LMFDB - Embedded newform 1205.2.b.c.724.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.3
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49572i q^{2} +1.66439i q^{3} -4.22863 q^{4} +(2.11925 - 0.713293i) q^{5} +4.15385 q^{6} +4.24911i q^{7} +5.56203i q^{8} +0.229807 q^{9} +O(q^{10})$	\(q-2.49572i q^{2} +1.66439i q^{3} -4.22863 q^{4} +(2.11925 - 0.713293i) q^{5} +4.15385 q^{6} +4.24911i q^{7} +5.56203i q^{8} +0.229807 q^{9} +(-1.78018 - 5.28905i) q^{10} -6.39942 q^{11} -7.03808i q^{12} -1.34094i q^{13} +10.6046 q^{14} +(1.18720 + 3.52726i) q^{15} +5.42403 q^{16} -1.79850i q^{17} -0.573534i q^{18} +3.80298 q^{19} +(-8.96151 + 3.01625i) q^{20} -7.07217 q^{21} +15.9712i q^{22} +5.33957i q^{23} -9.25739 q^{24} +(3.98243 - 3.02329i) q^{25} -3.34661 q^{26} +5.37566i q^{27} -17.9679i q^{28} -1.62578 q^{29} +(8.80305 - 2.96291i) q^{30} -3.96508 q^{31} -2.41281i q^{32} -10.6511i q^{33} -4.48857 q^{34} +(3.03086 + 9.00491i) q^{35} -0.971768 q^{36} +10.3760i q^{37} -9.49117i q^{38} +2.23185 q^{39} +(3.96736 + 11.7873i) q^{40} +2.25683 q^{41} +17.6502i q^{42} +1.94938i q^{43} +27.0608 q^{44} +(0.487018 - 0.163920i) q^{45} +13.3261 q^{46} +11.9862i q^{47} +9.02770i q^{48} -11.0549 q^{49} +(-7.54529 - 9.93903i) q^{50} +2.99341 q^{51} +5.67034i q^{52} +10.9623i q^{53} +13.4161 q^{54} +(-13.5620 + 4.56466i) q^{55} -23.6337 q^{56} +6.32964i q^{57} +4.05750i q^{58} -9.06104 q^{59} +(-5.02021 - 14.9154i) q^{60} +14.1035 q^{61} +9.89574i q^{62} +0.976474i q^{63} +4.82637 q^{64} +(-0.956483 - 2.84179i) q^{65} -26.5823 q^{66} +4.44323i q^{67} +7.60520i q^{68} -8.88712 q^{69} +(22.4737 - 7.56417i) q^{70} -6.47202 q^{71} +1.27819i q^{72} -4.44788i q^{73} +25.8956 q^{74} +(5.03193 + 6.62831i) q^{75} -16.0814 q^{76} -27.1918i q^{77} -5.57007i q^{78} +9.81502 q^{79} +(11.4949 - 3.86892i) q^{80} -8.25777 q^{81} -5.63241i q^{82} -14.6835i q^{83} +29.9056 q^{84} +(-1.28286 - 3.81148i) q^{85} +4.86511 q^{86} -2.70593i q^{87} -35.5938i q^{88} -10.4329 q^{89} +(-0.409098 - 1.21546i) q^{90} +5.69780 q^{91} -22.5790i q^{92} -6.59944i q^{93} +29.9143 q^{94} +(8.05945 - 2.71264i) q^{95} +4.01585 q^{96} -5.74102i q^{97} +27.5900i q^{98} -1.47063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.49572i		−	1.76474i	−0.470555	−	0.882371i	$-0.655946\pi$
$2$		−	2.49572i		−	1.76474i	0.470555	−	0.882371i	$-0.344054\pi$
$3$			1.66439i			0.960936i	0.877012	+	0.480468i	$0.159533\pi$
$3$			1.66439i			0.960936i	−0.877012	+	0.480468i	$0.840467\pi$
$4$	−4.22863			−2.11431
$5$	2.11925	−	0.713293i	0.947757	−	0.318994i
$5$	2.11925	−	0.713293i	0.947757	−	0.318994i
$6$	4.15385			1.69580
$7$			4.24911i			1.60601i	0.595972	+	0.803006i	$0.296767\pi$
$7$			4.24911i			1.60601i	−0.595972	+	0.803006i	$0.703233\pi$
$8$			5.56203i			1.96648i
$9$	0.229807			0.0766023
$10$	−1.78018	−	5.28905i	−0.562942	−	1.67255i
$11$	−6.39942			−1.92950			−0.964749	−	0.263170i	$-0.915232\pi$
$11$	−6.39942			−1.92950			−0.964749	+	0.263170i	$0.915232\pi$
$12$		−	7.03808i		−	2.03172i
$13$		−	1.34094i		−	0.371910i	−0.982558	−	0.185955i	$-0.940462\pi$
$13$		−	1.34094i		−	0.371910i	0.982558	−	0.185955i	$-0.0595379\pi$
$14$	10.6046			2.83419
$15$	1.18720	+	3.52726i	0.306533	+	0.910733i
$16$	5.42403			1.35601
$17$		−	1.79850i		−	0.436201i	−0.975926	−	0.218101i	$-0.930014\pi$
$17$		−	1.79850i		−	0.436201i	0.975926	−	0.218101i	$-0.0699861\pi$
$18$		−	0.573534i		−	0.135183i
$19$	3.80298			0.872463			0.436231	−	0.899835i	$-0.356313\pi$
$19$	3.80298			0.872463			0.436231	+	0.899835i	$0.356313\pi$
$20$	−8.96151	+	3.01625i	−2.00385	+	0.674454i
$21$	−7.07217			−1.54327
$22$			15.9712i			3.40507i
$23$			5.33957i			1.11338i	0.830721	+	0.556688i	$0.187928\pi$
$23$			5.33957i			1.11338i	−0.830721	+	0.556688i	$0.812072\pi$
$24$	−9.25739			−1.88966
$25$	3.98243	−	3.02329i	0.796485	−	0.604658i
$26$	−3.34661			−0.656325
$27$			5.37566i			1.03455i
$28$		−	17.9679i		−	3.39561i
$29$	−1.62578			−0.301900			−0.150950	−	0.988541i	$-0.548233\pi$
$29$	−1.62578			−0.301900			−0.150950	+	0.988541i	$0.548233\pi$
$30$	8.80305	−	2.96291i	1.60721	−	0.540952i
$31$	−3.96508			−0.712149			−0.356075	−	0.934458i	$-0.615885\pi$
$31$	−3.96508			−0.712149			−0.356075	+	0.934458i	$0.615885\pi$
$32$		−	2.41281i		−	0.426528i
$33$		−	10.6511i		−	1.85412i
$34$	−4.48857			−0.769783
$35$	3.03086	+	9.00491i	0.512308	+	1.52211i
$36$	−0.971768			−0.161961
$37$			10.3760i			1.70580i	0.522072	+	0.852901i	$0.325159\pi$
$37$			10.3760i			1.70580i	−0.522072	+	0.852901i	$0.674841\pi$
$38$		−	9.49117i		−	1.53967i
$39$	2.23185			0.357382
$40$	3.96736	+	11.7873i	0.627294	+	1.86374i
$41$	2.25683			0.352457			0.176228	−	0.984349i	$-0.443610\pi$
$41$	2.25683			0.352457			0.176228	+	0.984349i	$0.443610\pi$
$42$			17.6502i			2.72348i
$43$			1.94938i			0.297278i	0.988892	+	0.148639i	$0.0474892\pi$
$43$			1.94938i			0.297278i	−0.988892	+	0.148639i	$0.952511\pi$
$44$	27.0608			4.07957
$45$	0.487018	−	0.163920i	0.0726003	−	0.0244357i
$46$	13.3261			1.96482
$47$			11.9862i			1.74837i	0.485591	+	0.874186i	$0.338605\pi$
$47$			11.9862i			1.74837i	−0.485591	+	0.874186i	$0.661395\pi$
$48$			9.02770i			1.30304i
$49$	−11.0549			−1.57927
$50$	−7.54529	−	9.93903i	−1.06706	−	1.40559i
$51$	2.99341			0.419161
$52$			5.67034i			0.786334i
$53$			10.9623i			1.50578i	0.658145	+	0.752892i	$0.271342\pi$
$53$			10.9623i			1.50578i	−0.658145	+	0.752892i	$0.728658\pi$
$54$	13.4161			1.82571
$55$	−13.5620	+	4.56466i	−1.82870	+	0.615499i
$56$	−23.6337			−3.15818
$57$			6.32964i			0.838381i
$58$			4.05750i			0.532776i
$59$	−9.06104			−1.17965			−0.589823	−	0.807532i	$-0.700803\pi$
$59$	−9.06104			−1.17965			−0.589823	+	0.807532i	$0.700803\pi$
$60$	−5.02021	−	14.9154i	−0.648107	−	1.92558i
$61$	14.1035			1.80577			0.902885	−	0.429882i	$-0.141445\pi$
$61$	14.1035			1.80577			0.902885	+	0.429882i	$0.141445\pi$
$62$			9.89574i			1.25676i
$63$			0.976474i			0.123024i
$64$	4.82637			0.603296
$65$	−0.956483	−	2.84179i	−0.118637	−	0.352480i
$66$	−26.5823			−3.27205
$67$			4.44323i			0.542827i	0.962463	+	0.271413i	$0.0874911\pi$
$67$			4.44323i			0.542827i	−0.962463	+	0.271413i	$0.912509\pi$
$68$			7.60520i			0.922266i
$69$	−8.88712			−1.06988
$70$	22.4737	−	7.56417i	2.68613	−	0.904092i
$71$	−6.47202			−0.768087			−0.384044	−	0.923315i	$-0.625469\pi$
$71$	−6.47202			−0.768087			−0.384044	+	0.923315i	$0.625469\pi$
$72$			1.27819i			0.150637i
$73$		−	4.44788i		−	0.520585i	−0.965530	−	0.260293i	$-0.916181\pi$
$73$		−	4.44788i		−	0.520585i	0.965530	−	0.260293i	$-0.0838190\pi$
$74$	25.8956			3.01030
$75$	5.03193	+	6.62831i	0.581037	+	0.765371i
$76$	−16.0814			−1.84466
$77$		−	27.1918i		−	3.09880i
$78$		−	5.57007i		−	0.630686i
$79$	9.81502			1.10428			0.552138	−	0.833753i	$-0.313812\pi$
$79$	9.81502			1.10428			0.552138	+	0.833753i	$0.313812\pi$
$80$	11.4949	−	3.86892i	1.28517	−	0.432559i
$81$	−8.25777			−0.917530
$82$		−	5.63241i		−	0.621995i
$83$		−	14.6835i		−	1.61172i	−0.592105	−	0.805861i	$-0.701703\pi$
$83$		−	14.6835i		−	1.61172i	0.592105	−	0.805861i	$-0.298297\pi$
$84$	29.9056			3.26296
$85$	−1.28286	−	3.81148i	−0.139146	−	0.413413i
$86$	4.86511			0.524618
$87$		−	2.70593i		−	0.290107i
$88$		−	35.5938i		−	3.79431i
$89$	−10.4329			−1.10589			−0.552944	−	0.833219i	$-0.686496\pi$
$89$	−10.4329			−1.10589			−0.552944	+	0.833219i	$0.686496\pi$
$90$	−0.409098	−	1.21546i	−0.0431227	−	0.128121i
$91$	5.69780			0.597292
$92$		−	22.5790i		−	2.35403i
$93$		−	6.59944i		−	0.684330i
$94$	29.9143			3.08543
$95$	8.05945	−	2.71264i	0.826882	−	0.278311i
$96$	4.01585			0.409866
$97$		−	5.74102i		−	0.582913i	−0.956584	−	0.291456i	$-0.905860\pi$
$97$		−	5.74102i		−	0.582913i	0.956584	−	0.291456i	$-0.0941398\pi$
$98$			27.5900i			2.78701i
$99$	−1.47063			−0.147804
$100$	−16.8402	+	12.7844i	−1.68402	+	1.27844i
$101$	−1.30373			−0.129726			−0.0648630	−	0.997894i	$-0.520661\pi$
$101$	−1.30373			−0.129726			−0.0648630	+	0.997894i	$0.520661\pi$
$102$		−	7.47072i		−	0.739712i
$103$			12.0003i			1.18242i	0.806516	+	0.591212i	$0.201350\pi$
$103$			12.0003i			1.18242i	−0.806516	+	0.591212i	$0.798650\pi$
$104$	7.45836			0.731352
$105$	−14.9877	+	5.04453i	−1.46265	+	0.492295i
$106$	27.3588			2.65732
$107$		−	13.1936i		−	1.27547i	−0.770255	−	0.637736i	$-0.779871\pi$
$107$		−	13.1936i		−	1.27547i	0.770255	−	0.637736i	$-0.220129\pi$
$108$		−	22.7316i		−	2.18735i
$109$	−3.91188			−0.374690			−0.187345	−	0.982294i	$-0.559988\pi$
$109$	−3.91188			−0.374690			−0.187345	+	0.982294i	$0.559988\pi$
$110$	11.3921	+	33.8469i	1.08620	+	3.22718i
$111$	−17.2697			−1.63917
$112$			23.0473i			2.17776i
$113$		−	3.69680i		−	0.347765i	−0.984766	−	0.173883i	$-0.944369\pi$
$113$		−	3.69680i		−	0.347765i	0.984766	−	0.173883i	$-0.0556314\pi$
$114$	15.7970			1.47953
$115$	3.80867	+	11.3159i	0.355161	+	1.05521i
$116$	6.87482			0.638311
$117$		−	0.308157i		−	0.0284892i
$118$			22.6138i			2.08177i
$119$	7.64203			0.700544
$120$	−19.6187	+	6.60323i	−1.79093	+	0.602790i
$121$	29.9526			2.72297
$122$		−	35.1985i		−	3.18672i
$123$			3.75624i			0.338689i
$124$	16.7668			1.50571
$125$	6.28326	−	9.24774i	0.561992	−	0.827143i
$126$	2.43701			0.217106
$127$			3.75745i			0.333420i	0.986006	+	0.166710i	$0.0533143\pi$
$127$			3.75745i			0.333420i	−0.986006	+	0.166710i	$0.946686\pi$
$128$		−	16.8709i		−	1.49119i
$129$	−3.24453			−0.285665
$130$	−7.09231	+	2.38712i	−0.622037	+	0.209364i
$131$	−13.7718			−1.20325			−0.601625	−	0.798778i	$-0.705480\pi$
$131$	−13.7718			−1.20325			−0.601625	+	0.798778i	$0.705480\pi$
$132$			45.0397i			3.92020i
$133$			16.1593i			1.40119i
$134$	11.0891			0.957949
$135$	3.83442	+	11.3924i	0.330014	+	0.980498i
$136$	10.0033			0.857779
$137$		−	4.69491i		−	0.401113i	−0.979682	−	0.200557i	$-0.935725\pi$
$137$		−	4.69491i		−	0.401113i	0.979682	−	0.200557i	$-0.0642751\pi$
$138$			22.1798i			1.88807i
$139$	12.6737			1.07497			0.537483	−	0.843275i	$-0.319375\pi$
$139$	12.6737			1.07497			0.537483	+	0.843275i	$0.319375\pi$
$140$	−12.8164	−	38.0784i	−1.08318	−	3.21821i
$141$	−19.9498			−1.68007
$142$			16.1524i			1.35548i
$143$			8.58125i			0.717600i
$144$	1.24648			0.103873
$145$	−3.44544	+	1.15966i	−0.286128	+	0.0963044i
$146$	−11.1007			−0.918699
$147$		−	18.3997i		−	1.51758i
$148$		−	43.8762i		−	3.60660i
$149$	−0.645320			−0.0528667			−0.0264333	−	0.999651i	$-0.508415\pi$
$149$	−0.645320			−0.0528667			−0.0264333	+	0.999651i	$0.508415\pi$
$150$	16.5424	−	12.5583i	1.35068	−	1.02538i
$151$	8.32983			0.677872			0.338936	−	0.940809i	$-0.389933\pi$
$151$	8.32983			0.677872			0.338936	+	0.940809i	$0.389933\pi$
$152$			21.1523i			1.71568i
$153$		−	0.413309i		−	0.0334140i
$154$	−67.8632			−5.46858
$155$	−8.40299	+	2.82826i	−0.674944	+	0.227172i
$156$	−9.43765			−0.755617
$157$			2.68853i			0.214568i	0.994228	+	0.107284i	$0.0342154\pi$
$157$			2.68853i			0.214568i	−0.994228	+	0.107284i	$0.965785\pi$
$158$		−	24.4956i		−	1.94876i
$159$	−18.2455			−1.44696
$160$	−1.72104	−	5.11333i	−0.136060	−	0.404245i
$161$	−22.6884			−1.78810
$162$			20.6091i			1.61920i
$163$		−	16.9173i		−	1.32507i	−0.749033	−	0.662533i	$-0.769482\pi$
$163$		−	16.9173i		−	1.32507i	0.749033	−	0.662533i	$-0.230518\pi$
$164$	−9.54327			−0.745204
$165$	−7.59738	−	22.5724i	−0.591455	−	1.75726i
$166$	−36.6459			−2.84427
$167$		−	16.0096i		−	1.23886i	−0.785053	−	0.619428i	$-0.787365\pi$
$167$		−	16.0096i		−	1.23886i	0.785053	−	0.619428i	$-0.212635\pi$
$168$		−	39.3356i		−	3.03481i
$169$	11.2019			0.861683
$170$	−9.51238	+	3.20166i	−0.729567	+	0.245556i
$171$	0.873950			0.0668327
$172$		−	8.24320i		−	0.628538i
$173$			6.85866i			0.521454i	0.965413	+	0.260727i	$0.0839623\pi$
$173$			6.85866i			0.521454i	−0.965413	+	0.260727i	$0.916038\pi$
$174$	−6.75326			−0.511963
$175$	12.8463	+	16.9218i	0.971087	+	1.27916i
$176$	−34.7107			−2.61641
$177$		−	15.0811i		−	1.13356i
$178$			26.0377i			1.95161i
$179$	−4.54167			−0.339461			−0.169730	−	0.985491i	$-0.554290\pi$
$179$	−4.54167			−0.339461			−0.169730	+	0.985491i	$0.554290\pi$
$180$	−2.05942	+	0.693155i	−0.153500	+	0.0516647i
$181$	−21.3544			−1.58726			−0.793631	−	0.608399i	$-0.791812\pi$
$181$	−21.3544			−1.58726			−0.793631	+	0.608399i	$0.791812\pi$
$182$		−	14.2201i		−	1.05407i
$183$			23.4738i			1.73523i
$184$	−29.6988			−2.18943
$185$	7.40112	+	21.9893i	0.544141	+	1.61669i
$186$	−16.4704			−1.20767
$187$			11.5094i			0.841650i
$188$		−	50.6853i		−	3.69661i
$189$	−22.8417			−1.66149
$190$	−6.76999	−	20.1142i	−0.491146	−	1.45923i
$191$	6.63439			0.480047			0.240024	−	0.970767i	$-0.422845\pi$
$191$	6.63439			0.480047			0.240024	+	0.970767i	$0.422845\pi$
$192$			8.03296i			0.579729i
$193$		−	11.4179i		−	0.821878i	−0.911663	−	0.410939i	$-0.865201\pi$
$193$		−	11.4179i		−	0.821878i	0.911663	−	0.410939i	$-0.134799\pi$
$194$	−14.3280			−1.02869
$195$	4.72984	−	1.59196i	0.338711	−	0.114003i
$196$	46.7470			3.33907
$197$			22.5597i			1.60731i	0.595093	+	0.803657i	$0.297115\pi$
$197$			22.5597i			1.60731i	−0.595093	+	0.803657i	$0.702885\pi$
$198$			3.67029i			0.260836i
$199$	24.5485			1.74019			0.870097	−	0.492881i	$-0.164056\pi$
$199$	24.5485			1.74019			0.870097	+	0.492881i	$0.164056\pi$
$200$	16.8156	+	22.1504i	1.18904	+	1.56627i
$201$	−7.39526			−0.521622
$202$			3.25375i			0.228933i
$203$		−	6.90812i		−	0.484855i
$204$	−12.6580			−0.886239
$205$	4.78277	−	1.60978i	0.334043	−	0.112432i
$206$	29.9494			2.08667
$207$			1.22707i			0.0852872i
$208$		−	7.27330i		−	0.504313i
$209$	−24.3369			−1.68342
$210$	12.5897	+	37.4051i	0.868774	+	2.58120i
$211$	−5.29691			−0.364654			−0.182327	−	0.983238i	$-0.558363\pi$
$211$	−5.29691			−0.364654			−0.182327	+	0.983238i	$0.558363\pi$
$212$		−	46.3553i		−	3.18370i
$213$		−	10.7720i		−	0.738083i
$214$	−32.9275			−2.25088
$215$	1.39048	+	4.13122i	0.0948298	+	0.281747i
$216$	−29.8996			−2.03441
$217$		−	16.8480i		−	1.14372i
$218$			9.76296i			0.661231i
$219$	7.40301			0.500249
$220$	57.3485	−	19.3023i	3.86644	−	1.30136i
$221$	−2.41169			−0.162228
$222$			43.1004i			2.89271i
$223$		−	9.77130i		−	0.654335i	−0.944966	−	0.327167i	$-0.893906\pi$
$223$		−	9.77130i		−	0.654335i	0.944966	−	0.327167i	$-0.106094\pi$
$224$	10.2523			0.685008
$225$	0.915189	−	0.694773i	0.0610126	−	0.0463182i
$226$	−9.22618			−0.613716
$227$		−	6.78250i		−	0.450170i	−0.974339	−	0.225085i	$-0.927734\pi$
$227$		−	6.78250i		−	0.450170i	0.974339	−	0.225085i	$-0.0722660\pi$
$228$		−	26.7657i		−	1.77260i
$229$	−5.63514			−0.372381			−0.186190	−	0.982514i	$-0.559614\pi$
$229$	−5.63514			−0.372381			−0.186190	+	0.982514i	$0.559614\pi$
$230$	28.2413	−	9.50539i	1.86217	−	0.626767i
$231$	45.2578			2.97774
$232$		−	9.04265i		−	0.593679i
$233$		−	1.29396i		−	0.0847702i	−0.999101	−	0.0423851i	$-0.986504\pi$
$233$		−	1.29396i		−	0.0847702i	0.999101	−	0.0423851i	$-0.0134956\pi$
$234$	−0.769075			−0.0502760
$235$	8.54970	+	25.4018i	0.557721	+	1.65703i
$236$	38.3157			2.49414
$237$			16.3360i			1.06114i
$238$		−	19.0724i		−	1.23628i
$239$	0.893288			0.0577820			0.0288910	−	0.999583i	$-0.490802\pi$
$239$	0.893288			0.0577820			0.0288910	+	0.999583i	$0.490802\pi$
$240$	6.43939	+	19.1319i	0.415661	+	1.23496i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	74.7534i		−	4.80533i
$243$			2.38283i			0.152858i
$244$	−59.6385			−3.81796
$245$	−23.4281	+	7.88538i	−1.49677	+	0.503779i
$246$	9.37452			0.597698
$247$		−	5.09957i		−	0.324478i
$248$		−	22.0539i		−	1.40042i
$249$	24.4390			1.54876
$250$	−23.0798	−	15.6813i	−1.45969	−	0.991771i
$251$	15.9569			1.00719			0.503595	−	0.863940i	$-0.332010\pi$
$251$	15.9569			1.00719			0.503595	+	0.863940i	$0.332010\pi$
$252$		−	4.12914i		−	0.260112i
$253$		−	34.1702i		−	2.14826i
$254$	9.37754			0.588399
$255$	6.34378	−	2.13518i	0.397263	−	0.133710i
$256$	−32.4523			−2.02827
$257$		−	1.49006i		−	0.0929473i	−0.998920	−	0.0464736i	$-0.985202\pi$
$257$		−	1.49006i		−	0.0929473i	0.998920	−	0.0464736i	$-0.0147984\pi$
$258$			8.09744i			0.504124i
$259$	−44.0887			−2.73954
$260$	4.04461	+	12.0169i	0.250836	+	0.745254i
$261$	−0.373616			−0.0231262
$262$			34.3707i			2.12343i
$263$			17.3437i			1.06946i	0.845023	+	0.534731i	$0.179587\pi$
$263$			17.3437i			1.06946i	−0.845023	+	0.534731i	$0.820413\pi$
$264$	59.2420			3.64609
$265$	7.81931	+	23.2318i	0.480336	+	1.42712i
$266$	40.3290			2.47273
$267$		−	17.3644i		−	1.06269i
$268$		−	18.7888i		−	1.14771i
$269$	17.9557			1.09478			0.547388	−	0.836879i	$-0.315622\pi$
$269$	17.9557			1.09478			0.547388	+	0.836879i	$0.315622\pi$
$270$	28.4321	−	9.56964i	1.73033	−	0.582390i
$271$	−14.3727			−0.873078			−0.436539	−	0.899685i	$-0.643796\pi$
$271$	−14.3727			−0.873078			−0.436539	+	0.899685i	$0.643796\pi$
$272$		−	9.75514i		−	0.591492i
$273$			9.48336i			0.573959i
$274$	−11.7172			−0.707861
$275$	−25.4852	+	19.3473i	−1.53682	+	1.16669i
$276$	37.5803			2.26207
$277$		−	1.25592i		−	0.0754612i	−0.999288	−	0.0377306i	$-0.987987\pi$
$277$		−	1.25592i		−	0.0754612i	0.999288	−	0.0377306i	$-0.0120129\pi$
$278$		−	31.6299i		−	1.89704i
$279$	−0.911203			−0.0545523
$280$	−50.0856	+	16.8577i	−2.99319	+	1.00744i
$281$	22.3278			1.33197			0.665983	−	0.745967i	$-0.268012\pi$
$281$	22.3278			1.33197			0.665983	+	0.745967i	$0.268012\pi$
$282$			49.7891i			2.96490i
$283$		−	10.3956i		−	0.617952i	−0.951070	−	0.308976i	$-0.900014\pi$
$283$		−	10.3956i		−	0.617952i	0.951070	−	0.308976i	$-0.0999863\pi$
$284$	27.3678			1.62398
$285$	4.51488	+	13.4141i	0.267439	+	0.794581i
$286$	21.4164			1.26638
$287$			9.58949i			0.566050i
$288$		−	0.554479i		−	0.0326730i
$289$	13.7654			0.809728
$290$	2.89418	+	8.59885i	0.169952	+	0.504942i
$291$	9.55530			0.560142
$292$			18.8084i			1.10068i
$293$			23.3313i			1.36303i	0.731805	+	0.681514i	$0.238678\pi$
$293$			23.3313i			1.36303i	−0.731805	+	0.681514i	$0.761322\pi$
$294$	−45.9204			−2.67813
$295$	−19.2026	+	6.46317i	−1.11802	+	0.376300i
$296$	−57.7116			−3.35442
$297$		−	34.4011i		−	1.99615i
$298$			1.61054i			0.0932960i
$299$	7.16004			0.414076
$300$	−21.2782	−	28.0286i	−1.22850	−	1.61823i
$301$	−8.28312			−0.477431
$302$		−	20.7889i		−	1.19627i
$303$		−	2.16991i		−	0.124658i
$304$	20.6275			1.18307
$305$	29.8889	−	10.0599i	1.71143	−	0.576030i
$306$	−1.03150			−0.0589671
$307$			15.6330i			0.892220i	0.894978	+	0.446110i	$0.147191\pi$
$307$			15.6330i			0.892220i	−0.894978	+	0.446110i	$0.852809\pi$
$308$			114.984i			6.55183i
$309$	−19.9732			−1.13623
$310$	7.05856	+	20.9715i	0.400899	+	1.19110i
$311$	−26.6480			−1.51107			−0.755535	−	0.655108i	$-0.772623\pi$
$311$	−26.6480			−1.51107			−0.755535	+	0.655108i	$0.772623\pi$
$312$			12.4136i			0.702782i
$313$			2.78211i			0.157254i	0.996904	+	0.0786272i	$0.0250537\pi$
$313$			2.78211i			0.157254i	−0.996904	+	0.0786272i	$0.974946\pi$
$314$	6.70982			0.378657
$315$	0.696512	+	2.06939i	0.0392440	+	0.116597i
$316$	−41.5040			−2.33478
$317$		−	19.6989i		−	1.10640i	−0.833049	−	0.553200i	$-0.813407\pi$
$317$		−	19.6989i		−	1.10640i	0.833049	−	0.553200i	$-0.186593\pi$
$318$			45.5356i			2.55351i
$319$	10.4041			0.582516
$320$	10.2283	−	3.44261i	0.571778	−	0.192448i
$321$	21.9593			1.22565
$322$			56.6239i			3.15553i
$323$		−	6.83967i		−	0.380569i
$324$	34.9190			1.93995
$325$	−4.05405	−	5.34020i	−0.224878	−	0.296221i
$326$	−42.2209			−2.33840
$327$		−	6.51089i		−	0.360053i
$328$			12.5525i			0.693098i
$329$	−50.9308			−2.80791
$330$	−56.3344	+	18.9609i	−3.10111	+	1.04377i
$331$	15.0620			0.827882			0.413941	−	0.910304i	$-0.364152\pi$
$331$	15.0620			0.827882			0.413941	+	0.910304i	$0.364152\pi$
$332$			62.0910i			3.40768i
$333$			2.38448i			0.130668i
$334$	−39.9554			−2.18626
$335$	3.16932	+	9.41631i	0.173159	+	0.514468i
$336$	−38.3597			−2.09269
$337$			16.6018i			0.904359i	0.891927	+	0.452180i	$0.149353\pi$
$337$			16.6018i			0.904359i	−0.891927	+	0.452180i	$0.850647\pi$
$338$		−	27.9568i		−	1.52065i
$339$	6.15291			0.334180
$340$	5.42474	+	16.1173i	0.294198	+	0.874084i
$341$	25.3742			1.37409
$342$		−	2.18114i		−	0.117942i
$343$		−	17.2297i		−	0.930316i
$344$	−10.8425			−0.584589
$345$	−18.8340	+	6.33912i	−1.01399	+	0.341287i
$346$	17.1173			0.920232
$347$		−	15.8055i		−	0.848486i	−0.905549	−	0.424243i	$-0.860540\pi$
$347$		−	15.8055i		−	0.848486i	0.905549	−	0.424243i	$-0.139460\pi$
$348$			11.4424i			0.613376i
$349$	8.70148			0.465779			0.232890	−	0.972503i	$-0.425182\pi$
$349$	8.70148			0.465779			0.232890	+	0.972503i	$0.425182\pi$
$350$	42.2320	−	32.0607i	2.25739	−	1.71372i
$351$	7.20844			0.384758
$352$			15.4406i			0.822985i
$353$		−	21.5327i		−	1.14607i	−0.819531	−	0.573035i	$-0.805766\pi$
$353$		−	21.5327i		−	1.14607i	0.819531	−	0.573035i	$-0.194234\pi$
$354$	−37.6382			−2.00045
$355$	−13.7158	+	4.61644i	−0.727960	+	0.245015i
$356$	44.1169			2.33819
$357$			12.7193i			0.673178i
$358$			11.3348i			0.599060i
$359$	−10.5631			−0.557498			−0.278749	−	0.960364i	$-0.589920\pi$
$359$	−10.5631			−0.557498			−0.278749	+	0.960364i	$0.589920\pi$
$360$	0.911726	+	2.70881i	0.0480522	+	0.142767i
$361$	−4.53736			−0.238809
$362$			53.2947i			2.80111i
$363$			49.8528i			2.61660i
$364$	−24.0939			−1.26286
$365$	−3.17264	−	9.42617i	−0.166064	−	0.493388i
$366$	58.5840			3.06223
$367$		−	29.8064i		−	1.55588i	−0.628339	−	0.777939i	$-0.716265\pi$
$367$		−	29.8064i		−	1.55588i	0.628339	−	0.777939i	$-0.283735\pi$
$368$			28.9620i			1.50975i
$369$	0.518634			0.0269990
$370$	54.8792	−	18.4711i	2.85303	−	0.960269i
$371$	−46.5798			−2.41830
$372$			27.9066i			1.44689i
$373$			18.0975i			0.937051i	0.883450	+	0.468526i	$0.155215\pi$
$373$			18.0975i			0.937051i	−0.883450	+	0.468526i	$0.844785\pi$
$374$	28.7242			1.48529
$375$	15.3918	+	10.4578i	0.794831	+	0.540038i
$376$	−66.6678			−3.43813
$377$			2.18008i			0.112280i
$378$			57.0066i			2.93210i
$379$	−20.2276			−1.03902			−0.519512	−	0.854463i	$-0.673886\pi$
$379$	−20.2276			−1.03902			−0.519512	+	0.854463i	$0.673886\pi$
$380$	−34.0804	+	11.4707i	−1.74829	+	0.588436i
$381$	−6.25386			−0.320395
$382$		−	16.5576i		−	0.847160i
$383$			4.68748i			0.239519i	0.992803	+	0.119760i	$0.0382123\pi$
$383$			4.68748i			0.239519i	−0.992803	+	0.119760i	$0.961788\pi$
$384$	28.0797			1.43294
$385$	−19.3957	−	57.6262i	−0.988498	−	2.93691i
$386$	−28.4959			−1.45040
$387$			0.447981i			0.0227721i
$388$			24.2766i			1.23246i
$389$	15.4056			0.781094			0.390547	−	0.920583i	$-0.372286\pi$
$389$	15.4056			0.781094			0.390547	+	0.920583i	$0.372286\pi$
$390$	−3.97309	−	11.8044i	−0.201185	−	0.597737i
$391$	9.60323			0.485656
$392$		−	61.4877i		−	3.10560i
$393$		−	22.9217i		−	1.15625i
$394$	56.3028			2.83649
$395$	20.8005	−	7.00098i	1.04658	−	0.352258i
$396$	6.21875			0.312504
$397$		−	38.1510i		−	1.91474i	−0.288857	−	0.957372i	$-0.593275\pi$
$397$		−	38.1510i		−	1.91474i	0.288857	−	0.957372i	$-0.406725\pi$
$398$		−	61.2661i		−	3.07099i
$399$	−26.8953			−1.34645
$400$	21.6008	−	16.3984i	1.08004	−	0.819921i
$401$	32.9356			1.64472			0.822362	−	0.568965i	$-0.192656\pi$
$401$	32.9356			1.64472			0.822362	+	0.568965i	$0.192656\pi$
$402$			18.4565i			0.920528i
$403$			5.31694i			0.264856i
$404$	5.51299			0.274281
$405$	−17.5003	+	5.89021i	−0.869595	+	0.292687i
$406$	−17.2407			−0.855644
$407$		−	66.4004i		−	3.29134i
$408$			16.6494i			0.824271i
$409$	19.1149			0.945169			0.472584	−	0.881285i	$-0.343321\pi$
$409$	19.1149			0.945169			0.472584	+	0.881285i	$0.343321\pi$
$410$	−4.01756	−	11.9365i	−0.198413	−	0.589500i
$411$	7.81416			0.385444
$412$		−	50.7448i		−	2.50002i
$413$		−	38.5013i		−	1.89453i
$414$	3.06242			0.150510
$415$	−10.4736	−	31.1179i	−0.514130	−	1.52752i
$416$	−3.23543			−0.158630
$417$			21.0939i			1.03297i
$418$			60.7380i			2.97079i
$419$	−0.832487			−0.0406696			−0.0203348	−	0.999793i	$-0.506473\pi$
$419$	−0.832487			−0.0406696			−0.0203348	+	0.999793i	$0.506473\pi$
$420$	63.3773	−	21.3314i	3.09250	−	1.04087i
$421$	2.06135			0.100464			0.0502321	−	0.998738i	$-0.484004\pi$
$421$	2.06135			0.100464			0.0502321	+	0.998738i	$0.484004\pi$
$422$			13.2196i			0.643521i
$423$			2.75452i			0.133929i
$424$	−60.9725			−2.96109
$425$	−5.43740	−	7.16241i	−0.263753	−	0.347428i
$426$	−26.8838			−1.30253
$427$			59.9273i			2.90009i
$428$			55.7908i			2.69675i
$429$	−14.2825			−0.689568
$430$	10.3104	−	3.47025i	0.497210	−	0.167350i
$431$	−16.1802			−0.779375			−0.389688	−	0.920947i	$-0.627417\pi$
$431$	−16.1802			−0.779375			−0.389688	+	0.920947i	$0.627417\pi$
$432$			29.1577i			1.40285i
$433$			21.6854i			1.04213i	0.853517	+	0.521066i	$0.174465\pi$
$433$			21.6854i			1.04213i	−0.853517	+	0.521066i	$0.825535\pi$
$434$	−42.0480			−2.01837
$435$	−1.93012	−	5.73455i	−0.0925423	−	0.274950i
$436$	16.5419			0.792212
$437$			20.3063i			0.971380i
$438$		−	18.4759i		−	0.882810i
$439$	26.9940			1.28836			0.644178	−	0.764876i	$-0.277200\pi$
$439$	26.9940			1.28836			0.644178	+	0.764876i	$0.277200\pi$
$440$	−25.3888	−	75.4321i	−1.21036	−	3.59608i
$441$	−2.54049			−0.120976
$442$			6.01890i			0.286290i
$443$		−	26.0917i		−	1.23965i	−0.784739	−	0.619826i	$-0.787203\pi$
$443$		−	26.0917i		−	1.23965i	0.784739	−	0.619826i	$-0.212797\pi$
$444$	73.0271			3.46571
$445$	−22.1099	+	7.44173i	−1.04811	+	0.352772i
$446$	−24.3864			−1.15473
$447$		−	1.07406i		−	0.0508015i
$448$			20.5078i			0.968900i
$449$	21.4983			1.01457			0.507285	−	0.861778i	$-0.330649\pi$
$449$	21.4983			1.01457			0.507285	+	0.861778i	$0.330649\pi$
$450$	−1.73396	−	2.28406i	−0.0817396	−	0.107672i
$451$	−14.4424			−0.680065
$452$			15.6324i			0.735285i
$453$			13.8641i			0.651391i
$454$	−16.9272			−0.794434
$455$	12.0751	−	4.06420i	0.566087	−	0.190533i
$456$	−35.2056			−1.64866
$457$			17.4405i			0.815831i	0.913020	+	0.407915i	$0.133744\pi$
$457$			17.4405i			0.815831i	−0.913020	+	0.407915i	$0.866256\pi$
$458$			14.0637i			0.657156i
$459$	9.66814			0.451270
$460$	−16.1055	−	47.8506i	−0.750921	−	2.23104i
$461$	−4.48673			−0.208968			−0.104484	−	0.994527i	$-0.533319\pi$
$461$	−4.48673			−0.208968			−0.104484	+	0.994527i	$0.533319\pi$
$462$		−	112.951i		−	5.25495i
$463$			5.29000i			0.245847i	0.992416	+	0.122924i	$0.0392270\pi$
$463$			5.29000i			0.245847i	−0.992416	+	0.122924i	$0.960773\pi$
$464$	−8.81829			−0.409379
$465$	−4.70733	−	13.9858i	−0.218297	−	0.648578i
$466$	−3.22937			−0.149598
$467$			35.3907i			1.63768i	0.574018	+	0.818842i	$0.305384\pi$
$467$			35.3907i			1.63768i	−0.574018	+	0.818842i	$0.694616\pi$
$468$			1.30308i			0.0602350i
$469$	−18.8798			−0.871786
$470$	63.3959	−	21.3377i	2.92423	−	0.984233i
$471$	−4.47476			−0.206186
$472$		−	50.3978i		−	2.31975i
$473$		−	12.4749i		−	0.573597i
$474$	40.7701			1.87263
$475$	15.1451	−	11.4975i	0.694904	−	0.527542i
$476$	−32.3153			−1.48117
$477$			2.51920i			0.115346i
$478$		−	2.22940i		−	0.101970i
$479$	38.1256			1.74200			0.871002	−	0.491279i	$-0.163471\pi$
$479$	38.1256			1.74200			0.871002	+	0.491279i	$0.163471\pi$
$480$	8.51058	−	2.86448i	0.388453	−	0.130745i
$481$	13.9136			0.634405
$482$		−	2.49572i		−	0.113677i
$483$		−	37.7623i		−	1.71824i
$484$	−126.658			−5.75720
$485$	−4.09503	−	12.1667i	−0.185946	−	0.552459i
$486$	5.94688			0.269756
$487$		−	8.85116i		−	0.401084i	−0.979685	−	0.200542i	$-0.935730\pi$
$487$		−	8.85116i		−	0.401084i	0.979685	−	0.200542i	$-0.0642704\pi$
$488$			78.4442i			3.55100i
$489$	28.1570			1.27330
$490$	19.6797	+	58.4700i	0.889039	+	2.64140i
$491$	6.67644			0.301304			0.150652	−	0.988587i	$-0.451863\pi$
$491$	6.67644			0.301304			0.150652	+	0.988587i	$0.451863\pi$
$492$		−	15.8837i		−	0.716094i
$493$			2.92397i			0.131689i
$494$	−12.7271			−0.572619
$495$	−3.11663	+	1.04899i	−0.140082	+	0.0471486i
$496$	−21.5067			−0.965680
$497$		−	27.5003i		−	1.23356i
$498$		−	60.9930i		−	2.73316i
$499$	23.1701			1.03724			0.518619	−	0.855006i	$-0.326446\pi$
$499$	23.1701			1.03724			0.518619	+	0.855006i	$0.326446\pi$
$500$	−26.5696	+	39.1052i	−1.18823	+	1.74884i
$501$	26.6461			1.19046
$502$		−	39.8240i		−	1.77743i
$503$		−	2.36856i		−	0.105609i	−0.998605	−	0.0528044i	$-0.983184\pi$
$503$		−	2.36856i		−	0.105609i	0.998605	−	0.0528044i	$-0.0168160\pi$
$504$	−5.43118			−0.241924
$505$	−2.76293	+	0.929941i	−0.122949	+	0.0413818i
$506$	−85.2792			−3.79112
$507$			18.6443i			0.828022i
$508$		−	15.8888i		−	0.704954i
$509$	−11.4066			−0.505590			−0.252795	−	0.967520i	$-0.581350\pi$
$509$	−11.4066			−0.505590			−0.252795	+	0.967520i	$0.581350\pi$
$510$	−5.32881	−	15.8323i	−0.235964	−	0.701067i
$511$	18.8995			0.836066
$512$			47.2501i			2.08818i
$513$			20.4435i			0.902603i
$514$	−3.71877			−0.164028
$515$	8.55972	+	25.4316i	0.377187	+	1.12065i
$516$	13.7199			0.603985
$517$		−	76.7050i		−	3.37348i
$518$			110.033i			4.83458i
$519$	−11.4155			−0.501084
$520$	15.8061	−	5.31999i	0.693144	−	0.233297i
$521$	−8.79487			−0.385310			−0.192655	−	0.981267i	$-0.561710\pi$
$521$	−8.79487			−0.385310			−0.192655	+	0.981267i	$0.561710\pi$
$522$			0.932441i			0.0408118i
$523$		−	9.06170i		−	0.396241i	−0.980178	−	0.198120i	$-0.936516\pi$
$523$		−	9.06170i		−	0.396241i	0.980178	−	0.198120i	$-0.0634837\pi$
$524$	58.2359			2.54405
$525$	−28.1644	+	21.3812i	−1.22919	+	0.933152i
$526$	43.2852			1.88732
$527$			7.13121i			0.310640i
$528$		−	57.7721i		−	2.51421i
$529$	−5.51097			−0.239608
$530$	57.9800	−	19.5148i	2.51849	−	0.847669i
$531$	−2.08229			−0.0903636
$532$		−	68.3315i		−	2.96254i
$533$		−	3.02627i		−	0.131082i
$534$	−43.3368			−1.87537
$535$	−9.41090	−	27.9605i	−0.406869	−	1.20884i
$536$	−24.7134			−1.06746
$537$		−	7.55911i		−	0.326200i
$538$		−	44.8123i		−	1.93200i
$539$	70.7450			3.04720
$540$	−16.2143	−	48.1740i	−0.697753	−	2.07308i
$541$	−39.4094			−1.69434			−0.847171	−	0.531320i	$-0.821696\pi$
$541$	−39.4094			−1.69434			−0.847171	+	0.531320i	$0.821696\pi$
$542$			35.8702i			1.54076i
$543$		−	35.5421i		−	1.52526i
$544$	−4.33944			−0.186052
$545$	−8.29024	+	2.79032i	−0.355115	+	0.119524i
$546$	23.6678			1.01289
$547$			12.2963i			0.525753i	0.964829	+	0.262877i	$0.0846712\pi$
$547$			12.2963i			0.525753i	−0.964829	+	0.262877i	$0.915329\pi$
$548$			19.8530i			0.848079i
$549$	3.24109			0.138326
$550$	48.2855	+	63.6041i	2.05890	+	2.71209i
$551$	−6.18281			−0.263397
$552$		−	49.4304i		−	2.10390i
$553$			41.7050i			1.77348i
$554$	−3.13444			−0.133169
$555$	−36.5988	+	12.3184i	−1.55353	+	0.522885i
$556$	−53.5922			−2.27281
$557$			16.8825i			0.715333i	0.933849	+	0.357667i	$0.116428\pi$
$557$			16.8825i			0.715333i	−0.933849	+	0.357667i	$0.883572\pi$
$558$			2.27411i			0.0962707i
$559$	2.61400			0.110561
$560$	16.4395	+	48.8429i	0.694694	+	2.06399i
$561$	−19.1561			−0.808772
$562$		−	55.7240i		−	2.35058i
$563$			3.43922i			0.144946i	0.997370	+	0.0724729i	$0.0230891\pi$
$563$			3.43922i			0.144946i	−0.997370	+	0.0724729i	$0.976911\pi$
$564$	84.3601			3.55220
$565$	−2.63690	−	7.83443i	−0.110935	−	0.329597i
$566$	−25.9444			−1.09053
$567$		−	35.0881i		−	1.47356i
$568$		−	35.9976i		−	1.51042i
$569$	18.8153			0.788779			0.394390	−	0.918943i	$-0.370956\pi$
$569$	18.8153			0.788779			0.394390	+	0.918943i	$0.370956\pi$
$570$	33.4778	−	11.2679i	1.40223	−	0.471960i
$571$	−28.5582			−1.19512			−0.597562	−	0.801823i	$-0.703864\pi$
$571$	−28.5582			−1.19512			−0.597562	+	0.801823i	$0.703864\pi$
$572$		−	36.2869i		−	1.51723i
$573$			11.0422i			0.461295i
$574$	23.9327			0.998932
$575$	16.1431	+	21.2644i	0.673212	+	0.886788i
$576$	1.10913			0.0462139
$577$		−	10.0008i		−	0.416337i	−0.978093	−	0.208169i	$-0.933250\pi$
$577$		−	10.0008i		−	0.416337i	0.978093	−	0.208169i	$-0.0667503\pi$
$578$		−	34.3546i		−	1.42896i
$579$	19.0038			0.789772
$580$	14.5695	−	4.90376i	0.604964	−	0.203618i
$581$	62.3917			2.58844
$582$		−	23.8474i		−	0.988505i
$583$		−	70.1522i		−	2.90541i
$584$	24.7393			1.02372
$585$	−0.219806	−	0.653062i	−0.00908788	−	0.0270008i
$586$	58.2284			2.40539
$587$		−	26.7660i		−	1.10475i	−0.833595	−	0.552376i	$-0.813721\pi$
$587$		−	26.7660i		−	1.10475i	0.833595	−	0.552376i	$-0.186279\pi$
$588$			77.8053i			3.20864i
$589$	−15.0791			−0.621324
$590$	16.1303	+	47.9243i	0.664073	+	1.97301i
$591$	−37.5482			−1.54453
$592$			56.2797i			2.31308i
$593$			18.5431i			0.761472i	0.924684	+	0.380736i	$0.124329\pi$
$593$			18.5431i			0.761472i	−0.924684	+	0.380736i	$0.875671\pi$
$594$	−85.8556			−3.52270
$595$	16.1954	−	5.45101i	0.663945	−	0.223470i
$596$	2.72882			0.111777
$597$			40.8582i			1.67221i
$598$		−	17.8695i		−	0.730737i
$599$	0.913482			0.0373239			0.0186619	−	0.999826i	$-0.494059\pi$
$599$	0.913482			0.0373239			0.0186619	+	0.999826i	$0.494059\pi$
$600$	−36.8669	+	27.9878i	−1.50508	+	1.14260i
$601$	16.1779			0.659912			0.329956	−	0.943996i	$-0.392966\pi$
$601$	16.1779			0.659912			0.329956	+	0.943996i	$0.392966\pi$
$602$			20.6724i			0.842542i
$603$			1.02108i			0.0415818i
$604$	−35.2237			−1.43323
$605$	63.4771	−	21.3650i	2.58071	−	0.868610i
$606$	−5.41550			−0.219990
$607$		−	16.6396i		−	0.675380i	−0.941257	−	0.337690i	$-0.890354\pi$
$607$		−	16.6396i		−	0.675380i	0.941257	−	0.337690i	$-0.109646\pi$
$608$		−	9.17584i		−	0.372130i
$609$	11.4978			0.465914
$610$	−25.1068	−	74.5943i	−1.01654	−	3.02023i
$611$	16.0728			0.650237
$612$			1.74773i			0.0706477i
$613$			9.20938i			0.371963i	0.982553	+	0.185982i	$0.0595465\pi$
$613$			9.20938i			0.371963i	−0.982553	+	0.185982i	$0.940454\pi$
$614$	39.0155			1.57454
$615$	2.67930	+	7.96040i	0.108040	+	0.320994i
$616$	151.242			6.09371
$617$			14.7257i			0.592836i	0.955058	+	0.296418i	$0.0957922\pi$
$617$			14.7257i			0.592836i	−0.955058	+	0.296418i	$0.904208\pi$
$618$			49.8475i			2.00516i
$619$	−2.38884			−0.0960155			−0.0480077	−	0.998847i	$-0.515287\pi$
$619$	−2.38884			−0.0960155			−0.0480077	+	0.998847i	$0.515287\pi$
$620$	35.5331	−	11.9597i	1.42704	−	0.480312i
$621$	−28.7037			−1.15184
$622$			66.5060i			2.66665i
$623$		−	44.3306i		−	1.77607i
$624$	12.1056			0.484612
$625$	6.71945	−	24.0801i	0.268778	−	0.963202i
$626$	6.94338			0.277513
$627$		−	40.5060i		−	1.61765i
$628$		−	11.3688i		−	0.453664i
$629$	18.6613			0.744073
$630$	5.16462	−	1.73830i	0.205764	−	0.0692555i
$631$	−9.31118			−0.370672			−0.185336	−	0.982675i	$-0.559337\pi$
$631$	−9.31118			−0.370672			−0.185336	+	0.982675i	$0.559337\pi$
$632$			54.5914i			2.17153i
$633$		−	8.81612i		−	0.350409i
$634$	−49.1629			−1.95251
$635$	2.68016	+	7.96297i	0.106359	+	0.316001i
$636$	77.1533			3.05933
$637$			14.8240i			0.587347i
$638$		−	25.9657i		−	1.02799i
$639$	−1.48731			−0.0588373
$640$	−12.0339	−	35.7536i	−0.475681	−	1.41328i
$641$	8.83364			0.348908			0.174454	−	0.984665i	$-0.444184\pi$
$641$	8.83364			0.348908			0.174454	+	0.984665i	$0.444184\pi$
$642$		−	54.8043i		−	2.16295i
$643$		−	7.12073i		−	0.280814i	−0.990094	−	0.140407i	$-0.955159\pi$
$643$		−	7.12073i		−	0.280814i	0.990094	−	0.140407i	$-0.0448411\pi$
$644$	95.9407			3.78059
$645$	−6.87596	+	2.31430i	−0.270741	+	0.0911254i
$646$	−17.0699			−0.671607
$647$			25.6415i			1.00807i	0.863683	+	0.504036i	$0.168152\pi$
$647$			25.6415i			1.00807i	−0.863683	+	0.504036i	$0.831848\pi$
$648$		−	45.9300i		−	1.80430i
$649$	57.9854			2.27613
$650$	−13.3276	+	10.1178i	−0.522753	+	0.396852i
$651$	28.0417			1.09904
$652$			71.5370i			2.80160i
$653$			1.15251i			0.0451011i	0.999746	+	0.0225506i	$0.00717867\pi$
$653$			1.15251i			0.0451011i	−0.999746	+	0.0225506i	$0.992821\pi$
$654$	−16.2494			−0.635401
$655$	−29.1859	+	9.82335i	−1.14039	+	0.383830i
$656$	12.2411			0.477934
$657$		−	1.02215i		−	0.0398780i
$658$			127.109i			4.95523i
$659$	−40.1918			−1.56565			−0.782826	−	0.622241i	$-0.786223\pi$
$659$	−40.1918			−1.56565			−0.782826	+	0.622241i	$0.786223\pi$
$660$	32.1265	+	95.4503i	1.25052	+	3.71540i
$661$	−37.9960			−1.47787			−0.738937	−	0.673774i	$-0.764672\pi$
$661$	−37.9960			−1.47787			−0.738937	+	0.673774i	$0.764672\pi$
$662$		−	37.5905i		−	1.46100i
$663$		−	4.01399i		−	0.155890i
$664$	81.6700			3.16941
$665$	11.5263	+	34.2455i	0.446970	+	1.32798i
$666$	5.95099			0.230596
$667$		−	8.68097i		−	0.336129i
$668$			67.6984i			2.61933i
$669$	16.2633			0.628774
$670$	23.5005	−	7.90975i	0.907903	−	0.305580i
$671$	−90.2544			−3.48423
$672$			17.0638i			0.658249i
$673$			10.4706i			0.403611i	0.979426	+	0.201805i	$0.0646808\pi$
$673$			10.4706i			0.403611i	−0.979426	+	0.201805i	$0.935319\pi$
$674$	41.4336			1.59596
$675$	16.2522	+	21.4082i	0.625546	+	0.824001i
$676$	−47.3686			−1.82187
$677$		−	9.18573i		−	0.353036i	−0.984297	−	0.176518i	$-0.943517\pi$
$677$		−	9.18573i		−	0.353036i	0.984297	−	0.176518i	$-0.0564834\pi$
$678$		−	15.3560i		−	0.589742i
$679$	24.3942			0.936164
$680$	21.1996	−	7.13531i	0.812966	−	0.273627i
$681$	11.2887			0.432584
$682$		−	63.3270i		−	2.42492i
$683$			17.9966i			0.688620i	0.938856	+	0.344310i	$0.111887\pi$
$683$			17.9966i			0.688620i	−0.938856	+	0.344310i	$0.888113\pi$
$684$	−3.69561			−0.141305
$685$	−3.34885	−	9.94968i	−0.127953	−	0.380158i
$686$	−43.0005			−1.64177
$687$		−	9.37907i		−	0.357834i
$688$			10.5735i			0.403111i
$689$	14.6998			0.560016
$690$	15.8207	+	47.0045i	0.602283	+	1.78943i
$691$	49.5109			1.88349			0.941743	−	0.336335i	$-0.109187\pi$
$691$	49.5109			1.88349			0.941743	+	0.336335i	$0.109187\pi$
$692$		−	29.0027i		−	1.10252i
$693$		−	6.24887i		−	0.237375i
$694$	−39.4462			−1.49736
$695$	26.8586	−	9.04003i	1.01881	−	0.342908i
$696$	15.0505			0.570487
$697$		−	4.05891i		−	0.153742i
$698$		−	21.7165i		−	0.821980i
$699$	2.15366			0.0814587
$700$	−54.3221	−	71.5558i	−2.05318	−	2.70455i
$701$	−7.77497			−0.293657			−0.146828	−	0.989162i	$-0.546906\pi$
$701$	−7.77497			−0.293657			−0.146828	+	0.989162i	$0.546906\pi$
$702$		−	17.9903i		−	0.678998i
$703$			39.4597i			1.48825i
$704$	−30.8860			−1.16406
$705$	−42.2785	+	14.2300i	−1.59230	+	0.535934i
$706$	−53.7396			−2.02252
$707$		−	5.53969i		−	0.208341i
$708$			63.7723i			2.39671i
$709$	−0.260823			−0.00979541			−0.00489770	−	0.999988i	$-0.501559\pi$
$709$	−0.260823			−0.00979541			−0.00489770	+	0.999988i	$0.501559\pi$
$710$	11.5214	+	34.2309i	0.432389	+	1.28466i
$711$	2.25556			0.0845901
$712$		−	58.0282i		−	2.17470i
$713$		−	21.1718i		−	0.792890i
$714$	31.7439			1.18799
$715$	6.12094	+	18.1858i	0.228910	+	0.680110i
$716$	19.2050			0.717726
$717$			1.48678i			0.0555248i
$718$			26.3625i			0.983840i
$719$	−18.5739			−0.692688			−0.346344	−	0.938108i	$-0.612577\pi$
$719$	−18.5739			−0.692688			−0.346344	+	0.938108i	$0.612577\pi$
$720$	2.64160	−	0.889105i	0.0984466	−	0.0331350i
$721$	−50.9905			−1.89899
$722$			11.3240i			0.421435i
$723$			1.66439i			0.0618993i
$724$	90.2999			3.35597
$725$	−6.47456	+	4.91521i	−0.240459	+	0.182546i
$726$	124.419			4.61762
$727$			4.70298i			0.174424i	0.996190	+	0.0872119i	$0.0277957\pi$
$727$			4.70298i			0.174424i	−0.996190	+	0.0872119i	$0.972204\pi$
$728$			31.6913i			1.17456i
$729$	−28.7393			−1.06442
$730$	−23.5251	+	7.91803i	−0.870703	+	0.293060i
$731$	3.50597			0.129673
$732$		−	99.2617i		−	3.66882i
$733$		−	0.215894i		−	0.00797424i	−0.999992	−	0.00398712i	$-0.998731\pi$
$733$		−	0.215894i		−	0.00797424i	0.999992	−	0.00398712i	$-0.00126914\pi$
$734$	−74.3884			−2.74572
$735$	−13.1243	−	38.9935i	−0.484099	−	1.43830i
$736$	12.8833			0.474886
$737$		−	28.4341i		−	1.04738i
$738$		−	1.29437i		−	0.0476463i
$739$	−1.53528			−0.0564761			−0.0282381	−	0.999601i	$-0.508990\pi$
$739$	−1.53528			−0.0564761			−0.0282381	+	0.999601i	$0.508990\pi$
$740$	−31.2966	−	92.9846i	−1.15049	−	3.41818i
$741$	8.48767			0.311802
$742$			116.250i			4.26768i
$743$			19.5424i			0.716943i	0.933541	+	0.358471i	$0.116702\pi$
$743$			19.5424i			0.716943i	−0.933541	+	0.358471i	$0.883298\pi$
$744$	36.7063			1.34572
$745$	−1.36759	+	0.460302i	−0.0501047	+	0.0168642i
$746$	45.1662			1.65365
$747$		−	3.37437i		−	0.123462i
$748$		−	48.6689i		−	1.77951i
$749$	56.0610			2.04842
$750$	26.0997	−	38.4137i	0.953028	−	1.40267i
$751$	9.37833			0.342220			0.171110	−	0.985252i	$-0.445265\pi$
$751$	9.37833			0.342220			0.171110	+	0.985252i	$0.445265\pi$
$752$			65.0137i			2.37081i
$753$			26.5585i			0.967845i
$754$	5.44087			0.198145
$755$	17.6530	−	5.94161i	0.642458	−	0.216237i
$756$	96.5892			3.51291
$757$			28.5781i			1.03869i	0.854565	+	0.519344i	$0.173824\pi$
$757$			28.5781i			1.03869i	−0.854565	+	0.519344i	$0.826176\pi$
$758$			50.4826i			1.83361i
$759$	56.8724			2.06434
$760$	15.0878	+	44.8269i	0.547291	+	1.62604i
$761$	19.0881			0.691942			0.345971	−	0.938245i	$-0.387550\pi$
$761$	19.0881			0.691942			0.345971	+	0.938245i	$0.387550\pi$
$762$			15.6079i			0.565414i
$763$		−	16.6220i		−	0.601756i
$764$	−28.0543			−1.01497
$765$	−0.294810	−	0.875904i	−0.0106589	−	0.0316684i
$766$	11.6986			0.422689
$767$			12.1503i			0.438722i
$768$		−	54.0133i		−	1.94904i
$769$	−37.9012			−1.36675			−0.683376	−	0.730067i	$-0.739489\pi$
$769$	−37.9012			−1.36675			−0.683376	+	0.730067i	$0.739489\pi$
$770$	−143.819	+	48.4064i	−5.18288	+	1.74444i
$771$	2.48004			0.0893164
$772$			48.2820i			1.73771i
$773$			8.00091i			0.287773i	0.989594	+	0.143886i	$0.0459600\pi$
$773$			8.00091i			0.287773i	−0.989594	+	0.143886i	$0.954040\pi$
$774$	1.11804			0.0401870
$775$	−15.7906	+	11.9876i	−0.567217	+	0.430607i
$776$	31.9318			1.14628
$777$		−	73.3808i		−	2.63252i
$778$		−	38.4480i		−	1.37843i
$779$	8.58266			0.307506
$780$	−20.0007	+	6.73181i	−0.716141	+	0.241037i
$781$	41.4172			1.48202
$782$		−	23.9670i		−	0.857058i
$783$		−	8.73965i		−	0.312329i
$784$	−59.9621			−2.14150
$785$	1.91771	+	5.69766i	0.0684460	+	0.203358i
$786$	−57.2062			−2.04048
$787$		−	11.4339i		−	0.407576i	−0.979015	−	0.203788i	$-0.934675\pi$
$787$		−	11.4339i		−	0.407576i	0.979015	−	0.203788i	$-0.0653254\pi$
$788$		−	95.3966i		−	3.39836i
$789$	−28.8668			−1.02768
$790$	−17.4725	−	51.9122i	−0.621644	−	1.84695i
$791$	15.7081			0.558515
$792$		−	8.17970i		−	0.290653i
$793$		−	18.9120i		−	0.671584i
$794$	−95.2143			−3.37903
$795$	−38.6667	+	13.0144i	−1.37137	+	0.461572i
$796$	−103.806			−3.67931
$797$			29.3792i			1.04066i	0.853964	+	0.520332i	$0.174192\pi$
$797$			29.3792i			1.04066i	−0.853964	+	0.520332i	$0.825808\pi$
$798$			67.1232i			2.37613i
$799$	21.5573			0.762642
$800$	−7.29461	−	9.60882i	−0.257903	−	0.339723i
$801$	−2.39756			−0.0847135
$802$		−	82.1980i		−	2.90251i
$803$			28.4639i			1.00447i
$804$	31.2718			1.10287
$805$	−48.0823	+	16.1835i	−1.69468	+	0.570392i
$806$	13.2696			0.467402
$807$			29.8852i			1.05201i
$808$		−	7.25139i		−	0.255103i
$809$	−5.19954			−0.182806			−0.0914030	−	0.995814i	$-0.529135\pi$
$809$	−5.19954			−0.182806			−0.0914030	+	0.995814i	$0.529135\pi$
$810$	14.7003	+	43.6758i	0.516516	+	1.53461i
$811$	−9.70563			−0.340811			−0.170405	−	0.985374i	$-0.554508\pi$
$811$	−9.70563			−0.340811			−0.170405	+	0.985374i	$0.554508\pi$
$812$			29.2119i			1.02514i
$813$		−	23.9218i		−	0.838972i
$814$	−165.717			−5.80837
$815$	−12.0670	−	35.8520i	−0.422688	−	1.25584i
$816$	16.2364			0.568386
$817$			7.41345i			0.259364i
$818$		−	47.7054i		−	1.66798i
$819$	1.30939			0.0457539
$820$	−20.2246	+	6.80715i	−0.706272	+	0.237716i
$821$	−43.5252			−1.51904			−0.759521	−	0.650483i	$-0.774566\pi$
$821$	−43.5252			−1.51904			−0.759521	+	0.650483i	$0.774566\pi$
$822$		−	19.5020i		−	0.680209i
$823$			10.3541i			0.360920i	0.983582	+	0.180460i	$0.0577586\pi$
$823$			10.3541i			0.360920i	−0.983582	+	0.180460i	$0.942241\pi$
$824$	−66.7460			−2.32521
$825$	−32.2015	−	42.4174i	−1.12111	−	1.47678i
$826$	−96.0885			−3.34335
$827$		−	42.4097i		−	1.47473i	−0.675494	−	0.737366i	$-0.736069\pi$
$827$		−	42.4097i		−	1.47473i	0.675494	−	0.737366i	$-0.263931\pi$
$828$		−	5.18882i		−	0.180324i
$829$	−20.8325			−0.723543			−0.361772	−	0.932267i	$-0.617828\pi$
$829$	−20.8325			−0.723543			−0.361772	+	0.932267i	$0.617828\pi$
$830$	−77.6617	+	26.1392i	−2.69568	+	0.907307i
$831$	2.09035			0.0725133
$832$		−	6.47187i		−	0.224372i
$833$			19.8823i			0.688880i
$834$	52.6445			1.82293
$835$	−11.4195	−	33.9282i	−0.395188	−	1.17413i
$836$	102.912			3.55927
$837$		−	21.3149i		−	0.736751i
$838$			2.07765i			0.0717714i
$839$	42.8307			1.47868			0.739341	−	0.673332i	$-0.235137\pi$
$839$	42.8307			1.47868			0.739341	+	0.673332i	$0.235137\pi$
$840$	−28.0578	−	83.3620i	−0.968087	−	2.87626i
$841$	−26.3568			−0.908856
$842$		−	5.14457i		−	0.177293i
$843$			37.1622i			1.27993i
$844$	22.3986			0.770993
$845$	23.7396	−	7.99022i	0.816666	−	0.274872i
$846$	6.87452			0.236351
$847$			127.272i			4.37311i
$848$			59.4597i			2.04185i
$849$	17.3023			0.593813
$850$	−17.8754	+	13.5702i	−0.613121	+	0.465455i
$851$	−55.4033			−1.89920
$852$			45.5506i			1.56054i
$853$		−	14.7997i		−	0.506733i	−0.967370	−	0.253367i	$-0.918462\pi$
$853$		−	14.7997i		−	0.506733i	0.967370	−	0.253367i	$-0.0815379\pi$
$854$	149.562			5.11791
$855$	1.85212	−	0.623383i	0.0633411	−	0.0213192i
$856$	73.3832			2.50819
$857$		−	5.57859i		−	0.190561i	−0.995450	−	0.0952806i	$-0.969625\pi$
$857$		−	5.57859i		−	0.190561i	0.995450	−	0.0952806i	$-0.0303748\pi$
$858$			35.6452i			1.21691i
$859$	14.4231			0.492108			0.246054	−	0.969256i	$-0.420866\pi$
$859$	14.4231			0.492108			0.246054	+	0.969256i	$0.420866\pi$
$860$	−5.87981	−	17.4694i	−0.200500	−	0.595701i
$861$	−15.9607			−0.543938
$862$			40.3814i			1.37540i
$863$		−	47.4256i		−	1.61439i	−0.590287	−	0.807194i	$-0.700985\pi$
$863$		−	47.4256i		−	1.61439i	0.590287	−	0.807194i	$-0.299015\pi$
$864$	12.9704			0.441262
$865$	4.89223	+	14.5352i	0.166341	+	0.494212i
$866$	54.1206			1.83909
$867$			22.9110i			0.778097i
$868$			71.2441i			2.41818i
$869$	−62.8105			−2.13070
$870$	−14.3118	+	4.81705i	−0.485217	+	0.163313i
$871$	5.95811			0.201883
$872$		−	21.7580i		−	0.736819i
$873$		−	1.31933i		−	0.0446524i
$874$	50.6788			1.71423
$875$	39.2946	+	26.6982i	1.32840	+	0.902565i
$876$	−31.3046			−1.05768
$877$			47.9886i			1.62046i	0.586111	+	0.810231i	$0.300658\pi$
$877$			47.9886i			1.62046i	−0.586111	+	0.810231i	$0.699342\pi$
$878$		−	67.3696i		−	2.27361i
$879$	−38.8323			−1.30978
$880$	−73.5605	+	24.7589i	−2.47972	+	0.834621i
$881$	−7.04800			−0.237453			−0.118727	−	0.992927i	$-0.537881\pi$
$881$	−7.04800			−0.237453			−0.118727	+	0.992927i	$0.537881\pi$
$882$			6.34036i			0.213491i
$883$		−	20.6924i		−	0.696355i	−0.937429	−	0.348177i	$-0.886801\pi$
$883$		−	20.6924i		−	0.696355i	0.937429	−	0.348177i	$-0.113199\pi$
$884$	10.1981			0.343000
$885$	−10.7572	−	31.9606i	−0.361601	−	1.07434i
$886$	−65.1175			−2.18767
$887$			39.9150i			1.34022i	0.742264	+	0.670108i	$0.233752\pi$
$887$			39.9150i			1.34022i	−0.742264	+	0.670108i	$0.766248\pi$
$888$		−	96.0546i		−	3.22338i
$889$	−15.9658			−0.535476
$890$	18.5725	+	55.1803i	0.622551	+	1.84965i
$891$	52.8450			1.77037
$892$			41.3192i			1.38347i
$893$			45.5834i			1.52539i
$894$	−2.68056			−0.0896515
$895$	−9.62493	+	3.23954i	−0.321726	+	0.108286i
$896$	71.6862			2.39487
$897$			11.9171i			0.397900i
$898$		−	53.6539i		−	1.79045i
$899$	6.44635			0.214998
$900$	−3.86999	+	2.93793i	−0.129000	+	0.0979311i
$901$	19.7157			0.656825
$902$			36.0442i			1.20014i
$903$		−	13.7863i		−	0.458781i
$904$	20.5617			0.683872
$905$	−45.2554	+	15.2320i	−1.50434	+	0.506328i
$906$	34.6009			1.14954
$907$			30.9313i			1.02706i	0.858073	+	0.513528i	$0.171662\pi$
$907$			30.9313i			1.02706i	−0.858073	+	0.513528i	$0.828338\pi$
$908$			28.6806i			0.951800i
$909$	−0.299606			−0.00993731
$910$	−10.1431	−	30.1360i	−0.336241	−	0.998998i
$911$	2.92318			0.0968492			0.0484246	−	0.998827i	$-0.484580\pi$
$911$	2.92318			0.0968492			0.0484246	+	0.998827i	$0.484580\pi$
$912$			34.3321i			1.13685i
$913$			93.9658i			3.10982i
$914$	43.5266			1.43973
$915$	16.7437	+	49.7467i	0.553528	+	1.64458i
$916$	23.8289			0.787329
$917$		−	58.5180i		−	1.93243i
$918$		−	24.1290i		−	0.796375i
$919$	50.8708			1.67807			0.839036	−	0.544076i	$-0.183120\pi$
$919$	50.8708			1.67807			0.839036	+	0.544076i	$0.183120\pi$
$920$	−62.9392	+	21.1840i	−2.07504	+	0.698415i
$921$	−26.0193			−0.857366
$922$			11.1976i			0.368774i
$923$			8.67859i			0.285659i
$924$	−191.378			−6.29589
$925$	31.3696	+	41.3216i	1.03143	+	1.35865i
$926$	13.2024			0.433857
$927$			2.75775i			0.0905764i
$928$			3.92270i			0.128769i
$929$	−44.2087			−1.45044			−0.725220	−	0.688517i	$-0.758262\pi$
$929$	−44.2087			−1.45044			−0.725220	+	0.688517i	$0.758262\pi$
$930$	−34.9048	+	11.7482i	−1.14457	+	0.385238i
$931$	−42.0415			−1.37786
$932$			5.47168i			0.179231i
$933$		−	44.3527i		−	1.45204i
$934$	88.3252			2.89009
$935$	8.20956	+	24.3913i	0.268481	+	0.797679i
$936$	1.71398			0.0560232
$937$		−	20.4558i		−	0.668261i	−0.942527	−	0.334130i	$-0.891557\pi$
$937$		−	20.4558i		−	0.668261i	0.942527	−	0.334130i	$-0.108443\pi$
$938$			47.1186i			1.53848i
$939$	−4.63052			−0.151111
$940$	−36.1535	−	107.415i	−1.17920	−	3.50348i
$941$	−0.300822			−0.00980651			−0.00490325	−	0.999988i	$-0.501561\pi$
$941$	−0.300822			−0.00980651			−0.00490325	+	0.999988i	$0.501561\pi$
$942$			11.1678i			0.363865i
$943$			12.0505i			0.392417i
$944$	−49.1473			−1.59961
$945$	−48.4073	+	16.2928i	−1.57469	+	0.530006i
$946$	−31.1339			−1.01225
$947$		−	38.0133i		−	1.23526i	−0.786467	−	0.617632i	$-0.788092\pi$
$947$		−	38.0133i		−	1.23526i	0.786467	−	0.617632i	$-0.211908\pi$
$948$		−	69.0789i		−	2.24358i
$949$	−5.96435			−0.193611
$950$	−28.6946	−	37.7979i	−0.930975	−	1.22633i
$951$	32.7866			1.06318
$952$			42.5052i			1.37760i
$953$			19.9585i			0.646520i	0.946310	+	0.323260i	$0.104779\pi$
$953$			19.9585i			0.646520i	−0.946310	+	0.323260i	$0.895221\pi$
$954$	6.28723			0.203557
$955$	14.0599	−	4.73226i	0.454968	−	0.153132i
$956$	−3.77738			−0.122169
$957$			17.3164i			0.559760i
$958$		−	95.1509i		−	3.07419i
$959$	19.9492			0.644192
$960$	5.72985	+	17.0238i	0.184930	+	0.549442i
$961$	−15.2781			−0.492843
$962$		−	34.7245i		−	1.11956i
$963$		−	3.03198i		−	0.0977042i
$964$	−4.22863			−0.136195
$965$	−8.14430	−	24.1974i	−0.262174	−	0.778940i
$966$	−94.2442			−3.03226
$967$			11.6811i			0.375640i	0.982204	+	0.187820i	$0.0601421\pi$
$967$			11.6811i			0.375640i	−0.982204	+	0.187820i	$0.939858\pi$
$968$			166.597i			5.35464i
$969$	11.3839			0.365703
$970$	−30.3646	+	10.2201i	−0.974948	+	0.328146i
$971$	11.1262			0.357057			0.178529	−	0.983935i	$-0.442866\pi$
$971$	11.1262			0.357057			0.178529	+	0.983935i	$0.442866\pi$
$972$		−	10.0761i		−	0.323191i
$973$			53.8517i			1.72641i
$974$	−22.0900			−0.707810
$975$	8.88817	−	6.74752i	0.284649	−	0.216094i
$976$	76.4979			2.44864
$977$			62.1661i			1.98887i	0.105358	+	0.994434i	$0.466401\pi$
$977$			62.1661i			1.98887i	−0.105358	+	0.994434i	$0.533599\pi$
$978$		−	70.2720i		−	2.24705i
$979$	66.7647			2.13381
$980$	99.0686	−	33.3443i	3.16463	−	1.06515i
$981$	−0.898977			−0.0287021
$982$		−	16.6625i		−	0.531723i
$983$			39.9072i			1.27284i	0.771341	+	0.636422i	$0.219586\pi$
$983$			39.9072i			1.27284i	−0.771341	+	0.636422i	$0.780414\pi$
$984$	−20.8923			−0.666023
$985$	16.0917	+	47.8097i	0.512724	+	1.52334i
$986$	7.29743			0.232397
$987$		−	84.7687i		−	2.69822i
$988$			21.5642i			0.686048i
$989$	−10.4088			−0.330982
$990$	2.61799	+	7.77825i	0.0832052	+	0.247209i
$991$	28.5376			0.906527			0.453264	−	0.891376i	$-0.350260\pi$
$991$	28.5376			0.906527			0.453264	+	0.891376i	$0.350260\pi$
$992$			9.56697i			0.303751i
$993$			25.0690i			0.795541i
$994$	−68.6331			−2.17691
$995$	52.0243	−	17.5102i	1.64928	−	0.555112i
$996$	−103.344			−3.27457
$997$		−	30.6103i		−	0.969438i	−0.874670	−	0.484719i	$-0.838922\pi$
$997$		−	30.6103i		−	0.969438i	0.874670	−	0.484719i	$-0.161078\pi$
$998$		−	57.8262i		−	1.83046i
$999$	−55.7778			−1.76473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.3	✓	46
5.2	odd	4		6025.2.a.p.1.44		46
5.3	odd	4		6025.2.a.p.1.3		46
5.4	even	2	inner	1205.2.b.c.724.44	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.3	✓	46	1.1	even	1	trivial
1205.2.b.c.724.44	yes	46	5.4	even	2	inner
6025.2.a.p.1.3		46	5.3	odd	4
6025.2.a.p.1.44		46	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.49572i q^{2} +1.66439i q^{3} -4.22863 q^{4} +(2.11925 - 0.713293i) q^{5} +4.15385 q^{6} +4.24911i q^{7} +5.56203i q^{8} +0.229807 q^{9} +O(q^{10})\)	\(q-2.49572i q^{2} +1.66439i q^{3} -4.22863 q^{4} +(2.11925 - 0.713293i) q^{5} +4.15385 q^{6} +4.24911i q^{7} +5.56203i q^{8} +0.229807 q^{9} +(-1.78018 - 5.28905i) q^{10} -6.39942 q^{11} -7.03808i q^{12} -1.34094i q^{13} +10.6046 q^{14} +(1.18720 + 3.52726i) q^{15} +5.42403 q^{16} -1.79850i q^{17} -0.573534i q^{18} +3.80298 q^{19} +(-8.96151 + 3.01625i) q^{20} -7.07217 q^{21} +15.9712i q^{22} +5.33957i q^{23} -9.25739 q^{24} +(3.98243 - 3.02329i) q^{25} -3.34661 q^{26} +5.37566i q^{27} -17.9679i q^{28} -1.62578 q^{29} +(8.80305 - 2.96291i) q^{30} -3.96508 q^{31} -2.41281i q^{32} -10.6511i q^{33} -4.48857 q^{34} +(3.03086 + 9.00491i) q^{35} -0.971768 q^{36} +10.3760i q^{37} -9.49117i q^{38} +2.23185 q^{39} +(3.96736 + 11.7873i) q^{40} +2.25683 q^{41} +17.6502i q^{42} +1.94938i q^{43} +27.0608 q^{44} +(0.487018 - 0.163920i) q^{45} +13.3261 q^{46} +11.9862i q^{47} +9.02770i q^{48} -11.0549 q^{49} +(-7.54529 - 9.93903i) q^{50} +2.99341 q^{51} +5.67034i q^{52} +10.9623i q^{53} +13.4161 q^{54} +(-13.5620 + 4.56466i) q^{55} -23.6337 q^{56} +6.32964i q^{57} +4.05750i q^{58} -9.06104 q^{59} +(-5.02021 - 14.9154i) q^{60} +14.1035 q^{61} +9.89574i q^{62} +0.976474i q^{63} +4.82637 q^{64} +(-0.956483 - 2.84179i) q^{65} -26.5823 q^{66} +4.44323i q^{67} +7.60520i q^{68} -8.88712 q^{69} +(22.4737 - 7.56417i) q^{70} -6.47202 q^{71} +1.27819i q^{72} -4.44788i q^{73} +25.8956 q^{74} +(5.03193 + 6.62831i) q^{75} -16.0814 q^{76} -27.1918i q^{77} -5.57007i q^{78} +9.81502 q^{79} +(11.4949 - 3.86892i) q^{80} -8.25777 q^{81} -5.63241i q^{82} -14.6835i q^{83} +29.9056 q^{84} +(-1.28286 - 3.81148i) q^{85} +4.86511 q^{86} -2.70593i q^{87} -35.5938i q^{88} -10.4329 q^{89} +(-0.409098 - 1.21546i) q^{90} +5.69780 q^{91} -22.5790i q^{92} -6.59944i q^{93} +29.9143 q^{94} +(8.05945 - 2.71264i) q^{95} +4.01585 q^{96} -5.74102i q^{97} +27.5900i q^{98} -1.47063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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