LMFDB - Embedded newform 400.3.bg.b.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.2
Character	$\chi$	$=$	400.113
Dual form			400.3.bg.b.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.299213 - 0.587238i) q^{3} +(3.77205 - 3.28201i) q^{5} +(5.08008 - 5.08008i) q^{7} +(5.03475 + 6.92973i) q^{9} +O(q^{10})$	\(q+(0.299213 - 0.587238i) q^{3} +(3.77205 - 3.28201i) q^{5} +(5.08008 - 5.08008i) q^{7} +(5.03475 + 6.92973i) q^{9} +(15.3739 + 11.1698i) q^{11} +(-15.1469 - 2.39904i) q^{13} +(-0.798677 - 3.19712i) q^{15} +(2.06006 + 4.04310i) q^{17} +(-7.61807 - 2.47526i) q^{19} +(-1.46319 - 4.50324i) q^{21} +(-4.63577 - 29.2691i) q^{23} +(3.45678 - 24.7599i) q^{25} +(11.4345 - 1.81105i) q^{27} +(41.1843 - 13.3816i) q^{29} +(-7.78864 + 23.9710i) q^{31} +(11.1594 - 5.68602i) q^{33} +(2.48944 - 35.8352i) q^{35} +(-1.63663 + 10.3332i) q^{37} +(-5.94097 + 8.17704i) q^{39} +(31.9797 - 23.2346i) q^{41} +(16.0163 + 16.0163i) q^{43} +(41.7348 + 9.61523i) q^{45} +(-14.0708 - 7.16942i) q^{47} -2.61434i q^{49} +2.99066 q^{51} +(-22.4011 + 43.9646i) q^{53} +(94.6509 - 8.32431i) q^{55} +(-3.73299 + 3.73299i) q^{57} +(8.28306 + 11.4007i) q^{59} +(-52.4160 - 38.0825i) q^{61} +(60.7805 + 9.62668i) q^{63} +(-65.0087 + 40.6631i) q^{65} +(-1.12080 - 2.19970i) q^{67} +(-18.5750 - 6.03539i) q^{69} +(-34.1821 - 105.202i) q^{71} +(-20.0687 - 126.709i) q^{73} +(-13.5056 - 9.43842i) q^{75} +(134.844 - 21.3573i) q^{77} +(52.5356 - 17.0699i) q^{79} +(-21.4645 + 66.0609i) q^{81} +(-132.945 + 67.7386i) q^{83} +(21.0401 + 8.48963i) q^{85} +(4.46469 - 28.1889i) q^{87} +(-58.7326 + 80.8385i) q^{89} +(-89.1349 + 64.7603i) q^{91} +(11.7462 + 11.7462i) q^{93} +(-36.8596 + 15.6658i) q^{95} +(74.7286 + 38.0761i) q^{97} +162.775i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9}+O(q^{10}) $ 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9	$ 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9} + 32 q^{11} + 2 q^{13} + 20 q^{15} - 92 q^{17} + 230 q^{19} + 68 q^{21} + 18 q^{23} + 40 q^{25} - 260 q^{27} + 100 q^{29} + 132 q^{31} + 364 q^{33} - 50 q^{35} - 192 q^{37} + 80 q^{39} + 168 q^{41} + 78 q^{43} - 310 q^{45} + 22 q^{47} - 168 q^{51} - 108 q^{53} + 40 q^{55} + 280 q^{57} - 450 q^{59} - 492 q^{61} + 558 q^{63} + 120 q^{65} + 572 q^{67} - 670 q^{69} + 2 q^{71} + 262 q^{73} - 140 q^{75} + 496 q^{77} + 360 q^{79} - 46 q^{81} - 772 q^{83} + 490 q^{85} - 210 q^{87} + 900 q^{89} - 798 q^{91} + 294 q^{93} + 378 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9 + 32 * q^11 + 2 * q^13 + 20 * q^15 - 92 * q^17 + 230 * q^19 + 68 * q^21 + 18 * q^23 + 40 * q^25 - 260 * q^27 + 100 * q^29 + 132 * q^31 + 364 * q^33 - 50 * q^35 - 192 * q^37 + 80 * q^39 + 168 * q^41 + 78 * q^43 - 310 * q^45 + 22 * q^47 - 168 * q^51 - 108 * q^53 + 40 * q^55 + 280 * q^57 - 450 * q^59 - 492 * q^61 + 558 * q^63 + 120 * q^65 + 572 * q^67 - 670 * q^69 + 2 * q^71 + 262 * q^73 - 140 * q^75 + 496 * q^77 + 360 * q^79 - 46 * q^81 - 772 * q^83 + 490 * q^85 - 210 * q^87 + 900 * q^89 - 798 * q^91 + 294 * q^93 + 378 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.299213	−	0.587238i	0.0997376	−	0.195746i	−0.835746	−	0.549116i	$-0.814964\pi$
$3$	0.299213	−	0.587238i	0.0997376	−	0.195746i	0.935484	+	0.353370i	$0.114964\pi$
$4$		0			0
$5$	3.77205	−	3.28201i	0.754411	−	0.656403i
$5$	3.77205	−	3.28201i	0.754411	−	0.656403i
$6$		0			0
$7$	5.08008	−	5.08008i	0.725725	−	0.725725i	−0.244040	−	0.969765i	$-0.578473\pi$
$7$	5.08008	−	5.08008i	0.725725	−	0.725725i	0.969765	+	0.244040i	$0.0784728\pi$
$8$		0			0
$9$	5.03475	+	6.92973i	0.559416	+	0.769970i
$10$		0			0
$11$	15.3739	+	11.1698i	1.39763	+	1.01544i	0.994979	+	0.100086i	$0.0319117\pi$
$11$	15.3739	+	11.1698i	1.39763	+	1.01544i	0.402653	+	0.915353i	$0.368088\pi$
$12$		0			0
$13$	−15.1469	−	2.39904i	−1.16515	−	0.184541i	−0.456250	−	0.889852i	$-0.650808\pi$
$13$	−15.1469	−	2.39904i	−1.16515	−	0.184541i	−0.708899	+	0.705310i	$0.750808\pi$
$14$		0			0
$15$	−0.798677	−	3.19712i	−0.0532451	−	0.213141i
$16$		0			0
$17$	2.06006	+	4.04310i	0.121180	+	0.237829i	0.943626	−	0.331015i	$-0.107391\pi$
$17$	2.06006	+	4.04310i	0.121180	+	0.237829i	−0.822446	+	0.568844i	$0.807391\pi$
$18$		0			0
$19$	−7.61807	−	2.47526i	−0.400951	−	0.130277i	0.101598	−	0.994826i	$-0.467604\pi$
$19$	−7.61807	−	2.47526i	−0.400951	−	0.130277i	−0.502549	+	0.864549i	$0.667604\pi$
$20$		0			0
$21$	−1.46319	−	4.50324i	−0.0696758	−	0.214440i
$22$		0			0
$23$	−4.63577	−	29.2691i	−0.201555	−	1.27257i	−0.856204	−	0.516637i	$-0.827184\pi$
$23$	−4.63577	−	29.2691i	−0.201555	−	1.27257i	0.654649	−	0.755933i	$-0.272816\pi$
$24$		0			0
$25$	3.45678	−	24.7599i	0.138271	−	0.990394i
$26$		0			0
$27$	11.4345	−	1.81105i	0.423500	−	0.0670758i
$28$		0			0
$29$	41.1843	−	13.3816i	1.42015	−	0.461434i	0.504499	−	0.863412i	$-0.331677\pi$
$29$	41.1843	−	13.3816i	1.42015	−	0.461434i	0.915649	+	0.401979i	$0.131677\pi$
$30$		0			0
$31$	−7.78864	+	23.9710i	−0.251246	+	0.773257i	0.743300	+	0.668959i	$0.233260\pi$
$31$	−7.78864	+	23.9710i	−0.251246	+	0.773257i	−0.994546	+	0.104298i	$0.966740\pi$
$32$		0			0
$33$	11.1594	−	5.68602i	0.338165	−	0.172303i
$34$		0			0
$35$	2.48944	−	35.8352i	0.0711269	−	1.02386i
$36$		0			0
$37$	−1.63663	+	10.3332i	−0.0442331	+	0.279277i	−0.999884	−	0.0152247i	$-0.995154\pi$
$37$	−1.63663	+	10.3332i	−0.0442331	+	0.279277i	0.955651	+	0.294502i	$0.0951537\pi$
$38$		0			0
$39$	−5.94097	+	8.17704i	−0.152332	+	0.209668i
$40$		0			0
$41$	31.9797	−	23.2346i	0.779992	−	0.566698i	−0.124984	−	0.992159i	$-0.539888\pi$
$41$	31.9797	−	23.2346i	0.779992	−	0.566698i	0.904977	+	0.425461i	$0.139888\pi$
$42$		0			0
$43$	16.0163	+	16.0163i	0.372473	+	0.372473i	0.868377	−	0.495904i	$-0.165163\pi$
$43$	16.0163	+	16.0163i	0.372473	+	0.372473i	−0.495904	+	0.868377i	$0.665163\pi$
$44$		0			0
$45$	41.7348	+	9.61523i	0.927440	+	0.213672i
$46$		0			0
$47$	−14.0708	−	7.16942i	−0.299378	−	0.152541i	0.297849	−	0.954613i	$-0.403731\pi$
$47$	−14.0708	−	7.16942i	−0.299378	−	0.152541i	−0.597227	+	0.802072i	$0.703731\pi$
$48$		0			0
$49$		−	2.61434i		−	0.0533539i
$50$		0			0
$51$	2.99066			0.0586403
$52$		0			0
$53$	−22.4011	+	43.9646i	−0.422662	+	0.829521i	0.577254	+	0.816565i	$0.304124\pi$
$53$	−22.4011	+	43.9646i	−0.422662	+	0.829521i	−0.999916	+	0.0129566i	$0.995876\pi$
$54$		0			0
$55$	94.6509	−	8.32431i	1.72092	−	0.151351i
$56$		0			0
$57$	−3.73299	+	3.73299i	−0.0654911	+	0.0654911i
$58$		0			0
$59$	8.28306	+	11.4007i	0.140391	+	0.193231i	0.873423	−	0.486963i	$-0.161895\pi$
$59$	8.28306	+	11.4007i	0.140391	+	0.193231i	−0.733032	+	0.680194i	$0.761895\pi$
$60$		0			0
$61$	−52.4160	−	38.0825i	−0.859279	−	0.624303i	0.0684097	−	0.997657i	$-0.478207\pi$
$61$	−52.4160	−	38.0825i	−0.859279	−	0.624303i	−0.927689	+	0.373355i	$0.878207\pi$
$62$		0			0
$63$	60.7805	+	9.62668i	0.964769	+	0.152804i
$64$		0			0
$65$	−65.0087	+	40.6631i	−1.00013	+	0.625587i
$66$		0			0
$67$	−1.12080	−	2.19970i	−0.0167284	−	0.0328313i	0.882491	−	0.470329i	$-0.155865\pi$
$67$	−1.12080	−	2.19970i	−0.0167284	−	0.0328313i	−0.899219	+	0.437498i	$0.855865\pi$
$68$		0			0
$69$	−18.5750	−	6.03539i	−0.269203	−	0.0874695i
$70$		0			0
$71$	−34.1821	−	105.202i	−0.481438	−	1.48172i	−0.837074	−	0.547090i	$-0.815735\pi$
$71$	−34.1821	−	105.202i	−0.481438	−	1.48172i	0.355635	−	0.934625i	$-0.384265\pi$
$72$		0			0
$73$	−20.0687	−	126.709i	−0.274914	−	1.73574i	−0.608977	−	0.793188i	$-0.708420\pi$
$73$	−20.0687	−	126.709i	−0.274914	−	1.73574i	0.334063	−	0.942551i	$-0.391580\pi$
$74$		0			0
$75$	−13.5056	−	9.43842i	−0.180075	−	0.125846i
$76$		0			0
$77$	134.844	−	21.3573i	1.75123	−	0.277367i
$78$		0			0
$79$	52.5356	−	17.0699i	0.665008	−	0.216074i	0.0429880	−	0.999076i	$-0.486312\pi$
$79$	52.5356	−	17.0699i	0.665008	−	0.216074i	0.622020	+	0.783001i	$0.286312\pi$
$80$		0			0
$81$	−21.4645	+	66.0609i	−0.264994	+	0.815566i
$82$		0			0
$83$	−132.945	+	67.7386i	−1.60174	+	0.816128i	−0.601896	+	0.798574i	$0.705588\pi$
$83$	−132.945	+	67.7386i	−1.60174	+	0.816128i	−0.999846	+	0.0175538i	$0.994412\pi$
$84$		0			0
$85$	21.0401	+	8.48963i	0.247531	+	0.0998780i
$86$		0			0
$87$	4.46469	−	28.1889i	0.0513183	−	0.324011i
$88$		0			0
$89$	−58.7326	+	80.8385i	−0.659917	+	0.908298i	−0.999479	−	0.0322861i	$-0.989721\pi$
$89$	−58.7326	+	80.8385i	−0.659917	+	0.908298i	0.339562	+	0.940584i	$0.389721\pi$
$90$		0			0
$91$	−89.1349	+	64.7603i	−0.979504	+	0.711652i
$92$		0			0
$93$	11.7462	+	11.7462i	0.126303	+	0.126303i
$94$		0			0
$95$	−36.8596	+	15.6658i	−0.387996	+	0.164903i
$96$		0			0
$97$	74.7286	+	38.0761i	0.770398	+	0.392537i	0.794572	−	0.607171i	$-0.207696\pi$
$97$	74.7286	+	38.0761i	0.770398	+	0.392537i	−0.0241739	+	0.999708i	$0.507696\pi$
$98$		0			0
$99$			162.775i			1.64419i
$100$		0			0
$101$	−94.8804			−0.939410			−0.469705	−	0.882824i	$-0.655640\pi$
$101$	−94.8804			−0.939410			−0.469705	+	0.882824i	$0.655640\pi$
$102$		0			0
$103$	7.55549	−	14.8285i	0.0733543	−	0.143966i	−0.851417	−	0.524489i	$-0.824256\pi$
$103$	7.55549	−	14.8285i	0.0733543	−	0.143966i	0.924771	+	0.380524i	$0.124256\pi$
$104$		0			0
$105$	−20.2989	−	12.1842i	−0.193323	−	0.116040i
$106$		0			0
$107$	−6.28336	+	6.28336i	−0.0587230	+	0.0587230i	−0.735858	−	0.677135i	$-0.763221\pi$
$107$	−6.28336	+	6.28336i	−0.0587230	+	0.0587230i	0.677135	+	0.735858i	$0.263221\pi$
$108$		0			0
$109$	34.7441	+	47.8211i	0.318753	+	0.438726i	0.938086	−	0.346403i	$-0.112597\pi$
$109$	34.7441	+	47.8211i	0.318753	+	0.438726i	−0.619333	+	0.785128i	$0.712597\pi$
$110$		0			0
$111$	5.57838	+	4.05293i	0.0502557	+	0.0365129i
$112$		0			0
$113$	−79.1815	−	12.5411i	−0.700722	−	0.110983i	−0.204099	−	0.978950i	$-0.565427\pi$
$113$	−79.1815	−	12.5411i	−0.700722	−	0.110983i	−0.496622	+	0.867967i	$0.665427\pi$
$114$		0			0
$115$	−113.548	−	95.1900i	−0.987374	−	0.827739i
$116$		0			0
$117$	−59.6363	−	117.043i	−0.509712	−	1.00037i
$118$		0			0
$119$	31.0045	+	10.0740i	0.260542	+	0.0846552i
$120$		0			0
$121$	74.2022	+	228.371i	0.613241	+	1.88736i
$122$		0			0
$123$	−4.07552	−	25.7318i	−0.0331343	−	0.209202i
$124$		0			0
$125$	−68.2230	−	104.741i	−0.545784	−	0.837926i
$126$		0			0
$127$	173.820	−	27.5304i	1.36866	−	0.216775i	0.571530	−	0.820581i	$-0.306350\pi$
$127$	173.820	−	27.5304i	1.36866	−	0.216775i	0.797131	+	0.603806i	$0.206350\pi$
$128$		0			0
$129$	14.1977	−	4.61311i	0.110060	−	0.0357606i
$130$		0			0
$131$	−60.0918	+	184.943i	−0.458716	+	1.41178i	0.408001	+	0.912981i	$0.366226\pi$
$131$	−60.0918	+	184.943i	−0.458716	+	1.41178i	−0.866717	+	0.498800i	$0.833774\pi$
$132$		0			0
$133$	−51.2749	+	26.1258i	−0.385525	+	0.196435i
$134$		0			0
$135$	37.1877	−	44.3595i	0.275464	−	0.328589i
$136$		0			0
$137$	13.0753	−	82.5544i	0.0954404	−	0.602587i	−0.892892	−	0.450272i	$-0.851327\pi$
$137$	13.0753	−	82.5544i	0.0954404	−	0.602587i	0.988332	−	0.152315i	$-0.0486729\pi$
$138$		0			0
$139$	−59.6964	+	82.1651i	−0.429471	+	0.591116i	−0.967832	−	0.251599i	$-0.919044\pi$
$139$	−59.6964	+	82.1651i	−0.429471	+	0.591116i	0.538361	+	0.842714i	$0.319044\pi$
$140$		0			0
$141$	−8.42032	+	6.11772i	−0.0597185	+	0.0433881i
$142$		0			0
$143$	−206.071	−	206.071i	−1.44106	−	1.44106i
$144$		0			0
$145$	111.431	−	185.643i	0.768488	−	1.28030i
$146$		0			0
$147$	−1.53524	−	0.782244i	−0.0104438	−	0.00532139i
$148$		0			0
$149$			256.620i			1.72229i	0.508363	+	0.861143i	$0.330251\pi$
$149$			256.620i			1.72229i	−0.508363	+	0.861143i	$0.669749\pi$
$150$		0			0
$151$	−26.4378			−0.175085			−0.0875423	−	0.996161i	$-0.527901\pi$
$151$	−26.4378			−0.175085			−0.0875423	+	0.996161i	$0.527901\pi$
$152$		0			0
$153$	−17.6457	+	34.6316i	−0.115331	+	0.226350i
$154$		0			0
$155$	49.2939	+	115.982i	0.318025	+	0.748272i
$156$		0			0
$157$	−182.454	+	182.454i	−1.16213	+	1.16213i	−0.178119	+	0.984009i	$0.557001\pi$
$157$	−182.454	+	182.454i	−1.16213	+	1.16213i	−0.984009	+	0.178119i	$0.942999\pi$
$158$		0			0
$159$	19.1150	+	26.3096i	0.120220	+	0.165469i
$160$		0			0
$161$	−172.239	−	125.139i	−1.06981	−	0.777262i
$162$		0			0
$163$	−119.678	−	18.9551i	−0.734219	−	0.116289i	−0.221882	−	0.975074i	$-0.571220\pi$
$163$	−119.678	−	18.9551i	−0.734219	−	0.116289i	−0.512337	+	0.858785i	$0.671220\pi$
$164$		0			0
$165$	23.4324	−	58.0734i	0.142015	−	0.351960i
$166$		0			0
$167$	122.784	+	240.977i	0.735233	+	1.44298i	0.890443	+	0.455095i	$0.150395\pi$
$167$	122.784	+	240.977i	0.735233	+	1.44298i	−0.155210	+	0.987882i	$0.549605\pi$
$168$		0			0
$169$	62.9458	+	20.4523i	0.372460	+	0.121020i
$170$		0			0
$171$	−21.2021	−	65.2535i	−0.123989	−	0.381599i
$172$		0			0
$173$	0.0332496	+	0.209930i	0.000192194	+	0.00121347i	0.987784	−	0.155828i	$-0.0498045\pi$
$173$	0.0332496	+	0.209930i	0.000192194	+	0.00121347i	−0.987592	+	0.157041i	$0.949804\pi$
$174$		0			0
$175$	−108.221	−	143.343i	−0.618407	−	0.819101i
$176$		0			0
$177$	9.17330	−	1.45291i	0.0518266	−	0.00820852i
$178$		0			0
$179$	61.8454	−	20.0948i	0.345505	−	0.112261i	−0.131124	−	0.991366i	$-0.541859\pi$
$179$	61.8454	−	20.0948i	0.345505	−	0.112261i	0.476629	+	0.879105i	$0.341859\pi$
$180$		0			0
$181$	−34.0403	+	104.765i	−0.188068	+	0.578813i	−0.999988	−	0.00495553i	$-0.998423\pi$
$181$	−34.0403	+	104.765i	−0.188068	+	0.578813i	0.811920	+	0.583769i	$0.198423\pi$
$182$		0			0
$183$	−38.0470	+	19.3859i	−0.207907	+	0.105934i
$184$		0			0
$185$	27.7404	+	44.3490i	0.149948	+	0.239724i
$186$		0			0
$187$	−13.4894	+	85.1688i	−0.0721359	+	0.455448i
$188$		0			0
$189$	48.8879	−	67.2884i	0.258666	−	0.356023i
$190$		0			0
$191$	−45.3902	+	32.9779i	−0.237645	+	0.172659i	−0.700234	−	0.713914i	$-0.746921\pi$
$191$	−45.3902	+	32.9779i	−0.237645	+	0.172659i	0.462588	+	0.886573i	$0.346921\pi$
$192$		0			0
$193$	34.9311	+	34.9311i	0.180990	+	0.180990i	0.791787	−	0.610797i	$-0.209151\pi$
$193$	34.9311	+	34.9311i	0.180990	+	0.180990i	−0.610797	+	0.791787i	$0.709151\pi$
$194$		0			0
$195$	4.42751	+	50.3426i	0.0227052	+	0.258167i
$196$		0			0
$197$	30.7715	+	15.6789i	0.156201	+	0.0795882i	0.530343	−	0.847783i	$-0.322063\pi$
$197$	30.7715	+	15.6789i	0.156201	+	0.0795882i	−0.374143	+	0.927371i	$0.622063\pi$
$198$		0			0
$199$		−	102.272i		−	0.513928i	−0.966421	−	0.256964i	$-0.917278\pi$
$199$		−	102.272i		−	0.513928i	0.966421	−	0.256964i	$-0.0827221\pi$
$200$		0			0
$201$	−1.62711			−0.00809505
$202$		0			0
$203$	141.240	−	277.199i	0.695763	−	1.36551i
$204$		0			0
$205$	44.3728	−	192.600i	0.216453	−	0.939512i
$206$		0			0
$207$	179.487	−	179.487i	0.867088	−	0.867088i
$208$		0			0
$209$	−89.4715	−	123.147i	−0.428093	−	0.589220i
$210$		0			0
$211$	184.212	+	133.838i	0.873043	+	0.634303i	0.931402	−	0.363993i	$-0.118587\pi$
$211$	184.212	+	133.838i	0.873043	+	0.634303i	−0.0583587	+	0.998296i	$0.518587\pi$
$212$		0			0
$213$	−72.0063	−	11.4047i	−0.338058	−	0.0535431i
$214$		0			0
$215$	112.980	+	7.84865i	0.525490	+	0.0365054i
$216$		0			0
$217$	82.2075	+	161.341i	0.378836	+	0.743508i
$218$		0			0
$219$	−80.4131	−	26.1278i	−0.367183	−	0.119305i
$220$		0			0
$221$	−21.5041	−	66.1827i	−0.0973034	−	0.299469i
$222$		0			0
$223$	33.2206	+	209.747i	0.148971	+	0.940567i	0.943025	+	0.332720i	$0.107967\pi$
$223$	33.2206	+	209.747i	0.148971	+	0.940567i	−0.794054	+	0.607847i	$0.792033\pi$
$224$		0			0
$225$	188.983	−	100.705i	0.839926	−	0.447578i
$226$		0			0
$227$	−162.584	+	25.7507i	−0.716228	+	0.113439i	−0.503904	−	0.863760i	$-0.668103\pi$
$227$	−162.584	+	25.7507i	−0.716228	+	0.113439i	−0.212324	+	0.977199i	$0.568103\pi$
$228$		0			0
$229$	−123.207	+	40.0325i	−0.538023	+	0.174814i	−0.565409	−	0.824811i	$-0.691282\pi$
$229$	−123.207	+	40.0325i	−0.538023	+	0.174814i	0.0273861	+	0.999625i	$0.491282\pi$
$230$		0			0
$231$	27.8054	−	85.5762i	0.120370	−	0.370460i
$232$		0			0
$233$	−123.226	+	62.7869i	−0.528868	+	0.269472i	−0.697970	−	0.716127i	$-0.745913\pi$
$233$	−123.226	+	62.7869i	−0.528868	+	0.269472i	0.169102	+	0.985599i	$0.445913\pi$
$234$		0			0
$235$	−76.6058	+	19.1370i	−0.325982	+	0.0814342i
$236$		0			0
$237$	5.69526	−	35.9585i	0.0240306	−	0.151723i
$238$		0			0
$239$	124.760	−	171.718i	0.522009	−	0.718484i	−0.463877	−	0.885900i	$-0.653542\pi$
$239$	124.760	−	171.718i	0.522009	−	0.718484i	0.985886	+	0.167415i	$0.0535421\pi$
$240$		0			0
$241$	−211.841	+	153.912i	−0.879009	+	0.638637i	−0.932989	−	0.359905i	$-0.882809\pi$
$241$	−211.841	+	153.912i	−0.879009	+	0.638637i	0.0539800	+	0.998542i	$0.482809\pi$
$242$		0			0
$243$	106.047	+	106.047i	0.436407	+	0.436407i
$244$		0			0
$245$	−8.58030	−	9.86143i	−0.0350216	−	0.0402507i
$246$		0			0
$247$	109.452	+	55.7686i	0.443126	+	0.225784i
$248$		0			0
$249$			98.3384i			0.394933i
$250$		0			0
$251$	−257.619			−1.02637			−0.513185	−	0.858278i	$-0.671535\pi$
$251$	−257.619			−1.02637			−0.513185	+	0.858278i	$0.671535\pi$
$252$		0			0
$253$	255.661	−	501.763i	1.01052	−	1.98325i
$254$		0			0
$255$	11.2809	−	9.81538i	0.0442389	−	0.0384917i
$256$		0			0
$257$	253.093	−	253.093i	0.984798	−	0.984798i	−0.0150882	−	0.999886i	$-0.504803\pi$
$257$	253.093	−	253.093i	0.984798	−	0.984798i	0.999886	+	0.0150882i	$0.00480290\pi$
$258$		0			0
$259$	44.1795	+	60.8079i	0.170577	+	0.234779i
$260$		0			0
$261$	300.083	+	218.023i	1.14974	+	0.835338i
$262$		0			0
$263$	−403.221	−	63.8639i	−1.53316	−	0.242829i	−0.667938	−	0.744217i	$-0.732823\pi$
$263$	−403.221	−	63.8639i	−1.53316	−	0.242829i	−0.865222	+	0.501388i	$0.832823\pi$
$264$		0			0
$265$	59.7944	+	239.358i	0.225639	+	0.903236i
$266$		0			0
$267$	29.8979	+	58.6780i	0.111977	+	0.219768i
$268$		0			0
$269$	159.892	+	51.9520i	0.594393	+	0.193130i	0.590738	−	0.806863i	$-0.298837\pi$
$269$	159.892	+	51.9520i	0.594393	+	0.193130i	0.00365486	+	0.999993i	$0.498837\pi$
$270$		0			0
$271$	10.8829	+	33.4942i	0.0401584	+	0.123595i	0.969126	−	0.246567i	$-0.0793024\pi$
$271$	10.8829	+	33.4942i	0.0401584	+	0.123595i	−0.928967	+	0.370161i	$0.879302\pi$
$272$		0			0
$273$	11.3594	+	71.7205i	0.0416096	+	0.262713i
$274$		0			0
$275$	329.708	−	342.045i	1.19894	−	1.24380i
$276$		0			0
$277$	485.638	−	76.9174i	1.75320	−	0.277680i	0.804525	−	0.593919i	$-0.202420\pi$
$277$	485.638	−	76.9174i	1.75320	−	0.277680i	0.948680	+	0.316239i	$0.102420\pi$
$278$		0			0
$279$	−205.326	+	66.7146i	−0.735936	+	0.239120i
$280$		0			0
$281$	88.8094	−	273.327i	0.316048	−	0.972695i	−0.659273	−	0.751903i	$-0.729136\pi$
$281$	88.8094	−	273.327i	0.316048	−	0.972695i	0.975321	−	0.220791i	$-0.0708640\pi$
$282$		0			0
$283$	180.911	−	92.1790i	0.639263	−	0.325721i	−0.104142	−	0.994562i	$-0.533210\pi$
$283$	180.911	−	92.1790i	0.639263	−	0.325721i	0.743405	+	0.668842i	$0.233210\pi$
$284$		0			0
$285$	−1.82932	+	26.3328i	−0.00641866	+	0.0923957i
$286$		0			0
$287$	44.4257	−	280.493i	0.154793	−	0.977327i
$288$		0			0
$289$	157.767	−	217.148i	0.545907	−	0.751377i
$290$		0			0
$291$	44.7195	−	32.4906i	0.153675	−	0.111652i
$292$		0			0
$293$	−131.312	−	131.312i	−0.448164	−	0.448164i	0.446580	−	0.894744i	$-0.352642\pi$
$293$	−131.312	−	131.312i	−0.448164	−	0.448164i	−0.894744	+	0.446580i	$0.852642\pi$
$294$		0			0
$295$	68.6613	+	15.8188i	0.232750	+	0.0536229i
$296$		0			0
$297$	196.022	+	99.8784i	0.660008	+	0.336291i
$298$		0			0
$299$			454.459i			1.51993i
$300$		0			0
$301$	162.728			0.540626
$302$		0			0
$303$	−28.3894	+	55.7174i	−0.0936945	+	0.183886i
$304$		0			0
$305$	−322.703	+	28.3810i	−1.05804	+	0.0930523i
$306$		0			0
$307$	226.711	−	226.711i	0.738472	−	0.738472i	−0.233810	−	0.972282i	$-0.575119\pi$
$307$	226.711	−	226.711i	0.738472	−	0.738472i	0.972282	+	0.233810i	$0.0751194\pi$
$308$		0			0
$309$	−6.44715	−	8.87375i	−0.0208646	−	0.0287176i
$310$		0			0
$311$	−178.706	−	129.837i	−0.574617	−	0.417483i	0.262163	−	0.965024i	$-0.415564\pi$
$311$	−178.706	−	129.837i	−0.574617	−	0.417483i	−0.836779	+	0.547540i	$0.815564\pi$
$312$		0			0
$313$	−288.434	−	45.6834i	−0.921514	−	0.145953i	−0.322387	−	0.946608i	$-0.604485\pi$
$313$	−288.434	−	45.6834i	−0.921514	−	0.145953i	−0.599126	+	0.800654i	$0.704485\pi$
$314$		0			0
$315$	260.862	−	163.170i	0.828134	−	0.518000i
$316$		0			0
$317$	−85.6031	−	168.006i	−0.270041	−	0.529986i	0.715668	−	0.698441i	$-0.246122\pi$
$317$	−85.6031	−	168.006i	−0.270041	−	0.529986i	−0.985709	+	0.168455i	$0.946122\pi$
$318$		0			0
$319$	782.635	+	254.294i	2.45340	+	0.797158i
$320$		0			0
$321$	1.80977	+	5.56989i	0.00563791	+	0.0173517i
$322$		0			0
$323$	−5.68596	−	35.8997i	−0.0176036	−	0.111145i
$324$		0			0
$325$	−111.759	+	366.743i	−0.343875	+	1.12844i
$326$		0			0
$327$	38.4783	−	6.09436i	0.117671	−	0.0186372i
$328$		0			0
$329$	−107.902	+	35.0594i	−0.327969	+	0.106564i
$330$		0			0
$331$	−6.22386	+	19.1551i	−0.0188032	+	0.0578703i	−0.960018	−	0.279939i	$-0.909686\pi$
$331$	−6.22386	+	19.1551i	−0.0188032	+	0.0578703i	0.941215	+	0.337809i	$0.109686\pi$
$332$		0			0
$333$	−79.8467	+	40.6839i	−0.239780	+	0.122174i
$334$		0			0
$335$	−11.4472	−	4.61889i	−0.0341706	−	0.0137877i
$336$		0			0
$337$	0.112139	−	0.708016i	0.000332756	−	0.00210094i	−0.987521	−	0.157485i	$-0.949661\pi$
$337$	0.112139	−	0.708016i	0.000332756	−	0.00210094i	0.987854	+	0.155384i	$0.0496615\pi$
$338$		0			0
$339$	−31.0568	+	42.7460i	−0.0916129	+	0.126094i
$340$		0			0
$341$	−387.494	+	281.531i	−1.13635	+	0.825603i
$342$		0			0
$343$	235.643	+	235.643i	0.687005	+	0.687005i
$344$		0			0
$345$	−89.8743	+	38.1977i	−0.260505	+	0.110718i
$346$		0			0
$347$	−301.742	−	153.745i	−0.869573	−	0.443069i	−0.0385166	−	0.999258i	$-0.512263\pi$
$347$	−301.742	−	153.745i	−0.869573	−	0.443069i	−0.831056	+	0.556188i	$0.812263\pi$
$348$		0			0
$349$			16.5208i			0.0473377i	0.999720	+	0.0236688i	$0.00753473\pi$
$349$			16.5208i			0.0473377i	−0.999720	+	0.0236688i	$0.992465\pi$
$350$		0			0
$351$	−177.542			−0.505819
$352$		0			0
$353$	79.4588	−	155.947i	0.225096	−	0.441776i	−0.750645	−	0.660706i	$-0.770257\pi$
$353$	79.4588	−	155.947i	0.225096	−	0.441776i	0.975740	+	0.218931i	$0.0702569\pi$
$354$		0			0
$355$	−474.210	−	284.641i	−1.33580	−	0.801804i
$356$		0			0
$357$	15.1928	−	15.1928i	0.0425568	−	0.0425568i
$358$		0			0
$359$	−256.595	−	353.173i	−0.714751	−	0.983770i	−0.999682	−	0.0252219i	$-0.991971\pi$
$359$	−256.595	−	353.173i	−0.714751	−	0.983770i	0.284931	−	0.958548i	$-0.408029\pi$
$360$		0			0
$361$	−240.147	−	174.477i	−0.665227	−	0.483316i
$362$		0			0
$363$	156.310	+	24.7571i	0.430607	+	0.0682014i
$364$		0			0
$365$	−491.561	−	412.087i	−1.34674	−	1.12901i
$366$		0			0
$367$	−3.80774	−	7.47312i	−0.0103753	−	0.0203627i	0.885761	−	0.464142i	$-0.153637\pi$
$367$	−3.80774	−	7.47312i	−0.0103753	−	0.0203627i	−0.896136	+	0.443779i	$0.853637\pi$
$368$		0			0
$369$	322.019	+	104.630i	0.872681	+	0.283551i
$370$		0			0
$371$	109.544	+	337.143i	0.295268	+	0.908741i
$372$		0			0
$373$	60.0619	+	379.216i	0.161024	+	1.01667i	0.927345	+	0.374207i	$0.122085\pi$
$373$	60.0619	+	379.216i	0.161024	+	1.01667i	−0.766321	+	0.642458i	$0.777915\pi$
$374$		0			0
$375$	−81.9210	+	8.72341i	−0.218456	+	0.0232624i
$376$		0			0
$377$	−655.919	+	103.887i	−1.73984	+	0.275563i
$378$		0			0
$379$	−323.639	+	105.157i	−0.853928	+	0.277458i	−0.703090	−	0.711101i	$-0.748197\pi$
$379$	−323.639	+	105.157i	−0.853928	+	0.277458i	−0.150838	+	0.988559i	$0.548197\pi$
$380$		0			0
$381$	35.8423	−	110.311i	0.0940742	−	0.289531i
$382$		0			0
$383$	−67.0852	+	34.1816i	−0.175157	+	0.0892470i	−0.539371	−	0.842068i	$-0.681338\pi$
$383$	−67.0852	+	34.1816i	−0.175157	+	0.0892470i	0.364214	+	0.931315i	$0.381338\pi$
$384$		0			0
$385$	438.545	−	523.122i	1.13908	−	1.35876i
$386$		0			0
$387$	−30.3507	+	191.627i	−0.0784257	+	0.495160i
$388$		0			0
$389$	−3.14213	+	4.32477i	−0.00807745	+	0.0111177i	−0.813037	−	0.582213i	$-0.802187\pi$
$389$	−3.14213	+	4.32477i	−0.00807745	+	0.0111177i	0.804959	+	0.593330i	$0.202187\pi$
$390$		0			0
$391$	108.788	−	79.0390i	0.278230	−	0.202146i
$392$		0			0
$393$	90.6256	+	90.6256i	0.230600	+	0.230600i
$394$		0			0
$395$	142.144	−	236.811i	0.359857	−	0.599522i
$396$		0			0
$397$	255.655	+	130.263i	0.643968	+	0.328118i	0.745295	−	0.666735i	$-0.232309\pi$
$397$	255.655	+	130.263i	0.643968	+	0.328118i	−0.101327	+	0.994853i	$0.532309\pi$
$398$		0			0
$399$			37.9278i			0.0950570i
$400$		0			0
$401$	369.494			0.921432			0.460716	−	0.887548i	$-0.347593\pi$
$401$	369.494			0.921432			0.460716	+	0.887548i	$0.347593\pi$
$402$		0			0
$403$	175.481	−	344.402i	0.435438	−	0.854594i
$404$		0			0
$405$	135.847	+	319.632i	0.335426	+	0.789214i
$406$		0			0
$407$	−140.582	+	140.582i	−0.345410	+	0.345410i
$408$		0			0
$409$	195.858	+	269.576i	0.478871	+	0.659110i	0.978288	−	0.207252i	$-0.0664521\pi$
$409$	195.858	+	269.576i	0.478871	+	0.659110i	−0.499416	+	0.866362i	$0.666452\pi$
$410$		0			0
$411$	−44.5668	−	32.3797i	−0.108435	−	0.0787827i
$412$		0			0
$413$	99.9948	+	15.8376i	0.242118	+	0.0383477i
$414$		0			0
$415$	−279.155	+	691.840i	−0.672663	+	1.66708i
$416$		0			0
$417$	30.3885	+	59.6409i	0.0728742	+	0.143024i
$418$		0			0
$419$	−547.856	−	178.009i	−1.30753	−	0.424843i	−0.429337	−	0.903145i	$-0.641253\pi$
$419$	−547.856	−	178.009i	−1.30753	−	0.424843i	−0.878196	+	0.478302i	$0.841253\pi$
$420$		0			0
$421$	−239.932	−	738.435i	−0.569910	−	1.75400i	−0.652892	−	0.757451i	$-0.726444\pi$
$421$	−239.932	−	738.435i	−0.569910	−	1.75400i	0.0829823	−	0.996551i	$-0.473556\pi$
$422$		0			0
$423$	−21.1606	−	133.603i	−0.0500251	−	0.315846i
$424$		0			0
$425$	107.228	−	37.0307i	0.252300	−	0.0871311i
$426$		0			0
$427$	−459.739	+	72.8155i	−1.07667	+	0.170528i
$428$		0			0
$429$	−182.672	+	59.3538i	−0.425809	+	0.138354i
$430$		0			0
$431$	−95.6942	+	294.516i	−0.222028	+	0.683333i	0.776551	+	0.630054i	$0.216967\pi$
$431$	−95.6942	+	294.516i	−0.222028	+	0.683333i	−0.998580	+	0.0532789i	$0.983033\pi$
$432$		0			0
$433$	23.0174	−	11.7280i	0.0531581	−	0.0270854i	−0.427209	−	0.904153i	$-0.640503\pi$
$433$	23.0174	−	11.7280i	0.0531581	−	0.0270854i	0.480368	+	0.877067i	$0.340503\pi$
$434$		0			0
$435$	−75.6754	−	120.983i	−0.173966	−	0.278123i
$436$		0			0
$437$	−37.1330	+	234.449i	−0.0849726	+	0.536496i
$438$		0			0
$439$	173.704	−	239.083i	0.395682	−	0.544609i	−0.563972	−	0.825794i	$-0.690727\pi$
$439$	173.704	−	239.083i	0.395682	−	0.544609i	0.959654	+	0.281185i	$0.0907274\pi$
$440$		0			0
$441$	18.1167	−	13.1625i	0.0410809	−	0.0298470i
$442$		0			0
$443$	497.721	+	497.721i	1.12352	+	1.12352i	0.991208	+	0.132316i	$0.0422415\pi$
$443$	497.721	+	497.721i	1.12352	+	1.12352i	0.132316	+	0.991208i	$0.457759\pi$
$444$		0			0
$445$	43.7705	+	497.688i	0.0983606	+	1.11840i
$446$		0			0
$447$	150.697	+	76.7842i	0.337131	+	0.171777i
$448$		0			0
$449$		−	99.6032i		−	0.221833i	−0.993830	−	0.110917i	$-0.964621\pi$
$449$		−	99.6032i		−	0.221833i	0.993830	−	0.110917i	$-0.0353787\pi$
$450$		0			0
$451$	751.180			1.66559
$452$		0			0
$453$	−7.91052	+	15.5253i	−0.0174625	+	0.0342721i
$454$		0			0
$455$	−123.677	+	536.821i	−0.271819	+	1.17983i
$456$		0			0
$457$	−479.543	+	479.543i	−1.04933	+	1.04933i	−0.0506104	+	0.998718i	$0.516117\pi$
$457$	−479.543	+	479.543i	−1.04933	+	1.04933i	−0.998718	+	0.0506104i	$0.983883\pi$
$458$		0			0
$459$	30.8780	+	42.4999i	0.0672723	+	0.0925924i
$460$		0			0
$461$	73.4943	+	53.3967i	0.159424	+	0.115828i	0.664637	−	0.747166i	$-0.268586\pi$
$461$	73.4943	+	53.3967i	0.159424	+	0.115828i	−0.505213	+	0.862994i	$0.668586\pi$
$462$		0			0
$463$	−536.515	−	84.9756i	−1.15878	−	0.183533i	−0.452699	−	0.891664i	$-0.649539\pi$
$463$	−536.515	−	84.9756i	−1.15878	−	0.183533i	−0.706081	+	0.708131i	$0.749539\pi$
$464$		0			0
$465$	82.8586	+	5.75612i	0.178190	+	0.0123788i
$466$		0			0
$467$	−138.860	−	272.527i	−0.297344	−	0.583570i	0.693203	−	0.720742i	$-0.256199\pi$
$467$	−138.860	−	272.527i	−0.297344	−	0.583570i	−0.990547	+	0.137172i	$0.956199\pi$
$468$		0			0
$469$	−16.8684	−	5.48087i	−0.0359667	−	0.0116863i
$470$		0			0
$471$	52.5514	+	161.737i	0.111574	+	0.343390i
$472$		0			0
$473$	67.3346	+	425.134i	0.142356	+	0.898803i
$474$		0			0
$475$	−87.6211	+	180.066i	−0.184465	+	0.379086i
$476$		0			0
$477$	−417.447	+	66.1171i	−0.875151	+	0.138610i
$478$		0			0
$479$	−433.715	+	140.923i	−0.905459	+	0.294201i	−0.724488	−	0.689287i	$-0.757924\pi$
$479$	−433.715	+	140.923i	−0.905459	+	0.294201i	−0.180971	+	0.983488i	$0.557924\pi$
$480$		0			0
$481$	49.5797	−	152.591i	0.103076	−	0.317237i
$482$		0			0
$483$	−125.023	+	63.7023i	−0.258846	+	0.131889i
$484$		0			0
$485$	406.846	−	101.635i	0.838859	−	0.209557i
$486$		0			0
$487$	−58.1185	+	366.946i	−0.119340	+	0.753482i	0.853344	+	0.521348i	$0.174571\pi$
$487$	−58.1185	+	366.946i	−0.119340	+	0.753482i	−0.972684	+	0.232134i	$0.925429\pi$
$488$		0			0
$489$	−46.9402	+	64.6077i	−0.0959923	+	0.132122i
$490$		0			0
$491$	665.953	−	483.843i	1.35632	−	0.985425i	0.357651	−	0.933855i	$-0.383578\pi$
$491$	665.953	−	483.843i	1.35632	−	0.985425i	0.998669	−	0.0515692i	$-0.0164223\pi$
$492$		0			0
$493$	138.945	+	138.945i	0.281836	+	0.281836i
$494$		0			0
$495$	534.228	+	613.995i	1.07925	+	1.24039i
$496$		0			0
$497$	−708.081	−	360.785i	−1.42471	−	0.725926i
$498$		0			0
$499$		−	564.641i		−	1.13154i	−0.824562	−	0.565772i	$-0.808578\pi$
$499$		−	564.641i		−	1.13154i	0.824562	−	0.565772i	$-0.191422\pi$
$500$		0			0
$501$	178.250			0.355788
$502$		0			0
$503$	−87.1140	+	170.971i	−0.173189	+	0.339902i	−0.961243	−	0.275704i	$-0.911089\pi$
$503$	−87.1140	+	170.971i	−0.173189	+	0.339902i	0.788054	+	0.615607i	$0.211089\pi$
$504$		0			0
$505$	−357.894	+	311.399i	−0.708701	+	0.616631i
$506$		0			0
$507$	30.8446	−	30.8446i	0.0608375	−	0.0608375i
$508$		0			0
$509$	−457.051	−	629.076i	−0.897938	−	1.23591i	−0.971121	−	0.238588i	$-0.923316\pi$
$509$	−457.051	−	629.076i	−0.897938	−	1.23591i	0.0731825	−	0.997319i	$-0.476684\pi$
$510$		0			0
$511$	−745.641	−	541.740i	−1.45918	−	1.06016i
$512$		0			0
$513$	−91.5916	−	14.5067i	−0.178541	−	0.0282781i
$514$		0			0
$515$	−20.1676	−	80.7311i	−0.0391603	−	0.156759i
$516$		0			0
$517$	−136.242	−	267.390i	−0.263525	−	0.517196i
$518$		0			0
$519$	0.133228	+	0.0432883i	0.000256701	+	8.34071e-5i
$520$		0			0
$521$	165.034	+	507.924i	0.316765	+	0.974901i	0.975022	+	0.222108i	$0.0712939\pi$
$521$	165.034	+	507.924i	0.316765	+	0.974901i	−0.658257	+	0.752793i	$0.728706\pi$
$522$		0			0
$523$	−94.2656	−	595.170i	−0.180240	−	1.13799i	−0.897444	−	0.441129i	$-0.854578\pi$
$523$	−94.2656	−	595.170i	−0.180240	−	1.13799i	0.717204	−	0.696864i	$-0.245422\pi$
$524$		0			0
$525$	−116.558	+	20.6617i	−0.222014	+	0.0393556i
$526$		0			0
$527$	−112.962	+	17.8914i	−0.214349	+	0.0339496i
$528$		0			0
$529$	−332.082	+	107.900i	−0.627754	+	0.203970i
$530$		0			0
$531$	−37.3004	+	114.799i	−0.0702456	+	0.216194i
$532$		0			0
$533$	−540.135	+	275.213i	−1.01339	+	0.516346i
$534$		0			0
$535$	−3.07910	+	44.3233i	−0.00575533	+	0.0828472i
$536$		0			0
$537$	6.70451	−	42.3306i	0.0124851	−	0.0788280i
$538$		0			0
$539$	29.2017	−	40.1927i	0.0541776	−	0.0745691i
$540$		0			0
$541$	267.054	−	194.026i	0.493631	−	0.358644i	−0.312948	−	0.949770i	$-0.601317\pi$
$541$	267.054	−	194.026i	0.493631	−	0.358644i	0.806579	+	0.591126i	$0.201317\pi$
$542$		0			0
$543$	51.3369	+	51.3369i	0.0945430	+	0.0945430i
$544$		0			0
$545$	288.006	+	66.3533i	0.528451	+	0.121749i
$546$		0			0
$547$	−51.5761	−	26.2793i	−0.0942890	−	0.0480426i	0.406210	−	0.913780i	$-0.366850\pi$
$547$	−51.5761	−	26.2793i	−0.0942890	−	0.0480426i	−0.500499	+	0.865737i	$0.666850\pi$
$548$		0			0
$549$		−	554.965i		−	1.01086i
$550$		0			0
$551$	−346.867			−0.629524
$552$		0			0
$553$	180.169	−	353.601i	0.325803	−	0.639423i
$554$		0			0
$555$	34.3437	−	3.02045i	0.0618806	−	0.00544225i
$556$		0			0
$557$	292.810	−	292.810i	0.525692	−	0.525692i	−0.393593	−	0.919285i	$-0.628768\pi$
$557$	292.810	−	292.810i	0.525692	−	0.525692i	0.919285	+	0.393593i	$0.128768\pi$
$558$		0			0
$559$	−204.175	−	281.022i	−0.365250	−	0.502723i
$560$		0			0
$561$	45.9782	+	33.4051i	0.0819576	+	0.0595457i
$562$		0			0
$563$	294.479	+	46.6408i	0.523053	+	0.0828434i	0.412377	−	0.911013i	$-0.364699\pi$
$563$	294.479	+	46.6408i	0.523053	+	0.0828434i	0.110675	+	0.993857i	$0.464699\pi$
$564$		0			0
$565$	−339.837	+	212.569i	−0.601482	+	0.376228i
$566$		0			0
$567$	226.553	+	444.635i	0.399564	+	0.784189i
$568$		0			0
$569$	−400.352	−	130.082i	−0.703607	−	0.228616i	−0.0647055	−	0.997904i	$-0.520611\pi$
$569$	−400.352	−	130.082i	−0.703607	−	0.228616i	−0.638901	+	0.769289i	$0.720611\pi$
$570$		0			0
$571$	93.2408	+	286.966i	0.163294	+	0.502567i	0.998907	−	0.0467522i	$-0.0148871\pi$
$571$	93.2408	+	286.966i	0.163294	+	0.502567i	−0.835613	+	0.549319i	$0.814887\pi$
$572$		0			0
$573$	5.78457	+	36.5223i	0.0100952	+	0.0637388i
$574$		0			0
$575$	−740.724	+	13.6042i	−1.28822	+	0.0236595i
$576$		0			0
$577$	132.165	−	20.9329i	0.229056	−	0.0362788i	−0.0408514	−	0.999165i	$-0.513007\pi$
$577$	132.165	−	20.9329i	0.229056	−	0.0362788i	0.269907	+	0.962886i	$0.413007\pi$
$578$		0			0
$579$	30.9647	−	10.0610i	0.0534796	−	0.0173766i
$580$		0			0
$581$	−331.251	+	1019.49i	−0.570140	+	1.75471i
$582$		0			0
$583$	−835.471	+	425.694i	−1.43305	+	0.730178i
$584$		0			0
$585$	−609.087	−	245.765i	−1.04117	−	0.420111i
$586$		0			0
$587$	43.1900	−	272.691i	0.0735775	−	0.464550i	−0.923199	−	0.384322i	$-0.874435\pi$
$587$	43.1900	−	272.691i	0.0735775	−	0.464550i	0.996777	−	0.0802279i	$-0.0255648\pi$
$588$		0			0
$589$	118.669	−	163.334i	0.201475	−	0.277306i
$590$		0			0
$591$	18.4145	−	13.3789i	0.0311582	−	0.0226377i
$592$		0			0
$593$	617.372	+	617.372i	1.04110	+	1.04110i	0.999118	+	0.0419820i	$0.0133672\pi$
$593$	617.372	+	617.372i	1.04110	+	1.04110i	0.0419820	+	0.999118i	$0.486633\pi$
$594$		0			0
$595$	150.013	−	63.7576i	0.252124	−	0.107156i
$596$		0			0
$597$	−60.0578	−	30.6010i	−0.100599	−	0.0512579i
$598$		0			0
$599$		−	194.492i		−	0.324695i	−0.986734	−	0.162348i	$-0.948093\pi$
$599$		−	194.492i		−	0.324695i	0.986734	−	0.162348i	$-0.0519066\pi$
$600$		0			0
$601$	−5.84871			−0.00973163			−0.00486581	−	0.999988i	$-0.501549\pi$
$601$	−5.84871			−0.00973163			−0.00486581	+	0.999988i	$0.501549\pi$
$602$		0			0
$603$	9.60037	−	18.8418i	0.0159210	−	0.0312467i
$604$		0			0
$605$	1029.41	+	617.894i	1.70150	+	1.02131i
$606$		0			0
$607$	−368.811	+	368.811i	−0.607597	+	0.607597i	−0.942317	−	0.334721i	$-0.891358\pi$
$607$	−368.811	+	368.811i	−0.607597	+	0.607597i	0.334721	+	0.942317i	$0.391358\pi$
$608$		0			0
$609$	−120.521	−	165.883i	−0.197900	−	0.272386i
$610$		0			0
$611$	195.929	+	142.351i	0.320670	+	0.232980i
$612$		0			0
$613$	211.132	+	33.4401i	0.344425	+	0.0545515i	0.326251	−	0.945283i	$-0.394215\pi$
$613$	211.132	+	33.4401i	0.344425	+	0.0545515i	0.0181741	+	0.999835i	$0.494215\pi$
$614$		0			0
$615$	−99.8251	−	83.6858i	−0.162317	−	0.136074i
$616$		0			0
$617$	104.841	+	205.762i	0.169921	+	0.333488i	0.960225	−	0.279226i	$-0.0900779\pi$
$617$	104.841	+	205.762i	0.169921	+	0.333488i	−0.790305	+	0.612714i	$0.790078\pi$
$618$		0			0
$619$	1081.59	+	351.431i	1.74732	+	0.567739i	0.995766	−	0.0919290i	$-0.0293033\pi$
$619$	1081.59	+	351.431i	1.74732	+	0.567739i	0.751557	+	0.659668i	$0.229303\pi$
$620$		0			0
$621$	−106.015	−	326.282i	−0.170717	−	0.525414i
$622$		0			0
$623$	112.300	+	709.032i	0.180256	+	1.13809i
$624$		0			0
$625$	−601.101	−	171.179i	−0.961762	−	0.273886i
$626$		0			0
$627$	−99.0877	+	15.6939i	−0.158035	+	0.0250302i
$628$		0			0
$629$	−45.1499	+	14.6701i	−0.0717804	+	0.0233229i
$630$		0			0
$631$	385.541	−	1186.57i	0.611000	−	1.88047i	0.162423	−	0.986721i	$-0.448069\pi$
$631$	385.541	−	1186.57i	0.611000	−	1.88047i	0.448577	−	0.893744i	$-0.351931\pi$
$632$		0			0
$633$	133.713	−	68.1304i	0.211238	−	0.107631i
$634$		0			0
$635$	565.303	−	674.326i	0.890241	−	1.06193i
$636$		0			0
$637$	−6.27191	+	39.5993i	−0.00984601	+	0.0621652i
$638$		0			0
$639$	556.922	−	766.537i	0.871553	−	1.19959i
$640$		0			0
$641$	774.288	−	562.553i	1.20794	−	0.877618i	0.212896	−	0.977075i	$-0.431710\pi$
$641$	774.288	−	562.553i	1.20794	−	0.877618i	0.995042	+	0.0994564i	$0.0317104\pi$
$642$		0			0
$643$	564.710	+	564.710i	0.878243	+	0.878243i	0.993353	−	0.115109i	$-0.0367219\pi$
$643$	564.710	+	564.710i	0.878243	+	0.878243i	−0.115109	+	0.993353i	$0.536722\pi$
$644$		0			0
$645$	38.4142	−	63.9979i	0.0595569	−	0.0992216i
$646$		0			0
$647$	438.612	+	223.484i	0.677916	+	0.345415i	0.758814	−	0.651307i	$-0.225779\pi$
$647$	438.612	+	223.484i	0.677916	+	0.345415i	−0.0808985	+	0.996722i	$0.525779\pi$
$648$		0			0
$649$			267.793i			0.412625i
$650$		0			0
$651$	119.343			0.183323
$652$		0			0
$653$	245.470	−	481.761i	0.375911	−	0.737766i	−0.623104	−	0.782139i	$-0.714129\pi$
$653$	245.470	−	481.761i	0.375911	−	0.737766i	0.999015	+	0.0443726i	$0.0141289\pi$
$654$		0			0
$655$	380.317	+	894.838i	0.580637	+	1.36617i
$656$		0			0
$657$	777.018	−	777.018i	1.18268	−	1.18268i
$658$		0			0
$659$	247.804	+	341.073i	0.376030	+	0.517561i	0.954527	−	0.298123i	$-0.0963607\pi$
$659$	247.804	+	341.073i	0.376030	+	0.517561i	−0.578497	+	0.815684i	$0.696361\pi$
$660$		0			0
$661$	355.368	+	258.190i	0.537622	+	0.390606i	0.823201	−	0.567750i	$-0.192186\pi$
$661$	355.368	+	258.190i	0.537622	+	0.390606i	−0.285579	+	0.958355i	$0.592186\pi$
$662$		0			0
$663$	−45.2993	−	7.17470i	−0.0683247	−	0.0108216i
$664$		0			0
$665$	−107.666	+	266.833i	−0.161904	+	0.401252i
$666$		0			0
$667$	−582.588	−	1143.39i	−0.873446	−	1.71423i
$668$		0			0
$669$	133.111	+	43.2505i	0.198970	+	0.0646494i
$670$		0			0
$671$	−380.467	−	1170.96i	−0.567014	−	1.74509i
$672$		0			0
$673$	−192.174	−	1213.34i	−0.285548	−	1.80288i	−0.546425	−	0.837508i	$-0.684012\pi$
$673$	−192.174	−	1213.34i	−0.285548	−	1.80288i	0.260877	−	0.965372i	$-0.415988\pi$
$674$		0			0
$675$	−5.31473	−	289.377i	−0.00787367	−	0.428707i
$676$		0			0
$677$	−383.123	+	60.6808i	−0.565913	+	0.0896319i	−0.432834	−	0.901474i	$-0.642486\pi$
$677$	−383.123	+	60.6808i	−0.565913	+	0.0896319i	−0.133079	+	0.991105i	$0.542486\pi$
$678$		0			0
$679$	573.056	−	186.197i	0.843971	−	0.274223i
$680$		0			0
$681$	−33.5253	+	103.180i	−0.0492296	+	0.151513i
$682$		0			0
$683$	621.402	−	316.620i	0.909812	−	0.463572i	0.0645440	−	0.997915i	$-0.479441\pi$
$683$	621.402	−	316.620i	0.909812	−	0.463572i	0.845268	+	0.534342i	$0.179441\pi$
$684$		0			0
$685$	−221.624	−	354.313i	−0.323538	−	0.517246i
$686$		0			0
$687$	−13.3566	+	84.3302i	−0.0194419	+	0.122751i
$688$		0			0
$689$	444.781	−	612.188i	0.645546	−	0.888517i
$690$		0			0
$691$	−66.3377	+	48.1971i	−0.0960024	+	0.0697498i	−0.634751	−	0.772717i	$-0.718897\pi$
$691$	−66.3377	+	48.1971i	−0.0960024	+	0.0697498i	0.538749	+	0.842467i	$0.318897\pi$
$692$		0			0
$693$	826.907	+	826.907i	1.19323	+	1.19323i
$694$		0			0
$695$	44.4887	+	505.855i	0.0640126	+	0.727850i
$696$		0			0
$697$	159.820	+	81.4322i	0.229297	+	0.116832i
$698$		0			0
$699$			91.1498i			0.130400i
$700$		0			0
$701$	88.2963			0.125958			0.0629788	−	0.998015i	$-0.479940\pi$
$701$	88.2963			0.125958			0.0629788	+	0.998015i	$0.479940\pi$
$702$		0			0
$703$	38.0454	−	74.6683i	0.0541186	−	0.106214i
$704$		0			0
$705$	−11.6835	+	50.7119i	−0.0165723	+	0.0719318i
$706$		0			0
$707$	−482.000	+	482.000i	−0.681753	+	0.681753i
$708$		0			0
$709$	176.056	+	242.321i	0.248317	+	0.341778i	0.914921	−	0.403633i	$-0.132253\pi$
$709$	176.056	+	242.321i	0.248317	+	0.341778i	−0.666604	+	0.745412i	$0.732253\pi$
$710$		0			0
$711$	382.793	+	278.116i	0.538387	+	0.391161i
$712$		0			0
$713$	737.715	+	116.843i	1.03466	+	0.163875i
$714$		0			0
$715$	−1453.64	−	100.983i	−2.03306	−	0.141235i
$716$		0			0
$717$	−63.5094	−	124.644i	−0.0885765	−	0.173841i
$718$		0			0
$719$	−956.744	−	310.865i	−1.33066	−	0.432357i	−0.444517	−	0.895771i	$-0.646625\pi$
$719$	−956.744	−	310.865i	−1.33066	−	0.432357i	−0.886142	+	0.463413i	$0.846625\pi$
$720$		0			0
$721$	−36.9474	−	113.712i	−0.0512446	−	0.157715i
$722$		0			0
$723$	26.9972	+	170.454i	0.0373405	+	0.235759i
$724$		0			0
$725$	−188.961	−	1065.97i	−0.260636	−	1.47031i
$726$		0			0
$727$	175.309	−	27.7663i	0.241141	−	0.0381930i	−0.0346941	−	0.999398i	$-0.511046\pi$
$727$	175.309	−	27.7663i	0.241141	−	0.0381930i	0.275835	+	0.961205i	$0.411046\pi$
$728$		0			0
$729$	−500.542	+	162.636i	−0.686615	+	0.223095i
$730$		0			0
$731$	−31.7609	+	97.7501i	−0.0434486	+	0.133721i
$732$		0			0
$733$	−88.9443	+	45.3194i	−0.121343	+	0.0618273i	−0.513608	−	0.858025i	$-0.671691\pi$
$733$	−88.9443	+	45.3194i	−0.121343	+	0.0618273i	0.392265	+	0.919852i	$0.371691\pi$
$734$		0			0
$735$	−8.35835	+	2.08801i	−0.0113719	+	0.00284084i
$736$		0			0
$737$	7.33909	−	46.3372i	0.00995806	−	0.0628727i
$738$		0			0
$739$	−297.186	+	409.042i	−0.402147	+	0.553507i	−0.961281	−	0.275570i	$-0.911134\pi$
$739$	−297.186	+	409.042i	−0.402147	+	0.553507i	0.559134	+	0.829077i	$0.311134\pi$
$740$		0			0
$741$	65.4990	−	47.5878i	0.0883927	−	0.0642210i
$742$		0			0
$743$	477.643	+	477.643i	0.642858	+	0.642858i	0.951257	−	0.308399i	$-0.0997933\pi$
$743$	477.643	+	477.643i	0.642858	+	0.642858i	−0.308399	+	0.951257i	$0.599793\pi$
$744$		0			0
$745$	842.232	+	967.986i	1.13051	+	1.29931i
$746$		0			0
$747$	−1138.75	−	580.224i	−1.52444	−	0.776739i
$748$		0			0
$749$			63.8399i			0.0852335i
$750$		0			0
$751$	878.613			1.16992			0.584962	−	0.811061i	$-0.301109\pi$
$751$	878.613			1.16992			0.584962	+	0.811061i	$0.301109\pi$
$752$		0			0
$753$	−77.0829	+	151.284i	−0.102368	+	0.200908i
$754$		0			0
$755$	−99.7247	+	86.7691i	−0.132086	+	0.114926i
$756$		0			0
$757$	−780.141	+	780.141i	−1.03057	+	1.03057i	−0.0310514	+	0.999518i	$0.509886\pi$
$757$	−780.141	+	780.141i	−1.03057	+	1.03057i	−0.999518	+	0.0310514i	$0.990114\pi$
$758$		0			0
$759$	−218.157	−	300.268i	−0.287427	−	0.395610i
$760$		0			0
$761$	29.4845	+	21.4218i	0.0387445	+	0.0281495i	0.606989	−	0.794710i	$-0.292377\pi$
$761$	29.4845	+	21.4218i	0.0387445	+	0.0281495i	−0.568244	+	0.822860i	$0.692377\pi$
$762$		0			0
$763$	419.437	+	66.4323i	0.549721	+	0.0870673i
$764$		0			0
$765$	47.1009	+	188.546i	0.0615699	+	0.246465i
$766$		0			0
$767$	−98.1124	−	192.556i	−0.127917	−	0.251051i
$768$		0			0
$769$	182.285	+	59.2278i	0.237041	+	0.0770193i	0.425129	−	0.905133i	$-0.360229\pi$
$769$	182.285	+	59.2278i	0.237041	+	0.0770193i	−0.188088	+	0.982152i	$0.560229\pi$
$770$		0			0
$771$	−72.8973	−	224.355i	−0.0945490	−	0.290992i
$772$		0			0
$773$	−68.2028	−	430.615i	−0.0882313	−	0.557070i	−0.991716	−	0.128450i	$-0.959000\pi$
$773$	−68.2028	−	430.615i	−0.0882313	−	0.557070i	0.903485	−	0.428620i	$-0.141000\pi$
$774$		0			0
$775$	566.594	+	275.708i	0.731089	+	0.355752i
$776$		0			0
$777$	48.9278	−	7.74940i	0.0629701	−	0.00997349i
$778$		0			0
$779$	−301.135	+	97.8447i	−0.386566	+	0.125603i
$780$		0			0
$781$	649.571	−	1999.18i	0.831717	−	2.55976i
$782$		0			0
$783$	446.687	−	227.598i	0.570481	−	0.290675i
$784$		0			0
$785$	−89.4099	+	1287.04i	−0.113898	+	1.63955i
$786$		0			0
$787$	−75.0272	+	473.703i	−0.0953331	+	0.601910i	0.893054	+	0.449950i	$0.148558\pi$
$787$	−75.0272	+	473.703i	−0.0953331	+	0.601910i	−0.988387	+	0.151959i	$0.951442\pi$
$788$		0			0
$789$	−158.152	+	217.678i	−0.200447	+	0.275891i
$790$		0			0
$791$	−465.958	+	338.538i	−0.589075	+	0.427988i
$792$		0			0
$793$	702.581	+	702.581i	0.885978	+	0.885978i
$794$		0			0
$795$	158.451	+	36.5054i	0.199310	+	0.0459187i
$796$		0			0
$797$	−993.693	−	506.312i	−1.24679	−	0.635272i	−0.299027	−	0.954245i	$-0.596662\pi$
$797$	−993.693	−	506.312i	−1.24679	−	0.635272i	−0.947764	+	0.318973i	$0.896662\pi$
$798$		0			0
$799$		−	71.6589i		−	0.0896857i
$800$		0			0
$801$	−855.893			−1.06853
$802$		0			0
$803$	1106.78	−	2172.18i	1.37831	−	2.70508i
$804$		0			0
$805$	−1060.41	+	93.2600i	−1.31727	+	0.115851i
$806$		0			0
$807$	78.3499	−	78.3499i	0.0970878	−	0.0970878i
$808$		0			0
$809$	−682.133	−	938.876i	−0.843181	−	1.16054i	−0.985324	−	0.170693i	$-0.945400\pi$
$809$	−682.133	−	938.876i	−0.843181	−	1.16054i	0.142144	−	0.989846i	$-0.454600\pi$
$810$		0			0
$811$	1263.18	+	917.753i	1.55756	+	1.13163i	0.937977	+	0.346697i	$0.112697\pi$
$811$	1263.18	+	917.753i	1.55756	+	1.13163i	0.619579	+	0.784934i	$0.287303\pi$
$812$		0			0
$813$	22.9254	+	3.63103i	0.0281985	+	0.00446621i
$814$		0			0
$815$	−513.641	+	321.284i	−0.630235	+	0.394214i
$816$		0			0
$817$	−82.3689	−	161.658i	−0.100819	−	0.197868i
$818$		0			0
$819$	−897.543	−	291.629i	−1.09590	−	0.356080i
$820$		0			0
$821$	86.1613	+	265.177i	0.104947	+	0.322993i	0.989718	−	0.143033i	$-0.0456854\pi$
$821$	86.1613	+	265.177i	0.104947	+	0.322993i	−0.884771	+	0.466026i	$0.845685\pi$
$822$		0			0
$823$	−20.0293	−	126.460i	−0.0243370	−	0.153658i	0.972527	−	0.232789i	$-0.0747853\pi$
$823$	−20.0293	−	126.460i	−0.0243370	−	0.153658i	−0.996864	+	0.0791316i	$0.974785\pi$
$824$		0			0
$825$	−102.209	−	295.961i	−0.123890	−	0.358741i
$826$		0			0
$827$	1189.79	−	188.444i	1.43868	−	0.227865i	0.612144	−	0.790746i	$-0.290307\pi$
$827$	1189.79	−	188.444i	1.43868	−	0.227865i	0.826538	+	0.562881i	$0.190307\pi$
$828$		0			0
$829$	386.847	−	125.694i	0.466643	−	0.151622i	−0.0662518	−	0.997803i	$-0.521104\pi$
$829$	386.847	−	125.694i	0.466643	−	0.151622i	0.532895	+	0.846181i	$0.321104\pi$
$830$		0			0
$831$	100.140	−	308.200i	0.120506	−	0.370878i
$832$		0			0
$833$	10.5700	−	5.38570i	0.0126891	−	0.00646542i
$834$		0			0
$835$	1254.04	+	506.000i	1.50184	+	0.605988i
$836$		0			0
$837$	−45.6466	+	288.202i	−0.0545360	+	0.344327i
$838$		0			0
$839$	174.233	−	239.811i	0.207667	−	0.285829i	−0.692460	−	0.721456i	$-0.743473\pi$
$839$	174.233	−	239.811i	0.207667	−	0.285829i	0.900127	+	0.435627i	$0.143473\pi$
$840$		0			0
$841$	836.695	−	607.895i	0.994881	−	0.722824i
$842$		0			0
$843$	−133.935	−	133.935i	−0.158879	−	0.158879i
$844$		0			0
$845$	304.560	−	129.442i	0.360426	−	0.153185i
$846$		0			0
$847$	1537.09	+	783.188i	1.81475	+	0.924661i
$848$		0			0
$849$		−	133.819i		−	0.157620i
$850$		0			0
$851$	310.032			0.364315
$852$		0			0
$853$	−38.4795	+	75.5203i	−0.0451108	+	0.0885350i	−0.912462	−	0.409162i	$-0.865821\pi$
$853$	−38.4795	+	75.5203i	−0.0451108	+	0.0885350i	0.867351	+	0.497697i	$0.165821\pi$
$854$		0			0
$855$	−294.138	−	176.554i	−0.344022	−	0.206496i
$856$		0			0
$857$	−337.532	+	337.532i	−0.393853	+	0.393853i	−0.876058	−	0.482205i	$-0.839836\pi$
$857$	−337.532	+	337.532i	−0.393853	+	0.393853i	0.482205	+	0.876058i	$0.339836\pi$
$858$		0			0
$859$	−940.703	−	1294.77i	−1.09511	−	1.50730i	−0.841706	−	0.539937i	$-0.818448\pi$
$859$	−940.703	−	1294.77i	−1.09511	−	1.50730i	−0.253409	−	0.967359i	$-0.581552\pi$
$860$		0			0
$861$	−151.423	−	110.016i	−0.175869	−	0.127776i
$862$		0			0
$863$	55.7635	+	8.83207i	0.0646159	+	0.0102342i	0.188659	−	0.982043i	$-0.439586\pi$
$863$	55.7635	+	8.83207i	0.0646159	+	0.0102342i	−0.124043	+	0.992277i	$0.539586\pi$
$864$		0			0
$865$	0.814412	+	0.682741i	0.000941517	+	0.000789296i
$866$		0			0
$867$	−80.3116	−	157.620i	−0.0926316	−	0.181800i
$868$		0			0
$869$	998.347	+	324.383i	1.14885	+	0.373283i
$870$		0			0
$871$	11.6996	+	36.0075i	0.0134323	+	0.0413404i
$872$		0			0
$873$	112.382	+	709.553i	0.128731	+	0.812775i
$874$		0			0
$875$	−878.669	−	185.513i	−1.00419	−	0.212014i
$876$		0			0
$877$	−96.1339	+	15.2261i	−0.109617	+	0.0173616i	−0.211002	−	0.977486i	$-0.567673\pi$
$877$	−96.1339	+	15.2261i	−0.109617	+	0.0173616i	0.101385	+	0.994847i	$0.467673\pi$
$878$		0			0
$879$	−116.402	+	37.8212i	−0.132425	+	0.0430275i
$880$		0			0
$881$	−206.996	+	637.067i	−0.234955	+	0.723118i	0.762172	+	0.647375i	$0.224133\pi$
$881$	−206.996	+	637.067i	−0.234955	+	0.723118i	−0.997127	+	0.0757437i	$0.975867\pi$
$882$		0			0
$883$	−677.064	+	344.981i	−0.766777	+	0.390692i	−0.793202	−	0.608958i	$-0.791588\pi$
$883$	−677.064	+	344.981i	−0.766777	+	0.390692i	0.0264252	+	0.999651i	$0.491588\pi$
$884$		0			0
$885$	29.8337	−	35.5873i	0.0337104	−	0.0402117i
$886$		0			0
$887$	181.587	−	1146.50i	0.204721	−	1.29256i	−0.644535	−	0.764575i	$-0.722949\pi$
$887$	181.587	−	1146.50i	0.204721	−	1.29256i	0.849256	−	0.527981i	$-0.177051\pi$
$888$		0			0
$889$	743.162	−	1022.88i	0.835953	−	1.15059i
$890$		0			0
$891$	−1067.88	+	775.862i	−1.19852	+	0.870776i
$892$		0			0
$893$	89.4459	+	89.4459i	0.100163	+	0.100163i
$894$		0			0
$895$	167.333	−	278.776i	0.186964	−	0.311482i
$896$		0			0
$897$	266.876	+	135.980i	0.297520	+	0.151594i
$898$		0			0
$899$			1091.45i			1.21407i
$900$		0			0
$901$	−223.901			−0.248503
$902$		0			0
$903$	48.6904	−	95.5603i	0.0539207	−	0.105825i
$904$		0			0
$905$	215.439	+	506.901i	0.238054	+	0.560111i
$906$		0			0
$907$	−1184.92	+	1184.92i	−1.30642	+	1.30642i	−0.382441	+	0.923980i	$0.624916\pi$
$907$	−1184.92	+	1184.92i	−1.30642	+	1.30642i	−0.923980	+	0.382441i	$0.875084\pi$
$908$		0			0
$909$	−477.699	−	657.496i	−0.525521	−	0.723318i
$910$		0			0
$911$	−17.4528	−	12.6802i	−0.0191579	−	0.0139190i	0.578165	−	0.815920i	$-0.303769\pi$
$911$	−17.4528	−	12.6802i	−0.0191579	−	0.0139190i	−0.597323	+	0.802001i	$0.703769\pi$
$912$		0			0
$913$	−2800.51	−	443.557i	−3.06737	−	0.485824i
$914$		0			0
$915$	−79.8906	+	197.996i	−0.0873121	+	0.216389i
$916$		0			0
$917$	634.256	+	1244.80i	0.691664	+	1.35747i
$918$		0			0
$919$	902.139	+	293.123i	0.981652	+	0.318958i	0.755511	−	0.655136i	$-0.227389\pi$
$919$	902.139	+	293.123i	0.981652	+	0.318958i	0.226142	+	0.974094i	$0.427389\pi$
$920$		0			0
$921$	−65.2985	−	200.968i	−0.0708996	−	0.218207i
$922$		0			0
$923$	265.371	+	1675.49i	0.287510	+	1.81526i
$924$		0			0
$925$	250.192	+	76.2424i	0.270478	+	0.0824242i
$926$		0			0
$927$	140.797	−	22.3001i	0.151885	−	0.0240562i
$928$		0			0
$929$	−11.6467	+	3.78425i	−0.0125368	+	0.00407347i	−0.315279	−	0.948999i	$-0.602098\pi$
$929$	−11.6467	+	3.78425i	−0.0125368	+	0.00407347i	0.302742	+	0.953073i	$0.402098\pi$
$930$		0			0
$931$	−6.47117	+	19.9162i	−0.00695078	+	0.0213923i
$932$		0			0
$933$	−129.717	+	66.0939i	−0.139032	+	0.0708402i
$934$		0			0
$935$	228.642	+	365.534i	0.244537	+	0.390945i
$936$		0			0
$937$	−40.8249	+	257.758i	−0.0435698	+	0.275089i	−0.999849	−	0.0173657i	$-0.994472\pi$
$937$	−40.8249	+	257.758i	−0.0435698	+	0.275089i	0.956279	+	0.292455i	$0.0944720\pi$
$938$		0			0
$939$	−113.130	+	155.710i	−0.120479	+	0.165826i
$940$		0			0
$941$	432.619	−	314.316i	0.459744	−	0.334024i	−0.333687	−	0.942684i	$-0.608293\pi$
$941$	432.619	−	314.316i	0.459744	−	0.334024i	0.793431	+	0.608660i	$0.208293\pi$
$942$		0			0
$943$	−828.307	−	828.307i	−0.878374	−	0.878374i
$944$		0			0
$945$	−36.4337	−	414.266i	−0.0385541	−	0.438377i
$946$		0			0
$947$	−942.504	−	480.230i	−0.995252	−	0.507106i	−0.121038	−	0.992648i	$-0.538622\pi$
$947$	−942.504	−	480.230i	−0.995252	−	0.507106i	−0.874214	+	0.485542i	$0.838622\pi$
$948$		0			0
$949$			1967.40i			2.07313i
$950$		0			0
$951$	−124.273			−0.130676
$952$		0			0
$953$	254.659	−	499.796i	0.267218	−	0.524444i	−0.717938	−	0.696107i	$-0.754914\pi$
$953$	254.659	−	499.796i	0.267218	−	0.524444i	0.985156	+	0.171663i	$0.0549139\pi$
$954$		0			0
$955$	−62.9804	+	273.366i	−0.0659480	+	0.286247i
$956$		0			0
$957$	383.505	−	383.505i	0.400737	−	0.400737i
$958$		0			0
$959$	−352.959	−	485.806i	−0.368049	−	0.506576i
$960$		0			0
$961$	263.521	+	191.459i	0.274215	+	0.199229i
$962$		0			0
$963$	−75.1772	−	11.9069i	−0.0780656	−	0.0123644i
$964$		0			0
$965$	246.406	+	17.1176i	0.255343	+	0.0177385i
$966$		0			0
$967$	−459.689	−	902.191i	−0.475377	−	0.932979i	−0.996819	−	0.0796930i	$-0.974606\pi$
$967$	−459.689	−	902.191i	−0.475377	−	0.932979i	0.521443	−	0.853286i	$-0.325394\pi$
$968$		0			0
$969$	−22.7830	−	7.40265i	−0.0235119	−	0.00763948i
$970$		0			0
$971$	193.400	+	595.223i	0.199176	+	0.613000i	0.999902	+	0.0139699i	$0.00444691\pi$
$971$	193.400	+	595.223i	0.199176	+	0.613000i	−0.800727	+	0.599030i	$0.795553\pi$
$972$		0			0
$973$	114.142	+	720.667i	0.117310	+	0.740665i
$974$		0			0
$975$	181.926	+	175.364i	0.186591	+	0.179860i
$976$		0			0
$977$	1027.50	−	162.741i	1.05169	−	0.166572i	0.393426	−	0.919356i	$-0.371290\pi$
$977$	1027.50	−	162.741i	1.05169	−	0.166572i	0.658267	+	0.752785i	$0.271290\pi$
$978$		0			0
$979$	−1805.90	+	586.774i	−1.84464	+	0.599360i
$980$		0			0
$981$	−156.460	+	481.534i	−0.159490	+	0.490861i
$982$		0			0
$983$	−1732.04	+	882.521i	−1.76200	+	0.897783i	−0.813148	+	0.582056i	$0.802248\pi$
$983$	−1732.04	+	882.521i	−1.76200	+	0.897783i	−0.948850	+	0.315727i	$0.897752\pi$
$984$		0			0
$985$	167.530	−	41.8510i	0.170081	−	0.0424883i
$986$		0			0
$987$	−11.6974	+	73.8543i	−0.0118514	+	0.0748271i
$988$		0			0
$989$	394.536	−	543.032i	0.398924	−	0.549072i
$990$		0			0
$991$	−719.874	+	523.019i	−0.726411	+	0.527769i	−0.888426	−	0.459020i	$-0.848201\pi$
$991$	−719.874	+	523.019i	−0.726411	+	0.527769i	0.162015	+	0.986788i	$0.448201\pi$
$992$		0			0
$993$	9.38634	+	9.38634i	0.00945250	+	0.00945250i
$994$		0			0
$995$	−335.657	−	385.774i	−0.337343	−	0.387712i
$996$		0			0
$997$	−410.633	−	209.228i	−0.411869	−	0.209858i	0.235764	−	0.971810i	$-0.424241\pi$
$997$	−410.633	−	209.228i	−0.411869	−	0.209858i	−0.647633	+	0.761953i	$0.724241\pi$
$998$		0			0
$999$			121.120i			0.121241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.b.113.2		24
4.3	odd	2		50.3.f.b.13.2	✓	24
20.3	even	4		250.3.f.d.207.2		24
20.7	even	4		250.3.f.f.207.2		24
20.19	odd	2		250.3.f.e.43.2		24
25.2	odd	20	inner	400.3.bg.b.177.2		24
100.11	odd	10		250.3.f.f.93.2		24
100.23	even	20		250.3.f.e.157.2		24
100.27	even	20		50.3.f.b.27.2	yes	24
100.39	odd	10		250.3.f.d.93.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.b.13.2	✓	24	4.3	odd	2
50.3.f.b.27.2	yes	24	100.27	even	20
250.3.f.d.93.2		24	100.39	odd	10
250.3.f.d.207.2		24	20.3	even	4
250.3.f.e.43.2		24	20.19	odd	2
250.3.f.e.157.2		24	100.23	even	20
250.3.f.f.93.2		24	100.11	odd	10
250.3.f.f.207.2		24	20.7	even	4
400.3.bg.b.113.2		24	1.1	even	1	trivial
400.3.bg.b.177.2		24	25.2	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.299213 - 0.587238i) q^{3} +(3.77205 - 3.28201i) q^{5} +(5.08008 - 5.08008i) q^{7} +(5.03475 + 6.92973i) q^{9} +O(q^{10})\)	\(q+(0.299213 - 0.587238i) q^{3} +(3.77205 - 3.28201i) q^{5} +(5.08008 - 5.08008i) q^{7} +(5.03475 + 6.92973i) q^{9} +(15.3739 + 11.1698i) q^{11} +(-15.1469 - 2.39904i) q^{13} +(-0.798677 - 3.19712i) q^{15} +(2.06006 + 4.04310i) q^{17} +(-7.61807 - 2.47526i) q^{19} +(-1.46319 - 4.50324i) q^{21} +(-4.63577 - 29.2691i) q^{23} +(3.45678 - 24.7599i) q^{25} +(11.4345 - 1.81105i) q^{27} +(41.1843 - 13.3816i) q^{29} +(-7.78864 + 23.9710i) q^{31} +(11.1594 - 5.68602i) q^{33} +(2.48944 - 35.8352i) q^{35} +(-1.63663 + 10.3332i) q^{37} +(-5.94097 + 8.17704i) q^{39} +(31.9797 - 23.2346i) q^{41} +(16.0163 + 16.0163i) q^{43} +(41.7348 + 9.61523i) q^{45} +(-14.0708 - 7.16942i) q^{47} -2.61434i q^{49} +2.99066 q^{51} +(-22.4011 + 43.9646i) q^{53} +(94.6509 - 8.32431i) q^{55} +(-3.73299 + 3.73299i) q^{57} +(8.28306 + 11.4007i) q^{59} +(-52.4160 - 38.0825i) q^{61} +(60.7805 + 9.62668i) q^{63} +(-65.0087 + 40.6631i) q^{65} +(-1.12080 - 2.19970i) q^{67} +(-18.5750 - 6.03539i) q^{69} +(-34.1821 - 105.202i) q^{71} +(-20.0687 - 126.709i) q^{73} +(-13.5056 - 9.43842i) q^{75} +(134.844 - 21.3573i) q^{77} +(52.5356 - 17.0699i) q^{79} +(-21.4645 + 66.0609i) q^{81} +(-132.945 + 67.7386i) q^{83} +(21.0401 + 8.48963i) q^{85} +(4.46469 - 28.1889i) q^{87} +(-58.7326 + 80.8385i) q^{89} +(-89.1349 + 64.7603i) q^{91} +(11.7462 + 11.7462i) q^{93} +(-36.8596 + 15.6658i) q^{95} +(74.7286 + 38.0761i) q^{97} +162.775i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9}+O(q^{10}) \) 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9	\( 24 q - 2 q^{3} + 2 q^{7} + 40 q^{9} + 32 q^{11} + 2 q^{13} + 20 q^{15} - 92 q^{17} + 230 q^{19} + 68 q^{21} + 18 q^{23} + 40 q^{25} - 260 q^{27} + 100 q^{29} + 132 q^{31} + 364 q^{33} - 50 q^{35} - 192 q^{37} + 80 q^{39} + 168 q^{41} + 78 q^{43} - 310 q^{45} + 22 q^{47} - 168 q^{51} - 108 q^{53} + 40 q^{55} + 280 q^{57} - 450 q^{59} - 492 q^{61} + 558 q^{63} + 120 q^{65} + 572 q^{67} - 670 q^{69} + 2 q^{71} + 262 q^{73} - 140 q^{75} + 496 q^{77} + 360 q^{79} - 46 q^{81} - 772 q^{83} + 490 q^{85} - 210 q^{87} + 900 q^{89} - 798 q^{91} + 294 q^{93} + 378 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 2 * q^7 + 40 * q^9 + 32 * q^11 + 2 * q^13 + 20 * q^15 - 92 * q^17 + 230 * q^19 + 68 * q^21 + 18 * q^23 + 40 * q^25 - 260 * q^27 + 100 * q^29 + 132 * q^31 + 364 * q^33 - 50 * q^35 - 192 * q^37 + 80 * q^39 + 168 * q^41 + 78 * q^43 - 310 * q^45 + 22 * q^47 - 168 * q^51 - 108 * q^53 + 40 * q^55 + 280 * q^57 - 450 * q^59 - 492 * q^61 + 558 * q^63 + 120 * q^65 + 572 * q^67 - 670 * q^69 + 2 * q^71 + 262 * q^73 - 140 * q^75 + 496 * q^77 + 360 * q^79 - 46 * q^81 - 772 * q^83 + 490 * q^85 - 210 * q^87 + 900 * q^89 - 798 * q^91 + 294 * q^93 + 378 * q^97

Introduction

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Database

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