LMFDB - Embedded newform 350.3.p.c.93.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,3,Mod(93,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.93"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.p (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,4,0,0,-16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.3317760000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			93.2
Root			$-0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	350.93
Dual form			350.3.p.c.207.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 + 1.36603i) q^{2} +(0.636376 - 2.37499i) q^{3} +(-1.73205 + 1.00000i) q^{4} +3.47723 q^{6} +(-6.99656 + 0.219274i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.55863 + 1.47723i) q^{9} +(3.73861 + 6.47547i) q^{11} +(1.27275 + 4.74998i) q^{12} +(10.9545 + 10.9545i) q^{13} +(-2.86045 - 9.47723i) q^{14} +(2.00000 - 3.46410i) q^{16} +(20.4282 + 5.47371i) q^{17} +(-1.08140 + 4.03586i) q^{18} +(12.4982 + 7.21584i) q^{19} +(-3.93168 + 16.7563i) q^{21} +(-7.47723 + 7.47723i) q^{22} +(20.0711 - 5.37803i) q^{23} +(-6.02273 + 3.47723i) q^{24} +(-10.9545 + 18.9737i) q^{26} +(20.7842 - 20.7842i) q^{27} +(11.8991 - 7.37636i) q^{28} -15.8634i q^{29} +(-8.00000 - 13.8564i) q^{31} +(5.46410 + 1.46410i) q^{32} +(17.7583 - 4.75833i) q^{33} +29.9089i q^{34} -5.90890 q^{36} +(17.1865 + 64.1410i) q^{37} +(-5.28236 + 19.7140i) q^{38} +(32.9879 - 19.0455i) q^{39} -27.9545 q^{41} +(-24.3286 + 0.762464i) q^{42} +(-39.6475 - 39.6475i) q^{43} +(-12.9509 - 7.47723i) q^{44} +(14.6931 + 25.4491i) q^{46} +(18.6173 + 69.4806i) q^{47} +(-6.95445 - 6.95445i) q^{48} +(48.9038 - 3.06832i) q^{49} +(26.0000 - 45.0333i) q^{51} +(-29.9281 - 8.01921i) q^{52} +(10.9641 - 40.9185i) q^{53} +(35.9992 + 20.7842i) q^{54} +(14.4317 + 13.5546i) q^{56} +(25.0911 - 25.0911i) q^{57} +(21.6697 - 5.80639i) q^{58} +(-55.8784 + 32.2614i) q^{59} +(-29.5455 + 51.1744i) q^{61} +(16.0000 - 16.0000i) q^{62} +(-18.2255 - 9.77446i) q^{63} +8.00000i q^{64} +(13.0000 + 22.5167i) q^{66} +(-53.5698 - 14.3540i) q^{67} +(-40.8563 + 10.9474i) q^{68} -51.0911i q^{69} -36.3406 q^{71} +(-2.16281 - 8.07171i) q^{72} +(-17.1198 + 63.8921i) q^{73} +(-81.3275 + 46.9545i) q^{74} -28.8634 q^{76} +(-27.5773 - 44.4862i) q^{77} +(38.0911 + 38.0911i) q^{78} +(35.6837 + 20.6020i) q^{79} +(-22.8406 - 39.5610i) q^{81} +(-10.2320 - 38.1865i) q^{82} +(9.12474 + 9.12474i) q^{83} +(-9.94644 - 32.9545i) q^{84} +(39.6475 - 68.6715i) q^{86} +(-37.6753 - 10.0951i) q^{87} +(5.47371 - 20.4282i) q^{88} +(-42.1986 - 24.3634i) q^{89} +(-79.0455 - 74.2415i) q^{91} +(-29.3861 + 29.3861i) q^{92} +(-37.9998 + 10.1820i) q^{93} +(-88.0979 + 50.8634i) q^{94} +(6.95445 - 12.0455i) q^{96} +(63.7723 - 63.7723i) q^{97} +(22.0915 + 65.6808i) q^{98} +22.0911i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{3} - 16 q^{6} + 4 q^{7} - 16 q^{8} + 8 q^{11} + 8 q^{12} + 16 q^{16} + 16 q^{17} - 32 q^{18} + 100 q^{21} - 16 q^{22} + 4 q^{23} + 232 q^{27} + 40 q^{28} - 64 q^{31} + 16 q^{32} + 52 q^{33}+ \cdots + 132 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^3 - 16 * q^6 + 4 * q^7 - 16 * q^8 + 8 * q^11 + 8 * q^12 + 16 * q^16 + 16 * q^17 - 32 * q^18 + 100 * q^21 - 16 * q^22 + 4 * q^23 + 232 * q^27 + 40 * q^28 - 64 * q^31 + 16 * q^32 + 52 * q^33 + 128 * q^36 - 144 * q^37 - 8 * q^38 - 136 * q^41 - 188 * q^42 - 120 * q^43 + 8 * q^46 - 72 * q^47 + 32 * q^48 + 208 * q^51 - 76 * q^53 - 16 * q^56 + 376 * q^57 - 68 * q^58 - 324 * q^61 + 128 * q^62 - 112 * q^63 + 104 * q^66 - 124 * q^67 - 32 * q^68 + 16 * q^71 - 64 * q^72 - 32 * q^73 + 32 * q^76 - 20 * q^77 + 480 * q^78 + 124 * q^81 + 68 * q^82 - 168 * q^83 + 120 * q^86 - 428 * q^87 - 16 * q^88 - 720 * q^91 - 16 * q^92 + 64 * q^93 - 32 * q^96 + 72 * q^97 + 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$3$	0.636376	−	2.37499i	0.212125	−	0.791663i	−0.775033	−	0.631920i	$-0.782267\pi$
$3$	0.636376	−	2.37499i	0.212125	−	0.791663i	0.987159	−	0.159743i	$-0.0510664\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	3.47723			0.579538
$7$	−6.99656	+	0.219274i	−0.999509	+	0.0313248i
$7$	−6.99656	+	0.219274i	−0.999509	+	0.0313248i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	2.55863	+	1.47723i	0.284292	+	0.164136i
$10$		0			0
$11$	3.73861	+	6.47547i	0.339874	+	0.588679i	0.984409	−	0.175896i	$-0.0562823\pi$
$11$	3.73861	+	6.47547i	0.339874	+	0.588679i	−0.644535	+	0.764575i	$0.722949\pi$
$12$	1.27275	+	4.74998i	0.106063	+	0.395832i
$13$	10.9545	+	10.9545i	0.842650	+	0.842650i	0.989203	−	0.146553i	$-0.0468178\pi$
$13$	10.9545	+	10.9545i	0.842650	+	0.842650i	−0.146553	+	0.989203i	$0.546818\pi$
$14$	−2.86045	−	9.47723i	−0.204318	−	0.676945i
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	20.4282	+	5.47371i	1.20166	+	0.321983i	0.803483	−	0.595327i	$-0.202978\pi$
$17$	20.4282	+	5.47371i	1.20166	+	0.321983i	0.398173	+	0.917310i	$0.369644\pi$
$18$	−1.08140	+	4.03586i	−0.0600780	+	0.224214i
$19$	12.4982	+	7.21584i	0.657800	+	0.379781i	0.791438	−	0.611249i	$-0.209333\pi$
$19$	12.4982	+	7.21584i	0.657800	+	0.379781i	−0.133638	+	0.991030i	$0.542666\pi$
$20$		0			0
$21$	−3.93168	+	16.7563i	−0.187223	+	0.797919i
$22$	−7.47723	+	7.47723i	−0.339874	+	0.339874i
$23$	20.0711	−	5.37803i	0.872656	−	0.233828i	0.205420	−	0.978674i	$-0.434144\pi$
$23$	20.0711	−	5.37803i	0.872656	−	0.233828i	0.667236	+	0.744846i	$0.267477\pi$
$24$	−6.02273	+	3.47723i	−0.250947	+	0.144884i
$25$		0			0
$26$	−10.9545	+	18.9737i	−0.421325	+	0.729756i
$27$	20.7842	−	20.7842i	0.769784	−	0.769784i
$28$	11.8991	−	7.37636i	0.424969	−	0.263441i
$29$		−	15.8634i		−	0.547012i	−0.961870	−	0.273506i	$-0.911817\pi$
$29$		−	15.8634i		−	0.547012i	0.961870	−	0.273506i	$-0.0881834\pi$
$30$		0			0
$31$	−8.00000	−	13.8564i	−0.258065	−	0.446981i	0.707659	−	0.706554i	$-0.249751\pi$
$31$	−8.00000	−	13.8564i	−0.258065	−	0.446981i	−0.965723	+	0.259573i	$0.916418\pi$
$32$	5.46410	+	1.46410i	0.170753	+	0.0457532i
$33$	17.7583	−	4.75833i	0.538131	−	0.144192i
$34$			29.9089i			0.879674i
$35$		0			0
$36$	−5.90890			−0.164136
$37$	17.1865	+	64.1410i	0.464501	+	1.73354i	0.658540	+	0.752546i	$0.271174\pi$
$37$	17.1865	+	64.1410i	0.464501	+	1.73354i	−0.194039	+	0.980994i	$0.562159\pi$
$38$	−5.28236	+	19.7140i	−0.139009	+	0.518790i
$39$	32.9879	−	19.0455i	0.845843	−	0.488347i
$40$		0			0
$41$	−27.9545			−0.681816			−0.340908	−	0.940097i	$-0.610734\pi$
$41$	−27.9545			−0.681816			−0.340908	+	0.940097i	$0.610734\pi$
$42$	−24.3286	+	0.762464i	−0.579253	+	0.0181539i
$43$	−39.6475	−	39.6475i	−0.922035	−	0.922035i	0.0751379	−	0.997173i	$-0.476060\pi$
$43$	−39.6475	−	39.6475i	−0.922035	−	0.922035i	−0.997173	+	0.0751379i	$0.976060\pi$
$44$	−12.9509	−	7.47723i	−0.294339	−	0.169937i
$45$		0			0
$46$	14.6931	+	25.4491i	0.319414	+	0.553242i
$47$	18.6173	+	69.4806i	0.396112	+	1.47831i	0.819877	+	0.572539i	$0.194042\pi$
$47$	18.6173	+	69.4806i	0.396112	+	1.47831i	−0.423765	+	0.905772i	$0.639292\pi$
$48$	−6.95445	−	6.95445i	−0.144884	−	0.144884i
$49$	48.9038	−	3.06832i	0.998038	−	0.0626188i
$50$		0			0
$51$	26.0000	−	45.0333i	0.509804	−	0.883006i
$52$	−29.9281	−	8.01921i	−0.575541	−	0.154216i
$53$	10.9641	−	40.9185i	0.206870	−	0.772048i	−0.782002	−	0.623276i	$-0.785801\pi$
$53$	10.9641	−	40.9185i	0.206870	−	0.772048i	0.988872	−	0.148772i	$-0.0475320\pi$
$54$	35.9992	+	20.7842i	0.666652	+	0.384892i
$55$		0			0
$56$	14.4317	+	13.5546i	0.257709	+	0.242046i
$57$	25.0911	−	25.0911i	0.440195	−	0.440195i
$58$	21.6697	−	5.80639i	0.373616	−	0.100110i
$59$	−55.8784	+	32.2614i	−0.947091	+	0.546803i	−0.892176	−	0.451688i	$-0.850822\pi$
$59$	−55.8784	+	32.2614i	−0.947091	+	0.546803i	−0.0549148	+	0.998491i	$0.517489\pi$
$60$		0			0
$61$	−29.5455	+	51.1744i	−0.484353	+	0.838924i	−0.999838	−	0.0179740i	$-0.994278\pi$
$61$	−29.5455	+	51.1744i	−0.484353	+	0.838924i	0.515485	+	0.856898i	$0.327612\pi$
$62$	16.0000	−	16.0000i	0.258065	−	0.258065i
$63$	−18.2255	−	9.77446i	−0.289294	−	0.155150i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	13.0000	+	22.5167i	0.196970	+	0.341162i
$67$	−53.5698	−	14.3540i	−0.799550	−	0.214239i	−0.164163	−	0.986433i	$-0.552492\pi$
$67$	−53.5698	−	14.3540i	−0.799550	−	0.214239i	−0.635386	+	0.772194i	$0.719159\pi$
$68$	−40.8563	+	10.9474i	−0.600828	+	0.160991i
$69$		−	51.0911i		−	0.740451i
$70$		0			0
$71$	−36.3406			−0.511839			−0.255920	−	0.966698i	$-0.582378\pi$
$71$	−36.3406			−0.511839			−0.255920	+	0.966698i	$0.582378\pi$
$72$	−2.16281	−	8.07171i	−0.0300390	−	0.112107i
$73$	−17.1198	+	63.8921i	−0.234518	+	0.875234i	0.743847	+	0.668350i	$0.232999\pi$
$73$	−17.1198	+	63.8921i	−0.234518	+	0.875234i	−0.978365	+	0.206884i	$0.933668\pi$
$74$	−81.3275	+	46.9545i	−1.09902	+	0.634520i
$75$		0			0
$76$	−28.8634			−0.379781
$77$	−27.5773	−	44.4862i	−0.358147	−	0.577743i
$78$	38.0911	+	38.0911i	0.488347	+	0.488347i
$79$	35.6837	+	20.6020i	0.451692	+	0.260784i	0.708544	−	0.705666i	$-0.249352\pi$
$79$	35.6837	+	20.6020i	0.451692	+	0.260784i	−0.256853	+	0.966451i	$0.582686\pi$
$80$		0			0
$81$	−22.8406	−	39.5610i	−0.281982	−	0.488408i
$82$	−10.2320	−	38.1865i	−0.124781	−	0.465689i
$83$	9.12474	+	9.12474i	0.109937	+	0.109937i	0.759935	−	0.649999i	$-0.225231\pi$
$83$	9.12474	+	9.12474i	0.109937	+	0.109937i	−0.649999	+	0.759935i	$0.725231\pi$
$84$	−9.94644	−	32.9545i	−0.118410	−	0.392315i
$85$		0			0
$86$	39.6475	−	68.6715i	0.461018	−	0.798506i
$87$	−37.6753	−	10.0951i	−0.433049	−	0.116035i
$88$	5.47371	−	20.4282i	0.0622012	−	0.232138i
$89$	−42.1986	−	24.3634i	−0.474141	−	0.273746i	0.243830	−	0.969818i	$-0.421596\pi$
$89$	−42.1986	−	24.3634i	−0.474141	−	0.273746i	−0.717972	+	0.696072i	$0.754929\pi$
$90$		0			0
$91$	−79.0455	−	74.2415i	−0.868632	−	0.815841i
$92$	−29.3861	+	29.3861i	−0.319414	+	0.319414i
$93$	−37.9998	+	10.1820i	−0.408600	+	0.109484i
$94$	−88.0979	+	50.8634i	−0.937212	+	0.541100i
$95$		0			0
$96$	6.95445	−	12.0455i	0.0724422	−	0.125474i
$97$	63.7723	−	63.7723i	0.657446	−	0.657446i	−0.297329	−	0.954775i	$-0.596096\pi$
$97$	63.7723	−	63.7723i	0.657446	−	0.657446i	0.954775	+	0.297329i	$0.0960959\pi$
$98$	22.0915	+	65.6808i	0.225423	+	0.670212i
$99$			22.0911i			0.223142i
$100$		0			0
$101$	48.7495	+	84.4366i	0.482668	+	0.836006i	0.999802	−	0.0198988i	$-0.00633440\pi$
$101$	48.7495	+	84.4366i	0.482668	+	0.836006i	−0.517134	+	0.855905i	$0.673001\pi$
$102$	71.0333	+	19.0333i	0.696405	+	0.186601i
$103$	46.8019	−	12.5405i	0.454388	−	0.121753i	−0.0243641	−	0.999703i	$-0.507756\pi$
$103$	46.8019	−	12.5405i	0.454388	−	0.121753i	0.478752	+	0.877950i	$0.341089\pi$
$104$		−	43.8178i		−	0.421325i
$105$		0			0
$106$	59.9089			0.565178
$107$	−42.6126	−	159.032i	−0.398249	−	1.48628i	−0.816176	−	0.577803i	$-0.803910\pi$
$107$	−42.6126	−	159.032i	−0.398249	−	1.48628i	0.417927	−	0.908480i	$-0.362757\pi$
$108$	−15.2151	+	56.7834i	−0.140880	+	0.525772i
$109$	146.122	−	84.3634i	1.34057	−	0.773976i	0.353675	−	0.935368i	$-0.384932\pi$
$109$	146.122	−	84.3634i	1.34057	−	0.773976i	0.986890	+	0.161393i	$0.0515986\pi$
$110$		0			0
$111$	163.271			1.47091
$112$	−13.2335	+	24.6754i	−0.118157	+	0.220316i
$113$	−56.6356	−	56.6356i	−0.501200	−	0.501200i	0.410611	−	0.911811i	$-0.365316\pi$
$113$	−56.6356	−	56.6356i	−0.501200	−	0.501200i	−0.911811	+	0.410611i	$0.865316\pi$
$114$	43.4591	+	25.0911i	0.381220	+	0.220097i
$115$		0			0
$116$	15.8634	+	27.4761i	0.136753	+	0.236863i
$117$	11.8462	+	44.2106i	0.101249	+	0.377868i
$118$	−64.5228	−	64.5228i	−0.546803	−	0.546803i
$119$	−144.127	−	33.8178i	−1.21115	−	0.284183i
$120$		0			0
$121$	32.5455	−	56.3705i	0.268971	−	0.465872i
$122$	−80.7199	−	21.6288i	−0.661639	−	0.177286i
$123$	−17.7896	+	66.3915i	−0.144631	+	0.539768i
$124$	27.7128	+	16.0000i	0.223490	+	0.129032i
$125$		0			0
$126$	6.68116	−	28.4742i	0.0530251	−	0.225986i
$127$	−3.04555	+	3.04555i	−0.0239807	+	0.0239807i	−0.718995	−	0.695015i	$-0.755398\pi$
$127$	−3.04555	+	3.04555i	−0.0239807	+	0.0239807i	0.695015	+	0.718995i	$0.255398\pi$
$128$	−10.9282	+	2.92820i	−0.0853766	+	0.0228766i
$129$	−119.393	+	68.9317i	−0.925528	+	0.534354i
$130$		0			0
$131$	56.9545	−	98.6480i	0.434767	−	0.753038i	−0.562510	−	0.826791i	$-0.690164\pi$
$131$	56.9545	−	98.6480i	0.434767	−	0.753038i	0.997277	+	0.0737524i	$0.0234975\pi$
$132$	−26.0000	+	26.0000i	−0.196970	+	0.196970i
$133$	−89.0267	−	47.7456i	−0.669374	−	0.358989i
$134$		−	78.4317i		−	0.585311i
$135$		0			0
$136$	−29.9089	−	51.8037i	−0.219918	−	0.380910i
$137$	140.390	+	37.6173i	1.02474	+	0.274579i	0.731776	−	0.681545i	$-0.238692\pi$
$137$	140.390	+	37.6173i	1.02474	+	0.274579i	0.292965	+	0.956123i	$0.405358\pi$
$138$	69.7917	−	18.7006i	0.505737	−	0.135512i
$139$		−	177.022i		−	1.27354i	−0.771055	−	0.636769i	$-0.780271\pi$
$139$		−	177.022i		−	1.27354i	0.771055	−	0.636769i	$-0.219729\pi$
$140$		0			0
$141$	176.863			1.25435
$142$	−13.3016	−	49.6422i	−0.0936731	−	0.349593i
$143$	−29.9807	+	111.890i	−0.209656	+	0.782445i
$144$	10.2345	−	5.90890i	0.0710730	−	0.0410340i
$145$		0			0
$146$	−93.5445			−0.640716
$147$	23.8340	−	118.099i	0.162136	−	0.803393i
$148$	−93.9089	−	93.9089i	−0.634520	−	0.634520i
$149$	219.026	+	126.454i	1.46997	+	0.848688i	0.999432	−	0.0336923i	$-0.0107266\pi$
$149$	219.026	+	126.454i	1.46997	+	0.848688i	0.470538	+	0.882380i	$0.344060\pi$
$150$		0			0
$151$	−102.954	−	178.322i	−0.681818	−	1.18094i	−0.974426	−	0.224710i	$-0.927856\pi$
$151$	−102.954	−	178.322i	−0.681818	−	1.18094i	0.292608	−	0.956232i	$-0.405477\pi$
$152$	−10.5647	−	39.4281i	−0.0695047	−	0.259395i
$153$	44.1822	+	44.1822i	0.288773	+	0.288773i
$154$	50.6753	−	53.9545i	0.329061	−	0.350354i
$155$		0			0
$156$	−38.0911	+	65.9757i	−0.244174	+	0.422921i
$157$	−256.004	−	68.5960i	−1.63060	−	0.436917i	−0.676508	−	0.736436i	$-0.736507\pi$
$157$	−256.004	−	68.5960i	−1.63060	−	0.436917i	−0.954091	+	0.299518i	$0.903174\pi$
$158$	−15.0817	+	56.2856i	−0.0954537	+	0.356238i
$159$	−90.2038	−	52.0792i	−0.567320	−	0.327542i
$160$		0			0
$161$	−139.249	+	42.0288i	−0.864904	+	0.261049i
$162$	45.6812	−	45.6812i	0.281982	−	0.281982i
$163$	241.475	−	64.7031i	1.48144	−	0.396952i	0.574606	−	0.818430i	$-0.305155\pi$
$163$	241.475	−	64.7031i	1.48144	−	0.396952i	0.906838	+	0.421479i	$0.138489\pi$
$164$	48.4185	−	27.9545i	0.295235	−	0.170454i
$165$		0			0
$166$	−9.12474	+	15.8045i	−0.0549683	+	0.0952079i
$167$	−8.01191	+	8.01191i	−0.0479755	+	0.0479755i	−0.730688	−	0.682712i	$-0.760800\pi$
$167$	−8.01191	+	8.01191i	−0.0479755	+	0.0479755i	0.682712	+	0.730688i	$0.260800\pi$
$168$	41.3760	−	25.6493i	0.246286	−	0.152674i
$169$			71.0000i			0.420118i
$170$		0			0
$171$	21.3188	+	36.9253i	0.124672	+	0.215938i
$172$	108.319	+	29.0240i	0.629762	+	0.168744i
$173$	−119.961	+	32.1435i	−0.693418	+	0.185801i	−0.588281	−	0.808657i	$-0.700195\pi$
$173$	−119.961	+	32.1435i	−0.693418	+	0.185801i	−0.105138	+	0.994458i	$0.533528\pi$
$174$		−	55.1605i		−	0.317014i
$175$		0			0
$176$	29.9089			0.169937
$177$	41.0608	+	153.241i	0.231982	+	0.865768i
$178$	17.8352	−	66.5619i	0.100198	−	0.373943i
$179$	−114.000	+	65.8178i	−0.636870	+	0.367697i	−0.783408	−	0.621508i	$-0.786520\pi$
$179$	−114.000	+	65.8178i	−0.636870	+	0.367697i	0.146538	+	0.989205i	$0.453187\pi$
$180$		0			0
$181$	−149.681			−0.826968			−0.413484	−	0.910511i	$-0.635688\pi$
$181$	−149.681			−0.826968			−0.413484	+	0.910511i	$0.635688\pi$
$182$	72.4831	−	135.153i	0.398259	−	0.742596i
$183$	102.737	+	102.737i	0.561402	+	0.561402i
$184$	−50.8983	−	29.3861i	−0.276621	−	0.159707i
$185$		0			0
$186$	−27.8178	−	48.1819i	−0.149558	−	0.259042i
$187$	40.9282	+	152.746i	0.218867	+	0.816823i
$188$	−101.727	−	101.727i	−0.541100	−	0.541100i
$189$	−140.860	+	149.975i	−0.745293	+	0.793519i
$190$		0			0
$191$	−113.034	+	195.780i	−0.591799	+	1.02503i	0.402191	+	0.915556i	$0.368249\pi$
$191$	−113.034	+	195.780i	−0.591799	+	1.02503i	−0.993990	+	0.109470i	$0.965085\pi$
$192$	18.9999	+	5.09101i	0.0989579	+	0.0265157i
$193$	57.2326	−	213.595i	0.296542	−	1.10671i	−0.643443	−	0.765494i	$-0.722495\pi$
$193$	57.2326	−	213.595i	0.296542	−	1.10671i	0.939985	−	0.341215i	$-0.110839\pi$
$194$	110.457	+	63.7723i	0.569365	+	0.328723i
$195$		0			0
$196$	−81.6356	+	54.2183i	−0.416508	+	0.276624i
$197$	−84.9089	+	84.9089i	−0.431010	+	0.431010i	−0.888972	−	0.457962i	$-0.848580\pi$
$197$	−84.9089	+	84.9089i	−0.431010	+	0.431010i	0.457962	+	0.888972i	$0.348580\pi$
$198$	−30.1770	+	8.08590i	−0.152409	+	0.0408379i
$199$	−71.4085	+	41.2277i	−0.358837	+	0.207175i	−0.668570	−	0.743649i	$-0.733093\pi$
$199$	−71.4085	+	41.2277i	−0.358837	+	0.207175i	0.309734	+	0.950823i	$0.399760\pi$
$200$		0			0
$201$	−68.1812	+	118.093i	−0.339210	+	0.587529i
$202$	−97.4990	+	97.4990i	−0.482668	+	0.482668i
$203$	3.47841	+	110.989i	0.0171350	+	0.546744i
$204$			104.000i			0.509804i
$205$		0			0
$206$	34.2614	+	59.3425i	0.166317	+	0.288070i
$207$	59.2991	+	15.8891i	0.286469	+	0.0767591i
$208$	59.8562	−	16.0384i	0.287770	−	0.0771078i
$209$			107.909i			0.516311i
$210$		0			0
$211$	205.703			0.974895			0.487448	−	0.873152i	$-0.337928\pi$
$211$	205.703			0.974895			0.487448	+	0.873152i	$0.337928\pi$
$212$	21.9282	+	81.8371i	0.103435	+	0.386024i
$213$	−23.1263	+	86.3085i	−0.108574	+	0.405204i
$214$	201.645	−	116.420i	0.942266	−	0.544018i
$215$		0			0
$216$	−83.1366			−0.384892
$217$	59.0109	+	95.1931i	0.271939	+	0.438678i
$218$	168.727	+	168.727i	0.773976	+	0.773976i
$219$	140.848	+	81.3188i	0.643143	+	0.371319i
$220$		0			0
$221$	163.818	+	283.741i	0.741257	+	1.28389i
$222$	59.7614	+	223.033i	0.269196	+	1.00465i
$223$	−62.8872	−	62.8872i	−0.282005	−	0.282005i	0.551903	−	0.833908i	$-0.313902\pi$
$223$	−62.8872	−	62.8872i	−0.282005	−	0.282005i	−0.833908	+	0.551903i	$0.813902\pi$
$224$	−38.5510	−	9.04555i	−0.172103	−	0.0403819i
$225$		0			0
$226$	56.6356	−	98.0958i	0.250600	−	0.434052i
$227$	−249.547	−	66.8659i	−1.09933	−	0.294564i	−0.336836	−	0.941563i	$-0.609357\pi$
$227$	−249.547	−	66.8659i	−1.09933	−	0.294564i	−0.762490	+	0.647000i	$0.776024\pi$
$228$	−18.3680	+	68.5502i	−0.0805612	+	0.300659i
$229$	106.598	+	61.5445i	0.465494	+	0.268753i	0.714352	−	0.699787i	$-0.246722\pi$
$229$	106.598	+	61.5445i	0.465494	+	0.268753i	−0.248857	+	0.968540i	$0.580055\pi$
$230$		0			0
$231$	−123.204	+	37.1859i	−0.533350	+	0.160978i
$232$	−31.7267	+	31.7267i	−0.136753	+	0.136753i
$233$	−307.851	+	82.4883i	−1.32125	+	0.354027i	−0.849445	−	0.527677i	$-0.823063\pi$
$233$	−307.851	+	82.4883i	−1.32125	+	0.354027i	−0.471802	+	0.881704i	$0.656396\pi$
$234$	−56.0568	+	32.3644i	−0.239559	+	0.138309i
$235$		0			0
$236$	64.5228	−	111.757i	0.273402	−	0.473545i
$237$	71.6377	−	71.6377i	0.302269	−	0.302269i
$238$	−6.55823	−	209.260i	−0.0275556	−	0.879242i
$239$			174.725i			0.731065i	0.930798	+	0.365533i	$0.119113\pi$
$239$			174.725i			0.731065i	−0.930798	+	0.365533i	$0.880887\pi$
$240$		0			0
$241$	121.909	+	211.152i	0.505846	+	0.876151i	0.999977	+	0.00676366i	$0.00215296\pi$
$241$	121.909	+	211.152i	0.505846	+	0.876151i	−0.494131	+	0.869387i	$0.664514\pi$
$242$	88.9161	+	23.8250i	0.367422	+	0.0984504i
$243$	147.033	−	39.3974i	0.605074	−	0.162129i
$244$		−	118.182i		−	0.484353i
$245$		0			0
$246$	−97.2039			−0.395138
$247$	57.8654	+	215.956i	0.234273	+	0.874318i
$248$	−11.7128	+	43.7128i	−0.0472291	+	0.176261i
$249$	27.4779	−	15.8644i	0.110353	−	0.0637124i
$250$		0			0
$251$	54.2733			0.216228			0.108114	−	0.994138i	$-0.465519\pi$
$251$	54.2733			0.216228			0.108114	+	0.994138i	$0.465519\pi$
$252$	41.3420	−	1.29567i	0.164056	−	0.00514153i
$253$	109.863	+	109.863i	0.434243	+	0.434243i
$254$	−5.27505	−	3.04555i	−0.0207679	−	0.0119903i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−5.60709	−	20.9259i	−0.0218175	−	0.0814238i	0.954159	−	0.299301i	$-0.0967535\pi$
$257$	−5.60709	−	20.9259i	−0.0218175	−	0.0814238i	−0.975976	+	0.217877i	$0.930087\pi$
$258$	−137.863	−	137.863i	−0.534354	−	0.534354i
$259$	−134.311	−	444.998i	−0.518575	−	1.71814i
$260$		0			0
$261$	23.4338	−	40.5884i	0.0897845	−	0.155511i
$262$	155.602	+	41.6936i	0.593902	+	0.159136i
$263$	87.0184	−	324.757i	0.330868	−	1.23482i	−0.577411	−	0.816454i	$-0.695937\pi$
$263$	87.0184	−	324.757i	0.330868	−	1.23482i	0.908279	−	0.418364i	$-0.137396\pi$
$264$	−45.0333	−	26.0000i	−0.170581	−	0.0984848i
$265$		0			0
$266$	32.6356	−	139.089i	0.122690	−	0.522890i
$267$	−84.7169	+	84.7169i	−0.317292	+	0.317292i
$268$	107.140	−	28.7080i	0.399775	−	0.107119i
$269$	−93.6867	+	54.0901i	−0.348278	+	0.201078i	−0.663926	−	0.747798i	$-0.731111\pi$
$269$	−93.6867	+	54.0901i	−0.348278	+	0.201078i	0.315649	+	0.948876i	$0.397778\pi$
$270$		0			0
$271$	30.7603	−	53.2785i	0.113507	−	0.196600i	−0.803675	−	0.595068i	$-0.797125\pi$
$271$	30.7603	−	53.2785i	0.113507	−	0.196600i	0.917182	+	0.398469i	$0.130458\pi$
$272$	59.8178	−	59.8178i	0.219918	−	0.219918i
$273$	−226.626	+	140.487i	−0.830130	+	0.514604i
$274$			205.545i			0.750162i
$275$		0			0
$276$	51.0911	+	88.4924i	0.185113	+	0.320625i
$277$	−344.920	−	92.4210i	−1.24520	−	0.333650i	−0.424719	−	0.905325i	$-0.639627\pi$
$277$	−344.920	−	92.4210i	−1.24520	−	0.333650i	−0.820480	+	0.571675i	$0.806294\pi$
$278$	241.816	−	64.7945i	0.869842	−	0.233074i
$279$		−	47.2712i		−	0.169431i
$280$		0			0
$281$	−398.542			−1.41830			−0.709150	−	0.705057i	$-0.750921\pi$
$281$	−398.542			−1.41830			−0.709150	+	0.705057i	$0.750921\pi$
$282$	64.7365	+	241.600i	0.229562	+	0.856737i
$283$	127.393	−	475.436i	0.450151	−	1.67999i	−0.251814	−	0.967776i	$-0.581027\pi$
$283$	127.393	−	475.436i	0.450151	−	1.67999i	0.701965	−	0.712211i	$-0.252306\pi$
$284$	62.9437	−	36.3406i	0.221633	−	0.127960i
$285$		0			0
$286$	−163.818			−0.572790
$287$	195.585	−	6.12967i	0.681481	−	0.0213577i
$288$	11.8178	+	11.8178i	0.0410340	+	0.0410340i
$289$	137.067	+	79.1356i	0.474280	+	0.273826i
$290$		0			0
$291$	−110.875	−	192.042i	−0.381015	−	0.659937i
$292$	−34.2397	−	127.784i	−0.117259	−	0.437617i
$293$	187.818	+	187.818i	0.641016	+	0.641016i	0.950805	−	0.309789i	$-0.100258\pi$
$293$	187.818	+	187.818i	0.641016	+	0.641016i	−0.309789	+	0.950805i	$0.600258\pi$
$294$	170.050	−	10.6693i	0.578400	−	0.0362900i
$295$		0			0
$296$	93.9089	−	162.655i	0.317260	−	0.549510i
$297$	212.291	+	56.8832i	0.714785	+	0.191526i
$298$	−92.5711	+	345.480i	−0.310641	+	1.15933i
$299$	278.781	+	160.954i	0.932379	+	0.538309i
$300$		0			0
$301$	286.090	+	268.703i	0.950465	+	0.892700i
$302$	205.909	−	205.909i	0.681818	−	0.681818i
$303$	231.559	−	62.0460i	0.764221	−	0.204772i
$304$	49.9928	−	28.8634i	0.164450	−	0.0949452i
$305$		0			0
$306$	−44.1822	+	76.5258i	−0.144386	+	0.250084i
$307$	171.398	−	171.398i	0.558300	−	0.558300i	−0.370523	−	0.928823i	$-0.620822\pi$
$307$	171.398	−	171.398i	0.558300	−	0.558300i	0.928823	+	0.370523i	$0.120822\pi$
$308$	92.2516	+	49.4751i	0.299518	+	0.160633i
$309$		−	119.135i		−	0.385549i
$310$		0			0
$311$	1.73861	+	3.01137i	0.00559039	+	0.00968285i	0.868807	−	0.495151i	$-0.164887\pi$
$311$	1.73861	+	3.01137i	0.00559039	+	0.00968285i	−0.863217	+	0.504834i	$0.831554\pi$
$312$	−104.067	−	27.8846i	−0.333547	−	0.0893738i
$313$	20.6120	−	5.52297i	0.0658530	−	0.0176453i	−0.225742	−	0.974187i	$-0.572481\pi$
$313$	20.6120	−	5.52297i	0.0658530	−	0.0176453i	0.291595	+	0.956542i	$0.405814\pi$
$314$		−	374.816i		−	1.19368i
$315$		0			0
$316$	−82.4079			−0.260784
$317$	105.415	+	393.415i	0.332540	+	1.24106i	0.906511	+	0.422182i	$0.138736\pi$
$317$	105.415	+	393.415i	0.332540	+	1.24106i	−0.573971	+	0.818876i	$0.694598\pi$
$318$	38.1246	−	142.283i	0.119889	−	0.447431i
$319$	102.723	−	59.3069i	0.322015	−	0.185915i
$320$		0			0
$321$	−404.818			−1.26111
$322$	−108.381	−	174.835i	−0.336588	−	0.542965i
$323$	215.818	+	215.818i	0.668167	+	0.668167i
$324$	79.1221	+	45.6812i	0.244204	+	0.140991i
$325$		0			0
$326$	176.772	+	306.179i	0.542246	+	0.939198i
$327$	−107.374	−	400.724i	−0.328360	−	1.22546i
$328$	55.9089	+	55.9089i	0.170454	+	0.170454i
$329$	−145.492	−	482.043i	−0.442226	−	1.46518i
$330$		0			0
$331$	210.317	−	364.279i	0.635398	−	1.10054i	−0.351033	−	0.936363i	$-0.614169\pi$
$331$	210.317	−	364.279i	0.635398	−	1.10054i	0.986431	−	0.164179i	$-0.0524973\pi$
$332$	−24.9293	−	6.67977i	−0.0750881	−	0.0201198i
$333$	−50.7767	+	189.501i	−0.152483	+	0.569073i
$334$	−13.8770	−	8.01191i	−0.0415480	−	0.0239877i
$335$		0			0
$336$	50.1822	+	47.1323i	0.149352	+	0.140275i
$337$	34.2712	−	34.2712i	0.101695	−	0.101695i	−0.654429	−	0.756124i	$-0.727091\pi$
$337$	34.2712	−	34.2712i	0.101695	−	0.101695i	0.756124	+	0.654429i	$0.227091\pi$
$338$	−96.9878	+	25.9878i	−0.286946	+	0.0768870i
$339$	−170.551	+	98.4674i	−0.503099	+	0.290464i
$340$		0			0
$341$	59.8178	−	103.607i	0.175419	−	0.303834i
$342$	−42.6377	+	42.6377i	−0.124672	+	0.124672i
$343$	−341.486	+	32.1910i	−0.995586	+	0.0938514i
$344$			158.590i			0.461018i
$345$		0			0
$346$	−87.8178	−	152.105i	−0.253809	−	0.439610i
$347$	139.784	+	37.4549i	0.402834	+	0.107939i	0.454547	−	0.890723i	$-0.349801\pi$
$347$	139.784	+	37.4549i	0.402834	+	0.107939i	−0.0517123	+	0.998662i	$0.516468\pi$
$348$	75.3506	−	20.1901i	0.216525	−	0.0580176i
$349$			248.861i			0.713070i	0.934282	+	0.356535i	$0.116042\pi$
$349$			248.861i			0.713070i	−0.934282	+	0.356535i	$0.883958\pi$
$350$		0			0
$351$	455.358			1.29732
$352$	10.9474	+	40.8563i	0.0311006	+	0.116069i
$353$	−103.352	+	385.714i	−0.292781	+	1.09267i	0.650182	+	0.759778i	$0.274693\pi$
$353$	−103.352	+	385.714i	−0.292781	+	1.09267i	−0.942963	+	0.332896i	$0.891974\pi$
$354$	−194.302	+	112.180i	−0.548875	+	0.316893i
$355$		0			0
$356$	97.4534			0.273746
$357$	−172.036	+	320.780i	−0.481894	+	0.898542i
$358$	−131.636	−	131.636i	−0.367697	−	0.367697i
$359$	−370.734	−	214.043i	−1.03269	−	0.596221i	−0.114933	−	0.993373i	$-0.536665\pi$
$359$	−370.734	−	214.043i	−1.03269	−	0.596221i	−0.917753	+	0.397152i	$0.869999\pi$
$360$		0			0
$361$	−76.3634	−	132.265i	−0.211533	−	0.366386i
$362$	−54.7871	−	204.468i	−0.151346	−	0.564829i
$363$	−113.168	−	113.168i	−0.311758	−	0.311758i
$364$	211.152	+	49.5445i	0.580089	+	0.136111i
$365$		0			0
$366$	−102.737	+	177.945i	−0.280701	+	0.486188i
$367$	−227.458	−	60.9472i	−0.619777	−	0.166069i	−0.0647505	−	0.997901i	$-0.520625\pi$
$367$	−227.458	−	60.9472i	−0.619777	−	0.166069i	−0.555026	+	0.831833i	$0.687292\pi$
$368$	21.5121	−	80.2844i	0.0584569	−	0.218164i
$369$	−71.5251	−	41.2950i	−0.193835	−	0.111911i
$370$		0			0
$371$	−67.7386	+	288.693i	−0.182584	+	0.778149i
$372$	55.6356	−	55.6356i	0.149558	−	0.149558i
$373$	146.535	−	39.2640i	0.392856	−	0.105265i	−0.0569830	−	0.998375i	$-0.518148\pi$
$373$	146.535	−	39.2640i	0.392856	−	0.105265i	0.449839	+	0.893110i	$0.351481\pi$
$374$	−193.674	+	111.818i	−0.517845	+	0.298978i
$375$		0			0
$376$	101.727	−	176.196i	0.270550	−	0.468606i
$377$	173.774	−	173.774i	0.460940	−	0.460940i
$378$	−256.428	−	137.524i	−0.678382	−	0.363820i
$379$			66.4317i			0.175281i	0.996152	+	0.0876407i	$0.0279327\pi$
$379$			66.4317i			0.175281i	−0.996152	+	0.0876407i	$0.972067\pi$
$380$		0			0
$381$	5.29503	+	9.17126i	0.0138977	+	0.0240716i
$382$	−308.814	−	82.7464i	−0.808413	−	0.216614i
$383$	−657.478	+	176.171i	−1.71665	+	0.459975i	−0.977040	−	0.213058i	$-0.931658\pi$
$383$	−657.478	+	176.171i	−1.71665	+	0.459975i	−0.739612	+	0.673034i	$0.764991\pi$
$384$			27.8178i			0.0724422i
$385$		0			0
$386$	312.725			0.810167
$387$	−42.8750	−	160.012i	−0.110788	−	0.413467i
$388$	−46.6845	+	174.229i	−0.120321	+	0.449044i
$389$	−80.4633	+	46.4555i	−0.206846	+	0.119423i	−0.599845	−	0.800116i	$-0.704771\pi$
$389$	−80.4633	+	46.4555i	−0.206846	+	0.119423i	0.392999	+	0.919539i	$0.371438\pi$
$390$		0			0
$391$	439.453			1.12392
$392$	−103.944	−	91.6710i	−0.265164	−	0.233855i
$393$	−198.043	−	198.043i	−0.503927	−	0.503927i
$394$	−147.067	−	84.9089i	−0.373265	−	0.215505i
$395$		0			0
$396$	−22.0911	−	38.2629i	−0.0557856	−	0.0966235i
$397$	−93.6525	−	349.516i	−0.235900	−	0.880393i	−0.977741	−	0.209816i	$-0.932713\pi$
$397$	−93.6525	−	349.516i	−0.235900	−	0.880393i	0.741840	−	0.670576i	$-0.233953\pi$
$398$	−82.4555	−	82.4555i	−0.207175	−	0.207175i
$399$	−170.050	+	181.053i	−0.426190	+	0.453768i
$400$		0			0
$401$	315.270	−	546.064i	0.786210	−	1.36176i	−0.142064	−	0.989858i	$-0.545374\pi$
$401$	315.270	−	546.064i	0.786210	−	1.36176i	0.928274	−	0.371898i	$-0.121293\pi$
$402$	−186.274	−	49.9121i	−0.463369	−	0.124159i
$403$	64.1537	−	239.425i	0.159190	−	0.594107i
$404$	−168.873	−	97.4990i	−0.418003	−	0.241334i
$405$		0			0
$406$	−150.341	+	45.3764i	−0.370297	+	0.111765i
$407$	−351.089	+	351.089i	−0.862627	+	0.862627i
$408$	−142.067	+	38.0666i	−0.348203	+	0.0933006i
$409$	176.077	−	101.658i	0.430507	−	0.248554i	−0.269055	−	0.963125i	$-0.586711\pi$
$409$	176.077	−	101.658i	0.430507	−	0.248554i	0.699563	+	0.714571i	$0.253378\pi$
$410$		0			0
$411$	178.681	−	309.485i	0.434747	−	0.753004i
$412$	−68.5228	+	68.5228i	−0.166317	+	0.166317i
$413$	383.883	−	237.972i	0.929498	−	0.576202i
$414$			86.8199i			0.209710i
$415$		0			0
$416$	43.8178	+	75.8947i	0.105331	+	0.182439i
$417$	−420.425	−	112.652i	−1.00821	−	0.270150i
$418$	−147.406	+	39.4974i	−0.352647	+	0.0944914i
$419$			716.269i			1.70947i	0.519062	+	0.854736i	$0.326281\pi$
$419$			716.269i			1.70947i	−0.519062	+	0.854736i	$0.673719\pi$
$420$		0			0
$421$	−692.449			−1.64477			−0.822386	−	0.568929i	$-0.807358\pi$
$421$	−692.449			−1.64477			−0.822386	+	0.568929i	$0.807358\pi$
$422$	75.2925	+	280.995i	0.178418	+	0.665866i
$423$	−55.0038	+	205.277i	−0.130033	+	0.485289i
$424$	−103.765	+	59.9089i	−0.244729	+	0.141295i
$425$		0			0
$426$	−126.364			−0.296630
$427$	195.496	−	364.524i	0.457836	−	0.853685i
$428$	232.840	+	232.840i	0.544018	+	0.544018i
$429$	246.658	+	142.408i	0.574960	+	0.331953i
$430$		0			0
$431$	−248.737	−	430.824i	−0.577115	−	0.999592i	−0.995808	−	0.0914647i	$-0.970845\pi$
$431$	−248.737	−	430.824i	−0.577115	−	0.999592i	0.418693	−	0.908128i	$-0.362488\pi$
$432$	−30.4301	−	113.567i	−0.0704401	−	0.262886i
$433$	191.729	+	191.729i	0.442792	+	0.442792i	0.892949	−	0.450158i	$-0.148632\pi$
$433$	191.729	+	191.729i	0.442792	+	0.442792i	−0.450158	+	0.892949i	$0.648632\pi$
$434$	−108.437	+	115.453i	−0.249854	+	0.266022i
$435$		0			0
$436$	−168.727	+	292.243i	−0.386988	+	0.670283i
$437$	289.660	+	77.6141i	0.662837	+	0.177607i
$438$	−59.5295	+	222.167i	−0.135912	+	0.507231i
$439$	−460.252	−	265.727i	−1.04841	−	0.605300i	−0.126206	−	0.992004i	$-0.540280\pi$
$439$	−460.252	−	265.727i	−1.04841	−	0.605300i	−0.922204	+	0.386704i	$0.873614\pi$
$440$		0			0
$441$	129.659	+	64.3913i	0.294012	+	0.146012i
$442$	−327.636	+	327.636i	−0.741257	+	0.741257i
$443$	152.513	−	40.8658i	0.344274	−	0.0922479i	−0.0825391	−	0.996588i	$-0.526303\pi$
$443$	152.513	−	40.8658i	0.344274	−	0.0922479i	0.426813	+	0.904340i	$0.359636\pi$
$444$	−282.794	+	163.271i	−0.636924	+	0.367728i
$445$		0			0
$446$	62.8872	−	108.924i	0.141003	−	0.244224i
$447$	439.711	−	439.711i	0.983693	−	0.983693i
$448$	−1.75419	−	55.9725i	−0.00391560	−	0.124939i
$449$		−	297.590i		−	0.662784i	−0.943493	−	0.331392i	$-0.892482\pi$
$449$		−	297.590i		−	0.662784i	0.943493	−	0.331392i	$-0.107518\pi$
$450$		0			0
$451$	−104.511	−	181.018i	−0.231731	−	0.401371i
$452$	154.731	+	41.4601i	0.342326	+	0.0917260i
$453$	−489.031	+	131.036i	−1.07954	+	0.289262i
$454$		−	365.362i		−	0.804763i
$455$		0			0
$456$	−100.364			−0.220097
$457$	−188.834	−	704.739i	−0.413204	−	1.54210i	−0.788406	−	0.615155i	$-0.789093\pi$
$457$	−188.834	−	704.739i	−0.413204	−	1.54210i	0.375202	−	0.926943i	$-0.377573\pi$
$458$	−45.0537	+	168.143i	−0.0983705	+	0.367124i
$459$	538.349	−	310.816i	1.17287	−	0.677158i
$460$		0			0
$461$	−16.3644			−0.0354976			−0.0177488	−	0.999842i	$-0.505650\pi$
$461$	−16.3644			−0.0354976			−0.0177488	+	0.999842i	$0.505650\pi$
$462$	−95.8927	−	154.689i	−0.207560	−	0.334824i
$463$	−185.921	−	185.921i	−0.401557	−	0.401557i	0.477225	−	0.878781i	$-0.341643\pi$
$463$	−185.921	−	185.921i	−0.401557	−	0.401557i	−0.878781	+	0.477225i	$0.841643\pi$
$464$	−54.9523	−	31.7267i	−0.118432	−	0.0683765i
$465$		0			0
$466$	−225.362	−	390.339i	−0.483610	−	0.837637i
$467$	84.3641	+	314.851i	0.180651	+	0.674200i	0.995520	+	0.0945537i	$0.0301424\pi$
$467$	84.3641	+	314.851i	0.180651	+	0.674200i	−0.814869	+	0.579646i	$0.803191\pi$
$468$	−64.7288	−	64.7288i	−0.138309	−	0.138309i
$469$	377.952	+	88.6822i	0.805868	+	0.189088i
$470$		0			0
$471$	−325.830	+	564.354i	−0.691783	+	1.19820i
$472$	176.279	+	47.2339i	0.373474	+	0.100072i
$473$	108.509	−	404.963i	0.229407	−	0.856158i
$474$	124.080	+	71.6377i	0.261772	+	0.151134i
$475$		0			0
$476$	283.453	−	85.5530i	0.595490	−	0.179733i
$477$	88.4990	−	88.4990i	0.185532	−	0.185532i
$478$	−238.678	+	63.9537i	−0.499327	+	0.133794i
$479$	452.460	−	261.228i	0.944592	−	0.545361i	0.0531954	−	0.998584i	$-0.483059\pi$
$479$	452.460	−	261.228i	0.944592	−	0.545361i	0.891397	+	0.453223i	$0.149726\pi$
$480$		0			0
$481$	−514.360	+	890.898i	−1.06936	+	1.85218i
$482$	−243.818	+	243.818i	−0.505846	+	0.505846i
$483$	11.2029	+	357.462i	0.0231945	+	0.740087i
$484$			130.182i			0.268971i
$485$		0			0
$486$	107.636	+	186.430i	0.221472	+	0.383602i
$487$	286.054	+	76.6478i	0.587379	+	0.157388i	0.540255	−	0.841501i	$-0.318328\pi$
$487$	286.054	+	76.6478i	0.587379	+	0.157388i	0.0471240	+	0.998889i	$0.484994\pi$
$488$	161.440	−	43.2577i	0.330819	−	0.0886428i
$489$		−	614.677i		−	1.25701i
$490$		0			0
$491$	−232.000			−0.472505			−0.236253	−	0.971692i	$-0.575919\pi$
$491$	−232.000			−0.472505			−0.236253	+	0.971692i	$0.575919\pi$
$492$	−35.5791	−	132.783i	−0.0723153	−	0.269884i
$493$	86.8314	−	324.059i	0.176129	−	0.657321i
$494$	−273.822	+	158.091i	−0.554295	+	0.320022i
$495$		0			0
$496$	−64.0000			−0.129032
$497$	254.259	−	7.96853i	0.511588	−	0.0160333i
$498$	31.7288	+	31.7288i	0.0637124	+	0.0637124i
$499$	181.375	+	104.717i	0.363477	+	0.209853i	0.670605	−	0.741815i	$-0.266035\pi$
$499$	181.375	+	104.717i	0.363477	+	0.209853i	−0.307128	+	0.951668i	$0.599368\pi$
$500$		0			0
$501$	13.9296	+	24.1268i	0.0278036	+	0.0481572i
$502$	19.8654	+	74.1387i	0.0395725	+	0.147687i
$503$	104.055	+	104.055i	0.206870	+	0.206870i	0.802935	−	0.596066i	$-0.203270\pi$
$503$	104.055	+	104.055i	0.206870	+	0.206870i	−0.596066	+	0.802935i	$0.703270\pi$
$504$	16.9021	+	56.0000i	0.0335360	+	0.111111i
$505$		0			0
$506$	−109.863	+	190.289i	−0.217121	+	0.376065i
$507$	168.624	+	45.1827i	0.332592	+	0.0891178i
$508$	2.22950	−	8.32059i	0.00438877	−	0.0163791i
$509$	65.4629	+	37.7950i	0.128611	+	0.0742535i	0.562925	−	0.826508i	$-0.309676\pi$
$509$	65.4629	+	37.7950i	0.128611	+	0.0742535i	−0.434314	+	0.900761i	$0.643009\pi$
$510$		0			0
$511$	105.770	−	450.779i	0.206987	−	0.882151i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	409.740	−	109.789i	0.798713	−	0.214014i
$514$	26.5330	−	15.3188i	0.0516206	−	0.0298032i
$515$		0			0
$516$	137.863	−	238.786i	0.267177	−	0.462764i
$517$	−380.317	+	380.317i	−0.735622	+	0.735622i
$518$	558.717	−	346.353i	1.07860	−	0.668635i
$519$			305.362i			0.588367i
$520$		0			0
$521$	−172.135	−	298.146i	−0.330393	−	0.572257i	0.652196	−	0.758050i	$-0.273848\pi$
$521$	−172.135	−	298.146i	−0.330393	−	0.572257i	−0.982589	+	0.185793i	$0.940514\pi$
$522$	64.0222	+	17.1547i	0.122648	+	0.0328634i
$523$	−57.3080	+	15.3556i	−0.109576	+	0.0293607i	−0.313190	−	0.949690i	$-0.601398\pi$
$523$	−57.3080	+	15.3556i	−0.109576	+	0.0293607i	0.203615	+	0.979051i	$0.434731\pi$
$524$			227.818i			0.434767i
$525$		0			0
$526$	475.477			0.903949
$527$	−87.5793	−	326.851i	−0.166185	−	0.620210i
$528$	19.0333	−	71.0333i	0.0360480	−	0.134533i
$529$	−84.2017	+	48.6139i	−0.159171	+	0.0918977i
$530$		0			0
$531$	−190.629			−0.359001
$532$	201.944	−	6.32897i	0.379595	−	0.0118966i
$533$	−306.226	−	306.226i	−0.574532	−	0.574532i
$534$	−146.734	−	84.7169i	−0.274783	−	0.158646i
$535$		0			0
$536$	78.4317	+	135.848i	0.146328	+	0.253447i
$537$	83.7698	+	312.633i	0.155996	+	0.582185i
$538$	−108.180	−	108.180i	−0.201078	−	0.201078i
$539$	202.701	+	305.204i	0.376069	+	0.566241i
$540$		0			0
$541$	358.793	−	621.448i	0.663203	−	1.14870i	−0.316566	−	0.948571i	$-0.602530\pi$
$541$	358.793	−	621.448i	0.663203	−	1.14870i	0.979769	−	0.200131i	$-0.0641368\pi$
$542$	84.0388	+	22.5181i	0.155053	+	0.0415464i
$543$	−95.2536	+	355.491i	−0.175421	+	0.654680i
$544$	103.607	+	59.8178i	0.190455	+	0.109959i
$545$		0			0
$546$	−274.859	−	258.154i	−0.503405	−	0.472810i
$547$	−392.507	+	392.507i	−0.717563	+	0.717563i	−0.968105	−	0.250543i	$-0.919391\pi$
$547$	−392.507	+	392.507i	−0.717563	+	0.717563i	0.250543	+	0.968105i	$0.419391\pi$
$548$	−280.779	+	75.2345i	−0.512370	+	0.137289i
$549$	−151.192	+	87.2909i	−0.275396	+	0.159000i
$550$		0			0
$551$	114.467	−	198.263i	0.207745	−	0.359825i
$552$	−102.182	+	102.182i	−0.185113	+	0.185113i
$553$	−254.180	−	136.319i	−0.459639	−	0.246507i
$554$		−	504.998i		−	0.911549i
$555$		0			0
$556$	177.022	+	306.611i	0.318384	+	0.551458i
$557$	193.665	+	51.8922i	0.347692	+	0.0931638i	0.428439	−	0.903571i	$-0.359064\pi$
$557$	193.665	+	51.8922i	0.347692	+	0.0931638i	−0.0807466	+	0.996735i	$0.525730\pi$
$558$	64.5737	−	17.3025i	0.115723	−	0.0310080i
$559$		−	868.634i		−	1.55391i
$560$		0			0
$561$	388.816			0.693076
$562$	−145.877	−	544.419i	−0.259567	−	0.968717i
$563$	159.367	−	594.765i	0.283067	−	1.05642i	−0.667173	−	0.744903i	$-0.732496\pi$
$563$	159.367	−	594.765i	0.283067	−	1.05642i	0.950240	−	0.311518i	$-0.100837\pi$
$564$	−306.336	+	176.863i	−0.543149	+	0.313588i
$565$		0			0
$566$	696.087			1.22984
$567$	168.480	+	271.783i	0.297143	+	0.479335i
$568$	72.6812	+	72.6812i	0.127960	+	0.127960i
$569$	72.8214	+	42.0435i	0.127981	+	0.0738901i	0.562624	−	0.826713i	$-0.309792\pi$
$569$	72.8214	+	42.0435i	0.127981	+	0.0738901i	−0.434642	+	0.900603i	$0.643125\pi$
$570$		0			0
$571$	167.327	+	289.818i	0.293041	+	0.507562i	0.974527	−	0.224269i	$-0.0719993\pi$
$571$	167.327	+	289.818i	0.293041	+	0.507562i	−0.681486	+	0.731831i	$0.738666\pi$
$572$	−59.9615	−	223.779i	−0.104828	−	0.391223i
$573$	393.043	+	393.043i	0.685940	+	0.685940i
$574$	79.9624	+	264.931i	0.139307	+	0.461552i
$575$		0			0
$576$	−11.8178	+	20.4690i	−0.0205170	+	0.0355365i
$577$	444.640	+	119.141i	0.770606	+	0.206483i	0.622639	−	0.782509i	$-0.286060\pi$
$577$	444.640	+	119.141i	0.770606	+	0.206483i	0.147967	+	0.988992i	$0.452727\pi$
$578$	−57.9313	+	216.203i	−0.100227	+	0.374053i
$579$	−470.864	−	271.854i	−0.813237	−	0.469522i
$580$		0			0
$581$	−65.8427	−	61.8410i	−0.113326	−	0.106439i
$582$	221.751	−	221.751i	0.381015	−	0.381015i
$583$	305.957	−	81.9810i	0.524798	−	0.140619i
$584$	162.024	−	93.5445i	0.277438	−	0.160179i
$585$		0			0
$586$	−187.818	+	325.310i	−0.320508	+	0.555136i
$587$	−484.313	+	484.313i	−0.825064	+	0.825064i	−0.986829	−	0.161765i	$-0.948281\pi$
$587$	−484.313	+	484.313i	−0.825064	+	0.825064i	0.161765	+	0.986829i	$0.448281\pi$
$588$	76.8170	+	228.387i	0.130641	+	0.388413i
$589$		−	230.907i		−	0.392032i
$590$		0			0
$591$	147.624	+	255.692i	0.249786	+	0.432643i
$592$	256.564	+	68.7461i	0.433385	+	0.116125i
$593$	−206.021	+	55.2031i	−0.347422	+	0.0930913i	−0.428310	−	0.903632i	$-0.640891\pi$
$593$	−206.021	+	55.2031i	−0.347422	+	0.0930913i	0.0808885	+	0.996723i	$0.474224\pi$
$594$			310.816i			0.523259i
$595$		0			0
$596$	−505.818			−0.848688
$597$	52.4727	+	195.831i	0.0878940	+	0.328025i
$598$	−117.827	+	439.736i	−0.197035	+	0.735344i
$599$	71.5663	−	41.3188i	0.119476	−	0.0689797i	−0.439071	−	0.898452i	$-0.644692\pi$
$599$	71.5663	−	41.3188i	0.119476	−	0.0689797i	0.558547	+	0.829473i	$0.311359\pi$
$600$		0			0
$601$	785.362			1.30676			0.653380	−	0.757030i	$-0.273351\pi$
$601$	785.362			1.30676			0.653380	+	0.757030i	$0.273351\pi$
$602$	−262.339	+	489.158i	−0.435778	+	0.812555i
$603$	−115.861	−	115.861i	−0.192141	−	0.192141i
$604$	356.645	+	205.909i	0.590471	+	0.340909i
$605$		0			0
$606$	169.513	+	293.605i	0.279724	+	0.484497i
$607$	181.102	+	675.882i	0.298356	+	1.11348i	0.938515	+	0.345237i	$0.112202\pi$
$607$	181.102	+	675.882i	0.298356	+	1.11348i	−0.640159	+	0.768242i	$0.721132\pi$
$608$	57.7267	+	57.7267i	0.0949452	+	0.0949452i
$609$	265.811	+	62.3696i	0.436472	+	0.102413i
$610$		0			0
$611$	−557.180	+	965.064i	−0.911915	+	1.57948i
$612$	−120.708	−	32.3436i	−0.197235	−	0.0528490i
$613$	−49.4286	+	184.470i	−0.0806339	+	0.300930i	−0.994452	−	0.105195i	$-0.966453\pi$
$613$	−49.4286	+	184.470i	−0.0806339	+	0.300930i	0.913818	+	0.406125i	$0.133120\pi$
$614$	296.870	+	171.398i	0.483502	+	0.279150i
$615$		0			0
$616$	−33.8178	+	144.127i	−0.0548990	+	0.233973i
$617$	423.089	−	423.089i	0.685720	−	0.685720i	−0.275563	−	0.961283i	$-0.588864\pi$
$617$	423.089	−	423.089i	0.685720	−	0.685720i	0.961283	+	0.275563i	$0.0888644\pi$
$618$	162.741	−	43.6063i	0.263335	−	0.0705603i
$619$	93.5101	−	53.9881i	0.151066	−	0.0872182i	−0.422561	−	0.906334i	$-0.638869\pi$
$619$	93.5101	−	53.9881i	0.151066	−	0.0872182i	0.573628	+	0.819116i	$0.305536\pi$
$620$		0			0
$621$	305.383	−	528.939i	0.491760	−	0.851753i
$622$	−3.47723	+	3.47723i	−0.00559039	+	0.00559039i
$623$	300.587	+	161.207i	0.482484	+	0.258759i
$624$		−	152.364i		−	0.244174i
$625$		0			0
$626$	15.0890	+	26.1350i	0.0241039	+	0.0417491i
$627$	256.282	+	68.6707i	0.408744	+	0.109523i
$628$	512.008	−	137.192i	0.815299	−	0.218459i
$629$			1404.36i			2.23268i
$630$		0			0
$631$	−711.200			−1.12710			−0.563550	−	0.826082i	$-0.690565\pi$
$631$	−711.200			−1.12710			−0.563550	+	0.826082i	$0.690565\pi$
$632$	−30.1634	−	112.571i	−0.0477269	−	0.178119i
$633$	130.904	−	488.542i	0.206800	−	0.771789i
$634$	−498.831	+	288.000i	−0.786799	+	0.454259i
$635$		0			0
$636$	208.317			0.327542
$637$	569.327	+	502.103i	0.893762	+	0.788231i
$638$	118.614	+	118.614i	0.185915	+	0.185915i
$639$	−92.9821	−	53.6832i	−0.145512	−	0.0840113i
$640$		0			0
$641$	214.658	+	371.799i	0.334880	+	0.580030i	0.983462	−	0.181115i	$-0.0579707\pi$
$641$	214.658	+	371.799i	0.334880	+	0.580030i	−0.648581	+	0.761145i	$0.724637\pi$
$642$	−148.174	−	552.991i	−0.230800	−	0.861357i
$643$	289.770	+	289.770i	0.450653	+	0.450653i	0.895571	−	0.444918i	$-0.146767\pi$
$643$	289.770	+	289.770i	0.450653	+	0.450653i	−0.444918	+	0.895571i	$0.646767\pi$
$644$	199.158	−	212.046i	0.309252	−	0.329263i
$645$		0			0
$646$	−215.818	+	373.807i	−0.334083	+	0.578649i
$647$	−435.592	−	116.716i	−0.673248	−	0.180396i	−0.0940307	−	0.995569i	$-0.529975\pi$
$647$	−435.592	−	116.716i	−0.673248	−	0.180396i	−0.579218	+	0.815173i	$0.696642\pi$
$648$	−33.4409	+	124.803i	−0.0516064	+	0.192598i
$649$	−417.815	−	241.226i	−0.643783	−	0.371688i
$650$		0			0
$651$	263.636	−	79.5715i	0.404970	−	0.122230i
$652$	−353.545	+	353.545i	−0.542246	+	0.542246i
$653$	−340.019	+	91.1077i	−0.520702	+	0.139522i	−0.509592	−	0.860416i	$-0.670203\pi$
$653$	−340.019	+	91.1077i	−0.520702	+	0.139522i	−0.0111110	+	0.999938i	$0.503537\pi$
$654$	508.098	−	293.350i	0.776908	−	0.448548i
$655$		0			0
$656$	−55.9089	+	96.8371i	−0.0852270	+	0.147617i
$657$	−138.186	+	138.186i	−0.210329	+	0.210329i
$658$	605.230	−	375.186i	0.919802	−	0.570192i
$659$		−	900.158i		−	1.36595i	−0.730444	−	0.682973i	$-0.760687\pi$
$659$		−	900.158i		−	1.36595i	0.730444	−	0.682973i	$-0.239313\pi$
$660$		0			0
$661$	174.090	+	301.533i	0.263374	+	0.456177i	0.967136	−	0.254259i	$-0.0818314\pi$
$661$	174.090	+	301.533i	0.263374	+	0.456177i	−0.703763	+	0.710435i	$0.748498\pi$
$662$	574.596	+	153.963i	0.867970	+	0.232572i
$663$	778.131	−	208.500i	1.17365	−	0.314479i
$664$		−	36.4990i		−	0.0549683i
$665$		0			0
$666$	−277.449			−0.416590
$667$	−85.3137	−	318.395i	−0.127907	−	0.477354i
$668$	5.86512	−	21.8889i	0.00878012	−	0.0327679i
$669$	−189.376	+	109.336i	−0.283074	+	0.163433i
$670$		0			0
$671$	−441.837			−0.658476
$672$	−46.0160	+	85.8018i	−0.0684762	+	0.127681i
$673$	13.2277	+	13.2277i	0.0196549	+	0.0196549i	0.716866	−	0.697211i	$-0.245576\pi$
$673$	13.2277	+	13.2277i	0.0196549	+	0.0196549i	−0.697211	+	0.716866i	$0.745576\pi$
$674$	59.3595	+	34.2712i	0.0880705	+	0.0508475i
$675$		0			0
$676$	−71.0000	−	122.976i	−0.105030	−	0.181917i
$677$	153.597	+	573.233i	0.226879	+	0.846725i	0.981643	+	0.190728i	$0.0610849\pi$
$677$	153.597	+	573.233i	0.226879	+	0.846725i	−0.754764	+	0.655997i	$0.772248\pi$
$678$	−196.935	−	196.935i	−0.290464	−	0.290464i
$679$	−432.203	+	460.170i	−0.636529	+	0.677718i
$680$		0			0
$681$	−317.612	+	550.120i	−0.466390	+	0.807812i
$682$	163.425	+	43.7897i	0.239627	+	0.0642077i
$683$	−73.3428	+	273.719i	−0.107383	+	0.400760i	−0.998605	−	0.0528086i	$-0.983183\pi$
$683$	−73.3428	+	273.719i	−0.107383	+	0.400760i	0.891221	+	0.453569i	$0.149849\pi$
$684$	−73.8506	−	42.6377i	−0.107969	−	0.0623358i
$685$		0			0
$686$	−168.966	−	454.696i	−0.246307	−	0.662822i
$687$	214.004	−	214.004i	0.311505	−	0.311505i
$688$	−216.638	+	58.0480i	−0.314881	+	0.0843721i
$689$	568.346	−	328.135i	0.824885	−	0.476248i
$690$		0			0
$691$	−369.671	+	640.290i	−0.534980	+	0.926613i	0.464184	+	0.885739i	$0.346348\pi$
$691$	−369.671	+	640.290i	−0.534980	+	0.926613i	−0.999164	+	0.0408742i	$0.986986\pi$
$692$	175.636	−	175.636i	0.253809	−	0.253809i
$693$	−4.84399	−	154.562i	−0.00698989	−	0.223033i
$694$			204.657i			0.294895i
$695$		0			0
$696$	55.1605	+	95.5407i	0.0792535	+	0.137271i
$697$	−571.058	−	153.015i	−0.819308	−	0.219533i
$698$	−339.951	+	91.0896i	−0.487036	+	0.130501i
$699$			783.636i			1.12108i
$700$		0			0
$701$	189.638			0.270525			0.135262	−	0.990810i	$-0.456812\pi$
$701$	189.638			0.270525			0.135262	+	0.990810i	$0.456812\pi$
$702$	166.673	+	622.031i	0.237425	+	0.886084i
$703$	−248.030	+	925.662i	−0.352817	+	1.31673i
$704$	−51.8037	+	29.9089i	−0.0735849	+	0.0424842i
$705$		0			0
$706$	−564.725			−0.799893
$707$	−359.594	−	580.077i	−0.508619	−	0.820476i
$708$	−224.360	−	224.360i	−0.316893	−	0.316893i
$709$	−571.534	−	329.975i	−0.806112	−	0.465409i	0.0394916	−	0.999220i	$-0.487426\pi$
$709$	−571.534	−	329.975i	−0.806112	−	0.465409i	−0.845604	+	0.533811i	$0.820760\pi$
$710$		0			0
$711$	60.8675	+	105.426i	0.0856083	+	0.148278i
$712$	35.6704	+	133.124i	0.0500989	+	0.186972i
$713$	−235.089	−	235.089i	−0.329718	−	0.329718i
$714$	−501.163	−	117.592i	−0.701909	−	0.164695i
$715$		0			0
$716$	131.636	−	228.000i	0.183849	−	0.318435i
$717$	414.969	+	111.191i	0.578757	+	0.155078i
$718$	156.691	−	584.778i	0.218232	−	0.814454i
$719$	851.435	+	491.576i	1.18419	+	0.683694i	0.956981	−	0.290151i	$-0.0937056\pi$
$719$	851.435	+	491.576i	1.18419	+	0.683694i	0.227212	+	0.973845i	$0.427039\pi$
$720$		0			0
$721$	−324.703	+	98.0031i	−0.450351	+	0.135927i
$722$	152.727	−	152.727i	0.211533	−	0.211533i
$723$	579.065	−	155.160i	0.800919	−	0.214606i
$724$	259.255	−	149.681i	0.358088	−	0.206742i
$725$		0			0
$726$	113.168	−	196.013i	0.155879	−	0.269990i
$727$	−291.624	+	291.624i	−0.401133	+	0.401133i	−0.878632	−	0.477499i	$-0.841543\pi$
$727$	−291.624	+	291.624i	−0.401133	+	0.401133i	0.477499	+	0.878632i	$0.341543\pi$
$728$	9.60809	+	306.574i	0.0131979	+	0.421118i
$729$		−	785.404i		−	1.07737i
$730$		0			0
$731$	−592.907	−	1026.94i	−0.811090	−	1.40485i
$732$	−280.681	−	75.2084i	−0.383445	−	0.102744i
$733$	660.223	−	176.906i	0.900713	−	0.241345i	0.221391	−	0.975185i	$-0.428940\pi$
$733$	660.223	−	176.906i	0.900713	−	0.241345i	0.679323	+	0.733840i	$0.262274\pi$
$734$		−	333.022i		−	0.453708i
$735$		0			0
$736$	117.545			0.159707
$737$	−107.328	−	400.554i	−0.145628	−	0.543492i
$738$	30.2301	−	112.820i	0.0409621	−	0.152873i
$739$	110.947	−	64.0554i	0.150131	−	0.0866785i	−0.423052	−	0.906105i	$-0.639041\pi$
$739$	110.947	−	64.0554i	0.150131	−	0.0866785i	0.573184	+	0.819427i	$0.305708\pi$
$740$		0			0
$741$	549.718			0.741860
$742$	−419.157	+	13.1364i	−0.564901	+	0.0177041i
$743$	−443.624	−	443.624i	−0.597071	−	0.597071i	0.342461	−	0.939532i	$-0.388740\pi$
$743$	−443.624	−	443.624i	−0.597071	−	0.597071i	−0.939532	+	0.342461i	$0.888740\pi$
$744$	96.3637	+	55.6356i	0.129521	+	0.0747790i
$745$		0			0
$746$	107.271	+	185.799i	0.143795	+	0.249061i
$747$	9.86753	+	36.8261i	0.0132095	+	0.0492987i
$748$	−223.636	−	223.636i	−0.298978	−	0.298978i
$749$	333.013	+	1103.34i	0.444611	+	1.47308i
$750$		0			0
$751$	141.957	−	245.876i	0.189023	−	0.327398i	−0.755902	−	0.654685i	$-0.772801\pi$
$751$	141.957	−	245.876i	0.189023	−	0.327398i	0.944925	+	0.327287i	$0.106134\pi$
$752$	277.923	+	74.4691i	0.369578	+	0.0990281i
$753$	34.5382	−	128.898i	0.0458675	−	0.171180i
$754$	300.986	+	173.774i	0.399186	+	0.230470i
$755$		0			0
$756$	94.0021	−	400.625i	0.124341	−	0.529927i
$757$	494.590	−	494.590i	0.653355	−	0.653355i	−0.300444	−	0.953799i	$-0.597135\pi$
$757$	494.590	−	494.590i	0.653355	−	0.653355i	0.953799	+	0.300444i	$0.0971349\pi$
$758$	−90.7474	+	24.3157i	−0.119719	+	0.0320787i
$759$	330.839	−	191.010i	0.435888	−	0.251660i
$760$		0			0
$761$	17.7288	−	30.7072i	0.0232967	−	0.0403511i	−0.854142	−	0.520040i	$-0.825917\pi$
$761$	17.7288	−	30.7072i	0.0232967	−	0.0403511i	0.877439	+	0.479689i	$0.159250\pi$
$762$	−10.5901	+	10.5901i	−0.0138977	+	0.0138977i
$763$	−1003.85	+	622.294i	−1.31566	+	0.815589i
$764$		−	452.135i		−	0.591799i
$765$		0			0
$766$	−481.307	−	833.648i	−0.628338	−	1.08831i
$767$	−965.523	−	258.711i	−1.25883	−	0.337302i
$768$	−37.9998	+	10.1820i	−0.0494789	+	0.0132578i
$769$			702.447i			0.913455i	0.889607	+	0.456728i	$0.150979\pi$
$769$			702.447i			0.913455i	−0.889607	+	0.456728i	$0.849021\pi$
$770$		0			0
$771$	−53.2671			−0.0690883
$772$	114.465	+	427.190i	0.148271	+	0.553355i
$773$	216.901	−	809.487i	0.280597	−	1.04720i	−0.671400	−	0.741095i	$-0.734307\pi$
$773$	216.901	−	809.487i	0.280597	−	1.04720i	0.951997	−	0.306107i	$-0.0990266\pi$
$774$	202.887	−	117.137i	0.262127	−	0.151339i
$775$		0			0
$776$	−255.089			−0.328723
$777$	−1142.34	+	35.8011i	−1.47019	+	0.0460760i
$778$	−92.9110	−	92.9110i	−0.119423	−	0.119423i
$779$	−349.380	−	201.715i	−0.448498	−	0.258941i
$780$		0			0
$781$	−135.863	−	235.322i	−0.173961	−	0.301309i
$782$	160.851	+	600.305i	0.205692	+	0.767653i
$783$	−329.707	−	329.707i	−0.421081	−	0.421081i
$784$	87.1787	−	175.545i	0.111197	−	0.223909i
$785$		0			0
$786$	198.043	−	343.021i	0.251964	−	0.436414i
$787$	695.596	+	186.384i	0.883858	+	0.236829i	0.672071	−	0.740487i	$-0.265405\pi$
$787$	695.596	+	186.384i	0.883858	+	0.236829i	0.211787	+	0.977316i	$0.432072\pi$
$788$	62.1576	−	231.975i	0.0788802	−	0.294385i
$789$	−715.918	−	413.335i	−0.907374	−	0.523872i
$790$		0			0
$791$	408.673	+	383.836i	0.516654	+	0.485254i
$792$	44.1822	−	44.1822i	0.0557856	−	0.0557856i
$793$	−884.243	+	236.932i	−1.11506	+	0.298779i
$794$	443.168	−	255.863i	0.558147	−	0.322246i
$795$		0			0
$796$	82.4555	−	142.817i	0.103587	−	0.179418i
$797$	82.4079	−	82.4079i	0.103398	−	0.103398i	−0.653516	−	0.756913i	$-0.726707\pi$
$797$	82.4079	−	82.4079i	0.103398	−	0.103398i	0.756913	+	0.653516i	$0.226707\pi$
$798$	−309.566	−	166.022i	−0.387927	−	0.208048i
$799$			1521.27i			1.90396i
$800$		0			0
$801$	−71.9803	−	124.674i	−0.0898631	−	0.155647i
$802$	861.334	+	230.794i	1.07398	+	0.287773i
$803$	−477.736	+	128.009i	−0.594938	+	0.159413i
$804$		−	272.725i		−	0.339210i
$805$		0			0
$806$	350.542			0.434916
$807$	68.8433	+	256.927i	0.0853077	+	0.318373i
$808$	71.3742	−	266.372i	0.0883344	−	0.329668i
$809$	289.803	−	167.318i	0.358224	−	0.206821i	−0.310078	−	0.950711i	$-0.600355\pi$
$809$	289.803	−	167.318i	0.358224	−	0.206821i	0.668301	+	0.743891i	$0.267022\pi$
$810$		0			0
$811$	522.455			0.644211			0.322106	−	0.946704i	$-0.395609\pi$
$811$	522.455			0.644211			0.322106	+	0.946704i	$0.395609\pi$
$812$	−117.014	−	188.760i	−0.144106	−	0.232463i
$813$	−106.961	−	106.961i	−0.131563	−	0.131563i
$814$	−608.104	−	351.089i	−0.747057	−	0.431313i
$815$		0			0
$816$	−104.000	−	180.133i	−0.127451	−	0.220752i
$817$	−209.432	−	781.613i	−0.256343	−	0.956686i
$818$	203.317	+	203.317i	0.248554	+	0.248554i
$819$	−92.5768	−	306.725i	−0.113036	−	0.374511i
$820$		0			0
$821$	196.950	−	341.128i	0.239891	−	0.415503i	−0.720792	−	0.693151i	$-0.756222\pi$
$821$	196.950	−	341.128i	0.239891	−	0.415503i	0.960683	+	0.277648i	$0.0895550\pi$
$822$	488.166	+	130.804i	0.593876	+	0.159129i
$823$	67.2617	−	251.024i	0.0817275	−	0.305011i	−0.912947	−	0.408078i	$-0.866199\pi$
$823$	67.2617	−	251.024i	0.0817275	−	0.305011i	0.994674	+	0.103067i	$0.0328657\pi$
$824$	−118.685	−	68.5228i	−0.144035	−	0.0831587i
$825$		0			0
$826$	465.586	+	437.290i	0.563663	+	0.529406i
$827$	−143.561	+	143.561i	−0.173592	+	0.173592i	−0.788556	−	0.614964i	$-0.789171\pi$
$827$	−143.561	+	143.561i	−0.173592	+	0.173592i	0.614964	+	0.788556i	$0.289171\pi$
$828$	−118.598	+	31.7783i	−0.143234	+	0.0383796i
$829$	−566.219	+	326.907i	−0.683015	+	0.394339i	−0.800990	−	0.598678i	$-0.795693\pi$
$829$	−566.219	+	326.907i	−0.683015	+	0.394339i	0.117975	+	0.993017i	$0.462360\pi$
$830$		0			0
$831$	−438.998	+	760.367i	−0.528277	+	0.915002i
$832$	−87.6356	+	87.6356i	−0.105331	+	0.105331i
$833$	1015.81	+	205.005i	1.21946	+	0.246105i
$834$		−	615.545i		−	0.738063i
$835$		0			0
$836$	−107.909	−	186.904i	−0.129078	−	0.223569i
$837$	−454.267	−	121.720i	−0.542732	−	0.145425i
$838$	−978.442	+	262.173i	−1.16759	+	0.312855i
$839$			128.301i			0.152922i	0.997073	+	0.0764608i	$0.0243620\pi$
$839$			128.301i			0.152922i	−0.997073	+	0.0764608i	$0.975638\pi$
$840$		0			0
$841$	589.354			0.700778
$842$	−253.454	−	945.903i	−0.301014	−	1.12340i
$843$	−253.623	+	946.534i	−0.300858	+	1.12282i
$844$	−356.288	+	205.703i	−0.422142	+	0.243724i
$845$		0			0
$846$	−300.547			−0.355256
$847$	−215.346	+	401.537i	−0.254246	+	0.474069i
$848$	−119.818	−	119.818i	−0.141295	−	0.141295i
$849$	−1048.09	−	605.113i	−1.23449	−	0.712736i
$850$		0			0
$851$	689.905	+	1194.95i	0.810699	+	1.40417i
$852$	−46.2526	−	172.617i	−0.0542871	−	0.202602i
$853$	941.404	+	941.404i	1.10364	+	1.10364i	0.993968	+	0.109671i	$0.0349796\pi$
$853$	941.404	+	941.404i	1.10364	+	1.10364i	0.109671	+	0.993968i	$0.465020\pi$
$854$	569.505	+	133.628i	0.666868	+	0.156473i
$855$		0			0
$856$	−232.840	+	403.290i	−0.272009	+	0.471133i
$857$	−334.297	−	89.5747i	−0.390078	−	0.104521i	0.0584487	−	0.998290i	$-0.481385\pi$
$857$	−334.297	−	89.5747i	−0.390078	−	0.104521i	−0.448527	+	0.893769i	$0.648051\pi$
$858$	−104.250	+	389.066i	−0.121503	+	0.453456i
$859$	39.8336	+	22.9979i	0.0463720	+	0.0267729i	0.523007	−	0.852329i	$-0.324810\pi$
$859$	39.8336	+	22.9979i	0.0463720	+	0.0267729i	−0.476635	+	0.879101i	$0.658144\pi$
$860$		0			0
$861$	109.908	−	468.413i	0.127651	−	0.544034i
$862$	497.473	−	497.473i	0.577115	−	0.577115i
$863$	−1354.85	+	363.032i	−1.56993	+	0.420663i	−0.935792	−	0.352554i	$-0.885313\pi$
$863$	−1354.85	+	363.032i	−1.56993	+	0.420663i	−0.634143	+	0.773216i	$0.718647\pi$
$864$	143.997	−	83.1366i	0.166663	−	0.0962230i
$865$		0			0
$866$	−191.729	+	332.084i	−0.221396	+	0.383469i
$867$	275.172	−	275.172i	0.317385	−	0.317385i
$868$	−197.403	−	105.868i	−0.227423	−	0.121968i
$869$			308.091i			0.354535i
$870$		0			0
$871$	−429.588	−	744.068i	−0.493212	−	0.854269i
$872$	−460.970	−	123.517i	−0.528635	−	0.141647i
$873$	257.376	−	68.9636i	0.294817	−	0.0789961i
$874$			424.091i			0.485230i
$875$		0			0
$876$	−325.275			−0.371319
$877$	−288.777	−	1077.73i	−0.329278	−	1.22888i	−0.909941	−	0.414738i	$-0.863873\pi$
$877$	−288.777	−	1077.73i	−0.329278	−	1.22888i	0.580663	−	0.814144i	$-0.302793\pi$
$878$	194.525	−	725.979i	0.221555	−	0.826855i
$879$	565.588	−	326.542i	0.643445	−	0.371493i
$880$		0			0
$881$	−1392.40			−1.58048			−0.790239	−	0.612798i	$-0.790044\pi$
$881$	−1392.40			−1.58048			−0.790239	+	0.612798i	$0.790044\pi$
$882$	−40.5015	+	200.687i	−0.0459201	+	0.227536i
$883$	652.590	+	652.590i	0.739060	+	0.739060i	0.972396	−	0.233336i	$-0.0749642\pi$
$883$	652.590	+	652.590i	0.739060	+	0.739060i	−0.233336	+	0.972396i	$0.574964\pi$
$884$	−567.482	−	327.636i	−0.641947	−	0.370629i
$885$		0			0
$886$	111.648	+	193.379i	0.126013	+	0.218261i
$887$	−130.525	−	487.127i	−0.147154	−	0.549185i	−0.999650	−	0.0264521i	$-0.991579\pi$
$887$	−130.525	−	487.127i	−0.147154	−	0.549185i	0.852496	−	0.522733i	$-0.175088\pi$
$888$	−326.542	−	326.542i	−0.367728	−	0.367728i
$889$	20.6406	−	21.9762i	0.0232177	−	0.0247201i
$890$		0			0
$891$	170.784	−	295.807i	0.191677	−	0.331994i
$892$	171.811	+	46.0366i	0.192613	+	0.0516105i
$893$	−268.679	+	1002.72i	−0.300872	+	1.12287i
$894$	761.601	+	439.711i	0.851903	+	0.491846i
$895$		0			0
$896$	75.8178	−	22.8836i	0.0846181	−	0.0255398i
$897$	559.675	−	559.675i	0.623941	−	0.623941i
$898$	406.516	−	108.926i	0.452690	−	0.121298i
$899$	−219.809	+	126.907i	−0.244504	+	0.141164i
$900$		0			0
$901$	447.952	−	775.876i	0.497172	−	0.861128i
$902$	209.022	−	209.022i	0.231731	−	0.231731i
$903$	820.227	−	508.465i	0.908336	−	0.563084i
$904$			226.542i			0.250600i
$905$		0			0
$906$	−357.996	−	620.067i	−0.395139	−	0.684401i
$907$	1.84469	+	0.494284i	0.00203384	+	0.000544966i	0.259836	−	0.965653i	$-0.416332\pi$
$907$	1.84469	+	0.494284i	0.00203384	+	0.000544966i	−0.257802	+	0.966198i	$0.582998\pi$
$908$	499.094	−	133.732i	0.549663	−	0.147282i
$909$			288.056i			0.316893i
$910$		0			0
$911$	456.063			0.500618			0.250309	−	0.968166i	$-0.419468\pi$
$911$	456.063			0.500618			0.250309	+	0.968166i	$0.419468\pi$
$912$	−36.7359	−	137.100i	−0.0402806	−	0.150329i
$913$	−24.9731	+	93.2008i	−0.0273528	+	0.102082i
$914$	893.573	−	515.905i	0.977651	−	0.564447i
$915$		0			0
$916$	−246.178			−0.268753
$917$	−376.855	+	702.686i	−0.410965	+	0.766288i
$918$	621.631	+	621.631i	0.677158	+	0.677158i
$919$	−459.799	−	265.465i	−0.500326	−	0.288863i	0.228522	−	0.973539i	$-0.426611\pi$
$919$	−459.799	−	265.465i	−0.500326	−	0.288863i	−0.728848	+	0.684675i	$0.759944\pi$
$920$		0			0
$921$	−297.995	−	516.142i	−0.323556	−	0.560415i
$922$	−5.98978	−	22.3542i	−0.00649651	−	0.0242453i
$923$	−398.091	−	398.091i	−0.431301	−	0.431301i
$924$	176.210	−	187.612i	0.190703	−	0.203043i
$925$		0			0
$926$	185.921	−	322.024i	0.200778	−	0.347758i
$927$	138.274	+	37.0504i	0.149163	+	0.0399681i
$928$	23.2256	−	86.6790i	0.0250275	−	0.0934041i
$929$	−971.957	−	561.159i	−1.04624	−	0.604047i	−0.124645	−	0.992201i	$-0.539779\pi$
$929$	−971.957	−	561.159i	−1.04624	−	0.604047i	−0.921594	+	0.388155i	$0.873113\pi$
$930$		0			0
$931$	633.350	+	314.534i	0.680290	+	0.337845i
$932$	450.725	−	450.725i	0.483610	−	0.483610i
$933$	8.25837	−	2.21282i	0.00885142	−	0.00237173i
$934$	−399.215	+	230.487i	−0.427425	+	0.246774i
$935$		0			0
$936$	64.7288	−	112.114i	0.0691547	−	0.119779i
$937$	194.820	−	194.820i	0.207919	−	0.207919i	−0.595464	−	0.803382i	$-0.703032\pi$
$937$	194.820	−	194.820i	0.207919	−	0.207919i	0.803382	+	0.595464i	$0.203032\pi$
$938$	17.1980	+	548.752i	0.0183347	+	0.585024i
$939$		−	52.4679i		−	0.0558764i
$940$		0			0
$941$	−405.362	−	702.108i	−0.430778	−	0.746130i	0.566162	−	0.824294i	$-0.308428\pi$
$941$	−405.362	−	702.108i	−0.430778	−	0.746130i	−0.996941	+	0.0781640i	$0.975094\pi$
$942$	−890.183	−	238.524i	−0.944993	−	0.253210i
$943$	−561.077	+	150.340i	−0.594991	+	0.159427i
$944$			258.091i			0.273402i
$945$		0			0
$946$	592.907			0.626751
$947$	166.389	+	620.971i	0.175701	+	0.655724i	0.996431	+	0.0844087i	$0.0269001\pi$
$947$	166.389	+	620.971i	0.175701	+	0.655724i	−0.820730	+	0.571316i	$0.806433\pi$
$948$	−52.4424	+	195.718i	−0.0553190	+	0.206453i
$949$	−887.441	+	512.364i	−0.935133	+	0.539899i
$950$		0			0
$951$	1001.44			1.05304
$952$	220.619	+	355.890i	0.231742	+	0.373834i
$953$	−372.594	−	372.594i	−0.390970	−	0.390970i	0.484063	−	0.875033i	$-0.339160\pi$
$953$	−372.594	−	372.594i	−0.390970	−	0.390970i	−0.875033	+	0.484063i	$0.839160\pi$
$954$	153.285	+	88.4990i	0.160676	+	0.0927662i
$955$		0			0
$956$	−174.725	−	302.632i	−0.182766	−	0.316561i
$957$	−75.4831	−	281.707i	−0.0788747	−	0.294364i
$958$	522.455	+	522.455i	0.545361	+	0.545361i
$959$	−990.493	−	232.408i	−1.03284	−	0.242344i
$960$		0			0
$961$	352.500	−	610.548i	0.366805	−	0.635326i
$962$	−1405.26	−	376.538i	−1.46077	−	0.391411i
$963$	125.897	−	469.853i	0.130734	−	0.487906i
$964$	−422.305	−	243.818i	−0.438076	−	0.252923i
$965$		0			0
$966$	−484.202	+	146.144i	−0.501244	+	0.151287i
$967$	989.576	−	989.576i	1.02335	−	1.02335i	0.0236256	−	0.999721i	$-0.492479\pi$
$967$	989.576	−	989.576i	1.02335	−	1.02335i	0.999721	−	0.0236256i	$-0.00752097\pi$
$968$	−177.832	+	47.6500i	−0.183711	+	0.0492252i
$969$	649.906	−	375.224i	0.670698	−	0.387228i
$970$		0			0
$971$	−306.911	+	531.585i	−0.316077	+	0.547462i	−0.979666	−	0.200636i	$-0.935699\pi$
$971$	−306.911	+	531.585i	−0.316077	+	0.547462i	0.663589	+	0.748098i	$0.269033\pi$
$972$	−215.271	+	215.271i	−0.221472	+	0.221472i
$973$	38.8162	+	1238.54i	0.0398933	+	1.27291i
$974$			418.812i			0.429991i
$975$		0			0
$976$	118.182	+	204.698i	0.121088	+	0.209731i
$977$	−417.882	−	111.971i	−0.427720	−	0.114607i	0.0385359	−	0.999257i	$-0.487731\pi$
$977$	−417.882	−	111.971i	−0.427720	−	0.114607i	−0.466256	+	0.884650i	$0.654397\pi$
$978$	839.664	−	224.987i	0.858553	−	0.230048i
$979$		−	364.341i		−	0.372156i
$980$		0			0
$981$	498.495			0.508150
$982$	−84.9179	−	316.918i	−0.0864744	−	0.322727i
$983$	229.825	−	857.718i	0.233799	−	0.872551i	−0.744887	−	0.667191i	$-0.767497\pi$
$983$	229.825	−	857.718i	0.233799	−	0.872551i	0.978686	−	0.205360i	$-0.0658367\pi$
$984$	168.362	−	97.2039i	0.171100	−	0.0987845i
$985$		0			0
$986$	474.455			0.481192
$987$	−1237.44	+	38.7815i	−1.25373	+	0.0392923i
$988$	−316.182	−	316.182i	−0.320022	−	0.320022i
$989$	−1008.99	−	582.543i	−1.02022	−	0.589023i
$990$		0			0
$991$	426.768	+	739.184i	0.430644	+	0.745897i	0.996929	−	0.0783124i	$-0.0249532\pi$
$991$	426.768	+	739.184i	0.430644	+	0.745897i	−0.566285	+	0.824210i	$0.691620\pi$
$992$	−23.4256	−	87.4256i	−0.0236145	−	0.0881307i
$993$	−731.319	−	731.319i	−0.736474	−	0.736474i
$994$	103.951	+	344.408i	0.104578	+	0.346487i
$995$		0			0
$996$	−31.7288	+	54.9559i	−0.0318562	+	0.0551766i
$997$	−992.040	−	265.816i	−0.995025	−	0.266616i	−0.275665	−	0.961254i	$-0.588898\pi$
$997$	−992.040	−	265.816i	−0.995025	−	0.266616i	−0.719360	+	0.694638i	$0.755565\pi$
$998$	−76.6581	+	286.092i	−0.0768117	+	0.286665i
$999$	1690.32	+	975.909i	1.69202	+	0.976886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.p.c.93.2		8
5.2	odd	4	inner	350.3.p.c.107.1		8
5.3	odd	4		70.3.l.a.37.2	yes	8
5.4	even	2		70.3.l.a.23.1	✓	8
7.4	even	3	inner	350.3.p.c.193.1		8
35.4	even	6		70.3.l.a.53.2	yes	8
35.9	even	6		490.3.f.l.393.1		4
35.18	odd	12		70.3.l.a.67.1	yes	8
35.19	odd	6		490.3.f.e.393.2		4
35.23	odd	12		490.3.f.l.197.1		4
35.32	odd	12	inner	350.3.p.c.207.2		8
35.33	even	12		490.3.f.e.197.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.a.23.1	✓	8	5.4	even	2
70.3.l.a.37.2	yes	8	5.3	odd	4
70.3.l.a.53.2	yes	8	35.4	even	6
70.3.l.a.67.1	yes	8	35.18	odd	12
350.3.p.c.93.2		8	1.1	even	1	trivial
350.3.p.c.107.1		8	5.2	odd	4	inner
350.3.p.c.193.1		8	7.4	even	3	inner
350.3.p.c.207.2		8	35.32	odd	12	inner
490.3.f.e.197.2		4	35.33	even	12
490.3.f.e.393.2		4	35.19	odd	6
490.3.f.l.197.1		4	35.23	odd	12
490.3.f.l.393.1		4	35.9	even	6

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.636376 - 2.37499i) q^{3} +(-1.73205 + 1.00000i) q^{4} +3.47723 q^{6} +(-6.99656 + 0.219274i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.55863 + 1.47723i) q^{9} +(3.73861 + 6.47547i) q^{11} +(1.27275 + 4.74998i) q^{12} +(10.9545 + 10.9545i) q^{13} +(-2.86045 - 9.47723i) q^{14} +(2.00000 - 3.46410i) q^{16} +(20.4282 + 5.47371i) q^{17} +(-1.08140 + 4.03586i) q^{18} +(12.4982 + 7.21584i) q^{19} +(-3.93168 + 16.7563i) q^{21} +(-7.47723 + 7.47723i) q^{22} +(20.0711 - 5.37803i) q^{23} +(-6.02273 + 3.47723i) q^{24} +(-10.9545 + 18.9737i) q^{26} +(20.7842 - 20.7842i) q^{27} +(11.8991 - 7.37636i) q^{28} -15.8634i q^{29} +(-8.00000 - 13.8564i) q^{31} +(5.46410 + 1.46410i) q^{32} +(17.7583 - 4.75833i) q^{33} +29.9089i q^{34} -5.90890 q^{36} +(17.1865 + 64.1410i) q^{37} +(-5.28236 + 19.7140i) q^{38} +(32.9879 - 19.0455i) q^{39} -27.9545 q^{41} +(-24.3286 + 0.762464i) q^{42} +(-39.6475 - 39.6475i) q^{43} +(-12.9509 - 7.47723i) q^{44} +(14.6931 + 25.4491i) q^{46} +(18.6173 + 69.4806i) q^{47} +(-6.95445 - 6.95445i) q^{48} +(48.9038 - 3.06832i) q^{49} +(26.0000 - 45.0333i) q^{51} +(-29.9281 - 8.01921i) q^{52} +(10.9641 - 40.9185i) q^{53} +(35.9992 + 20.7842i) q^{54} +(14.4317 + 13.5546i) q^{56} +(25.0911 - 25.0911i) q^{57} +(21.6697 - 5.80639i) q^{58} +(-55.8784 + 32.2614i) q^{59} +(-29.5455 + 51.1744i) q^{61} +(16.0000 - 16.0000i) q^{62} +(-18.2255 - 9.77446i) q^{63} +8.00000i q^{64} +(13.0000 + 22.5167i) q^{66} +(-53.5698 - 14.3540i) q^{67} +(-40.8563 + 10.9474i) q^{68} -51.0911i q^{69} -36.3406 q^{71} +(-2.16281 - 8.07171i) q^{72} +(-17.1198 + 63.8921i) q^{73} +(-81.3275 + 46.9545i) q^{74} -28.8634 q^{76} +(-27.5773 - 44.4862i) q^{77} +(38.0911 + 38.0911i) q^{78} +(35.6837 + 20.6020i) q^{79} +(-22.8406 - 39.5610i) q^{81} +(-10.2320 - 38.1865i) q^{82} +(9.12474 + 9.12474i) q^{83} +(-9.94644 - 32.9545i) q^{84} +(39.6475 - 68.6715i) q^{86} +(-37.6753 - 10.0951i) q^{87} +(5.47371 - 20.4282i) q^{88} +(-42.1986 - 24.3634i) q^{89} +(-79.0455 - 74.2415i) q^{91} +(-29.3861 + 29.3861i) q^{92} +(-37.9998 + 10.1820i) q^{93} +(-88.0979 + 50.8634i) q^{94} +(6.95445 - 12.0455i) q^{96} +(63.7723 - 63.7723i) q^{97} +(22.0915 + 65.6808i) q^{98} +22.0911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 16 q^{6} + 4 q^{7} - 16 q^{8} + 8 q^{11} + 8 q^{12} + 16 q^{16} + 16 q^{17} - 32 q^{18} + 100 q^{21} - 16 q^{22} + 4 q^{23} + 232 q^{27} + 40 q^{28} - 64 q^{31} + 16 q^{32} + 52 q^{33}+ \cdots + 132 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^3 - 16 * q^6 + 4 * q^7 - 16 * q^8 + 8 * q^11 + 8 * q^12 + 16 * q^16 + 16 * q^17 - 32 * q^18 + 100 * q^21 - 16 * q^22 + 4 * q^23 + 232 * q^27 + 40 * q^28 - 64 * q^31 + 16 * q^32 + 52 * q^33 + 128 * q^36 - 144 * q^37 - 8 * q^38 - 136 * q^41 - 188 * q^42 - 120 * q^43 + 8 * q^46 - 72 * q^47 + 32 * q^48 + 208 * q^51 - 76 * q^53 - 16 * q^56 + 376 * q^57 - 68 * q^58 - 324 * q^61 + 128 * q^62 - 112 * q^63 + 104 * q^66 - 124 * q^67 - 32 * q^68 + 16 * q^71 - 64 * q^72 - 32 * q^73 + 32 * q^76 - 20 * q^77 + 480 * q^78 + 124 * q^81 + 68 * q^82 - 168 * q^83 + 120 * q^86 - 428 * q^87 - 16 * q^88 - 720 * q^91 - 16 * q^92 + 64 * q^93 - 32 * q^96 + 72 * q^97 + 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more