LMFDB - Embedded newform 1350.2.f.b.107.4

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			107.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.107
Dual form			1350.2.f.b.593.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.896575 - 0.896575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.896575 - 0.896575i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{11} +(-2.12132 + 2.12132i) q^{13} -1.26795 q^{14} -1.00000 q^{16} +(1.55291 - 1.55291i) q^{17} -6.19615i q^{19} +(-2.12132 - 2.12132i) q^{22} +(2.12132 + 2.12132i) q^{23} +3.00000i q^{26} +(-0.896575 + 0.896575i) q^{28} -8.19615 q^{29} -2.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} -2.19615i q^{34} +(-7.02030 - 7.02030i) q^{37} +(-4.38134 - 4.38134i) q^{38} -6.00000i q^{41} +(-7.58871 + 7.58871i) q^{43} -3.00000 q^{44} +3.00000 q^{46} +(6.36396 - 6.36396i) q^{47} -5.39230i q^{49} +(2.12132 + 2.12132i) q^{52} +(1.55291 + 1.55291i) q^{53} +1.26795i q^{56} +(-5.79555 + 5.79555i) q^{58} +13.3923 q^{59} -9.19615 q^{61} +(-1.41421 + 1.41421i) q^{62} +1.00000i q^{64} +(1.55291 + 1.55291i) q^{67} +(-1.55291 - 1.55291i) q^{68} -0.803848i q^{71} +(-6.03579 + 6.03579i) q^{73} -9.92820 q^{74} -6.19615 q^{76} +(-2.68973 + 2.68973i) q^{77} -10.1962i q^{79} +(-4.24264 - 4.24264i) q^{82} +(3.10583 + 3.10583i) q^{83} +10.7321i q^{86} +(-2.12132 + 2.12132i) q^{88} +8.19615 q^{89} +3.80385 q^{91} +(2.12132 - 2.12132i) q^{92} -9.00000i q^{94} +(1.88108 + 1.88108i) q^{97} +(-3.81294 - 3.81294i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−0.896575	−	0.896575i	−0.338874	−	0.338874i	0.517070	−	0.855943i	$-0.327023\pi$
$7$	−0.896575	−	0.896575i	−0.338874	−	0.338874i	−0.855943	+	0.517070i	$0.827023\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$		−	3.00000i		−	0.904534i	−0.891883	−	0.452267i	$-0.850615\pi$
$11$		−	3.00000i		−	0.904534i	0.891883	−	0.452267i	$-0.149385\pi$
$12$		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	$0.386577\pi$
$14$	−1.26795			−0.338874
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.55291	−	1.55291i	0.376637	−	0.376637i	−0.493250	−	0.869887i	$-0.664191\pi$
$17$	1.55291	−	1.55291i	0.376637	−	0.376637i	0.869887	+	0.493250i	$0.164191\pi$
$18$		0			0
$19$		−	6.19615i		−	1.42149i	−0.703447	−	0.710747i	$-0.748357\pi$
$19$		−	6.19615i		−	1.42149i	0.703447	−	0.710747i	$-0.251643\pi$
$20$		0			0
$21$		0			0
$22$	−2.12132	−	2.12132i	−0.452267	−	0.452267i
$23$	2.12132	+	2.12132i	0.442326	+	0.442326i	0.892793	−	0.450467i	$-0.148743\pi$
$23$	2.12132	+	2.12132i	0.442326	+	0.442326i	−0.450467	+	0.892793i	$0.648743\pi$
$24$		0			0
$25$		0			0
$26$			3.00000i			0.588348i
$27$		0			0
$28$	−0.896575	+	0.896575i	−0.169437	+	0.169437i
$29$	−8.19615			−1.52199			−0.760994	−	0.648759i	$-0.775288\pi$
$29$	−8.19615			−1.52199			−0.760994	+	0.648759i	$0.775288\pi$
$30$		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
$34$		−	2.19615i		−	0.376637i
$35$		0			0
$36$		0			0
$37$	−7.02030	−	7.02030i	−1.15413	−	1.15413i	−0.985716	−	0.168414i	$-0.946136\pi$
$37$	−7.02030	−	7.02030i	−1.15413	−	1.15413i	−0.168414	−	0.985716i	$-0.553864\pi$
$38$	−4.38134	−	4.38134i	−0.710747	−	0.710747i
$39$		0			0
$40$		0			0
$41$		−	6.00000i		−	0.937043i	−0.883452	−	0.468521i	$-0.844787\pi$
$41$		−	6.00000i		−	0.937043i	0.883452	−	0.468521i	$-0.155213\pi$
$42$		0			0
$43$	−7.58871	+	7.58871i	−1.15727	+	1.15727i	−0.172206	+	0.985061i	$0.555089\pi$
$43$	−7.58871	+	7.58871i	−1.15727	+	1.15727i	−0.985061	+	0.172206i	$0.944911\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	3.00000			0.442326
$47$	6.36396	−	6.36396i	0.928279	−	0.928279i	−0.0693157	−	0.997595i	$-0.522082\pi$
$47$	6.36396	−	6.36396i	0.928279	−	0.928279i	0.997595	+	0.0693157i	$0.0220816\pi$
$48$		0			0
$49$		−	5.39230i		−	0.770329i
$50$		0			0
$51$		0			0
$52$	2.12132	+	2.12132i	0.294174	+	0.294174i
$53$	1.55291	+	1.55291i	0.213309	+	0.213309i	0.805672	−	0.592362i	$-0.201805\pi$
$53$	1.55291	+	1.55291i	0.213309	+	0.213309i	−0.592362	+	0.805672i	$0.701805\pi$
$54$		0			0
$55$		0			0
$56$			1.26795i			0.169437i
$57$		0			0
$58$	−5.79555	+	5.79555i	−0.760994	+	0.760994i
$59$	13.3923			1.74353			0.871765	−	0.489925i	$-0.162976\pi$
$59$	13.3923			1.74353			0.871765	+	0.489925i	$0.162976\pi$
$60$		0			0
$61$	−9.19615			−1.17745			−0.588723	−	0.808335i	$-0.700369\pi$
$61$	−9.19615			−1.17745			−0.588723	+	0.808335i	$0.700369\pi$
$62$	−1.41421	+	1.41421i	−0.179605	+	0.179605i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	1.55291	+	1.55291i	0.189719	+	0.189719i	0.795574	−	0.605856i	$-0.207169\pi$
$67$	1.55291	+	1.55291i	0.189719	+	0.189719i	−0.605856	+	0.795574i	$0.707169\pi$
$68$	−1.55291	−	1.55291i	−0.188319	−	0.188319i
$69$		0			0
$70$		0			0
$71$		−	0.803848i		−	0.0953992i	−0.998862	−	0.0476996i	$-0.984811\pi$
$71$		−	0.803848i		−	0.0953992i	0.998862	−	0.0476996i	$-0.0151890\pi$
$72$		0			0
$73$	−6.03579	+	6.03579i	−0.706436	+	0.706436i	−0.965784	−	0.259348i	$-0.916492\pi$
$73$	−6.03579	+	6.03579i	−0.706436	+	0.706436i	0.259348	+	0.965784i	$0.416492\pi$
$74$	−9.92820			−1.15413
$75$		0			0
$76$	−6.19615			−0.710747
$77$	−2.68973	+	2.68973i	−0.306523	+	0.306523i
$78$		0			0
$79$		−	10.1962i		−	1.14716i	−0.819151	−	0.573578i	$-0.805555\pi$
$79$		−	10.1962i		−	1.14716i	0.819151	−	0.573578i	$-0.194445\pi$
$80$		0			0
$81$		0			0
$82$	−4.24264	−	4.24264i	−0.468521	−	0.468521i
$83$	3.10583	+	3.10583i	0.340909	+	0.340909i	0.856709	−	0.515800i	$-0.172505\pi$
$83$	3.10583	+	3.10583i	0.340909	+	0.340909i	−0.515800	+	0.856709i	$0.672505\pi$
$84$		0			0
$85$		0			0
$86$			10.7321i			1.15727i
$87$		0			0
$88$	−2.12132	+	2.12132i	−0.226134	+	0.226134i
$89$	8.19615			0.868790			0.434395	−	0.900722i	$-0.356962\pi$
$89$	8.19615			0.868790			0.434395	+	0.900722i	$0.356962\pi$
$90$		0			0
$91$	3.80385			0.398752
$92$	2.12132	−	2.12132i	0.221163	−	0.221163i
$93$		0			0
$94$		−	9.00000i		−	0.928279i
$95$		0			0
$96$		0			0
$97$	1.88108	+	1.88108i	0.190995	+	0.190995i	0.796126	−	0.605131i	$-0.206879\pi$
$97$	1.88108	+	1.88108i	0.190995	+	0.190995i	−0.605131	+	0.796126i	$0.706879\pi$
$98$	−3.81294	−	3.81294i	−0.385165	−	0.385165i
$99$		0			0
$100$		0			0
$101$		−	18.5885i		−	1.84962i	−0.380429	−	0.924810i	$-0.624224\pi$
$101$		−	18.5885i		−	1.84962i	0.380429	−	0.924810i	$-0.375776\pi$
$102$		0			0
$103$	0.656339	−	0.656339i	0.0646710	−	0.0646710i	−0.674032	−	0.738703i	$-0.735439\pi$
$103$	0.656339	−	0.656339i	0.0646710	−	0.0646710i	0.738703	+	0.674032i	$0.235439\pi$
$104$	3.00000			0.294174
$105$		0			0
$106$	2.19615			0.213309
$107$	−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
$112$	0.896575	+	0.896575i	0.0847184	+	0.0847184i
$113$	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
$116$			8.19615i			0.760994i
$117$		0			0
$118$	9.46979	−	9.46979i	0.871765	−	0.871765i
$119$	−2.78461			−0.255265
$120$		0			0
$121$	2.00000			0.181818
$122$	−6.50266	+	6.50266i	−0.588723	+	0.588723i
$123$		0			0
$124$			2.00000i			0.179605i
$125$		0			0
$126$		0			0
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	0.301420	−	0.953491i	$-0.402539\pi$
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	−0.953491	+	0.301420i	$0.902539\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$			13.3923i			1.17009i	0.811000	+	0.585046i	$0.198923\pi$
$131$			13.3923i			1.17009i	−0.811000	+	0.585046i	$0.801077\pi$
$132$		0			0
$133$	−5.55532	+	5.55532i	−0.481707	+	0.481707i
$134$	2.19615			0.189719
$135$		0			0
$136$	−2.19615			−0.188319
$137$	14.2808	−	14.2808i	1.22009	−	1.22009i	0.252496	−	0.967598i	$-0.418748\pi$
$137$	14.2808	−	14.2808i	1.22009	−	1.22009i	0.967598	−	0.252496i	$-0.0812516\pi$
$138$		0			0
$139$			16.1962i			1.37374i	0.726780	+	0.686870i	$0.241016\pi$
$139$			16.1962i			1.37374i	−0.726780	+	0.686870i	$0.758984\pi$
$140$		0			0
$141$		0			0
$142$	−0.568406	−	0.568406i	−0.0476996	−	0.0476996i
$143$	6.36396	+	6.36396i	0.532181	+	0.532181i
$144$		0			0
$145$		0			0
$146$			8.53590i			0.706436i
$147$		0			0
$148$	−7.02030	+	7.02030i	−0.577065	+	0.577065i
$149$	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
$151$	0.196152			0.0159627			0.00798133	−	0.999968i	$-0.497459\pi$
$151$	0.196152			0.0159627			0.00798133	+	0.999968i	$0.497459\pi$
$152$	−4.38134	+	4.38134i	−0.355374	+	0.355374i
$153$		0			0
$154$			3.80385i			0.306523i
$155$		0			0
$156$		0			0
$157$	4.89898	+	4.89898i	0.390981	+	0.390981i	0.875037	−	0.484056i	$-0.160837\pi$
$157$	4.89898	+	4.89898i	0.390981	+	0.390981i	−0.484056	+	0.875037i	$0.660837\pi$
$158$	−7.20977	−	7.20977i	−0.573578	−	0.573578i
$159$		0			0
$160$		0			0
$161$		−	3.80385i		−	0.299785i
$162$		0			0
$163$	1.13681	−	1.13681i	0.0890420	−	0.0890420i	−0.661183	−	0.750225i	$-0.729945\pi$
$163$	1.13681	−	1.13681i	0.0890420	−	0.0890420i	0.750225	+	0.661183i	$0.229945\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	4.39230			0.340909
$167$	−17.9551	+	17.9551i	−1.38941	+	1.38941i	−0.562838	+	0.826567i	$0.690290\pi$
$167$	−17.9551	+	17.9551i	−1.38941	+	1.38941i	−0.826567	+	0.562838i	$0.809710\pi$
$168$		0			0
$169$			4.00000i			0.307692i
$170$		0			0
$171$		0			0
$172$	7.58871	+	7.58871i	0.578633	+	0.578633i
$173$	−5.79555	−	5.79555i	−0.440628	−	0.440628i	0.451595	−	0.892223i	$-0.350855\pi$
$173$	−5.79555	−	5.79555i	−0.440628	−	0.440628i	−0.892223	+	0.451595i	$0.850855\pi$
$174$		0			0
$175$		0			0
$176$			3.00000i			0.226134i
$177$		0			0
$178$	5.79555	−	5.79555i	0.434395	−	0.434395i
$179$	25.3923			1.89791			0.948955	−	0.315412i	$-0.102143\pi$
$179$	25.3923			1.89791			0.948955	+	0.315412i	$0.102143\pi$
$180$		0			0
$181$	13.5885			1.01002			0.505011	−	0.863113i	$-0.331488\pi$
$181$	13.5885			1.01002			0.505011	+	0.863113i	$0.331488\pi$
$182$	2.68973	−	2.68973i	0.199376	−	0.199376i
$183$		0			0
$184$		−	3.00000i		−	0.221163i
$185$		0			0
$186$		0			0
$187$	−4.65874	−	4.65874i	−0.340681	−	0.340681i
$188$	−6.36396	−	6.36396i	−0.464140	−	0.464140i
$189$		0			0
$190$		0			0
$191$		−	4.39230i		−	0.317816i	−0.987293	−	0.158908i	$-0.949203\pi$
$191$		−	4.39230i		−	0.317816i	0.987293	−	0.158908i	$-0.0507973\pi$
$192$		0			0
$193$	18.2832	−	18.2832i	1.31606	−	1.31606i	0.399187	−	0.916870i	$-0.369292\pi$
$193$	18.2832	−	18.2832i	1.31606	−	1.31606i	0.916870	−	0.399187i	$-0.130708\pi$
$194$	2.66025			0.190995
$195$		0			0
$196$	−5.39230			−0.385165
$197$	3.10583	−	3.10583i	0.221281	−	0.221281i	−0.587757	−	0.809038i	$-0.699989\pi$
$197$	3.10583	−	3.10583i	0.221281	−	0.221281i	0.809038	+	0.587757i	$0.199989\pi$
$198$		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
$202$	−13.1440	−	13.1440i	−0.924810	−	0.924810i
$203$	7.34847	+	7.34847i	0.515761	+	0.515761i
$204$		0			0
$205$		0			0
$206$		−	0.928203i		−	0.0646710i
$207$		0			0
$208$	2.12132	−	2.12132i	0.147087	−	0.147087i
$209$	−18.5885			−1.28579
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	1.55291	−	1.55291i	0.106655	−	0.106655i
$213$		0			0
$214$			15.5885i			1.06561i
$215$		0			0
$216$		0			0
$217$	1.79315	+	1.79315i	0.121727	+	0.121727i
$218$	−5.65685	−	5.65685i	−0.383131	−	0.383131i
$219$		0			0
$220$		0			0
$221$			6.58846i			0.443188i
$222$		0			0
$223$	14.9372	−	14.9372i	1.00027	−	1.00027i	0.000267267	−	1.00000i	$-0.499915\pi$
$223$	14.9372	−	14.9372i	1.00027	−	1.00027i	1.00000		0.000267267i	$-8.50736e-5\pi$
$224$	1.26795			0.0847184
$225$		0			0
$226$	10.3923			0.691286
$227$	4.81105	−	4.81105i	0.319320	−	0.319320i	−0.529186	−	0.848506i	$-0.677503\pi$
$227$	4.81105	−	4.81105i	0.319320	−	0.319320i	0.848506	+	0.529186i	$0.177503\pi$
$228$		0			0
$229$			17.5885i			1.16228i	0.813804	+	0.581139i	$0.197393\pi$
$229$			17.5885i			1.16228i	−0.813804	+	0.581139i	$0.802607\pi$
$230$		0			0
$231$		0			0
$232$	5.79555	+	5.79555i	0.380497	+	0.380497i
$233$	10.0382	+	10.0382i	0.657624	+	0.657624i	0.954817	−	0.297193i	$-0.0960506\pi$
$233$	10.0382	+	10.0382i	0.657624	+	0.657624i	−0.297193	+	0.954817i	$0.596051\pi$
$234$		0			0
$235$		0			0
$236$		−	13.3923i		−	0.871765i
$237$		0			0
$238$	−1.96902	+	1.96902i	−0.127632	+	0.127632i
$239$	12.8038			0.828212			0.414106	−	0.910229i	$-0.364094\pi$
$239$	12.8038			0.828212			0.414106	+	0.910229i	$0.364094\pi$
$240$		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
$244$			9.19615i			0.588723i
$245$		0			0
$246$		0			0
$247$	13.1440	+	13.1440i	0.836334	+	0.836334i
$248$	1.41421	+	1.41421i	0.0898027	+	0.0898027i
$249$		0			0
$250$		0			0
$251$		−	1.39230i		−	0.0878815i	−0.999034	−	0.0439408i	$-0.986009\pi$
$251$		−	1.39230i		−	0.0878815i	0.999034	−	0.0439408i	$-0.0139913\pi$
$252$		0			0
$253$	6.36396	−	6.36396i	0.400099	−	0.400099i
$254$	−10.3923			−0.652071
$255$		0			0
$256$	1.00000			0.0625000
$257$	1.55291	−	1.55291i	0.0968681	−	0.0968681i	−0.657012	−	0.753880i	$-0.728180\pi$
$257$	1.55291	−	1.55291i	0.0968681	−	0.0968681i	0.753880	+	0.657012i	$0.228180\pi$
$258$		0			0
$259$			12.5885i			0.782209i
$260$		0			0
$261$		0			0
$262$	9.46979	+	9.46979i	0.585046	+	0.585046i
$263$	6.36396	+	6.36396i	0.392419	+	0.392419i	0.875549	−	0.483130i	$-0.160500\pi$
$263$	6.36396	+	6.36396i	0.392419	+	0.392419i	−0.483130	+	0.875549i	$0.660500\pi$
$264$		0			0
$265$		0			0
$266$			7.85641i			0.481707i
$267$		0			0
$268$	1.55291	−	1.55291i	0.0948593	−	0.0948593i
$269$	−24.0000			−1.46331			−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000			−1.46331			−0.731653	+	0.681677i	$0.761251\pi$
$270$		0			0
$271$	−20.3923			−1.23874			−0.619372	−	0.785098i	$-0.712613\pi$
$271$	−20.3923			−1.23874			−0.619372	+	0.785098i	$0.712613\pi$
$272$	−1.55291	+	1.55291i	−0.0941593	+	0.0941593i
$273$		0			0
$274$		−	20.1962i		−	1.22009i
$275$		0			0
$276$		0			0
$277$	15.1774	+	15.1774i	0.911922	+	0.911922i	0.996423	−	0.0845011i	$-0.0269296\pi$
$277$	15.1774	+	15.1774i	0.911922	+	0.911922i	−0.0845011	+	0.996423i	$0.526930\pi$
$278$	11.4524	+	11.4524i	0.686870	+	0.686870i
$279$		0			0
$280$		0			0
$281$		−	21.8038i		−	1.30071i	−0.759631	−	0.650354i	$-0.774620\pi$
$281$		−	21.8038i		−	1.30071i	0.759631	−	0.650354i	$-0.225380\pi$
$282$		0			0
$283$	7.58871	−	7.58871i	0.451102	−	0.451102i	−0.444618	−	0.895720i	$-0.646661\pi$
$283$	7.58871	−	7.58871i	0.451102	−	0.451102i	0.895720	+	0.444618i	$0.146661\pi$
$284$	−0.803848			−0.0476996
$285$		0			0
$286$	9.00000			0.532181
$287$	−5.37945	+	5.37945i	−0.317539	+	0.317539i
$288$		0			0
$289$			12.1769i			0.716289i
$290$		0			0
$291$		0			0
$292$	6.03579	+	6.03579i	0.353218	+	0.353218i
$293$	−20.4925	−	20.4925i	−1.19718	−	1.19718i	−0.975006	−	0.222178i	$-0.928683\pi$
$293$	−20.4925	−	20.4925i	−1.19718	−	1.19718i	−0.222178	−	0.975006i	$-0.571317\pi$
$294$		0			0
$295$		0			0
$296$			9.92820i			0.577065i
$297$		0			0
$298$	7.34847	−	7.34847i	0.425685	−	0.425685i
$299$	−9.00000			−0.520483
$300$		0			0
$301$	13.6077			0.784335
$302$	0.138701	−	0.138701i	0.00798133	−	0.00798133i
$303$		0			0
$304$			6.19615i			0.355374i
$305$		0			0
$306$		0			0
$307$	12.2474	+	12.2474i	0.698999	+	0.698999i	0.964195	−	0.265196i	$-0.0854366\pi$
$307$	12.2474	+	12.2474i	0.698999	+	0.698999i	−0.265196	+	0.964195i	$0.585437\pi$
$308$	2.68973	+	2.68973i	0.153261	+	0.153261i
$309$		0			0
$310$		0			0
$311$			0.803848i			0.0455820i	0.999740	+	0.0227910i	$0.00725523\pi$
$311$			0.803848i			0.0455820i	−0.999740	+	0.0227910i	$0.992745\pi$
$312$		0			0
$313$	1.13681	−	1.13681i	0.0642564	−	0.0642564i	−0.674248	−	0.738505i	$-0.735532\pi$
$313$	1.13681	−	1.13681i	0.0642564	−	0.0642564i	0.738505	+	0.674248i	$0.235532\pi$
$314$	6.92820			0.390981
$315$		0			0
$316$	−10.1962			−0.573578
$317$	18.5235	−	18.5235i	1.04038	−	1.04038i	0.0412325	−	0.999150i	$-0.486872\pi$
$317$	18.5235	−	18.5235i	1.04038	−	1.04038i	0.999150	−	0.0412325i	$-0.0131284\pi$
$318$		0			0
$319$			24.5885i			1.37669i
$320$		0			0
$321$		0			0
$322$	−2.68973	−	2.68973i	−0.149893	−	0.149893i
$323$	−9.62209	−	9.62209i	−0.535388	−	0.535388i
$324$		0			0
$325$		0			0
$326$		−	1.60770i		−	0.0890420i
$327$		0			0
$328$	−4.24264	+	4.24264i	−0.234261	+	0.234261i
$329$	−11.4115			−0.629139
$330$		0			0
$331$	34.7846			1.91194			0.955968	−	0.293472i	$-0.0948109\pi$
$331$	34.7846			1.91194			0.955968	+	0.293472i	$0.0948109\pi$
$332$	3.10583	−	3.10583i	0.170454	−	0.170454i
$333$		0			0
$334$			25.3923i			1.38941i
$335$		0			0
$336$		0			0
$337$	1.13681	+	1.13681i	0.0619261	+	0.0619261i	0.737392	−	0.675465i	$-0.236057\pi$
$337$	1.13681	+	1.13681i	0.0619261	+	0.0619261i	−0.675465	+	0.737392i	$0.736057\pi$
$338$	2.82843	+	2.82843i	0.153846	+	0.153846i
$339$		0			0
$340$		0			0
$341$			6.00000i			0.324918i
$342$		0			0
$343$	−11.1106	+	11.1106i	−0.599918	+	0.599918i
$344$	10.7321			0.578633
$345$		0			0
$346$	−8.19615			−0.440628
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$		0			0
$349$		−	14.3923i		−	0.770402i	−0.922833	−	0.385201i	$-0.874132\pi$
$349$		−	14.3923i		−	0.770402i	0.922833	−	0.385201i	$-0.125868\pi$
$350$		0			0
$351$		0			0
$352$	2.12132	+	2.12132i	0.113067	+	0.113067i
$353$	−2.68973	−	2.68973i	−0.143160	−	0.143160i	0.631895	−	0.775054i	$-0.282278\pi$
$353$	−2.68973	−	2.68973i	−0.143160	−	0.143160i	−0.775054	+	0.631895i	$0.782278\pi$
$354$		0			0
$355$		0			0
$356$		−	8.19615i		−	0.434395i
$357$		0			0
$358$	17.9551	−	17.9551i	0.948955	−	0.948955i
$359$	11.1962			0.590910			0.295455	−	0.955357i	$-0.404529\pi$
$359$	11.1962			0.590910			0.295455	+	0.955357i	$0.404529\pi$
$360$		0			0
$361$	−19.3923			−1.02065
$362$	9.60849	−	9.60849i	0.505011	−	0.505011i
$363$		0			0
$364$		−	3.80385i		−	0.199376i
$365$		0			0
$366$		0			0
$367$	−6.21166	−	6.21166i	−0.324246	−	0.324246i	0.526147	−	0.850393i	$-0.323636\pi$
$367$	−6.21166	−	6.21166i	−0.324246	−	0.324246i	−0.850393	+	0.526147i	$0.823636\pi$
$368$	−2.12132	−	2.12132i	−0.110581	−	0.110581i
$369$		0			0
$370$		0			0
$371$		−	2.78461i		−	0.144570i
$372$		0			0
$373$	23.8386	−	23.8386i	1.23431	−	1.23431i	0.272023	−	0.962291i	$-0.412307\pi$
$373$	23.8386	−	23.8386i	1.23431	−	1.23431i	0.962291	−	0.272023i	$-0.0876927\pi$
$374$	−6.58846			−0.340681
$375$		0			0
$376$	−9.00000			−0.464140
$377$	17.3867	−	17.3867i	0.895459	−	0.895459i
$378$		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
$382$	−3.10583	−	3.10583i	−0.158908	−	0.158908i
$383$	−2.12132	−	2.12132i	−0.108394	−	0.108394i	0.650830	−	0.759224i	$-0.274421\pi$
$383$	−2.12132	−	2.12132i	−0.108394	−	0.108394i	−0.759224	+	0.650830i	$0.774421\pi$
$384$		0			0
$385$		0			0
$386$		−	25.8564i		−	1.31606i
$387$		0			0
$388$	1.88108	−	1.88108i	0.0954976	−	0.0954976i
$389$	−32.1962			−1.63241			−0.816205	−	0.577763i	$-0.803926\pi$
$389$	−32.1962			−1.63241			−0.816205	+	0.577763i	$0.803926\pi$
$390$		0			0
$391$	6.58846			0.333193
$392$	−3.81294	+	3.81294i	−0.192582	+	0.192582i
$393$		0			0
$394$		−	4.39230i		−	0.221281i
$395$		0			0
$396$		0			0
$397$	1.46498	+	1.46498i	0.0735253	+	0.0735253i	0.742913	−	0.669388i	$-0.233444\pi$
$397$	1.46498	+	1.46498i	0.0735253	+	0.0735253i	−0.669388	+	0.742913i	$0.733444\pi$
$398$	−1.41421	−	1.41421i	−0.0708881	−	0.0708881i
$399$		0			0
$400$		0			0
$401$		−	3.80385i		−	0.189955i	−0.995479	−	0.0949775i	$-0.969722\pi$
$401$		−	3.80385i		−	0.189955i	0.995479	−	0.0949775i	$-0.0302779\pi$
$402$		0			0
$403$	4.24264	−	4.24264i	0.211341	−	0.211341i
$404$	−18.5885			−0.924810
$405$		0			0
$406$	10.3923			0.515761
$407$	−21.0609	+	21.0609i	−1.04395	+	1.04395i
$408$		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
$412$	−0.656339	−	0.656339i	−0.0323355	−	0.0323355i
$413$	−12.0072	−	12.0072i	−0.590836	−	0.590836i
$414$		0			0
$415$		0			0
$416$		−	3.00000i		−	0.147087i
$417$		0			0
$418$	−13.1440	+	13.1440i	−0.642895	+	0.642895i
$419$	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
$421$	−19.1962			−0.935563			−0.467782	−	0.883844i	$-0.654947\pi$
$421$	−19.1962			−0.935563			−0.467782	+	0.883844i	$0.654947\pi$
$422$	−2.82843	+	2.82843i	−0.137686	+	0.137686i
$423$		0			0
$424$		−	2.19615i		−	0.106655i
$425$		0			0
$426$		0			0
$427$	8.24504	+	8.24504i	0.399006	+	0.399006i
$428$	11.0227	+	11.0227i	0.532803	+	0.532803i
$429$		0			0
$430$		0			0
$431$			27.5885i			1.32889i	0.747338	+	0.664445i	$0.231332\pi$
$431$			27.5885i			1.32889i	−0.747338	+	0.664445i	$0.768668\pi$
$432$		0			0
$433$	−13.4722	+	13.4722i	−0.647432	+	0.647432i	−0.952372	−	0.304939i	$-0.901364\pi$
$433$	−13.4722	+	13.4722i	−0.647432	+	0.647432i	0.304939	+	0.952372i	$0.401364\pi$
$434$	2.53590			0.121727
$435$		0			0
$436$	−8.00000			−0.383131
$437$	13.1440	−	13.1440i	0.628764	−	0.628764i
$438$		0			0
$439$			10.5885i			0.505359i	0.967550	+	0.252680i	$0.0813119\pi$
$439$			10.5885i			0.505359i	−0.967550	+	0.252680i	$0.918688\pi$
$440$		0			0
$441$		0			0
$442$	4.65874	+	4.65874i	0.221594	+	0.221594i
$443$	−19.5080	−	19.5080i	−0.926852	−	0.926852i	0.0706489	−	0.997501i	$-0.477493\pi$
$443$	−19.5080	−	19.5080i	−0.926852	−	0.926852i	−0.997501	+	0.0706489i	$0.977493\pi$
$444$		0			0
$445$		0			0
$446$		−	21.1244i		−	1.00027i
$447$		0			0
$448$	0.896575	−	0.896575i	0.0423592	−	0.0423592i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$	7.34847	−	7.34847i	0.345643	−	0.345643i
$453$		0			0
$454$		−	6.80385i		−	0.319320i
$455$		0			0
$456$		0			0
$457$	−16.4022	−	16.4022i	−0.767261	−	0.767261i	0.210363	−	0.977623i	$-0.432535\pi$
$457$	−16.4022	−	16.4022i	−0.767261	−	0.767261i	−0.977623	+	0.210363i	$0.932535\pi$
$458$	12.4369	+	12.4369i	0.581139	+	0.581139i
$459$		0			0
$460$		0			0
$461$			32.7846i			1.52693i	0.645848	+	0.763466i	$0.276504\pi$
$461$			32.7846i			1.52693i	−0.645848	+	0.763466i	$0.723496\pi$
$462$		0			0
$463$	11.3509	−	11.3509i	0.527520	−	0.527520i	−0.392312	−	0.919832i	$-0.628325\pi$
$463$	11.3509	−	11.3509i	0.527520	−	0.527520i	0.919832	+	0.392312i	$0.128325\pi$
$464$	8.19615			0.380497
$465$		0			0
$466$	14.1962			0.657624
$467$	−9.88589	+	9.88589i	−0.457465	+	0.457465i	−0.897822	−	0.440358i	$-0.854852\pi$
$467$	−9.88589	+	9.88589i	−0.457465	+	0.457465i	0.440358	+	0.897822i	$0.354852\pi$
$468$		0			0
$469$		−	2.78461i		−	0.128581i
$470$		0			0
$471$		0			0
$472$	−9.46979	−	9.46979i	−0.435882	−	0.435882i
$473$	22.7661	+	22.7661i	1.04679	+	1.04679i
$474$		0			0
$475$		0			0
$476$			2.78461i			0.127632i
$477$		0			0
$478$	9.05369	−	9.05369i	0.414106	−	0.414106i
$479$	22.3923			1.02313			0.511565	−	0.859244i	$-0.329066\pi$
$479$	22.3923			1.02313			0.511565	+	0.859244i	$0.329066\pi$
$480$		0			0
$481$	29.7846			1.35806
$482$	−0.707107	+	0.707107i	−0.0322078	+	0.0322078i
$483$		0			0
$484$		−	2.00000i		−	0.0909091i
$485$		0			0
$486$		0			0
$487$	8.90138	+	8.90138i	0.403360	+	0.403360i	0.879415	−	0.476055i	$-0.157934\pi$
$487$	8.90138	+	8.90138i	0.403360	+	0.403360i	−0.476055	+	0.879415i	$0.657934\pi$
$488$	6.50266	+	6.50266i	0.294362	+	0.294362i
$489$		0			0
$490$		0			0
$491$			1.60770i			0.0725543i	0.999342	+	0.0362771i	$0.0115499\pi$
$491$			1.60770i			0.0725543i	−0.999342	+	0.0362771i	$0.988450\pi$
$492$		0			0
$493$	−12.7279	+	12.7279i	−0.573237	+	0.573237i
$494$	18.5885			0.836334
$495$		0			0
$496$	2.00000			0.0898027
$497$	−0.720710	+	0.720710i	−0.0323283	+	0.0323283i
$498$		0			0
$499$		−	33.1769i		−	1.48520i	−0.669734	−	0.742601i	$-0.733592\pi$
$499$		−	33.1769i		−	1.48520i	0.669734	−	0.742601i	$-0.266408\pi$
$500$		0			0
$501$		0			0
$502$	−0.984508	−	0.984508i	−0.0439408	−	0.0439408i
$503$	1.13681	+	1.13681i	0.0506879	+	0.0506879i	0.731996	−	0.681308i	$-0.238589\pi$
$503$	1.13681	+	1.13681i	0.0506879	+	0.0506879i	−0.681308	+	0.731996i	$0.738589\pi$
$504$		0			0
$505$		0			0
$506$		−	9.00000i		−	0.400099i
$507$		0			0
$508$	−7.34847	+	7.34847i	−0.326036	+	0.326036i
$509$	−38.7846			−1.71910			−0.859549	−	0.511054i	$-0.829255\pi$
$509$	−38.7846			−1.71910			−0.859549	+	0.511054i	$0.829255\pi$
$510$		0			0
$511$	10.8231			0.478785
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	2.19615i		−	0.0968681i
$515$		0			0
$516$		0			0
$517$	−19.0919	−	19.0919i	−0.839660	−	0.839660i
$518$	8.90138	+	8.90138i	0.391104	+	0.391104i
$519$		0			0
$520$		0			0
$521$		−	32.1962i		−	1.41054i	−0.708939	−	0.705270i	$-0.750826\pi$
$521$		−	32.1962i		−	1.41054i	0.708939	−	0.705270i	$-0.249174\pi$
$522$		0			0
$523$	−3.58630	+	3.58630i	−0.156818	+	0.156818i	−0.781155	−	0.624337i	$-0.785369\pi$
$523$	−3.58630	+	3.58630i	−0.156818	+	0.156818i	0.624337	+	0.781155i	$0.285369\pi$
$524$	13.3923			0.585046
$525$		0			0
$526$	9.00000			0.392419
$527$	−3.10583	+	3.10583i	−0.135292	+	0.135292i
$528$		0			0
$529$		−	14.0000i		−	0.608696i
$530$		0			0
$531$		0			0
$532$	5.55532	+	5.55532i	0.240854	+	0.240854i
$533$	12.7279	+	12.7279i	0.551308	+	0.551308i
$534$		0			0
$535$		0			0
$536$		−	2.19615i		−	0.0948593i
$537$		0			0
$538$	−16.9706	+	16.9706i	−0.731653	+	0.731653i
$539$	−16.1769			−0.696789
$540$		0			0
$541$	15.9808			0.687067			0.343533	−	0.939140i	$-0.388376\pi$
$541$	15.9808			0.687067			0.343533	+	0.939140i	$0.388376\pi$
$542$	−14.4195	+	14.4195i	−0.619372	+	0.619372i
$543$		0			0
$544$			2.19615i			0.0941593i
$545$		0			0
$546$		0			0
$547$	−26.7685	−	26.7685i	−1.14454	−	1.14454i	−0.987610	−	0.156930i	$-0.949840\pi$
$547$	−26.7685	−	26.7685i	−1.14454	−	1.14454i	−0.156930	−	0.987610i	$-0.550160\pi$
$548$	−14.2808	−	14.2808i	−0.610047	−	0.610047i
$549$		0			0
$550$		0			0
$551$			50.7846i			2.16350i
$552$		0			0
$553$	−9.14162	+	9.14162i	−0.388741	+	0.388741i
$554$	21.4641			0.911922
$555$		0			0
$556$	16.1962			0.686870
$557$	−12.0072	+	12.0072i	−0.508762	+	0.508762i	−0.914146	−	0.405384i	$-0.867138\pi$
$557$	−12.0072	+	12.0072i	−0.508762	+	0.508762i	0.405384	+	0.914146i	$0.367138\pi$
$558$		0			0
$559$		−	32.1962i		−	1.36175i
$560$		0			0
$561$		0			0
$562$	−15.4176	−	15.4176i	−0.650354	−	0.650354i
$563$	−16.4022	−	16.4022i	−0.691268	−	0.691268i	0.271243	−	0.962511i	$-0.412565\pi$
$563$	−16.4022	−	16.4022i	−0.691268	−	0.691268i	−0.962511	+	0.271243i	$0.912565\pi$
$564$		0			0
$565$		0			0
$566$		−	10.7321i		−	0.451102i
$567$		0			0
$568$	−0.568406	+	0.568406i	−0.0238498	+	0.0238498i
$569$	22.3923			0.938734			0.469367	−	0.883003i	$-0.344482\pi$
$569$	22.3923			0.938734			0.469367	+	0.883003i	$0.344482\pi$
$570$		0			0
$571$	−18.7846			−0.786111			−0.393056	−	0.919515i	$-0.628582\pi$
$571$	−18.7846			−0.786111			−0.393056	+	0.919515i	$0.628582\pi$
$572$	6.36396	−	6.36396i	0.266091	−	0.266091i
$573$		0			0
$574$			7.60770i			0.317539i
$575$		0			0
$576$		0			0
$577$	1.88108	+	1.88108i	0.0783105	+	0.0783105i	0.745177	−	0.666867i	$-0.232365\pi$
$577$	1.88108	+	1.88108i	0.0783105	+	0.0783105i	−0.666867	+	0.745177i	$0.732365\pi$
$578$	8.61038	+	8.61038i	0.358145	+	0.358145i
$579$		0			0
$580$		0			0
$581$		−	5.56922i		−	0.231050i
$582$		0			0
$583$	4.65874	−	4.65874i	0.192945	−	0.192945i
$584$	8.53590			0.353218
$585$		0			0
$586$	−28.9808			−1.19718
$587$	−15.8338	+	15.8338i	−0.653529	+	0.653529i	−0.953841	−	0.300312i	$-0.902909\pi$
$587$	−15.8338	+	15.8338i	−0.653529	+	0.653529i	0.300312	+	0.953841i	$0.402909\pi$
$588$		0			0
$589$			12.3923i			0.510616i
$590$		0			0
$591$		0			0
$592$	7.02030	+	7.02030i	0.288533	+	0.288533i
$593$	−31.6675	−	31.6675i	−1.30043	−	1.30043i	−0.928102	−	0.372327i	$-0.878560\pi$
$593$	−31.6675	−	31.6675i	−1.30043	−	1.30043i	−0.372327	−	0.928102i	$-0.621440\pi$
$594$		0			0
$595$		0			0
$596$		−	10.3923i		−	0.425685i
$597$		0			0
$598$	−6.36396	+	6.36396i	−0.260242	+	0.260242i
$599$	13.6077			0.555995			0.277998	−	0.960582i	$-0.410329\pi$
$599$	13.6077			0.555995			0.277998	+	0.960582i	$0.410329\pi$
$600$		0			0
$601$	−23.0000			−0.938190			−0.469095	−	0.883148i	$-0.655420\pi$
$601$	−23.0000			−0.938190			−0.469095	+	0.883148i	$0.655420\pi$
$602$	9.62209	−	9.62209i	0.392167	−	0.392167i
$603$		0			0
$604$		−	0.196152i		−	0.00798133i
$605$		0			0
$606$		0			0
$607$	14.0406	+	14.0406i	0.569890	+	0.569890i	0.932098	−	0.362207i	$-0.117977\pi$
$607$	14.0406	+	14.0406i	0.569890	+	0.569890i	−0.362207	+	0.932098i	$0.617977\pi$
$608$	4.38134	+	4.38134i	0.177687	+	0.177687i
$609$		0			0
$610$		0			0
$611$			27.0000i			1.09230i
$612$		0			0
$613$	−13.0561	+	13.0561i	−0.527331	+	0.527331i	−0.919776	−	0.392445i	$-0.871629\pi$
$613$	−13.0561	+	13.0561i	−0.527331	+	0.527331i	0.392445	+	0.919776i	$0.371629\pi$
$614$	17.3205			0.698999
$615$		0			0
$616$	3.80385			0.153261
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	−0.616530	−	0.787332i	$-0.711462\pi$
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	0.787332	+	0.616530i	$0.211462\pi$
$618$		0			0
$619$		−	42.3923i		−	1.70389i	−0.523631	−	0.851945i	$-0.675423\pi$
$619$		−	42.3923i		−	1.70389i	0.523631	−	0.851945i	$-0.324577\pi$
$620$		0			0
$621$		0			0
$622$	0.568406	+	0.568406i	0.0227910	+	0.0227910i
$623$	−7.34847	−	7.34847i	−0.294410	−	0.294410i
$624$		0			0
$625$		0			0
$626$		−	1.60770i		−	0.0642564i
$627$		0			0
$628$	4.89898	−	4.89898i	0.195491	−	0.195491i
$629$	−21.8038			−0.869376
$630$		0			0
$631$	8.58846			0.341901			0.170951	−	0.985280i	$-0.445316\pi$
$631$	8.58846			0.341901			0.170951	+	0.985280i	$0.445316\pi$
$632$	−7.20977	+	7.20977i	−0.286789	+	0.286789i
$633$		0			0
$634$		−	26.1962i		−	1.04038i
$635$		0			0
$636$		0			0
$637$	11.4388	+	11.4388i	0.453222	+	0.453222i
$638$	17.3867	+	17.3867i	0.688345	+	0.688345i
$639$		0			0
$640$		0			0
$641$		−	12.5885i		−	0.497214i	−0.968604	−	0.248607i	$-0.920027\pi$
$641$		−	12.5885i		−	0.497214i	0.968604	−	0.248607i	$-0.0799728\pi$
$642$		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	$0.365494\pi$
$644$	−3.80385			−0.149893
$645$		0			0
$646$	−13.6077			−0.535388
$647$	−5.22715	+	5.22715i	−0.205500	+	0.205500i	−0.802352	−	0.596851i	$-0.796418\pi$
$647$	−5.22715	+	5.22715i	−0.205500	+	0.205500i	0.596851	+	0.802352i	$0.296418\pi$
$648$		0			0
$649$		−	40.1769i		−	1.57708i
$650$		0			0
$651$		0			0
$652$	−1.13681	−	1.13681i	−0.0445210	−	0.0445210i
$653$	−20.4925	−	20.4925i	−0.801933	−	0.801933i	0.181464	−	0.983398i	$-0.441916\pi$
$653$	−20.4925	−	20.4925i	−0.801933	−	0.801933i	−0.983398	+	0.181464i	$0.941916\pi$
$654$		0			0
$655$		0			0
$656$			6.00000i			0.234261i
$657$		0			0
$658$	−8.06918	+	8.06918i	−0.314569	+	0.314569i
$659$	38.7846			1.51083			0.755417	−	0.655244i	$-0.227434\pi$
$659$	38.7846			1.51083			0.755417	+	0.655244i	$0.227434\pi$
$660$		0			0
$661$	−38.3731			−1.49254			−0.746270	−	0.665644i	$-0.768157\pi$
$661$	−38.3731			−1.49254			−0.746270	+	0.665644i	$0.768157\pi$
$662$	24.5964	−	24.5964i	0.955968	−	0.955968i
$663$		0			0
$664$		−	4.39230i		−	0.170454i
$665$		0			0
$666$		0			0
$667$	−17.3867	−	17.3867i	−0.673214	−	0.673214i
$668$	17.9551	+	17.9551i	0.694703	+	0.694703i
$669$		0			0
$670$		0			0
$671$			27.5885i			1.06504i
$672$		0			0
$673$	−24.4070	+	24.4070i	−0.940819	+	0.940819i	−0.998344	−	0.0575247i	$-0.981679\pi$
$673$	−24.4070	+	24.4070i	−0.940819	+	0.940819i	0.0575247	+	0.998344i	$0.481679\pi$
$674$	1.60770			0.0619261
$675$		0			0
$676$	4.00000			0.153846
$677$	−18.1074	+	18.1074i	−0.695923	+	0.695923i	−0.963529	−	0.267606i	$-0.913768\pi$
$677$	−18.1074	+	18.1074i	−0.695923	+	0.695923i	0.267606	+	0.963529i	$0.413768\pi$
$678$		0			0
$679$		−	3.37307i		−	0.129446i
$680$		0			0
$681$		0			0
$682$	4.24264	+	4.24264i	0.162459	+	0.162459i
$683$	27.9933	+	27.9933i	1.07113	+	1.07113i	0.997268	+	0.0738643i	$0.0235332\pi$
$683$	27.9933	+	27.9933i	1.07113	+	1.07113i	0.0738643	+	0.997268i	$0.476467\pi$
$684$		0			0
$685$		0			0
$686$			15.7128i			0.599918i
$687$		0			0
$688$	7.58871	−	7.58871i	0.289317	−	0.289317i
$689$	−6.58846			−0.251000
$690$		0			0
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$	−5.79555	+	5.79555i	−0.220314	+	0.220314i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−9.31749	−	9.31749i	−0.352925	−	0.352925i
$698$	−10.1769	−	10.1769i	−0.385201	−	0.385201i
$699$		0			0
$700$		0			0
$701$			30.5885i			1.15531i	0.816281	+	0.577655i	$0.196032\pi$
$701$			30.5885i			1.15531i	−0.816281	+	0.577655i	$0.803968\pi$
$702$		0			0
$703$	−43.4988	+	43.4988i	−1.64059	+	1.64059i
$704$	3.00000			0.113067
$705$		0			0
$706$	−3.80385			−0.143160
$707$	−16.6660	+	16.6660i	−0.626788	+	0.626788i
$708$		0			0
$709$			26.8038i			1.00664i	0.864100	+	0.503320i	$0.167888\pi$
$709$			26.8038i			1.00664i	−0.864100	+	0.503320i	$0.832112\pi$
$710$		0			0
$711$		0			0
$712$	−5.79555	−	5.79555i	−0.217198	−	0.217198i
$713$	−4.24264	−	4.24264i	−0.158888	−	0.158888i
$714$		0			0
$715$		0			0
$716$		−	25.3923i		−	0.948955i
$717$		0			0
$718$	7.91688	−	7.91688i	0.295455	−	0.295455i
$719$	−0.803848			−0.0299785			−0.0149892	−	0.999888i	$-0.504771\pi$
$719$	−0.803848			−0.0299785			−0.0149892	+	0.999888i	$0.504771\pi$
$720$		0			0
$721$	−1.17691			−0.0438306
$722$	−13.7124	+	13.7124i	−0.510324	+	0.510324i
$723$		0			0
$724$		−	13.5885i		−	0.505011i
$725$		0			0
$726$		0			0
$727$	−29.8744	−	29.8744i	−1.10798	−	1.10798i	−0.993416	−	0.114562i	$-0.963453\pi$
$727$	−29.8744	−	29.8744i	−1.10798	−	1.10798i	−0.114562	−	0.993416i	$-0.536547\pi$
$728$	−2.68973	−	2.68973i	−0.0996879	−	0.0996879i
$729$		0			0
$730$		0			0
$731$			23.5692i			0.871739i
$732$		0			0
$733$	−4.39494	+	4.39494i	−0.162331	+	0.162331i	−0.783599	−	0.621268i	$-0.786618\pi$
$733$	−4.39494	+	4.39494i	−0.162331	+	0.162331i	0.621268	+	0.783599i	$0.286618\pi$
$734$	−8.78461			−0.324246
$735$		0			0
$736$	−3.00000			−0.110581
$737$	4.65874	−	4.65874i	0.171607	−	0.171607i
$738$		0			0
$739$			44.5885i			1.64021i	0.572211	+	0.820106i	$0.306086\pi$
$739$			44.5885i			1.64021i	−0.572211	+	0.820106i	$0.693914\pi$
$740$		0			0
$741$		0			0
$742$	−1.96902	−	1.96902i	−0.0722849	−	0.0722849i
$743$	11.7434	+	11.7434i	0.430824	+	0.430824i	0.888909	−	0.458085i	$-0.151464\pi$
$743$	11.7434	+	11.7434i	0.430824	+	0.430824i	−0.458085	+	0.888909i	$0.651464\pi$
$744$		0			0
$745$		0			0
$746$		−	33.7128i		−	1.23431i
$747$		0			0
$748$	−4.65874	+	4.65874i	−0.170341	+	0.170341i
$749$	19.7654			0.722211
$750$		0			0
$751$	8.39230			0.306240			0.153120	−	0.988208i	$-0.451068\pi$
$751$	8.39230			0.306240			0.153120	+	0.988208i	$0.451068\pi$
$752$	−6.36396	+	6.36396i	−0.232070	+	0.232070i
$753$		0			0
$754$		−	24.5885i		−	0.895459i
$755$		0			0
$756$		0			0
$757$	−19.2677	−	19.2677i	−0.700298	−	0.700298i	0.264176	−	0.964474i	$-0.414900\pi$
$757$	−19.2677	−	19.2677i	−0.700298	−	0.700298i	−0.964474	+	0.264176i	$0.914900\pi$
$758$	1.41421	+	1.41421i	0.0513665	+	0.0513665i
$759$		0			0
$760$		0			0
$761$		−	22.3923i		−	0.811720i	−0.913935	−	0.405860i	$-0.866972\pi$
$761$		−	22.3923i		−	0.811720i	0.913935	−	0.405860i	$-0.133028\pi$
$762$		0			0
$763$	−7.17260	+	7.17260i	−0.259666	+	0.259666i
$764$	−4.39230			−0.158908
$765$		0			0
$766$	−3.00000			−0.108394
$767$	−28.4094	+	28.4094i	−1.02580	+	1.02580i
$768$		0			0
$769$		−	45.1769i		−	1.62912i	−0.580078	−	0.814561i	$-0.696978\pi$
$769$		−	45.1769i		−	1.62912i	0.580078	−	0.814561i	$-0.303022\pi$
$770$		0			0
$771$		0			0
$772$	−18.2832	−	18.2832i	−0.658028	−	0.658028i
$773$	−6.93237	−	6.93237i	−0.249340	−	0.249340i	0.571360	−	0.820700i	$-0.306416\pi$
$773$	−6.93237	−	6.93237i	−0.249340	−	0.249340i	−0.820700	+	0.571360i	$0.806416\pi$
$774$		0			0
$775$		0			0
$776$		−	2.66025i		−	0.0954976i
$777$		0			0
$778$	−22.7661	+	22.7661i	−0.816205	+	0.816205i
$779$	−37.1769			−1.33200
$780$		0			0
$781$	−2.41154			−0.0862918
$782$	4.65874	−	4.65874i	0.166596	−	0.166596i
$783$		0			0
$784$			5.39230i			0.192582i
$785$		0			0
$786$		0			0
$787$	16.4901	+	16.4901i	0.587808	+	0.587808i	0.937037	−	0.349229i	$-0.113557\pi$
$787$	16.4901	+	16.4901i	0.587808	+	0.587808i	−0.349229	+	0.937037i	$0.613557\pi$
$788$	−3.10583	−	3.10583i	−0.110641	−	0.110641i
$789$		0			0
$790$		0			0
$791$		−	13.1769i		−	0.468517i
$792$		0			0
$793$	19.5080	−	19.5080i	0.692749	−	0.692749i
$794$	2.07180			0.0735253
$795$		0			0
$796$	−2.00000			−0.0708881
$797$	38.5999	−	38.5999i	1.36728	−	1.36728i	0.502979	−	0.864299i	$-0.332237\pi$
$797$	38.5999	−	38.5999i	1.36728	−	1.36728i	0.864299	−	0.502979i	$-0.167763\pi$
$798$		0			0
$799$		−	19.7654i		−	0.699249i
$800$		0			0
$801$		0			0
$802$	−2.68973	−	2.68973i	−0.0949775	−	0.0949775i
$803$	18.1074	+	18.1074i	0.638995	+	0.638995i
$804$		0			0
$805$		0			0
$806$		−	6.00000i		−	0.211341i
$807$		0			0
$808$	−13.1440	+	13.1440i	−0.462405	+	0.462405i
$809$	−10.9808			−0.386063			−0.193032	−	0.981193i	$-0.561832\pi$
$809$	−10.9808			−0.386063			−0.193032	+	0.981193i	$0.561832\pi$
$810$		0			0
$811$	−32.5885			−1.14434			−0.572168	−	0.820137i	$-0.693897\pi$
$811$	−32.5885			−1.14434			−0.572168	+	0.820137i	$0.693897\pi$
$812$	7.34847	−	7.34847i	0.257881	−	0.257881i
$813$		0			0
$814$			29.7846i			1.04395i
$815$		0			0
$816$		0			0
$817$	47.0208	+	47.0208i	1.64505	+	1.64505i
$818$	16.2635	+	16.2635i	0.568638	+	0.568638i
$819$		0			0
$820$		0			0
$821$			50.7846i			1.77240i	0.463308	+	0.886198i	$0.346663\pi$
$821$			50.7846i			1.77240i	−0.463308	+	0.886198i	$0.653337\pi$
$822$		0			0
$823$	−30.9468	+	30.9468i	−1.07874	+	1.07874i	−0.0821144	+	0.996623i	$0.526167\pi$
$823$	−30.9468	+	30.9468i	−1.07874	+	1.07874i	−0.996623	+	0.0821144i	$0.973833\pi$
$824$	−0.928203			−0.0323355
$825$		0			0
$826$	−16.9808			−0.590836
$827$	35.3417	−	35.3417i	1.22895	−	1.22895i	0.264592	−	0.964360i	$-0.414763\pi$
$827$	35.3417	−	35.3417i	1.22895	−	1.22895i	0.964360	−	0.264592i	$-0.0852373\pi$
$828$		0			0
$829$		−	35.9808i		−	1.24966i	−0.780759	−	0.624832i	$-0.785168\pi$
$829$		−	35.9808i		−	1.24966i	0.780759	−	0.624832i	$-0.214832\pi$
$830$		0			0
$831$		0			0
$832$	−2.12132	−	2.12132i	−0.0735436	−	0.0735436i
$833$	−8.37379	−	8.37379i	−0.290135	−	0.290135i
$834$		0			0
$835$		0			0
$836$			18.5885i			0.642895i
$837$		0			0
$838$	7.34847	−	7.34847i	0.253849	−	0.253849i
$839$	19.9808			0.689813			0.344906	−	0.938637i	$-0.387911\pi$
$839$	19.9808			0.689813			0.344906	+	0.938637i	$0.387911\pi$
$840$		0			0
$841$	38.1769			1.31645
$842$	−13.5737	+	13.5737i	−0.467782	+	0.467782i
$843$		0			0
$844$			4.00000i			0.137686i
$845$		0			0
$846$		0			0
$847$	−1.79315	−	1.79315i	−0.0616134	−	0.0616134i
$848$	−1.55291	−	1.55291i	−0.0533273	−	0.0533273i
$849$		0			0
$850$		0			0
$851$		−	29.7846i		−	1.02100i
$852$		0			0
$853$	−9.46979	+	9.46979i	−0.324239	+	0.324239i	−0.850391	−	0.526151i	$-0.823634\pi$
$853$	−9.46979	+	9.46979i	−0.324239	+	0.324239i	0.526151	+	0.850391i	$0.323634\pi$
$854$	11.6603			0.399006
$855$		0			0
$856$	15.5885			0.532803
$857$	−8.48528	+	8.48528i	−0.289852	+	0.289852i	−0.837022	−	0.547170i	$-0.815705\pi$
$857$	−8.48528	+	8.48528i	−0.289852	+	0.289852i	0.547170	+	0.837022i	$0.315705\pi$
$858$		0			0
$859$			14.9808i			0.511137i	0.966791	+	0.255569i	$0.0822626\pi$
$859$			14.9808i			0.511137i	−0.966791	+	0.255569i	$0.917737\pi$
$860$		0			0
$861$		0			0
$862$	19.5080	+	19.5080i	0.664445	+	0.664445i
$863$	−21.2132	−	21.2132i	−0.722106	−	0.722106i	0.246928	−	0.969034i	$-0.420579\pi$
$863$	−21.2132	−	21.2132i	−0.722106	−	0.722106i	−0.969034	+	0.246928i	$0.920579\pi$
$864$		0			0
$865$		0			0
$866$			19.0526i			0.647432i
$867$		0			0
$868$	1.79315	−	1.79315i	0.0608635	−	0.0608635i
$869$	−30.5885			−1.03764
$870$		0			0
$871$	−6.58846			−0.223241
$872$	−5.65685	+	5.65685i	−0.191565	+	0.191565i
$873$		0			0
$874$		−	18.5885i		−	0.628764i
$875$		0			0
$876$		0			0
$877$	−22.6782	−	22.6782i	−0.765788	−	0.765788i	0.211574	−	0.977362i	$-0.432141\pi$
$877$	−22.6782	−	22.6782i	−0.765788	−	0.765788i	−0.977362	+	0.211574i	$0.932141\pi$
$878$	7.48717	+	7.48717i	0.252680	+	0.252680i
$879$		0			0
$880$		0			0
$881$		−	53.5692i		−	1.80479i	−0.430907	−	0.902396i	$-0.641806\pi$
$881$		−	53.5692i		−	1.80479i	0.430907	−	0.902396i	$-0.358194\pi$
$882$		0			0
$883$	21.1488	−	21.1488i	0.711715	−	0.711715i	−0.255179	−	0.966894i	$-0.582134\pi$
$883$	21.1488	−	21.1488i	0.711715	−	0.711715i	0.966894	+	0.255179i	$0.0821344\pi$
$884$	6.58846			0.221594
$885$		0			0
$886$	−27.5885			−0.926852
$887$	15.9861	−	15.9861i	0.536759	−	0.536759i	−0.385816	−	0.922576i	$-0.626080\pi$
$887$	15.9861	−	15.9861i	0.536759	−	0.536759i	0.922576	+	0.385816i	$0.126080\pi$
$888$		0			0
$889$			13.1769i			0.441940i
$890$		0			0
$891$		0			0
$892$	−14.9372	−	14.9372i	−0.500134	−	0.500134i
$893$	−39.4321	−	39.4321i	−1.31954	−	1.31954i
$894$		0			0
$895$		0			0
$896$		−	1.26795i		−	0.0423592i
$897$		0			0
$898$	−4.24264	+	4.24264i	−0.141579	+	0.141579i
$899$	16.3923			0.546714
$900$		0			0
$901$	4.82309			0.160680
$902$	−12.7279	+	12.7279i	−0.423793	+	0.423793i
$903$		0			0
$904$		−	10.3923i		−	0.345643i
$905$		0			0
$906$		0			0
$907$	−5.31508	−	5.31508i	−0.176484	−	0.176484i	0.613337	−	0.789821i	$-0.289827\pi$
$907$	−5.31508	−	5.31508i	−0.176484	−	0.176484i	−0.789821	+	0.613337i	$0.789827\pi$
$908$	−4.81105	−	4.81105i	−0.159660	−	0.159660i
$909$		0			0
$910$		0			0
$911$		−	47.1962i		−	1.56368i	−0.623480	−	0.781839i	$-0.714282\pi$
$911$		−	47.1962i		−	1.56368i	0.623480	−	0.781839i	$-0.285718\pi$
$912$		0			0
$913$	9.31749	−	9.31749i	0.308364	−	0.308364i
$914$	−23.1962			−0.767261
$915$		0			0
$916$	17.5885			0.581139
$917$	12.0072	−	12.0072i	0.396513	−	0.396513i
$918$		0			0
$919$		−	3.41154i		−	0.112536i	−0.998416	−	0.0562682i	$-0.982080\pi$
$919$		−	3.41154i		−	0.112536i	0.998416	−	0.0562682i	$-0.0179202\pi$
$920$		0			0
$921$		0			0
$922$	23.1822	+	23.1822i	0.763466	+	0.763466i
$923$	1.70522	+	1.70522i	0.0561279	+	0.0561279i
$924$		0			0
$925$		0			0
$926$		−	16.0526i		−	0.527520i
$927$		0			0
$928$	5.79555	−	5.79555i	0.190248	−	0.190248i
$929$	19.1769			0.629174			0.314587	−	0.949229i	$-0.398134\pi$
$929$	19.1769			0.629174			0.314587	+	0.949229i	$0.398134\pi$
$930$		0			0
$931$	−33.4115			−1.09502
$932$	10.0382	−	10.0382i	0.328812	−	0.328812i
$933$		0			0
$934$			13.9808i			0.457465i
$935$		0			0
$936$		0			0
$937$	−34.6854	−	34.6854i	−1.13312	−	1.13312i	−0.989655	−	0.143468i	$-0.954175\pi$
$937$	−34.6854	−	34.6854i	−1.13312	−	1.13312i	−0.143468	−	0.989655i	$-0.545825\pi$
$938$	−1.96902	−	1.96902i	−0.0642907	−	0.0642907i
$939$		0			0
$940$		0			0
$941$			27.3731i			0.892336i	0.894949	+	0.446168i	$0.147212\pi$
$941$			27.3731i			0.892336i	−0.894949	+	0.446168i	$0.852788\pi$
$942$		0			0
$943$	12.7279	−	12.7279i	0.414478	−	0.414478i
$944$	−13.3923			−0.435882
$945$		0			0
$946$	32.1962			1.04679
$947$	−13.8647	+	13.8647i	−0.450543	+	0.450543i	−0.895535	−	0.444991i	$-0.853207\pi$
$947$	−13.8647	+	13.8647i	−0.450543	+	0.450543i	0.444991	+	0.895535i	$0.353207\pi$
$948$		0			0
$949$		−	25.6077i		−	0.831261i
$950$		0			0
$951$		0			0
$952$	1.96902	+	1.96902i	0.0638162	+	0.0638162i
$953$	34.7733	+	34.7733i	1.12642	+	1.12642i	0.990755	+	0.135664i	$0.0433167\pi$
$953$	34.7733	+	34.7733i	1.12642	+	1.12642i	0.135664	+	0.990755i	$0.456683\pi$
$954$		0			0
$955$		0			0
$956$		−	12.8038i		−	0.414106i
$957$		0			0
$958$	15.8338	−	15.8338i	0.511565	−	0.511565i
$959$	−25.6077			−0.826916
$960$		0			0
$961$	−27.0000			−0.870968
$962$	21.0609	−	21.0609i	0.679031	−	0.679031i
$963$		0			0
$964$			1.00000i			0.0322078i
$965$		0			0
$966$		0			0
$967$	−4.06678	−	4.06678i	−0.130779	−	0.130779i	0.638688	−	0.769466i	$-0.279478\pi$
$967$	−4.06678	−	4.06678i	−0.130779	−	0.130779i	−0.769466	+	0.638688i	$0.779478\pi$
$968$	−1.41421	−	1.41421i	−0.0454545	−	0.0454545i
$969$		0			0
$970$		0			0
$971$			17.7846i			0.570735i	0.958418	+	0.285368i	$0.0921157\pi$
$971$			17.7846i			0.570735i	−0.958418	+	0.285368i	$0.907884\pi$
$972$		0			0
$973$	14.5211	−	14.5211i	0.465524	−	0.465524i
$974$	12.5885			0.403360
$975$		0			0
$976$	9.19615			0.294362
$977$	9.31749	−	9.31749i	0.298093	−	0.298093i	−0.542174	−	0.840266i	$-0.682399\pi$
$977$	9.31749	−	9.31749i	0.298093	−	0.298093i	0.840266	+	0.542174i	$0.182399\pi$
$978$		0			0
$979$		−	24.5885i		−	0.785851i
$980$		0			0
$981$		0			0
$982$	1.13681	+	1.13681i	0.0362771	+	0.0362771i
$983$	18.7873	+	18.7873i	0.599221	+	0.599221i	0.940105	−	0.340884i	$-0.110726\pi$
$983$	18.7873	+	18.7873i	0.599221	+	0.599221i	−0.340884	+	0.940105i	$0.610726\pi$
$984$		0			0
$985$		0			0
$986$			18.0000i			0.573237i
$987$		0			0
$988$	13.1440	−	13.1440i	0.418167	−	0.418167i
$989$	−32.1962			−1.02378
$990$		0			0
$991$	49.5692			1.57462			0.787309	−	0.616559i	$-0.211474\pi$
$991$	49.5692			1.57462			0.787309	+	0.616559i	$0.211474\pi$
$992$	1.41421	−	1.41421i	0.0449013	−	0.0449013i
$993$		0			0
$994$			1.01924i			0.0323283i
$995$		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	$0.609377\pi$
$998$	−23.4596	−	23.4596i	−0.742601	−	0.742601i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.896575 - 0.896575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.896575 - 0.896575i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.00000i q^{11} +(-2.12132 + 2.12132i) q^{13} -1.26795 q^{14} -1.00000 q^{16} +(1.55291 - 1.55291i) q^{17} -6.19615i q^{19} +(-2.12132 - 2.12132i) q^{22} +(2.12132 + 2.12132i) q^{23} +3.00000i q^{26} +(-0.896575 + 0.896575i) q^{28} -8.19615 q^{29} -2.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} -2.19615i q^{34} +(-7.02030 - 7.02030i) q^{37} +(-4.38134 - 4.38134i) q^{38} -6.00000i q^{41} +(-7.58871 + 7.58871i) q^{43} -3.00000 q^{44} +3.00000 q^{46} +(6.36396 - 6.36396i) q^{47} -5.39230i q^{49} +(2.12132 + 2.12132i) q^{52} +(1.55291 + 1.55291i) q^{53} +1.26795i q^{56} +(-5.79555 + 5.79555i) q^{58} +13.3923 q^{59} -9.19615 q^{61} +(-1.41421 + 1.41421i) q^{62} +1.00000i q^{64} +(1.55291 + 1.55291i) q^{67} +(-1.55291 - 1.55291i) q^{68} -0.803848i q^{71} +(-6.03579 + 6.03579i) q^{73} -9.92820 q^{74} -6.19615 q^{76} +(-2.68973 + 2.68973i) q^{77} -10.1962i q^{79} +(-4.24264 - 4.24264i) q^{82} +(3.10583 + 3.10583i) q^{83} +10.7321i q^{86} +(-2.12132 + 2.12132i) q^{88} +8.19615 q^{89} +3.80385 q^{91} +(2.12132 - 2.12132i) q^{92} -9.00000i q^{94} +(1.88108 + 1.88108i) q^{97} +(-3.81294 - 3.81294i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 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

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