LMFDB - Embedded newform 1216.2.i.p.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.39075800976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 12x^{6} - 13x^{5} + 125x^{4} - 116x^{3} + 232x^{2} + 96x + 64 $ x^8 - x^7 + 12x^6 - 13x^5 + 125x^4 - 116x^3 + 232x^2 + 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 608)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$-1.63248 + 2.82754i$ of defining polynomial
Character	$\chi$	$=$	1216.961
Dual form			1216.2.i.p.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59084 + 2.75542i) q^{3} +(-1.28078 + 2.21837i) q^{5} +(-3.56155 - 6.16879i) q^{9} +O(q^{10})$	\(q+(-1.59084 + 2.75542i) q^{3} +(-1.28078 + 2.21837i) q^{5} +(-3.56155 - 6.16879i) q^{9} +4.96837 q^{11} +(-2.28078 - 3.95042i) q^{13} +(-4.07502 - 7.05815i) q^{15} +(2.28078 - 3.95042i) q^{17} +(-0.697500 - 4.30273i) q^{19} +(-0.893341 - 1.54731i) q^{23} +(-0.780776 - 1.35234i) q^{25} +13.1184 q^{27} +(-3.84233 - 6.65511i) q^{29} +6.36337 q^{31} +(-7.90388 + 13.6899i) q^{33} -7.12311 q^{37} +14.5134 q^{39} +(-0.500000 + 0.866025i) q^{41} +(-2.28834 + 3.96352i) q^{43} +18.2462 q^{45} +(-4.07502 - 7.05815i) q^{47} -7.00000 q^{49} +(7.25671 + 12.5690i) q^{51} +(2.28078 + 3.95042i) q^{53} +(-6.36337 + 11.0217i) q^{55} +(12.9654 + 4.92306i) q^{57} +(1.59084 - 2.75542i) q^{59} +(-3.28078 - 5.68247i) q^{61} +11.6847 q^{65} +(2.98584 + 5.17163i) q^{67} +5.68466 q^{69} +(0.893341 - 1.54731i) q^{71} +(7.62311 - 13.2036i) q^{73} +4.96837 q^{75} +(-4.07502 + 7.05815i) q^{79} +(-10.1847 + 17.6403i) q^{81} +1.39500 q^{83} +(5.84233 + 10.1192i) q^{85} +24.4501 q^{87} +(-0.842329 - 1.45896i) q^{89} +(-10.1231 + 17.5337i) q^{93} +(10.4384 + 3.96352i) q^{95} +(2.62311 - 4.54335i) q^{97} +(-17.6951 - 30.6488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} - 12 q^{9}+O(q^{10}) $ 8 * q - 2 * q^5 - 12 * q^9	$ 8 q - 2 q^{5} - 12 q^{9} - 10 q^{13} + 10 q^{17} + 2 q^{25} - 6 q^{29} - 22 q^{33} - 24 q^{37} - 4 q^{41} + 80 q^{45} - 56 q^{49} + 10 q^{53} + 46 q^{57} - 18 q^{61} + 44 q^{65} - 4 q^{69} + 28 q^{73} - 32 q^{81} + 22 q^{85} + 18 q^{89} - 48 q^{93} - 12 q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 - 12 * q^9 - 10 * q^13 + 10 * q^17 + 2 * q^25 - 6 * q^29 - 22 * q^33 - 24 * q^37 - 4 * q^41 + 80 * q^45 - 56 * q^49 + 10 * q^53 + 46 * q^57 - 18 * q^61 + 44 * q^65 - 4 * q^69 + 28 * q^73 - 32 * q^81 + 22 * q^85 + 18 * q^89 - 48 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.59084	+	2.75542i	−0.918473	+	1.59084i	−0.116737	+	0.993163i	$0.537243\pi$
$3$	−1.59084	+	2.75542i	−0.918473	+	1.59084i	−0.801736	+	0.597679i	$0.796090\pi$
$4$		0			0
$5$	−1.28078	+	2.21837i	−0.572781	+	0.992085i	0.423498	+	0.905897i	$0.360802\pi$
$5$	−1.28078	+	2.21837i	−0.572781	+	0.992085i	−0.996279	+	0.0861882i	$0.972531\pi$
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$	−3.56155	−	6.16879i	−1.18718	−	2.05626i
$10$		0			0
$11$	4.96837			1.49802			0.749009	−	0.662559i	$-0.230530\pi$
$11$	4.96837			1.49802			0.749009	+	0.662559i	$0.230530\pi$
$12$		0			0
$13$	−2.28078	−	3.95042i	−0.632574	−	1.09565i	−0.987024	−	0.160575i	$-0.948665\pi$
$13$	−2.28078	−	3.95042i	−0.632574	−	1.09565i	0.354450	−	0.935075i	$-0.384668\pi$
$14$		0			0
$15$	−4.07502	−	7.05815i	−1.05217	−	1.82241i
$16$		0			0
$17$	2.28078	−	3.95042i	0.553170	−	0.958118i	−0.444874	−	0.895593i	$-0.646752\pi$
$17$	2.28078	−	3.95042i	0.553170	−	0.958118i	0.998043	−	0.0625245i	$-0.0199152\pi$
$18$		0			0
$19$	−0.697500	−	4.30273i	−0.160017	−	0.987114i
$19$	−0.697500	−	4.30273i	−0.160017	−	0.987114i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.893341	−	1.54731i	−0.186275	−	0.322637i	0.757731	−	0.652567i	$-0.226308\pi$
$23$	−0.893341	−	1.54731i	−0.186275	−	0.322637i	−0.944005	+	0.329930i	$0.892975\pi$
$24$		0			0
$25$	−0.780776	−	1.35234i	−0.156155	−	0.270469i
$26$		0			0
$27$	13.1184			2.52464
$28$		0			0
$29$	−3.84233	−	6.65511i	−0.713503	−	1.23582i	−0.963534	−	0.267585i	$-0.913774\pi$
$29$	−3.84233	−	6.65511i	−0.713503	−	1.23582i	0.250032	−	0.968238i	$-0.419559\pi$
$30$		0			0
$31$	6.36337			1.14289			0.571447	−	0.820639i	$-0.306382\pi$
$31$	6.36337			1.14289			0.571447	+	0.820639i	$0.306382\pi$
$32$		0			0
$33$	−7.90388	+	13.6899i	−1.37589	+	2.38311i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.12311			−1.17103			−0.585516	−	0.810661i	$-0.699108\pi$
$37$	−7.12311			−1.17103			−0.585516	+	0.810661i	$0.699108\pi$
$38$		0			0
$39$	14.5134			2.32401
$40$		0			0
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	−0.902424	−	0.430848i	$-0.858214\pi$
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	0.824338	+	0.566099i	$0.191548\pi$
$42$		0			0
$43$	−2.28834	+	3.96352i	−0.348969	+	0.604432i	−0.986067	−	0.166351i	$-0.946801\pi$
$43$	−2.28834	+	3.96352i	−0.348969	+	0.604432i	0.637098	+	0.770783i	$0.280135\pi$
$44$		0			0
$45$	18.2462			2.71998
$46$		0			0
$47$	−4.07502	−	7.05815i	−0.594403	−	1.02954i	−0.993631	−	0.112685i	$-0.964055\pi$
$47$	−4.07502	−	7.05815i	−0.594403	−	1.02954i	0.399227	−	0.916852i	$-0.369278\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$	7.25671	+	12.5690i	1.01614	+	1.76001i
$52$		0			0
$53$	2.28078	+	3.95042i	0.313289	+	0.542632i	0.979072	−	0.203513i	$-0.0652359\pi$
$53$	2.28078	+	3.95042i	0.313289	+	0.542632i	−0.665784	+	0.746145i	$0.731903\pi$
$54$		0			0
$55$	−6.36337	+	11.0217i	−0.858036	+	1.48616i
$56$		0			0
$57$	12.9654	+	4.92306i	1.71731	+	0.652075i
$58$		0			0
$59$	1.59084	−	2.75542i	0.207110	−	0.358725i	−0.743693	−	0.668521i	$-0.766928\pi$
$59$	1.59084	−	2.75542i	0.207110	−	0.358725i	0.950803	+	0.309796i	$0.100261\pi$
$60$		0			0
$61$	−3.28078	−	5.68247i	−0.420060	−	0.727566i	0.575885	−	0.817531i	$-0.304658\pi$
$61$	−3.28078	−	5.68247i	−0.420060	−	0.727566i	−0.995945	+	0.0899651i	$0.971324\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11.6847			1.44930
$66$		0			0
$67$	2.98584	+	5.17163i	0.364779	+	0.631815i	0.988741	−	0.149640i	$-0.0478114\pi$
$67$	2.98584	+	5.17163i	0.364779	+	0.631815i	−0.623962	+	0.781455i	$0.714478\pi$
$68$		0			0
$69$	5.68466			0.684352
$70$		0			0
$71$	0.893341	−	1.54731i	0.106020	−	0.183632i	−0.808134	−	0.588998i	$-0.799523\pi$
$71$	0.893341	−	1.54731i	0.106020	−	0.183632i	0.914155	+	0.405366i	$0.132856\pi$
$72$		0			0
$73$	7.62311	−	13.2036i	0.892217	−	1.54537i	0.0550055	−	0.998486i	$-0.482482\pi$
$73$	7.62311	−	13.2036i	0.892217	−	1.54537i	0.837212	−	0.546879i	$-0.184184\pi$
$74$		0			0
$75$	4.96837			0.573697
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.07502	+	7.05815i	−0.458476	+	0.794104i	−0.998881	−	0.0473015i	$-0.984938\pi$
$79$	−4.07502	+	7.05815i	−0.458476	+	0.794104i	0.540405	+	0.841405i	$0.318271\pi$
$80$		0			0
$81$	−10.1847	+	17.6403i	−1.13163	+	1.96004i
$82$		0			0
$83$	1.39500			0.153121			0.0765606	−	0.997065i	$-0.475606\pi$
$83$	1.39500			0.153121			0.0765606	+	0.997065i	$0.475606\pi$
$84$		0			0
$85$	5.84233	+	10.1192i	0.633690	+	1.09758i
$86$		0			0
$87$	24.4501			2.62133
$88$		0			0
$89$	−0.842329	−	1.45896i	−0.0892867	−	0.154649i	0.817923	−	0.575328i	$-0.195125\pi$
$89$	−0.842329	−	1.45896i	−0.0892867	−	0.154649i	−0.907210	+	0.420678i	$0.861792\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10.1231	+	17.5337i	−1.04972	+	1.81816i
$94$		0			0
$95$	10.4384	+	3.96352i	1.07096	+	0.406649i
$96$		0			0
$97$	2.62311	−	4.54335i	0.266336	−	0.461308i	−0.701577	−	0.712594i	$-0.747520\pi$
$97$	2.62311	−	4.54335i	0.266336	−	0.461308i	0.967913	+	0.251286i	$0.0808536\pi$
$98$		0			0
$99$	−17.6951	−	30.6488i	−1.77842	−	3.08032i
$100$		0			0
$101$	2.40388	+	4.16365i	0.239195	+	0.414298i	0.960484	−	0.278337i	$-0.0897831\pi$
$101$	2.40388	+	4.16365i	0.239195	+	0.414298i	−0.721288	+	0.692635i	$0.756450\pi$
$102$		0			0
$103$	−15.5167			−1.52891			−0.764454	−	0.644678i	$-0.776992\pi$
$103$	−15.5167			−1.52891			−0.764454	+	0.644678i	$0.776992\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.7267			−1.23034			−0.615170	−	0.788395i	$-0.710913\pi$
$107$	−12.7267			−1.23034			−0.615170	+	0.788395i	$0.710913\pi$
$108$		0			0
$109$	4.40388	−	7.62775i	0.421815	−	0.730606i	−0.574302	−	0.818644i	$-0.694726\pi$
$109$	4.40388	−	7.62775i	0.421815	−	0.730606i	0.996117	+	0.0880380i	$0.0280597\pi$
$110$		0			0
$111$	11.3317	−	19.6271i	1.07556	−	1.86293i
$112$		0			0
$113$	−2.43845			−0.229390			−0.114695	−	0.993401i	$-0.536589\pi$
$113$	−2.43845			−0.229390			−0.114695	+	0.993401i	$0.536589\pi$
$114$		0			0
$115$	4.57668			0.426778
$116$		0			0
$117$	−16.2462	+	28.1393i	−1.50196	+	2.60148i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	13.6847			1.24406
$122$		0			0
$123$	−1.59084	−	2.75542i	−0.143441	−	0.248448i
$124$		0			0
$125$	−8.80776			−0.787790
$126$		0			0
$127$	9.04339	+	15.6636i	0.802471	+	1.38992i	0.917985	+	0.396615i	$0.129815\pi$
$127$	9.04339	+	15.6636i	0.802471	+	1.38992i	−0.115514	+	0.993306i	$0.536852\pi$
$128$		0			0
$129$	−7.28078	−	12.6107i	−0.641037	−	1.11031i
$130$		0			0
$131$	11.1359	−	19.2879i	0.972947	−	1.68519i	0.286398	−	0.958111i	$-0.407542\pi$
$131$	11.1359	−	19.2879i	0.972947	−	1.68519i	0.686549	−	0.727083i	$-0.259125\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−16.8018	+	29.1015i	−1.44606	+	2.50466i
$136$		0			0
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	0.975913	−	0.218159i	$-0.0700052\pi$
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	−0.676888	+	0.736086i	$0.736672\pi$
$138$		0			0
$139$	−0.195842	−	0.339207i	−0.0166111	−	0.0287712i	0.857600	−	0.514317i	$-0.171954\pi$
$139$	−0.195842	−	0.339207i	−0.0166111	−	0.0287712i	−0.874211	+	0.485545i	$0.838621\pi$
$140$		0			0
$141$	25.9309			2.18377
$142$		0			0
$143$	−11.3317	−	19.6271i	−0.947607	−	1.64130i
$144$		0			0
$145$	19.6847			1.63472
$146$		0			0
$147$	11.1359	−	19.2879i	0.918473	−	1.59084i
$148$		0			0
$149$	9.96543	−	17.2606i	0.816400	−	1.41405i	−0.0919179	−	0.995767i	$-0.529300\pi$
$149$	9.96543	−	17.2606i	0.816400	−	1.41405i	0.908318	−	0.418280i	$-0.137367\pi$
$150$		0			0
$151$	9.93673			0.808640			0.404320	−	0.914618i	$-0.367508\pi$
$151$	9.93673			0.808640			0.404320	+	0.914618i	$0.367508\pi$
$152$		0			0
$153$	−32.4924			−2.62686
$154$		0			0
$155$	−8.15005	+	14.1163i	−0.654628	+	1.13385i
$156$		0			0
$157$	−0.403882	+	0.699544i	−0.0322333	+	0.0558297i	−0.881692	−	0.471825i	$-0.843595\pi$
$157$	−0.403882	+	0.699544i	−0.0322333	+	0.0558297i	0.849459	+	0.527655i	$0.176929\pi$
$158$		0			0
$159$	−14.5134			−1.15099
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.96837			−0.389152			−0.194576	−	0.980887i	$-0.562333\pi$
$163$	−4.96837			−0.389152			−0.194576	+	0.980887i	$0.562333\pi$
$164$		0			0
$165$	−20.2462	−	35.0675i	−1.57617	−	2.73000i
$166$		0			0
$167$	−6.86502	−	11.8906i	−0.531232	−	0.920120i	−0.999336	−	0.0364466i	$-0.988396\pi$
$167$	−6.86502	−	11.8906i	−0.531232	−	0.920120i	0.468104	−	0.883673i	$-0.344937\pi$
$168$		0			0
$169$	−3.90388	+	6.76172i	−0.300299	+	0.520132i
$170$		0			0
$171$	−24.0585	+	19.6271i	−1.83980	+	1.50092i
$172$		0			0
$173$	7.40388	−	12.8239i	0.562907	−	0.974983i	−0.434334	−	0.900752i	$-0.643016\pi$
$173$	7.40388	−	12.8239i	0.562907	−	0.974983i	0.997241	−	0.0742313i	$-0.0236503\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.06155	+	8.76687i	0.380450	+	0.658958i
$178$		0			0
$179$	−24.8418			−1.85677			−0.928383	−	0.371625i	$-0.878801\pi$
$179$	−24.8418			−1.85677			−0.928383	+	0.371625i	$0.878801\pi$
$180$		0			0
$181$	−3.96543	−	6.86833i	−0.294748	−	0.510519i	0.680178	−	0.733047i	$-0.261903\pi$
$181$	−3.96543	−	6.86833i	−0.294748	−	0.510519i	−0.974926	+	0.222528i	$0.928569\pi$
$182$		0			0
$183$	20.8768			1.54326
$184$		0			0
$185$	9.12311	−	15.8017i	0.670744	−	1.16176i
$186$		0			0
$187$	11.3317	−	19.6271i	0.828658	−	1.43528i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.58000			0.403755			0.201877	−	0.979411i	$-0.435296\pi$
$191$	5.58000			0.403755			0.201877	+	0.979411i	$0.435296\pi$
$192$		0			0
$193$	−5.40388	+	9.35980i	−0.388980	+	0.673733i	−0.992313	−	0.123757i	$-0.960506\pi$
$193$	−5.40388	+	9.35980i	−0.388980	+	0.673733i	0.603333	+	0.797490i	$0.293839\pi$
$194$		0			0
$195$	−18.5884	+	32.1961i	−1.33115	+	2.30561i
$196$		0			0
$197$	−5.36932			−0.382548			−0.191274	−	0.981537i	$-0.561262\pi$
$197$	−5.36932			−0.382548			−0.191274	+	0.981537i	$0.561262\pi$
$198$		0			0
$199$	10.8301	+	18.7582i	0.767724	+	1.32974i	0.938795	+	0.344477i	$0.111944\pi$
$199$	10.8301	+	18.7582i	0.767724	+	1.32974i	−0.171071	+	0.985259i	$0.554723\pi$
$200$		0			0
$201$	−19.0000			−1.34016
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.28078	−	2.21837i	−0.0894533	−	0.154938i
$206$		0			0
$207$	−6.36337	+	11.0217i	−0.442284	+	0.766059i
$208$		0			0
$209$	−3.46543	−	21.3775i	−0.239709	−	1.47872i
$210$		0			0
$211$	2.28834	−	3.96352i	0.157536	−	0.272860i	−0.776444	−	0.630187i	$-0.782978\pi$
$211$	2.28834	−	3.96352i	0.157536	−	0.272860i	0.933980	+	0.357327i	$0.116312\pi$
$212$		0			0
$213$	2.84233	+	4.92306i	0.194753	+	0.337322i
$214$		0			0
$215$	−5.86171	−	10.1528i	−0.399765	−	0.692413i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	24.2543	+	42.0097i	1.63895	+	2.83875i
$220$		0			0
$221$	−20.8078			−1.39968
$222$		0			0
$223$	−10.8301	+	18.7582i	−0.725235	+	1.25614i	0.233642	+	0.972323i	$0.424936\pi$
$223$	−10.8301	+	18.7582i	−0.725235	+	1.25614i	−0.958877	+	0.283822i	$0.908398\pi$
$224$		0			0
$225$	−5.56155	+	9.63289i	−0.370770	+	0.642193i
$226$		0			0
$227$	−14.9051			−0.989286			−0.494643	−	0.869096i	$-0.664701\pi$
$227$	−14.9051			−0.989286			−0.494643	+	0.869096i	$0.664701\pi$
$228$		0			0
$229$	26.2462			1.73440			0.867199	−	0.497961i	$-0.165918\pi$
$229$	26.2462			1.73440			0.867199	+	0.497961i	$0.165918\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.06155	+	10.4989i	−0.397106	+	0.687807i	−0.993367	−	0.114983i	$-0.963319\pi$
$233$	−6.06155	+	10.4989i	−0.397106	+	0.687807i	0.596262	+	0.802790i	$0.296652\pi$
$234$		0			0
$235$	20.8768			1.36185
$236$		0			0
$237$	−12.9654	−	22.4568i	−0.842195	−	1.45873i
$238$		0			0
$239$	−10.7201			−0.693425			−0.346713	−	0.937971i	$-0.612702\pi$
$239$	−10.7201			−0.693425			−0.346713	+	0.937971i	$0.612702\pi$
$240$		0			0
$241$	−6.74621	−	11.6848i	−0.434562	−	0.752683i	0.562698	−	0.826662i	$-0.309763\pi$
$241$	−6.74621	−	11.6848i	−0.434562	−	0.752683i	−0.997260	+	0.0739796i	$0.976430\pi$
$242$		0			0
$243$	−12.7267	−	22.0433i	−0.816420	−	1.41408i
$244$		0			0
$245$	8.96543	−	15.5286i	0.572781	−	0.992085i
$246$		0			0
$247$	−15.4068	+	12.5690i	−0.980308	+	0.799745i
$248$		0			0
$249$	−2.21922	+	3.84381i	−0.140638	+	0.243591i
$250$		0			0
$251$	1.98252	+	3.43383i	0.125136	+	0.216742i	0.921786	−	0.387699i	$-0.126730\pi$
$251$	1.98252	+	3.43383i	0.125136	+	0.216742i	−0.796650	+	0.604441i	$0.793397\pi$
$252$		0			0
$253$	−4.43845	−	7.68762i	−0.279043	−	0.483316i
$254$		0			0
$255$	−37.1769			−2.32811
$256$		0			0
$257$	−2.62311	−	4.54335i	−0.163625	−	0.283407i	0.772541	−	0.634965i	$-0.218985\pi$
$257$	−2.62311	−	4.54335i	−0.163625	−	0.283407i	−0.936166	+	0.351558i	$0.885652\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−27.3693	+	47.4050i	−1.69412	+	2.93430i
$262$		0			0
$263$	6.86502	−	11.8906i	0.423316	−	0.733204i	−0.572946	−	0.819593i	$-0.694200\pi$
$263$	6.86502	−	11.8906i	0.423316	−	0.733204i	0.996261	+	0.0863892i	$0.0275328\pi$
$264$		0			0
$265$	−11.6847			−0.717783
$266$		0			0
$267$	5.36005			0.328030
$268$		0			0
$269$	−6.71922	+	11.6380i	−0.409678	+	0.709584i	−0.994854	−	0.101323i	$-0.967692\pi$
$269$	−6.71922	+	11.6380i	−0.409678	+	0.709584i	0.585175	+	0.810907i	$0.301026\pi$
$270$		0			0
$271$	4.07502	−	7.05815i	0.247540	−	0.428752i	−0.715303	−	0.698815i	$-0.753711\pi$
$271$	4.07502	−	7.05815i	0.247540	−	0.428752i	0.962843	+	0.270063i	$0.0870445\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.87918	−	6.71894i	−0.233924	−	0.405167i
$276$		0			0
$277$	4.00000			0.240337			0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000			0.240337			0.120168	+	0.992754i	$0.461657\pi$
$278$		0			0
$279$	−22.6635	−	39.2543i	−1.35683	−	2.35009i
$280$		0			0
$281$	−11.5000	−	19.9186i	−0.686032	−	1.18824i	−0.973111	−	0.230336i	$-0.926017\pi$
$281$	−11.5000	−	19.9186i	−0.686032	−	1.18824i	0.287079	−	0.957907i	$-0.407316\pi$
$282$		0			0
$283$	11.1359	−	19.2879i	0.661960	−	1.14655i	−0.318140	−	0.948044i	$-0.603058\pi$
$283$	11.1359	−	19.2879i	0.661960	−	1.14655i	0.980100	−	0.198505i	$-0.0636085\pi$
$284$		0			0
$285$	−27.5270	+	22.4568i	−1.63056	+	1.33023i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.90388	−	3.29762i	−0.111993	−	0.193978i
$290$		0			0
$291$	8.34589	+	14.4555i	0.489245	+	0.847397i
$292$		0			0
$293$	4.00000			0.233682			0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000			0.233682			0.116841	+	0.993151i	$0.462723\pi$
$294$		0			0
$295$	4.07502	+	7.05815i	0.237257	+	0.410941i
$296$		0			0
$297$	65.1771			3.78196
$298$		0			0
$299$	−4.07502	+	7.05815i	−0.235665	+	0.408183i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−15.2968			−0.878777
$304$		0			0
$305$	16.8078			0.962410
$306$		0			0
$307$	−6.16752	+	10.6825i	−0.351999	+	0.609680i	−0.986600	−	0.163160i	$-0.947831\pi$
$307$	−6.16752	+	10.6825i	−0.351999	+	0.609680i	0.634600	+	0.772840i	$0.281165\pi$
$308$		0			0
$309$	24.6847	−	42.7551i	1.40426	−	2.43225i
$310$		0			0
$311$	31.8168			1.80417			0.902083	−	0.431562i	$-0.142037\pi$
$311$	31.8168			1.80417			0.902083	+	0.431562i	$0.142037\pi$
$312$		0			0
$313$	2.62311	+	4.54335i	0.148267	+	0.256805i	0.930587	−	0.366071i	$-0.119297\pi$
$313$	2.62311	+	4.54335i	0.148267	+	0.256805i	−0.782320	+	0.622876i	$0.785964\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.08854	+	12.2777i	0.398132	+	0.689585i	0.993495	−	0.113872i	$-0.0363252\pi$
$317$	7.08854	+	12.2777i	0.398132	+	0.689585i	−0.595363	+	0.803457i	$0.702992\pi$
$318$		0			0
$319$	−19.0901	−	33.0650i	−1.06884	−	1.85129i
$320$		0			0
$321$	20.2462	−	35.0675i	1.13003	−	1.95728i
$322$		0			0
$323$	−18.5884	−	7.05815i	−1.03429	−	0.392726i
$324$		0			0
$325$	−3.56155	+	6.16879i	−0.197559	+	0.342183i
$326$		0			0
$327$	14.0118	+	24.2691i	0.774852	+	1.34208i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.5484			−0.579791			−0.289895	−	0.957058i	$-0.593620\pi$
$331$	−10.5484			−0.579791			−0.289895	+	0.957058i	$0.593620\pi$
$332$		0			0
$333$	25.3693	+	43.9409i	1.39023	+	2.40795i
$334$		0			0
$335$	−15.2968			−0.835752
$336$		0			0
$337$	1.06155	−	1.83866i	0.0578265	−	0.100158i	−0.835663	−	0.549243i	$-0.814916\pi$
$337$	1.06155	−	1.83866i	0.0578265	−	0.100158i	0.893489	+	0.449084i	$0.148250\pi$
$338$		0			0
$339$	3.87918	−	6.71894i	0.210688	−	0.364923i
$340$		0			0
$341$	31.6155			1.71208
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−7.28078	+	12.6107i	−0.391984	+	0.678936i
$346$		0			0
$347$	−11.1359	+	19.2879i	−0.597806	+	1.03543i	0.395338	+	0.918536i	$0.370627\pi$
$347$	−11.1359	+	19.2879i	−0.597806	+	1.03543i	−0.993144	+	0.116895i	$0.962706\pi$
$348$		0			0
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$		0			0
$351$	−29.9202	−	51.8233i	−1.59702	−	2.76612i
$352$		0			0
$353$	−4.19224			−0.223130			−0.111565	−	0.993757i	$-0.535586\pi$
$353$	−4.19224			−0.223130			−0.111565	+	0.993757i	$0.535586\pi$
$354$		0			0
$355$	2.28834	+	3.96352i	0.121453	+	0.210362i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.893341	+	1.54731i	−0.0471488	+	0.0816640i	−0.888637	−	0.458612i	$-0.848347\pi$
$359$	−0.893341	+	1.54731i	−0.0471488	+	0.0816640i	0.841488	+	0.540276i	$0.181680\pi$
$360$		0			0
$361$	−18.0270	+	6.00231i	−0.948789	+	0.315911i
$362$		0			0
$363$	−21.7701	+	37.7070i	−1.14264	+	1.97910i
$364$		0			0
$365$	19.5270	+	33.8217i	1.02209	+	1.77031i
$366$		0			0
$367$	10.8301	+	18.7582i	0.565325	+	0.979172i	0.997019	+	0.0771519i	$0.0245827\pi$
$367$	10.8301	+	18.7582i	0.565325	+	0.979172i	−0.431694	+	0.902020i	$0.642084\pi$
$368$		0			0
$369$	7.12311			0.370814
$370$		0			0
$371$		0			0
$372$		0			0
$373$	13.6155			0.704985			0.352493	−	0.935815i	$-0.385334\pi$
$373$	13.6155			0.704985			0.352493	+	0.935815i	$0.385334\pi$
$374$		0			0
$375$	14.0118	−	24.2691i	0.723564	−	1.25325i
$376$		0			0
$377$	−17.5270	+	30.3576i	−0.902686	+	1.56350i
$378$		0			0
$379$	32.6002			1.67456			0.837280	−	0.546775i	$-0.184145\pi$
$379$	32.6002			1.67456			0.837280	+	0.546775i	$0.184145\pi$
$380$		0			0
$381$	−57.5464			−2.94819
$382$		0			0
$383$	5.86171	−	10.1528i	0.299519	−	0.518783i	−0.676507	−	0.736436i	$-0.736507\pi$
$383$	5.86171	−	10.1528i	0.299519	−	0.518783i	0.976026	+	0.217654i	$0.0698404\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	32.6002			1.65716
$388$		0			0
$389$	−12.6501	−	21.9106i	−0.641385	−	1.11091i	−0.985124	−	0.171846i	$-0.945027\pi$
$389$	−12.6501	−	21.9106i	−0.641385	−	1.11091i	0.343739	−	0.939065i	$-0.388307\pi$
$390$		0			0
$391$	−8.15005			−0.412166
$392$		0			0
$393$	35.4309	+	61.3681i	1.78725	+	3.09561i
$394$		0			0
$395$	−10.4384	−	18.0798i	−0.525212	−	0.909695i
$396$		0			0
$397$	−11.7192	+	20.2983i	−0.588171	+	1.01874i	0.406301	+	0.913739i	$0.366818\pi$
$397$	−11.7192	+	20.2983i	−0.588171	+	1.01874i	−0.994472	+	0.105003i	$0.966515\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	−0.996371	−	0.0851195i	$-0.972873\pi$
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	0.571901	+	0.820323i	$0.306206\pi$
$402$		0			0
$403$	−14.5134	−	25.1380i	−0.722965	−	1.25221i
$404$		0			0
$405$	−26.0885	−	45.1867i	−1.29635	−	2.24534i
$406$		0			0
$407$	−35.3902			−1.75423
$408$		0			0
$409$	−11.3078	−	19.5856i	−0.559133	−	0.968447i	−0.997569	−	0.0696843i	$-0.977801\pi$
$409$	−11.3078	−	19.5856i	−0.559133	−	0.968447i	0.438436	−	0.898762i	$-0.355533\pi$
$410$		0			0
$411$	−22.2718			−1.09859
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.78668	+	3.09463i	−0.0877048	+	0.151909i
$416$		0			0
$417$	1.24621			0.0610272
$418$		0			0
$419$	18.3067			0.894342			0.447171	−	0.894448i	$-0.352431\pi$
$419$	18.3067			0.894342			0.447171	+	0.894448i	$0.352431\pi$
$420$		0			0
$421$	2.52699	−	4.37687i	0.123158	−	0.213316i	−0.797854	−	0.602851i	$-0.794031\pi$
$421$	2.52699	−	4.37687i	0.123158	−	0.213316i	0.921011	+	0.389536i	$0.127365\pi$
$422$		0			0
$423$	−29.0268	+	50.2759i	−1.41133	+	2.44450i
$424$		0			0
$425$	−7.12311			−0.345521
$426$		0			0
$427$		0			0
$428$		0			0
$429$	72.1080			3.48140
$430$		0			0
$431$	1.89666	+	3.28511i	0.0913588	+	0.158238i	0.908083	−	0.418790i	$-0.137546\pi$
$431$	1.89666	+	3.28511i	0.0913588	+	0.158238i	−0.816724	+	0.577028i	$0.804212\pi$
$432$		0			0
$433$	7.08854	+	12.2777i	0.340654	+	0.590029i	0.984554	−	0.175080i	$-0.0560184\pi$
$433$	7.08854	+	12.2777i	0.340654	+	0.590029i	−0.643901	+	0.765109i	$0.722685\pi$
$434$		0			0
$435$	−31.3152	+	54.2395i	−1.50145	+	2.60058i
$436$		0			0
$437$	−6.03457	+	4.92306i	−0.288672	+	0.235502i
$438$		0			0
$439$	0.893341	−	1.54731i	0.0426369	−	0.0738492i	−0.843919	−	0.536470i	$-0.819757\pi$
$439$	0.893341	−	1.54731i	0.0426369	−	0.0738492i	0.886556	+	0.462621i	$0.153091\pi$
$440$		0			0
$441$	24.9309	+	43.1815i	1.18718	+	2.05626i
$442$		0			0
$443$	4.77252	+	8.26625i	0.226749	+	0.392742i	0.956843	−	0.290606i	$-0.0938568\pi$
$443$	4.77252	+	8.26625i	0.226749	+	0.392742i	−0.730093	+	0.683347i	$0.760523\pi$
$444$		0			0
$445$	4.31534			0.204567
$446$		0			0
$447$	31.7069	+	54.9179i	1.49968	+	2.59753i
$448$		0			0
$449$	4.19224			0.197844			0.0989219	−	0.995095i	$-0.468461\pi$
$449$	4.19224			0.197844			0.0989219	+	0.995095i	$0.468461\pi$
$450$		0			0
$451$	−2.48418	+	4.30273i	−0.116976	+	0.202608i
$452$		0			0
$453$	−15.8078	+	27.3799i	−0.742714	+	1.28642i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−28.4384			−1.33029			−0.665147	−	0.746712i	$-0.731631\pi$
$457$	−28.4384			−1.33029			−0.665147	+	0.746712i	$0.731631\pi$
$458$		0			0
$459$	29.9202	−	51.8233i	1.39655	−	2.41890i
$460$		0			0
$461$	11.7192	−	20.2983i	0.545819	−	0.945386i	−0.452736	−	0.891644i	$-0.649552\pi$
$461$	11.7192	−	20.2983i	0.545819	−	0.945386i	0.998555	−	0.0537412i	$-0.0171146\pi$
$462$		0			0
$463$	13.5101			0.627867			0.313934	−	0.949445i	$-0.398353\pi$
$463$	13.5101			0.627867			0.313934	+	0.949445i	$0.398353\pi$
$464$		0			0
$465$	−25.9309	−	44.9136i	−1.20252	−	2.08282i
$466$		0			0
$467$	20.4851			0.947937			0.473969	−	0.880542i	$-0.342821\pi$
$467$	20.4851			0.947937			0.473969	+	0.880542i	$0.342821\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.28502	−	2.22573i	−0.0592108	−	0.102556i
$472$		0			0
$473$	−11.3693	+	19.6922i	−0.522762	+	0.905450i
$474$		0			0
$475$	−5.27418	+	4.30273i	−0.241996	+	0.197423i
$476$		0			0
$477$	16.2462	−	28.1393i	0.743863	−	1.28841i
$478$		0			0
$479$	−16.8018	−	29.1015i	−0.767692	−	1.32968i	−0.938812	−	0.344431i	$-0.888072\pi$
$479$	−16.8018	−	29.1015i	−0.767692	−	1.32968i	0.171120	−	0.985250i	$-0.445261\pi$
$480$		0			0
$481$	16.2462	+	28.1393i	0.740763	+	1.28304i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.71922	+	11.6380i	0.305104	+	0.528456i
$486$		0			0
$487$	4.35673			0.197422			0.0987112	−	0.995116i	$-0.468528\pi$
$487$	4.35673			0.197422			0.0987112	+	0.995116i	$0.468528\pi$
$488$		0			0
$489$	7.90388	−	13.6899i	0.357426	−	0.619080i
$490$		0			0
$491$	5.07834	−	8.79594i	0.229182	−	0.396955i	−0.728384	−	0.685169i	$-0.759728\pi$
$491$	5.07834	−	8.79594i	0.229182	−	0.396955i	0.957566	+	0.288214i	$0.0930615\pi$
$492$		0			0
$493$	−35.0540			−1.57875
$494$		0			0
$495$	90.6539			4.07459
$496$		0			0
$497$		0			0
$498$		0			0
$499$	11.5276	−	19.9663i	0.516045	−	0.893816i	−0.483781	−	0.875189i	$-0.660737\pi$
$499$	11.5276	−	19.9663i	0.516045	−	0.893816i	0.999826	−	0.0186274i	$-0.00592962\pi$
$500$		0			0
$501$	43.6847			1.95169
$502$		0			0
$503$	1.89666	+	3.28511i	0.0845678	+	0.146476i	0.905207	−	0.424971i	$-0.139716\pi$
$503$	1.89666	+	3.28511i	0.0845678	+	0.146476i	−0.820639	+	0.571447i	$0.806382\pi$
$504$		0			0
$505$	−12.3153			−0.548026
$506$		0			0
$507$	−12.4209	−	21.5137i	−0.551632	−	0.955455i
$508$		0			0
$509$	−14.9654	−	25.9209i	−0.663331	−	1.14892i	−0.979735	−	0.200299i	$-0.935809\pi$
$509$	−14.9654	−	25.9209i	−0.663331	−	1.14892i	0.316404	−	0.948625i	$-0.397525\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−9.15009	−	56.4450i	−0.403986	−	2.49211i
$514$		0			0
$515$	19.8735	−	34.4218i	0.875729	−	1.51681i
$516$		0			0
$517$	−20.2462	−	35.0675i	−0.890427	−	1.54227i
$518$		0			0
$519$	23.5568	+	40.8016i	1.03403	+	1.79099i
$520$		0			0
$521$	−33.4233			−1.46430			−0.732151	−	0.681143i	$-0.761483\pi$
$521$	−33.4233			−1.46430			−0.732151	+	0.681143i	$0.761483\pi$
$522$		0			0
$523$	−5.86171	−	10.1528i	−0.256315	−	0.443950i	0.708937	−	0.705272i	$-0.249175\pi$
$523$	−5.86171	−	10.1528i	−0.256315	−	0.443950i	−0.965252	+	0.261322i	$0.915842\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.5134	−	25.1380i	0.632214	−	1.09503i
$528$		0			0
$529$	9.90388	−	17.1540i	0.430604	−	0.745827i
$530$		0			0
$531$	−22.6635			−0.983511
$532$		0			0
$533$	4.56155			0.197583
$534$		0			0
$535$	16.3001	−	28.2326i	0.704715	−	1.22060i
$536$		0			0
$537$	39.5194	−	68.4496i	1.70539	−	2.95382i
$538$		0			0
$539$	−34.7786			−1.49802
$540$		0			0
$541$	12.6501	+	21.9106i	0.543870	+	0.942010i	0.998677	+	0.0514205i	$0.0163749\pi$
$541$	12.6501	+	21.9106i	0.543870	+	0.942010i	−0.454807	+	0.890590i	$0.650292\pi$
$542$		0			0
$543$	25.2335			1.08287
$544$		0			0
$545$	11.2808	+	19.5389i	0.483215	+	0.836954i
$546$		0			0
$547$	5.86171	+	10.1528i	0.250629	+	0.434101i	0.963699	−	0.266991i	$-0.0860294\pi$
$547$	5.86171	+	10.1528i	0.250629	+	0.434101i	−0.713071	+	0.701092i	$0.752696\pi$
$548$		0			0
$549$	−23.3693	+	40.4768i	−0.997378	+	1.72751i
$550$		0			0
$551$	−25.9551	+	21.1744i	−1.10573	+	0.902062i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	29.0268	+	50.2759i	1.23212	+	2.13409i
$556$		0			0
$557$	−7.28078	−	12.6107i	−0.308496	−	0.534331i	0.669537	−	0.742778i	$-0.266492\pi$
$557$	−7.28078	−	12.6107i	−0.308496	−	0.534331i	−0.978034	+	0.208447i	$0.933159\pi$
$558$		0			0
$559$	20.8768			0.882994
$560$		0			0
$561$	36.0540	+	62.4473i	1.52220	+	2.63653i
$562$		0			0
$563$	36.0018			1.51730			0.758648	−	0.651501i	$-0.225860\pi$
$563$	36.0018			1.51730			0.758648	+	0.651501i	$0.225860\pi$
$564$		0			0
$565$	3.12311	−	5.40938i	0.131390	−	0.227574i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.3693			1.06354			0.531769	−	0.846890i	$-0.321528\pi$
$569$	25.3693			1.06354			0.531769	+	0.846890i	$0.321528\pi$
$570$		0			0
$571$	20.4851			0.857275			0.428637	−	0.903477i	$-0.358994\pi$
$571$	20.4851			0.857275			0.428637	+	0.903477i	$0.358994\pi$
$572$		0			0
$573$	−8.87689	+	15.3752i	−0.370838	+	0.642310i
$574$		0			0
$575$	−1.39500	+	2.41621i	−0.0581755	+	0.100763i
$576$		0			0
$577$	−21.1771			−0.881613			−0.440807	−	0.897602i	$-0.645308\pi$
$577$	−21.1771			−0.881613			−0.440807	+	0.897602i	$0.645308\pi$
$578$		0			0
$579$	−17.1934	−	29.7799i	−0.714535	−	1.23761i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	11.3317	+	19.6271i	0.469312	+	0.812873i
$584$		0			0
$585$	−41.6155	−	72.0802i	−1.72059	−	2.98015i
$586$		0			0
$587$	22.1618	−	38.3854i	0.914716	−	1.58433i	0.107398	−	0.994216i	$-0.465748\pi$
$587$	22.1618	−	38.3854i	0.914716	−	1.58433i	0.807317	−	0.590118i	$-0.200919\pi$
$588$		0			0
$589$	−4.43845	−	27.3799i	−0.182883	−	1.12817i
$590$		0			0
$591$	8.54173	−	14.7947i	0.351360	−	0.608573i
$592$		0			0
$593$	−1.18466	−	2.05189i	−0.0486481	−	0.0842610i	0.840676	−	0.541538i	$-0.182158\pi$
$593$	−1.18466	−	2.05189i	−0.0486481	−	0.0842610i	−0.889324	+	0.457278i	$0.848825\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−68.9157			−2.82053
$598$		0			0
$599$	11.8334	+	20.4960i	0.483499	+	0.837445i	0.999820	−	0.0189498i	$-0.00603227\pi$
$599$	11.8334	+	20.4960i	0.483499	+	0.837445i	−0.516321	+	0.856395i	$0.672699\pi$
$600$		0			0
$601$	−19.4233			−0.792293			−0.396146	−	0.918187i	$-0.629653\pi$
$601$	−19.4233			−0.792293			−0.396146	+	0.918187i	$0.629653\pi$
$602$		0			0
$603$	21.2685	−	36.8381i	0.866119	−	1.50016i
$604$		0			0
$605$	−17.5270	+	30.3576i	−0.712573	+	1.23421i
$606$		0			0
$607$	14.2935			0.580154			0.290077	−	0.957003i	$-0.406319\pi$
$607$	14.2935			0.580154			0.290077	+	0.957003i	$0.406319\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−18.5884	+	32.1961i	−0.752008	+	1.30252i
$612$		0			0
$613$	12.5961	−	21.8171i	0.508752	−	0.881185i	−0.491196	−	0.871049i	$-0.663440\pi$
$613$	12.5961	−	21.8171i	0.508752	−	0.881185i	0.999949	−	0.0101361i	$-0.00322647\pi$
$614$		0			0
$615$	8.15005			0.328642
$616$		0			0
$617$	−3.81534	−	6.60837i	−0.153600	−	0.266043i	0.778948	−	0.627088i	$-0.215753\pi$
$617$	−3.81534	−	6.60837i	−0.153600	−	0.266043i	−0.932548	+	0.361045i	$0.882420\pi$
$618$		0			0
$619$	−7.14673			−0.287251			−0.143626	−	0.989632i	$-0.545876\pi$
$619$	−7.14673			−0.287251			−0.143626	+	0.989632i	$0.545876\pi$
$620$		0			0
$621$	−11.7192	−	20.2983i	−0.470276	−	0.814542i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.1847	−	26.3006i	0.607386	−	1.05202i
$626$		0			0
$627$	64.4170	+	24.4596i	2.57257	+	0.976821i
$628$		0			0
$629$	−16.2462	+	28.1393i	−0.647779	+	1.12199i
$630$		0			0
$631$	−14.0118	−	24.2691i	−0.557799	−	0.966137i	−0.997680	−	0.0680803i	$-0.978313\pi$
$631$	−14.0118	−	24.2691i	−0.557799	−	0.966137i	0.439881	−	0.898056i	$-0.355021\pi$
$632$		0			0
$633$	7.28078	+	12.6107i	0.289385	+	0.501229i
$634$		0			0
$635$	−46.3302			−1.83856
$636$		0			0
$637$	15.9654	+	27.6529i	0.632574	+	1.09565i
$638$		0			0
$639$	−12.7267			−0.503462
$640$		0			0
$641$	5.18466	−	8.98009i	0.204782	−	0.354692i	−0.745281	−	0.666750i	$-0.767685\pi$
$641$	5.18466	−	8.98009i	0.204782	−	0.354692i	0.950063	+	0.312058i	$0.101018\pi$
$642$		0			0
$643$	−16.1043	+	27.8934i	−0.635090	+	1.10001i	0.351406	+	0.936223i	$0.385704\pi$
$643$	−16.1043	+	27.8934i	−0.635090	+	1.10001i	−0.986496	+	0.163785i	$0.947630\pi$
$644$		0			0
$645$	37.3002			1.46869
$646$		0			0
$647$	−40.9702			−1.61070			−0.805352	−	0.592797i	$-0.798024\pi$
$647$	−40.9702			−1.61070			−0.805352	+	0.592797i	$0.798024\pi$
$648$		0			0
$649$	7.90388	−	13.6899i	0.310255	−	0.537377i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.50758			0.293794			0.146897	−	0.989152i	$-0.453071\pi$
$653$	7.50758			0.293794			0.146897	+	0.989152i	$0.453071\pi$
$654$		0			0
$655$	28.5252	+	49.4070i	1.11457	+	1.93049i
$656$		0			0
$657$	−108.600			−4.23690
$658$		0			0
$659$	−5.86171	−	10.1528i	−0.228340	−	0.395496i	0.728976	−	0.684539i	$-0.239996\pi$
$659$	−5.86171	−	10.1528i	−0.228340	−	0.395496i	−0.957316	+	0.289043i	$0.906663\pi$
$660$		0			0
$661$	24.6501	+	42.6952i	0.958778	+	1.66065i	0.725477	+	0.688247i	$0.241619\pi$
$661$	24.6501	+	42.6952i	0.958778	+	1.66065i	0.233301	+	0.972405i	$0.425047\pi$
$662$		0			0
$663$	33.1019	−	57.3341i	1.28557	−	2.22667i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.86502	+	11.8906i	−0.265815	+	0.460405i
$668$		0			0
$669$	−34.4579	−	59.6828i	−1.33222	−	2.30747i
$670$		0			0
$671$	−16.3001	−	28.2326i	−0.629258	−	1.08991i
$672$		0			0
$673$	15.6155			0.601934			0.300967	−	0.953634i	$-0.402691\pi$
$673$	15.6155			0.601934			0.300967	+	0.953634i	$0.402691\pi$
$674$		0			0
$675$	−10.2425	−	17.7406i	−0.394236	−	0.682837i
$676$		0			0
$677$	7.12311			0.273763			0.136882	−	0.990587i	$-0.456292\pi$
$677$	7.12311			0.273763			0.136882	+	0.990587i	$0.456292\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	23.7116	−	41.0698i	0.908632	−	1.57380i
$682$		0			0
$683$	−23.4468			−0.897168			−0.448584	−	0.893741i	$-0.648072\pi$
$683$	−23.4468			−0.897168			−0.448584	+	0.893741i	$0.648072\pi$
$684$		0			0
$685$	−17.9309			−0.685103
$686$		0			0
$687$	−41.7536	+	72.3193i	−1.59300	+	2.75915i
$688$		0			0
$689$	10.4039	−	18.0201i	0.396356	−	0.686509i
$690$		0			0
$691$	−43.7602			−1.66472			−0.832358	−	0.554238i	$-0.813010\pi$
$691$	−43.7602			−1.66472			−0.832358	+	0.554238i	$0.813010\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.00332			0.0380580
$696$		0			0
$697$	2.28078	+	3.95042i	0.0863906	+	0.149633i
$698$		0			0
$699$	−19.2859	−	33.4042i	−0.729461	−	1.26346i
$700$		0			0
$701$	−10.7192	+	18.5662i	−0.404859	+	0.701237i	−0.994305	−	0.106571i	$-0.966013\pi$
$701$	−10.7192	+	18.5662i	−0.404859	+	0.701237i	0.589446	+	0.807808i	$0.299346\pi$
$702$		0			0
$703$	4.96837	+	30.6488i	0.187385	+	1.15594i
$704$		0			0
$705$	−33.2116	+	57.5243i	−1.25082	+	2.16649i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−2.59612	−	4.49661i	−0.0974993	−	0.168874i	0.813150	−	0.582055i	$-0.197751\pi$
$709$	−2.59612	−	4.49661i	−0.0974993	−	0.168874i	−0.910649	+	0.413181i	$0.864418\pi$
$710$		0			0
$711$	58.0537			2.17718
$712$		0			0
$713$	−5.68466	−	9.84612i	−0.212892	−	0.368740i
$714$		0			0
$715$	58.0537			2.17108
$716$		0			0
$717$	17.0540	−	29.5384i	0.636892	−	1.10313i
$718$		0			0
$719$	6.25339	−	10.8312i	0.233212	−	0.403935i	−0.725539	−	0.688181i	$-0.758410\pi$
$719$	6.25339	−	10.8312i	0.233212	−	0.403935i	0.958752	+	0.284245i	$0.0917430\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	42.9286			1.59653
$724$		0			0
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	1.28502	−	2.22573i	0.0476589	−	0.0825477i	−0.841212	−	0.540706i	$-0.818157\pi$
$727$	1.28502	−	2.22573i	0.0476589	−	0.0825477i	0.888871	+	0.458158i	$0.151491\pi$
$728$		0			0
$729$	19.8769			0.736181
$730$		0			0
$731$	10.4384	+	18.0798i	0.386078	+	0.668706i
$732$		0			0
$733$	−21.3693			−0.789294			−0.394647	−	0.918833i	$-0.629133\pi$
$733$	−21.3693			−0.789294			−0.394647	+	0.918833i	$0.629133\pi$
$734$		0			0
$735$	28.5252	+	49.4070i	1.05217	+	1.82241i
$736$		0			0
$737$	14.8348	+	25.6945i	0.546445	+	0.946471i
$738$		0			0
$739$	−11.1359	+	19.2879i	−0.409640	+	0.709518i	−0.994849	−	0.101365i	$-0.967679\pi$
$739$	−11.1359	+	19.2879i	−0.409640	+	0.709518i	0.585209	+	0.810882i	$0.301012\pi$
$740$		0			0
$741$	−10.1231	−	62.4473i	−0.371882	−	2.29406i
$742$		0			0
$743$	1.89666	−	3.28511i	0.0695816	−	0.120519i	−0.829136	−	0.559048i	$-0.811167\pi$
$743$	1.89666	−	3.28511i	0.0695816	−	0.120519i	0.898717	+	0.438529i	$0.144500\pi$
$744$		0			0
$745$	25.5270	+	44.2140i	0.935236	+	1.61988i
$746$		0			0
$747$	−4.96837	−	8.60546i	−0.181783	−	0.314857i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.04007	−	13.9258i	−0.293386	−	0.508160i	0.681222	−	0.732077i	$-0.261449\pi$
$751$	−8.04007	−	13.9258i	−0.293386	−	0.508160i	−0.974608	+	0.223917i	$0.928116\pi$
$752$		0			0
$753$	−12.6155			−0.459735
$754$		0			0
$755$	−12.7267	+	22.0433i	−0.463173	+	0.802239i
$756$		0			0
$757$	−10.8423	+	18.7795i	−0.394071	+	0.682551i	−0.992982	−	0.118264i	$-0.962267\pi$
$757$	−10.8423	+	18.7795i	−0.394071	+	0.682551i	0.598911	+	0.800816i	$0.295600\pi$
$758$		0			0
$759$	28.2435			1.02517
$760$		0			0
$761$	6.93087			0.251244			0.125622	−	0.992078i	$-0.459907\pi$
$761$	6.93087			0.251244			0.125622	+	0.992078i	$0.459907\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	41.6155	−	72.0802i	1.50461	−	2.60607i
$766$		0			0
$767$	−14.5134			−0.524049
$768$		0			0
$769$	0.842329	+	1.45896i	0.0303752	+	0.0526113i	0.880813	−	0.473464i	$-0.156996\pi$
$769$	0.842329	+	1.45896i	0.0303752	+	0.0526113i	−0.850438	+	0.526075i	$0.823663\pi$
$770$		0			0
$771$	16.6918			0.601140
$772$		0			0
$773$	−8.15767	−	14.1295i	−0.293411	−	0.508203i	0.681203	−	0.732095i	$-0.261457\pi$
$773$	−8.15767	−	14.1295i	−0.293411	−	0.508203i	−0.974614	+	0.223892i	$0.928124\pi$
$774$		0			0
$775$	−4.96837	−	8.60546i	−0.178469	−	0.309117i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.07502	+	1.54731i	0.146003	+	0.0554382i
$780$		0			0
$781$	4.43845	−	7.68762i	0.158820	−	0.275085i
$782$		0			0
$783$	−50.4053	−	87.3045i	−1.80134	−	3.12001i
$784$		0			0
$785$	−1.03457	−	1.79192i	−0.0369252	−	0.0639563i
$786$		0			0
$787$	−10.5484			−0.376009			−0.188004	−	0.982168i	$-0.560202\pi$
$787$	−10.5484			−0.376009			−0.188004	+	0.982168i	$0.560202\pi$
$788$		0			0
$789$	21.8423	+	37.8320i	0.777608	+	1.34686i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−14.9654	+	25.9209i	−0.531438	+	0.920478i
$794$		0			0
$795$	18.5884	−	32.1961i	0.659264	−	1.14188i
$796$		0			0
$797$	37.3693			1.32369			0.661845	−	0.749641i	$-0.269774\pi$
$797$	37.3693			1.32369			0.661845	+	0.749641i	$0.269774\pi$
$798$		0			0
$799$	−37.1769			−1.31522
$800$		0			0
$801$	−6.00000	+	10.3923i	−0.212000	+	0.367194i
$802$		0			0
$803$	37.8744	−	65.6003i	1.33656	−	2.31499i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.3784	−	37.0285i	−0.752557	−	1.30347i
$808$		0			0
$809$	5.17708			0.182016			0.0910082	−	0.995850i	$-0.470991\pi$
$809$	5.17708			0.182016			0.0910082	+	0.995850i	$0.470991\pi$
$810$		0			0
$811$	−1.50498	−	2.60669i	−0.0528468	−	0.0915334i	0.838392	−	0.545068i	$-0.183496\pi$
$811$	−1.50498	−	2.60669i	−0.0528468	−	0.0915334i	−0.891239	+	0.453535i	$0.850163\pi$
$812$		0			0
$813$	12.9654	+	22.4568i	0.454718	+	0.787594i
$814$		0			0
$815$	6.36337	−	11.0217i	0.222899	−	0.386072i
$816$		0			0
$817$	18.6501	+	7.08156i	0.652484	+	0.247752i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.2116	+	38.4717i	0.775192	+	1.34267i	0.934687	+	0.355473i	$0.115680\pi$
$821$	22.2116	+	38.4717i	0.775192	+	1.34267i	−0.159495	+	0.987199i	$0.550987\pi$
$822$		0			0
$823$	−16.1901	−	28.0421i	−0.564352	−	0.977487i	−0.997110	−	0.0759762i	$-0.975793\pi$
$823$	−16.1901	−	28.0421i	−0.564352	−	0.977487i	0.432757	−	0.901510i	$-0.357541\pi$
$824$		0			0
$825$	24.6847			0.859409
$826$		0			0
$827$	−7.95421	−	13.7771i	−0.276595	−	0.479076i	0.693941	−	0.720032i	$-0.255873\pi$
$827$	−7.95421	−	13.7771i	−0.276595	−	0.479076i	−0.970536	+	0.240955i	$0.922539\pi$
$828$		0			0
$829$	22.8769			0.794547			0.397274	−	0.917700i	$-0.369956\pi$
$829$	22.8769			0.794547			0.397274	+	0.917700i	$0.369956\pi$
$830$		0			0
$831$	−6.36337	+	11.0217i	−0.220743	+	0.382338i
$832$		0			0
$833$	−15.9654	+	27.6529i	−0.553170	+	0.958118i
$834$		0			0
$835$	35.1702			1.21712
$836$		0			0
$837$	83.4773			2.88540
$838$		0			0
$839$	−13.0084	+	22.5313i	−0.449101	+	0.777866i	−0.998328	−	0.0578074i	$-0.981589\pi$
$839$	−13.0084	+	22.5313i	−0.449101	+	0.777866i	0.549227	+	0.835673i	$0.314922\pi$
$840$		0			0
$841$	−15.0270	+	26.0275i	−0.518172	+	0.897500i
$842$		0			0
$843$	73.1787			2.52041
$844$		0			0
$845$	−10.0000	−	17.3205i	−0.344010	−	0.595844i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	35.4309	+	61.3681i	1.21598	+	2.10615i
$850$		0			0
$851$	6.36337	+	11.0217i	0.218133	+	0.377818i
$852$		0			0
$853$	0.280776	−	0.486319i	0.00961360	−	0.0166512i	−0.861179	−	0.508303i	$-0.830273\pi$
$853$	0.280776	−	0.486319i	0.00961360	−	0.0166512i	0.870792	+	0.491651i	$0.163607\pi$
$854$		0			0
$855$	−12.7267	−	78.5085i	−0.435245	−	2.68494i
$856$		0			0
$857$	13.1847	−	22.8365i	0.450379	−	0.780080i	−0.548030	−	0.836459i	$-0.684622\pi$
$857$	13.1847	−	22.8365i	0.450379	−	0.780080i	0.998409	+	0.0563787i	$0.0179554\pi$
$858$		0			0
$859$	−4.16089	−	7.20687i	−0.141968	−	0.245895i	0.786270	−	0.617883i	$-0.212010\pi$
$859$	−4.16089	−	7.20687i	−0.141968	−	0.245895i	−0.928238	+	0.371988i	$0.878676\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.6701			0.839780			0.419890	−	0.907575i	$-0.362069\pi$
$863$	24.6701			0.839780			0.419890	+	0.907575i	$0.362069\pi$
$864$		0			0
$865$	18.9654	+	32.8491i	0.644844	+	1.11690i
$866$		0			0
$867$	12.1151			0.411450
$868$		0			0
$869$	−20.2462	+	35.0675i	−0.686806	+	1.18958i
$870$		0			0
$871$	13.6201	−	23.5907i	0.461499	−	0.799339i
$872$		0			0
$873$	−37.3693			−1.26476
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.8423	+	44.7602i	−0.872633	+	1.51145i	−0.0133709	+	0.999911i	$0.504256\pi$
$877$	−25.8423	+	44.7602i	−0.872633	+	1.51145i	−0.859263	+	0.511535i	$0.829077\pi$
$878$		0			0
$879$	−6.36337	+	11.0217i	−0.214631	+	0.371752i
$880$		0			0
$881$	26.0540			0.877781			0.438890	−	0.898541i	$-0.355372\pi$
$881$	26.0540			0.877781			0.438890	+	0.898541i	$0.355372\pi$
$882$		0			0
$883$	11.9193	+	20.6448i	0.401115	+	0.694751i	0.993861	−	0.110638i	$-0.0352895\pi$
$883$	11.9193	+	20.6448i	0.401115	+	0.694751i	−0.592746	+	0.805390i	$0.701956\pi$
$884$		0			0
$885$	−25.9309			−0.871657
$886$		0			0
$887$	5.86171	+	10.1528i	0.196817	+	0.340897i	0.947495	−	0.319772i	$-0.103606\pi$
$887$	5.86171	+	10.1528i	0.196817	+	0.340897i	−0.750678	+	0.660669i	$0.770273\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−50.6011	+	87.6437i	−1.69520	+	2.93617i
$892$		0			0
$893$	−27.5270	+	22.4568i	−0.921156	+	0.751488i
$894$		0			0
$895$	31.8168	−	55.1084i	1.06352	−	1.84207i
$896$		0			0
$897$	−12.9654	−	22.4568i	−0.432903	−	0.749810i
$898$		0			0
$899$	−24.4501	−	42.3489i	−0.815458	−	1.41241i
$900$		0			0
$901$	20.8078			0.693207
$902$		0			0
$903$		0			0
$904$		0			0
$905$	20.3153			0.675305
$906$		0			0
$907$	−28.8310	+	49.9367i	−0.957317	+	1.65812i	−0.228343	+	0.973581i	$0.573331\pi$
$907$	−28.8310	+	49.9367i	−0.957317	+	1.65812i	−0.728974	+	0.684541i	$0.760003\pi$
$908$		0			0
$909$	17.1231	−	29.6581i	0.567938	−	0.983697i
$910$		0			0
$911$	−55.2637			−1.83097			−0.915483	−	0.402356i	$-0.868191\pi$
$911$	−55.2637			−1.83097			−0.915483	+	0.402356i	$0.868191\pi$
$912$		0			0
$913$	6.93087			0.229378
$914$		0			0
$915$	−26.7385	+	46.3124i	−0.883947	+	1.53104i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.22327			0.0403519			0.0201759	−	0.999796i	$-0.493577\pi$
$919$	1.22327			0.0403519			0.0201759	+	0.999796i	$0.493577\pi$
$920$		0			0
$921$	−19.6231	−	33.9882i	−0.646603	−	1.11995i
$922$		0			0
$923$	−8.15005			−0.268262
$924$		0			0
$925$	5.56155	+	9.63289i	0.182863	+	0.316728i
$926$		0			0
$927$	55.2637	+	95.7195i	1.81510	+	3.14384i
$928$		0			0
$929$	−1.93845	+	3.35749i	−0.0635984	+	0.110156i	−0.896071	−	0.443910i	$-0.853591\pi$
$929$	−1.93845	+	3.35749i	−0.0635984	+	0.110156i	0.832473	+	0.554066i	$0.186924\pi$
$930$		0			0
$931$	4.88250	+	30.1191i	0.160017	+	0.987114i
$932$		0			0
$933$	−50.6155	+	87.6687i	−1.65708	+	2.87014i
$934$		0			0
$935$	29.0268	+	50.2759i	0.949279	+	1.64420i
$936$		0			0
$937$	−11.9924	−	20.7715i	−0.391775	−	0.678575i	0.600908	−	0.799318i	$-0.294806\pi$
$937$	−11.9924	−	20.7715i	−0.391775	−	0.678575i	−0.992684	+	0.120743i	$0.961472\pi$
$938$		0			0
$939$	−16.6918			−0.544716
$940$		0			0
$941$	−1.71922	−	2.97778i	−0.0560451	−	0.0970729i	0.836642	−	0.547751i	$-0.184516\pi$
$941$	−1.71922	−	2.97778i	−0.0560451	−	0.0970729i	−0.892687	+	0.450678i	$0.851182\pi$
$942$		0			0
$943$	1.78668			0.0581824
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.85839	−	8.41498i	0.157876	−	0.273450i	−0.776226	−	0.630454i	$-0.782869\pi$
$947$	4.85839	−	8.41498i	0.157876	−	0.273450i	0.934103	+	0.357004i	$0.116202\pi$
$948$		0			0
$949$	−69.5464			−2.25757
$950$		0			0
$951$	−45.1070			−1.46269
$952$		0			0
$953$	−7.69224	+	13.3233i	−0.249176	+	0.431585i	−0.963297	−	0.268436i	$-0.913493\pi$
$953$	−7.69224	+	13.3233i	−0.249176	+	0.431585i	0.714121	+	0.700022i	$0.246826\pi$
$954$		0			0
$955$	−7.14673	+	12.3785i	−0.231263	+	0.400559i
$956$		0			0
$957$	121.477			3.92680
$958$		0			0
$959$		0			0
$960$		0			0
$961$	9.49242			0.306207
$962$		0			0
$963$	45.3269	+	78.5085i	1.46064	+	2.52990i
$964$		0			0
$965$	−13.8423	−	23.9756i	−0.445600	−	0.771802i
$966$		0			0
$967$	16.4101	−	28.4231i	0.527712	−	0.914025i	−0.471766	−	0.881724i	$-0.656383\pi$
$967$	16.4101	−	28.4231i	0.527712	−	0.914025i	0.999478	−	0.0323007i	$-0.0102834\pi$
$968$		0			0
$969$	49.0194	−	39.9905i	1.57473	−	1.28468i
$970$		0			0
$971$	−26.0410	+	45.1043i	−0.835695	+	1.44747i	0.0577682	+	0.998330i	$0.481602\pi$
$971$	−26.0410	+	45.1043i	−0.835695	+	1.44747i	−0.893463	+	0.449136i	$0.851732\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−11.3317	−	19.6271i	−0.362906	−	0.628571i
$976$		0			0
$977$	−16.3002			−0.521489			−0.260745	−	0.965408i	$-0.583968\pi$
$977$	−16.3002			−0.521489			−0.260745	+	0.965408i	$0.583968\pi$
$978$		0			0
$979$	−4.18500	−	7.24863i	−0.133753	−	0.231667i
$980$		0			0
$981$	−62.7386			−2.00309
$982$		0			0
$983$	11.4417	−	19.8176i	0.364934	−	0.632084i	−0.623832	−	0.781559i	$-0.714425\pi$
$983$	11.4417	−	19.8176i	0.364934	−	0.632084i	0.988766	+	0.149475i	$0.0477583\pi$
$984$		0			0
$985$	6.87689	−	11.9111i	0.219116	−	0.379520i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.17708			0.260016
$990$		0			0
$991$	−19.5918	+	33.9339i	−0.622353	+	1.07795i	0.366694	+	0.930342i	$0.380490\pi$
$991$	−19.5918	+	33.9339i	−0.622353	+	1.07795i	−0.989046	+	0.147605i	$0.952844\pi$
$992$		0			0
$993$	16.7808	−	29.0652i	0.532522	−	0.922355i
$994$		0			0
$995$	−55.4836			−1.75895
$996$		0			0
$997$	2.96543	+	5.13628i	0.0939163	+	0.162668i	0.909156	−	0.416456i	$-0.136728\pi$
$997$	2.96543	+	5.13628i	0.0939163	+	0.162668i	−0.815240	+	0.579124i	$0.803395\pi$
$998$		0			0
$999$	−93.4439			−2.95643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.p.961.1		8
4.3	odd	2	inner	1216.2.i.p.961.4		8
8.3	odd	2		608.2.i.d.353.1	✓	8
8.5	even	2		608.2.i.d.353.4	yes	8
19.7	even	3	inner	1216.2.i.p.577.1		8
76.7	odd	6	inner	1216.2.i.p.577.4		8
152.45	even	6		608.2.i.d.577.4	yes	8
152.83	odd	6		608.2.i.d.577.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.d.353.1	✓	8	8.3	odd	2
608.2.i.d.353.4	yes	8	8.5	even	2
608.2.i.d.577.1	yes	8	152.83	odd	6
608.2.i.d.577.4	yes	8	152.45	even	6
1216.2.i.p.577.1		8	19.7	even	3	inner
1216.2.i.p.577.4		8	76.7	odd	6	inner
1216.2.i.p.961.1		8	1.1	even	1	trivial
1216.2.i.p.961.4		8	4.3	odd	2	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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59084 + 2.75542i) q^{3} +(-1.28078 + 2.21837i) q^{5} +(-3.56155 - 6.16879i) q^{9} +O(q^{10})\)	\(q+(-1.59084 + 2.75542i) q^{3} +(-1.28078 + 2.21837i) q^{5} +(-3.56155 - 6.16879i) q^{9} +4.96837 q^{11} +(-2.28078 - 3.95042i) q^{13} +(-4.07502 - 7.05815i) q^{15} +(2.28078 - 3.95042i) q^{17} +(-0.697500 - 4.30273i) q^{19} +(-0.893341 - 1.54731i) q^{23} +(-0.780776 - 1.35234i) q^{25} +13.1184 q^{27} +(-3.84233 - 6.65511i) q^{29} +6.36337 q^{31} +(-7.90388 + 13.6899i) q^{33} -7.12311 q^{37} +14.5134 q^{39} +(-0.500000 + 0.866025i) q^{41} +(-2.28834 + 3.96352i) q^{43} +18.2462 q^{45} +(-4.07502 - 7.05815i) q^{47} -7.00000 q^{49} +(7.25671 + 12.5690i) q^{51} +(2.28078 + 3.95042i) q^{53} +(-6.36337 + 11.0217i) q^{55} +(12.9654 + 4.92306i) q^{57} +(1.59084 - 2.75542i) q^{59} +(-3.28078 - 5.68247i) q^{61} +11.6847 q^{65} +(2.98584 + 5.17163i) q^{67} +5.68466 q^{69} +(0.893341 - 1.54731i) q^{71} +(7.62311 - 13.2036i) q^{73} +4.96837 q^{75} +(-4.07502 + 7.05815i) q^{79} +(-10.1847 + 17.6403i) q^{81} +1.39500 q^{83} +(5.84233 + 10.1192i) q^{85} +24.4501 q^{87} +(-0.842329 - 1.45896i) q^{89} +(-10.1231 + 17.5337i) q^{93} +(10.4384 + 3.96352i) q^{95} +(2.62311 - 4.54335i) q^{97} +(-17.6951 - 30.6488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} - 12 q^{9}+O(q^{10}) \) 8 * q - 2 * q^5 - 12 * q^9	\( 8 q - 2 q^{5} - 12 q^{9} - 10 q^{13} + 10 q^{17} + 2 q^{25} - 6 q^{29} - 22 q^{33} - 24 q^{37} - 4 q^{41} + 80 q^{45} - 56 q^{49} + 10 q^{53} + 46 q^{57} - 18 q^{61} + 44 q^{65} - 4 q^{69} + 28 q^{73} - 32 q^{81} + 22 q^{85} + 18 q^{89} - 48 q^{93} - 12 q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 - 12 * q^9 - 10 * q^13 + 10 * q^17 + 2 * q^25 - 6 * q^29 - 22 * q^33 - 24 * q^37 - 4 * q^41 + 80 * q^45 - 56 * q^49 + 10 * q^53 + 46 * q^57 - 18 * q^61 + 44 * q^65 - 4 * q^69 + 28 * q^73 - 32 * q^81 + 22 * q^85 + 18 * q^89 - 48 * q^93 - 12 * q^97

Introduction

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