LMFDB - Embedded newform 1216.2.s.a.863.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(31,1216)]

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([3, 3, 5]))

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

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

chi := DirichletCharacter("1216.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			863.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1216.863
Dual form			1216.2.s.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{3} +(-2.36603 - 1.36603i) q^{5} -1.26795i q^{7} -4.46410 q^{11} +(2.36603 + 4.09808i) q^{15} +(2.73205 - 4.73205i) q^{17} +(-0.500000 - 4.33013i) q^{19} +(-1.09808 + 1.90192i) q^{21} +(-3.63397 + 2.09808i) q^{23} +(1.23205 + 2.13397i) q^{25} +5.19615i q^{27} +(1.09808 + 1.90192i) q^{29} -2.19615 q^{31} +(6.69615 + 3.86603i) q^{33} +(-1.73205 + 3.00000i) q^{35} -4.73205 q^{37} +(6.69615 + 3.86603i) q^{41} +(1.73205 - 3.00000i) q^{43} +(-8.36603 + 4.83013i) q^{47} +5.39230 q^{49} +(-8.19615 + 4.73205i) q^{51} +(4.73205 + 8.19615i) q^{53} +(10.5622 + 6.09808i) q^{55} +(-3.00000 + 6.92820i) q^{57} +(0.696152 + 0.401924i) q^{59} +(10.5622 - 6.09808i) q^{61} +(3.69615 - 2.13397i) q^{67} +7.26795 q^{69} +(-1.26795 + 2.19615i) q^{71} +(2.50000 - 4.33013i) q^{73} -4.26795i q^{75} +5.66025i q^{77} +(-8.19615 + 14.1962i) q^{79} +(4.50000 - 7.79423i) q^{81} +3.39230 q^{83} +(-12.9282 + 7.46410i) q^{85} -3.80385i q^{87} +(-11.1962 + 6.46410i) q^{89} +(3.29423 + 1.90192i) q^{93} +(-4.73205 + 10.9282i) q^{95} +(-6.69615 - 3.86603i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 6 q^{5} - 4 q^{11} + 6 q^{15} + 4 q^{17} - 2 q^{19} + 6 q^{21} - 18 q^{23} - 2 q^{25} - 6 q^{29} + 12 q^{31} + 6 q^{33} - 12 q^{37} + 6 q^{41} - 30 q^{47} - 20 q^{49} - 12 q^{51} + 12 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) $ 4 * q - 6 * q^3 - 6 * q^5 - 4 * q^11 + 6 * q^15 + 4 * q^17 - 2 * q^19 + 6 * q^21 - 18 * q^23 - 2 * q^25 - 6 * q^29 + 12 * q^31 + 6 * q^33 - 12 * q^37 + 6 * q^41 - 30 * q^47 - 20 * q^49 - 12 * q^51 + 12 * q^53 + 18 * q^55 - 12 * q^57 - 18 * q^59 + 18 * q^61 - 6 * q^67 + 36 * q^69 - 12 * q^71 + 10 * q^73 - 12 * q^79 + 18 * q^81 - 28 * q^83 - 24 * q^85 - 24 * q^89 - 18 * q^93 - 12 * q^95 - 6 * q^97

Character values

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

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	−2.36603	−	1.36603i	−1.05812	−	0.610905i	−0.133207	−	0.991088i	$-0.542528\pi$
$5$	−2.36603	−	1.36603i	−1.05812	−	0.610905i	−0.924911	+	0.380183i	$0.875861\pi$
$6$		0			0
$7$		−	1.26795i		−	0.479240i	−0.970867	−	0.239620i	$-0.922977\pi$
$7$		−	1.26795i		−	0.479240i	0.970867	−	0.239620i	$-0.0770228\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.46410			−1.34598			−0.672989	−	0.739653i	$-0.734990\pi$
$11$	−4.46410			−1.34598			−0.672989	+	0.739653i	$0.734990\pi$
$12$		0			0
$13$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$13$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$14$		0			0
$15$	2.36603	+	4.09808i	0.610905	+	1.05812i
$16$		0			0
$17$	2.73205	−	4.73205i	0.662620	−	1.14769i	−0.317305	−	0.948323i	$-0.602778\pi$
$17$	2.73205	−	4.73205i	0.662620	−	1.14769i	0.979925	−	0.199367i	$-0.0638887\pi$
$18$		0			0
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$20$		0			0
$21$	−1.09808	+	1.90192i	−0.239620	+	0.415034i
$22$		0			0
$23$	−3.63397	+	2.09808i	−0.757736	+	0.437479i	−0.828482	−	0.560015i	$-0.810795\pi$
$23$	−3.63397	+	2.09808i	−0.757736	+	0.437479i	0.0707462	+	0.997494i	$0.477462\pi$
$24$		0			0
$25$	1.23205	+	2.13397i	0.246410	+	0.426795i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	1.09808	+	1.90192i	0.203908	+	0.353178i	0.949784	−	0.312906i	$-0.101302\pi$
$29$	1.09808	+	1.90192i	0.203908	+	0.353178i	−0.745877	+	0.666084i	$0.767969\pi$
$30$		0			0
$31$	−2.19615			−0.394441			−0.197220	−	0.980359i	$-0.563191\pi$
$31$	−2.19615			−0.394441			−0.197220	+	0.980359i	$0.563191\pi$
$32$		0			0
$33$	6.69615	+	3.86603i	1.16565	+	0.672989i
$34$		0			0
$35$	−1.73205	+	3.00000i	−0.292770	+	0.507093i
$36$		0			0
$37$	−4.73205			−0.777944			−0.388972	−	0.921250i	$-0.627170\pi$
$37$	−4.73205			−0.777944			−0.388972	+	0.921250i	$0.627170\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.69615	+	3.86603i	1.04576	+	0.603772i	0.921460	−	0.388473i	$-0.126997\pi$
$41$	6.69615	+	3.86603i	1.04576	+	0.603772i	0.124303	+	0.992244i	$0.460331\pi$
$42$		0			0
$43$	1.73205	−	3.00000i	0.264135	−	0.457496i	−0.703201	−	0.710991i	$-0.748247\pi$
$43$	1.73205	−	3.00000i	0.264135	−	0.457496i	0.967337	+	0.253495i	$0.0815801\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.36603	+	4.83013i	−1.22031	+	0.704546i	−0.964984	−	0.262309i	$-0.915516\pi$
$47$	−8.36603	+	4.83013i	−1.22031	+	0.704546i	−0.255326	+	0.966855i	$0.582183\pi$
$48$		0			0
$49$	5.39230			0.770329
$50$		0			0
$51$	−8.19615	+	4.73205i	−1.14769	+	0.662620i
$52$		0			0
$53$	4.73205	+	8.19615i	0.649997	+	1.12583i	0.983123	+	0.182946i	$0.0585633\pi$
$53$	4.73205	+	8.19615i	0.649997	+	1.12583i	−0.333126	+	0.942882i	$0.608103\pi$
$54$		0			0
$55$	10.5622	+	6.09808i	1.42420	+	0.822264i
$56$		0			0
$57$	−3.00000	+	6.92820i	−0.397360	+	0.917663i
$58$		0			0
$59$	0.696152	+	0.401924i	0.0906313	+	0.0523260i	0.544631	−	0.838676i	$-0.316670\pi$
$59$	0.696152	+	0.401924i	0.0906313	+	0.0523260i	−0.453999	+	0.891002i	$0.650003\pi$
$60$		0			0
$61$	10.5622	−	6.09808i	1.35235	−	0.780779i	0.363770	−	0.931489i	$-0.381489\pi$
$61$	10.5622	−	6.09808i	1.35235	−	0.780779i	0.988578	+	0.150710i	$0.0481560\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.69615	−	2.13397i	0.451557	−	0.260706i	−0.256931	−	0.966430i	$-0.582711\pi$
$67$	3.69615	−	2.13397i	0.451557	−	0.260706i	0.708487	+	0.705723i	$0.249378\pi$
$68$		0			0
$69$	7.26795			0.874958
$70$		0			0
$71$	−1.26795	+	2.19615i	−0.150478	+	0.260635i	−0.931403	−	0.363989i	$-0.881415\pi$
$71$	−1.26795	+	2.19615i	−0.150478	+	0.260635i	0.780925	+	0.624624i	$0.214748\pi$
$72$		0			0
$73$	2.50000	−	4.33013i	0.292603	−	0.506803i	−0.681822	−	0.731519i	$-0.738812\pi$
$73$	2.50000	−	4.33013i	0.292603	−	0.506803i	0.974424	+	0.224716i	$0.0721453\pi$
$74$		0			0
$75$		−	4.26795i		−	0.492820i
$76$		0			0
$77$			5.66025i			0.645046i
$78$		0			0
$79$	−8.19615	+	14.1962i	−0.922139	+	1.59719i	−0.126041	+	0.992025i	$0.540227\pi$
$79$	−8.19615	+	14.1962i	−0.922139	+	1.59719i	−0.796099	+	0.605167i	$0.793106\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$	3.39230			0.372354			0.186177	−	0.982516i	$-0.440390\pi$
$83$	3.39230			0.372354			0.186177	+	0.982516i	$0.440390\pi$
$84$		0			0
$85$	−12.9282	+	7.46410i	−1.40226	+	0.809595i
$86$		0			0
$87$		−	3.80385i		−	0.407815i
$88$		0			0
$89$	−11.1962	+	6.46410i	−1.18679	+	0.685193i	−0.957575	−	0.288183i	$-0.906949\pi$
$89$	−11.1962	+	6.46410i	−1.18679	+	0.685193i	−0.229214	+	0.973376i	$0.573616\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.29423	+	1.90192i	0.341596	+	0.197220i
$94$		0			0
$95$	−4.73205	+	10.9282i	−0.485498	+	1.12121i
$96$		0			0
$97$	−6.69615	−	3.86603i	−0.679891	−	0.392535i	0.119923	−	0.992783i	$-0.461735\pi$
$97$	−6.69615	−	3.86603i	−0.679891	−	0.392535i	−0.799814	+	0.600248i	$0.795069\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−14.0263	+	8.09808i	−1.39567	+	0.805789i	−0.993935	−	0.109969i	$-0.964925\pi$
$101$	−14.0263	+	8.09808i	−1.39567	+	0.805789i	−0.401732	+	0.915757i	$0.631592\pi$
$102$		0			0
$103$	9.46410			0.932526			0.466263	−	0.884646i	$-0.345600\pi$
$103$	9.46410			0.932526			0.466263	+	0.884646i	$0.345600\pi$
$104$		0			0
$105$	5.19615	−	3.00000i	0.507093	−	0.292770i
$106$		0			0
$107$		−	4.39230i		−	0.424620i	−0.977202	−	0.212310i	$-0.931901\pi$
$107$		−	4.39230i		−	0.424620i	0.977202	−	0.212310i	$-0.0680987\pi$
$108$		0			0
$109$	−1.26795	+	2.19615i	−0.121448	+	0.210353i	−0.920339	−	0.391122i	$-0.872087\pi$
$109$	−1.26795	+	2.19615i	−0.121448	+	0.210353i	0.798891	+	0.601476i	$0.205420\pi$
$110$		0			0
$111$	7.09808	+	4.09808i	0.673720	+	0.388972i
$112$		0			0
$113$			15.5885i			1.46644i	0.679992	+	0.733219i	$0.261983\pi$
$113$			15.5885i			1.46644i	−0.679992	+	0.733219i	$0.738017\pi$
$114$		0			0
$115$	11.4641			1.06903
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.00000	−	3.46410i	−0.550019	−	0.317554i
$120$		0			0
$121$	8.92820			0.811655
$122$		0			0
$123$	−6.69615	−	11.5981i	−0.603772	−	1.04576i
$124$		0			0
$125$			6.92820i			0.619677i
$126$		0			0
$127$	−1.26795	−	2.19615i	−0.112512	−	0.194877i	0.804270	−	0.594264i	$-0.202556\pi$
$127$	−1.26795	−	2.19615i	−0.112512	−	0.194877i	−0.916783	+	0.399387i	$0.869223\pi$
$128$		0			0
$129$	−5.19615	+	3.00000i	−0.457496	+	0.264135i
$130$		0			0
$131$	0.964102	−	1.66987i	0.0842339	−	0.145897i	−0.820831	−	0.571172i	$-0.806489\pi$
$131$	0.964102	−	1.66987i	0.0842339	−	0.145897i	0.905065	+	0.425274i	$0.139822\pi$
$132$		0			0
$133$	−5.49038	+	0.633975i	−0.476076	+	0.0549726i
$134$		0			0
$135$	7.09808	−	12.2942i	0.610905	−	1.05812i
$136$		0			0
$137$	−8.96410	−	15.5263i	−0.765855	−	1.32650i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−8.96410	−	15.5263i	−0.765855	−	1.32650i	0.173939	−	0.984757i	$-0.444351\pi$
$138$		0			0
$139$	2.69615	+	4.66987i	0.228685	+	0.396093i	0.957419	−	0.288704i	$-0.0932242\pi$
$139$	2.69615	+	4.66987i	0.228685	+	0.396093i	−0.728734	+	0.684797i	$0.759891\pi$
$140$		0			0
$141$	16.7321			1.40909
$142$		0			0
$143$		0			0
$144$		0			0
$145$		−	6.00000i		−	0.498273i
$146$		0			0
$147$	−8.08846	−	4.66987i	−0.667125	−	0.385165i
$148$		0			0
$149$	−8.36603	−	4.83013i	−0.685372	−	0.395699i	0.116504	−	0.993190i	$-0.462831\pi$
$149$	−8.36603	−	4.83013i	−0.685372	−	0.395699i	−0.801876	+	0.597491i	$0.796164\pi$
$150$		0			0
$151$	16.7321			1.36163			0.680817	−	0.732453i	$-0.261625\pi$
$151$	16.7321			1.36163			0.680817	+	0.732453i	$0.261625\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.19615	+	3.00000i	0.417365	+	0.240966i
$156$		0			0
$157$	−0.339746	−	0.196152i	−0.0271147	−	0.0156547i	0.486381	−	0.873747i	$-0.338317\pi$
$157$	−0.339746	−	0.196152i	−0.0271147	−	0.0156547i	−0.513496	+	0.858092i	$0.671650\pi$
$158$		0			0
$159$		−	16.3923i		−	1.29999i
$160$		0			0
$161$	2.66025	+	4.60770i	0.209657	+	0.363137i
$162$		0			0
$163$	−9.39230			−0.735662			−0.367831	−	0.929893i	$-0.619900\pi$
$163$	−9.39230			−0.735662			−0.367831	+	0.929893i	$0.619900\pi$
$164$		0			0
$165$	−10.5622	−	18.2942i	−0.822264	−	1.42420i
$166$		0			0
$167$	−2.53590	−	4.39230i	−0.196234	−	0.339887i	0.751071	−	0.660222i	$-0.229538\pi$
$167$	−2.53590	−	4.39230i	−0.196234	−	0.339887i	−0.947304	+	0.320335i	$0.896204\pi$
$168$		0			0
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.9282	−	22.3923i	0.982913	−	1.70246i	0.332047	−	0.943263i	$-0.392261\pi$
$173$	12.9282	−	22.3923i	0.982913	−	1.70246i	0.650866	−	0.759193i	$-0.274406\pi$
$174$		0			0
$175$	2.70577	−	1.56218i	0.204537	−	0.118090i
$176$		0			0
$177$	−0.696152	−	1.20577i	−0.0523260	−	0.0906313i
$178$		0			0
$179$		−	5.19615i		−	0.388379i	−0.980964	−	0.194189i	$-0.937792\pi$
$179$		−	5.19615i		−	0.388379i	0.980964	−	0.194189i	$-0.0622076\pi$
$180$		0			0
$181$	−2.36603	−	4.09808i	−0.175865	−	0.304608i	0.764595	−	0.644511i	$-0.222939\pi$
$181$	−2.36603	−	4.09808i	−0.175865	−	0.304608i	−0.940460	+	0.339903i	$0.889606\pi$
$182$		0			0
$183$	−21.1244			−1.56156
$184$		0			0
$185$	11.1962	+	6.46410i	0.823157	+	0.475250i
$186$		0			0
$187$	−12.1962	+	21.1244i	−0.891871	+	1.54477i
$188$		0			0
$189$	6.58846			0.479240
$190$		0			0
$191$		−	17.8564i		−	1.29204i	−0.763319	−	0.646022i	$-0.776431\pi$
$191$		−	17.8564i		−	1.29204i	0.763319	−	0.646022i	$-0.223569\pi$
$192$		0			0
$193$	−21.5885	−	12.4641i	−1.55397	−	0.897186i	−0.997812	−	0.0661096i	$-0.978941\pi$
$193$	−21.5885	−	12.4641i	−1.55397	−	0.897186i	−0.556159	−	0.831076i	$-0.687725\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			7.80385i			0.556001i	0.960581	+	0.278001i	$0.0896717\pi$
$197$			7.80385i			0.556001i	−0.960581	+	0.278001i	$0.910328\pi$
$198$		0			0
$199$	−10.7321	+	6.19615i	−0.760775	+	0.439234i	−0.829574	−	0.558397i	$-0.811417\pi$
$199$	−10.7321	+	6.19615i	−0.760775	+	0.439234i	0.0687990	+	0.997631i	$0.478083\pi$
$200$		0			0
$201$	−7.39230			−0.521413
$202$		0			0
$203$	2.41154	−	1.39230i	0.169257	−	0.0977206i
$204$		0			0
$205$	−10.5622	−	18.2942i	−0.737694	−	1.27772i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.23205	+	19.3301i	0.154394	+	1.33709i
$210$		0			0
$211$	15.0000	+	8.66025i	1.03264	+	0.596196i	0.917741	−	0.397180i	$-0.130011\pi$
$211$	15.0000	+	8.66025i	1.03264	+	0.596196i	0.114902	+	0.993377i	$0.463345\pi$
$212$		0			0
$213$	3.80385	−	2.19615i	0.260635	−	0.150478i
$214$		0			0
$215$	−8.19615	+	4.73205i	−0.558973	+	0.322723i
$216$		0			0
$217$			2.78461i			0.189032i
$218$		0			0
$219$	−7.50000	+	4.33013i	−0.506803	+	0.292603i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	12.7583	−	22.0981i	0.854361	−	1.47980i	−0.0228756	−	0.999738i	$-0.507282\pi$
$223$	12.7583	−	22.0981i	0.854361	−	1.47980i	0.877237	−	0.480058i	$-0.159385\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			18.1244i			1.20296i	0.798889	+	0.601478i	$0.205421\pi$
$227$			18.1244i			1.20296i	−0.798889	+	0.601478i	$0.794579\pi$
$228$		0			0
$229$			12.7846i			0.844831i	0.906402	+	0.422415i	$0.138818\pi$
$229$			12.7846i			0.844831i	−0.906402	+	0.422415i	$0.861182\pi$
$230$		0			0
$231$	4.90192	−	8.49038i	0.322523	−	0.558626i
$232$		0			0
$233$	−3.42820	+	5.93782i	−0.224589	+	0.389000i	−0.956196	−	0.292727i	$-0.905437\pi$
$233$	−3.42820	+	5.93782i	−0.224589	+	0.389000i	0.731607	+	0.681727i	$0.238771\pi$
$234$		0			0
$235$	26.3923			1.72164
$236$		0			0
$237$	24.5885	−	14.1962i	1.59719	−	0.922139i
$238$		0			0
$239$			5.85641i			0.378819i	0.981898	+	0.189410i	$0.0606574\pi$
$239$			5.85641i			0.378819i	−0.981898	+	0.189410i	$0.939343\pi$
$240$		0			0
$241$	−22.2846	+	12.8660i	−1.43548	+	0.828774i	−0.997531	−	0.0702273i	$-0.977628\pi$
$241$	−22.2846	+	12.8660i	−1.43548	+	0.828774i	−0.437947	+	0.899001i	$0.644294\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.7583	−	7.36603i	−0.815100	−	0.470598i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−5.08846	−	2.93782i	−0.322468	−	0.186177i
$250$		0			0
$251$	−8.16025	−	14.1340i	−0.515071	−	0.892129i	−0.999847	−	0.0174904i	$-0.994432\pi$
$251$	−8.16025	−	14.1340i	−0.515071	−	0.892129i	0.484776	−	0.874638i	$-0.338901\pi$
$252$		0			0
$253$	16.2224	−	9.36603i	1.01990	−	0.588837i
$254$		0			0
$255$	25.8564			1.61919
$256$		0			0
$257$	11.3038	−	6.52628i	0.705115	−	0.407098i	−0.104135	−	0.994563i	$-0.533207\pi$
$257$	11.3038	−	6.52628i	0.705115	−	0.407098i	0.809250	+	0.587465i	$0.199874\pi$
$258$		0			0
$259$			6.00000i			0.372822i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.8301	−	6.83013i	−0.729477	−	0.421164i	0.0887539	−	0.996054i	$-0.471712\pi$
$263$	−11.8301	−	6.83013i	−0.729477	−	0.421164i	−0.818231	+	0.574890i	$0.805045\pi$
$264$		0			0
$265$		−	25.8564i		−	1.58835i
$266$		0			0
$267$	22.3923			1.37039
$268$		0			0
$269$	−10.7321	+	18.5885i	−0.654345	+	1.13336i	0.327713	+	0.944777i	$0.393722\pi$
$269$	−10.7321	+	18.5885i	−0.654345	+	1.13336i	−0.982058	+	0.188581i	$0.939611\pi$
$270$		0			0
$271$	−24.7583	−	14.2942i	−1.50396	−	0.868313i	−0.999989	−	0.00459256i	$-0.998538\pi$
$271$	−24.7583	−	14.2942i	−1.50396	−	0.868313i	−0.503972	−	0.863720i	$-0.668129\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.50000	−	9.52628i	−0.331662	−	0.574456i
$276$		0			0
$277$		−	4.19615i		−	0.252122i	−0.992022	−	0.126061i	$-0.959766\pi$
$277$		−	4.19615i		−	0.252122i	0.992022	−	0.126061i	$-0.0402336\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.8923	+	8.59808i	−0.888400	+	0.512918i	−0.873419	−	0.486970i	$-0.838102\pi$
$281$	−14.8923	+	8.59808i	−0.888400	+	0.512918i	−0.0149815	+	0.999888i	$0.504769\pi$
$282$		0			0
$283$	−9.23205	+	15.9904i	−0.548788	+	0.950529i	0.449569	+	0.893245i	$0.351577\pi$
$283$	−9.23205	+	15.9904i	−0.548788	+	0.950529i	−0.998358	+	0.0572841i	$0.981756\pi$
$284$		0			0
$285$	16.5622	−	12.2942i	0.981059	−	0.728247i
$286$		0			0
$287$	4.90192	−	8.49038i	0.289351	−	0.501171i
$288$		0			0
$289$	−6.42820	−	11.1340i	−0.378130	−	0.654940i
$290$		0			0
$291$	6.69615	+	11.5981i	0.392535	+	0.679891i
$292$		0			0
$293$	4.73205			0.276449			0.138225	−	0.990401i	$-0.455860\pi$
$293$	4.73205			0.276449			0.138225	+	0.990401i	$0.455860\pi$
$294$		0			0
$295$	−1.09808	−	1.90192i	−0.0639325	−	0.110734i
$296$		0			0
$297$		−	23.1962i		−	1.34598i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−3.80385	−	2.19615i	−0.219250	−	0.126584i
$302$		0			0
$303$	28.0526			1.61158
$304$		0			0
$305$	−33.3205			−1.90793
$306$		0			0
$307$	11.0885	+	6.40192i	0.632852	+	0.365377i	0.781856	−	0.623460i	$-0.214273\pi$
$307$	11.0885	+	6.40192i	0.632852	+	0.365377i	−0.149004	+	0.988837i	$0.547607\pi$
$308$		0			0
$309$	−14.1962	−	8.19615i	−0.807591	−	0.466263i
$310$		0			0
$311$			18.7321i			1.06220i	0.847310	+	0.531099i	$0.178221\pi$
$311$			18.7321i			1.06220i	−0.847310	+	0.531099i	$0.821779\pi$
$312$		0			0
$313$	9.69615	+	16.7942i	0.548059	+	0.949266i	0.998408	+	0.0564131i	$0.0179664\pi$
$313$	9.69615	+	16.7942i	0.548059	+	0.949266i	−0.450349	+	0.892853i	$0.648700\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.1244	−	26.1962i	−0.849468	−	1.47132i	−0.881683	−	0.471842i	$-0.843589\pi$
$317$	−15.1244	−	26.1962i	−0.849468	−	1.47132i	0.0322149	−	0.999481i	$-0.489744\pi$
$318$		0			0
$319$	−4.90192	−	8.49038i	−0.274455	−	0.475370i
$320$		0			0
$321$	−3.80385	+	6.58846i	−0.212310	+	0.367732i
$322$		0			0
$323$	−21.8564	−	9.46410i	−1.21612	−	0.526597i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.80385	−	2.19615i	0.210353	−	0.121448i
$328$		0			0
$329$	6.12436	+	10.6077i	0.337647	+	0.584821i
$330$		0			0
$331$		−	31.7321i		−	1.74415i	−0.489371	−	0.872076i	$-0.662774\pi$
$331$		−	31.7321i		−	1.74415i	0.489371	−	0.872076i	$-0.337226\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.6603			−0.637068
$336$		0			0
$337$	−5.89230	−	3.40192i	−0.320974	−	0.185315i	0.330852	−	0.943682i	$-0.392664\pi$
$337$	−5.89230	−	3.40192i	−0.320974	−	0.185315i	−0.651827	+	0.758368i	$0.725997\pi$
$338$		0			0
$339$	13.5000	−	23.3827i	0.733219	−	1.26997i
$340$		0			0
$341$	9.80385			0.530908
$342$		0			0
$343$		−	15.7128i		−	0.848412i
$344$		0			0
$345$	−17.1962	−	9.92820i	−0.925810	−	0.534516i
$346$		0			0
$347$	−1.23205	+	2.13397i	−0.0661400	+	0.114558i	−0.897199	−	0.441626i	$-0.854402\pi$
$347$	−1.23205	+	2.13397i	−0.0661400	+	0.114558i	0.831059	+	0.556184i	$0.187735\pi$
$348$		0			0
$349$			34.6410i			1.85429i	0.374701	+	0.927146i	$0.377745\pi$
$349$			34.6410i			1.85429i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	25.7846			1.37238			0.686188	−	0.727424i	$-0.259283\pi$
$353$	25.7846			1.37238			0.686188	+	0.727424i	$0.259283\pi$
$354$		0			0
$355$	6.00000	−	3.46410i	0.318447	−	0.183855i
$356$		0			0
$357$	6.00000	+	10.3923i	0.317554	+	0.550019i
$358$		0			0
$359$	−2.02628	−	1.16987i	−0.106943	−	0.0617435i	0.445575	−	0.895245i	$-0.352999\pi$
$359$	−2.02628	−	1.16987i	−0.106943	−	0.0617435i	−0.552517	+	0.833501i	$0.686333\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$		0			0
$363$	−13.3923	−	7.73205i	−0.702914	−	0.405827i
$364$		0			0
$365$	−11.8301	+	6.83013i	−0.619217	+	0.357505i
$366$		0			0
$367$	24.7583	−	14.2942i	1.29237	−	0.746153i	0.313300	−	0.949654i	$-0.398566\pi$
$367$	24.7583	−	14.2942i	1.29237	−	0.746153i	0.979075	+	0.203502i	$0.0652322\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10.3923	−	6.00000i	0.539542	−	0.311504i
$372$		0			0
$373$	−6.92820			−0.358729			−0.179364	−	0.983783i	$-0.557404\pi$
$373$	−6.92820			−0.358729			−0.179364	+	0.983783i	$0.557404\pi$
$374$		0			0
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$		0			0
$377$		0			0
$378$		0			0
$379$			17.3205i			0.889695i	0.895606	+	0.444847i	$0.146742\pi$
$379$			17.3205i			0.889695i	−0.895606	+	0.444847i	$0.853258\pi$
$380$		0			0
$381$			4.39230i			0.225025i
$382$		0			0
$383$	−8.36603	+	14.4904i	−0.427484	+	0.740424i	−0.996649	−	0.0817995i	$-0.973933\pi$
$383$	−8.36603	+	14.4904i	−0.427484	+	0.740424i	0.569165	+	0.822223i	$0.307267\pi$
$384$		0			0
$385$	7.73205	−	13.3923i	0.394062	−	0.682535i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−22.0526	+	12.7321i	−1.11811	+	0.645541i	−0.940918	−	0.338636i	$-0.890035\pi$
$389$	−22.0526	+	12.7321i	−1.11811	+	0.645541i	−0.177192	+	0.984176i	$0.556701\pi$
$390$		0			0
$391$			22.9282i			1.15953i
$392$		0			0
$393$	−2.89230	+	1.66987i	−0.145897	+	0.0842339i
$394$		0			0
$395$	38.7846	−	22.3923i	1.95147	−	1.12668i
$396$		0			0
$397$	30.0788	+	17.3660i	1.50961	+	0.871576i	0.999937	+	0.0112097i	$0.00356823\pi$
$397$	30.0788	+	17.3660i	1.50961	+	0.871576i	0.509676	+	0.860366i	$0.329765\pi$
$398$		0			0
$399$	8.78461	+	3.80385i	0.439781	+	0.190431i
$400$		0			0
$401$	17.0885	+	9.86603i	0.853357	+	0.492686i	0.861782	−	0.507279i	$-0.169349\pi$
$401$	17.0885	+	9.86603i	0.853357	+	0.492686i	−0.00842522	+	0.999965i	$0.502682\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−21.2942	+	12.2942i	−1.05812	+	0.610905i
$406$		0			0
$407$	21.1244			1.04710
$408$		0			0
$409$	−14.3038	+	8.25833i	−0.707280	+	0.408348i	−0.810053	−	0.586357i	$-0.800562\pi$
$409$	−14.3038	+	8.25833i	−0.707280	+	0.408348i	0.102773	+	0.994705i	$0.467228\pi$
$410$		0			0
$411$			31.0526i			1.53171i
$412$		0			0
$413$	0.509619	−	0.882686i	0.0250767	−	0.0434341i
$414$		0			0
$415$	−8.02628	−	4.63397i	−0.393995	−	0.227473i
$416$		0			0
$417$		−	9.33975i		−	0.457369i
$418$		0			0
$419$	35.1769			1.71850			0.859252	−	0.511552i	$-0.170929\pi$
$419$	35.1769			1.71850			0.859252	+	0.511552i	$0.170929\pi$
$420$		0			0
$421$	1.09808	−	1.90192i	0.0535170	−	0.0926941i	−0.838026	−	0.545631i	$-0.816290\pi$
$421$	1.09808	−	1.90192i	0.0535170	−	0.0926941i	0.891543	+	0.452936i	$0.149624\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	13.4641			0.653105
$426$		0			0
$427$	−7.73205	−	13.3923i	−0.374180	−	0.648099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.7321	−	18.5885i	−0.516945	−	0.895374i	−0.999806	−	0.0196778i	$-0.993736\pi$
$431$	−10.7321	−	18.5885i	−0.516945	−	0.895374i	0.482862	−	0.875697i	$-0.339597\pi$
$432$		0			0
$433$	−6.80385	+	3.92820i	−0.326972	+	0.188777i	−0.654496	−	0.756065i	$-0.727119\pi$
$433$	−6.80385	+	3.92820i	−0.326972	+	0.188777i	0.327524	+	0.944843i	$0.393786\pi$
$434$		0			0
$435$	−5.19615	+	9.00000i	−0.249136	+	0.431517i
$436$		0			0
$437$	10.9019	+	14.6865i	0.521510	+	0.702552i
$438$		0			0
$439$	−9.29423	+	16.0981i	−0.443589	+	0.768319i	−0.997953	−	0.0639555i	$-0.979628\pi$
$439$	−9.29423	+	16.0981i	−0.443589	+	0.768319i	0.554363	+	0.832275i	$0.312962\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.23205	+	2.13397i	0.0585365	+	0.101388i	0.893809	−	0.448449i	$-0.148023\pi$
$443$	1.23205	+	2.13397i	0.0585365	+	0.101388i	−0.835272	+	0.549837i	$0.814690\pi$
$444$		0			0
$445$	35.3205			1.67435
$446$		0			0
$447$	8.36603	+	14.4904i	0.395699	+	0.685372i
$448$		0			0
$449$		−	10.5167i		−	0.496312i	−0.968720	−	0.248156i	$-0.920175\pi$
$449$		−	10.5167i		−	0.496312i	0.968720	−	0.248156i	$-0.0798245\pi$
$450$		0			0
$451$	−29.8923	−	17.2583i	−1.40757	−	0.812663i
$452$		0			0
$453$	−25.0981	−	14.4904i	−1.17921	−	0.680817i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−24.1769			−1.13095			−0.565474	−	0.824766i	$-0.691307\pi$
$457$	−24.1769			−1.13095			−0.565474	+	0.824766i	$0.691307\pi$
$458$		0			0
$459$	24.5885	+	14.1962i	1.14769	+	0.662620i
$460$		0			0
$461$	−11.6603	−	6.73205i	−0.543072	−	0.313543i	0.203251	−	0.979127i	$-0.434849\pi$
$461$	−11.6603	−	6.73205i	−0.543072	−	0.313543i	−0.746323	+	0.665584i	$0.768183\pi$
$462$		0			0
$463$			16.7846i			0.780047i	0.920805	+	0.390023i	$0.127533\pi$
$463$			16.7846i			0.780047i	−0.920805	+	0.390023i	$0.872467\pi$
$464$		0			0
$465$	−5.19615	−	9.00000i	−0.240966	−	0.417365i
$466$		0			0
$467$	−4.46410			−0.206574			−0.103287	−	0.994652i	$-0.532936\pi$
$467$	−4.46410			−0.206574			−0.103287	+	0.994652i	$0.532936\pi$
$468$		0			0
$469$	−2.70577	−	4.68653i	−0.124941	−	0.216404i
$470$		0			0
$471$	0.339746	+	0.588457i	0.0156547	+	0.0271147i
$472$		0			0
$473$	−7.73205	+	13.3923i	−0.355520	+	0.615779i
$474$		0			0
$475$	8.62436	−	6.40192i	0.395713	−	0.293740i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−25.2679	+	14.5885i	−1.15452	+	0.666564i	−0.949985	−	0.312295i	$-0.898902\pi$
$479$	−25.2679	+	14.5885i	−1.15452	+	0.666564i	−0.204537	+	0.978859i	$0.565569\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		−	9.21539i		−	0.419315i
$484$		0			0
$485$	10.5622	+	18.2942i	0.479604	+	0.830698i
$486$		0			0
$487$	33.1244			1.50101			0.750504	−	0.660866i	$-0.229811\pi$
$487$	33.1244			1.50101			0.750504	+	0.660866i	$0.229811\pi$
$488$		0			0
$489$	14.0885	+	8.13397i	0.637102	+	0.367831i
$490$		0			0
$491$	−11.5885	+	20.0718i	−0.522980	+	0.905828i	0.476663	+	0.879086i	$0.341846\pi$
$491$	−11.5885	+	20.0718i	−0.522980	+	0.905828i	−0.999642	+	0.0267412i	$0.991487\pi$
$492$		0			0
$493$	12.0000			0.540453
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.78461	+	1.60770i	0.124907	+	0.0721150i
$498$		0			0
$499$	−15.0885	+	26.1340i	−0.675452	+	1.16992i	0.300884	+	0.953661i	$0.402718\pi$
$499$	−15.0885	+	26.1340i	−0.675452	+	1.16992i	−0.976337	+	0.216257i	$0.930615\pi$
$500$		0			0
$501$			8.78461i			0.392467i
$502$		0			0
$503$	−25.4378	+	14.6865i	−1.13422	+	0.654840i	−0.944992	−	0.327094i	$-0.893931\pi$
$503$	−25.4378	+	14.6865i	−1.13422	+	0.654840i	−0.189225	+	0.981934i	$0.560597\pi$
$504$		0			0
$505$	44.2487			1.96904
$506$		0			0
$507$	−19.5000	+	11.2583i	−0.866025	+	0.500000i
$508$		0			0
$509$	−13.8564	−	24.0000i	−0.614174	−	1.06378i	−0.990529	−	0.137305i	$-0.956156\pi$
$509$	−13.8564	−	24.0000i	−0.614174	−	1.06378i	0.376354	−	0.926476i	$-0.377178\pi$
$510$		0			0
$511$	−5.49038	−	3.16987i	−0.242880	−	0.140227i
$512$		0			0
$513$	22.5000	−	2.59808i	0.993399	−	0.114708i
$514$		0			0
$515$	−22.3923	−	12.9282i	−0.986723	−	0.569685i
$516$		0			0
$517$	37.3468	−	21.5622i	1.64251	−	0.948303i
$518$		0			0
$519$	−38.7846	+	22.3923i	−1.70246	+	0.982913i
$520$		0			0
$521$			19.0526i			0.834708i	0.908744	+	0.417354i	$0.137042\pi$
$521$			19.0526i			0.834708i	−0.908744	+	0.417354i	$0.862958\pi$
$522$		0			0
$523$	−16.9808	+	9.80385i	−0.742517	+	0.428692i	−0.822984	−	0.568065i	$-0.807692\pi$
$523$	−16.9808	+	9.80385i	−0.742517	+	0.428692i	0.0804668	+	0.996757i	$0.474359\pi$
$524$		0			0
$525$	−5.41154			−0.236179
$526$		0			0
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	−2.69615	+	4.66987i	−0.117224	+	0.203038i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$	−4.50000	+	7.79423i	−0.194189	+	0.336346i
$538$		0			0
$539$	−24.0718			−1.03685
$540$		0			0
$541$	−0.588457	+	0.339746i	−0.0252998	+	0.0146068i	−0.512597	−	0.858630i	$-0.671316\pi$
$541$	−0.588457	+	0.339746i	−0.0252998	+	0.0146068i	0.487297	+	0.873236i	$0.337983\pi$
$542$		0			0
$543$			8.19615i			0.351731i
$544$		0			0
$545$	6.00000	−	3.46410i	0.257012	−	0.148386i
$546$		0			0
$547$	−14.1962	+	8.19615i	−0.606984	+	0.350442i	−0.771784	−	0.635885i	$-0.780635\pi$
$547$	−14.1962	+	8.19615i	−0.606984	+	0.350442i	0.164800	+	0.986327i	$0.447302\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.68653	−	5.70577i	0.327457	−	0.243074i
$552$		0			0
$553$	18.0000	+	10.3923i	0.765438	+	0.441926i
$554$		0			0
$555$	−11.1962	−	19.3923i	−0.475250	−	0.823157i
$556$		0			0
$557$	−8.53590	+	4.92820i	−0.361678	+	0.208815i	−0.669816	−	0.742527i	$-0.733627\pi$
$557$	−8.53590	+	4.92820i	−0.361678	+	0.208815i	0.308139	+	0.951341i	$0.400294\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	36.5885	−	21.1244i	1.54477	−	0.891871i
$562$		0			0
$563$		−	35.1962i		−	1.48334i	−0.670764	−	0.741670i	$-0.734034\pi$
$563$		−	35.1962i		−	1.48334i	0.670764	−	0.741670i	$-0.265966\pi$
$564$		0			0
$565$	21.2942	−	36.8827i	0.895855	−	1.55167i
$566$		0			0
$567$	−9.88269	−	5.70577i	−0.415034	−	0.239620i
$568$		0			0
$569$		−	0.928203i		−	0.0389123i	−0.999811	−	0.0194562i	$-0.993807\pi$
$569$		−	0.928203i		−	0.0389123i	0.999811	−	0.0194562i	$-0.00619348\pi$
$570$		0			0
$571$	−4.60770			−0.192826			−0.0964130	−	0.995341i	$-0.530737\pi$
$571$	−4.60770			−0.192826			−0.0964130	+	0.995341i	$0.530737\pi$
$572$		0			0
$573$	−15.4641	+	26.7846i	−0.646022	+	1.11894i
$574$		0			0
$575$	−8.95448	−	5.16987i	−0.373428	−	0.215599i
$576$		0			0
$577$	10.8564			0.451958			0.225979	−	0.974132i	$-0.427442\pi$
$577$	10.8564			0.451958			0.225979	+	0.974132i	$0.427442\pi$
$578$		0			0
$579$	21.5885	+	37.3923i	0.897186	+	1.55397i
$580$		0			0
$581$		−	4.30127i		−	0.178447i
$582$		0			0
$583$	−21.1244	−	36.5885i	−0.874881	−	1.51534i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.26795	−	3.92820i	0.0936083	−	0.162134i	−0.815419	−	0.578872i	$-0.803493\pi$
$587$	2.26795	−	3.92820i	0.0936083	−	0.162134i	0.909027	+	0.416737i	$0.136827\pi$
$588$		0			0
$589$	1.09808	+	9.50962i	0.0452454	+	0.391837i
$590$		0			0
$591$	6.75833	−	11.7058i	0.278001	−	0.481511i
$592$		0			0
$593$	20.6962	+	35.8468i	0.849889	+	1.47205i	0.881307	+	0.472545i	$0.156665\pi$
$593$	20.6962	+	35.8468i	0.849889	+	1.47205i	−0.0314175	+	0.999506i	$0.510002\pi$
$594$		0			0
$595$	9.46410	+	16.3923i	0.387990	+	0.672019i
$596$		0			0
$597$	21.4641			0.878467
$598$		0			0
$599$	3.29423	+	5.70577i	0.134599	+	0.233131i	0.925444	−	0.378884i	$-0.123692\pi$
$599$	3.29423	+	5.70577i	0.134599	+	0.233131i	−0.790845	+	0.612016i	$0.790359\pi$
$600$		0			0
$601$			13.7321i			0.560142i	0.959979	+	0.280071i	$0.0903580\pi$
$601$			13.7321i			0.560142i	−0.959979	+	0.280071i	$0.909642\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−21.1244	−	12.1962i	−0.858827	−	0.495844i
$606$		0			0
$607$	42.5885			1.72861			0.864306	−	0.502966i	$-0.167758\pi$
$607$	42.5885			1.72861			0.864306	+	0.502966i	$0.167758\pi$
$608$		0			0
$609$	−4.82309			−0.195441
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−17.3205	−	10.0000i	−0.699569	−	0.403896i	0.107618	−	0.994192i	$-0.465678\pi$
$613$	−17.3205	−	10.0000i	−0.699569	−	0.403896i	−0.807187	+	0.590296i	$0.799011\pi$
$614$		0			0
$615$			36.5885i			1.47539i
$616$		0			0
$617$	5.16025	+	8.93782i	0.207744	+	0.359823i	0.951004	−	0.309180i	$-0.100055\pi$
$617$	5.16025	+	8.93782i	0.207744	+	0.359823i	−0.743260	+	0.669003i	$0.766721\pi$
$618$		0			0
$619$	−30.3923			−1.22157			−0.610785	−	0.791797i	$-0.709146\pi$
$619$	−30.3923			−1.22157			−0.610785	+	0.791797i	$0.709146\pi$
$620$		0			0
$621$	−10.9019	−	18.8827i	−0.437479	−	0.757736i
$622$		0			0
$623$	8.19615	+	14.1962i	0.328372	+	0.568757i
$624$		0			0
$625$	15.6244	−	27.0622i	0.624974	−	1.08249i
$626$		0			0
$627$	13.3923	−	30.9282i	0.534837	−	1.23515i
$628$		0			0
$629$	−12.9282	+	22.3923i	−0.515481	+	0.892840i
$630$		0			0
$631$	32.2750	−	18.6340i	1.28485	−	0.741807i	0.307117	−	0.951672i	$-0.400636\pi$
$631$	32.2750	−	18.6340i	1.28485	−	0.741807i	0.977730	+	0.209865i	$0.0673025\pi$
$632$		0			0
$633$	−15.0000	−	25.9808i	−0.596196	−	1.03264i
$634$		0			0
$635$			6.92820i			0.274937i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	31.5000	+	18.1865i	1.24418	+	0.718325i	0.969942	−	0.243338i	$-0.0782425\pi$
$641$	31.5000	+	18.1865i	1.24418	+	0.718325i	0.274234	+	0.961663i	$0.411576\pi$
$642$		0			0
$643$	−19.9641	+	34.5788i	−0.787307	+	1.36366i	0.140304	+	0.990109i	$0.455192\pi$
$643$	−19.9641	+	34.5788i	−0.787307	+	1.36366i	−0.927611	+	0.373548i	$0.878141\pi$
$644$		0			0
$645$	16.3923			0.645446
$646$		0			0
$647$			33.8564i			1.33103i	0.746383	+	0.665516i	$0.231789\pi$
$647$			33.8564i			1.33103i	−0.746383	+	0.665516i	$0.768211\pi$
$648$		0			0
$649$	−3.10770	−	1.79423i	−0.121988	−	0.0704296i
$650$		0			0
$651$	2.41154	−	4.17691i	0.0945158	−	0.163706i
$652$		0			0
$653$		−	3.32051i		−	0.129942i	−0.997887	−	0.0649708i	$-0.979305\pi$
$653$		−	3.32051i		−	0.129942i	0.997887	−	0.0649708i	$-0.0206954\pi$
$654$		0			0
$655$	−4.56218	+	2.63397i	−0.178259	+	0.102918i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−33.3731	+	19.2679i	−1.30003	+	0.750573i	−0.980409	−	0.196973i	$-0.936889\pi$
$659$	−33.3731	+	19.2679i	−1.30003	+	0.750573i	−0.319621	+	0.947545i	$0.603556\pi$
$660$		0			0
$661$	18.7583	+	32.4904i	0.729614	+	1.26373i	0.957046	+	0.289935i	$0.0936338\pi$
$661$	18.7583	+	32.4904i	0.729614	+	1.26373i	−0.227432	+	0.973794i	$0.573033\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	13.8564	+	6.00000i	0.537328	+	0.232670i
$666$		0			0
$667$	−7.98076	−	4.60770i	−0.309016	−	0.178411i
$668$		0			0
$669$	−38.2750	+	22.0981i	−1.47980	+	0.854361i
$670$		0			0
$671$	−47.1506	+	27.2224i	−1.82023	+	1.05091i
$672$		0			0
$673$		−	0.928203i		−	0.0357796i	−0.999840	−	0.0178898i	$-0.994305\pi$
$673$		−	0.928203i		−	0.0357796i	0.999840	−	0.0178898i	$-0.00569480\pi$
$674$		0			0
$675$	−11.0885	+	6.40192i	−0.426795	+	0.246410i
$676$		0			0
$677$	−3.21539			−0.123577			−0.0617887	−	0.998089i	$-0.519681\pi$
$677$	−3.21539			−0.123577			−0.0617887	+	0.998089i	$0.519681\pi$
$678$		0			0
$679$	−4.90192	+	8.49038i	−0.188119	+	0.325831i
$680$		0			0
$681$	15.6962	−	27.1865i	0.601478	−	1.04179i
$682$		0			0
$683$		−	51.0333i		−	1.95274i	−0.216115	−	0.976368i	$-0.569339\pi$
$683$		−	51.0333i		−	1.95274i	0.216115	−	0.976368i	$-0.430661\pi$
$684$		0			0
$685$			48.9808i			1.87146i
$686$		0			0
$687$	11.0718	−	19.1769i	0.422415	−	0.731645i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−17.3205			−0.658903			−0.329452	−	0.944172i	$-0.606864\pi$
$691$	−17.3205			−0.658903			−0.329452	+	0.944172i	$0.606864\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	14.7321i		−	0.558819i
$696$		0			0
$697$	36.5885	−	21.1244i	1.38589	−	0.800142i
$698$		0			0
$699$	10.2846	−	5.93782i	0.389000	−	0.224589i
$700$		0			0
$701$	−24.4186	−	14.0981i	−0.922277	−	0.532477i	−0.0379164	−	0.999281i	$-0.512072\pi$
$701$	−24.4186	−	14.0981i	−0.922277	−	0.532477i	−0.884361	+	0.466804i	$0.845405\pi$
$702$		0			0
$703$	2.36603	+	20.4904i	0.0892363	+	0.772809i
$704$		0			0
$705$	−39.5885	−	22.8564i	−1.49099	−	0.860822i
$706$		0			0
$707$	10.2679	+	17.7846i	0.386166	+	0.668859i
$708$		0			0
$709$	−31.6865	+	18.2942i	−1.19001	+	0.687054i	−0.958309	−	0.285732i	$-0.907763\pi$
$709$	−31.6865	+	18.2942i	−1.19001	+	0.687054i	−0.231703	+	0.972787i	$0.574430\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.98076	−	4.60770i	0.298882	−	0.172560i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.07180	−	8.78461i	0.189410	−	0.328067i
$718$		0			0
$719$	−19.8564	−	11.4641i	−0.740519	−	0.427539i	0.0817390	−	0.996654i	$-0.473953\pi$
$719$	−19.8564	−	11.4641i	−0.740519	−	0.427539i	−0.822258	+	0.569115i	$0.807286\pi$
$720$		0			0
$721$		−	12.0000i		−	0.446903i
$722$		0			0
$723$	44.5692			1.65755
$724$		0			0
$725$	−2.70577	+	4.68653i	−0.100490	+	0.174053i
$726$		0			0
$727$	0.679492	+	0.392305i	0.0252010	+	0.0145498i	0.512548	−	0.858659i	$-0.328702\pi$
$727$	0.679492	+	0.392305i	0.0252010	+	0.0145498i	−0.487347	+	0.873209i	$0.662035\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−9.46410	−	16.3923i	−0.350042	−	0.606291i
$732$		0			0
$733$		−	24.5885i		−	0.908195i	−0.890952	−	0.454098i	$-0.849962\pi$
$733$		−	24.5885i		−	0.908195i	0.890952	−	0.454098i	$-0.150038\pi$
$734$		0			0
$735$	12.7583	+	22.0981i	0.470598	+	0.815100i
$736$		0			0
$737$	−16.5000	+	9.52628i	−0.607785	+	0.350905i
$738$		0			0
$739$	21.8923	−	37.9186i	0.805321	−	1.39486i	−0.110752	−	0.993848i	$-0.535326\pi$
$739$	21.8923	−	37.9186i	0.805321	−	1.39486i	0.916074	−	0.401010i	$-0.131341\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.22243	−	7.31347i	0.154906	−	0.268305i	−0.778119	−	0.628117i	$-0.783826\pi$
$743$	4.22243	−	7.31347i	0.154906	−	0.268305i	0.933025	+	0.359812i	$0.117159\pi$
$744$		0			0
$745$	13.1962	+	22.8564i	0.483470	+	0.837394i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.56922			−0.203495
$750$		0			0
$751$	−0.928203	−	1.60770i	−0.0338706	−	0.0586656i	0.848593	−	0.529046i	$-0.177450\pi$
$751$	−0.928203	−	1.60770i	−0.0338706	−	0.0586656i	−0.882464	+	0.470380i	$0.844117\pi$
$752$		0			0
$753$			28.2679i			1.03014i
$754$		0			0
$755$	−39.5885	−	22.8564i	−1.44077	−	0.831830i
$756$		0			0
$757$	−14.5359	−	8.39230i	−0.528316	−	0.305024i	0.212014	−	0.977267i	$-0.431998\pi$
$757$	−14.5359	−	8.39230i	−0.528316	−	0.305024i	−0.740331	+	0.672243i	$0.765331\pi$
$758$		0			0
$759$	−32.4449			−1.17767
$760$		0			0
$761$	−6.85641			−0.248545			−0.124272	−	0.992248i	$-0.539660\pi$
$761$	−6.85641			−0.248545			−0.124272	+	0.992248i	$0.539660\pi$
$762$		0			0
$763$	2.78461	+	1.60770i	0.100810	+	0.0582025i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	21.1244	+	36.5885i	0.761764	+	1.31941i	0.941941	+	0.335779i	$0.109000\pi$
$769$	21.1244	+	36.5885i	0.761764	+	1.31941i	−0.180177	+	0.983634i	$0.557667\pi$
$770$		0			0
$771$	−22.6077			−0.814196
$772$		0			0
$773$	12.7583	+	22.0981i	0.458885	+	0.794813i	0.998902	−	0.0468415i	$-0.0149156\pi$
$773$	12.7583	+	22.0981i	0.458885	+	0.794813i	−0.540017	+	0.841654i	$0.681582\pi$
$774$		0			0
$775$	−2.70577	−	4.68653i	−0.0971942	−	0.168345i
$776$		0			0
$777$	5.19615	−	9.00000i	0.186411	−	0.322873i
$778$		0			0
$779$	13.3923	−	30.9282i	0.479829	−	1.10812i
$780$		0			0
$781$	5.66025	−	9.80385i	0.202540	−	0.350809i
$782$		0			0
$783$	−9.88269	+	5.70577i	−0.353178	+	0.203908i
$784$		0			0
$785$	0.535898	+	0.928203i	0.0191270	+	0.0331290i
$786$		0			0
$787$		−	30.8038i		−	1.09804i	−0.835810	−	0.549019i	$-0.815001\pi$
$787$		−	30.8038i		−	1.09804i	0.835810	−	0.549019i	$-0.184999\pi$
$788$		0			0
$789$	11.8301	+	20.4904i	0.421164	+	0.729477i
$790$		0			0
$791$	19.7654			0.702776
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−22.3923	+	38.7846i	−0.794173	+	1.37555i
$796$		0			0
$797$	28.7321			1.01774			0.508871	−	0.860843i	$-0.330063\pi$
$797$	28.7321			1.01774			0.508871	+	0.860843i	$0.330063\pi$
$798$		0			0
$799$			52.7846i			1.86739i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−11.1603	+	19.3301i	−0.393837	+	0.682145i
$804$		0			0
$805$		−	14.5359i		−	0.512323i
$806$		0			0
$807$	32.1962	−	18.5885i	1.13336	−	0.654345i
$808$		0			0
$809$	−0.320508			−0.0112685			−0.00563423	−	0.999984i	$-0.501793\pi$
$809$	−0.320508			−0.0112685			−0.00563423	+	0.999984i	$0.501793\pi$
$810$		0			0
$811$	40.9808	−	23.6603i	1.43903	−	0.830824i	0.441247	−	0.897386i	$-0.354536\pi$
$811$	40.9808	−	23.6603i	1.43903	−	0.830824i	0.997782	+	0.0665619i	$0.0212030\pi$
$812$		0			0
$813$	24.7583	+	42.8827i	0.868313	+	1.50396i
$814$		0			0
$815$	22.2224	+	12.8301i	0.778418	+	0.449420i
$816$		0			0
$817$	−13.8564	−	6.00000i	−0.484774	−	0.209913i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	36.8372	−	21.2679i	1.28563	−	0.742257i	0.307755	−	0.951466i	$-0.400422\pi$
$821$	36.8372	−	21.2679i	1.28563	−	0.742257i	0.977871	+	0.209209i	$0.0670889\pi$
$822$		0			0
$823$	46.9808	−	27.1244i	1.63765	−	0.945496i	0.656006	−	0.754756i	$-0.272245\pi$
$823$	46.9808	−	27.1244i	1.63765	−	0.945496i	0.981641	−	0.190740i	$-0.0610887\pi$
$824$		0			0
$825$			19.0526i			0.663325i
$826$		0			0
$827$	−27.6962	+	15.9904i	−0.963090	+	0.556040i	−0.897123	−	0.441782i	$-0.854347\pi$
$827$	−27.6962	+	15.9904i	−0.963090	+	0.556040i	−0.0659670	+	0.997822i	$0.521013\pi$
$828$		0			0
$829$	−40.3923			−1.40288			−0.701441	−	0.712727i	$-0.747460\pi$
$829$	−40.3923			−1.40288			−0.701441	+	0.712727i	$0.747460\pi$
$830$		0			0
$831$	−3.63397	+	6.29423i	−0.126061	+	0.218344i
$832$		0			0
$833$	14.7321	−	25.5167i	0.510435	−	0.884100i
$834$		0			0
$835$			13.8564i			0.479521i
$836$		0			0
$837$		−	11.4115i		−	0.394441i
$838$		0			0
$839$	−10.9019	+	18.8827i	−0.376376	+	0.651903i	−0.990532	−	0.137282i	$-0.956163\pi$
$839$	−10.9019	+	18.8827i	−0.376376	+	0.651903i	0.614156	+	0.789185i	$0.289497\pi$
$840$		0			0
$841$	12.0885	−	20.9378i	0.416843	−	0.721994i
$842$		0			0
$843$	29.7846			1.02584
$844$		0			0
$845$	−30.7583	+	17.7583i	−1.05812	+	0.610905i
$846$		0			0
$847$		−	11.3205i		−	0.388977i
$848$		0			0
$849$	27.6962	−	15.9904i	0.950529	−	0.548788i
$850$		0			0
$851$	17.1962	−	9.92820i	0.589477	−	0.340334i
$852$		0			0
$853$	−13.1769	−	7.60770i	−0.451169	−	0.260483i	0.257155	−	0.966370i	$-0.417215\pi$
$853$	−13.1769	−	7.60770i	−0.451169	−	0.260483i	−0.708324	+	0.705888i	$0.750548\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.50000	−	2.59808i	−0.153717	−	0.0887486i	0.421168	−	0.906982i	$-0.361620\pi$
$857$	−4.50000	−	2.59808i	−0.153717	−	0.0887486i	−0.574886	+	0.818234i	$0.694953\pi$
$858$		0			0
$859$	7.69615	+	13.3301i	0.262589	+	0.454818i	0.966929	−	0.255045i	$-0.0820902\pi$
$859$	7.69615	+	13.3301i	0.262589	+	0.454818i	−0.704340	+	0.709863i	$0.748757\pi$
$860$		0			0
$861$	−14.7058	+	8.49038i	−0.501171	+	0.289351i
$862$		0			0
$863$	8.44486			0.287467			0.143733	−	0.989616i	$-0.454089\pi$
$863$	8.44486			0.287467			0.143733	+	0.989616i	$0.454089\pi$
$864$		0			0
$865$	−61.1769	+	35.3205i	−2.08008	+	1.20093i
$866$		0			0
$867$			22.2679i			0.756259i
$868$		0			0
$869$	36.5885	−	63.3731i	1.24118	−	2.14978i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.78461			0.296974
$876$		0			0
$877$	−16.5622	+	28.6865i	−0.559265	+	0.968675i	0.438293	+	0.898832i	$0.355583\pi$
$877$	−16.5622	+	28.6865i	−0.559265	+	0.968675i	−0.997558	+	0.0698432i	$0.977750\pi$
$878$		0			0
$879$	−7.09808	−	4.09808i	−0.239412	−	0.138225i
$880$		0			0
$881$	−19.5359			−0.658181			−0.329091	−	0.944298i	$-0.606742\pi$
$881$	−19.5359			−0.658181			−0.329091	+	0.944298i	$0.606742\pi$
$882$		0			0
$883$	−3.50000	−	6.06218i	−0.117784	−	0.204009i	0.801105	−	0.598524i	$-0.204246\pi$
$883$	−3.50000	−	6.06218i	−0.117784	−	0.204009i	−0.918889	+	0.394515i	$0.870912\pi$
$884$		0			0
$885$			3.80385i			0.127865i
$886$		0			0
$887$	−24.2487	−	42.0000i	−0.814192	−	1.41022i	−0.909907	−	0.414813i	$-0.863847\pi$
$887$	−24.2487	−	42.0000i	−0.814192	−	1.41022i	0.0957146	−	0.995409i	$-0.469486\pi$
$888$		0			0
$889$	−2.78461	+	1.60770i	−0.0933928	+	0.0539204i
$890$		0			0
$891$	−20.0885	+	34.7942i	−0.672989	+	1.16565i
$892$		0			0
$893$	25.0981	+	33.8109i	0.839875	+	1.13144i
$894$		0			0
$895$	−7.09808	+	12.2942i	−0.237263	+	0.410951i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.41154	−	4.17691i	−0.0804295	−	0.139308i
$900$		0			0
$901$	51.7128			1.72280
$902$		0			0
$903$	3.80385	+	6.58846i	0.126584	+	0.219250i
$904$		0			0
$905$			12.9282i			0.429748i
$906$		0			0
$907$	46.5000	+	26.8468i	1.54401	+	0.891433i	0.998580	+	0.0532748i	$0.0169659\pi$
$907$	46.5000	+	26.8468i	1.54401	+	0.891433i	0.545427	+	0.838158i	$0.316367\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−49.5167			−1.64056			−0.820280	−	0.571962i	$-0.806182\pi$
$911$	−49.5167			−1.64056			−0.820280	+	0.571962i	$0.806182\pi$
$912$		0			0
$913$	−15.1436			−0.501180
$914$		0			0
$915$	49.9808	+	28.8564i	1.65231	+	0.953963i
$916$		0			0
$917$	−2.11731	−	1.22243i	−0.0699199	−	0.0403683i
$918$		0			0
$919$		−	8.78461i		−	0.289778i	−0.989448	−	0.144889i	$-0.953718\pi$
$919$		−	8.78461i		−	0.289778i	0.989448	−	0.144889i	$-0.0462824\pi$
$920$		0			0
$921$	−11.0885	−	19.2058i	−0.365377	−	0.632852i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−5.83013	−	10.0981i	−0.191693	−	0.332023i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.0885	+	33.0622i	−0.626272	+	1.08473i	0.362021	+	0.932170i	$0.382087\pi$
$929$	−19.0885	+	33.0622i	−0.626272	+	1.08473i	−0.988293	+	0.152565i	$0.951247\pi$
$930$		0			0
$931$	−2.69615	−	23.3494i	−0.0883628	−	0.765245i
$932$		0			0
$933$	16.2224	−	28.0981i	0.531099	−	0.919890i
$934$		0			0
$935$	57.7128	−	33.3205i	1.88741	−	1.08970i
$936$		0			0
$937$	−24.8923	−	43.1147i	−0.813196	−	1.40850i	−0.910616	−	0.413254i	$-0.864392\pi$
$937$	−24.8923	−	43.1147i	−0.813196	−	1.40850i	0.0974198	−	0.995243i	$-0.468941\pi$
$938$		0			0
$939$		−	33.5885i		−	1.09612i
$940$		0			0
$941$	−19.5167	−	33.8038i	−0.636225	−	1.10197i	−0.986254	−	0.165235i	$-0.947162\pi$
$941$	−19.5167	−	33.8038i	−0.636225	−	1.10197i	0.350029	−	0.936739i	$-0.386172\pi$
$942$		0			0
$943$	−32.4449			−1.05655
$944$		0			0
$945$	−15.5885	−	9.00000i	−0.507093	−	0.292770i
$946$		0			0
$947$	2.80385	−	4.85641i	0.0911128	−	0.157812i	−0.816867	−	0.576826i	$-0.804291\pi$
$947$	2.80385	−	4.85641i	0.0911128	−	0.157812i	0.907980	+	0.419014i	$0.137624\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$			52.3923i			1.69894i
$952$		0			0
$953$	14.3038	+	8.25833i	0.463347	+	0.267514i	0.713451	−	0.700706i	$-0.247131\pi$
$953$	14.3038	+	8.25833i	0.463347	+	0.267514i	−0.250104	+	0.968219i	$0.580465\pi$
$954$		0			0
$955$	−24.3923	+	42.2487i	−0.789316	+	1.36714i
$956$		0			0
$957$			16.9808i			0.548910i
$958$		0			0
$959$	−19.6865	+	11.3660i	−0.635711	+	0.367028i
$960$		0			0
$961$	−26.1769			−0.844417
$962$		0			0
$963$		0			0
$964$		0			0
$965$	34.0526	+	58.9808i	1.09619	+	1.89866i
$966$		0			0
$967$	−10.3923	−	6.00000i	−0.334194	−	0.192947i	0.323508	−	0.946226i	$-0.395138\pi$
$967$	−10.3923	−	6.00000i	−0.334194	−	0.192947i	−0.657702	+	0.753279i	$0.728471\pi$
$968$		0			0
$969$	24.5885	+	33.1244i	0.789895	+	1.06411i
$970$		0			0
$971$	9.10770	+	5.25833i	0.292280	+	0.168748i	0.638970	−	0.769232i	$-0.279361\pi$
$971$	9.10770	+	5.25833i	0.292280	+	0.168748i	−0.346690	+	0.937980i	$0.612694\pi$
$972$		0			0
$973$	5.92116	−	3.41858i	0.189824	−	0.109595i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	16.2679i		−	0.520458i	−0.965547	−	0.260229i	$-0.916202\pi$
$977$		−	16.2679i		−	0.520458i	0.965547	−	0.260229i	$-0.0837980\pi$
$978$		0			0
$979$	49.9808	−	28.8564i	1.59739	−	0.922255i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−12.5885	+	21.8038i	−0.401509	+	0.695435i	−0.993908	−	0.110210i	$-0.964848\pi$
$983$	−12.5885	+	21.8038i	−0.401509	+	0.695435i	0.592399	+	0.805645i	$0.298181\pi$
$984$		0			0
$985$	10.6603	−	18.4641i	0.339664	−	0.588315i
$986$		0			0
$987$		−	21.2154i		−	0.675293i
$988$		0			0
$989$			14.5359i			0.462215i
$990$		0			0
$991$	−16.0526	+	27.8038i	−0.509926	+	0.883218i	0.490008	+	0.871718i	$0.336994\pi$
$991$	−16.0526	+	27.8038i	−0.509926	+	0.883218i	−0.999934	+	0.0115001i	$0.996339\pi$
$992$		0			0
$993$	−27.4808	+	47.5981i	−0.872076	+	1.51048i
$994$		0			0
$995$	33.8564			1.07332
$996$		0			0
$997$	10.5622	−	6.09808i	0.334508	−	0.193128i	−0.323333	−	0.946285i	$-0.604803\pi$
$997$	10.5622	−	6.09808i	0.334508	−	0.193128i	0.657841	+	0.753157i	$0.271470\pi$
$998$		0			0
$999$		−	24.5885i		−	0.777944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.s.a.863.1	yes	4
4.3	odd	2		1216.2.s.e.863.1	yes	4
8.3	odd	2		1216.2.s.b.863.2	yes	4
8.5	even	2		1216.2.s.f.863.2	yes	4
19.12	odd	6		1216.2.s.b.31.2	yes	4
76.31	even	6		1216.2.s.f.31.2	yes	4
152.69	odd	6		1216.2.s.e.31.1	yes	4
152.107	even	6	inner	1216.2.s.a.31.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.s.a.31.1	✓	4	152.107	even	6	inner
1216.2.s.a.863.1	yes	4	1.1	even	1	trivial
1216.2.s.b.31.2	yes	4	19.12	odd	6
1216.2.s.b.863.2	yes	4	8.3	odd	2
1216.2.s.e.31.1	yes	4	152.69	odd	6
1216.2.s.e.863.1	yes	4	4.3	odd	2
1216.2.s.f.31.2	yes	4	76.31	even	6
1216.2.s.f.863.2	yes	4	8.5	even	2

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-2.36603 - 1.36603i) q^{5} -1.26795i q^{7} -4.46410 q^{11} +(2.36603 + 4.09808i) q^{15} +(2.73205 - 4.73205i) q^{17} +(-0.500000 - 4.33013i) q^{19} +(-1.09808 + 1.90192i) q^{21} +(-3.63397 + 2.09808i) q^{23} +(1.23205 + 2.13397i) q^{25} +5.19615i q^{27} +(1.09808 + 1.90192i) q^{29} -2.19615 q^{31} +(6.69615 + 3.86603i) q^{33} +(-1.73205 + 3.00000i) q^{35} -4.73205 q^{37} +(6.69615 + 3.86603i) q^{41} +(1.73205 - 3.00000i) q^{43} +(-8.36603 + 4.83013i) q^{47} +5.39230 q^{49} +(-8.19615 + 4.73205i) q^{51} +(4.73205 + 8.19615i) q^{53} +(10.5622 + 6.09808i) q^{55} +(-3.00000 + 6.92820i) q^{57} +(0.696152 + 0.401924i) q^{59} +(10.5622 - 6.09808i) q^{61} +(3.69615 - 2.13397i) q^{67} +7.26795 q^{69} +(-1.26795 + 2.19615i) q^{71} +(2.50000 - 4.33013i) q^{73} -4.26795i q^{75} +5.66025i q^{77} +(-8.19615 + 14.1962i) q^{79} +(4.50000 - 7.79423i) q^{81} +3.39230 q^{83} +(-12.9282 + 7.46410i) q^{85} -3.80385i q^{87} +(-11.1962 + 6.46410i) q^{89} +(3.29423 + 1.90192i) q^{93} +(-4.73205 + 10.9282i) q^{95} +(-6.69615 - 3.86603i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 6 q^{5} - 4 q^{11} + 6 q^{15} + 4 q^{17} - 2 q^{19} + 6 q^{21} - 18 q^{23} - 2 q^{25} - 6 q^{29} + 12 q^{31} + 6 q^{33} - 12 q^{37} + 6 q^{41} - 30 q^{47} - 20 q^{49} - 12 q^{51} + 12 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) \) 4 * q - 6 * q^3 - 6 * q^5 - 4 * q^11 + 6 * q^15 + 4 * q^17 - 2 * q^19 + 6 * q^21 - 18 * q^23 - 2 * q^25 - 6 * q^29 + 12 * q^31 + 6 * q^33 - 12 * q^37 + 6 * q^41 - 30 * q^47 - 20 * q^49 - 12 * q^51 + 12 * q^53 + 18 * q^55 - 12 * q^57 - 18 * q^59 + 18 * q^61 - 6 * q^67 + 36 * q^69 - 12 * q^71 + 10 * q^73 - 12 * q^79 + 18 * q^81 - 28 * q^83 - 24 * q^85 - 24 * q^89 - 18 * q^93 - 12 * q^95 - 6 * q^97

Introduction

L-functions

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