LMFDB - Embedded newform 235.2.c.a.189.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [235,2,Mod(189,235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(235, 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("235.189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 235 = 5 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	235.c (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:	$1.87648444750$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			189.16
Character	$\chi$	$=$	235.189
Dual form			235.2.c.a.189.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.29770i q^{2} +2.93223i q^{3} +0.315973 q^{4} +(1.39717 - 1.74583i) q^{5} -3.80515 q^{6} +1.39355i q^{7} +3.00544i q^{8} -5.59794 q^{9} +O(q^{10})$	\(q+1.29770i q^{2} +2.93223i q^{3} +0.315973 q^{4} +(1.39717 - 1.74583i) q^{5} -3.80515 q^{6} +1.39355i q^{7} +3.00544i q^{8} -5.59794 q^{9} +(2.26557 + 1.81310i) q^{10} +1.89487 q^{11} +0.926505i q^{12} -3.25256i q^{13} -1.80841 q^{14} +(5.11917 + 4.09681i) q^{15} -3.26821 q^{16} -6.69374i q^{17} -7.26445i q^{18} -2.33193 q^{19} +(0.441467 - 0.551636i) q^{20} -4.08620 q^{21} +2.45897i q^{22} +1.59282i q^{23} -8.81263 q^{24} +(-1.09585 - 4.87843i) q^{25} +4.22084 q^{26} -7.61776i q^{27} +0.440325i q^{28} +3.02593 q^{29} +(-5.31643 + 6.64315i) q^{30} -5.17742 q^{31} +1.76972i q^{32} +5.55618i q^{33} +8.68647 q^{34} +(2.43290 + 1.94702i) q^{35} -1.76880 q^{36} -6.68877i q^{37} -3.02614i q^{38} +9.53723 q^{39} +(5.24699 + 4.19910i) q^{40} +7.85273 q^{41} -5.30267i q^{42} +7.73676i q^{43} +0.598728 q^{44} +(-7.82126 + 9.77306i) q^{45} -2.06701 q^{46} +1.00000i q^{47} -9.58314i q^{48} +5.05802 q^{49} +(6.33075 - 1.42209i) q^{50} +19.6275 q^{51} -1.02772i q^{52} +12.7095i q^{53} +9.88557 q^{54} +(2.64745 - 3.30812i) q^{55} -4.18823 q^{56} -6.83773i q^{57} +3.92675i q^{58} -1.58640 q^{59} +(1.61752 + 1.29448i) q^{60} -13.4926 q^{61} -6.71874i q^{62} -7.80102i q^{63} -8.83299 q^{64} +(-5.67841 - 4.54436i) q^{65} -7.21026 q^{66} -10.9563i q^{67} -2.11504i q^{68} -4.67052 q^{69} +(-2.52665 + 3.15718i) q^{70} +3.67827 q^{71} -16.8243i q^{72} +15.0486i q^{73} +8.68002 q^{74} +(14.3047 - 3.21328i) q^{75} -0.736826 q^{76} +2.64059i q^{77} +12.3765i q^{78} -3.62442 q^{79} +(-4.56624 + 5.70575i) q^{80} +5.54314 q^{81} +10.1905i q^{82} -11.7569i q^{83} -1.29113 q^{84} +(-11.6861 - 9.35227i) q^{85} -10.0400 q^{86} +8.87270i q^{87} +5.69491i q^{88} +10.8341 q^{89} +(-12.6825 - 10.1497i) q^{90} +4.53260 q^{91} +0.503290i q^{92} -15.1814i q^{93} -1.29770 q^{94} +(-3.25809 + 4.07115i) q^{95} -5.18921 q^{96} +2.02835i q^{97} +6.56379i q^{98} -10.6074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 20 q^{4} - 2 q^{5} - 4 q^{6} - 18 q^{9}+O(q^{10}) $ 22 * q - 20 * q^4 - 2 * q^5 - 4 * q^6 - 18 * q^9	$ 22 q - 20 q^{4} - 2 q^{5} - 4 q^{6} - 18 q^{9} - 2 q^{15} + 24 q^{16} - 12 q^{21} + 24 q^{24} - 6 q^{25} + 12 q^{26} - 8 q^{29} - 10 q^{30} + 4 q^{31} + 32 q^{34} - 12 q^{35} - 16 q^{36} + 20 q^{39} + 14 q^{40} + 8 q^{41} - 48 q^{44} + 6 q^{45} - 32 q^{46} - 10 q^{49} - 20 q^{50} + 24 q^{51} + 52 q^{56} - 14 q^{59} + 34 q^{60} - 14 q^{61} - 48 q^{64} + 14 q^{65} + 24 q^{66} + 4 q^{69} - 18 q^{70} - 34 q^{71} + 32 q^{74} - 32 q^{75} - 20 q^{76} + 26 q^{79} + 28 q^{80} - 50 q^{81} + 8 q^{84} - 6 q^{85} - 12 q^{86} + 74 q^{89} - 58 q^{90} + 64 q^{91} + 8 q^{94} - 52 q^{95} - 12 q^{96} + 16 q^{99}+O(q^{100}) $ 22 * q - 20 * q^4 - 2 * q^5 - 4 * q^6 - 18 * q^9 - 2 * q^15 + 24 * q^16 - 12 * q^21 + 24 * q^24 - 6 * q^25 + 12 * q^26 - 8 * q^29 - 10 * q^30 + 4 * q^31 + 32 * q^34 - 12 * q^35 - 16 * q^36 + 20 * q^39 + 14 * q^40 + 8 * q^41 - 48 * q^44 + 6 * q^45 - 32 * q^46 - 10 * q^49 - 20 * q^50 + 24 * q^51 + 52 * q^56 - 14 * q^59 + 34 * q^60 - 14 * q^61 - 48 * q^64 + 14 * q^65 + 24 * q^66 + 4 * q^69 - 18 * q^70 - 34 * q^71 + 32 * q^74 - 32 * q^75 - 20 * q^76 + 26 * q^79 + 28 * q^80 - 50 * q^81 + 8 * q^84 - 6 * q^85 - 12 * q^86 + 74 * q^89 - 58 * q^90 + 64 * q^91 + 8 * q^94 - 52 * q^95 - 12 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/235\mathbb{Z}\right)^\times$.

$n$	$142$	$146$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.29770i			0.917613i	0.888536	+	0.458806i	$0.151723\pi$
$2$			1.29770i			0.917613i	−0.888536	+	0.458806i	$0.848277\pi$
$3$			2.93223i			1.69292i	0.532452	+	0.846460i	$0.321271\pi$
$3$			2.93223i			1.69292i	−0.532452	+	0.846460i	$0.678729\pi$
$4$	0.315973			0.157987
$5$	1.39717	−	1.74583i	0.624832	−	0.780759i
$5$	1.39717	−	1.74583i	0.624832	−	0.780759i
$6$	−3.80515			−1.55345
$7$			1.39355i			0.526713i	0.964699	+	0.263356i	$0.0848295\pi$
$7$			1.39355i			0.526713i	−0.964699	+	0.263356i	$0.915170\pi$
$8$			3.00544i			1.06258i
$9$	−5.59794			−1.86598
$10$	2.26557	+	1.81310i	0.716435	+	0.573354i
$11$	1.89487			0.571324			0.285662	−	0.958330i	$-0.407787\pi$
$11$	1.89487			0.571324			0.285662	+	0.958330i	$0.407787\pi$
$12$			0.926505i			0.267459i
$13$		−	3.25256i		−	0.902097i	−0.892499	−	0.451048i	$-0.851050\pi$
$13$		−	3.25256i		−	0.902097i	0.892499	−	0.451048i	$-0.148950\pi$
$14$	−1.80841			−0.483318
$15$	5.11917	+	4.09681i	1.32176	+	1.05779i
$16$	−3.26821			−0.817054
$17$		−	6.69374i		−	1.62347i	−0.584026	−	0.811735i	$-0.698524\pi$
$17$		−	6.69374i		−	1.62347i	0.584026	−	0.811735i	$-0.301476\pi$
$18$		−	7.26445i		−	1.71225i
$19$	−2.33193			−0.534981			−0.267490	−	0.963561i	$-0.586194\pi$
$19$	−2.33193			−0.534981			−0.267490	+	0.963561i	$0.586194\pi$
$20$	0.441467	−	0.551636i	0.0987151	−	0.123350i
$21$	−4.08620			−0.891683
$22$			2.45897i			0.524254i
$23$			1.59282i			0.332127i	0.986115	+	0.166063i	$0.0531056\pi$
$23$			1.59282i			0.332127i	−0.986115	+	0.166063i	$0.946894\pi$
$24$	−8.81263			−1.79887
$25$	−1.09585	−	4.87843i	−0.219170	−	0.975687i
$26$	4.22084			0.827776
$27$		−	7.61776i		−	1.46604i
$28$			0.440325i			0.0832136i
$29$	3.02593			0.561901			0.280950	−	0.959722i	$-0.409350\pi$
$29$	3.02593			0.561901			0.280950	+	0.959722i	$0.409350\pi$
$30$	−5.31643	+	6.64315i	−0.970643	+	1.21287i
$31$	−5.17742			−0.929892			−0.464946	−	0.885339i	$-0.653926\pi$
$31$	−5.17742			−0.929892			−0.464946	+	0.885339i	$0.653926\pi$
$32$			1.76972i			0.312845i
$33$			5.55618i			0.967207i
$34$	8.68647			1.48972
$35$	2.43290	+	1.94702i	0.411236	+	0.329107i
$36$	−1.76880			−0.294800
$37$		−	6.68877i		−	1.09963i	−0.835288	−	0.549813i	$-0.814699\pi$
$37$		−	6.68877i		−	1.09963i	0.835288	−	0.549813i	$-0.185301\pi$
$38$		−	3.02614i		−	0.490905i
$39$	9.53723			1.52718
$40$	5.24699	+	4.19910i	0.829622	+	0.663936i
$41$	7.85273			1.22639			0.613195	−	0.789931i	$-0.289884\pi$
$41$	7.85273			1.22639			0.613195	+	0.789931i	$0.289884\pi$
$42$		−	5.30267i		−	0.818220i
$43$			7.73676i			1.17985i	0.807460	+	0.589923i	$0.200842\pi$
$43$			7.73676i			1.17985i	−0.807460	+	0.589923i	$0.799158\pi$
$44$	0.598728			0.0902616
$45$	−7.82126	+	9.77306i	−1.16592	+	1.45688i
$46$	−2.06701			−0.304764
$47$			1.00000i			0.145865i
$47$			1.00000i			0.145865i
$48$		−	9.58314i		−	1.38321i
$49$	5.05802			0.722574
$50$	6.33075	−	1.42209i	0.895303	−	0.201113i
$51$	19.6275			2.74841
$52$		−	1.02772i		−	0.142519i
$53$			12.7095i			1.74578i	0.487918	+	0.872890i	$0.337757\pi$
$53$			12.7095i			1.74578i	−0.487918	+	0.872890i	$0.662243\pi$
$54$	9.88557			1.34526
$55$	2.64745	−	3.30812i	0.356982	−	0.446067i
$56$	−4.18823			−0.559676
$57$		−	6.83773i		−	0.905680i
$58$			3.92675i			0.515607i
$59$	−1.58640			−0.206532			−0.103266	−	0.994654i	$-0.532929\pi$
$59$	−1.58640			−0.206532			−0.103266	+	0.994654i	$0.532929\pi$
$60$	1.61752	+	1.29448i	0.208821	+	0.167117i
$61$	−13.4926			−1.72754			−0.863772	−	0.503882i	$-0.831905\pi$
$61$	−13.4926			−1.72754			−0.863772	+	0.503882i	$0.831905\pi$
$62$		−	6.71874i		−	0.853280i
$63$		−	7.80102i		−	0.982836i
$64$	−8.83299			−1.10412
$65$	−5.67841	−	4.54436i	−0.704321	−	0.563659i
$66$	−7.21026			−0.887521
$67$		−	10.9563i		−	1.33852i	−0.743027	−	0.669261i	$-0.766611\pi$
$67$		−	10.9563i		−	1.33852i	0.743027	−	0.669261i	$-0.233389\pi$
$68$		−	2.11504i		−	0.256487i
$69$	−4.67052			−0.562264
$70$	−2.52665	+	3.15718i	−0.301993	+	0.377355i
$71$	3.67827			0.436530			0.218265	−	0.975890i	$-0.429960\pi$
$71$	3.67827			0.436530			0.218265	+	0.975890i	$0.429960\pi$
$72$		−	16.8243i		−	1.98276i
$73$			15.0486i			1.76130i	0.473764	+	0.880652i	$0.342895\pi$
$73$			15.0486i			1.76130i	−0.473764	+	0.880652i	$0.657105\pi$
$74$	8.68002			1.00903
$75$	14.3047	−	3.21328i	1.65176	−	0.371038i
$76$	−0.736826			−0.0845198
$77$			2.64059i			0.300924i
$78$			12.3765i			1.40136i
$79$	−3.62442			−0.407779			−0.203889	−	0.978994i	$-0.565358\pi$
$79$	−3.62442			−0.407779			−0.203889	+	0.978994i	$0.565358\pi$
$80$	−4.56624	+	5.70575i	−0.510521	+	0.637922i
$81$	5.54314			0.615905
$82$			10.1905i			1.12535i
$83$		−	11.7569i		−	1.29049i	−0.763976	−	0.645245i	$-0.776755\pi$
$83$		−	11.7569i		−	1.29049i	0.763976	−	0.645245i	$-0.223245\pi$
$84$	−1.29113			−0.140874
$85$	−11.6861	−	9.35227i	−1.26754	−	1.01440i
$86$	−10.0400			−1.08264
$87$			8.87270i			0.951253i
$88$			5.69491i			0.607080i
$89$	10.8341			1.14841			0.574207	−	0.818710i	$-0.305310\pi$
$89$	10.8341			1.14841			0.574207	+	0.818710i	$0.305310\pi$
$90$	−12.6825	−	10.1497i	−1.33685	−	1.06987i
$91$	4.53260			0.475146
$92$			0.503290i			0.0524716i
$93$		−	15.1814i		−	1.57423i
$94$	−1.29770			−0.133848
$95$	−3.25809	+	4.07115i	−0.334273	+	0.417691i
$96$	−5.18921			−0.529621
$97$			2.02835i			0.205948i	0.994684	+	0.102974i	$0.0328358\pi$
$97$			2.02835i			0.205948i	−0.994684	+	0.102974i	$0.967164\pi$
$98$			6.56379i			0.663043i
$99$	−10.6074			−1.06608
$100$	−0.346259	−	1.54145i	−0.0346259	−	0.154145i
$101$	10.6122			1.05595			0.527974	−	0.849260i	$-0.322952\pi$
$101$	10.6122			1.05595			0.527974	+	0.849260i	$0.322952\pi$
$102$			25.4707i			2.52197i
$103$		−	13.4740i		−	1.32763i	−0.747896	−	0.663816i	$-0.768936\pi$
$103$		−	13.4740i		−	1.32763i	0.747896	−	0.663816i	$-0.231064\pi$
$104$	9.77536			0.958553
$105$	−5.70911	+	7.13382i	−0.557152	+	0.696190i
$106$	−16.4931			−1.60195
$107$			9.69212i			0.936973i	0.883471	+	0.468486i	$0.155200\pi$
$107$			9.69212i			0.936973i	−0.883471	+	0.468486i	$0.844800\pi$
$108$		−	2.40701i		−	0.231614i
$109$	−4.71780			−0.451884			−0.225942	−	0.974141i	$-0.572546\pi$
$109$	−4.71780			−0.451884			−0.225942	+	0.974141i	$0.572546\pi$
$110$	4.29295	+	3.43559i	0.409316	+	0.327571i
$111$	19.6130			1.86158
$112$		−	4.55442i		−	0.430353i
$113$		−	9.69806i		−	0.912317i	−0.889899	−	0.456158i	$-0.849225\pi$
$113$		−	9.69806i		−	0.912317i	0.889899	−	0.456158i	$-0.150775\pi$
$114$	8.87333			0.831063
$115$	2.78080	+	2.22544i	0.259311	+	0.207523i
$116$	0.956112			0.0887728
$117$			18.2076i			1.68330i
$118$		−	2.05868i		−	0.189517i
$119$	9.32806			0.855102
$120$	−12.3127	+	15.3854i	−1.12399	+	1.40448i
$121$	−7.40948			−0.673589
$122$		−	17.5093i		−	1.58522i
$123$			23.0260i			2.07618i
$124$	−1.63593			−0.146910
$125$	−10.0480	−	4.90282i	−0.898721	−	0.438521i
$126$	10.1234			0.901863
$127$		−	6.34822i		−	0.563313i	−0.959515	−	0.281657i	$-0.909116\pi$
$127$		−	6.34822i		−	0.563313i	0.959515	−	0.281657i	$-0.0908839\pi$
$128$		−	7.92314i		−	0.700314i
$129$	−22.6859			−1.99738
$130$	5.89722	−	7.36888i	0.517221	−	0.646294i
$131$	−5.52549			−0.482764			−0.241382	−	0.970430i	$-0.577601\pi$
$131$	−5.52549			−0.482764			−0.241382	+	0.970430i	$0.577601\pi$
$132$			1.75560i			0.152806i
$133$		−	3.24966i		−	0.281781i
$134$	14.2180			1.22825
$135$	−13.2993	−	10.6433i	−1.14462	−	0.916027i
$136$	20.1176			1.72507
$137$		−	9.99304i		−	0.853763i	−0.904308	−	0.426881i	$-0.859612\pi$
$137$		−	9.99304i		−	0.853763i	0.904308	−	0.426881i	$-0.140388\pi$
$138$		−	6.06093i		−	0.515941i
$139$	−12.9575			−1.09904			−0.549520	−	0.835480i	$-0.685190\pi$
$139$	−12.9575			−1.09904			−0.549520	+	0.835480i	$0.685190\pi$
$140$	0.768733	+	0.615207i	0.0649698	+	0.0519945i
$141$	−2.93223			−0.246938
$142$			4.77329i			0.400566i
$143$		−	6.16316i		−	0.515390i
$144$	18.2953			1.52461
$145$	4.22773	−	5.28276i	0.351094	−	0.438709i
$146$	−19.5286			−1.61620
$147$			14.8312i			1.22326i
$148$		−	2.11347i		−	0.173726i
$149$	−12.5053			−1.02447			−0.512235	−	0.858845i	$-0.671182\pi$
$149$	−12.5053			−1.02447			−0.512235	+	0.858845i	$0.671182\pi$
$150$	4.16987	+	18.5632i	0.340469	+	1.51568i
$151$	−15.3584			−1.24985			−0.624925	−	0.780685i	$-0.714871\pi$
$151$	−15.3584			−1.24985			−0.624925	+	0.780685i	$0.714871\pi$
$152$		−	7.00846i		−	0.568461i
$153$			37.4712i			3.02936i
$154$	−3.42670			−0.276131
$155$	−7.23371	+	9.03889i	−0.581026	+	0.726021i
$156$	3.01351			0.241274
$157$		−	0.665889i		−	0.0531437i	−0.999647	−	0.0265719i	$-0.991541\pi$
$157$		−	0.665889i		−	0.0531437i	0.999647	−	0.0265719i	$-0.00845908\pi$
$158$		−	4.70341i		−	0.374183i
$159$	−37.2670			−2.95547
$160$	3.08963	+	2.47259i	0.244256	+	0.195475i
$161$	−2.21968			−0.174935
$162$			7.19334i			0.565162i
$163$			12.5178i			0.980469i	0.871590	+	0.490235i	$0.163089\pi$
$163$			12.5178i			0.980469i	−0.871590	+	0.490235i	$0.836911\pi$
$164$	2.48125			0.193753
$165$	9.70015	+	7.76291i	0.755155	+	0.604342i
$166$	15.2570			1.18417
$167$		−	8.29432i		−	0.641833i	−0.947107	−	0.320917i	$-0.896009\pi$
$167$		−	8.29432i		−	0.641833i	0.947107	−	0.320917i	$-0.103991\pi$
$168$		−	12.2808i		−	0.947488i
$169$	2.42087			0.186221
$170$	12.1364	−	15.1651i	0.930822	−	1.16311i
$171$	13.0540			0.998264
$172$			2.44461i			0.186400i
$173$		−	7.03257i		−	0.534677i	−0.963603	−	0.267338i	$-0.913856\pi$
$173$		−	7.03257i		−	0.534677i	0.963603	−	0.267338i	$-0.0861441\pi$
$174$	−11.5141			−0.872882
$175$	6.79835	−	1.52712i	0.513907	−	0.115440i
$176$	−6.19283			−0.466802
$177$		−	4.65169i		−	0.349643i
$178$			14.0594i			1.05380i
$179$	20.5145			1.53333			0.766664	−	0.642048i	$-0.221915\pi$
$179$	20.5145			1.53333			0.766664	+	0.642048i	$0.221915\pi$
$180$	−2.47131	+	3.08803i	−0.184201	+	0.230168i
$181$	7.06632			0.525236			0.262618	−	0.964900i	$-0.415414\pi$
$181$	7.06632			0.525236			0.262618	+	0.964900i	$0.415414\pi$
$182$			5.88196i			0.436000i
$183$		−	39.5632i		−	2.92460i
$184$	−4.78714			−0.352912
$185$	−11.6775	−	9.34532i	−0.858544	−	0.687082i
$186$	19.7008			1.44454
$187$		−	12.6837i		−	0.927527i
$188$			0.315973i			0.0230447i
$189$	10.6157			0.772181
$190$	−5.28313	−	4.22802i	−0.383279	−	0.306733i
$191$	−26.3516			−1.90673			−0.953366	−	0.301816i	$-0.902407\pi$
$191$	−26.3516			−1.90673			−0.953366	+	0.301816i	$0.902407\pi$
$192$		−	25.9003i		−	1.86919i
$193$			17.1011i			1.23097i	0.788150	+	0.615483i	$0.211039\pi$
$193$			17.1011i			1.23097i	−0.788150	+	0.615483i	$0.788961\pi$
$194$	−2.63219			−0.188980
$195$	13.3251	−	16.6504i	0.954230	−	1.19236i
$196$	1.59820			0.114157
$197$			16.2855i			1.16029i	0.814512	+	0.580147i	$0.197005\pi$
$197$			16.2855i			1.16029i	−0.814512	+	0.580147i	$0.802995\pi$
$198$		−	13.7652i		−	0.978249i
$199$	3.59169			0.254608			0.127304	−	0.991864i	$-0.459368\pi$
$199$	3.59169			0.254608			0.127304	+	0.991864i	$0.459368\pi$
$200$	14.6618	−	3.29351i	1.03675	−	0.232886i
$201$	32.1263			2.26601
$202$			13.7714i			0.968952i
$203$			4.21678i			0.295960i
$204$	6.20178			0.434211
$205$	10.9716	−	13.7095i	0.766288	−	0.957516i
$206$	17.4852			1.21825
$207$		−	8.91654i		−	0.619742i
$208$			10.6301i			0.737062i
$209$	−4.41869			−0.305647
$210$	−9.25756	−	7.40871i	−0.638833	−	0.511250i
$211$	19.8861			1.36901			0.684507	−	0.729006i	$-0.260017\pi$
$211$	19.8861			1.36901			0.684507	+	0.729006i	$0.260017\pi$
$212$			4.01585i			0.275810i
$213$			10.7855i			0.739011i
$214$	−12.5775			−0.859778
$215$	13.5071	+	10.8095i	0.921175	+	0.737205i
$216$	22.8947			1.55779
$217$		−	7.21499i		−	0.489786i
$218$		−	6.12230i		−	0.414654i
$219$	−44.1258			−2.98175
$220$	0.836522	−	1.04528i	0.0563983	−	0.0704726i
$221$	−21.7718			−1.46453
$222$			25.4518i			1.70821i
$223$			0.488216i			0.0326934i	0.999866	+	0.0163467i	$0.00520354\pi$
$223$			0.488216i			0.0326934i	−0.999866	+	0.0163467i	$0.994796\pi$
$224$	−2.46619			−0.164779
$225$	6.13451	+	27.3092i	0.408967	+	1.82061i
$226$	12.5852			0.837153
$227$			5.47647i			0.363486i	0.983346	+	0.181743i	$0.0581739\pi$
$227$			5.47647i			0.363486i	−0.983346	+	0.181743i	$0.941826\pi$
$228$		−	2.16054i		−	0.143085i
$229$	27.9525			1.84715			0.923577	−	0.383413i	$-0.125252\pi$
$229$	27.9525			1.84715			0.923577	+	0.383413i	$0.125252\pi$
$230$	−2.88796	+	3.60865i	−0.190426	+	0.237947i
$231$	−7.74282			−0.509440
$232$			9.09424i			0.597066i
$233$			7.33594i			0.480593i	0.970699	+	0.240297i	$0.0772447\pi$
$233$			7.33594i			0.480593i	−0.970699	+	0.240297i	$0.922755\pi$
$234$	−23.6281			−1.54461
$235$	1.74583	+	1.39717i	0.113885	+	0.0911411i
$236$	−0.501261			−0.0326293
$237$		−	10.6276i		−	0.690337i
$238$			12.1050i			0.784653i
$239$	−16.6997			−1.08022			−0.540108	−	0.841596i	$-0.681617\pi$
$239$	−16.6997			−1.08022			−0.540108	+	0.841596i	$0.681617\pi$
$240$	−16.7305	−	13.3892i	−1.07995	−	0.864272i
$241$	−14.4137			−0.928469			−0.464235	−	0.885712i	$-0.653671\pi$
$241$	−14.4137			−0.928469			−0.464235	+	0.885712i	$0.653671\pi$
$242$		−	9.61528i		−	0.618094i
$243$		−	6.59952i		−	0.423360i
$244$	−4.26329			−0.272929
$245$	7.06689	−	8.83044i	0.451487	−	0.564156i
$246$	−29.8808			−1.90513
$247$			7.58472i			0.482604i
$248$		−	15.5604i		−	0.988087i
$249$	34.4739			2.18470
$250$	6.36239	−	13.0393i	0.402393	−	0.824678i
$251$	−5.87354			−0.370734			−0.185367	−	0.982669i	$-0.559347\pi$
$251$	−5.87354			−0.370734			−0.185367	+	0.982669i	$0.559347\pi$
$252$		−	2.46491i		−	0.155275i
$253$			3.01819i			0.189752i
$254$	8.23809			0.516904
$255$	27.4229	−	34.2664i	1.71729	−	2.14584i
$256$	−7.38411			−0.461507
$257$			25.4666i			1.58856i	0.607550	+	0.794281i	$0.292152\pi$
$257$			25.4666i			1.58856i	−0.607550	+	0.794281i	$0.707848\pi$
$258$		−	29.4395i		−	1.83283i
$259$	9.32114			0.579187
$260$	−1.79423	−	1.43590i	−0.111273	−	0.0890506i
$261$	−16.9390			−1.04850
$262$		−	7.17043i		−	0.442991i
$263$		−	5.72971i		−	0.353309i	−0.984273	−	0.176654i	$-0.943472\pi$
$263$		−	5.72971i		−	0.353309i	0.984273	−	0.176654i	$-0.0565275\pi$
$264$	−16.6988			−1.02774
$265$	22.1886	+	17.7572i	1.36303	+	1.09082i
$266$	4.21708			0.258566
$267$			31.7681i			1.94417i
$268$		−	3.46189i		−	0.211469i
$269$	13.4490			0.820002			0.410001	−	0.912085i	$-0.365528\pi$
$269$	13.4490			0.820002			0.410001	+	0.912085i	$0.365528\pi$
$270$	13.8118	−	17.2585i	0.840558	−	1.05032i
$271$	−11.6192			−0.705819			−0.352909	−	0.935657i	$-0.614808\pi$
$271$	−11.6192			−0.705819			−0.352909	+	0.935657i	$0.614808\pi$
$272$			21.8766i			1.32646i
$273$			13.2906i			0.804384i
$274$	12.9680			0.783424
$275$	−2.07649	−	9.24399i	−0.125217	−	0.557433i
$276$	−1.47576			−0.0888303
$277$		−	4.74524i		−	0.285114i	−0.989787	−	0.142557i	$-0.954468\pi$
$277$		−	4.74524i		−	0.285114i	0.989787	−	0.142557i	$-0.0455324\pi$
$278$		−	16.8150i		−	1.00849i
$279$	28.9829			1.73516
$280$	−5.85166	+	7.31195i	−0.349704	+	0.436972i
$281$	−11.6347			−0.694066			−0.347033	−	0.937853i	$-0.612811\pi$
$281$	−11.6347			−0.694066			−0.347033	+	0.937853i	$0.612811\pi$
$282$		−	3.80515i		−	0.226593i
$283$		−	29.1989i		−	1.73569i	−0.496831	−	0.867847i	$-0.665503\pi$
$283$		−	29.1989i		−	1.73569i	0.496831	−	0.867847i	$-0.334497\pi$
$284$	1.16223			0.0689659
$285$	−11.9375	−	9.55345i	−0.707118	−	0.565898i
$286$	7.99794			0.472928
$287$			10.9432i			0.645956i
$288$		−	9.90677i		−	0.583762i
$289$	−27.8061			−1.63565
$290$	6.85544	+	5.48632i	0.402565	+	0.322168i
$291$	−5.94758			−0.348653
$292$			4.75495i			0.278263i
$293$		−	20.8312i		−	1.21697i	−0.793565	−	0.608485i	$-0.791778\pi$
$293$		−	20.8312i		−	1.21697i	0.793565	−	0.608485i	$-0.208222\pi$
$294$	−19.2465			−1.12248
$295$	−2.21647	+	2.76959i	−0.129048	+	0.161252i
$296$	20.1027			1.16844
$297$		−	14.4346i		−	0.837583i
$298$		−	16.2281i		−	0.940068i
$299$	5.18075			0.299611
$300$	4.51989	−	1.01531i	0.260956	−	0.0586190i
$301$	−10.7816			−0.621439
$302$		−	19.9306i		−	1.14688i
$303$			31.1172i			1.78764i
$304$	7.62123			0.437108
$305$	−18.8514	+	23.5557i	−1.07943	+	1.34880i
$306$	−48.6263			−2.77978
$307$			26.9005i			1.53529i	0.640873	+	0.767647i	$0.278573\pi$
$307$			26.9005i			1.53529i	−0.640873	+	0.767647i	$0.721427\pi$
$308$			0.834357i			0.0475419i
$309$	39.5088			2.24758
$310$	−11.7298	−	9.38720i	−0.666207	−	0.533157i
$311$	17.3804			0.985552			0.492776	−	0.870156i	$-0.335982\pi$
$311$	17.3804			0.985552			0.492776	+	0.870156i	$0.335982\pi$
$312$			28.6636i			1.62275i
$313$			3.45677i			0.195388i	0.995216	+	0.0976942i	$0.0311467\pi$
$313$			3.45677i			0.195388i	−0.995216	+	0.0976942i	$0.968853\pi$
$314$	0.864125			0.0487654
$315$	−13.6193	−	10.8993i	−0.767358	−	0.614107i
$316$	−1.14522			−0.0644236
$317$		−	8.80669i		−	0.494633i	−0.968935	−	0.247317i	$-0.920451\pi$
$317$		−	8.80669i		−	0.494633i	0.968935	−	0.247317i	$-0.0795488\pi$
$318$		−	48.3614i		−	2.71197i
$319$	5.73373			0.321027
$320$	−12.3412	+	15.4209i	−0.689892	+	0.862055i
$321$	−28.4195			−1.58622
$322$		−	2.88048i		−	0.160523i
$323$			15.6093i			0.868525i
$324$	1.75149			0.0973048
$325$	−15.8674	+	3.56432i	−0.880164	+	0.197713i
$326$	−16.2443			−0.899691
$327$		−	13.8337i		−	0.765003i
$328$			23.6009i			1.30314i
$329$	−1.39355			−0.0768289
$330$	−10.0739	+	12.5879i	−0.554552	+	0.692940i
$331$	17.0896			0.939329			0.469664	−	0.882845i	$-0.344375\pi$
$331$	17.0896			0.939329			0.469664	+	0.882845i	$0.344375\pi$
$332$		−	3.71487i		−	0.203880i
$333$			37.4433i			2.05188i
$334$	10.7635			0.588955
$335$	−19.1278	−	15.3078i	−1.04506	−	0.836352i
$336$	13.3546			0.728553
$337$		−	10.1947i		−	0.555342i	−0.960676	−	0.277671i	$-0.910437\pi$
$337$		−	10.1947i		−	0.555342i	0.960676	−	0.277671i	$-0.0895625\pi$
$338$			3.14157i			0.170879i
$339$	28.4369			1.54448
$340$	−3.69251	−	2.95507i	−0.200254	−	0.160261i
$341$	−9.81052			−0.531269
$342$			16.9402i			0.916020i
$343$			16.8035i			0.907301i
$344$	−23.2524			−1.25368
$345$	−6.52549	+	8.15394i	−0.351321	+	0.438993i
$346$	9.12617			0.490626
$347$			23.9156i			1.28386i	0.766764	+	0.641929i	$0.221866\pi$
$347$			23.9156i			1.28386i	−0.766764	+	0.641929i	$0.778134\pi$
$348$			2.80354i			0.150285i
$349$	12.3584			0.661531			0.330765	−	0.943713i	$-0.392693\pi$
$349$	12.3584			0.661531			0.330765	+	0.943713i	$0.392693\pi$
$350$	1.98175	+	8.82222i	0.105929	+	0.471567i
$351$	−24.7772			−1.32251
$352$			3.35338i			0.178736i
$353$			2.25458i			0.119999i	0.998198	+	0.0599996i	$0.0191100\pi$
$353$			2.25458i			0.119999i	−0.998198	+	0.0599996i	$0.980890\pi$
$354$	6.03650			0.320837
$355$	5.13915	−	6.42163i	0.272758	−	0.340825i
$356$	3.42329			0.181434
$357$			27.3520i			1.44762i
$358$			26.6217i			1.40700i
$359$	−21.5837			−1.13914			−0.569571	−	0.821942i	$-0.692891\pi$
$359$	−21.5837			−1.13914			−0.569571	+	0.821942i	$0.692891\pi$
$360$	−29.3724	−	23.5063i	−1.54806	−	1.23889i
$361$	−13.5621			−0.713796
$362$			9.16997i			0.481963i
$363$		−	21.7263i		−	1.14033i
$364$	1.43218			0.0750667
$365$	26.2723	+	21.0254i	1.37515	+	1.10052i
$366$	51.3412			2.68365
$367$			15.0318i			0.784654i	0.919826	+	0.392327i	$0.128330\pi$
$367$			15.0318i			0.784654i	−0.919826	+	0.392327i	$0.871670\pi$
$368$		−	5.20569i		−	0.271365i
$369$	−43.9592			−2.28842
$370$	12.1274	−	15.1538i	0.630475	−	0.787811i
$371$	−17.7113			−0.919524
$372$		−	4.79690i		−	0.248708i
$373$			6.05672i			0.313605i	0.987630	+	0.156803i	$0.0501186\pi$
$373$			6.05672i			0.313605i	−0.987630	+	0.156803i	$0.949881\pi$
$374$	16.4597			0.851111
$375$	14.3762	−	29.4630i	0.742382	−	1.52146i
$376$	−3.00544			−0.154994
$377$		−	9.84200i		−	0.506889i
$378$			13.7760i			0.708563i
$379$	11.6087			0.596297			0.298148	−	0.954520i	$-0.403631\pi$
$379$	11.6087			0.596297			0.298148	+	0.954520i	$0.403631\pi$
$380$	−1.02947	+	1.28637i	−0.0528107	+	0.0659896i
$381$	18.6144			0.953645
$382$		−	34.1964i		−	1.74964i
$383$			20.8061i			1.06314i	0.847013	+	0.531572i	$0.178399\pi$
$383$			20.8061i			1.06314i	−0.847013	+	0.531572i	$0.821601\pi$
$384$	23.2324			1.18558
$385$	4.61003	+	3.68935i	0.234949	+	0.188027i
$386$	−22.1921			−1.12955
$387$		−	43.3100i		−	2.20157i
$388$			0.640905i			0.0325370i
$389$	13.4090			0.679866			0.339933	−	0.940450i	$-0.389596\pi$
$389$	13.4090			0.679866			0.339933	+	0.940450i	$0.389596\pi$
$390$	21.6072	+	17.2920i	1.09412	+	0.875614i
$391$	10.6619			0.539198
$392$			15.2016i			0.767795i
$393$		−	16.2020i		−	0.817282i
$394$	−21.1337			−1.06470
$395$	−5.06392	+	6.32762i	−0.254793	+	0.318377i
$396$	−3.35164			−0.168426
$397$			7.17418i			0.360062i	0.983661	+	0.180031i	$0.0576198\pi$
$397$			7.17418i			0.360062i	−0.983661	+	0.180031i	$0.942380\pi$
$398$			4.66093i			0.233632i
$399$	9.52873			0.477033
$400$	3.58147	+	15.9438i	0.179074	+	0.797188i
$401$	−22.4252			−1.11986			−0.559931	−	0.828539i	$-0.689172\pi$
$401$	−22.4252			−1.11986			−0.559931	+	0.828539i	$0.689172\pi$
$402$			41.6903i			2.07932i
$403$			16.8398i			0.838852i
$404$	3.35316			0.166826
$405$	7.74470	−	9.67739i	0.384837	−	0.480873i
$406$	−5.47212			−0.271577
$407$		−	12.6743i		−	0.628243i
$408$			58.9894i			2.92041i
$409$	−7.18162			−0.355108			−0.177554	−	0.984111i	$-0.556818\pi$
$409$	−7.18162			−0.355108			−0.177554	+	0.984111i	$0.556818\pi$
$410$	17.7909	+	14.2378i	0.878629	+	0.703156i
$411$	29.3018			1.44535
$412$		−	4.25742i		−	0.209748i
$413$		−	2.21073i		−	0.108783i
$414$	11.5710			0.568684
$415$	−20.5256	−	16.4264i	−1.00756	−	0.806339i
$416$	5.75610			0.282216
$417$		−	37.9943i		−	1.86059i
$418$		−	5.73414i		−	0.280466i
$419$	32.9500			1.60971			0.804857	−	0.593469i	$-0.202242\pi$
$419$	32.9500			1.60971			0.804857	+	0.593469i	$0.202242\pi$
$420$	−1.80393	+	2.25410i	−0.0880226	+	0.109989i
$421$	2.55607			0.124575			0.0622876	−	0.998058i	$-0.480160\pi$
$421$	2.55607			0.124575			0.0622876	+	0.998058i	$0.480160\pi$
$422$			25.8062i			1.25623i
$423$		−	5.59794i		−	0.272181i
$424$	−38.1975			−1.85504
$425$	−32.6549	+	7.33533i	−1.58400	+	0.355816i
$426$	−13.9964			−0.678126
$427$		−	18.8026i		−	0.909920i
$428$			3.06245i			0.148029i
$429$	18.0718			0.872514
$430$	−14.0276	+	17.5281i	−0.676469	+	0.845282i
$431$	0.389062			0.0187405			0.00937023	−	0.999956i	$-0.497017\pi$
$431$	0.389062			0.0187405			0.00937023	+	0.999956i	$0.497017\pi$
$432$			24.8965i			1.19783i
$433$		−	18.1300i		−	0.871273i	−0.900123	−	0.435637i	$-0.856523\pi$
$433$		−	18.1300i		−	0.871273i	0.900123	−	0.435637i	$-0.143477\pi$
$434$	9.36290			0.449434
$435$	15.4902	+	12.3966i	0.742700	+	0.594374i
$436$	−1.49070			−0.0713916
$437$		−	3.71435i		−	0.177681i
$438$		−	57.2621i		−	2.73609i
$439$	−4.40463			−0.210222			−0.105111	−	0.994461i	$-0.533520\pi$
$439$	−4.40463			−0.210222			−0.105111	+	0.994461i	$0.533520\pi$
$440$	9.94235	+	7.95674i	0.473983	+	0.379323i
$441$	−28.3145			−1.34831
$442$		−	28.2532i		−	1.34387i
$443$			14.4495i			0.686515i	0.939241	+	0.343257i	$0.111530\pi$
$443$			14.4495i			0.686515i	−0.939241	+	0.343257i	$0.888470\pi$
$444$	6.19717			0.294105
$445$	15.1371	−	18.9145i	0.717566	−	0.896635i
$446$	−0.633558			−0.0299999
$447$		−	36.6682i		−	1.73435i
$448$		−	12.3092i		−	0.581556i
$449$	29.9345			1.41270			0.706349	−	0.707864i	$-0.250341\pi$
$449$	29.9345			1.41270			0.706349	+	0.707864i	$0.250341\pi$
$450$	−35.4392	+	7.96076i	−1.67062	+	0.375274i
$451$	14.8799			0.700667
$452$		−	3.06433i		−	0.144134i
$453$		−	45.0343i		−	2.11590i
$454$	−7.10681			−0.333539
$455$	6.33280	−	7.91316i	0.296886	−	0.370975i
$456$	20.5504			0.962360
$457$			5.87957i			0.275035i	0.990499	+	0.137517i	$0.0439123\pi$
$457$			5.87957i			0.275035i	−0.990499	+	0.137517i	$0.956088\pi$
$458$			36.2740i			1.69497i
$459$	−50.9913			−2.38007
$460$	0.878659	+	0.703180i	0.0409677	+	0.0327859i
$461$	6.69236			0.311694			0.155847	−	0.987781i	$-0.450189\pi$
$461$	6.69236			0.311694			0.155847	+	0.987781i	$0.450189\pi$
$462$		−	10.0479i		−	0.467469i
$463$		−	0.108136i		−	0.00502551i	−0.999997	−	0.00251275i	$-0.999200\pi$
$463$		−	0.108136i		−	0.00502551i	0.999997	−	0.00251275i	$-0.000799835\pi$
$464$	−9.88938			−0.459103
$465$	−26.5041	−	21.2109i	−1.22910	−	0.983631i
$466$	−9.51985			−0.440999
$467$		−	12.7113i		−	0.588209i	−0.955773	−	0.294104i	$-0.904979\pi$
$467$		−	12.7113i		−	0.588209i	0.955773	−	0.294104i	$-0.0950213\pi$
$468$			5.75313i			0.265938i
$469$	15.2681			0.705017
$470$	−1.81310	+	2.26557i	−0.0836323	+	0.104503i
$471$	1.95254			0.0899681
$472$		−	4.76784i		−	0.219458i
$473$			14.6601i			0.674074i
$474$	13.7915			0.633462
$475$	2.55544	+	11.3761i	0.117252	+	0.521973i
$476$	2.94742			0.135095
$477$		−	71.1469i		−	3.25759i
$478$		−	21.6712i		−	0.991220i
$479$	−21.0716			−0.962787			−0.481394	−	0.876505i	$-0.659869\pi$
$479$	−21.0716			−0.962787			−0.481394	+	0.876505i	$0.659869\pi$
$480$	−7.25019	+	9.05948i	−0.330924	+	0.413507i
$481$	−21.7556			−0.991970
$482$		−	18.7047i		−	0.851975i
$483$		−	6.50861i		−	0.296152i
$484$	−2.34120			−0.106418
$485$	3.54116	+	2.83394i	0.160796	+	0.128683i
$486$	8.56420			0.388480
$487$		−	3.53445i		−	0.160161i	−0.996788	−	0.0800805i	$-0.974482\pi$
$487$		−	3.53445i		−	0.160161i	0.996788	−	0.0800805i	$-0.0255177\pi$
$488$		−	40.5511i		−	1.83566i
$489$	−36.7050			−1.65986
$490$	11.4593	+	9.17071i	0.517677	+	0.414290i
$491$	4.77004			0.215269			0.107634	−	0.994191i	$-0.465672\pi$
$491$	4.77004			0.215269			0.107634	+	0.994191i	$0.465672\pi$
$492$			7.27560i			0.328009i
$493$		−	20.2548i		−	0.912229i
$494$	−9.84270			−0.442844
$495$	−14.8203	+	18.5187i	−0.666121	+	0.832352i
$496$	16.9209			0.759771
$497$			5.12585i			0.229926i
$498$			44.7368i			2.00471i
$499$	−6.63631			−0.297082			−0.148541	−	0.988906i	$-0.547458\pi$
$499$	−6.63631			−0.297082			−0.148541	+	0.988906i	$0.547458\pi$
$500$	−3.17490	−	1.54916i	−0.141986	−	0.0692805i
$501$	24.3208			1.08657
$502$		−	7.62209i		−	0.340191i
$503$		−	15.0437i		−	0.670767i	−0.942082	−	0.335384i	$-0.891134\pi$
$503$		−	15.0437i		−	0.670767i	0.942082	−	0.335384i	$-0.108866\pi$
$504$	23.4455			1.04435
$505$	14.8269	−	18.5270i	0.659790	−	0.824442i
$506$	−3.91671			−0.174119
$507$			7.09855i			0.315258i
$508$		−	2.00587i		−	0.0889960i
$509$	−26.1240			−1.15793			−0.578963	−	0.815354i	$-0.696542\pi$
$509$	−26.1240			−1.15793			−0.578963	+	0.815354i	$0.696542\pi$
$510$	44.4675	+	35.5868i	1.96905	+	1.57581i
$511$	−20.9710			−0.927701
$512$		−	25.4287i		−	1.12380i
$513$			17.7640i			0.784302i
$514$	−33.0480			−1.45769
$515$	−23.5233	−	18.8254i	−1.03656	−	0.829547i
$516$	−7.16815			−0.315560
$517$			1.89487i			0.0833362i
$518$			12.0960i			0.531470i
$519$	20.6211			0.905165
$520$	13.6578	−	17.0661i	0.598935	−	0.748399i
$521$	12.6034			0.552167			0.276084	−	0.961134i	$-0.410963\pi$
$521$	12.6034			0.552167			0.276084	+	0.961134i	$0.410963\pi$
$522$		−	21.9817i		−	0.962114i
$523$		−	33.0171i		−	1.44374i	−0.692029	−	0.721869i	$-0.743283\pi$
$523$		−	33.0171i		−	1.44374i	0.692029	−	0.721869i	$-0.256717\pi$
$524$	−1.74591			−0.0762703
$525$	4.47787	+	19.9343i	0.195430	+	0.870003i
$526$	7.43544			0.324201
$527$			34.6563i			1.50965i
$528$		−	18.1588i		−	0.790260i
$529$	20.4629			0.889692
$530$	−23.0436	+	28.7941i	−1.00095	+	1.25074i
$531$	8.88060			0.385385
$532$		−	1.02681i		−	0.0445176i
$533$		−	25.5415i		−	1.10632i
$534$	−41.2254			−1.78400
$535$	16.9208	+	13.5415i	0.731550	+	0.585451i
$536$	32.9284			1.42229
$537$			60.1533i			2.59580i
$538$			17.4528i			0.752445i
$539$	9.58427			0.412824
$540$	−4.20223	−	3.36299i	−0.180835	−	0.144720i
$541$	27.6119			1.18713			0.593565	−	0.804786i	$-0.297720\pi$
$541$	27.6119			1.18713			0.593565	+	0.804786i	$0.297720\pi$
$542$		−	15.0783i		−	0.647668i
$543$			20.7201i			0.889183i
$544$	11.8460			0.507894
$545$	−6.59156	+	8.23649i	−0.282351	+	0.352812i
$546$	−17.2472			−0.738114
$547$			8.86100i			0.378869i	0.981893	+	0.189435i	$0.0606655\pi$
$547$			8.86100i			0.378869i	−0.981893	+	0.189435i	$0.939335\pi$
$548$		−	3.15753i		−	0.134883i
$549$	75.5306			3.22357
$550$	11.9959	−	2.69466i	0.511508	−	0.114901i
$551$	−7.05624			−0.300606
$552$		−	14.0370i		−	0.597453i
$553$		−	5.05081i		−	0.214782i
$554$	6.15790			0.261624
$555$	27.4026	−	34.2409i	1.16318	−	1.45345i
$556$	−4.09422			−0.173634
$557$			31.3684i			1.32912i	0.747234	+	0.664561i	$0.231381\pi$
$557$			31.3684i			1.32912i	−0.747234	+	0.664561i	$0.768619\pi$
$558$			37.6111i			1.59221i
$559$	25.1643			1.06433
$560$	−7.95125	−	6.36329i	−0.336002	−	0.268898i
$561$	37.1916			1.57023
$562$		−	15.0983i		−	0.636884i
$563$			24.1623i			1.01832i	0.860672	+	0.509160i	$0.170044\pi$
$563$			24.1623i			1.01832i	−0.860672	+	0.509160i	$0.829956\pi$
$564$	−0.926505			−0.0390129
$565$	−16.9312	−	13.5498i	−0.712300	−	0.570045i
$566$	37.8914			1.59270
$567$			7.72465i			0.324405i
$568$			11.0548i			0.463850i
$569$	−5.01744			−0.210342			−0.105171	−	0.994454i	$-0.533539\pi$
$569$	−5.01744			−0.210342			−0.105171	+	0.994454i	$0.533539\pi$
$570$	12.3975	−	15.4913i	0.519275	−	0.648860i
$571$	26.7388			1.11898			0.559491	−	0.828836i	$-0.310997\pi$
$571$	26.7388			1.11898			0.559491	+	0.828836i	$0.310997\pi$
$572$		−	1.94740i		−	0.0814247i
$573$		−	77.2687i		−	3.22795i
$574$	−14.2010			−0.592737
$575$	7.77049	−	1.74550i	0.324052	−	0.0727922i
$576$	49.4466			2.06027
$577$		−	6.92070i		−	0.288113i	−0.989569	−	0.144056i	$-0.953985\pi$
$577$		−	6.92070i		−	0.288113i	0.989569	−	0.144056i	$-0.0460146\pi$
$578$		−	36.0840i		−	1.50090i
$579$	−50.1444			−2.08393
$580$	1.33585	−	1.66921i	0.0554681	−	0.0693102i
$581$	16.3839			0.679717
$582$		−	7.71818i		−	0.319929i
$583$			24.0828i			0.997406i
$584$	−45.2276			−1.87153
$585$	31.7874	+	25.4391i	1.31425	+	1.05178i
$586$	27.0326			1.11671
$587$			46.4635i			1.91775i	0.283822	+	0.958877i	$0.408398\pi$
$587$			46.4635i			1.91775i	−0.283822	+	0.958877i	$0.591602\pi$
$588$			4.68628i			0.193259i
$589$	12.0734			0.497474
$590$	−3.59410	−	2.87631i	−0.147967	−	0.118416i
$591$	−47.7527			−1.96428
$592$			21.8603i			0.898454i
$593$		−	32.1098i		−	1.31859i	−0.751884	−	0.659295i	$-0.770855\pi$
$593$		−	32.1098i		−	1.31859i	0.751884	−	0.659295i	$-0.229145\pi$
$594$	18.7318			0.768577
$595$	13.0329	−	16.2852i	0.534295	−	0.667629i
$596$	−3.95133			−0.161853
$597$			10.5316i			0.431031i
$598$			6.72306i			0.274926i
$599$	3.11099			0.127112			0.0635558	−	0.997978i	$-0.479756\pi$
$599$	3.11099			0.127112			0.0635558	+	0.997978i	$0.479756\pi$
$600$	9.65732	+	42.9918i	0.394258	+	1.75513i
$601$	2.48083			0.101195			0.0505975	−	0.998719i	$-0.483887\pi$
$601$	2.48083			0.101195			0.0505975	+	0.998719i	$0.483887\pi$
$602$		−	13.9912i		−	0.570241i
$603$			61.3326i			2.49766i
$604$	−4.85285			−0.197460
$605$	−10.3523	+	12.9357i	−0.420880	+	0.525911i
$606$	−40.3808			−1.64036
$607$		−	37.9571i		−	1.54063i	−0.637664	−	0.770315i	$-0.720099\pi$
$607$		−	37.9571i		−	1.54063i	0.637664	−	0.770315i	$-0.279901\pi$
$608$		−	4.12685i		−	0.167366i
$609$	−12.3646			−0.501037
$610$	−30.5683	−	24.4634i	−1.23767	−	0.990494i
$611$	3.25256			0.131584
$612$			11.8399i			0.478599i
$613$			29.1282i			1.17648i	0.808687	+	0.588239i	$0.200178\pi$
$613$			29.1282i			1.17648i	−0.808687	+	0.588239i	$0.799822\pi$
$614$	−34.9088			−1.40881
$615$	40.1995	+	32.1711i	1.62100	+	1.29727i
$616$	−7.93615			−0.319757
$617$			7.32433i			0.294866i	0.989072	+	0.147433i	$0.0471011\pi$
$617$			7.32433i			0.294866i	−0.989072	+	0.147433i	$0.952899\pi$
$618$			51.2706i			2.06240i
$619$	−2.53651			−0.101951			−0.0509755	−	0.998700i	$-0.516233\pi$
$619$	−2.53651			−0.101951			−0.0509755	+	0.998700i	$0.516233\pi$
$620$	−2.28566	+	2.85605i	−0.0917943	+	0.114702i
$621$	12.1337			0.486910
$622$			22.5546i			0.904356i
$623$			15.0979i			0.604884i
$624$	−31.1697			−1.24779
$625$	−22.5982	+	10.6921i	−0.903929	+	0.427683i
$626$	−4.48586			−0.179291
$627$		−	12.9566i		−	0.517437i
$628$		−	0.210403i		−	0.00839600i
$629$	−44.7728			−1.78521
$630$	14.1441	−	17.6737i	0.563513	−	0.704138i
$631$	1.06954			0.0425778			0.0212889	−	0.999773i	$-0.493223\pi$
$631$	1.06954			0.0425778			0.0212889	+	0.999773i	$0.493223\pi$
$632$		−	10.8930i		−	0.433299i
$633$			58.3105i			2.31763i
$634$	11.4285			0.453882
$635$	−11.0829	−	8.86952i	−0.439812	−	0.351976i
$636$	−11.7754			−0.466924
$637$		−	16.4515i		−	0.651832i
$638$			7.44067i			0.294579i
$639$	−20.5907			−0.814557
$640$	−13.8325	−	11.0700i	−0.546776	−	0.437578i
$641$	40.4792			1.59883			0.799417	−	0.600777i	$-0.205142\pi$
$641$	40.4792			1.59883			0.799417	+	0.600777i	$0.205142\pi$
$642$		−	36.8800i		−	1.45554i
$643$			24.5046i			0.966368i	0.875519	+	0.483184i	$0.160520\pi$
$643$			24.5046i			0.966368i	−0.875519	+	0.483184i	$0.839480\pi$
$644$	−0.701360			−0.0276375
$645$	−31.6960	+	39.6058i	−1.24803	+	1.55948i
$646$	−20.2562			−0.796969
$647$			1.49656i			0.0588359i	0.999567	+	0.0294180i	$0.00936538\pi$
$647$			1.49656i			0.0588359i	−0.999567	+	0.0294180i	$0.990635\pi$
$648$			16.6596i			0.654450i
$649$	−3.00602			−0.117997
$650$	−4.62541	−	20.5911i	−0.181424	−	0.807650i
$651$	21.1560			0.829168
$652$			3.95529i			0.154901i
$653$		−	4.27935i		−	0.167464i	−0.996488	−	0.0837320i	$-0.973316\pi$
$653$		−	4.27935i		−	0.167464i	0.996488	−	0.0837320i	$-0.0266840\pi$
$654$	17.9520			0.701977
$655$	−7.72003	+	9.64657i	−0.301647	+	0.376923i
$656$	−25.6644			−1.00203
$657$		−	84.2411i		−	3.28656i
$658$		−	1.80841i		−	0.0704992i
$659$	14.3314			0.558271			0.279135	−	0.960252i	$-0.409952\pi$
$659$	14.3314			0.558271			0.279135	+	0.960252i	$0.409952\pi$
$660$	3.06499	+	2.45287i	0.119304	+	0.0954779i
$661$	19.4239			0.755501			0.377751	−	0.925907i	$-0.376698\pi$
$661$	19.4239			0.755501			0.377751	+	0.925907i	$0.376698\pi$
$662$			22.1772i			0.861940i
$663$		−	63.8397i		−	2.47933i
$664$	35.3347			1.37125
$665$	−5.67335	−	4.54031i	−0.220003	−	0.176066i
$666$	−48.5902			−1.88283
$667$			4.81977i			0.186622i
$668$		−	2.62078i		−	0.101401i
$669$	−1.43156			−0.0553473
$670$	19.8649	−	24.8222i	0.767447	−	0.958964i
$671$	−25.5666			−0.986988
$672$		−	7.23142i		−	0.278958i
$673$			29.3933i			1.13303i	0.824053	+	0.566513i	$0.191708\pi$
$673$			29.3933i			1.13303i	−0.824053	+	0.566513i	$0.808292\pi$
$674$	13.2297			0.509589
$675$	−37.1627	+	8.34792i	−1.43039	+	0.321312i
$676$	0.764932			0.0294205
$677$		−	36.2514i		−	1.39325i	−0.717434	−	0.696626i	$-0.754684\pi$
$677$		−	36.2514i		−	1.39325i	0.717434	−	0.696626i	$-0.245316\pi$
$678$			36.9026i			1.41723i
$679$	−2.82661			−0.108475
$680$	28.1077	−	35.1220i	1.07788	−	1.34687i
$681$	−16.0582			−0.615353
$682$		−	12.7311i		−	0.487500i
$683$		−	27.2333i		−	1.04205i	−0.853540	−	0.521027i	$-0.825549\pi$
$683$		−	27.2333i		−	1.04205i	0.853540	−	0.521027i	$-0.174451\pi$
$684$	4.12471			0.157712
$685$	−17.4461	−	13.9619i	−0.666583	−	0.533458i
$686$	−21.8059			−0.832552
$687$			81.9630i			3.12709i
$688$		−	25.2854i		−	0.963997i
$689$	41.3383			1.57486
$690$	−10.5814	−	8.46814i	−0.402826	−	0.322376i
$691$	−20.9110			−0.795493			−0.397747	−	0.917495i	$-0.630208\pi$
$691$	−20.9110			−0.795493			−0.397747	+	0.917495i	$0.630208\pi$
$692$		−	2.22211i		−	0.0844718i
$693$		−	14.7819i		−	0.561518i
$694$	−31.0353			−1.17808
$695$	−18.1038	+	22.6216i	−0.686716	+	0.858086i
$696$	−26.6664			−1.01079
$697$		−	52.5641i		−	1.99101i
$698$			16.0375i			0.607029i
$699$	−21.5106			−0.813607
$700$	2.14810	−	0.482530i	0.0811904	−	0.0182379i
$701$	−10.0458			−0.379425			−0.189712	−	0.981840i	$-0.560756\pi$
$701$	−10.0458			−0.379425			−0.189712	+	0.981840i	$0.560756\pi$
$702$		−	32.1534i		−	1.21355i
$703$			15.5977i			0.588279i
$704$	−16.7373			−0.630813
$705$	−4.09681	+	5.11917i	−0.154295	+	0.192799i
$706$	−2.92577			−0.110113
$707$			14.7886i			0.556182i
$708$		−	1.46981i		−	0.0552389i
$709$	−44.6066			−1.67524			−0.837619	−	0.546255i	$-0.816053\pi$
$709$	−44.6066			−1.67524			−0.837619	+	0.546255i	$0.816053\pi$
$710$	8.33336	+	6.66908i	0.312745	+	0.250286i
$711$	20.2893			0.760908
$712$			32.5613i			1.22029i
$713$		−	8.24671i		−	0.308842i
$714$	−35.4947			−1.32835
$715$	−10.7598	−	8.61097i	−0.402395	−	0.322032i
$716$	6.48205			0.242246
$717$		−	48.9674i		−	1.82872i
$718$		−	28.0091i		−	1.04529i
$719$	−6.92265			−0.258171			−0.129086	−	0.991633i	$-0.541204\pi$
$719$	−6.92265			−0.258171			−0.129086	+	0.991633i	$0.541204\pi$
$720$	25.5616	−	31.9405i	0.952623	−	1.19035i
$721$	18.7767			0.699280
$722$		−	17.5996i		−	0.654988i
$723$		−	42.2643i		−	1.57182i
$724$	2.23277			0.0829802
$725$	−3.31596	−	14.7618i	−0.123152	−	0.548239i
$726$	28.1942			1.04638
$727$		−	1.23977i		−	0.0459805i	−0.999736	−	0.0229902i	$-0.992681\pi$
$727$		−	1.23977i		−	0.0459805i	0.999736	−	0.0229902i	$-0.00731867\pi$
$728$			13.6225i			0.504882i
$729$	35.9807			1.33262
$730$	−27.2847	+	34.0936i	−1.00985	+	1.26186i
$731$	51.7878			1.91544
$732$		−	12.5009i		−	0.462047i
$733$			25.8685i			0.955474i	0.878503	+	0.477737i	$0.158543\pi$
$733$			25.8685i			0.955474i	−0.878503	+	0.477737i	$0.841457\pi$
$734$	−19.5068			−0.720008
$735$	25.8928	+	20.7217i	0.955072	+	0.764332i
$736$	−2.81885			−0.103904
$737$		−	20.7607i		−	0.764730i
$738$		−	57.0458i		−	2.09989i
$739$	−7.59657			−0.279445			−0.139722	−	0.990191i	$-0.544621\pi$
$739$	−7.59657			−0.279445			−0.139722	+	0.990191i	$0.544621\pi$
$740$	−3.68976	−	2.95287i	−0.135638	−	0.108550i
$741$	−22.2401			−0.817011
$742$		−	22.9839i		−	0.843767i
$743$			34.9507i			1.28222i	0.767450	+	0.641108i	$0.221525\pi$
$743$			34.9507i			1.28222i	−0.767450	+	0.641108i	$0.778475\pi$
$744$	45.6266			1.67275
$745$	−17.4719	+	21.8321i	−0.640122	+	0.799865i
$746$	−7.85981			−0.287768
$747$			65.8146i			2.40803i
$748$		−	4.00772i		−	0.146537i
$749$	−13.5065			−0.493515
$750$	38.2342	+	18.6559i	1.39611	+	0.681219i
$751$	3.08275			0.112491			0.0562455	−	0.998417i	$-0.482087\pi$
$751$	3.08275			0.112491			0.0562455	+	0.998417i	$0.482087\pi$
$752$		−	3.26821i		−	0.119180i
$753$		−	17.2225i		−	0.627624i
$754$	12.7720			0.465128
$755$	−21.4583	+	26.8132i	−0.780946	+	0.975832i
$756$	3.35429			0.121994
$757$		−	29.5454i		−	1.07385i	−0.843632	−	0.536923i	$-0.819587\pi$
$757$		−	29.5454i		−	1.07385i	0.843632	−	0.536923i	$-0.180413\pi$
$758$			15.0646i			0.547170i
$759$	−8.85001			−0.321235
$760$	−12.2356	−	9.79199i	−0.443832	−	0.355193i
$761$	20.9087			0.757939			0.378970	−	0.925409i	$-0.376279\pi$
$761$	20.9087			0.757939			0.378970	+	0.925409i	$0.376279\pi$
$762$			24.1559i			0.875077i
$763$		−	6.57450i		−	0.238013i
$764$	−8.32639			−0.301238
$765$	65.4183	+	52.3535i	2.36520	+	1.89284i
$766$	−27.0001			−0.975555
$767$			5.15987i			0.186312i
$768$		−	21.6519i		−	0.781295i
$769$	−17.0008			−0.613066			−0.306533	−	0.951860i	$-0.599169\pi$
$769$	−17.0008			−0.613066			−0.306533	+	0.951860i	$0.599169\pi$
$770$	−4.78767	+	5.98244i	−0.172536	+	0.215592i
$771$	−74.6738			−2.68931
$772$			5.40350i			0.194476i
$773$			6.51767i			0.234424i	0.993107	+	0.117212i	$0.0373958\pi$
$773$			6.51767i			0.234424i	−0.993107	+	0.117212i	$0.962604\pi$
$774$	56.2034			2.02019
$775$	5.67367	+	25.2577i	0.203804	+	0.907283i
$776$	−6.09609			−0.218837
$777$			27.3317i			0.980518i
$778$			17.4009i			0.623853i
$779$	−18.3120			−0.656095
$780$	4.21038	−	5.26108i	0.150756	−	0.188377i
$781$	6.96983			0.249400
$782$			13.8360i			0.494775i
$783$		−	23.0508i		−	0.823768i
$784$	−16.5307			−0.590381
$785$	−1.16253	−	0.930358i	−0.0414925	−	0.0332059i
$786$	21.0253			0.749948
$787$			4.22353i			0.150553i	0.997163	+	0.0752763i	$0.0239839\pi$
$787$			4.22353i			0.150553i	−0.997163	+	0.0752763i	$0.976016\pi$
$788$			5.14578i			0.183311i
$789$	16.8008			0.598124
$790$	−8.21136	−	6.57145i	−0.292147	−	0.233802i
$791$	13.5147			0.480529
$792$		−	31.8798i		−	1.13280i
$793$			43.8853i			1.55841i
$794$	−9.30994			−0.330397
$795$	−52.0682	+	65.0619i	−1.84667	+	2.30751i
$796$	1.13488			0.0402247
$797$			0.0413582i			0.00146498i	1.00000		0.000732491i	$0.000233159\pi$
$797$			0.0413582i			0.00146498i	−1.00000		0.000732491i	$0.999767\pi$
$798$			12.3654i			0.437732i
$799$	6.69374			0.236807
$800$	8.63344	−	1.93934i	0.305238	−	0.0685662i
$801$	−60.6488			−2.14292
$802$		−	29.1012i		−	1.02760i
$803$			28.5151i			1.00628i
$804$	10.1510			0.358000
$805$	−3.10126	+	3.87519i	−0.109305	+	0.136582i
$806$	−21.8531			−0.769742
$807$			39.4356i			1.38820i
$808$			31.8942i			1.12203i
$809$	−30.8971			−1.08628			−0.543142	−	0.839641i	$-0.682765\pi$
$809$	−30.8971			−1.08628			−0.543142	+	0.839641i	$0.682765\pi$
$810$	12.5584	+	10.0503i	0.441256	+	0.353131i
$811$	20.6037			0.723493			0.361746	−	0.932277i	$-0.382181\pi$
$811$	20.6037			0.723493			0.361746	+	0.932277i	$0.382181\pi$
$812$			1.33239i			0.0467578i
$813$		−	34.0702i		−	1.19490i
$814$	16.4475			0.576484
$815$	21.8540	+	17.4894i	0.765511	+	0.612629i
$816$	−64.1470			−2.24559
$817$		−	18.0416i		−	0.631194i
$818$		−	9.31959i		−	0.325852i
$819$	−25.3733			−0.886613
$820$	3.46673	−	4.33185i	0.121063	−	0.151275i
$821$	36.2733			1.26595			0.632974	−	0.774173i	$-0.281834\pi$
$821$	36.2733			1.26595			0.632974	+	0.774173i	$0.281834\pi$
$822$			38.0250i			1.32627i
$823$		−	51.4134i		−	1.79216i	−0.443896	−	0.896078i	$-0.646404\pi$
$823$		−	51.4134i		−	1.79216i	0.443896	−	0.896078i	$-0.353596\pi$
$824$	40.4953			1.41072
$825$	27.1054	−	6.08874i	0.943691	−	0.211983i
$826$	2.86887			0.0998208
$827$			24.4313i			0.849558i	0.905297	+	0.424779i	$0.139648\pi$
$827$			24.4313i			0.849558i	−0.905297	+	0.424779i	$0.860352\pi$
$828$		−	2.81739i		−	0.0979110i
$829$	4.34631			0.150954			0.0754768	−	0.997148i	$-0.475952\pi$
$829$	4.34631			0.150954			0.0754768	+	0.997148i	$0.475952\pi$
$830$	21.3165	−	26.6361i	0.739907	−	0.924551i
$831$	13.9141			0.482675
$832$			28.7298i			0.996027i
$833$		−	33.8570i		−	1.17308i
$834$	49.3052			1.70730
$835$	−14.4805	−	11.5885i	−0.501117	−	0.401038i
$836$	−1.39619			−0.0482882
$837$			39.4403i			1.36326i
$838$			42.7592i			1.47709i
$839$	50.2417			1.73454			0.867268	−	0.497841i	$-0.165874\pi$
$839$	50.2417			1.73454			0.867268	+	0.497841i	$0.165874\pi$
$840$	−21.4403	−	17.1584i	−0.739760	−	0.592021i
$841$	−19.8438			−0.684268
$842$			3.31701i			0.114312i
$843$		−	34.1155i		−	1.17500i
$844$	6.28347			0.216286
$845$	3.38237	−	4.22644i	0.116357	−	0.145394i
$846$	7.26445			0.249757
$847$		−	10.3255i		−	0.354788i
$848$		−	41.5373i		−	1.42640i
$849$	85.6177			2.93839
$850$	−9.51907	−	42.3763i	−0.326501	−	1.45350i
$851$	10.6540			0.365215
$852$			3.40793i			0.116754i
$853$			21.5835i			0.739006i	0.929230	+	0.369503i	$0.120472\pi$
$853$			21.5835i			0.739006i	−0.929230	+	0.369503i	$0.879528\pi$
$854$	24.4001			0.834954
$855$	18.2386	−	22.7901i	0.623747	−	0.779404i
$856$	−29.1291			−0.995612
$857$		−	28.6381i		−	0.978258i	−0.872211	−	0.489129i	$-0.837315\pi$
$857$		−	28.6381i		−	0.978258i	0.872211	−	0.489129i	$-0.162685\pi$
$858$			23.4518i			0.800630i
$859$	16.2773			0.555374			0.277687	−	0.960672i	$-0.410432\pi$
$859$	16.2773			0.555374			0.277687	+	0.960672i	$0.410432\pi$
$860$	4.26788	+	3.41553i	0.145533	+	0.116469i
$861$	−32.0879			−1.09355
$862$			0.504886i			0.0171965i
$863$			28.4598i			0.968782i	0.874852	+	0.484391i	$0.160959\pi$
$863$			28.4598i			0.968782i	−0.874852	+	0.484391i	$0.839041\pi$
$864$	13.4813			0.458642
$865$	−12.2777	−	9.82568i	−0.417454	−	0.334083i
$866$	23.5273			0.799491
$867$		−	81.5338i		−	2.76903i
$868$		−	2.27975i		−	0.0773796i
$869$	−6.86779			−0.232974
$870$	−16.0871	+	20.1017i	−0.545405	+	0.681511i
$871$	−35.6359			−1.20748
$872$		−	14.1791i		−	0.480164i
$873$		−	11.3546i		−	0.384295i
$874$	4.82011			0.163043
$875$	6.83232	−	14.0024i	0.230975	−	0.473368i
$876$	−13.9426			−0.471076
$877$			3.33339i			0.112561i	0.998415	+	0.0562804i	$0.0179241\pi$
$877$			3.33339i			0.112561i	−0.998415	+	0.0562804i	$0.982076\pi$
$878$		−	5.71590i		−	0.192902i
$879$	61.0817			2.06023
$880$	−8.65242	+	10.8116i	−0.291673	+	0.364460i
$881$	9.45635			0.318593			0.159296	−	0.987231i	$-0.449077\pi$
$881$	9.45635			0.318593			0.159296	+	0.987231i	$0.449077\pi$
$882$		−	36.7437i		−	1.23723i
$883$			2.82689i			0.0951323i	0.998868	+	0.0475662i	$0.0151465\pi$
$883$			2.82689i			0.0951323i	−0.998868	+	0.0475662i	$0.984854\pi$
$884$	−6.87929			−0.231376
$885$	−8.12107	−	6.49919i	−0.272987	−	0.218468i
$886$	−18.7511			−0.629955
$887$		−	22.3355i		−	0.749952i	−0.927035	−	0.374976i	$-0.877651\pi$
$887$		−	22.3355i		−	0.749952i	0.927035	−	0.374976i	$-0.122349\pi$
$888$			58.9456i			1.97808i
$889$	8.84657			0.296704
$890$	24.5454	+	19.6434i	0.822764	+	0.658447i
$891$	10.5035			0.351881
$892$			0.154263i			0.00516512i
$893$		−	2.33193i		−	0.0780349i
$894$	47.5844			1.59146
$895$	28.6622	−	35.8149i	0.958073	−	1.19716i
$896$	11.0413			0.368864
$897$			15.1911i			0.507217i
$898$			38.8461i			1.29631i
$899$	−15.6665			−0.522507
$900$	1.93834	+	8.62898i	0.0646114	+	0.287633i
$901$	85.0738			2.83422
$902$			19.3096i			0.642941i
$903$		−	31.6140i		−	1.05205i
$904$	29.1469			0.969412
$905$	9.87283	−	12.3366i	0.328184	−	0.410083i
$906$	58.4411			1.94158
$907$		−	17.1828i		−	0.570545i	−0.958446	−	0.285272i	$-0.907916\pi$
$907$		−	17.1828i		−	0.570545i	0.958446	−	0.285272i	$-0.0920841\pi$
$908$			1.73042i			0.0574259i
$909$	−59.4062			−1.97038
$910$	10.2689	+	8.21808i	0.340411	+	0.272427i
$911$	−20.7182			−0.686425			−0.343213	−	0.939258i	$-0.611515\pi$
$911$	−20.7182			−0.686425			−0.343213	+	0.939258i	$0.611515\pi$
$912$			22.3472i			0.739989i
$913$		−	22.2778i		−	0.737288i
$914$	−7.62992			−0.252375
$915$	−69.0707	−	55.2764i	−2.28341	−	1.82738i
$916$	8.83225			0.291826
$917$		−	7.70005i		−	0.254278i
$918$		−	66.1714i		−	2.18398i
$919$	40.9712			1.35151			0.675757	−	0.737125i	$-0.263817\pi$
$919$	40.9712			1.35151			0.675757	+	0.737125i	$0.263817\pi$
$920$	−6.68843	+	8.35753i	−0.220511	+	0.275540i
$921$	−78.8784			−2.59913
$922$			8.68468i			0.286015i
$923$		−	11.9638i		−	0.393792i
$924$	−2.44652			−0.0804847
$925$	−32.6307	+	7.32989i	−1.07289	+	0.241005i
$926$	0.140328			0.00461147
$927$			75.4266i			2.47734i
$928$			5.35503i			0.175788i
$929$	−43.5119			−1.42758			−0.713790	−	0.700360i	$-0.753023\pi$
$929$	−43.5119			−1.42758			−0.713790	+	0.700360i	$0.753023\pi$
$930$	27.5254	−	34.3943i	0.902592	−	1.12784i
$931$	−11.7949			−0.386563
$932$			2.31796i			0.0759274i
$933$			50.9633i			1.66846i
$934$	16.4955			0.539748
$935$	−22.1437	−	17.7213i	−0.724176	−	0.579549i
$936$	−54.7219			−1.78864
$937$			38.2212i			1.24863i	0.781172	+	0.624316i	$0.214622\pi$
$937$			38.2212i			1.24863i	−0.781172	+	0.624316i	$0.785378\pi$
$938$			19.8135i			0.646933i
$939$	−10.1360			−0.330777
$940$	0.551636	+	0.441467i	0.0179924	+	0.0143991i
$941$	−15.5248			−0.506095			−0.253048	−	0.967454i	$-0.581433\pi$
$941$	−15.5248			−0.506095			−0.253048	+	0.967454i	$0.581433\pi$
$942$			2.53381i			0.0825559i
$943$			12.5080i			0.407317i
$944$	5.18471			0.168748
$945$	14.8319	−	18.5333i	0.482483	−	0.602887i
$946$	−19.0245			−0.618539
$947$			12.9251i			0.420008i	0.977701	+	0.210004i	$0.0673477\pi$
$947$			12.9251i			0.420008i	−0.977701	+	0.210004i	$0.932652\pi$
$948$		−	3.35804i		−	0.109064i
$949$	48.9464			1.58887
$950$	−14.7628	+	3.31620i	−0.478970	+	0.107592i
$951$	25.8232			0.837375
$952$			28.0349i			0.908617i
$953$		−	6.03650i		−	0.195542i	−0.995209	−	0.0977708i	$-0.968829\pi$
$953$		−	6.03650i		−	0.195542i	0.995209	−	0.0977708i	$-0.0311712\pi$
$954$	92.3273			2.98921
$955$	−36.8175	+	46.0054i	−1.19139	+	1.48870i
$956$	−5.27667			−0.170660
$957$			16.8126i			0.543474i
$958$		−	27.3447i		−	0.883466i
$959$	13.9258			0.449688
$960$	−45.2176	−	36.1871i	−1.45939	−	1.16793i
$961$	−4.19435			−0.135302
$962$		−	28.2322i		−	0.910244i
$963$		−	54.2560i		−	1.74837i
$964$	−4.55435			−0.146686
$965$	29.8557	+	23.8931i	0.961088	+	0.769147i
$966$	8.44622			0.271753
$967$			56.7615i			1.82533i	0.408711	+	0.912664i	$0.365979\pi$
$967$			56.7615i			1.82533i	−0.408711	+	0.912664i	$0.634021\pi$
$968$		−	22.2687i		−	0.715744i
$969$	−45.7700			−1.47034
$970$	−3.67761	+	4.59536i	−0.118081	+	0.147548i
$971$	−23.7181			−0.761149			−0.380574	−	0.924750i	$-0.624274\pi$
$971$	−23.7181			−0.761149			−0.380574	+	0.924750i	$0.624274\pi$
$972$		−	2.08527i		−	0.0668852i
$973$		−	18.0569i		−	0.578879i
$974$	4.58665			0.146966
$975$	−10.4514	−	46.5267i	−0.334712	−	1.49005i
$976$	44.0966			1.41150
$977$		−	47.6492i		−	1.52443i	−0.647322	−	0.762217i	$-0.724111\pi$
$977$		−	47.6492i		−	1.52443i	0.647322	−	0.762217i	$-0.275889\pi$
$978$		−	47.6321i		−	1.52311i
$979$	20.5292			0.656117
$980$	2.23295	−	2.79018i	0.0713289	−	0.0891291i
$981$	26.4100			0.843206
$982$			6.19008i			0.197533i
$983$		−	44.8564i		−	1.43070i	−0.698769	−	0.715348i	$-0.746268\pi$
$983$		−	44.8564i		−	1.43070i	0.698769	−	0.715348i	$-0.253732\pi$
$984$	−69.2032			−2.20612
$985$	28.4317	+	22.7535i	0.905910	+	0.724988i
$986$	26.2846			0.837073
$987$		−	4.08620i		−	0.130065i
$988$			2.39657i			0.0762450i
$989$	−12.3233			−0.391858
$990$	−24.0317	−	19.2323i	−0.763777	−	0.611241i
$991$	−51.3548			−1.63134			−0.815670	−	0.578517i	$-0.803632\pi$
$991$	−51.3548			−1.63134			−0.815670	+	0.578517i	$0.803632\pi$
$992$		−	9.16256i		−	0.290912i
$993$			50.1105i			1.59021i
$994$	−6.65182			−0.210983
$995$	5.01819	−	6.27048i	0.159087	−	0.198788i
$996$	10.8928			0.345153
$997$			17.4060i			0.551255i	0.961265	+	0.275627i	$0.0888856\pi$
$997$			17.4060i			0.551255i	−0.961265	+	0.275627i	$0.911114\pi$
$998$		−	8.61195i		−	0.272606i
$999$	−50.9534			−1.61209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	235.2.c.a.189.16	yes	22
5.2	odd	4		1175.2.a.j.1.3		11
5.3	odd	4		1175.2.a.i.1.9		11
5.4	even	2	inner	235.2.c.a.189.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.c.a.189.7	✓	22	5.4	even	2	inner
235.2.c.a.189.16	yes	22	1.1	even	1	trivial
1175.2.a.i.1.9		11	5.3	odd	4
1175.2.a.j.1.3		11	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:	\( N \)	\(=\)	\( 235 = 5 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	235.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.29770i q^{2} +2.93223i q^{3} +0.315973 q^{4} +(1.39717 - 1.74583i) q^{5} -3.80515 q^{6} +1.39355i q^{7} +3.00544i q^{8} -5.59794 q^{9} +O(q^{10})\)	\(q+1.29770i q^{2} +2.93223i q^{3} +0.315973 q^{4} +(1.39717 - 1.74583i) q^{5} -3.80515 q^{6} +1.39355i q^{7} +3.00544i q^{8} -5.59794 q^{9} +(2.26557 + 1.81310i) q^{10} +1.89487 q^{11} +0.926505i q^{12} -3.25256i q^{13} -1.80841 q^{14} +(5.11917 + 4.09681i) q^{15} -3.26821 q^{16} -6.69374i q^{17} -7.26445i q^{18} -2.33193 q^{19} +(0.441467 - 0.551636i) q^{20} -4.08620 q^{21} +2.45897i q^{22} +1.59282i q^{23} -8.81263 q^{24} +(-1.09585 - 4.87843i) q^{25} +4.22084 q^{26} -7.61776i q^{27} +0.440325i q^{28} +3.02593 q^{29} +(-5.31643 + 6.64315i) q^{30} -5.17742 q^{31} +1.76972i q^{32} +5.55618i q^{33} +8.68647 q^{34} +(2.43290 + 1.94702i) q^{35} -1.76880 q^{36} -6.68877i q^{37} -3.02614i q^{38} +9.53723 q^{39} +(5.24699 + 4.19910i) q^{40} +7.85273 q^{41} -5.30267i q^{42} +7.73676i q^{43} +0.598728 q^{44} +(-7.82126 + 9.77306i) q^{45} -2.06701 q^{46} +1.00000i q^{47} -9.58314i q^{48} +5.05802 q^{49} +(6.33075 - 1.42209i) q^{50} +19.6275 q^{51} -1.02772i q^{52} +12.7095i q^{53} +9.88557 q^{54} +(2.64745 - 3.30812i) q^{55} -4.18823 q^{56} -6.83773i q^{57} +3.92675i q^{58} -1.58640 q^{59} +(1.61752 + 1.29448i) q^{60} -13.4926 q^{61} -6.71874i q^{62} -7.80102i q^{63} -8.83299 q^{64} +(-5.67841 - 4.54436i) q^{65} -7.21026 q^{66} -10.9563i q^{67} -2.11504i q^{68} -4.67052 q^{69} +(-2.52665 + 3.15718i) q^{70} +3.67827 q^{71} -16.8243i q^{72} +15.0486i q^{73} +8.68002 q^{74} +(14.3047 - 3.21328i) q^{75} -0.736826 q^{76} +2.64059i q^{77} +12.3765i q^{78} -3.62442 q^{79} +(-4.56624 + 5.70575i) q^{80} +5.54314 q^{81} +10.1905i q^{82} -11.7569i q^{83} -1.29113 q^{84} +(-11.6861 - 9.35227i) q^{85} -10.0400 q^{86} +8.87270i q^{87} +5.69491i q^{88} +10.8341 q^{89} +(-12.6825 - 10.1497i) q^{90} +4.53260 q^{91} +0.503290i q^{92} -15.1814i q^{93} -1.29770 q^{94} +(-3.25809 + 4.07115i) q^{95} -5.18921 q^{96} +2.02835i q^{97} +6.56379i q^{98} -10.6074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 20 q^{4} - 2 q^{5} - 4 q^{6} - 18 q^{9}+O(q^{10}) \) 22 * q - 20 * q^4 - 2 * q^5 - 4 * q^6 - 18 * q^9	\( 22 q - 20 q^{4} - 2 q^{5} - 4 q^{6} - 18 q^{9} - 2 q^{15} + 24 q^{16} - 12 q^{21} + 24 q^{24} - 6 q^{25} + 12 q^{26} - 8 q^{29} - 10 q^{30} + 4 q^{31} + 32 q^{34} - 12 q^{35} - 16 q^{36} + 20 q^{39} + 14 q^{40} + 8 q^{41} - 48 q^{44} + 6 q^{45} - 32 q^{46} - 10 q^{49} - 20 q^{50} + 24 q^{51} + 52 q^{56} - 14 q^{59} + 34 q^{60} - 14 q^{61} - 48 q^{64} + 14 q^{65} + 24 q^{66} + 4 q^{69} - 18 q^{70} - 34 q^{71} + 32 q^{74} - 32 q^{75} - 20 q^{76} + 26 q^{79} + 28 q^{80} - 50 q^{81} + 8 q^{84} - 6 q^{85} - 12 q^{86} + 74 q^{89} - 58 q^{90} + 64 q^{91} + 8 q^{94} - 52 q^{95} - 12 q^{96} + 16 q^{99}+O(q^{100}) \) 22 * q - 20 * q^4 - 2 * q^5 - 4 * q^6 - 18 * q^9 - 2 * q^15 + 24 * q^16 - 12 * q^21 + 24 * q^24 - 6 * q^25 + 12 * q^26 - 8 * q^29 - 10 * q^30 + 4 * q^31 + 32 * q^34 - 12 * q^35 - 16 * q^36 + 20 * q^39 + 14 * q^40 + 8 * q^41 - 48 * q^44 + 6 * q^45 - 32 * q^46 - 10 * q^49 - 20 * q^50 + 24 * q^51 + 52 * q^56 - 14 * q^59 + 34 * q^60 - 14 * q^61 - 48 * q^64 + 14 * q^65 + 24 * q^66 + 4 * q^69 - 18 * q^70 - 34 * q^71 + 32 * q^74 - 32 * q^75 - 20 * q^76 + 26 * q^79 + 28 * q^80 - 50 * q^81 + 8 * q^84 - 6 * q^85 - 12 * q^86 + 74 * q^89 - 58 * q^90 + 64 * q^91 + 8 * q^94 - 52 * q^95 - 12 * q^96 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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