LMFDB - Embedded newform 585.2.c.b.469.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(469,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("585.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.c (of order $2$, degree $1$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.5
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.b.469.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.53919i q^{2} -0.369102 q^{4} +(-0.539189 + 2.17009i) q^{5} +1.70928i q^{7} +2.51026i q^{8} +O(q^{10})$	\(q+1.53919i q^{2} -0.369102 q^{4} +(-0.539189 + 2.17009i) q^{5} +1.70928i q^{7} +2.51026i q^{8} +(-3.34017 - 0.829914i) q^{10} +2.53919 q^{11} -1.00000i q^{13} -2.63090 q^{14} -4.60197 q^{16} +0.921622i q^{17} +0.539189 q^{19} +(0.199016 - 0.800984i) q^{20} +3.90829i q^{22} -2.82991i q^{23} +(-4.41855 - 2.34017i) q^{25} +1.53919 q^{26} -0.630898i q^{28} -5.12783 q^{29} +0.879362 q^{31} -2.06278i q^{32} -1.41855 q^{34} +(-3.70928 - 0.921622i) q^{35} +6.04945i q^{37} +0.829914i q^{38} +(-5.44748 - 1.35350i) q^{40} -1.26180 q^{41} +6.43188i q^{43} -0.937221 q^{44} +4.35577 q^{46} +5.70928i q^{47} +4.07838 q^{49} +(3.60197 - 6.80098i) q^{50} +0.369102i q^{52} -8.49693i q^{53} +(-1.36910 + 5.51026i) q^{55} -4.29072 q^{56} -7.89269i q^{58} -4.72261 q^{59} +8.04945 q^{61} +1.35350i q^{62} -6.02893 q^{64} +(2.17009 + 0.539189i) q^{65} -7.86603i q^{67} -0.340173i q^{68} +(1.41855 - 5.70928i) q^{70} +14.4813 q^{71} -1.95055i q^{73} -9.31124 q^{74} -0.199016 q^{76} +4.34017i q^{77} -0.496928 q^{79} +(2.48133 - 9.98667i) q^{80} -1.94214i q^{82} -8.63090i q^{83} +(-2.00000 - 0.496928i) q^{85} -9.89988 q^{86} +6.37402i q^{88} +12.8371 q^{89} +1.70928 q^{91} +1.04453i q^{92} -8.78765 q^{94} +(-0.290725 + 1.17009i) q^{95} -5.91548i q^{97} +6.27739i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4}+O(q^{10}) $ 6 * q - 10 * q^4	$ 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50} - 16 q^{55} - 40 q^{56} - 16 q^{59} + 12 q^{61} - 66 q^{64} + 2 q^{65} - 20 q^{70} + 24 q^{71} - 4 q^{74} - 20 q^{76} + 32 q^{79} - 48 q^{80} - 12 q^{85} + 32 q^{86} + 20 q^{89} - 4 q^{91} - 32 q^{94} - 16 q^{95}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^10 + 12 * q^11 - 8 * q^14 + 10 * q^16 + 20 * q^20 + 2 * q^25 + 6 * q^26 + 12 * q^29 - 20 * q^31 + 20 * q^34 - 8 * q^35 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 32 * q^46 + 18 * q^49 - 16 * q^50 - 16 * q^55 - 40 * q^56 - 16 * q^59 + 12 * q^61 - 66 * q^64 + 2 * q^65 - 20 * q^70 + 24 * q^71 - 4 * q^74 - 20 * q^76 + 32 * q^79 - 48 * q^80 - 12 * q^85 + 32 * q^86 + 20 * q^89 - 4 * q^91 - 32 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.53919i			1.08837i	0.838965	+	0.544185i	$0.183161\pi$
$2$			1.53919i			1.08837i	−0.838965	+	0.544185i	$0.816839\pi$
$3$		0			0
$3$		0			0
$4$	−0.369102			−0.184551
$5$	−0.539189	+	2.17009i	−0.241133	+	0.970492i
$5$	−0.539189	+	2.17009i	−0.241133	+	0.970492i
$6$		0			0
$7$			1.70928i			0.646045i	0.946391	+	0.323023i	$0.104699\pi$
$7$			1.70928i			0.646045i	−0.946391	+	0.323023i	$0.895301\pi$
$8$			2.51026i			0.887511i
$9$		0			0
$10$	−3.34017	−	0.829914i	−1.05626	−	0.262442i
$11$	2.53919			0.765594			0.382797	−	0.923832i	$-0.374961\pi$
$11$	2.53919			0.765594			0.382797	+	0.923832i	$0.374961\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−2.63090			−0.703137
$15$		0			0
$16$	−4.60197			−1.15049
$17$			0.921622i			0.223526i	0.993735	+	0.111763i	$0.0356498\pi$
$17$			0.921622i			0.223526i	−0.993735	+	0.111763i	$0.964350\pi$
$18$		0			0
$19$	0.539189			0.123698			0.0618492	−	0.998086i	$-0.480300\pi$
$19$	0.539189			0.123698			0.0618492	+	0.998086i	$0.480300\pi$
$20$	0.199016	−	0.800984i	0.0445013	−	0.179105i
$21$		0			0
$22$			3.90829i			0.833250i
$23$		−	2.82991i		−	0.590078i	−0.955485	−	0.295039i	$-0.904667\pi$
$23$		−	2.82991i		−	0.590078i	0.955485	−	0.295039i	$-0.0953326\pi$
$24$		0			0
$25$	−4.41855	−	2.34017i	−0.883710	−	0.468035i
$26$	1.53919			0.301860
$27$		0			0
$28$		−	0.630898i		−	0.119228i
$29$	−5.12783			−0.952213			−0.476107	−	0.879388i	$-0.657952\pi$
$29$	−5.12783			−0.952213			−0.476107	+	0.879388i	$0.657952\pi$
$30$		0			0
$31$	0.879362			0.157938			0.0789690	−	0.996877i	$-0.474837\pi$
$31$	0.879362			0.157938			0.0789690	+	0.996877i	$0.474837\pi$
$32$		−	2.06278i		−	0.364651i
$33$		0			0
$34$	−1.41855			−0.243279
$35$	−3.70928	−	0.921622i	−0.626982	−	0.155783i
$36$		0			0
$37$			6.04945i			0.994523i	0.867601	+	0.497262i	$0.165661\pi$
$37$			6.04945i			0.994523i	−0.867601	+	0.497262i	$0.834339\pi$
$38$			0.829914i			0.134630i
$39$		0			0
$40$	−5.44748	−	1.35350i	−0.861322	−	0.214008i
$41$	−1.26180			−0.197059			−0.0985297	−	0.995134i	$-0.531414\pi$
$41$	−1.26180			−0.197059			−0.0985297	+	0.995134i	$0.531414\pi$
$42$		0			0
$43$			6.43188i			0.980853i	0.871483	+	0.490426i	$0.163159\pi$
$43$			6.43188i			0.980853i	−0.871483	+	0.490426i	$0.836841\pi$
$44$	−0.937221			−0.141291
$45$		0			0
$46$	4.35577			0.642223
$47$			5.70928i			0.832783i	0.909185	+	0.416392i	$0.136705\pi$
$47$			5.70928i			0.832783i	−0.909185	+	0.416392i	$0.863295\pi$
$48$		0			0
$49$	4.07838			0.582625
$50$	3.60197	−	6.80098i	0.509395	−	0.961804i
$51$		0			0
$52$			0.369102i			0.0511853i
$53$		−	8.49693i		−	1.16714i	−0.812062	−	0.583571i	$-0.801655\pi$
$53$		−	8.49693i		−	1.16714i	0.812062	−	0.583571i	$-0.198345\pi$
$54$		0			0
$55$	−1.36910	+	5.51026i	−0.184610	+	0.743003i
$56$	−4.29072			−0.573372
$57$		0			0
$58$		−	7.89269i		−	1.03636i
$59$	−4.72261			−0.614831			−0.307415	−	0.951575i	$-0.599464\pi$
$59$	−4.72261			−0.614831			−0.307415	+	0.951575i	$0.599464\pi$
$60$		0			0
$61$	8.04945			1.03063			0.515313	−	0.857002i	$-0.327676\pi$
$61$	8.04945			1.03063			0.515313	+	0.857002i	$0.327676\pi$
$62$			1.35350i			0.171895i
$63$		0			0
$64$	−6.02893			−0.753616
$65$	2.17009	+	0.539189i	0.269166	+	0.0668781i
$66$		0			0
$67$		−	7.86603i		−	0.960989i	−0.876998	−	0.480494i	$-0.840457\pi$
$67$		−	7.86603i		−	0.960989i	0.876998	−	0.480494i	$-0.159543\pi$
$68$		−	0.340173i		−	0.0412520i
$69$		0			0
$70$	1.41855	−	5.70928i	0.169549	−	0.682389i
$71$	14.4813			1.71862			0.859309	−	0.511457i	$-0.170894\pi$
$71$	14.4813			1.71862			0.859309	+	0.511457i	$0.170894\pi$
$72$		0			0
$73$		−	1.95055i		−	0.228295i	−0.993464	−	0.114147i	$-0.963586\pi$
$73$		−	1.95055i		−	0.228295i	0.993464	−	0.114147i	$-0.0364136\pi$
$74$	−9.31124			−1.08241
$75$		0			0
$76$	−0.199016			−0.0228287
$77$			4.34017i			0.494609i
$78$		0			0
$79$	−0.496928			−0.0559088			−0.0279544	−	0.999609i	$-0.508899\pi$
$79$	−0.496928			−0.0559088			−0.0279544	+	0.999609i	$0.508899\pi$
$80$	2.48133	−	9.98667i	0.277421	−	1.11654i
$81$		0			0
$82$		−	1.94214i		−	0.214474i
$83$		−	8.63090i		−	0.947364i	−0.880696	−	0.473682i	$-0.842925\pi$
$83$		−	8.63090i		−	0.947364i	0.880696	−	0.473682i	$-0.157075\pi$
$84$		0			0
$85$	−2.00000	−	0.496928i	−0.216930	−	0.0538995i
$86$	−9.89988			−1.06753
$87$		0			0
$88$			6.37402i			0.679473i
$89$	12.8371			1.36073			0.680365	−	0.732873i	$-0.261821\pi$
$89$	12.8371			1.36073			0.680365	+	0.732873i	$0.261821\pi$
$90$		0			0
$91$	1.70928			0.179181
$92$			1.04453i			0.108900i
$93$		0			0
$94$	−8.78765			−0.906377
$95$	−0.290725	+	1.17009i	−0.0298277	+	0.120048i
$96$		0			0
$97$		−	5.91548i		−	0.600626i	−0.953841	−	0.300313i	$-0.902909\pi$
$97$		−	5.91548i		−	0.600626i	0.953841	−	0.300313i	$-0.0970911\pi$
$98$			6.27739i			0.634113i
$99$		0			0
$100$	1.63090	+	0.863763i	0.163090	+	0.0863763i
$101$	16.4391			1.63575			0.817874	−	0.575397i	$-0.195152\pi$
$101$	16.4391			1.63575			0.817874	+	0.575397i	$0.195152\pi$
$102$		0			0
$103$		−	10.1906i		−	1.00411i	−0.864836	−	0.502055i	$-0.832577\pi$
$103$		−	10.1906i		−	1.00411i	0.864836	−	0.502055i	$-0.167423\pi$
$104$	2.51026			0.246151
$105$		0			0
$106$	13.0784			1.27028
$107$			9.75154i			0.942717i	0.881942	+	0.471358i	$0.156236\pi$
$107$			9.75154i			0.942717i	−0.881942	+	0.471358i	$0.843764\pi$
$108$		0			0
$109$	16.8638			1.61526			0.807628	−	0.589693i	$-0.200751\pi$
$109$	16.8638			1.61526			0.807628	+	0.589693i	$0.200751\pi$
$110$	−8.48133	−	2.10731i	−0.808663	−	0.200924i
$111$		0			0
$112$		−	7.86603i		−	0.743270i
$113$			11.7587i			1.10617i	0.833126	+	0.553084i	$0.186549\pi$
$113$			11.7587i			1.10617i	−0.833126	+	0.553084i	$0.813451\pi$
$114$		0			0
$115$	6.14116	+	1.52586i	0.572666	+	0.142287i
$116$	1.89269			0.175732
$117$		0			0
$118$		−	7.26898i		−	0.669164i
$119$	−1.57531			−0.144408
$120$		0			0
$121$	−4.55252			−0.413865
$122$			12.3896i			1.12170i
$123$		0			0
$124$	−0.324575			−0.0291477
$125$	7.46081	−	8.32684i	0.667315	−	0.744775i
$126$		0			0
$127$			18.0072i			1.59788i	0.601411	+	0.798940i	$0.294605\pi$
$127$			18.0072i			1.59788i	−0.601411	+	0.798940i	$0.705395\pi$
$128$		−	13.4052i		−	1.18487i
$129$		0			0
$130$	−0.829914	+	3.34017i	−0.0727882	+	0.292953i
$131$	−14.2557			−1.24552			−0.622761	−	0.782412i	$-0.713989\pi$
$131$	−14.2557			−1.24552			−0.622761	+	0.782412i	$0.713989\pi$
$132$		0			0
$133$			0.921622i			0.0799148i
$134$	12.1073			1.04591
$135$		0			0
$136$	−2.31351			−0.198382
$137$			13.7854i			1.17776i	0.808219	+	0.588882i	$0.200432\pi$
$137$			13.7854i			1.17776i	−0.808219	+	0.588882i	$0.799568\pi$
$138$		0			0
$139$	6.65368			0.564358			0.282179	−	0.959362i	$-0.408943\pi$
$139$	6.65368			0.564358			0.282179	+	0.959362i	$0.408943\pi$
$140$	1.36910	+	0.340173i	0.115710	+	0.0287499i
$141$		0			0
$142$			22.2895i			1.87049i
$143$		−	2.53919i		−	0.212338i
$144$		0			0
$145$	2.76487	−	11.1278i	0.229610	−	0.924116i
$146$	3.00227			0.248469
$147$		0			0
$148$		−	2.23287i		−	0.183540i
$149$	−9.07838			−0.743730			−0.371865	−	0.928287i	$-0.621282\pi$
$149$	−9.07838			−0.743730			−0.371865	+	0.928287i	$0.621282\pi$
$150$		0			0
$151$	3.27739			0.266711			0.133355	−	0.991068i	$-0.457425\pi$
$151$	3.27739			0.266711			0.133355	+	0.991068i	$0.457425\pi$
$152$			1.35350i			0.109784i
$153$		0			0
$154$	−6.68035			−0.538318
$155$	−0.474142	+	1.90829i	−0.0380840	+	0.153278i
$156$		0			0
$157$		−	12.8371i		−	1.02451i	−0.858833	−	0.512256i	$-0.828810\pi$
$157$		−	12.8371i		−	1.02451i	0.858833	−	0.512256i	$-0.171190\pi$
$158$		−	0.764867i		−	0.0608495i
$159$		0			0
$160$	4.47641	+	1.11223i	0.353891	+	0.0879293i
$161$	4.83710			0.381217
$162$		0			0
$163$			12.0494i			0.943786i	0.881656	+	0.471893i	$0.156429\pi$
$163$			12.0494i			0.943786i	−0.881656	+	0.471893i	$0.843571\pi$
$164$	0.465732			0.0363675
$165$		0			0
$166$	13.2846			1.03108
$167$			8.72979i			0.675532i	0.941230	+	0.337766i	$0.109671\pi$
$167$			8.72979i			0.675532i	−0.941230	+	0.337766i	$0.890329\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	0.764867	−	3.07838i	0.0586626	−	0.236101i
$171$		0			0
$172$		−	2.37402i		−	0.181018i
$173$		−	0.863763i		−	0.0656707i	−0.999461	−	0.0328354i	$-0.989546\pi$
$173$		−	0.863763i		−	0.0656707i	0.999461	−	0.0328354i	$-0.0104537\pi$
$174$		0			0
$175$	4.00000	−	7.55252i	0.302372	−	0.570917i
$176$	−11.6853			−0.880810
$177$		0			0
$178$			19.7587i			1.48098i
$179$	19.9155			1.48855			0.744276	−	0.667872i	$-0.232795\pi$
$179$	19.9155			1.48855			0.744276	+	0.667872i	$0.232795\pi$
$180$		0			0
$181$	14.3896			1.06957			0.534786	−	0.844987i	$-0.320392\pi$
$181$	14.3896			1.06957			0.534786	+	0.844987i	$0.320392\pi$
$182$			2.63090i			0.195015i
$183$		0			0
$184$	7.10382			0.523700
$185$	−13.1278	−	3.26180i	−0.965177	−	0.239812i
$186$		0			0
$187$			2.34017i			0.171130i
$188$		−	2.10731i		−	0.153691i
$189$		0			0
$190$	−1.80098	−	0.447480i	−0.130657	−	0.0324636i
$191$	−1.47641			−0.106829			−0.0534146	−	0.998572i	$-0.517010\pi$
$191$	−1.47641			−0.106829			−0.0534146	+	0.998572i	$0.517010\pi$
$192$		0			0
$193$		−	17.7321i		−	1.27638i	−0.769878	−	0.638191i	$-0.779683\pi$
$193$		−	17.7321i		−	1.27638i	0.769878	−	0.638191i	$-0.220317\pi$
$194$	9.10504			0.653704
$195$		0			0
$196$	−1.50534			−0.107524
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$		0			0
$199$	5.39189			0.382221			0.191110	−	0.981569i	$-0.438791\pi$
$199$	5.39189			0.382221			0.191110	+	0.981569i	$0.438791\pi$
$200$	5.87444	−	11.0917i	0.415386	−	0.784302i
$201$		0			0
$202$			25.3028i			1.78030i
$203$		−	8.76487i		−	0.615173i
$204$		0			0
$205$	0.680346	−	2.73820i	0.0475174	−	0.191245i
$206$	15.6853			1.09284
$207$		0			0
$208$			4.60197i			0.319089i
$209$	1.36910			0.0947028
$210$		0			0
$211$	−22.7526			−1.56635			−0.783176	−	0.621800i	$-0.786402\pi$
$211$	−22.7526			−1.56635			−0.783176	+	0.621800i	$0.786402\pi$
$212$			3.13624i			0.215398i
$213$		0			0
$214$	−15.0095			−1.02603
$215$	−13.9577	−	3.46800i	−0.951910	−	0.236516i
$216$		0			0
$217$			1.50307i			0.102035i
$218$			25.9565i			1.75800i
$219$		0			0
$220$	0.505339	−	2.03385i	0.0340699	−	0.137122i
$221$	0.921622			0.0619950
$222$		0			0
$223$			8.76099i			0.586679i	0.956008	+	0.293340i	$0.0947667\pi$
$223$			8.76099i			0.586679i	−0.956008	+	0.293340i	$0.905233\pi$
$224$	3.52586			0.235581
$225$		0			0
$226$	−18.0989			−1.20392
$227$		−	17.2267i		−	1.14338i	−0.820470	−	0.571689i	$-0.806288\pi$
$227$		−	17.2267i		−	1.14338i	0.820470	−	0.571689i	$-0.193712\pi$
$228$		0			0
$229$	−3.07838			−0.203425			−0.101712	−	0.994814i	$-0.532432\pi$
$229$	−3.07838			−0.203425			−0.101712	+	0.994814i	$0.532432\pi$
$230$	−2.34858	+	9.45240i	−0.154861	+	0.623273i
$231$		0			0
$232$		−	12.8722i		−	0.845100i
$233$		−	18.9360i		−	1.24054i	−0.784389	−	0.620269i	$-0.787023\pi$
$233$		−	18.9360i		−	1.24054i	0.784389	−	0.620269i	$-0.212977\pi$
$234$		0			0
$235$	−12.3896	−	3.07838i	−0.808210	−	0.200811i
$236$	1.74313			0.113468
$237$		0			0
$238$		−	2.42469i		−	0.157170i
$239$	6.63809			0.429382			0.214691	−	0.976682i	$-0.431126\pi$
$239$	6.63809			0.429382			0.214691	+	0.976682i	$0.431126\pi$
$240$		0			0
$241$	−9.47641			−0.610429			−0.305215	−	0.952284i	$-0.598728\pi$
$241$	−9.47641			−0.610429			−0.305215	+	0.952284i	$0.598728\pi$
$242$		−	7.00719i		−	0.450439i
$243$		0			0
$244$	−2.97107			−0.190203
$245$	−2.19902	+	8.85043i	−0.140490	+	0.565433i
$246$		0			0
$247$		−	0.539189i		−	0.0343078i
$248$			2.20743i			0.140172i
$249$		0			0
$250$	12.8166	+	11.4836i	0.810592	+	0.726286i
$251$	−29.4596			−1.85947			−0.929736	−	0.368226i	$-0.879965\pi$
$251$	−29.4596			−1.85947			−0.929736	+	0.368226i	$0.879965\pi$
$252$		0			0
$253$		−	7.18568i		−	0.451760i
$254$	−27.7165			−1.73909
$255$		0			0
$256$	8.57531			0.535957
$257$		−	20.4657i		−	1.27662i	−0.769781	−	0.638309i	$-0.779634\pi$
$257$		−	20.4657i		−	1.27662i	0.769781	−	0.638309i	$-0.220366\pi$
$258$		0			0
$259$	−10.3402			−0.642507
$260$	−0.800984	−	0.199016i	−0.0496749	−	0.0123424i
$261$		0			0
$262$		−	21.9421i		−	1.35559i
$263$		−	9.14342i		−	0.563808i	−0.959443	−	0.281904i	$-0.909034\pi$
$263$		−	9.14342i		−	0.563808i	0.959443	−	0.281904i	$-0.0909659\pi$
$264$		0			0
$265$	18.4391	+	4.58145i	1.13270	+	0.281436i
$266$	−1.41855			−0.0869769
$267$		0			0
$268$			2.90337i			0.177352i
$269$	11.3919			0.694576			0.347288	−	0.937759i	$-0.387103\pi$
$269$	11.3919			0.694576			0.347288	+	0.937759i	$0.387103\pi$
$270$		0			0
$271$	−21.1350			−1.28386			−0.641930	−	0.766763i	$-0.721866\pi$
$271$	−21.1350			−1.28386			−0.641930	+	0.766763i	$0.721866\pi$
$272$		−	4.24128i		−	0.257165i
$273$		0			0
$274$	−21.2183			−1.28185
$275$	−11.2195	−	5.94214i	−0.676563	−	0.358325i
$276$		0			0
$277$			13.0784i			0.785804i	0.919580	+	0.392902i	$0.128529\pi$
$277$			13.0784i			0.785804i	−0.919580	+	0.392902i	$0.871471\pi$
$278$			10.2413i			0.614231i
$279$		0			0
$280$	2.31351	−	9.31124i	0.138259	−	0.556453i
$281$	0.680346			0.0405860			0.0202930	−	0.999794i	$-0.493540\pi$
$281$	0.680346			0.0405860			0.0202930	+	0.999794i	$0.493540\pi$
$282$		0			0
$283$		−	19.2956i		−	1.14701i	−0.819203	−	0.573504i	$-0.805584\pi$
$283$		−	19.2956i		−	1.14701i	0.819203	−	0.573504i	$-0.194416\pi$
$284$	−5.34509			−0.317173
$285$		0			0
$286$	3.90829			0.231102
$287$		−	2.15676i		−	0.127309i
$288$		0			0
$289$	16.1506			0.950036
$290$	17.1278	+	4.25565i	1.00578	+	0.249900i
$291$		0			0
$292$			0.719953i			0.0421321i
$293$			9.46800i			0.553126i	0.960996	+	0.276563i	$0.0891955\pi$
$293$			9.46800i			0.553126i	−0.960996	+	0.276563i	$0.910804\pi$
$294$		0			0
$295$	2.54638	−	10.2485i	0.148256	−	0.596689i
$296$	−15.1857			−0.882650
$297$		0			0
$298$		−	13.9733i		−	0.809454i
$299$	−2.82991			−0.163658
$300$		0			0
$301$	−10.9939			−0.633675
$302$			5.04453i			0.290280i
$303$		0			0
$304$	−2.48133			−0.142314
$305$	−4.34017	+	17.4680i	−0.248518	+	1.00021i
$306$		0			0
$307$			0.264063i			0.0150709i	0.999972	+	0.00753543i	$0.00239862\pi$
$307$			0.264063i			0.0150709i	−0.999972	+	0.00753543i	$0.997601\pi$
$308$		−	1.60197i		−	0.0912806i
$309$		0			0
$310$	−2.93722	−	0.729794i	−0.166823	−	0.0414495i
$311$	−13.0472			−0.739838			−0.369919	−	0.929064i	$-0.620615\pi$
$311$	−13.0472			−0.739838			−0.369919	+	0.929064i	$0.620615\pi$
$312$		0			0
$313$		−	33.7009i		−	1.90489i	−0.304718	−	0.952443i	$-0.598562\pi$
$313$		−	33.7009i		−	1.90489i	0.304718	−	0.952443i	$-0.401438\pi$
$314$	19.7587			1.11505
$315$		0			0
$316$	0.183417			0.0103180
$317$		−	13.9506i		−	0.783541i	−0.920063	−	0.391771i	$-0.871863\pi$
$317$		−	13.9506i		−	0.783541i	0.920063	−	0.391771i	$-0.128137\pi$
$318$		0			0
$319$	−13.0205			−0.729009
$320$	3.25073	−	13.0833i	0.181721	−	0.731379i
$321$		0			0
$322$			7.44521i			0.414905i
$323$			0.496928i			0.0276498i
$324$		0			0
$325$	−2.34017	+	4.41855i	−0.129809	+	0.245097i
$326$	−18.5464			−1.02719
$327$		0			0
$328$		−	3.16743i		−	0.174892i
$329$	−9.75872			−0.538016
$330$		0			0
$331$	−18.4547			−1.01436			−0.507180	−	0.861840i	$-0.669312\pi$
$331$	−18.4547			−1.01436			−0.507180	+	0.861840i	$0.669312\pi$
$332$			3.18568i			0.174837i
$333$		0			0
$334$	−13.4368			−0.735229
$335$	17.0700	+	4.24128i	0.932632	+	0.231726i
$336$		0			0
$337$			15.8576i			0.863820i	0.901917	+	0.431910i	$0.142160\pi$
$337$			15.8576i			0.863820i	−0.901917	+	0.431910i	$0.857840\pi$
$338$		−	1.53919i		−	0.0837208i
$339$		0			0
$340$	0.738205	+	0.183417i	0.0400348	+	0.00994721i
$341$	2.23287			0.120916
$342$		0			0
$343$			18.9360i			1.02245i
$344$	−16.1457			−0.870517
$345$		0			0
$346$	1.32950			0.0714741
$347$			9.72487i			0.522059i	0.965331	+	0.261029i	$0.0840619\pi$
$347$			9.72487i			0.522059i	−0.965331	+	0.261029i	$0.915938\pi$
$348$		0			0
$349$	30.9093			1.65454			0.827269	−	0.561805i	$-0.189893\pi$
$349$	30.9093			1.65454			0.827269	+	0.561805i	$0.189893\pi$
$350$	11.6248	+	6.15676i	0.621369	+	0.329092i
$351$		0			0
$352$		−	5.23779i		−	0.279175i
$353$		−	5.95055i		−	0.316716i	−0.987382	−	0.158358i	$-0.949380\pi$
$353$		−	5.95055i		−	0.316716i	0.987382	−	0.158358i	$-0.0506200\pi$
$354$		0			0
$355$	−7.80817	+	31.4257i	−0.414415	+	1.66791i
$356$	−4.73820			−0.251124
$357$		0			0
$358$			30.6537i			1.62010i
$359$	10.9783			0.579410			0.289705	−	0.957116i	$-0.406443\pi$
$359$	10.9783			0.579410			0.289705	+	0.957116i	$0.406443\pi$
$360$		0			0
$361$	−18.7093			−0.984699
$362$			22.1483i			1.16409i
$363$		0			0
$364$	−0.630898			−0.0330680
$365$	4.23287	+	1.05172i	0.221558	+	0.0550493i
$366$		0			0
$367$		−	10.3740i		−	0.541520i	−0.962647	−	0.270760i	$-0.912725\pi$
$367$		−	10.3740i		−	0.541520i	0.962647	−	0.270760i	$-0.0872749\pi$
$368$			13.0232i			0.678880i
$369$		0			0
$370$	5.02052	−	20.2062i	0.261004	−	1.05047i
$371$	14.5236			0.754027
$372$		0			0
$373$			23.9877i			1.24204i	0.783796	+	0.621018i	$0.213281\pi$
$373$			23.9877i			1.24204i	−0.783796	+	0.621018i	$0.786719\pi$
$374$	−3.60197			−0.186253
$375$		0			0
$376$	−14.3318			−0.739104
$377$			5.12783i			0.264096i
$378$		0			0
$379$	−29.7575			−1.52854			−0.764270	−	0.644896i	$-0.776901\pi$
$379$	−29.7575			−1.52854			−0.764270	+	0.644896i	$0.776901\pi$
$380$	0.107307	−	0.431882i	0.00550474	−	0.0221551i
$381$		0			0
$382$		−	2.27247i		−	0.116270i
$383$		−	12.4163i		−	0.634442i	−0.948352	−	0.317221i	$-0.897250\pi$
$383$		−	12.4163i		−	0.634442i	0.948352	−	0.317221i	$-0.102750\pi$
$384$		0			0
$385$	−9.41855	−	2.34017i	−0.480014	−	0.119266i
$386$	27.2930			1.38918
$387$		0			0
$388$			2.18342i			0.110846i
$389$	−16.8371			−0.853675			−0.426837	−	0.904328i	$-0.640372\pi$
$389$	−16.8371			−0.853675			−0.426837	+	0.904328i	$0.640372\pi$
$390$		0			0
$391$	2.60811			0.131898
$392$			10.2378i			0.517086i
$393$		0			0
$394$	−3.07838			−0.155086
$395$	0.267938	−	1.07838i	0.0134814	−	0.0542591i
$396$		0			0
$397$			3.89269i			0.195369i	0.995217	+	0.0976843i	$0.0311436\pi$
$397$			3.89269i			0.195369i	−0.995217	+	0.0976843i	$0.968856\pi$
$398$			8.29914i			0.415998i
$399$		0			0
$400$	20.3340	+	10.7694i	1.01670	+	0.538470i
$401$	9.10504			0.454684			0.227342	−	0.973815i	$-0.426996\pi$
$401$	9.10504			0.454684			0.227342	+	0.973815i	$0.426996\pi$
$402$		0			0
$403$		−	0.879362i		−	0.0438041i
$404$	−6.06770			−0.301879
$405$		0			0
$406$	13.4908			0.669536
$407$			15.3607i			0.761401i
$408$		0			0
$409$	19.4186			0.960186			0.480093	−	0.877218i	$-0.340603\pi$
$409$	19.4186			0.960186			0.480093	+	0.877218i	$0.340603\pi$
$410$	4.21461	+	1.04718i	0.208145	+	0.0517166i
$411$		0			0
$412$			3.76138i			0.185310i
$413$		−	8.07223i		−	0.397209i
$414$		0			0
$415$	18.7298	+	4.65368i	0.919409	+	0.228440i
$416$	−2.06278			−0.101136
$417$		0			0
$418$			2.10731i			0.103072i
$419$	−16.7792			−0.819720			−0.409860	−	0.912149i	$-0.634422\pi$
$419$	−16.7792			−0.819720			−0.409860	+	0.912149i	$0.634422\pi$
$420$		0			0
$421$	−19.0205			−0.927003			−0.463502	−	0.886096i	$-0.653407\pi$
$421$	−19.0205			−0.927003			−0.463502	+	0.886096i	$0.653407\pi$
$422$		−	35.0205i		−	1.70477i
$423$		0			0
$424$	21.3295			1.03585
$425$	2.15676	−	4.07223i	0.104618	−	0.197532i
$426$		0			0
$427$			13.7587i			0.665831i
$428$		−	3.59932i		−	0.173979i
$429$		0			0
$430$	5.33791	−	21.4836i	0.257417	−	1.03603i
$431$	−8.02997			−0.386790			−0.193395	−	0.981121i	$-0.561950\pi$
$431$	−8.02997			−0.386790			−0.193395	+	0.981121i	$0.561950\pi$
$432$		0			0
$433$			13.0472i			0.627008i	0.949587	+	0.313504i	$0.101503\pi$
$433$			13.0472i			0.627008i	−0.949587	+	0.313504i	$0.898497\pi$
$434$	−2.31351			−0.111052
$435$		0			0
$436$	−6.22446			−0.298097
$437$		−	1.52586i		−	0.0729917i
$438$		0			0
$439$	7.70086			0.367542			0.183771	−	0.982969i	$-0.441169\pi$
$439$	7.70086			0.367542			0.183771	+	0.982969i	$0.441169\pi$
$440$	−13.8322	−	3.43680i	−0.659423	−	0.163843i
$441$		0			0
$442$			1.41855i			0.0674736i
$443$		−	6.39084i		−	0.303638i	−0.988408	−	0.151819i	$-0.951487\pi$
$443$		−	6.39084i		−	0.303638i	0.988408	−	0.151819i	$-0.0485131\pi$
$444$		0			0
$445$	−6.92162	+	27.8576i	−0.328116	+	1.32058i
$446$	−13.4848			−0.638525
$447$		0			0
$448$		−	10.3051i		−	0.486870i
$449$	31.6163			1.49207			0.746034	−	0.665908i	$-0.231956\pi$
$449$	31.6163			1.49207			0.746034	+	0.665908i	$0.231956\pi$
$450$		0			0
$451$	−3.20394			−0.150867
$452$		−	4.34017i		−	0.204145i
$453$		0			0
$454$	26.5152			1.24442
$455$	−0.921622	+	3.70928i	−0.0432063	+	0.173894i
$456$		0			0
$457$		−	35.6430i		−	1.66731i	−0.552286	−	0.833655i	$-0.686244\pi$
$457$		−	35.6430i		−	1.66731i	0.552286	−	0.833655i	$-0.313756\pi$
$458$		−	4.73820i		−	0.221402i
$459$		0			0
$460$	−2.26672	−	0.563198i	−0.105686	−	0.0262592i
$461$	14.9795			0.697664			0.348832	−	0.937185i	$-0.386578\pi$
$461$	14.9795			0.697664			0.348832	+	0.937185i	$0.386578\pi$
$462$		0			0
$463$			9.09663i			0.422756i	0.977404	+	0.211378i	$0.0677951\pi$
$463$			9.09663i			0.422756i	−0.977404	+	0.211378i	$0.932205\pi$
$464$	23.5981			1.09551
$465$		0			0
$466$	29.1461			1.35017
$467$		−	1.87709i		−	0.0868616i	−0.999056	−	0.0434308i	$-0.986171\pi$
$467$		−	1.87709i		−	0.0868616i	0.999056	−	0.0434308i	$-0.0138288\pi$
$468$		0			0
$469$	13.4452			0.620842
$470$	4.73820	−	19.0700i	0.218557	−	0.879632i
$471$		0			0
$472$		−	11.8550i		−	0.545669i
$473$			16.3318i			0.750935i
$474$		0			0
$475$	−2.38243	−	1.26180i	−0.109314	−	0.0578951i
$476$	0.581449			0.0266507
$477$		0			0
$478$			10.2173i			0.467327i
$479$	−15.7431			−0.719322			−0.359661	−	0.933083i	$-0.617108\pi$
$479$	−15.7431			−0.719322			−0.359661	+	0.933083i	$0.617108\pi$
$480$		0			0
$481$	6.04945			0.275831
$482$		−	14.5860i		−	0.664373i
$483$		0			0
$484$	1.68035			0.0763794
$485$	12.8371	+	3.18956i	0.582903	+	0.144830i
$486$		0			0
$487$			4.94441i			0.224053i	0.993705	+	0.112026i	$0.0357341\pi$
$487$			4.94441i			0.224053i	−0.993705	+	0.112026i	$0.964266\pi$
$488$			20.2062i			0.914692i
$489$		0			0
$490$	−13.6225	−	3.38470i	−0.615401	−	0.152905i
$491$	−39.4863			−1.78199			−0.890995	−	0.454014i	$-0.849992\pi$
$491$	−39.4863			−1.78199			−0.890995	+	0.454014i	$0.849992\pi$
$492$		0			0
$493$		−	4.72592i		−	0.212845i
$494$	0.829914			0.0373396
$495$		0			0
$496$	−4.04680			−0.181706
$497$			24.7526i			1.11030i
$498$		0			0
$499$	−1.67089			−0.0747993			−0.0373997	−	0.999300i	$-0.511907\pi$
$499$	−1.67089			−0.0747993			−0.0373997	+	0.999300i	$0.511907\pi$
$500$	−2.75380	+	3.07346i	−0.123154	+	0.137449i
$501$		0			0
$502$		−	45.3439i		−	2.02380i
$503$			9.08557i			0.405105i	0.979271	+	0.202553i	$0.0649237\pi$
$503$			9.08557i			0.405105i	−0.979271	+	0.202553i	$0.935076\pi$
$504$		0			0
$505$	−8.86376	+	35.6742i	−0.394432	+	1.58748i
$506$	11.0601			0.491683
$507$		0			0
$508$		−	6.64650i		−	0.294891i
$509$	−19.5441			−0.866277			−0.433139	−	0.901327i	$-0.642594\pi$
$509$	−19.5441			−0.866277			−0.433139	+	0.901327i	$0.642594\pi$
$510$		0			0
$511$	3.33403			0.147489
$512$		−	13.6114i		−	0.601546i
$513$		0			0
$514$	31.5006			1.38943
$515$	22.1145	+	5.49466i	0.974481	+	0.242124i
$516$		0			0
$517$			14.4969i			0.637574i
$518$		−	15.9155i		−	0.699286i
$519$		0			0
$520$	−1.35350	+	5.44748i	−0.0593551	+	0.238888i
$521$	−6.50534			−0.285004			−0.142502	−	0.989795i	$-0.545515\pi$
$521$	−6.50534			−0.285004			−0.142502	+	0.989795i	$0.545515\pi$
$522$		0			0
$523$		−	36.5452i		−	1.59801i	−0.601326	−	0.799004i	$-0.705361\pi$
$523$		−	36.5452i		−	1.59801i	0.601326	−	0.799004i	$-0.294639\pi$
$524$	5.26180			0.229863
$525$		0			0
$526$	14.0735			0.613632
$527$			0.810439i			0.0353033i
$528$		0			0
$529$	14.9916			0.651808
$530$	−7.05172	+	28.3812i	−0.306307	+	1.23280i
$531$		0			0
$532$		−	0.340173i		−	0.0147484i
$533$			1.26180i			0.0546544i
$534$		0			0
$535$	−21.1617	−	5.25792i	−0.914899	−	0.227320i
$536$	19.7458			0.852888
$537$		0			0
$538$			17.5343i			0.755956i
$539$	10.3558			0.446055
$540$		0			0
$541$	20.3402			0.874492			0.437246	−	0.899342i	$-0.355954\pi$
$541$	20.3402			0.874492			0.437246	+	0.899342i	$0.355954\pi$
$542$		−	32.5308i		−	1.39732i
$543$		0			0
$544$	1.90110			0.0815091
$545$	−9.09275	+	36.5958i	−0.389491	+	1.56759i
$546$		0			0
$547$		−	11.5948i		−	0.495757i	−0.968791	−	0.247879i	$-0.920267\pi$
$547$		−	11.5948i		−	0.495757i	0.968791	−	0.247879i	$-0.0797334\pi$
$548$		−	5.08822i		−	0.217358i
$549$		0			0
$550$	9.14608	−	17.2690i	0.389990	−	0.736352i
$551$	−2.76487			−0.117787
$552$		0			0
$553$		−	0.849388i		−	0.0361196i
$554$	−20.1301			−0.855246
$555$		0			0
$556$	−2.45589			−0.104153
$557$		−	10.7298i		−	0.454636i	−0.973821	−	0.227318i	$-0.927004\pi$
$557$		−	10.7298i		−	0.454636i	0.973821	−	0.227318i	$-0.0729957\pi$
$558$		0			0
$559$	6.43188			0.272040
$560$	17.0700	+	4.24128i	0.721338	+	0.179227i
$561$		0			0
$562$			1.04718i			0.0441727i
$563$			10.2485i			0.431921i	0.976402	+	0.215961i	$0.0692883\pi$
$563$			10.2485i			0.431921i	−0.976402	+	0.215961i	$0.930712\pi$
$564$		0			0
$565$	−25.5174	−	6.34017i	−1.07353	−	0.266733i
$566$	29.6996			1.24837
$567$		0			0
$568$			36.3519i			1.52529i
$569$	−8.84551			−0.370823			−0.185412	−	0.982661i	$-0.559362\pi$
$569$	−8.84551			−0.370823			−0.185412	+	0.982661i	$0.559362\pi$
$570$		0			0
$571$	9.29299			0.388900			0.194450	−	0.980912i	$-0.437708\pi$
$571$	9.29299			0.388900			0.194450	+	0.980912i	$0.437708\pi$
$572$			0.937221i			0.0391872i
$573$		0			0
$574$	3.31965			0.138560
$575$	−6.62249	+	12.5041i	−0.276177	+	0.521458i
$576$		0			0
$577$		−	19.5259i		−	0.812872i	−0.913679	−	0.406436i	$-0.866771\pi$
$577$		−	19.5259i		−	0.812872i	0.913679	−	0.406436i	$-0.133229\pi$
$578$			24.8588i			1.03399i
$579$		0			0
$580$	−1.02052	+	4.10731i	−0.0423747	+	0.170547i
$581$	14.7526			0.612040
$582$		0			0
$583$		−	21.5753i		−	0.893558i
$584$	4.89639			0.202614
$585$		0			0
$586$	−14.5730			−0.602007
$587$		−	22.5029i		−	0.928794i	−0.885627	−	0.464397i	$-0.846271\pi$
$587$		−	22.5029i		−	0.928794i	0.885627	−	0.464397i	$-0.153729\pi$
$588$		0			0
$589$	0.474142			0.0195367
$590$	15.7743	+	3.91935i	0.649419	+	0.161357i
$591$		0			0
$592$		−	27.8394i		−	1.14419i
$593$			4.43907i			0.182291i	0.995838	+	0.0911454i	$0.0290528\pi$
$593$			4.43907i			0.182291i	−0.995838	+	0.0911454i	$0.970947\pi$
$594$		0			0
$595$	0.849388	−	3.41855i	0.0348215	−	0.140147i
$596$	3.35085			0.137256
$597$		0			0
$598$		−	4.35577i		−	0.178121i
$599$	33.3607			1.36308			0.681540	−	0.731780i	$-0.261310\pi$
$599$	33.3607			1.36308			0.681540	+	0.731780i	$0.261310\pi$
$600$		0			0
$601$	13.3197			0.543320			0.271660	−	0.962393i	$-0.412427\pi$
$601$	13.3197			0.543320			0.271660	+	0.962393i	$0.412427\pi$
$602$		−	16.9216i		−	0.689674i
$603$		0			0
$604$	−1.20969			−0.0492217
$605$	2.45467	−	9.87936i	0.0997964	−	0.401653i
$606$		0			0
$607$			14.1184i			0.573047i	0.958073	+	0.286523i	$0.0924996\pi$
$607$			14.1184i			0.573047i	−0.958073	+	0.286523i	$0.907500\pi$
$608$		−	1.11223i		−	0.0451068i
$609$		0			0
$610$	−26.8865	−	6.68035i	−1.08860	−	0.270479i
$611$	5.70928			0.230973
$612$		0			0
$613$			26.8104i			1.08286i	0.840745	+	0.541432i	$0.182118\pi$
$613$			26.8104i			1.08286i	−0.840745	+	0.541432i	$0.817882\pi$
$614$	−0.406442			−0.0164027
$615$		0			0
$616$	−10.8950			−0.438970
$617$		−	14.8950i		−	0.599649i	−0.953994	−	0.299824i	$-0.903072\pi$
$617$		−	14.8950i		−	0.599649i	0.953994	−	0.299824i	$-0.0969280\pi$
$618$		0			0
$619$	−45.3184			−1.82150			−0.910751	−	0.412956i	$-0.864496\pi$
$619$	−45.3184			−1.82150			−0.910751	+	0.412956i	$0.864496\pi$
$620$	0.175007	−	0.704355i	0.00702845	−	0.0282876i
$621$		0			0
$622$		−	20.0821i		−	0.805218i
$623$			21.9421i			0.879093i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	51.8720			2.07322
$627$		0			0
$628$			4.73820i			0.189075i
$629$	−5.57531			−0.222302
$630$		0			0
$631$	37.8876			1.50828			0.754141	−	0.656713i	$-0.228054\pi$
$631$	37.8876			1.50828			0.754141	+	0.656713i	$0.228054\pi$
$632$		−	1.24742i		−	0.0496197i
$633$		0			0
$634$	21.4725			0.852783
$635$	−39.0772	−	9.70928i	−1.55073	−	0.385301i
$636$		0			0
$637$		−	4.07838i		−	0.161591i
$638$		−	20.0410i		−	0.793432i
$639$		0			0
$640$	29.0905	+	7.22795i	1.14990	+	0.285710i
$641$	8.47027			0.334555			0.167278	−	0.985910i	$-0.446502\pi$
$641$	8.47027			0.334555			0.167278	+	0.985910i	$0.446502\pi$
$642$		0			0
$643$		−	34.1750i		−	1.34773i	−0.738854	−	0.673865i	$-0.764633\pi$
$643$		−	34.1750i		−	1.34773i	0.738854	−	0.673865i	$-0.235367\pi$
$644$	−1.78539			−0.0703541
$645$		0			0
$646$	−0.764867			−0.0300933
$647$			13.8238i			0.543468i	0.962372	+	0.271734i	$0.0875972\pi$
$647$			13.8238i			0.543468i	−0.962372	+	0.271734i	$0.912403\pi$
$648$		0			0
$649$	−11.9916			−0.470711
$650$	−6.80098	−	3.60197i	−0.266757	−	0.141281i
$651$		0			0
$652$		−	4.44748i		−	0.174177i
$653$		−	42.8781i		−	1.67795i	−0.544169	−	0.838976i	$-0.683155\pi$
$653$		−	42.8781i		−	1.67795i	0.544169	−	0.838976i	$-0.316845\pi$
$654$		0			0
$655$	7.68649	−	30.9360i	0.300336	−	1.20877i
$656$	5.80674			0.226715
$657$		0			0
$658$		−	15.0205i		−	0.585561i
$659$	−23.2495			−0.905672			−0.452836	−	0.891594i	$-0.649588\pi$
$659$	−23.2495			−0.905672			−0.452836	+	0.891594i	$0.649588\pi$
$660$		0			0
$661$	27.0661			1.05275			0.526374	−	0.850253i	$-0.323551\pi$
$661$	27.0661			1.05275			0.526374	+	0.850253i	$0.323551\pi$
$662$		−	28.4052i		−	1.10400i
$663$		0			0
$664$	21.6658			0.840796
$665$	−2.00000	−	0.496928i	−0.0775567	−	0.0192701i
$666$		0			0
$667$			14.5113i			0.561880i
$668$		−	3.22219i		−	0.124670i
$669$		0			0
$670$	−6.52813	+	26.2739i	−0.252203	+	1.01505i
$671$	20.4391			0.789042
$672$		0			0
$673$		−	16.1711i		−	0.623351i	−0.950189	−	0.311676i	$-0.899110\pi$
$673$		−	16.1711i		−	0.623351i	0.950189	−	0.311676i	$-0.100890\pi$
$674$	−24.4079			−0.940156
$675$		0			0
$676$	0.369102			0.0141962
$677$		−	43.1194i		−	1.65721i	−0.559831	−	0.828607i	$-0.689134\pi$
$677$		−	43.1194i		−	1.65721i	0.559831	−	0.828607i	$-0.310866\pi$
$678$		0			0
$679$	10.1112			0.388032
$680$	1.24742	−	5.02052i	0.0478363	−	0.192528i
$681$		0			0
$682$			3.43680i			0.131602i
$683$		−	17.7093i		−	0.677627i	−0.940854	−	0.338813i	$-0.889974\pi$
$683$		−	17.7093i		−	0.677627i	0.940854	−	0.338813i	$-0.110026\pi$
$684$		0			0
$685$	−29.9155	−	7.43293i	−1.14301	−	0.283998i
$686$	−29.1461			−1.11280
$687$		0			0
$688$		−	29.5993i		−	1.12846i
$689$	−8.49693			−0.323707
$690$		0			0
$691$	−24.8794			−0.946456			−0.473228	−	0.880940i	$-0.656911\pi$
$691$	−24.8794			−0.946456			−0.473228	+	0.880940i	$0.656911\pi$
$692$			0.318817i			0.0121196i
$693$		0			0
$694$	−14.9684			−0.568193
$695$	−3.58759	+	14.4391i	−0.136085	+	0.547705i
$696$		0			0
$697$		−	1.16290i		−	0.0440479i
$698$			47.5753i			1.80075i
$699$		0			0
$700$	−1.47641	+	2.78765i	−0.0558030	+	0.105363i
$701$	−33.0661			−1.24889			−0.624445	−	0.781069i	$-0.714675\pi$
$701$	−33.0661			−1.24889			−0.624445	+	0.781069i	$0.714675\pi$
$702$		0			0
$703$			3.26180i			0.123021i
$704$	−15.3086			−0.576964
$705$		0			0
$706$	9.15902			0.344704
$707$			28.0989i			1.05677i
$708$		0			0
$709$	−2.18342			−0.0820000			−0.0410000	−	0.999159i	$-0.513054\pi$
$709$	−2.18342			−0.0820000			−0.0410000	+	0.999159i	$0.513054\pi$
$710$	−48.3701	−	12.0183i	−1.81530	−	0.451037i
$711$		0			0
$712$			32.2245i			1.20766i
$713$		−	2.48852i		−	0.0931957i
$714$		0			0
$715$	5.51026	+	1.36910i	0.206072	+	0.0512015i
$716$	−7.35085			−0.274714
$717$		0			0
$718$			16.8976i			0.630613i
$719$	5.20847			0.194243			0.0971216	−	0.995273i	$-0.469036\pi$
$719$	5.20847			0.194243			0.0971216	+	0.995273i	$0.469036\pi$
$720$		0			0
$721$	17.4186			0.648701
$722$		−	28.7971i		−	1.07172i
$723$		0			0
$724$	−5.31124			−0.197391
$725$	22.6576	+	12.0000i	0.841481	+	0.445669i
$726$		0			0
$727$		−	3.52464i		−	0.130721i	−0.997862	−	0.0653607i	$-0.979180\pi$
$727$		−	3.52464i		−	0.130721i	0.997862	−	0.0653607i	$-0.0208198\pi$
$728$			4.29072i			0.159025i
$729$		0			0
$730$	−1.61879	+	6.51518i	−0.0599141	+	0.241138i
$731$	−5.92777			−0.219246
$732$		0			0
$733$			21.8310i			0.806345i	0.915124	+	0.403172i	$0.132093\pi$
$733$			21.8310i			0.806345i	−0.915124	+	0.403172i	$0.867907\pi$
$734$	15.9676			0.589374
$735$		0			0
$736$	−5.83749			−0.215173
$737$		−	19.9733i		−	0.735727i
$738$		0			0
$739$	−50.3533			−1.85228			−0.926139	−	0.377184i	$-0.876893\pi$
$739$	−50.3533			−1.85228			−0.926139	+	0.377184i	$0.876893\pi$
$740$	4.84551	+	1.20394i	0.178125	+	0.0442576i
$741$		0			0
$742$			22.3545i			0.820661i
$743$			30.7877i			1.12949i	0.825266	+	0.564745i	$0.191025\pi$
$743$			30.7877i			1.12949i	−0.825266	+	0.564745i	$0.808975\pi$
$744$		0			0
$745$	4.89496	−	19.7009i	0.179337	−	0.721784i
$746$	−36.9216			−1.35180
$747$		0			0
$748$		−	0.863763i		−	0.0315823i
$749$	−16.6681			−0.609038
$750$		0			0
$751$	−10.6225			−0.387620			−0.193810	−	0.981039i	$-0.562085\pi$
$751$	−10.6225			−0.387620			−0.193810	+	0.981039i	$0.562085\pi$
$752$		−	26.2739i		−	0.958111i
$753$		0			0
$754$	−7.89269			−0.287435
$755$	−1.76713	+	7.11223i	−0.0643126	+	0.258840i
$756$		0			0
$757$		−	7.98562i		−	0.290242i	−0.989414	−	0.145121i	$-0.953643\pi$
$757$		−	7.98562i		−	0.290242i	0.989414	−	0.145121i	$-0.0463572\pi$
$758$		−	45.8024i		−	1.66362i
$759$		0			0
$760$	−2.93722	−	0.729794i	−0.106544	−	0.0264724i
$761$	48.9360			1.77393			0.886964	−	0.461838i	$-0.152810\pi$
$761$	48.9360			1.77393			0.886964	+	0.461838i	$0.152810\pi$
$762$		0			0
$763$			28.8248i			1.04353i
$764$	0.544946			0.0197155
$765$		0			0
$766$	19.1110			0.690509
$767$			4.72261i			0.170523i
$768$		0			0
$769$	7.99547			0.288324			0.144162	−	0.989554i	$-0.453951\pi$
$769$	7.99547			0.288324			0.144162	+	0.989554i	$0.453951\pi$
$770$	3.60197	−	14.4969i	0.129806	−	0.522433i
$771$		0			0
$772$			6.54495i			0.235558i
$773$			26.6141i			0.957242i	0.878022	+	0.478621i	$0.158863\pi$
$773$			26.6141i			0.957242i	−0.878022	+	0.478621i	$0.841137\pi$
$774$		0			0
$775$	−3.88550	−	2.05786i	−0.139571	−	0.0739205i
$776$	14.8494			0.533062
$777$		0			0
$778$		−	25.9155i		−	0.929115i
$779$	−0.680346			−0.0243759
$780$		0			0
$781$	36.7708			1.31576
$782$			4.01438i			0.143554i
$783$		0			0
$784$	−18.7686			−0.670306
$785$	27.8576	+	6.92162i	0.994281	+	0.247043i
$786$		0			0
$787$			9.25792i			0.330009i	0.986293	+	0.165005i	$0.0527639\pi$
$787$			9.25792i			0.330009i	−0.986293	+	0.165005i	$0.947236\pi$
$788$		−	0.738205i		−	0.0262975i
$789$		0			0
$790$	1.65983	+	0.412408i	0.0590540	+	0.0146728i
$791$	−20.0989			−0.714634
$792$		0			0
$793$		−	8.04945i		−	0.285844i
$794$	−5.99159			−0.212634
$795$		0			0
$796$	−1.99016			−0.0705393
$797$		−	15.9421i		−	0.564700i	−0.959312	−	0.282350i	$-0.908886\pi$
$797$		−	15.9421i		−	0.564700i	0.959312	−	0.282350i	$-0.0911139\pi$
$798$		0			0
$799$	−5.26180			−0.186149
$800$	−4.82726	+	9.11450i	−0.170669	+	0.322246i
$801$		0			0
$802$			14.0144i			0.494865i
$803$		−	4.95282i		−	0.174781i
$804$		0			0
$805$	−2.60811	+	10.4969i	−0.0919238	+	0.369968i
$806$	1.35350			0.0476751
$807$		0			0
$808$			41.2663i			1.45174i
$809$	17.9239			0.630170			0.315085	−	0.949063i	$-0.397967\pi$
$809$	17.9239			0.630170			0.315085	+	0.949063i	$0.397967\pi$
$810$		0			0
$811$	7.43415			0.261048			0.130524	−	0.991445i	$-0.458334\pi$
$811$	7.43415			0.261048			0.130524	+	0.991445i	$0.458334\pi$
$812$			3.23513i			0.113531i
$813$		0			0
$814$	−23.6430			−0.828687
$815$	−26.1483	−	6.49693i	−0.915937	−	0.227577i
$816$		0			0
$817$			3.46800i			0.121330i
$818$			29.8888i			1.04504i
$819$		0			0
$820$	−0.251117	+	1.01068i	−0.00876940	+	0.0352944i
$821$	−20.4801			−0.714761			−0.357380	−	0.933959i	$-0.616330\pi$
$821$	−20.4801			−0.714761			−0.357380	+	0.933959i	$0.616330\pi$
$822$		0			0
$823$			3.75154i			0.130770i	0.997860	+	0.0653852i	$0.0208276\pi$
$823$			3.75154i			0.130770i	−0.997860	+	0.0653852i	$0.979172\pi$
$824$	25.5811			0.891159
$825$		0			0
$826$	12.4247			0.432310
$827$			48.1483i			1.67428i	0.546987	+	0.837141i	$0.315775\pi$
$827$			48.1483i			1.67428i	−0.546987	+	0.837141i	$0.684225\pi$
$828$		0			0
$829$	−36.5608			−1.26981			−0.634904	−	0.772591i	$-0.718960\pi$
$829$	−36.5608			−1.26981			−0.634904	+	0.772591i	$0.718960\pi$
$830$	−7.16290	+	28.8287i	−0.248628	+	1.00066i
$831$		0			0
$832$			6.02893i			0.209016i
$833$			3.75872i			0.130232i
$834$		0			0
$835$	−18.9444	−	4.70701i	−0.655598	−	0.162893i
$836$	−0.505339			−0.0174775
$837$		0			0
$838$		−	25.8264i		−	0.892159i
$839$	45.2294			1.56149			0.780746	−	0.624849i	$-0.214839\pi$
$839$	45.2294			1.56149			0.780746	+	0.624849i	$0.214839\pi$
$840$		0			0
$841$	−2.70540			−0.0932896
$842$		−	29.2762i		−	1.00892i
$843$		0			0
$844$	8.39803			0.289072
$845$	0.539189	−	2.17009i	0.0185487	−	0.0746532i
$846$		0			0
$847$		−	7.78151i		−	0.267376i
$848$			39.1026i			1.34279i
$849$		0			0
$850$	6.26794	+	3.31965i	0.214989	+	0.113863i
$851$	17.1194			0.586846
$852$		0			0
$853$			37.2534i			1.27553i	0.770230	+	0.637766i	$0.220141\pi$
$853$			37.2534i			1.27553i	−0.770230	+	0.637766i	$0.779859\pi$
$854$	−21.1773			−0.724671
$855$		0			0
$856$	−24.4789			−0.836671
$857$		−	10.8371i		−	0.370188i	−0.982721	−	0.185094i	$-0.940741\pi$
$857$		−	10.8371i		−	0.370188i	0.982721	−	0.185094i	$-0.0592590\pi$
$858$		0			0
$859$	−14.6081			−0.498422			−0.249211	−	0.968449i	$-0.580171\pi$
$859$	−14.6081			−0.498422			−0.249211	+	0.968449i	$0.580171\pi$
$860$	5.15183	+	1.28005i	0.175676	+	0.0436492i
$861$		0			0
$862$		−	12.3596i		−	0.420971i
$863$		−	10.3440i		−	0.352116i	−0.984380	−	0.176058i	$-0.943665\pi$
$863$		−	10.3440i		−	0.352116i	0.984380	−	0.176058i	$-0.0563345\pi$
$864$		0			0
$865$	1.87444	+	0.465732i	0.0637329	+	0.0158354i
$866$	−20.0821			−0.682417
$867$		0			0
$868$		−	0.554787i		−	0.0188307i
$869$	−1.26180			−0.0428035
$870$		0			0
$871$	−7.86603			−0.266530
$872$			42.3324i			1.43356i
$873$		0			0
$874$	2.34858			0.0794420
$875$	14.2329	+	12.7526i	0.481159	+	0.431116i
$876$		0			0
$877$			38.0677i			1.28545i	0.766095	+	0.642727i	$0.222197\pi$
$877$			38.0677i			1.28545i	−0.766095	+	0.642727i	$0.777803\pi$
$878$			11.8531i			0.400022i
$879$		0			0
$880$	6.30057	−	25.3580i	0.212392	−	0.854819i
$881$	−12.0494			−0.405956			−0.202978	−	0.979183i	$-0.565062\pi$
$881$	−12.0494			−0.405956			−0.202978	+	0.979183i	$0.565062\pi$
$882$		0			0
$883$			0.320699i			0.0107924i	0.999985	+	0.00539619i	$0.00171767\pi$
$883$			0.320699i			0.0107924i	−0.999985	+	0.00539619i	$0.998282\pi$
$884$	−0.340173			−0.0114413
$885$		0			0
$886$	9.83672			0.330471
$887$		−	3.62144i		−	0.121596i	−0.998150	−	0.0607981i	$-0.980635\pi$
$887$		−	3.62144i		−	0.121596i	0.998150	−	0.0607981i	$-0.0193646\pi$
$888$		0			0
$889$	−30.7792			−1.03230
$890$	−42.8781	−	10.6537i	−1.43728	−	0.357112i
$891$		0			0
$892$		−	3.23370i		−	0.108272i
$893$			3.07838i			0.103014i
$894$		0			0
$895$	−10.7382	+	43.2183i	−0.358939	+	1.44463i
$896$	22.9132			0.765477
$897$		0			0
$898$			48.6635i			1.62392i
$899$	−4.50921			−0.150391
$900$		0			0
$901$	7.83096			0.260887
$902$		−	4.93146i		−	0.164200i
$903$		0			0
$904$	−29.5174			−0.981736
$905$	−7.75872	+	31.2267i	−0.257909	+	1.03801i
$906$		0			0
$907$			10.9333i			0.363036i	0.983388	+	0.181518i	$0.0581010\pi$
$907$			10.9333i			0.363036i	−0.983388	+	0.181518i	$0.941899\pi$
$908$			6.35842i			0.211012i
$909$		0			0
$910$	−5.70928	−	1.41855i	−0.189261	−	0.0470245i
$911$	37.5897			1.24540			0.622701	−	0.782460i	$-0.286035\pi$
$911$	37.5897			1.24540			0.622701	+	0.782460i	$0.286035\pi$
$912$		0			0
$913$		−	21.9155i		−	0.725297i
$914$	54.8613			1.81465
$915$		0			0
$916$	1.13624			0.0375423
$917$		−	24.3668i		−	0.804664i
$918$		0			0
$919$	−33.6742			−1.11081			−0.555405	−	0.831580i	$-0.687437\pi$
$919$	−33.6742			−1.11081			−0.555405	+	0.831580i	$0.687437\pi$
$920$	−3.83030	+	15.4159i	−0.126281	+	0.508247i
$921$		0			0
$922$			23.0563i			0.759317i
$923$		−	14.4813i		−	0.476659i
$924$		0			0
$925$	14.1568	−	26.7298i	0.465471	−	0.878870i
$926$	−14.0014			−0.460116
$927$		0			0
$928$			10.5776i			0.347226i
$929$	−43.2039			−1.41748			−0.708738	−	0.705472i	$-0.750735\pi$
$929$	−43.2039			−1.41748			−0.708738	+	0.705472i	$0.750735\pi$
$930$		0			0
$931$	2.19902			0.0720698
$932$			6.98932i			0.228943i
$933$		0			0
$934$	2.88920			0.0945376
$935$	−5.07838	−	1.26180i	−0.166081	−	0.0412651i
$936$		0			0
$937$		−	27.5630i		−	0.900445i	−0.892916	−	0.450222i	$-0.851345\pi$
$937$		−	27.5630i		−	0.900445i	0.892916	−	0.450222i	$-0.148655\pi$
$938$			20.6947i			0.675707i
$939$		0			0
$940$	4.57304	+	1.13624i	0.149156	+	0.0370600i
$941$	−58.1666			−1.89618			−0.948088	−	0.318007i	$-0.896987\pi$
$941$	−58.1666			−1.89618			−0.948088	+	0.318007i	$0.896987\pi$
$942$		0			0
$943$			3.57077i			0.116280i
$944$	21.7333			0.707358
$945$		0			0
$946$	−25.1377			−0.817296
$947$			48.5152i			1.57653i	0.615335	+	0.788266i	$0.289021\pi$
$947$			48.5152i			1.57653i	−0.615335	+	0.788266i	$0.710979\pi$
$948$		0			0
$949$	−1.95055			−0.0633176
$950$	1.94214	−	3.66701i	0.0630114	−	0.118974i
$951$		0			0
$952$		−	3.95443i		−	0.128164i
$953$			23.0349i			0.746173i	0.927796	+	0.373087i	$0.121701\pi$
$953$			23.0349i			0.746173i	−0.927796	+	0.373087i	$0.878299\pi$
$954$		0			0
$955$	0.796064	−	3.20394i	0.0257600	−	0.103677i
$956$	−2.45013			−0.0792430
$957$		0			0
$958$		−	24.2316i		−	0.782889i
$959$	−23.5630			−0.760890
$960$		0			0
$961$	−30.2267			−0.975056
$962$			9.31124i			0.300207i
$963$		0			0
$964$	3.49777			0.112655
$965$	38.4801	+	9.56093i	1.23872	+	0.307777i
$966$		0			0
$967$		−	54.9998i		−	1.76868i	−0.466848	−	0.884338i	$-0.654611\pi$
$967$		−	54.9998i		−	1.76868i	0.466848	−	0.884338i	$-0.345389\pi$
$968$		−	11.4280i		−	0.367310i
$969$		0			0
$970$	−4.90934	+	19.7587i	−0.157629	+	0.634414i
$971$	−9.70540			−0.311461			−0.155731	−	0.987800i	$-0.549773\pi$
$971$	−9.70540			−0.311461			−0.155731	+	0.987800i	$0.549773\pi$
$972$		0			0
$973$			11.3730i			0.364601i
$974$	−7.61038			−0.243852
$975$		0			0
$976$	−37.0433			−1.18573
$977$			32.2062i			1.03037i	0.857080	+	0.515184i	$0.172276\pi$
$977$			32.2062i			1.03037i	−0.857080	+	0.515184i	$0.827724\pi$
$978$		0			0
$979$	32.5958			1.04177
$980$	0.811662	−	3.26672i	0.0259276	−	0.104351i
$981$		0			0
$982$		−	60.7768i		−	1.93947i
$983$		−	44.0782i		−	1.40588i	−0.711251	−	0.702938i	$-0.751871\pi$
$983$		−	44.0782i		−	1.40588i	0.711251	−	0.702938i	$-0.248129\pi$
$984$		0			0
$985$	−4.34017	−	1.07838i	−0.138289	−	0.0343600i
$986$	7.27408			0.231654
$987$		0			0
$988$			0.199016i			0.00633154i
$989$	18.2017			0.578779
$990$		0			0
$991$	12.0677			0.383343			0.191672	−	0.981459i	$-0.438609\pi$
$991$	12.0677			0.383343			0.191672	+	0.981459i	$0.438609\pi$
$992$		−	1.81393i		−	0.0575923i
$993$		0			0
$994$	−38.0989			−1.20842
$995$	−2.90725	+	11.7009i	−0.0921659	+	0.370942i
$996$		0			0
$997$		−	45.7587i		−	1.44919i	−0.689173	−	0.724597i	$-0.742026\pi$
$997$		−	45.7587i		−	1.44919i	0.689173	−	0.724597i	$-0.257974\pi$
$998$		−	2.57182i		−	0.0814094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.b.469.5		6
3.2	odd	2		65.2.b.a.14.2	✓	6
5.2	odd	4		2925.2.a.bf.1.2		3
5.3	odd	4		2925.2.a.bj.1.2		3
5.4	even	2	inner	585.2.c.b.469.2		6
12.11	even	2		1040.2.d.c.209.1		6
15.2	even	4		325.2.a.k.1.2		3
15.8	even	4		325.2.a.j.1.2		3
15.14	odd	2		65.2.b.a.14.5	yes	6
39.2	even	12		845.2.l.e.654.3		12
39.5	even	4		845.2.d.a.844.4		6
39.8	even	4		845.2.d.b.844.4		6
39.11	even	12		845.2.l.d.654.3		12
39.17	odd	6		845.2.n.g.484.5		12
39.20	even	12		845.2.l.d.699.4		12
39.23	odd	6		845.2.n.g.529.2		12
39.29	odd	6		845.2.n.f.529.5		12
39.32	even	12		845.2.l.e.699.4		12
39.35	odd	6		845.2.n.f.484.2		12
39.38	odd	2		845.2.b.c.339.5		6
60.23	odd	4		5200.2.a.cj.1.3		3
60.47	odd	4		5200.2.a.cb.1.1		3
60.59	even	2		1040.2.d.c.209.6		6
195.29	odd	6		845.2.n.f.529.2		12
195.38	even	4		4225.2.a.bh.1.2		3
195.44	even	4		845.2.d.b.844.3		6
195.59	even	12		845.2.l.e.699.3		12
195.74	odd	6		845.2.n.f.484.5		12
195.77	even	4		4225.2.a.ba.1.2		3
195.89	even	12		845.2.l.e.654.4		12
195.119	even	12		845.2.l.d.654.4		12
195.134	odd	6		845.2.n.g.484.2		12
195.149	even	12		845.2.l.d.699.3		12
195.164	even	4		845.2.d.a.844.3		6
195.179	odd	6		845.2.n.g.529.5		12
195.194	odd	2		845.2.b.c.339.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.2	✓	6	3.2	odd	2
65.2.b.a.14.5	yes	6	15.14	odd	2
325.2.a.j.1.2		3	15.8	even	4
325.2.a.k.1.2		3	15.2	even	4
585.2.c.b.469.2		6	5.4	even	2	inner
585.2.c.b.469.5		6	1.1	even	1	trivial
845.2.b.c.339.2		6	195.194	odd	2
845.2.b.c.339.5		6	39.38	odd	2
845.2.d.a.844.3		6	195.164	even	4
845.2.d.a.844.4		6	39.5	even	4
845.2.d.b.844.3		6	195.44	even	4
845.2.d.b.844.4		6	39.8	even	4
845.2.l.d.654.3		12	39.11	even	12
845.2.l.d.654.4		12	195.119	even	12
845.2.l.d.699.3		12	195.149	even	12
845.2.l.d.699.4		12	39.20	even	12
845.2.l.e.654.3		12	39.2	even	12
845.2.l.e.654.4		12	195.89	even	12
845.2.l.e.699.3		12	195.59	even	12
845.2.l.e.699.4		12	39.32	even	12
845.2.n.f.484.2		12	39.35	odd	6
845.2.n.f.484.5		12	195.74	odd	6
845.2.n.f.529.2		12	195.29	odd	6
845.2.n.f.529.5		12	39.29	odd	6
845.2.n.g.484.2		12	195.134	odd	6
845.2.n.g.484.5		12	39.17	odd	6
845.2.n.g.529.2		12	39.23	odd	6
845.2.n.g.529.5		12	195.179	odd	6
1040.2.d.c.209.1		6	12.11	even	2
1040.2.d.c.209.6		6	60.59	even	2
2925.2.a.bf.1.2		3	5.2	odd	4
2925.2.a.bj.1.2		3	5.3	odd	4
4225.2.a.ba.1.2		3	195.77	even	4
4225.2.a.bh.1.2		3	195.38	even	4
5200.2.a.cb.1.1		3	60.47	odd	4
5200.2.a.cj.1.3		3	60.23	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.53919i q^{2} -0.369102 q^{4} +(-0.539189 + 2.17009i) q^{5} +1.70928i q^{7} +2.51026i q^{8} +O(q^{10})\)	\(q+1.53919i q^{2} -0.369102 q^{4} +(-0.539189 + 2.17009i) q^{5} +1.70928i q^{7} +2.51026i q^{8} +(-3.34017 - 0.829914i) q^{10} +2.53919 q^{11} -1.00000i q^{13} -2.63090 q^{14} -4.60197 q^{16} +0.921622i q^{17} +0.539189 q^{19} +(0.199016 - 0.800984i) q^{20} +3.90829i q^{22} -2.82991i q^{23} +(-4.41855 - 2.34017i) q^{25} +1.53919 q^{26} -0.630898i q^{28} -5.12783 q^{29} +0.879362 q^{31} -2.06278i q^{32} -1.41855 q^{34} +(-3.70928 - 0.921622i) q^{35} +6.04945i q^{37} +0.829914i q^{38} +(-5.44748 - 1.35350i) q^{40} -1.26180 q^{41} +6.43188i q^{43} -0.937221 q^{44} +4.35577 q^{46} +5.70928i q^{47} +4.07838 q^{49} +(3.60197 - 6.80098i) q^{50} +0.369102i q^{52} -8.49693i q^{53} +(-1.36910 + 5.51026i) q^{55} -4.29072 q^{56} -7.89269i q^{58} -4.72261 q^{59} +8.04945 q^{61} +1.35350i q^{62} -6.02893 q^{64} +(2.17009 + 0.539189i) q^{65} -7.86603i q^{67} -0.340173i q^{68} +(1.41855 - 5.70928i) q^{70} +14.4813 q^{71} -1.95055i q^{73} -9.31124 q^{74} -0.199016 q^{76} +4.34017i q^{77} -0.496928 q^{79} +(2.48133 - 9.98667i) q^{80} -1.94214i q^{82} -8.63090i q^{83} +(-2.00000 - 0.496928i) q^{85} -9.89988 q^{86} +6.37402i q^{88} +12.8371 q^{89} +1.70928 q^{91} +1.04453i q^{92} -8.78765 q^{94} +(-0.290725 + 1.17009i) q^{95} -5.91548i q^{97} +6.27739i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4}+O(q^{10}) \) 6 * q - 10 * q^4	\( 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50} - 16 q^{55} - 40 q^{56} - 16 q^{59} + 12 q^{61} - 66 q^{64} + 2 q^{65} - 20 q^{70} + 24 q^{71} - 4 q^{74} - 20 q^{76} + 32 q^{79} - 48 q^{80} - 12 q^{85} + 32 q^{86} + 20 q^{89} - 4 q^{91} - 32 q^{94} - 16 q^{95}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^10 + 12 * q^11 - 8 * q^14 + 10 * q^16 + 20 * q^20 + 2 * q^25 + 6 * q^26 + 12 * q^29 - 20 * q^31 + 20 * q^34 - 8 * q^35 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 32 * q^46 + 18 * q^49 - 16 * q^50 - 16 * q^55 - 40 * q^56 - 16 * q^59 + 12 * q^61 - 66 * q^64 + 2 * q^65 - 20 * q^70 + 24 * q^71 - 4 * q^74 - 20 * q^76 + 32 * q^79 - 48 * q^80 - 12 * q^85 + 32 * q^86 + 20 * q^89 - 4 * q^91 - 32 * q^94 - 16 * q^95

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