LMFDB - Embedded newform 185.2.c.b.36.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(36,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.36"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
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} + 21x^{10} + 162x^{8} + 574x^{6} + 985x^{4} + 765x^{2} + 196 $ x^12 + 21x^10 + 162x^8 + 574x^6 + 985x^4 + 765*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			36.4
Root			$-1.36551i$ of defining polynomial
Character	$\chi$	$=$	185.36
Dual form			185.2.c.b.36.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.36551i q^{2} +2.79310 q^{3} +0.135372 q^{4} +1.00000i q^{5} -3.81402i q^{6} -4.67865 q^{7} -2.91588i q^{8} +4.80143 q^{9} +1.36551 q^{10} -0.186084 q^{11} +0.378109 q^{12} +4.24161i q^{13} +6.38876i q^{14} +2.79310i q^{15} -3.71093 q^{16} +3.61534i q^{17} -6.55641i q^{18} -7.92848i q^{19} +0.135372i q^{20} -13.0679 q^{21} +0.254101i q^{22} +3.32146i q^{23} -8.14435i q^{24} -1.00000 q^{25} +5.79198 q^{26} +5.03157 q^{27} -0.633360 q^{28} +2.01664i q^{29} +3.81402 q^{30} -2.04293i q^{31} -0.764435i q^{32} -0.519752 q^{33} +4.93680 q^{34} -4.67865i q^{35} +0.649980 q^{36} +(-5.30231 + 2.98085i) q^{37} -10.8264 q^{38} +11.8473i q^{39} +2.91588 q^{40} +1.03061 q^{41} +17.8445i q^{42} -4.05248i q^{43} -0.0251907 q^{44} +4.80143i q^{45} +4.53549 q^{46} -2.78341 q^{47} -10.3650 q^{48} +14.8897 q^{49} +1.36551i q^{50} +10.0980i q^{51} +0.574197i q^{52} +7.67087 q^{53} -6.87067i q^{54} -0.186084i q^{55} +13.6424i q^{56} -22.1451i q^{57} +2.75376 q^{58} +9.12948i q^{59} +0.378109i q^{60} -12.5713i q^{61} -2.78965 q^{62} -22.4642 q^{63} -8.46571 q^{64} -4.24161 q^{65} +0.709729i q^{66} +7.35469 q^{67} +0.489417i q^{68} +9.27717i q^{69} -6.38876 q^{70} +15.2343 q^{71} -14.0004i q^{72} -0.622606 q^{73} +(4.07040 + 7.24038i) q^{74} -2.79310 q^{75} -1.07330i q^{76} +0.870623 q^{77} +16.1776 q^{78} -0.662906i q^{79} -3.71093i q^{80} -0.350591 q^{81} -1.40732i q^{82} -9.75304 q^{83} -1.76904 q^{84} -3.61534 q^{85} -5.53372 q^{86} +5.63270i q^{87} +0.542599i q^{88} -6.06313i q^{89} +6.55641 q^{90} -19.8450i q^{91} +0.449633i q^{92} -5.70612i q^{93} +3.80078i q^{94} +7.92848 q^{95} -2.13515i q^{96} -10.2018i q^{97} -20.3322i q^{98} -0.893470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 18 q^{4} - 18 q^{7} + 22 q^{9} - 2 q^{10} + 2 q^{11} - 36 q^{12} + 30 q^{16} - 6 q^{21} - 12 q^{25} - 12 q^{26} + 26 q^{27} + 24 q^{28} - 12 q^{30} - 18 q^{33} + 4 q^{34} - 22 q^{36} + 10 q^{37}+ \cdots - 84 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 - 18 * q^4 - 18 * q^7 + 22 * q^9 - 2 * q^10 + 2 * q^11 - 36 * q^12 + 30 * q^16 - 6 * q^21 - 12 * q^25 - 12 * q^26 + 26 * q^27 + 24 * q^28 - 12 * q^30 - 18 * q^33 + 4 * q^34 - 22 * q^36 + 10 * q^37 + 12 * q^38 + 6 * q^40 - 10 * q^41 + 44 * q^44 - 24 * q^46 + 2 * q^47 + 60 * q^48 + 30 * q^49 - 6 * q^53 - 24 * q^58 + 44 * q^62 - 16 * q^63 - 126 * q^64 + 20 * q^65 + 16 * q^67 - 28 * q^70 + 42 * q^71 - 46 * q^73 + 50 * q^74 - 2 * q^75 + 30 * q^77 + 132 * q^78 - 12 * q^81 - 62 * q^83 - 84 * q^84 - 12 * q^85 - 64 * q^86 - 26 * q^90 + 44 * q^95 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.36551i		−	0.965564i	−0.875741	−	0.482782i	$-0.839626\pi$
$2$		−	1.36551i		−	0.965564i	0.875741	−	0.482782i	$-0.160374\pi$
$3$	2.79310			1.61260			0.806299	−	0.591508i	$-0.201467\pi$
$3$	2.79310			1.61260			0.806299	+	0.591508i	$0.201467\pi$
$4$	0.135372			0.0676862
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		−	3.81402i		−	1.55707i
$7$	−4.67865			−1.76836			−0.884181	−	0.467144i	$-0.845283\pi$
$7$	−4.67865			−1.76836			−0.884181	+	0.467144i	$0.845283\pi$
$8$		−	2.91588i		−	1.03092i
$9$	4.80143			1.60048
$10$	1.36551			0.431813
$11$	−0.186084			−0.0561065			−0.0280533	−	0.999606i	$-0.508931\pi$
$11$	−0.186084			−0.0561065			−0.0280533	+	0.999606i	$0.508931\pi$
$12$	0.378109			0.109151
$13$			4.24161i			1.17641i	0.808712	+	0.588205i	$0.200165\pi$
$13$			4.24161i			1.17641i	−0.808712	+	0.588205i	$0.799835\pi$
$14$			6.38876i			1.70747i
$15$			2.79310i			0.721176i
$16$	−3.71093			−0.927732
$17$			3.61534i			0.876849i	0.898768	+	0.438424i	$0.144463\pi$
$17$			3.61534i			0.876849i	−0.898768	+	0.438424i	$0.855537\pi$
$18$		−	6.55641i		−	1.54536i
$19$		−	7.92848i		−	1.81892i	−0.415795	−	0.909459i	$-0.636497\pi$
$19$		−	7.92848i		−	1.81892i	0.415795	−	0.909459i	$-0.363503\pi$
$20$			0.135372i			0.0302702i
$21$	−13.0679			−2.85166
$22$			0.254101i			0.0541744i
$23$			3.32146i			0.692572i	0.938129	+	0.346286i	$0.112557\pi$
$23$			3.32146i			0.692572i	−0.938129	+	0.346286i	$0.887443\pi$
$24$		−	8.14435i		−	1.66246i
$25$	−1.00000			−0.200000
$26$	5.79198			1.13590
$27$	5.03157			0.968325
$28$	−0.633360			−0.119694
$29$			2.01664i			0.374481i	0.982314	+	0.187241i	$0.0599544\pi$
$29$			2.01664i			0.374481i	−0.982314	+	0.187241i	$0.940046\pi$
$30$	3.81402			0.696342
$31$		−	2.04293i		−	0.366921i	−0.983027	−	0.183461i	$-0.941270\pi$
$31$		−	2.04293i		−	0.366921i	0.983027	−	0.183461i	$-0.0587300\pi$
$32$		−	0.764435i		−	0.135134i
$33$	−0.519752			−0.0904773
$34$	4.93680			0.846654
$35$		−	4.67865i		−	0.790836i
$36$	0.649980			0.108330
$37$	−5.30231	+	2.98085i	−0.871695	+	0.490049i
$37$	−5.30231	+	2.98085i	−0.871695	+	0.490049i
$38$	−10.8264			−1.75628
$39$			11.8473i			1.89708i
$40$	2.91588			0.461041
$41$	1.03061			0.160955			0.0804774	−	0.996756i	$-0.474356\pi$
$41$	1.03061			0.160955			0.0804774	+	0.996756i	$0.474356\pi$
$42$			17.8445i			2.75346i
$43$		−	4.05248i		−	0.617998i	−0.951062	−	0.308999i	$-0.900006\pi$
$43$		−	4.05248i		−	0.617998i	0.951062	−	0.308999i	$-0.0999940\pi$
$44$	−0.0251907			−0.00379764
$45$			4.80143i			0.715754i
$46$	4.53549			0.668722
$47$	−2.78341			−0.406002			−0.203001	−	0.979179i	$-0.565069\pi$
$47$	−2.78341			−0.406002			−0.203001	+	0.979179i	$0.565069\pi$
$48$	−10.3650			−1.49606
$49$	14.8897			2.12711
$50$			1.36551i			0.193113i
$51$			10.0980i			1.41401i
$52$			0.574197i			0.0796268i
$53$	7.67087			1.05367			0.526837	−	0.849966i	$-0.323378\pi$
$53$	7.67087			1.05367			0.526837	+	0.849966i	$0.323378\pi$
$54$		−	6.87067i		−	0.934980i
$55$		−	0.186084i		−	0.0250916i
$56$			13.6424i			1.82304i
$57$		−	22.1451i		−	2.93318i
$58$	2.75376			0.361586
$59$			9.12948i			1.18856i	0.804259	+	0.594279i	$0.202562\pi$
$59$			9.12948i			1.18856i	−0.804259	+	0.594279i	$0.797438\pi$
$60$			0.378109i			0.0488137i
$61$		−	12.5713i		−	1.60959i	−0.593550	−	0.804797i	$-0.702274\pi$
$61$		−	12.5713i		−	1.60959i	0.593550	−	0.804797i	$-0.297726\pi$
$62$	−2.78965			−0.354286
$63$	−22.4642			−2.83022
$64$	−8.46571			−1.05821
$65$	−4.24161			−0.526107
$66$			0.709729i			0.0873616i
$67$	7.35469			0.898518			0.449259	−	0.893401i	$-0.351688\pi$
$67$	7.35469			0.898518			0.449259	+	0.893401i	$0.351688\pi$
$68$			0.489417i			0.0593506i
$69$			9.27717i			1.11684i
$70$	−6.38876			−0.763603
$71$	15.2343			1.80798			0.903992	−	0.427549i	$-0.140623\pi$
$71$	15.2343			1.80798			0.903992	+	0.427549i	$0.140623\pi$
$72$		−	14.0004i		−	1.64996i
$73$	−0.622606			−0.0728705			−0.0364352	−	0.999336i	$-0.511600\pi$
$73$	−0.622606			−0.0728705			−0.0364352	+	0.999336i	$0.511600\pi$
$74$	4.07040	+	7.24038i	0.473174	+	0.841677i
$75$	−2.79310			−0.322520
$76$		−	1.07330i		−	0.123116i
$77$	0.870623			0.0992167
$78$	16.1776			1.83175
$79$		−	0.662906i		−	0.0745828i	−0.999304	−	0.0372914i	$-0.988127\pi$
$79$		−	0.662906i		−	0.0745828i	0.999304	−	0.0372914i	$-0.0118730\pi$
$80$		−	3.71093i		−	0.414895i
$81$	−0.350591			−0.0389546
$82$		−	1.40732i		−	0.155412i
$83$	−9.75304			−1.07054			−0.535268	−	0.844683i	$-0.679789\pi$
$83$	−9.75304			−1.07054			−0.535268	+	0.844683i	$0.679789\pi$
$84$	−1.76904			−0.193018
$85$	−3.61534			−0.392139
$86$	−5.53372			−0.596717
$87$			5.63270i			0.603888i
$88$			0.542599i			0.0578413i
$89$		−	6.06313i		−	0.642691i	−0.946962	−	0.321345i	$-0.895865\pi$
$89$		−	6.06313i		−	0.642691i	0.946962	−	0.321345i	$-0.104135\pi$
$90$	6.55641			0.691106
$91$		−	19.8450i		−	2.08032i
$92$			0.449633i			0.0468775i
$93$		−	5.70612i		−	0.591697i
$94$			3.80078i			0.392020i
$95$	7.92848			0.813444
$96$		−	2.13515i		−	0.217917i
$97$		−	10.2018i		−	1.03584i	−0.855430	−	0.517919i	$-0.826707\pi$
$97$		−	10.2018i		−	1.03584i	0.855430	−	0.517919i	$-0.173293\pi$
$98$		−	20.3322i		−	2.05386i
$99$	−0.893470			−0.0897971
$100$	−0.135372			−0.0135372
$101$	5.22165			0.519573			0.259787	−	0.965666i	$-0.416348\pi$
$101$	5.22165			0.519573			0.259787	+	0.965666i	$0.416348\pi$
$102$	13.7890			1.36531
$103$		−	13.4563i		−	1.32589i	−0.748670	−	0.662943i	$-0.769307\pi$
$103$		−	13.4563i		−	1.32589i	0.748670	−	0.662943i	$-0.230693\pi$
$104$	12.3680			1.21278
$105$		−	13.0679i		−	1.27530i
$106$		−	10.4747i		−	1.01739i
$107$	3.61849			0.349812			0.174906	−	0.984585i	$-0.444038\pi$
$107$	3.61849			0.349812			0.174906	+	0.984585i	$0.444038\pi$
$108$	0.681135			0.0655423
$109$			15.9453i			1.52728i	0.645642	+	0.763640i	$0.276590\pi$
$109$			15.9453i			1.52728i	−0.645642	+	0.763640i	$0.723410\pi$
$110$	−0.254101			−0.0242275
$111$	−14.8099	+	8.32583i	−1.40569	+	0.790253i
$112$	17.3621			1.64057
$113$			7.28167i			0.685002i	0.939517	+	0.342501i	$0.111274\pi$
$113$			7.28167i			0.685002i	−0.939517	+	0.342501i	$0.888726\pi$
$114$	−30.2394			−2.83218
$115$	−3.32146			−0.309727
$116$			0.272998i			0.0253472i
$117$			20.3658i			1.88282i
$118$	12.4664			1.14763
$119$		−	16.9149i		−	1.55059i
$120$	8.14435			0.743474
$121$	−10.9654			−0.996852
$122$	−17.1663			−1.55417
$123$	2.87861			0.259556
$124$		−	0.276556i		−	0.0248355i
$125$		−	1.00000i		−	0.0894427i
$126$			30.6751i			2.73276i
$127$	−12.3627			−1.09701			−0.548505	−	0.836148i	$-0.684803\pi$
$127$	−12.3627			−1.09701			−0.548505	+	0.836148i	$0.684803\pi$
$128$			10.0312i			0.886638i
$129$		−	11.3190i		−	0.996583i
$130$			5.79198i			0.507990i
$131$			7.80186i			0.681652i	0.940126	+	0.340826i	$0.110707\pi$
$131$			7.80186i			0.681652i	−0.940126	+	0.340826i	$0.889293\pi$
$132$	−0.0703601			−0.00612406
$133$			37.0945i			3.21651i
$134$		−	10.0429i		−	0.867577i
$135$			5.03157i			0.433048i
$136$	10.5419			0.903961
$137$	1.28562			0.109838			0.0549188	−	0.998491i	$-0.482510\pi$
$137$	1.28562			0.109838			0.0549188	+	0.998491i	$0.482510\pi$
$138$	12.6681			1.07838
$139$	3.93652			0.333891			0.166946	−	0.985966i	$-0.446610\pi$
$139$	3.93652			0.333891			0.166946	+	0.985966i	$0.446610\pi$
$140$		−	0.633360i		−	0.0535287i
$141$	−7.77434			−0.654718
$142$		−	20.8027i		−	1.74572i
$143$		−	0.789297i		−	0.0660043i
$144$	−17.8178			−1.48481
$145$	−2.01664			−0.167473
$146$			0.850177i			0.0703611i
$147$	41.5886			3.43017
$148$	−0.717786	+	0.403525i	−0.0590017	+	0.0331696i
$149$	−15.5509			−1.27398			−0.636988	−	0.770873i	$-0.719820\pi$
$149$	−15.5509			−1.27398			−0.636988	+	0.770873i	$0.719820\pi$
$150$			3.81402i			0.311413i
$151$	15.0928			1.22824			0.614119	−	0.789213i	$-0.289511\pi$
$151$	15.0928			1.22824			0.614119	+	0.789213i	$0.289511\pi$
$152$	−23.1185			−1.87516
$153$			17.3588i			1.40337i
$154$		−	1.18885i		−	0.0958000i
$155$	2.04293			0.164092
$156$			1.60379i			0.128406i
$157$	−6.89821			−0.550537			−0.275269	−	0.961367i	$-0.588767\pi$
$157$	−6.89821			−0.550537			−0.275269	+	0.961367i	$0.588767\pi$
$158$	−0.905208			−0.0720144
$159$	21.4255			1.69915
$160$	0.764435			0.0604339
$161$		−	15.5399i		−	1.22472i
$162$			0.478737i			0.0376131i
$163$			4.42444i			0.346549i	0.984874	+	0.173275i	$0.0554348\pi$
$163$			4.42444i			0.346549i	−0.984874	+	0.173275i	$0.944565\pi$
$164$	0.139517			0.0108944
$165$		−	0.519752i		−	0.0404627i
$166$			13.3179i			1.03367i
$167$		−	16.1383i		−	1.24882i	−0.781096	−	0.624411i	$-0.785339\pi$
$167$		−	16.1383i		−	1.24882i	0.781096	−	0.624411i	$-0.214661\pi$
$168$			38.1046i			2.93983i
$169$	−4.99126			−0.383943
$170$			4.93680i			0.378635i
$171$		−	38.0680i		−	2.91113i
$172$		−	0.548594i		−	0.0418299i
$173$	23.7342			1.80448			0.902239	−	0.431236i	$-0.141922\pi$
$173$	23.7342			1.80448			0.902239	+	0.431236i	$0.141922\pi$
$174$	7.69152			0.583093
$175$	4.67865			0.353673
$176$	0.690545			0.0520518
$177$			25.4996i			1.91667i
$178$	−8.27929			−0.620559
$179$		−	7.66128i		−	0.572631i	−0.958135	−	0.286315i	$-0.907570\pi$
$179$		−	7.66128i		−	0.572631i	0.958135	−	0.286315i	$-0.0924305\pi$
$180$			0.649980i			0.0484467i
$181$	−13.9590			−1.03756			−0.518781	−	0.854907i	$-0.673614\pi$
$181$	−13.9590			−1.03756			−0.518781	+	0.854907i	$0.673614\pi$
$182$	−27.0986			−2.00868
$183$		−	35.1130i		−	2.59563i
$184$	9.68497			0.713985
$185$	−2.98085	−	5.30231i	−0.219157	−	0.389834i
$186$	−7.79178			−0.571321
$187$		−	0.672758i		−	0.0491969i
$188$	−0.376796			−0.0274807
$189$	−23.5409			−1.71235
$190$		−	10.8264i		−	0.785433i
$191$			20.7490i			1.50134i	0.660675	+	0.750672i	$0.270270\pi$
$191$			20.7490i			1.50134i	−0.660675	+	0.750672i	$0.729730\pi$
$192$	−23.6456			−1.70647
$193$			9.18440i			0.661108i	0.943787	+	0.330554i	$0.107236\pi$
$193$			9.18440i			0.661108i	−0.943787	+	0.330554i	$0.892764\pi$
$194$	−13.9307			−1.00017
$195$	−11.8473			−0.848400
$196$	2.01566			0.143976
$197$	−8.62507			−0.614511			−0.307255	−	0.951627i	$-0.599411\pi$
$197$	−8.62507			−0.614511			−0.307255	+	0.951627i	$0.599411\pi$
$198$			1.22004i			0.0867048i
$199$			1.09459i			0.0775938i	0.999247	+	0.0387969i	$0.0123525\pi$
$199$			1.09459i			0.0775938i	−0.999247	+	0.0387969i	$0.987647\pi$
$200$			2.91588i			0.206184i
$201$	20.5424			1.44895
$202$		−	7.13023i		−	0.501681i
$203$		−	9.43517i		−	0.662219i
$204$			1.36699i			0.0957087i
$205$			1.03061i			0.0719812i
$206$	−18.3747			−1.28023
$207$			15.9477i			1.10844i
$208$		−	15.7403i		−	1.09139i
$209$			1.47536i			0.102053i
$210$	−17.8445			−1.23138
$211$	6.92566			0.476782			0.238391	−	0.971169i	$-0.423380\pi$
$211$	6.92566			0.476782			0.238391	+	0.971169i	$0.423380\pi$
$212$	1.03842			0.0713192
$213$	42.5511			2.91555
$214$		−	4.94109i		−	0.337766i
$215$	4.05248			0.276377
$216$		−	14.6714i		−	0.998265i
$217$			9.55815i			0.648850i
$218$	21.7735			1.47469
$219$	−1.73900			−0.117511
$220$		−	0.0251907i		−	0.00169835i
$221$	−15.3349			−1.03153
$222$	11.3690	+	20.2231i	0.763040	+	1.35729i
$223$	5.75304			0.385252			0.192626	−	0.981272i	$-0.438300\pi$
$223$	5.75304			0.385252			0.192626	+	0.981272i	$0.438300\pi$
$224$			3.57652i			0.238967i
$225$	−4.80143			−0.320095
$226$	9.94322			0.661413
$227$		−	7.56947i		−	0.502404i	−0.967935	−	0.251202i	$-0.919174\pi$
$227$		−	7.56947i		−	0.502404i	0.967935	−	0.251202i	$-0.0808258\pi$
$228$		−	2.99783i		−	0.198536i
$229$	−19.8975			−1.31487			−0.657433	−	0.753513i	$-0.728358\pi$
$229$	−19.8975			−1.31487			−0.657433	+	0.753513i	$0.728358\pi$
$230$			4.53549i			0.299062i
$231$	2.43174			0.159997
$232$	5.88029			0.386060
$233$	17.7494			1.16280			0.581402	−	0.813616i	$-0.302504\pi$
$233$	17.7494			1.16280			0.581402	+	0.813616i	$0.302504\pi$
$234$	27.8097			1.81798
$235$		−	2.78341i		−	0.181569i
$236$			1.23588i			0.0804489i
$237$		−	1.85157i		−	0.120272i
$238$	−23.0975			−1.49719
$239$		−	9.34261i		−	0.604323i	−0.953257	−	0.302162i	$-0.902292\pi$
$239$		−	9.34261i		−	0.604323i	0.953257	−	0.302162i	$-0.0977082\pi$
$240$		−	10.3650i		−	0.669058i
$241$			13.0233i			0.838903i	0.907778	+	0.419452i	$0.137778\pi$
$241$			13.0233i			0.838903i	−0.907778	+	0.419452i	$0.862222\pi$
$242$			14.9734i			0.962524i
$243$	−16.0739			−1.03114
$244$		−	1.70181i		−	0.108947i
$245$			14.8897i			0.951271i
$246$		−	3.93078i		−	0.250618i
$247$	33.6295			2.13979
$248$	−5.95694			−0.378266
$249$	−27.2412			−1.72634
$250$	−1.36551			−0.0863627
$251$			7.49230i			0.472910i	0.971642	+	0.236455i	$0.0759856\pi$
$251$			7.49230i			0.472910i	−0.971642	+	0.236455i	$0.924014\pi$
$252$	−3.04103			−0.191567
$253$		−	0.618071i		−	0.0388578i
$254$			16.8814i			1.05923i
$255$	−10.0980			−0.632363
$256$	−3.23372			−0.202107
$257$		−	2.57062i		−	0.160351i	−0.996781	−	0.0801756i	$-0.974452\pi$
$257$		−	2.57062i		−	0.160351i	0.996781	−	0.0801756i	$-0.0255481\pi$
$258$	−15.4563			−0.962265
$259$	24.8076	−	13.9464i	1.54147	−	0.866585i
$260$	−0.574197			−0.0356102
$261$			9.68277i			0.599348i
$262$	10.6535			0.658178
$263$	−18.2800			−1.12719			−0.563597	−	0.826050i	$-0.690583\pi$
$263$	−18.2800			−1.12719			−0.563597	+	0.826050i	$0.690583\pi$
$264$			1.51554i			0.0932748i
$265$			7.67087i			0.471218i
$266$	50.6531			3.10574
$267$		−	16.9350i		−	1.03640i
$268$	0.995622			0.0608173
$269$	−2.38487			−0.145408			−0.0727040	−	0.997354i	$-0.523163\pi$
$269$	−2.38487			−0.145408			−0.0727040	+	0.997354i	$0.523163\pi$
$270$	6.87067			0.418136
$271$	−8.55124			−0.519451			−0.259725	−	0.965683i	$-0.583632\pi$
$271$	−8.55124			−0.519451			−0.259725	+	0.965683i	$0.583632\pi$
$272$		−	13.4163i		−	0.813481i
$273$		−	55.4291i		−	3.35472i
$274$		−	1.75553i		−	0.106055i
$275$	0.186084			0.0112213
$276$			1.25587i			0.0755947i
$277$			19.1136i			1.14843i	0.818705	+	0.574214i	$0.194692\pi$
$277$			19.1136i			1.14843i	−0.818705	+	0.574214i	$0.805308\pi$
$278$		−	5.37537i		−	0.322393i
$279$		−	9.80898i		−	0.587248i
$280$	−13.6424			−0.815288
$281$			4.61050i			0.275039i	0.990499	+	0.137520i	$0.0439130\pi$
$281$			4.61050i			0.275039i	−0.990499	+	0.137520i	$0.956087\pi$
$282$			10.6160i			0.632172i
$283$			11.3598i			0.675273i	0.941277	+	0.337636i	$0.109627\pi$
$283$			11.3598i			0.675273i	−0.941277	+	0.337636i	$0.890373\pi$
$284$	2.06231			0.122376
$285$	22.1451			1.31176
$286$	−1.07780			−0.0637314
$287$	−4.82188			−0.284627
$288$		−	3.67038i		−	0.216279i
$289$	3.92931			0.231136
$290$			2.75376i			0.161706i
$291$		−	28.4948i		−	1.67039i
$292$	−0.0842836			−0.00493233
$293$	−14.0612			−0.821466			−0.410733	−	0.911756i	$-0.634727\pi$
$293$	−14.0612			−0.821466			−0.410733	+	0.911756i	$0.634727\pi$
$294$		−	56.7898i		−	3.31205i
$295$	−9.12948			−0.531539
$296$	8.69182	+	15.4609i	0.505201	+	0.898647i
$297$	−0.936295			−0.0543294
$298$			21.2349i			1.23011i
$299$	−14.0883			−0.814749
$300$	−0.378109			−0.0218301
$301$			18.9601i			1.09284i
$302$		−	20.6095i		−	1.18594i
$303$	14.5846			0.837863
$304$			29.4220i			1.68747i
$305$	12.5713			0.719833
$306$	23.7037			1.35505
$307$	−9.03504			−0.515657			−0.257829	−	0.966191i	$-0.583007\pi$
$307$	−9.03504			−0.515657			−0.257829	+	0.966191i	$0.583007\pi$
$308$	0.117858			0.00671560
$309$		−	37.5847i		−	2.13812i
$310$		−	2.78965i		−	0.158441i
$311$		−	28.0432i		−	1.59019i	−0.606487	−	0.795093i	$-0.707422\pi$
$311$		−	28.0432i		−	1.59019i	0.606487	−	0.795093i	$-0.292578\pi$
$312$	34.5452			1.95574
$313$			15.7374i			0.889528i	0.895648	+	0.444764i	$0.146713\pi$
$313$			15.7374i			0.889528i	−0.895648	+	0.444764i	$0.853287\pi$
$314$			9.41961i			0.531579i
$315$		−	22.4642i		−	1.26571i
$316$		−	0.0897392i		−	0.00504822i
$317$	32.4811			1.82432			0.912159	−	0.409836i	$-0.134414\pi$
$317$	32.4811			1.82432			0.912159	+	0.409836i	$0.134414\pi$
$318$		−	29.2568i		−	1.64064i
$319$		−	0.375266i		−	0.0210108i
$320$		−	8.46571i		−	0.473247i
$321$	10.1068			0.564107
$322$	−21.2200			−1.18254
$323$	28.6641			1.59492
$324$	−0.0474604			−0.00263669
$325$		−	4.24161i		−	0.235282i
$326$	6.04164			0.334615
$327$			44.5368i			2.46289i
$328$		−	3.00515i		−	0.165931i
$329$	13.0226			0.717958
$330$	−0.709729			−0.0390693
$331$			23.2086i			1.27566i	0.770177	+	0.637830i	$0.220168\pi$
$331$			23.2086i			1.27566i	−0.770177	+	0.637830i	$0.779832\pi$
$332$	−1.32029			−0.0724605
$333$	−25.4587	+	14.3124i	−1.39513	+	0.784312i
$334$	−22.0371			−1.20582
$335$			7.35469i			0.401830i
$336$	48.4942			2.64558
$337$	−4.46538			−0.243245			−0.121622	−	0.992576i	$-0.538810\pi$
$337$	−4.46538			−0.243245			−0.121622	+	0.992576i	$0.538810\pi$
$338$			6.81563i			0.370721i
$339$			20.3385i			1.10463i
$340$	−0.489417			−0.0265424
$341$			0.380157i			0.0205867i
$342$	−51.9824			−2.81088
$343$	−36.9134			−1.99313
$344$	−11.8166			−0.637106
$345$	−9.27717			−0.499466
$346$		−	32.4094i		−	1.74234i
$347$			9.36350i			0.502659i	0.967902	+	0.251330i	$0.0808678\pi$
$347$			9.36350i			0.502659i	−0.967902	+	0.251330i	$0.919132\pi$
$348$			0.762511i			0.0408749i
$349$	15.2015			0.813720			0.406860	−	0.913490i	$-0.366624\pi$
$349$	15.2015			0.813720			0.406860	+	0.913490i	$0.366624\pi$
$350$		−	6.38876i		−	0.341493i
$351$			21.3419i			1.13915i
$352$			0.142249i			0.00758192i
$353$		−	4.76686i		−	0.253714i	−0.991921	−	0.126857i	$-0.959511\pi$
$353$		−	4.76686i		−	0.253714i	0.991921	−	0.126857i	$-0.0404889\pi$
$354$	34.8200			1.85066
$355$			15.2343i			0.808555i
$356$		−	0.820781i		−	0.0435013i
$357$		−	47.2451i		−	2.50048i
$358$	−10.4616			−0.552911
$359$	4.76777			0.251633			0.125817	−	0.992054i	$-0.459845\pi$
$359$	4.76777			0.251633			0.125817	+	0.992054i	$0.459845\pi$
$360$	14.0004			0.737885
$361$	−43.8607			−2.30846
$362$			19.0612i			1.00183i
$363$	−30.6274			−1.60752
$364$		−	2.68647i		−	0.140809i
$365$		−	0.622606i		−	0.0325887i
$366$	−47.9473			−2.50625
$367$	−13.5255			−0.706027			−0.353014	−	0.935618i	$-0.614843\pi$
$367$	−13.5255			−0.706027			−0.353014	+	0.935618i	$0.614843\pi$
$368$		−	12.3257i		−	0.642521i
$369$	4.94842			0.257604
$370$	−7.24038	+	4.07040i	−0.376409	+	0.211610i
$371$	−35.8893			−1.86328
$372$		−	0.772450i		−	0.0400497i
$373$	−17.6980			−0.916366			−0.458183	−	0.888858i	$-0.651500\pi$
$373$	−17.6980			−0.916366			−0.458183	+	0.888858i	$0.651500\pi$
$374$	−0.918660			−0.0475028
$375$		−	2.79310i		−	0.144235i
$376$			8.11608i			0.418555i
$377$	−8.55382			−0.440544
$378$			32.1455i			1.65338i
$379$	10.1646			0.522123			0.261061	−	0.965322i	$-0.415927\pi$
$379$	10.1646			0.522123			0.261061	+	0.965322i	$0.415927\pi$
$380$	1.07330			0.0550590
$381$	−34.5302			−1.76904
$382$	28.3330			1.44964
$383$			36.9494i			1.88802i	0.329911	+	0.944012i	$0.392981\pi$
$383$			36.9494i			1.88802i	−0.329911	+	0.944012i	$0.607019\pi$
$384$			28.0181i			1.42979i
$385$			0.870623i			0.0443710i
$386$	12.5414			0.638342
$387$		−	19.4577i		−	0.989090i
$388$		−	1.38105i		−	0.0701120i
$389$		−	24.8802i		−	1.26148i	−0.775995	−	0.630739i	$-0.782752\pi$
$389$		−	24.8802i		−	1.26148i	0.775995	−	0.630739i	$-0.217248\pi$
$390$			16.1776i			0.819184i
$391$	−12.0082			−0.607281
$392$		−	43.4167i		−	2.19288i
$393$			21.7914i			1.09923i
$394$			11.7776i			0.593349i
$395$	0.662906			0.0333544
$396$	−0.120951			−0.00607802
$397$	−3.14936			−0.158062			−0.0790308	−	0.996872i	$-0.525183\pi$
$397$	−3.14936			−0.158062			−0.0790308	+	0.996872i	$0.525183\pi$
$398$	1.49468			0.0749218
$399$			103.609i			5.18693i
$400$	3.71093			0.185546
$401$			37.0988i			1.85263i	0.376756	+	0.926313i	$0.377040\pi$
$401$			37.0988i			1.85263i	−0.376756	+	0.926313i	$0.622960\pi$
$402$		−	28.0509i		−	1.39905i
$403$	8.66531			0.431650
$404$	0.706867			0.0351679
$405$		−	0.350591i		−	0.0174210i
$406$	−12.8839			−0.639415
$407$	0.986677	−	0.554690i	0.0489077	−	0.0274950i
$408$	29.4446			1.45773
$409$			16.6487i			0.823226i	0.911359	+	0.411613i	$0.135034\pi$
$409$			16.6487i			0.823226i	−0.911359	+	0.411613i	$0.864966\pi$
$410$	1.40732			0.0695025
$411$	3.59086			0.177124
$412$		−	1.82161i		−	0.0897441i
$413$		−	42.7136i		−	2.10180i
$414$	21.7768			1.07027
$415$		−	9.75304i		−	0.478758i
$416$	3.24244			0.158974
$417$	10.9951			0.538433
$418$	2.01463			0.0985388
$419$	−8.08323			−0.394892			−0.197446	−	0.980314i	$-0.563265\pi$
$419$	−8.08323			−0.394892			−0.197446	+	0.980314i	$0.563265\pi$
$420$		−	1.76904i		−	0.0863203i
$421$		−	14.4462i		−	0.704067i	−0.935987	−	0.352034i	$-0.885490\pi$
$421$		−	14.4462i		−	0.704067i	0.935987	−	0.352034i	$-0.114510\pi$
$422$		−	9.45708i		−	0.460363i
$423$	−13.3643			−0.649795
$424$		−	22.3673i		−	1.08625i
$425$		−	3.61534i		−	0.175370i
$426$		−	58.1041i		−	2.81515i
$427$			58.8169i			2.84635i
$428$	0.489843			0.0236775
$429$		−	2.20459i		−	0.106438i
$430$		−	5.53372i		−	0.266860i
$431$			13.8283i			0.666086i	0.942912	+	0.333043i	$0.108075\pi$
$431$			13.8283i			0.666086i	−0.942912	+	0.333043i	$0.891925\pi$
$432$	−18.6718			−0.898347
$433$	18.0931			0.869497			0.434749	−	0.900552i	$-0.356837\pi$
$433$	18.0931			0.869497			0.434749	+	0.900552i	$0.356837\pi$
$434$	13.0518			0.626506
$435$	−5.63270			−0.270067
$436$			2.15855i			0.103376i
$437$	26.3341			1.25973
$438$			2.37463i			0.113464i
$439$		−	0.179590i		−	0.00857135i	−0.999991	−	0.00428567i	$-0.998636\pi$
$439$		−	0.179590i		−	0.00857135i	0.999991	−	0.00428567i	$-0.00136418\pi$
$440$	−0.542599			−0.0258674
$441$	71.4920			3.40438
$442$			20.9400i			0.996013i
$443$	3.43515			0.163209			0.0816045	−	0.996665i	$-0.473996\pi$
$443$	3.43515			0.163209			0.0816045	+	0.996665i	$0.473996\pi$
$444$	−2.00485	+	1.12709i	−0.0951461	+	0.0534892i
$445$	6.06313			0.287420
$446$		−	7.85586i		−	0.371986i
$447$	−43.4352			−2.05441
$448$	39.6081			1.87130
$449$			26.3383i			1.24298i	0.783422	+	0.621490i	$0.213472\pi$
$449$			26.3383i			1.24298i	−0.783422	+	0.621490i	$0.786528\pi$
$450$			6.55641i			0.309072i
$451$	−0.191781			−0.00903062
$452$			0.985737i			0.0463652i
$453$	42.1559			1.98066
$454$	−10.3362			−0.485103
$455$	19.8450			0.930348
$456$	−64.5723			−3.02388
$457$		−	9.74641i		−	0.455918i	−0.973671	−	0.227959i	$-0.926795\pi$
$457$		−	9.74641i		−	0.455918i	0.973671	−	0.227959i	$-0.0732052\pi$
$458$			27.1704i			1.26959i
$459$			18.1908i			0.849075i
$460$	−0.449633			−0.0209643
$461$			17.7513i			0.826763i	0.910558	+	0.413381i	$0.135652\pi$
$461$			17.7513i			0.826763i	−0.910558	+	0.413381i	$0.864348\pi$
$462$		−	3.32057i		−	0.154487i
$463$		−	32.0881i		−	1.49126i	−0.666361	−	0.745629i	$-0.732149\pi$
$463$		−	32.0881i		−	1.49126i	0.666361	−	0.745629i	$-0.267851\pi$
$464$		−	7.48362i		−	0.347419i
$465$	5.70612			0.264615
$466$		−	24.2371i		−	1.12276i
$467$		−	28.3944i		−	1.31393i	−0.753919	−	0.656967i	$-0.771839\pi$
$467$		−	28.3944i		−	1.31393i	0.753919	−	0.656967i	$-0.228161\pi$
$468$			2.75696i			0.127441i
$469$	−34.4100			−1.58891
$470$	−3.80078			−0.175317
$471$	−19.2674			−0.887796
$472$	26.6205			1.22531
$473$			0.754103i			0.0346737i
$474$	−2.52834			−0.116130
$475$			7.92848i			0.363783i
$476$		−	2.28981i		−	0.104953i
$477$	36.8311			1.68638
$478$	−12.7575			−0.583513
$479$			1.49825i			0.0684567i	0.999414	+	0.0342283i	$0.0108973\pi$
$479$			1.49825i			0.0684567i	−0.999414	+	0.0342283i	$0.989103\pi$
$480$	2.13515			0.0974557
$481$	−12.6436	−	22.4903i	−0.576500	−	1.02547i
$482$	17.7835			0.810015
$483$		−	43.4046i		−	1.97498i
$484$	−1.48441			−0.0674731
$485$	10.2018			0.463241
$486$			21.9492i			0.995635i
$487$		−	31.5505i		−	1.42969i	−0.699284	−	0.714844i	$-0.746498\pi$
$487$		−	31.5505i		−	1.42969i	0.699284	−	0.714844i	$-0.253502\pi$
$488$	−36.6565			−1.65936
$489$			12.3579i			0.558845i
$490$	20.3322			0.918513
$491$	16.9549			0.765166			0.382583	−	0.923921i	$-0.375035\pi$
$491$	16.9549			0.765166			0.382583	+	0.923921i	$0.375035\pi$
$492$	0.389684			0.0175683
$493$	−7.29086			−0.328364
$494$		−	45.9215i		−	2.06611i
$495$		−	0.893470i		−	0.0401585i
$496$			7.58117i			0.340405i
$497$	−71.2761			−3.19717
$498$			37.1983i			1.66690i
$499$		−	15.1962i		−	0.680274i	−0.940376	−	0.340137i	$-0.889527\pi$
$499$		−	15.1962i		−	0.680274i	0.940376	−	0.340137i	$-0.110473\pi$
$500$		−	0.135372i		−	0.00605404i
$501$		−	45.0761i		−	2.01385i
$502$	10.2308			0.456625
$503$			2.02764i			0.0904081i	0.998978	+	0.0452040i	$0.0143938\pi$
$503$			2.02764i			0.0904081i	−0.998978	+	0.0452040i	$0.985606\pi$
$504$			65.5029i			2.91773i
$505$			5.22165i			0.232360i
$506$	−0.843984			−0.0375197
$507$	−13.9411			−0.619146
$508$	−1.67356			−0.0742524
$509$	−4.66055			−0.206575			−0.103288	−	0.994652i	$-0.532936\pi$
$509$	−4.66055			−0.206575			−0.103288	+	0.994652i	$0.532936\pi$
$510$			13.7890i			0.610587i
$511$	2.91295			0.128861
$512$			24.4780i			1.08179i
$513$		−	39.8927i		−	1.76130i
$514$	−3.51022			−0.154829
$515$	13.4563			0.592954
$516$		−	1.53228i		−	0.0674549i
$517$	0.517948			0.0227793
$518$	−19.0440	−	33.8752i	−0.836744	−	1.48839i
$519$	66.2921			2.90990
$520$			12.3680i			0.542374i
$521$	23.5400			1.03130			0.515652	−	0.856798i	$-0.327550\pi$
$521$	23.5400			1.03130			0.515652	+	0.856798i	$0.327550\pi$
$522$	13.2219			0.578709
$523$			11.4942i			0.502607i	0.967908	+	0.251303i	$0.0808592\pi$
$523$			11.4942i			0.502607i	−0.967908	+	0.251303i	$0.919141\pi$
$524$			1.05616i			0.0461384i
$525$	13.0679			0.570332
$526$			24.9616i			1.08838i
$527$	7.38589			0.321734
$528$	1.92876			0.0839387
$529$	11.9679			0.520345
$530$	10.4747			0.454991
$531$			43.8345i			1.90226i
$532$			5.02158i			0.217713i
$533$			4.37146i			0.189349i
$534$	−23.1249			−1.00071
$535$			3.61849i			0.156441i
$536$		−	21.4454i		−	0.926300i
$537$		−	21.3987i		−	0.923423i
$538$			3.25657i			0.140401i
$539$	−2.77075			−0.119345
$540$			0.681135i			0.0293114i
$541$		−	27.6299i		−	1.18790i	−0.804500	−	0.593952i	$-0.797567\pi$
$541$		−	27.6299i		−	1.18790i	0.804500	−	0.593952i	$-0.202433\pi$
$542$			11.6768i			0.501563i
$543$	−38.9888			−1.67317
$544$	2.76369			0.118492
$545$	−15.9453			−0.683021
$546$	−75.6892			−3.23920
$547$		−	32.6357i		−	1.39540i	−0.716390	−	0.697700i	$-0.754207\pi$
$547$		−	32.6357i		−	1.39540i	0.716390	−	0.697700i	$-0.245793\pi$
$548$	0.174037			0.00743449
$549$		−	60.3603i		−	2.57612i
$550$		−	0.254101i		−	0.0108349i
$551$	15.9889			0.681151
$552$	27.0511			1.15137
$553$			3.10150i			0.131889i
$554$	26.0999			1.10888
$555$	−8.32583	−	14.8099i	−0.353412	−	0.628645i
$556$	0.532896			0.0225998
$557$			23.9676i			1.01554i	0.861492	+	0.507771i	$0.169530\pi$
$557$			23.9676i			1.01554i	−0.861492	+	0.507771i	$0.830470\pi$
$558$	−13.3943			−0.567026
$559$	17.1891			0.727020
$560$			17.3621i			0.733684i
$561$		−	1.87908i		−	0.0793349i
$562$	6.29570			0.265568
$563$			15.7977i			0.665792i	0.942964	+	0.332896i	$0.108026\pi$
$563$			15.7977i			0.665792i	−0.942964	+	0.332896i	$0.891974\pi$
$564$	−1.05243			−0.0443153
$565$	−7.28167			−0.306342
$566$	15.5120			0.652019
$567$	1.64029			0.0688858
$568$		−	44.4215i		−	1.86389i
$569$		−	24.2188i		−	1.01530i	−0.861562	−	0.507652i	$-0.830514\pi$
$569$		−	24.2188i		−	1.01530i	0.861562	−	0.507652i	$-0.169486\pi$
$570$		−	30.2394i		−	1.26659i
$571$	24.0429			1.00617			0.503083	−	0.864238i	$-0.332199\pi$
$571$	24.0429			1.00617			0.503083	+	0.864238i	$0.332199\pi$
$572$		−	0.106849i		−	0.00446758i
$573$			57.9540i			2.42106i
$574$			6.58434i			0.274825i
$575$		−	3.32146i		−	0.138514i
$576$	−40.6475			−1.69364
$577$		−	23.8305i		−	0.992076i	−0.868301	−	0.496038i	$-0.834788\pi$
$577$		−	23.8305i		−	0.992076i	0.868301	−	0.496038i	$-0.165212\pi$
$578$		−	5.36553i		−	0.223176i
$579$			25.6530i			1.06610i
$580$	−0.272998			−0.0113356
$581$	45.6310			1.89309
$582$	−38.9100			−1.61287
$583$	−1.42743			−0.0591180
$584$			1.81544i			0.0751236i
$585$	−20.3658			−0.842021
$586$			19.2008i			0.793178i
$587$			7.16402i			0.295691i	0.989010	+	0.147845i	$0.0472338\pi$
$587$			7.16402i			0.295691i	−0.989010	+	0.147845i	$0.952766\pi$
$588$	5.62995			0.232175
$589$	−16.1973			−0.667399
$590$			12.4664i			0.513235i
$591$	−24.0907			−0.990959
$592$	19.6765	−	11.0617i	0.808699	−	0.454635i
$593$	−33.0533			−1.35734			−0.678668	−	0.734445i	$-0.737442\pi$
$593$	−33.0533			−1.35734			−0.678668	+	0.734445i	$0.737442\pi$
$594$			1.27852i			0.0524585i
$595$	16.9149			0.693444
$596$	−2.10516			−0.0862306
$597$			3.05732i			0.125128i
$598$			19.2378i			0.786692i
$599$	−40.2670			−1.64527			−0.822633	−	0.568572i	$-0.807496\pi$
$599$	−40.2670			−1.64527			−0.822633	+	0.568572i	$0.807496\pi$
$600$			8.14435i			0.332492i
$601$	6.28442			0.256347			0.128173	−	0.991752i	$-0.459089\pi$
$601$	6.28442			0.256347			0.128173	+	0.991752i	$0.459089\pi$
$602$	25.8903			1.05521
$603$	35.3130			1.43806
$604$	2.04315			0.0831348
$605$		−	10.9654i		−	0.445806i
$606$		−	19.9155i		−	0.809010i
$607$			26.3428i			1.06922i	0.845098	+	0.534611i	$0.179542\pi$
$607$			26.3428i			1.06922i	−0.845098	+	0.534611i	$0.820458\pi$
$608$	−6.06081			−0.245798
$609$		−	26.3534i		−	1.06789i
$610$		−	17.1663i		−	0.695044i
$611$		−	11.8061i		−	0.477625i
$612$			2.34990i			0.0949891i
$613$	29.2189			1.18014			0.590070	−	0.807352i	$-0.299100\pi$
$613$	29.2189			1.18014			0.590070	+	0.807352i	$0.299100\pi$
$614$			12.3375i			0.497900i
$615$			2.87861i			0.116077i
$616$		−	2.53863i		−	0.102284i
$617$	−6.55954			−0.264077			−0.132039	−	0.991245i	$-0.542152\pi$
$617$	−6.55954			−0.264077			−0.132039	+	0.991245i	$0.542152\pi$
$618$	−51.3225			−2.06449
$619$	11.6979			0.470177			0.235088	−	0.971974i	$-0.424462\pi$
$619$	11.6979			0.470177			0.235088	+	0.971974i	$0.424462\pi$
$620$	0.276556			0.0111068
$621$			16.7121i			0.670635i
$622$	−38.2934			−1.53543
$623$			28.3673i			1.13651i
$624$		−	43.9643i		−	1.75998i
$625$	1.00000			0.0400000
$626$	21.4896			0.858897
$627$			4.12084i			0.164571i
$628$	−0.933828			−0.0372638
$629$	−10.7768	−	19.1697i	−0.429699	−	0.764345i
$630$	−30.6751			−1.22213
$631$		−	7.02214i		−	0.279547i	−0.990183	−	0.139774i	$-0.955363\pi$
$631$		−	7.02214i		−	0.279547i	0.990183	−	0.139774i	$-0.0446375\pi$
$632$	−1.93296			−0.0768888
$633$	19.3441			0.768858
$634$		−	44.3533i		−	1.76150i
$635$		−	12.3627i		−	0.490597i
$636$	2.90042			0.115009
$637$			63.1565i			2.50235i
$638$	−0.512430			−0.0202873
$639$	73.1466			2.89363
$640$	−10.0312			−0.396517
$641$	36.0787			1.42502			0.712511	−	0.701661i	$-0.247558\pi$
$641$	36.0787			1.42502			0.712511	+	0.701661i	$0.247558\pi$
$642$		−	13.8010i		−	0.544681i
$643$		−	46.9144i		−	1.85012i	−0.379817	−	0.925062i	$-0.624013\pi$
$643$		−	46.9144i		−	1.85012i	0.379817	−	0.925062i	$-0.375987\pi$
$644$		−	2.10368i		−	0.0828965i
$645$	11.3190			0.445685
$646$		−	39.1413i		−	1.53999i
$647$		−	6.09043i		−	0.239439i	−0.992808	−	0.119720i	$-0.961800\pi$
$647$		−	6.09043i		−	0.239439i	0.992808	−	0.119720i	$-0.0381996\pi$
$648$			1.02228i			0.0401590i
$649$		−	1.69885i		−	0.0666858i
$650$	−5.79198			−0.227180
$651$			26.6969i			1.04633i
$652$			0.598947i			0.0234566i
$653$		−	37.3874i		−	1.46308i	−0.681798	−	0.731540i	$-0.738802\pi$
$653$		−	37.3874i		−	1.46308i	0.681798	−	0.731540i	$-0.261198\pi$
$654$	60.8156			2.37808
$655$	−7.80186			−0.304844
$656$	−3.82454			−0.149323
$657$	−2.98940			−0.116627
$658$		−	17.7825i		−	0.693234i
$659$	6.06336			0.236195			0.118098	−	0.993002i	$-0.462320\pi$
$659$	6.06336			0.236195			0.118098	+	0.993002i	$0.462320\pi$
$660$		−	0.0703601i		−	0.00273876i
$661$		−	1.09225i		−	0.0424835i	−0.999774	−	0.0212418i	$-0.993238\pi$
$661$		−	1.09225i		−	0.0424835i	0.999774	−	0.0212418i	$-0.00676197\pi$
$662$	31.6917			1.23173
$663$	−42.8319			−1.66345
$664$			28.4387i			1.10364i
$665$	−37.0945			−1.43846
$666$	19.5437	+	34.7641i	0.757303	+	1.34708i
$667$	−6.69820			−0.259355
$668$		−	2.18469i		−	0.0845280i
$669$	16.0688			0.621257
$670$	10.0429			0.387992
$671$			2.33933i			0.0903087i
$672$			9.98960i			0.385357i
$673$	−10.6301			−0.409762			−0.204881	−	0.978787i	$-0.565681\pi$
$673$	−10.6301			−0.409762			−0.204881	+	0.978787i	$0.565681\pi$
$674$			6.09753i			0.234868i
$675$	−5.03157			−0.193665
$676$	−0.675678			−0.0259876
$677$	15.3033			0.588153			0.294076	−	0.955782i	$-0.404988\pi$
$677$	15.3033			0.588153			0.294076	+	0.955782i	$0.404988\pi$
$678$	27.7724			1.06659
$679$			47.7308i			1.83174i
$680$			10.5419i			0.404263i
$681$		−	21.1423i		−	0.810175i
$682$	0.519110			0.0198777
$683$		−	23.6010i		−	0.903066i	−0.892255	−	0.451533i	$-0.850877\pi$
$683$		−	23.6010i		−	0.903066i	0.892255	−	0.451533i	$-0.149123\pi$
$684$		−	5.15335i		−	0.197043i
$685$			1.28562i			0.0491209i
$686$			50.4057i			1.92450i
$687$	−55.5759			−2.12035
$688$			15.0385i			0.573337i
$689$			32.5368i			1.23955i
$690$			12.6681i			0.482266i
$691$	−32.4523			−1.23454			−0.617271	−	0.786751i	$-0.711762\pi$
$691$	−32.4523			−1.23454			−0.617271	+	0.786751i	$0.711762\pi$
$692$	3.21296			0.122138
$693$	4.18023			0.158794
$694$	12.7860			0.485350
$695$			3.93652i			0.149321i
$696$	16.4243			0.622560
$697$			3.72602i			0.141133i
$698$		−	20.7579i		−	0.785699i
$699$	49.5760			1.87514
$700$	0.633360			0.0239387
$701$		−	29.6756i		−	1.12083i	−0.828211	−	0.560416i	$-0.810641\pi$
$701$		−	29.6756i		−	1.12083i	0.828211	−	0.560416i	$-0.189359\pi$
$702$	29.1427			1.09992
$703$	23.6336	+	42.0392i	0.891359	+	1.58554i
$704$	1.57533			0.0593727
$705$		−	7.77434i		−	0.292799i
$706$	−6.50921			−0.244977
$707$	−24.4302			−0.918794
$708$			3.45194i			0.129732i
$709$			2.33245i			0.0875969i	0.999040	+	0.0437985i	$0.0139459\pi$
$709$			2.33245i			0.0875969i	−0.999040	+	0.0437985i	$0.986054\pi$
$710$	20.8027			0.780712
$711$		−	3.18289i		−	0.119368i
$712$	−17.6794			−0.662562
$713$	6.78550			0.254119
$714$	−64.5138			−2.41437
$715$	0.789297			0.0295180
$716$		−	1.03713i		−	0.0387592i
$717$		−	26.0949i		−	0.974531i
$718$		−	6.51045i		−	0.242968i
$719$	−38.0117			−1.41760			−0.708799	−	0.705410i	$-0.750763\pi$
$719$	−38.0117			−1.41760			−0.708799	+	0.705410i	$0.750763\pi$
$720$		−	17.8178i		−	0.664028i
$721$			62.9572i			2.34465i
$722$			59.8924i			2.22897i
$723$			36.3754i			1.35281i
$724$	−1.88966			−0.0702286
$725$		−	2.01664i		−	0.0748963i
$726$			41.8222i			1.55217i
$727$			11.8176i			0.438289i	0.975692	+	0.219145i	$0.0703267\pi$
$727$			11.8176i			0.438289i	−0.975692	+	0.219145i	$0.929673\pi$
$728$	−57.8656			−2.14464
$729$	−43.8444			−1.62387
$730$	−0.850177			−0.0314665
$731$	14.6511			0.541891
$732$		−	4.75333i		−	0.175688i
$733$	26.8937			0.993340			0.496670	−	0.867939i	$-0.334556\pi$
$733$	26.8937			0.993340			0.496670	+	0.867939i	$0.334556\pi$
$734$			18.4693i			0.681715i
$735$			41.5886i			1.53402i
$736$	2.53904			0.0935902
$737$	−1.36859			−0.0504127
$738$		−	6.75713i		−	0.248733i
$739$	−19.0328			−0.700134			−0.350067	−	0.936725i	$-0.613841\pi$
$739$	−19.0328			−0.700134			−0.350067	+	0.936725i	$0.613841\pi$
$740$	−0.403525	−	0.717786i	−0.0148339	−	0.0263864i
$741$	93.9307			3.45063
$742$			49.0073i			1.79912i
$743$	22.1010			0.810806			0.405403	−	0.914138i	$-0.367131\pi$
$743$	22.1010			0.810806			0.405403	+	0.914138i	$0.367131\pi$
$744$	−16.6383			−0.609991
$745$		−	15.5509i		−	0.569740i
$746$			24.1668i			0.884810i
$747$	−46.8285			−1.71337
$748$		−	0.0910728i		−	0.00332995i
$749$	−16.9296			−0.618595
$750$	−3.81402			−0.139268
$751$	−35.7157			−1.30328			−0.651641	−	0.758527i	$-0.725919\pi$
$751$	−35.7157			−1.30328			−0.651641	+	0.758527i	$0.725919\pi$
$752$	10.3290			0.376661
$753$			20.9268i			0.762614i
$754$			11.6804i			0.425373i
$755$			15.0928i			0.549285i
$756$	−3.18679			−0.115902
$757$			9.16811i			0.333221i	0.986023	+	0.166610i	$0.0532822\pi$
$757$			9.16811i			0.333221i	−0.986023	+	0.166610i	$0.946718\pi$
$758$		−	13.8800i		−	0.504143i
$759$		−	1.72634i		−	0.0626620i
$760$		−	23.1185i		−	0.838596i
$761$	−33.4346			−1.21200			−0.606001	−	0.795464i	$-0.707227\pi$
$761$	−33.4346			−1.21200			−0.606001	+	0.795464i	$0.707227\pi$
$762$			47.1515i			1.70812i
$763$		−	74.6023i		−	2.70079i
$764$			2.80884i			0.101620i
$765$	−17.3588			−0.627608
$766$	50.4549			1.82301
$767$	−38.7237			−1.39823
$768$	−9.03210			−0.325918
$769$		−	33.3999i		−	1.20443i	−0.798333	−	0.602216i	$-0.794284\pi$
$769$		−	33.3999i		−	1.20443i	0.798333	−	0.602216i	$-0.205716\pi$
$770$	1.18885			0.0428431
$771$		−	7.18002i		−	0.258582i
$772$			1.24331i			0.0447479i
$773$	−33.6561			−1.21053			−0.605263	−	0.796026i	$-0.706932\pi$
$773$	−33.6561			−1.21053			−0.605263	+	0.796026i	$0.706932\pi$
$774$	−26.5698			−0.955030
$775$			2.04293i			0.0733842i
$776$	−29.7473			−1.06787
$777$	69.2903	−	38.9537i	2.48578	−	1.39745i
$778$	−33.9743			−1.21804
$779$		−	8.17120i		−	0.292764i
$780$	−1.60379			−0.0574249
$781$	−2.83487			−0.101440
$782$			16.3974i			0.586368i
$783$			10.1469i			0.362620i
$784$	−55.2548			−1.97339
$785$		−	6.89821i		−	0.246208i
$786$	29.7565			1.06138
$787$	1.05415			0.0375764			0.0187882	−	0.999823i	$-0.494019\pi$
$787$	1.05415			0.0375764			0.0187882	+	0.999823i	$0.494019\pi$
$788$	−1.16760			−0.0415939
$789$	−51.0579			−1.81771
$790$		−	0.905208i		−	0.0322058i
$791$		−	34.0684i		−	1.21133i
$792$			2.60525i			0.0925735i
$793$	53.3227			1.89354
$794$			4.30049i			0.152619i
$795$			21.4255i			0.759885i
$796$			0.148178i			0.00525203i
$797$		−	26.3106i		−	0.931970i	−0.884793	−	0.465985i	$-0.845700\pi$
$797$		−	26.3106i		−	0.931970i	0.884793	−	0.465985i	$-0.154300\pi$
$798$	141.479			5.00832
$799$		−	10.0630i		−	0.356002i
$800$			0.764435i			0.0270269i
$801$		−	29.1117i		−	1.02861i
$802$	50.6589			1.78883
$803$	0.115857			0.00408851
$804$	2.78087			0.0980739
$805$	15.5399			0.547710
$806$		−	11.8326i		−	0.416786i
$807$	−6.66118			−0.234485
$808$		−	15.2257i		−	0.535638i
$809$			15.9357i			0.560271i	0.959960	+	0.280136i	$0.0903794\pi$
$809$			15.9357i			0.560271i	−0.959960	+	0.280136i	$0.909621\pi$
$810$	−0.478737			−0.0168211
$811$	14.8155			0.520242			0.260121	−	0.965576i	$-0.416238\pi$
$811$	14.8155			0.520242			0.260121	+	0.965576i	$0.416238\pi$
$812$		−	1.27726i		−	0.0448231i
$813$	−23.8845			−0.837665
$814$	−0.757437	−	1.34732i	−0.0265481	−	0.0472236i
$815$	−4.42444			−0.154981
$816$		−	37.4730i		−	1.31182i
$817$	−32.1300			−1.12409
$818$	22.7340			0.794877
$819$		−	95.2843i		−	3.32950i
$820$			0.139517i			0.00487213i
$821$	−15.9564			−0.556882			−0.278441	−	0.960453i	$-0.589818\pi$
$821$	−15.9564			−0.556882			−0.278441	+	0.960453i	$0.589818\pi$
$822$		−	4.90337i		−	0.171025i
$823$	−10.3719			−0.361542			−0.180771	−	0.983525i	$-0.557859\pi$
$823$	−10.3719			−0.361542			−0.180771	+	0.983525i	$0.557859\pi$
$824$	−39.2369			−1.36688
$825$	0.519752			0.0180955
$826$	−58.3261			−2.02942
$827$		−	54.8138i		−	1.90606i	−0.302871	−	0.953032i	$-0.597945\pi$
$827$		−	54.8138i		−	1.90606i	0.302871	−	0.953032i	$-0.402055\pi$
$828$			2.15888i			0.0750263i
$829$		−	18.7538i		−	0.651347i	−0.945482	−	0.325674i	$-0.894409\pi$
$829$		−	18.7538i		−	0.651347i	0.945482	−	0.325674i	$-0.105591\pi$
$830$	−13.3179			−0.462271
$831$			53.3864i			1.85195i
$832$		−	35.9082i		−	1.24489i
$833$			53.8315i			1.86515i
$834$		−	15.0140i		−	0.519891i
$835$	16.1383			0.558490
$836$			0.199724i			0.00690758i
$837$		−	10.2791i		−	0.355299i
$838$			11.0378i			0.381293i
$839$	−27.0261			−0.933043			−0.466522	−	0.884510i	$-0.654493\pi$
$839$	−27.0261			−0.933043			−0.466522	+	0.884510i	$0.654493\pi$
$840$	−38.1046			−1.31473
$841$	24.9331			0.859764
$842$	−19.7266			−0.679822
$843$			12.8776i			0.443528i
$844$	0.937543			0.0322716
$845$		−	4.99126i		−	0.171704i
$846$			18.2492i			0.627419i
$847$	51.3031			1.76280
$848$	−28.4660			−0.977528
$849$			31.7292i			1.08894i
$850$	−4.93680			−0.169331
$851$	−9.90078	−	17.6114i	−0.339394	−	0.603711i
$852$	5.76024			0.197343
$853$			32.8016i			1.12311i	0.827441	+	0.561553i	$0.189796\pi$
$853$			32.8016i			1.12311i	−0.827441	+	0.561553i	$0.810204\pi$
$854$	80.3152			2.74833
$855$	38.0680			1.30190
$856$		−	10.5511i		−	0.360628i
$857$			44.9972i			1.53707i	0.639805	+	0.768537i	$0.279015\pi$
$857$			44.9972i			1.53707i	−0.639805	+	0.768537i	$0.720985\pi$
$858$	−3.01039			−0.102773
$859$		−	38.4263i		−	1.31109i	−0.755157	−	0.655543i	$-0.772440\pi$
$859$		−	38.4263i		−	1.31109i	0.755157	−	0.655543i	$-0.227560\pi$
$860$	0.548594			0.0187069
$861$	−13.4680			−0.458989
$862$	18.8827			0.643149
$863$	11.3362			0.385890			0.192945	−	0.981210i	$-0.438196\pi$
$863$	11.3362			0.385890			0.192945	+	0.981210i	$0.438196\pi$
$864$		−	3.84631i		−	0.130854i
$865$			23.7342i			0.806987i
$866$		−	24.7063i		−	0.839555i
$867$	10.9750			0.372729
$868$			1.29391i			0.0439182i
$869$			0.123356i			0.00418458i
$870$			7.69152i			0.260767i
$871$			31.1957i			1.05703i
$872$	46.4945			1.57450
$873$		−	48.9833i		−	1.65783i
$874$		−	35.9596i		−	1.21635i
$875$			4.67865i			0.158167i
$876$	−0.235413			−0.00795386
$877$	−15.7379			−0.531433			−0.265716	−	0.964051i	$-0.585608\pi$
$877$	−15.7379			−0.531433			−0.265716	+	0.964051i	$0.585608\pi$
$878$	−0.245232			−0.00827618
$879$	−39.2745			−1.32469
$880$			0.690545i			0.0232783i
$881$	−19.4357			−0.654804			−0.327402	−	0.944885i	$-0.606173\pi$
$881$	−19.4357			−0.654804			−0.327402	+	0.944885i	$0.606173\pi$
$882$		−	97.6233i		−	3.28715i
$883$		−	20.2319i		−	0.680858i	−0.940270	−	0.340429i	$-0.889428\pi$
$883$		−	20.2319i		−	0.680858i	0.940270	−	0.340429i	$-0.110572\pi$
$884$	−2.07592			−0.0698207
$885$	−25.4996			−0.857159
$886$		−	4.69075i		−	0.157589i
$887$	−10.5339			−0.353695			−0.176847	−	0.984238i	$-0.556590\pi$
$887$	−10.5339			−0.353695			−0.176847	+	0.984238i	$0.556590\pi$
$888$	24.2771	+	43.1839i	0.814687	+	1.44916i
$889$	57.8406			1.93991
$890$		−	8.27929i		−	0.277522i
$891$	0.0652395			0.00218561
$892$	0.778803			0.0260762
$893$			22.0682i			0.738483i
$894$			59.3113i			1.98367i
$895$	7.66128			0.256088
$896$		−	46.9323i		−	1.56790i
$897$	−39.3501			−1.31386
$898$	35.9653			1.20018
$899$	4.11986			0.137405
$900$	−0.649980			−0.0216660
$901$			27.7328i			0.923914i
$902$			0.261880i			0.00871964i
$903$			52.9576i			1.76232i
$904$	21.2325			0.706182
$905$		−	13.9590i		−	0.464012i
$906$		−	57.5644i		−	1.91245i
$907$			9.71635i			0.322626i	0.986903	+	0.161313i	$0.0515729\pi$
$907$			9.71635i			0.322626i	−0.986903	+	0.161313i	$0.948427\pi$
$908$		−	1.02470i		−	0.0340058i
$909$	25.0713			0.831564
$910$		−	27.0986i		−	0.898311i
$911$		−	9.06312i		−	0.300274i	−0.988665	−	0.150137i	$-0.952028\pi$
$911$		−	9.06312i		−	0.300274i	0.988665	−	0.150137i	$-0.0479715\pi$
$912$			82.1787i			2.72121i
$913$	1.81489			0.0600640
$914$	−13.3089			−0.440218
$915$	35.1130			1.16080
$916$	−2.69358			−0.0889983
$917$		−	36.5022i		−	1.20541i
$918$	24.8398			0.819836
$919$		−	16.9169i		−	0.558036i	−0.960286	−	0.279018i	$-0.909991\pi$
$919$		−	16.9169i		−	0.558036i	0.960286	−	0.279018i	$-0.0900089\pi$
$920$			9.68497i			0.319304i
$921$	−25.2358			−0.831548
$922$	24.2397			0.798292
$923$			64.6182i			2.12693i
$924$	0.329190			0.0108296
$925$	5.30231	−	2.98085i	0.174339	−	0.0980099i
$926$	−43.8167			−1.43991
$927$		−	64.6093i		−	2.12205i
$928$	1.54159			0.0506053
$929$	−22.5222			−0.738930			−0.369465	−	0.929245i	$-0.620459\pi$
$929$	−22.5222			−0.738930			−0.369465	+	0.929245i	$0.620459\pi$
$930$		−	7.79178i		−	0.255502i
$931$		−	118.053i		−	3.86903i
$932$	2.40278			0.0787058
$933$		−	78.3277i		−	2.56433i
$934$	−38.7729			−1.26869
$935$	0.672758			0.0220015
$936$	59.3842			1.94103
$937$	30.8630			1.00825			0.504126	−	0.863630i	$-0.331815\pi$
$937$	30.8630			1.00825			0.504126	+	0.863630i	$0.331815\pi$
$938$			46.9873i			1.53419i
$939$			43.9561i			1.43445i
$940$		−	0.376796i		−	0.0122897i
$941$	−54.0573			−1.76222			−0.881108	−	0.472914i	$-0.843202\pi$
$941$	−54.0573			−1.76222			−0.881108	+	0.472914i	$0.843202\pi$
$942$			26.3099i			0.857224i
$943$			3.42314i			0.111473i
$944$		−	33.8789i		−	1.10266i
$945$		−	23.5409i		−	0.765787i
$946$	1.02974			0.0334797
$947$			53.5495i			1.74013i	0.492941	+	0.870063i	$0.335922\pi$
$947$			53.5495i			1.74013i	−0.492941	+	0.870063i	$0.664078\pi$
$948$		−	0.250651i		−	0.00814076i
$949$		−	2.64085i		−	0.0857256i
$950$	10.8264			0.351256
$951$	90.7230			2.94189
$952$	−49.3218			−1.59853
$953$	32.2122			1.04346			0.521728	−	0.853112i	$-0.325288\pi$
$953$	32.2122			1.04346			0.521728	+	0.853112i	$0.325288\pi$
$954$		−	50.2934i		−	1.62831i
$955$	−20.7490			−0.671421
$956$		−	1.26473i		−	0.0409043i
$957$		−	1.04816i		−	0.0338821i
$958$	2.04588			0.0660993
$959$	−6.01495			−0.194233
$960$		−	23.6456i		−	0.763158i
$961$	26.8264			0.865369
$962$	−30.7109	+	17.2650i	−0.990158	+	0.556647i
$963$	17.3739			0.559866
$964$			1.76299i			0.0567822i
$965$	−9.18440			−0.295656
$966$	−59.2696			−1.90697
$967$		−	25.9095i		−	0.833193i	−0.909091	−	0.416597i	$-0.863223\pi$
$967$		−	25.9095i		−	0.833193i	0.909091	−	0.416597i	$-0.136777\pi$
$968$			31.9737i			1.02767i
$969$	80.0619			2.57196
$970$		−	13.9307i		−	0.447289i
$971$	7.44649			0.238969			0.119485	−	0.992836i	$-0.461876\pi$
$971$	7.44649			0.238969			0.119485	+	0.992836i	$0.461876\pi$
$972$	−2.17597			−0.0697942
$973$	−18.4176			−0.590441
$974$	−43.0826			−1.38046
$975$		−	11.8473i		−	0.379416i
$976$			46.6513i			1.49327i
$977$			5.21832i			0.166949i	0.996510	+	0.0834744i	$0.0266017\pi$
$977$			5.21832i			0.166949i	−0.996510	+	0.0834744i	$0.973398\pi$
$978$	16.8749			0.539600
$979$			1.12825i			0.0360591i
$980$			2.01566i			0.0643879i
$981$			76.5600i			2.44437i
$982$		−	23.1522i		−	0.738816i
$983$	30.9100			0.985874			0.492937	−	0.870065i	$-0.335923\pi$
$983$	30.9100			0.985874			0.492937	+	0.870065i	$0.335923\pi$
$984$		−	8.39369i		−	0.267581i
$985$		−	8.62507i		−	0.274818i
$986$			9.95576i			0.317056i
$987$	36.3734			1.15778
$988$	4.55251			0.144834
$989$	13.4601			0.428008
$990$	−1.22004			−0.0387756
$991$			37.9145i			1.20439i	0.798348	+	0.602196i	$0.205708\pi$
$991$			37.9145i			1.20439i	−0.798348	+	0.602196i	$0.794292\pi$
$992$	−1.56169			−0.0495836
$993$			64.8240i			2.05713i
$994$			97.3285i			3.08707i
$995$	−1.09459			−0.0347010
$996$	−3.68771			−0.116850
$997$		−	43.7248i		−	1.38478i	−0.721525	−	0.692389i	$-0.756558\pi$
$997$		−	43.7248i		−	1.38478i	0.721525	−	0.692389i	$-0.243442\pi$
$998$	−20.7506			−0.656848
$999$	−26.6789	+	14.9984i	−0.844084	+	0.474527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.c.b.36.4	✓	12
3.2	odd	2		1665.2.e.e.406.9		12
4.3	odd	2		2960.2.p.h.961.4		12
5.2	odd	4		925.2.d.e.924.9		12
5.3	odd	4		925.2.d.f.924.4		12
5.4	even	2		925.2.c.c.776.9		12
37.6	odd	4		6845.2.a.i.1.2		6
37.31	odd	4		6845.2.a.h.1.5		6
37.36	even	2	inner	185.2.c.b.36.9	yes	12
111.110	odd	2		1665.2.e.e.406.4		12
148.147	odd	2		2960.2.p.h.961.3		12
185.73	odd	4		925.2.d.e.924.10		12
185.147	odd	4		925.2.d.f.924.3		12
185.184	even	2		925.2.c.c.776.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.c.b.36.4	✓	12	1.1	even	1	trivial
185.2.c.b.36.9	yes	12	37.36	even	2	inner
925.2.c.c.776.4		12	185.184	even	2
925.2.c.c.776.9		12	5.4	even	2
925.2.d.e.924.9		12	5.2	odd	4
925.2.d.e.924.10		12	185.73	odd	4
925.2.d.f.924.3		12	185.147	odd	4
925.2.d.f.924.4		12	5.3	odd	4
1665.2.e.e.406.4		12	111.110	odd	2
1665.2.e.e.406.9		12	3.2	odd	2
2960.2.p.h.961.3		12	148.147	odd	2
2960.2.p.h.961.4		12	4.3	odd	2
6845.2.a.h.1.5		6	37.31	odd	4
6845.2.a.i.1.2		6	37.6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.36551i q^{2} +2.79310 q^{3} +0.135372 q^{4} +1.00000i q^{5} -3.81402i q^{6} -4.67865 q^{7} -2.91588i q^{8} +4.80143 q^{9} +1.36551 q^{10} -0.186084 q^{11} +0.378109 q^{12} +4.24161i q^{13} +6.38876i q^{14} +2.79310i q^{15} -3.71093 q^{16} +3.61534i q^{17} -6.55641i q^{18} -7.92848i q^{19} +0.135372i q^{20} -13.0679 q^{21} +0.254101i q^{22} +3.32146i q^{23} -8.14435i q^{24} -1.00000 q^{25} +5.79198 q^{26} +5.03157 q^{27} -0.633360 q^{28} +2.01664i q^{29} +3.81402 q^{30} -2.04293i q^{31} -0.764435i q^{32} -0.519752 q^{33} +4.93680 q^{34} -4.67865i q^{35} +0.649980 q^{36} +(-5.30231 + 2.98085i) q^{37} -10.8264 q^{38} +11.8473i q^{39} +2.91588 q^{40} +1.03061 q^{41} +17.8445i q^{42} -4.05248i q^{43} -0.0251907 q^{44} +4.80143i q^{45} +4.53549 q^{46} -2.78341 q^{47} -10.3650 q^{48} +14.8897 q^{49} +1.36551i q^{50} +10.0980i q^{51} +0.574197i q^{52} +7.67087 q^{53} -6.87067i q^{54} -0.186084i q^{55} +13.6424i q^{56} -22.1451i q^{57} +2.75376 q^{58} +9.12948i q^{59} +0.378109i q^{60} -12.5713i q^{61} -2.78965 q^{62} -22.4642 q^{63} -8.46571 q^{64} -4.24161 q^{65} +0.709729i q^{66} +7.35469 q^{67} +0.489417i q^{68} +9.27717i q^{69} -6.38876 q^{70} +15.2343 q^{71} -14.0004i q^{72} -0.622606 q^{73} +(4.07040 + 7.24038i) q^{74} -2.79310 q^{75} -1.07330i q^{76} +0.870623 q^{77} +16.1776 q^{78} -0.662906i q^{79} -3.71093i q^{80} -0.350591 q^{81} -1.40732i q^{82} -9.75304 q^{83} -1.76904 q^{84} -3.61534 q^{85} -5.53372 q^{86} +5.63270i q^{87} +0.542599i q^{88} -6.06313i q^{89} +6.55641 q^{90} -19.8450i q^{91} +0.449633i q^{92} -5.70612i q^{93} +3.80078i q^{94} +7.92848 q^{95} -2.13515i q^{96} -10.2018i q^{97} -20.3322i q^{98} -0.893470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 18 q^{4} - 18 q^{7} + 22 q^{9} - 2 q^{10} + 2 q^{11} - 36 q^{12} + 30 q^{16} - 6 q^{21} - 12 q^{25} - 12 q^{26} + 26 q^{27} + 24 q^{28} - 12 q^{30} - 18 q^{33} + 4 q^{34} - 22 q^{36} + 10 q^{37}+ \cdots - 84 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 - 18 * q^4 - 18 * q^7 + 22 * q^9 - 2 * q^10 + 2 * q^11 - 36 * q^12 + 30 * q^16 - 6 * q^21 - 12 * q^25 - 12 * q^26 + 26 * q^27 + 24 * q^28 - 12 * q^30 - 18 * q^33 + 4 * q^34 - 22 * q^36 + 10 * q^37 + 12 * q^38 + 6 * q^40 - 10 * q^41 + 44 * q^44 - 24 * q^46 + 2 * q^47 + 60 * q^48 + 30 * q^49 - 6 * q^53 - 24 * q^58 + 44 * q^62 - 16 * q^63 - 126 * q^64 + 20 * q^65 + 16 * q^67 - 28 * q^70 + 42 * q^71 - 46 * q^73 + 50 * q^74 - 2 * q^75 + 30 * q^77 + 132 * q^78 - 12 * q^81 - 62 * q^83 - 84 * q^84 - 12 * q^85 - 64 * q^86 - 26 * q^90 + 44 * q^95 - 84 * q^99

Introduction

L-functions

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