LMFDB - Embedded newform 1998.2.t.a.397.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1998,2,Mod(307,1998)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1998.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1998, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1998 = 2 \cdot 3^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1998.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$15.9541103239$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 666)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			397.37
Character	$\chi$	$=$	1998.397
Dual form			1998.2.t.a.307.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.98479 + 1.72327i) q^{5} -0.480194 q^{7} -1.00000i q^{8} +3.44654 q^{10} +(-1.57883 + 2.73461i) q^{11} +(1.16995 + 0.675468i) q^{13} +(-0.415860 + 0.240097i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.944880 - 0.545527i) q^{17} +(0.333391 - 0.192483i) q^{19} +(2.98479 - 1.72327i) q^{20} +3.15766i q^{22} +(6.91907 - 3.99473i) q^{23} +(3.43932 + 5.95707i) q^{25} +1.35094 q^{26} +(-0.240097 + 0.415860i) q^{28} +(5.40267 + 3.11923i) q^{29} +(-3.60235 + 2.07982i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.09105 q^{34} +(-1.43328 - 0.827504i) q^{35} +(5.65702 + 2.23564i) q^{37} +(0.192483 - 0.333391i) q^{38} +(1.72327 - 2.98479i) q^{40} +(-1.65030 + 2.85840i) q^{41} +(7.47606 + 4.31631i) q^{43} +(1.57883 + 2.73461i) q^{44} +(3.99473 - 6.91907i) q^{46} +(5.93648 - 10.2823i) q^{47} -6.76941 q^{49} +(5.95707 + 3.43932i) q^{50} +(1.16995 - 0.675468i) q^{52} +(-1.47126 + 2.54830i) q^{53} +(-9.42495 + 5.44150i) q^{55} +0.480194i q^{56} +6.23847 q^{58} +0.340484i q^{59} +14.2169i q^{61} +(-2.07982 + 3.60235i) q^{62} -1.00000 q^{64} +(2.32803 + 4.03226i) q^{65} +(4.44667 - 7.70185i) q^{67} +(-0.944880 + 0.545527i) q^{68} -1.65501 q^{70} +(-1.04493 - 1.80988i) q^{71} -7.32053 q^{73} +(6.01695 - 0.892387i) q^{74} -0.384966i q^{76} +(0.758145 - 1.31315i) q^{77} +16.2973i q^{79} -3.44654i q^{80} +3.30060i q^{82} +(-5.37919 - 9.31702i) q^{83} +(-1.88018 - 3.25657i) q^{85} +8.63261 q^{86} +(2.73461 + 1.57883i) q^{88} +(-2.15753 - 1.24565i) q^{89} +(-0.561801 - 0.324356i) q^{91} -7.98946i q^{92} -11.8730i q^{94} +1.32680 q^{95} +(-10.9363 - 6.31410i) q^{97} +(-5.86248 + 3.38471i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) $ 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1998\mathbb{Z}\right)^\times$.

$n$	$1297$	$1703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.98479	+	1.72327i	1.33484	+	0.770670i	0.986037	−	0.166527i	$-0.0532553\pi$
$5$	2.98479	+	1.72327i	1.33484	+	0.770670i	0.348802	+	0.937196i	$0.386589\pi$
$6$		0			0
$7$	−0.480194			−0.181496			−0.0907482	−	0.995874i	$-0.528926\pi$
$7$	−0.480194			−0.181496			−0.0907482	+	0.995874i	$0.528926\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	3.44654			1.08989
$11$	−1.57883	+	2.73461i	−0.476035	+	0.824517i	−0.999623	−	0.0274546i	$-0.991260\pi$
$11$	−1.57883	+	2.73461i	−0.476035	+	0.824517i	0.523588	+	0.851972i	$0.324593\pi$
$12$		0			0
$13$	1.16995	+	0.675468i	0.324484	+	0.187341i	0.653390	−	0.757022i	$-0.273346\pi$
$13$	1.16995	+	0.675468i	0.324484	+	0.187341i	−0.328905	+	0.944363i	$0.606680\pi$
$14$	−0.415860	+	0.240097i	−0.111143	+	0.0641687i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.944880	−	0.545527i	−0.229167	−	0.132310i	0.381021	−	0.924567i	$-0.375573\pi$
$17$	−0.944880	−	0.545527i	−0.229167	−	0.132310i	−0.610188	+	0.792257i	$0.708906\pi$
$18$		0			0
$19$	0.333391	−	0.192483i	0.0764851	−	0.0441587i	−0.461270	−	0.887260i	$-0.652606\pi$
$19$	0.333391	−	0.192483i	0.0764851	−	0.0441587i	0.537755	+	0.843101i	$0.319273\pi$
$20$	2.98479	−	1.72327i	0.667419	−	0.385335i
$21$		0			0
$22$			3.15766i			0.673215i
$23$	6.91907	−	3.99473i	1.44273	−	0.832958i	0.444695	−	0.895682i	$-0.353312\pi$
$23$	6.91907	−	3.99473i	1.44273	−	0.832958i	0.998031	+	0.0627234i	$0.0199786\pi$
$24$		0			0
$25$	3.43932	+	5.95707i	0.687863	+	1.19141i
$26$	1.35094			0.264940
$27$		0			0
$28$	−0.240097	+	0.415860i	−0.0453741	+	0.0785902i
$29$	5.40267	+	3.11923i	1.00325	+	0.579227i	0.909209	−	0.416341i	$-0.136688\pi$
$29$	5.40267	+	3.11923i	1.00325	+	0.579227i	0.0940423	+	0.995568i	$0.470021\pi$
$30$		0			0
$31$	−3.60235	+	2.07982i	−0.647001	+	0.373546i	−0.787306	−	0.616562i	$-0.788525\pi$
$31$	−3.60235	+	2.07982i	−0.647001	+	0.373546i	0.140305	+	0.990108i	$0.455192\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−1.09105			−0.187114
$35$	−1.43328	−	0.827504i	−0.242268	−	0.139874i
$36$		0			0
$37$	5.65702	+	2.23564i	0.930009	+	0.367538i
$37$	5.65702	+	2.23564i	0.930009	+	0.367538i
$38$	0.192483	−	0.333391i	0.0312249	−	0.0540831i
$39$		0			0
$40$	1.72327	−	2.98479i	0.272473	−	0.471937i
$41$	−1.65030	+	2.85840i	−0.257733	+	0.446407i	−0.965634	−	0.259905i	$-0.916309\pi$
$41$	−1.65030	+	2.85840i	−0.257733	+	0.446407i	0.707901	+	0.706312i	$0.249642\pi$
$42$		0			0
$43$	7.47606	+	4.31631i	1.14009	+	0.658231i	0.946453	−	0.322843i	$-0.104638\pi$
$43$	7.47606	+	4.31631i	1.14009	+	0.658231i	0.193636	+	0.981073i	$0.437972\pi$
$44$	1.57883	+	2.73461i	0.238018	+	0.412259i
$45$		0			0
$46$	3.99473	−	6.91907i	0.588991	−	1.02016i
$47$	5.93648	−	10.2823i	0.865925	−	1.49983i	−0.000200737	−	1.00000i	$-0.500064\pi$
$47$	5.93648	−	10.2823i	0.865925	−	1.49983i	0.866126	−	0.499826i	$-0.166603\pi$
$48$		0			0
$49$	−6.76941			−0.967059
$50$	5.95707	+	3.43932i	0.842457	+	0.486393i
$51$		0			0
$52$	1.16995	−	0.675468i	0.162242	−	0.0936706i
$53$	−1.47126	+	2.54830i	−0.202094	+	0.350037i	−0.949203	−	0.314665i	$-0.898108\pi$
$53$	−1.47126	+	2.54830i	−0.202094	+	0.350037i	0.747109	+	0.664701i	$0.231441\pi$
$54$		0			0
$55$	−9.42495	+	5.44150i	−1.27086	+	0.733732i
$56$			0.480194i			0.0641687i
$57$		0			0
$58$	6.23847			0.819151
$59$			0.340484i			0.0443273i	0.999754	+	0.0221636i	$0.00705548\pi$
$59$			0.340484i			0.0443273i	−0.999754	+	0.0221636i	$0.992945\pi$
$60$		0			0
$61$			14.2169i			1.82029i	0.414286	+	0.910147i	$0.364031\pi$
$61$			14.2169i			1.82029i	−0.414286	+	0.910147i	$0.635969\pi$
$62$	−2.07982	+	3.60235i	−0.264137	+	0.457499i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.32803	+	4.03226i	0.288756	+	0.500140i
$66$		0			0
$67$	4.44667	−	7.70185i	0.543247	−	0.940931i	−0.455468	−	0.890252i	$-0.650528\pi$
$67$	4.44667	−	7.70185i	0.543247	−	0.940931i	0.998715	−	0.0506791i	$-0.0161386\pi$
$68$	−0.944880	+	0.545527i	−0.114584	+	0.0661549i
$69$		0			0
$70$	−1.65501			−0.197811
$71$	−1.04493	−	1.80988i	−0.124011	−	0.214793i	0.797335	−	0.603537i	$-0.206242\pi$
$71$	−1.04493	−	1.80988i	−0.124011	−	0.214793i	−0.921346	+	0.388744i	$0.872909\pi$
$72$		0			0
$73$	−7.32053			−0.856803			−0.428402	−	0.903588i	$-0.640923\pi$
$73$	−7.32053			−0.856803			−0.428402	+	0.903588i	$0.640923\pi$
$74$	6.01695	−	0.892387i	0.699456	−	0.103738i
$75$		0			0
$76$		−	0.384966i		−	0.0441587i
$77$	0.758145	−	1.31315i	0.0863987	−	0.149647i
$78$		0			0
$79$			16.2973i			1.83359i	0.399361	+	0.916794i	$0.369232\pi$
$79$			16.2973i			1.83359i	−0.399361	+	0.916794i	$0.630768\pi$
$80$		−	3.44654i		−	0.385335i
$81$		0			0
$82$			3.30060i			0.364490i
$83$	−5.37919	−	9.31702i	−0.590442	−	1.02268i	−0.994173	−	0.107798i	$-0.965620\pi$
$83$	−5.37919	−	9.31702i	−0.590442	−	1.02268i	0.403730	−	0.914878i	$-0.367713\pi$
$84$		0			0
$85$	−1.88018	−	3.25657i	−0.203934	−	0.353224i
$86$	8.63261			0.930879
$87$		0			0
$88$	2.73461	+	1.57883i	0.291511	+	0.168304i
$89$	−2.15753	−	1.24565i	−0.228697	−	0.132038i	0.381274	−	0.924462i	$-0.375486\pi$
$89$	−2.15753	−	1.24565i	−0.228697	−	0.132038i	−0.609971	+	0.792424i	$0.708819\pi$
$90$		0			0
$91$	−0.561801	−	0.324356i	−0.0588927	−	0.0340017i
$92$		−	7.98946i		−	0.832958i
$93$		0			0
$94$		−	11.8730i		−	1.22460i
$95$	1.32680			0.136127
$96$		0			0
$97$	−10.9363	−	6.31410i	−1.11042	−	0.641100i	−0.171480	−	0.985188i	$-0.554855\pi$
$97$	−10.9363	−	6.31410i	−1.11042	−	0.641100i	−0.938938	+	0.344088i	$0.888188\pi$
$98$	−5.86248	+	3.38471i	−0.592200	+	0.341907i
$99$		0			0
$100$	6.87863			0.687863
$101$	−0.492396	+	0.852854i	−0.0489952	+	0.0848622i	−0.889483	−	0.456968i	$-0.848935\pi$
$101$	−0.492396	+	0.852854i	−0.0489952	+	0.0848622i	0.840488	+	0.541831i	$0.182269\pi$
$102$		0			0
$103$	−1.04404	+	0.602776i	−0.102872	+	0.0593933i	−0.550553	−	0.834800i	$-0.685583\pi$
$103$	−1.04404	+	0.602776i	−0.102872	+	0.0593933i	0.447681	+	0.894193i	$0.352250\pi$
$104$	0.675468	−	1.16995i	0.0662351	−	0.114723i
$105$		0			0
$106$			2.94253i			0.285804i
$107$	−7.88782	−	13.6621i	−0.762544	−	1.32077i	−0.941535	−	0.336915i	$-0.890617\pi$
$107$	−7.88782	−	13.6621i	−0.762544	−	1.32077i	0.178991	−	0.983851i	$-0.442717\pi$
$108$		0			0
$109$	4.39231	+	2.53590i	0.420707	+	0.242895i	0.695380	−	0.718643i	$-0.255236\pi$
$109$	4.39231	+	2.53590i	0.420707	+	0.242895i	−0.274673	+	0.961538i	$0.588570\pi$
$110$	−5.44150	+	9.42495i	−0.518827	+	0.898634i
$111$		0			0
$112$	0.240097	+	0.415860i	0.0226870	+	0.0392951i
$113$		−	0.595128i		−	0.0559850i	−0.999608	−	0.0279925i	$-0.991089\pi$
$113$		−	0.595128i		−	0.0559850i	0.999608	−	0.0279925i	$-0.00891145\pi$
$114$		0			0
$115$	27.5360			2.56774
$116$	5.40267	−	3.11923i	0.501625	−	0.289614i
$117$		0			0
$118$	0.170242	+	0.294868i	0.0156721	+	0.0271448i
$119$	0.453726	+	0.261959i	0.0415930	+	0.0240137i
$120$		0			0
$121$	0.514592	+	0.891300i	0.0467811	+	0.0810272i
$122$	7.10847	+	12.3122i	0.643571	+	1.11470i
$123$		0			0
$124$			4.15963i			0.373546i
$125$			6.47477i			0.579121i
$126$		0			0
$127$	3.39075	−	5.87296i	0.300881	−	0.521141i	−0.675455	−	0.737401i	$-0.736053\pi$
$127$	3.39075	−	5.87296i	0.300881	−	0.521141i	0.976336	+	0.216261i	$0.0693861\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	4.03226	+	2.32803i	0.353653	+	0.204181i
$131$		−	8.07078i		−	0.705148i	−0.935784	−	0.352574i	$-0.885307\pi$
$131$		−	8.07078i		−	0.705148i	0.935784	−	0.352574i	$-0.114693\pi$
$132$		0			0
$133$	−0.160092	+	0.0924293i	−0.0138818	+	0.00801464i
$134$		−	8.89333i		−	0.768267i
$135$		0			0
$136$	−0.545527	+	0.944880i	−0.0467785	+	0.0810228i
$137$	−0.0848084	+	0.146893i	−0.00724567	+	0.0125499i	−0.869626	−	0.493712i	$-0.835640\pi$
$137$	−0.0848084	+	0.146893i	−0.00724567	+	0.0125499i	0.862380	+	0.506262i	$0.168973\pi$
$138$		0			0
$139$	8.65398			0.734021			0.367011	−	0.930217i	$-0.380381\pi$
$139$	8.65398			0.734021			0.367011	+	0.930217i	$0.380381\pi$
$140$	−1.43328	+	0.827504i	−0.121134	+	0.0699369i
$141$		0			0
$142$	−1.80988	−	1.04493i	−0.151881	−	0.0876888i
$143$	−3.69429	+	2.13290i	−0.308932	+	0.178362i
$144$		0			0
$145$	10.7506	+	18.6205i	0.892785	+	1.54635i
$146$	−6.33976	+	3.66026i	−0.524683	+	0.302926i
$147$		0			0
$148$	4.76464	−	3.78130i	0.391651	−	0.310821i
$149$	2.53720	+	4.39456i	0.207855	+	0.360016i	0.951039	−	0.309072i	$-0.100018\pi$
$149$	2.53720	+	4.39456i	0.207855	+	0.360016i	−0.743183	+	0.669088i	$0.766685\pi$
$150$		0			0
$151$	4.93152			0.401321			0.200661	−	0.979661i	$-0.435691\pi$
$151$	4.93152			0.401321			0.200661	+	0.979661i	$0.435691\pi$
$152$	−0.192483	−	0.333391i	−0.0156125	−	0.0270416i
$153$		0			0
$154$		−	1.51629i		−	0.122186i
$155$	−14.3363			−1.15152
$156$		0			0
$157$	7.07318			0.564501			0.282251	−	0.959341i	$-0.408919\pi$
$157$	7.07318			0.564501			0.282251	+	0.959341i	$0.408919\pi$
$158$	8.14864	+	14.1139i	0.648271	+	1.12284i
$159$		0			0
$160$	−1.72327	−	2.98479i	−0.136236	−	0.235968i
$161$	−3.32250	+	1.91825i	−0.261850	+	0.151179i
$162$		0			0
$163$	−16.5023	−	9.52761i	−1.29256	−	0.746260i	−0.313452	−	0.949604i	$-0.601486\pi$
$163$	−16.5023	−	9.52761i	−1.29256	−	0.746260i	−0.979107	+	0.203344i	$0.934819\pi$
$164$	1.65030	+	2.85840i	0.128867	+	0.223204i
$165$		0			0
$166$	−9.31702	−	5.37919i	−0.723141	−	0.417506i
$167$	−8.96444	−	5.17562i	−0.693689	−	0.400501i	0.111304	−	0.993786i	$-0.464497\pi$
$167$	−8.96444	−	5.17562i	−0.693689	−	0.400501i	−0.804993	+	0.593285i	$0.797831\pi$
$168$		0			0
$169$	−5.58749	−	9.67781i	−0.429807	−	0.744447i
$170$	−3.25657	−	1.88018i	−0.249767	−	0.144203i
$171$		0			0
$172$	7.47606	−	4.31631i	0.570044	−	0.329115i
$173$	−1.93394	−	3.34967i	−0.147034	−	0.254671i	0.783096	−	0.621901i	$-0.213639\pi$
$173$	−1.93394	−	3.34967i	−0.147034	−	0.254671i	−0.930130	+	0.367230i	$0.880306\pi$
$174$		0			0
$175$	−1.65154	−	2.86055i	−0.124845	−	0.216237i
$176$	3.15766			0.238018
$177$		0			0
$178$	−2.49130			−0.186731
$179$			2.26842i			0.169550i	0.996400	+	0.0847748i	$0.0270171\pi$
$179$			2.26842i			0.169550i	−0.996400	+	0.0847748i	$0.972983\pi$
$180$		0			0
$181$	−1.66515	−	2.88412i	−0.123769	−	0.214375i	0.797482	−	0.603343i	$-0.206165\pi$
$181$	−1.66515	−	2.88412i	−0.123769	−	0.214375i	−0.921251	+	0.388968i	$0.872832\pi$
$182$	−0.648712			−0.0480857
$183$		0			0
$184$	−3.99473	−	6.91907i	−0.294495	−	0.510081i
$185$	13.0324	+	16.4215i	0.958162	+	1.20733i
$186$		0			0
$187$	2.98361	−	1.72259i	0.218183	−	0.125968i
$188$	−5.93648	−	10.2823i	−0.432963	−	0.749913i
$189$		0			0
$190$	1.14904	−	0.663401i	0.0833604	−	0.0481282i
$191$	4.54498	+	2.62405i	0.328863	+	0.189869i	0.655336	−	0.755337i	$-0.272527\pi$
$191$	4.54498	+	2.62405i	0.328863	+	0.189869i	−0.326473	+	0.945207i	$0.605860\pi$
$192$		0			0
$193$	−5.51469	+	3.18391i	−0.396956	+	0.229183i	−0.685170	−	0.728384i	$-0.740272\pi$
$193$	−5.51469	+	3.18391i	−0.396956	+	0.229183i	0.288214	+	0.957566i	$0.406939\pi$
$194$	−12.6282			−0.906652
$195$		0			0
$196$	−3.38471	+	5.86248i	−0.241765	+	0.418749i
$197$	3.14271	−	5.44333i	0.223909	−	0.387821i	−0.732083	−	0.681216i	$-0.761452\pi$
$197$	3.14271	−	5.44333i	0.223909	−	0.387821i	0.955991	+	0.293394i	$0.0947849\pi$
$198$		0			0
$199$		−	13.2707i		−	0.940735i	−0.882471	−	0.470368i	$-0.844121\pi$
$199$		−	13.2707i		−	0.940735i	0.882471	−	0.470368i	$-0.155879\pi$
$200$	5.95707	−	3.43932i	0.421228	−	0.243196i
$201$		0			0
$202$			0.984791i			0.0692897i
$203$	−2.59433	−	1.49784i	−0.182086	−	0.105128i
$204$		0			0
$205$	−9.85159	+	5.68782i	−0.688065	+	0.397254i
$206$	−0.602776	+	1.04404i	−0.0419974	+	0.0727417i
$207$		0			0
$208$		−	1.35094i		−	0.0936706i
$209$			1.21559i			0.0840843i
$210$		0			0
$211$	−8.29561	−	14.3684i	−0.571093	−	0.989163i	−0.996454	−	0.0841389i	$-0.973186\pi$
$211$	−8.29561	−	14.3684i	−0.571093	−	0.989163i	0.425361	−	0.905024i	$-0.360147\pi$
$212$	1.47126	+	2.54830i	0.101047	+	0.175018i
$213$		0			0
$214$	−13.6621	−	7.88782i	−0.933922	−	0.539200i
$215$	14.8763	+	25.7665i	1.01456	+	1.75726i
$216$		0			0
$217$	1.72983	−	0.998716i	0.117428	−	0.0677973i
$218$	5.07180			0.343506
$219$		0			0
$220$			10.8830i			0.733732i
$221$	−0.736972	−	1.27647i	−0.0495741	−	0.0858649i
$222$		0			0
$223$	−9.16344	+	15.8715i	−0.613629	+	1.06284i	0.376994	+	0.926216i	$0.376958\pi$
$223$	−9.16344	+	15.8715i	−0.613629	+	1.06284i	−0.990623	+	0.136621i	$0.956376\pi$
$224$	0.415860	+	0.240097i	0.0277858	+	0.0160422i
$225$		0			0
$226$	−0.297564	−	0.515396i	−0.0197937	−	0.0342837i
$227$		−	1.86789i		−	0.123977i	−0.998077	−	0.0619883i	$-0.980256\pi$
$227$		−	1.86789i		−	0.123977i	0.998077	−	0.0619883i	$-0.0197441\pi$
$228$		0			0
$229$	−3.40970	+	5.90577i	−0.225319	+	0.390264i	−0.956415	−	0.292011i	$-0.905676\pi$
$229$	−3.40970	+	5.90577i	−0.225319	+	0.390264i	0.731096	+	0.682275i	$0.239009\pi$
$230$	23.8469	−	13.7680i	1.57241	−	0.907834i
$231$		0			0
$232$	3.11923	−	5.40267i	0.204788	−	0.354703i
$233$	28.3171			1.85512			0.927559	−	0.373678i	$-0.121903\pi$
$233$	28.3171			1.85512			0.927559	+	0.373678i	$0.121903\pi$
$234$		0			0
$235$	35.4383	−	20.4603i	2.31174	−	1.33468i
$236$	0.294868	+	0.170242i	0.0191943	+	0.0110818i
$237$		0			0
$238$	0.523918			0.0339605
$239$		−	19.4823i		−	1.26021i	−0.776511	−	0.630104i	$-0.783012\pi$
$239$		−	19.4823i		−	1.26021i	0.776511	−	0.630104i	$-0.216988\pi$
$240$		0			0
$241$		−	23.8689i		−	1.53753i	−0.639530	−	0.768766i	$-0.720871\pi$
$241$		−	23.8689i		−	1.53753i	0.639530	−	0.768766i	$-0.279129\pi$
$242$	0.891300	+	0.514592i	0.0572949	+	0.0330792i
$243$		0			0
$244$	12.3122	+	7.10847i	0.788210	+	0.455073i
$245$	−20.2053	−	11.6655i	−1.29087	−	0.745283i
$246$		0			0
$247$	0.520065			0.0330909
$248$	2.07982	+	3.60235i	0.132069	+	0.228749i
$249$		0			0
$250$	3.23739	+	5.60732i	0.204750	+	0.354638i
$251$		−	15.8983i		−	1.00349i	−0.865016	−	0.501745i	$-0.832692\pi$
$251$		−	15.8983i		−	1.00349i	0.865016	−	0.501745i	$-0.167308\pi$
$252$		0			0
$253$			25.2280i			1.58607i
$254$		−	6.78151i		−	0.425510i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	16.9104i		−	1.05484i	−0.849604	−	0.527421i	$-0.823159\pi$
$257$		−	16.9104i		−	1.05484i	0.849604	−	0.527421i	$-0.176841\pi$
$258$		0			0
$259$	−2.71647	−	1.07354i	−0.168793	−	0.0667067i
$260$	4.65605			0.288756
$261$		0			0
$262$	−4.03539	−	6.98950i	−0.249307	−	0.431813i
$263$	−22.9136			−1.41291			−0.706455	−	0.707757i	$-0.749707\pi$
$263$	−22.9136			−1.41291			−0.706455	+	0.707757i	$0.749707\pi$
$264$		0			0
$265$	−8.78283	+	5.07077i	−0.539525	+	0.311495i
$266$	−0.0924293	+	0.160092i	−0.00566721	+	0.00981589i
$267$		0			0
$268$	−4.44667	−	7.70185i	−0.271623	−	0.470466i
$269$	18.9536			1.15562			0.577812	−	0.816170i	$-0.303907\pi$
$269$	18.9536			1.15562			0.577812	+	0.816170i	$0.303907\pi$
$270$		0			0
$271$	2.10857	−	3.65215i	0.128086	−	0.221852i	−0.794849	−	0.606808i	$-0.792450\pi$
$271$	2.10857	−	3.65215i	0.128086	−	0.221852i	0.922935	+	0.384955i	$0.125783\pi$
$272$			1.09105i			0.0661549i
$273$		0			0
$274$			0.169617i			0.0102469i
$275$	−21.7204			−1.30979
$276$		0			0
$277$			30.8890i			1.85594i	0.372654	+	0.927971i	$0.378448\pi$
$277$			30.8890i			1.85594i	−0.372654	+	0.927971i	$0.621552\pi$
$278$	7.49457	−	4.32699i	0.449494	−	0.259516i
$279$		0			0
$280$	−0.827504	+	1.43328i	−0.0494528	+	0.0856548i
$281$	−28.0267	+	16.1812i	−1.67193	+	0.965290i	−0.705375	+	0.708834i	$0.749222\pi$
$281$	−28.0267	+	16.1812i	−1.67193	+	0.965290i	−0.966556	+	0.256456i	$0.917445\pi$
$282$		0			0
$283$	−14.1673	−	8.17949i	−0.842158	−	0.486220i	0.0158393	−	0.999875i	$-0.494958\pi$
$283$	−14.1673	−	8.17949i	−0.842158	−	0.486220i	−0.857997	+	0.513655i	$0.828291\pi$
$284$	−2.08986			−0.124011
$285$		0			0
$286$	−2.13290	+	3.69429i	−0.126121	+	0.218448i
$287$	0.792464	−	1.37259i	0.0467776	−	0.0810213i
$288$		0			0
$289$	−7.90480	−	13.6915i	−0.464988	−	0.805383i
$290$	18.6205	+	10.7506i	1.09343	+	0.631295i
$291$		0			0
$292$	−3.66026	+	6.33976i	−0.214201	+	0.371007i
$293$	8.99539	−	15.5805i	0.525516	−	0.910221i	−0.474042	−	0.880502i	$-0.657206\pi$
$293$	8.99539	−	15.5805i	0.525516	−	0.910221i	0.999558	−	0.0297185i	$-0.00946110\pi$
$294$		0			0
$295$	−0.586746	+	1.01627i	−0.0341617	+	0.0591698i
$296$	2.23564	−	5.65702i	0.129944	−	0.328808i
$297$		0			0
$298$	4.39456	+	2.53720i	0.254570	+	0.146976i
$299$	10.7932			0.624190
$300$		0			0
$301$	−3.58996	−	2.07267i	−0.206922	−	0.119466i
$302$	4.27082	−	2.46576i	0.245758	−	0.141889i
$303$		0			0
$304$	−0.333391	−	0.192483i	−0.0191213	−	0.0110397i
$305$	−24.4996	+	42.4346i	−1.40285	+	2.42980i
$306$		0			0
$307$	−8.71513			−0.497399			−0.248699	−	0.968581i	$-0.580003\pi$
$307$	−8.71513			−0.497399			−0.248699	+	0.968581i	$0.580003\pi$
$308$	−0.758145	−	1.31315i	−0.0431993	−	0.0748234i
$309$		0			0
$310$	−12.4156	+	7.16817i	−0.705161	+	0.407125i
$311$		−	24.5989i		−	1.39487i	−0.716646	−	0.697437i	$-0.754324\pi$
$311$		−	24.5989i		−	1.39487i	0.716646	−	0.697437i	$-0.245676\pi$
$312$		0			0
$313$	−8.97718	+	5.18298i	−0.507420	+	0.292959i	−0.731773	−	0.681549i	$-0.761307\pi$
$313$	−8.97718	+	5.18298i	−0.507420	+	0.292959i	0.224352	+	0.974508i	$0.427973\pi$
$314$	6.12555	−	3.53659i	0.345685	−	0.199581i
$315$		0			0
$316$	14.1139	+	8.14864i	0.793967	+	0.458397i
$317$	14.9365	+	25.8708i	0.838918	+	1.45305i	0.890800	+	0.454396i	$0.150145\pi$
$317$	14.9365	+	25.8708i	0.838918	+	1.45305i	−0.0518816	+	0.998653i	$0.516522\pi$
$318$		0			0
$319$	−17.0598	+	9.84948i	−0.955165	+	0.551465i
$320$	−2.98479	−	1.72327i	−0.166855	−	0.0963337i
$321$		0			0
$322$	−1.91825	+	3.32250i	−0.106900	+	0.185156i
$323$	−0.420019			−0.0233705
$324$		0			0
$325$			9.29259i			0.515460i
$326$	−19.0552			−1.05537
$327$		0			0
$328$	2.85840	+	1.65030i	0.157829	+	0.0911224i
$329$	−2.85067	+	4.93750i	−0.157162	+	0.272213i
$330$		0			0
$331$	−20.3700	+	11.7606i	−1.11964	+	0.646423i	−0.941308	−	0.337548i	$-0.890403\pi$
$331$	−20.3700	+	11.7606i	−1.11964	+	0.646423i	−0.178329	+	0.983971i	$0.557069\pi$
$332$	−10.7584			−0.590442
$333$		0			0
$334$	−10.3512			−0.566395
$335$	26.5447	−	15.3256i	1.45029	−	0.837328i
$336$		0			0
$337$	2.11229	−	3.65859i	0.115064	−	0.199296i	−0.802741	−	0.596327i	$-0.796626\pi$
$337$	2.11229	−	3.65859i	0.115064	−	0.199296i	0.917805	+	0.397031i	$0.129959\pi$
$338$	−9.67781	−	5.58749i	−0.526403	−	0.303919i
$339$		0			0
$340$	−3.76036			−0.203934
$341$		−	13.1347i		−	0.711285i
$342$		0			0
$343$	6.61199			0.357014
$344$	4.31631	−	7.47606i	0.232720	−	0.403082i
$345$		0			0
$346$	−3.34967	−	1.93394i	−0.180080	−	0.103969i
$347$	−22.1211	+	12.7716i	−1.18752	+	0.685616i	−0.957743	−	0.287627i	$-0.907134\pi$
$347$	−22.1211	+	12.7716i	−1.18752	+	0.685616i	−0.229779	+	0.973243i	$0.573800\pi$
$348$		0			0
$349$	−12.8280	−	22.2188i	−0.686667	−	1.18934i	−0.972910	−	0.231185i	$-0.925740\pi$
$349$	−12.8280	−	22.2188i	−0.686667	−	1.18934i	0.286243	−	0.958157i	$-0.407594\pi$
$350$	−2.86055	−	1.65154i	−0.152903	−	0.0882785i
$351$		0			0
$352$	2.73461	−	1.57883i	0.145755	−	0.0841519i
$353$	15.7201	−	9.07598i	0.836695	−	0.483066i	−0.0194447	−	0.999811i	$-0.506190\pi$
$353$	15.7201	−	9.07598i	0.836695	−	0.483066i	0.856139	+	0.516745i	$0.172857\pi$
$354$		0			0
$355$		−	7.20280i		−	0.382285i
$356$	−2.15753	+	1.24565i	−0.114349	+	0.0660192i
$357$		0			0
$358$	1.13421	+	1.96451i	0.0599449	+	0.103828i
$359$	−3.62838			−0.191499			−0.0957493	−	0.995405i	$-0.530525\pi$
$359$	−3.62838			−0.191499			−0.0957493	+	0.995405i	$0.530525\pi$
$360$		0			0
$361$	−9.42590	+	16.3261i	−0.496100	+	0.859270i
$362$	−2.88412	−	1.66515i	−0.151586	−	0.0875182i
$363$		0			0
$364$	−0.561801	+	0.324356i	−0.0294464	+	0.0170009i
$365$	−21.8502	−	12.6152i	−1.14369	−	0.660312i
$366$		0			0
$367$	−22.6758			−1.18367			−0.591835	−	0.806059i	$-0.701596\pi$
$367$	−22.6758			−1.18367			−0.591835	+	0.806059i	$0.701596\pi$
$368$	−6.91907	−	3.99473i	−0.360682	−	0.208240i
$369$		0			0
$370$	19.4971	+	7.70523i	1.01361	+	0.400576i
$371$	0.706493	−	1.22368i	0.0366793	−	0.0635304i
$372$		0			0
$373$	13.3477	−	23.1189i	0.691117	−	1.19705i	−0.280355	−	0.959896i	$-0.590452\pi$
$373$	13.3477	−	23.1189i	0.691117	−	1.19705i	0.971472	−	0.237154i	$-0.0762145\pi$
$374$	1.72259	−	2.98361i	0.0890729	−	0.154279i
$375$		0			0
$376$	−10.2823	−	5.93648i	−0.530269	−	0.306151i
$377$	4.21389	+	7.29866i	0.217026	+	0.375900i
$378$		0			0
$379$	−11.6509	+	20.1799i	−0.598466	+	1.03657i	0.394582	+	0.918861i	$0.370889\pi$
$379$	−11.6509	+	20.1799i	−0.598466	+	1.03657i	−0.993048	+	0.117712i	$0.962444\pi$
$380$	0.663401	−	1.14904i	0.0340317	−	0.0589447i
$381$		0			0
$382$	5.24809			0.268516
$383$	−12.3960	−	7.15683i	−0.633406	−	0.365697i	0.148664	−	0.988888i	$-0.452503\pi$
$383$	−12.3960	−	7.15683i	−0.633406	−	0.365697i	−0.782070	+	0.623191i	$0.785836\pi$
$384$		0			0
$385$	4.52581	−	2.61298i	0.230657	−	0.133170i
$386$	−3.18391	+	5.51469i	−0.162057	+	0.280690i
$387$		0			0
$388$	−10.9363	+	6.31410i	−0.555209	+	0.320550i
$389$			18.7709i			0.951722i	0.879520	+	0.475861i	$0.157864\pi$
$389$			18.7709i			0.951722i	−0.879520	+	0.475861i	$0.842136\pi$
$390$		0			0
$391$	−8.71693			−0.440834
$392$			6.76941i			0.341907i
$393$		0			0
$394$		−	6.28542i		−	0.316655i
$395$	−28.0846	+	48.6440i	−1.41309	+	2.44754i
$396$		0			0
$397$	39.5953			1.98723			0.993616	−	0.112812i	$-0.0359857\pi$
$397$	39.5953			1.98723			0.993616	+	0.112812i	$0.0359857\pi$
$398$	−6.63535	−	11.4928i	−0.332600	−	0.576080i
$399$		0			0
$400$	3.43932	−	5.95707i	0.171966	−	0.297853i
$401$	−24.0748	+	13.8996i	−1.20224	+	0.694111i	−0.961052	−	0.276368i	$-0.910869\pi$
$401$	−24.0748	+	13.8996i	−1.20224	+	0.694111i	−0.241184	+	0.970479i	$0.577536\pi$
$402$		0			0
$403$	−5.61940			−0.279922
$404$	0.492396	+	0.852854i	0.0244976	+	0.0424311i
$405$		0			0
$406$	−2.99568			−0.148673
$407$	−15.0451	+	11.9401i	−0.745758	+	0.591847i
$408$		0			0
$409$			14.7125i			0.727486i	0.931499	+	0.363743i	$0.118501\pi$
$409$			14.7125i			0.727486i	−0.931499	+	0.363743i	$0.881499\pi$
$410$	−5.68782	+	9.85159i	−0.280901	+	0.486535i
$411$		0			0
$412$			1.20555i			0.0593933i
$413$		−	0.163499i		−	0.00804524i
$414$		0			0
$415$		−	37.0792i		−	1.82014i
$416$	−0.675468	−	1.16995i	−0.0331175	−	0.0573613i
$417$		0			0
$418$	0.607797	+	1.05273i	0.0297283	+	0.0514909i
$419$	0.661695			0.0323259			0.0161630	−	0.999869i	$-0.494855\pi$
$419$	0.661695			0.0323259			0.0161630	+	0.999869i	$0.494855\pi$
$420$		0			0
$421$	−19.0635	−	11.0063i	−0.929098	−	0.536415i	−0.0425721	−	0.999093i	$-0.513555\pi$
$421$	−19.0635	−	11.0063i	−0.929098	−	0.536415i	−0.886526	+	0.462678i	$0.846889\pi$
$422$	−14.3684	−	8.29561i	−0.699444	−	0.403824i
$423$		0			0
$424$	2.54830	+	1.47126i	0.123757	+	0.0714509i
$425$		−	7.50496i		−	0.364044i
$426$		0			0
$427$		−	6.82690i		−	0.330377i
$428$	−15.7756			−0.762544
$429$		0			0
$430$	25.7665	+	14.8763i	1.24257	+	0.717400i
$431$	5.70464	−	3.29357i	0.274783	−	0.158646i	−0.356276	−	0.934381i	$-0.615954\pi$
$431$	5.70464	−	3.29357i	0.274783	−	0.158646i	0.631059	+	0.775735i	$0.282621\pi$
$432$		0			0
$433$	−12.7700			−0.613686			−0.306843	−	0.951760i	$-0.599273\pi$
$433$	−12.7700			−0.613686			−0.306843	+	0.951760i	$0.599273\pi$
$434$	0.998716	−	1.72983i	0.0479399	−	0.0830344i
$435$		0			0
$436$	4.39231	−	2.53590i	0.210353	−	0.121448i
$437$	1.53784	−	2.66361i	0.0735647	−	0.127418i
$438$		0			0
$439$			35.9750i			1.71699i	0.512819	+	0.858497i	$0.328601\pi$
$439$			35.9750i			1.71699i	−0.512819	+	0.858497i	$0.671399\pi$
$440$	5.44150	+	9.42495i	0.259413	+	0.449317i
$441$		0			0
$442$	−1.27647	−	0.736972i	−0.0607156	−	0.0350542i
$443$	7.80056	−	13.5110i	0.370616	−	0.641925i	−0.619045	−	0.785356i	$-0.712480\pi$
$443$	7.80056	−	13.5110i	0.370616	−	0.641925i	0.989660	+	0.143430i	$0.0458133\pi$
$444$		0			0
$445$	−4.29318	−	7.43600i	−0.203516	−	0.352500i
$446$			18.3269i			0.867803i
$447$		0			0
$448$	0.480194			0.0226870
$449$	7.19308	−	4.15293i	0.339462	−	0.195989i	−0.320572	−	0.947224i	$-0.603875\pi$
$449$	7.19308	−	4.15293i	0.339462	−	0.195989i	0.660034	+	0.751235i	$0.270542\pi$
$450$		0			0
$451$	−5.21108	−	9.02585i	−0.245380	−	0.425011i
$452$	−0.515396	−	0.297564i	−0.0242422	−	0.0139962i
$453$		0			0
$454$	−0.933947	−	1.61764i	−0.0438323	−	0.0759198i
$455$	−1.11791	−	1.93627i	−0.0524082	−	0.0907737i
$456$		0			0
$457$			3.28231i			0.153540i	0.997049	+	0.0767700i	$0.0244607\pi$
$457$			3.28231i			0.153540i	−0.997049	+	0.0767700i	$0.975539\pi$
$458$			6.81939i			0.318649i
$459$		0			0
$460$	13.7680	−	23.8469i	0.641936	−	1.11187i
$461$	−27.7237	+	16.0063i	−1.29122	+	0.745487i	−0.978871	−	0.204480i	$-0.934450\pi$
$461$	−27.7237	+	16.0063i	−1.29122	+	0.745487i	−0.312351	+	0.949967i	$0.601116\pi$
$462$		0			0
$463$	−18.2739	−	10.5505i	−0.849261	−	0.490321i	0.0111402	−	0.999938i	$-0.496454\pi$
$463$	−18.2739	−	10.5505i	−0.849261	−	0.490321i	−0.860402	+	0.509617i	$0.829787\pi$
$464$		−	6.23847i		−	0.289614i
$465$		0			0
$466$	24.5234	−	14.1586i	1.13602	−	0.655883i
$467$			26.7437i			1.23755i	0.785568	+	0.618776i	$0.212371\pi$
$467$			26.7437i			1.23755i	−0.785568	+	0.618776i	$0.787629\pi$
$468$		0			0
$469$	−2.13526	+	3.69839i	−0.0985973	+	0.170776i
$470$	20.4603	−	35.4383i	0.943764	−	1.63465i
$471$		0			0
$472$	0.340484			0.0156721
$473$	−23.6069	+	13.6294i	−1.08544	+	0.626682i
$474$		0			0
$475$	2.29327	+	1.32402i	0.105223	+	0.0607502i
$476$	0.453726	−	0.261959i	0.0207965	−	0.0120069i
$477$		0			0
$478$	−9.74117	−	16.8722i	−0.445551	−	0.771716i
$479$	6.20074	−	3.58000i	0.283319	−	0.163574i	−0.351606	−	0.936148i	$-0.614364\pi$
$479$	6.20074	−	3.58000i	0.283319	−	0.163574i	0.634925	+	0.772574i	$0.281031\pi$
$480$		0			0
$481$	5.10830	+	6.43672i	0.232918	+	0.293489i
$482$	−11.9345	−	20.6711i	−0.543600	−	0.941542i
$483$		0			0
$484$	1.02918			0.0467811
$485$	−21.7618	−	37.6925i	−0.988153	−	1.71153i
$486$		0			0
$487$			24.2615i			1.09939i	0.835364	+	0.549697i	$0.185257\pi$
$487$			24.2615i			1.09939i	−0.835364	+	0.549697i	$0.814743\pi$
$488$	14.2169			0.643571
$489$		0			0
$490$	−23.3310			−1.05399
$491$	16.1023	+	27.8901i	0.726688	+	1.25866i	0.958275	+	0.285847i	$0.0922749\pi$
$491$	16.1023	+	27.8901i	0.726688	+	1.25866i	−0.231587	+	0.972814i	$0.574392\pi$
$492$		0			0
$493$	−3.40325	−	5.89460i	−0.153275	−	0.265480i
$494$	0.450390	−	0.260033i	0.0202640	−	0.0116994i
$495$		0			0
$496$	3.60235	+	2.07982i	0.161750	+	0.0933866i
$497$	0.501770	+	0.869092i	0.0225075	+	0.0389841i
$498$		0			0
$499$	−15.9643	−	9.21700i	−0.714661	−	0.412610i	0.0981237	−	0.995174i	$-0.468716\pi$
$499$	−15.9643	−	9.21700i	−0.714661	−	0.412610i	−0.812784	+	0.582565i	$0.802049\pi$
$500$	5.60732	+	3.23739i	0.250767	+	0.144780i
$501$		0			0
$502$	−7.94913	−	13.7683i	−0.354787	−	0.614509i
$503$	28.9751	+	16.7288i	1.29193	+	0.745898i	0.978997	−	0.203876i	$-0.0653538\pi$
$503$	28.9751	+	16.7288i	1.29193	+	0.745898i	0.312937	+	0.949774i	$0.398687\pi$
$504$		0			0
$505$	−2.93940	+	1.69706i	−0.130801	+	0.0755182i
$506$	12.6140	+	21.8481i	0.560760	+	0.971266i
$507$		0			0
$508$	−3.39075	−	5.87296i	−0.150440	−	0.260570i
$509$	19.1727			0.849817			0.424908	−	0.905236i	$-0.360306\pi$
$509$	19.1727			0.849817			0.424908	+	0.905236i	$0.360306\pi$
$510$		0			0
$511$	3.51528			0.155507
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−8.45521	−	14.6449i	−0.372943	−	0.645957i
$515$	−4.15498			−0.183091
$516$		0			0
$517$	18.7454	+	32.4680i	0.824421	+	1.42794i
$518$	−2.88930	+	0.428519i	−0.126949	+	0.0188280i
$519$		0			0
$520$	4.03226	−	2.32803i	0.176826	−	0.102091i
$521$	−18.7964	−	32.5563i	−0.823485	−	1.42632i	−0.903072	−	0.429489i	$-0.858694\pi$
$521$	−18.7964	−	32.5563i	−0.823485	−	1.42632i	0.0795871	−	0.996828i	$-0.474640\pi$
$522$		0			0
$523$	−5.51977	+	3.18684i	−0.241363	+	0.139351i	−0.615803	−	0.787900i	$-0.711168\pi$
$523$	−5.51977	+	3.18684i	−0.241363	+	0.139351i	0.374440	+	0.927251i	$0.377835\pi$
$524$	−6.98950	−	4.03539i	−0.305338	−	0.176287i
$525$		0			0
$526$	−19.8437	+	11.4568i	−0.865228	+	0.499539i
$527$	4.53839			0.197695
$528$		0			0
$529$	20.4157	−	35.3610i	0.887640	−	1.53744i
$530$	−5.07077	+	8.78283i	−0.220260	+	0.381502i
$531$		0			0
$532$			0.184859i			0.00801464i
$533$	−3.86152	+	2.22945i	−0.167261	+	0.0965681i
$534$		0			0
$535$		−	54.3713i		−	2.35068i
$536$	−7.70185	−	4.44667i	−0.332669	−	0.192067i
$537$		0			0
$538$	16.4143	−	9.47682i	0.707672	−	0.408575i
$539$	10.6878	−	18.5117i	0.460354	−	0.797357i
$540$		0			0
$541$		−	8.62312i		−	0.370737i	−0.982669	−	0.185369i	$-0.940652\pi$
$541$		−	8.62312i		−	0.370737i	0.982669	−	0.185369i	$-0.0593479\pi$
$542$		−	4.21714i		−	0.181142i
$543$		0			0
$544$	0.545527	+	0.944880i	0.0233893	+	0.0405114i
$545$	8.74007	+	15.1383i	0.374384	+	0.648452i
$546$		0			0
$547$	7.56083	+	4.36525i	0.323278	+	0.186644i	0.652853	−	0.757485i	$-0.273572\pi$
$547$	7.56083	+	4.36525i	0.323278	+	0.186644i	−0.329575	+	0.944129i	$0.606905\pi$
$548$	0.0848084	+	0.146893i	0.00362284	+	0.00627494i
$549$		0			0
$550$	−18.8104	+	10.8602i	−0.802078	+	0.463080i
$551$	2.40160			0.102312
$552$		0			0
$553$		−	7.82586i		−	0.332790i
$554$	15.4445	+	26.7507i	0.656174	+	1.13653i
$555$		0			0
$556$	4.32699	−	7.49457i	0.183505	−	0.317841i
$557$	−24.9911	−	14.4286i	−1.05891	−	0.611361i	−0.133778	−	0.991011i	$-0.542711\pi$
$557$	−24.9911	−	14.4286i	−1.05891	−	0.611361i	−0.925130	+	0.379651i	$0.876044\pi$
$558$		0			0
$559$	5.83106	+	10.0997i	0.246627	+	0.427171i
$560$			1.65501i			0.0699369i
$561$		0			0
$562$	−16.1812	+	28.0267i	−0.682563	+	1.18223i
$563$	39.2375	−	22.6538i	1.65366	−	0.954742i	0.678114	−	0.734957i	$-0.262798\pi$
$563$	39.2375	−	22.6538i	1.65366	−	0.954742i	0.975548	−	0.219785i	$-0.0705357\pi$
$564$		0			0
$565$	1.02557	−	1.77633i	0.0431459	−	0.0747309i
$566$	−16.3590			−0.687619
$567$		0			0
$568$	−1.80988	+	1.04493i	−0.0759407	+	0.0438444i
$569$	−7.70454	−	4.44822i	−0.322991	−	0.186479i	0.329734	−	0.944074i	$-0.393041\pi$
$569$	−7.70454	−	4.44822i	−0.322991	−	0.186479i	−0.652725	+	0.757595i	$0.726374\pi$
$570$		0			0
$571$	32.1759			1.34652			0.673259	−	0.739406i	$-0.264894\pi$
$571$	32.1759			1.34652			0.673259	+	0.739406i	$0.264894\pi$
$572$			4.26580i			0.178362i
$573$		0			0
$574$		−	1.58493i		−	0.0661536i
$575$	47.5937	+	27.4783i	1.98480	+	1.14592i
$576$		0			0
$577$	25.1077	+	14.4959i	1.04525	+	0.603474i	0.921315	−	0.388817i	$-0.127116\pi$
$577$	25.1077	+	14.4959i	1.04525	+	0.603474i	0.123933	+	0.992291i	$0.460449\pi$
$578$	−13.6915	−	7.90480i	−0.569492	−	0.328796i
$579$		0			0
$580$	21.5011			0.892785
$581$	2.58305	+	4.47398i	0.107163	+	0.185612i
$582$		0			0
$583$	−4.64575	−	8.04668i	−0.192407	−	0.333259i
$584$			7.32053i			0.302926i
$585$		0			0
$586$		−	17.9908i		−	0.743192i
$587$			5.24695i			0.216565i	0.994120	+	0.108282i	$0.0345351\pi$
$587$			5.24695i			0.216565i	−0.994120	+	0.108282i	$0.965465\pi$
$588$		0			0
$589$	−0.800660	+	1.38678i	−0.0329906	+	0.0571414i
$590$			1.17349i			0.0483119i
$591$		0			0
$592$	−0.892387	−	6.01695i	−0.0366769	−	0.247295i
$593$	8.42504			0.345975			0.172987	−	0.984924i	$-0.444658\pi$
$593$	8.42504			0.345975			0.172987	+	0.984924i	$0.444658\pi$
$594$		0			0
$595$	0.902852	+	1.56378i	0.0370133	+	0.0641089i
$596$	5.07440			0.207855
$597$		0			0
$598$	9.34723	−	5.39662i	0.382236	−	0.220684i
$599$	−16.0499	+	27.7993i	−0.655781	+	1.13585i	0.325916	+	0.945399i	$0.394327\pi$
$599$	−16.0499	+	27.7993i	−0.655781	+	1.13585i	−0.981697	+	0.190448i	$0.939006\pi$
$600$		0			0
$601$	1.21888	+	2.11117i	0.0497193	+	0.0861163i	0.889814	−	0.456323i	$-0.150834\pi$
$601$	1.21888	+	2.11117i	0.0497193	+	0.0861163i	−0.840095	+	0.542440i	$0.817501\pi$
$602$	−4.14533			−0.168951
$603$		0			0
$604$	2.46576	−	4.27082i	0.100330	−	0.173777i
$605$			3.54712i			0.144211i
$606$		0			0
$607$			1.71604i			0.0696518i	0.999393	+	0.0348259i	$0.0110877\pi$
$607$			1.71604i			0.0696518i	−0.999393	+	0.0348259i	$0.988912\pi$
$608$	−0.384966			−0.0156125
$609$		0			0
$610$			48.9993i			1.98392i
$611$	13.8907	−	8.01981i	0.561958	−	0.324447i
$612$		0			0
$613$	17.8592	−	30.9331i	0.721327	−	1.24938i	−0.239141	−	0.970985i	$-0.576866\pi$
$613$	17.8592	−	30.9331i	0.721327	−	1.24938i	0.960468	−	0.278390i	$-0.0898009\pi$
$614$	−7.54752	+	4.35756i	−0.304593	+	0.175857i
$615$		0			0
$616$	−1.31315	−	0.758145i	−0.0529082	−	0.0305465i
$617$	−47.0472			−1.89405			−0.947025	−	0.321159i	$-0.895928\pi$
$617$	−47.0472			−1.89405			−0.947025	+	0.321159i	$0.895928\pi$
$618$		0			0
$619$	17.1311	−	29.6720i	0.688558	−	1.19262i	−0.283747	−	0.958899i	$-0.591578\pi$
$619$	17.1311	−	29.6720i	0.688558	−	1.19262i	0.972304	−	0.233718i	$-0.0750892\pi$
$620$	−7.16817	+	12.4156i	−0.287881	+	0.498624i
$621$		0			0
$622$	−12.2994	−	21.3032i	−0.493162	−	0.854182i
$623$	1.03603	+	0.598153i	0.0415077	+	0.0239645i
$624$		0			0
$625$	6.03880	−	10.4595i	0.241552	−	0.418380i
$626$	−5.18298	+	8.97718i	−0.207153	+	0.358800i
$627$		0			0
$628$	3.53659	−	6.12555i	0.141125	−	0.244436i
$629$	−4.12560	−	5.19847i	−0.164499	−	0.207277i
$630$		0			0
$631$	8.67244	+	5.00704i	0.345244	+	0.199327i	0.662589	−	0.748983i	$-0.269458\pi$
$631$	8.67244	+	5.00704i	0.345244	+	0.199327i	−0.317344	+	0.948310i	$0.602791\pi$
$632$	16.2973			0.648271
$633$		0			0
$634$	25.8708	+	14.9365i	1.02746	+	0.593205i
$635$	20.2414	−	11.6864i	0.803254	−	0.463759i
$636$		0			0
$637$	−7.91984	−	4.57252i	−0.313796	−	0.181170i
$638$	−9.84948	+	17.0598i	−0.389945	+	0.675404i
$639$		0			0
$640$	−3.44654			−0.136236
$641$	2.64011	+	4.57281i	0.104278	+	0.180615i	0.913443	−	0.406967i	$-0.133413\pi$
$641$	2.64011	+	4.57281i	0.104278	+	0.180615i	−0.809165	+	0.587582i	$0.800080\pi$
$642$		0			0
$643$	−2.93253	+	1.69309i	−0.115648	+	0.0667691i	−0.556708	−	0.830708i	$-0.687936\pi$
$643$	−2.93253	+	1.69309i	−0.115648	+	0.0667691i	0.441060	+	0.897477i	$0.354602\pi$
$644$			3.83649i			0.151179i
$645$		0			0
$646$	−0.363747	+	0.210010i	−0.0143114	+	0.00826271i
$647$	−15.0995	+	8.71769i	−0.593622	+	0.342728i	−0.766528	−	0.642211i	$-0.778017\pi$
$647$	−15.0995	+	8.71769i	−0.593622	+	0.342728i	0.172907	+	0.984938i	$0.444684\pi$
$648$		0			0
$649$	−0.931093	−	0.537567i	−0.0365486	−	0.0211013i
$650$	4.64630	+	8.04762i	0.182243	+	0.315654i
$651$		0			0
$652$	−16.5023	+	9.52761i	−0.646280	+	0.373130i
$653$	41.2587	+	23.8207i	1.61458	+	0.932178i	0.988290	+	0.152587i	$0.0487604\pi$
$653$	41.2587	+	23.8207i	1.61458	+	0.932178i	0.626289	+	0.779591i	$0.284573\pi$
$654$		0			0
$655$	13.9081	−	24.0896i	0.543436	−	0.941258i
$656$	3.30060			0.128867
$657$		0			0
$658$			5.70133i			0.222261i
$659$	3.97201			0.154728			0.0773638	−	0.997003i	$-0.475350\pi$
$659$	3.97201			0.154728			0.0773638	+	0.997003i	$0.475350\pi$
$660$		0			0
$661$	18.4962	+	10.6788i	0.719420	+	0.415357i	0.814539	−	0.580109i	$-0.196990\pi$
$661$	18.4962	+	10.6788i	0.719420	+	0.415357i	−0.0951192	+	0.995466i	$0.530323\pi$
$662$	−11.7606	+	20.3700i	−0.457090	+	0.791704i
$663$		0			0
$664$	−9.31702	+	5.37919i	−0.361571	+	0.208753i
$665$	−0.637123			−0.0247066
$666$		0			0
$667$	49.8420			1.92989
$668$	−8.96444	+	5.17562i	−0.346844	+	0.200251i
$669$		0			0
$670$	15.3256	−	26.5447i	0.592080	−	1.02551i
$671$	−38.8779	−	22.4461i	−1.50086	−	0.866524i
$672$		0			0
$673$	−22.8244			−0.879816			−0.439908	−	0.898043i	$-0.644989\pi$
$673$	−22.8244			−0.879816			−0.439908	+	0.898043i	$0.644989\pi$
$674$		−	4.22458i		−	0.162725i
$675$		0			0
$676$	−11.1750			−0.429807
$677$	6.16271	−	10.6741i	0.236852	−	0.410240i	−0.722957	−	0.690893i	$-0.757218\pi$
$677$	6.16271	−	10.6741i	0.236852	−	0.410240i	0.959809	+	0.280653i	$0.0905510\pi$
$678$		0			0
$679$	5.25157	+	3.03200i	0.201537	+	0.116357i
$680$	−3.25657	+	1.88018i	−0.124884	+	0.0721016i
$681$		0			0
$682$	−6.56736	−	11.3750i	−0.251477	−	0.435571i
$683$	−2.66192	−	1.53686i	−0.101855	−	0.0588063i	0.448207	−	0.893930i	$-0.352063\pi$
$683$	−2.66192	−	1.53686i	−0.101855	−	0.0588063i	−0.550062	+	0.835124i	$0.685396\pi$
$684$		0			0
$685$	−0.506271	+	0.292296i	−0.0193436	+	0.0111680i
$686$	5.72615	−	3.30600i	0.218626	−	0.126224i
$687$		0			0
$688$		−	8.63261i		−	0.329115i
$689$	−3.44260	+	1.98758i	−0.131152	+	0.0757209i
$690$		0			0
$691$	8.09830	+	14.0267i	0.308074	+	0.533600i	0.977941	−	0.208881i	$-0.0669822\pi$
$691$	8.09830	+	14.0267i	0.308074	+	0.533600i	−0.669867	+	0.742481i	$0.733649\pi$
$692$	−3.86787			−0.147034
$693$		0			0
$694$	−12.7716	+	22.1211i	−0.484804	+	0.839705i
$695$	25.8303	+	14.9131i	0.979800	+	0.565688i
$696$		0			0
$697$	3.11867	−	1.80056i	0.118128	−	0.0682012i
$698$	−22.2188	−	12.8280i	−0.840992	−	0.485547i
$699$		0			0
$700$	−3.30308			−0.124845
$701$	3.84777	+	2.22151i	0.145328	+	0.0839052i	0.570901	−	0.821019i	$-0.306594\pi$
$701$	3.84777	+	2.22151i	0.145328	+	0.0839052i	−0.425573	+	0.904924i	$0.639927\pi$
$702$		0			0
$703$	2.31632	−	0.343539i	0.0873618	−	0.0129568i
$704$	1.57883	−	2.73461i	0.0595044	−	0.103065i
$705$		0			0
$706$	9.07598	−	15.7201i	0.341579	−	0.591632i
$707$	0.236446	−	0.409536i	0.00889245	−	0.0154022i
$708$		0			0
$709$	26.3142	+	15.1925i	0.988252	+	0.570567i	0.904751	−	0.425940i	$-0.140057\pi$
$709$	26.3142	+	15.1925i	0.988252	+	0.570567i	0.0835004	+	0.996508i	$0.473390\pi$
$710$	−3.60140	−	6.23781i	−0.135158	−	0.234101i
$711$		0			0
$712$	−1.24565	+	2.15753i	−0.0466826	+	0.0808567i
$713$	−16.6166	+	28.7808i	−0.622297	+	1.07785i
$714$		0			0
$715$	−14.7022			−0.549832
$716$	1.96451	+	1.13421i	0.0734172	+	0.0423874i
$717$		0			0
$718$	−3.14227	+	1.81419i	−0.117268	+	0.0677050i
$719$	20.5554	−	35.6030i	0.766588	−	1.32777i	−0.172816	−	0.984954i	$-0.555286\pi$
$719$	20.5554	−	35.6030i	0.766588	−	1.32777i	0.939403	−	0.342814i	$-0.111380\pi$
$720$		0			0
$721$	0.501342	−	0.289450i	0.0186709	−	0.0107797i
$722$			18.8518i			0.701591i
$723$		0			0
$724$	−3.33029			−0.123769
$725$			42.9121i			1.59372i
$726$		0			0
$727$		−	7.32555i		−	0.271689i	−0.990730	−	0.135845i	$-0.956625\pi$
$727$		−	7.32555i		−	0.271689i	0.990730	−	0.135845i	$-0.0433748\pi$
$728$	−0.324356	+	0.561801i	−0.0120214	+	0.0208217i
$729$		0			0
$730$	−25.2305			−0.933822
$731$	−4.70932	−	8.15679i	−0.174181	−	0.301690i
$732$		0			0
$733$	6.48200	−	11.2272i	0.239418	−	0.414685i	−0.721129	−	0.692801i	$-0.756377\pi$
$733$	6.48200	−	11.2272i	0.239418	−	0.414685i	0.960548	+	0.278116i	$0.0897099\pi$
$734$	−19.6379	+	11.3379i	−0.724846	+	0.418490i
$735$		0			0
$736$	−7.98946			−0.294495
$737$	14.0411	+	24.3198i	0.517209	+	0.895833i
$738$		0			0
$739$	23.1115			0.850172			0.425086	−	0.905153i	$-0.360244\pi$
$739$	23.1115			0.850172			0.425086	+	0.905153i	$0.360244\pi$
$740$	20.7376	−	3.07565i	0.762331	−	0.113063i
$741$		0			0
$742$		−	1.41299i		−	0.0518723i
$743$	19.9229	−	34.5075i	0.730901	−	1.26596i	−0.225598	−	0.974220i	$-0.572434\pi$
$743$	19.9229	−	34.5075i	0.730901	−	1.26596i	0.956499	−	0.291736i	$-0.0942330\pi$
$744$		0			0
$745$			17.4891i			0.640751i
$746$		−	26.6954i		−	0.977387i
$747$		0			0
$748$		−	3.44518i		−	0.125968i
$749$	3.78769	+	6.56046i	0.138399	+	0.239714i
$750$		0			0
$751$	−0.276749	−	0.479344i	−0.0100987	−	0.0174915i	0.860932	−	0.508720i	$-0.169881\pi$
$751$	−0.276749	−	0.479344i	−0.0100987	−	0.0174915i	−0.871031	+	0.491229i	$0.836548\pi$
$752$	−11.8730			−0.432963
$753$		0			0
$754$	7.29866	+	4.21389i	0.265802	+	0.153461i
$755$	14.7196	+	8.49834i	0.535699	+	0.309286i
$756$		0			0
$757$	−4.11305	−	2.37467i	−0.149491	−	0.0863088i	0.423389	−	0.905948i	$-0.360841\pi$
$757$	−4.11305	−	2.37467i	−0.149491	−	0.0863088i	−0.572880	+	0.819639i	$0.694174\pi$
$758$			23.3018i			0.846358i
$759$		0			0
$760$		−	1.32680i		−	0.0481282i
$761$	−7.11945			−0.258080			−0.129040	−	0.991639i	$-0.541190\pi$
$761$	−7.11945			−0.258080			−0.129040	+	0.991639i	$0.541190\pi$
$762$		0			0
$763$	−2.10916	−	1.21772i	−0.0763567	−	0.0440846i
$764$	4.54498	−	2.62405i	0.164432	−	0.0949347i
$765$		0			0
$766$	−14.3137			−0.517174
$767$	−0.229986	+	0.398348i	−0.00830432	+	0.0143835i
$768$		0			0
$769$	−31.9973	+	18.4736i	−1.15385	+	0.666177i	−0.949823	−	0.312788i	$-0.898737\pi$
$769$	−31.9973	+	18.4736i	−1.15385	+	0.666177i	−0.204029	+	0.978965i	$0.565404\pi$
$770$	2.61298	−	4.52581i	0.0941651	−	0.163099i
$771$		0			0
$772$			6.36781i			0.229183i
$773$	−9.49564	−	16.4469i	−0.341534	−	0.591555i	0.643184	−	0.765712i	$-0.277613\pi$
$773$	−9.49564	−	16.4469i	−0.341534	−	0.591555i	−0.984718	+	0.174157i	$0.944280\pi$
$774$		0			0
$775$	−24.7792	−	14.3063i	−0.890096	−	0.513897i
$776$	−6.31410	+	10.9363i	−0.226663	+	0.392592i
$777$		0			0
$778$	9.38545	+	16.2561i	0.336485	+	0.582808i
$779$			1.27062i			0.0455246i
$780$		0			0
$781$	6.59908			0.236134
$782$	−7.54908	+	4.35846i	−0.269955	+	0.155858i
$783$		0			0
$784$	3.38471	+	5.86248i	0.120882	+	0.209374i
$785$	21.1120	+	12.1890i	0.753518	+	0.435044i
$786$		0			0
$787$	26.4114	+	45.7459i	0.941465	+	1.63067i	0.762678	+	0.646778i	$0.223884\pi$
$787$	26.4114	+	45.7459i	0.941465	+	1.63067i	0.178787	+	0.983888i	$0.442783\pi$
$788$	−3.14271	−	5.44333i	−0.111954	−	0.193911i
$789$		0			0
$790$			56.1692i			1.99841i
$791$			0.285777i			0.0101611i
$792$		0			0
$793$	−9.60310	+	16.6331i	−0.341016	+	0.590657i
$794$	34.2906	−	19.7977i	1.21693	−	0.702593i
$795$		0			0
$796$	−11.4928	−	6.63535i	−0.407350	−	0.235184i
$797$		−	0.582881i		−	0.0206467i	−0.999947	−	0.0103233i	$-0.996714\pi$
$797$		−	0.582881i		−	0.0206467i	0.999947	−	0.0103233i	$-0.00328608\pi$
$798$		0			0
$799$	−11.2185	+	6.47702i	−0.396883	+	0.229141i
$800$		−	6.87863i		−	0.243196i
$801$		0			0
$802$	−13.8996	+	24.0748i	−0.490811	+	0.850109i
$803$	11.5579	−	20.0188i	0.407868	−	0.706449i
$804$		0			0
$805$	−13.2226			−0.466036
$806$	−4.86654	+	2.80970i	−0.171417	+	0.0989675i
$807$		0			0
$808$	0.852854	+	0.492396i	0.0300033	+	0.0173224i
$809$	0.932228	−	0.538222i	0.0327754	−	0.0189229i	−0.483523	−	0.875332i	$-0.660643\pi$
$809$	0.932228	−	0.538222i	0.0327754	−	0.0189229i	0.516298	+	0.856409i	$0.327310\pi$
$810$		0			0
$811$	−9.15259	−	15.8527i	−0.321391	−	0.556665i	0.659384	−	0.751806i	$-0.270817\pi$
$811$	−9.15259	−	15.8527i	−0.321391	−	0.556665i	−0.980775	+	0.195141i	$0.937484\pi$
$812$	−2.59433	+	1.49784i	−0.0910432	+	0.0525638i
$813$		0			0
$814$	−7.05940	+	17.8630i	−0.247432	+	0.626096i
$815$	−32.8373	−	56.8758i	−1.15024	−	1.99227i
$816$		0			0
$817$	3.32327			0.116266
$818$	7.35625	+	12.7414i	0.257205	+	0.445492i
$819$		0			0
$820$			11.3756i			0.397254i
$821$	−36.4894			−1.27349			−0.636744	−	0.771075i	$-0.719719\pi$
$821$	−36.4894			−1.27349			−0.636744	+	0.771075i	$0.719719\pi$
$822$		0			0
$823$	−48.4327			−1.68826			−0.844130	−	0.536139i	$-0.819882\pi$
$823$	−48.4327			−1.68826			−0.844130	+	0.536139i	$0.819882\pi$
$824$	0.602776	+	1.04404i	0.0209987	+	0.0363708i
$825$		0			0
$826$	−0.0817493	−	0.141594i	−0.00284442	−	0.00492668i
$827$	41.2844	−	23.8356i	1.43560	−	0.828845i	0.438061	−	0.898945i	$-0.355665\pi$
$827$	41.2844	−	23.8356i	1.43560	−	0.828845i	0.997540	+	0.0701008i	$0.0223321\pi$
$828$		0			0
$829$	−2.70886	−	1.56396i	−0.0940825	−	0.0543186i	0.452221	−	0.891906i	$-0.350632\pi$
$829$	−2.70886	−	1.56396i	−0.0940825	−	0.0543186i	−0.546303	+	0.837588i	$0.683965\pi$
$830$	−18.5396	−	32.1115i	−0.643518	−	1.11461i
$831$		0			0
$832$	−1.16995	−	0.675468i	−0.0405605	−	0.0234176i
$833$	6.39629	+	3.69290i	0.221618	+	0.127951i
$834$		0			0
$835$	−17.8380	−	30.8963i	−0.617309	−	1.06921i
$836$	1.05273	+	0.607797i	0.0364096	+	0.0210211i
$837$		0			0
$838$	0.573045	−	0.330848i	0.0197955	−	0.0114289i
$839$	−24.9335	−	43.1861i	−0.860800	−	1.49095i	−0.871158	−	0.491003i	$-0.836631\pi$
$839$	−24.9335	−	43.1861i	−0.860800	−	1.49095i	0.0103583	−	0.999946i	$-0.496703\pi$
$840$		0			0
$841$	4.95924	+	8.58965i	0.171008	+	0.296195i
$842$	−22.0126			−0.758606
$843$		0			0
$844$	−16.5912			−0.571093
$845$		−	38.5150i		−	1.32496i
$846$		0			0
$847$	−0.247104	−	0.427997i	−0.00849060	−	0.0147061i
$848$	2.94253			0.101047
$849$		0			0
$850$	−3.75248	−	6.49948i	−0.128709	−	0.222930i
$851$	48.0721	−	7.12968i	1.64789	−	0.244402i
$852$		0			0
$853$	−2.06294	+	1.19104i	−0.0706337	+	0.0407804i	−0.534901	−	0.844915i	$-0.679651\pi$
$853$	−2.06294	+	1.19104i	−0.0706337	+	0.0407804i	0.464267	+	0.885695i	$0.346318\pi$
$854$	−3.41345	−	5.91227i	−0.116806	−	0.202314i
$855$		0			0
$856$	−13.6621	+	7.88782i	−0.466961	+	0.269600i
$857$	36.0471	+	20.8118i	1.23135	+	0.710918i	0.967311	−	0.253595i	$-0.0816129\pi$
$857$	36.0471	+	20.8118i	1.23135	+	0.710918i	0.264036	+	0.964513i	$0.414946\pi$
$858$		0			0
$859$	−18.8119	+	10.8611i	−0.641854	+	0.370574i	−0.785328	−	0.619080i	$-0.787506\pi$
$859$	−18.8119	+	10.8611i	−0.641854	+	0.370574i	0.143475	+	0.989654i	$0.454172\pi$
$860$	29.7526			1.01456
$861$		0			0
$862$	3.29357	−	5.70464i	0.112180	−	0.194301i
$863$	7.13935	−	12.3657i	0.243026	−	0.420934i	−0.718549	−	0.695477i	$-0.755193\pi$
$863$	7.13935	−	12.3657i	0.243026	−	0.420934i	0.961575	+	0.274543i	$0.0885266\pi$
$864$		0			0
$865$		−	13.3308i		−	0.453260i
$866$	−11.0591	+	6.38499i	−0.375804	+	0.216971i
$867$		0			0
$868$		−	1.99743i		−	0.0677973i
$869$	−44.5668	−	25.7306i	−1.51182	−	0.872852i
$870$		0			0
$871$	10.4047	−	6.00716i	0.352550	−	0.203545i
$872$	2.53590	−	4.39231i	0.0858764	−	0.148742i
$873$		0			0
$874$		−	3.07567i		−	0.104036i
$875$		−	3.10915i		−	0.105108i
$876$		0			0
$877$	8.18576	+	14.1781i	0.276413	+	0.478762i	0.970491	−	0.241138i	$-0.0775208\pi$
$877$	8.18576	+	14.1781i	0.276413	+	0.478762i	−0.694077	+	0.719900i	$0.744187\pi$
$878$	17.9875	+	31.1553i	0.607049	+	1.05144i
$879$		0			0
$880$	9.42495	+	5.44150i	0.317715	+	0.183433i
$881$	−12.4391	−	21.5451i	−0.419082	−	0.725872i	0.576765	−	0.816910i	$-0.304315\pi$
$881$	−12.4391	−	21.5451i	−0.419082	−	0.725872i	−0.995847	+	0.0910380i	$0.970982\pi$
$882$		0			0
$883$	−38.8179	+	22.4115i	−1.30633	+	0.754208i	−0.981481	−	0.191559i	$-0.938646\pi$
$883$	−38.8179	+	22.4115i	−1.30633	+	0.754208i	−0.324845	+	0.945767i	$0.605312\pi$
$884$	−1.47394			−0.0495741
$885$		0			0
$886$		−	15.6011i		−	0.524130i
$887$	16.8558	+	29.1951i	0.565962	+	0.980275i	0.996959	+	0.0779220i	$0.0248285\pi$
$887$	16.8558	+	29.1951i	0.565962	+	0.980275i	−0.430997	+	0.902353i	$0.641838\pi$
$888$		0			0
$889$	−1.62822	+	2.82016i	−0.0546088	+	0.0945851i
$890$	−7.43600	−	4.29318i	−0.249255	−	0.143908i
$891$		0			0
$892$	9.16344	+	15.8715i	0.306815	+	0.531419i
$893$		−	4.57069i		−	0.152952i
$894$		0			0
$895$	−3.90910	+	6.77076i	−0.130667	+	0.226321i
$896$	0.415860	−	0.240097i	0.0138929	−	0.00802108i
$897$		0			0
$898$	4.15293	−	7.19308i	0.138585	−	0.240036i
$899$	−25.9497			−0.865472
$900$		0			0
$901$	2.78034	−	1.60523i	0.0926265	−	0.0534779i
$902$	−9.02585	−	5.21108i	−0.300528	−	0.173510i
$903$		0			0
$904$	−0.595128			−0.0197937
$905$		−	11.4780i		−	0.381541i
$906$		0			0
$907$		−	25.7604i		−	0.855360i	−0.903930	−	0.427680i	$-0.859331\pi$
$907$		−	25.7604i		−	0.855360i	0.903930	−	0.427680i	$-0.140669\pi$
$908$	−1.61764	−	0.933947i	−0.0536834	−	0.0309941i
$909$		0			0
$910$	−1.93627	−	1.11791i	−0.0641867	−	0.0370582i
$911$	45.3764	+	26.1981i	1.50339	+	0.867982i	0.999992	+	0.00392616i	$0.00124974\pi$
$911$	45.3764	+	26.1981i	1.50339	+	0.867982i	0.503396	+	0.864056i	$0.332084\pi$
$912$		0			0
$913$	33.9713			1.12429
$914$	1.64116	+	2.84257i	0.0542846	+	0.0940237i
$915$		0			0
$916$	3.40970	+	5.90577i	0.112660	+	0.195132i
$917$			3.87554i			0.127982i
$918$		0			0
$919$		−	20.5345i		−	0.677371i	−0.940900	−	0.338686i	$-0.890018\pi$
$919$		−	20.5345i		−	0.677371i	0.940900	−	0.338686i	$-0.109982\pi$
$920$		−	27.5360i		−	0.907834i
$921$		0			0
$922$	−16.0063	+	27.7237i	−0.527139	+	0.913032i
$923$		−	2.82327i		−	0.0929292i
$924$		0			0
$925$	6.13840	+	41.3884i	0.201829	+	1.36084i
$926$	−21.1009			−0.693419
$927$		0			0
$928$	−3.11923	−	5.40267i	−0.102394	−	0.177351i
$929$	−42.6476			−1.39922			−0.699610	−	0.714525i	$-0.746643\pi$
$929$	−42.6476			−1.39922			−0.699610	+	0.714525i	$0.746643\pi$
$930$		0			0
$931$	−2.25686	+	1.30300i	−0.0739656	+	0.0427040i
$932$	14.1586	−	24.5234i	0.463779	−	0.803289i
$933$		0			0
$934$	13.3719	+	23.1607i	0.437541	+	0.757842i
$935$	11.8739			0.388319
$936$		0			0
$937$	4.08392	−	7.07356i	0.133416	−	0.231083i	−0.791575	−	0.611072i	$-0.790739\pi$
$937$	4.08392	−	7.07356i	0.133416	−	0.231083i	0.924991	+	0.379989i	$0.124072\pi$
$938$			4.27053i			0.139438i
$939$		0			0
$940$		−	40.9206i		−	1.33468i
$941$	54.7952			1.78627			0.893136	−	0.449787i	$-0.148500\pi$
$941$	54.7952			1.78627			0.893136	+	0.449787i	$0.148500\pi$
$942$		0			0
$943$			26.3700i			0.858724i
$944$	0.294868	−	0.170242i	0.00959714	−	0.00554091i
$945$		0			0
$946$	−13.6294	+	23.6069i	−0.443131	+	0.767525i
$947$	−35.7426	+	20.6360i	−1.16148	+	0.670580i	−0.951658	−	0.307159i	$-0.900622\pi$
$947$	−35.7426	+	20.6360i	−1.16148	+	0.670580i	−0.209821	+	0.977740i	$0.567288\pi$
$948$		0			0
$949$	−8.56462	−	4.94478i	−0.278019	−	0.160514i
$950$	2.64804			0.0859138
$951$		0			0
$952$	0.261959	−	0.453726i	0.00849014	−	0.0147053i
$953$	0.885286	−	1.53336i	0.0286772	−	0.0496704i	−0.851331	−	0.524630i	$-0.824204\pi$
$953$	0.885286	−	1.53336i	0.0286772	−	0.0496704i	0.880008	+	0.474959i	$0.157537\pi$
$954$		0			0
$955$	9.04388	+	15.6645i	0.292653	+	0.506890i
$956$	−16.8722	−	9.74117i	−0.545686	−	0.315052i
$957$		0			0
$958$	3.58000	−	6.20074i	0.115665	−	0.200337i
$959$	0.0407245	−	0.0705370i	0.00131506	−	0.00227776i
$960$		0			0
$961$	−6.84872	+	11.8623i	−0.220926	+	0.382656i
$962$	7.64228	+	3.02021i	0.246397	+	0.0973756i
$963$		0			0
$964$	−20.6711	−	11.9345i	−0.665771	−	0.384383i
$965$	−21.9469			−0.706496
$966$		0			0
$967$	50.7037	+	29.2738i	1.63052	+	0.941382i	0.983932	+	0.178543i	$0.0571383\pi$
$967$	50.7037	+	29.2738i	1.63052	+	0.941382i	0.646589	+	0.762839i	$0.276195\pi$
$968$	0.891300	−	0.514592i	0.0286475	−	0.0165396i
$969$		0			0
$970$	−37.6925	−	21.7618i	−1.21023	−	0.698729i
$971$	0.0438050	−	0.0758725i	0.00140577	−	0.00243486i	−0.865322	−	0.501217i	$-0.832886\pi$
$971$	0.0438050	−	0.0758725i	0.00140577	−	0.00243486i	0.866727	+	0.498782i	$0.166219\pi$
$972$		0			0
$973$	−4.15559			−0.133222
$974$	12.1307	+	21.0111i	0.388694	+	0.673238i
$975$		0			0
$976$	12.3122	−	7.10847i	0.394105	−	0.227537i
$977$		−	57.6325i		−	1.84383i	−0.387396	−	0.921913i	$-0.626625\pi$
$977$		−	57.6325i		−	1.84383i	0.387396	−	0.921913i	$-0.373375\pi$
$978$		0			0
$979$	6.81273	−	3.93333i	0.217736	−	0.125710i
$980$	−20.2053	+	11.6655i	−0.645434	+	0.372641i
$981$		0			0
$982$	27.8901	+	16.1023i	0.890008	+	0.513846i
$983$	19.8239	+	34.3361i	0.632286	+	1.09515i	0.987083	+	0.160208i	$0.0512164\pi$
$983$	19.8239	+	34.3361i	0.632286	+	1.09515i	−0.354798	+	0.934943i	$0.615450\pi$
$984$		0			0
$985$	18.7607	−	10.8315i	0.597764	−	0.345119i
$986$	−5.89460	−	3.40325i	−0.187722	−	0.108382i
$987$		0			0
$988$	0.260033	−	0.450390i	0.00827274	−	0.0143288i
$989$	68.9699			2.19312
$990$		0			0
$991$			18.8014i			0.597247i	0.954371	+	0.298624i	$0.0965275\pi$
$991$			18.8014i			0.597247i	−0.954371	+	0.298624i	$0.903472\pi$
$992$	4.15963			0.132069
$993$		0			0
$994$	0.869092	+	0.501770i	0.0275659	+	0.0159152i
$995$	22.8690	−	39.6103i	0.724996	−	1.25573i
$996$		0			0
$997$	−27.1011	+	15.6468i	−0.858300	+	0.495540i	−0.863443	−	0.504447i	$-0.831696\pi$
$997$	−27.1011	+	15.6468i	−0.858300	+	0.495540i	0.00514262	+	0.999987i	$0.498363\pi$
$998$	−18.4340			−0.583518
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1998.2.t.a.397.37		76
3.2	odd	2		666.2.t.a.619.3	yes	76
9.4	even	3		1998.2.k.a.1063.37		76
9.5	odd	6		666.2.k.a.175.16	✓	76
37.11	even	6		1998.2.k.a.1639.2		76
111.11	odd	6		666.2.k.a.529.35	yes	76
333.85	even	6	inner	1998.2.t.a.307.37		76
333.122	odd	6		666.2.t.a.85.3	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.16	✓	76	9.5	odd	6
666.2.k.a.529.35	yes	76	111.11	odd	6
666.2.t.a.85.3	yes	76	333.122	odd	6
666.2.t.a.619.3	yes	76	3.2	odd	2
1998.2.k.a.1063.37		76	9.4	even	3
1998.2.k.a.1639.2		76	37.11	even	6
1998.2.t.a.307.37		76	333.85	even	6	inner
1998.2.t.a.397.37		76	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1998 = 2 \cdot 3^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1998.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.98479 + 1.72327i) q^{5} -0.480194 q^{7} -1.00000i q^{8} +3.44654 q^{10} +(-1.57883 + 2.73461i) q^{11} +(1.16995 + 0.675468i) q^{13} +(-0.415860 + 0.240097i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.944880 - 0.545527i) q^{17} +(0.333391 - 0.192483i) q^{19} +(2.98479 - 1.72327i) q^{20} +3.15766i q^{22} +(6.91907 - 3.99473i) q^{23} +(3.43932 + 5.95707i) q^{25} +1.35094 q^{26} +(-0.240097 + 0.415860i) q^{28} +(5.40267 + 3.11923i) q^{29} +(-3.60235 + 2.07982i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.09105 q^{34} +(-1.43328 - 0.827504i) q^{35} +(5.65702 + 2.23564i) q^{37} +(0.192483 - 0.333391i) q^{38} +(1.72327 - 2.98479i) q^{40} +(-1.65030 + 2.85840i) q^{41} +(7.47606 + 4.31631i) q^{43} +(1.57883 + 2.73461i) q^{44} +(3.99473 - 6.91907i) q^{46} +(5.93648 - 10.2823i) q^{47} -6.76941 q^{49} +(5.95707 + 3.43932i) q^{50} +(1.16995 - 0.675468i) q^{52} +(-1.47126 + 2.54830i) q^{53} +(-9.42495 + 5.44150i) q^{55} +0.480194i q^{56} +6.23847 q^{58} +0.340484i q^{59} +14.2169i q^{61} +(-2.07982 + 3.60235i) q^{62} -1.00000 q^{64} +(2.32803 + 4.03226i) q^{65} +(4.44667 - 7.70185i) q^{67} +(-0.944880 + 0.545527i) q^{68} -1.65501 q^{70} +(-1.04493 - 1.80988i) q^{71} -7.32053 q^{73} +(6.01695 - 0.892387i) q^{74} -0.384966i q^{76} +(0.758145 - 1.31315i) q^{77} +16.2973i q^{79} -3.44654i q^{80} +3.30060i q^{82} +(-5.37919 - 9.31702i) q^{83} +(-1.88018 - 3.25657i) q^{85} +8.63261 q^{86} +(2.73461 + 1.57883i) q^{88} +(-2.15753 - 1.24565i) q^{89} +(-0.561801 - 0.324356i) q^{91} -7.98946i q^{92} -11.8730i q^{94} +1.32680 q^{95} +(-10.9363 - 6.31410i) q^{97} +(-5.86248 + 3.38471i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) \) 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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