LMFDB - Embedded newform 253.3.c.a.208.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [253,3,Mod(208,253)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(253, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("253.208");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.c (of order $2$, degree $1$, 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:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.20
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.703600i q^{2} +3.72628 q^{3} +3.50495 q^{4} -1.98039 q^{5} -2.62181i q^{6} +11.6103i q^{7} -5.28048i q^{8} +4.88516 q^{9} +1.39340i q^{10} +(10.9993 - 0.121761i) q^{11} +13.0604 q^{12} +9.72682i q^{13} +8.16898 q^{14} -7.37949 q^{15} +10.3044 q^{16} +0.249882i q^{17} -3.43720i q^{18} -29.1859i q^{19} -6.94116 q^{20} +43.2631i q^{21} +(-0.0856712 - 7.73913i) q^{22} +4.79583 q^{23} -19.6765i q^{24} -21.0781 q^{25} +6.84379 q^{26} -15.3330 q^{27} +40.6933i q^{28} -32.3885i q^{29} +5.19221i q^{30} -43.2877 q^{31} -28.3721i q^{32} +(40.9866 - 0.453716i) q^{33} +0.175817 q^{34} -22.9928i q^{35} +17.1222 q^{36} +42.4881 q^{37} -20.5352 q^{38} +36.2448i q^{39} +10.4574i q^{40} -34.4997i q^{41} +30.4399 q^{42} +32.0435i q^{43} +(38.5521 - 0.426767i) q^{44} -9.67452 q^{45} -3.37435i q^{46} +18.1225 q^{47} +38.3972 q^{48} -85.7980 q^{49} +14.8305i q^{50} +0.931132i q^{51} +34.0920i q^{52} +48.8222 q^{53} +10.7883i q^{54} +(-21.7830 + 0.241135i) q^{55} +61.3077 q^{56} -108.755i q^{57} -22.7885 q^{58} -27.2925 q^{59} -25.8647 q^{60} -46.8028i q^{61} +30.4572i q^{62} +56.7180i q^{63} +21.2551 q^{64} -19.2629i q^{65} +(-0.319235 - 28.8381i) q^{66} -35.9957 q^{67} +0.875825i q^{68} +17.8706 q^{69} -16.1778 q^{70} -63.5621 q^{71} -25.7960i q^{72} -59.6102i q^{73} -29.8946i q^{74} -78.5427 q^{75} -102.295i q^{76} +(1.41368 + 127.705i) q^{77} +25.5019 q^{78} +119.784i q^{79} -20.4068 q^{80} -101.102 q^{81} -24.2740 q^{82} +139.132i q^{83} +151.635i q^{84} -0.494865i q^{85} +22.5458 q^{86} -120.689i q^{87} +(-0.642958 - 58.0817i) q^{88} -9.28094 q^{89} +6.80699i q^{90} -112.931 q^{91} +16.8091 q^{92} -161.302 q^{93} -12.7510i q^{94} +57.7995i q^{95} -105.722i q^{96} -122.884 q^{97} +60.3675i q^{98} +(53.7335 - 0.594823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) $ 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.703600i		−	0.351800i	−0.984408	−	0.175900i	$-0.943716\pi$
$2$		−	0.703600i		−	0.351800i	0.984408	−	0.175900i	$-0.0562835\pi$
$3$	3.72628			1.24209			0.621047	−	0.783774i	$-0.286708\pi$
$3$	3.72628			1.24209			0.621047	+	0.783774i	$0.286708\pi$
$4$	3.50495			0.876237
$5$	−1.98039			−0.396078			−0.198039	−	0.980194i	$-0.563457\pi$
$5$	−1.98039			−0.396078			−0.198039	+	0.980194i	$0.563457\pi$
$6$		−	2.62181i		−	0.436968i
$7$			11.6103i			1.65861i	0.558798	+	0.829304i	$0.311263\pi$
$7$			11.6103i			1.65861i	−0.558798	+	0.829304i	$0.688737\pi$
$8$		−	5.28048i		−	0.660060i
$9$	4.88516			0.542796
$10$			1.39340i			0.139340i
$11$	10.9993	−	0.121761i	0.999939	−	0.0110692i
$11$	10.9993	−	0.121761i	0.999939	−	0.0110692i
$12$	13.0604			1.08837
$13$			9.72682i			0.748217i	0.927385	+	0.374108i	$0.122051\pi$
$13$			9.72682i			0.748217i	−0.927385	+	0.374108i	$0.877949\pi$
$14$	8.16898			0.583498
$15$	−7.37949			−0.491966
$16$	10.3044			0.644028
$17$			0.249882i			0.0146990i	0.999973	+	0.00734948i	$0.00233943\pi$
$17$			0.249882i			0.0146990i	−0.999973	+	0.00734948i	$0.997661\pi$
$18$		−	3.43720i		−	0.190955i
$19$		−	29.1859i		−	1.53610i	−0.640389	−	0.768050i	$-0.721227\pi$
$19$		−	29.1859i		−	1.53610i	0.640389	−	0.768050i	$-0.278773\pi$
$20$	−6.94116			−0.347058
$21$			43.2631i			2.06015i
$22$	−0.0856712	−	7.73913i	−0.00389414	−	0.351778i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$		−	19.6765i		−	0.819856i
$25$	−21.0781			−0.843122
$26$	6.84379			0.263223
$27$	−15.3330			−0.567890
$28$			40.6933i			1.45333i
$29$		−	32.3885i		−	1.11684i	−0.829557	−	0.558422i	$-0.811407\pi$
$29$		−	32.3885i		−	1.11684i	0.829557	−	0.558422i	$-0.188593\pi$
$30$			5.19221i			0.173074i
$31$	−43.2877			−1.39638			−0.698189	−	0.715914i	$-0.746010\pi$
$31$	−43.2877			−1.39638			−0.698189	+	0.715914i	$0.746010\pi$
$32$		−	28.3721i		−	0.886629i
$33$	40.9866	−	0.453716i	1.24202	−	0.0137490i
$34$	0.175817			0.00517110
$35$		−	22.9928i		−	0.656938i
$36$	17.1222			0.475617
$37$	42.4881			1.14833			0.574164	−	0.818741i	$-0.305327\pi$
$37$	42.4881			1.14833			0.574164	+	0.818741i	$0.305327\pi$
$38$	−20.5352			−0.540400
$39$			36.2448i			0.929355i
$40$			10.4574i			0.261435i
$41$		−	34.4997i		−	0.841455i	−0.907187	−	0.420728i	$-0.861775\pi$
$41$		−	34.4997i		−	0.841455i	0.907187	−	0.420728i	$-0.138225\pi$
$42$	30.4399			0.724759
$43$			32.0435i			0.745197i	0.927993	+	0.372598i	$0.121533\pi$
$43$			32.0435i			0.745197i	−0.927993	+	0.372598i	$0.878467\pi$
$44$	38.5521	−	0.426767i	0.876183	−	0.00969924i
$45$	−9.67452			−0.214989
$46$		−	3.37435i		−	0.0733554i
$47$	18.1225			0.385586			0.192793	−	0.981239i	$-0.438245\pi$
$47$	18.1225			0.385586			0.192793	+	0.981239i	$0.438245\pi$
$48$	38.3972			0.799942
$49$	−85.7980			−1.75098
$50$			14.8305i			0.296610i
$51$			0.931132i			0.0182575i
$52$			34.0920i			0.655615i
$53$	48.8222			0.921174			0.460587	−	0.887614i	$-0.347639\pi$
$53$	48.8222			0.921174			0.460587	+	0.887614i	$0.347639\pi$
$54$			10.7883i			0.199784i
$55$	−21.7830	+	0.241135i	−0.396054	+	0.00438427i
$56$	61.3077			1.09478
$57$		−	108.755i		−	1.90798i
$58$	−22.7885			−0.392906
$59$	−27.2925			−0.462585			−0.231292	−	0.972884i	$-0.574295\pi$
$59$	−27.2925			−0.462585			−0.231292	+	0.972884i	$0.574295\pi$
$60$	−25.8647			−0.431078
$61$		−	46.8028i		−	0.767259i	−0.923487	−	0.383629i	$-0.874674\pi$
$61$		−	46.8028i		−	0.767259i	0.923487	−	0.383629i	$-0.125326\pi$
$62$			30.4572i			0.491245i
$63$			56.7180i			0.900285i
$64$	21.2551			0.332112
$65$		−	19.2629i		−	0.296352i
$66$	−0.319235	−	28.8381i	−0.00483689	−	0.436942i
$67$	−35.9957			−0.537249			−0.268625	−	0.963245i	$-0.586569\pi$
$67$	−35.9957			−0.537249			−0.268625	+	0.963245i	$0.586569\pi$
$68$			0.875825i			0.0128798i
$69$	17.8706			0.258994
$70$	−16.1778			−0.231111
$71$	−63.5621			−0.895241			−0.447620	−	0.894224i	$-0.647728\pi$
$71$	−63.5621			−0.895241			−0.447620	+	0.894224i	$0.647728\pi$
$72$		−	25.7960i		−	0.358278i
$73$		−	59.6102i		−	0.816578i	−0.912853	−	0.408289i	$-0.866126\pi$
$73$		−	59.6102i		−	0.816578i	0.912853	−	0.408289i	$-0.133874\pi$
$74$		−	29.8946i		−	0.403982i
$75$	−78.5427			−1.04724
$76$		−	102.295i		−	1.34599i
$77$	1.41368	+	127.705i	0.0183595	+	1.65851i
$78$	25.5019			0.326947
$79$			119.784i			1.51625i	0.652109	+	0.758125i	$0.273884\pi$
$79$			119.784i			1.51625i	−0.652109	+	0.758125i	$0.726116\pi$
$80$	−20.4068			−0.255085
$81$	−101.102			−1.24817
$82$	−24.2740			−0.296024
$83$			139.132i			1.67629i	0.545448	+	0.838145i	$0.316360\pi$
$83$			139.132i			1.67629i	−0.545448	+	0.838145i	$0.683640\pi$
$84$			151.635i			1.80518i
$85$		−	0.494865i		−	0.00582194i
$86$	22.5458			0.262160
$87$		−	120.689i		−	1.38723i
$88$	−0.642958	−	58.0817i	−0.00730634	−	0.660020i
$89$	−9.28094			−0.104280			−0.0521401	−	0.998640i	$-0.516604\pi$
$89$	−9.28094			−0.104280			−0.0521401	+	0.998640i	$0.516604\pi$
$90$			6.80699i			0.0756333i
$91$	−112.931			−1.24100
$92$	16.8091			0.182708
$93$	−161.302			−1.73443
$94$		−	12.7510i		−	0.135649i
$95$			57.7995i			0.608416i
$96$		−	105.722i		−	1.10128i
$97$	−122.884			−1.26685			−0.633423	−	0.773806i	$-0.718351\pi$
$97$	−122.884			−1.26685			−0.633423	+	0.773806i	$0.718351\pi$
$98$			60.3675i			0.615995i
$99$	53.7335	−	0.594823i	0.542762	−	0.00600831i
$100$	−73.8775			−0.738775
$101$			35.5807i			0.352285i	0.984365	+	0.176142i	$0.0563619\pi$
$101$			35.5807i			0.352285i	−0.984365	+	0.176142i	$0.943638\pi$
$102$	0.655144			0.00642298
$103$	−5.72707			−0.0556026			−0.0278013	−	0.999613i	$-0.508851\pi$
$103$	−5.72707			−0.0556026			−0.0278013	+	0.999613i	$0.508851\pi$
$104$	51.3623			0.493868
$105$		−	85.6777i		−	0.815978i
$106$		−	34.3513i		−	0.324069i
$107$		−	2.39079i		−	0.0223438i	−0.999938	−	0.0111719i	$-0.996444\pi$
$107$		−	2.39079i		−	0.0223438i	0.999938	−	0.0111719i	$-0.00355620\pi$
$108$	−53.7415			−0.497607
$109$			38.3646i			0.351969i	0.984393	+	0.175984i	$0.0563108\pi$
$109$			38.3646i			0.351969i	−0.984393	+	0.175984i	$0.943689\pi$
$110$	0.169662	+	15.3265i	0.00154238	+	0.139332i
$111$	158.323			1.42633
$112$			119.637i			1.06819i
$113$	99.2696			0.878492			0.439246	−	0.898367i	$-0.355246\pi$
$113$	99.2696			0.878492			0.439246	+	0.898367i	$0.355246\pi$
$114$	−76.5199			−0.671227
$115$	−9.49761			−0.0825880
$116$		−	113.520i		−	0.978620i
$117$			47.5171i			0.406129i
$118$			19.2030i			0.162737i
$119$	−2.90120			−0.0243798
$120$			38.9672i			0.324727i
$121$	120.970	−	2.67858i	0.999755	−	0.0221370i
$122$	−32.9304			−0.269922
$123$		−	128.555i		−	1.04517i
$124$	−151.721			−1.22356
$125$	91.2525			0.730020
$126$	39.9068			0.316720
$127$		−	90.5479i		−	0.712975i	−0.934300	−	0.356488i	$-0.883974\pi$
$127$		−	90.5479i		−	0.712975i	0.934300	−	0.356488i	$-0.116026\pi$
$128$		−	128.444i		−	1.00347i
$129$			119.403i			0.925604i
$130$	−13.5534			−0.104257
$131$		−	158.767i		−	1.21196i	−0.795480	−	0.605980i	$-0.792781\pi$
$131$		−	158.767i		−	1.21196i	0.795480	−	0.605980i	$-0.207219\pi$
$132$	143.656	−	1.59025i	1.08830	−	0.0120474i
$133$	338.856			2.54779
$134$			25.3266i			0.189004i
$135$	30.3654			0.224929
$136$	1.31950			0.00970220
$137$	−118.158			−0.862467			−0.431233	−	0.902240i	$-0.641921\pi$
$137$	−118.158			−0.862467			−0.431233	+	0.902240i	$0.641921\pi$
$138$		−	12.5738i		−	0.0911142i
$139$		−	181.525i		−	1.30594i	−0.757384	−	0.652969i	$-0.773523\pi$
$139$		−	181.525i		−	1.30594i	0.757384	−	0.652969i	$-0.226477\pi$
$140$		−	80.5886i		−	0.575633i
$141$	67.5297			0.478934
$142$			44.7223i			0.314946i
$143$	1.18435	+	106.988i	0.00828216	+	0.748171i
$144$	50.3389			0.349575
$145$			64.1418i			0.442357i
$146$	−41.9417			−0.287272
$147$	−319.707			−2.17488
$148$	148.919			1.00621
$149$			1.28535i			0.00862653i	0.999991	+	0.00431326i	$0.00137296\pi$
$149$			1.28535i			0.00862653i	−0.999991	+	0.00431326i	$0.998627\pi$
$150$			55.2627i			0.368418i
$151$			299.741i			1.98504i	0.122095	+	0.992518i	$0.461039\pi$
$151$			299.741i			1.98504i	−0.122095	+	0.992518i	$0.538961\pi$
$152$	−154.116			−1.01392
$153$			1.22072i			0.00797853i
$154$	89.8532	−	0.994664i	0.583463	−	0.00645886i
$155$	85.7265			0.553074
$156$			127.036i			0.814335i
$157$	161.320			1.02752			0.513758	−	0.857935i	$-0.328253\pi$
$157$	161.320			1.02752			0.513758	+	0.857935i	$0.328253\pi$
$158$	84.2798			0.533417
$159$	181.925			1.14418
$160$			56.1879i			0.351174i
$161$			55.6808i			0.345844i
$162$			71.1351i			0.439106i
$163$	−139.594			−0.856407			−0.428204	−	0.903682i	$-0.640853\pi$
$163$	−139.594			−0.856407			−0.428204	+	0.903682i	$0.640853\pi$
$164$		−	120.919i		−	0.737314i
$165$	−81.1694	+	0.898535i	−0.491936	+	0.00544567i
$166$	97.8933			0.589719
$167$		−	308.264i		−	1.84589i	−0.384931	−	0.922945i	$-0.625775\pi$
$167$		−	308.264i		−	1.84589i	0.384931	−	0.922945i	$-0.374225\pi$
$168$	228.450			1.35982
$169$	74.3890			0.440172
$170$	−0.348187			−0.00204816
$171$		−	142.578i		−	0.833789i
$172$			112.311i			0.652969i
$173$			254.331i			1.47012i	0.678002	+	0.735060i	$0.262846\pi$
$173$			254.331i			1.47012i	−0.678002	+	0.735060i	$0.737154\pi$
$174$	−84.9165			−0.488026
$175$		−	244.722i		−	1.39841i
$176$	113.342	−	1.25468i	0.643988	−	0.00712887i
$177$	−101.699			−0.574573
$178$			6.53007i			0.0366858i
$179$	319.298			1.78379			0.891894	−	0.452245i	$-0.149377\pi$
$179$	319.298			1.78379			0.891894	+	0.452245i	$0.149377\pi$
$180$	−33.9087			−0.188382
$181$	−133.229			−0.736074			−0.368037	−	0.929811i	$-0.619970\pi$
$181$	−133.229			−0.736074			−0.368037	+	0.929811i	$0.619970\pi$
$182$			79.4581i			0.436583i
$183$		−	174.400i		−	0.953007i
$184$		−	25.3243i		−	0.137632i
$185$	−84.1430			−0.454827
$186$			113.492i			0.610173i
$187$	0.0304260	+	2.74854i	0.000162706	+	0.0146981i
$188$	63.5186			0.337865
$189$		−	178.021i		−	0.941908i
$190$	40.6677			0.214041
$191$	−120.382			−0.630275			−0.315137	−	0.949046i	$-0.602051\pi$
$191$	−120.382			−0.630275			−0.315137	+	0.949046i	$0.602051\pi$
$192$	79.2026			0.412513
$193$		−	57.4217i		−	0.297522i	−0.988873	−	0.148761i	$-0.952472\pi$
$193$		−	57.4217i		−	0.297522i	0.988873	−	0.148761i	$-0.0475284\pi$
$194$			86.4612i			0.445676i
$195$		−	71.7789i		−	0.368097i
$196$	−300.718			−1.53427
$197$			129.654i			0.658140i	0.944305	+	0.329070i	$0.106735\pi$
$197$			129.654i			0.658140i	−0.944305	+	0.329070i	$0.893265\pi$
$198$	−0.418517	−	37.8069i	−0.00211372	−	0.190944i
$199$	−8.56995			−0.0430651			−0.0215325	−	0.999768i	$-0.506855\pi$
$199$	−8.56995			−0.0430651			−0.0215325	+	0.999768i	$0.506855\pi$
$200$			111.302i			0.556511i
$201$	−134.130			−0.667314
$202$	25.0346			0.123934
$203$	376.039			1.85241
$204$			3.26357i			0.0159979i
$205$			68.3228i			0.333282i
$206$			4.02957i			0.0195610i
$207$	23.4284			0.113181
$208$			100.229i			0.481872i
$209$	−3.55371	−	321.025i	−0.0170034	−	1.53601i
$210$	−60.2828			−0.287061
$211$			417.822i			1.98020i	0.140364	+	0.990100i	$0.455173\pi$
$211$			417.822i			1.98020i	−0.140364	+	0.990100i	$0.544827\pi$
$212$	171.119			0.807167
$213$	−236.850			−1.11197
$214$	−1.68216			−0.00786055
$215$		−	63.4585i		−	0.295156i
$216$			80.9658i			0.374842i
$217$		−	502.581i		−	2.31604i
$218$	26.9933			0.123823
$219$		−	222.124i		−	1.01427i
$220$	−76.3481	+	0.845164i	−0.347037	+	0.00384165i
$221$	−2.43056			−0.0109980
$222$		−	111.396i		−	0.501783i
$223$	197.298			0.884744			0.442372	−	0.896832i	$-0.354137\pi$
$223$	197.298			0.884744			0.442372	+	0.896832i	$0.354137\pi$
$224$	329.408			1.47057
$225$	−102.970			−0.457643
$226$		−	69.8461i		−	0.309053i
$227$			197.950i			0.872024i	0.899941	+	0.436012i	$0.143610\pi$
$227$			197.950i			0.872024i	−0.899941	+	0.436012i	$0.856390\pi$
$228$		−	381.180i		−	1.67184i
$229$	−172.651			−0.753933			−0.376967	−	0.926227i	$-0.623033\pi$
$229$	−172.651			−0.753933			−0.376967	+	0.926227i	$0.623033\pi$
$230$			6.68252i			0.0290544i
$231$	5.26776	+	475.864i	0.0228042	+	2.06002i
$232$	−171.027			−0.737185
$233$		−	52.6488i		−	0.225960i	−0.993597	−	0.112980i	$-0.963960\pi$
$233$		−	52.6488i		−	0.225960i	0.993597	−	0.112980i	$-0.0360397\pi$
$234$	33.4330			0.142876
$235$	−35.8897			−0.152722
$236$	−95.6587			−0.405334
$237$			446.348i			1.88332i
$238$			2.04128i			0.00857682i
$239$			39.7110i			0.166155i	0.996543	+	0.0830775i	$0.0264749\pi$
$239$			39.7110i			0.166155i	−0.996543	+	0.0830775i	$0.973525\pi$
$240$	−76.0415			−0.316839
$241$			435.488i			1.80700i	0.428584	+	0.903502i	$0.359013\pi$
$241$			435.488i			1.80700i	−0.428584	+	0.903502i	$0.640987\pi$
$242$	−1.88465	−	85.1147i	−0.00778781	−	0.351714i
$243$	−238.736			−0.982451
$244$		−	164.041i		−	0.672300i
$245$	169.914			0.693525
$246$	−90.4516			−0.367689
$247$	283.886			1.14934
$248$			228.580i			0.921693i
$249$			518.445i			2.08211i
$250$		−	64.2053i		−	0.256821i
$251$	144.086			0.574047			0.287024	−	0.957924i	$-0.407334\pi$
$251$	144.086			0.574047			0.287024	+	0.957924i	$0.407334\pi$
$252$			198.793i			0.788863i
$253$	52.7509	−	0.583946i	0.208502	−	0.00230809i
$254$	−63.7095			−0.250825
$255$		−	1.84400i		−	0.00723139i
$256$	−5.35239			−0.0209078
$257$	−427.768			−1.66447			−0.832234	−	0.554424i	$-0.812938\pi$
$257$	−427.768			−1.66447			−0.832234	+	0.554424i	$0.812938\pi$
$258$	84.0119			0.325627
$259$			493.298i			1.90462i
$260$		−	67.5154i		−	0.259675i
$261$		−	158.223i		−	0.606218i
$262$	−111.708			−0.426368
$263$		−	228.378i		−	0.868356i	−0.900827	−	0.434178i	$-0.857039\pi$
$263$		−	228.378i		−	0.868356i	0.900827	−	0.434178i	$-0.142961\pi$
$264$	−2.39584	−	216.429i	−0.00907515	−	0.819806i
$265$	−96.6871			−0.364857
$266$		−	238.419i		−	0.896312i
$267$	−34.5834			−0.129526
$268$	−126.163			−0.470758
$269$	432.507			1.60783			0.803916	−	0.594743i	$-0.202746\pi$
$269$	432.507			1.60783			0.803916	+	0.594743i	$0.202746\pi$
$270$		−	21.3651i		−	0.0791300i
$271$		−	105.523i		−	0.389382i	−0.980865	−	0.194691i	$-0.937630\pi$
$271$		−	105.523i		−	0.389382i	0.980865	−	0.194691i	$-0.0623704\pi$
$272$			2.57490i			0.00946654i
$273$	−420.812			−1.54144
$274$			83.1359i			0.303416i
$275$	−231.844	+	2.56649i	−0.843071	+	0.00933269i
$276$	62.6355			0.226940
$277$		−	199.847i		−	0.721471i	−0.932668	−	0.360735i	$-0.882526\pi$
$277$		−	199.847i		−	0.721471i	0.932668	−	0.360735i	$-0.117474\pi$
$278$	−127.721			−0.459429
$279$	−211.467			−0.757947
$280$	−121.413			−0.433619
$281$		−	467.449i		−	1.66352i	−0.555137	−	0.831759i	$-0.687334\pi$
$281$		−	467.449i		−	1.66352i	0.555137	−	0.831759i	$-0.312666\pi$
$282$		−	47.5139i		−	0.168489i
$283$		−	394.206i		−	1.39295i	−0.717579	−	0.696477i	$-0.754750\pi$
$283$		−	394.206i		−	1.39295i	0.717579	−	0.696477i	$-0.245250\pi$
$284$	−222.782			−0.784443
$285$			215.377i			0.755709i
$286$	75.2771	−	0.833308i	0.263206	−	0.00291366i
$287$	400.550			1.39564
$288$		−	138.602i		−	0.481258i
$289$	288.938			0.999784
$290$	45.1302			0.155621
$291$	−457.900			−1.57354
$292$		−	208.931i		−	0.715516i
$293$		−	500.325i		−	1.70759i	−0.520606	−	0.853797i	$-0.674294\pi$
$293$		−	500.325i		−	1.70759i	0.520606	−	0.853797i	$-0.325706\pi$
$294$			224.946i			0.765123i
$295$	54.0498			0.183220
$296$		−	224.358i		−	0.757965i
$297$	−168.653	+	1.86697i	−0.567856	+	0.00628609i
$298$	0.904374			0.00303481
$299$			46.6482i			0.156014i
$300$	−275.288			−0.917627
$301$	−372.033			−1.23599
$302$	210.897			0.698336
$303$			132.584i			0.437570i
$304$		−	300.745i		−	0.989291i
$305$			92.6877i			0.303894i
$306$	0.858896			0.00280685
$307$			291.289i			0.948824i	0.880303	+	0.474412i	$0.157339\pi$
$307$			291.289i			0.948824i	−0.880303	+	0.474412i	$0.842661\pi$
$308$	4.95487	+	447.599i	0.0160872	+	1.45324i
$309$	−21.3407			−0.0690636
$310$		−	60.3172i		−	0.194571i
$311$	399.315			1.28397			0.641985	−	0.766717i	$-0.278111\pi$
$311$	399.315			1.28397			0.641985	+	0.766717i	$0.278111\pi$
$312$	191.390			0.613430
$313$	96.6616			0.308823			0.154411	−	0.988007i	$-0.450652\pi$
$313$	96.6616			0.308823			0.154411	+	0.988007i	$0.450652\pi$
$314$		−	113.505i		−	0.361480i
$315$		−	112.324i		−	0.356583i
$316$			419.836i			1.32859i
$317$	295.212			0.931269			0.465635	−	0.884977i	$-0.345826\pi$
$317$	295.212			0.931269			0.465635	+	0.884977i	$0.345826\pi$
$318$		−	128.003i		−	0.402524i
$319$	−3.94366	−	356.252i	−0.0123626	−	1.11678i
$320$	−42.0935			−0.131542
$321$		−	8.90874i		−	0.0277531i
$322$	39.1770			0.121668
$323$	7.29305			0.0225791
$324$	−354.356			−1.09369
$325$		−	205.022i		−	0.630838i
$326$			98.2186i			0.301284i
$327$			142.957i			0.437178i
$328$	−182.175			−0.555411
$329$			210.407i			0.639536i
$330$	0.632209	+	57.1108i	0.00191579	+	0.173063i
$331$	−45.1322			−0.136351			−0.0681755	−	0.997673i	$-0.521718\pi$
$331$	−45.1322			−0.136351			−0.0681755	+	0.997673i	$0.521718\pi$
$332$			487.650i			1.46883i
$333$	207.561			0.623307
$334$	−216.894			−0.649384
$335$	71.2855			0.212793
$336$			445.802i			1.32679i
$337$			169.284i			0.502328i	0.967945	+	0.251164i	$0.0808133\pi$
$337$			169.284i			0.502328i	−0.967945	+	0.251164i	$0.919187\pi$
$338$		−	52.3401i		−	0.154852i
$339$	369.906			1.09117
$340$		−	1.73447i		−	0.00510139i
$341$	−476.135	+	5.27076i	−1.39629	+	0.0154568i
$342$	−100.318			−0.293327
$343$		−	427.234i		−	1.24558i
$344$	169.205			0.491875
$345$	−35.3908			−0.102582
$346$	178.947			0.517188
$347$			310.292i			0.894214i	0.894481	+	0.447107i	$0.147546\pi$
$347$			310.292i			0.894214i	−0.894481	+	0.447107i	$0.852454\pi$
$348$		−	423.007i		−	1.21554i
$349$			114.024i			0.326717i	0.986567	+	0.163359i	$0.0522328\pi$
$349$			114.024i			0.326717i	−0.986567	+	0.163359i	$0.947767\pi$
$350$	−172.186			−0.491960
$351$		−	149.142i		−	0.424905i
$352$	−3.45462	−	312.074i	−0.00981427	−	0.886575i
$353$	−63.6894			−0.180423			−0.0902116	−	0.995923i	$-0.528754\pi$
$353$	−63.6894			−0.180423			−0.0902116	+	0.995923i	$0.528754\pi$
$354$			71.5557i			0.202135i
$355$	125.878			0.354585
$356$	−32.5292			−0.0913741
$357$	−10.8107			−0.0302820
$358$		−	224.658i		−	0.627536i
$359$			96.2534i			0.268115i	0.990974	+	0.134058i	$0.0428008\pi$
$359$			96.2534i			0.268115i	−0.990974	+	0.134058i	$0.957199\pi$
$360$			51.0861i			0.141906i
$361$	−490.818			−1.35961
$362$			93.7402i			0.258951i
$363$	450.769	−	9.98115i	1.24179	−	0.0274963i
$364$	−395.817			−1.08741
$365$			118.051i			0.323429i
$366$	−122.708			−0.335268
$367$	284.656			0.775630			0.387815	−	0.921737i	$-0.373230\pi$
$367$	284.656			0.775630			0.387815	+	0.921737i	$0.373230\pi$
$368$	49.4184			0.134289
$369$		−	168.536i		−	0.456738i
$370$			59.2030i			0.160008i
$371$			566.839i			1.52787i
$372$	−565.355			−1.51977
$373$			595.762i			1.59722i	0.601851	+	0.798608i	$0.294430\pi$
$373$			595.762i			1.59722i	−0.601851	+	0.798608i	$0.705570\pi$
$374$	1.93387	−	0.0214077i	0.00517078	−	5.72399e-5i
$375$	340.032			0.906753
$376$		−	95.6958i		−	0.254510i
$377$	315.037			0.835642
$378$	−125.255			−0.331363
$379$	280.699			0.740631			0.370315	−	0.928906i	$-0.379250\pi$
$379$	280.699			0.740631			0.370315	+	0.928906i	$0.379250\pi$
$380$			202.584i			0.533116i
$381$		−	337.407i		−	0.885582i
$382$			84.7011i			0.221731i
$383$	−394.446			−1.02989			−0.514943	−	0.857225i	$-0.672187\pi$
$383$	−394.446			−1.02989			−0.514943	+	0.857225i	$0.672187\pi$
$384$		−	478.617i		−	1.24640i
$385$	−2.79963	−	252.906i	−0.00727178	−	0.656898i
$386$	−40.4019			−0.104668
$387$			156.537i			0.404489i
$388$	−430.702			−1.11006
$389$	−493.302			−1.26813			−0.634064	−	0.773280i	$-0.718615\pi$
$389$	−493.302			−1.26813			−0.634064	+	0.773280i	$0.718615\pi$
$390$	−50.5036			−0.129496
$391$			1.19839i			0.00306495i
$392$			453.055i			1.15575i
$393$		−	591.609i		−	1.50537i
$394$	91.2243			0.231534
$395$		−	237.218i		−	0.600553i
$396$	188.333	−	2.08482i	0.475588	−	0.00526470i
$397$	−420.647			−1.05956			−0.529782	−	0.848134i	$-0.677726\pi$
$397$	−420.647			−1.05956			−0.529782	+	0.848134i	$0.677726\pi$
$398$			6.02981i			0.0151503i
$399$	1262.67			3.16459
$400$	−217.198			−0.542994
$401$	−719.525			−1.79433			−0.897164	−	0.441698i	$-0.854376\pi$
$401$	−719.525			−1.79433			−0.897164	+	0.441698i	$0.854376\pi$
$402$			94.3739i			0.234761i
$403$		−	421.051i		−	1.04479i
$404$			124.709i			0.308685i
$405$	200.221			0.494372
$406$		−	264.581i		−	0.651677i
$407$	467.341	−	5.17340i	1.14826	−	0.0127111i
$408$	4.91682			0.0120510
$409$			377.723i			0.923528i	0.887003	+	0.461764i	$0.152783\pi$
$409$			377.723i			0.923528i	−0.887003	+	0.461764i	$0.847217\pi$
$410$	48.0719			0.117249
$411$	−440.289			−1.07126
$412$	−20.0731			−0.0487210
$413$		−	316.873i		−	0.767246i
$414$		−	16.4842i		−	0.0398170i
$415$		−	275.536i		−	0.663941i
$416$	275.970			0.663391
$417$		−	676.415i		−	1.62210i
$418$	−225.873	+	2.50039i	−0.540367	+	0.00598180i
$419$	674.048			1.60871			0.804354	−	0.594151i	$-0.202512\pi$
$419$	674.048			1.60871			0.804354	+	0.594151i	$0.202512\pi$
$420$		−	300.296i		−	0.714990i
$421$	454.458			1.07947			0.539737	−	0.841834i	$-0.318524\pi$
$421$	454.458			1.07947			0.539737	+	0.841834i	$0.318524\pi$
$422$	293.980			0.696634
$423$	88.5315			0.209294
$424$		−	257.805i		−	0.608030i
$425$		−	5.26704i		−	0.0123930i
$426$			166.648i			0.391192i
$427$	543.392			1.27258
$428$		−	8.37958i		−	0.0195785i
$429$	4.41322	+	398.669i	0.0102872	+	0.929298i
$430$	−44.6494			−0.103836
$431$			594.735i			1.37990i	0.723859	+	0.689948i	$0.242367\pi$
$431$			594.735i			1.37990i	−0.723859	+	0.689948i	$0.757633\pi$
$432$	−157.998			−0.365737
$433$	382.466			0.883294			0.441647	−	0.897189i	$-0.354394\pi$
$433$	382.466			0.883294			0.441647	+	0.897189i	$0.354394\pi$
$434$	−353.616			−0.814784
$435$			239.010i			0.549449i
$436$			134.466i			0.308408i
$437$		−	139.971i		−	0.320299i
$438$	−156.287			−0.356819
$439$			457.197i			1.04145i	0.853724	+	0.520725i	$0.174338\pi$
$439$			457.197i			1.04145i	−0.853724	+	0.520725i	$0.825662\pi$
$440$	1.27331	+	115.024i	0.00289388	+	0.261419i
$441$	−419.137			−0.950424
$442$			1.71014i			0.00386910i
$443$	182.385			0.411704			0.205852	−	0.978583i	$-0.434003\pi$
$443$	182.385			0.411704			0.205852	+	0.978583i	$0.434003\pi$
$444$	554.912			1.24980
$445$	18.3799			0.0413031
$446$		−	138.819i		−	0.311253i
$447$			4.78958i			0.0107150i
$448$			246.778i			0.550843i
$449$	−97.9290			−0.218105			−0.109052	−	0.994036i	$-0.534782\pi$
$449$	−97.9290			−0.218105			−0.109052	+	0.994036i	$0.534782\pi$
$450$			72.4495i			0.160999i
$451$	−4.20072	−	379.473i	−0.00931424	−	0.841404i
$452$	347.935			0.769767
$453$			1116.92i			2.46560i
$454$	139.277			0.306778
$455$	223.647			0.491532
$456$	−574.278			−1.25938
$457$			233.838i			0.511680i	0.966719	+	0.255840i	$0.0823521\pi$
$457$			233.838i			0.511680i	−0.966719	+	0.255840i	$0.917648\pi$
$458$			121.477i			0.265234i
$459$		−	3.83146i		−	0.00834740i
$460$	−33.2886			−0.0723666
$461$		−	121.687i		−	0.263962i	−0.991252	−	0.131981i	$-0.957866\pi$
$461$		−	121.687i		−	0.263962i	0.991252	−	0.131981i	$-0.0421339\pi$
$462$	334.818	−	3.70640i	0.724715	−	0.00802250i
$463$	279.698			0.604099			0.302050	−	0.953292i	$-0.402329\pi$
$463$	279.698			0.604099			0.302050	+	0.953292i	$0.402329\pi$
$464$		−	333.745i		−	0.719279i
$465$	319.441			0.686970
$466$	−37.0437			−0.0794928
$467$	239.544			0.512943			0.256471	−	0.966552i	$-0.417440\pi$
$467$	239.544			0.512943			0.256471	+	0.966552i	$0.417440\pi$
$468$			166.545i			0.355865i
$469$		−	417.919i		−	0.891086i
$470$			25.2520i			0.0537276i
$471$	601.123			1.27627
$472$			144.117i			0.305334i
$473$	3.90165	+	352.456i	0.00824873	+	0.745151i
$474$	314.050			0.662553
$475$			615.182i			1.29512i
$476$	−10.1685			−0.0213625
$477$	238.504			0.500009
$478$	27.9407			0.0584533
$479$		−	209.126i		−	0.436588i	−0.975883	−	0.218294i	$-0.929951\pi$
$479$		−	209.126i		−	0.436588i	0.975883	−	0.218294i	$-0.0700492\pi$
$480$			209.372i			0.436191i
$481$			413.274i			0.859198i
$482$	306.409			0.635704
$483$			207.482i			0.429570i
$484$	423.995	−	9.38829i	0.876022	−	0.0193973i
$485$	243.358			0.501770
$486$			167.974i			0.345626i
$487$	−426.918			−0.876629			−0.438315	−	0.898822i	$-0.644424\pi$
$487$	−426.918			−0.876629			−0.438315	+	0.898822i	$0.644424\pi$
$488$	−247.141			−0.506437
$489$	−520.168			−1.06374
$490$		−	119.551i		−	0.243982i
$491$			18.9288i			0.0385515i	0.999814	+	0.0192758i	$0.00613605\pi$
$491$			18.9288i			0.0385515i	−0.999814	+	0.0192758i	$0.993864\pi$
$492$		−	450.580i		−	0.915813i
$493$	8.09331			0.0164165
$494$		−	199.742i		−	0.404336i
$495$	−106.413	+	1.17798i	−0.214976	+	0.00237976i
$496$	−446.055			−0.899305
$497$		−	737.972i		−	1.48485i
$498$	364.778			0.732486
$499$	−125.159			−0.250819			−0.125410	−	0.992105i	$-0.540025\pi$
$499$	−125.159			−0.250819			−0.125410	+	0.992105i	$0.540025\pi$
$500$	319.835			0.639670
$501$		−	1148.68i		−	2.29277i
$502$		−	101.379i		−	0.201950i
$503$			442.570i			0.879860i	0.898032	+	0.439930i	$0.144997\pi$
$503$			442.570i			0.879860i	−0.898032	+	0.439930i	$0.855003\pi$
$504$	299.498			0.594242
$505$		−	70.4637i		−	0.139532i
$506$	−0.410865	−	37.1155i	−0.000811985	−	0.0733509i
$507$	277.194			0.546734
$508$		−	317.365i		−	0.624735i
$509$	−482.080			−0.947111			−0.473556	−	0.880764i	$-0.657030\pi$
$509$	−482.080			−0.947111			−0.473556	+	0.880764i	$0.657030\pi$
$510$	−1.29744			−0.00254400
$511$	692.090			1.35438
$512$		−	510.009i		−	0.996110i
$513$			447.509i			0.872337i
$514$			300.978i			0.585560i
$515$	11.3418			0.0220230
$516$			418.501i			0.811048i
$517$	199.336	−	2.20662i	0.385562	−	0.00426813i
$518$	347.084			0.670047
$519$			947.707i			1.82603i
$520$	−101.717			−0.195610
$521$	−329.382			−0.632212			−0.316106	−	0.948724i	$-0.602376\pi$
$521$	−329.382			−0.632212			−0.316106	+	0.948724i	$0.602376\pi$
$522$	−111.326			−0.213268
$523$			104.255i			0.199340i	0.995021	+	0.0996699i	$0.0317787\pi$
$523$			104.255i			0.199340i	−0.995021	+	0.0996699i	$0.968221\pi$
$524$		−	556.469i		−	1.06196i
$525$		−	911.901i		−	1.73695i
$526$	−160.686			−0.305488
$527$		−	10.8168i		−	0.0205253i
$528$	422.344	−	4.67529i	0.799893	−	0.00885472i
$529$	23.0000			0.0434783
$530$			68.0290i			0.128357i
$531$	−133.328			−0.251089
$532$	1187.67			2.23247
$533$	335.572			0.629591
$534$			24.3329i			0.0455672i
$535$			4.73469i			0.00884988i
$536$			190.075i			0.354617i
$537$	1189.79			2.21563
$538$		−	304.312i		−	0.565635i
$539$	−943.720	+	10.4469i	−1.75087	+	0.0193819i
$540$	106.429			0.197091
$541$		−	289.851i		−	0.535768i	−0.963451	−	0.267884i	$-0.913676\pi$
$541$		−	289.851i		−	0.535768i	0.963451	−	0.267884i	$-0.0863244\pi$
$542$	−74.2457			−0.136985
$543$	−496.450			−0.914273
$544$	7.08970			0.0130325
$545$		−	75.9769i		−	0.139407i
$546$			296.083i			0.542277i
$547$		−	249.772i		−	0.456621i	−0.973588	−	0.228311i	$-0.926680\pi$
$547$		−	249.772i		−	0.456621i	0.973588	−	0.228311i	$-0.0733202\pi$
$548$	−414.137			−0.755725
$549$		−	228.639i		−	0.416465i
$550$	1.80578	+	163.126i	0.00328324	+	0.296592i
$551$	−945.288			−1.71559
$552$		−	94.3654i		−	0.170952i
$553$	−1390.72			−2.51486
$554$	−140.613			−0.253813
$555$	−313.540			−0.564938
$556$		−	636.237i		−	1.14431i
$557$			275.005i			0.493726i	0.969050	+	0.246863i	$0.0793997\pi$
$557$			275.005i			0.493726i	−0.969050	+	0.246863i	$0.920600\pi$
$558$			148.788i			0.266646i
$559$	−311.681			−0.557568
$560$		−	236.928i		−	0.423086i
$561$	0.113376	+	10.2418i	0.000202096	+	0.0182564i
$562$	−328.897			−0.585226
$563$		−	796.938i		−	1.41552i	−0.706453	−	0.707760i	$-0.749706\pi$
$563$		−	796.938i		−	1.41552i	0.706453	−	0.707760i	$-0.250294\pi$
$564$	236.688			0.419659
$565$	−196.592			−0.347951
$566$	−277.363			−0.490041
$567$		−	1173.82i		−	2.07022i
$568$			335.638i			0.590913i
$569$		−	451.435i		−	0.793383i	−0.917952	−	0.396692i	$-0.870158\pi$
$569$		−	451.435i		−	0.793383i	0.917952	−	0.396692i	$-0.129842\pi$
$570$	151.539			0.265858
$571$			102.109i			0.178825i	0.995995	+	0.0894125i	$0.0284989\pi$
$571$			102.109i			0.178825i	−0.995995	+	0.0894125i	$0.971501\pi$
$572$	4.15108	+	374.989i	0.00725713	+	0.655575i
$573$	−448.579			−0.782860
$574$		−	281.827i		−	0.490988i
$575$	−101.087			−0.175803
$576$	103.835			0.180269
$577$	−250.493			−0.434130			−0.217065	−	0.976157i	$-0.569648\pi$
$577$	−250.493			−0.434130			−0.217065	+	0.976157i	$0.569648\pi$
$578$		−	203.296i		−	0.351724i
$579$		−	213.969i		−	0.369549i
$580$			224.814i			0.387610i
$581$	−1615.36			−2.78031
$582$			322.179i			0.553572i
$583$	537.012	−	5.94465i	0.921118	−	0.0101967i
$584$	−314.771			−0.538991
$585$		−	94.1023i		−	0.160859i
$586$	−352.029			−0.600732
$587$	−76.0110			−0.129491			−0.0647453	−	0.997902i	$-0.520623\pi$
$587$	−76.0110			−0.129491			−0.0647453	+	0.997902i	$0.520623\pi$
$588$	−1120.56			−1.90571
$589$			1263.39i			2.14498i
$590$		−	38.0294i		−	0.0644566i
$591$			483.126i			0.817472i
$592$	437.816			0.739554
$593$		−	194.178i		−	0.327450i	−0.986506	−	0.163725i	$-0.947649\pi$
$593$		−	194.178i		−	0.327450i	0.986506	−	0.163725i	$-0.0523509\pi$
$594$	1.31360	+	118.664i	0.00221145	+	0.199772i
$595$	5.74550			0.00965631
$596$			4.50509i			0.00755888i
$597$	−31.9340			−0.0534908
$598$	32.8217			0.0548857
$599$	−365.873			−0.610806			−0.305403	−	0.952223i	$-0.598791\pi$
$599$	−365.873			−0.610806			−0.305403	+	0.952223i	$0.598791\pi$
$600$			414.743i			0.691239i
$601$			573.111i			0.953596i	0.879013	+	0.476798i	$0.158203\pi$
$601$			573.111i			0.953596i	−0.879013	+	0.476798i	$0.841797\pi$
$602$			261.762i			0.434821i
$603$	−175.845			−0.291617
$604$			1050.57i			1.73936i
$605$	−239.568	+	5.30464i	−0.395981	+	0.00876799i
$606$	93.2859			0.153937
$607$		−	110.986i		−	0.182844i	−0.995812	−	0.0914221i	$-0.970859\pi$
$607$		−	110.986i		−	0.182844i	0.995812	−	0.0914221i	$-0.0291412\pi$
$608$	−828.067			−1.36195
$609$	1401.23			2.30086
$610$	65.2151			0.106910
$611$			176.275i			0.288502i
$612$			4.27854i			0.00699108i
$613$			759.528i			1.23903i	0.784983	+	0.619517i	$0.212671\pi$
$613$			759.528i			1.23903i	−0.784983	+	0.619517i	$0.787329\pi$
$614$	204.951			0.333796
$615$			254.590i			0.413967i
$616$	674.344	−	7.46490i	1.09471	−	0.0121183i
$617$	−960.616			−1.55691			−0.778457	−	0.627698i	$-0.783997\pi$
$617$	−960.616			−1.55691			−0.778457	+	0.627698i	$0.783997\pi$
$618$			15.0153i			0.0242966i
$619$	−993.833			−1.60555			−0.802773	−	0.596285i	$-0.796643\pi$
$619$	−993.833			−1.60555			−0.802773	+	0.596285i	$0.796643\pi$
$620$	300.467			0.484624
$621$	−73.5347			−0.118413
$622$		−	280.958i		−	0.451701i
$623$		−	107.754i		−	0.172960i
$624$			373.483i			0.598530i
$625$	346.236			0.553977
$626$		−	68.0111i		−	0.108644i
$627$	−13.2421	−	1196.23i	−0.0211198	−	1.90786i
$628$	565.418			0.900347
$629$			10.6170i			0.0168792i
$630$	−79.0309			−0.125446
$631$	−1038.08			−1.64513			−0.822564	−	0.568672i	$-0.807457\pi$
$631$	−1038.08			−1.64513			−0.822564	+	0.568672i	$0.807457\pi$
$632$	632.516			1.00082
$633$			1556.92i			2.45959i
$634$		−	207.711i		−	0.327620i
$635$			179.320i			0.282394i
$636$	637.639			1.00258
$637$		−	834.542i		−	1.31011i
$638$	−250.659	+	2.77476i	−0.392882	+	0.00434915i
$639$	−310.511			−0.485933
$640$			254.368i			0.397451i
$641$	−1100.66			−1.71710			−0.858551	−	0.512729i	$-0.828635\pi$
$641$	−1100.66			−1.71710			−0.858551	+	0.512729i	$0.828635\pi$
$642$	−6.26819			−0.00976353
$643$	614.843			0.956210			0.478105	−	0.878303i	$-0.341324\pi$
$643$	614.843			0.956210			0.478105	+	0.878303i	$0.341324\pi$
$644$			195.158i			0.303041i
$645$		−	236.464i		−	0.366611i
$646$		−	5.13139i		−	0.00794332i
$647$	139.332			0.215351			0.107676	−	0.994186i	$-0.465659\pi$
$647$	139.332			0.215351			0.107676	+	0.994186i	$0.465659\pi$
$648$			533.865i			0.823866i
$649$	−300.199	+	3.32317i	−0.462556	+	0.00512044i
$650$	−144.254			−0.221929
$651$		−	1872.76i		−	2.87674i
$652$	−489.271			−0.750416
$653$	323.650			0.495635			0.247817	−	0.968807i	$-0.420287\pi$
$653$	323.650			0.495635			0.247817	+	0.968807i	$0.420287\pi$
$654$	100.585			0.153799
$655$			314.420i			0.480031i
$656$		−	355.500i		−	0.541920i
$657$		−	291.205i		−	0.443235i
$658$	148.043			0.224989
$659$		−	423.958i		−	0.643335i	−0.946853	−	0.321667i	$-0.895757\pi$
$659$		−	423.958i		−	0.643335i	0.946853	−	0.321667i	$-0.104243\pi$
$660$	−284.494	+	3.14932i	−0.431052	+	0.00477169i
$661$	396.034			0.599144			0.299572	−	0.954074i	$-0.403156\pi$
$661$	396.034			0.599144			0.299572	+	0.954074i	$0.403156\pi$
$662$			31.7550i			0.0479683i
$663$	−9.05695			−0.0136606
$664$	734.684			1.10645
$665$	−671.067			−1.00912
$666$		−	146.040i		−	0.219279i
$667$		−	155.330i		−	0.232878i
$668$		−	1080.45i		−	1.61744i
$669$	735.187			1.09893
$670$		−	50.1565i		−	0.0748605i
$671$	−5.69876	−	514.799i	−0.00849294	−	0.767212i
$672$	1227.47			1.82658
$673$			762.021i			1.13228i	0.824311	+	0.566138i	$0.191563\pi$
$673$			762.021i			1.13228i	−0.824311	+	0.566138i	$0.808437\pi$
$674$	119.109			0.176719
$675$	323.191			0.478801
$676$	260.730			0.385695
$677$			877.508i			1.29617i	0.761567	+	0.648086i	$0.224430\pi$
$677$			877.508i			1.29617i	−0.761567	+	0.648086i	$0.775570\pi$
$678$		−	260.266i		−	0.383873i
$679$		−	1426.71i		−	2.10120i
$680$	−2.61312			−0.00384283
$681$			737.615i			1.08314i
$682$	3.70851	+	335.009i	0.00543769	+	0.491215i
$683$	808.057			1.18310			0.591550	−	0.806268i	$-0.298516\pi$
$683$	808.057			1.18310			0.591550	+	0.806268i	$0.298516\pi$
$684$		−	499.728i		−	0.730596i
$685$	233.999			0.341604
$686$	−300.602			−0.438196
$687$	−643.345			−0.936455
$688$			330.190i			0.479927i
$689$			474.885i			0.689238i
$690$			24.9009i			0.0360883i
$691$	−671.447			−0.971704			−0.485852	−	0.874041i	$-0.661491\pi$
$691$	−671.447			−0.971704			−0.485852	+	0.874041i	$0.661491\pi$
$692$			891.416i			1.28817i
$693$	6.90605	+	623.859i	0.00996544	+	0.900230i
$694$	218.322			0.314584
$695$			359.491i			0.517254i
$696$	−637.294			−0.915652
$697$	8.62086			0.0123685
$698$	80.2276			0.114939
$699$		−	196.184i		−	0.280664i
$700$		−	857.736i		−	1.22534i
$701$		−	1063.53i		−	1.51716i	−0.651580	−	0.758580i	$-0.725893\pi$
$701$		−	1063.53i		−	1.51716i	0.651580	−	0.758580i	$-0.274107\pi$
$702$	−104.936			−0.149482
$703$		−	1240.05i		−	1.76395i
$704$	233.792	−	2.58805i	0.332091	−	0.00367621i
$705$	−133.735			−0.189695
$706$			44.8118i			0.0634729i
$707$	−413.101			−0.584302
$708$	−356.451			−0.503462
$709$	646.580			0.911960			0.455980	−	0.889990i	$-0.349289\pi$
$709$	646.580			0.911960			0.455980	+	0.889990i	$0.349289\pi$
$710$		−	88.5675i		−	0.124743i
$711$			585.163i			0.823014i
$712$			49.0078i			0.0688312i
$713$	−207.600			−0.291165
$714$			7.60639i			0.0106532i
$715$	−2.34547	−	211.879i	−0.00328038	−	0.296334i
$716$	1119.12			1.56302
$717$			147.974i			0.206380i
$718$	67.7239			0.0943230
$719$	−1075.38			−1.49565			−0.747827	−	0.663893i	$-0.768903\pi$
$719$	−1075.38			−1.49565			−0.747827	+	0.663893i	$0.768903\pi$
$720$	−99.6905			−0.138459
$721$		−	66.4927i		−	0.0922229i
$722$			345.339i			0.478309i
$723$			1622.75i			2.24447i
$724$	−466.962			−0.644975
$725$			682.687i			0.941637i
$726$	−7.02273	−	317.161i	−0.00967319	−	0.436861i
$727$	722.664			0.994036			0.497018	−	0.867740i	$-0.334428\pi$
$727$	722.664			0.994036			0.497018	+	0.867740i	$0.334428\pi$
$728$			596.329i			0.819133i
$729$	20.3191			0.0278725
$730$	83.0610			0.113782
$731$	−8.00710			−0.0109536
$732$		−	611.264i		−	0.835060i
$733$		−	856.241i		−	1.16813i	−0.811706	−	0.584066i	$-0.801461\pi$
$733$		−	856.241i		−	1.16813i	0.811706	−	0.584066i	$-0.198539\pi$
$734$		−	200.284i		−	0.272866i
$735$	633.145			0.861422
$736$		−	136.068i		−	0.184875i
$737$	−395.929	+	4.38288i	−0.537217	+	0.00594692i
$738$	−118.582			−0.160680
$739$			934.190i			1.26413i	0.774916	+	0.632064i	$0.217792\pi$
$739$			934.190i			1.26413i	−0.774916	+	0.632064i	$0.782208\pi$
$740$	−294.917			−0.398536
$741$	1057.84			1.42758
$742$	398.828			0.537504
$743$			1281.71i			1.72505i	0.506012	+	0.862527i	$0.331119\pi$
$743$			1281.71i			1.72505i	−0.506012	+	0.862527i	$0.668881\pi$
$744$			851.752i			1.14483i
$745$		−	2.54550i		−	0.00341678i
$746$	419.178			0.561901
$747$			679.682i			0.909883i
$748$	0.106641	+	9.63348i	0.000142569	+	0.0128790i
$749$	27.7576			0.0370596
$750$		−	239.247i		−	0.318996i
$751$	382.291			0.509043			0.254521	−	0.967067i	$-0.418082\pi$
$751$	382.291			0.509043			0.254521	+	0.967067i	$0.418082\pi$
$752$	186.743			0.248328
$753$	536.904			0.713020
$754$		−	221.660i		−	0.293979i
$755$		−	593.603i		−	0.786229i
$756$		−	623.953i		−	0.825334i
$757$	477.647			0.630974			0.315487	−	0.948930i	$-0.397832\pi$
$757$	477.647			0.630974			0.315487	+	0.948930i	$0.397832\pi$
$758$		−	197.500i		−	0.260554i
$759$	196.565	−	2.17595i	0.258978	−	0.00286686i
$760$	305.209			0.401591
$761$		−	1243.89i		−	1.63455i	−0.576247	−	0.817275i	$-0.695484\pi$
$761$		−	1243.89i		−	1.63455i	0.576247	−	0.817275i	$-0.304516\pi$
$762$	−237.399			−0.311548
$763$	−445.423			−0.583778
$764$	−421.934			−0.552270
$765$		−	2.41749i		−	0.00316012i
$766$			277.532i			0.362314i
$767$		−	265.469i		−	0.346113i
$768$	−19.9445			−0.0259694
$769$		−	216.593i		−	0.281655i	−0.990034	−	0.140828i	$-0.955024\pi$
$769$		−	216.593i		−	0.281655i	0.990034	−	0.140828i	$-0.0449763\pi$
$770$	−177.944	+	1.96982i	−0.231097	+	0.00255821i
$771$	−1593.98			−2.06742
$772$		−	201.260i		−	0.260699i
$773$	−900.023			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$773$	−900.023			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$774$	110.140			0.142299
$775$	912.420			1.17732
$776$			648.887i			0.836194i
$777$			1838.17i			2.36572i
$778$			347.087i			0.446128i
$779$	−1006.90			−1.29256
$780$		−	251.581i		−	0.322540i
$781$	−699.140	+	7.73940i	−0.895186	+	0.00990960i
$782$	0.843190			0.00107825
$783$			496.614i			0.634245i
$784$	−884.101			−1.12768
$785$	−319.476			−0.406976
$786$	−416.256			−0.529588
$787$		−	187.916i		−	0.238774i	−0.992848	−	0.119387i	$-0.961907\pi$
$787$		−	187.916i		−	0.238774i	0.992848	−	0.119387i	$-0.0380930\pi$
$788$			454.429i			0.576687i
$789$		−	850.999i		−	1.07858i
$790$	−166.907			−0.211275
$791$			1152.55i			1.45707i
$792$	−3.14095	−	283.739i	−0.00396585	−	0.358256i
$793$	455.242			0.574076
$794$			295.967i			0.372755i
$795$	−360.283			−0.453186
$796$	−30.0372			−0.0377352
$797$	−506.433			−0.635425			−0.317712	−	0.948187i	$-0.602915\pi$
$797$	−506.433			−0.635425			−0.317712	+	0.948187i	$0.602915\pi$
$798$		−	888.416i		−	1.11330i
$799$			4.52851i			0.00566772i
$800$			598.029i			0.747537i
$801$	−45.3389			−0.0566028
$802$			506.258i			0.631245i
$803$	−7.25821	−	655.672i	−0.00903887	−	0.816528i
$804$	−470.119			−0.584725
$805$		−	110.270i		−	0.136981i
$806$	−296.252			−0.367558
$807$	1611.64			1.99708
$808$	187.883			0.232529
$809$		−	1150.44i		−	1.42205i	−0.703166	−	0.711026i	$-0.748231\pi$
$809$		−	1150.44i		−	1.42205i	0.703166	−	0.711026i	$-0.251769\pi$
$810$		−	140.875i		−	0.173920i
$811$		−	579.421i		−	0.714453i	−0.934018	−	0.357226i	$-0.883722\pi$
$811$		−	579.421i		−	0.714453i	0.934018	−	0.357226i	$-0.116278\pi$
$812$	1318.00			1.62315
$813$		−	393.206i		−	0.483649i
$814$	−3.64001	−	328.821i	−0.00447175	−	0.403957i
$815$	276.451			0.339204
$816$			9.59479i			0.0117583i
$817$	935.217			1.14470
$818$	265.766			0.324897
$819$	−551.685			−0.673608
$820$			239.468i			0.292034i
$821$		−	575.883i		−	0.701441i	−0.936480	−	0.350721i	$-0.885937\pi$
$821$		−	575.883i		−	0.701441i	0.936480	−	0.350721i	$-0.114063\pi$
$822$			309.788i			0.376871i
$823$	236.800			0.287728			0.143864	−	0.989597i	$-0.454047\pi$
$823$	236.800			0.287728			0.143864	+	0.989597i	$0.454047\pi$
$824$			30.2417i			0.0367011i
$825$	−863.917	+	9.56346i	−1.04717	+	0.0115921i
$826$	−222.952			−0.269917
$827$			1004.62i			1.21478i	0.794404	+	0.607389i	$0.207783\pi$
$827$			1004.62i			1.21478i	−0.794404	+	0.607389i	$0.792217\pi$
$828$	82.1153			0.0991731
$829$	1062.33			1.28146			0.640729	−	0.767767i	$-0.278632\pi$
$829$	1062.33			1.28146			0.640729	+	0.767767i	$0.278632\pi$
$830$	−193.867			−0.233575
$831$		−	744.687i		−	0.896134i
$832$			206.745i			0.248491i
$833$		−	21.4394i		−	0.0257376i
$834$	−475.925			−0.570654
$835$			610.482i			0.731117i
$836$	−12.4556	−	1125.18i	−0.0148990	−	1.34591i
$837$	663.732			0.792989
$838$		−	474.261i		−	0.565943i
$839$	720.469			0.858724			0.429362	−	0.903133i	$-0.358738\pi$
$839$	720.469			0.858724			0.429362	+	0.903133i	$0.358738\pi$
$840$	−452.419			−0.538595
$841$	−208.014			−0.247342
$842$		−	319.757i		−	0.379759i
$843$		−	1741.84i		−	2.06624i
$844$			1464.44i			1.73512i
$845$	−147.319			−0.174342
$846$		−	62.2908i		−	0.0736298i
$847$	31.0990	+	1404.50i	0.0367167	+	1.65820i
$848$	503.086			0.593262
$849$		−	1468.92i		−	1.73018i
$850$	−3.70589			−0.00435987
$851$	203.766			0.239443
$852$	−830.147			−0.974351
$853$			461.992i			0.541609i	0.962634	+	0.270804i	$0.0872897\pi$
$853$			461.992i			0.541609i	−0.962634	+	0.270804i	$0.912710\pi$
$854$		−	382.331i		−	0.447694i
$855$			282.360i			0.330245i
$856$	−12.6245			−0.0147482
$857$			306.615i			0.357777i	0.983869	+	0.178888i	$0.0572501\pi$
$857$			306.615i			0.357777i	−0.983869	+	0.178888i	$0.942750\pi$
$858$	280.503	−	3.10514i	0.326927	−	0.00361904i
$859$	−620.173			−0.721971			−0.360985	−	0.932572i	$-0.617560\pi$
$859$	−620.173			−0.721971			−0.360985	+	0.932572i	$0.617560\pi$
$860$		−	222.419i		−	0.258626i
$861$	1492.56			1.73352
$862$	418.456			0.485447
$863$	698.049			0.808863			0.404431	−	0.914568i	$-0.367469\pi$
$863$	698.049			0.808863			0.404431	+	0.914568i	$0.367469\pi$
$864$			435.031i			0.503508i
$865$		−	503.674i		−	0.582282i
$866$		−	269.103i		−	0.310743i
$867$	1076.66			1.24182
$868$		−	1761.52i		−	2.02940i
$869$	14.5850	+	1317.54i	0.0167837	+	1.51616i
$870$	168.168			0.193296
$871$		−	350.124i		−	0.401979i
$872$	202.584			0.232321
$873$	−600.308			−0.687638
$874$	−98.4834			−0.112681
$875$			1059.46i			1.21082i
$876$		−	778.534i		−	0.888737i
$877$		−	791.973i		−	0.903048i	−0.892259	−	0.451524i	$-0.850881\pi$
$877$		−	791.973i		−	0.903048i	0.892259	−	0.451524i	$-0.149119\pi$
$878$	321.684			0.366382
$879$		−	1864.35i		−	2.12099i
$880$	−224.461	+	2.48476i	−0.255069	+	0.00282359i
$881$	−1106.71			−1.25620			−0.628098	−	0.778134i	$-0.716166\pi$
$881$	−1106.71			−1.25620			−0.628098	+	0.778134i	$0.716166\pi$
$882$			294.905i			0.334359i
$883$	−483.052			−0.547058			−0.273529	−	0.961864i	$-0.588191\pi$
$883$	−483.052			−0.547058			−0.273529	+	0.961864i	$0.588191\pi$
$884$	−8.51899			−0.00963686
$885$	201.405			0.227576
$886$		−	128.326i		−	0.144837i
$887$			841.033i			0.948177i	0.880477	+	0.474088i	$0.157222\pi$
$887$			841.033i			0.948177i	−0.880477	+	0.474088i	$0.842778\pi$
$888$		−	836.019i		−	0.941463i
$889$	1051.28			1.18255
$890$		−	12.9321i		−	0.0145304i
$891$	−1112.05	+	12.3103i	−1.24809	+	0.0138162i
$892$	691.518			0.775245
$893$		−	528.923i		−	0.592299i
$894$	3.36995			0.00376952
$895$	−632.334			−0.706519
$896$	1491.26			1.66436
$897$			173.824i			0.193784i
$898$			68.9028i			0.0767292i
$899$			1402.02i			1.55954i
$900$	−360.903			−0.401004
$901$			12.1998i			0.0135403i
$902$	−266.997	+	2.95563i	−0.296006	+	0.00327675i
$903$	−1386.30			−1.53521
$904$		−	524.191i		−	0.579858i
$905$	263.846			0.291543
$906$	785.863			0.867398
$907$	1522.59			1.67871			0.839357	−	0.543580i	$-0.182931\pi$
$907$	1522.59			1.67871			0.839357	+	0.543580i	$0.182931\pi$
$908$			693.803i			0.764100i
$909$			173.818i			0.191218i
$910$		−	157.358i		−	0.172921i
$911$	501.279			0.550251			0.275125	−	0.961408i	$-0.411281\pi$
$911$	501.279			0.550251			0.275125	+	0.961408i	$0.411281\pi$
$912$		−	1120.66i		−	1.22879i
$913$	16.9409	+	1530.36i	0.0185552	+	1.67619i
$914$	164.528			0.180009
$915$			345.380i			0.377465i
$916$	−605.131			−0.660624
$917$	1843.32			2.01017
$918$	−2.69581			−0.00293662
$919$			337.336i			0.367068i	0.983013	+	0.183534i	$0.0587538\pi$
$919$			337.336i			0.367068i	−0.983013	+	0.183534i	$0.941246\pi$
$920$			50.1520i			0.0545130i
$921$			1085.42i			1.17853i
$922$	−85.6187			−0.0928620
$923$		−	618.257i		−	0.669834i
$924$	18.4632	+	1667.88i	0.0199818	+	1.80506i
$925$	−895.567			−0.968180
$926$		−	196.796i		−	0.212522i
$927$	−27.9776			−0.0301808
$928$	−918.930			−0.990227
$929$	1214.27			1.30708			0.653538	−	0.756894i	$-0.273284\pi$
$929$	1214.27			1.30708			0.653538	+	0.756894i	$0.273284\pi$
$930$		−	224.759i		−	0.241676i
$931$			2504.09i			2.68968i
$932$		−	184.531i		−	0.197995i
$933$	1487.96			1.59481
$934$		−	168.543i		−	0.180453i
$935$	−0.0602553	−	5.44318i	−6.44442e−5	−	0.00582158i
$936$	250.913			0.268069
$937$			357.662i			0.381710i	0.981618	+	0.190855i	$0.0611260\pi$
$937$			357.662i			0.381710i	−0.981618	+	0.190855i	$0.938874\pi$
$938$	−294.048			−0.313484
$939$	360.188			0.383587
$940$	−125.792			−0.133821
$941$			89.8930i			0.0955292i	0.998859	+	0.0477646i	$0.0152097\pi$
$941$			89.8930i			0.0955292i	−0.998859	+	0.0477646i	$0.984790\pi$
$942$		−	422.950i		−	0.448992i
$943$		−	165.455i		−	0.175456i
$944$	−281.234			−0.297917
$945$			352.550i			0.373069i
$946$	247.988	−	2.74520i	0.262144	−	0.00290190i
$947$	118.257			0.124875			0.0624375	−	0.998049i	$-0.480113\pi$
$947$	118.257			0.124875			0.0624375	+	0.998049i	$0.480113\pi$
$948$			1564.43i			1.65024i
$949$	579.818			0.610977
$950$	432.842			0.455623
$951$	1100.04			1.15672
$952$			15.3197i			0.0160921i
$953$		−	1376.56i		−	1.44445i	−0.691660	−	0.722223i	$-0.743120\pi$
$953$		−	1376.56i		−	1.44445i	0.691660	−	0.722223i	$-0.256880\pi$
$954$		−	167.812i		−	0.175903i
$955$	238.404			0.249638
$956$			139.185i			0.145591i
$957$	−14.6952	−	1327.49i	−0.0153555	−	1.38714i
$958$	−147.141			−0.153592
$959$		−	1371.84i		−	1.43049i
$960$	−156.852			−0.163387
$961$	912.824			0.949869
$962$	290.780			0.302266
$963$		−	11.6794i		−	0.0121281i
$964$			1526.36i			1.58336i
$965$			113.717i			0.117842i
$966$	145.985			0.151123
$967$		−	1127.11i		−	1.16558i	−0.812624	−	0.582789i	$-0.801962\pi$
$967$		−	1127.11i		−	1.16558i	0.812624	−	0.582789i	$-0.198038\pi$
$968$	−14.1442	−	638.782i	−0.0146118	−	0.659898i
$969$	27.1759			0.0280453
$970$		−	171.227i		−	0.176523i
$971$	−1563.51			−1.61020			−0.805102	−	0.593136i	$-0.797890\pi$
$971$	−1563.51			−1.61020			−0.805102	+	0.593136i	$0.797890\pi$
$972$	−836.756			−0.860860
$973$	2107.56			2.16604
$974$			300.380i			0.308398i
$975$		−	763.971i		−	0.783560i
$976$		−	482.277i		−	0.494136i
$977$	37.5412			0.0384250			0.0192125	−	0.999815i	$-0.493884\pi$
$977$	37.5412			0.0384250			0.0192125	+	0.999815i	$0.493884\pi$
$978$			365.990i			0.374223i
$979$	−102.084	+	1.13006i	−0.104274	+	0.00115430i
$980$	595.538			0.607692
$981$			187.417i			0.191047i
$982$	13.3183			0.0135624
$983$	436.375			0.443921			0.221961	−	0.975056i	$-0.428754\pi$
$983$	436.375			0.443921			0.221961	+	0.975056i	$0.428754\pi$
$984$	−678.834			−0.689872
$985$		−	256.765i		−	0.260675i
$986$		−	5.69446i		−	0.00577531i
$987$			784.037i			0.794363i
$988$	995.005			1.00709
$989$			153.675i			0.155384i
$990$	0.828828	+	74.8723i	0.000837200	+	0.0756286i
$991$	421.446			0.425273			0.212637	−	0.977131i	$-0.431795\pi$
$991$	421.446			0.425273			0.212637	+	0.977131i	$0.431795\pi$
$992$			1228.16i			1.23807i
$993$	−168.175			−0.169361
$994$	−519.237			−0.522371
$995$	16.9718			0.0170571
$996$			1817.12i			1.82442i
$997$		−	1400.04i		−	1.40425i	−0.712053	−	0.702126i	$-0.752235\pi$
$997$		−	1400.04i		−	1.40425i	0.712053	−	0.702126i	$-0.247765\pi$
$998$			88.0617i			0.0882382i
$999$	−651.472			−0.652124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.20	✓	44
11.10	odd	2	inner	253.3.c.a.208.25	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.20	✓	44	1.1	even	1	trivial
253.3.c.a.208.25	yes	44	11.10	odd	2	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:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.703600i q^{2} +3.72628 q^{3} +3.50495 q^{4} -1.98039 q^{5} -2.62181i q^{6} +11.6103i q^{7} -5.28048i q^{8} +4.88516 q^{9} +1.39340i q^{10} +(10.9993 - 0.121761i) q^{11} +13.0604 q^{12} +9.72682i q^{13} +8.16898 q^{14} -7.37949 q^{15} +10.3044 q^{16} +0.249882i q^{17} -3.43720i q^{18} -29.1859i q^{19} -6.94116 q^{20} +43.2631i q^{21} +(-0.0856712 - 7.73913i) q^{22} +4.79583 q^{23} -19.6765i q^{24} -21.0781 q^{25} +6.84379 q^{26} -15.3330 q^{27} +40.6933i q^{28} -32.3885i q^{29} +5.19221i q^{30} -43.2877 q^{31} -28.3721i q^{32} +(40.9866 - 0.453716i) q^{33} +0.175817 q^{34} -22.9928i q^{35} +17.1222 q^{36} +42.4881 q^{37} -20.5352 q^{38} +36.2448i q^{39} +10.4574i q^{40} -34.4997i q^{41} +30.4399 q^{42} +32.0435i q^{43} +(38.5521 - 0.426767i) q^{44} -9.67452 q^{45} -3.37435i q^{46} +18.1225 q^{47} +38.3972 q^{48} -85.7980 q^{49} +14.8305i q^{50} +0.931132i q^{51} +34.0920i q^{52} +48.8222 q^{53} +10.7883i q^{54} +(-21.7830 + 0.241135i) q^{55} +61.3077 q^{56} -108.755i q^{57} -22.7885 q^{58} -27.2925 q^{59} -25.8647 q^{60} -46.8028i q^{61} +30.4572i q^{62} +56.7180i q^{63} +21.2551 q^{64} -19.2629i q^{65} +(-0.319235 - 28.8381i) q^{66} -35.9957 q^{67} +0.875825i q^{68} +17.8706 q^{69} -16.1778 q^{70} -63.5621 q^{71} -25.7960i q^{72} -59.6102i q^{73} -29.8946i q^{74} -78.5427 q^{75} -102.295i q^{76} +(1.41368 + 127.705i) q^{77} +25.5019 q^{78} +119.784i q^{79} -20.4068 q^{80} -101.102 q^{81} -24.2740 q^{82} +139.132i q^{83} +151.635i q^{84} -0.494865i q^{85} +22.5458 q^{86} -120.689i q^{87} +(-0.642958 - 58.0817i) q^{88} -9.28094 q^{89} +6.80699i q^{90} -112.931 q^{91} +16.8091 q^{92} -161.302 q^{93} -12.7510i q^{94} +57.7995i q^{95} -105.722i q^{96} -122.884 q^{97} +60.3675i q^{98} +(53.7335 - 0.594823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more