LMFDB - Embedded newform 702.2.bc.a.305.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(305,702)]

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([2, 5]))

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

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

chi := DirichletCharacter("702.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (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			305.13
Character	$\chi$	$=$	702.305
Dual form			702.2.bc.a.557.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707650 - 2.64098i) q^{5} +(-2.46440 - 2.46440i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707650 - 2.64098i) q^{5} +(-2.46440 - 2.46440i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.36784 - 1.36707i) q^{10} +(1.76278 + 0.472336i) q^{11} +(-3.37968 + 1.25609i) q^{13} +(-3.01826 + 1.74260i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.419403 - 0.726428i) q^{17} +(-6.94825 - 1.86178i) q^{19} +(-1.93334 + 1.93334i) q^{20} +(0.912483 - 1.58047i) q^{22} +6.37931 q^{23} +(-2.14391 - 1.23778i) q^{25} +(0.338562 + 3.58962i) q^{26} +(0.902034 + 3.36644i) q^{28} +(-5.24032 + 3.02550i) q^{29} +(7.43873 + 1.99320i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.810225 + 0.217099i) q^{34} +(-8.25239 + 4.76452i) q^{35} +(-4.09570 + 1.09744i) q^{37} +(-3.59668 + 6.22963i) q^{38} +(1.36707 + 2.36784i) q^{40} +(-2.93930 - 2.93930i) q^{41} -8.62974i q^{43} +(-1.29045 - 1.29045i) q^{44} +(1.65109 - 6.16194i) q^{46} +(-2.00059 - 7.46630i) q^{47} +5.14656i q^{49} +(-1.75049 + 1.75049i) q^{50} +(3.55493 + 0.602036i) q^{52} +3.92979i q^{53} +(2.49486 - 4.32123i) q^{55} +3.48519 q^{56} +(1.56612 + 5.84482i) q^{58} +(-1.92746 - 7.19337i) q^{59} -0.494876 q^{61} +(3.85057 - 6.66938i) q^{62} -1.00000i q^{64} +(0.925680 + 9.81456i) q^{65} +(-3.91359 + 3.91359i) q^{67} +0.838806i q^{68} +(2.46630 + 9.20434i) q^{70} +(1.48865 - 5.55573i) q^{71} +(-9.66963 - 9.66963i) q^{73} +4.24018i q^{74} +(5.08647 + 5.08647i) q^{76} +(-3.18018 - 5.50823i) q^{77} +(-0.892374 + 1.54564i) q^{79} +(2.64098 - 0.707650i) q^{80} +(-3.59989 + 2.07840i) q^{82} +(15.2034 - 4.07375i) q^{83} +(-2.21527 + 0.593581i) q^{85} +(-8.33569 - 2.23354i) q^{86} +(-1.58047 + 0.912483i) q^{88} +(0.385644 + 1.43924i) q^{89} +(11.4244 + 5.23339i) q^{91} +(-5.52464 - 3.18965i) q^{92} -7.72968 q^{94} +(-9.83385 + 17.0327i) q^{95} +(12.2984 - 12.2984i) q^{97} +(4.97120 + 1.33203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73} + 4 q^{76} - 24 q^{77} - 24 q^{79} + 96 q^{83} - 72 q^{85} + 4 q^{91} + 24 q^{92} - 52 q^{97} - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.707650	−	2.64098i	0.316471	−	1.18108i	−0.606142	−	0.795356i	$-0.707284\pi$
$5$	0.707650	−	2.64098i	0.316471	−	1.18108i	0.922613	−	0.385728i	$-0.126050\pi$
$6$		0			0
$7$	−2.46440	−	2.46440i	−0.931457	−	0.931457i	0.0663403	−	0.997797i	$-0.478868\pi$
$7$	−2.46440	−	2.46440i	−0.931457	−	0.931457i	−0.997797	+	0.0663403i	$0.978868\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.36784	−	1.36707i	−0.748777	−	0.432307i
$11$	1.76278	+	0.472336i	0.531499	+	0.142415i	0.514580	−	0.857442i	$-0.327948\pi$
$11$	1.76278	+	0.472336i	0.531499	+	0.142415i	0.0169185	+	0.999857i	$0.494614\pi$
$12$		0			0
$13$	−3.37968	+	1.25609i	−0.937355	+	0.348376i
$13$	−3.37968	+	1.25609i	−0.937355	+	0.348376i
$14$	−3.01826	+	1.74260i	−0.806665	+	0.465728i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.419403	−	0.726428i	−0.101720	−	0.176185i	0.810673	−	0.585499i	$-0.199101\pi$
$17$	−0.419403	−	0.726428i	−0.101720	−	0.176185i	−0.912393	+	0.409314i	$0.865768\pi$
$18$		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	$0.892234\pi$
$20$	−1.93334	+	1.93334i	−0.432307	+	0.432307i
$21$		0			0
$22$	0.912483	−	1.58047i	0.194542	−	0.336957i
$23$	6.37931			1.33018			0.665089	−	0.746764i	$-0.268394\pi$
$23$	6.37931			1.33018			0.665089	+	0.746764i	$0.268394\pi$
$24$		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
$29$	−5.24032	+	3.02550i	−0.973104	+	0.561822i	−0.900181	−	0.435516i	$-0.856566\pi$
$29$	−5.24032	+	3.02550i	−0.973104	+	0.561822i	−0.0729226	+	0.997338i	$0.523233\pi$
$30$		0			0
$31$	7.43873	+	1.99320i	1.33604	+	0.357990i	0.854962	−	0.518691i	$-0.173580\pi$
$31$	7.43873	+	1.99320i	1.33604	+	0.357990i	0.481074	+	0.876680i	$0.340247\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	−0.810225	+	0.217099i	−0.138952	+	0.0372322i
$35$	−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
$41$	−2.93930	−	2.93930i	−0.459041	−	0.459041i	0.439300	−	0.898341i	$-0.355227\pi$
$41$	−2.93930	−	2.93930i	−0.459041	−	0.459041i	−0.898341	+	0.439300i	$0.855227\pi$
$42$		0			0
$43$		−	8.62974i		−	1.31602i	−0.753008	−	0.658011i	$-0.771398\pi$
$43$		−	8.62974i		−	1.31602i	0.753008	−	0.658011i	$-0.228602\pi$
$44$	−1.29045	−	1.29045i	−0.194542	−	0.194542i
$45$		0			0
$46$	1.65109	−	6.16194i	0.243439	−	0.908528i
$47$	−2.00059	−	7.46630i	−0.291816	−	1.08907i	−0.943713	−	0.330765i	$-0.892693\pi$
$47$	−2.00059	−	7.46630i	−0.291816	−	1.08907i	0.651897	−	0.758307i	$-0.273973\pi$
$48$		0			0
$49$			5.14656i			0.735223i
$50$	−1.75049	+	1.75049i	−0.247557	+	0.247557i
$51$		0			0
$52$	3.55493	+	0.602036i	0.492981	+	0.0834874i
$53$			3.92979i			0.539798i	0.962889	+	0.269899i	$0.0869903\pi$
$53$			3.92979i			0.539798i	−0.962889	+	0.269899i	$0.913010\pi$
$54$		0			0
$55$	2.49486	−	4.32123i	0.336408	−	0.582675i
$56$	3.48519			0.465728
$57$		0			0
$58$	1.56612	+	5.84482i	0.205641	+	0.767463i
$59$	−1.92746	−	7.19337i	−0.250934	−	0.936497i	−0.970308	−	0.241874i	$-0.922238\pi$
$59$	−1.92746	−	7.19337i	−0.250934	−	0.936497i	0.719374	−	0.694623i	$-0.244429\pi$
$60$		0			0
$61$	−0.494876			−0.0633624			−0.0316812	−	0.999498i	$-0.510086\pi$
$61$	−0.494876			−0.0633624			−0.0316812	+	0.999498i	$0.510086\pi$
$62$	3.85057	−	6.66938i	0.489023	−	0.847013i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.925680	+	9.81456i	0.114816	+	1.21735i
$66$		0			0
$67$	−3.91359	+	3.91359i	−0.478121	+	0.478121i	−0.904530	−	0.426409i	$-0.859778\pi$
$67$	−3.91359	+	3.91359i	−0.478121	+	0.478121i	0.426409	+	0.904530i	$0.359778\pi$
$68$			0.838806i			0.101720i
$69$		0			0
$70$	2.46630	+	9.20434i	0.294779	+	1.10013i
$71$	1.48865	−	5.55573i	0.176671	−	0.659344i	−0.819591	−	0.572950i	$-0.805799\pi$
$71$	1.48865	−	5.55573i	0.176671	−	0.659344i	0.996261	−	0.0863938i	$-0.0275343\pi$
$72$		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	$-0.545307\pi$
$74$			4.24018i			0.492910i
$75$		0			0
$76$	5.08647	+	5.08647i	0.583458	+	0.583458i
$77$	−3.18018	−	5.50823i	−0.362415	−	0.627721i
$78$		0			0
$79$	−0.892374	+	1.54564i	−0.100400	+	0.173898i	−0.911849	−	0.410525i	$-0.865346\pi$
$79$	−0.892374	+	1.54564i	−0.100400	+	0.173898i	0.811450	+	0.584422i	$0.198679\pi$
$80$	2.64098	−	0.707650i	0.295271	−	0.0791177i
$81$		0			0
$82$	−3.59989	+	2.07840i	−0.397541	+	0.229520i
$83$	15.2034	−	4.07375i	1.66879	−	0.447152i	0.704009	−	0.710191i	$-0.251391\pi$
$83$	15.2034	−	4.07375i	1.66879	−	0.447152i	0.964785	+	0.263039i	$0.0847248\pi$
$84$		0			0
$85$	−2.21527	+	0.593581i	−0.240280	+	0.0643829i
$86$	−8.33569	−	2.23354i	−0.898860	−	0.240849i
$87$		0			0
$88$	−1.58047	+	0.912483i	−0.168478	+	0.0972710i
$89$	0.385644	+	1.43924i	0.0408782	+	0.152559i	0.983348	−	0.181731i	$-0.0581700\pi$
$89$	0.385644	+	1.43924i	0.0408782	+	0.152559i	−0.942470	+	0.334290i	$0.891503\pi$
$90$		0			0
$91$	11.4244	+	5.23339i	1.19760	+	0.548608i
$92$	−5.52464	−	3.18965i	−0.575984	−	0.332544i
$93$		0			0
$94$	−7.72968			−0.797256
$95$	−9.83385	+	17.0327i	−1.00893	+	1.74752i
$96$		0			0
$97$	12.2984	−	12.2984i	1.24872	−	1.24872i	0.292430	−	0.956287i	$-0.405536\pi$
$97$	12.2984	−	12.2984i	1.24872	−	1.24872i	0.956287	−	0.292430i	$-0.0944638\pi$
$98$	4.97120	+	1.33203i	0.502167	+	0.134555i
$99$		0			0
$100$	1.23778	+	2.14391i	0.123778	+	0.214391i
$101$	−0.0423653	−	0.0733788i	−0.00421550	−	0.00730146i	0.863910	−	0.503646i	$-0.168009\pi$
$101$	−0.0423653	−	0.0733788i	−0.00421550	−	0.00730146i	−0.868125	+	0.496345i	$0.834675\pi$
$102$		0			0
$103$	7.73765	−	4.46733i	0.762413	−	0.440179i	−0.0677484	−	0.997702i	$-0.521582\pi$
$103$	7.73765	−	4.46733i	0.762413	−	0.440179i	0.830161	+	0.557523i	$0.188248\pi$
$104$	1.50161	−	3.27798i	0.147245	−	0.321433i
$105$		0			0
$106$	3.79588	+	1.01710i	0.368689	+	0.0987899i
$107$	12.3692	+	7.14138i	1.19578	+	0.690384i	0.959611	−	0.281329i	$-0.0907751\pi$
$107$	12.3692	+	7.14138i	1.19578	+	0.690384i	0.236168	+	0.971712i	$0.424108\pi$
$108$		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	$0.477730\pi$
$110$	−3.52827	−	3.52827i	−0.336408	−	0.336408i
$111$		0			0
$112$	0.902034	−	3.36644i	0.0852342	−	0.318098i
$113$	6.89055	+	3.97826i	0.648209	+	0.374244i	0.787770	−	0.615970i	$-0.211236\pi$
$113$	6.89055	+	3.97826i	0.648209	+	0.374244i	−0.139561	+	0.990213i	$0.544569\pi$
$114$		0			0
$115$	4.51432	−	16.8477i	0.420962	−	1.57105i
$116$	6.05100			0.561822
$117$		0			0
$118$	−7.44713			−0.685564
$119$	−0.756632	+	2.82379i	−0.0693603	+	0.258856i
$120$		0			0
$121$	−6.64198	−	3.83475i	−0.603816	−	0.348614i
$122$	−0.128083	+	0.478014i	−0.0115961	+	0.0432773i
$123$		0			0
$124$	−5.44553	−	5.44553i	−0.489023	−	0.489023i
$125$	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	$0.494238\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	9.71972	+	1.64606i	0.852476	+	0.144369i
$131$	4.16625	−	2.40538i	0.364007	−	0.210159i	−0.306830	−	0.951764i	$-0.599268\pi$
$131$	4.16625	−	2.40538i	0.364007	−	0.210159i	0.670837	+	0.741605i	$0.265935\pi$
$132$		0			0
$133$	12.5351	+	21.7114i	1.08693	+	1.88262i
$134$	2.76733	+	4.79315i	0.239061	+	0.414065i
$135$		0			0
$136$	0.810225	+	0.217099i	0.0694762	+	0.0186161i
$137$	5.48363	−	5.48363i	0.468498	−	0.468498i	−0.432930	−	0.901428i	$-0.642520\pi$
$137$	5.48363	−	5.48363i	0.468498	−	0.468498i	0.901428	+	0.432930i	$0.142520\pi$
$138$		0			0
$139$	2.41353	−	4.18036i	0.204713	−	0.354574i	−0.745328	−	0.666698i	$-0.767707\pi$
$139$	2.41353	−	4.18036i	0.204713	−	0.354574i	0.950041	+	0.312124i	$0.101040\pi$
$140$	9.52903			0.805350
$141$		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
$146$	−11.8428	+	6.83746i	−0.980120	+	0.565872i
$147$		0			0
$148$	4.09570	+	1.09744i	0.336664	+	0.0902089i
$149$	12.6085	−	3.37842i	1.03292	−	0.276771i	0.297746	−	0.954645i	$-0.403765\pi$
$149$	12.6085	−	3.37842i	1.03292	−	0.276771i	0.735178	+	0.677874i	$0.237098\pi$
$150$		0			0
$151$	−11.0213	+	2.95315i	−0.896900	+	0.240324i	−0.677685	−	0.735353i	$-0.737016\pi$
$151$	−11.0213	+	2.95315i	−0.896900	+	0.240324i	−0.219216	+	0.975676i	$0.570350\pi$
$152$	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	0.939498	−	0.342554i	$-0.111292\pi$
$157$	2.16879	+	3.75646i	0.173089	+	0.299798i	−0.766409	+	0.642352i	$0.777959\pi$
$158$	1.26201	+	1.26201i	0.100400	+	0.100400i
$159$		0			0
$160$		−	2.73415i		−	0.216153i
$161$	−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	$-0.172052\pi$
$164$	1.07586	+	4.01515i	0.0840103	+	0.313531i
$165$		0			0
$166$		−	15.7398i		−	1.22164i
$167$	−1.72148	+	1.72148i	−0.133212	+	0.133212i	−0.770569	−	0.637357i	$-0.780028\pi$
$167$	−1.72148	+	1.72148i	−0.133212	+	0.133212i	0.637357	+	0.770569i	$0.280028\pi$
$168$		0			0
$169$	9.84448	−	8.49035i	0.757268	−	0.653104i
$170$			2.29342i			0.175897i
$171$		0			0
$172$	−4.31487	+	7.47357i	−0.329006	+	0.569855i
$173$	−10.1751			−0.773602			−0.386801	−	0.922163i	$-0.626420\pi$
$173$	−10.1751			−0.773602			−0.386801	+	0.922163i	$0.626420\pi$
$174$		0			0
$175$	2.23305	+	8.33385i	0.168803	+	0.629980i
$176$	0.472336	+	1.76278i	0.0356037	+	0.132875i
$177$		0			0
$178$	1.49001			0.111681
$179$	6.54598	−	11.3380i	0.489270	−	0.847440i	−0.510654	−	0.859786i	$-0.670597\pi$
$179$	6.54598	−	11.3380i	0.489270	−	0.847440i	0.999924	+	0.0123463i	$0.00393003\pi$
$180$		0			0
$181$			10.0606i			0.747798i	0.927469	+	0.373899i	$0.121979\pi$
$181$			10.0606i			0.747798i	−0.927469	+	0.373899i	$0.878021\pi$
$182$	8.01192	−	9.68063i	0.593883	−	0.717576i
$183$		0			0
$184$	−4.51085	+	4.51085i	−0.332544	+	0.332544i
$185$			11.5933i			0.852354i
$186$		0			0
$187$	−0.396198	−	1.47863i	−0.0289729	−	0.108128i
$188$	−2.00059	+	7.46630i	−0.145908	+	0.544536i
$189$		0			0
$190$	13.9072	+	13.9072i	1.00893	+	1.00893i
$191$		−	18.6945i		−	1.35269i	−0.736587	−	0.676343i	$-0.763564\pi$
$191$		−	18.6945i		−	1.35269i	0.736587	−	0.676343i	$-0.236436\pi$
$192$		0			0
$193$	−3.65707	−	3.65707i	−0.263242	−	0.263242i	0.563128	−	0.826370i	$-0.309598\pi$
$193$	−3.65707	−	3.65707i	−0.263242	−	0.263242i	−0.826370	+	0.563128i	$0.809598\pi$
$194$	−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	0.0709764	−	0.997478i	$-0.477388\pi$
$197$	8.85907	−	2.37378i	0.631183	−	0.169125i	0.560206	+	0.828353i	$0.310722\pi$
$198$		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	$0.490395\pi$
$200$	2.39122	−	0.640725i	0.169085	−	0.0453061i
$201$		0			0
$202$	−0.0818434	+	0.0219299i	−0.00575848	+	0.00154298i
$203$	20.3703	+	5.45821i	1.42972	+	0.383091i
$204$		0			0
$205$	−9.84263	+	5.68265i	−0.687439	+	0.396893i
$206$	−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
$211$	−11.9791			−0.824672			−0.412336	−	0.911032i	$-0.635287\pi$
$211$	−11.9791			−0.824672			−0.412336	+	0.911032i	$0.635287\pi$
$212$	1.96489	−	3.40330i	0.134949	−	0.233739i
$213$		0			0
$214$	10.0994	−	10.0994i	0.690384	−	0.690384i
$215$	−22.7910	−	6.10683i	−1.55433	−	0.416483i
$216$		0			0
$217$	−13.4200	−	23.2441i	−0.911007	−	1.57791i
$218$	6.84827	+	11.8616i	0.463823	+	0.803366i
$219$		0			0
$220$	−4.32123	+	2.49486i	−0.291337	+	0.168204i
$221$	2.32991	+	1.92829i	0.156726	+	0.129711i
$222$		0			0
$223$	1.69696	+	0.454698i	0.113637	+	0.0304489i	0.315189	−	0.949029i	$-0.397932\pi$
$223$	1.69696	+	0.454698i	0.113637	+	0.0304489i	−0.201553	+	0.979478i	$0.564599\pi$
$224$	−3.01826	−	1.74260i	−0.201666	−	0.116432i
$225$		0			0
$226$	5.62611	−	5.62611i	0.374244	−	0.374244i
$227$	−7.63479	−	7.63479i	−0.506739	−	0.506739i	0.406785	−	0.913524i	$-0.366650\pi$
$227$	−7.63479	−	7.63479i	−0.506739	−	0.506739i	−0.913524	+	0.406785i	$0.866650\pi$
$228$		0			0
$229$	−0.614457	+	2.29318i	−0.0406044	+	0.151538i	−0.983252	−	0.182253i	$-0.941661\pi$
$229$	−0.614457	+	2.29318i	−0.0406044	+	0.151538i	0.942647	+	0.333790i	$0.108328\pi$
$230$	−15.1052	−	8.72099i	−0.996007	−	0.575045i
$231$		0			0
$232$	1.56612	−	5.84482i	0.102820	−	0.383731i
$233$	−14.8461			−0.972602			−0.486301	−	0.873791i	$-0.661654\pi$
$233$	−14.8461			−0.972602			−0.486301	+	0.873791i	$0.661654\pi$
$234$		0			0
$235$	−21.1341			−1.37864
$236$	−1.92746	+	7.19337i	−0.125467	+	0.468249i
$237$		0			0
$238$	2.53174	+	1.46170i	0.164108	+	0.0947480i
$239$	−7.64464	+	28.5302i	−0.494491	+	1.84546i	0.0383723	+	0.999264i	$0.487783\pi$
$239$	−7.64464	+	28.5302i	−0.494491	+	1.84546i	−0.532863	+	0.846201i	$0.678884\pi$
$240$		0			0
$241$	14.5621	+	14.5621i	0.938026	+	0.938026i	0.998189	−	0.0601623i	$-0.0191618\pi$
$241$	14.5621	+	14.5621i	0.938026	+	0.938026i	−0.0601623	+	0.998189i	$0.519162\pi$
$242$	−5.42315	+	5.42315i	−0.348614	+	0.348614i
$243$		0			0
$244$	0.428575	+	0.247438i	0.0274367	+	0.0158406i
$245$	13.5920	+	3.64197i	0.868361	+	0.232677i
$246$		0			0
$247$	25.8214	−	2.43540i	1.64298	−	0.154961i
$248$	−6.66938	+	3.85057i	−0.423506	+	0.244511i
$249$		0			0
$250$	−3.45108	−	5.97745i	−0.218266	−	0.378047i
$251$	10.3116	+	17.8602i	0.650861	+	1.12732i	0.982914	+	0.184064i	$0.0589253\pi$
$251$	10.3116	+	17.8602i	0.650861	+	1.12732i	−0.332053	+	0.943261i	$0.607741\pi$
$252$		0			0
$253$	11.2453	+	3.01318i	0.706988	+	0.189437i
$254$	8.21722	−	8.21722i	0.515594	−	0.515594i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.53934			0.532669			0.266335	−	0.963881i	$-0.414187\pi$
$257$	8.53934			0.532669			0.266335	+	0.963881i	$0.414187\pi$
$258$		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
$263$	2.29077	−	1.32258i	0.141255	−	0.0815535i	−0.427707	−	0.903917i	$-0.640679\pi$
$263$	2.29077	−	1.32258i	0.141255	−	0.0815535i	0.568962	+	0.822364i	$0.307345\pi$
$264$		0			0
$265$	10.3785	+	2.78091i	0.637547	+	0.170830i
$266$	24.2160	−	6.48865i	1.48478	−	0.397845i
$267$		0			0
$268$	5.34607	−	1.43247i	0.326563	−	0.0875023i
$269$	−14.9308	+	8.62028i	−0.910345	+	0.525588i	−0.880542	−	0.473968i	$-0.842821\pi$
$269$	−14.9308	+	8.62028i	−0.910345	+	0.525588i	−0.0298029	+	0.999556i	$0.509488\pi$
$270$		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
$275$	−3.19459	−	3.19459i	−0.192641	−	0.192641i
$276$		0			0
$277$			13.6780i			0.821833i	0.911673	+	0.410916i	$0.134791\pi$
$277$			13.6780i			0.821833i	−0.911673	+	0.410916i	$0.865209\pi$
$278$	−3.41325	−	3.41325i	−0.204713	−	0.204713i
$279$		0			0
$280$	2.46630	−	9.20434i	0.147389	−	0.550065i
$281$	3.44720	+	12.8651i	0.205643	+	0.767468i	0.989253	+	0.146216i	$0.0467093\pi$
$281$	3.44720	+	12.8651i	0.205643	+	0.767468i	−0.783610	+	0.621253i	$0.786624\pi$
$282$		0			0
$283$		−	2.53856i		−	0.150902i	−0.997150	−	0.0754510i	$-0.975960\pi$
$283$		−	2.53856i		−	0.150902i	0.997150	−	0.0754510i	$-0.0240396\pi$
$284$	−4.06707	+	4.06707i	−0.241336	+	0.241336i
$285$		0			0
$286$	−1.09870	+	6.48763i	−0.0649672	+	0.383622i
$287$			14.4872i			0.855154i
$288$		0			0
$289$	8.14820	−	14.1131i	0.479306	−	0.830182i
$290$	16.5443			0.971517
$291$		0			0
$292$	3.53933	+	13.2090i	0.207124	+	0.772996i
$293$	−3.60679	−	13.4607i	−0.210711	−	0.786385i	−0.987632	−	0.156787i	$-0.949886\pi$
$293$	−3.60679	−	13.4607i	−0.210711	−	0.786385i	0.776921	−	0.629598i	$-0.216780\pi$
$294$		0			0
$295$	−20.3616			−1.18550
$296$	2.12009	−	3.67210i	0.123228	−	0.213436i
$297$		0			0
$298$		−	13.0532i		−	0.756153i
$299$	−21.5600	+	8.01297i	−1.24685	+	0.463402i
$300$		0			0
$301$	−21.2672	+	21.2672i	−1.22582	+	1.22582i
$302$			11.4101i			0.656576i
$303$		0			0
$304$	−1.86178	−	6.94825i	−0.106780	−	0.398509i
$305$	−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	$0.835072\pi$
$308$			6.36036i			0.362415i
$309$		0			0
$310$	−14.8889	−	14.8889i	−0.845632	−	0.845632i
$311$	−8.02003	−	13.8911i	−0.454774	−	0.787692i	0.543901	−	0.839149i	$-0.316947\pi$
$311$	−8.02003	−	13.8911i	−0.454774	−	0.787692i	−0.998675	+	0.0514573i	$0.983613\pi$
$312$		0			0
$313$	−9.30369	+	16.1145i	−0.525875	+	0.910843i	0.473670	+	0.880702i	$0.342929\pi$
$313$	−9.30369	+	16.1145i	−0.525875	+	0.910843i	−0.999546	+	0.0301408i	$0.990404\pi$
$314$	4.18979	−	1.12265i	0.236444	−	0.0633549i
$315$		0			0
$316$	1.54564	−	0.892374i	0.0869489	−	0.0501999i
$317$	−7.22395	+	1.93565i	−0.405737	+	0.108717i	−0.455915	−	0.890023i	$-0.650688\pi$
$317$	−7.22395	+	1.93565i	−0.405737	+	0.108717i	0.0501776	+	0.998740i	$0.484021\pi$
$318$		0			0
$319$	−10.6666	+	2.85811i	−0.597215	+	0.160023i
$320$	−2.64098	−	0.707650i	−0.147636	−	0.0395588i
$321$		0			0
$322$	−19.2544	+	11.1166i	−1.07301	+	0.619501i
$323$	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
$328$	4.15679			0.229520
$329$	−13.4697	+	23.3302i	−0.742609	+	1.28624i
$330$		0			0
$331$	−8.05567	+	8.05567i	−0.442779	+	0.442779i	−0.892945	−	0.450166i	$-0.851365\pi$
$331$	−8.05567	+	8.05567i	−0.442779	+	0.442779i	0.450166	+	0.892945i	$0.351365\pi$
$332$	−15.2034	−	4.07375i	−0.834397	−	0.223576i
$333$		0			0
$334$	1.21727	+	2.10838i	0.0666062	+	0.115365i
$335$	7.56629	+	13.1052i	0.413390	+	0.716013i
$336$		0			0
$337$	14.3804	−	8.30252i	0.783349	−	0.452267i	−0.0542666	−	0.998526i	$-0.517282\pi$
$337$	14.3804	−	8.30252i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$338$	−5.65311	−	11.7065i	−0.307489	−	0.636750i
$339$		0			0
$340$	2.21527	+	0.593581i	0.120140	+	0.0321915i
$341$	12.1714	+	7.02716i	0.659118	+	0.380542i
$342$		0			0
$343$	−4.56761	+	4.56761i	−0.246628	+	0.246628i
$344$	6.10215	+	6.10215i	0.329006	+	0.329006i
$345$		0			0
$346$	−2.63352	+	9.82844i	−0.141579	+	0.528380i
$347$	12.1916	+	7.03881i	0.654478	+	0.377863i	0.790170	−	0.612888i	$-0.209992\pi$
$347$	12.1916	+	7.03881i	0.654478	+	0.377863i	−0.135692	+	0.990751i	$0.543326\pi$
$348$		0			0
$349$	−0.665385	+	2.48325i	−0.0356172	+	0.132925i	−0.981445	−	0.191743i	$-0.938586\pi$
$349$	−0.665385	+	2.48325i	−0.0356172	+	0.132925i	0.945828	+	0.324668i	$0.105253\pi$
$350$	8.62784			0.461177
$351$		0			0
$352$	1.82497			0.0972710
$353$	1.64048	−	6.12235i	0.0873139	−	0.325860i	−0.908428	−	0.418040i	$-0.862717\pi$
$353$	1.64048	−	6.12235i	0.0873139	−	0.325860i	0.995742	+	0.0921806i	$0.0293837\pi$
$354$		0			0
$355$	−13.6191	−	7.86302i	−0.722829	−	0.417326i
$356$	0.385644	−	1.43924i	0.0204391	−	0.0762797i
$357$		0			0
$358$	−9.25742	−	9.25742i	−0.489270	−	0.489270i
$359$	−15.0107	+	15.0107i	−0.792236	+	0.792236i	−0.981857	−	0.189622i	$-0.939274\pi$
$359$	−15.0107	+	15.0107i	−0.792236	+	0.792236i	0.189622	+	0.981857i	$0.439274\pi$
$360$		0			0
$361$	28.3574	+	16.3722i	1.49250	+	0.861693i
$362$	9.71779	+	2.60387i	0.510756	+	0.136857i
$363$		0			0
$364$	−7.27713	−	10.2444i	−0.381425	−	0.536955i
$365$	−32.3801	+	18.6946i	−1.69485	+	0.978522i
$366$		0			0
$367$	−8.38757	−	14.5277i	−0.437828	−	0.758340i	0.559694	−	0.828699i	$-0.310919\pi$
$367$	−8.38757	−	14.5277i	−0.437828	−	0.758340i	−0.997522	+	0.0703596i	$0.977585\pi$
$368$	3.18965	+	5.52464i	0.166272	+	0.287992i
$369$		0			0
$370$	11.1982	+	3.00056i	0.582169	+	0.155992i
$371$	9.68458	−	9.68458i	0.502798	−	0.502798i
$372$		0			0
$373$	5.46023	−	9.45739i	0.282720	−	0.489685i	−0.689334	−	0.724444i	$-0.742097\pi$
$373$	5.46023	−	9.45739i	0.282720	−	0.489685i	0.972054	+	0.234759i	$0.0754300\pi$
$374$	−1.53079			−0.0791554
$375$		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	$0.866639\pi$
$380$	17.0327	−	9.83385i	0.873760	−	0.504466i
$381$		0			0
$382$	−18.0575	−	4.83849i	−0.923901	−	0.247559i
$383$	30.9806	−	8.30124i	1.58304	−	0.424173i	0.643172	−	0.765722i	$-0.277618\pi$
$383$	30.9806	−	8.30124i	1.58304	−	0.424173i	0.939864	+	0.341548i	$0.110951\pi$
$384$		0			0
$385$	−16.7976	+	4.50091i	−0.856086	+	0.229387i
$386$	−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	0.0367925	+	0.999323i	$0.488286\pi$
$389$	−16.7063	+	28.9362i	−0.847043	+	1.46712i	−0.883835	+	0.467798i	$0.845047\pi$
$390$		0			0
$391$	−2.67550	−	4.63411i	−0.135306	−	0.234357i
$392$	−3.63917	−	3.63917i	−0.183806	−	0.183806i
$393$		0			0
$394$		−	9.17159i		−	0.462058i
$395$	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	$0.908982\pi$
$398$	3.45864	+	12.9078i	0.173366	+	0.647010i
$399$		0			0
$400$		−	2.47557i		−	0.123778i
$401$	−14.3386	+	14.3386i	−0.716037	+	0.716037i	−0.967791	−	0.251754i	$-0.918993\pi$
$401$	−14.3386	+	14.3386i	−0.716037	+	0.716037i	0.251754	+	0.967791i	$0.418993\pi$
$402$		0			0
$403$	−27.6442	+	2.60732i	−1.37705	+	0.129880i
$404$			0.0847306i			0.00421550i
$405$		0			0
$406$	10.5445	−	18.2635i	0.523313	−	0.906404i
$407$	−7.73818			−0.383567
$408$		0			0
$409$	1.44482	+	5.39214i	0.0714418	+	0.266624i	0.992403	−	0.123030i	$-0.0392611\pi$
$409$	1.44482	+	5.39214i	0.0714418	+	0.266624i	−0.920961	+	0.389654i	$0.872594\pi$
$410$	2.94155	+	10.9780i	0.145273	+	0.542166i
$411$		0			0
$412$	−8.93467			−0.440179
$413$	−12.9773	+	22.4774i	−0.638573	+	1.10604i
$414$		0			0
$415$		−	43.0348i		−	2.11250i
$416$	−2.93942	+	2.08801i	−0.144117	+	0.102373i
$417$		0			0
$418$	−9.28264	+	9.28264i	−0.454029	+	0.454029i
$419$		−	31.3420i		−	1.53116i	−0.643343	−	0.765578i	$-0.722453\pi$
$419$		−	31.3420i		−	1.53116i	0.643343	−	0.765578i	$-0.277547\pi$
$420$		0			0
$421$	−7.11743	−	26.5626i	−0.346882	−	1.29458i	−0.890398	−	0.455183i	$-0.849574\pi$
$421$	−7.11743	−	26.5626i	−0.346882	−	1.29458i	0.543516	−	0.839399i	$-0.317093\pi$
$422$	−3.10041	+	11.5709i	−0.150925	+	0.563261i
$423$		0			0
$424$	−2.77878	−	2.77878i	−0.134949	−	0.134949i
$425$			2.07652i			0.100726i
$426$		0			0
$427$	1.21957	+	1.21957i	0.0590193	+	0.0590193i
$428$	−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	0.451274	−	0.892386i	$-0.350970\pi$
$431$	26.7454	−	7.16641i	1.28828	−	0.345194i	0.837007	+	0.547192i	$0.184303\pi$
$432$		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	$0.606346\pi$
$434$	−25.9254	+	6.94669i	−1.24446	+	0.333452i
$435$		0			0
$436$	13.2298	−	3.54493i	0.633595	−	0.169771i
$437$	−44.3250	−	11.8768i	−2.12035	−	0.568147i
$438$		0			0
$439$	22.7395	−	13.1286i	1.08530	−	0.626596i	0.152976	−	0.988230i	$-0.451114\pi$
$439$	22.7395	−	13.1286i	1.08530	−	0.626596i	0.932320	+	0.361634i	$0.117781\pi$
$440$	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	0.937815	−	0.347136i	$-0.112846\pi$
$443$	23.2806	+	13.4410i	1.10609	+	0.638604i	0.168279	+	0.985739i	$0.446179\pi$
$444$		0			0
$445$	4.07392			0.193122
$446$	0.878410	−	1.52145i	0.0415939	−	0.0720428i
$447$		0			0
$448$	−2.46440	+	2.46440i	−0.116432	+	0.116432i
$449$	−1.60200	−	0.429254i	−0.0756029	−	0.0202577i	0.220819	−	0.975315i	$-0.429127\pi$
$449$	−1.60200	−	0.429254i	−0.0756029	−	0.0202577i	−0.296422	+	0.955057i	$0.595794\pi$
$450$		0			0
$451$	−3.79300	−	6.56968i	−0.178606	−	0.309354i
$452$	−3.97826	−	6.89055i	−0.187122	−	0.324104i
$453$		0			0
$454$	−9.35067	+	5.39861i	−0.438849	+	0.253369i
$455$	21.9058	−	26.4683i	1.02696	−	1.24085i
$456$		0			0
$457$	−35.0473	−	9.39089i	−1.63944	−	0.439287i	−0.682812	−	0.730594i	$-0.739243\pi$
$457$	−35.0473	−	9.39089i	−1.63944	−	0.439287i	−0.956630	+	0.291307i	$0.905910\pi$
$458$	2.05601	+	1.18704i	0.0960711	+	0.0554667i
$459$		0			0
$460$	−12.3333	+	12.3333i	−0.575045	+	0.575045i
$461$	15.6720	+	15.6720i	0.729919	+	0.729919i	0.970603	−	0.240685i	$-0.0773720\pi$
$461$	15.6720	+	15.6720i	0.729919	+	0.729919i	−0.240685	+	0.970603i	$0.577372\pi$
$462$		0			0
$463$	7.73679	−	28.8741i	0.359559	−	1.34189i	−0.515090	−	0.857136i	$-0.672242\pi$
$463$	7.73679	−	28.8741i	0.359559	−	1.34189i	0.874649	−	0.484756i	$-0.161092\pi$
$464$	−5.24032	−	3.02550i	−0.243276	−	0.140455i
$465$		0			0
$466$	−3.84246	+	14.3403i	−0.177999	+	0.664300i
$467$	−36.5666			−1.69210			−0.846051	−	0.533102i	$-0.821026\pi$
$467$	−36.5666			−1.69210			−0.846051	+	0.533102i	$0.821026\pi$
$468$		0			0
$469$	19.2893			0.890699
$470$	−5.46991	+	20.4140i	−0.252308	+	0.941627i
$471$		0			0
$472$	6.44940	+	3.72356i	0.296858	+	0.171391i
$473$	4.07614	−	15.2123i	0.187421	−	0.699465i
$474$		0			0
$475$	12.5919	+	12.5919i	0.577756	+	0.577756i
$476$	2.06716	−	2.06716i	0.0947480	−	0.0947480i
$477$		0			0
$478$	25.5795	+	14.7683i	1.16998	+	0.675487i
$479$	−32.8503	−	8.80222i	−1.50097	−	0.402184i	−0.587545	−	0.809191i	$-0.699906\pi$
$479$	−32.8503	−	8.80222i	−1.50097	−	0.402184i	−0.913425	+	0.407007i	$0.866572\pi$
$480$		0			0
$481$	12.4637	−	8.85355i	0.568294	−	0.403687i
$482$	17.8348	−	10.2969i	0.812355	−	0.469013i
$483$		0			0
$484$	3.83475	+	6.64198i	0.174307	+	0.301908i
$485$	−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	$0.492170\pi$
$488$	0.349930	−	0.349930i	0.0158406	−	0.0158406i
$489$		0			0
$490$	7.03574	−	12.1863i	0.317842	−	0.550519i
$491$	5.53351			0.249724			0.124862	−	0.992174i	$-0.460151\pi$
$491$	5.53351			0.249724			0.124862	+	0.992174i	$0.460151\pi$
$492$		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
$497$	−17.3602	+	10.0229i	−0.778711	+	0.449589i
$498$		0			0
$499$	2.39294	+	0.641188i	0.107123	+	0.0287035i	0.311982	−	0.950088i	$-0.399007\pi$
$499$	2.39294	+	0.641188i	0.107123	+	0.0287035i	−0.204859	+	0.978791i	$0.565674\pi$
$500$	−6.66698	+	1.78641i	−0.298157	+	0.0798908i
$501$		0			0
$502$	19.9204	−	5.33767i	0.889093	−	0.238232i
$503$	32.0788	−	18.5207i	1.43032	−	0.825798i	0.433179	−	0.901308i	$-0.357392\pi$
$503$	32.0788	−	18.5207i	1.43032	−	0.825798i	0.997145	+	0.0755096i	$0.0240583\pi$
$504$		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
$509$	23.6343	+	23.6343i	1.04757	+	1.04757i	0.998810	+	0.0487610i	$0.0155273\pi$
$509$	23.6343	+	23.6343i	1.04757	+	1.04757i	0.0487610	+	0.998810i	$0.484473\pi$
$510$		0			0
$511$			47.6597i			2.10834i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	2.21014	−	8.24837i	0.0974853	−	0.363820i
$515$	−6.32261	−	23.5963i	−0.278608	−	1.03978i
$516$		0			0
$517$		−	14.1064i		−	0.620399i
$518$	10.4495	−	10.4495i	0.459125	−	0.459125i
$519$		0			0
$520$	−7.59449	−	6.28539i	−0.333041	−	0.275632i
$521$		−	6.65944i		−	0.291755i	−0.989303	−	0.145878i	$-0.953399\pi$
$521$		−	6.65944i		−	0.291755i	0.989303	−	0.145878i	$-0.0466006\pi$
$522$		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	$0.158576\pi$
$524$	−4.81077			−0.210159
$525$		0			0
$526$	−0.684615	−	2.55502i	−0.0298506	−	0.111404i
$527$	−1.67191	−	6.23965i	−0.0728296	−	0.271804i
$528$		0			0
$529$	17.6956			0.769373
$530$	5.37231	−	9.30512i	0.233358	−	0.404189i
$531$		0			0
$532$		−	25.0702i		−	1.08693i
$533$	13.6259	+	6.24187i	0.590203	+	0.270365i
$534$		0			0
$535$	27.6134	−	27.6134i	1.19383	−	1.19383i
$536$		−	5.53466i		−	0.239061i
$537$		0			0
$538$	4.46219	+	16.6531i	0.192379	+	0.717967i
$539$	−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	$0.593113\pi$
$542$		−	15.0655i		−	0.647119i
$543$		0			0
$544$	−0.593126	−	0.593126i	−0.0254301	−	0.0254301i
$545$	18.7242	+	32.4313i	0.802056	+	1.38920i
$546$		0			0
$547$	−4.14533	+	7.17992i	−0.177241	+	0.306991i	−0.940935	−	0.338588i	$-0.890051\pi$
$547$	−4.14533	+	7.17992i	−0.177241	+	0.306991i	0.763693	+	0.645579i	$0.223384\pi$
$548$	−7.49077	+	2.00715i	−0.319990	+	0.0857411i
$549$		0			0
$550$	−3.91256	+	2.25892i	−0.166832	+	0.0963205i
$551$	42.0439	−	11.2656i	1.79113	−	0.479932i
$552$		0			0
$553$	6.00824	−	1.60990i	0.255496	−	0.0684600i
$554$	13.2120	+	3.54013i	0.561322	+	0.150406i
$555$		0			0
$556$	−4.18036	+	2.41353i	−0.177287	+	0.102357i
$557$	5.76476	+	21.5144i	0.244261	+	0.911594i	0.973754	+	0.227605i	$0.0730895\pi$
$557$	5.76476	+	21.5144i	0.244261	+	0.911594i	−0.729493	+	0.683989i	$0.760244\pi$
$558$		0			0
$559$	10.8397	+	29.1658i	0.458471	+	1.23358i
$560$	−8.25239	−	4.76452i	−0.348727	−	0.201338i
$561$		0			0
$562$	13.3189			0.561826
$563$	−14.0872	+	24.3998i	−0.593707	+	1.02833i	0.400021	+	0.916506i	$0.369003\pi$
$563$	−14.0872	+	24.3998i	−0.593707	+	1.02833i	−0.993728	+	0.111824i	$0.964331\pi$
$564$		0			0
$565$	15.3826	−	15.3826i	0.647152	−	0.647152i
$566$	−2.45206	−	0.657028i	−0.103068	−	0.0276170i
$567$		0			0
$568$	2.87586	+	4.98113i	0.120668	+	0.209004i
$569$	−14.5939	−	25.2774i	−0.611808	−	1.05968i	−0.990936	−	0.134338i	$-0.957109\pi$
$569$	−14.5939	−	25.2774i	−0.611808	−	1.05968i	0.379128	−	0.925344i	$-0.376224\pi$
$570$		0			0
$571$	−36.5099	+	21.0790i	−1.52789	+	0.882129i	−0.528443	+	0.848969i	$0.677224\pi$
$571$	−36.5099	+	21.0790i	−1.52789	+	0.882129i	−0.999450	+	0.0331604i	$0.989443\pi$
$572$	5.98221	+	2.74038i	0.250129	+	0.114581i
$573$		0			0
$574$	13.9936	+	3.74957i	0.584081	+	0.156504i
$575$	−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	$0.116121\pi$
$578$	−11.5233	−	11.5233i	−0.479306	−	0.479306i
$579$		0			0
$580$	4.28199	−	15.9806i	0.177800	−	0.663559i
$581$	−47.5068	−	27.4280i	−1.97091	−	1.13791i
$582$		0			0
$583$	−1.85618	+	6.92736i	−0.0768752	+	0.286902i
$584$	13.6749			0.565872
$585$		0			0
$586$	−13.9356			−0.575674
$587$	−2.05358	+	7.66407i	−0.0847604	+	0.316330i	−0.995269	−	0.0971607i	$-0.969024\pi$
$587$	−2.05358	+	7.66407i	−0.0847604	+	0.316330i	0.910508	+	0.413491i	$0.135691\pi$
$588$		0			0
$589$	−47.9752	−	27.6985i	−1.97679	−	1.14130i
$590$	−5.26996	+	19.6678i	−0.216961	+	0.809708i
$591$		0			0
$592$	−2.99826	−	2.99826i	−0.123228	−	0.123228i
$593$	23.8412	−	23.8412i	0.979040	−	0.979040i	−0.0207452	−	0.999785i	$-0.506604\pi$
$593$	23.8412	−	23.8412i	0.979040	−	0.979040i	0.999785	+	0.0207452i	$0.00660388\pi$
$594$		0			0
$595$	6.92215	+	3.99651i	0.283781	+	0.163841i
$596$	−12.6085	−	3.37842i	−0.516462	−	0.138386i
$597$		0			0
$598$	2.15979	+	22.8993i	0.0883205	+	0.936422i
$599$	−5.64668	+	3.26011i	−0.230717	+	0.133205i	−0.610903	−	0.791706i	$-0.709193\pi$
$599$	−5.64668	+	3.26011i	−0.230717	+	0.133205i	0.380186	+	0.924910i	$0.375860\pi$
$600$		0			0
$601$	13.7872	+	23.8801i	0.562390	+	0.974088i	0.997287	+	0.0736083i	$0.0234515\pi$
$601$	13.7872	+	23.8801i	0.562390	+	0.974088i	−0.434897	+	0.900480i	$0.643215\pi$
$602$	15.0381	+	26.0468i	0.612909	+	1.06159i
$603$		0			0
$604$	11.0213	+	2.95315i	0.448450	+	0.120162i
$605$	−14.8277	+	14.8277i	−0.602832	+	0.602832i
$606$		0			0
$607$	−2.95810	+	5.12359i	−0.120066	+	0.207960i	−0.919793	−	0.392403i	$-0.871644\pi$
$607$	−2.95810	+	5.12359i	−0.120066	+	0.207960i	0.799728	+	0.600363i	$0.204977\pi$
$608$	−7.19335			−0.291729
$609$		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	$0.812987\pi$
$614$	−8.01466	+	4.62727i	−0.323445	+	0.186741i
$615$		0			0
$616$	6.14363	+	1.64618i	0.247534	+	0.0663266i
$617$	25.2301	−	6.76037i	1.01572	−	0.272162i	0.287705	−	0.957719i	$-0.407108\pi$
$617$	25.2301	−	6.76037i	1.01572	−	0.272162i	0.728019	+	0.685557i	$0.240441\pi$
$618$		0			0
$619$	11.8178	−	3.16658i	0.474999	−	0.127276i	−0.0133740	−	0.999911i	$-0.504257\pi$
$619$	11.8178	−	3.16658i	0.474999	−	0.127276i	0.488373	+	0.872635i	$0.337591\pi$
$620$	−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
$626$	13.1574	+	13.1574i	0.525875	+	0.525875i
$627$		0			0
$628$		−	4.33759i		−	0.173089i
$629$	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	$0.0161528\pi$
$632$	−0.461927	−	1.72393i	−0.0183745	−	0.0685744i
$633$		0			0
$634$			7.47878i			0.297020i
$635$	22.4671	−	22.4671i	0.891580	−	0.891580i
$636$		0			0
$637$	−6.46454	−	17.3937i	−0.256134	−	0.689165i
$638$			11.0429i			0.437192i
$639$		0			0
$640$	−1.36707	+	2.36784i	−0.0540384	+	0.0935972i
$641$	−4.92012			−0.194333			−0.0971666	−	0.995268i	$-0.530978\pi$
$641$	−4.92012			−0.194333			−0.0971666	+	0.995268i	$0.530978\pi$
$642$		0			0
$643$	8.73497	+	32.5993i	0.344473	+	1.28559i	0.893226	+	0.449608i	$0.148436\pi$
$643$	8.73497	+	32.5993i	0.344473	+	1.28559i	−0.548753	+	0.835985i	$0.684897\pi$
$644$	5.75435	+	21.4755i	0.226753	+	0.846255i
$645$		0			0
$646$	6.03383			0.237398
$647$	−2.54755	+	4.41248i	−0.100154	+	0.173473i	−0.911748	−	0.410750i	$-0.865267\pi$
$647$	−2.54755	+	4.41248i	−0.100154	+	0.173473i	0.811594	+	0.584222i	$0.198600\pi$
$648$		0			0
$649$		−	13.5908i		−	0.533484i
$650$	3.71733	−	8.11488i	0.145806	−	0.318292i
$651$		0			0
$652$	−12.9813	+	12.9813i	−0.508388	+	0.508388i
$653$		−	39.5640i		−	1.54826i	−0.633028	−	0.774129i	$-0.718188\pi$
$653$		−	39.5640i		−	1.54826i	0.633028	−	0.774129i	$-0.281812\pi$
$654$		0			0
$655$	−3.40434	−	12.7052i	−0.133019	−	0.496432i
$656$	1.07586	−	4.01515i	0.0420052	−	0.156765i
$657$		0			0
$658$	19.0491	+	19.0491i	0.742609	+	0.742609i
$659$		−	15.2097i		−	0.592484i	−0.955113	−	0.296242i	$-0.904267\pi$
$659$		−	15.2097i		−	0.592484i	0.955113	−	0.296242i	$-0.0957335\pi$
$660$		0			0
$661$	8.36737	+	8.36737i	0.325453	+	0.325453i	0.850854	−	0.525401i	$-0.176085\pi$
$661$	8.36737	+	8.36737i	0.325453	+	0.325453i	−0.525401	+	0.850854i	$0.676085\pi$
$662$	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
$668$	2.35159	−	0.630107i	0.0909858	−	0.0243796i
$669$		0			0
$670$	14.6169	−	3.91660i	0.564702	−	0.151311i
$671$	−0.872359	−	0.233748i	−0.0336770	−	0.00902373i
$672$		0			0
$673$	16.9241	−	9.77114i	0.652376	−	0.376650i	−0.136990	−	0.990572i	$-0.543743\pi$
$673$	16.9241	−	9.77114i	0.652376	−	0.376650i	0.789366	+	0.613923i	$0.210409\pi$
$674$	−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	0.634327	−	0.773065i	$-0.281277\pi$
$677$	7.33732	+	4.23620i	0.281996	+	0.162811i	−0.352331	+	0.935876i	$0.614611\pi$
$678$		0			0
$679$	−60.6166			−2.32625
$680$	1.14671	−	1.98616i	0.0439743	−	0.0761658i
$681$		0			0
$682$	9.93791	−	9.93791i	0.380542	−	0.380542i
$683$	13.4051	+	3.59188i	0.512930	+	0.137439i	0.505995	−	0.862537i	$-0.331126\pi$
$683$	13.4051	+	3.59188i	0.512930	+	0.137439i	0.00693584	+	0.999976i	$0.497792\pi$
$684$		0			0
$685$	−10.6017	−	18.3627i	−0.405070	−	0.701601i
$686$	3.22979	+	5.59416i	0.123314	+	0.213586i
$687$		0			0
$688$	7.47357	−	4.31487i	0.284927	−	0.164503i
$689$	−4.93616	−	13.2814i	−0.188053	−	0.505982i
$690$		0			0
$691$	−4.44039	−	1.18980i	−0.168920	−	0.0452620i	0.173368	−	0.984857i	$-0.444535\pi$
$691$	−4.44039	−	1.18980i	−0.168920	−	0.0452620i	−0.342288	+	0.939595i	$0.611202\pi$
$692$	8.81194	+	5.08757i	0.334980	+	0.193401i
$693$		0			0
$694$	9.95438	−	9.95438i	0.377863	−	0.377863i
$695$	−9.33234	−	9.33234i	−0.353996	−	0.353996i
$696$		0			0
$697$	−0.902436	+	3.36794i	−0.0341822	+	0.127570i
$698$	2.22642	+	1.28542i	0.0842712	+	0.0486540i
$699$		0			0
$700$	2.23305	−	8.33385i	0.0844013	−	0.314990i
$701$	−3.27106			−0.123546			−0.0617731	−	0.998090i	$-0.519676\pi$
$701$	−3.27106			−0.123546			−0.0617731	+	0.998090i	$0.519676\pi$
$702$		0			0
$703$	30.5011			1.15037
$704$	0.472336	−	1.76278i	0.0178018	−	0.0664374i
$705$		0			0
$706$	−5.48915	−	3.16916i	−0.206587	−	0.119273i
$707$	−0.0764298	+	0.285240i	−0.00287444	+	0.0107276i
$708$		0			0
$709$	−13.1692	−	13.1692i	−0.494578	−	0.494578i	0.415167	−	0.909745i	$-0.363723\pi$
$709$	−13.1692	−	13.1692i	−0.494578	−	0.494578i	−0.909745	+	0.415167i	$0.863723\pi$
$710$	−11.1200	+	11.1200i	−0.417326	+	0.417326i
$711$		0			0
$712$	−1.29039	−	0.745007i	−0.0483594	−	0.0279203i
$713$	47.4540	+	12.7152i	1.77716	+	0.476190i
$714$		0			0
$715$	−3.00400	+	17.7382i	−0.112343	+	0.663370i
$716$	−11.3380	+	6.54598i	−0.423720	+	0.244635i
$717$		0			0
$718$	10.6142	+	18.3843i	0.396118	+	0.686096i
$719$	−6.22658	−	10.7848i	−0.232212	−	0.402204i	0.726247	−	0.687434i	$-0.241263\pi$
$719$	−6.22658	−	10.7848i	−0.232212	−	0.402204i	−0.958459	+	0.285231i	$0.907930\pi$
$720$		0			0
$721$	−30.0780	−	8.05937i	−1.12016	−	0.300147i
$722$	23.1537	−	23.1537i	0.861693	−	0.861693i
$723$		0			0
$724$	5.03030	−	8.71273i	0.186950	−	0.323806i
$725$	14.9797			0.556331
$726$		0			0
$727$	−0.202128	−	0.116699i	−0.00749650	−	0.00432811i	0.496247	−	0.868181i	$-0.334711\pi$
$727$	−0.202128	−	0.116699i	−0.00749650	−	0.00432811i	−0.503744	+	0.863853i	$0.668044\pi$
$728$	−11.7788	+	4.37771i	−0.436553	+	0.162249i
$729$		0			0
$730$	9.67706	+	36.1153i	0.358164	+	1.33669i
$731$	−6.26888	+	3.61934i	−0.231863	+	0.133866i
$732$		0			0
$733$	27.3080	+	7.31715i	1.00864	+	0.270265i	0.725062	−	0.688684i	$-0.241811\pi$
$733$	27.3080	+	7.31715i	1.00864	+	0.270265i	0.283580	+	0.958948i	$0.408478\pi$
$734$	−16.2035	+	4.34173i	−0.598084	+	0.160256i
$735$		0			0
$736$	6.16194	−	1.65109i	0.227132	−	0.0608599i
$737$	−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
$743$	18.5235	+	18.5235i	0.679560	+	0.679560i	0.959901	−	0.280340i	$-0.0904473\pi$
$743$	18.5235	+	18.5235i	0.679560	+	0.679560i	−0.280340	+	0.959901i	$0.590447\pi$
$744$		0			0
$745$		−	35.6895i		−	1.30756i
$746$	−7.72193	−	7.72193i	−0.282720	−	0.282720i
$747$		0			0
$748$	−0.396198	+	1.47863i	−0.0144865	+	0.0540642i
$749$	−12.8835	−	48.0820i	−0.470754	−	1.75688i
$750$		0			0
$751$			29.2381i			1.06691i	0.845827	+	0.533457i	$0.179108\pi$
$751$			29.2381i			1.06691i	−0.845827	+	0.533457i	$0.820892\pi$
$752$	5.46571	−	5.46571i	0.199314	−	0.199314i
$753$		0			0
$754$	−12.6346	−	17.7865i	−0.460124	−	0.647744i
$755$			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	$0.160187\pi$
$758$	6.09421			0.221352
$759$		0			0
$760$	−5.09038	−	18.9975i	−0.184647	−	0.689113i
$761$	−3.20044	−	11.9442i	−0.116016	−	0.432977i	0.883345	−	0.468723i	$-0.155286\pi$
$761$	−3.20044	−	11.9442i	−0.116016	−	0.432977i	−0.999361	+	0.0357464i	$0.988619\pi$
$762$		0			0
$763$	47.7351			1.72813
$764$	−9.34724	+	16.1899i	−0.338171	+	0.585730i
$765$		0			0
$766$		−	32.0735i		−	1.15886i
$767$	15.5497	+	21.8902i	0.561467	+	0.790411i
$768$		0			0
$769$	15.5698	−	15.5698i	0.561462	−	0.561462i	−0.368261	−	0.929723i	$-0.620047\pi$
$769$	15.5698	−	15.5698i	0.561462	−	0.561462i	0.929723	+	0.368261i	$0.120047\pi$
$770$			17.3902i			0.626698i
$771$		0			0
$772$	1.33858	+	4.99566i	0.0481766	+	0.179798i
$773$	4.66222	−	17.3997i	0.167689	−	0.625822i	−0.829993	−	0.557773i	$-0.811656\pi$
$773$	4.66222	−	17.3997i	0.167689	−	0.625822i	0.997682	−	0.0680490i	$-0.0216774\pi$
$774$		0			0
$775$	−13.4808	−	13.4808i	−0.484244	−	0.484244i
$776$			17.3926i			0.624358i
$777$		0			0
$778$	23.6263	+	23.6263i	0.847043	+	0.847043i
$779$	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
$785$	11.4555	−	3.06949i	0.408865	−	0.109555i
$786$		0			0
$787$	35.9348	−	9.62869i	1.28094	−	0.343226i	0.446725	−	0.894671i	$-0.352590\pi$
$787$	35.9348	−	9.62869i	1.28094	−	0.343226i	0.834211	+	0.551446i	$0.185924\pi$
$788$	−8.85907	−	2.37378i	−0.315591	−	0.0845625i
$789$		0			0
$790$	4.22600	−	2.43988i	0.150354	−	0.0868071i
$791$	−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
$796$	13.3632			0.473644
$797$	7.46000	−	12.9211i	0.264247	−	0.457689i	−0.703119	−	0.711072i	$-0.748210\pi$
$797$	7.46000	−	12.9211i	0.264247	−	0.457689i	0.967366	+	0.253383i	$0.0815433\pi$
$798$		0			0
$799$	−4.58467	+	4.58467i	−0.162194	+	0.162194i
$800$	−2.39122	−	0.640725i	−0.0845423	−	0.0226530i
$801$		0			0
$802$	10.1389	+	17.5612i	0.358019	+	0.620106i
$803$	−12.4781	−	21.6128i	−0.440344	−	0.762698i
$804$		0			0
$805$	−52.6445	+	30.3943i	−1.85548	+	1.07126i
$806$	−4.63636	+	27.3770i	−0.163309	+	0.964315i
$807$		0			0
$808$	0.0818434	+	0.0219299i	0.00287924	+	0.000771491i
$809$	42.8291	+	24.7274i	1.50579	+	0.869368i	0.999977	+	0.00672439i	$0.00214046\pi$
$809$	42.8291	+	24.7274i	1.50579	+	0.869368i	0.505812	+	0.862644i	$0.331193\pi$
$810$		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	$0.0672178\pi$
$812$	−14.9121	−	14.9121i	−0.523313	−	0.523313i
$813$		0			0
$814$	−2.00279	+	7.47451i	−0.0701977	+	0.261981i
$815$	−43.4697	−	25.0972i	−1.52268	−	0.879118i
$816$		0			0
$817$	−16.0666	+	59.9615i	−0.562101	+	2.09779i
$818$	5.58236			0.195183
$819$		0			0
$820$	11.3653			0.396893
$821$	−3.90063	+	14.5574i	−0.136133	+	0.508055i	0.863858	+	0.503736i	$0.168042\pi$
$821$	−3.90063	+	14.5574i	−0.136133	+	0.508055i	−0.999991	+	0.00431939i	$0.998625\pi$
$822$		0			0
$823$	45.9939	+	26.5546i	1.60325	+	0.925635i	0.990832	+	0.135097i	$0.0431346\pi$
$823$	45.9939	+	26.5546i	1.60325	+	0.925635i	0.612414	+	0.790537i	$0.290199\pi$
$824$	−2.31246	+	8.63023i	−0.0805584	+	0.300648i
$825$		0			0
$826$	18.3527	+	18.3527i	0.638573	+	0.638573i
$827$	7.98942	−	7.98942i	0.277819	−	0.277819i	−0.554419	−	0.832238i	$-0.687059\pi$
$827$	7.98942	−	7.98942i	0.277819	−	0.277819i	0.832238	+	0.554419i	$0.187059\pi$
$828$		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	$0.870005\pi$
$830$	−41.5685	−	11.1382i	−1.44286	−	0.386614i
$831$		0			0
$832$	1.25609	+	3.37968i	0.0435470	+	0.117169i
$833$	3.73861	−	2.15849i	0.129535	−	0.0747871i
$834$		0			0
$835$	3.32821	+	5.76462i	0.115177	+	0.199493i
$836$	6.56381	+	11.3689i	0.227014	+	0.393200i
$837$		0			0
$838$	−30.2740	−	8.11190i	−1.04580	−	0.280221i
$839$	−27.7133	+	27.7133i	−0.956769	+	0.956769i	−0.999104	−	0.0423341i	$-0.986521\pi$
$839$	−27.7133	+	27.7133i	−0.956769	+	0.956769i	0.0423341	+	0.999104i	$0.486521\pi$
$840$		0			0
$841$	3.80732	−	6.59448i	0.131287	−	0.227396i
$842$	−27.4996			−0.947700
$843$		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
$848$	−3.40330	+	1.96489i	−0.116870	+	0.0674747i
$849$		0			0
$850$	2.00577	+	0.537444i	0.0687973	+	0.0184342i
$851$	−26.1277	+	7.00090i	−0.895646	+	0.239988i
$852$		0			0
$853$	−20.9221	+	5.60605i	−0.716358	+	0.191948i	−0.598546	−	0.801088i	$-0.704255\pi$
$853$	−20.9221	+	5.60605i	−0.716358	+	0.191948i	−0.117812	+	0.993036i	$0.537588\pi$
$854$	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	$-0.710313\pi$
$857$	11.0344	−	19.1122i	0.376930	−	0.652861i	0.990614	+	0.136690i	$0.0436465\pi$
$858$		0			0
$859$	−15.1793	−	26.2913i	−0.517911	−	0.897048i	−0.999784	−	0.0208071i	$-0.993376\pi$
$859$	−15.1793	−	26.2913i	−0.517911	−	0.897048i	0.481872	−	0.876241i	$-0.339957\pi$
$860$	16.6842	+	16.6842i	0.568926	+	0.568926i
$861$		0			0
$862$		−	27.6889i		−	0.943087i
$863$	10.7391	+	10.7391i	0.365563	+	0.365563i	0.865856	−	0.500293i	$-0.166775\pi$
$863$	10.7391	+	10.7391i	0.365563	+	0.365563i	−0.500293	+	0.865856i	$0.666775\pi$
$864$		0			0
$865$	−7.20044	+	26.8724i	−0.244822	+	0.913689i
$866$	8.14676	+	30.4041i	0.276838	+	1.03317i
$867$		0			0
$868$			26.8400i			0.911007i
$869$	−2.30312	+	2.30312i	−0.0781280	+	0.0781280i
$870$		0			0
$871$	8.31088	−	18.1425i	0.281603	−	0.614736i
$872$		−	13.6965i		−	0.463823i
$873$		0			0
$874$	−22.9443	+	39.7407i	−0.776103	+	1.34425i
$875$	−24.0554			−0.813220
$876$		0			0
$877$	8.37899	+	31.2708i	0.282938	+	1.05594i	0.950333	+	0.311236i	$0.100743\pi$
$877$	8.37899	+	31.2708i	0.282938	+	1.05594i	−0.667394	+	0.744705i	$0.732590\pi$
$878$	−6.79588	−	25.3626i	−0.229350	−	0.855946i
$879$		0			0
$880$	4.98973			0.168204
$881$	−2.90596	+	5.03326i	−0.0979041	+	0.169575i	−0.910817	−	0.412810i	$-0.864547\pi$
$881$	−2.90596	+	5.03326i	−0.0979041	+	0.169575i	0.812913	+	0.582385i	$0.197881\pi$
$882$		0			0
$883$			10.3443i			0.348115i	0.984735	+	0.174058i	$0.0556879\pi$
$883$			10.3443i			0.348115i	−0.984735	+	0.174058i	$0.944312\pi$
$884$	−1.05361	−	2.83490i	−0.0354369	−	0.0953479i
$885$		0			0
$886$	19.0085	−	19.0085i	0.638604	−	0.638604i
$887$		−	14.8439i		−	0.498411i	−0.968451	−	0.249205i	$-0.919831\pi$
$887$		−	14.8439i		−	0.498411i	0.968451	−	0.249205i	$-0.0801694\pi$
$888$		0			0
$889$	−10.4824	−	39.1210i	−0.351570	−	1.31208i
$890$	1.05441	−	3.93511i	0.0353438	−	0.131905i
$891$		0			0
$892$	−1.24226	−	1.24226i	−0.0415939	−	0.0415939i
$893$			55.6023i			1.86066i
$894$		0			0
$895$	−25.3112	−	25.3112i	−0.846059	−	0.846059i
$896$	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
$902$	−7.32752	+	1.96340i	−0.243980	+	0.0653742i
$903$		0			0
$904$	−7.68541	+	2.05930i	−0.255613	+	0.0684913i
$905$	26.5699	+	7.11938i	0.883213	+	0.236656i
$906$		0			0
$907$	−4.98924	+	2.88054i	−0.165665	+	0.0956467i	−0.580540	−	0.814232i	$-0.697159\pi$
$907$	−4.98924	+	2.88054i	−0.165665	+	0.0956467i	0.414875	+	0.909878i	$0.363825\pi$
$908$	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	0.879361	−	0.476155i	$-0.157970\pi$
$911$	27.3661	+	15.7998i	0.906680	+	0.523472i	0.0273186	+	0.999627i	$0.491303\pi$
$912$		0			0
$913$	28.7245			0.950643
$914$	−18.1418	+	31.4225i	−0.600077	+	1.03936i
$915$		0			0
$916$	1.67873	−	1.67873i	0.0554667	−	0.0554667i
$917$	−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	$0.799693\pi$
$920$	8.72099	+	15.1052i	0.287522	+	0.498004i
$921$		0			0
$922$	19.1942	−	11.0818i	0.632128	−	0.364959i
$923$	1.94731	+	20.6465i	0.0640966	+	0.679587i
$924$		0			0
$925$	10.1392	+	2.71679i	0.333374	+	0.0893273i
$926$	−25.8878	−	14.9463i	−0.850726	−	0.491167i
$927$		0			0
$928$	−4.27871	+	4.27871i	−0.140455	+	0.140455i
$929$	11.5077	+	11.5077i	0.377556	+	0.377556i	0.870220	−	0.492664i	$-0.163977\pi$
$929$	11.5077	+	11.5077i	0.377556	+	0.377556i	−0.492664	+	0.870220i	$0.663977\pi$
$930$		0			0
$931$	9.58175	−	35.7596i	0.314029	−	1.17197i
$932$	12.8571	+	7.42307i	0.421149	+	0.243151i
$933$		0			0
$934$	−9.46414	+	35.3206i	−0.309676	+	1.15573i
$935$	−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	$0.137811\pi$
$938$	4.99245	−	18.6321i	0.163009	−	0.608359i
$939$		0			0
$940$	18.3027	+	10.5671i	0.596967	+	0.344659i
$941$	7.74269	−	28.8961i	0.252404	−	0.941986i	−0.717112	−	0.696958i	$-0.754536\pi$
$941$	7.74269	−	28.8961i	0.252404	−	0.941986i	0.969516	−	0.245028i	$-0.0787970\pi$
$942$		0			0
$943$	−18.7507	−	18.7507i	−0.610606	−	0.610606i
$944$	5.26591	−	5.26591i	0.171391	−	0.171391i
$945$		0			0
$946$	−13.6390	−	7.87449i	−0.443443	−	0.256022i
$947$	−1.42283	−	0.381246i	−0.0462357	−	0.0123888i	0.235627	−	0.971844i	$-0.424286\pi$
$947$	−1.42283	−	0.381246i	−0.0462357	−	0.0123888i	−0.281863	+	0.959455i	$0.590952\pi$
$948$		0			0
$949$	44.8262	+	20.5344i	1.45512	+	0.666573i
$950$	15.4219	−	8.90382i	0.500352	−	0.288878i
$951$		0			0
$952$	−1.46170	−	2.53174i	−0.0473740	−	0.0820542i
$953$	12.8169	+	22.1996i	0.415181	+	0.719114i	0.995447	−	0.0953124i	$-0.0303850\pi$
$953$	12.8169	+	22.1996i	0.415181	+	0.719114i	−0.580267	+	0.814427i	$0.697052\pi$
$954$		0			0
$955$	−49.3719	−	13.2291i	−1.59764	−	0.428085i
$956$	20.8856	−	20.8856i	0.675487	−	0.675487i
$957$		0			0
$958$	−17.0046	+	29.4528i	−0.549393	+	0.951577i
$959$	−27.0277			−0.872771
$960$		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
$965$	−12.2462	+	7.07035i	−0.394219	+	0.227603i
$966$		0			0
$967$	−0.179048	−	0.0479759i	−0.00575781	−	0.00154280i	0.255939	−	0.966693i	$-0.417615\pi$
$967$	−0.179048	−	0.0479759i	−0.00575781	−	0.00154280i	−0.261697	+	0.965150i	$0.584282\pi$
$968$	7.40817	−	1.98501i	0.238107	−	0.0638007i
$969$		0			0
$970$	−45.9336	+	12.3079i	−1.47484	+	0.395182i
$971$	−16.6170	+	9.59381i	−0.533264	+	0.307880i	−0.742344	−	0.670018i	$-0.766286\pi$
$971$	−16.6170	+	9.59381i	−0.533264	+	0.307880i	0.209081	+	0.977898i	$0.432953\pi$
$972$		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
$977$	−37.3613	−	37.3613i	−1.19529	−	1.19529i	−0.975560	−	0.219733i	$-0.929481\pi$
$977$	−37.3613	−	37.3613i	−1.19529	−	1.19529i	−0.219733	−	0.975560i	$-0.570519\pi$
$978$		0			0
$979$			2.71923i			0.0869068i
$980$	−9.95003	−	9.95003i	−0.317842	−	0.317842i
$981$		0			0
$982$	1.43218	−	5.34496i	0.0457027	−	0.170565i
$983$	−2.75711	−	10.2897i	−0.0879382	−	0.328190i	0.907916	−	0.419152i	$-0.137673\pi$
$983$	−2.75711	−	10.2897i	−0.0879382	−	0.328190i	−0.995854	+	0.0909619i	$0.971006\pi$
$984$		0			0
$985$		−	25.0765i		−	0.799003i
$986$	3.58901	−	3.58901i	0.114297	−	0.114297i
$987$		0			0
$988$	−23.5797	−	10.8016i	−0.750170	−	0.343644i
$989$		−	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	$0.296759\pi$
$992$	7.70114			0.244511
$993$		0			0
$994$	5.18824	+	19.3628i	0.164561	+	0.614150i
$995$	9.45643	+	35.2919i	0.299789	+	1.11883i
$996$		0			0
$997$	−19.2289			−0.608984			−0.304492	−	0.952515i	$-0.598487\pi$
$997$	−19.2289			−0.608984			−0.304492	+	0.952515i	$0.598487\pi$
$998$	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.bc.a.305.13		56
3.2	odd	2		234.2.z.a.227.3	yes	56
9.4	even	3		234.2.y.a.149.14	yes	56
9.5	odd	6		702.2.bb.a.71.6		56
13.11	odd	12		702.2.bb.a.89.6		56
39.11	even	12		234.2.y.a.11.14	✓	56
117.50	even	12	inner	702.2.bc.a.557.13		56
117.76	odd	12		234.2.z.a.167.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.14	✓	56	39.11	even	12
234.2.y.a.149.14	yes	56	9.4	even	3
234.2.z.a.167.3	yes	56	117.76	odd	12
234.2.z.a.227.3	yes	56	3.2	odd	2
702.2.bb.a.71.6		56	9.5	odd	6
702.2.bb.a.89.6		56	13.11	odd	12
702.2.bc.a.305.13		56	1.1	even	1	trivial
702.2.bc.a.557.13		56	117.50	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707650 - 2.64098i) q^{5} +(-2.46440 - 2.46440i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707650 - 2.64098i) q^{5} +(-2.46440 - 2.46440i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.36784 - 1.36707i) q^{10} +(1.76278 + 0.472336i) q^{11} +(-3.37968 + 1.25609i) q^{13} +(-3.01826 + 1.74260i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.419403 - 0.726428i) q^{17} +(-6.94825 - 1.86178i) q^{19} +(-1.93334 + 1.93334i) q^{20} +(0.912483 - 1.58047i) q^{22} +6.37931 q^{23} +(-2.14391 - 1.23778i) q^{25} +(0.338562 + 3.58962i) q^{26} +(0.902034 + 3.36644i) q^{28} +(-5.24032 + 3.02550i) q^{29} +(7.43873 + 1.99320i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.810225 + 0.217099i) q^{34} +(-8.25239 + 4.76452i) q^{35} +(-4.09570 + 1.09744i) q^{37} +(-3.59668 + 6.22963i) q^{38} +(1.36707 + 2.36784i) q^{40} +(-2.93930 - 2.93930i) q^{41} -8.62974i q^{43} +(-1.29045 - 1.29045i) q^{44} +(1.65109 - 6.16194i) q^{46} +(-2.00059 - 7.46630i) q^{47} +5.14656i q^{49} +(-1.75049 + 1.75049i) q^{50} +(3.55493 + 0.602036i) q^{52} +3.92979i q^{53} +(2.49486 - 4.32123i) q^{55} +3.48519 q^{56} +(1.56612 + 5.84482i) q^{58} +(-1.92746 - 7.19337i) q^{59} -0.494876 q^{61} +(3.85057 - 6.66938i) q^{62} -1.00000i q^{64} +(0.925680 + 9.81456i) q^{65} +(-3.91359 + 3.91359i) q^{67} +0.838806i q^{68} +(2.46630 + 9.20434i) q^{70} +(1.48865 - 5.55573i) q^{71} +(-9.66963 - 9.66963i) q^{73} +4.24018i q^{74} +(5.08647 + 5.08647i) q^{76} +(-3.18018 - 5.50823i) q^{77} +(-0.892374 + 1.54564i) q^{79} +(2.64098 - 0.707650i) q^{80} +(-3.59989 + 2.07840i) q^{82} +(15.2034 - 4.07375i) q^{83} +(-2.21527 + 0.593581i) q^{85} +(-8.33569 - 2.23354i) q^{86} +(-1.58047 + 0.912483i) q^{88} +(0.385644 + 1.43924i) q^{89} +(11.4244 + 5.23339i) q^{91} +(-5.52464 - 3.18965i) q^{92} -7.72968 q^{94} +(-9.83385 + 17.0327i) q^{95} +(12.2984 - 12.2984i) q^{97} +(4.97120 + 1.33203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73} + 4 q^{76} - 24 q^{77} - 24 q^{79} + 96 q^{83} - 72 q^{85} + 4 q^{91} + 24 q^{92} - 52 q^{97} - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more