805821\pi$
$912$		0			0
$913$			7.76623i			0.257025i
$914$		0			0
$915$	−18.6114	−	3.97388i	−0.615274	−	0.131372i
$916$		0			0
$917$	1.01912	+	1.01912i	0.0336544	+	0.0336544i
$918$		0			0
$919$		−	4.92570i		−	0.162484i	−0.996694	−	0.0812420i	$-0.974111\pi$
$919$		−	4.92570i		−	0.162484i	0.996694	−	0.0812420i	$-0.0258886\pi$
$920$		0			0
$921$		−	8.52184i		−	0.280804i
$922$		0			0
$923$	12.2502	+	12.2502i	0.403219	+	0.403219i
$924$		0			0
$925$	−13.5116	−	35.3935i	−0.444259	−	1.16373i
$926$		0			0
$927$			14.9978i			0.492592i
$928$		0			0
$929$	15.7829			0.517822			0.258911	−	0.965901i	$-0.416636\pi$
$929$	15.7829			0.517822			0.258911	+	0.965901i	$0.416636\pi$
$930$		0			0
$931$	32.0330	+	32.0330i	1.04984	+	1.04984i
$932$		0			0
$933$	14.9748	+	14.9748i	0.490254	+	0.490254i
$934$		0			0
$935$	−5.66525	−	8.74132i	−0.185274	−	0.285872i
$936$		0			0
$937$	23.6323			0.772033			0.386017	−	0.922492i	$-0.373851\pi$
$937$	23.6323			0.772033			0.386017	+	0.922492i	$0.373851\pi$
$938$		0			0
$939$	3.04366	−	3.04366i	0.0993259	−	0.0993259i
$940$		0			0
$941$	22.0372	+	22.0372i	0.718391	+	0.718391i	0.968276	−	0.249884i	$-0.0803926\pi$
$941$	22.0372	+	22.0372i	0.718391	+	0.718391i	−0.249884	+	0.968276i	$0.580393\pi$
$942$		0			0
$943$		−	1.58594i		−	0.0516452i
$944$		0			0
$945$	1.21625	+	1.87663i	0.0395645	+	0.0610469i
$946$		0			0
$947$	−8.89469	+	8.89469i	−0.289039	+	0.289039i	−0.836700	−	0.547661i	$-0.815518\pi$
$947$	−8.89469	+	8.89469i	−0.289039	+	0.289039i	0.547661	+	0.836700i	$0.315518\pi$
$948$		0			0
$949$	32.4204	−	32.4204i	1.05241	−	1.05241i
$950$		0			0
$951$		−	33.1382i		−	1.07458i
$952$		0			0
$953$	−24.1239			−0.781450			−0.390725	−	0.920507i	$-0.627776\pi$
$953$	−24.1239			−0.781450			−0.390725	+	0.920507i	$0.627776\pi$
$954$		0			0
$955$	−21.4449	−	4.57888i	−0.693941	−	0.148169i
$956$		0			0
$957$	−7.24325	+	7.24325i	−0.234141	+	0.234141i
$958$		0			0
$959$	−11.1588			−0.360335
$960$		0			0
$961$	−9.44370			−0.304636
$962$		0			0
$963$	1.22436	−	1.22436i	0.0394544	−	0.0394544i
$964$		0			0
$965$	3.18514	−	14.9174i	0.102533	−	0.480208i
$966$		0			0
$967$	−17.5889			−0.565620			−0.282810	−	0.959176i	$-0.591267\pi$
$967$	−17.5889			−0.565620			−0.282810	+	0.959176i	$0.591267\pi$
$968$		0			0
$969$		−	13.1255i		−	0.421652i
$970$		0			0
$971$	−4.45325	+	4.45325i	−0.142911	+	0.142911i	−0.774943	−	0.632031i	$-0.782221\pi$
$971$	−4.45325	+	4.45325i	−0.142911	+	0.142911i	0.632031	+	0.774943i	$0.282221\pi$
$972$		0			0
$973$	−15.9673	+	15.9673i	−0.511888	+	0.511888i
$974$		0			0
$975$	−7.67948	+	17.1633i	−0.245940	+	0.549666i
$976$		0			0
$977$		−	33.1408i		−	1.06027i	−0.847914	−	0.530134i	$-0.822142\pi$
$977$		−	33.1408i		−	1.06027i	0.847914	−	0.530134i	$-0.177858\pi$
$978$		0			0
$979$	−28.4967	−	28.4967i	−0.910757	−	0.910757i
$980$		0			0
$981$	−5.31222	+	5.31222i	−0.169606	+	0.169606i
$982$		0			0
$983$	27.3732			0.873070			0.436535	−	0.899687i	$-0.356206\pi$
$983$	27.3732			0.873070			0.436535	+	0.899687i	$0.356206\pi$
$984$		0			0
$985$	−26.6822	−	41.1699i	−0.850167	−	1.31178i
$986$		0			0
$987$	3.39151	+	3.39151i	0.107953	+	0.107953i
$988$		0			0
$989$	1.15873	+	1.15873i	0.0368454	+	0.0368454i
$990$		0			0
$991$	−11.5423			−0.366653			−0.183327	−	0.983052i	$-0.558687\pi$
$991$	−11.5423			−0.366653			−0.183327	+	0.983052i	$0.558687\pi$
$992$		0			0
$993$			7.12489i			0.226102i
$994$		0			0
$995$	3.69822	−	17.3204i	0.117241	−	0.549092i
$996$		0			0
$997$	−28.5401	−	28.5401i	−0.903874	−	0.903874i	0.0918946	−	0.995769i	$-0.470708\pi$
$997$	−28.5401	−	28.5401i	−0.903874	−	0.903874i	−0.995769	+	0.0918946i	$0.970708\pi$
$998$		0			0
$999$			7.57698i			0.239725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.a.289.19		48
4.3	odd	2		1920.2.bl.b.289.6		48
5.4	even	2	inner	1920.2.bl.a.289.6		48
8.3	odd	2		960.2.bl.a.529.23		48
8.5	even	2		240.2.bl.a.109.1	✓	48
16.3	odd	4		960.2.bl.a.49.5		48
16.5	even	4	inner	1920.2.bl.a.1249.6		48
16.11	odd	4		1920.2.bl.b.1249.19		48
16.13	even	4		240.2.bl.a.229.24	yes	48
20.19	odd	2		1920.2.bl.b.289.19		48
24.5	odd	2		720.2.bm.h.109.24		48
40.19	odd	2		960.2.bl.a.529.5		48
40.29	even	2		240.2.bl.a.109.24	yes	48
48.29	odd	4		720.2.bm.h.469.1		48
80.19	odd	4		960.2.bl.a.49.23		48
80.29	even	4		240.2.bl.a.229.1	yes	48
80.59	odd	4		1920.2.bl.b.1249.6		48
80.69	even	4	inner	1920.2.bl.a.1249.19		48
120.29	odd	2		720.2.bm.h.109.1		48
240.29	odd	4		720.2.bm.h.469.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.1	✓	48	8.5	even	2
240.2.bl.a.109.24	yes	48	40.29	even	2
240.2.bl.a.229.1	yes	48	80.29	even	4
240.2.bl.a.229.24	yes	48	16.13	even	4
720.2.bm.h.109.1		48	120.29	odd	2
720.2.bm.h.109.24		48	24.5	odd	2
720.2.bm.h.469.1		48	48.29	odd	4
720.2.bm.h.469.24		48	240.29	odd	4
960.2.bl.a.49.5		48	16.3	odd	4
960.2.bl.a.49.23		48	80.19	odd	4
960.2.bl.a.529.5		48	40.19	odd	2
960.2.bl.a.529.23		48	8.3	odd	2
1920.2.bl.a.289.6		48	5.4	even	2	inner
1920.2.bl.a.289.19		48	1.1	even	1	trivial
1920.2.bl.a.1249.6		48	16.5	even	4	inner
1920.2.bl.a.1249.19		48	80.69	even	4	inner
1920.2.bl.b.289.6		48	4.3	odd	2
1920.2.bl.b.289.19		48	20.19	odd	2
1920.2.bl.b.1249.6		48	80.59	odd	4
1920.2.bl.b.1249.19		48	16.11	odd	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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.18678 - 0.466917i) q^{5} +1.00010 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.18678 - 0.466917i) q^{5} +1.00010 q^{7} -1.00000i q^{9} +(1.89490 - 1.89490i) q^{11} +(-2.65915 + 2.65915i) q^{13} +(-1.87644 + 1.21612i) q^{15} +1.73836i q^{17} +(-5.33902 - 5.33902i) q^{19} +(0.707179 - 0.707179i) q^{21} +0.160230 q^{23} +(4.56398 + 2.04209i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-2.70291 - 2.70291i) q^{29} -4.64288 q^{31} -2.67980i q^{33} +(-2.18700 - 0.466965i) q^{35} +(-5.35773 - 5.35773i) q^{37} +3.76061i q^{39} -9.89786i q^{41} +(7.23165 + 7.23165i) q^{43} +(-0.466917 + 2.18678i) q^{45} +4.79583i q^{47} -5.99980 q^{49} +(1.22921 + 1.22921i) q^{51} +(-3.44618 - 3.44618i) q^{53} +(-5.02849 + 3.25896i) q^{55} -7.55051 q^{57} +(-0.101729 + 0.101729i) q^{59} +(6.01811 + 6.01811i) q^{61} -1.00010i q^{63} +(7.05657 - 4.57336i) q^{65} +(-9.04430 + 9.04430i) q^{67} +(0.113300 - 0.113300i) q^{69} -4.60679i q^{71} -12.1920 q^{73} +(4.67119 - 1.78325i) q^{75} +(1.89509 - 1.89509i) q^{77} -5.73529 q^{79} -1.00000 q^{81} +(-2.04924 + 2.04924i) q^{83} +(0.811670 - 3.80140i) q^{85} -3.82249 q^{87} -15.0386i q^{89} +(-2.65942 + 2.65942i) q^{91} +(-3.28301 + 3.28301i) q^{93} +(9.18235 + 14.1681i) q^{95} +3.84735i q^{97} +(-1.89490 - 1.89490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) \) 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

Introduction

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