LMFDB - Embedded newform 275.3.bk.c.207.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(82,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			207.11
Character	$\chi$	$=$	275.207
Dual form			275.3.bk.c.93.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04950 - 0.534746i) q^{2} +(0.902907 - 5.70073i) q^{3} +(-1.53565 + 2.11364i) q^{4} +(-2.10084 - 6.46573i) q^{6} +(-0.308752 - 1.94938i) q^{7} +(-1.21844 + 7.69295i) q^{8} +(-23.1236 - 7.51330i) q^{9} +(-9.40014 - 5.71291i) q^{11} +(10.6627 + 10.6627i) q^{12} +(-7.55546 - 14.8284i) q^{13} +(-1.36646 - 1.88077i) q^{14} +(-0.394331 - 1.21363i) q^{16} +(-2.20061 + 4.31894i) q^{17} +(-28.2858 + 4.48004i) q^{18} +(8.23200 + 11.3304i) q^{19} -11.3917 q^{21} +(-12.9204 - 0.968994i) q^{22} +(20.5117 - 20.5117i) q^{23} +(42.7553 + 13.8920i) q^{24} +(-15.8589 - 11.5221i) q^{26} +(-40.1266 + 78.7530i) q^{27} +(4.59443 + 2.34098i) q^{28} +(25.5765 - 35.2031i) q^{29} +(-3.79161 + 11.6694i) q^{31} +(-23.0930 - 23.0930i) q^{32} +(-41.0552 + 48.4294i) q^{33} +5.70948i q^{34} +(51.3900 - 37.3370i) q^{36} +(0.0304356 + 0.192163i) q^{37} +(14.6984 + 7.48918i) q^{38} +(-91.3546 + 29.6829i) q^{39} +(-35.3846 + 25.7084i) q^{41} +(-11.9555 + 6.09166i) q^{42} +(19.6401 - 19.6401i) q^{43} +(26.5103 - 11.0955i) q^{44} +(10.5585 - 32.4956i) q^{46} +(48.5817 + 7.69458i) q^{47} +(-7.27460 + 1.15218i) q^{48} +(42.8970 - 13.9381i) q^{49} +(22.6341 + 16.4447i) q^{51} +(42.9444 + 6.80173i) q^{52} +(2.54841 + 5.00155i) q^{53} +104.109i q^{54} +15.3727 q^{56} +(72.0242 - 36.6981i) q^{57} +(8.01782 - 50.6225i) q^{58} +(-1.39664 + 1.92231i) q^{59} +(-36.3443 - 111.856i) q^{61} +(2.26086 + 14.2745i) q^{62} +(-7.50685 + 47.3964i) q^{63} +(-31.7305 - 10.3099i) q^{64} +(-17.1899 + 72.7807i) q^{66} +(-50.5862 - 50.5862i) q^{67} +(-5.74931 - 11.2837i) q^{68} +(-98.4116 - 135.452i) q^{69} +(-0.478560 - 1.47286i) q^{71} +(85.9742 - 168.734i) q^{72} +(89.5842 - 14.1887i) q^{73} +(0.134700 + 0.185399i) q^{74} -36.5898 q^{76} +(-8.23433 + 20.0884i) q^{77} +(-80.0037 + 80.0037i) q^{78} +(-47.9857 - 15.5915i) q^{79} +(235.688 + 171.237i) q^{81} +(-23.3886 + 45.9027i) q^{82} +(-12.4452 - 6.34114i) q^{83} +(17.4936 - 24.0779i) q^{84} +(10.1098 - 31.1147i) q^{86} +(-177.590 - 177.590i) q^{87} +(55.4026 - 65.3540i) q^{88} -80.6579i q^{89} +(-26.5735 + 19.3068i) q^{91} +(11.8556 + 74.8532i) q^{92} +(63.1004 + 32.1513i) q^{93} +(55.1010 - 17.9034i) q^{94} +(-152.498 + 110.796i) q^{96} +(96.8143 - 49.3293i) q^{97} +(37.5670 - 37.5670i) q^{98} +(174.442 + 202.729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) $ 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.04950	−	0.534746i	0.524749	−	0.267373i	−0.171486	−	0.985186i	$-0.554857\pi$
$2$	1.04950	−	0.534746i	0.524749	−	0.267373i	0.696235	+	0.717813i	$0.254857\pi$
$3$	0.902907	−	5.70073i	0.300969	−	1.90024i	−0.119326	−	0.992855i	$-0.538073\pi$
$3$	0.902907	−	5.70073i	0.300969	−	1.90024i	0.420295	−	0.907388i	$-0.361927\pi$
$4$	−1.53565	+	2.11364i	−0.383912	+	0.528410i
$5$		0			0
$5$		0			0
$6$	−2.10084	−	6.46573i	−0.350140	−	1.07762i
$7$	−0.308752	−	1.94938i	−0.0441074	−	0.278483i	0.955770	−	0.294114i	$-0.0950245\pi$
$7$	−0.308752	−	1.94938i	−0.0441074	−	0.278483i	−0.999878	+	0.0156304i	$0.995024\pi$
$8$	−1.21844	+	7.69295i	−0.152305	+	0.961619i
$9$	−23.1236	−	7.51330i	−2.56928	−	0.834811i
$10$		0			0
$11$	−9.40014	−	5.71291i	−0.854559	−	0.519355i
$11$	−9.40014	−	5.71291i	−0.854559	−	0.519355i
$12$	10.6627	+	10.6627i	0.888561	+	0.888561i
$13$	−7.55546	−	14.8284i	−0.581189	−	1.14065i	−0.975155	−	0.221523i	$-0.928897\pi$
$13$	−7.55546	−	14.8284i	−0.581189	−	1.14065i	0.393966	−	0.919125i	$-0.371103\pi$
$14$	−1.36646	−	1.88077i	−0.0976043	−	0.134341i
$15$		0			0
$16$	−0.394331	−	1.21363i	−0.0246457	−	0.0758516i
$17$	−2.20061	+	4.31894i	−0.129448	+	0.254055i	−0.946629	−	0.322326i	$-0.895535\pi$
$17$	−2.20061	+	4.31894i	−0.129448	+	0.254055i	0.817181	+	0.576381i	$0.195535\pi$
$18$	−28.2858	+	4.48004i	−1.57144	+	0.248891i
$19$	8.23200	+	11.3304i	0.433263	+	0.596336i	0.968698	−	0.248240i	$-0.0798523\pi$
$19$	8.23200	+	11.3304i	0.433263	+	0.596336i	−0.535435	+	0.844576i	$0.679852\pi$
$20$		0			0
$21$	−11.3917			−0.542461
$22$	−12.9204	−	0.968994i	−0.587290	−	0.0440452i
$23$	20.5117	−	20.5117i	0.891814	−	0.891814i	−0.102879	−	0.994694i	$-0.532806\pi$
$23$	20.5117	−	20.5117i	0.891814	−	0.891814i	0.994694	+	0.102879i	$0.0328056\pi$
$24$	42.7553	+	13.8920i	1.78147	+	0.578835i
$25$		0			0
$26$	−15.8589	−	11.5221i	−0.609957	−	0.443159i
$27$	−40.1266	+	78.7530i	−1.48617	+	2.91678i
$28$	4.59443	+	2.34098i	0.164087	+	0.0836063i
$29$	25.5765	−	35.2031i	0.881949	−	1.21390i	−0.0939277	−	0.995579i	$-0.529942\pi$
$29$	25.5765	−	35.2031i	0.881949	−	1.21390i	0.975877	−	0.218320i	$-0.0700577\pi$
$30$		0			0
$31$	−3.79161	+	11.6694i	−0.122310	+	0.376431i	−0.993401	−	0.114690i	$-0.963413\pi$
$31$	−3.79161	+	11.6694i	−0.122310	+	0.376431i	0.871091	+	0.491121i	$0.163413\pi$
$32$	−23.0930	−	23.0930i	−0.721657	−	0.721657i
$33$	−41.0552	+	48.4294i	−1.24410	+	1.46756i
$34$			5.70948i			0.167926i
$35$		0			0
$36$	51.3900	−	37.3370i	1.42750	−	1.03714i
$37$	0.0304356	+	0.192163i	0.000822583	+	0.00519359i	0.988096	−	0.153837i	$-0.0491631\pi$
$37$	0.0304356	+	0.192163i	0.000822583	+	0.00519359i	−0.987274	+	0.159031i	$0.949163\pi$
$38$	14.6984	+	7.48918i	0.386799	+	0.197084i
$39$	−91.3546	+	29.6829i	−2.34243	+	0.761101i
$40$		0			0
$41$	−35.3846	+	25.7084i	−0.863039	+	0.627034i	−0.928710	−	0.370807i	$-0.879081\pi$
$41$	−35.3846	+	25.7084i	−0.863039	+	0.627034i	0.0656713	+	0.997841i	$0.479081\pi$
$42$	−11.9555	+	6.09166i	−0.284656	+	0.145039i
$43$	19.6401	−	19.6401i	0.456746	−	0.456746i	−0.440840	−	0.897586i	$-0.645319\pi$
$43$	19.6401	−	19.6401i	0.456746	−	0.456746i	0.897586	+	0.440840i	$0.145319\pi$
$44$	26.5103	−	11.0955i	0.602507	−	0.252170i
$45$		0			0
$46$	10.5585	−	32.4956i	0.229532	−	0.706426i
$47$	48.5817	+	7.69458i	1.03365	+	0.163714i	0.650135	−	0.759819i	$-0.274712\pi$
$47$	48.5817	+	7.69458i	1.03365	+	0.163714i	0.383518	+	0.923533i	$0.374712\pi$
$48$	−7.27460	+	1.15218i	−0.151554	+	0.0240038i
$49$	42.8970	−	13.9381i	0.875449	−	0.284451i
$50$		0			0
$51$	22.6341	+	16.4447i	0.443807	+	0.322444i
$52$	42.9444	+	6.80173i	0.825854	+	0.130802i
$53$	2.54841	+	5.00155i	0.0480833	+	0.0943688i	0.913798	−	0.406169i	$-0.133136\pi$
$53$	2.54841	+	5.00155i	0.0480833	+	0.0943688i	−0.865715	+	0.500538i	$0.833136\pi$
$54$			104.109i			1.92794i
$55$		0			0
$56$	15.3727			0.274513
$57$	72.0242	−	36.6981i	1.26358	−	0.643827i
$58$	8.01782	−	50.6225i	0.138238	−	0.872802i
$59$	−1.39664	+	1.92231i	−0.0236719	+	0.0325816i	−0.820689	−	0.571375i	$-0.806410\pi$
$59$	−1.39664	+	1.92231i	−0.0236719	+	0.0325816i	0.797017	+	0.603957i	$0.206410\pi$
$60$		0			0
$61$	−36.3443	−	111.856i	−0.595809	−	1.83371i	−0.550659	−	0.834731i	$-0.685623\pi$
$61$	−36.3443	−	111.856i	−0.595809	−	1.83371i	−0.0451502	−	0.998980i	$-0.514377\pi$
$62$	2.26086	+	14.2745i	0.0364655	+	0.230234i
$63$	−7.50685	+	47.3964i	−0.119156	+	0.752324i
$64$	−31.7305	−	10.3099i	−0.495789	−	0.161091i
$65$		0			0
$66$	−17.1899	+	72.7807i	−0.260453	+	1.10274i
$67$	−50.5862	−	50.5862i	−0.755018	−	0.755018i	0.220393	−	0.975411i	$-0.429266\pi$
$67$	−50.5862	−	50.5862i	−0.755018	−	0.755018i	−0.975411	+	0.220393i	$0.929266\pi$
$68$	−5.74931	−	11.2837i	−0.0845487	−	0.165936i
$69$	−98.4116	−	135.452i	−1.42626	−	1.96307i
$70$		0			0
$71$	−0.478560	−	1.47286i	−0.00674028	−	0.0207445i	0.947630	−	0.319371i	$-0.103472\pi$
$71$	−0.478560	−	1.47286i	−0.00674028	−	0.0207445i	−0.954370	+	0.298626i	$0.903472\pi$
$72$	85.9742	−	168.734i	1.19409	−	2.34353i
$73$	89.5842	−	14.1887i	1.22718	−	0.194366i	0.491005	−	0.871157i	$-0.336630\pi$
$73$	89.5842	−	14.1887i	1.22718	−	0.194366i	0.736176	+	0.676790i	$0.236630\pi$
$74$	0.134700	+	0.185399i	0.00182028	+	0.00250539i
$75$		0			0
$76$	−36.5898			−0.481445
$77$	−8.23433	+	20.0884i	−0.106939	+	0.260888i
$78$	−80.0037	+	80.0037i	−1.02569	+	1.02569i
$79$	−47.9857	−	15.5915i	−0.607414	−	0.197361i	−0.0108696	−	0.999941i	$-0.503460\pi$
$79$	−47.9857	−	15.5915i	−0.607414	−	0.197361i	−0.596544	+	0.802580i	$0.703460\pi$
$80$		0			0
$81$	235.688	+	171.237i	2.90973	+	2.11404i
$82$	−23.3886	+	45.9027i	−0.285227	+	0.559789i
$83$	−12.4452	−	6.34114i	−0.149942	−	0.0763993i	0.377410	−	0.926046i	$-0.376815\pi$
$83$	−12.4452	−	6.34114i	−0.149942	−	0.0763993i	−0.527352	+	0.849647i	$0.676815\pi$
$84$	17.4936	−	24.0779i	0.208257	−	0.286642i
$85$		0			0
$86$	10.1098	−	31.1147i	0.117555	−	0.361799i
$87$	−177.590	−	177.590i	−2.04126	−	2.04126i
$88$	55.4026	−	65.3540i	0.629576	−	0.742659i
$89$		−	80.6579i		−	0.906269i	−0.891442	−	0.453135i	$-0.850306\pi$
$89$		−	80.6579i		−	0.906269i	0.891442	−	0.453135i	$-0.149694\pi$
$90$		0			0
$91$	−26.5735	+	19.3068i	−0.292017	+	0.212162i
$92$	11.8556	+	74.8532i	0.128865	+	0.813621i
$93$	63.1004	+	32.1513i	0.678499	+	0.345713i
$94$	55.1010	−	17.9034i	0.586181	−	0.190462i
$95$		0			0
$96$	−152.498	+	110.796i	−1.58852	+	1.15413i
$97$	96.8143	−	49.3293i	0.998085	−	0.508550i	0.122942	−	0.992414i	$-0.460767\pi$
$97$	96.8143	−	49.3293i	0.998085	−	0.508550i	0.875143	+	0.483864i	$0.160767\pi$
$98$	37.5670	−	37.5670i	0.383337	−	0.383337i
$99$	174.442	+	202.729i	1.76204	+	2.04777i
$100$		0			0
$101$	−10.2333	+	31.4947i	−0.101319	+	0.311829i	−0.988849	−	0.148922i	$-0.952420\pi$
$101$	−10.2333	+	31.4947i	−0.101319	+	0.311829i	0.887530	+	0.460751i	$0.152420\pi$
$102$	32.5482	+	5.15513i	0.319100	+	0.0505405i
$103$	71.7554	−	11.3649i	0.696654	−	0.110339i	0.201944	−	0.979397i	$-0.435274\pi$
$103$	71.7554	−	11.3649i	0.696654	−	0.110339i	0.494710	+	0.869058i	$0.335274\pi$
$104$	123.280	−	40.0562i	1.18539	−	0.385155i
$105$		0			0
$106$	5.34911	+	3.88636i	0.0504633	+	0.0366638i
$107$	−47.8637	−	7.58086i	−0.447324	−	0.0708492i	−0.0712913	−	0.997456i	$-0.522712\pi$
$107$	−47.8637	−	7.58086i	−0.447324	−	0.0708492i	−0.376033	+	0.926606i	$0.622712\pi$
$108$	−104.835	−	205.750i	−0.970693	−	1.90509i
$109$			151.952i			1.39405i	0.717045	+	0.697026i	$0.245494\pi$
$109$			151.952i			1.39405i	−0.717045	+	0.697026i	$0.754506\pi$
$110$		0			0
$111$	1.12295			0.0101166
$112$	−2.24407	+	1.14341i	−0.0200364	+	0.0102090i
$113$	−20.7537	+	131.034i	−0.183661	+	1.15959i	0.707773	+	0.706440i	$0.249700\pi$
$113$	−20.7537	+	131.034i	−0.183661	+	1.15959i	−0.891434	+	0.453150i	$0.850300\pi$
$114$	55.9650	−	77.0293i	0.490921	−	0.675695i
$115$		0			0
$116$	35.1300	+	108.119i	0.302845	+	0.932061i
$117$	63.2987	+	399.652i	0.541014	+	3.41583i
$118$	−0.437825	+	2.76432i	−0.00371038	+	0.0234264i
$119$	9.09870	+	2.95635i	0.0764597	+	0.0248433i
$120$		0			0
$121$	55.7254	+	107.404i	0.460541	+	0.887639i
$122$	−97.9581	−	97.9581i	−0.802935	−	0.802935i
$123$	114.608	+	224.930i	0.931770	+	1.82870i
$124$	−18.8422	−	25.9341i	−0.151954	−	0.209146i
$125$		0			0
$126$	17.4666	+	53.7567i	0.138624	+	0.426641i
$127$	−26.6924	+	52.3868i	−0.210176	+	0.412495i	−0.971895	−	0.235413i	$-0.924356\pi$
$127$	−26.6924	+	52.3868i	−0.210176	+	0.412495i	0.761719	+	0.647908i	$0.224356\pi$
$128$	90.2113	−	14.2881i	0.704776	−	0.111625i
$129$	−94.2296	−	129.696i	−0.730462	−	1.00539i
$130$		0			0
$131$	−175.310			−1.33825			−0.669124	−	0.743151i	$-0.733330\pi$
$131$	−175.310			−1.33825			−0.669124	+	0.743151i	$0.733330\pi$
$132$	−39.3160	−	161.146i	−0.297849	−	1.22081i
$133$	19.5456	−	19.5456i	0.146959	−	0.146959i
$134$	−80.1409	−	26.0394i	−0.598066	−	0.194324i
$135$		0			0
$136$	−30.5440	−	22.1916i	−0.224589	−	0.163173i
$137$	3.67581	−	7.21419i	0.0268308	−	0.0526583i	−0.877202	−	0.480121i	$-0.840593\pi$
$137$	3.67581	−	7.21419i	0.0268308	−	0.0526583i	0.904033	+	0.427463i	$0.140593\pi$
$138$	−175.715	−	89.5314i	−1.27330	−	0.648778i
$139$	−79.9474	+	110.038i	−0.575161	+	0.791641i	−0.993154	−	0.116809i	$-0.962734\pi$
$139$	−79.9474	+	110.038i	−0.575161	+	0.791641i	0.417993	+	0.908450i	$0.362734\pi$
$140$		0			0
$141$	87.7294	−	270.003i	0.622195	−	1.91492i
$142$	−1.28985	−	1.28985i	−0.00908347	−	0.00908347i
$143$	−13.6910	+	182.553i	−0.0957410	+	1.27659i
$144$			31.0261i			0.215459i
$145$		0			0
$146$	86.4311	−	62.7959i	0.591994	−	0.430109i
$147$	−40.7252	−	257.129i	−0.277042	−	1.74918i
$148$	−0.452901	−	0.230765i	−0.00306014	−	0.00155922i
$149$	−75.9893	+	24.6904i	−0.509995	+	0.165707i	−0.552700	−	0.833380i	$-0.686402\pi$
$149$	−75.9893	+	24.6904i	−0.509995	+	0.165707i	0.0427049	+	0.999088i	$0.486402\pi$
$150$		0			0
$151$	73.7929	−	53.6137i	0.488695	−	0.355058i	−0.315987	−	0.948763i	$-0.602336\pi$
$151$	73.7929	−	53.6137i	0.488695	−	0.355058i	0.804682	+	0.593706i	$0.202336\pi$
$152$	−97.1943	+	49.5230i	−0.639436	+	0.325809i
$153$	83.3353	−	83.3353i	0.544675	−	0.544675i
$154$	2.10026	+	25.4860i	0.0136380	+	0.165493i
$155$		0			0
$156$	77.5496	−	238.673i	0.497113	−	1.52996i
$157$	249.034	+	39.4430i	1.58620	+	0.251230i	0.886335	−	0.463045i	$-0.153243\pi$
$157$	249.034	+	39.4430i	1.58620	+	0.251230i	0.699866	+	0.714274i	$0.253243\pi$
$158$	−58.6984	+	9.29691i	−0.371509	+	0.0588412i
$159$	30.8134	−	10.0119i	0.193795	−	0.0629679i
$160$		0			0
$161$	−46.3183	−	33.6522i	−0.287691	−	0.209020i
$162$	338.923	+	53.6801i	2.09212	+	0.331358i
$163$	−104.075	−	204.260i	−0.638500	−	1.25313i	−0.952741	−	0.303783i	$-0.901750\pi$
$163$	−104.075	−	204.260i	−0.638500	−	1.25313i	0.314242	−	0.949343i	$-0.398250\pi$
$164$		−	114.269i		−	0.696764i
$165$		0			0
$166$	−16.4521			−0.0991091
$167$	−92.0535	+	46.9036i	−0.551219	+	0.280860i	−0.707335	−	0.706879i	$-0.750103\pi$
$167$	−92.0535	+	46.9036i	−0.551219	+	0.280860i	0.156116	+	0.987739i	$0.450103\pi$
$168$	13.8801	−	87.6356i	0.0826198	−	0.521641i
$169$	−63.4613	+	87.3470i	−0.375511	+	0.516846i
$170$		0			0
$171$	−105.225	−	323.848i	−0.615349	−	1.89385i
$172$	11.3518	+	71.6723i	0.0659987	+	0.416699i
$173$	−1.00807	+	6.36471i	−0.00582700	+	0.0367902i	−0.990431	−	0.138012i	$-0.955929\pi$
$173$	−1.00807	+	6.36471i	−0.00582700	+	0.0367902i	0.984604	+	0.174802i	$0.0559287\pi$
$174$	−281.346	−	91.4148i	−1.61693	−	0.525372i
$175$		0			0
$176$	−3.22656	+	13.6610i	−0.0183327	+	0.0776195i
$177$	9.69756	+	9.69756i	0.0547885	+	0.0547885i
$178$	−43.1315	−	84.6504i	−0.242312	−	0.475564i
$179$	−50.2025	−	69.0978i	−0.280461	−	0.386021i	0.645426	−	0.763823i	$-0.276680\pi$
$179$	−50.2025	−	69.0978i	−0.280461	−	0.386021i	−0.925886	+	0.377802i	$0.876680\pi$
$180$		0			0
$181$	−49.5631	−	152.540i	−0.273829	−	0.842760i	−0.989527	−	0.144350i	$-0.953891\pi$
$181$	−49.5631	−	152.540i	−0.273829	−	0.842760i	0.715697	−	0.698411i	$-0.246109\pi$
$182$	−17.5646	+	34.4725i	−0.0965089	+	0.189409i
$183$	−670.478	+	106.193i	−3.66382	+	0.580291i
$184$	132.803	+	182.788i	0.721757	+	0.993414i
$185$		0			0
$186$	83.4166			0.448476
$187$	45.3597	−	28.0268i	0.242565	−	0.149876i
$188$	−90.8679	+	90.8679i	−0.483340	+	0.483340i
$189$	165.909	+	53.9071i	0.877825	+	0.285223i
$190$		0			0
$191$	105.149	+	76.3950i	0.550517	+	0.399974i	0.827976	−	0.560764i	$-0.189492\pi$
$191$	105.149	+	76.3950i	0.550517	+	0.399974i	−0.277459	+	0.960737i	$0.589492\pi$
$192$	−87.4233	+	171.578i	−0.455330	+	0.893635i
$193$	289.915	+	147.719i	1.50215	+	0.765383i	0.995317	−	0.0966622i	$-0.0308166\pi$
$193$	289.915	+	147.719i	1.50215	+	0.765383i	0.506831	+	0.862045i	$0.330817\pi$
$194$	75.2277	−	103.542i	0.387772	−	0.533722i
$195$		0			0
$196$	−36.4146	+	112.073i	−0.185789	+	0.571800i
$197$	4.22058	+	4.22058i	0.0214242	+	0.0214242i	0.717738	−	0.696314i	$-0.245178\pi$
$197$	4.22058	+	4.22058i	0.0214242	+	0.0214242i	−0.696314	+	0.717738i	$0.745178\pi$
$198$	291.485	+	119.481i	1.47215	+	0.603441i
$199$			231.739i			1.16452i	0.813003	+	0.582260i	$0.197831\pi$
$199$			231.739i			1.16452i	−0.813003	+	0.582260i	$0.802169\pi$
$200$		0			0
$201$	−334.053	+	242.704i	−1.66195	+	1.20748i
$202$	6.10189	+	38.5258i	0.0302074	+	0.190722i
$203$	−76.5211	−	38.9895i	−0.376951	−	0.192066i
$204$	−69.5161	+	22.5872i	−0.340765	+	0.110721i
$205$		0			0
$206$	69.2298	−	50.2984i	0.336067	−	0.244167i
$207$	−628.415	+	320.193i	−3.03582	+	1.54683i
$208$	−15.0168	+	15.0168i	−0.0721962	+	0.0721962i
$209$	−12.6526	−	153.536i	−0.0605389	−	0.734622i
$210$		0			0
$211$	−46.5064	+	143.132i	−0.220409	+	0.678350i	0.778316	+	0.627873i	$0.216074\pi$
$211$	−46.5064	+	143.132i	−0.220409	+	0.678350i	−0.998725	+	0.0504773i	$0.983926\pi$
$212$	−14.4849	−	2.29419i	−0.0683251	−	0.0108216i
$213$	−8.82845	+	1.39829i	−0.0414481	+	0.00656474i
$214$	−54.2867	+	17.6388i	−0.253676	+	0.0824243i
$215$		0			0
$216$	−556.951	−	404.648i	−2.57848	−	1.87337i
$217$	23.9187	+	3.78836i	0.110225	+	0.0174579i
$218$	81.2556	+	159.473i	0.372732	+	0.731528i
$219$		−	523.506i		−	2.39044i
$220$		0			0
$221$	80.6696			0.365021
$222$	1.17853	−	0.600492i	0.00530870	−	0.00270492i
$223$	21.7436	−	137.283i	0.0975048	−	0.615621i	−0.889747	−	0.456454i	$-0.849119\pi$
$223$	21.7436	−	137.283i	0.0975048	−	0.615621i	0.987252	−	0.159167i	$-0.0508807\pi$
$224$	−37.8871	+	52.1472i	−0.169139	+	0.232800i
$225$		0			0
$226$	48.2887	+	148.617i	0.213667	+	0.657600i
$227$	0.159379	+	1.00628i	0.000702112	+	0.00443296i	0.988037	−	0.154218i	$-0.0492857\pi$
$227$	0.159379	+	1.00628i	0.000702112	+	0.00443296i	−0.987335	+	0.158651i	$0.949286\pi$
$228$	−33.0372	+	208.588i	−0.144900	+	0.914862i
$229$	−8.36376	−	2.71755i	−0.0365230	−	0.0118670i	0.290699	−	0.956815i	$-0.406112\pi$
$229$	−8.36376	−	2.71755i	−0.0365230	−	0.0118670i	−0.327222	+	0.944948i	$0.606112\pi$
$230$		0			0
$231$	107.083	+	65.0796i	0.463565	+	0.281730i
$232$	239.652	+	239.652i	1.03298	+	1.03298i
$233$	−188.847	−	370.632i	−0.810500	−	1.59070i	−0.806889	−	0.590703i	$-0.798850\pi$
$233$	−188.847	−	370.632i	−0.810500	−	1.59070i	−0.00361160	−	0.999993i	$-0.501150\pi$
$234$	280.144	+	385.585i	1.19720	+	1.64780i
$235$		0			0
$236$	−1.91833	−	5.90400i	−0.00812850	−	0.0250169i
$237$	−132.209	+	259.476i	−0.557846	+	1.09483i
$238$	11.1300	−	1.76281i	0.0467646	−	0.00740678i
$239$	168.700	+	232.195i	0.705857	+	0.971529i	0.999876	+	0.0157295i	$0.00500705\pi$
$239$	168.700	+	232.195i	0.705857	+	0.971529i	−0.294019	+	0.955800i	$0.594993\pi$
$240$		0			0
$241$	317.030			1.31548			0.657738	−	0.753247i	$-0.271513\pi$
$241$	317.030			1.31548			0.657738	+	0.753247i	$0.271513\pi$
$242$	115.918	+	82.9216i	0.478999	+	0.342651i
$243$	626.494	−	626.494i	2.57816	−	2.57816i
$244$	292.236	+	94.9532i	1.19769	+	0.389153i
$245$		0			0
$246$	240.561	+	174.778i	0.977890	+	0.710479i
$247$	105.815	−	207.674i	0.428401	−	0.840785i
$248$	−85.1520	−	43.3871i	−0.343355	−	0.174948i
$249$	−47.3860	+	65.2212i	−0.190305	+	0.261933i
$250$		0			0
$251$	21.5845	−	66.4304i	0.0859942	−	0.264663i	−0.898808	−	0.438342i	$-0.855566\pi$
$251$	21.5845	−	66.4304i	0.0859942	−	0.264663i	0.984802	+	0.173680i	$0.0555657\pi$
$252$	−88.6510	−	88.6510i	−0.351790	−	0.351790i
$253$	−309.995	+	75.6317i	−1.22528	+	0.298939i
$254$			69.2535i			0.272652i
$255$		0			0
$256$	195.002	−	141.677i	0.761728	−	0.553427i
$257$	−45.1789	−	285.248i	−0.175793	−	1.10992i	−0.904934	−	0.425552i	$-0.860080\pi$
$257$	−45.1789	−	285.248i	−0.175793	−	1.10992i	0.729141	−	0.684364i	$-0.239920\pi$
$258$	−168.248	−	85.7267i	−0.652124	−	0.332274i
$259$	0.365202	−	0.118661i	0.00141005	−	0.000458152i
$260$		0			0
$261$	−855.912	+	621.856i	−3.27935	+	2.38259i
$262$	−183.988	+	93.7465i	−0.702244	+	0.357811i
$263$	6.71971	−	6.71971i	0.0255502	−	0.0255502i	−0.694216	−	0.719766i	$-0.744249\pi$
$263$	6.71971	−	6.71971i	0.0255502	−	0.0255502i	0.719766	+	0.694216i	$0.244249\pi$
$264$	−322.542	−	374.844i	−1.22175	−	1.41986i
$265$		0			0
$266$	10.0611	−	30.9650i	0.0378239	−	0.116410i
$267$	−459.809	−	72.8266i	−1.72213	−	0.272759i
$268$	184.604	−	29.2383i	0.688819	−	0.109098i
$269$	−99.7989	+	32.4266i	−0.371000	+	0.120545i	−0.488582	−	0.872518i	$-0.662486\pi$
$269$	−99.7989	+	32.4266i	−0.371000	+	0.120545i	0.117582	+	0.993063i	$0.462486\pi$
$270$		0			0
$271$	76.1609	+	55.3341i	0.281037	+	0.204185i	0.719369	−	0.694628i	$-0.244431\pi$
$271$	76.1609	+	55.3341i	0.281037	+	0.204185i	−0.438333	+	0.898813i	$0.644431\pi$
$272$	6.10934	+	0.967625i	0.0224608	+	0.00355744i
$273$	86.0693	+	168.921i	0.315272	+	0.618757i
$274$		−	9.53691i		−	0.0348062i
$275$		0			0
$276$	437.422			1.58486
$277$	206.076	−	105.001i	0.743956	−	0.379065i	−0.0405564	−	0.999177i	$-0.512913\pi$
$277$	206.076	−	105.001i	0.743956	−	0.379065i	0.784513	+	0.620113i	$0.212913\pi$
$278$	−25.0622	+	158.236i	−0.0901517	+	0.569196i
$279$	175.351	−	241.350i	0.628498	−	0.865053i
$280$		0			0
$281$	88.5075	+	272.398i	0.314973	+	0.969388i	0.975765	+	0.218819i	$0.0702204\pi$
$281$	88.5075	+	272.398i	0.314973	+	0.969388i	−0.660792	+	0.750569i	$0.729780\pi$
$282$	−52.3114	−	330.281i	−0.185501	−	1.17121i
$283$	26.6596	−	168.322i	0.0942035	−	0.594777i	−0.894752	−	0.446564i	$-0.852648\pi$
$283$	26.6596	−	168.322i	0.0942035	−	0.594777i	0.988955	−	0.148214i	$-0.0473524\pi$
$284$	3.84799	+	1.25029i	0.0135492	+	0.00440242i
$285$		0			0
$286$	83.2508	+	198.910i	0.291087	+	0.695490i
$287$	61.0406	+	61.0406i	0.212685	+	0.212685i
$288$	360.488	+	707.497i	1.25169	+	2.45659i
$289$	156.059	+	214.797i	0.539998	+	0.743243i
$290$		0			0
$291$	−193.799	−	596.452i	−0.665976	−	2.04966i
$292$	−107.580	+	211.138i	−0.368425	+	0.723074i
$293$	−268.654	+	42.5506i	−0.916907	+	0.145224i	−0.597015	−	0.802230i	$-0.703647\pi$
$293$	−268.654	+	42.5506i	−0.916907	+	0.145224i	−0.319892	+	0.947454i	$0.603647\pi$
$294$	−180.240	−	248.079i	−0.613060	−	0.843805i
$295$		0			0
$296$	−1.51538			−0.00511954
$297$	827.104	−	511.050i	2.78486	−	1.72071i
$298$	−66.5475	+	66.5475i	−0.223314	+	0.223314i
$299$	−459.132	−	149.181i	−1.53556	−	0.498933i
$300$		0			0
$301$	−44.3500	−	32.2221i	−0.147342	−	0.107050i
$302$	48.7758	−	95.7279i	0.161509	−	0.316980i
$303$	170.303	+	86.7738i	0.562056	+	0.286382i
$304$	10.5047	−	14.4585i	0.0345550	−	0.0475609i
$305$		0			0
$306$	42.8970	−	132.023i	0.140186	−	0.431449i
$307$	141.243	+	141.243i	0.460075	+	0.460075i	0.898680	−	0.438605i	$-0.144527\pi$
$307$	141.243	+	141.243i	0.460075	+	0.460075i	−0.438605	+	0.898680i	$0.644527\pi$
$308$	−29.8145	−	48.2530i	−0.0968003	−	0.156666i
$309$		−	419.319i		−	1.35702i
$310$		0			0
$311$	39.1515	−	28.4453i	0.125889	−	0.0914639i	−0.523059	−	0.852297i	$-0.675209\pi$
$311$	39.1515	−	28.4453i	0.125889	−	0.0914639i	0.648948	+	0.760833i	$0.275209\pi$
$312$	−117.039	−	738.954i	−0.375124	−	2.36844i
$313$	−29.6215	−	15.0929i	−0.0946374	−	0.0482202i	0.406031	−	0.913859i	$-0.366912\pi$
$313$	−29.6215	−	15.0929i	−0.0946374	−	0.0482202i	−0.500669	+	0.865639i	$0.666912\pi$
$314$	282.452	−	91.7743i	0.899529	−	0.292275i
$315$		0			0
$316$	106.644	−	77.4813i	0.337481	−	0.245194i
$317$	242.086	−	123.349i	0.763678	−	0.389113i	−0.0283501	−	0.999598i	$-0.509025\pi$
$317$	242.086	−	123.349i	0.763678	−	0.389113i	0.792028	+	0.610485i	$0.209025\pi$
$318$	26.9848	−	26.9848i	0.0848579	−	0.0848579i
$319$	−441.535	+	184.798i	−1.38412	+	0.579303i
$320$		0			0
$321$	−86.4329	+	266.013i	−0.269261	+	0.828701i
$322$	−66.6063	−	10.5494i	−0.206852	−	0.0327621i
$323$	−67.0506	+	10.6198i	−0.207587	+	0.0328786i
$324$	−723.868	+	235.199i	−2.23416	+	0.725922i
$325$		0			0
$326$	−218.454	−	158.716i	−0.670104	−	0.486859i
$327$	866.236	+	137.198i	2.64904	+	0.419567i
$328$	−154.659	−	303.536i	−0.471523	−	0.925415i
$329$		−	97.0800i		−	0.295076i
$330$		0			0
$331$	−114.527			−0.346003			−0.173001	−	0.984922i	$-0.555347\pi$
$331$	−114.527			−0.346003			−0.173001	+	0.984922i	$0.555347\pi$
$332$	32.5143	−	16.5669i	0.0979347	−	0.0499002i
$333$	0.739997	−	4.67216i	0.00222221	−	0.0140305i
$334$	−71.5285	+	98.4505i	−0.214157	+	0.294762i
$335$		0			0
$336$	4.49209	+	13.8252i	0.0133693	+	0.0411466i
$337$	−19.8459	−	125.302i	−0.0588899	−	0.371816i	−0.999479	−	0.0322698i	$-0.989726\pi$
$337$	−19.8459	−	125.302i	−0.0588899	−	0.371816i	0.940589	−	0.339546i	$-0.110274\pi$
$338$	−19.8941	+	125.606i	−0.0588582	+	0.371616i
$339$	728.248	+	236.622i	2.14823	+	0.698001i
$340$		0			0
$341$	102.308	−	88.0327i	0.300022	−	0.258160i
$342$	−283.610	−	283.610i	−0.829268	−	0.829268i
$343$	−84.3208	−	165.489i	−0.245833	−	0.482475i
$344$	127.160	+	175.020i	0.369651	+	0.508780i
$345$		0			0
$346$	2.34554	+	7.21882i	0.00677900	+	0.0208636i
$347$	68.3476	−	134.140i	0.196967	−	0.386570i	−0.771306	−	0.636465i	$-0.780396\pi$
$347$	68.3476	−	134.140i	0.196967	−	0.386570i	0.968273	+	0.249895i	$0.0803961\pi$
$348$	648.077	−	102.645i	1.86229	−	0.294958i
$349$	205.310	+	282.585i	0.588281	+	0.809699i	0.994573	−	0.104045i	$-0.0331785\pi$
$349$	205.310	+	282.585i	0.588281	+	0.809699i	−0.406292	+	0.913743i	$0.633178\pi$
$350$		0			0
$351$	1470.96			4.19076
$352$	85.1495	+	349.006i	0.241902	+	0.991494i
$353$	−362.555	+	362.555i	−1.02707	+	1.02707i	−0.0274434	+	0.999623i	$0.508737\pi$
$353$	−362.555	+	362.555i	−1.02707	+	1.02707i	−0.999623	+	0.0274434i	$0.991263\pi$
$354$	15.3633	+	4.99184i	0.0433991	+	0.0141012i
$355$		0			0
$356$	170.482	+	123.862i	0.478881	+	0.347928i
$357$	25.0686	−	49.1999i	0.0702202	−	0.137815i
$358$	−89.6372	−	45.6724i	−0.250383	−	0.127577i
$359$	−285.929	+	393.548i	−0.796461	+	1.09623i	0.196812	+	0.980441i	$0.436941\pi$
$359$	−285.929	+	393.548i	−0.796461	+	1.09623i	−0.993273	+	0.115793i	$0.963059\pi$
$360$		0			0
$361$	50.9435	−	156.788i	0.141118	−	0.434315i
$362$	−133.586	−	133.586i	−0.369023	−	0.369023i
$363$	662.597	−	220.700i	1.82534	−	0.607988i
$364$		−	85.8152i		−	0.235756i
$365$		0			0
$366$	−646.879	+	469.985i	−1.76743	+	1.28411i
$367$	−1.49280	−	9.42516i	−0.00406757	−	0.0256816i	0.985571	−	0.169262i	$-0.0541384\pi$
$367$	−1.49280	−	9.42516i	−0.00406757	−	0.0256816i	−0.989639	+	0.143580i	$0.954138\pi$
$368$	−32.9820	−	16.8052i	−0.0896250	−	0.0456662i
$369$	1011.37	−	328.615i	2.74085	−	0.890555i
$370$		0			0
$371$	8.96310	−	6.51208i	0.0241593	−	0.0175528i
$372$	−164.856	+	83.9984i	−0.443162	+	0.225802i
$373$	268.508	−	268.508i	0.719862	−	0.719862i	−0.248715	−	0.968577i	$-0.580008\pi$
$373$	268.508	−	268.508i	0.719862	−	0.719862i	0.968577	+	0.248715i	$0.0800082\pi$
$374$	32.6177	−	53.6700i	0.0872132	−	0.143503i
$375$		0			0
$376$	−118.388	+	364.361i	−0.314862	+	0.969045i
$377$	−715.248	−	113.284i	−1.89721	−	0.300489i
$378$	202.948	−	32.1438i	0.536899	−	0.0850364i
$379$	329.126	−	106.940i	0.868406	−	0.282162i	0.159271	−	0.987235i	$-0.449086\pi$
$379$	329.126	−	106.940i	0.868406	−	0.282162i	0.709135	+	0.705073i	$0.249086\pi$
$380$		0			0
$381$	274.542	+	199.467i	0.720583	+	0.523534i
$382$	151.205	+	23.9486i	0.395825	+	0.0626926i
$383$	39.7395	+	77.9932i	0.103758	+	0.203638i	0.937049	−	0.349198i	$-0.113546\pi$
$383$	39.7395	+	77.9932i	0.103758	+	0.203638i	−0.833291	+	0.552835i	$0.813546\pi$
$384$		−	527.171i		−	1.37284i
$385$		0			0
$386$	383.257			0.992894
$387$	−601.710	+	306.587i	−1.55481	+	0.792213i
$388$	−44.4083	+	280.383i	−0.114454	+	0.722636i
$389$	−246.055	+	338.666i	−0.632533	+	0.870607i	−0.998190	−	0.0601430i	$-0.980844\pi$
$389$	−246.055	+	338.666i	−0.632533	+	0.870607i	0.365657	+	0.930750i	$0.380844\pi$
$390$		0			0
$391$	43.4506	+	133.727i	0.111127	+	0.342013i
$392$	54.9574	+	346.987i	0.140197	+	0.885172i
$393$	−158.289	+	999.397i	−0.402771	+	2.54299i
$394$	6.68642	+	2.17255i	0.0169706	+	0.00551409i
$395$		0			0
$396$	−696.377	+	57.3872i	−1.75853	+	0.144917i
$397$	−434.845	−	434.845i	−1.09533	−	1.09533i	−0.994950	−	0.100377i	$-0.967995\pi$
$397$	−434.845	−	434.845i	−1.09533	−	1.09533i	−0.100377	−	0.994950i	$-0.532005\pi$
$398$	123.922	+	243.210i	0.311361	+	0.611080i
$399$	−93.7764	−	129.072i	−0.235028	−	0.323489i
$400$		0			0
$401$	−166.418	−	512.181i	−0.415007	−	1.27726i	−0.912245	−	0.409645i	$-0.865653\pi$
$401$	−166.418	−	512.181i	−0.415007	−	1.27726i	0.497238	−	0.867614i	$-0.334347\pi$
$402$	−220.803	+	433.350i	−0.549261	+	1.07799i
$403$	201.686	−	31.9439i	0.500461	−	0.0792652i
$404$	−50.8537	−	69.9942i	−0.125876	−	0.173253i
$405$		0			0
$406$	−101.158			−0.249158
$407$	0.811709	−	1.98023i	0.00199437	−	0.00486544i
$408$	−154.086	+	154.086i	−0.377663	+	0.377663i
$409$	−2.27154	−	0.738069i	−0.00555390	−	0.00180457i	0.306239	−	0.951955i	$-0.400929\pi$
$409$	−2.27154	−	0.738069i	−0.00555390	−	0.00180457i	−0.311793	+	0.950150i	$0.600929\pi$
$410$		0			0
$411$	−37.8072	−	27.4686i	−0.0919884	−	0.0668335i
$412$	−86.1696	+	169.117i	−0.209150	+	0.410479i
$413$	4.17855	+	2.12908i	0.0101175	+	0.00515515i
$414$	−488.298	+	672.085i	−1.17946	+	1.62339i
$415$		0			0
$416$	−167.955	+	516.911i	−0.403737	+	1.24257i
$417$	555.113	+	555.113i	1.33121	+	1.33121i
$418$	−95.3816	−	154.370i	−0.228186	−	0.369305i
$419$		−	235.871i		−	0.562937i	−0.959570	−	0.281469i	$-0.909178\pi$
$419$		−	235.871i		−	0.562937i	0.959570	−	0.281469i	$-0.0908215\pi$
$420$		0			0
$421$	492.334	−	357.702i	1.16944	−	0.849648i	0.178498	−	0.983940i	$-0.442876\pi$
$421$	492.334	−	357.702i	1.16944	−	0.849648i	0.990942	+	0.134293i	$0.0428762\pi$
$422$	27.7309	+	175.086i	0.0657129	+	0.414895i
$423$	−1065.57	−	542.935i	−2.51908	−	1.28353i
$424$	−41.5817	+	13.5107i	−0.0980702	+	0.0318649i
$425$		0			0
$426$	−8.51771	+	6.18848i	−0.0199946	+	0.0145270i
$427$	−206.830	+	105.385i	−0.484378	+	0.246803i
$428$	89.5249	−	89.5249i	0.209170	−	0.209170i
$429$	1028.32	+	242.877i	2.39702	+	0.566146i
$430$		0			0
$431$	−125.771	+	387.085i	−0.291813	+	0.898108i	0.692460	+	0.721456i	$0.256527\pi$
$431$	−125.771	+	387.085i	−0.291813	+	0.898108i	−0.984273	+	0.176652i	$0.943473\pi$
$432$	111.400	+	17.6440i	0.257870	+	0.0408426i
$433$	508.392	−	80.5214i	1.17412	−	0.185962i	0.461255	−	0.887267i	$-0.347399\pi$
$433$	508.392	−	80.5214i	1.17412	−	0.185962i	0.712861	+	0.701306i	$0.247399\pi$
$434$	27.1285	−	8.81458i	0.0625080	−	0.0203101i
$435$		0			0
$436$	−321.171	−	233.344i	−0.736631	−	0.535194i
$437$	401.258	+	63.5531i	0.918211	+	0.145430i
$438$	−279.943	−	549.419i	−0.639139	−	1.25438i
$439$		−	352.062i		−	0.801963i	−0.916086	−	0.400982i	$-0.868669\pi$
$439$		−	352.062i		−	0.801963i	0.916086	−	0.400982i	$-0.131331\pi$
$440$		0			0
$441$	−1096.65			−2.48674
$442$	84.6626	−	43.1377i	0.191544	−	0.0975967i
$443$	1.16390	−	7.34858i	0.00262732	−	0.0165882i	−0.986340	−	0.164723i	$-0.947327\pi$
$443$	1.16390	−	7.34858i	0.00262732	−	0.0165882i	0.988967	+	0.148135i	$0.0473270\pi$
$444$	−1.72445	+	2.37351i	−0.00388390	+	0.00534573i
$445$		0			0
$446$	−50.5920	−	155.706i	−0.113435	−	0.349117i
$447$	72.1421	+	455.487i	0.161392	+	1.01899i
$448$	−10.3010	+	65.0380i	−0.0229933	+	0.145174i
$449$	175.258	+	56.9447i	0.390329	+	0.126826i	0.497605	−	0.867404i	$-0.334213\pi$
$449$	175.258	+	56.9447i	0.390329	+	0.126826i	−0.107276	+	0.994229i	$0.534213\pi$
$450$		0			0
$451$	479.490	−	39.5139i	1.06317	−	0.0876141i
$452$	−245.087	−	245.087i	−0.542229	−	0.542229i
$453$	−239.009	−	469.082i	−0.527614	−	1.03550i
$454$	0.705374	+	0.970864i	0.00155369	+	0.00213847i
$455$		0			0
$456$	194.560	+	598.793i	0.426666	+	1.31314i
$457$	−106.600	+	209.215i	−0.233261	+	0.457800i	−0.977733	−	0.209854i	$-0.932701\pi$
$457$	−106.600	+	209.215i	−0.233261	+	0.457800i	0.744472	+	0.667654i	$0.232701\pi$
$458$	−10.2310	+	1.62042i	−0.0223383	+	0.00353804i
$459$	−251.826	−	346.609i	−0.548641	−	0.755139i
$460$		0			0
$461$	−542.586			−1.17698			−0.588488	−	0.808506i	$-0.700277\pi$
$461$	−542.586			−1.17698			−0.588488	+	0.808506i	$0.700277\pi$
$462$	147.185	+	11.0385i	0.318582	+	0.0238928i
$463$	−48.2381	+	48.2381i	−0.104186	+	0.104186i	−0.757278	−	0.653092i	$-0.773471\pi$
$463$	−48.2381	+	48.2381i	−0.104186	+	0.104186i	0.653092	+	0.757278i	$0.273471\pi$
$464$	−52.8090	−	17.1587i	−0.113813	−	0.0369799i
$465$		0			0
$466$	−396.388	−	287.993i	−0.850619	−	0.618011i
$467$	284.997	−	559.339i	0.610272	−	1.19773i	−0.354602	−	0.935017i	$-0.615384\pi$
$467$	284.997	−	559.339i	0.610272	−	1.19773i	0.964875	−	0.262710i	$-0.0846162\pi$
$468$	−941.924	−	479.934i	−2.01266	−	1.02550i
$469$	−82.9933	+	114.231i	−0.176958	+	0.243562i
$470$		0			0
$471$	449.708	−	1384.06i	0.954794	−	2.93855i
$472$	−13.0865	−	13.0865i	−0.0277257	−	0.0277257i
$473$	−296.821	+	72.4177i	−0.627529	+	0.153103i
$474$			343.018i			0.723666i
$475$		0			0
$476$	−20.2211	+	14.6915i	−0.0424812	+	0.0308644i
$477$	−21.3503	−	134.801i	−0.0447595	−	0.282601i
$478$	301.216	+	153.477i	0.630159	+	0.321082i
$479$	−553.115	+	179.718i	−1.15473	+	0.375194i	−0.822922	−	0.568154i	$-0.807658\pi$
$479$	−553.115	+	179.718i	−1.15473	+	0.375194i	−0.331806	+	0.943348i	$0.607658\pi$
$480$		0			0
$481$	2.61951	−	1.90319i	0.00544598	−	0.00395673i
$482$	332.722	−	169.530i	0.690295	−	0.351723i
$483$	−233.663	+	233.663i	−0.483774	+	0.483774i
$484$	−312.588	−	47.1518i	−0.645844	−	0.0974210i
$485$		0			0
$486$	322.489	−	992.519i	0.663557	−	2.04222i
$487$	172.226	+	27.2780i	0.353647	+	0.0560122i	0.330731	−	0.943725i	$-0.392705\pi$
$487$	172.226	+	27.2780i	0.353647	+	0.0560122i	0.0229166	+	0.999737i	$0.492705\pi$
$488$	904.789	−	143.305i	1.85408	−	0.293657i
$489$	−1258.40	+	408.878i	−2.57341	+	0.836152i
$490$		0			0
$491$	−216.106	−	157.010i	−0.440134	−	0.319776i	0.345554	−	0.938399i	$-0.387691\pi$
$491$	−216.106	−	157.010i	−0.440134	−	0.319776i	−0.785688	+	0.618623i	$0.787691\pi$
$492$	−651.418	−	103.174i	−1.32402	−	0.209704i
$493$	95.7559	+	187.932i	0.194231	+	0.381200i
$494$		−	274.537i		−	0.555744i
$495$		0			0
$496$	15.6574			0.0315673
$497$	−2.72341	+	1.38764i	−0.00547969	+	0.00279204i
$498$	−14.8547	+	93.7890i	−0.0298287	+	0.188331i
$499$	552.387	−	760.296i	1.10699	−	1.52364i	0.281207	−	0.959647i	$-0.409265\pi$
$499$	552.387	−	760.296i	1.10699	−	1.52364i	0.825781	−	0.563991i	$-0.190735\pi$
$500$		0			0
$501$	184.269	+	567.122i	0.367802	+	1.13198i
$502$	−12.8704	−	81.2608i	−0.0256383	−	0.161874i
$503$	80.9416	−	511.045i	0.160918	−	1.01599i	−0.766576	−	0.642154i	$-0.778041\pi$
$503$	80.9416	−	511.045i	0.160918	−	1.01599i	0.927493	−	0.373840i	$-0.121959\pi$
$504$	−355.472	−	115.500i	−0.705301	−	0.229166i
$505$		0			0
$506$	−284.895	+	245.144i	−0.563034	+	0.484474i
$507$	440.642	+	440.642i	0.869116	+	0.869116i
$508$	−69.7366	−	136.866i	−0.137277	−	0.269421i
$509$	−359.646	−	495.010i	−0.706573	−	0.972515i	−0.999864	−	0.0164915i	$-0.994750\pi$
$509$	−359.646	−	495.010i	−0.706573	−	0.972515i	0.293291	−	0.956023i	$-0.405250\pi$
$510$		0			0
$511$	−55.3186	−	170.253i	−0.108256	−	0.333177i
$512$	−36.9692	+	72.5562i	−0.0722055	+	0.141711i
$513$	−1222.62	+	193.645i	−2.38328	+	0.377475i
$514$	−199.951	−	275.208i	−0.389009	−	0.535425i
$515$		0			0
$516$	418.834			0.811693
$517$	−412.716	−	349.873i	−0.798291	−	0.676736i
$518$	0.319825	−	0.319825i	0.000617423	−	0.000617423i
$519$	35.3733	+	11.4935i	0.0681566	+	0.0221454i
$520$		0			0
$521$	−755.178	−	548.669i	−1.44948	−	1.05311i	−0.985953	−	0.167025i	$-0.946584\pi$
$521$	−755.178	−	548.669i	−1.44948	−	1.05311i	−0.463526	−	0.886083i	$-0.653416\pi$
$522$	−565.742	+	1110.33i	−1.08380	+	2.12707i
$523$	329.945	+	168.115i	0.630870	+	0.321444i	0.740024	−	0.672581i	$-0.234814\pi$
$523$	329.945	+	168.115i	0.630870	+	0.321444i	−0.109154	+	0.994025i	$0.534814\pi$
$524$	269.215	−	370.543i	0.513769	−	0.707143i
$525$		0			0
$526$	3.45898	−	10.6457i	0.00657601	−	0.0202389i
$527$	−42.0554	−	42.0554i	−0.0798016	−	0.0798016i
$528$	74.9646	+	30.7284i	0.141978	+	0.0581977i
$529$		−	312.462i		−	0.590666i
$530$		0			0
$531$	46.7383	−	33.9574i	0.0880194	−	0.0639498i
$532$	11.2972	+	71.3275i	0.0212353	+	0.134074i
$533$	648.562	+	330.459i	1.21681	+	0.619997i
$534$	−521.512	+	169.450i	−0.976615	+	0.317321i
$535$		0			0
$536$	450.794	−	327.521i	0.841033	−	0.611046i
$537$	−439.236	+	223.802i	−0.817944	+	0.416763i
$538$	−87.3988	+	87.3988i	−0.162451	+	0.162451i
$539$	−482.865	−	114.047i	−0.895853	−	0.211589i
$540$		0			0
$541$	−135.828	+	418.036i	−0.251069	+	0.772711i	0.743510	+	0.668725i	$0.233160\pi$
$541$	−135.828	+	418.036i	−0.251069	+	0.772711i	−0.994579	+	0.103986i	$0.966840\pi$
$542$	109.520	+	17.3463i	0.202067	+	0.0320043i
$543$	−914.338	+	144.817i	−1.68386	+	0.266698i
$544$	150.556	−	48.9186i	0.276757	−	0.0899239i
$545$		0			0
$546$	180.659	+	131.257i	0.330878	+	0.240397i
$547$	53.7219	+	8.50871i	0.0982119	+	0.0155552i	0.205347	−	0.978689i	$-0.434168\pi$
$547$	53.7219	+	8.50871i	0.0982119	+	0.0155552i	−0.107135	+	0.994244i	$0.534168\pi$
$548$	9.60343	+	18.8478i	0.0175245	+	0.0343938i
$549$			2859.58i			5.20871i
$550$		0			0
$551$	609.411			1.10601
$552$	1161.93	−	592.035i	2.10495	−	1.07253i
$553$	−15.5781	+	98.3564i	−0.0281702	+	0.177860i
$554$	160.127	−	220.397i	0.289039	−	0.397828i
$555$		0			0
$556$	−109.810	−	337.960i	−0.197500	−	0.607841i
$557$	82.1439	+	518.636i	0.147476	+	0.931124i	0.944818	+	0.327596i	$0.106239\pi$
$557$	82.1439	+	518.636i	0.147476	+	0.931124i	−0.797342	+	0.603527i	$0.793761\pi$
$558$	54.9696	−	347.064i	0.0985118	−	0.621979i
$559$	−439.621	−	142.841i	−0.786442	−	0.255530i
$560$		0			0
$561$	−118.817	−	283.889i	−0.211796	−	0.506041i
$562$	238.552	+	238.552i	0.424470	+	0.424470i
$563$	−345.855	−	678.778i	−0.614307	−	1.20565i	−0.963277	−	0.268511i	$-0.913468\pi$
$563$	−345.855	−	678.778i	−0.614307	−	1.20565i	0.348970	−	0.937134i	$-0.386532\pi$
$564$	435.968	+	600.058i	0.772993	+	1.06393i
$565$		0			0
$566$	−62.0303	−	190.910i	−0.109594	−	0.337296i
$567$	261.038	−	512.316i	0.460385	−	0.903556i
$568$	11.9137	−	1.88695i	0.0209748	−	0.00332209i
$569$	522.049	+	718.539i	0.917485	+	1.26281i	0.964545	+	0.263918i	$0.0850148\pi$
$569$	522.049	+	718.539i	0.917485	+	1.26281i	−0.0470600	+	0.998892i	$0.514985\pi$
$570$		0			0
$571$	−943.557			−1.65246			−0.826232	−	0.563330i	$-0.809520\pi$
$571$	−943.557			−1.65246			−0.826232	+	0.563330i	$0.809520\pi$
$572$	−364.826	−	309.275i	−0.637808	−	0.540690i
$573$	530.447	−	530.447i	0.925736	−	0.925736i
$574$	96.7032	+	31.4208i	0.168473	+	0.0547400i
$575$		0			0
$576$	656.260	+	476.801i	1.13934	+	0.827779i
$577$	−59.2654	+	116.315i	−0.102713	+	0.201585i	−0.936644	−	0.350284i	$-0.886085\pi$
$577$	−59.2654	+	116.315i	−0.102713	+	0.201585i	0.833931	+	0.551869i	$0.186085\pi$
$578$	278.646	+	141.977i	0.482087	+	0.245635i
$579$	1103.87	−	1519.35i	1.90651	−	2.62409i
$580$		0			0
$581$	−8.51884	+	26.2183i	−0.0146624	+	0.0451261i
$582$	−522.342	−	522.342i	−0.897494	−	0.897494i
$583$	4.61789	−	61.5741i	0.00792091	−	0.105616i
$584$			706.455i			1.20968i
$585$		0			0
$586$	−259.198	+	188.318i	−0.442317	+	0.321362i
$587$	98.2417	+	620.273i	0.167362	+	1.05668i	0.918177	+	0.396171i	$0.129661\pi$
$587$	98.2417	+	620.273i	0.167362	+	1.05668i	−0.750815	+	0.660513i	$0.770339\pi$
$588$	606.017	+	308.781i	1.03064	+	0.525138i
$589$	−163.431	+	53.1019i	−0.277472	+	0.0901561i
$590$		0			0
$591$	27.8711	−	20.2496i	0.0471593	−	0.0342632i
$592$	0.221212	−	0.112713i	0.000373669	−	0.000190394i
$593$	543.917	−	543.917i	0.917229	−	0.917229i	−0.0795984	−	0.996827i	$-0.525364\pi$
$593$	543.917	−	543.917i	0.917229	−	0.917229i	0.996827	+	0.0795984i	$0.0253638\pi$
$594$	594.763	−	978.636i	1.00128	−	1.64754i
$595$		0			0
$596$	64.5062	−	198.530i	0.108232	−	0.333103i
$597$	1321.08	+	209.239i	2.21287	+	0.350484i
$598$	−561.632	+	88.9538i	−0.939184	+	0.148752i
$599$	955.576	−	310.485i	1.59529	−	0.518340i	0.629350	−	0.777122i	$-0.283321\pi$
$599$	955.576	−	310.485i	1.59529	−	0.518340i	0.965936	+	0.258783i	$0.0833213\pi$
$600$		0			0
$601$	−211.574	−	153.717i	−0.352036	−	0.255769i	0.397686	−	0.917521i	$-0.369813\pi$
$601$	−211.574	−	153.717i	−0.352036	−	0.255769i	−0.749723	+	0.661752i	$0.769813\pi$
$602$	−63.7758	−	10.1011i	−0.105940	−	0.0167792i
$603$	789.663	+	1549.80i	1.30956	+	2.57015i
$604$			238.303i			0.394542i
$605$		0			0
$606$	225.135			0.371509
$607$	−810.971	+	413.211i	−1.33603	+	0.680742i	−0.968440	−	0.249245i	$-0.919817\pi$
$607$	−810.971	+	413.211i	−1.33603	+	0.680742i	−0.367591	+	0.929987i	$0.619817\pi$
$608$	71.5509	−	451.754i	0.117682	−	0.743017i
$609$	−291.360	+	401.022i	−0.478423	+	0.658493i
$610$		0			0
$611$	−252.958	−	778.525i	−0.414007	−	1.27418i
$612$	48.1670	+	304.114i	0.0787042	+	0.496919i
$613$	−121.222	+	765.368i	−0.197753	+	1.24856i	0.666501	+	0.745504i	$0.267791\pi$
$613$	−121.222	+	765.368i	−0.197753	+	1.24856i	−0.864254	+	0.503057i	$0.832209\pi$
$614$	223.764	+	72.7052i	0.364436	+	0.118412i
$615$		0			0
$616$	−144.506	−	87.8228i	−0.234587	−	0.142570i
$617$	204.509	+	204.509i	0.331457	+	0.331457i	0.853140	−	0.521682i	$-0.174695\pi$
$617$	204.509	+	204.509i	0.331457	+	0.331457i	−0.521682	+	0.853140i	$0.674695\pi$
$618$	−224.229	−	440.075i	−0.362831	−	0.712095i
$619$	−149.114	−	205.237i	−0.240894	−	0.331563i	0.671402	−	0.741093i	$-0.265692\pi$
$619$	−149.114	−	205.237i	−0.240894	−	0.331563i	−0.912296	+	0.409531i	$0.865692\pi$
$620$		0			0
$621$	792.293	+	2438.43i	1.27583	+	3.92661i
$622$	25.8785	−	50.7894i	0.0416053	−	0.0816550i
$623$	−157.233	+	24.9033i	−0.252381	+	0.0399732i
$624$	72.0479	+	99.1655i	0.115461	+	0.158919i
$625$		0			0
$626$	−39.1586			−0.0625537
$627$	−886.691	−	66.4994i	−1.41418	−	0.106060i
$628$	−465.796	+	465.796i	−0.741714	+	0.741714i
$629$	−0.896915	−	0.291425i	−0.00142594	−	0.000463316i
$630$		0			0
$631$	884.455	+	642.594i	1.40167	+	1.01837i	0.994468	+	0.105038i	$0.0334963\pi$
$631$	884.455	+	642.594i	1.40167	+	1.01837i	0.407204	+	0.913337i	$0.366504\pi$
$632$	178.413	−	350.154i	0.282298	−	0.554042i
$633$	773.965	+	394.355i	1.22269	+	0.622994i
$634$	188.108	−	258.909i	0.296701	−	0.408374i
$635$		0			0
$636$	−26.1571	+	80.5032i	−0.0411275	+	0.126577i
$637$	−530.786	−	530.786i	−0.833259	−	0.833259i
$638$	−364.570	+	430.054i	−0.571427	+	0.674066i
$639$			37.6532i			0.0589253i
$640$		0			0
$641$	−327.130	+	237.674i	−0.510343	+	0.370786i	−0.812954	−	0.582328i	$-0.802142\pi$
$641$	−327.130	+	237.674i	−0.510343	+	0.370786i	0.302610	+	0.953114i	$0.402142\pi$
$642$	51.5383	+	325.400i	0.0802777	+	0.506853i
$643$	257.491	+	131.198i	0.400452	+	0.204040i	0.642605	−	0.766198i	$-0.277854\pi$
$643$	257.491	+	131.198i	0.400452	+	0.204040i	−0.242153	+	0.970238i	$0.577854\pi$
$644$	142.257	−	46.2221i	0.220896	−	0.0717735i
$645$		0			0
$646$	−64.6906	+	47.0005i	−0.100140	+	0.0727562i
$647$	−447.585	+	228.056i	−0.691785	+	0.352482i	−0.764278	−	0.644887i	$-0.776904\pi$
$647$	−447.585	+	228.056i	−0.691785	+	0.352482i	0.0724932	+	0.997369i	$0.476904\pi$
$648$	−1604.49	+	1604.49i	−2.47607	+	2.47607i
$649$	24.1107	−	10.0911i	0.0371505	−	0.0155488i
$650$		0			0
$651$	43.1928	−	132.934i	0.0663484	−	0.204199i
$652$	591.554	+	93.6929i	0.907291	+	0.143701i
$653$	766.801	−	121.449i	1.17427	−	0.185987i	0.461343	−	0.887222i	$-0.347368\pi$
$653$	766.801	−	121.449i	1.17427	−	0.185987i	0.712930	+	0.701235i	$0.247368\pi$
$654$	982.479	−	319.227i	1.50226	−	0.488114i
$655$		0			0
$656$	45.1536	+	32.8060i	0.0688318	+	0.0500092i
$657$	−2178.11	−	344.979i	−3.31524	−	0.525082i
$658$	−51.9132	−	101.885i	−0.0788954	−	0.154841i
$659$			167.781i			0.254599i	0.991864	+	0.127299i	$0.0406309\pi$
$659$			167.781i			0.254599i	−0.991864	+	0.127299i	$0.959369\pi$
$660$		0			0
$661$	6.21057			0.00939572			0.00469786	−	0.999989i	$-0.498505\pi$
$661$	6.21057			0.00939572			0.00469786	+	0.999989i	$0.498505\pi$
$662$	−120.196	+	61.2428i	−0.181565	+	0.0925119i
$663$	72.8371	−	459.875i	0.109860	−	0.693628i
$664$	63.9459	−	88.0139i	0.0963040	−	0.132551i
$665$		0			0
$666$	−1.72179	−	5.29913i	−0.00258527	−	0.00795665i
$667$	−197.457	−	1246.70i	−0.296038	−	1.86911i
$668$	42.2246	−	266.595i	0.0632104	−	0.399095i
$669$	−762.983	−	247.908i	−1.14048	−	0.370565i
$670$		0			0
$671$	−297.383	+	1259.10i	−0.443193	+	1.87645i
$672$	263.068	+	263.068i	0.391471	+	0.391471i
$673$	−374.572	−	735.139i	−0.556570	−	1.09233i	−0.982271	−	0.187467i	$-0.939972\pi$
$673$	−374.572	−	735.139i	−0.556570	−	1.09233i	0.425701	−	0.904864i	$-0.360028\pi$
$674$	−87.8330	−	120.892i	−0.130316	−	0.179365i
$675$		0			0
$676$	−87.1657	−	268.269i	−0.128943	−	0.396847i
$677$	459.592	−	901.999i	0.678865	−	1.33235i	−0.252264	−	0.967658i	$-0.581175\pi$
$677$	459.592	−	901.999i	0.678865	−	1.33235i	0.931129	−	0.364689i	$-0.118825\pi$
$678$	890.828	−	141.093i	1.31391	−	0.208102i
$679$	−126.053	−	173.498i	−0.185646	−	0.255519i
$680$		0			0
$681$	5.88044			0.00863501
$682$	60.2966	−	147.099i	0.0884114	−	0.215687i
$683$	229.153	−	229.153i	0.335510	−	0.335510i	−0.519164	−	0.854674i	$-0.673757\pi$
$683$	229.153	−	229.153i	0.335510	−	0.335510i	0.854674	+	0.519164i	$0.173757\pi$
$684$	846.086	+	274.910i	1.23697	+	0.401915i
$685$		0			0
$686$	−176.989	−	128.590i	−0.258002	−	0.187449i
$687$	−23.0437	+	45.2258i	−0.0335425	+	0.0658309i
$688$	−31.5804	−	16.0910i	−0.0459017	−	0.0233881i
$689$	54.9106	−	75.5779i	0.0796960	−	0.109692i
$690$		0			0
$691$	−74.3036	+	228.683i	−0.107531	+	0.330945i	−0.990316	−	0.138831i	$-0.955665\pi$
$691$	−74.3036	+	228.683i	−0.107531	+	0.330945i	0.882786	+	0.469776i	$0.155665\pi$
$692$	−11.9047	−	11.9047i	−0.0172033	−	0.0172033i
$693$	341.337	−	402.647i	0.492549	−	0.581021i
$694$		−	177.328i		−	0.255516i
$695$		0			0
$696$	1582.57	−	1149.81i	2.27381	−	1.65202i
$697$	−33.1654	−	209.398i	−0.0475830	−	0.300427i
$698$	366.583	+	186.784i	0.525191	+	0.267598i
$699$	−2283.39	+	741.917i	−3.26665	+	1.06140i
$700$		0			0
$701$	198.550	−	144.255i	0.283238	−	0.205785i	−0.437090	−	0.899418i	$-0.643991\pi$
$701$	198.550	−	144.255i	0.283238	−	0.205785i	0.720329	+	0.693633i	$0.243991\pi$
$702$	1543.77	−	786.588i	2.19910	−	1.12050i
$703$	−1.92673	+	1.92673i	−0.00274073	+	0.00274073i
$704$	239.372	+	278.187i	0.340017	+	0.395152i
$705$		0			0
$706$	−186.626	+	574.375i	−0.264342	+	0.813562i
$707$	64.5548	+	10.2245i	0.0913081	+	0.0144618i
$708$	−35.3892	+	5.60509i	−0.0499847	+	0.00791680i
$709$	853.145	−	277.204i	1.20331	−	0.390979i	0.362331	−	0.932049i	$-0.381981\pi$
$709$	853.145	−	277.204i	1.20331	−	0.390979i	0.840977	+	0.541071i	$0.181981\pi$
$710$		0			0
$711$	992.456	+	721.062i	1.39586	+	1.01415i
$712$	620.498	+	98.2772i	0.871486	+	0.138030i
$713$	161.587	+	317.131i	0.226629	+	0.444785i
$714$		−	65.0406i		−	0.0910933i
$715$		0			0
$716$	223.141			0.311649
$717$	1476.00	−	752.061i	2.05858	−	1.04890i
$718$	−89.6341	+	565.928i	−0.124839	+	0.788200i
$719$	119.555	−	164.554i	0.166280	−	0.228865i	−0.717743	−	0.696308i	$-0.754825\pi$
$719$	119.555	−	164.554i	0.166280	−	0.228865i	0.884023	+	0.467443i	$0.154825\pi$
$720$		0			0
$721$	−44.3092	−	136.370i	−0.0614552	−	0.189140i
$722$	−30.3766	−	191.790i	−0.0420729	−	0.265638i
$723$	286.248	−	1807.30i	0.395917	−	2.49972i
$724$	398.525	+	129.489i	0.550449	+	0.178852i
$725$		0			0
$726$	577.377	−	585.945i	0.795284	−	0.807087i
$727$	−373.051	−	373.051i	−0.513137	−	0.513137i	0.402349	−	0.915486i	$-0.368194\pi$
$727$	−373.051	−	373.051i	−0.513137	−	0.513137i	−0.915486	+	0.402349i	$0.868194\pi$
$728$	−116.148	−	227.953i	−0.159544	−	0.313122i
$729$	−1464.67	−	2015.94i	−2.00915	−	2.76535i
$730$		0			0
$731$	41.6041	+	128.044i	0.0569140	+	0.175163i
$732$	805.164	−	1580.22i	1.09995	−	2.15878i
$733$	502.338	−	79.5625i	0.685318	−	0.108544i	0.195940	−	0.980616i	$-0.437224\pi$
$733$	502.338	−	79.5625i	0.685318	−	0.108544i	0.489377	+	0.872072i	$0.337224\pi$
$734$	−6.60676	−	9.09342i	−0.00900103	−	0.0123889i
$735$		0			0
$736$	−947.355			−1.28717
$737$	186.523	+	764.512i	0.253085	+	1.03733i
$738$	885.708	−	885.708i	1.20015	−	1.20015i
$739$	−334.582	−	108.712i	−0.452750	−	0.147107i	0.0737605	−	0.997276i	$-0.476500\pi$
$739$	−334.582	−	108.712i	−0.452750	−	0.147107i	−0.526511	+	0.850169i	$0.676500\pi$
$740$		0			0
$741$	−1088.35	−	790.733i	−1.46876	−	1.06712i
$742$	5.92445	−	11.6274i	0.00798444	−	0.0156703i
$743$	−1028.21	−	523.897i	−1.38386	−	0.705110i	−0.405900	−	0.913918i	$-0.633042\pi$
$743$	−1028.21	−	523.897i	−1.38386	−	0.705110i	−0.977957	+	0.208807i	$0.933042\pi$
$744$	−324.223	+	446.254i	−0.435783	+	0.599804i
$745$		0			0
$746$	138.215	−	425.383i	0.185275	−	0.570218i
$747$	240.134	+	240.134i	0.321465	+	0.321465i
$748$	−10.4181	+	138.913i	−0.0139280	+	0.185713i
$749$			95.6453i			0.127697i
$750$		0			0
$751$	−199.691	+	145.084i	−0.265900	+	0.193188i	−0.712744	−	0.701424i	$-0.752548\pi$
$751$	−199.691	+	145.084i	−0.265900	+	0.193188i	0.446844	+	0.894612i	$0.352548\pi$
$752$	−9.81892	−	61.9942i	−0.0130571	−	0.0824391i
$753$	−359.213	−	183.028i	−0.477042	−	0.243065i
$754$	−811.230	+	263.585i	−1.07590	+	0.349582i
$755$		0			0
$756$	−368.718	+	267.889i	−0.487722	+	0.354351i
$757$	1034.03	−	526.866i	1.36596	−	0.695992i	0.391422	−	0.920211i	$-0.371983\pi$
$757$	1034.03	−	526.866i	1.36596	−	0.695992i	0.974539	+	0.224220i	$0.0719834\pi$
$758$	288.232	−	288.232i	0.380253	−	0.380253i
$759$	151.259	+	1835.48i	0.199287	+	2.41829i
$760$		0			0
$761$	160.769	−	494.797i	0.211260	−	0.650193i	−0.788138	−	0.615499i	$-0.788954\pi$
$761$	160.769	−	494.797i	0.211260	−	0.650193i	0.999398	−	0.0346936i	$-0.0110455\pi$
$762$	394.796	+	62.5295i	0.518104	+	0.0820597i
$763$	296.212	−	46.9154i	0.388221	−	0.0614881i
$764$	−322.943	+	104.930i	−0.422700	+	0.137344i
$765$		0			0
$766$	83.4131	+	60.6031i	0.108894	+	0.0791164i
$767$	39.0572	+	6.18605i	0.0509220	+	0.00806525i
$768$	−631.596	−	1239.58i	−0.822390	−	1.61403i
$769$		−	801.838i		−	1.04270i	−0.853342	−	0.521351i	$-0.825428\pi$
$769$		−	801.838i		−	1.04270i	0.853342	−	0.521351i	$-0.174572\pi$
$770$		0			0
$771$	−1666.92			−2.16202
$772$	−757.431	+	385.930i	−0.981129	+	0.499910i
$773$	−108.787	+	686.852i	−0.140733	+	0.888553i	0.811760	+	0.583992i	$0.198510\pi$
$773$	−108.787	+	686.852i	−0.140733	+	0.888553i	−0.952493	+	0.304561i	$0.901490\pi$
$774$	−467.548	+	643.524i	−0.604067	+	0.831426i
$775$		0			0
$776$	261.525	+	804.893i	0.337017	+	1.03723i
$777$	−0.346712	−	2.18906i	−0.000446219	−	0.00281732i
$778$	−77.1342	+	487.006i	−0.0991443	+	0.625972i
$779$	−582.572	−	189.289i	−0.747846	−	0.242990i
$780$		0			0
$781$	−3.91576	+	16.5790i	−0.00501377	+	0.0212280i
$782$	117.111	+	117.111i	0.149759	+	0.149759i
$783$	1746.05	+	3426.81i	2.22994	+	4.37651i
$784$	−33.8312	−	46.5647i	−0.0431521	−	0.0593938i
$785$		0			0
$786$	368.300	+	1133.51i	0.468574	+	1.44212i
$787$	68.6427	−	134.719i	0.0872207	−	0.171180i	−0.843276	−	0.537481i	$-0.819376\pi$
$787$	68.6427	−	134.719i	0.0872207	−	0.171180i	0.930496	+	0.366301i	$0.119376\pi$
$788$	−15.4021	+	2.43945i	−0.0195458	+	0.00309575i
$789$	−32.2399	−	44.3745i	−0.0408618	−	0.0562414i
$790$		0			0
$791$	261.843			0.331027
$792$	−1772.13	+	1094.96i	−2.23754	+	1.38253i
$793$	−1384.05	+	1384.05i	−1.74534	+	1.74534i
$794$	−688.900	−	223.837i	−0.867632	−	0.281911i
$795$		0			0
$796$	−489.813	−	355.870i	−0.615343	−	0.447073i
$797$	−560.165	+	1099.39i	−0.702842	+	1.37941i	0.212674	+	0.977123i	$0.431783\pi$
$797$	−560.165	+	1099.39i	−0.702842	+	1.37941i	−0.915516	+	0.402282i	$0.868217\pi$
$798$	−167.439	−	85.3144i	−0.209823	−	0.106910i
$799$	−140.142	+	192.888i	−0.175396	+	0.241412i
$800$		0			0
$801$	−606.007	+	1865.10i	−0.756563	+	2.32846i
$802$	−448.542	−	448.542i	−0.559279	−	0.559279i
$803$	−923.164	−	378.410i	−1.14964	−	0.471245i
$804$		−	1078.77i		−	1.34176i
$805$		0			0
$806$	194.587	−	141.376i	0.241423	−	0.175404i
$807$	94.7463	+	598.205i	0.117406	+	0.741270i
$808$	−229.819	−	117.098i	−0.284429	−	0.144924i
$809$	896.054	−	291.145i	1.10761	−	0.359883i	0.302581	−	0.953124i	$-0.402152\pi$
$809$	896.054	−	291.145i	1.10761	−	0.359883i	0.805025	+	0.593241i	$0.202152\pi$
$810$		0			0
$811$	972.098	−	706.271i	1.19864	−	0.870864i	0.204491	−	0.978868i	$-0.434446\pi$
$811$	972.098	−	706.271i	1.19864	−	0.870864i	0.994150	+	0.108005i	$0.0344461\pi$
$812$	199.919	−	101.864i	0.246206	−	0.125448i
$813$	384.211	−	384.211i	0.472584	−	0.472584i
$814$	−0.207035	−	2.51231i	−0.000254343	−	0.00308637i
$815$		0			0
$816$	11.0323	−	33.9540i	0.0135200	−	0.0416103i
$817$	384.207	+	60.8524i	0.470265	+	0.0744827i
$818$	−2.77866	+	0.440097i	−0.00339690	+	0.000538015i
$819$	759.532	−	246.787i	0.927389	−	0.301327i
$820$		0			0
$821$	805.110	+	584.947i	0.980645	+	0.712481i	0.957853	−	0.287260i	$-0.0927443\pi$
$821$	805.110	+	584.947i	0.980645	+	0.712481i	0.0227926	+	0.999740i	$0.492744\pi$
$822$	−54.3673	−	8.61093i	−0.0661403	−	0.0104756i
$823$	−82.4626	−	161.842i	−0.100198	−	0.196649i	0.835466	−	0.549542i	$-0.185198\pi$
$823$	−82.4626	−	161.842i	−0.100198	−	0.196649i	−0.935664	+	0.352893i	$0.885198\pi$
$824$			565.858i			0.686721i
$825$		0			0
$826$	5.52389			0.00668752
$827$	−1062.27	+	541.252i	−1.28448	+	0.654477i	−0.956920	−	0.290352i	$-0.906228\pi$
$827$	−1062.27	+	541.252i	−1.28448	+	0.654477i	−0.327564	+	0.944829i	$0.606228\pi$
$828$	288.251	−	1819.95i	0.348129	−	2.19800i
$829$	529.845	−	729.269i	0.639137	−	0.879697i	−0.359432	−	0.933171i	$-0.617030\pi$
$829$	529.845	−	729.269i	0.639137	−	0.879697i	0.998569	+	0.0534743i	$0.0170295\pi$
$830$		0			0
$831$	−412.514	−	1269.59i	−0.496407	−	1.52778i
$832$	86.8593	+	548.408i	0.104398	+	0.659144i
$833$	−34.2018	+	215.942i	−0.0410586	+	0.259234i
$834$	879.434	+	285.745i	1.05448	+	0.342620i
$835$		0			0
$836$	343.949	+	209.034i	0.411423	+	0.250041i
$837$	−766.853	−	766.853i	−0.916192	−	0.916192i
$838$	−126.131	−	247.546i	−0.150514	−	0.295401i
$839$	588.099	+	809.448i	0.700952	+	0.964778i	0.999945	+	0.0105222i	$0.00334938\pi$
$839$	588.099	+	809.448i	0.700952	+	0.964778i	−0.298993	+	0.954255i	$0.596651\pi$
$840$		0			0
$841$	−325.214	−	1000.91i	−0.386700	−	1.19014i
$842$	325.424	−	638.681i	0.386489	−	0.758528i
$843$	1632.78	−	258.607i	1.93687	−	0.306770i
$844$	−231.112	−	318.098i	−0.273829	−	0.376893i
$845$		0			0
$846$	−1408.65			−1.66507
$847$	192.167	−	141.792i	0.226879	−	0.167404i
$848$	5.06509	−	5.06509i	0.00597298	−	0.00597298i
$849$	−935.487	−	303.958i	−1.10187	−	0.358019i
$850$		0			0
$851$	4.56588	+	3.31730i	0.00536531	+	0.00389812i
$852$	10.6019	−	20.8074i	0.0124436	−	0.0244219i
$853$	−83.5210	−	42.5561i	−0.0979145	−	0.0498899i	0.404347	−	0.914605i	$-0.367499\pi$
$853$	−83.5210	−	42.5561i	−0.0979145	−	0.0498899i	−0.502262	+	0.864716i	$0.667499\pi$
$854$	−160.713	+	221.203i	−0.188189	+	0.259019i
$855$		0			0
$856$	116.638	−	358.976i	0.136260	−	0.419365i
$857$	521.312	+	521.312i	0.608299	+	0.608299i	0.942501	−	0.334202i	$-0.108467\pi$
$857$	521.312	+	521.312i	0.608299	+	0.608299i	−0.334202	+	0.942501i	$0.608467\pi$
$858$	1209.10	−	294.993i	1.40921	−	0.343814i
$859$			385.080i			0.448289i	0.974556	+	0.224144i	$0.0719587\pi$
$859$			385.080i			0.448289i	−0.974556	+	0.224144i	$0.928041\pi$
$860$		0			0
$861$	403.090	−	292.862i	0.468165	−	0.340142i
$862$	74.9951	+	473.500i	0.0870013	+	0.549304i
$863$	−625.137	−	318.523i	−0.724377	−	0.369088i	0.0526018	−	0.998616i	$-0.483249\pi$
$863$	−625.137	−	318.523i	−0.724377	−	0.369088i	−0.776978	+	0.629527i	$0.783249\pi$
$864$	2745.29	−	891.998i	3.17742	−	1.03241i
$865$		0			0
$866$	490.498	−	356.368i	0.566395	−	0.411510i
$867$	1365.41	−	695.710i	1.57487	−	0.802434i
$868$	−44.7380	+	44.7380i	−0.0515415	+	0.0515415i
$869$	362.000	+	420.700i	0.416570	+	0.484120i
$870$		0			0
$871$	−367.911	+	1132.32i	−0.422401	+	1.30002i
$872$	−1168.96	−	185.145i	−1.34055	−	0.212322i
$873$	−2609.32	+	413.275i	−2.98891	+	0.473396i
$874$	455.105	−	147.872i	0.520715	−	0.169190i
$875$		0			0
$876$	1106.50	+	803.922i	1.26313	+	0.917719i
$877$	−980.068	−	155.228i	−1.11752	−	0.176998i	−0.429767	−	0.902940i	$-0.641404\pi$
$877$	−980.068	−	155.228i	−1.11752	−	0.176998i	−0.687756	+	0.725941i	$0.741404\pi$
$878$	−188.264	−	369.488i	−0.214423	−	0.420829i
$879$			1569.94i			1.78605i
$880$		0			0
$881$	1602.32			1.81875			0.909376	−	0.415974i	$-0.136559\pi$
$881$	1602.32			1.81875			0.909376	+	0.415974i	$0.136559\pi$
$882$	−1150.93	+	586.430i	−1.30491	+	0.664887i
$883$	−60.0009	+	378.831i	−0.0679512	+	0.429027i	0.930137	+	0.367214i	$0.119688\pi$
$883$	−60.0009	+	378.831i	−0.0679512	+	0.429027i	−0.998088	+	0.0618131i	$0.980312\pi$
$884$	−123.880	+	170.506i	−0.140136	+	0.192880i
$885$		0			0
$886$	−2.70811	−	8.33471i	−0.00305656	−	0.00940713i
$887$	130.534	+	824.162i	0.147164	+	0.929157i	0.945187	+	0.326530i	$0.105879\pi$
$887$	130.534	+	824.162i	0.147164	+	0.929157i	−0.798023	+	0.602627i	$0.794121\pi$
$888$	−1.36825	+	8.63878i	−0.00154082	+	0.00972836i
$889$	110.363	+	35.8592i	0.124143	+	0.0403366i
$890$		0			0
$891$	−1237.24	−	2956.12i	−1.38860	−	3.31775i
$892$	256.777	+	256.777i	0.287867	+	0.287867i
$893$	312.742	+	613.791i	0.350215	+	0.687336i
$894$	319.283	+	439.455i	0.357140	+	0.491561i
$895$		0			0
$896$	−55.7058	−	171.445i	−0.0621717	−	0.191345i
$897$	−1264.99	+	2482.69i	−1.41025	+	2.76777i
$898$	214.384	−	33.9550i	0.238734	−	0.0378118i
$899$	313.822	+	431.938i	0.349078	+	0.480465i
$900$		0			0
$901$	−27.2094			−0.0301991
$902$	482.094	−	297.875i	0.534472	−	0.330238i
$903$	−223.733	+	223.733i	−0.247767	+	0.247767i
$904$	−982.748	−	319.314i	−1.08711	−	0.353224i
$905$		0			0
$906$	−501.679	−	364.491i	−0.553730	−	0.402308i
$907$	193.184	−	379.145i	0.212992	−	0.418021i	−0.759649	−	0.650333i	$-0.774629\pi$
$907$	193.184	−	379.145i	0.212992	−	0.418021i	0.972641	+	0.232313i	$0.0746293\pi$
$908$	−2.37167	−	1.20842i	−0.00261197	−	0.00133086i
$909$	473.258	−	651.384i	0.520636	−	0.716594i
$910$		0			0
$911$	−488.370	+	1503.05i	−0.536081	+	1.64989i	0.205219	+	0.978716i	$0.434209\pi$
$911$	−488.370	+	1503.05i	−0.536081	+	1.64989i	−0.741301	+	0.671173i	$0.765791\pi$
$912$	−72.9392	−	72.9392i	−0.0799772	−	0.0799772i
$913$	80.7603	+	130.706i	0.0884559	+	0.143161i
$914$			276.574i			0.302598i
$915$		0			0
$916$	18.5877	−	13.5048i	0.0202923	−	0.0147432i
$917$	54.1274	+	341.747i	0.0590266	+	0.372680i
$918$	−449.639	−	229.102i	−0.489802	−	0.249567i
$919$	−19.2879	+	6.26701i	−0.0209879	+	0.00681938i	−0.319492	−	0.947589i	$-0.603512\pi$
$919$	−19.2879	+	6.26701i	−0.0209879	+	0.00681938i	0.298504	+	0.954408i	$0.403512\pi$
$920$		0			0
$921$	932.718	−	677.660i	1.01272	−	0.735787i
$922$	−569.443	+	290.146i	−0.617617	+	0.314692i
$923$	−18.2244	+	18.2244i	−0.0197447	+	0.0197447i
$924$	−301.997	+	126.396i	−0.326837	+	0.136793i
$925$		0			0
$926$	−24.8307	+	76.4210i	−0.0268150	+	0.0825281i
$927$	−1744.63	−	276.322i	−1.88201	−	0.298082i
$928$	−1403.58	+	222.306i	−1.51248	+	0.239554i
$929$	640.531	−	208.121i	0.689484	−	0.224027i	0.0567411	−	0.998389i	$-0.481929\pi$
$929$	640.531	−	208.121i	0.689484	−	0.224027i	0.632743	+	0.774362i	$0.281929\pi$
$930$		0			0
$931$	511.052	+	371.301i	0.548928	+	0.398820i
$932$	1073.38	+	170.007i	1.15170	+	0.182411i
$933$	−126.809	−	248.876i	−0.135915	−	0.266748i
$934$		−	739.426i		−	0.791677i
$935$		0			0
$936$	−3151.63			−3.36713
$937$	258.180	−	131.549i	0.275539	−	0.140394i	−0.310761	−	0.950488i	$-0.600584\pi$
$937$	258.180	−	131.549i	0.275539	−	0.140394i	0.586300	+	0.810094i	$0.300584\pi$
$938$	−26.0170	+	164.265i	−0.0277367	+	0.175123i
$939$	−112.786	+	155.237i	−0.120113	+	0.165321i
$940$		0			0
$941$	−1.31431	−	4.04503i	−0.00139672	−	0.00429865i	0.950356	−	0.311166i	$-0.100719\pi$
$941$	−1.31431	−	4.04503i	−0.00139672	−	0.00429865i	−0.951752	+	0.306867i	$0.900719\pi$
$942$	−268.152	−	1693.05i	−0.284663	−	1.79729i
$943$	−198.475	+	1253.12i	−0.210472	+	1.32887i
$944$	2.88371	+	0.936975i	0.00305478	+	0.000992558i
$945$		0			0
$946$	−272.788	+	234.726i	−0.288360	+	0.248125i
$947$	779.521	+	779.521i	0.823148	+	0.823148i	0.986558	−	0.163410i	$-0.0522495\pi$
$947$	779.521	+	779.521i	0.823148	+	0.823148i	−0.163410	+	0.986558i	$0.552249\pi$
$948$	−345.411	−	677.906i	−0.364357	−	0.715091i
$949$	−887.246	−	1221.19i	−0.934928	−	1.28682i
$950$		0			0
$951$	−484.598	−	1491.44i	−0.509567	−	1.56828i
$952$	−33.8293	+	66.3938i	−0.0355350	+	0.0697413i
$953$	571.006	−	90.4385i	0.599167	−	0.0948987i	0.150519	−	0.988607i	$-0.451906\pi$
$953$	571.006	−	90.4385i	0.599167	−	0.0948987i	0.448648	+	0.893708i	$0.351906\pi$
$954$	−94.4911	−	130.056i	−0.0990473	−	0.136327i
$955$		0			0
$956$	−749.841			−0.784352
$957$	654.817	+	2683.93i	0.684239	+	2.80452i
$958$	−484.389	+	484.389i	−0.505626	+	0.505626i
$959$	−15.1981	−	4.93817i	−0.0158479	−	0.00514930i
$960$		0			0
$961$	655.667	+	476.370i	0.682276	+	0.495703i
$962$	1.73145	−	3.39817i	0.00179985	−	0.00353240i
$963$	1049.82	+	534.910i	1.09016	+	0.555463i
$964$	−486.846	+	670.086i	−0.505027	+	0.695110i
$965$		0			0
$966$	−120.279	+	370.179i	−0.124512	+	0.383208i
$967$	−115.321	−	115.321i	−0.119256	−	0.119256i	0.644960	−	0.764216i	$-0.276874\pi$
$967$	−115.321	−	115.321i	−0.119256	−	0.119256i	−0.764216	+	0.644960i	$0.776874\pi$
$968$	−894.154	+	297.827i	−0.923713	+	0.307672i
$969$			391.826i			0.404361i
$970$		0			0
$971$	−305.877	+	222.233i	−0.315012	+	0.228870i	−0.734044	−	0.679102i	$-0.762370\pi$
$971$	−305.877	+	222.233i	−0.315012	+	0.228870i	0.419032	+	0.907971i	$0.362370\pi$
$972$	362.107	+	2286.25i	0.372538	+	2.35211i
$973$	239.190	+	121.874i	0.245828	+	0.125256i
$974$	195.338	−	63.4691i	0.200552	−	0.0651634i
$975$		0			0
$976$	−121.420	+	88.2169i	−0.124406	+	0.0903861i
$977$	169.433	−	86.3306i	0.173422	−	0.0883629i	−0.365125	−	0.930959i	$-0.618974\pi$
$977$	169.433	−	86.3306i	0.173422	−	0.0883629i	0.538547	+	0.842596i	$0.318974\pi$
$978$	−1102.04	+	1102.04i	−1.12683	+	1.12683i
$979$	−460.791	+	758.196i	−0.470675	+	0.774460i
$980$		0			0
$981$	1141.66	−	3513.66i	1.16377	−	3.58172i
$982$	−310.763	−	49.2201i	−0.316460	−	0.0501223i
$983$	1232.11	−	195.147i	1.25342	−	0.198522i	0.505799	−	0.862651i	$-0.331198\pi$
$983$	1232.11	−	195.147i	1.25342	−	0.198522i	0.747618	+	0.664129i	$0.231198\pi$
$984$	−1870.02	+	607.606i	−1.90043	+	0.617486i
$985$		0			0
$986$	200.991	+	146.029i	0.203845	+	0.148102i
$987$	−553.427	−	87.6542i	−0.560716	−	0.0888087i
$988$	276.453	+	542.569i	0.279810	+	0.549159i
$989$		−	805.704i		−	0.814665i
$990$		0			0
$991$	1692.83			1.70821			0.854103	−	0.520104i	$-0.174107\pi$
$991$	1692.83			1.70821			0.854103	+	0.520104i	$0.174107\pi$
$992$	357.041	−	181.921i	0.359920	−	0.183388i
$993$	−103.407	+	652.887i	−0.104136	+	0.657490i
$994$	−2.11617	+	2.91266i	−0.00212895	+	0.00293024i
$995$		0			0
$996$	−65.0858	−	200.314i	−0.0653472	−	0.201118i
$997$	−185.327	−	1170.11i	−0.185885	−	1.17363i	−0.887409	−	0.460983i	$-0.847497\pi$
$997$	−185.327	−	1170.11i	−0.185885	−	1.17363i	0.701524	−	0.712646i	$-0.252503\pi$
$998$	173.164	−	1093.32i	0.173511	−	1.09551i
$999$	−16.3547	−	5.31395i	−0.0163710	−	0.00531927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.207.11	yes	128
5.2	odd	4	inner	275.3.bk.c.218.11	yes	128
5.3	odd	4	inner	275.3.bk.c.218.6	yes	128
5.4	even	2	inner	275.3.bk.c.207.6	yes	128
11.5	even	5	inner	275.3.bk.c.82.6	✓	128
55.27	odd	20	inner	275.3.bk.c.93.6	yes	128
55.38	odd	20	inner	275.3.bk.c.93.11	yes	128
55.49	even	10	inner	275.3.bk.c.82.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.6	✓	128	11.5	even	5	inner
275.3.bk.c.82.11	yes	128	55.49	even	10	inner
275.3.bk.c.93.6	yes	128	55.27	odd	20	inner
275.3.bk.c.93.11	yes	128	55.38	odd	20	inner
275.3.bk.c.207.6	yes	128	5.4	even	2	inner
275.3.bk.c.207.11	yes	128	1.1	even	1	trivial
275.3.bk.c.218.6	yes	128	5.3	odd	4	inner
275.3.bk.c.218.11	yes	128	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04950 - 0.534746i) q^{2} +(0.902907 - 5.70073i) q^{3} +(-1.53565 + 2.11364i) q^{4} +(-2.10084 - 6.46573i) q^{6} +(-0.308752 - 1.94938i) q^{7} +(-1.21844 + 7.69295i) q^{8} +(-23.1236 - 7.51330i) q^{9} +(-9.40014 - 5.71291i) q^{11} +(10.6627 + 10.6627i) q^{12} +(-7.55546 - 14.8284i) q^{13} +(-1.36646 - 1.88077i) q^{14} +(-0.394331 - 1.21363i) q^{16} +(-2.20061 + 4.31894i) q^{17} +(-28.2858 + 4.48004i) q^{18} +(8.23200 + 11.3304i) q^{19} -11.3917 q^{21} +(-12.9204 - 0.968994i) q^{22} +(20.5117 - 20.5117i) q^{23} +(42.7553 + 13.8920i) q^{24} +(-15.8589 - 11.5221i) q^{26} +(-40.1266 + 78.7530i) q^{27} +(4.59443 + 2.34098i) q^{28} +(25.5765 - 35.2031i) q^{29} +(-3.79161 + 11.6694i) q^{31} +(-23.0930 - 23.0930i) q^{32} +(-41.0552 + 48.4294i) q^{33} +5.70948i q^{34} +(51.3900 - 37.3370i) q^{36} +(0.0304356 + 0.192163i) q^{37} +(14.6984 + 7.48918i) q^{38} +(-91.3546 + 29.6829i) q^{39} +(-35.3846 + 25.7084i) q^{41} +(-11.9555 + 6.09166i) q^{42} +(19.6401 - 19.6401i) q^{43} +(26.5103 - 11.0955i) q^{44} +(10.5585 - 32.4956i) q^{46} +(48.5817 + 7.69458i) q^{47} +(-7.27460 + 1.15218i) q^{48} +(42.8970 - 13.9381i) q^{49} +(22.6341 + 16.4447i) q^{51} +(42.9444 + 6.80173i) q^{52} +(2.54841 + 5.00155i) q^{53} +104.109i q^{54} +15.3727 q^{56} +(72.0242 - 36.6981i) q^{57} +(8.01782 - 50.6225i) q^{58} +(-1.39664 + 1.92231i) q^{59} +(-36.3443 - 111.856i) q^{61} +(2.26086 + 14.2745i) q^{62} +(-7.50685 + 47.3964i) q^{63} +(-31.7305 - 10.3099i) q^{64} +(-17.1899 + 72.7807i) q^{66} +(-50.5862 - 50.5862i) q^{67} +(-5.74931 - 11.2837i) q^{68} +(-98.4116 - 135.452i) q^{69} +(-0.478560 - 1.47286i) q^{71} +(85.9742 - 168.734i) q^{72} +(89.5842 - 14.1887i) q^{73} +(0.134700 + 0.185399i) q^{74} -36.5898 q^{76} +(-8.23433 + 20.0884i) q^{77} +(-80.0037 + 80.0037i) q^{78} +(-47.9857 - 15.5915i) q^{79} +(235.688 + 171.237i) q^{81} +(-23.3886 + 45.9027i) q^{82} +(-12.4452 - 6.34114i) q^{83} +(17.4936 - 24.0779i) q^{84} +(10.1098 - 31.1147i) q^{86} +(-177.590 - 177.590i) q^{87} +(55.4026 - 65.3540i) q^{88} -80.6579i q^{89} +(-26.5735 + 19.3068i) q^{91} +(11.8556 + 74.8532i) q^{92} +(63.1004 + 32.1513i) q^{93} +(55.1010 - 17.9034i) q^{94} +(-152.498 + 110.796i) q^{96} +(96.8143 - 49.3293i) q^{97} +(37.5670 - 37.5670i) q^{98} +(174.442 + 202.729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) \) 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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