LMFDB - Embedded newform 400.3.bg.f.17.8

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			17.8
Character	$\chi$	$=$	400.17
Dual form			400.3.bg.f.353.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.898945 - 5.67572i) q^{3} +(-0.177358 - 4.99685i) q^{5} +(8.20346 + 8.20346i) q^{7} +(-22.8462 - 7.42316i) q^{9} +O(q^{10})$	\(q+(0.898945 - 5.67572i) q^{3} +(-0.177358 - 4.99685i) q^{5} +(8.20346 + 8.20346i) q^{7} +(-22.8462 - 7.42316i) q^{9} +(-3.33578 - 10.2665i) q^{11} +(-5.40675 - 10.6114i) q^{13} +(-28.5202 - 3.48526i) q^{15} +(-0.503045 - 3.17610i) q^{17} +(3.81089 - 5.24524i) q^{19} +(53.9350 - 39.1861i) q^{21} +(20.6552 + 10.5244i) q^{23} +(-24.9371 + 1.77246i) q^{25} +(-39.1897 + 76.9140i) q^{27} +(8.64761 + 11.9024i) q^{29} +(-12.6901 - 9.21987i) q^{31} +(-61.2684 + 9.70395i) q^{33} +(39.5365 - 42.4464i) q^{35} +(-33.1914 + 16.9119i) q^{37} +(-65.0874 + 21.1482i) q^{39} +(-2.62592 + 8.08176i) q^{41} +(2.91650 - 2.91650i) q^{43} +(-33.0405 + 115.475i) q^{45} +(48.8132 + 7.73125i) q^{47} +85.5936i q^{49} -18.4789 q^{51} +(12.6010 - 79.5595i) q^{53} +(-50.7085 + 18.4893i) q^{55} +(-26.3447 - 26.3447i) q^{57} +(91.0169 + 29.5732i) q^{59} +(-5.81815 - 17.9064i) q^{61} +(-126.522 - 248.313i) q^{63} +(-52.0644 + 28.8988i) q^{65} +(-4.71815 - 29.7892i) q^{67} +(78.3012 - 107.772i) q^{69} +(19.7162 - 14.3246i) q^{71} +(57.2768 + 29.1840i) q^{73} +(-12.3571 + 143.129i) q^{75} +(56.8557 - 111.586i) q^{77} +(1.98385 + 2.73053i) q^{79} +(226.406 + 164.494i) q^{81} +(-38.7880 + 6.14342i) q^{83} +(-15.7813 + 3.07695i) q^{85} +(75.3284 - 38.3818i) q^{87} +(104.031 - 33.8016i) q^{89} +(42.6957 - 131.404i) q^{91} +(-63.7371 + 63.7371i) q^{93} +(-26.8856 - 18.1122i) q^{95} +(-128.316 - 20.3232i) q^{97} +259.312i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$	$1$

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
$3$	0.898945	−	5.67572i	0.299648	−	1.89191i	−0.134256	−	0.990947i	$-0.542864\pi$
$3$	0.898945	−	5.67572i	0.299648	−	1.89191i	0.433904	−	0.900959i	$-0.357136\pi$
$4$		0			0
$5$	−0.177358	−	4.99685i	−0.0354716	−	0.999371i
$5$	−0.177358	−	4.99685i	−0.0354716	−	0.999371i
$6$		0			0
$7$	8.20346	+	8.20346i	1.17192	+	1.17192i	0.981751	+	0.190172i	$0.0609047\pi$
$7$	8.20346	+	8.20346i	1.17192	+	1.17192i	0.190172	+	0.981751i	$0.439095\pi$
$8$		0			0
$9$	−22.8462	−	7.42316i	−2.53846	−	0.824796i
$10$		0			0
$11$	−3.33578	−	10.2665i	−0.303253	−	0.933317i	−0.980323	−	0.197398i	$-0.936751\pi$
$11$	−3.33578	−	10.2665i	−0.303253	−	0.933317i	0.677070	−	0.735918i	$-0.263249\pi$
$12$		0			0
$13$	−5.40675	−	10.6114i	−0.415904	−	0.816258i	−0.999990	−	0.00456565i	$-0.998547\pi$
$13$	−5.40675	−	10.6114i	−0.415904	−	0.816258i	0.584085	−	0.811692i	$-0.301453\pi$
$14$		0			0
$15$	−28.5202	−	3.48526i	−1.90134	−	0.232351i
$16$		0			0
$17$	−0.503045	−	3.17610i	−0.0295909	−	0.186830i	0.968465	−	0.249148i	$-0.0801506\pi$
$17$	−0.503045	−	3.17610i	−0.0295909	−	0.186830i	−0.998056	+	0.0623184i	$0.980151\pi$
$18$		0			0
$19$	3.81089	−	5.24524i	0.200573	−	0.276065i	−0.696868	−	0.717199i	$-0.745424\pi$
$19$	3.81089	−	5.24524i	0.200573	−	0.276065i	0.897441	+	0.441134i	$0.145424\pi$
$20$		0			0
$21$	53.9350	−	39.1861i	2.56833	−	1.86600i
$22$		0			0
$23$	20.6552	+	10.5244i	0.898053	+	0.457581i	0.841152	−	0.540799i	$-0.181878\pi$
$23$	20.6552	+	10.5244i	0.898053	+	0.457581i	0.0569010	+	0.998380i	$0.481878\pi$
$24$		0			0
$25$	−24.9371	+	1.77246i	−0.997484	+	0.0708985i
$26$		0			0
$27$	−39.1897	+	76.9140i	−1.45147	+	2.84867i
$28$		0			0
$29$	8.64761	+	11.9024i	0.298193	+	0.410428i	0.931654	−	0.363347i	$-0.118366\pi$
$29$	8.64761	+	11.9024i	0.298193	+	0.410428i	−0.633460	+	0.773775i	$0.718366\pi$
$30$		0			0
$31$	−12.6901	−	9.21987i	−0.409357	−	0.297415i	0.363984	−	0.931405i	$-0.381416\pi$
$31$	−12.6901	−	9.21987i	−0.409357	−	0.297415i	−0.773341	+	0.633990i	$0.781416\pi$
$32$		0			0
$33$	−61.2684	+	9.70395i	−1.85662	+	0.294059i
$34$		0			0
$35$	39.5365	−	42.4464i	1.12962	−	1.21276i
$36$		0			0
$37$	−33.1914	+	16.9119i	−0.897066	+	0.457078i	−0.840805	−	0.541338i	$-0.817918\pi$
$37$	−33.1914	+	16.9119i	−0.897066	+	0.457078i	−0.0562608	+	0.998416i	$0.517918\pi$
$38$		0			0
$39$	−65.0874	+	21.1482i	−1.66891	+	0.542261i
$40$		0			0
$41$	−2.62592	+	8.08176i	−0.0640469	+	0.197116i	−0.977959	−	0.208795i	$-0.933046\pi$
$41$	−2.62592	+	8.08176i	−0.0640469	+	0.197116i	0.913912	+	0.405911i	$0.133046\pi$
$42$		0			0
$43$	2.91650	−	2.91650i	0.0678255	−	0.0678255i	−0.672380	−	0.740206i	$-0.734728\pi$
$43$	2.91650	−	2.91650i	0.0678255	−	0.0678255i	0.740206	+	0.672380i	$0.234728\pi$
$44$		0			0
$45$	−33.0405	+	115.475i	−0.734234	+	2.56612i
$46$		0			0
$47$	48.8132	+	7.73125i	1.03858	+	0.164495i	0.652357	−	0.757911i	$-0.273780\pi$
$47$	48.8132	+	7.73125i	1.03858	+	0.164495i	0.386221	+	0.922406i	$0.373780\pi$
$48$		0			0
$49$			85.5936i			1.74681i
$50$		0			0
$51$	−18.4789			−0.362331
$52$		0			0
$53$	12.6010	−	79.5595i	0.237754	−	1.50112i	−0.523140	−	0.852246i	$-0.675240\pi$
$53$	12.6010	−	79.5595i	0.237754	−	1.50112i	0.760895	−	0.648875i	$-0.224760\pi$
$54$		0			0
$55$	−50.7085	+	18.4893i	−0.921973	+	0.336168i
$56$		0			0
$57$	−26.3447	−	26.3447i	−0.462188	−	0.462188i
$58$		0			0
$59$	91.0169	+	29.5732i	1.54266	+	0.501240i	0.952108	−	0.305761i	$-0.0989107\pi$
$59$	91.0169	+	29.5732i	1.54266	+	0.501240i	0.590550	+	0.807001i	$0.298911\pi$
$60$		0			0
$61$	−5.81815	−	17.9064i	−0.0953795	−	0.293548i	0.891973	−	0.452089i	$-0.149321\pi$
$61$	−5.81815	−	17.9064i	−0.0953795	−	0.293548i	−0.987352	+	0.158541i	$0.949321\pi$
$62$		0			0
$63$	−126.522	−	248.313i	−2.00828	−	3.94148i
$64$		0			0
$65$	−52.0644	+	28.8988i	−0.800991	+	0.444596i
$66$		0			0
$67$	−4.71815	−	29.7892i	−0.0704202	−	0.444615i	−0.997555	−	0.0698873i	$-0.977736\pi$
$67$	−4.71815	−	29.7892i	−0.0704202	−	0.444615i	0.927135	−	0.374728i	$-0.122264\pi$
$68$		0			0
$69$	78.3012	−	107.772i	1.13480	−	1.56192i
$70$		0			0
$71$	19.7162	−	14.3246i	0.277692	−	0.201755i	−0.440218	−	0.897891i	$-0.645099\pi$
$71$	19.7162	−	14.3246i	0.277692	−	0.201755i	0.717910	+	0.696136i	$0.245099\pi$
$72$		0			0
$73$	57.2768	+	29.1840i	0.784614	+	0.399781i	0.799923	−	0.600102i	$-0.204873\pi$
$73$	57.2768	+	29.1840i	0.784614	+	0.399781i	−0.0153096	+	0.999883i	$0.504873\pi$
$74$		0			0
$75$	−12.3571	+	143.129i	−0.164761	+	1.90839i
$76$		0			0
$77$	56.8557	−	111.586i	0.738386	−	1.44916i
$78$		0			0
$79$	1.98385	+	2.73053i	0.0251120	+	0.0345637i	0.821388	−	0.570369i	$-0.193200\pi$
$79$	1.98385	+	2.73053i	0.0251120	+	0.0345637i	−0.796276	+	0.604933i	$0.793200\pi$
$80$		0			0
$81$	226.406	+	164.494i	2.79514	+	2.03079i
$82$		0			0
$83$	−38.7880	+	6.14342i	−0.467326	+	0.0740171i	−0.385657	−	0.922642i	$-0.626025\pi$
$83$	−38.7880	+	6.14342i	−0.467326	+	0.0740171i	−0.0816691	+	0.996659i	$0.526025\pi$
$84$		0			0
$85$	−15.7813	+	3.07695i	−0.185662	+	0.0361994i
$86$		0			0
$87$	75.3284	−	38.3818i	0.865844	−	0.441170i
$88$		0			0
$89$	104.031	−	33.8016i	1.16888	−	0.379793i	0.340657	−	0.940188i	$-0.389350\pi$
$89$	104.031	−	33.8016i	1.16888	−	0.379793i	0.828226	+	0.560394i	$0.189350\pi$
$90$		0			0
$91$	42.6957	−	131.404i	0.469184	−	1.44400i
$92$		0			0
$93$	−63.7371	+	63.7371i	−0.685345	+	0.685345i
$94$		0			0
$95$	−26.8856	−	18.1122i	−0.283006	−	0.190654i
$96$		0			0
$97$	−128.316	−	20.3232i	−1.32284	−	0.209518i	−0.545244	−	0.838277i	$-0.683563\pi$
$97$	−128.316	−	20.3232i	−1.32284	−	0.209518i	−0.777600	+	0.628760i	$0.783563\pi$
$98$		0			0
$99$			259.312i			2.61931i
$100$		0			0
$101$	−92.1276			−0.912155			−0.456077	−	0.889940i	$-0.650746\pi$
$101$	−92.1276			−0.912155			−0.456077	+	0.889940i	$0.650746\pi$
$102$		0			0
$103$	23.6180	−	149.118i	0.229301	−	1.44775i	−0.557311	−	0.830304i	$-0.688167\pi$
$103$	23.6180	−	149.118i	0.229301	−	1.44775i	0.786613	−	0.617447i	$-0.211833\pi$
$104$		0			0
$105$	−205.373	−	262.555i	−1.95593	−	2.50053i
$106$		0			0
$107$	−73.2850	−	73.2850i	−0.684906	−	0.684906i	0.276195	−	0.961102i	$-0.410926\pi$
$107$	−73.2850	−	73.2850i	−0.684906	−	0.684906i	−0.961102	+	0.276195i	$0.910926\pi$
$108$		0			0
$109$	4.78691	+	1.55536i	0.0439166	+	0.0142694i	0.330893	−	0.943668i	$-0.392650\pi$
$109$	4.78691	+	1.55536i	0.0439166	+	0.0142694i	−0.286976	+	0.957938i	$0.592650\pi$
$110$		0			0
$111$	66.1498	+	203.588i	0.595944	+	1.83413i
$112$		0			0
$113$	−23.1893	−	45.5116i	−0.205215	−	0.402758i	0.765343	−	0.643622i	$-0.222569\pi$
$113$	−23.1893	−	45.5116i	−0.205215	−	0.402758i	−0.970559	+	0.240864i	$0.922569\pi$
$114$		0			0
$115$	48.9253	−	105.078i	0.425437	−	0.913719i
$116$		0			0
$117$	44.7537	+	282.564i	0.382510	+	2.41507i
$118$		0			0
$119$	21.9283	−	30.1818i	0.184272	−	0.253628i
$120$		0			0
$121$	3.61779	−	2.62848i	0.0298991	−	0.0217230i
$122$		0			0
$123$	43.5092	+	22.1691i	0.353733	+	0.180236i
$124$		0			0
$125$	13.2795	+	124.293i	0.106236	+	0.994341i
$126$		0			0
$127$	42.7821	−	83.9647i	0.336867	−	0.661139i	−0.658982	−	0.752159i	$-0.729013\pi$
$127$	42.7821	−	83.9647i	0.336867	−	0.661139i	0.995849	+	0.0910197i	$0.0290126\pi$
$128$		0			0
$129$	−13.9314	−	19.1750i	−0.107996	−	0.148643i
$130$		0			0
$131$	26.6662	+	19.3741i	0.203559	+	0.147894i	0.684895	−	0.728642i	$-0.259848\pi$
$131$	26.6662	+	19.3741i	0.203559	+	0.147894i	−0.481336	+	0.876536i	$0.659848\pi$
$132$		0			0
$133$	74.2916	−	11.7666i	0.558583	−	0.0884709i
$134$		0			0
$135$	391.279	+	182.184i	2.89836	+	1.34951i
$136$		0			0
$137$	217.591	−	110.868i	1.58826	−	0.809258i	0.588258	−	0.808673i	$-0.299814\pi$
$137$	217.591	−	110.868i	1.58826	−	0.809258i	1.00000		0.000584728i	$-0.000186125\pi$
$138$		0			0
$139$	−251.507	+	81.7196i	−1.80940	+	0.587911i	−0.809405	+	0.587251i	$0.800210\pi$
$139$	−251.507	+	81.7196i	−1.80940	+	0.587911i	−1.00000		0.000659663i	$0.999790\pi$
$140$		0			0
$141$	87.7608	−	270.100i	0.622417	−	1.91560i
$142$		0			0
$143$	−90.9055	+	90.9055i	−0.635703	+	0.635703i
$144$		0			0
$145$	57.9409	−	45.3218i	0.399592	−	0.312564i
$146$		0			0
$147$	485.805	+	76.9439i	3.30480	+	0.523428i
$148$		0			0
$149$		−	236.879i		−	1.58979i	−0.606745	−	0.794896i	$-0.707525\pi$
$149$		−	236.879i		−	1.58979i	0.606745	−	0.794896i	$-0.292475\pi$
$150$		0			0
$151$	237.432			1.57240			0.786199	−	0.617973i	$-0.212046\pi$
$151$	237.432			1.57240			0.786199	+	0.617973i	$0.212046\pi$
$152$		0			0
$153$	−12.0841	+	76.2959i	−0.0789810	+	0.498666i
$154$		0			0
$155$	−43.8197	+	65.0456i	−0.282708	+	0.419649i
$156$		0			0
$157$	11.3169	+	11.3169i	0.0720823	+	0.0720823i	0.742229	−	0.670147i	$-0.233769\pi$
$157$	11.3169	+	11.3169i	0.0720823	+	0.0720823i	−0.670147	+	0.742229i	$0.733769\pi$
$158$		0			0
$159$	−440.229	−	143.039i	−2.76874	−	0.899618i
$160$		0			0
$161$	83.1081	+	255.780i	0.516199	+	1.58870i
$162$		0			0
$163$	44.3488	+	87.0395i	0.272079	+	0.533985i	0.986103	−	0.166137i	$-0.0531293\pi$
$163$	44.3488	+	87.0395i	0.272079	+	0.533985i	−0.714024	+	0.700121i	$0.753129\pi$
$164$		0			0
$165$	59.3557	+	304.428i	0.359731	+	1.84502i
$166$		0			0
$167$	38.7842	+	244.874i	0.232241	+	1.46631i	0.777945	+	0.628333i	$0.216262\pi$
$167$	38.7842	+	244.874i	0.232241	+	1.46631i	−0.545704	+	0.837978i	$0.683738\pi$
$168$		0			0
$169$	15.9679	−	21.9779i	0.0944847	−	0.130047i
$170$		0			0
$171$	−126.000	+	91.5446i	−0.736844	+	0.535349i
$172$		0			0
$173$	130.591	+	66.5394i	0.754861	+	0.384621i	0.788677	−	0.614807i	$-0.210766\pi$
$173$	130.591	+	66.5394i	0.754861	+	0.384621i	−0.0338167	+	0.999428i	$0.510766\pi$
$174$		0			0
$175$	−219.111	−	190.030i	−1.25206	−	1.08589i
$176$		0			0
$177$	249.668	−	490.001i	1.41055	−	2.76837i
$178$		0			0
$179$	60.0821	+	82.6959i	0.335654	+	0.461988i	0.943166	−	0.332323i	$-0.107832\pi$
$179$	60.0821	+	82.6959i	0.335654	+	0.461988i	−0.607512	+	0.794311i	$0.707832\pi$
$180$		0			0
$181$	169.731	+	123.316i	0.937738	+	0.681306i	0.947875	−	0.318642i	$-0.103227\pi$
$181$	169.731	+	123.316i	0.937738	+	0.681306i	−0.0101373	+	0.999949i	$0.503227\pi$
$182$		0			0
$183$	−106.862	+	16.9253i	−0.583946	+	0.0924879i
$184$		0			0
$185$	90.3929	+	162.853i	0.488610	+	0.880288i
$186$		0			0
$187$	−30.9294	+	15.7593i	−0.165398	+	0.0842744i
$188$		0			0
$189$	−952.452	+	309.470i	−5.03943	+	1.63741i
$190$		0			0
$191$	21.4525	−	66.0240i	0.112317	−	0.345676i	−0.879061	−	0.476709i	$-0.841830\pi$
$191$	21.4525	−	66.0240i	0.112317	−	0.345676i	0.991378	+	0.131033i	$0.0418295\pi$
$192$		0			0
$193$	−44.3005	+	44.3005i	−0.229536	+	0.229536i	−0.812499	−	0.582963i	$-0.801893\pi$
$193$	−44.3005	+	44.3005i	−0.229536	+	0.229536i	0.582963	+	0.812499i	$0.301893\pi$
$194$		0			0
$195$	117.218	+	321.481i	0.601119	+	1.64862i
$196$		0			0
$197$	−226.578	−	35.8864i	−1.15014	−	0.182164i	−0.447887	−	0.894090i	$-0.647823\pi$
$197$	−226.578	−	35.8864i	−1.15014	−	0.182164i	−0.702255	+	0.711926i	$0.747823\pi$
$198$		0			0
$199$		−	262.444i		−	1.31881i	−0.751787	−	0.659406i	$-0.770808\pi$
$199$		−	262.444i		−	1.31881i	0.751787	−	0.659406i	$-0.229192\pi$
$200$		0			0
$201$	−173.317			−0.862272
$202$		0			0
$203$	−26.7007	+	168.581i	−0.131530	+	0.830450i
$204$		0			0
$205$	40.8491	+	11.6880i	0.199264	+	0.0570146i
$206$		0			0
$207$	−393.768	−	393.768i	−1.90226	−	1.90226i
$208$		0			0
$209$	−66.5624	−	21.6274i	−0.318481	−	0.103481i
$210$		0			0
$211$	64.4677	+	198.411i	0.305534	+	0.940337i	0.979477	+	0.201554i	$0.0645991\pi$
$211$	64.4677	+	198.411i	0.305534	+	0.940337i	−0.673943	+	0.738783i	$0.735401\pi$
$212$		0			0
$213$	−63.5788	−	124.780i	−0.298492	−	0.585823i
$214$		0			0
$215$	−15.0906	−	14.0561i	−0.0701887	−	0.0653770i
$216$		0			0
$217$	−28.4676	−	179.737i	−0.131187	−	0.828283i
$218$		0			0
$219$	217.129	−	298.852i	0.991456	−	1.36462i
$220$		0			0
$221$	−30.9829	+	22.5104i	−0.140194	+	0.101857i
$222$		0			0
$223$	187.758	+	95.6674i	0.841964	+	0.429002i	0.821103	−	0.570780i	$-0.193359\pi$
$223$	187.758	+	95.6674i	0.841964	+	0.429002i	0.0208610	+	0.999782i	$0.493359\pi$
$224$		0			0
$225$	582.874	+	144.618i	2.59055	+	0.642747i
$226$		0			0
$227$	38.3290	−	75.2249i	0.168850	−	0.331387i	−0.791039	−	0.611765i	$-0.790460\pi$
$227$	38.3290	−	75.2249i	0.168850	−	0.331387i	0.959890	+	0.280378i	$0.0904598\pi$
$228$		0			0
$229$	95.7508	+	131.790i	0.418126	+	0.575500i	0.965177	−	0.261599i	$-0.0842497\pi$
$229$	95.7508	+	131.790i	0.418126	+	0.575500i	−0.547051	+	0.837099i	$0.684250\pi$
$230$		0			0
$231$	−582.219	−	423.007i	−2.52043	−	1.83120i
$232$		0			0
$233$	−104.403	+	16.5358i	−0.448081	+	0.0709691i	−0.376397	−	0.926458i	$-0.622837\pi$
$233$	−104.403	+	16.5358i	−0.448081	+	0.0709691i	−0.0716839	+	0.997427i	$0.522837\pi$
$234$		0			0
$235$	29.9745	−	245.284i	0.127551	−	1.04376i
$236$		0			0
$237$	17.2811	−	8.80516i	0.0729161	−	0.0371526i
$238$		0			0
$239$	86.1231	−	27.9831i	0.360348	−	0.117084i	−0.123247	−	0.992376i	$-0.539331\pi$
$239$	86.1231	−	27.9831i	0.360348	−	0.117084i	0.483595	+	0.875292i	$0.339331\pi$
$240$		0			0
$241$	−43.0659	+	132.543i	−0.178697	+	0.549972i	−0.999783	−	0.0208319i	$-0.993369\pi$
$241$	−43.0659	+	132.543i	−0.178697	+	0.549972i	0.821086	+	0.570804i	$0.193369\pi$
$242$		0			0
$243$	587.792	−	587.792i	2.41890	−	2.41890i
$244$		0			0
$245$	427.699	−	15.1807i	1.74571	−	0.0619620i
$246$		0			0
$247$	−76.2636	−	12.0790i	−0.308759	−	0.0489027i
$248$		0			0
$249$			225.673i			0.906316i
$250$		0			0
$251$	49.1319			0.195745			0.0978723	−	0.995199i	$-0.468796\pi$
$251$	49.1319			0.195745			0.0978723	+	0.995199i	$0.468796\pi$
$252$		0			0
$253$	39.1468	−	247.163i	0.154731	−	0.976931i
$254$		0			0
$255$	3.27737	+	92.3362i	0.0128524	+	0.362103i
$256$		0			0
$257$	−151.413	−	151.413i	−0.589155	−	0.589155i	0.348247	−	0.937403i	$-0.386777\pi$
$257$	−151.413	−	151.413i	−0.589155	−	0.589155i	−0.937403	+	0.348247i	$0.886777\pi$
$258$		0			0
$259$	−411.021	−	133.549i	−1.58695	−	0.515632i
$260$		0			0
$261$	−109.211	−	336.117i	−0.418433	−	1.28780i
$262$		0			0
$263$	28.1502	+	55.2479i	0.107035	+	0.210068i	0.938312	−	0.345791i	$-0.112389\pi$
$263$	28.1502	+	55.2479i	0.107035	+	0.210068i	−0.831277	+	0.555859i	$0.812389\pi$
$264$		0			0
$265$	−399.782	−	48.8548i	−1.50861	−	0.184358i
$266$		0			0
$267$	−98.3304	−	620.834i	−0.368279	−	2.32522i
$268$		0			0
$269$	68.7404	−	94.6131i	0.255541	−	0.351721i	−0.661902	−	0.749591i	$-0.730250\pi$
$269$	68.7404	−	94.6131i	0.255541	−	0.351721i	0.917442	+	0.397869i	$0.130250\pi$
$270$		0			0
$271$	−91.2818	+	66.3201i	−0.336833	+	0.244724i	−0.743325	−	0.668931i	$-0.766752\pi$
$271$	−91.2818	+	66.3201i	−0.336833	+	0.244724i	0.406491	+	0.913655i	$0.366752\pi$
$272$		0			0
$273$	−707.430	−	360.454i	−2.59132	−	1.32034i
$274$		0			0
$275$	101.382	+	250.104i	0.368661	+	0.909468i
$276$		0			0
$277$	−70.6927	+	138.742i	−0.255208	+	0.500874i	−0.982691	−	0.185252i	$-0.940690\pi$
$277$	−70.6927	+	138.742i	−0.255208	+	0.500874i	0.727483	+	0.686126i	$0.240690\pi$
$278$		0			0
$279$	221.479	+	304.839i	0.793830	+	1.09261i
$280$		0			0
$281$	46.3618	+	33.6838i	0.164989	+	0.119871i	0.667216	−	0.744864i	$-0.267486\pi$
$281$	46.3618	+	33.6838i	0.164989	+	0.119871i	−0.502227	+	0.864736i	$0.667486\pi$
$282$		0			0
$283$	−497.619	+	78.8151i	−1.75837	+	0.278499i	−0.950469	−	0.310818i	$-0.899397\pi$
$283$	−497.619	+	78.8151i	−1.75837	+	0.278499i	−0.807902	+	0.589317i	$0.799397\pi$
$284$		0			0
$285$	−126.968	+	136.313i	−0.445502	+	0.478291i
$286$		0			0
$287$	−87.8401	+	44.7567i	−0.306063	+	0.155947i
$288$		0			0
$289$	265.021	−	86.1105i	0.917027	−	0.297960i
$290$		0			0
$291$	−230.698	+	710.015i	−0.792776	+	2.43991i
$292$		0			0
$293$	30.9139	−	30.9139i	0.105508	−	0.105508i	−0.652382	−	0.757890i	$-0.726230\pi$
$293$	30.9139	−	30.9139i	0.105508	−	0.105508i	0.757890	+	0.652382i	$0.226230\pi$
$294$		0			0
$295$	131.630	−	460.043i	0.446204	−	1.55947i
$296$		0			0
$297$	920.365	+	145.771i	3.09887	+	0.490813i
$298$		0			0
$299$		−	276.082i		−	0.923352i
$300$		0			0
$301$	47.8508			0.158973
$302$		0			0
$303$	−82.8177	+	522.890i	−0.273326	+	1.72571i
$304$		0			0
$305$	−88.4439	+	32.2483i	−0.289980	+	0.105732i
$306$		0			0
$307$	−248.964	−	248.964i	−0.810957	−	0.810957i	0.173821	−	0.984777i	$-0.444389\pi$
$307$	−248.964	−	248.964i	−0.810957	−	0.810957i	−0.984777	+	0.173821i	$0.944389\pi$
$308$		0			0
$309$	−825.122	−	268.098i	−2.67030	−	0.867632i
$310$		0			0
$311$	129.319	+	398.003i	0.415817	+	1.27975i	0.911519	+	0.411259i	$0.134911\pi$
$311$	129.319	+	398.003i	0.415817	+	1.27975i	−0.495702	+	0.868493i	$0.665089\pi$
$312$		0			0
$313$	−23.7574	−	46.6266i	−0.0759023	−	0.148967i	0.849937	−	0.526885i	$-0.176640\pi$
$313$	−23.7574	−	46.6266i	−0.0759023	−	0.148967i	−0.925839	+	0.377918i	$0.876640\pi$
$314$		0			0
$315$	−1218.34	+	676.252i	−3.86776	+	2.14683i
$316$		0			0
$317$	−1.61990	−	10.2277i	−0.00511010	−	0.0322639i	0.985002	−	0.172546i	$-0.0551992\pi$
$317$	−1.61990	−	10.2277i	−0.00511010	−	0.0322639i	−0.990112	+	0.140282i	$0.955199\pi$
$318$		0			0
$319$	93.3494	−	128.484i	0.292631	−	0.402772i
$320$		0			0
$321$	−481.824	+	350.066i	−1.50101	+	1.09055i
$322$		0			0
$323$	−18.5765	−	9.46518i	−0.0575123	−	0.0293040i
$324$		0			0
$325$	153.637	+	255.033i	0.472729	+	0.784717i
$326$		0			0
$327$	13.1309	−	25.7709i	0.0401558	−	0.0788102i
$328$		0			0
$329$	337.014	+	463.860i	1.02436	+	1.40991i
$330$		0			0
$331$	264.164	+	191.927i	0.798079	+	0.579839i	0.910350	−	0.413839i	$-0.135812\pi$
$331$	264.164	+	191.927i	0.798079	+	0.579839i	−0.112271	+	0.993678i	$0.535812\pi$
$332$		0			0
$333$	883.836	−	139.986i	2.65416	−	0.420378i
$334$		0			0
$335$	−148.016	+	28.8593i	−0.441838	+	0.0861471i
$336$		0			0
$337$	−549.351	+	279.909i	−1.63012	+	0.830589i	−0.631655	+	0.775249i	$0.717624\pi$
$337$	−549.351	+	279.909i	−1.63012	+	0.830589i	−0.998468	+	0.0553396i	$0.982376\pi$
$338$		0			0
$339$	−279.157	+	90.7036i	−0.823472	+	0.267562i
$340$		0			0
$341$	−52.3244	+	161.038i	−0.153444	+	0.472252i
$342$		0			0
$343$	−300.194	+	300.194i	−0.875201	+	0.875201i
$344$		0			0
$345$	−552.410	−	372.145i	−1.60119	−	1.07868i
$346$		0			0
$347$	642.564	+	101.772i	1.85177	+	0.293292i	0.980353	−	0.197251i	$-0.0632012\pi$
$347$	642.564	+	101.772i	1.85177	+	0.293292i	0.871417	+	0.490542i	$0.163201\pi$
$348$		0			0
$349$			199.472i			0.571553i	0.958296	+	0.285777i	$0.0922515\pi$
$349$			199.472i			0.571553i	−0.958296	+	0.285777i	$0.907748\pi$
$350$		0			0
$351$	1028.05			2.92892
$352$		0			0
$353$	−43.6436	+	275.555i	−0.123636	+	0.780609i	0.845481	+	0.534006i	$0.179314\pi$
$353$	−43.6436	+	275.555i	−0.123636	+	0.780609i	−0.969117	+	0.246602i	$0.920686\pi$
$354$		0			0
$355$	−75.0749	−	95.9782i	−0.211479	−	0.270361i
$356$		0			0
$357$	−151.591	−	151.591i	−0.424624	−	0.424624i
$358$		0			0
$359$	293.603	+	95.3974i	0.817836	+	0.265731i	0.687913	−	0.725793i	$-0.258527\pi$
$359$	293.603	+	95.3974i	0.817836	+	0.265731i	0.129923	+	0.991524i	$0.458527\pi$
$360$		0			0
$361$	98.5655	+	303.353i	0.273035	+	0.840314i
$362$		0			0
$363$	−11.6663	−	22.8964i	−0.0321386	−	0.0630755i
$364$		0			0
$365$	135.670	−	291.380i	0.371698	−	0.798301i
$366$		0			0
$367$	86.0321	+	543.186i	0.234420	+	1.48007i	0.771333	+	0.636432i	$0.219590\pi$
$367$	86.0321	+	543.186i	0.234420	+	1.48007i	−0.536913	+	0.843638i	$0.680410\pi$
$368$		0			0
$369$	119.984	−	165.144i	0.325161	−	0.447546i
$370$		0			0
$371$	756.035	−	549.291i	2.03783	−	1.48057i
$372$		0			0
$373$	−430.983	−	219.597i	−1.15545	−	0.588731i	−0.232101	−	0.972692i	$-0.574560\pi$
$373$	−430.983	−	219.597i	−1.15545	−	0.588731i	−0.923349	+	0.383961i	$0.874560\pi$
$374$		0			0
$375$	717.387	+	36.3615i	1.91303	+	0.0969639i
$376$		0			0
$377$	79.5452	−	156.116i	0.210995	−	0.414101i
$378$		0			0
$379$	355.236	+	488.940i	0.937297	+	1.29008i	0.956944	+	0.290272i	$0.0937456\pi$
$379$	355.236	+	488.940i	0.937297	+	1.29008i	−0.0196474	+	0.999807i	$0.506254\pi$
$380$		0			0
$381$	−438.101	−	318.299i	−1.14987	−	0.835430i
$382$		0			0
$383$	−112.861	+	17.8755i	−0.294677	+	0.0466723i	−0.302023	−	0.953301i	$-0.597662\pi$
$383$	−112.861	+	17.8755i	−0.294677	+	0.0466723i	0.00734545	+	0.999973i	$0.497662\pi$
$384$		0			0
$385$	−567.661	−	264.309i	−1.47444	−	0.686518i
$386$		0			0
$387$	−88.2804	+	44.9811i	−0.228115	+	0.116230i
$388$		0			0
$389$	391.781	−	127.297i	1.00715	−	0.327243i	0.241431	−	0.970418i	$-0.422383\pi$
$389$	391.781	−	127.297i	1.00715	−	0.327243i	0.765719	+	0.643175i	$0.222383\pi$
$390$		0			0
$391$	23.0359	−	70.8973i	0.0589155	−	0.181323i
$392$		0			0
$393$	133.934	−	133.934i	0.340798	−	0.340798i
$394$		0			0
$395$	13.2922	−	10.3973i	0.0336512	−	0.0263222i
$396$		0			0
$397$	616.042	+	97.5715i	1.55174	+	0.245772i	0.872674	−	0.488303i	$-0.162384\pi$
$397$	616.042	+	97.5715i	1.55174	+	0.245772i	0.679069	+	0.734075i	$0.262384\pi$
$398$		0			0
$399$		−	432.235i		−	1.08330i
$400$		0			0
$401$	−416.207			−1.03792			−0.518961	−	0.854798i	$-0.673681\pi$
$401$	−416.207			−1.03792			−0.518961	+	0.854798i	$0.673681\pi$
$402$		0			0
$403$	−29.2233	+	184.508i	−0.0725143	+	0.457837i
$404$		0			0
$405$	781.796	−	1160.49i	1.93036	−	2.86541i
$406$		0			0
$407$	284.345	+	284.345i	0.698636	+	0.698636i
$408$		0			0
$409$	−198.025	−	64.3422i	−0.484168	−	0.157316i	0.0567544	−	0.998388i	$-0.481925\pi$
$409$	−198.025	−	64.3422i	−0.484168	−	0.157316i	−0.540923	+	0.841072i	$0.681925\pi$
$410$		0			0
$411$	−433.655	−	1334.65i	−1.05512	−	3.24733i
$412$		0			0
$413$	504.051	+	989.256i	1.22046	+	2.39529i
$414$		0			0
$415$	37.5771	+	192.729i	0.0905473	+	0.464406i
$416$		0			0
$417$	237.726	+	1500.95i	0.570087	+	3.59939i
$418$		0			0
$419$	−279.939	+	385.303i	−0.668112	+	0.919577i	−0.999716	−	0.0238417i	$-0.992410\pi$
$419$	−279.939	+	385.303i	−0.668112	+	0.919577i	0.331604	+	0.943419i	$0.392410\pi$
$420$		0			0
$421$	−15.9320	+	11.5753i	−0.0378432	+	0.0274947i	−0.606546	−	0.795048i	$-0.707445\pi$
$421$	−15.9320	+	11.5753i	−0.0378432	+	0.0274947i	0.568703	+	0.822543i	$0.307445\pi$
$422$		0			0
$423$	−1057.80	−	538.978i	−2.50072	−	1.27418i
$424$		0			0
$425$	18.1740	+	78.3112i	0.0427624	+	0.184262i
$426$		0			0
$427$	99.1657	−	194.624i	0.232238	−	0.455793i
$428$		0			0
$429$	434.235	+	597.673i	1.01220	+	1.39318i
$430$		0			0
$431$	421.159	+	305.990i	0.977166	+	0.709953i	0.957074	−	0.289845i	$-0.0936039\pi$
$431$	421.159	+	305.990i	0.977166	+	0.709953i	0.0200927	+	0.999798i	$0.493604\pi$
$432$		0			0
$433$	−555.667	+	88.0090i	−1.28330	+	0.203254i	−0.760575	−	0.649250i	$-0.775083\pi$
$433$	−555.667	+	88.0090i	−1.28330	+	0.203254i	−0.522721	+	0.852504i	$0.675083\pi$
$434$		0			0
$435$	−205.148	−	369.598i	−0.471605	−	0.849650i
$436$		0			0
$437$	133.917	−	68.2343i	0.306447	−	0.156143i
$438$		0			0
$439$	47.1785	−	15.3292i	0.107468	−	0.0349185i	−0.254789	−	0.966997i	$-0.582006\pi$
$439$	47.1785	−	15.3292i	0.107468	−	0.0349185i	0.362257	+	0.932078i	$0.382006\pi$
$440$		0			0
$441$	635.375	−	1955.48i	1.44076	−	4.43420i
$442$		0			0
$443$	−73.9373	+	73.9373i	−0.166901	+	0.166901i	−0.785616	−	0.618715i	$-0.787654\pi$
$443$	−73.9373	+	73.9373i	−0.166901	+	0.166901i	0.618715	+	0.785616i	$0.287654\pi$
$444$		0			0
$445$	−187.352	−	513.831i	−0.421016	−	1.15468i
$446$		0			0
$447$	−1344.46	−	212.941i	−3.00774	−	0.476379i
$448$		0			0
$449$		−	308.992i		−	0.688178i	−0.938937	−	0.344089i	$-0.888188\pi$
$449$		−	308.992i		−	0.688178i	0.938937	−	0.344089i	$-0.111812\pi$
$450$		0			0
$451$	91.7308			0.203394
$452$		0			0
$453$	213.439	−	1347.60i	0.471167	−	2.97483i
$454$		0			0
$455$	−664.179	−	190.039i	−1.45973	−	0.417668i
$456$		0			0
$457$	−458.273	−	458.273i	−1.00279	−	1.00279i	−0.999996	−	0.00279045i	$-0.999112\pi$
$457$	−458.273	−	458.273i	−1.00279	−	1.00279i	−0.00279045	−	0.999996i	$-0.500888\pi$
$458$		0			0
$459$	264.001	+	85.7792i	0.575166	+	0.186883i
$460$		0			0
$461$	40.6987	+	125.258i	0.0882835	+	0.271709i	0.985445	−	0.169994i	$-0.0543747\pi$
$461$	40.6987	+	125.258i	0.0882835	+	0.271709i	−0.897162	+	0.441702i	$0.854375\pi$
$462$		0			0
$463$	107.595	+	211.167i	0.232387	+	0.456084i	0.977523	−	0.210827i	$-0.0676158\pi$
$463$	107.595	+	211.167i	0.232387	+	0.456084i	−0.745137	+	0.666912i	$0.767616\pi$
$464$		0			0
$465$	329.789	+	307.181i	0.709224	+	0.660603i
$466$		0			0
$467$	−6.50487	−	41.0702i	−0.0139291	−	0.0879447i	0.979744	−	0.200252i	$-0.0641760\pi$
$467$	−6.50487	−	41.0702i	−0.0139291	−	0.0879447i	−0.993674	+	0.112307i	$0.964176\pi$
$468$		0			0
$469$	205.670	−	283.080i	0.438528	−	0.603582i
$470$		0			0
$471$	74.4050	−	54.0584i	0.157972	−	0.114774i
$472$		0			0
$473$	−39.6710	−	20.2134i	−0.0838710	−	0.0427344i
$474$		0			0
$475$	−85.7355	+	137.556i	−0.180496	+	0.289591i
$476$		0			0
$477$	−878.467	+	1724.09i	−1.84165	+	3.61444i
$478$		0			0
$479$	−15.5947	−	21.4643i	−0.0325568	−	0.0448106i	0.792428	−	0.609965i	$-0.208817\pi$
$479$	−15.5947	−	21.4643i	−0.0325568	−	0.0448106i	−0.824985	+	0.565154i	$0.808817\pi$
$480$		0			0
$481$	358.916	+	260.768i	0.746187	+	0.542136i
$482$		0			0
$483$	1526.45	−	241.765i	3.16035	−	0.500550i
$484$		0			0
$485$	−78.7944	+	644.780i	−0.162463	+	1.32944i
$486$		0			0
$487$	515.276	−	262.546i	1.05806	−	0.539110i	0.163726	−	0.986506i	$-0.447649\pi$
$487$	515.276	−	262.546i	1.05806	−	0.539110i	0.894336	+	0.447396i	$0.147649\pi$
$488$		0			0
$489$	533.879	−	173.468i	1.09178	−	0.354740i
$490$		0			0
$491$	−9.71110	+	29.8877i	−0.0197782	+	0.0608711i	−0.960458	−	0.278423i	$-0.910188\pi$
$491$	−9.71110	+	29.8877i	−0.0197782	+	0.0608711i	0.940680	+	0.339294i	$0.110188\pi$
$492$		0			0
$493$	33.4532	−	33.4532i	0.0678563	−	0.0678563i
$494$		0			0
$495$	1295.74	−	45.9910i	2.61766	−	0.0929110i
$496$		0			0
$497$	279.252	+	44.2292i	0.561876	+	0.0889924i
$498$		0			0
$499$			500.655i			1.00332i	0.865066	+	0.501658i	$0.167277\pi$
$499$			500.655i			1.00332i	−0.865066	+	0.501658i	$0.832723\pi$
$500$		0			0
$501$	1424.70			2.84371
$502$		0			0
$503$	92.5078	−	584.072i	0.183912	−	1.16118i	−0.707072	−	0.707142i	$-0.749984\pi$
$503$	92.5078	−	584.072i	0.183912	−	1.16118i	0.890984	−	0.454034i	$-0.150016\pi$
$504$		0			0
$505$	16.3396	+	460.348i	0.0323556	+	0.911581i
$506$		0			0
$507$	−110.386	−	110.386i	−0.217724	−	0.217724i
$508$		0			0
$509$	280.871	+	91.2606i	0.551810	+	0.179294i	0.571633	−	0.820510i	$-0.306310\pi$
$509$	280.871	+	91.2606i	0.551810	+	0.179294i	−0.0198228	+	0.999804i	$0.506310\pi$
$510$		0			0
$511$	230.458	+	709.278i	0.450995	+	1.38802i
$512$		0			0
$513$	254.085	+	498.670i	0.495292	+	0.972066i
$514$		0			0
$515$	−749.311	−	91.5685i	−1.45497	−	0.177803i
$516$		0			0
$517$	−83.4575	−	526.930i	−0.161426	−	1.01921i
$518$		0			0
$519$	495.053	−	681.382i	0.953859	−	1.31287i
$520$		0			0
$521$	−497.333	+	361.333i	−0.954574	+	0.693538i	−0.951884	−	0.306458i	$-0.900856\pi$
$521$	−497.333	+	361.333i	−0.954574	+	0.693538i	−0.00268941	+	0.999996i	$0.500856\pi$
$522$		0			0
$523$	727.367	+	370.612i	1.39076	+	0.708627i	0.979227	−	0.202769i	$-0.0649940\pi$
$523$	727.367	+	370.612i	1.39076	+	0.708627i	0.411532	+	0.911395i	$0.364994\pi$
$524$		0			0
$525$	−1275.53	+	1072.78i	−2.42957	+	2.04340i
$526$		0			0
$527$	−22.8996	+	44.9430i	−0.0434528	+	0.0852808i
$528$		0			0
$529$	4.93737	+	6.79571i	0.00933341	+	0.0128463i
$530$		0			0
$531$	−1859.86	−	1351.27i	−3.50256	−	2.54476i
$532$		0			0
$533$	99.9561	−	15.8315i	0.187535	−	0.0297026i
$534$		0			0
$535$	−353.197	+	379.192i	−0.660181	+	0.708770i
$536$		0			0
$537$	523.369	−	266.670i	0.974616	−	0.496592i
$538$		0			0
$539$	878.745	−	285.522i	1.63033	−	0.529725i
$540$		0			0
$541$	−21.2774	+	65.4852i	−0.0393298	+	0.121045i	−0.968794	−	0.247868i	$-0.920270\pi$
$541$	−21.2774	+	65.4852i	−0.0393298	+	0.121045i	0.929464	+	0.368913i	$0.120270\pi$
$542$		0			0
$543$	852.488	−	852.488i	1.56996	−	1.56996i
$544$		0			0
$545$	6.92291	−	24.1953i	0.0127026	−	0.0443951i
$546$		0			0
$547$	−825.615	−	130.765i	−1.50935	−	0.239058i	−0.653757	−	0.756704i	$-0.726808\pi$
$547$	−825.615	−	130.765i	−1.50935	−	0.239058i	−0.855595	+	0.517646i	$0.826808\pi$
$548$		0			0
$549$			452.282i			0.823829i
$550$		0			0
$551$	95.3860			0.173114
$552$		0			0
$553$	−6.12540	+	38.6743i	−0.0110767	+	0.0699354i
$554$		0			0
$555$	1005.57	−	366.649i	1.81183	−	0.660628i
$556$		0			0
$557$	−375.063	−	375.063i	−0.673363	−	0.673363i	0.285127	−	0.958490i	$-0.407964\pi$
$557$	−375.063	−	375.063i	−0.673363	−	0.673363i	−0.958490	+	0.285127i	$0.907964\pi$
$558$		0			0
$559$	−46.7168	−	15.1792i	−0.0835721	−	0.0271542i
$560$		0			0
$561$	61.6415	+	189.713i	0.109878	+	0.338170i
$562$		0			0
$563$	−431.040	−	845.964i	−0.765613	−	1.50260i	−0.861806	−	0.507238i	$-0.830666\pi$
$563$	−431.040	−	845.964i	−0.765613	−	1.50260i	0.0961924	−	0.995363i	$-0.469334\pi$
$564$		0			0
$565$	−223.302	+	123.946i	−0.395225	+	0.219373i
$566$		0			0
$567$	507.896	+	3206.73i	0.895760	+	5.65561i
$568$		0			0
$569$	−446.211	+	614.157i	−0.784202	+	1.07936i	0.210604	+	0.977571i	$0.432457\pi$
$569$	−446.211	+	614.157i	−0.784202	+	1.07936i	−0.994806	+	0.101790i	$0.967543\pi$
$570$		0			0
$571$	−47.5659	+	34.5586i	−0.0833028	+	0.0605230i	−0.628657	−	0.777683i	$-0.716395\pi$
$571$	−47.5659	+	34.5586i	−0.0833028	+	0.0605230i	0.545354	+	0.838206i	$0.316395\pi$
$572$		0			0
$573$	−355.449	−	181.110i	−0.620330	−	0.316074i
$574$		0			0
$575$	−533.735	−	225.836i	−0.928235	−	0.392759i
$576$		0			0
$577$	−267.568	+	525.131i	−0.463722	+	0.910106i	0.534180	+	0.845371i	$0.320620\pi$
$577$	−267.568	+	525.131i	−0.463722	+	0.910106i	−0.997902	+	0.0647353i	$0.979380\pi$
$578$		0			0
$579$	211.614	+	291.261i	0.365481	+	0.503042i
$580$		0			0
$581$	−368.594	−	267.799i	−0.634412	−	0.460928i
$582$		0			0
$583$	−858.830	+	136.025i	−1.47312	+	0.233320i
$584$		0			0
$585$	1403.99	−	273.743i	2.39999	−	0.467936i
$586$		0			0
$587$	−308.454	+	157.165i	−0.525475	+	0.267743i	−0.696542	−	0.717516i	$-0.745279\pi$
$587$	−308.454	+	157.165i	−0.525475	+	0.267743i	0.171066	+	0.985260i	$0.445279\pi$
$588$		0			0
$589$	−96.7209	+	31.4265i	−0.164212	+	0.0533557i
$590$		0			0
$591$	−407.362	+	1253.73i	−0.689276	+	2.12137i
$592$		0			0
$593$	108.207	−	108.207i	0.182475	−	0.182475i	−0.609959	−	0.792433i	$-0.708814\pi$
$593$	108.207	−	108.207i	0.182475	−	0.182475i	0.792433	+	0.609959i	$0.208814\pi$
$594$		0			0
$595$	−154.703	−	104.220i	−0.260005	−	0.175159i
$596$		0			0
$597$	−1489.56	−	235.922i	−2.49507	−	0.395180i
$598$		0			0
$599$			847.939i			1.41559i	0.706418	+	0.707795i	$0.250310\pi$
$599$			847.939i			1.41559i	−0.706418	+	0.707795i	$0.749690\pi$
$600$		0			0
$601$	200.362			0.333381			0.166690	−	0.986009i	$-0.446692\pi$
$601$	200.362			0.333381			0.166690	+	0.986009i	$0.446692\pi$
$602$		0			0
$603$	−113.339	+	715.593i	−0.187958	+	1.18672i
$604$		0			0
$605$	−13.7758	−	17.6114i	−0.0227699	−	0.0291097i
$606$		0			0
$607$	187.186	+	187.186i	0.308380	+	0.308380i	0.844281	−	0.535901i	$-0.180028\pi$
$607$	187.186	+	187.186i	0.308380	+	0.308380i	−0.535901	+	0.844281i	$0.680028\pi$
$608$		0			0
$609$	932.817	+	303.091i	1.53172	+	0.497686i
$610$		0			0
$611$	−181.882	−	559.775i	−0.297679	−	0.916162i
$612$		0			0
$613$	−53.6620	−	105.318i	−0.0875399	−	0.171807i	0.843086	−	0.537779i	$-0.180737\pi$
$613$	−53.6620	−	105.318i	−0.0875399	−	0.171807i	−0.930626	+	0.365972i	$0.880737\pi$
$614$		0			0
$615$	103.059	−	221.341i	0.167575	−	0.359904i
$616$		0			0
$617$	−85.8328	−	541.927i	−0.139113	−	0.878326i	−0.954240	−	0.299043i	$-0.903333\pi$
$617$	−85.8328	−	541.927i	−0.139113	−	0.878326i	0.815127	−	0.579283i	$-0.196667\pi$
$618$		0			0
$619$	670.533	−	922.909i	1.08325	−	1.49097i	0.227362	−	0.973810i	$-0.426990\pi$
$619$	670.533	−	922.909i	1.08325	−	1.49097i	0.855890	−	0.517158i	$-0.173010\pi$
$620$		0			0
$621$	−1618.94	+	1176.23i	−2.60699	+	1.89409i
$622$		0			0
$623$	1130.70	+	576.121i	1.81493	+	0.924753i
$624$		0			0
$625$	618.717	−	88.4001i	0.989947	−	0.141440i
$626$		0			0
$627$	−182.587	+	358.348i	−0.291208	+	0.571527i
$628$		0			0
$629$	70.4107	+	96.9120i	0.111941	+	0.154073i
$630$		0			0
$631$	−846.485	−	615.007i	−1.34150	−	0.974655i	−0.999387	−	0.0349948i	$-0.988859\pi$
$631$	−846.485	−	615.007i	−1.34150	−	0.974655i	−0.342110	−	0.939660i	$-0.611141\pi$
$632$		0			0
$633$	1184.08	−	187.540i	1.87058	−	0.296271i
$634$		0			0
$635$	−427.147	−	198.884i	−0.672672	−	0.313204i
$636$		0			0
$637$	908.264	−	462.783i	1.42585	−	0.726505i
$638$		0			0
$639$	−556.772	+	180.906i	−0.871318	+	0.283109i
$640$		0			0
$641$	115.068	−	354.142i	0.179513	−	0.552483i	−0.820298	−	0.571936i	$-0.806193\pi$
$641$	115.068	−	354.142i	0.179513	−	0.552483i	0.999811	+	0.0194532i	$0.00619253\pi$
$642$		0			0
$643$	−798.965	+	798.965i	−1.24256	+	1.24256i	−0.283623	+	0.958936i	$0.591537\pi$
$643$	−798.965	+	798.965i	−1.24256	+	1.24256i	−0.958936	+	0.283623i	$0.908463\pi$
$644$		0			0
$645$	−93.3438	+	73.0142i	−0.144719	+	0.113200i
$646$		0			0
$647$	−12.9722	−	2.05459i	−0.0200497	−	0.00317556i	0.146402	−	0.989225i	$-0.453231\pi$
$647$	−12.9722	−	2.05459i	−0.0200497	−	0.00317556i	−0.166451	+	0.986050i	$0.553231\pi$
$648$		0			0
$649$		−	1033.07i		−	1.59179i
$650$		0			0
$651$	−1045.73			−1.60634
$652$		0			0
$653$	−200.420	+	1265.41i	−0.306923	+	1.93783i	0.0381867	+	0.999271i	$0.487842\pi$
$653$	−200.420	+	1265.41i	−0.306923	+	1.93783i	−0.345109	+	0.938562i	$0.612158\pi$
$654$		0			0
$655$	92.0802	−	136.683i	0.140580	−	0.208677i
$656$		0			0
$657$	−1091.92	−	1091.92i	−1.66197	−	1.66197i
$658$		0			0
$659$	584.477	+	189.908i	0.886914	+	0.288176i	0.716825	−	0.697253i	$-0.245594\pi$
$659$	584.477	+	189.908i	0.886914	+	0.288176i	0.170089	+	0.985429i	$0.445594\pi$
$660$		0			0
$661$	−138.504	−	426.271i	−0.209537	−	0.644889i	−0.999496	−	0.0317296i	$-0.989898\pi$
$661$	−138.504	−	426.271i	−0.209537	−	0.644889i	0.789959	−	0.613159i	$-0.210102\pi$
$662$		0			0
$663$	99.9107	+	196.086i	0.150695	+	0.295755i
$664$		0			0
$665$	−71.9723	−	369.137i	−0.108229	−	0.555094i
$666$		0			0
$667$	53.3530	+	336.857i	0.0799894	+	0.505033i
$668$		0			0
$669$	711.765	−	979.661i	1.06392	−	1.46437i
$670$		0			0
$671$	−164.428	+	119.464i	−0.245049	+	0.178039i
$672$		0			0
$673$	1027.11	+	523.337i	1.52616	+	0.777617i	0.997463	−	0.0711927i	$-0.0226805\pi$
$673$	1027.11	+	523.337i	1.52616	+	0.777617i	0.528698	+	0.848810i	$0.322681\pi$
$674$		0			0
$675$	840.949	−	1987.47i	1.24585	−	2.94441i
$676$		0			0
$677$	564.133	−	1107.17i	0.833284	−	1.63541i	0.0627368	−	0.998030i	$-0.480017\pi$
$677$	564.133	−	1107.17i	0.833284	−	1.63541i	0.770548	−	0.637382i	$-0.219983\pi$
$678$		0			0
$679$	−885.913	−	1219.36i	−1.30473	−	1.79581i
$680$		0			0
$681$	−392.500	−	285.168i	−0.576358	−	0.418748i
$682$		0			0
$683$	−70.0579	+	11.0961i	−0.102574	+	0.0162461i	−0.207510	−	0.978233i	$-0.566536\pi$
$683$	−70.0579	+	11.0961i	−0.102574	+	0.0162461i	0.104937	+	0.994479i	$0.466536\pi$
$684$		0			0
$685$	−592.584	−	1067.61i	−0.865087	−	1.55855i
$686$		0			0
$687$	834.075	−	424.983i	1.21408	−	0.618606i
$688$		0			0
$689$	−912.364	+	296.445i	−1.32419	+	0.430254i
$690$		0			0
$691$	−297.511	+	915.643i	−0.430551	+	1.32510i	0.467027	+	0.884243i	$0.345325\pi$
$691$	−297.511	+	915.643i	−0.430551	+	1.32510i	−0.897578	+	0.440856i	$0.854675\pi$
$692$		0			0
$693$	−2127.25	+	2127.25i	−3.06963	+	3.06963i
$694$		0			0
$695$	452.948	+	1242.25i	0.651724	+	1.78741i
$696$		0			0
$697$	26.9895	+	4.27471i	0.0387223	+	0.00613302i
$698$		0			0
$699$			607.426i			0.868993i
$700$		0			0
$701$	639.816			0.912719			0.456359	−	0.889796i	$-0.349153\pi$
$701$	639.816			0.912719			0.456359	+	0.889796i	$0.349153\pi$
$702$		0			0
$703$	−37.7820	+	238.546i	−0.0537440	+	0.339326i
$704$		0			0
$705$	−1365.21	−	390.623i	−1.93647	−	0.554076i
$706$		0			0
$707$	−755.766	−	755.766i	−1.06898	−	1.06898i
$708$		0			0
$709$	867.869	+	281.988i	1.22407	+	0.397726i	0.848564	−	0.529092i	$-0.177468\pi$
$709$	867.869	+	281.988i	1.22407	+	0.397726i	0.375510	+	0.926818i	$0.377468\pi$
$710$		0			0
$711$	−25.0541	−	77.1086i	−0.0352378	−	0.108451i
$712$		0			0
$713$	−165.083	−	323.993i	−0.231533	−	0.454409i
$714$		0			0
$715$	470.364	+	438.119i	0.657852	+	0.612754i
$716$		0			0
$717$	−81.4041	−	513.965i	−0.113534	−	0.716828i
$718$		0			0
$719$	−124.914	+	171.930i	−0.173733	+	0.239123i	−0.887000	−	0.461769i	$-0.847215\pi$
$719$	−124.914	+	171.930i	−0.173733	+	0.239123i	0.713267	+	0.700893i	$0.247215\pi$
$720$		0			0
$721$	1417.04	−	1029.54i	1.96538	−	1.42793i
$722$		0			0
$723$	713.565	+	363.579i	0.986950	+	0.502876i
$724$		0			0
$725$	−236.743	−	281.484i	−0.326542	−	0.388254i
$726$		0			0
$727$	191.041	−	374.939i	0.262780	−	0.515734i	−0.721486	−	0.692429i	$-0.756541\pi$
$727$	191.041	−	374.939i	0.262780	−	0.515734i	0.984266	+	0.176695i	$0.0565406\pi$
$728$		0			0
$729$	−1327.31	−	1826.88i	−1.82072	−	2.50601i
$730$		0			0
$731$	−10.7302	−	7.79597i	−0.0146788	−	0.0106648i
$732$		0			0
$733$	−1307.24	+	207.047i	−1.78342	+	0.282465i	−0.958976	−	0.283486i	$-0.908509\pi$
$733$	−1307.24	+	207.047i	−1.78342	+	0.282465i	−0.824439	+	0.565951i	$0.808509\pi$
$734$		0			0
$735$	298.316	−	2441.14i	0.405873	−	3.32128i
$736$		0			0
$737$	−290.092	+	147.809i	−0.393612	+	0.200555i
$738$		0			0
$739$	−223.114	+	72.4940i	−0.301913	+	0.0980974i	−0.456056	−	0.889951i	$-0.650738\pi$
$739$	−223.114	+	72.4940i	−0.301913	+	0.0980974i	0.154143	+	0.988049i	$0.450738\pi$
$740$		0			0
$741$	−137.114	+	421.992i	−0.185039	+	0.569490i
$742$		0			0
$743$	−441.715	+	441.715i	−0.594503	+	0.594503i	−0.938844	−	0.344342i	$-0.888102\pi$
$743$	−441.715	+	441.715i	−0.594503	+	0.594503i	0.344342	+	0.938844i	$0.388102\pi$
$744$		0			0
$745$	−1183.65	+	42.0124i	−1.58879	+	0.0563924i
$746$		0			0
$747$	931.761	+	147.576i	1.24734	+	0.197559i
$748$		0			0
$749$		−	1202.38i		−	1.60532i
$750$		0			0
$751$	490.378			0.652966			0.326483	−	0.945203i	$-0.394136\pi$
$751$	490.378			0.652966			0.326483	+	0.945203i	$0.394136\pi$
$752$		0			0
$753$	44.1669	−	278.859i	0.0586545	−	0.370330i
$754$		0			0
$755$	−42.1105	−	1186.41i	−0.0557754	−	1.57141i
$756$		0			0
$757$	708.614	+	708.614i	0.936082	+	0.936082i	0.998076	−	0.0619946i	$-0.0197462\pi$
$757$	708.614	+	708.614i	0.936082	+	0.936082i	−0.0619946	+	0.998076i	$0.519746\pi$
$758$		0			0
$759$	−1367.64	−	444.373i	−1.80190	−	0.585471i
$760$		0			0
$761$	467.060	+	1437.46i	0.613745	+	1.88891i	0.418717	+	0.908117i	$0.362480\pi$
$761$	467.060	+	1437.46i	0.613745	+	1.88891i	0.195029	+	0.980798i	$0.437520\pi$
$762$		0			0
$763$	26.5099	+	52.0285i	0.0347442	+	0.0681894i
$764$		0			0
$765$	383.383	+	46.8508i	0.501154	+	0.0612428i
$766$		0			0
$767$	−178.294	−	1125.71i	−0.232457	−	1.46768i
$768$		0			0
$769$	51.7980	−	71.2939i	0.0673577	−	0.0927099i	−0.774009	−	0.633175i	$-0.781752\pi$
$769$	51.7980	−	71.2939i	0.0673577	−	0.0927099i	0.841367	+	0.540465i	$0.181752\pi$
$770$		0			0
$771$	−995.489	+	723.265i	−1.29117	+	0.938087i
$772$		0			0
$773$	752.978	+	383.661i	0.974098	+	0.496328i	0.867210	−	0.497943i	$-0.165911\pi$
$773$	752.978	+	383.661i	0.974098	+	0.496328i	0.106889	+	0.994271i	$0.465911\pi$
$774$		0			0
$775$	332.795	+	207.424i	0.429413	+	0.267644i
$776$		0			0
$777$	−1127.47	+	2212.78i	−1.45105	+	2.84786i
$778$		0			0
$779$	32.3836	+	44.5723i	0.0415708	+	0.0572173i
$780$		0			0
$781$	−212.832	−	154.632i	−0.272513	−	0.197992i
$782$		0			0
$783$	−1254.36	+	198.671i	−1.60199	+	0.253730i
$784$		0			0
$785$	54.5419	−	58.5562i	0.0694801	−	0.0745938i
$786$		0			0
$787$	1045.60	−	532.761i	1.32859	−	0.676952i	0.361739	−	0.932279i	$-0.382183\pi$
$787$	1045.60	−	532.761i	1.32859	−	0.676952i	0.966855	+	0.255327i	$0.0821832\pi$
$788$		0			0
$789$	338.877	−	110.108i	0.429501	−	0.139553i
$790$		0			0
$791$	183.120	−	563.586i	0.231505	−	0.712498i
$792$		0			0
$793$	−158.554	+	158.554i	−0.199942	+	0.199942i
$794$		0			0
$795$	−636.668	+	2225.13i	−0.800840	+	2.79891i
$796$		0			0
$797$	1013.42	+	160.509i	1.27154	+	0.201392i	0.755485	−	0.655165i	$-0.227401\pi$
$797$	1013.42	+	160.509i	1.27154	+	0.201392i	0.516052	+	0.856557i	$0.327401\pi$
$798$		0			0
$799$		−	158.925i		−	0.198905i
$800$		0			0
$801$	−2627.61			−3.28042
$802$		0			0
$803$	108.554	−	685.383i	0.135186	−	0.853528i
$804$		0			0
$805$	1263.36	−	460.644i	1.56939	−	0.572228i
$806$		0			0
$807$	−475.203	−	475.203i	−0.588851	−	0.588851i
$808$		0			0
$809$	−577.085	−	187.506i	−0.713331	−	0.231775i	−0.0702014	−	0.997533i	$-0.522364\pi$
$809$	−577.085	−	187.506i	−0.713331	−	0.231775i	−0.643129	+	0.765758i	$0.722364\pi$
$810$		0			0
$811$	−78.3357	−	241.093i	−0.0965915	−	0.297278i	0.891074	−	0.453859i	$-0.149953\pi$
$811$	−78.3357	−	241.093i	−0.0965915	−	0.297278i	−0.987665	+	0.156581i	$0.949953\pi$
$812$		0			0
$813$	294.357	+	577.708i	0.362063	+	0.710588i
$814$		0			0
$815$	427.058	−	237.042i	0.523997	−	0.290849i
$816$		0			0
$817$	−4.18328	−	26.4122i	−0.00512029	−	0.0323282i
$818$		0			0
$819$	−1950.87	+	2685.14i	−2.38201	+	3.27855i
$820$		0			0
$821$	−121.934	+	88.5899i	−0.148518	+	0.107905i	−0.659563	−	0.751649i	$-0.729259\pi$
$821$	−121.934	+	88.5899i	−0.148518	+	0.107905i	0.511045	+	0.859554i	$0.329259\pi$
$822$		0			0
$823$	−50.9426	−	25.9566i	−0.0618987	−	0.0315390i	0.422767	−	0.906238i	$-0.361059\pi$
$823$	−50.9426	−	25.9566i	−0.0618987	−	0.0315390i	−0.484666	+	0.874699i	$0.661059\pi$
$824$		0			0
$825$	1510.65	−	350.584i	1.83110	−	0.424950i
$826$		0			0
$827$	−49.0040	+	96.1757i	−0.0592551	+	0.116295i	−0.918735	−	0.394875i	$-0.870788\pi$
$827$	−49.0040	+	96.1757i	−0.0592551	+	0.116295i	0.859480	+	0.511170i	$0.170788\pi$
$828$		0			0
$829$	−425.540	−	585.705i	−0.513317	−	0.706520i	0.471157	−	0.882049i	$-0.343836\pi$
$829$	−425.540	−	585.705i	−0.513317	−	0.706520i	−0.984474	+	0.175529i	$0.943836\pi$
$830$		0			0
$831$	723.912	+	525.953i	0.871134	+	0.632916i
$832$		0			0
$833$	271.854	−	43.0575i	0.326355	−	0.0516896i
$834$		0			0
$835$	1216.72	−	237.229i	1.45715	−	0.284107i
$836$		0			0
$837$	1206.46	−	614.721i	1.44141	−	0.734433i
$838$		0			0
$839$	685.108	−	222.605i	0.816577	−	0.265322i	0.129196	−	0.991619i	$-0.458760\pi$
$839$	685.108	−	222.605i	0.816577	−	0.265322i	0.687381	+	0.726297i	$0.258760\pi$
$840$		0			0
$841$	192.997	−	593.984i	0.229485	−	0.706283i
$842$		0			0
$843$	232.857	−	232.857i	0.276224	−	0.276224i
$844$		0			0
$845$	−112.653	−	75.8913i	−0.133317	−	0.0898122i
$846$		0			0
$847$	51.2410	+	8.11578i	0.0604971	+	0.00958179i
$848$		0			0
$849$			2895.20i			3.41012i
$850$		0			0
$851$	−863.563			−1.01476
$852$		0			0
$853$	−143.794	+	907.882i	−0.168575	+	1.06434i	0.747772	+	0.663955i	$0.231123\pi$
$853$	−143.794	+	907.882i	−0.168575	+	1.06434i	−0.916347	+	0.400385i	$0.868877\pi$
$854$		0			0
$855$	479.782	+	613.369i	0.561149	+	0.717391i
$856$		0			0
$857$	−514.604	−	514.604i	−0.600472	−	0.600472i	0.339966	−	0.940438i	$-0.389584\pi$
$857$	−514.604	−	514.604i	−0.600472	−	0.600472i	−0.940438	+	0.339966i	$0.889584\pi$
$858$		0			0
$859$	146.679	+	47.6588i	0.170755	+	0.0554817i	0.393147	−	0.919476i	$-0.371386\pi$
$859$	146.679	+	47.6588i	0.170755	+	0.0554817i	−0.222392	+	0.974957i	$0.571386\pi$
$860$		0			0
$861$	175.063	+	538.789i	0.203325	+	0.625771i
$862$		0			0
$863$	−337.322	−	662.031i	−0.390871	−	0.767128i	0.608785	−	0.793335i	$-0.291657\pi$
$863$	−337.322	−	662.031i	−0.390871	−	0.767128i	−0.999657	+	0.0262073i	$0.991657\pi$
$864$		0			0
$865$	309.326	−	664.345i	0.357603	−	0.768029i
$866$		0			0
$867$	−250.499	−	1581.59i	−0.288927	−	1.82421i
$868$		0			0
$869$	21.4153	−	29.4756i	0.0246436	−	0.0339190i
$870$		0			0
$871$	−290.594	+	211.129i	−0.333633	+	0.242398i
$872$		0			0
$873$	2780.66	+	1416.82i	3.18518	+	1.62293i
$874$		0			0
$875$	−910.692	+	1128.57i	−1.04079	+	1.28979i
$876$		0			0
$877$	−262.696	+	515.569i	−0.299539	+	0.587878i	−0.990895	−	0.134636i	$-0.957014\pi$
$877$	−262.696	+	515.569i	−0.299539	+	0.587878i	0.691356	+	0.722514i	$0.257014\pi$
$878$		0			0
$879$	−147.669	−	203.248i	−0.167996	−	0.231227i
$880$		0			0
$881$	712.382	+	517.576i	0.808606	+	0.587487i	0.913426	−	0.407004i	$-0.133427\pi$
$881$	712.382	+	517.576i	0.808606	+	0.587487i	−0.104820	+	0.994491i	$0.533427\pi$
$882$		0			0
$883$	277.896	−	44.0144i	0.314718	−	0.0498465i	0.00292285	−	0.999996i	$-0.499070\pi$
$883$	277.896	−	44.0144i	0.314718	−	0.0498465i	0.311795	+	0.950149i	$0.399070\pi$
$884$		0			0
$885$	−2492.75	−	1160.65i	−2.81666	−	1.31147i
$886$		0			0
$887$	−1067.41	+	543.872i	−1.20339	+	0.613159i	−0.936534	−	0.350577i	$-0.885985\pi$
$887$	−1067.41	+	543.872i	−1.20339	+	0.613159i	−0.266858	+	0.963736i	$0.585985\pi$
$888$		0			0
$889$	1039.76	−	337.839i	1.16959	−	0.380022i
$890$		0			0
$891$	933.530	−	2873.11i	1.04773	−	3.22459i
$892$		0			0
$893$	226.574	−	226.574i	0.253722	−	0.253722i
$894$		0			0
$895$	402.563	−	314.888i	0.449791	−	0.351830i
$896$		0			0
$897$	−1566.97	−	248.183i	−1.74690	−	0.276681i
$898$		0			0
$899$		−	230.772i		−	0.256699i
$900$		0			0
$901$	−259.028			−0.287489
$902$		0			0
$903$	43.0152	−	271.587i	0.0476359	−	0.300761i
$904$		0			0
$905$	586.091	−	869.990i	0.647615	−	0.961315i
$906$		0			0
$907$	707.177	+	707.177i	0.779687	+	0.779687i	0.979778	−	0.200090i	$-0.0641235\pi$
$907$	707.177	+	707.177i	0.779687	+	0.779687i	−0.200090	+	0.979778i	$0.564123\pi$
$908$		0			0
$909$	2104.76	+	683.879i	2.31547	+	0.752342i
$910$		0			0
$911$	21.9156	+	67.4493i	0.0240567	+	0.0740388i	0.962364	−	0.271763i	$-0.0876068\pi$
$911$	21.9156	+	67.4493i	0.0240567	+	0.0740388i	−0.938307	+	0.345802i	$0.887607\pi$
$912$		0			0
$913$	192.460	+	377.724i	0.210799	+	0.413717i
$914$		0			0
$915$	103.526	+	530.972i	0.113143	+	0.580297i
$916$		0			0
$917$	59.8202	+	377.690i	0.0652347	+	0.411876i
$918$		0			0
$919$	428.164	−	589.318i	0.465903	−	0.641260i	−0.509817	−	0.860283i	$-0.670287\pi$
$919$	428.164	−	589.318i	0.465903	−	0.641260i	0.975720	+	0.219023i	$0.0702869\pi$
$920$		0			0
$921$	−1636.85	+	1189.24i	−1.77726	+	1.29125i
$922$		0			0
$923$	−258.604	−	131.765i	−0.280178	−	0.142758i
$924$		0			0
$925$	797.722	−	480.564i	0.862402	−	0.519528i
$926$		0			0
$927$	−1646.51	+	3231.46i	−1.77617	+	3.48593i
$928$		0			0
$929$	−809.240	−	1113.82i	−0.871088	−	1.19895i	−0.978810	−	0.204768i	$-0.934356\pi$
$929$	−809.240	−	1113.82i	−0.871088	−	1.19895i	0.107723	−	0.994181i	$-0.465644\pi$
$930$		0			0
$931$	448.959	+	326.187i	0.482233	+	0.350363i
$932$		0			0
$933$	2375.20	−	376.195i	2.54577	−	0.403210i
$934$		0			0
$935$	84.2325	+	151.755i	0.0900882	+	0.162304i
$936$		0			0
$937$	−937.621	+	477.742i	−1.00066	+	0.509863i	−0.875987	−	0.482334i	$-0.839789\pi$
$937$	−937.621	+	477.742i	−1.00066	+	0.509863i	−0.124676	+	0.992198i	$0.539789\pi$
$938$		0			0
$939$	−285.996	+	92.9257i	−0.304575	+	0.0989624i
$940$		0			0
$941$	−300.343	+	924.361i	−0.319174	+	0.982318i	0.654828	+	0.755778i	$0.272741\pi$
$941$	−300.343	+	924.361i	−0.319174	+	0.982318i	−0.974002	+	0.226539i	$0.927259\pi$
$942$		0			0
$943$	−139.294	+	139.294i	−0.147714	+	0.147714i
$944$		0			0
$945$	1715.30	+	4704.38i	1.81514	+	4.97818i
$946$		0			0
$947$	−1027.02	−	162.664i	−1.08450	−	0.171768i	−0.411500	−	0.911410i	$-0.634995\pi$
$947$	−1027.02	−	162.664i	−1.08450	−	0.171768i	−0.673001	+	0.739642i	$0.734995\pi$
$948$		0			0
$949$		−	765.575i		−	0.806718i
$950$		0			0
$951$	−59.5055			−0.0625715
$952$		0			0
$953$	−58.3458	+	368.381i	−0.0612233	+	0.386549i	0.937982	+	0.346684i	$0.112693\pi$
$953$	−58.3458	+	368.381i	−0.0612233	+	0.386549i	−0.999205	+	0.0398642i	$0.987307\pi$
$954$		0			0
$955$	−333.717	−	95.4852i	−0.349442	−	0.0999845i
$956$		0			0
$957$	−645.325	−	645.325i	−0.674321	−	0.674321i
$958$		0			0
$959$	2694.51	+	875.498i	2.80970	+	0.912928i
$960$		0			0
$961$	−220.934	−	679.964i	−0.229900	−	0.707558i
$962$		0			0
$963$	1130.27	+	2218.29i	1.17370	+	2.30352i
$964$		0			0
$965$	229.220	+	213.506i	0.237534	+	0.221250i
$966$		0			0
$967$	−247.128	−	1560.30i	−0.255561	−	1.61355i	−0.697555	−	0.716531i	$-0.745729\pi$
$967$	−247.128	−	1560.30i	−0.255561	−	1.61355i	0.441994	−	0.897018i	$-0.354271\pi$
$968$		0			0
$969$	−70.4209	+	96.9261i	−0.0726738	+	0.100027i
$970$		0			0
$971$	88.6237	−	64.3889i	0.0912705	−	0.0663119i	−0.541214	−	0.840885i	$-0.682035\pi$
$971$	88.6237	−	64.3889i	0.0912705	−	0.0663119i	0.632485	+	0.774573i	$0.282035\pi$
$972$		0			0
$973$	−2733.61	−	1392.85i	−2.80947	−	1.43150i
$974$		0			0
$975$	1585.61	−	642.739i	1.62626	−	0.659219i
$976$		0			0
$977$	626.873	−	1230.31i	0.641630	−	1.25927i	−0.309623	−	0.950859i	$-0.600203\pi$
$977$	626.873	−	1230.31i	0.641630	−	1.25927i	0.951253	−	0.308411i	$-0.0997973\pi$
$978$		0			0
$979$	−694.047	−	955.274i	−0.708935	−	0.975765i
$980$		0			0
$981$	−97.8167	−	71.0680i	−0.0997112	−	0.0724444i
$982$		0			0
$983$	−866.267	+	137.203i	−0.881248	+	0.139576i	−0.580629	−	0.814168i	$-0.697193\pi$
$983$	−866.267	+	137.203i	−0.881248	+	0.139576i	−0.300619	+	0.953744i	$0.597193\pi$
$984$		0			0
$985$	−139.134	+	1138.54i	−0.141253	+	1.15588i
$986$		0			0
$987$	2935.70	−	1495.81i	2.97436	−	1.51551i
$988$		0			0
$989$	90.9352	−	29.5466i	0.0919466	−	0.0298753i
$990$		0			0
$991$	139.471	−	429.248i	0.140738	−	0.433146i	−0.855701	−	0.517471i	$-0.826873\pi$
$991$	139.471	−	429.248i	0.140738	−	0.433146i	0.996438	+	0.0843250i	$0.0268734\pi$
$992$		0			0
$993$	1326.79	−	1326.79i	1.33614	−	1.33614i
$994$		0			0
$995$	−1311.39	+	46.5464i	−1.31798	+	0.0467803i
$996$		0			0
$997$	994.264	+	157.476i	0.997256	+	0.157950i	0.633664	−	0.773608i	$-0.281550\pi$
$997$	994.264	+	157.476i	0.997256	+	0.157950i	0.363592	+	0.931558i	$0.381550\pi$
$998$		0			0
$999$		−	3215.66i		−	3.21888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.17.8		64
4.3	odd	2		200.3.u.b.17.1	✓	64
25.3	odd	20	inner	400.3.bg.f.353.8		64
100.3	even	20		200.3.u.b.153.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.17.1	✓	64	4.3	odd	2
200.3.u.b.153.1	yes	64	100.3	even	20
400.3.bg.f.17.8		64	1.1	even	1	trivial
400.3.bg.f.353.8		64	25.3	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)

\(f(q)\)	\(=\)	\(q+(0.898945 - 5.67572i) q^{3} +(-0.177358 - 4.99685i) q^{5} +(8.20346 + 8.20346i) q^{7} +(-22.8462 - 7.42316i) q^{9} +O(q^{10})\)	\(q+(0.898945 - 5.67572i) q^{3} +(-0.177358 - 4.99685i) q^{5} +(8.20346 + 8.20346i) q^{7} +(-22.8462 - 7.42316i) q^{9} +(-3.33578 - 10.2665i) q^{11} +(-5.40675 - 10.6114i) q^{13} +(-28.5202 - 3.48526i) q^{15} +(-0.503045 - 3.17610i) q^{17} +(3.81089 - 5.24524i) q^{19} +(53.9350 - 39.1861i) q^{21} +(20.6552 + 10.5244i) q^{23} +(-24.9371 + 1.77246i) q^{25} +(-39.1897 + 76.9140i) q^{27} +(8.64761 + 11.9024i) q^{29} +(-12.6901 - 9.21987i) q^{31} +(-61.2684 + 9.70395i) q^{33} +(39.5365 - 42.4464i) q^{35} +(-33.1914 + 16.9119i) q^{37} +(-65.0874 + 21.1482i) q^{39} +(-2.62592 + 8.08176i) q^{41} +(2.91650 - 2.91650i) q^{43} +(-33.0405 + 115.475i) q^{45} +(48.8132 + 7.73125i) q^{47} +85.5936i q^{49} -18.4789 q^{51} +(12.6010 - 79.5595i) q^{53} +(-50.7085 + 18.4893i) q^{55} +(-26.3447 - 26.3447i) q^{57} +(91.0169 + 29.5732i) q^{59} +(-5.81815 - 17.9064i) q^{61} +(-126.522 - 248.313i) q^{63} +(-52.0644 + 28.8988i) q^{65} +(-4.71815 - 29.7892i) q^{67} +(78.3012 - 107.772i) q^{69} +(19.7162 - 14.3246i) q^{71} +(57.2768 + 29.1840i) q^{73} +(-12.3571 + 143.129i) q^{75} +(56.8557 - 111.586i) q^{77} +(1.98385 + 2.73053i) q^{79} +(226.406 + 164.494i) q^{81} +(-38.7880 + 6.14342i) q^{83} +(-15.7813 + 3.07695i) q^{85} +(75.3284 - 38.3818i) q^{87} +(104.031 - 33.8016i) q^{89} +(42.6957 - 131.404i) q^{91} +(-63.7371 + 63.7371i) q^{93} +(-26.8856 - 18.1122i) q^{95} +(-128.316 - 20.3232i) q^{97} +259.312i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 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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