LMFDB - Embedded newform 1575.2.m.d.1268.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(1268,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1575.1268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.m (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:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1268.5
Root			$2.01185i$ of defining polynomial
Character	$\chi$	$=$	1575.1268
Dual form			1575.2.m.d.1457.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28118 + 1.28118i) q^{2} +1.28283i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.918816 - 0.918816i) q^{8} +O(q^{10})$	\(q+(1.28118 + 1.28118i) q^{2} +1.28283i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.918816 - 0.918816i) q^{8} -4.14225i q^{11} +(-4.57421 - 4.57421i) q^{13} -1.81186 q^{14} +4.92000 q^{16} +(-5.27126 - 5.27126i) q^{17} -3.06412i q^{19} +(5.30696 - 5.30696i) q^{22} +(-3.82371 + 3.82371i) q^{23} -11.7208i q^{26} +(-0.907101 - 0.907101i) q^{28} +5.24853 q^{29} -2.42509 q^{31} +(4.46577 + 4.46577i) q^{32} -13.5068i q^{34} +(0.834319 - 0.834319i) q^{37} +(3.92569 - 3.92569i) q^{38} +4.19215i q^{41} +(-3.71717 - 3.71717i) q^{43} +5.31382 q^{44} -9.79772 q^{46} +(3.14814 + 3.14814i) q^{47} -1.00000i q^{49} +(5.86796 - 5.86796i) q^{52} +(-4.79411 + 4.79411i) q^{53} +1.29940i q^{56} +(6.72431 + 6.72431i) q^{58} +1.97629 q^{59} +1.88920 q^{61} +(-3.10697 - 3.10697i) q^{62} +1.60288i q^{64} +(10.7350 - 10.7350i) q^{67} +(6.76215 - 6.76215i) q^{68} +9.76123i q^{71} +(-0.978941 - 0.978941i) q^{73} +2.13782 q^{74} +3.93076 q^{76} +(2.92901 + 2.92901i) q^{77} +4.09428i q^{79} +(-5.37089 + 5.37089i) q^{82} +(3.68028 - 3.68028i) q^{83} -9.52470i q^{86} +(-3.80597 - 3.80597i) q^{88} +7.39217 q^{89} +6.46891 q^{91} +(-4.90519 - 4.90519i) q^{92} +8.06666i q^{94} +(3.07322 - 3.07322i) q^{97} +(1.28118 - 1.28118i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{8}+O(q^{10}) $ 12 * q + 24 * q^8	$ 12 q + 24 q^{8} + 4 q^{13} + 4 q^{14} - 20 q^{16} + 8 q^{17} + 8 q^{22} + 8 q^{23} + 32 q^{29} + 48 q^{32} - 4 q^{37} + 24 q^{38} - 40 q^{43} + 64 q^{44} + 16 q^{46} + 24 q^{47} - 36 q^{52} - 40 q^{53} + 28 q^{58} + 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{67} + 32 q^{68} + 20 q^{73} + 64 q^{74} + 16 q^{76} - 20 q^{82} + 24 q^{83} + 56 q^{89} + 8 q^{92} - 12 q^{97}+O(q^{100}) $ 12 * q + 24 * q^8 + 4 * q^13 + 4 * q^14 - 20 * q^16 + 8 * q^17 + 8 * q^22 + 8 * q^23 + 32 * q^29 + 48 * q^32 - 4 * q^37 + 24 * q^38 - 40 * q^43 + 64 * q^44 + 16 * q^46 + 24 * q^47 - 36 * q^52 - 40 * q^53 + 28 * q^58 + 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^67 + 32 * q^68 + 20 * q^73 + 64 * q^74 + 16 * q^76 - 20 * q^82 + 24 * q^83 + 56 * q^89 + 8 * q^92 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	1.28118	+	1.28118i	0.905930	+	0.905930i	0.995941	−	0.0900110i	$-0.0286902\pi$
$2$	1.28118	+	1.28118i	0.905930	+	0.905930i	−0.0900110	+	0.995941i	$0.528690\pi$
$3$		0			0
$3$		0			0
$4$			1.28283i			0.641417i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.918816	−	0.918816i	0.324851	−	0.324851i
$9$		0			0
$10$		0			0
$11$		−	4.14225i		−	1.24894i	−0.781051	−	0.624468i	$-0.785316\pi$
$11$		−	4.14225i		−	1.24894i	0.781051	−	0.624468i	$-0.214684\pi$
$12$		0			0
$13$	−4.57421	−	4.57421i	−1.26866	−	1.26866i	−0.946782	−	0.321876i	$-0.895687\pi$
$13$	−4.57421	−	4.57421i	−1.26866	−	1.26866i	−0.321876	−	0.946782i	$-0.604313\pi$
$14$	−1.81186			−0.484240
$15$		0			0
$16$	4.92000			1.23000
$17$	−5.27126	−	5.27126i	−1.27847	−	1.27847i	−0.941525	−	0.336943i	$-0.890607\pi$
$17$	−5.27126	−	5.27126i	−1.27847	−	1.27847i	−0.336943	−	0.941525i	$-0.609393\pi$
$18$		0			0
$19$		−	3.06412i		−	0.702958i	−0.936196	−	0.351479i	$-0.885679\pi$
$19$		−	3.06412i		−	0.702958i	0.936196	−	0.351479i	$-0.114321\pi$
$20$		0			0
$21$		0			0
$22$	5.30696	−	5.30696i	1.13145	−	1.13145i
$23$	−3.82371	+	3.82371i	−0.797299	+	0.797299i	−0.982669	−	0.185370i	$-0.940652\pi$
$23$	−3.82371	+	3.82371i	−0.797299	+	0.797299i	0.185370	+	0.982669i	$0.440652\pi$
$24$		0			0
$25$		0			0
$26$		−	11.7208i		−	2.29863i
$27$		0			0
$28$	−0.907101	−	0.907101i	−0.171426	−	0.171426i
$29$	5.24853			0.974628			0.487314	−	0.873227i	$-0.337977\pi$
$29$	5.24853			0.974628			0.487314	+	0.873227i	$0.337977\pi$
$30$		0			0
$31$	−2.42509			−0.435558			−0.217779	−	0.975998i	$-0.569881\pi$
$31$	−2.42509			−0.435558			−0.217779	+	0.975998i	$0.569881\pi$
$32$	4.46577	+	4.46577i	0.789444	+	0.789444i
$33$		0			0
$34$		−	13.5068i		−	2.31640i
$35$		0			0
$36$		0			0
$37$	0.834319	−	0.834319i	0.137161	−	0.137161i	−0.635193	−	0.772354i	$-0.719079\pi$
$37$	0.834319	−	0.834319i	0.137161	−	0.137161i	0.772354	+	0.635193i	$0.219079\pi$
$38$	3.92569	−	3.92569i	0.636831	−	0.636831i
$39$		0			0
$40$		0			0
$41$			4.19215i			0.654704i	0.944902	+	0.327352i	$0.106156\pi$
$41$			4.19215i			0.654704i	−0.944902	+	0.327352i	$0.893844\pi$
$42$		0			0
$43$	−3.71717	−	3.71717i	−0.566862	−	0.566862i	0.364386	−	0.931248i	$-0.381279\pi$
$43$	−3.71717	−	3.71717i	−0.566862	−	0.566862i	−0.931248	+	0.364386i	$0.881279\pi$
$44$	5.31382			0.801089
$45$		0			0
$46$	−9.79772			−1.44459
$47$	3.14814	+	3.14814i	0.459204	+	0.459204i	0.898394	−	0.439190i	$-0.144735\pi$
$47$	3.14814	+	3.14814i	0.459204	+	0.459204i	−0.439190	+	0.898394i	$0.644735\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		0			0
$52$	5.86796	−	5.86796i	0.813739	−	0.813739i
$53$	−4.79411	+	4.79411i	−0.658522	+	0.658522i	−0.955030	−	0.296508i	$-0.904178\pi$
$53$	−4.79411	+	4.79411i	−0.658522	+	0.658522i	0.296508	+	0.955030i	$0.404178\pi$
$54$		0			0
$55$		0			0
$56$			1.29940i			0.173640i
$57$		0			0
$58$	6.72431	+	6.72431i	0.882945	+	0.882945i
$59$	1.97629			0.257291			0.128646	−	0.991691i	$-0.458937\pi$
$59$	1.97629			0.257291			0.128646	+	0.991691i	$0.458937\pi$
$60$		0			0
$61$	1.88920			0.241887			0.120944	−	0.992659i	$-0.461408\pi$
$61$	1.88920			0.241887			0.120944	+	0.992659i	$0.461408\pi$
$62$	−3.10697	−	3.10697i	−0.394585	−	0.394585i
$63$		0			0
$64$			1.60288i			0.200360i
$65$		0			0
$66$		0			0
$67$	10.7350	−	10.7350i	1.31149	−	1.31149i	0.391167	−	0.920320i	$-0.372072\pi$
$67$	10.7350	−	10.7350i	1.31149	−	1.31149i	0.920320	−	0.391167i	$-0.127928\pi$
$68$	6.76215	−	6.76215i	0.820032	−	0.820032i
$69$		0			0
$70$		0			0
$71$			9.76123i			1.15844i	0.815170	+	0.579222i	$0.196644\pi$
$71$			9.76123i			1.15844i	−0.815170	+	0.579222i	$0.803356\pi$
$72$		0			0
$73$	−0.978941	−	0.978941i	−0.114576	−	0.114576i	0.647494	−	0.762070i	$-0.275817\pi$
$73$	−0.978941	−	0.978941i	−0.114576	−	0.114576i	−0.762070	+	0.647494i	$0.775817\pi$
$74$	2.13782			0.248517
$75$		0			0
$76$	3.93076			0.450890
$77$	2.92901	+	2.92901i	0.333792	+	0.333792i
$78$		0			0
$79$			4.09428i			0.460642i	0.973115	+	0.230321i	$0.0739776\pi$
$79$			4.09428i			0.460642i	−0.973115	+	0.230321i	$0.926022\pi$
$80$		0			0
$81$		0			0
$82$	−5.37089	+	5.37089i	−0.593116	+	0.593116i
$83$	3.68028	−	3.68028i	0.403964	−	0.403964i	−0.475664	−	0.879627i	$-0.657792\pi$
$83$	3.68028	−	3.68028i	0.403964	−	0.403964i	0.879627	+	0.475664i	$0.157792\pi$
$84$		0			0
$85$		0			0
$86$		−	9.52470i		−	1.02707i
$87$		0			0
$88$	−3.80597	−	3.80597i	−0.405717	−	0.405717i
$89$	7.39217			0.783569			0.391784	−	0.920057i	$-0.371858\pi$
$89$	7.39217			0.783569			0.391784	+	0.920057i	$0.371858\pi$
$90$		0			0
$91$	6.46891			0.678126
$92$	−4.90519	−	4.90519i	−0.511402	−	0.511402i
$93$		0			0
$94$			8.06666i			0.832013i
$95$		0			0
$96$		0			0
$97$	3.07322	−	3.07322i	0.312038	−	0.312038i	−0.533661	−	0.845699i	$-0.679184\pi$
$97$	3.07322	−	3.07322i	0.312038	−	0.312038i	0.845699	+	0.533661i	$0.179184\pi$
$98$	1.28118	−	1.28118i	0.129419	−	0.129419i
$99$		0			0
$100$		0			0
$101$		−	0.759784i		−	0.0756013i	−0.999285	−	0.0378006i	$-0.987965\pi$
$101$		−	0.759784i		−	0.0756013i	0.999285	−	0.0378006i	$-0.0120352\pi$
$102$		0			0
$103$	1.96312	+	1.96312i	0.193432	+	0.193432i	0.797177	−	0.603745i	$-0.206326\pi$
$103$	1.96312	+	1.96312i	0.193432	+	0.193432i	−0.603745	+	0.797177i	$0.706326\pi$
$104$	−8.40572			−0.824248
$105$		0			0
$106$	−12.2842			−1.19315
$107$	11.4237	+	11.4237i	1.10437	+	1.10437i	0.993876	+	0.110497i	$0.0352441\pi$
$107$	11.4237	+	11.4237i	1.10437	+	1.10437i	0.110497	+	0.993876i	$0.464756\pi$
$108$		0			0
$109$		−	18.1899i		−	1.74228i	−0.491034	−	0.871140i	$-0.663381\pi$
$109$		−	18.1899i		−	1.74228i	0.491034	−	0.871140i	$-0.336619\pi$
$110$		0			0
$111$		0			0
$112$	−3.47897	+	3.47897i	−0.328732	+	0.328732i
$113$	5.30459	−	5.30459i	0.499014	−	0.499014i	−0.412117	−	0.911131i	$-0.635211\pi$
$113$	5.30459	−	5.30459i	0.499014	−	0.499014i	0.911131	+	0.412117i	$0.135211\pi$
$114$		0			0
$115$		0			0
$116$			6.73300i			0.625143i
$117$		0			0
$118$	2.53198	+	2.53198i	0.233088	+	0.233088i
$119$	7.45469			0.683370
$120$		0			0
$121$	−6.15824			−0.559840
$122$	2.42040	+	2.42040i	0.219133	+	0.219133i
$123$		0			0
$124$		−	3.11098i		−	0.279375i
$125$		0			0
$126$		0			0
$127$	−4.46393	+	4.46393i	−0.396110	+	0.396110i	−0.876858	−	0.480749i	$-0.840365\pi$
$127$	−4.46393	+	4.46393i	−0.396110	+	0.396110i	0.480749	+	0.876858i	$0.340365\pi$
$128$	6.87796	−	6.87796i	0.607931	−	0.607931i
$129$		0			0
$130$		0			0
$131$		−	2.72941i		−	0.238470i	−0.992866	−	0.119235i	$-0.961956\pi$
$131$		−	2.72941i		−	0.238470i	0.992866	−	0.119235i	$-0.0380441\pi$
$132$		0			0
$133$	2.16666	+	2.16666i	0.187873	+	0.187873i
$134$	27.5068			2.37623
$135$		0			0
$136$	−9.68664			−0.830622
$137$	−0.0524664	−	0.0524664i	−0.00448250	−	0.00448250i	0.704862	−	0.709344i	$-0.251009\pi$
$137$	−0.0524664	−	0.0524664i	−0.00448250	−	0.00448250i	−0.709344	+	0.704862i	$0.751009\pi$
$138$		0			0
$139$		−	15.6674i		−	1.32890i	−0.747335	−	0.664448i	$-0.768667\pi$
$139$		−	15.6674i		−	1.32890i	0.747335	−	0.664448i	$-0.231333\pi$
$140$		0			0
$141$		0			0
$142$	−12.5059	+	12.5059i	−1.04947	+	1.04947i
$143$	−18.9475	+	18.9475i	−1.58447	+	1.58447i
$144$		0			0
$145$		0			0
$146$		−	2.50839i		−	0.207596i
$147$		0			0
$148$	1.07029	+	1.07029i	0.0879776	+	0.0879776i
$149$	−5.10614			−0.418312			−0.209156	−	0.977882i	$-0.567072\pi$
$149$	−5.10614			−0.418312			−0.209156	+	0.977882i	$0.567072\pi$
$150$		0			0
$151$	2.13920			0.174085			0.0870426	−	0.996205i	$-0.472258\pi$
$151$	2.13920			0.174085			0.0870426	+	0.996205i	$0.472258\pi$
$152$	−2.81537	−	2.81537i	−0.228356	−	0.228356i
$153$		0			0
$154$			7.50518i			0.604784i
$155$		0			0
$156$		0			0
$157$	−5.17676	+	5.17676i	−0.413150	+	0.413150i	−0.882835	−	0.469684i	$-0.844368\pi$
$157$	−5.17676	+	5.17676i	−0.413150	+	0.413150i	0.469684	+	0.882835i	$0.344368\pi$
$158$	−5.24550	+	5.24550i	−0.417309	+	0.417309i
$159$		0			0
$160$		0			0
$161$		−	5.40755i		−	0.426174i
$162$		0			0
$163$	−5.45330	−	5.45330i	−0.427135	−	0.427135i	0.460516	−	0.887651i	$-0.347664\pi$
$163$	−5.45330	−	5.45330i	−0.427135	−	0.427135i	−0.887651	+	0.460516i	$0.847664\pi$
$164$	−5.37784			−0.419938
$165$		0			0
$166$	9.43020			0.731925
$167$	13.4700	+	13.4700i	1.04234	+	1.04234i	0.999063	+	0.0432737i	$0.0137787\pi$
$167$	13.4700	+	13.4700i	1.04234	+	1.04234i	0.0432737	+	0.999063i	$0.486221\pi$
$168$		0			0
$169$			28.8468i			2.21898i
$170$		0			0
$171$		0			0
$172$	4.76851	−	4.76851i	0.363595	−	0.363595i
$173$	4.88296	−	4.88296i	0.371244	−	0.371244i	−0.496686	−	0.867930i	$-0.665450\pi$
$173$	4.88296	−	4.88296i	0.371244	−	0.371244i	0.867930	+	0.496686i	$0.165450\pi$
$174$		0			0
$175$		0			0
$176$		−	20.3799i		−	1.53619i
$177$		0			0
$178$	9.47069	+	9.47069i	0.709858	+	0.709858i
$179$	−17.0489			−1.27429			−0.637147	−	0.770742i	$-0.719886\pi$
$179$	−17.0489			−1.27429			−0.637147	+	0.770742i	$0.719886\pi$
$180$		0			0
$181$	−15.8349			−1.17700			−0.588498	−	0.808498i	$-0.700281\pi$
$181$	−15.8349			−1.17700			−0.588498	+	0.808498i	$0.700281\pi$
$182$	8.28783	+	8.28783i	0.614335	+	0.614335i
$183$		0			0
$184$			7.02658i			0.518006i
$185$		0			0
$186$		0			0
$187$	−21.8349	+	21.8349i	−1.59672	+	1.59672i
$188$	−4.03855	+	4.03855i	−0.294541	+	0.294541i
$189$		0			0
$190$		0			0
$191$			0.295615i			0.0213899i	0.999943	+	0.0106950i	$0.00340438\pi$
$191$			0.295615i			0.0213899i	−0.999943	+	0.0106950i	$0.996596\pi$
$192$		0			0
$193$	11.5473	+	11.5473i	0.831190	+	0.831190i	0.987680	−	0.156490i	$-0.0500178\pi$
$193$	11.5473	+	11.5473i	0.831190	+	0.831190i	−0.156490	+	0.987680i	$0.550018\pi$
$194$	7.87468			0.565369
$195$		0			0
$196$	1.28283			0.0916311
$197$	5.30459	+	5.30459i	0.377936	+	0.377936i	0.870357	−	0.492421i	$-0.163888\pi$
$197$	5.30459	+	5.30459i	0.377936	+	0.377936i	−0.492421	+	0.870357i	$0.663888\pi$
$198$		0			0
$199$		−	7.06135i		−	0.500566i	−0.968173	−	0.250283i	$-0.919476\pi$
$199$		−	7.06135i		−	0.500566i	0.968173	−	0.250283i	$-0.0805236\pi$
$200$		0			0
$201$		0			0
$202$	0.973418	−	0.973418i	0.0684895	−	0.0684895i
$203$	−3.71127	+	3.71127i	−0.260480	+	0.260480i
$204$		0			0
$205$		0			0
$206$			5.03021i			0.350471i
$207$		0			0
$208$	−22.5051	−	22.5051i	−1.56045	−	1.56045i
$209$	−12.6924			−0.877950
$210$		0			0
$211$	14.2937			0.984019			0.492010	−	0.870590i	$-0.336263\pi$
$211$	14.2937			0.984019			0.492010	+	0.870590i	$0.336263\pi$
$212$	−6.15006	−	6.15006i	−0.422388	−	0.422388i
$213$		0			0
$214$			29.2717i			2.00097i
$215$		0			0
$216$		0			0
$217$	1.71479	−	1.71479i	0.116408	−	0.116408i
$218$	23.3046	−	23.3046i	1.57838	−	1.57838i
$219$		0			0
$220$		0			0
$221$			48.2237i			3.24388i
$222$		0			0
$223$	−14.7096	−	14.7096i	−0.985027	−	0.985027i	0.0148628	−	0.999890i	$-0.495269\pi$
$223$	−14.7096	−	14.7096i	−0.985027	−	0.985027i	−0.999890	+	0.0148628i	$0.995269\pi$
$224$	−6.31555			−0.421976
$225$		0			0
$226$	13.5923			0.904143
$227$	−0.813981	−	0.813981i	−0.0540258	−	0.0540258i	0.679578	−	0.733604i	$-0.262163\pi$
$227$	−0.813981	−	0.813981i	−0.0540258	−	0.0540258i	−0.733604	+	0.679578i	$0.762163\pi$
$228$		0			0
$229$		−	19.2790i		−	1.27399i	−0.770866	−	0.636997i	$-0.780176\pi$
$229$		−	19.2790i		−	1.27399i	0.770866	−	0.636997i	$-0.219824\pi$
$230$		0			0
$231$		0			0
$232$	4.82244	−	4.82244i	0.316609	−	0.316609i
$233$	0.00390031	−	0.00390031i	0.000255518	−	0.000255518i	−0.706979	−	0.707235i	$-0.749942\pi$
$233$	0.00390031	−	0.00390031i	0.000255518	−	0.000255518i	0.707235	+	0.706979i	$0.249942\pi$
$234$		0			0
$235$		0			0
$236$			2.53526i			0.165031i
$237$		0			0
$238$	9.55078	+	9.55078i	0.619085	+	0.619085i
$239$	−1.26696			−0.0819530			−0.0409765	−	0.999160i	$-0.513047\pi$
$239$	−1.26696			−0.0819530			−0.0409765	+	0.999160i	$0.513047\pi$
$240$		0			0
$241$	−6.14879			−0.396078			−0.198039	−	0.980194i	$-0.563457\pi$
$241$	−6.14879			−0.396078			−0.198039	+	0.980194i	$0.563457\pi$
$242$	−7.88980	−	7.88980i	−0.507176	−	0.507176i
$243$		0			0
$244$			2.42353i			0.155151i
$245$		0			0
$246$		0			0
$247$	−14.0159	+	14.0159i	−0.891813	+	0.891813i
$248$	−2.22821	+	2.22821i	−0.141491	+	0.141491i
$249$		0			0
$250$		0			0
$251$		−	1.50823i		−	0.0951987i	−0.998867	−	0.0475994i	$-0.984843\pi$
$251$		−	1.50823i		−	0.0951987i	0.998867	−	0.0475994i	$-0.0151571\pi$
$252$		0			0
$253$	15.8388	+	15.8388i	0.995776	+	0.995776i
$254$	−11.4382			−0.717695
$255$		0			0
$256$	20.8296			1.30185
$257$	−6.44051	−	6.44051i	−0.401748	−	0.401748i	0.477101	−	0.878849i	$-0.341688\pi$
$257$	−6.44051	−	6.44051i	−0.401748	−	0.401748i	−0.878849	+	0.477101i	$0.841688\pi$
$258$		0			0
$259$			1.17991i			0.0733158i
$260$		0			0
$261$		0			0
$262$	3.49686	−	3.49686i	0.216037	−	0.216037i
$263$	10.3565	−	10.3565i	0.638611	−	0.638611i	−0.311602	−	0.950213i	$-0.600866\pi$
$263$	10.3565	−	10.3565i	0.638611	−	0.638611i	0.950213	+	0.311602i	$0.100866\pi$
$264$		0			0
$265$		0			0
$266$			5.55176i			0.340400i
$267$		0			0
$268$	13.7712	+	13.7712i	0.841210	+	0.841210i
$269$	−8.28454			−0.505117			−0.252559	−	0.967582i	$-0.581272\pi$
$269$	−8.28454			−0.505117			−0.252559	+	0.967582i	$0.581272\pi$
$270$		0			0
$271$	−18.8028			−1.14219			−0.571093	−	0.820885i	$-0.693480\pi$
$271$	−18.8028			−1.14219			−0.571093	+	0.820885i	$0.693480\pi$
$272$	−25.9346	−	25.9346i	−1.57252	−	1.57252i
$273$		0			0
$274$		−	0.134438i		−	0.00812167i
$275$		0			0
$276$		0			0
$277$	−4.60162	+	4.60162i	−0.276485	+	0.276485i	−0.831704	−	0.555219i	$-0.812634\pi$
$277$	−4.60162	+	4.60162i	−0.276485	+	0.276485i	0.555219	+	0.831704i	$0.312634\pi$
$278$	20.0728	−	20.0728i	1.20389	−	1.20389i
$279$		0			0
$280$		0			0
$281$		−	14.7052i		−	0.877236i	−0.898673	−	0.438618i	$-0.855468\pi$
$281$		−	14.7052i		−	0.877236i	0.898673	−	0.438618i	$-0.144532\pi$
$282$		0			0
$283$	−1.84999	−	1.84999i	−0.109970	−	0.109970i	0.649980	−	0.759951i	$-0.274777\pi$
$283$	−1.84999	−	1.84999i	−0.109970	−	0.109970i	−0.759951	+	0.649980i	$0.774777\pi$
$284$	−12.5220			−0.743047
$285$		0			0
$286$	−48.5503			−2.87084
$287$	−2.96430	−	2.96430i	−0.174977	−	0.174977i
$288$		0			0
$289$			38.5723i			2.26896i
$290$		0			0
$291$		0			0
$292$	1.25582	−	1.25582i	0.0734913	−	0.0734913i
$293$	−10.9840	+	10.9840i	−0.641692	+	0.641692i	−0.950971	−	0.309279i	$-0.899912\pi$
$293$	−10.9840	+	10.9840i	−0.641692	+	0.641692i	0.309279	+	0.950971i	$0.399912\pi$
$294$		0			0
$295$		0			0
$296$		−	1.53317i		−	0.0891138i
$297$		0			0
$298$	−6.54188	−	6.54188i	−0.378961	−	0.378961i
$299$	34.9809			2.02300
$300$		0			0
$301$	5.25687			0.303001
$302$	2.74069	+	2.74069i	0.157709	+	0.157709i
$303$		0			0
$304$		−	15.0755i		−	0.864639i
$305$		0			0
$306$		0			0
$307$	24.6231	−	24.6231i	1.40531	−	1.40531i	0.623448	−	0.781865i	$-0.285731\pi$
$307$	24.6231	−	24.6231i	1.40531	−	1.40531i	0.781865	−	0.623448i	$-0.214269\pi$
$308$	−3.75744	+	3.75744i	−0.214100	+	0.214100i
$309$		0			0
$310$		0			0
$311$			22.5359i			1.27789i	0.769251	+	0.638947i	$0.220630\pi$
$311$			22.5359i			1.27789i	−0.769251	+	0.638947i	$0.779370\pi$
$312$		0			0
$313$	13.0467	+	13.0467i	0.737444	+	0.737444i	0.972083	−	0.234639i	$-0.0753908\pi$
$313$	13.0467	+	13.0467i	0.737444	+	0.737444i	−0.234639	+	0.972083i	$0.575391\pi$
$314$	−13.2647			−0.748571
$315$		0			0
$316$	−5.25228			−0.295464
$317$	−1.48198	−	1.48198i	−0.0832361	−	0.0832361i	0.664263	−	0.747499i	$-0.268746\pi$
$317$	−1.48198	−	1.48198i	−0.0832361	−	0.0832361i	−0.747499	+	0.664263i	$0.768746\pi$
$318$		0			0
$319$		−	21.7407i		−	1.21725i
$320$		0			0
$321$		0			0
$322$	6.92803	−	6.92803i	0.386084	−	0.386084i
$323$	−16.1518	+	16.1518i	−0.898710	+	0.898710i
$324$		0			0
$325$		0			0
$326$		−	13.9733i		−	0.773909i
$327$		0			0
$328$	3.85182	+	3.85182i	0.212681	+	0.212681i
$329$	−4.45215			−0.245455
$330$		0			0
$331$	23.4613			1.28955			0.644775	−	0.764372i	$-0.276951\pi$
$331$	23.4613			1.28955			0.644775	+	0.764372i	$0.276951\pi$
$332$	4.72120	+	4.72120i	0.259109	+	0.259109i
$333$		0			0
$334$			34.5148i			1.88857i
$335$		0			0
$336$		0			0
$337$	−8.87106	+	8.87106i	−0.483238	+	0.483238i	−0.906164	−	0.422926i	$-0.861003\pi$
$337$	−8.87106	+	8.87106i	−0.483238	+	0.483238i	0.422926	+	0.906164i	$0.361003\pi$
$338$	−36.9579	+	36.9579i	−2.01024	+	2.01024i
$339$		0			0
$340$		0			0
$341$			10.0453i			0.543984i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−6.83078			−0.368291
$345$		0			0
$346$	12.5119			0.672642
$347$	−4.80618	−	4.80618i	−0.258009	−	0.258009i	0.566235	−	0.824244i	$-0.308400\pi$
$347$	−4.80618	−	4.80618i	−0.258009	−	0.258009i	−0.824244	+	0.566235i	$0.808400\pi$
$348$		0			0
$349$		−	35.9770i		−	1.92580i	−0.269854	−	0.962901i	$-0.586975\pi$
$349$		−	35.9770i		−	1.92580i	0.269854	−	0.962901i	$-0.413025\pi$
$350$		0			0
$351$		0			0
$352$	18.4983	−	18.4983i	0.985965	−	0.985965i
$353$	−17.0253	+	17.0253i	−0.906166	+	0.906166i	−0.995960	−	0.0897948i	$-0.971379\pi$
$353$	−17.0253	+	17.0253i	−0.906166	+	0.906166i	0.0897948	+	0.995960i	$0.471379\pi$
$354$		0			0
$355$		0			0
$356$			9.48294i			0.502595i
$357$		0			0
$358$	−21.8427	−	21.8427i	−1.15442	−	1.15442i
$359$	−3.02758			−0.159789			−0.0798947	−	0.996803i	$-0.525458\pi$
$359$	−3.02758			−0.159789			−0.0798947	+	0.996803i	$0.525458\pi$
$360$		0			0
$361$	9.61114			0.505850
$362$	−20.2873	−	20.2873i	−1.06628	−	1.06628i
$363$		0			0
$364$			8.29854i			0.434962i
$365$		0			0
$366$		0			0
$367$	9.75566	−	9.75566i	0.509241	−	0.509241i	−0.405052	−	0.914293i	$-0.632747\pi$
$367$	9.75566	−	9.75566i	0.509241	−	0.509241i	0.914293	+	0.405052i	$0.132747\pi$
$368$	−18.8127	+	18.8127i	−0.980679	+	0.980679i
$369$		0			0
$370$		0			0
$371$		−	6.77990i		−	0.351995i
$372$		0			0
$373$	16.4680	+	16.4680i	0.852682	+	0.852682i	0.990463	−	0.137781i	$-0.0439970\pi$
$373$	16.4680	+	16.4680i	0.852682	+	0.852682i	−0.137781	+	0.990463i	$0.543997\pi$
$374$	−55.9487			−2.89304
$375$		0			0
$376$	5.78513			0.298345
$377$	−24.0079	−	24.0079i	−1.23647	−	1.23647i
$378$		0			0
$379$		−	37.2929i		−	1.91561i	−0.287422	−	0.957804i	$-0.592798\pi$
$379$		−	37.2929i		−	1.91561i	0.287422	−	0.957804i	$-0.407202\pi$
$380$		0			0
$381$		0			0
$382$	−0.378735	+	0.378735i	−0.0193778	+	0.0193778i
$383$	13.0112	−	13.0112i	0.664841	−	0.664841i	−0.291676	−	0.956517i	$-0.594213\pi$
$383$	13.0112	−	13.0112i	0.664841	−	0.664841i	0.956517	+	0.291676i	$0.0942130\pi$
$384$		0			0
$385$		0			0
$386$			29.5882i			1.50600i
$387$		0			0
$388$	3.94243	+	3.94243i	0.200147	+	0.200147i
$389$	−9.87898			−0.500884			−0.250442	−	0.968132i	$-0.580576\pi$
$389$	−9.87898			−0.500884			−0.250442	+	0.968132i	$0.580576\pi$
$390$		0			0
$391$	40.3116			2.03864
$392$	−0.918816	−	0.918816i	−0.0464072	−	0.0464072i
$393$		0			0
$394$			13.5923i			0.684768i
$395$		0			0
$396$		0			0
$397$	0.381469	−	0.381469i	0.0191454	−	0.0191454i	−0.697469	−	0.716615i	$-0.745691\pi$
$397$	0.381469	−	0.381469i	0.0191454	−	0.0191454i	0.716615	+	0.697469i	$0.245691\pi$
$398$	9.04684	−	9.04684i	0.453477	−	0.453477i
$399$		0			0
$400$		0			0
$401$			20.9162i			1.04450i	0.852792	+	0.522251i	$0.174908\pi$
$401$			20.9162i			1.04450i	−0.852792	+	0.522251i	$0.825092\pi$
$402$		0			0
$403$	11.0929	+	11.0929i	0.552574	+	0.552574i
$404$	0.974677			0.0484920
$405$		0			0
$406$	−9.50960			−0.471954
$407$	−3.45596	−	3.45596i	−0.171306	−	0.171306i
$408$		0			0
$409$			15.9561i			0.788976i	0.918901	+	0.394488i	$0.129078\pi$
$409$			15.9561i			0.788976i	−0.918901	+	0.394488i	$0.870922\pi$
$410$		0			0
$411$		0			0
$412$	−2.51836	+	2.51836i	−0.124071	+	0.124071i
$413$	−1.39745	+	1.39745i	−0.0687640	+	0.0687640i
$414$		0			0
$415$		0			0
$416$		−	40.8547i		−	2.00307i
$417$		0			0
$418$	−16.2612	−	16.2612i	−0.795361	−	0.795361i
$419$	14.6415			0.715286			0.357643	−	0.933858i	$-0.383581\pi$
$419$	14.6415			0.715286			0.357643	+	0.933858i	$0.383581\pi$
$420$		0			0
$421$	29.4256			1.43412			0.717058	−	0.697014i	$-0.245488\pi$
$421$	29.4256			1.43412			0.717058	+	0.697014i	$0.245488\pi$
$422$	18.3128	+	18.3128i	0.891452	+	0.891452i
$423$		0			0
$424$			8.80982i			0.427843i
$425$		0			0
$426$		0			0
$427$	−1.33586	+	1.33586i	−0.0646470	+	0.0646470i
$428$	−14.6548	+	14.6548i	−0.708364	+	0.708364i
$429$		0			0
$430$		0			0
$431$		−	22.9228i		−	1.10415i	−0.833794	−	0.552076i	$-0.813836\pi$
$431$		−	22.9228i		−	1.10415i	0.833794	−	0.552076i	$-0.186164\pi$
$432$		0			0
$433$	−14.3689	−	14.3689i	−0.690527	−	0.690527i	0.271821	−	0.962348i	$-0.412374\pi$
$433$	−14.3689	−	14.3689i	−0.690527	−	0.690527i	−0.962348	+	0.271821i	$0.912374\pi$
$434$	4.39391			0.210915
$435$		0			0
$436$	23.3347			1.11753
$437$	11.7163	+	11.7163i	0.560468	+	0.560468i
$438$		0			0
$439$			29.7425i			1.41953i	0.704437	+	0.709767i	$0.251200\pi$
$439$			29.7425i			1.41953i	−0.704437	+	0.709767i	$0.748800\pi$
$440$		0			0
$441$		0			0
$442$	−61.7831	+	61.7831i	−2.93872	+	2.93872i
$443$	14.9597	−	14.9597i	0.710754	−	0.710754i	−0.255939	−	0.966693i	$-0.582384\pi$
$443$	14.9597	−	14.9597i	0.710754	−	0.710754i	0.966693	+	0.255939i	$0.0823845\pi$
$444$		0			0
$445$		0			0
$446$		−	37.6912i		−	1.78473i
$447$		0			0
$448$	−1.13341	−	1.13341i	−0.0535486	−	0.0535486i
$449$	−12.6248			−0.595801			−0.297900	−	0.954597i	$-0.596286\pi$
$449$	−12.6248			−0.595801			−0.297900	+	0.954597i	$0.596286\pi$
$450$		0			0
$451$	17.3649			0.817683
$452$	6.80491	+	6.80491i	0.320076	+	0.320076i
$453$		0			0
$454$		−	2.08571i		−	0.0978871i
$455$		0			0
$456$		0			0
$457$	23.0026	−	23.0026i	1.07602	−	1.07602i	0.0791546	−	0.996862i	$-0.474778\pi$
$457$	23.0026	−	23.0026i	1.07602	−	1.07602i	0.996862	−	0.0791546i	$-0.0252221\pi$
$458$	24.6999	−	24.6999i	1.15415	−	1.15415i
$459$		0			0
$460$		0			0
$461$			33.6976i			1.56945i	0.619842	+	0.784727i	$0.287197\pi$
$461$			33.6976i			1.56945i	−0.619842	+	0.784727i	$0.712803\pi$
$462$		0			0
$463$	−10.5496	−	10.5496i	−0.490280	−	0.490280i	0.418115	−	0.908394i	$-0.362691\pi$
$463$	−10.5496	−	10.5496i	−0.490280	−	0.490280i	−0.908394	+	0.418115i	$0.862691\pi$
$464$	25.8228			1.19879
$465$		0			0
$466$	0.00999398			0.000462962
$467$	−9.72972	−	9.72972i	−0.450238	−	0.450238i	0.445196	−	0.895433i	$-0.353134\pi$
$467$	−9.72972	−	9.72972i	−0.450238	−	0.450238i	−0.895433	+	0.445196i	$0.853134\pi$
$468$		0			0
$469$			15.1816i			0.701019i
$470$		0			0
$471$		0			0
$472$	1.81585	−	1.81585i	0.0835812	−	0.0835812i
$473$	−15.3974	+	15.3974i	−0.707975	+	0.707975i
$474$		0			0
$475$		0			0
$476$			9.56313i			0.438325i
$477$		0			0
$478$	−1.62321	−	1.62321i	−0.0742437	−	0.0742437i
$479$	29.8978			1.36607			0.683033	−	0.730388i	$-0.260661\pi$
$479$	29.8978			1.36607			0.683033	+	0.730388i	$0.260661\pi$
$480$		0			0
$481$	−7.63270			−0.348021
$482$	−7.87770	−	7.87770i	−0.358819	−	0.358819i
$483$		0			0
$484$		−	7.90001i		−	0.359091i
$485$		0			0
$486$		0			0
$487$	6.74208	−	6.74208i	0.305513	−	0.305513i	−0.537653	−	0.843166i	$-0.680689\pi$
$487$	6.74208	−	6.74208i	0.305513	−	0.305513i	0.843166	+	0.537653i	$0.180689\pi$
$488$	1.73583	−	1.73583i	0.0785772	−	0.0785772i
$489$		0			0
$490$		0			0
$491$		−	39.9275i		−	1.80190i	−0.433921	−	0.900951i	$-0.642870\pi$
$491$		−	39.9275i		−	1.80190i	0.433921	−	0.900951i	$-0.357130\pi$
$492$		0			0
$493$	−27.6664	−	27.6664i	−1.24603	−	1.24603i
$494$	−35.9138			−1.61584
$495$		0			0
$496$	−11.9314			−0.535737
$497$	−6.90223	−	6.90223i	−0.309607	−	0.309607i
$498$		0			0
$499$		−	21.0239i		−	0.941159i	−0.882358	−	0.470579i	$-0.844045\pi$
$499$		−	21.0239i		−	0.941159i	0.882358	−	0.470579i	$-0.155955\pi$
$500$		0			0
$501$		0			0
$502$	1.93231	−	1.93231i	0.0862434	−	0.0862434i
$503$	−2.83078	+	2.83078i	−0.126218	+	0.126218i	−0.767394	−	0.641176i	$-0.778447\pi$
$503$	−2.83078	+	2.83078i	−0.126218	+	0.126218i	0.641176	+	0.767394i	$0.278447\pi$
$504$		0			0
$505$		0			0
$506$			40.5846i			1.80421i
$507$		0			0
$508$	−5.72649	−	5.72649i	−0.254072	−	0.254072i
$509$	−21.7097			−0.962267			−0.481133	−	0.876647i	$-0.659775\pi$
$509$	−21.7097			−0.962267			−0.481133	+	0.876647i	$0.659775\pi$
$510$		0			0
$511$	1.38443			0.0612436
$512$	12.9304	+	12.9304i	0.571450	+	0.571450i
$513$		0			0
$514$		−	16.5029i		−	0.727911i
$515$		0			0
$516$		0			0
$517$	13.0404	−	13.0404i	0.573516	−	0.573516i
$518$	−1.51167	+	1.51167i	−0.0664189	+	0.0664189i
$519$		0			0
$520$		0			0
$521$			10.1879i			0.446338i	0.974780	+	0.223169i	$0.0716402\pi$
$521$			10.1879i			0.446338i	−0.974780	+	0.223169i	$0.928360\pi$
$522$		0			0
$523$	−17.9604	−	17.9604i	−0.785353	−	0.785353i	0.195375	−	0.980729i	$-0.437408\pi$
$523$	−17.9604	−	17.9604i	−0.785353	−	0.785353i	−0.980729	+	0.195375i	$0.937408\pi$
$524$	3.50138			0.152959
$525$		0			0
$526$	26.5371			1.15707
$527$	12.7833	+	12.7833i	0.556847	+	0.556847i
$528$		0			0
$529$		−	6.24157i		−	0.271373i
$530$		0			0
$531$		0			0
$532$	−2.77947	+	2.77947i	−0.120505	+	0.120505i
$533$	19.1758	−	19.1758i	0.830595	−	0.830595i
$534$		0			0
$535$		0			0
$536$		−	19.7270i		−	0.852075i
$537$		0			0
$538$	−10.6140	−	10.6140i	−0.457601	−	0.457601i
$539$	−4.14225			−0.178419
$540$		0			0
$541$	−19.8027			−0.851385			−0.425693	−	0.904868i	$-0.639970\pi$
$541$	−19.8027			−0.851385			−0.425693	+	0.904868i	$0.639970\pi$
$542$	−24.0897	−	24.0897i	−1.03474	−	1.03474i
$543$		0			0
$544$		−	47.0805i		−	2.01856i
$545$		0			0
$546$		0			0
$547$	3.17046	−	3.17046i	0.135559	−	0.135559i	−0.636071	−	0.771630i	$-0.719442\pi$
$547$	3.17046	−	3.17046i	0.135559	−	0.135559i	0.771630	+	0.636071i	$0.219442\pi$
$548$	0.0673057	−	0.0673057i	0.00287516	−	0.00287516i
$549$		0			0
$550$		0			0
$551$		−	16.0822i		−	0.685123i
$552$		0			0
$553$	−2.89509	−	2.89509i	−0.123112	−	0.123112i
$554$	−11.7910			−0.500951
$555$		0			0
$556$	20.0987			0.852377
$557$	21.0318	+	21.0318i	0.891144	+	0.891144i	0.994631	−	0.103487i	$-0.0329999\pi$
$557$	21.0318	+	21.0318i	0.891144	+	0.891144i	−0.103487	+	0.994631i	$0.533000\pi$
$558$		0			0
$559$			34.0062i			1.43831i
$560$		0			0
$561$		0			0
$562$	18.8399	−	18.8399i	0.794715	−	0.794715i
$563$	11.8395	−	11.8395i	0.498977	−	0.498977i	−0.412142	−	0.911119i	$-0.635219\pi$
$563$	11.8395	−	11.8395i	0.498977	−	0.498977i	0.911119	+	0.412142i	$0.135219\pi$
$564$		0			0
$565$		0			0
$566$		−	4.74033i		−	0.199251i
$567$		0			0
$568$	8.96878	+	8.96878i	0.376321	+	0.376321i
$569$	−3.22907			−0.135370			−0.0676848	−	0.997707i	$-0.521561\pi$
$569$	−3.22907			−0.135370			−0.0676848	+	0.997707i	$0.521561\pi$
$570$		0			0
$571$	−45.1687			−1.89025			−0.945126	−	0.326706i	$-0.894061\pi$
$571$	−45.1687			−1.89025			−0.945126	+	0.326706i	$0.894061\pi$
$572$	−24.3065	−	24.3065i	−1.01631	−	1.01631i
$573$		0			0
$574$		−	7.59559i		−	0.317034i
$575$		0			0
$576$		0			0
$577$	−11.7379	+	11.7379i	−0.488655	+	0.488655i	−0.907882	−	0.419226i	$-0.862301\pi$
$577$	−11.7379	+	11.7379i	−0.488655	+	0.488655i	0.419226	+	0.907882i	$0.362301\pi$
$578$	−49.4180	+	49.4180i	−2.05552	+	2.05552i
$579$		0			0
$580$		0			0
$581$			5.20471i			0.215928i
$582$		0			0
$583$	19.8584	+	19.8584i	0.822452	+	0.822452i
$584$	−1.79893			−0.0744404
$585$		0			0
$586$	−28.1449			−1.16266
$587$	7.69625	+	7.69625i	0.317658	+	0.317658i	0.847867	−	0.530209i	$-0.177886\pi$
$587$	7.69625	+	7.69625i	0.317658	+	0.317658i	−0.530209	+	0.847867i	$0.677886\pi$
$588$		0			0
$589$			7.43076i			0.306179i
$590$		0			0
$591$		0			0
$592$	4.10485	−	4.10485i	0.168708	−	0.168708i
$593$	0.772725	−	0.772725i	0.0317320	−	0.0317320i	−0.691063	−	0.722795i	$-0.742857\pi$
$593$	0.772725	−	0.772725i	0.0317320	−	0.0317320i	0.722795	+	0.691063i	$0.242857\pi$
$594$		0			0
$595$		0			0
$596$		−	6.55034i		−	0.268312i
$597$		0			0
$598$	44.8168	+	44.8168i	1.83270	+	1.83270i
$599$	−7.19884			−0.294136			−0.147068	−	0.989126i	$-0.546984\pi$
$599$	−7.19884			−0.294136			−0.147068	+	0.989126i	$0.546984\pi$
$600$		0			0
$601$	14.3551			0.585559			0.292779	−	0.956180i	$-0.405420\pi$
$601$	14.3551			0.585559			0.292779	+	0.956180i	$0.405420\pi$
$602$	6.73498	+	6.73498i	0.274497	+	0.274497i
$603$		0			0
$604$			2.74423i			0.111661i
$605$		0			0
$606$		0			0
$607$	18.1909	−	18.1909i	0.738347	−	0.738347i	−0.233911	−	0.972258i	$-0.575152\pi$
$607$	18.1909	−	18.1909i	0.738347	−	0.738347i	0.972258	+	0.233911i	$0.0751523\pi$
$608$	13.6837	−	13.6837i	0.554946	−	0.554946i
$609$		0			0
$610$		0			0
$611$		−	28.8005i		−	1.16514i
$612$		0			0
$613$	26.8922	+	26.8922i	1.08616	+	1.08616i	0.995920	+	0.0902447i	$0.0287649\pi$
$613$	26.8922	+	26.8922i	1.08616	+	1.08616i	0.0902447	+	0.995920i	$0.471235\pi$
$614$	63.0931			2.54623
$615$		0			0
$616$	5.38245			0.216865
$617$	−32.4145	−	32.4145i	−1.30496	−	1.30496i	−0.925006	−	0.379952i	$-0.875941\pi$
$617$	−32.4145	−	32.4145i	−1.30496	−	1.30496i	−0.379952	−	0.925006i	$-0.624059\pi$
$618$		0			0
$619$			44.1635i			1.77508i	0.460729	+	0.887541i	$0.347588\pi$
$619$			44.1635i			1.77508i	−0.460729	+	0.887541i	$0.652412\pi$
$620$		0			0
$621$		0			0
$622$	−28.8725	+	28.8725i	−1.15768	+	1.15768i
$623$	−5.22706	+	5.22706i	−0.209418	+	0.209418i
$624$		0			0
$625$		0			0
$626$			33.4303i			1.33614i
$627$		0			0
$628$	−6.64093	−	6.64093i	−0.265002	−	0.265002i
$629$	−8.79582			−0.350712
$630$		0			0
$631$	−23.5286			−0.936659			−0.468330	−	0.883554i	$-0.655144\pi$
$631$	−23.5286			−0.936659			−0.468330	+	0.883554i	$0.655144\pi$
$632$	3.76189	+	3.76189i	0.149640	+	0.149640i
$633$		0			0
$634$		−	3.79735i		−	0.150812i
$635$		0			0
$636$		0			0
$637$	−4.57421	+	4.57421i	−0.181237	+	0.181237i
$638$	27.8538	−	27.8538i	1.10274	−	1.10274i
$639$		0			0
$640$		0			0
$641$		−	6.92503i		−	0.273522i	−0.990604	−	0.136761i	$-0.956331\pi$
$641$		−	6.92503i		−	0.273522i	0.990604	−	0.136761i	$-0.0436693\pi$
$642$		0			0
$643$	33.4615	+	33.4615i	1.31959	+	1.31959i	0.914097	+	0.405495i	$0.132901\pi$
$643$	33.4615	+	33.4615i	1.31959	+	1.31959i	0.405495	+	0.914097i	$0.367099\pi$
$644$	6.93699			0.273356
$645$		0			0
$646$	−41.3866			−1.62834
$647$	33.6527	+	33.6527i	1.32302	+	1.32302i	0.911317	+	0.411706i	$0.135067\pi$
$647$	33.6527	+	33.6527i	1.32302	+	1.32302i	0.411706	+	0.911317i	$0.364933\pi$
$648$		0			0
$649$		−	8.18630i		−	0.321340i
$650$		0			0
$651$		0			0
$652$	6.99568	−	6.99568i	0.273972	−	0.273972i
$653$	−29.4549	+	29.4549i	−1.15266	+	1.15266i	−0.166643	+	0.986017i	$0.553293\pi$
$653$	−29.4549	+	29.4549i	−1.15266	+	1.15266i	−0.986017	+	0.166643i	$0.946707\pi$
$654$		0			0
$655$		0			0
$656$			20.6254i			0.805286i
$657$		0			0
$658$	−5.70399	−	5.70399i	−0.222365	−	0.222365i
$659$	29.4372			1.14671			0.573354	−	0.819307i	$-0.305642\pi$
$659$	29.4372			1.14671			0.573354	+	0.819307i	$0.305642\pi$
$660$		0			0
$661$	16.3460			0.635787			0.317893	−	0.948126i	$-0.397025\pi$
$661$	16.3460			0.635787			0.317893	+	0.948126i	$0.397025\pi$
$662$	30.0581	+	30.0581i	1.16824	+	1.16824i
$663$		0			0
$664$		−	6.76301i		−	0.262456i
$665$		0			0
$666$		0			0
$667$	−20.0689	+	20.0689i	−0.777070	+	0.777070i
$668$	−17.2797	+	17.2797i	−0.668573	+	0.668573i
$669$		0			0
$670$		0			0
$671$		−	7.82553i		−	0.302101i
$672$		0			0
$673$	5.86468	+	5.86468i	0.226067	+	0.226067i	0.811047	−	0.584981i	$-0.198898\pi$
$673$	5.86468	+	5.86468i	0.226067	+	0.226067i	−0.584981	+	0.811047i	$0.698898\pi$
$674$	−22.7308			−0.875559
$675$		0			0
$676$	−37.0057			−1.42330
$677$	8.34109	+	8.34109i	0.320574	+	0.320574i	0.848987	−	0.528413i	$-0.177213\pi$
$677$	8.34109	+	8.34109i	0.320574	+	0.320574i	−0.528413	+	0.848987i	$0.677213\pi$
$678$		0			0
$679$			4.34618i			0.166791i
$680$		0			0
$681$		0			0
$682$	−12.8698	+	12.8698i	−0.492811	+	0.492811i
$683$	21.9309	−	21.9309i	0.839162	−	0.839162i	−0.149587	−	0.988749i	$-0.547794\pi$
$683$	21.9309	−	21.9309i	0.839162	−	0.839162i	0.988749	+	0.149587i	$0.0477943\pi$
$684$		0			0
$685$		0			0
$686$			1.81186i			0.0691771i
$687$		0			0
$688$	−18.2885	−	18.2885i	−0.697241	−	0.697241i
$689$	43.8586			1.67088
$690$		0			0
$691$	−31.5075			−1.19860			−0.599300	−	0.800525i	$-0.704554\pi$
$691$	−31.5075			−1.19860			−0.599300	+	0.800525i	$0.704554\pi$
$692$	6.26402	+	6.26402i	0.238123	+	0.238123i
$693$		0			0
$694$		−	12.3151i		−	0.467476i
$695$		0			0
$696$		0			0
$697$	22.0979	−	22.0979i	0.837018	−	0.837018i
$698$	46.0929	−	46.0929i	1.74464	−	1.74464i
$699$		0			0
$700$		0			0
$701$		−	37.1532i		−	1.40326i	−0.712543	−	0.701628i	$-0.752457\pi$
$701$		−	37.1532i		−	1.40326i	0.712543	−	0.701628i	$-0.247543\pi$
$702$		0			0
$703$	−2.55646	−	2.55646i	−0.0964186	−	0.0964186i
$704$	6.63955			0.250237
$705$		0			0
$706$	−43.6249			−1.64184
$707$	0.537248	+	0.537248i	0.0202053	+	0.0202053i
$708$		0			0
$709$			17.8148i			0.669048i	0.942387	+	0.334524i	$0.108576\pi$
$709$			17.8148i			0.669048i	−0.942387	+	0.334524i	$0.891424\pi$
$710$		0			0
$711$		0			0
$712$	6.79205	−	6.79205i	0.254543	−	0.254543i
$713$	9.27283	−	9.27283i	0.347270	−	0.347270i
$714$		0			0
$715$		0			0
$716$		−	21.8709i		−	0.817355i
$717$		0			0
$718$	−3.87886	−	3.87886i	−0.144758	−	0.144758i
$719$	26.0712			0.972292			0.486146	−	0.873878i	$-0.338402\pi$
$719$	26.0712			0.972292			0.486146	+	0.873878i	$0.338402\pi$
$720$		0			0
$721$	−2.77627			−0.103394
$722$	12.3136	+	12.3136i	0.458264	+	0.458264i
$723$		0			0
$724$		−	20.3135i		−	0.754946i
$725$		0			0
$726$		0			0
$727$	−14.3966	+	14.3966i	−0.533941	+	0.533941i	−0.921743	−	0.387802i	$-0.873234\pi$
$727$	−14.3966	+	14.3966i	−0.533941	+	0.533941i	0.387802	+	0.921743i	$0.373234\pi$
$728$	5.94374	−	5.94374i	0.220290	−	0.220290i
$729$		0			0
$730$		0			0
$731$			39.1883i			1.44943i
$732$		0			0
$733$	−0.715347	−	0.715347i	−0.0264219	−	0.0264219i	0.693772	−	0.720194i	$-0.255947\pi$
$733$	−0.715347	−	0.715347i	−0.0264219	−	0.0264219i	−0.720194	+	0.693772i	$0.755947\pi$
$734$	24.9975			0.922673
$735$		0			0
$736$	−34.1516			−1.25885
$737$	−44.4670	−	44.4670i	−1.63796	−	1.63796i
$738$		0			0
$739$			24.4989i			0.901205i	0.892725	+	0.450602i	$0.148791\pi$
$739$			24.4989i			0.901205i	−0.892725	+	0.450602i	$0.851209\pi$
$740$		0			0
$741$		0			0
$742$	8.68626	−	8.68626i	0.318883	−	0.318883i
$743$	24.0536	−	24.0536i	0.882441	−	0.882441i	−0.111341	−	0.993782i	$-0.535515\pi$
$743$	24.0536	−	24.0536i	0.882441	−	0.882441i	0.993782	+	0.111341i	$0.0355145\pi$
$744$		0			0
$745$		0			0
$746$			42.1969i			1.54494i
$747$		0			0
$748$	−28.0105	−	28.0105i	−1.02417	−	1.02417i
$749$	−16.1556			−0.590312
$750$		0			0
$751$	−9.50757			−0.346936			−0.173468	−	0.984839i	$-0.555497\pi$
$751$	−9.50757			−0.346936			−0.173468	+	0.984839i	$0.555497\pi$
$752$	15.4889	+	15.4889i	0.564821	+	0.564821i
$753$		0			0
$754$		−	61.5168i		−	2.24031i
$755$		0			0
$756$		0			0
$757$	−9.69461	+	9.69461i	−0.352357	+	0.352357i	−0.860986	−	0.508629i	$-0.830152\pi$
$757$	−9.69461	+	9.69461i	−0.352357	+	0.352357i	0.508629	+	0.860986i	$0.330152\pi$
$758$	47.7789	−	47.7789i	1.73541	−	1.73541i
$759$		0			0
$760$		0			0
$761$		−	1.20458i		−	0.0436662i	−0.999762	−	0.0218331i	$-0.993050\pi$
$761$		−	1.20458i		−	0.0436662i	0.999762	−	0.0218331i	$-0.00695024\pi$
$762$		0			0
$763$	12.8622	+	12.8622i	0.465644	+	0.465644i
$764$	−0.379225			−0.0137199
$765$		0			0
$766$	33.3393			1.20460
$767$	−9.03998	−	9.03998i	−0.326415	−	0.326415i
$768$		0			0
$769$			32.3602i			1.16694i	0.812135	+	0.583469i	$0.198305\pi$
$769$			32.3602i			1.16694i	−0.812135	+	0.583469i	$0.801695\pi$
$770$		0			0
$771$		0			0
$772$	−14.8132	+	14.8132i	−0.533140	+	0.533140i
$773$	25.3066	−	25.3066i	0.910216	−	0.910216i	−0.0860725	−	0.996289i	$-0.527432\pi$
$773$	25.3066	−	25.3066i	0.910216	−	0.910216i	0.996289	+	0.0860725i	$0.0274317\pi$
$774$		0			0
$775$		0			0
$776$		−	5.64744i		−	0.202731i
$777$		0			0
$778$	−12.6567	−	12.6567i	−0.453766	−	0.453766i
$779$	12.8453			0.460229
$780$		0			0
$781$	40.4335			1.44682
$782$	51.6463	+	51.6463i	1.84687	+	1.84687i
$783$		0			0
$784$		−	4.92000i		−	0.175714i
$785$		0			0
$786$		0			0
$787$	25.4112	−	25.4112i	0.905810	−	0.905810i	−0.0901209	−	0.995931i	$-0.528725\pi$
$787$	25.4112	−	25.4112i	0.905810	−	0.905810i	0.995931	+	0.0901209i	$0.0287253\pi$
$788$	−6.80491	+	6.80491i	−0.242415	+	0.242415i
$789$		0			0
$790$		0			0
$791$			7.50182i			0.266734i
$792$		0			0
$793$	−8.64159	−	8.64159i	−0.306872	−	0.306872i
$794$	0.977459			0.0346887
$795$		0			0
$796$	9.05854			0.321071
$797$	7.39217	+	7.39217i	0.261844	+	0.261844i	0.825803	−	0.563959i	$-0.190722\pi$
$797$	7.39217	+	7.39217i	0.261844	+	0.261844i	−0.563959	+	0.825803i	$0.690722\pi$
$798$		0			0
$799$		−	33.1893i		−	1.17415i
$800$		0			0
$801$		0			0
$802$	−26.7973	+	26.7973i	−0.946246	+	0.946246i
$803$	−4.05502	+	4.05502i	−0.143098	+	0.143098i
$804$		0			0
$805$		0			0
$806$			28.4238i			1.00119i
$807$		0			0
$808$	−0.698102	−	0.698102i	−0.0245591	−	0.0245591i
$809$	1.56712			0.0550969			0.0275485	−	0.999620i	$-0.491230\pi$
$809$	1.56712			0.0550969			0.0275485	+	0.999620i	$0.491230\pi$
$810$		0			0
$811$	13.6470			0.479210			0.239605	−	0.970870i	$-0.422982\pi$
$811$	13.6470			0.479210			0.239605	+	0.970870i	$0.422982\pi$
$812$	−4.76095	−	4.76095i	−0.167077	−	0.167077i
$813$		0			0
$814$		−	8.85540i		−	0.310382i
$815$		0			0
$816$		0			0
$817$	−11.3899	+	11.3899i	−0.398481	+	0.398481i
$818$	−20.4425	+	20.4425i	−0.714757	+	0.714757i
$819$		0			0
$820$		0			0
$821$			21.7023i			0.757414i	0.925517	+	0.378707i	$0.123631\pi$
$821$			21.7023i			0.757414i	−0.925517	+	0.378707i	$0.876369\pi$
$822$		0			0
$823$	9.66959	+	9.66959i	0.337061	+	0.337061i	0.855260	−	0.518199i	$-0.173397\pi$
$823$	9.66959	+	9.66959i	0.337061	+	0.337061i	−0.518199	+	0.855260i	$0.673397\pi$
$824$	3.60749			0.125673
$825$		0			0
$826$	−3.58076			−0.124591
$827$	0.682391	+	0.682391i	0.0237291	+	0.0237291i	0.718872	−	0.695143i	$-0.244659\pi$
$827$	0.682391	+	0.682391i	0.0237291	+	0.0237291i	−0.695143	+	0.718872i	$0.744659\pi$
$828$		0			0
$829$		−	10.3444i		−	0.359276i	−0.983733	−	0.179638i	$-0.942507\pi$
$829$		−	10.3444i		−	0.359276i	0.983733	−	0.179638i	$-0.0574926\pi$
$830$		0			0
$831$		0			0
$832$	7.33193	−	7.33193i	0.254189	−	0.254189i
$833$	−5.27126	+	5.27126i	−0.182638	+	0.182638i
$834$		0			0
$835$		0			0
$836$		−	16.2822i		−	0.563132i
$837$		0			0
$838$	18.7584	+	18.7584i	0.647999	+	0.647999i
$839$	43.5272			1.50273			0.751363	−	0.659889i	$-0.229397\pi$
$839$	43.5272			1.50273			0.751363	+	0.659889i	$0.229397\pi$
$840$		0			0
$841$	−1.45290			−0.0501001
$842$	37.6994	+	37.6994i	1.29921	+	1.29921i
$843$		0			0
$844$			18.3365i			0.631167i
$845$		0			0
$846$		0			0
$847$	4.35453	−	4.35453i	0.149624	−	0.149624i
$848$	−23.5871	+	23.5871i	−0.809983	+	0.809983i
$849$		0			0
$850$		0			0
$851$			6.38039i			0.218717i
$852$		0			0
$853$	0.0328516	+	0.0328516i	0.00112482	+	0.00112482i	0.707669	−	0.706544i	$-0.249747\pi$
$853$	0.0328516	+	0.0328516i	0.00112482	+	0.00112482i	−0.706544	+	0.707669i	$0.749747\pi$
$854$	−3.42296			−0.117131
$855$		0			0
$856$	20.9926			0.717513
$857$	32.6070	+	32.6070i	1.11384	+	1.11384i	0.992627	+	0.121208i	$0.0386769\pi$
$857$	32.6070	+	32.6070i	1.11384	+	1.11384i	0.121208	+	0.992627i	$0.461323\pi$
$858$		0			0
$859$			3.46726i			0.118301i	0.998249	+	0.0591506i	$0.0188392\pi$
$859$			3.46726i			0.118301i	−0.998249	+	0.0591506i	$0.981161\pi$
$860$		0			0
$861$		0			0
$862$	29.3682	−	29.3682i	1.00028	−	1.00028i
$863$	−31.7372	+	31.7372i	−1.08035	+	1.08035i	−0.0838692	+	0.996477i	$0.526728\pi$
$863$	−31.7372	+	31.7372i	−1.08035	+	1.08035i	−0.996477	+	0.0838692i	$0.973272\pi$
$864$		0			0
$865$		0			0
$866$		−	36.8183i		−	1.25114i
$867$		0			0
$868$	2.19980	+	2.19980i	0.0746660	+	0.0746660i
$869$	16.9595			0.575312
$870$		0			0
$871$	−98.2081			−3.32766
$872$	−16.7132	−	16.7132i	−0.565981	−	0.565981i
$873$		0			0
$874$			30.0214i			1.01549i
$875$		0			0
$876$		0			0
$877$	5.46491	−	5.46491i	0.184537	−	0.184537i	−0.608793	−	0.793329i	$-0.708346\pi$
$877$	5.46491	−	5.46491i	0.184537	−	0.184537i	0.793329	+	0.608793i	$0.208346\pi$
$878$	−38.1055	+	38.1055i	−1.28600	+	1.28600i
$879$		0			0
$880$		0			0
$881$		−	49.0241i		−	1.65166i	−0.563916	−	0.825832i	$-0.690706\pi$
$881$		−	49.0241i		−	1.65166i	0.563916	−	0.825832i	$-0.309294\pi$
$882$		0			0
$883$	−9.34962	−	9.34962i	−0.314640	−	0.314640i	0.532064	−	0.846704i	$-0.321416\pi$
$883$	−9.34962	−	9.34962i	−0.314640	−	0.314640i	−0.846704	+	0.532064i	$0.821416\pi$
$884$	−61.8630			−2.08068
$885$		0			0
$886$	38.3320			1.28779
$887$	−32.1054	−	32.1054i	−1.07799	−	1.07799i	−0.996689	−	0.0813035i	$-0.974092\pi$
$887$	−32.1054	−	32.1054i	−1.07799	−	1.07799i	−0.0813035	−	0.996689i	$-0.525908\pi$
$888$		0			0
$889$		−	6.31295i		−	0.211730i
$890$		0			0
$891$		0			0
$892$	18.8700	−	18.8700i	0.631813	−	0.631813i
$893$	9.64630	−	9.64630i	0.322801	−	0.322801i
$894$		0			0
$895$		0			0
$896$			9.72690i			0.324953i
$897$		0			0
$898$	−16.1746	−	16.1746i	−0.539754	−	0.539754i
$899$	−12.7281			−0.424507
$900$		0			0
$901$	50.5420			1.68380
$902$	22.2476	+	22.2476i	0.740763	+	0.740763i
$903$		0			0
$904$		−	9.74789i		−	0.324210i
$905$		0			0
$906$		0			0
$907$	−2.35659	+	2.35659i	−0.0782493	+	0.0782493i	−0.745148	−	0.666899i	$-0.767621\pi$
$907$	−2.35659	+	2.35659i	−0.0782493	+	0.0782493i	0.666899	+	0.745148i	$0.267621\pi$
$908$	1.04420	−	1.04420i	0.0346531	−	0.0346531i
$909$		0			0
$910$		0			0
$911$			19.2308i			0.637144i	0.947899	+	0.318572i	$0.103203\pi$
$911$			19.2308i			0.637144i	−0.947899	+	0.318572i	$0.896797\pi$
$912$		0			0
$913$	−15.2447	−	15.2447i	−0.504525	−	0.504525i
$914$	58.9409			1.94959
$915$		0			0
$916$	24.7318			0.817162
$917$	1.92998	+	1.92998i	0.0637337	+	0.0637337i
$918$		0			0
$919$		−	29.2988i		−	0.966478i	−0.875489	−	0.483239i	$-0.839460\pi$
$919$		−	29.2988i		−	0.966478i	0.875489	−	0.483239i	$-0.160540\pi$
$920$		0			0
$921$		0			0
$922$	−43.1726	+	43.1726i	−1.42181	+	1.42181i
$923$	44.6499	−	44.6499i	1.46967	−	1.46967i
$924$		0			0
$925$		0			0
$926$		−	27.0317i		−	0.888318i
$927$		0			0
$928$	23.4387	+	23.4387i	0.769414	+	0.769414i
$929$	−30.3363			−0.995301			−0.497651	−	0.867378i	$-0.665804\pi$
$929$	−30.3363			−0.995301			−0.497651	+	0.867378i	$0.665804\pi$
$930$		0			0
$931$	−3.06412			−0.100423
$932$	0.00500345	+	0.00500345i	0.000163893	+	0.000163893i
$933$		0			0
$934$		−	24.9310i		−	0.815768i
$935$		0			0
$936$		0			0
$937$	−18.7277	+	18.7277i	−0.611808	+	0.611808i	−0.943417	−	0.331609i	$-0.892409\pi$
$937$	−18.7277	+	18.7277i	−0.611808	+	0.611808i	0.331609	+	0.943417i	$0.392409\pi$
$938$	−19.4503	+	19.4503i	−0.635074	+	0.635074i
$939$		0			0
$940$		0			0
$941$			2.53282i			0.0825676i	0.999147	+	0.0412838i	$0.0131448\pi$
$941$			2.53282i			0.0825676i	−0.999147	+	0.0412838i	$0.986855\pi$
$942$		0			0
$943$	−16.0296	−	16.0296i	−0.521995	−	0.521995i
$944$	9.72337			0.316469
$945$		0			0
$946$	−39.4537			−1.28275
$947$	17.4742	+	17.4742i	0.567834	+	0.567834i	0.931521	−	0.363687i	$-0.118482\pi$
$947$	17.4742	+	17.4742i	0.567834	+	0.567834i	−0.363687	+	0.931521i	$0.618482\pi$
$948$		0			0
$949$			8.95576i			0.290716i
$950$		0			0
$951$		0			0
$952$	6.84949	−	6.84949i	0.221993	−	0.221993i
$953$	−30.4565	+	30.4565i	−0.986584	+	0.986584i	−0.999911	−	0.0133276i	$-0.995758\pi$
$953$	−30.4565	+	30.4565i	−0.986584	+	0.986584i	0.0133276	+	0.999911i	$0.495758\pi$
$954$		0			0
$955$		0			0
$956$		−	1.62530i		−	0.0525661i
$957$		0			0
$958$	38.3044	+	38.3044i	1.23756	+	1.23756i
$959$	0.0741987			0.00239600
$960$		0			0
$961$	−25.1190			−0.810289
$962$	−9.77885	−	9.77885i	−0.315283	−	0.315283i
$963$		0			0
$964$		−	7.88788i		−	0.254052i
$965$		0			0
$966$		0			0
$967$	18.0985	−	18.0985i	0.582009	−	0.582009i	−0.353446	−	0.935455i	$-0.614990\pi$
$967$	18.0985	−	18.0985i	0.582009	−	0.582009i	0.935455	+	0.353446i	$0.114990\pi$
$968$	−5.65829	+	5.65829i	−0.181864	+	0.181864i
$969$		0			0
$970$		0			0
$971$			38.7995i			1.24514i	0.782566	+	0.622568i	$0.213911\pi$
$971$			38.7995i			1.24514i	−0.782566	+	0.622568i	$0.786089\pi$
$972$		0			0
$973$	11.0786	+	11.0786i	0.355162	+	0.355162i
$974$	17.2756			0.553546
$975$		0			0
$976$	9.29486			0.297521
$977$	22.3872	+	22.3872i	0.716231	+	0.716231i	0.967831	−	0.251601i	$-0.0809569\pi$
$977$	22.3872	+	22.3872i	0.716231	+	0.716231i	−0.251601	+	0.967831i	$0.580957\pi$
$978$		0			0
$979$		−	30.6202i		−	0.978627i
$980$		0			0
$981$		0			0
$982$	51.1542	−	51.1542i	1.63240	−	1.63240i
$983$	−26.6802	+	26.6802i	−0.850968	+	0.850968i	−0.990252	−	0.139285i	$-0.955520\pi$
$983$	−26.6802	+	26.6802i	−0.850968	+	0.850968i	0.139285	+	0.990252i	$0.455520\pi$
$984$		0			0
$985$		0			0
$986$		−	70.8911i		−	2.25763i
$987$		0			0
$988$	−17.9801	−	17.9801i	−0.572025	−	0.572025i
$989$	28.4267			0.903918
$990$		0			0
$991$	44.0522			1.39936			0.699682	−	0.714454i	$-0.253325\pi$
$991$	44.0522			1.39936			0.699682	+	0.714454i	$0.253325\pi$
$992$	−10.8299	−	10.8299i	−0.343849	−	0.343849i
$993$		0			0
$994$		−	17.6860i		−	0.560965i
$995$		0			0
$996$		0			0
$997$	−33.6548	+	33.6548i	−1.06586	+	1.06586i	−0.0681847	+	0.997673i	$0.521721\pi$
$997$	−33.6548	+	33.6548i	−1.06586	+	1.06586i	−0.997673	+	0.0681847i	$0.978279\pi$
$998$	26.9354	−	26.9354i	0.852624	−	0.852624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.m.d.1268.5		12
3.2	odd	2		1575.2.m.c.1268.2		12
5.2	odd	4		1575.2.m.c.1457.2		12
5.3	odd	4		315.2.m.a.197.5	yes	12
5.4	even	2		315.2.m.b.8.2	yes	12
15.2	even	4	inner	1575.2.m.d.1457.5		12
15.8	even	4		315.2.m.b.197.2	yes	12
15.14	odd	2		315.2.m.a.8.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.5	✓	12	15.14	odd	2
315.2.m.a.197.5	yes	12	5.3	odd	4
315.2.m.b.8.2	yes	12	5.4	even	2
315.2.m.b.197.2	yes	12	15.8	even	4
1575.2.m.c.1268.2		12	3.2	odd	2
1575.2.m.c.1457.2		12	5.2	odd	4
1575.2.m.d.1268.5		12	1.1	even	1	trivial
1575.2.m.d.1457.5		12	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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28118 + 1.28118i) q^{2} +1.28283i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.918816 - 0.918816i) q^{8} +O(q^{10})\)	\(q+(1.28118 + 1.28118i) q^{2} +1.28283i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.918816 - 0.918816i) q^{8} -4.14225i q^{11} +(-4.57421 - 4.57421i) q^{13} -1.81186 q^{14} +4.92000 q^{16} +(-5.27126 - 5.27126i) q^{17} -3.06412i q^{19} +(5.30696 - 5.30696i) q^{22} +(-3.82371 + 3.82371i) q^{23} -11.7208i q^{26} +(-0.907101 - 0.907101i) q^{28} +5.24853 q^{29} -2.42509 q^{31} +(4.46577 + 4.46577i) q^{32} -13.5068i q^{34} +(0.834319 - 0.834319i) q^{37} +(3.92569 - 3.92569i) q^{38} +4.19215i q^{41} +(-3.71717 - 3.71717i) q^{43} +5.31382 q^{44} -9.79772 q^{46} +(3.14814 + 3.14814i) q^{47} -1.00000i q^{49} +(5.86796 - 5.86796i) q^{52} +(-4.79411 + 4.79411i) q^{53} +1.29940i q^{56} +(6.72431 + 6.72431i) q^{58} +1.97629 q^{59} +1.88920 q^{61} +(-3.10697 - 3.10697i) q^{62} +1.60288i q^{64} +(10.7350 - 10.7350i) q^{67} +(6.76215 - 6.76215i) q^{68} +9.76123i q^{71} +(-0.978941 - 0.978941i) q^{73} +2.13782 q^{74} +3.93076 q^{76} +(2.92901 + 2.92901i) q^{77} +4.09428i q^{79} +(-5.37089 + 5.37089i) q^{82} +(3.68028 - 3.68028i) q^{83} -9.52470i q^{86} +(-3.80597 - 3.80597i) q^{88} +7.39217 q^{89} +6.46891 q^{91} +(-4.90519 - 4.90519i) q^{92} +8.06666i q^{94} +(3.07322 - 3.07322i) q^{97} +(1.28118 - 1.28118i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{8}+O(q^{10}) \) 12 * q + 24 * q^8	\( 12 q + 24 q^{8} + 4 q^{13} + 4 q^{14} - 20 q^{16} + 8 q^{17} + 8 q^{22} + 8 q^{23} + 32 q^{29} + 48 q^{32} - 4 q^{37} + 24 q^{38} - 40 q^{43} + 64 q^{44} + 16 q^{46} + 24 q^{47} - 36 q^{52} - 40 q^{53} + 28 q^{58} + 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{67} + 32 q^{68} + 20 q^{73} + 64 q^{74} + 16 q^{76} - 20 q^{82} + 24 q^{83} + 56 q^{89} + 8 q^{92} - 12 q^{97}+O(q^{100}) \) 12 * q + 24 * q^8 + 4 * q^13 + 4 * q^14 - 20 * q^16 + 8 * q^17 + 8 * q^22 + 8 * q^23 + 32 * q^29 + 48 * q^32 - 4 * q^37 + 24 * q^38 - 40 * q^43 + 64 * q^44 + 16 * q^46 + 24 * q^47 - 36 * q^52 - 40 * q^53 + 28 * q^58 + 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^67 + 32 * q^68 + 20 * q^73 + 64 * q^74 + 16 * q^76 - 20 * q^82 + 24 * q^83 + 56 * q^89 + 8 * q^92 - 12 * q^97

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