LMFDB - Embedded newform 605.2.b.h.364.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(364,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + x^{10} + 34 x^{9} - 123 x^{8} - 20 x^{7} + 516 x^{6} - 668 x^{5} - 67 x^{4} + \cdots + 1089 $ x^12 - 4x^11 + x^10 + 34x^9 - 123x^8 - 20x^7 + 516x^6 - 668x^5 - 67x^4 + 3848x^3 + 6697x^2 + 4398x + 1089
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.4
Root			$1.38187 + 2.46878i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.h.364.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02281i q^{2} +2.91475i q^{3} -2.09174 q^{4} +(1.20202 - 1.88551i) q^{5} +5.89598 q^{6} -3.21128i q^{7} +0.185581i q^{8} -5.49579 q^{9} +O(q^{10})$	\(q-2.02281i q^{2} +2.91475i q^{3} -2.09174 q^{4} +(1.20202 - 1.88551i) q^{5} +5.89598 q^{6} -3.21128i q^{7} +0.185581i q^{8} -5.49579 q^{9} +(-3.81402 - 2.43146i) q^{10} -6.09692i q^{12} -0.648753i q^{13} -6.49579 q^{14} +(5.49579 + 3.50360i) q^{15} -3.80809 q^{16} -1.18847i q^{17} +11.1169i q^{18} -1.89096 q^{19} +(-2.51433 + 3.94400i) q^{20} +9.36008 q^{21} -4.35986i q^{23} -0.540924 q^{24} +(-2.11028 - 4.53285i) q^{25} -1.31230 q^{26} -7.27462i q^{27} +6.71717i q^{28} +4.16393 q^{29} +(7.08711 - 11.1169i) q^{30} +7.89984 q^{31} +8.07420i q^{32} -2.40405 q^{34} +(-6.05489 - 3.86003i) q^{35} +11.4958 q^{36} -2.05849i q^{37} +3.82504i q^{38} +1.89096 q^{39} +(0.349915 + 0.223073i) q^{40} -3.30520 q^{41} -18.9336i q^{42} -10.9313i q^{43} +(-6.60607 + 10.3624i) q^{45} -8.81916 q^{46} +2.91475i q^{47} -11.0997i q^{48} -3.31230 q^{49} +(-9.16908 + 4.26869i) q^{50} +3.46410 q^{51} +1.35703i q^{52} +6.41836i q^{53} -14.7151 q^{54} +0.595953 q^{56} -5.51167i q^{57} -8.42283i q^{58} +3.71635 q^{59} +(-11.4958 - 7.32864i) q^{60} -7.78694 q^{61} -15.9798i q^{62} +17.6485i q^{63} +8.71635 q^{64} +(-1.22323 - 0.779817i) q^{65} -2.37993i q^{67} +2.48598i q^{68} +12.7079 q^{69} +(-7.80809 + 12.2479i) q^{70} +15.7163 q^{71} -1.01992i q^{72} +5.71428i q^{73} -4.16393 q^{74} +(13.2121 - 6.15094i) q^{75} +3.95540 q^{76} -3.82504i q^{78} +15.2561 q^{79} +(-4.57742 + 7.18019i) q^{80} +4.71635 q^{81} +6.68577i q^{82} +10.6367i q^{83} -19.5789 q^{84} +(-2.24087 - 1.42857i) q^{85} -22.1120 q^{86} +12.1368i q^{87} -9.00000 q^{89} +(20.9610 + 13.3628i) q^{90} -2.08333 q^{91} +9.11972i q^{92} +23.0261i q^{93} +5.89598 q^{94} +(-2.27297 + 3.56541i) q^{95} -23.5343 q^{96} +15.1381i q^{97} +6.70015i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9}+O(q^{10}) $ 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9	$ 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9} - 32 q^{14} + 20 q^{15} + 36 q^{16} + 26 q^{20} - 10 q^{25} + 20 q^{26} + 8 q^{31} + 12 q^{34} + 92 q^{36} - 18 q^{45} - 4 q^{49} + 48 q^{56} - 32 q^{59} - 92 q^{60} + 28 q^{64} - 16 q^{69} - 12 q^{70} + 112 q^{71} + 36 q^{75} - 106 q^{80} - 20 q^{81} - 56 q^{86} - 108 q^{89} + 72 q^{91}+O(q^{100}) $ 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9 - 32 * q^14 + 20 * q^15 + 36 * q^16 + 26 * q^20 - 10 * q^25 + 20 * q^26 + 8 * q^31 + 12 * q^34 + 92 * q^36 - 18 * q^45 - 4 * q^49 + 48 * q^56 - 32 * q^59 - 92 * q^60 + 28 * q^64 - 16 * q^69 - 12 * q^70 + 112 * q^71 + 36 * q^75 - 106 * q^80 - 20 * q^81 - 56 * q^86 - 108 * q^89 + 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.02281i		−	1.43034i	−0.698951	−	0.715170i	$-0.746349\pi$
$2$		−	2.02281i		−	1.43034i	0.698951	−	0.715170i	$-0.253651\pi$
$3$			2.91475i			1.68283i	0.540386	+	0.841417i	$0.318278\pi$
$3$			2.91475i			1.68283i	−0.540386	+	0.841417i	$0.681722\pi$
$4$	−2.09174			−1.04587
$5$	1.20202	−	1.88551i	0.537561	−	0.843225i
$5$	1.20202	−	1.88551i	0.537561	−	0.843225i
$6$	5.89598			2.40702
$7$		−	3.21128i		−	1.21375i	−0.794798	−	0.606874i	$-0.792423\pi$
$7$		−	3.21128i		−	1.21375i	0.794798	−	0.606874i	$-0.207577\pi$
$8$			0.185581i			0.0656129i
$9$	−5.49579			−1.83193
$10$	−3.81402	−	2.43146i	−1.20610	−	0.768895i
$11$		0			0
$11$		0			0
$12$		−	6.09692i		−	1.76003i
$13$		−	0.648753i		−	0.179932i	−0.995945	−	0.0899659i	$-0.971324\pi$
$13$		−	0.648753i		−	0.179932i	0.995945	−	0.0899659i	$-0.0286758\pi$
$14$	−6.49579			−1.73607
$15$	5.49579	+	3.50360i	1.41901	+	0.904626i
$16$	−3.80809			−0.952023
$17$		−	1.18847i		−	0.288247i	−0.989560	−	0.144123i	$-0.953964\pi$
$17$		−	1.18847i		−	0.288247i	0.989560	−	0.144123i	$-0.0460362\pi$
$18$			11.1169i			2.62028i
$19$	−1.89096			−0.433815			−0.216908	−	0.976192i	$-0.569597\pi$
$19$	−1.89096			−0.433815			−0.216908	+	0.976192i	$0.569597\pi$
$20$	−2.51433	+	3.94400i	−0.562220	+	0.881905i
$21$	9.36008			2.04254
$22$		0			0
$23$		−	4.35986i		−	0.909095i	−0.890723	−	0.454547i	$-0.849801\pi$
$23$		−	4.35986i		−	0.909095i	0.890723	−	0.454547i	$-0.150199\pi$
$24$	−0.540924			−0.110416
$25$	−2.11028	−	4.53285i	−0.422056	−	0.906570i
$26$	−1.31230			−0.257364
$27$		−	7.27462i		−	1.40000i
$28$			6.71717i			1.26943i
$29$	4.16393			0.773223			0.386611	−	0.922243i	$-0.373645\pi$
$29$	4.16393			0.773223			0.386611	+	0.922243i	$0.373645\pi$
$30$	7.08711	−	11.1169i	1.29392	−	2.02966i
$31$	7.89984			1.41885			0.709426	−	0.704779i	$-0.248954\pi$
$31$	7.89984			1.41885			0.709426	+	0.704779i	$0.248954\pi$
$32$			8.07420i			1.42733i
$33$		0			0
$34$	−2.40405			−0.412291
$35$	−6.05489	−	3.86003i	−1.02346	−	0.652464i
$36$	11.4958			1.91597
$37$		−	2.05849i		−	0.338414i	−0.985581	−	0.169207i	$-0.945879\pi$
$37$		−	2.05849i		−	0.338414i	0.985581	−	0.169207i	$-0.0541207\pi$
$38$			3.82504i			0.620503i
$39$	1.89096			0.302795
$40$	0.349915	+	0.223073i	0.0553264	+	0.0352709i
$41$	−3.30520			−0.516185			−0.258092	−	0.966120i	$-0.583094\pi$
$41$	−3.30520			−0.516185			−0.258092	+	0.966120i	$0.583094\pi$
$42$		−	18.9336i		−	2.92152i
$43$		−	10.9313i		−	1.66701i	−0.552509	−	0.833507i	$-0.686330\pi$
$43$		−	10.9313i		−	1.66701i	0.552509	−	0.833507i	$-0.313670\pi$
$44$		0			0
$45$	−6.60607	+	10.3624i	−0.984775	+	1.54473i
$46$	−8.81916			−1.30031
$47$			2.91475i			0.425161i	0.977144	+	0.212580i	$0.0681867\pi$
$47$			2.91475i			0.425161i	−0.977144	+	0.212580i	$0.931813\pi$
$48$		−	11.0997i		−	1.60210i
$49$	−3.31230			−0.473186
$50$	−9.16908	+	4.26869i	−1.29670	+	0.603683i
$51$	3.46410			0.485071
$52$			1.35703i			0.188186i
$53$			6.41836i			0.881629i	0.897598	+	0.440815i	$0.145310\pi$
$53$			6.41836i			0.881629i	−0.897598	+	0.440815i	$0.854690\pi$
$54$	−14.7151			−2.00248
$55$		0			0
$56$	0.595953			0.0796376
$57$		−	5.51167i		−	0.730039i
$58$		−	8.42283i		−	1.10597i
$59$	3.71635			0.483827			0.241914	−	0.970298i	$-0.422225\pi$
$59$	3.71635			0.483827			0.241914	+	0.970298i	$0.422225\pi$
$60$	−11.4958	−	7.32864i	−1.48410	−	0.946124i
$61$	−7.78694			−0.997015			−0.498508	−	0.866885i	$-0.666118\pi$
$61$	−7.78694			−0.997015			−0.498508	+	0.866885i	$0.666118\pi$
$62$		−	15.9798i		−	2.02944i
$63$			17.6485i			2.22350i
$64$	8.71635			1.08954
$65$	−1.22323	−	0.779817i	−0.151723	−	0.0967244i
$66$		0			0
$67$		−	2.37993i		−	0.290755i	−0.989376	−	0.145377i	$-0.953560\pi$
$67$		−	2.37993i		−	0.290755i	0.989376	−	0.145377i	$-0.0464396\pi$
$68$			2.48598i			0.301469i
$69$	12.7079			1.52986
$70$	−7.80809	+	12.2479i	−0.933246	+	1.46390i
$71$	15.7163			1.86519			0.932594	−	0.360928i	$-0.117540\pi$
$71$	15.7163			1.86519			0.932594	+	0.360928i	$0.117540\pi$
$72$		−	1.01992i		−	0.120198i
$73$			5.71428i			0.668806i	0.942430	+	0.334403i	$0.108535\pi$
$73$			5.71428i			0.668806i	−0.942430	+	0.334403i	$0.891465\pi$
$74$	−4.16393			−0.484047
$75$	13.2121	−	6.15094i	1.52561	−	0.710250i
$76$	3.95540			0.453715
$77$		0			0
$78$		−	3.82504i		−	0.433100i
$79$	15.2561			1.71644			0.858221	−	0.513281i	$-0.171570\pi$
$79$	15.2561			1.71644			0.858221	+	0.513281i	$0.171570\pi$
$80$	−4.57742	+	7.18019i	−0.511771	+	0.802770i
$81$	4.71635			0.524039
$82$			6.68577i			0.738320i
$83$			10.6367i			1.16753i	0.811922	+	0.583766i	$0.198421\pi$
$83$			10.6367i			1.16753i	−0.811922	+	0.583766i	$0.801579\pi$
$84$	−19.5789			−2.13623
$85$	−2.24087	−	1.42857i	−0.243057	−	0.154950i
$86$	−22.1120			−2.38440
$87$			12.1368i			1.30121i
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	20.9610	+	13.3628i	2.20949	+	1.40856i
$91$	−2.08333			−0.218392
$92$			9.11972i			0.950797i
$93$			23.0261i			2.38769i
$94$	5.89598			0.608124
$95$	−2.27297	+	3.56541i	−0.233202	+	0.365804i
$96$	−23.5343			−2.40196
$97$			15.1381i			1.53704i	0.639826	+	0.768520i	$0.279006\pi$
$97$			15.1381i			1.53704i	−0.639826	+	0.768520i	$0.720994\pi$
$98$			6.70015i			0.676817i
$99$		0			0
$100$	4.41416	+	9.48156i	0.441416	+	0.948156i
$101$	−5.57817			−0.555049			−0.277524	−	0.960719i	$-0.589514\pi$
$101$	−5.57817			−0.555049			−0.277524	+	0.960719i	$0.589514\pi$
$102$		−	7.00721i		−	0.693817i
$103$			3.18217i			0.313548i	0.987634	+	0.156774i	$0.0501095\pi$
$103$			3.18217i			0.313548i	−0.987634	+	0.156774i	$0.949891\pi$
$104$	0.120397			0.0118058
$105$	11.2510	−	17.6485i	1.09799	−	1.72232i
$106$	12.9831			1.26103
$107$			3.96907i			0.383704i	0.981424	+	0.191852i	$0.0614494\pi$
$107$			3.96907i			0.383704i	−0.981424	+	0.191852i	$0.938551\pi$
$108$			15.2166i			1.46422i
$109$	15.4150			1.47649			0.738243	−	0.674535i	$-0.235656\pi$
$109$	15.4150			1.47649			0.738243	+	0.674535i	$0.235656\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$			12.2288i			1.15552i
$113$			10.1353i			0.953453i	0.879052	+	0.476727i	$0.158177\pi$
$113$			10.1353i			0.953453i	−0.879052	+	0.476727i	$0.841823\pi$
$114$	−11.1490			−1.04420
$115$	−8.22056	−	5.24066i	−0.766571	−	0.488694i
$116$	−8.70988			−0.808692
$117$			3.56541i			0.329623i
$118$		−	7.51745i		−	0.692038i
$119$	−3.81651			−0.349859
$120$	−0.650203	+	1.01992i	−0.0593552	+	0.0931052i
$121$		0			0
$122$			15.7515i			1.42607i
$123$		−	9.63383i		−	0.868653i
$124$	−16.5244			−1.48394
$125$	−11.0833	−	1.46964i	−0.991323	−	0.131449i
$126$	35.6995			3.18037
$127$		−	16.4430i		−	1.45908i	−0.683937	−	0.729541i	$-0.739734\pi$
$127$		−	16.4430i		−	1.45908i	0.683937	−	0.729541i	$-0.260266\pi$
$128$		−	1.48309i		−	0.131088i
$129$	31.8622			2.80531
$130$	−1.57742	+	2.47436i	−0.138349	+	0.217015i
$131$	−14.0007			−1.22325			−0.611625	−	0.791148i	$-0.709484\pi$
$131$	−14.0007			−1.22325			−0.611625	+	0.791148i	$0.709484\pi$
$132$		0			0
$133$			6.07239i			0.526543i
$134$	−4.81413			−0.415878
$135$	−13.7163	−	8.74426i	−1.18052	−	0.752586i
$136$	0.220558			0.0189127
$137$		−	13.7715i		−	1.17658i	−0.808650	−	0.588291i	$-0.799801\pi$
$137$		−	13.7715i		−	1.17658i	0.808650	−	0.588291i	$-0.200199\pi$
$138$		−	25.7057i		−	2.18821i
$139$	6.75472			0.572928			0.286464	−	0.958091i	$-0.407520\pi$
$139$	6.75472			0.572928			0.286464	+	0.958091i	$0.407520\pi$
$140$	12.6653	+	8.07420i	1.07041	+	0.682394i
$141$	−8.49579			−0.715475
$142$		−	31.7911i		−	2.66785i
$143$		0			0
$144$	20.9285			1.74404
$145$	5.00514	−	7.85113i	0.415655	−	0.652000i
$146$	11.5589			0.956620
$147$		−	9.65455i		−	0.796294i
$148$			4.30584i			0.353938i
$149$	−19.1969			−1.57267			−0.786335	−	0.617800i	$-0.788024\pi$
$149$	−19.1969			−1.57267			−0.786335	+	0.617800i	$0.788024\pi$
$150$	−12.4422	−	26.7256i	−1.01590	−	2.18214i
$151$	3.29062			0.267787			0.133893	−	0.990996i	$-0.457252\pi$
$151$	3.29062			0.267787			0.133893	+	0.990996i	$0.457252\pi$
$152$		−	0.350926i		−	0.0284639i
$153$			6.53159i			0.528048i
$154$		0			0
$155$	9.49579	−	14.8952i	0.762720	−	1.19641i
$156$	−3.95540			−0.316685
$157$			14.0144i			1.11847i	0.829009	+	0.559236i	$0.188905\pi$
$157$			14.0144i			1.11847i	−0.829009	+	0.559236i	$0.811095\pi$
$158$		−	30.8601i		−	2.45509i
$159$	−18.7079			−1.48364
$160$	15.2240	+	9.70538i	1.20356	+	0.767277i
$161$	−14.0007			−1.10341
$162$		−	9.54026i		−	0.749554i
$163$		−	10.3220i		−	0.808478i	−0.914653	−	0.404239i	$-0.867536\pi$
$163$		−	10.3220i		−	0.808478i	0.914653	−	0.404239i	$-0.132464\pi$
$164$	6.91362			0.539863
$165$		0			0
$166$	21.5160			1.66997
$167$			14.6058i			1.13023i	0.825012	+	0.565115i	$0.191168\pi$
$167$			14.6058i			1.13023i	−0.825012	+	0.565115i	$0.808832\pi$
$168$			1.73706i			0.134017i
$169$	12.5791			0.967625
$170$	−2.88972	+	4.53285i	−0.221631	+	0.347654i
$171$	10.3923			0.794719
$172$			22.8656i			1.74348i
$173$		−	2.20839i		−	0.167901i	−0.996470	−	0.0839503i	$-0.973246\pi$
$173$		−	2.20839i		−	0.167901i	0.996470	−	0.0839503i	$-0.0267537\pi$
$174$	24.5505			1.86117
$175$	−14.5562	+	6.77669i	−1.10035	+	0.512270i
$176$		0			0
$177$			10.8322i			0.814201i
$178$			18.2053i			1.36454i
$179$	−10.8081			−0.807835			−0.403917	−	0.914795i	$-0.632352\pi$
$179$	−10.8081			−0.807835			−0.403917	+	0.914795i	$0.632352\pi$
$180$	13.8182	−	21.6754i	1.02995	−	1.61559i
$181$	−3.36698			−0.250265			−0.125133	−	0.992140i	$-0.539936\pi$
$181$	−3.36698			−0.250265			−0.125133	+	0.992140i	$0.539936\pi$
$182$			4.21417i			0.312375i
$183$		−	22.6970i		−	1.67781i
$184$	0.809109			0.0596483
$185$	−3.88130	−	2.47436i	−0.285359	−	0.181918i
$186$	46.5773			3.41521
$187$		0			0
$188$		−	6.09692i		−	0.444664i
$189$	−23.3608			−1.69925
$190$	7.21214	+	4.59779i	0.523224	+	0.333559i
$191$	9.27523			0.671132			0.335566	−	0.942017i	$-0.391072\pi$
$191$	9.27523			0.671132			0.335566	+	0.942017i	$0.391072\pi$
$192$			25.4060i			1.83352i
$193$			4.86292i			0.350041i	0.984565	+	0.175020i	$0.0559991\pi$
$193$			4.86292i			0.350041i	−0.984565	+	0.175020i	$0.944001\pi$
$194$	30.6214			2.19849
$195$	2.27297	−	3.56541i	0.162771	−	0.255325i
$196$	6.92849			0.494892
$197$			11.8747i			0.846038i	0.906121	+	0.423019i	$0.139030\pi$
$197$			11.8747i			0.846038i	−0.906121	+	0.423019i	$0.860970\pi$
$198$		0			0
$199$	4.99158			0.353844			0.176922	−	0.984225i	$-0.443386\pi$
$199$	4.99158			0.353844			0.176922	+	0.984225i	$0.443386\pi$
$200$	0.841212	−	0.391628i	0.0594827	−	0.0276923i
$201$	6.93691			0.489292
$202$			11.2836i			0.793908i
$203$		−	13.3715i		−	0.938498i
$204$	−7.24602			−0.507323
$205$	−3.97292	+	6.23197i	−0.277481	+	0.435260i
$206$	6.43691			0.448481
$207$			23.9609i			1.66540i
$208$			2.47051i			0.171299i
$209$		0			0
$210$	−35.6995	−	22.7587i	−2.46350	−	1.57050i
$211$	−1.57314			−0.108300			−0.0541499	−	0.998533i	$-0.517245\pi$
$211$	−1.57314			−0.108300			−0.0541499	+	0.998533i	$0.517245\pi$
$212$		−	13.4256i		−	0.922071i
$213$			45.8093i			3.13880i
$214$	8.02865			0.548827
$215$	−20.6111	−	13.1397i	−1.40567	−	0.896122i
$216$	1.35003			0.0918581
$217$		−	25.3686i		−	1.72213i
$218$		−	31.1815i		−	2.11188i
$219$	−16.6557			−1.12549
$220$		0			0
$221$	−0.771025			−0.0518647
$222$		−	12.1368i		−	0.814571i
$223$			3.31475i			0.221972i	0.993822	+	0.110986i	$0.0354009\pi$
$223$			3.31475i			0.221972i	−0.993822	+	0.110986i	$0.964599\pi$
$224$	25.9285			1.73242
$225$	11.5977	+	24.9116i	0.773177	+	1.66077i
$226$	20.5018			1.36376
$227$			2.84011i			0.188505i	0.995548	+	0.0942525i	$0.0300461\pi$
$227$			2.84011i			0.188505i	−0.995548	+	0.0942525i	$0.969954\pi$
$228$			11.5290i			0.763528i
$229$	1.99158			0.131608			0.0658038	−	0.997833i	$-0.479039\pi$
$229$	1.99158			0.131608			0.0658038	+	0.997833i	$0.479039\pi$
$230$	−10.6008	+	16.6286i	−0.698999	+	1.09646i
$231$		0			0
$232$			0.772748i			0.0507334i
$233$			20.2535i			1.32685i	0.748242	+	0.663426i	$0.230898\pi$
$233$			20.2535i			1.32685i	−0.748242	+	0.663426i	$0.769102\pi$
$234$	7.21214			0.471472
$235$	5.49579	+	3.50360i	0.358506	+	0.228550i
$236$	−7.77365			−0.506022
$237$			44.4677i			2.88849i
$238$			7.72006i			0.500417i
$239$	−1.89096			−0.122316			−0.0611579	−	0.998128i	$-0.519479\pi$
$239$	−1.89096			−0.122316			−0.0611579	+	0.998128i	$0.519479\pi$
$240$	−20.9285	−	13.3420i	−1.35093	−	0.861226i
$241$	4.00503			0.257986			0.128993	−	0.991645i	$-0.458825\pi$
$241$	4.00503			0.257986			0.128993	+	0.991645i	$0.458825\pi$
$242$		0			0
$243$		−	8.07686i		−	0.518131i
$244$	16.2883			1.04275
$245$	−3.98147	+	6.24537i	−0.254366	+	0.399002i
$246$	−19.4874			−1.24247
$247$			1.22676i			0.0780572i
$248$			1.46606i			0.0930950i
$249$	−31.0034			−1.96476
$250$	−2.97280	+	22.4194i	−0.188017	+	1.41793i
$251$	22.7079			1.43331			0.716656	−	0.697427i	$-0.245672\pi$
$251$	22.7079			1.43331			0.716656	+	0.697427i	$0.245672\pi$
$252$		−	36.9162i		−	2.32550i
$253$		0			0
$254$	−33.2610			−2.08698
$255$	4.16393	−	6.53159i	0.260756	−	0.409024i
$256$	14.4327			0.902044
$257$			4.06296i			0.253441i	0.991938	+	0.126720i	$0.0404451\pi$
$257$			4.06296i			0.253441i	−0.991938	+	0.126720i	$0.959555\pi$
$258$		−	64.4510i		−	4.01254i
$259$	−6.61039			−0.410750
$260$	2.55868	+	1.63118i	0.158683	+	0.101161i
$261$	−22.8841			−1.41649
$262$			28.3208i			1.74966i
$263$		−	12.3054i		−	0.758783i	−0.925236	−	0.379391i	$-0.876133\pi$
$263$		−	12.3054i		−	0.758783i	0.925236	−	0.379391i	$-0.123867\pi$
$264$		0			0
$265$	12.1019	+	7.71502i	0.743411	+	0.473930i
$266$	12.2833			0.753135
$267$		−	26.2328i		−	1.60542i
$268$			4.97820i			0.304092i
$269$	7.70793			0.469961			0.234980	−	0.972000i	$-0.424497\pi$
$269$	7.70793			0.469961			0.234980	+	0.972000i	$0.424497\pi$
$270$	−17.6879	+	27.7455i	−1.07645	+	1.68854i
$271$	15.5739			0.946046			0.473023	−	0.881050i	$-0.343163\pi$
$271$	15.5739			0.946046			0.473023	+	0.881050i	$0.343163\pi$
$272$			4.52581i			0.274418i
$273$		−	6.07239i		−	0.367518i
$274$	−27.8571			−1.68291
$275$		0			0
$276$	−26.5817			−1.60003
$277$		−	20.3030i		−	1.21989i	−0.792443	−	0.609946i	$-0.791191\pi$
$277$		−	20.3030i		−	1.21989i	0.792443	−	0.609946i	$-0.208809\pi$
$278$		−	13.6635i		−	0.819481i
$279$	−43.4159			−2.59924
$280$	0.716350	−	1.12367i	0.0428101	−	0.0671524i
$281$	24.2196			1.44482			0.722409	−	0.691466i	$-0.243035\pi$
$281$	24.2196			1.44482			0.722409	+	0.691466i	$0.243035\pi$
$282$			17.1853i			1.02337i
$283$		−	14.4372i		−	0.858204i	−0.903256	−	0.429102i	$-0.858830\pi$
$283$		−	14.4372i		−	0.858204i	0.903256	−	0.429102i	$-0.141170\pi$
$284$	−32.8746			−1.95075
$285$	−10.3923	−	6.62516i	−0.615587	−	0.392441i
$286$		0			0
$287$			10.6139i			0.626519i
$288$		−	44.3741i		−	2.61477i
$289$	15.5875			0.916914
$290$	−15.8813	−	10.1244i	−0.932582	−	0.594527i
$291$	−44.1238			−2.58658
$292$		−	11.9528i		−	0.699486i
$293$		−	15.1625i		−	0.885805i	−0.896570	−	0.442902i	$-0.853949\pi$
$293$		−	15.1625i		−	0.885805i	0.896570	−	0.442902i	$-0.146051\pi$
$294$	−19.5293			−1.13897
$295$	4.46714	−	7.00721i	0.260087	−	0.407975i
$296$	0.382018			0.0222043
$297$		0			0
$298$			38.8316i			2.24945i
$299$	−2.82848			−0.163575
$300$	−27.6364	+	12.8662i	−1.59559	+	0.742831i
$301$	−35.1036			−2.02334
$302$		−	6.65628i		−	0.383026i
$303$		−	16.2590i		−	0.934055i
$304$	7.20094			0.413002
$305$	−9.36008	+	14.6823i	−0.535957	+	0.840708i
$306$	13.2121			0.755288
$307$			8.04171i			0.458965i	0.973313	+	0.229482i	$0.0737033\pi$
$307$			8.04171i			0.458965i	−0.973313	+	0.229482i	$0.926297\pi$
$308$		0			0
$309$	−9.27523			−0.527650
$310$	−30.1301	−	19.2081i	−1.71128	−	1.09095i
$311$	22.2668			1.26264			0.631318	−	0.775524i	$-0.282514\pi$
$311$	22.2668			1.26264			0.631318	+	0.775524i	$0.282514\pi$
$312$			0.350926i			0.0198673i
$313$			2.35044i			0.132855i	0.997791	+	0.0664273i	$0.0211601\pi$
$313$			2.35044i			0.132855i	−0.997791	+	0.0664273i	$0.978840\pi$
$314$	28.3484			1.59979
$315$	33.2764	+	21.2139i	1.87491	+	1.19527i
$316$	−31.9118			−1.79518
$317$		−	18.0233i		−	1.01229i	−0.862448	−	0.506146i	$-0.831070\pi$
$317$		−	18.0233i		−	1.01229i	0.862448	−	0.506146i	$-0.168930\pi$
$318$			37.8425i			2.12210i
$319$		0			0
$320$	10.4773	−	16.4347i	0.585696	−	0.918730i
$321$	−11.5689			−0.645710
$322$			28.3208i			1.57825i
$323$			2.24735i			0.125046i
$324$	−9.86540			−0.548078
$325$	−2.94070	+	1.36905i	−0.163121	+	0.0759413i
$326$	−20.8793			−1.15640
$327$			44.9309i			2.48468i
$328$		−	0.613382i		−	0.0338684i
$329$	9.36008			0.516038
$330$		0			0
$331$	−3.09174			−0.169938			−0.0849688	−	0.996384i	$-0.527079\pi$
$331$	−3.09174			−0.169938			−0.0849688	+	0.996384i	$0.527079\pi$
$332$		−	22.2493i		−	1.22109i
$333$			11.3130i			0.619951i
$334$	29.5447			1.61661
$335$	−4.48737	−	2.86073i	−0.245171	−	0.156298i
$336$	−35.6441			−1.94454
$337$			35.9458i			1.95809i	0.203641	+	0.979046i	$0.434722\pi$
$337$			35.9458i			1.95809i	−0.203641	+	0.979046i	$0.565278\pi$
$338$		−	25.4451i		−	1.38403i
$339$	−29.5420			−1.60450
$340$	4.68733	+	2.98820i	0.254206	+	0.162058i
$341$		0			0
$342$		−	21.0216i		−	1.13672i
$343$		−	11.8422i		−	0.639420i
$344$	2.02865			0.109378
$345$	15.2752	−	23.9609i	0.822391	−	1.29001i
$346$	−4.46714			−0.240155
$347$			12.2629i			0.658307i	0.944276	+	0.329153i	$0.106763\pi$
$347$			12.2629i			0.658307i	−0.944276	+	0.329153i	$0.893237\pi$
$348$		−	25.3872i		−	1.36089i
$349$	−17.6734			−0.946034			−0.473017	−	0.881053i	$-0.656835\pi$
$349$	−17.6734			−0.946034			−0.473017	+	0.881053i	$0.656835\pi$
$350$	13.7079	+	29.4444i	0.732720	+	1.57387i
$351$	−4.71943			−0.251905
$352$		0			0
$353$		−	18.7202i		−	0.996378i	−0.867068	−	0.498189i	$-0.833999\pi$
$353$		−	18.7202i		−	0.996378i	0.867068	−	0.498189i	$-0.166001\pi$
$354$	21.9115			1.16458
$355$	18.8914	−	29.6333i	1.00265	−	1.57277i
$356$	18.8257			0.997760
$357$		−	11.1242i		−	0.588755i
$358$			21.8627i			1.15548i
$359$	−37.2669			−1.96687			−0.983435	−	0.181263i	$-0.941981\pi$
$359$	−37.2669			−1.96687			−0.983435	+	0.181263i	$0.941981\pi$
$360$	−1.92306	−	1.22596i	−0.101354	−	0.0646139i
$361$	−15.4243			−0.811804
$362$			6.81074i			0.357965i
$363$		0			0
$364$	4.35779			0.228410
$365$	10.7743	+	6.86870i	0.563954	+	0.359524i
$366$	−45.9117			−2.39984
$367$		−	17.9988i		−	0.939531i	−0.882791	−	0.469765i	$-0.844339\pi$
$367$		−	17.9988i		−	0.939531i	0.882791	−	0.469765i	$-0.155661\pi$
$368$			16.6028i			0.865479i
$369$	18.1647			0.945615
$370$	−5.00514	+	7.85113i	−0.260205	+	0.408161i
$371$	20.6111			1.07008
$372$		−	48.1647i		−	2.49722i
$373$		−	0.202607i		−	0.0104906i	−0.999986	−	0.00524531i	$-0.998330\pi$
$373$		−	0.202607i		−	0.0104906i	0.999986	−	0.00524531i	$-0.00166964\pi$
$374$		0			0
$375$	4.28365	−	32.3052i	0.221207	−	1.66823i
$376$	−0.540924			−0.0278960
$377$		−	2.70137i		−	0.139127i
$378$			47.2544i			2.43050i
$379$	33.9832			1.74560			0.872799	−	0.488080i	$-0.162303\pi$
$379$	33.9832			1.74560			0.872799	+	0.488080i	$0.162303\pi$
$380$	4.75448	−	7.45793i	0.243900	−	0.382584i
$381$	47.9273			2.45539
$382$		−	18.7620i		−	0.959947i
$383$		−	7.14204i		−	0.364941i	−0.983211	−	0.182471i	$-0.941591\pi$
$383$		−	7.14204i		−	0.364941i	0.983211	−	0.182471i	$-0.0584094\pi$
$384$	4.32284			0.220599
$385$		0			0
$386$	9.83675			0.500677
$387$			60.0764i			3.05385i
$388$		−	31.6650i		−	1.60755i
$389$	−13.2668			−0.672654			−0.336327	−	0.941745i	$-0.609185\pi$
$389$	−13.2668			−0.672654			−0.336327	+	0.941745i	$0.609185\pi$
$390$	−7.21214	−	4.59779i	−0.365201	−	0.232818i
$391$	−5.18157			−0.262043
$392$		−	0.614701i		−	0.0310471i
$393$		−	40.8087i		−	2.05853i
$394$	24.0202			1.21012
$395$	18.3382	−	28.7654i	0.922692	−	1.44735i
$396$		0			0
$397$		−	33.5614i		−	1.68440i	−0.539165	−	0.842200i	$-0.681260\pi$
$397$		−	33.5614i		−	1.68440i	0.539165	−	0.842200i	$-0.318740\pi$
$398$		−	10.0970i		−	0.506117i
$399$	−17.6995			−0.886084
$400$	8.03614	+	17.2615i	0.401807	+	0.863076i
$401$	33.5909			1.67745			0.838726	−	0.544554i	$-0.183301\pi$
$401$	33.5909			1.67745			0.838726	+	0.544554i	$0.183301\pi$
$402$		−	14.0320i		−	0.699853i
$403$		−	5.12505i		−	0.255297i
$404$	11.6681			0.580510
$405$	5.66916	−	8.89271i	0.281703	−	0.441882i
$406$	−27.0480			−1.34237
$407$		0			0
$408$			0.642872i			0.0318269i
$409$	−8.16896			−0.403929			−0.201964	−	0.979393i	$-0.564733\pi$
$409$	−8.16896			−0.403929			−0.201964	+	0.979393i	$0.564733\pi$
$410$	12.6061	+	8.03645i	0.622569	+	0.396892i
$411$	40.1406			1.97999
$412$		−	6.65628i		−	0.327931i
$413$		−	11.9342i		−	0.587245i
$414$	48.4683			2.38209
$415$	20.0556	+	12.7856i	0.984492	+	0.627620i
$416$	5.23816			0.256822
$417$			19.6883i			0.964142i
$418$		0			0
$419$	−19.5329			−0.954243			−0.477121	−	0.878837i	$-0.658320\pi$
$419$	−19.5329			−0.954243			−0.477121	+	0.878837i	$0.658320\pi$
$420$	−23.5343	+	36.9162i	−1.14836	+	1.80132i
$421$	−23.9083			−1.16522			−0.582609	−	0.812753i	$-0.697968\pi$
$421$	−23.9083			−1.16522			−0.582609	+	0.812753i	$0.697968\pi$
$422$			3.18217i			0.154905i
$423$		−	16.0189i		−	0.778865i
$424$	−1.19113			−0.0578462
$425$	−5.38716	+	2.50801i	−0.261316	+	0.121656i
$426$	92.6633			4.48955
$427$			25.0060i			1.21013i
$428$		−	8.30227i		−	0.401306i
$429$		0			0
$430$	−26.5791	+	41.6923i	−1.28176	+	2.01058i
$431$	−7.56383			−0.364337			−0.182168	−	0.983267i	$-0.558312\pi$
$431$	−7.56383			−0.364337			−0.182168	+	0.983267i	$0.558312\pi$
$432$			27.7024i			1.33283i
$433$		−	25.6194i		−	1.23119i	−0.788063	−	0.615595i	$-0.788916\pi$
$433$		−	25.6194i		−	1.23119i	0.788063	−	0.615595i	$-0.211084\pi$
$434$	−51.3157			−2.46323
$435$	22.8841	+	14.5888i	1.09721	+	0.699478i
$436$	−32.2442			−1.54422
$437$			8.24432i			0.394379i
$438$			33.6913i			1.60983i
$439$	20.4668			0.976827			0.488413	−	0.872612i	$-0.337576\pi$
$439$	20.4668			0.976827			0.488413	+	0.872612i	$0.337576\pi$
$440$		0			0
$441$	18.2037			0.866844
$442$			1.55963i			0.0741842i
$443$		−	10.1648i		−	0.482946i	−0.970408	−	0.241473i	$-0.922369\pi$
$443$		−	10.1648i		−	0.482946i	0.970408	−	0.241473i	$-0.0776305\pi$
$444$	−12.5505			−0.595619
$445$	−10.8182	+	16.9696i	−0.512832	+	0.804435i
$446$	6.70509			0.317495
$447$		−	55.9542i		−	2.64654i
$448$		−	27.9906i		−	1.32243i
$449$	14.6995			0.693713			0.346857	−	0.937918i	$-0.387249\pi$
$449$	14.6995			0.693713			0.346857	+	0.937918i	$0.387249\pi$
$450$	50.3913	−	23.4598i	2.37547	−	1.10591i
$451$		0			0
$452$		−	21.2006i		−	0.997190i
$453$			9.59134i			0.450640i
$454$	5.74500			0.269626
$455$	−2.50421	+	3.92813i	−0.117399	+	0.184154i
$456$	1.02286			0.0479000
$457$			3.36281i			0.157305i	0.996902	+	0.0786527i	$0.0250618\pi$
$457$			3.36281i			0.157305i	−0.996902	+	0.0786527i	$0.974938\pi$
$458$		−	4.02859i		−	0.188243i
$459$	−8.64568			−0.403546
$460$	17.1953	+	10.9621i	0.801735	+	0.511111i
$461$	−1.41424			−0.0658677			−0.0329338	−	0.999458i	$-0.510485\pi$
$461$	−1.41424			−0.0658677			−0.0329338	+	0.999458i	$0.510485\pi$
$462$		0			0
$463$			15.4595i			0.718465i	0.933248	+	0.359232i	$0.116961\pi$
$463$			15.4595i			0.718465i	−0.933248	+	0.359232i	$0.883039\pi$
$464$	−15.8566			−0.736126
$465$	43.4159	+	27.6779i	2.01336	+	1.28353i
$466$	40.9690			1.89785
$467$			18.6908i			0.864905i	0.901657	+	0.432453i	$0.142352\pi$
$467$			18.6908i			0.864905i	−0.901657	+	0.432453i	$0.857648\pi$
$468$		−	7.45793i		−	0.344743i
$469$	−7.64261			−0.352903
$470$	7.08711	−	11.1169i	0.326904	−	0.512785i
$471$	−40.8486			−1.88220
$472$			0.689685i			0.0317453i
$473$		0			0
$474$	89.9495			4.13152
$475$	3.99045	+	8.57142i	0.183094	+	0.393284i
$476$	7.98317			0.365908
$477$		−	35.2740i		−	1.61508i
$478$			3.82504i			0.174953i
$479$	29.8765			1.36509			0.682546	−	0.730842i	$-0.260873\pi$
$479$	29.8765			1.36509			0.682546	+	0.730842i	$0.260873\pi$
$480$	−28.2888	+	44.3741i	−1.29120	+	2.02539i
$481$	−1.33545			−0.0608915
$482$		−	8.10139i		−	0.369008i
$483$		−	40.8087i		−	1.85686i
$484$		0			0
$485$	28.5430	+	18.1963i	1.29607	+	0.826253i
$486$	−16.3379			−0.741103
$487$			0.934819i			0.0423607i	0.999776	+	0.0211803i	$0.00674242\pi$
$487$			0.934819i			0.0423607i	−0.999776	+	0.0211803i	$0.993258\pi$
$488$		−	1.44511i		−	0.0654171i
$489$	30.0860			1.36053
$490$	12.6332	+	8.05373i	0.570709	+	0.363831i
$491$	−32.8944			−1.48450			−0.742251	−	0.670121i	$-0.766242\pi$
$491$	−32.8944			−1.48450			−0.742251	+	0.670121i	$0.766242\pi$
$492$			20.1515i			0.908500i
$493$		−	4.94871i		−	0.222879i
$494$	2.48151			0.111648
$495$		0			0
$496$	−30.0833			−1.35078
$497$		−	50.4696i		−	2.26387i
$498$			62.7139i			2.81028i
$499$	−8.99158			−0.402519			−0.201259	−	0.979538i	$-0.564503\pi$
$499$	−8.99158			−0.402519			−0.201259	+	0.979538i	$0.564503\pi$
$500$	23.1835	+	3.07412i	1.03680	+	0.137479i
$501$	−42.5723			−1.90199
$502$		−	45.9337i		−	2.05012i
$503$			1.22096i			0.0544400i	0.999629	+	0.0272200i	$0.00866546\pi$
$503$			1.22096i			0.0544400i	−0.999629	+	0.0272200i	$0.991335\pi$
$504$	−3.27523			−0.145890
$505$	−6.70509	+	10.5177i	−0.298373	+	0.468031i
$506$		0			0
$507$			36.6650i			1.62835i
$508$			34.3946i			1.52601i
$509$	−24.1953			−1.07244			−0.536219	−	0.844079i	$-0.680148\pi$
$509$	−24.1953			−1.07244			−0.536219	+	0.844079i	$0.680148\pi$
$510$	−13.2121	−	8.42283i	−0.585043	−	0.372969i
$511$	18.3501			0.811763
$512$		−	32.1607i		−	1.42132i
$513$			13.7560i			0.607342i
$514$	8.21858			0.362506
$515$	6.00000	+	3.82504i	0.264392	+	0.168551i
$516$	−66.6475			−2.93399
$517$		0			0
$518$			13.3715i			0.587512i
$519$	6.43691			0.282549
$520$	0.144719	−	0.227009i	0.00634637	−	0.00995498i
$521$	−4.85358			−0.212639			−0.106320	−	0.994332i	$-0.533907\pi$
$521$	−4.85358			−0.212639			−0.106320	+	0.994332i	$0.533907\pi$
$522$			46.2901i			2.02606i
$523$			7.33344i			0.320669i	0.987063	+	0.160334i	$0.0512572\pi$
$523$			7.33344i			0.320669i	−0.987063	+	0.160334i	$0.948743\pi$
$524$	29.2860			1.27936
$525$	−19.7524	−	42.4278i	−0.862065	−	1.85170i
$526$	−24.8914			−1.08532
$527$		−	9.38873i		−	0.408980i
$528$		0			0
$529$	3.99158			0.173547
$530$	15.6060	−	24.4797i	0.677881	−	1.06333i
$531$	−20.4243			−0.886338
$532$		−	12.7019i		−	0.550696i
$533$			2.14426i			0.0928781i
$534$	−53.0638			−2.29630
$535$	7.48371	+	4.77091i	0.323549	+	0.206264i
$536$	0.441670			0.0190773
$537$		−	31.5029i		−	1.35945i
$538$		−	15.5917i		−	0.672204i
$539$		0			0
$540$	28.6911	+	18.2908i	1.23467	+	0.787109i
$541$	28.0803			1.20726			0.603632	−	0.797263i	$-0.293720\pi$
$541$	28.0803			1.20726			0.603632	+	0.797263i	$0.293720\pi$
$542$		−	31.5029i		−	1.35317i
$543$		−	9.81391i		−	0.421155i
$544$	9.59595			0.411423
$545$	18.5292	−	29.0651i	0.793702	−	1.24501i
$546$	−12.2833			−0.525675
$547$		−	23.3628i		−	0.998921i	−0.866337	−	0.499460i	$-0.833532\pi$
$547$		−	23.3628i		−	0.998921i	0.866337	−	0.499460i	$-0.166468\pi$
$548$			28.8065i			1.23055i
$549$	42.7954			1.82646
$550$		0			0
$551$	−7.87382			−0.335436
$552$			2.35835i			0.100378i
$553$		−	48.9915i		−	2.08333i
$554$	−41.0691			−1.74486
$555$	7.21214	−	11.3130i	0.306138	−	0.480212i
$556$	−14.1291			−0.599209
$557$		−	0.0340521i		−	0.00144283i	−1.00000		0.000721417i	$-0.999770\pi$
$557$		−	0.0340521i		−	0.00144283i	1.00000		0.000721417i	$-0.000229634\pi$
$558$			87.8219i			3.71780i
$559$	−7.09174			−0.299949
$560$	23.0576	+	14.6994i	0.974361	+	0.621161i
$561$		0			0
$562$		−	48.9915i		−	2.06658i
$563$			23.6574i			0.997041i	0.866878	+	0.498520i	$0.166123\pi$
$563$			23.6574i			0.997041i	−0.866878	+	0.498520i	$0.833877\pi$
$564$	17.7710			0.748295
$565$	19.1103	+	12.1829i	0.803975	+	0.512540i
$566$	−29.2037			−1.22752
$567$		−	15.1455i		−	0.636051i
$568$			2.91666i			0.122380i
$569$	−30.7352			−1.28849			−0.644244	−	0.764820i	$-0.722828\pi$
$569$	−30.7352			−1.28849			−0.644244	+	0.764820i	$0.722828\pi$
$570$	−13.4014	+	21.0216i	−0.561324	+	0.880499i
$571$	−28.4768			−1.19172			−0.595860	−	0.803089i	$-0.703188\pi$
$571$	−28.4768			−1.19172			−0.595860	+	0.803089i	$0.703188\pi$
$572$		0			0
$573$			27.0350i			1.12940i
$574$	21.4699			0.896135
$575$	−19.7626	+	9.20053i	−0.824158	+	0.383689i
$576$	−47.9032			−1.99597
$577$		−	38.6132i		−	1.60749i	−0.594974	−	0.803745i	$-0.702838\pi$
$577$		−	38.6132i		−	1.60749i	0.594974	−	0.803745i	$-0.297162\pi$
$578$		−	31.5306i		−	1.31150i
$579$	−14.1742			−0.589060
$580$	−10.4695	+	16.4225i	−0.434722	+	0.681909i
$581$	34.1575			1.41709
$582$			89.2539i			3.69969i
$583$		0			0
$584$	−1.06046			−0.0438823
$585$	6.72262	+	4.28571i	0.277946	+	0.177192i
$586$	−30.6709			−1.26700
$587$			14.2818i			0.589474i	0.955578	+	0.294737i	$0.0952320\pi$
$587$			14.2818i			0.589474i	−0.955578	+	0.294737i	$0.904768\pi$
$588$			20.1948i			0.832821i
$589$	−14.9383			−0.615520
$590$	−14.1742	−	9.03616i	−0.583543	−	0.372013i
$591$	−34.6119			−1.42374
$592$			7.83893i			0.322178i
$593$			36.4700i			1.49764i	0.662771	+	0.748822i	$0.269380\pi$
$593$			36.4700i			1.49764i	−0.662771	+	0.748822i	$0.730620\pi$
$594$		0			0
$595$	−4.58754	+	7.19606i	−0.188071	+	0.295010i
$596$	40.1550			1.64481
$597$			14.5492i			0.595461i
$598$			5.72146i			0.233968i
$599$	−30.3410			−1.23970			−0.619849	−	0.784721i	$-0.712806\pi$
$599$	−30.3410			−1.23970			−0.619849	+	0.784721i	$0.712806\pi$
$600$	1.14150	+	2.45193i	0.0466016	+	0.100099i
$601$	37.8224			1.54281			0.771403	−	0.636347i	$-0.219555\pi$
$601$	37.8224			1.54281			0.771403	+	0.636347i	$0.219555\pi$
$602$			71.0077i			2.89406i
$603$			13.0796i			0.532642i
$604$	−6.88313			−0.280071
$605$		0			0
$606$	−32.8888			−1.33602
$607$			31.0829i			1.26161i	0.775940	+	0.630807i	$0.217276\pi$
$607$			31.0829i			1.26161i	−0.775940	+	0.630807i	$0.782724\pi$
$608$		−	15.2680i		−	0.619198i
$609$	38.9747			1.57934
$610$	29.6995	+	18.9336i	1.20250	+	0.766600i
$611$	1.89096			0.0764999
$612$		−	13.6624i		−	0.552271i
$613$			36.2674i			1.46483i	0.680860	+	0.732414i	$0.261606\pi$
$613$			36.2674i			1.46483i	−0.680860	+	0.732414i	$0.738394\pi$
$614$	16.2668			0.656475
$615$	−18.1647	−	11.5801i	−0.732470	−	0.466954i
$616$		0			0
$617$		−	1.28079i		−	0.0515626i	−0.999668	−	0.0257813i	$-0.991793\pi$
$617$		−	1.28079i		−	0.0515626i	0.999668	−	0.0257813i	$-0.00820735\pi$
$618$			18.7620i			0.754718i
$619$	−8.24079			−0.331225			−0.165613	−	0.986191i	$-0.552960\pi$
$619$	−8.24079			−0.331225			−0.165613	+	0.986191i	$0.552960\pi$
$620$	−19.8628	+	31.1570i	−0.797708	+	1.25129i
$621$	−31.7163			−1.27273
$622$		−	45.0415i		−	1.80600i
$623$			28.9015i			1.15791i
$624$	−7.20094			−0.288268
$625$	−16.0934	+	19.1312i	−0.643738	+	0.765246i
$626$	4.75448			0.190027
$627$		0			0
$628$		−	29.3146i		−	1.16978i
$629$	−2.44646			−0.0975467
$630$	42.9117	−	67.3117i	1.70964	−	2.68176i
$631$	−12.4074			−0.493933			−0.246966	−	0.969024i	$-0.579434\pi$
$631$	−12.4074			−0.493933			−0.246966	+	0.969024i	$0.579434\pi$
$632$			2.83124i			0.112621i
$633$		−	4.58533i		−	0.182251i
$634$	−36.4577			−1.44792
$635$	−31.0034	−	19.7649i	−1.23033	−	0.784346i
$636$	39.1322			1.55169
$637$			2.14887i			0.0851412i
$638$		0			0
$639$	−86.3738			−3.41689
$640$	−2.79637	−	1.78271i	−0.110536	−	0.0704677i
$641$	−5.42930			−0.214444			−0.107222	−	0.994235i	$-0.534196\pi$
$641$	−5.42930			−0.214444			−0.107222	+	0.994235i	$0.534196\pi$
$642$			23.4015i			0.923585i
$643$			2.08798i			0.0823420i	0.999152	+	0.0411710i	$0.0131088\pi$
$643$			2.08798i			0.0823420i	−0.999152	+	0.0411710i	$0.986891\pi$
$644$	29.2860			1.15403
$645$	38.2991	−	60.0764i	1.50802	−	2.36550i
$646$	4.54595			0.178858
$647$		−	24.7631i		−	0.973540i	−0.873530	−	0.486770i	$-0.838175\pi$
$647$		−	24.7631i		−	0.973540i	0.873530	−	0.486770i	$-0.161825\pi$
$648$			0.875266i			0.0343837i
$649$		0			0
$650$	2.76932	+	5.94847i	0.108622	+	0.233318i
$651$	73.9432			2.89806
$652$			21.5909i			0.845564i
$653$		−	6.89916i		−	0.269985i	−0.990847	−	0.134992i	$-0.956899\pi$
$653$		−	6.89916i		−	0.269985i	0.990847	−	0.134992i	$-0.0431010\pi$
$654$	90.8864			3.55394
$655$	−16.8292	+	26.3985i	−0.657572	+	1.03147i
$656$	12.5865			0.491420
$657$		−	31.4045i		−	1.22521i
$658$		−	18.9336i		−	0.738110i
$659$	12.4567			0.485246			0.242623	−	0.970121i	$-0.421992\pi$
$659$	12.4567			0.485246			0.242623	+	0.970121i	$0.421992\pi$
$660$		0			0
$661$	17.8173			0.693012			0.346506	−	0.938048i	$-0.387368\pi$
$661$	17.8173			0.693012			0.346506	+	0.938048i	$0.387368\pi$
$662$			6.25400i			0.243069i
$663$		−	2.24735i		−	0.0872798i
$664$	−1.97398			−0.0766052
$665$	11.4495	+	7.29915i	0.443994	+	0.283049i
$666$	22.8841			0.886741
$667$		−	18.1542i		−	0.702933i
$668$		−	30.5516i		−	1.18208i
$669$	−9.66167			−0.373542
$670$	−5.78670	+	9.07709i	−0.223560	+	0.350679i
$671$		0			0
$672$			75.5752i			2.91538i
$673$		−	29.0771i		−	1.12084i	−0.828209	−	0.560419i	$-0.810640\pi$
$673$		−	29.0771i		−	1.12084i	0.828209	−	0.560419i	$-0.189360\pi$
$674$	72.7113			2.80074
$675$	−32.9747	+	15.3515i	−1.26920	+	0.590879i
$676$	−26.3123			−1.01201
$677$			40.8682i			1.57069i	0.619056	+	0.785347i	$0.287515\pi$
$677$			40.8682i			1.57069i	−0.619056	+	0.785347i	$0.712485\pi$
$678$			59.7578i			2.29499i
$679$	48.6126			1.86558
$680$	0.265116	−	0.415864i	0.0101667	−	0.0159477i
$681$	−8.27824			−0.317223
$682$		0			0
$683$			17.2211i			0.658948i	0.944165	+	0.329474i	$0.106871\pi$
$683$			17.2211i			0.658948i	−0.944165	+	0.329474i	$0.893129\pi$
$684$	−21.7380			−0.831175
$685$	−25.9663	−	16.5537i	−0.992123	−	0.632485i
$686$	−23.9545			−0.914588
$687$			5.80497i			0.221474i
$688$			41.6276i			1.58704i
$689$	4.16393			0.158633
$690$	−48.4683	−	30.8988i	−1.84516	−	1.17630i
$691$	20.1406			0.766186			0.383093	−	0.923710i	$-0.374859\pi$
$691$	20.1406			0.766186			0.383093	+	0.923710i	$0.374859\pi$
$692$			4.61938i			0.175603i
$693$		0			0
$694$	24.8055			0.941603
$695$	8.11933	−	12.7361i	0.307984	−	0.483107i
$696$	−2.25237			−0.0853759
$697$			3.92813i			0.148789i
$698$			35.7498i			1.35315i
$699$	−59.0341			−2.23287
$700$	30.4479	−	14.1751i	1.15082	−	0.535769i
$701$	21.1666			0.799452			0.399726	−	0.916635i	$-0.369105\pi$
$701$	21.1666			0.799452			0.399726	+	0.916635i	$0.369105\pi$
$702$			9.54650i			0.360309i
$703$			3.89252i			0.146809i
$704$		0			0
$705$	−10.2121	+	16.0189i	−0.384611	+	0.603306i
$706$	−37.8674			−1.42516
$707$			17.9131i			0.673690i
$708$		−	22.6583i		−	0.851551i
$709$	−20.5623			−0.772233			−0.386116	−	0.922450i	$-0.626184\pi$
$709$	−20.5623			−0.772233			−0.386116	+	0.922450i	$0.626184\pi$
$710$	−59.9424	−	38.2137i	−2.24960	−	1.43413i
$711$	−83.8442			−3.14440
$712$		−	1.67023i		−	0.0625946i
$713$		−	34.4422i		−	1.28987i
$714$	−22.5021			−0.842119
$715$		0			0
$716$	22.6078			0.844892
$717$		−	5.51167i		−	0.205837i
$718$			75.3836i			2.81329i
$719$	18.2500			0.680609			0.340305	−	0.940315i	$-0.389470\pi$
$719$	18.2500			0.680609			0.340305	+	0.940315i	$0.389470\pi$
$720$	25.1565	−	39.4608i	0.937529	−	1.47062i
$721$	10.2188			0.380569
$722$			31.2003i			1.16116i
$723$			11.6737i			0.434148i
$724$	7.04286			0.261746
$725$	−8.78706	−	18.8745i	−0.326343	−	0.700980i
$726$		0			0
$727$		−	0.218345i		−	0.00809798i	−0.999992	−	0.00404899i	$-0.998711\pi$
$727$		−	0.218345i		−	0.00809798i	0.999992	−	0.00404899i	$-0.00128884\pi$
$728$		−	0.386627i		−	0.0143293i
$729$	37.6911			1.39597
$730$	13.8941	−	21.7944i	0.514242	−	0.806646i
$731$	−12.9916			−0.480511
$732$			47.4764i			1.75478i
$733$			1.74365i			0.0644033i	0.999481	+	0.0322016i	$0.0102519\pi$
$733$			1.74365i			0.0644033i	−0.999481	+	0.0322016i	$0.989748\pi$
$734$	−36.4081			−1.34385
$735$	−18.2037	−	11.6050i	−0.671454	−	0.428057i
$736$	35.2024			1.29758
$737$		0			0
$738$		−	36.7436i		−	1.35255i
$739$	−30.3837			−1.11768			−0.558842	−	0.829274i	$-0.688754\pi$
$739$	−30.3837			−1.11768			−0.558842	+	0.829274i	$0.688754\pi$
$740$	8.11870	+	5.17572i	0.298449	+	0.190263i
$741$	−3.57572			−0.131357
$742$		−	41.6923i		−	1.53057i
$743$			34.6653i			1.27175i	0.771794	+	0.635873i	$0.219360\pi$
$743$			34.6653i			1.27175i	−0.771794	+	0.635873i	$0.780640\pi$
$744$	−4.27321			−0.156664
$745$	−23.0751	+	36.1959i	−0.845407	+	1.32611i
$746$	−0.409835			−0.0150051
$747$		−	58.4572i		−	2.13884i
$748$		0			0
$749$	12.7458			0.465720
$750$	−65.3471	−	8.66499i	−2.38614	−	0.316401i
$751$	9.55888			0.348809			0.174404	−	0.984674i	$-0.444200\pi$
$751$	9.55888			0.348809			0.174404	+	0.984674i	$0.444200\pi$
$752$		−	11.0997i		−	0.404763i
$753$			66.1880i			2.41203i
$754$	−5.46434			−0.198999
$755$	3.95540	−	6.20448i	0.143952	−	0.225804i
$756$	48.8649			1.77720
$757$		−	6.26124i		−	0.227569i	−0.993505	−	0.113784i	$-0.963703\pi$
$757$		−	6.26124i		−	0.227569i	0.993505	−	0.113784i	$-0.0362973\pi$
$758$		−	68.7414i		−	2.49680i
$759$		0			0
$760$	−0.661674	−	0.421822i	−0.0240014	−	0.0153011i
$761$	26.6660			0.966642			0.483321	−	0.875443i	$-0.339430\pi$
$761$	26.6660			0.966642			0.483321	+	0.875443i	$0.339430\pi$
$762$		−	96.9477i		−	3.51205i
$763$		−	49.5018i		−	1.79208i
$764$	−19.4014			−0.701919
$765$	12.3154	+	7.85113i	0.445263	+	0.283858i
$766$	−14.4470			−0.521990
$767$		−	2.41099i		−	0.0870560i
$768$			42.0678i			1.51799i
$769$	−42.2399			−1.52321			−0.761605	−	0.648042i	$-0.775588\pi$
$769$	−42.2399			−1.52321			−0.761605	+	0.648042i	$0.775588\pi$
$770$		0			0
$771$	−11.8425			−0.426498
$772$		−	10.1720i		−	0.366098i
$773$			46.2951i			1.66512i	0.553937	+	0.832559i	$0.313125\pi$
$773$			46.2951i			1.66512i	−0.553937	+	0.832559i	$0.686875\pi$
$774$	121.523			4.36805
$775$	−16.6709	−	35.8088i	−0.598835	−	1.28629i
$776$	−2.80935			−0.100850
$777$		−	19.2677i		−	0.691224i
$778$			26.8362i			0.962124i
$779$	6.24998			0.223929
$780$	−4.75448	+	7.45793i	−0.170238	+	0.267037i
$781$		0			0
$782$			10.4813i			0.374811i
$783$		−	30.2910i		−	1.08251i
$784$	12.6136			0.450484
$785$	26.4243	+	16.8457i	0.943123	+	0.601247i
$786$	−82.5481			−2.94439
$787$		−	49.1450i		−	1.75183i	−0.482465	−	0.875915i	$-0.660258\pi$
$787$		−	49.1450i		−	1.75183i	0.482465	−	0.875915i	$-0.339742\pi$
$788$		−	24.8389i		−	0.884848i
$789$	35.8672			1.27691
$790$	−58.1869	−	37.0945i	−2.07020	−	1.31976i
$791$	32.5474			1.15725
$792$		0			0
$793$			5.05180i			0.179395i
$794$	−67.8883			−2.40926
$795$	−22.4874	+	35.2740i	−0.797545	+	1.25104i
$796$	−10.4411			−0.370076
$797$			43.6700i			1.54687i	0.633875	+	0.773435i	$0.281463\pi$
$797$			43.6700i			1.54687i	−0.633875	+	0.773435i	$0.718537\pi$
$798$			35.8027i			1.26740i
$799$	3.46410			0.122551
$800$	36.5991	−	17.0388i	1.29397	−	0.602413i
$801$	49.4621			1.74766
$802$		−	67.9480i		−	2.39933i
$803$		0			0
$804$	−14.5102			−0.511737
$805$	−16.8292	+	26.3985i	−0.593152	+	0.930425i
$806$	−10.3670			−0.365161
$807$			22.4667i			0.790866i
$808$		−	1.03520i		−	0.0364184i
$809$	39.5048			1.38891			0.694457	−	0.719534i	$-0.255645\pi$
$809$	39.5048			1.38891			0.694457	+	0.719534i	$0.255645\pi$
$810$	−17.9882	−	11.4676i	−0.632042	−	0.402931i
$811$	46.5773			1.63555			0.817775	−	0.575538i	$-0.195207\pi$
$811$	46.5773			1.63555			0.817775	+	0.575538i	$0.195207\pi$
$812$			27.9698i			0.981549i
$813$			45.3940i			1.59204i
$814$		0			0
$815$	−19.4621	−	12.4072i	−0.681728	−	0.434606i
$816$	−13.1916			−0.461799
$817$			20.6707i			0.723176i
$818$			16.5242i			0.577756i
$819$	11.4495			0.400079
$820$	8.31034	−	13.0357i	0.290210	−	0.455226i
$821$	29.2072			1.01934			0.509669	−	0.860371i	$-0.329768\pi$
$821$	29.2072			1.01934			0.509669	+	0.860371i	$0.329768\pi$
$822$		−	81.1967i		−	2.83206i
$823$		−	13.8818i		−	0.483890i	−0.970290	−	0.241945i	$-0.922215\pi$
$823$		−	13.8818i		−	0.483890i	0.970290	−	0.241945i	$-0.0777854\pi$
$824$	−0.590551			−0.0205728
$825$		0			0
$826$	−24.1406			−0.839960
$827$			9.55026i			0.332095i	0.986118	+	0.166048i	$0.0531005\pi$
$827$			9.55026i			0.332095i	−0.986118	+	0.166048i	$0.946899\pi$
$828$		−	50.1201i		−	1.74179i
$829$	−37.3241			−1.29632			−0.648160	−	0.761504i	$-0.724461\pi$
$829$	−37.3241			−1.29632			−0.648160	+	0.761504i	$0.724461\pi$
$830$	25.8628	−	40.5686i	0.897710	−	1.40816i
$831$	59.1784			2.05288
$832$		−	5.65476i		−	0.196044i
$833$			3.93658i			0.136394i
$834$	39.8257			1.37905
$835$	27.5393	+	17.5565i	0.953038	+	0.607568i
$836$		0			0
$837$		−	57.4683i		−	1.98640i
$838$			39.5112i			1.36489i
$839$	1.43270			0.0494623			0.0247311	−	0.999694i	$-0.492127\pi$
$839$	1.43270			0.0494623			0.0247311	+	0.999694i	$0.492127\pi$
$840$	3.27523	+	2.08798i	0.113006	+	0.0720422i
$841$	−11.6617			−0.402127
$842$			48.3618i			1.66666i
$843$			70.5940i			2.43139i
$844$	3.29062			0.113268
$845$	15.1204	−	23.7180i	0.520157	−	0.815925i
$846$	−32.4031			−1.11404
$847$		0			0
$848$		−	24.4417i		−	0.839332i
$849$	42.0810			1.44422
$850$	5.07321	+	10.8972i	0.174010	+	0.373770i
$851$	−8.97475			−0.307650
$852$		−	95.8213i		−	3.28278i
$853$		−	28.1421i		−	0.963569i	−0.876290	−	0.481784i	$-0.839989\pi$
$853$		−	28.1421i		−	0.963569i	0.876290	−	0.481784i	$-0.160011\pi$
$854$	50.5823			1.73089
$855$	12.4918	−	19.5948i	0.427210	−	0.670127i
$856$	−0.736584			−0.0251759
$857$			4.04561i			0.138195i	0.997610	+	0.0690977i	$0.0220120\pi$
$857$			4.04561i			0.138195i	−0.997610	+	0.0690977i	$0.977988\pi$
$858$		0			0
$859$	55.2064			1.88362			0.941808	−	0.336151i	$-0.109125\pi$
$859$	55.2064			1.88362			0.941808	+	0.336151i	$0.109125\pi$
$860$	43.1132	+	27.4850i	1.47015	+	0.937229i
$861$	−30.9369			−1.05433
$862$			15.3002i			0.521125i
$863$		−	30.1927i		−	1.02777i	−0.857859	−	0.513885i	$-0.828206\pi$
$863$		−	30.1927i		−	1.02777i	0.857859	−	0.513885i	$-0.171794\pi$
$864$	58.7367			1.99826
$865$	−4.16393	−	2.65453i	−0.141578	−	0.0902568i
$866$	−51.8231			−1.76102
$867$			45.4338i			1.54301i
$868$			53.0646i			1.80113i
$869$		0			0
$870$	29.5102	−	46.2901i	1.00049	−	1.56938i
$871$	−1.54399			−0.0523160
$872$			2.86073i			0.0968766i
$873$		−	83.1958i		−	2.81575i
$874$	16.6767			0.564096
$875$	−4.71943	+	35.5916i	−0.159546	+	1.20322i
$876$	34.8395			1.17712
$877$		−	30.9398i		−	1.04476i	−0.852712	−	0.522381i	$-0.825044\pi$
$877$		−	30.9398i		−	1.04476i	0.852712	−	0.522381i	$-0.174956\pi$
$878$		−	41.4004i		−	1.39719i
$879$	44.1951			1.49066
$880$		0			0
$881$	−8.25840			−0.278233			−0.139116	−	0.990276i	$-0.544426\pi$
$881$	−8.25840			−0.278233			−0.139116	+	0.990276i	$0.544426\pi$
$882$		−	36.8226i		−	1.23988i
$883$		−	40.0289i		−	1.34708i	−0.739152	−	0.673539i	$-0.764773\pi$
$883$		−	40.0289i		−	1.34708i	0.739152	−	0.673539i	$-0.235227\pi$
$884$	1.61279			0.0542439
$885$	20.4243	+	13.0206i	0.686555	+	0.437683i
$886$	−20.5615			−0.690777
$887$			37.7350i			1.26702i	0.773735	+	0.633509i	$0.218386\pi$
$887$			37.7350i			1.26702i	−0.773735	+	0.633509i	$0.781614\pi$
$888$			1.11349i			0.0373662i
$889$	−52.8031			−1.77096
$890$	34.3261	+	21.8831i	1.15062	+	0.733525i
$891$		0			0
$892$		−	6.93360i		−	0.232154i
$893$		−	5.51167i		−	0.184441i
$894$	−113.185			−3.78546
$895$	−12.9916	+	20.3787i	−0.434261	+	0.681186i
$896$	−4.76261			−0.159108
$897$		−	8.24432i		−	0.275270i
$898$		−	29.7343i		−	0.992245i
$899$	32.8944			1.09709
$900$	−24.2593	−	52.1087i	−0.808644	−	1.73696i
$901$	7.62803			0.254127
$902$		0			0
$903$		−	102.318i		−	3.40494i
$904$	−1.88093			−0.0625588
$905$	−4.04719	+	6.34846i	−0.134533	+	0.211030i
$906$	19.4014			0.644569
$907$			33.5319i			1.11341i	0.830710	+	0.556705i	$0.187935\pi$
$907$			33.5319i			1.11341i	−0.830710	+	0.556705i	$0.812065\pi$
$908$		−	5.94079i		−	0.197152i
$909$	30.6565			1.01681
$910$	7.94585	+	5.06553i	0.263402	+	0.167921i
$911$	−13.7828			−0.456646			−0.228323	−	0.973585i	$-0.573324\pi$
$911$	−13.7828			−0.456646			−0.228323	+	0.973585i	$0.573324\pi$
$912$			20.9890i			0.695014i
$913$		0			0
$914$	6.80231			0.225000
$915$	−42.7954	−	27.2823i	−1.41477	−	0.901926i
$916$	−4.16588			−0.137645
$917$			44.9602i			1.48472i
$918$			17.4885i			0.577207i
$919$	−41.8128			−1.37928			−0.689639	−	0.724154i	$-0.742231\pi$
$919$	−41.8128			−1.37928			−0.689639	+	0.724154i	$0.742231\pi$
$920$	0.972568	−	1.52558i	0.0320646	−	0.0502969i
$921$	−23.4396			−0.772361
$922$			2.86073i			0.0942131i
$923$		−	10.1960i		−	0.335607i
$924$		0			0
$925$	−9.33084	+	4.34399i	−0.306796	+	0.142830i
$926$	31.2716			1.02765
$927$		−	17.4885i		−	0.574399i
$928$			33.6204i			1.10364i
$929$	−13.1028			−0.429889			−0.214944	−	0.976626i	$-0.568957\pi$
$929$	−13.1028			−0.429889			−0.214944	+	0.976626i	$0.568957\pi$
$930$	55.9870	−	87.8219i	1.83589	−	2.87979i
$931$	6.26342			0.205275
$932$		−	42.3652i		−	1.38772i
$933$			64.9023i			2.12481i
$934$	37.8078			1.23711
$935$		0			0
$936$	−0.661674			−0.0216275
$937$		−	8.75544i		−	0.286028i	−0.989721	−	0.143014i	$-0.954321\pi$
$937$		−	8.75544i		−	0.286028i	0.989721	−	0.143014i	$-0.0456794\pi$
$938$			15.4595i			0.504771i
$939$	−6.85095			−0.223572
$940$	−11.4958	−	7.32864i	−0.374951	−	0.239034i
$941$	−17.6529			−0.575468			−0.287734	−	0.957710i	$-0.592902\pi$
$941$	−17.6529			−0.575468			−0.287734	+	0.957710i	$0.592902\pi$
$942$			82.6287i			2.69219i
$943$			14.4102i			0.469261i
$944$	−14.1522			−0.460615
$945$	−28.0803	+	44.0470i	−0.913451	+	1.43285i
$946$		0			0
$947$			56.2415i			1.82760i	0.406159	+	0.913802i	$0.366868\pi$
$947$			56.2415i			1.82760i	−0.406159	+	0.913802i	$0.633132\pi$
$948$		−	93.0150i		−	3.02099i
$949$	3.70716			0.120340
$950$	17.3383	−	8.07190i	0.562530	−	0.261887i
$951$	52.5336			1.70352
$952$		−	0.708273i		−	0.0229553i
$953$			4.74388i			0.153669i	0.997044	+	0.0768347i	$0.0244814\pi$
$953$			4.74388i			0.153669i	−0.997044	+	0.0768347i	$0.975519\pi$
$954$	−71.3524			−2.31012
$955$	11.1490	−	17.4885i	0.360775	−	0.565915i
$956$	3.95540			0.127927
$957$		0			0
$958$		−	60.4344i		−	1.95255i
$959$	−44.2242			−1.42807
$960$	47.9032	+	30.5386i	1.54607	+	0.985630i
$961$	31.4074			1.01314
$962$			2.70137i			0.0870955i
$963$		−	21.8132i		−	0.702919i
$964$	−8.37749			−0.269821
$965$	9.16908	+	5.84535i	0.295163	+	0.188168i
$966$	−82.5481			−2.65594
$967$			33.8619i			1.08892i	0.838785	+	0.544462i	$0.183266\pi$
$967$			33.8619i			1.08892i	−0.838785	+	0.544462i	$0.816734\pi$
$968$		0			0
$969$	−6.55047			−0.210431
$970$	36.8077	−	57.7369i	1.18182	−	1.85382i
$971$	−19.7828			−0.634862			−0.317431	−	0.948281i	$-0.602820\pi$
$971$	−19.7828			−0.634862			−0.317431	+	0.948281i	$0.602820\pi$
$972$			16.8947i			0.541898i
$973$		−	21.6913i		−	0.695390i
$974$	1.89096			0.0605902
$975$	−3.99045	−	8.57142i	−0.127797	−	0.274505i
$976$	29.6534			0.949182
$977$		−	6.66124i		−	0.213112i	−0.994307	−	0.106556i	$-0.966018\pi$
$977$		−	6.66124i		−	0.213112i	0.994307	−	0.106556i	$-0.0339823\pi$
$978$		−	60.8581i		−	1.94603i
$979$		0			0
$980$	8.32821	−	13.0637i	0.266035	−	0.417305i
$981$	−84.7175			−2.70482
$982$			66.5390i			2.12334i
$983$			5.16210i			0.164645i	0.996606	+	0.0823227i	$0.0262338\pi$
$983$			5.16210i			0.164645i	−0.996606	+	0.0823227i	$0.973766\pi$
$984$	1.78786			0.0569949
$985$	22.3899	+	14.2737i	0.713400	+	0.454797i
$986$	−10.0103			−0.318792
$987$			27.2823i			0.868407i
$988$		−	2.56608i		−	0.0816378i
$989$	−47.6592			−1.51547
$990$		0			0
$991$	−23.8830			−0.758669			−0.379334	−	0.925260i	$-0.623847\pi$
$991$	−23.8830			−0.758669			−0.379334	+	0.925260i	$0.623847\pi$
$992$			63.7849i			2.02517i
$993$		−	9.01167i		−	0.285977i
$994$	−102.090			−3.23810
$995$	6.00000	−	9.41167i	0.190213	−	0.298370i
$996$	64.8513			2.05489
$997$			29.6423i			0.938780i	0.882991	+	0.469390i	$0.155526\pi$
$997$			29.6423i			0.938780i	−0.882991	+	0.469390i	$0.844474\pi$
$998$			18.1882i			0.575738i
$999$	−14.9747			−0.473780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.b.h.364.4	yes	12
5.2	odd	4		3025.2.a.bo.1.10		12
5.3	odd	4		3025.2.a.bo.1.3		12
5.4	even	2	inner	605.2.b.h.364.9	yes	12
11.2	odd	10		605.2.j.k.444.10		48
11.3	even	5		605.2.j.k.9.3		48
11.4	even	5		605.2.j.k.269.10		48
11.5	even	5		605.2.j.k.124.9		48
11.6	odd	10		605.2.j.k.124.3		48
11.7	odd	10		605.2.j.k.269.4		48
11.8	odd	10		605.2.j.k.9.9		48
11.9	even	5		605.2.j.k.444.4		48
11.10	odd	2	inner	605.2.b.h.364.10	yes	12
55.4	even	10		605.2.j.k.269.3		48
55.9	even	10		605.2.j.k.444.9		48
55.14	even	10		605.2.j.k.9.10		48
55.19	odd	10		605.2.j.k.9.4		48
55.24	odd	10		605.2.j.k.444.3		48
55.29	odd	10		605.2.j.k.269.9		48
55.32	even	4		3025.2.a.bo.1.4		12
55.39	odd	10		605.2.j.k.124.10		48
55.43	even	4		3025.2.a.bo.1.9		12
55.49	even	10		605.2.j.k.124.4		48
55.54	odd	2	inner	605.2.b.h.364.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.h.364.3	✓	12	55.54	odd	2	inner
605.2.b.h.364.4	yes	12	1.1	even	1	trivial
605.2.b.h.364.9	yes	12	5.4	even	2	inner
605.2.b.h.364.10	yes	12	11.10	odd	2	inner
605.2.j.k.9.3		48	11.3	even	5
605.2.j.k.9.4		48	55.19	odd	10
605.2.j.k.9.9		48	11.8	odd	10
605.2.j.k.9.10		48	55.14	even	10
605.2.j.k.124.3		48	11.6	odd	10
605.2.j.k.124.4		48	55.49	even	10
605.2.j.k.124.9		48	11.5	even	5
605.2.j.k.124.10		48	55.39	odd	10
605.2.j.k.269.3		48	55.4	even	10
605.2.j.k.269.4		48	11.7	odd	10
605.2.j.k.269.9		48	55.29	odd	10
605.2.j.k.269.10		48	11.4	even	5
605.2.j.k.444.3		48	55.24	odd	10
605.2.j.k.444.4		48	11.9	even	5
605.2.j.k.444.9		48	55.9	even	10
605.2.j.k.444.10		48	11.2	odd	10
3025.2.a.bo.1.3		12	5.3	odd	4
3025.2.a.bo.1.4		12	55.32	even	4
3025.2.a.bo.1.9		12	55.43	even	4
3025.2.a.bo.1.10		12	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.02281i q^{2} +2.91475i q^{3} -2.09174 q^{4} +(1.20202 - 1.88551i) q^{5} +5.89598 q^{6} -3.21128i q^{7} +0.185581i q^{8} -5.49579 q^{9} +O(q^{10})\)	\(q-2.02281i q^{2} +2.91475i q^{3} -2.09174 q^{4} +(1.20202 - 1.88551i) q^{5} +5.89598 q^{6} -3.21128i q^{7} +0.185581i q^{8} -5.49579 q^{9} +(-3.81402 - 2.43146i) q^{10} -6.09692i q^{12} -0.648753i q^{13} -6.49579 q^{14} +(5.49579 + 3.50360i) q^{15} -3.80809 q^{16} -1.18847i q^{17} +11.1169i q^{18} -1.89096 q^{19} +(-2.51433 + 3.94400i) q^{20} +9.36008 q^{21} -4.35986i q^{23} -0.540924 q^{24} +(-2.11028 - 4.53285i) q^{25} -1.31230 q^{26} -7.27462i q^{27} +6.71717i q^{28} +4.16393 q^{29} +(7.08711 - 11.1169i) q^{30} +7.89984 q^{31} +8.07420i q^{32} -2.40405 q^{34} +(-6.05489 - 3.86003i) q^{35} +11.4958 q^{36} -2.05849i q^{37} +3.82504i q^{38} +1.89096 q^{39} +(0.349915 + 0.223073i) q^{40} -3.30520 q^{41} -18.9336i q^{42} -10.9313i q^{43} +(-6.60607 + 10.3624i) q^{45} -8.81916 q^{46} +2.91475i q^{47} -11.0997i q^{48} -3.31230 q^{49} +(-9.16908 + 4.26869i) q^{50} +3.46410 q^{51} +1.35703i q^{52} +6.41836i q^{53} -14.7151 q^{54} +0.595953 q^{56} -5.51167i q^{57} -8.42283i q^{58} +3.71635 q^{59} +(-11.4958 - 7.32864i) q^{60} -7.78694 q^{61} -15.9798i q^{62} +17.6485i q^{63} +8.71635 q^{64} +(-1.22323 - 0.779817i) q^{65} -2.37993i q^{67} +2.48598i q^{68} +12.7079 q^{69} +(-7.80809 + 12.2479i) q^{70} +15.7163 q^{71} -1.01992i q^{72} +5.71428i q^{73} -4.16393 q^{74} +(13.2121 - 6.15094i) q^{75} +3.95540 q^{76} -3.82504i q^{78} +15.2561 q^{79} +(-4.57742 + 7.18019i) q^{80} +4.71635 q^{81} +6.68577i q^{82} +10.6367i q^{83} -19.5789 q^{84} +(-2.24087 - 1.42857i) q^{85} -22.1120 q^{86} +12.1368i q^{87} -9.00000 q^{89} +(20.9610 + 13.3628i) q^{90} -2.08333 q^{91} +9.11972i q^{92} +23.0261i q^{93} +5.89598 q^{94} +(-2.27297 + 3.56541i) q^{95} -23.5343 q^{96} +15.1381i q^{97} +6.70015i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9}+O(q^{10}) \) 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9	\( 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9} - 32 q^{14} + 20 q^{15} + 36 q^{16} + 26 q^{20} - 10 q^{25} + 20 q^{26} + 8 q^{31} + 12 q^{34} + 92 q^{36} - 18 q^{45} - 4 q^{49} + 48 q^{56} - 32 q^{59} - 92 q^{60} + 28 q^{64} - 16 q^{69} - 12 q^{70} + 112 q^{71} + 36 q^{75} - 106 q^{80} - 20 q^{81} - 56 q^{86} - 108 q^{89} + 72 q^{91}+O(q^{100}) \) 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9 - 32 * q^14 + 20 * q^15 + 36 * q^16 + 26 * q^20 - 10 * q^25 + 20 * q^26 + 8 * q^31 + 12 * q^34 + 92 * q^36 - 18 * q^45 - 4 * q^49 + 48 * q^56 - 32 * q^59 - 92 * q^60 + 28 * q^64 - 16 * q^69 - 12 * q^70 + 112 * q^71 + 36 * q^75 - 106 * q^80 - 20 * q^81 - 56 * q^86 - 108 * q^89 + 72 * q^91

Introduction

L-functions

Modular forms

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Database

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