LMFDB - Embedded newform 702.2.bb.a.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("702.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.6
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.64098 - 0.707650i) q^{5} +(3.36644 - 0.902034i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.64098 - 0.707650i) q^{5} +(3.36644 - 0.902034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.36784 - 1.36707i) q^{10} +(1.29045 - 1.29045i) q^{11} +(2.77764 + 2.29885i) q^{13} +(-3.01826 - 1.74260i) q^{14} -1.00000 q^{16} +(0.419403 + 0.726428i) q^{17} +(-6.94825 - 1.86178i) q^{19} +(0.707650 + 2.64098i) q^{20} -1.82497 q^{22} +(3.18965 + 5.52464i) q^{23} +(2.14391 - 1.23778i) q^{25} +(-0.338562 - 3.58962i) q^{26} +(0.902034 + 3.36644i) q^{28} +6.05100i q^{29} +(-1.99320 - 7.43873i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.217099 - 0.810225i) q^{34} +(8.25239 - 4.76452i) q^{35} +(-4.09570 + 1.09744i) q^{37} +(3.59668 + 6.22963i) q^{38} +(1.36707 - 2.36784i) q^{40} +(1.07586 - 4.01515i) q^{41} +(7.47357 + 4.31487i) q^{43} +(1.29045 + 1.29045i) q^{44} +(1.65109 - 6.16194i) q^{46} +(-7.46630 - 2.00059i) q^{47} +(4.45706 - 2.57328i) q^{49} +(-2.39122 - 0.640725i) q^{50} +(-2.29885 + 2.77764i) q^{52} -3.92979i q^{53} +(2.49486 - 4.32123i) q^{55} +(1.74260 - 3.01826i) q^{56} +(4.27871 - 4.27871i) q^{58} +(5.26591 - 5.26591i) q^{59} +(0.247438 - 0.428575i) q^{61} +(-3.85057 + 6.66938i) q^{62} -1.00000i q^{64} +(8.96250 + 4.10562i) q^{65} +(5.34607 + 1.43247i) q^{67} +(-0.726428 + 0.419403i) q^{68} +(-9.20434 - 2.46630i) q^{70} +(-1.48865 + 5.55573i) q^{71} +(-9.66963 - 9.66963i) q^{73} +(3.67210 + 2.12009i) q^{74} +(1.86178 - 6.94825i) q^{76} +(3.18018 - 5.50823i) q^{77} +(-0.892374 - 1.54564i) q^{79} +(-2.64098 + 0.707650i) q^{80} +(-3.59989 + 2.07840i) q^{82} +(4.07375 - 15.2034i) q^{83} +(1.62169 + 1.62169i) q^{85} +(-2.23354 - 8.33569i) q^{86} -1.82497i q^{88} +(-0.385644 - 1.43924i) q^{89} +(11.4244 + 5.23339i) q^{91} +(-5.52464 + 3.18965i) q^{92} +(3.86484 + 6.69410i) q^{94} -19.6677 q^{95} +(4.50154 + 16.8000i) q^{97} +(-4.97120 - 1.33203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	2.64098	−	0.707650i	1.18108	−	0.316471i	0.385728	−	0.922613i	$-0.373950\pi$
$5$	2.64098	−	0.707650i	1.18108	−	0.316471i	0.795356	+	0.606142i	$0.207284\pi$
$6$		0			0
$7$	3.36644	−	0.902034i	1.27239	−	0.340937i	0.441446	−	0.897288i	$-0.354466\pi$
$7$	3.36644	−	0.902034i	1.27239	−	0.340937i	0.830947	+	0.556351i	$0.187799\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−2.36784	−	1.36707i	−0.748777	−	0.432307i
$11$	1.29045	−	1.29045i	0.389084	−	0.389084i	−0.485277	−	0.874361i	$-0.661281\pi$
$11$	1.29045	−	1.29045i	0.389084	−	0.389084i	0.874361	+	0.485277i	$0.161281\pi$
$12$		0			0
$13$	2.77764	+	2.29885i	0.770380	+	0.637585i
$13$	2.77764	+	2.29885i	0.770380	+	0.637585i
$14$	−3.01826	−	1.74260i	−0.806665	−	0.465728i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.419403	+	0.726428i	0.101720	+	0.176185i	0.912393	−	0.409314i	$-0.134232\pi$
$17$	0.419403	+	0.726428i	0.101720	+	0.176185i	−0.810673	+	0.585499i	$0.800899\pi$
$18$		0			0
$19$	−6.94825	−	1.86178i	−1.59404	−	0.427121i	−0.650802	−	0.759247i	$-0.725567\pi$
$19$	−6.94825	−	1.86178i	−1.59404	−	0.427121i	−0.943235	+	0.332126i	$0.892234\pi$
$20$	0.707650	+	2.64098i	0.158235	+	0.590542i
$21$		0			0
$22$	−1.82497			−0.389084
$23$	3.18965	+	5.52464i	0.665089	+	1.15197i	0.979261	+	0.202602i	$0.0649397\pi$
$23$	3.18965	+	5.52464i	0.665089	+	1.15197i	−0.314172	+	0.949366i	$0.601727\pi$
$24$		0			0
$25$	2.14391	−	1.23778i	0.428781	−	0.247557i
$26$	−0.338562	−	3.58962i	−0.0663975	−	0.703983i
$27$		0			0
$28$	0.902034	+	3.36644i	0.170468	+	0.636197i
$29$			6.05100i			1.12364i	0.827258	+	0.561822i	$0.189899\pi$
$29$			6.05100i			1.12364i	−0.827258	+	0.561822i	$0.810101\pi$
$30$		0			0
$31$	−1.99320	−	7.43873i	−0.357990	−	1.33604i	−0.876680	−	0.481074i	$-0.840247\pi$
$31$	−1.99320	−	7.43873i	−0.357990	−	1.33604i	0.518691	−	0.854962i	$-0.326420\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	0.217099	−	0.810225i	0.0372322	−	0.138952i
$35$	8.25239	−	4.76452i	1.39491	−	0.805350i
$36$		0			0
$37$	−4.09570	+	1.09744i	−0.673328	+	0.180418i	−0.579254	−	0.815147i	$-0.696656\pi$
$37$	−4.09570	+	1.09744i	−0.673328	+	0.180418i	−0.0940746	+	0.995565i	$0.529989\pi$
$38$	3.59668	+	6.22963i	0.583458	+	1.01058i
$39$		0			0
$40$	1.36707	−	2.36784i	0.216153	−	0.374389i
$41$	1.07586	−	4.01515i	0.168021	−	0.627062i	−0.829615	−	0.558336i	$-0.811440\pi$
$41$	1.07586	−	4.01515i	0.168021	−	0.627062i	0.997636	−	0.0687257i	$-0.0218933\pi$
$42$		0			0
$43$	7.47357	+	4.31487i	1.13971	+	0.658011i	0.946359	−	0.323118i	$-0.104731\pi$
$43$	7.47357	+	4.31487i	1.13971	+	0.658011i	0.193351	+	0.981130i	$0.438065\pi$
$44$	1.29045	+	1.29045i	0.194542	+	0.194542i
$45$		0			0
$46$	1.65109	−	6.16194i	0.243439	−	0.908528i
$47$	−7.46630	−	2.00059i	−1.08907	−	0.291816i	−0.330765	−	0.943713i	$-0.607307\pi$
$47$	−7.46630	−	2.00059i	−1.08907	−	0.291816i	−0.758307	+	0.651897i	$0.773973\pi$
$48$		0			0
$49$	4.45706	−	2.57328i	0.636722	−	0.367612i
$50$	−2.39122	−	0.640725i	−0.338169	−	0.0906121i
$51$		0			0
$52$	−2.29885	+	2.77764i	−0.318792	+	0.385190i
$53$		−	3.92979i		−	0.539798i	−0.962889	−	0.269899i	$-0.913010\pi$
$53$		−	3.92979i		−	0.539798i	0.962889	−	0.269899i	$-0.0869903\pi$
$54$		0			0
$55$	2.49486	−	4.32123i	0.336408	−	0.582675i
$56$	1.74260	−	3.01826i	0.232864	−	0.403333i
$57$		0			0
$58$	4.27871	−	4.27871i	0.561822	−	0.561822i
$59$	5.26591	−	5.26591i	0.685564	−	0.685564i	−0.275685	−	0.961248i	$-0.588905\pi$
$59$	5.26591	−	5.26591i	0.685564	−	0.685564i	0.961248	+	0.275685i	$0.0889045\pi$
$60$		0			0
$61$	0.247438	−	0.428575i	0.0316812	−	0.0548734i	−0.849750	−	0.527186i	$-0.823247\pi$
$61$	0.247438	−	0.428575i	0.0316812	−	0.0548734i	0.881431	+	0.472312i	$0.156581\pi$
$62$	−3.85057	+	6.66938i	−0.489023	+	0.847013i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	8.96250	+	4.10562i	1.11166	+	0.509239i
$66$		0			0
$67$	5.34607	+	1.43247i	0.653126	+	0.175005i	0.570142	−	0.821546i	$-0.306888\pi$
$67$	5.34607	+	1.43247i	0.653126	+	0.175005i	0.0829842	+	0.996551i	$0.473555\pi$
$68$	−0.726428	+	0.419403i	−0.0880923	+	0.0508601i
$69$		0			0
$70$	−9.20434	−	2.46630i	−1.10013	−	0.294779i
$71$	−1.48865	+	5.55573i	−0.176671	+	0.659344i	0.819591	+	0.572950i	$0.194201\pi$
$71$	−1.48865	+	5.55573i	−0.176671	+	0.659344i	−0.996261	+	0.0863938i	$0.972466\pi$
$72$		0			0
$73$	−9.66963	−	9.66963i	−1.13174	−	1.13174i	−0.989887	−	0.141858i	$-0.954693\pi$
$73$	−9.66963	−	9.66963i	−1.13174	−	1.13174i	−0.141858	−	0.989887i	$-0.545307\pi$
$74$	3.67210	+	2.12009i	0.426873	+	0.246455i
$75$		0			0
$76$	1.86178	−	6.94825i	0.213560	−	0.797018i
$77$	3.18018	−	5.50823i	0.362415	−	0.627721i
$78$		0			0
$79$	−0.892374	−	1.54564i	−0.100400	−	0.173898i	0.811450	−	0.584422i	$-0.198679\pi$
$79$	−0.892374	−	1.54564i	−0.100400	−	0.173898i	−0.911849	+	0.410525i	$0.865346\pi$
$80$	−2.64098	+	0.707650i	−0.295271	+	0.0791177i
$81$		0			0
$82$	−3.59989	+	2.07840i	−0.397541	+	0.229520i
$83$	4.07375	−	15.2034i	0.447152	−	1.66879i	−0.263039	−	0.964785i	$-0.584725\pi$
$83$	4.07375	−	15.2034i	0.447152	−	1.66879i	0.710191	−	0.704009i	$-0.248609\pi$
$84$		0			0
$85$	1.62169	+	1.62169i	0.175897	+	0.175897i
$86$	−2.23354	−	8.33569i	−0.240849	−	0.898860i
$87$		0			0
$88$		−	1.82497i		−	0.194542i
$89$	−0.385644	−	1.43924i	−0.0408782	−	0.152559i	0.942470	−	0.334290i	$-0.108497\pi$
$89$	−0.385644	−	1.43924i	−0.0408782	−	0.152559i	−0.983348	+	0.181731i	$0.941830\pi$
$90$		0			0
$91$	11.4244	+	5.23339i	1.19760	+	0.548608i
$92$	−5.52464	+	3.18965i	−0.575984	+	0.332544i
$93$		0			0
$94$	3.86484	+	6.69410i	0.398628	+	0.690444i
$95$	−19.6677			−2.01786
$96$		0			0
$97$	4.50154	+	16.8000i	0.457062	+	1.70578i	0.681954	+	0.731395i	$0.261130\pi$
$97$	4.50154	+	16.8000i	0.457062	+	1.70578i	−0.224892	+	0.974384i	$0.572203\pi$
$98$	−4.97120	−	1.33203i	−0.502167	−	0.134555i
$99$		0			0
$100$	1.23778	+	2.14391i	0.123778	+	0.214391i
$101$	−0.0847306			−0.00843101			−0.00421550	−	0.999991i	$-0.501342\pi$
$101$	−0.0847306			−0.00843101			−0.00421550	+	0.999991i	$0.501342\pi$
$102$		0			0
$103$	−7.73765	−	4.46733i	−0.762413	−	0.440179i	0.0677484	−	0.997702i	$-0.478418\pi$
$103$	−7.73765	−	4.46733i	−0.762413	−	0.440179i	−0.830161	+	0.557523i	$0.811752\pi$
$104$	3.58962	−	0.338562i	0.351991	−	0.0331988i
$105$		0			0
$106$	−2.77878	+	2.77878i	−0.269899	+	0.269899i
$107$	−12.3692	−	7.14138i	−1.19578	−	0.690384i	−0.236168	−	0.971712i	$-0.575892\pi$
$107$	−12.3692	−	7.14138i	−1.19578	−	0.690384i	−0.959611	+	0.281329i	$0.909225\pi$
$108$		0			0
$109$	−9.68492	+	9.68492i	−0.927647	+	0.927647i	−0.997554	−	0.0699067i	$-0.977730\pi$
$109$	−9.68492	+	9.68492i	−0.927647	+	0.927647i	0.0699067	+	0.997554i	$0.477730\pi$
$110$	−4.81971	+	1.29144i	−0.459541	+	0.123134i
$111$		0			0
$112$	−3.36644	+	0.902034i	−0.318098	+	0.0852342i
$113$			7.95653i			0.748487i	0.927330	+	0.374244i	$0.122098\pi$
$113$			7.95653i			0.748487i	−0.927330	+	0.374244i	$0.877902\pi$
$114$		0			0
$115$	12.3333	+	12.3333i	1.15009	+	1.15009i
$116$	−6.05100			−0.561822
$117$		0			0
$118$	−7.44713			−0.685564
$119$	2.06716	+	2.06716i	0.189496	+	0.189496i
$120$		0			0
$121$			7.66950i			0.697227i
$122$	−0.478014	+	0.128083i	−0.0432773	+	0.0115961i
$123$		0			0
$124$	7.43873	−	1.99320i	0.668018	−	0.178995i
$125$	−4.88057	+	4.88057i	−0.436531	+	0.436531i
$126$		0			0
$127$	10.0640	+	5.81045i	0.893035	+	0.515594i	0.874934	−	0.484242i	$-0.160905\pi$
$127$	10.0640	+	5.81045i	0.893035	+	0.515594i	0.0181011	+	0.999836i	$0.494238\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−3.43433	−	9.24055i	−0.301211	−	0.810450i
$131$	4.16625	+	2.40538i	0.364007	+	0.210159i	0.670837	−	0.741605i	$-0.265935\pi$
$131$	4.16625	+	2.40538i	0.364007	+	0.210159i	−0.306830	+	0.951764i	$0.599268\pi$
$132$		0			0
$133$	−25.0702			−2.17386
$134$	−2.76733	−	4.79315i	−0.239061	−	0.414065i
$135$		0			0
$136$	0.810225	+	0.217099i	0.0694762	+	0.0186161i
$137$	−2.00715	−	7.49077i	−0.171482	−	0.639980i	−0.997124	−	0.0757856i	$-0.975854\pi$
$137$	−2.00715	−	7.49077i	−0.171482	−	0.639980i	0.825642	−	0.564194i	$-0.190813\pi$
$138$		0			0
$139$	−4.82707			−0.409427			−0.204713	−	0.978822i	$-0.565626\pi$
$139$	−4.82707			−0.409427			−0.204713	+	0.978822i	$0.565626\pi$
$140$	4.76452	+	8.25239i	0.402675	+	0.697454i
$141$		0			0
$142$	4.98113	−	2.87586i	0.418007	−	0.241336i
$143$	6.55094	−	0.617865i	0.547817	−	0.0516685i
$144$		0			0
$145$	4.28199	+	15.9806i	0.355600	+	1.32712i
$146$			13.6749i			1.13174i
$147$		0			0
$148$	−1.09744	−	4.09570i	−0.0902089	−	0.336664i
$149$	9.23003	+	9.23003i	0.756153	+	0.756153i	0.975620	−	0.219467i	$-0.0704317\pi$
$149$	9.23003	+	9.23003i	0.756153	+	0.756153i	−0.219467	+	0.975620i	$0.570432\pi$
$150$		0			0
$151$	2.95315	−	11.0213i	0.240324	−	0.896900i	−0.735353	−	0.677685i	$-0.762984\pi$
$151$	2.95315	−	11.0213i	0.240324	−	0.896900i	0.975676	−	0.219216i	$-0.0703498\pi$
$152$	−6.22963	+	3.59668i	−0.505289	+	0.291729i
$153$		0			0
$154$	−6.14363	+	1.64618i	−0.495068	+	0.132653i
$155$	−10.5280	−	18.2351i	−0.845632	−	1.46468i
$156$		0			0
$157$	2.16879	−	3.75646i	0.173089	−	0.299798i	−0.766409	−	0.642352i	$-0.777959\pi$
$157$	2.16879	−	3.75646i	0.173089	−	0.299798i	0.939498	+	0.342554i	$0.111292\pi$
$158$	−0.461927	+	1.72393i	−0.0367489	+	0.137149i
$159$		0			0
$160$	2.36784	+	1.36707i	0.187194	+	0.108077i
$161$	15.7212	+	15.7212i	1.23900	+	1.23900i
$162$		0			0
$163$	4.75149	−	17.7328i	0.372166	−	1.38894i	−0.485277	−	0.874361i	$-0.661281\pi$
$163$	4.75149	−	17.7328i	0.372166	−	1.38894i	0.857442	−	0.514580i	$-0.172052\pi$
$164$	4.01515	+	1.07586i	0.313531	+	0.0840103i
$165$		0			0
$166$	−13.6310	+	7.86988i	−1.05797	+	0.610821i
$167$	−2.35159	−	0.630107i	−0.181972	−	0.0487591i	0.166682	−	0.986011i	$-0.446695\pi$
$167$	−2.35159	−	0.630107i	−0.181972	−	0.0487591i	−0.348654	+	0.937251i	$0.613361\pi$
$168$		0			0
$169$	2.43062	+	12.7708i	0.186971	+	0.982365i
$170$		−	2.29342i		−	0.175897i
$171$		0			0
$172$	−4.31487	+	7.47357i	−0.329006	+	0.569855i
$173$	−5.08757	+	8.81194i	−0.386801	+	0.669959i	−0.992017	−	0.126102i	$-0.959753\pi$
$173$	−5.08757	+	8.81194i	−0.386801	+	0.669959i	0.605216	+	0.796061i	$0.293087\pi$
$174$		0			0
$175$	6.10080	−	6.10080i	0.461177	−	0.461177i
$176$	−1.29045	+	1.29045i	−0.0972710	+	0.0972710i
$177$		0			0
$178$	−0.745007	+	1.29039i	−0.0558406	+	0.0967188i
$179$	−6.54598	+	11.3380i	−0.489270	+	0.847440i	−0.999924	−	0.0123463i	$-0.996070\pi$
$179$	−6.54598	+	11.3380i	−0.489270	+	0.847440i	0.510654	+	0.859786i	$0.329403\pi$
$180$		0			0
$181$			10.0606i			0.747798i	0.927469	+	0.373899i	$0.121979\pi$
$181$			10.0606i			0.747798i	−0.927469	+	0.373899i	$0.878021\pi$
$182$	−4.37771	−	11.7788i	−0.324497	−	0.873105i
$183$		0			0
$184$	6.16194	+	1.65109i	0.454264	+	0.121720i
$185$	−10.0401	+	5.79664i	−0.738160	+	0.426177i
$186$		0			0
$187$	1.47863	+	0.396198i	0.108128	+	0.0289729i
$188$	2.00059	−	7.46630i	0.145908	−	0.544536i
$189$		0			0
$190$	13.9072	+	13.9072i	1.00893	+	1.00893i
$191$	−16.1899	−	9.34724i	−1.17146	−	0.676343i	−0.217437	−	0.976074i	$-0.569770\pi$
$191$	−16.1899	−	9.34724i	−1.17146	−	0.676343i	−0.954024	+	0.299732i	$0.903103\pi$
$192$		0			0
$193$	−1.33858	+	4.99566i	−0.0963533	+	0.359595i	−0.997221	−	0.0744981i	$-0.976265\pi$
$193$	−1.33858	+	4.99566i	−0.0963533	+	0.359595i	0.900868	+	0.434093i	$0.142931\pi$
$194$	8.69631	−	15.0624i	0.624358	−	1.08142i
$195$		0			0
$196$	2.57328	+	4.45706i	0.183806	+	0.318361i
$197$	−8.85907	+	2.37378i	−0.631183	+	0.169125i	−0.560206	−	0.828353i	$-0.689278\pi$
$197$	−8.85907	+	2.37378i	−0.631183	+	0.169125i	−0.0709764	+	0.997478i	$0.522612\pi$
$198$		0			0
$199$	−11.5728	+	6.68158i	−0.820376	+	0.473644i	−0.850546	−	0.525900i	$-0.823728\pi$
$199$	−11.5728	+	6.68158i	−0.820376	+	0.473644i	0.0301700	+	0.999545i	$0.490395\pi$
$200$	0.640725	−	2.39122i	0.0453061	−	0.169085i
$201$		0			0
$202$	0.0599135	+	0.0599135i	0.00421550	+	0.00421550i
$203$	5.45821	+	20.3703i	0.383091	+	1.42972i
$204$		0			0
$205$		−	11.3653i		−	0.793786i
$206$	2.31246	+	8.63023i	0.161117	+	0.601296i
$207$		0			0
$208$	−2.77764	−	2.29885i	−0.192595	−	0.159396i
$209$	−11.3689	+	6.56381i	−0.786401	+	0.454029i
$210$		0			0
$211$	5.98953	+	10.3742i	0.412336	+	0.714187i	0.995145	−	0.0984226i	$-0.0313797\pi$
$211$	5.98953	+	10.3742i	0.412336	+	0.714187i	−0.582809	+	0.812609i	$0.698046\pi$
$212$	3.92979			0.269899
$213$		0			0
$214$	3.69665	+	13.7961i	0.252698	+	0.943081i
$215$	22.7910	+	6.10683i	1.55433	+	0.416483i
$216$		0			0
$217$	−13.4200	−	23.2441i	−0.911007	−	1.57791i
$218$	13.6965			0.927647
$219$		0			0
$220$	4.32123	+	2.49486i	0.291337	+	0.168204i
$221$	−0.504992	+	2.98190i	−0.0339694	+	0.200584i
$222$		0			0
$223$	−1.24226	+	1.24226i	−0.0831878	+	0.0831878i	−0.747476	−	0.664288i	$-0.768735\pi$
$223$	−1.24226	+	1.24226i	−0.0831878	+	0.0831878i	0.664288	+	0.747476i	$0.268735\pi$
$224$	3.01826	+	1.74260i	0.201666	+	0.116432i
$225$		0			0
$226$	5.62611	−	5.62611i	0.374244	−	0.374244i
$227$	−10.4293	+	2.79453i	−0.692218	+	0.185479i	−0.587742	−	0.809048i	$-0.699983\pi$
$227$	−10.4293	+	2.79453i	−0.692218	+	0.185479i	−0.104476	+	0.994527i	$0.533316\pi$
$228$		0			0
$229$	2.29318	−	0.614457i	0.151538	−	0.0406044i	−0.182253	−	0.983252i	$-0.558339\pi$
$229$	2.29318	−	0.614457i	0.151538	−	0.0406044i	0.333790	+	0.942647i	$0.391672\pi$
$230$		−	17.4420i		−	1.15009i
$231$		0			0
$232$	4.27871	+	4.27871i	0.280911	+	0.280911i
$233$	14.8461			0.972602			0.486301	−	0.873791i	$-0.338346\pi$
$233$	14.8461			0.972602			0.486301	+	0.873791i	$0.338346\pi$
$234$		0			0
$235$	−21.1341			−1.37864
$236$	5.26591	+	5.26591i	0.342782	+	0.342782i
$237$		0			0
$238$		−	2.92340i		−	0.189496i
$239$	−28.5302	+	7.64464i	−1.84546	+	0.494491i	−0.999264	−	0.0383723i	$-0.987783\pi$
$239$	−28.5302	+	7.64464i	−1.84546	+	0.494491i	−0.846201	+	0.532863i	$0.821116\pi$
$240$		0			0
$241$	−19.8922	+	5.33009i	−1.28137	+	0.343341i	−0.834376	−	0.551196i	$-0.814171\pi$
$241$	−19.8922	+	5.33009i	−1.28137	+	0.343341i	−0.446992	+	0.894538i	$0.647505\pi$
$242$	5.42315	−	5.42315i	0.348614	−	0.348614i
$243$		0			0
$244$	0.428575	+	0.247438i	0.0274367	+	0.0158406i
$245$	9.95003	−	9.95003i	0.635684	−	0.635684i
$246$		0			0
$247$	−15.0198	−	21.1443i	−0.955688	−	1.34538i
$248$	−6.66938	−	3.85057i	−0.423506	−	0.244511i
$249$		0			0
$250$	6.90217			0.436531
$251$	−10.3116	−	17.8602i	−0.650861	−	1.12732i	−0.982914	−	0.184064i	$-0.941075\pi$
$251$	−10.3116	−	17.8602i	−0.650861	−	1.12732i	0.332053	−	0.943261i	$-0.392259\pi$
$252$		0			0
$253$	11.2453	+	3.01318i	0.706988	+	0.189437i
$254$	−3.00771	−	11.2249i	−0.188721	−	0.704315i
$255$		0			0
$256$	1.00000			0.0625000
$257$	4.26967	+	7.39529i	0.266335	+	0.461305i	0.967912	−	0.251288i	$-0.0808540\pi$
$257$	4.26967	+	7.39529i	0.266335	+	0.461305i	−0.701578	+	0.712593i	$0.747521\pi$
$258$		0			0
$259$	−12.7980	+	7.38891i	−0.795227	+	0.459125i
$260$	−4.10562	+	8.96250i	−0.254620	+	0.555830i
$261$		0			0
$262$	−1.24512	−	4.64685i	−0.0769237	−	0.287083i
$263$		−	2.64515i		−	0.163107i	−0.996669	−	0.0815535i	$-0.974012\pi$
$263$		−	2.64515i		−	0.163107i	0.996669	−	0.0815535i	$-0.0259881\pi$
$264$		0			0
$265$	−2.78091	−	10.3785i	−0.170830	−	0.637547i
$266$	17.7273	+	17.7273i	1.08693	+	1.08693i
$267$		0			0
$268$	−1.43247	+	5.34607i	−0.0875023	+	0.326563i
$269$	14.9308	−	8.62028i	0.910345	−	0.525588i	0.0298029	−	0.999556i	$-0.490512\pi$
$269$	14.9308	−	8.62028i	0.910345	−	0.525588i	0.880542	+	0.473968i	$0.157179\pi$
$270$		0			0
$271$	14.5522	−	3.89924i	0.883981	−	0.236862i	0.211857	−	0.977301i	$-0.432049\pi$
$271$	14.5522	−	3.89924i	0.883981	−	0.236862i	0.672124	+	0.740439i	$0.265382\pi$
$272$	−0.419403	−	0.726428i	−0.0254301	−	0.0440461i
$273$		0			0
$274$	−3.87751	+	6.71604i	−0.234249	+	0.405731i
$275$	1.16930	−	4.36389i	0.0705115	−	0.263153i
$276$		0			0
$277$	−11.8455	−	6.83901i	−0.711728	−	0.410916i	0.0999726	−	0.994990i	$-0.468124\pi$
$277$	−11.8455	−	6.83901i	−0.711728	−	0.410916i	−0.811700	+	0.584074i	$0.801458\pi$
$278$	3.41325	+	3.41325i	0.204713	+	0.204713i
$279$		0			0
$280$	2.46630	−	9.20434i	0.147389	−	0.550065i
$281$	12.8651	+	3.44720i	0.767468	+	0.205643i	0.621253	−	0.783610i	$-0.286624\pi$
$281$	12.8651	+	3.44720i	0.767468	+	0.205643i	0.146216	+	0.989253i	$0.453291\pi$
$282$		0			0
$283$	−2.19846	+	1.26928i	−0.130685	+	0.0754510i	−0.563917	−	0.825831i	$-0.690706\pi$
$283$	−2.19846	+	1.26928i	−0.130685	+	0.0754510i	0.433232	+	0.901282i	$0.357373\pi$
$284$	−5.55573	−	1.48865i	−0.329672	−	0.0883353i
$285$		0			0
$286$	−5.06911	−	4.19532i	−0.299743	−	0.248074i
$287$		−	14.4872i		−	0.855154i
$288$		0			0
$289$	8.14820	−	14.1131i	0.479306	−	0.830182i
$290$	8.27217	−	14.3278i	0.485759	−	0.841359i
$291$		0			0
$292$	9.66963	−	9.66963i	0.565872	−	0.565872i
$293$	9.85394	−	9.85394i	0.575674	−	0.575674i	−0.358035	−	0.933708i	$-0.616553\pi$
$293$	9.85394	−	9.85394i	0.575674	−	0.575674i	0.933708	+	0.358035i	$0.116553\pi$
$294$		0			0
$295$	10.1808	−	17.6336i	0.592748	−	1.02667i
$296$	−2.12009	+	3.67210i	−0.123228	+	0.213436i
$297$		0			0
$298$		−	13.0532i		−	0.756153i
$299$	−3.84057	+	22.6780i	−0.222106	+	1.31150i
$300$		0			0
$301$	29.0515	+	7.78432i	1.67450	+	0.448681i
$302$	−9.88142	+	5.70504i	−0.568612	+	0.328288i
$303$		0			0
$304$	6.94825	+	1.86178i	0.398509	+	0.106780i
$305$	0.350199	−	1.30696i	0.0200523	−	0.0748363i
$306$		0			0
$307$	−6.54395	−	6.54395i	−0.373483	−	0.373483i	0.495261	−	0.868744i	$-0.335072\pi$
$307$	−6.54395	−	6.54395i	−0.373483	−	0.373483i	−0.868744	+	0.495261i	$0.835072\pi$
$308$	5.50823	+	3.18018i	0.313861	+	0.181208i
$309$		0			0
$310$	−5.44971	+	20.3386i	−0.309523	+	1.15515i
$311$	8.02003	−	13.8911i	0.454774	−	0.787692i	−0.543901	−	0.839149i	$-0.683053\pi$
$311$	8.02003	−	13.8911i	0.454774	−	0.787692i	0.998675	+	0.0514573i	$0.0163866\pi$
$312$		0			0
$313$	−9.30369	−	16.1145i	−0.525875	−	0.910843i	−0.999546	−	0.0301408i	$-0.990404\pi$
$313$	−9.30369	−	16.1145i	−0.525875	−	0.910843i	0.473670	−	0.880702i	$-0.342929\pi$
$314$	−4.18979	+	1.12265i	−0.236444	+	0.0633549i
$315$		0			0
$316$	1.54564	−	0.892374i	0.0869489	−	0.0501999i
$317$	−1.93565	+	7.22395i	−0.108717	+	0.405737i	−0.998740	−	0.0501776i	$-0.984021\pi$
$317$	−1.93565	+	7.22395i	−0.108717	+	0.405737i	0.890023	+	0.455915i	$0.150688\pi$
$318$		0			0
$319$	7.80849	+	7.80849i	0.437192	+	0.437192i
$320$	−0.707650	−	2.64098i	−0.0395588	−	0.147636i
$321$		0			0
$322$		−	22.2331i		−	1.23900i
$323$	−1.56167	−	5.82823i	−0.0868937	−	0.324292i
$324$		0			0
$325$	8.80049	+	1.49038i	0.488163	+	0.0826715i
$326$	−15.8988	+	9.17918i	−0.880553	+	0.508388i
$327$		0			0
$328$	−2.07840	−	3.59989i	−0.114760	−	0.198771i
$329$	−26.9394			−1.48522
$330$		0			0
$331$	−2.94858	−	11.0042i	−0.162069	−	0.604848i	−0.998396	−	0.0566177i	$-0.981968\pi$
$331$	−2.94858	−	11.0042i	−0.162069	−	0.604848i	0.836327	−	0.548230i	$-0.184698\pi$
$332$	15.2034	+	4.07375i	0.834397	+	0.223576i
$333$		0			0
$334$	1.21727	+	2.10838i	0.0666062	+	0.115365i
$335$	15.1326			0.826781
$336$		0			0
$337$	−14.3804	−	8.30252i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$337$	−14.3804	−	8.30252i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$338$	7.31158	−	10.7490i	0.397697	−	0.584668i
$339$		0			0
$340$	−1.62169	+	1.62169i	−0.0879487	+	0.0879487i
$341$	−12.1714	−	7.02716i	−0.659118	−	0.380542i
$342$		0			0
$343$	−4.56761	+	4.56761i	−0.246628	+	0.246628i
$344$	8.33569	−	2.23354i	0.449430	−	0.120424i
$345$		0			0
$346$	9.82844	−	2.63352i	0.528380	−	0.141579i
$347$			14.0776i			0.755726i	0.925862	+	0.377863i	$0.123341\pi$
$347$			14.0776i			0.755726i	−0.925862	+	0.377863i	$0.876659\pi$
$348$		0			0
$349$	−1.81786	−	1.81786i	−0.0973080	−	0.0973080i	0.656777	−	0.754085i	$-0.271919\pi$
$349$	−1.81786	−	1.81786i	−0.0973080	−	0.0973080i	−0.754085	+	0.656777i	$0.771919\pi$
$350$	−8.62784			−0.461177
$351$		0			0
$352$	1.82497			0.0972710
$353$	−4.48187	−	4.48187i	−0.238546	−	0.238546i	0.577702	−	0.816248i	$-0.303950\pi$
$353$	−4.48187	−	4.48187i	−0.238546	−	0.238546i	−0.816248	+	0.577702i	$0.803950\pi$
$354$		0			0
$355$			15.7260i			0.834651i
$356$	1.43924	−	0.385644i	0.0762797	−	0.0204391i
$357$		0			0
$358$	12.6459	−	3.38845i	0.668355	−	0.179085i
$359$	15.0107	−	15.0107i	0.792236	−	0.792236i	−0.189622	−	0.981857i	$-0.560726\pi$
$359$	15.0107	−	15.0107i	0.792236	−	0.792236i	0.981857	+	0.189622i	$0.0607261\pi$
$360$		0			0
$361$	28.3574	+	16.3722i	1.49250	+	0.861693i
$362$	7.11392	−	7.11392i	0.373899	−	0.373899i
$363$		0			0
$364$	−5.23339	+	11.4244i	−0.274304	+	0.598801i
$365$	−32.3801	−	18.6946i	−1.69485	−	0.978522i
$366$		0			0
$367$	16.7751			0.875655			0.437828	−	0.899059i	$-0.355748\pi$
$367$	16.7751			0.875655			0.437828	+	0.899059i	$0.355748\pi$
$368$	−3.18965	−	5.52464i	−0.166272	−	0.287992i
$369$		0			0
$370$	11.1982	+	3.00056i	0.582169	+	0.155992i
$371$	−3.54480	−	13.2294i	−0.184037	−	0.686835i
$372$		0			0
$373$	−10.9205			−0.565440			−0.282720	−	0.959202i	$-0.591237\pi$
$373$	−10.9205			−0.565440			−0.282720	+	0.959202i	$0.591237\pi$
$374$	−0.765397	−	1.32571i	−0.0395777	−	0.0685506i
$375$		0			0
$376$	−6.69410	+	3.86484i	−0.345222	+	0.199314i
$377$	−13.9103	+	16.8075i	−0.716418	+	0.865632i
$378$		0			0
$379$	1.57730	+	5.88656i	0.0810203	+	0.302372i	0.994531	−	0.104443i	$-0.0333060\pi$
$379$	1.57730	+	5.88656i	0.0810203	+	0.302372i	−0.913511	+	0.406815i	$0.866639\pi$
$380$		−	19.6677i		−	1.00893i
$381$		0			0
$382$	4.83849	+	18.0575i	0.247559	+	0.923901i
$383$	22.6794	+	22.6794i	1.15886	+	1.15886i	0.984720	+	0.174143i	$0.0557154\pi$
$383$	22.6794	+	22.6794i	1.15886	+	1.15886i	0.174143	+	0.984720i	$0.444285\pi$
$384$		0			0
$385$	4.50091	−	16.7976i	0.229387	−	0.856086i
$386$	4.47898	−	2.58594i	0.227974	−	0.131621i
$387$		0			0
$388$	−16.8000	+	4.50154i	−0.852889	+	0.228531i
$389$	16.7063	+	28.9362i	0.847043	+	1.46712i	0.883835	+	0.467798i	$0.154953\pi$
$389$	16.7063	+	28.9362i	0.847043	+	1.46712i	−0.0367925	+	0.999323i	$0.511714\pi$
$390$		0			0
$391$	−2.67550	+	4.63411i	−0.135306	+	0.234357i
$392$	1.33203	−	4.97120i	0.0672776	−	0.251083i
$393$		0			0
$394$	7.94283	+	4.58579i	0.400154	+	0.231029i
$395$	−3.45052	−	3.45052i	−0.173614	−	0.173614i
$396$		0			0
$397$	−5.37105	+	20.0450i	−0.269565	+	1.00603i	0.689832	+	0.723970i	$0.257685\pi$
$397$	−5.37105	+	20.0450i	−0.269565	+	1.00603i	−0.959397	+	0.282061i	$0.908982\pi$
$398$	12.9078	+	3.45864i	0.647010	+	0.173366i
$399$		0			0
$400$	−2.14391	+	1.23778i	−0.107195	+	0.0618892i
$401$	−19.5869	−	5.24830i	−0.978125	−	0.262088i	−0.265870	−	0.964009i	$-0.585659\pi$
$401$	−19.5869	−	5.24830i	−0.978125	−	0.262088i	−0.712255	+	0.701921i	$0.752326\pi$
$402$		0			0
$403$	11.5641	−	25.2442i	0.576048	−	1.25750i
$404$		−	0.0847306i		−	0.00421550i
$405$		0			0
$406$	10.5445	−	18.2635i	0.523313	−	0.906404i
$407$	−3.86909	+	6.70146i	−0.191784	+	0.332179i
$408$		0			0
$409$	3.94732	−	3.94732i	0.195183	−	0.195183i	−0.602749	−	0.797931i	$-0.705928\pi$
$409$	3.94732	−	3.94732i	0.195183	−	0.195183i	0.797931	+	0.602749i	$0.205928\pi$
$410$	−8.03647	+	8.03647i	−0.396893	+	0.396893i
$411$		0			0
$412$	4.46733	−	7.73765i	0.220090	−	0.381207i
$413$	12.9773	−	22.4774i	0.638573	−	1.10604i
$414$		0			0
$415$		−	43.0348i		−	2.11250i
$416$	0.338562	+	3.58962i	0.0165994	+	0.175996i
$417$		0			0
$418$	12.6803	+	3.39768i	0.620215	+	0.166186i
$419$	27.1430	−	15.6710i	1.32602	−	0.765578i	0.341339	−	0.939940i	$-0.389120\pi$
$419$	27.1430	−	15.6710i	1.32602	−	0.765578i	0.984682	+	0.174362i	$0.0557863\pi$
$420$		0			0
$421$	26.5626	+	7.11743i	1.29458	+	0.346882i	0.839399	−	0.543516i	$-0.182907\pi$
$421$	26.5626	+	7.11743i	1.29458	+	0.346882i	0.455183	+	0.890398i	$0.349574\pi$
$422$	3.10041	−	11.5709i	0.150925	−	0.563261i
$423$		0			0
$424$	−2.77878	−	2.77878i	−0.134949	−	0.134949i
$425$	1.79832	+	1.03826i	0.0872314	+	0.0503631i
$426$		0			0
$427$	0.446395	−	1.66597i	0.0216026	−	0.0806219i
$428$	7.14138	−	12.3692i	0.345192	−	0.597890i
$429$		0			0
$430$	−11.7975	−	20.4339i	−0.568926	−	0.985408i
$431$	−26.7454	+	7.16641i	−1.28828	+	0.345194i	−0.837007	−	0.547192i	$-0.815697\pi$
$431$	−26.7454	+	7.16641i	−1.28828	+	0.345194i	−0.451274	+	0.892386i	$0.649030\pi$
$432$		0			0
$433$	−27.2596	+	15.7383i	−1.31001	+	0.756336i	−0.982098	−	0.188372i	$-0.939679\pi$
$433$	−27.2596	+	15.7383i	−1.31001	+	0.756336i	−0.327914	+	0.944708i	$0.606346\pi$
$434$	−6.94669	+	25.9254i	−0.333452	+	1.24446i
$435$		0			0
$436$	−9.68492	−	9.68492i	−0.463823	−	0.463823i
$437$	−11.8768	−	44.3250i	−0.568147	−	2.12035i
$438$		0			0
$439$			26.2573i			1.25319i	0.779344	+	0.626596i	$0.215552\pi$
$439$			26.2573i			1.25319i	−0.779344	+	0.626596i	$0.784448\pi$
$440$	−1.29144	−	4.81971i	−0.0615669	−	0.229771i
$441$		0			0
$442$	2.46561	−	1.75144i	0.117277	−	0.0833075i
$443$	23.2806	−	13.4410i	1.10609	−	0.638604i	0.168279	−	0.985739i	$-0.446179\pi$
$443$	23.2806	−	13.4410i	1.10609	−	0.638604i	0.937815	+	0.347136i	$0.112846\pi$
$444$		0			0
$445$	−2.03696	−	3.52812i	−0.0965612	−	0.167249i
$446$	1.75682			0.0831878
$447$		0			0
$448$	−0.902034	−	3.36644i	−0.0426171	−	0.159049i
$449$	1.60200	+	0.429254i	0.0756029	+	0.0202577i	0.296422	−	0.955057i	$-0.404206\pi$
$449$	1.60200	+	0.429254i	0.0756029	+	0.0202577i	−0.220819	+	0.975315i	$0.570873\pi$
$450$		0			0
$451$	−3.79300	−	6.56968i	−0.178606	−	0.309354i
$452$	−7.95653			−0.374244
$453$		0			0
$454$	9.35067	+	5.39861i	0.438849	+	0.253369i
$455$	33.8751	+	5.73682i	1.58809	+	0.268946i
$456$		0			0
$457$	25.6564	−	25.6564i	1.20015	−	1.20015i	0.226036	−	0.974119i	$-0.427423\pi$
$457$	25.6564	−	25.6564i	1.20015	−	1.20015i	0.974119	−	0.226036i	$-0.0725767\pi$
$458$	−2.05601	−	1.18704i	−0.0960711	−	0.0554667i
$459$		0			0
$460$	−12.3333	+	12.3333i	−0.575045	+	0.575045i
$461$	21.4084	−	5.73636i	0.997087	−	0.267169i	0.276863	−	0.960910i	$-0.410705\pi$
$461$	21.4084	−	5.73636i	0.997087	−	0.267169i	0.720225	+	0.693741i	$0.244039\pi$
$462$		0			0
$463$	−28.8741	+	7.73679i	−1.34189	+	0.359559i	−0.857136	−	0.515090i	$-0.827758\pi$
$463$	−28.8741	+	7.73679i	−1.34189	+	0.359559i	−0.484756	+	0.874649i	$0.661092\pi$
$464$		−	6.05100i		−	0.280911i
$465$		0			0
$466$	−10.4978	−	10.4978i	−0.486301	−	0.486301i
$467$	36.5666			1.69210			0.846051	−	0.533102i	$-0.178974\pi$
$467$	36.5666			1.69210			0.846051	+	0.533102i	$0.178974\pi$
$468$		0			0
$469$	19.2893			0.890699
$470$	14.9441	+	14.9441i	0.689318	+	0.689318i
$471$		0			0
$472$		−	7.44713i		−	0.342782i
$473$	15.2123	−	4.07614i	0.699465	−	0.187421i
$474$		0			0
$475$	−17.2009	+	4.60896i	−0.789230	+	0.211474i
$476$	−2.06716	+	2.06716i	−0.0947480	+	0.0947480i
$477$		0			0
$478$	25.5795	+	14.7683i	1.16998	+	0.675487i
$479$	−24.0481	+	24.0481i	−1.09879	+	1.09879i	−0.104234	+	0.994553i	$0.533239\pi$
$479$	−24.0481	+	24.0481i	−1.09879	+	1.09879i	−0.994553	+	0.104234i	$0.966761\pi$
$480$		0			0
$481$	−13.8992	−	6.36708i	−0.633750	−	0.290314i
$482$	17.8348	+	10.2969i	0.812355	+	0.469013i
$483$		0			0
$484$	−7.66950			−0.348614
$485$	23.7770	+	41.1830i	1.07966	+	1.87002i
$486$		0			0
$487$	12.0435	+	3.22705i	0.545744	+	0.146232i	0.521149	−	0.853466i	$-0.325504\pi$
$487$	12.0435	+	3.22705i	0.545744	+	0.146232i	0.0245951	+	0.999697i	$0.492170\pi$
$488$	−0.128083	−	0.478014i	−0.00579806	−	0.0216387i
$489$		0			0
$490$	−14.0715			−0.635684
$491$	2.76676	+	4.79216i	0.124862	+	0.216267i	0.921679	−	0.387953i	$-0.126818\pi$
$491$	2.76676	+	4.79216i	0.124862	+	0.216267i	−0.796817	+	0.604221i	$0.793485\pi$
$492$		0			0
$493$	−4.39562	+	2.53781i	−0.197969	+	0.114297i
$494$	−4.33066	+	25.5719i	−0.194846	+	1.15053i
$495$		0			0
$496$	1.99320	+	7.43873i	0.0894974	+	0.334009i
$497$			20.0458i			0.899178i
$498$		0			0
$499$	−0.641188	−	2.39294i	−0.0287035	−	0.107123i	0.950088	−	0.311982i	$-0.100993\pi$
$499$	−0.641188	−	2.39294i	−0.0287035	−	0.107123i	−0.978791	+	0.204859i	$0.934326\pi$
$500$	−4.88057	−	4.88057i	−0.218266	−	0.218266i
$501$		0			0
$502$	−5.33767	+	19.9204i	−0.238232	+	0.889093i
$503$	−32.0788	+	18.5207i	−1.43032	+	0.825798i	−0.997145	−	0.0755096i	$-0.975942\pi$
$503$	−32.0788	+	18.5207i	−1.43032	+	0.825798i	−0.433179	+	0.901308i	$0.642608\pi$
$504$		0			0
$505$	−0.223772	+	0.0599596i	−0.00995773	+	0.00266817i
$506$	−5.82101	−	10.0823i	−0.258776	−	0.448212i
$507$		0			0
$508$	−5.81045	+	10.0640i	−0.257797	+	0.446518i
$509$	−8.65075	+	32.2850i	−0.383438	+	1.43101i	0.457177	+	0.889376i	$0.348861\pi$
$509$	−8.65075	+	32.2850i	−0.383438	+	1.43101i	−0.840615	+	0.541634i	$0.817806\pi$
$510$		0			0
$511$	−41.2745	−	23.8299i	−1.82588	−	1.05417i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	2.21014	−	8.24837i	0.0974853	−	0.363820i
$515$	−23.5963	−	6.32261i	−1.03978	−	0.278608i
$516$		0			0
$517$	−12.2165	+	7.05321i	−0.537282	+	0.310200i
$518$	14.2743	+	3.82478i	0.627176	+	0.168051i
$519$		0			0
$520$	9.24055	−	3.43433i	0.405225	−	0.150605i
$521$			6.65944i			0.291755i	0.989303	+	0.145878i	$0.0466006\pi$
$521$			6.65944i			0.291755i	−0.989303	+	0.145878i	$0.953399\pi$
$522$		0			0
$523$	0.581243	−	1.00674i	0.0254160	−	0.0440218i	−0.853038	−	0.521849i	$-0.825242\pi$
$523$	0.581243	−	1.00674i	0.0254160	−	0.0440218i	0.878454	+	0.477828i	$0.158576\pi$
$524$	−2.40538	+	4.16625i	−0.105080	+	0.182003i
$525$		0			0
$526$	−1.87040	+	1.87040i	−0.0815535	+	0.0815535i
$527$	4.56774	−	4.56774i	0.198974	−	0.198974i
$528$		0			0
$529$	−8.84778	+	15.3248i	−0.384686	+	0.666296i
$530$	−5.37231	+	9.30512i	−0.233358	+	0.404189i
$531$		0			0
$532$		−	25.0702i		−	1.08693i
$533$	12.2186	−	8.67944i	0.529245	−	0.375948i
$534$		0			0
$535$	−37.7206	−	10.1072i	−1.63080	−	0.436972i
$536$	4.79315	−	2.76733i	0.207033	−	0.119530i
$537$		0			0
$538$	−16.6531	−	4.46219i	−0.717967	−	0.192379i
$539$	2.43091	−	9.07227i	0.104707	−	0.390770i
$540$		0			0
$541$	15.5641	+	15.5641i	0.669152	+	0.669152i	0.957520	−	0.288368i	$-0.0931126\pi$
$541$	15.5641	+	15.5641i	0.669152	+	0.669152i	−0.288368	+	0.957520i	$0.593113\pi$
$542$	−13.0471	−	7.53275i	−0.560421	−	0.323559i
$543$		0			0
$544$	−0.217099	+	0.810225i	−0.00930805	+	0.0347381i
$545$	−18.7242	+	32.4313i	−0.802056	+	1.38920i
$546$		0			0
$547$	−4.14533	−	7.17992i	−0.177241	−	0.306991i	0.763693	−	0.645579i	$-0.223384\pi$
$547$	−4.14533	−	7.17992i	−0.177241	−	0.306991i	−0.940935	+	0.338588i	$0.890051\pi$
$548$	7.49077	−	2.00715i	0.319990	−	0.0857411i
$549$		0			0
$550$	−3.91256	+	2.25892i	−0.166832	+	0.0963205i
$551$	11.2656	−	42.0439i	0.479932	−	1.79113i
$552$		0			0
$553$	−4.39834	−	4.39834i	−0.187036	−	0.187036i
$554$	3.54013	+	13.2120i	0.150406	+	0.561322i
$555$		0			0
$556$		−	4.82707i		−	0.204713i
$557$	−5.76476	−	21.5144i	−0.244261	−	0.911594i	−0.973754	−	0.227605i	$-0.926910\pi$
$557$	−5.76476	−	21.5144i	−0.244261	−	0.911594i	0.729493	−	0.683989i	$-0.239756\pi$
$558$		0			0
$559$	10.8397	+	29.1658i	0.458471	+	1.23358i
$560$	−8.25239	+	4.76452i	−0.348727	+	0.201338i
$561$		0			0
$562$	−6.65947	−	11.5345i	−0.280913	−	0.486555i
$563$	−28.1745			−1.18741			−0.593707	−	0.804682i	$-0.702336\pi$
$563$	−28.1745			−1.18741			−0.593707	+	0.804682i	$0.702336\pi$
$564$		0			0
$565$	5.63043	+	21.0131i	0.236874	+	0.884026i
$566$	2.45206	+	0.657028i	0.103068	+	0.0276170i
$567$		0			0
$568$	2.87586	+	4.98113i	0.120668	+	0.209004i
$569$	−29.1878			−1.22362			−0.611808	−	0.791007i	$-0.709557\pi$
$569$	−29.1878			−1.22362			−0.611808	+	0.791007i	$0.709557\pi$
$570$		0			0
$571$	36.5099	+	21.0790i	1.52789	+	0.882129i	0.999450	+	0.0331604i	$0.0105572\pi$
$571$	36.5099	+	21.0790i	1.52789	+	0.882129i	0.528443	+	0.848969i	$0.322776\pi$
$572$	0.617865	+	6.55094i	0.0258342	+	0.273908i
$573$		0			0
$574$	−10.2440	+	10.2440i	−0.427577	+	0.427577i
$575$	13.6766	+	7.89621i	0.570355	+	0.329295i
$576$		0			0
$577$	13.8702	−	13.8702i	0.577425	−	0.577425i	−0.356768	−	0.934193i	$-0.616121\pi$
$577$	13.8702	−	13.8702i	0.577425	−	0.577425i	0.934193	+	0.356768i	$0.116121\pi$
$578$	−15.7411	+	4.21782i	−0.654744	+	0.175438i
$579$		0			0
$580$	−15.9806	+	4.28199i	−0.663559	+	0.177800i
$581$		−	54.8561i		−	2.27581i
$582$		0			0
$583$	−5.07118	−	5.07118i	−0.210027	−	0.210027i
$584$	−13.6749			−0.565872
$585$		0			0
$586$	−13.9356			−0.575674
$587$	5.61049	+	5.61049i	0.231570	+	0.231570i	0.813348	−	0.581778i	$-0.197643\pi$
$587$	5.61049	+	5.61049i	0.231570	+	0.231570i	−0.581778	+	0.813348i	$0.697643\pi$
$588$		0			0
$589$			55.3970i			2.28259i
$590$	−19.6678	+	5.26996i	−0.809708	+	0.216961i
$591$		0			0
$592$	4.09570	−	1.09744i	0.168332	−	0.0451044i
$593$	−23.8412	+	23.8412i	−0.979040	+	0.979040i	−0.999785	−	0.0207452i	$-0.993396\pi$
$593$	−23.8412	+	23.8412i	−0.979040	+	0.979040i	0.0207452	+	0.999785i	$0.493396\pi$
$594$		0			0
$595$	6.92215	+	3.99651i	0.283781	+	0.163841i
$596$	−9.23003	+	9.23003i	−0.378077	+	0.378077i
$597$		0			0
$598$	18.7515	−	13.3201i	0.766805	−	0.544699i
$599$	−5.64668	−	3.26011i	−0.230717	−	0.133205i	0.380186	−	0.924910i	$-0.375860\pi$
$599$	−5.64668	−	3.26011i	−0.230717	−	0.133205i	−0.610903	+	0.791706i	$0.709193\pi$
$600$		0			0
$601$	−27.5743			−1.12478			−0.562390	−	0.826872i	$-0.690118\pi$
$601$	−27.5743			−1.12478			−0.562390	+	0.826872i	$0.690118\pi$
$602$	−15.0381	−	26.0468i	−0.612909	−	1.06159i
$603$		0			0
$604$	11.0213	+	2.95315i	0.448450	+	0.120162i
$605$	5.42732	+	20.2550i	0.220652	+	0.823484i
$606$		0			0
$607$	5.91621			0.240132			0.120066	−	0.992766i	$-0.461689\pi$
$607$	5.91621			0.240132			0.120066	+	0.992766i	$0.461689\pi$
$608$	−3.59668	−	6.22963i	−0.145865	−	0.252645i
$609$		0			0
$610$	−1.17179	+	0.676532i	−0.0474443	+	0.0273920i
$611$	−16.1397	−	22.7208i	−0.652942	−	0.919185i
$612$		0			0
$613$	4.10104	+	15.3053i	0.165639	+	0.618175i	0.997958	+	0.0638768i	$0.0203465\pi$
$613$	4.10104	+	15.3053i	0.165639	+	0.618175i	−0.832318	+	0.554298i	$0.812987\pi$
$614$			9.25454i			0.373483i
$615$		0			0
$616$	−1.64618	−	6.14363i	−0.0663266	−	0.247534i
$617$	18.4697	+	18.4697i	0.743561	+	0.743561i	0.973261	−	0.229700i	$-0.0737746\pi$
$617$	18.4697	+	18.4697i	0.743561	+	0.743561i	−0.229700	+	0.973261i	$0.573775\pi$
$618$		0			0
$619$	−3.16658	+	11.8178i	−0.127276	+	0.474999i	−0.999911	−	0.0133740i	$-0.995743\pi$
$619$	−3.16658	+	11.8178i	−0.127276	+	0.474999i	0.872635	+	0.488373i	$0.162409\pi$
$620$	18.2351	−	10.5280i	0.732339	−	0.422816i
$621$		0			0
$622$	−15.4935	+	4.15147i	−0.621233	+	0.166459i
$623$	−2.59649	−	4.49726i	−0.104026	−	0.180179i
$624$		0			0
$625$	−15.6247	+	27.0628i	−0.624988	+	1.08251i
$626$	−4.81594	+	17.9733i	−0.192484	+	0.718359i
$627$		0			0
$628$	3.75646	+	2.16879i	0.149899	+	0.0865443i
$629$	−2.51496	−	2.51496i	−0.100278	−	0.100278i
$630$		0			0
$631$	2.72399	−	10.1661i	0.108440	−	0.404704i	−0.890272	−	0.455428i	$-0.849486\pi$
$631$	2.72399	−	10.1661i	0.108440	−	0.404704i	0.998713	+	0.0507238i	$0.0161528\pi$
$632$	−1.72393	−	0.461927i	−0.0685744	−	0.0183745i
$633$		0			0
$634$	6.47682	−	3.73939i	0.257227	−	0.148510i
$635$	30.6906	+	8.22353i	1.21792	+	0.326341i
$636$		0			0
$637$	18.2957	+	3.09842i	0.724902	+	0.122764i
$638$		−	11.0429i		−	0.437192i
$639$		0			0
$640$	−1.36707	+	2.36784i	−0.0540384	+	0.0935972i
$641$	−2.46006	+	4.26095i	−0.0971666	+	0.168297i	−0.910511	−	0.413485i	$-0.864311\pi$
$641$	−2.46006	+	4.26095i	−0.0971666	+	0.168297i	0.813344	+	0.581783i	$0.197645\pi$
$642$		0			0
$643$	23.8644	−	23.8644i	0.941119	−	0.941119i	−0.0572415	−	0.998360i	$-0.518230\pi$
$643$	23.8644	−	23.8644i	0.941119	−	0.941119i	0.998360	+	0.0572415i	$0.0182305\pi$
$644$	−15.7212	+	15.7212i	−0.619501	+	0.619501i
$645$		0			0
$646$	−3.01692	+	5.22545i	−0.118699	+	0.205593i
$647$	2.54755	−	4.41248i	0.100154	−	0.173473i	−0.811594	−	0.584222i	$-0.801400\pi$
$647$	2.54755	−	4.41248i	0.100154	−	0.173473i	0.911748	+	0.410750i	$0.134733\pi$
$648$		0			0
$649$		−	13.5908i		−	0.533484i
$650$	−5.16902	−	7.27674i	−0.202746	−	0.285417i
$651$		0			0
$652$	17.7328	+	4.75149i	0.694470	+	0.186083i
$653$	34.2634	−	19.7820i	1.34083	−	0.774129i	0.353901	−	0.935283i	$-0.384855\pi$
$653$	34.2634	−	19.7820i	1.34083	−	0.774129i	0.986929	+	0.161154i	$0.0515216\pi$
$654$		0			0
$655$	12.7052	+	3.40434i	0.496432	+	0.133019i
$656$	−1.07586	+	4.01515i	−0.0420052	+	0.156765i
$657$		0			0
$658$	19.0491	+	19.0491i	0.742609	+	0.742609i
$659$	−13.1719	−	7.60483i	−0.513106	−	0.296242i	0.221003	−	0.975273i	$-0.429067\pi$
$659$	−13.1719	−	7.60483i	−0.513106	−	0.296242i	−0.734110	+	0.679031i	$0.762400\pi$
$660$		0			0
$661$	3.06267	−	11.4300i	0.119124	−	0.444577i	−0.880438	−	0.474161i	$-0.842752\pi$
$661$	3.06267	−	11.4300i	0.119124	−	0.444577i	0.999562	+	0.0295837i	$0.00941817\pi$
$662$	−5.69622	+	9.86614i	−0.221390	+	0.383458i
$663$		0			0
$664$	−7.86988	−	13.6310i	−0.305411	−	0.528987i
$665$	−66.2101	+	17.7409i	−2.56752	+	0.687964i
$666$		0			0
$667$	−33.4296	+	19.3006i	−1.29440	+	0.747323i
$668$	0.630107	−	2.35159i	0.0243796	−	0.0909858i
$669$		0			0
$670$	−10.7003	−	10.7003i	−0.413390	−	0.413390i
$671$	−0.233748	−	0.872359i	−0.00902373	−	0.0336770i
$672$		0			0
$673$			19.5423i			0.753299i	0.926356	+	0.376650i	$0.122924\pi$
$673$			19.5423i			0.753299i	−0.926356	+	0.376650i	$0.877076\pi$
$674$	4.29770	+	16.0392i	0.165541	+	0.617808i
$675$		0			0
$676$	−12.7708	+	2.43062i	−0.491183	+	0.0934854i
$677$	7.33732	−	4.23620i	0.281996	−	0.162811i	−0.352331	−	0.935876i	$-0.614611\pi$
$677$	7.33732	−	4.23620i	0.281996	−	0.162811i	0.634327	+	0.773065i	$0.281277\pi$
$678$		0			0
$679$	30.3083	+	52.4955i	1.16313	+	2.01459i
$680$	2.29342			0.0879487
$681$		0			0
$682$	3.63753	+	13.5754i	0.139288	+	0.519830i
$683$	−13.4051	−	3.59188i	−0.512930	−	0.137439i	−0.00693584	−	0.999976i	$-0.502208\pi$
$683$	−13.4051	−	3.59188i	−0.512930	−	0.137439i	−0.505995	+	0.862537i	$0.668874\pi$
$684$		0			0
$685$	−10.6017	−	18.3627i	−0.405070	−	0.701601i
$686$	6.45958			0.246628
$687$		0			0
$688$	−7.47357	−	4.31487i	−0.284927	−	0.164503i
$689$	9.03398	−	10.9156i	0.344167	−	0.415850i
$690$		0			0
$691$	3.25059	−	3.25059i	0.123658	−	0.123658i	−0.642569	−	0.766228i	$-0.722132\pi$
$691$	3.25059	−	3.25059i	0.123658	−	0.123658i	0.766228	+	0.642569i	$0.222132\pi$
$692$	−8.81194	−	5.08757i	−0.334980	−	0.193401i
$693$		0			0
$694$	9.95438	−	9.95438i	0.377863	−	0.377863i
$695$	−12.7482	+	3.41587i	−0.483567	+	0.129571i
$696$		0			0
$697$	3.36794	−	0.902436i	0.127570	−	0.0341822i
$698$			2.57085i			0.0973080i
$699$		0			0
$700$	6.10080	+	6.10080i	0.230589	+	0.230589i
$701$	3.27106			0.123546			0.0617731	−	0.998090i	$-0.480324\pi$
$701$	3.27106			0.123546			0.0617731	+	0.998090i	$0.480324\pi$
$702$		0			0
$703$	30.5011			1.15037
$704$	−1.29045	−	1.29045i	−0.0486355	−	0.0486355i
$705$		0			0
$706$			6.33832i			0.238546i
$707$	−0.285240	+	0.0764298i	−0.0107276	+	0.00287444i
$708$		0			0
$709$	17.9894	−	4.82025i	0.675606	−	0.181028i	0.0953275	−	0.995446i	$-0.469610\pi$
$709$	17.9894	−	4.82025i	0.675606	−	0.181028i	0.580279	+	0.814418i	$0.302944\pi$
$710$	11.1200	−	11.1200i	0.417326	−	0.417326i
$711$		0			0
$712$	−1.29039	−	0.745007i	−0.0483594	−	0.0279203i
$713$	34.7387	−	34.7387i	1.30097	−	1.30097i
$714$		0			0
$715$	16.8637	−	6.26754i	0.630666	−	0.234393i
$716$	−11.3380	−	6.54598i	−0.423720	−	0.244635i
$717$		0			0
$718$	−21.2284			−0.792236
$719$	6.22658	+	10.7848i	0.232212	+	0.402204i	0.958459	−	0.285231i	$-0.0920703\pi$
$719$	6.22658	+	10.7848i	0.232212	+	0.402204i	−0.726247	+	0.687434i	$0.758737\pi$
$720$		0			0
$721$	−30.0780	−	8.05937i	−1.12016	−	0.300147i
$722$	−8.47486	−	31.6286i	−0.315402	−	1.17709i
$723$		0			0
$724$	−10.0606			−0.373899
$725$	7.48984	+	12.9728i	0.278166	+	0.481797i
$726$		0			0
$727$	0.202128	−	0.116699i	0.00749650	−	0.00432811i	−0.496247	−	0.868181i	$-0.665289\pi$
$727$	0.202128	−	0.116699i	0.00749650	−	0.00432811i	0.503744	+	0.863853i	$0.331956\pi$
$728$	11.7788	−	4.37771i	0.436553	−	0.162249i
$729$		0			0
$730$	9.67706	+	36.1153i	0.358164	+	1.33669i
$731$			7.23868i			0.267732i
$732$		0			0
$733$	−7.31715	−	27.3080i	−0.270265	−	1.00864i	−0.958948	−	0.283580i	$-0.908478\pi$
$733$	−7.31715	−	27.3080i	−0.270265	−	1.00864i	0.688684	−	0.725062i	$-0.258189\pi$
$734$	−11.8618	−	11.8618i	−0.437828	−	0.437828i
$735$		0			0
$736$	−1.65109	+	6.16194i	−0.0608599	+	0.227132i
$737$	8.74734	−	5.05028i	0.322213	−	0.186030i
$738$		0			0
$739$	34.3558	−	9.20561i	1.26380	−	0.338634i	0.436146	−	0.899876i	$-0.356343\pi$
$739$	34.3558	−	9.20561i	1.26380	−	0.338634i	0.827652	+	0.561242i	$0.189676\pi$
$740$	−5.79664	−	10.0401i	−0.213089	−	0.369080i
$741$		0			0
$742$	−6.84803	+	11.8611i	−0.251399	+	0.435436i
$743$	−6.78006	+	25.3035i	−0.248736	+	0.928297i	0.722732	+	0.691128i	$0.242886\pi$
$743$	−6.78006	+	25.3035i	−0.248736	+	0.928297i	−0.971469	+	0.237168i	$0.923781\pi$
$744$		0			0
$745$	30.9080	+	17.8447i	1.13238	+	0.653781i
$746$	7.72193	+	7.72193i	0.282720	+	0.282720i
$747$		0			0
$748$	−0.396198	+	1.47863i	−0.0144865	+	0.0540642i
$749$	−48.0820	−	12.8835i	−1.75688	−	0.470754i
$750$		0			0
$751$	25.3210	−	14.6191i	0.923975	−	0.533457i	0.0390742	−	0.999236i	$-0.487559\pi$
$751$	25.3210	−	14.6191i	0.923975	−	0.533457i	0.884901	+	0.465779i	$0.154226\pi$
$752$	7.46630	+	2.00059i	0.272268	+	0.0729540i
$753$		0			0
$754$	21.7208	−	2.04864i	0.791025	−	0.0746071i
$755$		−	31.1969i		−	1.13537i
$756$		0			0
$757$	0.560080	−	0.970087i	0.0203565	−	0.0352584i	−0.855668	−	0.517526i	$-0.826853\pi$
$757$	0.560080	−	0.970087i	0.0203565	−	0.0352584i	0.876024	+	0.482267i	$0.160187\pi$
$758$	3.04711	−	5.27774i	0.110676	−	0.191696i
$759$		0			0
$760$	−13.9072	+	13.9072i	−0.504466	+	0.504466i
$761$	8.74376	−	8.74376i	0.316961	−	0.316961i	−0.530638	−	0.847599i	$-0.678048\pi$
$761$	8.74376	−	8.74376i	0.316961	−	0.316961i	0.847599	+	0.530638i	$0.178048\pi$
$762$		0			0
$763$	−23.8675	+	41.3398i	−0.864063	+	1.49660i
$764$	9.34724	−	16.1899i	0.338171	−	0.585730i
$765$		0			0
$766$		−	32.0735i		−	1.15886i
$767$	26.7324	−	2.52132i	0.965250	−	0.0910395i
$768$		0			0
$769$	−21.2688	−	5.69895i	−0.766971	−	0.205509i	−0.145938	−	0.989294i	$-0.546620\pi$
$769$	−21.2688	−	5.69895i	−0.766971	−	0.205509i	−0.621033	+	0.783785i	$0.713287\pi$
$770$	−15.0603	+	8.69508i	−0.542737	+	0.313349i
$771$		0			0
$772$	−4.99566	−	1.33858i	−0.179798	−	0.0481766i
$773$	−4.66222	+	17.3997i	−0.167689	+	0.625822i	0.829993	+	0.557773i	$0.188344\pi$
$773$	−4.66222	+	17.3997i	−0.167689	+	0.625822i	−0.997682	+	0.0680490i	$0.978323\pi$
$774$		0			0
$775$	−13.4808	−	13.4808i	−0.484244	−	0.484244i
$776$	15.0624	+	8.69631i	0.540710	+	0.312179i
$777$		0			0
$778$	8.64781	−	32.2741i	0.310039	−	1.15708i
$779$	−14.9506	+	25.8953i	−0.535662	+	0.927794i
$780$		0			0
$781$	5.24834	+	9.09039i	0.187800	+	0.325280i
$782$	5.16867	−	1.38494i	0.184831	−	0.0495254i
$783$		0			0
$784$	−4.45706	+	2.57328i	−0.159181	+	0.0919029i
$785$	3.06949	−	11.4555i	0.109555	−	0.408865i
$786$		0			0
$787$	−26.3061	−	26.3061i	−0.937710	−	0.937710i	0.0604604	−	0.998171i	$-0.480743\pi$
$787$	−26.3061	−	26.3061i	−0.937710	−	0.937710i	−0.998171	+	0.0604604i	$0.980743\pi$
$788$	−2.37378	−	8.85907i	−0.0845625	−	0.315591i
$789$		0			0
$790$			4.87977i			0.173614i
$791$	7.17706	+	26.7851i	0.255187	+	0.952370i
$792$		0			0
$793$	1.67252	−	0.621608i	0.0593930	−	0.0220739i
$794$	17.9719	−	10.3761i	0.637798	−	0.368233i
$795$		0			0
$796$	−6.68158	−	11.5728i	−0.236822	−	0.410188i
$797$	14.9200			0.528494			0.264247	−	0.964455i	$-0.414877\pi$
$797$	14.9200			0.528494			0.264247	+	0.964455i	$0.414877\pi$
$798$		0			0
$799$	−1.67811	−	6.26278i	−0.0593672	−	0.221561i
$800$	2.39122	+	0.640725i	0.0845423	+	0.0226530i
$801$		0			0
$802$	10.1389	+	17.5612i	0.358019	+	0.620106i
$803$	−24.9563			−0.880688
$804$		0			0
$805$	52.6445	+	30.3943i	1.85548	+	1.07126i
$806$	−26.0274	+	9.67331i	−0.916776	+	0.340728i
$807$		0			0
$808$	−0.0599135	+	0.0599135i	−0.00210775	+	0.00210775i
$809$	−42.8291	−	24.7274i	−1.50579	−	0.869368i	−0.999977	−	0.00672439i	$-0.997860\pi$
$809$	−42.8291	−	24.7274i	−1.50579	−	0.869368i	−0.505812	−	0.862644i	$-0.668807\pi$
$810$		0			0
$811$	21.8763	−	21.8763i	0.768181	−	0.768181i	−0.209605	−	0.977786i	$-0.567218\pi$
$811$	21.8763	−	21.8763i	0.768181	−	0.768181i	0.977786	+	0.209605i	$0.0672178\pi$
$812$	−20.3703	+	5.45821i	−0.714858	+	0.191546i
$813$		0			0
$814$	7.47451	−	2.00279i	0.261981	−	0.0701977i
$815$		−	50.1945i		−	1.75824i
$816$		0			0
$817$	−43.8949	−	43.8949i	−1.53569	−	1.53569i
$818$	−5.58236			−0.195183
$819$		0			0
$820$	11.3653			0.396893
$821$	10.6567	+	10.6567i	0.371922	+	0.371922i	0.868177	−	0.496255i	$-0.165292\pi$
$821$	10.6567	+	10.6567i	0.371922	+	0.371922i	−0.496255	+	0.868177i	$0.665292\pi$
$822$		0			0
$823$		−	53.1092i		−	1.85127i	−0.378419	−	0.925635i	$-0.623532\pi$
$823$		−	53.1092i		−	1.85127i	0.378419	−	0.925635i	$-0.376468\pi$
$824$	−8.63023	+	2.31246i	−0.300648	+	0.0805584i
$825$		0			0
$826$	−25.0703	+	6.71756i	−0.872307	+	0.233734i
$827$	−7.98942	+	7.98942i	−0.277819	+	0.277819i	−0.832238	−	0.554419i	$-0.812941\pi$
$827$	−7.98942	+	7.98942i	−0.277819	+	0.277819i	0.554419	+	0.832238i	$0.312941\pi$
$828$		0			0
$829$	−29.7343	−	17.1671i	−1.03271	−	0.596238i	−0.114953	−	0.993371i	$-0.536672\pi$
$829$	−29.7343	−	17.1671i	−1.03271	−	0.596238i	−0.917761	+	0.397133i	$0.870005\pi$
$830$	−30.4302	+	30.4302i	−1.05625	+	1.05625i
$831$		0			0
$832$	2.29885	−	2.77764i	0.0796981	−	0.0962975i
$833$	3.73861	+	2.15849i	0.129535	+	0.0747871i
$834$		0			0
$835$	−6.65641			−0.230355
$836$	−6.56381	−	11.3689i	−0.227014	−	0.393200i
$837$		0			0
$838$	−30.2740	−	8.11190i	−1.04580	−	0.280221i
$839$	10.1438	+	37.8571i	0.350202	+	1.30697i	0.886416	+	0.462889i	$0.153187\pi$
$839$	10.1438	+	37.8571i	0.350202	+	1.30697i	−0.536214	+	0.844082i	$0.680146\pi$
$840$		0			0
$841$	−7.61465			−0.262574
$842$	−13.7498	−	23.8154i	−0.473850	−	0.820732i
$843$		0			0
$844$	−10.3742	+	5.98953i	−0.357093	+	0.206168i
$845$	15.4565	+	32.0073i	0.531718	+	1.10109i
$846$		0			0
$847$	6.91815	+	25.8189i	0.237710	+	0.887147i
$848$			3.92979i			0.134949i
$849$		0			0
$850$	−0.537444	−	2.00577i	−0.0184342	−	0.0687973i
$851$	−19.1268	−	19.1268i	−0.655658	−	0.655658i
$852$		0			0
$853$	5.60605	−	20.9221i	0.191948	−	0.716358i	−0.801088	−	0.598546i	$-0.795745\pi$
$853$	5.60605	−	20.9221i	0.191948	−	0.716358i	0.993036	−	0.117812i	$-0.0375880\pi$
$854$	−1.49367	+	0.862369i	−0.0511122	+	0.0295097i
$855$		0			0
$856$	−13.7961	+	3.69665i	−0.471541	+	0.126349i
$857$	−11.0344	−	19.1122i	−0.376930	−	0.652861i	0.613684	−	0.789552i	$-0.289687\pi$
$857$	−11.0344	−	19.1122i	−0.376930	−	0.652861i	−0.990614	+	0.136690i	$0.956353\pi$
$858$		0			0
$859$	−15.1793	+	26.2913i	−0.517911	+	0.897048i	0.481872	+	0.876241i	$0.339957\pi$
$859$	−15.1793	+	26.2913i	−0.517911	+	0.897048i	−0.999784	+	0.0208071i	$0.993376\pi$
$860$	−6.10683	+	22.7910i	−0.208241	+	0.777167i
$861$		0			0
$862$	23.9793	+	13.8444i	0.816737	+	0.471543i
$863$	−10.7391	−	10.7391i	−0.365563	−	0.365563i	0.500293	−	0.865856i	$-0.333225\pi$
$863$	−10.7391	−	10.7391i	−0.365563	−	0.365563i	−0.865856	+	0.500293i	$0.833225\pi$
$864$		0			0
$865$	−7.20044	+	26.8724i	−0.244822	+	0.913689i
$866$	30.4041	+	8.14676i	1.03317	+	0.276838i
$867$		0			0
$868$	23.2441	−	13.4200i	0.788956	−	0.455504i
$869$	−3.14612	−	0.843001i	−0.106725	−	0.0285968i
$870$		0			0
$871$	11.5564	+	16.2687i	0.391575	+	0.551243i
$872$			13.6965i			0.463823i
$873$		0			0
$874$	−22.9443	+	39.7407i	−0.776103	+	1.34425i
$875$	−12.0277	+	20.8326i	−0.406610	+	0.704269i
$876$		0			0
$877$	22.8918	−	22.8918i	0.773002	−	0.773002i	−0.205628	−	0.978630i	$-0.565924\pi$
$877$	22.8918	−	22.8918i	0.773002	−	0.773002i	0.978630	+	0.205628i	$0.0659237\pi$
$878$	18.5667	−	18.5667i	0.626596	−	0.626596i
$879$		0			0
$880$	−2.49486	+	4.32123i	−0.0841019	+	0.145669i
$881$	2.90596	−	5.03326i	0.0979041	−	0.169575i	−0.812913	−	0.582385i	$-0.802119\pi$
$881$	2.90596	−	5.03326i	0.0979041	−	0.169575i	0.910817	+	0.412810i	$0.135453\pi$
$882$		0			0
$883$			10.3443i			0.348115i	0.984735	+	0.174058i	$0.0556879\pi$
$883$			10.3443i			0.348115i	−0.984735	+	0.174058i	$0.944312\pi$
$884$	−2.98190	−	0.504992i	−0.100292	−	0.0169847i
$885$		0			0
$886$	−25.9661	−	6.95760i	−0.872349	−	0.233745i
$887$	12.8552	−	7.42197i	0.431636	−	0.249205i	−0.268407	−	0.963306i	$-0.586497\pi$
$887$	12.8552	−	7.42197i	0.431636	−	0.249205i	0.700043	+	0.714100i	$0.253164\pi$
$888$		0			0
$889$	39.1210	+	10.4824i	1.31208	+	0.351570i
$890$	−1.05441	+	3.93511i	−0.0353438	+	0.131905i
$891$		0			0
$892$	−1.24226	−	1.24226i	−0.0415939	−	0.0415939i
$893$	48.1530	+	27.8012i	1.61138	+	0.930331i
$894$		0			0
$895$	−9.26453	+	34.5757i	−0.309679	+	1.15574i
$896$	−1.74260	+	3.01826i	−0.0582160	+	0.100833i
$897$		0			0
$898$	−0.829255	−	1.43631i	−0.0276726	−	0.0479303i
$899$	45.0118	−	12.0609i	1.50123	−	0.402253i
$900$		0			0
$901$	2.85471	−	1.64817i	0.0951041	−	0.0549084i
$902$	−1.96340	+	7.32752i	−0.0653742	+	0.243980i
$903$		0			0
$904$	5.62611	+	5.62611i	0.187122	+	0.187122i
$905$	7.11938	+	26.5699i	0.236656	+	0.883213i
$906$		0			0
$907$		−	5.76107i		−	0.191293i	−0.995415	−	0.0956467i	$-0.969508\pi$
$907$		−	5.76107i		−	0.191293i	0.995415	−	0.0956467i	$-0.0304919\pi$
$908$	−2.79453	−	10.4293i	−0.0927396	−	0.346109i
$909$		0			0
$910$	−19.8968	−	28.0098i	−0.659571	−	0.928517i
$911$	27.3661	−	15.7998i	0.906680	−	0.523472i	0.0273186	−	0.999627i	$-0.491303\pi$
$911$	27.3661	−	15.7998i	0.906680	−	0.523472i	0.879361	+	0.476155i	$0.157970\pi$
$912$		0			0
$913$	−14.3623	−	24.8762i	−0.475322	−	0.823281i
$914$	−36.2836			−1.20015
$915$		0			0
$916$	0.614457	+	2.29318i	0.0203022	+	0.0757689i
$917$	16.1952	+	4.33948i	0.534811	+	0.143302i
$918$		0			0
$919$	3.19782	+	5.53878i	0.105486	+	0.182708i	0.913937	−	0.405857i	$-0.133027\pi$
$919$	3.19782	+	5.53878i	0.105486	+	0.182708i	−0.808451	+	0.588564i	$0.799693\pi$
$920$	17.4420			0.575045
$921$		0			0
$922$	−19.1942	−	11.0818i	−0.632128	−	0.364959i
$923$	−16.9067	+	12.0097i	−0.556491	+	0.395303i
$924$		0			0
$925$	−7.42240	+	7.42240i	−0.244047	+	0.244047i
$926$	25.8878	+	14.9463i	0.850726	+	0.491167i
$927$		0			0
$928$	−4.27871	+	4.27871i	−0.140455	+	0.140455i
$929$	15.7198	−	4.21211i	0.515750	−	0.138195i	0.00845022	−	0.999964i	$-0.497310\pi$
$929$	15.7198	−	4.21211i	0.515750	−	0.138195i	0.507300	+	0.861769i	$0.330644\pi$
$930$		0			0
$931$	−35.7596	+	9.58175i	−1.17197	+	0.314029i
$932$			14.8461i			0.486301i
$933$		0			0
$934$	−25.8565	−	25.8565i	−0.846051	−	0.846051i
$935$	4.18542			0.136878
$936$		0			0
$937$	55.5723			1.81547			0.907734	−	0.419547i	$-0.137811\pi$
$937$	55.5723			1.81547			0.907734	+	0.419547i	$0.137811\pi$
$938$	−13.6396	−	13.6396i	−0.445350	−	0.445350i
$939$		0			0
$940$		−	21.1341i		−	0.689318i
$941$	28.8961	−	7.74269i	0.941986	−	0.252404i	0.245028	−	0.969516i	$-0.421203\pi$
$941$	28.8961	−	7.74269i	0.941986	−	0.252404i	0.696958	+	0.717112i	$0.254536\pi$
$942$		0			0
$943$	25.6139	−	6.86322i	0.834103	−	0.223497i
$944$	−5.26591	+	5.26591i	−0.171391	+	0.171391i
$945$		0			0
$946$	−13.6390	−	7.87449i	−0.443443	−	0.256022i
$947$	−1.04158	+	1.04158i	−0.0338469	+	0.0338469i	−0.723828	−	0.689981i	$-0.757619\pi$
$947$	−1.04158	+	1.04158i	−0.0338469	+	0.0338469i	0.689981	+	0.723828i	$0.257619\pi$
$948$		0			0
$949$	−4.62981	−	49.0878i	−0.150290	−	1.59346i
$950$	15.4219	+	8.90382i	0.500352	+	0.288878i
$951$		0			0
$952$	2.92340			0.0947480
$953$	−12.8169	−	22.1996i	−0.415181	−	0.719114i	0.580267	−	0.814427i	$-0.302948\pi$
$953$	−12.8169	−	22.1996i	−0.415181	−	0.719114i	−0.995447	+	0.0953124i	$0.969615\pi$
$954$		0			0
$955$	−49.3719	−	13.2291i	−1.59764	−	0.428085i
$956$	−7.64464	−	28.5302i	−0.247245	−	0.922732i
$957$		0			0
$958$	34.0092			1.09879
$959$	−13.5139	−	23.4067i	−0.436386	−	0.755842i
$960$		0			0
$961$	−24.5151	+	14.1538i	−0.790809	+	0.456574i
$962$	5.32604	+	14.3304i	0.171718	+	0.462032i
$963$		0			0
$964$	−5.33009	−	19.8922i	−0.171671	−	0.640684i
$965$			14.1407i			0.455205i
$966$		0			0
$967$	0.0479759	+	0.179048i	0.00154280	+	0.00575781i	0.966693	−	0.255939i	$-0.0823846\pi$
$967$	0.0479759	+	0.179048i	0.00154280	+	0.00575781i	−0.965150	+	0.261697i	$0.915718\pi$
$968$	5.42315	+	5.42315i	0.174307	+	0.174307i
$969$		0			0
$970$	12.3079	−	45.9336i	0.395182	−	1.47484i
$971$	16.6170	−	9.59381i	0.533264	−	0.307880i	−0.209081	−	0.977898i	$-0.567047\pi$
$971$	16.6170	−	9.59381i	0.533264	−	0.307880i	0.742344	+	0.670018i	$0.233714\pi$
$972$		0			0
$973$	−16.2500	+	4.35418i	−0.520952	+	0.139589i
$974$	−6.23418	−	10.7979i	−0.199756	−	0.345988i
$975$		0			0
$976$	−0.247438	+	0.428575i	−0.00792030	+	0.0137184i
$977$	13.6752	−	51.0365i	0.437508	−	1.63280i	−0.297485	−	0.954726i	$-0.596148\pi$
$977$	13.6752	−	51.0365i	0.437508	−	1.63280i	0.734993	−	0.678075i	$-0.237185\pi$
$978$		0			0
$979$	−2.35492	−	1.35961i	−0.0752635	−	0.0434534i
$980$	9.95003	+	9.95003i	0.317842	+	0.317842i
$981$		0			0
$982$	1.43218	−	5.34496i	0.0457027	−	0.170565i
$983$	−10.2897	−	2.75711i	−0.328190	−	0.0879382i	0.0909619	−	0.995854i	$-0.471006\pi$
$983$	−10.2897	−	2.75711i	−0.328190	−	0.0879382i	−0.419152	+	0.907916i	$0.637673\pi$
$984$		0			0
$985$	−21.7169	+	12.5382i	−0.691957	+	0.399502i
$986$	4.90267	+	1.31367i	0.156133	+	0.0418357i
$987$		0			0
$988$	21.1443	−	15.0198i	0.672690	−	0.477844i
$989$			55.0518i			1.75054i
$990$		0			0
$991$	−12.5106	+	21.6690i	−0.397413	+	0.688339i	−0.993406	−	0.114651i	$-0.963425\pi$
$991$	−12.5106	+	21.6690i	−0.397413	+	0.688339i	0.595993	+	0.802989i	$0.296759\pi$
$992$	3.85057	−	6.66938i	0.122256	−	0.211753i
$993$		0			0
$994$	14.1745	−	14.1745i	0.449589	−	0.449589i
$995$	−25.8355	+	25.8355i	−0.819039	+	0.819039i
$996$		0			0
$997$	9.61444	−	16.6527i	0.304492	−	0.527396i	−0.672656	−	0.739955i	$-0.734847\pi$
$997$	9.61444	−	16.6527i	0.304492	−	0.527396i	0.977148	+	0.212559i	$0.0681799\pi$
$998$	−1.23868	+	2.14546i	−0.0392097	+	0.0679132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.71.6		56
3.2	odd	2		234.2.y.a.149.14	yes	56
9.2	odd	6		702.2.bc.a.305.13		56
9.7	even	3		234.2.z.a.227.3	yes	56
13.11	odd	12		702.2.bc.a.557.13		56
39.11	even	12		234.2.z.a.167.3	yes	56
117.11	even	12	inner	702.2.bb.a.89.6		56
117.115	odd	12		234.2.y.a.11.14	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.14	✓	56	117.115	odd	12
234.2.y.a.149.14	yes	56	3.2	odd	2
234.2.z.a.167.3	yes	56	39.11	even	12
234.2.z.a.227.3	yes	56	9.7	even	3
702.2.bb.a.71.6		56	1.1	even	1	trivial
702.2.bb.a.89.6		56	117.11	even	12	inner
702.2.bc.a.305.13		56	9.2	odd	6
702.2.bc.a.557.13		56	13.11	odd	12

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.64098 - 0.707650i) q^{5} +(3.36644 - 0.902034i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(2.64098 - 0.707650i) q^{5} +(3.36644 - 0.902034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.36784 - 1.36707i) q^{10} +(1.29045 - 1.29045i) q^{11} +(2.77764 + 2.29885i) q^{13} +(-3.01826 - 1.74260i) q^{14} -1.00000 q^{16} +(0.419403 + 0.726428i) q^{17} +(-6.94825 - 1.86178i) q^{19} +(0.707650 + 2.64098i) q^{20} -1.82497 q^{22} +(3.18965 + 5.52464i) q^{23} +(2.14391 - 1.23778i) q^{25} +(-0.338562 - 3.58962i) q^{26} +(0.902034 + 3.36644i) q^{28} +6.05100i q^{29} +(-1.99320 - 7.43873i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.217099 - 0.810225i) q^{34} +(8.25239 - 4.76452i) q^{35} +(-4.09570 + 1.09744i) q^{37} +(3.59668 + 6.22963i) q^{38} +(1.36707 - 2.36784i) q^{40} +(1.07586 - 4.01515i) q^{41} +(7.47357 + 4.31487i) q^{43} +(1.29045 + 1.29045i) q^{44} +(1.65109 - 6.16194i) q^{46} +(-7.46630 - 2.00059i) q^{47} +(4.45706 - 2.57328i) q^{49} +(-2.39122 - 0.640725i) q^{50} +(-2.29885 + 2.77764i) q^{52} -3.92979i q^{53} +(2.49486 - 4.32123i) q^{55} +(1.74260 - 3.01826i) q^{56} +(4.27871 - 4.27871i) q^{58} +(5.26591 - 5.26591i) q^{59} +(0.247438 - 0.428575i) q^{61} +(-3.85057 + 6.66938i) q^{62} -1.00000i q^{64} +(8.96250 + 4.10562i) q^{65} +(5.34607 + 1.43247i) q^{67} +(-0.726428 + 0.419403i) q^{68} +(-9.20434 - 2.46630i) q^{70} +(-1.48865 + 5.55573i) q^{71} +(-9.66963 - 9.66963i) q^{73} +(3.67210 + 2.12009i) q^{74} +(1.86178 - 6.94825i) q^{76} +(3.18018 - 5.50823i) q^{77} +(-0.892374 - 1.54564i) q^{79} +(-2.64098 + 0.707650i) q^{80} +(-3.59989 + 2.07840i) q^{82} +(4.07375 - 15.2034i) q^{83} +(1.62169 + 1.62169i) q^{85} +(-2.23354 - 8.33569i) q^{86} -1.82497i q^{88} +(-0.385644 - 1.43924i) q^{89} +(11.4244 + 5.23339i) q^{91} +(-5.52464 + 3.18965i) q^{92} +(3.86484 + 6.69410i) q^{94} -19.6677 q^{95} +(4.50154 + 16.8000i) q^{97} +(-4.97120 - 1.33203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73} - 48 q^{74} + 4 q^{76} + 24 q^{77} - 24 q^{79} + 60 q^{83} - 48 q^{86} + 4 q^{91} + 24 q^{92} + 20 q^{97} + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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