LMFDB - Embedded newform 700.2.p.e.451.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(451,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			451.15
Character	$\chi$	$=$	700.451
Dual form			700.2.p.e.551.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34238 + 0.444985i) q^{2} +(1.29809 - 2.24836i) q^{3} +(1.60398 + 1.19468i) q^{4} +(2.74302 - 2.44053i) q^{6} +(-0.603960 - 2.57589i) q^{7} +(1.62154 + 2.31746i) q^{8} +(-1.87009 - 3.23909i) q^{9} +(3.12008 + 1.80138i) q^{11} +(4.76818 - 2.05552i) q^{12} -0.818282i q^{13} +(0.335489 - 3.72659i) q^{14} +(1.14549 + 3.83247i) q^{16} +(-6.40537 - 3.69814i) q^{17} +(-1.06903 - 5.18026i) q^{18} +(1.65329 + 2.86358i) q^{19} +(-6.57554 - 1.98583i) q^{21} +(3.38675 + 3.80652i) q^{22} +(-2.19550 + 1.26758i) q^{23} +(7.31540 - 0.637523i) q^{24} +(0.364123 - 1.09845i) q^{26} -1.92166 q^{27} +(2.10863 - 4.85321i) q^{28} +2.04334 q^{29} +(-0.955727 + 1.65537i) q^{31} +(-0.167714 + 5.65437i) q^{32} +(8.10030 - 4.67671i) q^{33} +(-6.95283 - 7.81461i) q^{34} +(0.870092 - 7.42959i) q^{36} +(3.58360 + 6.20697i) q^{37} +(0.945096 + 4.57971i) q^{38} +(-1.83980 - 1.06221i) q^{39} -2.65824i q^{41} +(-7.94322 - 5.59176i) q^{42} -2.39696i q^{43} +(2.85246 + 6.61686i) q^{44} +(-3.51126 + 0.724604i) q^{46} +(-0.667376 - 1.15593i) q^{47} +(10.1037 + 2.39944i) q^{48} +(-6.27046 + 3.11147i) q^{49} +(-16.6295 + 9.60106i) q^{51} +(0.977584 - 1.31251i) q^{52} +(-0.905503 + 1.56838i) q^{53} +(-2.57960 - 0.855108i) q^{54} +(4.99019 - 5.57656i) q^{56} +8.58450 q^{57} +(2.74295 + 0.909256i) q^{58} +(-0.955727 + 1.65537i) q^{59} +(-8.46625 + 4.88799i) q^{61} +(-2.01956 + 1.79685i) q^{62} +(-7.21411 + 6.77344i) q^{63} +(-2.74124 + 7.51569i) q^{64} +(12.9548 - 2.67342i) q^{66} +(8.02134 + 4.63112i) q^{67} +(-5.85597 - 13.5841i) q^{68} +6.58172i q^{69} +1.38422i q^{71} +(4.47405 - 9.58617i) q^{72} +(-6.40537 - 3.69814i) q^{73} +(2.04855 + 9.92677i) q^{74} +(-0.769222 + 6.56827i) q^{76} +(2.75576 - 9.12495i) q^{77} +(-1.99704 - 2.24457i) q^{78} +(-6.70979 + 3.87390i) q^{79} +(3.11579 - 5.39670i) q^{81} +(1.18287 - 3.56837i) q^{82} +10.4973 q^{83} +(-8.17459 - 11.0409i) q^{84} +(1.06661 - 3.21763i) q^{86} +(2.65245 - 4.59418i) q^{87} +(0.884696 + 10.1516i) q^{88} +(9.19133 - 5.30662i) q^{89} +(-2.10781 + 0.494210i) q^{91} +(-5.03589 - 0.589761i) q^{92} +(2.48125 + 4.29764i) q^{93} +(-0.381503 - 1.84867i) q^{94} +(12.4954 + 7.71698i) q^{96} +7.32005i q^{97} +(-9.80192 + 1.38652i) q^{98} -13.4750i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) $ 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Character values

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

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

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 $

$2$	1.34238	+	0.444985i	0.949207	+	0.314652i
$2$	1.34238	+	0.444985i	0.949207	+	0.314652i
$3$	1.29809	−	2.24836i	0.749454	−	1.29809i	−0.198630	−	0.980075i	$-0.563649\pi$
$3$	1.29809	−	2.24836i	0.749454	−	1.29809i	0.948084	−	0.318019i	$-0.103017\pi$
$4$	1.60398	+	1.19468i	0.801989	+	0.597339i
$5$		0			0
$5$		0			0
$6$	2.74302	−	2.44053i	1.11983	−	0.996342i
$7$	−0.603960	−	2.57589i	−0.228275	−	0.973597i
$7$	−0.603960	−	2.57589i	−0.228275	−	0.973597i
$8$	1.62154	+	2.31746i	0.573300	+	0.819346i
$9$	−1.87009	−	3.23909i	−0.623364	−	1.07970i
$10$		0			0
$11$	3.12008	+	1.80138i	0.940738	+	0.543136i	0.890192	−	0.455586i	$-0.150570\pi$
$11$	3.12008	+	1.80138i	0.940738	+	0.543136i	0.0505467	+	0.998722i	$0.483904\pi$
$12$	4.76818	−	2.05552i	1.37646	−	0.593377i
$13$		−	0.818282i		−	0.226951i	−0.993541	−	0.113475i	$-0.963802\pi$
$13$		−	0.818282i		−	0.226951i	0.993541	−	0.113475i	$-0.0361983\pi$
$14$	0.335489	−	3.72659i	0.0896632	−	0.995972i
$15$		0			0
$16$	1.14549	+	3.83247i	0.286371	+	0.958119i
$17$	−6.40537	−	3.69814i	−1.55353	−	0.896931i	−0.997850	−	0.0655347i	$-0.979125\pi$
$17$	−6.40537	−	3.69814i	−1.55353	−	0.896931i	−0.555680	−	0.831396i	$-0.687542\pi$
$18$	−1.06903	−	5.18026i	−0.251973	−	1.22100i
$19$	1.65329	+	2.86358i	0.379291	+	0.656951i	0.990959	−	0.134163i	$-0.0428346\pi$
$19$	1.65329	+	2.86358i	0.379291	+	0.656951i	−0.611668	+	0.791114i	$0.709501\pi$
$20$		0			0
$21$	−6.57554	−	1.98583i	−1.43490	−	0.433344i
$22$	3.38675	+	3.80652i	0.722057	+	0.811553i
$23$	−2.19550	+	1.26758i	−0.457794	+	0.264308i	−0.711116	−	0.703074i	$-0.751810\pi$
$23$	−2.19550	+	1.26758i	−0.457794	+	0.264308i	0.253322	+	0.967382i	$0.418477\pi$
$24$	7.31540	−	0.637523i	1.49325	−	0.130134i
$25$		0			0
$26$	0.364123	−	1.09845i	0.0714104	−	0.215423i
$27$	−1.92166			−0.369823
$28$	2.10863	−	4.85321i	0.398493	−	0.917171i
$29$	2.04334			0.379439			0.189720	−	0.981838i	$-0.439242\pi$
$29$	2.04334			0.379439			0.189720	+	0.981838i	$0.439242\pi$
$30$		0			0
$31$	−0.955727	+	1.65537i	−0.171654	+	0.297313i	−0.938998	−	0.343922i	$-0.888244\pi$
$31$	−0.955727	+	1.65537i	−0.171654	+	0.297313i	0.767345	+	0.641235i	$0.221578\pi$
$32$	−0.167714	+	5.65437i	−0.0296479	+	0.999560i
$33$	8.10030	−	4.67671i	1.41008	−	0.814111i
$34$	−6.95283	−	7.81461i	−1.19240	−	1.34019i
$35$		0			0
$36$	0.870092	−	7.42959i	0.145015	−	1.23827i
$37$	3.58360	+	6.20697i	0.589140	+	1.02042i	0.994345	+	0.106195i	$0.0338666\pi$
$37$	3.58360	+	6.20697i	0.589140	+	1.02042i	−0.405206	+	0.914226i	$0.632800\pi$
$38$	0.945096	+	4.57971i	0.153315	+	0.742927i
$39$	−1.83980	−	1.06221i	−0.294603	−	0.170089i
$40$		0			0
$41$		−	2.65824i		−	0.415147i	−0.978219	−	0.207573i	$-0.933443\pi$
$41$		−	2.65824i		−	0.415147i	0.978219	−	0.207573i	$-0.0665566\pi$
$42$	−7.94322	−	5.59176i	−1.22567	−	0.862827i
$43$		−	2.39696i		−	0.365533i	−0.983156	−	0.182766i	$-0.941495\pi$
$43$		−	2.39696i		−	0.365533i	0.983156	−	0.182766i	$-0.0585052\pi$
$44$	2.85246	+	6.61686i	0.430025	+	0.997529i
$45$		0			0
$46$	−3.51126	+	0.724604i	−0.517707	+	0.106837i
$47$	−0.667376	−	1.15593i	−0.0973468	−	0.168610i	0.813239	−	0.581930i	$-0.197702\pi$
$47$	−0.667376	−	1.15593i	−0.0973468	−	0.168610i	−0.910586	+	0.413320i	$0.864369\pi$
$48$	10.1037	+	2.39944i	1.45835	+	0.346330i
$49$	−6.27046	+	3.11147i	−0.895781	+	0.444496i
$50$		0			0
$51$	−16.6295	+	9.60106i	−2.32860	+	1.34442i
$52$	0.977584	−	1.31251i	0.135567	−	0.182012i
$53$	−0.905503	+	1.56838i	−0.124380	+	0.215433i	−0.921491	−	0.388401i	$-0.873028\pi$
$53$	−0.905503	+	1.56838i	−0.124380	+	0.215433i	0.797110	+	0.603834i	$0.206361\pi$
$54$	−2.57960	−	0.855108i	−0.351039	−	0.116365i
$55$		0			0
$56$	4.99019	−	5.57656i	0.666842	−	0.745199i
$57$	8.58450			1.13705
$58$	2.74295	+	0.909256i	0.360166	+	0.119391i
$59$	−0.955727	+	1.65537i	−0.124425	+	0.215510i	−0.921508	−	0.388359i	$-0.873042\pi$
$59$	−0.955727	+	1.65537i	−0.124425	+	0.215510i	0.797083	+	0.603870i	$0.206375\pi$
$60$		0			0
$61$	−8.46625	+	4.88799i	−1.08399	+	0.625843i	−0.931970	−	0.362534i	$-0.881912\pi$
$61$	−8.46625	+	4.88799i	−1.08399	+	0.625843i	−0.152021	+	0.988377i	$0.548578\pi$
$62$	−2.01956	+	1.79685i	−0.256485	+	0.228200i
$63$	−7.21411	+	6.77344i	−0.908892	+	0.853374i
$64$	−2.74124	+	7.51569i	−0.342655	+	0.939461i
$65$		0			0
$66$	12.9548	−	2.67342i	1.59462	−	0.329075i
$67$	8.02134	+	4.63112i	0.979963	+	0.565782i	0.902259	−	0.431195i	$-0.141908\pi$
$67$	8.02134	+	4.63112i	0.979963	+	0.565782i	0.0777041	+	0.996976i	$0.475241\pi$
$68$	−5.85597	−	13.5841i	−0.710141	−	1.64731i
$69$			6.58172i			0.792346i
$70$		0			0
$71$			1.38422i			0.164277i	0.996621	+	0.0821385i	$0.0261750\pi$
$71$			1.38422i			0.164277i	−0.996621	+	0.0821385i	$0.973825\pi$
$72$	4.47405	−	9.58617i	0.527272	−	1.12974i
$73$	−6.40537	−	3.69814i	−0.749692	−	0.432835i	0.0758908	−	0.997116i	$-0.475820\pi$
$73$	−6.40537	−	3.69814i	−0.749692	−	0.432835i	−0.825583	+	0.564281i	$0.809153\pi$
$74$	2.04855	+	9.92677i	0.238139	+	1.15396i
$75$		0			0
$76$	−0.769222	+	6.56827i	−0.0882358	+	0.753433i
$77$	2.75576	−	9.12495i	0.314048	−	1.03988i
$78$	−1.99704	−	2.24457i	−0.226121	−	0.254147i
$79$	−6.70979	+	3.87390i	−0.754910	+	0.435848i	−0.827465	−	0.561517i	$-0.810218\pi$
$79$	−6.70979	+	3.87390i	−0.754910	+	0.435848i	0.0725552	+	0.997364i	$0.476885\pi$
$80$		0			0
$81$	3.11579	−	5.39670i	0.346199	−	0.599634i
$82$	1.18287	−	3.56837i	0.130627	−	0.394060i
$83$	10.4973			1.15223			0.576113	−	0.817370i	$-0.304569\pi$
$83$	10.4973			1.15223			0.576113	+	0.817370i	$0.304569\pi$
$84$	−8.17459	−	11.0409i	−0.891921	−	1.20466i
$85$		0			0
$86$	1.06661	−	3.21763i	0.115015	−	0.346966i
$87$	2.65245	−	4.59418i	0.284372	−	0.492547i
$88$	0.884696	+	10.1516i	0.0943090	+	1.08217i
$89$	9.19133	−	5.30662i	0.974279	−	0.562500i	0.0737410	−	0.997277i	$-0.476506\pi$
$89$	9.19133	−	5.30662i	0.974279	−	0.562500i	0.900538	+	0.434777i	$0.143173\pi$
$90$		0			0
$91$	−2.10781	+	0.494210i	−0.220958	+	0.0518073i
$92$	−5.03589	−	0.589761i	−0.525027	−	0.0614868i
$93$	2.48125	+	4.29764i	0.257293	+	0.445645i
$94$	−0.381503	−	1.84867i	−0.0393490	−	0.190676i
$95$		0			0
$96$	12.4954	+	7.71698i	1.27530	+	0.787611i
$97$			7.32005i			0.743239i	0.928385	+	0.371619i	$0.121197\pi$
$97$			7.32005i			0.743239i	−0.928385	+	0.371619i	$0.878803\pi$
$98$	−9.80192	+	1.38652i	−0.990143	+	0.140060i
$99$		−	13.4750i		−	1.35428i
$100$		0			0
$101$	−5.50608	−	3.17894i	−0.547875	−	0.316316i	0.200389	−	0.979716i	$-0.435779\pi$
$101$	−5.50608	−	3.17894i	−0.547875	−	0.316316i	−0.748265	+	0.663400i	$0.769113\pi$
$102$	−26.5955	+	5.48841i	−2.63335	+	0.543433i
$103$	0.511038	+	0.885144i	0.0503541	+	0.0872158i	0.890104	−	0.455758i	$-0.150632\pi$
$103$	0.511038	+	0.885144i	0.0503541	+	0.0872158i	−0.839750	+	0.542974i	$0.817298\pi$
$104$	1.89634	−	1.32687i	0.185951	−	0.130111i
$105$		0			0
$106$	−1.91343	+	1.70243i	−0.185849	+	0.165354i
$107$	−6.28003	+	3.62578i	−0.607114	+	0.350517i	−0.771835	−	0.635823i	$-0.780661\pi$
$107$	−6.28003	+	3.62578i	−0.607114	+	0.350517i	0.164721	+	0.986340i	$0.447328\pi$
$108$	−3.08229	−	2.29576i	−0.296594	−	0.220910i
$109$	−3.98588	+	6.90375i	−0.381778	+	0.661259i	−0.991316	−	0.131498i	$-0.958021\pi$
$109$	−3.98588	+	6.90375i	−0.381778	+	0.661259i	0.609538	+	0.792756i	$0.291355\pi$
$110$		0			0
$111$	18.6074			1.76613
$112$	9.18022	−	5.26531i	0.867450	−	0.497525i
$113$	−7.61610			−0.716462			−0.358231	−	0.933633i	$-0.616620\pi$
$113$	−7.61610			−0.716462			−0.358231	+	0.933633i	$0.616620\pi$
$114$	11.5237	+	3.81997i	1.07929	+	0.357773i
$115$		0			0
$116$	3.27747	+	2.44114i	0.304306	+	0.226654i
$117$	−2.65049	+	1.53026i	−0.245038	+	0.141473i
$118$	−2.01956	+	1.79685i	−0.185916	+	0.165414i
$119$	−5.65744	+	18.7331i	−0.518616	+	1.71726i
$120$		0			0
$121$	0.989917	+	1.71459i	0.0899925	+	0.155872i
$122$	−13.5400	+	2.79420i	−1.22586	+	0.252975i
$123$	−5.97668	−	3.45064i	−0.538899	−	0.311134i
$124$	−3.51060	+	1.51339i	−0.315261	+	0.135906i
$125$		0			0
$126$	−12.6982	+	5.88238i	−1.13124	+	0.524044i
$127$			8.78136i			0.779220i	0.920980	+	0.389610i	$0.127390\pi$
$127$			8.78136i			0.779220i	−0.920980	+	0.389610i	$0.872610\pi$
$128$	−7.02416	+	8.86911i	−0.620854	+	0.783926i
$129$	−5.38923	−	3.11147i	−0.474495	−	0.273950i
$130$		0			0
$131$	6.69467	+	11.5955i	0.584916	+	1.01310i	0.994886	+	0.101005i	$0.0322059\pi$
$131$	6.69467	+	11.5955i	0.584916	+	1.01310i	−0.409970	+	0.912099i	$0.634461\pi$
$132$	18.5799	+	2.17592i	1.61717	+	0.189389i
$133$	6.37777	−	5.98819i	0.553023	−	0.519242i
$134$	8.70692	+	9.78611i	0.752164	+	0.845391i
$135$		0			0
$136$	−1.81624	−	20.8409i	−0.155741	−	1.78709i
$137$	2.61208	−	4.52425i	0.223165	−	0.386533i	−0.732602	−	0.680657i	$-0.761694\pi$
$137$	2.61208	−	4.52425i	0.223165	−	0.386533i	0.955767	+	0.294124i	$0.0950278\pi$
$138$	−2.92877	+	8.83519i	−0.249313	+	0.752101i
$139$	21.9442			1.86128			0.930641	−	0.365933i	$-0.119250\pi$
$139$	21.9442			1.86128			0.930641	+	0.365933i	$0.119250\pi$
$140$		0			0
$141$	−3.46527			−0.291828
$142$	−0.615958	+	1.85816i	−0.0516901	+	0.155933i
$143$	1.47403	−	2.55310i	0.123265	−	0.213501i
$144$	10.2716	−	10.8774i	0.855965	−	0.906451i
$145$		0			0
$146$	−6.95283	−	7.81461i	−0.575421	−	0.646742i
$147$	−1.14392	+	18.1373i	−0.0943492	+	1.49594i
$148$	−1.66733	+	14.2371i	−0.137054	+	1.17028i
$149$	−11.9749	−	20.7411i	−0.981019	−	1.69917i	−0.658444	−	0.752630i	$-0.728785\pi$
$149$	−11.9749	−	20.7411i	−0.981019	−	1.69917i	−0.322575	−	0.946544i	$-0.604548\pi$
$150$		0			0
$151$	−6.06876	−	3.50380i	−0.493869	−	0.285135i	0.232309	−	0.972642i	$-0.425372\pi$
$151$	−6.06876	−	3.50380i	−0.493869	−	0.285135i	−0.726178	+	0.687507i	$0.758705\pi$
$152$	−3.95537	+	8.47484i	−0.320823	+	0.687400i
$153$			27.6635i			2.23646i
$154$	7.75974	−	11.0229i	0.625297	−	0.888250i
$155$		0			0
$156$	−1.68200	−	3.90172i	−0.134667	−	0.312388i
$157$	−5.56468	−	3.21277i	−0.444110	−	0.256407i	0.261229	−	0.965277i	$-0.415872\pi$
$157$	−5.56468	−	3.21277i	−0.444110	−	0.256407i	−0.705340	+	0.708870i	$0.749205\pi$
$158$	−10.7309	+	2.21450i	−0.853706	+	0.176176i
$159$	2.35085	+	4.07180i	0.186435	+	0.322915i
$160$		0			0
$161$	4.59114	+	4.88982i	0.361832	+	0.385372i
$162$	6.58403	−	5.85796i	0.517290	−	0.460245i
$163$	16.0033	−	9.23950i	1.25347	−	0.723693i	0.281676	−	0.959510i	$-0.409110\pi$
$163$	16.0033	−	9.23950i	1.25347	−	0.723693i	0.971798	+	0.235816i	$0.0757764\pi$
$164$	3.17574	−	4.26375i	0.247983	−	0.332943i
$165$		0			0
$166$	14.0913	+	4.67113i	1.09370	+	0.362550i
$167$	−1.82894			−0.141527			−0.0707637	−	0.997493i	$-0.522544\pi$
$167$	−1.82894			−0.141527			−0.0707637	+	0.997493i	$0.522544\pi$
$168$	−6.06040	−	18.4587i	−0.467570	−	1.42412i
$169$	12.3304			0.948493
$170$		0			0
$171$	6.18361	−	10.7103i	0.472873	−	0.819039i
$172$	2.86359	−	3.84466i	0.218347	−	0.293153i
$173$	−13.2065	+	7.62476i	−1.00407	+	0.579700i	−0.909450	−	0.415814i	$-0.863497\pi$
$173$	−13.2065	+	7.62476i	−1.00407	+	0.579700i	−0.0946193	+	0.995514i	$0.530163\pi$
$174$	5.60494	−	4.98684i	0.424909	−	0.378051i
$175$		0			0
$176$	−3.32973	+	14.0211i	−0.250988	+	1.05688i
$177$	2.48125	+	4.29764i	0.186502	+	0.323031i
$178$	14.6996	−	3.03350i	1.10178	−	0.227371i
$179$	−10.8572	−	6.26844i	−0.811509	−	0.468525i	0.0359707	−	0.999353i	$-0.488548\pi$
$179$	−10.8572	−	6.26844i	−0.811509	−	0.468525i	−0.847480	+	0.530828i	$0.821881\pi$
$180$		0			0
$181$			8.01839i			0.596002i	0.954566	+	0.298001i	$0.0963199\pi$
$181$			8.01839i			0.596002i	−0.954566	+	0.298001i	$0.903680\pi$
$182$	−3.04940	−	0.274525i	−0.226037	−	0.0203491i
$183$			25.3803i			1.87616i
$184$	−6.49765	−	3.03258i	−0.479013	−	0.223564i
$185$		0			0
$186$	1.41839	+	6.87319i	0.104002	+	0.503967i
$187$	−13.3235	−	23.0770i	−0.974310	−	1.68755i
$188$	0.310508	−	2.65139i	0.0226461	−	0.193372i
$189$	1.16060	+	4.94998i	0.0844215	+	0.360058i
$190$		0			0
$191$	−5.85379	+	3.37969i	−0.423565	+	0.244546i	−0.696602	−	0.717458i	$-0.745305\pi$
$191$	−5.85379	+	3.37969i	−0.423565	+	0.244546i	0.273036	+	0.962004i	$0.411972\pi$
$192$	13.3396	+	15.9194i	0.962704	+	1.14888i
$193$	1.18001	−	2.04384i	0.0849392	−	0.147119i	−0.820426	−	0.571753i	$-0.806264\pi$
$193$	1.18001	−	2.04384i	0.0849392	−	0.147119i	0.905365	+	0.424634i	$0.139597\pi$
$194$	−3.25731	+	9.82631i	−0.233861	+	0.705488i
$195$		0			0
$196$	−13.7749	−	2.50046i	−0.983921	−	0.178604i
$197$	−20.3205			−1.44777			−0.723887	−	0.689918i	$-0.757647\pi$
$197$	−20.3205			−1.44777			−0.723887	+	0.689918i	$0.757647\pi$
$198$	5.99615	−	18.0885i	0.426128	−	1.28550i
$199$	5.72909	−	9.92308i	0.406125	−	0.703429i	−0.588327	−	0.808623i	$-0.700213\pi$
$199$	5.72909	−	9.92308i	0.406125	−	0.703429i	0.994452	+	0.105195i	$0.0335465\pi$
$200$		0			0
$201$	20.8249	−	12.0233i	1.46888	−	0.848056i
$202$	−5.97668	−	6.71746i	−0.420518	−	0.472639i
$203$	−1.23410	−	5.26343i	−0.0866166	−	0.369421i
$204$	−38.1436	−	4.46706i	−2.67058	−	0.312757i
$205$		0			0
$206$	0.292133	+	1.41560i	0.0203538	+	0.0986298i
$207$	8.21159	+	4.74097i	0.570745	+	0.329520i
$208$	3.13605	−	0.937331i	0.217446	−	0.0649922i
$209$			11.9128i			0.824026i
$210$		0			0
$211$		−	22.0647i		−	1.51900i	−0.650510	−	0.759498i	$-0.725445\pi$
$211$		−	22.0647i		−	1.51900i	0.650510	−	0.759498i	$-0.274555\pi$
$212$	−3.32611	+	1.43386i	−0.228438	+	0.0984776i
$213$	3.11224	+	1.79685i	0.213247	+	0.123118i
$214$	−10.0436	+	2.07266i	−0.686568	+	0.141684i
$215$		0			0
$216$	−3.11603	−	4.45336i	−0.212019	−	0.303013i
$217$	4.84127	+	1.46208i	0.328647	+	0.0992522i
$218$	−8.42263	+	7.49381i	−0.570453	+	0.507545i
$219$	−16.6295	+	9.60106i	−1.12372	+	0.648780i
$220$		0			0
$221$	−3.02612	+	5.24140i	−0.203559	+	0.352575i
$222$	24.9782	+	8.28000i	1.67643	+	0.555717i
$223$	−23.5776			−1.57887			−0.789436	−	0.613833i	$-0.789627\pi$
$223$	−23.5776			−1.57887			−0.789436	+	0.613833i	$0.789627\pi$
$224$	14.6663	−	2.98300i	0.979936	−	0.199310i
$225$		0			0
$226$	−10.2237	−	3.38905i	−0.680071	−	0.225436i
$227$	10.4634	−	18.1231i	0.694478	−	1.20287i	−0.275879	−	0.961192i	$-0.588969\pi$
$227$	10.4634	−	18.1231i	0.694478	−	1.20287i	0.970356	−	0.241678i	$-0.0776978\pi$
$228$	13.7693	+	10.2557i	0.911897	+	0.679202i
$229$	−4.48735	+	2.59077i	−0.296533	+	0.171203i	−0.640884	−	0.767638i	$-0.721432\pi$
$229$	−4.48735	+	2.59077i	−0.296533	+	0.171203i	0.344352	+	0.938841i	$0.388099\pi$
$230$		0			0
$231$	−16.9390	−	18.0410i	−1.11450	−	1.18701i
$232$	3.31335	+	4.73536i	0.217532	+	0.310892i
$233$	−10.3847	−	17.9868i	−0.680324	−	1.17836i	−0.974882	−	0.222722i	$-0.928506\pi$
$233$	−10.3847	−	17.9868i	−0.680324	−	1.17836i	0.294558	−	0.955634i	$-0.404828\pi$
$234$	−4.23892	+	0.874768i	−0.277107	+	0.0571854i
$235$		0			0
$236$	−3.51060	+	1.51339i	−0.228520	+	0.0985130i
$237$			20.1147i			1.30659i
$238$	−15.9304	+	22.6295i	−1.03261	+	1.46685i
$239$		−	21.1286i		−	1.36670i	−0.730092	−	0.683349i	$-0.760523\pi$
$239$		−	21.1286i		−	1.36670i	0.730092	−	0.683349i	$-0.239477\pi$
$240$		0			0
$241$	1.57448	+	0.909029i	0.101421	+	0.0585557i	0.549853	−	0.835262i	$-0.314684\pi$
$241$	1.57448	+	0.909029i	0.101421	+	0.0585557i	−0.448431	+	0.893817i	$0.648017\pi$
$242$	0.565882	+	2.74213i	0.0363763	+	0.176271i
$243$	−10.9716	−	19.0035i	−0.703832	−	1.21907i
$244$	−19.4192	−	2.27422i	−1.24319	−	0.145592i
$245$		0			0
$246$	−6.48750	−	7.29160i	−0.413628	−	0.464896i
$247$	2.34322	−	1.35286i	0.149095	−	0.0860803i
$248$	−5.38599	+	0.469379i	−0.342011	+	0.0298056i
$249$	13.6264	−	23.6017i	0.863540	−	1.49570i
$250$		0			0
$251$	−14.0187			−0.884856			−0.442428	−	0.896804i	$-0.645883\pi$
$251$	−14.0187			−0.884856			−0.442428	+	0.896804i	$0.645883\pi$
$252$	−19.6633	+	2.24591i	−1.23867	+	0.141479i
$253$	−9.13352			−0.574220
$254$	−3.90757	+	11.7879i	−0.245183	+	0.739641i
$255$		0			0
$256$	−13.3757	+	8.78009i	−0.835983	+	0.548756i
$257$	−15.4780	+	8.93624i	−0.965492	+	0.557427i	−0.897859	−	0.440283i	$-0.854878\pi$
$257$	−15.4780	+	8.93624i	−0.965492	+	0.557427i	−0.0676333	+	0.997710i	$0.521545\pi$
$258$	−5.84985	−	6.57491i	−0.364196	−	0.409336i
$259$	13.8242	−	12.9797i	0.858991	−	0.806521i
$260$		0			0
$261$	−3.82124	−	6.61858i	−0.236529	−	0.409680i
$262$	3.82698	+	18.5446i	0.236432	+	1.14569i
$263$	18.9629	+	10.9482i	1.16930	+	0.675097i	0.953516	−	0.301343i	$-0.0974349\pi$
$263$	18.9629	+	10.9482i	1.16930	+	0.675097i	0.215787	+	0.976440i	$0.430768\pi$
$264$	23.9730	+	11.1887i	1.47544	+	0.688615i
$265$		0			0
$266$	11.2261	−	5.20043i	0.688313	−	0.318859i
$267$		−	27.5539i		−	1.68627i
$268$	7.33335	+	17.0111i	0.447955	+	1.03912i
$269$	−2.49661	−	1.44142i	−0.152221	−	0.0878847i	0.421955	−	0.906617i	$-0.361344\pi$
$269$	−2.49661	−	1.44142i	−0.152221	−	0.0878847i	−0.574176	+	0.818732i	$0.694677\pi$
$270$		0			0
$271$	8.47793	+	14.6842i	0.514997	+	0.892002i	0.999849	+	0.0174049i	$0.00554042\pi$
$271$	8.47793	+	14.6842i	0.514997	+	0.892002i	−0.484851	+	0.874597i	$0.661126\pi$
$272$	6.83578	−	28.7846i	0.414480	−	1.74532i
$273$	−1.62497	+	5.38065i	−0.0983476	+	0.325652i
$274$	5.51963	−	4.91094i	0.333453	−	0.296681i
$275$		0			0
$276$	−7.86305	+	10.5569i	−0.473300	+	0.635453i
$277$	13.4258	−	23.2541i	0.806677	−	1.39720i	−0.108477	−	0.994099i	$-0.534597\pi$
$277$	13.4258	−	23.2541i	0.806677	−	1.39720i	0.915153	−	0.403106i	$-0.132069\pi$
$278$	29.4575	+	9.76483i	1.76674	+	0.585656i
$279$	7.14919			0.428011
$280$		0			0
$281$	24.9497			1.48838			0.744188	−	0.667971i	$-0.232837\pi$
$281$	24.9497			1.48838			0.744188	+	0.667971i	$0.232837\pi$
$282$	−4.65171	−	1.54199i	−0.277005	−	0.0918242i
$283$	4.91910	−	8.52014i	0.292410	−	0.506470i	−0.681969	−	0.731381i	$-0.738876\pi$
$283$	4.91910	−	8.52014i	0.292410	−	0.506470i	0.974379	+	0.224912i	$0.0722093\pi$
$284$	−1.65370	+	2.22026i	−0.0981292	+	0.131748i
$285$		0			0
$286$	3.11481	−	2.77132i	0.184183	−	0.163871i
$287$	−6.84733	+	1.60547i	−0.404185	+	0.0947678i
$288$	18.6287	−	10.0309i	1.09770	−	0.591079i
$289$	18.8525	+	32.6535i	1.10897	+	1.92079i
$290$		0			0
$291$	16.4581	+	9.50211i	0.964793	+	0.557024i
$292$	−5.85597	−	13.5841i	−0.342695	−	0.794949i
$293$		−	23.4039i		−	1.36727i	−0.729823	−	0.683636i	$-0.760398\pi$
$293$		−	23.4039i		−	1.36727i	0.729823	−	0.683636i	$-0.239602\pi$
$294$	−9.60639	+	23.8381i	−0.560256	+	1.39027i
$295$		0			0
$296$	−8.57348	+	18.3697i	−0.498323	+	1.06772i
$297$	−5.99571	−	3.46163i	−0.347907	−	0.200864i
$298$	−6.84537	−	33.1710i	−0.396542	−	1.92155i
$299$	1.03723	+	1.79654i	0.0599848	+	0.103897i
$300$		0			0
$301$	−6.17431	+	1.44767i	−0.355881	+	0.0834421i
$302$	−6.58746	−	7.40395i	−0.379066	−	0.426049i
$303$	−14.2948	+	8.25311i	−0.821215	+	0.474129i
$304$	−9.08079	+	9.61639i	−0.520819	+	0.551538i
$305$		0			0
$306$	−12.3098	+	37.1349i	−0.703705	+	2.12286i
$307$	2.18529			0.124721			0.0623606	−	0.998054i	$-0.480137\pi$
$307$	2.18529			0.124721			0.0623606	+	0.998054i	$0.480137\pi$
$308$	15.3215	−	11.3440i	0.873026	−	0.646382i
$309$	2.65350			0.150952
$310$		0			0
$311$	14.4501	−	25.0282i	0.819388	−	1.41922i	−0.0867457	−	0.996230i	$-0.527647\pi$
$311$	14.4501	−	25.0282i	0.819388	−	1.41922i	0.906134	−	0.422991i	$-0.139020\pi$
$312$	−0.521673	−	5.98606i	−0.0295339	−	0.338894i
$313$	5.50189	−	3.17652i	0.310985	−	0.179548i	−0.336382	−	0.941726i	$-0.609203\pi$
$313$	5.50189	−	3.17652i	0.310985	−	0.179548i	0.647367	+	0.762178i	$0.275870\pi$
$314$	−6.04030	−	6.78897i	−0.340874	−	0.383124i
$315$		0			0
$316$	−15.3904	−	1.80240i	−0.865778	−	0.101393i
$317$	−9.40153	−	16.2839i	−0.528043	−	0.914597i	−0.999466	−	0.0326894i	$-0.989593\pi$
$317$	−9.40153	−	16.2839i	−0.528043	−	0.914597i	0.471423	−	0.881907i	$-0.343741\pi$
$318$	1.34386	+	6.51200i	0.0753597	+	0.365175i
$319$	6.37538	+	3.68083i	0.356953	+	0.206087i
$320$		0			0
$321$			18.8264i			1.05079i
$322$	3.98716	+	8.60700i	0.222196	+	0.479649i
$323$		−	24.4564i		−	1.36079i
$324$	11.4450	−	4.93382i	0.635832	−	0.274101i
$325$		0			0
$326$	25.5939	−	5.28172i	1.41752	−	0.292527i
$327$	10.3481	+	17.9234i	0.572250	+	0.991167i
$328$	6.16035	−	4.31042i	0.340149	−	0.238003i
$329$	−2.57448	+	2.41723i	−0.141936	+	0.133266i
$330$		0			0
$331$	11.3353	−	6.54441i	0.623042	−	0.359713i	−0.155010	−	0.987913i	$-0.549541\pi$
$331$	11.3353	−	6.54441i	0.623042	−	0.359713i	0.778052	+	0.628199i	$0.216208\pi$
$332$	16.8374	+	12.5409i	0.924071	+	0.688269i
$333$	13.4033	−	23.2152i	0.734497	−	1.27219i
$334$	−2.45513	−	0.813849i	−0.134339	−	0.0445318i
$335$		0			0
$336$	0.0784518	−	27.4753i	0.00427990	−	1.49890i
$337$	−11.7319			−0.639079			−0.319539	−	0.947573i	$-0.603528\pi$
$337$	−11.7319			−0.639079			−0.319539	+	0.947573i	$0.603528\pi$
$338$	16.5521	+	5.48685i	0.900317	+	0.298445i
$339$	−9.88640	+	17.1238i	−0.536956	+	0.930035i
$340$		0			0
$341$	−5.96388	+	3.44325i	−0.322962	+	0.186462i
$342$	13.0667	−	11.6257i	0.706566	−	0.628648i
$343$	11.8019	+	14.2729i	0.637245	+	0.770661i
$344$	5.55485	−	3.88675i	0.299498	−	0.209560i
$345$		0			0
$346$	−21.1210	+	4.35866i	−1.13547	+	0.234323i
$347$	−3.82065	−	2.20585i	−0.205103	−	0.118416i	0.393930	−	0.919140i	$-0.371115\pi$
$347$	−3.82065	−	2.20585i	−0.205103	−	0.118416i	−0.599034	+	0.800724i	$0.704448\pi$
$348$	9.74303	−	4.20013i	0.522281	−	0.225151i
$349$			18.3479i			0.982142i	0.871120	+	0.491071i	$0.163394\pi$
$349$			18.3479i			0.982142i	−0.871120	+	0.491071i	$0.836606\pi$
$350$		0			0
$351$			1.57246i			0.0839316i
$352$	−10.7089	+	17.3399i	−0.570788	+	0.924222i
$353$	10.1742	+	5.87406i	0.541516	+	0.312645i	0.745693	−	0.666289i	$-0.232118\pi$
$353$	10.1742	+	5.87406i	0.541516	+	0.312645i	−0.204177	+	0.978934i	$0.565452\pi$
$354$	1.41839	+	6.87319i	0.0753867	+	0.365306i
$355$		0			0
$356$	21.0824	+	2.46899i	1.11736	+	0.130856i
$357$	34.7749	+	37.0373i	1.84048	+	1.96022i
$358$	−11.7852	−	13.2459i	−0.622868	−	0.700070i
$359$	−0.171388	+	0.0989510i	−0.00904552	+	0.00522243i	−0.504516	−	0.863402i	$-0.668329\pi$
$359$	−0.171388	+	0.0989510i	−0.00904552	+	0.00522243i	0.495470	+	0.868625i	$0.334996\pi$
$360$		0			0
$361$	4.03326	−	6.98581i	0.212277	−	0.367674i
$362$	−3.56806	+	10.7637i	−0.187533	+	0.565730i
$363$	5.14002			0.269781
$364$	−3.97130	−	1.72545i	−0.208153	−	0.0904383i
$365$		0			0
$366$	−11.2938	+	34.0700i	−0.590338	+	1.78087i
$367$	−3.76412	+	6.51964i	−0.196485	+	0.340323i	−0.947386	−	0.320092i	$-0.896286\pi$
$367$	−3.76412	+	6.51964i	−0.196485	+	0.340323i	0.750901	+	0.660415i	$0.229619\pi$
$368$	−7.37287	−	6.96223i	−0.384337	−	0.362931i
$369$	−8.61028	+	4.97115i	−0.448233	+	0.258787i
$370$		0			0
$371$	4.58686	+	1.38524i	0.238138	+	0.0719182i
$372$	−1.15444	+	9.85761i	−0.0598550	+	0.511093i
$373$	15.5696	+	26.9674i	0.806164	+	1.39632i	0.915503	+	0.402312i	$0.131793\pi$
$373$	15.5696	+	26.9674i	0.806164	+	1.39632i	−0.109339	+	0.994005i	$0.534873\pi$
$374$	−7.61632	−	36.9068i	−0.393830	−	1.90841i
$375$		0			0
$376$	1.59665	−	3.42100i	0.0823408	−	0.176425i
$377$		−	1.67203i		−	0.0861140i
$378$	−0.644694	+	7.16122i	−0.0331595	+	0.368333i
$379$			16.3396i			0.839307i	0.907684	+	0.419654i	$0.137848\pi$
$379$			16.3396i			0.839307i	−0.907684	+	0.419654i	$0.862152\pi$
$380$		0			0
$381$	19.7437	+	11.3990i	1.01150	+	0.583990i
$382$	−9.36193	+	1.93198i	−0.478998	+	0.0988489i
$383$	4.42434	+	7.66318i	0.226073	+	0.391570i	0.956641	−	0.291270i	$-0.0940778\pi$
$383$	4.42434	+	7.66318i	0.226073	+	0.391570i	−0.730568	+	0.682840i	$0.760744\pi$
$384$	10.8230	+	27.3058i	0.552307	+	1.39344i
$385$		0			0
$386$	2.49351	−	2.21853i	0.126916	−	0.112920i
$387$	−7.76397	+	4.48253i	−0.394665	+	0.227860i
$388$	−8.74511	+	11.7412i	−0.443966	+	0.596069i
$389$	4.67264	−	8.09325i	0.236912	−	0.410344i	−0.722915	−	0.690937i	$-0.757198\pi$
$389$	4.67264	−	8.09325i	0.236912	−	0.410344i	0.959827	+	0.280594i	$0.0905313\pi$
$390$		0			0
$391$	18.7507			0.948263
$392$	−17.3785	−	9.48619i	−0.877747	−	0.479125i
$393$	34.7612			1.75347
$394$	−27.2779	−	9.04231i	−1.37424	−	0.455545i
$395$		0			0
$396$	16.0983	−	21.6135i	0.808968	−	1.08612i
$397$	17.5826	−	10.1513i	0.882446	−	0.509480i	0.0109817	−	0.999940i	$-0.496504\pi$
$397$	17.5826	−	10.1513i	0.882446	−	0.509480i	0.871464	+	0.490459i	$0.163171\pi$
$398$	12.1063	−	10.7712i	0.606831	−	0.539912i
$399$	−5.18470	−	22.1128i	−0.259559	−	1.10702i
$400$		0			0
$401$	5.54334	+	9.60135i	0.276821	+	0.479469i	0.970593	−	0.240726i	$-0.0773857\pi$
$401$	5.54334	+	9.60135i	0.276821	+	0.479469i	−0.693772	+	0.720195i	$0.744052\pi$
$402$	33.3051	−	6.87304i	1.66111	−	0.342796i
$403$	1.35456	+	0.782054i	0.0674753	+	0.0389569i
$404$	−5.03382	−	11.6769i	−0.250442	−	0.580949i
$405$		0			0
$406$	0.685519	−	7.61469i	0.0340217	−	0.377911i
$407$			25.8216i			1.27993i
$408$	−49.2155	−	22.9698i	−2.43653	−	1.13717i
$409$	−5.09812	−	2.94340i	−0.252086	−	0.145542i	0.368633	−	0.929575i	$-0.379826\pi$
$409$	−5.09812	−	2.94340i	−0.252086	−	0.145542i	−0.620719	+	0.784033i	$0.713159\pi$
$410$		0			0
$411$	−6.78145	−	11.7458i	−0.334504	−	0.579378i
$412$	−0.237769	+	2.03028i	−0.0117140	+	0.100025i
$413$	4.84127	+	1.46208i	0.238223	+	0.0719441i
$414$	8.91343	+	10.0182i	0.438071	+	0.492369i
$415$		0			0
$416$	4.62687	+	0.137237i	0.226851	+	0.00672860i
$417$	28.4856	−	49.3385i	1.39495	−	2.41612i
$418$	−5.30101	+	15.9915i	−0.259281	+	0.782171i
$419$	−16.7262			−0.817126			−0.408563	−	0.912730i	$-0.633970\pi$
$419$	−16.7262			−0.817126			−0.408563	+	0.912730i	$0.633970\pi$
$420$		0			0
$421$	−1.18823			−0.0579109			−0.0289555	−	0.999581i	$-0.509218\pi$
$421$	−1.18823			−0.0579109			−0.0289555	+	0.999581i	$0.509218\pi$
$422$	9.81845	−	29.6192i	0.477955	−	1.44184i
$423$	−2.49611	+	4.32339i	−0.121365	+	0.210210i
$424$	−5.10296	+	0.444713i	−0.247822	+	0.0215972i
$425$		0			0
$426$	3.37824	+	3.79696i	0.163676	+	0.183963i
$427$	17.7042	+	18.8560i	0.856767	+	0.912506i
$428$	−14.4047	−	1.68696i	−0.696276	−	0.0815421i
$429$	−3.82687	−	6.62833i	−0.184763	−	0.320019i
$430$		0			0
$431$	−20.8669	−	12.0475i	−1.00512	−	0.580307i	−0.0953622	−	0.995443i	$-0.530401\pi$
$431$	−20.8669	−	12.0475i	−1.00512	−	0.580307i	−0.909760	+	0.415135i	$0.863734\pi$
$432$	−2.20123	−	7.36470i	−0.105907	−	0.354334i
$433$		−	14.9805i		−	0.719916i	−0.932968	−	0.359958i	$-0.882791\pi$
$433$		−	14.9805i		−	0.719916i	0.932968	−	0.359958i	$-0.117209\pi$
$434$	5.84823	+	4.11696i	0.280724	+	0.197620i
$435$		0			0
$436$	−14.6410	+	6.31161i	−0.701178	+	0.302271i
$437$	−7.25962	−	4.19134i	−0.347275	−	0.200499i
$438$	−26.5955	+	5.48841i	−1.27078	+	0.262246i
$439$	−8.66266	−	15.0042i	−0.413446	−	0.716110i	0.581818	−	0.813319i	$-0.302342\pi$
$439$	−8.66266	−	15.0042i	−0.413446	−	0.716110i	−0.995264	+	0.0972091i	$0.969008\pi$
$440$		0			0
$441$	21.8047	+	14.4919i	1.03832	+	0.690090i
$442$	−6.39456	+	5.68938i	−0.304158	+	0.270616i
$443$	−21.8520	+	12.6162i	−1.03822	+	0.599416i	−0.919328	−	0.393492i	$-0.871267\pi$
$443$	−21.8520	+	12.6162i	−1.03822	+	0.599416i	−0.118890	+	0.992907i	$0.537934\pi$
$444$	29.8458	+	22.2298i	1.41642	+	1.05498i
$445$		0			0
$446$	−31.6501	−	10.4917i	−1.49868	−	0.496795i
$447$	−62.1779			−2.94091
$448$	21.0152	+	2.52198i	0.992876	+	0.119152i
$449$	−7.06145			−0.333251			−0.166625	−	0.986020i	$-0.553287\pi$
$449$	−7.06145			−0.333251			−0.166625	+	0.986020i	$0.553287\pi$
$450$		0			0
$451$	4.78848	−	8.29390i	0.225481	−	0.390544i
$452$	−12.2160	−	9.09879i	−0.574594	−	0.427971i
$453$	−15.7556	+	9.09653i	−0.740265	+	0.427392i
$454$	22.1103	−	19.6720i	1.03769	−	0.923255i
$455$		0			0
$456$	13.9201	+	19.8942i	0.651867	+	0.931633i
$457$	9.44078	+	16.3519i	0.441621	+	0.764910i	0.997810	−	0.0661459i	$-0.0210703\pi$
$457$	9.44078	+	16.3519i	0.441621	+	0.764910i	−0.556189	+	0.831056i	$0.687737\pi$
$458$	−7.17660	+	1.48100i	−0.335340	+	0.0692028i
$459$	12.3089	+	7.10656i	0.574531	+	0.331706i
$460$		0			0
$461$		−	34.6087i		−	1.61189i	−0.591992	−	0.805944i	$-0.701658\pi$
$461$		−	34.6087i		−	1.61189i	0.591992	−	0.805944i	$-0.298342\pi$
$462$	−14.7106	−	31.7555i	−0.684399	−	1.47740i
$463$		−	15.0235i		−	0.698202i	−0.937085	−	0.349101i	$-0.886487\pi$
$463$		−	15.0235i		−	0.698202i	0.937085	−	0.349101i	$-0.113513\pi$
$464$	2.34062	+	7.83106i	0.108661	+	0.363548i
$465$		0			0
$466$	−5.93636	−	28.7662i	−0.274997	−	1.33257i
$467$	12.7195	+	22.0309i	0.588590	+	1.01947i	0.994417	+	0.105518i	$0.0336500\pi$
$467$	12.7195	+	22.0309i	0.588590	+	1.01947i	−0.405828	+	0.913950i	$0.633017\pi$
$468$	−6.07950	−	0.711981i	−0.281025	−	0.0329113i
$469$	7.08472	−	23.4591i	0.327142	−	1.08324i
$470$		0			0
$471$	−14.4470	+	8.34096i	−0.665681	+	0.384331i
$472$	−5.38599	+	0.469379i	−0.247910	+	0.0216049i
$473$	4.31782	−	7.47869i	0.198534	−	0.343871i
$474$	−8.95074	+	27.0016i	−0.411121	+	1.24023i
$475$		0			0
$476$	−31.4544	+	23.2886i	−1.44171	+	1.06743i
$477$	6.77350			0.310137
$478$	9.40192	−	28.3627i	0.430034	−	1.29728i
$479$	10.2844	−	17.8131i	0.469905	−	0.813900i	−0.529502	−	0.848308i	$-0.677621\pi$
$479$	10.2844	−	17.8131i	0.469905	−	0.813900i	0.999408	+	0.0344084i	$0.0109547\pi$
$480$		0			0
$481$	5.07906	−	2.93239i	0.231585	−	0.133706i
$482$	1.70906	+	1.92089i	0.0778453	+	0.0874939i
$483$	16.9538	−	3.97510i	0.771426	−	0.180873i
$484$	−0.460576	+	3.93279i	−0.0209353	+	0.178763i
$485$		0			0
$486$	−6.27189	−	30.3921i	−0.284499	−	1.37861i
$487$	25.1658	+	14.5295i	1.14037	+	0.658394i	0.946522	−	0.322638i	$-0.104570\pi$
$487$	25.1658	+	14.5295i	1.14037	+	0.658394i	0.193849	+	0.981031i	$0.437903\pi$
$488$	−25.0560	−	11.6941i	−1.13423	−	0.529369i
$489$		−	47.9749i		−	2.16950i
$490$		0			0
$491$		−	9.51815i		−	0.429548i	−0.976664	−	0.214774i	$-0.931098\pi$
$491$		−	9.51815i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$492$	−5.46405	−	12.6750i	−0.246339	−	0.571431i
$493$	−13.0884	−	7.55657i	−0.589470	−	0.340331i
$494$	3.74750	−	0.773356i	0.168608	−	0.0347949i
$495$		0			0
$496$	−7.43893	−	1.76660i	−0.334018	−	0.0793226i
$497$	3.56561	−	0.836015i	0.159940	−	0.0375004i
$498$	28.7943	−	25.6189i	1.29030	−	1.14801i
$499$	17.4855	−	10.0953i	0.782760	−	0.451927i	−0.0546477	−	0.998506i	$-0.517404\pi$
$499$	17.4855	−	10.0953i	0.782760	−	0.451927i	0.837407	+	0.546579i	$0.184070\pi$
$500$		0			0
$501$	−2.37413	+	4.11211i	−0.106068	+	0.183716i
$502$	−18.8185	−	6.23813i	−0.839911	−	0.278421i
$503$	−13.3134			−0.593616			−0.296808	−	0.954937i	$-0.595922\pi$
$503$	−13.3134			−0.593616			−0.296808	+	0.954937i	$0.595922\pi$
$504$	−27.3951	−	5.73502i	−1.22028	−	0.255458i
$505$		0			0
$506$	−12.2607	−	4.06428i	−0.545053	−	0.180679i
$507$	16.0060	−	27.7233i	0.710853	−	1.23123i
$508$	−10.4909	+	14.0851i	−0.465459	+	0.624926i
$509$	−12.4294	+	7.17613i	−0.550925	+	0.318077i	−0.749495	−	0.662010i	$-0.769704\pi$
$509$	−12.4294	+	7.17613i	−0.550925	+	0.318077i	0.198570	+	0.980087i	$0.436370\pi$
$510$		0			0
$511$	−5.65744	+	18.7331i	−0.250270	+	0.828703i
$512$	−21.8623	+	5.83424i	−0.966188	+	0.257839i
$513$	−3.17706	−	5.50282i	−0.140270	−	0.242956i
$514$	−24.7539	+	5.10836i	−1.09185	+	0.225320i
$515$		0			0
$516$	−4.92699	−	11.4291i	−0.216899	−	0.503140i
$517$		−	4.80879i		−	0.211490i
$518$	24.3331	−	11.2722i	1.06913	−	0.495273i
$519$			39.5906i			1.73783i
$520$		0			0
$521$	−31.9571	−	18.4505i	−1.40007	−	0.808330i	−0.405669	−	0.914020i	$-0.632961\pi$
$521$	−31.9571	−	18.4505i	−1.40007	−	0.808330i	−0.994399	+	0.105690i	$0.966295\pi$
$522$	−2.18439	−	10.5851i	−0.0956083	−	0.463295i
$523$	9.07509	+	15.7185i	0.396826	+	0.687323i	0.993332	−	0.115285i	$-0.0367783\pi$
$523$	9.07509	+	15.7185i	0.396826	+	0.687323i	−0.596506	+	0.802608i	$0.703445\pi$
$524$	−3.11481	+	26.5969i	−0.136071	+	1.16189i
$525$		0			0
$526$	20.5837	+	23.1349i	0.897490	+	1.00873i
$527$	12.2436	−	7.06883i	0.533338	−	0.307923i
$528$	27.2022	+	25.6871i	1.18382	+	1.11789i
$529$	−8.28651	+	14.3526i	−0.360283	+	0.624028i
$530$		0			0
$531$	7.14919			0.310248
$532$	17.3838	−	1.98554i	0.753682	−	0.0860841i
$533$	−2.17519			−0.0942178
$534$	12.2611	−	36.9879i	0.530589	−	1.60062i
$535$		0			0
$536$	2.27445	+	26.0987i	0.0982412	+	1.12729i
$537$	−28.1874	+	16.2740i	−1.21638	+	0.702276i
$538$	−2.70999	−	3.04588i	−0.116836	−	0.131317i
$539$	−25.1693	−	1.58743i	−1.08412	−	0.0683756i
$540$		0			0
$541$	9.37629	+	16.2402i	0.403118	+	0.698221i	0.994100	−	0.108463i	$-0.0345930\pi$
$541$	9.37629	+	16.2402i	0.403118	+	0.698221i	−0.590982	+	0.806685i	$0.701260\pi$
$542$	4.84637	+	23.4843i	0.208169	+	1.00874i
$543$	18.0283	+	10.4086i	0.773667	+	0.446677i
$544$	21.9849	−	35.5981i	0.942596	−	1.52626i
$545$		0			0
$546$	−4.57564	+	6.49980i	−0.195819	+	0.278166i
$547$		−	34.1580i		−	1.46049i	−0.683185	−	0.730246i	$-0.739406\pi$
$547$		−	34.1580i		−	1.46049i	0.683185	−	0.730246i	$-0.260594\pi$
$548$	9.59475	−	4.13621i	0.409867	−	0.176690i
$549$	31.6653	+	18.2820i	1.35144	+	0.780256i
$550$		0			0
$551$	3.37824	+	5.85128i	0.143918	+	0.249273i
$552$	−15.2529	+	10.6725i	−0.649206	+	0.454252i
$553$	14.0312	+	14.9440i	0.596667	+	0.635485i
$554$	28.3702	−	25.2416i	1.20534	−	1.07241i
$555$		0			0
$556$	35.1980	+	26.2163i	1.49273	+	1.11182i
$557$	−20.2183	+	35.0192i	−0.856679	+	1.48381i	0.0184005	+	0.999831i	$0.494143\pi$
$557$	−20.2183	+	35.0192i	−0.856679	+	1.48381i	−0.875079	+	0.483980i	$0.839191\pi$
$558$	9.59694	+	3.18128i	0.406271	+	0.134674i
$559$	−1.96139			−0.0829579
$560$		0			0
$561$	−69.1805			−2.92080
$562$	33.4920	+	11.1022i	1.41278	+	0.468320i
$563$	0.159465	−	0.276201i	0.00672065	−	0.0116405i	−0.862646	−	0.505809i	$-0.831194\pi$
$563$	0.159465	−	0.276201i	0.00672065	−	0.0116405i	0.869366	+	0.494168i	$0.164527\pi$
$564$	−5.55821	−	4.13988i	−0.234043	−	0.174320i
$565$		0			0
$566$	10.3946	−	9.24835i	0.436920	−	0.388737i
$567$	−15.7831	−	4.76655i	−0.662830	−	0.200176i
$568$	−3.20788	+	2.24457i	−0.134600	+	0.0941800i
$569$	15.3058	+	26.5104i	0.641651	+	1.11137i	0.985064	+	0.172188i	$0.0550836\pi$
$569$	15.3058	+	26.5104i	0.641651	+	1.11137i	−0.343413	+	0.939184i	$0.611583\pi$
$570$		0			0
$571$	−7.35081	−	4.24399i	−0.307622	−	0.177606i	0.338240	−	0.941060i	$-0.390168\pi$
$571$	−7.35081	−	4.24399i	−0.307622	−	0.177606i	−0.645862	+	0.763454i	$0.723502\pi$
$572$	5.41446	−	2.33412i	0.226390	−	0.0975945i
$573$			17.5486i			0.733103i
$574$	−9.90614	−	0.891809i	−0.413474	−	0.0372234i
$575$		0			0
$576$	29.4704	−	5.17589i	1.22793	−	0.215662i
$577$	−2.91419	−	1.68251i	−0.121319	−	0.0700438i	0.438112	−	0.898920i	$-0.355647\pi$
$577$	−2.91419	−	1.68251i	−0.121319	−	0.0700438i	−0.559432	+	0.828876i	$0.688981\pi$
$578$	10.7769	+	52.2225i	0.448262	+	2.17217i
$579$	−3.06354	−	5.30620i	−0.127316	−	0.220518i
$580$		0			0
$581$	−6.33993	−	27.0399i	−0.263025	−	1.12180i
$582$	17.8648	+	20.0791i	0.740520	+	0.832305i
$583$	−5.65048	+	3.26230i	−0.234019	+	0.135111i
$584$	−1.81624	−	20.8409i	−0.0751565	−	0.862401i
$585$		0			0
$586$	10.4144	−	31.4170i	0.430215	−	1.29782i
$587$	2.02359			0.0835225			0.0417613	−	0.999128i	$-0.486703\pi$
$587$	2.02359			0.0835225			0.0417613	+	0.999128i	$0.486703\pi$
$588$	−23.5030	+	27.7251i	−0.969249	+	1.14337i
$589$	−6.32038			−0.260427
$590$		0			0
$591$	−26.3779	+	45.6878i	−1.08504	+	1.87935i
$592$	−19.6831	+	20.8440i	−0.808971	+	0.856685i
$593$	−23.2318	+	13.4129i	−0.954016	+	0.550802i	−0.894326	−	0.447415i	$-0.852345\pi$
$593$	−23.2318	+	13.4129i	−0.954016	+	0.550802i	−0.0596901	+	0.998217i	$0.519011\pi$
$594$	−6.50817	−	7.31483i	−0.267033	−	0.300131i
$595$		0			0
$596$	5.57151	−	47.5743i	0.228218	−	1.94872i
$597$	−14.8738	−	25.7622i	−0.608744	−	1.05438i
$598$	0.592930	+	2.87320i	0.0242467	+	0.117494i
$599$	32.0964	+	18.5309i	1.31143	+	0.757152i	0.982332	−	0.187146i	$-0.0599237\pi$
$599$	32.0964	+	18.5309i	1.31143	+	0.757152i	0.329093	+	0.944297i	$0.393257\pi$
$600$		0			0
$601$		−	1.27911i		−	0.0521761i	−0.999660	−	0.0260880i	$-0.991695\pi$
$601$		−	1.27911i		−	0.0521761i	0.999660	−	0.0260880i	$-0.00830503\pi$
$602$	−8.93247	−	0.804153i	−0.364060	−	0.0327748i
$603$		−	34.6425i		−	1.41075i
$604$	−5.54824	−	12.8702i	−0.225755	−	0.523683i
$605$		0			0
$606$	−22.8616	+	4.71785i	−0.928689	+	0.191650i
$607$	−11.3045	−	19.5800i	−0.458836	−	0.794727i	0.540064	−	0.841624i	$-0.318400\pi$
$607$	−11.3045	−	19.5800i	−0.458836	−	0.794727i	−0.998900	+	0.0468970i	$0.985067\pi$
$608$	−16.4690	+	8.86805i	−0.667907	+	0.359647i
$609$	−13.4361	−	4.05773i	−0.544458	−	0.164428i
$610$		0			0
$611$	−0.945877	+	0.546102i	−0.0382661	+	0.0220929i
$612$	−33.0489	+	44.3716i	−1.33592	+	1.79361i
$613$	1.50973	−	2.61492i	0.0609773	−	0.105616i	−0.833925	−	0.551877i	$-0.813912\pi$
$613$	1.50973	−	2.61492i	0.0609773	−	0.105616i	0.894903	+	0.446262i	$0.147245\pi$
$614$	2.93350	+	0.972422i	0.118386	+	0.0392437i
$615$		0			0
$616$	25.6153	−	8.41007i	1.03207	−	0.338852i
$617$	14.3344			0.577081			0.288540	−	0.957468i	$-0.406830\pi$
$617$	14.3344			0.577081			0.288540	+	0.957468i	$0.406830\pi$
$618$	3.56201	+	1.18077i	0.143285	+	0.0474974i
$619$	10.8987	−	18.8771i	0.438055	−	0.758733i	−0.559485	−	0.828841i	$-0.689001\pi$
$619$	10.8987	−	18.8771i	0.438055	−	0.758733i	0.997539	+	0.0701078i	$0.0223343\pi$
$620$		0			0
$621$	4.21901	−	2.43584i	0.169303	−	0.0977471i
$622$	30.5347	−	27.1674i	1.22433	−	1.08931i
$623$	−19.2205	−	20.4709i	−0.770052	−	0.820150i
$624$	1.96342	−	8.26771i	0.0785997	−	0.330973i
$625$		0			0
$626$	8.79915	−	1.81584i	0.351685	−	0.0725757i
$627$	26.7843	+	15.4639i	1.06966	+	0.617570i
$628$	−5.08740	−	11.8012i	−0.203009	−	0.470920i
$629$		−	53.0106i		−	2.11367i
$630$		0			0
$631$			15.1512i			0.603160i	0.953441	+	0.301580i	$0.0975140\pi$
$631$			15.1512i			0.603160i	−0.953441	+	0.301580i	$0.902486\pi$
$632$	−19.8578	−	9.26800i	−0.789899	−	0.368661i
$633$	−49.6094	−	28.6420i	−1.97180	−	1.13842i
$634$	−5.37434	−	26.0428i	−0.213442	−	1.03429i
$635$		0			0
$636$	−1.09378	+	9.33959i	−0.0433710	+	0.370339i
$637$	2.54606	+	5.13101i	0.100879	+	0.203298i
$638$	6.92029	+	7.77803i	0.273977	+	0.307935i
$639$	4.48363	−	2.58863i	0.177370	−	0.102404i
$640$		0			0
$641$	−14.9960	+	25.9739i	−0.592308	+	1.02591i	0.401613	+	0.915809i	$0.368450\pi$
$641$	−14.9960	+	25.9739i	−0.592308	+	1.02591i	−0.993921	+	0.110098i	$0.964884\pi$
$642$	−8.37746	+	25.2722i	−0.330632	+	0.997415i
$643$	−1.63196			−0.0643583			−0.0321792	−	0.999482i	$-0.510245\pi$
$643$	−1.63196			−0.0643583			−0.0321792	+	0.999482i	$0.510245\pi$
$644$	1.52231	+	13.3281i	0.0599874	+	0.525201i
$645$		0			0
$646$	10.8827	−	32.8298i	0.428175	−	1.29167i
$647$	16.3832	−	28.3765i	0.644090	−	1.11560i	−0.340421	−	0.940273i	$-0.610570\pi$
$647$	16.3832	−	28.3765i	0.644090	−	1.11560i	0.984511	−	0.175323i	$-0.0560971\pi$
$648$	17.5590	−	1.53023i	0.689783	−	0.0601132i
$649$	−5.96388	+	3.44325i	−0.234103	+	0.135159i
$650$		0			0
$651$	9.57170	−	8.98703i	0.375145	−	0.352229i
$652$	36.7071	+	4.29883i	1.43756	+	0.168355i
$653$	11.2646	+	19.5109i	0.440819	+	0.763521i	0.997750	−	0.0670377i	$-0.0213548\pi$
$653$	11.2646	+	19.5109i	0.440819	+	0.763521i	−0.556932	+	0.830558i	$0.688021\pi$
$654$	5.91544	+	28.6648i	0.231312	+	1.12088i
$655$		0			0
$656$	10.1876	−	3.04497i	0.397760	−	0.118886i
$657$			27.6635i			1.07925i
$658$	−4.53157	+	2.09923i	−0.176659	+	0.0818367i
$659$			19.2525i			0.749969i	0.927031	+	0.374985i	$0.122352\pi$
$659$			19.2525i			0.749969i	−0.927031	+	0.374985i	$0.877648\pi$
$660$		0			0
$661$	30.1079	+	17.3828i	1.17106	+	0.676113i	0.953930	−	0.300030i	$-0.0969966\pi$
$661$	30.1079	+	17.3828i	1.17106	+	0.676113i	0.217132	+	0.976142i	$0.430330\pi$
$662$	18.1284	−	3.74108i	0.704580	−	0.145401i
$663$	7.85638	+	13.6077i	0.305117	+	0.528477i
$664$	17.0217	+	24.3270i	0.660570	+	0.944071i
$665$		0			0
$666$	28.3228	−	25.1994i	1.09749	−	0.976458i
$667$	−4.48617	+	2.59009i	−0.173705	+	0.100289i
$668$	−2.93357	−	2.18499i	−0.113503	−	0.0845398i
$669$	−30.6059	+	53.0110i	−1.18329	+	2.04952i
$670$		0			0
$671$	−35.2205			−1.35967
$672$	12.3314	−	36.8475i	0.475695	−	1.42142i
$673$	−42.6368			−1.64353			−0.821764	−	0.569827i	$-0.807010\pi$
$673$	−42.6368			−1.64353			−0.821764	+	0.569827i	$0.807010\pi$
$674$	−15.7487	−	5.22053i	−0.606618	−	0.201087i
$675$		0			0
$676$	19.7777	+	14.7309i	0.760681	+	0.566572i
$677$	−1.54611	+	0.892648i	−0.0594219	+	0.0343073i	−0.529417	−	0.848362i	$-0.677589\pi$
$677$	−1.54611	+	0.892648i	−0.0594219	+	0.0343073i	0.469995	+	0.882669i	$0.344256\pi$
$678$	−20.8911	+	18.5873i	−0.802319	+	0.713842i
$679$	18.8557	−	4.42102i	0.723615	−	0.169663i
$680$		0			0
$681$	−27.1648	−	47.0509i	−1.04096	−	1.80299i
$682$	−9.53800	+	1.96832i	−0.365229	+	0.0753708i
$683$	−7.45237	−	4.30263i	−0.285157	−	0.164636i	0.350599	−	0.936526i	$-0.385978\pi$
$683$	−7.45237	−	4.30263i	−0.285157	−	0.164636i	−0.635756	+	0.771890i	$0.719311\pi$
$684$	22.7138	−	9.79170i	0.868483	−	0.374395i
$685$		0			0
$686$	9.49151	+	24.4113i	0.362387	+	0.932028i
$687$			13.4523i			0.513236i
$688$	9.18628	−	2.74568i	0.350224	−	0.104678i
$689$	1.28338	+	0.740957i	0.0488927	+	0.0282282i
$690$		0			0
$691$	20.1511	+	34.9027i	0.766583	+	1.32776i	0.939405	+	0.342808i	$0.111378\pi$
$691$	20.1511	+	34.9027i	0.766583	+	1.32776i	−0.172822	+	0.984953i	$0.555289\pi$
$692$	−30.2920	−	3.54755i	−1.15153	−	0.134858i
$693$	−34.7101	+	8.13834i	−1.31853	+	0.309150i
$694$	−4.14720	−	4.66123i	−0.157426	−	0.176938i
$695$		0			0
$696$	14.9479	−	1.30268i	0.566597	−	0.0493778i
$697$	−9.83053	+	17.0270i	−0.372358	+	0.644943i
$698$	−8.16454	+	24.6299i	−0.309033	+	0.932256i
$699$	−53.9212			−2.03949
$700$		0			0
$701$	37.3051			1.40899			0.704497	−	0.709707i	$-0.251172\pi$
$701$	37.3051			1.40899			0.704497	+	0.709707i	$0.251172\pi$
$702$	−0.699719	+	2.11084i	−0.0264092	+	0.0796684i
$703$	−11.8495	+	20.5239i	−0.446911	+	0.774072i
$704$	−22.0915	+	18.5115i	−0.832604	+	0.697679i
$705$		0			0
$706$	11.0438	+	12.4126i	0.415637	+	0.467154i
$707$	−4.86315	+	16.1030i	−0.182898	+	0.605617i
$708$	−1.15444	+	9.85761i	−0.0433866	+	0.370472i
$709$	−4.02866	−	6.97784i	−0.151299	−	0.262058i	0.780406	−	0.625273i	$-0.215012\pi$
$709$	−4.02866	−	6.97784i	−0.151299	−	0.262058i	−0.931705	+	0.363215i	$0.881679\pi$
$710$		0			0
$711$	25.0958	+	14.4891i	0.941168	+	0.543383i
$712$	27.2019	+	12.6957i	1.01944	+	0.475790i
$713$		−	4.84582i		−	0.181477i
$714$	30.2002	+	65.1924i	1.13021	+	2.43977i
$715$		0			0
$716$	−9.92601	−	23.0254i	−0.370953	−	0.860498i
$717$	−47.5049	−	27.4269i	−1.77410	−	1.02428i
$718$	−0.274100	+	0.0565649i	−0.0102293	+	0.00211098i
$719$	5.87241	+	10.1713i	0.219004	+	0.379326i	0.954504	−	0.298199i	$-0.0963859\pi$
$719$	5.87241	+	10.1713i	0.219004	+	0.379326i	−0.735500	+	0.677525i	$0.763053\pi$
$720$		0			0
$721$	1.97139	−	1.85097i	0.0734184	−	0.0689338i
$722$	8.52275	−	7.58289i	0.317184	−	0.282206i
$723$	4.08766	−	2.36001i	0.152022	−	0.0877697i
$724$	−9.57940	+	12.8613i	−0.356016	+	0.477987i
$725$		0			0
$726$	6.89987	+	2.28723i	0.256078	+	0.0848871i
$727$	−33.3549			−1.23706			−0.618532	−	0.785760i	$-0.712272\pi$
$727$	−33.3549			−1.23706			−0.618532	+	0.785760i	$0.712272\pi$
$728$	−4.56320	−	4.08338i	−0.169123	−	0.151340i
$729$	−38.2742			−1.41756
$730$		0			0
$731$	−8.86429	+	15.3534i	−0.327857	+	0.567866i
$732$	−30.3213	+	40.7094i	−1.12071	+	1.50466i
$733$	9.95934	−	5.75003i	0.367856	−	0.212382i	−0.304665	−	0.952460i	$-0.598545\pi$
$733$	9.95934	−	5.75003i	0.367856	−	0.212382i	0.672522	+	0.740077i	$0.265211\pi$
$734$	−7.95403	+	7.07688i	−0.293588	+	0.261212i
$735$		0			0
$736$	−6.79912	−	12.6268i	−0.250619	−	0.465429i
$737$	16.6848	+	28.8989i	0.614593	+	1.06451i
$738$	−13.7704	+	2.84173i	−0.506894	+	0.104606i
$739$	−9.70301	−	5.60203i	−0.356931	−	0.206074i	0.310803	−	0.950474i	$-0.399402\pi$
$739$	−9.70301	−	5.60203i	−0.356931	−	0.206074i	−0.667734	+	0.744400i	$0.732735\pi$
$740$		0			0
$741$		−	7.02455i		−	0.258053i
$742$	5.54091	+	3.90061i	0.203413	+	0.143196i
$743$			43.7950i			1.60668i	0.595520	+	0.803341i	$0.296946\pi$
$743$			43.7950i			1.60668i	−0.595520	+	0.803341i	$0.703054\pi$
$744$	−5.93619	+	12.7190i	−0.217631	+	0.466300i
$745$		0			0
$746$	8.90030	+	43.1287i	0.325863	+	1.57905i
$747$	−19.6309	−	34.0017i	−0.718256	−	1.24406i
$748$	6.19898	−	52.9322i	0.226657	−	1.93539i
$749$	13.1325	+	13.9869i	0.479852	+	0.511069i
$750$		0			0
$751$	44.5322	−	25.7107i	1.62500	−	0.938196i	0.639450	−	0.768832i	$-0.279162\pi$
$751$	44.5322	−	25.7107i	1.62500	−	0.938196i	0.985554	−	0.169364i	$-0.0541714\pi$
$752$	3.66560	−	3.88180i	0.133671	−	0.141555i
$753$	−18.1976	+	31.5192i	−0.663159	+	1.14862i
$754$	0.744028	−	2.24450i	0.0270959	−	0.0817400i
$755$		0			0
$756$	−4.05206	+	9.32621i	−0.147372	+	0.339191i
$757$	−18.1453			−0.659502			−0.329751	−	0.944068i	$-0.606965\pi$
$757$	−18.1453			−0.659502			−0.329751	+	0.944068i	$0.606965\pi$
$758$	−7.27086	+	21.9339i	−0.264089	+	0.796676i
$759$	−11.8562	+	20.5355i	−0.430352	+	0.745391i
$760$		0			0
$761$	−28.4860	+	16.4464i	−1.03262	+	0.596181i	−0.917733	−	0.397198i	$-0.869983\pi$
$761$	−28.4860	+	16.4464i	−1.03262	+	0.596181i	−0.114883	+	0.993379i	$0.536649\pi$
$762$	21.4312	+	24.0875i	0.776370	+	0.872598i
$763$	20.1906	+	6.09762i	0.730950	+	0.220749i
$764$	−13.4270	−	1.57246i	−0.485771	−	0.0568895i
$765$		0			0
$766$	2.52915	+	12.2557i	0.0913821	+	0.442816i
$767$	1.35456	+	0.782054i	0.0489102	+	0.0282383i
$768$	2.37790	+	41.4709i	0.0858049	+	1.49645i
$769$			20.8502i			0.751876i	0.926645	+	0.375938i	$0.122679\pi$
$769$			20.8502i			0.751876i	−0.926645	+	0.375938i	$0.877321\pi$
$770$		0			0
$771$			46.4003i			1.67107i
$772$	4.33445	−	1.86854i	0.156000	−	0.0672503i
$773$	7.52368	+	4.34380i	0.270608	+	0.156236i	0.629164	−	0.777273i	$-0.283397\pi$
$773$	7.52368	+	4.34380i	0.270608	+	0.156236i	−0.358556	+	0.933508i	$0.616731\pi$
$774$	−12.4169	+	2.56242i	−0.446315	+	0.0921042i
$775$		0			0
$776$	−16.9639	+	11.8697i	−0.608970	+	0.426099i
$777$	−11.2381	−	47.9306i	−0.403165	−	1.71950i
$778$	9.87384	−	8.78497i	0.353994	−	0.314957i
$779$	7.61208	−	4.39484i	0.272731	−	0.157461i
$780$		0			0
$781$	−2.49351	+	4.31888i	−0.0892247	+	0.154542i
$782$	25.1706	+	8.34377i	0.900098	+	0.298373i
$783$	−3.92660			−0.140325
$784$	−19.1074	−	20.4672i	−0.682406	−	0.730973i
$785$		0			0
$786$	46.6628	+	15.4682i	1.66441	+	0.551733i
$787$	−18.6062	+	32.2270i	−0.663241	+	1.14877i	0.316518	+	0.948586i	$0.397486\pi$
$787$	−18.6062	+	32.2270i	−0.663241	+	1.14877i	−0.979759	+	0.200180i	$0.935847\pi$
$788$	−32.5936	−	24.2765i	−1.16110	−	0.864813i
$789$	49.2312	−	28.4237i	1.75268	−	1.01191i
$790$		0			0
$791$	4.59982	+	19.6183i	0.163551	+	0.697545i
$792$	31.2277	−	21.8501i	1.10963	−	0.776411i
$793$	3.99976	+	6.92778i	0.142036	+	0.246013i
$794$	28.1198	−	5.80296i	0.997933	−	0.205939i
$795$		0			0
$796$	21.0442	−	9.07197i	0.745893	−	0.321547i
$797$			21.3900i			0.757671i	0.925464	+	0.378835i	$0.123675\pi$
$797$			21.3900i			0.757671i	−0.925464	+	0.378835i	$0.876325\pi$
$798$	2.88001	−	31.9909i	0.101951	−	1.13247i
$799$			9.87221i			0.349254i
$800$		0			0
$801$	−34.3773	−	19.8477i	−1.21466	−	0.701285i
$802$	3.16883	+	15.3554i	0.111895	+	0.542217i
$803$	−13.3235	−	23.0770i	−0.470176	−	0.814368i
$804$	47.7666	+	5.59403i	1.68460	+	0.197286i
$805$		0			0
$806$	1.47033	+	1.65257i	0.0517902	+	0.0582094i
$807$	−6.48166	+	3.74219i	−0.228165	+	0.131731i
$808$	−1.56125	−	17.9149i	−0.0549244	−	0.630243i
$809$	12.1707	−	21.0803i	0.427900	−	0.741144i	−0.568787	−	0.822485i	$-0.692587\pi$
$809$	12.1707	−	21.0803i	0.427900	−	0.741144i	0.996686	+	0.0813411i	$0.0259203\pi$
$810$		0			0
$811$	−31.3778			−1.10183			−0.550913	−	0.834563i	$-0.685720\pi$
$811$	−31.3778			−1.10183			−0.550913	+	0.834563i	$0.685720\pi$
$812$	4.30865	−	9.91678i	0.151204	−	0.348011i
$813$	44.0206			1.54387
$814$	−11.4902	+	34.6625i	−0.402733	+	1.21492i
$815$		0			0
$816$	−55.8447	−	52.7344i	−1.95496	−	1.84607i
$817$	6.86389	−	3.96287i	0.240137	−	0.138643i
$818$	−5.53386	−	6.21976i	−0.193487	−	0.217469i
$819$	5.54259	+	5.90317i	0.193674	+	0.206274i
$820$		0			0
$821$	−0.0785681	−	0.136084i	−0.00274204	−	0.00474936i	0.864651	−	0.502373i	$-0.167539\pi$
$821$	−0.0785681	−	0.136084i	−0.00274204	−	0.00474936i	−0.867393	+	0.497623i	$0.834206\pi$
$822$	−3.87658	−	18.7850i	−0.135211	−	0.655202i
$823$	−16.1904	−	9.34753i	−0.564362	−	0.325835i	0.190532	−	0.981681i	$-0.438979\pi$
$823$	−16.1904	−	9.34753i	−0.564362	−	0.325835i	−0.754894	+	0.655846i	$0.772312\pi$
$824$	−1.22262	+	2.61960i	−0.0425919	+	0.0912582i
$825$		0			0
$826$	5.84823	+	4.11696i	0.203486	+	0.143247i
$827$		−	35.2960i		−	1.22736i	−0.789554	−	0.613681i	$-0.789688\pi$
$827$		−	35.2960i		−	1.22736i	0.789554	−	0.613681i	$-0.210312\pi$
$828$	7.50728	+	17.4146i	0.260896	+	0.605200i
$829$	14.2590	+	8.23245i	0.495237	+	0.285925i	0.726744	−	0.686908i	$-0.241033\pi$
$829$	14.2590	+	8.23245i	0.495237	+	0.285925i	−0.231508	+	0.972833i	$0.574366\pi$
$830$		0			0
$831$	−34.8558	−	60.3720i	−1.20913	−	2.09428i
$832$	6.14996	+	2.24311i	0.213211	+	0.0777659i
$833$	51.6713	+	3.25893i	1.79030	+	0.112915i
$834$	60.1934	−	53.5555i	2.08433	−	1.85447i
$835$		0			0
$836$	−14.2320	+	19.1079i	−0.492223	+	0.660859i
$837$	1.83658	−	3.18105i	0.0634814	−	0.109953i
$838$	−22.4529	−	7.44288i	−0.775622	−	0.257110i
$839$	−54.8000			−1.89191			−0.945953	−	0.324303i	$-0.894870\pi$
$839$	−54.8000			−1.89191			−0.945953	+	0.324303i	$0.894870\pi$
$840$		0			0
$841$	−24.8248			−0.856026
$842$	−1.59506	−	0.528745i	−0.0549694	−	0.0182218i
$843$	32.3871	−	56.0960i	1.11547	−	1.93205i
$844$	26.3602	−	35.3913i	0.907356	−	1.21822i
$845$		0			0
$846$	−5.27458	+	4.69291i	−0.181344	+	0.161346i
$847$	3.81872	−	3.58546i	0.131213	−	0.123198i
$848$	−7.04801	−	1.67376i	−0.242030	−	0.0574773i
$849$	−12.7709	−	22.1199i	−0.438297	−	0.759152i
$850$		0			0
$851$	−15.7356	−	9.08496i	−0.539410	−	0.311428i
$852$	2.84530	+	6.60023i	0.0974783	+	0.226120i
$853$			38.9225i			1.33268i	0.745648	+	0.666340i	$0.232140\pi$
$853$			38.9225i			1.33268i	−0.745648	+	0.666340i	$0.767860\pi$
$854$	15.3752	+	33.1901i	0.526128	+	1.13574i
$855$		0			0
$856$	−18.5859	−	8.67440i	−0.635253	−	0.296485i
$857$	−25.4206	−	14.6766i	−0.868350	−	0.501342i	−0.00155047	−	0.999999i	$-0.500494\pi$
$857$	−25.4206	−	14.6766i	−0.868350	−	0.501342i	−0.866800	+	0.498657i	$0.833827\pi$
$858$	−2.18761	−	10.6006i	−0.0746839	−	0.361900i
$859$	23.6874	+	41.0277i	0.808202	+	1.39985i	0.914108	+	0.405471i	$0.132893\pi$
$859$	23.6874	+	41.0277i	0.808202	+	1.39985i	−0.105905	+	0.994376i	$0.533774\pi$
$860$		0			0
$861$	−5.27880	+	17.4793i	−0.179901	+	0.595694i
$862$	−22.6504	−	25.4578i	−0.771474	−	0.867095i
$863$	20.5257	−	11.8505i	0.698704	−	0.403397i	−0.108161	−	0.994133i	$-0.534496\pi$
$863$	20.5257	−	11.8505i	0.698704	−	0.403397i	0.806865	+	0.590737i	$0.201163\pi$
$864$	0.322288	−	10.8658i	0.0109645	−	0.369660i
$865$		0			0
$866$	6.66609	−	20.1095i	0.226523	−	0.683350i
$867$	97.8892			3.32449
$868$	6.01858	+	8.12890i	0.204284	+	0.275913i
$869$	−27.9134			−0.946897
$870$		0			0
$871$	3.78957	−	6.56372i	0.128405	−	0.222403i
$872$	−22.4624	+	1.95755i	−0.760673	+	0.0662912i
$873$	23.7103	−	13.6892i	0.802474	−	0.463308i
$874$	−7.88009	−	8.85680i	−0.266548	−	0.299586i
$875$		0			0
$876$	−38.1436	−	4.46706i	−1.28875	−	0.150928i
$877$	16.6020	+	28.7555i	0.560610	+	0.971004i	0.997443	+	0.0714621i	$0.0227665\pi$
$877$	16.6020	+	28.7555i	0.560610	+	0.971004i	−0.436834	+	0.899542i	$0.643900\pi$
$878$	−4.95197	−	23.9961i	−0.167121	−	0.809829i
$879$	−52.6205	−	30.3805i	−1.77485	−	1.02471i
$880$		0			0
$881$			19.2043i			0.647008i	0.946227	+	0.323504i	$0.104861\pi$
$881$			19.2043i			0.647008i	−0.946227	+	0.323504i	$0.895139\pi$
$882$	22.8216	+	29.1564i	0.768442	+	0.981747i
$883$		−	8.57526i		−	0.288581i	−0.989535	−	0.144290i	$-0.953910\pi$
$883$		−	8.57526i		−	0.288581i	0.989535	−	0.144290i	$-0.0460899\pi$
$884$	−11.1156	+	4.79184i	−0.373859	+	0.161167i
$885$		0			0
$886$	−34.9477	+	7.21202i	−1.17409	+	0.242292i
$887$	7.37543	+	12.7746i	0.247643	+	0.428930i	0.962871	−	0.269961i	$-0.0870108\pi$
$887$	7.37543	+	12.7746i	0.247643	+	0.428930i	−0.715229	+	0.698891i	$0.753677\pi$
$888$	30.1725	+	43.1219i	1.01252	+	1.44707i
$889$	22.6199	−	5.30359i	0.758646	−	0.177877i
$890$		0			0
$891$	19.4430	−	11.2254i	0.651365	−	0.376066i
$892$	−37.8179	−	28.1676i	−1.26624	−	0.943122i
$893$	2.20673	−	3.82218i	0.0738455	−	0.127904i
$894$	−83.4665	−	27.6682i	−2.79154	−	0.925364i
$895$		0			0
$896$	27.0882	+	12.7369i	0.904954	+	0.425510i
$897$	5.38571			0.179824
$898$	−9.47917	−	3.14224i	−0.316324	−	0.104858i
$899$	−1.95288	+	3.38248i	−0.0651321	+	0.112812i
$900$		0			0
$901$	11.6002	−	6.69736i	0.386457	−	0.223121i
$902$	10.1186	−	9.00277i	0.336914	−	0.299760i
$903$	−4.75995	+	15.7613i	−0.158401	+	0.524503i
$904$	−12.3498	−	17.6500i	−0.410747	−	0.587030i
$905$		0			0
$906$	−25.1979	+	5.19999i	−0.837144	+	0.172758i
$907$	−41.2134	−	23.7946i	−1.36847	−	0.790085i	−0.377736	−	0.925914i	$-0.623297\pi$
$907$	−41.2134	−	23.7946i	−1.36847	−	0.790085i	−0.990732	+	0.135828i	$0.956631\pi$
$908$	38.4342	−	16.5686i	1.27548	−	0.549850i
$909$			23.7796i			0.788720i
$910$		0			0
$911$			34.7074i			1.14991i	0.818186	+	0.574954i	$0.194980\pi$
$911$			34.7074i			1.14991i	−0.818186	+	0.574954i	$0.805020\pi$
$912$	9.83342	+	32.8999i	0.325617	+	1.08942i
$913$	32.7523	+	18.9095i	1.08394	+	0.625814i
$914$	5.39678	+	26.1515i	0.178510	+	0.865015i
$915$		0			0
$916$	−10.2928	−	1.20540i	−0.340082	−	0.0398276i
$917$	25.8255	−	24.2480i	0.852833	−	0.800739i
$918$	13.3610	+	15.0170i	0.440977	+	0.495635i
$919$	44.9270	−	25.9386i	1.48200	−	0.855635i	0.482212	−	0.876055i	$-0.339833\pi$
$919$	44.9270	−	25.9386i	1.48200	−	0.855635i	0.999792	+	0.0204194i	$0.00650013\pi$
$920$		0			0
$921$	2.83671	−	4.91333i	0.0934729	−	0.161900i
$922$	15.4003	−	46.4581i	0.507183	−	1.53001i
$923$	1.13269			0.0372828
$924$	−5.61655	−	49.1739i	−0.184771	−	1.61770i
$925$		0			0
$926$	6.68524	−	20.1673i	0.219690	−	0.662738i
$927$	1.91138	−	3.31060i	0.0627778	−	0.108734i
$928$	−0.342696	+	11.5538i	−0.0112496	+	0.379272i
$929$	−37.9198	+	21.8930i	−1.24411	+	0.718286i	−0.969928	−	0.243393i	$-0.921740\pi$
$929$	−37.9198	+	21.8930i	−1.24411	+	0.718286i	−0.274180	+	0.961678i	$0.588406\pi$
$930$		0			0
$931$	−19.2769	−	12.8118i	−0.631774	−	0.419891i
$932$	4.83166	−	41.2568i	0.158266	−	1.35141i
$933$	−37.5151	−	64.9780i	−1.22819	−	2.12728i
$934$	7.27106	+	35.2338i	0.237916	+	1.15289i
$935$		0			0
$936$	−7.84419	−	3.66104i	−0.256396	−	0.119665i
$937$		−	14.2224i		−	0.464624i	−0.972641	−	0.232312i	$-0.925371\pi$
$937$		−	14.2224i		−	0.464624i	0.972641	−	0.232312i	$-0.0746290\pi$
$938$	19.9494	−	28.3385i	0.651370	−	0.925286i
$939$		−	16.4937i		−	0.538251i
$940$		0			0
$941$	4.80070	+	2.77169i	0.156498	+	0.0903544i	0.576204	−	0.817306i	$-0.304533\pi$
$941$	4.80070	+	2.77169i	0.156498	+	0.0903544i	−0.419706	+	0.907660i	$0.637867\pi$
$942$	−23.1049	+	4.76807i	−0.752799	+	0.155352i
$943$	3.36951	+	5.83617i	0.109726	+	0.190052i
$944$	−7.43893	−	1.76660i	−0.242116	−	0.0574979i
$945$		0			0
$946$	9.12407	−	8.11789i	0.296649	−	0.263935i
$947$	−51.5945	+	29.7881i	−1.67660	+	0.967983i	−0.712791	+	0.701377i	$0.752569\pi$
$947$	−51.5945	+	29.7881i	−1.67660	+	0.967983i	−0.963805	+	0.266607i	$0.914098\pi$
$948$	−24.0306	+	32.2636i	−0.780479	+	1.04787i
$949$	−3.02612	+	5.24140i	−0.0982321	+	0.170143i
$950$		0			0
$951$	−48.8163			−1.58298
$952$	−52.5869	+	17.2655i	−1.70435	+	0.559578i
$953$	−12.2577			−0.397065			−0.198532	−	0.980094i	$-0.563617\pi$
$953$	−12.2577			−0.397065			−0.198532	+	0.980094i	$0.563617\pi$
$954$	9.09262	+	3.01410i	0.294384	+	0.0975852i
$955$		0			0
$956$	25.2419	−	33.8899i	0.816383	−	1.09608i
$957$	16.5517	−	9.55612i	0.535040	−	0.308906i
$958$	21.7321	−	19.3355i	0.702133	−	0.624703i
$959$	−13.2316	−	3.99597i	−0.427270	−	0.129037i
$960$		0			0
$961$	13.6732	+	23.6826i	0.441070	+	0.763956i
$962$	8.12290	−	1.67629i	0.261893	−	0.0540458i
$963$	23.4885	+	13.5611i	0.756906	+	0.437000i
$964$	1.43944	+	3.33907i	0.0463612	+	0.107544i
$965$		0			0
$966$	24.5274	+	2.20810i	0.789155	+	0.0710443i
$967$			53.4551i			1.71900i	0.511137	+	0.859499i	$0.329225\pi$
$967$			53.4551i			1.71900i	−0.511137	+	0.859499i	$0.670775\pi$
$968$	−2.36830	+	5.07436i	−0.0761201	+	0.163096i
$969$	−54.9869	−	31.7467i	−1.76643	−	1.01985i
$970$		0			0
$971$	−11.1284	−	19.2749i	−0.357126	−	0.618561i	0.630353	−	0.776308i	$-0.282910\pi$
$971$	−11.1284	−	19.2749i	−0.357126	−	0.618561i	−0.987479	+	0.157748i	$0.949577\pi$
$972$	5.10475	−	43.5887i	0.163735	−	1.39811i
$973$	−13.2534	−	56.5259i	−0.424885	−	1.81214i
$974$	27.3167	+	30.7025i	0.875284	+	0.983772i
$975$		0			0
$976$	−28.4311	−	26.8476i	−0.910056	−	0.859369i
$977$	15.8974	−	27.5351i	0.508603	−	0.880926i	−0.491347	−	0.870964i	$-0.663495\pi$
$977$	15.8974	−	27.5351i	0.508603	−	0.880926i	0.999950	−	0.00996251i	$-0.00317122\pi$
$978$	21.3481	−	64.4006i	0.682637	−	2.05931i
$979$	38.2369			1.22206
$980$		0			0
$981$	29.8158			0.951947
$982$	4.23543	−	12.7770i	0.135158	−	0.407730i
$983$	−10.2927	+	17.8275i	−0.328287	+	0.568609i	−0.982172	−	0.187985i	$-0.939805\pi$
$983$	−10.2927	+	17.8275i	−0.328287	+	0.568609i	0.653885	+	0.756594i	$0.273138\pi$
$984$	−1.69469	−	19.4460i	−0.0540246	−	0.619917i
$985$		0			0
$986$	−14.2070	−	15.9679i	−0.452444	−	0.508522i
$987$	2.09288	+	8.92616i	0.0666172	+	0.284123i
$988$	5.37470	+	0.629440i	0.170992	+	0.0200252i
$989$	3.03832	+	5.26253i	0.0966131	+	0.167339i
$990$		0			0
$991$	32.2836	+	18.6390i	1.02552	+	0.592086i	0.915699	−	0.401865i	$-0.131638\pi$
$991$	32.2836	+	18.6390i	1.02552	+	0.592086i	0.109824	+	0.993951i	$0.464971\pi$
$992$	−9.19977	−	5.68166i	−0.292093	−	0.180393i
$993$		−	33.9810i		−	1.07836i
$994$	5.15843	+	0.464392i	0.163615	+	0.0147296i
$995$		0			0
$996$	50.0529	−	21.5773i	1.58599	−	0.683704i
$997$	10.9485	+	6.32111i	0.346742	+	0.200191i	0.663249	−	0.748399i	$-0.269177\pi$
$997$	10.9485	+	6.32111i	0.346742	+	0.200191i	−0.316508	+	0.948590i	$0.602510\pi$
$998$	27.9645	−	5.77092i	0.885201	−	0.182675i
$999$	−6.88644	−	11.9277i	−0.217877	−	0.377375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.e.451.15		32
4.3	odd	2	inner	700.2.p.e.451.7		32
5.2	odd	4		140.2.s.b.59.7	yes	32
5.3	odd	4		140.2.s.b.59.10	yes	32
5.4	even	2	inner	700.2.p.e.451.2		32
7.5	odd	6	inner	700.2.p.e.551.7		32
20.3	even	4		140.2.s.b.59.15	yes	32
20.7	even	4		140.2.s.b.59.2	yes	32
20.19	odd	2	inner	700.2.p.e.451.10		32
28.19	even	6	inner	700.2.p.e.551.15		32
35.2	odd	12		980.2.s.e.19.15		32
35.3	even	12		980.2.c.d.979.28		32
35.12	even	12		140.2.s.b.19.15	yes	32
35.13	even	4		980.2.s.e.619.10		32
35.17	even	12		980.2.c.d.979.5		32
35.18	odd	12		980.2.c.d.979.27		32
35.19	odd	6	inner	700.2.p.e.551.10		32
35.23	odd	12		980.2.s.e.19.2		32
35.27	even	4		980.2.s.e.619.7		32
35.32	odd	12		980.2.c.d.979.6		32
35.33	even	12		140.2.s.b.19.2	✓	32
140.3	odd	12		980.2.c.d.979.7		32
140.19	even	6	inner	700.2.p.e.551.2		32
140.23	even	12		980.2.s.e.19.7		32
140.27	odd	4		980.2.s.e.619.2		32
140.47	odd	12		140.2.s.b.19.10	yes	32
140.67	even	12		980.2.c.d.979.25		32
140.83	odd	4		980.2.s.e.619.15		32
140.87	odd	12		980.2.c.d.979.26		32
140.103	odd	12		140.2.s.b.19.7	yes	32
140.107	even	12		980.2.s.e.19.10		32
140.123	even	12		980.2.c.d.979.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.2	✓	32	35.33	even	12
140.2.s.b.19.7	yes	32	140.103	odd	12
140.2.s.b.19.10	yes	32	140.47	odd	12
140.2.s.b.19.15	yes	32	35.12	even	12
140.2.s.b.59.2	yes	32	20.7	even	4
140.2.s.b.59.7	yes	32	5.2	odd	4
140.2.s.b.59.10	yes	32	5.3	odd	4
140.2.s.b.59.15	yes	32	20.3	even	4
700.2.p.e.451.2		32	5.4	even	2	inner
700.2.p.e.451.7		32	4.3	odd	2	inner
700.2.p.e.451.10		32	20.19	odd	2	inner
700.2.p.e.451.15		32	1.1	even	1	trivial
700.2.p.e.551.2		32	140.19	even	6	inner
700.2.p.e.551.7		32	7.5	odd	6	inner
700.2.p.e.551.10		32	35.19	odd	6	inner
700.2.p.e.551.15		32	28.19	even	6	inner
980.2.c.d.979.5		32	35.17	even	12
980.2.c.d.979.6		32	35.32	odd	12
980.2.c.d.979.7		32	140.3	odd	12
980.2.c.d.979.8		32	140.123	even	12
980.2.c.d.979.25		32	140.67	even	12
980.2.c.d.979.26		32	140.87	odd	12
980.2.c.d.979.27		32	35.18	odd	12
980.2.c.d.979.28		32	35.3	even	12
980.2.s.e.19.2		32	35.23	odd	12
980.2.s.e.19.7		32	140.23	even	12
980.2.s.e.19.10		32	140.107	even	12
980.2.s.e.19.15		32	35.2	odd	12
980.2.s.e.619.2		32	140.27	odd	4
980.2.s.e.619.7		32	35.27	even	4
980.2.s.e.619.10		32	35.13	even	4
980.2.s.e.619.15		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34238 + 0.444985i) q^{2} +(1.29809 - 2.24836i) q^{3} +(1.60398 + 1.19468i) q^{4} +(2.74302 - 2.44053i) q^{6} +(-0.603960 - 2.57589i) q^{7} +(1.62154 + 2.31746i) q^{8} +(-1.87009 - 3.23909i) q^{9} +(3.12008 + 1.80138i) q^{11} +(4.76818 - 2.05552i) q^{12} -0.818282i q^{13} +(0.335489 - 3.72659i) q^{14} +(1.14549 + 3.83247i) q^{16} +(-6.40537 - 3.69814i) q^{17} +(-1.06903 - 5.18026i) q^{18} +(1.65329 + 2.86358i) q^{19} +(-6.57554 - 1.98583i) q^{21} +(3.38675 + 3.80652i) q^{22} +(-2.19550 + 1.26758i) q^{23} +(7.31540 - 0.637523i) q^{24} +(0.364123 - 1.09845i) q^{26} -1.92166 q^{27} +(2.10863 - 4.85321i) q^{28} +2.04334 q^{29} +(-0.955727 + 1.65537i) q^{31} +(-0.167714 + 5.65437i) q^{32} +(8.10030 - 4.67671i) q^{33} +(-6.95283 - 7.81461i) q^{34} +(0.870092 - 7.42959i) q^{36} +(3.58360 + 6.20697i) q^{37} +(0.945096 + 4.57971i) q^{38} +(-1.83980 - 1.06221i) q^{39} -2.65824i q^{41} +(-7.94322 - 5.59176i) q^{42} -2.39696i q^{43} +(2.85246 + 6.61686i) q^{44} +(-3.51126 + 0.724604i) q^{46} +(-0.667376 - 1.15593i) q^{47} +(10.1037 + 2.39944i) q^{48} +(-6.27046 + 3.11147i) q^{49} +(-16.6295 + 9.60106i) q^{51} +(0.977584 - 1.31251i) q^{52} +(-0.905503 + 1.56838i) q^{53} +(-2.57960 - 0.855108i) q^{54} +(4.99019 - 5.57656i) q^{56} +8.58450 q^{57} +(2.74295 + 0.909256i) q^{58} +(-0.955727 + 1.65537i) q^{59} +(-8.46625 + 4.88799i) q^{61} +(-2.01956 + 1.79685i) q^{62} +(-7.21411 + 6.77344i) q^{63} +(-2.74124 + 7.51569i) q^{64} +(12.9548 - 2.67342i) q^{66} +(8.02134 + 4.63112i) q^{67} +(-5.85597 - 13.5841i) q^{68} +6.58172i q^{69} +1.38422i q^{71} +(4.47405 - 9.58617i) q^{72} +(-6.40537 - 3.69814i) q^{73} +(2.04855 + 9.92677i) q^{74} +(-0.769222 + 6.56827i) q^{76} +(2.75576 - 9.12495i) q^{77} +(-1.99704 - 2.24457i) q^{78} +(-6.70979 + 3.87390i) q^{79} +(3.11579 - 5.39670i) q^{81} +(1.18287 - 3.56837i) q^{82} +10.4973 q^{83} +(-8.17459 - 11.0409i) q^{84} +(1.06661 - 3.21763i) q^{86} +(2.65245 - 4.59418i) q^{87} +(0.884696 + 10.1516i) q^{88} +(9.19133 - 5.30662i) q^{89} +(-2.10781 + 0.494210i) q^{91} +(-5.03589 - 0.589761i) q^{92} +(2.48125 + 4.29764i) q^{93} +(-0.381503 - 1.84867i) q^{94} +(12.4954 + 7.71698i) q^{96} +7.32005i q^{97} +(-9.80192 + 1.38652i) q^{98} -13.4750i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) \) 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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