LMFDB - Embedded newform 253.3.c.a.208.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(208,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("253.208"); S:= CuspForms(chi, 3); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			208.27
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.09200i q^{2} +1.62306 q^{3} +2.80754 q^{4} +7.64004 q^{5} +1.77238i q^{6} +6.41879i q^{7} +7.43383i q^{8} -6.36568 q^{9} +8.34293i q^{10} +(-5.22182 + 9.68156i) q^{11} +4.55680 q^{12} -11.7166i q^{13} -7.00932 q^{14} +12.4002 q^{15} +3.11239 q^{16} -28.2618i q^{17} -6.95132i q^{18} +0.740083i q^{19} +21.4497 q^{20} +10.4181i q^{21} +(-10.5723 - 5.70223i) q^{22} -4.79583 q^{23} +12.0656i q^{24} +33.3702 q^{25} +12.7945 q^{26} -24.9394 q^{27} +18.0210i q^{28} -9.49203i q^{29} +13.5411i q^{30} -46.8460 q^{31} +33.1341i q^{32} +(-8.47532 + 15.7138i) q^{33} +30.8619 q^{34} +49.0398i q^{35} -17.8719 q^{36} +67.1068 q^{37} -0.808171 q^{38} -19.0167i q^{39} +56.7948i q^{40} -10.1557i q^{41} -11.3766 q^{42} -53.5537i q^{43} +(-14.6604 + 27.1813i) q^{44} -48.6340 q^{45} -5.23705i q^{46} +10.1611 q^{47} +5.05160 q^{48} +7.79912 q^{49} +36.4403i q^{50} -45.8706i q^{51} -32.8947i q^{52} -4.65727 q^{53} -27.2339i q^{54} +(-39.8949 + 73.9675i) q^{55} -47.7162 q^{56} +1.20120i q^{57} +10.3653 q^{58} +56.0868 q^{59} +34.8141 q^{60} -13.8941i q^{61} -51.1558i q^{62} -40.8599i q^{63} -23.7328 q^{64} -89.5151i q^{65} +(-17.1594 - 9.25506i) q^{66} -4.31938 q^{67} -79.3459i q^{68} -7.78392 q^{69} -53.5515 q^{70} +6.30778 q^{71} -47.3214i q^{72} +64.0503i q^{73} +73.2807i q^{74} +54.1619 q^{75} +2.07781i q^{76} +(-62.1439 - 33.5178i) q^{77} +20.7663 q^{78} -31.1637i q^{79} +23.7788 q^{80} +16.8129 q^{81} +11.0900 q^{82} +109.725i q^{83} +29.2491i q^{84} -215.921i q^{85} +58.4807 q^{86} -15.4061i q^{87} +(-71.9711 - 38.8181i) q^{88} -93.6954 q^{89} -53.1084i q^{90} +75.2063 q^{91} -13.4645 q^{92} -76.0338 q^{93} +11.0959i q^{94} +5.65426i q^{95} +53.7786i q^{96} +1.35617 q^{97} +8.51664i q^{98} +(33.2404 - 61.6297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.09200i			0.546000i	0.962014	+	0.273000i	$0.0880159\pi$
$2$			1.09200i			0.546000i	−0.962014	+	0.273000i	$0.911984\pi$
$3$	1.62306			0.541020			0.270510	−	0.962717i	$-0.412808\pi$
$3$	1.62306			0.541020			0.270510	+	0.962717i	$0.412808\pi$
$4$	2.80754			0.701884
$5$	7.64004			1.52801			0.764004	−	0.645212i	$-0.223231\pi$
$5$	7.64004			1.52801			0.764004	+	0.645212i	$0.223231\pi$
$6$			1.77238i			0.295397i
$7$			6.41879i			0.916970i	0.888702	+	0.458485i	$0.151608\pi$
$7$			6.41879i			0.916970i	−0.888702	+	0.458485i	$0.848392\pi$
$8$			7.43383i			0.929229i
$9$	−6.36568			−0.707297
$10$			8.34293i			0.834293i
$11$	−5.22182	+	9.68156i	−0.474711	+	0.880142i
$11$	−5.22182	+	9.68156i	−0.474711	+	0.880142i
$12$	4.55680			0.379733
$13$		−	11.7166i		−	0.901275i	−0.892707	−	0.450638i	$-0.851197\pi$
$13$		−	11.7166i		−	0.901275i	0.892707	−	0.450638i	$-0.148803\pi$
$14$	−7.00932			−0.500666
$15$	12.4002			0.826683
$16$	3.11239			0.194525
$17$		−	28.2618i		−	1.66246i	−0.555931	−	0.831229i	$-0.687638\pi$
$17$		−	28.2618i		−	1.66246i	0.555931	−	0.831229i	$-0.312362\pi$
$18$		−	6.95132i		−	0.386184i
$19$			0.740083i			0.0389517i	0.999810	+	0.0194759i	$0.00619975\pi$
$19$			0.740083i			0.0389517i	−0.999810	+	0.0194759i	$0.993800\pi$
$20$	21.4497			1.07248
$21$			10.4181i			0.496099i
$22$	−10.5723	−	5.70223i	−0.480558	−	0.259192i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$			12.0656i			0.502731i
$25$	33.3702			1.33481
$26$	12.7945			0.492096
$27$	−24.9394			−0.923682
$28$			18.0210i			0.643606i
$29$		−	9.49203i		−	0.327311i	−0.986518	−	0.163656i	$-0.947671\pi$
$29$		−	9.49203i		−	0.327311i	0.986518	−	0.163656i	$-0.0523286\pi$
$30$			13.5411i			0.451369i
$31$	−46.8460			−1.51116			−0.755580	−	0.655056i	$-0.772645\pi$
$31$	−46.8460			−1.51116			−0.755580	+	0.655056i	$0.772645\pi$
$32$			33.1341i			1.03544i
$33$	−8.47532	+	15.7138i	−0.256828	+	0.476174i
$34$	30.8619			0.907702
$35$			49.0398i			1.40114i
$36$	−17.8719			−0.496440
$37$	67.1068			1.81370			0.906849	−	0.421456i	$-0.138481\pi$
$37$	67.1068			1.81370			0.906849	+	0.421456i	$0.138481\pi$
$38$	−0.808171			−0.0212677
$39$		−	19.0167i		−	0.487608i
$40$			56.7948i			1.41987i
$41$		−	10.1557i		−	0.247700i	−0.992301	−	0.123850i	$-0.960476\pi$
$41$		−	10.1557i		−	0.247700i	0.992301	−	0.123850i	$-0.0395241\pi$
$42$	−11.3766			−0.270870
$43$		−	53.5537i		−	1.24544i	−0.782447	−	0.622718i	$-0.786029\pi$
$43$		−	53.5537i		−	1.24544i	0.782447	−	0.622718i	$-0.213971\pi$
$44$	−14.6604	+	27.1813i	−0.333192	+	0.617757i
$45$	−48.6340			−1.08076
$46$		−	5.23705i		−	0.113849i
$47$	10.1611			0.216193			0.108096	−	0.994140i	$-0.465525\pi$
$47$	10.1611			0.216193			0.108096	+	0.994140i	$0.465525\pi$
$48$	5.05160			0.105242
$49$	7.79912			0.159166
$50$			36.4403i			0.728806i
$51$		−	45.8706i		−	0.899423i
$52$		−	32.8947i		−	0.632590i
$53$	−4.65727			−0.0878731			−0.0439366	−	0.999034i	$-0.513990\pi$
$53$	−4.65727			−0.0878731			−0.0439366	+	0.999034i	$0.513990\pi$
$54$		−	27.2339i		−	0.504331i
$55$	−39.8949	+	73.9675i	−0.725362	+	1.34486i
$56$	−47.7162			−0.852075
$57$			1.20120i			0.0210737i
$58$	10.3653			0.178712
$59$	56.0868			0.950623			0.475311	−	0.879818i	$-0.342335\pi$
$59$	56.0868			0.950623			0.475311	+	0.879818i	$0.342335\pi$
$60$	34.8141			0.580235
$61$		−	13.8941i		−	0.227771i	−0.993494	−	0.113886i	$-0.963670\pi$
$61$		−	13.8941i		−	0.227771i	0.993494	−	0.113886i	$-0.0363298\pi$
$62$		−	51.1558i		−	0.825094i
$63$		−	40.8599i		−	0.648571i
$64$	−23.7328			−0.370826
$65$		−	89.5151i		−	1.37716i
$66$	−17.1594	−	9.25506i	−0.259991	−	0.140228i
$67$	−4.31938			−0.0644683			−0.0322341	−	0.999480i	$-0.510262\pi$
$67$	−4.31938			−0.0644683			−0.0322341	+	0.999480i	$0.510262\pi$
$68$		−	79.3459i		−	1.16685i
$69$	−7.78392			−0.112810
$70$	−53.5515			−0.765021
$71$	6.30778			0.0888420			0.0444210	−	0.999013i	$-0.485856\pi$
$71$	6.30778			0.0888420			0.0444210	+	0.999013i	$0.485856\pi$
$72$		−	47.3214i		−	0.657241i
$73$			64.0503i			0.877402i	0.898633	+	0.438701i	$0.144561\pi$
$73$			64.0503i			0.877402i	−0.898633	+	0.438701i	$0.855439\pi$
$74$			73.2807i			0.990279i
$75$	54.1619			0.722158
$76$			2.07781i			0.0273396i
$77$	−62.1439	−	33.5178i	−0.807064	−	0.435295i
$78$	20.7663			0.266234
$79$		−	31.1637i		−	0.394478i	−0.980355	−	0.197239i	$-0.936803\pi$
$79$		−	31.1637i		−	0.394478i	0.980355	−	0.197239i	$-0.0631975\pi$
$80$	23.7788			0.297235
$81$	16.8129			0.207567
$82$	11.0900			0.135244
$83$			109.725i			1.32199i	0.750391	+	0.660994i	$0.229865\pi$
$83$			109.725i			1.32199i	−0.750391	+	0.660994i	$0.770135\pi$
$84$			29.2491i			0.348204i
$85$		−	215.921i		−	2.54025i
$86$	58.4807			0.680008
$87$		−	15.4061i		−	0.177082i
$88$	−71.9711	−	38.8181i	−0.817853	−	0.441115i
$89$	−93.6954			−1.05276			−0.526379	−	0.850250i	$-0.676451\pi$
$89$	−93.6954			−1.05276			−0.526379	+	0.850250i	$0.676451\pi$
$90$		−	53.1084i		−	0.590093i
$91$	75.2063			0.826442
$92$	−13.4645			−0.146353
$93$	−76.0338			−0.817568
$94$			11.0959i			0.118041i
$95$			5.65426i			0.0595186i
$96$			53.7786i			0.560193i
$97$	1.35617			0.0139812			0.00699058	−	0.999976i	$-0.497775\pi$
$97$	1.35617			0.0139812			0.00699058	+	0.999976i	$0.497775\pi$
$98$			8.51664i			0.0869045i
$99$	33.2404	−	61.6297i	0.335762	−	0.622522i
$100$	93.6880			0.936880
$101$		−	1.02162i		−	0.0101150i	−0.999987	−	0.00505751i	$-0.998390\pi$
$101$		−	1.02162i		−	0.0101150i	0.999987	−	0.00505751i	$-0.00160986\pi$
$102$	50.0907			0.491085
$103$	−137.376			−1.33375			−0.666874	−	0.745170i	$-0.732368\pi$
$103$	−137.376			−1.33375			−0.666874	+	0.745170i	$0.732368\pi$
$104$	87.0991			0.837491
$105$			79.5946i			0.758044i
$106$		−	5.08575i		−	0.0479787i
$107$			147.336i			1.37697i	0.725250	+	0.688486i	$0.241724\pi$
$107$			147.336i			1.37697i	−0.725250	+	0.688486i	$0.758276\pi$
$108$	−70.0183			−0.648317
$109$		−	204.845i		−	1.87931i	−0.342122	−	0.939656i	$-0.611146\pi$
$109$		−	204.845i		−	1.87931i	0.342122	−	0.939656i	$-0.388854\pi$
$110$	−80.7726	−	43.5652i	−0.734296	−	0.396048i
$111$	108.918			0.981247
$112$			19.9778i			0.178373i
$113$	−120.078			−1.06263			−0.531317	−	0.847173i	$-0.678303\pi$
$113$	−120.078			−1.06263			−0.531317	+	0.847173i	$0.678303\pi$
$114$	−1.31171			−0.0115062
$115$	−36.6403			−0.318612
$116$		−	26.6492i		−	0.229734i
$117$			74.5839i			0.637469i
$118$			61.2468i			0.519040i
$119$	181.406			1.52442
$120$			92.1813i			0.768178i
$121$	−66.4653	−	101.111i	−0.549300	−	0.835625i
$122$	15.1723			0.124363
$123$		−	16.4833i		−	0.134010i
$124$	−131.522			−1.06066
$125$	63.9487			0.511590
$126$	44.6191			0.354120
$127$		−	235.090i		−	1.85110i	−0.378624	−	0.925551i	$-0.623603\pi$
$127$		−	235.090i		−	1.85110i	0.378624	−	0.925551i	$-0.376397\pi$
$128$			106.620i			0.832969i
$129$		−	86.9209i		−	0.673806i
$130$	97.7505			0.751927
$131$		−	5.90984i		−	0.0451133i	−0.999746	−	0.0225566i	$-0.992819\pi$
$131$		−	5.90984i		−	0.0451133i	0.999746	−	0.0225566i	$-0.00718061\pi$
$132$	−23.7948	+	44.1169i	−0.180263	+	0.334219i
$133$	−4.75044			−0.0357176
$134$		−	4.71676i		−	0.0351997i
$135$	−190.538			−1.41139
$136$	210.093			1.54480
$137$	−50.7013			−0.370083			−0.185041	−	0.982731i	$-0.559242\pi$
$137$	−50.7013			−0.370083			−0.185041	+	0.982731i	$0.559242\pi$
$138$		−	8.50005i		−	0.0615945i
$139$			49.2168i			0.354078i	0.984204	+	0.177039i	$0.0566519\pi$
$139$			49.2168i			0.354078i	−0.984204	+	0.177039i	$0.943348\pi$
$140$			137.681i			0.983436i
$141$	16.4920			0.116965
$142$			6.88810i			0.0485077i
$143$	113.435	+	61.1818i	0.793250	+	0.427845i
$144$	−19.8125			−0.137587
$145$		−	72.5195i		−	0.500134i
$146$	−69.9430			−0.479062
$147$	12.6584			0.0861118
$148$	188.405			1.27300
$149$			213.132i			1.43042i	0.698911	+	0.715208i	$0.253668\pi$
$149$			213.132i			1.43042i	−0.698911	+	0.715208i	$0.746332\pi$
$150$			59.1448i			0.394298i
$151$		−	93.7847i		−	0.621091i	−0.950559	−	0.310545i	$-0.899488\pi$
$151$		−	93.7847i		−	0.621091i	0.950559	−	0.310545i	$-0.100512\pi$
$152$	−5.50165			−0.0361951
$153$			179.905i			1.17585i
$154$	36.6014	−	67.8612i	0.237671	−	0.440657i
$155$	−357.905			−2.30906
$156$		−	53.3901i		−	0.342244i
$157$	−258.359			−1.64560			−0.822799	−	0.568332i	$-0.807589\pi$
$157$	−258.359			−1.64560			−0.822799	+	0.568332i	$0.807589\pi$
$158$	34.0308			0.215385
$159$	−7.55904			−0.0475411
$160$			253.146i			1.58216i
$161$		−	30.7834i		−	0.191202i
$162$			18.3597i			0.113331i
$163$	92.2391			0.565884			0.282942	−	0.959137i	$-0.408690\pi$
$163$	92.2391			0.565884			0.282942	+	0.959137i	$0.408690\pi$
$164$		−	28.5124i		−	0.173856i
$165$	−64.7518	+	120.054i	−0.392435	+	0.727598i
$166$	−119.820			−0.721806
$167$			129.704i			0.776668i	0.921519	+	0.388334i	$0.126949\pi$
$167$			129.704i			0.776668i	−0.921519	+	0.388334i	$0.873051\pi$
$168$	−77.4463			−0.460990
$169$	31.7218			0.187703
$170$	235.786			1.38698
$171$		−	4.71113i		−	0.0275505i
$172$		−	150.354i		−	0.874151i
$173$			271.696i			1.57049i	0.619182	+	0.785247i	$0.287464\pi$
$173$			271.696i			1.57049i	−0.619182	+	0.785247i	$0.712536\pi$
$174$	16.8235			0.0966868
$175$			214.196i			1.22398i
$176$	−16.2523	+	30.1328i	−0.0923429	+	0.171209i
$177$	91.0322			0.514306
$178$		−	102.315i		−	0.574806i
$179$	157.143			0.877894			0.438947	−	0.898513i	$-0.355352\pi$
$179$	157.143			0.877894			0.438947	+	0.898513i	$0.355352\pi$
$180$	−136.542			−0.758565
$181$	130.345			0.720140			0.360070	−	0.932925i	$-0.382753\pi$
$181$	130.345			0.720140			0.360070	+	0.932925i	$0.382753\pi$
$182$			82.1253i			0.451238i
$183$		−	22.5509i		−	0.123229i
$184$		−	35.6514i		−	0.193758i
$185$	512.699			2.77134
$186$		−	83.0289i		−	0.446392i
$187$	273.618	+	147.578i	1.46320	+	0.789186i
$188$	28.5275			0.151742
$189$		−	160.081i		−	0.846989i
$190$	−6.17446			−0.0324971
$191$	−5.67086			−0.0296904			−0.0148452	−	0.999890i	$-0.504726\pi$
$191$	−5.67086			−0.0296904			−0.0148452	+	0.999890i	$0.504726\pi$
$192$	−38.5198			−0.200624
$193$			267.014i			1.38349i	0.722140	+	0.691747i	$0.243159\pi$
$193$			267.014i			1.38349i	−0.722140	+	0.691747i	$0.756841\pi$
$194$			1.48094i			0.00763371i
$195$		−	145.288i		−	0.745069i
$196$	21.8963			0.111716
$197$		−	63.8217i		−	0.323968i	−0.986793	−	0.161984i	$-0.948211\pi$
$197$		−	63.8217i		−	0.323968i	0.986793	−	0.161984i	$-0.0517893\pi$
$198$	67.2996	+	36.2985i	0.339897	+	0.183326i
$199$	−253.734			−1.27504			−0.637522	−	0.770432i	$-0.720041\pi$
$199$	−253.734			−1.27504			−0.637522	+	0.770432i	$0.720041\pi$
$200$			248.068i			1.24034i
$201$	−7.01061			−0.0348786
$202$	1.11561			0.00552280
$203$	60.9273			0.300135
$204$		−	128.783i		−	0.631290i
$205$		−	77.5898i		−	0.378487i
$206$		−	150.015i		−	0.728227i
$207$	30.5287			0.147482
$208$		−	36.4666i		−	0.175320i
$209$	−7.16516	−	3.86458i	−0.0342831	−	0.0184908i
$210$	−86.9173			−0.413892
$211$			75.1073i			0.355959i	0.984034	+	0.177979i	$0.0569560\pi$
$211$			75.1073i			0.355959i	−0.984034	+	0.177979i	$0.943044\pi$
$212$	−13.0755			−0.0616767
$213$	10.2379			0.0480653
$214$	−160.891			−0.751827
$215$		−	409.153i		−	1.90304i
$216$		−	185.395i		−	0.858312i
$217$		−	300.694i		−	1.38569i
$218$	223.691			1.02610
$219$			103.958i			0.474692i
$220$	−112.006	+	207.666i	−0.509120	+	0.943938i
$221$	−331.131			−1.49833
$222$			118.939i			0.535761i
$223$	−165.774			−0.743380			−0.371690	−	0.928357i	$-0.621222\pi$
$223$	−165.774			−0.743380			−0.371690	+	0.928357i	$0.621222\pi$
$224$	−212.681			−0.949467
$225$	−212.424			−0.944106
$226$		−	131.125i		−	0.580198i
$227$			335.726i			1.47897i	0.673174	+	0.739484i	$0.264930\pi$
$227$			335.726i			1.47897i	−0.673174	+	0.739484i	$0.735070\pi$
$228$			3.37241i			0.0147913i
$229$	289.563			1.26447			0.632234	−	0.774778i	$-0.282138\pi$
$229$	289.563			1.26447			0.632234	+	0.774778i	$0.282138\pi$
$230$		−	40.0113i		−	0.173962i
$231$	−100.863	−	54.4013i	−0.436638	−	0.235504i
$232$	70.5621			0.304147
$233$		−	121.192i		−	0.520138i	−0.965590	−	0.260069i	$-0.916255\pi$
$233$		−	121.192i		−	0.520138i	0.965590	−	0.260069i	$-0.0837454\pi$
$234$	−81.4457			−0.348058
$235$	77.6309			0.330344
$236$	157.466			0.667227
$237$		−	50.5806i		−	0.213420i
$238$			198.096i			0.832336i
$239$			359.123i			1.50261i	0.659958	+	0.751303i	$0.270574\pi$
$239$			359.123i			1.50261i	−0.659958	+	0.751303i	$0.729426\pi$
$240$	38.5944			0.160810
$241$		−	249.115i		−	1.03367i	−0.856085	−	0.516836i	$-0.827110\pi$
$241$		−	249.115i		−	1.03367i	0.856085	−	0.516836i	$-0.172890\pi$
$242$	110.413	−	72.5801i	0.456252	−	0.299918i
$243$	251.743			1.03598
$244$		−	39.0080i		−	0.159869i
$245$	59.5856			0.243206
$246$	17.9998			0.0731697
$247$	8.67124			0.0351062
$248$		−	348.245i		−	1.40421i
$249$			178.090i			0.715223i
$250$			69.8320i			0.279328i
$251$	−172.223			−0.686146			−0.343073	−	0.939309i	$-0.611468\pi$
$251$	−172.223			−0.686146			−0.343073	+	0.939309i	$0.611468\pi$
$252$		−	114.716i		−	0.455221i
$253$	25.0430	−	46.4311i	0.0989840	−	0.183522i
$254$	256.718			1.01070
$255$		−	350.453i		−	1.37433i
$256$	−211.360			−0.825627
$257$	268.046			1.04298			0.521490	−	0.853258i	$-0.325377\pi$
$257$	268.046			1.04298			0.521490	+	0.853258i	$0.325377\pi$
$258$	94.9177			0.367898
$259$			430.745i			1.66311i
$260$		−	251.317i		−	0.966603i
$261$			60.4232i			0.231506i
$262$	6.45355			0.0246319
$263$		−	213.813i		−	0.812977i	−0.913656	−	0.406488i	$-0.866753\pi$
$263$		−	213.813i		−	0.812977i	0.913656	−	0.406488i	$-0.133247\pi$
$264$	−116.813	−	63.0041i	−0.442475	−	0.238652i
$265$	−35.5818			−0.134271
$266$		−	5.18748i		−	0.0195018i
$267$	−152.073			−0.569563
$268$	−12.1268			−0.0452492
$269$	−233.791			−0.869111			−0.434555	−	0.900645i	$-0.643094\pi$
$269$	−233.791			−0.869111			−0.434555	+	0.900645i	$0.643094\pi$
$270$		−	208.068i		−	0.770621i
$271$		−	170.435i		−	0.628910i	−0.949272	−	0.314455i	$-0.898178\pi$
$271$		−	170.435i		−	0.628910i	0.949272	−	0.314455i	$-0.101822\pi$
$272$		−	87.9618i		−	0.323389i
$273$	122.064			0.447122
$274$		−	55.3659i		−	0.202065i
$275$	−174.253	+	323.076i	−0.633648	+	1.17482i
$276$	−21.8536			−0.0791798
$277$			291.870i			1.05368i	0.849964	+	0.526841i	$0.176624\pi$
$277$			291.870i			1.05368i	−0.849964	+	0.526841i	$0.823376\pi$
$278$	−53.7448			−0.193327
$279$	298.206			1.06884
$280$	−364.554			−1.30198
$281$		−	177.126i		−	0.630341i	−0.949035	−	0.315171i	$-0.897938\pi$
$281$		−	177.126i		−	0.630341i	0.949035	−	0.315171i	$-0.102062\pi$
$282$			18.0093i			0.0638627i
$283$		−	139.267i		−	0.492110i	−0.969256	−	0.246055i	$-0.920866\pi$
$283$		−	139.267i		−	0.492110i	0.969256	−	0.246055i	$-0.0791344\pi$
$284$	17.7093			0.0623567
$285$			9.17721i			0.0322007i
$286$	−66.8106	+	123.871i	−0.233603	+	0.433115i
$287$	65.1872			0.227133
$288$		−	210.921i		−	0.732363i
$289$	−509.728			−1.76376
$290$	79.1913			0.273073
$291$	2.20115			0.00756409
$292$			179.824i			0.615834i
$293$			454.142i			1.54997i	0.631978	+	0.774986i	$0.282243\pi$
$293$			454.142i			1.54997i	−0.631978	+	0.774986i	$0.717757\pi$
$294$			13.8230i			0.0470171i
$295$	428.505			1.45256
$296$			498.861i			1.68534i
$297$	130.229	−	241.452i	0.438482	−	0.812971i
$298$	−232.740			−0.781008
$299$			56.1907i			0.187929i
$300$	152.061			0.506871
$301$	343.750			1.14203
$302$	102.413			0.339116
$303$		−	1.65815i		−	0.00547243i
$304$			2.30343i			0.00757707i
$305$		−	106.151i		−	0.348036i
$306$	−196.457			−0.642015
$307$			160.556i			0.522982i	0.965206	+	0.261491i	$0.0842142\pi$
$307$			160.556i			0.522982i	−0.965206	+	0.261491i	$0.915786\pi$
$308$	−174.471	−	94.1023i	−0.566465	−	0.305527i
$309$	−222.970			−0.721585
$310$		−	390.832i		−	1.26075i
$311$	−151.792			−0.488077			−0.244038	−	0.969766i	$-0.578472\pi$
$311$	−151.792			−0.488077			−0.244038	+	0.969766i	$0.578472\pi$
$312$	141.367			0.453099
$313$	−518.355			−1.65609			−0.828043	−	0.560664i	$-0.810546\pi$
$313$	−518.355			−1.65609			−0.828043	+	0.560664i	$0.810546\pi$
$314$		−	282.128i		−	0.898497i
$315$		−	312.172i		−	0.991021i
$316$		−	87.4933i		−	0.276878i
$317$	−160.589			−0.506591			−0.253295	−	0.967389i	$-0.581514\pi$
$317$	−160.589			−0.506591			−0.253295	+	0.967389i	$0.581514\pi$
$318$		−	8.25447i		−	0.0259575i
$319$	91.8976	+	49.5656i	0.288080	+	0.155378i
$320$	−181.320			−0.566624
$321$			239.135i			0.744970i
$322$	33.6155			0.104396
$323$	20.9161			0.0647556
$324$	47.2028			0.145688
$325$		−	390.985i		−	1.20303i
$326$			100.725i			0.308973i
$327$		−	332.476i		−	1.01675i
$328$	75.4956			0.230170
$329$			65.2217i			0.198242i
$330$	−131.099	−	70.7090i	−0.397269	−	0.214270i
$331$	170.115			0.513941			0.256971	−	0.966419i	$-0.417276\pi$
$331$	170.115			0.513941			0.256971	+	0.966419i	$0.417276\pi$
$332$			308.057i			0.927883i
$333$	−427.180			−1.28282
$334$	−141.636			−0.424061
$335$	−33.0002			−0.0985081
$336$			32.4252i			0.0965035i
$337$		−	439.608i		−	1.30447i	−0.758015	−	0.652237i	$-0.773831\pi$
$337$		−	439.608i		−	1.30447i	0.758015	−	0.652237i	$-0.226169\pi$
$338$			34.6402i			0.102486i
$339$	−194.893			−0.574906
$340$		−	606.206i		−	1.78296i
$341$	244.621	−	453.542i	0.717364	−	1.33004i
$342$	5.14455			0.0150426
$343$			364.582i			1.06292i
$344$	398.109			1.15729
$345$	−59.4695			−0.172375
$346$	−296.692			−0.857490
$347$			276.110i			0.795705i	0.917449	+	0.397853i	$0.130244\pi$
$347$			276.110i			0.795705i	−0.917449	+	0.397853i	$0.869756\pi$
$348$		−	43.2532i		−	0.124291i
$349$			458.907i			1.31492i	0.753489	+	0.657460i	$0.228369\pi$
$349$			458.907i			1.31492i	−0.753489	+	0.657460i	$0.771631\pi$
$350$	−233.903			−0.668293
$351$			292.205i			0.832492i
$352$	−320.789	−	173.020i	−0.911334	−	0.491534i
$353$	57.7569			0.163617			0.0818087	−	0.996648i	$-0.473930\pi$
$353$	57.7569			0.163617			0.0818087	+	0.996648i	$0.473930\pi$
$354$			99.4072i			0.280811i
$355$	48.1917			0.135751
$356$	−263.053			−0.738913
$357$	294.434			0.824744
$358$			171.600i			0.479330i
$359$		−	683.381i		−	1.90357i	−0.306767	−	0.951785i	$-0.599247\pi$
$359$		−	683.381i		−	1.90357i	0.306767	−	0.951785i	$-0.400753\pi$
$360$		−	361.537i		−	1.00427i
$361$	360.452			0.998483
$362$			142.337i			0.393197i
$363$	−107.877	−	164.109i	−0.297182	−	0.452090i
$364$	211.144			0.580067
$365$			489.347i			1.34068i
$366$	24.6256			0.0672830
$367$	529.091			1.44167			0.720833	−	0.693109i	$-0.243760\pi$
$367$	529.091			1.44167			0.720833	+	0.693109i	$0.243760\pi$
$368$	−14.9265			−0.0405612
$369$			64.6478i			0.175197i
$370$			559.867i			1.51315i
$371$		−	29.8941i		−	0.0805770i
$372$	−213.468			−0.573838
$373$		−	420.707i		−	1.12790i	−0.825809	−	0.563950i	$-0.809281\pi$
$373$		−	420.707i		−	1.12790i	0.825809	−	0.563950i	$-0.190719\pi$
$374$	−161.155	+	298.791i	−0.430896	+	0.798907i
$375$	103.793			0.276780
$376$			75.5356i			0.200892i
$377$	−111.214			−0.294998
$378$	174.808			0.462456
$379$	188.323			0.496896			0.248448	−	0.968645i	$-0.420080\pi$
$379$	188.323			0.496896			0.248448	+	0.968645i	$0.420080\pi$
$380$			15.8745i			0.0417751i
$381$		−	381.565i		−	1.00148i
$382$		−	6.19258i		−	0.0162110i
$383$	−250.445			−0.653904			−0.326952	−	0.945041i	$-0.606022\pi$
$383$	−250.445			−0.653904			−0.326952	+	0.945041i	$0.606022\pi$
$384$			173.051i			0.450653i
$385$	−474.782	−	256.077i	−1.23320	−	0.665135i
$386$	−291.580			−0.755388
$387$			340.906i			0.880893i
$388$	3.80750			0.00981315
$389$	618.618			1.59028			0.795139	−	0.606428i	$-0.207398\pi$
$389$	618.618			1.59028			0.795139	+	0.606428i	$0.207398\pi$
$390$	158.655			0.406808
$391$			135.539i			0.346646i
$392$			57.9773i			0.147901i
$393$		−	9.59203i		−	0.0244072i
$394$	69.6933			0.176887
$395$		−	238.092i		−	0.602765i
$396$	93.3236	−	173.027i	0.235666	−	0.436938i
$397$	669.346			1.68601			0.843005	−	0.537906i	$-0.180785\pi$
$397$	669.346			1.68601			0.843005	+	0.537906i	$0.180785\pi$
$398$		−	277.077i		−	0.696174i
$399$	−7.71025			−0.0193239
$400$	103.861			0.259653
$401$	118.969			0.296681			0.148341	−	0.988936i	$-0.452607\pi$
$401$	118.969			0.296681			0.148341	+	0.988936i	$0.452607\pi$
$402$		−	7.65558i		−	0.0190437i
$403$			548.874i			1.36197i
$404$		−	2.86823i		−	0.00709957i
$405$	128.451			0.317164
$406$			66.5327i			0.163874i
$407$	−350.419	+	649.699i	−0.860981	+	1.59631i
$408$	340.994			0.835770
$409$			132.590i			0.324180i	0.986776	+	0.162090i	$0.0518235\pi$
$409$			132.590i			0.324180i	−0.986776	+	0.162090i	$0.948176\pi$
$410$	84.7281			0.206654
$411$	−82.2913			−0.200222
$412$	−385.688			−0.936137
$413$			360.009i			0.871693i
$414$			33.3374i			0.0805250i
$415$			838.304i			2.02001i
$416$	388.218			0.933216
$417$			79.8819i			0.191563i
$418$	4.22012	−	7.82436i	0.0100960	−	0.0187186i
$419$	−134.730			−0.321550			−0.160775	−	0.986991i	$-0.551399\pi$
$419$	−134.730			−0.321550			−0.160775	+	0.986991i	$0.551399\pi$
$420$			223.465i			0.532059i
$421$	−142.606			−0.338732			−0.169366	−	0.985553i	$-0.554172\pi$
$421$	−142.606			−0.338732			−0.169366	+	0.985553i	$0.554172\pi$
$422$	−82.0172			−0.194353
$423$	−64.6820			−0.152912
$424$		−	34.6214i		−	0.0816542i
$425$		−	943.101i		−	2.21906i
$426$			11.1798i			0.0262437i
$427$	89.1830			0.208860
$428$			413.651i			0.966474i
$429$	184.111	+	99.3018i	0.429164	+	0.231473i
$430$	446.795			1.03906
$431$		−	664.557i		−	1.54190i	−0.636898	−	0.770948i	$-0.719783\pi$
$431$		−	664.557i		−	1.54190i	0.636898	−	0.770948i	$-0.280217\pi$
$432$	−77.6213			−0.179679
$433$	−251.446			−0.580707			−0.290353	−	0.956920i	$-0.593773\pi$
$433$	−251.446			−0.580707			−0.290353	+	0.956920i	$0.593773\pi$
$434$	328.358			0.756586
$435$		−	117.703i		−	0.270583i
$436$		−	575.109i		−	1.31906i
$437$		−	3.54931i		−	0.00812200i
$438$	−113.522			−0.259182
$439$			496.366i			1.13067i	0.824860	+	0.565337i	$0.191254\pi$
$439$			496.366i			1.13067i	−0.824860	+	0.565337i	$0.808746\pi$
$440$	−549.862	−	296.572i	−1.24969	−	0.674027i
$441$	−49.6467			−0.112577
$442$		−	361.596i		−	0.818089i
$443$	735.902			1.66118			0.830589	−	0.556886i	$-0.188004\pi$
$443$	735.902			1.66118			0.830589	+	0.556886i	$0.188004\pi$
$444$	305.792			0.688721
$445$	−715.836			−1.60862
$446$		−	181.025i		−	0.405886i
$447$			345.926i			0.773884i
$448$		−	152.336i		−	0.340036i
$449$	741.308			1.65102			0.825510	−	0.564387i	$-0.190887\pi$
$449$	741.308			1.65102			0.825510	+	0.564387i	$0.190887\pi$
$450$		−	231.967i		−	0.515482i
$451$	98.3229	+	53.0311i	0.218011	+	0.117586i
$452$	−337.122			−0.745845
$453$		−	152.218i		−	0.336023i
$454$	−366.612			−0.807516
$455$	574.579			1.26281
$456$	−8.92951			−0.0195823
$457$			575.862i			1.26009i	0.776558	+	0.630046i	$0.216964\pi$
$457$			575.862i			1.26009i	−0.776558	+	0.630046i	$0.783036\pi$
$458$			316.203i			0.690400i
$459$			704.832i			1.53558i
$460$	−102.869			−0.223628
$461$			348.384i			0.755713i	0.925864	+	0.377857i	$0.123339\pi$
$461$			348.384i			0.755713i	−0.925864	+	0.377857i	$0.876661\pi$
$462$	59.4063	−	110.143i	0.128585	−	0.238404i
$463$	−62.7153			−0.135454			−0.0677271	−	0.997704i	$-0.521575\pi$
$463$	−62.7153			−0.135454			−0.0677271	+	0.997704i	$0.521575\pi$
$464$		−	29.5429i		−	0.0636701i
$465$	−580.901			−1.24925
$466$	132.342			0.283996
$467$	722.228			1.54653			0.773264	−	0.634085i	$-0.218623\pi$
$467$	722.228			1.54653			0.773264	+	0.634085i	$0.218623\pi$
$468$			209.397i			0.447429i
$469$		−	27.7252i		−	0.0591155i
$470$			84.7729i			0.180368i
$471$	−419.332			−0.890302
$472$			416.939i			0.883346i
$473$	518.484	+	279.648i	1.09616	+	0.591221i
$474$	55.2341			0.116528
$475$			24.6967i			0.0519931i
$476$	509.305			1.06997
$477$	29.6467			0.0621524
$478$	−392.162			−0.820423
$479$			632.481i			1.32042i	0.751081	+	0.660210i	$0.229533\pi$
$479$			632.481i			1.32042i	−0.751081	+	0.660210i	$0.770467\pi$
$480$			410.870i			0.855980i
$481$		−	786.262i		−	1.63464i
$482$	272.034			0.564385
$483$		−	49.9634i		−	0.103444i
$484$	−186.604	−	283.872i	−0.385545	−	0.586512i
$485$	10.3612			0.0213633
$486$			274.904i			0.565645i
$487$	586.950			1.20524			0.602618	−	0.798030i	$-0.294124\pi$
$487$	586.950			1.20524			0.602618	+	0.798030i	$0.294124\pi$
$488$	103.286			0.211652
$489$	149.710			0.306155
$490$			65.0675i			0.132791i
$491$		−	666.289i		−	1.35700i	−0.734598	−	0.678502i	$-0.762629\pi$
$491$		−	666.289i		−	1.35700i	0.734598	−	0.678502i	$-0.237371\pi$
$492$		−	46.2774i		−	0.0940597i
$493$	−268.262			−0.544141
$494$			9.46900i			0.0191680i
$495$	253.958	−	470.853i	0.513046	−	0.951219i
$496$	−145.803			−0.293958
$497$			40.4883i			0.0814654i
$498$	−194.475			−0.390512
$499$	−146.172			−0.292930			−0.146465	−	0.989216i	$-0.546790\pi$
$499$	−146.172			−0.292930			−0.146465	+	0.989216i	$0.546790\pi$
$500$	179.538			0.359076
$501$			210.517i			0.420193i
$502$		−	188.067i		−	0.374636i
$503$			416.063i			0.827164i	0.910467	+	0.413582i	$0.135722\pi$
$503$			416.063i			0.827164i	−0.910467	+	0.413582i	$0.864278\pi$
$504$	303.746			0.602670
$505$		−	7.80520i		−	0.0154558i
$506$	50.7028	+	27.3469i	0.100203	+	0.0540453i
$507$	51.4864			0.101551
$508$		−	660.023i		−	1.29926i
$509$	−397.969			−0.781865			−0.390932	−	0.920419i	$-0.627847\pi$
$509$	−397.969			−0.781865			−0.390932	+	0.920419i	$0.627847\pi$
$510$	382.695			0.750382
$511$	−411.126			−0.804551
$512$			195.674i			0.382176i
$513$		−	18.4572i		−	0.0359790i
$514$			292.706i			0.569467i
$515$	−1049.56			−2.03798
$516$		−	244.034i		−	0.472933i
$517$	−53.0592	+	98.3749i	−0.102629	+	0.190280i
$518$	−470.373			−0.908057
$519$			440.978i			0.849669i
$520$	665.440			1.27969
$521$	−916.115			−1.75838			−0.879189	−	0.476473i	$-0.841915\pi$
$521$	−916.115			−1.75838			−0.879189	+	0.476473i	$0.841915\pi$
$522$	−65.9821			−0.126403
$523$		−	671.538i		−	1.28401i	−0.766700	−	0.642006i	$-0.778103\pi$
$523$		−	671.538i		−	1.28401i	0.766700	−	0.642006i	$-0.221897\pi$
$524$		−	16.5921i		−	0.0316643i
$525$			347.654i			0.662197i
$526$	233.484			0.443885
$527$			1323.95i			2.51224i
$528$	−26.3785	+	48.9074i	−0.0499594	+	0.0926276i
$529$	23.0000			0.0434783
$530$		−	38.8553i		−	0.0733119i
$531$	−357.030			−0.672373
$532$	−13.3370			−0.0250696
$533$	−118.990			−0.223245
$534$		−	166.064i		−	0.310981i
$535$			1125.65i			2.10402i
$536$		−	32.1095i		−	0.0599058i
$537$	255.053			0.474958
$538$		−	255.300i		−	0.474535i
$539$	−40.7256	+	75.5076i	−0.0755576	+	0.140088i
$540$	−534.942			−0.990634
$541$		−	754.982i		−	1.39553i	−0.716326	−	0.697765i	$-0.754178\pi$
$541$		−	754.982i		−	1.39553i	0.716326	−	0.697765i	$-0.245822\pi$
$542$	186.115			0.343385
$543$	211.558			0.389610
$544$	936.427			1.72137
$545$		−	1565.02i		−	2.87160i
$546$			133.294i			0.244129i
$547$		−	433.105i		−	0.791783i	−0.918297	−	0.395892i	$-0.870436\pi$
$547$		−	433.105i		−	0.791783i	0.918297	−	0.395892i	$-0.129564\pi$
$548$	−142.346			−0.259755
$549$			88.4450i			0.161102i
$550$	−352.799	−	190.284i	−0.641452	−	0.345972i
$551$	7.02489			0.0127493
$552$		−	57.8644i		−	0.104827i
$553$	200.034			0.361724
$554$	−318.722			−0.575310
$555$	832.141			1.49935
$556$			138.178i			0.248522i
$557$			26.3908i			0.0473802i	0.999719	+	0.0236901i	$0.00754150\pi$
$557$			26.3908i			0.0473802i	−0.999719	+	0.0236901i	$0.992458\pi$
$558$			325.641i			0.583586i
$559$	−627.466			−1.12248
$560$			152.631i			0.272556i
$561$	444.099	+	239.528i	0.791620	+	0.426966i
$562$	193.422			0.344167
$563$			144.090i			0.255933i	0.991778	+	0.127967i	$0.0408451\pi$
$563$			144.090i			0.255933i	−0.991778	+	0.127967i	$0.959155\pi$
$564$	46.3019			0.0820955
$565$	−917.397			−1.62371
$566$	152.080			0.268692
$567$			107.919i			0.190332i
$568$			46.8910i			0.0825545i
$569$		−	723.390i		−	1.27134i	−0.771963	−	0.635668i	$-0.780725\pi$
$569$		−	723.390i		−	1.27134i	0.771963	−	0.635668i	$-0.219275\pi$
$570$	−10.0215			−0.0175816
$571$			126.844i			0.222143i	0.993812	+	0.111071i	$0.0354282\pi$
$571$			126.844i			0.222143i	−0.993812	+	0.111071i	$0.964572\pi$
$572$	318.472	+	171.770i	0.556769	+	0.300297i
$573$	−9.20415			−0.0160631
$574$			71.1845i			0.124015i
$575$	−160.038			−0.278327
$576$	151.076			0.262284
$577$	46.2464			0.0801498			0.0400749	−	0.999197i	$-0.487240\pi$
$577$	46.2464			0.0801498			0.0400749	+	0.999197i	$0.487240\pi$
$578$		−	556.623i		−	0.963016i
$579$			433.380i			0.748498i
$580$		−	203.601i		−	0.351036i
$581$	−704.302			−1.21222
$582$			2.40366i			0.00412999i
$583$	24.3194	−	45.0897i	0.0417143	−	0.0773408i
$584$	−476.139			−0.815307
$585$			569.824i			0.974058i
$586$	−495.923			−0.846286
$587$	−966.024			−1.64570			−0.822848	−	0.568261i	$-0.807616\pi$
$587$	−966.024			−1.64570			−0.822848	+	0.568261i	$0.807616\pi$
$588$	35.5390			0.0604405
$589$		−	34.6699i		−	0.0588623i
$590$			467.928i			0.793098i
$591$		−	103.586i		−	0.175273i
$592$	208.863			0.352809
$593$		−	883.864i		−	1.49050i	−0.666788	−	0.745248i	$-0.732331\pi$
$593$		−	883.864i		−	1.49050i	0.666788	−	0.745248i	$-0.267669\pi$
$594$	263.666	+	142.210i	0.443883	+	0.239411i
$595$	1385.95			2.32933
$596$			598.376i			1.00399i
$597$	−411.825			−0.689825
$598$	−61.3603			−0.102609
$599$	857.927			1.43227			0.716133	−	0.697964i	$-0.245910\pi$
$599$	857.927			1.43227			0.716133	+	0.697964i	$0.245910\pi$
$600$			402.630i			0.671050i
$601$		−	733.292i		−	1.22012i	−0.792355	−	0.610060i	$-0.791145\pi$
$601$		−	733.292i		−	1.22012i	0.792355	−	0.610060i	$-0.208855\pi$
$602$			375.375i			0.623547i
$603$	27.4957			0.0455982
$604$		−	263.304i		−	0.435934i
$605$	−507.797	−	772.490i	−0.839334	−	1.27684i
$606$	1.81070			0.00298795
$607$			233.363i			0.384453i	0.981351	+	0.192226i	$0.0615708\pi$
$607$			233.363i			0.384453i	−0.981351	+	0.192226i	$0.938429\pi$
$608$	−24.5220			−0.0403322
$609$	98.8887			0.162379
$610$	115.917			0.190028
$611$		−	119.053i		−	0.194849i
$612$			505.090i			0.825311i
$613$			650.289i			1.06083i	0.847738	+	0.530415i	$0.177964\pi$
$613$			650.289i			1.06083i	−0.847738	+	0.530415i	$0.822036\pi$
$614$	−175.327			−0.285548
$615$		−	125.933i		−	0.204769i
$616$	249.165	−	461.967i	0.404489	−	0.749947i
$617$	−1142.33			−1.85142			−0.925711	−	0.378233i	$-0.876532\pi$
$617$	−1142.33			−1.85142			−0.925711	+	0.378233i	$0.876532\pi$
$618$		−	243.483i		−	0.393985i
$619$	638.219			1.03105			0.515524	−	0.856875i	$-0.327597\pi$
$619$	638.219			1.03105			0.515524	+	0.856875i	$0.327597\pi$
$620$	−1004.83			−1.62069
$621$	119.605			0.192601
$622$		−	165.757i		−	0.266490i
$623$		−	601.411i		−	0.965347i
$624$		−	59.1875i		−	0.0948517i
$625$	−345.684			−0.553095
$626$		−	566.044i		−	0.904224i
$627$	−11.6295	−	6.27244i	−0.0185478	−	0.0100039i
$628$	−725.352			−1.15502
$629$		−	1896.56i		−	3.01520i
$630$	340.891			0.541098
$631$	662.231			1.04950			0.524748	−	0.851258i	$-0.324160\pi$
$631$	662.231			1.04950			0.524748	+	0.851258i	$0.324160\pi$
$632$	231.666			0.366560
$633$			121.904i			0.192581i
$634$		−	175.364i		−	0.276599i
$635$		−	1796.10i		−	2.82850i
$636$	−21.2223			−0.0333683
$637$		−	91.3790i		−	0.143452i
$638$	−54.1257	+	100.352i	−0.0848365	+	0.157292i
$639$	−40.1533			−0.0628377
$640$			814.581i			1.27278i
$641$	−373.060			−0.581996			−0.290998	−	0.956724i	$-0.593987\pi$
$641$	−373.060			−0.581996			−0.290998	+	0.956724i	$0.593987\pi$
$642$	−261.136			−0.406754
$643$	−745.562			−1.15951			−0.579753	−	0.814792i	$-0.696851\pi$
$643$	−745.562			−1.15951			−0.579753	+	0.814792i	$0.696851\pi$
$644$		−	86.4256i		−	0.134201i
$645$		−	664.079i		−	1.02958i
$646$			22.8403i			0.0353566i
$647$	−405.581			−0.626864			−0.313432	−	0.949611i	$-0.601479\pi$
$647$	−405.581			−0.626864			−0.313432	+	0.949611i	$0.601479\pi$
$648$			124.984i			0.192877i
$649$	−292.875	+	543.007i	−0.451271	+	0.836683i
$650$	426.955			0.656854
$651$		−	488.045i		−	0.749685i
$652$	258.965			0.397185
$653$	1017.79			1.55864			0.779318	−	0.626628i	$-0.215566\pi$
$653$	1017.79			1.55864			0.779318	+	0.626628i	$0.215566\pi$
$654$	363.064			0.555143
$655$		−	45.1514i		−	0.0689335i
$656$		−	31.6085i		−	0.0481837i
$657$		−	407.724i		−	0.620584i
$658$	−71.2221			−0.108240
$659$		−	836.253i		−	1.26897i	−0.772934	−	0.634486i	$-0.781212\pi$
$659$		−	836.253i		−	1.26897i	0.772934	−	0.634486i	$-0.218788\pi$
$660$	−181.793	+	337.055i	−0.275444	+	0.510689i
$661$	414.058			0.626411			0.313205	−	0.949685i	$-0.398597\pi$
$661$	414.058			0.626411			0.313205	+	0.949685i	$0.398597\pi$
$662$			185.765i			0.280612i
$663$	−537.446			−0.810628
$664$	−815.678			−1.22843
$665$	−36.2935			−0.0545767
$666$		−	466.481i		−	0.700422i
$667$			45.5222i			0.0682491i
$668$			364.147i			0.545131i
$669$	−269.061			−0.402184
$670$		−	36.0362i		−	0.0537854i
$671$	134.516	+	72.5522i	0.200471	+	0.108125i
$672$	−345.193			−0.513681
$673$		−	119.258i		−	0.177204i	−0.996067	−	0.0886020i	$-0.971760\pi$
$673$		−	119.258i		−	0.177204i	0.996067	−	0.0886020i	$-0.0282399\pi$
$674$	480.052			0.712243
$675$	−832.233			−1.23294
$676$	89.0601			0.131746
$677$			187.148i			0.276437i	0.990402	+	0.138218i	$0.0441376\pi$
$677$			187.148i			0.276437i	−0.990402	+	0.138218i	$0.955862\pi$
$678$		−	212.823i		−	0.313899i
$679$			8.70499i			0.0128203i
$680$	1605.12			2.36047
$681$			544.903i			0.800151i
$682$	495.268	+	267.126i	0.726199	+	0.391681i
$683$	323.044			0.472977			0.236489	−	0.971634i	$-0.424003\pi$
$683$	323.044			0.472977			0.236489	+	0.971634i	$0.424003\pi$
$684$		−	13.2267i		−	0.0193372i
$685$	−387.360			−0.565489
$686$	−398.123			−0.580355
$687$	469.978			0.684102
$688$		−	166.680i		−	0.242268i
$689$			54.5673i			0.0791978i
$690$		−	64.9407i		−	0.0941170i
$691$	−981.418			−1.42029			−0.710143	−	0.704057i	$-0.751370\pi$
$691$	−981.418			−1.42029			−0.710143	+	0.704057i	$0.751370\pi$
$692$			762.795i			1.10230i
$693$	395.588	+	213.363i	0.570834	+	0.307883i
$694$	−301.512			−0.434455
$695$			376.019i			0.541034i
$696$	114.527			0.164550
$697$	−287.018			−0.411790
$698$	−501.127			−0.717947
$699$		−	196.702i		−	0.281405i
$700$			601.364i			0.859091i
$701$		−	122.016i		−	0.174059i	−0.996206	−	0.0870296i	$-0.972263\pi$
$701$		−	122.016i		−	0.174059i	0.996206	−	0.0870296i	$-0.0277375\pi$
$702$	−319.088			−0.454541
$703$			49.6646i			0.0706467i
$704$	123.929	−	229.771i	0.176035	−	0.326379i
$705$	126.000			0.178723
$706$			63.0706i			0.0893351i
$707$	6.55755			0.00927517
$708$	255.576			0.360983
$709$	998.822			1.40878			0.704388	−	0.709815i	$-0.251222\pi$
$709$	998.822			1.40878			0.704388	+	0.709815i	$0.251222\pi$
$710$			52.6253i			0.0741202i
$711$			198.378i			0.279013i
$712$		−	696.516i		−	0.978252i
$713$	224.665			0.315099
$714$			321.522i			0.450310i
$715$	866.646	+	467.432i	1.21209	+	0.653750i
$716$	441.185			0.616179
$717$			582.878i			0.812940i
$718$	746.253			1.03935
$719$	−505.751			−0.703409			−0.351704	−	0.936111i	$-0.614398\pi$
$719$	−505.751			−0.703409			−0.351704	+	0.936111i	$0.614398\pi$
$720$	−151.368			−0.210234
$721$		−	881.789i		−	1.22301i
$722$			393.614i			0.545172i
$723$		−	404.328i		−	0.559237i
$724$	365.949			0.505455
$725$		−	316.751i		−	0.436898i
$726$	179.207	−	117.802i	0.246841	−	0.162262i
$727$	817.446			1.12441			0.562205	−	0.826998i	$-0.309953\pi$
$727$	817.446			1.12441			0.562205	+	0.826998i	$0.309953\pi$
$728$			559.071i			0.767954i
$729$	257.278			0.352919
$730$	−534.367			−0.732010
$731$	−1513.52			−2.07048
$732$		−	63.3124i		−	0.0864923i
$733$		−	836.566i		−	1.14129i	−0.821197	−	0.570645i	$-0.806693\pi$
$733$		−	836.566i		−	1.14129i	0.821197	−	0.570645i	$-0.193307\pi$
$734$			577.768i			0.787149i
$735$	96.7110			0.131580
$736$		−	158.905i		−	0.215904i
$737$	22.5550	−	41.8183i	0.0306038	−	0.0567412i
$738$	−70.5954			−0.0956577
$739$			1258.25i			1.70264i	0.524644	+	0.851322i	$0.324198\pi$
$739$			1258.25i			1.70264i	−0.524644	+	0.851322i	$0.675802\pi$
$740$	1439.42			1.94516
$741$	14.0739			0.0189932
$742$	32.6443			0.0439951
$743$		−	81.6684i		−	0.109917i	−0.998489	−	0.0549585i	$-0.982497\pi$
$743$		−	81.6684i		−	0.109917i	0.998489	−	0.0549585i	$-0.0175027\pi$
$744$		−	565.222i		−	0.759708i
$745$			1628.34i			2.18569i
$746$	459.412			0.615834
$747$		−	698.474i		−	0.935039i
$748$	768.192	+	414.330i	1.02700	+	0.553917i
$749$	−945.719			−1.26264
$750$			113.342i			0.151122i
$751$	119.746			0.159449			0.0797244	−	0.996817i	$-0.474596\pi$
$751$	119.746			0.159449			0.0797244	+	0.996817i	$0.474596\pi$
$752$	31.6252			0.0420548
$753$	−279.528			−0.371219
$754$		−	121.446i		−	0.161069i
$755$		−	716.519i		−	0.949032i
$756$		−	449.433i		−	0.594488i
$757$	97.0977			0.128266			0.0641332	−	0.997941i	$-0.479572\pi$
$757$	97.0977			0.128266			0.0641332	+	0.997941i	$0.479572\pi$
$758$			205.649i			0.271305i
$759$	40.6462	−	75.3605i	0.0535523	−	0.0992892i
$760$	−42.0328			−0.0553064
$761$		−	360.307i		−	0.473465i	−0.971575	−	0.236732i	$-0.923924\pi$
$761$		−	360.307i		−	0.473465i	0.971575	−	0.236732i	$-0.0760764\pi$
$762$	416.669			0.546810
$763$	1314.86			1.72327
$764$	−15.9211			−0.0208392
$765$			1374.48i			1.79671i
$766$		−	273.486i		−	0.357032i
$767$		−	657.145i		−	0.856773i
$768$	−343.051			−0.446681
$769$			1105.53i			1.43762i	0.695205	+	0.718812i	$0.255314\pi$
$769$			1105.53i			1.43762i	−0.695205	+	0.718812i	$0.744686\pi$
$770$	279.636	−	518.462i	0.363164	−	0.673328i
$771$	435.054			0.564273
$772$			749.652i			0.971052i
$773$	−327.176			−0.423255			−0.211628	−	0.977350i	$-0.567876\pi$
$773$	−327.176			−0.423255			−0.211628	+	0.977350i	$0.567876\pi$
$774$	−372.269			−0.480968
$775$	−1563.26			−2.01711
$776$			10.0816i			0.0129917i
$777$			699.124i			0.899774i
$778$			675.531i			0.868292i
$779$	7.51605			0.00964833
$780$		−	407.902i		−	0.522952i
$781$	−32.9381	+	61.0691i	−0.0421742	+	0.0781935i
$782$	−148.008			−0.189269
$783$			236.726i			0.302332i
$784$	24.2739			0.0309616
$785$	−1973.87			−2.51449
$786$	10.4745			0.0133263
$787$			255.482i			0.324627i	0.986739	+	0.162314i	$0.0518956\pi$
$787$			255.482i			0.324627i	−0.986739	+	0.162314i	$0.948104\pi$
$788$		−	179.182i		−	0.227388i
$789$		−	347.031i		−	0.439837i
$790$	259.997			0.329110
$791$		−	770.753i		−	0.974403i
$792$	458.145	+	247.103i	0.578465	+	0.311999i
$793$	−162.791			−0.205285
$794$			730.926i			0.920561i
$795$	−57.7513			−0.0726432
$796$	−712.367			−0.894933
$797$	945.887			1.18681			0.593404	−	0.804904i	$-0.297783\pi$
$797$	945.887			1.18681			0.593404	+	0.804904i	$0.297783\pi$
$798$		−	8.41959i		−	0.0105509i
$799$		−	287.169i		−	0.359411i
$800$			1105.69i			1.38211i
$801$	596.434			0.744612
$802$			129.914i			0.161988i
$803$	−620.107	−	334.459i	−0.772238	−	0.416512i
$804$	−19.6825			−0.0244807
$805$		−	235.187i		−	0.292157i
$806$	−599.371			−0.743636
$807$	−379.457			−0.470206
$808$	7.59453			0.00939917
$809$			895.925i			1.10745i	0.832700	+	0.553724i	$0.186794\pi$
$809$			895.925i			1.10745i	−0.832700	+	0.553724i	$0.813206\pi$
$810$			140.269i			0.173171i
$811$		−	954.586i		−	1.17705i	−0.808479	−	0.588524i	$-0.799709\pi$
$811$		−	954.586i		−	1.17705i	0.808479	−	0.588524i	$-0.200291\pi$
$812$	171.056			0.210660
$813$		−	276.626i		−	0.340253i
$814$	−709.471	−	382.658i	−0.871586	−	0.470096i
$815$	704.711			0.864676
$816$		−	142.767i		−	0.174960i
$817$	39.6342			0.0485119
$818$	−144.788			−0.177002
$819$	−478.739			−0.584541
$820$		−	217.836i		−	0.265654i
$821$		−	632.016i		−	0.769812i	−0.922956	−	0.384906i	$-0.874234\pi$
$821$		−	632.016i		−	0.769812i	0.922956	−	0.384906i	$-0.125766\pi$
$822$		−	89.8622i		−	0.109321i
$823$	−361.628			−0.439402			−0.219701	−	0.975567i	$-0.570508\pi$
$823$	−361.628			−0.439402			−0.219701	+	0.975567i	$0.570508\pi$
$824$		−	1021.23i		−	1.23936i
$825$	−282.823	+	524.371i	−0.342816	+	0.635602i
$826$	−393.130			−0.475945
$827$		−	1292.02i		−	1.56229i	−0.624349	−	0.781146i	$-0.714636\pi$
$827$		−	1292.02i		−	1.56229i	0.624349	−	0.781146i	$-0.285364\pi$
$828$	85.7104			0.103515
$829$	678.938			0.818984			0.409492	−	0.912314i	$-0.365706\pi$
$829$	678.938			0.818984			0.409492	+	0.912314i	$0.365706\pi$
$830$	−915.428			−1.10293
$831$			473.722i			0.570063i
$832$			278.068i			0.334216i
$833$		−	220.417i		−	0.264606i
$834$	−87.2310			−0.104594
$835$			990.940i			1.18675i
$836$	−20.1164	−	10.8499i	−0.0240627	−	0.0129784i
$837$	1168.31			1.39583
$838$		−	147.125i		−	0.175567i
$839$	−888.769			−1.05932			−0.529660	−	0.848210i	$-0.677680\pi$
$839$	−888.769			−1.05932			−0.529660	+	0.848210i	$0.677680\pi$
$840$	−591.693			−0.704396
$841$	750.901			0.892867
$842$		−	155.726i		−	0.184948i
$843$		−	287.486i		−	0.341027i
$844$			210.866i			0.249842i
$845$	242.356			0.286812
$846$		−	70.6328i		−	0.0834903i
$847$	649.008	−	426.627i	0.766244	−	0.503691i
$848$	−14.4953			−0.0170935
$849$		−	226.039i		−	0.266241i
$850$	1029.87			1.21161
$851$	−321.833			−0.378182
$852$	28.7433			0.0337362
$853$			403.297i			0.472799i	0.971656	+	0.236399i	$0.0759674\pi$
$853$			403.297i			0.472799i	−0.971656	+	0.236399i	$0.924033\pi$
$854$			97.3879i			0.114037i
$855$		−	35.9932i		−	0.0420973i
$856$	−1095.27			−1.27952
$857$		−	193.500i		−	0.225788i	−0.993607	−	0.112894i	$-0.963988\pi$
$857$		−	193.500i		−	0.225788i	0.993607	−	0.112894i	$-0.0360120\pi$
$858$	−108.438	+	201.050i	−0.126384	+	0.234324i
$859$	163.433			0.190260			0.0951300	−	0.995465i	$-0.469673\pi$
$859$	163.433			0.190260			0.0951300	+	0.995465i	$0.469673\pi$
$860$		−	1148.71i		−	1.33571i
$861$	105.803			0.122884
$862$	725.697			0.841876
$863$	755.373			0.875288			0.437644	−	0.899148i	$-0.355813\pi$
$863$	755.373			0.875288			0.437644	+	0.899148i	$0.355813\pi$
$864$		−	826.344i		−	0.956417i
$865$			2075.77i			2.39973i
$866$		−	274.579i		−	0.317066i
$867$	−827.319			−0.954232
$868$		−	844.210i		−	0.972592i
$869$	301.714	+	162.731i	0.347196	+	0.187263i
$870$	128.532			0.147738
$871$			50.6083i			0.0581037i
$872$	1522.78			1.74631
$873$	−8.63295			−0.00988883
$874$	3.87585			0.00443461
$875$			410.473i			0.469112i
$876$			291.864i			0.333179i
$877$			818.563i			0.933367i	0.884424	+	0.466684i	$0.154551\pi$
$877$			818.563i			0.933367i	−0.884424	+	0.466684i	$0.845449\pi$
$878$	−542.031			−0.617348
$879$			737.100i			0.838566i
$880$	−124.169	+	230.216i	−0.141101	+	0.261609i
$881$	−541.369			−0.614493			−0.307247	−	0.951630i	$-0.599408\pi$
$881$	−541.369			−0.614493			−0.307247	+	0.951630i	$0.599408\pi$
$882$		−	54.2142i		−	0.0614673i
$883$	1147.58			1.29963			0.649817	−	0.760091i	$-0.274845\pi$
$883$	1147.58			1.29963			0.649817	+	0.760091i	$0.274845\pi$
$884$	−929.663			−1.05165
$885$	695.489			0.785864
$886$			803.605i			0.907004i
$887$			1718.65i			1.93760i	0.247843	+	0.968800i	$0.420278\pi$
$887$			1718.65i			1.93760i	−0.247843	+	0.968800i	$0.579722\pi$
$888$			809.681i			0.911803i
$889$	1508.99			1.69740
$890$		−	781.694i		−	0.878308i
$891$	−87.7939	+	162.775i	−0.0985341	+	0.182688i
$892$	−465.416			−0.521767
$893$			7.52002i			0.00842108i
$894$	−377.752			−0.422541
$895$	1200.58			1.34143
$896$	−684.371			−0.763807
$897$			91.2009i			0.101673i
$898$			809.509i			0.901457i
$899$			444.663i			0.494620i
$900$	−596.388			−0.662653
$901$			131.623i			0.146085i
$902$	−57.9100	+	107.369i	−0.0642018	+	0.119034i
$903$	557.927			0.617860
$904$		−	892.636i		−	0.987430i
$905$	995.844			1.10038
$906$	166.222			0.183468
$907$	−1632.71			−1.80012			−0.900062	−	0.435762i	$-0.856479\pi$
$907$	−1632.71			−1.80012			−0.900062	+	0.435762i	$0.856479\pi$
$908$			942.561i			1.03806i
$909$			6.50328i			0.00715433i
$910$			627.440i			0.689495i
$911$	−1125.41			−1.23536			−0.617679	−	0.786430i	$-0.711927\pi$
$911$	−1125.41			−1.23536			−0.617679	+	0.786430i	$0.711927\pi$
$912$			3.73860i			0.00409935i
$913$	−1062.31	−	572.964i	−1.16354	−	0.627562i
$914$	−628.841			−0.688010
$915$		−	172.290i		−	0.188295i
$916$	812.959			0.887509
$917$	37.9340			0.0413676
$918$	−769.677			−0.838428
$919$		−	493.122i		−	0.536586i	−0.963337	−	0.268293i	$-0.913541\pi$
$919$		−	493.122i		−	0.536586i	0.963337	−	0.268293i	$-0.0864595\pi$
$920$		−	272.378i		−	0.296063i
$921$			260.591i			0.282944i
$922$	−380.435			−0.412620
$923$		−	73.9056i		−	0.0800711i
$924$	−283.177	−	152.734i	−0.306469	−	0.165296i
$925$	2239.37			2.42094
$926$		−	68.4851i		−	0.0739580i
$927$	874.492			0.943357
$928$	314.509			0.338911
$929$	−378.116			−0.407014			−0.203507	−	0.979074i	$-0.565234\pi$
$929$	−378.116			−0.407014			−0.203507	+	0.979074i	$0.565234\pi$
$930$		−	634.344i		−	0.682091i
$931$			5.77199i			0.00619978i
$932$		−	340.252i		−	0.365077i
$933$	−246.367			−0.264059
$934$			788.673i			0.844404i
$935$	2090.45	+	1127.50i	2.23578	+	1.20588i
$936$	−554.444			−0.592355
$937$			375.108i			0.400329i	0.979762	+	0.200164i	$0.0641477\pi$
$937$			375.108i			0.400329i	−0.979762	+	0.200164i	$0.935852\pi$
$938$	30.2759			0.0322771
$939$	−841.321			−0.895976
$940$	217.951			0.231863
$941$			1149.02i			1.22106i	0.791993	+	0.610530i	$0.209044\pi$
$941$			1149.02i			1.22106i	−0.791993	+	0.610530i	$0.790956\pi$
$942$		−	457.911i		−	0.486105i
$943$			48.7049i			0.0516489i
$944$	174.564			0.184920
$945$		−	1223.02i		−	1.29421i
$946$	−305.375	+	566.184i	−0.322807	+	0.598504i
$947$	−780.204			−0.823869			−0.411934	−	0.911213i	$-0.635147\pi$
$947$	−780.204			−0.823869			−0.411934	+	0.911213i	$0.635147\pi$
$948$		−	142.007i		−	0.149796i
$949$	750.451			0.790781
$950$	−26.9688			−0.0283882
$951$	−260.646			−0.274076
$952$			1348.54i			1.41654i
$953$			1645.77i			1.72694i	0.504404	+	0.863468i	$0.331712\pi$
$953$			1645.77i			1.72694i	−0.504404	+	0.863468i	$0.668288\pi$
$954$			32.3742i			0.0339352i
$955$	−43.3256			−0.0453671
$956$			1008.25i			1.05465i
$957$	149.155	+	80.4480i	0.155857	+	0.0840627i
$958$	−690.670			−0.720950
$959$		−	325.441i		−	0.339355i
$960$	−294.293			−0.306555
$961$	1233.54			1.28360
$962$	858.599			0.892514
$963$		−	937.893i		−	0.973929i
$964$		−	699.399i		−	0.725517i
$965$			2040.00i			2.11399i
$966$	54.5600			0.0564804
$967$		−	1583.76i		−	1.63781i	−0.573928	−	0.818906i	$-0.694581\pi$
$967$		−	1583.76i		−	1.63781i	0.573928	−	0.818906i	$-0.305419\pi$
$968$	751.640	−	494.092i	0.776487	−	0.510425i
$969$	33.9480			0.0350341
$970$			11.3144i			0.0116644i
$971$	−225.914			−0.232662			−0.116331	−	0.993211i	$-0.537113\pi$
$971$	−225.914			−0.232662			−0.116331	+	0.993211i	$0.537113\pi$
$972$	706.778			0.727137
$973$	−315.913			−0.324679
$974$			640.949i			0.658059i
$975$		−	634.592i		−	0.650863i
$976$		−	43.2438i		−	0.0443071i
$977$	−1755.73			−1.79707			−0.898533	−	0.438905i	$-0.855366\pi$
$977$	−1755.73			−1.79707			−0.898533	+	0.438905i	$0.855366\pi$
$978$			163.483i			0.167161i
$979$	489.260	−	907.118i	0.499755	−	0.926576i
$980$	167.289			0.170703
$981$			1303.98i			1.32923i
$982$	727.588			0.740925
$983$	1512.85			1.53902			0.769508	−	0.638638i	$-0.220502\pi$
$983$	1512.85			1.53902			0.769508	+	0.638638i	$0.220502\pi$
$984$	122.534			0.124526
$985$		−	487.600i		−	0.495025i
$986$		−	292.942i		−	0.297101i
$987$			105.859i			0.107253i
$988$	24.3448			0.0246405
$989$			256.835i			0.259691i
$990$	514.172	+	277.322i	0.519366	+	0.280123i
$991$	31.4683			0.0317541			0.0158771	−	0.999874i	$-0.494946\pi$
$991$	31.4683			0.0317541			0.0158771	+	0.999874i	$0.494946\pi$
$992$		−	1552.20i		−	1.56471i
$993$	276.106			0.278052
$994$	−44.2133			−0.0444801
$995$	−1938.54			−1.94828
$996$			499.995i			0.502003i
$997$			1336.93i			1.34096i	0.741929	+	0.670478i	$0.233911\pi$
$997$			1336.93i			1.34096i	−0.741929	+	0.670478i	$0.766089\pi$
$998$		−	159.620i		−	0.159940i
$999$	−1673.60			−1.67528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.27	yes	44
11.10	odd	2	inner	253.3.c.a.208.18	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.18	✓	44	11.10	odd	2	inner
253.3.c.a.208.27	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.09200i q^{2} +1.62306 q^{3} +2.80754 q^{4} +7.64004 q^{5} +1.77238i q^{6} +6.41879i q^{7} +7.43383i q^{8} -6.36568 q^{9} +8.34293i q^{10} +(-5.22182 + 9.68156i) q^{11} +4.55680 q^{12} -11.7166i q^{13} -7.00932 q^{14} +12.4002 q^{15} +3.11239 q^{16} -28.2618i q^{17} -6.95132i q^{18} +0.740083i q^{19} +21.4497 q^{20} +10.4181i q^{21} +(-10.5723 - 5.70223i) q^{22} -4.79583 q^{23} +12.0656i q^{24} +33.3702 q^{25} +12.7945 q^{26} -24.9394 q^{27} +18.0210i q^{28} -9.49203i q^{29} +13.5411i q^{30} -46.8460 q^{31} +33.1341i q^{32} +(-8.47532 + 15.7138i) q^{33} +30.8619 q^{34} +49.0398i q^{35} -17.8719 q^{36} +67.1068 q^{37} -0.808171 q^{38} -19.0167i q^{39} +56.7948i q^{40} -10.1557i q^{41} -11.3766 q^{42} -53.5537i q^{43} +(-14.6604 + 27.1813i) q^{44} -48.6340 q^{45} -5.23705i q^{46} +10.1611 q^{47} +5.05160 q^{48} +7.79912 q^{49} +36.4403i q^{50} -45.8706i q^{51} -32.8947i q^{52} -4.65727 q^{53} -27.2339i q^{54} +(-39.8949 + 73.9675i) q^{55} -47.7162 q^{56} +1.20120i q^{57} +10.3653 q^{58} +56.0868 q^{59} +34.8141 q^{60} -13.8941i q^{61} -51.1558i q^{62} -40.8599i q^{63} -23.7328 q^{64} -89.5151i q^{65} +(-17.1594 - 9.25506i) q^{66} -4.31938 q^{67} -79.3459i q^{68} -7.78392 q^{69} -53.5515 q^{70} +6.30778 q^{71} -47.3214i q^{72} +64.0503i q^{73} +73.2807i q^{74} +54.1619 q^{75} +2.07781i q^{76} +(-62.1439 - 33.5178i) q^{77} +20.7663 q^{78} -31.1637i q^{79} +23.7788 q^{80} +16.8129 q^{81} +11.0900 q^{82} +109.725i q^{83} +29.2491i q^{84} -215.921i q^{85} +58.4807 q^{86} -15.4061i q^{87} +(-71.9711 - 38.8181i) q^{88} -93.6954 q^{89} -53.1084i q^{90} +75.2063 q^{91} -13.4645 q^{92} -76.0338 q^{93} +11.0959i q^{94} +5.65426i q^{95} +53.7786i q^{96} +1.35617 q^{97} +8.51664i q^{98} +(33.2404 - 61.6297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 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

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