LMFDB - Embedded newform 819.2.bm.h.550.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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:	$6.53974792554$
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			550.2
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.h.478.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62688i q^{2} -4.90051 q^{4} +(-2.99000 + 1.72628i) q^{5} +(-2.63476 - 0.240965i) q^{7} +7.61930i q^{8} +O(q^{10})$	\(q-2.62688i q^{2} -4.90051 q^{4} +(-2.99000 + 1.72628i) q^{5} +(-2.63476 - 0.240965i) q^{7} +7.61930i q^{8} +(4.53473 + 7.85438i) q^{10} +(4.24816 - 2.45267i) q^{11} +(-3.59418 + 0.286096i) q^{13} +(-0.632988 + 6.92119i) q^{14} +10.2140 q^{16} +2.16734 q^{17} +(1.83239 + 1.05793i) q^{19} +(14.6525 - 8.45964i) q^{20} +(-6.44289 - 11.1594i) q^{22} +7.75943 q^{23} +(3.46006 - 5.99301i) q^{25} +(0.751541 + 9.44150i) q^{26} +(12.9116 + 1.18085i) q^{28} +(-4.61504 + 7.99349i) q^{29} +(-3.33239 - 1.92395i) q^{31} -11.5923i q^{32} -5.69336i q^{34} +(8.29389 - 3.82783i) q^{35} -0.456008i q^{37} +(2.77905 - 4.81346i) q^{38} +(-13.1530 - 22.7817i) q^{40} +(3.36535 + 1.94298i) q^{41} +(-0.634118 - 1.09832i) q^{43} +(-20.8181 + 12.0194i) q^{44} -20.3831i q^{46} +(5.62318 - 3.24654i) q^{47} +(6.88387 + 1.26977i) q^{49} +(-15.7429 - 9.08918i) q^{50} +(17.6133 - 1.40202i) q^{52} +(0.681202 - 1.17988i) q^{53} +(-8.46799 + 14.6670i) q^{55} +(1.83599 - 20.0750i) q^{56} +(20.9979 + 12.1232i) q^{58} +4.35931i q^{59} +(-7.21014 + 12.4883i) q^{61} +(-5.05400 + 8.75379i) q^{62} -10.0237 q^{64} +(10.2527 - 7.05998i) q^{65} +(6.34516 - 3.66338i) q^{67} -10.6211 q^{68} +(-10.0553 - 21.7871i) q^{70} +(6.96362 - 4.02045i) q^{71} +(4.12289 + 2.38035i) q^{73} -1.19788 q^{74} +(-8.97963 - 5.18439i) q^{76} +(-11.7839 + 5.43854i) q^{77} +(4.74876 + 8.22509i) q^{79} +(-30.5398 + 17.6322i) q^{80} +(5.10399 - 8.84037i) q^{82} +6.37170i q^{83} +(-6.48036 + 3.74144i) q^{85} +(-2.88517 + 1.66575i) q^{86} +(18.6877 + 32.3680i) q^{88} +2.15742i q^{89} +(9.53873 + 0.112281i) q^{91} -38.0252 q^{92} +(-8.52829 - 14.7714i) q^{94} -7.30511 q^{95} +(-12.9589 + 7.48185i) q^{97} +(3.33554 - 18.0831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) $ 36 * q - 44 * q^4 + 8 * q^7	$ 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) $ 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	2.62688i		−	1.85749i	−0.370724	−	0.928743i	$-0.620890\pi$
$2$		−	2.62688i		−	1.85749i	0.370724	−	0.928743i	$-0.379110\pi$
$3$		0			0
$3$		0			0
$4$	−4.90051			−2.45026
$5$	−2.99000	+	1.72628i	−1.33717	+	0.772015i	−0.986387	−	0.164443i	$-0.947417\pi$
$5$	−2.99000	+	1.72628i	−1.33717	+	0.772015i	−0.350782	+	0.936457i	$0.614084\pi$
$6$		0			0
$7$	−2.63476	−	0.240965i	−0.995844	−	0.0910764i
$7$	−2.63476	−	0.240965i	−0.995844	−	0.0910764i
$8$			7.61930i			2.69383i
$9$		0			0
$10$	4.53473	+	7.85438i	1.43401	+	2.48377i
$11$	4.24816	−	2.45267i	1.28087	−	0.739509i	0.303860	−	0.952717i	$-0.401724\pi$
$11$	4.24816	−	2.45267i	1.28087	−	0.739509i	0.977007	+	0.213208i	$0.0683910\pi$
$12$		0			0
$13$	−3.59418	+	0.286096i	−0.996847	+	0.0793488i
$13$	−3.59418	+	0.286096i	−0.996847	+	0.0793488i
$14$	−0.632988	+	6.92119i	−0.169173	+	1.84977i
$15$		0			0
$16$	10.2140			2.55350
$17$	2.16734			0.525658			0.262829	−	0.964842i	$-0.415344\pi$
$17$	2.16734			0.525658			0.262829	+	0.964842i	$0.415344\pi$
$18$		0			0
$19$	1.83239	+	1.05793i	0.420378	+	0.242705i	0.695239	−	0.718779i	$-0.255298\pi$
$19$	1.83239	+	1.05793i	0.420378	+	0.242705i	−0.274861	+	0.961484i	$0.588632\pi$
$20$	14.6525	−	8.45964i	3.27640	−	1.89163i
$21$		0			0
$22$	−6.44289	−	11.1594i	−1.37363	−	2.37919i
$23$	7.75943			1.61795			0.808976	−	0.587842i	$-0.200022\pi$
$23$	7.75943			1.61795			0.808976	+	0.587842i	$0.200022\pi$
$24$		0			0
$25$	3.46006	−	5.99301i	0.692013	−	1.19860i
$26$	0.751541	+	9.44150i	0.147389	+	1.85163i
$27$		0			0
$28$	12.9116	+	1.18085i	2.44007	+	0.223160i
$29$	−4.61504	+	7.99349i	−0.856992	+	1.48435i	0.0177932	+	0.999842i	$0.494336\pi$
$29$	−4.61504	+	7.99349i	−0.856992	+	1.48435i	−0.874785	+	0.484511i	$0.838997\pi$
$30$		0			0
$31$	−3.33239	−	1.92395i	−0.598514	−	0.345552i	0.169943	−	0.985454i	$-0.445642\pi$
$31$	−3.33239	−	1.92395i	−0.598514	−	0.345552i	−0.768457	+	0.639902i	$0.778975\pi$
$32$		−	11.5923i		−	2.04926i
$33$		0			0
$34$		−	5.69336i		−	0.976403i
$35$	8.29389	−	3.82783i	1.40192	−	0.647022i
$36$		0			0
$37$		−	0.456008i		−	0.0749672i	−0.999297	−	0.0374836i	$-0.988066\pi$
$37$		−	0.456008i		−	0.0749672i	0.999297	−	0.0374836i	$-0.0119342\pi$
$38$	2.77905	−	4.81346i	0.450822	−	0.780847i
$39$		0			0
$40$	−13.1530	−	22.7817i	−2.07968	−	3.60210i
$41$	3.36535	+	1.94298i	0.525579	+	0.303443i	0.739214	−	0.673470i	$-0.235197\pi$
$41$	3.36535	+	1.94298i	0.525579	+	0.303443i	−0.213635	+	0.976913i	$0.568530\pi$
$42$		0			0
$43$	−0.634118	−	1.09832i	−0.0967021	−	0.167493i	0.813616	−	0.581403i	$-0.197496\pi$
$43$	−0.634118	−	1.09832i	−0.0967021	−	0.167493i	−0.910318	+	0.413910i	$0.864163\pi$
$44$	−20.8181	+	12.0194i	−3.13845	+	1.81199i
$45$		0			0
$46$		−	20.3831i		−	3.00532i
$47$	5.62318	−	3.24654i	0.820225	−	0.473557i	−0.0302690	−	0.999542i	$-0.509636\pi$
$47$	5.62318	−	3.24654i	0.820225	−	0.473557i	0.850494	+	0.525985i	$0.176303\pi$
$48$		0			0
$49$	6.88387	+	1.26977i	0.983410	+	0.181396i
$50$	−15.7429	−	9.08918i	−2.22639	−	1.28540i
$51$		0			0
$52$	17.6133	−	1.40202i	2.44253	−	0.194425i
$53$	0.681202	−	1.17988i	0.0935702	−	0.162068i	−0.815441	−	0.578841i	$-0.803505\pi$
$53$	0.681202	−	1.17988i	0.0935702	−	0.162068i	0.909011	+	0.416772i	$0.136839\pi$
$54$		0			0
$55$	−8.46799	+	14.6670i	−1.14182	+	1.97770i
$56$	1.83599	−	20.0750i	0.245344	−	2.68263i
$57$		0			0
$58$	20.9979	+	12.1232i	2.75717	+	1.59185i
$59$			4.35931i			0.567534i	0.958893	+	0.283767i	$0.0915843\pi$
$59$			4.35931i			0.567534i	−0.958893	+	0.283767i	$0.908416\pi$
$60$		0			0
$61$	−7.21014	+	12.4883i	−0.923164	+	1.59897i	−0.128676	+	0.991687i	$0.541073\pi$
$61$	−7.21014	+	12.4883i	−0.923164	+	1.59897i	−0.794488	+	0.607280i	$0.792261\pi$
$62$	−5.05400	+	8.75379i	−0.641859	+	1.11173i
$63$		0			0
$64$	−10.0237			−1.25297
$65$	10.2527	−	7.05998i	1.27169	−	0.875683i
$66$		0			0
$67$	6.34516	−	3.66338i	0.775184	−	0.447553i	−0.0595366	−	0.998226i	$-0.518962\pi$
$67$	6.34516	−	3.66338i	0.775184	−	0.447553i	0.834721	+	0.550673i	$0.185629\pi$
$68$	−10.6211			−1.28800
$69$		0			0
$70$	−10.0553	−	21.7871i	−1.20183	−	2.60405i
$71$	6.96362	−	4.02045i	0.826429	−	0.477139i	−0.0261993	−	0.999657i	$-0.508340\pi$
$71$	6.96362	−	4.02045i	0.826429	−	0.477139i	0.852628	+	0.522518i	$0.175007\pi$
$72$		0			0
$73$	4.12289	+	2.38035i	0.482548	+	0.278599i	0.721478	−	0.692438i	$-0.243463\pi$
$73$	4.12289	+	2.38035i	0.482548	+	0.278599i	−0.238930	+	0.971037i	$0.576797\pi$
$74$	−1.19788			−0.139251
$75$		0			0
$76$	−8.97963	−	5.18439i	−1.03003	−	0.594690i
$77$	−11.7839	+	5.43854i	−1.34290	+	0.619779i
$78$		0			0
$79$	4.74876	+	8.22509i	0.534277	+	0.925395i	0.999198	+	0.0400431i	$0.0127495\pi$
$79$	4.74876	+	8.22509i	0.534277	+	0.925395i	−0.464921	+	0.885352i	$0.653917\pi$
$80$	−30.5398	+	17.6322i	−3.41446	+	1.97134i
$81$		0			0
$82$	5.10399	−	8.84037i	0.563642	−	0.976256i
$83$			6.37170i			0.699385i	0.936865	+	0.349692i	$0.113714\pi$
$83$			6.37170i			0.699385i	−0.936865	+	0.349692i	$0.886286\pi$
$84$		0			0
$85$	−6.48036	+	3.74144i	−0.702894	+	0.405816i
$86$	−2.88517	+	1.66575i	−0.311116	+	0.179623i
$87$		0			0
$88$	18.6877	+	32.3680i	1.99211	+	3.45044i
$89$			2.15742i			0.228686i	0.993441	+	0.114343i	$0.0364763\pi$
$89$			2.15742i			0.228686i	−0.993441	+	0.114343i	$0.963524\pi$
$90$		0			0
$91$	9.53873	+	0.112281i	0.999931	+	0.0117702i
$92$	−38.0252			−3.96440
$93$		0			0
$94$	−8.52829	−	14.7714i	−0.879626	−	1.52356i
$95$	−7.30511			−0.749488
$96$		0			0
$97$	−12.9589	+	7.48185i	−1.31578	+	0.759666i	−0.983047	−	0.183354i	$-0.941304\pi$
$97$	−12.9589	+	7.48185i	−1.31578	+	0.759666i	−0.332734	+	0.943021i	$0.607971\pi$
$98$	3.33554	−	18.0831i	0.336940	−	1.82667i
$99$		0			0
$100$	−16.9561	+	29.3688i	−1.69561	+	2.93688i
$101$	4.47933	+	7.75842i	0.445709	+	0.771991i	0.998101	−	0.0615931i	$-0.0196181\pi$
$101$	4.47933	+	7.75842i	0.445709	+	0.771991i	−0.552392	+	0.833585i	$0.686285\pi$
$102$		0			0
$103$	6.41683	+	11.1143i	0.632269	+	1.09512i	0.987087	+	0.160187i	$0.0512096\pi$
$103$	6.41683	+	11.1143i	0.632269	+	1.09512i	−0.354818	+	0.934935i	$0.615457\pi$
$104$	−2.17985	−	27.3852i	−0.213752	−	2.68534i
$105$		0			0
$106$	−3.09940	−	1.78944i	−0.301040	−	0.173805i
$107$	6.55276			0.633479			0.316739	−	0.948513i	$-0.397412\pi$
$107$	6.55276			0.633479			0.316739	+	0.948513i	$0.397412\pi$
$108$		0			0
$109$	6.04410	+	3.48956i	0.578920	+	0.334239i	0.760704	−	0.649099i	$-0.224854\pi$
$109$	6.04410	+	3.48956i	0.578920	+	0.334239i	−0.181784	+	0.983338i	$0.558187\pi$
$110$	38.5285	+	22.2444i	3.67354	+	2.12092i
$111$		0			0
$112$	−26.9114	−	2.46122i	−2.54288	−	0.232563i
$113$	4.11671	+	7.13036i	0.387268	+	0.670768i	0.992081	−	0.125600i	$-0.0400855\pi$
$113$	4.11671	+	7.13036i	0.387268	+	0.670768i	−0.604813	+	0.796367i	$0.706752\pi$
$114$		0			0
$115$	−23.2007	+	13.3949i	−2.16347	+	1.24908i
$116$	22.6161	−	39.1722i	2.09985	−	3.63704i
$117$		0			0
$118$	11.4514			1.05419
$119$	−5.71042	−	0.522255i	−0.523474	−	0.0478750i
$120$		0			0
$121$	6.53122	−	11.3124i	0.593747	−	1.02840i
$122$	32.8054	+	18.9402i	2.97006	+	1.71476i
$123$		0			0
$124$	16.3304	+	9.42836i	1.46651	+	0.846691i
$125$			6.62935i			0.592947i
$126$		0			0
$127$	−3.73689	+	6.47249i	−0.331596	+	0.574340i	−0.982825	−	0.184541i	$-0.940920\pi$
$127$	−3.73689	+	6.47249i	−0.331596	+	0.574340i	0.651229	+	0.758881i	$0.274254\pi$
$128$			3.14651i			0.278115i
$129$		0			0
$130$	−18.5457	−	26.9327i	−1.62657	−	2.36215i
$131$	−5.88165	−	10.1873i	−0.513882	−	0.890070i	−0.999870	−	0.0161048i	$-0.994873\pi$
$131$	−5.88165	−	10.1873i	−0.513882	−	0.890070i	0.485988	−	0.873966i	$-0.338460\pi$
$132$		0			0
$133$	−4.57296	−	3.22892i	−0.396526	−	0.279983i
$134$	−9.62326	−	16.6680i	−0.831323	−	1.43989i
$135$		0			0
$136$			16.5137i			1.41603i
$137$		−	6.04040i		−	0.516066i	−0.966136	−	0.258033i	$-0.916926\pi$
$137$		−	6.04040i		−	0.516066i	0.966136	−	0.258033i	$-0.0830743\pi$
$138$		0			0
$139$	0.168366	+	0.291618i	0.0142806	+	0.0247347i	0.873077	−	0.487582i	$-0.162121\pi$
$139$	0.168366	+	0.291618i	0.0142806	+	0.0247347i	−0.858797	+	0.512316i	$0.828788\pi$
$140$	−40.6443	+	18.7583i	−3.43507	+	1.58537i
$141$		0			0
$142$	−10.5612	−	18.2926i	−0.886279	−	1.53508i
$143$	−14.5669	+	10.0307i	−1.21815	+	0.838813i
$144$		0			0
$145$		−	31.8674i		−	2.64644i
$146$	6.25290	−	10.8303i	0.517494	−	0.896326i
$147$		0			0
$148$			2.23467i			0.183689i
$149$	−16.4590	−	9.50259i	−1.34837	−	0.778483i	−0.360352	−	0.932816i	$-0.617344\pi$
$149$	−16.4590	−	9.50259i	−1.34837	−	0.778483i	−0.988019	+	0.154334i	$0.950677\pi$
$150$		0			0
$151$	−6.20378	−	3.58176i	−0.504857	−	0.291479i	0.225860	−	0.974160i	$-0.427481\pi$
$151$	−6.20378	−	3.58176i	−0.504857	−	0.291479i	−0.730717	+	0.682681i	$0.760814\pi$
$152$	−8.06068	+	13.9615i	−0.653807	+	1.13243i
$153$		0			0
$154$	14.2864	+	30.9548i	1.15123	+	2.49441i
$155$	13.2851			1.06709
$156$		0			0
$157$	9.75074	−	16.8888i	0.778194	−	1.34787i	−0.154788	−	0.987948i	$-0.549470\pi$
$157$	9.75074	−	16.8888i	0.778194	−	1.34787i	0.932982	−	0.359923i	$-0.117197\pi$
$158$	21.6064	−	12.4744i	1.71891	−	0.992413i
$159$		0			0
$160$	20.0116	+	34.6611i	1.58206	+	2.74020i
$161$	−20.4442	−	1.86975i	−1.61123	−	0.147357i
$162$		0			0
$163$	−17.8891	−	10.3283i	−1.40118	−	0.808972i	−0.406667	−	0.913577i	$-0.633309\pi$
$163$	−17.8891	−	10.3283i	−1.40118	−	0.808972i	−0.994514	+	0.104605i	$0.966642\pi$
$164$	−16.4919	−	9.52162i	−1.28780	−	0.743513i
$165$		0			0
$166$	16.7377			1.29910
$167$	1.21761	+	0.702986i	0.0942214	+	0.0543987i	0.546370	−	0.837544i	$-0.316009\pi$
$167$	1.21761	+	0.702986i	0.0942214	+	0.0543987i	−0.452149	+	0.891942i	$0.649342\pi$
$168$		0			0
$169$	12.8363	−	2.05656i	0.987408	−	0.158197i
$170$	9.82832	+	17.0231i	0.753798	+	1.30562i
$171$		0			0
$172$	3.10750	+	5.38235i	0.236945	+	0.410400i
$173$	−3.02576	+	5.24076i	−0.230044	+	0.398448i	−0.957821	−	0.287366i	$-0.907220\pi$
$173$	−3.02576	+	5.24076i	−0.230044	+	0.398448i	0.727777	+	0.685814i	$0.240554\pi$
$174$		0			0
$175$	−10.5605	+	14.9564i	−0.798301	+	1.13059i
$176$	43.3906	−	25.0516i	3.27069	−	1.88833i
$177$		0			0
$178$	5.66728			0.424781
$179$	9.56570	+	16.5683i	0.714974	+	1.23837i	0.962970	+	0.269610i	$0.0868947\pi$
$179$	9.56570	+	16.5683i	0.714974	+	1.23837i	−0.247996	+	0.968761i	$0.579772\pi$
$180$		0			0
$181$	−6.46184			−0.480305			−0.240153	−	0.970735i	$-0.577197\pi$
$181$	−6.46184			−0.480305			−0.240153	+	0.970735i	$0.577197\pi$
$182$	0.294948	−	25.0571i	0.0218630	−	1.85736i
$183$		0			0
$184$			59.1214i			4.35849i
$185$	0.787196	+	1.36346i	0.0578758	+	0.100244i
$186$		0			0
$187$	9.20722	−	5.31579i	0.673299	−	0.388729i
$188$	−27.5565	+	15.9097i	−2.00976	+	1.16034i
$189$		0			0
$190$			19.1897i			1.39216i
$191$	−2.25437	+	3.90469i	−0.163121	+	0.282533i	−0.935986	−	0.352036i	$-0.885489\pi$
$191$	−2.25437	+	3.90469i	−0.163121	+	0.282533i	0.772866	+	0.634570i	$0.218823\pi$
$192$		0			0
$193$	−1.70737	+	0.985752i	−0.122899	+	0.0709560i	−0.560189	−	0.828365i	$-0.689272\pi$
$193$	−1.70737	+	0.985752i	−0.122899	+	0.0709560i	0.437290	+	0.899321i	$0.355938\pi$
$194$	19.6539	+	34.0416i	1.41107	+	2.44405i
$195$		0			0
$196$	−33.7345	−	6.22252i	−2.40961	−	0.444466i
$197$	5.47035	+	3.15831i	0.389747	+	0.225020i	0.682050	−	0.731305i	$-0.261088\pi$
$197$	5.47035	+	3.15831i	0.389747	+	0.225020i	−0.292304	+	0.956326i	$0.594422\pi$
$198$		0			0
$199$	21.5007			1.52414			0.762072	−	0.647493i	$-0.224182\pi$
$199$	21.5007			1.52414			0.762072	+	0.647493i	$0.224182\pi$
$200$	45.6625	+	26.3633i	3.22883	+	1.86417i
$201$		0			0
$202$	20.3805	−	11.7667i	1.43396	−	0.827899i
$203$	14.0857	−	19.9488i	0.988619	−	1.40013i
$204$		0			0
$205$	−13.4165			−0.937050
$206$	29.1959	−	16.8563i	2.03417	−	1.17443i
$207$		0			0
$208$	−36.7109	+	2.92218i	−2.54545	+	0.202617i
$209$	10.3790			0.717931
$210$		0			0
$211$	−4.84093	+	8.38474i	−0.333263	+	0.577229i	−0.983150	−	0.182802i	$-0.941483\pi$
$211$	−4.84093	+	8.38474i	−0.333263	+	0.577229i	0.649886	+	0.760031i	$0.274816\pi$
$212$	−3.33824	+	5.78200i	−0.229271	+	0.397109i
$213$		0			0
$214$		−	17.2133i		−	1.17668i
$215$	3.79202	+	2.18933i	0.258614	+	0.149311i
$216$		0			0
$217$	8.31641	+	5.87214i	0.564555	+	0.398627i
$218$	9.16667	−	15.8771i	0.620845	−	1.07534i
$219$		0			0
$220$	41.4975	−	71.8757i	2.79776	−	4.84586i
$221$	−7.78983	+	0.620069i	−0.524001	+	0.0417103i
$222$		0			0
$223$	1.50960	+	0.871568i	0.101090	+	0.0583645i	0.549693	−	0.835367i	$-0.314745\pi$
$223$	1.50960	+	0.871568i	0.101090	+	0.0583645i	−0.448603	+	0.893731i	$0.648078\pi$
$224$	−2.79335	+	30.5430i	−0.186639	+	2.04074i
$225$		0			0
$226$	18.7306	−	10.8141i	1.24594	−	0.719345i
$227$		−	4.32040i		−	0.286755i	−0.989668	−	0.143378i	$-0.954204\pi$
$227$		−	4.32040i		−	0.286755i	0.989668	−	0.143378i	$-0.0457963\pi$
$228$		0			0
$229$	−14.0353	+	8.10328i	−0.927478	+	0.535480i	−0.886013	−	0.463660i	$-0.846536\pi$
$229$	−14.0353	+	8.10328i	−0.927478	+	0.535480i	−0.0414648	+	0.999140i	$0.513202\pi$
$230$	35.1869	+	60.9455i	2.32015	+	4.01862i
$231$		0			0
$232$	−60.9048	−	35.1634i	−3.99860	−	2.30859i
$233$	6.48983	+	11.2407i	0.425163	+	0.736404i	0.996436	−	0.0843565i	$-0.0268835\pi$
$233$	6.48983	+	11.2407i	0.425163	+	0.736404i	−0.571273	+	0.820760i	$0.693550\pi$
$234$		0			0
$235$	−11.2089	+	19.4143i	−0.731186	+	1.26645i
$236$		−	21.3629i		−	1.39060i
$237$		0			0
$238$	−1.37190	+	15.0006i	−0.0889273	+	0.972345i
$239$		−	7.03023i		−	0.454748i	−0.973808	−	0.227374i	$-0.926986\pi$
$239$		−	7.03023i		−	0.454748i	0.973808	−	0.227374i	$-0.0730140\pi$
$240$		0			0
$241$			3.63439i			0.234112i	0.993125	+	0.117056i	$0.0373456\pi$
$241$			3.63439i			0.234112i	−0.993125	+	0.117056i	$0.962654\pi$
$242$	−29.7164	−	17.1567i	−1.91024	−	1.10288i
$243$		0			0
$244$	35.3334	−	61.1992i	2.26199	−	3.91788i
$245$	−22.7747	+	8.08686i	−1.45503	+	0.516650i
$246$		0			0
$247$	−6.88860	−	3.27815i	−0.438311	−	0.208584i
$248$	14.6592	−	25.3905i	0.930859	−	1.61230i
$249$		0			0
$250$	17.4145			1.10139
$251$	9.31585	+	16.1355i	0.588011	+	1.01847i	0.994493	+	0.104807i	$0.0334223\pi$
$251$	9.31585	+	16.1355i	0.588011	+	1.01847i	−0.406481	+	0.913659i	$0.633244\pi$
$252$		0			0
$253$	32.9633	−	19.0313i	2.07238	−	1.19649i
$254$	17.0025	+	9.81638i	1.06683	+	0.615934i
$255$		0			0
$256$	−11.7820			−0.736373
$257$	8.89164			0.554645			0.277323	−	0.960777i	$-0.410553\pi$
$257$	8.89164			0.554645			0.277323	+	0.960777i	$0.410553\pi$
$258$		0			0
$259$	−0.109882	+	1.20147i	−0.00682774	+	0.0746557i
$260$	−50.2436	+	34.5975i	−3.11598	+	2.14565i
$261$		0			0
$262$	−26.7609	+	15.4504i	−1.65329	+	0.954529i
$263$	−3.62190	−	6.27331i	−0.223336	−	0.386829i	0.732483	−	0.680785i	$-0.238361\pi$
$263$	−3.62190	−	6.27331i	−0.223336	−	0.386829i	−0.955819	+	0.293956i	$0.905028\pi$
$264$		0			0
$265$			4.70377i			0.288950i
$266$	−8.48200	+	12.0126i	−0.520065	+	0.736542i
$267$		0			0
$268$	−31.0945	+	17.9524i	−1.89940	+	1.09662i
$269$	6.19214			0.377541			0.188771	−	0.982021i	$-0.439550\pi$
$269$	6.19214			0.377541			0.188771	+	0.982021i	$0.439550\pi$
$270$		0			0
$271$			16.0187i			0.973066i	0.873662	+	0.486533i	$0.161739\pi$
$271$			16.0187i			0.973066i	−0.873662	+	0.486533i	$0.838261\pi$
$272$	22.1372			1.34227
$273$		0			0
$274$	−15.8674			−0.958586
$275$		−	33.9456i		−	2.04700i
$276$		0			0
$277$	17.8367			1.07170			0.535852	−	0.844312i	$-0.319990\pi$
$277$	17.8367			1.07170			0.535852	+	0.844312i	$0.319990\pi$
$278$	0.766047	−	0.442277i	0.0459444	−	0.0265260i
$279$		0			0
$280$	29.1654	+	63.1937i	1.74297	+	3.77654i
$281$			2.96366i			0.176797i	0.996085	+	0.0883984i	$0.0281749\pi$
$281$			2.96366i			0.176797i	−0.996085	+	0.0883984i	$0.971825\pi$
$282$		0			0
$283$	1.18285	+	2.04875i	0.0703131	+	0.121786i	0.899038	−	0.437870i	$-0.144267\pi$
$283$	1.18285	+	2.04875i	0.0703131	+	0.121786i	−0.828725	+	0.559655i	$0.810934\pi$
$284$	−34.1253	+	19.7022i	−2.02496	+	1.16911i
$285$		0			0
$286$	26.3496	+	38.2657i	1.55808	+	2.26270i
$287$	−8.39868	−	5.93022i	−0.495758	−	0.350050i
$288$		0			0
$289$	−12.3026			−0.723683
$290$	−83.7118			−4.91573
$291$		0			0
$292$	−20.2043	−	11.6649i	−1.18237	−	0.682639i
$293$	15.8683	−	9.16158i	0.927038	−	0.535226i	0.0411643	−	0.999152i	$-0.486893\pi$
$293$	15.8683	−	9.16158i	0.927038	−	0.535226i	0.885873	+	0.463927i	$0.153560\pi$
$294$		0			0
$295$	−7.52538	−	13.0343i	−0.438145	−	0.758889i
$296$	3.47446			0.201949
$297$		0			0
$298$	−24.9622	+	43.2358i	−1.44602	+	2.50458i
$299$	−27.8888	+	2.21994i	−1.61285	+	0.128382i
$300$		0			0
$301$	1.40609	+	3.04662i	0.0810455	+	0.175604i
$302$	−9.40885	+	16.2966i	−0.541419	+	0.937765i
$303$		0			0
$304$	18.7160	+	10.8057i	1.07343	+	0.619748i
$305$		−	49.7868i		−	2.85078i
$306$		0			0
$307$		−	28.0663i		−	1.60183i	−0.598778	−	0.800915i	$-0.704347\pi$
$307$		−	28.0663i		−	1.60183i	0.598778	−	0.800915i	$-0.295653\pi$
$308$	57.7469	−	26.6516i	3.29044	−	1.51862i
$309$		0			0
$310$		−	34.8984i		−	1.98210i
$311$	0.765793	−	1.32639i	0.0434241	−	0.0752128i	−0.843496	−	0.537135i	$-0.819507\pi$
$311$	0.765793	−	1.32639i	0.0434241	−	0.0752128i	0.886921	+	0.461922i	$0.152840\pi$
$312$		0			0
$313$	−0.281485	−	0.487547i	−0.0159105	−	0.0275578i	0.857961	−	0.513716i	$-0.171731\pi$
$313$	−0.281485	−	0.487547i	−0.0159105	−	0.0275578i	−0.873871	+	0.486158i	$0.838398\pi$
$314$	−44.3648	−	25.6140i	−2.50365	−	1.44548i
$315$		0			0
$316$	−23.2714	−	40.3072i	−1.30912	−	2.26746i
$317$	15.4668	−	8.92979i	0.868705	−	0.501547i	0.00178709	−	0.999998i	$-0.499431\pi$
$317$	15.4668	−	8.92979i	0.868705	−	0.501547i	0.866918	+	0.498452i	$0.166098\pi$
$318$		0			0
$319$			45.2768i			2.53501i
$320$	29.9710	−	17.3038i	1.67543	−	0.967310i
$321$		0			0
$322$	−4.91162	+	53.7045i	−0.273714	+	2.99283i
$323$	3.97141	+	2.29290i	0.220975	+	0.127580i
$324$		0			0
$325$	−10.7215	+	22.5299i	−0.594723	+	1.24973i
$326$	−27.1311	+	46.9925i	−1.50265	+	2.60267i
$327$		0			0
$328$	−14.8042	+	25.6416i	−0.817424	+	1.41582i
$329$	−15.5980	+	7.19886i	−0.859946	+	0.396886i
$330$		0			0
$331$	24.0949	+	13.9112i	1.32438	+	0.764629i	0.984424	−	0.175813i	$-0.0562554\pi$
$331$	24.0949	+	13.9112i	1.32438	+	0.764629i	0.339953	+	0.940442i	$0.389589\pi$
$332$		−	31.2246i		−	1.71367i
$333$		0			0
$334$	1.84666	−	3.19851i	0.101045	−	0.175015i
$335$	−12.6480	+	21.9070i	−0.691035	+	1.19691i
$336$		0			0
$337$	5.61976			0.306128			0.153064	−	0.988216i	$-0.451086\pi$
$337$	5.61976			0.306128			0.153064	+	0.988216i	$0.451086\pi$
$338$	−5.40235	−	33.7194i	−0.293849	−	1.83410i
$339$		0			0
$340$	31.7571	−	18.3350i	1.72227	−	0.994353i
$341$	−18.8753			−1.02216
$342$		0			0
$343$	−17.8313	−	5.00431i	−0.962802	−	0.270207i
$344$	8.36847	−	4.83154i	0.451197	−	0.260499i
$345$		0			0
$346$	13.7669	+	7.94831i	0.740112	+	0.427304i
$347$	−30.6459			−1.64516			−0.822579	−	0.568650i	$-0.807466\pi$
$347$	−30.6459			−1.64516			−0.822579	+	0.568650i	$0.807466\pi$
$348$		0			0
$349$	23.9956	+	13.8538i	1.28445	+	0.741579i	0.977659	−	0.210197i	$-0.0674104\pi$
$349$	23.9956	+	13.8538i	1.28445	+	0.741579i	0.306794	+	0.951776i	$0.400744\pi$
$350$	39.2886	+	27.7413i	2.10006	+	1.48283i
$351$		0			0
$352$	−28.4322	−	49.2461i	−1.51544	−	2.62483i
$353$	25.6271	−	14.7958i	1.36399	−	0.787500i	0.373838	−	0.927494i	$-0.378041\pi$
$353$	25.6271	−	14.7958i	1.36399	−	0.787500i	0.990152	+	0.139993i	$0.0447081\pi$
$354$		0			0
$355$	−13.8808	+	24.0423i	−0.736717	+	1.27603i
$356$		−	10.5725i		−	0.560339i
$357$		0			0
$358$	43.5229	−	25.1280i	2.30026	−	1.32805i
$359$	−1.71255	+	0.988741i	−0.0903849	+	0.0521838i	−0.544511	−	0.838754i	$-0.683285\pi$
$359$	−1.71255	+	0.988741i	−0.0903849	+	0.0521838i	0.454126	+	0.890937i	$0.349951\pi$
$360$		0			0
$361$	−7.26158	−	12.5774i	−0.382188	−	0.661969i
$362$			16.9745i			0.892160i
$363$		0			0
$364$	−46.7447	−	0.550233i	−2.45009	−	0.0288400i
$365$	−16.4366			−0.860330
$366$		0			0
$367$	−7.87543	−	13.6406i	−0.411094	−	0.712036i	0.583916	−	0.811814i	$-0.301520\pi$
$367$	−7.87543	−	13.6406i	−0.411094	−	0.712036i	−0.995010	+	0.0997786i	$0.968187\pi$
$368$	79.2547			4.13144
$369$		0			0
$370$	3.58166	−	2.06787i	0.186202	−	0.107503i
$371$	−2.07911	+	2.94454i	−0.107942	+	0.152873i
$372$		0			0
$373$	−0.579376	+	1.00351i	−0.0299989	+	0.0519597i	−0.880635	−	0.473795i	$-0.842884\pi$
$373$	−0.579376	+	1.00351i	−0.0299989	+	0.0519597i	0.850636	+	0.525755i	$0.176217\pi$
$374$	−13.9640	−	24.1863i	−0.722059	−	1.25064i
$375$		0			0
$376$	24.7364	+	42.8447i	1.27568	+	2.20955i
$377$	14.3004	−	30.0504i	0.736508	−	1.54767i
$378$		0			0
$379$	−21.8580	−	12.6197i	−1.12277	−	0.648231i	−0.180663	−	0.983545i	$-0.557824\pi$
$379$	−21.8580	−	12.6197i	−1.12277	−	0.648231i	−0.942106	+	0.335314i	$0.891158\pi$
$380$	35.7988			1.83644
$381$		0			0
$382$	10.2572	+	5.92197i	0.524802	+	0.302994i
$383$	−11.9354	−	6.89090i	−0.609870	−	0.352109i	0.163045	−	0.986619i	$-0.447869\pi$
$383$	−11.9354	−	6.89090i	−0.609870	−	0.352109i	−0.772915	+	0.634510i	$0.781202\pi$
$384$		0			0
$385$	25.8453	−	36.6034i	1.31720	−	1.86548i
$386$	2.58945	+	4.48507i	0.131800	+	0.228284i
$387$		0			0
$388$	63.5054	−	36.6649i	3.22400	−	1.86138i
$389$	−9.79332	+	16.9625i	−0.496541	+	0.860035i	−0.999992	−	0.00398932i	$-0.998730\pi$
$389$	−9.79332	+	16.9625i	−0.496541	+	0.860035i	0.503451	+	0.864024i	$0.332063\pi$
$390$		0			0
$391$	16.8174			0.850490
$392$	−9.67476	+	52.4503i	−0.488649	+	2.64914i
$393$		0			0
$394$	8.29651	−	14.3700i	0.417972	−	0.723949i
$395$	−28.3976	−	16.3954i	−1.42884	−	0.824940i
$396$		0			0
$397$	−28.3285	−	16.3555i	−1.42177	−	0.820859i	−0.425319	−	0.905044i	$-0.639838\pi$
$397$	−28.3285	−	16.3555i	−1.42177	−	0.820859i	−0.996450	+	0.0841850i	$0.973171\pi$
$398$		−	56.4798i		−	2.83108i
$399$		0			0
$400$	35.3411	−	61.2125i	1.76705	−	3.06063i
$401$			18.0781i			0.902779i	0.892327	+	0.451390i	$0.149071\pi$
$401$			18.0781i			0.902779i	−0.892327	+	0.451390i	$0.850929\pi$
$402$		0			0
$403$	12.5276	+	5.96166i	0.624046	+	0.296971i
$404$	−21.9510	−	38.0202i	−1.09210	−	1.89158i
$405$		0			0
$406$	−52.4032	−	37.0014i	−2.60073	−	1.83635i
$407$	−1.11844	−	1.93719i	−0.0554389	−	0.0960231i
$408$		0			0
$409$		−	20.9447i		−	1.03565i	−0.855486	−	0.517825i	$-0.826742\pi$
$409$		−	20.9447i		−	1.03565i	0.855486	−	0.517825i	$-0.173258\pi$
$410$			35.2436i			1.74056i
$411$		0			0
$412$	−31.4457	−	54.4656i	−1.54922	−	2.68333i
$413$	1.05044	−	11.4857i	0.0516890	−	0.565176i
$414$		0			0
$415$	−10.9993	−	19.0514i	−0.539935	−	0.935195i
$416$	3.31652	+	41.6650i	0.162606	+	2.04279i
$417$		0			0
$418$		−	27.2644i		−	1.33355i
$419$	1.13951	−	1.97369i	0.0556686	−	0.0964209i	−0.836848	−	0.547435i	$-0.815604\pi$
$419$	1.13951	−	1.97369i	0.0556686	−	0.0964209i	0.892517	+	0.451014i	$0.148938\pi$
$420$		0			0
$421$			35.8575i			1.74759i	0.486296	+	0.873794i	$0.338348\pi$
$421$			35.8575i			1.74759i	−0.486296	+	0.873794i	$0.661652\pi$
$422$	22.0257	+	12.7166i	1.07219	+	0.619032i
$423$		0			0
$424$	8.98983	+	5.19028i	0.436585	+	0.252062i
$425$	7.49915	−	12.9889i	0.363762	−	0.630055i
$426$		0			0
$427$	22.0062	−	31.1663i	1.06496	−	1.50824i
$428$	−32.1119			−1.55219
$429$		0			0
$430$	5.75110	−	9.96120i	0.277343	−	0.480372i
$431$	−2.62617	+	1.51622i	−0.126498	+	0.0730338i	−0.561914	−	0.827196i	$-0.689935\pi$
$431$	−2.62617	+	1.51622i	−0.126498	+	0.0730338i	0.435416	+	0.900230i	$0.356601\pi$
$432$		0			0
$433$	2.38738	+	4.13507i	0.114730	+	0.198719i	0.917672	−	0.397339i	$-0.130066\pi$
$433$	2.38738	+	4.13507i	0.114730	+	0.198719i	−0.802942	+	0.596058i	$0.796733\pi$
$434$	15.4254	−	21.8462i	0.740444	−	1.04865i
$435$		0			0
$436$	−29.6192	−	17.1006i	−1.41850	−	0.818972i
$437$	14.2183	+	8.20892i	0.680152	+	0.392686i
$438$		0			0
$439$	−22.8816			−1.09208			−0.546040	−	0.837759i	$-0.683865\pi$
$439$	−22.8816			−1.09208			−0.546040	+	0.837759i	$0.683865\pi$
$440$	−111.752	−	64.5202i	−5.32758	−	3.07588i
$441$		0			0
$442$	1.62885	+	20.4630i	0.0774764	+	0.973325i
$443$	3.94834	+	6.83873i	0.187591	+	0.324918i	0.944447	−	0.328665i	$-0.106599\pi$
$443$	3.94834	+	6.83873i	0.187591	+	0.324918i	−0.756855	+	0.653582i	$0.773265\pi$
$444$		0			0
$445$	−3.72430	−	6.45068i	−0.176549	−	0.305791i
$446$	2.28951	−	3.96554i	0.108411	−	0.187774i
$447$		0			0
$448$	26.4101	+	2.41538i	1.24776	+	0.114116i
$449$	11.4618	−	6.61749i	0.540917	−	0.312298i	−0.204534	−	0.978860i	$-0.565568\pi$
$449$	11.4618	−	6.61749i	0.540917	−	0.312298i	0.745450	+	0.666561i	$0.232234\pi$
$450$		0			0
$451$	19.0620			0.897596
$452$	−20.1740	−	34.9424i	−0.948905	−	1.64355i
$453$		0			0
$454$	−11.3492			−0.532644
$455$	−28.7146	+	16.1308i	−1.34616	+	0.756222i
$456$		0			0
$457$			25.2528i			1.18128i	0.806936	+	0.590638i	$0.201124\pi$
$457$			25.2528i			1.18128i	−0.806936	+	0.590638i	$0.798876\pi$
$458$	21.2864	+	36.8690i	0.994646	+	1.72278i
$459$		0			0
$460$	113.695	−	65.6419i	5.30107	−	3.06057i
$461$	−26.9528	+	15.5612i	−1.25532	+	0.724758i	−0.972161	−	0.234315i	$-0.924715\pi$
$461$	−26.9528	+	15.5612i	−1.25532	+	0.724758i	−0.283157	+	0.959073i	$0.591382\pi$
$462$		0			0
$463$			18.9663i			0.881439i	0.897645	+	0.440719i	$0.145277\pi$
$463$			18.9663i			0.881439i	−0.897645	+	0.440719i	$0.854723\pi$
$464$	−47.1380	+	81.6454i	−2.18833	+	3.79029i
$465$		0			0
$466$	29.5280	−	17.0480i	1.36786	−	0.789734i
$467$	6.96276	+	12.0599i	0.322198	+	0.558063i	0.980941	−	0.194304i	$-0.0622450\pi$
$467$	6.96276	+	12.0599i	0.322198	+	0.558063i	−0.658743	+	0.752368i	$0.728912\pi$
$468$		0			0
$469$	−17.6007	+	8.12314i	−0.812724	+	0.375092i
$470$	50.9992	+	29.4444i	2.35242	+	1.35817i
$471$		0			0
$472$	−33.2149			−1.52884
$473$	−5.38766	−	3.11057i	−0.247725	−	0.143024i
$474$		0			0
$475$	12.6803	−	7.32100i	0.581814	−	0.335911i
$476$	27.9840	+	2.55932i	1.28264	+	0.117306i
$477$		0			0
$478$	−18.4676			−0.844688
$479$	13.1603	−	7.59810i	0.601309	−	0.347166i	−0.168247	−	0.985745i	$-0.553811\pi$
$479$	13.1603	−	7.59810i	0.601309	−	0.347166i	0.769556	+	0.638579i	$0.220477\pi$
$480$		0			0
$481$	0.130462	+	1.63898i	0.00594856	+	0.0747308i
$482$	9.54711			0.434859
$483$		0			0
$484$	−32.0063	+	55.4366i	−1.45483	+	2.51984i
$485$	25.8315	−	44.7414i	1.17295	−	2.03160i
$486$		0			0
$487$		−	3.63315i		−	0.164634i	−0.996606	−	0.0823169i	$-0.973768\pi$
$487$		−	3.63315i		−	0.164634i	0.996606	−	0.0823169i	$-0.0262320\pi$
$488$	−95.1524	−	54.9362i	−4.30734	−	2.48685i
$489$		0			0
$490$	21.2432	+	59.8266i	0.959671	+	2.70269i
$491$	−15.6429	+	27.0943i	−0.705953	+	1.22275i	0.260393	+	0.965503i	$0.416148\pi$
$491$	−15.6429	+	27.0943i	−0.705953	+	1.22275i	−0.966346	+	0.257244i	$0.917186\pi$
$492$		0			0
$493$	−10.0024	+	17.3246i	−0.450485	+	0.780263i
$494$	−8.61131	+	18.0955i	−0.387441	+	0.814157i
$495$		0			0
$496$	−34.0369	−	19.6512i	−1.52830	−	0.882367i
$497$	−19.3162	+	8.91490i	−0.866451	+	0.399888i
$498$		0			0
$499$	8.90798	−	5.14302i	0.398776	−	0.230233i	−0.287180	−	0.957877i	$-0.592718\pi$
$499$	8.90798	−	5.14302i	0.398776	−	0.230233i	0.685956	+	0.727643i	$0.259384\pi$
$500$		−	32.4872i		−	1.45287i
$501$		0			0
$502$	42.3861	−	24.4717i	1.89179	−	1.09222i
$503$	20.8076	+	36.0399i	0.927766	+	1.60694i	0.787051	+	0.616888i	$0.211607\pi$
$503$	20.8076	+	36.0399i	0.927766	+	1.60694i	0.140716	+	0.990050i	$0.455060\pi$
$504$		0			0
$505$	−26.7864	−	15.4651i	−1.19198	−	0.688188i
$506$	−49.9931	−	86.5906i	−2.22246	−	3.84942i
$507$		0			0
$508$	18.3127	−	31.7185i	0.812494	−	1.40728i
$509$			22.5979i			1.00163i	0.865553	+	0.500817i	$0.166967\pi$
$509$			22.5979i			1.00163i	−0.865553	+	0.500817i	$0.833033\pi$
$510$		0			0
$511$	−10.2892	−	7.26512i	−0.455168	−	0.321390i
$512$			37.2429i			1.64592i
$513$		0			0
$514$		−	23.3573i		−	1.03025i
$515$	−38.3726	−	22.1545i	−1.69090	−	0.976242i
$516$		0			0
$517$	15.9254	−	27.5837i	0.700400	−	1.21313i
$518$	3.15612	+	0.288647i	0.138672	+	0.0126824i
$519$		0			0
$520$	53.7921	+	78.1186i	2.35894	+	3.42573i
$521$	−5.11486	+	8.85920i	−0.224086	+	0.388129i	−0.956045	−	0.293220i	$-0.905273\pi$
$521$	−5.11486	+	8.85920i	−0.224086	+	0.388129i	0.731959	+	0.681349i	$0.238606\pi$
$522$		0			0
$523$	29.5218			1.29090			0.645449	−	0.763803i	$-0.276670\pi$
$523$	29.5218			1.29090			0.645449	+	0.763803i	$0.276670\pi$
$524$	28.8231	+	49.9231i	1.25914	+	2.18090i
$525$		0			0
$526$	−16.4792	+	9.51430i	−0.718529	+	0.414843i
$527$	−7.22243	−	4.16987i	−0.314614	−	0.181642i
$528$		0			0
$529$	37.2087			1.61777
$530$	12.3563			0.536721
$531$		0			0
$532$	22.4099	+	15.8234i	0.971591	+	0.686030i
$533$	−12.6516	−	6.02063i	−0.548000	−	0.260782i
$534$		0			0
$535$	−19.5927	+	11.3119i	−0.847068	+	0.489055i
$536$	27.9124	+	48.3457i	1.20563	+	2.08821i
$537$		0			0
$538$		−	16.2660i		−	0.701278i
$539$	32.3581	−	11.4897i	1.39376	−	0.494897i
$540$		0			0
$541$	22.7558	−	13.1381i	0.978350	−	0.564851i	0.0765785	−	0.997064i	$-0.475600\pi$
$541$	22.7558	−	13.1381i	0.978350	−	0.564851i	0.901772	+	0.432213i	$0.142267\pi$
$542$	42.0792			1.80746
$543$		0			0
$544$		−	25.1246i		−	1.07721i
$545$	−24.0958			−1.03215
$546$		0			0
$547$	−9.82751			−0.420194			−0.210097	−	0.977681i	$-0.567378\pi$
$547$	−9.82751			−0.420194			−0.210097	+	0.977681i	$0.567378\pi$
$548$			29.6010i			1.26449i
$549$		0			0
$550$	−89.1712			−3.80227
$551$	−16.9131	+	9.76477i	−0.720521	+	0.415993i
$552$		0			0
$553$	−10.5299	−	22.8154i	−0.447775	−	0.970209i
$554$		−	46.8550i		−	1.99068i
$555$		0			0
$556$	−0.825079	−	1.42908i	−0.0349911	−	0.0606064i
$557$	14.2945	−	8.25293i	0.605677	−	0.349688i	−0.165595	−	0.986194i	$-0.552954\pi$
$557$	14.2945	−	8.25293i	0.605677	−	0.349688i	0.771272	+	0.636506i	$0.219621\pi$
$558$		0			0
$559$	2.59336	+	3.76616i	0.109688	+	0.159292i
$560$	84.7137	−	39.0974i	3.57981	−	1.65217i
$561$		0			0
$562$	7.78517			0.328398
$563$	35.1106			1.47973			0.739867	−	0.672753i	$-0.234888\pi$
$563$	35.1106			1.47973			0.739867	+	0.672753i	$0.234888\pi$
$564$		0			0
$565$	−24.6179	−	14.2132i	−1.03568	−	0.597953i
$566$	5.38184	−	3.10720i	0.226215	−	0.130606i
$567$		0			0
$568$	30.6330	+	53.0579i	1.28533	+	2.22626i
$569$	45.1105			1.89113			0.945564	−	0.325435i	$-0.105511\pi$
$569$	45.1105			1.89113			0.945564	+	0.325435i	$0.105511\pi$
$570$		0			0
$571$	−12.6060	+	21.8342i	−0.527545	+	0.913735i	0.471939	+	0.881631i	$0.343554\pi$
$571$	−12.6060	+	21.8342i	−0.527545	+	0.913735i	−0.999485	+	0.0321039i	$0.989779\pi$
$572$	71.3855	−	49.1558i	2.98478	−	2.05531i
$573$		0			0
$574$	−15.5780	+	22.0623i	−0.650213	+	0.920864i
$575$	26.8481	−	46.5023i	1.11964	−	1.93928i
$576$		0			0
$577$	−37.0651	−	21.3996i	−1.54304	−	0.890875i	−0.998645	−	0.0520469i	$-0.983425\pi$
$577$	−37.0651	−	21.3996i	−1.54304	−	0.890875i	−0.544396	−	0.838828i	$-0.683241\pi$
$578$			32.3175i			1.34423i
$579$		0			0
$580$			156.166i			6.48446i
$581$	1.53536	−	16.7879i	0.0636974	−	0.696478i
$582$		0			0
$583$		−	6.68306i		−	0.276784i
$584$	−18.1366	+	31.4135i	−0.750499	+	1.29990i
$585$		0			0
$586$	−24.0664	−	41.6842i	−0.994174	−	1.72196i
$587$	28.0352	+	16.1861i	1.15714	+	0.668073i	0.950616	−	0.310370i	$-0.100453\pi$
$587$	28.0352	+	16.1861i	1.15714	+	0.668073i	0.206520	+	0.978442i	$0.433786\pi$
$588$		0			0
$589$	−4.07081	−	7.05085i	−0.167735	−	0.290525i
$590$	−34.2397	+	19.7683i	−1.40963	+	0.813848i
$591$		0			0
$592$		−	4.65766i		−	0.191429i
$593$	4.43914	−	2.56294i	0.182294	−	0.105247i	−0.406076	−	0.913839i	$-0.633103\pi$
$593$	4.43914	−	2.56294i	0.182294	−	0.105247i	0.588370	+	0.808592i	$0.299770\pi$
$594$		0			0
$595$	17.9757	−	8.29623i	0.736933	−	0.340112i
$596$	80.6574	+	46.5676i	3.30385	+	1.90748i
$597$		0			0
$598$	5.83152	+	73.2606i	0.238469	+	2.99585i
$599$	−16.4903	+	28.5621i	−0.673777	+	1.16702i	0.303047	+	0.952975i	$0.401996\pi$
$599$	−16.4903	+	28.5621i	−0.673777	+	1.16702i	−0.976825	+	0.214041i	$0.931337\pi$
$600$		0			0
$601$	10.1310	−	17.5474i	0.413251	−	0.715772i	−0.581992	−	0.813194i	$-0.697727\pi$
$601$	10.1310	−	17.5474i	0.413251	−	0.715772i	0.995243	+	0.0974227i	$0.0310599\pi$
$602$	8.00310	−	3.69363i	0.326182	−	0.150541i
$603$		0			0
$604$	30.4017	+	17.5524i	1.23703	+	0.714199i
$605$			45.0988i			1.83353i
$606$		0			0
$607$	−3.47379	+	6.01677i	−0.140997	+	0.244213i	−0.927872	−	0.372898i	$-0.878364\pi$
$607$	−3.47379	+	6.01677i	−0.140997	+	0.244213i	0.786876	+	0.617112i	$0.211697\pi$
$608$	12.2639	−	21.2416i	0.497366	−	0.861462i
$609$		0			0
$610$	−130.784			−5.29529
$611$	−19.2819	+	13.2774i	−0.780063	+	0.537148i
$612$		0			0
$613$	12.1814	−	7.03292i	0.492001	−	0.284057i	−0.233403	−	0.972380i	$-0.574986\pi$
$613$	12.1814	−	7.03292i	0.492001	−	0.284057i	0.725404	+	0.688323i	$0.241653\pi$
$614$	−73.7269			−2.97538
$615$		0			0
$616$	−41.4379	−	89.7848i	−1.66958	−	3.61753i
$617$	22.0937	−	12.7558i	0.889459	−	0.513529i	0.0156936	−	0.999877i	$-0.495004\pi$
$617$	22.0937	−	12.7558i	0.889459	−	0.513529i	0.873766	+	0.486347i	$0.161671\pi$
$618$		0			0
$619$	−35.4441	−	20.4637i	−1.42462	−	0.822504i	−0.427929	−	0.903812i	$-0.640757\pi$
$619$	−35.4441	−	20.4637i	−1.42462	−	0.822504i	−0.996689	+	0.0813086i	$0.974090\pi$
$620$	−65.1038			−2.61463
$621$		0			0
$622$	−3.48428	−	2.01165i	−0.139707	−	0.0806597i
$623$	0.519863	−	5.68427i	0.0208279	−	0.227735i
$624$		0			0
$625$	5.85623	+	10.1433i	0.234249	+	0.405731i
$626$	−1.28073	+	0.739429i	−0.0511882	+	0.0295535i
$627$		0			0
$628$	−47.7836	+	82.7636i	−1.90677	+	3.30263i
$629$		−	0.988326i		−	0.0394071i
$630$		0			0
$631$	15.4257	−	8.90600i	0.614086	−	0.354542i	−0.160477	−	0.987040i	$-0.551303\pi$
$631$	15.4257	−	8.90600i	0.614086	−	0.354542i	0.774563	+	0.632497i	$0.217970\pi$
$632$	−62.6695	+	36.1822i	−2.49286	+	1.43925i
$633$		0			0
$634$	−23.4575	−	40.6296i	−0.931616	−	1.61361i
$635$		−	25.8036i		−	1.02399i
$636$		0			0
$637$	−25.1052	−	2.59434i	−0.994703	−	0.102791i
$638$	118.937			4.70875
$639$		0			0
$640$	−5.43175	−	9.40807i	−0.214709	−	0.371887i
$641$	−24.4348			−0.965115			−0.482557	−	0.875864i	$-0.660292\pi$
$641$	−24.4348			−0.965115			−0.482557	+	0.875864i	$0.660292\pi$
$642$		0			0
$643$	−11.6547	+	6.72885i	−0.459617	+	0.265360i	−0.711883	−	0.702298i	$-0.752158\pi$
$643$	−11.6547	+	6.72885i	−0.459617	+	0.265360i	0.252266	+	0.967658i	$0.418824\pi$
$644$	100.187	+	9.16275i	3.94792	+	0.361063i
$645$		0			0
$646$	6.02317	−	10.4324i	0.236978	−	0.410459i
$647$	−4.15531	−	7.19720i	−0.163362	−	0.282951i	0.772710	−	0.634759i	$-0.218901\pi$
$647$	−4.15531	−	7.19720i	−0.163362	−	0.282951i	−0.936072	+	0.351807i	$0.885567\pi$
$648$		0			0
$649$	10.6920	+	18.5190i	0.419697	+	0.726936i
$650$	59.1833	+	28.1642i	2.32136	+	1.10469i
$651$		0			0
$652$	87.6656	+	50.6138i	3.43325	+	1.98219i
$653$	−32.4735			−1.27079			−0.635393	−	0.772189i	$-0.719162\pi$
$653$	−32.4735			−1.27079			−0.635393	+	0.772189i	$0.719162\pi$
$654$		0			0
$655$	35.1723	+	20.3067i	1.37429	+	0.793449i
$656$	34.3736	+	19.8456i	1.34206	+	0.774841i
$657$		0			0
$658$	18.9106	+	40.9741i	0.737210	+	1.59734i
$659$	−6.60168	−	11.4345i	−0.257165	−	0.445423i	0.708316	−	0.705895i	$-0.249455\pi$
$659$	−6.60168	−	11.4345i	−0.257165	−	0.445423i	−0.965481	+	0.260472i	$0.916122\pi$
$660$		0			0
$661$	14.4854	−	8.36313i	0.563415	−	0.325288i	−0.191100	−	0.981571i	$-0.561205\pi$
$661$	14.4854	−	8.36313i	0.563415	−	0.325288i	0.754515	+	0.656283i	$0.227872\pi$
$662$	36.5431	−	63.2945i	1.42029	−	2.46001i
$663$		0			0
$664$	−48.5479			−1.88402
$665$	19.2472	+	1.76028i	0.746373	+	0.0682607i
$666$		0			0
$667$	−35.8101	+	62.0249i	−1.38657	+	2.40161i
$668$	−5.96690	−	3.44499i	−0.230866	−	0.133291i
$669$		0			0
$670$	57.5471	+	33.2248i	2.22324	+	1.28359i
$671$			70.7365i			2.73075i
$672$		0			0
$673$	5.44712	−	9.43469i	0.209971	−	0.363681i	−0.741734	−	0.670694i	$-0.765996\pi$
$673$	5.44712	−	9.43469i	0.209971	−	0.363681i	0.951705	+	0.307013i	$0.0993297\pi$
$674$		−	14.7624i		−	0.568628i
$675$		0			0
$676$	−62.9044	+	10.0782i	−2.41940	+	0.387623i
$677$	10.4984	+	18.1837i	0.403486	+	0.698857i	0.994144	−	0.108064i	$-0.0344652\pi$
$677$	10.4984	+	18.1837i	0.403486	+	0.698857i	−0.590658	+	0.806922i	$0.701132\pi$
$678$		0			0
$679$	35.9465	−	16.5902i	1.37950	−	0.636673i
$680$	−28.5071	−	49.3758i	−1.09320	−	1.89348i
$681$		0			0
$682$			49.5833i			1.89864i
$683$			40.0533i			1.53260i	0.642486	+	0.766298i	$0.277903\pi$
$683$			40.0533i			1.53260i	−0.642486	+	0.766298i	$0.722097\pi$
$684$		0			0
$685$	10.4274	+	18.0608i	0.398410	+	0.690067i
$686$	−13.1457	+	46.8409i	−0.501906	+	1.78839i
$687$		0			0
$688$	−6.47687	−	11.2183i	−0.246928	−	0.427693i
$689$	−2.11081	+	4.43558i	−0.0804153	+	0.168982i
$690$		0			0
$691$			3.27012i			0.124401i	0.998064	+	0.0622006i	$0.0198118\pi$
$691$			3.27012i			0.124401i	−0.998064	+	0.0622006i	$0.980188\pi$
$692$	14.8278	−	25.6824i	0.563667	−	0.976299i
$693$		0			0
$694$			80.5032i			3.05586i
$695$	−1.00683	−	0.581292i	−0.0381912	−	0.0220497i
$696$		0			0
$697$	7.29387	+	4.21112i	0.276275	+	0.159507i
$698$	36.3924	−	63.0335i	1.37747	−	2.38585i
$699$		0			0
$700$	51.7520	−	73.2938i	1.95604	−	2.77024i
$701$	−10.0906			−0.381118			−0.190559	−	0.981676i	$-0.561030\pi$
$701$	−10.0906			−0.381118			−0.190559	+	0.981676i	$0.561030\pi$
$702$		0			0
$703$	0.482424	−	0.835582i	0.0181950	−	0.0315146i
$704$	−42.5824	+	24.5850i	−1.60489	+	0.926581i
$705$		0			0
$706$	−38.8668	−	67.3193i	−1.46277	−	2.53359i
$707$	−9.93242	−	21.5209i	−0.373547	−	0.809377i
$708$		0			0
$709$	38.9731	+	22.5011i	1.46366	+	0.845047i	0.999178	−	0.0405331i	$-0.0129056\pi$
$709$	38.9731	+	22.5011i	1.46366	+	0.845047i	0.464486	+	0.885580i	$0.346239\pi$
$710$	63.1562	+	36.4632i	2.37021	+	1.36844i
$711$		0			0
$712$	−16.4380			−0.616041
$713$	−25.8574	−	14.9288i	−0.968367	−	0.559087i
$714$		0			0
$715$	26.2393	−	55.1385i	0.981296	−	2.06206i
$716$	−46.8768	−	81.1930i	−1.75187	−	3.03433i
$717$		0			0
$718$	2.59731	+	4.49867i	0.0969306	+	0.167889i
$719$	9.82990	−	17.0259i	0.366593	−	0.634958i	−0.622437	−	0.782670i	$-0.713857\pi$
$719$	9.82990	−	17.0259i	0.366593	−	0.634958i	0.989030	+	0.147712i	$0.0471907\pi$
$720$		0			0
$721$	−14.2286	−	30.8296i	−0.529902	−	1.14816i
$722$	−33.0394	+	19.0753i	−1.22960	+	0.709909i
$723$		0			0
$724$	31.6663			1.17687
$725$	31.9367	+	55.3160i	1.18610	+	2.05438i
$726$		0			0
$727$	11.8574			0.439767			0.219883	−	0.975526i	$-0.429432\pi$
$727$	11.8574			0.439767			0.219883	+	0.975526i	$0.429432\pi$
$728$	−0.855500	+	72.6785i	−0.0317069	+	2.69364i
$729$		0			0
$730$			43.1770i			1.59805i
$731$	−1.37435	−	2.38045i	−0.0508323	−	0.0880440i
$732$		0			0
$733$	−2.42527	+	1.40023i	−0.0895794	+	0.0517187i	−0.544121	−	0.839007i	$-0.683137\pi$
$733$	−2.42527	+	1.40023i	−0.0895794	+	0.0517187i	0.454541	+	0.890726i	$0.349803\pi$
$734$	−35.8324	+	20.6878i	−1.32260	+	0.763602i
$735$		0			0
$736$		−	89.9499i		−	3.31560i
$737$	17.9701	−	31.1252i	0.661939	−	1.14651i
$738$		0			0
$739$	−13.3386	+	7.70102i	−0.490667	+	0.283287i	−0.724851	−	0.688906i	$-0.758091\pi$
$739$	−13.3386	+	7.70102i	−0.490667	+	0.283287i	0.234184	+	0.972192i	$0.424758\pi$
$740$	−3.85766	−	6.68167i	−0.141810	−	0.245623i
$741$		0			0
$742$	7.73496	+	5.46158i	0.283959	+	0.200501i
$743$	−25.2013	−	14.5500i	−0.924545	−	0.533786i	−0.0394629	−	0.999221i	$-0.512565\pi$
$743$	−25.2013	−	14.5500i	−0.924545	−	0.533786i	−0.885082	+	0.465435i	$0.845898\pi$
$744$		0			0
$745$	65.6164			2.40400
$746$	2.63610	+	1.52195i	0.0965144	+	0.0557226i
$747$		0			0
$748$	−45.1201	+	26.0501i	−1.64975	+	0.952486i
$749$	−17.2649	−	1.57899i	−0.630846	−	0.0576949i
$750$		0			0
$751$	7.23690			0.264078			0.132039	−	0.991245i	$-0.457848\pi$
$751$	7.23690			0.264078			0.132039	+	0.991245i	$0.457848\pi$
$752$	57.4351	−	33.1602i	2.09444	−	1.20923i
$753$		0			0
$754$	−78.9389	−	37.5655i	−2.87478	−	1.36805i
$755$	24.7324			0.900105
$756$		0			0
$757$	16.4315	−	28.4602i	0.597214	−	1.03440i	−0.396016	−	0.918243i	$-0.629608\pi$
$757$	16.4315	−	28.4602i	0.597214	−	1.03440i	0.993230	−	0.116161i	$-0.0370590\pi$
$758$	−33.1505	+	57.4184i	−1.20408	+	2.08553i
$759$		0			0
$760$		−	55.6598i		−	2.01899i
$761$	16.2280	+	9.36925i	0.588265	+	0.339635i	0.764411	−	0.644729i	$-0.223030\pi$
$761$	16.2280	+	9.36925i	0.588265	+	0.339635i	−0.176146	+	0.984364i	$0.556363\pi$
$762$		0			0
$763$	−15.0839	−	10.6506i	−0.546072	−	0.385576i
$764$	11.0476	−	19.1350i	0.399687	−	0.692279i
$765$		0			0
$766$	−18.1016	+	31.3529i	−0.654037	+	1.13283i
$767$	−1.24718	−	15.6682i	−0.0450331	−	0.565745i
$768$		0			0
$769$	6.43052	+	3.71266i	0.231890	+	0.133882i	0.611444	−	0.791288i	$-0.290589\pi$
$769$	6.43052	+	3.71266i	0.231890	+	0.133882i	−0.379553	+	0.925170i	$0.623922\pi$
$770$	−96.1529	−	67.8926i	−3.46511	−	2.44668i
$771$		0			0
$772$	8.36700	−	4.83069i	0.301135	−	0.173860i
$773$		−	51.6169i		−	1.85653i	−0.371920	−	0.928265i	$-0.621300\pi$
$773$		−	51.6169i		−	1.85653i	0.371920	−	0.928265i	$-0.378700\pi$
$774$		0			0
$775$	−23.0605	+	13.3140i	−0.828359	+	0.478253i
$776$	−57.0065	−	98.7381i	−2.04641	−	3.54449i
$777$		0			0
$778$	44.5586	+	25.7259i	1.59750	+	0.922318i
$779$	4.11108	+	7.12059i	0.147295	+	0.255122i
$780$		0			0
$781$	19.7217	−	34.1590i	0.705697	−	1.22230i
$782$		−	44.1772i		−	1.57977i
$783$		0			0
$784$	70.3118	+	12.9694i	2.51114	+	0.463193i
$785$			67.3299i			2.40311i
$786$		0			0
$787$			42.6019i			1.51859i	0.650744	+	0.759297i	$0.274457\pi$
$787$			42.6019i			1.51859i	−0.650744	+	0.759297i	$0.725543\pi$
$788$	−26.8075	−	15.4773i	−0.954979	−	0.551357i
$789$		0			0
$790$	−43.0687	+	74.5971i	−1.53231	+	2.65405i
$791$	−9.12836	−	19.7787i	−0.324567	−	0.703251i
$792$		0			0
$793$	22.3417	−	46.9481i	0.793377	−	1.66718i
$794$	−42.9640	+	74.4158i	−1.52473	+	2.64092i
$795$		0			0
$796$	−105.364			−3.73454
$797$	−7.61743	−	13.1938i	−0.269823	−	0.467348i	0.698993	−	0.715129i	$-0.253632\pi$
$797$	−7.61743	−	13.1938i	−0.269823	−	0.467348i	−0.968816	+	0.247781i	$0.920299\pi$
$798$		0			0
$799$	12.1874	−	7.03638i	0.431158	−	0.248929i
$800$	−69.4730	−	40.1103i	−2.45624	−	1.41811i
$801$		0			0
$802$	47.4891			1.67690
$803$	23.3529			0.824106
$804$		0			0
$805$	64.3558	−	29.7018i	2.26824	−	1.04685i
$806$	15.6606	−	32.9086i	0.551620	−	1.15916i
$807$		0			0
$808$	−59.1137	+	34.1293i	−2.07961	+	1.20067i
$809$	11.2114	+	19.4188i	0.394173	+	0.682728i	0.992995	−	0.118154i	$-0.0376978\pi$
$809$	11.2114	+	19.4188i	0.394173	+	0.682728i	−0.598822	+	0.800882i	$0.704364\pi$
$810$		0			0
$811$			49.8853i			1.75171i	0.482574	+	0.875855i	$0.339702\pi$
$811$			49.8853i			1.75171i	−0.482574	+	0.875855i	$0.660298\pi$
$812$	−69.0269	+	97.7594i	−2.42237	+	3.43068i
$813$		0			0
$814$	−5.08878	+	2.93801i	−0.178362	+	0.102977i
$815$	71.3178			2.49815
$816$		0			0
$817$		−	2.68341i		−	0.0938805i
$818$	−55.0194			−1.92371
$819$		0			0
$820$	65.7478			2.29601
$821$		−	42.9908i		−	1.50039i	−0.661218	−	0.750194i	$-0.729960\pi$
$821$		−	42.9908i		−	1.50039i	0.661218	−	0.750194i	$-0.270040\pi$
$822$		0			0
$823$	−25.5674			−0.891225			−0.445613	−	0.895226i	$-0.647014\pi$
$823$	−25.5674			−0.891225			−0.445613	+	0.895226i	$0.647014\pi$
$824$	−84.6830	+	48.8918i	−2.95007	+	1.70323i
$825$		0			0
$826$	−30.1717	−	2.75939i	−1.04981	−	0.0960115i
$827$			11.3034i			0.393058i	0.980498	+	0.196529i	$0.0629670\pi$
$827$			11.3034i			0.393058i	−0.980498	+	0.196529i	$0.937033\pi$
$828$		0			0
$829$	−17.8147	−	30.8560i	−0.618731	−	1.07167i	−0.989718	−	0.143036i	$-0.954314\pi$
$829$	−17.8147	−	30.8560i	−0.618731	−	1.07167i	0.370986	−	0.928638i	$-0.379020\pi$
$830$	−50.0457	+	28.8939i	−1.73711	+	1.00292i
$831$		0			0
$832$	36.0272	−	2.86775i	1.24902	−	0.0994215i
$833$	14.9197	+	2.75203i	0.516938	+	0.0953522i
$834$		0			0
$835$	−4.85420			−0.167986
$836$	−50.8625			−1.75912
$837$		0			0
$838$	−5.18464	−	2.99335i	−0.179100	−	0.103404i
$839$	−11.3481	+	6.55181i	−0.391779	+	0.226194i	−0.682931	−	0.730483i	$-0.739295\pi$
$839$	−11.3481	+	6.55181i	−0.391779	+	0.226194i	0.291152	+	0.956677i	$0.405962\pi$
$840$		0			0
$841$	−28.0972	−	48.6658i	−0.968870	−	1.67813i
$842$	94.1935			3.24612
$843$		0			0
$844$	23.7230	−	41.0895i	0.816580	−	1.41436i
$845$	−34.8303	+	28.3081i	−1.19820	+	0.973829i
$846$		0			0
$847$	−19.9341	+	28.2316i	−0.684943	+	0.970050i
$848$	6.95779	−	12.0512i	0.238931	−	0.413841i
$849$		0			0
$850$	−34.1204	−	19.6994i	−1.17032	−	0.675684i
$851$		−	3.53836i		−	0.121293i
$852$		0			0
$853$			14.7766i			0.505940i	0.967474	+	0.252970i	$0.0814074\pi$
$853$			14.7766i			0.505940i	−0.967474	+	0.252970i	$0.918593\pi$
$854$	−81.8702	−	57.8077i	−2.80154	−	1.97814i
$855$		0			0
$856$			49.9274i			1.70648i
$857$	−13.1008	+	22.6912i	−0.447514	+	0.775118i	−0.998224	−	0.0595795i	$-0.981024\pi$
$857$	−13.1008	+	22.6912i	−0.447514	+	0.775118i	0.550709	+	0.834697i	$0.314357\pi$
$858$		0			0
$859$	−23.0108	−	39.8558i	−0.785117	−	1.35986i	−0.928929	−	0.370258i	$-0.879269\pi$
$859$	−23.0108	−	39.8558i	−0.785117	−	1.35986i	0.143811	−	0.989605i	$-0.454064\pi$
$860$	−18.5829	−	10.7288i	−0.633670	−	0.365850i
$861$		0			0
$862$	3.98293	+	6.89865i	0.135659	+	0.234969i
$863$	18.6631	−	10.7751i	0.635298	−	0.366789i	−0.147503	−	0.989062i	$-0.547124\pi$
$863$	18.6631	−	10.7751i	0.635298	−	0.366789i	0.782801	+	0.622272i	$0.213790\pi$
$864$		0			0
$865$		−	20.8932i		−	0.710389i
$866$	10.8623	−	6.27137i	0.369117	−	0.213110i
$867$		0			0
$868$	−40.7547	−	28.7765i	−1.38330	−	0.976737i
$869$	40.3470	+	23.2943i	1.36868	+	0.790206i
$870$		0			0
$871$	−21.7576	+	14.9822i	−0.737227	+	0.507652i
$872$	−26.5880	+	46.0518i	−0.900384	+	1.55951i
$873$		0			0
$874$	21.5639	−	37.3497i	0.729408	−	1.26337i
$875$	1.59744	−	17.4667i	0.0540035	−	0.590483i
$876$		0			0
$877$	−0.960199	−	0.554371i	−0.0324236	−	0.0187198i	0.483701	−	0.875234i	$-0.339292\pi$
$877$	−0.960199	−	0.554371i	−0.0324236	−	0.0187198i	−0.516124	+	0.856514i	$0.672626\pi$
$878$			60.1073i			2.02852i
$879$		0			0
$880$	−86.4920	+	149.808i	−2.91564	+	5.05004i
$881$	10.8855	−	18.8543i	0.366742	−	0.635216i	−0.622312	−	0.782769i	$-0.713806\pi$
$881$	10.8855	−	18.8543i	0.366742	−	0.635216i	0.989054	+	0.147553i	$0.0471398\pi$
$882$		0			0
$883$	2.96578			0.0998063			0.0499032	−	0.998754i	$-0.484109\pi$
$883$	2.96578			0.0998063			0.0499032	+	0.998754i	$0.484109\pi$
$884$	38.1742	−	3.03865i	1.28394	−	0.102201i
$885$		0			0
$886$	17.9645	−	10.3718i	0.603530	−	0.348448i
$887$	35.2167			1.18246			0.591231	−	0.806502i	$-0.298642\pi$
$887$	35.2167			1.18246			0.591231	+	0.806502i	$0.298642\pi$
$888$		0			0
$889$	11.4054	−	16.1530i	0.382526	−	0.541753i
$890$	−16.9452	+	9.78330i	−0.568004	+	0.327937i
$891$		0			0
$892$	−7.39781	−	4.27113i	−0.247697	−	0.143008i
$893$	13.7384			0.459740
$894$		0			0
$895$	−57.2029	−	33.0261i	−1.91208	−	1.10394i
$896$	0.758201	−	8.29029i	0.0253297	−	0.276959i
$897$		0			0
$898$	−17.3834	−	30.1089i	−0.580090	−	1.00475i
$899$	30.7582	−	17.7583i	1.02584	−	0.592271i
$900$		0			0
$901$	1.47640	−	2.55720i	0.0491860	−	0.0851926i
$902$		−	50.0737i		−	1.66727i
$903$		0			0
$904$	−54.3283	+	31.3665i	−1.80693	+	1.04323i
$905$	19.3209	−	11.1549i	0.642249	−	0.370803i
$906$		0			0
$907$	−0.709165	−	1.22831i	−0.0235474	−	0.0407853i	0.854012	−	0.520254i	$-0.174163\pi$
$907$	−0.709165	−	1.22831i	−0.0235474	−	0.0407853i	−0.877559	+	0.479469i	$0.840829\pi$
$908$			21.1722i			0.702624i
$909$		0			0
$910$	42.3736	+	75.4300i	1.40467	+	2.50048i
$911$	22.3775			0.741400			0.370700	−	0.928753i	$-0.379118\pi$
$911$	22.3775			0.741400			0.370700	+	0.928753i	$0.379118\pi$
$912$		0			0
$913$	15.6277	+	27.0680i	0.517201	+	0.895819i
$914$	66.3362			2.19421
$915$		0			0
$916$	68.7801	−	39.7102i	2.27256	−	1.31206i
$917$	13.0419	+	28.2584i	0.430682	+	0.933174i
$918$		0			0
$919$	12.2763	−	21.2631i	0.404957	−	0.701406i	−0.589359	−	0.807871i	$-0.700620\pi$
$919$	12.2763	−	21.2631i	0.404957	−	0.701406i	0.994316	+	0.106465i	$0.0339531\pi$
$920$	−102.060	−	176.773i	−3.36482	−	5.82803i
$921$		0			0
$922$	40.8775	+	70.8019i	1.34623	+	2.33174i
$923$	−23.8783	+	16.4425i	−0.785963	+	0.541211i
$924$		0			0
$925$	−2.73286	−	1.57782i	−0.0898558	−	0.0518783i
$926$	49.8223			1.63726
$927$		0			0
$928$	92.6632	+	53.4991i	3.04182	+	1.75620i
$929$	21.4886	+	12.4065i	0.705018	+	0.407043i	0.809214	−	0.587514i	$-0.199893\pi$
$929$	21.4886	+	12.4065i	0.705018	+	0.407043i	−0.104195	+	0.994557i	$0.533227\pi$
$930$		0			0
$931$	11.2706	+	9.60935i	0.369378	+	0.314934i
$932$	−31.8035	−	55.0853i	−1.04176	−	1.80438i
$933$		0			0
$934$	31.6798	−	18.2903i	1.03659	−	0.598478i
$935$	−18.3531	+	31.7884i	−0.600209	+	1.03959i
$936$		0			0
$937$	−48.1764			−1.57386			−0.786928	−	0.617045i	$-0.788330\pi$
$937$	−48.1764			−1.57386			−0.786928	+	0.617045i	$0.788330\pi$
$938$	21.3385	+	46.2349i	0.696728	+	1.50962i
$939$		0			0
$940$	54.9292	−	95.1402i	1.79159	−	3.10313i
$941$	−4.49213	−	2.59353i	−0.146439	−	0.0845467i	0.424990	−	0.905198i	$-0.360278\pi$
$941$	−4.49213	−	2.59353i	−0.146439	−	0.0845467i	−0.571429	+	0.820651i	$0.693611\pi$
$942$		0			0
$943$	26.1132	+	15.0764i	0.850362	+	0.490957i
$944$			44.5260i			1.44920i
$945$		0			0
$946$	−8.17110	+	14.1528i	−0.265665	+	0.460146i
$947$		−	34.5590i		−	1.12302i	−0.827471	−	0.561508i	$-0.810221\pi$
$947$		−	34.5590i		−	1.12302i	0.827471	−	0.561508i	$-0.189779\pi$
$948$		0			0
$949$	−15.4994	−	7.37588i	−0.503133	−	0.239431i
$950$	−19.2314	−	33.3098i	−0.623949	−	1.08071i
$951$		0			0
$952$	3.97922	−	43.5094i	0.128967	−	1.41015i
$953$	2.08313	+	3.60809i	0.0674793	+	0.116878i	0.897791	−	0.440422i	$-0.145171\pi$
$953$	2.08313	+	3.60809i	0.0674793	+	0.116878i	−0.830312	+	0.557299i	$0.811838\pi$
$954$		0			0
$955$		−	15.5667i		−	0.503726i
$956$			34.4517i			1.11425i
$957$		0			0
$958$	−19.9593	−	34.5705i	−0.644856	−	1.11692i
$959$	−1.45553	+	15.9150i	−0.0470014	+	0.513921i
$960$		0			0
$961$	−8.09680	−	14.0241i	−0.261187	−	0.452390i
$962$	4.30540	−	0.342708i	0.138812	−	0.0110494i
$963$		0			0
$964$		−	17.8104i		−	0.573633i
$965$	3.40336	−	5.89479i	0.109558	−	0.189760i
$966$		0			0
$967$		−	16.8795i		−	0.542810i	−0.962465	−	0.271405i	$-0.912512\pi$
$967$		−	16.8795i		−	0.542810i	0.962465	−	0.271405i	$-0.0874882\pi$
$968$	86.1926	+	49.7633i	2.77034	+	1.59945i
$969$		0			0
$970$	−117.530	−	67.8563i	−3.77368	−	2.17873i
$971$	−21.7964	+	37.7525i	−0.699479	+	1.21153i	0.269168	+	0.963093i	$0.413251\pi$
$971$	−21.7964	+	37.7525i	−0.699479	+	1.21153i	−0.968647	+	0.248441i	$0.920082\pi$
$972$		0			0
$973$	−0.373333	−	0.808913i	−0.0119685	−	0.0259326i
$974$	−9.54387			−0.305805
$975$		0			0
$976$	−73.6443	+	127.556i	−2.35730	+	4.08296i
$977$	13.3292	−	7.69560i	0.426438	−	0.246204i	−0.271390	−	0.962469i	$-0.587483\pi$
$977$	13.3292	−	7.69560i	0.426438	−	0.246204i	0.697828	+	0.716265i	$0.254150\pi$
$978$		0			0
$979$	5.29144	+	9.16505i	0.169115	+	0.292916i
$980$	111.608	−	39.6297i	3.56518	−	1.26593i
$981$		0			0
$982$	71.1734	+	41.0920i	2.27124	+	1.31130i
$983$	−20.8358	−	12.0295i	−0.664558	−	0.383683i	0.129453	−	0.991585i	$-0.458678\pi$
$983$	−20.8358	−	12.0295i	−0.664558	−	0.383683i	−0.794011	+	0.607903i	$0.792011\pi$
$984$		0			0
$985$	−21.8085			−0.694876
$986$	45.5098	+	26.2751i	1.44933	+	0.836769i
$987$		0			0
$988$	33.7577	+	16.0646i	1.07397	+	0.511083i
$989$	−4.92039	−	8.52237i	−0.156459	−	0.270995i
$990$		0			0
$991$	19.8512	+	34.3834i	0.630595	+	1.09222i	0.987430	+	0.158056i	$0.0505225\pi$
$991$	19.8512	+	34.3834i	0.630595	+	1.09222i	−0.356835	+	0.934167i	$0.616144\pi$
$992$	−22.3031	+	38.6302i	−0.708125	+	1.22651i
$993$		0			0
$994$	23.4184	+	50.7414i	0.742786	+	1.60942i
$995$	−64.2871	+	37.1161i	−2.03804	+	1.17666i
$996$		0			0
$997$	−21.4077			−0.677987			−0.338994	−	0.940789i	$-0.610087\pi$
$997$	−21.4077			−0.677987			−0.338994	+	0.940789i	$0.610087\pi$
$998$	−13.5101	−	23.4002i	−0.427655	−	0.740721i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.h.550.2	yes	36
3.2	odd	2	inner	819.2.bm.h.550.17	yes	36
7.2	even	3		819.2.do.h.667.2	yes	36
13.10	even	6		819.2.do.h.361.2	yes	36
21.2	odd	6		819.2.do.h.667.17	yes	36
39.23	odd	6		819.2.do.h.361.17	yes	36
91.23	even	6	inner	819.2.bm.h.478.17	yes	36
273.23	odd	6	inner	819.2.bm.h.478.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bm.h.478.2	✓	36	273.23	odd	6	inner
819.2.bm.h.478.17	yes	36	91.23	even	6	inner
819.2.bm.h.550.2	yes	36	1.1	even	1	trivial
819.2.bm.h.550.17	yes	36	3.2	odd	2	inner
819.2.do.h.361.2	yes	36	13.10	even	6
819.2.do.h.361.17	yes	36	39.23	odd	6
819.2.do.h.667.2	yes	36	7.2	even	3
819.2.do.h.667.17	yes	36	21.2	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.62688i q^{2} -4.90051 q^{4} +(-2.99000 + 1.72628i) q^{5} +(-2.63476 - 0.240965i) q^{7} +7.61930i q^{8} +O(q^{10})\)	\(q-2.62688i q^{2} -4.90051 q^{4} +(-2.99000 + 1.72628i) q^{5} +(-2.63476 - 0.240965i) q^{7} +7.61930i q^{8} +(4.53473 + 7.85438i) q^{10} +(4.24816 - 2.45267i) q^{11} +(-3.59418 + 0.286096i) q^{13} +(-0.632988 + 6.92119i) q^{14} +10.2140 q^{16} +2.16734 q^{17} +(1.83239 + 1.05793i) q^{19} +(14.6525 - 8.45964i) q^{20} +(-6.44289 - 11.1594i) q^{22} +7.75943 q^{23} +(3.46006 - 5.99301i) q^{25} +(0.751541 + 9.44150i) q^{26} +(12.9116 + 1.18085i) q^{28} +(-4.61504 + 7.99349i) q^{29} +(-3.33239 - 1.92395i) q^{31} -11.5923i q^{32} -5.69336i q^{34} +(8.29389 - 3.82783i) q^{35} -0.456008i q^{37} +(2.77905 - 4.81346i) q^{38} +(-13.1530 - 22.7817i) q^{40} +(3.36535 + 1.94298i) q^{41} +(-0.634118 - 1.09832i) q^{43} +(-20.8181 + 12.0194i) q^{44} -20.3831i q^{46} +(5.62318 - 3.24654i) q^{47} +(6.88387 + 1.26977i) q^{49} +(-15.7429 - 9.08918i) q^{50} +(17.6133 - 1.40202i) q^{52} +(0.681202 - 1.17988i) q^{53} +(-8.46799 + 14.6670i) q^{55} +(1.83599 - 20.0750i) q^{56} +(20.9979 + 12.1232i) q^{58} +4.35931i q^{59} +(-7.21014 + 12.4883i) q^{61} +(-5.05400 + 8.75379i) q^{62} -10.0237 q^{64} +(10.2527 - 7.05998i) q^{65} +(6.34516 - 3.66338i) q^{67} -10.6211 q^{68} +(-10.0553 - 21.7871i) q^{70} +(6.96362 - 4.02045i) q^{71} +(4.12289 + 2.38035i) q^{73} -1.19788 q^{74} +(-8.97963 - 5.18439i) q^{76} +(-11.7839 + 5.43854i) q^{77} +(4.74876 + 8.22509i) q^{79} +(-30.5398 + 17.6322i) q^{80} +(5.10399 - 8.84037i) q^{82} +6.37170i q^{83} +(-6.48036 + 3.74144i) q^{85} +(-2.88517 + 1.66575i) q^{86} +(18.6877 + 32.3680i) q^{88} +2.15742i q^{89} +(9.53873 + 0.112281i) q^{91} -38.0252 q^{92} +(-8.52829 - 14.7714i) q^{94} -7.30511 q^{95} +(-12.9589 + 7.48185i) q^{97} +(3.33554 - 18.0831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) \) 36 * q - 44 * q^4 + 8 * q^7	\( 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) \) 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

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