LMFDB - Embedded newform 253.3.c.a.208.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("253.208");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.42
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.51900i q^{2} -4.54425 q^{3} -8.38333 q^{4} -6.03619 q^{5} -15.9912i q^{6} +3.84661i q^{7} -15.4249i q^{8} +11.6502 q^{9} -21.2413i q^{10} +(-9.75758 + 5.07834i) q^{11} +38.0960 q^{12} -10.2362i q^{13} -13.5362 q^{14} +27.4300 q^{15} +20.7469 q^{16} +14.5992i q^{17} +40.9971i q^{18} +25.7209i q^{19} +50.6034 q^{20} -17.4799i q^{21} +(-17.8707 - 34.3369i) q^{22} -4.79583 q^{23} +70.0947i q^{24} +11.4356 q^{25} +36.0213 q^{26} -12.0433 q^{27} -32.2474i q^{28} -3.68185i q^{29} +96.5259i q^{30} +47.7130 q^{31} +11.3086i q^{32} +(44.3409 - 23.0773i) q^{33} -51.3745 q^{34} -23.2188i q^{35} -97.6677 q^{36} -22.3475 q^{37} -90.5118 q^{38} +46.5160i q^{39} +93.1077i q^{40} -42.7410i q^{41} +61.5119 q^{42} -52.1839i q^{43} +(81.8010 - 42.5734i) q^{44} -70.3230 q^{45} -16.8765i q^{46} -4.97317 q^{47} -94.2792 q^{48} +34.2036 q^{49} +40.2417i q^{50} -66.3424i q^{51} +85.8137i q^{52} -50.4936 q^{53} -42.3804i q^{54} +(58.8986 - 30.6538i) q^{55} +59.3336 q^{56} -116.882i q^{57} +12.9564 q^{58} -98.9956 q^{59} -229.954 q^{60} -64.8384i q^{61} +167.902i q^{62} +44.8138i q^{63} +43.1928 q^{64} +61.7878i q^{65} +(81.2088 + 156.036i) q^{66} +68.1495 q^{67} -122.390i q^{68} +21.7935 q^{69} +81.7070 q^{70} +83.2800 q^{71} -179.704i q^{72} +128.060i q^{73} -78.6407i q^{74} -51.9661 q^{75} -215.627i q^{76} +(-19.5344 - 37.5336i) q^{77} -163.690 q^{78} -65.3432i q^{79} -125.232 q^{80} -50.1242 q^{81} +150.406 q^{82} +136.036i q^{83} +146.540i q^{84} -88.1235i q^{85} +183.635 q^{86} +16.7312i q^{87} +(78.3330 + 150.510i) q^{88} +40.2404 q^{89} -247.466i q^{90} +39.3747 q^{91} +40.2050 q^{92} -216.820 q^{93} -17.5006i q^{94} -155.256i q^{95} -51.3890i q^{96} -102.539 q^{97} +120.362i q^{98} +(-113.678 + 59.1639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			3.51900i			1.75950i	0.475439	+	0.879749i	$0.342289\pi$
$2$			3.51900i			1.75950i	−0.475439	+	0.879749i	$0.657711\pi$
$3$	−4.54425			−1.51475			−0.757375	−	0.652980i	$-0.773519\pi$
$3$	−4.54425			−1.51475			−0.757375	+	0.652980i	$0.773519\pi$
$4$	−8.38333			−2.09583
$5$	−6.03619			−1.20724			−0.603619	−	0.797273i	$-0.706275\pi$
$5$	−6.03619			−1.20724			−0.603619	+	0.797273i	$0.706275\pi$
$6$		−	15.9912i		−	2.66520i
$7$			3.84661i			0.549515i	0.961514	+	0.274758i	$0.0885976\pi$
$7$			3.84661i			0.549515i	−0.961514	+	0.274758i	$0.911402\pi$
$8$		−	15.4249i		−	1.92811i
$9$	11.6502			1.29447
$10$		−	21.2413i		−	2.12413i
$11$	−9.75758	+	5.07834i	−0.887053	+	0.461668i
$11$	−9.75758	+	5.07834i	−0.887053	+	0.461668i
$12$	38.0960			3.17466
$13$		−	10.2362i		−	0.787402i	−0.919238	−	0.393701i	$-0.871194\pi$
$13$		−	10.2362i		−	0.787402i	0.919238	−	0.393701i	$-0.128806\pi$
$14$	−13.5362			−0.966871
$15$	27.4300			1.82866
$16$	20.7469			1.29668
$17$			14.5992i			0.858776i	0.903120	+	0.429388i	$0.141271\pi$
$17$			14.5992i			0.858776i	−0.903120	+	0.429388i	$0.858729\pi$
$18$			40.9971i			2.27762i
$19$			25.7209i			1.35373i	0.736106	+	0.676866i	$0.236663\pi$
$19$			25.7209i			1.35373i	−0.736106	+	0.676866i	$0.763337\pi$
$20$	50.6034			2.53017
$21$		−	17.4799i		−	0.832379i
$22$	−17.8707	−	34.3369i	−0.812303	−	1.56077i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$			70.0947i			2.92061i
$25$	11.4356			0.457423
$26$	36.0213			1.38543
$27$	−12.0433			−0.446049
$28$		−	32.2474i		−	1.15169i
$29$		−	3.68185i		−	0.126960i	−0.997983	−	0.0634801i	$-0.979780\pi$
$29$		−	3.68185i		−	0.126960i	0.997983	−	0.0634801i	$-0.0202199\pi$
$30$			96.5259i			3.21753i
$31$	47.7130			1.53913			0.769564	−	0.638570i	$-0.220474\pi$
$31$	47.7130			1.53913			0.769564	+	0.638570i	$0.220474\pi$
$32$			11.3086i			0.353393i
$33$	44.3409	−	23.0773i	1.34366	−	0.699311i
$34$	−51.3745			−1.51101
$35$		−	23.2188i		−	0.663395i
$36$	−97.6677			−2.71299
$37$	−22.3475			−0.603986			−0.301993	−	0.953310i	$-0.597652\pi$
$37$	−22.3475			−0.603986			−0.301993	+	0.953310i	$0.597652\pi$
$38$	−90.5118			−2.38189
$39$			46.5160i			1.19272i
$40$			93.1077i			2.32769i
$41$		−	42.7410i		−	1.04246i	−0.853415	−	0.521232i	$-0.825473\pi$
$41$		−	42.7410i		−	1.04246i	0.853415	−	0.521232i	$-0.174527\pi$
$42$	61.5119			1.46457
$43$		−	52.1839i		−	1.21358i	−0.794863	−	0.606789i	$-0.792457\pi$
$43$		−	52.1839i		−	1.21358i	0.794863	−	0.606789i	$-0.207543\pi$
$44$	81.8010	−	42.5734i	1.85911	−	0.967578i
$45$	−70.3230			−1.56273
$46$		−	16.8765i		−	0.366881i
$47$	−4.97317			−0.105812			−0.0529061	−	0.998599i	$-0.516848\pi$
$47$	−4.97317			−0.105812			−0.0529061	+	0.998599i	$0.516848\pi$
$48$	−94.2792			−1.96415
$49$	34.2036			0.698033
$50$			40.2417i			0.804834i
$51$		−	66.3424i		−	1.30083i
$52$			85.8137i			1.65026i
$53$	−50.4936			−0.952710			−0.476355	−	0.879253i	$-0.658042\pi$
$53$	−50.4936			−0.952710			−0.476355	+	0.879253i	$0.658042\pi$
$54$		−	42.3804i		−	0.784822i
$55$	58.8986	−	30.6538i	1.07088	−	0.557343i
$56$	59.3336			1.05953
$57$		−	116.882i		−	2.05057i
$58$	12.9564			0.223386
$59$	−98.9956			−1.67789			−0.838946	−	0.544215i	$-0.816828\pi$
$59$	−98.9956			−1.67789			−0.838946	+	0.544215i	$0.816828\pi$
$60$	−229.954			−3.83257
$61$		−	64.8384i		−	1.06293i	−0.847082	−	0.531463i	$-0.821643\pi$
$61$		−	64.8384i		−	1.06293i	0.847082	−	0.531463i	$-0.178357\pi$
$62$			167.902i			2.70809i
$63$			44.8138i			0.711331i
$64$	43.1928			0.674887
$65$			61.7878i			0.950582i
$66$	81.2088	+	156.036i	1.23044	+	2.36417i
$67$	68.1495			1.01716			0.508579	−	0.861016i	$-0.330171\pi$
$67$	68.1495			1.01716			0.508579	+	0.861016i	$0.330171\pi$
$68$		−	122.390i		−	1.79985i
$69$	21.7935			0.315847
$70$	81.7070			1.16724
$71$	83.2800			1.17296			0.586479	−	0.809964i	$-0.300514\pi$
$71$	83.2800			1.17296			0.586479	+	0.809964i	$0.300514\pi$
$72$		−	179.704i		−	2.49589i
$73$			128.060i			1.75425i	0.480263	+	0.877124i	$0.340541\pi$
$73$			128.060i			1.75425i	−0.480263	+	0.877124i	$0.659459\pi$
$74$		−	78.6407i		−	1.06271i
$75$	−51.9661			−0.692882
$76$		−	215.627i		−	2.83720i
$77$	−19.5344	−	37.5336i	−0.253693	−	0.487449i
$78$	−163.690			−2.09859
$79$		−	65.3432i		−	0.827129i	−0.910475	−	0.413565i	$-0.864284\pi$
$79$		−	65.3432i		−	0.827129i	0.910475	−	0.413565i	$-0.135716\pi$
$80$	−125.232			−1.56540
$81$	−50.1242			−0.618817
$82$	150.406			1.83421
$83$			136.036i			1.63899i	0.573086	+	0.819495i	$0.305746\pi$
$83$			136.036i			1.63899i	−0.573086	+	0.819495i	$0.694254\pi$
$84$			146.540i			1.74453i
$85$		−	88.1235i		−	1.03675i
$86$	183.635			2.13529
$87$			16.7312i			0.192313i
$88$	78.3330	+	150.510i	0.890148	+	1.71034i
$89$	40.2404			0.452140			0.226070	−	0.974111i	$-0.427412\pi$
$89$	40.2404			0.452140			0.226070	+	0.974111i	$0.427412\pi$
$90$		−	247.466i		−	2.74963i
$91$	39.3747			0.432690
$92$	40.2050			0.437011
$93$	−216.820			−2.33140
$94$		−	17.5006i		−	0.186176i
$95$		−	155.256i		−	1.63428i
$96$		−	51.3890i		−	0.535303i
$97$	−102.539			−1.05710			−0.528551	−	0.848901i	$-0.677265\pi$
$97$	−102.539			−1.05710			−0.528551	+	0.848901i	$0.677265\pi$
$98$			120.362i			1.22819i
$99$	−113.678	+	59.1639i	−1.14826	+	0.597615i
$100$	−95.8682			−0.958682
$101$		−	12.0813i		−	0.119616i	−0.998210	−	0.0598082i	$-0.980951\pi$
$101$		−	12.0813i		−	0.119616i	0.998210	−	0.0598082i	$-0.0190489\pi$
$102$	233.459			2.28881
$103$	−83.9717			−0.815259			−0.407630	−	0.913147i	$-0.633645\pi$
$103$	−83.9717			−0.815259			−0.407630	+	0.913147i	$0.633645\pi$
$104$	−157.893			−1.51820
$105$			105.512i			1.00488i
$106$		−	177.687i		−	1.67629i
$107$		−	80.2454i		−	0.749957i	−0.927034	−	0.374978i	$-0.877650\pi$
$107$		−	80.2454i		−	0.749957i	0.927034	−	0.374978i	$-0.122350\pi$
$108$	100.963			0.934844
$109$		−	153.452i		−	1.40782i	−0.710289	−	0.703910i	$-0.751436\pi$
$109$		−	153.452i		−	1.40782i	0.710289	−	0.703910i	$-0.248564\pi$
$110$	107.871	+	207.264i	0.980643	+	1.88422i
$111$	101.553			0.914888
$112$			79.8052i			0.712546i
$113$	−198.954			−1.76066			−0.880330	−	0.474363i	$-0.842679\pi$
$113$	−198.954			−1.76066			−0.880330	+	0.474363i	$0.842679\pi$
$114$	411.309			3.60797
$115$	28.9485			0.251726
$116$			30.8661i			0.266087i
$117$		−	119.254i		−	1.01927i
$118$		−	348.365i		−	2.95225i
$119$	−56.1574			−0.471911
$120$		−	423.105i		−	3.52587i
$121$	69.4209	−	99.1047i	0.573726	−	0.819047i
$122$	228.166			1.87021
$123$			194.226i			1.57907i
$124$	−399.994			−3.22575
$125$	81.8775			0.655020
$126$	−157.700			−1.25159
$127$			25.8605i			0.203626i	0.994804	+	0.101813i	$0.0324643\pi$
$127$			25.8605i			0.203626i	−0.994804	+	0.101813i	$0.967536\pi$
$128$			197.229i			1.54086i
$129$			237.137i			1.83827i
$130$	−217.431			−1.67255
$131$			114.023i			0.870401i	0.900334	+	0.435201i	$0.143323\pi$
$131$			114.023i			0.870401i	−0.900334	+	0.435201i	$0.856677\pi$
$132$	−371.725	+	193.464i	−2.81610	+	1.46564i
$133$	−98.9383			−0.743897
$134$			239.818i			1.78969i
$135$	72.6958			0.538487
$136$	225.191			1.65582
$137$	−50.9224			−0.371696			−0.185848	−	0.982578i	$-0.559503\pi$
$137$	−50.9224			−0.371696			−0.185848	+	0.982578i	$0.559503\pi$
$138$			76.6911i			0.555733i
$139$		−	64.3952i		−	0.463275i	−0.972802	−	0.231637i	$-0.925592\pi$
$139$		−	64.3952i		−	0.463275i	0.972802	−	0.231637i	$-0.0744083\pi$
$140$			194.651i			1.39037i
$141$	22.5993			0.160279
$142$			293.062i			2.06382i
$143$	51.9831	+	99.8809i	0.363518	+	0.698468i
$144$	241.706			1.67852
$145$			22.2243i			0.153271i
$146$	−450.643			−3.08660
$147$	−155.430			−1.05735
$148$	187.346			1.26585
$149$			268.852i			1.80437i	0.431346	+	0.902187i	$0.358039\pi$
$149$			268.852i			1.80437i	−0.431346	+	0.902187i	$0.641961\pi$
$150$		−	182.869i		−	1.21912i
$151$		−	159.152i		−	1.05399i	−0.849869	−	0.526994i	$-0.823319\pi$
$151$		−	159.152i		−	1.05399i	0.849869	−	0.526994i	$-0.176681\pi$
$152$	396.743			2.61015
$153$			170.084i			1.11166i
$154$	132.080	−	68.7414i	0.857666	−	0.446373i
$155$	−288.004			−1.85809
$156$		−	389.959i		−	2.49974i
$157$	−48.8691			−0.311268			−0.155634	−	0.987815i	$-0.549742\pi$
$157$	−48.8691			−0.311268			−0.155634	+	0.987815i	$0.549742\pi$
$158$	229.943			1.45533
$159$	229.456			1.44312
$160$		−	68.2607i		−	0.426630i
$161$		−	18.4477i		−	0.114582i
$162$		−	176.387i		−	1.08881i
$163$	191.044			1.17205			0.586025	−	0.810293i	$-0.300692\pi$
$163$	191.044			1.17205			0.586025	+	0.810293i	$0.300692\pi$
$164$			358.312i			2.18483i
$165$	−267.650	+	139.299i	−1.62212	+	0.844235i
$166$	−478.711			−2.88380
$167$		−	27.5575i		−	0.165015i	−0.996590	−	0.0825074i	$-0.973707\pi$
$167$		−	27.5575i		−	0.165015i	0.996590	−	0.0825074i	$-0.0262928\pi$
$168$	−269.627			−1.60492
$169$	64.2196			0.379998
$170$	310.106			1.82415
$171$			299.655i			1.75237i
$172$			437.475i			2.54346i
$173$		−	291.735i		−	1.68633i	−0.537655	−	0.843165i	$-0.680690\pi$
$173$		−	291.735i		−	1.68633i	0.537655	−	0.843165i	$-0.319310\pi$
$174$	−58.8771			−0.338374
$175$			43.9881i			0.251361i
$176$	−202.440	+	105.360i	−1.15023	+	0.598636i
$177$	449.861			2.54159
$178$			141.606i			0.795539i
$179$	42.5320			0.237609			0.118804	−	0.992918i	$-0.462094\pi$
$179$	42.5320			0.237609			0.118804	+	0.992918i	$0.462094\pi$
$180$	589.541			3.27523
$181$	−39.3354			−0.217323			−0.108661	−	0.994079i	$-0.534656\pi$
$181$	−39.3354			−0.217323			−0.108661	+	0.994079i	$0.534656\pi$
$182$			138.560i			0.761316i
$183$			294.642i			1.61007i
$184$			73.9753i			0.402040i
$185$	134.894			0.729154
$186$		−	762.988i		−	4.10208i
$187$	−74.1397	−	142.453i	−0.396469	−	0.761780i
$188$	41.6917			0.221765
$189$		−	46.3259i		−	0.245111i
$190$	546.346			2.87551
$191$	113.290			0.593140			0.296570	−	0.955011i	$-0.404157\pi$
$191$	113.290			0.593140			0.296570	+	0.955011i	$0.404157\pi$
$192$	−196.279			−1.02229
$193$			10.2043i			0.0528718i	0.999651	+	0.0264359i	$0.00841579\pi$
$193$			10.2043i			0.0528718i	−0.999651	+	0.0264359i	$0.991584\pi$
$194$		−	360.834i		−	1.85997i
$195$		−	280.779i		−	1.43989i
$196$	−286.740			−1.46296
$197$		−	275.324i		−	1.39758i	−0.715326	−	0.698791i	$-0.753722\pi$
$197$		−	275.324i		−	1.39758i	0.715326	−	0.698791i	$-0.246278\pi$
$198$	−208.197	−	400.033i	−1.05150	−	2.02037i
$199$	217.171			1.09131			0.545656	−	0.838009i	$-0.316280\pi$
$199$	217.171			1.09131			0.545656	+	0.838009i	$0.316280\pi$
$200$		−	176.393i		−	0.881964i
$201$	−309.689			−1.54074
$202$	42.5139			0.210465
$203$	14.1626			0.0697665
$204$			556.171i			2.72633i
$205$			257.993i			1.25850i
$206$		−	295.496i		−	1.43445i
$207$	−55.8725			−0.269916
$208$		−	212.370i		−	1.02101i
$209$	−130.620	−	250.974i	−0.624975	−	1.20083i
$210$	−371.297			−1.76808
$211$		−	155.342i		−	0.736218i	−0.929783	−	0.368109i	$-0.880005\pi$
$211$		−	155.342i		−	0.736218i	0.929783	−	0.368109i	$-0.119995\pi$
$212$	423.305			1.99672
$213$	−378.446			−1.77674
$214$	282.383			1.31955
$215$			314.992i			1.46508i
$216$			185.767i			0.860034i
$217$			183.533i			0.845774i
$218$	539.999			2.47706
$219$		−	581.938i		−	2.65725i
$220$	−493.766	+	256.981i	−2.24439	+	1.16810i
$221$	149.441			0.676202
$222$			357.363i			1.60974i
$223$	−2.33090			−0.0104525			−0.00522623	−	0.999986i	$-0.501664\pi$
$223$	−2.33090			−0.0104525			−0.00522623	+	0.999986i	$0.501664\pi$
$224$	−43.4997			−0.194195
$225$	133.227			0.592120
$226$		−	700.120i		−	3.09788i
$227$			432.665i			1.90601i	0.302950	+	0.953006i	$0.402028\pi$
$227$			432.665i			1.90601i	−0.302950	+	0.953006i	$0.597972\pi$
$228$			979.863i			4.29765i
$229$	−274.772			−1.19988			−0.599938	−	0.800047i	$-0.704808\pi$
$229$	−274.772			−1.19988			−0.599938	+	0.800047i	$0.704808\pi$
$230$			101.870i			0.442912i
$231$	88.7692	+	170.562i	0.384282	+	0.738364i
$232$	−56.7922			−0.244794
$233$		−	251.514i		−	1.07946i	−0.841838	−	0.539730i	$-0.818526\pi$
$233$		−	251.514i		−	1.07946i	0.841838	−	0.539730i	$-0.181474\pi$
$234$	419.656			1.79340
$235$	30.0190			0.127740
$236$	829.913			3.51658
$237$			296.936i			1.25289i
$238$		−	197.617i		−	0.830326i
$239$		−	150.972i		−	0.631680i	−0.948812	−	0.315840i	$-0.897714\pi$
$239$		−	150.972i		−	0.631680i	0.948812	−	0.315840i	$-0.102286\pi$
$240$	569.087			2.37119
$241$		−	229.369i		−	0.951738i	−0.879516	−	0.475869i	$-0.842134\pi$
$241$		−	229.369i		−	0.951738i	0.879516	−	0.475869i	$-0.157866\pi$
$242$	348.749	+	244.292i	1.44111	+	1.00947i
$243$	336.167			1.38340
$244$			543.562i			2.22771i
$245$	−206.460			−0.842692
$246$	−683.481			−2.77838
$247$	263.285			1.06593
$248$		−	735.969i		−	2.96762i
$249$		−	618.183i		−	2.48266i
$250$			288.126i			1.15251i
$251$	145.913			0.581328			0.290664	−	0.956825i	$-0.406124\pi$
$251$	145.913			0.581328			0.290664	+	0.956825i	$0.406124\pi$
$252$		−	375.689i		−	1.49083i
$253$	46.7957	−	24.3549i	0.184963	−	0.0962643i
$254$	−91.0028			−0.358279
$255$			400.455i			1.57041i
$256$	−521.279			−2.03624
$257$	−145.701			−0.566931			−0.283465	−	0.958982i	$-0.591484\pi$
$257$	−145.701			−0.566931			−0.283465	+	0.958982i	$0.591484\pi$
$258$	−834.483			−3.23443
$259$		−	85.9619i		−	0.331899i
$260$		−	517.988i		−	1.99226i
$261$		−	42.8943i		−	0.164346i
$262$	−401.245			−1.53147
$263$			175.157i			0.665998i	0.942927	+	0.332999i	$0.108061\pi$
$263$			175.157i			0.665998i	−0.942927	+	0.332999i	$0.891939\pi$
$264$	−355.965	−	683.955i	−1.34835	−	2.59074i
$265$	304.789			1.15015
$266$		−	348.163i		−	1.30888i
$267$	−182.863			−0.684879
$268$	−571.320			−2.13179
$269$	−231.022			−0.858818			−0.429409	−	0.903110i	$-0.641278\pi$
$269$	−231.022			−0.858818			−0.429409	+	0.903110i	$0.641278\pi$
$270$			255.816i			0.947467i
$271$			299.480i			1.10509i	0.833482	+	0.552546i	$0.186344\pi$
$271$			299.480i			1.10509i	−0.833482	+	0.552546i	$0.813656\pi$
$272$			302.888i			1.11356i
$273$	−178.929			−0.655417
$274$		−	179.196i		−	0.653999i
$275$	−111.584	+	58.0737i	−0.405758	+	0.211177i
$276$	−182.702			−0.661963
$277$		−	32.1710i		−	0.116141i	−0.998312	−	0.0580704i	$-0.981505\pi$
$277$		−	32.1710i		−	0.116141i	0.998312	−	0.0580704i	$-0.0184948\pi$
$278$	226.606			0.815131
$279$	555.867			1.99236
$280$	−358.149			−1.27910
$281$		−	126.109i		−	0.448787i	−0.974499	−	0.224394i	$-0.927960\pi$
$281$		−	126.109i		−	0.448787i	0.974499	−	0.224394i	$-0.0720401\pi$
$282$			79.5270i			0.282011i
$283$		−	337.808i		−	1.19367i	−0.802364	−	0.596834i	$-0.796425\pi$
$283$		−	337.808i		−	1.19367i	0.802364	−	0.596834i	$-0.203575\pi$
$284$	−698.164			−2.45832
$285$			705.524i			2.47552i
$286$	−351.480	+	182.928i	−1.22895	+	0.639609i
$287$	164.408			0.572850
$288$			131.748i			0.457457i
$289$	75.8635			0.262503
$290$	−78.2072			−0.269680
$291$	465.963			1.60125
$292$		−	1073.57i		−	3.67661i
$293$		−	272.615i		−	0.930427i	−0.885198	−	0.465214i	$-0.845977\pi$
$293$		−	272.615i		−	0.930427i	0.885198	−	0.465214i	$-0.154023\pi$
$294$		−	546.957i		−	1.86040i
$295$	597.556			2.02561
$296$			344.708i			1.16455i
$297$	117.514	−	61.1601i	0.395669	−	0.205926i
$298$	−946.088			−3.17479
$299$			49.0912i			0.164185i
$300$	435.649			1.45216
$301$	200.731			0.666880
$302$	560.056			1.85449
$303$			54.9003i			0.181189i
$304$			533.629i			1.75536i
$305$			391.377i			1.28320i
$306$	−598.525			−1.95596
$307$			360.807i			1.17527i	0.809127	+	0.587634i	$0.199941\pi$
$307$			360.807i			1.17527i	−0.809127	+	0.587634i	$0.800059\pi$
$308$	163.763	+	314.656i	0.531699	+	1.02161i
$309$	381.589			1.23491
$310$		−	1013.49i		−	3.26931i
$311$	578.159			1.85903			0.929515	−	0.368783i	$-0.120226\pi$
$311$	578.159			1.85903			0.929515	+	0.368783i	$0.120226\pi$
$312$	717.506			2.29970
$313$	−366.449			−1.17076			−0.585382	−	0.810758i	$-0.699055\pi$
$313$	−366.449			−1.17076			−0.585382	+	0.810758i	$0.699055\pi$
$314$		−	171.970i		−	0.547676i
$315$		−	270.505i		−	0.858746i
$316$			547.794i			1.73352i
$317$	−545.515			−1.72087			−0.860434	−	0.509562i	$-0.829807\pi$
$317$	−545.515			−1.72087			−0.860434	+	0.509562i	$0.829807\pi$
$318$			807.454i			2.53916i
$319$	18.6977	+	35.9259i	0.0586134	+	0.112620i
$320$	−260.720			−0.814749
$321$			364.655i			1.13600i
$322$	64.9173			0.201606
$323$	−375.505			−1.16255
$324$	420.208			1.29694
$325$		−	117.057i		−	0.360176i
$326$			672.283i			2.06222i
$327$			697.327i			2.13250i
$328$	−659.277			−2.00999
$329$		−	19.1298i		−	0.0581454i
$330$	−490.192	−	941.860i	−1.48543	−	2.85412i
$331$	−346.822			−1.04780			−0.523900	−	0.851780i	$-0.675524\pi$
$331$	−346.822			−1.04780			−0.523900	+	0.851780i	$0.675524\pi$
$332$		−	1140.44i		−	3.43505i
$333$	−260.353			−0.781842
$334$	96.9747			0.290343
$335$	−411.363			−1.22795
$336$		−	362.655i		−	1.07933i
$337$		−	330.456i		−	0.980582i	−0.871559	−	0.490291i	$-0.836891\pi$
$337$		−	330.456i		−	0.980582i	0.871559	−	0.490291i	$-0.163109\pi$
$338$			225.988i			0.668605i
$339$	904.099			2.66696
$340$			738.768i			2.17285i
$341$	−465.563	+	242.303i	−1.36529	+	0.710565i
$342$	−1054.48			−3.08329
$343$			320.052i			0.933095i
$344$	−804.932			−2.33992
$345$	−131.549			−0.381303
$346$	1026.61			2.96709
$347$		−	303.213i		−	0.873812i	−0.899507	−	0.436906i	$-0.856074\pi$
$347$		−	303.213i		−	0.873812i	0.899507	−	0.436906i	$-0.143926\pi$
$348$		−	140.263i		−	0.403056i
$349$		−	389.099i		−	1.11490i	−0.830211	−	0.557449i	$-0.811780\pi$
$349$		−	389.099i		−	1.11490i	0.830211	−	0.557449i	$-0.188220\pi$
$350$	−154.794			−0.442269
$351$			123.278i			0.351220i
$352$	−57.4289	−	110.344i	−0.163150	−	0.313478i
$353$	511.608			1.44932			0.724658	−	0.689109i	$-0.241998\pi$
$353$	511.608			1.44932			0.724658	+	0.689109i	$0.241998\pi$
$354$			1583.06i			4.47192i
$355$	−502.694			−1.41604
$356$	−337.349			−0.947609
$357$	255.193			0.714827
$358$			149.670i			0.418072i
$359$		−	16.2891i		−	0.0453735i	−0.999743	−	0.0226868i	$-0.992778\pi$
$359$		−	16.2891i		−	0.0453735i	0.999743	−	0.0226868i	$-0.00722204\pi$
$360$			1084.73i			3.01313i
$361$	−300.566			−0.832592
$362$		−	138.421i		−	0.382379i
$363$	−315.466	+	450.357i	−0.869052	+	1.24065i
$364$	−330.091			−0.906845
$365$		−	772.995i		−	2.11780i
$366$	−1036.84			−2.83291
$367$	165.576			0.451161			0.225581	−	0.974225i	$-0.427572\pi$
$367$	165.576			0.451161			0.225581	+	0.974225i	$0.427572\pi$
$368$	−99.4986			−0.270377
$369$		−	497.943i		−	1.34944i
$370$			474.690i			1.28295i
$371$		−	194.229i		−	0.523528i
$372$	1817.67			4.88621
$373$			90.6069i			0.242914i	0.992597	+	0.121457i	$0.0387566\pi$
$373$			90.6069i			0.242914i	−0.992597	+	0.121457i	$0.961243\pi$
$374$	501.291	−	260.897i	1.34035	−	0.697587i
$375$	−372.072			−0.992192
$376$			76.7108i			0.204018i
$377$	−37.6882			−0.0999687
$378$	163.021			0.431272
$379$	−220.619			−0.582109			−0.291055	−	0.956706i	$-0.594006\pi$
$379$	−220.619			−0.582109			−0.291055	+	0.956706i	$0.594006\pi$
$380$			1301.57i			3.42517i
$381$		−	117.516i		−	0.308442i
$382$			398.666i			1.04363i
$383$	−377.307			−0.985136			−0.492568	−	0.870274i	$-0.663942\pi$
$383$	−377.307			−0.985136			−0.492568	+	0.870274i	$0.663942\pi$
$384$		−	896.260i		−	2.33401i
$385$	117.913	+	226.560i	0.306268	+	0.588467i
$386$	−35.9088			−0.0930279
$387$		−	607.954i		−	1.57094i
$388$	859.618			2.21551
$389$	182.321			0.468691			0.234346	−	0.972153i	$-0.424705\pi$
$389$	182.321			0.468691			0.234346	+	0.972153i	$0.424705\pi$
$390$	988.062			2.53349
$391$		−	70.0153i		−	0.179067i
$392$		−	527.588i		−	1.34589i
$393$		−	518.147i		−	1.31844i
$394$	968.863			2.45904
$395$			394.424i			0.998542i
$396$	953.001	−	495.990i	2.40657	−	1.25250i
$397$	264.719			0.666797			0.333399	−	0.942786i	$-0.391805\pi$
$397$	264.719			0.666797			0.333399	+	0.942786i	$0.391805\pi$
$398$			764.225i			1.92016i
$399$	449.600			1.12682
$400$	237.253			0.593132
$401$	173.087			0.431637			0.215819	−	0.976433i	$-0.430758\pi$
$401$	173.087			0.431637			0.215819	+	0.976433i	$0.430758\pi$
$402$		−	1089.79i		−	2.71093i
$403$		−	488.401i		−	1.21191i
$404$			101.281i			0.250696i
$405$	302.559			0.747059
$406$			49.8382i			0.122754i
$407$	218.057	−	113.488i	0.535767	−	0.278841i
$408$	−1023.33			−2.50815
$409$			13.8640i			0.0338972i	0.999856	+	0.0169486i	$0.00539517\pi$
$409$			13.8640i			0.0338972i	−0.999856	+	0.0169486i	$0.994605\pi$
$410$	−907.876			−2.21433
$411$	231.404			0.563027
$412$	703.963			1.70865
$413$		−	380.797i		−	0.922027i
$414$		−	196.615i		−	0.474916i
$415$		−	821.140i		−	1.97865i
$416$	115.757			0.278263
$417$			292.628i			0.701746i
$418$	883.177	−	459.650i	2.11286	−	1.09964i
$419$	213.432			0.509383			0.254692	−	0.967022i	$-0.418026\pi$
$419$	213.432			0.509383			0.254692	+	0.967022i	$0.418026\pi$
$420$		−	884.544i		−	2.10606i
$421$	280.888			0.667192			0.333596	−	0.942716i	$-0.391738\pi$
$421$	280.888			0.667192			0.333596	+	0.942716i	$0.391738\pi$
$422$	546.648			1.29537
$423$	−57.9386			−0.136971
$424$			778.860i			1.83693i
$425$			166.950i			0.392824i
$426$		−	1331.75i		−	3.12617i
$427$	249.408			0.584094
$428$			672.724i			1.57178i
$429$	−236.224	−	453.884i	−0.550639	−	1.05800i
$430$	−1108.45			−2.57780
$431$		−	100.549i		−	0.233292i	−0.993174	−	0.116646i	$-0.962786\pi$
$431$		−	100.549i		−	0.233292i	0.993174	−	0.116646i	$-0.0372143\pi$
$432$	−249.862			−0.578383
$433$	576.821			1.33215			0.666075	−	0.745884i	$-0.267973\pi$
$433$	576.821			1.33215			0.666075	+	0.745884i	$0.267973\pi$
$434$	−645.852			−1.48814
$435$		−	100.993i		−	0.232168i
$436$			1286.44i			2.95056i
$437$		−	123.353i		−	0.282273i
$438$	2047.84			4.67543
$439$		−	403.246i		−	0.918556i	−0.888293	−	0.459278i	$-0.848108\pi$
$439$		−	403.246i		−	0.918556i	0.888293	−	0.459278i	$-0.151892\pi$
$440$	−472.833	−	908.506i	−1.07462	−	2.06479i
$441$	398.480			0.903583
$442$			525.881i			1.18978i
$443$	115.561			0.260860			0.130430	−	0.991458i	$-0.458364\pi$
$443$	115.561			0.260860			0.130430	+	0.991458i	$0.458364\pi$
$444$	−851.349			−1.91745
$445$	−242.899			−0.545840
$446$		−	8.20242i		−	0.0183911i
$447$		−	1221.73i		−	2.73318i
$448$			166.146i			0.370861i
$449$	−189.439			−0.421914			−0.210957	−	0.977495i	$-0.567658\pi$
$449$	−189.439			−0.421914			−0.210957	+	0.977495i	$0.567658\pi$
$450$			468.825i			1.04183i
$451$	217.054	+	417.049i	0.481272	+	0.924721i
$452$	1667.90			3.69005
$453$			723.227i			1.59653i
$454$	−1522.55			−3.35363
$455$	−237.673			−0.522359
$456$	−1802.90			−3.95373
$457$			406.406i			0.889291i	0.895707	+	0.444645i	$0.146670\pi$
$457$			406.406i			0.889291i	−0.895707	+	0.444645i	$0.853330\pi$
$458$		−	966.920i		−	2.11118i
$459$		−	175.823i		−	0.383056i
$460$	−242.685			−0.527576
$461$			791.137i			1.71613i	0.513539	+	0.858066i	$0.328334\pi$
$461$			791.137i			1.71613i	−0.513539	+	0.858066i	$0.671666\pi$
$462$	−600.207	+	312.378i	−1.29915	+	0.676144i
$463$	−906.642			−1.95819			−0.979095	−	0.203403i	$-0.934800\pi$
$463$	−906.642			−1.95819			−0.979095	+	0.203403i	$0.934800\pi$
$464$		−	76.3869i		−	0.164627i
$465$	1308.76			2.81455
$466$	885.078			1.89931
$467$	−735.795			−1.57558			−0.787789	−	0.615946i	$-0.788774\pi$
$467$	−735.795			−1.57558			−0.787789	+	0.615946i	$0.788774\pi$
$468$			999.749i			2.13622i
$469$			262.144i			0.558943i
$470$			105.637i			0.224759i
$471$	222.074			0.471494
$472$			1527.00i			3.23517i
$473$	265.008	+	509.189i	0.560270	+	1.07651i
$474$	−1044.92			−2.20447
$475$			294.133i			0.619228i
$476$	470.786			0.989045
$477$	−588.262			−1.23325
$478$	531.268			1.11144
$479$		−	631.339i		−	1.31804i	−0.752127	−	0.659018i	$-0.770972\pi$
$479$		−	631.339i		−	1.31804i	0.752127	−	0.659018i	$-0.229028\pi$
$480$			310.194i			0.646237i
$481$			228.754i			0.475580i
$482$	807.148			1.67458
$483$			83.8309i			0.173563i
$484$	−581.978	+	830.828i	−1.20243	+	1.71659i
$485$	618.944			1.27617
$486$			1182.97i			2.43409i
$487$	−598.624			−1.22921			−0.614604	−	0.788836i	$-0.710684\pi$
$487$	−598.624			−1.22921			−0.614604	+	0.788836i	$0.710684\pi$
$488$	−1000.13			−2.04944
$489$	−868.153			−1.77536
$490$		−	726.530i		−	1.48271i
$491$		−	861.107i		−	1.75378i	−0.480690	−	0.876891i	$-0.659614\pi$
$491$		−	861.107i		−	1.75378i	0.480690	−	0.876891i	$-0.340386\pi$
$492$		−	1628.26i		−	3.30948i
$493$	53.7520			0.109030
$494$			926.500i			1.87551i
$495$	686.182	−	357.124i	1.38623	−	0.721463i
$496$	989.896			1.99576
$497$			320.345i			0.644558i
$498$	2175.38			4.36824
$499$	−648.476			−1.29955			−0.649776	−	0.760126i	$-0.725137\pi$
$499$	−648.476			−1.29955			−0.649776	+	0.760126i	$0.725137\pi$
$500$	−686.406			−1.37281
$501$			125.228i			0.249956i
$502$			513.468i			1.02284i
$503$			362.946i			0.721563i	0.932650	+	0.360782i	$0.117490\pi$
$503$			362.946i			0.721563i	−0.932650	+	0.360782i	$0.882510\pi$
$504$	691.250			1.37153
$505$			72.9248i			0.144406i
$506$	85.7047	+	164.674i	0.169377	+	0.325443i
$507$	−291.830			−0.575602
$508$		−	216.797i		−	0.426765i
$509$	568.354			1.11661			0.558305	−	0.829636i	$-0.311452\pi$
$509$	568.354			1.11661			0.558305	+	0.829636i	$0.311452\pi$
$510$	−1409.20			−2.76314
$511$	−492.597			−0.963986
$512$		−	1045.46i		−	2.04191i
$513$		−	309.765i		−	0.603831i
$514$		−	512.722i		−	0.997514i
$515$	506.869			0.984212
$516$		−	1988.00i		−	3.85271i
$517$	48.5261	−	25.2555i	0.0938610	−	0.0488500i
$518$	302.500			0.583976
$519$			1325.72i			2.55437i
$520$	953.072			1.83283
$521$	−685.533			−1.31580			−0.657901	−	0.753104i	$-0.728556\pi$
$521$	−685.533			−1.31580			−0.657901	+	0.753104i	$0.728556\pi$
$522$	150.945			0.289167
$523$			385.804i			0.737674i	0.929494	+	0.368837i	$0.120244\pi$
$523$			385.804i			0.737674i	−0.929494	+	0.368837i	$0.879756\pi$
$524$		−	955.889i		−	1.82422i
$525$		−	199.893i		−	0.380749i
$526$	−616.378			−1.17182
$527$			696.571i			1.32177i
$528$	919.937	−	478.782i	1.74230	−	0.906784i
$529$	23.0000			0.0434783
$530$			1072.55i			2.02368i
$531$	−1153.32			−2.17198
$532$	829.432			1.55908
$533$	−437.507			−0.820839
$534$		−	643.493i		−	1.20504i
$535$			484.376i			0.905376i
$536$		−	1051.20i		−	1.96120i
$537$	−193.276			−0.359918
$538$		−	812.966i		−	1.51109i
$539$	−333.745	+	173.698i	−0.619192	+	0.322259i
$540$	−609.433			−1.12858
$541$			45.1903i			0.0835311i	0.999127	+	0.0417656i	$0.0132983\pi$
$541$			45.1903i			0.0835311i	−0.999127	+	0.0417656i	$0.986702\pi$
$542$	−1053.87			−1.94441
$543$	178.750			0.329190
$544$	−165.096			−0.303486
$545$			926.268i			1.69957i
$546$		−	629.650i		−	1.15320i
$547$		−	142.344i		−	0.260226i	−0.991499	−	0.130113i	$-0.958466\pi$
$547$		−	142.344i		−	0.260226i	0.991499	−	0.130113i	$-0.0415341\pi$
$548$	426.899			0.779013
$549$		−	755.383i		−	1.37593i
$550$	−204.361	−	392.662i	−0.371566	−	0.713931i
$551$	94.7005			0.171870
$552$		−	336.163i		−	0.608990i
$553$	251.350			0.454520
$554$	113.210			0.204350
$555$	−612.990			−1.10449
$556$			539.846i			0.970946i
$557$		−	681.844i		−	1.22414i	−0.790805	−	0.612068i	$-0.790338\pi$
$557$		−	681.844i		−	1.22414i	0.790805	−	0.612068i	$-0.209662\pi$
$558$			1956.09i			3.50554i
$559$	−534.166			−0.955575
$560$		−	481.719i		−	0.860212i
$561$	336.910	+	647.342i	0.600552	+	1.15391i
$562$	443.778			0.789640
$563$			661.817i			1.17552i	0.809036	+	0.587759i	$0.199990\pi$
$563$			661.817i			1.17552i	−0.809036	+	0.587759i	$0.800010\pi$
$564$	−189.458			−0.335918
$565$	1200.93			2.12553
$566$	1188.75			2.10026
$567$		−	192.808i		−	0.340049i
$568$		−	1284.59i		−	2.26160i
$569$		−	202.274i		−	0.355490i	−0.984077	−	0.177745i	$-0.943120\pi$
$569$		−	202.274i		−	0.355490i	0.984077	−	0.177745i	$-0.0568803\pi$
$570$	−2482.74			−4.35568
$571$			75.3621i			0.131983i	0.997820	+	0.0659913i	$0.0210210\pi$
$571$			75.3621i			0.131983i	−0.997820	+	0.0659913i	$0.978979\pi$
$572$	−435.791	−	837.334i	−0.761873	−	1.46387i
$573$	−514.817			−0.898459
$574$			578.551i			1.00793i
$575$	−54.8431			−0.0953792
$576$	503.206			0.873621
$577$	362.063			0.627493			0.313746	−	0.949507i	$-0.398416\pi$
$577$	362.063			0.627493			0.313746	+	0.949507i	$0.398416\pi$
$578$			266.963i			0.461874i
$579$		−	46.3707i		−	0.0800876i
$580$		−	186.314i		−	0.321231i
$581$	−523.278			−0.900650
$582$			1639.72i			2.81739i
$583$	492.696	−	256.424i	0.845104	−	0.439835i
$584$	1975.32			3.38239
$585$			719.842i			1.23050i
$586$	959.332			1.63709
$587$	−617.263			−1.05156			−0.525778	−	0.850622i	$-0.676226\pi$
$587$	−617.263			−1.05156			−0.525778	+	0.850622i	$0.676226\pi$
$588$	1303.02			2.21602
$589$			1227.22i			2.08357i
$590$			2102.80i			3.56406i
$591$			1251.14i			2.11699i
$592$	−463.641			−0.783177
$593$		−	767.497i		−	1.29426i	−0.762379	−	0.647131i	$-0.775969\pi$
$593$		−	767.497i		−	1.29426i	0.762379	−	0.647131i	$-0.224031\pi$
$594$	215.222	+	413.530i	0.362327	+	0.696179i
$595$	338.976			0.569708
$596$		−	2253.87i		−	3.78166i
$597$	−986.881			−1.65307
$598$	−172.752			−0.288883
$599$	−885.062			−1.47757			−0.738783	−	0.673943i	$-0.764599\pi$
$599$	−885.062			−1.47757			−0.738783	+	0.673943i	$0.764599\pi$
$600$			801.573i			1.33596i
$601$			297.619i			0.495206i	0.968862	+	0.247603i	$0.0796429\pi$
$601$			297.619i			0.495206i	−0.968862	+	0.247603i	$0.920357\pi$
$602$			706.371i			1.17337i
$603$	793.958			1.31668
$604$			1334.22i			2.20898i
$605$	−419.037	+	598.215i	−0.692624	+	0.988785i
$606$	−193.194			−0.318802
$607$			581.248i			0.957575i	0.877931	+	0.478787i	$0.158924\pi$
$607$			581.248i			0.957575i	−0.877931	+	0.478787i	$0.841076\pi$
$608$	−290.867			−0.478400
$609$	−64.3585			−0.105679
$610$	−1377.25			−2.25779
$611$			50.9065i			0.0833167i
$612$		−	1425.87i		−	2.32985i
$613$		−	121.527i		−	0.198249i	−0.995075	−	0.0991245i	$-0.968396\pi$
$613$		−	121.527i		−	0.198249i	0.995075	−	0.0991245i	$-0.0316042\pi$
$614$	−1269.68			−2.06788
$615$		−	1172.39i		−	1.90632i
$616$	−578.952	+	301.316i	−0.939858	+	0.489150i
$617$	−428.754			−0.694901			−0.347450	−	0.937698i	$-0.612953\pi$
$617$	−428.754			−0.694901			−0.347450	+	0.937698i	$0.612953\pi$
$618$			1342.81i			2.17283i
$619$	487.783			0.788017			0.394009	−	0.919107i	$-0.371088\pi$
$619$	487.783			0.788017			0.394009	+	0.919107i	$0.371088\pi$
$620$	2414.44			3.89425
$621$	57.7577			0.0930076
$622$			2034.54i			3.27096i
$623$			154.789i			0.248458i
$624$			965.063i			1.54658i
$625$	−780.117			−1.24819
$626$		−	1289.53i		−	2.05996i
$627$	593.569	+	1140.49i	0.946681	+	1.81896i
$628$	409.686			0.652366
$629$		−	326.255i		−	0.518689i
$630$	951.905			1.51096
$631$	−150.320			−0.238224			−0.119112	−	0.992881i	$-0.538005\pi$
$631$	−150.320			−0.238224			−0.119112	+	0.992881i	$0.538005\pi$
$632$	−1007.91			−1.59480
$633$			705.913i			1.11519i
$634$		−	1919.66i		−	3.02786i
$635$		−	156.099i		−	0.245825i
$636$	−1923.60			−3.02453
$637$		−	350.116i		−	0.549633i
$638$	−126.423	+	65.7970i	−0.198155	+	0.103130i
$639$	970.232			1.51836
$640$		−	1190.51i		−	1.86018i
$641$	−54.9906			−0.0857887			−0.0428944	−	0.999080i	$-0.513658\pi$
$641$	−54.9906			−0.0857887			−0.0428944	+	0.999080i	$0.513658\pi$
$642$	−1283.22			−1.99879
$643$	−55.8584			−0.0868716			−0.0434358	−	0.999056i	$-0.513830\pi$
$643$	−55.8584			−0.0868716			−0.0434358	+	0.999056i	$0.513830\pi$
$644$			154.653i			0.240144i
$645$		−	1431.40i		−	2.21923i
$646$		−	1321.40i		−	2.04551i
$647$	313.952			0.485243			0.242621	−	0.970121i	$-0.421993\pi$
$647$	313.952			0.485243			0.242621	+	0.970121i	$0.421993\pi$
$648$			773.162i			1.19315i
$649$	965.958	−	502.734i	1.48838	−	0.774628i
$650$	411.924			0.633728
$651$		−	834.020i		−	1.28114i
$652$	−1601.59			−2.45642
$653$	84.3835			0.129224			0.0646122	−	0.997910i	$-0.479419\pi$
$653$	84.3835			0.129224			0.0646122	+	0.997910i	$0.479419\pi$
$654$	−2453.89			−3.75212
$655$		−	688.262i		−	1.05078i
$656$		−	886.744i		−	1.35174i
$657$			1491.93i			2.27082i
$658$	67.3178			0.102307
$659$		−	1080.54i		−	1.63966i	−0.572606	−	0.819831i	$-0.694068\pi$
$659$		−	1080.54i		−	1.63966i	0.572606	−	0.819831i	$-0.305932\pi$
$660$	2243.80	−	1167.79i	3.39970	−	1.76938i
$661$	178.384			0.269870			0.134935	−	0.990854i	$-0.456917\pi$
$661$	178.384			0.269870			0.134935	+	0.990854i	$0.456917\pi$
$662$		−	1220.46i		−	1.84360i
$663$	−679.096			−1.02428
$664$	2098.35			3.16016
$665$	597.210			0.898060
$666$		−	916.182i		−	1.37565i
$667$			17.6575i			0.0264730i
$668$			231.024i			0.345844i
$669$	10.5922			0.0158329
$670$		−	1447.59i		−	2.16058i
$671$	329.272	+	632.667i	0.490718	+	0.942871i
$672$	197.673			0.294157
$673$		−	1119.98i		−	1.66416i	−0.554652	−	0.832082i	$-0.687149\pi$
$673$		−	1119.98i		−	1.66416i	0.554652	−	0.832082i	$-0.312851\pi$
$674$	1162.87			1.72533
$675$	−137.722			−0.204033
$676$	−538.374			−0.796411
$677$			453.505i			0.669874i	0.942240	+	0.334937i	$0.108715\pi$
$677$			453.505i			0.669874i	−0.942240	+	0.334937i	$0.891285\pi$
$678$			3181.52i			4.69251i
$679$		−	394.427i		−	0.580894i
$680$	−1359.30			−1.99897
$681$		−	1966.14i		−	2.88713i
$682$	−852.663	−	1638.31i	−1.25024	−	2.40222i
$683$	60.1606			0.0880828			0.0440414	−	0.999030i	$-0.485977\pi$
$683$	60.1606			0.0880828			0.0440414	+	0.999030i	$0.485977\pi$
$684$		−	2512.10i		−	3.67267i
$685$	307.377			0.448726
$686$	−1126.26			−1.64178
$687$	1248.63			1.81751
$688$		−	1082.65i		−	1.57363i
$689$			516.864i			0.750166i
$690$		−	462.922i		−	0.670902i
$691$	−1001.51			−1.44936			−0.724682	−	0.689083i	$-0.758013\pi$
$691$	−1001.51			−1.44936			−0.724682	+	0.689083i	$0.758013\pi$
$692$			2445.71i			3.53427i
$693$	−227.580	−	437.275i	−0.328398	−	0.630988i
$694$	1067.00			1.53747
$695$			388.701i			0.559283i
$696$	258.078			0.370802
$697$	623.985			0.895244
$698$	1369.24			1.96166
$699$			1142.94i			1.63511i
$700$		−	368.767i		−	0.526810i
$701$			265.925i			0.379350i	0.981847	+	0.189675i	$0.0607435\pi$
$701$			265.925i			0.379350i	−0.981847	+	0.189675i	$0.939257\pi$
$702$	−433.816			−0.617971
$703$		−	574.798i		−	0.817635i
$704$	−421.457	+	219.348i	−0.598660	+	0.311573i
$705$	−136.414			−0.193495
$706$			1800.35i			2.55007i
$707$	46.4719			0.0657311
$708$	−3771.33			−5.32674
$709$	−42.2360			−0.0595712			−0.0297856	−	0.999556i	$-0.509482\pi$
$709$	−42.2360			−0.0595712			−0.0297856	+	0.999556i	$0.509482\pi$
$710$		−	1768.98i		−	2.49152i
$711$		−	761.264i		−	1.07069i
$712$		−	620.706i		−	0.871778i
$713$	−228.823			−0.320930
$714$			898.024i			1.25774i
$715$	−313.780	−	602.900i	−0.438853	−	0.843216i
$716$	−356.560			−0.497988
$717$			686.053i			0.956838i
$718$	57.3212			0.0798346
$719$	97.0504			0.134980			0.0674898	−	0.997720i	$-0.478501\pi$
$719$	97.0504			0.134980			0.0674898	+	0.997720i	$0.478501\pi$
$720$	−1458.98			−2.02637
$721$		−	323.006i		−	0.447997i
$722$		−	1057.69i		−	1.46494i
$723$			1042.31i			1.44165i
$724$	329.762			0.455472
$725$		−	42.1040i		−	0.0580745i
$726$	−1584.80	−	1110.12i	−2.18293	−	1.52910i
$727$	104.621			0.143907			0.0719537	−	0.997408i	$-0.477077\pi$
$727$	104.621			0.143907			0.0719537	+	0.997408i	$0.477077\pi$
$728$		−	607.352i		−	0.834275i
$729$	−1076.51			−1.47669
$730$	2720.17			3.72626
$731$	761.843			1.04219
$732$		−	2470.08i		−	3.37443i
$733$		−	1114.36i		−	1.52028i	−0.649760	−	0.760140i	$-0.725130\pi$
$733$		−	1114.36i		−	1.52028i	0.649760	−	0.760140i	$-0.274870\pi$
$734$			582.662i			0.793817i
$735$	938.204			1.27647
$736$		−	54.2341i		−	0.0736876i
$737$	−664.975	+	346.087i	−0.902272	+	0.469589i
$738$	1752.26			2.37434
$739$		−	570.688i		−	0.772244i	−0.922448	−	0.386122i	$-0.873814\pi$
$739$		−	570.688i		−	0.772244i	0.922448	−	0.386122i	$-0.126186\pi$
$740$	−1130.86			−1.52819
$741$	−1196.43			−1.61462
$742$	683.491			0.921147
$743$		−	721.901i		−	0.971603i	−0.874069	−	0.485802i	$-0.838528\pi$
$743$		−	721.901i		−	0.971603i	0.874069	−	0.485802i	$-0.161472\pi$
$744$			3344.43i			4.49520i
$745$		−	1622.84i		−	2.17831i
$746$	−318.845			−0.427406
$747$			1584.85i			2.12162i
$748$	621.538	+	1194.23i	0.830933	+	1.59656i
$749$	308.672			0.412113
$750$		−	1309.32i		−	1.74576i
$751$	−800.941			−1.06650			−0.533250	−	0.845958i	$-0.679029\pi$
$751$	−800.941			−1.06650			−0.533250	+	0.845958i	$0.679029\pi$
$752$	−103.178			−0.137205
$753$	−663.067			−0.880567
$754$		−	132.625i		−	0.175895i
$755$			960.672i			1.27241i
$756$			388.365i			0.513711i
$757$	306.780			0.405258			0.202629	−	0.979256i	$-0.435051\pi$
$757$	306.780			0.405258			0.202629	+	0.979256i	$0.435051\pi$
$758$		−	776.359i		−	1.02422i
$759$	−212.652	+	110.675i	−0.280173	+	0.145817i
$760$	−2394.82			−3.15107
$761$			1280.14i			1.68218i	0.540896	+	0.841089i	$0.318085\pi$
$761$			1280.14i			1.68218i	−0.540896	+	0.841089i	$0.681915\pi$
$762$	413.540			0.542703
$763$	590.271			0.773619
$764$	−949.745			−1.24312
$765$		−	1026.66i		−	1.34204i
$766$		−	1327.74i		−	1.73334i
$767$			1013.34i			1.32118i
$768$	2368.82			3.08440
$769$			414.515i			0.539031i	0.962996	+	0.269515i	$0.0868635\pi$
$769$			414.515i			0.539031i	−0.962996	+	0.269515i	$0.913137\pi$
$770$	−797.263	+	414.936i	−1.03541	+	0.538878i
$771$	662.103			0.858759
$772$		−	85.5457i		−	0.110810i
$773$	−956.266			−1.23708			−0.618542	−	0.785752i	$-0.712276\pi$
$773$	−956.266			−1.23708			−0.618542	+	0.785752i	$0.712276\pi$
$774$	2139.39			2.76407
$775$	545.625			0.704032
$776$			1581.66i			2.03822i
$777$			390.633i			0.502745i
$778$			641.586i			0.824661i
$779$	1099.34			1.41122
$780$			2353.87i			3.01778i
$781$	−812.612	+	422.925i	−1.04048	+	0.541517i
$782$	246.383			0.315068
$783$			44.3416i			0.0566305i
$784$	709.619			0.905127
$785$	294.983			0.375775
$786$	1823.36			2.31979
$787$		−	486.888i		−	0.618664i	−0.950954	−	0.309332i	$-0.899895\pi$
$787$		−	486.888i		−	0.618664i	0.950954	−	0.309332i	$-0.100105\pi$
$788$			2308.13i			2.92910i
$789$		−	795.960i		−	1.00882i
$790$	−1387.98			−1.75693
$791$		−	765.299i		−	0.967509i
$792$	912.598	+	1753.48i	1.15227	+	2.21398i
$793$	−663.701			−0.836950
$794$			931.543i			1.17323i
$795$	−1385.04			−1.74219
$796$	−1820.62			−2.28721
$797$	−513.113			−0.643806			−0.321903	−	0.946773i	$-0.604323\pi$
$797$	−513.113			−0.643806			−0.321903	+	0.946773i	$0.604323\pi$
$798$			1582.14i			1.98263i
$799$		−	72.6043i		−	0.0908690i
$800$			129.320i			0.161650i
$801$	468.811			0.585282
$802$			609.091i			0.759465i
$803$	−650.334	−	1249.56i	−0.809880	−	1.55611i
$804$	2596.22			3.22913
$805$			111.354i			0.138327i
$806$	1718.68			2.13236
$807$	1049.82			1.30090
$808$	−186.353			−0.230634
$809$		−	1334.98i		−	1.65016i	−0.565015	−	0.825080i	$-0.691130\pi$
$809$		−	1334.98i		−	1.65016i	0.565015	−	0.825080i	$-0.308870\pi$
$810$			1064.70i			1.31445i
$811$		−	1023.77i		−	1.26236i	−0.775638	−	0.631178i	$-0.782572\pi$
$811$		−	1023.77i		−	1.26236i	0.775638	−	0.631178i	$-0.217428\pi$
$812$	−118.730			−0.146219
$813$		−	1360.91i		−	1.67394i
$814$	399.364	+	767.343i	0.490620	+	0.942682i
$815$	−1153.18			−1.41494
$816$		−	1376.40i		−	1.68676i
$817$	1342.22			1.64286
$818$	−48.7872			−0.0596421
$819$	458.725			0.560104
$820$		−	2162.84i		−	2.63761i
$821$			1043.61i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$821$			1043.61i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$822$			814.310i			0.990645i
$823$	172.394			0.209471			0.104735	−	0.994500i	$-0.466600\pi$
$823$	172.394			0.209471			0.104735	+	0.994500i	$0.466600\pi$
$824$			1295.26i			1.57191i
$825$	507.064	−	263.902i	0.614623	−	0.319881i
$826$	1340.02			1.62230
$827$			111.451i			0.134765i	0.997727	+	0.0673825i	$0.0214648\pi$
$827$			111.451i			0.134765i	−0.997727	+	0.0673825i	$0.978535\pi$
$828$	468.398			0.565698
$829$	−69.3115			−0.0836086			−0.0418043	−	0.999126i	$-0.513311\pi$
$829$	−69.3115			−0.0836086			−0.0418043	+	0.999126i	$0.513311\pi$
$830$	2889.59			3.48143
$831$			146.193i			0.175924i
$832$		−	442.131i		−	0.531408i
$833$			499.345i			0.599454i
$834$	−1029.76			−1.23472
$835$			166.342i			0.199212i
$836$	1095.03	+	2104.00i	1.30984	+	2.51674i
$837$	−574.623			−0.686526
$838$			751.065i			0.896259i
$839$	−659.164			−0.785654			−0.392827	−	0.919612i	$-0.628503\pi$
$839$	−659.164			−0.785654			−0.392827	+	0.919612i	$0.628503\pi$
$840$	1627.52			1.93752
$841$	827.444			0.983881
$842$			988.444i			1.17392i
$843$			573.072i			0.679801i
$844$			1302.28i			1.54299i
$845$	−387.641			−0.458747
$846$		−	203.886i		−	0.241000i
$847$	381.217	+	267.035i	0.450079	+	0.315271i
$848$	−1047.59			−1.23536
$849$			1535.09i			1.80811i
$850$	−587.497			−0.691173
$851$	107.175			0.125940
$852$	3172.63			3.72375
$853$		−	151.287i		−	0.177358i	−0.996060	−	0.0886792i	$-0.971735\pi$
$853$		−	151.287i		−	0.177358i	0.996060	−	0.0886792i	$-0.0282646\pi$
$854$			877.666i			1.02771i
$855$		−	1808.77i		−	2.11552i
$856$	−1237.78			−1.44600
$857$		−	331.113i		−	0.386363i	−0.981163	−	0.193182i	$-0.938119\pi$
$857$		−	331.113i		−	0.386363i	0.981163	−	0.193182i	$-0.0618807\pi$
$858$	1597.22	−	831.272i	1.86156	−	0.968849i
$859$	−207.832			−0.241946			−0.120973	−	0.992656i	$-0.538602\pi$
$859$	−207.832			−0.241946			−0.120973	+	0.992656i	$0.538602\pi$
$860$		−	2640.68i		−	3.07056i
$861$	−747.111			−0.867725
$862$	353.831			0.410477
$863$	−355.725			−0.412195			−0.206098	−	0.978531i	$-0.566076\pi$
$863$	−355.725			−0.412195			−0.206098	+	0.978531i	$0.566076\pi$
$864$		−	136.193i		−	0.157631i
$865$			1760.97i			2.03580i
$866$			2029.83i			2.34392i
$867$	−344.743			−0.397627
$868$		−	1538.62i		−	1.77260i
$869$	331.835	+	637.592i	0.381859	+	0.733708i
$870$	355.393			0.408498
$871$		−	697.594i		−	0.800912i
$872$	−2366.99			−2.71444
$873$	−1194.60			−1.36839
$874$	434.079			0.496658
$875$			314.950i			0.359943i
$876$			4878.58i			5.56915i
$877$			1147.95i			1.30895i	0.756083	+	0.654475i	$0.227110\pi$
$877$			1147.95i			1.30895i	−0.756083	+	0.654475i	$0.772890\pi$
$878$	1419.02			1.61620
$879$			1238.83i			1.40937i
$880$	1221.96	−	635.972i	1.38860	−	0.722696i
$881$	856.484			0.972173			0.486086	−	0.873911i	$-0.338424\pi$
$881$	856.484			0.972173			0.486086	+	0.873911i	$0.338424\pi$
$882$			1402.25i			1.58985i
$883$	−444.279			−0.503148			−0.251574	−	0.967838i	$-0.580948\pi$
$883$	−444.279			−0.503148			−0.251574	+	0.967838i	$0.580948\pi$
$884$	−1252.81			−1.41721
$885$	−2715.45			−3.06830
$886$			406.658i			0.458982i
$887$		−	1153.66i		−	1.30063i	−0.759663	−	0.650317i	$-0.774636\pi$
$887$		−	1153.66i		−	1.30063i	0.759663	−	0.650317i	$-0.225364\pi$
$888$		−	1566.44i		−	1.76401i
$889$	−99.4750			−0.111895
$890$		−	854.760i		−	0.960405i
$891$	489.091	−	254.548i	0.548924	−	0.285688i
$892$	19.5407			0.0219066
$893$		−	127.915i		−	0.143241i
$894$	4299.26			4.80902
$895$	−256.731			−0.286850
$896$	−758.664			−0.846723
$897$		−	223.083i		−	0.248699i
$898$		−	666.636i		−	0.742356i
$899$		−	175.672i		−	0.195408i
$900$	−1116.89			−1.24098
$901$		−	737.166i		−	0.818164i
$902$	−1467.59	+	763.811i	−1.62705	+	0.846797i
$903$	−912.172			−1.01016
$904$			3068.86i			3.39475i
$905$	237.436			0.262360
$906$	−2545.03			−2.80909
$907$	638.739			0.704232			0.352116	−	0.935956i	$-0.385462\pi$
$907$	638.739			0.704232			0.352116	+	0.935956i	$0.385462\pi$
$908$		−	3627.17i		−	3.99468i
$909$		−	140.750i		−	0.154840i
$910$		−	836.372i		−	0.919090i
$911$	917.274			1.00689			0.503444	−	0.864028i	$-0.332066\pi$
$911$	917.274			1.00689			0.503444	+	0.864028i	$0.332066\pi$
$912$		−	2424.95i		−	2.65893i
$913$	−690.838	−	1327.38i	−0.756669	−	1.45387i
$914$	−1430.14			−1.56471
$915$		−	1778.52i		−	1.94373i
$916$	2303.50			2.51474
$917$	−438.600			−0.478299
$918$	618.720			0.673987
$919$			1455.34i			1.58361i	0.610774	+	0.791805i	$0.290859\pi$
$919$			1455.34i			1.58361i	−0.610774	+	0.791805i	$0.709141\pi$
$920$		−	446.529i		−	0.485358i
$921$		−	1639.60i		−	1.78024i
$922$	−2784.01			−3.01953
$923$		−	852.474i		−	0.923590i
$924$	−744.181	−	1429.88i	−0.805391	−	1.54749i
$925$	−255.556			−0.276277
$926$		−	3190.47i		−	3.44543i
$927$	−978.290			−1.05533
$928$	41.6364			0.0448669
$929$	−708.446			−0.762590			−0.381295	−	0.924453i	$-0.624522\pi$
$929$	−708.446			−0.762590			−0.381295	+	0.924453i	$0.624522\pi$
$930$			4605.54i			4.95219i
$931$			879.749i			0.944950i
$932$			2108.53i			2.26237i
$933$	−2627.30			−2.81597
$934$		−	2589.26i		−	2.77223i
$935$	447.521	+	859.872i	0.478632	+	0.919650i
$936$	−1839.49			−1.96527
$937$			526.093i			0.561465i	0.959786	+	0.280733i	$0.0905774\pi$
$937$			526.093i			0.561465i	−0.959786	+	0.280733i	$0.909423\pi$
$938$	−922.485			−0.983459
$939$	1665.24			1.77342
$940$	−251.659			−0.267723
$941$		−	911.336i		−	0.968477i	−0.874936	−	0.484238i	$-0.839097\pi$
$941$		−	911.336i		−	0.968477i	0.874936	−	0.484238i	$-0.160903\pi$
$942$			781.476i			0.829593i
$943$			204.979i			0.217369i
$944$	−2053.85			−2.17569
$945$			279.632i			0.295907i
$946$	−1791.83	+	932.561i	−1.89411	+	0.985794i
$947$	50.6201			0.0534532			0.0267266	−	0.999643i	$-0.491492\pi$
$947$	50.6201			0.0534532			0.0267266	+	0.999643i	$0.491492\pi$
$948$		−	2489.31i		−	2.62586i
$949$	1310.85			1.38130
$950$	−1035.05			−1.08953
$951$	2478.96			2.60669
$952$			866.223i			0.909898i
$953$		−	1229.09i		−	1.28971i	−0.764305	−	0.644855i	$-0.776918\pi$
$953$		−	1229.09i		−	1.28971i	0.764305	−	0.644855i	$-0.223082\pi$
$954$		−	2070.09i		−	2.16991i
$955$	−683.838			−0.716061
$956$			1265.64i			1.32390i
$957$	−84.9670	−	163.256i	−0.0887847	−	0.170592i
$958$	2221.68			2.31908
$959$		−	195.878i		−	0.204253i
$960$	1184.78			1.23414
$961$	1315.53			1.36891
$962$	−804.984			−0.836782
$963$		−	934.877i		−	0.970797i
$964$			1922.88i			1.99468i
$965$		−	61.5948i		−	0.0638289i
$966$	−295.001			−0.305384
$967$			977.279i			1.01063i	0.862935	+	0.505315i	$0.168624\pi$
$967$			977.279i			1.01063i	−0.862935	+	0.505315i	$0.831376\pi$
$968$	−1528.68	−	1070.81i	−1.57922	−	1.10621i
$969$	1706.39			1.76098
$970$			2178.06i			2.24543i
$971$	0.106966			0.000110161			5.50805e−5	−	1.00000i	$-0.499982\pi$
$971$	0.106966			0.000110161			5.50805e−5		1.00000i	$0.499982\pi$
$972$	−2818.20			−2.89938
$973$	247.703			0.254576
$974$		−	2106.56i		−	2.16279i
$975$			531.937i			0.545577i
$976$		−	1345.20i		−	1.37828i
$977$	−948.278			−0.970602			−0.485301	−	0.874347i	$-0.661290\pi$
$977$	−948.278			−0.970602			−0.485301	+	0.874347i	$0.661290\pi$
$978$		−	3055.03i		−	3.12375i
$979$	−392.650	+	204.355i	−0.401072	+	0.208738i
$980$	1730.82			1.76614
$981$		−	1787.76i		−	1.82238i
$982$	3030.23			3.08578
$983$	247.226			0.251502			0.125751	−	0.992062i	$-0.459866\pi$
$983$	247.226			0.251502			0.125751	+	0.992062i	$0.459866\pi$
$984$	2995.92			3.04464
$985$			1661.91i			1.68721i
$986$			189.153i			0.191839i
$987$			86.9308i			0.0880758i
$988$	−2207.21			−2.23402
$989$			250.265i			0.253049i
$990$	1256.72	+	2414.67i	1.26941	+	2.43906i
$991$	−1442.49			−1.45559			−0.727795	−	0.685795i	$-0.759455\pi$
$991$	−1442.49			−1.45559			−0.727795	+	0.685795i	$0.759455\pi$
$992$			539.566i			0.543917i
$993$	1576.05			1.58716
$994$	−1127.29			−1.13410
$995$	−1310.89			−1.31747
$996$			5182.43i			5.20324i
$997$		−	815.435i		−	0.817889i	−0.912559	−	0.408944i	$-0.865897\pi$
$997$		−	815.435i		−	0.817889i	0.912559	−	0.408944i	$-0.134103\pi$
$998$		−	2281.98i		−	2.28656i
$999$	269.138			0.269407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.42	yes	44
11.10	odd	2	inner	253.3.c.a.208.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.3	✓	44	11.10	odd	2	inner
253.3.c.a.208.42	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+3.51900i q^{2} -4.54425 q^{3} -8.38333 q^{4} -6.03619 q^{5} -15.9912i q^{6} +3.84661i q^{7} -15.4249i q^{8} +11.6502 q^{9} -21.2413i q^{10} +(-9.75758 + 5.07834i) q^{11} +38.0960 q^{12} -10.2362i q^{13} -13.5362 q^{14} +27.4300 q^{15} +20.7469 q^{16} +14.5992i q^{17} +40.9971i q^{18} +25.7209i q^{19} +50.6034 q^{20} -17.4799i q^{21} +(-17.8707 - 34.3369i) q^{22} -4.79583 q^{23} +70.0947i q^{24} +11.4356 q^{25} +36.0213 q^{26} -12.0433 q^{27} -32.2474i q^{28} -3.68185i q^{29} +96.5259i q^{30} +47.7130 q^{31} +11.3086i q^{32} +(44.3409 - 23.0773i) q^{33} -51.3745 q^{34} -23.2188i q^{35} -97.6677 q^{36} -22.3475 q^{37} -90.5118 q^{38} +46.5160i q^{39} +93.1077i q^{40} -42.7410i q^{41} +61.5119 q^{42} -52.1839i q^{43} +(81.8010 - 42.5734i) q^{44} -70.3230 q^{45} -16.8765i q^{46} -4.97317 q^{47} -94.2792 q^{48} +34.2036 q^{49} +40.2417i q^{50} -66.3424i q^{51} +85.8137i q^{52} -50.4936 q^{53} -42.3804i q^{54} +(58.8986 - 30.6538i) q^{55} +59.3336 q^{56} -116.882i q^{57} +12.9564 q^{58} -98.9956 q^{59} -229.954 q^{60} -64.8384i q^{61} +167.902i q^{62} +44.8138i q^{63} +43.1928 q^{64} +61.7878i q^{65} +(81.2088 + 156.036i) q^{66} +68.1495 q^{67} -122.390i q^{68} +21.7935 q^{69} +81.7070 q^{70} +83.2800 q^{71} -179.704i q^{72} +128.060i q^{73} -78.6407i q^{74} -51.9661 q^{75} -215.627i q^{76} +(-19.5344 - 37.5336i) q^{77} -163.690 q^{78} -65.3432i q^{79} -125.232 q^{80} -50.1242 q^{81} +150.406 q^{82} +136.036i q^{83} +146.540i q^{84} -88.1235i q^{85} +183.635 q^{86} +16.7312i q^{87} +(78.3330 + 150.510i) q^{88} +40.2404 q^{89} -247.466i q^{90} +39.3747 q^{91} +40.2050 q^{92} -216.820 q^{93} -17.5006i q^{94} -155.256i q^{95} -51.3890i q^{96} -102.539 q^{97} +120.362i q^{98} +(-113.678 + 59.1639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 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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