LMFDB - Embedded newform 275.3.bk.c.82.11

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			82.11
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.534746 - 1.04950i) q^{2} +(-5.70073 + 0.902907i) q^{3} +(1.53565 + 2.11364i) q^{4} +(-2.10084 + 6.46573i) q^{6} +(1.94938 + 0.308752i) q^{7} +(7.69295 - 1.21844i) q^{8} +(23.1236 - 7.51330i) q^{9} +(-9.40014 + 5.71291i) q^{11} +(-10.6627 - 10.6627i) q^{12} +(-14.8284 - 7.55546i) q^{13} +(1.36646 - 1.88077i) q^{14} +(-0.394331 + 1.21363i) q^{16} +(-4.31894 + 2.20061i) q^{17} +(4.48004 - 28.2858i) q^{18} +(-8.23200 + 11.3304i) q^{19} -11.3917 q^{21} +(0.968994 + 12.9204i) q^{22} +(-20.5117 + 20.5117i) q^{23} +(-42.7553 + 13.8920i) q^{24} +(-15.8589 + 11.5221i) q^{26} +(-78.7530 + 40.1266i) q^{27} +(2.34098 + 4.59443i) q^{28} +(-25.5765 - 35.2031i) q^{29} +(-3.79161 - 11.6694i) q^{31} +(23.0930 + 23.0930i) q^{32} +(48.4294 - 41.0552i) q^{33} +5.70948i q^{34} +(51.3900 + 37.3370i) q^{36} +(-0.192163 - 0.0304356i) q^{37} +(7.48918 + 14.6984i) q^{38} +(91.3546 + 29.6829i) q^{39} +(-35.3846 - 25.7084i) q^{41} +(-6.09166 + 11.9555i) q^{42} +(-19.6401 + 19.6401i) q^{43} +(-26.5103 - 11.0955i) q^{44} +(10.5585 + 32.4956i) q^{46} +(-7.69458 - 48.5817i) q^{47} +(1.15218 - 7.27460i) q^{48} +(-42.8970 - 13.9381i) q^{49} +(22.6341 - 16.4447i) q^{51} +(-6.80173 - 42.9444i) q^{52} +(5.00155 + 2.54841i) q^{53} +104.109i q^{54} +15.3727 q^{56} +(36.6981 - 72.0242i) q^{57} +(-50.6225 + 8.01782i) q^{58} +(1.39664 + 1.92231i) q^{59} +(-36.3443 + 111.856i) q^{61} +(-14.2745 - 2.26086i) q^{62} +(47.3964 - 7.50685i) q^{63} +(31.7305 - 10.3099i) q^{64} +(-17.1899 - 72.7807i) q^{66} +(50.5862 + 50.5862i) q^{67} +(-11.2837 - 5.74931i) q^{68} +(98.4116 - 135.452i) q^{69} +(-0.478560 + 1.47286i) q^{71} +(168.734 - 85.9742i) q^{72} +(-14.1887 + 89.5842i) q^{73} +(-0.134700 + 0.185399i) q^{74} -36.5898 q^{76} +(-20.0884 + 8.23433i) q^{77} +(80.0037 - 80.0037i) q^{78} +(47.9857 - 15.5915i) q^{79} +(235.688 - 171.237i) q^{81} +(-45.9027 + 23.3886i) q^{82} +(-6.34114 - 12.4452i) q^{83} +(-17.4936 - 24.0779i) q^{84} +(10.1098 + 31.1147i) q^{86} +(177.590 + 177.590i) q^{87} +(-65.3540 + 55.4026i) q^{88} -80.6579i q^{89} +(-26.5735 - 19.3068i) q^{91} +(-74.8532 - 11.8556i) q^{92} +(32.1513 + 63.1004i) q^{93} +(-55.1010 - 17.9034i) q^{94} +(-152.498 - 110.796i) q^{96} +(49.3293 - 96.8143i) 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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.534746	−	1.04950i	0.267373	−	0.524749i	−0.717813	−	0.696235i	$-0.754857\pi$
$2$	0.534746	−	1.04950i	0.267373	−	0.524749i	0.985186	+	0.171486i	$0.0548570\pi$
$3$	−5.70073	+	0.902907i	−1.90024	+	0.300969i	−0.992855	−	0.119326i	$-0.961927\pi$
$3$	−5.70073	+	0.902907i	−1.90024	+	0.300969i	−0.907388	+	0.420295i	$0.861927\pi$
$4$	1.53565	+	2.11364i	0.383912	+	0.528410i
$5$		0			0
$5$		0			0
$6$	−2.10084	+	6.46573i	−0.350140	+	1.07762i
$7$	1.94938	+	0.308752i	0.278483	+	0.0441074i	0.294114	−	0.955770i	$-0.404976\pi$
$7$	1.94938	+	0.308752i	0.278483	+	0.0441074i	−0.0156304	+	0.999878i	$0.504976\pi$
$8$	7.69295	−	1.21844i	0.961619	−	0.152305i
$9$	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
$13$	−14.8284	−	7.55546i	−1.14065	−	0.581189i	−0.221523	−	0.975155i	$-0.571103\pi$
$13$	−14.8284	−	7.55546i	−1.14065	−	0.581189i	−0.919125	+	0.393966i	$0.871103\pi$
$14$	1.36646	−	1.88077i	0.0976043	−	0.134341i
$15$		0			0
$16$	−0.394331	+	1.21363i	−0.0246457	+	0.0758516i
$17$	−4.31894	+	2.20061i	−0.254055	+	0.129448i	−0.576381	−	0.817181i	$-0.695535\pi$
$17$	−4.31894	+	2.20061i	−0.254055	+	0.129448i	0.322326	+	0.946629i	$0.395535\pi$
$18$	4.48004	−	28.2858i	0.248891	−	1.57144i
$19$	−8.23200	+	11.3304i	−0.433263	+	0.596336i	−0.968698	−	0.248240i	$-0.920148\pi$
$19$	−8.23200	+	11.3304i	−0.433263	+	0.596336i	0.535435	+	0.844576i	$0.320148\pi$
$20$		0			0
$21$	−11.3917			−0.542461
$22$	0.968994	+	12.9204i	0.0440452	+	0.587290i
$23$	−20.5117	+	20.5117i	−0.891814	+	0.891814i	−0.994694	−	0.102879i	$-0.967194\pi$
$23$	−20.5117	+	20.5117i	−0.891814	+	0.891814i	0.102879	+	0.994694i	$0.467194\pi$
$24$	−42.7553	+	13.8920i	−1.78147	+	0.578835i
$25$		0			0
$26$	−15.8589	+	11.5221i	−0.609957	+	0.443159i
$27$	−78.7530	+	40.1266i	−2.91678	+	1.48617i
$28$	2.34098	+	4.59443i	0.0836063	+	0.164087i
$29$	−25.5765	−	35.2031i	−0.881949	−	1.21390i	−0.975877	−	0.218320i	$-0.929942\pi$
$29$	−25.5765	−	35.2031i	−0.881949	−	1.21390i	0.0939277	−	0.995579i	$-0.470058\pi$
$30$		0			0
$31$	−3.79161	−	11.6694i	−0.122310	−	0.376431i	0.871091	−	0.491121i	$-0.163413\pi$
$31$	−3.79161	−	11.6694i	−0.122310	−	0.376431i	−0.993401	+	0.114690i	$0.963413\pi$
$32$	23.0930	+	23.0930i	0.721657	+	0.721657i
$33$	48.4294	−	41.0552i	1.46756	−	1.24410i
$34$			5.70948i			0.167926i
$35$		0			0
$36$	51.3900	+	37.3370i	1.42750	+	1.03714i
$37$	−0.192163	−	0.0304356i	−0.00519359	−	0.000822583i	0.153837	−	0.988096i	$-0.450837\pi$
$37$	−0.192163	−	0.0304356i	−0.00519359	−	0.000822583i	−0.159031	+	0.987274i	$0.550837\pi$
$38$	7.48918	+	14.6984i	0.197084	+	0.386799i
$39$	91.3546	+	29.6829i	2.34243	+	0.761101i
$40$		0			0
$41$	−35.3846	−	25.7084i	−0.863039	−	0.627034i	0.0656713	−	0.997841i	$-0.479081\pi$
$41$	−35.3846	−	25.7084i	−0.863039	−	0.627034i	−0.928710	+	0.370807i	$0.879081\pi$
$42$	−6.09166	+	11.9555i	−0.145039	+	0.284656i
$43$	−19.6401	+	19.6401i	−0.456746	+	0.456746i	−0.897586	−	0.440840i	$-0.854681\pi$
$43$	−19.6401	+	19.6401i	−0.456746	+	0.456746i	0.440840	+	0.897586i	$0.354681\pi$
$44$	−26.5103	−	11.0955i	−0.602507	−	0.252170i
$45$		0			0
$46$	10.5585	+	32.4956i	0.229532	+	0.706426i
$47$	−7.69458	−	48.5817i	−0.163714	−	1.03365i	−0.923533	−	0.383518i	$-0.874712\pi$
$47$	−7.69458	−	48.5817i	−0.163714	−	1.03365i	0.759819	−	0.650135i	$-0.225288\pi$
$48$	1.15218	−	7.27460i	0.0240038	−	0.151554i
$49$	−42.8970	−	13.9381i	−0.875449	−	0.284451i
$50$		0			0
$51$	22.6341	−	16.4447i	0.443807	−	0.322444i
$52$	−6.80173	−	42.9444i	−0.130802	−	0.825854i
$53$	5.00155	+	2.54841i	0.0943688	+	0.0480833i	0.500538	−	0.865715i	$-0.333136\pi$
$53$	5.00155	+	2.54841i	0.0943688	+	0.0480833i	−0.406169	+	0.913798i	$0.633136\pi$
$54$			104.109i			1.92794i
$55$		0			0
$56$	15.3727			0.274513
$57$	36.6981	−	72.0242i	0.643827	−	1.26358i
$58$	−50.6225	+	8.01782i	−0.872802	+	0.138238i
$59$	1.39664	+	1.92231i	0.0236719	+	0.0325816i	0.820689	−	0.571375i	$-0.193590\pi$
$59$	1.39664	+	1.92231i	0.0236719	+	0.0325816i	−0.797017	+	0.603957i	$0.793590\pi$
$60$		0			0
$61$	−36.3443	+	111.856i	−0.595809	+	1.83371i	−0.0451502	+	0.998980i	$0.514377\pi$
$61$	−36.3443	+	111.856i	−0.595809	+	1.83371i	−0.550659	+	0.834731i	$0.685623\pi$
$62$	−14.2745	−	2.26086i	−0.230234	−	0.0364655i
$63$	47.3964	−	7.50685i	0.752324	−	0.119156i
$64$	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	0.975411	−	0.220393i	$-0.0707340\pi$
$67$	50.5862	+	50.5862i	0.755018	+	0.755018i	−0.220393	+	0.975411i	$0.570734\pi$
$68$	−11.2837	−	5.74931i	−0.165936	−	0.0845487i
$69$	98.4116	−	135.452i	1.42626	−	1.96307i
$70$		0			0
$71$	−0.478560	+	1.47286i	−0.00674028	+	0.0207445i	−0.954370	−	0.298626i	$-0.903472\pi$
$71$	−0.478560	+	1.47286i	−0.00674028	+	0.0207445i	0.947630	+	0.319371i	$0.103472\pi$
$72$	168.734	−	85.9742i	2.34353	−	1.19409i
$73$	−14.1887	+	89.5842i	−0.194366	+	1.22718i	0.676790	+	0.736176i	$0.263370\pi$
$73$	−14.1887	+	89.5842i	−0.194366	+	1.22718i	−0.871157	+	0.491005i	$0.836630\pi$
$74$	−0.134700	+	0.185399i	−0.00182028	+	0.00250539i
$75$		0			0
$76$	−36.5898			−0.481445
$77$	−20.0884	+	8.23433i	−0.260888	+	0.106939i
$78$	80.0037	−	80.0037i	1.02569	−	1.02569i
$79$	47.9857	−	15.5915i	0.607414	−	0.197361i	0.0108696	−	0.999941i	$-0.496540\pi$
$79$	47.9857	−	15.5915i	0.607414	−	0.197361i	0.596544	+	0.802580i	$0.296540\pi$
$80$		0			0
$81$	235.688	−	171.237i	2.90973	−	2.11404i
$82$	−45.9027	+	23.3886i	−0.559789	+	0.285227i
$83$	−6.34114	−	12.4452i	−0.0763993	−	0.149942i	0.849647	−	0.527352i	$-0.176815\pi$
$83$	−6.34114	−	12.4452i	−0.0763993	−	0.149942i	−0.926046	+	0.377410i	$0.876815\pi$
$84$	−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
$88$	−65.3540	+	55.4026i	−0.742659	+	0.629576i
$89$		−	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
$92$	−74.8532	−	11.8556i	−0.813621	−	0.128865i
$93$	32.1513	+	63.1004i	0.345713	+	0.678499i
$94$	−55.1010	−	17.9034i	−0.586181	−	0.190462i
$95$		0			0
$96$	−152.498	−	110.796i	−1.58852	−	1.15413i
$97$	49.3293	−	96.8143i	0.508550	−	0.998085i	−0.483864	−	0.875143i	$-0.660767\pi$
$97$	49.3293	−	96.8143i	0.508550	−	0.998085i	0.992414	−	0.122942i	$-0.0392330\pi$
$98$	−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	0.887530	−	0.460751i	$-0.152420\pi$
$101$	−10.2333	−	31.4947i	−0.101319	−	0.311829i	−0.988849	+	0.148922i	$0.952420\pi$
$102$	−5.15513	−	32.5482i	−0.0505405	−	0.319100i
$103$	−11.3649	+	71.7554i	−0.110339	+	0.696654i	0.869058	+	0.494710i	$0.164726\pi$
$103$	−11.3649	+	71.7554i	−0.110339	+	0.696654i	−0.979397	+	0.201944i	$0.935274\pi$
$104$	−123.280	−	40.0562i	−1.18539	−	0.385155i
$105$		0			0
$106$	5.34911	−	3.88636i	0.0504633	−	0.0366638i
$107$	7.58086	+	47.8637i	0.0708492	+	0.447324i	0.997456	+	0.0712913i	$0.0227120\pi$
$107$	7.58086	+	47.8637i	0.0708492	+	0.447324i	−0.926606	+	0.376033i	$0.877288\pi$
$108$	−205.750	−	104.835i	−1.90509	−	0.970693i
$109$			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
$112$	−1.14341	+	2.24407i	−0.0102090	+	0.0200364i
$113$	131.034	−	20.7537i	1.15959	−	0.183661i	0.453150	−	0.891434i	$-0.350300\pi$
$113$	131.034	−	20.7537i	1.15959	−	0.183661i	0.706440	+	0.707773i	$0.250300\pi$
$114$	−55.9650	−	77.0293i	−0.490921	−	0.675695i
$115$		0			0
$116$	35.1300	−	108.119i	0.302845	−	0.932061i
$117$	−399.652	−	63.2987i	−3.41583	−	0.541014i
$118$	2.76432	−	0.437825i	0.0234264	−	0.00371038i
$119$	−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
$123$	224.930	+	114.608i	1.82870	+	0.931770i
$124$	18.8422	−	25.9341i	0.151954	−	0.209146i
$125$		0			0
$126$	17.4666	−	53.7567i	0.138624	−	0.426641i
$127$	−52.3868	+	26.6924i	−0.412495	+	0.210176i	−0.647908	−	0.761719i	$-0.724356\pi$
$127$	−52.3868	+	26.6924i	−0.412495	+	0.210176i	0.235413	+	0.971895i	$0.424356\pi$
$128$	−14.2881	+	90.2113i	−0.111625	+	0.704776i
$129$	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	$0.733330\pi$
$132$	161.146	+	39.3160i	1.22081	+	0.297849i
$133$	−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
$137$	7.21419	−	3.67581i	0.0526583	−	0.0268308i	−0.427463	−	0.904033i	$-0.640593\pi$
$137$	7.21419	−	3.67581i	0.0526583	−	0.0268308i	0.480121	+	0.877202i	$0.340593\pi$
$138$	−89.5314	−	175.715i	−0.648778	−	1.27330i
$139$	79.9474	+	110.038i	0.575161	+	0.791641i	0.993154	−	0.116809i	$-0.0372665\pi$
$139$	79.9474	+	110.038i	0.575161	+	0.791641i	−0.417993	+	0.908450i	$0.637266\pi$
$140$		0			0
$141$	87.7294	+	270.003i	0.622195	+	1.91492i
$142$	1.28985	+	1.28985i	0.00908347	+	0.00908347i
$143$	182.553	−	13.6910i	1.27659	−	0.0957410i
$144$			31.0261i			0.215459i
$145$		0			0
$146$	86.4311	+	62.7959i	0.591994	+	0.430109i
$147$	257.129	+	40.7252i	1.74918	+	0.277042i
$148$	−0.230765	−	0.452901i	−0.00155922	−	0.00306014i
$149$	75.9893	+	24.6904i	0.509995	+	0.165707i	0.552700	−	0.833380i	$-0.313598\pi$
$149$	75.9893	+	24.6904i	0.509995	+	0.165707i	−0.0427049	+	0.999088i	$0.513598\pi$
$150$		0			0
$151$	73.7929	+	53.6137i	0.488695	+	0.355058i	0.804682	−	0.593706i	$-0.202336\pi$
$151$	73.7929	+	53.6137i	0.488695	+	0.355058i	−0.315987	+	0.948763i	$0.602336\pi$
$152$	−49.5230	+	97.1943i	−0.325809	+	0.639436i
$153$	−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
$157$	−39.4430	−	249.034i	−0.251230	−	1.58620i	−0.714274	−	0.699866i	$-0.753243\pi$
$157$	−39.4430	−	249.034i	−0.251230	−	1.58620i	0.463045	−	0.886335i	$-0.346757\pi$
$158$	9.29691	−	58.6984i	0.0588412	−	0.371509i
$159$	−30.8134	−	10.0119i	−0.193795	−	0.0629679i
$160$		0			0
$161$	−46.3183	+	33.6522i	−0.287691	+	0.209020i
$162$	−53.6801	−	338.923i	−0.331358	−	2.09212i
$163$	−204.260	−	104.075i	−1.25313	−	0.638500i	−0.303783	−	0.952741i	$-0.598250\pi$
$163$	−204.260	−	104.075i	−1.25313	−	0.638500i	−0.949343	+	0.314242i	$0.898250\pi$
$164$		−	114.269i		−	0.696764i
$165$		0			0
$166$	−16.4521			−0.0991091
$167$	−46.9036	+	92.0535i	−0.280860	+	0.551219i	−0.987739	−	0.156116i	$-0.950103\pi$
$167$	−46.9036	+	92.0535i	−0.280860	+	0.551219i	0.706879	+	0.707335i	$0.250103\pi$
$168$	−87.6356	+	13.8801i	−0.521641	+	0.0826198i
$169$	63.4613	+	87.3470i	0.375511	+	0.516846i
$170$		0			0
$171$	−105.225	+	323.848i	−0.615349	+	1.89385i
$172$	−71.6723	−	11.3518i	−0.416699	−	0.0659987i
$173$	6.36471	−	1.00807i	0.0367902	−	0.00582700i	−0.138012	−	0.990431i	$-0.544071\pi$
$173$	6.36471	−	1.00807i	0.0367902	−	0.00582700i	0.174802	+	0.984604i	$0.444071\pi$
$174$	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
$178$	−84.6504	−	43.1315i	−0.475564	−	0.242312i
$179$	50.2025	−	69.0978i	0.280461	−	0.386021i	−0.645426	−	0.763823i	$-0.723320\pi$
$179$	50.2025	−	69.0978i	0.280461	−	0.386021i	0.925886	+	0.377802i	$0.123320\pi$
$180$		0			0
$181$	−49.5631	+	152.540i	−0.273829	+	0.842760i	0.715697	+	0.698411i	$0.246109\pi$
$181$	−49.5631	+	152.540i	−0.273829	+	0.842760i	−0.989527	+	0.144350i	$0.953891\pi$
$182$	−34.4725	+	17.5646i	−0.189409	+	0.0965089i
$183$	106.193	−	670.478i	0.580291	−	3.66382i
$184$	−132.803	+	182.788i	−0.721757	+	0.993414i
$185$		0			0
$186$	83.4166			0.448476
$187$	28.0268	−	45.3597i	0.149876	−	0.242565i
$188$	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	−0.277459	−	0.960737i	$-0.589492\pi$
$191$	105.149	−	76.3950i	0.550517	−	0.399974i	0.827976	+	0.560764i	$0.189492\pi$
$192$	−171.578	+	87.4233i	−0.893635	+	0.455330i
$193$	147.719	+	289.915i	0.765383	+	1.50215i	0.862045	+	0.506831i	$0.169183\pi$
$193$	147.719	+	289.915i	0.765383	+	1.50215i	−0.0966622	+	0.995317i	$0.530817\pi$
$194$	−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	0.696314	−	0.717738i	$-0.254822\pi$
$197$	−4.22058	−	4.22058i	−0.0214242	−	0.0214242i	−0.717738	+	0.696314i	$0.754822\pi$
$198$	119.481	+	291.485i	0.603441	+	1.47215i
$199$			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
$202$	−38.5258	−	6.10189i	−0.190722	−	0.0302074i
$203$	−38.9895	−	76.5211i	−0.192066	−	0.376951i
$204$	69.5161	+	22.5872i	0.340765	+	0.110721i
$205$		0			0
$206$	69.2298	+	50.2984i	0.336067	+	0.244167i
$207$	−320.193	+	628.415i	−1.54683	+	3.03582i
$208$	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	−0.998725	−	0.0504773i	$-0.983926\pi$
$211$	−46.5064	−	143.132i	−0.220409	−	0.678350i	0.778316	−	0.627873i	$-0.216074\pi$
$212$	2.29419	+	14.4849i	0.0108216	+	0.0683251i
$213$	1.39829	−	8.82845i	0.00656474	−	0.0414481i
$214$	54.2867	+	17.6388i	0.253676	+	0.0824243i
$215$		0			0
$216$	−556.951	+	404.648i	−2.57848	+	1.87337i
$217$	−3.78836	−	23.9187i	−0.0174579	−	0.110225i
$218$	159.473	+	81.2556i	0.731528	+	0.372732i
$219$		−	523.506i		−	2.39044i
$220$		0			0
$221$	80.6696			0.365021
$222$	0.600492	−	1.17853i	0.00270492	−	0.00530870i
$223$	−137.283	+	21.7436i	−0.615621	+	0.0975048i	−0.456454	−	0.889747i	$-0.650881\pi$
$223$	−137.283	+	21.7436i	−0.615621	+	0.0975048i	−0.159167	+	0.987252i	$0.550881\pi$
$224$	37.8871	+	52.1472i	0.169139	+	0.232800i
$225$		0			0
$226$	48.2887	−	148.617i	0.213667	−	0.657600i
$227$	−1.00628	−	0.159379i	−0.00443296	−	0.000702112i	0.154218	−	0.988037i	$-0.450714\pi$
$227$	−1.00628	−	0.159379i	−0.00443296	−	0.000702112i	−0.158651	+	0.987335i	$0.550714\pi$
$228$	208.588	−	33.0372i	0.914862	−	0.144900i
$229$	8.36376	−	2.71755i	0.0365230	−	0.0118670i	−0.290699	−	0.956815i	$-0.593888\pi$
$229$	8.36376	−	2.71755i	0.0365230	−	0.0118670i	0.327222	+	0.944948i	$0.393888\pi$
$230$		0			0
$231$	107.083	−	65.0796i	0.463565	−	0.281730i
$232$	−239.652	−	239.652i	−1.03298	−	1.03298i
$233$	−370.632	−	188.847i	−1.59070	−	0.810500i	−0.999993	−	0.00361160i	$-0.998850\pi$
$233$	−370.632	−	188.847i	−1.59070	−	0.810500i	−0.590703	−	0.806889i	$-0.701150\pi$
$234$	−280.144	+	385.585i	−1.19720	+	1.64780i
$235$		0			0
$236$	−1.91833	+	5.90400i	−0.00812850	+	0.0250169i
$237$	−259.476	+	132.209i	−1.09483	+	0.557846i
$238$	−1.76281	+	11.1300i	−0.00740678	+	0.0467646i
$239$	−168.700	+	232.195i	−0.705857	+	0.971529i	0.294019	+	0.955800i	$0.405007\pi$
$239$	−168.700	+	232.195i	−0.705857	+	0.971529i	−0.999876	+	0.0157295i	$0.994993\pi$
$240$		0			0
$241$	317.030			1.31548			0.657738	−	0.753247i	$-0.271513\pi$
$241$	317.030			1.31548			0.657738	+	0.753247i	$0.271513\pi$
$242$	−82.9216	−	115.918i	−0.342651	−	0.478999i
$243$	−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
$247$	207.674	−	105.815i	0.840785	−	0.428401i
$248$	−43.3871	−	85.1520i	−0.174948	−	0.343355i
$249$	47.3860	+	65.2212i	0.190305	+	0.261933i
$250$		0			0
$251$	21.5845	+	66.4304i	0.0859942	+	0.264663i	0.984802	−	0.173680i	$-0.0555657\pi$
$251$	21.5845	+	66.4304i	0.0859942	+	0.264663i	−0.898808	+	0.438342i	$0.855566\pi$
$252$	88.6510	+	88.6510i	0.351790	+	0.351790i
$253$	75.6317	−	309.995i	0.298939	−	1.22528i
$254$			69.2535i			0.272652i
$255$		0			0
$256$	195.002	+	141.677i	0.761728	+	0.553427i
$257$	285.248	+	45.1789i	1.10992	+	0.175793i	0.684364	−	0.729141i	$-0.260080\pi$
$257$	285.248	+	45.1789i	1.10992	+	0.175793i	0.425552	+	0.904934i	$0.360080\pi$
$258$	−85.7267	−	168.248i	−0.332274	−	0.652124i
$259$	−0.365202	−	0.118661i	−0.00141005	−	0.000458152i
$260$		0			0
$261$	−855.912	−	621.856i	−3.27935	−	2.38259i
$262$	−93.7465	+	183.988i	−0.357811	+	0.702244i
$263$	−6.71971	+	6.71971i	−0.0255502	+	0.0255502i	−0.719766	−	0.694216i	$-0.755751\pi$
$263$	−6.71971	+	6.71971i	−0.0255502	+	0.0255502i	0.694216	+	0.719766i	$0.255751\pi$
$264$	322.542	−	374.844i	1.22175	−	1.41986i
$265$		0			0
$266$	10.0611	+	30.9650i	0.0378239	+	0.116410i
$267$	72.8266	+	459.809i	0.272759	+	1.72213i
$268$	−29.2383	+	184.604i	−0.109098	+	0.688819i
$269$	99.7989	+	32.4266i	0.371000	+	0.120545i	0.488582	−	0.872518i	$-0.337514\pi$
$269$	99.7989	+	32.4266i	0.371000	+	0.120545i	−0.117582	+	0.993063i	$0.537514\pi$
$270$		0			0
$271$	76.1609	−	55.3341i	0.281037	−	0.204185i	−0.438333	−	0.898813i	$-0.644431\pi$
$271$	76.1609	−	55.3341i	0.281037	−	0.204185i	0.719369	+	0.694628i	$0.244431\pi$
$272$	−0.967625	−	6.10934i	−0.00355744	−	0.0224608i
$273$	168.921	+	86.0693i	0.618757	+	0.315272i
$274$		−	9.53691i		−	0.0348062i
$275$		0			0
$276$	437.422			1.58486
$277$	105.001	−	206.076i	0.379065	−	0.743956i	−0.620113	−	0.784513i	$-0.712913\pi$
$277$	105.001	−	206.076i	0.379065	−	0.743956i	0.999177	+	0.0405564i	$0.0129131\pi$
$278$	158.236	−	25.0622i	0.569196	−	0.0901517i
$279$	−175.351	−	241.350i	−0.628498	−	0.865053i
$280$		0			0
$281$	88.5075	−	272.398i	0.314973	−	0.969388i	−0.660792	−	0.750569i	$-0.729780\pi$
$281$	88.5075	−	272.398i	0.314973	−	0.969388i	0.975765	−	0.218819i	$-0.0702204\pi$
$282$	330.281	+	52.3114i	1.17121	+	0.185501i
$283$	−168.322	+	26.6596i	−0.594777	+	0.0942035i	−0.446564	−	0.894752i	$-0.647352\pi$
$283$	−168.322	+	26.6596i	−0.594777	+	0.0942035i	−0.148214	+	0.988955i	$0.547352\pi$
$284$	−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
$288$	707.497	+	360.488i	2.45659	+	1.25169i
$289$	−156.059	+	214.797i	−0.539998	+	0.743243i
$290$		0			0
$291$	−193.799	+	596.452i	−0.665976	+	2.04966i
$292$	−211.138	+	107.580i	−0.723074	+	0.368425i
$293$	42.5506	−	268.654i	0.145224	−	0.916907i	−0.802230	−	0.597015i	$-0.796353\pi$
$293$	42.5506	−	268.654i	0.145224	−	0.916907i	0.947454	−	0.319892i	$-0.103647\pi$
$294$	180.240	−	248.079i	0.613060	−	0.843805i
$295$		0			0
$296$	−1.51538			−0.00511954
$297$	511.050	−	827.104i	1.72071	−	2.78486i
$298$	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
$302$	95.7279	−	48.7758i	0.316980	−	0.161509i
$303$	86.7738	+	170.303i	0.286382	+	0.562056i
$304$	−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	0.438605	−	0.898680i	$-0.355473\pi$
$307$	−141.243	−	141.243i	−0.460075	−	0.460075i	−0.898680	+	0.438605i	$0.855473\pi$
$308$	−48.2530	−	29.8145i	−0.156666	−	0.0968003i
$309$		−	419.319i		−	1.35702i
$310$		0			0
$311$	39.1515	+	28.4453i	0.125889	+	0.0914639i	0.648948	−	0.760833i	$-0.275209\pi$
$311$	39.1515	+	28.4453i	0.125889	+	0.0914639i	−0.523059	+	0.852297i	$0.675209\pi$
$312$	738.954	+	117.039i	2.36844	+	0.375124i
$313$	−15.0929	−	29.6215i	−0.0482202	−	0.0946374i	0.865639	−	0.500669i	$-0.166912\pi$
$313$	−15.0929	−	29.6215i	−0.0482202	−	0.0946374i	−0.913859	+	0.406031i	$0.866912\pi$
$314$	−282.452	−	91.7743i	−0.899529	−	0.292275i
$315$		0			0
$316$	106.644	+	77.4813i	0.337481	+	0.245194i
$317$	123.349	−	242.086i	0.389113	−	0.763678i	−0.610485	−	0.792028i	$-0.709025\pi$
$317$	123.349	−	242.086i	0.389113	−	0.763678i	0.999598	+	0.0283501i	$0.00902532\pi$
$318$	−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
$322$	10.5494	+	66.6063i	0.0327621	+	0.206852i
$323$	10.6198	−	67.0506i	0.0328786	−	0.207587i
$324$	723.868	+	235.199i	2.23416	+	0.725922i
$325$		0			0
$326$	−218.454	+	158.716i	−0.670104	+	0.486859i
$327$	−137.198	−	866.236i	−0.419567	−	2.64904i
$328$	−303.536	−	154.659i	−0.925415	−	0.471523i
$329$		−	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	$0.555347\pi$
$332$	16.5669	−	32.5143i	0.0499002	−	0.0979347i
$333$	−4.67216	+	0.739997i	−0.0140305	+	0.00222221i
$334$	71.5285	+	98.4505i	0.214157	+	0.294762i
$335$		0			0
$336$	4.49209	−	13.8252i	0.0133693	−	0.0411466i
$337$	125.302	+	19.8459i	0.371816	+	0.0588899i	0.339546	−	0.940589i	$-0.389726\pi$
$337$	125.302	+	19.8459i	0.371816	+	0.0588899i	0.0322698	+	0.999479i	$0.489726\pi$
$338$	125.606	−	19.8941i	0.371616	−	0.0588582i
$339$	−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
$343$	−165.489	−	84.3208i	−0.482475	−	0.245833i
$344$	−127.160	+	175.020i	−0.369651	+	0.508780i
$345$		0			0
$346$	2.34554	−	7.21882i	0.00677900	−	0.0208636i
$347$	134.140	−	68.3476i	0.386570	−	0.196967i	−0.249895	−	0.968273i	$-0.580396\pi$
$347$	134.140	−	68.3476i	0.386570	−	0.196967i	0.636465	+	0.771306i	$0.280396\pi$
$348$	−102.645	+	648.077i	−0.294958	+	1.86229i
$349$	−205.310	+	282.585i	−0.588281	+	0.809699i	−0.994573	−	0.104045i	$-0.966822\pi$
$349$	−205.310	+	282.585i	−0.588281	+	0.809699i	0.406292	+	0.913743i	$0.366822\pi$
$350$		0			0
$351$	1470.96			4.19076
$352$	−349.006	−	85.1495i	−0.991494	−	0.241902i
$353$	362.555	−	362.555i	1.02707	−	1.02707i	0.0274434	−	0.999623i	$-0.491263\pi$
$353$	362.555	−	362.555i	1.02707	−	1.02707i	0.999623	−	0.0274434i	$-0.00873660\pi$
$354$	−15.3633	+	4.99184i	−0.0433991	+	0.0141012i
$355$		0			0
$356$	170.482	−	123.862i	0.478881	−	0.347928i
$357$	49.1999	−	25.0686i	0.137815	−	0.0702202i
$358$	−45.6724	−	89.6372i	−0.127577	−	0.250383i
$359$	285.929	+	393.548i	0.796461	+	1.09623i	0.993273	+	0.115793i	$0.0369410\pi$
$359$	285.929	+	393.548i	0.796461	+	1.09623i	−0.196812	+	0.980441i	$0.563059\pi$
$360$		0			0
$361$	50.9435	+	156.788i	0.141118	+	0.434315i
$362$	133.586	+	133.586i	0.369023	+	0.369023i
$363$	−220.700	+	662.597i	−0.607988	+	1.82534i
$364$		−	85.8152i		−	0.235756i
$365$		0			0
$366$	−646.879	−	469.985i	−1.76743	−	1.28411i
$367$	9.42516	+	1.49280i	0.0256816	+	0.00406757i	0.169262	−	0.985571i	$-0.445862\pi$
$367$	9.42516	+	1.49280i	0.0256816	+	0.00406757i	−0.143580	+	0.989639i	$0.545862\pi$
$368$	−16.8052	−	32.9820i	−0.0456662	−	0.0896250i
$369$	−1011.37	−	328.615i	−2.74085	−	0.890555i
$370$		0			0
$371$	8.96310	+	6.51208i	0.0241593	+	0.0175528i
$372$	−83.9984	+	164.856i	−0.225802	+	0.443162i
$373$	−268.508	+	268.508i	−0.719862	+	0.719862i	−0.968577	−	0.248715i	$-0.919992\pi$
$373$	−268.508	+	268.508i	−0.719862	+	0.719862i	0.248715	+	0.968577i	$0.419992\pi$
$374$	−32.6177	−	53.6700i	−0.0872132	−	0.143503i
$375$		0			0
$376$	−118.388	−	364.361i	−0.314862	−	0.969045i
$377$	113.284	+	715.248i	0.300489	+	1.89721i
$378$	−32.1438	+	202.948i	−0.0850364	+	0.536899i
$379$	−329.126	−	106.940i	−0.868406	−	0.282162i	−0.159271	−	0.987235i	$-0.550914\pi$
$379$	−329.126	−	106.940i	−0.868406	−	0.282162i	−0.709135	+	0.705073i	$0.750914\pi$
$380$		0			0
$381$	274.542	−	199.467i	0.720583	−	0.523534i
$382$	−23.9486	−	151.205i	−0.0626926	−	0.395825i
$383$	77.9932	+	39.7395i	0.203638	+	0.103758i	0.552835	−	0.833291i	$-0.313546\pi$
$383$	77.9932	+	39.7395i	0.203638	+	0.103758i	−0.349198	+	0.937049i	$0.613546\pi$
$384$		−	527.171i		−	1.37284i
$385$		0			0
$386$	383.257			0.992894
$387$	−306.587	+	601.710i	−0.792213	+	1.55481i
$388$	280.383	−	44.4083i	0.722636	−	0.114454i
$389$	246.055	+	338.666i	0.632533	+	0.870607i	0.998190	−	0.0601430i	$-0.0191557\pi$
$389$	246.055	+	338.666i	0.632533	+	0.870607i	−0.365657	+	0.930750i	$0.619156\pi$
$390$		0			0
$391$	43.4506	−	133.727i	0.111127	−	0.342013i
$392$	−346.987	−	54.9574i	−0.885172	−	0.140197i
$393$	999.397	−	158.289i	2.54299	−	0.402771i
$394$	−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	$0.0320048\pi$
$397$	434.845	+	434.845i	1.09533	+	1.09533i	0.100377	+	0.994950i	$0.467995\pi$
$398$	243.210	+	123.922i	0.611080	+	0.311361i
$399$	93.7764	−	129.072i	0.235028	−	0.323489i
$400$		0			0
$401$	−166.418	+	512.181i	−0.415007	+	1.27726i	0.497238	+	0.867614i	$0.334347\pi$
$401$	−166.418	+	512.181i	−0.415007	+	1.27726i	−0.912245	+	0.409645i	$0.865653\pi$
$402$	−433.350	+	220.803i	−1.07799	+	0.549261i
$403$	−31.9439	+	201.686i	−0.0792652	+	0.500461i
$404$	50.8537	−	69.9942i	0.125876	−	0.173253i
$405$		0			0
$406$	−101.158			−0.249158
$407$	1.98023	−	0.811709i	0.00486544	−	0.00199437i
$408$	154.086	−	154.086i	0.377663	−	0.377663i
$409$	2.27154	−	0.738069i	0.00555390	−	0.00180457i	−0.306239	−	0.951955i	$-0.599071\pi$
$409$	2.27154	−	0.738069i	0.00555390	−	0.00180457i	0.311793	+	0.950150i	$0.399071\pi$
$410$		0			0
$411$	−37.8072	+	27.4686i	−0.0919884	+	0.0668335i
$412$	−169.117	+	86.1696i	−0.410479	+	0.209150i
$413$	2.12908	+	4.17855i	0.00515515	+	0.0101175i
$414$	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
$418$	−154.370	−	95.3816i	−0.369305	−	0.228186i
$419$		−	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	0.990942	−	0.134293i	$-0.0428762\pi$
$421$	492.334	+	357.702i	1.16944	+	0.849648i	0.178498	+	0.983940i	$0.442876\pi$
$422$	−175.086	−	27.7309i	−0.414895	−	0.0657129i
$423$	−542.935	−	1065.57i	−1.28353	−	2.51908i
$424$	41.5817	+	13.5107i	0.0980702	+	0.0318649i
$425$		0			0
$426$	−8.51771	−	6.18848i	−0.0199946	−	0.0145270i
$427$	−105.385	+	206.830i	−0.246803	+	0.484378i
$428$	−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	−0.984273	−	0.176652i	$-0.943473\pi$
$431$	−125.771	−	387.085i	−0.291813	−	0.898108i	0.692460	−	0.721456i	$-0.256527\pi$
$432$	−17.6440	−	111.400i	−0.0408426	−	0.257870i
$433$	−80.5214	+	508.392i	−0.185962	+	1.17412i	0.701306	+	0.712861i	$0.252601\pi$
$433$	−80.5214	+	508.392i	−0.185962	+	1.17412i	−0.887267	+	0.461255i	$0.847399\pi$
$434$	−27.1285	−	8.81458i	−0.0625080	−	0.0203101i
$435$		0			0
$436$	−321.171	+	233.344i	−0.736631	+	0.535194i
$437$	−63.5531	−	401.258i	−0.145430	−	0.918211i
$438$	−549.419	−	279.943i	−1.25438	−	0.639139i
$439$		−	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
$442$	43.1377	−	84.6626i	0.0975967	−	0.191544i
$443$	−7.34858	+	1.16390i	−0.0165882	+	0.00262732i	−0.164723	−	0.986340i	$-0.552673\pi$
$443$	−7.34858	+	1.16390i	−0.0165882	+	0.00262732i	0.148135	+	0.988967i	$0.452673\pi$
$444$	1.72445	+	2.37351i	0.00388390	+	0.00534573i
$445$		0			0
$446$	−50.5920	+	155.706i	−0.113435	+	0.349117i
$447$	−455.487	−	72.1421i	−1.01899	−	0.161392i
$448$	65.0380	−	10.3010i	0.145174	−	0.0229933i
$449$	−175.258	+	56.9447i	−0.390329	+	0.126826i	−0.497605	−	0.867404i	$-0.665787\pi$
$449$	−175.258	+	56.9447i	−0.390329	+	0.126826i	0.107276	+	0.994229i	$0.465787\pi$
$450$		0			0
$451$	479.490	+	39.5139i	1.06317	+	0.0876141i
$452$	245.087	+	245.087i	0.542229	+	0.542229i
$453$	−469.082	−	239.009i	−1.03550	−	0.527614i
$454$	−0.705374	+	0.970864i	−0.00155369	+	0.00213847i
$455$		0			0
$456$	194.560	−	598.793i	0.426666	−	1.31314i
$457$	−209.215	+	106.600i	−0.457800	+	0.233261i	−0.667654	−	0.744472i	$-0.732701\pi$
$457$	−209.215	+	106.600i	−0.457800	+	0.233261i	0.209854	+	0.977733i	$0.432701\pi$
$458$	1.62042	−	10.2310i	0.00353804	−	0.0223383i
$459$	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	$0.700277\pi$
$462$	−11.0385	−	147.185i	−0.0238928	−	0.318582i
$463$	48.2381	−	48.2381i	0.104186	−	0.104186i	−0.653092	−	0.757278i	$-0.726529\pi$
$463$	48.2381	−	48.2381i	0.104186	−	0.104186i	0.757278	+	0.653092i	$0.226529\pi$
$464$	52.8090	−	17.1587i	0.113813	−	0.0369799i
$465$		0			0
$466$	−396.388	+	287.993i	−0.850619	+	0.618011i
$467$	559.339	−	284.997i	1.19773	−	0.610272i	0.262710	−	0.964875i	$-0.415384\pi$
$467$	559.339	−	284.997i	1.19773	−	0.610272i	0.935017	+	0.354602i	$0.115384\pi$
$468$	−479.934	−	941.924i	−1.02550	−	2.01266i
$469$	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
$473$	72.4177	−	296.821i	0.153103	−	0.627529i
$474$			343.018i			0.723666i
$475$		0			0
$476$	−20.2211	−	14.6915i	−0.0424812	−	0.0308644i
$477$	134.801	+	21.3503i	0.282601	+	0.0447595i
$478$	153.477	+	301.216i	0.321082	+	0.630159i
$479$	553.115	+	179.718i	1.15473	+	0.375194i	0.822922	−	0.568154i	$-0.192342\pi$
$479$	553.115	+	179.718i	1.15473	+	0.375194i	0.331806	+	0.943348i	$0.392342\pi$
$480$		0			0
$481$	2.61951	+	1.90319i	0.00544598	+	0.00395673i
$482$	169.530	−	332.722i	0.351723	−	0.690295i
$483$	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
$487$	−27.2780	−	172.226i	−0.0560122	−	0.353647i	−0.999737	−	0.0229166i	$-0.992705\pi$
$487$	−27.2780	−	172.226i	−0.0560122	−	0.353647i	0.943725	−	0.330731i	$-0.107295\pi$
$488$	−143.305	+	904.789i	−0.293657	+	1.85408i
$489$	1258.40	+	408.878i	2.57341	+	0.836152i
$490$		0			0
$491$	−216.106	+	157.010i	−0.440134	+	0.319776i	−0.785688	−	0.618623i	$-0.787691\pi$
$491$	−216.106	+	157.010i	−0.440134	+	0.319776i	0.345554	+	0.938399i	$0.387691\pi$
$492$	103.174	+	651.418i	0.209704	+	1.32402i
$493$	187.932	+	95.7559i	0.381200	+	0.194231i
$494$		−	274.537i		−	0.555744i
$495$		0			0
$496$	15.6574			0.0315673
$497$	−1.38764	+	2.72341i	−0.00279204	+	0.00547969i
$498$	93.7890	−	14.8547i	0.188331	−	0.0298287i
$499$	−552.387	−	760.296i	−1.10699	−	1.52364i	−0.825781	−	0.563991i	$-0.809265\pi$
$499$	−552.387	−	760.296i	−1.10699	−	1.52364i	−0.281207	−	0.959647i	$-0.590735\pi$
$500$		0			0
$501$	184.269	−	567.122i	0.367802	−	1.13198i
$502$	81.2608	+	12.8704i	0.161874	+	0.0256383i
$503$	−511.045	+	80.9416i	−1.01599	+	0.160918i	−0.642154	−	0.766576i	$-0.721959\pi$
$503$	−511.045	+	80.9416i	−1.01599	+	0.160918i	−0.373840	+	0.927493i	$0.621959\pi$
$504$	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
$508$	−136.866	−	69.7366i	−0.269421	−	0.137277i
$509$	359.646	−	495.010i	0.706573	−	0.972515i	−0.293291	−	0.956023i	$-0.594750\pi$
$509$	359.646	−	495.010i	0.706573	−	0.972515i	0.999864	−	0.0164915i	$-0.00524964\pi$
$510$		0			0
$511$	−55.3186	+	170.253i	−0.108256	+	0.333177i
$512$	−72.5562	+	36.9692i	−0.141711	+	0.0722055i
$513$	193.645	−	1222.62i	0.377475	−	2.38328i
$514$	199.951	−	275.208i	0.389009	−	0.535425i
$515$		0			0
$516$	418.834			0.811693
$517$	349.873	+	412.716i	0.676736	+	0.798291i
$518$	−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	−0.463526	+	0.886083i	$0.653416\pi$
$521$	−755.178	+	548.669i	−1.44948	+	1.05311i	−0.985953	+	0.167025i	$0.946584\pi$
$522$	−1110.33	+	565.742i	−2.12707	+	1.08380i
$523$	168.115	+	329.945i	0.321444	+	0.630870i	0.994025	−	0.109154i	$-0.0348141\pi$
$523$	168.115	+	329.945i	0.321444	+	0.630870i	−0.672581	+	0.740024i	$0.734814\pi$
$524$	−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
$528$	30.7284	+	74.9646i	0.0581977	+	0.141978i
$529$		−	312.462i		−	0.590666i
$530$		0			0
$531$	46.7383	+	33.9574i	0.0880194	+	0.0639498i
$532$	−71.3275	−	11.2972i	−0.134074	−	0.0212353i
$533$	330.459	+	648.562i	0.619997	+	1.21681i
$534$	521.512	+	169.450i	0.976615	+	0.317321i
$535$		0			0
$536$	450.794	+	327.521i	0.841033	+	0.611046i
$537$	−223.802	+	439.236i	−0.416763	+	0.817944i
$538$	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	−0.994579	−	0.103986i	$-0.966840\pi$
$541$	−135.828	−	418.036i	−0.251069	−	0.772711i	0.743510	−	0.668725i	$-0.233160\pi$
$542$	−17.3463	−	109.520i	−0.0320043	−	0.202067i
$543$	144.817	−	914.338i	0.266698	−	1.68386i
$544$	−150.556	−	48.9186i	−0.276757	−	0.0899239i
$545$		0			0
$546$	180.659	−	131.257i	0.330878	−	0.240397i
$547$	−8.50871	−	53.7219i	−0.0155552	−	0.0982119i	0.978689	−	0.205347i	$-0.0658323\pi$
$547$	−8.50871	−	53.7219i	−0.0155552	−	0.0982119i	−0.994244	+	0.107135i	$0.965832\pi$
$548$	18.8478	+	9.60343i	0.0343938	+	0.0175245i
$549$			2859.58i			5.20871i
$550$		0			0
$551$	609.411			1.10601
$552$	592.035	−	1161.93i	1.07253	−	2.10495i
$553$	98.3564	−	15.5781i	0.177860	−	0.0281702i
$554$	−160.127	−	220.397i	−0.289039	−	0.397828i
$555$		0			0
$556$	−109.810	+	337.960i	−0.197500	+	0.607841i
$557$	−518.636	−	82.1439i	−0.931124	−	0.147476i	−0.327596	−	0.944818i	$-0.606239\pi$
$557$	−518.636	−	82.1439i	−0.931124	−	0.147476i	−0.603527	+	0.797342i	$0.706239\pi$
$558$	−347.064	+	54.9696i	−0.621979	+	0.0985118i
$559$	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
$563$	−678.778	−	345.855i	−1.20565	−	0.614307i	−0.268511	−	0.963277i	$-0.586532\pi$
$563$	−678.778	−	345.855i	−1.20565	−	0.614307i	−0.937134	+	0.348970i	$0.886532\pi$
$564$	−435.968	+	600.058i	−0.772993	+	1.06393i
$565$		0			0
$566$	−62.0303	+	190.910i	−0.109594	+	0.337296i
$567$	512.316	−	261.038i	0.903556	−	0.460385i
$568$	−1.88695	+	11.9137i	−0.00332209	+	0.0209748i
$569$	−522.049	+	718.539i	−0.917485	+	1.26281i	0.0470600	+	0.998892i	$0.485015\pi$
$569$	−522.049	+	718.539i	−0.917485	+	1.26281i	−0.964545	+	0.263918i	$0.914985\pi$
$570$		0			0
$571$	−943.557			−1.65246			−0.826232	−	0.563330i	$-0.809520\pi$
$571$	−943.557			−1.65246			−0.826232	+	0.563330i	$0.809520\pi$
$572$	309.275	+	364.826i	0.540690	+	0.637808i
$573$	−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
$577$	−116.315	+	59.2654i	−0.201585	+	0.102713i	−0.551869	−	0.833931i	$-0.686085\pi$
$577$	−116.315	+	59.2654i	−0.201585	+	0.102713i	0.350284	+	0.936644i	$0.386085\pi$
$578$	141.977	+	278.646i	0.245635	+	0.482087i
$579$	−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
$583$	−61.5741	+	4.61789i	−0.105616	+	0.00792091i
$584$			706.455i			1.20968i
$585$		0			0
$586$	−259.198	−	188.318i	−0.442317	−	0.321362i
$587$	−620.273	−	98.2417i	−1.05668	−	0.167362i	−0.396171	−	0.918177i	$-0.629661\pi$
$587$	−620.273	−	98.2417i	−1.05668	−	0.167362i	−0.660513	+	0.750815i	$0.729661\pi$
$588$	308.781	+	606.017i	0.525138	+	1.03064i
$589$	163.431	+	53.1019i	0.277472	+	0.0901561i
$590$		0			0
$591$	27.8711	+	20.2496i	0.0471593	+	0.0342632i
$592$	0.112713	−	0.221212i	0.000190394	−	0.000373669i
$593$	−543.917	+	543.917i	−0.917229	+	0.917229i	−0.996827	−	0.0795984i	$-0.974636\pi$
$593$	−543.917	+	543.917i	−0.917229	+	0.917229i	0.0795984	+	0.996827i	$0.474636\pi$
$594$	−594.763	−	978.636i	−1.00128	−	1.64754i
$595$		0			0
$596$	64.5062	+	198.530i	0.108232	+	0.333103i
$597$	−209.239	−	1321.08i	−0.350484	−	2.21287i
$598$	88.9538	−	561.632i	0.148752	−	0.939184i
$599$	−955.576	−	310.485i	−1.59529	−	0.518340i	−0.629350	−	0.777122i	$-0.716679\pi$
$599$	−955.576	−	310.485i	−1.59529	−	0.518340i	−0.965936	+	0.258783i	$0.916679\pi$
$600$		0			0
$601$	−211.574	+	153.717i	−0.352036	+	0.255769i	−0.749723	−	0.661752i	$-0.769813\pi$
$601$	−211.574	+	153.717i	−0.352036	+	0.255769i	0.397686	+	0.917521i	$0.369813\pi$
$602$	10.1011	+	63.7758i	0.0167792	+	0.105940i
$603$	1549.80	+	789.663i	2.57015	+	1.30956i
$604$			238.303i			0.394542i
$605$		0			0
$606$	225.135			0.371509
$607$	−413.211	+	810.971i	−0.680742	+	1.33603i	0.249245	+	0.968440i	$0.419817\pi$
$607$	−413.211	+	810.971i	−0.680742	+	1.33603i	−0.929987	+	0.367591i	$0.880183\pi$
$608$	−451.754	+	71.5509i	−0.743017	+	0.117682i
$609$	291.360	+	401.022i	0.478423	+	0.658493i
$610$		0			0
$611$	−252.958	+	778.525i	−0.414007	+	1.27418i
$612$	−304.114	−	48.1670i	−0.496919	−	0.0787042i
$613$	765.368	−	121.222i	1.24856	−	0.197753i	0.503057	−	0.864254i	$-0.332209\pi$
$613$	765.368	−	121.222i	1.24856	−	0.197753i	0.745504	+	0.666501i	$0.232209\pi$
$614$	−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	0.521682	−	0.853140i	$-0.325305\pi$
$617$	−204.509	−	204.509i	−0.331457	−	0.331457i	−0.853140	+	0.521682i	$0.825305\pi$
$618$	−440.075	−	224.229i	−0.712095	−	0.362831i
$619$	149.114	−	205.237i	0.240894	−	0.331563i	−0.671402	−	0.741093i	$-0.734308\pi$
$619$	149.114	−	205.237i	0.240894	−	0.331563i	0.912296	+	0.409531i	$0.134308\pi$
$620$		0			0
$621$	792.293	−	2438.43i	1.27583	−	3.92661i
$622$	50.7894	−	25.8785i	0.0816550	−	0.0416053i
$623$	24.9033	−	157.233i	0.0399732	−	0.252381i
$624$	−72.0479	+	99.1655i	−0.115461	+	0.158919i
$625$		0			0
$626$	−39.1586			−0.0625537
$627$	66.4994	+	886.691i	0.106060	+	1.41418i
$628$	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	0.407204	−	0.913337i	$-0.366504\pi$
$631$	884.455	−	642.594i	1.40167	−	1.01837i	0.994468	−	0.105038i	$-0.0334963\pi$
$632$	350.154	−	178.413i	0.554042	−	0.282298i
$633$	394.355	+	773.965i	0.622994	+	1.22269i
$634$	−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
$638$	430.054	−	364.570i	0.674066	−	0.571427i
$639$			37.6532i			0.0589253i
$640$		0			0
$641$	−327.130	−	237.674i	−0.510343	−	0.370786i	0.302610	−	0.953114i	$-0.402142\pi$
$641$	−327.130	−	237.674i	−0.510343	−	0.370786i	−0.812954	+	0.582328i	$0.802142\pi$
$642$	−325.400	−	51.5383i	−0.506853	−	0.0802777i
$643$	131.198	+	257.491i	0.204040	+	0.400452i	0.970238	−	0.242153i	$-0.0778536\pi$
$643$	131.198	+	257.491i	0.204040	+	0.400452i	−0.766198	+	0.642605i	$0.777854\pi$
$644$	−142.257	−	46.2221i	−0.220896	−	0.0717735i
$645$		0			0
$646$	−64.6906	−	47.0005i	−0.100140	−	0.0727562i
$647$	−228.056	+	447.585i	−0.352482	+	0.691785i	−0.997369	−	0.0724932i	$-0.976904\pi$
$647$	−228.056	+	447.585i	−0.352482	+	0.691785i	0.644887	+	0.764278i	$0.276904\pi$
$648$	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
$652$	−93.6929	−	591.554i	−0.143701	−	0.907291i
$653$	−121.449	+	766.801i	−0.185987	+	1.17427i	0.701235	+	0.712930i	$0.252632\pi$
$653$	−121.449	+	766.801i	−0.185987	+	1.17427i	−0.887222	+	0.461343i	$0.847368\pi$
$654$	−982.479	−	319.227i	−1.50226	−	0.488114i
$655$		0			0
$656$	45.1536	−	32.8060i	0.0688318	−	0.0500092i
$657$	344.979	+	2178.11i	0.525082	+	3.31524i
$658$	−101.885	−	51.9132i	−0.154841	−	0.0788954i
$659$			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	$0.498505\pi$
$662$	−61.2428	+	120.196i	−0.0925119	+	0.181565i
$663$	−459.875	+	72.8371i	−0.693628	+	0.109860i
$664$	−63.9459	−	88.0139i	−0.0963040	−	0.132551i
$665$		0			0
$666$	−1.72179	+	5.29913i	−0.00258527	+	0.00795665i
$667$	1246.70	+	197.457i	1.86911	+	0.296038i
$668$	−266.595	+	42.2246i	−0.399095	+	0.0632104i
$669$	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
$673$	−735.139	−	374.572i	−1.09233	−	0.556570i	−0.187467	−	0.982271i	$-0.560028\pi$
$673$	−735.139	−	374.572i	−1.09233	−	0.556570i	−0.904864	+	0.425701i	$0.860028\pi$
$674$	87.8330	−	120.892i	0.130316	−	0.179365i
$675$		0			0
$676$	−87.1657	+	268.269i	−0.128943	+	0.396847i
$677$	901.999	−	459.592i	1.33235	−	0.678865i	0.364689	−	0.931129i	$-0.381175\pi$
$677$	901.999	−	459.592i	1.33235	−	0.678865i	0.967658	+	0.252264i	$0.0811753\pi$
$678$	−141.093	+	890.828i	−0.208102	+	1.31391i
$679$	126.053	−	173.498i	0.185646	−	0.255519i
$680$		0			0
$681$	5.88044			0.00863501
$682$	147.099	−	60.2966i	0.215687	−	0.0884114i
$683$	−229.153	+	229.153i	−0.335510	+	0.335510i	−0.854674	−	0.519164i	$-0.826243\pi$
$683$	−229.153	+	229.153i	−0.335510	+	0.335510i	0.519164	+	0.854674i	$0.326243\pi$
$684$	−846.086	+	274.910i	−1.23697	+	0.401915i
$685$		0			0
$686$	−176.989	+	128.590i	−0.258002	+	0.187449i
$687$	−45.2258	+	23.0437i	−0.0658309	+	0.0335425i
$688$	−16.0910	−	31.5804i	−0.0233881	−	0.0459017i
$689$	−54.9106	−	75.5779i	−0.0796960	−	0.109692i
$690$		0			0
$691$	−74.3036	−	228.683i	−0.107531	−	0.330945i	0.882786	−	0.469776i	$-0.155665\pi$
$691$	−74.3036	−	228.683i	−0.107531	−	0.330945i	−0.990316	+	0.138831i	$0.955665\pi$
$692$	11.9047	+	11.9047i	0.0172033	+	0.0172033i
$693$	−402.647	+	341.337i	−0.581021	+	0.492549i
$694$		−	177.328i		−	0.255516i
$695$		0			0
$696$	1582.57	+	1149.81i	2.27381	+	1.65202i
$697$	209.398	+	33.1654i	0.300427	+	0.0475830i
$698$	186.784	+	366.583i	0.267598	+	0.525191i
$699$	2283.39	+	741.917i	3.26665	+	1.06140i
$700$		0			0
$701$	198.550	+	144.255i	0.283238	+	0.205785i	0.720329	−	0.693633i	$-0.243991\pi$
$701$	198.550	+	144.255i	0.283238	+	0.205785i	−0.437090	+	0.899418i	$0.643991\pi$
$702$	786.588	−	1543.77i	1.12050	−	2.19910i
$703$	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
$707$	−10.2245	−	64.5548i	−0.0144618	−	0.0913081i
$708$	5.60509	−	35.3892i	0.00791680	−	0.0499847i
$709$	−853.145	−	277.204i	−1.20331	−	0.390979i	−0.362331	−	0.932049i	$-0.618019\pi$
$709$	−853.145	−	277.204i	−1.20331	−	0.390979i	−0.840977	+	0.541071i	$0.818019\pi$
$710$		0			0
$711$	992.456	−	721.062i	1.39586	−	1.01415i
$712$	−98.2772	−	620.498i	−0.138030	−	0.871486i
$713$	317.131	+	161.587i	0.444785	+	0.226629i
$714$		−	65.0406i		−	0.0910933i
$715$		0			0
$716$	223.141			0.311649
$717$	752.061	−	1476.00i	1.04890	−	2.05858i
$718$	565.928	−	89.6341i	0.788200	−	0.124839i
$719$	−119.555	−	164.554i	−0.166280	−	0.228865i	0.717743	−	0.696308i	$-0.245175\pi$
$719$	−119.555	−	164.554i	−0.166280	−	0.228865i	−0.884023	+	0.467443i	$0.845175\pi$
$720$		0			0
$721$	−44.3092	+	136.370i	−0.0614552	+	0.189140i
$722$	191.790	+	30.3766i	0.265638	+	0.0420729i
$723$	−1807.30	+	286.248i	−2.49972	+	0.395917i
$724$	−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	0.915486	−	0.402349i	$-0.131806\pi$
$727$	373.051	+	373.051i	0.513137	+	0.513137i	−0.402349	+	0.915486i	$0.631806\pi$
$728$	−227.953	−	116.148i	−0.313122	−	0.159544i
$729$	1464.67	−	2015.94i	2.00915	−	2.76535i
$730$		0			0
$731$	41.6041	−	128.044i	0.0569140	−	0.175163i
$732$	1580.22	−	805.164i	2.15878	−	1.09995i
$733$	−79.5625	+	502.338i	−0.108544	+	0.685318i	0.872072	+	0.489377i	$0.162776\pi$
$733$	−79.5625	+	502.338i	−0.108544	+	0.685318i	−0.980616	+	0.195940i	$0.937224\pi$
$734$	6.60676	−	9.09342i	0.00900103	−	0.0123889i
$735$		0			0
$736$	−947.355			−1.28717
$737$	−764.512	−	186.523i	−1.03733	−	0.253085i
$738$	−885.708	+	885.708i	−1.20015	+	1.20015i
$739$	334.582	−	108.712i	0.452750	−	0.147107i	−0.0737605	−	0.997276i	$-0.523500\pi$
$739$	334.582	−	108.712i	0.452750	−	0.147107i	0.526511	+	0.850169i	$0.323500\pi$
$740$		0			0
$741$	−1088.35	+	790.733i	−1.46876	+	1.06712i
$742$	11.6274	−	5.92445i	0.0156703	−	0.00798444i
$743$	−523.897	−	1028.21i	−0.705110	−	1.38386i	−0.913918	−	0.405900i	$-0.866958\pi$
$743$	−523.897	−	1028.21i	−0.705110	−	1.38386i	0.208807	−	0.977957i	$-0.433042\pi$
$744$	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
$748$	138.913	−	10.4181i	0.185713	−	0.0139280i
$749$			95.6453i			0.127697i
$750$		0			0
$751$	−199.691	−	145.084i	−0.265900	−	0.193188i	0.446844	−	0.894612i	$-0.352548\pi$
$751$	−199.691	−	145.084i	−0.265900	−	0.193188i	−0.712744	+	0.701424i	$0.752548\pi$
$752$	61.9942	+	9.81892i	0.0824391	+	0.0130571i
$753$	−183.028	−	359.213i	−0.243065	−	0.477042i
$754$	811.230	+	263.585i	1.07590	+	0.349582i
$755$		0			0
$756$	−368.718	−	267.889i	−0.487722	−	0.354351i
$757$	526.866	−	1034.03i	0.695992	−	1.36596i	−0.224220	−	0.974539i	$-0.571983\pi$
$757$	526.866	−	1034.03i	0.695992	−	1.36596i	0.920211	−	0.391422i	$-0.128017\pi$
$758$	−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	0.999398	+	0.0346936i	$0.0110455\pi$
$761$	160.769	+	494.797i	0.211260	+	0.650193i	−0.788138	+	0.615499i	$0.788954\pi$
$762$	−62.5295	−	394.796i	−0.0820597	−	0.518104i
$763$	−46.9154	+	296.212i	−0.0614881	+	0.388221i
$764$	322.943	+	104.930i	0.422700	+	0.137344i
$765$		0			0
$766$	83.4131	−	60.6031i	0.108894	−	0.0791164i
$767$	−6.18605	−	39.0572i	−0.00806525	−	0.0509220i
$768$	−1239.58	−	631.596i	−1.61403	−	0.822390i
$769$		−	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
$772$	−385.930	+	757.431i	−0.499910	+	0.981129i
$773$	686.852	−	108.787i	0.888553	−	0.140733i	0.304561	−	0.952493i	$-0.401490\pi$
$773$	686.852	−	108.787i	0.888553	−	0.140733i	0.583992	+	0.811760i	$0.301490\pi$
$774$	467.548	+	643.524i	0.604067	+	0.831426i
$775$		0			0
$776$	261.525	−	804.893i	0.337017	−	1.03723i
$777$	2.18906	+	0.346712i	0.00281732	+	0.000446219i
$778$	487.006	−	77.1342i	0.625972	−	0.0991443i
$779$	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
$783$	3426.81	+	1746.05i	4.37651	+	2.22994i
$784$	33.8312	−	46.5647i	0.0431521	−	0.0593938i
$785$		0			0
$786$	368.300	−	1133.51i	0.468574	−	1.44212i
$787$	134.719	−	68.6427i	0.171180	−	0.0872207i	−0.366301	−	0.930496i	$-0.619376\pi$
$787$	134.719	−	68.6427i	0.171180	−	0.0872207i	0.537481	+	0.843276i	$0.319376\pi$
$788$	2.43945	−	15.4021i	0.00309575	−	0.0195458i
$789$	32.2399	−	44.3745i	0.0408618	−	0.0562414i
$790$		0			0
$791$	261.843			0.331027
$792$	−1094.96	+	1772.13i	−1.38253	+	2.23754i
$793$	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
$797$	−1099.39	+	560.165i	−1.37941	+	0.702842i	−0.977123	−	0.212674i	$-0.931783\pi$
$797$	−1099.39	+	560.165i	−1.37941	+	0.702842i	−0.402282	+	0.915516i	$0.631783\pi$
$798$	−85.3144	−	167.439i	−0.106910	−	0.209823i
$799$	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
$803$	−378.410	−	923.164i	−0.471245	−	1.14964i
$804$		−	1078.77i		−	1.34176i
$805$		0			0
$806$	194.587	+	141.376i	0.241423	+	0.175404i
$807$	−598.205	−	94.7463i	−0.741270	−	0.117406i
$808$	−117.098	−	229.819i	−0.144924	−	0.284429i
$809$	−896.054	−	291.145i	−1.10761	−	0.359883i	−0.302581	−	0.953124i	$-0.597848\pi$
$809$	−896.054	−	291.145i	−1.10761	−	0.359883i	−0.805025	+	0.593241i	$0.797848\pi$
$810$		0			0
$811$	972.098	+	706.271i	1.19864	+	0.870864i	0.994150	−	0.108005i	$-0.0344461\pi$
$811$	972.098	+	706.271i	1.19864	+	0.870864i	0.204491	+	0.978868i	$0.434446\pi$
$812$	101.864	−	199.919i	0.125448	−	0.246206i
$813$	−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
$817$	−60.8524	−	384.207i	−0.0744827	−	0.470265i
$818$	0.440097	−	2.77866i	0.000538015	−	0.00339690i
$819$	−759.532	−	246.787i	−0.927389	−	0.301327i
$820$		0			0
$821$	805.110	−	584.947i	0.980645	−	0.712481i	0.0227926	−	0.999740i	$-0.492744\pi$
$821$	805.110	−	584.947i	0.980645	−	0.712481i	0.957853	+	0.287260i	$0.0927443\pi$
$822$	8.61093	+	54.3673i	0.0104756	+	0.0661403i
$823$	−161.842	−	82.4626i	−0.196649	−	0.100198i	0.352893	−	0.935664i	$-0.385198\pi$
$823$	−161.842	−	82.4626i	−0.196649	−	0.100198i	−0.549542	+	0.835466i	$0.685198\pi$
$824$			565.858i			0.686721i
$825$		0			0
$826$	5.52389			0.00668752
$827$	−541.252	+	1062.27i	−0.654477	+	1.28448i	0.290352	+	0.956920i	$0.406228\pi$
$827$	−541.252	+	1062.27i	−0.654477	+	1.28448i	−0.944829	+	0.327564i	$0.893772\pi$
$828$	−1819.95	+	288.251i	−2.19800	+	0.348129i
$829$	−529.845	−	729.269i	−0.639137	−	0.879697i	0.359432	−	0.933171i	$-0.382970\pi$
$829$	−529.845	−	729.269i	−0.639137	−	0.879697i	−0.998569	+	0.0534743i	$0.982970\pi$
$830$		0			0
$831$	−412.514	+	1269.59i	−0.496407	+	1.52778i
$832$	−548.408	−	86.8593i	−0.659144	−	0.104398i
$833$	215.942	−	34.2018i	0.259234	−	0.0410586i
$834$	−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
$838$	−247.546	−	126.131i	−0.295401	−	0.150514i
$839$	−588.099	+	809.448i	−0.700952	+	0.964778i	0.298993	+	0.954255i	$0.403349\pi$
$839$	−588.099	+	809.448i	−0.700952	+	0.964778i	−0.999945	+	0.0105222i	$0.996651\pi$
$840$		0			0
$841$	−325.214	+	1000.91i	−0.386700	+	1.19014i
$842$	638.681	−	325.424i	0.758528	−	0.386489i
$843$	−258.607	+	1632.78i	−0.306770	+	1.93687i
$844$	231.112	−	318.098i	0.273829	−	0.376893i
$845$		0			0
$846$	−1408.65			−1.66507
$847$	141.792	−	192.167i	0.167404	−	0.226879i
$848$	−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
$852$	20.8074	−	10.6019i	0.0244219	−	0.0124436i
$853$	−42.5561	−	83.5210i	−0.0498899	−	0.0979145i	0.864716	−	0.502262i	$-0.167499\pi$
$853$	−42.5561	−	83.5210i	−0.0498899	−	0.0979145i	−0.914605	+	0.404347i	$0.867499\pi$
$854$	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	0.334202	−	0.942501i	$-0.391533\pi$
$857$	−521.312	−	521.312i	−0.608299	−	0.608299i	−0.942501	+	0.334202i	$0.891533\pi$
$858$	−294.993	+	1209.10i	−0.343814	+	1.40921i
$859$			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
$862$	−473.500	−	74.9951i	−0.549304	−	0.0870013i
$863$	−318.523	−	625.137i	−0.369088	−	0.724377i	0.629527	−	0.776978i	$-0.283249\pi$
$863$	−318.523	−	625.137i	−0.369088	−	0.724377i	−0.998616	+	0.0526018i	$0.983249\pi$
$864$	−2745.29	−	891.998i	−3.17742	−	1.03241i
$865$		0			0
$866$	490.498	+	356.368i	0.566395	+	0.411510i
$867$	695.710	−	1365.41i	0.802434	−	1.57487i
$868$	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
$872$	185.145	+	1168.96i	0.212322	+	1.34055i
$873$	413.275	−	2609.32i	0.473396	−	2.98891i
$874$	−455.105	−	147.872i	−0.520715	−	0.169190i
$875$		0			0
$876$	1106.50	−	803.922i	1.26313	−	0.917719i
$877$	155.228	+	980.068i	0.176998	+	1.11752i	0.902940	+	0.429767i	$0.141404\pi$
$877$	155.228	+	980.068i	0.176998	+	1.11752i	−0.725941	+	0.687756i	$0.758596\pi$
$878$	−369.488	−	188.264i	−0.420829	−	0.214423i
$879$			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	$0.136559\pi$
$882$	−586.430	+	1150.93i	−0.664887	+	1.30491i
$883$	378.831	−	60.0009i	0.429027	−	0.0679512i	0.0618131	−	0.998088i	$-0.480312\pi$
$883$	378.831	−	60.0009i	0.429027	−	0.0679512i	0.367214	+	0.930137i	$0.380312\pi$
$884$	123.880	+	170.506i	0.140136	+	0.192880i
$885$		0			0
$886$	−2.70811	+	8.33471i	−0.00305656	+	0.00940713i
$887$	−824.162	−	130.534i	−0.929157	−	0.147164i	−0.326530	−	0.945187i	$-0.605879\pi$
$887$	−824.162	−	130.534i	−0.929157	−	0.147164i	−0.602627	+	0.798023i	$0.705879\pi$
$888$	8.63878	−	1.36825i	0.00972836	−	0.00154082i
$889$	−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
$893$	613.791	+	312.742i	0.687336	+	0.350215i
$894$	−319.283	+	439.455i	−0.357140	+	0.491561i
$895$		0			0
$896$	−55.7058	+	171.445i	−0.0621717	+	0.191345i
$897$	−2482.69	+	1264.99i	−2.76777	+	1.41025i
$898$	−33.9550	+	214.384i	−0.0378118	+	0.238734i
$899$	−313.822	+	431.938i	−0.349078	+	0.480465i
$900$		0			0
$901$	−27.2094			−0.0301991
$902$	297.875	−	482.094i	0.330238	−	0.534472i
$903$	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
$907$	379.145	−	193.184i	0.418021	−	0.212992i	−0.232313	−	0.972641i	$-0.574629\pi$
$907$	379.145	−	193.184i	0.418021	−	0.212992i	0.650333	+	0.759649i	$0.274629\pi$
$908$	−1.20842	−	2.37167i	−0.00133086	−	0.00261197i
$909$	−473.258	−	651.384i	−0.520636	−	0.716594i
$910$		0			0
$911$	−488.370	−	1503.05i	−0.536081	−	1.64989i	−0.741301	−	0.671173i	$-0.765791\pi$
$911$	−488.370	−	1503.05i	−0.536081	−	1.64989i	0.205219	−	0.978716i	$-0.434209\pi$
$912$	72.9392	+	72.9392i	0.0799772	+	0.0799772i
$913$	130.706	+	80.7603i	0.143161	+	0.0884559i
$914$			276.574i			0.302598i
$915$		0			0
$916$	18.5877	+	13.5048i	0.0202923	+	0.0147432i
$917$	−341.747	−	54.1274i	−0.372680	−	0.0590266i
$918$	−229.102	−	449.639i	−0.249567	−	0.489802i
$919$	19.2879	+	6.26701i	0.0209879	+	0.00681938i	0.319492	−	0.947589i	$-0.396488\pi$
$919$	19.2879	+	6.26701i	0.0209879	+	0.00681938i	−0.298504	+	0.954408i	$0.596488\pi$
$920$		0			0
$921$	932.718	+	677.660i	1.01272	+	0.735787i
$922$	−290.146	+	569.443i	−0.314692	+	0.617617i
$923$	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
$927$	276.322	+	1744.63i	0.298082	+	1.88201i
$928$	222.306	−	1403.58i	0.239554	−	1.51248i
$929$	−640.531	−	208.121i	−0.689484	−	0.224027i	−0.0567411	−	0.998389i	$-0.518071\pi$
$929$	−640.531	−	208.121i	−0.689484	−	0.224027i	−0.632743	+	0.774362i	$0.718071\pi$
$930$		0			0
$931$	511.052	−	371.301i	0.548928	−	0.398820i
$932$	−170.007	−	1073.38i	−0.182411	−	1.15170i
$933$	−248.876	−	126.809i	−0.266748	−	0.135915i
$934$		−	739.426i		−	0.791677i
$935$		0			0
$936$	−3151.63			−3.36713
$937$	131.549	−	258.180i	0.140394	−	0.275539i	−0.810094	−	0.586300i	$-0.800584\pi$
$937$	131.549	−	258.180i	0.140394	−	0.275539i	0.950488	+	0.310761i	$0.100584\pi$
$938$	164.265	−	26.0170i	0.175123	−	0.0277367i
$939$	112.786	+	155.237i	0.120113	+	0.165321i
$940$		0			0
$941$	−1.31431	+	4.04503i	−0.00139672	+	0.00429865i	−0.951752	−	0.306867i	$-0.900719\pi$
$941$	−1.31431	+	4.04503i	−0.00139672	+	0.00429865i	0.950356	+	0.311166i	$0.100719\pi$
$942$	1693.05	+	268.152i	1.79729	+	0.284663i
$943$	1253.12	−	198.475i	1.32887	−	0.210472i
$944$	−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	0.163410	−	0.986558i	$-0.447751\pi$
$947$	−779.521	−	779.521i	−0.823148	−	0.823148i	−0.986558	+	0.163410i	$0.947751\pi$
$948$	−677.906	−	345.411i	−0.715091	−	0.364357i
$949$	887.246	−	1221.19i	0.934928	−	1.28682i
$950$		0			0
$951$	−484.598	+	1491.44i	−0.509567	+	1.56828i
$952$	−66.3938	+	33.8293i	−0.0697413	+	0.0355350i
$953$	−90.4385	+	571.006i	−0.0948987	+	0.599167i	0.893708	+	0.448648i	$0.148094\pi$
$953$	−90.4385	+	571.006i	−0.0948987	+	0.599167i	−0.988607	+	0.150519i	$0.951906\pi$
$954$	94.4911	−	130.056i	0.0990473	−	0.136327i
$955$		0			0
$956$	−749.841			−0.784352
$957$	−2683.93	−	654.817i	−2.80452	−	0.684239i
$958$	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
$962$	3.39817	−	1.73145i	0.00353240	−	0.00179985i
$963$	534.910	+	1049.82i	0.555463	+	1.09016i
$964$	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	0.764216	−	0.644960i	$-0.223126\pi$
$967$	115.321	+	115.321i	0.119256	+	0.119256i	−0.644960	+	0.764216i	$0.723126\pi$
$968$	297.827	−	894.154i	0.307672	−	0.923713i
$969$			391.826i			0.404361i
$970$		0			0
$971$	−305.877	−	222.233i	−0.315012	−	0.228870i	0.419032	−	0.907971i	$-0.362370\pi$
$971$	−305.877	−	222.233i	−0.315012	−	0.228870i	−0.734044	+	0.679102i	$0.762370\pi$
$972$	−2286.25	−	362.107i	−2.35211	−	0.372538i
$973$	121.874	+	239.190i	0.125256	+	0.245828i
$974$	−195.338	−	63.4691i	−0.200552	−	0.0651634i
$975$		0			0
$976$	−121.420	−	88.2169i	−0.124406	−	0.0903861i
$977$	86.3306	−	169.433i	0.0883629	−	0.173422i	−0.842596	−	0.538547i	$-0.818974\pi$
$977$	86.3306	−	169.433i	0.0883629	−	0.173422i	0.930959	+	0.365125i	$0.118974\pi$
$978$	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
$982$	49.2201	+	310.763i	0.0501223	+	0.316460i
$983$	−195.147	+	1232.11i	−0.198522	+	1.25342i	0.664129	+	0.747618i	$0.268802\pi$
$983$	−195.147	+	1232.11i	−0.198522	+	1.25342i	−0.862651	+	0.505799i	$0.831198\pi$
$984$	1870.02	+	607.606i	1.90043	+	0.617486i
$985$		0			0
$986$	200.991	−	146.029i	0.203845	−	0.148102i
$987$	87.6542	+	553.427i	0.0888087	+	0.560716i
$988$	542.569	+	276.453i	0.549159	+	0.279810i
$989$		−	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	$0.174107\pi$
$992$	181.921	−	357.041i	0.183388	−	0.359920i
$993$	652.887	−	103.407i	0.657490	−	0.104136i
$994$	2.11617	+	2.91266i	0.00212895	+	0.00293024i
$995$		0			0
$996$	−65.0858	+	200.314i	−0.0653472	+	0.201118i
$997$	1170.11	+	185.327i	1.17363	+	0.185885i	0.712646	−	0.701524i	$-0.247497\pi$
$997$	1170.11	+	185.327i	1.17363	+	0.185885i	0.460983	+	0.887409i	$0.347497\pi$
$998$	−1093.32	+	173.164i	−1.09551	+	0.173511i
$999$	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.82.11	yes	128
5.2	odd	4	inner	275.3.bk.c.93.11	yes	128
5.3	odd	4	inner	275.3.bk.c.93.6	yes	128
5.4	even	2	inner	275.3.bk.c.82.6	✓	128
11.9	even	5	inner	275.3.bk.c.207.6	yes	128
55.9	even	10	inner	275.3.bk.c.207.11	yes	128
55.42	odd	20	inner	275.3.bk.c.218.6	yes	128
55.53	odd	20	inner	275.3.bk.c.218.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.6	✓	128	5.4	even	2	inner
275.3.bk.c.82.11	yes	128	1.1	even	1	trivial
275.3.bk.c.93.6	yes	128	5.3	odd	4	inner
275.3.bk.c.93.11	yes	128	5.2	odd	4	inner
275.3.bk.c.207.6	yes	128	11.9	even	5	inner
275.3.bk.c.207.11	yes	128	55.9	even	10	inner
275.3.bk.c.218.6	yes	128	55.42	odd	20	inner
275.3.bk.c.218.11	yes	128	55.53	odd	20	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+(0.534746 - 1.04950i) q^{2} +(-5.70073 + 0.902907i) q^{3} +(1.53565 + 2.11364i) q^{4} +(-2.10084 + 6.46573i) q^{6} +(1.94938 + 0.308752i) q^{7} +(7.69295 - 1.21844i) q^{8} +(23.1236 - 7.51330i) q^{9} +(-9.40014 + 5.71291i) q^{11} +(-10.6627 - 10.6627i) q^{12} +(-14.8284 - 7.55546i) q^{13} +(1.36646 - 1.88077i) q^{14} +(-0.394331 + 1.21363i) q^{16} +(-4.31894 + 2.20061i) q^{17} +(4.48004 - 28.2858i) q^{18} +(-8.23200 + 11.3304i) q^{19} -11.3917 q^{21} +(0.968994 + 12.9204i) q^{22} +(-20.5117 + 20.5117i) q^{23} +(-42.7553 + 13.8920i) q^{24} +(-15.8589 + 11.5221i) q^{26} +(-78.7530 + 40.1266i) q^{27} +(2.34098 + 4.59443i) q^{28} +(-25.5765 - 35.2031i) q^{29} +(-3.79161 - 11.6694i) q^{31} +(23.0930 + 23.0930i) q^{32} +(48.4294 - 41.0552i) q^{33} +5.70948i q^{34} +(51.3900 + 37.3370i) q^{36} +(-0.192163 - 0.0304356i) q^{37} +(7.48918 + 14.6984i) q^{38} +(91.3546 + 29.6829i) q^{39} +(-35.3846 - 25.7084i) q^{41} +(-6.09166 + 11.9555i) q^{42} +(-19.6401 + 19.6401i) q^{43} +(-26.5103 - 11.0955i) q^{44} +(10.5585 + 32.4956i) q^{46} +(-7.69458 - 48.5817i) q^{47} +(1.15218 - 7.27460i) q^{48} +(-42.8970 - 13.9381i) q^{49} +(22.6341 - 16.4447i) q^{51} +(-6.80173 - 42.9444i) q^{52} +(5.00155 + 2.54841i) q^{53} +104.109i q^{54} +15.3727 q^{56} +(36.6981 - 72.0242i) q^{57} +(-50.6225 + 8.01782i) q^{58} +(1.39664 + 1.92231i) q^{59} +(-36.3443 + 111.856i) q^{61} +(-14.2745 - 2.26086i) q^{62} +(47.3964 - 7.50685i) q^{63} +(31.7305 - 10.3099i) q^{64} +(-17.1899 - 72.7807i) q^{66} +(50.5862 + 50.5862i) q^{67} +(-11.2837 - 5.74931i) q^{68} +(98.4116 - 135.452i) q^{69} +(-0.478560 + 1.47286i) q^{71} +(168.734 - 85.9742i) q^{72} +(-14.1887 + 89.5842i) q^{73} +(-0.134700 + 0.185399i) q^{74} -36.5898 q^{76} +(-20.0884 + 8.23433i) q^{77} +(80.0037 - 80.0037i) q^{78} +(47.9857 - 15.5915i) q^{79} +(235.688 - 171.237i) q^{81} +(-45.9027 + 23.3886i) q^{82} +(-6.34114 - 12.4452i) q^{83} +(-17.4936 - 24.0779i) q^{84} +(10.1098 + 31.1147i) q^{86} +(177.590 + 177.590i) q^{87} +(-65.3540 + 55.4026i) q^{88} -80.6579i q^{89} +(-26.5735 - 19.3068i) q^{91} +(-74.8532 - 11.8556i) q^{92} +(32.1513 + 63.1004i) q^{93} +(-55.1010 - 17.9034i) q^{94} +(-152.498 - 110.796i) q^{96} +(49.3293 - 96.8143i) 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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