LMFDB - Embedded newform 700.2.t.c.299.10

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			299.10
Character	$\chi$	$=$	700.299
Dual form			700.2.t.c.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.334637 + 1.37405i) q^{2} +(-0.963833 + 0.556469i) q^{3} +(-1.77604 + 0.919616i) 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} +(1.20006 - 1.87467i) q^{12} +2.45950 q^{13} +(2.77035 - 2.51499i) q^{14} +(2.30861 - 3.26654i) q^{16} +(-3.10946 - 5.38574i) q^{17} +(-2.39067 - 0.699655i) 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} +(2.97747 + 1.02162i) q^{24} +(0.823038 + 3.37948i) q^{26} -5.29911i q^{27} +(4.38279 + 2.96499i) q^{28} +2.47123 q^{29} +(-0.0819131 - 0.141878i) q^{31} +(5.26095 + 2.07905i) 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} +(-0.293869 - 0.0860036i) q^{38} +(-2.37054 + 1.36863i) q^{39} -8.34130i q^{41} +(-1.27063 + 3.96564i) q^{42} -1.89449 q^{43} +(1.84793 - 2.88672i) q^{44} +(8.91268 + 2.60838i) 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} +(-4.36816 + 2.26179i) q^{52} +(-11.2823 + 6.51382i) q^{53} +(7.28125 - 1.77328i) q^{54} +(-2.60741 + 7.01437i) q^{56} -0.240965i q^{57} +(0.826965 + 3.39560i) 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} +(2.58877 + 0.757629i) q^{66} +(-2.58708 - 4.48095i) q^{67} +(10.4753 + 6.70576i) q^{68} +7.30818i q^{69} -5.04201i q^{71} +(4.88934 - 0.955891i) q^{72} +(-3.80759 - 6.59493i) q^{73} +(3.05734 - 10.4467i) 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} +(11.4614 - 2.79131i) q^{82} +5.47827i q^{83} +(-5.87420 - 0.418869i) q^{84} +(-0.633967 - 2.60313i) q^{86} +(-2.38185 + 1.37516i) q^{87} +(4.58489 + 1.57315i) 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} +(-4.64929 + 15.8863i) q^{94} +(-6.22760 + 0.923701i) q^{96} -10.5305 q^{97} +(-9.34775 - 3.25878i) 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 $

$2$	0.334637	+	1.37405i	0.236624	+	0.971601i
$2$	0.334637	+	1.37405i	0.236624	+	0.971601i
$3$	−0.963833	+	0.556469i	−0.556469	+	0.321278i	−0.751727	−	0.659474i	$-0.770779\pi$
$3$	−0.963833	+	0.556469i	−0.556469	+	0.321278i	0.195258	+	0.980752i	$0.437446\pi$
$4$	−1.77604	+	0.919616i	−0.888018	+	0.459808i
$5$		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	−0.706771	−	0.707442i	$-0.749849\pi$
$11$	−1.48417	+	0.856885i	−0.447493	+	0.258360i	0.259278	+	0.965803i	$0.416516\pi$
$12$	1.20006	−	1.87467i	0.346429	−	0.541169i
$13$	2.45950			0.682142			0.341071	−	0.940038i	$-0.389210\pi$
$13$	2.45950			0.682142			0.341071	+	0.940038i	$0.389210\pi$
$14$	2.77035	−	2.51499i	0.740406	−	0.672160i
$15$		0			0
$16$	2.30861	−	3.26654i	0.577153	−	0.816636i
$17$	−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	$-0.438620\pi$
$18$	−2.39067	−	0.699655i	−0.563487	−	0.164910i
$19$	−0.108256	+	0.187505i	−0.0248357	+	0.0430167i	−0.878176	−	0.478337i	$-0.841240\pi$
$19$	−0.108256	+	0.187505i	−0.0248357	+	0.0430167i	0.853340	+	0.521354i	$0.174573\pi$
$20$		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	$-0.593305\pi$
$23$	3.28328	−	5.68681i	0.684612	−	1.18578i	0.973559	−	0.228437i	$-0.0733615\pi$
$24$	2.97747	+	1.02162i	0.607774	+	0.208537i
$25$		0			0
$26$	0.823038	+	3.37948i	0.161411	+	0.662770i
$27$		−	5.29911i		−	1.01981i
$28$	4.38279	+	2.96499i	0.828269	+	0.560331i
$29$	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	0.858576	−	0.512687i	$-0.171350\pi$
$31$	−0.0819131	−	0.141878i	−0.0147120	−	0.0254820i	−0.873288	+	0.487205i	$0.838016\pi$
$32$	5.26095	+	2.07905i	0.930013	+	0.367527i
$33$	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	$0.884709\pi$
$38$	−0.293869	−	0.0860036i	−0.0476718	−	0.0139516i
$39$	−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	$-0.225795\pi$
$42$	−1.27063	+	3.96564i	−0.196063	+	0.611912i
$43$	−1.89449			−0.288907			−0.144454	−	0.989512i	$-0.546142\pi$
$43$	−1.89449			−0.288907			−0.144454	+	0.989512i	$0.546142\pi$
$44$	1.84793	−	2.88672i	0.278586	−	0.435190i
$45$		0			0
$46$	8.91268	+	2.60838i	1.31410	+	0.384585i
$47$	10.1364	+	5.85225i	1.47855	+	0.853639i	0.999706	−	0.0242630i	$-0.00772390\pi$
$47$	10.1364	+	5.85225i	1.47855	+	0.853639i	0.478840	+	0.877902i	$0.341057\pi$
$48$	−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
$52$	−4.36816	+	2.26179i	−0.605754	+	0.313654i
$53$	−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	$0.980692\pi$
$54$	7.28125	−	1.77328i	0.990853	−	0.241312i
$55$		0			0
$56$	−2.60741	+	7.01437i	−0.348430	+	0.937335i
$57$		−	0.240965i		−	0.0319166i
$58$	0.826965	+	3.39560i	0.108586	+	0.445864i
$59$	−2.14379	−	3.71315i	−0.279098	−	0.483411i	0.692063	−	0.721837i	$-0.256702\pi$
$59$	−2.14379	−	3.71315i	−0.279098	−	0.483411i	−0.971161	+	0.238426i	$0.923369\pi$
$60$		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
$66$	2.58877	+	0.757629i	0.318656	+	0.0932577i
$67$	−2.58708	−	4.48095i	−0.316062	−	0.547435i	0.663601	−	0.748087i	$-0.269027\pi$
$67$	−2.58708	−	4.48095i	−0.316062	−	0.547435i	−0.979663	+	0.200652i	$0.935694\pi$
$68$	10.4753	+	6.70576i	1.27032	+	0.813193i
$69$			7.30818i			0.879801i
$70$		0			0
$71$		−	5.04201i		−	0.598376i	−0.954194	−	0.299188i	$-0.903284\pi$
$71$		−	5.04201i		−	0.598376i	0.954194	−	0.299188i	$-0.0967158\pi$
$72$	4.88934	−	0.955891i	0.576214	−	0.112653i
$73$	−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	$0.980359\pi$
$74$	3.05734	−	10.4467i	0.355408	−	1.21441i
$75$		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	$-0.978919\pi$
$79$	−13.8125	−	7.97463i	−1.55402	−	0.897216i	−0.556216	−	0.831038i	$-0.687747\pi$
$80$		0			0
$81$	0.306736	+	0.531282i	0.0340817	+	0.0590313i
$82$	11.4614	−	2.79131i	1.26570	−	0.308248i
$83$			5.47827i			0.601318i	0.953732	+	0.300659i	$0.0972066\pi$
$83$			5.47827i			0.601318i	−0.953732	+	0.300659i	$0.902793\pi$
$84$	−5.87420	−	0.418869i	−0.640928	−	0.0457024i
$85$		0			0
$86$	−0.633967	−	2.60313i	−0.0683624	−	0.280703i
$87$	−2.38185	+	1.37516i	−0.255362	+	0.147433i
$88$	4.58489	+	1.57315i	0.488751	+	0.167698i
$89$	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
$94$	−4.64929	+	15.8863i	−0.479537	+	1.63855i
$95$		0			0
$96$	−6.22760	+	0.923701i	−0.635601	+	0.0942748i
$97$	−10.5305			−1.06921			−0.534606	−	0.845101i	$-0.679540\pi$
$97$	−10.5305			−1.06921			−0.534606	+	0.845101i	$0.679540\pi$
$98$	−9.34775	−	3.25878i	−0.944265	−	0.329187i
$99$		−	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	$0.340457\pi$
$102$	−2.74928	+	9.39411i	−0.272219	+	0.930156i
$103$	−8.03841	−	4.64098i	−0.792048	−	0.457289i	0.0486348	−	0.998817i	$-0.484513\pi$
$103$	−8.03841	−	4.64098i	−0.792048	−	0.457289i	−0.840683	+	0.541527i	$0.817846\pi$
$104$	−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	$-0.480229\pi$
$107$	9.26201	−	16.0423i	0.895392	−	1.55086i	0.833318	−	0.552793i	$-0.186438\pi$
$108$	4.87315	+	9.41141i	0.468919	+	0.905613i
$109$	−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
$112$	−10.5106	−	1.23545i	−0.993163	−	0.116739i
$113$		−	0.333646i		−	0.0313868i	−0.999877	−	0.0156934i	$-0.995004\pi$
$113$		−	0.333646i		−	0.0313868i	0.999877	−	0.0156934i	$-0.00499557\pi$
$114$	0.331098	−	0.0806358i	0.0310102	−	0.00755223i
$115$		0			0
$116$	−4.38900	+	2.27259i	−0.407508	+	0.211004i
$117$	−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
$122$	−2.78071	+	9.50150i	−0.251753	+	0.860225i
$123$	4.64168	+	8.03962i	0.418526	+	0.724908i
$124$	0.275954	+	0.176651i	0.0247814	+	0.0158638i
$125$		0			0
$126$	1.39654	+	6.44077i	0.124414	+	0.573790i
$127$	−15.8806			−1.40918			−0.704589	−	0.709616i	$-0.748869\pi$
$127$	−15.8806			−1.40918			−0.704589	+	0.709616i	$0.748869\pi$
$128$	−11.2556	+	1.14559i	−0.994860	+	0.101257i
$129$	1.82597	−	1.05423i	0.160768	−	0.0928195i
$130$		0			0
$131$	−1.60328	+	2.77697i	−0.140080	+	0.242625i	−0.927526	−	0.373758i	$-0.878069\pi$
$131$	−1.60328	+	2.77697i	−0.140080	+	0.242625i	0.787447	+	0.616383i	$0.211402\pi$
$132$	−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
$136$	−5.70864	+	16.6376i	−0.489512	+	1.42667i
$137$	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	$0.315599\pi$
$138$	−10.0418	+	2.44558i	−0.854816	+	0.208182i
$139$	20.8813			1.77113			0.885563	−	0.464519i	$-0.153773\pi$
$139$	20.8813			1.77113			0.885563	+	0.464519i	$0.153773\pi$
$140$		0			0
$141$	−13.0264			−1.09702
$142$	6.92798	−	1.68724i	0.581383	−	0.141590i
$143$	−3.65031	+	2.10750i	−0.305254	+	0.176238i
$144$	2.94960	+	6.39833i	0.245800	+	0.533194i
$145$		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	−0.923408	−	0.383821i	$-0.874608\pi$
$151$	−12.9360	+	7.46858i	−1.05271	+	0.607784i	−0.129306	+	0.991605i	$0.541275\pi$
$152$	0.601012	−	0.117501i	0.0487485	−	0.00953058i
$153$	10.9538			0.885563
$154$	−1.95660	+	6.10654i	−0.157667	+	0.492079i
$155$		0			0
$156$	2.95155	−	4.61073i	0.236313	−	0.369154i
$157$	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	$0.726892\pi$
$158$	6.33540	−	21.6476i	0.504017	−	1.72219i
$159$	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	−0.529958	−	0.848024i	$-0.677792\pi$
$163$	5.99330	−	10.3807i	0.469431	−	0.813079i	0.999389	+	0.0349450i	$0.0111256\pi$
$164$	7.67080	+	14.8145i	0.598989	+	1.15681i
$165$		0			0
$166$	−7.52742	+	1.83323i	−0.584241	+	0.142286i
$167$			14.8103i			1.14606i	0.819535	+	0.573029i	$0.194232\pi$
$167$			14.8103i			1.14606i	−0.819535	+	0.573029i	$0.805768\pi$
$168$	−1.39017	−	8.21162i	−0.107254	−	0.633540i
$169$	−6.95088			−0.534683
$170$		0			0
$171$	−0.190679	−	0.330266i	−0.0145816	−	0.0252561i
$172$	3.36469	−	1.74221i	0.256555	−	0.132842i
$173$	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
$178$	−0.708516	+	2.42095i	−0.0531055	+	0.181458i
$179$	−5.53306	+	3.19451i	−0.413560	+	0.238769i	−0.692318	−	0.721592i	$-0.743411\pi$
$179$	−5.53306	+	3.19451i	−0.413560	+	0.238769i	0.278758	+	0.960361i	$0.410077\pi$
$180$		0			0
$181$		−	1.18770i		−	0.0882808i	−0.999025	−	0.0441404i	$-0.985945\pi$
$181$		−	1.18770i		−	0.0882808i	0.999025	−	0.0441404i	$-0.0140549\pi$
$182$	6.81366	−	6.18561i	0.505062	−	0.458508i
$183$	−7.79100			−0.575927
$184$	−18.2280	+	3.56366i	−1.34378	+	0.262716i
$185$		0			0
$186$	−0.0724249	+	0.247471i	−0.00531045	+	0.0181455i
$187$	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	0.131170	−	0.991360i	$-0.458126\pi$
$191$	−9.14608	−	5.28049i	−0.661787	−	0.382083i	−0.792958	+	0.609277i	$0.791460\pi$
$192$	−3.35319	−	8.24794i	−0.241996	−	0.595244i
$193$	−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	$0.395687\pi$
$194$	−3.52390	−	14.4695i	−0.253001	−	1.03885i
$195$		0			0
$196$	1.34964	−	13.9348i	0.0964025	−	0.995342i
$197$			17.9504i			1.27892i	0.768826	+	0.639458i	$0.220841\pi$
$197$			17.9504i			1.27892i	−0.768826	+	0.639458i	$0.779159\pi$
$198$	4.14769	−	1.01013i	0.294763	−	0.0717867i
$199$	3.82538	+	6.62575i	0.271174	+	0.469687i	0.969163	−	0.246422i	$-0.0792548\pi$
$199$	3.82538	+	6.62575i	0.271174	+	0.469687i	−0.697989	+	0.716109i	$0.745921\pi$
$200$		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
$206$	3.68700	−	12.5982i	0.256885	−	0.877761i
$207$	5.78307	+	10.0166i	0.401951	+	0.696200i
$208$	5.67802	−	8.03405i	0.393700	−	0.557061i
$209$		−	0.371053i		−	0.0256662i
$210$		0			0
$211$			15.5710i			1.07195i	0.844234	+	0.535975i	$0.180056\pi$
$211$			15.5710i			1.07195i	−0.844234	+	0.535975i	$0.819944\pi$
$212$	14.0475	−	21.9442i	0.964787	−	1.50713i
$213$	2.80572	+	4.85965i	0.192245	+	0.332978i
$214$	25.1423	+	7.35815i	1.71869	+	0.502993i
$215$		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
$222$	2.86652	+	11.7702i	0.192388	+	0.789964i
$223$		−	11.4678i		−	0.767938i	−0.923346	−	0.383969i	$-0.874557\pi$
$223$		−	11.4678i		−	0.767938i	0.923346	−	0.383969i	$-0.125443\pi$
$224$	−1.81968	−	14.8556i	−0.121582	−	0.992581i
$225$		0			0
$226$	0.458447	−	0.111650i	0.0304954	−	0.00742686i
$227$	−7.75470	+	4.47718i	−0.514697	+	0.297161i	−0.734762	−	0.678325i	$-0.762706\pi$
$227$	−7.75470	+	4.47718i	−0.514697	+	0.297161i	0.220065	+	0.975485i	$0.429373\pi$
$228$	0.221595	+	0.427963i	0.0146755	+	0.0283425i
$229$	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	$0.693398\pi$
$234$	−5.87986	−	1.72080i	−0.384378	−	0.112492i
$235$		0			0
$236$	7.22213	+	4.62323i	0.470120	+	0.300947i
$237$	17.7505			1.15302
$238$	−22.1594	−	7.10010i	−1.43638	−	0.460231i
$239$		−	6.31200i		−	0.408289i	−0.978941	−	0.204145i	$-0.934559\pi$
$239$		−	6.31200i		−	0.408289i	0.978941	−	0.204145i	$-0.0654413\pi$
$240$		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	$0.232992\pi$
$242$	−10.9438	−	3.20280i	−0.703491	−	0.205884i
$243$	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
$248$	−0.150384	+	0.438289i	−0.00954938	+	0.0278314i
$249$	−3.04848	−	5.28013i	−0.193190	−	0.334615i
$250$		0			0
$251$	24.9508			1.57488			0.787440	−	0.616391i	$-0.211406\pi$
$251$	24.9508			1.57488			0.787440	+	0.616391i	$0.211406\pi$
$252$	−8.38262	+	4.07424i	−0.528056	+	0.256653i
$253$			11.2536i			0.707506i
$254$	−5.31424	−	21.8208i	−0.333445	−	1.36916i
$255$		0			0
$256$	−5.34062	−	15.0824i	−0.333789	−	0.942648i
$257$	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
$262$	−4.35222	−	1.27372i	−0.268881	−	0.0786906i
$263$	7.51675	+	13.0194i	0.463503	+	0.802810i	0.999133	−	0.0416428i	$-0.0132591\pi$
$263$	7.51675	+	13.0194i	0.463503	+	0.802810i	−0.535630	+	0.844453i	$0.679926\pi$
$264$	−5.29448	+	1.03510i	−0.325853	+	0.0637059i
$265$		0			0
$266$	0.171667	+	0.791719i	0.0105256	+	0.0485434i
$267$	−1.98512			−0.121487
$268$	8.71550	+	5.57921i	0.532384	+	0.340805i
$269$	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	−0.811233	−	0.584723i	$-0.801203\pi$
$271$	1.65885	−	2.87322i	0.100768	−	0.174536i	0.912001	+	0.410187i	$0.134537\pi$
$272$	−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
$276$	−6.72072	−	12.9796i	−0.404540	−	0.781280i
$277$	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	$0.187249\pi$
$278$	6.98764	+	28.6919i	0.419091	+	1.72083i
$279$	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	$0.290056\pi$
$282$	−4.35911	−	17.8989i	−0.259581	−	1.06587i
$283$	−24.1069	+	13.9181i	−1.43301	+	0.827346i	−0.997349	−	0.0727665i	$-0.976817\pi$
$283$	−24.1069	+	13.9181i	−1.43301	+	0.827346i	−0.435657	+	0.900113i	$0.643484\pi$
$284$	4.63671	+	8.95479i	0.275138	+	0.531369i
$285$		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
$292$	12.8272	+	8.21132i	0.750656	+	0.480531i
$293$	4.28428			0.250290			0.125145	−	0.992138i	$-0.460060\pi$
$293$	4.28428			0.250290			0.125145	+	0.992138i	$0.460060\pi$
$294$	10.8231	−	2.06081i	0.631214	−	0.120189i
$295$		0			0
$296$	4.17703	+	21.3653i	0.242785	+	1.24183i
$297$	4.54072	+	7.86477i	0.263480	+	0.456360i
$298$	13.2131	+	3.86693i	0.765412	+	0.224005i
$299$	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
$304$	0.362573	+	0.786501i	0.0207950	+	0.0451089i
$305$		0			0
$306$	3.66555	+	15.0511i	0.209545	+	0.860414i
$307$			14.3171i			0.817117i	0.912732	+	0.408559i	$0.133968\pi$
$307$			14.3171i			0.817117i	−0.912732	+	0.408559i	$0.866032\pi$
$308$	−9.04545	−	0.645000i	−0.515412	−	0.0367523i
$309$	10.3302			0.587667
$310$		0			0
$311$	−12.8315	−	22.2249i	−0.727609	−	1.26026i	−0.957891	−	0.287132i	$-0.907298\pi$
$311$	−12.8315	−	22.2249i	−0.727609	−	1.26026i	0.230281	−	0.973124i	$-0.426035\pi$
$312$	7.32308	+	2.51267i	0.414588	+	0.142252i
$313$	−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	$0.692804\pi$
$318$	19.6792	+	5.75931i	1.10355	+	0.322966i
$319$	−3.66772	+	2.11756i	−0.205353	+	0.118561i
$320$		0			0
$321$			20.6161i			1.15068i
$322$	−5.20645	−	24.0119i	−0.290144	−	1.33813i
$323$	1.34647			0.0749198
$324$	−1.03335	−	0.661497i	−0.0574083	−	0.0367498i
$325$		0			0
$326$	16.2692	+	4.76134i	0.901067	+	0.263706i
$327$	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	0.591027	−	0.806652i	$-0.298723\pi$
$331$	3.41964	+	1.97433i	0.187960	+	0.108519i	−0.403067	+	0.915170i	$0.632056\pi$
$332$	−5.03790	−	9.72960i	−0.276491	−	0.533981i
$333$	11.7406	−	6.77845i	0.643382	−	0.371457i
$334$	−20.3502	+	4.95608i	−1.11351	+	0.271185i
$335$		0			0
$336$	10.8180	−	4.65808i	0.590170	−	0.254119i
$337$		−	10.0467i		−	0.547280i	−0.961832	−	0.273640i	$-0.911772\pi$
$337$		−	10.0467i		−	0.547280i	0.961832	−	0.273640i	$-0.0882277\pi$
$338$	−2.32602	−	9.55087i	−0.126519	−	0.519499i
$339$	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
$346$	21.2019	+	6.20496i	1.13982	+	0.333581i
$347$	−0.0100550	−	0.0174157i	−0.000539780	−	0.000934926i	0.865755	−	0.500467i	$-0.166838\pi$
$347$	−0.0100550	−	0.0174157i	−0.000539780	−	0.000934926i	−0.866295	+	0.499532i	$0.833505\pi$
$348$	2.96564	−	4.63274i	0.158975	−	0.248341i
$349$			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
$352$	−9.58963	+	1.42237i	−0.511129	+	0.0758126i
$353$	−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	$-0.403905\pi$
$354$	−1.89547	+	6.47669i	−0.100743	+	0.344232i
$355$		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	0.872094	−	0.489339i	$-0.162762\pi$
$359$	16.7562	+	9.67422i	0.884361	+	0.510586i	0.0122672	+	0.999925i	$0.496095\pi$
$360$		0			0
$361$	9.47656	+	16.4139i	0.498766	+	0.863889i
$362$	1.63196	−	0.397447i	0.0857737	−	0.0208893i
$363$		−	8.97361i		−	0.470993i
$364$	10.7795	+	7.29238i	0.564997	+	0.382225i
$365$		0			0
$366$	−2.60715	−	10.7052i	−0.136278	−	0.559571i
$367$	−14.9780	+	8.64757i	−0.781846	+	0.451399i	−0.837084	−	0.547074i	$-0.815742\pi$
$367$	−14.9780	+	8.64757i	−0.781846	+	0.451399i	0.0552378	+	0.998473i	$0.482408\pi$
$368$	−10.9964	−	23.8536i	−0.573227	−	1.24346i
$369$	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	$0.573803\pi$
$374$	−4.23351	+	14.4656i	−0.218910	+	0.748000i
$375$		0			0
$376$	−6.35201	−	32.4902i	−0.327580	−	1.67556i
$377$	6.07799			0.313032
$378$	−13.3272	−	14.6804i	−0.685478	−	0.755076i
$379$			14.3198i			0.735558i	0.929913	+	0.367779i	$0.119882\pi$
$379$			14.3198i			0.735558i	−0.929913	+	0.367779i	$0.880118\pi$
$380$		0			0
$381$	15.3063	−	8.83707i	0.784164	−	0.452737i
$382$	4.19506	−	14.3342i	0.214638	−	0.733403i
$383$	9.05330	+	5.22693i	0.462602	+	0.267084i	0.713138	−	0.701024i	$-0.247273\pi$
$383$	9.05330	+	5.22693i	0.462602	+	0.267084i	−0.250536	+	0.968107i	$0.580607\pi$
$384$	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
$388$	18.7026	−	9.68403i	0.949480	−	0.491632i
$389$	−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
$392$	19.5988	−	2.80862i	0.989887	−	0.141857i
$393$		−	3.56871i		−	0.180018i
$394$	−24.6648	+	6.00688i	−1.24260	+	0.302622i
$395$		0			0
$396$	2.77594	+	5.36111i	0.139496	+	0.269406i
$397$	−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	$-0.0897497\pi$
$402$	−2.28741	+	7.81593i	−0.114086	+	0.389823i
$403$	−0.201465	−	0.348948i	−0.0100357	−	0.0173823i
$404$	0.484981	−	0.757607i	0.0241287	−	0.0376924i
$405$		0			0
$406$	6.84617	−	6.21513i	0.339770	−	0.308452i
$407$	13.1905			0.653830
$408$	−3.75616	−	19.2126i	−0.185957	−	0.951164i
$409$	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
$416$	12.9393	+	5.11341i	0.634400	+	0.250705i
$417$	−20.1260	+	11.6198i	−0.985577	+	0.569023i
$418$	0.509846	−	0.124168i	0.0249374	−	0.00607325i
$419$	28.1022			1.37288			0.686441	−	0.727185i	$-0.259172\pi$
$419$	28.1022			1.37288			0.686441	+	0.727185i	$0.259172\pi$
$420$		0			0
$421$	15.6269			0.761608			0.380804	−	0.924656i	$-0.375647\pi$
$421$	15.6269			0.761608			0.380804	+	0.924656i	$0.375647\pi$
$422$	−21.3953	+	5.21062i	−1.04151	+	0.253649i
$423$	−17.8539	+	10.3080i	−0.868088	+	0.501191i
$424$	34.8532	+	11.9587i	1.69262	+	0.580765i
$425$		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	−0.854609	−	0.519273i	$-0.826203\pi$
$431$	−17.2771	+	9.97495i	−0.832210	+	0.480477i	0.0223988	+	0.999749i	$0.492870\pi$
$432$	−17.3098	−	12.2336i	−0.832817	−	0.588589i
$433$	11.8294			0.568487			0.284243	−	0.958752i	$-0.408258\pi$
$433$	11.8294			0.568487			0.284243	+	0.958752i	$0.408258\pi$
$434$	−0.583749	−	0.187039i	−0.0280208	−	0.00897818i
$435$		0			0
$436$	11.7424	+	7.51687i	0.562359	+	0.359993i
$437$	0.710872	+	1.23127i	0.0340056	+	0.0588995i
$438$	−3.36654	+	11.5033i	−0.160860	+	0.549647i
$439$	13.9474	−	24.1577i	0.665675	−	1.15298i	−0.313427	−	0.949612i	$-0.601477\pi$
$439$	13.9474	−	24.1577i	0.665675	−	1.15298i	0.979102	−	0.203371i	$-0.0651897\pi$
$440$		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	−0.998750	−	0.0499830i	$-0.984083\pi$
$443$	−9.59955	+	16.6269i	−0.456088	+	0.789968i	0.542662	+	0.839951i	$0.317417\pi$
$444$	−15.2136	+	7.87748i	−0.722007	+	0.373849i
$445$		0			0
$446$	15.7573	−	3.83753i	0.746130	−	0.181713i
$447$			10.8344i			0.512449i
$448$	19.8034	−	7.47156i	0.935624	−	0.352998i
$449$	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
$452$	0.306826	+	0.592568i	0.0144319	+	0.0278720i
$453$	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	$0.457425\pi$
$458$	−0.956014	+	3.26664i	−0.0446716	+	0.152640i
$459$	−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	$0.899067\pi$
$462$	−1.51226	−	6.97447i	−0.0703568	−	0.324482i
$463$	−16.4019			−0.762259			−0.381130	−	0.924522i	$-0.624465\pi$
$463$	−16.4019			−0.762259			−0.381130	+	0.924522i	$0.624465\pi$
$464$	5.70512	−	8.07239i	0.264853	−	0.374751i
$465$		0			0
$466$	1.01719	−	3.47567i	0.0471203	−	0.161007i
$467$	−10.3345	−	5.96663i	−0.478224	−	0.276103i	0.241452	−	0.970413i	$-0.422376\pi$
$467$	−10.3345	−	5.96663i	−0.478224	−	0.276103i	−0.719676	+	0.694310i	$0.755710\pi$
$468$	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
$472$	−3.93577	+	11.4707i	−0.181159	+	0.527981i
$473$	2.81175	−	1.62336i	0.129284	−	0.0746423i
$474$	5.93998	+	24.3902i	0.272832	+	1.12028i
$475$		0			0
$476$	2.34057	−	32.8241i	0.107280	−	1.50449i
$477$		−	22.9465i		−	1.05065i
$478$	8.67301	−	2.11223i	0.396694	−	0.0966110i
$479$	−18.5889	−	32.1969i	−0.849347	−	1.47111i	−0.881792	−	0.471639i	$-0.843663\pi$
$479$	−18.5889	−	32.1969i	−0.849347	−	1.47111i	0.0324444	−	0.999474i	$-0.489671\pi$
$480$		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
$486$	−6.04356	+	20.6505i	−0.274142	+	0.936724i
$487$	−0.489188	−	0.847298i	−0.0221672	−	0.0383948i	0.854729	−	0.519075i	$-0.173723\pi$
$487$	−0.489188	−	0.847298i	−0.0221672	−	0.0383948i	−0.876896	+	0.480680i	$0.840390\pi$
$488$	−3.79909	−	19.4322i	−0.171977	−	0.879654i
$489$			13.3403i			0.603271i
$490$		0			0
$491$		−	18.4167i		−	0.831132i	−0.909563	−	0.415566i	$-0.863583\pi$
$491$		−	18.4167i		−	0.831132i	0.909563	−	0.415566i	$-0.136417\pi$
$492$	−15.6372	−	10.0101i	−0.704977	−	0.451290i
$493$	−7.68420	−	13.3094i	−0.346079	−	0.599426i
$494$	−0.722769	−	0.211525i	−0.0325189	−	0.00951698i
$495$		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	0.0710273	−	0.997474i	$-0.477372\pi$
$499$	−16.9167	−	9.76688i	−0.757297	−	0.437226i	−0.828324	+	0.560249i	$0.810706\pi$
$500$		0			0
$501$	−8.24149	−	14.2747i	−0.368203	−	0.637746i
$502$	8.34945	+	34.2837i	0.372654	+	1.53016i
$503$			11.7007i			0.521707i	0.965378	+	0.260853i	$0.0840039\pi$
$503$			11.7007i			0.521707i	−0.965378	+	0.260853i	$0.915996\pi$
$504$	−8.40335	−	10.1548i	−0.374315	−	0.452329i
$505$		0			0
$506$	−15.4630	+	3.76586i	−0.687414	+	0.167413i
$507$	6.69948	−	3.86795i	0.297534	−	0.171782i
$508$	28.2046	−	14.6041i	1.25138	−	0.647951i
$509$	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
$514$	23.0416	+	6.74335i	1.01632	+	0.297436i
$515$		0			0
$516$	−2.27351	+	3.55154i	−0.100086	+	0.156348i
$517$	−20.0588			−0.882186
$518$	−28.1448	+	6.10258i	−1.23661	+	0.268132i
$519$			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	$0.430146\pi$
$522$	−5.90792	−	1.72901i	−0.258582	−	0.0756767i
$523$	−32.5328	−	18.7828i	−1.42256	−	0.821316i	−0.426043	−	0.904703i	$-0.640093\pi$
$523$	−32.5328	−	18.7828i	−1.42256	−	0.821316i	−0.996517	+	0.0833873i	$0.973426\pi$
$524$	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
$528$	−3.19400	−	6.92851i	−0.139001	−	0.301524i
$529$	−10.0599	−	17.4242i	−0.437386	−	0.757575i
$530$		0			0
$531$	7.55201			0.327729
$532$	−1.03042	+	0.500818i	−0.0446742	+	0.0217132i
$533$		−	20.5154i		−	0.888621i
$534$	−0.664294	−	2.72766i	−0.0287468	−	0.118037i
$535$		0			0
$536$	−4.74960	+	13.8426i	−0.205152	+	0.597907i
$537$	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	$0.972821\pi$
$542$	4.50306	+	1.31787i	0.193423	+	0.0566072i
$543$	0.660916	+	1.14474i	0.0283626	+	0.0491255i
$544$	−5.16149	−	34.7988i	−0.221297	−	1.49199i
$545$		0			0
$546$	−3.12512	+	9.75348i	−0.133743	+	0.417411i
$547$	24.0582			1.02865			0.514327	−	0.857594i	$-0.328042\pi$
$547$	24.0582			1.02865			0.514327	+	0.857594i	$0.328042\pi$
$548$	−1.40562	+	2.19578i	−0.0600452	+	0.0937990i
$549$	−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
$556$	−37.0859	+	19.2028i	−1.57279	+	0.814378i
$557$	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	$0.141613\pi$
$558$	0.0965622	+	0.396494i	0.00408780	+	0.0167849i
$559$	−4.65950			−0.197076
$560$		0			0
$561$	−11.8615			−0.500791
$562$	6.87470	+	28.2282i	0.289992	+	1.19073i
$563$	15.1306	−	8.73567i	0.637680	−	0.368165i	−0.146041	−	0.989279i	$-0.546653\pi$
$563$	15.1306	−	8.73567i	0.637680	−	0.368165i	0.783720	+	0.621114i	$0.213320\pi$
$564$	23.1353	−	11.9793i	0.974174	−	0.504419i
$565$		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	−0.0391963	−	0.999232i	$-0.512480\pi$
$571$	19.2734	−	11.1275i	0.806565	−	0.465671i	0.845762	+	0.533561i	$0.179146\pi$
$572$	4.54498	−	7.09989i	0.190035	−	0.296861i
$573$	11.7537			0.491019
$574$	−20.9783	−	23.1083i	−0.875618	−	0.964522i
$575$		0			0
$576$	−11.1226	−	8.65117i	−0.463442	−	0.360465i
$577$	−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	$0.839768\pi$
$578$	−29.4190	−	8.60976i	−1.22367	−	0.358119i
$579$	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
$584$	−6.99033	+	20.3731i	−0.289262	+	0.843044i
$585$		0			0
$586$	1.43368	+	5.88682i	0.0592246	+	0.243182i
$587$		−	17.6042i		−	0.726602i	−0.931672	−	0.363301i	$-0.881650\pi$
$587$		−	17.6042i		−	0.726602i	0.931672	−	0.363301i	$-0.118350\pi$
$588$	6.45346	+	14.1818i	0.266136	+	0.584849i
$589$	0.0354704			0.00146153
$590$		0			0
$591$	−9.98887	−	17.3012i	−0.410887	−	0.711677i
$592$	−27.9593	+	12.8891i	−1.14912	+	0.529738i
$593$	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
$598$	21.9207	+	6.41531i	0.896404	+	0.262342i
$599$	−15.9061	+	9.18338i	−0.649905	+	0.375223i	−0.788420	−	0.615137i	$-0.789100\pi$
$599$	−15.9061	+	9.18338i	−0.649905	+	0.375223i	0.138515	+	0.990360i	$0.455767\pi$
$600$		0			0
$601$			11.9668i			0.488136i	0.969758	+	0.244068i	$0.0784820\pi$
$601$			11.9668i			0.488136i	−0.969758	+	0.244068i	$0.921518\pi$
$602$	−5.24840	+	4.76463i	−0.213909	+	0.194192i
$603$	9.11360			0.371134
$604$	16.1065	−	25.1606i	0.655365	−	1.02377i
$605$		0			0
$606$	0.679410	+	0.198836i	0.0275992	+	0.00807717i
$607$	−14.1791	−	8.18629i	−0.575511	−	0.332271i	0.183837	−	0.982957i	$-0.441148\pi$
$607$	−14.1791	−	8.18629i	−0.575511	−	0.332271i	−0.759347	+	0.650686i	$0.774482\pi$
$608$	−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
$612$	−19.4544	+	10.0733i	−0.786396	+	0.407189i
$613$	−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	$0.958414\pi$
$614$	−19.6724	+	4.79101i	−0.793912	+	0.193349i
$615$		0			0
$616$	−2.14068	−	12.6448i	−0.0862503	−	0.509472i
$617$			3.88479i			0.156396i	0.996938	+	0.0781979i	$0.0249166\pi$
$617$			3.88479i			0.156396i	−0.996938	+	0.0781979i	$0.975083\pi$
$618$	3.45688	+	14.1943i	0.139056	+	0.570978i
$619$	−10.2165	−	17.6955i	−0.410636	−	0.711242i	0.584323	−	0.811521i	$-0.301360\pi$
$619$	−10.2165	−	17.6955i	−0.410636	−	0.711242i	−0.994959	+	0.100278i	$0.968027\pi$
$620$		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
$626$	−44.1189	−	12.9118i	−1.76335	−	0.516061i
$627$	0.206479	+	0.357633i	0.00824599	+	0.0142825i
$628$	−13.8538	−	8.86849i	−0.552827	−	0.353891i
$629$			47.8657i			1.90853i
$630$		0			0
$631$			23.7070i			0.943762i	0.881662	+	0.471881i	$0.156425\pi$
$631$			23.7070i			0.943762i	−0.881662	+	0.471881i	$0.843575\pi$
$632$	8.65563	+	44.2731i	0.344302	+	1.76109i
$633$	−8.66476	−	15.0078i	−0.344393	−	0.596507i
$634$	1.16015	−	3.96417i	0.0460756	−	0.157437i
$635$		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	$0.925080\pi$
$642$	−28.3276	+	6.89890i	−1.11800	+	0.272278i
$643$		−	47.6127i		−	1.87766i	−0.344380	−	0.938830i	$-0.611911\pi$
$643$		−	47.6127i		−	1.87766i	0.344380	−	0.938830i	$-0.388089\pi$
$644$	31.2513	−	15.1892i	1.23147	−	0.598538i
$645$		0			0
$646$	0.450580	+	1.85012i	0.0177278	+	0.0727922i
$647$	−0.00937783	+	0.00541429i	−0.000368680	+	0.000212858i	−0.500184	−	0.865919i	$-0.666734\pi$
$647$	−0.00937783	+	0.00541429i	−0.000368680	+	0.000212858i	0.499816	+	0.866132i	$0.333401\pi$
$648$	0.563134	−	1.64124i	0.0221220	−	0.0644738i
$649$	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	$0.733310\pi$
$654$	−3.08183	+	10.5304i	−0.120509	+	0.411771i
$655$		0			0
$656$	−27.2472	−	19.2568i	−1.06383	−	0.751853i
$657$	13.4131			0.523296
$658$	42.7997	−	9.28019i	1.66851	−	0.361780i
$659$			13.3688i			0.520773i	0.965505	+	0.260386i	$0.0838499\pi$
$659$			13.3688i			0.520773i	−0.965505	+	0.260386i	$0.916150\pi$
$660$		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	$0.379961\pi$
$662$	−1.56849	+	5.35944i	−0.0609612	+	0.208301i
$663$	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
$668$	−13.6198	−	26.3037i	−0.526967	−	1.01772i
$669$	6.38146	+	11.0530i	0.246721	+	0.427334i
$670$		0			0
$671$	−11.9970			−0.463141
$672$	10.0205	+	13.3057i	0.386551	+	0.513279i
$673$		−	19.9107i		−	0.767501i	−0.923437	−	0.383751i	$-0.874632\pi$
$673$		−	19.9107i		−	0.767501i	0.923437	−	0.383751i	$-0.125368\pi$
$674$	13.8047	−	3.36200i	0.531738	−	0.129500i
$675$		0			0
$676$	12.3450	−	6.39214i	0.474808	−	0.245852i
$677$	−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
$682$	−0.111524	+	0.381071i	−0.00427048	+	0.0145920i
$683$	7.41000	+	12.8345i	0.283536	+	0.491098i	0.972253	−	0.233932i	$-0.0751592\pi$
$683$	7.41000	+	12.8345i	0.283536	+	0.491098i	−0.688717	+	0.725030i	$0.741826\pi$
$684$	0.642372	+	0.411213i	0.0245617	+	0.0157231i
$685$		0			0
$686$	4.24493	+	25.8453i	0.162072	+	0.986779i
$687$	−2.67856			−0.102194
$688$	−4.37365	+	6.18844i	−0.166744	+	0.235932i
$689$	−27.7487	+	16.0207i	−1.05714	+	0.610341i
$690$		0			0
$691$	13.2455	−	22.9418i	0.503882	−	0.872749i	−0.496108	−	0.868261i	$-0.665238\pi$
$691$	13.2455	−	22.9418i	0.503882	−	0.872749i	0.999990	−	0.00448815i	$-0.00142863\pi$
$692$	−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
$696$	7.35803	+	2.52466i	0.278905	+	0.0956969i
$697$	−44.9241	+	25.9369i	−1.70162	+	0.982432i
$698$	−7.69971	+	1.87519i	−0.291438	+	0.0709769i
$699$	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	$0.504289\pi$
$702$	17.9082	−	4.36137i	0.675902	−	0.164609i
$703$	1.44319	−	0.833226i	0.0544310	−	0.0314257i
$704$	−5.16345	−	12.7007i	−0.194605	−	0.478675i
$705$		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
$712$	−0.967997	−	4.95126i	−0.0362772	−	0.185556i
$713$	−1.07578			−0.0402881
$714$	25.3089	−	5.48769i	0.947162	−	0.205372i
$715$		0			0
$716$	6.88919	−	10.7619i	0.257461	−	0.402190i
$717$	3.51243	+	6.08371i	0.131174	+	0.227200i
$718$	−7.68563	+	26.2613i	−0.286825	+	0.980063i
$719$	−20.0286	+	34.6906i	−0.746941	+	1.29374i	0.202341	+	0.979315i	$0.435145\pi$
$719$	−20.0286	+	34.6906i	−0.746941	+	1.29374i	−0.949282	+	0.314425i	$0.898188\pi$
$720$		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
$724$	1.09222	+	2.10939i	0.0405922	+	0.0783949i
$725$		0			0
$726$	12.3302	−	3.00290i	0.457617	−	0.111448i
$727$		−	14.4074i		−	0.534341i	−0.963649	−	0.267171i	$-0.913911\pi$
$727$		−	14.4074i		−	0.534341i	0.963649	−	0.267171i	$-0.0860887\pi$
$728$	−6.41291	+	17.2518i	−0.237678	+	0.639395i
$729$	−18.7733			−0.695307
$730$		0			0
$731$	5.89085	+	10.2032i	0.217881	+	0.377381i
$732$	13.8371	−	7.16473i	0.511434	−	0.264816i
$733$	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
$738$	−5.83603	+	19.9413i	−0.214827	+	0.734051i
$739$	−7.09915	+	4.09870i	−0.261147	+	0.150773i	−0.624858	−	0.780739i	$-0.714843\pi$
$739$	−7.09915	+	4.09870i	−0.261147	+	0.150773i	0.363711	+	0.931512i	$0.381510\pi$
$740$		0			0
$741$		−	0.592653i		−	0.0217716i
$742$	−14.8736	+	46.4204i	−0.546027	+	1.70415i
$743$	8.66498			0.317887			0.158944	−	0.987288i	$-0.449191\pi$
$743$	8.66498			0.317887			0.158944	+	0.987288i	$0.449191\pi$
$744$	−0.0989492	−	0.506121i	−0.00362765	−	0.0185553i
$745$		0			0
$746$	−4.41301	+	15.0790i	−0.161572	+	0.552080i
$747$	−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	0.372117	−	0.928186i	$-0.378632\pi$
$751$	−6.73208	−	3.88677i	−0.245657	−	0.141830i	−0.617774	+	0.786356i	$0.711965\pi$
$752$	42.5177	−	19.6004i	1.55046	−	0.714754i
$753$	−24.0484	+	13.8843i	−0.876372	+	0.505974i
$754$	2.03392	+	8.35147i	0.0740709	+	0.304143i
$755$		0			0
$756$	15.7118	−	23.2249i	0.571433	−	0.844680i
$757$		−	5.10767i		−	0.185641i	−0.995683	−	0.0928206i	$-0.970412\pi$
$757$		−	5.10767i		−	0.185641i	0.995683	−	0.0928206i	$-0.0295883\pi$
$758$	−19.6761	+	4.79192i	−0.714669	+	0.174050i
$759$	−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
$766$	−4.15250	+	14.1888i	−0.150036	+	0.512663i
$767$	−5.27264	−	9.13249i	−0.190384	−	0.329755i
$768$	13.5403	+	11.5650i	0.488595	+	0.417315i
$769$		−	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
$772$	5.83144	−	9.10951i	0.209878	−	0.327858i
$773$	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	$0.682899\pi$
$774$	4.52912	+	1.32549i	0.162796	+	0.0476438i
$775$		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
$782$	−13.6655	−	56.1120i	−0.488678	−	2.00656i
$783$		−	13.0953i		−	0.467989i
$784$	10.4177	+	25.9899i	0.372059	+	0.928209i
$785$		0			0
$786$	4.90359	−	1.19422i	0.174905	−	0.0425965i
$787$	43.2134	−	24.9493i	1.54039	−	0.889345i	0.541577	−	0.840651i	$-0.317827\pi$
$787$	43.2134	−	24.9493i	1.54039	−	0.889345i	0.998814	−	0.0486943i	$-0.0155060\pi$
$788$	−16.5075	−	31.8806i	−0.588056	−	1.13570i
$789$	−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
$794$	−18.2390	−	5.33783i	−0.647279	−	0.189433i
$795$		0			0
$796$	−12.8872	−	8.24969i	−0.456773	−	0.292403i
$797$	−38.2770			−1.35584			−0.677921	−	0.735135i	$-0.737119\pi$
$797$	−38.2770			−1.35584			−0.677921	+	0.735135i	$0.737119\pi$
$798$	−0.606025	−	0.667557i	−0.0214531	−	0.0236313i
$799$		−	72.7894i		−	2.57510i
$800$		0			0
$801$	−2.72080	+	1.57086i	−0.0961349	+	0.0555035i
$802$	39.2046	+	11.4736i	1.38436	+	0.405148i
$803$	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
$808$	1.20328	+	0.412866i	0.0423314	+	0.0145246i
$809$	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	$-0.473412\pi$
$811$	4.75188			0.166861			0.0834305	+	0.996514i	$0.473412\pi$
$812$	10.8309	+	7.32718i	0.380090	+	0.257134i
$813$			3.69240i			0.129498i
$814$	4.41404	+	18.1245i	0.154712	+	0.635262i
$815$		0			0
$816$	25.1421	−	11.5904i	0.880150	−	0.405745i
$817$	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	$0.254751\pi$
$822$	−1.96914	−	0.576288i	−0.0686816	−	0.0201004i
$823$	9.89848	+	17.1447i	0.345039	+	0.597626i	0.985361	−	0.170481i	$-0.0545322\pi$
$823$	9.89848	+	17.1447i	0.345039	+	0.597626i	−0.640322	+	0.768107i	$0.721199\pi$
$824$	5.03730	+	25.7656i	0.175483	+	0.897586i
$825$		0			0
$826$	−15.2776	−	4.89511i	−0.531575	−	0.170323i
$827$	13.0808			0.454863			0.227431	−	0.973794i	$-0.426967\pi$
$827$	13.0808			0.454863			0.227431	+	0.973794i	$0.426967\pi$
$828$	−19.4824	−	12.4716i	−0.677059	−	0.433418i
$829$	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
$836$	0.341226	+	0.659003i	0.0118015	+	0.0227921i
$837$	−0.751825	+	0.434066i	−0.0259869	+	0.0150035i
$838$	9.40403	+	38.6139i	0.324857	+	1.33389i
$839$	−32.1347			−1.10941			−0.554707	−	0.832046i	$-0.687170\pi$
$839$	−32.1347			−1.10941			−0.554707	+	0.832046i	$0.687170\pi$
$840$		0			0
$841$	−22.8930			−0.789414
$842$	5.22933	+	21.4722i	0.180215	+	0.739980i
$843$	−19.8007	+	11.4320i	−0.681974	+	0.393738i
$844$	−14.3193	−	27.6546i	−0.492891	−	0.951911i
$845$		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
$852$	−9.45208	−	6.05073i	−0.323823	−	0.207295i
$853$	−45.8238			−1.56898			−0.784489	−	0.620142i	$-0.787075\pi$
$853$	−45.8238			−1.56898			−0.784489	+	0.620142i	$0.787075\pi$
$854$	25.5982	−	5.55042i	0.875953	−	0.189931i
$855$		0			0
$856$	−51.4204	+	10.0529i	−1.75751	+	0.343603i
$857$	−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	$-0.386703\pi$
$858$	6.36707	+	1.86339i	0.217368	+	0.0636150i
$859$	−6.62605	+	11.4767i	−0.226078	+	0.391579i	−0.956642	−	0.291265i	$-0.905924\pi$
$859$	−6.62605	+	11.4767i	−0.226078	+	0.391579i	0.730564	+	0.682844i	$0.239257\pi$
$860$		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	−0.925613	−	0.378471i	$-0.876450\pi$
$863$	−3.96707	+	6.87116i	−0.135041	+	0.233897i	0.790572	+	0.612369i	$0.209783\pi$
$864$	11.0171	−	27.8783i	0.374809	−	0.948440i
$865$		0			0
$866$	3.95857	+	16.2543i	0.134518	+	0.552342i
$867$		−	24.1229i		−	0.819255i
$868$	0.0616582	−	0.864691i	0.00209281	−	0.0293495i
$869$	27.3334			0.927221
$870$		0			0
$871$	−6.36291	−	11.0209i	−0.215599	−	0.373428i
$872$	−6.39914	+	18.6501i	−0.216702	+	0.631571i
$873$	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	$-0.671687\pi$
$878$	37.8612	+	11.0805i	1.27775	+	0.373948i
$879$	−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	$0.958635\pi$
$882$	13.2033	−	11.3890i	0.444579	−	0.383488i
$883$	35.2766			1.18715			0.593575	−	0.804778i	$-0.297716\pi$
$883$	35.2766			1.18715			0.593575	+	0.804778i	$0.297716\pi$
$884$	25.7640	+	16.4928i	0.866538	+	0.554713i
$885$		0			0
$886$	−26.0586	−	7.62631i	−0.875456	−	0.256211i
$887$	−10.0685	−	5.81304i	−0.338067	−	0.195183i	0.321350	−	0.946960i	$-0.395863\pi$
$887$	−10.0685	−	5.81304i	−0.338067	−	0.195183i	−0.659417	+	0.751778i	$0.729197\pi$
$888$	−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
$892$	10.5459	+	20.3672i	0.353104	+	0.681943i
$893$	−2.19466	+	1.26709i	−0.0734414	+	0.0424014i
$894$	−14.8870	+	3.62558i	−0.497896	+	0.121258i
$895$		0			0
$896$	16.8933	+	24.7107i	0.564364	+	0.825526i
$897$			17.9744i			0.600149i
$898$	1.65322	+	6.78830i	0.0551688	+	0.226529i
$899$	−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
$906$	22.5636	+	6.60347i	0.749626	+	0.219386i
$907$	−11.5887	−	20.0723i	−0.384798	−	0.666490i	0.606943	−	0.794745i	$-0.292396\pi$
$907$	−11.5887	−	20.0723i	−0.384798	−	0.666490i	−0.991741	+	0.128256i	$0.959062\pi$
$908$	9.65534	−	15.0830i	0.320424	−	0.500546i
$909$		−	0.792212i		−	0.0262760i
$910$		0			0
$911$		−	43.0818i		−	1.42737i	−0.700469	−	0.713683i	$-0.747026\pi$
$911$		−	43.0818i		−	1.42737i	0.700469	−	0.713683i	$-0.252974\pi$
$912$	−0.787123	−	0.556295i	−0.0260642	−	0.0184208i
$913$	−4.69424	−	8.13067i	−0.155357	−	0.269086i
$914$	−10.3772	+	35.4581i	−0.343246	+	1.17285i
$915$		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	0.768476	−	0.639878i	$-0.221015\pi$
$919$	18.1455	+	10.4763i	0.598564	+	0.345581i	−0.169912	+	0.985459i	$0.554348\pi$
$920$		0			0
$921$	−7.96699	−	13.7992i	−0.262521	−	0.454700i
$922$	−18.3978	+	4.48060i	−0.605899	+	0.147561i
$923$		−	12.4008i		−	0.408177i
$924$	9.07722	−	4.41184i	0.298619	−	0.145139i
$925$		0			0
$926$	−5.48867	−	22.5370i	−0.180369	−	0.740612i
$927$	14.1586	−	8.17448i	0.465030	−	0.268485i
$928$	13.0010	+	5.13781i	0.426780	+	0.168657i
$929$	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
$934$	4.74016	−	16.1968i	0.155103	−	0.529976i
$935$		0			0
$936$	12.0253	−	2.35101i	0.393060	−	0.0768452i
$937$	38.3992			1.25445			0.627224	−	0.778839i	$-0.284191\pi$
$937$	38.3992			1.25445			0.627224	+	0.778839i	$0.284191\pi$
$938$	−18.4366	−	5.90730i	−0.601978	−	0.192880i
$939$		−	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	$0.413802\pi$
$942$	3.63597	−	12.4239i	0.118466	−	0.404792i
$943$	−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	−0.997093	−	0.0761928i	$-0.975724\pi$
$947$	−13.3114	+	23.0560i	−0.432562	+	0.749219i	0.564531	+	0.825412i	$0.309057\pi$
$948$	−31.5256	+	16.3237i	−1.02390	+	0.530169i
$949$	−9.36474	−	16.2202i	−0.303992	−	0.526530i
$950$		0			0
$951$	3.25052			0.105405
$952$	45.8852	−	7.76807i	1.48715	−	0.251765i
$953$		−	5.39146i		−	0.174646i	−0.996180	−	0.0873232i	$-0.972169\pi$
$953$		−	5.39146i		−	0.174646i	0.996180	−	0.0873232i	$-0.0278313\pi$
$954$	31.5297	−	7.67874i	1.02081	−	0.248608i
$955$		0			0
$956$	5.80462	+	11.2103i	0.187735	+	0.362568i
$957$	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
$962$	7.51951	−	25.6937i	0.242439	−	0.828397i
$963$	16.3138	+	28.2564i	0.525705	+	0.910548i
$964$	−10.3797	+	16.2146i	−0.334309	+	0.522237i
$965$		0			0
$966$	18.3800	+	20.2462i	0.591367	+	0.651410i
$967$	6.14901			0.197739			0.0988694	−	0.995100i	$-0.468477\pi$
$967$	6.14901			0.197739			0.0988694	+	0.995100i	$0.468477\pi$
$968$	22.3819	−	4.37577i	0.719380	−	0.140643i
$969$	−1.29778	+	0.749271i	−0.0416906	+	0.0240701i
$970$		0			0
$971$	15.6816	−	27.1613i	0.503247	−	0.871649i	−0.496746	−	0.867896i	$-0.665472\pi$
$971$	15.6816	−	27.1613i	0.503247	−	0.871649i	0.999993	−	0.00375309i	$-0.00119465\pi$
$972$	−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
$976$	25.4295	−	11.7229i	0.813979	−	0.375240i
$977$	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	$0.116863\pi$
$978$	−18.3303	+	4.46417i	−0.586139	+	0.142748i
$979$	−3.05681			−0.0976961
$980$		0			0
$981$	12.2787			0.392030
$982$	25.3054	−	6.16289i	0.807529	−	0.196666i
$983$	26.4013	−	15.2428i	0.842072	−	0.486170i	−0.0158960	−	0.999874i	$-0.505060\pi$
$983$	26.4013	−	15.2428i	0.842072	−	0.486170i	0.857968	+	0.513703i	$0.171727\pi$
$984$	8.52163	−	24.8360i	0.271660	−	0.791743i
$985$		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	−0.669835	−	0.742510i	$-0.733635\pi$
$991$	−11.3870	+	6.57431i	−0.361721	+	0.208840i	0.308114	+	0.951349i	$0.400302\pi$
$992$	−0.135970	−	0.916712i	−0.00431706	−	0.0291056i
$993$	−4.39461			−0.139459
$994$	−12.6806	−	13.9681i	−0.402204	−	0.443041i
$995$		0			0
$996$	10.2699	+	6.57427i	0.325415	+	0.208314i
$997$	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	$0.775970\pi$
$998$	7.75924	−	26.5128i	0.245615	−	0.839249i
$999$	−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.299.10		32
4.3	odd	2	inner	700.2.t.c.299.15		32
5.2	odd	4		700.2.p.c.551.2		32
5.3	odd	4		140.2.o.a.131.15	yes	32
5.4	even	2		700.2.t.d.299.7		32
7.3	odd	6		700.2.t.d.199.2		32
20.3	even	4		140.2.o.a.131.7	yes	32
20.7	even	4		700.2.p.c.551.10		32
20.19	odd	2		700.2.t.d.299.2		32
28.3	even	6		700.2.t.d.199.7		32
35.3	even	12		140.2.o.a.31.7	✓	32
35.13	even	4		980.2.o.f.411.15		32
35.17	even	12		700.2.p.c.451.10		32
35.18	odd	12		980.2.o.f.31.7		32
35.23	odd	12		980.2.g.a.391.10		32
35.24	odd	6	inner	700.2.t.c.199.15		32
35.33	even	12		980.2.g.a.391.9		32
140.3	odd	12		140.2.o.a.31.15	yes	32
140.23	even	12		980.2.g.a.391.11		32
140.59	even	6	inner	700.2.t.c.199.10		32
140.83	odd	4		980.2.o.f.411.7		32
140.87	odd	12		700.2.p.c.451.2		32
140.103	odd	12		980.2.g.a.391.12		32
140.123	even	12		980.2.o.f.31.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.7	✓	32	35.3	even	12
140.2.o.a.31.15	yes	32	140.3	odd	12
140.2.o.a.131.7	yes	32	20.3	even	4
140.2.o.a.131.15	yes	32	5.3	odd	4
700.2.p.c.451.2		32	140.87	odd	12
700.2.p.c.451.10		32	35.17	even	12
700.2.p.c.551.2		32	5.2	odd	4
700.2.p.c.551.10		32	20.7	even	4
700.2.t.c.199.10		32	140.59	even	6	inner
700.2.t.c.199.15		32	35.24	odd	6	inner
700.2.t.c.299.10		32	1.1	even	1	trivial
700.2.t.c.299.15		32	4.3	odd	2	inner
700.2.t.d.199.2		32	7.3	odd	6
700.2.t.d.199.7		32	28.3	even	6
700.2.t.d.299.2		32	20.19	odd	2
700.2.t.d.299.7		32	5.4	even	2
980.2.g.a.391.9		32	35.33	even	12
980.2.g.a.391.10		32	35.23	odd	12
980.2.g.a.391.11		32	140.23	even	12
980.2.g.a.391.12		32	140.103	odd	12
980.2.o.f.31.7		32	35.18	odd	12
980.2.o.f.31.15		32	140.123	even	12
980.2.o.f.411.7		32	140.83	odd	4
980.2.o.f.411.15		32	35.13	even	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+(0.334637 + 1.37405i) q^{2} +(-0.963833 + 0.556469i) q^{3} +(-1.77604 + 0.919616i) 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} +(1.20006 - 1.87467i) q^{12} +2.45950 q^{13} +(2.77035 - 2.51499i) q^{14} +(2.30861 - 3.26654i) q^{16} +(-3.10946 - 5.38574i) q^{17} +(-2.39067 - 0.699655i) 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} +(2.97747 + 1.02162i) q^{24} +(0.823038 + 3.37948i) q^{26} -5.29911i q^{27} +(4.38279 + 2.96499i) q^{28} +2.47123 q^{29} +(-0.0819131 - 0.141878i) q^{31} +(5.26095 + 2.07905i) 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} +(-0.293869 - 0.0860036i) q^{38} +(-2.37054 + 1.36863i) q^{39} -8.34130i q^{41} +(-1.27063 + 3.96564i) q^{42} -1.89449 q^{43} +(1.84793 - 2.88672i) q^{44} +(8.91268 + 2.60838i) 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} +(-4.36816 + 2.26179i) q^{52} +(-11.2823 + 6.51382i) q^{53} +(7.28125 - 1.77328i) q^{54} +(-2.60741 + 7.01437i) q^{56} -0.240965i q^{57} +(0.826965 + 3.39560i) 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} +(2.58877 + 0.757629i) q^{66} +(-2.58708 - 4.48095i) q^{67} +(10.4753 + 6.70576i) q^{68} +7.30818i q^{69} -5.04201i q^{71} +(4.88934 - 0.955891i) q^{72} +(-3.80759 - 6.59493i) q^{73} +(3.05734 - 10.4467i) 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} +(11.4614 - 2.79131i) q^{82} +5.47827i q^{83} +(-5.87420 - 0.418869i) q^{84} +(-0.633967 - 2.60313i) q^{86} +(-2.38185 + 1.37516i) q^{87} +(4.58489 + 1.57315i) 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} +(-4.64929 + 15.8863i) q^{94} +(-6.22760 + 0.923701i) q^{96} -10.5305 q^{97} +(-9.34775 - 3.25878i) 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

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Database

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