LMFDB - Embedded newform 400.3.bg.f.33.2

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:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	400.33
Dual form			400.3.bg.f.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.88880 - 0.615926i) q^{3} +(2.05707 + 4.55724i) q^{5} +(-5.11305 + 5.11305i) q^{7} +(6.18393 + 2.00928i) q^{9} +O(q^{10})$	\(q+(-3.88880 - 0.615926i) q^{3} +(2.05707 + 4.55724i) q^{5} +(-5.11305 + 5.11305i) q^{7} +(6.18393 + 2.00928i) q^{9} +(0.0865225 + 0.266289i) q^{11} +(-5.04080 + 2.56841i) q^{13} +(-5.19263 - 18.9892i) q^{15} +(9.22052 - 1.46039i) q^{17} +(14.8832 - 20.4849i) q^{19} +(23.0329 - 16.7344i) q^{21} +(-11.5801 + 22.7271i) q^{23} +(-16.5369 + 18.7492i) q^{25} +(8.76274 + 4.46484i) q^{27} +(-26.1473 - 35.9887i) q^{29} +(-44.2788 - 32.1704i) q^{31} +(-0.172455 - 1.08884i) q^{33} +(-33.8193 - 12.7835i) q^{35} +(-17.6833 - 34.7055i) q^{37} +(21.1846 - 6.88330i) q^{39} +(5.93471 - 18.2652i) q^{41} +(-23.5671 - 23.5671i) q^{43} +(3.56401 + 32.3149i) q^{45} +(2.94533 - 18.5961i) q^{47} -3.28662i q^{49} -36.7563 q^{51} +(-49.6251 - 7.85985i) q^{53} +(-1.03556 + 0.942080i) q^{55} +(-70.4949 + 70.4949i) q^{57} +(73.1755 + 23.7762i) q^{59} +(-32.1545 - 98.9614i) q^{61} +(-41.8923 + 21.3452i) q^{63} +(-22.0742 - 17.6887i) q^{65} +(29.9952 - 4.75077i) q^{67} +(59.0308 - 81.2490i) q^{69} +(-18.4157 + 13.3798i) q^{71} +(-4.79456 + 9.40984i) q^{73} +(75.8569 - 62.7263i) q^{75} +(-1.80394 - 0.919155i) q^{77} +(71.4829 + 98.3877i) q^{79} +(-78.6699 - 57.1570i) q^{81} +(-4.05019 - 25.5719i) q^{83} +(25.6226 + 39.0160i) q^{85} +(79.5155 + 156.058i) q^{87} +(-19.5716 + 6.35919i) q^{89} +(12.6414 - 38.9063i) q^{91} +(152.377 + 152.377i) q^{93} +(123.970 + 25.6872i) q^{95} +(-23.4342 + 147.957i) q^{97} +1.82056i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$	$1$

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
$3$	−3.88880	−	0.615926i	−1.29627	−	0.205309i	−0.530093	−	0.847940i	$-0.677843\pi$
$3$	−3.88880	−	0.615926i	−1.29627	−	0.205309i	−0.766176	+	0.642631i	$0.777843\pi$
$4$		0			0
$5$	2.05707	+	4.55724i	0.411414	+	0.911448i
$5$	2.05707	+	4.55724i	0.411414	+	0.911448i
$6$		0			0
$7$	−5.11305	+	5.11305i	−0.730436	+	0.730436i	−0.970706	−	0.240270i	$-0.922764\pi$
$7$	−5.11305	+	5.11305i	−0.730436	+	0.730436i	0.240270	+	0.970706i	$0.422764\pi$
$8$		0			0
$9$	6.18393	+	2.00928i	0.687103	+	0.223253i
$10$		0			0
$11$	0.0865225	+	0.266289i	0.00786568	+	0.0242081i	0.954912	−	0.296888i	$-0.0959488\pi$
$11$	0.0865225	+	0.266289i	0.00786568	+	0.0242081i	−0.947047	+	0.321096i	$0.895949\pi$
$12$		0			0
$13$	−5.04080	+	2.56841i	−0.387754	+	0.197570i	−0.636990	−	0.770872i	$-0.719821\pi$
$13$	−5.04080	+	2.56841i	−0.387754	+	0.197570i	0.249236	+	0.968443i	$0.419821\pi$
$14$		0			0
$15$	−5.19263	−	18.9892i	−0.346175	−	1.26595i
$16$		0			0
$17$	9.22052	−	1.46039i	0.542384	−	0.0859051i	0.120770	−	0.992681i	$-0.461464\pi$
$17$	9.22052	−	1.46039i	0.542384	−	0.0859051i	0.421614	+	0.906775i	$0.361464\pi$
$18$		0			0
$19$	14.8832	−	20.4849i	0.783324	−	1.07815i	−0.211583	−	0.977360i	$-0.567862\pi$
$19$	14.8832	−	20.4849i	0.783324	−	1.07815i	0.994907	−	0.100793i	$-0.0321381\pi$
$20$		0			0
$21$	23.0329	−	16.7344i	1.09681	−	0.796876i
$22$		0			0
$23$	−11.5801	+	22.7271i	−0.503481	+	0.988136i	0.489737	+	0.871870i	$0.337093\pi$
$23$	−11.5801	+	22.7271i	−0.503481	+	0.988136i	−0.993218	+	0.116266i	$0.962907\pi$
$24$		0			0
$25$	−16.5369	+	18.7492i	−0.661476	+	0.749966i
$26$		0			0
$27$	8.76274	+	4.46484i	0.324546	+	0.165365i
$28$		0			0
$29$	−26.1473	−	35.9887i	−0.901632	−	1.24099i	−0.969945	−	0.243326i	$-0.921762\pi$
$29$	−26.1473	−	35.9887i	−0.901632	−	1.24099i	0.0683127	−	0.997664i	$-0.478238\pi$
$30$		0			0
$31$	−44.2788	−	32.1704i	−1.42835	−	1.03776i	−0.990321	−	0.138794i	$-0.955677\pi$
$31$	−44.2788	−	32.1704i	−1.42835	−	1.03776i	−0.438027	−	0.898962i	$-0.644323\pi$
$32$		0			0
$33$	−0.172455	−	1.08884i	−0.00522591	−	0.0329951i
$34$		0			0
$35$	−33.8193	−	12.7835i	−0.966267	−	0.365243i
$36$		0			0
$37$	−17.6833	−	34.7055i	−0.477928	−	0.937987i	−0.996551	−	0.0829838i	$-0.973555\pi$
$37$	−17.6833	−	34.7055i	−0.477928	−	0.937987i	0.518623	−	0.855003i	$-0.326445\pi$
$38$		0			0
$39$	21.1846	−	6.88330i	0.543196	−	0.176495i
$40$		0			0
$41$	5.93471	−	18.2652i	0.144749	−	0.445492i	−0.852230	−	0.523168i	$-0.824750\pi$
$41$	5.93471	−	18.2652i	0.144749	−	0.445492i	0.996979	+	0.0776760i	$0.0247500\pi$
$42$		0			0
$43$	−23.5671	−	23.5671i	−0.548073	−	0.548073i	0.377810	−	0.925883i	$-0.376677\pi$
$43$	−23.5671	−	23.5671i	−0.548073	−	0.548073i	−0.925883	+	0.377810i	$0.876677\pi$
$44$		0			0
$45$	3.56401	+	32.3149i	0.0792003	+	0.718109i
$46$		0			0
$47$	2.94533	−	18.5961i	0.0626666	−	0.395661i	−0.936340	−	0.351095i	$-0.885809\pi$
$47$	2.94533	−	18.5961i	0.0626666	−	0.395661i	0.999006	−	0.0445663i	$-0.0141906\pi$
$48$		0			0
$49$		−	3.28662i		−	0.0670739i
$50$		0			0
$51$	−36.7563			−0.720712
$52$		0			0
$53$	−49.6251	−	7.85985i	−0.936323	−	0.148299i	−0.330417	−	0.943835i	$-0.607189\pi$
$53$	−49.6251	−	7.85985i	−0.936323	−	0.148299i	−0.605906	+	0.795536i	$0.707189\pi$
$54$		0			0
$55$	−1.03556	+	0.942080i	−0.0188284	+	0.0171287i
$56$		0			0
$57$	−70.4949	+	70.4949i	−1.23675	+	1.23675i
$58$		0			0
$59$	73.1755	+	23.7762i	1.24026	+	0.402986i	0.854422	−	0.519580i	$-0.173911\pi$
$59$	73.1755	+	23.7762i	1.24026	+	0.402986i	0.385841	+	0.922565i	$0.373911\pi$
$60$		0			0
$61$	−32.1545	−	98.9614i	−0.527123	−	1.62232i	−0.760079	−	0.649831i	$-0.774840\pi$
$61$	−32.1545	−	98.9614i	−0.527123	−	1.62232i	0.232955	−	0.972487i	$-0.425160\pi$
$62$		0			0
$63$	−41.8923	+	21.3452i	−0.664957	+	0.338813i
$64$		0			0
$65$	−22.0742	−	17.6887i	−0.339603	−	0.272134i
$66$		0			0
$67$	29.9952	−	4.75077i	0.447690	−	0.0709071i	0.0714809	−	0.997442i	$-0.477228\pi$
$67$	29.9952	−	4.75077i	0.447690	−	0.0709071i	0.376209	+	0.926535i	$0.377228\pi$
$68$		0			0
$69$	59.0308	−	81.2490i	0.855519	−	1.17752i
$70$		0			0
$71$	−18.4157	+	13.3798i	−0.259377	+	0.188448i	−0.709872	−	0.704330i	$-0.751247\pi$
$71$	−18.4157	+	13.3798i	−0.259377	+	0.188448i	0.450496	+	0.892779i	$0.351247\pi$
$72$		0			0
$73$	−4.79456	+	9.40984i	−0.0656788	+	0.128902i	−0.921512	−	0.388350i	$-0.873045\pi$
$73$	−4.79456	+	9.40984i	−0.0656788	+	0.128902i	0.855833	+	0.517252i	$0.173045\pi$
$74$		0			0
$75$	75.8569	−	62.7263i	1.01143	−	0.836350i
$76$		0			0
$77$	−1.80394	−	0.919155i	−0.0234278	−	0.0119371i
$78$		0			0
$79$	71.4829	+	98.3877i	0.904847	+	1.24541i	0.968896	+	0.247468i	$0.0795984\pi$
$79$	71.4829	+	98.3877i	0.904847	+	1.24541i	−0.0640496	+	0.997947i	$0.520402\pi$
$80$		0			0
$81$	−78.6699	−	57.1570i	−0.971233	−	0.705642i
$82$		0			0
$83$	−4.05019	−	25.5719i	−0.0487975	−	0.308095i	0.951202	−	0.308568i	$-0.0998497\pi$
$83$	−4.05019	−	25.5719i	−0.0487975	−	0.308095i	−1.00000		0.000472307i	$0.999850\pi$
$84$		0			0
$85$	25.6226	+	39.0160i	0.301443	+	0.459012i
$86$		0			0
$87$	79.5155	+	156.058i	0.913971	+	1.79377i
$88$		0			0
$89$	−19.5716	+	6.35919i	−0.219905	+	0.0714516i	−0.416898	−	0.908953i	$-0.636883\pi$
$89$	−19.5716	+	6.35919i	−0.219905	+	0.0714516i	0.196992	+	0.980405i	$0.436883\pi$
$90$		0			0
$91$	12.6414	−	38.9063i	0.138917	−	0.427542i
$92$		0			0
$93$	152.377	+	152.377i	1.63846	+	1.63846i
$94$		0			0
$95$	123.970	+	25.6872i	1.30495	+	0.270392i
$96$		0			0
$97$	−23.4342	+	147.957i	−0.241589	+	1.52533i	0.506793	+	0.862068i	$0.330831\pi$
$97$	−23.4342	+	147.957i	−0.241589	+	1.52533i	−0.748383	+	0.663267i	$0.769169\pi$
$98$		0			0
$99$			1.82056i			0.0183895i
$100$		0			0
$101$	−48.4125			−0.479332			−0.239666	−	0.970855i	$-0.577038\pi$
$101$	−48.4125			−0.479332			−0.239666	+	0.970855i	$0.577038\pi$
$102$		0			0
$103$	−120.042	−	19.0128i	−1.16546	−	0.184590i	−0.456422	−	0.889763i	$-0.650869\pi$
$103$	−120.042	−	19.0128i	−1.16546	−	0.184590i	−0.709035	+	0.705173i	$0.750869\pi$
$104$		0			0
$105$	123.643	+	70.5428i	1.17755	+	0.671836i
$106$		0			0
$107$	104.833	−	104.833i	0.979751	−	0.979751i	−0.0200477	−	0.999799i	$-0.506382\pi$
$107$	104.833	−	104.833i	0.979751	−	0.979751i	0.999799	+	0.0200477i	$0.00638180\pi$
$108$		0			0
$109$	136.885	+	44.4765i	1.25582	+	0.408041i	0.860004	−	0.510287i	$-0.170461\pi$
$109$	136.885	+	44.4765i	1.25582	+	0.408041i	0.395818	+	0.918329i	$0.370461\pi$
$110$		0			0
$111$	47.3910	+	145.855i	0.426946	+	1.31401i
$112$		0			0
$113$	122.130	−	62.2282i	1.08079	−	0.550692i	0.179438	−	0.983769i	$-0.442572\pi$
$113$	122.130	−	62.2282i	1.08079	−	0.550692i	0.901357	+	0.433077i	$0.142572\pi$
$114$		0			0
$115$	−127.394	−	6.02175i	−1.10777	−	0.0523631i
$116$		0			0
$117$	−36.3326	+	5.75452i	−0.310535	+	0.0491839i
$118$		0			0
$119$	−39.6780	+	54.6121i	−0.333428	+	0.458925i
$120$		0			0
$121$	97.8276	−	71.0759i	0.808493	−	0.587404i
$122$		0			0
$123$	−34.3289	+	67.3744i	−0.279097	+	0.547759i
$124$		0			0
$125$	−119.462	−	36.7943i	−0.955696	−	0.294355i
$126$		0			0
$127$	−108.864	−	55.4692i	−0.857200	−	0.436765i	−0.0305846	−	0.999532i	$-0.509737\pi$
$127$	−108.864	−	55.4692i	−0.857200	−	0.436765i	−0.826616	+	0.562767i	$0.809737\pi$
$128$		0			0
$129$	77.1324	+	106.164i	0.597925	+	0.822974i
$130$		0			0
$131$	−146.603	−	106.513i	−1.11911	−	0.813079i	−0.135033	−	0.990841i	$-0.543114\pi$
$131$	−146.603	−	106.513i	−1.11911	−	0.813079i	−0.984073	+	0.177762i	$0.943114\pi$
$132$		0			0
$133$	28.6421	+	180.839i	0.215354	+	1.35969i
$134$		0			0
$135$	−2.32176	+	49.1184i	−0.0171983	+	0.363840i
$136$		0			0
$137$	16.0731	+	31.5452i	0.117322	+	0.230257i	0.942198	−	0.335056i	$-0.108755\pi$
$137$	16.0731	+	31.5452i	0.117322	+	0.230257i	−0.824876	+	0.565313i	$0.808755\pi$
$138$		0			0
$139$	−54.9774	+	17.8632i	−0.395521	+	0.128513i	−0.500023	−	0.866012i	$-0.666675\pi$
$139$	−54.9774	+	17.8632i	−0.395521	+	0.128513i	0.104502	+	0.994525i	$0.466675\pi$
$140$		0			0
$141$	−22.9076	+	70.5024i	−0.162465	+	0.500017i
$142$		0			0
$143$	−1.12008	−	1.12008i	−0.00783275	−	0.00783275i
$144$		0			0
$145$	110.222	−	193.191i	0.760154	−	1.33235i
$146$		0			0
$147$	−2.02432	+	12.7810i	−0.0137709	+	0.0869458i
$148$		0			0
$149$		−	241.873i		−	1.62331i	−0.584140	−	0.811653i	$-0.698568\pi$
$149$		−	241.873i		−	1.62331i	0.584140	−	0.811653i	$-0.301432\pi$
$150$		0			0
$151$	−94.4994			−0.625824			−0.312912	−	0.949782i	$-0.601304\pi$
$151$	−94.4994			−0.625824			−0.312912	+	0.949782i	$0.601304\pi$
$152$		0			0
$153$	59.9534	+	9.49568i	0.391852	+	0.0620633i
$154$		0			0
$155$	55.5238	−	267.966i	0.358218	−	1.72881i
$156$		0			0
$157$	−187.357	+	187.357i	−1.19336	+	1.19336i	−0.217241	+	0.976118i	$0.569706\pi$
$157$	−187.357	+	187.357i	−1.19336	+	1.19336i	−0.976118	+	0.217241i	$0.930294\pi$
$158$		0			0
$159$	188.141	+	61.1308i	1.18328	+	0.384471i
$160$		0			0
$161$	−56.9956	−	175.415i	−0.354010	−	1.08953i
$162$		0			0
$163$	39.7438	−	20.2505i	0.243827	−	0.124236i	−0.327807	−	0.944745i	$-0.606310\pi$
$163$	39.7438	−	20.2505i	0.243827	−	0.124236i	0.571634	+	0.820509i	$0.306310\pi$
$164$		0			0
$165$	4.60734	−	3.02574i	0.0279233	−	0.0183378i
$166$		0			0
$167$	−234.821	+	37.1920i	−1.40612	+	0.222707i	−0.812931	−	0.582360i	$-0.802129\pi$
$167$	−234.821	+	37.1920i	−1.40612	+	0.222707i	−0.593184	+	0.805067i	$0.702129\pi$
$168$		0			0
$169$	−80.5228	+	110.830i	−0.476466	+	0.655800i
$170$		0			0
$171$	133.196	−	96.7728i	0.778926	−	0.565923i
$172$		0			0
$173$	−126.827	+	248.913i	−0.733107	+	1.43880i	0.159140	+	0.987256i	$0.449128\pi$
$173$	−126.827	+	248.913i	−0.733107	+	1.43880i	−0.892247	+	0.451547i	$0.850872\pi$
$174$		0			0
$175$	−11.3113	−	180.419i	−0.0646361	−	1.03097i
$176$		0			0
$177$	−269.921	−	137.532i	−1.52498	−	0.777014i
$178$		0			0
$179$	54.7109	+	75.3030i	0.305647	+	0.420687i	0.934018	−	0.357227i	$-0.116278\pi$
$179$	54.7109	+	75.3030i	0.305647	+	0.420687i	−0.628370	+	0.777914i	$0.716278\pi$
$180$		0			0
$181$	282.031	+	204.908i	1.55818	+	1.13209i	0.937479	+	0.348041i	$0.113153\pi$
$181$	282.031	+	204.908i	1.55818	+	1.13209i	0.620703	+	0.784046i	$0.286847\pi$
$182$		0			0
$183$	64.0897	+	404.646i	0.350217	+	2.21118i
$184$		0			0
$185$	121.786	−	151.979i	0.658300	−	0.821508i
$186$		0			0
$187$	1.18667	+	2.32897i	0.00634582	+	0.0124544i
$188$		0			0
$189$	−67.6333	+	21.9754i	−0.357848	+	0.116272i
$190$		0			0
$191$	−29.5335	+	90.8949i	−0.154626	+	0.475890i	−0.998123	−	0.0612445i	$-0.980493\pi$
$191$	−29.5335	+	90.8949i	−0.154626	+	0.475890i	0.843497	+	0.537134i	$0.180493\pi$
$192$		0			0
$193$	−45.2300	−	45.2300i	−0.234352	−	0.234352i	0.580154	−	0.814507i	$-0.302992\pi$
$193$	−45.2300	−	45.2300i	−0.234352	−	0.234352i	−0.814507	+	0.580154i	$0.802992\pi$
$194$		0			0
$195$	74.9472	+	82.3840i	0.384345	+	0.422482i
$196$		0			0
$197$	20.3420	−	128.434i	0.103259	−	0.651950i	−0.880716	−	0.473644i	$-0.842938\pi$
$197$	20.3420	−	128.434i	0.103259	−	0.651950i	0.983975	−	0.178306i	$-0.0570617\pi$
$198$		0			0
$199$		−	165.880i		−	0.833568i	−0.909006	−	0.416784i	$-0.863157\pi$
$199$		−	165.880i		−	0.833568i	0.909006	−	0.416784i	$-0.136843\pi$
$200$		0			0
$201$	−119.572			−0.594884
$202$		0			0
$203$	317.705	+	50.3195i	1.56505	+	0.247879i
$204$		0			0
$205$	95.4470	−	10.5268i	0.465595	−	0.0513505i
$206$		0			0
$207$	−117.275	+	117.275i	−0.566548	+	0.566548i
$208$		0			0
$209$	6.74263	+	2.19081i	0.0322614	+	0.0104824i
$210$		0			0
$211$	34.9729	+	107.635i	0.165748	+	0.510121i	0.999091	−	0.0426364i	$-0.0135757\pi$
$211$	34.9729	+	107.635i	0.165748	+	0.510121i	−0.833342	+	0.552757i	$0.813576\pi$
$212$		0			0
$213$	79.8562	−	40.6888i	0.374912	−	0.191027i
$214$		0			0
$215$	58.9218	−	155.880i	0.274055	−	0.725025i
$216$		0			0
$217$	390.889	−	61.9107i	1.80133	−	0.285303i
$218$		0			0
$219$	24.4409	−	33.6400i	0.111602	−	0.153607i
$220$		0			0
$221$	−42.7279	+	31.0436i	−0.193339	+	0.140469i
$222$		0			0
$223$	76.8865	−	150.898i	0.344782	−	0.676674i	−0.651879	−	0.758323i	$-0.726019\pi$
$223$	76.8865	−	150.898i	0.344782	−	0.676674i	0.996661	+	0.0816497i	$0.0260189\pi$
$224$		0			0
$225$	−139.935	+	82.7162i	−0.621935	+	0.367627i
$226$		0			0
$227$	−354.121	−	180.434i	−1.56001	−	0.794863i	−0.560559	−	0.828115i	$-0.689414\pi$
$227$	−354.121	−	180.434i	−1.56001	−	0.794863i	−0.999447	+	0.0332522i	$0.989414\pi$
$228$		0			0
$229$	108.078	+	148.756i	0.471955	+	0.649590i	0.976934	−	0.213542i	$-0.0684999\pi$
$229$	108.078	+	148.756i	0.471955	+	0.649590i	−0.504979	+	0.863131i	$0.668500\pi$
$230$		0			0
$231$	6.44905	+	4.68551i	0.0279180	+	0.0202836i
$232$		0			0
$233$	−45.9121	−	289.878i	−0.197048	−	1.24411i	−0.865711	−	0.500545i	$-0.833133\pi$
$233$	−45.9121	−	289.878i	−0.197048	−	1.24411i	0.668663	−	0.743566i	$-0.266867\pi$
$234$		0			0
$235$	90.8056	−	24.8309i	0.386407	−	0.105663i
$236$		0			0
$237$	−217.383	−	426.639i	−0.917229	−	1.80016i
$238$		0			0
$239$	−17.8751	+	5.80798i	−0.0747913	+	0.0243012i	−0.346174	−	0.938170i	$-0.612519\pi$
$239$	−17.8751	+	5.80798i	−0.0747913	+	0.0243012i	0.271382	+	0.962472i	$0.412519\pi$
$240$		0			0
$241$	−107.483	+	330.799i	−0.445989	+	1.37261i	0.435408	+	0.900233i	$0.356604\pi$
$241$	−107.483	+	330.799i	−0.445989	+	1.37261i	−0.881396	+	0.472378i	$0.843396\pi$
$242$		0			0
$243$	208.140	+	208.140i	0.856543	+	0.856543i
$244$		0			0
$245$	14.9779	−	6.76082i	0.0611344	−	0.0275952i
$246$		0			0
$247$	−22.4092	+	141.486i	−0.0907257	+	0.572819i
$248$		0			0
$249$			101.939i			0.409393i
$250$		0			0
$251$	−358.291			−1.42746			−0.713728	−	0.700423i	$-0.752995\pi$
$251$	−358.291			−1.42746			−0.713728	+	0.700423i	$0.752995\pi$
$252$		0			0
$253$	−7.05392	−	1.11723i	−0.0278811	−	0.00441593i
$254$		0			0
$255$	−75.6104	−	167.507i	−0.296511	−	0.656892i
$256$		0			0
$257$	−93.9152	+	93.9152i	−0.365429	+	0.365429i	−0.865807	−	0.500378i	$-0.833194\pi$
$257$	−93.9152	+	93.9152i	−0.365429	+	0.365429i	0.500378	+	0.865807i	$0.333194\pi$
$258$		0			0
$259$	267.867	+	87.0353i	1.03424	+	0.336044i
$260$		0			0
$261$	−89.3818	−	275.089i	−0.342459	−	1.05398i
$262$		0			0
$263$	−32.3684	+	16.4925i	−0.123074	+	0.0627092i	−0.514443	−	0.857524i	$-0.672001\pi$
$263$	−32.3684	+	16.4925i	−0.123074	+	0.0627092i	0.391370	+	0.920234i	$0.372001\pi$
$264$		0			0
$265$	−66.2633	−	242.322i	−0.250050	−	0.914423i
$266$		0			0
$267$	80.0269	−	12.6750i	0.299726	−	0.0474719i
$268$		0			0
$269$	−126.562	+	174.198i	−0.470491	+	0.647575i	−0.976643	−	0.214869i	$-0.931068\pi$
$269$	−126.562	+	174.198i	−0.470491	+	0.647575i	0.506152	+	0.862444i	$0.331068\pi$
$270$		0			0
$271$	152.245	−	110.612i	0.561789	−	0.408164i	−0.270324	−	0.962769i	$-0.587131\pi$
$271$	152.245	−	110.612i	0.561789	−	0.408164i	0.832113	+	0.554606i	$0.187131\pi$
$272$		0			0
$273$	−73.1234	+	143.513i	−0.267851	+	0.525688i
$274$		0			0
$275$	−6.42351	−	2.78137i	−0.0233582	−	0.0101141i
$276$		0			0
$277$	−181.467	−	92.4618i	−0.655114	−	0.333797i	0.0946423	−	0.995511i	$-0.469829\pi$
$277$	−181.467	−	92.4618i	−0.655114	−	0.333797i	−0.749756	+	0.661714i	$0.769829\pi$
$278$		0			0
$279$	−209.178	−	287.908i	−0.749740	−	1.03193i
$280$		0			0
$281$	−259.573	−	188.591i	−0.923747	−	0.671142i	0.0207066	−	0.999786i	$-0.493408\pi$
$281$	−259.573	−	188.591i	−0.923747	−	0.671142i	−0.944454	+	0.328644i	$0.893408\pi$
$282$		0			0
$283$	16.3976	+	103.531i	0.0579422	+	0.365833i	0.999574	+	0.0291880i	$0.00929215\pi$
$283$	16.3976	+	103.531i	0.0579422	+	0.365833i	−0.941632	+	0.336645i	$0.890708\pi$
$284$		0			0
$285$	−466.275	−	176.249i	−1.63605	−	0.618418i
$286$		0			0
$287$	63.0463	+	123.735i	0.219673	+	0.431134i
$288$		0			0
$289$	−191.970	+	62.3748i	−0.664256	+	0.215830i
$290$		0			0
$291$	182.262	−	560.944i	0.626329	−	1.92764i
$292$		0			0
$293$	−60.8637	−	60.8637i	−0.207726	−	0.207726i	0.595574	−	0.803300i	$-0.296925\pi$
$293$	−60.8637	−	60.8637i	−0.207726	−	0.207726i	−0.803300	+	0.595574i	$0.796925\pi$
$294$		0			0
$295$	42.1736	+	382.388i	0.142961	+	1.29623i
$296$		0			0
$297$	−0.430763	+	2.71973i	−0.00145038	+	0.00915735i
$298$		0			0
$299$		−	144.305i		−	0.482626i
$300$		0			0
$301$	241.000			0.800665
$302$		0			0
$303$	188.267	+	29.8185i	0.621343	+	0.0984110i
$304$		0			0
$305$	384.847	−	350.107i	1.26179	−	1.14789i
$306$		0			0
$307$	−382.682	+	382.682i	−1.24652	+	1.24652i	−0.289274	+	0.957246i	$0.593414\pi$
$307$	−382.682	+	382.682i	−1.24652	+	1.24652i	−0.957246	+	0.289274i	$0.906586\pi$
$308$		0			0
$309$	455.110	+	147.874i	1.47285	+	0.478557i
$310$		0			0
$311$	13.8868	+	42.7392i	0.0446521	+	0.137425i	0.970897	−	0.239497i	$-0.0769825\pi$
$311$	13.8868	+	42.7392i	0.0446521	+	0.137425i	−0.926245	+	0.376922i	$0.876982\pi$
$312$		0			0
$313$	−2.01992	+	1.02920i	−0.00645342	+	0.00328818i	−0.457214	−	0.889357i	$-0.651153\pi$
$313$	−2.01992	+	1.02920i	−0.00645342	+	0.00328818i	0.450761	+	0.892645i	$0.351153\pi$
$314$		0			0
$315$	−183.451	−	147.005i	−0.582383	−	0.466682i
$316$		0			0
$317$	157.199	−	24.8979i	0.495896	−	0.0785422i	0.0965228	−	0.995331i	$-0.469228\pi$
$317$	157.199	−	24.8979i	0.495896	−	0.0785422i	0.399373	+	0.916789i	$0.369228\pi$
$318$		0			0
$319$	7.32106	−	10.0766i	0.0229500	−	0.0315880i
$320$		0			0
$321$	−472.246	+	343.107i	−1.47117	+	1.06887i
$322$		0			0
$323$	107.315	−	210.617i	0.332243	−	0.652064i
$324$		0			0
$325$	35.2036	−	136.984i	0.108319	−	0.421490i
$326$		0			0
$327$	−504.923	−	257.271i	−1.54411	−	0.786762i
$328$		0			0
$329$	80.0231	+	110.142i	0.243231	+	0.334779i
$330$		0			0
$331$	−251.942	−	183.047i	−0.761155	−	0.553011i	0.138110	−	0.990417i	$-0.455897\pi$
$331$	−251.942	−	183.047i	−0.761155	−	0.553011i	−0.899264	+	0.437406i	$0.855897\pi$
$332$		0			0
$333$	−39.6194	−	250.147i	−0.118977	−	0.751193i
$334$		0			0
$335$	83.3527	+	126.923i	0.248814	+	0.378874i
$336$		0			0
$337$	280.615	+	550.737i	0.832684	+	1.63423i	0.771605	+	0.636102i	$0.219454\pi$
$337$	280.615	+	550.737i	0.832684	+	1.63423i	0.0610793	+	0.998133i	$0.480546\pi$
$338$		0			0
$339$	−513.267	+	166.770i	−1.51406	+	0.491948i
$340$		0			0
$341$	4.73552	−	14.5744i	0.0138871	−	0.0427402i
$342$		0			0
$343$	−233.735	−	233.735i	−0.681443	−	0.681443i
$344$		0			0
$345$	491.702	+	101.883i	1.42522	+	0.295312i
$346$		0			0
$347$	60.4828	−	381.874i	0.174302	−	1.10050i	−0.733064	−	0.680159i	$-0.761911\pi$
$347$	60.4828	−	381.874i	0.174302	−	1.10050i	0.907366	−	0.420341i	$-0.138089\pi$
$348$		0			0
$349$		−	324.359i		−	0.929396i	−0.885469	−	0.464698i	$-0.846163\pi$
$349$		−	324.359i		−	0.929396i	0.885469	−	0.464698i	$-0.153837\pi$
$350$		0			0
$351$	−55.6388			−0.158515
$352$		0			0
$353$	−573.272	−	90.7973i	−1.62400	−	0.257216i	−0.722940	−	0.690911i	$-0.757210\pi$
$353$	−573.272	−	90.7973i	−1.62400	−	0.257216i	−0.901060	+	0.433695i	$0.857210\pi$
$354$		0			0
$355$	−98.8576	−	56.4017i	−0.278472	−	0.158878i
$356$		0			0
$357$	187.937	−	187.937i	0.526434	−	0.526434i
$358$		0			0
$359$	−348.589	−	113.264i	−0.971001	−	0.315497i	−0.219781	−	0.975549i	$-0.570534\pi$
$359$	−348.589	−	113.264i	−0.971001	−	0.315497i	−0.751220	+	0.660052i	$0.770534\pi$
$360$		0			0
$361$	−86.5680	−	266.429i	−0.239801	−	0.738030i
$362$		0			0
$363$	−424.210	+	216.146i	−1.16862	+	0.595443i
$364$		0			0
$365$	−52.7457	−	2.49322i	−0.144509	−	0.00683074i
$366$		0			0
$367$	410.639	−	65.0389i	1.11891	−	0.177218i	0.430534	−	0.902574i	$-0.358325\pi$
$367$	410.639	−	65.0389i	1.11891	−	0.177218i	0.688373	+	0.725357i	$0.258325\pi$
$368$		0			0
$369$	73.3997	−	101.026i	0.198915	−	0.273783i
$370$		0			0
$371$	293.924	−	213.548i	0.792247	−	0.575601i
$372$		0			0
$373$	1.77772	−	3.48897i	0.00476600	−	0.00935381i	−0.888611	−	0.458661i	$-0.848329\pi$
$373$	1.77772	−	3.48897i	0.00476600	−	0.00935381i	0.893377	+	0.449307i	$0.148329\pi$
$374$		0			0
$375$	441.902	+	216.666i	1.17841	+	0.577775i
$376$		0			0
$377$	224.237	+	114.255i	0.594794	+	0.303063i
$378$		0			0
$379$	155.189	+	213.599i	0.409470	+	0.563586i	0.963089	−	0.269183i	$-0.0867538\pi$
$379$	155.189	+	213.599i	0.409470	+	0.563586i	−0.553619	+	0.832770i	$0.686754\pi$
$380$		0			0
$381$	389.188	+	282.761i	1.02149	+	0.742156i
$382$		0			0
$383$	−78.4913	−	495.574i	−0.204938	−	1.29393i	−0.848770	−	0.528761i	$-0.822657\pi$
$383$	−78.4913	−	495.574i	−0.204938	−	1.29393i	0.643832	−	0.765167i	$-0.277343\pi$
$384$		0			0
$385$	0.477970	−	10.1118i	0.00124148	−	0.0262644i
$386$		0			0
$387$	−98.3845	−	193.091i	−0.254224	−	0.498942i
$388$		0			0
$389$	364.326	−	118.377i	0.936571	−	0.304310i	0.199324	−	0.979934i	$-0.436125\pi$
$389$	364.326	−	118.377i	0.936571	−	0.304310i	0.737247	+	0.675623i	$0.236125\pi$
$390$		0			0
$391$	−73.5837	+	226.467i	−0.188194	+	0.579201i
$392$		0			0
$393$	504.506	+	504.506i	1.28373	+	1.28373i
$394$		0			0
$395$	−301.331	+	528.155i	−0.762864	+	1.33710i
$396$		0			0
$397$	−51.3528	+	324.229i	−0.129352	+	0.816697i	0.834646	+	0.550787i	$0.185672\pi$
$397$	−51.3528	+	324.229i	−0.129352	+	0.816697i	−0.963998	+	0.265910i	$0.914328\pi$
$398$		0			0
$399$		−	720.888i		−	1.80674i
$400$		0			0
$401$	−54.4458			−0.135775			−0.0678875	−	0.997693i	$-0.521626\pi$
$401$	−54.4458			−0.135775			−0.0678875	+	0.997693i	$0.521626\pi$
$402$		0			0
$403$	305.827	+	48.4383i	0.758877	+	0.120194i
$404$		0			0
$405$	98.6487	−	476.094i	0.243577	−	1.17554i
$406$		0			0
$407$	7.71169	−	7.71169i	0.0189476	−	0.0189476i
$408$		0			0
$409$	149.018	+	48.4188i	0.364347	+	0.118383i	0.485468	−	0.874254i	$-0.338649\pi$
$409$	149.018	+	48.4188i	0.364347	+	0.118383i	−0.121122	+	0.992638i	$0.538649\pi$
$410$		0			0
$411$	−43.0756	−	132.573i	−0.104807	−	0.322562i
$412$		0			0
$413$	−495.719	+	252.581i	−1.20029	+	0.611577i
$414$		0			0
$415$	108.206	−	71.0610i	0.260737	−	0.171231i
$416$		0			0
$417$	224.799	−	35.6046i	0.539086	−	0.0853828i
$418$		0			0
$419$	−296.787	+	408.492i	−0.708321	+	0.974920i	0.291510	+	0.956568i	$0.405842\pi$
$419$	−296.787	+	408.492i	−0.708321	+	0.974920i	−0.999832	+	0.0183527i	$0.994158\pi$
$420$		0			0
$421$	−599.885	+	435.842i	−1.42491	+	1.03525i	−0.433969	+	0.900928i	$0.642887\pi$
$421$	−599.885	+	435.842i	−1.42491	+	1.03525i	−0.990937	+	0.134327i	$0.957113\pi$
$422$		0			0
$423$	55.5785	−	109.079i	0.131391	−	0.257870i
$424$		0			0
$425$	−125.098	+	197.027i	−0.294348	+	0.463594i
$426$		0			0
$427$	670.403	+	341.587i	1.57003	+	0.799970i
$428$		0			0
$429$	3.66590	+	5.04567i	0.00854521	+	0.0117615i
$430$		0			0
$431$	588.734	+	427.740i	1.36597	+	0.992437i	0.998040	+	0.0625850i	$0.0199345\pi$
$431$	588.734	+	427.740i	1.36597	+	0.992437i	0.367933	+	0.929852i	$0.380066\pi$
$432$		0			0
$433$	−34.7237	−	219.237i	−0.0801932	−	0.506320i	−0.994789	−	0.101952i	$-0.967491\pi$
$433$	−34.7237	−	219.237i	−0.0801932	−	0.506320i	0.914596	−	0.404369i	$-0.132509\pi$
$434$		0			0
$435$	−547.624	+	683.393i	−1.25891	+	1.57102i
$436$		0			0
$437$	293.216	+	575.468i	0.670974	+	1.31686i
$438$		0			0
$439$	245.012	−	79.6092i	0.558113	−	0.181342i	−0.0163587	−	0.999866i	$-0.505207\pi$
$439$	245.012	−	79.6092i	0.558113	−	0.181342i	0.574472	+	0.818524i	$0.305207\pi$
$440$		0			0
$441$	6.60374	−	20.3242i	0.0149745	−	0.0460867i
$442$		0			0
$443$	60.0305	+	60.0305i	0.135509	+	0.135509i	0.771608	−	0.636099i	$-0.219453\pi$
$443$	60.0305	+	60.0305i	0.135509	+	0.135509i	−0.636099	+	0.771608i	$0.719453\pi$
$444$		0			0
$445$	−69.2405	−	76.1111i	−0.155597	−	0.171036i
$446$		0			0
$447$	−148.976	+	940.596i	−0.333279	+	2.10424i
$448$		0			0
$449$			142.467i			0.317299i	0.987335	+	0.158649i	$0.0507139\pi$
$449$			142.467i			0.317299i	−0.987335	+	0.158649i	$0.949286\pi$
$450$		0			0
$451$	5.37730			0.0119231
$452$		0			0
$453$	367.490	+	58.2046i	0.811235	+	0.128487i
$454$		0			0
$455$	203.310	−	22.4230i	0.446835	−	0.0492814i
$456$		0			0
$457$	265.053	−	265.053i	0.579986	−	0.579986i	−0.354914	−	0.934899i	$-0.615490\pi$
$457$	265.053	−	265.053i	0.579986	−	0.579986i	0.934899	+	0.354914i	$0.115490\pi$
$458$		0			0
$459$	87.3175	+	28.3712i	0.190234	+	0.0618108i
$460$		0			0
$461$	−221.105	−	680.490i	−0.479620	−	1.47612i	−0.839624	−	0.543167i	$-0.817225\pi$
$461$	−221.105	−	680.490i	−0.479620	−	1.47612i	0.360005	−	0.932950i	$-0.382775\pi$
$462$		0			0
$463$	−520.235	+	265.073i	−1.12362	+	0.572512i	−0.914179	−	0.405310i	$-0.867164\pi$
$463$	−520.235	+	265.073i	−1.12362	+	0.572512i	−0.209439	+	0.977822i	$0.567164\pi$
$464$		0			0
$465$	−380.968	+	1007.87i	−0.819287	+	2.16746i
$466$		0			0
$467$	826.139	−	130.848i	1.76903	−	0.280187i	0.814907	−	0.579591i	$-0.196788\pi$
$467$	826.139	−	130.848i	1.76903	−	0.280187i	0.954126	+	0.299404i	$0.0967879\pi$
$468$		0			0
$469$	−129.076	+	177.658i	−0.275216	+	0.378802i
$470$		0			0
$471$	843.995	−	613.198i	1.79192	−	1.30191i
$472$		0			0
$473$	4.23658	−	8.31476i	0.00895683	−	0.0175788i
$474$		0			0
$475$	137.953	+	617.804i	0.290428	+	1.30064i
$476$		0			0
$477$	−291.086	−	148.316i	−0.610243	−	0.310934i
$478$		0			0
$479$	229.058	+	315.271i	0.478201	+	0.658187i	0.978158	−	0.207863i	$-0.0666509\pi$
$479$	229.058	+	315.271i	0.478201	+	0.658187i	−0.499957	+	0.866050i	$0.666651\pi$
$480$		0			0
$481$	178.276	+	129.525i	0.370637	+	0.269283i
$482$		0			0
$483$	113.602	+	717.258i	0.235202	+	1.48501i
$484$		0			0
$485$	−722.484	+	197.564i	−1.48966	+	0.407349i
$486$		0			0
$487$	−81.6474	−	160.242i	−0.167654	−	0.329039i	0.791859	−	0.610704i	$-0.209113\pi$
$487$	−81.6474	−	160.242i	−0.167654	−	0.329039i	−0.959513	+	0.281665i	$0.909113\pi$
$488$		0			0
$489$	−167.029	+	54.2709i	−0.341572	+	0.110983i
$490$		0			0
$491$	−147.768	+	454.783i	−0.300953	+	0.926239i	0.680203	+	0.733024i	$0.261892\pi$
$491$	−147.768	+	454.783i	−0.300953	+	0.926239i	−0.981156	+	0.193215i	$0.938108\pi$
$492$		0			0
$493$	−293.649	−	293.649i	−0.595638	−	0.595638i
$494$		0			0
$495$	−8.29673	+	3.74502i	−0.0167611	+	0.00756571i
$496$		0			0
$497$	25.7489	−	162.572i	0.0518087	−	0.327107i
$498$		0			0
$499$			112.565i			0.225581i	0.993619	+	0.112791i	$0.0359789\pi$
$499$			112.565i			0.225581i	−0.993619	+	0.112791i	$0.964021\pi$
$500$		0			0
$501$	936.082			1.86843
$502$		0			0
$503$	211.275	+	33.4627i	0.420031	+	0.0665263i	0.362872	−	0.931839i	$-0.381796\pi$
$503$	211.275	+	33.4627i	0.420031	+	0.0665263i	0.0571582	+	0.998365i	$0.481796\pi$
$504$		0			0
$505$	−99.5880	−	220.628i	−0.197204	−	0.436886i
$506$		0			0
$507$	381.401	−	381.401i	0.752270	−	0.752270i
$508$		0			0
$509$	295.169	+	95.9061i	0.579899	+	0.188421i	0.584255	−	0.811570i	$-0.301387\pi$
$509$	295.169	+	95.9061i	0.579899	+	0.188421i	−0.00435637	+	0.999991i	$0.501387\pi$
$510$		0			0
$511$	−23.5982	−	72.6278i	−0.0461805	−	0.142129i
$512$		0			0
$513$	221.879	−	113.053i	0.432513	−	0.220376i
$514$		0			0
$515$	−160.289	−	586.172i	−0.311241	−	1.13820i
$516$		0			0
$517$	5.20677	−	0.824671i	0.0100711	−	0.00159511i
$518$		0			0
$519$	646.519	−	889.858i	1.24570	−	1.71456i
$520$		0			0
$521$	399.823	−	290.488i	0.767414	−	0.557559i	−0.133761	−	0.991014i	$-0.542706\pi$
$521$	399.823	−	290.488i	0.767414	−	0.557559i	0.901175	+	0.433455i	$0.142706\pi$
$522$		0			0
$523$	−34.6555	+	68.0152i	−0.0662628	+	0.130048i	−0.921762	−	0.387756i	$-0.873250\pi$
$523$	−34.6555	+	68.0152i	−0.0662628	+	0.130048i	0.855499	+	0.517804i	$0.173250\pi$
$524$		0			0
$525$	−67.1376	+	708.583i	−0.127881	+	1.34968i
$526$		0			0
$527$	−455.255	−	231.964i	−0.863861	−	0.440159i
$528$		0			0
$529$	−71.4868	−	98.3931i	−0.135136	−	0.185998i
$530$		0			0
$531$	404.739	+	294.060i	0.762221	+	0.553786i
$532$		0			0
$533$	16.9968	+	107.314i	0.0318890	+	0.201339i
$534$		0			0
$535$	693.401	+	262.101i	1.29608	+	0.489909i
$536$		0			0
$537$	−166.379	−	326.537i	−0.309830	−	0.608076i
$538$		0			0
$539$	0.875191	−	0.284367i	0.00162373	−	0.000527582i
$540$		0			0
$541$	−111.558	+	343.339i	−0.206207	+	0.634639i	0.793455	+	0.608629i	$0.208280\pi$
$541$	−111.558	+	343.339i	−0.206207	+	0.634639i	−0.999662	+	0.0260098i	$0.991720\pi$
$542$		0			0
$543$	−970.556	−	970.556i	−1.78740	−	1.78740i
$544$		0			0
$545$	78.8913	+	715.308i	0.144755	+	1.31249i
$546$		0			0
$547$	−80.2610	+	506.748i	−0.146729	+	0.926413i	0.798970	+	0.601371i	$0.205379\pi$
$547$	−80.2610	+	506.748i	−0.146729	+	0.926413i	−0.945699	+	0.325042i	$0.894621\pi$
$548$		0			0
$549$		−	676.578i		−	1.23238i
$550$		0			0
$551$	−1126.38			−2.04425
$552$		0			0
$553$	−868.557	−	137.566i	−1.57063	−	0.248763i
$554$		0			0
$555$	−567.208	+	516.006i	−1.02200	+	0.929741i
$556$		0			0
$557$	633.877	−	633.877i	1.13802	−	1.13802i	0.149215	−	0.988805i	$-0.452325\pi$
$557$	633.877	−	633.877i	1.13802	−	1.13802i	0.988805	−	0.149215i	$-0.0476747\pi$
$558$		0			0
$559$	179.327	+	58.2670i	0.320800	+	0.104234i
$560$		0			0
$561$	−3.18025	−	9.78780i	−0.00566889	−	0.0174471i
$562$		0			0
$563$	554.252	−	282.405i	0.984462	−	0.501608i	0.113807	−	0.993503i	$-0.463695\pi$
$563$	554.252	−	282.405i	0.984462	−	0.501608i	0.870655	+	0.491895i	$0.163695\pi$
$564$		0			0
$565$	534.819	+	428.567i	0.946582	+	0.758526i
$566$		0			0
$567$	694.490	−	109.996i	1.22485	−	0.193997i
$568$		0			0
$569$	448.044	−	616.680i	0.787423	−	1.08380i	−0.207001	−	0.978341i	$-0.566370\pi$
$569$	448.044	−	616.680i	0.787423	−	1.08380i	0.994424	−	0.105455i	$-0.0336297\pi$
$570$		0			0
$571$	−104.927	+	76.2337i	−0.183760	+	0.133509i	−0.675862	−	0.737028i	$-0.736229\pi$
$571$	−104.927	+	76.2337i	−0.183760	+	0.133509i	0.492103	+	0.870537i	$0.336229\pi$
$572$		0			0
$573$	170.835	−	335.282i	0.298141	−	0.585135i
$574$		0			0
$575$	−234.616	−	592.953i	−0.408028	−	1.03122i
$576$		0			0
$577$	−667.653	−	340.186i	−1.15711	−	0.589578i	−0.233292	−	0.972407i	$-0.574950\pi$
$577$	−667.653	−	340.186i	−1.15711	−	0.589578i	−0.923819	+	0.382829i	$0.874950\pi$
$578$		0			0
$579$	148.032	+	203.749i	0.255669	+	0.351898i
$580$		0			0
$581$	151.459	+	110.042i	0.260688	+	0.189401i
$582$		0			0
$583$	−2.20070	−	13.8947i	−0.00377479	−	0.0238331i
$584$		0			0
$585$	−100.964	−	153.739i	−0.172587	−	0.262802i
$586$		0			0
$587$	−207.881	−	407.988i	−0.354141	−	0.695040i	0.643370	−	0.765555i	$-0.277536\pi$
$587$	−207.881	−	407.988i	−0.354141	−	0.695040i	−0.997511	+	0.0705153i	$0.977536\pi$
$588$		0			0
$589$	−1318.02	+	428.250i	−2.23772	+	0.727079i
$590$		0			0
$591$	−158.212	+	486.926i	−0.267702	+	0.823902i
$592$		0			0
$593$	−142.290	−	142.290i	−0.239950	−	0.239950i	0.576879	−	0.816829i	$-0.304270\pi$
$593$	−142.290	−	142.290i	−0.239950	−	0.239950i	−0.816829	+	0.576879i	$0.804270\pi$
$594$		0			0
$595$	−330.501	−	68.4812i	−0.555464	−	0.115094i
$596$		0			0
$597$	−102.170	+	645.075i	−0.171139	+	1.08053i
$598$		0			0
$599$		−	123.484i		−	0.206150i	−0.994674	−	0.103075i	$-0.967132\pi$
$599$		−	123.484i		−	0.206150i	0.994674	−	0.103075i	$-0.0328682\pi$
$600$		0			0
$601$	512.898			0.853407			0.426704	−	0.904392i	$-0.359675\pi$
$601$	512.898			0.853407			0.426704	+	0.904392i	$0.359675\pi$
$602$		0			0
$603$	195.034	+	30.8903i	0.323439	+	0.0512278i
$604$		0			0
$605$	525.149	+	299.616i	0.868014	+	0.495233i
$606$		0			0
$607$	−164.317	+	164.317i	−0.270703	+	0.270703i	−0.829383	−	0.558680i	$-0.811308\pi$
$607$	−164.317	+	164.317i	−0.270703	+	0.270703i	0.558680	+	0.829383i	$0.311308\pi$
$608$		0			0
$609$	−1204.50	−	391.365i	−1.97783	−	0.642636i
$610$		0			0
$611$	32.9156	+	101.304i	0.0538717	+	0.165800i
$612$		0			0
$613$	794.593	−	404.865i	1.29624	−	0.660465i	0.336583	−	0.941654i	$-0.390729\pi$
$613$	794.593	−	404.865i	1.29624	−	0.660465i	0.959653	+	0.281189i	$0.0907286\pi$
$614$		0			0
$615$	−377.658	−	17.8514i	−0.614079	−	0.0290267i
$616$		0			0
$617$	430.183	−	68.1342i	0.697217	−	0.110428i	0.202242	−	0.979336i	$-0.435177\pi$
$617$	430.183	−	68.1342i	0.697217	−	0.110428i	0.494975	+	0.868907i	$0.335177\pi$
$618$		0			0
$619$	−446.704	+	614.835i	−0.721654	+	0.993271i	0.277813	+	0.960635i	$0.410390\pi$
$619$	−446.704	+	614.835i	−0.721654	+	0.993271i	−0.999467	+	0.0326364i	$0.989610\pi$
$620$		0			0
$621$	−202.946	+	147.449i	−0.326805	+	0.237438i
$622$		0			0
$623$	67.5557	−	132.585i	0.108436	−	0.212818i
$624$		0			0
$625$	−78.0613	−	620.106i	−0.124898	−	0.992170i
$626$		0			0
$627$	−24.8714	−	12.6726i	−0.0396673	−	0.0202115i
$628$		0			0
$629$	−213.733	−	294.178i	−0.339798	−	0.467692i
$630$		0			0
$631$	496.536	+	360.754i	0.786903	+	0.571719i	0.907043	−	0.421038i	$-0.138334\pi$
$631$	496.536	+	360.754i	0.786903	+	0.571719i	−0.120140	+	0.992757i	$0.538334\pi$
$632$		0			0
$633$	−69.7072	−	440.114i	−0.110122	−	0.695283i
$634$		0			0
$635$	28.8446	−	610.226i	0.0454245	−	0.960985i
$636$		0			0
$637$	8.44140	+	16.5672i	0.0132518	+	0.0260081i
$638$		0			0
$639$	−140.765	+	45.7375i	−0.220290	+	0.0715767i
$640$		0			0
$641$	8.01015	−	24.6527i	0.0124963	−	0.0384598i	−0.944614	−	0.328184i	$-0.893563\pi$
$641$	8.01015	−	24.6527i	0.0124963	−	0.0384598i	0.957110	+	0.289724i	$0.0935635\pi$
$642$		0			0
$643$	−307.458	−	307.458i	−0.478162	−	0.478162i	0.426381	−	0.904543i	$-0.359788\pi$
$643$	−307.458	−	307.458i	−0.478162	−	0.478162i	−0.904543	+	0.426381i	$0.859788\pi$
$644$		0			0
$645$	−325.146	+	569.897i	−0.504103	+	0.883561i
$646$		0			0
$647$	25.5238	−	161.151i	0.0394494	−	0.249074i	−0.960081	−	0.279723i	$-0.909757\pi$
$647$	25.5238	−	161.151i	0.0394494	−	0.249074i	0.999530	+	0.0306491i	$0.00975744\pi$
$648$		0			0
$649$			21.5430i			0.0331941i
$650$		0			0
$651$	−1558.22			−2.39358
$652$		0			0
$653$	−181.554	−	28.7553i	−0.278030	−	0.0440357i	0.0158620	−	0.999874i	$-0.494951\pi$
$653$	−181.554	−	28.7553i	−0.278030	−	0.0440357i	−0.293892	+	0.955838i	$0.594951\pi$
$654$		0			0
$655$	183.834	−	887.211i	0.280663	−	1.35452i
$656$		0			0
$657$	−48.5562	+	48.5562i	−0.0739060	+	0.0739060i
$658$		0			0
$659$	−308.361	−	100.193i	−0.467923	−	0.152038i	0.0655590	−	0.997849i	$-0.479117\pi$
$659$	−308.361	−	100.193i	−0.467923	−	0.152038i	−0.533482	+	0.845811i	$0.679117\pi$
$660$		0			0
$661$	−121.643	−	374.378i	−0.184028	−	0.566381i	0.815902	−	0.578190i	$-0.196241\pi$
$661$	−121.643	−	374.378i	−0.184028	−	0.566381i	−0.999930	+	0.0118092i	$0.996241\pi$
$662$		0			0
$663$	185.281	−	94.4054i	0.279459	−	0.142391i
$664$		0			0
$665$	−765.207	+	502.527i	−1.15069	+	0.755680i
$666$		0			0
$667$	1120.71	−	177.503i	1.68022	−	0.266121i
$668$		0			0
$669$	−391.939	+	539.457i	−0.585857	+	0.806364i
$670$		0			0
$671$	23.5702	−	17.1248i	0.0351270	−	0.0255213i
$672$		0			0
$673$	−208.434	+	409.074i	−0.309708	+	0.607837i	−0.992426	−	0.122846i	$-0.960798\pi$
$673$	−208.434	+	409.074i	−0.309708	+	0.607837i	0.682718	+	0.730682i	$0.260798\pi$
$674$		0			0
$675$	−228.621	+	90.4594i	−0.338697	+	0.134014i
$676$		0			0
$677$	−49.8554	−	25.4026i	−0.0736417	−	0.0375223i	0.416782	−	0.909007i	$-0.363158\pi$
$677$	−49.8554	−	25.4026i	−0.0736417	−	0.0375223i	−0.490424	+	0.871484i	$0.663158\pi$
$678$		0			0
$679$	−636.694	−	876.335i	−0.937694	−	1.29063i
$680$		0			0
$681$	1265.97	+	919.784i	1.85899	+	1.35064i
$682$		0			0
$683$	−0.429989	−	2.71484i	−0.000629559	−	0.00397488i	0.987372	−	0.158422i	$-0.0506405\pi$
$683$	−0.429989	−	2.71484i	−0.000629559	−	0.00397488i	−0.988001	+	0.154447i	$0.950641\pi$
$684$		0			0
$685$	−110.696	+	138.140i	−0.161599	+	0.201664i
$686$		0			0
$687$	−328.670	−	645.051i	−0.478413	−	0.938939i
$688$		0			0
$689$	270.338	−	87.8380i	0.392362	−	0.127486i
$690$		0			0
$691$	−41.5358	+	127.834i	−0.0601097	+	0.184999i	−0.976602	−	0.215053i	$-0.931008\pi$
$691$	−41.5358	+	127.834i	−0.0601097	+	0.184999i	0.916493	+	0.400051i	$0.131008\pi$
$692$		0			0
$693$	−9.30862	−	9.30862i	−0.0134324	−	0.0134324i
$694$		0			0
$695$	−194.500	−	213.799i	−0.279855	−	0.307625i
$696$		0			0
$697$	28.0469	−	177.081i	0.0402395	−	0.254062i
$698$		0			0
$699$			1155.56i			1.65316i
$700$		0			0
$701$	−264.123			−0.376780			−0.188390	−	0.982094i	$-0.560327\pi$
$701$	−264.123			−0.376780			−0.188390	+	0.982094i	$0.560327\pi$
$702$		0			0
$703$	−974.124	−	154.286i	−1.38567	−	0.219468i
$704$		0			0
$705$	−368.419	+	40.6330i	−0.522580	+	0.0576354i
$706$		0			0
$707$	247.536	−	247.536i	0.350121	−	0.350121i
$708$		0			0
$709$	−854.165	−	277.535i	−1.20475	−	0.391446i	−0.363242	−	0.931695i	$-0.618330\pi$
$709$	−854.165	−	277.535i	−1.20475	−	0.391446i	−0.841505	+	0.540249i	$0.818330\pi$
$710$		0			0
$711$	244.357	+	752.052i	0.343680	+	1.05774i
$712$		0			0
$713$	1243.89	−	633.795i	1.74459	−	0.888913i
$714$		0			0
$715$	2.80040	−	7.40858i	0.00391664	−	0.0103617i
$716$		0			0
$717$	73.0902	−	11.5763i	0.101939	−	0.0161455i
$718$		0			0
$719$	−719.629	+	990.484i	−1.00087	+	1.37759i	−0.0760877	+	0.997101i	$0.524243\pi$
$719$	−719.629	+	990.484i	−1.00087	+	1.37759i	−0.924787	+	0.380485i	$0.875757\pi$
$720$		0			0
$721$	710.995	−	516.568i	0.986124	−	0.716461i
$722$		0			0
$723$	621.729	−	1220.21i	0.859930	−	1.68771i
$724$		0			0
$725$	1107.15	+	104.902i	1.52711	+	0.144692i
$726$		0			0
$727$	597.726	+	304.557i	0.822182	+	0.418923i	0.813873	−	0.581043i	$-0.197355\pi$
$727$	597.726	+	304.557i	0.822182	+	0.418923i	0.00830916	+	0.999965i	$0.497355\pi$
$728$		0			0
$729$	−166.804	−	229.586i	−0.228812	−	0.314932i
$730$		0			0
$731$	−251.718	−	182.884i	−0.344348	−	0.250184i
$732$		0			0
$733$	23.5240	+	148.525i	0.0320928	+	0.202626i	0.998525	−	0.0542964i	$-0.0172916\pi$
$733$	23.5240	+	148.525i	0.0320928	+	0.202626i	−0.966432	+	0.256922i	$0.917292\pi$
$734$		0			0
$735$	−62.4104	+	17.0662i	−0.0849121	+	0.0232193i
$736$		0			0
$737$	3.86034	+	7.57635i	0.00523791	+	0.0102800i
$738$		0			0
$739$	−62.7595	+	20.3918i	−0.0849249	+	0.0275938i	−0.351171	−	0.936311i	$-0.614217\pi$
$739$	−62.7595	+	20.3918i	−0.0849249	+	0.0275938i	0.266246	+	0.963905i	$0.414217\pi$
$740$		0			0
$741$	174.290	−	536.411i	0.235210	−	0.723901i
$742$		0			0
$743$	−425.112	−	425.112i	−0.572156	−	0.572156i	0.360574	−	0.932730i	$-0.382581\pi$
$743$	−425.112	−	425.112i	−0.572156	−	0.572156i	−0.932730	+	0.360574i	$0.882581\pi$
$744$		0			0
$745$	1102.27	−	497.550i	1.47956	−	0.667852i
$746$		0			0
$747$	26.3351	−	166.273i	0.0352544	−	0.222588i
$748$		0			0
$749$			1072.04i			1.43129i
$750$		0			0
$751$	903.975			1.20370			0.601848	−	0.798611i	$-0.294431\pi$
$751$	903.975			1.20370			0.601848	+	0.798611i	$0.294431\pi$
$752$		0			0
$753$	1393.33	+	220.681i	1.85037	+	0.293069i
$754$		0			0
$755$	−194.392	−	430.656i	−0.257473	−	0.570406i
$756$		0			0
$757$	334.979	−	334.979i	0.442508	−	0.442508i	−0.450346	−	0.892854i	$-0.648699\pi$
$757$	334.979	−	334.979i	0.442508	−	0.442508i	0.892854	+	0.450346i	$0.148699\pi$
$758$		0			0
$759$	26.7432	+	8.68939i	0.0352348	+	0.0114485i
$760$		0			0
$761$	43.3702	+	133.480i	0.0569911	+	0.175401i	0.975500	−	0.220000i	$-0.0706058\pi$
$761$	43.3702	+	133.480i	0.0569911	+	0.175401i	−0.918509	+	0.395401i	$0.870606\pi$
$762$		0			0
$763$	−927.309	+	472.488i	−1.21535	+	0.619250i
$764$		0			0
$765$	80.0543	+	292.755i	0.104646	+	0.382687i
$766$		0			0
$767$	−429.930	+	68.0942i	−0.560534	+	0.0887799i
$768$		0			0
$769$	52.0992	−	71.7085i	0.0677493	−	0.0932490i	−0.773798	−	0.633433i	$-0.781645\pi$
$769$	52.0992	−	71.7085i	0.0677493	−	0.0932490i	0.841547	+	0.540184i	$0.181645\pi$
$770$		0			0
$771$	423.063	−	307.373i	0.548719	−	0.398668i
$772$		0			0
$773$	431.889	−	847.630i	0.558718	−	1.09655i	−0.422986	−	0.906136i	$-0.639018\pi$
$773$	431.889	−	847.630i	0.558718	−	1.09655i	0.981705	−	0.190410i	$-0.0609818\pi$
$774$		0			0
$775$	1335.40	−	298.190i	1.72310	−	0.384762i
$776$		0			0
$777$	−988.075	−	503.450i	−1.27165	−	0.647940i
$778$		0			0
$779$	−285.833	−	393.416i	−0.366923	−	0.505026i
$780$		0			0
$781$	−5.15628	−	3.74625i	−0.00660215	−	0.00479674i
$782$		0			0
$783$	−68.4385	−	432.103i	−0.0874055	−	0.551856i
$784$		0			0
$785$	−1239.24	−	468.425i	−1.57865	−	0.596720i
$786$		0			0
$787$	−146.845	−	288.200i	−0.186589	−	0.366201i	0.778696	−	0.627401i	$-0.215881\pi$
$787$	−146.845	−	288.200i	−0.186589	−	0.366201i	−0.965284	+	0.261201i	$0.915881\pi$
$788$		0			0
$789$	136.033	−	44.1997i	0.172411	−	0.0560198i
$790$		0			0
$791$	−306.280	+	942.632i	−0.387206	+	1.19170i
$792$		0			0
$793$	416.258	+	416.258i	0.524916	+	0.524916i
$794$		0			0
$795$	108.432	+	983.156i	0.136393	+	1.23667i
$796$		0			0
$797$	−132.525	+	836.730i	−0.166280	+	1.04985i	0.753510	+	0.657437i	$0.228359\pi$
$797$	−132.525	+	836.730i	−0.166280	+	1.04985i	−0.919789	+	0.392412i	$0.871641\pi$
$798$		0			0
$799$		−	175.767i		−	0.219984i
$800$		0			0
$801$	−133.807			−0.167050
$802$		0			0
$803$	−2.92057	−	0.462574i	−0.00363708	−	0.000576057i
$804$		0			0
$805$	682.162	−	620.583i	0.847406	−	0.770911i
$806$		0			0
$807$	599.468	−	599.468i	0.742835	−	0.742835i
$808$		0			0
$809$	−209.176	−	67.9655i	−0.258561	−	0.0840117i	0.176868	−	0.984235i	$-0.443403\pi$
$809$	−209.176	−	67.9655i	−0.258561	−	0.0840117i	−0.435429	+	0.900223i	$0.643403\pi$
$810$		0			0
$811$	77.6057	+	238.846i	0.0956913	+	0.294508i	0.987433	−	0.158037i	$-0.0505164\pi$
$811$	77.6057	+	238.846i	0.0956913	+	0.294508i	−0.891742	+	0.452544i	$0.850516\pi$
$812$		0			0
$813$	−660.180	+	336.378i	−0.812029	+	0.413750i
$814$		0			0
$815$	174.042	+	139.465i	0.213549	+	0.171123i
$816$		0			0
$817$	−833.524	+	132.017i	−1.02023	+	0.161588i
$818$		0			0
$819$	156.347	−	215.194i	0.190900	−	0.262752i
$820$		0			0
$821$	−1005.92	+	730.846i	−1.22524	+	0.890190i	−0.996524	−	0.0833033i	$-0.973453\pi$
$821$	−1005.92	+	730.846i	−1.22524	+	0.890190i	−0.228717	+	0.973493i	$0.573453\pi$
$822$		0			0
$823$	−58.3047	+	114.429i	−0.0708442	+	0.139039i	−0.923712	−	0.383087i	$-0.874861\pi$
$823$	−58.3047	+	114.429i	−0.0708442	+	0.139039i	0.852868	+	0.522126i	$0.174861\pi$
$824$		0			0
$825$	23.2666	+	14.7726i	0.0282020	+	0.0179062i
$826$		0			0
$827$	−611.364	−	311.506i	−0.739255	−	0.376669i	0.0434552	−	0.999055i	$-0.486163\pi$
$827$	−611.364	−	311.506i	−0.739255	−	0.376669i	−0.782710	+	0.622386i	$0.786163\pi$
$828$		0			0
$829$	−722.996	−	995.118i	−0.872130	−	1.20038i	−0.978539	−	0.206061i	$-0.933935\pi$
$829$	−722.996	−	995.118i	−0.872130	−	1.20038i	0.106409	−	0.994322i	$-0.466065\pi$
$830$		0			0
$831$	648.738	+	471.336i	0.780672	+	0.567191i
$832$		0			0
$833$	−4.79974	−	30.3044i	−0.00576199	−	0.0363798i
$834$		0			0
$835$	−652.537	−	993.631i	−0.781482	−	1.18998i
$836$		0			0
$837$	−244.368	−	479.599i	−0.291957	−	0.572998i
$838$		0			0
$839$	−358.353	+	116.436i	−0.427120	+	0.138780i	−0.514685	−	0.857379i	$-0.672091\pi$
$839$	−358.353	+	116.436i	−0.427120	+	0.138780i	0.0875656	+	0.996159i	$0.472091\pi$
$840$		0			0
$841$	−351.621	+	1082.18i	−0.418099	+	1.28678i
$842$		0			0
$843$	893.271	+	893.271i	1.05963	+	1.05963i
$844$		0			0
$845$	−670.721	−	138.976i	−0.793753	−	0.164469i
$846$		0			0
$847$	−136.783	+	863.613i	−0.161491	+	1.01961i
$848$		0			0
$849$		−	412.710i		−	0.486113i
$850$		0			0
$851$	993.531			1.16749
$852$		0			0
$853$	30.6258	+	4.85064i	0.0359036	+	0.00568657i	0.174360	−	0.984682i	$-0.444214\pi$
$853$	30.6258	+	4.85064i	0.0359036	+	0.00568657i	−0.138457	+	0.990368i	$0.544214\pi$
$854$		0			0
$855$	715.012	+	407.939i	0.836271	+	0.477122i
$856$		0			0
$857$	−530.847	+	530.847i	−0.619424	+	0.619424i	−0.945384	−	0.325959i	$-0.894313\pi$
$857$	−530.847	+	530.847i	−0.619424	+	0.619424i	0.325959	+	0.945384i	$0.394313\pi$
$858$		0			0
$859$	−1220.02	−	396.408i	−1.42028	−	0.461476i	−0.504588	−	0.863360i	$-0.668355\pi$
$859$	−1220.02	−	396.408i	−1.42028	−	0.461476i	−0.915691	+	0.401884i	$0.868355\pi$
$860$		0			0
$861$	−168.963	−	520.014i	−0.196240	−	0.603966i
$862$		0			0
$863$	583.573	−	297.345i	0.676214	−	0.344548i	−0.0819275	−	0.996638i	$-0.526108\pi$
$863$	583.573	−	297.345i	0.676214	−	0.344548i	0.758142	+	0.652090i	$0.226108\pi$
$864$		0			0
$865$	−1395.25	−	65.9516i	−1.61301	−	0.0762447i
$866$		0			0
$867$	784.952	−	124.324i	0.905366	−	0.143396i
$868$		0			0
$869$	−20.0147	+	27.5479i	−0.0230319	+	0.0317006i
$870$		0			0
$871$	−138.998	+	100.988i	−0.159584	+	0.115945i
$872$		0			0
$873$	−442.203	+	867.873i	−0.506533	+	0.994127i
$874$		0			0
$875$	798.947	−	422.684i	0.913082	−	0.483068i
$876$		0			0
$877$	−99.6739	−	50.7864i	−0.113653	−	0.0579092i	0.396240	−	0.918147i	$-0.370315\pi$
$877$	−99.6739	−	50.7864i	−0.113653	−	0.0579092i	−0.509893	+	0.860238i	$0.670315\pi$
$878$		0			0
$879$	199.199	+	274.174i	0.226620	+	0.311916i
$880$		0			0
$881$	−1204.60	−	875.195i	−1.36731	−	0.993411i	−0.997942	−	0.0641289i	$-0.979573\pi$
$881$	−1204.60	−	875.195i	−1.36731	−	0.993411i	−0.369371	−	0.929282i	$-0.620427\pi$
$882$		0			0
$883$	−162.958	−	1028.88i	−0.184551	−	1.16521i	−0.889834	−	0.456283i	$-0.849180\pi$
$883$	−162.958	−	1028.88i	−0.184551	−	1.16521i	0.705284	−	0.708925i	$-0.250820\pi$
$884$		0			0
$885$	71.5178	−	1513.01i	0.0808111	−	1.70961i
$886$		0			0
$887$	83.4425	+	163.765i	0.0940727	+	0.184628i	0.933248	−	0.359233i	$-0.116962\pi$
$887$	83.4425	+	163.765i	0.0940727	+	0.184628i	−0.839175	+	0.543861i	$0.816962\pi$
$888$		0			0
$889$	840.247	−	273.013i	0.945159	−	0.307101i
$890$		0			0
$891$	8.41357	−	25.8943i	0.00944283	−	0.0290621i
$892$		0			0
$893$	−337.103	−	337.103i	−0.377495	−	0.377495i
$894$		0			0
$895$	−230.630	+	404.234i	−0.257687	+	0.451659i
$896$		0			0
$897$	−88.8814	+	561.175i	−0.0990874	+	0.625613i
$898$		0			0
$899$			2434.71i			2.70824i
$900$		0			0
$901$	−469.048			−0.520586
$902$		0			0
$903$	−937.202	−	148.438i	−1.03788	−	0.164383i
$904$		0			0
$905$	−353.655	+	1706.79i	−0.390779	+	1.88596i
$906$		0			0
$907$	1195.59	−	1195.59i	1.31818	−	1.31818i	0.402959	−	0.915218i	$-0.367982\pi$
$907$	1195.59	−	1195.59i	1.31818	−	1.31818i	0.915218	−	0.402959i	$-0.132018\pi$
$908$		0			0
$909$	−299.380	−	97.2743i	−0.329350	−	0.107012i
$910$		0			0
$911$	461.192	+	1419.40i	0.506248	+	1.55807i	0.798662	+	0.601780i	$0.205542\pi$
$911$	461.192	+	1419.40i	0.506248	+	1.55807i	−0.292414	+	0.956292i	$0.594458\pi$
$912$		0			0
$913$	6.45909	−	3.29107i	0.00707458	−	0.00360468i
$914$		0			0
$915$	−1712.23	+	1124.46i	−1.87129	+	1.22892i
$916$		0			0
$917$	1294.20	−	204.981i	1.41134	−	0.223534i
$918$		0			0
$919$	812.353	−	1118.11i	0.883953	−	1.21666i	−0.0913577	−	0.995818i	$-0.529121\pi$
$919$	812.353	−	1118.11i	0.883953	−	1.21666i	0.975310	−	0.220838i	$-0.0708793\pi$
$920$		0			0
$921$	1723.88	−	1252.47i	1.87175	−	1.35990i
$922$		0			0
$923$	58.4651	−	114.744i	0.0633425	−	0.124317i
$924$		0			0
$925$	943.127	+	242.374i	1.01960	+	0.262026i
$926$		0			0
$927$	−704.130	−	358.772i	−0.759579	−	0.387025i
$928$		0			0
$929$	−47.2332	−	65.0109i	−0.0508431	−	0.0699795i	0.782838	−	0.622225i	$-0.213771\pi$
$929$	−47.2332	−	65.0109i	−0.0508431	−	0.0699795i	−0.833682	+	0.552246i	$0.813771\pi$
$930$		0			0
$931$	−67.3261	−	48.9153i	−0.0723159	−	0.0525406i
$932$		0			0
$933$	−27.6789	−	174.758i	−0.0296665	−	0.187307i
$934$		0			0
$935$	−8.17260	+	10.1988i	−0.00874075	+	0.0109078i
$936$		0			0
$937$	−677.385	−	1329.44i	−0.722930	−	1.41883i	−0.900560	−	0.434732i	$-0.856843\pi$
$937$	−677.385	−	1329.44i	−0.722930	−	1.41883i	0.177630	−	0.984097i	$-0.443157\pi$
$938$		0			0
$939$	8.48898	−	2.75824i	0.00904045	−	0.00293742i
$940$		0			0
$941$	−156.957	+	483.065i	−0.166798	+	0.513353i	−0.999164	−	0.0408737i	$-0.986986\pi$
$941$	−156.957	+	483.065i	−0.166798	+	0.513353i	0.832366	+	0.554227i	$0.186986\pi$
$942$		0			0
$943$	346.391	+	346.391i	0.367329	+	0.367329i
$944$		0			0
$945$	−239.274	−	263.017i	−0.253200	−	0.278324i
$946$		0			0
$947$	4.90723	−	30.9831i	0.00518187	−	0.0327171i	−0.984962	−	0.172772i	$-0.944728\pi$
$947$	4.90723	−	30.9831i	0.00518187	−	0.0327171i	0.990144	+	0.140054i	$0.0447278\pi$
$948$		0			0
$949$		−	59.7475i		−	0.0629584i
$950$		0			0
$951$	−626.651			−0.658939
$952$		0			0
$953$	−907.936	−	143.803i	−0.952714	−	0.150895i	−0.339319	−	0.940671i	$-0.610197\pi$
$953$	−907.936	−	143.803i	−0.952714	−	0.150895i	−0.613395	+	0.789776i	$0.710197\pi$
$954$		0			0
$955$	−474.983	+	52.3859i	−0.497364	+	0.0548543i
$956$		0			0
$957$	−34.6766	+	34.6766i	−0.0362347	+	0.0362347i
$958$		0			0
$959$	−243.475	−	79.1098i	−0.253884	−	0.0824919i
$960$		0			0
$961$	628.710	+	1934.97i	0.654225	+	2.01350i
$962$		0			0
$963$	858.922	−	437.643i	0.891923	−	0.454458i
$964$		0			0
$965$	113.083	−	299.165i	0.117184	−	0.310016i
$966$		0			0
$967$	−714.279	+	113.131i	−0.738654	+	0.116991i	−0.514413	−	0.857542i	$-0.671990\pi$
$967$	−714.279	+	113.131i	−0.738654	+	0.116991i	−0.224241	+	0.974534i	$0.571990\pi$
$968$		0			0
$969$	−547.050	+	752.950i	−0.564551	+	0.777038i
$970$		0			0
$971$	1077.34	−	782.736i	1.10952	−	0.806113i	0.126932	−	0.991911i	$-0.459487\pi$
$971$	1077.34	−	782.736i	1.10952	−	0.806113i	0.982588	+	0.185798i	$0.0594870\pi$
$972$		0			0
$973$	189.767	−	372.438i	0.195033	−	0.382773i
$974$		0			0
$975$	−221.272	+	511.022i	−0.226946	+	0.524126i
$976$		0			0
$977$	812.379	+	413.928i	0.831503	+	0.423672i	0.817290	−	0.576227i	$-0.195476\pi$
$977$	812.379	+	413.928i	0.831503	+	0.423672i	0.0142134	+	0.999899i	$0.495476\pi$
$978$		0			0
$979$	−3.38677	−	4.66148i	−0.00345941	−	0.00476147i
$980$		0			0
$981$	757.119	+	550.079i	0.771783	+	0.560733i
$982$		0			0
$983$	166.604	+	1051.90i	0.169485	+	1.07009i	0.914957	+	0.403551i	$0.132224\pi$
$983$	166.604	+	1051.90i	0.169485	+	1.07009i	−0.745472	+	0.666537i	$0.767776\pi$
$984$		0			0
$985$	627.150	−	171.495i	0.636701	−	0.174107i
$986$		0			0
$987$	−243.355	−	477.611i	−0.246560	−	0.483901i
$988$		0			0
$989$	808.522	−	262.705i	0.817515	−	0.265627i
$990$		0			0
$991$	45.3053	−	139.435i	0.0457167	−	0.140702i	−0.925593	−	0.378521i	$-0.876433\pi$
$991$	45.3053	−	139.435i	0.0457167	−	0.140702i	0.971309	+	0.237820i	$0.0764327\pi$
$992$		0			0
$993$	867.011	+	867.011i	0.873123	+	0.873123i
$994$		0			0
$995$	755.955	−	341.227i	0.759754	−	0.342942i
$996$		0			0
$997$	−163.370	+	1031.48i	−0.163862	+	1.03458i	0.759460	+	0.650554i	$0.225463\pi$
$997$	−163.370	+	1031.48i	−0.163862	+	1.03458i	−0.923322	+	0.384028i	$0.874537\pi$
$998$		0			0
$999$		−	383.069i		−	0.383452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.33.2		64
4.3	odd	2		200.3.u.b.33.7	✓	64
25.22	odd	20	inner	400.3.bg.f.97.2		64
100.47	even	20		200.3.u.b.97.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.33.7	✓	64	4.3	odd	2
200.3.u.b.97.7	yes	64	100.47	even	20
400.3.bg.f.33.2		64	1.1	even	1	trivial
400.3.bg.f.97.2		64	25.22	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)

\(f(q)\)	\(=\)	\(q+(-3.88880 - 0.615926i) q^{3} +(2.05707 + 4.55724i) q^{5} +(-5.11305 + 5.11305i) q^{7} +(6.18393 + 2.00928i) q^{9} +O(q^{10})\)	\(q+(-3.88880 - 0.615926i) q^{3} +(2.05707 + 4.55724i) q^{5} +(-5.11305 + 5.11305i) q^{7} +(6.18393 + 2.00928i) q^{9} +(0.0865225 + 0.266289i) q^{11} +(-5.04080 + 2.56841i) q^{13} +(-5.19263 - 18.9892i) q^{15} +(9.22052 - 1.46039i) q^{17} +(14.8832 - 20.4849i) q^{19} +(23.0329 - 16.7344i) q^{21} +(-11.5801 + 22.7271i) q^{23} +(-16.5369 + 18.7492i) q^{25} +(8.76274 + 4.46484i) q^{27} +(-26.1473 - 35.9887i) q^{29} +(-44.2788 - 32.1704i) q^{31} +(-0.172455 - 1.08884i) q^{33} +(-33.8193 - 12.7835i) q^{35} +(-17.6833 - 34.7055i) q^{37} +(21.1846 - 6.88330i) q^{39} +(5.93471 - 18.2652i) q^{41} +(-23.5671 - 23.5671i) q^{43} +(3.56401 + 32.3149i) q^{45} +(2.94533 - 18.5961i) q^{47} -3.28662i q^{49} -36.7563 q^{51} +(-49.6251 - 7.85985i) q^{53} +(-1.03556 + 0.942080i) q^{55} +(-70.4949 + 70.4949i) q^{57} +(73.1755 + 23.7762i) q^{59} +(-32.1545 - 98.9614i) q^{61} +(-41.8923 + 21.3452i) q^{63} +(-22.0742 - 17.6887i) q^{65} +(29.9952 - 4.75077i) q^{67} +(59.0308 - 81.2490i) q^{69} +(-18.4157 + 13.3798i) q^{71} +(-4.79456 + 9.40984i) q^{73} +(75.8569 - 62.7263i) q^{75} +(-1.80394 - 0.919155i) q^{77} +(71.4829 + 98.3877i) q^{79} +(-78.6699 - 57.1570i) q^{81} +(-4.05019 - 25.5719i) q^{83} +(25.6226 + 39.0160i) q^{85} +(79.5155 + 156.058i) q^{87} +(-19.5716 + 6.35919i) q^{89} +(12.6414 - 38.9063i) q^{91} +(152.377 + 152.377i) q^{93} +(123.970 + 25.6872i) q^{95} +(-23.4342 + 147.957i) q^{97} +1.82056i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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