LMFDB - Embedded newform 925.2.y.b.532.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			532.9
Character	$\chi$	$=$	925.532
Dual form			925.2.y.b.193.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212566 + 0.122725i) q^{2} +(0.491666 - 1.83492i) q^{3} +(-0.969877 - 1.67988i) q^{4} +(0.329702 - 0.329702i) q^{6} +(-1.00868 + 3.76446i) q^{7} -0.967013i q^{8} +(-0.527123 - 0.304334i) q^{9} +4.37395i q^{11} +(-3.55930 + 0.953710i) q^{12} +(-4.43371 + 2.55980i) q^{13} +(-0.676405 + 0.676405i) q^{14} +(-1.82108 + 3.15420i) q^{16} +(-1.24200 + 2.15121i) q^{17} +(-0.0746989 - 0.129382i) q^{18} +(-0.196130 + 0.731966i) q^{19} +(6.41155 + 3.70171i) q^{21} +(-0.536793 + 0.929753i) q^{22} +3.38111i q^{23} +(-1.77439 - 0.475447i) q^{24} -1.25661 q^{26} +(3.21217 - 3.21217i) q^{27} +(7.30213 - 1.95660i) q^{28} +(-4.99116 + 4.99116i) q^{29} +(-5.96470 - 5.96470i) q^{31} +(-2.44911 + 1.41400i) q^{32} +(8.02585 + 2.15052i) q^{33} +(-0.528015 + 0.304850i) q^{34} +1.18067i q^{36} +(3.11652 - 5.22373i) q^{37} +(-0.131521 + 0.131521i) q^{38} +(2.51713 + 9.39407i) q^{39} +(4.18352 - 2.41536i) q^{41} +(0.908585 + 1.57371i) q^{42} -3.40053i q^{43} +(7.34770 - 4.24219i) q^{44} +(-0.414947 + 0.718709i) q^{46} +(-5.91409 - 5.91409i) q^{47} +(4.89234 + 4.89234i) q^{48} +(-7.09153 - 4.09430i) q^{49} +(3.33665 + 3.33665i) q^{51} +(8.60030 + 4.96539i) q^{52} +(0.158224 + 0.590502i) q^{53} +(1.07701 - 0.288584i) q^{54} +(3.64028 + 0.975410i) q^{56} +(1.24667 + 0.719765i) q^{57} +(-1.67349 + 0.448410i) q^{58} +(-9.92739 + 2.66004i) q^{59} +(-2.63598 + 9.83759i) q^{61} +(-0.535874 - 1.99991i) q^{62} +(1.67735 - 1.67735i) q^{63} +6.59018 q^{64} +(1.44210 + 1.44210i) q^{66} +(12.4015 + 3.32297i) q^{67} +4.81836 q^{68} +(6.20407 + 1.66238i) q^{69} +(5.23213 + 9.06231i) q^{71} +(-0.294295 + 0.509734i) q^{72} +(3.10809 + 3.10809i) q^{73} +(1.30355 - 0.727912i) q^{74} +(1.41983 - 0.380443i) q^{76} +(-16.4656 - 4.41193i) q^{77} +(-0.617830 + 2.30577i) q^{78} +(-0.743780 + 2.77583i) q^{79} +(-5.22776 - 9.05475i) q^{81} +1.18570 q^{82} +(-1.55418 - 5.80029i) q^{83} -14.3608i q^{84} +(0.417330 - 0.722837i) q^{86} +(6.70440 + 11.6124i) q^{87} +4.22967 q^{88} +(-0.387792 - 1.44726i) q^{89} +(-5.16406 - 19.2725i) q^{91} +(5.67985 - 3.27926i) q^{92} +(-13.8774 + 8.01211i) q^{93} +(-0.531327 - 1.98294i) q^{94} +(1.39043 + 5.18914i) q^{96} -6.03559 q^{97} +(-1.00495 - 1.74062i) q^{98} +(1.33114 - 2.30561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.212566	+	0.122725i	0.150307	+	0.0867797i	0.573267	−	0.819369i	$-0.305676\pi$
$2$	0.212566	+	0.122725i	0.150307	+	0.0867797i	−0.422960	+	0.906148i	$0.639009\pi$
$3$	0.491666	−	1.83492i	0.283863	−	1.05939i	−0.665803	−	0.746128i	$-0.731911\pi$
$3$	0.491666	−	1.83492i	0.283863	−	1.05939i	0.949666	−	0.313264i	$-0.101423\pi$
$4$	−0.969877	−	1.67988i	−0.484939	−	0.839938i
$5$		0			0
$5$		0			0
$6$	0.329702	−	0.329702i	0.134600	−	0.134600i
$7$	−1.00868	+	3.76446i	−0.381247	+	1.42283i	0.462753	+	0.886487i	$0.346862\pi$
$7$	−1.00868	+	3.76446i	−0.381247	+	1.42283i	−0.843999	+	0.536344i	$0.819805\pi$
$8$		−	0.967013i		−	0.341891i
$9$	−0.527123	−	0.304334i	−0.175708	−	0.101445i
$10$		0			0
$11$			4.37395i			1.31880i	0.751794	+	0.659398i	$0.229189\pi$
$11$			4.37395i			1.31880i	−0.751794	+	0.659398i	$0.770811\pi$
$12$	−3.55930	+	0.953710i	−1.02748	+	0.275312i
$13$	−4.43371	+	2.55980i	−1.22969	+	0.709961i	−0.966965	−	0.254909i	$-0.917954\pi$
$13$	−4.43371	+	2.55980i	−1.22969	+	0.709961i	−0.262724	+	0.964871i	$0.584621\pi$
$14$	−0.676405	+	0.676405i	−0.180777	+	0.180777i
$15$		0			0
$16$	−1.82108	+	3.15420i	−0.455269	+	0.788550i
$17$	−1.24200	+	2.15121i	−0.301230	+	0.521746i	−0.976415	−	0.215903i	$-0.930731\pi$
$17$	−1.24200	+	2.15121i	−0.301230	+	0.521746i	0.675185	+	0.737649i	$0.264064\pi$
$18$	−0.0746989	−	0.129382i	−0.0176067	−	0.0304957i
$19$	−0.196130	+	0.731966i	−0.0449952	+	0.167924i	−0.984767	−	0.173877i	$-0.944370\pi$
$19$	−0.196130	+	0.731966i	−0.0449952	+	0.167924i	0.939772	+	0.341802i	$0.111037\pi$
$20$		0			0
$21$	6.41155	+	3.70171i	1.39911	+	0.807779i
$22$	−0.536793	+	0.929753i	−0.114445	+	0.198224i
$23$			3.38111i			0.705010i	0.935810	+	0.352505i	$0.114670\pi$
$23$			3.38111i			0.705010i	−0.935810	+	0.352505i	$0.885330\pi$
$24$	−1.77439	−	0.475447i	−0.362196	−	0.0970502i
$25$		0			0
$26$	−1.25661			−0.246441
$27$	3.21217	−	3.21217i	0.618182	−	0.618182i
$28$	7.30213	−	1.95660i	1.37997	−	0.369762i
$29$	−4.99116	+	4.99116i	−0.926835	+	0.926835i	−0.997500	−	0.0706651i	$-0.977488\pi$
$29$	−4.99116	+	4.99116i	−0.926835	+	0.926835i	0.0706651	+	0.997500i	$0.477488\pi$
$30$		0			0
$31$	−5.96470	−	5.96470i	−1.07129	−	1.07129i	−0.997256	−	0.0740358i	$-0.976412\pi$
$31$	−5.96470	−	5.96470i	−1.07129	−	1.07129i	−0.0740358	−	0.997256i	$-0.523588\pi$
$32$	−2.44911	+	1.41400i	−0.432946	+	0.249962i
$33$	8.02585	+	2.15052i	1.39712	+	0.374358i
$34$	−0.528015	+	0.304850i	−0.0905538	+	0.0522813i
$35$		0			0
$36$			1.18067i			0.196778i
$37$	3.11652	−	5.22373i	0.512352	−	0.858775i
$37$	3.11652	−	5.22373i	0.512352	−	0.858775i
$38$	−0.131521	+	0.131521i	−0.0213355	+	0.0213355i
$39$	2.51713	+	9.39407i	0.403064	+	1.50425i
$40$		0			0
$41$	4.18352	−	2.41536i	0.653357	−	0.377216i	−0.136384	−	0.990656i	$-0.543548\pi$
$41$	4.18352	−	2.41536i	0.653357	−	0.377216i	0.789741	+	0.613440i	$0.210215\pi$
$42$	0.908585	+	1.57371i	0.140198	+	0.242829i
$43$		−	3.40053i		−	0.518576i	−0.965800	−	0.259288i	$-0.916512\pi$
$43$		−	3.40053i		−	0.518576i	0.965800	−	0.259288i	$-0.0834879\pi$
$44$	7.34770	−	4.24219i	1.10771	−	0.639535i
$45$		0			0
$46$	−0.414947	+	0.718709i	−0.0611806	+	0.105968i
$47$	−5.91409	−	5.91409i	−0.862659	−	0.862659i	0.128987	−	0.991646i	$-0.458827\pi$
$47$	−5.91409	−	5.91409i	−0.862659	−	0.862659i	−0.991646	+	0.128987i	$0.958827\pi$
$48$	4.89234	+	4.89234i	0.706149	+	0.706149i
$49$	−7.09153	−	4.09430i	−1.01308	−	0.584900i
$50$		0			0
$51$	3.33665	+	3.33665i	0.467225	+	0.467225i
$52$	8.60030	+	4.96539i	1.19265	+	0.688575i
$53$	0.158224	+	0.590502i	0.0217338	+	0.0811116i	0.975941	−	0.218035i	$-0.0699647\pi$
$53$	0.158224	+	0.590502i	0.0217338	+	0.0811116i	−0.954207	+	0.299147i	$0.903298\pi$
$54$	1.07701	−	0.288584i	0.146563	−	0.0392713i
$55$		0			0
$56$	3.64028	+	0.975410i	0.486453	+	0.130345i
$57$	1.24667	+	0.719765i	0.165125	+	0.0953352i
$58$	−1.67349	+	0.448410i	−0.219740	+	0.0588792i
$59$	−9.92739	+	2.66004i	−1.29244	+	0.346307i	−0.838585	−	0.544771i	$-0.816617\pi$
$59$	−9.92739	+	2.66004i	−1.29244	+	0.346307i	−0.453851	+	0.891078i	$0.649950\pi$
$60$		0			0
$61$	−2.63598	+	9.83759i	−0.337502	+	1.25957i	0.563629	+	0.826028i	$0.309405\pi$
$61$	−2.63598	+	9.83759i	−0.337502	+	1.25957i	−0.901131	+	0.433547i	$0.857262\pi$
$62$	−0.535874	−	1.99991i	−0.0680561	−	0.253989i
$63$	1.67735	−	1.67735i	0.211327	−	0.211327i
$64$	6.59018			0.823773
$65$		0			0
$66$	1.44210	+	1.44210i	0.177510	+	0.177510i
$67$	12.4015	+	3.32297i	1.51508	+	0.405966i	0.918120	−	0.396302i	$-0.129707\pi$
$67$	12.4015	+	3.32297i	1.51508	+	0.405966i	0.596964	+	0.802268i	$0.296373\pi$
$68$	4.81836			0.584312
$69$	6.20407	+	1.66238i	0.746882	+	0.200126i
$70$		0			0
$71$	5.23213	+	9.06231i	0.620940	+	1.07550i	0.989311	+	0.145820i	$0.0465821\pi$
$71$	5.23213	+	9.06231i	0.620940	+	1.07550i	−0.368372	+	0.929679i	$0.620085\pi$
$72$	−0.294295	+	0.509734i	−0.0346830	+	0.0600727i
$73$	3.10809	+	3.10809i	0.363775	+	0.363775i	0.865201	−	0.501426i	$-0.167191\pi$
$73$	3.10809	+	3.10809i	0.363775	+	0.363775i	−0.501426	+	0.865201i	$0.667191\pi$
$74$	1.30355	−	0.727912i	0.151534	−	0.0846180i
$75$		0			0
$76$	1.41983	−	0.380443i	0.162866	−	0.0436398i
$77$	−16.4656	−	4.41193i	−1.87642	−	0.502786i
$78$	−0.617830	+	2.30577i	−0.0699555	+	0.261077i
$79$	−0.743780	+	2.77583i	−0.0836818	+	0.312305i	−0.995061	−	0.0992622i	$-0.968352\pi$
$79$	−0.743780	+	2.77583i	−0.0836818	+	0.312305i	0.911379	+	0.411567i	$0.135018\pi$
$80$		0			0
$81$	−5.22776	−	9.05475i	−0.580863	−	1.00608i
$82$	1.18570			0.130939
$83$	−1.55418	−	5.80029i	−0.170594	−	0.636664i	−0.997260	−	0.0739721i	$-0.976432\pi$
$83$	−1.55418	−	5.80029i	−0.170594	−	0.636664i	0.826667	−	0.562692i	$-0.190234\pi$
$84$		−	14.3608i		−	1.56689i
$85$		0			0
$86$	0.417330	−	0.722837i	0.0450019	−	0.0779456i
$87$	6.70440	+	11.6124i	0.718787	+	1.24498i
$88$	4.22967			0.450884
$89$	−0.387792	−	1.44726i	−0.0411059	−	0.153409i	0.942322	−	0.334706i	$-0.108637\pi$
$89$	−0.387792	−	1.44726i	−0.0411059	−	0.153409i	−0.983428	+	0.181297i	$0.941970\pi$
$90$		0			0
$91$	−5.16406	−	19.2725i	−0.541341	−	2.02031i
$92$	5.67985	−	3.27926i	0.592165	−	0.341887i
$93$	−13.8774	+	8.01211i	−1.43902	+	0.830817i
$94$	−0.531327	−	1.98294i	−0.0548022	−	0.204525i
$95$		0			0
$96$	1.39043	+	5.18914i	0.141910	+	0.529614i
$97$	−6.03559			−0.612821			−0.306411	−	0.951899i	$-0.599128\pi$
$97$	−6.03559			−0.612821			−0.306411	+	0.951899i	$0.599128\pi$
$98$	−1.00495	−	1.74062i	−0.101515	−	0.175829i
$99$	1.33114	−	2.30561i	0.133785	−	0.231722i
$100$		0			0
$101$			1.89841i			0.188899i	0.995530	+	0.0944493i	$0.0301090\pi$
$101$			1.89841i			0.188899i	−0.995530	+	0.0944493i	$0.969891\pi$
$102$	0.299768	+	1.11875i	0.0296815	+	0.110773i
$103$	−4.74353			−0.467394			−0.233697	−	0.972309i	$-0.575082\pi$
$103$	−4.74353			−0.467394			−0.233697	+	0.972309i	$0.575082\pi$
$104$	2.47536	+	4.28745i	0.242729	+	0.420419i
$105$		0			0
$106$	−0.0388362	+	0.144939i	−0.00377210	+	0.0140777i
$107$	−0.157247	+	0.586853i	−0.0152016	+	0.0567332i	−0.973110	−	0.230341i	$-0.926016\pi$
$107$	−0.157247	+	0.586853i	−0.0152016	+	0.0567332i	0.957908	+	0.287074i	$0.0926826\pi$
$108$	−8.51145	−	2.28064i	−0.819015	−	0.219454i
$109$	6.60438	−	1.76964i	0.632585	−	0.169501i	0.0717424	−	0.997423i	$-0.477144\pi$
$109$	6.60438	−	1.76964i	0.632585	−	0.169501i	0.560842	+	0.827923i	$0.310477\pi$
$110$		0			0
$111$	−8.05284	−	8.28689i	−0.764342	−	0.786556i
$112$	−10.0370	−	10.0370i	−0.948404	−	0.948404i
$113$	−0.890996	+	1.54325i	−0.0838178	+	0.145177i	−0.904887	−	0.425652i	$-0.860045\pi$
$113$	−0.890996	+	1.54325i	−0.0838178	+	0.145177i	0.821069	+	0.570829i	$0.193378\pi$
$114$	0.176666	+	0.305995i	0.0165463	+	0.0286590i
$115$		0			0
$116$	13.2253	+	3.54372i	1.22794	+	0.329026i
$117$	3.11614			0.288088
$118$	−2.43668	−	0.652906i	−0.224314	−	0.0601048i
$119$	−6.84536	−	6.84536i	−0.627513	−	0.627513i
$120$		0			0
$121$	−8.13144			−0.739222
$122$	−1.76764	+	1.76764i	−0.160034	+	0.160034i
$123$	−2.37510	−	8.86398i	−0.214155	−	0.799238i
$124$	−4.23493	+	15.8050i	−0.380308	+	1.41933i
$125$		0			0
$126$	0.562402	−	0.150695i	0.0501027	−	0.0134250i
$127$	3.66591	−	0.982278i	0.325297	−	0.0871631i	−0.0924749	−	0.995715i	$-0.529478\pi$
$127$	3.66591	−	0.982278i	0.325297	−	0.0871631i	0.417772	+	0.908552i	$0.362811\pi$
$128$	6.29907	+	3.63677i	0.556765	+	0.321448i
$129$	−6.23971	−	1.67192i	−0.549376	−	0.147205i
$130$		0			0
$131$	15.2542	−	4.08734i	1.33276	−	0.357113i	0.479019	−	0.877805i	$-0.340993\pi$
$131$	15.2542	−	4.08734i	1.33276	−	0.357113i	0.853745	+	0.520692i	$0.174326\pi$
$132$	−4.17148	−	15.5682i	−0.363081	−	1.35504i
$133$	−2.55762	−	1.47664i	−0.221774	−	0.128041i
$134$	2.22832	+	2.22832i	0.192498	+	0.192498i
$135$		0			0
$136$	2.08025	+	1.20103i	0.178380	+	0.102988i
$137$	9.67862	+	9.67862i	0.826900	+	0.826900i	0.987087	−	0.160186i	$-0.0512095\pi$
$137$	9.67862	+	9.67862i	0.826900	+	0.826900i	−0.160186	+	0.987087i	$0.551210\pi$
$138$	1.11476	+	1.11476i	0.0948946	+	0.0948946i
$139$	−8.37582	+	14.5073i	−0.710427	+	1.23050i	0.254269	+	0.967133i	$0.418165\pi$
$139$	−8.37582	+	14.5073i	−0.710427	+	1.23050i	−0.964697	+	0.263363i	$0.915168\pi$
$140$		0			0
$141$	−13.7596	+	7.94413i	−1.15877	+	0.669017i
$142$			2.56845i			0.215540i
$143$	−11.1964	−	19.3928i	−0.936294	−	1.62171i
$144$	1.91986	−	1.10843i	0.159989	−	0.0923694i
$145$		0			0
$146$	0.279234	+	1.04211i	0.0231096	+	0.0862460i
$147$	−10.9994	+	10.9994i	−0.907213	+	0.907213i
$148$	−11.7979	−	0.168989i	−0.969778	−	0.0138908i
$149$		−	2.73367i		−	0.223951i	−0.993711	−	0.111976i	$-0.964282\pi$
$149$		−	2.73367i		−	0.223951i	0.993711	−	0.111976i	$-0.0357179\pi$
$150$		0			0
$151$	−13.6955	+	7.90713i	−1.11453	+	0.643473i	−0.939998	−	0.341179i	$-0.889174\pi$
$151$	−13.6955	+	7.90713i	−1.11453	+	0.643473i	−0.174530	+	0.984652i	$0.555840\pi$
$152$	0.707820	+	0.189660i	0.0574118	+	0.0153834i
$153$	1.30938	−	0.755968i	0.105857	−	0.0611164i
$154$	−2.95856	−	2.95856i	−0.238408	−	0.238408i
$155$		0			0
$156$	13.3396	−	13.3396i	1.06802	−	1.06802i
$157$	−4.78011	+	1.28083i	−0.381494	+	0.102221i	−0.444469	−	0.895794i	$-0.646608\pi$
$157$	−4.78011	+	1.28083i	−0.381494	+	0.102221i	0.0629751	+	0.998015i	$0.479941\pi$
$158$	−0.498766	+	0.498766i	−0.0396797	+	0.0396797i
$159$	1.16132			0.0920984
$160$		0			0
$161$	−12.7281	−	3.41047i	−1.00311	−	0.268783i
$162$		−	2.56631i		−	0.201628i
$163$	−8.18168	+	14.1711i	−0.640839	+	1.10996i	0.344407	+	0.938820i	$0.388080\pi$
$163$	−8.18168	+	14.1711i	−0.640839	+	1.10996i	−0.985246	+	0.171145i	$0.945253\pi$
$164$	−8.11501	−	4.68520i	−0.633676	−	0.365853i
$165$		0			0
$166$	0.381474	−	1.42368i	0.0296081	−	0.110499i
$167$	−3.90611	−	6.76558i	−0.302264	−	0.523537i	0.674384	−	0.738380i	$-0.264409\pi$
$167$	−3.90611	−	6.76558i	−0.302264	−	0.523537i	−0.976648	+	0.214844i	$0.931076\pi$
$168$	3.57960	−	6.20005i	0.276172	−	0.478344i
$169$	6.60518	−	11.4405i	0.508091	−	0.880039i
$170$		0			0
$171$	0.326147	−	0.326147i	0.0249411	−	0.0249411i
$172$	−5.71248	+	3.29810i	−0.435572	+	0.251478i
$173$	20.1044	−	5.38695i	1.52851	−	0.409562i	0.605976	−	0.795483i	$-0.292783\pi$
$173$	20.1044	−	5.38695i	1.52851	−	0.409562i	0.922532	+	0.385921i	$0.126116\pi$
$174$			3.29119i			0.249504i
$175$		0			0
$176$	−13.7963	−	7.96530i	−1.03994	−	0.600407i
$177$			19.5238i			1.46750i
$178$	0.0951836	−	0.355230i	0.00713431	−	0.0266256i
$179$	8.72104	−	8.72104i	0.651841	−	0.651841i	−0.301595	−	0.953436i	$-0.597519\pi$
$179$	8.72104	−	8.72104i	0.651841	−	0.651841i	0.953436	+	0.301595i	$0.0975190\pi$
$180$		0			0
$181$	−1.85478	−	3.21258i	−0.137865	−	0.238789i	0.788823	−	0.614620i	$-0.210691\pi$
$181$	−1.85478	−	3.21258i	−0.137865	−	0.238789i	−0.926688	+	0.375831i	$0.877357\pi$
$182$	1.26752	−	4.73045i	0.0939548	−	0.350644i
$183$	16.7552	+	9.67361i	1.23858	+	0.715094i
$184$	3.26958			0.241036
$185$		0			0
$186$	−3.93314			−0.288392
$187$	−9.40930	−	5.43246i	−0.688076	−	0.397261i
$188$	−4.19900	+	15.6709i	−0.306244	+	1.14292i
$189$	8.85201	+	15.3321i	0.643889	+	1.11525i
$190$		0			0
$191$	7.04757	−	7.04757i	0.509945	−	0.509945i	−0.404565	−	0.914509i	$-0.632577\pi$
$191$	7.04757	−	7.04757i	0.509945	−	0.509945i	0.914509	+	0.404565i	$0.132577\pi$
$192$	3.24016	−	12.0925i	0.233839	−	0.872698i
$193$			4.50078i			0.323974i	0.986793	+	0.161987i	$0.0517902\pi$
$193$			4.50078i			0.323974i	−0.986793	+	0.161987i	$0.948210\pi$
$194$	−1.28296	−	0.740718i	−0.0921112	−	0.0531804i
$195$		0			0
$196$			15.8839i			1.13456i
$197$	4.63427	−	1.24175i	0.330178	−	0.0884710i	−0.0899217	−	0.995949i	$-0.528662\pi$
$197$	4.63427	−	1.24175i	0.330178	−	0.0884710i	0.420100	+	0.907478i	$0.361995\pi$
$198$	0.565911	−	0.326729i	0.0402176	−	0.0232196i
$199$	−2.93495	+	2.93495i	−0.208053	+	0.208053i	−0.803440	−	0.595386i	$-0.796999\pi$
$199$	−2.93495	+	2.93495i	−0.208053	+	0.208053i	0.595386	+	0.803440i	$0.296999\pi$
$200$		0			0
$201$	12.1948	−	21.1220i	0.860153	−	1.48983i
$202$	−0.232982	+	0.403537i	−0.0163926	+	0.0283927i
$203$	−13.7545	−	23.8235i	−0.965378	−	1.67208i
$204$	2.36902	−	8.84131i	0.165865	−	0.619015i
$205$		0			0
$206$	−1.00831	−	0.582150i	−0.0702525	−	0.0405603i
$207$	1.02899	−	1.78226i	0.0715196	−	0.123876i
$208$		−	18.6464i		−	1.29290i
$209$	−3.20158	−	0.857861i	−0.221458	−	0.0593395i
$210$		0			0
$211$	−16.2172			−1.11644			−0.558221	−	0.829692i	$-0.688516\pi$
$211$	−16.2172			−1.11644			−0.558221	+	0.829692i	$0.688516\pi$
$212$	0.838512	−	0.838512i	0.0575892	−	0.0575892i
$213$	19.2011	−	5.14492i	1.31564	−	0.352524i
$214$	−0.105447	+	0.105447i	−0.00720819	+	0.00720819i
$215$		0			0
$216$	−3.10621	−	3.10621i	−0.211351	−	0.211351i
$217$	28.4704	−	16.4374i	1.93269	−	1.11584i
$218$	1.62104	+	0.434358i	0.109791	+	0.0294184i
$219$	7.23124	−	4.17496i	0.488642	−	0.282118i
$220$		0			0
$221$		−	12.7171i		−	0.855447i
$222$	−0.694751	−	2.74979i	−0.0466287	−	0.184554i
$223$	−12.0819	+	12.0819i	−0.809065	+	0.809065i	−0.984492	−	0.175427i	$-0.943869\pi$
$223$	−12.0819	+	12.0819i	−0.809065	+	0.809065i	0.175427	+	0.984492i	$0.443869\pi$
$224$	−2.85255	−	10.6459i	−0.190594	−	0.711307i
$225$		0			0
$226$	−0.378791	+	0.218695i	−0.0251968	+	0.0145474i
$227$	2.22445	+	3.85285i	0.147642	+	0.255723i	0.930355	−	0.366659i	$-0.119498\pi$
$227$	2.22445	+	3.85285i	0.147642	+	0.255723i	−0.782714	+	0.622382i	$0.786165\pi$
$228$		−	2.79233i		−	0.184927i
$229$	7.06526	−	4.07913i	0.466886	−	0.269556i	−0.248050	−	0.968747i	$-0.579790\pi$
$229$	7.06526	−	4.07913i	0.466886	−	0.269556i	0.714935	+	0.699191i	$0.246456\pi$
$230$		0			0
$231$	−16.1911	+	28.0438i	−1.06530	+	1.84515i
$232$	4.82651	+	4.82651i	0.316876	+	0.316876i
$233$	9.86567	+	9.86567i	0.646322	+	0.646322i	0.952102	−	0.305780i	$-0.0989173\pi$
$233$	9.86567	+	9.86567i	0.646322	+	0.646322i	−0.305780	+	0.952102i	$0.598917\pi$
$234$	0.662386	+	0.382429i	0.0433015	+	0.0250001i
$235$		0			0
$236$	14.0969	+	14.0969i	0.917629	+	0.917629i
$237$	4.72773	+	2.72956i	0.307099	+	0.177304i
$238$	−0.614994	−	2.29519i	−0.0398641	−	0.148775i
$239$	15.3216	−	4.10540i	0.991069	−	0.265556i	0.273369	−	0.961909i	$-0.411862\pi$
$239$	15.3216	−	4.10540i	0.991069	−	0.265556i	0.717699	+	0.696353i	$0.245195\pi$
$240$		0			0
$241$	15.9979	+	4.28663i	1.03052	+	0.276126i	0.734178	−	0.678957i	$-0.237568\pi$
$241$	15.9979	+	4.28663i	1.03052	+	0.276126i	0.296338	+	0.955083i	$0.404235\pi$
$242$	−1.72847	−	0.997931i	−0.111110	−	0.0641495i
$243$	−6.02136	+	1.61342i	−0.386270	+	0.103501i
$244$	19.0825	−	5.11314i	1.22163	−	0.327336i
$245$		0			0
$246$	0.582967	−	2.17566i	0.0371686	−	0.138715i
$247$	−1.00411	−	3.74738i	−0.0638898	−	0.238440i
$248$	−5.76794	+	5.76794i	−0.366264	+	0.366264i
$249$	−11.4072			−0.722902
$250$		0			0
$251$	3.53612	+	3.53612i	0.223198	+	0.223198i	0.809844	−	0.586646i	$-0.199552\pi$
$251$	3.53612	+	3.53612i	0.223198	+	0.223198i	−0.586646	+	0.809844i	$0.699552\pi$
$252$	−4.44458	−	1.19092i	−0.279982	−	0.0750209i
$253$	−14.7888			−0.929765
$254$	0.899798	+	0.241100i	0.0564583	+	0.0151280i
$255$		0			0
$256$	−5.69753	−	9.86842i	−0.356096	−	0.616776i
$257$	10.4856	−	18.1616i	0.654073	−	1.13289i	−0.328052	−	0.944660i	$-0.606392\pi$
$257$	10.4856	−	18.1616i	0.654073	−	1.13289i	0.982125	−	0.188229i	$-0.0602746\pi$
$258$	−1.12116	−	1.12116i	−0.0698005	−	0.0698005i
$259$	16.5209	+	17.0011i	1.02656	+	1.05640i
$260$		0			0
$261$	4.14993	−	1.11197i	0.256874	−	0.0688293i
$262$	3.74414	+	1.00324i	0.231314	+	0.0619803i
$263$	−3.00781	+	11.2253i	−0.185470	+	0.692182i	0.809060	+	0.587726i	$0.199977\pi$
$263$	−3.00781	+	11.2253i	−0.185470	+	0.692182i	−0.994530	+	0.104456i	$0.966690\pi$
$264$	2.07958	−	7.76110i	0.127989	−	0.477663i
$265$		0			0
$266$	−0.362442	−	0.627768i	−0.0222228	−	0.0384910i
$267$	−2.84627			−0.174189
$268$	−6.44575	−	24.0559i	−0.393737	−	1.46945i
$269$			20.4566i			1.24726i	0.781719	+	0.623631i	$0.214343\pi$
$269$			20.4566i			1.24726i	−0.781719	+	0.623631i	$0.785657\pi$
$270$		0			0
$271$	11.4239	−	19.7867i	0.693951	−	1.20196i	−0.276582	−	0.960990i	$-0.589202\pi$
$271$	11.4239	−	19.7867i	0.693951	−	1.20196i	0.970533	−	0.240968i	$-0.0774650\pi$
$272$	−4.52357	−	7.83505i	−0.274282	−	0.475070i
$273$	−37.9026			−2.29397
$274$	0.869536	+	3.24515i	0.0525306	+	0.196047i
$275$		0			0
$276$	−3.22460	−	12.0344i	−0.194098	−	0.724384i
$277$	−11.9296	+	6.88756i	−0.716780	+	0.413833i	−0.813567	−	0.581472i	$-0.802477\pi$
$277$	−11.9296	+	6.88756i	−0.716780	+	0.413833i	0.0967861	+	0.995305i	$0.469144\pi$
$278$	−3.56083	+	2.05584i	−0.213564	+	0.123301i
$279$	1.32886	+	4.95939i	0.0795570	+	0.296911i
$280$		0			0
$281$	−6.14362	−	22.9283i	−0.366498	−	1.36779i	−0.865379	−	0.501118i	$-0.832922\pi$
$281$	−6.14362	−	22.9283i	−0.366498	−	1.36779i	0.498881	−	0.866670i	$-0.333744\pi$
$282$	−3.89978			−0.232228
$283$	10.5663	+	18.3014i	0.628102	+	1.08790i	0.987932	+	0.154887i	$0.0495013\pi$
$283$	10.5663	+	18.3014i	0.628102	+	1.08790i	−0.359830	+	0.933018i	$0.617165\pi$
$284$	10.1490	−	17.5787i	0.602235	−	1.04310i
$285$		0			0
$286$		−	5.49634i		−	0.325005i
$287$	4.87267	+	18.1850i	0.287624	+	1.07343i
$288$	1.72131			0.101429
$289$	5.41486	+	9.37881i	0.318521	+	0.551695i
$290$		0			0
$291$	−2.96749	+	11.0748i	−0.173957	+	0.649218i
$292$	2.20674	−	8.23568i	0.129140	−	0.481957i
$293$	0.477628	+	0.127980i	0.0279033	+	0.00747667i	0.272744	−	0.962087i	$-0.412069\pi$
$293$	0.477628	+	0.127980i	0.0279033	+	0.00747667i	−0.244840	+	0.969563i	$0.578736\pi$
$294$	−3.68799	+	0.988194i	−0.215088	+	0.0576326i
$295$		0			0
$296$	−5.05141	−	3.01371i	−0.293607	−	0.175168i
$297$	14.0499	+	14.0499i	0.815256	+	0.815256i
$298$	0.335490	−	0.581086i	0.0194344	−	0.0336614i
$299$	−8.65498	−	14.9909i	−0.500530	−	0.866944i
$300$		0			0
$301$	12.8012	+	3.43006i	0.737847	+	0.197706i
$302$	−3.88161			−0.223362
$303$	3.48343	+	0.933381i	0.200118	+	0.0536214i
$304$	−1.95160	−	1.95160i	−0.111932	−	0.111932i
$305$		0			0
$306$	0.371105			0.0212146
$307$	−13.0911	+	13.0911i	−0.747149	+	0.747149i	−0.973943	−	0.226794i	$-0.927176\pi$
$307$	−13.0911	+	13.0911i	−0.747149	+	0.747149i	0.226794	+	0.973943i	$0.427176\pi$
$308$	8.55807	+	31.9391i	0.487641	+	1.81990i
$309$	−2.33223	+	8.70400i	−0.132676	+	0.495153i
$310$		0			0
$311$	−25.2278	+	6.75978i	−1.43054	+	0.383312i	−0.889210	−	0.457499i	$-0.848745\pi$
$311$	−25.2278	+	6.75978i	−1.43054	+	0.383312i	−0.541329	+	0.840811i	$0.682079\pi$
$312$	9.08418	−	2.43410i	0.514291	−	0.137804i
$313$	14.5726	+	8.41349i	0.823691	+	0.475558i	0.851688	−	0.524050i	$-0.175579\pi$
$313$	14.5726	+	8.41349i	0.823691	+	0.475558i	−0.0279965	+	0.999608i	$0.508913\pi$
$314$	−1.17328	−	0.314379i	−0.0662119	−	0.0177414i
$315$		0			0
$316$	5.38442	−	1.44275i	0.302897	−	0.0811611i
$317$	−4.65369	−	17.3678i	−0.261377	−	0.975472i	−0.964431	−	0.264336i	$-0.914847\pi$
$317$	−4.65369	−	17.3678i	−0.261377	−	0.975472i	0.703054	−	0.711137i	$-0.251819\pi$
$318$	0.246856	+	0.142523i	0.0138430	+	0.00799227i
$319$	−21.8311	−	21.8311i	−1.22231	−	1.22231i
$320$		0			0
$321$	0.999515	+	0.577070i	0.0557875	+	0.0322089i
$322$	−2.28700	−	2.28700i	−0.127450	−	0.127450i
$323$	−1.33102	−	1.33102i	−0.0740599	−	0.0740599i
$324$	−10.1406	+	17.5640i	−0.563365	+	0.975778i
$325$		0			0
$326$	−3.47829	+	2.00819i	−0.192645	+	0.111224i
$327$		−	12.9886i		−	0.718270i
$328$	−2.33568	−	4.04552i	−0.128966	−	0.223376i
$329$	28.2288	−	16.2979i	1.55630	−	0.898533i
$330$		0			0
$331$	−1.17108	−	4.37053i	−0.0643683	−	0.240226i	0.926245	−	0.376923i	$-0.123018\pi$
$331$	−1.17108	−	4.37053i	−0.0643683	−	0.240226i	−0.990613	+	0.136697i	$0.956351\pi$
$332$	−8.23640	+	8.23640i	−0.452031	+	0.452031i
$333$	−3.23255	+	1.80508i	−0.177142	+	0.0989178i
$334$		−	1.91751i		−	0.104921i
$335$		0			0
$336$	−23.3519	+	13.4822i	−1.27395	+	0.735514i
$337$	−0.483946	−	0.129673i	−0.0263622	−	0.00706374i	0.245614	−	0.969368i	$-0.421010\pi$
$337$	−0.483946	−	0.129673i	−0.0263622	−	0.00706374i	−0.271976	+	0.962304i	$0.587677\pi$
$338$	2.80807	−	1.62124i	0.152739	−	0.0881839i
$339$	2.39367	+	2.39367i	0.130006	+	0.130006i
$340$		0			0
$341$	26.0893	−	26.0893i	1.41281	−	1.41281i
$342$	0.109354	−	0.0293013i	0.00591319	−	0.00158443i
$343$	3.27551	−	3.27551i	0.176861	−	0.176861i
$344$	−3.28836			−0.177296
$345$		0			0
$346$	4.93462	+	1.32223i	0.265287	+	0.0710834i
$347$		−	5.86619i		−	0.314914i	−0.987526	−	0.157457i	$-0.949670\pi$
$347$		−	5.86619i		−	0.314914i	0.987526	−	0.157457i	$-0.0503295\pi$
$348$	13.0049	−	22.5251i	0.697135	−	1.20747i
$349$	−18.2252	−	10.5223i	−0.975571	−	0.563246i	−0.0746410	−	0.997210i	$-0.523781\pi$
$349$	−18.2252	−	10.5223i	−0.975571	−	0.563246i	−0.900930	+	0.433964i	$0.857114\pi$
$350$		0			0
$351$	−6.01930	+	22.4643i	−0.321286	+	1.19906i
$352$	−6.18475	−	10.7123i	−0.329648	−	0.570967i
$353$	7.69762	−	13.3327i	0.409703	−	0.709627i	−0.585153	−	0.810923i	$-0.698966\pi$
$353$	7.69762	−	13.3327i	0.409703	−	0.709627i	0.994856	+	0.101296i	$0.0322989\pi$
$354$	−2.39606	+	4.15010i	−0.127349	+	0.220575i
$355$		0			0
$356$	−2.05511	+	2.05511i	−0.108920	+	0.108920i
$357$	−15.9263	+	9.19507i	−0.842910	+	0.486655i
$358$	2.92409	−	0.783507i	0.154543	−	0.0414096i
$359$			28.7191i			1.51574i	0.652407	+	0.757869i	$0.273759\pi$
$359$			28.7191i			1.51574i	−0.652407	+	0.757869i	$0.726241\pi$
$360$		0			0
$361$	15.9572	+	9.21288i	0.839851	+	0.484888i
$362$		−	0.910513i		−	0.0478555i
$363$	−3.99795	+	14.9206i	−0.209838	+	0.783126i
$364$	−27.3670	+	27.3670i	−1.43442	+	1.43442i
$365$		0			0
$366$	2.37439	+	4.11256i	0.124111	+	0.214967i
$367$	−2.96732	+	11.0742i	−0.154893	+	0.578068i	0.844222	+	0.535994i	$0.180063\pi$
$367$	−2.96732	+	11.0742i	−0.154893	+	0.578068i	−0.999115	+	0.0420738i	$0.986604\pi$
$368$	−10.6647	−	6.15727i	−0.555936	−	0.320970i
$369$	−2.94031			−0.153066
$370$		0			0
$371$	−2.38252			−0.123694
$372$	26.9187	+	15.5415i	1.39567	+	0.805791i
$373$	2.85417	−	10.6519i	0.147783	−	0.551535i	−0.851832	−	0.523815i	$-0.824508\pi$
$373$	2.85417	−	10.6519i	0.147783	−	0.551535i	0.999616	−	0.0277207i	$-0.00882491\pi$
$374$	−1.33340	−	2.30951i	−0.0689483	−	0.119422i
$375$		0			0
$376$	−5.71900	+	5.71900i	−0.294935	+	0.294935i
$377$	9.35296	−	34.9057i	0.481702	−	1.79774i
$378$			4.34545i			0.223506i
$379$	−24.3009	−	14.0302i	−1.24826	−	0.720681i	−0.277494	−	0.960727i	$-0.589504\pi$
$379$	−24.3009	−	14.0302i	−1.24826	−	0.720681i	−0.970761	+	0.240046i	$0.922837\pi$
$380$		0			0
$381$		−	7.20961i		−	0.369359i
$382$	2.36299	−	0.633161i	0.120901	−	0.0323953i
$383$	−7.08041	+	4.08788i	−0.361792	+	0.208881i	−0.669867	−	0.742481i	$-0.733649\pi$
$383$	−7.08041	+	4.08788i	−0.361792	+	0.208881i	0.308075	+	0.951362i	$0.400315\pi$
$384$	9.77022	−	9.77022i	0.498585	−	0.498585i
$385$		0			0
$386$	−0.552359	+	0.956713i	−0.0281143	+	0.0486954i
$387$	−1.03490	+	1.79250i	−0.0526069	+	0.0911178i
$388$	5.85378	+	10.1390i	0.297181	+	0.514732i
$389$	6.73768	−	25.1454i	0.341614	−	1.27492i	−0.554904	−	0.831914i	$-0.687245\pi$
$389$	6.73768	−	25.1454i	0.341614	−	1.27492i	0.896518	−	0.443007i	$-0.146088\pi$
$390$		0			0
$391$	−7.27349	−	4.19935i	−0.367836	−	0.212370i
$392$	−3.95924	+	6.85760i	−0.199972	+	0.346361i
$393$		−	29.9998i		−	1.51329i
$394$	1.13748	+	0.304787i	0.0573055	+	0.0153550i
$395$		0			0
$396$	−5.16418			−0.259510
$397$	−24.8666	+	24.8666i	−1.24802	+	1.24802i	−0.291423	+	0.956594i	$0.594129\pi$
$397$	−24.8666	+	24.8666i	−1.24802	+	1.24802i	−0.956594	+	0.291423i	$0.905871\pi$
$398$	−0.984063	+	0.263679i	−0.0493266	+	0.0132170i
$399$	−3.96702	+	3.96702i	−0.198599	+	0.198599i
$400$		0			0
$401$	21.5174	+	21.5174i	1.07453	+	1.07453i	0.996990	+	0.0775363i	$0.0247054\pi$
$401$	21.5174	+	21.5174i	1.07453	+	1.07453i	0.0775363	+	0.996990i	$0.475295\pi$
$402$	5.18439	−	2.99321i	0.258574	−	0.149288i
$403$	41.7142	+	11.1773i	2.07793	+	0.556780i
$404$	3.18909	−	1.84122i	0.158663	−	0.0916042i
$405$		0			0
$406$		−	6.75209i		−	0.335101i
$407$	22.8483	+	13.6315i	1.13255	+	0.675688i
$408$	3.22659	−	3.22659i	0.159740	−	0.159740i
$409$	4.96725	+	18.5380i	0.245615	+	0.916647i	0.973073	+	0.230495i	$0.0740346\pi$
$409$	4.96725	+	18.5380i	0.245615	+	0.916647i	−0.727459	+	0.686151i	$0.759299\pi$
$410$		0			0
$411$	22.5181	−	13.0009i	1.11074	−	0.641285i
$412$	4.60064	+	7.96855i	0.226657	+	0.392582i
$413$		−	40.0544i		−	1.97095i
$414$	0.437456	−	0.252565i	0.0214998	−	0.0124129i
$415$		0			0
$416$	7.23910	−	12.5385i	0.354926	−	0.614750i
$417$	22.5017	+	22.5017i	1.10191	+	1.10191i
$418$	−0.575266	−	0.575266i	−0.0281372	−	0.0281372i
$419$	−14.4238	−	8.32758i	−0.704649	−	0.406829i	0.104428	−	0.994532i	$-0.466699\pi$
$419$	−14.4238	−	8.32758i	−0.704649	−	0.406829i	−0.809076	+	0.587703i	$0.800032\pi$
$420$		0			0
$421$	−1.63243	−	1.63243i	−0.0795600	−	0.0795600i	0.666207	−	0.745767i	$-0.267917\pi$
$421$	−1.63243	−	1.63243i	−0.0795600	−	0.0795600i	−0.745767	+	0.666207i	$0.767917\pi$
$422$	−3.44723	−	1.99026i	−0.167809	−	0.0968844i
$423$	1.31759	+	4.91731i	0.0640634	+	0.239088i
$424$	0.571022	−	0.153005i	0.0277313	−	0.00743058i
$425$		0			0
$426$	4.71291	+	1.26282i	0.228341	+	0.0611838i
$427$	−34.3744	−	19.8460i	−1.66349	−	0.960417i
$428$	1.13835	−	0.305020i	0.0550242	−	0.0147437i
$429$	−41.0892	+	11.0098i	−1.98380	+	0.531559i
$430$		0			0
$431$	−4.00348	+	14.9412i	−0.192841	+	0.719692i	0.799974	+	0.600034i	$0.204846\pi$
$431$	−4.00348	+	14.9412i	−0.192841	+	0.719692i	−0.992815	+	0.119658i	$0.961820\pi$
$432$	4.28221	+	15.9814i	0.206028	+	0.768907i
$433$	25.3131	−	25.3131i	1.21647	−	1.21647i	0.247609	−	0.968860i	$-0.420355\pi$
$433$	25.3131	−	25.3131i	1.21647	−	1.21647i	0.968860	−	0.247609i	$-0.0796449\pi$
$434$	8.06910			0.387329
$435$		0			0
$436$	−9.37821	−	9.37821i	−0.449135	−	0.449135i
$437$	−2.47486	−	0.663136i	−0.118388	−	0.0317221i
$438$	2.04949			0.0979283
$439$	19.5391	+	5.23549i	0.932551	+	0.249876i	0.692942	−	0.720993i	$-0.256314\pi$
$439$	19.5391	+	5.23549i	0.932551	+	0.249876i	0.239609	+	0.970870i	$0.422981\pi$
$440$		0			0
$441$	2.49207	+	4.31639i	0.118670	+	0.205543i
$442$	1.56071	−	2.70323i	0.0742354	−	0.128579i
$443$	14.1936	+	14.1936i	0.674357	+	0.674357i	0.958717	−	0.284360i	$-0.0917813\pi$
$443$	14.1936	+	14.1936i	0.674357	+	0.674357i	−0.284360	+	0.958717i	$0.591781\pi$
$444$	−6.11068	+	21.5650i	−0.290000	+	1.02343i
$445$		0			0
$446$	−4.05096	+	1.08545i	−0.191818	+	0.0513976i
$447$	−5.01607	−	1.34405i	−0.237252	−	0.0635715i
$448$	−6.64741	+	24.8085i	−0.314061	+	1.17209i
$449$	0.795805	−	2.96998i	0.0375563	−	0.140162i	−0.944602	−	0.328218i	$-0.893552\pi$
$449$	0.795805	−	2.96998i	0.0375563	−	0.140162i	0.982158	+	0.188056i	$0.0602186\pi$
$450$		0			0
$451$	10.5647	+	18.2985i	0.497470	+	0.861644i
$452$	3.45663			0.162586
$453$	7.77533	+	29.0179i	0.365317	+	1.36338i
$454$			1.09198i			0.0512492i
$455$		0			0
$456$	0.696022	−	1.20554i	0.0325942	−	0.0564548i
$457$	1.90857	+	3.30575i	0.0892793	+	0.154636i	0.907207	−	0.420685i	$-0.138210\pi$
$457$	1.90857	+	3.30575i	0.0892793	+	0.154636i	−0.817927	+	0.575321i	$0.804877\pi$
$458$	2.00244			0.0935681
$459$	2.92053	+	10.8996i	0.136319	+	0.508749i
$460$		0			0
$461$	9.05566	+	33.7962i	0.421764	+	1.57404i	0.770890	+	0.636969i	$0.219812\pi$
$461$	9.05566	+	33.7962i	0.421764	+	1.57404i	−0.349126	+	0.937076i	$0.613521\pi$
$462$	−6.88335	+	3.97410i	−0.320242	+	0.184892i
$463$	−24.4405	+	14.1107i	−1.13585	+	0.655782i	−0.945399	−	0.325915i	$-0.894328\pi$
$463$	−24.4405	+	14.1107i	−1.13585	+	0.655782i	−0.190449	+	0.981697i	$0.560994\pi$
$464$	−6.65382	−	24.8324i	−0.308896	−	1.15282i
$465$		0			0
$466$	0.886341	+	3.30787i	0.0410590	+	0.153234i
$467$	−15.9774			−0.739345			−0.369672	−	0.929162i	$-0.620530\pi$
$467$	−15.9774			−0.739345			−0.369672	+	0.929162i	$0.620530\pi$
$468$	−3.02228	−	5.23474i	−0.139705	−	0.241976i
$469$	−25.0184	+	43.3331i	−1.15524	+	2.00094i
$470$		0			0
$471$			9.40086i			0.433169i
$472$	2.57229	+	9.59991i	0.118399	+	0.441872i
$473$	14.8738			0.683896
$474$	0.669969	+	1.16042i	0.0307727	+	0.0532999i
$475$		0			0
$476$	−4.86020	+	18.1385i	−0.222767	+	0.831378i
$477$	0.0963063	−	0.359420i	0.00440956	−	0.0164567i
$478$	3.76067	+	1.00767i	0.172009	+	0.0460897i
$479$	−19.8825	+	5.32750i	−0.908454	+	0.243420i	−0.682643	−	0.730752i	$-0.739170\pi$
$479$	−19.8825	+	5.32750i	−0.908454	+	0.243420i	−0.225811	+	0.974171i	$0.572503\pi$
$480$		0			0
$481$	−0.446015	+	31.1381i	−0.0203365	+	1.41978i
$482$	2.87453	+	2.87453i	0.130931	+	0.130931i
$483$	−12.5159	+	21.6782i	−0.569493	+	0.986390i
$484$	7.88650	+	13.6598i	0.358477	+	0.620901i
$485$		0			0
$486$	−1.47794	−	0.396013i	−0.0670408	−	0.0179635i
$487$	6.61449			0.299731			0.149866	−	0.988706i	$-0.452116\pi$
$487$	6.61449			0.299731			0.149866	+	0.988706i	$0.452116\pi$
$488$	9.51308	+	2.54902i	0.430637	+	0.115389i
$489$	21.9802	+	21.9802i	0.993977	+	0.993977i
$490$		0			0
$491$	−5.57169			−0.251447			−0.125723	−	0.992065i	$-0.540125\pi$
$491$	−5.57169			−0.251447			−0.125723	+	0.992065i	$0.540125\pi$
$492$	−12.5868	+	12.5868i	−0.567459	+	0.567459i
$493$	−4.53801	−	16.9361i	−0.204382	−	0.762762i
$494$	0.246458	−	0.919793i	0.0110887	−	0.0413835i
$495$		0			0
$496$	29.6760	−	7.95167i	1.33249	−	0.357040i
$497$	−39.3923	+	10.5551i	−1.76699	+	0.473462i
$498$	−2.42478	−	1.39995i	−0.108657	−	0.0627332i
$499$	5.11780	+	1.37131i	0.229104	+	0.0613883i	0.371545	−	0.928415i	$-0.378828\pi$
$499$	5.11780	+	1.37131i	0.229104	+	0.0613883i	−0.142440	+	0.989803i	$0.545495\pi$
$500$		0			0
$501$	−14.3348	+	3.84100i	−0.640432	+	0.171603i
$502$	0.317689	+	1.18563i	0.0141791	+	0.0529172i
$503$	−5.01801	−	2.89715i	−0.223742	−	0.129178i	0.383940	−	0.923358i	$-0.374567\pi$
$503$	−5.01801	−	2.89715i	−0.223742	−	0.129178i	−0.607682	+	0.794181i	$0.707900\pi$
$504$	−1.62202	−	1.62202i	−0.0722506	−	0.0722506i
$505$		0			0
$506$	−3.14360	−	1.81496i	−0.139750	−	0.0806847i
$507$	−17.7449	−	17.7449i	−0.788078	−	0.788078i
$508$	−5.20559	−	5.20559i	−0.230961	−	0.230961i
$509$	18.5930	−	32.2040i	0.824118	−	1.42742i	−0.0784727	−	0.996916i	$-0.525004\pi$
$509$	18.5930	−	32.2040i	0.824118	−	1.42742i	0.902591	−	0.430499i	$-0.141662\pi$
$510$		0			0
$511$	−14.8354	+	8.56520i	−0.656278	+	0.378902i
$512$		−	17.3440i		−	0.766504i
$513$	1.72120	+	2.98120i	0.0759927	+	0.131623i
$514$	4.45776	−	2.57369i	0.196623	−	0.113521i
$515$		0			0
$516$	3.24312	+	12.1035i	0.142771	+	0.532827i
$517$	25.8679	−	25.8679i	1.13767	−	1.13767i
$518$	1.42533	+	5.64138i	0.0626253	+	0.247868i
$519$		−	39.5385i		−	1.73555i
$520$		0			0
$521$	−29.0910	+	16.7957i	−1.27450	+	0.735832i	−0.975831	−	0.218525i	$-0.929876\pi$
$521$	−29.0910	+	16.7957i	−1.27450	+	0.735832i	−0.298668	+	0.954357i	$0.596542\pi$
$522$	1.01860	+	0.272933i	0.0445830	+	0.0119460i
$523$	−26.7199	+	15.4267i	−1.16838	+	0.674564i	−0.953298	−	0.302031i	$-0.902335\pi$
$523$	−26.7199	+	15.4267i	−1.16838	+	0.674564i	−0.215082	+	0.976596i	$0.569002\pi$
$524$	−21.6609	−	21.6609i	−0.946261	−	0.946261i
$525$		0			0
$526$	−2.01698	+	2.01698i	−0.0879447	+	0.0879447i
$527$	20.2395	−	5.42316i	0.881647	−	0.236236i
$528$	−21.3989	+	21.3989i	−0.931266	+	0.931266i
$529$	11.5681			0.502960
$530$		0			0
$531$	6.04249	+	1.61908i	0.262222	+	0.0702621i
$532$			5.72865i			0.248369i
$533$	−12.3657	+	21.4180i	−0.535617	+	0.927716i
$534$	−0.605020	−	0.349309i	−0.0261818	−	0.0151161i
$535$		0			0
$536$	3.21336	−	11.9924i	0.138796	−	0.517993i
$537$	−11.7146	−	20.2903i	−0.505522	−	0.875589i
$538$	−2.51054	+	4.34838i	−0.108237	+	0.187472i
$539$	17.9083	−	31.0180i	0.771363	−	1.33604i
$540$		0			0
$541$	−11.6465	+	11.6465i	−0.500724	+	0.500724i	−0.911663	−	0.410939i	$-0.865201\pi$
$541$	−11.6465	+	11.6465i	−0.500724	+	0.500724i	0.410939	+	0.911663i	$0.365201\pi$
$542$	4.85665	−	2.80399i	0.208611	−	0.120442i
$543$	−6.80676	+	1.82387i	−0.292106	+	0.0782696i
$544$		−	7.02475i		−	0.301184i
$545$		0			0
$546$	−8.05680	−	4.65159i	−0.344799	−	0.199070i
$547$			18.6903i			0.799142i	0.916702	+	0.399571i	$0.130841\pi$
$547$			18.6903i			0.799142i	−0.916702	+	0.399571i	$0.869159\pi$
$548$	6.87182	−	25.6460i	0.293549	−	1.09554i
$549$	4.38340	−	4.38340i	0.187079	−	0.187079i
$550$		0			0
$551$	−2.67444	−	4.63227i	−0.113935	−	0.197341i
$552$	1.60754	−	5.99941i	0.0684214	−	0.255352i
$553$	−9.69925	−	5.59986i	−0.412454	−	0.238130i
$554$	−3.38110			−0.143649
$555$		0			0
$556$	32.4941			1.37805
$557$	−5.33894	−	3.08244i	−0.226218	−	0.130607i	0.382608	−	0.923911i	$-0.375026\pi$
$557$	−5.33894	−	3.08244i	−0.226218	−	0.130607i	−0.608826	+	0.793304i	$0.708359\pi$
$558$	−0.326170	+	1.21728i	−0.0138079	+	0.0515317i
$559$	8.70469	+	15.0770i	0.368169	+	0.637688i
$560$		0			0
$561$	−14.5944	+	14.5944i	−0.616174	+	0.616174i
$562$	1.50795	−	5.62775i	0.0636091	−	0.237392i
$563$		−	24.5838i		−	1.03609i	−0.855355	−	0.518043i	$-0.826661\pi$
$563$		−	24.5838i		−	1.03609i	0.855355	−	0.518043i	$-0.173339\pi$
$564$	26.6903	+	15.4097i	1.12387	+	0.648864i
$565$		0			0
$566$			5.18700i			0.218026i
$567$	39.3594	−	10.5463i	1.65294	−	0.442904i
$568$	8.76337	−	5.05954i	0.367703	−	0.212293i
$569$	−24.7919	+	24.7919i	−1.03933	+	1.03933i	−0.0401367	+	0.999194i	$0.512779\pi$
$569$	−24.7919	+	24.7919i	−1.03933	+	1.03933i	−0.999194	+	0.0401367i	$0.987221\pi$
$570$		0			0
$571$	10.8132	−	18.7289i	0.452516	−	0.783781i	−0.546025	−	0.837769i	$-0.683860\pi$
$571$	10.8132	−	18.7289i	0.452516	−	0.783781i	0.998542	+	0.0539873i	$0.0171930\pi$
$572$	−21.7184	+	37.6173i	−0.908090	+	1.57286i
$573$	−9.46669	−	16.3968i	−0.395477	−	0.684986i
$574$	−1.19600	+	4.46352i	−0.0499199	+	0.186304i
$575$		0			0
$576$	−3.47383	−	2.00562i	−0.144743	−	0.0835674i
$577$	−1.76397	+	3.05528i	−0.0734348	+	0.127193i	−0.900405	−	0.435054i	$-0.856729\pi$
$577$	−1.76397	+	3.05528i	−0.0734348	+	0.127193i	0.826970	+	0.562246i	$0.190063\pi$
$578$			2.65815i			0.110565i
$579$	8.25858	+	2.21288i	0.343215	+	0.0919642i
$580$		0			0
$581$	23.4026			0.970904
$582$	−1.98995	+	1.98995i	−0.0824859	+	0.0824859i
$583$	−2.58282	+	0.692066i	−0.106970	+	0.0286624i
$584$	3.00556	−	3.00556i	0.124371	−	0.124371i
$585$		0			0
$586$	0.0858211	+	0.0858211i	0.00354524	+	0.00354524i
$587$	−30.6172	+	17.6768i	−1.26371	+	0.729601i	−0.973790	−	0.227451i	$-0.926961\pi$
$587$	−30.6172	+	17.6768i	−1.26371	+	0.729601i	−0.289917	+	0.957052i	$0.593628\pi$
$588$	29.1456	+	7.80955i	1.20195	+	0.322060i
$589$	5.53581	−	3.19610i	0.228099	−	0.131693i
$590$		0			0
$591$		−	9.11405i		−	0.374902i
$592$	10.8013	+	19.3429i	0.443929	+	0.794989i
$593$	25.5343	−	25.5343i	1.04857	−	1.04857i	0.0498107	−	0.998759i	$-0.484138\pi$
$593$	25.5343	−	25.5343i	1.04857	−	1.04857i	0.998759	−	0.0498107i	$-0.0158618\pi$
$594$	1.26225	+	4.71079i	0.0517909	+	0.193286i
$595$		0			0
$596$	−4.59223	+	2.65133i	−0.188105	+	0.108603i
$597$	3.94239	+	6.82842i	0.161351	+	0.279469i
$598$		−	4.24873i		−	0.173743i
$599$	8.97611	−	5.18236i	0.366754	−	0.211745i	−0.305286	−	0.952261i	$-0.598752\pi$
$599$	8.97611	−	5.18236i	0.366754	−	0.211745i	0.672039	+	0.740515i	$0.265419\pi$
$600$		0			0
$601$	18.8695	−	32.6829i	0.769702	−	1.33316i	−0.168023	−	0.985783i	$-0.553738\pi$
$601$	18.8695	−	32.6829i	0.769702	−	1.33316i	0.937725	−	0.347379i	$-0.112928\pi$
$602$	2.30014	+	2.30014i	0.0937466	+	0.0937466i
$603$	−5.52582	−	5.52582i	−0.225029	−	0.225029i
$604$	26.5660	+	15.3379i	1.08096	+	0.624090i
$605$		0			0
$606$	0.625909	+	0.625909i	0.0254258	+	0.0254258i
$607$	28.4843	+	16.4454i	1.15614	+	0.667500i	0.950377	−	0.311101i	$-0.100698\pi$
$607$	28.4843	+	16.4454i	1.15614	+	0.667500i	0.205767	+	0.978601i	$0.434031\pi$
$608$	−0.554653	−	2.06999i	−0.0224942	−	0.0839493i
$609$	−50.4769	+	13.5252i	−2.04543	+	0.548070i
$610$		0			0
$611$	41.3603	+	11.0824i	1.67326	+	0.448348i
$612$	−2.53987	−	1.46639i	−0.102668	−	0.0592754i
$613$	24.0323	−	6.43944i	0.970657	−	0.260087i	0.261552	−	0.965190i	$-0.415766\pi$
$613$	24.0323	−	6.43944i	0.970657	−	0.260087i	0.709105	+	0.705103i	$0.249099\pi$
$614$	−4.38933	+	1.17612i	−0.177139	+	0.0474642i
$615$		0			0
$616$	−4.26639	+	15.9224i	−0.171898	+	0.641532i
$617$	−3.98826	−	14.8844i	−0.160561	−	0.599223i	−0.998565	−	0.0535581i	$-0.982944\pi$
$617$	−3.98826	−	14.8844i	−0.160561	−	0.599223i	0.838003	−	0.545665i	$-0.183723\pi$
$618$	−1.56395	+	1.56395i	−0.0629113	+	0.0629113i
$619$	9.03986			0.363343			0.181671	−	0.983359i	$-0.441849\pi$
$619$	9.03986			0.363343			0.181671	+	0.983359i	$0.441849\pi$
$620$		0			0
$621$	10.8607	+	10.8607i	0.435825	+	0.435825i
$622$	−6.19217	−	1.65919i	−0.248283	−	0.0665274i
$623$	5.83931			0.233947
$624$	−34.2147	−	9.16779i	−1.36968	−	0.367005i
$625$		0			0
$626$	2.06509	+	3.57684i	0.0825376	+	0.142959i
$627$	−3.14822	+	5.45287i	−0.125728	+	0.217767i
$628$	6.78775	+	6.78775i	0.270861	+	0.270861i
$629$	7.36662	+	13.1922i	0.293726	+	0.526006i
$630$		0			0
$631$	0.852346	−	0.228386i	0.0339314	−	0.00909188i	−0.241813	−	0.970323i	$-0.577742\pi$
$631$	0.852346	−	0.228386i	0.0339314	−	0.00909188i	0.275745	+	0.961231i	$0.411076\pi$
$632$	2.68426	+	0.719245i	0.106774	+	0.0286100i
$633$	−7.97346	+	29.7574i	−0.316917	+	1.18275i
$634$	1.14225	−	4.26292i	0.0453644	−	0.169302i
$635$		0			0
$636$	−1.12633	−	1.95087i	−0.0446621	−	0.0773570i
$637$	41.9224			1.66103
$638$	−1.96132	−	7.31976i	−0.0776496	−	0.289792i
$639$		−	6.36927i		−	0.251964i
$640$		0			0
$641$	23.9371	−	41.4602i	0.945458	−	1.63758i	0.190626	−	0.981663i	$-0.438948\pi$
$641$	23.9371	−	41.4602i	0.945458	−	1.63758i	0.754832	−	0.655918i	$-0.227718\pi$
$642$	0.141642	+	0.245331i	0.00559016	+	0.00968244i
$643$	−2.96948			−0.117105			−0.0585523	−	0.998284i	$-0.518648\pi$
$643$	−2.96948			−0.117105			−0.0585523	+	0.998284i	$0.518648\pi$
$644$	6.61548	+	24.6893i	0.260686	+	0.972895i
$645$		0			0
$646$	−0.119580	−	0.446279i	−0.00470482	−	0.0175586i
$647$	3.18505	−	1.83889i	0.125217	−	0.0722941i	−0.436083	−	0.899906i	$-0.643635\pi$
$647$	3.18505	−	1.83889i	0.125217	−	0.0722941i	0.561300	+	0.827612i	$0.310301\pi$
$648$	−8.75606	+	5.05531i	−0.343971	+	0.198591i
$649$	−11.6349	−	43.4219i	−0.456708	−	1.70446i
$650$		0			0
$651$	−16.1634	−	60.3225i	−0.633493	−	2.36423i
$652$	31.7409			1.24307
$653$	3.43864	+	5.95590i	0.134564	+	0.233072i	0.925431	−	0.378916i	$-0.123703\pi$
$653$	3.43864	+	5.95590i	0.134564	+	0.233072i	−0.790867	+	0.611989i	$0.790370\pi$
$654$	1.59402	−	2.76093i	0.0623312	−	0.107961i
$655$		0			0
$656$			17.5942i			0.686939i
$657$	−0.692446	−	2.58424i	−0.0270149	−	0.100821i
$658$	8.00064			0.311898
$659$	−9.37543	−	16.2387i	−0.365215	−	0.632571i	0.623596	−	0.781747i	$-0.285671\pi$
$659$	−9.37543	−	16.2387i	−0.365215	−	0.632571i	−0.988811	+	0.149176i	$0.952338\pi$
$660$		0			0
$661$	−7.54321	+	28.1516i	−0.293397	+	1.09497i	0.649086	+	0.760715i	$0.275152\pi$
$661$	−7.54321	+	28.1516i	−0.293397	+	1.09497i	−0.942482	+	0.334256i	$0.891515\pi$
$662$	0.287441	−	1.07275i	0.0111717	−	0.0416934i
$663$	−23.3349	−	6.25257i	−0.906253	−	0.242830i
$664$	−5.60895	+	1.50291i	−0.217669	+	0.0583243i
$665$		0			0
$666$	−0.908658	−	0.0130154i	−0.0352098	−	0.000504336i
$667$	−16.8757	−	16.8757i	−0.653428	−	0.653428i
$668$	−7.57690	+	13.1236i	−0.293159	+	0.507766i
$669$	16.2291	+	28.1096i	0.627453	+	1.08678i
$670$		0			0
$671$	−43.0292	−	11.5296i	−1.66112	−	0.445096i
$672$	−20.9368			−0.807655
$673$	27.3184	+	7.31994i	1.05305	+	0.282163i	0.743510	−	0.668725i	$-0.233160\pi$
$673$	27.3184	+	7.31994i	1.05305	+	0.282163i	0.309536	+	0.950888i	$0.399826\pi$
$674$	−0.0869564	−	0.0869564i	−0.00334943	−	0.00334943i
$675$		0			0
$676$	−25.6248			−0.985571
$677$	11.9853	−	11.9853i	0.460633	−	0.460633i	−0.438230	−	0.898863i	$-0.644395\pi$
$677$	11.9853	−	11.9853i	0.460633	−	0.460633i	0.898863	+	0.438230i	$0.144395\pi$
$678$	0.215049	+	0.802575i	0.00825892	+	0.0308227i
$679$	6.08800	−	22.7207i	0.233636	−	0.871942i
$680$		0			0
$681$	8.16336	−	2.18737i	0.312821	−	0.0838201i
$682$	8.74750	−	2.34389i	0.334959	−	0.0897520i
$683$	11.8491	+	6.84107i	0.453393	+	0.261766i	0.709262	−	0.704945i	$-0.249028\pi$
$683$	11.8491	+	6.84107i	0.453393	+	0.261766i	−0.255869	+	0.966711i	$0.582362\pi$
$684$	−0.864208	−	0.231564i	−0.0330438	−	0.00885407i
$685$		0			0
$686$	1.09825	−	0.294275i	0.0419313	−	0.0112355i
$687$	−4.01113	−	14.9698i	−0.153034	−	0.571132i
$688$	10.7260	+	6.19263i	0.408923	+	0.236092i
$689$	−2.21309	−	2.21309i	−0.0843120	−	0.0843120i
$690$		0			0
$691$	−12.5733	−	7.25918i	−0.478310	−	0.276152i	0.241402	−	0.970425i	$-0.422393\pi$
$691$	−12.5733	−	7.25918i	−0.478310	−	0.276152i	−0.719712	+	0.694273i	$0.755726\pi$
$692$	−28.5482	−	28.5482i	−1.08524	−	1.08524i
$693$	7.33666	+	7.33666i	0.278697	+	0.278697i
$694$	0.719928	−	1.24695i	0.0273281	−	0.0473337i
$695$		0			0
$696$	11.2293	−	6.48324i	0.425646	−	0.245747i
$697$			11.9995i			0.454515i
$698$	−2.58270	−	4.47337i	−0.0977566	−	0.169319i
$699$	22.9533	−	13.2521i	0.868175	−	0.501241i
$700$		0			0
$701$	−6.61099	−	24.6725i	−0.249693	−	0.931869i	−0.970966	−	0.239217i	$-0.923109\pi$
$701$	−6.61099	−	24.6725i	−0.249693	−	0.931869i	0.721273	−	0.692651i	$-0.243558\pi$
$702$	−4.03643	+	4.03643i	−0.152345	+	0.152345i
$703$	3.21235	+	3.30571i	0.121156	+	0.124677i
$704$			28.8251i			1.08639i
$705$		0			0
$706$	3.27251	−	1.88938i	0.123162	−	0.0711078i
$707$	−7.14648	−	1.91489i	−0.268771	−	0.0720170i
$708$	32.7976	−	18.9357i	1.23261	−	0.711647i
$709$	−0.827189	−	0.827189i	−0.0310657	−	0.0310657i	0.691403	−	0.722469i	$-0.256993\pi$
$709$	−0.827189	−	0.827189i	−0.0310657	−	0.0310657i	−0.722469	+	0.691403i	$0.756993\pi$
$710$		0			0
$711$	1.23684	−	1.23684i	0.0463852	−	0.0463852i
$712$	−1.39952	+	0.375000i	−0.0524492	+	0.0140537i
$713$	20.1673	−	20.1673i	0.755271	−	0.755271i
$714$	−4.51386			−0.168927
$715$		0			0
$716$	−23.1086	−	6.19193i	−0.863610	−	0.231403i
$717$		−	30.1323i		−	1.12531i
$718$	−3.52456	+	6.10471i	−0.131535	+	0.227826i
$719$	−5.80482	−	3.35141i	−0.216483	−	0.124987i	0.387838	−	0.921728i	$-0.373222\pi$
$719$	−5.80482	−	3.35141i	−0.216483	−	0.124987i	−0.604321	+	0.796741i	$0.706555\pi$
$720$		0			0
$721$	4.78472	−	17.8568i	0.178192	−	0.665023i
$722$	2.26130	+	3.91669i	0.0841569	+	0.145764i
$723$	15.7312	−	27.2473i	0.585051	−	1.01334i
$724$	−3.59782	+	6.23161i	−0.133712	+	0.231596i
$725$		0			0
$726$	−2.68095	+	2.68095i	−0.0994995	+	0.0994995i
$727$	−18.2215	+	10.5202i	−0.675797	+	0.390171i	−0.798270	−	0.602300i	$-0.794251\pi$
$727$	−18.2215	+	10.5202i	−0.675797	+	0.390171i	0.122473	+	0.992472i	$0.460918\pi$
$728$	−18.6368	+	4.99371i	−0.690726	+	0.185079i
$729$		−	19.5246i		−	0.723134i
$730$		0			0
$731$	7.31527	+	4.22347i	0.270565	+	0.156211i
$732$		−	37.5289i		−	1.38711i
$733$	−6.79083	+	25.3437i	−0.250825	+	0.936092i	0.719541	+	0.694450i	$0.244352\pi$
$733$	−6.79083	+	25.3437i	−0.250825	+	0.936092i	−0.970366	+	0.241641i	$0.922314\pi$
$734$	−1.98983	+	1.98983i	−0.0734460	+	0.0734460i
$735$		0			0
$736$	−4.78088	−	8.28072i	−0.176225	−	0.305231i
$737$	−14.5345	+	54.2435i	−0.535386	+	1.99809i
$738$	−0.625009	−	0.360849i	−0.0230069	−	0.0132830i
$739$	−33.7980			−1.24328			−0.621640	−	0.783303i	$-0.713533\pi$
$739$	−33.7980			−1.24328			−0.621640	+	0.783303i	$0.713533\pi$
$740$		0			0
$741$	−7.36982			−0.270737
$742$	−0.506442	−	0.292394i	−0.0185921	−	0.0107341i
$743$	0.130195	−	0.485894i	0.00477639	−	0.0178257i	−0.963497	−	0.267721i	$-0.913729\pi$
$743$	0.130195	−	0.485894i	0.00477639	−	0.0178257i	0.968273	+	0.249895i	$0.0803962\pi$
$744$	7.74781	+	13.4196i	0.284049	+	0.491987i
$745$		0			0
$746$	1.91396	−	1.91396i	0.0700749	−	0.0700749i
$747$	−0.945982	+	3.53045i	−0.0346117	+	0.129172i
$748$			21.0753i			0.770588i
$749$	−2.05057	−	1.18390i	−0.0749262	−	0.0432587i
$750$		0			0
$751$			16.9759i			0.619459i	0.950825	+	0.309730i	$0.100239\pi$
$751$			16.9759i			0.619459i	−0.950825	+	0.309730i	$0.899761\pi$
$752$	29.4242	−	7.88420i	1.07299	−	0.287507i
$753$	8.22709	−	4.74991i	0.299812	−	0.173097i
$754$	6.27192	−	6.27192i	0.228410	−	0.228410i
$755$		0			0
$756$	17.1707	−	29.7406i	0.624494	−	1.08165i
$757$	−10.7520	+	18.6230i	−0.390789	+	0.676866i	−0.992554	−	0.121807i	$-0.961131\pi$
$757$	−10.7520	+	18.6230i	−0.390789	+	0.676866i	0.601765	+	0.798673i	$0.294464\pi$
$758$	−3.44370	−	5.96467i	−0.125081	−	0.216646i
$759$	−7.27115	+	27.1363i	−0.263926	+	0.984985i
$760$		0			0
$761$	5.87890	+	3.39418i	0.213110	+	0.123039i	0.602756	−	0.797926i	$-0.294069\pi$
$761$	5.87890	+	3.39418i	0.213110	+	0.123039i	−0.389646	+	0.920965i	$0.627403\pi$
$762$	0.884799	−	1.53252i	0.0320529	−	0.0555172i
$763$			26.6469i			0.964683i
$764$	−18.6743	−	5.00377i	−0.675614	−	0.181030i
$765$		0			0
$766$	−2.00674			−0.0725064
$767$	37.2060	−	37.2060i	1.34343	−	1.34343i
$768$	−20.9090	+	5.60256i	−0.754490	+	0.202165i
$769$	7.17556	−	7.17556i	0.258757	−	0.258757i	−0.565791	−	0.824549i	$-0.691429\pi$
$769$	7.17556	−	7.17556i	0.258757	−	0.258757i	0.824549	+	0.565791i	$0.191429\pi$
$770$		0			0
$771$	−28.1697	−	28.1697i	−1.01451	−	1.01451i
$772$	7.56076	−	4.36521i	0.272118	−	0.157107i
$773$	−27.1353	−	7.27088i	−0.975988	−	0.261515i	−0.264634	−	0.964349i	$-0.585251\pi$
$773$	−27.1353	−	7.27088i	−0.975988	−	0.261515i	−0.711354	+	0.702834i	$0.751918\pi$
$774$	−0.439968	+	0.254016i	−0.0158143	+	0.00913041i
$775$		0			0
$776$			5.83649i			0.209518i
$777$	39.3184	−	21.9557i	1.41054	−	0.787658i
$778$	4.51817	−	4.51817i	0.161984	−	0.161984i
$779$	0.947447	+	3.53592i	0.0339458	+	0.126687i
$780$		0			0
$781$	−39.6381	+	22.8851i	−1.41836	+	0.818892i
$782$	−1.03073	−	1.78528i	−0.0368588	−	0.0638414i
$783$			32.0649i			1.14591i
$784$	25.8285	−	14.9121i	0.922445	−	0.532574i
$785$		0			0
$786$	3.68173	−	6.37694i	0.131323	−	0.227458i
$787$	−9.47199	−	9.47199i	−0.337640	−	0.337640i	0.517838	−	0.855478i	$-0.326737\pi$
$787$	−9.47199	−	9.47199i	−0.337640	−	0.337640i	−0.855478	+	0.517838i	$0.826737\pi$
$788$	−6.58066	−	6.58066i	−0.234426	−	0.234426i
$789$	19.1187	+	11.0382i	0.680644	+	0.392970i
$790$		0			0
$791$	−4.91077	−	4.91077i	−0.174607	−	0.174607i
$792$	−2.22955	−	1.28723i	−0.0792237	−	0.0457398i
$793$	−13.4952	−	50.3646i	−0.479227	−	1.78850i
$794$	−8.33753	+	2.23404i	−0.295888	+	0.0792829i
$795$		0			0
$796$	7.77690	+	2.08381i	0.275645	+	0.0738588i
$797$	−29.9455	−	17.2891i	−1.06072	−	0.612410i	−0.135092	−	0.990833i	$-0.543133\pi$
$797$	−29.9455	−	17.2891i	−1.06072	−	0.612410i	−0.925633	+	0.378423i	$0.876466\pi$
$798$	−1.33011	+	0.356401i	−0.0470852	+	0.0126164i
$799$	20.0678	−	5.37715i	0.709947	−	0.190230i
$800$		0			0
$801$	−0.236037	+	0.880902i	−0.00833996	+	0.0311251i
$802$	1.93314	+	7.21458i	0.0682615	+	0.254756i
$803$	−13.5946	+	13.5946i	−0.479744	+	0.479744i
$804$	−47.3097			−1.66849
$805$		0			0
$806$	7.49528	+	7.49528i	0.264010	+	0.264010i
$807$	37.5363	+	10.0578i	1.32134	+	0.354052i
$808$	1.83578			0.0645826
$809$	28.4366	+	7.61955i	0.999776	+	0.267889i	0.721352	−	0.692569i	$-0.243521\pi$
$809$	28.4366	+	7.61955i	0.999776	+	0.267889i	0.278424	+	0.960458i	$0.410188\pi$
$810$		0			0
$811$	−3.59932	−	6.23420i	−0.126389	−	0.218912i	0.795886	−	0.605447i	$-0.207005\pi$
$811$	−3.59932	−	6.23420i	−0.126389	−	0.218912i	−0.922275	+	0.386534i	$0.873672\pi$
$812$	−26.6804	+	46.2118i	−0.936298	+	1.62172i
$813$	−30.6904	−	30.6904i	−1.07636	−	1.07636i
$814$	3.18385	+	5.70165i	0.111594	+	0.199843i
$815$		0			0
$816$	−16.6008	+	4.44816i	−0.581143	+	0.155717i
$817$	2.48907	+	0.666945i	0.0870817	+	0.0233335i
$818$	−1.21921	+	4.55016i	−0.0426287	+	0.159093i
$819$	−3.14320	+	11.7306i	−0.109832	+	0.409900i
$820$		0			0
$821$	−10.3931	−	18.0014i	−0.362721	−	0.628252i	0.625686	−	0.780075i	$-0.284819\pi$
$821$	−10.3931	−	18.0014i	−0.362721	−	0.628252i	−0.988408	+	0.151823i	$0.951486\pi$
$822$	6.38212			0.222602
$823$	−5.31233	−	19.8259i	−0.185176	−	0.691087i	−0.994593	−	0.103852i	$-0.966883\pi$
$823$	−5.31233	−	19.8259i	−0.185176	−	0.691087i	0.809417	−	0.587235i	$-0.199784\pi$
$824$			4.58705i			0.159798i
$825$		0			0
$826$	4.91567	−	8.51420i	0.171038	−	0.296247i
$827$	−10.2930	−	17.8279i	−0.357921	−	0.619937i	0.629692	−	0.776845i	$-0.283181\pi$
$827$	−10.2930	−	17.8279i	−0.357921	−	0.619937i	−0.987613	+	0.156907i	$0.949848\pi$
$828$	−3.99197			−0.138730
$829$	0.0273552	+	0.102091i	0.000950086	+	0.00354577i	0.966399	−	0.257046i	$-0.0827491\pi$
$829$	0.0273552	+	0.102091i	0.000950086	+	0.00354577i	−0.965449	+	0.260591i	$0.916082\pi$
$830$		0			0
$831$	6.77275	+	25.2763i	0.234944	+	0.876823i
$832$	−29.2189	+	16.8696i	−1.01298	+	0.584847i
$833$	17.6154	−	10.1703i	0.610338	−	0.352379i
$834$	2.02157	+	7.54462i	0.0700014	+	0.261249i
$835$		0			0
$836$	1.66404	+	6.21028i	0.0575520	+	0.214787i
$837$	−38.3192			−1.32451
$838$	−2.04400	−	3.54032i	−0.0706090	−	0.122298i
$839$	25.4547	−	44.0888i	0.878793	−	1.52211i	0.0261266	−	0.999659i	$-0.491683\pi$
$839$	25.4547	−	44.0888i	0.878793	−	1.52211i	0.852666	−	0.522456i	$-0.174984\pi$
$840$		0			0
$841$		−	20.8233i		−	0.718046i
$842$	−0.146659	−	0.547340i	−0.00505422	−	0.0188626i
$843$	−45.0922			−1.55306
$844$	15.7287	+	27.2430i	0.541406	+	0.937742i
$845$		0			0
$846$	−0.323402	+	1.20695i	−0.0111188	+	0.0414959i
$847$	8.20206	−	30.6105i	0.281826	−	1.05179i
$848$	−2.15070	−	0.576278i	−0.0738553	−	0.0197895i
$849$	38.7767	−	10.3902i	1.33081	−	0.356590i
$850$		0			0
$851$	17.6620	+	10.5373i	0.605446	+	0.361214i
$852$	−27.2655	−	27.2655i	−0.934101	−	0.934101i
$853$	−10.8258	+	18.7508i	−0.370667	+	0.642014i	−0.989668	−	0.143376i	$-0.954204\pi$
$853$	−10.8258	+	18.7508i	−0.370667	+	0.642014i	0.619001	+	0.785390i	$0.287538\pi$
$854$	−4.87121	−	8.43718i	−0.166689	−	0.288715i
$855$		0			0
$856$	0.567494	+	0.152059i	0.0193965	+	0.00519729i
$857$	−8.91910			−0.304670			−0.152335	−	0.988329i	$-0.548679\pi$
$857$	−8.91910			−0.304670			−0.152335	+	0.988329i	$0.548679\pi$
$858$	−10.0853	−	2.70236i	−0.344308	−	0.0922570i
$859$	−34.0010	−	34.0010i	−1.16010	−	1.16010i	−0.984453	−	0.175647i	$-0.943798\pi$
$859$	−34.0010	−	34.0010i	−1.16010	−	1.16010i	−0.175647	−	0.984453i	$-0.556202\pi$
$860$		0			0
$861$	35.7638			1.21883
$862$	−2.68466	+	2.68466i	−0.0914399	+	0.0914399i
$863$	12.2844	+	45.8461i	0.418166	+	1.56062i	0.778408	+	0.627759i	$0.216028\pi$
$863$	12.2844	+	45.8461i	0.418166	+	1.56062i	−0.360241	+	0.932859i	$0.617306\pi$
$864$	−3.32497	+	12.4090i	−0.113118	+	0.422161i
$865$		0			0
$866$	8.48725	−	2.27415i	0.288408	−	0.0772788i
$867$	19.8717	−	5.32460i	0.674877	−	0.180833i
$868$	−55.2255	−	31.8845i	−1.87448	−	1.08223i
$869$	−12.1413	−	3.25326i	−0.411866	−	0.110359i
$870$		0			0
$871$	−63.4908	+	17.0123i	−2.15130	+	0.576440i
$872$	−1.71126	−	6.38652i	−0.0579507	−	0.216275i
$873$	3.18150	+	1.83684i	0.107677	+	0.0621675i
$874$	−0.444687	−	0.444687i	−0.0150418	−	0.0150418i
$875$		0			0
$876$	−14.0268	−	8.09840i	−0.473923	−	0.273619i
$877$	34.2418	+	34.2418i	1.15626	+	1.15626i	0.985273	+	0.170989i	$0.0546963\pi$
$877$	34.2418	+	34.2418i	1.15626	+	1.15626i	0.170989	+	0.985273i	$0.445304\pi$
$878$	3.51082	+	3.51082i	0.118485	+	0.118485i
$879$	0.469666	−	0.813486i	0.0158415	−	0.0274382i
$880$		0			0
$881$	28.3215	−	16.3514i	0.954175	−	0.550893i	0.0597995	−	0.998210i	$-0.480954\pi$
$881$	28.3215	−	16.3514i	0.954175	−	0.550893i	0.894375	+	0.447317i	$0.147621\pi$
$882$			1.22336i			0.0411926i
$883$	1.57439	+	2.72693i	0.0529825	+	0.0917684i	0.891300	−	0.453414i	$-0.149794\pi$
$883$	1.57439	+	2.72693i	0.0529825	+	0.0917684i	−0.838318	+	0.545182i	$0.816461\pi$
$884$	−21.3632	+	12.3341i	−0.718522	+	0.414839i
$885$		0			0
$886$	1.27516	+	4.75898i	0.0428400	+	0.159881i
$887$	−1.64239	+	1.64239i	−0.0551461	+	0.0551461i	−0.734142	−	0.678996i	$-0.762415\pi$
$887$	−1.64239	+	1.64239i	−0.0551461	+	0.0551461i	0.678996	+	0.734142i	$0.262415\pi$
$888$	−8.01352	+	7.78720i	−0.268916	+	0.261321i
$889$			14.7910i			0.496074i
$890$		0			0
$891$	39.6050	−	22.8660i	1.32682	−	0.766039i
$892$	32.0141	+	8.57815i	1.07191	+	0.287218i
$893$	5.48884	−	3.16898i	0.183677	−	0.106046i
$894$	−0.901297	−	0.901297i	−0.0301439	−	0.0301439i
$895$		0			0
$896$	−20.0443	+	20.0443i	−0.669632	+	0.669632i
$897$	−31.7624	+	8.51071i	−1.06052	+	0.284164i
$898$	0.533652	−	0.533652i	0.0178082	−	0.0178082i
$899$	59.5415			1.98582
$900$		0			0
$901$	−1.46681	−	0.393030i	−0.0488665	−	0.0130937i
$902$			5.18619i			0.172681i
$903$	12.5878	−	21.8027i	0.418895	−	0.725548i
$904$	1.49234	+	0.861604i	0.0496346	+	0.0286565i
$905$		0			0
$906$	−1.90845	+	7.12244i	−0.0634041	+	0.236627i
$907$	4.16760	+	7.21849i	0.138383	+	0.239686i	0.926885	−	0.375346i	$-0.122476\pi$
$907$	4.16760	+	7.21849i	0.138383	+	0.239686i	−0.788502	+	0.615032i	$0.789143\pi$
$908$	4.31488	−	7.47359i	0.143194	−	0.248020i
$909$	0.577751	−	1.00069i	0.0191628	−	0.0331909i
$910$		0			0
$911$	26.7018	−	26.7018i	0.884669	−	0.884669i	−0.109336	−	0.994005i	$-0.534872\pi$
$911$	26.7018	−	26.7018i	0.884669	−	0.884669i	0.994005	+	0.109336i	$0.0348725\pi$
$912$	−4.54056	+	2.62149i	−0.150353	+	0.0868064i
$913$	25.3702	−	6.79791i	0.839630	−	0.224978i
$914$			0.936919i			0.0309905i
$915$		0			0
$916$	−13.7049	−	7.91251i	−0.452822	−	0.261437i
$917$			61.5466i			2.03245i
$918$	−0.716845	+	2.67530i	−0.0236594	+	0.0882981i
$919$	41.4518	−	41.4518i	1.36737	−	1.36737i	0.503195	−	0.864173i	$-0.332158\pi$
$919$	41.4518	−	41.4518i	1.36737	−	1.36737i	0.864173	−	0.503195i	$-0.167842\pi$
$920$		0			0
$921$	17.5847	+	30.4576i	0.579436	+	1.00361i
$922$	−2.22271	+	8.29527i	−0.0732011	+	0.273190i
$923$	−46.3955	−	26.7864i	−1.52713	−	0.881686i
$924$	62.8135			2.06641
$925$		0			0
$926$	−6.92697			−0.227634
$927$	2.50042	+	1.44362i	0.0821246	+	0.0474147i
$928$	5.16643	−	19.2814i	0.169596	−	0.632943i
$929$	17.9777	+	31.1383i	0.589830	+	1.02162i	0.994254	+	0.107044i	$0.0341386\pi$
$929$	17.9777	+	31.1383i	0.589830	+	1.02162i	−0.404424	+	0.914571i	$0.632528\pi$
$930$		0			0
$931$	4.38775	−	4.38775i	0.143803	−	0.143803i
$932$	7.00462	−	26.1416i	0.229444	−	0.856297i
$933$			49.6146i			1.62431i
$934$	−3.39624	−	1.96082i	−0.111129	−	0.0641601i
$935$		0			0
$936$		−	3.01335i		−	0.0984944i
$937$	26.9183	−	7.21273i	0.879381	−	0.235629i	0.209241	−	0.977864i	$-0.432901\pi$
$937$	26.9183	−	7.21273i	0.879381	−	0.235629i	0.670140	+	0.742235i	$0.266234\pi$
$938$	−10.6361	+	6.14076i	−0.347281	+	0.200503i
$939$	22.6029	−	22.6029i	0.737618	−	0.737618i
$940$		0			0
$941$	−21.5873	+	37.3903i	−0.703725	+	1.21889i	0.263425	+	0.964680i	$0.415148\pi$
$941$	−21.5873	+	37.3903i	−0.703725	+	1.21889i	−0.967150	+	0.254208i	$0.918185\pi$
$942$	−1.15372	+	1.99830i	−0.0375902	+	0.0651082i
$943$	8.16659	+	14.1450i	0.265941	+	0.460623i
$944$	9.68826	−	36.1571i	0.315326	−	1.17681i
$945$		0			0
$946$	3.16165	+	1.82538i	0.102794	+	0.0593483i
$947$	13.5641	−	23.4937i	0.440773	−	0.763442i	−0.556974	−	0.830530i	$-0.688038\pi$
$947$	13.5641	−	23.4937i	0.440773	−	0.763442i	0.997747	+	0.0670885i	$0.0213710\pi$
$948$		−	10.5893i		−	0.343926i
$949$	−21.7365	−	5.82427i	−0.705596	−	0.189064i
$950$		0			0
$951$	−34.1566			−1.10760
$952$	−6.61955	+	6.61955i	−0.214541	+	0.214541i
$953$	−12.8110	+	3.43270i	−0.414989	+	0.111196i	−0.460271	−	0.887778i	$-0.652248\pi$
$953$	−12.8110	+	3.43270i	−0.414989	+	0.111196i	0.0452823	+	0.998974i	$0.485581\pi$
$954$	0.0645812	−	0.0645812i	0.00209089	−	0.00209089i
$955$		0			0
$956$	−21.7566	−	21.7566i	−0.703658	−	0.703658i
$957$	−50.7919	+	29.3247i	−1.64187	+	0.947933i
$958$	−4.88016	−	1.30763i	−0.157671	−	0.0422477i
$959$	−46.1974	+	26.6721i	−1.49179	+	0.861287i
$960$		0			0
$961$			40.1552i			1.29533i
$962$	−3.91624	+	6.56417i	−0.126265	+	0.211637i
$963$	0.261488	−	0.261488i	0.00842632	−	0.00842632i
$964$	−8.31500	−	31.0320i	−0.267808	−	0.999474i
$965$		0			0
$966$	−5.32090	+	3.07202i	−0.171197	+	0.0988408i
$967$	−20.5372	−	35.5714i	−0.660431	−	1.14390i	−0.980503	−	0.196506i	$-0.937040\pi$
$967$	−20.5372	−	35.5714i	−0.660431	−	1.14390i	0.320072	−	0.947393i	$-0.396293\pi$
$968$			7.86321i			0.252733i
$969$	−3.09673	+	1.78790i	−0.0994814	+	0.0574356i
$970$		0			0
$971$	−10.9286	+	18.9288i	−0.350714	+	0.607455i	−0.986375	−	0.164514i	$-0.947395\pi$
$971$	−10.9286	+	18.9288i	−0.350714	+	0.607455i	0.635660	+	0.771969i	$0.280728\pi$
$972$	8.55032	+	8.55032i	0.274252	+	0.274252i
$973$	−46.1637	−	46.1637i	−1.47994	−	1.47994i
$974$	1.40602	+	0.811763i	0.0450516	+	0.0260106i
$975$		0			0
$976$	−26.2294	−	26.2294i	−0.839583	−	0.839583i
$977$	32.8873	+	18.9875i	1.05216	+	0.607464i	0.923253	−	0.384192i	$-0.125520\pi$
$977$	32.8873	+	18.9875i	1.05216	+	0.607464i	0.128906	+	0.991657i	$0.458853\pi$
$978$	1.97472	+	7.36975i	0.0631445	+	0.235659i
$979$	6.33024	−	1.69618i	0.202316	−	0.0542103i
$980$		0			0
$981$	−4.01988	−	1.07712i	−0.128345	−	0.0343899i
$982$	−1.18435	−	0.683786i	−0.0377942	−	0.0218205i
$983$	39.6755	−	10.6310i	1.26545	−	0.339077i	0.437166	−	0.899381i	$-0.355982\pi$
$983$	39.6755	−	10.6310i	1.26545	−	0.339077i	0.828287	+	0.560304i	$0.189316\pi$
$984$	−8.57158	+	2.29675i	−0.273252	+	0.0732177i
$985$		0			0
$986$	1.11385	−	4.15696i	0.0354723	−	0.132385i
$987$	−16.0262	−	59.8107i	−0.510121	−	1.90380i
$988$	−5.32127	+	5.32127i	−0.169292	+	0.169292i
$989$	11.4976			0.365602
$990$		0			0
$991$	9.05454	+	9.05454i	0.287627	+	0.287627i	0.836141	−	0.548514i	$-0.184806\pi$
$991$	9.05454	+	9.05454i	0.287627	+	0.287627i	−0.548514	+	0.836141i	$0.684806\pi$
$992$	23.0423	+	6.17416i	0.731593	+	0.196030i
$993$	−8.59535			−0.272765
$994$	−9.66883	−	2.59076i	−0.306677	−	0.0821738i
$995$		0			0
$996$	11.0636	+	19.1627i	0.350563	+	0.607193i
$997$	28.4758	−	49.3216i	0.901838	−	1.56203i	0.0767317	−	0.997052i	$-0.475551\pi$
$997$	28.4758	−	49.3216i	0.901838	−	1.56203i	0.825106	−	0.564978i	$-0.191115\pi$
$998$	0.919576	+	0.919576i	0.0291087	+	0.0291087i
$999$	−6.76871	−	26.7903i	−0.214153	−	0.847606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.532.9		68
5.2	odd	4		185.2.p.a.88.9	yes	68
5.3	odd	4		925.2.t.b.643.9		68
5.4	even	2		185.2.u.a.162.9	yes	68
37.8	odd	12		925.2.t.b.82.9		68
185.8	even	12	inner	925.2.y.b.193.9		68
185.82	even	12		185.2.u.a.8.9	yes	68
185.119	odd	12		185.2.p.a.82.9	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.9	✓	68	185.119	odd	12
185.2.p.a.88.9	yes	68	5.2	odd	4
185.2.u.a.8.9	yes	68	185.82	even	12
185.2.u.a.162.9	yes	68	5.4	even	2
925.2.t.b.82.9		68	37.8	odd	12
925.2.t.b.643.9		68	5.3	odd	4
925.2.y.b.193.9		68	185.8	even	12	inner
925.2.y.b.532.9		68	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.212566 + 0.122725i) q^{2} +(0.491666 - 1.83492i) q^{3} +(-0.969877 - 1.67988i) q^{4} +(0.329702 - 0.329702i) q^{6} +(-1.00868 + 3.76446i) q^{7} -0.967013i q^{8} +(-0.527123 - 0.304334i) q^{9} +4.37395i q^{11} +(-3.55930 + 0.953710i) q^{12} +(-4.43371 + 2.55980i) q^{13} +(-0.676405 + 0.676405i) q^{14} +(-1.82108 + 3.15420i) q^{16} +(-1.24200 + 2.15121i) q^{17} +(-0.0746989 - 0.129382i) q^{18} +(-0.196130 + 0.731966i) q^{19} +(6.41155 + 3.70171i) q^{21} +(-0.536793 + 0.929753i) q^{22} +3.38111i q^{23} +(-1.77439 - 0.475447i) q^{24} -1.25661 q^{26} +(3.21217 - 3.21217i) q^{27} +(7.30213 - 1.95660i) q^{28} +(-4.99116 + 4.99116i) q^{29} +(-5.96470 - 5.96470i) q^{31} +(-2.44911 + 1.41400i) q^{32} +(8.02585 + 2.15052i) q^{33} +(-0.528015 + 0.304850i) q^{34} +1.18067i q^{36} +(3.11652 - 5.22373i) q^{37} +(-0.131521 + 0.131521i) q^{38} +(2.51713 + 9.39407i) q^{39} +(4.18352 - 2.41536i) q^{41} +(0.908585 + 1.57371i) q^{42} -3.40053i q^{43} +(7.34770 - 4.24219i) q^{44} +(-0.414947 + 0.718709i) q^{46} +(-5.91409 - 5.91409i) q^{47} +(4.89234 + 4.89234i) q^{48} +(-7.09153 - 4.09430i) q^{49} +(3.33665 + 3.33665i) q^{51} +(8.60030 + 4.96539i) q^{52} +(0.158224 + 0.590502i) q^{53} +(1.07701 - 0.288584i) q^{54} +(3.64028 + 0.975410i) q^{56} +(1.24667 + 0.719765i) q^{57} +(-1.67349 + 0.448410i) q^{58} +(-9.92739 + 2.66004i) q^{59} +(-2.63598 + 9.83759i) q^{61} +(-0.535874 - 1.99991i) q^{62} +(1.67735 - 1.67735i) q^{63} +6.59018 q^{64} +(1.44210 + 1.44210i) q^{66} +(12.4015 + 3.32297i) q^{67} +4.81836 q^{68} +(6.20407 + 1.66238i) q^{69} +(5.23213 + 9.06231i) q^{71} +(-0.294295 + 0.509734i) q^{72} +(3.10809 + 3.10809i) q^{73} +(1.30355 - 0.727912i) q^{74} +(1.41983 - 0.380443i) q^{76} +(-16.4656 - 4.41193i) q^{77} +(-0.617830 + 2.30577i) q^{78} +(-0.743780 + 2.77583i) q^{79} +(-5.22776 - 9.05475i) q^{81} +1.18570 q^{82} +(-1.55418 - 5.80029i) q^{83} -14.3608i q^{84} +(0.417330 - 0.722837i) q^{86} +(6.70440 + 11.6124i) q^{87} +4.22967 q^{88} +(-0.387792 - 1.44726i) q^{89} +(-5.16406 - 19.2725i) q^{91} +(5.67985 - 3.27926i) q^{92} +(-13.8774 + 8.01211i) q^{93} +(-0.531327 - 1.98294i) q^{94} +(1.39043 + 5.18914i) q^{96} -6.03559 q^{97} +(-1.00495 - 1.74062i) q^{98} +(1.33114 - 2.30561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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