LMFDB - Embedded newform 363.3.b.m.122.5

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			122.5
Root			$1.65816i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.m.122.4

$q$-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	$0.136057\pi$
$2$			1.65816i			0.829080i	−0.910031	+	0.414540i	$0.863943\pi$
$3$	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	$-0.440329\pi$
$7$	2.60911			0.372730			0.186365	+	0.982481i	$0.440329\pi$
$8$			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	$-0.271257\pi$
$13$	17.1169			1.31669			0.658344	+	0.752717i	$0.271257\pi$
$14$			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	$0.157154\pi$
$17$			16.1125i			0.947797i	−0.880579	+	0.473898i	$0.842846\pi$
$18$	14.6452	+	2.86845i	0.813620	+	0.159359i
$19$	−15.9263			−0.838229			−0.419114	−	0.907933i	$-0.637659\pi$
$19$	−15.9263			−0.838229			−0.419114	+	0.907933i	$0.637659\pi$
$20$			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	$0.0294909\pi$
$29$			5.36592i			0.185032i	−0.995711	+	0.0925158i	$0.970509\pi$
$30$	−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	$-0.692628\pi$
$41$		−	67.4378i		−	1.64482i	0.568893	−	0.822412i	$-0.307372\pi$
$42$	8.24848	+	10.0208i	0.196392	+	0.238590i
$43$	−22.6622			−0.527028			−0.263514	−	0.964656i	$-0.584882\pi$
$43$	−22.6622			−0.527028			−0.263514	+	0.964656i	$0.584882\pi$
$44$		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	$-0.623910\pi$
$61$	−46.3013			−0.759037			−0.379519	+	0.925184i	$0.623910\pi$
$62$		−	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	$-0.627129\pi$
$73$	−56.7729			−0.777711			−0.388856	+	0.921299i	$0.627129\pi$
$74$			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	$-0.604460\pi$
$79$	−50.9253			−0.644624			−0.322312	+	0.946633i	$0.604460\pi$
$80$		−	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	$-0.883907\pi$
$83$		−	59.2098i		−	0.713371i	0.934225	−	0.356685i	$-0.116093\pi$
$84$	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	$-0.827490\pi$
$101$		−	104.194i		−	1.03163i	0.856701	−	0.515814i	$-0.172510\pi$
$102$	−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	$-0.957622\pi$
$107$		−	28.4068i		−	0.265484i	0.991151	−	0.132742i	$-0.0423782\pi$
$108$	−16.0470	−	29.7066i	−0.148583	−	0.275061i
$109$	−41.2540			−0.378477			−0.189238	−	0.981931i	$-0.560602\pi$
$109$	−41.2540			−0.378477			−0.189238	+	0.981931i	$0.560602\pi$
$110$		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	$-0.755680\pi$
$127$	−182.781			−1.43922			−0.719612	+	0.694376i	$0.755680\pi$
$128$		−	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	$0.104544\pi$
$131$			84.5109i			0.645121i	−0.946549	+	0.322561i	$0.895456\pi$
$132$		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	$-0.557844\pi$
$139$	−50.2414			−0.361449			−0.180724	+	0.983534i	$0.557844\pi$
$140$			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	$-0.822869\pi$
$149$		−	157.402i		−	1.05639i	0.849123	−	0.528195i	$-0.177131\pi$
$150$	77.4929	+	94.1433i	0.516619	+	0.627622i
$151$	−171.381			−1.13498			−0.567488	−	0.823382i	$-0.692085\pi$
$151$	−171.381			−1.13498			−0.567488	+	0.823382i	$0.692085\pi$
$152$		−	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	$0.152648\pi$
$167$			154.104i			0.922776i	−0.887198	+	0.461388i	$0.847352\pi$
$168$	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	$-0.976886\pi$
$173$		−	25.1030i		−	0.145104i	0.997365	−	0.0725520i	$-0.0231143\pi$
$174$	−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	$-0.372088\pi$
$193$	150.972			0.782239			0.391119	+	0.920340i	$0.372088\pi$
$194$			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	$-0.981944\pi$
$197$		−	22.3374i		−	0.113388i	0.998392	−	0.0566938i	$-0.0180559\pi$
$198$		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	$-0.358415\pi$
$211$	181.578			0.860559			0.430279	+	0.902696i	$0.358415\pi$
$212$			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	$0.394361\pi$
$227$			429.227i			1.89087i	−0.325815	+	0.945434i	$0.605639\pi$
$228$	−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	$0.247477\pi$
$233$			326.889i			1.40296i	−0.712690	+	0.701479i	$0.752523\pi$
$234$	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	$-0.937364\pi$
$239$		−	93.4530i		−	0.391017i	0.980702	−	0.195508i	$-0.0626357\pi$
$240$	−12.5640	−	15.2636i	−0.0523501	−	0.0635983i
$241$	206.766			0.857952			0.428976	−	0.903316i	$-0.358875\pi$
$241$	206.766			0.857952			0.428976	+	0.903316i	$0.358875\pi$
$242$		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	$-0.743713\pi$
$263$		−	379.212i		−	1.44187i	0.693003	−	0.720935i	$-0.256287\pi$
$264$		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	$-0.0948672\pi$
$271$	518.106			1.91183			0.955916	+	0.293641i	$0.0948672\pi$
$272$		−	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	$-0.268779\pi$
$277$	367.958			1.32837			0.664184	+	0.747570i	$0.268779\pi$
$278$		−	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	$0.193093\pi$
$281$			320.392i			1.14019i	−0.821580	+	0.570093i	$0.806907\pi$
$282$	−283.523	+	233.378i	−1.00540	+	0.827583i
$283$	−160.795			−0.568180			−0.284090	−	0.958798i	$-0.591691\pi$
$283$	−160.795			−0.568180			−0.284090	+	0.958798i	$0.591691\pi$
$284$			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	$-0.834623\pi$
$293$		−	290.942i		−	0.992976i	0.868043	−	0.496488i	$-0.165377\pi$
$294$	−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	$-0.651777\pi$
$307$	−281.800			−0.917915			−0.458957	+	0.888458i	$0.651777\pi$
$308$		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	$-0.473804\pi$
$337$	55.4053			0.164408			0.0822038	+	0.996616i	$0.473804\pi$
$338$			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	$0.0639732\pi$
$347$			138.541i			0.399255i	−0.979872	+	0.199627i	$0.936027\pi$
$348$	12.7934	+	15.5422i	0.0367626	+	0.0446615i
$349$	226.516			0.649044			0.324522	−	0.945878i	$-0.394797\pi$
$349$	226.516			0.649044			0.324522	+	0.945878i	$0.394797\pi$
$350$			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	$-0.882512\pi$
$359$		−	259.036i		−	0.721549i	0.932653	−	0.360774i	$-0.117488\pi$
$360$	−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	$-0.144477\pi$
$373$	670.467			1.79750			0.898750	+	0.438462i	$0.144477\pi$
$374$		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	$-0.379889\pi$
$409$	301.390			0.736896			0.368448	+	0.929648i	$0.379889\pi$
$410$			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	$-0.925525\pi$
$431$		−	199.847i		−	0.463682i	0.972754	−	0.231841i	$-0.0744750\pi$
$432$	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	$-0.772175\pi$
$439$	−662.550			−1.50923			−0.754613	+	0.656171i	$0.772175\pi$
$440$		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	$-0.490704\pi$
$457$	26.6877			0.0583975			0.0291988	+	0.999574i	$0.490704\pi$
$458$			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	$0.140212\pi$
$461$			393.125i			0.852766i	−0.904543	+	0.426383i	$0.859788\pi$
$462$		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	$-0.809502\pi$
$479$		−	539.714i		−	1.12675i	0.826200	−	0.563376i	$-0.190498\pi$
$480$	−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	$-0.981554\pi$
$491$		−	56.8741i		−	0.115833i	0.998321	−	0.0579166i	$-0.0184458\pi$
$492$	−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	$-0.849482\pi$
$503$		−	458.172i		−	0.910879i	0.890267	−	0.455439i	$-0.150518\pi$
$504$	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	$-0.457088\pi$
$523$	140.587			0.268808			0.134404	+	0.990927i	$0.457088\pi$
$524$			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	$-0.312576\pi$
$541$	600.914			1.11075			0.555373	+	0.831601i	$0.312576\pi$
$542$			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	$-0.692099\pi$
$547$	−620.873			−1.13505			−0.567525	+	0.823356i	$0.692099\pi$
$548$		−	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	$-0.838906\pi$
$557$		−	540.026i		−	0.969526i	0.874645	−	0.484763i	$-0.161094\pi$
$558$	−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	$0.0796036\pi$
$563$			278.666i			0.494967i	−0.968892	+	0.247483i	$0.920396\pi$
$564$	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	$0.389050\pi$
$569$			1069.57i			1.87973i	−0.341546	+	0.939865i	$0.610950\pi$
$570$	42.7262	−	35.1695i	0.0749582	−	0.0617009i
$571$	470.660			0.824274			0.412137	−	0.911122i	$-0.364783\pi$
$571$	470.660			0.824274			0.412137	+	0.911122i	$0.364783\pi$
$572$		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	$0.138057\pi$
$593$			498.413i			0.840494i	−0.907410	+	0.420247i	$0.861943\pi$
$594$		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	$-0.256864\pi$
$601$	831.418			1.38339			0.691696	+	0.722189i	$0.256864\pi$
$602$		−	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	$-0.274564\pi$
$607$	789.695			1.30098			0.650490	+	0.759515i	$0.274564\pi$
$608$		−	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	$-0.572597\pi$
$613$	−277.196			−0.452196			−0.226098	+	0.974105i	$0.572597\pi$
$614$		−	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	$-0.741572\pi$
$659$		−	956.314i		−	1.45116i	0.688138	−	0.725580i	$-0.258428\pi$
$660$		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	$-0.281936\pi$
$673$	851.648			1.26545			0.632725	+	0.774377i	$0.281936\pi$
$674$			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	$-0.936163\pi$
$677$		−	269.729i		−	0.398418i	0.979957	−	0.199209i	$-0.0638373\pi$
$678$	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	$0.0732867\pi$
$701$			319.948i			0.456416i	−0.973612	+	0.228208i	$0.926713\pi$
$702$	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	$-0.664566\pi$
$733$	−724.606			−0.988548			−0.494274	+	0.869306i	$0.664566\pi$
$734$		−	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	$-0.697767\pi$
$739$	−860.336			−1.16419			−0.582095	+	0.813121i	$0.697767\pi$
$740$			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	$-0.915400\pi$
$743$		−	390.314i		−	0.525322i	0.964888	−	0.262661i	$-0.0846000\pi$
$744$	−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	$-0.963134\pi$
$761$		−	175.879i		−	0.231116i	0.993301	−	0.115558i	$-0.0368656\pi$
$762$	−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	$-0.162861\pi$
$769$	1341.04			1.74388			0.871941	+	0.489611i	$0.162861\pi$
$770$		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	$-0.872001\pi$
$787$	−1448.45			−1.84047			−0.920233	+	0.391372i	$0.872001\pi$
$788$		−	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	$-0.895188\pi$
$809$		−	523.195i		−	0.646718i	0.946276	−	0.323359i	$-0.104812\pi$
$810$	86.8845	+	35.3928i	0.107265	+	0.0436948i
$811$	−1033.47			−1.27431			−0.637156	−	0.770735i	$-0.719889\pi$
$811$	−1033.47			−1.27431			−0.637156	+	0.770735i	$0.719889\pi$
$812$			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	$-0.981034\pi$
$821$		−	97.7784i		−	0.119097i	0.998225	−	0.0595484i	$-0.0189661\pi$
$822$	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	$-0.733303\pi$
$827$		−	1229.27i		−	1.48642i	0.669059	−	0.743209i	$-0.266697\pi$
$828$	−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	$-0.581341\pi$
$853$	−431.225			−0.505539			−0.252770	+	0.967527i	$0.581341\pi$
$854$		−	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	$-0.890027\pi$
$857$		−	580.461i		−	0.677317i	0.940909	−	0.338659i	$-0.109973\pi$
$858$		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	$-0.259973\pi$
$877$	1200.80			1.36922			0.684608	+	0.728911i	$0.259973\pi$
$878$		−	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	$-0.764791\pi$
$887$		−	1194.79i		−	1.34700i	0.739189	−	0.673499i	$-0.235209\pi$
$888$	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	$-0.751337\pi$
$919$	−1305.11			−1.42014			−0.710070	+	0.704131i	$0.751337\pi$
$920$			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	$-0.625405\pi$
$937$	−719.352			−0.767718			−0.383859	+	0.923392i	$0.625405\pi$
$938$		−	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	$0.214260\pi$
$941$			1173.29i			1.24685i	−0.781882	+	0.623426i	$0.785740\pi$
$942$	−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	$-0.978582\pi$
$953$		−	128.153i		−	0.134474i	0.997737	−	0.0672369i	$-0.0214183\pi$
$954$	−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	$-0.259941\pi$
$967$	1324.17			1.36936			0.684682	+	0.728842i	$0.259941\pi$
$968$		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	$-0.628174\pi$
$997$	−781.403			−0.783754			−0.391877	+	0.920018i	$0.628174\pi$
$998$			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.m.122.5		8
3.2	odd	2	inner	363.3.b.m.122.4		8
11.2	odd	10		363.3.h.j.323.2		16
11.3	even	5		363.3.h.o.251.3		16
11.4	even	5		363.3.h.o.269.2		16
11.5	even	5		33.3.h.b.14.2	✓	16
11.6	odd	10		363.3.h.j.245.3		16
11.7	odd	10		363.3.h.n.269.3		16
11.8	odd	10		363.3.h.n.251.2		16
11.9	even	5		33.3.h.b.26.3	yes	16
11.10	odd	2		363.3.b.l.122.4		8
33.2	even	10		363.3.h.j.323.3		16
33.5	odd	10		33.3.h.b.14.3	yes	16
33.8	even	10		363.3.h.n.251.3		16
33.14	odd	10		363.3.h.o.251.2		16
33.17	even	10		363.3.h.j.245.2		16
33.20	odd	10		33.3.h.b.26.2	yes	16
33.26	odd	10		363.3.h.o.269.3		16
33.29	even	10		363.3.h.n.269.2		16
33.32	even	2		363.3.b.l.122.5		8

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