LMFDB - Embedded newform 804.2.o.d.641.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.2
Character	$\chi$	$=$	804.641
Dual form			804.2.o.d.365.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71192 - 0.263286i) q^{3} -0.454473 q^{5} +(-0.768091 + 0.443457i) q^{7} +(2.86136 + 0.901449i) q^{9} +O(q^{10})$	\(q+(-1.71192 - 0.263286i) q^{3} -0.454473 q^{5} +(-0.768091 + 0.443457i) q^{7} +(2.86136 + 0.901449i) q^{9} +(-1.57034 - 2.71991i) q^{11} +(2.43029 + 1.40313i) q^{13} +(0.778023 + 0.119656i) q^{15} +(0.940366 + 0.542920i) q^{17} +(0.289306 - 0.501092i) q^{19} +(1.43167 - 0.556938i) q^{21} +(-3.87917 - 2.23964i) q^{23} -4.79345 q^{25} +(-4.66109 - 2.29657i) q^{27} +(-8.89584 + 5.13602i) q^{29} +(-3.83109 + 2.21188i) q^{31} +(1.97219 + 5.06972i) q^{33} +(0.349077 - 0.201540i) q^{35} +(2.10137 - 3.63968i) q^{37} +(-3.79105 - 3.04191i) q^{39} +(0.941989 + 1.63157i) q^{41} -0.668277i q^{43} +(-1.30041 - 0.409685i) q^{45} +(-4.28992 + 2.47679i) q^{47} +(-3.10669 + 5.38095i) q^{49} +(-1.46689 - 1.17702i) q^{51} +1.78184 q^{53} +(0.713678 + 1.23613i) q^{55} +(-0.627199 + 0.781661i) q^{57} -1.78284i q^{59} +(-11.7989 - 6.81208i) q^{61} +(-2.59754 + 0.576497i) q^{63} +(-1.10450 - 0.637685i) q^{65} +(-7.95026 - 1.94764i) q^{67} +(6.05117 + 4.85542i) q^{69} +(-7.11599 + 4.10842i) q^{71} +(-5.50162 + 9.52908i) q^{73} +(8.20602 + 1.26205i) q^{75} +(2.41233 + 1.39276i) q^{77} +(-2.39051 + 1.38016i) q^{79} +(7.37478 + 5.15874i) q^{81} +(3.07529 + 1.77552i) q^{83} +(-0.427371 - 0.246743i) q^{85} +(16.5812 - 6.45032i) q^{87} -8.06035i q^{89} -2.48891 q^{91} +(7.14089 - 2.77790i) q^{93} +(-0.131482 + 0.227733i) q^{95} +(1.99555 + 1.15213i) q^{97} +(-2.04145 - 9.19823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{9}+O(q^{10}) $ 36 * q + 4 * q^9	$ 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) $ 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.71192	−	0.263286i	−0.988379	−	0.152008i
$3$	−1.71192	−	0.263286i	−0.988379	−	0.152008i
$4$		0			0
$5$	−0.454473			−0.203247			−0.101623	−	0.994823i	$-0.532404\pi$
$5$	−0.454473			−0.203247			−0.101623	+	0.994823i	$0.532404\pi$
$6$		0			0
$7$	−0.768091	+	0.443457i	−0.290311	+	0.167611i	−0.638082	−	0.769968i	$-0.720272\pi$
$7$	−0.768091	+	0.443457i	−0.290311	+	0.167611i	0.347771	+	0.937579i	$0.386939\pi$
$8$		0			0
$9$	2.86136	+	0.901449i	0.953787	+	0.300483i
$10$		0			0
$11$	−1.57034	−	2.71991i	−0.473476	−	0.820084i	0.526063	−	0.850445i	$-0.323667\pi$
$11$	−1.57034	−	2.71991i	−0.473476	−	0.820084i	−0.999539	+	0.0303616i	$0.990334\pi$
$12$		0			0
$13$	2.43029	+	1.40313i	0.674042	+	0.389158i	0.797606	−	0.603178i	$-0.206099\pi$
$13$	2.43029	+	1.40313i	0.674042	+	0.389158i	−0.123564	+	0.992337i	$0.539433\pi$
$14$		0			0
$15$	0.778023	+	0.119656i	0.200885	+	0.0308951i
$16$		0			0
$17$	0.940366	+	0.542920i	0.228072	+	0.131678i	0.609682	−	0.792646i	$-0.291297\pi$
$17$	0.940366	+	0.542920i	0.228072	+	0.131678i	−0.381610	+	0.924323i	$0.624630\pi$
$18$		0			0
$19$	0.289306	−	0.501092i	0.0663713	−	0.114958i	−0.830930	−	0.556377i	$-0.812191\pi$
$19$	0.289306	−	0.501092i	0.0663713	−	0.114958i	0.897301	+	0.441418i	$0.145524\pi$
$20$		0			0
$21$	1.43167	−	0.556938i	0.312416	−	0.121534i
$22$		0			0
$23$	−3.87917	−	2.23964i	−0.808862	−	0.466997i	0.0376983	−	0.999289i	$-0.487997\pi$
$23$	−3.87917	−	2.23964i	−0.808862	−	0.466997i	−0.846561	+	0.532292i	$0.821331\pi$
$24$		0			0
$25$	−4.79345			−0.958691
$26$		0			0
$27$	−4.66109	−	2.29657i	−0.897028	−	0.441975i
$28$		0			0
$29$	−8.89584	+	5.13602i	−1.65192	+	0.953734i	−0.675633	+	0.737238i	$0.736130\pi$
$29$	−8.89584	+	5.13602i	−1.65192	+	0.953734i	−0.976283	+	0.216496i	$0.930537\pi$
$30$		0			0
$31$	−3.83109	+	2.21188i	−0.688085	+	0.397266i	−0.802894	−	0.596122i	$-0.796708\pi$
$31$	−3.83109	+	2.21188i	−0.688085	+	0.397266i	0.114809	+	0.993388i	$0.463374\pi$
$32$		0			0
$33$	1.97219	+	5.06972i	0.343314	+	0.882526i
$34$		0			0
$35$	0.349077	−	0.201540i	0.0590048	−	0.0340664i
$36$		0			0
$37$	2.10137	−	3.63968i	0.345464	−	0.598360i	−0.639974	−	0.768396i	$-0.721055\pi$
$37$	2.10137	−	3.63968i	0.345464	−	0.598360i	0.985438	+	0.170036i	$0.0543884\pi$
$38$		0			0
$39$	−3.79105	−	3.04191i	−0.607054	−	0.487096i
$40$		0			0
$41$	0.941989	+	1.63157i	0.147114	+	0.254809i	0.930160	−	0.367155i	$-0.119668\pi$
$41$	0.941989	+	1.63157i	0.147114	+	0.254809i	−0.783046	+	0.621964i	$0.786335\pi$
$42$		0			0
$43$		−	0.668277i		−	0.101911i	−0.998701	−	0.0509556i	$-0.983773\pi$
$43$		−	0.668277i		−	0.101911i	0.998701	−	0.0509556i	$-0.0162267\pi$
$44$		0			0
$45$	−1.30041	−	0.409685i	−0.193854	−	0.0610722i
$46$		0			0
$47$	−4.28992	+	2.47679i	−0.625749	+	0.361277i	−0.779104	−	0.626895i	$-0.784326\pi$
$47$	−4.28992	+	2.47679i	−0.625749	+	0.361277i	0.153355	+	0.988171i	$0.450992\pi$
$48$		0			0
$49$	−3.10669	+	5.38095i	−0.443813	+	0.768707i
$50$		0			0
$51$	−1.46689	−	1.17702i	−0.205406	−	0.164816i
$52$		0			0
$53$	1.78184			0.244754			0.122377	−	0.992484i	$-0.460948\pi$
$53$	1.78184			0.244754			0.122377	+	0.992484i	$0.460948\pi$
$54$		0			0
$55$	0.713678	+	1.23613i	0.0962323	+	0.166679i
$56$		0			0
$57$	−0.627199	+	0.781661i	−0.0830746	+	0.103534i
$58$		0			0
$59$		−	1.78284i		−	0.232106i	−0.993243	−	0.116053i	$-0.962976\pi$
$59$		−	1.78284i		−	0.232106i	0.993243	−	0.116053i	$-0.0370243\pi$
$60$		0			0
$61$	−11.7989	−	6.81208i	−1.51069	−	0.872198i	−0.999922	−	0.0124800i	$-0.996027\pi$
$61$	−11.7989	−	6.81208i	−1.51069	−	0.872198i	−0.510769	−	0.859718i	$-0.670639\pi$
$62$		0			0
$63$	−2.59754	+	0.576497i	−0.327259	+	0.0726318i
$64$		0			0
$65$	−1.10450	−	0.637685i	−0.136997	−	0.0790951i
$66$		0			0
$67$	−7.95026	−	1.94764i	−0.971279	−	0.237942i
$67$	−7.95026	−	1.94764i	−0.971279	−	0.237942i
$68$		0			0
$69$	6.05117	+	4.85542i	0.728475	+	0.584524i
$70$		0			0
$71$	−7.11599	+	4.10842i	−0.844513	+	0.487580i	−0.858796	−	0.512318i	$-0.828787\pi$
$71$	−7.11599	+	4.10842i	−0.844513	+	0.487580i	0.0142830	+	0.999898i	$0.495453\pi$
$72$		0			0
$73$	−5.50162	+	9.52908i	−0.643916	+	1.11529i	0.340635	+	0.940196i	$0.389358\pi$
$73$	−5.50162	+	9.52908i	−0.643916	+	1.11529i	−0.984551	+	0.175099i	$0.943975\pi$
$74$		0			0
$75$	8.20602	+	1.26205i	0.947550	+	0.145729i
$76$		0			0
$77$	2.41233	+	1.39276i	0.274910	+	0.158720i
$78$		0			0
$79$	−2.39051	+	1.38016i	−0.268953	+	0.155280i	−0.628412	−	0.777881i	$-0.716295\pi$
$79$	−2.39051	+	1.38016i	−0.268953	+	0.155280i	0.359459	+	0.933161i	$0.382961\pi$
$80$		0			0
$81$	7.37478	+	5.15874i	0.819420	+	0.573194i
$82$		0			0
$83$	3.07529	+	1.77552i	0.337557	+	0.194889i	0.659191	−	0.751975i	$-0.270899\pi$
$83$	3.07529	+	1.77552i	0.337557	+	0.194889i	−0.321634	+	0.946864i	$0.604232\pi$
$84$		0			0
$85$	−0.427371	−	0.246743i	−0.0463549	−	0.0267630i
$86$		0			0
$87$	16.5812	−	6.45032i	1.77770	−	0.691547i
$88$		0			0
$89$		−	8.06035i		−	0.854395i	−0.904158	−	0.427198i	$-0.859501\pi$
$89$		−	8.06035i		−	0.854395i	0.904158	−	0.427198i	$-0.140499\pi$
$90$		0			0
$91$	−2.48891			−0.260909
$92$		0			0
$93$	7.14089	−	2.77790i	0.740476	−	0.288055i
$94$		0			0
$95$	−0.131482	+	0.227733i	−0.0134897	+	0.0233649i
$96$		0			0
$97$	1.99555	+	1.15213i	0.202618	+	0.116981i	0.597876	−	0.801589i	$-0.296012\pi$
$97$	1.99555	+	1.15213i	0.202618	+	0.116981i	−0.395258	+	0.918570i	$0.629345\pi$
$98$		0			0
$99$	−2.04145	−	9.19823i	−0.205174	−	0.924457i
$100$		0			0
$101$	−0.409789	−	0.709775i	−0.0407755	−	0.0706252i	0.844917	−	0.534897i	$-0.179650\pi$
$101$	−0.409789	−	0.709775i	−0.0407755	−	0.0706252i	−0.885693	+	0.464272i	$0.846316\pi$
$102$		0			0
$103$	−5.36487	−	9.29223i	−0.528617	−	0.915591i	−0.999443	−	0.0333652i	$-0.989378\pi$
$103$	−5.36487	−	9.29223i	−0.528617	−	0.915591i	0.470827	−	0.882226i	$-0.343956\pi$
$104$		0			0
$105$	−0.650655	+	0.253113i	−0.0634974	+	0.0247013i
$106$		0			0
$107$		−	8.46063i		−	0.817920i	−0.912552	−	0.408960i	$-0.865891\pi$
$107$		−	8.46063i		−	0.817920i	0.912552	−	0.408960i	$-0.134109\pi$
$108$		0			0
$109$		−	10.3730i		−	0.993552i	−0.867879	−	0.496776i	$-0.834517\pi$
$109$		−	10.3730i		−	0.993552i	0.867879	−	0.496776i	$-0.165483\pi$
$110$		0			0
$111$	−4.55566	+	5.67760i	−0.432405	+	0.538894i
$112$		0			0
$113$	7.11361	+	12.3211i	0.669192	+	1.15907i	0.978130	+	0.207993i	$0.0666931\pi$
$113$	7.11361	+	12.3211i	0.669192	+	1.15907i	−0.308938	+	0.951082i	$0.599974\pi$
$114$		0			0
$115$	1.76298	+	1.01786i	0.164399	+	0.0949156i
$116$		0			0
$117$	5.68910	+	6.20565i	0.525957	+	0.573712i
$118$		0			0
$119$	−0.963048			−0.0882825
$120$		0			0
$121$	0.568059	−	0.983908i	0.0516418	−	0.0894462i
$122$		0			0
$123$	−1.18304	−	3.04114i	−0.106671	−	0.274210i
$124$		0			0
$125$	4.45086			0.398097
$126$		0			0
$127$	7.31681	+	12.6731i	0.649262	+	1.12455i	0.983300	+	0.181994i	$0.0582553\pi$
$127$	7.31681	+	12.6731i	0.649262	+	1.12455i	−0.334038	+	0.942560i	$0.608411\pi$
$128$		0			0
$129$	−0.175948	+	1.14404i	−0.0154913	+	0.100727i
$130$		0			0
$131$		−	16.7935i		−	1.46726i	−0.679551	−	0.733628i	$-0.737825\pi$
$131$		−	16.7935i		−	1.46726i	0.679551	−	0.733628i	$-0.262175\pi$
$132$		0			0
$133$			0.513179i			0.0444983i
$134$		0			0
$135$	2.11834	+	1.04373i	0.182318	+	0.0898298i
$136$		0			0
$137$	19.7518			1.68751			0.843754	−	0.536731i	$-0.180341\pi$
$137$	19.7518			1.68751			0.843754	+	0.536731i	$0.180341\pi$
$138$		0			0
$139$			6.61168i			0.560796i	0.959884	+	0.280398i	$0.0904664\pi$
$139$			6.61168i			0.560796i	−0.959884	+	0.280398i	$0.909534\pi$
$140$		0			0
$141$	7.99612	−	3.11059i	0.673395	−	0.261959i
$142$		0			0
$143$		−	8.81357i		−	0.737028i
$144$		0			0
$145$	4.04292	−	2.33418i	0.335746	−	0.193843i
$146$		0			0
$147$	6.73514	−	8.39382i	0.555505	−	0.692311i
$148$		0			0
$149$			12.3454i			1.01137i	0.862718	+	0.505686i	$0.168761\pi$
$149$			12.3454i			1.01137i	−0.862718	+	0.505686i	$0.831239\pi$
$150$		0			0
$151$	−7.15252	+	12.3885i	−0.582064	+	1.00816i	0.413171	+	0.910654i	$0.364421\pi$
$151$	−7.15252	+	12.3885i	−0.582064	+	1.00816i	−0.995234	+	0.0975106i	$0.968912\pi$
$152$		0			0
$153$	2.20131	+	2.40118i	0.177965	+	0.194124i
$154$		0			0
$155$	1.74113	−	1.00524i	0.139851	−	0.0807430i
$156$		0			0
$157$	5.20590	−	9.01689i	0.415476	−	0.719626i	−0.580002	−	0.814615i	$-0.696948\pi$
$157$	5.20590	−	9.01689i	0.415476	−	0.719626i	0.995478	+	0.0949890i	$0.0302816\pi$
$158$		0			0
$159$	−3.05037	−	0.469132i	−0.241910	−	0.0372046i
$160$		0			0
$161$	3.97274			0.313096
$162$		0			0
$163$	−0.971234	−	1.68223i	−0.0760729	−	0.131762i	0.825479	−	0.564432i	$-0.190905\pi$
$163$	−0.971234	−	1.68223i	−0.0760729	−	0.131762i	−0.901552	+	0.432670i	$0.857572\pi$
$164$		0			0
$165$	−0.896308	−	2.30405i	−0.0697775	−	0.179370i
$166$		0			0
$167$	6.06888	−	3.50387i	0.469624	−	0.271137i	−0.246459	−	0.969153i	$-0.579267\pi$
$167$	6.06888	−	3.50387i	0.469624	−	0.271137i	0.716082	+	0.698016i	$0.245934\pi$
$168$		0			0
$169$	−2.56245	−	4.43829i	−0.197112	−	0.341407i
$170$		0			0
$171$	1.27952	−	1.17301i	0.0978471	−	0.0897024i
$172$		0			0
$173$	13.5486	+	7.82227i	1.03008	+	0.594716i	0.917007	−	0.398871i	$-0.130598\pi$
$173$	13.5486	+	7.82227i	1.03008	+	0.594716i	0.113071	+	0.993587i	$0.463931\pi$
$174$		0			0
$175$	3.68181	−	2.12569i	0.278319	−	0.160687i
$176$		0			0
$177$	−0.469397	+	3.05209i	−0.0352820	+	0.229409i
$178$		0			0
$179$	−1.50694			−0.112634			−0.0563169	−	0.998413i	$-0.517936\pi$
$179$	−1.50694			−0.112634			−0.0563169	+	0.998413i	$0.517936\pi$
$180$		0			0
$181$	−6.36939	−	11.0321i	−0.473433	−	0.820011i	0.526104	−	0.850420i	$-0.323652\pi$
$181$	−6.36939	−	11.0321i	−0.473433	−	0.820011i	−0.999538	+	0.0304096i	$0.990319\pi$
$182$		0			0
$183$	18.4052	+	14.7682i	1.36055	+	1.09170i
$184$		0			0
$185$	−0.955018	+	1.65414i	−0.0702143	+	0.121615i
$186$		0			0
$187$		−	3.41028i		−	0.249384i
$188$		0			0
$189$	4.59857	−	0.303024i	0.334497	−	0.0220417i
$190$		0			0
$191$	−3.79740	+	6.57728i	−0.274770	+	0.475916i	−0.970077	−	0.242797i	$-0.921935\pi$
$191$	−3.79740	+	6.57728i	−0.274770	+	0.475916i	0.695307	+	0.718713i	$0.255268\pi$
$192$		0			0
$193$	−3.58658			−0.258168			−0.129084	−	0.991634i	$-0.541204\pi$
$193$	−3.58658			−0.258168			−0.129084	+	0.991634i	$0.541204\pi$
$194$		0			0
$195$	1.72293	+	1.38247i	0.123382	+	0.0990006i
$196$		0			0
$197$	0.585266	+	1.01371i	0.0416985	+	0.0722239i	0.886121	−	0.463453i	$-0.153390\pi$
$197$	0.585266	+	1.01371i	0.0416985	+	0.0722239i	−0.844423	+	0.535677i	$0.820056\pi$
$198$		0			0
$199$	1.39811	−	2.42159i	0.0991092	−	0.171662i	−0.812207	−	0.583369i	$-0.801734\pi$
$199$	1.39811	−	2.42159i	0.0991092	−	0.171662i	0.911316	+	0.411707i	$0.135067\pi$
$200$		0			0
$201$	13.0975	+	5.42740i	0.923823	+	0.382819i
$202$		0			0
$203$	4.55521	−	7.88985i	0.319713	−	0.553759i
$204$		0			0
$205$	−0.428109	−	0.741506i	−0.0299004	−	0.0517890i
$206$		0			0
$207$	−9.08078	−	9.90529i	−0.631158	−	0.688465i
$208$		0			0
$209$	−1.81723			−0.125701
$210$		0			0
$211$	−2.07752	+	3.59838i	−0.143023	+	0.247723i	−0.928633	−	0.370998i	$-0.879016\pi$
$211$	−2.07752	+	3.59838i	−0.143023	+	0.247723i	0.785611	+	0.618721i	$0.212349\pi$
$212$		0			0
$213$	13.2637	−	5.15976i	0.908815	−	0.353541i
$214$		0			0
$215$			0.303714i			0.0207131i
$216$		0			0
$217$	1.96175	−	3.39785i	0.133172	−	0.230661i
$218$		0			0
$219$	11.9272	−	14.8646i	0.805967	−	1.00445i
$220$		0			0
$221$	1.52358	+	2.63891i	0.102487	+	0.177512i
$222$		0			0
$223$	−13.0738			−0.875486			−0.437743	−	0.899100i	$-0.644222\pi$
$223$	−13.0738			−0.875486			−0.437743	+	0.899100i	$0.644222\pi$
$224$		0			0
$225$	−13.7158	−	4.32106i	−0.914387	−	0.288070i
$226$		0			0
$227$	6.62946	−	3.82752i	0.440013	−	0.254042i	−0.263590	−	0.964635i	$-0.584907\pi$
$227$	6.62946	−	3.82752i	0.440013	−	0.254042i	0.703603	+	0.710593i	$0.251573\pi$
$228$		0			0
$229$	6.93933	+	4.00642i	0.458564	+	0.264752i	0.711440	−	0.702747i	$-0.248043\pi$
$229$	6.93933	+	4.00642i	0.458564	+	0.264752i	−0.252876	+	0.967499i	$0.581377\pi$
$230$		0			0
$231$	−3.76303	−	3.01943i	−0.247589	−	0.198664i
$232$		0			0
$233$	5.31630	+	9.20811i	0.348283	+	0.603243i	0.985945	−	0.167073i	$-0.0534316\pi$
$233$	5.31630	+	9.20811i	0.348283	+	0.603243i	−0.637662	+	0.770316i	$0.720098\pi$
$234$		0			0
$235$	1.94965	−	1.12563i	0.127181	−	0.0734283i
$236$		0			0
$237$	4.45574	−	1.73334i	0.289432	−	0.112593i
$238$		0			0
$239$	5.76948	+	9.99303i	0.373197	+	0.646395i	0.990055	−	0.140678i	$-0.0449284\pi$
$239$	5.76948	+	9.99303i	0.373197	+	0.646395i	−0.616859	+	0.787074i	$0.711595\pi$
$240$		0			0
$241$	−20.2180			−1.30236			−0.651179	−	0.758924i	$-0.725725\pi$
$241$	−20.2180			−1.30236			−0.651179	+	0.758924i	$0.725725\pi$
$242$		0			0
$243$	−11.2668	−	10.7730i	−0.722768	−	0.691091i
$244$		0			0
$245$	1.41191	−	2.44550i	0.0902035	−	0.156237i
$246$		0			0
$247$	1.40619	−	0.811867i	0.0894740	−	0.0516579i
$248$		0			0
$249$	−4.79720	−	3.84924i	−0.304010	−	0.243935i
$250$		0			0
$251$	0.299630	−	0.518975i	0.0189125	−	0.0327574i	−0.856414	−	0.516289i	$-0.827313\pi$
$251$	0.299630	−	0.518975i	0.0189125	−	0.0327574i	0.875327	+	0.483532i	$0.160646\pi$
$252$		0			0
$253$			14.0680i			0.884446i
$254$		0			0
$255$	0.666663	+	0.534925i	0.0417480	+	0.0334983i
$256$		0			0
$257$	−11.2264	+	6.48159i	−0.700286	+	0.404310i	−0.807454	−	0.589931i	$-0.799155\pi$
$257$	−11.2264	+	6.48159i	−0.700286	+	0.404310i	0.107168	+	0.994241i	$0.465822\pi$
$258$		0			0
$259$			3.72748i			0.231614i
$260$		0			0
$261$	−30.0841	+	6.67685i	−1.86216	+	0.413287i
$262$		0			0
$263$		−	9.24643i		−	0.570159i	−0.958504	−	0.285080i	$-0.907980\pi$
$263$		−	9.24643i		−	0.570159i	0.958504	−	0.285080i	$-0.0920201\pi$
$264$		0			0
$265$	−0.809798			−0.0497455
$266$		0			0
$267$	−2.12217	+	13.7987i	−0.129875	+	0.844466i
$268$		0			0
$269$		−	1.74249i		−	0.106241i	−0.998588	−	0.0531206i	$-0.983083\pi$
$269$		−	1.74249i		−	0.106241i	0.998588	−	0.0531206i	$-0.0169168\pi$
$270$		0			0
$271$			10.6969i			0.649792i	0.945750	+	0.324896i	$0.105329\pi$
$271$			10.6969i			0.649792i	−0.945750	+	0.324896i	$0.894671\pi$
$272$		0			0
$273$	4.26083	+	0.655295i	0.257877	+	0.0396603i
$274$		0			0
$275$	7.52736	+	13.0378i	0.453917	+	0.786207i
$276$		0			0
$277$	−18.1918			−1.09304			−0.546519	−	0.837447i	$-0.684047\pi$
$277$	−18.1918			−1.09304			−0.546519	+	0.837447i	$0.684047\pi$
$278$		0			0
$279$	−12.9560	+	2.87546i	−0.775658	+	0.172149i
$280$		0			0
$281$	−6.44830	+	11.1688i	−0.384673	+	0.666273i	−0.991724	−	0.128390i	$-0.959019\pi$
$281$	−6.44830	+	11.1688i	−0.384673	+	0.666273i	0.607051	+	0.794663i	$0.292353\pi$
$282$		0			0
$283$	26.0361			1.54769			0.773844	−	0.633376i	$-0.218332\pi$
$283$	26.0361			1.54769			0.773844	+	0.633376i	$0.218332\pi$
$284$		0			0
$285$	0.285045	−	0.355244i	0.0168846	−	0.0210428i
$286$		0			0
$287$	−1.44707	−	0.835464i	−0.0854176	−	0.0493159i
$288$		0			0
$289$	−7.91048	−	13.7013i	−0.465322	−	0.805961i
$290$		0			0
$291$	−3.11289	−	2.49776i	−0.182481	−	0.146421i
$292$		0			0
$293$		−	22.5354i		−	1.31653i	−0.752785	−	0.658267i	$-0.771290\pi$
$293$		−	22.5354i		−	1.31653i	0.752785	−	0.658267i	$-0.228710\pi$
$294$		0			0
$295$			0.810255i			0.0471749i
$296$		0			0
$297$	1.07305	+	16.2841i	0.0622645	+	0.944902i
$298$		0			0
$299$	−6.28501	−	10.8860i	−0.363471	−	0.629551i
$300$		0			0
$301$	0.296352	+	0.513297i	0.0170815	+	0.0295860i
$302$		0			0
$303$	0.514653	+	1.32297i	0.0295660	+	0.0760027i
$304$		0			0
$305$	5.36227	+	3.09591i	0.307043	+	0.177271i
$306$		0			0
$307$	−7.55191	+	13.0803i	−0.431010	+	0.746531i	−0.996961	−	0.0779079i	$-0.975176\pi$
$307$	−7.55191	+	13.0803i	−0.431010	+	0.746531i	0.565950	+	0.824439i	$0.308509\pi$
$308$		0			0
$309$	6.73774	+	17.3201i	0.383297	+	0.985305i
$310$		0			0
$311$	−21.5110			−1.21978			−0.609888	−	0.792488i	$-0.708786\pi$
$311$	−21.5110			−1.21978			−0.609888	+	0.792488i	$0.708786\pi$
$312$		0			0
$313$		−	23.3867i		−	1.32190i	−0.750432	−	0.660948i	$-0.770155\pi$
$313$		−	23.3867i		−	1.32190i	0.750432	−	0.660948i	$-0.229845\pi$
$314$		0			0
$315$	1.18051	−	0.262003i	0.0665144	−	0.0147622i
$316$		0			0
$317$	−20.3050	−	11.7231i	−1.14044	−	0.658435i	−0.193903	−	0.981021i	$-0.562115\pi$
$317$	−20.3050	−	11.7231i	−1.14044	−	0.658435i	−0.946540	+	0.322585i	$0.895448\pi$
$318$		0			0
$319$	27.9390	+	16.1306i	1.56428	+	0.903140i
$320$		0			0
$321$	−2.22756	+	14.4840i	−0.124330	+	0.808416i
$322$		0			0
$323$	0.544106	−	0.314140i	0.0302749	−	0.0174792i
$324$		0			0
$325$	−11.6495	−	6.72584i	−0.646198	−	0.373083i
$326$		0			0
$327$	−2.73106	+	17.7578i	−0.151028	+	0.982006i
$328$		0			0
$329$	2.19670	−	3.80480i	0.121108	−	0.209765i
$330$		0			0
$331$	−11.2791	+	6.51201i	−0.619957	+	0.357932i	−0.776852	−	0.629683i	$-0.783185\pi$
$331$	−11.2791	+	6.51201i	−0.619957	+	0.357932i	0.156895	+	0.987615i	$0.449852\pi$
$332$		0			0
$333$	9.29378	−	8.52017i	0.509296	−	0.466902i
$334$		0			0
$335$	3.61318	+	0.885151i	0.197409	+	0.0483609i
$336$		0			0
$337$	−11.9751	−	6.91380i	−0.652323	−	0.376619i	0.137023	−	0.990568i	$-0.456247\pi$
$337$	−11.9751	−	6.91380i	−0.652323	−	0.376619i	−0.789346	+	0.613949i	$0.789580\pi$
$338$		0			0
$339$	−8.93398	−	22.9657i	−0.485227	−	1.24733i
$340$		0			0
$341$	12.0322	+	6.94682i	0.651583	+	0.376191i
$342$		0			0
$343$		−	11.7191i		−	0.632774i
$344$		0			0
$345$	−2.75010	−	2.20666i	−0.148060	−	0.118802i
$346$		0			0
$347$	4.06467	+	7.04022i	0.218203	+	0.377939i	0.954259	−	0.298982i	$-0.0966471\pi$
$347$	4.06467	+	7.04022i	0.218203	+	0.377939i	−0.736056	+	0.676921i	$0.763314\pi$
$348$		0			0
$349$	8.64336			0.462669			0.231334	−	0.972874i	$-0.425691\pi$
$349$	8.64336			0.462669			0.231334	+	0.972874i	$0.425691\pi$
$350$		0			0
$351$	−8.10544	−	12.1215i	−0.432636	−	0.646995i
$352$		0			0
$353$	12.0880	−	20.9370i	0.643377	−	1.11436i	−0.341296	−	0.939956i	$-0.610866\pi$
$353$	12.0880	−	20.9370i	0.643377	−	1.11436i	0.984674	−	0.174406i	$-0.0558007\pi$
$354$		0			0
$355$	3.23403	−	1.86717i	0.171644	−	0.0990989i
$356$		0			0
$357$	1.64866	+	0.253557i	0.0872566	+	0.0134196i
$358$		0			0
$359$			21.9880i			1.16048i	0.814445	+	0.580240i	$0.197041\pi$
$359$			21.9880i			1.16048i	−0.814445	+	0.580240i	$0.802959\pi$
$360$		0			0
$361$	9.33260	+	16.1645i	0.491190	+	0.850766i
$362$		0			0
$363$	−1.23152	+	1.53481i	−0.0646382	+	0.0805568i
$364$		0			0
$365$	2.50034	−	4.33071i	0.130874	−	0.226680i
$366$		0			0
$367$	25.9627	−	14.9895i	1.35524	−	0.782448i	0.366262	−	0.930512i	$-0.380638\pi$
$367$	25.9627	−	14.9895i	1.35524	−	0.782448i	0.988978	+	0.148064i	$0.0473042\pi$
$368$		0			0
$369$	1.22459	+	5.51767i	0.0637496	+	0.287239i
$370$		0			0
$371$	−1.36861	+	0.790169i	−0.0710549	+	0.0410235i
$372$		0			0
$373$	14.4060	−	8.31733i	0.745917	−	0.430655i	−0.0783000	−	0.996930i	$-0.524949\pi$
$373$	14.4060	−	8.31733i	0.745917	−	0.430655i	0.824217	+	0.566275i	$0.191616\pi$
$374$		0			0
$375$	−7.61954	−	1.17185i	−0.393471	−	0.0605140i
$376$		0			0
$377$	−28.8260			−1.48461
$378$		0			0
$379$	29.1548	+	16.8325i	1.49758	+	0.864628i	0.999996	−	0.00278882i	$-0.000887710\pi$
$379$	29.1548	+	16.8325i	1.49758	+	0.864628i	0.497583	+	0.867416i	$0.334221\pi$
$380$		0			0
$381$	−9.18917	−	23.6218i	−0.470776	−	1.21018i
$382$		0			0
$383$	4.79079	−	8.29789i	0.244798	−	0.424002i	−0.717277	−	0.696788i	$-0.754612\pi$
$383$	4.79079	−	8.29789i	0.244798	−	0.424002i	0.962075	+	0.272786i	$0.0879450\pi$
$384$		0			0
$385$	−1.09634	−	0.632972i	−0.0558746	−	0.0322592i
$386$		0			0
$387$	0.602417	−	1.91218i	0.0306226	−	0.0972016i
$388$		0			0
$389$	−13.4626	−	7.77266i	−0.682583	−	0.394089i	0.118245	−	0.992984i	$-0.462273\pi$
$389$	−13.4626	−	7.77266i	−0.682583	−	0.394089i	−0.800827	+	0.598895i	$0.795607\pi$
$390$		0			0
$391$	−2.43189	−	4.21216i	−0.122986	−	0.213018i
$392$		0			0
$393$	−4.42149	+	28.7492i	−0.223035	+	1.45021i
$394$		0			0
$395$	1.08642	−	0.627246i	0.0546638	−	0.0315602i
$396$		0			0
$397$	14.6879			0.737166			0.368583	−	0.929595i	$-0.379843\pi$
$397$	14.6879			0.737166			0.368583	+	0.929595i	$0.379843\pi$
$398$		0			0
$399$	0.135113	−	0.878523i	0.00676409	−	0.0439811i
$400$		0			0
$401$	−28.1226			−1.40438			−0.702188	−	0.711991i	$-0.747793\pi$
$401$	−28.1226			−1.40438			−0.702188	+	0.711991i	$0.747793\pi$
$402$		0			0
$403$	−12.4142			−0.618397
$404$		0			0
$405$	−3.35164	−	2.34451i	−0.166544	−	0.116500i
$406$		0			0
$407$	−13.1995			−0.654274
$408$		0			0
$409$	30.8767	−	17.8267i	1.52676	−	0.881473i	0.527260	−	0.849704i	$-0.323219\pi$
$409$	30.8767	−	17.8267i	1.52676	−	0.881473i	0.999495	−	0.0317691i	$-0.0101141\pi$
$410$		0			0
$411$	−33.8135	−	5.20035i	−1.66790	−	0.256515i
$412$		0			0
$413$	0.790615	+	1.36939i	0.0389036	+	0.0673831i
$414$		0			0
$415$	−1.39764	−	0.806927i	−0.0686074	−	0.0396105i
$416$		0			0
$417$	1.74076	−	11.3187i	0.0852454	−	0.554279i
$418$		0			0
$419$	−0.734762	−	0.424215i	−0.0358955	−	0.0207243i	0.481945	−	0.876202i	$-0.339931\pi$
$419$	−0.734762	−	0.424215i	−0.0358955	−	0.0207243i	−0.517840	+	0.855477i	$0.673264\pi$
$420$		0			0
$421$	−15.7950	+	27.3578i	−0.769803	+	1.33334i	0.167866	+	0.985810i	$0.446312\pi$
$421$	−15.7950	+	27.3578i	−0.769803	+	1.33334i	−0.937669	+	0.347528i	$0.887021\pi$
$422$		0			0
$423$	−14.5077	+	3.21984i	−0.705389	+	0.156554i
$424$		0			0
$425$	−4.50760	−	2.60246i	−0.218651	−	0.126238i
$426$		0			0
$427$	12.0835			0.584760
$428$		0			0
$429$	−2.32049	+	15.0882i	−0.112034	+	0.728463i
$430$		0			0
$431$	−20.3659	+	11.7582i	−0.980990	+	0.566375i	−0.902569	−	0.430546i	$-0.858321\pi$
$431$	−20.3659	+	11.7582i	−0.980990	+	0.566375i	−0.0784210	+	0.996920i	$0.524988\pi$
$432$		0			0
$433$	16.1116	−	9.30203i	0.774273	−	0.447027i	−0.0601236	−	0.998191i	$-0.519149\pi$
$433$	16.1116	−	9.30203i	0.774273	−	0.447027i	0.834397	+	0.551164i	$0.185816\pi$
$434$		0			0
$435$	−7.53573	+	2.93150i	−0.361311	+	0.140555i
$436$		0			0
$437$	−2.24453	+	1.29588i	−0.107370	+	0.0619903i
$438$		0			0
$439$	−11.4753	+	19.8759i	−0.547688	+	0.948623i	0.450744	+	0.892653i	$0.351159\pi$
$439$	−11.4753	+	19.8759i	−0.547688	+	0.948623i	−0.998432	+	0.0559704i	$0.982175\pi$
$440$		0			0
$441$	−13.7400	+	12.5963i	−0.654286	+	0.599824i
$442$		0			0
$443$	10.1155	+	17.5205i	0.480600	+	0.832423i	0.999752	−	0.0222583i	$-0.00708561\pi$
$443$	10.1155	+	17.5205i	0.480600	+	0.832423i	−0.519152	+	0.854682i	$0.673752\pi$
$444$		0			0
$445$			3.66321i			0.173653i
$446$		0			0
$447$	3.25036	−	21.1343i	0.153737	−	0.999619i
$448$		0			0
$449$	−15.9654	+	9.21762i	−0.753453	+	0.435006i	−0.826940	−	0.562290i	$-0.809921\pi$
$449$	−15.9654	+	9.21762i	−0.753453	+	0.435006i	0.0734872	+	0.997296i	$0.476587\pi$
$450$		0			0
$451$	2.95849	−	5.12425i	0.139310	−	0.241292i
$452$		0			0
$453$	15.5063	−	19.3251i	0.728549	−	0.907970i
$454$		0			0
$455$	1.13115			0.0530289
$456$		0			0
$457$	3.13294	+	5.42641i	0.146553	+	0.253837i	0.929951	−	0.367683i	$-0.119849\pi$
$457$	3.13294	+	5.42641i	0.146553	+	0.253837i	−0.783398	+	0.621520i	$0.786516\pi$
$458$		0			0
$459$	−3.13628	−	4.69021i	−0.146389	−	0.218920i
$460$		0			0
$461$			24.5187i			1.14195i	0.820968	+	0.570974i	$0.193434\pi$
$461$			24.5187i			1.14195i	−0.820968	+	0.570974i	$0.806566\pi$
$462$		0			0
$463$	13.9884	+	8.07623i	0.650098	+	0.375334i	0.788494	−	0.615043i	$-0.210861\pi$
$463$	13.9884	+	8.07623i	0.650098	+	0.375334i	−0.138396	+	0.990377i	$0.544195\pi$
$464$		0			0
$465$	−3.24535	+	1.26248i	−0.150499	+	0.0585462i
$466$		0			0
$467$	−31.1246	−	17.9698i	−1.44028	−	0.831544i	−0.442409	−	0.896814i	$-0.645876\pi$
$467$	−31.1246	−	17.9698i	−1.44028	−	0.831544i	−0.997868	+	0.0652696i	$0.979209\pi$
$468$		0			0
$469$	6.97022	−	2.02964i	0.321855	−	0.0937200i
$470$		0			0
$471$	−11.2861	+	14.0656i	−0.520037	+	0.648108i
$472$		0			0
$473$	−1.81765	+	1.04942i	−0.0835757	+	0.0482525i
$474$		0			0
$475$	−1.38677	+	2.40196i	−0.0636295	+	0.110210i
$476$		0			0
$477$	5.09848	+	1.60624i	0.233443	+	0.0735445i
$478$		0			0
$479$	−23.6111	−	13.6319i	−1.07882	−	0.622856i	−0.148241	−	0.988951i	$-0.547361\pi$
$479$	−23.6111	−	13.6319i	−1.07882	−	0.622856i	−0.930577	+	0.366095i	$0.880694\pi$
$480$		0			0
$481$	10.2139	−	5.89700i	0.465714	−	0.268880i
$482$		0			0
$483$	−6.80102	−	1.04596i	−0.309457	−	0.0475930i
$484$		0			0
$485$	−0.906925	−	0.523614i	−0.0411814	−	0.0237761i
$486$		0			0
$487$	15.5990	+	9.00608i	0.706857	+	0.408104i	0.809896	−	0.586573i	$-0.199523\pi$
$487$	15.5990	+	9.00608i	0.706857	+	0.408104i	−0.103039	+	0.994677i	$0.532857\pi$
$488$		0			0
$489$	1.21977	+	3.13556i	0.0551600	+	0.141795i
$490$		0			0
$491$		−	20.1778i		−	0.910613i	−0.890335	−	0.455306i	$-0.849530\pi$
$491$		−	20.1778i		−	0.910613i	0.890335	−	0.455306i	$-0.150470\pi$
$492$		0			0
$493$	−11.1538			−0.502341
$494$		0			0
$495$	0.927785	+	4.18035i	0.0417009	+	0.187893i
$496$		0			0
$497$	3.64382	−	6.31128i	0.163448	−	0.283099i
$498$		0			0
$499$	−2.20200	−	1.27132i	−0.0985750	−	0.0569123i	0.449902	−	0.893078i	$-0.351459\pi$
$499$	−2.20200	−	1.27132i	−0.0985750	−	0.0569123i	−0.548477	+	0.836166i	$0.684792\pi$
$500$		0			0
$501$	−11.3120	+	4.40050i	−0.505381	+	0.196600i
$502$		0			0
$503$	14.2788	+	24.7316i	0.636660	+	1.10273i	0.986161	+	0.165792i	$0.0530180\pi$
$503$	14.2788	+	24.7316i	0.636660	+	1.10273i	−0.349500	+	0.936936i	$0.613649\pi$
$504$		0			0
$505$	0.186238	+	0.322574i	0.00828748	+	0.0143543i
$506$		0			0
$507$	3.21818	+	8.27267i	0.142924	+	0.367402i
$508$		0			0
$509$		−	22.7159i		−	1.00686i	−0.864035	−	0.503432i	$-0.832071\pi$
$509$		−	22.7159i		−	1.00686i	0.864035	−	0.503432i	$-0.167929\pi$
$510$		0			0
$511$		−	9.75893i		−	0.431710i
$512$		0			0
$513$	−2.49927	+	1.67123i	−0.110346	+	0.0737864i
$514$		0			0
$515$	2.43819	+	4.22307i	0.107440	+	0.186091i
$516$		0			0
$517$	13.4733	+	7.77880i	0.592554	+	0.342111i
$518$		0			0
$519$	−21.1346	−	16.9583i	−0.927706	−	0.744385i
$520$		0			0
$521$	1.61192			0.0706195			0.0353098	−	0.999376i	$-0.488758\pi$
$521$	1.61192			0.0706195			0.0353098	+	0.999376i	$0.488758\pi$
$522$		0			0
$523$	12.0755	−	20.9154i	0.528025	−	0.914567i	−0.471441	−	0.881898i	$-0.656266\pi$
$523$	12.0755	−	20.9154i	0.528025	−	0.914567i	0.999466	−	0.0326691i	$-0.0104008\pi$
$524$		0			0
$525$	−6.86264	+	2.66966i	−0.299510	+	0.116513i
$526$		0			0
$527$	−4.80350			−0.209244
$528$		0			0
$529$	−1.46804	−	2.54272i	−0.0638279	−	0.110553i
$530$		0			0
$531$	1.60714	−	5.10136i	0.0697441	−	0.221380i
$532$		0			0
$533$			5.28693i			0.229003i
$534$		0			0
$535$			3.84513i			0.166240i
$536$		0			0
$537$	2.57976	+	0.396755i	0.111325	+	0.0171212i
$538$		0			0
$539$	19.5143			0.840538
$540$		0			0
$541$		−	10.1497i		−	0.436371i	−0.975907	−	0.218185i	$-0.929986\pi$
$541$		−	10.1497i		−	0.436371i	0.975907	−	0.218185i	$-0.0700137\pi$
$542$		0			0
$543$	7.99932	+	20.5631i	0.343283	+	0.882447i
$544$		0			0
$545$			4.71425i			0.201936i
$546$		0			0
$547$	−28.0100	+	16.1716i	−1.19762	+	0.691447i	−0.960024	−	0.279916i	$-0.909693\pi$
$547$	−28.0100	+	16.1716i	−1.19762	+	0.691447i	−0.237598	+	0.971364i	$0.576360\pi$
$548$		0			0
$549$	−27.6201	−	30.1279i	−1.17880	−	1.28583i
$550$		0			0
$551$			5.94351i			0.253202i
$552$		0			0
$553$	1.22409	−	2.12018i	0.0520534	−	0.0901591i
$554$		0			0
$555$	2.07043	−	2.58032i	0.0878848	−	0.109528i
$556$		0			0
$557$	−14.8089	+	8.54990i	−0.627471	+	0.362271i	−0.779772	−	0.626063i	$-0.784665\pi$
$557$	−14.8089	+	8.54990i	−0.627471	+	0.362271i	0.152301	+	0.988334i	$0.451332\pi$
$558$		0			0
$559$	0.937679	−	1.62411i	0.0396596	−	0.0686925i
$560$		0			0
$561$	−0.897877	+	5.83814i	−0.0379084	+	0.246486i
$562$		0			0
$563$	32.9197			1.38740			0.693701	−	0.720263i	$-0.255979\pi$
$563$	32.9197			1.38740			0.693701	+	0.720263i	$0.255979\pi$
$564$		0			0
$565$	−3.23295	−	5.59963i	−0.136011	−	0.235578i
$566$		0			0
$567$	−7.95218	−	0.691984i	−0.333960	−	0.0290606i
$568$		0			0
$569$	10.7811	−	6.22446i	0.451966	−	0.260943i	−0.256694	−	0.966493i	$-0.582633\pi$
$569$	10.7811	−	6.22446i	0.451966	−	0.260943i	0.708660	+	0.705550i	$0.249300\pi$
$570$		0			0
$571$	−5.45567	−	9.44949i	−0.228313	−	0.395449i	0.728996	−	0.684518i	$-0.239987\pi$
$571$	−5.45567	−	9.44949i	−0.228313	−	0.395449i	−0.957308	+	0.289069i	$0.906654\pi$
$572$		0			0
$573$	8.23255	−	10.2600i	0.343920	−	0.428618i
$574$		0			0
$575$	18.5946	+	10.7356i	0.775449	+	0.447706i
$576$		0			0
$577$	3.20633	−	1.85118i	0.133481	−	0.0770655i	−0.431772	−	0.901983i	$-0.642112\pi$
$577$	3.20633	−	1.85118i	0.133481	−	0.0770655i	0.565254	+	0.824917i	$0.308778\pi$
$578$		0			0
$579$	6.13996	+	0.944296i	0.255168	+	0.0392436i
$580$		0			0
$581$	−3.14947			−0.130662
$582$		0			0
$583$	−2.79809	−	4.84644i	−0.115885	−	0.200719i
$584$		0			0
$585$	−2.58554	−	2.82030i	−0.106899	−	0.116605i
$586$		0			0
$587$	1.89035	−	3.27418i	0.0780230	−	0.135140i	−0.824374	−	0.566046i	$-0.808473\pi$
$587$	1.89035	−	3.27418i	0.0780230	−	0.135140i	0.902397	+	0.430906i	$0.141806\pi$
$588$		0			0
$589$			2.55964i			0.105468i
$590$		0			0
$591$	−0.735036	−	1.88949i	−0.0302353	−	0.0777231i
$592$		0			0
$593$	15.8575	−	27.4659i	0.651188	−	1.12789i	−0.331647	−	0.943404i	$-0.607604\pi$
$593$	15.8575	−	27.4659i	0.651188	−	1.12789i	0.982835	−	0.184487i	$-0.0590625\pi$
$594$		0			0
$595$	0.437680			0.0179431
$596$		0			0
$597$	−3.03102	+	3.77748i	−0.124052	+	0.154602i
$598$		0			0
$599$	18.4877	+	32.0216i	0.755386	+	1.30837i	0.945182	+	0.326544i	$0.105884\pi$
$599$	18.4877	+	32.0216i	0.755386	+	1.30837i	−0.189796	+	0.981824i	$0.560783\pi$
$600$		0			0
$601$	−12.2885	+	21.2843i	−0.501258	+	0.868204i	0.498741	+	0.866751i	$0.333796\pi$
$601$	−12.2885	+	21.2843i	−0.501258	+	0.868204i	−0.999999	+	0.00145305i	$0.999537\pi$
$602$		0			0
$603$	−20.9929	−	12.7397i	−0.854896	−	0.518799i
$604$		0			0
$605$	−0.258168	+	0.447160i	−0.0104960	+	0.0181796i
$606$		0			0
$607$	3.37950	+	5.85347i	0.137170	+	0.237585i	0.926424	−	0.376481i	$-0.122866\pi$
$607$	3.37950	+	5.85347i	0.137170	+	0.237585i	−0.789254	+	0.614066i	$0.789533\pi$
$608$		0			0
$609$	−9.87545	+	12.3075i	−0.400174	+	0.498725i
$610$		0			0
$611$	−13.9010			−0.562375
$612$		0			0
$613$	−13.7833	+	23.8734i	−0.556703	+	0.964239i	0.441065	+	0.897475i	$0.354601\pi$
$613$	−13.7833	+	23.8734i	−0.556703	+	0.964239i	−0.997769	+	0.0667637i	$0.978733\pi$
$614$		0			0
$615$	0.537662	+	1.38212i	0.0216806	+	0.0557323i
$616$		0			0
$617$		−	28.0718i		−	1.13013i	−0.825048	−	0.565063i	$-0.808852\pi$
$617$		−	28.0718i		−	1.13013i	0.825048	−	0.565063i	$-0.191148\pi$
$618$		0			0
$619$	11.4083	−	19.7597i	0.458538	−	0.794211i	−0.540346	−	0.841443i	$-0.681707\pi$
$619$	11.4083	−	19.7597i	0.458538	−	0.794211i	0.998884	+	0.0472318i	$0.0150400\pi$
$620$		0			0
$621$	12.9377	+	19.3479i	0.519171	+	0.776406i
$622$		0			0
$623$	3.57442	+	6.19108i	0.143206	+	0.248040i
$624$		0			0
$625$	21.9445			0.877779
$626$		0			0
$627$	3.11096	+	0.478451i	0.124240	+	0.0191075i
$628$		0			0
$629$	3.95212	−	2.28176i	0.157581	−	0.0909795i
$630$		0			0
$631$	−15.5905	−	9.00120i	−0.620650	−	0.358332i	0.156472	−	0.987682i	$-0.449988\pi$
$631$	−15.5905	−	9.00120i	−0.620650	−	0.358332i	−0.777122	+	0.629350i	$0.783321\pi$
$632$		0			0
$633$	4.50396	−	5.61316i	0.179016	−	0.223103i
$634$		0			0
$635$	−3.32529	−	5.75958i	−0.131960	−	0.228562i
$636$		0			0
$637$	−15.1003	+	8.71819i	−0.598297	+	0.345427i
$638$		0			0
$639$	−24.0649	+	5.34097i	−0.951995	+	0.211285i
$640$		0			0
$641$	4.21389	+	7.29868i	0.166439	+	0.288280i	0.937165	−	0.348886i	$-0.113440\pi$
$641$	4.21389	+	7.29868i	0.166439	+	0.288280i	−0.770726	+	0.637166i	$0.780107\pi$
$642$		0			0
$643$	−2.19834			−0.0866940			−0.0433470	−	0.999060i	$-0.513802\pi$
$643$	−2.19834			−0.0866940			−0.0433470	+	0.999060i	$0.513802\pi$
$644$		0			0
$645$	0.0799635	−	0.519935i	0.00314856	−	0.0204724i
$646$		0			0
$647$	−13.2373	+	22.9277i	−0.520413	+	0.901381i	0.479306	+	0.877648i	$0.340889\pi$
$647$	−13.2373	+	22.9277i	−0.520413	+	0.901381i	−0.999718	+	0.0237331i	$0.992445\pi$
$648$		0			0
$649$	−4.84917	+	2.79967i	−0.190347	+	0.109897i
$650$		0			0
$651$	−4.25297	+	5.30036i	−0.166687	+	0.207738i
$652$		0			0
$653$	−9.81418	+	16.9987i	−0.384058	+	0.665209i	−0.991638	−	0.129050i	$-0.958807\pi$
$653$	−9.81418	+	16.9987i	−0.384058	+	0.665209i	0.607580	+	0.794259i	$0.292141\pi$
$654$		0			0
$655$			7.63221i			0.298215i
$656$		0			0
$657$	−24.3321	+	22.3067i	−0.949286	+	0.870268i
$658$		0			0
$659$	14.6413	−	8.45315i	0.570344	−	0.329288i	−0.186943	−	0.982371i	$-0.559858\pi$
$659$	14.6413	−	8.45315i	0.570344	−	0.329288i	0.757287	+	0.653083i	$0.226525\pi$
$660$		0			0
$661$			5.50572i			0.214148i	0.994251	+	0.107074i	$0.0341481\pi$
$661$			5.50572i			0.214148i	−0.994251	+	0.107074i	$0.965852\pi$
$662$		0			0
$663$	−1.91346	−	4.91875i	−0.0743125	−	0.191028i
$664$		0			0
$665$		−	0.233226i		−	0.00904412i
$666$		0			0
$667$	46.0113			1.78156
$668$		0			0
$669$	22.3813	+	3.44214i	0.865312	+	0.133081i
$670$		0			0
$671$			42.7892i			1.65186i
$672$		0			0
$673$		−	10.9196i		−	0.420921i	−0.977602	−	0.210460i	$-0.932504\pi$
$673$		−	10.9196i		−	0.420921i	0.977602	−	0.210460i	$-0.0674963\pi$
$674$		0			0
$675$	22.3427	+	11.0085i	0.859972	+	0.423717i
$676$		0			0
$677$	−8.49515	−	14.7140i	−0.326495	−	0.565506i	0.655319	−	0.755353i	$-0.272534\pi$
$677$	−8.49515	−	14.7140i	−0.326495	−	0.565506i	−0.981814	+	0.189846i	$0.939201\pi$
$678$		0			0
$679$	−2.04369			−0.0784295
$680$		0			0
$681$	−12.3569	+	4.80698i	−0.473516	+	0.184204i
$682$		0			0
$683$	21.4485	−	37.1500i	0.820706	−	1.42150i	−0.0844513	−	0.996428i	$-0.526914\pi$
$683$	21.4485	−	37.1500i	0.820706	−	1.42150i	0.905157	−	0.425077i	$-0.139753\pi$
$684$		0			0
$685$	−8.97665			−0.342980
$686$		0			0
$687$	−10.8248	−	8.68572i	−0.412991	−	0.331381i
$688$		0			0
$689$	4.33039	+	2.50015i	0.164975	+	0.0952481i
$690$		0			0
$691$	−11.8056	−	20.4480i	−0.449108	−	0.777877i	0.549220	−	0.835677i	$-0.314925\pi$
$691$	−11.8056	−	20.4480i	−0.449108	−	0.777877i	−0.998328	+	0.0578001i	$0.981591\pi$
$692$		0			0
$693$	5.64704	+	6.15978i	0.214513	+	0.233991i
$694$		0			0
$695$		−	3.00483i		−	0.113980i
$696$		0			0
$697$			2.04570i			0.0774864i
$698$		0			0
$699$	−6.67674	−	17.1633i	−0.252538	−	0.649175i
$700$		0			0
$701$	−22.5818	−	39.1128i	−0.852903	−	1.47727i	−0.878577	−	0.477601i	$-0.841507\pi$
$701$	−22.5818	−	39.1128i	−0.852903	−	1.47727i	0.0256744	−	0.999670i	$-0.491827\pi$
$702$		0			0
$703$	−1.21588	−	2.10596i	−0.0458577	−	0.0794278i
$704$		0			0
$705$	−3.63402	+	1.41368i	−0.136865	+	0.0532424i
$706$		0			0
$707$	0.629510	+	0.363448i	0.0236751	+	0.0136689i
$708$		0			0
$709$	17.9070	−	31.0158i	0.672510	−	1.16482i	−0.304680	−	0.952455i	$-0.598549\pi$
$709$	17.9070	−	31.0158i	0.672510	−	1.16482i	0.977190	−	0.212367i	$-0.0681172\pi$
$710$		0			0
$711$	−8.08425	+	1.79422i	−0.303183	+	0.0672884i
$712$		0			0
$713$	19.8153			0.742088
$714$		0			0
$715$			4.00553i			0.149798i
$716$		0			0
$717$	−7.24588	−	18.6263i	−0.270602	−	0.695613i
$718$		0			0
$719$	11.2895	+	6.51798i	0.421026	+	0.243080i	0.695516	−	0.718510i	$-0.255176\pi$
$719$	11.2895	+	6.51798i	0.421026	+	0.243080i	−0.274490	+	0.961590i	$0.588509\pi$
$720$		0			0
$721$	8.24142	+	4.75819i	0.306927	+	0.177204i
$722$		0			0
$723$	34.6117	+	5.32312i	1.28722	+	0.197969i
$724$		0			0
$725$	42.6418	−	24.6193i	1.58368	−	0.914336i
$726$		0			0
$727$	−4.61348	−	2.66360i	−0.171105	−	0.0987873i	0.412002	−	0.911183i	$-0.364830\pi$
$727$	−4.61348	−	2.66360i	−0.171105	−	0.0987873i	−0.583107	+	0.812396i	$0.698163\pi$
$728$		0			0
$729$	16.4516	+	21.4090i	0.609317	+	0.792927i
$730$		0			0
$731$	0.362821	−	0.628424i	0.0134194	−	0.0232431i
$732$		0			0
$733$	−17.2290	+	9.94716i	−0.636367	+	0.367407i	−0.783214	−	0.621752i	$-0.786421\pi$
$733$	−17.2290	+	9.94716i	−0.636367	+	0.367407i	0.146847	+	0.989159i	$0.453088\pi$
$734$		0			0
$735$	−3.06094	+	3.81477i	−0.112905	+	0.140710i
$736$		0			0
$737$	7.18722	+	24.6825i	0.264745	+	0.909190i
$738$		0			0
$739$	11.5120	+	6.64648i	0.423477	+	0.244495i	0.696564	−	0.717495i	$-0.254711\pi$
$739$	11.5120	+	6.64648i	0.423477	+	0.244495i	−0.273087	+	0.961989i	$0.588045\pi$
$740$		0			0
$741$	−2.62105	+	1.01962i	−0.0962867	+	0.0374568i
$742$		0			0
$743$	25.5477	+	14.7500i	0.937255	+	0.541124i	0.889099	−	0.457716i	$-0.151332\pi$
$743$	25.5477	+	14.7500i	0.937255	+	0.541124i	0.0481561	+	0.998840i	$0.484666\pi$
$744$		0			0
$745$		−	5.61064i		−	0.205558i
$746$		0			0
$747$	7.19898	+	7.85263i	0.263397	+	0.287313i
$748$		0			0
$749$	3.75193	+	6.49854i	0.137093	+	0.237451i
$750$		0			0
$751$	45.8887			1.67450			0.837251	−	0.546819i	$-0.184161\pi$
$751$	45.8887			1.67450			0.837251	+	0.546819i	$0.184161\pi$
$752$		0			0
$753$	−0.649582	+	0.809556i	−0.0236721	+	0.0295019i
$754$		0			0
$755$	3.25063	−	5.63026i	0.118303	−	0.204906i
$756$		0			0
$757$	22.3193	−	12.8861i	0.811210	−	0.468352i	−0.0361658	−	0.999346i	$-0.511514\pi$
$757$	22.3193	−	12.8861i	0.811210	−	0.468352i	0.847376	+	0.530993i	$0.178181\pi$
$758$		0			0
$759$	3.70390	−	24.0833i	0.134443	−	0.874168i
$760$		0			0
$761$		−	52.3227i		−	1.89670i	−0.317229	−	0.948349i	$-0.602752\pi$
$761$		−	52.3227i		−	1.89670i	0.317229	−	0.948349i	$-0.397248\pi$
$762$		0			0
$763$	4.59998	+	7.96740i	0.166530	+	0.288439i
$764$		0			0
$765$	−1.00044	−	1.09127i	−0.0361709	−	0.0394551i
$766$		0			0
$767$	2.50156	−	4.33283i	0.0903262	−	0.156449i
$768$		0			0
$769$	31.8998	−	18.4173i	1.15033	−	0.664146i	0.201366	−	0.979516i	$-0.435462\pi$
$769$	31.8998	−	18.4173i	1.15033	−	0.664146i	0.948969	+	0.315370i	$0.102129\pi$
$770$		0			0
$771$	20.9253	−	8.14022i	0.753606	−	0.293163i
$772$		0			0
$773$	16.5606	−	9.56127i	0.595644	−	0.343895i	−0.171682	−	0.985152i	$-0.554920\pi$
$773$	16.5606	−	9.56127i	0.595644	−	0.343895i	0.767326	+	0.641257i	$0.221587\pi$
$774$		0			0
$775$	18.3642	−	10.6026i	0.659660	−	0.380855i
$776$		0			0
$777$	0.981391	−	6.38115i	0.0352072	−	0.228923i
$778$		0			0
$779$	1.09009			0.0390566
$780$		0			0
$781$	22.3491	+	12.9032i	0.799712	+	0.461714i
$782$		0			0
$783$	53.2595	−	3.50955i	1.90334	−	0.125421i
$784$		0			0
$785$	−2.36594	+	4.09794i	−0.0844442	+	0.146262i
$786$		0			0
$787$	−4.76419	−	2.75061i	−0.169825	−	0.0980486i	0.412678	−	0.910877i	$-0.364593\pi$
$787$	−4.76419	−	2.75061i	−0.169825	−	0.0980486i	−0.582503	+	0.812828i	$0.697927\pi$
$788$		0			0
$789$	−2.43445	+	15.8292i	−0.0866688	+	0.563534i
$790$		0			0
$791$	−10.9278	−	6.30917i	−0.388548	−	0.224328i
$792$		0			0
$793$	−19.1165	−	33.1107i	−0.678846	−	1.17580i
$794$		0			0
$795$	1.38631	+	0.213208i	0.0491674	+	0.00756171i
$796$		0			0
$797$	−41.7760	+	24.1194i	−1.47978	+	0.854353i	−0.999738	−	0.0228910i	$-0.992713\pi$
$797$	−41.7760	+	24.1194i	−1.47978	+	0.854353i	−0.480045	+	0.877244i	$0.659380\pi$
$798$		0			0
$799$	−5.37879			−0.190288
$800$		0			0
$801$	7.26599	−	23.0636i	0.256731	−	0.814911i
$802$		0			0
$803$	34.5577			1.21951
$804$		0			0
$805$	−1.80550			−0.0636356
$806$		0			0
$807$	−0.458771	+	2.98300i	−0.0161495	+	0.105007i
$808$		0			0
$809$	30.8603			1.08499			0.542495	−	0.840059i	$-0.317480\pi$
$809$	30.8603			1.08499			0.542495	+	0.840059i	$0.317480\pi$
$810$		0			0
$811$	−11.9408	+	6.89404i	−0.419299	+	0.242082i	−0.694777	−	0.719225i	$-0.744497\pi$
$811$	−11.9408	+	6.89404i	−0.419299	+	0.242082i	0.275478	+	0.961307i	$0.411164\pi$
$812$		0			0
$813$	2.81634	−	18.3123i	0.0987735	−	0.642241i
$814$		0			0
$815$	0.441400	+	0.764527i	0.0154616	+	0.0267802i
$816$		0			0
$817$	−0.334868	−	0.193336i	−0.0117156	−	0.00676398i
$818$		0			0
$819$	−7.12168	−	2.24363i	−0.248852	−	0.0783988i
$820$		0			0
$821$	25.4665	+	14.7031i	0.888787	+	0.513141i	0.873546	−	0.486742i	$-0.161815\pi$
$821$	25.4665	+	14.7031i	0.888787	+	0.513141i	0.0152414	+	0.999884i	$0.495148\pi$
$822$		0			0
$823$	−18.1702	+	31.4717i	−0.633373	+	1.09703i	0.353484	+	0.935441i	$0.384997\pi$
$823$	−18.1702	+	31.4717i	−0.633373	+	1.09703i	−0.986857	+	0.161594i	$0.948336\pi$
$824$		0			0
$825$	−9.45360	−	24.3015i	−0.329132	−	0.846069i
$826$		0			0
$827$	7.17226	+	4.14091i	0.249404	+	0.143993i	0.619491	−	0.785003i	$-0.287339\pi$
$827$	7.17226	+	4.14091i	0.249404	+	0.143993i	−0.370087	+	0.928997i	$0.620672\pi$
$828$		0			0
$829$	−17.3733			−0.603399			−0.301699	−	0.953403i	$-0.597554\pi$
$829$	−17.3733			−0.603399			−0.301699	+	0.953403i	$0.597554\pi$
$830$		0			0
$831$	31.1429	+	4.78963i	1.08034	+	0.166150i
$832$		0			0
$833$	−5.84285	+	3.37337i	−0.202443	+	0.116880i
$834$		0			0
$835$	−2.75814	+	1.59241i	−0.0954494	+	0.0551078i
$836$		0			0
$837$	22.9368	−	1.51143i	0.792812	−	0.0522425i
$838$		0			0
$839$	−11.6744	+	6.74020i	−0.403044	+	0.232698i	−0.687797	−	0.725903i	$-0.741422\pi$
$839$	−11.6744	+	6.74020i	−0.403044	+	0.232698i	0.284753	+	0.958601i	$0.408089\pi$
$840$		0			0
$841$	38.2573	−	66.2637i	1.31922	−	2.28495i
$842$		0			0
$843$	13.9796	−	17.4223i	0.481482	−	0.600057i
$844$		0			0
$845$	1.16457	+	2.01709i	0.0400623	+	0.0693899i
$846$		0			0
$847$			1.00764i			0.0346229i
$848$		0			0
$849$	−44.5719	−	6.85494i	−1.52970	−	0.235261i
$850$		0			0
$851$	−16.3032	+	9.41263i	−0.558865	+	0.322661i
$852$		0			0
$853$	−21.3000	+	36.8928i	−0.729300	+	1.26318i	0.227880	+	0.973689i	$0.426821\pi$
$853$	−21.3000	+	36.8928i	−0.729300	+	1.26318i	−0.957180	+	0.289495i	$0.906513\pi$
$854$		0			0
$855$	−0.581506	+	0.533102i	−0.0198871	+	0.0182317i
$856$		0			0
$857$	43.5827			1.48876			0.744378	−	0.667758i	$-0.232746\pi$
$857$	43.5827			1.48876			0.744378	+	0.667758i	$0.232746\pi$
$858$		0			0
$859$	18.3100	+	31.7138i	0.624728	+	1.08206i	0.988593	+	0.150609i	$0.0481234\pi$
$859$	18.3100	+	31.7138i	0.624728	+	1.08206i	−0.363866	+	0.931451i	$0.618543\pi$
$860$		0			0
$861$	2.25730	+	1.81124i	0.0769286	+	0.0617270i
$862$		0			0
$863$			13.4088i			0.456441i	0.973610	+	0.228220i	$0.0732906\pi$
$863$			13.4088i			0.456441i	−0.973610	+	0.228220i	$0.926709\pi$
$864$		0			0
$865$	−6.15746	−	3.55501i	−0.209360	−	0.120874i
$866$		0			0
$867$	9.93476	+	25.5384i	0.337402	+	0.867328i
$868$		0			0
$869$	7.50783	+	4.33465i	0.254686	+	0.147043i
$870$		0			0
$871$	−16.5887	−	15.8886i	−0.562086	−	0.538364i
$872$		0			0
$873$	4.67141	+	5.09556i	0.158103	+	0.172458i
$874$		0			0
$875$	−3.41867	+	1.97377i	−0.115572	+	0.0667256i
$876$		0			0
$877$	−17.4202	+	30.1727i	−0.588238	+	1.01886i	0.406225	+	0.913773i	$0.366845\pi$
$877$	−17.4202	+	30.1727i	−0.588238	+	1.01886i	−0.994463	+	0.105085i	$0.966488\pi$
$878$		0			0
$879$	−5.93325	+	38.5789i	−0.200124	+	1.30123i
$880$		0			0
$881$	−22.1161	−	12.7688i	−0.745112	−	0.430190i	0.0788132	−	0.996889i	$-0.474887\pi$
$881$	−22.1161	−	12.7688i	−0.745112	−	0.430190i	−0.823925	+	0.566699i	$0.808220\pi$
$882$		0			0
$883$	−39.3876	+	22.7405i	−1.32550	+	0.765277i	−0.984600	−	0.174823i	$-0.944065\pi$
$883$	−39.3876	+	22.7405i	−1.32550	+	0.765277i	−0.340899	+	0.940100i	$0.610731\pi$
$884$		0			0
$885$	0.213328	−	1.38709i	0.00717096	−	0.0466266i
$886$		0			0
$887$	30.0692	+	17.3605i	1.00962	+	0.582907i	0.911082	−	0.412226i	$-0.135249\pi$
$887$	30.0692	+	17.3605i	1.00962	+	0.582907i	0.0985427	+	0.995133i	$0.468582\pi$
$888$		0			0
$889$	−11.2399	−	6.48939i	−0.376976	−	0.217647i
$890$		0			0
$891$	2.45041	−	28.1597i	0.0820917	−	0.943386i
$892$		0			0
$893$			2.86619i			0.0959135i
$894$		0			0
$895$	0.684863			0.0228924
$896$		0			0
$897$	7.89334	+	20.2907i	0.263551	+	0.677486i
$898$		0			0
$899$	22.7205	−	39.3531i	0.757772	−	1.31250i
$900$		0			0
$901$	1.67558	+	0.967396i	0.0558216	+	0.0322286i
$902$		0			0
$903$	−0.372189	−	0.956751i	−0.0123857	−	0.0318387i
$904$		0			0
$905$	2.89472	+	5.01380i	0.0962237	+	0.166664i
$906$		0			0
$907$	−9.04923	−	15.6737i	−0.300475	−	0.520437i	0.675769	−	0.737114i	$-0.263812\pi$
$907$	−9.04923	−	15.6737i	−0.300475	−	0.520437i	−0.976244	+	0.216676i	$0.930478\pi$
$908$		0			0
$909$	−0.532727	−	2.40033i	−0.0176694	−	0.0796138i
$910$		0			0
$911$			8.24693i			0.273233i	0.990624	+	0.136616i	$0.0436228\pi$
$911$			8.24693i			0.273233i	−0.990624	+	0.136616i	$0.956377\pi$
$912$		0			0
$913$		−	11.1527i		−	0.369100i
$914$		0			0
$915$	−8.36469	−	6.71177i	−0.276528	−	0.221884i
$916$		0			0
$917$	7.44721	+	12.8989i	0.245929	+	0.425961i
$918$		0			0
$919$	45.4603	+	26.2465i	1.49960	+	0.865793i	1.00000		0.000463933i	$-0.000147675\pi$
$919$	45.4603	+	26.2465i	1.49960	+	0.865793i	0.499598	+	0.866257i	$0.333481\pi$
$920$		0			0
$921$	16.3721	−	20.4041i	0.539480	−	0.672339i
$922$		0			0
$923$	−23.0586			−0.758983
$924$		0			0
$925$	−10.0728	+	17.4467i	−0.331193	+	0.573643i
$926$		0			0
$927$	−6.97436	−	31.4246i	−0.229068	−	1.03212i
$928$		0			0
$929$	−59.1597			−1.94097			−0.970484	−	0.241165i	$-0.922470\pi$
$929$	−59.1597			−1.94097			−0.970484	+	0.241165i	$0.922470\pi$
$930$		0			0
$931$	1.79757	+	3.11348i	0.0589128	+	0.102040i
$932$		0			0
$933$	36.8251	+	5.66353i	1.20560	+	0.185416i
$934$		0			0
$935$			1.54988i			0.0506865i
$936$		0			0
$937$		−	23.9234i		−	0.781543i	−0.920488	−	0.390772i	$-0.872208\pi$
$937$		−	23.9234i		−	0.781543i	0.920488	−	0.390772i	$-0.127792\pi$
$938$		0			0
$939$	−6.15738	+	40.0362i	−0.200939	+	1.30653i
$940$		0			0
$941$	−28.6942			−0.935405			−0.467703	−	0.883886i	$-0.654918\pi$
$941$	−28.6942			−0.935405			−0.467703	+	0.883886i	$0.654918\pi$
$942$		0			0
$943$		−	8.43886i		−	0.274807i
$944$		0			0
$945$	−2.08993	+	0.137716i	−0.0679854	+	0.00447991i
$946$		0			0
$947$			33.6240i			1.09263i	0.837579	+	0.546316i	$0.183970\pi$
$947$			33.6240i			1.09263i	−0.837579	+	0.546316i	$0.816030\pi$
$948$		0			0
$949$	−26.7411	+	15.4390i	−0.868053	+	0.501170i
$950$		0			0
$951$	31.6741	+	25.4151i	1.02710	+	0.824140i
$952$		0			0
$953$		−	16.4616i		−	0.533243i	−0.963801	−	0.266621i	$-0.914093\pi$
$953$		−	16.4616i		−	0.533243i	0.963801	−	0.266621i	$-0.0859073\pi$
$954$		0			0
$955$	1.72582	−	2.98920i	0.0558461	−	0.0967282i
$956$		0			0
$957$	−43.5825	−	34.9703i	−1.40882	−	1.13043i
$958$		0			0
$959$	−15.1712	+	8.75907i	−0.489902	+	0.282845i
$960$		0			0
$961$	−5.71515	+	9.89893i	−0.184360	+	0.319320i
$962$		0			0
$963$	7.62683	−	24.2089i	0.245771	−	0.780122i
$964$		0			0
$965$	1.63001			0.0524718
$966$		0			0
$967$	−15.1624	−	26.2620i	−0.487589	−	0.844530i	0.512309	−	0.858801i	$-0.328790\pi$
$967$	−15.1624	−	26.2620i	−0.487589	−	0.844530i	−0.999898	+	0.0142716i	$0.995457\pi$
$968$		0			0
$969$	−1.01418	+	0.394528i	−0.0325800	+	0.0126741i
$970$		0			0
$971$	22.8976	−	13.2199i	0.734820	−	0.424248i	−0.0853631	−	0.996350i	$-0.527205\pi$
$971$	22.8976	−	13.2199i	0.734820	−	0.424248i	0.820183	+	0.572102i	$0.193872\pi$
$972$		0			0
$973$	−2.93200	−	5.07837i	−0.0939956	−	0.162805i
$974$		0			0
$975$	18.1722	+	14.5813i	0.581977	+	0.466974i
$976$		0			0
$977$	−40.0709	−	23.1349i	−1.28198	−	0.740153i	−0.304771	−	0.952426i	$-0.598580\pi$
$977$	−40.0709	−	23.1349i	−1.28198	−	0.740153i	−0.977210	+	0.212273i	$0.931913\pi$
$978$		0			0
$979$	−21.9234	+	12.6575i	−0.700676	+	0.404535i
$980$		0			0
$981$	9.35072	−	29.6809i	0.298546	−	0.947637i
$982$		0			0
$983$	−24.3280			−0.775943			−0.387971	−	0.921671i	$-0.626824\pi$
$983$	−24.3280			−0.775943			−0.387971	+	0.921671i	$0.626824\pi$
$984$		0			0
$985$	−0.265988	−	0.460705i	−0.00847508	−	0.0146793i
$986$		0			0
$987$	−4.76233	+	5.93516i	−0.151587	+	0.188918i
$988$		0			0
$989$	−1.49670	+	2.59236i	−0.0475922	+	0.0824322i
$990$		0			0
$991$			2.16786i			0.0688643i	0.999407	+	0.0344321i	$0.0109623\pi$
$991$			2.16786i			0.0688643i	−0.999407	+	0.0344321i	$0.989038\pi$
$992$		0			0
$993$	21.0235	−	8.17843i	0.667161	−	0.259535i
$994$		0			0
$995$	−0.635403	+	1.10055i	−0.0201436	+	0.0348898i
$996$		0			0
$997$	−40.1380			−1.27118			−0.635592	−	0.772025i	$-0.719244\pi$
$997$	−40.1380			−1.27118			−0.635592	+	0.772025i	$0.719244\pi$
$998$		0			0
$999$	−18.1535	+	12.1390i	−0.574350	+	0.384060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.641.2	yes	36
3.2	odd	2	inner	804.2.o.d.641.17	yes	36
67.30	odd	6	inner	804.2.o.d.365.17	yes	36
201.164	even	6	inner	804.2.o.d.365.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.2	✓	36	201.164	even	6	inner
804.2.o.d.365.17	yes	36	67.30	odd	6	inner
804.2.o.d.641.2	yes	36	1.1	even	1	trivial
804.2.o.d.641.17	yes	36	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71192 - 0.263286i) q^{3} -0.454473 q^{5} +(-0.768091 + 0.443457i) q^{7} +(2.86136 + 0.901449i) q^{9} +O(q^{10})\)	\(q+(-1.71192 - 0.263286i) q^{3} -0.454473 q^{5} +(-0.768091 + 0.443457i) q^{7} +(2.86136 + 0.901449i) q^{9} +(-1.57034 - 2.71991i) q^{11} +(2.43029 + 1.40313i) q^{13} +(0.778023 + 0.119656i) q^{15} +(0.940366 + 0.542920i) q^{17} +(0.289306 - 0.501092i) q^{19} +(1.43167 - 0.556938i) q^{21} +(-3.87917 - 2.23964i) q^{23} -4.79345 q^{25} +(-4.66109 - 2.29657i) q^{27} +(-8.89584 + 5.13602i) q^{29} +(-3.83109 + 2.21188i) q^{31} +(1.97219 + 5.06972i) q^{33} +(0.349077 - 0.201540i) q^{35} +(2.10137 - 3.63968i) q^{37} +(-3.79105 - 3.04191i) q^{39} +(0.941989 + 1.63157i) q^{41} -0.668277i q^{43} +(-1.30041 - 0.409685i) q^{45} +(-4.28992 + 2.47679i) q^{47} +(-3.10669 + 5.38095i) q^{49} +(-1.46689 - 1.17702i) q^{51} +1.78184 q^{53} +(0.713678 + 1.23613i) q^{55} +(-0.627199 + 0.781661i) q^{57} -1.78284i q^{59} +(-11.7989 - 6.81208i) q^{61} +(-2.59754 + 0.576497i) q^{63} +(-1.10450 - 0.637685i) q^{65} +(-7.95026 - 1.94764i) q^{67} +(6.05117 + 4.85542i) q^{69} +(-7.11599 + 4.10842i) q^{71} +(-5.50162 + 9.52908i) q^{73} +(8.20602 + 1.26205i) q^{75} +(2.41233 + 1.39276i) q^{77} +(-2.39051 + 1.38016i) q^{79} +(7.37478 + 5.15874i) q^{81} +(3.07529 + 1.77552i) q^{83} +(-0.427371 - 0.246743i) q^{85} +(16.5812 - 6.45032i) q^{87} -8.06035i q^{89} -2.48891 q^{91} +(7.14089 - 2.77790i) q^{93} +(-0.131482 + 0.227733i) q^{95} +(1.99555 + 1.15213i) q^{97} +(-2.04145 - 9.19823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 36 * q + 4 * q^9	\( 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) \) 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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