LMFDB - Embedded newform 1344.2.s.d.239.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, degree $2$, not 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.13
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.d.911.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.223071 + 1.71763i) q^{3} +(2.27022 + 2.27022i) q^{5} -1.00000 q^{7} +(-2.90048 + 0.766304i) q^{9} +O(q^{10})$	\(q+(0.223071 + 1.71763i) q^{3} +(2.27022 + 2.27022i) q^{5} -1.00000 q^{7} +(-2.90048 + 0.766304i) q^{9} +(1.53672 - 1.53672i) q^{11} +(-3.63094 - 3.63094i) q^{13} +(-3.39297 + 4.40581i) q^{15} +1.81890i q^{17} +(-4.98250 + 4.98250i) q^{19} +(-0.223071 - 1.71763i) q^{21} +7.21608i q^{23} +5.30780i q^{25} +(-1.96324 - 4.81100i) q^{27} +(-2.77187 + 2.77187i) q^{29} +4.14621i q^{31} +(2.98230 + 2.29671i) q^{33} +(-2.27022 - 2.27022i) q^{35} +(-1.77185 + 1.77185i) q^{37} +(5.42665 - 7.04656i) q^{39} +0.517924 q^{41} +(4.67423 + 4.67423i) q^{43} +(-8.32441 - 4.84505i) q^{45} -1.19336 q^{47} +1.00000 q^{49} +(-3.12419 + 0.405744i) q^{51} +(-7.94384 - 7.94384i) q^{53} +6.97737 q^{55} +(-9.66952 - 7.44662i) q^{57} +(-1.94904 + 1.94904i) q^{59} +(2.94791 + 2.94791i) q^{61} +(2.90048 - 0.766304i) q^{63} -16.4861i q^{65} +(7.85747 - 7.85747i) q^{67} +(-12.3945 + 1.60970i) q^{69} -10.9009i q^{71} +15.7454i q^{73} +(-9.11682 + 1.18402i) q^{75} +(-1.53672 + 1.53672i) q^{77} -5.40437i q^{79} +(7.82556 - 4.44530i) q^{81} +(7.12290 + 7.12290i) q^{83} +(-4.12931 + 4.12931i) q^{85} +(-5.37937 - 4.14272i) q^{87} +11.1745 q^{89} +(3.63094 + 3.63094i) q^{91} +(-7.12163 + 0.924898i) q^{93} -22.6227 q^{95} +12.3244 q^{97} +(-3.27962 + 5.63480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{7}+O(q^{10}) $ 48 * q - 48 * q^7	$ 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) $ 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	0.223071	+	1.71763i	0.128790	+	0.991672i
$3$	0.223071	+	1.71763i	0.128790	+	0.991672i
$4$		0			0
$5$	2.27022	+	2.27022i	1.01527	+	1.01527i	0.999882	+	0.0153920i	$0.00489963\pi$
$5$	2.27022	+	2.27022i	1.01527	+	1.01527i	0.0153920	+	0.999882i	$0.495100\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$		0			0
$9$	−2.90048	+	0.766304i	−0.966826	+	0.255435i
$10$		0			0
$11$	1.53672	−	1.53672i	0.463337	−	0.463337i	−0.436411	−	0.899748i	$-0.643750\pi$
$11$	1.53672	−	1.53672i	0.463337	−	0.463337i	0.899748	+	0.436411i	$0.143750\pi$
$12$		0			0
$13$	−3.63094	−	3.63094i	−1.00704	−	1.00704i	−0.999975	−	0.00706768i	$-0.997750\pi$
$13$	−3.63094	−	3.63094i	−1.00704	−	1.00704i	−0.00706768	−	0.999975i	$-0.502250\pi$
$14$		0			0
$15$	−3.39297	+	4.40581i	−0.876061	+	1.13758i
$16$		0			0
$17$			1.81890i			0.441148i	0.975370	+	0.220574i	$0.0707931\pi$
$17$			1.81890i			0.441148i	−0.975370	+	0.220574i	$0.929207\pi$
$18$		0			0
$19$	−4.98250	+	4.98250i	−1.14306	+	1.14306i	−0.155177	+	0.987887i	$0.549595\pi$
$19$	−4.98250	+	4.98250i	−1.14306	+	1.14306i	−0.987887	+	0.155177i	$0.950405\pi$
$20$		0			0
$21$	−0.223071	−	1.71763i	−0.0486780	−	0.374817i
$22$		0			0
$23$			7.21608i			1.50466i	0.658789	+	0.752328i	$0.271069\pi$
$23$			7.21608i			1.50466i	−0.658789	+	0.752328i	$0.728931\pi$
$24$		0			0
$25$			5.30780i			1.06156i
$26$		0			0
$27$	−1.96324	−	4.81100i	−0.377825	−	0.925877i
$28$		0			0
$29$	−2.77187	+	2.77187i	−0.514724	+	0.514724i	−0.915970	−	0.401246i	$-0.868577\pi$
$29$	−2.77187	+	2.77187i	−0.514724	+	0.514724i	0.401246	+	0.915970i	$0.368577\pi$
$30$		0			0
$31$			4.14621i			0.744681i	0.928096	+	0.372340i	$0.121445\pi$
$31$			4.14621i			0.744681i	−0.928096	+	0.372340i	$0.878555\pi$
$32$		0			0
$33$	2.98230	+	2.29671i	0.519151	+	0.399805i
$34$		0			0
$35$	−2.27022	−	2.27022i	−0.383737	−	0.383737i
$36$		0			0
$37$	−1.77185	+	1.77185i	−0.291290	+	0.291290i	−0.837590	−	0.546300i	$-0.816036\pi$
$37$	−1.77185	+	1.77185i	−0.291290	+	0.291290i	0.546300	+	0.837590i	$0.316036\pi$
$38$		0			0
$39$	5.42665	−	7.04656i	0.868959	−	1.12835i
$40$		0			0
$41$	0.517924			0.0808862			0.0404431	−	0.999182i	$-0.487123\pi$
$41$	0.517924			0.0808862			0.0404431	+	0.999182i	$0.487123\pi$
$42$		0			0
$43$	4.67423	+	4.67423i	0.712813	+	0.712813i	0.967123	−	0.254310i	$-0.0818483\pi$
$43$	4.67423	+	4.67423i	0.712813	+	0.712813i	−0.254310	+	0.967123i	$0.581848\pi$
$44$		0			0
$45$	−8.32441	−	4.84505i	−1.24093	−	0.722257i
$46$		0			0
$47$	−1.19336			−0.174069			−0.0870346	−	0.996205i	$-0.527739\pi$
$47$	−1.19336			−0.174069			−0.0870346	+	0.996205i	$0.527739\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−3.12419	+	0.405744i	−0.437474	+	0.0568155i
$52$		0			0
$53$	−7.94384	−	7.94384i	−1.09117	−	1.09117i	−0.995404	−	0.0957666i	$-0.969470\pi$
$53$	−7.94384	−	7.94384i	−1.09117	−	1.09117i	−0.0957666	−	0.995404i	$-0.530530\pi$
$54$		0			0
$55$	6.97737			0.940828
$56$		0			0
$57$	−9.66952	−	7.44662i	−1.28076	−	0.986329i
$58$		0			0
$59$	−1.94904	+	1.94904i	−0.253744	+	0.253744i	−0.822504	−	0.568760i	$-0.807423\pi$
$59$	−1.94904	+	1.94904i	−0.253744	+	0.253744i	0.568760	+	0.822504i	$0.307423\pi$
$60$		0			0
$61$	2.94791	+	2.94791i	0.377441	+	0.377441i	0.870178	−	0.492737i	$-0.164004\pi$
$61$	2.94791	+	2.94791i	0.377441	+	0.377441i	−0.492737	+	0.870178i	$0.664004\pi$
$62$		0			0
$63$	2.90048	−	0.766304i	0.365426	−	0.0965453i
$64$		0			0
$65$		−	16.4861i		−	2.04485i
$66$		0			0
$67$	7.85747	−	7.85747i	0.959943	−	0.959943i	−0.0392854	−	0.999228i	$-0.512508\pi$
$67$	7.85747	−	7.85747i	0.959943	−	0.959943i	0.999228	+	0.0392854i	$0.0125082\pi$
$68$		0			0
$69$	−12.3945	+	1.60970i	−1.49212	+	0.193785i
$70$		0			0
$71$		−	10.9009i		−	1.29370i	−0.762619	−	0.646848i	$-0.776087\pi$
$71$		−	10.9009i		−	1.29370i	0.762619	−	0.646848i	$-0.223913\pi$
$72$		0			0
$73$			15.7454i			1.84286i	0.388539	+	0.921432i	$0.372980\pi$
$73$			15.7454i			1.84286i	−0.388539	+	0.921432i	$0.627020\pi$
$74$		0			0
$75$	−9.11682	+	1.18402i	−1.05272	+	0.136718i
$76$		0			0
$77$	−1.53672	+	1.53672i	−0.175125	+	0.175125i
$78$		0			0
$79$		−	5.40437i		−	0.608039i	−0.952666	−	0.304019i	$-0.901671\pi$
$79$		−	5.40437i		−	0.608039i	0.952666	−	0.304019i	$-0.0983288\pi$
$80$		0			0
$81$	7.82556	−	4.44530i	0.869506	−	0.493922i
$82$		0			0
$83$	7.12290	+	7.12290i	0.781840	+	0.781840i	0.980141	−	0.198301i	$-0.0635425\pi$
$83$	7.12290	+	7.12290i	0.781840	+	0.781840i	−0.198301	+	0.980141i	$0.563542\pi$
$84$		0			0
$85$	−4.12931	+	4.12931i	−0.447886	+	0.447886i
$86$		0			0
$87$	−5.37937	−	4.14272i	−0.576729	−	0.444146i
$88$		0			0
$89$	11.1745			1.18449			0.592246	−	0.805758i	$-0.298242\pi$
$89$	11.1745			1.18449			0.592246	+	0.805758i	$0.298242\pi$
$90$		0			0
$91$	3.63094	+	3.63094i	0.380626	+	0.380626i
$92$		0			0
$93$	−7.12163	+	0.924898i	−0.738479	+	0.0959074i
$94$		0			0
$95$	−22.6227			−2.32105
$96$		0			0
$97$	12.3244			1.25136			0.625678	−	0.780081i	$-0.284822\pi$
$97$	12.3244			1.25136			0.625678	+	0.780081i	$0.284822\pi$
$98$		0			0
$99$	−3.27962	+	5.63480i	−0.329614	+	0.566319i
$100$		0			0
$101$	−8.72339	−	8.72339i	−0.868009	−	0.868009i	0.124242	−	0.992252i	$-0.460350\pi$
$101$	−8.72339	−	8.72339i	−0.868009	−	0.868009i	−0.992252	+	0.124242i	$0.960350\pi$
$102$		0			0
$103$	1.74109			0.171555			0.0857774	−	0.996314i	$-0.472663\pi$
$103$	1.74109			0.171555			0.0857774	+	0.996314i	$0.472663\pi$
$104$		0			0
$105$	3.39297	−	4.40581i	0.331120	−	0.429963i
$106$		0			0
$107$	−0.640107	+	0.640107i	−0.0618814	+	0.0618814i	−0.737370	−	0.675489i	$-0.763933\pi$
$107$	−0.640107	+	0.640107i	−0.0618814	+	0.0618814i	0.675489	+	0.737370i	$0.263933\pi$
$108$		0			0
$109$	4.52892	+	4.52892i	0.433791	+	0.433791i	0.889916	−	0.456125i	$-0.150763\pi$
$109$	4.52892	+	4.52892i	0.433791	+	0.433791i	−0.456125	+	0.889916i	$0.650763\pi$
$110$		0			0
$111$	−3.43862	−	2.64812i	−0.326379	−	0.251349i
$112$		0			0
$113$		−	2.86038i		−	0.269082i	−0.990908	−	0.134541i	$-0.957044\pi$
$113$		−	2.86038i		−	0.269082i	0.990908	−	0.134541i	$-0.0429559\pi$
$114$		0			0
$115$	−16.3821	+	16.3821i	−1.52764	+	1.52764i
$116$		0			0
$117$	13.3139	+	7.74907i	1.23087	+	0.716402i
$118$		0			0
$119$		−	1.81890i		−	0.166738i
$120$		0			0
$121$			6.27701i			0.570638i
$122$		0			0
$123$	0.115534	+	0.889601i	0.0104173	+	0.0802126i
$124$		0			0
$125$	−0.698783	+	0.698783i	−0.0625011	+	0.0625011i
$126$		0			0
$127$		−	6.44899i		−	0.572256i	−0.958191	−	0.286128i	$-0.907632\pi$
$127$		−	6.44899i		−	0.572256i	0.958191	−	0.286128i	$-0.0923682\pi$
$128$		0			0
$129$	−6.98589	+	9.07126i	−0.615073	+	0.798680i
$130$		0			0
$131$	2.83186	+	2.83186i	0.247421	+	0.247421i	0.819911	−	0.572491i	$-0.194023\pi$
$131$	2.83186	+	2.83186i	0.247421	+	0.247421i	−0.572491	+	0.819911i	$0.694023\pi$
$132$		0			0
$133$	4.98250	−	4.98250i	0.432038	−	0.432038i
$134$		0			0
$135$	6.46505	−	15.3790i	0.556423	−	1.32361i
$136$		0			0
$137$	14.1051			1.20508			0.602538	−	0.798090i	$-0.294156\pi$
$137$	14.1051			1.20508			0.602538	+	0.798090i	$0.294156\pi$
$138$		0			0
$139$	5.16493	+	5.16493i	0.438083	+	0.438083i	0.891367	−	0.453283i	$-0.149747\pi$
$139$	5.16493	+	5.16493i	0.438083	+	0.438083i	−0.453283	+	0.891367i	$0.649747\pi$
$140$		0			0
$141$	−0.266203	−	2.04974i	−0.0224184	−	0.172619i
$142$		0			0
$143$	−11.1595			−0.933200
$144$		0			0
$145$	−12.5855			−1.04517
$146$		0			0
$147$	0.223071	+	1.71763i	0.0183986	+	0.141667i
$148$		0			0
$149$	11.3665	+	11.3665i	0.931178	+	0.931178i	0.997780	−	0.0666019i	$-0.0212157\pi$
$149$	11.3665	+	11.3665i	0.931178	+	0.931178i	−0.0666019	+	0.997780i	$0.521216\pi$
$150$		0			0
$151$	−20.4171			−1.66152			−0.830758	−	0.556634i	$-0.812093\pi$
$151$	−20.4171			−1.66152			−0.830758	+	0.556634i	$0.812093\pi$
$152$		0			0
$153$	−1.39383	−	5.27569i	−0.112685	−	0.426514i
$154$		0			0
$155$	−9.41281	+	9.41281i	−0.756055	+	0.756055i
$156$		0			0
$157$	−6.20353	−	6.20353i	−0.495096	−	0.495096i	0.414812	−	0.909907i	$-0.363847\pi$
$157$	−6.20353	−	6.20353i	−0.495096	−	0.495096i	−0.909907	+	0.414812i	$0.863847\pi$
$158$		0			0
$159$	11.8725	−	15.4166i	0.941551	−	1.22261i
$160$		0			0
$161$		−	7.21608i		−	0.568706i
$162$		0			0
$163$	−3.87321	+	3.87321i	−0.303373	+	0.303373i	−0.842332	−	0.538959i	$-0.818818\pi$
$163$	−3.87321	+	3.87321i	−0.303373	+	0.303373i	0.538959	+	0.842332i	$0.318818\pi$
$164$		0			0
$165$	1.55645	+	11.9845i	0.121169	+	0.932992i
$166$		0			0
$167$			6.25436i			0.483977i	0.970279	+	0.241989i	$0.0777996\pi$
$167$			6.25436i			0.483977i	−0.970279	+	0.241989i	$0.922200\pi$
$168$		0			0
$169$			13.3675i			1.02827i
$170$		0			0
$171$	10.6335	−	18.2697i	0.813166	−	1.39712i
$172$		0			0
$173$	−14.7186	+	14.7186i	−1.11903	+	1.11903i	−0.127148	+	0.991884i	$0.540582\pi$
$173$	−14.7186	+	14.7186i	−1.11903	+	1.11903i	−0.991884	+	0.127148i	$0.959418\pi$
$174$		0			0
$175$		−	5.30780i		−	0.401232i
$176$		0			0
$177$	−3.78251	−	2.91296i	−0.284310	−	0.218951i
$178$		0			0
$179$	−12.4907	−	12.4907i	−0.933596	−	0.933596i	0.0643321	−	0.997929i	$-0.479508\pi$
$179$	−12.4907	−	12.4907i	−0.933596	−	0.933596i	−0.997929	+	0.0643321i	$0.979508\pi$
$180$		0			0
$181$	1.06356	−	1.06356i	0.0790541	−	0.0790541i	−0.666474	−	0.745528i	$-0.732197\pi$
$181$	1.06356	−	1.06356i	0.0790541	−	0.0790541i	0.745528	+	0.666474i	$0.232197\pi$
$182$		0			0
$183$	−4.40581	+	5.72099i	−0.325687	+	0.422908i
$184$		0			0
$185$	−8.04497			−0.591478
$186$		0			0
$187$	2.79513	+	2.79513i	0.204400	+	0.204400i
$188$		0			0
$189$	1.96324	+	4.81100i	0.142804	+	0.349949i
$190$		0			0
$191$	18.9350			1.37009			0.685044	−	0.728502i	$-0.259783\pi$
$191$	18.9350			1.37009			0.685044	+	0.728502i	$0.259783\pi$
$192$		0			0
$193$	−1.39738			−0.100585			−0.0502927	−	0.998735i	$-0.516015\pi$
$193$	−1.39738			−0.100585			−0.0502927	+	0.998735i	$0.516015\pi$
$194$		0			0
$195$	28.3169	−	3.67756i	2.02782	−	0.263356i
$196$		0			0
$197$	−8.87505	−	8.87505i	−0.632321	−	0.632321i	0.316328	−	0.948650i	$-0.397550\pi$
$197$	−8.87505	−	8.87505i	−0.632321	−	0.632321i	−0.948650	+	0.316328i	$0.897550\pi$
$198$		0			0
$199$	21.8865			1.55149			0.775747	−	0.631044i	$-0.217373\pi$
$199$	21.8865			1.55149			0.775747	+	0.631044i	$0.217373\pi$
$200$		0			0
$201$	15.2490	+	11.7434i	1.07558	+	0.828317i
$202$		0			0
$203$	2.77187	−	2.77187i	0.194547	−	0.194547i
$204$		0			0
$205$	1.17580	+	1.17580i	0.0821216	+	0.0821216i
$206$		0			0
$207$	−5.52971	−	20.9301i	−0.384341	−	1.45474i
$208$		0			0
$209$			15.3134i			1.05925i
$210$		0			0
$211$	−6.14716	+	6.14716i	−0.423188	+	0.423188i	−0.886300	−	0.463112i	$-0.846733\pi$
$211$	−6.14716	+	6.14716i	−0.423188	+	0.423188i	0.463112	+	0.886300i	$0.346733\pi$
$212$		0			0
$213$	18.7236	−	2.43167i	1.28292	−	0.166615i
$214$		0			0
$215$			21.2231i			1.44740i
$216$		0			0
$217$		−	4.14621i		−	0.281463i
$218$		0			0
$219$	−27.0448	+	3.51235i	−1.82752	+	0.237342i
$220$		0			0
$221$	6.60433	−	6.60433i	0.444255	−	0.444255i
$222$		0			0
$223$			22.5496i			1.51004i	0.655704	+	0.755018i	$0.272372\pi$
$223$			22.5496i			1.51004i	−0.655704	+	0.755018i	$0.727628\pi$
$224$		0			0
$225$	−4.06739	−	15.3952i	−0.271160	−	1.02634i
$226$		0			0
$227$	−7.88171	−	7.88171i	−0.523127	−	0.523127i	0.395387	−	0.918515i	$-0.370610\pi$
$227$	−7.88171	−	7.88171i	−0.523127	−	0.523127i	−0.918515	+	0.395387i	$0.870610\pi$
$228$		0			0
$229$	9.66460	−	9.66460i	0.638654	−	0.638654i	−0.311569	−	0.950224i	$-0.600855\pi$
$229$	9.66460	−	9.66460i	0.638654	−	0.638654i	0.950224	+	0.311569i	$0.100855\pi$
$230$		0			0
$231$	−2.98230	−	2.29671i	−0.196221	−	0.151112i
$232$		0			0
$233$	20.8685			1.36714			0.683571	−	0.729884i	$-0.260426\pi$
$233$	20.8685			1.36714			0.683571	+	0.729884i	$0.260426\pi$
$234$		0			0
$235$	−2.70919	−	2.70919i	−0.176728	−	0.176728i
$236$		0			0
$237$	9.28268	−	1.20556i	0.602975	−	0.0783093i
$238$		0			0
$239$	9.99752			0.646686			0.323343	−	0.946282i	$-0.395193\pi$
$239$	9.99752			0.646686			0.323343	+	0.946282i	$0.395193\pi$
$240$		0			0
$241$	16.6499			1.07251			0.536256	−	0.844055i	$-0.319838\pi$
$241$	16.6499			1.07251			0.536256	+	0.844055i	$0.319838\pi$
$242$		0			0
$243$	9.38101	+	12.4498i	0.601792	+	0.798653i
$244$		0			0
$245$	2.27022	+	2.27022i	0.145039	+	0.145039i
$246$		0			0
$247$	36.1824			2.30223
$248$		0			0
$249$	−10.6456	+	13.8234i	−0.674635	+	0.876021i
$250$		0			0
$251$	13.9403	−	13.9403i	0.879903	−	0.879903i	−0.113621	−	0.993524i	$-0.536245\pi$
$251$	13.9403	−	13.9403i	0.879903	−	0.879903i	0.993524	+	0.113621i	$0.0362451\pi$
$252$		0			0
$253$	11.0891	+	11.0891i	0.697163	+	0.697163i
$254$		0			0
$255$	−8.01374	−	6.17148i	−0.501840	−	0.386473i
$256$		0			0
$257$			8.37152i			0.522201i	0.965312	+	0.261100i	$0.0840854\pi$
$257$			8.37152i			0.522201i	−0.965312	+	0.261100i	$0.915915\pi$
$258$		0			0
$259$	1.77185	−	1.77185i	0.110097	−	0.110097i
$260$		0			0
$261$	5.91566	−	10.1639i	0.366170	−	0.629127i
$262$		0			0
$263$			3.62005i			0.223222i	0.993752	+	0.111611i	$0.0356011\pi$
$263$			3.62005i			0.223222i	−0.993752	+	0.111611i	$0.964399\pi$
$264$		0			0
$265$		−	36.0685i		−	2.21567i
$266$		0			0
$267$	2.49270	+	19.1936i	0.152551	+	1.17463i
$268$		0			0
$269$	0.136662	−	0.136662i	0.00833240	−	0.00833240i	−0.702928	−	0.711261i	$-0.748125\pi$
$269$	0.136662	−	0.136662i	0.00833240	−	0.00833240i	0.711261	+	0.702928i	$0.248125\pi$
$270$		0			0
$271$		−	22.1261i		−	1.34406i	−0.740523	−	0.672031i	$-0.765422\pi$
$271$		−	22.1261i		−	1.34406i	0.740523	−	0.672031i	$-0.234578\pi$
$272$		0			0
$273$	−5.42665	+	7.04656i	−0.328436	+	0.426477i
$274$		0			0
$275$	8.15658	+	8.15658i	0.491860	+	0.491860i
$276$		0			0
$277$	−7.42315	+	7.42315i	−0.446014	+	0.446014i	−0.894027	−	0.448013i	$-0.852132\pi$
$277$	−7.42315	+	7.42315i	−0.446014	+	0.446014i	0.448013	+	0.894027i	$0.352132\pi$
$278$		0			0
$279$	−3.17726	−	12.0260i	−0.190217	−	0.719977i
$280$		0			0
$281$	−2.16601			−0.129213			−0.0646067	−	0.997911i	$-0.520579\pi$
$281$	−2.16601			−0.129213			−0.0646067	+	0.997911i	$0.520579\pi$
$282$		0			0
$283$	10.6179	+	10.6179i	0.631171	+	0.631171i	0.948362	−	0.317190i	$-0.102739\pi$
$283$	10.6179	+	10.6179i	0.631171	+	0.631171i	−0.317190	+	0.948362i	$0.602739\pi$
$284$		0			0
$285$	−5.04647	−	38.8574i	−0.298927	−	2.30172i
$286$		0			0
$287$	−0.517924			−0.0305721
$288$		0			0
$289$	13.6916			0.805388
$290$		0			0
$291$	2.74922	+	21.1688i	0.161162	+	1.24094i
$292$		0			0
$293$	6.34724	+	6.34724i	0.370810	+	0.370810i	0.867772	−	0.496962i	$-0.165551\pi$
$293$	6.34724	+	6.34724i	0.370810	+	0.370810i	−0.496962	+	0.867772i	$0.665551\pi$
$294$		0			0
$295$	−8.84952			−0.515239
$296$		0			0
$297$	−10.4101	−	4.37620i	−0.604053	−	0.253933i
$298$		0			0
$299$	26.2012	−	26.2012i	1.51525	−	1.51525i
$300$		0			0
$301$	−4.67423	−	4.67423i	−0.269418	−	0.269418i
$302$		0			0
$303$	13.0376	−	16.9294i	0.748990	−	0.972571i
$304$		0			0
$305$			13.3848i			0.766411i
$306$		0			0
$307$	−12.0463	+	12.0463i	−0.687521	+	0.687521i	−0.961683	−	0.274162i	$-0.911599\pi$
$307$	−12.0463	+	12.0463i	−0.687521	+	0.687521i	0.274162	+	0.961683i	$0.411599\pi$
$308$		0			0
$309$	0.388386	+	2.99054i	0.0220945	+	0.170126i
$310$		0			0
$311$			18.3544i			1.04078i	0.853928	+	0.520392i	$0.174214\pi$
$311$			18.3544i			1.04078i	−0.853928	+	0.520392i	$0.825786\pi$
$312$		0			0
$313$			11.8602i			0.670379i	0.942151	+	0.335190i	$0.108800\pi$
$313$			11.8602i			0.670379i	−0.942151	+	0.335190i	$0.891200\pi$
$314$		0			0
$315$	8.32441	+	4.84505i	0.469027	+	0.272988i
$316$		0			0
$317$	7.44587	−	7.44587i	0.418201	−	0.418201i	−0.466382	−	0.884583i	$-0.654443\pi$
$317$	7.44587	−	7.44587i	0.418201	−	0.418201i	0.884583	+	0.466382i	$0.154443\pi$
$318$		0			0
$319$			8.51916i			0.476981i
$320$		0			0
$321$	−1.24225	−	0.956675i	−0.0693358	−	0.0533964i
$322$		0			0
$323$	−9.06268	−	9.06268i	−0.504261	−	0.504261i
$324$		0			0
$325$	19.2723	−	19.2723i	1.06904	−	1.06904i
$326$		0			0
$327$	−6.76871	+	8.78925i	−0.374311	+	0.486047i
$328$		0			0
$329$	1.19336			0.0657919
$330$		0			0
$331$	−18.1210	−	18.1210i	−0.996018	−	0.996018i	0.00397423	−	0.999992i	$-0.498735\pi$
$331$	−18.1210	−	18.1210i	−0.996018	−	0.996018i	−0.999992	+	0.00397423i	$0.998735\pi$
$332$		0			0
$333$	3.78143	−	6.49698i	0.207221	−	0.356032i
$334$		0			0
$335$	35.6764			1.94921
$336$		0			0
$337$	−9.87814			−0.538096			−0.269048	−	0.963127i	$-0.586709\pi$
$337$	−9.87814			−0.538096			−0.269048	+	0.963127i	$0.586709\pi$
$338$		0			0
$339$	4.91306	−	0.638066i	0.266841	−	0.0346550i
$340$		0			0
$341$	6.37154	+	6.37154i	0.345038	+	0.345038i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−31.7927	−	24.4839i	−1.71166	−	1.31817i
$346$		0			0
$347$	−7.05190	+	7.05190i	−0.378566	+	0.378566i	−0.870585	−	0.492019i	$-0.836259\pi$
$347$	−7.05190	+	7.05190i	−0.378566	+	0.378566i	0.492019	+	0.870585i	$0.336259\pi$
$348$		0			0
$349$	−24.5451	−	24.5451i	−1.31387	−	1.31387i	−0.918539	−	0.395331i	$-0.870630\pi$
$349$	−24.5451	−	24.5451i	−1.31387	−	1.31387i	−0.395331	−	0.918539i	$-0.629370\pi$
$350$		0			0
$351$	−10.3401	+	24.5969i	−0.551912	+	1.31288i
$352$		0			0
$353$		−	20.0409i		−	1.06667i	−0.845905	−	0.533334i	$-0.820939\pi$
$353$		−	20.0409i		−	1.06667i	0.845905	−	0.533334i	$-0.179061\pi$
$354$		0			0
$355$	24.7474	−	24.7474i	1.31346	−	1.31346i
$356$		0			0
$357$	3.12419	−	0.405744i	0.165350	−	0.0214742i
$358$		0			0
$359$		−	9.58285i		−	0.505763i	−0.967497	−	0.252882i	$-0.918622\pi$
$359$		−	9.58285i		−	0.505763i	0.967497	−	0.252882i	$-0.0813784\pi$
$360$		0			0
$361$		−	30.6506i		−	1.61319i
$362$		0			0
$363$	−10.7816	+	1.40022i	−0.565885	+	0.0734924i
$364$		0			0
$365$	−35.7456	+	35.7456i	−1.87101	+	1.87101i
$366$		0			0
$367$			13.5432i			0.706952i	0.935444	+	0.353476i	$0.115000\pi$
$367$			13.5432i			0.706952i	−0.935444	+	0.353476i	$0.885000\pi$
$368$		0			0
$369$	−1.50223	+	0.396888i	−0.0782029	+	0.0206611i
$370$		0			0
$371$	7.94384	+	7.94384i	0.412424	+	0.412424i
$372$		0			0
$373$	−17.3451	+	17.3451i	−0.898095	+	0.898095i	−0.995268	−	0.0971728i	$-0.969020\pi$
$373$	−17.3451	+	17.3451i	−0.898095	+	0.898095i	0.0971728	+	0.995268i	$0.469020\pi$
$374$		0			0
$375$	−1.35613	−	1.04437i	−0.0700301	−	0.0539311i
$376$		0			0
$377$	20.1290			1.03670
$378$		0			0
$379$	−3.61555	−	3.61555i	−0.185718	−	0.185718i	0.608124	−	0.793842i	$-0.291922\pi$
$379$	−3.61555	−	3.61555i	−0.185718	−	0.185718i	−0.793842	+	0.608124i	$0.791922\pi$
$380$		0			0
$381$	11.0770	−	1.43858i	0.567490	−	0.0737008i
$382$		0			0
$383$	3.95251			0.201964			0.100982	−	0.994888i	$-0.467802\pi$
$383$	3.95251			0.201964			0.100982	+	0.994888i	$0.467802\pi$
$384$		0			0
$385$	−6.97737			−0.355599
$386$		0			0
$387$	−17.1394	−	9.97562i	−0.871243	−	0.507089i
$388$		0			0
$389$	−7.65725	−	7.65725i	−0.388238	−	0.388238i	0.485821	−	0.874059i	$-0.338521\pi$
$389$	−7.65725	−	7.65725i	−0.388238	−	0.388238i	−0.874059	+	0.485821i	$0.838521\pi$
$390$		0			0
$391$	−13.1253			−0.663777
$392$		0			0
$393$	−4.23237	+	5.49578i	−0.213495	+	0.277225i
$394$		0			0
$395$	12.2691	−	12.2691i	0.617326	−	0.617326i
$396$		0			0
$397$	11.5714	+	11.5714i	0.580750	+	0.580750i	0.935109	−	0.354359i	$-0.115301\pi$
$397$	11.5714	+	11.5714i	0.580750	+	0.580750i	−0.354359	+	0.935109i	$0.615301\pi$
$398$		0			0
$399$	9.66952	+	7.44662i	0.484082	+	0.372797i
$400$		0			0
$401$			4.44074i			0.221760i	0.993834	+	0.110880i	$0.0353670\pi$
$401$			4.44074i			0.221760i	−0.993834	+	0.110880i	$0.964633\pi$
$402$		0			0
$403$	15.0546	−	15.0546i	0.749925	−	0.749925i
$404$		0			0
$405$	27.8575	+	7.67393i	1.38425	+	0.381321i
$406$		0			0
$407$			5.44565i			0.269931i
$408$		0			0
$409$			33.0682i			1.63512i	0.575846	+	0.817558i	$0.304673\pi$
$409$			33.0682i			1.63512i	−0.575846	+	0.817558i	$0.695327\pi$
$410$		0			0
$411$	3.14642	+	24.2272i	0.155202	+	1.19504i
$412$		0			0
$413$	1.94904	−	1.94904i	0.0959062	−	0.0959062i
$414$		0			0
$415$			32.3411i			1.58756i
$416$		0			0
$417$	−7.71927	+	10.0236i	−0.378014	+	0.490856i
$418$		0			0
$419$	4.39061	+	4.39061i	0.214495	+	0.214495i	0.806174	−	0.591679i	$-0.201535\pi$
$419$	4.39061	+	4.39061i	0.214495	+	0.214495i	−0.591679	+	0.806174i	$0.701535\pi$
$420$		0			0
$421$	−28.6244	+	28.6244i	−1.39507	+	1.39507i	−0.581581	+	0.813488i	$0.697566\pi$
$421$	−28.6244	+	28.6244i	−1.39507	+	1.39507i	−0.813488	+	0.581581i	$0.802434\pi$
$422$		0			0
$423$	3.46131	−	0.914475i	0.168295	−	0.0444633i
$424$		0			0
$425$	−9.65437			−0.468306
$426$		0			0
$427$	−2.94791	−	2.94791i	−0.142659	−	0.142659i
$428$		0			0
$429$	−2.48935	−	19.1678i	−0.120187	−	0.925429i
$430$		0			0
$431$	15.8985			0.765805			0.382903	−	0.923789i	$-0.374924\pi$
$431$	15.8985			0.765805			0.382903	+	0.923789i	$0.374924\pi$
$432$		0			0
$433$	24.4239			1.17374			0.586870	−	0.809681i	$-0.300360\pi$
$433$	24.4239			1.17374			0.586870	+	0.809681i	$0.300360\pi$
$434$		0			0
$435$	−2.80746	−	21.6172i	−0.134608	−	1.03647i
$436$		0			0
$437$	−35.9541	−	35.9541i	−1.71992	−	1.71992i
$438$		0			0
$439$	−2.55315			−0.121855			−0.0609277	−	0.998142i	$-0.519406\pi$
$439$	−2.55315			−0.121855			−0.0609277	+	0.998142i	$0.519406\pi$
$440$		0			0
$441$	−2.90048	+	0.766304i	−0.138118	+	0.0364907i
$442$		0			0
$443$	−6.64628	+	6.64628i	−0.315774	+	0.315774i	−0.847142	−	0.531367i	$-0.821678\pi$
$443$	−6.64628	+	6.64628i	−0.315774	+	0.315774i	0.531367	+	0.847142i	$0.321678\pi$
$444$		0			0
$445$	25.3685	+	25.3685i	1.20258	+	1.20258i
$446$		0			0
$447$	−16.9878	+	22.0589i	−0.803496	+	1.04335i
$448$		0			0
$449$			0.463395i			0.0218689i	0.999940	+	0.0109345i	$0.00348062\pi$
$449$			0.463395i			0.0218689i	−0.999940	+	0.0109345i	$0.996519\pi$
$450$		0			0
$451$	0.795902	−	0.795902i	0.0374776	−	0.0374776i
$452$		0			0
$453$	−4.55445	−	35.0689i	−0.213987	−	1.64768i
$454$		0			0
$455$			16.4861i			0.772880i
$456$		0			0
$457$		−	12.8788i		−	0.602445i	−0.953554	−	0.301222i	$-0.902605\pi$
$457$		−	12.8788i		−	0.602445i	0.953554	−	0.301222i	$-0.0973947\pi$
$458$		0			0
$459$	8.75073	−	3.57093i	0.408449	−	0.166677i
$460$		0			0
$461$	9.25658	−	9.25658i	0.431122	−	0.431122i	−0.457888	−	0.889010i	$-0.651394\pi$
$461$	9.25658	−	9.25658i	0.431122	−	0.431122i	0.889010	+	0.457888i	$0.151394\pi$
$462$		0			0
$463$			22.2993i			1.03634i	0.855278	+	0.518169i	$0.173386\pi$
$463$			22.2993i			1.03634i	−0.855278	+	0.518169i	$0.826614\pi$
$464$		0			0
$465$	−18.2674	−	14.0680i	−0.847131	−	0.652386i
$466$		0			0
$467$	−14.3536	−	14.3536i	−0.664205	−	0.664205i	0.292163	−	0.956368i	$-0.405625\pi$
$467$	−14.3536	−	14.3536i	−0.664205	−	0.664205i	−0.956368	+	0.292163i	$0.905625\pi$
$468$		0			0
$469$	−7.85747	+	7.85747i	−0.362824	+	0.362824i
$470$		0			0
$471$	9.27152	−	12.0392i	0.427209	−	0.554736i
$472$		0			0
$473$	14.3659			0.660545
$474$		0			0
$475$	−26.4461	−	26.4461i	−1.21343	−	1.21343i
$476$		0			0
$477$	29.1283	+	16.9535i	1.33370	+	0.776249i
$478$		0			0
$479$	−5.08030			−0.232125			−0.116062	−	0.993242i	$-0.537027\pi$
$479$	−5.08030			−0.232125			−0.116062	+	0.993242i	$0.537027\pi$
$480$		0			0
$481$	12.8670			0.586683
$482$		0			0
$483$	12.3945	−	1.60970i	0.563970	−	0.0732437i
$484$		0			0
$485$	27.9792	+	27.9792i	1.27047	+	1.27047i
$486$		0			0
$487$	−15.3722			−0.696582			−0.348291	−	0.937386i	$-0.613238\pi$
$487$	−15.3722			−0.696582			−0.348291	+	0.937386i	$0.613238\pi$
$488$		0			0
$489$	−7.51672	−	5.78873i	−0.339918	−	0.261775i
$490$		0			0
$491$	17.6352	−	17.6352i	0.795867	−	0.795867i	−0.186574	−	0.982441i	$-0.559738\pi$
$491$	17.6352	−	17.6352i	0.795867	−	0.795867i	0.982441	+	0.186574i	$0.0597384\pi$
$492$		0			0
$493$	−5.04177	−	5.04177i	−0.227070	−	0.227070i
$494$		0			0
$495$	−20.2377	+	5.34678i	−0.909617	+	0.240320i
$496$		0			0
$497$			10.9009i			0.488971i
$498$		0			0
$499$	27.5178	−	27.5178i	1.23187	−	1.23187i	0.268622	−	0.963246i	$-0.413432\pi$
$499$	27.5178	−	27.5178i	1.23187	−	1.23187i	0.963246	−	0.268622i	$-0.0865683\pi$
$500$		0			0
$501$	−10.7427	+	1.39517i	−0.479946	+	0.0623314i
$502$		0			0
$503$		−	8.92907i		−	0.398128i	−0.979987	−	0.199064i	$-0.936210\pi$
$503$		−	8.92907i		−	0.398128i	0.979987	−	0.199064i	$-0.0637901\pi$
$504$		0			0
$505$		−	39.6080i		−	1.76253i
$506$		0			0
$507$	−22.9604	+	2.98190i	−1.01971	+	0.132431i
$508$		0			0
$509$	16.3303	−	16.3303i	0.723829	−	0.723829i	−0.245554	−	0.969383i	$-0.578970\pi$
$509$	16.3303	−	16.3303i	0.723829	−	0.723829i	0.969383	+	0.245554i	$0.0789698\pi$
$510$		0			0
$511$		−	15.7454i		−	0.696537i
$512$		0			0
$513$	33.7526	+	14.1890i	1.49021	+	0.626459i
$514$		0			0
$515$	3.95266	+	3.95266i	0.174175	+	0.174175i
$516$		0			0
$517$	−1.83385	+	1.83385i	−0.0806527	+	0.0806527i
$518$		0			0
$519$	−28.5643	−	21.9977i	−1.25383	−	0.965592i
$520$		0			0
$521$	10.4790			0.459093			0.229547	−	0.973298i	$-0.426276\pi$
$521$	10.4790			0.459093			0.229547	+	0.973298i	$0.426276\pi$
$522$		0			0
$523$	1.75338	+	1.75338i	0.0766700	+	0.0766700i	0.744402	−	0.667732i	$-0.232735\pi$
$523$	1.75338	+	1.75338i	0.0766700	+	0.0766700i	−0.667732	+	0.744402i	$0.732735\pi$
$524$		0			0
$525$	9.11682	−	1.18402i	0.397891	−	0.0516747i
$526$		0			0
$527$	−7.54154			−0.328515
$528$		0			0
$529$	−29.0718			−1.26399
$530$		0			0
$531$	4.15960	−	7.14672i	0.180511	−	0.310141i
$532$		0			0
$533$	−1.88055	−	1.88055i	−0.0814559	−	0.0814559i
$534$		0			0
$535$	−2.90637			−0.125653
$536$		0			0
$537$	18.6680	−	24.2406i	0.805584	−	1.04606i
$538$		0			0
$539$	1.53672	−	1.53672i	0.0661910	−	0.0661910i
$540$		0			0
$541$	21.1268	+	21.1268i	0.908311	+	0.908311i	0.996136	−	0.0878251i	$-0.0279917\pi$
$541$	21.1268	+	21.1268i	0.908311	+	0.908311i	−0.0878251	+	0.996136i	$0.527992\pi$
$542$		0			0
$543$	2.06405	+	1.58955i	0.0885771	+	0.0682143i
$544$		0			0
$545$			20.5633i			0.880834i
$546$		0			0
$547$	−10.0948	+	10.0948i	−0.431622	+	0.431622i	−0.889180	−	0.457558i	$-0.848724\pi$
$547$	−10.0948	+	10.0948i	−0.431622	+	0.431622i	0.457558	+	0.889180i	$0.348724\pi$
$548$		0			0
$549$	−10.8093	−	6.29135i	−0.461331	−	0.268508i
$550$		0			0
$551$		−	27.6217i		−	1.17672i
$552$		0			0
$553$			5.40437i			0.229817i
$554$		0			0
$555$	−1.79460	−	13.8182i	−0.0761764	−	0.586552i
$556$		0			0
$557$	−6.89116	+	6.89116i	−0.291988	+	0.291988i	−0.837865	−	0.545877i	$-0.816197\pi$
$557$	−6.89116	+	6.89116i	−0.291988	+	0.291988i	0.545877	+	0.837865i	$0.316197\pi$
$558$		0			0
$559$		−	33.9437i		−	1.43567i
$560$		0			0
$561$	−4.17748	+	5.42451i	−0.176373	+	0.229023i
$562$		0			0
$563$	−20.3031	−	20.3031i	−0.855675	−	0.855675i	0.135150	−	0.990825i	$-0.456848\pi$
$563$	−20.3031	−	20.3031i	−0.855675	−	0.855675i	−0.990825	+	0.135150i	$0.956848\pi$
$564$		0			0
$565$	6.49369	−	6.49369i	0.273192	−	0.273192i
$566$		0			0
$567$	−7.82556	+	4.44530i	−0.328642	+	0.186685i
$568$		0			0
$569$	−24.5437			−1.02893			−0.514463	−	0.857512i	$-0.672009\pi$
$569$	−24.5437			−1.02893			−0.514463	+	0.857512i	$0.672009\pi$
$570$		0			0
$571$	24.2789	+	24.2789i	1.01604	+	1.01604i	0.999869	+	0.0161720i	$0.00514793\pi$
$571$	24.2789	+	24.2789i	1.01604	+	1.01604i	0.0161720	+	0.999869i	$0.494852\pi$
$572$		0			0
$573$	4.22384	+	32.5232i	0.176454	+	1.35868i
$574$		0			0
$575$	−38.3015			−1.59728
$576$		0			0
$577$	−37.2283			−1.54983			−0.774916	−	0.632064i	$-0.782208\pi$
$577$	−37.2283			−1.54983			−0.774916	+	0.632064i	$0.782208\pi$
$578$		0			0
$579$	−0.311714	−	2.40017i	−0.0129544	−	0.0997478i
$580$		0			0
$581$	−7.12290	−	7.12290i	−0.295508	−	0.295508i
$582$		0			0
$583$	−24.4148			−1.01116
$584$		0			0
$585$	12.6334	+	47.8176i	0.522325	+	1.97701i
$586$		0			0
$587$	−16.9789	+	16.9789i	−0.700796	+	0.700796i	−0.964581	−	0.263785i	$-0.915029\pi$
$587$	−16.9789	+	16.9789i	−0.700796	+	0.700796i	0.263785	+	0.964581i	$0.415029\pi$
$588$		0			0
$589$	−20.6585	−	20.6585i	−0.851218	−	0.851218i
$590$		0			0
$591$	13.2643	−	17.2238i	0.545619	−	0.708492i
$592$		0			0
$593$			17.6074i			0.723050i	0.932362	+	0.361525i	$0.117744\pi$
$593$			17.6074i			0.723050i	−0.932362	+	0.361525i	$0.882256\pi$
$594$		0			0
$595$	4.12931	−	4.12931i	0.169285	−	0.169285i
$596$		0			0
$597$	4.88224	+	37.5929i	0.199817	+	1.53857i
$598$		0			0
$599$			27.5694i			1.12646i	0.826302	+	0.563228i	$0.190441\pi$
$599$			27.5694i			1.12646i	−0.826302	+	0.563228i	$0.809559\pi$
$600$		0			0
$601$			4.35161i			0.177506i	0.996054	+	0.0887529i	$0.0282881\pi$
$601$			4.35161i			0.177506i	−0.996054	+	0.0887529i	$0.971712\pi$
$602$		0			0
$603$	−16.7692	+	28.8116i	−0.682895	+	1.17330i
$604$		0			0
$605$	−14.2502	+	14.2502i	−0.579353	+	0.579353i
$606$		0			0
$607$			7.85518i			0.318832i	0.987212	+	0.159416i	$0.0509611\pi$
$607$			7.85518i			0.318832i	−0.987212	+	0.159416i	$0.949039\pi$
$608$		0			0
$609$	5.37937	+	4.14272i	0.217983	+	0.167871i
$610$		0			0
$611$	4.33302	+	4.33302i	0.175295	+	0.175295i
$612$		0			0
$613$	8.45171	−	8.45171i	0.341361	−	0.341361i	−0.515518	−	0.856879i	$-0.672400\pi$
$613$	8.45171	−	8.45171i	0.341361	−	0.341361i	0.856879	+	0.515518i	$0.172400\pi$
$614$		0			0
$615$	−1.75730	+	2.28188i	−0.0708613	+	0.0920142i
$616$		0			0
$617$	−29.2865			−1.17903			−0.589515	−	0.807758i	$-0.700681\pi$
$617$	−29.2865			−1.17903			−0.589515	+	0.807758i	$0.700681\pi$
$618$		0			0
$619$	26.8403	+	26.8403i	1.07880	+	1.07880i	0.996617	+	0.0821872i	$0.0261905\pi$
$619$	26.8403	+	26.8403i	1.07880	+	1.07880i	0.0821872	+	0.996617i	$0.473809\pi$
$620$		0			0
$621$	34.7165	−	14.1669i	1.39313	−	0.568497i
$622$		0			0
$623$	−11.1745			−0.447696
$624$		0			0
$625$	23.3662			0.934649
$626$		0			0
$627$	−26.3026	+	3.41596i	−1.05043	+	0.136420i
$628$		0			0
$629$	−3.22282	−	3.22282i	−0.128502	−	0.128502i
$630$		0			0
$631$	−0.489937			−0.0195041			−0.00975204	−	0.999952i	$-0.503104\pi$
$631$	−0.489937			−0.0195041			−0.00975204	+	0.999952i	$0.503104\pi$
$632$		0			0
$633$	−11.9298	−	9.18726i	−0.474166	−	0.365161i
$634$		0			0
$635$	14.6406	−	14.6406i	0.580996	−	0.580996i
$636$		0			0
$637$	−3.63094	−	3.63094i	−0.143863	−	0.143863i
$638$		0			0
$639$	8.35339	+	31.6178i	0.330455	+	1.25078i
$640$		0			0
$641$		−	23.0818i		−	0.911676i	−0.890063	−	0.455838i	$-0.849340\pi$
$641$		−	23.0818i		−	0.911676i	0.890063	−	0.455838i	$-0.150660\pi$
$642$		0			0
$643$	4.66945	−	4.66945i	0.184145	−	0.184145i	−0.609014	−	0.793159i	$-0.708435\pi$
$643$	4.66945	−	4.66945i	0.184145	−	0.184145i	0.793159	+	0.609014i	$0.208435\pi$
$644$		0			0
$645$	−36.4533	+	4.73424i	−1.43535	+	0.186411i
$646$		0			0
$647$			2.56882i			0.100991i	0.998724	+	0.0504953i	$0.0160800\pi$
$647$			2.56882i			0.100991i	−0.998724	+	0.0504953i	$0.983920\pi$
$648$		0			0
$649$			5.99025i			0.235138i
$650$		0			0
$651$	7.12163	−	0.924898i	0.279119	−	0.0362496i
$652$		0			0
$653$	0.969829	−	0.969829i	0.0379523	−	0.0379523i	−0.687876	−	0.725828i	$-0.741457\pi$
$653$	0.969829	−	0.969829i	0.0379523	−	0.0379523i	0.725828	+	0.687876i	$0.241457\pi$
$654$		0			0
$655$			12.8579i			0.502399i
$656$		0			0
$657$	−12.0658	−	45.6693i	−0.470732	−	1.78173i
$658$		0			0
$659$	−30.8082	−	30.8082i	−1.20012	−	1.20012i	−0.974131	−	0.225985i	$-0.927440\pi$
$659$	−30.8082	−	30.8082i	−1.20012	−	1.20012i	−0.225985	−	0.974131i	$-0.572560\pi$
$660$		0			0
$661$	−1.86728	+	1.86728i	−0.0726286	+	0.0726286i	−0.742488	−	0.669859i	$-0.766354\pi$
$661$	−1.86728	+	1.86728i	−0.0726286	+	0.0726286i	0.669859	+	0.742488i	$0.266354\pi$
$662$		0			0
$663$	12.8170	+	9.87054i	0.497771	+	0.383340i
$664$		0			0
$665$	22.6227			0.877273
$666$		0			0
$667$	−20.0021	−	20.0021i	−0.774482	−	0.774482i
$668$		0			0
$669$	−38.7319	+	5.03017i	−1.49746	+	0.194477i
$670$		0			0
$671$	9.06019			0.349765
$672$		0			0
$673$	−10.3158			−0.397643			−0.198822	−	0.980036i	$-0.563711\pi$
$673$	−10.3158			−0.397643			−0.198822	+	0.980036i	$0.563711\pi$
$674$		0			0
$675$	25.5358	−	10.4205i	0.982875	−	0.401084i
$676$		0			0
$677$	−26.2802	−	26.2802i	−1.01003	−	1.01003i	−0.999949	−	0.0100808i	$-0.996791\pi$
$677$	−26.2802	−	26.2802i	−1.01003	−	1.01003i	−0.0100808	−	0.999949i	$-0.503209\pi$
$678$		0			0
$679$	−12.3244			−0.472968
$680$		0			0
$681$	11.7797	−	15.2960i	0.451397	−	0.586144i
$682$		0			0
$683$	−23.4251	+	23.4251i	−0.896335	+	0.896335i	−0.995110	−	0.0987751i	$-0.968508\pi$
$683$	−23.4251	+	23.4251i	−0.896335	+	0.896335i	0.0987751	+	0.995110i	$0.468508\pi$
$684$		0			0
$685$	32.0216	+	32.0216i	1.22348	+	1.22348i
$686$		0			0
$687$	18.7561	+	14.4443i	0.715588	+	0.551083i
$688$		0			0
$689$			57.6873i			2.19771i
$690$		0			0
$691$	9.99950	−	9.99950i	0.380399	−	0.380399i	−0.490847	−	0.871246i	$-0.663313\pi$
$691$	9.99950	−	9.99950i	0.380399	−	0.380399i	0.871246	+	0.490847i	$0.163313\pi$
$692$		0			0
$693$	3.27962	−	5.63480i	0.124582	−	0.214048i
$694$		0			0
$695$			23.4510i			0.889549i
$696$		0			0
$697$			0.942054i			0.0356828i
$698$		0			0
$699$	4.65516	+	35.8443i	0.176074	+	1.35576i
$700$		0			0
$701$	28.9895	−	28.9895i	1.09492	−	1.09492i	0.0999251	−	0.994995i	$-0.468140\pi$
$701$	28.9895	−	28.9895i	1.09492	−	1.09492i	0.994995	−	0.0999251i	$-0.0318603\pi$
$702$		0			0
$703$		−	17.6565i		−	0.665926i
$704$		0			0
$705$	4.04903	−	5.25771i	0.152495	−	0.198017i
$706$		0			0
$707$	8.72339	+	8.72339i	0.328077	+	0.328077i
$708$		0			0
$709$	0.235410	−	0.235410i	0.00884102	−	0.00884102i	−0.702672	−	0.711513i	$-0.748010\pi$
$709$	0.235410	−	0.235410i	0.00884102	−	0.00884102i	0.711513	+	0.702672i	$0.248010\pi$
$710$		0			0
$711$	4.14139	+	15.6753i	0.155314	+	0.587868i
$712$		0			0
$713$	−29.9193			−1.12049
$714$		0			0
$715$	−25.3344	−	25.3344i	−0.947454	−	0.947454i
$716$		0			0
$717$	2.23016	+	17.1720i	0.0832867	+	0.641300i
$718$		0			0
$719$	15.4145			0.574864			0.287432	−	0.957801i	$-0.407198\pi$
$719$	15.4145			0.574864			0.287432	+	0.957801i	$0.407198\pi$
$720$		0			0
$721$	−1.74109			−0.0648416
$722$		0			0
$723$	3.71410	+	28.5983i	0.138129	+	1.06358i
$724$		0			0
$725$	−14.7126	−	14.7126i	−0.546411	−	0.546411i
$726$		0			0
$727$	35.3548			1.31124			0.655619	−	0.755092i	$-0.272408\pi$
$727$	35.3548			1.31124			0.655619	+	0.755092i	$0.272408\pi$
$728$		0			0
$729$	−19.2914	+	18.8903i	−0.714497	+	0.699639i
$730$		0			0
$731$	−8.50196	+	8.50196i	−0.314456	+	0.314456i
$732$		0			0
$733$	8.83561	+	8.83561i	0.326351	+	0.326351i	0.851197	−	0.524846i	$-0.175877\pi$
$733$	8.83561	+	8.83561i	0.326351	+	0.326351i	−0.524846	+	0.851197i	$0.675877\pi$
$734$		0			0
$735$	−3.39297	+	4.40581i	−0.125152	+	0.162511i
$736$		0			0
$737$		−	24.1494i		−	0.889554i
$738$		0			0
$739$	6.37067	−	6.37067i	0.234349	−	0.234349i	−0.580156	−	0.814505i	$-0.697009\pi$
$739$	6.37067	−	6.37067i	0.234349	−	0.234349i	0.814505	+	0.580156i	$0.197009\pi$
$740$		0			0
$741$	8.07123	+	62.1478i	0.296504	+	2.28306i
$742$		0			0
$743$			7.69026i			0.282128i	0.990000	+	0.141064i	$0.0450524\pi$
$743$			7.69026i			0.282128i	−0.990000	+	0.141064i	$0.954948\pi$
$744$		0			0
$745$			51.6088i			1.89080i
$746$		0			0
$747$	−26.1181	−	15.2015i	−0.955612	−	0.556194i
$748$		0			0
$749$	0.640107	−	0.640107i	0.0233890	−	0.0233890i
$750$		0			0
$751$			18.7075i			0.682646i	0.939946	+	0.341323i	$0.110875\pi$
$751$			18.7075i			0.682646i	−0.939946	+	0.341323i	$0.889125\pi$
$752$		0			0
$753$	27.0539	+	20.8345i	0.985897	+	0.759252i
$754$		0			0
$755$	−46.3512	−	46.3512i	−1.68689	−	1.68689i
$756$		0			0
$757$	11.2403	−	11.2403i	0.408537	−	0.408537i	−0.472691	−	0.881228i	$-0.656717\pi$
$757$	11.2403	−	11.2403i	0.408537	−	0.408537i	0.881228	+	0.472691i	$0.156717\pi$
$758$		0			0
$759$	−16.5732	+	21.5205i	−0.601569	+	0.781144i
$760$		0			0
$761$	−6.13022			−0.222220			−0.111110	−	0.993808i	$-0.535441\pi$
$761$	−6.13022			−0.222220			−0.111110	+	0.993808i	$0.535441\pi$
$762$		0			0
$763$	−4.52892	−	4.52892i	−0.163958	−	0.163958i
$764$		0			0
$765$	8.81266	−	15.1413i	0.318623	−	0.547434i
$766$		0			0
$767$	14.1537			0.511062
$768$		0			0
$769$	−48.7274			−1.75716			−0.878578	−	0.477599i	$-0.841507\pi$
$769$	−48.7274			−1.75716			−0.878578	+	0.477599i	$0.841507\pi$
$770$		0			0
$771$	−14.3791	+	1.86744i	−0.517852	+	0.0672542i
$772$		0			0
$773$	27.8293	+	27.8293i	1.00095	+	1.00095i	1.00000		0.000951442i	$0.000302853\pi$
$773$	27.8293	+	27.8293i	1.00095	+	1.00095i	0.000951442		1.00000i	$0.499697\pi$
$774$		0			0
$775$	−22.0073			−0.790524
$776$		0			0
$777$	3.43862	+	2.64812i	0.123360	+	0.0950009i
$778$		0			0
$779$	−2.58056	+	2.58056i	−0.0924581	+	0.0924581i
$780$		0			0
$781$	−16.7515	−	16.7515i	−0.599417	−	0.599417i
$782$		0			0
$783$	18.7773	+	7.89364i	0.671047	+	0.282096i
$784$		0			0
$785$		−	28.1668i		−	1.00532i
$786$		0			0
$787$	−27.1930	+	27.1930i	−0.969327	+	0.969327i	−0.999543	−	0.0302163i	$-0.990380\pi$
$787$	−27.1930	+	27.1930i	−0.969327	+	0.969327i	0.0302163	+	0.999543i	$0.490380\pi$
$788$		0			0
$789$	−6.21790	+	0.807528i	−0.221363	+	0.0287488i
$790$		0			0
$791$			2.86038i			0.101703i
$792$		0			0
$793$		−	21.4074i		−	0.760198i
$794$		0			0
$795$	61.9523	−	8.04584i	2.19722	−	0.285356i
$796$		0			0
$797$	4.82223	−	4.82223i	0.170812	−	0.170812i	−0.616524	−	0.787336i	$-0.711460\pi$
$797$	4.82223	−	4.82223i	0.170812	−	0.170812i	0.787336	+	0.616524i	$0.211460\pi$
$798$		0			0
$799$		−	2.17060i		−	0.0767903i
$800$		0			0
$801$	−32.4113	+	8.56304i	−1.14520	+	0.302560i
$802$		0			0
$803$	24.1963	+	24.1963i	0.853868	+	0.853868i
$804$		0			0
$805$	16.3821	−	16.3821i	0.577393	−	0.577393i
$806$		0			0
$807$	0.265219	+	0.204248i	0.00933614	+	0.00718988i
$808$		0			0
$809$	−41.7157			−1.46665			−0.733323	−	0.679880i	$-0.762032\pi$
$809$	−41.7157			−1.46665			−0.733323	+	0.679880i	$0.762032\pi$
$810$		0			0
$811$	−2.12966	−	2.12966i	−0.0747826	−	0.0747826i	0.668726	−	0.743509i	$-0.266840\pi$
$811$	−2.12966	−	2.12966i	−0.0747826	−	0.0747826i	−0.743509	+	0.668726i	$0.766840\pi$
$812$		0			0
$813$	38.0043	−	4.93568i	1.33287	−	0.173102i
$814$		0			0
$815$	−17.5861			−0.616013
$816$		0			0
$817$	−46.5787			−1.62958
$818$		0			0
$819$	−13.3139	−	7.74907i	−0.465225	−	0.270774i
$820$		0			0
$821$	17.6123	+	17.6123i	0.614675	+	0.614675i	0.944161	−	0.329485i	$-0.106875\pi$
$821$	17.6123	+	17.6123i	0.614675	+	0.614675i	−0.329485	+	0.944161i	$0.606875\pi$
$822$		0			0
$823$	−22.8604			−0.796864			−0.398432	−	0.917198i	$-0.630446\pi$
$823$	−22.8604			−0.796864			−0.398432	+	0.917198i	$0.630446\pi$
$824$		0			0
$825$	−12.1905	+	15.8295i	−0.424418	+	0.551111i
$826$		0			0
$827$	17.8096	−	17.8096i	0.619299	−	0.619299i	−0.326052	−	0.945352i	$-0.605719\pi$
$827$	17.8096	−	17.8096i	0.619299	−	0.619299i	0.945352	+	0.326052i	$0.105719\pi$
$828$		0			0
$829$	18.5707	+	18.5707i	0.644986	+	0.644986i	0.951777	−	0.306791i	$-0.0992553\pi$
$829$	18.5707	+	18.5707i	0.644986	+	0.644986i	−0.306791	+	0.951777i	$0.599255\pi$
$830$		0			0
$831$	−14.4061	−	11.0943i	−0.499742	−	0.384857i
$832$		0			0
$833$			1.81890i			0.0630212i
$834$		0			0
$835$	−14.1988	+	14.1988i	−0.491369	+	0.491369i
$836$		0			0
$837$	19.9474	−	8.13998i	0.689483	−	0.281359i
$838$		0			0
$839$		−	9.12371i		−	0.314986i	−0.987520	−	0.157493i	$-0.949659\pi$
$839$		−	9.12371i		−	0.314986i	0.987520	−	0.157493i	$-0.0503411\pi$
$840$		0			0
$841$			13.6334i			0.470118i
$842$		0			0
$843$	−0.483174	−	3.72040i	−0.0166414	−	0.128137i
$844$		0			0
$845$	−30.3472	+	30.3472i	−1.04398	+	1.04398i
$846$		0			0
$847$		−	6.27701i		−	0.215681i
$848$		0			0
$849$	−15.8691	+	20.6062i	−0.544626	+	0.707204i
$850$		0			0
$851$	−12.7858	−	12.7858i	−0.438291	−	0.438291i
$852$		0			0
$853$	0.691738	−	0.691738i	0.0236846	−	0.0236846i	−0.695165	−	0.718850i	$-0.744669\pi$
$853$	0.691738	−	0.691738i	0.0236846	−	0.0236846i	0.718850	+	0.695165i	$0.244669\pi$
$854$		0			0
$855$	65.6168	−	17.3359i	2.24405	−	0.592876i
$856$		0			0
$857$	28.5386			0.974860			0.487430	−	0.873162i	$-0.337934\pi$
$857$	28.5386			0.974860			0.487430	+	0.873162i	$0.337934\pi$
$858$		0			0
$859$	16.6833	+	16.6833i	0.569228	+	0.569228i	0.931912	−	0.362684i	$-0.118140\pi$
$859$	16.6833	+	16.6833i	0.569228	+	0.569228i	−0.362684	+	0.931912i	$0.618140\pi$
$860$		0			0
$861$	−0.115534	−	0.889601i	−0.00393738	−	0.0303175i
$862$		0			0
$863$	−17.7028			−0.602610			−0.301305	−	0.953528i	$-0.597422\pi$
$863$	−17.7028			−0.602610			−0.301305	+	0.953528i	$0.597422\pi$
$864$		0			0
$865$	−66.8288			−2.27225
$866$		0			0
$867$	3.05419	+	23.5170i	0.103726	+	0.798681i
$868$		0			0
$869$	−8.30497	−	8.30497i	−0.281727	−	0.281727i
$870$		0			0
$871$	−57.0601			−1.93341
$872$		0			0
$873$	−35.7468	+	9.44427i	−1.20984	+	0.319640i
$874$		0			0
$875$	0.698783	−	0.698783i	0.0236232	−	0.0236232i
$876$		0			0
$877$	−25.5896	−	25.5896i	−0.864099	−	0.864099i	0.127712	−	0.991811i	$-0.459237\pi$
$877$	−25.5896	−	25.5896i	−0.864099	−	0.864099i	−0.991811	+	0.127712i	$0.959237\pi$
$878$		0			0
$879$	−9.48631	+	12.3181i	−0.319965	+	0.415478i
$880$		0			0
$881$		−	52.2911i		−	1.76173i	−0.473367	−	0.880865i	$-0.656961\pi$
$881$		−	52.2911i		−	1.76173i	0.473367	−	0.880865i	$-0.343039\pi$
$882$		0			0
$883$	−1.05344	+	1.05344i	−0.0354512	+	0.0354512i	−0.724610	−	0.689159i	$-0.757980\pi$
$883$	−1.05344	+	1.05344i	−0.0354512	+	0.0354512i	0.689159	+	0.724610i	$0.257980\pi$
$884$		0			0
$885$	−1.97407	−	15.2002i	−0.0663576	−	0.510948i
$886$		0			0
$887$		−	7.92643i		−	0.266143i	−0.991106	−	0.133072i	$-0.957516\pi$
$887$		−	7.92643i		−	0.266143i	0.991106	−	0.133072i	$-0.0424841\pi$
$888$		0			0
$889$			6.44899i			0.216292i
$890$		0			0
$891$	5.19449	−	18.8568i	0.174022	−	0.631727i
$892$		0			0
$893$	5.94590	−	5.94590i	0.198972	−	0.198972i
$894$		0			0
$895$		−	56.7132i		−	1.89571i
$896$		0			0
$897$	50.8485	+	39.1591i	1.69778	+	1.30748i
$898$		0			0
$899$	−11.4928	−	11.4928i	−0.383305	−	0.383305i
$900$		0			0
$901$	14.4491	−	14.4491i	0.481368	−	0.481368i
$902$		0			0
$903$	6.98589	−	9.07126i	0.232476	−	0.301873i
$904$		0			0
$905$	4.82905			0.160523
$906$		0			0
$907$	−19.6768	−	19.6768i	−0.653358	−	0.653358i	0.300442	−	0.953800i	$-0.402866\pi$
$907$	−19.6768	−	19.6768i	−0.653358	−	0.653358i	−0.953800	+	0.300442i	$0.902866\pi$
$908$		0			0
$909$	31.9868	+	18.6172i	1.06093	+	0.617495i
$910$		0			0
$911$	−32.4338			−1.07458			−0.537291	−	0.843397i	$-0.680552\pi$
$911$	−32.4338			−1.07458			−0.537291	+	0.843397i	$0.680552\pi$
$912$		0			0
$913$	21.8917			0.724511
$914$		0			0
$915$	−22.9901	+	2.98576i	−0.760029	+	0.0987061i
$916$		0			0
$917$	−2.83186	−	2.83186i	−0.0935162	−	0.0935162i
$918$		0			0
$919$	18.6029			0.613653			0.306827	−	0.951765i	$-0.400733\pi$
$919$	18.6029			0.613653			0.306827	+	0.951765i	$0.400733\pi$
$920$		0			0
$921$	−23.3783	−	18.0039i	−0.770341	−	0.593250i
$922$		0			0
$923$	−39.5805	+	39.5805i	−1.30281	+	1.30281i
$924$		0			0
$925$	−9.40462	−	9.40462i	−0.309222	−	0.309222i
$926$		0			0
$927$	−5.05000	+	1.33421i	−0.165864	+	0.0438210i
$928$		0			0
$929$		−	8.43671i		−	0.276800i	−0.990376	−	0.138400i	$-0.955804\pi$
$929$		−	8.43671i		−	0.276800i	0.990376	−	0.138400i	$-0.0441959\pi$
$930$		0			0
$931$	−4.98250	+	4.98250i	−0.163295	+	0.163295i
$932$		0			0
$933$	−31.5260	+	4.09433i	−1.03212	+	0.134042i
$934$		0			0
$935$			12.6911i			0.415045i
$936$		0			0
$937$		−	19.1378i		−	0.625206i	−0.949884	−	0.312603i	$-0.898799\pi$
$937$		−	19.1378i		−	0.625206i	0.949884	−	0.312603i	$-0.101201\pi$
$938$		0			0
$939$	−20.3714	+	2.64567i	−0.664796	+	0.0863381i
$940$		0			0
$941$	29.2568	−	29.2568i	0.953745	−	0.953745i	−0.0452313	−	0.998977i	$-0.514402\pi$
$941$	29.2568	−	29.2568i	0.953745	−	0.953745i	0.998977	+	0.0452313i	$0.0144025\pi$
$942$		0			0
$943$			3.73738i			0.121706i
$944$		0			0
$945$	−6.46505	+	15.3790i	−0.210308	+	0.500279i
$946$		0			0
$947$	−5.36713	−	5.36713i	−0.174408	−	0.174408i	0.614505	−	0.788913i	$-0.289356\pi$
$947$	−5.36713	−	5.36713i	−0.174408	−	0.174408i	−0.788913	+	0.614505i	$0.789356\pi$
$948$		0			0
$949$	57.1708	−	57.1708i	1.85584	−	1.85584i
$950$		0			0
$951$	14.4502	+	11.1283i	0.468579	+	0.360859i
$952$		0			0
$953$	−36.7962			−1.19195			−0.595973	−	0.803004i	$-0.703234\pi$
$953$	−36.7962			−1.19195			−0.595973	+	0.803004i	$0.703234\pi$
$954$		0			0
$955$	42.9866	+	42.9866i	1.39101	+	1.39101i
$956$		0			0
$957$	−14.6327	+	1.90038i	−0.473009	+	0.0614304i
$958$		0			0
$959$	−14.1051			−0.455476
$960$		0			0
$961$	13.8090			0.445450
$962$		0			0
$963$	1.36610	−	2.34713i	0.0440219	−	0.0756353i
$964$		0			0
$965$	−3.17236	−	3.17236i	−0.102122	−	0.102122i
$966$		0			0
$967$	28.6511			0.921358			0.460679	−	0.887567i	$-0.347606\pi$
$967$	28.6511			0.921358			0.460679	+	0.887567i	$0.347606\pi$
$968$		0			0
$969$	13.5447	−	17.5879i	0.435118	−	0.565005i
$970$		0			0
$971$	22.5134	−	22.5134i	0.722489	−	0.722489i	−0.246623	−	0.969112i	$-0.579321\pi$
$971$	22.5134	−	22.5134i	0.722489	−	0.722489i	0.969112	+	0.246623i	$0.0793209\pi$
$972$		0			0
$973$	−5.16493	−	5.16493i	−0.165580	−	0.165580i
$974$		0			0
$975$	37.4018	+	28.8036i	1.19782	+	0.922453i
$976$		0			0
$977$		−	10.6244i		−	0.339906i	−0.985452	−	0.169953i	$-0.945638\pi$
$977$		−	10.6244i		−	0.339906i	0.985452	−	0.169953i	$-0.0543616\pi$
$978$		0			0
$979$	17.1720	−	17.1720i	0.548819	−	0.548819i
$980$		0			0
$981$	−16.6066	−	9.66550i	−0.530206	−	0.308596i
$982$		0			0
$983$			45.6286i			1.45533i	0.685935	+	0.727663i	$0.259394\pi$
$983$			45.6286i			1.45533i	−0.685935	+	0.727663i	$0.740606\pi$
$984$		0			0
$985$		−	40.2967i		−	1.28396i
$986$		0			0
$987$	0.266203	+	2.04974i	0.00847334	+	0.0652440i
$988$		0			0
$989$	−33.7296	+	33.7296i	−1.07254	+	1.07254i
$990$		0			0
$991$		−	39.6701i		−	1.26016i	−0.776529	−	0.630082i	$-0.783021\pi$
$991$		−	39.6701i		−	1.26016i	0.776529	−	0.630082i	$-0.216979\pi$
$992$		0			0
$993$	27.0828	−	35.1673i	0.859446	−	1.11600i
$994$		0			0
$995$	49.6872	+	49.6872i	1.57519	+	1.57519i
$996$		0			0
$997$	−17.7009	+	17.7009i	−0.560594	+	0.560594i	−0.929476	−	0.368883i	$-0.879740\pi$
$997$	−17.7009	+	17.7009i	−0.560594	+	0.560594i	0.368883	+	0.929476i	$0.379740\pi$
$998$		0			0
$999$	12.0029	+	5.04580i	0.379755	+	0.159642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.d.239.13		48
3.2	odd	2	inner	1344.2.s.d.239.1		48
4.3	odd	2		336.2.s.d.323.21	yes	48
12.11	even	2		336.2.s.d.323.4	yes	48
16.5	even	4		336.2.s.d.155.4	✓	48
16.11	odd	4	inner	1344.2.s.d.911.1		48
48.5	odd	4		336.2.s.d.155.21	yes	48
48.11	even	4	inner	1344.2.s.d.911.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.4	✓	48	16.5	even	4
336.2.s.d.155.21	yes	48	48.5	odd	4
336.2.s.d.323.4	yes	48	12.11	even	2
336.2.s.d.323.21	yes	48	4.3	odd	2
1344.2.s.d.239.1		48	3.2	odd	2	inner
1344.2.s.d.239.13		48	1.1	even	1	trivial
1344.2.s.d.911.1		48	16.11	odd	4	inner
1344.2.s.d.911.13		48	48.11	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.223071 + 1.71763i) q^{3} +(2.27022 + 2.27022i) q^{5} -1.00000 q^{7} +(-2.90048 + 0.766304i) q^{9} +O(q^{10})\)	\(q+(0.223071 + 1.71763i) q^{3} +(2.27022 + 2.27022i) q^{5} -1.00000 q^{7} +(-2.90048 + 0.766304i) q^{9} +(1.53672 - 1.53672i) q^{11} +(-3.63094 - 3.63094i) q^{13} +(-3.39297 + 4.40581i) q^{15} +1.81890i q^{17} +(-4.98250 + 4.98250i) q^{19} +(-0.223071 - 1.71763i) q^{21} +7.21608i q^{23} +5.30780i q^{25} +(-1.96324 - 4.81100i) q^{27} +(-2.77187 + 2.77187i) q^{29} +4.14621i q^{31} +(2.98230 + 2.29671i) q^{33} +(-2.27022 - 2.27022i) q^{35} +(-1.77185 + 1.77185i) q^{37} +(5.42665 - 7.04656i) q^{39} +0.517924 q^{41} +(4.67423 + 4.67423i) q^{43} +(-8.32441 - 4.84505i) q^{45} -1.19336 q^{47} +1.00000 q^{49} +(-3.12419 + 0.405744i) q^{51} +(-7.94384 - 7.94384i) q^{53} +6.97737 q^{55} +(-9.66952 - 7.44662i) q^{57} +(-1.94904 + 1.94904i) q^{59} +(2.94791 + 2.94791i) q^{61} +(2.90048 - 0.766304i) q^{63} -16.4861i q^{65} +(7.85747 - 7.85747i) q^{67} +(-12.3945 + 1.60970i) q^{69} -10.9009i q^{71} +15.7454i q^{73} +(-9.11682 + 1.18402i) q^{75} +(-1.53672 + 1.53672i) q^{77} -5.40437i q^{79} +(7.82556 - 4.44530i) q^{81} +(7.12290 + 7.12290i) q^{83} +(-4.12931 + 4.12931i) q^{85} +(-5.37937 - 4.14272i) q^{87} +11.1745 q^{89} +(3.63094 + 3.63094i) q^{91} +(-7.12163 + 0.924898i) q^{93} -22.6227 q^{95} +12.3244 q^{97} +(-3.27962 + 5.63480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{7}+O(q^{10}) \) 48 * q - 48 * q^7	\( 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) \) 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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