LMFDB - Embedded newform 1205.2.b.c.724.15

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			724.15
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.09514i q^{2} +0.223927i q^{3} +0.800662 q^{4} +(-1.50518 + 1.65361i) q^{5} +0.245232 q^{6} -2.26365i q^{7} -3.06713i q^{8} +2.94986 q^{9} +O(q^{10})$	\(q-1.09514i q^{2} +0.223927i q^{3} +0.800662 q^{4} +(-1.50518 + 1.65361i) q^{5} +0.245232 q^{6} -2.26365i q^{7} -3.06713i q^{8} +2.94986 q^{9} +(1.81094 + 1.64839i) q^{10} -3.16701 q^{11} +0.179290i q^{12} -0.0649874i q^{13} -2.47902 q^{14} +(-0.370288 - 0.337051i) q^{15} -1.75761 q^{16} -4.44087i q^{17} -3.23051i q^{18} -7.82407 q^{19} +(-1.20514 + 1.32398i) q^{20} +0.506893 q^{21} +3.46833i q^{22} -2.53175i q^{23} +0.686812 q^{24} +(-0.468844 - 4.97797i) q^{25} -0.0711705 q^{26} +1.33233i q^{27} -1.81242i q^{28} +6.53411 q^{29} +(-0.369119 + 0.405518i) q^{30} +8.27459 q^{31} -4.20941i q^{32} -0.709178i q^{33} -4.86338 q^{34} +(3.74319 + 3.40721i) q^{35} +2.36184 q^{36} +2.73984i q^{37} +8.56847i q^{38} +0.0145524 q^{39} +(5.07183 + 4.61659i) q^{40} -7.52088 q^{41} -0.555120i q^{42} -10.7428i q^{43} -2.53570 q^{44} +(-4.44008 + 4.87791i) q^{45} -2.77262 q^{46} -8.53037i q^{47} -0.393577i q^{48} +1.87588 q^{49} +(-5.45159 + 0.513451i) q^{50} +0.994430 q^{51} -0.0520330i q^{52} +0.0654906i q^{53} +1.45909 q^{54} +(4.76693 - 5.23699i) q^{55} -6.94290 q^{56} -1.75202i q^{57} -7.15578i q^{58} -11.9066 q^{59} +(-0.296475 - 0.269864i) q^{60} +7.88792 q^{61} -9.06186i q^{62} -6.67745i q^{63} -8.12514 q^{64} +(0.107464 + 0.0978179i) q^{65} -0.776651 q^{66} +13.3617i q^{67} -3.55564i q^{68} +0.566926 q^{69} +(3.73138 - 4.09933i) q^{70} -8.56086 q^{71} -9.04758i q^{72} -16.6336i q^{73} +3.00052 q^{74} +(1.11470 - 0.104987i) q^{75} -6.26444 q^{76} +7.16900i q^{77} -0.0159370i q^{78} +0.725508 q^{79} +(2.64553 - 2.90641i) q^{80} +8.55123 q^{81} +8.23644i q^{82} -6.57206i q^{83} +0.405850 q^{84} +(7.34346 + 6.68432i) q^{85} -11.7649 q^{86} +1.46316i q^{87} +9.71361i q^{88} +10.8164 q^{89} +(5.34201 + 4.86252i) q^{90} -0.147109 q^{91} -2.02707i q^{92} +1.85290i q^{93} -9.34197 q^{94} +(11.7767 - 12.9380i) q^{95} +0.942600 q^{96} +9.64642i q^{97} -2.05436i q^{98} -9.34222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.09514i		−	0.774383i	−0.921999	−	0.387191i	$-0.873445\pi$
$2$		−	1.09514i		−	0.774383i	0.921999	−	0.387191i	$-0.126555\pi$
$3$			0.223927i			0.129284i	0.997909	+	0.0646421i	$0.0205906\pi$
$3$			0.223927i			0.129284i	−0.997909	+	0.0646421i	$0.979409\pi$
$4$	0.800662			0.400331
$5$	−1.50518	+	1.65361i	−0.673139	+	0.739516i
$5$	−1.50518	+	1.65361i	−0.673139	+	0.739516i
$6$	0.245232			0.100116
$7$		−	2.26365i		−	0.855580i	−0.903878	−	0.427790i	$-0.859292\pi$
$7$		−	2.26365i		−	0.855580i	0.903878	−	0.427790i	$-0.140708\pi$
$8$		−	3.06713i		−	1.08439i
$9$	2.94986			0.983286
$10$	1.81094	+	1.64839i	0.572669	+	0.521267i
$11$	−3.16701			−0.954889			−0.477444	−	0.878662i	$-0.658437\pi$
$11$	−3.16701			−0.954889			−0.477444	+	0.878662i	$0.658437\pi$
$12$			0.179290i			0.0517565i
$13$		−	0.0649874i		−	0.0180243i	−0.999959	−	0.00901213i	$-0.997131\pi$
$13$		−	0.0649874i		−	0.0180243i	0.999959	−	0.00901213i	$-0.00286869\pi$
$14$	−2.47902			−0.662546
$15$	−0.370288	−	0.337051i	−0.0956078	−	0.0870262i
$16$	−1.75761			−0.439404
$17$		−	4.44087i		−	1.07707i	−0.842604	−	0.538534i	$-0.818978\pi$
$17$		−	4.44087i		−	1.07707i	0.842604	−	0.538534i	$-0.181022\pi$
$18$		−	3.23051i		−	0.761439i
$19$	−7.82407			−1.79496			−0.897482	−	0.441050i	$-0.854606\pi$
$19$	−7.82407			−1.79496			−0.897482	+	0.441050i	$0.854606\pi$
$20$	−1.20514	+	1.32398i	−0.269478	+	0.296051i
$21$	0.506893			0.110613
$22$			3.46833i			0.739450i
$23$		−	2.53175i		−	0.527906i	−0.964536	−	0.263953i	$-0.914974\pi$
$23$		−	2.53175i		−	0.527906i	0.964536	−	0.263953i	$-0.0850263\pi$
$24$	0.686812			0.140195
$25$	−0.468844	−	4.97797i	−0.0937689	−	0.995594i
$26$	−0.0711705			−0.0139577
$27$			1.33233i			0.256408i
$28$		−	1.81242i		−	0.342515i
$29$	6.53411			1.21335			0.606677	−	0.794949i	$-0.292502\pi$
$29$	6.53411			1.21335			0.606677	+	0.794949i	$0.292502\pi$
$30$	−0.369119	+	0.405518i	−0.0673916	+	0.0740371i
$31$	8.27459			1.48616			0.743080	−	0.669202i	$-0.233364\pi$
$31$	8.27459			1.48616			0.743080	+	0.669202i	$0.233364\pi$
$32$		−	4.20941i		−	0.744126i
$33$		−	0.709178i		−	0.123452i
$34$	−4.86338			−0.834063
$35$	3.74319	+	3.40721i	0.632715	+	0.575924i
$36$	2.36184			0.393640
$37$			2.73984i			0.450428i	0.974309	+	0.225214i	$0.0723081\pi$
$37$			2.73984i			0.450428i	−0.974309	+	0.225214i	$0.927692\pi$
$38$			8.56847i			1.38999i
$39$	0.0145524			0.00233025
$40$	5.07183	+	4.61659i	0.801926	+	0.729946i
$41$	−7.52088			−1.17456			−0.587282	−	0.809382i	$-0.699802\pi$
$41$	−7.52088			−1.17456			−0.587282	+	0.809382i	$0.699802\pi$
$42$		−	0.555120i		−	0.0856568i
$43$		−	10.7428i		−	1.63827i	−0.573603	−	0.819134i	$-0.694455\pi$
$43$		−	10.7428i		−	1.63827i	0.573603	−	0.819134i	$-0.305545\pi$
$44$	−2.53570			−0.382272
$45$	−4.44008	+	4.87791i	−0.661887	+	0.727156i
$46$	−2.77262			−0.408801
$47$		−	8.53037i		−	1.24428i	−0.782905	−	0.622141i	$-0.786263\pi$
$47$		−	8.53037i		−	1.24428i	0.782905	−	0.622141i	$-0.213737\pi$
$48$		−	0.393577i		−	0.0568080i
$49$	1.87588			0.267983
$50$	−5.45159	+	0.513451i	−0.770971	+	0.0726130i
$51$	0.994430			0.139248
$52$		−	0.0520330i		−	0.00721567i
$53$			0.0654906i			0.00899583i	0.999990	+	0.00449791i	$0.00143174\pi$
$53$			0.0654906i			0.00899583i	−0.999990	+	0.00449791i	$0.998568\pi$
$54$	1.45909			0.198558
$55$	4.76693	−	5.23699i	0.642773	−	0.706156i
$56$	−6.94290			−0.927784
$57$		−	1.75202i		−	0.232061i
$58$		−	7.15578i		−	0.939600i
$59$	−11.9066			−1.55011			−0.775055	−	0.631894i	$-0.782278\pi$
$59$	−11.9066			−1.55011			−0.775055	+	0.631894i	$0.782278\pi$
$60$	−0.296475	−	0.269864i	−0.0382748	−	0.0348393i
$61$	7.88792			1.00995			0.504973	−	0.863135i	$-0.331503\pi$
$61$	7.88792			1.00995			0.504973	+	0.863135i	$0.331503\pi$
$62$		−	9.06186i		−	1.15086i
$63$		−	6.67745i		−	0.841279i
$64$	−8.12514			−1.01564
$65$	0.107464	+	0.0978179i	0.0133292	+	0.0121328i
$66$	−0.776651			−0.0955992
$67$			13.3617i			1.63240i	0.577771	+	0.816199i	$0.303923\pi$
$67$			13.3617i			1.63240i	−0.577771	+	0.816199i	$0.696077\pi$
$68$		−	3.55564i		−	0.431184i
$69$	0.566926			0.0682499
$70$	3.73138	−	4.09933i	0.445986	−	0.489964i
$71$	−8.56086			−1.01599			−0.507994	−	0.861361i	$-0.669613\pi$
$71$	−8.56086			−1.01599			−0.507994	+	0.861361i	$0.669613\pi$
$72$		−	9.04758i		−	1.06627i
$73$		−	16.6336i		−	1.94682i	−0.229068	−	0.973410i	$-0.573568\pi$
$73$		−	16.6336i		−	1.94682i	0.229068	−	0.973410i	$-0.426432\pi$
$74$	3.00052			0.348803
$75$	1.11470	−	0.104987i	0.128715	−	0.0121228i
$76$	−6.26444			−0.718580
$77$			7.16900i			0.816984i
$78$		−	0.0159370i		−	0.00180451i
$79$	0.725508			0.0816260			0.0408130	−	0.999167i	$-0.487005\pi$
$79$	0.725508			0.0816260			0.0408130	+	0.999167i	$0.487005\pi$
$80$	2.64553	−	2.90641i	0.295780	−	0.324946i
$81$	8.55123			0.950136
$82$			8.23644i			0.909562i
$83$		−	6.57206i		−	0.721378i	−0.932686	−	0.360689i	$-0.882542\pi$
$83$		−	6.57206i		−	0.721378i	0.932686	−	0.360689i	$-0.117458\pi$
$84$	0.405850			0.0442818
$85$	7.34346	+	6.68432i	0.796510	+	0.725016i
$86$	−11.7649			−1.26865
$87$			1.46316i			0.156868i
$88$			9.71361i			1.03547i
$89$	10.8164			1.14654			0.573269	−	0.819367i	$-0.305675\pi$
$89$	10.8164			1.14654			0.573269	+	0.819367i	$0.305675\pi$
$90$	5.34201	+	4.86252i	0.563097	+	0.512554i
$91$	−0.147109			−0.0154212
$92$		−	2.02707i		−	0.211337i
$93$			1.85290i			0.192137i
$94$	−9.34197			−0.963551
$95$	11.7767	−	12.9380i	1.20826	−	1.32741i
$96$	0.942600			0.0962038
$97$			9.64642i			0.979445i	0.871878	+	0.489723i	$0.162902\pi$
$97$			9.64642i			0.979445i	−0.871878	+	0.489723i	$0.837098\pi$
$98$		−	2.05436i		−	0.207521i
$99$	−9.34222			−0.938928
$100$	−0.375386	−	3.98567i	−0.0375386	−	0.398567i
$101$	−16.4798			−1.63980			−0.819902	−	0.572504i	$-0.805972\pi$
$101$	−16.4798			−1.63980			−0.819902	+	0.572504i	$0.805972\pi$
$102$		−	1.08904i		−	0.107831i
$103$			10.7964i			1.06380i	0.846808	+	0.531898i	$0.178521\pi$
$103$			10.7964i			1.06380i	−0.846808	+	0.531898i	$0.821479\pi$
$104$	−0.199324			−0.0195454
$105$	−0.762966	+	0.838202i	−0.0744579	+	0.0818001i
$106$	0.0717216			0.00696622
$107$		−	1.67365i		−	0.161798i	−0.996722	−	0.0808988i	$-0.974221\pi$
$107$		−	1.67365i		−	0.161798i	0.996722	−	0.0808988i	$-0.0257791\pi$
$108$			1.06675i			0.102648i
$109$	16.9594			1.62442			0.812208	−	0.583368i	$-0.198265\pi$
$109$	16.9594			1.62442			0.812208	+	0.583368i	$0.198265\pi$
$110$	−5.73525	−	5.22047i	−0.546835	−	0.497752i
$111$	−0.613525			−0.0582332
$112$			3.97863i			0.375945i
$113$		−	8.64948i		−	0.813675i	−0.913501	−	0.406837i	$-0.866632\pi$
$113$		−	8.64948i		−	0.813675i	0.913501	−	0.406837i	$-0.133368\pi$
$114$	−1.91871			−0.179704
$115$	4.18652	+	3.81074i	0.390395	+	0.355354i
$116$	5.23162			0.485743
$117$		−	0.191703i		−	0.0177230i
$118$			13.0394i			1.20038i
$119$	−10.0526			−0.921518
$120$	−1.03378	+	1.13572i	−0.0943706	+	0.103676i
$121$	−0.970060			−0.0881872
$122$		−	8.63840i		−	0.782084i
$123$		−	1.68413i		−	0.151853i
$124$	6.62515			0.594956
$125$	8.93731	+	6.71747i	0.799377	+	0.600829i
$126$	−7.31276			−0.651472
$127$		−	6.06109i		−	0.537835i	−0.963163	−	0.268918i	$-0.913334\pi$
$127$		−	6.06109i		−	0.537835i	0.963163	−	0.268918i	$-0.0866659\pi$
$128$			0.479360i			0.0423699i
$129$	2.40561			0.211802
$130$	0.107125	−	0.117688i	0.00939545	−	0.0103219i
$131$	−6.54103			−0.571493			−0.285746	−	0.958305i	$-0.592241\pi$
$131$	−6.54103			−0.571493			−0.285746	+	0.958305i	$0.592241\pi$
$132$		−	0.567812i		−	0.0494217i
$133$			17.7110i			1.53574i
$134$	14.6330			1.26410
$135$	−2.20316	−	2.00541i	−0.189618	−	0.172598i
$136$	−13.6207			−1.16797
$137$			8.14464i			0.695844i	0.937524	+	0.347922i	$0.113113\pi$
$137$			8.14464i			0.695844i	−0.937524	+	0.347922i	$0.886887\pi$
$138$		−	0.620865i		−	0.0528515i
$139$	6.38850			0.541865			0.270933	−	0.962598i	$-0.412668\pi$
$139$	6.38850			0.541865			0.270933	+	0.962598i	$0.412668\pi$
$140$	2.99704	+	2.72803i	0.253296	+	0.230560i
$141$	1.91018			0.160866
$142$			9.37537i			0.786763i
$143$			0.205816i			0.0172112i
$144$	−5.18471			−0.432059
$145$	−9.83503	+	10.8049i	−0.816755	+	0.897295i
$146$	−18.2162			−1.50758
$147$			0.420060i			0.0346460i
$148$			2.19369i			0.180320i
$149$	−9.29157			−0.761195			−0.380598	−	0.924741i	$-0.624282\pi$
$149$	−9.29157			−0.761195			−0.380598	+	0.924741i	$0.624282\pi$
$150$	−0.114976	−	1.22076i	−0.00938772	−	0.0996744i
$151$	−4.44437			−0.361677			−0.180839	−	0.983513i	$-0.557881\pi$
$151$	−4.44437			−0.361677			−0.180839	+	0.983513i	$0.557881\pi$
$152$			23.9974i			1.94645i
$153$		−	13.0999i		−	1.05907i
$154$	7.85108			0.632658
$155$	−12.4548	+	13.6829i	−1.00039	+	1.09904i
$156$	0.0116516			0.000932873
$157$			0.260484i			0.0207889i	0.999946	+	0.0103944i	$0.00330871\pi$
$157$			0.260484i			0.0207889i	−0.999946	+	0.0103944i	$0.996691\pi$
$158$		−	0.794534i		−	0.0632098i
$159$	−0.0146651			−0.00116302
$160$	6.96072	+	6.33594i	0.550293	+	0.500900i
$161$	−5.73099			−0.451666
$162$		−	9.36481i		−	0.735769i
$163$			5.42016i			0.424539i	0.977211	+	0.212270i	$0.0680855\pi$
$163$			5.42016i			0.424539i	−0.977211	+	0.212270i	$0.931914\pi$
$164$	−6.02169			−0.470215
$165$	1.17270	+	1.06744i	0.0912948	+	0.0831004i
$166$	−7.19735			−0.558623
$167$			22.0325i			1.70492i	0.522789	+	0.852462i	$0.324891\pi$
$167$			22.0325i			1.70492i	−0.522789	+	0.852462i	$0.675109\pi$
$168$		−	1.55470i		−	0.119948i
$169$	12.9958			0.999675
$170$	7.32029	−	8.04213i	0.561440	−	0.616804i
$171$	−23.0799			−1.76496
$172$		−	8.60139i		−	0.655849i
$173$			18.0964i			1.37584i	0.725785	+	0.687922i	$0.241477\pi$
$173$			18.0964i			1.37584i	−0.725785	+	0.687922i	$0.758523\pi$
$174$	1.60237			0.121476
$175$	−11.2684	+	1.06130i	−0.851810	+	0.0802268i
$176$	5.56638			0.419582
$177$		−	2.66621i		−	0.200405i
$178$		−	11.8455i		−	0.887859i
$179$	17.4131			1.30151			0.650757	−	0.759286i	$-0.274452\pi$
$179$	17.4131			1.30151			0.650757	+	0.759286i	$0.274452\pi$
$180$	−3.55500	+	3.90556i	−0.264974	+	0.291103i
$181$	6.69828			0.497879			0.248940	−	0.968519i	$-0.419918\pi$
$181$	6.69828			0.497879			0.248940	+	0.968519i	$0.419918\pi$
$182$			0.161105i			0.0119419i
$183$			1.76632i			0.130570i
$184$	−7.76518			−0.572457
$185$	−4.53063	−	4.12397i	−0.333099	−	0.303200i
$186$	2.02919			0.148788
$187$			14.0643i			1.02848i
$188$		−	6.82995i		−	0.498125i
$189$	3.01594			0.219377
$190$	−14.1689	−	12.8971i	−1.02792	−	0.935656i
$191$	18.2205			1.31839			0.659196	−	0.751971i	$-0.270897\pi$
$191$	18.2205			1.31839			0.659196	+	0.751971i	$0.270897\pi$
$192$		−	1.81944i		−	0.131307i
$193$		−	5.88201i		−	0.423396i	−0.977335	−	0.211698i	$-0.932101\pi$
$193$		−	5.88201i		−	0.423396i	0.977335	−	0.211698i	$-0.0678993\pi$
$194$	10.5642			0.758466
$195$	−0.0219041	+	0.0240640i	−0.00156858	+	0.00172326i
$196$	1.50195			0.107282
$197$		−	18.3999i		−	1.31094i	−0.755223	−	0.655468i	$-0.772472\pi$
$197$		−	18.3999i		−	1.31094i	0.755223	−	0.655468i	$-0.227528\pi$
$198$			10.2311i			0.727090i
$199$	−11.8695			−0.841404			−0.420702	−	0.907199i	$-0.638216\pi$
$199$	−11.8695			−0.841404			−0.420702	+	0.907199i	$0.638216\pi$
$200$	−15.2681	+	1.43800i	−1.07961	+	0.101682i
$201$	−2.99206			−0.211043
$202$			18.0478i			1.26984i
$203$		−	14.7909i		−	1.03812i
$204$	0.796203			0.0557453
$205$	11.3203	−	12.4366i	0.790644	−	0.868609i
$206$	11.8235			0.823786
$207$		−	7.46829i		−	0.519082i
$208$			0.114223i			0.00791992i
$209$	24.7789			1.71399
$210$	0.917951	+	0.835557i	0.0633446	+	0.0576589i
$211$	17.3377			1.19358			0.596788	−	0.802399i	$-0.296443\pi$
$211$	17.3377			1.19358			0.596788	+	0.802399i	$0.296443\pi$
$212$			0.0524359i			0.00360131i
$213$		−	1.91701i		−	0.131351i
$214$	−1.83288			−0.125293
$215$	17.7644	+	16.1699i	1.21153	+	1.10278i
$216$	4.08643			0.278046
$217$		−	18.7308i		−	1.27153i
$218$		−	18.5730i		−	1.25792i
$219$	3.72472			0.251693
$220$	3.81670	−	4.19306i	0.257322	−	0.282696i
$221$	−0.288600			−0.0194134
$222$			0.671897i			0.0450948i
$223$		−	0.685671i		−	0.0459159i	−0.999736	−	0.0229580i	$-0.992692\pi$
$223$		−	0.685671i		−	0.0459159i	0.999736	−	0.0229580i	$-0.00730838\pi$
$224$	−9.52864			−0.636659
$225$	−1.38302	−	14.6843i	−0.0922016	−	0.978953i
$226$	−9.47242			−0.630096
$227$			23.7034i			1.57325i	0.617429	+	0.786626i	$0.288174\pi$
$227$			23.7034i			1.57325i	−0.617429	+	0.786626i	$0.711826\pi$
$228$		−	1.40278i		−	0.0929011i
$229$	18.1670			1.20051			0.600254	−	0.799810i	$-0.295066\pi$
$229$	18.1670			1.20051			0.600254	+	0.799810i	$0.295066\pi$
$230$	4.17331	−	4.58484i	0.275180	−	0.302315i
$231$	−1.60533			−0.105623
$232$		−	20.0409i		−	1.31575i
$233$		−	1.69882i		−	0.111293i	−0.998451	−	0.0556466i	$-0.982278\pi$
$233$		−	1.69882i		−	0.111293i	0.998451	−	0.0556466i	$-0.0177220\pi$
$234$	−0.209943			−0.0137244
$235$	14.1059	+	12.8398i	0.920167	+	0.837574i
$236$	−9.53318			−0.620557
$237$			0.162461i			0.0105530i
$238$			11.0090i			0.713608i
$239$	−4.67855			−0.302631			−0.151315	−	0.988486i	$-0.548351\pi$
$239$	−4.67855			−0.302631			−0.151315	+	0.988486i	$0.548351\pi$
$240$	0.650823	+	0.592406i	0.0420104	+	0.0382396i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$			1.06235i			0.0682907i
$243$			5.91185i			0.379245i
$244$	6.31556			0.404313
$245$	−2.82355	+	3.10197i	−0.180390	+	0.198178i
$246$	−1.84436			−0.117592
$247$			0.508466i			0.0323529i
$248$		−	25.3792i		−	1.61158i
$249$	1.47166			0.0932628
$250$	7.35659	−	9.78763i	0.465272	−	0.619024i
$251$	−6.44769			−0.406974			−0.203487	−	0.979078i	$-0.565228\pi$
$251$	−6.44769			−0.406974			−0.203487	+	0.979078i	$0.565228\pi$
$252$		−	5.34638i		−	0.336790i
$253$			8.01806i			0.504091i
$254$	−6.63776			−0.416490
$255$	−1.49680	+	1.64440i	−0.0937332	+	0.102976i
$256$	−15.7253			−0.982831
$257$			15.0125i			0.936452i	0.883609	+	0.468226i	$0.155107\pi$
$257$			15.0125i			0.936452i	−0.883609	+	0.468226i	$0.844893\pi$
$258$		−	2.63449i		−	0.164016i
$259$	6.20205			0.385377
$260$	0.0860422	+	0.0783192i	0.00533611	+	0.00485715i
$261$	19.2747			1.19307
$262$			7.16336i			0.442554i
$263$			11.1566i			0.687945i	0.938980	+	0.343973i	$0.111773\pi$
$263$			11.1566i			0.687945i	−0.938980	+	0.343973i	$0.888227\pi$
$264$	−2.17514			−0.133871
$265$	−0.108296	−	0.0985754i	−0.00665256	−	0.00605544i
$266$	19.3960			1.18925
$267$			2.42209i			0.148229i
$268$			10.6983i			0.653500i
$269$	13.5075			0.823569			0.411785	−	0.911281i	$-0.364906\pi$
$269$	13.5075			0.823569			0.411785	+	0.911281i	$0.364906\pi$
$270$	−2.19621	+	2.41277i	−0.133657	+	0.146837i
$271$	13.0987			0.795687			0.397844	−	0.917453i	$-0.369759\pi$
$271$	13.0987			0.795687			0.397844	+	0.917453i	$0.369759\pi$
$272$			7.80533i			0.473268i
$273$		−	0.0329416i		−	0.00199372i
$274$	8.91954			0.538849
$275$	1.48483	+	15.7653i	0.0895388	+	0.950682i
$276$	0.453917			0.0273226
$277$		−	14.4487i		−	0.868135i	−0.900880	−	0.434068i	$-0.857078\pi$
$277$		−	14.4487i		−	0.868135i	0.900880	−	0.434068i	$-0.142922\pi$
$278$		−	6.99631i		−	0.419611i
$279$	24.4089			1.46132
$280$	10.4503	−	11.4808i	0.624528	−	0.686112i
$281$	1.77667			0.105988			0.0529938	−	0.998595i	$-0.483124\pi$
$281$	1.77667			0.105988			0.0529938	+	0.998595i	$0.483124\pi$
$282$		−	2.09192i		−	0.124572i
$283$			18.4509i			1.09679i	0.836218	+	0.548397i	$0.184762\pi$
$283$			18.4509i			1.09679i	−0.836218	+	0.548397i	$0.815238\pi$
$284$	−6.85436			−0.406732
$285$	2.89716	+	2.63711i	0.171613	+	0.156209i
$286$	0.225397			0.0133280
$287$			17.0247i			1.00493i
$288$		−	12.4172i		−	0.731688i
$289$	−2.72130			−0.160077
$290$	11.8329	+	10.7708i	0.694850	+	0.632481i
$291$	−2.16009			−0.126627
$292$		−	13.3179i		−	0.779373i
$293$		−	8.65394i		−	0.505569i	−0.967523	−	0.252784i	$-0.918654\pi$
$293$		−	8.65394i		−	0.505569i	0.967523	−	0.252784i	$-0.0813463\pi$
$294$	0.460026			0.0268293
$295$	17.9216	−	19.6889i	1.04344	−	1.14633i
$296$	8.40345			0.488440
$297$		−	4.21951i		−	0.244841i
$298$			10.1756i			0.589456i
$299$	−0.164532			−0.00951511
$300$	0.892500	−	0.0840590i	0.0515285	−	0.00485315i
$301$	−24.3180			−1.40167
$302$			4.86722i			0.280077i
$303$		−	3.69028i		−	0.212001i
$304$	13.7517			0.788714
$305$	−11.8728	+	13.0435i	−0.679833	+	0.746871i
$306$	−14.3463			−0.820123
$307$			6.61143i			0.377334i	0.982041	+	0.188667i	$0.0604167\pi$
$307$			6.61143i			0.377334i	−0.982041	+	0.188667i	$0.939583\pi$
$308$			5.73995i			0.327064i
$309$	−2.41759			−0.137532
$310$	14.9848	+	13.6398i	0.851078	+	0.774686i
$311$	−19.4206			−1.10124			−0.550622	−	0.834755i	$-0.685609\pi$
$311$	−19.4206			−1.10124			−0.550622	+	0.834755i	$0.685609\pi$
$312$		−	0.0446341i		−	0.00252691i
$313$			19.4518i			1.09948i	0.835336	+	0.549740i	$0.185273\pi$
$313$			19.4518i			1.09948i	−0.835336	+	0.549740i	$0.814727\pi$
$314$	0.285267			0.0160986
$315$	11.0419	+	10.0508i	0.622140	+	0.566298i
$316$	0.580887			0.0326774
$317$		−	0.792618i		−	0.0445179i	−0.999752	−	0.0222589i	$-0.992914\pi$
$317$		−	0.792618i		−	0.0445179i	0.999752	−	0.0222589i	$-0.00708583\pi$
$318$			0.0160604i			0.000900622i
$319$	−20.6936			−1.15862
$320$	12.2298	−	13.4358i	0.683668	−	0.751084i
$321$	0.374775			0.0209179
$322$			6.27626i			0.349762i
$323$			34.7457i			1.93330i
$324$	6.84664			0.380369
$325$	−0.323505	+	0.0304690i	−0.0179448	+	0.00169011i
$326$	5.93584			0.328756
$327$			3.79767i			0.210011i
$328$			23.0675i			1.27369i
$329$	−19.3098			−1.06458
$330$	1.16900	−	1.28428i	0.0643515	−	0.0706972i
$331$	14.6988			0.807917			0.403958	−	0.914777i	$-0.367634\pi$
$331$	14.6988			0.807917			0.403958	+	0.914777i	$0.367634\pi$
$332$		−	5.26201i		−	0.288790i
$333$			8.08215i			0.442899i
$334$	24.1287			1.32026
$335$	−22.0951	−	20.1119i	−1.20718	−	1.09883i
$336$	−0.890922			−0.0486038
$337$			17.3385i			0.944487i	0.881468	+	0.472244i	$0.156556\pi$
$337$			17.3385i			0.944487i	−0.881468	+	0.472244i	$0.843444\pi$
$338$		−	14.2322i		−	0.774131i
$339$	1.93685			0.105195
$340$	5.87963	+	5.35189i	0.318868	+	0.290247i
$341$	−26.2057			−1.41912
$342$			25.2758i			1.36676i
$343$		−	20.0919i		−	1.08486i
$344$	−32.9496			−1.77652
$345$	−0.853328	+	0.937474i	−0.0459416	+	0.0504719i
$346$	19.8181			1.06543
$347$		−	13.9745i		−	0.750188i	−0.926987	−	0.375094i	$-0.877610\pi$
$347$		−	13.9745i		−	0.750188i	0.926987	−	0.375094i	$-0.122390\pi$
$348$			1.17150i			0.0627990i
$349$	−18.2257			−0.975600			−0.487800	−	0.872955i	$-0.662200\pi$
$349$	−18.2257			−0.975600			−0.487800	+	0.872955i	$0.662200\pi$
$350$	1.16228	+	12.3405i	0.0621262	+	0.659627i
$351$	0.0865848			0.00462156
$352$			13.3312i			0.710557i
$353$		−	25.1550i		−	1.33886i	−0.742873	−	0.669432i	$-0.766537\pi$
$353$		−	25.1550i		−	1.33886i	0.742873	−	0.669432i	$-0.233463\pi$
$354$	−2.91988			−0.155190
$355$	12.8857	−	14.1563i	0.683900	−	0.751339i
$356$	8.66030			0.458995
$357$		−	2.25104i		−	0.119138i
$358$		−	19.0698i		−	1.00787i
$359$	6.05193			0.319409			0.159704	−	0.987165i	$-0.448946\pi$
$359$	6.05193			0.319409			0.159704	+	0.987165i	$0.448946\pi$
$360$	14.9612	+	13.6183i	0.788522	+	0.717746i
$361$	42.2161			2.22190
$362$		−	7.33558i		−	0.385549i
$363$		−	0.217222i		−	0.0114012i
$364$	−0.117784			−0.00617359
$365$	27.5055	+	25.0367i	1.43971	+	1.31048i
$366$	1.93437			0.101111
$367$		−	31.3055i		−	1.63413i	−0.576543	−	0.817067i	$-0.695599\pi$
$367$		−	31.3055i		−	1.63413i	0.576543	−	0.817067i	$-0.304401\pi$
$368$			4.44984i			0.231964i
$369$	−22.1855			−1.15493
$370$	−4.51633	+	4.96169i	−0.234793	+	0.257946i
$371$	0.148248			0.00769665
$372$			1.48355i			0.0769185i
$373$			17.5060i			0.906424i	0.891403	+	0.453212i	$0.149722\pi$
$373$			17.5060i			0.906424i	−0.891403	+	0.453212i	$0.850278\pi$
$374$	15.4024			0.796438
$375$	−1.50422	+	2.00130i	−0.0776777	+	0.103347i
$376$	−26.1637			−1.34929
$377$		−	0.424635i		−	0.0218698i
$378$		−	3.30288i		−	0.169882i
$379$	−0.569958			−0.0292768			−0.0146384	−	0.999893i	$-0.504660\pi$
$379$	−0.569958			−0.0292768			−0.0146384	+	0.999893i	$0.504660\pi$
$380$	9.42913	−	10.3589i	0.483704	−	0.531402i
$381$	1.35724			0.0695336
$382$		−	19.9541i		−	1.02094i
$383$			24.0263i			1.22769i	0.789428	+	0.613843i	$0.210377\pi$
$383$			24.0263i			1.22769i	−0.789428	+	0.613843i	$0.789623\pi$
$384$	−0.107342			−0.00547776
$385$	−11.8547	−	10.7907i	−0.604173	−	0.549943i
$386$	−6.44164			−0.327871
$387$		−	31.6898i		−	1.61088i
$388$			7.72353i			0.392103i
$389$	13.5820			0.688633			0.344317	−	0.938854i	$-0.388111\pi$
$389$	13.5820			0.688633			0.344317	+	0.938854i	$0.388111\pi$
$390$	0.0263535	+	0.0239881i	0.00133446	+	0.00121468i
$391$	−11.2432			−0.568591
$392$		−	5.75356i		−	0.290599i
$393$		−	1.46471i		−	0.0738850i
$394$	−20.1505			−1.01517
$395$	−1.09202	+	1.19971i	−0.0549456	+	0.0603638i
$396$	−7.47997			−0.375882
$397$		−	9.52930i		−	0.478262i	−0.970987	−	0.239131i	$-0.923137\pi$
$397$		−	9.52930i		−	0.478262i	0.970987	−	0.239131i	$-0.0768625\pi$
$398$			12.9988i			0.651569i
$399$	−3.96596			−0.198546
$400$	0.824048	+	8.74935i	0.0412024	+	0.437468i
$401$	9.98608			0.498681			0.249341	−	0.968416i	$-0.419786\pi$
$401$	9.98608			0.498681			0.249341	+	0.968416i	$0.419786\pi$
$402$			3.27673i			0.163428i
$403$		−	0.537744i		−	0.0267869i
$404$	−13.1948			−0.656465
$405$	−12.8712	+	14.1404i	−0.639573	+	0.702641i
$406$	−16.1982			−0.803903
$407$		−	8.67711i		−	0.430108i
$408$		−	3.05004i		−	0.150999i
$409$	1.85693			0.0918193			0.0459097	−	0.998946i	$-0.485381\pi$
$409$	1.85693			0.0918193			0.0459097	+	0.998946i	$0.485381\pi$
$410$	−13.6198	−	12.3974i	−0.672636	−	0.612261i
$411$	−1.82380			−0.0899616
$412$			8.64424i			0.425871i
$413$			26.9524i			1.32624i
$414$	−8.17884			−0.401968
$415$	10.8676	+	9.89216i	0.533471	+	0.485587i
$416$	−0.273559			−0.0134123
$417$			1.43056i			0.0700546i
$418$		−	27.1364i		−	1.32729i
$419$	9.53574			0.465851			0.232926	−	0.972495i	$-0.425170\pi$
$419$	9.53574			0.465851			0.232926	+	0.972495i	$0.425170\pi$
$420$	−0.610879	+	0.671117i	−0.0298078	+	0.0327471i
$421$	−21.1822			−1.03235			−0.516177	−	0.856482i	$-0.672645\pi$
$421$	−21.1822			−1.03235			−0.516177	+	0.856482i	$0.672645\pi$
$422$		−	18.9872i		−	0.924284i
$423$		−	25.1634i		−	1.22348i
$424$	0.200868			0.00975501
$425$	−22.1065	+	2.08208i	−1.07232	+	0.100995i
$426$	−2.09940			−0.101716
$427$		−	17.8555i		−	0.864089i
$428$		−	1.34003i		−	0.0647726i
$429$	−0.0460876			−0.00222513
$430$	17.7084	−	19.4546i	0.853975	−	0.938184i
$431$	−35.7158			−1.72037			−0.860186	−	0.509981i	$-0.829652\pi$
$431$	−35.7158			−1.72037			−0.860186	+	0.509981i	$0.829652\pi$
$432$		−	2.34173i		−	0.112666i
$433$			11.8322i			0.568618i	0.958733	+	0.284309i	$0.0917642\pi$
$433$			11.8322i			0.568618i	−0.958733	+	0.284309i	$0.908236\pi$
$434$	−20.5129			−0.984650
$435$	−2.41950	−	2.20233i	−0.116006	−	0.105594i
$436$	13.5788			0.650305
$437$			19.8086i			0.947572i
$438$		−	4.07910i		−	0.194907i
$439$	−2.11764			−0.101069			−0.0505347	−	0.998722i	$-0.516093\pi$
$439$	−2.11764			−0.101069			−0.0505347	+	0.998722i	$0.516093\pi$
$440$	−16.0625	−	14.6208i	−0.765750	−	0.697018i
$441$	5.53358			0.263504
$442$			0.316059i			0.0150334i
$443$			26.8075i			1.27366i	0.771002	+	0.636832i	$0.219756\pi$
$443$			26.8075i			1.27366i	−0.771002	+	0.636832i	$0.780244\pi$
$444$	−0.491226			−0.0233126
$445$	−16.2807	+	17.8861i	−0.771779	+	0.847883i
$446$	−0.750907			−0.0355565
$447$		−	2.08063i		−	0.0984106i
$448$			18.3925i			0.868963i
$449$	35.6307			1.68152			0.840759	−	0.541409i	$-0.182109\pi$
$449$	35.6307			1.68152			0.840759	+	0.541409i	$0.182109\pi$
$450$	−16.0814	+	1.51461i	−0.758085	+	0.0713993i
$451$	23.8187			1.12158
$452$		−	6.92532i		−	0.325739i
$453$		−	0.995213i		−	0.0467592i
$454$	25.9587			1.21830
$455$	0.221426	−	0.243260i	0.0103806	−	0.0114042i
$456$	−5.37366			−0.251645
$457$			4.37323i			0.204571i	0.994755	+	0.102286i	$0.0326156\pi$
$457$			4.37323i			0.204571i	−0.994755	+	0.102286i	$0.967384\pi$
$458$		−	19.8954i		−	0.929652i
$459$	5.91671			0.276169
$460$	3.35199	+	3.05112i	0.156287	+	0.142259i
$461$	2.32865			0.108456			0.0542281	−	0.998529i	$-0.482730\pi$
$461$	2.32865			0.108456			0.0542281	+	0.998529i	$0.482730\pi$
$462$			1.75807i			0.0817927i
$463$		−	24.3683i		−	1.13249i	−0.824236	−	0.566246i	$-0.808395\pi$
$463$		−	24.3683i		−	1.13249i	0.824236	−	0.566246i	$-0.191605\pi$
$464$	−11.4844			−0.533152
$465$	−3.06398	−	2.78896i	−0.142089	−	0.129335i
$466$	−1.86045			−0.0861835
$467$		−	42.0547i		−	1.94606i	−0.230678	−	0.973030i	$-0.574094\pi$
$467$		−	42.0547i		−	1.94606i	0.230678	−	0.973030i	$-0.425906\pi$
$468$		−	0.153490i		−	0.00709507i
$469$	30.2463			1.39665
$470$	14.0614	−	15.4480i	0.648603	−	0.712562i
$471$	−0.0583294			−0.00268768
$472$			36.5191i			1.68093i
$473$			34.0226i			1.56436i
$474$	0.177918			0.00817203
$475$	3.66827	+	38.9480i	0.168312	+	1.78706i
$476$	−8.04872			−0.368913
$477$			0.193188i			0.00884547i
$478$			5.12369i			0.234352i
$479$	30.3166			1.38520			0.692600	−	0.721322i	$-0.256465\pi$
$479$	30.3166			1.38520			0.692600	+	0.721322i	$0.256465\pi$
$480$	−1.41879	+	1.55869i	−0.0647585	+	0.0711442i
$481$	0.178055			0.00811862
$482$		−	1.09514i		−	0.0498824i
$483$		−	1.28332i		−	0.0583932i
$484$	−0.776690			−0.0353041
$485$	−15.9514	−	14.5196i	−0.724316	−	0.659303i
$486$	6.47432			0.293681
$487$		−	16.4118i		−	0.743692i	−0.928295	−	0.371846i	$-0.878725\pi$
$487$		−	16.4118i		−	0.743692i	0.928295	−	0.371846i	$-0.121275\pi$
$488$		−	24.1932i		−	1.09518i
$489$	−1.21372			−0.0548863
$490$	3.39710	+	3.09218i	0.153465	+	0.139691i
$491$	−0.561056			−0.0253201			−0.0126600	−	0.999920i	$-0.504030\pi$
$491$	−0.561056			−0.0253201			−0.0126600	+	0.999920i	$0.504030\pi$
$492$		−	1.34842i		−	0.0607914i
$493$		−	29.0171i		−	1.30686i
$494$	0.556843			0.0250535
$495$	14.0618	−	15.4484i	0.632029	−	0.694353i
$496$	−14.5435			−0.653024
$497$			19.3788i			0.869258i
$498$		−	1.61168i		−	0.0722211i
$499$	39.1100			1.75080			0.875401	−	0.483397i	$-0.160597\pi$
$499$	39.1100			1.75080			0.875401	+	0.483397i	$0.160597\pi$
$500$	7.15577	+	5.37843i	0.320016	+	0.240531i
$501$	−4.93366			−0.220420
$502$			7.06114i			0.315154i
$503$		−	36.7064i		−	1.63666i	−0.574750	−	0.818329i	$-0.694901\pi$
$503$		−	36.7064i		−	1.63666i	0.574750	−	0.818329i	$-0.305099\pi$
$504$	−20.4806			−0.912277
$505$	24.8052	−	27.2512i	1.10382	−	1.21266i
$506$	8.78092			0.390360
$507$			2.91010i			0.129242i
$508$		−	4.85289i		−	0.215312i
$509$	20.8479			0.924065			0.462033	−	0.886863i	$-0.347120\pi$
$509$	20.8479			0.924065			0.462033	+	0.886863i	$0.347120\pi$
$510$	1.80085	+	1.63921i	0.0797430	+	0.0725854i
$511$	−37.6528			−1.66566
$512$			18.1802i			0.803458i
$513$		−	10.4243i		−	0.460243i
$514$	16.4408			0.725172
$515$	−17.8529	−	16.2505i	−0.786695	−	0.716082i
$516$	1.92608			0.0847910
$517$			27.0158i			1.18815i
$518$		−	6.79213i		−	0.298429i
$519$	−4.05227			−0.177875
$520$	0.300020	−	0.329605i	0.0131567	−	0.0144541i
$521$	−23.2776			−1.01981			−0.509904	−	0.860231i	$-0.670319\pi$
$521$	−23.2776			−1.01981			−0.509904	+	0.860231i	$0.670319\pi$
$522$		−	21.1085i		−	0.923895i
$523$			16.3641i			0.715552i	0.933807	+	0.357776i	$0.116465\pi$
$523$			16.3641i			0.715552i	−0.933807	+	0.357776i	$0.883535\pi$
$524$	−5.23716			−0.228786
$525$	−0.237654	−	2.52330i	−0.0103721	−	0.110126i
$526$	12.2181			0.532733
$527$		−	36.7464i		−	1.60070i
$528$			1.24646i			0.0542453i
$529$	16.5903			0.721316
$530$	−0.107954	+	0.118599i	−0.00468923	+	0.00515163i
$531$	−35.1228			−1.52420
$532$			14.1805i			0.614803i
$533$			0.488762i			0.0211706i
$534$	2.65253			0.114786
$535$	2.76756	+	2.51915i	0.119652	+	0.108912i
$536$	40.9822			1.77016
$537$			3.89926i			0.168265i
$538$		−	14.7927i		−	0.637758i
$539$	−5.94093			−0.255894
$540$	−1.76399	−	1.60565i	−0.0759099	−	0.0690963i
$541$	−23.0819			−0.992369			−0.496184	−	0.868217i	$-0.665266\pi$
$541$	−23.0819			−0.992369			−0.496184	+	0.868217i	$0.665266\pi$
$542$		−	14.3449i		−	0.616166i
$543$			1.49993i			0.0643680i
$544$	−18.6934			−0.801475
$545$	−25.5270	+	28.0442i	−1.09346	+	1.20128i
$546$	−0.0360758			−0.00154390
$547$		−	17.3551i		−	0.742049i	−0.928623	−	0.371024i	$-0.879007\pi$
$547$		−	17.3551i		−	0.742049i	0.928623	−	0.371024i	$-0.120993\pi$
$548$			6.52111i			0.278568i
$549$	23.2682			0.993064
$550$	17.2652	−	1.62610i	0.736192	−	0.0693373i
$551$	−51.1233			−2.17793
$552$		−	1.73883i		−	0.0740097i
$553$		−	1.64230i		−	0.0698376i
$554$	−15.8233			−0.672269
$555$	0.923468	−	1.01453i	0.0391990	−	0.0430644i
$556$	5.11503			0.216926
$557$			6.28655i			0.266370i	0.991091	+	0.133185i	$0.0425204\pi$
$557$			6.28655i			0.266370i	−0.991091	+	0.133185i	$0.957480\pi$
$558$		−	26.7312i		−	1.13162i
$559$	−0.698149			−0.0295285
$560$	−6.57909	−	5.98857i	−0.278017	−	0.253063i
$561$	−3.14937			−0.132966
$562$		−	1.94571i		−	0.0820749i
$563$			6.26725i			0.264133i	0.991241	+	0.132067i	$0.0421613\pi$
$563$			6.26725i			0.264133i	−0.991241	+	0.132067i	$0.957839\pi$
$564$	1.52941			0.0643997
$565$	14.3029	+	13.0191i	0.601726	+	0.547716i
$566$	20.2064			0.849338
$567$		−	19.3570i		−	0.812917i
$568$			26.2572i			1.10173i
$569$	−21.6171			−0.906234			−0.453117	−	0.891451i	$-0.649688\pi$
$569$	−21.6171			−0.906234			−0.453117	+	0.891451i	$0.649688\pi$
$570$	2.88801	−	3.17280i	0.120966	−	0.132894i
$571$	−36.4039			−1.52345			−0.761727	−	0.647898i	$-0.775648\pi$
$571$	−36.4039			−1.52345			−0.761727	+	0.647898i	$0.775648\pi$
$572$			0.164789i			0.00689017i
$573$			4.08007i			0.170447i
$574$	18.6444			0.778203
$575$	−12.6030	+	1.18700i	−0.525580	+	0.0495011i
$576$	−23.9680			−0.998666
$577$		−	31.3479i		−	1.30503i	−0.757776	−	0.652514i	$-0.773714\pi$
$577$		−	31.3479i		−	1.30503i	0.757776	−	0.652514i	$-0.226286\pi$
$578$			2.98022i			0.123961i
$579$	1.31714			0.0547385
$580$	−7.87454	+	8.65105i	−0.326973	+	0.359215i
$581$	−14.8769			−0.617196
$582$			2.36561i			0.0980577i
$583$		−	0.207409i		−	0.00859002i
$584$	−51.0175			−2.11112
$585$	0.317003	+	0.288549i	0.0131064	+	0.0119300i
$586$	−9.47730			−0.391504
$587$			44.4381i			1.83416i	0.398705	+	0.917079i	$0.369460\pi$
$587$			44.4381i			1.83416i	−0.398705	+	0.917079i	$0.630540\pi$
$588$			0.336326i			0.0138699i
$589$	−64.7410			−2.66761
$590$	−21.5621	−	19.6268i	−0.887699	−	0.808021i
$591$	4.12022			0.169483
$592$		−	4.81559i		−	0.197920i
$593$		−	6.62491i		−	0.272052i	−0.990705	−	0.136026i	$-0.956567\pi$
$593$		−	6.62491i		−	0.272052i	0.990705	−	0.136026i	$-0.0434331\pi$
$594$	−4.62096			−0.189600
$595$	15.1310	−	16.6230i	0.620310	−	0.681478i
$596$	−7.43941			−0.304730
$597$		−	2.65789i		−	0.108780i
$598$			0.180186i			0.00736834i
$599$	−24.8397			−1.01492			−0.507460	−	0.861675i	$-0.669416\pi$
$599$	−24.8397			−1.01492			−0.507460	+	0.861675i	$0.669416\pi$
$600$	−0.322008	−	3.41893i	−0.0131459	−	0.139577i
$601$	−6.70931			−0.273679			−0.136839	−	0.990593i	$-0.543694\pi$
$601$	−6.70931			−0.273679			−0.136839	+	0.990593i	$0.543694\pi$
$602$			26.6317i			1.08543i
$603$			39.4152i			1.60511i
$604$	−3.55844			−0.144791
$605$	1.46012	−	1.60410i	0.0593622	−	0.0652159i
$606$	−4.04138			−0.164170
$607$			18.3020i			0.742857i	0.928462	+	0.371428i	$0.121132\pi$
$607$			18.3020i			0.742857i	−0.928462	+	0.371428i	$0.878868\pi$
$608$			32.9347i			1.33568i
$609$	3.31209			0.134213
$610$	14.2845	+	13.0024i	0.578364	+	0.526451i
$611$	−0.554366			−0.0224273
$612$		−	10.4886i		−	0.423977i
$613$		−	26.7397i		−	1.08000i	−0.841664	−	0.540002i	$-0.818423\pi$
$613$		−	26.7397i		−	1.08000i	0.841664	−	0.540002i	$-0.181577\pi$
$614$	7.24045			0.292201
$615$	2.78489	+	2.53492i	0.112298	+	0.102218i
$616$	21.9882			0.885931
$617$			44.9237i			1.80856i	0.426939	+	0.904280i	$0.359592\pi$
$617$			44.9237i			1.80856i	−0.426939	+	0.904280i	$0.640408\pi$
$618$			2.64761i			0.106503i
$619$	−34.7225			−1.39562			−0.697808	−	0.716285i	$-0.745841\pi$
$619$	−34.7225			−1.39562			−0.697808	+	0.716285i	$0.745841\pi$
$620$	−9.97207	+	10.9554i	−0.400488	+	0.439980i
$621$	3.37313			0.135359
$622$			21.2684i			0.852784i
$623$		−	24.4846i		−	0.980954i
$624$	−0.0255776			−0.00102392
$625$	−24.5604	+	4.66779i	−0.982415	+	0.186711i
$626$	21.3025			0.851418
$627$			5.54866i			0.221592i
$628$			0.208560i			0.00832244i
$629$	12.1673			0.485142
$630$	11.0070	−	12.0924i	0.438531	−	0.481774i
$631$	−30.3033			−1.20635			−0.603177	−	0.797607i	$-0.706099\pi$
$631$	−30.3033			−1.20635			−0.603177	+	0.797607i	$0.706099\pi$
$632$		−	2.22522i		−	0.0885146i
$633$			3.88237i			0.154311i
$634$	−0.868030			−0.0344739
$635$	10.0227	+	9.12306i	0.397738	+	0.362038i
$636$	−0.0117418			−0.000465593
$637$		−	0.121909i		−	0.00483019i
$638$			22.6624i			0.897214i
$639$	−25.2533			−0.999006
$640$	−0.792674	−	0.721525i	−0.0313332	−	0.0285208i
$641$	44.8929			1.77316			0.886582	−	0.462571i	$-0.153073\pi$
$641$	44.8929			1.77316			0.886582	+	0.462571i	$0.153073\pi$
$642$		−	0.410432i		−	0.0161984i
$643$		−	0.746188i		−	0.0294268i	−0.999892	−	0.0147134i	$-0.995316\pi$
$643$		−	0.746188i		−	0.0294268i	0.999892	−	0.0147134i	$-0.00468359\pi$
$644$	−4.58859			−0.180816
$645$	−3.62088	+	3.97794i	−0.142572	+	0.156631i
$646$	38.0515			1.49711
$647$		−	25.5099i		−	1.00290i	−0.865188	−	0.501448i	$-0.832801\pi$
$647$		−	25.5099i		−	1.00290i	0.865188	−	0.501448i	$-0.167199\pi$
$648$		−	26.2277i		−	1.03032i
$649$	37.7084			1.48018
$650$	0.0333679	+	0.354284i	0.00130880	+	0.0138962i
$651$	4.19433			0.164389
$652$			4.33972i			0.169956i
$653$		−	28.7035i		−	1.12325i	−0.827391	−	0.561627i	$-0.810176\pi$
$653$		−	28.7035i		−	1.12325i	0.827391	−	0.561627i	$-0.189824\pi$
$654$	4.15899			0.162629
$655$	9.84546	−	10.8163i	0.384694	−	0.422628i
$656$	13.2188			0.516108
$657$		−	49.0669i		−	1.91428i
$658$			21.1470i			0.824395i
$659$	−15.5090			−0.604146			−0.302073	−	0.953285i	$-0.597679\pi$
$659$	−15.5090			−0.604146			−0.302073	+	0.953285i	$0.597679\pi$
$660$	0.938940	+	0.854662i	0.0365482	+	0.0332677i
$661$	−28.9524			−1.12612			−0.563058	−	0.826417i	$-0.690375\pi$
$661$	−28.9524			−1.12612			−0.563058	+	0.826417i	$0.690375\pi$
$662$		−	16.0972i		−	0.625637i
$663$		−	0.0646254i		−	0.00250984i
$664$	−20.1573			−0.782257
$665$	−29.2870	−	26.6583i	−1.13570	−	1.03376i
$666$	8.85111			0.342973
$667$		−	16.5427i		−	0.640536i
$668$			17.6406i			0.682534i
$669$	0.153540			0.00593620
$670$	−22.0254	+	24.1973i	−0.850915	+	0.934823i
$671$	−24.9811			−0.964385
$672$		−	2.13372i		−	0.0823100i
$673$			35.4119i			1.36503i	0.730873	+	0.682513i	$0.239113\pi$
$673$			35.4119i			1.36503i	−0.730873	+	0.682513i	$0.760887\pi$
$674$	18.9881			0.731395
$675$	6.63231	−	0.624657i	0.255278	−	0.0240430i
$676$	10.4052			0.400201
$677$		−	17.5836i		−	0.675791i	−0.941184	−	0.337896i	$-0.890285\pi$
$677$		−	17.5836i		−	0.675791i	0.941184	−	0.337896i	$-0.109715\pi$
$678$		−	2.12113i		−	0.0814615i
$679$	21.8361			0.837994
$680$	20.5016	−	22.5233i	0.786202	−	0.863729i
$681$	−5.30784			−0.203397
$682$			28.6990i			1.09894i
$683$		−	29.9328i		−	1.14535i	−0.819783	−	0.572674i	$-0.805906\pi$
$683$		−	29.9328i		−	1.14535i	0.819783	−	0.572674i	$-0.194094\pi$
$684$	−18.4792			−0.706570
$685$	−13.4680	−	12.2592i	−0.514588	−	0.468399i
$686$	−22.0035			−0.840098
$687$			4.06807i			0.155207i
$688$			18.8818i			0.719861i
$689$	0.00425606			0.000162143
$690$	1.02667	+	0.934516i	0.0390846	+	0.0355764i
$691$	13.2291			0.503260			0.251630	−	0.967823i	$-0.419033\pi$
$691$	13.2291			0.503260			0.251630	+	0.967823i	$0.419033\pi$
$692$			14.4891i			0.550793i
$693$			21.1475i			0.803328i
$694$	−15.3040			−0.580933
$695$	−9.61586	+	10.5641i	−0.364750	+	0.400718i
$696$	4.48770			0.170106
$697$			33.3992i			1.26509i
$698$			19.9598i			0.755488i
$699$	0.380411			0.0143884
$700$	−9.02218	+	0.849743i	−0.341006	+	0.0321173i
$701$	15.9444			0.602214			0.301107	−	0.953590i	$-0.402644\pi$
$701$	15.9444			0.602214			0.301107	+	0.953590i	$0.402644\pi$
$702$		−	0.0948228i		−	0.00357885i
$703$		−	21.4367i		−	0.808502i
$704$	25.7324			0.969825
$705$	−2.87517	+	3.15869i	−0.108285	+	0.118963i
$706$	−27.5483			−1.03679
$707$			37.3046i			1.40298i
$708$		−	2.13474i		−	0.0802283i
$709$	−37.1049			−1.39351			−0.696753	−	0.717312i	$-0.745372\pi$
$709$	−37.1049			−1.39351			−0.696753	+	0.717312i	$0.745372\pi$
$710$	−15.5032	−	14.1116i	−0.581824	−	0.529601i
$711$	2.14014			0.0802617
$712$		−	33.1753i		−	1.24330i
$713$		−	20.9492i		−	0.784552i
$714$	−2.46521			−0.0922583
$715$	−0.340338	−	0.309790i	−0.0127279	−	0.0115855i
$716$	13.9420			0.521037
$717$		−	1.04765i		−	0.0391254i
$718$		−	6.62773i		−	0.247345i
$719$	−5.70240			−0.212664			−0.106332	−	0.994331i	$-0.533911\pi$
$719$	−5.70240			−0.212664			−0.106332	+	0.994331i	$0.533911\pi$
$720$	7.80394	−	8.57348i	0.290836	−	0.319515i
$721$	24.4392			0.910163
$722$		−	46.2326i		−	1.72060i
$723$			0.223927i			0.00832793i
$724$	5.36306			0.199317
$725$	−3.06348	−	32.5266i	−0.113775	−	1.20801i
$726$	−0.237890			−0.00882891
$727$			5.81600i			0.215703i	0.994167	+	0.107852i	$0.0343972\pi$
$727$			5.81600i			0.215703i	−0.994167	+	0.107852i	$0.965603\pi$
$728$			0.451201i			0.0167226i
$729$	24.3299			0.901106
$730$	27.4187	−	30.1225i	1.01481	−	1.11488i
$731$	−47.7075			−1.76453
$732$			1.41422i			0.0522712i
$733$			43.9492i			1.62330i	0.584143	+	0.811651i	$0.301431\pi$
$733$			43.9492i			1.62330i	−0.584143	+	0.811651i	$0.698569\pi$
$734$	−34.2840			−1.26545
$735$	−0.694615	−	0.632268i	−0.0256213	−	0.0233215i
$736$	−10.6572			−0.392828
$737$		−	42.3168i		−	1.55876i
$738$			24.2963i			0.894359i
$739$	22.5626			0.829979			0.414989	−	0.909826i	$-0.363785\pi$
$739$	22.5626			0.829979			0.414989	+	0.909826i	$0.363785\pi$
$740$	−3.62751	−	3.30191i	−0.133350	−	0.121381i
$741$	−0.113859			−0.00418272
$742$		−	0.162353i		−	0.00596015i
$743$			7.18672i			0.263655i	0.991273	+	0.131828i	$0.0420845\pi$
$743$			7.18672i			0.263655i	−0.991273	+	0.131828i	$0.957915\pi$
$744$	5.68309			0.208352
$745$	13.9855	−	15.3646i	0.512390	−	0.562916i
$746$	19.1715			0.701919
$747$		−	19.3866i		−	0.709320i
$748$			11.2607i			0.411733i
$749$	−3.78855			−0.138431
$750$	2.19171	+	1.64734i	0.0800301	+	0.0601523i
$751$	30.0828			1.09774			0.548868	−	0.835909i	$-0.315059\pi$
$751$	30.0828			1.09774			0.548868	+	0.835909i	$0.315059\pi$
$752$			14.9931i			0.546742i
$753$		−	1.44381i		−	0.0526154i
$754$	−0.465036			−0.0169356
$755$	6.68959	−	7.34924i	0.243459	−	0.267466i
$756$	2.41475			0.0878235
$757$			6.52000i			0.236973i	0.992956	+	0.118487i	$0.0378043\pi$
$757$			6.52000i			0.236973i	−0.992956	+	0.118487i	$0.962196\pi$
$758$			0.624185i			0.0226714i
$759$	−1.79546			−0.0651711
$760$	−39.6823	−	36.1205i	−1.43943	−	1.31023i
$761$	14.1010			0.511162			0.255581	−	0.966788i	$-0.417733\pi$
$761$	14.1010			0.511162			0.255581	+	0.966788i	$0.417733\pi$
$762$		−	1.48637i		−	0.0538456i
$763$		−	38.3902i		−	1.38982i
$764$	14.5885			0.527793
$765$	21.6621	+	19.7178i	0.783197	+	0.712898i
$766$	26.3122			0.950699
$767$			0.773780i			0.0279396i
$768$		−	3.52132i		−	0.127065i
$769$	−18.1800			−0.655589			−0.327795	−	0.944749i	$-0.606305\pi$
$769$	−18.1800			−0.655589			−0.327795	+	0.944749i	$0.606305\pi$
$770$	−11.8173	+	12.9826i	−0.425867	+	0.467861i
$771$	−3.36169			−0.121068
$772$		−	4.70950i		−	0.169499i
$773$			43.7032i			1.57190i	0.618293	+	0.785948i	$0.287825\pi$
$773$			43.7032i			1.57190i	−0.618293	+	0.785948i	$0.712175\pi$
$774$	−34.7049			−1.24744
$775$	−3.87949	−	41.1907i	−0.139356	−	1.47961i
$776$	29.5868			1.06210
$777$			1.38881i			0.0498232i
$778$		−	14.8742i		−	0.533266i
$779$	58.8439			2.10830
$780$	−0.0175378	+	0.0192672i	−0.000627953	+	0.000689875i
$781$	27.1123			0.970155
$782$			12.3129i			0.440307i
$783$			8.70561i			0.311113i
$784$	−3.29708			−0.117753
$785$	−0.430739	−	0.392076i	−0.0153737	−	0.0139938i
$786$	−1.60407			−0.0572153
$787$		−	20.3278i		−	0.724608i	−0.932060	−	0.362304i	$-0.881990\pi$
$787$		−	20.3278i		−	0.724608i	0.932060	−	0.362304i	$-0.118010\pi$
$788$		−	14.7321i		−	0.524808i
$789$	−2.49826			−0.0889405
$790$	1.31385	+	1.19592i	0.0467447	+	0.0425489i
$791$	−19.5794			−0.696164
$792$			28.6538i			1.01817i
$793$		−	0.512615i		−	0.0182035i
$794$	−10.4359			−0.370358
$795$	0.0220737	−	0.0242504i	0.000782873	−	0.000860072i
$796$	−9.50343			−0.336840
$797$			8.91772i			0.315882i	0.987449	+	0.157941i	$0.0504856\pi$
$797$			8.91772i			0.315882i	−0.987449	+	0.157941i	$0.949514\pi$
$798$			4.34329i			0.153751i
$799$	−37.8822			−1.34018
$800$	−20.9543	+	1.97356i	−0.740847	+	0.0697758i
$801$	31.9069			1.12737
$802$		−	10.9362i		−	0.386170i
$803$			52.6789i			1.85900i
$804$	−2.39563			−0.0844872
$805$	8.62620	−	9.47682i	0.304034	−	0.334014i
$806$	−0.588906			−0.0207433
$807$			3.02470i			0.106475i
$808$			50.5457i			1.77819i
$809$	23.4279			0.823680			0.411840	−	0.911256i	$-0.364886\pi$
$809$	23.4279			0.823680			0.411840	+	0.911256i	$0.364886\pi$
$810$	15.4857	+	14.0958i	0.544113	+	0.495275i
$811$	17.8208			0.625774			0.312887	−	0.949790i	$-0.398704\pi$
$811$	17.8208			0.625774			0.312887	+	0.949790i	$0.398704\pi$
$812$		−	11.8426i		−	0.415592i
$813$			2.93314i			0.102870i
$814$	−9.50267			−0.333069
$815$	−8.96282	−	8.15833i	−0.313954	−	0.285774i
$816$	−1.74782			−0.0611861
$817$			84.0527i			2.94063i
$818$		−	2.03360i		−	0.0711033i
$819$	−0.433950			−0.0151634
$820$	9.06374	−	9.95751i	0.316520	−	0.347731i
$821$	33.2196			1.15937			0.579686	−	0.814840i	$-0.303175\pi$
$821$	33.2196			1.15937			0.579686	+	0.814840i	$0.303175\pi$
$822$			1.99733i			0.0696647i
$823$			13.2155i			0.460663i	0.973112	+	0.230331i	$0.0739810\pi$
$823$			13.2155i			0.460663i	−0.973112	+	0.230331i	$0.926019\pi$
$824$	33.1138			1.15357
$825$	−3.53027	+	0.332494i	−0.122908	+	0.0115760i
$826$	29.5168			1.02702
$827$		−	47.8885i		−	1.66525i	−0.553840	−	0.832623i	$-0.686838\pi$
$827$		−	47.8885i		−	1.66525i	0.553840	−	0.832623i	$-0.313162\pi$
$828$		−	5.97958i		−	0.207805i
$829$	−50.0186			−1.73722			−0.868609	−	0.495498i	$-0.834985\pi$
$829$	−50.0186			−1.73722			−0.868609	+	0.495498i	$0.834985\pi$
$830$	10.8333	−	11.9016i	0.376030	−	0.413111i
$831$	3.23544			0.112236
$832$			0.528031i			0.0183062i
$833$		−	8.33054i		−	0.288636i
$834$	1.56666			0.0542491
$835$	−36.4331	−	33.1629i	−1.26082	−	1.14765i
$836$	19.8395			0.686164
$837$			11.0245i			0.381063i
$838$		−	10.4430i		−	0.360747i
$839$	23.0264			0.794958			0.397479	−	0.917611i	$-0.369885\pi$
$839$	23.0264			0.794958			0.397479	+	0.917611i	$0.369885\pi$
$840$	2.57087	+	2.34011i	0.0887034	+	0.0807416i
$841$	13.6946			0.472227
$842$			23.1975i			0.799438i
$843$			0.397845i			0.0137025i
$844$	13.8816			0.477826
$845$	−19.5610	+	21.4899i	−0.672920	+	0.739276i
$846$	−27.5575			−0.947446
$847$			2.19588i			0.0754512i
$848$		−	0.115107i		−	0.00395280i
$849$	−4.13166			−0.141798
$850$	2.28017	+	24.2098i	0.0782092	+	0.830389i
$851$	6.93659			0.237783
$852$		−	1.53488i		−	0.0525840i
$853$		−	39.2071i		−	1.34243i	−0.741265	−	0.671213i	$-0.765774\pi$
$853$		−	39.2071i		−	1.34243i	0.741265	−	0.671213i	$-0.234226\pi$
$854$	−19.5543			−0.669135
$855$	34.7395	−	38.1651i	1.18806	−	1.30522i
$856$	−5.13328			−0.175452
$857$			36.7331i			1.25478i	0.778706	+	0.627389i	$0.215876\pi$
$857$			36.7331i			1.25478i	−0.778706	+	0.627389i	$0.784124\pi$
$858$			0.0504725i			0.00172310i
$859$	47.6475			1.62571			0.812856	−	0.582465i	$-0.197912\pi$
$859$	47.6475			1.62571			0.812856	+	0.582465i	$0.197912\pi$
$860$	14.2233	+	12.9467i	0.485011	+	0.441478i
$861$	−3.81228			−0.129922
$862$			39.1139i			1.33223i
$863$		−	35.6174i		−	1.21243i	−0.795301	−	0.606215i	$-0.792687\pi$
$863$		−	35.6174i		−	1.21243i	0.795301	−	0.606215i	$-0.207313\pi$
$864$	5.60834			0.190800
$865$	−29.9243	−	27.2384i	−1.01746	−	0.926133i
$866$	12.9579			0.440328
$867$		−	0.609373i		−	0.0206954i
$868$		−	14.9970i		−	0.509033i
$869$	−2.29769			−0.0779438
$870$	−2.41186	+	2.64970i	−0.0817699	+	0.0898331i
$871$	0.868345			0.0294228
$872$		−	52.0166i		−	1.76150i
$873$			28.4556i			0.963075i
$874$	21.6932			0.733784
$875$	15.2060	−	20.2310i	0.514057	−	0.683931i
$876$	2.98224			0.100761
$877$		−	39.1576i		−	1.32226i	−0.750272	−	0.661129i	$-0.770078\pi$
$877$		−	39.1576i		−	1.32226i	0.750272	−	0.661129i	$-0.229922\pi$
$878$			2.31912i			0.0782664i
$879$	1.93785			0.0653621
$880$	−8.37842	+	9.20461i	−0.282437	+	0.310288i
$881$	−30.9027			−1.04114			−0.520569	−	0.853820i	$-0.674280\pi$
$881$	−30.9027			−1.04114			−0.520569	+	0.853820i	$0.674280\pi$
$882$		−	6.06006i		−	0.204053i
$883$		−	9.36408i		−	0.315126i	−0.987509	−	0.157563i	$-0.949636\pi$
$883$		−	9.36408i		−	0.315126i	0.987509	−	0.157563i	$-0.0503638\pi$
$884$	−0.231071			−0.00777177
$885$	4.40887	+	4.01314i	0.148203	+	0.134900i
$886$	29.3581			0.986304
$887$		−	48.6485i		−	1.63346i	−0.577023	−	0.816728i	$-0.695786\pi$
$887$		−	48.6485i		−	1.63346i	0.577023	−	0.816728i	$-0.304214\pi$
$888$			1.88176i			0.0631477i
$889$	−13.7202			−0.460161
$890$	19.5878	+	17.8297i	0.656586	+	0.597652i
$891$	−27.0818			−0.907274
$892$		−	0.548991i		−	0.0183816i
$893$			66.7422i			2.23344i
$894$	−2.27859			−0.0762074
$895$	−26.2099	+	28.7944i	−0.876099	+	0.962491i
$896$	1.08510			0.0362508
$897$		−	0.0368431i		−	0.00123015i
$898$		−	39.0207i		−	1.30214i
$899$	54.0671			1.80324
$900$	−1.10733	−	11.7572i	−0.0369112	−	0.391906i
$901$	0.290835			0.00968913
$902$		−	26.0849i		−	0.868531i
$903$		−	5.44546i		−	0.181214i
$904$	−26.5290			−0.882343
$905$	−10.0821	+	11.0763i	−0.335142	+	0.368190i
$906$	−1.08990			−0.0362095
$907$		−	42.3130i		−	1.40498i	−0.711694	−	0.702489i	$-0.752072\pi$
$907$		−	42.3130i		−	1.40498i	0.711694	−	0.702489i	$-0.247928\pi$
$908$			18.9785i			0.629822i
$909$	−48.6131			−1.61240
$910$	−0.266405	−	0.242493i	−0.00883124	−	0.00803856i
$911$	2.03059			0.0672763			0.0336382	−	0.999434i	$-0.489291\pi$
$911$	2.03059			0.0672763			0.0336382	+	0.999434i	$0.489291\pi$
$912$			3.07938i			0.101968i
$913$			20.8138i			0.688836i
$914$	4.78931			0.158416
$915$	−2.92080	−	2.65863i	−0.0965586	−	0.0878917i
$916$	14.5456			0.480601
$917$			14.8066i			0.488958i
$918$		−	6.47965i		−	0.213860i
$919$	24.5581			0.810097			0.405048	−	0.914295i	$-0.367255\pi$
$919$	24.5581			0.810097			0.405048	+	0.914295i	$0.367255\pi$
$920$	11.6880	−	12.8406i	0.385343	−	0.423341i
$921$	−1.48048			−0.0487833
$922$		−	2.55021i		−	0.0839866i
$923$			0.556348i			0.0183124i
$924$	−1.28533			−0.0422842
$925$	13.6389	−	1.28456i	0.448443	−	0.0422361i
$926$	−26.6868			−0.876983
$927$			31.8477i			1.04602i
$928$		−	27.5048i		−	0.902888i
$929$	−6.26058			−0.205403			−0.102702	−	0.994712i	$-0.532749\pi$
$929$	−6.26058			−0.205403			−0.102702	+	0.994712i	$0.532749\pi$
$930$	−3.05431	+	3.35549i	−0.100155	+	0.110031i
$931$	−14.6770			−0.481020
$932$		−	1.36018i		−	0.0445541i
$933$		−	4.34881i		−	0.142374i
$934$	−46.0559			−1.50700
$935$	−23.2568	−	21.1693i	−0.760578	−	0.692310i
$936$	−0.587979			−0.0192187
$937$		−	21.1381i		−	0.690552i	−0.938501	−	0.345276i	$-0.887785\pi$
$937$		−	21.1381i		−	0.690552i	0.938501	−	0.345276i	$-0.112215\pi$
$938$		−	33.1241i		−	1.08154i
$939$	−4.35577			−0.142145
$940$	11.2941	+	10.2803i	0.368372	+	0.335307i
$941$	−3.32725			−0.108465			−0.0542327	−	0.998528i	$-0.517271\pi$
$941$	−3.32725			−0.108465			−0.0542327	+	0.998528i	$0.517271\pi$
$942$			0.0638790i			0.00208129i
$943$			19.0410i			0.620059i
$944$	20.9272			0.681124
$945$	−4.53954	+	4.98718i	−0.147671	+	0.162233i
$946$	37.2597			1.21142
$947$		−	3.04446i		−	0.0989318i	−0.998776	−	0.0494659i	$-0.984248\pi$
$947$		−	3.04446i		−	0.0989318i	0.998776	−	0.0494659i	$-0.0157519\pi$
$948$			0.130076i			0.00422468i
$949$	−1.08098			−0.0350900
$950$	42.6536	−	4.01728i	1.38387	−	0.130338i
$951$	0.177489			0.00575546
$952$			30.8325i			0.999287i
$953$		−	9.75807i		−	0.316095i	−0.987432	−	0.158047i	$-0.949480\pi$
$953$		−	9.75807i		−	0.316095i	0.987432	−	0.158047i	$-0.0505199\pi$
$954$	0.211568			0.00684978
$955$	−27.4253	+	30.1296i	−0.887460	+	0.974972i
$956$	−3.74594			−0.121152
$957$		−	4.63385i		−	0.149791i
$958$		−	33.2010i		−	1.07267i
$959$	18.4366			0.595350
$960$	3.00864	+	2.73859i	0.0971033	+	0.0883875i
$961$	37.4688			1.20867
$962$		−	0.194996i		−	0.00628692i
$963$		−	4.93702i		−	0.159093i
$964$	0.800662			0.0257876
$965$	9.72654	+	8.85350i	0.313108	+	0.285004i
$966$	−1.40542			−0.0452187
$967$		−	8.16066i		−	0.262429i	−0.991354	−	0.131215i	$-0.958112\pi$
$967$		−	8.16066i		−	0.262429i	0.991354	−	0.131215i	$-0.0418877\pi$
$968$			2.97529i			0.0956296i
$969$	−7.78049			−0.249945
$970$	−15.9011	+	17.4691i	−0.510553	+	0.560898i
$971$	16.0914			0.516398			0.258199	−	0.966092i	$-0.416871\pi$
$971$	16.0914			0.516398			0.258199	+	0.966092i	$0.416871\pi$
$972$			4.73340i			0.151824i
$973$		−	14.4613i		−	0.463609i
$974$	−17.9733			−0.575902
$975$	−0.00682282	−	0.0724415i	−0.000218505	−	0.00231999i
$976$	−13.8639			−0.443774
$977$			23.1058i			0.739220i	0.929187	+	0.369610i	$0.120509\pi$
$977$			23.1058i			0.739220i	−0.929187	+	0.369610i	$0.879491\pi$
$978$			1.32920i			0.0425030i
$979$	−34.2557			−1.09482
$980$	−2.26071	+	2.48363i	−0.0722156	+	0.0793368i
$981$	50.0278			1.59727
$982$			0.614436i			0.0196074i
$983$		−	44.1346i		−	1.40768i	−0.710361	−	0.703838i	$-0.751468\pi$
$983$		−	44.1346i		−	1.40768i	0.710361	−	0.703838i	$-0.248532\pi$
$984$	−5.16543			−0.164668
$985$	30.4262	+	27.6952i	0.969458	+	0.882441i
$986$	−31.7779			−1.01201
$987$		−	4.32398i		−	0.137634i
$988$			0.407110i			0.0129519i
$989$	−27.1981			−0.864851
$990$	−16.9182	−	15.3996i	−0.537695	−	0.489432i
$991$	−5.42300			−0.172267			−0.0861337	−	0.996284i	$-0.527451\pi$
$991$	−5.42300			−0.172267			−0.0861337	+	0.996284i	$0.527451\pi$
$992$		−	34.8312i		−	1.10589i
$993$			3.29145i			0.104451i
$994$	21.2226			0.673139
$995$	17.8657	−	19.6275i	0.566382	−	0.622232i
$996$	1.17830			0.0373360
$997$		−	56.5705i		−	1.79161i	−0.444451	−	0.895803i	$-0.646601\pi$
$997$		−	56.5705i		−	1.79161i	0.444451	−	0.895803i	$-0.353399\pi$
$998$		−	42.8310i		−	1.35579i
$999$	−3.65039			−0.115493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.15	✓	46
5.2	odd	4		6025.2.a.p.1.32		46
5.3	odd	4		6025.2.a.p.1.15		46
5.4	even	2	inner	1205.2.b.c.724.32	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.15	✓	46	1.1	even	1	trivial
1205.2.b.c.724.32	yes	46	5.4	even	2	inner
6025.2.a.p.1.15		46	5.3	odd	4
6025.2.a.p.1.32		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)

\(f(q)\)	\(=\)	\(q-1.09514i q^{2} +0.223927i q^{3} +0.800662 q^{4} +(-1.50518 + 1.65361i) q^{5} +0.245232 q^{6} -2.26365i q^{7} -3.06713i q^{8} +2.94986 q^{9} +O(q^{10})\)	\(q-1.09514i q^{2} +0.223927i q^{3} +0.800662 q^{4} +(-1.50518 + 1.65361i) q^{5} +0.245232 q^{6} -2.26365i q^{7} -3.06713i q^{8} +2.94986 q^{9} +(1.81094 + 1.64839i) q^{10} -3.16701 q^{11} +0.179290i q^{12} -0.0649874i q^{13} -2.47902 q^{14} +(-0.370288 - 0.337051i) q^{15} -1.75761 q^{16} -4.44087i q^{17} -3.23051i q^{18} -7.82407 q^{19} +(-1.20514 + 1.32398i) q^{20} +0.506893 q^{21} +3.46833i q^{22} -2.53175i q^{23} +0.686812 q^{24} +(-0.468844 - 4.97797i) q^{25} -0.0711705 q^{26} +1.33233i q^{27} -1.81242i q^{28} +6.53411 q^{29} +(-0.369119 + 0.405518i) q^{30} +8.27459 q^{31} -4.20941i q^{32} -0.709178i q^{33} -4.86338 q^{34} +(3.74319 + 3.40721i) q^{35} +2.36184 q^{36} +2.73984i q^{37} +8.56847i q^{38} +0.0145524 q^{39} +(5.07183 + 4.61659i) q^{40} -7.52088 q^{41} -0.555120i q^{42} -10.7428i q^{43} -2.53570 q^{44} +(-4.44008 + 4.87791i) q^{45} -2.77262 q^{46} -8.53037i q^{47} -0.393577i q^{48} +1.87588 q^{49} +(-5.45159 + 0.513451i) q^{50} +0.994430 q^{51} -0.0520330i q^{52} +0.0654906i q^{53} +1.45909 q^{54} +(4.76693 - 5.23699i) q^{55} -6.94290 q^{56} -1.75202i q^{57} -7.15578i q^{58} -11.9066 q^{59} +(-0.296475 - 0.269864i) q^{60} +7.88792 q^{61} -9.06186i q^{62} -6.67745i q^{63} -8.12514 q^{64} +(0.107464 + 0.0978179i) q^{65} -0.776651 q^{66} +13.3617i q^{67} -3.55564i q^{68} +0.566926 q^{69} +(3.73138 - 4.09933i) q^{70} -8.56086 q^{71} -9.04758i q^{72} -16.6336i q^{73} +3.00052 q^{74} +(1.11470 - 0.104987i) q^{75} -6.26444 q^{76} +7.16900i q^{77} -0.0159370i q^{78} +0.725508 q^{79} +(2.64553 - 2.90641i) q^{80} +8.55123 q^{81} +8.23644i q^{82} -6.57206i q^{83} +0.405850 q^{84} +(7.34346 + 6.68432i) q^{85} -11.7649 q^{86} +1.46316i q^{87} +9.71361i q^{88} +10.8164 q^{89} +(5.34201 + 4.86252i) q^{90} -0.147109 q^{91} -2.02707i q^{92} +1.85290i q^{93} -9.34197 q^{94} +(11.7767 - 12.9380i) q^{95} +0.942600 q^{96} +9.64642i q^{97} -2.05436i q^{98} -9.34222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more