LMFDB - Embedded newform 700.2.t.c.299.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(199,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("700.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.15
Character	$\chi$	$=$	700.299
Dual form			700.2.t.c.199.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35728 - 0.397222i) q^{2} +(0.963833 - 0.556469i) q^{3} +(1.68443 - 1.07828i) q^{4} +(1.08715 - 1.13814i) q^{6} +(1.26433 + 2.32410i) q^{7} +(1.85793 - 2.13263i) q^{8} +(-0.880685 + 1.52539i) q^{9} +(1.48417 - 0.856885i) q^{11} +(1.02348 - 1.97662i) q^{12} +2.45950 q^{13} +(2.63924 + 2.65224i) q^{14} +(1.67460 - 3.63259i) q^{16} +(-3.10946 - 5.38574i) q^{17} +(-0.589419 + 2.42021i) q^{18} +(0.108256 - 0.187505i) q^{19} +(2.51190 + 1.53648i) q^{21} +(1.67406 - 1.75258i) q^{22} +(-3.28328 + 5.68681i) q^{23} +(0.603989 - 3.08938i) q^{24} +(3.33823 - 0.976966i) q^{26} +5.29911i q^{27} +(4.63573 + 2.55148i) q^{28} +2.47123 q^{29} +(0.0819131 + 0.141878i) q^{31} +(0.829966 - 5.59564i) q^{32} +(0.953659 - 1.65179i) q^{33} +(-6.35975 - 6.07482i) q^{34} +(0.161354 + 3.51904i) q^{36} +(-6.66562 - 3.84840i) q^{37} +(0.0724531 - 0.297500i) q^{38} +(2.37054 - 1.36863i) q^{39} -8.34130i q^{41} +(4.01968 + 1.08766i) q^{42} +1.89449 q^{43} +(1.57601 - 3.04372i) q^{44} +(-2.19741 + 9.02280i) q^{46} +(-10.1364 - 5.85225i) q^{47} +(-0.407385 - 4.43307i) q^{48} +(-3.80292 + 5.87689i) q^{49} +(-5.99399 - 3.46063i) q^{51} +(4.14285 - 2.65204i) q^{52} +(-11.2823 + 6.51382i) q^{53} +(2.10492 + 7.19238i) q^{54} +(7.30549 + 1.62166i) q^{56} -0.240965i q^{57} +(3.35416 - 0.981628i) q^{58} +(2.14379 + 3.71315i) q^{59} +(6.06251 + 3.50019i) q^{61} +(0.167536 + 0.160030i) q^{62} +(-4.65865 - 0.118198i) q^{63} +(-1.09621 - 7.92454i) q^{64} +(0.638259 - 2.62076i) q^{66} +(2.58708 + 4.48095i) q^{67} +(-11.0450 - 5.71902i) q^{68} +7.30818i q^{69} +5.04201i q^{71} +(1.61684 + 4.71224i) q^{72} +(-3.80759 - 6.59493i) q^{73} +(-10.5758 - 2.57563i) q^{74} +(-0.0198341 - 0.432571i) q^{76} +(3.86797 + 2.36597i) q^{77} +(2.67384 - 2.79925i) q^{78} +(13.8125 + 7.97463i) q^{79} +(0.306736 + 0.531282i) q^{81} +(-3.31335 - 11.3215i) q^{82} -5.47827i q^{83} +(5.88788 - 0.120443i) q^{84} +(2.57136 - 0.752534i) q^{86} +(2.38185 - 1.37516i) q^{87} +(0.930059 - 4.75721i) q^{88} +(1.54471 + 0.891838i) q^{89} +(3.10963 + 5.71612i) q^{91} +(0.601545 + 13.1193i) q^{92} +(0.157901 + 0.0911642i) q^{93} +(-16.0826 - 3.91676i) q^{94} +(-2.31385 - 5.85511i) q^{96} -10.5305 q^{97} +(-2.82720 + 9.48720i) q^{98} +3.01858i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100}) $ 32 * q + 2 * q^4 + 16 * q^9 - 14 * q^12 - 8 * q^13 - 2 * q^14 - 14 * q^16 + 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 + 32 * q^28 + 40 * q^29 + 60 * q^32 - 24 * q^33 + 60 * q^36 - 60 * q^37 - 46 * q^38 + 78 * q^42 + 18 * q^44 + 2 * q^46 - 28 * q^48 + 16 * q^49 - 46 * q^52 - 12 * q^53 - 12 * q^54 - 4 * q^56 + 42 * q^58 + 24 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 - 4 * q^68 + 90 * q^72 - 24 * q^73 - 38 * q^74 + 20 * q^77 - 36 * q^81 + 8 * q^82 + 20 * q^84 + 28 * q^86 - 78 * q^88 + 60 * q^89 + 72 * q^93 - 18 * q^94 - 60 * q^96 - 48 * q^97 - 124 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.35728	−	0.397222i	0.959743	−	0.280878i
$2$	1.35728	−	0.397222i	0.959743	−	0.280878i
$3$	0.963833	−	0.556469i	0.556469	−	0.321278i	−0.195258	−	0.980752i	$-0.562554\pi$
$3$	0.963833	−	0.556469i	0.556469	−	0.321278i	0.751727	+	0.659474i	$0.229221\pi$
$4$	1.68443	−	1.07828i	0.842215	−	0.539142i
$5$		0			0
$5$		0			0
$6$	1.08715	−	1.13814i	0.443827	−	0.464644i
$7$	1.26433	+	2.32410i	0.477874	+	0.878429i
$7$	1.26433	+	2.32410i	0.477874	+	0.878429i
$8$	1.85793	−	2.13263i	0.656876	−	0.753998i
$9$	−0.880685	+	1.52539i	−0.293562	+	0.508463i
$10$		0			0
$11$	1.48417	−	0.856885i	0.447493	−	0.258360i	−0.259278	−	0.965803i	$-0.583484\pi$
$11$	1.48417	−	0.856885i	0.447493	−	0.258360i	0.706771	+	0.707442i	$0.250151\pi$
$12$	1.02348	−	1.97662i	0.295452	−	0.570601i
$13$	2.45950			0.682142			0.341071	−	0.940038i	$-0.389210\pi$
$13$	2.45950			0.682142			0.341071	+	0.940038i	$0.389210\pi$
$14$	2.63924	+	2.65224i	0.705368	+	0.708842i
$15$		0			0
$16$	1.67460	−	3.63259i	0.418651	−	0.908147i
$17$	−3.10946	−	5.38574i	−0.754155	−	1.30623i	−0.945794	−	0.324768i	$-0.894714\pi$
$17$	−3.10946	−	5.38574i	−0.754155	−	1.30623i	0.191639	−	0.981465i	$-0.438620\pi$
$18$	−0.589419	+	2.42021i	−0.138927	+	0.570450i
$19$	0.108256	−	0.187505i	0.0248357	−	0.0430167i	−0.853340	−	0.521354i	$-0.825427\pi$
$19$	0.108256	−	0.187505i	0.0248357	−	0.0430167i	0.878176	+	0.478337i	$0.158760\pi$
$20$		0			0
$21$	2.51190	+	1.53648i	0.548141	+	0.335288i
$22$	1.67406	−	1.75258i	0.356911	−	0.373651i
$23$	−3.28328	+	5.68681i	−0.684612	+	1.18578i	0.288947	+	0.957345i	$0.406695\pi$
$23$	−3.28328	+	5.68681i	−0.684612	+	1.18578i	−0.973559	+	0.228437i	$0.926638\pi$
$24$	0.603989	−	3.08938i	0.123289	−	0.630616i
$25$		0			0
$26$	3.33823	−	0.976966i	0.654681	−	0.191599i
$27$			5.29911i			1.01981i
$28$	4.63573	+	2.55148i	0.876070	+	0.482184i
$29$	2.47123			0.458896			0.229448	−	0.973321i	$-0.426308\pi$
$29$	2.47123			0.458896			0.229448	+	0.973321i	$0.426308\pi$
$30$		0			0
$31$	0.0819131	+	0.141878i	0.0147120	+	0.0254820i	0.873288	−	0.487205i	$-0.161984\pi$
$31$	0.0819131	+	0.141878i	0.0147120	+	0.0254820i	−0.858576	+	0.512687i	$0.828650\pi$
$32$	0.829966	−	5.59564i	0.146719	−	0.989178i
$33$	0.953659	−	1.65179i	0.166011	−	0.287539i
$34$	−6.35975	−	6.07482i	−1.09069	−	1.04182i
$35$		0			0
$36$	0.161354	+	3.51904i	0.0268924	+	0.586507i
$37$	−6.66562	−	3.84840i	−1.09582	−	0.632673i	−0.160701	−	0.987003i	$-0.551375\pi$
$37$	−6.66562	−	3.84840i	−1.09582	−	0.632673i	−0.935120	+	0.354331i	$0.884709\pi$
$38$	0.0724531	−	0.297500i	0.0117534	−	0.0482608i
$39$	2.37054	−	1.36863i	0.379591	−	0.219157i
$40$		0			0
$41$		−	8.34130i		−	1.30269i	−0.758781	−	0.651346i	$-0.774205\pi$
$41$		−	8.34130i		−	1.30269i	0.758781	−	0.651346i	$-0.225795\pi$
$42$	4.01968	+	1.08766i	0.620250	+	0.167830i
$43$	1.89449			0.288907			0.144454	−	0.989512i	$-0.453858\pi$
$43$	1.89449			0.288907			0.144454	+	0.989512i	$0.453858\pi$
$44$	1.57601	−	3.04372i	0.237592	−	0.458858i
$45$		0			0
$46$	−2.19741	+	9.02280i	−0.323991	+	1.33034i
$47$	−10.1364	−	5.85225i	−1.47855	−	0.853639i	−0.478840	−	0.877902i	$-0.658943\pi$
$47$	−10.1364	−	5.85225i	−1.47855	−	0.853639i	−0.999706	+	0.0242630i	$0.992276\pi$
$48$	−0.407385	−	4.43307i	−0.0588010	−	0.639859i
$49$	−3.80292	+	5.87689i	−0.543274	+	0.839556i
$50$		0			0
$51$	−5.99399	−	3.46063i	−0.839327	−	0.484586i
$52$	4.14285	−	2.65204i	0.574510	−	0.367771i
$53$	−11.2823	+	6.51382i	−1.54974	+	0.894743i	−0.551579	+	0.834123i	$0.685974\pi$
$53$	−11.2823	+	6.51382i	−1.54974	+	0.894743i	−0.998161	+	0.0606196i	$0.980692\pi$
$54$	2.10492	+	7.19238i	0.286444	+	0.978760i
$55$		0			0
$56$	7.30549	+	1.62166i	0.976238	+	0.216703i
$57$		−	0.240965i		−	0.0319166i
$58$	3.35416	−	0.981628i	0.440423	−	0.128894i
$59$	2.14379	+	3.71315i	0.279098	+	0.483411i	0.971161	−	0.238426i	$-0.0766313\pi$
$59$	2.14379	+	3.71315i	0.279098	+	0.483411i	−0.692063	+	0.721837i	$0.743298\pi$
$60$		0			0
$61$	6.06251	+	3.50019i	0.776225	+	0.448154i	0.835091	−	0.550112i	$-0.185415\pi$
$61$	6.06251	+	3.50019i	0.776225	+	0.448154i	−0.0588657	+	0.998266i	$0.518748\pi$
$62$	0.167536	+	0.160030i	0.0212771	+	0.0203239i
$63$	−4.65865	−	0.118198i	−0.586934	−	0.0148916i
$64$	−1.09621	−	7.92454i	−0.137027	−	0.990567i
$65$		0			0
$66$	0.638259	−	2.62076i	0.0785642	−	0.322593i
$67$	2.58708	+	4.48095i	0.316062	+	0.547435i	0.979663	−	0.200652i	$-0.0643060\pi$
$67$	2.58708	+	4.48095i	0.316062	+	0.547435i	−0.663601	+	0.748087i	$0.730973\pi$
$68$	−11.0450	−	5.71902i	−1.33941	−	0.693533i
$69$			7.30818i			0.879801i
$70$		0			0
$71$			5.04201i			0.598376i	0.954194	+	0.299188i	$0.0967158\pi$
$71$			5.04201i			0.598376i	−0.954194	+	0.299188i	$0.903284\pi$
$72$	1.61684	+	4.71224i	0.190547	+	0.555343i
$73$	−3.80759	−	6.59493i	−0.445644	−	0.771878i	0.552453	−	0.833544i	$-0.313692\pi$
$73$	−3.80759	−	6.59493i	−0.445644	−	0.771878i	−0.998097	+	0.0616659i	$0.980359\pi$
$74$	−10.5758	−	2.57563i	−1.22941	−	0.299411i
$75$		0			0
$76$	−0.0198341	−	0.432571i	−0.00227513	−	0.0496193i
$77$	3.86797	+	2.36597i	0.440797	+	0.269627i
$78$	2.67384	−	2.79925i	0.302753	−	0.316953i
$79$	13.8125	+	7.97463i	1.55402	+	0.897216i	0.997808	+	0.0661781i	$0.0210805\pi$
$79$	13.8125	+	7.97463i	1.55402	+	0.897216i	0.556216	+	0.831038i	$0.312253\pi$
$80$		0			0
$81$	0.306736	+	0.531282i	0.0340817	+	0.0590313i
$82$	−3.31335	−	11.3215i	−0.365898	−	1.25025i
$83$		−	5.47827i		−	0.601318i	−0.953732	−	0.300659i	$-0.902793\pi$
$83$		−	5.47827i		−	0.601318i	0.953732	−	0.300659i	$-0.0972066\pi$
$84$	5.88788	−	0.120443i	0.642421	−	0.0131414i
$85$		0			0
$86$	2.57136	−	0.752534i	0.277277	−	0.0811479i
$87$	2.38185	−	1.37516i	0.255362	−	0.147433i
$88$	0.930059	−	4.75721i	0.0991446	−	0.507120i
$89$	1.54471	+	0.891838i	0.163739	+	0.0945347i	0.579630	−	0.814880i	$-0.303197\pi$
$89$	1.54471	+	0.891838i	0.163739	+	0.0945347i	−0.415891	+	0.909414i	$0.636530\pi$
$90$		0			0
$91$	3.10963	+	5.71612i	0.325977	+	0.599213i
$92$	0.601545	+	13.1193i	0.0627154	+	1.36779i
$93$	0.157901	+	0.0911642i	0.0163736	+	0.00945329i
$94$	−16.0826	−	3.91676i	−1.65879	−	0.403983i
$95$		0			0
$96$	−2.31385	−	5.85511i	−0.236156	−	0.597584i
$97$	−10.5305			−1.06921			−0.534606	−	0.845101i	$-0.679540\pi$
$97$	−10.5305			−1.06921			−0.534606	+	0.845101i	$0.679540\pi$
$98$	−2.82720	+	9.48720i	−0.285590	+	0.958352i
$99$			3.01858i			0.303379i
$100$		0			0
$101$	−0.389513	+	0.224885i	−0.0387580	+	0.0223769i	−0.519254	−	0.854620i	$-0.673790\pi$
$101$	−0.389513	+	0.224885i	−0.0387580	+	0.0223769i	0.480496	+	0.876997i	$0.340457\pi$
$102$	−9.51018	−	2.31611i	−0.941648	−	0.229329i
$103$	8.03841	+	4.64098i	0.792048	+	0.457289i	0.840683	−	0.541527i	$-0.182154\pi$
$103$	8.03841	+	4.64098i	0.792048	+	0.457289i	−0.0486348	+	0.998817i	$0.515487\pi$
$104$	4.56957	−	5.24519i	0.448083	−	0.514334i
$105$		0			0
$106$	−12.7258	+	13.3227i	−1.23604	+	1.29401i
$107$	−9.26201	+	16.0423i	−0.895392	+	1.55086i	−0.0620738	+	0.998072i	$0.519771\pi$
$107$	−9.26201	+	16.0423i	−0.895392	+	1.55086i	−0.833318	+	0.552793i	$0.813562\pi$
$108$	5.71395	+	8.92597i	0.549825	+	0.858902i
$109$	−3.48557	−	6.03718i	−0.333857	−	0.578257i	0.649408	−	0.760441i	$-0.275017\pi$
$109$	−3.48557	−	6.03718i	−0.333857	−	0.578257i	−0.983265	+	0.182183i	$0.941684\pi$
$110$		0			0
$111$	−8.56605			−0.813054
$112$	10.5598	−	0.700854i	0.997805	−	0.0662245i
$113$		−	0.333646i		−	0.0313868i	−0.999877	−	0.0156934i	$-0.995004\pi$
$113$		−	0.333646i		−	0.0313868i	0.999877	−	0.0156934i	$-0.00499557\pi$
$114$	−0.0957166	−	0.327058i	−0.00896468	−	0.0306317i
$115$		0			0
$116$	4.16262	−	2.66469i	0.386489	−	0.247411i
$117$	−2.16604	+	3.75169i	−0.200251	+	0.346844i
$118$	4.38467	+	4.18824i	0.403642	+	0.385558i
$119$	8.58562	−	14.0361i	0.787043	−	1.28669i
$120$		0			0
$121$	−4.03150	+	6.98276i	−0.366500	+	0.634796i
$122$	9.61889	+	2.34259i	0.870854	+	0.212088i
$123$	−4.64168	−	8.03962i	−0.418526	−	0.724908i
$124$	0.290961	+	0.150657i	0.0261291	+	0.0135294i
$125$		0			0
$126$	−6.37005	+	1.69009i	−0.567489	+	0.150565i
$127$	15.8806			1.40918			0.704589	−	0.709616i	$-0.251131\pi$
$127$	15.8806			1.40918			0.704589	+	0.709616i	$0.251131\pi$
$128$	−4.63567	−	10.3204i	−0.409739	−	0.912203i
$129$	1.82597	−	1.05423i	0.160768	−	0.0928195i
$130$		0			0
$131$	1.60328	−	2.77697i	0.140080	−	0.242625i	−0.787447	−	0.616383i	$-0.788598\pi$
$131$	1.60328	−	2.77697i	0.140080	−	0.242625i	0.927526	+	0.373758i	$0.121931\pi$
$132$	−0.174724	−	3.81063i	−0.0152078	−	0.331673i
$133$	0.572654	+	0.0145293i	0.0496554	+	0.00125985i
$134$	5.29133	+	5.05427i	0.457101	+	0.436622i
$135$		0			0
$136$	−17.2629	−	3.37499i	−1.48028	−	0.289403i
$137$	1.12893	−	0.651787i	0.0964508	−	0.0556859i	−0.450999	−	0.892525i	$-0.648932\pi$
$137$	1.12893	−	0.651787i	0.0964508	−	0.0556859i	0.547450	+	0.836839i	$0.315599\pi$
$138$	2.90297	+	9.91926i	0.247117	+	0.844383i
$139$	−20.8813			−1.77113			−0.885563	−	0.464519i	$-0.846227\pi$
$139$	−20.8813			−1.77113			−0.885563	+	0.464519i	$0.846227\pi$
$140$		0			0
$141$	−13.0264			−1.09702
$142$	2.00280	+	6.84343i	0.168071	+	0.574288i
$143$	3.65031	−	2.10750i	0.305254	−	0.176238i
$144$	4.06632	+	5.75359i	0.338860	+	0.479466i
$145$		0			0
$146$	−7.78762	−	7.43873i	−0.644508	−	0.615633i
$147$	−0.395068	+	7.78054i	−0.0325846	+	0.641728i
$148$	−15.3774	+	0.705083i	−1.26402	+	0.0579574i
$149$	4.86747	−	8.43071i	0.398759	−	0.690670i	−0.594814	−	0.803863i	$-0.702774\pi$
$149$	4.86747	−	8.43071i	0.398759	−	0.690670i	0.993573	+	0.113193i	$0.0361078\pi$
$150$		0			0
$151$	12.9360	−	7.46858i	1.05271	−	0.607784i	0.129306	−	0.991605i	$-0.458725\pi$
$151$	12.9360	−	7.46858i	1.05271	−	0.607784i	0.923408	+	0.383821i	$0.125392\pi$
$152$	−0.198747	−	0.579242i	−0.0161205	−	0.0469827i
$153$	10.9538			0.885563
$154$	6.18975	+	1.67485i	0.498784	+	0.134963i
$155$		0			0
$156$	2.51723	−	4.86149i	0.201540	−	0.389230i
$157$	4.11231	+	7.12273i	0.328198	+	0.568456i	0.982154	−	0.188076i	$-0.0602252\pi$
$157$	4.11231	+	7.12273i	0.328198	+	0.568456i	−0.653956	+	0.756532i	$0.726892\pi$
$158$	21.9151	+	5.33721i	1.74347	+	0.424605i
$159$	−7.24948	+	12.5565i	−0.574921	+	0.995793i
$160$		0			0
$161$	−17.3679	−	0.440656i	−1.36878	−	0.0347285i
$162$	0.627364	+	0.599257i	0.0492903	+	0.0470821i
$163$	−5.99330	+	10.3807i	−0.469431	+	0.813079i	−0.999389	−	0.0349450i	$-0.988874\pi$
$163$	−5.99330	+	10.3807i	−0.469431	+	0.813079i	0.529958	+	0.848024i	$0.322208\pi$
$164$	−8.99430	−	14.0503i	−0.702337	−	1.09715i
$165$		0			0
$166$	−2.17609	−	7.43555i	−0.168897	−	0.577111i
$167$		−	14.8103i		−	1.14606i	−0.819535	−	0.573029i	$-0.805768\pi$
$167$		−	14.8103i		−	1.14606i	0.819535	−	0.573029i	$-0.194232\pi$
$168$	7.94367	−	2.50227i	0.612868	−	0.193054i
$169$	−6.95088			−0.534683
$170$		0			0
$171$	0.190679	+	0.330266i	0.0145816	+	0.0252561i
$172$	3.19114	−	2.04280i	0.243322	−	0.155762i
$173$	7.81044	−	13.5281i	0.593817	−	1.02852i	−0.399896	−	0.916561i	$-0.630954\pi$
$173$	7.81044	−	13.5281i	0.593817	−	1.02852i	0.993713	−	0.111960i	$-0.0357129\pi$
$174$	2.68660	−	2.81261i	0.203671	−	0.213224i
$175$		0			0
$176$	−0.627316	−	6.82631i	−0.0472857	−	0.514553i
$177$	4.13251	+	2.38591i	0.310618	+	0.179336i
$178$	2.45086	+	0.596884i	0.183700	+	0.0447383i
$179$	5.53306	−	3.19451i	0.413560	−	0.238769i	−0.278758	−	0.960361i	$-0.589923\pi$
$179$	5.53306	−	3.19451i	0.413560	−	0.238769i	0.692318	+	0.721592i	$0.256589\pi$
$180$		0			0
$181$		−	1.18770i		−	0.0882808i	−0.999025	−	0.0441404i	$-0.985945\pi$
$181$		−	1.18770i		−	0.0882808i	0.999025	−	0.0441404i	$-0.0140549\pi$
$182$	6.49121	+	6.52318i	0.481161	+	0.483530i
$183$	7.79100			0.575927
$184$	6.02776	+	17.5677i	0.444372	+	1.29511i
$185$		0			0
$186$	0.250529	+	0.0610138i	0.0183697	+	0.00447375i
$187$	−9.22992	−	5.32890i	−0.674958	−	0.389687i
$188$	−23.3844	+	1.07222i	−1.70549	+	0.0781996i
$189$	−12.3157	+	6.69985i	−0.895834	+	0.487342i
$190$		0			0
$191$	9.14608	+	5.28049i	0.661787	+	0.382083i	0.792958	−	0.609277i	$-0.208540\pi$
$191$	9.14608	+	5.28049i	0.661787	+	0.382083i	−0.131170	+	0.991360i	$0.541874\pi$
$192$	−5.46633	−	7.02792i	−0.394498	−	0.507196i
$193$	−4.68353	+	2.70403i	−0.337128	+	0.194641i	−0.659001	−	0.752142i	$-0.729021\pi$
$193$	−4.68353	+	2.70403i	−0.337128	+	0.194641i	0.321874	+	0.946783i	$0.395687\pi$
$194$	−14.2929	+	4.18295i	−1.02617	+	0.300319i
$195$		0			0
$196$	−0.0687835	+	13.9998i	−0.00491310	+	0.999988i
$197$			17.9504i			1.27892i	0.768826	+	0.639458i	$0.220841\pi$
$197$			17.9504i			1.27892i	−0.768826	+	0.639458i	$0.779159\pi$
$198$	1.19905	+	4.09707i	0.0852125	+	0.291166i
$199$	−3.82538	−	6.62575i	−0.271174	−	0.469687i	0.697989	−	0.716109i	$-0.254079\pi$
$199$	−3.82538	−	6.62575i	−0.271174	−	0.469687i	−0.969163	+	0.246422i	$0.920745\pi$
$200$		0			0
$201$	4.98702	+	2.87926i	0.351757	+	0.203087i
$202$	−0.439349	+	0.459956i	−0.0309125	+	0.0323624i
$203$	3.12447	+	5.74340i	0.219294	+	0.403108i
$204$	−13.8280	+	0.634039i	−0.968154	+	0.0443916i
$205$		0			0
$206$	12.7539	+	3.10608i	0.888606	+	0.216411i
$207$	−5.78307	−	10.0166i	−0.401951	−	0.696200i
$208$	4.11868	−	8.93434i	0.285579	−	0.619485i
$209$		−	0.371053i		−	0.0256662i
$210$		0			0
$211$		−	15.5710i		−	1.07195i	−0.844234	−	0.535975i	$-0.819944\pi$
$211$		−	15.5710i		−	1.07195i	0.844234	−	0.535975i	$-0.180056\pi$
$212$	−11.9804	+	23.1376i	−0.822820	+	1.58910i
$213$	2.80572	+	4.85965i	0.192245	+	0.332978i
$214$	−6.19882	+	25.4530i	−0.423742	+	1.73993i
$215$		0			0
$216$	11.3010	+	9.84536i	0.768938	+	0.669892i
$217$	−0.226173	+	0.369755i	−0.0153536	+	0.0251006i
$218$	−7.12900	−	6.80962i	−0.482837	−	0.461205i
$219$	−7.33975	−	4.23761i	−0.495974	−	0.286351i
$220$		0			0
$221$	−7.64770	−	13.2462i	−0.514440	−	0.891036i
$222$	−11.6266	+	3.40263i	−0.780323	+	0.228369i
$223$			11.4678i			0.767938i	0.923346	+	0.383969i	$0.125443\pi$
$223$			11.4678i			0.767938i	−0.923346	+	0.383969i	$0.874557\pi$
$224$	14.0542	−	5.14583i	0.939035	−	0.343820i
$225$		0			0
$226$	−0.132532	−	0.452852i	−0.00881587	−	0.0301233i
$227$	7.75470	−	4.47718i	0.514697	−	0.297161i	−0.220065	−	0.975485i	$-0.570627\pi$
$227$	7.75470	−	4.47718i	0.514697	−	0.297161i	0.734762	+	0.678325i	$0.237294\pi$
$228$	−0.259829	−	0.405889i	−0.0172076	−	0.0268806i
$229$	2.08431	+	1.20337i	0.137735	+	0.0795212i	0.567284	−	0.823522i	$-0.307994\pi$
$229$	2.08431	+	1.20337i	0.137735	+	0.0795212i	−0.429549	+	0.903043i	$0.641328\pi$
$230$		0			0
$231$	5.04467	+	0.127993i	0.331915	+	0.00842129i
$232$	4.59137	−	5.27022i	0.301438	−	0.346007i
$233$	−2.21768	−	1.28038i	−0.145285	−	0.0838803i	0.425595	−	0.904914i	$-0.360065\pi$
$233$	−2.21768	−	1.28038i	−0.145285	−	0.0838803i	−0.570880	+	0.821033i	$0.693398\pi$
$234$	−1.44967	+	5.95250i	−0.0947681	+	0.389127i
$235$		0			0
$236$	7.61490	+	3.94293i	0.495688	+	0.256663i
$237$	17.7505			1.15302
$238$	6.07767	−	22.4613i	0.393957	−	1.45595i
$239$			6.31200i			0.408289i	0.978941	+	0.204145i	$0.0654413\pi$
$239$			6.31200i			0.408289i	−0.978941	+	0.204145i	$0.934559\pi$
$240$		0			0
$241$	8.33650	−	4.81308i	0.537001	−	0.310038i	−0.206862	−	0.978370i	$-0.566325\pi$
$241$	8.33650	−	4.81308i	0.537001	−	0.310038i	0.743863	+	0.668332i	$0.232992\pi$
$242$	−2.69817	+	11.0790i	−0.173445	+	0.712183i
$243$	−13.1762	−	7.60728i	−0.845254	−	0.488008i
$244$	13.9861	−	0.641286i	0.895367	−	0.0410542i
$245$		0			0
$246$	−9.49358	−	9.06825i	−0.605288	−	0.578171i
$247$	0.266256	−	0.461169i	0.0169415	−	0.0293435i
$248$	0.454761	+	0.0889081i	0.0288773	+	0.00564567i
$249$	−3.04848	−	5.28013i	−0.193190	−	0.334615i
$250$		0			0
$251$	−24.9508			−1.57488			−0.787440	−	0.616391i	$-0.788594\pi$
$251$	−24.9508			−1.57488			−0.787440	+	0.616391i	$0.788594\pi$
$252$	−7.97461	+	4.82425i	−0.502353	+	0.303899i
$253$			11.2536i			0.707506i
$254$	21.5545	−	6.30813i	1.35245	−	0.395808i
$255$		0			0
$256$	−10.3914	−	12.1663i	−0.649463	−	0.760394i
$257$	8.48813	−	14.7019i	0.529475	−	0.917078i	−0.469934	−	0.882702i	$-0.655722\pi$
$257$	8.48813	−	14.7019i	0.529475	−	0.917078i	0.999409	−	0.0343764i	$-0.0109445\pi$
$258$	2.05960	−	2.15620i	0.128225	−	0.134239i
$259$	0.516501	−	20.3573i	0.0320938	−	1.26494i
$260$		0			0
$261$	−2.17638	+	3.76960i	−0.134714	+	0.233332i
$262$	1.07303	−	4.40599i	0.0662923	−	0.272203i
$263$	−7.51675	−	13.0194i	−0.463503	−	0.802810i	0.535630	−	0.844453i	$-0.320074\pi$
$263$	−7.51675	−	13.0194i	−0.463503	−	0.802810i	−0.999133	+	0.0416428i	$0.986741\pi$
$264$	−1.75082	−	5.10270i	−0.107755	−	0.314050i
$265$		0			0
$266$	0.783025	−	0.207751i	0.0480103	−	0.0127380i
$267$	1.98512			0.121487
$268$	9.18949	+	4.75824i	0.561337	+	0.290656i
$269$	27.2203	−	15.7157i	1.65965	−	0.958201i	0.686778	−	0.726867i	$-0.259025\pi$
$269$	27.2203	−	15.7157i	1.65965	−	0.958201i	0.972875	−	0.231333i	$-0.0743088\pi$
$270$		0			0
$271$	−1.65885	+	2.87322i	−0.100768	+	0.174536i	−0.912001	−	0.410187i	$-0.865463\pi$
$271$	−1.65885	+	2.87322i	−0.100768	+	0.174536i	0.811233	+	0.584723i	$0.198797\pi$
$272$	−24.7713	+	2.27640i	−1.50198	+	0.138027i
$273$	6.17800	+	3.77898i	0.373910	+	0.228714i
$274$	1.27337	−	1.33309i	0.0769270	−	0.0805351i
$275$		0			0
$276$	7.88030	+	12.3101i	0.474338	+	0.740982i
$277$	12.7703	−	7.37294i	0.767293	−	0.442997i	−0.0646150	−	0.997910i	$-0.520582\pi$
$277$	12.7703	−	7.37294i	0.767293	−	0.442997i	0.831908	+	0.554913i	$0.187249\pi$
$278$	−28.3418	+	8.29450i	−1.69983	+	0.497471i
$279$	−0.288558			−0.0172755
$280$		0			0
$281$	20.5438			1.22554			0.612769	−	0.790262i	$-0.290056\pi$
$281$	20.5438			1.22554			0.612769	+	0.790262i	$0.290056\pi$
$282$	−17.6805	+	5.17437i	−1.05286	+	0.308129i
$283$	24.1069	−	13.9181i	1.43301	−	0.827346i	0.435657	−	0.900113i	$-0.356516\pi$
$283$	24.1069	−	13.9181i	1.43301	−	0.827346i	0.997349	+	0.0727665i	$0.0231828\pi$
$284$	5.43672	+	8.49290i	0.322610	+	0.503961i
$285$		0			0
$286$	4.11735	−	4.31046i	0.243464	−	0.254883i
$287$	19.3861	−	10.5462i	1.14432	−	0.622522i
$288$	7.80459	+	6.19401i	0.459890	+	0.364986i
$289$	−10.8375	+	18.7710i	−0.637498	+	1.10418i
$290$		0			0
$291$	−10.1497	+	5.85991i	−0.594983	+	0.343514i
$292$	−13.5248	−	7.00304i	−0.791480	−	0.409822i
$293$	4.28428			0.250290			0.125145	−	0.992138i	$-0.460060\pi$
$293$	4.28428			0.250290			0.125145	+	0.992138i	$0.460060\pi$
$294$	2.55438	+	10.7173i	0.148975	+	0.625047i
$295$		0			0
$296$	−20.5914	+	7.06525i	−1.19685	+	0.410659i
$297$	4.54072	+	7.86477i	0.263480	+	0.456360i
$298$	3.25767	−	13.3763i	0.188712	−	0.774869i
$299$	−8.07522	+	13.9867i	−0.467002	+	0.808871i
$300$		0			0
$301$	2.39527	+	4.40300i	0.138061	+	0.253785i
$302$	14.5911	−	15.2754i	0.839621	−	0.879001i
$303$	−0.250283	+	0.433504i	−0.0143784	+	0.0249041i
$304$	−0.499844	−	0.707248i	−0.0286680	−	0.0405635i
$305$		0			0
$306$	14.8674	−	4.35109i	0.849913	−	0.248736i
$307$		−	14.3171i		−	0.817117i	−0.912732	−	0.408559i	$-0.866032\pi$
$307$		−	14.3171i		−	0.817117i	0.912732	−	0.408559i	$-0.133968\pi$
$308$	9.06652	−	0.185466i	0.516613	−	0.0105679i
$309$	10.3302			0.587667
$310$		0			0
$311$	12.8315	+	22.2249i	0.727609	+	1.26026i	0.957891	+	0.287132i	$0.0927020\pi$
$311$	12.8315	+	22.2249i	0.727609	+	1.26026i	−0.230281	+	0.973124i	$0.573965\pi$
$312$	1.48551	−	7.59831i	0.0841004	−	0.430170i
$313$	−16.2527	+	28.1505i	−0.918656	+	1.59116i	−0.117196	+	0.993109i	$0.537391\pi$
$313$	−16.2527	+	28.1505i	−0.918656	+	1.59116i	−0.801459	+	0.598049i	$0.795943\pi$
$314$	8.41088	+	8.03406i	0.474653	+	0.453388i
$315$		0			0
$316$	31.8650	−	1.46107i	1.79255	−	0.0821915i
$317$	−2.52937	−	1.46033i	−0.142064	−	0.0820205i	0.427284	−	0.904118i	$-0.359471\pi$
$317$	−2.52937	−	1.46033i	−0.142064	−	0.0820205i	−0.569347	+	0.822097i	$0.692804\pi$
$318$	−4.85188	+	19.9223i	−0.272080	+	1.11719i
$319$	3.66772	−	2.11756i	0.205353	−	0.118561i
$320$		0			0
$321$			20.6161i			1.15068i
$322$	−23.7482	+	6.30082i	−1.32343	+	0.351131i
$323$	−1.34647			−0.0749198
$324$	1.08955	+	0.564158i	0.0605304	+	0.0313421i
$325$		0			0
$326$	−4.01115	+	16.4702i	−0.222157	+	0.912200i
$327$	−6.71901	−	3.87922i	−0.371562	−	0.214522i
$328$	−17.7889	−	15.4975i	−0.982228	−	0.855708i
$329$	0.785443	−	30.9573i	0.0433029	−	1.70673i
$330$		0			0
$331$	−3.41964	−	1.97433i	−0.187960	−	0.108519i	0.403067	−	0.915170i	$-0.367944\pi$
$331$	−3.41964	−	1.97433i	−0.187960	−	0.108519i	−0.591027	+	0.806652i	$0.701277\pi$
$332$	−5.90713	−	9.22775i	−0.324196	−	0.506439i
$333$	11.7406	−	6.77845i	0.643382	−	0.371457i
$334$	−5.88299	−	20.1018i	−0.321903	−	1.09992i
$335$		0			0
$336$	9.78785	−	6.55169i	0.533971	−	0.357424i
$337$		−	10.0467i		−	0.547280i	−0.961832	−	0.273640i	$-0.911772\pi$
$337$		−	10.0467i		−	0.547280i	0.961832	−	0.273640i	$-0.0882277\pi$
$338$	−9.43430	+	2.76104i	−0.513158	+	0.150181i
$339$	−0.185664	−	0.321579i	−0.0100839	−	0.0174658i
$340$		0			0
$341$	0.243146	+	0.140380i	0.0131671	+	0.00760201i
$342$	0.389995	+	0.372522i	0.0210885	+	0.0201437i
$343$	−18.4667	−	1.40802i	−0.997106	−	0.0760258i
$344$	3.51983	−	4.04025i	0.189776	−	0.217836i
$345$		0			0
$346$	5.22732	−	21.4639i	0.281022	−	1.15391i
$347$	0.0100550	+	0.0174157i	0.000539780	+	0.000934926i	0.866295	−	0.499532i	$-0.166495\pi$
$347$	0.0100550	+	0.0174157i	0.000539780	+	0.000934926i	−0.865755	+	0.500467i	$0.833162\pi$
$348$	2.52925	−	4.88469i	0.135582	−	0.261847i
$349$			5.60366i			0.299957i	0.988689	+	0.149978i	$0.0479204\pi$
$349$			5.60366i			0.299957i	−0.988689	+	0.149978i	$0.952080\pi$
$350$		0			0
$351$			13.0331i			0.695657i
$352$	−3.56301	−	9.01605i	−0.189909	−	0.480557i
$353$	−12.7422	−	22.0701i	−0.678198	−	1.17467i	−0.975523	−	0.219897i	$-0.929428\pi$
$353$	−12.7422	−	22.0701i	−0.678198	−	1.17467i	0.297325	−	0.954776i	$-0.403905\pi$
$354$	6.55672	+	1.59682i	0.348485	+	0.0848702i
$355$		0			0
$356$	3.56361	−	0.163398i	0.188871	−	0.00866007i
$357$	0.464459	−	18.3061i	0.0245818	−	0.968860i
$358$	6.24099	−	6.53371i	0.329847	−	0.345317i
$359$	−16.7562	−	9.67422i	−0.884361	−	0.510586i	−0.0122672	−	0.999925i	$-0.503905\pi$
$359$	−16.7562	−	9.67422i	−0.884361	−	0.510586i	−0.872094	+	0.489339i	$0.837238\pi$
$360$		0			0
$361$	9.47656	+	16.4139i	0.498766	+	0.863889i
$362$	−0.471779	−	1.61204i	−0.0247962	−	0.0847269i
$363$			8.97361i			0.470993i
$364$	11.4016	+	6.27535i	0.597604	+	0.328917i
$365$		0			0
$366$	10.5746	−	3.09476i	0.552742	−	0.161765i
$367$	14.9780	−	8.64757i	0.781846	−	0.451399i	−0.0552378	−	0.998473i	$-0.517592\pi$
$367$	14.9780	−	8.64757i	0.781846	−	0.451399i	0.837084	+	0.547074i	$0.184258\pi$
$368$	15.1596	+	21.4500i	0.790251	+	1.11816i
$369$	12.7237	+	7.34606i	0.662372	+	0.382420i
$370$		0			0
$371$	−29.4034	−	17.9855i	−1.52655	−	0.933762i
$372$	0.364274	−	0.0167026i	0.0188867	−	0.000865990i
$373$	9.62126	+	5.55483i	0.498170	+	0.287618i	0.727957	−	0.685622i	$-0.240470\pi$
$373$	9.62126	+	5.55483i	0.498170	+	0.287618i	−0.229788	+	0.973241i	$0.573803\pi$
$374$	−14.6444	−	3.56649i	−0.757242	−	0.184419i
$375$		0			0
$376$	−31.3134	+	10.7441i	−1.61486	+	0.554086i
$377$	6.07799			0.313032
$378$	−14.0545	+	13.9856i	−0.722887	+	0.719344i
$379$		−	14.3198i		−	0.735558i	−0.929913	−	0.367779i	$-0.880118\pi$
$379$		−	14.3198i		−	0.735558i	0.929913	−	0.367779i	$-0.119882\pi$
$380$		0			0
$381$	15.3063	−	8.83707i	0.784164	−	0.452737i
$382$	14.5113	+	3.53409i	0.742465	+	0.180820i
$383$	−9.05330	−	5.22693i	−0.462602	−	0.267084i	0.250536	−	0.968107i	$-0.419393\pi$
$383$	−9.05330	−	5.22693i	−0.462602	−	0.267084i	−0.713138	+	0.701024i	$0.752727\pi$
$384$	−10.2110	−	7.36753i	−0.521077	−	0.375972i
$385$		0			0
$386$	−5.28276	+	5.53054i	−0.268886	+	0.281497i
$387$	−1.66845	+	2.88984i	−0.0848121	+	0.146899i
$388$	−17.7379	+	11.3549i	−0.900506	+	0.576457i
$389$	−15.0629	−	26.0897i	−0.763718	−	1.32280i	−0.940922	−	0.338624i	$-0.890038\pi$
$389$	−15.0629	−	26.0897i	−0.763718	−	1.32280i	0.177204	−	0.984174i	$-0.443295\pi$
$390$		0			0
$391$	40.8369			2.06521
$392$	5.46768	+	19.0290i	0.276160	+	0.961112i
$393$		−	3.56871i		−	0.180018i
$394$	7.13031	+	24.3638i	0.359220	+	1.22743i
$395$		0			0
$396$	3.25489	+	5.08459i	0.163564	+	0.255510i
$397$	−6.71896	+	11.6376i	−0.337215	+	0.584073i	−0.983908	−	0.178677i	$-0.942818\pi$
$397$	−6.71896	+	11.6376i	−0.337215	+	0.584073i	0.646693	+	0.762750i	$0.276151\pi$
$398$	−7.82401	−	7.47349i	−0.392182	−	0.374612i
$399$	0.560028	−	0.304660i	0.0280365	−	0.0152521i
$400$		0			0
$401$	14.4423	−	25.0149i	0.721216	−	1.24918i	−0.239297	−	0.970946i	$-0.576917\pi$
$401$	14.4423	−	25.0149i	0.721216	−	1.24918i	0.960513	−	0.278236i	$-0.0897497\pi$
$402$	7.91250	+	1.92701i	0.394639	+	0.0961105i
$403$	0.201465	+	0.348948i	0.0100357	+	0.0173823i
$404$	−0.413616	+	0.798809i	−0.0205782	+	0.0397422i
$405$		0			0
$406$	6.52219	+	6.55431i	0.323691	+	0.325285i
$407$	−13.1905			−0.653830
$408$	−18.5167	+	6.35336i	−0.916711	+	0.314538i
$409$	22.4328	−	12.9516i	1.10923	−	0.640413i	0.170599	−	0.985341i	$-0.445430\pi$
$409$	22.4328	−	12.9516i	1.10923	−	0.640413i	0.938629	+	0.344927i	$0.112096\pi$
$410$		0			0
$411$	0.725398	−	1.25643i	0.0357813	−	0.0619749i
$412$	18.5444	−	0.850295i	0.913619	−	0.0418910i
$413$	−5.91929	+	9.67706i	−0.291269	+	0.476177i
$414$	−11.8281	−	11.2982i	−0.581318	−	0.555274i
$415$		0			0
$416$	2.04130	−	13.7624i	0.100083	−	0.674760i
$417$	−20.1260	+	11.6198i	−0.985577	+	0.569023i
$418$	−0.147390	−	0.503623i	−0.00720909	−	0.0246330i
$419$	−28.1022			−1.37288			−0.686441	−	0.727185i	$-0.740828\pi$
$419$	−28.1022			−1.37288			−0.686441	+	0.727185i	$0.740828\pi$
$420$		0			0
$421$	15.6269			0.761608			0.380804	−	0.924656i	$-0.375647\pi$
$421$	15.6269			0.761608			0.380804	+	0.924656i	$0.375647\pi$
$422$	−6.18513	−	21.1342i	−0.301087	−	1.02880i
$423$	17.8539	−	10.3080i	0.868088	−	0.501191i
$424$	−7.07007	+	36.1631i	−0.343353	+	1.75624i
$425$		0			0
$426$	5.73851	+	5.48142i	0.278032	+	0.265576i
$427$	−0.469768	+	18.5153i	−0.0227337	+	0.896019i
$428$	1.69694	+	37.0092i	0.0820245	+	1.78890i
$429$	2.34552	−	4.06256i	0.113243	−	0.196142i
$430$		0			0
$431$	17.2771	−	9.97495i	0.832210	−	0.480477i	−0.0223988	−	0.999749i	$-0.507130\pi$
$431$	17.2771	−	9.97495i	0.832210	−	0.480477i	0.854609	+	0.519273i	$0.173797\pi$
$432$	19.2495	+	8.87391i	0.926141	+	0.426946i
$433$	11.8294			0.568487			0.284243	−	0.958752i	$-0.408258\pi$
$433$	11.8294			0.568487			0.284243	+	0.958752i	$0.408258\pi$
$434$	−0.160105	+	0.591703i	−0.00768530	+	0.0284027i
$435$		0			0
$436$	−12.3810	−	6.41077i	−0.592942	−	0.307020i
$437$	0.710872	+	1.23127i	0.0340056	+	0.0588995i
$438$	−11.6454	−	2.83612i	−0.556438	−	0.135515i
$439$	−13.9474	+	24.1577i	−0.665675	+	1.15298i	0.313427	+	0.949612i	$0.398523\pi$
$439$	−13.9474	+	24.1577i	−0.665675	+	1.15298i	−0.979102	+	0.203371i	$0.934810\pi$
$440$		0			0
$441$	−5.61538	−	10.9766i	−0.267399	−	0.522696i
$442$	−15.6418	−	14.9410i	−0.744003	−	0.710671i
$443$	9.59955	−	16.6269i	0.456088	−	0.789968i	−0.542662	−	0.839951i	$-0.682583\pi$
$443$	9.59955	−	16.6269i	0.456088	−	0.789968i	0.998750	+	0.0499830i	$0.0159167\pi$
$444$	−14.4289	+	9.23665i	−0.684766	+	0.438352i
$445$		0			0
$446$	4.55525	+	15.5650i	0.215697	+	0.737024i
$447$		−	10.8344i		−	0.512449i
$448$	17.0315	−	12.5670i	0.804661	−	0.593734i
$449$	4.94035			0.233150			0.116575	−	0.993182i	$-0.462809\pi$
$449$	4.94035			0.233150			0.116575	+	0.993182i	$0.462809\pi$
$450$		0			0
$451$	−7.14753	−	12.3799i	−0.336564	−	0.582946i
$452$	−0.359765	−	0.562003i	−0.0169219	−	0.0264344i
$453$	8.31206	−	14.3969i	0.390535	−	0.676426i
$454$	8.74688	−	9.15713i	0.410511	−	0.429765i
$455$		0			0
$456$	−0.513889	−	0.447696i	−0.0240651	−	0.0209653i
$457$	22.6243	+	13.0622i	1.05832	+	0.611022i	0.924967	−	0.380046i	$-0.124092\pi$
$457$	22.6243	+	13.0622i	1.05832	+	0.611022i	0.133354	+	0.991068i	$0.457425\pi$
$458$	3.30700	+	0.805387i	0.154526	+	0.0376332i
$459$	28.5396	−	16.4774i	1.33212	−	0.769097i
$460$		0			0
$461$			13.3894i			0.623609i	0.950146	+	0.311804i	$0.100933\pi$
$461$			13.3894i			0.623609i	−0.950146	+	0.311804i	$0.899067\pi$
$462$	6.89788	−	1.83013i	0.320918	−	0.0851454i
$463$	16.4019			0.762259			0.381130	−	0.924522i	$-0.375535\pi$
$463$	16.4019			0.762259			0.381130	+	0.924522i	$0.375535\pi$
$464$	4.13834	−	8.97697i	0.192117	−	0.416746i
$465$		0			0
$466$	−3.51861	−	0.856922i	−0.162996	−	0.0396962i
$467$	10.3345	+	5.96663i	0.478224	+	0.276103i	0.719676	−	0.694310i	$-0.244290\pi$
$467$	10.3345	+	5.96663i	0.478224	+	0.276103i	−0.241452	+	0.970413i	$0.577624\pi$
$468$	0.396850	+	8.65507i	0.0183444	+	0.400081i
$469$	−7.14326	+	11.6781i	−0.329845	+	0.539242i
$470$		0			0
$471$	7.92716	+	4.57675i	0.365264	+	0.210885i
$472$	11.9018	+	2.32686i	0.547824	+	0.107102i
$473$	2.81175	−	1.62336i	0.129284	−	0.0746423i
$474$	24.0925	−	7.05090i	1.10660	−	0.323859i
$475$		0			0
$476$	−0.673018	−	32.9005i	−0.0308477	−	1.50799i
$477$		−	22.9465i		−	1.05065i
$478$	2.50726	+	8.56716i	0.114680	+	0.391853i
$479$	18.5889	+	32.1969i	0.849347	+	1.47111i	0.881792	+	0.471639i	$0.156337\pi$
$479$	18.5889	+	32.1969i	0.849347	+	1.47111i	−0.0324444	+	0.999474i	$0.510329\pi$
$480$		0			0
$481$	−16.3941	−	9.46512i	−0.747505	−	0.431572i
$482$	9.40312	−	9.84415i	0.428300	−	0.448389i
$483$	−16.9850	+	9.23998i	−0.772843	+	0.420434i
$484$	0.738629	+	16.1091i	0.0335741	+	0.732230i
$485$		0			0
$486$	−20.9056	−	5.09135i	−0.948298	−	0.230948i
$487$	0.489188	+	0.847298i	0.0221672	+	0.0383948i	0.876896	−	0.480680i	$-0.159610\pi$
$487$	0.489188	+	0.847298i	0.0221672	+	0.0383948i	−0.854729	+	0.519075i	$0.826277\pi$
$488$	18.7283	−	6.42599i	0.847791	−	0.290891i
$489$			13.3403i			0.603271i
$490$		0			0
$491$			18.4167i			0.831132i	0.909563	+	0.415566i	$0.136417\pi$
$491$			18.4167i			0.831132i	−0.909563	+	0.415566i	$0.863583\pi$
$492$	−16.4876	−	8.53712i	−0.743317	−	0.384883i
$493$	−7.68420	−	13.3094i	−0.346079	−	0.599426i
$494$	0.178198	−	0.731699i	0.00801751	−	0.0329207i
$495$		0			0
$496$	0.652555	−	0.0599677i	0.0293006	−	0.00269263i
$497$	−11.7181	+	6.37478i	−0.525631	+	0.285948i
$498$	−6.23504	−	5.95570i	−0.279399	−	0.266881i
$499$	16.9167	+	9.76688i	0.757297	+	0.437226i	0.828324	−	0.560249i	$-0.189294\pi$
$499$	16.9167	+	9.76688i	0.757297	+	0.437226i	−0.0710273	+	0.997474i	$0.522628\pi$
$500$		0			0
$501$	−8.24149	−	14.2747i	−0.368203	−	0.637746i
$502$	−33.8653	+	9.91101i	−1.51148	+	0.442350i
$503$		−	11.7007i		−	0.521707i	−0.965378	−	0.260853i	$-0.915996\pi$
$503$		−	11.7007i		−	0.521707i	0.965378	−	0.260853i	$-0.0840039\pi$
$504$	−8.90750	+	9.71556i	−0.396771	+	0.432765i
$505$		0			0
$506$	4.47017	+	15.2743i	0.198723	+	0.679025i
$507$	−6.69948	+	3.86795i	−0.297534	+	0.171782i
$508$	26.7498	−	17.1238i	1.18683	−	0.759747i
$509$	1.85583	+	1.07147i	0.0822584	+	0.0474919i	0.540565	−	0.841302i	$-0.318211\pi$
$509$	1.85583	+	1.07147i	0.0822584	+	0.0474919i	−0.458307	+	0.888794i	$0.651544\pi$
$510$		0			0
$511$	10.5132	−	17.1874i	0.465079	−	0.760327i
$512$	−18.9368	−	12.3854i	−0.836896	−	0.547363i
$513$	0.993611	+	0.573662i	0.0438690	+	0.0253278i
$514$	5.68088	−	23.3263i	0.250573	−	1.02888i
$515$		0			0
$516$	1.93897	−	3.74469i	0.0853583	−	0.164851i
$517$	−20.0588			−0.882186
$518$	−7.38531	−	27.8357i	−0.324492	−	1.22303i
$519$		−	17.3851i		−	0.763120i
$520$		0			0
$521$	−11.8399	+	6.83576i	−0.518714	+	0.299480i	−0.736408	−	0.676537i	$-0.763480\pi$
$521$	−11.8399	+	6.83576i	−0.518714	+	0.299480i	0.217694	+	0.976017i	$0.430146\pi$
$522$	−1.45659	+	5.98091i	−0.0637533	+	0.261777i
$523$	32.5328	+	18.7828i	1.42256	+	0.821316i	0.996517	−	0.0833873i	$-0.0265739\pi$
$523$	32.5328	+	18.7828i	1.42256	+	0.821316i	0.426043	+	0.904703i	$0.359907\pi$
$524$	−0.293745	−	6.40640i	−0.0128323	−	0.279865i
$525$		0			0
$526$	−15.3739	−	14.6852i	−0.670336	−	0.640304i
$527$	0.509411	−	0.882325i	0.0221903	−	0.0384347i
$528$	−4.40326	−	6.23034i	−0.191627	−	0.271141i
$529$	−10.0599	−	17.4242i	−0.437386	−	0.757575i
$530$		0			0
$531$	−7.55201			−0.327729
$532$	0.980262	−	0.593011i	0.0424998	−	0.0257103i
$533$		−	20.5154i		−	0.888621i
$534$	2.69437	−	0.788534i	0.116597	−	0.0341232i
$535$		0			0
$536$	14.3628	+	2.80800i	0.620379	+	0.121287i
$537$	3.55530	−	6.15795i	0.153422	−	0.265735i
$538$	30.7030	−	32.1431i	1.32370	−	1.38579i
$539$	−0.608349	+	11.9810i	−0.0262035	+	0.516056i
$540$		0			0
$541$	−13.3052	+	23.0452i	−0.572034	+	0.990793i	0.424323	+	0.905511i	$0.360512\pi$
$541$	−13.3052	+	23.0452i	−0.572034	+	0.990793i	−0.996357	+	0.0852815i	$0.972821\pi$
$542$	−1.11023	+	4.55870i	−0.0476883	+	0.195813i
$543$	−0.660916	−	1.14474i	−0.0283626	−	0.0491255i
$544$	−32.7174	+	12.9294i	−1.40275	+	0.554344i
$545$		0			0
$546$	9.88639	+	2.67510i	0.423098	+	0.114484i
$547$	−24.0582			−1.02865			−0.514327	−	0.857594i	$-0.671958\pi$
$547$	−24.0582			−1.02865			−0.514327	+	0.857594i	$0.671958\pi$
$548$	1.19879	−	2.31519i	0.0512097	−	0.0989002i
$549$	−10.6783	+	6.16513i	−0.455740	+	0.263121i
$550$		0			0
$551$	0.267527	−	0.463370i	0.0113970	−	0.0197402i
$552$	15.5856	+	13.5781i	0.663369	+	0.577921i
$553$	−1.07029	+	42.1842i	−0.0455134	+	1.79385i
$554$	14.4042	−	15.0798i	0.611976	−	0.640679i
$555$		0			0
$556$	−35.1730	+	22.5160i	−1.49167	+	0.954889i
$557$	23.1592	−	13.3710i	0.981286	−	0.566546i	0.0786280	−	0.996904i	$-0.474946\pi$
$557$	23.1592	−	13.3710i	0.981286	−	0.566546i	0.902658	+	0.430358i	$0.141613\pi$
$558$	−0.391655	+	0.114622i	−0.0165801	+	0.00485233i
$559$	4.65950			0.197076
$560$		0			0
$561$	−11.8615			−0.500791
$562$	27.8837	−	8.16043i	1.17620	−	0.344227i
$563$	−15.1306	+	8.73567i	−0.637680	+	0.368165i	−0.783720	−	0.621114i	$-0.786680\pi$
$563$	−15.1306	+	8.73567i	−0.637680	+	0.368165i	0.146041	+	0.989279i	$0.453347\pi$
$564$	−21.9420	+	14.0462i	−0.923926	+	0.591450i
$565$		0			0
$566$	27.1913	−	28.4666i	1.14293	−	1.19654i
$567$	−0.846937	+	1.38460i	−0.0355680	+	0.0581479i
$568$	10.7527	+	9.36768i	0.451175	+	0.393059i
$569$	−10.1792	+	17.6309i	−0.426734	+	0.739125i	−0.996581	−	0.0826258i	$-0.973669\pi$
$569$	−10.1792	+	17.6309i	−0.426734	+	0.739125i	0.569846	+	0.821751i	$0.307003\pi$
$570$		0			0
$571$	−19.2734	+	11.1275i	−0.806565	+	0.465671i	−0.845762	−	0.533561i	$-0.820854\pi$
$571$	−19.2734	+	11.1275i	−0.806565	+	0.465671i	0.0391963	+	0.999232i	$0.487520\pi$
$572$	3.87619	−	7.48601i	0.162072	−	0.313006i
$573$	11.7537			0.491019
$574$	22.1232	−	22.0147i	0.923403	−	0.918877i
$575$		0			0
$576$	13.0534	+	5.30687i	0.543893	+	0.221119i
$577$	−0.485564	−	0.841022i	−0.0202143	−	0.0350122i	0.855741	−	0.517404i	$-0.173102\pi$
$577$	−0.485564	−	0.841022i	−0.0202143	−	0.0350122i	−0.875956	+	0.482392i	$0.839768\pi$
$578$	−7.25323	+	29.7825i	−0.301694	+	1.23879i
$579$	−3.00942	+	5.21247i	−0.125067	+	0.216623i
$580$		0			0
$581$	12.7321	−	6.92636i	0.528215	−	0.287354i
$582$	−11.4483	+	11.9852i	−0.474546	+	0.496803i
$583$	−11.1632	+	19.3352i	−0.462332	+	0.800783i
$584$	−21.1388	−	4.13274i	−0.874728	−	0.171014i
$585$		0			0
$586$	5.81497	−	1.70181i	0.240214	−	0.0703011i
$587$			17.6042i			0.726602i	0.931672	+	0.363301i	$0.118350\pi$
$587$			17.6042i			0.726602i	−0.931672	+	0.363301i	$0.881650\pi$
$588$	7.72418	+	13.5318i	0.318540	+	0.558041i
$589$	0.0354704			0.00146153
$590$		0			0
$591$	9.98887	+	17.3012i	0.410887	+	0.711677i
$592$	−25.1419	+	17.7689i	−1.03333	+	0.730298i
$593$	11.1886	−	19.3792i	0.459461	−	0.795810i	−0.539471	−	0.842004i	$-0.681376\pi$
$593$	11.1886	−	19.3792i	0.459461	−	0.795810i	0.998932	+	0.0461938i	$0.0147092\pi$
$594$	9.28710	+	8.87103i	0.381054	+	0.363983i
$595$		0			0
$596$	−0.891792	−	19.4494i	−0.0365292	−	0.796680i
$597$	−7.37405	−	4.25741i	−0.301800	−	0.174244i
$598$	−5.40453	+	22.1915i	−0.221008	+	0.907480i
$599$	15.9061	−	9.18338i	0.649905	−	0.375223i	−0.138515	−	0.990360i	$-0.544233\pi$
$599$	15.9061	−	9.18338i	0.649905	−	0.375223i	0.788420	+	0.615137i	$0.210900\pi$
$600$		0			0
$601$			11.9668i			0.488136i	0.969758	+	0.244068i	$0.0784820\pi$
$601$			11.9668i			0.488136i	−0.969758	+	0.244068i	$0.921518\pi$
$602$	5.00003	+	5.02465i	0.203786	+	0.204790i
$603$	−9.11360			−0.371134
$604$	13.7365	−	26.5289i	0.558928	−	1.07945i
$605$		0			0
$606$	−0.167508	+	0.687805i	−0.00680455	+	0.0279402i
$607$	14.1791	+	8.18629i	0.575511	+	0.332271i	0.759347	−	0.650686i	$-0.225518\pi$
$607$	14.1791	+	8.18629i	0.575511	+	0.332271i	−0.183837	+	0.982957i	$0.558852\pi$
$608$	−0.959363	−	0.761386i	−0.0389073	−	0.0308783i
$609$	6.20749	+	3.79701i	0.251540	+	0.153863i
$610$		0			0
$611$	−24.9304	−	14.3936i	−1.00858	−	0.582303i
$612$	18.4509	−	11.8113i	0.745834	−	0.477445i
$613$	−39.6151	+	22.8718i	−1.60004	+	0.923783i	−0.608561	+	0.793507i	$0.708253\pi$
$613$	−39.6151	+	22.8718i	−1.60004	+	0.923783i	−0.991478	+	0.130276i	$0.958414\pi$
$614$	−5.68705	−	19.4323i	−0.229511	−	0.784223i
$615$		0			0
$616$	12.2322	−	3.85315i	0.492847	−	0.155248i
$617$			3.88479i			0.156396i	0.996938	+	0.0781979i	$0.0249166\pi$
$617$			3.88479i			0.156396i	−0.996938	+	0.0781979i	$0.975083\pi$
$618$	14.0211	−	4.10340i	0.564010	−	0.165063i
$619$	10.2165	+	17.6955i	0.410636	+	0.711242i	0.994959	−	0.100278i	$-0.0319734\pi$
$619$	10.2165	+	17.6955i	0.410636	+	0.711242i	−0.584323	+	0.811521i	$0.698640\pi$
$620$		0			0
$621$	−30.1350	−	17.3985i	−1.20928	−	0.698176i
$622$	26.2442	+	25.0684i	1.05230	+	1.00515i
$623$	−0.119695	+	4.71765i	−0.00479549	+	0.189009i
$624$	−1.00196	−	10.9031i	−0.0401106	−	0.436474i
$625$		0			0
$626$	−10.8775	+	44.6640i	−0.434752	+	1.78513i
$627$	−0.206479	−	0.357633i	−0.00824599	−	0.0142825i
$628$	14.6072	+	7.56350i	0.582892	+	0.301816i
$629$			47.8657i			1.90853i
$630$		0			0
$631$		−	23.7070i		−	0.943762i	−0.881662	−	0.471881i	$-0.843575\pi$
$631$		−	23.7070i		−	0.943762i	0.881662	−	0.471881i	$-0.156425\pi$
$632$	42.6695	−	14.6406i	1.69730	−	0.582371i
$633$	−8.66476	−	15.0078i	−0.344393	−	0.596507i
$634$	−4.01315	−	0.977362i	−0.159382	−	0.0388160i
$635$		0			0
$636$	1.32821	+	28.9675i	0.0526670	+	1.14864i
$637$	−9.35326	+	14.4542i	−0.370590	+	0.572696i
$638$	4.13700	−	4.33103i	0.163785	−	0.171467i
$639$	−7.69103	−	4.44042i	−0.304252	−	0.175660i
$640$		0			0
$641$	−7.19683	−	12.4653i	−0.284258	−	0.492349i	0.688171	−	0.725548i	$-0.258414\pi$
$641$	−7.19683	−	12.4653i	−0.284258	−	0.492349i	−0.972429	+	0.233200i	$0.925080\pi$
$642$	8.18916	+	27.9818i	0.323200	+	1.10436i
$643$			47.6127i			1.87766i	0.344380	+	0.938830i	$0.388089\pi$
$643$			47.6127i			1.87766i	−0.344380	+	0.938830i	$0.611911\pi$
$644$	−29.7302	+	17.9853i	−1.17153	+	0.708720i
$645$		0			0
$646$	−1.82754	+	0.534849i	−0.0719038	+	0.0210434i
$647$	0.00937783	−	0.00541429i	0.000368680	−	0.000212858i	−0.499816	−	0.866132i	$-0.666599\pi$
$647$	0.00937783	−	0.00541429i	0.000368680	−	0.000212858i	0.500184	+	0.865919i	$0.333266\pi$
$648$	1.70292	+	0.332929i	0.0668970	+	0.0130787i
$649$	6.36349	+	3.67396i	0.249789	+	0.144216i
$650$		0			0
$651$	−0.0122353	+	0.482240i	−0.000479540	+	0.0189005i
$652$	1.09806	+	23.9480i	0.0430033	+	0.937877i
$653$	−9.19915	−	5.31113i	−0.359990	−	0.207841i	0.309086	−	0.951034i	$-0.399977\pi$
$653$	−9.19915	−	5.31113i	−0.359990	−	0.207841i	−0.669077	+	0.743193i	$0.733310\pi$
$654$	−10.6605	−	2.59626i	−0.416859	−	0.101522i
$655$		0			0
$656$	−30.3005	−	13.9684i	−1.18304	−	0.545374i
$657$	13.4131			0.523296
$658$	−11.2308	−	42.3297i	−0.437824	−	1.65018i
$659$		−	13.3688i		−	0.520773i	−0.965505	−	0.260386i	$-0.916150\pi$
$659$		−	13.3688i		−	0.520773i	0.965505	−	0.260386i	$-0.0838499\pi$
$660$		0			0
$661$	−6.49983	+	3.75268i	−0.252814	+	0.145962i	−0.621052	−	0.783769i	$-0.713294\pi$
$661$	−6.49983	+	3.75268i	−0.252814	+	0.145962i	0.368238	+	0.929732i	$0.379961\pi$
$662$	−5.42566	−	1.32137i	−0.210874	−	0.0513563i
$663$	−14.7422	−	8.51142i	−0.572540	−	0.330556i
$664$	−11.6831	−	10.1782i	−0.453393	−	0.394992i
$665$		0			0
$666$	13.2428	−	13.8639i	0.513147	−	0.537215i
$667$	−8.11376	+	14.0534i	−0.314166	+	0.544151i
$668$	−15.9698	−	24.9470i	−0.617889	−	0.965227i
$669$	6.38146	+	11.0530i	0.246721	+	0.427334i
$670$		0			0
$671$	11.9970			0.463141
$672$	10.6824	−	12.7804i	0.412082	−	0.493016i
$673$		−	19.9107i		−	0.767501i	−0.923437	−	0.383751i	$-0.874632\pi$
$673$		−	19.9107i		−	0.767501i	0.923437	−	0.383751i	$-0.125368\pi$
$674$	−3.99078	−	13.6362i	−0.153719	−	0.525249i
$675$		0			0
$676$	−11.7083	+	7.49503i	−0.450318	+	0.288270i
$677$	−13.0027	+	22.5213i	−0.499733	+	0.865563i	−1.00000		0.000308393i	$-0.999902\pi$
$677$	−13.0027	+	22.5213i	−0.499733	+	0.865563i	0.500267	+	0.865871i	$0.333235\pi$
$678$	−0.379736	−	0.362724i	−0.0145837	−	0.0139303i
$679$	−13.3141	−	24.4740i	−0.510948	−	0.939226i
$680$		0			0
$681$	4.98282	−	8.63049i	0.190942	−	0.330721i
$682$	0.385779	+	0.0939527i	0.0147722	+	0.00359763i
$683$	−7.41000	−	12.8345i	−0.283536	−	0.491098i	0.688717	−	0.725030i	$-0.258174\pi$
$683$	−7.41000	−	12.8345i	−0.283536	−	0.491098i	−0.972253	+	0.233932i	$0.924841\pi$
$684$	0.677307	+	0.350704i	0.0258975	+	0.0134095i
$685$		0			0
$686$	−25.6238	+	5.42429i	−0.978320	+	0.207100i
$687$	2.67856			0.102194
$688$	3.17253	−	6.88191i	0.120951	−	0.262370i
$689$	−27.7487	+	16.0207i	−1.05714	+	0.610341i
$690$		0			0
$691$	−13.2455	+	22.9418i	−0.503882	+	0.872749i	0.496108	+	0.868261i	$0.334762\pi$
$691$	−13.2455	+	22.9418i	−0.503882	+	0.872749i	−0.999990	+	0.00448815i	$0.998571\pi$
$692$	−1.43099	−	31.2090i	−0.0543980	−	1.18639i
$693$	−7.01549	+	3.81650i	−0.266497	+	0.144977i
$694$	0.0205654	+	0.0196440i	0.000780651	+	0.000745677i
$695$		0			0
$696$	1.49260	−	7.63457i	0.0565768	−	0.289388i
$697$	−44.9241	+	25.9369i	−1.70162	+	0.982432i
$698$	2.22590	+	7.60574i	0.0842514	+	0.287882i
$699$	−2.84996			−0.107795
$700$		0			0
$701$	−0.713553			−0.0269505			−0.0134753	−	0.999909i	$-0.504289\pi$
$701$	−0.713553			−0.0269505			−0.0134753	+	0.999909i	$0.504289\pi$
$702$	5.17705	+	17.6896i	0.195395	+	0.667653i
$703$	−1.44319	+	0.833226i	−0.0544310	+	0.0314257i
$704$	−8.41738	−	10.8220i	−0.317242	−	0.407870i
$705$		0			0
$706$	−26.0615	−	24.8939i	−0.980836	−	0.936893i
$707$	−1.01513	−	0.620938i	−0.0381779	−	0.0233528i
$708$	9.53361	−	0.437133i	0.358295	−	0.0164285i
$709$	−9.56584	+	16.5685i	−0.359253	+	0.622244i	−0.987836	−	0.155498i	$-0.950302\pi$
$709$	−9.56584	+	16.5685i	−0.359253	+	0.622244i	0.628584	+	0.777742i	$0.283635\pi$
$710$		0			0
$711$	−24.3288	+	14.0463i	−0.912403	+	0.526776i
$712$	4.77192	−	1.63732i	0.178835	−	0.0613612i
$713$	−1.07578			−0.0402881
$714$	−6.64117	−	25.0310i	−0.248540	−	0.936761i
$715$		0			0
$716$	5.87545	−	11.3471i	0.219576	−	0.424063i
$717$	3.51243	+	6.08371i	0.131174	+	0.227200i
$718$	−26.5858	−	6.47470i	−0.992172	−	0.241634i
$719$	20.0286	−	34.6906i	0.746941	−	1.29374i	−0.202341	−	0.979315i	$-0.564855\pi$
$719$	20.0286	−	34.6906i	0.746941	−	1.29374i	0.949282	−	0.314425i	$-0.101812\pi$
$720$		0			0
$721$	−0.622875	+	24.5499i	−0.0231971	+	0.914284i
$722$	19.3823	+	18.5140i	0.721335	+	0.689019i
$723$	5.35666	−	9.27801i	0.199216	−	0.345053i
$724$	−1.28067	−	2.00059i	−0.0475959	−	0.0743514i
$725$		0			0
$726$	3.56452	+	12.1797i	0.132292	+	0.452032i
$727$			14.4074i			0.534341i	0.963649	+	0.267171i	$0.0860887\pi$
$727$			14.4074i			0.534341i	−0.963649	+	0.267171i	$0.913911\pi$
$728$	17.9678	+	3.98846i	0.665932	+	0.147822i
$729$	−18.7733			−0.695307
$730$		0			0
$731$	−5.89085	−	10.2032i	−0.217881	−	0.377381i
$732$	13.1234	−	8.40091i	0.485054	−	0.310507i
$733$	0.387263	−	0.670759i	0.0143039	−	0.0247751i	−0.858785	−	0.512336i	$-0.828780\pi$
$733$	0.387263	−	0.670759i	0.0143039	−	0.0247751i	0.873089	+	0.487561i	$0.162113\pi$
$734$	16.8944	−	17.6868i	0.623584	−	0.652831i
$735$		0			0
$736$	29.0963	+	23.0919i	1.07250	+	0.851179i
$737$	7.67931	+	4.43365i	0.282871	+	0.163316i
$738$	20.1877	+	4.91652i	0.743120	+	0.180980i
$739$	7.09915	−	4.09870i	0.261147	−	0.150773i	−0.363711	−	0.931512i	$-0.618490\pi$
$739$	7.09915	−	4.09870i	0.261147	−	0.150773i	0.624858	+	0.780739i	$0.285157\pi$
$740$		0			0
$741$		−	0.592653i		−	0.0217716i
$742$	−47.0529	−	12.7318i	−1.72737	−	0.467398i
$743$	−8.66498			−0.317887			−0.158944	−	0.987288i	$-0.550809\pi$
$743$	−8.66498			−0.317887			−0.158944	+	0.987288i	$0.550809\pi$
$744$	0.487788	−	0.167368i	0.0178832	−	0.00613600i
$745$		0			0
$746$	15.2653	+	3.71770i	0.558901	+	0.136115i
$747$	8.35649	+	4.82462i	0.305748	+	0.176524i
$748$	−21.2932	+	0.976331i	−0.778557	+	0.0356982i
$749$	−48.9942	−	1.24307i	−1.79021	−	0.0454209i
$750$		0			0
$751$	6.73208	+	3.88677i	0.245657	+	0.141830i	0.617774	−	0.786356i	$-0.288035\pi$
$751$	6.73208	+	3.88677i	0.245657	+	0.141830i	−0.372117	+	0.928186i	$0.621368\pi$
$752$	−38.2333	+	27.0212i	−1.39422	+	0.985361i
$753$	−24.0484	+	13.8843i	−0.876372	+	0.505974i
$754$	8.24955	−	2.41431i	0.300431	−	0.0879240i
$755$		0			0
$756$	−13.5205	+	24.5652i	−0.491738	+	0.893429i
$757$		−	5.10767i		−	0.185641i	−0.995683	−	0.0928206i	$-0.970412\pi$
$757$		−	5.10767i		−	0.185641i	0.995683	−	0.0928206i	$-0.0295883\pi$
$758$	−5.68813	−	19.4360i	−0.206602	−	0.705946i
$759$	6.26227	+	10.8466i	0.227306	+	0.393705i
$760$		0			0
$761$	−4.16241	−	2.40317i	−0.150887	−	0.0871149i	0.422655	−	0.906290i	$-0.361098\pi$
$761$	−4.16241	−	2.40317i	−0.150887	−	0.0871149i	−0.573543	+	0.819176i	$0.694431\pi$
$762$	17.2646	−	18.0744i	0.625432	−	0.654766i
$763$	9.62411	−	15.7338i	0.348416	−	0.569603i
$764$	21.0998	−	0.967463i	0.763364	−	0.0350016i
$765$		0			0
$766$	−14.3641	−	3.49824i	−0.518997	−	0.126397i
$767$	5.27264	+	9.13249i	0.190384	+	0.329755i
$768$	−16.7857	−	5.94378i	−0.605703	−	0.214478i
$769$		−	24.7841i		−	0.893738i	−0.894600	−	0.446869i	$-0.852539\pi$
$769$		−	24.7841i		−	0.893738i	0.894600	−	0.446869i	$-0.147461\pi$
$770$		0			0
$771$		−	18.8935i		−	0.680434i
$772$	−4.97335	+	9.60493i	−0.178995	+	0.345689i
$773$	12.6560	+	21.9209i	0.455205	+	0.788438i	0.998700	−	0.0509742i	$-0.0162326\pi$
$773$	12.6560	+	21.9209i	0.455205	+	0.788438i	−0.543495	+	0.839412i	$0.682899\pi$
$774$	−1.11665	+	4.58507i	−0.0401371	+	0.164807i
$775$		0			0
$776$	−19.5649	+	22.4577i	−0.702340	+	0.806184i
$777$	−10.8304	−	19.9084i	−0.388537	−	0.714210i
$778$	−30.8080	−	29.4277i	−1.10452	−	1.05504i
$779$	−1.56404	−	0.902999i	−0.0560375	−	0.0323533i
$780$		0			0
$781$	4.32042	+	7.48318i	0.154597	+	0.267769i
$782$	55.4272	−	16.2213i	1.98207	−	0.580073i
$783$			13.0953i			0.467989i
$784$	14.9799	+	23.6559i	0.534998	+	0.844853i
$785$		0			0
$786$	−1.41757	−	4.84375i	−0.0505631	−	0.172771i
$787$	−43.2134	+	24.9493i	−1.54039	+	0.889345i	−0.541577	+	0.840651i	$0.682173\pi$
$787$	−43.2134	+	24.9493i	−1.54039	+	0.889345i	−0.998814	+	0.0486943i	$0.984494\pi$
$788$	19.3557	+	30.2363i	0.689518	+	1.07712i
$789$	−14.4898	−	8.36567i	−0.515850	−	0.297826i
$790$		0			0
$791$	0.775428	−	0.421840i	0.0275711	−	0.0149989i
$792$	6.43751	+	5.60830i	0.228747	+	0.199282i
$793$	14.9107	+	8.60871i	0.529495	+	0.305704i
$794$	−4.49682	+	18.4644i	−0.159586	+	0.655277i
$795$		0			0
$796$	−13.5880	−	7.03576i	−0.481615	−	0.249376i
$797$	−38.2770			−1.35584			−0.677921	−	0.735135i	$-0.737119\pi$
$797$	−38.2770			−1.35584			−0.677921	+	0.735135i	$0.737119\pi$
$798$	0.639098	−	0.635966i	0.0226238	−	0.0225129i
$799$			72.7894i			2.57510i
$800$		0			0
$801$	−2.72080	+	1.57086i	−0.0961349	+	0.0555035i
$802$	9.66587	−	39.6890i	0.341314	−	1.40147i
$803$	−11.3022	−	6.52532i	−0.398846	−	0.230274i
$804$	11.5049	−	0.527522i	0.405748	−	0.0186043i
$805$		0			0
$806$	0.412054	+	0.393594i	0.0145140	+	0.0138638i
$807$	17.4906	−	30.2945i	0.615697	−	1.06642i
$808$	−0.244090	+	1.24851i	−0.00858704	+	0.0439223i
$809$	4.90151	+	8.48966i	0.172328	+	0.298480i	0.939233	−	0.343280i	$-0.111538\pi$
$809$	4.90151	+	8.48966i	0.172328	+	0.298480i	−0.766906	+	0.641760i	$0.778205\pi$
$810$		0			0
$811$	−4.75188			−0.166861			−0.0834305	−	0.996514i	$-0.526588\pi$
$811$	−4.75188			−0.166861			−0.0834305	+	0.996514i	$0.526588\pi$
$812$	11.4560	+	6.30529i	0.402026	+	0.221272i
$813$			3.69240i			0.129498i
$814$	−17.9033	+	5.23957i	−0.627509	+	0.183647i
$815$		0			0
$816$	−22.6086	+	15.9785i	−0.791460	+	0.559360i
$817$	0.205091	−	0.355228i	0.00717522	−	0.0124278i
$818$	25.3029	−	26.4897i	0.884696	−	0.926191i
$819$	−11.4579	−	0.290709i	−0.400372	−	0.0101582i
$820$		0			0
$821$	−7.82822	+	13.5589i	−0.273207	+	0.473208i	−0.969681	−	0.244374i	$-0.921418\pi$
$821$	−7.82822	+	13.5589i	−0.273207	+	0.473208i	0.696474	+	0.717582i	$0.254751\pi$
$822$	0.485490	−	1.99347i	0.0169334	−	0.0695302i
$823$	−9.89848	−	17.1447i	−0.345039	−	0.597626i	0.640322	−	0.768107i	$-0.278801\pi$
$823$	−9.89848	−	17.1447i	−0.345039	−	0.597626i	−0.985361	+	0.170481i	$0.945468\pi$
$824$	24.8323	−	8.52035i	0.865073	−	0.296820i
$825$		0			0
$826$	−4.19020	+	15.4858i	−0.145796	+	0.538819i
$827$	−13.0808			−0.454863			−0.227431	−	0.973794i	$-0.573033\pi$
$827$	−13.0808			−0.454863			−0.227431	+	0.973794i	$0.573033\pi$
$828$	−20.5419	−	10.6364i	−0.713880	−	0.369641i
$829$	21.7092	−	12.5338i	0.753990	−	0.435316i	−0.0731437	−	0.997321i	$-0.523303\pi$
$829$	21.7092	−	12.5338i	0.753990	−	0.435316i	0.827134	+	0.562005i	$0.189970\pi$
$830$		0			0
$831$	8.20562	−	14.2126i	0.284650	−	0.493028i
$832$	−2.69613	−	19.4904i	−0.0934715	−	0.675707i
$833$	43.4764	+	2.20757i	1.50637	+	0.0764879i
$834$	−22.7011	+	23.7658i	−0.786074	+	0.822943i
$835$		0			0
$836$	−0.400100	−	0.625012i	−0.0138378	−	0.0216165i
$837$	−0.751825	+	0.434066i	−0.0259869	+	0.0150035i
$838$	−38.1426	+	11.1628i	−1.31761	+	0.385613i
$839$	32.1347			1.10941			0.554707	−	0.832046i	$-0.312830\pi$
$839$	32.1347			1.10941			0.554707	+	0.832046i	$0.312830\pi$
$840$		0			0
$841$	−22.8930			−0.789414
$842$	21.2101	−	6.20735i	0.730948	−	0.213919i
$843$	19.8007	−	11.4320i	0.681974	−	0.393738i
$844$	−16.7899	−	26.2282i	−0.577933	−	0.902811i
$845$		0			0
$846$	20.1383	−	21.0828i	0.692368	−	0.724842i
$847$	−21.3258	−	0.541075i	−0.732764	−	0.0185916i
$848$	4.76870	+	51.8919i	0.163758	+	1.78198i
$849$	15.4900	−	26.8295i	0.531616	−	0.920785i
$850$		0			0
$851$	43.7702	−	25.2707i	1.50042	−	0.866270i
$852$	9.96612	+	5.16037i	0.341434	+	0.176791i
$853$	−45.8238			−1.56898			−0.784489	−	0.620142i	$-0.787075\pi$
$853$	−45.8238			−1.56898			−0.784489	+	0.620142i	$0.787075\pi$
$854$	6.71709	+	25.3171i	0.229854	+	0.866334i
$855$		0			0
$856$	17.0041	+	49.5578i	0.581187	+	1.69385i
$857$	−18.6629	−	32.3250i	−0.637512	−	1.10420i	−0.985977	−	0.166881i	$-0.946630\pi$
$857$	−18.6629	−	32.3250i	−0.637512	−	1.10420i	0.348465	−	0.937322i	$-0.386703\pi$
$858$	1.56980	−	6.44574i	0.0535919	−	0.220054i
$859$	6.62605	−	11.4767i	0.226078	−	0.391579i	−0.730564	−	0.682844i	$-0.760743\pi$
$859$	6.62605	−	11.4767i	0.226078	−	0.391579i	0.956642	+	0.291265i	$0.0940762\pi$
$860$		0			0
$861$	12.8163	−	20.9525i	0.436778	−	0.714059i
$862$	19.4877	−	20.4017i	0.663752	−	0.694884i
$863$	3.96707	−	6.87116i	0.135041	−	0.233897i	−0.790572	−	0.612369i	$-0.790217\pi$
$863$	3.96707	−	6.87116i	0.135041	−	0.233897i	0.925613	+	0.378471i	$0.123550\pi$
$864$	29.6519	+	4.39808i	1.00878	+	0.149626i
$865$		0			0
$866$	16.0559	−	4.69892i	0.545601	−	0.159676i
$867$			24.1229i			0.819255i
$868$	0.0177294	+	0.866705i	0.000601776	+	0.0294179i
$869$	27.3334			0.927221
$870$		0			0
$871$	6.36291	+	11.0209i	0.215599	+	0.373428i
$872$	−19.3510	−	3.78322i	−0.655308	−	0.128116i
$873$	9.27406	−	16.0631i	0.313879	−	0.543655i
$874$	1.45394	+	1.38880i	0.0491803	+	0.0469769i
$875$		0			0
$876$	−16.9326	+	0.776391i	−0.572101	+	0.0262318i
$877$	−44.8202	−	25.8770i	−1.51347	−	0.873803i	−0.999876	−	0.0157714i	$-0.994980\pi$
$877$	−44.8202	−	25.8770i	−1.51347	−	0.873803i	−0.513596	−	0.858032i	$-0.671687\pi$
$878$	−9.33465	+	38.3290i	−0.315029	+	1.29354i
$879$	4.12932	−	2.38407i	0.139279	−	0.0804126i
$880$		0			0
$881$			7.69261i			0.259171i	0.991568	+	0.129585i	$0.0413646\pi$
$881$			7.69261i			0.259171i	−0.991568	+	0.129585i	$0.958635\pi$
$882$	−11.9818	−	12.6678i	−0.403449	−	0.426547i
$883$	−35.2766			−1.18715			−0.593575	−	0.804778i	$-0.702284\pi$
$883$	−35.2766			−1.18715			−0.593575	+	0.804778i	$0.702284\pi$
$884$	−27.1652	−	14.0659i	−0.913665	−	0.473087i
$885$		0			0
$886$	6.42472	−	26.3806i	0.215843	−	0.886272i
$887$	10.0685	+	5.81304i	0.338067	+	0.195183i	0.659417	−	0.751778i	$-0.270803\pi$
$887$	10.0685	+	5.81304i	0.338067	+	0.195183i	−0.321350	+	0.946960i	$0.604137\pi$
$888$	−15.9151	+	18.2682i	−0.534076	+	0.613041i
$889$	20.0784	+	36.9082i	0.673409	+	1.23786i
$890$		0			0
$891$	0.910494	+	0.525674i	0.0305027	+	0.0176107i
$892$	12.3655	+	19.3166i	0.414028	+	0.646769i
$893$	−2.19466	+	1.26709i	−0.0734414	+	0.0424014i
$894$	−4.30366	−	14.7053i	−0.143936	−	0.491819i
$895$		0			0
$896$	18.1246	−	23.8222i	0.605501	−	0.795844i
$897$			17.9744i			0.600149i
$898$	6.70545	−	1.96242i	0.223764	−	0.0654867i
$899$	0.202426	+	0.350613i	0.00675130	+	0.0116936i
$900$		0			0
$901$	70.1635	+	40.5089i	2.33749	+	1.34955i
$902$	−14.6188	−	13.9638i	−0.486752	−	0.464945i
$903$	4.75877	+	2.91086i	0.158362	+	0.0968673i
$904$	−0.711543	−	0.619890i	−0.0236656	−	0.0206172i
$905$		0			0
$906$	5.56304	−	22.8424i	0.184820	−	0.758888i
$907$	11.5887	+	20.0723i	0.384798	+	0.666490i	0.991741	−	0.128256i	$-0.0409378\pi$
$907$	11.5887	+	20.0723i	0.384798	+	0.666490i	−0.606943	+	0.794745i	$0.707604\pi$
$908$	8.23457	−	15.9033i	0.273274	−	0.527768i
$909$		−	0.792212i		−	0.0262760i
$910$		0			0
$911$			43.0818i			1.42737i	0.700469	+	0.713683i	$0.252974\pi$
$911$			43.0818i			1.42737i	−0.700469	+	0.713683i	$0.747026\pi$
$912$	−0.875327	−	0.403521i	−0.0289850	−	0.0133619i
$913$	−4.69424	−	8.13067i	−0.155357	−	0.269086i
$914$	35.8962	+	8.74216i	1.18734	+	0.289165i
$915$		0			0
$916$	4.80845	−	0.220476i	0.158876	−	0.00728473i
$917$	8.48105	+	0.215180i	0.280069	+	0.00710587i
$918$	32.1911	−	33.7010i	1.06247	−	1.11230i
$919$	−18.1455	−	10.4763i	−0.598564	−	0.345581i	0.169912	−	0.985459i	$-0.445652\pi$
$919$	−18.1455	−	10.4763i	−0.598564	−	0.345581i	−0.768476	+	0.639878i	$0.778985\pi$
$920$		0			0
$921$	−7.96699	−	13.7992i	−0.262521	−	0.454700i
$922$	5.31858	+	18.1733i	0.175158	+	0.598504i
$923$			12.4008i			0.408177i
$924$	8.63540	−	5.22399i	0.284084	−	0.171857i
$925$		0			0
$926$	22.2620	−	6.51518i	0.731573	−	0.214102i
$927$	−14.1586	+	8.17448i	−0.465030	+	0.268485i
$928$	2.05104	−	13.8281i	0.0673287	−	0.453930i
$929$	8.90058	+	5.13875i	0.292019	+	0.168597i	0.638852	−	0.769330i	$-0.279410\pi$
$929$	8.90058	+	5.13875i	0.292019	+	0.168597i	−0.346833	+	0.937927i	$0.612743\pi$
$930$		0			0
$931$	0.690259	+	1.34928i	0.0226223	+	0.0442208i
$932$	−5.11613	+	0.234584i	−0.167585	+	0.00768405i
$933$	24.7349	+	14.2807i	0.809784	+	0.467529i
$934$	16.3969	+	3.99331i	0.536524	+	0.130665i
$935$		0			0
$936$	3.97662	+	11.5897i	0.129980	+	0.378822i
$937$	38.3992			1.25445			0.627224	−	0.778839i	$-0.284191\pi$
$937$	38.3992			1.25445			0.627224	+	0.778839i	$0.284191\pi$
$938$	−5.05664	+	18.6879i	−0.165105	+	0.610181i
$939$			36.1764i			1.18057i
$940$		0			0
$941$	−13.2891	+	7.67245i	−0.433211	+	0.250115i	−0.700714	−	0.713443i	$-0.747135\pi$
$941$	−13.2891	+	7.67245i	−0.433211	+	0.250115i	0.267502	+	0.963557i	$0.413802\pi$
$942$	12.5774	+	3.06310i	0.409793	+	0.0998011i
$943$	47.4354	+	27.3869i	1.54471	+	0.891839i
$944$	17.0784	−	1.56945i	0.555853	−	0.0510811i
$945$		0			0
$946$	3.17150	−	3.32025i	0.103114	−	0.107951i
$947$	13.3114	−	23.0560i	0.432562	−	0.749219i	−0.564531	−	0.825412i	$-0.690943\pi$
$947$	13.3114	−	23.0560i	0.432562	−	0.749219i	0.997093	+	0.0761928i	$0.0242764\pi$
$948$	29.8995	−	19.1401i	0.971091	−	0.621643i
$949$	−9.36474	−	16.2202i	−0.303992	−	0.526530i
$950$		0			0
$951$	−3.25052			−0.105405
$952$	−13.9823	−	44.3880i	−0.453169	−	1.43862i
$953$		−	5.39146i		−	0.174646i	−0.996180	−	0.0873232i	$-0.972169\pi$
$953$		−	5.39146i		−	0.174646i	0.996180	−	0.0873232i	$-0.0278313\pi$
$954$	−9.11485	−	31.1449i	−0.295104	−	1.00835i
$955$		0			0
$956$	6.80613	+	10.6321i	0.220126	+	0.343867i
$957$	2.35672	−	4.08195i	0.0761818	−	0.131951i
$958$	38.0197	+	36.3163i	1.22836	+	1.17333i
$959$	2.94216	+	1.79967i	0.0950074	+	0.0581143i
$960$		0			0
$961$	15.4866	−	26.8235i	0.499567	−	0.865276i
$962$	−26.0111	−	6.33475i	−0.838632	−	0.204241i
$963$	−16.3138	−	28.2564i	−0.525705	−	0.910548i
$964$	8.85237	−	17.0964i	0.285116	−	0.550638i
$965$		0			0
$966$	−19.3831	+	19.2881i	−0.623640	+	0.620583i
$967$	−6.14901			−0.197739			−0.0988694	−	0.995100i	$-0.531523\pi$
$967$	−6.14901			−0.197739			−0.0988694	+	0.995100i	$0.531523\pi$
$968$	7.40140	+	21.5711i	0.237890	+	0.693323i
$969$	−1.29778	+	0.749271i	−0.0416906	+	0.0240701i
$970$		0			0
$971$	−15.6816	+	27.1613i	−0.503247	+	0.871649i	0.496746	+	0.867896i	$0.334528\pi$
$971$	−15.6816	+	27.1613i	−0.503247	+	0.871649i	−0.999993	+	0.00375309i	$0.998805\pi$
$972$	−30.3972	+	1.39377i	−0.974991	+	0.0447051i
$973$	−26.4009	−	48.5302i	−0.846374	−	1.55581i
$974$	1.00053	+	0.955707i	0.0320591	+	0.0306228i
$975$		0			0
$976$	22.8671	−	16.1612i	0.731957	−	0.517307i
$977$	34.0446	−	19.6557i	1.08918	−	0.628841i	0.155825	−	0.987785i	$-0.450196\pi$
$977$	34.0446	−	19.6557i	1.08918	−	0.628841i	0.933359	+	0.358944i	$0.116863\pi$
$978$	5.29908	+	18.1066i	0.169446	+	0.578985i
$979$	3.05681			0.0976961
$980$		0			0
$981$	12.2787			0.392030
$982$	7.31550	+	24.9966i	0.233447	+	0.797674i
$983$	−26.4013	+	15.2428i	−0.842072	+	0.486170i	−0.857968	−	0.513703i	$-0.828273\pi$
$983$	−26.4013	+	15.2428i	−0.842072	+	0.486170i	0.0158960	+	0.999874i	$0.494940\pi$
$984$	−25.7694	−	5.03805i	−0.821499	−	0.160607i
$985$		0			0
$986$	−15.7164	−	15.0123i	−0.500513	−	0.478089i
$987$	−16.4697	−	30.2747i	−0.524237	−	0.963654i
$988$	−0.0487820	−	1.06391i	−0.00155196	−	0.0338474i
$989$	−6.22015	+	10.7736i	−0.197789	+	0.342581i
$990$		0			0
$991$	11.3870	−	6.57431i	0.361721	−	0.208840i	−0.308114	−	0.951349i	$-0.599698\pi$
$991$	11.3870	−	6.57431i	0.361721	−	0.208840i	0.669835	+	0.742510i	$0.266365\pi$
$992$	0.861881	−	0.340602i	0.0273647	−	0.0108141i
$993$	−4.39461			−0.139459
$994$	−13.3726	+	13.3071i	−0.424154	+	0.422075i
$995$		0			0
$996$	−10.8284	−	5.60687i	−0.343112	−	0.177661i
$997$	5.65950	+	9.80253i	0.179238	+	0.310449i	0.941620	−	0.336678i	$-0.109303\pi$
$997$	5.65950	+	9.80253i	0.179238	+	0.310449i	−0.762382	+	0.647128i	$0.775970\pi$
$998$	26.8404	+	6.53671i	0.849618	+	0.206916i
$999$	20.3931	−	35.3218i	0.645208	−	1.11753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.c.299.15		32
4.3	odd	2	inner	700.2.t.c.299.10		32
5.2	odd	4		700.2.p.c.551.10		32
5.3	odd	4		140.2.o.a.131.7	yes	32
5.4	even	2		700.2.t.d.299.2		32
7.3	odd	6		700.2.t.d.199.7		32
20.3	even	4		140.2.o.a.131.15	yes	32
20.7	even	4		700.2.p.c.551.2		32
20.19	odd	2		700.2.t.d.299.7		32
28.3	even	6		700.2.t.d.199.2		32
35.3	even	12		140.2.o.a.31.15	yes	32
35.13	even	4		980.2.o.f.411.7		32
35.17	even	12		700.2.p.c.451.2		32
35.18	odd	12		980.2.o.f.31.15		32
35.23	odd	12		980.2.g.a.391.11		32
35.24	odd	6	inner	700.2.t.c.199.10		32
35.33	even	12		980.2.g.a.391.12		32
140.3	odd	12		140.2.o.a.31.7	✓	32
140.23	even	12		980.2.g.a.391.10		32
140.59	even	6	inner	700.2.t.c.199.15		32
140.83	odd	4		980.2.o.f.411.15		32
140.87	odd	12		700.2.p.c.451.10		32
140.103	odd	12		980.2.g.a.391.9		32
140.123	even	12		980.2.o.f.31.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.7	✓	32	140.3	odd	12
140.2.o.a.31.15	yes	32	35.3	even	12
140.2.o.a.131.7	yes	32	5.3	odd	4
140.2.o.a.131.15	yes	32	20.3	even	4
700.2.p.c.451.2		32	35.17	even	12
700.2.p.c.451.10		32	140.87	odd	12
700.2.p.c.551.2		32	20.7	even	4
700.2.p.c.551.10		32	5.2	odd	4
700.2.t.c.199.10		32	35.24	odd	6	inner
700.2.t.c.199.15		32	140.59	even	6	inner
700.2.t.c.299.10		32	4.3	odd	2	inner
700.2.t.c.299.15		32	1.1	even	1	trivial
700.2.t.d.199.2		32	28.3	even	6
700.2.t.d.199.7		32	7.3	odd	6
700.2.t.d.299.2		32	5.4	even	2
700.2.t.d.299.7		32	20.19	odd	2
980.2.g.a.391.9		32	140.103	odd	12
980.2.g.a.391.10		32	140.23	even	12
980.2.g.a.391.11		32	35.23	odd	12
980.2.g.a.391.12		32	35.33	even	12
980.2.o.f.31.7		32	140.123	even	12
980.2.o.f.31.15		32	35.18	odd	12
980.2.o.f.411.7		32	35.13	even	4
980.2.o.f.411.15		32	140.83	odd	4

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35728 - 0.397222i) q^{2} +(0.963833 - 0.556469i) q^{3} +(1.68443 - 1.07828i) q^{4} +(1.08715 - 1.13814i) q^{6} +(1.26433 + 2.32410i) q^{7} +(1.85793 - 2.13263i) q^{8} +(-0.880685 + 1.52539i) q^{9} +(1.48417 - 0.856885i) q^{11} +(1.02348 - 1.97662i) q^{12} +2.45950 q^{13} +(2.63924 + 2.65224i) q^{14} +(1.67460 - 3.63259i) q^{16} +(-3.10946 - 5.38574i) q^{17} +(-0.589419 + 2.42021i) q^{18} +(0.108256 - 0.187505i) q^{19} +(2.51190 + 1.53648i) q^{21} +(1.67406 - 1.75258i) q^{22} +(-3.28328 + 5.68681i) q^{23} +(0.603989 - 3.08938i) q^{24} +(3.33823 - 0.976966i) q^{26} +5.29911i q^{27} +(4.63573 + 2.55148i) q^{28} +2.47123 q^{29} +(0.0819131 + 0.141878i) q^{31} +(0.829966 - 5.59564i) q^{32} +(0.953659 - 1.65179i) q^{33} +(-6.35975 - 6.07482i) q^{34} +(0.161354 + 3.51904i) q^{36} +(-6.66562 - 3.84840i) q^{37} +(0.0724531 - 0.297500i) q^{38} +(2.37054 - 1.36863i) q^{39} -8.34130i q^{41} +(4.01968 + 1.08766i) q^{42} +1.89449 q^{43} +(1.57601 - 3.04372i) q^{44} +(-2.19741 + 9.02280i) q^{46} +(-10.1364 - 5.85225i) q^{47} +(-0.407385 - 4.43307i) q^{48} +(-3.80292 + 5.87689i) q^{49} +(-5.99399 - 3.46063i) q^{51} +(4.14285 - 2.65204i) q^{52} +(-11.2823 + 6.51382i) q^{53} +(2.10492 + 7.19238i) q^{54} +(7.30549 + 1.62166i) q^{56} -0.240965i q^{57} +(3.35416 - 0.981628i) q^{58} +(2.14379 + 3.71315i) q^{59} +(6.06251 + 3.50019i) q^{61} +(0.167536 + 0.160030i) q^{62} +(-4.65865 - 0.118198i) q^{63} +(-1.09621 - 7.92454i) q^{64} +(0.638259 - 2.62076i) q^{66} +(2.58708 + 4.48095i) q^{67} +(-11.0450 - 5.71902i) q^{68} +7.30818i q^{69} +5.04201i q^{71} +(1.61684 + 4.71224i) q^{72} +(-3.80759 - 6.59493i) q^{73} +(-10.5758 - 2.57563i) q^{74} +(-0.0198341 - 0.432571i) q^{76} +(3.86797 + 2.36597i) q^{77} +(2.67384 - 2.79925i) q^{78} +(13.8125 + 7.97463i) q^{79} +(0.306736 + 0.531282i) q^{81} +(-3.31335 - 11.3215i) q^{82} -5.47827i q^{83} +(5.88788 - 0.120443i) q^{84} +(2.57136 - 0.752534i) q^{86} +(2.38185 - 1.37516i) q^{87} +(0.930059 - 4.75721i) q^{88} +(1.54471 + 0.891838i) q^{89} +(3.10963 + 5.71612i) q^{91} +(0.601545 + 13.1193i) q^{92} +(0.157901 + 0.0911642i) q^{93} +(-16.0826 - 3.91676i) q^{94} +(-2.31385 - 5.85511i) q^{96} -10.5305 q^{97} +(-2.82720 + 9.48720i) q^{98} +3.01858i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100}) \) 32 * q + 2 * q^4 + 16 * q^9 - 14 * q^12 - 8 * q^13 - 2 * q^14 - 14 * q^16 + 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 + 32 * q^28 + 40 * q^29 + 60 * q^32 - 24 * q^33 + 60 * q^36 - 60 * q^37 - 46 * q^38 + 78 * q^42 + 18 * q^44 + 2 * q^46 - 28 * q^48 + 16 * q^49 - 46 * q^52 - 12 * q^53 - 12 * q^54 - 4 * q^56 + 42 * q^58 + 24 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 - 4 * q^68 + 90 * q^72 - 24 * q^73 - 38 * q^74 + 20 * q^77 - 36 * q^81 + 8 * q^82 + 20 * q^84 + 28 * q^86 - 78 * q^88 + 60 * q^89 + 72 * q^93 - 18 * q^94 - 60 * q^96 - 48 * q^97 - 124 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more