LMFDB - Embedded newform 253.3.c.a.208.2

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			208.2
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.43

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.71224i q^{2} -2.82013 q^{3} -9.78074 q^{4} +2.21957 q^{5} +10.4690i q^{6} +5.12153i q^{7} +21.4595i q^{8} -1.04689 q^{9} -8.23959i q^{10} +(9.16580 + 6.08179i) q^{11} +27.5829 q^{12} -2.92352i q^{13} +19.0123 q^{14} -6.25947 q^{15} +40.5400 q^{16} +12.0416i q^{17} +3.88631i q^{18} +1.76698i q^{19} -21.7091 q^{20} -14.4433i q^{21} +(22.5771 - 34.0257i) q^{22} +4.79583 q^{23} -60.5186i q^{24} -20.0735 q^{25} -10.8528 q^{26} +28.3335 q^{27} -50.0923i q^{28} +7.43658i q^{29} +23.2367i q^{30} -15.3983 q^{31} -64.6562i q^{32} +(-25.8487 - 17.1514i) q^{33} +44.7013 q^{34} +11.3676i q^{35} +10.2394 q^{36} +53.4251 q^{37} +6.55946 q^{38} +8.24470i q^{39} +47.6310i q^{40} +58.9509i q^{41} -53.6172 q^{42} +45.8154i q^{43} +(-89.6483 - 59.4844i) q^{44} -2.32365 q^{45} -17.8033i q^{46} +5.73259 q^{47} -114.328 q^{48} +22.7700 q^{49} +74.5177i q^{50} -33.9588i q^{51} +28.5942i q^{52} -90.1928 q^{53} -105.181i q^{54} +(20.3441 + 13.4990i) q^{55} -109.906 q^{56} -4.98311i q^{57} +27.6064 q^{58} +71.4856 q^{59} +61.2223 q^{60} +26.1146i q^{61} +57.1623i q^{62} -5.36168i q^{63} -77.8594 q^{64} -6.48897i q^{65} +(-63.6702 + 95.9567i) q^{66} +20.7812 q^{67} -117.776i q^{68} -13.5248 q^{69} +42.1993 q^{70} +20.2277 q^{71} -22.4658i q^{72} +111.200i q^{73} -198.327i q^{74} +56.6098 q^{75} -17.2824i q^{76} +(-31.1480 + 46.9429i) q^{77} +30.6063 q^{78} +13.9473i q^{79} +89.9814 q^{80} -70.4820 q^{81} +218.840 q^{82} +86.4589i q^{83} +141.267i q^{84} +26.7272i q^{85} +170.078 q^{86} -20.9721i q^{87} +(-130.512 + 196.694i) q^{88} -29.8456 q^{89} +8.62595i q^{90} +14.9729 q^{91} -46.9068 q^{92} +43.4252 q^{93} -21.2808i q^{94} +3.92194i q^{95} +182.339i q^{96} -79.0787 q^{97} -84.5277i q^{98} +(-9.59559 - 6.36697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.71224i		−	1.85612i	−0.372429	−	0.928061i	$-0.621475\pi$
$2$		−	3.71224i		−	1.85612i	0.372429	−	0.928061i	$-0.378525\pi$
$3$	−2.82013			−0.940042			−0.470021	−	0.882655i	$-0.655754\pi$
$3$	−2.82013			−0.940042			−0.470021	+	0.882655i	$0.655754\pi$
$4$	−9.78074			−2.44519
$5$	2.21957			0.443914			0.221957	−	0.975056i	$-0.428755\pi$
$5$	2.21957			0.443914			0.221957	+	0.975056i	$0.428755\pi$
$6$			10.4690i			1.74483i
$7$			5.12153i			0.731647i	0.930684	+	0.365823i	$0.119213\pi$
$7$			5.12153i			0.731647i	−0.930684	+	0.365823i	$0.880787\pi$
$8$			21.4595i			2.68244i
$9$	−1.04689			−0.116321
$10$		−	8.23959i		−	0.823959i
$11$	9.16580	+	6.08179i	0.833254	+	0.552890i
$11$	9.16580	+	6.08179i	0.833254	+	0.552890i
$12$	27.5829			2.29858
$13$		−	2.92352i		−	0.224886i	−0.993658	−	0.112443i	$-0.964132\pi$
$13$		−	2.92352i		−	0.224886i	0.993658	−	0.112443i	$-0.0358676\pi$
$14$	19.0123			1.35802
$15$	−6.25947			−0.417298
$16$	40.5400			2.53375
$17$			12.0416i			0.708329i	0.935183	+	0.354164i	$0.115235\pi$
$17$			12.0416i			0.708329i	−0.935183	+	0.354164i	$0.884765\pi$
$18$			3.88631i			0.215906i
$19$			1.76698i			0.0929990i	0.998918	+	0.0464995i	$0.0148066\pi$
$19$			1.76698i			0.0929990i	−0.998918	+	0.0464995i	$0.985193\pi$
$20$	−21.7091			−1.08545
$21$		−	14.4433i		−	0.687778i
$22$	22.5771	−	34.0257i	1.02623	−	1.54662i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$		−	60.5186i		−	2.52161i
$25$	−20.0735			−0.802940
$26$	−10.8528			−0.417416
$27$	28.3335			1.04939
$28$		−	50.0923i		−	1.78901i
$29$			7.43658i			0.256434i	0.991746	+	0.128217i	$0.0409254\pi$
$29$			7.43658i			0.256434i	−0.991746	+	0.128217i	$0.959075\pi$
$30$			23.2367i			0.774556i
$31$	−15.3983			−0.496720			−0.248360	−	0.968668i	$-0.579892\pi$
$31$	−15.3983			−0.496720			−0.248360	+	0.968668i	$0.579892\pi$
$32$		−	64.6562i		−	2.02051i
$33$	−25.8487	−	17.1514i	−0.783294	−	0.519739i
$34$	44.7013			1.31474
$35$			11.3676i			0.324788i
$36$	10.2394			0.284427
$37$	53.4251			1.44392			0.721960	−	0.691934i	$-0.243241\pi$
$37$	53.4251			1.44392			0.721960	+	0.691934i	$0.243241\pi$
$38$	6.55946			0.172617
$39$			8.24470i			0.211403i
$40$			47.6310i			1.19077i
$41$			58.9509i			1.43783i	0.695100	+	0.718913i	$0.255360\pi$
$41$			58.9509i			1.43783i	−0.695100	+	0.718913i	$0.744640\pi$
$42$	−53.6172			−1.27660
$43$			45.8154i			1.06547i	0.846281	+	0.532737i	$0.178837\pi$
$43$			45.8154i			1.06547i	−0.846281	+	0.532737i	$0.821163\pi$
$44$	−89.6483	−	59.4844i	−2.03746	−	1.35192i
$45$	−2.32365			−0.0516367
$46$		−	17.8033i		−	0.387028i
$47$	5.73259			0.121970			0.0609850	−	0.998139i	$-0.480576\pi$
$47$	5.73259			0.121970			0.0609850	+	0.998139i	$0.480576\pi$
$48$	−114.328			−2.38183
$49$	22.7700			0.464693
$50$			74.5177i			1.49035i
$51$		−	33.9588i		−	0.665859i
$52$			28.5942i			0.549889i
$53$	−90.1928			−1.70175			−0.850875	−	0.525368i	$-0.823928\pi$
$53$	−90.1928			−1.70175			−0.850875	+	0.525368i	$0.823928\pi$
$54$		−	105.181i		−	1.94779i
$55$	20.3441	+	13.4990i	0.369894	+	0.245436i
$56$	−109.906			−1.96260
$57$		−	4.98311i		−	0.0874229i
$58$	27.6064			0.475972
$59$	71.4856			1.21162			0.605810	−	0.795609i	$-0.292849\pi$
$59$	71.4856			1.21162			0.605810	+	0.795609i	$0.292849\pi$
$60$	61.2223			1.02037
$61$			26.1146i			0.428109i	0.976822	+	0.214054i	$0.0686670\pi$
$61$			26.1146i			0.428109i	−0.976822	+	0.214054i	$0.931333\pi$
$62$			57.1623i			0.921972i
$63$		−	5.36168i		−	0.0851060i
$64$	−77.8594			−1.21655
$65$		−	6.48897i		−	0.0998303i
$66$	−63.6702	+	95.9567i	−0.964699	+	1.45389i
$67$	20.7812			0.310167			0.155084	−	0.987901i	$-0.450435\pi$
$67$	20.7812			0.310167			0.155084	+	0.987901i	$0.450435\pi$
$68$		−	117.776i		−	1.73200i
$69$	−13.5248			−0.196012
$70$	42.1993			0.602847
$71$	20.2277			0.284897			0.142449	−	0.989802i	$-0.454502\pi$
$71$	20.2277			0.284897			0.142449	+	0.989802i	$0.454502\pi$
$72$		−	22.4658i		−	0.312025i
$73$			111.200i			1.52328i	0.647998	+	0.761642i	$0.275606\pi$
$73$			111.200i			1.52328i	−0.647998	+	0.761642i	$0.724394\pi$
$74$		−	198.327i		−	2.68009i
$75$	56.6098			0.754797
$76$		−	17.2824i		−	0.227400i
$77$	−31.1480	+	46.9429i	−0.404520	+	0.609648i
$78$	30.6063			0.392389
$79$			13.9473i			0.176548i	0.996096	+	0.0882738i	$0.0281350\pi$
$79$			13.9473i			0.176548i	−0.996096	+	0.0882738i	$0.971865\pi$
$80$	89.9814			1.12477
$81$	−70.4820			−0.870148
$82$	218.840			2.66878
$83$			86.4589i			1.04167i	0.853656	+	0.520837i	$0.174380\pi$
$83$			86.4589i			1.04167i	−0.853656	+	0.520837i	$0.825620\pi$
$84$			141.267i			1.68175i
$85$			26.7272i			0.314437i
$86$	170.078			1.97765
$87$		−	20.9721i		−	0.241059i
$88$	−130.512	+	196.694i	−1.48309	+	2.23516i
$89$	−29.8456			−0.335344			−0.167672	−	0.985843i	$-0.553625\pi$
$89$	−29.8456			−0.335344			−0.167672	+	0.985843i	$0.553625\pi$
$90$			8.62595i			0.0958439i
$91$	14.9729			0.164537
$92$	−46.9068			−0.509857
$93$	43.4252			0.466938
$94$		−	21.2808i		−	0.226391i
$95$			3.92194i			0.0412836i
$96$			182.339i			1.89936i
$97$	−79.0787			−0.815244			−0.407622	−	0.913151i	$-0.633642\pi$
$97$	−79.0787			−0.815244			−0.407622	+	0.913151i	$0.633642\pi$
$98$		−	84.5277i		−	0.862527i
$99$	−9.59559	−	6.36697i	−0.0969252	−	0.0643128i
$100$	196.334			1.96334
$101$		−	52.3826i		−	0.518640i	−0.965791	−	0.259320i	$-0.916502\pi$
$101$		−	52.3826i		−	0.518640i	0.965791	−	0.259320i	$-0.0834984\pi$
$102$	−126.063			−1.23591
$103$	−29.0550			−0.282087			−0.141044	−	0.990003i	$-0.545046\pi$
$103$	−29.0550			−0.282087			−0.141044	+	0.990003i	$0.545046\pi$
$104$	62.7374			0.603244
$105$		−	32.0580i		−	0.305315i
$106$			334.818i			3.15866i
$107$		−	151.941i		−	1.42001i	−0.704197	−	0.710005i	$-0.748693\pi$
$107$		−	151.941i		−	1.42001i	0.704197	−	0.710005i	$-0.251307\pi$
$108$	−277.123			−2.56595
$109$			42.5027i			0.389933i	0.980810	+	0.194966i	$0.0624598\pi$
$109$			42.5027i			0.389933i	−0.980810	+	0.194966i	$0.937540\pi$
$110$	50.1114	−	75.5224i	0.455558	−	0.686567i
$111$	−150.665			−1.35735
$112$			207.627i			1.85381i
$113$	−138.904			−1.22924			−0.614619	−	0.788825i	$-0.710690\pi$
$113$	−138.904			−1.22924			−0.614619	+	0.788825i	$0.710690\pi$
$114$	−18.4985			−0.162268
$115$	10.6447			0.0925625
$116$		−	72.7353i		−	0.627029i
$117$			3.06061i			0.0261591i
$118$		−	265.372i		−	2.24892i
$119$	−61.6713			−0.518246
$120$		−	134.325i		−	1.11938i
$121$	47.0237	+	111.489i	0.388626	+	0.921396i
$122$	96.9439			0.794622
$123$		−	166.249i		−	1.35162i
$124$	150.607			1.21457
$125$	−100.044			−0.800351
$126$	−19.9039			−0.157967
$127$		−	29.5374i		−	0.232578i	−0.993215	−	0.116289i	$-0.962900\pi$
$127$		−	29.5374i		−	0.232578i	0.993215	−	0.116289i	$-0.0370998\pi$
$128$			30.4084i			0.237566i
$129$		−	129.205i		−	1.00159i
$130$	−24.0886			−0.185297
$131$			195.824i			1.49484i	0.664353	+	0.747419i	$0.268707\pi$
$131$			195.824i			1.49484i	−0.664353	+	0.747419i	$0.731293\pi$
$132$	252.820	+	167.753i	1.91530	+	1.27086i
$133$	−9.04963			−0.0680424
$134$		−	77.1448i		−	0.575708i
$135$	62.8882			0.465839
$136$	−258.407			−1.90005
$137$	−167.319			−1.22131			−0.610654	−	0.791898i	$-0.709093\pi$
$137$	−167.319			−1.22131			−0.610654	+	0.791898i	$0.709093\pi$
$138$			50.2075i			0.363823i
$139$		−	140.313i		−	1.00945i	−0.863281	−	0.504723i	$-0.831595\pi$
$139$		−	140.313i		−	1.00945i	0.863281	−	0.504723i	$-0.168405\pi$
$140$		−	111.184i		−	0.794168i
$141$	−16.1666			−0.114657
$142$		−	75.0901i		−	0.528804i
$143$	17.7802	−	26.7964i	0.124337	−	0.187388i
$144$	−42.4410			−0.294729
$145$			16.5060i			0.113835i
$146$	412.800			2.82740
$147$	−64.2142			−0.436831
$148$	−522.537			−3.53066
$149$			185.326i			1.24380i	0.783097	+	0.621900i	$0.213639\pi$
$149$			185.326i			1.24380i	−0.783097	+	0.621900i	$0.786361\pi$
$150$		−	210.149i		−	1.40100i
$151$		−	106.855i		−	0.707647i	−0.935312	−	0.353823i	$-0.884881\pi$
$151$		−	106.855i		−	0.707647i	0.935312	−	0.353823i	$-0.115119\pi$
$152$	−37.9186			−0.249464
$153$		−	12.6062i		−	0.0823937i
$154$	174.263	+	115.629i	1.13158	+	0.750838i
$155$	−34.1777			−0.220501
$156$		−	80.6393i		−	0.516919i
$157$	−117.148			−0.746165			−0.373082	−	0.927798i	$-0.621699\pi$
$157$	−117.148			−0.746165			−0.373082	+	0.927798i	$0.621699\pi$
$158$	51.7756			0.327694
$159$	254.355			1.59972
$160$		−	143.509i		−	0.896931i
$161$			24.5620i			0.152559i
$162$			261.646i			1.61510i
$163$	−82.1719			−0.504122			−0.252061	−	0.967711i	$-0.581108\pi$
$163$	−82.1719			−0.504122			−0.252061	+	0.967711i	$0.581108\pi$
$164$		−	576.584i		−	3.51575i
$165$	−57.3731	−	38.0688i	−0.347715	−	0.230720i
$166$	320.956			1.93347
$167$		−	324.085i		−	1.94063i	−0.241842	−	0.970316i	$-0.577752\pi$
$167$		−	324.085i		−	1.94063i	0.241842	−	0.970316i	$-0.422248\pi$
$168$	309.947			1.84492
$169$	160.453			0.949426
$170$	99.2177			0.583634
$171$		−	1.84984i		−	0.0108178i
$172$		−	448.109i		−	2.60528i
$173$		−	206.843i		−	1.19563i	−0.801636	−	0.597813i	$-0.796037\pi$
$173$		−	206.843i		−	1.19563i	0.801636	−	0.597813i	$-0.203963\pi$
$174$	−77.8535			−0.447434
$175$		−	102.807i		−	0.587468i
$176$	371.581	+	246.556i	2.11126	+	1.40088i
$177$	−201.598			−1.13897
$178$			110.794i			0.622438i
$179$	106.200			0.593295			0.296647	−	0.954987i	$-0.404131\pi$
$179$	106.200			0.593295			0.296647	+	0.954987i	$0.404131\pi$
$180$	22.7270			0.126261
$181$	−307.206			−1.69727			−0.848635	−	0.528979i	$-0.822575\pi$
$181$	−307.206			−1.69727			−0.848635	+	0.528979i	$0.822575\pi$
$182$		−	55.5830i		−	0.305401i
$183$		−	73.6466i		−	0.402440i
$184$			102.916i			0.559328i
$185$	118.581			0.640977
$186$		−	161.205i		−	0.866693i
$187$	−73.2344	+	110.371i	−0.391628	+	0.590218i
$188$	−56.0690			−0.298239
$189$			145.111i			0.767782i
$190$	14.5592			0.0766273
$191$	86.8653			0.454792			0.227396	−	0.973802i	$-0.426979\pi$
$191$	86.8653			0.454792			0.227396	+	0.973802i	$0.426979\pi$
$192$	219.573			1.14361
$193$			319.471i			1.65529i	0.561251	+	0.827646i	$0.310320\pi$
$193$			319.471i			1.65529i	−0.561251	+	0.827646i	$0.689680\pi$
$194$			293.559i			1.51319i
$195$			18.2997i			0.0938446i
$196$	−222.707			−1.13626
$197$			257.423i			1.30672i	0.757048	+	0.653359i	$0.226641\pi$
$197$			257.423i			1.30672i	−0.757048	+	0.653359i	$0.773359\pi$
$198$	−23.6357	+	35.6212i	−0.119372	+	0.179905i
$199$	208.481			1.04764			0.523821	−	0.851828i	$-0.324506\pi$
$199$	208.481			1.04764			0.523821	+	0.851828i	$0.324506\pi$
$200$		−	430.768i		−	2.15384i
$201$	−58.6056			−0.291570
$202$	−194.457			−0.962658
$203$	−38.0867			−0.187619
$204$			332.142i			1.62815i
$205$			130.846i			0.638272i
$206$			107.859i			0.523588i
$207$	−5.02071			−0.0242547
$208$		−	118.520i		−	0.569806i
$209$	−10.7464	+	16.1958i	−0.0514182	+	0.0774918i
$210$	−119.007			−0.566701
$211$			232.777i			1.10321i	0.834107	+	0.551603i	$0.185984\pi$
$211$			232.777i			1.10321i	−0.834107	+	0.551603i	$0.814016\pi$
$212$	882.153			4.16110
$213$	−57.0446			−0.267815
$214$	−564.042			−2.63571
$215$			101.691i			0.472979i
$216$			608.023i			2.81492i
$217$		−	78.8629i		−	0.363423i
$218$	157.780			0.723763
$219$		−	313.597i		−	1.43195i
$220$	−198.981	−	132.030i	−0.904459	−	0.600136i
$221$	35.2039			0.159293
$222$			559.307i			2.51940i
$223$	129.675			0.581502			0.290751	−	0.956799i	$-0.406095\pi$
$223$	129.675			0.581502			0.290751	+	0.956799i	$0.406095\pi$
$224$	331.138			1.47830
$225$	21.0148			0.0933990
$226$			515.645i			2.28161i
$227$		−	354.790i		−	1.56295i	−0.623936	−	0.781475i	$-0.714467\pi$
$227$		−	354.790i		−	1.56295i	0.623936	−	0.781475i	$-0.285533\pi$
$228$			48.7385i			0.213765i
$229$	306.280			1.33747			0.668733	−	0.743503i	$-0.266837\pi$
$229$	306.280			1.33747			0.668733	+	0.743503i	$0.266837\pi$
$230$		−	39.5157i		−	0.171807i
$231$	87.8414	−	132.385i	0.380266	−	0.573094i
$232$	−159.586			−0.687869
$233$		−	365.395i		−	1.56822i	−0.620621	−	0.784110i	$-0.713120\pi$
$233$		−	365.395i		−	1.56822i	0.620621	−	0.784110i	$-0.286880\pi$
$234$	11.3617			0.0485544
$235$	12.7239			0.0541442
$236$	−699.183			−2.96264
$237$		−	39.3330i		−	0.165962i
$238$			228.939i			0.961928i
$239$			403.911i			1.69000i	0.534764	+	0.845002i	$0.320401\pi$
$239$			403.911i			1.69000i	−0.534764	+	0.845002i	$0.679599\pi$
$240$	−253.759			−1.05733
$241$		−	298.240i		−	1.23751i	−0.785584	−	0.618755i	$-0.787637\pi$
$241$		−	298.240i		−	1.23751i	0.785584	−	0.618755i	$-0.212363\pi$
$242$	413.874	−	174.564i	1.71022	−	0.721337i
$243$	−56.2334			−0.231413
$244$		−	255.421i		−	1.04681i
$245$	50.5396			0.206284
$246$	−617.156			−2.50877
$247$	5.16581			0.0209142
$248$		−	330.441i		−	1.33242i
$249$		−	243.825i		−	0.979216i
$250$			371.387i			1.48555i
$251$	286.597			1.14182			0.570911	−	0.821012i	$-0.306590\pi$
$251$	286.597			1.14182			0.570911	+	0.821012i	$0.306590\pi$
$252$			52.4412i			0.208100i
$253$	43.9576	+	29.1672i	0.173746	+	0.115285i
$254$	−109.650			−0.431693
$255$		−	75.3740i		−	0.295584i
$256$	−198.554			−0.775603
$257$	407.438			1.58536			0.792681	−	0.609637i	$-0.208685\pi$
$257$	407.438			1.58536			0.792681	+	0.609637i	$0.208685\pi$
$258$	−479.641			−1.85907
$259$			273.618i			1.05644i
$260$			63.4669i			0.244104i
$261$		−	7.78529i		−	0.0298287i
$262$	726.945			2.77460
$263$			122.177i			0.464550i	0.972650	+	0.232275i	$0.0746169\pi$
$263$			122.177i			0.464550i	−0.972650	+	0.232275i	$0.925383\pi$
$264$	368.061	−	554.701i	1.39417	−	2.10114i
$265$	−200.189			−0.755432
$266$			33.5944i			0.126295i
$267$	84.1683			0.315237
$268$	−203.256			−0.758416
$269$	256.340			0.952937			0.476469	−	0.879191i	$-0.341917\pi$
$269$	256.340			0.952937			0.476469	+	0.879191i	$0.341917\pi$
$270$		−	233.456i		−	0.864653i
$271$		−	239.693i		−	0.884476i	−0.896898	−	0.442238i	$-0.854185\pi$
$271$		−	239.693i		−	0.884476i	0.896898	−	0.442238i	$-0.145815\pi$
$272$			488.166i			1.79473i
$273$	−42.2255			−0.154672
$274$			621.129i			2.26690i
$275$	−183.990	−	122.083i	−0.669053	−	0.443937i
$276$	132.283			0.479287
$277$			19.9293i			0.0719469i	0.999353	+	0.0359734i	$0.0114532\pi$
$277$			19.9293i			0.0719469i	−0.999353	+	0.0359734i	$0.988547\pi$
$278$	−520.876			−1.87366
$279$	16.1204			0.0577791
$280$	−243.943			−0.871226
$281$		−	38.9019i		−	0.138441i	−0.997601	−	0.0692204i	$-0.977949\pi$
$281$		−	38.9019i		−	0.138441i	0.997601	−	0.0692204i	$-0.0220512\pi$
$282$			60.0144i			0.212817i
$283$		−	25.5351i		−	0.0902301i	−0.998982	−	0.0451151i	$-0.985635\pi$
$283$		−	25.5351i		−	0.0902301i	0.998982	−	0.0451151i	$-0.0143654\pi$
$284$	−197.842			−0.696627
$285$		−	11.0604i		−	0.0388083i
$286$	−99.4748	−	66.0046i	−0.347814	−	0.230785i
$287$	−301.919			−1.05198
$288$			67.6880i			0.235028i
$289$	144.000			0.498271
$290$	61.2744			0.211291
$291$	223.012			0.766364
$292$		−	1087.62i		−	3.72471i
$293$		−	135.217i		−	0.461490i	−0.973014	−	0.230745i	$-0.925884\pi$
$293$		−	135.217i		−	0.461490i	0.973014	−	0.230745i	$-0.0741164\pi$
$294$			238.379i			0.810812i
$295$	158.667			0.537856
$296$			1146.48i			3.87323i
$297$	259.699	+	172.318i	0.874408	+	0.580196i
$298$	687.976			2.30864
$299$		−	14.0207i		−	0.0468920i
$300$	−553.686			−1.84562
$301$	−234.645			−0.779551
$302$	−396.670			−1.31348
$303$			147.726i			0.487543i
$304$			71.6334i			0.235636i
$305$			57.9633i			0.190044i
$306$	−46.7974			−0.152933
$307$			33.0151i			0.107541i	0.998553	+	0.0537705i	$0.0171239\pi$
$307$			33.0151i			0.107541i	−0.998553	+	0.0537705i	$0.982876\pi$
$308$	304.651	−	459.136i	0.989126	−	1.49070i
$309$	81.9387			0.265174
$310$			126.876i			0.409277i
$311$	−178.502			−0.573961			−0.286980	−	0.957936i	$-0.592651\pi$
$311$	−178.502			−0.573961			−0.286980	+	0.957936i	$0.592651\pi$
$312$	−176.927			−0.567075
$313$	237.007			0.757209			0.378605	−	0.925558i	$-0.376404\pi$
$313$	237.007			0.757209			0.378605	+	0.925558i	$0.376404\pi$
$314$			434.881i			1.38497i
$315$		−	11.9006i		−	0.0377798i
$316$		−	136.415i		−	0.431692i
$317$	−585.587			−1.84728			−0.923638	−	0.383266i	$-0.874799\pi$
$317$	−585.587			−1.84728			−0.923638	+	0.383266i	$0.874799\pi$
$318$		−	944.228i		−	2.96927i
$319$	−45.2277	+	68.1622i	−0.141780	+	0.213675i
$320$	−172.815			−0.540046
$321$			428.493i			1.33487i
$322$	91.1800			0.283168
$323$	−21.2772			−0.0658738
$324$	689.366			2.12767
$325$			58.6853i			0.180570i
$326$			305.042i			0.935711i
$327$		−	119.863i		−	0.366553i
$328$	−1265.06			−3.85689
$329$			29.3596i			0.0892389i
$330$	−141.320	+	212.983i	−0.428244	+	0.645402i
$331$	167.197			0.505126			0.252563	−	0.967580i	$-0.418726\pi$
$331$	167.197			0.505126			0.252563	+	0.967580i	$0.418726\pi$
$332$		−	845.632i		−	2.54708i
$333$	−55.9302			−0.167959
$334$	−1203.08			−3.60205
$335$	46.1253			0.137688
$336$		−	585.533i		−	1.74266i
$337$		−	437.087i		−	1.29699i	−0.761217	−	0.648497i	$-0.775398\pi$
$337$		−	437.087i		−	1.29699i	0.761217	−	0.648497i	$-0.224602\pi$
$338$		−	595.641i		−	1.76225i
$339$	391.726			1.15553
$340$		−	261.412i		−	0.768858i
$341$	−141.138	−	93.6493i	−0.413894	−	0.274631i
$342$	−6.86704			−0.0200791
$343$			367.572i			1.07164i
$344$	−983.177			−2.85807
$345$	−30.0194			−0.0870127
$346$	−767.852			−2.21923
$347$			119.686i			0.344918i	0.985017	+	0.172459i	$0.0551712\pi$
$347$			119.686i			0.344918i	−0.985017	+	0.172459i	$0.944829\pi$
$348$			205.123i			0.589433i
$349$		−	20.2005i		−	0.0578811i	−0.999581	−	0.0289406i	$-0.990787\pi$
$349$		−	20.2005i		−	0.0578811i	0.999581	−	0.0289406i	$-0.00921335\pi$
$350$	−381.644			−1.09041
$351$		−	82.8336i		−	0.235993i
$352$	393.225	−	592.625i	1.11712	−	1.68360i
$353$	−428.808			−1.21475			−0.607377	−	0.794414i	$-0.707778\pi$
$353$	−428.808			−1.21475			−0.607377	+	0.794414i	$0.707778\pi$
$354$			748.382i			2.11407i
$355$	44.8968			0.126470
$356$	291.912			0.819977
$357$	173.921			0.487173
$358$		−	394.239i		−	1.10123i
$359$			498.002i			1.38719i	0.720364	+	0.693596i	$0.243975\pi$
$359$			498.002i			1.38719i	−0.720364	+	0.693596i	$0.756025\pi$
$360$		−	49.8644i		−	0.138512i
$361$	357.878			0.991351
$362$			1140.42i			3.15034i
$363$	−132.613	−	314.413i	−0.365325	−	0.866150i
$364$	−146.446			−0.402324
$365$			246.816i			0.676207i
$366$	−273.394			−0.746978
$367$	577.389			1.57327			0.786634	−	0.617420i	$-0.211822\pi$
$367$	577.389			1.57327			0.786634	+	0.617420i	$0.211822\pi$
$368$	194.423			0.528323
$369$		−	61.7152i		−	0.167250i
$370$		−	440.201i		−	1.18973i
$371$		−	461.925i		−	1.24508i
$372$	−424.731			−1.14175
$373$			402.439i			1.07893i	0.842009	+	0.539463i	$0.181373\pi$
$373$			402.439i			1.07893i	−0.842009	+	0.539463i	$0.818627\pi$
$374$	409.723	+	271.864i	1.09552	+	0.726908i
$375$	282.136			0.752363
$376$			123.019i			0.327177i
$377$	21.7410			0.0576685
$378$	538.686			1.42510
$379$	253.217			0.668120			0.334060	−	0.942552i	$-0.391581\pi$
$379$	253.217			0.668120			0.334060	+	0.942552i	$0.391581\pi$
$380$		−	38.3595i		−	0.100946i
$381$			83.2991i			0.218633i
$382$		−	322.465i		−	0.844150i
$383$	−597.161			−1.55917			−0.779584	−	0.626298i	$-0.784570\pi$
$383$	−597.161			−1.55917			−0.779584	+	0.626298i	$0.784570\pi$
$384$		−	85.7555i		−	0.223322i
$385$	−69.1353	+	104.193i	−0.179572	+	0.270631i
$386$	1185.95			3.07242
$387$		−	47.9637i		−	0.123937i
$388$	773.448			1.99342
$389$	−606.242			−1.55846			−0.779231	−	0.626737i	$-0.784390\pi$
$389$	−606.242			−1.55846			−0.779231	+	0.626737i	$0.784390\pi$
$390$	67.9329			0.174187
$391$			57.7494i			0.147697i
$392$			488.633i			1.24651i
$393$		−	552.248i		−	1.40521i
$394$	955.618			2.42543
$395$			30.9569i			0.0783720i
$396$	93.8520	+	62.2737i	0.237000	+	0.157257i
$397$	62.0969			0.156415			0.0782077	−	0.996937i	$-0.475080\pi$
$397$	62.0969			0.156415			0.0782077	+	0.996937i	$0.475080\pi$
$398$		−	773.931i		−	1.94455i
$399$	25.5211			0.0639627
$400$	−813.780			−2.03445
$401$	440.712			1.09903			0.549516	−	0.835483i	$-0.314812\pi$
$401$	440.712			1.09903			0.549516	+	0.835483i	$0.314812\pi$
$402$			217.558i			0.541189i
$403$			45.0173i			0.111706i
$404$			512.341i			1.26817i
$405$	−156.440			−0.386271
$406$			141.387i			0.348244i
$407$	489.683	+	324.920i	1.20315	+	0.798329i
$408$	728.740			1.78613
$409$			550.963i			1.34710i	0.739142	+	0.673549i	$0.235231\pi$
$409$			550.963i			1.34710i	−0.739142	+	0.673549i	$0.764769\pi$
$410$	485.731			1.18471
$411$	471.861			1.14808
$412$	284.179			0.689755
$413$			366.116i			0.886478i
$414$			18.6381i			0.0450196i
$415$			191.902i			0.462414i
$416$	−189.024			−0.454384
$417$			395.700i			0.948922i
$418$	60.1227	+	39.8932i	0.143834	+	0.0954383i
$419$	−380.148			−0.907274			−0.453637	−	0.891187i	$-0.649874\pi$
$419$	−380.148			−0.907274			−0.453637	+	0.891187i	$0.649874\pi$
$420$			313.552i			0.746551i
$421$	753.520			1.78983			0.894917	−	0.446232i	$-0.147234\pi$
$421$	753.520			1.78983			0.894917	+	0.446232i	$0.147234\pi$
$422$	864.123			2.04769
$423$	−6.00140			−0.0141877
$424$		−	1935.49i		−	4.56485i
$425$		−	241.717i		−	0.568745i
$426$			211.764i			0.497098i
$427$	−133.747			−0.313224
$428$			1486.10i			3.47219i
$429$	−50.1425	+	75.5693i	−0.116882	+	0.176152i
$430$	377.500			0.877907
$431$		−	252.854i		−	0.586668i	−0.956010	−	0.293334i	$-0.905235\pi$
$431$		−	252.854i		−	0.586668i	0.956010	−	0.293334i	$-0.0947648\pi$
$432$	1148.64			2.65889
$433$	−62.3560			−0.144009			−0.0720047	−	0.997404i	$-0.522940\pi$
$433$	−62.3560			−0.144009			−0.0720047	+	0.997404i	$0.522940\pi$
$434$	−292.758			−0.674558
$435$		−	46.5491i		−	0.107009i
$436$		−	415.708i		−	0.953458i
$437$			8.47414i			0.0193916i
$438$	−1164.15			−2.65787
$439$		−	424.263i		−	0.966431i	−0.875501	−	0.483215i	$-0.839469\pi$
$439$		−	424.263i		−	0.966431i	0.875501	−	0.483215i	$-0.160531\pi$
$440$	−289.681	+	436.576i	−0.658367	+	0.992218i
$441$	−23.8377			−0.0540537
$442$		−	130.685i		−	0.295668i
$443$	420.565			0.949356			0.474678	−	0.880159i	$-0.342564\pi$
$443$	420.565			0.949356			0.474678	+	0.880159i	$0.342564\pi$
$444$	1473.62			3.31896
$445$	−66.2444			−0.148864
$446$		−	481.385i		−	1.07934i
$447$		−	522.643i		−	1.16922i
$448$		−	398.759i		−	0.890087i
$449$	−508.999			−1.13363			−0.566814	−	0.823846i	$-0.691824\pi$
$449$	−508.999			−1.13363			−0.566814	+	0.823846i	$0.691824\pi$
$450$		−	78.0119i		−	0.173360i
$451$	−358.527	+	540.332i	−0.794960	+	1.19808i
$452$	1358.58			3.00571
$453$			301.344i			0.665218i
$454$	−1317.07			−2.90103
$455$	33.2334			0.0730405
$456$	106.935			0.234507
$457$		−	577.760i		−	1.26425i	−0.774868	−	0.632123i	$-0.782184\pi$
$457$		−	577.760i		−	1.26425i	0.774868	−	0.632123i	$-0.217816\pi$
$458$		−	1136.98i		−	2.48250i
$459$			341.180i			0.743312i
$460$	−104.113			−0.226333
$461$		−	359.507i		−	0.779841i	−0.920848	−	0.389921i	$-0.872502\pi$
$461$		−	359.507i		−	0.779841i	0.920848	−	0.389921i	$-0.127498\pi$
$462$	−491.445	−	326.088i	−1.06373	−	0.705819i
$463$	197.014			0.425516			0.212758	−	0.977105i	$-0.431755\pi$
$463$	197.014			0.425516			0.212758	+	0.977105i	$0.431755\pi$
$464$			301.479i			0.649739i
$465$	96.3853			0.207280
$466$	−1356.44			−2.91081
$467$	−452.306			−0.968536			−0.484268	−	0.874920i	$-0.660914\pi$
$467$	−452.306			−0.968536			−0.484268	+	0.874920i	$0.660914\pi$
$468$		−	29.9350i		−	0.0639638i
$469$			106.431i			0.226933i
$470$		−	47.2342i		−	0.100498i
$471$	330.372			0.701426
$472$			1534.05i			3.25010i
$473$	−278.639	+	419.935i	−0.589090	+	0.887811i
$474$	−146.014			−0.308046
$475$		−	35.4695i		−	0.0746726i
$476$	603.191			1.26721
$477$	94.4220			0.197950
$478$	1499.42			3.13685
$479$			165.332i			0.345161i	0.984995	+	0.172581i	$0.0552105\pi$
$479$			165.332i			0.345161i	−0.984995	+	0.172581i	$0.944789\pi$
$480$			404.713i			0.843153i
$481$		−	156.189i		−	0.324718i
$482$	−1107.14			−2.29697
$483$		−	69.2679i		−	0.143412i
$484$	−459.927	−	1090.44i	−0.950263	−	2.25298i
$485$	−175.521			−0.361899
$486$			208.752i			0.429531i
$487$	397.583			0.816391			0.408196	−	0.912894i	$-0.366158\pi$
$487$	397.583			0.816391			0.408196	+	0.912894i	$0.366158\pi$
$488$	−560.408			−1.14838
$489$	231.735			0.473896
$490$		−	187.615i		−	0.382888i
$491$		−	261.902i		−	0.533405i	−0.963779	−	0.266703i	$-0.914066\pi$
$491$		−	261.902i		−	0.533405i	0.963779	−	0.266703i	$-0.0859341\pi$
$492$			1626.04i			3.30496i
$493$	−89.5483			−0.181639
$494$		−	19.1767i		−	0.0388193i
$495$	−21.2981	−	14.1319i	−0.0430265	−	0.0285494i
$496$	−624.248			−1.25856
$497$			103.597i			0.208444i
$498$	−905.137			−1.81754
$499$	−197.738			−0.396268			−0.198134	−	0.980175i	$-0.563488\pi$
$499$	−197.738			−0.396268			−0.198134	+	0.980175i	$0.563488\pi$
$500$	978.503			1.95701
$501$			913.962i			1.82427i
$502$		−	1063.92i		−	2.11936i
$503$		−	802.955i		−	1.59633i	−0.602438	−	0.798166i	$-0.705804\pi$
$503$		−	802.955i		−	1.59633i	0.602438	−	0.798166i	$-0.294196\pi$
$504$	115.059			0.228292
$505$		−	116.267i		−	0.230232i
$506$	108.276	−	163.181i	0.213984	−	0.322493i
$507$	−452.498			−0.892500
$508$			288.898i			0.568696i
$509$	−662.471			−1.30151			−0.650757	−	0.759286i	$-0.725548\pi$
$509$	−662.471			−1.30151			−0.650757	+	0.759286i	$0.725548\pi$
$510$	−279.806			−0.548640
$511$	−569.512			−1.11451
$512$			858.716i			1.67718i
$513$			50.0647i			0.0975921i
$514$		−	1512.51i		−	2.94262i
$515$	−64.4896			−0.125222
$516$			1263.72i			2.44908i
$517$	52.5438	+	34.8644i	0.101632	+	0.0674360i
$518$	1015.74			1.96088
$519$			583.324i			1.12394i
$520$	139.250			0.267789
$521$	39.6154			0.0760372			0.0380186	−	0.999277i	$-0.487895\pi$
$521$	39.6154			0.0760372			0.0380186	+	0.999277i	$0.487895\pi$
$522$	−28.9009			−0.0553657
$523$		−	401.452i		−	0.767595i	−0.923417	−	0.383798i	$-0.874616\pi$
$523$		−	401.452i		−	0.767595i	0.923417	−	0.383798i	$-0.125384\pi$
$524$		−	1915.30i		−	3.65516i
$525$			289.929i			0.552245i
$526$	453.549			0.862260
$527$		−	185.420i		−	0.351841i
$528$	−1047.91	−	695.318i	−1.98467	−	1.31689i
$529$	23.0000			0.0434783
$530$			743.151i			1.40217i
$531$	−74.8377			−0.140937
$532$	88.5122			0.166376
$533$	172.344			0.323348
$534$		−	312.453i		−	0.585118i
$535$		−	337.244i		−	0.630362i
$536$			445.955i			0.832005i
$537$	−299.497			−0.557722
$538$		−	951.597i		−	1.76877i
$539$	208.705	+	138.482i	0.387208	+	0.256924i
$540$	−615.094			−1.13906
$541$		−	513.423i		−	0.949027i	−0.880248	−	0.474513i	$-0.842624\pi$
$541$		−	513.423i		−	0.949027i	0.880248	−	0.474513i	$-0.157376\pi$
$542$	−889.799			−1.64169
$543$	866.359			1.59551
$544$	778.563			1.43118
$545$			94.3377i			0.173097i
$546$			156.751i			0.287090i
$547$			1024.91i			1.87369i	0.349750	+	0.936843i	$0.386266\pi$
$547$			1024.91i			1.87369i	−0.349750	+	0.936843i	$0.613734\pi$
$548$	1636.51			2.98633
$549$		−	27.3392i		−	0.0497981i
$550$	−453.201	+	683.014i	−0.824001	+	1.24184i
$551$	−13.1403			−0.0238481
$552$		−	290.237i		−	0.525791i
$553$	−71.4312			−0.129170
$554$	73.9823			0.133542
$555$	−334.413			−0.602545
$556$			1372.37i			2.46828i
$557$		−	611.991i		−	1.09873i	−0.835584	−	0.549363i	$-0.814870\pi$
$557$		−	611.991i		−	1.09873i	0.835584	−	0.549363i	$-0.185130\pi$
$558$		−	59.8427i		−	0.107245i
$559$	133.942			0.239611
$560$			460.842i			0.822932i
$561$	206.530	−	311.259i	0.368146	−	0.554830i
$562$	−144.413			−0.256963
$563$			718.045i			1.27539i	0.770289	+	0.637695i	$0.220112\pi$
$563$			718.045i			1.27539i	−0.770289	+	0.637695i	$0.779888\pi$
$564$	158.122			0.280358
$565$	−308.307			−0.545676
$566$	−94.7926			−0.167478
$567$		−	360.975i		−	0.636641i
$568$			434.077i			0.764220i
$569$		−	757.312i		−	1.33095i	−0.746419	−	0.665476i	$-0.768228\pi$
$569$		−	757.312i		−	1.33095i	0.746419	−	0.665476i	$-0.231772\pi$
$570$	−41.0587			−0.0720329
$571$		−	383.124i		−	0.670971i	−0.942045	−	0.335485i	$-0.891100\pi$
$571$		−	383.124i		−	0.670971i	0.942045	−	0.335485i	$-0.108900\pi$
$572$	−173.904	+	262.089i	−0.304028	+	0.458198i
$573$	−244.971			−0.427524
$574$			1120.80i			1.95260i
$575$	−96.2691			−0.167425
$576$	81.5103			0.141511
$577$	749.516			1.29899			0.649494	−	0.760367i	$-0.274981\pi$
$577$	749.516			1.29899			0.649494	+	0.760367i	$0.274981\pi$
$578$		−	534.564i		−	0.924851i
$579$		−	900.949i		−	1.55604i
$580$		−	161.441i		−	0.278347i
$581$	−442.801			−0.762137
$582$		−	827.874i		−	1.42246i
$583$	−826.689	−	548.533i	−1.41799	−	0.940880i
$584$	−2386.29			−4.08612
$585$			6.79324i			0.0116124i
$586$	−501.957			−0.856582
$587$	−427.646			−0.728528			−0.364264	−	0.931296i	$-0.618679\pi$
$587$	−427.646			−0.728528			−0.364264	+	0.931296i	$0.618679\pi$
$588$	628.063			1.06813
$589$		−	27.2085i		−	0.0461944i
$590$		−	589.012i		−	0.998326i
$591$		−	725.967i		−	1.22837i
$592$	2165.85			3.65853
$593$		−	1117.61i		−	1.88468i	−0.334663	−	0.942338i	$-0.608623\pi$
$593$		−	1117.61i		−	1.88468i	0.334663	−	0.942338i	$-0.391377\pi$
$594$	639.687	−	964.066i	1.07691	−	1.62301i
$595$	−136.884			−0.230057
$596$		−	1812.63i		−	3.04132i
$597$	−587.942			−0.984828
$598$	−52.0483			−0.0870373
$599$	603.509			1.00753			0.503763	−	0.863842i	$-0.331948\pi$
$599$	603.509			1.00753			0.503763	+	0.863842i	$0.331948\pi$
$600$			1214.82i			2.02470i
$601$		−	248.929i		−	0.414191i	−0.978321	−	0.207096i	$-0.933599\pi$
$601$		−	248.929i		−	0.414191i	0.978321	−	0.207096i	$-0.0664011\pi$
$602$			871.058i			1.44694i
$603$	−21.7556			−0.0360790
$604$			1045.12i			1.73033i
$605$	104.373	+	247.458i	0.172517	+	0.409021i
$606$	548.393			0.904939
$607$			3.45150i			0.00568616i	0.999996	+	0.00284308i	$0.000904982\pi$
$607$			3.45150i			0.00568616i	−0.999996	+	0.00284308i	$0.999095\pi$
$608$	114.246			0.187905
$609$	107.409			0.176370
$610$	215.174			0.352744
$611$		−	16.7594i		−	0.0274294i
$612$			123.298i			0.201468i
$613$		−	334.538i		−	0.545738i	−0.962051	−	0.272869i	$-0.912027\pi$
$613$		−	334.538i		−	0.545738i	0.962051	−	0.272869i	$-0.0879726\pi$
$614$	122.560			0.199609
$615$		−	369.001i		−	0.600002i
$616$	−1007.37	−	668.422i	−1.63534	−	1.08510i
$617$	−566.449			−0.918070			−0.459035	−	0.888418i	$-0.651805\pi$
$617$	−566.449			−0.918070			−0.459035	+	0.888418i	$0.651805\pi$
$618$		−	304.176i		−	0.492195i
$619$	−571.422			−0.923137			−0.461569	−	0.887104i	$-0.652713\pi$
$619$	−571.422			−0.923137			−0.461569	+	0.887104i	$0.652713\pi$
$620$	334.283			0.539166
$621$	135.883			0.218813
$622$			662.642i			1.06534i
$623$		−	152.855i		−	0.245353i
$624$			334.240i			0.535641i
$625$	279.783			0.447653
$626$		−	879.826i		−	1.40547i
$627$	30.3062	−	45.6742i	0.0483352	−	0.0728455i
$628$	1145.79			1.82451
$629$			643.323i			1.02277i
$630$	−44.1780			−0.0701239
$631$	166.216			0.263417			0.131708	−	0.991289i	$-0.457954\pi$
$631$	166.216			0.263417			0.131708	+	0.991289i	$0.457954\pi$
$632$	−299.302			−0.473578
$633$		−	656.459i		−	1.03706i
$634$			2173.84i			3.42877i
$635$		−	65.5603i		−	0.103245i
$636$	−2487.78			−3.91161
$637$		−	66.5685i		−	0.104503i
$638$	253.035	+	167.896i	0.396606	+	0.263160i
$639$	−21.1762			−0.0331396
$640$			67.4936i			0.105459i
$641$	627.233			0.978523			0.489261	−	0.872137i	$-0.337266\pi$
$641$	627.233			0.978523			0.489261	+	0.872137i	$0.337266\pi$
$642$	1590.67			2.47768
$643$	604.826			0.940631			0.470315	−	0.882498i	$-0.344140\pi$
$643$	604.826			0.940631			0.470315	+	0.882498i	$0.344140\pi$
$644$		−	240.234i		−	0.373035i
$645$		−	286.780i		−	0.444620i
$646$			78.9863i			0.122270i
$647$	514.851			0.795751			0.397876	−	0.917439i	$-0.369748\pi$
$647$	514.851			0.795751			0.397876	+	0.917439i	$0.369748\pi$
$648$		−	1512.51i		−	2.33412i
$649$	655.223	+	434.760i	1.00959	+	0.669893i
$650$	217.854			0.335160
$651$			222.403i			0.341633i
$652$	803.702			1.23267
$653$	−764.189			−1.17027			−0.585137	−	0.810934i	$-0.698959\pi$
$653$	−764.189			−1.17027			−0.585137	+	0.810934i	$0.698959\pi$
$654$	−444.960			−0.680367
$655$			434.645i			0.663580i
$656$			2389.87i			3.64309i
$657$		−	116.414i		−	0.177190i
$658$	108.990			0.165638
$659$			527.152i			0.799928i	0.916531	+	0.399964i	$0.130977\pi$
$659$			527.152i			0.799928i	−0.916531	+	0.399964i	$0.869023\pi$
$660$	561.151	+	372.341i	0.850229	+	0.564153i
$661$	−829.561			−1.25501			−0.627504	−	0.778613i	$-0.715924\pi$
$661$	−829.561			−1.25501			−0.627504	+	0.778613i	$0.715924\pi$
$662$		−	620.675i		−	0.937576i
$663$	−99.2793			−0.149743
$664$	−1855.37			−2.79423
$665$	−20.0863			−0.0302050
$666$			207.627i			0.311752i
$667$			35.6646i			0.0534702i
$668$			3169.80i			4.74520i
$669$	−365.700			−0.546636
$670$		−	171.228i		−	0.255565i
$671$	−158.824	+	239.362i	−0.236697	+	0.356724i
$672$	−933.851			−1.38966
$673$			1094.63i			1.62649i	0.581920	+	0.813246i	$0.302302\pi$
$673$			1094.63i			1.62649i	−0.581920	+	0.813246i	$0.697698\pi$
$674$	−1622.57			−2.40738
$675$	−568.752			−0.842596
$676$	−1569.35			−2.32152
$677$		−	631.668i		−	0.933040i	−0.884511	−	0.466520i	$-0.845508\pi$
$677$		−	631.668i		−	0.933040i	0.884511	−	0.466520i	$-0.154492\pi$
$678$		−	1454.18i		−	2.14481i
$679$		−	405.004i		−	0.596471i
$680$	−573.552			−0.843459
$681$			1000.55i			1.46924i
$682$	−347.649	+	523.938i	−0.509749	+	0.768238i
$683$	124.032			0.181599			0.0907993	−	0.995869i	$-0.471058\pi$
$683$	124.032			0.181599			0.0907993	+	0.995869i	$0.471058\pi$
$684$			18.0928i			0.0264514i
$685$	−371.377			−0.542156
$686$	1364.52			1.98909
$687$	−863.747			−1.25727
$688$			1857.36i			2.69965i
$689$			263.681i			0.382701i
$690$			111.439i			0.161506i
$691$	720.430			1.04259			0.521296	−	0.853376i	$-0.325449\pi$
$691$	720.430			1.04259			0.521296	+	0.853376i	$0.325449\pi$
$692$			2023.08i			2.92353i
$693$	32.6086	−	49.1441i	0.0470542	−	0.0709150i
$694$	444.305			0.640209
$695$		−	311.435i		−	0.448108i
$696$	450.051			0.646626
$697$	−709.862			−1.01845
$698$	−74.9892			−0.107434
$699$			1030.46i			1.47419i
$700$			1005.53i			1.43647i
$701$			765.277i			1.09169i	0.837885	+	0.545847i	$0.183792\pi$
$701$			765.277i			1.09169i	−0.837885	+	0.545847i	$0.816208\pi$
$702$	−307.498			−0.438032
$703$			94.4010i			0.134283i
$704$	−713.644	−	473.524i	−1.01370	−	0.672620i
$705$	−35.8830			−0.0508979
$706$			1591.84i			2.25473i
$707$	268.279			0.379461
$708$	1971.78			2.78500
$709$	−181.165			−0.255522			−0.127761	−	0.991805i	$-0.540779\pi$
$709$	−181.165			−0.255522			−0.127761	+	0.991805i	$0.540779\pi$
$710$		−	166.668i		−	0.234743i
$711$		−	14.6013i		−	0.0205362i
$712$		−	640.472i		−	0.899539i
$713$	−73.8477			−0.103573
$714$		−	645.636i		−	0.904252i
$715$	39.4645	−	59.4766i	0.0551951	−	0.0831840i
$716$	−1038.71			−1.45072
$717$		−	1139.08i		−	1.58867i
$718$	1848.70			2.57480
$719$	381.476			0.530565			0.265283	−	0.964171i	$-0.414535\pi$
$719$	381.476			0.530565			0.265283	+	0.964171i	$0.414535\pi$
$720$	−94.2007			−0.130834
$721$		−	148.806i		−	0.206388i
$722$		−	1328.53i		−	1.84007i
$723$			841.075i			1.16331i
$724$	3004.70			4.15014
$725$		−	149.278i		−	0.205901i
$726$	−1167.18	+	492.291i	−1.60768	+	0.678087i
$727$	−60.3143			−0.0829633			−0.0414816	−	0.999139i	$-0.513208\pi$
$727$	−60.3143			−0.0829633			−0.0414816	+	0.999139i	$0.513208\pi$
$728$			321.311i			0.441362i
$729$	792.923			1.08769
$730$	916.240			1.25512
$731$	−551.690			−0.754706
$732$			720.318i			0.984041i
$733$			886.156i			1.20894i	0.796626	+	0.604472i	$0.206616\pi$
$733$			886.156i			1.20894i	−0.796626	+	0.604472i	$0.793384\pi$
$734$		−	2143.41i		−	2.92018i
$735$	−142.528			−0.193916
$736$		−	310.080i		−	0.421304i
$737$	190.476	+	126.387i	0.258448	+	0.171488i
$738$	−229.102			−0.310436
$739$			531.318i			0.718968i	0.933151	+	0.359484i	$0.117047\pi$
$739$			531.318i			0.718968i	−0.933151	+	0.359484i	$0.882953\pi$
$740$	−1159.81			−1.56731
$741$	−14.5682			−0.0196602
$742$	−1714.78			−2.31102
$743$		−	181.095i		−	0.243735i	−0.992546	−	0.121868i	$-0.961112\pi$
$743$		−	181.095i		−	0.243735i	0.992546	−	0.121868i	$-0.0388883\pi$
$744$			931.884i			1.25253i
$745$			411.345i			0.552141i
$746$	1493.95			2.00262
$747$		−	90.5130i		−	0.121169i
$748$	716.287	−	1079.51i	0.957602	−	1.44319i
$749$	778.170			1.03894
$750$		−	1047.36i		−	1.39648i
$751$	452.551			0.602597			0.301299	−	0.953530i	$-0.402580\pi$
$751$	452.551			0.602597			0.301299	+	0.953530i	$0.402580\pi$
$752$	232.399			0.309041
$753$	−808.240			−1.07336
$754$		−	80.7079i		−	0.107040i
$755$		−	237.172i		−	0.314135i
$756$		−	1419.29i		−	1.87737i
$757$	−387.825			−0.512318			−0.256159	−	0.966635i	$-0.582457\pi$
$757$	−387.825			−0.512318			−0.256159	+	0.966635i	$0.582457\pi$
$758$		−	940.004i		−	1.24011i
$759$	−123.966	−	82.2552i	−0.163328	−	0.108373i
$760$	−84.1630			−0.110741
$761$		−	133.741i		−	0.175743i	−0.996132	−	0.0878717i	$-0.971993\pi$
$761$		−	133.741i		−	0.175743i	0.996132	−	0.0878717i	$-0.0280066\pi$
$762$	309.227			0.405809
$763$	−217.679			−0.285293
$764$	−849.608			−1.11205
$765$		−	27.9804i		−	0.0365757i
$766$			2216.81i			2.89401i
$767$		−	208.990i		−	0.272477i
$768$	559.948			0.729099
$769$			1434.15i			1.86495i	0.361234	+	0.932475i	$0.382355\pi$
$769$			1434.15i			1.86495i	−0.361234	+	0.932475i	$0.617645\pi$
$770$	386.790	+	256.647i	0.502325	+	0.333308i
$771$	−1149.03			−1.49031
$772$		−	3124.67i		−	4.04750i
$773$	270.299			0.349676			0.174838	−	0.984597i	$-0.444060\pi$
$773$	270.299			0.349676			0.174838	+	0.984597i	$0.444060\pi$
$774$	−178.053			−0.230043
$775$	309.098			0.398836
$776$		−	1696.99i		−	2.18684i
$777$		−	771.637i		−	0.993098i
$778$			2250.52i			2.89269i
$779$	−104.165			−0.133716
$780$		−	178.985i		−	0.229468i
$781$	185.403	+	123.021i	0.237392	+	0.157517i
$782$	214.380			0.274143
$783$			210.704i			0.269099i
$784$	923.094			1.17742
$785$	−260.018			−0.331233
$786$	−2050.08			−2.60824
$787$			820.972i			1.04317i	0.853200	+	0.521583i	$0.174658\pi$
$787$			820.972i			1.04317i	−0.853200	+	0.521583i	$0.825342\pi$
$788$		−	2517.79i		−	3.19517i
$789$		−	344.553i		−	0.436696i
$790$	114.920			0.145468
$791$		−	711.399i		−	0.899367i
$792$	136.632	−	205.917i	0.172515	−	0.259996i
$793$	76.3467			0.0962758
$794$		−	230.519i		−	0.290326i
$795$	564.559			0.710137
$796$	−2039.10			−2.56168
$797$	696.476			0.873872			0.436936	−	0.899493i	$-0.356064\pi$
$797$	696.476			0.873872			0.436936	+	0.899493i	$0.356064\pi$
$798$		−	94.7405i		−	0.118722i
$799$			69.0295i			0.0863949i
$800$			1297.88i			1.62234i
$801$	31.2451			0.0390076
$802$		−	1636.03i		−	2.03994i
$803$	−676.293	+	1019.23i	−0.842208	+	1.26928i
$804$	573.206			0.712943
$805$			54.5171i			0.0677231i
$806$	167.115			0.207339
$807$	−722.911			−0.895801
$808$	1124.11			1.39122
$809$			494.088i			0.610739i	0.952234	+	0.305369i	$0.0987800\pi$
$809$			494.088i			0.610739i	−0.952234	+	0.305369i	$0.901220\pi$
$810$			580.743i			0.716966i
$811$		−	1323.70i		−	1.63218i	−0.577926	−	0.816089i	$-0.696138\pi$
$811$		−	1323.70i		−	1.63218i	0.577926	−	0.816089i	$-0.303862\pi$
$812$	372.516			0.458763
$813$			675.964i			0.831445i
$814$	1206.18	−	1817.82i	1.48180	−	2.23320i
$815$	−182.386			−0.223787
$816$		−	1376.69i		−	1.68712i
$817$	−80.9549			−0.0990880
$818$	2045.31			2.50038
$819$	−15.6750			−0.0191392
$820$		−	1279.77i		−	1.56069i
$821$			1347.93i			1.64182i	0.571060	+	0.820908i	$0.306532\pi$
$821$			1347.93i			1.64182i	−0.571060	+	0.820908i	$0.693468\pi$
$822$		−	1751.66i		−	2.13098i
$823$	−121.479			−0.147605			−0.0738025	−	0.997273i	$-0.523513\pi$
$823$	−121.479			−0.147605			−0.0738025	+	0.997273i	$0.523513\pi$
$824$		−	623.506i		−	0.756682i
$825$	518.874	+	344.289i	0.628938	+	0.417320i
$826$	1359.11			1.64541
$827$			98.2407i			0.118792i	0.998235	+	0.0593958i	$0.0189174\pi$
$827$			98.2407i			0.118792i	−0.998235	+	0.0593958i	$0.981083\pi$
$828$	49.1063			0.0593071
$829$	431.135			0.520067			0.260033	−	0.965600i	$-0.416266\pi$
$829$	431.135			0.520067			0.260033	+	0.965600i	$0.416266\pi$
$830$	712.385			0.858296
$831$		−	56.2031i		−	0.0676331i
$832$			227.624i			0.273586i
$833$			274.187i			0.329156i
$834$	1468.94			1.76131
$835$		−	719.331i		−	0.861474i
$836$	105.108	−	158.407i	0.125727	−	0.189482i
$837$	−436.288			−0.521252
$838$			1411.20i			1.68401i
$839$	1585.87			1.89019			0.945095	−	0.326795i	$-0.105969\pi$
$839$	1585.87			1.89019			0.945095	+	0.326795i	$0.105969\pi$
$840$	687.950			0.818989
$841$	785.697			0.934242
$842$		−	2797.25i		−	3.32215i
$843$			109.708i			0.130140i
$844$		−	2276.73i		−	2.69755i
$845$	356.137			0.421464
$846$			22.2786i			0.0263341i
$847$	−570.993	+	240.833i	−0.674136	+	0.284337i
$848$	−3656.42			−4.31181
$849$			72.0123i			0.0848201i
$850$	−897.311			−1.05566
$851$	256.218			0.301078
$852$	557.939			0.654858
$853$			82.0178i			0.0961522i	0.998844	+	0.0480761i	$0.0153090\pi$
$853$			82.0178i			0.0961522i	−0.998844	+	0.0480761i	$0.984691\pi$
$854$			496.501i			0.581382i
$855$		−	4.10584i		−	0.00480215i
$856$	3260.58			3.80909
$857$			505.321i			0.589640i	0.955553	+	0.294820i	$0.0952597\pi$
$857$			505.321i			0.589640i	−0.955553	+	0.294820i	$0.904740\pi$
$858$	280.531	+	186.141i	0.326960	+	0.216948i
$859$	747.706			0.870438			0.435219	−	0.900325i	$-0.356671\pi$
$859$	747.706			0.870438			0.435219	+	0.900325i	$0.356671\pi$
$860$		−	994.609i		−	1.15652i
$861$	851.448			0.988906
$862$	−938.655			−1.08893
$863$	−817.340			−0.947092			−0.473546	−	0.880769i	$-0.657026\pi$
$863$	−817.340			−0.947092			−0.473546	+	0.880769i	$0.657026\pi$
$864$		−	1831.94i		−	2.12030i
$865$		−	459.103i		−	0.530755i
$866$			231.481i			0.267299i
$867$	−406.099			−0.468395
$868$			771.338i			0.888638i
$869$	−84.8242	+	127.838i	−0.0976113	+	0.147109i
$870$	−172.801			−0.198622
$871$		−	60.7543i		−	0.0697523i
$872$	−912.087			−1.04597
$873$	82.7868			0.0948302
$874$	31.4581			0.0359932
$875$		−	512.377i		−	0.585574i
$876$			3067.21i			3.50139i
$877$		−	679.794i		−	0.775135i	−0.921841	−	0.387568i	$-0.873315\pi$
$877$		−	679.794i		−	0.775135i	0.921841	−	0.387568i	$-0.126685\pi$
$878$	−1574.97			−1.79381
$879$			381.328i			0.433820i
$880$	824.752	+	547.248i	0.937218	+	0.621872i
$881$	−151.442			−0.171898			−0.0859488	−	0.996300i	$-0.527392\pi$
$881$	−151.442			−0.171898			−0.0859488	+	0.996300i	$0.527392\pi$
$882$			88.4912i			0.100330i
$883$	938.406			1.06275			0.531374	−	0.847138i	$-0.321676\pi$
$883$	938.406			1.06275			0.531374	+	0.847138i	$0.321676\pi$
$884$	−344.320			−0.389502
$885$	−447.462			−0.505607
$886$		−	1561.24i		−	1.76212i
$887$			1176.26i			1.32611i	0.748573	+	0.663053i	$0.230740\pi$
$887$			1176.26i			1.32611i	−0.748573	+	0.663053i	$0.769260\pi$
$888$		−	3233.21i		−	3.64100i
$889$	151.276			0.170165
$890$			245.915i			0.276309i
$891$	−646.024	−	428.656i	−0.725055	−	0.481096i
$892$	−1268.32			−1.42188
$893$			10.1294i			0.0113431i
$894$	−1940.18			−2.17022
$895$	235.718			0.263372
$896$	−155.737			−0.173814
$897$			39.5402i			0.0440805i
$898$			1889.53i			2.10415i
$899$		−	114.511i		−	0.127376i
$900$	−205.540			−0.228378
$901$		−	1086.06i		−	1.20540i
$902$	2005.84	+	1330.94i	2.22377	+	1.47554i
$903$	661.728			0.732810
$904$		−	2980.81i		−	3.29736i
$905$	−681.866			−0.753443
$906$	1118.66			1.23472
$907$	−764.106			−0.842455			−0.421227	−	0.906955i	$-0.638401\pi$
$907$	−764.106			−0.842455			−0.421227	+	0.906955i	$0.638401\pi$
$908$			3470.11i			3.82171i
$909$			54.8389i			0.0603288i
$910$		−	123.371i		−	0.135572i
$911$	350.637			0.384892			0.192446	−	0.981308i	$-0.438358\pi$
$911$	350.637			0.384892			0.192446	+	0.981308i	$0.438358\pi$
$912$		−	202.015i		−	0.221508i
$913$	−525.824	+	792.465i	−0.575930	+	0.867979i
$914$	−2144.79			−2.34659
$915$		−	163.464i		−	0.178649i
$916$	−2995.64			−3.27035
$917$	−1002.92			−1.09369
$918$	1266.54			1.37968
$919$			696.005i			0.757350i	0.925530	+	0.378675i	$0.123620\pi$
$919$			696.005i			0.757350i	−0.925530	+	0.378675i	$0.876380\pi$
$920$			228.430i			0.248294i
$921$		−	93.1067i		−	0.101093i
$922$	−1334.58			−1.44748
$923$		−	59.1361i		−	0.0640695i
$924$	−859.154	+	1294.82i	−0.929820	+	1.40132i
$925$	−1072.43			−1.15938
$926$		−	731.363i		−	0.789809i
$927$	30.4174			0.0328127
$928$	480.821			0.518126
$929$	−1697.97			−1.82774			−0.913868	−	0.406012i	$-0.866919\pi$
$929$	−1697.97			−1.82774			−0.913868	+	0.406012i	$0.866919\pi$
$930$		−	357.806i		−	0.384737i
$931$			40.2341i			0.0432160i
$932$			3573.84i			3.83459i
$933$	503.398			0.539547
$934$			1679.07i			1.79772i
$935$	−162.549	+	244.976i	−0.173849	+	0.262006i
$936$	−65.6792			−0.0701701
$937$		−	1484.61i		−	1.58443i	−0.610240	−	0.792217i	$-0.708927\pi$
$937$		−	1484.61i		−	1.58443i	0.610240	−	0.792217i	$-0.291073\pi$
$938$	395.099			0.421214
$939$	−668.388			−0.711808
$940$	−124.449			−0.132393
$941$		−	472.563i		−	0.502192i	−0.967962	−	0.251096i	$-0.919209\pi$
$941$		−	472.563i		−	0.502192i	0.967962	−	0.251096i	$-0.0807910\pi$
$942$		−	1226.42i		−	1.30193i
$943$			282.719i			0.299808i
$944$	2898.03			3.06994
$945$			322.084i			0.340829i
$946$	1558.90	+	1034.38i	1.64789	+	1.09342i
$947$	−1719.70			−1.81595			−0.907973	−	0.419030i	$-0.862370\pi$
$947$	−1719.70			−1.81595			−0.907973	+	0.419030i	$0.862370\pi$
$948$			384.706i			0.405808i
$949$	325.095			0.342566
$950$	−131.671			−0.138601
$951$	1651.43			1.73652
$952$		−	1323.44i		−	1.39016i
$953$			1271.44i			1.33414i	0.744994	+	0.667071i	$0.232452\pi$
$953$			1271.44i			1.33414i	−0.744994	+	0.667071i	$0.767548\pi$
$954$		−	350.517i		−	0.367419i
$955$	192.804			0.201889
$956$		−	3950.55i		−	4.13237i
$957$	127.548	−	192.226i	0.133279	−	0.200863i
$958$	613.753			0.640661
$959$		−	856.930i		−	0.893566i
$960$	487.359			0.507665
$961$	−723.892			−0.753269
$962$	−579.813			−0.602716
$963$			159.066i			0.165177i
$964$			2917.01i			3.02594i
$965$			709.089i			0.734808i
$966$	−257.139			−0.266190
$967$		−	744.849i		−	0.770267i	−0.922861	−	0.385134i	$-0.874155\pi$
$967$		−	744.849i		−	0.770267i	0.922861	−	0.385134i	$-0.125845\pi$
$968$	−2392.50	+	1009.11i	−2.47159	+	1.04247i
$969$	60.0045			0.0619242
$970$			651.576i			0.671728i
$971$	−471.281			−0.485357			−0.242678	−	0.970107i	$-0.578026\pi$
$971$	−471.281			−0.485357			−0.242678	+	0.970107i	$0.578026\pi$
$972$	550.004			0.565848
$973$	718.617			0.738558
$974$		−	1475.92i		−	1.51532i
$975$		−	165.500i		−	0.169744i
$976$			1058.69i			1.08472i
$977$	1666.47			1.70570			0.852849	−	0.522158i	$-0.174873\pi$
$977$	1666.47			1.70570			0.852849	+	0.522158i	$0.174873\pi$
$978$		−	860.256i		−	0.879608i
$979$	−273.559	−	181.514i	−0.279426	−	0.185408i
$980$	−494.315			−0.504403
$981$		−	44.4957i		−	0.0453575i
$982$	−972.243			−0.990065
$983$	−198.420			−0.201852			−0.100926	−	0.994894i	$-0.532180\pi$
$983$	−198.420			−0.201852			−0.100926	+	0.994894i	$0.532180\pi$
$984$	3567.62			3.62563
$985$			571.370i			0.580071i
$986$			332.425i			0.337145i
$987$		−	82.7978i		−	0.0838883i
$988$	−50.5254			−0.0511391
$989$			219.723i			0.222167i
$990$	−52.4612	+	79.0637i	−0.0529911	+	0.0798624i
$991$	1482.44			1.49590			0.747951	−	0.663754i	$-0.231038\pi$
$991$	1482.44			1.49590			0.747951	+	0.663754i	$0.231038\pi$
$992$			995.596i			1.00363i
$993$	−471.516			−0.474840
$994$	384.576			0.386897
$995$	462.738			0.465063
$996$			2384.79i			2.39437i
$997$		−	1521.12i		−	1.52570i	−0.646576	−	0.762850i	$-0.723799\pi$
$997$		−	1521.12i		−	1.52570i	0.646576	−	0.762850i	$-0.276201\pi$
$998$			734.051i			0.735522i
$999$	1513.72			1.51523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.2	✓	44
11.10	odd	2	inner	253.3.c.a.208.43	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.2	✓	44	1.1	even	1	trivial
253.3.c.a.208.43	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-3.71224i q^{2} -2.82013 q^{3} -9.78074 q^{4} +2.21957 q^{5} +10.4690i q^{6} +5.12153i q^{7} +21.4595i q^{8} -1.04689 q^{9} -8.23959i q^{10} +(9.16580 + 6.08179i) q^{11} +27.5829 q^{12} -2.92352i q^{13} +19.0123 q^{14} -6.25947 q^{15} +40.5400 q^{16} +12.0416i q^{17} +3.88631i q^{18} +1.76698i q^{19} -21.7091 q^{20} -14.4433i q^{21} +(22.5771 - 34.0257i) q^{22} +4.79583 q^{23} -60.5186i q^{24} -20.0735 q^{25} -10.8528 q^{26} +28.3335 q^{27} -50.0923i q^{28} +7.43658i q^{29} +23.2367i q^{30} -15.3983 q^{31} -64.6562i q^{32} +(-25.8487 - 17.1514i) q^{33} +44.7013 q^{34} +11.3676i q^{35} +10.2394 q^{36} +53.4251 q^{37} +6.55946 q^{38} +8.24470i q^{39} +47.6310i q^{40} +58.9509i q^{41} -53.6172 q^{42} +45.8154i q^{43} +(-89.6483 - 59.4844i) q^{44} -2.32365 q^{45} -17.8033i q^{46} +5.73259 q^{47} -114.328 q^{48} +22.7700 q^{49} +74.5177i q^{50} -33.9588i q^{51} +28.5942i q^{52} -90.1928 q^{53} -105.181i q^{54} +(20.3441 + 13.4990i) q^{55} -109.906 q^{56} -4.98311i q^{57} +27.6064 q^{58} +71.4856 q^{59} +61.2223 q^{60} +26.1146i q^{61} +57.1623i q^{62} -5.36168i q^{63} -77.8594 q^{64} -6.48897i q^{65} +(-63.6702 + 95.9567i) q^{66} +20.7812 q^{67} -117.776i q^{68} -13.5248 q^{69} +42.1993 q^{70} +20.2277 q^{71} -22.4658i q^{72} +111.200i q^{73} -198.327i q^{74} +56.6098 q^{75} -17.2824i q^{76} +(-31.1480 + 46.9429i) q^{77} +30.6063 q^{78} +13.9473i q^{79} +89.9814 q^{80} -70.4820 q^{81} +218.840 q^{82} +86.4589i q^{83} +141.267i q^{84} +26.7272i q^{85} +170.078 q^{86} -20.9721i q^{87} +(-130.512 + 196.694i) q^{88} -29.8456 q^{89} +8.62595i q^{90} +14.9729 q^{91} -46.9068 q^{92} +43.4252 q^{93} -21.2808i q^{94} +3.92194i q^{95} +182.339i q^{96} -79.0787 q^{97} -84.5277i q^{98} +(-9.59559 - 6.36697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 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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