LMFDB - Embedded newform 1512.2.j.c.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 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("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.3
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33436 - 0.468477i) q^{2} +(1.56106 + 1.25024i) q^{4} -3.47003 q^{5} +1.00000i q^{7} +(-1.49731 - 2.39959i) q^{8} +O(q^{10})$	\(q+(-1.33436 - 0.468477i) q^{2} +(1.56106 + 1.25024i) q^{4} -3.47003 q^{5} +1.00000i q^{7} +(-1.49731 - 2.39959i) q^{8} +(4.63028 + 1.62563i) q^{10} +5.11891i q^{11} -0.268602i q^{13} +(0.468477 - 1.33436i) q^{14} +(0.873805 + 3.90339i) q^{16} +1.96616i q^{17} +0.909926 q^{19} +(-5.41692 - 4.33836i) q^{20} +(2.39809 - 6.83050i) q^{22} -5.86455 q^{23} +7.04110 q^{25} +(-0.125834 + 0.358413i) q^{26} +(-1.25024 + 1.56106i) q^{28} +7.19959 q^{29} -4.57491i q^{31} +(0.662675 - 5.61791i) q^{32} +(0.921102 - 2.62358i) q^{34} -3.47003i q^{35} +6.98312i q^{37} +(-1.21417 - 0.426280i) q^{38} +(5.19572 + 8.32666i) q^{40} -8.34605i q^{41} -9.25237 q^{43} +(-6.39986 + 7.99092i) q^{44} +(7.82544 + 2.74741i) q^{46} +6.49316 q^{47} -1.00000 q^{49} +(-9.39539 - 3.29859i) q^{50} +(0.335817 - 0.419304i) q^{52} -4.54325 q^{53} -17.7628i q^{55} +(2.39959 - 1.49731i) q^{56} +(-9.60688 - 3.37285i) q^{58} +3.50524i q^{59} +1.96254i q^{61} +(-2.14324 + 6.10459i) q^{62} +(-3.51611 + 7.18589i) q^{64} +0.932057i q^{65} -11.0280 q^{67} +(-2.45817 + 3.06929i) q^{68} +(-1.62563 + 4.63028i) q^{70} -1.20092 q^{71} -9.01697 q^{73} +(3.27143 - 9.31802i) q^{74} +(1.42045 + 1.13762i) q^{76} -5.11891 q^{77} -13.5570i q^{79} +(-3.03213 - 13.5449i) q^{80} +(-3.90994 + 11.1367i) q^{82} -4.96335i q^{83} -6.82263i q^{85} +(12.3460 + 4.33452i) q^{86} +(12.2833 - 7.66461i) q^{88} -18.2032i q^{89} +0.268602 q^{91} +(-9.15490 - 7.33208i) q^{92} +(-8.66424 - 3.04190i) q^{94} -3.15747 q^{95} +3.39139 q^{97} +(1.33436 + 0.468477i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.33436	−	0.468477i	−0.943538	−	0.331263i
$2$	−1.33436	−	0.468477i	−0.943538	−	0.331263i
$3$		0			0
$3$		0			0
$4$	1.56106	+	1.25024i	0.780529	+	0.625119i
$5$	−3.47003			−1.55184			−0.775922	−	0.630829i	$-0.782715\pi$
$5$	−3.47003			−1.55184			−0.775922	+	0.630829i	$0.782715\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.49731	−	2.39959i	−0.529380	−	0.848385i
$9$		0			0
$10$	4.63028	+	1.62563i	1.46422	+	0.514069i
$11$			5.11891i			1.54341i	0.635981	+	0.771705i	$0.280596\pi$
$11$			5.11891i			1.54341i	−0.635981	+	0.771705i	$0.719404\pi$
$12$		0			0
$13$		−	0.268602i		−	0.0744968i	−0.999306	−	0.0372484i	$-0.988141\pi$
$13$		−	0.268602i		−	0.0744968i	0.999306	−	0.0372484i	$-0.0118593\pi$
$14$	0.468477	−	1.33436i	0.125206	−	0.356624i
$15$		0			0
$16$	0.873805	+	3.90339i	0.218451	+	0.975848i
$17$			1.96616i			0.476864i	0.971159	+	0.238432i	$0.0766334\pi$
$17$			1.96616i			0.476864i	−0.971159	+	0.238432i	$0.923367\pi$
$18$		0			0
$19$	0.909926			0.208751			0.104376	−	0.994538i	$-0.466716\pi$
$19$	0.909926			0.208751			0.104376	+	0.994538i	$0.466716\pi$
$20$	−5.41692	−	4.33836i	−1.21126	−	0.970088i
$21$		0			0
$22$	2.39809	−	6.83050i	0.511275	−	1.45627i
$23$	−5.86455			−1.22284			−0.611421	−	0.791305i	$-0.709402\pi$
$23$	−5.86455			−1.22284			−0.611421	+	0.791305i	$0.709402\pi$
$24$		0			0
$25$	7.04110			1.40822
$26$	−0.125834	+	0.358413i	−0.0246781	+	0.0702906i
$27$		0			0
$28$	−1.25024	+	1.56106i	−0.236273	+	0.295012i
$29$	7.19959			1.33693			0.668466	−	0.743743i	$-0.266951\pi$
$29$	7.19959			1.33693			0.668466	+	0.743743i	$0.266951\pi$
$30$		0			0
$31$		−	4.57491i		−	0.821678i	−0.911708	−	0.410839i	$-0.865236\pi$
$31$		−	4.57491i		−	0.821678i	0.911708	−	0.410839i	$-0.134764\pi$
$32$	0.662675	−	5.61791i	0.117145	−	0.993115i
$33$		0			0
$34$	0.921102	−	2.62358i	0.157968	−	0.449940i
$35$		−	3.47003i		−	0.586542i
$36$		0			0
$37$			6.98312i			1.14802i	0.818849	+	0.574009i	$0.194612\pi$
$37$			6.98312i			1.14802i	−0.818849	+	0.574009i	$0.805388\pi$
$38$	−1.21417	−	0.426280i	−0.196965	−	0.0691517i
$39$		0			0
$40$	5.19572	+	8.32666i	0.821515	+	1.31656i
$41$		−	8.34605i		−	1.30343i	−0.758462	−	0.651717i	$-0.774049\pi$
$41$		−	8.34605i		−	1.30343i	0.758462	−	0.651717i	$-0.225951\pi$
$42$		0			0
$43$	−9.25237			−1.41097			−0.705487	−	0.708723i	$-0.749272\pi$
$43$	−9.25237			−1.41097			−0.705487	+	0.708723i	$0.749272\pi$
$44$	−6.39986	+	7.99092i	−0.964816	+	1.20468i
$45$		0			0
$46$	7.82544	+	2.74741i	1.15380	+	0.405083i
$47$	6.49316			0.947125			0.473562	−	0.880760i	$-0.342968\pi$
$47$	6.49316			0.947125			0.473562	+	0.880760i	$0.342968\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−9.39539	−	3.29859i	−1.32871	−	0.466491i
$51$		0			0
$52$	0.335817	−	0.419304i	0.0465694	−	0.0581470i
$53$	−4.54325			−0.624063			−0.312032	−	0.950072i	$-0.601010\pi$
$53$	−4.54325			−0.624063			−0.312032	+	0.950072i	$0.601010\pi$
$54$		0			0
$55$		−	17.7628i		−	2.39513i
$56$	2.39959	−	1.49731i	0.320659	−	0.200087i
$57$		0			0
$58$	−9.60688	−	3.37285i	−1.26145	−	0.442876i
$59$			3.50524i			0.456344i	0.973621	+	0.228172i	$0.0732748\pi$
$59$			3.50524i			0.456344i	−0.973621	+	0.228172i	$0.926725\pi$
$60$		0			0
$61$			1.96254i			0.251278i	0.992076	+	0.125639i	$0.0400980\pi$
$61$			1.96254i			0.251278i	−0.992076	+	0.125639i	$0.959902\pi$
$62$	−2.14324	+	6.10459i	−0.272192	+	0.775284i
$63$		0			0
$64$	−3.51611	+	7.18589i	−0.439514	+	0.898236i
$65$			0.932057i			0.115607i
$66$		0			0
$67$	−11.0280			−1.34728			−0.673641	−	0.739059i	$-0.735271\pi$
$67$	−11.0280			−1.34728			−0.673641	+	0.739059i	$0.735271\pi$
$68$	−2.45817	+	3.06929i	−0.298097	+	0.372206i
$69$		0			0
$70$	−1.62563	+	4.63028i	−0.194300	+	0.553425i
$71$	−1.20092			−0.142523			−0.0712616	−	0.997458i	$-0.522703\pi$
$71$	−1.20092			−0.142523			−0.0712616	+	0.997458i	$0.522703\pi$
$72$		0			0
$73$	−9.01697			−1.05536			−0.527679	−	0.849444i	$-0.676937\pi$
$73$	−9.01697			−1.05536			−0.527679	+	0.849444i	$0.676937\pi$
$74$	3.27143	−	9.31802i	0.380296	−	1.08320i
$75$		0			0
$76$	1.42045	+	1.13762i	0.162937	+	0.130495i
$77$	−5.11891			−0.583354
$78$		0			0
$79$		−	13.5570i		−	1.52528i	−0.646825	−	0.762638i	$-0.723904\pi$
$79$		−	13.5570i		−	1.52528i	0.646825	−	0.762638i	$-0.276096\pi$
$80$	−3.03213	−	13.5449i	−0.339002	−	1.51436i
$81$		0			0
$82$	−3.90994	+	11.1367i	−0.431780	+	1.22984i
$83$		−	4.96335i		−	0.544799i	−0.962184	−	0.272399i	$-0.912183\pi$
$83$		−	4.96335i		−	0.544799i	0.962184	−	0.272399i	$-0.0878172\pi$
$84$		0			0
$85$		−	6.82263i		−	0.740019i
$86$	12.3460	+	4.33452i	1.33131	+	0.467404i
$87$		0			0
$88$	12.2833	−	7.66461i	1.30941	−	0.817050i
$89$		−	18.2032i		−	1.92954i	−0.263100	−	0.964769i	$-0.584745\pi$
$89$		−	18.2032i		−	1.92954i	0.263100	−	0.964769i	$-0.415255\pi$
$90$		0			0
$91$	0.268602			0.0281572
$92$	−9.15490	−	7.33208i	−0.954464	−	0.764423i
$93$		0			0
$94$	−8.66424	−	3.04190i	−0.893649	−	0.313748i
$95$	−3.15747			−0.323949
$96$		0			0
$97$	3.39139			0.344344			0.172172	−	0.985067i	$-0.444922\pi$
$97$	3.39139			0.344344			0.172172	+	0.985067i	$0.444922\pi$
$98$	1.33436	+	0.468477i	0.134791	+	0.0473233i
$99$		0			0
$100$	10.9916	+	8.80305i	1.09916	+	0.880305i
$101$	−8.18671			−0.814608			−0.407304	−	0.913293i	$-0.633531\pi$
$101$	−8.18671			−0.814608			−0.407304	+	0.913293i	$0.633531\pi$
$102$		0			0
$103$			16.5624i			1.63194i	0.578093	+	0.815971i	$0.303797\pi$
$103$			16.5624i			1.63194i	−0.578093	+	0.815971i	$0.696203\pi$
$104$	−0.644536	+	0.402181i	−0.0632020	+	0.0394371i
$105$		0			0
$106$	6.06235	+	2.12841i	0.588828	+	0.206729i
$107$			15.1480i			1.46441i	0.681083	+	0.732206i	$0.261509\pi$
$107$			15.1480i			1.46441i	−0.681083	+	0.732206i	$0.738491\pi$
$108$		0			0
$109$		−	7.70038i		−	0.737562i	−0.929516	−	0.368781i	$-0.879775\pi$
$109$		−	7.70038i		−	0.737562i	0.929516	−	0.368781i	$-0.120225\pi$
$110$	−8.32145	+	23.7020i	−0.793419	+	2.25990i
$111$		0			0
$112$	−3.90339	+	0.873805i	−0.368836	+	0.0825668i
$113$		−	14.5822i		−	1.37178i	−0.727706	−	0.685889i	$-0.759413\pi$
$113$		−	14.5822i		−	1.37178i	0.727706	−	0.685889i	$-0.240587\pi$
$114$		0			0
$115$	20.3501			1.89766
$116$	11.2390	+	9.00121i	1.04351	+	0.835742i
$117$		0			0
$118$	1.64213	−	4.67727i	0.151170	−	0.430578i
$119$	−1.96616			−0.180238
$120$		0			0
$121$	−15.2033			−1.38211
$122$	0.919406	−	2.61874i	0.0832391	−	0.237090i
$123$		0			0
$124$	5.71973	−	7.14170i	0.513647	−	0.641343i
$125$	−7.08266			−0.633492
$126$		0			0
$127$		−	13.7782i		−	1.22262i	−0.791392	−	0.611309i	$-0.790643\pi$
$127$		−	13.7782i		−	1.22262i	0.791392	−	0.611309i	$-0.209357\pi$
$128$	8.05820	−	7.94138i	0.712251	−	0.701925i
$129$		0			0
$130$	0.436648	−	1.24370i	0.0382965	−	0.109080i
$131$		−	11.4226i		−	0.997997i	−0.866603	−	0.498999i	$-0.833701\pi$
$131$		−	11.4226i		−	0.997997i	0.866603	−	0.498999i	$-0.166299\pi$
$132$		0			0
$133$			0.909926i			0.0789006i
$134$	14.7153	+	5.16636i	1.27121	+	0.446305i
$135$		0			0
$136$	4.71799	−	2.94396i	0.404564	−	0.252442i
$137$			5.89343i			0.503510i	0.967791	+	0.251755i	$0.0810077\pi$
$137$			5.89343i			0.503510i	−0.967791	+	0.251755i	$0.918992\pi$
$138$		0			0
$139$	3.67309			0.311547			0.155774	−	0.987793i	$-0.450213\pi$
$139$	3.67309			0.311547			0.155774	+	0.987793i	$0.450213\pi$
$140$	4.33836	−	5.41692i	0.366659	−	0.457813i
$141$		0			0
$142$	1.60247	+	0.562604i	0.134476	+	0.0472127i
$143$	1.37495			0.114979
$144$		0			0
$145$	−24.9828			−2.07471
$146$	12.0319	+	4.22425i	0.995770	+	0.349601i
$147$		0			0
$148$	−8.73056	+	10.9010i	−0.717648	+	0.896061i
$149$	−23.0240			−1.88620			−0.943102	−	0.332504i	$-0.892106\pi$
$149$	−23.0240			−1.88620			−0.943102	+	0.332504i	$0.892106\pi$
$150$		0			0
$151$		−	1.33860i		−	0.108934i	−0.998516	−	0.0544669i	$-0.982654\pi$
$151$		−	1.33860i		−	0.108934i	0.998516	−	0.0544669i	$-0.0173459\pi$
$152$	−1.36244	−	2.18345i	−0.110509	−	0.177101i
$153$		0			0
$154$	6.83050	+	2.39809i	0.550417	+	0.193244i
$155$			15.8751i			1.27512i
$156$		0			0
$157$		−	21.7839i		−	1.73854i	−0.494333	−	0.869272i	$-0.664588\pi$
$157$		−	21.7839i		−	1.73854i	0.494333	−	0.869272i	$-0.335412\pi$
$158$	−6.35112	+	18.0899i	−0.505268	+	1.43916i
$159$		0			0
$160$	−2.29950	+	19.4943i	−0.181792	+	1.54116i
$161$		−	5.86455i		−	0.462191i
$162$		0			0
$163$	−20.2710			−1.58775			−0.793875	−	0.608082i	$-0.791939\pi$
$163$	−20.2710			−1.58775			−0.793875	+	0.608082i	$0.791939\pi$
$164$	10.4346	−	13.0287i	0.814802	−	1.01737i
$165$		0			0
$166$	−2.32522	+	6.62292i	−0.180472	+	0.514039i
$167$	−6.57632			−0.508891			−0.254445	−	0.967087i	$-0.581893\pi$
$167$	−6.57632			−0.508891			−0.254445	+	0.967087i	$0.581893\pi$
$168$		0			0
$169$	12.9279			0.994450
$170$	−3.19625	+	9.10388i	−0.245141	+	0.698236i
$171$		0			0
$172$	−14.4435	−	11.5677i	−1.10131	−	0.882027i
$173$	13.3399			1.01421			0.507105	−	0.861884i	$-0.330716\pi$
$173$	13.3399			1.01421			0.507105	+	0.861884i	$0.330716\pi$
$174$		0			0
$175$			7.04110i			0.532257i
$176$	−19.9811	+	4.47293i	−1.50613	+	0.337160i
$177$		0			0
$178$	−8.52779	+	24.2897i	−0.639185	+	1.82059i
$179$			9.82571i			0.734408i	0.930140	+	0.367204i	$0.119685\pi$
$179$			9.82571i			0.734408i	−0.930140	+	0.367204i	$0.880315\pi$
$180$		0			0
$181$		−	4.88753i		−	0.363287i	−0.983364	−	0.181643i	$-0.941858\pi$
$181$		−	4.88753i		−	0.363287i	0.983364	−	0.181643i	$-0.0581417\pi$
$182$	−0.358413	−	0.125834i	−0.0265674	−	0.00932744i
$183$		0			0
$184$	8.78106	+	14.0725i	0.647348	+	1.03744i
$185$		−	24.2316i		−	1.78154i
$186$		0			0
$187$	−10.0646			−0.735997
$188$	10.1362	+	8.11800i	0.739258	+	0.592066i
$189$		0			0
$190$	4.21322	+	1.47920i	0.305659	+	0.107313i
$191$	−11.6129			−0.840281			−0.420141	−	0.907459i	$-0.638019\pi$
$191$	−11.6129			−0.840281			−0.420141	+	0.907459i	$0.638019\pi$
$192$		0			0
$193$	−12.8166			−0.922562			−0.461281	−	0.887254i	$-0.652610\pi$
$193$	−12.8166			−0.922562			−0.461281	+	0.887254i	$0.652610\pi$
$194$	−4.52536	−	1.58879i	−0.324902	−	0.114069i
$195$		0			0
$196$	−1.56106	−	1.25024i	−0.111504	−	0.0893028i
$197$	−4.69147			−0.334253			−0.167127	−	0.985935i	$-0.553449\pi$
$197$	−4.69147			−0.334253			−0.167127	+	0.985935i	$0.553449\pi$
$198$		0			0
$199$		−	15.3555i		−	1.08852i	−0.838915	−	0.544262i	$-0.816810\pi$
$199$		−	15.3555i		−	1.08852i	0.838915	−	0.544262i	$-0.183190\pi$
$200$	−10.5427	−	16.8958i	−0.745483	−	1.19471i
$201$		0			0
$202$	10.9241	+	3.83529i	0.768614	+	0.269850i
$203$			7.19959i			0.505312i
$204$		0			0
$205$			28.9610i			2.02273i
$206$	7.75911	−	22.1003i	0.540603	−	1.53980i
$207$		0			0
$208$	1.04846	−	0.234706i	0.0726976	−	0.0162739i
$209$			4.65783i			0.322189i
$210$		0			0
$211$	5.09850			0.350995			0.175497	−	0.984480i	$-0.443847\pi$
$211$	5.09850			0.350995			0.175497	+	0.984480i	$0.443847\pi$
$212$	−7.09228	−	5.68015i	−0.487100	−	0.390114i
$213$		0			0
$214$	7.09649	−	20.2130i	0.485106	−	1.38173i
$215$	32.1060			2.18961
$216$		0			0
$217$	4.57491			0.310565
$218$	−3.60745	+	10.2751i	−0.244327	+	0.695918i
$219$		0			0
$220$	22.2077	−	27.7287i	1.49724	−	1.86947i
$221$	0.528115			0.0355249
$222$		0			0
$223$			29.5118i			1.97625i	0.153636	+	0.988127i	$0.450902\pi$
$223$			29.5118i			1.97625i	−0.153636	+	0.988127i	$0.549098\pi$
$224$	5.61791	+	0.662675i	0.375362	+	0.0442768i
$225$		0			0
$226$	−6.83143	+	19.4580i	−0.454420	+	1.29433i
$227$		−	14.4769i		−	0.960868i	−0.877031	−	0.480434i	$-0.840479\pi$
$227$		−	14.4769i		−	0.960868i	0.877031	−	0.480434i	$-0.159521\pi$
$228$		0			0
$229$		−	11.9120i		−	0.787168i	−0.919289	−	0.393584i	$-0.871235\pi$
$229$		−	11.9120i		−	0.787168i	0.919289	−	0.393584i	$-0.128765\pi$
$230$	−27.1545	−	9.53358i	−1.79052	−	0.628625i
$231$		0			0
$232$	−10.7800	−	17.2761i	−0.707744	−	1.13423i
$233$			13.2938i			0.870904i	0.900212	+	0.435452i	$0.143411\pi$
$233$			13.2938i			0.870904i	−0.900212	+	0.435452i	$0.856589\pi$
$234$		0			0
$235$	−22.5315			−1.46979
$236$	−4.38239	+	5.47189i	−0.285269	+	0.356190i
$237$		0			0
$238$	2.62358	+	0.921102i	0.170061	+	0.0597062i
$239$	11.7744			0.761624			0.380812	−	0.924652i	$-0.375644\pi$
$239$	11.7744			0.761624			0.380812	+	0.924652i	$0.375644\pi$
$240$		0			0
$241$	−23.3009			−1.50094			−0.750471	−	0.660903i	$-0.770173\pi$
$241$	−23.3009			−1.50094			−0.750471	+	0.660903i	$0.770173\pi$
$242$	20.2867	+	7.12238i	1.30408	+	0.457844i
$243$		0			0
$244$	−2.45364	+	3.06364i	−0.157079	+	0.196129i
$245$	3.47003			0.221692
$246$		0			0
$247$		−	0.244408i		−	0.0155513i
$248$	−10.9779	+	6.85007i	−0.697099	+	0.434980i
$249$		0			0
$250$	9.45085	+	3.31806i	0.597724	+	0.209853i
$251$			18.5562i			1.17126i	0.810579	+	0.585629i	$0.199153\pi$
$251$			18.5562i			1.17126i	−0.810579	+	0.585629i	$0.800847\pi$
$252$		0			0
$253$		−	30.0201i		−	1.88735i
$254$	−6.45477	+	18.3851i	−0.405009	+	1.15359i
$255$		0			0
$256$	−14.4729	+	6.82161i	−0.904558	+	0.426351i
$257$		−	12.7179i		−	0.793318i	−0.917966	−	0.396659i	$-0.870169\pi$
$257$		−	12.7179i		−	0.793318i	0.917966	−	0.396659i	$-0.129831\pi$
$258$		0			0
$259$	−6.98312			−0.433910
$260$	−1.16529	+	1.45500i	−0.0722685	+	0.0902350i
$261$		0			0
$262$	−5.35123	+	15.2419i	−0.330600	+	0.941648i
$263$	4.04929			0.249690			0.124845	−	0.992176i	$-0.460157\pi$
$263$	4.04929			0.249690			0.124845	+	0.992176i	$0.460157\pi$
$264$		0			0
$265$	15.7652			0.968449
$266$	0.426280	−	1.21417i	0.0261369	−	0.0744457i
$267$		0			0
$268$	−17.2153	−	13.7876i	−1.05159	−	0.842212i
$269$	22.6641			1.38185			0.690926	−	0.722925i	$-0.257203\pi$
$269$	22.6641			1.38185			0.690926	+	0.722925i	$0.257203\pi$
$270$		0			0
$271$			0.0619260i			0.00376174i	0.999998	+	0.00188087i	$0.000598699\pi$
$271$			0.0619260i			0.00376174i	−0.999998	+	0.00188087i	$0.999401\pi$
$272$	−7.67470	+	1.71804i	−0.465347	+	0.104172i
$273$		0			0
$274$	2.76094	−	7.86399i	0.166794	−	0.475081i
$275$			36.0427i			2.17346i
$276$		0			0
$277$		−	24.9177i		−	1.49716i	−0.663045	−	0.748580i	$-0.730736\pi$
$277$		−	24.9177i		−	1.49716i	0.663045	−	0.748580i	$-0.269264\pi$
$278$	−4.90124	−	1.72076i	−0.293957	−	0.103204i
$279$		0			0
$280$	−8.32666	+	5.19572i	−0.497613	+	0.310503i
$281$			8.26290i			0.492923i	0.969153	+	0.246462i	$0.0792679\pi$
$281$			8.26290i			0.492923i	−0.969153	+	0.246462i	$0.920732\pi$
$282$		0			0
$283$	23.4764			1.39553			0.697763	−	0.716329i	$-0.254179\pi$
$283$	23.4764			1.39553			0.697763	+	0.716329i	$0.254179\pi$
$284$	−1.87471	−	1.50144i	−0.111243	−	0.0890940i
$285$		0			0
$286$	−1.83469	−	0.644133i	−0.108487	−	0.0380884i
$287$	8.34605			0.492652
$288$		0			0
$289$	13.1342			0.772601
$290$	33.3362	+	11.7039i	1.95757	+	0.687275i
$291$		0			0
$292$	−14.0760	−	11.2734i	−0.823737	−	0.659724i
$293$	−6.18958			−0.361599			−0.180800	−	0.983520i	$-0.557869\pi$
$293$	−6.18958			−0.361599			−0.180800	+	0.983520i	$0.557869\pi$
$294$		0			0
$295$		−	12.1633i		−	0.708174i
$296$	16.7566	−	10.4559i	0.973960	−	0.607737i
$297$		0			0
$298$	30.7225	+	10.7862i	1.77971	+	0.624830i
$299$			1.57523i			0.0910979i
$300$		0			0
$301$		−	9.25237i		−	0.533298i
$302$	−0.627104	+	1.78618i	−0.0360858	+	0.102783i
$303$		0			0
$304$	0.795098	+	3.55180i	0.0456020	+	0.203710i
$305$		−	6.81007i		−	0.389944i
$306$		0			0
$307$	−25.4140			−1.45045			−0.725226	−	0.688511i	$-0.758265\pi$
$307$	−25.4140			−1.45045			−0.725226	+	0.688511i	$0.758265\pi$
$308$	−7.99092	−	6.39986i	−0.455325	−	0.364666i
$309$		0			0
$310$	7.43710	−	21.1831i	0.422399	−	1.20312i
$311$	7.55273			0.428276			0.214138	−	0.976803i	$-0.431306\pi$
$311$	7.55273			0.428276			0.214138	+	0.976803i	$0.431306\pi$
$312$		0			0
$313$	2.49790			0.141190			0.0705948	−	0.997505i	$-0.477510\pi$
$313$	2.49790			0.141190			0.0705948	+	0.997505i	$0.477510\pi$
$314$	−10.2053	+	29.0677i	−0.575916	+	1.64038i
$315$		0			0
$316$	16.9494	−	21.1632i	0.953480	−	1.19052i
$317$	−10.9643			−0.615815			−0.307908	−	0.951416i	$-0.599629\pi$
$317$	−10.9643			−0.615815			−0.307908	+	0.951416i	$0.599629\pi$
$318$		0			0
$319$			36.8541i			2.06343i
$320$	12.2010	−	24.9352i	0.682057	−	1.39392i
$321$		0			0
$322$	−2.74741	+	7.82544i	−0.153107	+	0.436095i
$323$			1.78906i			0.0995460i
$324$		0			0
$325$		−	1.89125i		−	0.104908i
$326$	27.0489	+	9.49651i	1.49810	+	0.525963i
$327$		0			0
$328$	−20.0271	+	12.4967i	−1.10581	+	0.690012i
$329$			6.49316i			0.357980i
$330$		0			0
$331$	35.6043			1.95699			0.978494	−	0.206275i	$-0.0661341\pi$
$331$	35.6043			1.95699			0.978494	+	0.206275i	$0.0661341\pi$
$332$	6.20538	−	7.74808i	0.340564	−	0.425231i
$333$		0			0
$334$	8.77521	+	3.08086i	0.480158	+	0.168577i
$335$	38.2674			2.09077
$336$		0			0
$337$	18.4308			1.00399			0.501995	−	0.864871i	$-0.332600\pi$
$337$	18.4308			1.00399			0.501995	+	0.864871i	$0.332600\pi$
$338$	−17.2505	−	6.05640i	−0.938302	−	0.329425i
$339$		0			0
$340$	8.52992	−	10.6505i	0.462600	−	0.577606i
$341$	23.4185			1.26819
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	13.8537	+	22.2019i	0.746941	+	1.19705i
$345$		0			0
$346$	−17.8002	−	6.24942i	−0.956946	−	0.335971i
$347$			25.2141i			1.35356i	0.736184	+	0.676782i	$0.236626\pi$
$347$			25.2141i			1.35356i	−0.736184	+	0.676782i	$0.763374\pi$
$348$		0			0
$349$		−	4.82396i		−	0.258221i	−0.991630	−	0.129110i	$-0.958788\pi$
$349$		−	4.82396i		−	0.258221i	0.991630	−	0.129110i	$-0.0412121\pi$
$350$	3.29859	−	9.39539i	0.176317	−	0.502205i
$351$		0			0
$352$	28.7576	+	3.39217i	1.53278	+	0.180804i
$353$		−	21.2660i		−	1.13187i	−0.824448	−	0.565937i	$-0.808514\pi$
$353$		−	21.2660i		−	1.13187i	0.824448	−	0.565937i	$-0.191486\pi$
$354$		0			0
$355$	4.16723			0.221174
$356$	22.7584	−	28.4163i	1.20619	−	1.50606i
$357$		0			0
$358$	4.60312	−	13.1111i	0.243282	−	0.692942i
$359$	24.9785			1.31832			0.659158	−	0.752004i	$-0.270913\pi$
$359$	24.9785			1.31832			0.659158	+	0.752004i	$0.270913\pi$
$360$		0			0
$361$	−18.1720			−0.956423
$362$	−2.28969	+	6.52174i	−0.120344	+	0.342775i
$363$		0			0
$364$	0.419304	+	0.335817i	0.0219775	+	0.0176016i
$365$	31.2892			1.63775
$366$		0			0
$367$			13.8851i			0.724795i	0.932024	+	0.362397i	$0.118042\pi$
$367$			13.8851i			0.724795i	−0.932024	+	0.362397i	$0.881958\pi$
$368$	−5.12447	−	22.8916i	−0.267132	−	1.19331i
$369$		0			0
$370$	−11.3520	+	32.3338i	−0.590160	+	1.68095i
$371$		−	4.54325i		−	0.235874i
$372$		0			0
$373$		−	0.513970i		−	0.0266123i	−0.999911	−	0.0133062i	$-0.995764\pi$
$373$		−	0.513970i		−	0.0266123i	0.999911	−	0.0133062i	$-0.00423561\pi$
$374$	13.4299	+	4.71504i	0.694441	+	0.243809i
$375$		0			0
$376$	−9.72229	−	15.5810i	−0.501389	−	0.803526i
$377$		−	1.93383i		−	0.0995972i
$378$		0			0
$379$	−7.97711			−0.409757			−0.204878	−	0.978787i	$-0.565680\pi$
$379$	−7.97711			−0.409757			−0.204878	+	0.978787i	$0.565680\pi$
$380$	−4.92899	−	3.94759i	−0.252852	−	0.202507i
$381$		0			0
$382$	15.4959	+	5.44039i	0.792837	+	0.278354i
$383$	8.03401			0.410519			0.205259	−	0.978708i	$-0.434196\pi$
$383$	8.03401			0.410519			0.205259	+	0.978708i	$0.434196\pi$
$384$		0			0
$385$	17.7628			0.905275
$386$	17.1021	+	6.00430i	0.870472	+	0.305611i
$387$		0			0
$388$	5.29416	+	4.24005i	0.268770	+	0.215256i
$389$	6.60733			0.335005			0.167503	−	0.985872i	$-0.446430\pi$
$389$	6.60733			0.335005			0.167503	+	0.985872i	$0.446430\pi$
$390$		0			0
$391$		−	11.5306i		−	0.583130i
$392$	1.49731	+	2.39959i	0.0756257	+	0.121198i
$393$		0			0
$394$	6.26013	+	2.19785i	0.315381	+	0.110726i
$395$			47.0430i			2.36699i
$396$		0			0
$397$			17.4642i			0.876502i	0.898853	+	0.438251i	$0.144402\pi$
$397$			17.4642i			0.876502i	−0.898853	+	0.438251i	$0.855598\pi$
$398$	−7.19372	+	20.4899i	−0.360588	+	1.02706i
$399$		0			0
$400$	6.15255	+	27.4842i	0.307627	+	1.37421i
$401$			18.6133i			0.929503i	0.885441	+	0.464751i	$0.153856\pi$
$401$			18.6133i			0.929503i	−0.885441	+	0.464751i	$0.846144\pi$
$402$		0			0
$403$	−1.22883			−0.0612124
$404$	−12.7799	−	10.2353i	−0.635825	−	0.509227i
$405$		0			0
$406$	3.37285	−	9.60688i	0.167392	−	0.476782i
$407$	−35.7460			−1.77186
$408$		0			0
$409$	3.72844			0.184359			0.0921797	−	0.995742i	$-0.470617\pi$
$409$	3.72844			0.184359			0.0921797	+	0.995742i	$0.470617\pi$
$410$	13.5676	−	38.6446i	0.670055	−	1.90852i
$411$		0			0
$412$	−20.7070	+	25.8549i	−1.02016	+	1.27378i
$413$	−3.50524			−0.172482
$414$		0			0
$415$			17.2230i			0.845443i
$416$	−1.50898	−	0.177996i	−0.0739839	−	0.00872697i
$417$		0			0
$418$	2.18209	−	6.21525i	0.106729	−	0.303998i
$419$			30.1591i			1.47337i	0.676237	+	0.736684i	$0.263609\pi$
$419$			30.1591i			1.47337i	−0.676237	+	0.736684i	$0.736391\pi$
$420$		0			0
$421$			4.17416i			0.203436i	0.994813	+	0.101718i	$0.0324340\pi$
$421$			4.17416i			0.203436i	−0.994813	+	0.101718i	$0.967566\pi$
$422$	−6.80325	−	2.38853i	−0.331177	−	0.116272i
$423$		0			0
$424$	6.80266	+	10.9020i	0.330367	+	0.529446i
$425$			13.8439i			0.671529i
$426$		0			0
$427$	−1.96254			−0.0949740
$428$	−18.9386	+	23.6469i	−0.915433	+	1.14302i
$429$		0			0
$430$	−42.8411	−	15.0409i	−2.06598	−	0.725338i
$431$	−20.3147			−0.978524			−0.489262	−	0.872137i	$-0.662734\pi$
$431$	−20.3147			−0.978524			−0.489262	+	0.872137i	$0.662734\pi$
$432$		0			0
$433$	37.5740			1.80569			0.902847	−	0.429963i	$-0.141473\pi$
$433$	37.5740			1.80569			0.902847	+	0.429963i	$0.141473\pi$
$434$	−6.10459	−	2.14324i	−0.293030	−	0.102879i
$435$		0			0
$436$	9.62731	−	12.0207i	0.461064	−	0.575689i
$437$	−5.33630			−0.255270
$438$		0			0
$439$			12.2219i			0.583317i	0.956522	+	0.291659i	$0.0942072\pi$
$439$			12.2219i			0.583317i	−0.956522	+	0.291659i	$0.905793\pi$
$440$	−42.6234	+	26.5964i	−2.03199	+	1.26793i
$441$		0			0
$442$	−0.704698	−	0.247410i	−0.0335191	−	0.0117681i
$443$		−	2.13132i		−	0.101262i	−0.998717	−	0.0506311i	$-0.983877\pi$
$443$		−	2.13132i		−	0.101262i	0.998717	−	0.0506311i	$-0.0161233\pi$
$444$		0			0
$445$			63.1657i			2.99434i
$446$	13.8256	−	39.3795i	0.654661	−	1.86467i
$447$		0			0
$448$	−7.18589	−	3.51611i	−0.339501	−	0.166121i
$449$		−	24.6873i		−	1.16506i	−0.812807	−	0.582532i	$-0.802062\pi$
$449$		−	24.6873i		−	1.16506i	0.812807	−	0.582532i	$-0.197938\pi$
$450$		0			0
$451$	42.7227			2.01173
$452$	18.2312	−	22.7637i	0.857526	−	1.07071i
$453$		0			0
$454$	−6.78211	+	19.3175i	−0.318300	+	0.906615i
$455$	−0.932057			−0.0436955
$456$		0			0
$457$	−33.2814			−1.55684			−0.778419	−	0.627745i	$-0.783978\pi$
$457$	−33.2814			−1.55684			−0.778419	+	0.627745i	$0.783978\pi$
$458$	−5.58051	+	15.8950i	−0.260760	+	0.742723i
$459$		0			0
$460$	31.7678	+	25.4425i	1.48118	+	1.18626i
$461$	−15.2279			−0.709233			−0.354617	−	0.935012i	$-0.615389\pi$
$461$	−15.2279			−0.709233			−0.354617	+	0.935012i	$0.615389\pi$
$462$		0			0
$463$			3.21883i			0.149592i	0.997199	+	0.0747959i	$0.0238305\pi$
$463$			3.21883i			0.149592i	−0.997199	+	0.0747959i	$0.976169\pi$
$464$	6.29104	+	28.1028i	0.292054	+	1.30464i
$465$		0			0
$466$	6.22783	−	17.7387i	0.288499	−	0.821731i
$467$		−	22.5827i		−	1.04500i	−0.852638	−	0.522502i	$-0.824999\pi$
$467$		−	22.5827i		−	1.04500i	0.852638	−	0.522502i	$-0.175001\pi$
$468$		0			0
$469$		−	11.0280i		−	0.509225i
$470$	30.0652	+	10.5555i	1.38680	+	0.486888i
$471$		0			0
$472$	8.41117	−	5.24845i	0.387155	−	0.241579i
$473$		−	47.3621i		−	2.17771i
$474$		0			0
$475$	6.40688			0.293968
$476$	−3.06929	−	2.45817i	−0.140681	−	0.112670i
$477$		0			0
$478$	−15.7114	−	5.51605i	−0.718622	−	0.252298i
$479$	−28.0140			−1.27999			−0.639995	−	0.768379i	$-0.721064\pi$
$479$	−28.0140			−1.27999			−0.639995	+	0.768379i	$0.721064\pi$
$480$		0			0
$481$	1.87568			0.0855237
$482$	31.0919	+	10.9159i	1.41620	+	0.497207i
$483$		0			0
$484$	−23.7332	−	19.0077i	−1.07878	−	0.863987i
$485$	−11.7682			−0.534368
$486$		0			0
$487$		−	2.55321i		−	0.115697i	−0.998325	−	0.0578485i	$-0.981576\pi$
$487$		−	2.55321i		−	0.115697i	0.998325	−	0.0578485i	$-0.0184240\pi$
$488$	4.70930	−	2.93854i	0.213180	−	0.133021i
$489$		0			0
$490$	−4.63028	−	1.62563i	−0.209175	−	0.0734384i
$491$		−	0.803432i		−	0.0362584i	−0.999836	−	0.0181292i	$-0.994229\pi$
$491$		−	0.803432i		−	0.0362584i	0.999836	−	0.0181292i	$-0.00577102\pi$
$492$		0			0
$493$			14.1556i			0.637534i
$494$	−0.114500	+	0.326130i	−0.00515158	+	0.0146733i
$495$		0			0
$496$	17.8577	−	3.99758i	0.801832	−	0.179497i
$497$		−	1.20092i		−	0.0538687i
$498$		0			0
$499$	32.6029			1.45950			0.729752	−	0.683712i	$-0.239635\pi$
$499$	32.6029			1.45950			0.729752	+	0.683712i	$0.239635\pi$
$500$	−11.0564	−	8.85502i	−0.494459	−	0.396008i
$501$		0			0
$502$	8.69317	−	24.7608i	0.387995	−	1.10513i
$503$	11.6962			0.521508			0.260754	−	0.965405i	$-0.416029\pi$
$503$	11.6962			0.521508			0.260754	+	0.965405i	$0.416029\pi$
$504$		0			0
$505$	28.4081			1.26414
$506$	−14.0637	+	40.0578i	−0.625209	+	1.78078i
$507$		0			0
$508$	17.2260	−	21.5086i	0.764282	−	0.954289i
$509$	−40.0087			−1.77335			−0.886676	−	0.462391i	$-0.846992\pi$
$509$	−40.0087			−1.77335			−0.886676	+	0.462391i	$0.846992\pi$
$510$		0			0
$511$		−	9.01697i		−	0.398887i
$512$	22.5079	−	2.32228i	0.994719	−	0.102631i
$513$		0			0
$514$	−5.95803	+	16.9703i	−0.262797	+	0.748526i
$515$		−	57.4720i		−	2.53252i
$516$		0			0
$517$			33.2379i			1.46180i
$518$	9.31802	+	3.27143i	0.409410	+	0.143738i
$519$		0			0
$520$	2.23656	−	1.39558i	0.0980796	−	0.0612003i
$521$			5.13277i			0.224871i	0.993659	+	0.112435i	$0.0358651\pi$
$521$			5.13277i			0.224871i	−0.993659	+	0.112435i	$0.964135\pi$
$522$		0			0
$523$	35.3652			1.54641			0.773207	−	0.634154i	$-0.218652\pi$
$523$	35.3652			1.54641			0.773207	+	0.634154i	$0.218652\pi$
$524$	14.2810	−	17.8313i	0.623867	−	0.778966i
$525$		0			0
$526$	−5.40324	−	1.89700i	−0.235592	−	0.0827132i
$527$	8.99500			0.391829
$528$		0			0
$529$	11.3929			0.495344
$530$	−21.0365	−	7.38564i	−0.913769	−	0.320812i
$531$		0			0
$532$	−1.13762	+	1.42045i	−0.0493223	+	0.0615842i
$533$	−2.24177			−0.0971018
$534$		0			0
$535$		−	52.5640i		−	2.27254i
$536$	16.5123	+	26.4627i	0.713224	+	1.14301i
$537$		0			0
$538$	−30.2421	−	10.6176i	−1.30383	−	0.457757i
$539$		−	5.11891i		−	0.220487i
$540$		0			0
$541$		−	30.7038i		−	1.32006i	−0.751240	−	0.660029i	$-0.770544\pi$
$541$		−	30.7038i		−	1.32006i	0.751240	−	0.660029i	$-0.229456\pi$
$542$	0.0290109	−	0.0826319i	0.00124613	−	0.00354934i
$543$		0			0
$544$	11.0457	+	1.30293i	0.473581	+	0.0558625i
$545$			26.7205i			1.14458i
$546$		0			0
$547$	−2.21526			−0.0947175			−0.0473588	−	0.998878i	$-0.515080\pi$
$547$	−2.21526			−0.0947175			−0.0473588	+	0.998878i	$0.515080\pi$
$548$	−7.36820	+	9.19999i	−0.314754	+	0.393004i
$549$		0			0
$550$	16.8852	−	48.0942i	0.719988	−	2.05074i
$551$	6.55110			0.279086
$552$		0			0
$553$	13.5570			0.576500
$554$	−11.6734	+	33.2493i	−0.495954	+	1.41263i
$555$		0			0
$556$	5.73390	+	4.59224i	0.243172	+	0.194754i
$557$	−8.88158			−0.376325			−0.188162	−	0.982138i	$-0.560253\pi$
$557$	−8.88158			−0.376325			−0.188162	+	0.982138i	$0.560253\pi$
$558$		0			0
$559$			2.48521i			0.105113i
$560$	13.5449	−	3.03213i	0.572376	−	0.128131i
$561$		0			0
$562$	3.87098	−	11.0257i	0.163287	−	0.465092i
$563$		−	28.9398i		−	1.21967i	−0.792529	−	0.609834i	$-0.791236\pi$
$563$		−	28.9398i		−	1.21967i	0.792529	−	0.609834i	$-0.208764\pi$
$564$		0			0
$565$			50.6007i			2.12879i
$566$	−31.3260	−	10.9981i	−1.31673	−	0.462287i
$567$		0			0
$568$	1.79815	+	2.88173i	0.0754489	+	0.120915i
$569$			30.8816i			1.29463i	0.762224	+	0.647313i	$0.224107\pi$
$569$			30.8816i			1.29463i	−0.762224	+	0.647313i	$0.775893\pi$
$570$		0			0
$571$	−31.5945			−1.32219			−0.661094	−	0.750303i	$-0.729908\pi$
$571$	−31.5945			−1.32219			−0.661094	+	0.750303i	$0.729908\pi$
$572$	2.14638	+	1.71902i	0.0897446	+	0.0718757i
$573$		0			0
$574$	−11.1367	−	3.90994i	−0.464836	−	0.163198i
$575$	−41.2928			−1.72203
$576$		0			0
$577$	−37.6007			−1.56534			−0.782669	−	0.622438i	$-0.786142\pi$
$577$	−37.6007			−1.56534			−0.782669	+	0.622438i	$0.786142\pi$
$578$	−17.5258	−	6.15308i	−0.728978	−	0.255934i
$579$		0			0
$580$	−38.9996	−	31.2345i	−1.61937	−	1.29694i
$581$	4.96335			0.205915
$582$		0			0
$583$		−	23.2565i		−	0.963186i
$584$	13.5012	+	21.6371i	0.558685	+	0.895349i
$585$		0			0
$586$	8.25916	+	2.89968i	0.341183	+	0.119785i
$587$		−	22.0321i		−	0.909361i	−0.890655	−	0.454680i	$-0.849754\pi$
$587$		−	22.0321i		−	0.909361i	0.890655	−	0.454680i	$-0.150246\pi$
$588$		0			0
$589$		−	4.16283i		−	0.171526i
$590$	−5.69823	+	16.2303i	−0.234592	+	0.668190i
$591$		0			0
$592$	−27.2578	+	6.10188i	−1.12029	+	0.250786i
$593$		−	17.8392i		−	0.732569i	−0.930503	−	0.366284i	$-0.880630\pi$
$593$		−	17.8392i		−	0.732569i	0.930503	−	0.366284i	$-0.119370\pi$
$594$		0			0
$595$	6.82263			0.279701
$596$	−35.9419	−	28.7856i	−1.47224	−	1.17910i
$597$		0			0
$598$	0.737959	−	2.10193i	0.0301774	−	0.0859544i
$599$	19.5363			0.798230			0.399115	−	0.916901i	$-0.369317\pi$
$599$	19.5363			0.798230			0.399115	+	0.916901i	$0.369317\pi$
$600$		0			0
$601$	−20.1240			−0.820877			−0.410438	−	0.911888i	$-0.634624\pi$
$601$	−20.1240			−0.820877			−0.410438	+	0.911888i	$0.634624\pi$
$602$	−4.33452	+	12.3460i	−0.176662	+	0.503187i
$603$		0			0
$604$	1.67357	−	2.08963i	0.0680966	−	0.0850260i
$605$	52.7557			2.14483
$606$		0			0
$607$		−	15.3972i		−	0.624951i	−0.949926	−	0.312476i	$-0.898842\pi$
$607$		−	15.3972i		−	0.624951i	0.949926	−	0.312476i	$-0.101158\pi$
$608$	0.602985	−	5.11188i	0.0244543	−	0.207314i
$609$		0			0
$610$	−3.19036	+	9.08712i	−0.129174	+	0.367927i
$611$		−	1.74408i		−	0.0705578i
$612$		0			0
$613$			37.9629i			1.53331i	0.642061	+	0.766653i	$0.278079\pi$
$613$			37.9629i			1.53331i	−0.642061	+	0.766653i	$0.721921\pi$
$614$	33.9115	+	11.9059i	1.36856	+	0.480482i
$615$		0			0
$616$	7.66461	+	12.2833i	0.308816	+	0.494909i
$617$		−	43.0532i		−	1.73326i	−0.498953	−	0.866629i	$-0.666282\pi$
$617$		−	43.0532i		−	1.73326i	0.498953	−	0.866629i	$-0.333718\pi$
$618$		0			0
$619$	−6.75463			−0.271491			−0.135746	−	0.990744i	$-0.543343\pi$
$619$	−6.75463			−0.271491			−0.135746	+	0.990744i	$0.543343\pi$
$620$	−19.8476	+	24.7819i	−0.797099	+	0.995265i
$621$		0			0
$622$	−10.0781	−	3.53828i	−0.404095	−	0.141872i
$623$	18.2032			0.729297
$624$		0			0
$625$	−10.6285			−0.425138
$626$	−3.33311	−	1.17021i	−0.133218	−	0.0467710i
$627$		0			0
$628$	27.2351	−	34.0059i	1.08680	−	1.35698i
$629$	−13.7299			−0.547448
$630$		0			0
$631$			1.96735i			0.0783189i	0.999233	+	0.0391594i	$0.0124680\pi$
$631$			1.96735i			0.0783189i	−0.999233	+	0.0391594i	$0.987532\pi$
$632$	−32.5312	+	20.2990i	−1.29402	+	0.807451i
$633$		0			0
$634$	14.6303	+	5.13652i	0.581045	+	0.203997i
$635$			47.8108i			1.89731i
$636$		0			0
$637$			0.268602i			0.0106424i
$638$	17.2653	−	49.1768i	0.683540	−	1.94693i
$639$		0			0
$640$	−27.9622	+	27.5568i	−1.10530	+	1.08928i
$641$		−	30.2998i		−	1.19677i	−0.801209	−	0.598385i	$-0.795809\pi$
$641$		−	30.2998i		−	1.19677i	0.801209	−	0.598385i	$-0.204191\pi$
$642$		0			0
$643$	3.85901			0.152185			0.0760923	−	0.997101i	$-0.475756\pi$
$643$	3.85901			0.152185			0.0760923	+	0.997101i	$0.475756\pi$
$644$	7.33208	−	9.15490i	0.288925	−	0.360754i
$645$		0			0
$646$	0.838134	−	2.38726i	0.0329760	−	0.0939255i
$647$	−33.4004			−1.31310			−0.656552	−	0.754281i	$-0.727986\pi$
$647$	−33.4004			−1.31310			−0.656552	+	0.754281i	$0.727986\pi$
$648$		0			0
$649$	−17.9430			−0.704326
$650$	−0.886009	+	2.52362i	−0.0347521	+	0.0989846i
$651$		0			0
$652$	−31.6442	−	25.3436i	−1.23928	−	0.992533i
$653$	−26.9899			−1.05620			−0.528098	−	0.849184i	$-0.677095\pi$
$653$	−26.9899			−1.05620			−0.528098	+	0.849184i	$0.677095\pi$
$654$		0			0
$655$			39.6367i			1.54874i
$656$	32.5779	−	7.29283i	1.27195	−	0.284737i
$657$		0			0
$658$	3.04190	−	8.66424i	0.118586	−	0.337767i
$659$			13.1888i			0.513763i	0.966443	+	0.256881i	$0.0826950\pi$
$659$			13.1888i			0.513763i	−0.966443	+	0.256881i	$0.917305\pi$
$660$		0			0
$661$			33.5767i			1.30598i	0.757366	+	0.652990i	$0.226486\pi$
$661$			33.5767i			1.30598i	−0.757366	+	0.652990i	$0.773514\pi$
$662$	−47.5091	−	16.6798i	−1.84649	−	0.648279i
$663$		0			0
$664$	−11.9100	+	7.43169i	−0.462199	+	0.288406i
$665$		−	3.15747i		−	0.122441i
$666$		0			0
$667$	−42.2224			−1.63486
$668$	−10.2660	−	8.22197i	−0.397204	−	0.318118i
$669$		0			0
$670$	−51.0627	−	17.9274i	−1.97272	−	0.692596i
$671$	−10.0461			−0.387824
$672$		0			0
$673$	13.5269			0.521424			0.260712	−	0.965417i	$-0.416043\pi$
$673$	13.5269			0.521424			0.260712	+	0.965417i	$0.416043\pi$
$674$	−24.5934	−	8.63441i	−0.947303	−	0.332585i
$675$		0			0
$676$	20.1811	+	16.1629i	0.776197	+	0.621650i
$677$	−25.3388			−0.973850			−0.486925	−	0.873444i	$-0.661882\pi$
$677$	−25.3388			−0.973850			−0.486925	+	0.873444i	$0.661882\pi$
$678$		0			0
$679$			3.39139i			0.130150i
$680$	−16.3716	+	10.2156i	−0.627821	+	0.391751i
$681$		0			0
$682$	−31.2489	−	10.9711i	−1.19658	−	0.420103i
$683$			4.74712i			0.181644i	0.995867	+	0.0908218i	$0.0289494\pi$
$683$			4.74712i			0.181644i	−0.995867	+	0.0908218i	$0.971051\pi$
$684$		0			0
$685$		−	20.4504i		−	0.781369i
$686$	−0.468477	+	1.33436i	−0.0178865	+	0.0509463i
$687$		0			0
$688$	−8.08477	−	36.1156i	−0.308229	−	1.37690i
$689$			1.22033i			0.0464908i
$690$		0			0
$691$	−46.8908			−1.78381			−0.891904	−	0.452224i	$-0.850631\pi$
$691$	−46.8908			−1.78381			−0.891904	+	0.452224i	$0.850631\pi$
$692$	20.8243	+	16.6780i	0.791620	+	0.634002i
$693$		0			0
$694$	11.8122	−	33.6448i	0.448386	−	1.27714i
$695$	−12.7457			−0.483472
$696$		0			0
$697$	16.4097			0.621561
$698$	−2.25991	+	6.43692i	−0.0855390	+	0.243641i
$699$		0			0
$700$	−8.80305	+	10.9916i	−0.332724	+	0.415442i
$701$	−11.8394			−0.447166			−0.223583	−	0.974685i	$-0.571775\pi$
$701$	−11.8394			−0.447166			−0.223583	+	0.974685i	$0.571775\pi$
$702$		0			0
$703$			6.35412i			0.239650i
$704$	−36.7839	−	17.9987i	−1.38635	−	0.678350i
$705$		0			0
$706$	−9.96263	+	28.3766i	−0.374949	+	1.06797i
$707$		−	8.18671i		−	0.307893i
$708$		0			0
$709$			3.55487i			0.133506i	0.997770	+	0.0667530i	$0.0212639\pi$
$709$			3.55487i			0.133506i	−0.997770	+	0.0667530i	$0.978736\pi$
$710$	−5.56061	−	1.95225i	−0.208686	−	0.0732668i
$711$		0			0
$712$	−43.6803	+	27.2559i	−1.63699	+	1.02146i
$713$			26.8298i			1.00478i
$714$		0			0
$715$	−4.77112			−0.178430
$716$	−12.2845	+	15.3385i	−0.459093	+	0.573227i
$717$		0			0
$718$	−33.3305	−	11.7019i	−1.24388	−	0.436710i
$719$	−0.174626			−0.00651246			−0.00325623	−	0.999995i	$-0.501036\pi$
$719$	−0.174626			−0.00651246			−0.00325623	+	0.999995i	$0.501036\pi$
$720$		0			0
$721$	−16.5624			−0.616816
$722$	24.2481	+	8.51318i	0.902422	+	0.316828i
$723$		0			0
$724$	6.11058	−	7.62971i	0.227098	−	0.283556i
$725$	50.6930			1.88269
$726$		0			0
$727$			8.37928i			0.310770i	0.987854	+	0.155385i	$0.0496619\pi$
$727$			8.37928i			0.310770i	−0.987854	+	0.155385i	$0.950338\pi$
$728$	−0.402181	−	0.644536i	−0.0149058	−	0.0238881i
$729$		0			0
$730$	−41.7511	−	14.6583i	−1.54528	−	0.542526i
$731$		−	18.1917i		−	0.672843i
$732$		0			0
$733$			15.6312i			0.577351i	0.957427	+	0.288676i	$0.0932149\pi$
$733$			15.6312i			0.577351i	−0.957427	+	0.288676i	$0.906785\pi$
$734$	6.50484	−	18.5277i	0.240098	−	0.683872i
$735$		0			0
$736$	−3.88629	+	32.9465i	−0.143250	+	1.21442i
$737$		−	56.4512i		−	2.07941i
$738$		0			0
$739$	−25.4382			−0.935760			−0.467880	−	0.883792i	$-0.654982\pi$
$739$	−25.4382			−0.935760			−0.467880	+	0.883792i	$0.654982\pi$
$740$	30.2953	−	37.8269i	1.11368	−	1.39055i
$741$		0			0
$742$	−2.12841	+	6.06235i	−0.0781364	+	0.222556i
$743$	−33.0542			−1.21264			−0.606320	−	0.795220i	$-0.707355\pi$
$743$	−33.0542			−1.21264			−0.606320	+	0.795220i	$0.707355\pi$
$744$		0			0
$745$	79.8941			2.92709
$746$	−0.240783	+	0.685823i	−0.00881570	+	0.0251098i
$747$		0			0
$748$	−15.7114	−	12.5832i	−0.574467	−	0.460086i
$749$	−15.1480			−0.553496
$750$		0			0
$751$			40.4075i			1.47449i	0.675625	+	0.737246i	$0.263874\pi$
$751$			40.4075i			1.47449i	−0.675625	+	0.737246i	$0.736126\pi$
$752$	5.67376	+	25.3453i	0.206901	+	0.924250i
$753$		0			0
$754$	−0.905954	+	2.58043i	−0.0329929	+	0.0939737i
$755$			4.64498i			0.169048i
$756$		0			0
$757$		−	30.0219i		−	1.09116i	−0.838057	−	0.545582i	$-0.816309\pi$
$757$		−	30.0219i		−	1.09116i	0.838057	−	0.545582i	$-0.183691\pi$
$758$	10.6444	+	3.73710i	0.386621	+	0.135737i
$759$		0			0
$760$	4.72772	+	7.57665i	0.171492	+	0.274834i
$761$		−	13.9651i		−	0.506234i	−0.967436	−	0.253117i	$-0.918544\pi$
$761$		−	13.9651i		−	0.506234i	0.967436	−	0.253117i	$-0.0814557\pi$
$762$		0			0
$763$	7.70038			0.278772
$764$	−18.1284	−	14.5189i	−0.655864	−	0.525276i
$765$		0			0
$766$	−10.7203	−	3.76375i	−0.387340	−	0.135990i
$767$	0.941516			0.0339962
$768$		0			0
$769$	17.9999			0.649094			0.324547	−	0.945869i	$-0.394788\pi$
$769$	17.9999			0.649094			0.324547	+	0.945869i	$0.394788\pi$
$770$	−23.7020	−	8.32145i	−0.854161	−	0.299884i
$771$		0			0
$772$	−20.0075	−	16.0239i	−0.720086	−	0.576711i
$773$	−27.2134			−0.978798			−0.489399	−	0.872060i	$-0.662784\pi$
$773$	−27.2134			−0.978798			−0.489399	+	0.872060i	$0.662784\pi$
$774$		0			0
$775$		−	32.2124i		−	1.15710i
$776$	−5.07798	−	8.13797i	−0.182289	−	0.292136i
$777$		0			0
$778$	−8.81659	−	3.09539i	−0.316090	−	0.110975i
$779$		−	7.59429i		−	0.272094i
$780$		0			0
$781$		−	6.14741i		−	0.219972i
$782$	−5.40184	+	15.3861i	−0.193170	+	0.550205i
$783$		0			0
$784$	−0.873805	−	3.90339i	−0.0312073	−	0.139407i
$785$			75.5908i			2.69795i
$786$		0			0
$787$	3.45794			0.123262			0.0616312	−	0.998099i	$-0.480370\pi$
$787$	3.45794			0.123262			0.0616312	+	0.998099i	$0.480370\pi$
$788$	−7.32365	−	5.86546i	−0.260894	−	0.208948i
$789$		0			0
$790$	22.0386	−	62.7725i	0.784097	−	2.23335i
$791$	14.5822			0.518484
$792$		0			0
$793$	0.527143			0.0187194
$794$	8.18157	−	23.3036i	0.290353	−	0.827013i
$795$		0			0
$796$	19.1981	−	23.9709i	0.680458	−	0.849625i
$797$	−44.2671			−1.56802			−0.784010	−	0.620748i	$-0.786829\pi$
$797$	−44.2671			−1.56802			−0.784010	+	0.620748i	$0.786829\pi$
$798$		0			0
$799$			12.7666i			0.451650i
$800$	4.66596	−	39.5562i	0.164967	−	1.39852i
$801$		0			0
$802$	8.71989	−	24.8369i	0.307910	−	0.877021i
$803$		−	46.1571i		−	1.62885i
$804$		0			0
$805$			20.3501i			0.717248i
$806$	1.63971	+	0.575679i	0.0577562	+	0.0202774i
$807$		0			0
$808$	12.2581	+	19.6448i	0.431237	+	0.691101i
$809$			14.4191i			0.506949i	0.967342	+	0.253475i	$0.0815734\pi$
$809$			14.4191i			0.506949i	−0.967342	+	0.253475i	$0.918427\pi$
$810$		0			0
$811$	24.3314			0.854389			0.427195	−	0.904160i	$-0.359502\pi$
$811$	24.3314			0.854389			0.427195	+	0.904160i	$0.359502\pi$
$812$	−9.00121	+	11.2390i	−0.315881	+	0.394411i
$813$		0			0
$814$	47.6981	+	16.7462i	1.67182	+	0.586953i
$815$	70.3410			2.46394
$816$		0			0
$817$	−8.41897			−0.294543
$818$	−4.97510	−	1.74669i	−0.173950	−	0.0610715i
$819$		0			0
$820$	−36.2082	+	45.2099i	−1.26445	+	1.57880i
$821$	3.63626			0.126906			0.0634532	−	0.997985i	$-0.479789\pi$
$821$	3.63626			0.126906			0.0634532	+	0.997985i	$0.479789\pi$
$822$		0			0
$823$			0.408592i			0.0142426i	0.999975	+	0.00712132i	$0.00226681\pi$
$823$			0.408592i			0.0142426i	−0.999975	+	0.00712132i	$0.997733\pi$
$824$	39.7431	−	24.7991i	1.38451	−	0.863917i
$825$		0			0
$826$	4.67727	+	1.64213i	0.162743	+	0.0571369i
$827$			39.3528i			1.36843i	0.729280	+	0.684215i	$0.239855\pi$
$827$			39.3528i			1.36843i	−0.729280	+	0.684215i	$0.760145\pi$
$828$		0			0
$829$			37.5641i			1.30465i	0.757938	+	0.652327i	$0.226207\pi$
$829$			37.5641i			1.30465i	−0.757938	+	0.652327i	$0.773793\pi$
$830$	8.06857	−	22.9817i	0.280064	−	0.797707i
$831$		0			0
$832$	1.93014	+	0.944435i	0.0669157	+	0.0327424i
$833$		−	1.96616i		−	0.0681234i
$834$		0			0
$835$	22.8200			0.789719
$836$	−5.82340	+	7.27115i	−0.201407	+	0.251478i
$837$		0			0
$838$	14.1288	−	40.2432i	0.488073	−	1.39018i
$839$	−35.7770			−1.23516			−0.617579	−	0.786509i	$-0.711887\pi$
$839$	−35.7770			−1.23516			−0.617579	+	0.786509i	$0.711887\pi$
$840$		0			0
$841$	22.8342			0.787385
$842$	1.95550	−	5.56986i	0.0673910	−	0.191950i
$843$		0			0
$844$	7.95905	+	6.37434i	0.273962	+	0.219414i
$845$	−44.8600			−1.54323
$846$		0			0
$847$		−	15.2033i		−	0.522390i
$848$	−3.96992	−	17.7341i	−0.136327	−	0.608991i
$849$		0			0
$850$	6.48556	−	18.4728i	0.222453	−	0.633613i
$851$		−	40.9528i		−	1.40384i
$852$		0			0
$853$		−	52.3988i		−	1.79410i	−0.441929	−	0.897050i	$-0.645706\pi$
$853$		−	52.3988i		−	1.79410i	0.441929	−	0.897050i	$-0.354294\pi$
$854$	2.61874	+	0.919406i	0.0896116	+	0.0314614i
$855$		0			0
$856$	36.3491	−	22.6813i	1.24239	−	0.775230i
$857$			19.1325i			0.653553i	0.945102	+	0.326777i	$0.105963\pi$
$857$			19.1325i			0.653553i	−0.945102	+	0.326777i	$0.894037\pi$
$858$		0			0
$859$	−12.1998			−0.416253			−0.208127	−	0.978102i	$-0.566737\pi$
$859$	−12.1998			−0.416253			−0.208127	+	0.978102i	$0.566737\pi$
$860$	50.1193	+	40.1402i	1.70905	+	1.36877i
$861$		0			0
$862$	27.1072	+	9.51696i	0.923275	+	0.324149i
$863$	−31.3575			−1.06742			−0.533711	−	0.845667i	$-0.679203\pi$
$863$	−31.3575			−1.06742			−0.533711	+	0.845667i	$0.679203\pi$
$864$		0			0
$865$	−46.2897			−1.57390
$866$	−50.1375	−	17.6026i	−1.70374	−	0.598160i
$867$		0			0
$868$	7.14170	+	5.71973i	0.242405	+	0.194140i
$869$	69.3968			2.35413
$870$		0			0
$871$			2.96214i			0.100368i
$872$	−18.4778	+	11.5299i	−0.625737	+	0.390451i
$873$		0			0
$874$	7.12057	+	2.49994i	0.240857	+	0.0845616i
$875$		−	7.08266i		−	0.239438i
$876$		0			0
$877$		−	4.64956i		−	0.157004i	−0.996914	−	0.0785022i	$-0.974986\pi$
$877$		−	4.64956i		−	0.157004i	0.996914	−	0.0785022i	$-0.0250138\pi$
$878$	5.72566	−	16.3084i	0.193232	−	0.550382i
$879$		0			0
$880$	69.3350	−	15.5212i	2.33728	−	0.523220i
$881$			43.3414i			1.46021i	0.683336	+	0.730104i	$0.260528\pi$
$881$			43.3414i			1.46021i	−0.683336	+	0.730104i	$0.739472\pi$
$882$		0			0
$883$	0.420653			0.0141561			0.00707805	−	0.999975i	$-0.497747\pi$
$883$	0.420653			0.0141561			0.00707805	+	0.999975i	$0.497747\pi$
$884$	0.824419	+	0.660270i	0.0277282	+	0.0222073i
$885$		0			0
$886$	−0.998477	+	2.84396i	−0.0335445	+	0.0955448i
$887$	14.5102			0.487204			0.243602	−	0.969875i	$-0.421671\pi$
$887$	14.5102			0.487204			0.243602	+	0.969875i	$0.421671\pi$
$888$		0			0
$889$	13.7782			0.462106
$890$	29.5917	−	84.2860i	0.991915	−	2.82527i
$891$		0			0
$892$	−36.8968	+	46.0696i	−1.23540	+	1.54252i
$893$	5.90830			0.197714
$894$		0			0
$895$		−	34.0955i		−	1.13969i
$896$	7.94138	+	8.05820i	0.265303	+	0.269206i
$897$		0			0
$898$	−11.5654	+	32.9418i	−0.385943	+	1.09928i
$899$		−	32.9375i		−	1.09853i
$900$		0			0
$901$		−	8.93276i		−	0.297593i
$902$	−57.0077	−	20.0146i	−1.89815	−	0.666414i
$903$		0			0
$904$	−34.9914	+	21.8341i	−1.16380	+	0.726192i
$905$			16.9599i			0.563765i
$906$		0			0
$907$	−30.1284			−1.00040			−0.500198	−	0.865911i	$-0.666740\pi$
$907$	−30.1284			−1.00040			−0.500198	+	0.865911i	$0.666740\pi$
$908$	18.0996	−	22.5993i	0.600657	−	0.749985i
$909$		0			0
$910$	1.24370	+	0.436648i	0.0412284	+	0.0144747i
$911$	−15.1934			−0.503379			−0.251689	−	0.967808i	$-0.580986\pi$
$911$	−15.1934			−0.503379			−0.251689	+	0.967808i	$0.580986\pi$
$912$		0			0
$913$	25.4070			0.840848
$914$	44.4095	+	15.5916i	1.46894	+	0.515724i
$915$		0			0
$916$	14.8929	−	18.5954i	0.492074	−	0.614408i
$917$	11.4226			0.377207
$918$		0			0
$919$			38.7985i			1.27984i	0.768440	+	0.639922i	$0.221033\pi$
$919$			38.7985i			1.27984i	−0.768440	+	0.639922i	$0.778967\pi$
$920$	−30.4705	−	48.8321i	−1.00458	−	1.60995i
$921$		0			0
$922$	20.3195	+	7.13392i	0.669189	+	0.234943i
$923$			0.322570i			0.0106175i
$924$		0			0
$925$			49.1688i			1.61666i
$926$	1.50795	−	4.29509i	0.0495543	−	0.141146i
$927$		0			0
$928$	4.77099	−	40.4466i	0.156615	−	1.32773i
$929$			43.7700i			1.43605i	0.696019	+	0.718023i	$0.254953\pi$
$929$			43.7700i			1.43605i	−0.696019	+	0.718023i	$0.745047\pi$
$930$		0			0
$931$	−0.909926			−0.0298216
$932$	−16.6204	+	20.7524i	−0.544419	+	0.679766i
$933$		0			0
$934$	−10.5795	+	30.1336i	−0.346171	+	0.986001i
$935$	34.9245			1.14215
$936$		0			0
$937$	17.7605			0.580209			0.290104	−	0.956995i	$-0.406310\pi$
$937$	17.7605			0.580209			0.290104	+	0.956995i	$0.406310\pi$
$938$	−5.16636	+	14.7153i	−0.168688	+	0.480473i
$939$		0			0
$940$	−35.1729	−	28.1697i	−1.14721	−	0.918794i
$941$	32.6364			1.06392			0.531958	−	0.846771i	$-0.321456\pi$
$941$	32.6364			1.06392			0.531958	+	0.846771i	$0.321456\pi$
$942$		0			0
$943$			48.9458i			1.59390i
$944$	−13.6823	+	3.06290i	−0.445322	+	0.0996889i
$945$		0			0
$946$	−22.1881	+	63.1983i	−0.721396	+	2.05475i
$947$			14.9843i			0.486925i	0.969910	+	0.243462i	$0.0782832\pi$
$947$			14.9843i			0.486925i	−0.969910	+	0.243462i	$0.921717\pi$
$948$		0			0
$949$			2.42198i			0.0786208i
$950$	−8.54911	−	3.00148i	−0.277370	−	0.0973807i
$951$		0			0
$952$	2.94396	+	4.71799i	0.0954142	+	0.152911i
$953$			23.1053i			0.748453i	0.927337	+	0.374226i	$0.122092\pi$
$953$			23.1053i			0.748453i	−0.927337	+	0.374226i	$0.877908\pi$
$954$		0			0
$955$	40.2971			1.30398
$956$	18.3806	+	14.7208i	0.594470	+	0.476106i
$957$		0			0
$958$	37.3808	+	13.1239i	1.20772	+	0.424014i
$959$	−5.89343			−0.190309
$960$		0			0
$961$	10.0702			0.324846
$962$	−2.50284	−	0.878713i	−0.0806948	−	0.0283309i
$963$		0			0
$964$	−36.3740	−	29.1317i	−1.17153	−	0.938268i
$965$	44.4741			1.43167
$966$		0			0
$967$			25.1604i			0.809103i	0.914515	+	0.404552i	$0.132572\pi$
$967$			25.1604i			0.809103i	−0.914515	+	0.404552i	$0.867428\pi$
$968$	22.7640	+	36.4817i	0.731664	+	1.17257i
$969$		0			0
$970$	15.7031	+	5.51315i	0.504197	+	0.177017i
$971$		−	24.0973i		−	0.773318i	−0.922223	−	0.386659i	$-0.873629\pi$
$971$		−	24.0973i		−	0.773318i	0.922223	−	0.386659i	$-0.126371\pi$
$972$		0			0
$973$			3.67309i			0.117754i
$974$	−1.19612	+	3.40691i	−0.0383262	+	0.109164i
$975$		0			0
$976$	−7.66056	+	1.71488i	−0.245209	+	0.0548919i
$977$			30.9215i			0.989267i	0.869102	+	0.494634i	$0.164698\pi$
$977$			30.9215i			0.989267i	−0.869102	+	0.494634i	$0.835302\pi$
$978$		0			0
$979$	93.1807			2.97807
$980$	5.41692	+	4.33836i	0.173037	+	0.138584i
$981$		0			0
$982$	−0.376390	+	1.07207i	−0.0120111	+	0.0342112i
$983$	1.67927			0.0535602			0.0267801	−	0.999641i	$-0.491475\pi$
$983$	1.67927			0.0535602			0.0267801	+	0.999641i	$0.491475\pi$
$984$		0			0
$985$	16.2795			0.518709
$986$	6.63156	−	18.8887i	0.211192	−	0.601538i
$987$		0			0
$988$	0.305569	−	0.381535i	0.00972143	−	0.0121383i
$989$	54.2610			1.72540
$990$		0			0
$991$			7.63921i			0.242667i	0.992612	+	0.121334i	$0.0387171\pi$
$991$			7.63921i			0.242667i	−0.992612	+	0.121334i	$0.961283\pi$
$992$	−25.7014	−	3.03168i	−0.816020	−	0.0962558i
$993$		0			0
$994$	−0.562604	+	1.60247i	−0.0178447	+	0.0508272i
$995$			53.2841i			1.68922i
$996$		0			0
$997$		−	57.4039i		−	1.81800i	−0.416798	−	0.908999i	$-0.636848\pi$
$997$		−	57.4039i		−	1.81800i	0.416798	−	0.908999i	$-0.363152\pi$
$998$	−43.5041	−	15.2737i	−1.37710	−	0.483480i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.c.323.3	✓	32
3.2	odd	2	inner	1512.2.j.c.323.30	yes	32
4.3	odd	2		6048.2.j.c.5615.4		32
8.3	odd	2	inner	1512.2.j.c.323.29	yes	32
8.5	even	2		6048.2.j.c.5615.30		32
12.11	even	2		6048.2.j.c.5615.29		32
24.5	odd	2		6048.2.j.c.5615.3		32
24.11	even	2	inner	1512.2.j.c.323.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.c.323.3	✓	32	1.1	even	1	trivial
1512.2.j.c.323.4	yes	32	24.11	even	2	inner
1512.2.j.c.323.29	yes	32	8.3	odd	2	inner
1512.2.j.c.323.30	yes	32	3.2	odd	2	inner
6048.2.j.c.5615.3		32	24.5	odd	2
6048.2.j.c.5615.4		32	4.3	odd	2
6048.2.j.c.5615.29		32	12.11	even	2
6048.2.j.c.5615.30		32	8.5	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33436 - 0.468477i) q^{2} +(1.56106 + 1.25024i) q^{4} -3.47003 q^{5} +1.00000i q^{7} +(-1.49731 - 2.39959i) q^{8} +O(q^{10})\)	\(q+(-1.33436 - 0.468477i) q^{2} +(1.56106 + 1.25024i) q^{4} -3.47003 q^{5} +1.00000i q^{7} +(-1.49731 - 2.39959i) q^{8} +(4.63028 + 1.62563i) q^{10} +5.11891i q^{11} -0.268602i q^{13} +(0.468477 - 1.33436i) q^{14} +(0.873805 + 3.90339i) q^{16} +1.96616i q^{17} +0.909926 q^{19} +(-5.41692 - 4.33836i) q^{20} +(2.39809 - 6.83050i) q^{22} -5.86455 q^{23} +7.04110 q^{25} +(-0.125834 + 0.358413i) q^{26} +(-1.25024 + 1.56106i) q^{28} +7.19959 q^{29} -4.57491i q^{31} +(0.662675 - 5.61791i) q^{32} +(0.921102 - 2.62358i) q^{34} -3.47003i q^{35} +6.98312i q^{37} +(-1.21417 - 0.426280i) q^{38} +(5.19572 + 8.32666i) q^{40} -8.34605i q^{41} -9.25237 q^{43} +(-6.39986 + 7.99092i) q^{44} +(7.82544 + 2.74741i) q^{46} +6.49316 q^{47} -1.00000 q^{49} +(-9.39539 - 3.29859i) q^{50} +(0.335817 - 0.419304i) q^{52} -4.54325 q^{53} -17.7628i q^{55} +(2.39959 - 1.49731i) q^{56} +(-9.60688 - 3.37285i) q^{58} +3.50524i q^{59} +1.96254i q^{61} +(-2.14324 + 6.10459i) q^{62} +(-3.51611 + 7.18589i) q^{64} +0.932057i q^{65} -11.0280 q^{67} +(-2.45817 + 3.06929i) q^{68} +(-1.62563 + 4.63028i) q^{70} -1.20092 q^{71} -9.01697 q^{73} +(3.27143 - 9.31802i) q^{74} +(1.42045 + 1.13762i) q^{76} -5.11891 q^{77} -13.5570i q^{79} +(-3.03213 - 13.5449i) q^{80} +(-3.90994 + 11.1367i) q^{82} -4.96335i q^{83} -6.82263i q^{85} +(12.3460 + 4.33452i) q^{86} +(12.2833 - 7.66461i) q^{88} -18.2032i q^{89} +0.268602 q^{91} +(-9.15490 - 7.33208i) q^{92} +(-8.66424 - 3.04190i) q^{94} -3.15747 q^{95} +3.39139 q^{97} +(1.33436 + 0.468477i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

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