LMFDB - Embedded newform 363.3.b.l.122.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(122,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, 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("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.b (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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 $ x^8 + 29x^6 + 282x^4 + 1061*x^2 + 1331
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.4
Root			$-1.65816i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.l.122.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.65816i q^{2} +(2.31624 - 1.90658i) q^{3} +1.25051 q^{4} +0.698503i q^{5} +(-3.16141 - 3.84069i) q^{6} -2.60911 q^{7} -8.70618i q^{8} +(1.72990 - 8.83218i) q^{9} +O(q^{10})$	\(q-1.65816i q^{2} +(2.31624 - 1.90658i) q^{3} +1.25051 q^{4} +0.698503i q^{5} +(-3.16141 - 3.84069i) q^{6} -2.60911 q^{7} -8.70618i q^{8} +(1.72990 - 8.83218i) q^{9} +1.15823 q^{10} +(2.89647 - 2.38419i) q^{12} -17.1169 q^{13} +4.32632i q^{14} +(1.33175 + 1.61790i) q^{15} -9.43421 q^{16} -16.1125i q^{17} +(-14.6452 - 2.86845i) q^{18} +15.9263 q^{19} +0.873483i q^{20} +(-6.04332 + 4.97448i) q^{21} -23.1295i q^{23} +(-16.5990 - 20.1656i) q^{24} +24.5121 q^{25} +28.3826i q^{26} +(-12.8324 - 23.7556i) q^{27} -3.26271 q^{28} -5.36592i q^{29} +(2.68273 - 2.20826i) q^{30} -4.06259 q^{31} -19.1813i q^{32} -26.7172 q^{34} -1.82247i q^{35} +(2.16325 - 11.0447i) q^{36} +63.5312 q^{37} -26.4084i q^{38} +(-39.6469 + 32.6348i) q^{39} +6.08130 q^{40} +67.4378i q^{41} +(8.24848 + 10.0208i) q^{42} +22.6622 q^{43} +(6.16931 + 1.20834i) q^{45} -38.3523 q^{46} +73.8208i q^{47} +(-21.8519 + 17.9871i) q^{48} -42.1925 q^{49} -40.6450i q^{50} +(-30.7199 - 37.3205i) q^{51} -21.4048 q^{52} +42.8512i q^{53} +(-39.3906 + 21.2782i) q^{54} +22.7154i q^{56} +(36.8892 - 30.3649i) q^{57} -8.89755 q^{58} -28.7381i q^{59} +(1.66537 + 2.02319i) q^{60} +46.3013 q^{61} +6.73643i q^{62} +(-4.51350 + 23.0441i) q^{63} -69.5425 q^{64} -11.9562i q^{65} -77.2821 q^{67} -20.1489i q^{68} +(-44.0982 - 53.5733i) q^{69} -3.02195 q^{70} +41.2629i q^{71} +(-76.8946 - 15.0608i) q^{72} +56.7729 q^{73} -105.345i q^{74} +(56.7758 - 46.7343i) q^{75} +19.9160 q^{76} +(54.1137 + 65.7409i) q^{78} +50.9253 q^{79} -6.58983i q^{80} +(-75.0149 - 30.5576i) q^{81} +111.823 q^{82} +59.2098i q^{83} +(-7.55721 + 6.22062i) q^{84} +11.2547 q^{85} -37.5776i q^{86} +(-10.2306 - 12.4287i) q^{87} +38.1909i q^{89} +(2.00362 - 10.2297i) q^{90} +44.6600 q^{91} -28.9235i q^{92} +(-9.40993 + 7.74566i) q^{93} +122.407 q^{94} +11.1246i q^{95} +(-36.5707 - 44.4284i) q^{96} +16.2924 q^{97} +69.9620i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9	$ 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9} + 6 q^{10} + 53 q^{12} - 44 q^{13} - 54 q^{15} - 14 q^{16} - q^{18} - 68 q^{19} + 6 q^{21} - 33 q^{24} + 42 q^{25} - 25 q^{27} + 118 q^{28} - 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} - 38 q^{39} - 58 q^{40} + 174 q^{42} + 78 q^{43} - 36 q^{45} + 286 q^{46} - 285 q^{48} - 140 q^{49} - 58 q^{51} + 102 q^{52} - 523 q^{54} + 22 q^{57} - 68 q^{58} + 262 q^{60} - 22 q^{61} - 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} - 489 q^{72} + 378 q^{73} - 33 q^{75} + 450 q^{76} - 246 q^{78} + 252 q^{79} + 11 q^{81} - 200 q^{82} - 450 q^{84} + 156 q^{85} - 66 q^{87} - 598 q^{90} - 148 q^{91} + 380 q^{93} + 460 q^{94} - 399 q^{96} - 324 q^{97}+O(q^{100}) $ 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9 + 6 * q^10 + 53 * q^12 - 44 * q^13 - 54 * q^15 - 14 * q^16 - q^18 - 68 * q^19 + 6 * q^21 - 33 * q^24 + 42 * q^25 - 25 * q^27 + 118 * q^28 - 10 * q^30 + 2 * q^31 - 66 * q^34 - 7 * q^36 + 140 * q^37 - 38 * q^39 - 58 * q^40 + 174 * q^42 + 78 * q^43 - 36 * q^45 + 286 * q^46 - 285 * q^48 - 140 * q^49 - 58 * q^51 + 102 * q^52 - 523 * q^54 + 22 * q^57 - 68 * q^58 + 262 * q^60 - 22 * q^61 - 246 * q^63 - 52 * q^64 + 184 * q^67 - 176 * q^69 + 374 * q^70 - 489 * q^72 + 378 * q^73 - 33 * q^75 + 450 * q^76 - 246 * q^78 + 252 * q^79 + 11 * q^81 - 200 * q^82 - 450 * q^84 + 156 * q^85 - 66 * q^87 - 598 * q^90 - 148 * q^91 + 380 * q^93 + 460 * q^94 - 399 * q^96 - 324 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.65816i		−	0.829080i	−0.910031	−	0.414540i	$-0.863943\pi$
$2$		−	1.65816i		−	0.829080i	0.910031	−	0.414540i	$-0.136057\pi$
$3$	2.31624	−	1.90658i	0.772079	−	0.635527i
$3$	2.31624	−	1.90658i	0.772079	−	0.635527i
$4$	1.25051			0.312627
$5$			0.698503i			0.139701i	0.997557	+	0.0698503i	$0.0222522\pi$
$5$			0.698503i			0.139701i	−0.997557	+	0.0698503i	$0.977748\pi$
$6$	−3.16141	−	3.84069i	−0.526902	−	0.640115i
$7$	−2.60911			−0.372730			−0.186365	−	0.982481i	$-0.559671\pi$
$7$	−2.60911			−0.372730			−0.186365	+	0.982481i	$0.559671\pi$
$8$		−	8.70618i		−	1.08827i
$9$	1.72990	−	8.83218i	0.192211	−	0.981354i
$10$	1.15823			0.115823
$11$		0			0
$11$		0			0
$12$	2.89647	−	2.38419i	0.241372	−	0.198683i
$13$	−17.1169			−1.31669			−0.658344	−	0.752717i	$-0.728743\pi$
$13$	−17.1169			−1.31669			−0.658344	+	0.752717i	$0.728743\pi$
$14$			4.32632i			0.309023i
$15$	1.33175	+	1.61790i	0.0887835	+	0.107860i
$16$	−9.43421			−0.589638
$17$		−	16.1125i		−	0.947797i	−0.880579	−	0.473898i	$-0.842846\pi$
$17$		−	16.1125i		−	0.947797i	0.880579	−	0.473898i	$-0.157154\pi$
$18$	−14.6452	−	2.86845i	−0.813620	−	0.159359i
$19$	15.9263			0.838229			0.419114	−	0.907933i	$-0.362341\pi$
$19$	15.9263			0.838229			0.419114	+	0.907933i	$0.362341\pi$
$20$			0.873483i			0.0436742i
$21$	−6.04332	+	4.97448i	−0.287777	+	0.236880i
$22$		0			0
$23$		−	23.1295i		−	1.00563i	−0.864395	−	0.502814i	$-0.832298\pi$
$23$		−	23.1295i		−	1.00563i	0.864395	−	0.502814i	$-0.167702\pi$
$24$	−16.5990	−	20.1656i	−0.691626	−	0.840232i
$25$	24.5121			0.980484
$26$			28.3826i			1.09164i
$27$	−12.8324	−	23.7556i	−0.475274	−	0.879838i
$28$	−3.26271			−0.116525
$29$		−	5.36592i		−	0.185032i	−0.995711	−	0.0925158i	$-0.970509\pi$
$29$		−	5.36592i		−	0.185032i	0.995711	−	0.0925158i	$-0.0294909\pi$
$30$	2.68273	−	2.20826i	0.0894245	−	0.0736086i
$31$	−4.06259			−0.131051			−0.0655257	−	0.997851i	$-0.520872\pi$
$31$	−4.06259			−0.131051			−0.0655257	+	0.997851i	$0.520872\pi$
$32$		−	19.1813i		−	0.599415i
$33$		0			0
$34$	−26.7172			−0.785799
$35$		−	1.82247i		−	0.0520706i
$36$	2.16325	−	11.0447i	0.0600904	−	0.306797i
$37$	63.5312			1.71706			0.858529	−	0.512765i	$-0.171379\pi$
$37$	63.5312			1.71706			0.858529	+	0.512765i	$0.171379\pi$
$38$		−	26.4084i		−	0.694958i
$39$	−39.6469	+	32.6348i	−1.01659	+	0.836790i
$40$	6.08130			0.152032
$41$			67.4378i			1.64482i	0.568893	+	0.822412i	$0.307372\pi$
$41$			67.4378i			1.64482i	−0.568893	+	0.822412i	$0.692628\pi$
$42$	8.24848	+	10.0208i	0.196392	+	0.238590i
$43$	22.6622			0.527028			0.263514	−	0.964656i	$-0.415118\pi$
$43$	22.6622			0.527028			0.263514	+	0.964656i	$0.415118\pi$
$44$		0			0
$45$	6.16931	+	1.20834i	0.137096	+	0.0268521i
$46$	−38.3523			−0.833746
$47$			73.8208i			1.57066i	0.619080	+	0.785328i	$0.287506\pi$
$47$			73.8208i			1.57066i	−0.619080	+	0.785328i	$0.712494\pi$
$48$	−21.8519	+	17.9871i	−0.455247	+	0.374731i
$49$	−42.1925			−0.861072
$50$		−	40.6450i		−	0.812899i
$51$	−30.7199	−	37.3205i	−0.602350	−	0.731774i
$52$	−21.4048			−0.411632
$53$			42.8512i			0.808513i	0.914646	+	0.404256i	$0.132470\pi$
$53$			42.8512i			0.808513i	−0.914646	+	0.404256i	$0.867530\pi$
$54$	−39.3906	+	21.2782i	−0.729456	+	0.394040i
$55$		0			0
$56$			22.7154i			0.405632i
$57$	36.8892	−	30.3649i	0.647179	−	0.532717i
$58$	−8.89755			−0.153406
$59$		−	28.7381i		−	0.487086i	−0.969890	−	0.243543i	$-0.921690\pi$
$59$		−	28.7381i		−	0.487086i	0.969890	−	0.243543i	$-0.0783098\pi$
$60$	1.66537	+	2.02319i	0.0277561	+	0.0337199i
$61$	46.3013			0.759037			0.379519	−	0.925184i	$-0.376090\pi$
$61$	46.3013			0.759037			0.379519	+	0.925184i	$0.376090\pi$
$62$			6.73643i			0.108652i
$63$	−4.51350	+	23.0441i	−0.0716429	+	0.365780i
$64$	−69.5425			−1.08660
$65$		−	11.9562i		−	0.183942i
$66$		0			0
$67$	−77.2821			−1.15346			−0.576732	−	0.816933i	$-0.695672\pi$
$67$	−77.2821			−1.15346			−0.576732	+	0.816933i	$0.695672\pi$
$68$		−	20.1489i		−	0.296307i
$69$	−44.0982	−	53.5733i	−0.639104	−	0.776424i
$70$	−3.02195			−0.0431707
$71$			41.2629i			0.581167i	0.956850	+	0.290584i	$0.0938494\pi$
$71$			41.2629i			0.581167i	−0.956850	+	0.290584i	$0.906151\pi$
$72$	−76.8946	−	15.0608i	−1.06798	−	0.209178i
$73$	56.7729			0.777711			0.388856	−	0.921299i	$-0.372871\pi$
$73$	56.7729			0.777711			0.388856	+	0.921299i	$0.372871\pi$
$74$		−	105.345i		−	1.42358i
$75$	56.7758	−	46.7343i	0.757011	−	0.623124i
$76$	19.9160			0.262053
$77$		0			0
$78$	54.1137	+	65.7409i	0.693766	+	0.842831i
$79$	50.9253			0.644624			0.322312	−	0.946633i	$-0.395540\pi$
$79$	50.9253			0.644624			0.322312	+	0.946633i	$0.395540\pi$
$80$		−	6.58983i		−	0.0823728i
$81$	−75.0149	−	30.5576i	−0.926110	−	0.377255i
$82$	111.823			1.36369
$83$			59.2098i			0.713371i	0.934225	+	0.356685i	$0.116093\pi$
$83$			59.2098i			0.713371i	−0.934225	+	0.356685i	$0.883907\pi$
$84$	−7.55721	+	6.22062i	−0.0899668	+	0.0740550i
$85$	11.2547			0.132408
$86$		−	37.5776i		−	0.436948i
$87$	−10.2306	−	12.4287i	−0.117593	−	0.142859i
$88$		0			0
$89$			38.1909i			0.429112i	0.976712	+	0.214556i	$0.0688304\pi$
$89$			38.1909i			0.429112i	−0.976712	+	0.214556i	$0.931170\pi$
$90$	2.00362	−	10.2297i	0.0222625	−	0.113663i
$91$	44.6600			0.490769
$92$		−	28.9235i		−	0.314386i
$93$	−9.40993	+	7.74566i	−0.101182	+	0.0832867i
$94$	122.407			1.30220
$95$			11.1246i			0.117101i
$96$	−36.5707	−	44.4284i	−0.380945	−	0.462796i
$97$	16.2924			0.167963			0.0839815	−	0.996467i	$-0.473236\pi$
$97$	16.2924			0.167963			0.0839815	+	0.996467i	$0.473236\pi$
$98$			69.9620i			0.713898i
$99$		0			0
$100$	30.6525			0.306525
$101$			104.194i			1.03163i	0.856701	+	0.515814i	$0.172510\pi$
$101$			104.194i			1.03163i	−0.856701	+	0.515814i	$0.827490\pi$
$102$	−61.8833	+	50.9384i	−0.606699	+	0.499397i
$103$	54.4065			0.528219			0.264109	−	0.964493i	$-0.414922\pi$
$103$	54.4065			0.528219			0.264109	+	0.964493i	$0.414922\pi$
$104$			149.023i			1.43291i
$105$	−3.47469	−	4.22128i	−0.0330923	−	0.0402026i
$106$	71.0541			0.670321
$107$			28.4068i			0.265484i	0.991151	+	0.132742i	$0.0423782\pi$
$107$			28.4068i			0.265484i	−0.991151	+	0.132742i	$0.957622\pi$
$108$	−16.0470	−	29.7066i	−0.148583	−	0.275061i
$109$	41.2540			0.378477			0.189238	−	0.981931i	$-0.439398\pi$
$109$	41.2540			0.378477			0.189238	+	0.981931i	$0.439398\pi$
$110$		0			0
$111$	147.153	−	121.127i	1.32570	−	1.09124i
$112$	24.6149			0.219776
$113$		−	145.178i		−	1.28476i	−0.766386	−	0.642381i	$-0.777947\pi$
$113$		−	145.178i		−	1.28476i	0.766386	−	0.642381i	$-0.222053\pi$
$114$	−50.3498	−	61.1681i	−0.441665	−	0.536563i
$115$	16.1560			0.140487
$116$		−	6.71012i		−	0.0578458i
$117$	−29.6106	+	151.180i	−0.253082	+	1.29214i
$118$	−47.6524			−0.403834
$119$			42.0394i			0.353272i
$120$	14.0857	−	11.5945i	0.117381	−	0.0966207i
$121$		0			0
$122$		−	76.7749i		−	0.629303i
$123$	128.576	+	156.202i	1.04533	+	1.26993i
$124$	−5.08030			−0.0409702
$125$			34.5844i			0.276675i
$126$	38.2109	+	7.48411i	0.303261	+	0.0593977i
$127$	182.781			1.43922			0.719612	−	0.694376i	$-0.244320\pi$
$127$	182.781			1.43922			0.719612	+	0.694376i	$0.244320\pi$
$128$			38.5873i			0.301464i
$129$	52.4910	−	43.2073i	0.406907	−	0.334940i
$130$	−19.8254			−0.152503
$131$		−	84.5109i		−	0.645121i	−0.946549	−	0.322561i	$-0.895456\pi$
$131$		−	84.5109i		−	0.645121i	0.946549	−	0.322561i	$-0.104544\pi$
$132$		0			0
$133$	−41.5536			−0.312433
$134$			128.146i			0.956314i
$135$	16.5934	−	8.96348i	0.122914	−	0.0663961i
$136$	−140.279			−1.03146
$137$		−	204.373i		−	1.49177i	−0.666075	−	0.745885i	$-0.732027\pi$
$137$		−	204.373i		−	1.49177i	0.666075	−	0.745885i	$-0.267973\pi$
$138$	−88.8330	+	73.1218i	−0.643718	+	0.529868i
$139$	50.2414			0.361449			0.180724	−	0.983534i	$-0.442156\pi$
$139$	50.2414			0.361449			0.180724	+	0.983534i	$0.442156\pi$
$140$		−	2.27901i		−	0.0162787i
$141$	140.745	+	170.987i	0.998194	+	1.21267i
$142$	68.4204			0.481834
$143$		0			0
$144$	−16.3203	+	83.3246i	−0.113335	+	0.578643i
$145$	3.74811			0.0258490
$146$		−	94.1385i		−	0.644785i
$147$	−97.7279	+	80.4435i	−0.664816	+	0.547235i
$148$	79.4461			0.536798
$149$			157.402i			1.05639i	0.849123	+	0.528195i	$0.177131\pi$
$149$			157.402i			1.05639i	−0.849123	+	0.528195i	$0.822869\pi$
$150$	−77.4929	−	94.1433i	−0.516619	−	0.627622i
$151$	171.381			1.13498			0.567488	−	0.823382i	$-0.307915\pi$
$151$	171.381			1.13498			0.567488	+	0.823382i	$0.307915\pi$
$152$		−	138.658i		−	0.912221i
$153$	−142.309	−	27.8731i	−0.930124	−	0.182177i
$154$		0			0
$155$		−	2.83774i		−	0.0183080i
$156$	−49.5787	+	40.8101i	−0.317812	+	0.261603i
$157$	−65.3379			−0.416165			−0.208083	−	0.978111i	$-0.566722\pi$
$157$	−65.3379			−0.416165			−0.208083	+	0.978111i	$0.566722\pi$
$158$		−	84.4423i		−	0.534445i
$159$	81.6992	+	99.2534i	0.513831	+	0.624235i
$160$	13.3982			0.0837387
$161$			60.3473i			0.374828i
$162$	−50.6694	+	124.387i	−0.312774	+	0.767819i
$163$	−15.4384			−0.0947144			−0.0473572	−	0.998878i	$-0.515080\pi$
$163$	−15.4384			−0.0947144			−0.0473572	+	0.998878i	$0.515080\pi$
$164$			84.3314i			0.514216i
$165$		0			0
$166$	98.1792			0.591441
$167$		−	154.104i		−	0.922776i	−0.887198	−	0.461388i	$-0.847352\pi$
$167$		−	154.104i		−	0.922776i	0.887198	−	0.461388i	$-0.152648\pi$
$168$	43.3087	+	52.6142i	0.257790	+	0.313180i
$169$	123.990			0.733667
$170$		−	18.6620i		−	0.109777i
$171$	27.5510	−	140.664i	0.161117	−	0.822599i
$172$	28.3392			0.164763
$173$			25.1030i			0.145104i	0.997365	+	0.0725520i	$0.0231143\pi$
$173$			25.1030i			0.145104i	−0.997365	+	0.0725520i	$0.976886\pi$
$174$	−20.6088	+	16.9639i	−0.118442	+	0.0974936i
$175$	−63.9548			−0.365456
$176$		0			0
$177$	−54.7915	−	66.5642i	−0.309556	−	0.376069i
$178$	63.3267			0.355768
$179$			61.8050i			0.345279i	0.984985	+	0.172640i	$0.0552296\pi$
$179$			61.8050i			0.345279i	−0.984985	+	0.172640i	$0.944770\pi$
$180$	7.71476	+	1.51104i	0.0428598	+	0.00839467i
$181$	−148.405			−0.819915			−0.409958	−	0.912105i	$-0.634456\pi$
$181$	−148.405			−0.819915			−0.409958	+	0.912105i	$0.634456\pi$
$182$		−	74.0534i		−	0.406887i
$183$	107.245	−	88.2771i	0.586037	−	0.482389i
$184$	−201.369			−1.09440
$185$			44.3767i			0.239874i
$186$	12.8435	+	15.6032i	0.0690513	+	0.0838880i
$187$		0			0
$188$			92.3135i			0.491029i
$189$	33.4812	+	61.9810i	0.177149	+	0.327942i
$190$	18.4464			0.0970862
$191$		−	56.2029i		−	0.294256i	−0.989117	−	0.147128i	$-0.952997\pi$
$191$		−	56.2029i		−	0.294256i	0.989117	−	0.147128i	$-0.0470029\pi$
$192$	−161.077	+	132.588i	−0.838942	+	0.690564i
$193$	−150.972			−0.782239			−0.391119	−	0.920340i	$-0.627912\pi$
$193$	−150.972			−0.782239			−0.391119	+	0.920340i	$0.627912\pi$
$194$		−	27.0154i		−	0.139255i
$195$	−22.7955	−	27.6935i	−0.116900	−	0.142018i
$196$	−52.7621			−0.269194
$197$			22.3374i			0.113388i	0.998392	+	0.0566938i	$0.0180559\pi$
$197$			22.3374i			0.113388i	−0.998392	+	0.0566938i	$0.981944\pi$
$198$		0			0
$199$	−150.930			−0.758444			−0.379222	−	0.925306i	$-0.623808\pi$
$199$	−150.930			−0.758444			−0.379222	+	0.925306i	$0.623808\pi$
$200$		−	213.407i		−	1.06703i
$201$	−179.004	+	147.344i	−0.890565	+	0.733057i
$202$	172.771			0.855302
$203$			14.0003i			0.0689668i
$204$	−38.4154	−	46.6695i	−0.188311	−	0.228772i
$205$	−47.1055			−0.229783
$206$		−	90.2147i		−	0.437935i
$207$	−204.284	−	40.0117i	−0.986877	−	0.193293i
$208$	161.485			0.776369
$209$		0			0
$210$	−6.99955	+	5.76159i	−0.0333312	+	0.0274362i
$211$	−181.578			−0.860559			−0.430279	−	0.902696i	$-0.641585\pi$
$211$	−181.578			−0.860559			−0.430279	+	0.902696i	$0.641585\pi$
$212$			53.5857i			0.252763i
$213$	78.6710	+	95.5745i	0.369347	+	0.448707i
$214$	47.1030			0.220107
$215$			15.8296i			0.0736262i
$216$	−206.821	+	111.721i	−0.957503	+	0.517228i
$217$	10.5998			0.0488468
$218$		−	68.4057i		−	0.313788i
$219$	131.499	−	108.242i	0.600454	−	0.494256i
$220$		0			0
$221$			275.798i			1.24795i
$222$	−200.848	−	244.003i	−0.904722	−	1.09911i
$223$	188.035			0.843204			0.421602	−	0.906781i	$-0.361468\pi$
$223$	188.035			0.843204			0.421602	+	0.906781i	$0.361468\pi$
$224$			50.0461i			0.223420i
$225$	42.4035	−	216.495i	0.188460	−	0.962201i
$226$	−240.728			−1.06517
$227$		−	429.227i		−	1.89087i	−0.325815	−	0.945434i	$-0.605639\pi$
$227$		−	429.227i		−	1.89087i	0.325815	−	0.945434i	$-0.394361\pi$
$228$	46.1302	−	37.9715i	0.202325	−	0.166541i
$229$	135.775			0.592906			0.296453	−	0.955047i	$-0.404196\pi$
$229$	135.775			0.592906			0.296453	+	0.955047i	$0.404196\pi$
$230$		−	26.7892i		−	0.116475i
$231$		0			0
$232$	−46.7166			−0.201365
$233$		−	326.889i		−	1.40296i	−0.712690	−	0.701479i	$-0.752523\pi$
$233$		−	326.889i		−	1.40296i	0.712690	−	0.701479i	$-0.247477\pi$
$234$	250.680	+	49.0991i	1.07128	+	0.209825i
$235$	−51.5641			−0.219422
$236$		−	35.9372i		−	0.152276i
$237$	117.955	−	97.0932i	0.497701	−	0.409676i
$238$	69.7081			0.292891
$239$			93.4530i			0.391017i	0.980702	+	0.195508i	$0.0626357\pi$
$239$			93.4530i			0.391017i	−0.980702	+	0.195508i	$0.937364\pi$
$240$	−12.5640	−	15.2636i	−0.0523501	−	0.0635983i
$241$	−206.766			−0.857952			−0.428976	−	0.903316i	$-0.641125\pi$
$241$	−206.766			−0.857952			−0.428976	+	0.903316i	$0.641125\pi$
$242$		0			0
$243$	−232.013	+	72.2432i	−0.954785	+	0.297297i
$244$	57.9001			0.237295
$245$		−	29.4716i		−	0.120292i
$246$	259.007	−	213.199i	1.05288	−	0.866661i
$247$	−272.610			−1.10369
$248$			35.3697i			0.142620i
$249$	112.888	+	137.144i	0.453366	+	0.550778i
$250$	57.3464			0.229386
$251$			2.79029i			0.0111167i	0.999985	+	0.00555834i	$0.00176928\pi$
$251$			2.79029i			0.0111167i	−0.999985	+	0.00555834i	$0.998231\pi$
$252$	−5.64417	+	28.8168i	−0.0223975	+	0.114353i
$253$		0			0
$254$		−	303.081i		−	1.19323i
$255$	26.0685	−	21.4579i	0.102229	−	0.0841488i
$256$	−214.186			−0.836664
$257$			400.206i			1.55722i	0.627506	+	0.778611i	$0.284076\pi$
$257$			400.206i			1.55722i	−0.627506	+	0.778611i	$0.715924\pi$
$258$	−71.6446	−	87.0385i	−0.277692	−	0.337358i
$259$	−165.760			−0.639999
$260$		−	14.9514i		−	0.0575052i
$261$	−47.3928	−	9.28251i	−0.181581	−	0.0355652i
$262$	−140.133			−0.534857
$263$			379.212i			1.44187i	0.693003	+	0.720935i	$0.256287\pi$
$263$			379.212i			1.44187i	−0.693003	+	0.720935i	$0.743713\pi$
$264$		0			0
$265$	−29.9317			−0.112950
$266$			68.9025i			0.259032i
$267$	72.8141	+	88.4592i	0.272712	+	0.331308i
$268$	−96.6418			−0.360604
$269$			31.2008i			0.115988i	0.998317	+	0.0579940i	$0.0184704\pi$
$269$			31.2008i			0.115988i	−0.998317	+	0.0579940i	$0.981530\pi$
$270$	−14.8629	−	27.5145i	−0.0550477	−	0.101905i
$271$	−518.106			−1.91183			−0.955916	−	0.293641i	$-0.905133\pi$
$271$	−518.106			−1.91183			−0.955916	+	0.293641i	$0.905133\pi$
$272$			152.009i			0.558857i
$273$	103.443	−	85.1479i	0.378912	−	0.311897i
$274$	−338.882			−1.23680
$275$		0			0
$276$	−55.1450	−	66.9937i	−0.199801	−	0.242731i
$277$	−367.958			−1.32837			−0.664184	−	0.747570i	$-0.731221\pi$
$277$	−367.958			−1.32837			−0.664184	+	0.747570i	$0.731221\pi$
$278$		−	83.3082i		−	0.299670i
$279$	−7.02789	+	35.8816i	−0.0251896	+	0.128608i
$280$	−15.8668			−0.0566670
$281$		−	320.392i		−	1.14019i	−0.821580	−	0.570093i	$-0.806907\pi$
$281$		−	320.392i		−	1.14019i	0.821580	−	0.570093i	$-0.193093\pi$
$282$	283.523	−	233.378i	1.00540	−	0.827583i
$283$	160.795			0.568180			0.284090	−	0.958798i	$-0.408309\pi$
$283$	160.795			0.568180			0.284090	+	0.958798i	$0.408309\pi$
$284$			51.5995i			0.181688i
$285$	21.2100	+	25.7672i	0.0744209	+	0.0904113i
$286$		0			0
$287$		−	175.953i		−	0.613075i
$288$	−169.413	−	33.1818i	−0.588238	−	0.115214i
$289$	29.3858			0.101681
$290$		−	6.21497i		−	0.0214309i
$291$	37.7371	−	31.0628i	0.129681	−	0.106745i
$292$	70.9949			0.243133
$293$			290.942i			0.992976i	0.868043	+	0.496488i	$0.165377\pi$
$293$			290.942i			0.992976i	−0.868043	+	0.496488i	$0.834623\pi$
$294$	133.388	+	162.048i	0.453701	+	0.551185i
$295$	20.0737			0.0680463
$296$		−	553.114i		−	1.86863i
$297$		0			0
$298$	260.998			0.875832
$299$			395.905i			1.32410i
$300$	70.9985	−	58.4415i	0.236662	−	0.194805i
$301$	−59.1282			−0.196439
$302$		−	284.178i		−	0.940986i
$303$	198.655	+	241.339i	0.655627	+	0.796498i
$304$	−150.252			−0.494251
$305$			32.3416i			0.106038i
$306$	−46.2181	+	235.971i	−0.151040	+	0.771147i
$307$	281.800			0.917915			0.458957	−	0.888458i	$-0.348223\pi$
$307$	281.800			0.917915			0.458957	+	0.888458i	$0.348223\pi$
$308$		0			0
$309$	126.018	−	103.730i	0.407826	−	0.335697i
$310$	−4.70542			−0.0151788
$311$			473.753i			1.52332i	0.647977	+	0.761660i	$0.275615\pi$
$311$			473.753i			1.52332i	−0.647977	+	0.761660i	$0.724385\pi$
$312$	284.125	+	345.173i	0.910656	+	1.10632i
$313$	−29.9742			−0.0957641			−0.0478820	−	0.998853i	$-0.515247\pi$
$313$	−29.9742			−0.0957641			−0.0478820	+	0.998853i	$0.515247\pi$
$314$			108.341i			0.345034i
$315$	−16.0964	−	3.15270i	−0.0510997	−	0.0100086i
$316$	63.6824			0.201527
$317$			159.277i			0.502450i	0.967929	+	0.251225i	$0.0808334\pi$
$317$			159.277i			0.502450i	−0.967929	+	0.251225i	$0.919167\pi$
$318$	164.578	−	135.470i	0.517541	−	0.426007i
$319$		0			0
$320$		−	48.5757i		−	0.151799i
$321$	54.1598	+	65.7968i	0.168722	+	0.204974i
$322$	100.065			0.310762
$323$		−	256.614i		−	0.794471i
$324$	−93.8066	−	38.2125i	−0.289527	−	0.117940i
$325$	−419.572			−1.29099
$326$			25.5994i			0.0785258i
$327$	95.5540	−	78.6540i	0.292214	−	0.240532i
$328$	587.125			1.79002
$329$		−	192.607i		−	0.585431i
$330$		0			0
$331$	332.709			1.00516			0.502582	−	0.864530i	$-0.332384\pi$
$331$	332.709			1.00516			0.502582	+	0.864530i	$0.332384\pi$
$332$			74.0422i			0.223019i
$333$	109.903	−	561.119i	0.330038	−	1.68504i
$334$	−255.528			−0.765055
$335$		−	53.9818i		−	0.161140i
$336$	57.0139	−	46.9303i	0.169684	−	0.139673i
$337$	−55.4053			−0.164408			−0.0822038	−	0.996616i	$-0.526196\pi$
$337$	−55.4053			−0.164408			−0.0822038	+	0.996616i	$0.526196\pi$
$338$		−	205.595i		−	0.608268i
$339$	−276.794	−	336.267i	−0.816500	−	0.991937i
$340$	14.0740			0.0413942
$341$		0			0
$342$	−233.244	−	45.6840i	−0.682000	−	0.133579i
$343$	237.931			0.693678
$344$		−	197.301i		−	0.573550i
$345$	37.4211	−	30.8027i	0.108467	−	0.0892832i
$346$	41.6247			0.120303
$347$		−	138.541i		−	0.399255i	−0.979872	−	0.199627i	$-0.936027\pi$
$347$		−	138.541i		−	0.399255i	0.979872	−	0.199627i	$-0.0639732\pi$
$348$	−12.7934	−	15.5422i	−0.0367626	−	0.0446615i
$349$	−226.516			−0.649044			−0.324522	−	0.945878i	$-0.605203\pi$
$349$	−226.516			−0.649044			−0.324522	+	0.945878i	$0.605203\pi$
$350$			106.047i			0.302992i
$351$	219.652	+	406.624i	0.625788	+	1.15847i
$352$		0			0
$353$		−	258.939i		−	0.733538i	−0.930312	−	0.366769i	$-0.880464\pi$
$353$		−	258.939i		−	0.733538i	0.930312	−	0.366769i	$-0.119536\pi$
$354$	−110.374	+	90.8530i	−0.311791	+	0.256647i
$355$	−28.8223			−0.0811894
$356$			47.7580i			0.134152i
$357$	80.1515	+	97.3732i	0.224514	+	0.272754i
$358$	102.482			0.286264
$359$			259.036i			0.721549i	0.932653	+	0.360774i	$0.117488\pi$
$359$			259.036i			0.721549i	−0.932653	+	0.360774i	$0.882512\pi$
$360$	10.5200	−	53.7111i	0.0292223	−	0.149198i
$361$	−107.352			−0.297373
$362$			246.079i			0.679775i
$363$		0			0
$364$	55.8476			0.153428
$365$			39.6561i			0.108647i
$366$	−146.378	−	177.829i	−0.399939	−	0.485871i
$367$	−198.777			−0.541627			−0.270814	−	0.962632i	$-0.587293\pi$
$367$	−198.777			−0.541627			−0.270814	+	0.962632i	$0.587293\pi$
$368$			218.208i			0.592957i
$369$	595.623	+	116.661i	1.61415	+	0.316154i
$370$	73.5837			0.198875
$371$		−	111.803i		−	0.301357i
$372$	−11.7672	+	9.68600i	−0.0316322	+	0.0260376i
$373$	−670.467			−1.79750			−0.898750	−	0.438462i	$-0.855523\pi$
$373$	−670.467			−1.79750			−0.898750	+	0.438462i	$0.855523\pi$
$374$		0			0
$375$	65.9379	+	80.1056i	0.175834	+	0.213615i
$376$	642.697			1.70930
$377$			91.8481i			0.243629i
$378$	102.774	−	55.5171i	0.271890	−	0.146871i
$379$	392.391			1.03533			0.517666	−	0.855583i	$-0.326801\pi$
$379$	392.391			1.03533			0.517666	+	0.855583i	$0.326801\pi$
$380$			13.9114i			0.0366089i
$381$	423.365	−	348.488i	1.11119	−	0.914666i
$382$	−93.1933			−0.243962
$383$		−	497.702i		−	1.29948i	−0.760155	−	0.649741i	$-0.774877\pi$
$383$		−	497.702i		−	1.29948i	0.760155	−	0.649741i	$-0.225123\pi$
$384$	73.5699	+	89.3774i	0.191588	+	0.232754i
$385$		0			0
$386$			250.336i			0.648538i
$387$	39.2034	−	200.157i	0.101301	−	0.517201i
$388$	20.3738			0.0525097
$389$		−	412.280i		−	1.05985i	−0.848046	−	0.529923i	$-0.822221\pi$
$389$		−	412.280i		−	1.05985i	0.848046	−	0.529923i	$-0.177779\pi$
$390$	−45.9202	+	37.7986i	−0.117744	+	0.0969196i
$391$	−372.674			−0.953131
$392$			367.336i			0.937081i
$393$	−161.127	−	195.747i	−0.409992	−	0.498084i
$394$	37.0389			0.0940074
$395$			35.5715i			0.0900544i
$396$		0			0
$397$	171.230			0.431310			0.215655	−	0.976470i	$-0.430811\pi$
$397$	171.230			0.431310			0.215655	+	0.976470i	$0.430811\pi$
$398$			250.267i			0.628810i
$399$	−96.2479	+	79.2253i	−0.241223	+	0.198560i
$400$	−231.252			−0.578130
$401$			726.019i			1.81052i	0.424858	+	0.905260i	$0.360324\pi$
$401$			726.019i			1.81052i	−0.424858	+	0.905260i	$0.639676\pi$
$402$	244.321	+	296.816i	0.607763	+	0.738349i
$403$	69.5392			0.172554
$404$			130.296i			0.322514i
$405$	21.3446	−	52.3982i	0.0527027	−	0.129378i
$406$	23.2147			0.0571790
$407$		0			0
$408$	−324.919	+	267.453i	−0.796369	+	0.655521i
$409$	−301.390			−0.736896			−0.368448	−	0.929648i	$-0.620111\pi$
$409$	−301.390			−0.736896			−0.368448	+	0.929648i	$0.620111\pi$
$410$			78.1084i			0.190508i
$411$	−389.653	−	473.375i	−0.948060	−	1.15176i
$412$	68.0357			0.165135
$413$			74.9809i			0.181552i
$414$	−66.3458	+	338.735i	−0.160255	+	0.818200i
$415$	−41.3582			−0.0996584
$416$			328.325i			0.789243i
$417$	116.371	−	95.7892i	0.279067	−	0.229710i
$418$		0			0
$419$			573.195i			1.36801i	0.729478	+	0.684004i	$0.239763\pi$
$419$			573.195i			1.36801i	−0.729478	+	0.684004i	$0.760237\pi$
$420$	−4.34512	−	5.27874i	−0.0103455	−	0.0125684i
$421$	−559.281			−1.32846			−0.664229	−	0.747529i	$-0.731240\pi$
$421$	−559.281			−1.32846			−0.664229	+	0.747529i	$0.731240\pi$
$422$			301.085i			0.713472i
$423$	651.999	+	127.703i	1.54137	+	0.301898i
$424$	373.070			0.879882
$425$		−	394.952i		−	0.929299i
$426$	158.478	−	130.449i	0.372014	−	0.306218i
$427$	−120.805			−0.282916
$428$			35.5229i			0.0829973i
$429$		0			0
$430$	26.2480			0.0610420
$431$			199.847i			0.463682i	0.972754	+	0.231841i	$0.0744750\pi$
$431$			199.847i			0.463682i	−0.972754	+	0.231841i	$0.925525\pi$
$432$	121.064	+	224.115i	0.280240	+	0.518786i
$433$	−103.486			−0.238999			−0.119499	−	0.992834i	$-0.538129\pi$
$433$	−103.486			−0.238999			−0.119499	+	0.992834i	$0.538129\pi$
$434$		−	17.5761i		−	0.0404979i
$435$	8.68151	−	7.14608i	0.0199575	−	0.0164278i
$436$	51.5884			0.118322
$437$		−	368.368i		−	0.842947i
$438$	−179.483	−	218.047i	−0.409778	−	0.497824i
$439$	662.550			1.50923			0.754613	−	0.656171i	$-0.227825\pi$
$439$	662.550			1.50923			0.754613	+	0.656171i	$0.227825\pi$
$440$		0			0
$441$	−72.9890	+	372.652i	−0.165508	+	0.845016i
$442$	457.316			1.03465
$443$		−	210.829i		−	0.475913i	−0.971276	−	0.237956i	$-0.923522\pi$
$443$		−	210.829i		−	0.475913i	0.971276	−	0.237956i	$-0.0764775\pi$
$444$	184.016	−	151.470i	0.414451	−	0.341150i
$445$	−26.6765			−0.0599472
$446$		−	311.791i		−	0.699084i
$447$	300.100	+	364.581i	0.671365	+	0.815617i
$448$	181.444			0.405009
$449$			239.271i			0.532897i	0.963849	+	0.266448i	$0.0858502\pi$
$449$			239.271i			0.532897i	−0.963849	+	0.266448i	$0.914150\pi$
$450$	−358.984	−	70.3118i	−0.797742	−	0.156248i
$451$		0			0
$452$		−	181.546i		−	0.401651i
$453$	396.960	−	326.752i	0.876291	−	0.721308i
$454$	−711.727			−1.56768
$455$			31.1952i			0.0685608i
$456$	−264.362	−	321.164i	−0.579741	−	0.704307i
$457$	−26.6877			−0.0583975			−0.0291988	−	0.999574i	$-0.509296\pi$
$457$	−26.6877			−0.0583975			−0.0291988	+	0.999574i	$0.509296\pi$
$458$		−	225.137i		−	0.491566i
$459$	−382.764	+	206.763i	−0.833908	+	0.450463i
$460$	20.2032			0.0439200
$461$		−	393.125i		−	0.852766i	−0.904543	−	0.426383i	$-0.859788\pi$
$461$		−	393.125i		−	0.852766i	0.904543	−	0.426383i	$-0.140212\pi$
$462$		0			0
$463$	106.954			0.231002			0.115501	−	0.993307i	$-0.463153\pi$
$463$	106.954			0.231002			0.115501	+	0.993307i	$0.463153\pi$
$464$			50.6232i			0.109102i
$465$	−5.41037	−	6.57287i	−0.0116352	−	0.0141352i
$466$	−542.035			−1.16316
$467$			422.909i			0.905588i	0.891615	+	0.452794i	$0.149573\pi$
$467$			422.909i			0.905588i	−0.891615	+	0.452794i	$0.850427\pi$
$468$	−37.0283	+	189.052i	−0.0791203	+	0.403956i
$469$	201.637			0.429931
$470$			85.5015i			0.181918i
$471$	−151.338	+	124.572i	−0.321312	+	0.264484i
$472$	−250.199			−0.530083
$473$		0			0
$474$	−160.996	−	195.588i	−0.339654	−	0.412634i
$475$	390.388			0.821870
$476$			52.5706i			0.110442i
$477$	378.469	+	74.1283i	0.793437	+	0.155405i
$478$	154.960			0.324184
$479$			539.714i			1.12675i	0.826200	+	0.563376i	$0.190498\pi$
$479$			539.714i			1.12675i	−0.826200	+	0.563376i	$0.809502\pi$
$480$	31.0334	−	25.5447i	0.0646529	−	0.0532182i
$481$	−1087.46			−2.26083
$482$			342.852i			0.711311i
$483$	115.057	+	139.779i	0.238213	+	0.289397i
$484$		0			0
$485$			11.3803i			0.0234645i
$486$	119.791	+	384.714i	0.246483	+	0.791593i
$487$	610.646			1.25389			0.626947	−	0.779062i	$-0.284304\pi$
$487$	610.646			1.25389			0.626947	+	0.779062i	$0.284304\pi$
$488$		−	403.107i		−	0.826039i
$489$	−35.7591	+	29.4346i	−0.0731270	+	0.0601935i
$490$	−48.8687			−0.0997320
$491$			56.8741i			0.115833i	0.998321	+	0.0579166i	$0.0184458\pi$
$491$			56.8741i			0.115833i	−0.998321	+	0.0579166i	$0.981554\pi$
$492$	160.785	+	195.331i	0.326798	+	0.397015i
$493$	−86.4586			−0.175372
$494$			452.031i			0.915043i
$495$		0			0
$496$	38.3274			0.0772729
$497$		−	107.659i		−	0.216618i
$498$	227.406	−	187.187i	0.456639	−	0.375877i
$499$	468.878			0.939635			0.469818	−	0.882763i	$-0.344320\pi$
$499$	468.878			0.939635			0.469818	+	0.882763i	$0.344320\pi$
$500$			43.2480i			0.0864960i
$501$	−293.811	−	356.940i	−0.586449	−	0.712456i
$502$	4.62674			0.00921661
$503$			458.172i			0.910879i	0.890267	+	0.455439i	$0.150518\pi$
$503$			458.172i			0.910879i	−0.890267	+	0.455439i	$0.849482\pi$
$504$	200.626	+	39.2954i	0.398068	+	0.0779670i
$505$	−72.7802			−0.144119
$506$		0			0
$507$	287.189	−	236.396i	0.566448	−	0.466265i
$508$	228.569			0.449940
$509$		−	274.849i		−	0.539978i	−0.962863	−	0.269989i	$-0.912980\pi$
$509$		−	274.849i		−	0.539978i	0.962863	−	0.269989i	$-0.0870201\pi$
$510$	−35.5807	−	43.2257i	−0.0697660	−	0.0847563i
$511$	−148.127			−0.289876
$512$			509.504i			0.995125i
$513$	−204.373	−	378.340i	−0.398388	−	0.737505i
$514$	663.606			1.29106
$515$			38.0031i			0.0737925i
$516$	65.6404	−	54.0310i	0.127210	−	0.104711i
$517$		0			0
$518$			274.856i			0.530610i
$519$	47.8609	+	58.1444i	0.0922174	+	0.112032i
$520$	−104.093			−0.200179
$521$		−	248.396i		−	0.476768i	−0.971171	−	0.238384i	$-0.923382\pi$
$521$		−	248.396i		−	0.476768i	0.971171	−	0.238384i	$-0.0766177\pi$
$522$	−15.3919	+	78.5848i	−0.0294864	+	0.150546i
$523$	−140.587			−0.268808			−0.134404	−	0.990927i	$-0.542912\pi$
$523$	−140.587			−0.268808			−0.134404	+	0.990927i	$0.542912\pi$
$524$		−	105.681i		−	0.201682i
$525$	−148.134	+	121.935i	−0.282161	+	0.232257i
$526$	628.794			1.19543
$527$			65.4587i			0.124210i
$528$		0			0
$529$	−5.97152			−0.0112883
$530$			49.6315i			0.0936444i
$531$	−253.820	−	49.7141i	−0.478004	−	0.0936235i
$532$	−51.9630			−0.0976749
$533$		−	1154.33i		−	2.16572i
$534$	146.680	−	120.737i	0.274681	−	0.226100i
$535$	−19.8422			−0.0370883
$536$			672.832i			1.25528i
$537$	117.836	+	143.155i	0.219434	+	0.266583i
$538$	51.7358			0.0961633
$539$		0			0
$540$	20.7501	−	11.2089i	0.0384262	−	0.0207572i
$541$	−600.914			−1.11075			−0.555373	−	0.831601i	$-0.687424\pi$
$541$	−600.914			−1.11075			−0.555373	+	0.831601i	$0.687424\pi$
$542$			859.103i			1.58506i
$543$	−343.740	+	282.945i	−0.633039	+	0.521078i
$544$	−309.060			−0.568124
$545$			28.8160i			0.0528735i
$546$	−141.189	−	171.525i	−0.258587	−	0.314149i
$547$	620.873			1.13505			0.567525	−	0.823356i	$-0.307901\pi$
$547$	620.873			1.13505			0.567525	+	0.823356i	$0.307901\pi$
$548$		−	255.569i		−	0.466367i
$549$	80.0967	−	408.941i	0.145896	−	0.744884i
$550$		0			0
$551$		−	85.4594i		−	0.155099i
$552$	−466.418	+	383.926i	−0.844961	+	0.695519i
$553$	−132.870			−0.240271
$554$			610.133i			1.10132i
$555$	84.6078	+	102.787i	0.152447	+	0.185202i
$556$	62.8272			0.112998
$557$			540.026i			0.969526i	0.874645	+	0.484763i	$0.161094\pi$
$557$			540.026i			0.969526i	−0.874645	+	0.484763i	$0.838906\pi$
$558$	59.4974	+	11.6534i	0.106626	+	0.0208842i
$559$	−387.908			−0.693931
$560$			17.1936i			0.0307028i
$561$		0			0
$562$	−531.261			−0.945305
$563$		−	278.666i		−	0.494967i	−0.968892	−	0.247483i	$-0.920396\pi$
$563$		−	278.666i		−	0.494967i	0.968892	−	0.247483i	$-0.0796036\pi$
$564$	176.003	+	213.820i	0.312062	+	0.379113i
$565$	101.407			0.179482
$566$		−	266.624i		−	0.471066i
$567$	195.722	+	79.7282i	0.345189	+	0.140614i
$568$	359.242			0.632468
$569$		−	1069.57i		−	1.87973i	−0.341546	−	0.939865i	$-0.610950\pi$
$569$		−	1069.57i		−	1.87973i	0.341546	−	0.939865i	$-0.389050\pi$
$570$	42.7262	−	35.1695i	0.0749582	−	0.0617009i
$571$	−470.660			−0.824274			−0.412137	−	0.911122i	$-0.635217\pi$
$571$	−470.660			−0.824274			−0.412137	+	0.911122i	$0.635217\pi$
$572$		0			0
$573$	−107.155	−	130.179i	−0.187007	−	0.227189i
$574$	−291.757			−0.508288
$575$		−	566.951i		−	0.986002i
$576$	−120.302	+	614.212i	−0.208857	+	1.06634i
$577$	229.146			0.397133			0.198567	−	0.980087i	$-0.436371\pi$
$577$	229.146			0.397133			0.198567	+	0.980087i	$0.436371\pi$
$578$		−	48.7263i		−	0.0843016i
$579$	−349.687	+	287.840i	−0.603950	+	0.497134i
$580$	4.68704			0.00808110
$581$		−	154.485i		−	0.265895i
$582$	−51.5071	−	62.5741i	−0.0885001	−	0.107516i
$583$		0			0
$584$		−	494.275i		−	0.846361i
$585$	−105.600	−	20.6831i	−0.180512	−	0.0353558i
$586$	482.428			0.823257
$587$		−	0.740839i		−	0.00126208i	−1.00000		0.000631038i	$-0.999799\pi$
$587$		−	0.740839i		−	0.00126208i	1.00000		0.000631038i	$-0.000200866\pi$
$588$	−122.209	+	100.595i	−0.207839	+	0.171080i
$589$	−64.7023			−0.109851
$590$		−	33.2853i		−	0.0564158i
$591$	42.5880	+	51.7386i	0.0720608	+	0.0875441i
$592$	−599.366			−1.01244
$593$		−	498.413i		−	0.840494i	−0.907410	−	0.420247i	$-0.861943\pi$
$593$		−	498.413i		−	0.840494i	0.907410	−	0.420247i	$-0.138057\pi$
$594$		0			0
$595$	−29.3647			−0.0493524
$596$			196.832i			0.330256i
$597$	−349.590	+	287.761i	−0.585578	+	0.482011i
$598$	656.474			1.09778
$599$			191.403i			0.319537i	0.987154	+	0.159769i	$0.0510748\pi$
$599$			191.403i			0.319537i	−0.987154	+	0.159769i	$0.948925\pi$
$600$	−406.877	−	494.300i	−0.678128	−	0.823834i
$601$	−831.418			−1.38339			−0.691696	−	0.722189i	$-0.743136\pi$
$601$	−831.418			−1.38339			−0.691696	+	0.722189i	$0.743136\pi$
$602$			98.0440i			0.162864i
$603$	−133.690	+	682.569i	−0.221709	+	1.13196i
$604$	214.314			0.354824
$605$		0			0
$606$	400.178	−	329.402i	0.660361	−	0.543567i
$607$	−789.695			−1.30098			−0.650490	−	0.759515i	$-0.725436\pi$
$607$	−789.695			−1.30098			−0.650490	+	0.759515i	$0.725436\pi$
$608$		−	305.488i		−	0.502447i
$609$	26.6926	+	32.4279i	0.0438303	+	0.0532478i
$610$	53.6275			0.0879140
$611$		−	1263.59i		−	2.06806i
$612$	−177.958	−	34.8555i	−0.290782	−	0.0569535i
$613$	277.196			0.452196			0.226098	−	0.974105i	$-0.427403\pi$
$613$	277.196			0.452196			0.226098	+	0.974105i	$0.427403\pi$
$614$		−	467.269i		−	0.761025i
$615$	−109.107	+	89.8104i	−0.177411	+	0.146033i
$616$		0			0
$617$		−	928.547i		−	1.50494i	−0.658628	−	0.752469i	$-0.728863\pi$
$617$		−	928.547i		−	1.50494i	0.658628	−	0.752469i	$-0.271137\pi$
$618$	−172.002	−	208.959i	−0.278320	−	0.338121i
$619$	955.674			1.54390			0.771950	−	0.635683i	$-0.219282\pi$
$619$	955.674			1.54390			0.771950	+	0.635683i	$0.219282\pi$
$620$		−	3.54861i		−	0.00572356i
$621$	−549.454	+	296.806i	−0.884790	+	0.477949i
$622$	785.557			1.26295
$623$		−	99.6443i		−	0.159943i
$624$	374.037	−	307.884i	0.599418	−	0.493403i
$625$	588.645			0.941832
$626$			49.7019i			0.0793961i
$627$		0			0
$628$	−81.7055			−0.130104
$629$		−	1023.65i		−	1.62742i
$630$	−5.22768	+	26.6904i	−0.00829790	+	0.0423657i
$631$	−5.25949			−0.00833517			−0.00416759	−	0.999991i	$-0.501327\pi$
$631$	−5.25949			−0.00833517			−0.00416759	+	0.999991i	$0.501327\pi$
$632$		−	443.365i		−	0.701527i
$633$	−420.577	+	346.193i	−0.664419	+	0.546908i
$634$	264.106			0.416571
$635$			127.673i			0.201061i
$636$	102.165	+	124.117i	0.160637	+	0.195153i
$637$	722.207			1.13376
$638$		0			0
$639$	364.441	+	71.3807i	0.570330	+	0.111707i
$640$	−26.9534			−0.0421147
$641$		−	486.004i		−	0.758196i	−0.925356	−	0.379098i	$-0.876234\pi$
$641$		−	486.004i		−	0.758196i	0.925356	−	0.379098i	$-0.123766\pi$
$642$	109.102	−	89.8056i	0.169940	−	0.139884i
$643$	−738.878			−1.14911			−0.574555	−	0.818466i	$-0.694825\pi$
$643$	−738.878			−1.14911			−0.574555	+	0.818466i	$0.694825\pi$
$644$			75.4647i			0.117181i
$645$	30.1805	+	36.6652i	0.0467914	+	0.0568452i
$646$	−425.507			−0.658680
$647$		−	1150.29i		−	1.77788i	−0.458027	−	0.888938i	$-0.651444\pi$
$647$		−	1150.29i		−	1.77788i	0.458027	−	0.888938i	$-0.348556\pi$
$648$	−266.040	+	653.093i	−0.410556	+	1.00786i
$649$		0			0
$650$			695.717i			1.07033i
$651$	24.5515	−	20.2093i	0.0377136	−	0.0310435i
$652$	−19.3059			−0.0296102
$653$			605.052i			0.926573i	0.886208	+	0.463287i	$0.153330\pi$
$653$			605.052i			0.926573i	−0.886208	+	0.463287i	$0.846670\pi$
$654$	−130.421	−	158.444i	−0.199420	−	0.242269i
$655$	59.0311			0.0901239
$656$		−	636.222i		−	0.969850i
$657$	98.2116	−	501.429i	0.149485	−	0.763209i
$658$	−319.373			−0.485369
$659$			956.314i			1.45116i	0.688138	+	0.725580i	$0.258428\pi$
$659$			956.314i			1.45116i	−0.688138	+	0.725580i	$0.741572\pi$
$660$		0			0
$661$	57.8747			0.0875563			0.0437781	−	0.999041i	$-0.486061\pi$
$661$	57.8747			0.0875563			0.0437781	+	0.999041i	$0.486061\pi$
$662$		−	551.685i		−	0.833361i
$663$	525.830	+	638.812i	0.793107	+	0.963518i
$664$	515.491			0.776342
$665$		−	29.0253i		−	0.0436471i
$666$	−930.425	−	182.236i	−1.39703	−	0.273628i
$667$	−124.111			−0.186073
$668$		−	192.708i		−	0.288484i
$669$	435.532	−	358.503i	0.651020	−	0.535879i
$670$	−89.5104			−0.133598
$671$		0			0
$672$	95.4169	+	115.919i	0.141989	+	0.172498i
$673$	−851.648			−1.26545			−0.632725	−	0.774377i	$-0.718064\pi$
$673$	−851.648			−1.26545			−0.632725	+	0.774377i	$0.718064\pi$
$674$			91.8709i			0.136307i
$675$	−314.549	−	582.300i	−0.465999	−	0.862667i
$676$	155.050			0.229364
$677$			269.729i			0.398418i	0.979957	+	0.199209i	$0.0638373\pi$
$677$			269.729i			0.398418i	−0.979957	+	0.199209i	$0.936163\pi$
$678$	−557.584	+	458.968i	−0.822395	+	0.676944i
$679$	−42.5087			−0.0626049
$680$		−	97.9852i		−	0.144096i
$681$	−818.355	−	994.191i	−1.20170	−	1.45990i
$682$		0			0
$683$			254.016i			0.371913i	0.982558	+	0.185956i	$0.0595383\pi$
$683$			254.016i			0.371913i	−0.982558	+	0.185956i	$0.940462\pi$
$684$	34.4527	−	175.902i	0.0503695	−	0.257166i
$685$	142.755			0.208401
$686$		−	394.528i		−	0.575114i
$687$	314.488	−	258.867i	0.457770	−	0.376808i
$688$	−213.800			−0.310756
$689$		−	733.481i		−	1.06456i
$690$	−51.0758	−	62.0502i	−0.0740229	−	0.0899278i
$691$	−378.595			−0.547894			−0.273947	−	0.961745i	$-0.588329\pi$
$691$	−378.595			−0.547894			−0.273947	+	0.961745i	$0.588329\pi$
$692$			31.3914i			0.0453634i
$693$		0			0
$694$	−229.724			−0.331014
$695$			35.0938i			0.0504946i
$696$	−108.207	+	89.0690i	−0.155469	+	0.127973i
$697$	1086.59			1.55896
$698$			375.600i			0.538109i
$699$	−623.241	−	757.153i	−0.891618	−	1.08319i
$700$	−79.9759			−0.114251
$701$		−	319.948i		−	0.456416i	−0.973612	−	0.228208i	$-0.926713\pi$
$701$		−	319.948i		−	0.456416i	0.973612	−	0.228208i	$-0.0732867\pi$
$702$	674.247	−	364.217i	0.960465	−	0.518828i
$703$	1011.82			1.43929
$704$		0			0
$705$	−119.435	+	98.3111i	−0.169411	+	0.139448i
$706$	−429.362			−0.608161
$707$		−	271.855i		−	0.384519i
$708$	−68.5171	−	83.2390i	−0.0967756	−	0.117569i
$709$	−228.519			−0.322311			−0.161156	−	0.986929i	$-0.551522\pi$
$709$	−228.519			−0.322311			−0.161156	+	0.986929i	$0.551522\pi$
$710$			47.7919i			0.0673125i
$711$	88.0958	−	449.782i	0.123904	−	0.632604i
$712$	332.497			0.466990
$713$			93.9656i			0.131789i
$714$	161.460	−	132.904i	0.226135	−	0.186140i
$715$		0			0
$716$			77.2875i			0.107943i
$717$	178.176	+	216.459i	0.248502	+	0.301896i
$718$	429.523			0.598222
$719$			805.149i			1.11982i	0.828554	+	0.559909i	$0.189164\pi$
$719$			805.149i			1.11982i	−0.828554	+	0.559909i	$0.810836\pi$
$720$	−58.2025	−	11.3998i	−0.0808369	−	0.0158330i
$721$	−141.953			−0.196883
$722$			178.006i			0.246546i
$723$	−478.920	+	394.217i	−0.662406	+	0.545251i
$724$	−185.581			−0.256327
$725$		−	131.530i		−	0.181420i
$726$		0			0
$727$	−1002.31			−1.37869			−0.689345	−	0.724434i	$-0.742101\pi$
$727$	−1002.31			−1.37869			−0.689345	+	0.724434i	$0.742101\pi$
$728$		−	388.818i		−	0.534090i
$729$	−399.659	+	609.683i	−0.548229	+	0.836328i
$730$	65.7561			0.0900768
$731$		−	365.146i		−	0.499516i
$732$	134.110	−	110.391i	0.183211	−	0.150808i
$733$	724.606			0.988548			0.494274	−	0.869306i	$-0.335434\pi$
$733$	724.606			0.988548			0.494274	+	0.869306i	$0.335434\pi$
$734$			329.604i			0.449052i
$735$	−56.1900	−	68.2633i	−0.0764490	−	0.0928752i
$736$	−443.653			−0.602789
$737$		0			0
$738$	193.442	−	987.637i	0.262117	−	1.33826i
$739$	860.336			1.16419			0.582095	−	0.813121i	$-0.302233\pi$
$739$	860.336			1.16419			0.582095	+	0.813121i	$0.302233\pi$
$740$			55.4934i			0.0749911i
$741$	−631.430	+	519.753i	−0.852132	+	0.701422i
$742$	−185.388			−0.249849
$743$			390.314i			0.525322i	0.964888	+	0.262661i	$0.0846000\pi$
$743$			390.314i			0.525322i	−0.964888	+	0.262661i	$0.915400\pi$
$744$	67.4351	+	81.9245i	0.0906386	+	0.110114i
$745$	−109.946			−0.147578
$746$			1111.74i			1.49027i
$747$	522.951	+	102.427i	0.700069	+	0.137118i
$748$		0			0
$749$		−	74.1164i		−	0.0989538i
$750$	132.828	−	109.336i	0.177104	−	0.145781i
$751$	−863.735			−1.15011			−0.575057	−	0.818113i	$-0.695020\pi$
$751$	−863.735			−1.15011			−0.575057	+	0.818113i	$0.695020\pi$
$752$		−	696.441i		−	0.926118i
$753$	5.31990	+	6.46296i	0.00706495	+	0.00858295i
$754$	152.299			0.201988
$755$			119.710i			0.158557i
$756$	41.8684	+	77.5077i	0.0553815	+	0.102523i
$757$	−845.429			−1.11681			−0.558407	−	0.829567i	$-0.688587\pi$
$757$	−845.429			−1.11681			−0.558407	+	0.829567i	$0.688587\pi$
$758$		−	650.647i		−	0.858373i
$759$		0			0
$760$	96.8528			0.127438
$761$			175.879i			0.231116i	0.993301	+	0.115558i	$0.0368656\pi$
$761$			175.879i			0.231116i	−0.993301	+	0.115558i	$0.963134\pi$
$762$	−577.848	−	702.007i	−0.758331	−	0.921269i
$763$	−107.636			−0.141070
$764$		−	70.2821i		−	0.0919922i
$765$	19.4695	−	99.4033i	0.0254503	−	0.129939i
$766$	−825.269			−1.07737
$767$			491.908i			0.641341i
$768$	−496.105	+	408.363i	−0.645970	+	0.531722i
$769$	−1341.04			−1.74388			−0.871941	−	0.489611i	$-0.837139\pi$
$769$	−1341.04			−1.74388			−0.871941	+	0.489611i	$0.837139\pi$
$770$		0			0
$771$	763.025	+	926.972i	0.989657	+	1.20230i
$772$	−188.792			−0.244549
$773$			784.632i			1.01505i	0.861637	+	0.507524i	$0.169439\pi$
$773$			784.632i			1.01505i	−0.861637	+	0.507524i	$0.830561\pi$
$774$	−331.892	−	65.0055i	−0.428801	−	0.0839864i
$775$	−99.5827			−0.128494
$776$		−	141.845i		−	0.182789i
$777$	−383.939	+	316.034i	−0.494130	+	0.406737i
$778$	−683.626			−0.878696
$779$			1074.04i			1.37874i
$780$	−28.5060	−	34.6309i	−0.0365461	−	0.0443986i
$781$		0			0
$782$			617.954i			0.790222i
$783$	−127.471	+	68.8576i	−0.162798	+	0.0879408i
$784$	398.053			0.507721
$785$		−	45.6388i		−	0.0581386i
$786$	−324.580	+	267.174i	−0.412952	+	0.339916i
$787$	1448.45			1.84047			0.920233	−	0.391372i	$-0.127999\pi$
$787$	1448.45			1.84047			0.920233	+	0.391372i	$0.127999\pi$
$788$			27.9330i			0.0354480i
$789$	722.998	+	878.344i	0.916347	+	1.11324i
$790$	58.9832			0.0746623
$791$			378.785i			0.478869i
$792$		0			0
$793$	−792.536			−0.999415
$794$		−	283.927i		−	0.357590i
$795$	−69.3289	+	57.0672i	−0.0872061	+	0.0717826i
$796$	−188.739			−0.237110
$797$			346.393i			0.434621i	0.976102	+	0.217311i	$0.0697285\pi$
$797$			346.393i			0.434621i	−0.976102	+	0.217311i	$0.930272\pi$
$798$	131.368	+	159.594i	0.164622	+	0.199993i
$799$	1189.44			1.48866
$800$		−	470.174i		−	0.587717i
$801$	337.309	+	66.0666i	0.421110	+	0.0824801i
$802$	1203.85			1.50107
$803$		0			0
$804$	−223.845	+	184.255i	−0.278414	+	0.229173i
$805$	−42.1528			−0.0523637
$806$		−	115.307i		−	0.143061i
$807$	59.4868	+	72.2683i	0.0737135	+	0.0895518i
$808$	907.135			1.12269
$809$			523.195i			0.646718i	0.946276	+	0.323359i	$0.104812\pi$
$809$			523.195i			0.646718i	−0.946276	+	0.323359i	$0.895188\pi$
$810$	−86.8845	−	35.3928i	−0.107265	−	0.0436948i
$811$	1033.47			1.27431			0.637156	−	0.770735i	$-0.280111\pi$
$811$	1033.47			1.27431			0.637156	+	0.770735i	$0.280111\pi$
$812$			17.5074i			0.0215609i
$813$	−1200.06	+	987.811i	−1.47608	+	1.21502i
$814$		0			0
$815$		−	10.7838i		−	0.0132317i
$816$	289.818	+	352.089i	0.355169	+	0.431482i
$817$	360.926			0.441770
$818$			499.753i			0.610946i
$819$	77.2574	−	394.445i	0.0943314	−	0.481618i
$820$	−58.9058			−0.0718363
$821$			97.7784i			0.119097i	0.998225	+	0.0595484i	$0.0189661\pi$
$821$			97.7784i			0.119097i	−0.998225	+	0.0595484i	$0.981034\pi$
$822$	−784.932	+	646.106i	−0.954905	+	0.786017i
$823$	721.665			0.876871			0.438436	−	0.898763i	$-0.355533\pi$
$823$	721.665			0.876871			0.438436	+	0.898763i	$0.355533\pi$
$824$		−	473.673i		−	0.574846i
$825$		0			0
$826$	124.330			0.150521
$827$			1229.27i			1.48642i	0.669059	+	0.743209i	$0.266697\pi$
$827$			1229.27i			1.48642i	−0.669059	+	0.743209i	$0.733303\pi$
$828$	−255.458	−	50.0349i	−0.308524	−	0.0604286i
$829$	−193.404			−0.233298			−0.116649	−	0.993173i	$-0.537215\pi$
$829$	−193.404			−0.233298			−0.116649	+	0.993173i	$0.537215\pi$
$830$			68.5785i			0.0826248i
$831$	−852.277	+	701.541i	−1.02560	+	0.844213i
$832$	1190.35			1.43071
$833$			679.829i			0.816122i
$834$	−158.834	−	192.961i	−0.190448	−	0.231369i
$835$	107.642			0.128912
$836$		0			0
$837$	52.1329	+	96.5094i	0.0622854	+	0.115304i
$838$	950.449			1.13419
$839$			583.289i			0.695220i	0.937639	+	0.347610i	$0.113007\pi$
$839$			583.289i			0.695220i	−0.937639	+	0.347610i	$0.886993\pi$
$840$	−36.7512	+	30.2513i	−0.0437514	+	0.0360134i
$841$	812.207			0.965763
$842$			927.377i			1.10140i
$843$	−610.853	−	742.104i	−0.724618	−	0.880313i
$844$	−227.064			−0.269034
$845$			86.6072i			0.102494i
$846$	211.752	−	1081.12i	0.250297	−	1.27792i
$847$		0			0
$848$		−	404.267i		−	0.476730i
$849$	372.439	−	306.568i	0.438679	−	0.361093i
$850$	−654.894			−0.770463
$851$		−	1469.44i		−	1.72672i
$852$	98.3786	+	119.517i	0.115468	+	0.140278i
$853$	431.225			0.505539			0.252770	−	0.967527i	$-0.418659\pi$
$853$	431.225			0.505539			0.252770	+	0.967527i	$0.418659\pi$
$854$			200.314i			0.234560i
$855$	98.2546	+	19.2445i	0.114918	+	0.0225082i
$856$	247.314			0.288919
$857$			580.461i			0.677317i	0.940909	+	0.338659i	$0.109973\pi$
$857$			580.461i			0.677317i	−0.940909	+	0.338659i	$0.890027\pi$
$858$		0			0
$859$	−812.241			−0.945566			−0.472783	−	0.881179i	$-0.656751\pi$
$859$	−812.241			−0.945566			−0.472783	+	0.881179i	$0.656751\pi$
$860$			19.7951i			0.0230175i
$861$	−335.468	−	407.548i	−0.389626	−	0.473342i
$862$	331.378			0.384430
$863$		−	628.218i		−	0.727947i	−0.931409	−	0.363973i	$-0.881420\pi$
$863$		−	628.218i		−	0.727947i	0.931409	−	0.363973i	$-0.118580\pi$
$864$	−455.663	+	246.142i	−0.527388	+	0.284887i
$865$	−17.5345			−0.0202711
$866$			171.597i			0.198149i
$867$	68.0644	−	56.0264i	0.0785057	−	0.0646209i
$868$	13.2551			0.0152708
$869$		0			0
$870$	−11.8493	−	14.3953i	−0.0136199	−	0.0165464i
$871$	1322.83			1.51875
$872$		−	359.164i		−	0.411886i
$873$	28.1843	−	143.898i	0.0322844	−	0.164831i
$874$	−610.812			−0.698870
$875$		−	90.2344i		−	0.103125i
$876$	164.441	−	135.357i	0.187718	−	0.154518i
$877$	−1200.80			−1.36922			−0.684608	−	0.728911i	$-0.740027\pi$
$877$	−1200.80			−1.36922			−0.684608	+	0.728911i	$0.740027\pi$
$878$		−	1098.61i		−	1.25127i
$879$	554.704	+	673.891i	0.631063	+	0.766656i
$880$		0			0
$881$			131.219i			0.148943i	0.997223	+	0.0744714i	$0.0237269\pi$
$881$			131.219i			0.148943i	−0.997223	+	0.0744714i	$0.976273\pi$
$882$	617.917	+	121.027i	0.700586	+	0.137219i
$883$	−127.000			−0.143828			−0.0719138	−	0.997411i	$-0.522911\pi$
$883$	−127.000			−0.143828			−0.0719138	+	0.997411i	$0.522911\pi$
$884$			344.887i			0.390143i
$885$	46.4953	−	38.2721i	0.0525371	−	0.0432453i
$886$	−349.589			−0.394570
$887$			1194.79i			1.34700i	0.739189	+	0.673499i	$0.235209\pi$
$887$			1194.79i			1.34700i	−0.739189	+	0.673499i	$0.764791\pi$
$888$	−1054.56	−	1281.14i	−1.18756	−	1.44273i
$889$	−476.897			−0.536442
$890$			44.2339i			0.0497010i
$891$		0			0
$892$	235.138			0.263608
$893$			1175.70i			1.31657i
$894$	604.533	−	497.614i	0.676211	−	0.556615i
$895$	−43.1710			−0.0482357
$896$		−	100.679i		−	0.112365i
$897$	754.826	+	917.011i	0.841500	+	1.02231i
$898$	396.749			0.441814
$899$			21.7995i			0.0242487i
$900$	53.0259	−	270.729i	0.0589176	−	0.300810i
$901$	690.442			0.766306
$902$		0			0
$903$	−136.955	+	112.733i	−0.151667	+	0.124842i
$904$	−1263.95			−1.39817
$905$		−	103.661i		−	0.114543i
$906$	−541.808	−	658.223i	−0.598022	−	0.726515i
$907$	524.583			0.578372			0.289186	−	0.957273i	$-0.406615\pi$
$907$	524.583			0.578372			0.289186	+	0.957273i	$0.406615\pi$
$908$		−	536.751i		−	0.591135i
$909$	920.264	+	180.246i	1.01239	+	0.198291i
$910$	51.7265			0.0568424
$911$			175.608i			0.192764i	0.995344	+	0.0963822i	$0.0307271\pi$
$911$			175.608i			0.192764i	−0.995344	+	0.0963822i	$0.969273\pi$
$912$	−348.020	+	286.468i	−0.381601	+	0.314110i
$913$		0			0
$914$			44.2524i			0.0484162i
$915$	61.6619	+	74.9108i	0.0673900	+	0.0818697i
$916$	169.788			0.185358
$917$			220.498i			0.240456i
$918$	342.846	+	634.683i	0.373470	+	0.691376i
$919$	1305.11			1.42014			0.710070	−	0.704131i	$-0.248663\pi$
$919$	1305.11			1.42014			0.710070	+	0.704131i	$0.248663\pi$
$920$		−	140.657i		−	0.152888i
$921$	652.715	−	537.274i	0.708702	−	0.583359i
$922$	−651.864			−0.707011
$923$		−	706.294i		−	0.765216i
$924$		0			0
$925$	1557.28			1.68355
$926$		−	177.347i		−	0.191519i
$927$	94.1179	−	480.528i	0.101530	−	0.518369i
$928$	−102.925			−0.110911
$929$			1559.50i			1.67869i	0.543600	+	0.839344i	$0.317061\pi$
$929$			1559.50i			1.67869i	−0.543600	+	0.839344i	$0.682939\pi$
$930$	−10.8989	+	8.97126i	−0.0117192	+	0.00964652i
$931$	−671.973			−0.721776
$932$		−	408.777i		−	0.438602i
$933$	903.247	+	1097.32i	0.968111	+	1.17612i
$934$	701.251			0.750804
$935$		0			0
$936$	1316.20	+	257.795i	1.40620	+	0.275422i
$937$	719.352			0.767718			0.383859	−	0.923392i	$-0.374595\pi$
$937$	719.352			0.767718			0.383859	+	0.923392i	$0.374595\pi$
$938$		−	334.347i		−	0.356447i
$939$	−69.4272	+	57.1481i	−0.0739374	+	0.0608606i
$940$	−64.4813			−0.0685971
$941$		−	1173.29i		−	1.24685i	−0.781882	−	0.623426i	$-0.785740\pi$
$941$		−	1173.29i		−	1.24685i	0.781882	−	0.623426i	$-0.214260\pi$
$942$	206.560	+	250.943i	0.219278	+	0.266394i
$943$	1559.80			1.65408
$944$			271.121i			0.287205i
$945$	−43.2940	+	23.3867i	−0.0458137	+	0.0247478i
$946$		0			0
$947$		−	266.119i		−	0.281013i	−0.990080	−	0.140506i	$-0.955127\pi$
$947$		−	266.119i		−	0.281013i	0.990080	−	0.140506i	$-0.0448730\pi$
$948$	147.504	−	121.416i	0.155595	−	0.128076i
$949$	−971.778			−1.02400
$950$		−	647.326i		−	0.681395i
$951$	303.674	+	368.922i	0.319320	+	0.387931i
$952$	366.003			0.384457
$953$			128.153i			0.134474i	0.997737	+	0.0672369i	$0.0214183\pi$
$953$			128.153i			0.134474i	−0.997737	+	0.0672369i	$0.978582\pi$
$954$	122.917	−	627.563i	0.128843	−	0.657822i
$955$	39.2579			0.0411077
$956$			116.864i			0.122242i
$957$		0			0
$958$	894.933			0.934168
$959$			533.231i			0.556028i
$960$	−92.6134	−	112.513i	−0.0964723	−	0.117201i
$961$	−944.495			−0.982826
$962$			1803.18i			1.87441i
$963$	250.894	+	49.1409i	0.260534	+	0.0510290i
$964$	−258.563			−0.268219
$965$		−	105.455i		−	0.109279i
$966$	231.775	−	190.783i	0.239933	−	0.197498i
$967$	−1324.17			−1.36936			−0.684682	−	0.728842i	$-0.740059\pi$
$967$	−1324.17			−1.36936			−0.684682	+	0.728842i	$0.740059\pi$
$968$		0			0
$969$	−489.255	−	594.379i	−0.504907	−	0.613394i
$970$	18.8704			0.0194540
$971$			584.878i			0.602346i	0.953570	+	0.301173i	$0.0973781\pi$
$971$			584.878i			0.602346i	−0.953570	+	0.301173i	$0.902622\pi$
$972$	−290.134	+	90.3407i	−0.298491	+	0.0929431i
$973$	−131.085			−0.134723
$974$		−	1012.55i		−	1.03958i
$975$	−971.828	+	799.948i	−0.996747	+	0.820459i
$976$	−436.816			−0.447557
$977$		−	691.347i		−	0.707622i	−0.935317	−	0.353811i	$-0.884886\pi$
$977$		−	691.347i		−	0.707622i	0.935317	−	0.353811i	$-0.115114\pi$
$978$	48.8073	+	59.2943i	0.0499052	+	0.0606281i
$979$		0			0
$980$		−	36.8545i		−	0.0376066i
$981$	71.3653	−	364.363i	0.0727475	−	0.371420i
$982$	94.3064			0.0960350
$983$			655.489i			0.666825i	0.942781	+	0.333413i	$0.108200\pi$
$983$			655.489i			0.666825i	−0.942781	+	0.333413i	$0.891800\pi$
$984$	1359.92	−	1119.40i	1.38203	−	1.13760i
$985$	−15.6027			−0.0158403
$986$			143.362i			0.145398i
$987$	−367.220	−	446.123i	−0.372057	−	0.451999i
$988$	−340.901			−0.345042
$989$		−	524.164i		−	0.529994i
$990$		0			0
$991$	95.0559			0.0959192			0.0479596	−	0.998849i	$-0.484728\pi$
$991$	95.0559			0.0959192			0.0479596	+	0.998849i	$0.484728\pi$
$992$			77.9258i			0.0785542i
$993$	770.633	−	634.337i	0.776066	−	0.638809i
$994$	−178.516			−0.179594
$995$		−	105.425i		−	0.105955i
$996$	141.167	+	171.499i	0.141734	+	0.172188i
$997$	781.403			0.783754			0.391877	−	0.920018i	$-0.371826\pi$
$997$	781.403			0.783754			0.391877	+	0.920018i	$0.371826\pi$
$998$		−	777.475i		−	0.779033i
$999$	−815.258	−	1509.22i	−0.816074	−	1.51073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.l.122.4		8
3.2	odd	2	inner	363.3.b.l.122.5		8
11.2	odd	10		33.3.h.b.26.3	yes	16
11.3	even	5		363.3.h.n.251.2		16
11.4	even	5		363.3.h.n.269.3		16
11.5	even	5		363.3.h.j.245.3		16
11.6	odd	10		33.3.h.b.14.2	✓	16
11.7	odd	10		363.3.h.o.269.2		16
11.8	odd	10		363.3.h.o.251.3		16
11.9	even	5		363.3.h.j.323.2		16
11.10	odd	2		363.3.b.m.122.5		8
33.2	even	10		33.3.h.b.26.2	yes	16
33.5	odd	10		363.3.h.j.245.2		16
33.8	even	10		363.3.h.o.251.2		16
33.14	odd	10		363.3.h.n.251.3		16
33.17	even	10		33.3.h.b.14.3	yes	16
33.20	odd	10		363.3.h.j.323.3		16
33.26	odd	10		363.3.h.n.269.2		16
33.29	even	10		363.3.h.o.269.3		16
33.32	even	2		363.3.b.m.122.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.2	✓	16	11.6	odd	10
33.3.h.b.14.3	yes	16	33.17	even	10
33.3.h.b.26.2	yes	16	33.2	even	10
33.3.h.b.26.3	yes	16	11.2	odd	10
363.3.b.l.122.4		8	1.1	even	1	trivial
363.3.b.l.122.5		8	3.2	odd	2	inner
363.3.b.m.122.4		8	33.32	even	2
363.3.b.m.122.5		8	11.10	odd	2
363.3.h.j.245.2		16	33.5	odd	10
363.3.h.j.245.3		16	11.5	even	5
363.3.h.j.323.2		16	11.9	even	5
363.3.h.j.323.3		16	33.20	odd	10
363.3.h.n.251.2		16	11.3	even	5
363.3.h.n.251.3		16	33.14	odd	10
363.3.h.n.269.2		16	33.26	odd	10
363.3.h.n.269.3		16	11.4	even	5
363.3.h.o.251.2		16	33.8	even	10
363.3.h.o.251.3		16	11.8	odd	10
363.3.h.o.269.2		16	11.7	odd	10
363.3.h.o.269.3		16	33.29	even	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.65816i q^{2} +(2.31624 - 1.90658i) q^{3} +1.25051 q^{4} +0.698503i q^{5} +(-3.16141 - 3.84069i) q^{6} -2.60911 q^{7} -8.70618i q^{8} +(1.72990 - 8.83218i) q^{9} +O(q^{10})\)	\(q-1.65816i q^{2} +(2.31624 - 1.90658i) q^{3} +1.25051 q^{4} +0.698503i q^{5} +(-3.16141 - 3.84069i) q^{6} -2.60911 q^{7} -8.70618i q^{8} +(1.72990 - 8.83218i) q^{9} +1.15823 q^{10} +(2.89647 - 2.38419i) q^{12} -17.1169 q^{13} +4.32632i q^{14} +(1.33175 + 1.61790i) q^{15} -9.43421 q^{16} -16.1125i q^{17} +(-14.6452 - 2.86845i) q^{18} +15.9263 q^{19} +0.873483i q^{20} +(-6.04332 + 4.97448i) q^{21} -23.1295i q^{23} +(-16.5990 - 20.1656i) q^{24} +24.5121 q^{25} +28.3826i q^{26} +(-12.8324 - 23.7556i) q^{27} -3.26271 q^{28} -5.36592i q^{29} +(2.68273 - 2.20826i) q^{30} -4.06259 q^{31} -19.1813i q^{32} -26.7172 q^{34} -1.82247i q^{35} +(2.16325 - 11.0447i) q^{36} +63.5312 q^{37} -26.4084i q^{38} +(-39.6469 + 32.6348i) q^{39} +6.08130 q^{40} +67.4378i q^{41} +(8.24848 + 10.0208i) q^{42} +22.6622 q^{43} +(6.16931 + 1.20834i) q^{45} -38.3523 q^{46} +73.8208i q^{47} +(-21.8519 + 17.9871i) q^{48} -42.1925 q^{49} -40.6450i q^{50} +(-30.7199 - 37.3205i) q^{51} -21.4048 q^{52} +42.8512i q^{53} +(-39.3906 + 21.2782i) q^{54} +22.7154i q^{56} +(36.8892 - 30.3649i) q^{57} -8.89755 q^{58} -28.7381i q^{59} +(1.66537 + 2.02319i) q^{60} +46.3013 q^{61} +6.73643i q^{62} +(-4.51350 + 23.0441i) q^{63} -69.5425 q^{64} -11.9562i q^{65} -77.2821 q^{67} -20.1489i q^{68} +(-44.0982 - 53.5733i) q^{69} -3.02195 q^{70} +41.2629i q^{71} +(-76.8946 - 15.0608i) q^{72} +56.7729 q^{73} -105.345i q^{74} +(56.7758 - 46.7343i) q^{75} +19.9160 q^{76} +(54.1137 + 65.7409i) q^{78} +50.9253 q^{79} -6.58983i q^{80} +(-75.0149 - 30.5576i) q^{81} +111.823 q^{82} +59.2098i q^{83} +(-7.55721 + 6.22062i) q^{84} +11.2547 q^{85} -37.5776i q^{86} +(-10.2306 - 12.4287i) q^{87} +38.1909i q^{89} +(2.00362 - 10.2297i) q^{90} +44.6600 q^{91} -28.9235i q^{92} +(-9.40993 + 7.74566i) q^{93} +122.407 q^{94} +11.1246i q^{95} +(-36.5707 - 44.4284i) q^{96} +16.2924 q^{97} +69.9620i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9	\( 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9} + 6 q^{10} + 53 q^{12} - 44 q^{13} - 54 q^{15} - 14 q^{16} - q^{18} - 68 q^{19} + 6 q^{21} - 33 q^{24} + 42 q^{25} - 25 q^{27} + 118 q^{28} - 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} - 38 q^{39} - 58 q^{40} + 174 q^{42} + 78 q^{43} - 36 q^{45} + 286 q^{46} - 285 q^{48} - 140 q^{49} - 58 q^{51} + 102 q^{52} - 523 q^{54} + 22 q^{57} - 68 q^{58} + 262 q^{60} - 22 q^{61} - 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} - 489 q^{72} + 378 q^{73} - 33 q^{75} + 450 q^{76} - 246 q^{78} + 252 q^{79} + 11 q^{81} - 200 q^{82} - 450 q^{84} + 156 q^{85} - 66 q^{87} - 598 q^{90} - 148 q^{91} + 380 q^{93} + 460 q^{94} - 399 q^{96} - 324 q^{97}+O(q^{100}) \) 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9 + 6 * q^10 + 53 * q^12 - 44 * q^13 - 54 * q^15 - 14 * q^16 - q^18 - 68 * q^19 + 6 * q^21 - 33 * q^24 + 42 * q^25 - 25 * q^27 + 118 * q^28 - 10 * q^30 + 2 * q^31 - 66 * q^34 - 7 * q^36 + 140 * q^37 - 38 * q^39 - 58 * q^40 + 174 * q^42 + 78 * q^43 - 36 * q^45 + 286 * q^46 - 285 * q^48 - 140 * q^49 - 58 * q^51 + 102 * q^52 - 523 * q^54 + 22 * q^57 - 68 * q^58 + 262 * q^60 - 22 * q^61 - 246 * q^63 - 52 * q^64 + 184 * q^67 - 176 * q^69 + 374 * q^70 - 489 * q^72 + 378 * q^73 - 33 * q^75 + 450 * q^76 - 246 * q^78 + 252 * q^79 + 11 * q^81 - 200 * q^82 - 450 * q^84 + 156 * q^85 - 66 * q^87 - 598 * q^90 - 148 * q^91 + 380 * q^93 + 460 * q^94 - 399 * q^96 - 324 * q^97

Introduction

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