LMFDB - Embedded newform 1638.2.cm.a.341.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(269,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("1638.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.cm (of order $6$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.5
Character	$\chi$	$=$	1638.341
Dual form			1638.2.cm.a.269.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-1.60179 + 2.77439i) q^{5} +(0.817803 - 2.51619i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.60179 + 2.77439i) q^{5} +(0.817803 - 2.51619i) q^{7} +1.00000i q^{8} +(2.77439 + 1.60179i) q^{10} +(-3.80949 - 2.19941i) q^{11} +(1.68024 + 3.19011i) q^{13} +(-2.51619 - 0.817803i) q^{14} +1.00000 q^{16} +1.88224 q^{17} +(-0.507247 + 0.292859i) q^{19} +(1.60179 - 2.77439i) q^{20} +(-2.19941 + 3.80949i) q^{22} -4.42465i q^{23} +(-2.63149 - 4.55787i) q^{25} +(3.19011 - 1.68024i) q^{26} +(-0.817803 + 2.51619i) q^{28} +(-2.61944 + 1.51233i) q^{29} +(5.58151 - 3.22249i) q^{31} -1.00000i q^{32} -1.88224i q^{34} +(5.67093 + 6.29932i) q^{35} +5.37400 q^{37} +(0.292859 + 0.507247i) q^{38} +(-2.77439 - 1.60179i) q^{40} +(2.62311 + 4.54336i) q^{41} +(4.11310 - 7.12409i) q^{43} +(3.80949 + 2.19941i) q^{44} -4.42465 q^{46} +(0.908990 - 1.57442i) q^{47} +(-5.66240 - 4.11549i) q^{49} +(-4.55787 + 2.63149i) q^{50} +(-1.68024 - 3.19011i) q^{52} +(1.48629 - 0.858108i) q^{53} +(12.2040 - 7.04601i) q^{55} +(2.51619 + 0.817803i) q^{56} +(1.51233 + 2.61944i) q^{58} +1.92677 q^{59} +(-1.62388 + 0.937547i) q^{61} +(-3.22249 - 5.58151i) q^{62} -1.00000 q^{64} +(-11.5420 - 0.448247i) q^{65} +(7.01339 - 12.1475i) q^{67} -1.88224 q^{68} +(6.29932 - 5.67093i) q^{70} +(-3.32098 - 1.91737i) q^{71} +(12.9992 - 7.50506i) q^{73} -5.37400i q^{74} +(0.507247 - 0.292859i) q^{76} +(-8.64955 + 7.78671i) q^{77} +(0.244870 - 0.424127i) q^{79} +(-1.60179 + 2.77439i) q^{80} +(4.54336 - 2.62311i) q^{82} +9.42846 q^{83} +(-3.01497 + 5.22208i) q^{85} +(-7.12409 - 4.11310i) q^{86} +(2.19941 - 3.80949i) q^{88} +9.26784 q^{89} +(9.40101 - 1.61893i) q^{91} +4.42465i q^{92} +(-1.57442 - 0.908990i) q^{94} -1.87640i q^{95} +(-1.90859 - 1.10192i) q^{97} +(-4.11549 + 5.66240i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) $ 72 * q - 72 * q^4 - 4 * q^7	$ 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) $ 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.60179	+	2.77439i	−0.716344	+	1.24074i	0.246095	+	0.969246i	$0.420853\pi$
$5$	−1.60179	+	2.77439i	−0.716344	+	1.24074i	−0.962439	+	0.271499i	$0.912481\pi$
$6$		0			0
$7$	0.817803	−	2.51619i	0.309101	−	0.951029i
$7$	0.817803	−	2.51619i	0.309101	−	0.951029i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.77439	+	1.60179i	0.877339	+	0.506532i
$11$	−3.80949	−	2.19941i	−1.14861	−	0.663148i	−0.200059	−	0.979784i	$-0.564113\pi$
$11$	−3.80949	−	2.19941i	−1.14861	−	0.663148i	−0.948547	+	0.316636i	$0.897447\pi$
$12$		0			0
$13$	1.68024	+	3.19011i	0.466016	+	0.884776i
$13$	1.68024	+	3.19011i	0.466016	+	0.884776i
$14$	−2.51619	−	0.817803i	−0.672479	−	0.218567i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.88224			0.456511			0.228256	−	0.973601i	$-0.426698\pi$
$17$	1.88224			0.456511			0.228256	+	0.973601i	$0.426698\pi$
$18$		0			0
$19$	−0.507247	+	0.292859i	−0.116370	+	0.0671865i	−0.557055	−	0.830475i	$-0.688069\pi$
$19$	−0.507247	+	0.292859i	−0.116370	+	0.0671865i	0.440685	+	0.897662i	$0.354736\pi$
$20$	1.60179	−	2.77439i	0.358172	−	0.620372i
$21$		0			0
$22$	−2.19941	+	3.80949i	−0.468916	+	0.812187i
$23$		−	4.42465i		−	0.922603i	−0.887244	−	0.461301i	$-0.847383\pi$
$23$		−	4.42465i		−	0.922603i	0.887244	−	0.461301i	$-0.152617\pi$
$24$		0			0
$25$	−2.63149	−	4.55787i	−0.526298	−	0.911575i
$26$	3.19011	−	1.68024i	0.625631	−	0.329523i
$27$		0			0
$28$	−0.817803	+	2.51619i	−0.154550	+	0.475515i
$29$	−2.61944	+	1.51233i	−0.486417	+	0.280833i	−0.723087	−	0.690757i	$-0.757277\pi$
$29$	−2.61944	+	1.51233i	−0.486417	+	0.280833i	0.236670	+	0.971590i	$0.423944\pi$
$30$		0			0
$31$	5.58151	−	3.22249i	1.00247	−	0.578776i	0.0934909	−	0.995620i	$-0.470197\pi$
$31$	5.58151	−	3.22249i	1.00247	−	0.578776i	0.908978	+	0.416845i	$0.136864\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		−	1.88224i		−	0.322802i
$35$	5.67093	+	6.29932i	0.958562	+	1.06478i
$36$		0			0
$37$	5.37400			0.883479			0.441740	−	0.897143i	$-0.354361\pi$
$37$	5.37400			0.883479			0.441740	+	0.897143i	$0.354361\pi$
$38$	0.292859	+	0.507247i	0.0475081	+	0.0822864i
$39$		0			0
$40$	−2.77439	−	1.60179i	−0.438669	−	0.253266i
$41$	2.62311	+	4.54336i	0.409661	+	0.709554i	0.994852	−	0.101342i	$-0.0323135\pi$
$41$	2.62311	+	4.54336i	0.409661	+	0.709554i	−0.585190	+	0.810896i	$0.698980\pi$
$42$		0			0
$43$	4.11310	−	7.12409i	0.627241	−	1.08641i	−0.360862	−	0.932619i	$-0.617517\pi$
$43$	4.11310	−	7.12409i	0.627241	−	1.08641i	0.988103	−	0.153794i	$-0.0491493\pi$
$44$	3.80949	+	2.19941i	0.574303	+	0.331574i
$45$		0			0
$46$	−4.42465			−0.652379
$47$	0.908990	−	1.57442i	0.132590	−	0.229652i	−0.792084	−	0.610412i	$-0.791004\pi$
$47$	0.908990	−	1.57442i	0.132590	−	0.229652i	0.924674	+	0.380759i	$0.124337\pi$
$48$		0			0
$49$	−5.66240	−	4.11549i	−0.808914	−	0.587928i
$50$	−4.55787	+	2.63149i	−0.644581	+	0.372149i
$51$		0			0
$52$	−1.68024	−	3.19011i	−0.233008	−	0.442388i
$53$	1.48629	−	0.858108i	0.204157	−	0.117870i	−0.394436	−	0.918923i	$-0.629060\pi$
$53$	1.48629	−	0.858108i	0.204157	−	0.117870i	0.598593	+	0.801053i	$0.295727\pi$
$54$		0			0
$55$	12.2040	−	7.04601i	1.64559	−	0.950084i
$56$	2.51619	+	0.817803i	0.336240	+	0.109284i
$57$		0			0
$58$	1.51233	+	2.61944i	0.198579	+	0.343949i
$59$	1.92677			0.250844			0.125422	−	0.992103i	$-0.459972\pi$
$59$	1.92677			0.250844			0.125422	+	0.992103i	$0.459972\pi$
$60$		0			0
$61$	−1.62388	+	0.937547i	−0.207916	+	0.120041i	−0.600343	−	0.799743i	$-0.704969\pi$
$61$	−1.62388	+	0.937547i	−0.207916	+	0.120041i	0.392426	+	0.919783i	$0.371636\pi$
$62$	−3.22249	−	5.58151i	−0.409256	−	0.708852i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−11.5420	−	0.448247i	−1.43161	−	0.0555982i
$66$		0			0
$67$	7.01339	−	12.1475i	0.856821	−	1.48406i	−0.0181234	−	0.999836i	$-0.505769\pi$
$67$	7.01339	−	12.1475i	0.856821	−	1.48406i	0.874945	−	0.484223i	$-0.160897\pi$
$68$	−1.88224			−0.228256
$69$		0			0
$70$	6.29932	−	5.67093i	0.752913	−	0.677806i
$71$	−3.32098	−	1.91737i	−0.394128	−	0.227550i	0.289819	−	0.957081i	$-0.406405\pi$
$71$	−3.32098	−	1.91737i	−0.394128	−	0.227550i	−0.683947	+	0.729532i	$0.739738\pi$
$72$		0			0
$73$	12.9992	−	7.50506i	1.52144	−	0.878401i	0.521756	−	0.853095i	$-0.325277\pi$
$73$	12.9992	−	7.50506i	1.52144	−	0.878401i	0.999680	−	0.0253062i	$-0.00805608\pi$
$74$		−	5.37400i		−	0.624714i
$75$		0			0
$76$	0.507247	−	0.292859i	0.0581852	−	0.0335933i
$77$	−8.64955	+	7.78671i	−0.985708	+	0.887378i
$78$		0			0
$79$	0.244870	−	0.424127i	0.0275500	−	0.0477180i	−0.851922	−	0.523669i	$-0.824563\pi$
$79$	0.244870	−	0.424127i	0.0275500	−	0.0477180i	0.879472	+	0.475951i	$0.157896\pi$
$80$	−1.60179	+	2.77439i	−0.179086	+	0.310186i
$81$		0			0
$82$	4.54336	−	2.62311i	0.501731	−	0.289674i
$83$	9.42846			1.03491			0.517454	−	0.855711i	$-0.326880\pi$
$83$	9.42846			1.03491			0.517454	+	0.855711i	$0.326880\pi$
$84$		0			0
$85$	−3.01497	+	5.22208i	−0.327019	+	0.566414i
$86$	−7.12409	−	4.11310i	−0.768211	−	0.443527i
$87$		0			0
$88$	2.19941	−	3.80949i	0.234458	−	0.406093i
$89$	9.26784			0.982390			0.491195	−	0.871050i	$-0.336560\pi$
$89$	9.26784			0.982390			0.491195	+	0.871050i	$0.336560\pi$
$90$		0			0
$91$	9.40101	−	1.61893i	0.985494	−	0.169710i
$92$			4.42465i			0.461301i
$93$		0			0
$94$	−1.57442	−	0.908990i	−0.162389	−	0.0937551i
$95$		−	1.87640i		−	0.192515i
$96$		0			0
$97$	−1.90859	−	1.10192i	−0.193787	−	0.111883i	0.399967	−	0.916530i	$-0.369022\pi$
$97$	−1.90859	−	1.10192i	−0.193787	−	0.111883i	−0.593754	+	0.804646i	$0.702355\pi$
$98$	−4.11549	+	5.66240i	−0.415728	+	0.571988i
$99$		0			0
$100$	2.63149	+	4.55787i	0.263149	+	0.455787i
$101$	7.02406	−	12.1660i	0.698921	−	1.21057i	−0.269921	−	0.962883i	$-0.586997\pi$
$101$	7.02406	−	12.1660i	0.698921	−	1.21057i	0.968841	−	0.247683i	$-0.0796692\pi$
$102$		0			0
$103$	−13.3597	−	7.71320i	−1.31637	−	0.760004i	−0.333224	−	0.942848i	$-0.608137\pi$
$103$	−13.3597	−	7.71320i	−1.31637	−	0.760004i	−0.983142	+	0.182843i	$0.941470\pi$
$104$	−3.19011	+	1.68024i	−0.312816	+	0.164761i
$105$		0			0
$106$	−0.858108	−	1.48629i	−0.0833468	−	0.144361i
$107$		−	6.55593i		−	0.633786i	−0.948461	−	0.316893i	$-0.897360\pi$
$107$		−	6.55593i		−	0.633786i	0.948461	−	0.316893i	$-0.102640\pi$
$108$		0			0
$109$	6.40585	+	11.0953i	0.613569	+	1.06273i	0.990634	+	0.136546i	$0.0436000\pi$
$109$	6.40585	+	11.0953i	0.613569	+	1.06273i	−0.377065	+	0.926187i	$0.623067\pi$
$110$	−7.04601	−	12.2040i	−0.671811	−	1.16361i
$111$		0			0
$112$	0.817803	−	2.51619i	0.0772752	−	0.237757i
$113$	10.7839	+	6.22608i	1.01446	+	0.585700i	0.912495	−	0.409088i	$-0.134153\pi$
$113$	10.7839	+	6.22608i	1.01446	+	0.585700i	0.101967	+	0.994788i	$0.467486\pi$
$114$		0			0
$115$	12.2757	+	7.08737i	1.14471	+	0.660901i
$116$	2.61944	−	1.51233i	0.243208	−	0.140416i
$117$		0			0
$118$		−	1.92677i		−	0.177374i
$119$	1.53931	−	4.73608i	0.141108	−	0.434156i
$120$		0			0
$121$	4.17483	+	7.23101i	0.379530	+	0.657365i
$122$	0.937547	+	1.62388i	0.0848815	+	0.147019i
$123$		0			0
$124$	−5.58151	+	3.22249i	−0.501234	+	0.289388i
$125$	0.842475			0.0753533
$126$		0			0
$127$	−7.26430	−	12.5821i	−0.644602	−	1.11648i	−0.984393	−	0.175983i	$-0.943690\pi$
$127$	−7.26430	−	12.5821i	−0.644602	−	1.11648i	0.339791	−	0.940501i	$-0.389644\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−0.448247	+	11.5420i	−0.0393138	+	1.01230i
$131$	1.16756	−	2.02228i	0.102010	−	0.176687i	−0.810502	−	0.585735i	$-0.800806\pi$
$131$	1.16756	−	2.02228i	0.102010	−	0.176687i	0.912513	+	0.409048i	$0.134139\pi$
$132$		0			0
$133$	0.322060	+	1.51583i	0.0279262	+	0.131439i
$134$	−12.1475	−	7.01339i	−1.04939	−	0.605864i
$135$		0			0
$136$			1.88224i			0.161401i
$137$		−	17.2694i		−	1.47542i	−0.675117	−	0.737711i	$-0.735907\pi$
$137$		−	17.2694i		−	1.47542i	0.675117	−	0.737711i	$-0.264093\pi$
$138$		0			0
$139$	−14.5977	−	8.42796i	−1.23816	−	0.714851i	−0.269440	−	0.963017i	$-0.586839\pi$
$139$	−14.5977	−	8.42796i	−1.23816	−	0.714851i	−0.968717	+	0.248167i	$0.920172\pi$
$140$	−5.67093	−	6.29932i	−0.479281	−	0.532390i
$141$		0			0
$142$	−1.91737	+	3.32098i	−0.160902	+	0.278690i
$143$	0.615484	−	15.8482i	0.0514694	−	1.32530i
$144$		0			0
$145$		−	9.68978i		−	0.804692i
$146$	−7.50506	−	12.9992i	−0.621123	−	1.07582i
$147$		0			0
$148$	−5.37400			−0.441740
$149$	−6.87749	+	3.97072i	−0.563426	+	0.325294i	−0.754519	−	0.656278i	$-0.772130\pi$
$149$	−6.87749	+	3.97072i	−0.563426	+	0.325294i	0.191093	+	0.981572i	$0.438797\pi$
$150$		0			0
$151$	3.37816	+	5.85115i	0.274911	+	0.476160i	0.970113	−	0.242655i	$-0.0780182\pi$
$151$	3.37816	+	5.85115i	0.274911	+	0.476160i	−0.695202	+	0.718815i	$0.744685\pi$
$152$	−0.292859	−	0.507247i	−0.0237540	−	0.0411432i
$153$		0			0
$154$	7.78671	+	8.64955i	0.627471	+	0.697001i
$155$			20.6470i			1.65841i
$156$		0			0
$157$	−4.14370	+	2.39237i	−0.330703	+	0.190932i	−0.656153	−	0.754628i	$-0.727818\pi$
$157$	−4.14370	+	2.39237i	−0.330703	+	0.190932i	0.325450	+	0.945559i	$0.394484\pi$
$158$	−0.424127	−	0.244870i	−0.0337418	−	0.0194808i
$159$		0			0
$160$	2.77439	+	1.60179i	0.219335	+	0.126633i
$161$	−11.1332	−	3.61849i	−0.877422	−	0.285177i
$162$		0			0
$163$	12.3870	+	21.4548i	0.970221	+	1.68047i	0.694880	+	0.719126i	$0.255457\pi$
$163$	12.3870	+	21.4548i	0.970221	+	1.68047i	0.275341	+	0.961347i	$0.411209\pi$
$164$	−2.62311	−	4.54336i	−0.204831	−	0.354777i
$165$		0			0
$166$		−	9.42846i		−	0.731791i
$167$	2.98452	+	5.16935i	0.230949	+	0.400016i	0.958088	−	0.286475i	$-0.0924835\pi$
$167$	2.98452	+	5.16935i	0.230949	+	0.400016i	−0.727138	+	0.686491i	$0.759150\pi$
$168$		0			0
$169$	−7.35357	+	10.7203i	−0.565659	+	0.824639i
$170$	5.22208	+	3.01497i	0.400515	+	0.231237i
$171$		0			0
$172$	−4.11310	+	7.12409i	−0.313621	+	0.543207i
$173$	3.13211	+	5.42498i	0.238130	+	0.412453i	0.960178	−	0.279390i	$-0.0901322\pi$
$173$	3.13211	+	5.42498i	0.238130	+	0.412453i	−0.722048	+	0.691843i	$0.756799\pi$
$174$		0			0
$175$	−13.6205	+	2.89388i	−1.02961	+	0.218756i
$176$	−3.80949	−	2.19941i	−0.287151	−	0.165787i
$177$		0			0
$178$		−	9.26784i		−	0.694654i
$179$	−5.10712	−	2.94859i	−0.381724	−	0.220388i	0.296844	−	0.954926i	$-0.404066\pi$
$179$	−5.10712	−	2.94859i	−0.381724	−	0.220388i	−0.678568	+	0.734538i	$0.737399\pi$
$180$		0			0
$181$			23.4079i			1.73990i	0.493141	+	0.869949i	$0.335849\pi$
$181$			23.4079i			1.73990i	−0.493141	+	0.869949i	$0.664151\pi$
$182$	−1.61893	−	9.40101i	−0.120003	−	0.696850i
$183$		0			0
$184$	4.42465			0.326189
$185$	−8.60803	+	14.9096i	−0.632875	+	1.09617i
$186$		0			0
$187$	−7.17040	−	4.13983i	−0.524351	−	0.302734i
$188$	−0.908990	+	1.57442i	−0.0662949	+	0.114826i
$189$		0			0
$190$	−1.87640			−0.136128
$191$	−14.6500	+	8.45819i	−1.06004	+	0.612013i	−0.925443	−	0.378887i	$-0.876307\pi$
$191$	−14.6500	+	8.45819i	−1.06004	+	0.612013i	−0.134595	+	0.990901i	$0.542973\pi$
$192$		0			0
$193$	−1.55884	+	2.69999i	−0.112208	+	0.194349i	−0.916660	−	0.399668i	$-0.869126\pi$
$193$	−1.55884	+	2.69999i	−0.112208	+	0.194349i	0.804452	+	0.594017i	$0.202459\pi$
$194$	−1.10192	+	1.90859i	−0.0791134	+	0.137028i
$195$		0			0
$196$	5.66240	+	4.11549i	0.404457	+	0.293964i
$197$	4.97546	−	2.87258i	0.354487	−	0.204663i	−0.312173	−	0.950025i	$-0.601057\pi$
$197$	4.97546	−	2.87258i	0.354487	−	0.204663i	0.666660	+	0.745362i	$0.267723\pi$
$198$		0			0
$199$		−	19.2077i		−	1.36160i	−0.732471	−	0.680799i	$-0.761633\pi$
$199$		−	19.2077i		−	1.36160i	0.732471	−	0.680799i	$-0.238367\pi$
$200$	4.55787	−	2.63149i	0.322290	−	0.186074i
$201$		0			0
$202$	−12.1660	−	7.02406i	−0.855999	−	0.494211i
$203$	1.66313	+	7.82778i	0.116729	+	0.549402i
$204$		0			0
$205$	−16.8067			−1.17383
$206$	−7.71320	+	13.3597i	−0.537404	+	0.930812i
$207$		0			0
$208$	1.68024	+	3.19011i	0.116504	+	0.221194i
$209$	2.57647			0.178218
$210$		0			0
$211$	5.23782	+	9.07217i	0.360587	+	0.624554i	0.988057	−	0.154086i	$-0.0492432\pi$
$211$	5.23782	+	9.07217i	0.360587	+	0.624554i	−0.627471	+	0.778640i	$0.715910\pi$
$212$	−1.48629	+	0.858108i	−0.102079	+	0.0589351i
$213$		0			0
$214$	−6.55593			−0.448154
$215$	13.1767	+	22.8227i	0.898641	+	1.55649i
$216$		0			0
$217$	−3.54380	−	16.6795i	−0.240569	−	1.13228i
$218$	11.0953	−	6.40585i	0.751465	−	0.433859i
$219$		0			0
$220$	−12.2040	+	7.04601i	−0.822797	+	0.475042i
$221$	3.16263	+	6.00456i	0.212741	+	0.403910i
$222$		0			0
$223$	−10.1635	+	5.86791i	−0.680599	+	0.392944i	−0.800081	−	0.599892i	$-0.795210\pi$
$223$	−10.1635	+	5.86791i	−0.680599	+	0.392944i	0.119482	+	0.992836i	$0.461877\pi$
$224$	−2.51619	−	0.817803i	−0.168120	−	0.0546418i
$225$		0			0
$226$	6.22608	−	10.7839i	0.414153	−	0.717333i
$227$	−26.8747			−1.78374			−0.891869	−	0.452293i	$-0.850606\pi$
$227$	−26.8747			−1.78374			−0.891869	+	0.452293i	$0.850606\pi$
$228$		0			0
$229$	16.7640	+	9.67870i	1.10780	+	0.639586i	0.938258	−	0.345937i	$-0.112439\pi$
$229$	16.7640	+	9.67870i	1.10780	+	0.639586i	0.169538	+	0.985524i	$0.445772\pi$
$230$	7.08737	−	12.2757i	0.467328	−	0.809435i
$231$		0			0
$232$	−1.51233	−	2.61944i	−0.0992894	−	0.171974i
$233$	−19.3444	−	11.1685i	−1.26729	−	0.731672i	−0.292818	−	0.956168i	$-0.594593\pi$
$233$	−19.3444	−	11.1685i	−1.26729	−	0.731672i	−0.974475	+	0.224496i	$0.927926\pi$
$234$		0			0
$235$	2.91203	+	5.04378i	0.189960	+	0.329020i
$236$	−1.92677			−0.125422
$237$		0			0
$238$	−4.73608	−	1.53931i	−0.306994	−	0.0997784i
$239$			21.2454i			1.37425i	0.726538	+	0.687126i	$0.241128\pi$
$239$			21.2454i			1.37425i	−0.726538	+	0.687126i	$0.758872\pi$
$240$		0			0
$241$		−	3.87232i		−	0.249438i	−0.992192	−	0.124719i	$-0.960197\pi$
$241$		−	3.87232i		−	0.249438i	0.992192	−	0.124719i	$-0.0398030\pi$
$242$	7.23101	−	4.17483i	0.464827	−	0.268368i
$243$		0			0
$244$	1.62388	−	0.937547i	0.103958	−	0.0600203i
$245$	20.4880	−	9.11751i	1.30893	−	0.582497i
$246$		0			0
$247$	−1.78655	−	1.12610i	−0.113676	−	0.0716519i
$248$	3.22249	+	5.58151i	0.204628	+	0.354426i
$249$		0			0
$250$		−	0.842475i		−	0.0532828i
$251$	−1.22143	+	2.11557i	−0.0770958	+	0.133534i	−0.901996	−	0.431745i	$-0.857898\pi$
$251$	−1.22143	+	2.11557i	−0.0770958	+	0.133534i	0.824900	+	0.565279i	$0.191231\pi$
$252$		0			0
$253$	−9.73162	+	16.8557i	−0.611822	+	1.05971i
$254$	−12.5821	+	7.26430i	−0.789473	+	0.455802i
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.7336			0.856676			0.428338	−	0.903619i	$-0.359099\pi$
$257$	13.7336			0.856676			0.428338	+	0.903619i	$0.359099\pi$
$258$		0			0
$259$	4.39487	−	13.5220i	0.273084	−	0.840215i
$260$	11.5420	+	0.448247i	0.715805	+	0.0277991i
$261$		0			0
$262$	−2.02228	−	1.16756i	−0.124937	−	0.0721323i
$263$	5.45312	+	3.14836i	0.336254	+	0.194136i	0.658614	−	0.752481i	$-0.271143\pi$
$263$	5.45312	+	3.14836i	0.336254	+	0.194136i	−0.322360	+	0.946617i	$0.604476\pi$
$264$		0			0
$265$			5.49805i			0.337743i
$266$	1.51583	−	0.322060i	0.0929415	−	0.0197468i
$267$		0			0
$268$	−7.01339	+	12.1475i	−0.428411	+	0.742029i
$269$	10.9628			0.668416			0.334208	−	0.942499i	$-0.391531\pi$
$269$	10.9628			0.668416			0.334208	+	0.942499i	$0.391531\pi$
$270$		0			0
$271$		−	17.8787i		−	1.08606i	−0.839715	−	0.543028i	$-0.817278\pi$
$271$		−	17.8787i		−	1.08606i	0.839715	−	0.543028i	$-0.182722\pi$
$272$	1.88224			0.114128
$273$		0			0
$274$	−17.2694			−1.04328
$275$			23.1509i			1.39605i
$276$		0			0
$277$	21.5869			1.29703			0.648514	−	0.761203i	$-0.275391\pi$
$277$	21.5869			1.29703			0.648514	+	0.761203i	$0.275391\pi$
$278$	−8.42796	+	14.5977i	−0.505476	+	0.875509i
$279$		0			0
$280$	−6.29932	+	5.67093i	−0.376456	+	0.338903i
$281$		−	26.4550i		−	1.57817i	−0.614283	−	0.789086i	$-0.710555\pi$
$281$		−	26.4550i		−	1.57817i	0.614283	−	0.789086i	$-0.289445\pi$
$282$		0			0
$283$	13.8612	+	8.00274i	0.823960	+	0.475714i	0.851780	−	0.523899i	$-0.175523\pi$
$283$	13.8612	+	8.00274i	0.823960	+	0.475714i	−0.0278199	+	0.999613i	$0.508856\pi$
$284$	3.32098	+	1.91737i	0.197064	+	0.113775i
$285$		0			0
$286$	−15.8482	−	0.615484i	−0.937126	−	0.0363944i
$287$	13.5771	−	2.88466i	0.801434	−	0.170276i
$288$		0			0
$289$	−13.4572			−0.791597
$290$	−9.68978			−0.569003
$291$		0			0
$292$	−12.9992	+	7.50506i	−0.760718	+	0.439201i
$293$	9.15472	−	15.8564i	0.534824	−	0.926343i	−0.464347	−	0.885653i	$-0.653711\pi$
$293$	9.15472	−	15.8564i	0.534824	−	0.926343i	0.999172	−	0.0406898i	$-0.0129555\pi$
$294$		0			0
$295$	−3.08629	+	5.34561i	−0.179691	+	0.311233i
$296$			5.37400i			0.312357i
$297$		0			0
$298$	3.97072	+	6.87749i	0.230018	+	0.398402i
$299$	14.1151	−	7.43448i	0.816297	−	0.429947i
$300$		0			0
$301$	−14.5618	−	16.1754i	−0.839331	−	0.932336i
$302$	5.85115	−	3.37816i	0.336696	−	0.194391i
$303$		0			0
$304$	−0.507247	+	0.292859i	−0.0290926	+	0.0167966i
$305$		−	6.00703i		−	0.343962i
$306$		0			0
$307$		−	9.21783i		−	0.526089i	−0.964784	−	0.263045i	$-0.915273\pi$
$307$		−	9.21783i		−	0.526089i	0.964784	−	0.263045i	$-0.0847266\pi$
$308$	8.64955	−	7.78671i	0.492854	−	0.443689i
$309$		0			0
$310$	20.6470			1.17267
$311$	−10.6192	−	18.3930i	−0.602161	−	1.04297i	−0.992493	−	0.122299i	$-0.960973\pi$
$311$	−10.6192	−	18.3930i	−0.602161	−	1.04297i	0.390332	−	0.920674i	$-0.372360\pi$
$312$		0			0
$313$	14.3626	+	8.29225i	0.811822	+	0.468706i	0.847588	−	0.530654i	$-0.178054\pi$
$313$	14.3626	+	8.29225i	0.811822	+	0.468706i	−0.0357660	+	0.999360i	$0.511387\pi$
$314$	2.39237	+	4.14370i	0.135009	+	0.233842i
$315$		0			0
$316$	−0.244870	+	0.424127i	−0.0137750	+	0.0238590i
$317$	28.0236	+	16.1794i	1.57396	+	0.908727i	0.995676	+	0.0928925i	$0.0296113\pi$
$317$	28.0236	+	16.1794i	1.57396	+	0.908727i	0.578285	+	0.815835i	$0.303722\pi$
$318$		0			0
$319$	13.3050			0.744935
$320$	1.60179	−	2.77439i	0.0895430	−	0.155093i
$321$		0			0
$322$	−3.61849	+	11.1332i	−0.201651	+	0.620431i
$323$	−0.954763	+	0.551233i	−0.0531244	+	0.0306714i
$324$		0			0
$325$	10.1186	−	16.0531i	0.561277	−	0.890464i
$326$	21.4548	−	12.3870i	1.18827	−	0.686050i
$327$		0			0
$328$	−4.54336	+	2.62311i	−0.250865	+	0.144837i
$329$	−3.21815	−	3.57475i	−0.177422	−	0.197082i
$330$		0			0
$331$	6.39485	+	11.0762i	0.351493	+	0.608803i	0.986511	−	0.163694i	$-0.0523409\pi$
$331$	6.39485	+	11.0762i	0.351493	+	0.608803i	−0.635019	+	0.772497i	$0.719008\pi$
$332$	−9.42846			−0.517454
$333$		0			0
$334$	5.16935	−	2.98452i	0.282854	−	0.163306i
$335$	22.4680	+	38.9157i	1.22756	+	2.12619i
$336$		0			0
$337$	−14.0245			−0.763961			−0.381980	−	0.924170i	$-0.624758\pi$
$337$	−14.0245			−0.763961			−0.381980	+	0.924170i	$0.624758\pi$
$338$	10.7203	+	7.35357i	0.583108	+	0.399981i
$339$		0			0
$340$	3.01497	−	5.22208i	0.163510	−	0.283207i
$341$	−28.3503			−1.53525
$342$		0			0
$343$	−14.9861	+	10.8820i	−0.809172	+	0.587572i
$344$	7.12409	+	4.11310i	0.384105	+	0.221763i
$345$		0			0
$346$	5.42498	−	3.13211i	0.291649	−	0.168383i
$347$		−	24.4041i		−	1.31008i	−0.755593	−	0.655041i	$-0.772651\pi$
$347$		−	24.4041i		−	1.31008i	0.755593	−	0.655041i	$-0.227349\pi$
$348$		0			0
$349$	−23.1005	+	13.3371i	−1.23654	+	0.713918i	−0.968386	−	0.249457i	$-0.919748\pi$
$349$	−23.1005	+	13.3371i	−1.23654	+	0.713918i	−0.268157	+	0.963375i	$0.586415\pi$
$350$	2.89388	+	13.6205i	0.154684	+	0.728047i
$351$		0			0
$352$	−2.19941	+	3.80949i	−0.117229	+	0.203047i
$353$	−0.0811128	+	0.140491i	−0.00431720	+	0.00747760i	−0.868176	−	0.496257i	$-0.834708\pi$
$353$	−0.0811128	+	0.140491i	−0.00431720	+	0.00747760i	0.863859	+	0.503734i	$0.168041\pi$
$354$		0			0
$355$	10.6391	−	6.14246i	0.564662	−	0.326008i
$356$	−9.26784			−0.491195
$357$		0			0
$358$	−2.94859	+	5.10712i	−0.155838	+	0.269919i
$359$	28.3547	+	16.3706i	1.49651	+	0.864008i	0.999992	−	0.00402165i	$-0.00128013\pi$
$359$	28.3547	+	16.3706i	1.49651	+	0.864008i	0.496513	+	0.868029i	$0.334613\pi$
$360$		0			0
$361$	−9.32847	+	16.1574i	−0.490972	+	0.850388i
$362$	23.4079			1.23029
$363$		0			0
$364$	−9.40101	+	1.61893i	−0.492747	+	0.0848548i
$365$			48.0863i			2.51695i
$366$		0			0
$367$	−1.63841	−	0.945934i	−0.0855240	−	0.0493773i	0.456628	−	0.889658i	$-0.349057\pi$
$367$	−1.63841	−	0.945934i	−0.0855240	−	0.0493773i	−0.542152	+	0.840280i	$0.682390\pi$
$368$		−	4.42465i		−	0.230651i
$369$		0			0
$370$	14.9096	+	8.60803i	0.775111	+	0.447510i
$371$	−0.943670	−	4.44154i	−0.0489929	−	0.230593i
$372$		0			0
$373$	−1.83238	−	3.17377i	−0.0948770	−	0.164332i	0.814680	−	0.579910i	$-0.196912\pi$
$373$	−1.83238	−	3.17377i	−0.0948770	−	0.164332i	−0.909557	+	0.415579i	$0.863579\pi$
$374$	−4.13983	+	7.17040i	−0.214066	+	0.370772i
$375$		0			0
$376$	1.57442	+	0.908990i	0.0811943	+	0.0468776i
$377$	−9.22579	−	5.81519i	−0.475152	−	0.299498i
$378$		0			0
$379$	−4.68225	−	8.10990i	−0.240511	−	0.416578i	0.720349	−	0.693612i	$-0.243982\pi$
$379$	−4.68225	−	8.10990i	−0.240511	−	0.416578i	−0.960860	+	0.277034i	$0.910648\pi$
$380$			1.87640i			0.0962574i
$381$		0			0
$382$	8.45819	+	14.6500i	0.432759	+	0.749560i
$383$	4.34328	+	7.52277i	0.221931	+	0.384396i	0.955394	−	0.295333i	$-0.0954307\pi$
$383$	4.34328	+	7.52277i	0.221931	+	0.384396i	−0.733463	+	0.679729i	$0.762097\pi$
$384$		0			0
$385$	−7.74857	−	36.4699i	−0.394904	−	1.85868i
$386$	2.69999	+	1.55884i	0.137426	+	0.0793428i
$387$		0			0
$388$	1.90859	+	1.10192i	0.0968937	+	0.0559416i
$389$	−0.171158	+	0.0988184i	−0.00867808	+	0.00501029i	−0.504333	−	0.863509i	$-0.668261\pi$
$389$	−0.171158	+	0.0988184i	−0.00867808	+	0.00501029i	0.495655	+	0.868520i	$0.334928\pi$
$390$		0			0
$391$		−	8.32827i		−	0.421178i
$392$	4.11549	−	5.66240i	0.207864	−	0.285994i
$393$		0			0
$394$	−2.87258	−	4.97546i	−0.144719	−	0.250660i
$395$	0.784463	+	1.35873i	0.0394706	+	0.0683651i
$396$		0			0
$397$	23.3981	−	13.5089i	1.17431	−	0.677991i	0.219622	−	0.975585i	$-0.429518\pi$
$397$	23.3981	−	13.5089i	1.17431	−	0.677991i	0.954692	+	0.297594i	$0.0961843\pi$
$398$	−19.2077			−0.962795
$399$		0			0
$400$	−2.63149	−	4.55787i	−0.131574	−	0.227894i
$401$		−	21.4390i		−	1.07061i	−0.844659	−	0.535306i	$-0.820196\pi$
$401$		−	21.4390i		−	1.07061i	0.844659	−	0.535306i	$-0.179804\pi$
$402$		0			0
$403$	19.6584	+	12.3911i	0.979253	+	0.617242i
$404$	−7.02406	+	12.1660i	−0.349460	+	0.605283i
$405$		0			0
$406$	7.82778	−	1.66313i	0.388486	−	0.0825396i
$407$	−20.4722	−	11.8196i	−1.01477	−	0.585877i
$408$		0			0
$409$		−	19.3524i		−	0.956913i	−0.878111	−	0.478457i	$-0.841196\pi$
$409$		−	19.3524i		−	0.956913i	0.878111	−	0.478457i	$-0.158804\pi$
$410$			16.8067i			0.830026i
$411$		0			0
$412$	13.3597	+	7.71320i	0.658183	+	0.380002i
$413$	1.57572	−	4.84811i	0.0775361	−	0.238560i
$414$		0			0
$415$	−15.1025	+	26.1582i	−0.741350	+	1.28406i
$416$	3.19011	−	1.68024i	0.156408	−	0.0823807i
$417$		0			0
$418$		−	2.57647i		−	0.126019i
$419$	7.07461	+	12.2536i	0.345618	+	0.598627i	0.985466	−	0.169874i	$-0.0543361\pi$
$419$	7.07461	+	12.2536i	0.345618	+	0.598627i	−0.639848	+	0.768501i	$0.721003\pi$
$420$		0			0
$421$	−19.4735			−0.949078			−0.474539	−	0.880234i	$-0.657385\pi$
$421$	−19.4735			−0.949078			−0.474539	+	0.880234i	$0.657385\pi$
$422$	9.07217	−	5.23782i	0.441626	−	0.254973i
$423$		0			0
$424$	0.858108	+	1.48629i	0.0416734	+	0.0721805i
$425$	−4.95311	−	8.57903i	−0.240261	−	0.416144i
$426$		0			0
$427$	1.03103	+	4.85271i	0.0498950	+	0.234839i
$428$			6.55593i			0.316893i
$429$		0			0
$430$	22.8227	−	13.1767i	1.10061	−	0.635435i
$431$	11.1103	+	6.41451i	0.535162	+	0.308976i	0.743116	−	0.669162i	$-0.233347\pi$
$431$	11.1103	+	6.41451i	0.535162	+	0.308976i	−0.207954	+	0.978139i	$0.566680\pi$
$432$		0			0
$433$	9.20595	+	5.31506i	0.442410	+	0.255425i	0.704619	−	0.709586i	$-0.251118\pi$
$433$	9.20595	+	5.31506i	0.442410	+	0.255425i	−0.262209	+	0.965011i	$0.584451\pi$
$434$	−16.6795	+	3.54380i	−0.800641	+	0.170108i
$435$		0			0
$436$	−6.40585	−	11.0953i	−0.306784	−	0.531366i
$437$	1.29580	+	2.24439i	0.0619865	+	0.107364i
$438$		0			0
$439$			30.0083i			1.43222i	0.697989	+	0.716108i	$0.254078\pi$
$439$			30.0083i			1.43222i	−0.697989	+	0.716108i	$0.745922\pi$
$440$	7.04601	+	12.2040i	0.335905	+	0.581805i
$441$		0			0
$442$	6.00456	−	3.16263i	0.285608	−	0.150431i
$443$	31.2015	+	18.0142i	1.48243	+	0.855882i	0.999801	−	0.0199432i	$-0.00634855\pi$
$443$	31.2015	+	18.0142i	1.48243	+	0.855882i	0.482629	+	0.875825i	$0.339682\pi$
$444$		0			0
$445$	−14.8452	+	25.7126i	−0.703729	+	1.21889i
$446$	5.86791	+	10.1635i	0.277853	+	0.481256i
$447$		0			0
$448$	−0.817803	+	2.51619i	−0.0386376	+	0.118879i
$449$	−31.7884	−	18.3530i	−1.50019	−	0.866134i	−1.00000		0.000216651i	$-0.999931\pi$
$449$	−31.7884	−	18.3530i	−1.50019	−	0.866134i	−0.500188	−	0.865917i	$-0.666736\pi$
$450$		0			0
$451$		−	23.0772i		−	1.08666i
$452$	−10.7839	−	6.22608i	−0.507231	−	0.292850i
$453$		0			0
$454$			26.8747i			1.26129i
$455$	−10.5670	+	28.6753i	−0.495387	+	1.34432i
$456$		0			0
$457$	−36.3165			−1.69881			−0.849407	−	0.527738i	$-0.823040\pi$
$457$	−36.3165			−1.69881			−0.849407	+	0.527738i	$0.823040\pi$
$458$	9.67870	−	16.7640i	0.452256	−	0.783330i
$459$		0			0
$460$	−12.2757	−	7.08737i	−0.572357	−	0.330450i
$461$	9.31532	−	16.1346i	0.433858	−	0.751463i	−0.563344	−	0.826222i	$-0.690485\pi$
$461$	9.31532	−	16.1346i	0.433858	−	0.751463i	0.997202	+	0.0747590i	$0.0238188\pi$
$462$		0			0
$463$	26.9786			1.25380			0.626901	−	0.779099i	$-0.284323\pi$
$463$	26.9786			1.25380			0.626901	+	0.779099i	$0.284323\pi$
$464$	−2.61944	+	1.51233i	−0.121604	+	0.0702082i
$465$		0			0
$466$	−11.1685	+	19.3444i	−0.517370	+	0.896112i
$467$	−20.2900	+	35.1434i	−0.938911	+	1.62624i	−0.171405	+	0.985201i	$0.554831\pi$
$467$	−20.2900	+	35.1434i	−0.938911	+	1.62624i	−0.767507	+	0.641041i	$0.778503\pi$
$468$		0			0
$469$	−24.8299	−	27.5813i	−1.14654	−	1.27359i
$470$	5.04378	−	2.91203i	0.232652	−	0.134322i
$471$		0			0
$472$			1.92677i			0.0886868i
$473$	−31.3376	+	18.0928i	−1.44091	+	0.831907i
$474$		0			0
$475$	2.66963	+	1.54131i	0.122491	+	0.0707203i
$476$	−1.53931	+	4.73608i	−0.0705540	+	0.217078i
$477$		0			0
$478$	21.2454			0.971743
$479$	15.8075	−	27.3794i	0.722262	−	1.25099i	−0.237829	−	0.971307i	$-0.576436\pi$
$479$	15.8075	−	27.3794i	0.722262	−	1.25099i	0.960091	−	0.279688i	$-0.0902309\pi$
$480$		0			0
$481$	9.02962	+	17.1436i	0.411715	+	0.781682i
$482$	−3.87232			−0.176380
$483$		0			0
$484$	−4.17483	−	7.23101i	−0.189765	−	0.328682i
$485$	6.11432	−	3.53011i	0.277637	−	0.160294i
$486$		0			0
$487$	−35.5216			−1.60964			−0.804818	−	0.593522i	$-0.797737\pi$
$487$	−35.5216			−1.60964			−0.804818	+	0.593522i	$0.797737\pi$
$488$	−0.937547	−	1.62388i	−0.0424408	−	0.0735096i
$489$		0			0
$490$	−9.11751	−	20.4880i	−0.411887	−	0.925552i
$491$	9.49939	−	5.48447i	0.428701	−	0.247511i	−0.270092	−	0.962835i	$-0.587054\pi$
$491$	9.49939	−	5.48447i	0.428701	−	0.247511i	0.698793	+	0.715324i	$0.253721\pi$
$492$		0			0
$493$	−4.93042	+	2.84658i	−0.222055	+	0.128203i
$494$	−1.12610	+	1.78655i	−0.0506655	+	0.0803807i
$495$		0			0
$496$	5.58151	−	3.22249i	0.250617	−	0.144694i
$497$	−7.54037	+	6.78818i	−0.338232	+	0.304491i
$498$		0			0
$499$	0.378099	−	0.654887i	0.0169261	−	0.0293168i	−0.857438	−	0.514587i	$-0.827945\pi$
$499$	0.378099	−	0.654887i	0.0169261	−	0.0293168i	0.874364	+	0.485270i	$0.161279\pi$
$500$	−0.842475			−0.0376766
$501$		0			0
$502$	2.11557	+	1.22143i	0.0944227	+	0.0545150i
$503$	5.70627	−	9.88354i	0.254430	−	0.440685i	−0.710311	−	0.703888i	$-0.751446\pi$
$503$	5.70627	−	9.88354i	0.254430	−	0.440685i	0.964740	+	0.263203i	$0.0847789\pi$
$504$		0			0
$505$	22.5022	+	38.9750i	1.00134	+	1.73436i
$506$	16.8557	+	9.73162i	0.749326	+	0.432623i
$507$		0			0
$508$	7.26430	+	12.5821i	0.322301	+	0.558242i
$509$	−9.45790			−0.419214			−0.209607	−	0.977786i	$-0.567218\pi$
$509$	−9.45790			−0.419214			−0.209607	+	0.977786i	$0.567218\pi$
$510$		0			0
$511$	−8.25339	−	38.8460i	−0.365109	−	1.71844i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	13.7336i		−	0.605761i
$515$	42.7988	−	24.7099i	1.88594	−	1.08885i
$516$		0			0
$517$	−6.92558	+	3.99849i	−0.304587	+	0.175853i
$518$	−13.5220	−	4.39487i	−0.594122	−	0.193100i
$519$		0			0
$520$	0.448247	−	11.5420i	0.0196569	−	0.506150i
$521$	−20.5740	−	35.6352i	−0.901362	−	1.56120i	−0.825728	−	0.564069i	$-0.809235\pi$
$521$	−20.5740	−	35.6352i	−0.901362	−	1.56120i	−0.0756338	−	0.997136i	$-0.524098\pi$
$522$		0			0
$523$			18.1574i			0.793965i	0.917826	+	0.396983i	$0.129943\pi$
$523$			18.1574i			0.793965i	−0.917826	+	0.396983i	$0.870057\pi$
$524$	−1.16756	+	2.02228i	−0.0510052	+	0.0883436i
$525$		0			0
$526$	3.14836	−	5.45312i	0.137275	−	0.237767i
$527$	10.5058	−	6.06551i	0.457638	−	0.264218i
$528$		0			0
$529$	3.42250			0.148804
$530$	5.49805			0.238820
$531$		0			0
$532$	−0.322060	−	1.51583i	−0.0139631	−	0.0657196i
$533$	−10.0864	+	16.0020i	−0.436888	+	0.693122i
$534$		0			0
$535$	18.1887	+	10.5013i	0.786367	+	0.454009i
$536$	12.1475	+	7.01339i	0.524694	+	0.302932i
$537$		0			0
$538$		−	10.9628i		−	0.472641i
$539$	12.5192	+	28.1319i	0.539240	+	1.21173i
$540$		0			0
$541$	0.971610	−	1.68288i	0.0417728	−	0.0723526i	−0.844383	−	0.535740i	$-0.820033\pi$
$541$	0.971610	−	1.68288i	0.0417728	−	0.0723526i	0.886156	+	0.463387i	$0.153366\pi$
$542$	−17.8787			−0.767958
$543$		0			0
$544$		−	1.88224i		−	0.0807006i
$545$	−41.0434			−1.75811
$546$		0			0
$547$	−29.5878			−1.26508			−0.632542	−	0.774526i	$-0.717988\pi$
$547$	−29.5878			−1.26508			−0.632542	+	0.774526i	$0.717988\pi$
$548$			17.2694i			0.737711i
$549$		0			0
$550$	23.1509			0.987159
$551$	0.885801	−	1.53425i	0.0377364	−	0.0653613i
$552$		0			0
$553$	−0.866928	−	0.962991i	−0.0368655	−	0.0409506i
$554$		−	21.5869i		−	0.917137i
$555$		0			0
$556$	14.5977	+	8.42796i	0.619079	+	0.357425i
$557$	−21.4400	−	12.3784i	−0.908442	−	0.524489i	−0.0285126	−	0.999593i	$-0.509077\pi$
$557$	−21.4400	−	12.3784i	−0.908442	−	0.524489i	−0.879930	+	0.475104i	$0.842410\pi$
$558$		0			0
$559$	29.6376	+	1.15101i	1.25354	+	0.0486826i
$560$	5.67093	+	6.29932i	0.239640	+	0.266195i
$561$		0			0
$562$	−26.4550			−1.11594
$563$	−31.4957			−1.32739			−0.663694	−	0.748004i	$-0.731012\pi$
$563$	−31.4957			−1.32739			−0.663694	+	0.748004i	$0.731012\pi$
$564$		0			0
$565$	−34.5471	+	19.9458i	−1.45341	+	0.839126i
$566$	8.00274	−	13.8612i	0.336380	−	0.582628i
$567$		0			0
$568$	1.91737	−	3.32098i	0.0804510	−	0.139345i
$569$		−	23.3074i		−	0.977097i	−0.872537	−	0.488549i	$-0.837527\pi$
$569$		−	23.3074i		−	0.977097i	0.872537	−	0.488549i	$-0.162473\pi$
$570$		0			0
$571$	1.93361	+	3.34910i	0.0809189	+	0.140156i	0.903645	−	0.428283i	$-0.140881\pi$
$571$	1.93361	+	3.34910i	0.0809189	+	0.140156i	−0.822726	+	0.568438i	$0.807548\pi$
$572$	−0.615484	+	15.8482i	−0.0257347	+	0.662648i
$573$		0			0
$574$	−2.88466	−	13.5771i	−0.120404	−	0.566699i
$575$	−20.1670	+	11.6434i	−0.841021	+	0.485564i
$576$		0			0
$577$	−35.0818	+	20.2545i	−1.46048	+	0.843206i	−0.999033	−	0.0439640i	$-0.986001\pi$
$577$	−35.0818	+	20.2545i	−1.46048	+	0.843206i	−0.461443	+	0.887170i	$0.652668\pi$
$578$			13.4572i			0.559744i
$579$		0			0
$580$			9.68978i			0.402346i
$581$	7.71063	−	23.7238i	0.319891	−	0.984228i
$582$		0			0
$583$	−7.54933			−0.312661
$584$	7.50506	+	12.9992i	0.310562	+	0.537909i
$585$		0			0
$586$	−15.8564	−	9.15472i	−0.655023	−	0.378178i
$587$	17.2225	+	29.8302i	0.710849	+	1.23123i	0.964539	+	0.263940i	$0.0850222\pi$
$587$	17.2225	+	29.8302i	0.710849	+	1.23123i	−0.253690	+	0.967285i	$0.581644\pi$
$588$		0			0
$589$	−1.88747	+	3.26919i	−0.0777719	+	0.134705i
$590$	5.34561	+	3.08629i	0.220075	+	0.127060i
$591$		0			0
$592$	5.37400			0.220870
$593$	−14.9527	+	25.8988i	−0.614033	+	1.06354i	0.376520	+	0.926409i	$0.377121\pi$
$593$	−14.9527	+	25.8988i	−0.614033	+	1.06354i	−0.990553	+	0.137129i	$0.956213\pi$
$594$		0			0
$595$	10.6741	+	11.8569i	0.437594	+	0.486084i
$596$	6.87749	−	3.97072i	0.281713	−	0.162647i
$597$		0			0
$598$	−7.43448	−	14.1151i	−0.304019	−	0.577209i
$599$	−5.91232	+	3.41348i	−0.241571	+	0.139471i	−0.615899	−	0.787826i	$-0.711207\pi$
$599$	−5.91232	+	3.41348i	−0.241571	+	0.139471i	0.374328	+	0.927297i	$0.377874\pi$
$600$		0			0
$601$	33.0338	−	19.0721i	1.34748	−	0.777966i	0.359586	−	0.933112i	$-0.382918\pi$
$601$	33.0338	−	19.0721i	1.34748	−	0.777966i	0.987892	+	0.155146i	$0.0495847\pi$
$602$	−16.1754	+	14.5618i	−0.659261	+	0.593496i
$603$		0			0
$604$	−3.37816	−	5.85115i	−0.137456	−	0.238080i
$605$	−26.7489			−1.08750
$606$		0			0
$607$	5.57498	−	3.21871i	0.226281	−	0.130644i	−0.382574	−	0.923925i	$-0.624962\pi$
$607$	5.57498	−	3.21871i	0.226281	−	0.130644i	0.608855	+	0.793281i	$0.291629\pi$
$608$	0.292859	+	0.507247i	0.0118770	+	0.0205716i
$609$		0			0
$610$	−6.00703			−0.243218
$611$	6.54988	+	0.254372i	0.264980	+	0.0102908i
$612$		0			0
$613$	−2.41457	+	4.18215i	−0.0975234	+	0.168916i	−0.910659	−	0.413159i	$-0.864425\pi$
$613$	−2.41457	+	4.18215i	−0.0975234	+	0.168916i	0.813136	+	0.582074i	$0.197759\pi$
$614$	−9.21783			−0.372001
$615$		0			0
$616$	−7.78671	−	8.64955i	−0.313736	−	0.348500i
$617$	38.2836	+	22.1031i	1.54124	+	0.889836i	0.998761	+	0.0497673i	$0.0158480\pi$
$617$	38.2836	+	22.1031i	1.54124	+	0.889836i	0.542480	+	0.840069i	$0.317485\pi$
$618$		0			0
$619$	−17.5183	+	10.1142i	−0.704120	+	0.406524i	−0.808880	−	0.587974i	$-0.799926\pi$
$619$	−17.5183	+	10.1142i	−0.704120	+	0.406524i	0.104760	+	0.994498i	$0.466592\pi$
$620$		−	20.6470i		−	0.829205i
$621$		0			0
$622$	−18.3930	+	10.6192i	−0.737494	+	0.425792i
$623$	7.57927	−	23.3196i	0.303657	−	0.934281i
$624$		0			0
$625$	11.8080	−	20.4520i	0.472319	−	0.818080i
$626$	8.29225	−	14.3626i	0.331425	−	0.574045i
$627$		0			0
$628$	4.14370	−	2.39237i	0.165352	−	0.0954658i
$629$	10.1152			0.403318
$630$		0			0
$631$	−21.9165	+	37.9604i	−0.872481	+	1.51118i	−0.0130581	+	0.999915i	$0.504157\pi$
$631$	−21.9165	+	37.9604i	−0.872481	+	1.51118i	−0.859423	+	0.511266i	$0.829177\pi$
$632$	0.424127	+	0.244870i	0.0168709	+	0.00974040i
$633$		0			0
$634$	16.1794	−	28.0236i	0.642567	−	1.11296i
$635$	46.5436			1.84703
$636$		0			0
$637$	3.61466	−	24.9787i	0.143218	−	0.989691i
$638$		−	13.3050i		−	0.526749i
$639$		0			0
$640$	−2.77439	−	1.60179i	−0.109667	−	0.0633165i
$641$		−	36.7993i		−	1.45349i	−0.686910	−	0.726743i	$-0.741033\pi$
$641$		−	36.7993i		−	1.45349i	0.686910	−	0.726743i	$-0.258967\pi$
$642$		0			0
$643$	−11.2923	−	6.51958i	−0.445323	−	0.257107i	0.260530	−	0.965466i	$-0.416103\pi$
$643$	−11.2923	−	6.51958i	−0.445323	−	0.257107i	−0.705853	+	0.708358i	$0.749436\pi$
$644$	11.1332	+	3.61849i	0.438711	+	0.142589i
$645$		0			0
$646$	0.551233	+	0.954763i	0.0216880	+	0.0375647i
$647$	1.16813	−	2.02325i	0.0459237	−	0.0795422i	−0.842150	−	0.539244i	$-0.818710\pi$
$647$	1.16813	−	2.02325i	0.0459237	−	0.0795422i	0.888074	+	0.459701i	$0.152044\pi$
$648$		0			0
$649$	−7.34002	−	4.23776i	−0.288121	−	0.166347i
$650$	−16.0531	−	10.1186i	−0.629653	−	0.396883i
$651$		0			0
$652$	−12.3870	−	21.4548i	−0.485111	−	0.840236i
$653$		−	32.5681i		−	1.27449i	−0.770663	−	0.637243i	$-0.780075\pi$
$653$		−	32.5681i		−	1.27449i	0.770663	−	0.637243i	$-0.219925\pi$
$654$		0			0
$655$	3.74039	+	6.47854i	0.146149	+	0.253138i
$656$	2.62311	+	4.54336i	0.102415	+	0.177389i
$657$		0			0
$658$	−3.57475	+	3.21815i	−0.139358	+	0.125457i
$659$	−39.1411	−	22.5981i	−1.52472	−	0.880299i	−0.999571	−	0.0292894i	$-0.990676\pi$
$659$	−39.1411	−	22.5981i	−1.52472	−	0.880299i	−0.525151	−	0.851009i	$-0.675991\pi$
$660$		0			0
$661$	42.3436	+	24.4471i	1.64697	+	0.950881i	0.978265	+	0.207356i	$0.0664860\pi$
$661$	42.3436	+	24.4471i	1.64697	+	0.950881i	0.668709	+	0.743525i	$0.266847\pi$
$662$	11.0762	−	6.39485i	0.430489	−	0.248543i
$663$		0			0
$664$			9.42846i			0.365895i
$665$	−4.72138	−	1.53453i	−0.183087	−	0.0595064i
$666$		0			0
$667$	6.69153	+	11.5901i	0.259097	+	0.448770i
$668$	−2.98452	−	5.16935i	−0.115475	−	0.200008i
$669$		0			0
$670$	38.9157	−	22.4680i	1.50345	−	0.868015i
$671$	8.24821			0.318419
$672$		0			0
$673$	−5.13668	−	8.89699i	−0.198005	−	0.342954i	0.749877	−	0.661578i	$-0.230113\pi$
$673$	−5.13668	−	8.89699i	−0.198005	−	0.342954i	−0.947881	+	0.318624i	$0.896779\pi$
$674$			14.0245i			0.540202i
$675$		0			0
$676$	7.35357	−	10.7203i	0.282829	−	0.412320i
$677$	14.9488	−	25.8921i	0.574530	−	0.995115i	−0.421563	−	0.906799i	$-0.638518\pi$
$677$	14.9488	−	25.8921i	0.574530	−	0.995115i	0.996093	−	0.0883155i	$-0.0281484\pi$
$678$		0			0
$679$	−4.33349	+	3.90120i	−0.166304	+	0.149714i
$680$	−5.22208	−	3.01497i	−0.200258	−	0.115619i
$681$		0			0
$682$			28.3503i			1.08559i
$683$		−	4.70026i		−	0.179850i	−0.995949	−	0.0899252i	$-0.971337\pi$
$683$		−	4.70026i		−	0.179850i	0.995949	−	0.0899252i	$-0.0286628\pi$
$684$		0			0
$685$	47.9119	+	27.6620i	1.83062	+	1.05691i
$686$	10.8820	+	14.9861i	0.415476	+	0.572171i
$687$		0			0
$688$	4.11310	−	7.12409i	0.156810	−	0.271603i
$689$	5.23478	+	3.29958i	0.199429	+	0.125704i
$690$		0			0
$691$		−	2.88905i		−	0.109905i	−0.998489	−	0.0549524i	$-0.982499\pi$
$691$		−	2.88905i		−	0.109905i	0.998489	−	0.0549524i	$-0.0175007\pi$
$692$	−3.13211	−	5.42498i	−0.119065	−	0.206227i
$693$		0			0
$694$	−24.4041			−0.926368
$695$	46.7649	−	26.9997i	1.77389	−	1.02416i
$696$		0			0
$697$	4.93734	+	8.55172i	0.187015	+	0.323920i
$698$	13.3371	+	23.1005i	0.504817	+	0.874368i
$699$		0			0
$700$	13.6205	−	2.89388i	0.514807	−	0.109378i
$701$			39.6677i			1.49823i	0.662441	+	0.749114i	$0.269521\pi$
$701$			39.6677i			1.49823i	−0.662441	+	0.749114i	$0.730479\pi$
$702$		0			0
$703$	−2.72594	+	1.57382i	−0.102811	+	0.0593579i
$704$	3.80949	+	2.19941i	0.143576	+	0.0828935i
$705$		0			0
$706$	0.140491	+	0.0811128i	0.00528746	+	0.00305272i
$707$	−24.8677	−	27.6233i	−0.935247	−	1.03888i
$708$		0			0
$709$	−4.96967	−	8.60773i	−0.186640	−	0.323270i	0.757488	−	0.652849i	$-0.226426\pi$
$709$	−4.96967	−	8.60773i	−0.186640	−	0.323270i	−0.944128	+	0.329579i	$0.893093\pi$
$710$	−6.14246	−	10.6391i	−0.230522	−	0.399277i
$711$		0			0
$712$			9.26784i			0.347327i
$713$	−14.2584	−	24.6962i	−0.533980	−	0.924880i
$714$		0			0
$715$	42.9833	+	27.0932i	1.60748	+	1.01323i
$716$	5.10712	+	2.94859i	0.190862	+	0.110194i
$717$		0			0
$718$	16.3706	−	28.3547i	0.610946	−	1.05819i
$719$	6.70671	+	11.6164i	0.250118	+	0.433217i	0.963558	−	0.267499i	$-0.0861972\pi$
$719$	6.70671	+	11.6164i	0.250118	+	0.433217i	−0.713440	+	0.700716i	$0.752864\pi$
$720$		0			0
$721$	−30.3334	+	27.3075i	−1.12968	+	1.01699i
$722$	16.1574	+	9.32847i	0.601315	+	0.347170i
$723$		0			0
$724$		−	23.4079i		−	0.869949i
$725$	13.7860	+	7.95937i	0.512000	+	0.295604i
$726$		0			0
$727$		−	18.8373i		−	0.698636i	−0.937004	−	0.349318i	$-0.886413\pi$
$727$		−	18.8373i		−	0.698636i	0.937004	−	0.349318i	$-0.113587\pi$
$728$	1.61893	+	9.40101i	0.0600014	+	0.348425i
$729$		0			0
$730$	48.0863			1.77975
$731$	7.74185	−	13.4093i	0.286343	−	0.495960i
$732$		0			0
$733$	−24.0582	−	13.8900i	−0.888611	−	0.513040i	−0.0151230	−	0.999886i	$-0.504814\pi$
$733$	−24.0582	−	13.8900i	−0.888611	−	0.513040i	−0.873488	+	0.486846i	$0.838147\pi$
$734$	−0.945934	+	1.63841i	−0.0349150	+	0.0604746i
$735$		0			0
$736$	−4.42465			−0.163095
$737$	−53.4349	+	30.8507i	−1.96830	+	1.13640i
$738$		0			0
$739$	−3.06172	+	5.30306i	−0.112627	+	0.195076i	−0.916829	−	0.399281i	$-0.869260\pi$
$739$	−3.06172	+	5.30306i	−0.112627	+	0.195076i	0.804202	+	0.594357i	$0.202593\pi$
$740$	8.60803	−	14.9096i	0.316438	−	0.548086i
$741$		0			0
$742$	−4.44154	+	0.943670i	−0.163054	+	0.0346432i
$743$	−2.68842	+	1.55216i	−0.0986286	+	0.0569432i	−0.548503	−	0.836149i	$-0.684802\pi$
$743$	−2.68842	+	1.55216i	−0.0986286	+	0.0569432i	0.449874	+	0.893092i	$0.351469\pi$
$744$		0			0
$745$		−	25.4411i		−	0.932090i
$746$	−3.17377	+	1.83238i	−0.116200	+	0.0670882i
$747$		0			0
$748$	7.17040	+	4.13983i	0.262176	+	0.151367i
$749$	−16.4960	−	5.36147i	−0.602749	−	0.195904i
$750$		0			0
$751$	33.9571			1.23911			0.619556	−	0.784952i	$-0.287313\pi$
$751$	33.9571			1.23911			0.619556	+	0.784952i	$0.287313\pi$
$752$	0.908990	−	1.57442i	0.0331474	−	0.0574131i
$753$		0			0
$754$	−5.81519	+	9.22579i	−0.211777	+	0.335983i
$755$	−21.6445			−0.787724
$756$		0			0
$757$	−17.1841	−	29.7638i	−0.624568	−	1.08178i	−0.988624	−	0.150406i	$-0.951942\pi$
$757$	−17.1841	−	29.7638i	−0.624568	−	1.08178i	0.364057	−	0.931377i	$-0.381391\pi$
$758$	−8.10990	+	4.68225i	−0.294565	+	0.170067i
$759$		0			0
$760$	1.87640			0.0680642
$761$	12.8454	+	22.2488i	0.465644	+	0.806519i	0.999230	−	0.0392266i	$-0.0124894\pi$
$761$	12.8454	+	22.2488i	0.465644	+	0.806519i	−0.533586	+	0.845746i	$0.679156\pi$
$762$		0			0
$763$	33.1565	−	7.04457i	1.20034	−	0.255031i
$764$	14.6500	−	8.45819i	0.530019	−	0.306007i
$765$		0			0
$766$	7.52277	−	4.34328i	0.271809	−	0.156929i
$767$	3.23744	+	6.14660i	0.116897	+	0.221941i
$768$		0			0
$769$	29.3811	−	16.9632i	1.05951	−	0.611708i	0.134212	−	0.990953i	$-0.457150\pi$
$769$	29.3811	−	16.9632i	1.05951	−	0.611708i	0.925296	+	0.379245i	$0.123816\pi$
$770$	−36.4699	+	7.74857i	−1.31428	+	0.279239i
$771$		0			0
$772$	1.55884	−	2.69999i	0.0561038	−	0.0971747i
$773$	29.1552			1.04864			0.524321	−	0.851521i	$-0.324319\pi$
$773$	29.1552			1.04864			0.524321	+	0.851521i	$0.324319\pi$
$774$		0			0
$775$	−29.3754	−	16.9599i	−1.05519	−	0.609217i
$776$	1.10192	−	1.90859i	0.0395567	−	0.0685142i
$777$		0			0
$778$	0.0988184	+	0.171158i	0.00354281	+	0.00613633i
$779$	−2.66113	−	1.53641i	−0.0953450	−	0.0550475i
$780$		0			0
$781$	8.43417	+	14.6084i	0.301798	+	0.522730i
$782$	−8.32827			−0.297818
$783$		0			0
$784$	−5.66240	−	4.11549i	−0.202228	−	0.146982i
$785$		−	15.3283i		−	0.547091i
$786$		0			0
$787$		−	24.0139i		−	0.856003i	−0.903778	−	0.428001i	$-0.859218\pi$
$787$		−	24.0139i		−	0.856003i	0.903778	−	0.428001i	$-0.140782\pi$
$788$	−4.97546	+	2.87258i	−0.177244	+	0.102332i
$789$		0			0
$790$	1.35873	−	0.784463i	0.0483414	−	0.0279099i
$791$	24.4851	−	22.0426i	0.870589	−	0.783743i
$792$		0			0
$793$	−5.71939	−	3.60504i	−0.203101	−	0.128019i
$794$	−13.5089	−	23.3981i	−0.479412	−	0.830366i
$795$		0			0
$796$			19.2077i			0.680799i
$797$	0.568935	−	0.985424i	0.0201527	−	0.0349055i	−0.855773	−	0.517351i	$-0.826918\pi$
$797$	0.568935	−	0.985424i	0.0201527	−	0.0349055i	0.875926	+	0.482446i	$0.160251\pi$
$798$		0			0
$799$	1.71094	−	2.96344i	0.0605287	−	0.104839i
$800$	−4.55787	+	2.63149i	−0.161145	+	0.0930372i
$801$		0			0
$802$	−21.4390			−0.757036
$803$	−66.0269			−2.33004
$804$		0			0
$805$	27.8723	−	25.0919i	0.982368	−	0.884372i
$806$	12.3911	−	19.6584i	0.436456	−	0.692437i
$807$		0			0
$808$	12.1660	+	7.02406i	0.428000	+	0.247106i
$809$	7.15729	+	4.13227i	0.251637	+	0.145283i	0.620514	−	0.784196i	$-0.286924\pi$
$809$	7.15729	+	4.13227i	0.251637	+	0.145283i	−0.368877	+	0.929478i	$0.620257\pi$
$810$		0			0
$811$		−	41.3783i		−	1.45299i	−0.687173	−	0.726494i	$-0.741149\pi$
$811$		−	41.3783i		−	1.45299i	0.687173	−	0.726494i	$-0.258851\pi$
$812$	−1.66313	−	7.82778i	−0.0583643	−	0.274701i
$813$		0			0
$814$	−11.8196	+	20.4722i	−0.414278	+	0.717550i
$815$	−79.3654			−2.78005
$816$		0			0
$817$			4.81823i			0.168569i
$818$	−19.3524			−0.676640
$819$		0			0
$820$	16.8067			0.586917
$821$		−	25.6758i		−	0.896090i	−0.894011	−	0.448045i	$-0.852120\pi$
$821$		−	25.6758i		−	0.896090i	0.894011	−	0.448045i	$-0.147880\pi$
$822$		0			0
$823$	35.4083			1.23426			0.617128	−	0.786863i	$-0.288296\pi$
$823$	35.4083			1.23426			0.617128	+	0.786863i	$0.288296\pi$
$824$	7.71320	−	13.3597i	0.268702	−	0.465406i
$825$		0			0
$826$	−4.84811	−	1.57572i	−0.168687	−	0.0548263i
$827$			40.1435i			1.39592i	0.716135	+	0.697962i	$0.245910\pi$
$827$			40.1435i			1.39592i	−0.716135	+	0.697962i	$0.754090\pi$
$828$		0			0
$829$	−21.2078	−	12.2443i	−0.736578	−	0.425263i	0.0842460	−	0.996445i	$-0.473152\pi$
$829$	−21.2078	−	12.2443i	−0.736578	−	0.425263i	−0.820824	+	0.571182i	$0.806485\pi$
$830$	26.1582	+	15.1025i	0.907965	+	0.524214i
$831$		0			0
$832$	−1.68024	−	3.19011i	−0.0582520	−	0.110597i
$833$	−10.6580	−	7.74636i	−0.369278	−	0.268396i
$834$		0			0
$835$	−19.1224			−0.661757
$836$	−2.57647			−0.0891092
$837$		0			0
$838$	12.2536	−	7.07461i	0.423293	−	0.244388i
$839$	10.0592	−	17.4230i	0.347281	−	0.601507i	−0.638485	−	0.769634i	$-0.720439\pi$
$839$	10.0592	−	17.4230i	0.347281	−	0.601507i	0.985765	+	0.168127i	$0.0537718\pi$
$840$		0			0
$841$	−9.92570	+	17.1918i	−0.342266	+	0.592822i
$842$			19.4735i			0.671100i
$843$		0			0
$844$	−5.23782	−	9.07217i	−0.180293	−	0.312277i
$845$	−17.9634	−	37.5734i	−0.617960	−	1.29256i
$846$		0			0
$847$	21.6088	−	4.59110i	0.742486	−	0.157752i
$848$	1.48629	−	0.858108i	0.0510393	−	0.0294676i
$849$		0			0
$850$	−8.57903	+	4.95311i	−0.294258	+	0.169890i
$851$		−	23.7780i		−	0.815100i
$852$		0			0
$853$		−	23.9060i		−	0.818525i	−0.912417	−	0.409263i	$-0.865786\pi$
$853$		−	23.9060i		−	0.818525i	0.912417	−	0.409263i	$-0.134214\pi$
$854$	4.85271	−	1.03103i	0.166056	−	0.0352811i
$855$		0			0
$856$	6.55593			0.224077
$857$	−0.331806	−	0.574705i	−0.0113343	−	0.0196316i	0.860303	−	0.509784i	$-0.170275\pi$
$857$	−0.331806	−	0.574705i	−0.0113343	−	0.0196316i	−0.871637	+	0.490152i	$0.836941\pi$
$858$		0			0
$859$	−33.7633	−	19.4932i	−1.15199	−	0.665101i	−0.202617	−	0.979258i	$-0.564945\pi$
$859$	−33.7633	−	19.4932i	−1.15199	−	0.665101i	−0.949371	+	0.314157i	$0.898278\pi$
$860$	−13.1767	−	22.8227i	−0.449321	−	0.778246i
$861$		0			0
$862$	6.41451	−	11.1103i	0.218479	−	0.378417i
$863$	12.6438	+	7.29991i	0.430400	+	0.248492i	0.699517	−	0.714616i	$-0.253398\pi$
$863$	12.6438	+	7.29991i	0.430400	+	0.248492i	−0.269117	+	0.963108i	$0.586732\pi$
$864$		0			0
$865$	−20.0680			−0.682332
$866$	5.31506	−	9.20595i	0.180613	−	0.312831i
$867$		0			0
$868$	3.54380	+	16.6795i	0.120284	+	0.566139i
$869$	−1.86566	+	1.07714i	−0.0632882	+	0.0365395i
$870$		0			0
$871$	50.5361	+	1.96263i	1.71235	+	0.0665011i
$872$	−11.0953	+	6.40585i	−0.375733	+	0.216929i
$873$		0			0
$874$	2.24439	−	1.29580i	0.0759176	−	0.0438311i
$875$	0.688979	−	2.11983i	0.0232918	−	0.0716632i
$876$		0			0
$877$	11.3154	+	19.5988i	0.382094	+	0.661805i	0.991361	−	0.131159i	$-0.0418699\pi$
$877$	11.3154	+	19.5988i	0.382094	+	0.661805i	−0.609268	+	0.792965i	$0.708537\pi$
$878$	30.0083			1.01273
$879$		0			0
$880$	12.2040	−	7.04601i	0.411398	−	0.237521i
$881$	5.53432	+	9.58572i	0.186456	+	0.322951i	0.944066	−	0.329756i	$-0.106967\pi$
$881$	5.53432	+	9.58572i	0.186456	+	0.322951i	−0.757610	+	0.652707i	$0.773633\pi$
$882$		0			0
$883$	−40.4115			−1.35995			−0.679977	−	0.733233i	$-0.738010\pi$
$883$	−40.4115			−1.35995			−0.679977	+	0.733233i	$0.738010\pi$
$884$	−3.16263	−	6.00456i	−0.106371	−	0.201955i
$885$		0			0
$886$	18.0142	−	31.2015i	0.605200	−	1.04824i
$887$	−42.2930			−1.42006			−0.710031	−	0.704171i	$-0.751319\pi$
$887$	−42.2930			−1.42006			−0.710031	+	0.704171i	$0.751319\pi$
$888$		0			0
$889$	−37.5998	+	7.98862i	−1.26106	+	0.267930i
$890$	25.7126	+	14.8452i	0.861888	+	0.497612i
$891$		0			0
$892$	10.1635	−	5.86791i	0.340300	−	0.196472i
$893$			1.06482i			0.0356330i
$894$		0			0
$895$	16.3611	−	9.44608i	0.546891	−	0.315748i
$896$	2.51619	+	0.817803i	0.0840599	+	0.0273209i
$897$		0			0
$898$	−18.3530	+	31.7884i	−0.612449	+	1.06079i
$899$	−9.74694	+	16.8822i	−0.325079	+	0.563053i
$900$		0			0
$901$	2.79755	−	1.61517i	0.0932001	−	0.0538091i
$902$	−23.0772			−0.768388
$903$		0			0
$904$	−6.22608	+	10.7839i	−0.207076	+	0.358667i
$905$	−64.9427	−	37.4947i	−2.15877	−	1.24637i
$906$		0			0
$907$	−19.0603	+	33.0133i	−0.632885	+	1.09619i	0.354074	+	0.935217i	$0.384796\pi$
$907$	−19.0603	+	33.0133i	−0.632885	+	1.09619i	−0.986959	+	0.160972i	$0.948537\pi$
$908$	26.8747			0.891869
$909$		0			0
$910$	28.6753	+	10.5670i	0.950576	+	0.350291i
$911$		−	48.0230i		−	1.59107i	−0.605905	−	0.795537i	$-0.707189\pi$
$911$		−	48.0230i		−	1.59107i	0.605905	−	0.795537i	$-0.292811\pi$
$912$		0			0
$913$	−35.9177	−	20.7371i	−1.18870	−	0.686297i
$914$			36.3165i			1.20124i
$915$		0			0
$916$	−16.7640	−	9.67870i	−0.553898	−	0.319793i
$917$	−4.13359	−	4.59163i	−0.136503	−	0.151629i
$918$		0			0
$919$	2.22846	+	3.85981i	0.0735102	+	0.127323i	0.900437	−	0.434986i	$-0.143247\pi$
$919$	2.22846	+	3.85981i	0.0735102	+	0.127323i	−0.826927	+	0.562309i	$0.809913\pi$
$920$	−7.08737	+	12.2757i	−0.233664	+	0.404718i
$921$		0			0
$922$	−16.1346	−	9.31532i	−0.531365	−	0.306784i
$923$	0.536557	−	13.8159i	0.0176610	−	0.454757i
$924$		0			0
$925$	−14.1416	−	24.4940i	−0.464973	−	0.805357i
$926$		−	26.9786i		−	0.886571i
$927$		0			0
$928$	1.51233	+	2.61944i	0.0496447	+	0.0859872i
$929$	−29.4900	−	51.0781i	−0.967534	−	1.67582i	−0.702646	−	0.711540i	$-0.747998\pi$
$929$	−29.4900	−	51.0781i	−0.967534	−	1.67582i	−0.264889	−	0.964279i	$-0.585335\pi$
$930$		0			0
$931$	4.07749	+	0.429287i	0.133634	+	0.0140693i
$932$	19.3444	+	11.1685i	0.633647	+	0.365836i
$933$		0			0
$934$	35.1434	+	20.2900i	1.14993	+	0.663910i
$935$	22.9710	−	13.2623i	0.751232	−	0.433724i
$936$		0			0
$937$			5.16469i			0.168723i	0.996435	+	0.0843615i	$0.0268850\pi$
$937$			5.16469i			0.168723i	−0.996435	+	0.0843615i	$0.973115\pi$
$938$	−27.5813	+	24.8299i	−0.900561	+	0.810725i
$939$		0			0
$940$	−2.91203	−	5.04378i	−0.0949799	−	0.164510i
$941$	23.6183	+	40.9082i	0.769936	+	1.33357i	0.937597	+	0.347724i	$0.113045\pi$
$941$	23.6183	+	40.9082i	0.769936	+	1.33357i	−0.167661	+	0.985845i	$0.553621\pi$
$942$		0			0
$943$	20.1028	−	11.6063i	0.654637	−	0.377955i
$944$	1.92677			0.0627110
$945$		0			0
$946$	18.0928	+	31.3376i	0.588247	+	1.01887i
$947$			18.6002i			0.604425i	0.953241	+	0.302213i	$0.0977253\pi$
$947$			18.6002i			0.604425i	−0.953241	+	0.302213i	$0.902275\pi$
$948$		0			0
$949$	45.7837	+	28.8583i	1.48620	+	0.936782i
$950$	1.54131	−	2.66963i	0.0500068	−	0.0866143i
$951$		0			0
$952$	4.73608	+	1.53931i	0.153497	+	0.0498892i
$953$	−27.1451	−	15.6722i	−0.879317	−	0.507674i	−0.00888383	−	0.999961i	$-0.502828\pi$
$953$	−27.1451	−	15.6722i	−0.879317	−	0.507674i	−0.870433	+	0.492287i	$0.836161\pi$
$954$		0			0
$955$		−	54.1931i		−	1.75365i
$956$		−	21.2454i		−	0.687126i
$957$		0			0
$958$	−27.3794	−	15.8075i	−0.884587	−	0.510716i
$959$	−43.4530	−	14.1229i	−1.40317	−	0.456054i
$960$		0			0
$961$	5.26883	−	9.12588i	0.169962	−	0.294383i
$962$	17.1436	−	9.02962i	0.552733	−	0.291127i
$963$		0			0
$964$			3.87232i			0.124719i
$965$	−4.99388	−	8.64965i	−0.160759	−	0.278442i
$966$		0			0
$967$	23.6188			0.759528			0.379764	−	0.925083i	$-0.376005\pi$
$967$	23.6188			0.759528			0.379764	+	0.925083i	$0.376005\pi$
$968$	−7.23101	+	4.17483i	−0.232414	+	0.134184i
$969$		0			0
$970$	−3.53011	−	6.11432i	−0.113345	−	0.196319i
$971$	−13.7566	−	23.8271i	−0.441470	−	0.764648i	0.556329	−	0.830962i	$-0.312209\pi$
$971$	−13.7566	−	23.8271i	−0.441470	−	0.764648i	−0.997799	+	0.0663139i	$0.978876\pi$
$972$		0			0
$973$	−33.1443	+	29.8380i	−1.06256	+	0.956563i
$974$			35.5216i			1.13818i
$975$		0			0
$976$	−1.62388	+	0.937547i	−0.0519791	+	0.0300102i
$977$	−13.9295	−	8.04219i	−0.445644	−	0.257293i	0.260345	−	0.965516i	$-0.416164\pi$
$977$	−13.9295	−	8.04219i	−0.445644	−	0.257293i	−0.705989	+	0.708223i	$0.749497\pi$
$978$		0			0
$979$	−35.3058	−	20.3838i	−1.12838	−	0.651469i
$980$	−20.4880	+	9.11751i	−0.654464	+	0.291248i
$981$		0			0
$982$	−5.48447	−	9.49939i	−0.175017	−	0.303138i
$983$	3.25142	+	5.63162i	0.103704	+	0.179621i	0.913208	−	0.407494i	$-0.133597\pi$
$983$	3.25142	+	5.63162i	0.103704	+	0.179621i	−0.809504	+	0.587114i	$0.800264\pi$
$984$		0			0
$985$			18.4052i			0.586437i
$986$	2.84658	+	4.93042i	0.0906535	+	0.157016i
$987$		0			0
$988$	1.78655	+	1.12610i	0.0568378	+	0.0358260i
$989$	−31.5216	−	18.1990i	−1.00233	−	0.578694i
$990$		0			0
$991$	18.9755	−	32.8666i	0.602778	−	1.04404i	−0.389621	−	0.920975i	$-0.627394\pi$
$991$	18.9755	−	32.8666i	0.602778	−	1.04404i	0.992398	−	0.123066i	$-0.0392728\pi$
$992$	−3.22249	−	5.58151i	−0.102314	−	0.177213i
$993$		0			0
$994$	6.78818	+	7.54037i	0.215308	+	0.239166i
$995$	53.2896	+	30.7668i	1.68939	+	0.975372i
$996$		0			0
$997$			42.3287i			1.34056i	0.742107	+	0.670281i	$0.233827\pi$
$997$			42.3287i			1.34056i	−0.742107	+	0.670281i	$0.766173\pi$
$998$	−0.654887	−	0.378099i	−0.0207301	−	0.0119685i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.cm.a.341.5	yes	72
3.2	odd	2	inner	1638.2.cm.a.341.32	yes	72
7.3	odd	6		1638.2.bq.a.1277.22	yes	72
13.9	even	3		1638.2.bq.a.971.15	✓	72
21.17	even	6		1638.2.bq.a.1277.15	yes	72
39.35	odd	6		1638.2.bq.a.971.22	yes	72
91.87	odd	6	inner	1638.2.cm.a.269.32	yes	72
273.269	even	6	inner	1638.2.cm.a.269.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bq.a.971.15	✓	72	13.9	even	3
1638.2.bq.a.971.22	yes	72	39.35	odd	6
1638.2.bq.a.1277.15	yes	72	21.17	even	6
1638.2.bq.a.1277.22	yes	72	7.3	odd	6
1638.2.cm.a.269.5	yes	72	273.269	even	6	inner
1638.2.cm.a.269.32	yes	72	91.87	odd	6	inner
1638.2.cm.a.341.5	yes	72	1.1	even	1	trivial
1638.2.cm.a.341.32	yes	72	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.cm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.60179 + 2.77439i) q^{5} +(0.817803 - 2.51619i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.60179 + 2.77439i) q^{5} +(0.817803 - 2.51619i) q^{7} +1.00000i q^{8} +(2.77439 + 1.60179i) q^{10} +(-3.80949 - 2.19941i) q^{11} +(1.68024 + 3.19011i) q^{13} +(-2.51619 - 0.817803i) q^{14} +1.00000 q^{16} +1.88224 q^{17} +(-0.507247 + 0.292859i) q^{19} +(1.60179 - 2.77439i) q^{20} +(-2.19941 + 3.80949i) q^{22} -4.42465i q^{23} +(-2.63149 - 4.55787i) q^{25} +(3.19011 - 1.68024i) q^{26} +(-0.817803 + 2.51619i) q^{28} +(-2.61944 + 1.51233i) q^{29} +(5.58151 - 3.22249i) q^{31} -1.00000i q^{32} -1.88224i q^{34} +(5.67093 + 6.29932i) q^{35} +5.37400 q^{37} +(0.292859 + 0.507247i) q^{38} +(-2.77439 - 1.60179i) q^{40} +(2.62311 + 4.54336i) q^{41} +(4.11310 - 7.12409i) q^{43} +(3.80949 + 2.19941i) q^{44} -4.42465 q^{46} +(0.908990 - 1.57442i) q^{47} +(-5.66240 - 4.11549i) q^{49} +(-4.55787 + 2.63149i) q^{50} +(-1.68024 - 3.19011i) q^{52} +(1.48629 - 0.858108i) q^{53} +(12.2040 - 7.04601i) q^{55} +(2.51619 + 0.817803i) q^{56} +(1.51233 + 2.61944i) q^{58} +1.92677 q^{59} +(-1.62388 + 0.937547i) q^{61} +(-3.22249 - 5.58151i) q^{62} -1.00000 q^{64} +(-11.5420 - 0.448247i) q^{65} +(7.01339 - 12.1475i) q^{67} -1.88224 q^{68} +(6.29932 - 5.67093i) q^{70} +(-3.32098 - 1.91737i) q^{71} +(12.9992 - 7.50506i) q^{73} -5.37400i q^{74} +(0.507247 - 0.292859i) q^{76} +(-8.64955 + 7.78671i) q^{77} +(0.244870 - 0.424127i) q^{79} +(-1.60179 + 2.77439i) q^{80} +(4.54336 - 2.62311i) q^{82} +9.42846 q^{83} +(-3.01497 + 5.22208i) q^{85} +(-7.12409 - 4.11310i) q^{86} +(2.19941 - 3.80949i) q^{88} +9.26784 q^{89} +(9.40101 - 1.61893i) q^{91} +4.42465i q^{92} +(-1.57442 - 0.908990i) q^{94} -1.87640i q^{95} +(-1.90859 - 1.10192i) q^{97} +(-4.11549 + 5.66240i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) \) 72 * q - 72 * q^4 - 4 * q^7	\( 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) \) 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more