LMFDB - Embedded newform 1350.2.f.e.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(107,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("1350.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1350.107
Dual form			1350.2.f.e.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-3.34607 - 3.34607i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-3.34607 - 3.34607i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.00000i q^{11} +(-2.12132 + 2.12132i) q^{13} +4.73205 q^{14} -1.00000 q^{16} +(5.79555 - 5.79555i) q^{17} +4.19615i q^{19} +(-2.12132 - 2.12132i) q^{22} +(-2.12132 - 2.12132i) q^{23} -3.00000i q^{26} +(-3.34607 + 3.34607i) q^{28} -2.19615 q^{29} -2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +8.19615i q^{34} +(2.77766 + 2.77766i) q^{37} +(-2.96713 - 2.96713i) q^{38} +6.00000i q^{41} +(-5.13922 + 5.13922i) q^{43} +3.00000 q^{44} +3.00000 q^{46} +(-6.36396 + 6.36396i) q^{47} +15.3923i q^{49} +(2.12132 + 2.12132i) q^{52} +(5.79555 + 5.79555i) q^{53} -4.73205i q^{56} +(1.55291 - 1.55291i) q^{58} +7.39230 q^{59} +1.19615 q^{61} +(1.41421 - 1.41421i) q^{62} +1.00000i q^{64} +(-5.79555 - 5.79555i) q^{67} +(-5.79555 - 5.79555i) q^{68} +11.1962i q^{71} +(-10.9348 + 10.9348i) q^{73} -3.92820 q^{74} +4.19615 q^{76} +(10.0382 - 10.0382i) q^{77} +0.196152i q^{79} +(-4.24264 - 4.24264i) q^{82} +(11.5911 + 11.5911i) q^{83} -7.26795i q^{86} +(-2.12132 + 2.12132i) q^{88} +2.19615 q^{89} +14.1962 q^{91} +(-2.12132 + 2.12132i) q^{92} -9.00000i q^{94} +(-10.3664 - 10.3664i) q^{97} +(-10.8840 - 10.8840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 24 q^{14} - 8 q^{16} + 24 q^{29} - 16 q^{31} + 24 q^{44} + 24 q^{46} - 24 q^{59} - 32 q^{61} + 24 q^{74} - 8 q^{76} - 24 q^{89} + 72 q^{91}+O(q^{100}) $ 8 * q + 24 * q^14 - 8 * q^16 + 24 * q^29 - 16 * q^31 + 24 * q^44 + 24 * q^46 - 24 * q^59 - 32 * q^61 + 24 * q^74 - 8 * q^76 - 24 * q^89 + 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.34607	−	3.34607i	−1.26469	−	1.26469i	−0.948792	−	0.315902i	$-0.897693\pi$
$7$	−3.34607	−	3.34607i	−1.26469	−	1.26469i	−0.315902	−	0.948792i	$-0.602307\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$			3.00000i			0.904534i	0.891883	+	0.452267i	$0.149385\pi$
$11$			3.00000i			0.904534i	−0.891883	+	0.452267i	$0.850615\pi$
$12$		0			0
$13$	−2.12132	+	2.12132i	−0.588348	+	0.588348i	−0.937184	−	0.348836i	$-0.886577\pi$
$13$	−2.12132	+	2.12132i	−0.588348	+	0.588348i	0.348836	+	0.937184i	$0.386577\pi$
$14$	4.73205			1.26469
$15$		0			0
$16$	−1.00000			−0.250000
$17$	5.79555	−	5.79555i	1.40563	−	1.40563i	0.625019	−	0.780610i	$-0.285091\pi$
$17$	5.79555	−	5.79555i	1.40563	−	1.40563i	0.780610	−	0.625019i	$-0.214909\pi$
$18$		0			0
$19$			4.19615i			0.962663i	0.876539	+	0.481332i	$0.159847\pi$
$19$			4.19615i			0.962663i	−0.876539	+	0.481332i	$0.840153\pi$
$20$		0			0
$21$		0			0
$22$	−2.12132	−	2.12132i	−0.452267	−	0.452267i
$23$	−2.12132	−	2.12132i	−0.442326	−	0.442326i	0.450467	−	0.892793i	$-0.351257\pi$
$23$	−2.12132	−	2.12132i	−0.442326	−	0.442326i	−0.892793	+	0.450467i	$0.851257\pi$
$24$		0			0
$25$		0			0
$26$		−	3.00000i		−	0.588348i
$27$		0			0
$28$	−3.34607	+	3.34607i	−0.632347	+	0.632347i
$29$	−2.19615			−0.407815			−0.203908	−	0.978990i	$-0.565364\pi$
$29$	−2.19615			−0.407815			−0.203908	+	0.978990i	$0.565364\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			8.19615i			1.40563i
$35$		0			0
$36$		0			0
$37$	2.77766	+	2.77766i	0.456644	+	0.456644i	0.897552	−	0.440908i	$-0.145343\pi$
$37$	2.77766	+	2.77766i	0.456644	+	0.456644i	−0.440908	+	0.897552i	$0.645343\pi$
$38$	−2.96713	−	2.96713i	−0.481332	−	0.481332i
$39$		0			0
$40$		0			0
$41$			6.00000i			0.937043i	0.883452	+	0.468521i	$0.155213\pi$
$41$			6.00000i			0.937043i	−0.883452	+	0.468521i	$0.844787\pi$
$42$		0			0
$43$	−5.13922	+	5.13922i	−0.783723	+	0.783723i	−0.980457	−	0.196734i	$-0.936967\pi$
$43$	−5.13922	+	5.13922i	−0.783723	+	0.783723i	0.196734	+	0.980457i	$0.436967\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	3.00000			0.442326
$47$	−6.36396	+	6.36396i	−0.928279	+	0.928279i	−0.997595	−	0.0693157i	$-0.977918\pi$
$47$	−6.36396	+	6.36396i	−0.928279	+	0.928279i	0.0693157	+	0.997595i	$0.477918\pi$
$48$		0			0
$49$			15.3923i			2.19890i
$50$		0			0
$51$		0			0
$52$	2.12132	+	2.12132i	0.294174	+	0.294174i
$53$	5.79555	+	5.79555i	0.796081	+	0.796081i	0.982475	−	0.186394i	$-0.0596802\pi$
$53$	5.79555	+	5.79555i	0.796081	+	0.796081i	−0.186394	+	0.982475i	$0.559680\pi$
$54$		0			0
$55$		0			0
$56$		−	4.73205i		−	0.632347i
$57$		0			0
$58$	1.55291	−	1.55291i	0.203908	−	0.203908i
$59$	7.39230			0.962396			0.481198	−	0.876612i	$-0.340202\pi$
$59$	7.39230			0.962396			0.481198	+	0.876612i	$0.340202\pi$
$60$		0			0
$61$	1.19615			0.153152			0.0765758	−	0.997064i	$-0.475601\pi$
$61$	1.19615			0.153152			0.0765758	+	0.997064i	$0.475601\pi$
$62$	1.41421	−	1.41421i	0.179605	−	0.179605i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−5.79555	−	5.79555i	−0.708040	−	0.708040i	0.258083	−	0.966123i	$-0.416909\pi$
$67$	−5.79555	−	5.79555i	−0.708040	−	0.708040i	−0.966123	+	0.258083i	$0.916909\pi$
$68$	−5.79555	−	5.79555i	−0.702814	−	0.702814i
$69$		0			0
$70$		0			0
$71$			11.1962i			1.32874i	0.747404	+	0.664369i	$0.231300\pi$
$71$			11.1962i			1.32874i	−0.747404	+	0.664369i	$0.768700\pi$
$72$		0			0
$73$	−10.9348	+	10.9348i	−1.27982	+	1.27982i	−0.339050	+	0.940768i	$0.610105\pi$
$73$	−10.9348	+	10.9348i	−1.27982	+	1.27982i	−0.940768	+	0.339050i	$0.889895\pi$
$74$	−3.92820			−0.456644
$75$		0			0
$76$	4.19615			0.481332
$77$	10.0382	−	10.0382i	1.14396	−	1.14396i
$78$		0			0
$79$			0.196152i			0.0220689i	0.999939	+	0.0110344i	$0.00351244\pi$
$79$			0.196152i			0.0220689i	−0.999939	+	0.0110344i	$0.996488\pi$
$80$		0			0
$81$		0			0
$82$	−4.24264	−	4.24264i	−0.468521	−	0.468521i
$83$	11.5911	+	11.5911i	1.27229	+	1.27229i	0.944884	+	0.327406i	$0.106174\pi$
$83$	11.5911	+	11.5911i	1.27229	+	1.27229i	0.327406	+	0.944884i	$0.393826\pi$
$84$		0			0
$85$		0			0
$86$		−	7.26795i		−	0.783723i
$87$		0			0
$88$	−2.12132	+	2.12132i	−0.226134	+	0.226134i
$89$	2.19615			0.232792			0.116396	−	0.993203i	$-0.462866\pi$
$89$	2.19615			0.232792			0.116396	+	0.993203i	$0.462866\pi$
$90$		0			0
$91$	14.1962			1.48816
$92$	−2.12132	+	2.12132i	−0.221163	+	0.221163i
$93$		0			0
$94$		−	9.00000i		−	0.928279i
$95$		0			0
$96$		0			0
$97$	−10.3664	−	10.3664i	−1.05254	−	1.05254i	−0.998541	−	0.0540042i	$-0.982802\pi$
$97$	−10.3664	−	10.3664i	−1.05254	−	1.05254i	−0.0540042	−	0.998541i	$-0.517198\pi$
$98$	−10.8840	−	10.8840i	−1.09945	−	1.09945i
$99$		0			0
$100$		0			0
$101$		−	12.5885i		−	1.25260i	−0.779583	−	0.626299i	$-0.784569\pi$
$101$		−	12.5885i		−	1.25260i	0.779583	−	0.626299i	$-0.215431\pi$
$102$		0			0
$103$	−9.14162	+	9.14162i	−0.900751	+	0.900751i	−0.995501	−	0.0947505i	$-0.969795\pi$
$103$	−9.14162	+	9.14162i	−0.900751	+	0.900751i	0.0947505	+	0.995501i	$0.469795\pi$
$104$	−3.00000			−0.294174
$105$		0			0
$106$	−8.19615			−0.796081
$107$	−11.0227	+	11.0227i	−1.06561	+	1.06561i	−0.0679138	+	0.997691i	$0.521634\pi$
$107$	−11.0227	+	11.0227i	−1.06561	+	1.06561i	−0.997691	+	0.0679138i	$0.978366\pi$
$108$		0			0
$109$		−	8.00000i		−	0.766261i	−0.923694	−	0.383131i	$-0.874846\pi$
$109$		−	8.00000i		−	0.766261i	0.923694	−	0.383131i	$-0.125154\pi$
$110$		0			0
$111$		0			0
$112$	3.34607	+	3.34607i	0.316173	+	0.316173i
$113$	7.34847	+	7.34847i	0.691286	+	0.691286i	0.962515	−	0.271229i	$-0.0874301\pi$
$113$	7.34847	+	7.34847i	0.691286	+	0.691286i	−0.271229	+	0.962515i	$0.587430\pi$
$114$		0			0
$115$		0			0
$116$			2.19615i			0.203908i
$117$		0			0
$118$	−5.22715	+	5.22715i	−0.481198	+	0.481198i
$119$	−38.7846			−3.55538
$120$		0			0
$121$	2.00000			0.181818
$122$	−0.845807	+	0.845807i	−0.0765758	+	0.0765758i
$123$		0			0
$124$			2.00000i			0.179605i
$125$		0			0
$126$		0			0
$127$	7.34847	+	7.34847i	0.652071	+	0.652071i	0.953491	−	0.301420i	$-0.0974607\pi$
$127$	7.34847	+	7.34847i	0.652071	+	0.652071i	−0.301420	+	0.953491i	$0.597461\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$			7.39230i			0.645869i	0.946421	+	0.322934i	$0.104669\pi$
$131$			7.39230i			0.645869i	−0.946421	+	0.322934i	$0.895331\pi$
$132$		0			0
$133$	14.0406	−	14.0406i	1.21747	−	1.21747i
$134$	8.19615			0.708040
$135$		0			0
$136$	8.19615			0.702814
$137$	−6.93237	+	6.93237i	−0.592272	+	0.592272i	−0.938245	−	0.345973i	$-0.887549\pi$
$137$	−6.93237	+	6.93237i	−0.592272	+	0.592272i	0.345973	+	0.938245i	$0.387549\pi$
$138$		0			0
$139$			5.80385i			0.492276i	0.969235	+	0.246138i	$0.0791616\pi$
$139$			5.80385i			0.492276i	−0.969235	+	0.246138i	$0.920838\pi$
$140$		0			0
$141$		0			0
$142$	−7.91688	−	7.91688i	−0.664369	−	0.664369i
$143$	−6.36396	−	6.36396i	−0.532181	−	0.532181i
$144$		0			0
$145$		0			0
$146$		−	15.4641i		−	1.27982i
$147$		0			0
$148$	2.77766	−	2.77766i	0.228322	−	0.228322i
$149$	10.3923			0.851371			0.425685	−	0.904871i	$-0.360033\pi$
$149$	10.3923			0.851371			0.425685	+	0.904871i	$0.360033\pi$
$150$		0			0
$151$	−10.1962			−0.829751			−0.414876	−	0.909878i	$-0.636175\pi$
$151$	−10.1962			−0.829751			−0.414876	+	0.909878i	$0.636175\pi$
$152$	−2.96713	+	2.96713i	−0.240666	+	0.240666i
$153$		0			0
$154$			14.1962i			1.14396i
$155$		0			0
$156$		0			0
$157$	−4.89898	−	4.89898i	−0.390981	−	0.390981i	0.484056	−	0.875037i	$-0.339163\pi$
$157$	−4.89898	−	4.89898i	−0.390981	−	0.390981i	−0.875037	+	0.484056i	$0.839163\pi$
$158$	−0.138701	−	0.138701i	−0.0110344	−	0.0110344i
$159$		0			0
$160$		0			0
$161$			14.1962i			1.11881i
$162$		0			0
$163$	15.8338	−	15.8338i	1.24020	−	1.24020i	0.280275	−	0.959920i	$-0.409574\pi$
$163$	15.8338	−	15.8338i	1.24020	−	1.24020i	0.959920	−	0.280275i	$-0.0904258\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	−16.3923			−1.27229
$167$	3.25813	−	3.25813i	0.252122	−	0.252122i	−0.569718	−	0.821840i	$-0.692948\pi$
$167$	3.25813	−	3.25813i	0.252122	−	0.252122i	0.821840	+	0.569718i	$0.192948\pi$
$168$		0			0
$169$			4.00000i			0.307692i
$170$		0			0
$171$		0			0
$172$	5.13922	+	5.13922i	0.391862	+	0.391862i
$173$	−1.55291	−	1.55291i	−0.118066	−	0.118066i	0.645605	−	0.763671i	$-0.276605\pi$
$173$	−1.55291	−	1.55291i	−0.118066	−	0.118066i	−0.763671	+	0.645605i	$0.776605\pi$
$174$		0			0
$175$		0			0
$176$		−	3.00000i		−	0.226134i
$177$		0			0
$178$	−1.55291	+	1.55291i	−0.116396	+	0.116396i
$179$	−4.60770			−0.344395			−0.172198	−	0.985062i	$-0.555087\pi$
$179$	−4.60770			−0.344395			−0.172198	+	0.985062i	$0.555087\pi$
$180$		0			0
$181$	−17.5885			−1.30734			−0.653670	−	0.756780i	$-0.726771\pi$
$181$	−17.5885			−1.30734			−0.653670	+	0.756780i	$0.726771\pi$
$182$	−10.0382	+	10.0382i	−0.744081	+	0.744081i
$183$		0			0
$184$		−	3.00000i		−	0.221163i
$185$		0			0
$186$		0			0
$187$	17.3867	+	17.3867i	1.27144	+	1.27144i
$188$	6.36396	+	6.36396i	0.464140	+	0.464140i
$189$		0			0
$190$		0			0
$191$		−	16.3923i		−	1.18611i	−0.805164	−	0.593053i	$-0.797923\pi$
$191$		−	16.3923i		−	1.18611i	0.805164	−	0.593053i	$-0.202077\pi$
$192$		0			0
$193$	−1.31268	+	1.31268i	−0.0944886	+	0.0944886i	−0.752771	−	0.658282i	$-0.771283\pi$
$193$	−1.31268	+	1.31268i	−0.0944886	+	0.0944886i	0.658282	+	0.752771i	$0.271283\pi$
$194$	14.6603			1.05254
$195$		0			0
$196$	15.3923			1.09945
$197$	11.5911	−	11.5911i	0.825832	−	0.825832i	−0.161105	−	0.986937i	$-0.551506\pi$
$197$	11.5911	−	11.5911i	0.825832	−	0.825832i	0.986937	+	0.161105i	$0.0515057\pi$
$198$		0			0
$199$		−	2.00000i		−	0.141776i	−0.997484	−	0.0708881i	$-0.977417\pi$
$199$		−	2.00000i		−	0.141776i	0.997484	−	0.0708881i	$-0.0225833\pi$
$200$		0			0
$201$		0			0
$202$	8.90138	+	8.90138i	0.626299	+	0.626299i
$203$	7.34847	+	7.34847i	0.515761	+	0.515761i
$204$		0			0
$205$		0			0
$206$		−	12.9282i		−	0.900751i
$207$		0			0
$208$	2.12132	−	2.12132i	0.147087	−	0.147087i
$209$	−12.5885			−0.870762
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	5.79555	−	5.79555i	0.398040	−	0.398040i
$213$		0			0
$214$		−	15.5885i		−	1.06561i
$215$		0			0
$216$		0			0
$217$	6.69213	+	6.69213i	0.454291	+	0.454291i
$218$	5.65685	+	5.65685i	0.383131	+	0.383131i
$219$		0			0
$220$		0			0
$221$			24.5885i			1.65400i
$222$		0			0
$223$	−2.20925	+	2.20925i	−0.147943	+	0.147943i	−0.777198	−	0.629256i	$-0.783360\pi$
$223$	−2.20925	+	2.20925i	−0.147943	+	0.147943i	0.629256	+	0.777198i	$0.283360\pi$
$224$	−4.73205			−0.316173
$225$		0			0
$226$	−10.3923			−0.691286
$227$	−12.1595	+	12.1595i	−0.807055	+	0.807055i	−0.984187	−	0.177132i	$-0.943318\pi$
$227$	−12.1595	+	12.1595i	−0.807055	+	0.807055i	0.177132	+	0.984187i	$0.443318\pi$
$228$		0			0
$229$		−	13.5885i		−	0.897951i	−0.893544	−	0.448975i	$-0.851789\pi$
$229$		−	13.5885i		−	0.897951i	0.893544	−	0.448975i	$-0.148211\pi$
$230$		0			0
$231$		0			0
$232$	−1.55291	−	1.55291i	−0.101954	−	0.101954i
$233$	−2.68973	−	2.68973i	−0.176210	−	0.176210i	0.613491	−	0.789701i	$-0.289764\pi$
$233$	−2.68973	−	2.68973i	−0.176210	−	0.176210i	−0.789701	+	0.613491i	$0.789764\pi$
$234$		0			0
$235$		0			0
$236$		−	7.39230i		−	0.481198i
$237$		0			0
$238$	27.4249	−	27.4249i	1.77769	−	1.77769i
$239$	−23.1962			−1.50043			−0.750217	−	0.661191i	$-0.770051\pi$
$239$	−23.1962			−1.50043			−0.750217	+	0.661191i	$0.770051\pi$
$240$		0			0
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$	−1.41421	+	1.41421i	−0.0909091	+	0.0909091i
$243$		0			0
$244$		−	1.19615i		−	0.0765758i
$245$		0			0
$246$		0			0
$247$	−8.90138	−	8.90138i	−0.566381	−	0.566381i
$248$	−1.41421	−	1.41421i	−0.0898027	−	0.0898027i
$249$		0			0
$250$		0			0
$251$		−	19.3923i		−	1.22403i	−0.790846	−	0.612016i	$-0.790359\pi$
$251$		−	19.3923i		−	1.22403i	0.790846	−	0.612016i	$-0.209641\pi$
$252$		0			0
$253$	6.36396	−	6.36396i	0.400099	−	0.400099i
$254$	−10.3923			−0.652071
$255$		0			0
$256$	1.00000			0.0625000
$257$	5.79555	−	5.79555i	0.361517	−	0.361517i	−0.502854	−	0.864371i	$-0.667717\pi$
$257$	5.79555	−	5.79555i	0.361517	−	0.361517i	0.864371	+	0.502854i	$0.167717\pi$
$258$		0			0
$259$		−	18.5885i		−	1.15503i
$260$		0			0
$261$		0			0
$262$	−5.22715	−	5.22715i	−0.322934	−	0.322934i
$263$	−6.36396	−	6.36396i	−0.392419	−	0.392419i	0.483130	−	0.875549i	$-0.339500\pi$
$263$	−6.36396	−	6.36396i	−0.392419	−	0.392419i	−0.875549	+	0.483130i	$0.839500\pi$
$264$		0			0
$265$		0			0
$266$			19.8564i			1.21747i
$267$		0			0
$268$	−5.79555	+	5.79555i	−0.354020	+	0.354020i
$269$	24.0000			1.46331			0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000			1.46331			0.731653	+	0.681677i	$0.238749\pi$
$270$		0			0
$271$	0.392305			0.0238308			0.0119154	−	0.999929i	$-0.496207\pi$
$271$	0.392305			0.0238308			0.0119154	+	0.999929i	$0.496207\pi$
$272$	−5.79555	+	5.79555i	−0.351407	+	0.351407i
$273$		0			0
$274$		−	9.80385i		−	0.592272i
$275$		0			0
$276$		0			0
$277$	10.2784	+	10.2784i	0.617571	+	0.617571i	0.944908	−	0.327337i	$-0.106151\pi$
$277$	10.2784	+	10.2784i	0.617571	+	0.617571i	−0.327337	+	0.944908i	$0.606151\pi$
$278$	−4.10394	−	4.10394i	−0.246138	−	0.246138i
$279$		0			0
$280$		0			0
$281$			32.1962i			1.92066i	0.278864	+	0.960331i	$0.410042\pi$
$281$			32.1962i			1.92066i	−0.278864	+	0.960331i	$0.589958\pi$
$282$		0			0
$283$	5.13922	−	5.13922i	0.305495	−	0.305495i	−0.537664	−	0.843159i	$-0.680693\pi$
$283$	5.13922	−	5.13922i	0.305495	−	0.305495i	0.843159	+	0.537664i	$0.180693\pi$
$284$	11.1962			0.664369
$285$		0			0
$286$	9.00000			0.532181
$287$	20.0764	−	20.0764i	1.18507	−	1.18507i
$288$		0			0
$289$		−	50.1769i		−	2.95158i
$290$		0			0
$291$		0			0
$292$	10.9348	+	10.9348i	0.639909	+	0.639909i
$293$	−16.2499	−	16.2499i	−0.949327	−	0.949327i	0.0494501	−	0.998777i	$-0.484253\pi$
$293$	−16.2499	−	16.2499i	−0.949327	−	0.949327i	−0.998777	+	0.0494501i	$0.984253\pi$
$294$		0			0
$295$		0			0
$296$			3.92820i			0.228322i
$297$		0			0
$298$	−7.34847	+	7.34847i	−0.425685	+	0.425685i
$299$	9.00000			0.520483
$300$		0			0
$301$	34.3923			1.98234
$302$	7.20977	−	7.20977i	0.414876	−	0.414876i
$303$		0			0
$304$		−	4.19615i		−	0.240666i
$305$		0			0
$306$		0			0
$307$	−12.2474	−	12.2474i	−0.698999	−	0.698999i	0.265196	−	0.964195i	$-0.414563\pi$
$307$	−12.2474	−	12.2474i	−0.698999	−	0.698999i	−0.964195	+	0.265196i	$0.914563\pi$
$308$	−10.0382	−	10.0382i	−0.571979	−	0.571979i
$309$		0			0
$310$		0			0
$311$		−	11.1962i		−	0.634876i	−0.948279	−	0.317438i	$-0.897178\pi$
$311$		−	11.1962i		−	0.634876i	0.948279	−	0.317438i	$-0.102822\pi$
$312$		0			0
$313$	15.8338	−	15.8338i	0.894976	−	0.894976i	−0.100010	−	0.994986i	$-0.531887\pi$
$313$	15.8338	−	15.8338i	0.894976	−	0.894976i	0.994986	+	0.100010i	$0.0318875\pi$
$314$	6.92820			0.390981
$315$		0			0
$316$	0.196152			0.0110344
$317$	−11.1750	+	11.1750i	−0.627651	+	0.627651i	−0.947476	−	0.319825i	$-0.896376\pi$
$317$	−11.1750	+	11.1750i	−0.627651	+	0.627651i	0.319825	+	0.947476i	$0.396376\pi$
$318$		0			0
$319$		−	6.58846i		−	0.368883i
$320$		0			0
$321$		0			0
$322$	−10.0382	−	10.0382i	−0.559407	−	0.559407i
$323$	24.3190	+	24.3190i	1.35315	+	1.35315i
$324$		0			0
$325$		0			0
$326$			22.3923i			1.24020i
$327$		0			0
$328$	−4.24264	+	4.24264i	−0.234261	+	0.234261i
$329$	42.5885			2.34798
$330$		0			0
$331$	−6.78461			−0.372916			−0.186458	−	0.982463i	$-0.559701\pi$
$331$	−6.78461			−0.372916			−0.186458	+	0.982463i	$0.559701\pi$
$332$	11.5911	−	11.5911i	0.636145	−	0.636145i
$333$		0			0
$334$			4.60770i			0.252122i
$335$		0			0
$336$		0			0
$337$	15.8338	+	15.8338i	0.862519	+	0.862519i	0.991630	−	0.129111i	$-0.0412123\pi$
$337$	15.8338	+	15.8338i	0.862519	+	0.862519i	−0.129111	+	0.991630i	$0.541212\pi$
$338$	−2.82843	−	2.82843i	−0.153846	−	0.153846i
$339$		0			0
$340$		0			0
$341$		−	6.00000i		−	0.324918i
$342$		0			0
$343$	28.0812	−	28.0812i	1.51624	−	1.51624i
$344$	−7.26795			−0.391862
$345$		0			0
$346$	2.19615			0.118066
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$		0			0
$349$			6.39230i			0.342172i	0.985256	+	0.171086i	$0.0547276\pi$
$349$			6.39230i			0.342172i	−0.985256	+	0.171086i	$0.945272\pi$
$350$		0			0
$351$		0			0
$352$	2.12132	+	2.12132i	0.113067	+	0.113067i
$353$	10.0382	+	10.0382i	0.534279	+	0.534279i	0.921843	−	0.387564i	$-0.126683\pi$
$353$	10.0382	+	10.0382i	0.534279	+	0.534279i	−0.387564	+	0.921843i	$0.626683\pi$
$354$		0			0
$355$		0			0
$356$		−	2.19615i		−	0.116396i
$357$		0			0
$358$	3.25813	−	3.25813i	0.172198	−	0.172198i
$359$	−0.803848			−0.0424255			−0.0212127	−	0.999775i	$-0.506753\pi$
$359$	−0.803848			−0.0424255			−0.0212127	+	0.999775i	$0.506753\pi$
$360$		0			0
$361$	1.39230			0.0732792
$362$	12.4369	−	12.4369i	0.653670	−	0.653670i
$363$		0			0
$364$		−	14.1962i		−	0.744081i
$365$		0			0
$366$		0			0
$367$	23.1822	+	23.1822i	1.21010	+	1.21010i	0.970993	+	0.239109i	$0.0768555\pi$
$367$	23.1822	+	23.1822i	1.21010	+	1.21010i	0.239109	+	0.970993i	$0.423145\pi$
$368$	2.12132	+	2.12132i	0.110581	+	0.110581i
$369$		0			0
$370$		0			0
$371$		−	38.7846i		−	2.01360i
$372$		0			0
$373$	−15.3533	+	15.3533i	−0.794963	+	0.794963i	−0.982296	−	0.187334i	$-0.940015\pi$
$373$	−15.3533	+	15.3533i	−0.794963	+	0.794963i	0.187334	+	0.982296i	$0.440015\pi$
$374$	−24.5885			−1.27144
$375$		0			0
$376$	−9.00000			−0.464140
$377$	4.65874	−	4.65874i	0.239937	−	0.239937i
$378$		0			0
$379$			2.00000i			0.102733i	0.998680	+	0.0513665i	$0.0163577\pi$
$379$			2.00000i			0.102733i	−0.998680	+	0.0513665i	$0.983642\pi$
$380$		0			0
$381$		0			0
$382$	11.5911	+	11.5911i	0.593053	+	0.593053i
$383$	2.12132	+	2.12132i	0.108394	+	0.108394i	0.759224	−	0.650830i	$-0.225579\pi$
$383$	2.12132	+	2.12132i	0.108394	+	0.108394i	−0.650830	+	0.759224i	$0.725579\pi$
$384$		0			0
$385$		0			0
$386$		−	1.85641i		−	0.0944886i
$387$		0			0
$388$	−10.3664	+	10.3664i	−0.526272	+	0.526272i
$389$	21.8038			1.10550			0.552749	−	0.833347i	$-0.313579\pi$
$389$	21.8038			1.10550			0.552749	+	0.833347i	$0.313579\pi$
$390$		0			0
$391$	−24.5885			−1.24349
$392$	−10.8840	+	10.8840i	−0.549725	+	0.549725i
$393$		0			0
$394$			16.3923i			0.825832i
$395$		0			0
$396$		0			0
$397$	11.2629	+	11.2629i	0.565271	+	0.565271i	0.930800	−	0.365529i	$-0.119112\pi$
$397$	11.2629	+	11.2629i	0.565271	+	0.565271i	−0.365529	+	0.930800i	$0.619112\pi$
$398$	1.41421	+	1.41421i	0.0708881	+	0.0708881i
$399$		0			0
$400$		0			0
$401$			14.1962i			0.708922i	0.935071	+	0.354461i	$0.115336\pi$
$401$			14.1962i			0.708922i	−0.935071	+	0.354461i	$0.884664\pi$
$402$		0			0
$403$	4.24264	−	4.24264i	0.211341	−	0.211341i
$404$	−12.5885			−0.626299
$405$		0			0
$406$	−10.3923			−0.515761
$407$	−8.33298	+	8.33298i	−0.413050	+	0.413050i
$408$		0			0
$409$			23.0000i			1.13728i	0.822588	+	0.568638i	$0.192530\pi$
$409$			23.0000i			1.13728i	−0.822588	+	0.568638i	$0.807470\pi$
$410$		0			0
$411$		0			0
$412$	9.14162	+	9.14162i	0.450375	+	0.450375i
$413$	−24.7351	−	24.7351i	−1.21714	−	1.21714i
$414$		0			0
$415$		0			0
$416$			3.00000i			0.147087i
$417$		0			0
$418$	8.90138	−	8.90138i	0.435381	−	0.435381i
$419$	10.3923			0.507697			0.253849	−	0.967244i	$-0.418303\pi$
$419$	10.3923			0.507697			0.253849	+	0.967244i	$0.418303\pi$
$420$		0			0
$421$	−8.80385			−0.429073			−0.214537	−	0.976716i	$-0.568824\pi$
$421$	−8.80385			−0.429073			−0.214537	+	0.976716i	$0.568824\pi$
$422$	2.82843	−	2.82843i	0.137686	−	0.137686i
$423$		0			0
$424$			8.19615i			0.398040i
$425$		0			0
$426$		0			0
$427$	−4.00240	−	4.00240i	−0.193690	−	0.193690i
$428$	11.0227	+	11.0227i	0.532803	+	0.532803i
$429$		0			0
$430$		0			0
$431$			3.58846i			0.172850i	0.996258	+	0.0864250i	$0.0275443\pi$
$431$			3.58846i			0.172850i	−0.996258	+	0.0864250i	$0.972456\pi$
$432$		0			0
$433$	13.4722	−	13.4722i	0.647432	−	0.647432i	−0.304939	−	0.952372i	$-0.598636\pi$
$433$	13.4722	−	13.4722i	0.647432	−	0.647432i	0.952372	+	0.304939i	$0.0986362\pi$
$434$	−9.46410			−0.454291
$435$		0			0
$436$	−8.00000			−0.383131
$437$	8.90138	−	8.90138i	0.425811	−	0.425811i
$438$		0			0
$439$		−	20.5885i		−	0.982633i	−0.870981	−	0.491317i	$-0.836516\pi$
$439$		−	20.5885i		−	0.982633i	0.870981	−	0.491317i	$-0.163484\pi$
$440$		0			0
$441$		0			0
$442$	−17.3867	−	17.3867i	−0.826999	−	0.826999i
$443$	−2.53742	−	2.53742i	−0.120557	−	0.120557i	0.644255	−	0.764811i	$-0.277168\pi$
$443$	−2.53742	−	2.53742i	−0.120557	−	0.120557i	−0.764811	+	0.644255i	$0.777168\pi$
$444$		0			0
$445$		0			0
$446$		−	3.12436i		−	0.147943i
$447$		0			0
$448$	3.34607	−	3.34607i	0.158087	−	0.158087i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$	7.34847	−	7.34847i	0.345643	−	0.345643i
$453$		0			0
$454$		−	17.1962i		−	0.807055i
$455$		0			0
$456$		0			0
$457$	−9.05369	−	9.05369i	−0.423514	−	0.423514i	0.462898	−	0.886412i	$-0.346810\pi$
$457$	−9.05369	−	9.05369i	−0.423514	−	0.423514i	−0.886412	+	0.462898i	$0.846810\pi$
$458$	9.60849	+	9.60849i	0.448975	+	0.448975i
$459$		0			0
$460$		0			0
$461$			8.78461i			0.409140i	0.978852	+	0.204570i	$0.0655796\pi$
$461$			8.78461i			0.409140i	−0.978852	+	0.204570i	$0.934420\pi$
$462$		0			0
$463$	−15.5935	+	15.5935i	−0.724692	+	0.724692i	−0.969557	−	0.244865i	$-0.921256\pi$
$463$	−15.5935	+	15.5935i	−0.724692	+	0.724692i	0.244865	+	0.969557i	$0.421256\pi$
$464$	2.19615			0.101954
$465$		0			0
$466$	3.80385			0.176210
$467$	−26.8565	+	26.8565i	−1.24277	+	1.24277i	−0.283921	+	0.958848i	$0.591635\pi$
$467$	−26.8565	+	26.8565i	−1.24277	+	1.24277i	−0.958848	+	0.283921i	$0.908365\pi$
$468$		0			0
$469$			38.7846i			1.79091i
$470$		0			0
$471$		0			0
$472$	5.22715	+	5.22715i	0.240599	+	0.240599i
$473$	−15.4176	−	15.4176i	−0.708904	−	0.708904i
$474$		0			0
$475$		0			0
$476$			38.7846i			1.77769i
$477$		0			0
$478$	16.4022	−	16.4022i	0.750217	−	0.750217i
$479$	−1.60770			−0.0734575			−0.0367287	−	0.999325i	$-0.511694\pi$
$479$	−1.60770			−0.0734575			−0.0367287	+	0.999325i	$0.511694\pi$
$480$		0			0
$481$	−11.7846			−0.537332
$482$	0.707107	−	0.707107i	0.0322078	−	0.0322078i
$483$		0			0
$484$		−	2.00000i		−	0.0909091i
$485$		0			0
$486$		0			0
$487$	−13.1440	−	13.1440i	−0.595613	−	0.595613i	0.343529	−	0.939142i	$-0.388378\pi$
$487$	−13.1440	−	13.1440i	−0.595613	−	0.595613i	−0.939142	+	0.343529i	$0.888378\pi$
$488$	0.845807	+	0.845807i	0.0382879	+	0.0382879i
$489$		0			0
$490$		0			0
$491$		−	22.3923i		−	1.01055i	−0.862958	−	0.505275i	$-0.831391\pi$
$491$		−	22.3923i		−	1.01055i	0.862958	−	0.505275i	$-0.168609\pi$
$492$		0			0
$493$	−12.7279	+	12.7279i	−0.573237	+	0.573237i
$494$	12.5885			0.566381
$495$		0			0
$496$	2.00000			0.0898027
$497$	37.4631	−	37.4631i	1.68045	−	1.68045i
$498$		0			0
$499$			29.1769i			1.30614i	0.757298	+	0.653069i	$0.226519\pi$
$499$			29.1769i			1.30614i	−0.757298	+	0.653069i	$0.773481\pi$
$500$		0			0
$501$		0			0
$502$	13.7124	+	13.7124i	0.612016	+	0.612016i
$503$	−15.8338	−	15.8338i	−0.705992	−	0.705992i	0.259698	−	0.965690i	$-0.416377\pi$
$503$	−15.8338	−	15.8338i	−0.705992	−	0.705992i	−0.965690	+	0.259698i	$0.916377\pi$
$504$		0			0
$505$		0			0
$506$			9.00000i			0.400099i
$507$		0			0
$508$	7.34847	−	7.34847i	0.326036	−	0.326036i
$509$	−2.78461			−0.123426			−0.0617128	−	0.998094i	$-0.519656\pi$
$509$	−2.78461			−0.123426			−0.0617128	+	0.998094i	$0.519656\pi$
$510$		0			0
$511$	73.1769			3.23716
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			8.19615i			0.361517i
$515$		0			0
$516$		0			0
$517$	−19.0919	−	19.0919i	−0.839660	−	0.839660i
$518$	13.1440	+	13.1440i	0.577515	+	0.577515i
$519$		0			0
$520$		0			0
$521$			21.8038i			0.955244i	0.878565	+	0.477622i	$0.158501\pi$
$521$			21.8038i			0.955244i	−0.878565	+	0.477622i	$0.841499\pi$
$522$		0			0
$523$	−13.3843	+	13.3843i	−0.585253	+	0.585253i	−0.936342	−	0.351089i	$-0.885811\pi$
$523$	−13.3843	+	13.3843i	−0.585253	+	0.585253i	0.351089	+	0.936342i	$0.385811\pi$
$524$	7.39230			0.322934
$525$		0			0
$526$	9.00000			0.392419
$527$	−11.5911	+	11.5911i	−0.504917	+	0.504917i
$528$		0			0
$529$		−	14.0000i		−	0.608696i
$530$		0			0
$531$		0			0
$532$	−14.0406	−	14.0406i	−0.608737	−	0.608737i
$533$	−12.7279	−	12.7279i	−0.551308	−	0.551308i
$534$		0			0
$535$		0			0
$536$		−	8.19615i		−	0.354020i
$537$		0			0
$538$	−16.9706	+	16.9706i	−0.731653	+	0.731653i
$539$	−46.1769			−1.98898
$540$		0			0
$541$	−35.9808			−1.54693			−0.773467	−	0.633837i	$-0.781479\pi$
$541$	−35.9808			−1.54693			−0.773467	+	0.633837i	$0.781479\pi$
$542$	−0.277401	+	0.277401i	−0.0119154	+	0.0119154i
$543$		0			0
$544$		−	8.19615i		−	0.351407i
$545$		0			0
$546$		0			0
$547$	−7.17260	−	7.17260i	−0.306678	−	0.306678i	0.536941	−	0.843620i	$-0.319580\pi$
$547$	−7.17260	−	7.17260i	−0.306678	−	0.306678i	−0.843620	+	0.536941i	$0.819580\pi$
$548$	6.93237	+	6.93237i	0.296136	+	0.296136i
$549$		0			0
$550$		0			0
$551$		−	9.21539i		−	0.392589i
$552$		0			0
$553$	0.656339	−	0.656339i	0.0279104	−	0.0279104i
$554$	−14.5359			−0.617571
$555$		0			0
$556$	5.80385			0.246138
$557$	−24.7351	+	24.7351i	−1.04806	+	1.04806i	−0.0492761	+	0.998785i	$0.515691\pi$
$557$	−24.7351	+	24.7351i	−1.04806	+	1.04806i	−0.998785	+	0.0492761i	$0.984309\pi$
$558$		0			0
$559$		−	21.8038i		−	0.922204i
$560$		0			0
$561$		0			0
$562$	−22.7661	−	22.7661i	−0.960331	−	0.960331i
$563$	9.05369	+	9.05369i	0.381567	+	0.381567i	0.871667	−	0.490099i	$-0.163039\pi$
$563$	9.05369	+	9.05369i	0.381567	+	0.381567i	−0.490099	+	0.871667i	$0.663039\pi$
$564$		0			0
$565$		0			0
$566$			7.26795i			0.305495i
$567$		0			0
$568$	−7.91688	+	7.91688i	−0.332185	+	0.332185i
$569$	−1.60770			−0.0673981			−0.0336990	−	0.999432i	$-0.510729\pi$
$569$	−1.60770			−0.0673981			−0.0336990	+	0.999432i	$0.510729\pi$
$570$		0			0
$571$	22.7846			0.953506			0.476753	−	0.879037i	$-0.341814\pi$
$571$	22.7846			0.953506			0.476753	+	0.879037i	$0.341814\pi$
$572$	−6.36396	+	6.36396i	−0.266091	+	0.266091i
$573$		0			0
$574$			28.3923i			1.18507i
$575$		0			0
$576$		0			0
$577$	−10.3664	−	10.3664i	−0.431557	−	0.431557i	0.457600	−	0.889158i	$-0.348709\pi$
$577$	−10.3664	−	10.3664i	−0.431557	−	0.431557i	−0.889158	+	0.457600i	$0.848709\pi$
$578$	35.4804	+	35.4804i	1.47579	+	1.47579i
$579$		0			0
$580$		0			0
$581$		−	77.5692i		−	3.21811i
$582$		0			0
$583$	−17.3867	+	17.3867i	−0.720082	+	0.720082i
$584$	−15.4641			−0.639909
$585$		0			0
$586$	22.9808			0.949327
$587$	1.13681	−	1.13681i	0.0469213	−	0.0469213i	−0.683257	−	0.730178i	$-0.739437\pi$
$587$	1.13681	−	1.13681i	0.0469213	−	0.0469213i	0.730178	+	0.683257i	$0.239437\pi$
$588$		0			0
$589$		−	8.39230i		−	0.345799i
$590$		0			0
$591$		0			0
$592$	−2.77766	−	2.77766i	−0.114161	−	0.114161i
$593$	2.27362	+	2.27362i	0.0933666	+	0.0933666i	0.752247	−	0.658881i	$-0.228970\pi$
$593$	2.27362	+	2.27362i	0.0933666	+	0.0933666i	−0.658881	+	0.752247i	$0.728970\pi$
$594$		0			0
$595$		0			0
$596$		−	10.3923i		−	0.425685i
$597$		0			0
$598$	−6.36396	+	6.36396i	−0.260242	+	0.260242i
$599$	−34.3923			−1.40523			−0.702616	−	0.711569i	$-0.747985\pi$
$599$	−34.3923			−1.40523			−0.702616	+	0.711569i	$0.747985\pi$
$600$		0			0
$601$	−23.0000			−0.938190			−0.469095	−	0.883148i	$-0.655420\pi$
$601$	−23.0000			−0.938190			−0.469095	+	0.883148i	$0.655420\pi$
$602$	−24.3190	+	24.3190i	−0.991170	+	0.991170i
$603$		0			0
$604$			10.1962i			0.414876i
$605$		0			0
$606$		0			0
$607$	−5.55532	−	5.55532i	−0.225483	−	0.225483i	0.585319	−	0.810803i	$-0.300969\pi$
$607$	−5.55532	−	5.55532i	−0.225483	−	0.225483i	−0.810803	+	0.585319i	$0.800969\pi$
$608$	2.96713	+	2.96713i	0.120333	+	0.120333i
$609$		0			0
$610$		0			0
$611$		−	27.0000i		−	1.09230i
$612$		0			0
$613$	−8.15711	+	8.15711i	−0.329463	+	0.329463i	−0.852382	−	0.522919i	$-0.824843\pi$
$613$	−8.15711	+	8.15711i	−0.329463	+	0.329463i	0.522919	+	0.852382i	$0.324843\pi$
$614$	17.3205			0.698999
$615$		0			0
$616$	14.1962			0.571979
$617$	−4.24264	+	4.24264i	−0.170802	+	0.170802i	−0.787332	−	0.616530i	$-0.788538\pi$
$617$	−4.24264	+	4.24264i	−0.170802	+	0.170802i	0.616530	+	0.787332i	$0.288538\pi$
$618$		0			0
$619$		−	21.6077i		−	0.868487i	−0.900796	−	0.434243i	$-0.857016\pi$
$619$		−	21.6077i		−	0.868487i	0.900796	−	0.434243i	$-0.142984\pi$
$620$		0			0
$621$		0			0
$622$	7.91688	+	7.91688i	0.317438	+	0.317438i
$623$	−7.34847	−	7.34847i	−0.294410	−	0.294410i
$624$		0			0
$625$		0			0
$626$			22.3923i			0.894976i
$627$		0			0
$628$	−4.89898	+	4.89898i	−0.195491	+	0.195491i
$629$	32.1962			1.28374
$630$		0			0
$631$	−22.5885			−0.899232			−0.449616	−	0.893222i	$-0.648439\pi$
$631$	−22.5885			−0.899232			−0.449616	+	0.893222i	$0.648439\pi$
$632$	−0.138701	+	0.138701i	−0.00551722	+	0.00551722i
$633$		0			0
$634$		−	15.8038i		−	0.627651i
$635$		0			0
$636$		0			0
$637$	−32.6520	−	32.6520i	−1.29372	−	1.29372i
$638$	4.65874	+	4.65874i	0.184441	+	0.184441i
$639$		0			0
$640$		0			0
$641$		−	18.5885i		−	0.734200i	−0.930181	−	0.367100i	$-0.880351\pi$
$641$		−	18.5885i		−	0.734200i	0.930181	−	0.367100i	$-0.119649\pi$
$642$		0			0
$643$	−12.7279	+	12.7279i	−0.501940	+	0.501940i	−0.912040	−	0.410100i	$-0.865494\pi$
$643$	−12.7279	+	12.7279i	−0.501940	+	0.501940i	0.410100	+	0.912040i	$0.365494\pi$
$644$	14.1962			0.559407
$645$		0			0
$646$	−34.3923			−1.35315
$647$	−9.46979	+	9.46979i	−0.372296	+	0.372296i	−0.868313	−	0.496017i	$-0.834795\pi$
$647$	−9.46979	+	9.46979i	−0.372296	+	0.372296i	0.496017	+	0.868313i	$0.334795\pi$
$648$		0			0
$649$			22.1769i			0.870520i
$650$		0			0
$651$		0			0
$652$	−15.8338	−	15.8338i	−0.620098	−	0.620098i
$653$	−16.2499	−	16.2499i	−0.635906	−	0.635906i	0.313637	−	0.949543i	$-0.398452\pi$
$653$	−16.2499	−	16.2499i	−0.635906	−	0.635906i	−0.949543	+	0.313637i	$0.898452\pi$
$654$		0			0
$655$		0			0
$656$		−	6.00000i		−	0.234261i
$657$		0			0
$658$	−30.1146	+	30.1146i	−1.17399	+	1.17399i
$659$	2.78461			0.108473			0.0542365	−	0.998528i	$-0.482728\pi$
$659$	2.78461			0.108473			0.0542365	+	0.998528i	$0.482728\pi$
$660$		0			0
$661$	34.3731			1.33696			0.668479	−	0.743731i	$-0.266946\pi$
$661$	34.3731			1.33696			0.668479	+	0.743731i	$0.266946\pi$
$662$	4.79744	−	4.79744i	0.186458	−	0.186458i
$663$		0			0
$664$			16.3923i			0.636145i
$665$		0			0
$666$		0			0
$667$	4.65874	+	4.65874i	0.180387	+	0.180387i
$668$	−3.25813	−	3.25813i	−0.126061	−	0.126061i
$669$		0			0
$670$		0			0
$671$			3.58846i			0.138531i
$672$		0			0
$673$	7.43640	−	7.43640i	0.286652	−	0.286652i	−0.549103	−	0.835755i	$-0.685030\pi$
$673$	7.43640	−	7.43640i	0.286652	−	0.286652i	0.835755	+	0.549103i	$0.185030\pi$
$674$	−22.3923			−0.862519
$675$		0			0
$676$	4.00000			0.153846
$677$	32.8043	−	32.8043i	1.26077	−	1.26077i	0.310053	−	0.950719i	$-0.399653\pi$
$677$	32.8043	−	32.8043i	1.26077	−	1.26077i	0.950719	−	0.310053i	$-0.100347\pi$
$678$		0			0
$679$			69.3731i			2.66229i
$680$		0			0
$681$		0			0
$682$	4.24264	+	4.24264i	0.162459	+	0.162459i
$683$	−5.94786	−	5.94786i	−0.227588	−	0.227588i	0.584096	−	0.811685i	$-0.301449\pi$
$683$	−5.94786	−	5.94786i	−0.227588	−	0.227588i	−0.811685	+	0.584096i	$0.801449\pi$
$684$		0			0
$685$		0			0
$686$			39.7128i			1.51624i
$687$		0			0
$688$	5.13922	−	5.13922i	0.195931	−	0.195931i
$689$	−24.5885			−0.936746
$690$		0			0
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$	−1.55291	+	1.55291i	−0.0590329	+	0.0590329i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	34.7733	+	34.7733i	1.31713	+	1.31713i
$698$	−4.52004	−	4.52004i	−0.171086	−	0.171086i
$699$		0			0
$700$		0			0
$701$			0.588457i			0.0222257i	0.999938	+	0.0111129i	$0.00353741\pi$
$701$			0.588457i			0.0222257i	−0.999938	+	0.0111129i	$0.996463\pi$
$702$		0			0
$703$	−11.6555	+	11.6555i	−0.439595	+	0.439595i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	−14.1962			−0.534279
$707$	−42.1218	+	42.1218i	−1.58415	+	1.58415i
$708$		0			0
$709$			37.1962i			1.39693i	0.715644	+	0.698465i	$0.246133\pi$
$709$			37.1962i			1.39693i	−0.715644	+	0.698465i	$0.753867\pi$
$710$		0			0
$711$		0			0
$712$	1.55291	+	1.55291i	0.0581979	+	0.0581979i
$713$	4.24264	+	4.24264i	0.158888	+	0.158888i
$714$		0			0
$715$		0			0
$716$			4.60770i			0.172198i
$717$		0			0
$718$	0.568406	−	0.568406i	0.0212127	−	0.0212127i
$719$	11.1962			0.417546			0.208773	−	0.977964i	$-0.433053\pi$
$719$	11.1962			0.417546			0.208773	+	0.977964i	$0.433053\pi$
$720$		0			0
$721$	61.1769			2.27835
$722$	−0.984508	+	0.984508i	−0.0366396	+	0.0366396i
$723$		0			0
$724$			17.5885i			0.653670i
$725$		0			0
$726$		0			0
$727$	4.41851	+	4.41851i	0.163873	+	0.163873i	0.784280	−	0.620407i	$-0.213032\pi$
$727$	4.41851	+	4.41851i	0.163873	+	0.163873i	−0.620407	+	0.784280i	$0.713032\pi$
$728$	10.0382	+	10.0382i	0.372040	+	0.372040i
$729$		0			0
$730$		0			0
$731$			59.5692i			2.20325i
$732$		0			0
$733$	−33.7888	+	33.7888i	−1.24802	+	1.24802i	−0.291425	+	0.956594i	$0.594129\pi$
$733$	−33.7888	+	33.7888i	−1.24802	+	1.24802i	−0.956594	+	0.291425i	$0.905871\pi$
$734$	−32.7846			−1.21010
$735$		0			0
$736$	−3.00000			−0.110581
$737$	17.3867	−	17.3867i	0.640446	−	0.640446i
$738$		0			0
$739$			13.4115i			0.493352i	0.969098	+	0.246676i	$0.0793383\pi$
$739$			13.4115i			0.493352i	−0.969098	+	0.246676i	$0.920662\pi$
$740$		0			0
$741$		0			0
$742$	27.4249	+	27.4249i	1.00680	+	1.00680i
$743$	−26.4404	−	26.4404i	−0.970002	−	0.970002i	0.0295605	−	0.999563i	$-0.490589\pi$
$743$	−26.4404	−	26.4404i	−0.970002	−	0.970002i	−0.999563	+	0.0295605i	$0.990589\pi$
$744$		0			0
$745$		0			0
$746$		−	21.7128i		−	0.794963i
$747$		0			0
$748$	17.3867	−	17.3867i	0.635719	−	0.635719i
$749$	73.7654			2.69533
$750$		0			0
$751$	−12.3923			−0.452202			−0.226101	−	0.974104i	$-0.572598\pi$
$751$	−12.3923			−0.452202			−0.226101	+	0.974104i	$0.572598\pi$
$752$	6.36396	−	6.36396i	0.232070	−	0.232070i
$753$		0			0
$754$			6.58846i			0.239937i
$755$		0			0
$756$		0			0
$757$	15.0251	+	15.0251i	0.546097	+	0.546097i	0.925310	−	0.379213i	$-0.123805\pi$
$757$	15.0251	+	15.0251i	0.546097	+	0.546097i	−0.379213	+	0.925310i	$0.623805\pi$
$758$	−1.41421	−	1.41421i	−0.0513665	−	0.0513665i
$759$		0			0
$760$		0			0
$761$			1.60770i			0.0582789i	0.999575	+	0.0291395i	$0.00927669\pi$
$761$			1.60770i			0.0582789i	−0.999575	+	0.0291395i	$0.990723\pi$
$762$		0			0
$763$	−26.7685	+	26.7685i	−0.969086	+	0.969086i
$764$	−16.3923			−0.593053
$765$		0			0
$766$	−3.00000			−0.108394
$767$	−15.6814	+	15.6814i	−0.566224	+	0.566224i
$768$		0			0
$769$			17.1769i			0.619415i	0.950832	+	0.309708i	$0.100231\pi$
$769$			17.1769i			0.619415i	−0.950832	+	0.309708i	$0.899769\pi$
$770$		0			0
$771$		0			0
$772$	1.31268	+	1.31268i	0.0472443	+	0.0472443i
$773$	14.2808	+	14.2808i	0.513646	+	0.513646i	0.915642	−	0.401996i	$-0.131683\pi$
$773$	14.2808	+	14.2808i	0.513646	+	0.513646i	−0.401996	+	0.915642i	$0.631683\pi$
$774$		0			0
$775$		0			0
$776$		−	14.6603i		−	0.526272i
$777$		0			0
$778$	−15.4176	+	15.4176i	−0.552749	+	0.552749i
$779$	−25.1769			−0.902057
$780$		0			0
$781$	−33.5885			−1.20189
$782$	17.3867	−	17.3867i	0.621746	−	0.621746i
$783$		0			0
$784$		−	15.3923i		−	0.549725i
$785$		0			0
$786$		0			0
$787$	−8.00481	−	8.00481i	−0.285341	−	0.285341i	0.549894	−	0.835235i	$-0.314668\pi$
$787$	−8.00481	−	8.00481i	−0.285341	−	0.285341i	−0.835235	+	0.549894i	$0.814668\pi$
$788$	−11.5911	−	11.5911i	−0.412916	−	0.412916i
$789$		0			0
$790$		0			0
$791$		−	49.1769i		−	1.74853i
$792$		0			0
$793$	−2.53742	+	2.53742i	−0.0901065	+	0.0901065i
$794$	−15.9282			−0.565271
$795$		0			0
$796$	−2.00000			−0.0708881
$797$	−16.5545	+	16.5545i	−0.586389	+	0.586389i	−0.936652	−	0.350262i	$-0.886092\pi$
$797$	−16.5545	+	16.5545i	−0.586389	+	0.586389i	0.350262	+	0.936652i	$0.386092\pi$
$798$		0			0
$799$			73.7654i			2.60963i
$800$		0			0
$801$		0			0
$802$	−10.0382	−	10.0382i	−0.354461	−	0.354461i
$803$	−32.8043	−	32.8043i	−1.15764	−	1.15764i
$804$		0			0
$805$		0			0
$806$			6.00000i			0.211341i
$807$		0			0
$808$	8.90138	−	8.90138i	0.313150	−	0.313150i
$809$	−40.9808			−1.44081			−0.720403	−	0.693555i	$-0.756043\pi$
$809$	−40.9808			−1.44081			−0.720403	+	0.693555i	$0.756043\pi$
$810$		0			0
$811$	−1.41154			−0.0495660			−0.0247830	−	0.999693i	$-0.507889\pi$
$811$	−1.41154			−0.0495660			−0.0247830	+	0.999693i	$0.507889\pi$
$812$	7.34847	−	7.34847i	0.257881	−	0.257881i
$813$		0			0
$814$		−	11.7846i		−	0.413050i
$815$		0			0
$816$		0			0
$817$	−21.5649	−	21.5649i	−0.754462	−	0.754462i
$818$	−16.2635	−	16.2635i	−0.568638	−	0.568638i
$819$		0			0
$820$		0			0
$821$		−	9.21539i		−	0.321619i	−0.986985	−	0.160810i	$-0.948589\pi$
$821$		−	9.21539i		−	0.321619i	0.986985	−	0.160810i	$-0.0514105\pi$
$822$		0			0
$823$	35.1894	−	35.1894i	1.22663	−	1.22663i	0.261394	−	0.965232i	$-0.415818\pi$
$823$	35.1894	−	35.1894i	1.22663	−	1.22663i	0.965232	−	0.261394i	$-0.0841823\pi$
$824$	−12.9282			−0.450375
$825$		0			0
$826$	34.9808			1.21714
$827$	1.40061	−	1.40061i	0.0487040	−	0.0487040i	−0.682335	−	0.731039i	$-0.739036\pi$
$827$	1.40061	−	1.40061i	0.0487040	−	0.0487040i	0.731039	+	0.682335i	$0.239036\pi$
$828$		0			0
$829$			15.9808i			0.555035i	0.960721	+	0.277517i	$0.0895116\pi$
$829$			15.9808i			0.555035i	−0.960721	+	0.277517i	$0.910488\pi$
$830$		0			0
$831$		0			0
$832$	−2.12132	−	2.12132i	−0.0735436	−	0.0735436i
$833$	89.2069	+	89.2069i	3.09084	+	3.09084i
$834$		0			0
$835$		0			0
$836$			12.5885i			0.435381i
$837$		0			0
$838$	−7.34847	+	7.34847i	−0.253849	+	0.253849i
$839$	31.9808			1.10410			0.552049	−	0.833811i	$-0.313846\pi$
$839$	31.9808			1.10410			0.552049	+	0.833811i	$0.313846\pi$
$840$		0			0
$841$	−24.1769			−0.833687
$842$	6.22526	−	6.22526i	0.214537	−	0.214537i
$843$		0			0
$844$			4.00000i			0.137686i
$845$		0			0
$846$		0			0
$847$	−6.69213	−	6.69213i	−0.229944	−	0.229944i
$848$	−5.79555	−	5.79555i	−0.199020	−	0.199020i
$849$		0			0
$850$		0			0
$851$		−	11.7846i		−	0.403971i
$852$		0			0
$853$	5.22715	−	5.22715i	0.178974	−	0.178974i	−0.611934	−	0.790909i	$-0.709608\pi$
$853$	5.22715	−	5.22715i	0.178974	−	0.178974i	0.790909	+	0.611934i	$0.209608\pi$
$854$	5.66025			0.193690
$855$		0			0
$856$	−15.5885			−0.532803
$857$	8.48528	−	8.48528i	0.289852	−	0.289852i	−0.547170	−	0.837022i	$-0.684295\pi$
$857$	8.48528	−	8.48528i	0.289852	−	0.289852i	0.837022	+	0.547170i	$0.184295\pi$
$858$		0			0
$859$		−	36.9808i		−	1.26177i	−0.775877	−	0.630884i	$-0.782693\pi$
$859$		−	36.9808i		−	1.26177i	0.775877	−	0.630884i	$-0.217307\pi$
$860$		0			0
$861$		0			0
$862$	−2.53742	−	2.53742i	−0.0864250	−	0.0864250i
$863$	21.2132	+	21.2132i	0.722106	+	0.722106i	0.969034	−	0.246928i	$-0.0794211\pi$
$863$	21.2132	+	21.2132i	0.722106	+	0.722106i	−0.246928	+	0.969034i	$0.579421\pi$
$864$		0			0
$865$		0			0
$866$			19.0526i			0.647432i
$867$		0			0
$868$	6.69213	−	6.69213i	0.227146	−	0.227146i
$869$	−0.588457			−0.0199620
$870$		0			0
$871$	24.5885			0.833148
$872$	5.65685	−	5.65685i	0.191565	−	0.191565i
$873$		0			0
$874$			12.5885i			0.425811i
$875$		0			0
$876$		0			0
$877$	−32.4761	−	32.4761i	−1.09664	−	1.09664i	−0.994801	−	0.101841i	$-0.967527\pi$
$877$	−32.4761	−	32.4761i	−1.09664	−	1.09664i	−0.101841	−	0.994801i	$-0.532473\pi$
$878$	14.5582	+	14.5582i	0.491317	+	0.491317i
$879$		0			0
$880$		0			0
$881$		−	29.5692i		−	0.996212i	−0.867116	−	0.498106i	$-0.834029\pi$
$881$		−	29.5692i		−	0.996212i	0.867116	−	0.498106i	$-0.165971\pi$
$882$		0			0
$883$	−25.3915	+	25.3915i	−0.854491	+	0.854491i	−0.990683	−	0.136191i	$-0.956514\pi$
$883$	−25.3915	+	25.3915i	−0.854491	+	0.854491i	0.136191	+	0.990683i	$0.456514\pi$
$884$	24.5885			0.826999
$885$		0			0
$886$	3.58846			0.120557
$887$	−30.6830	+	30.6830i	−1.03023	+	1.03023i	−0.0307056	+	0.999528i	$0.509775\pi$
$887$	−30.6830	+	30.6830i	−1.03023	+	1.03023i	−0.999528	+	0.0307056i	$0.990225\pi$
$888$		0			0
$889$		−	49.1769i		−	1.64934i
$890$		0			0
$891$		0			0
$892$	2.20925	+	2.20925i	0.0739713	+	0.0739713i
$893$	−26.7042	−	26.7042i	−0.893620	−	0.893620i
$894$		0			0
$895$		0			0
$896$			4.73205i			0.158087i
$897$		0			0
$898$	−4.24264	+	4.24264i	−0.141579	+	0.141579i
$899$	4.39230			0.146492
$900$		0			0
$901$	67.1769			2.23799
$902$	12.7279	−	12.7279i	0.423793	−	0.423793i
$903$		0			0
$904$			10.3923i			0.345643i
$905$		0			0
$906$		0			0
$907$	26.5283	+	26.5283i	0.880857	+	0.880857i	0.993622	−	0.112764i	$-0.0359706\pi$
$907$	26.5283	+	26.5283i	0.880857	+	0.880857i	−0.112764	+	0.993622i	$0.535971\pi$
$908$	12.1595	+	12.1595i	0.403528	+	0.403528i
$909$		0			0
$910$		0			0
$911$			36.8038i			1.21937i	0.792645	+	0.609683i	$0.208703\pi$
$911$			36.8038i			1.21937i	−0.792645	+	0.609683i	$0.791297\pi$
$912$		0			0
$913$	−34.7733	+	34.7733i	−1.15083	+	1.15083i
$914$	12.8038			0.423514
$915$		0			0
$916$	−13.5885			−0.448975
$917$	24.7351	−	24.7351i	0.816826	−	0.816826i
$918$		0			0
$919$		−	34.5885i		−	1.14097i	−0.821309	−	0.570484i	$-0.806756\pi$
$919$		−	34.5885i		−	1.14097i	0.821309	−	0.570484i	$-0.193244\pi$
$920$		0			0
$921$		0			0
$922$	−6.21166	−	6.21166i	−0.204570	−	0.204570i
$923$	−23.7506	−	23.7506i	−0.781761	−	0.781761i
$924$		0			0
$925$		0			0
$926$		−	22.0526i		−	0.724692i
$927$		0			0
$928$	−1.55291	+	1.55291i	−0.0509769	+	0.0509769i
$929$	43.1769			1.41659			0.708294	−	0.705917i	$-0.249465\pi$
$929$	43.1769			1.41659			0.708294	+	0.705917i	$0.249465\pi$
$930$		0			0
$931$	−64.5885			−2.11680
$932$	−2.68973	+	2.68973i	−0.0881049	+	0.0881049i
$933$		0			0
$934$		−	37.9808i		−	1.24277i
$935$		0			0
$936$		0			0
$937$	−7.74101	−	7.74101i	−0.252888	−	0.252888i	0.569266	−	0.822154i	$-0.307228\pi$
$937$	−7.74101	−	7.74101i	−0.252888	−	0.252888i	−0.822154	+	0.569266i	$0.807228\pi$
$938$	−27.4249	−	27.4249i	−0.895453	−	0.895453i
$939$		0			0
$940$		0			0
$941$			45.3731i			1.47912i	0.673091	+	0.739560i	$0.264966\pi$
$941$			45.3731i			1.47912i	−0.673091	+	0.739560i	$0.735034\pi$
$942$		0			0
$943$	12.7279	−	12.7279i	0.414478	−	0.414478i
$944$	−7.39230			−0.240599
$945$		0			0
$946$	21.8038			0.708904
$947$	28.5617	−	28.5617i	0.928130	−	0.928130i	−0.0694554	−	0.997585i	$-0.522126\pi$
$947$	28.5617	−	28.5617i	0.928130	−	0.928130i	0.997585	+	0.0694554i	$0.0221262\pi$
$948$		0			0
$949$		−	46.3923i		−	1.50596i
$950$		0			0
$951$		0			0
$952$	−27.4249	−	27.4249i	−0.888845	−	0.888845i
$953$	9.31749	+	9.31749i	0.301823	+	0.301823i	0.841727	−	0.539904i	$-0.181539\pi$
$953$	9.31749	+	9.31749i	0.301823	+	0.301823i	−0.539904	+	0.841727i	$0.681539\pi$
$954$		0			0
$955$		0			0
$956$			23.1962i			0.750217i
$957$		0			0
$958$	1.13681	−	1.13681i	0.0367287	−	0.0367287i
$959$	46.3923			1.49809
$960$		0			0
$961$	−27.0000			−0.870968
$962$	8.33298	−	8.33298i	0.268666	−	0.268666i
$963$		0			0
$964$			1.00000i			0.0322078i
$965$		0			0
$966$		0			0
$967$	−38.3596	−	38.3596i	−1.23356	−	1.23356i	−0.962586	−	0.270977i	$-0.912653\pi$
$967$	−38.3596	−	38.3596i	−1.23356	−	1.23356i	−0.270977	−	0.962586i	$-0.587347\pi$
$968$	1.41421	+	1.41421i	0.0454545	+	0.0454545i
$969$		0			0
$970$		0			0
$971$			23.7846i			0.763284i	0.924310	+	0.381642i	$0.124641\pi$
$971$			23.7846i			0.763284i	−0.924310	+	0.381642i	$0.875359\pi$
$972$		0			0
$973$	19.4201	−	19.4201i	0.622578	−	0.622578i
$974$	18.5885			0.595613
$975$		0			0
$976$	−1.19615			−0.0382879
$977$	34.7733	−	34.7733i	1.11250	−	1.11250i	0.119686	−	0.992812i	$-0.461811\pi$
$977$	34.7733	−	34.7733i	1.11250	−	1.11250i	0.992812	−	0.119686i	$-0.0381886\pi$
$978$		0			0
$979$			6.58846i			0.210568i
$980$		0			0
$981$		0			0
$982$	15.8338	+	15.8338i	0.505275	+	0.505275i
$983$	40.0005	+	40.0005i	1.27582	+	1.27582i	0.942987	+	0.332830i	$0.108004\pi$
$983$	40.0005	+	40.0005i	1.27582	+	1.27582i	0.332830	+	0.942987i	$0.391996\pi$
$984$		0			0
$985$		0			0
$986$		−	18.0000i		−	0.573237i
$987$		0			0
$988$	−8.90138	+	8.90138i	−0.283191	+	0.283191i
$989$	21.8038			0.693322
$990$		0			0
$991$	−33.5692			−1.06636			−0.533181	−	0.846001i	$-0.679003\pi$
$991$	−33.5692			−1.06636			−0.533181	+	0.846001i	$0.679003\pi$
$992$	−1.41421	+	1.41421i	−0.0449013	+	0.0449013i
$993$		0			0
$994$			52.9808i			1.68045i
$995$		0			0
$996$		0			0
$997$	19.0919	+	19.0919i	0.604646	+	0.604646i	0.941542	−	0.336896i	$-0.109377\pi$
$997$	19.0919	+	19.0919i	0.604646	+	0.604646i	−0.336896	+	0.941542i	$0.609377\pi$
$998$	−20.6312	−	20.6312i	−0.653069	−	0.653069i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.f.e.107.1	yes	8
3.2	odd	2		1350.2.f.b.107.3	yes	8
5.2	odd	4		1350.2.f.b.593.2	yes	8
5.3	odd	4		1350.2.f.b.593.3	yes	8
5.4	even	2	inner	1350.2.f.e.107.4	yes	8
15.2	even	4	inner	1350.2.f.e.593.4	yes	8
15.8	even	4	inner	1350.2.f.e.593.1	yes	8
15.14	odd	2		1350.2.f.b.107.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1350.2.f.b.107.2	✓	8	15.14	odd	2
1350.2.f.b.107.3	yes	8	3.2	odd	2
1350.2.f.b.593.2	yes	8	5.2	odd	4
1350.2.f.b.593.3	yes	8	5.3	odd	4
1350.2.f.e.107.1	yes	8	1.1	even	1	trivial
1350.2.f.e.107.4	yes	8	5.4	even	2	inner
1350.2.f.e.593.1	yes	8	15.8	even	4	inner
1350.2.f.e.593.4	yes	8	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-3.34607 - 3.34607i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-3.34607 - 3.34607i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.00000i q^{11} +(-2.12132 + 2.12132i) q^{13} +4.73205 q^{14} -1.00000 q^{16} +(5.79555 - 5.79555i) q^{17} +4.19615i q^{19} +(-2.12132 - 2.12132i) q^{22} +(-2.12132 - 2.12132i) q^{23} -3.00000i q^{26} +(-3.34607 + 3.34607i) q^{28} -2.19615 q^{29} -2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +8.19615i q^{34} +(2.77766 + 2.77766i) q^{37} +(-2.96713 - 2.96713i) q^{38} +6.00000i q^{41} +(-5.13922 + 5.13922i) q^{43} +3.00000 q^{44} +3.00000 q^{46} +(-6.36396 + 6.36396i) q^{47} +15.3923i q^{49} +(2.12132 + 2.12132i) q^{52} +(5.79555 + 5.79555i) q^{53} -4.73205i q^{56} +(1.55291 - 1.55291i) q^{58} +7.39230 q^{59} +1.19615 q^{61} +(1.41421 - 1.41421i) q^{62} +1.00000i q^{64} +(-5.79555 - 5.79555i) q^{67} +(-5.79555 - 5.79555i) q^{68} +11.1962i q^{71} +(-10.9348 + 10.9348i) q^{73} -3.92820 q^{74} +4.19615 q^{76} +(10.0382 - 10.0382i) q^{77} +0.196152i q^{79} +(-4.24264 - 4.24264i) q^{82} +(11.5911 + 11.5911i) q^{83} -7.26795i q^{86} +(-2.12132 + 2.12132i) q^{88} +2.19615 q^{89} +14.1962 q^{91} +(-2.12132 + 2.12132i) q^{92} -9.00000i q^{94} +(-10.3664 - 10.3664i) q^{97} +(-10.8840 - 10.8840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 24 q^{14} - 8 q^{16} + 24 q^{29} - 16 q^{31} + 24 q^{44} + 24 q^{46} - 24 q^{59} - 32 q^{61} + 24 q^{74} - 8 q^{76} - 24 q^{89} + 72 q^{91}+O(q^{100}) \) 8 * q + 24 * q^14 - 8 * q^16 + 24 * q^29 - 16 * q^31 + 24 * q^44 + 24 * q^46 - 24 * q^59 - 32 * q^61 + 24 * q^74 - 8 * q^76 - 24 * q^89 + 72 * q^91

Introduction

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