LMFDB - Embedded newform 354.3.d.a.235.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.d (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:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 $ x^20 - 300x^18 - 88x^17 + 37952x^16 + 27000x^15 - 2574056x^14 - 3295208x^13 + 98138134x^12 + 195465720x^11 - 1935828112x^10 - 5590976152x^9 + 12661641204x^8 + 55962519336x^7 + 75365256136x^6 + 219349710792x^5 + 570681930321x^4 + 614778274152x^3 + 1559028888924x^2 + 534075251472x + 2455573689828
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.19
Root			$0.969662 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +0.969662 q^{5} +2.44949i q^{6} +3.05407 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +0.969662 q^{5} +2.44949i q^{6} +3.05407 q^{7} -2.82843i q^{8} +3.00000 q^{9} +1.37131i q^{10} +3.80377i q^{11} -3.46410 q^{12} +11.7231i q^{13} +4.31911i q^{14} +1.67950 q^{15} +4.00000 q^{16} +18.5750 q^{17} +4.24264i q^{18} +19.0796 q^{19} -1.93932 q^{20} +5.28981 q^{21} -5.37934 q^{22} +12.7703i q^{23} -4.89898i q^{24} -24.0598 q^{25} -16.5790 q^{26} +5.19615 q^{27} -6.10814 q^{28} +33.5722 q^{29} +2.37518i q^{30} +34.8029i q^{31} +5.65685i q^{32} +6.58832i q^{33} +26.2690i q^{34} +2.96142 q^{35} -6.00000 q^{36} +5.62133i q^{37} +26.9826i q^{38} +20.3050i q^{39} -2.74262i q^{40} +2.32258 q^{41} +7.48091i q^{42} -3.84313i q^{43} -7.60754i q^{44} +2.90899 q^{45} -18.0599 q^{46} -53.4193i q^{47} +6.92820 q^{48} -39.6727 q^{49} -34.0256i q^{50} +32.1728 q^{51} -23.4462i q^{52} +9.70038 q^{53} +7.34847i q^{54} +3.68837i q^{55} -8.63822i q^{56} +33.0468 q^{57} +47.4783i q^{58} +(-57.6355 - 12.6155i) q^{59} -3.35901 q^{60} +6.26746i q^{61} -49.2188 q^{62} +9.16221 q^{63} -8.00000 q^{64} +11.3674i q^{65} -9.31729 q^{66} +46.7320i q^{67} -37.1500 q^{68} +22.1188i q^{69} +4.18807i q^{70} +58.6411 q^{71} -8.48528i q^{72} +3.41033i q^{73} -7.94975 q^{74} -41.6727 q^{75} -38.1592 q^{76} +11.6170i q^{77} -28.7156 q^{78} -44.9144 q^{79} +3.87865 q^{80} +9.00000 q^{81} +3.28463i q^{82} -147.198i q^{83} -10.5796 q^{84} +18.0115 q^{85} +5.43500 q^{86} +58.1488 q^{87} +10.7587 q^{88} -92.3380i q^{89} +4.11393i q^{90} +35.8032i q^{91} -25.5406i q^{92} +60.2804i q^{93} +75.5463 q^{94} +18.5008 q^{95} +9.79796i q^{96} +123.134i q^{97} -56.1056i q^{98} +11.4113i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) $ 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9	$ 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9} - 24 q^{15} + 80 q^{16} + 72 q^{19} + 16 q^{22} + 140 q^{25} + 64 q^{26} - 16 q^{28} + 56 q^{29} - 80 q^{35} - 120 q^{36} - 8 q^{41} + 16 q^{46} + 52 q^{49} + 32 q^{53} - 48 q^{57} + 192 q^{59} + 48 q^{60} - 16 q^{62} + 24 q^{63} - 160 q^{64} + 96 q^{66} - 568 q^{71} - 288 q^{74} - 96 q^{75} - 144 q^{76} + 192 q^{78} + 528 q^{79} + 180 q^{81} + 568 q^{85} - 416 q^{86} - 216 q^{87} - 32 q^{88} - 480 q^{94} - 456 q^{95}+O(q^{100}) $ 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9 - 24 * q^15 + 80 * q^16 + 72 * q^19 + 16 * q^22 + 140 * q^25 + 64 * q^26 - 16 * q^28 + 56 * q^29 - 80 * q^35 - 120 * q^36 - 8 * q^41 + 16 * q^46 + 52 * q^49 + 32 * q^53 - 48 * q^57 + 192 * q^59 + 48 * q^60 - 16 * q^62 + 24 * q^63 - 160 * q^64 + 96 * q^66 - 568 * q^71 - 288 * q^74 - 96 * q^75 - 144 * q^76 + 192 * q^78 + 528 * q^79 + 180 * q^81 + 568 * q^85 - 416 * q^86 - 216 * q^87 - 32 * q^88 - 480 * q^94 - 456 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−2.00000			−0.500000
$5$	0.969662			0.193932			0.0969662	−	0.995288i	$-0.469086\pi$
$5$	0.969662			0.193932			0.0969662	+	0.995288i	$0.469086\pi$
$6$			2.44949i			0.408248i
$7$	3.05407			0.436296			0.218148	−	0.975916i	$-0.429998\pi$
$7$	3.05407			0.436296			0.218148	+	0.975916i	$0.429998\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$			1.37131i			0.137131i
$11$			3.80377i			0.345797i	0.984940	+	0.172899i	$0.0553133\pi$
$11$			3.80377i			0.345797i	−0.984940	+	0.172899i	$0.944687\pi$
$12$	−3.46410			−0.288675
$13$			11.7231i			0.901777i	0.892580	+	0.450889i	$0.148893\pi$
$13$			11.7231i			0.901777i	−0.892580	+	0.450889i	$0.851107\pi$
$14$			4.31911i			0.308508i
$15$	1.67950			0.111967
$16$	4.00000			0.250000
$17$	18.5750			1.09265			0.546323	−	0.837574i	$-0.316027\pi$
$17$	18.5750			1.09265			0.546323	+	0.837574i	$0.316027\pi$
$18$			4.24264i			0.235702i
$19$	19.0796			1.00419			0.502095	−	0.864813i	$-0.332563\pi$
$19$	19.0796			1.00419			0.502095	+	0.864813i	$0.332563\pi$
$20$	−1.93932			−0.0969662
$21$	5.28981			0.251895
$22$	−5.37934			−0.244516
$23$			12.7703i			0.555230i	0.960692	+	0.277615i	$0.0895439\pi$
$23$			12.7703i			0.555230i	−0.960692	+	0.277615i	$0.910456\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−24.0598			−0.962390
$26$	−16.5790			−0.637653
$27$	5.19615			0.192450
$28$	−6.10814			−0.218148
$29$	33.5722			1.15766			0.578832	−	0.815447i	$-0.303509\pi$
$29$	33.5722			1.15766			0.578832	+	0.815447i	$0.303509\pi$
$30$			2.37518i			0.0791726i
$31$			34.8029i			1.12267i	0.827587	+	0.561337i	$0.189713\pi$
$31$			34.8029i			1.12267i	−0.827587	+	0.561337i	$0.810287\pi$
$32$			5.65685i			0.176777i
$33$			6.58832i			0.199646i
$34$			26.2690i			0.772618i
$35$	2.96142			0.0846119
$36$	−6.00000			−0.166667
$37$			5.62133i			0.151928i	0.997111	+	0.0759639i	$0.0242034\pi$
$37$			5.62133i			0.151928i	−0.997111	+	0.0759639i	$0.975797\pi$
$38$			26.9826i			0.710069i
$39$			20.3050i			0.520641i
$40$		−	2.74262i		−	0.0685655i
$41$	2.32258			0.0566483			0.0283242	−	0.999599i	$-0.490983\pi$
$41$	2.32258			0.0566483			0.0283242	+	0.999599i	$0.490983\pi$
$42$			7.48091i			0.178117i
$43$		−	3.84313i		−	0.0893750i	−0.999001	−	0.0446875i	$-0.985771\pi$
$43$		−	3.84313i		−	0.0893750i	0.999001	−	0.0446875i	$-0.0142292\pi$
$44$		−	7.60754i		−	0.172899i
$45$	2.90899			0.0646441
$46$	−18.0599			−0.392607
$47$		−	53.4193i		−	1.13658i	−0.822828	−	0.568291i	$-0.807605\pi$
$47$		−	53.4193i		−	1.13658i	0.822828	−	0.568291i	$-0.192395\pi$
$48$	6.92820			0.144338
$49$	−39.6727			−0.809646
$50$		−	34.0256i		−	0.680513i
$51$	32.1728			0.630840
$52$		−	23.4462i		−	0.450889i
$53$	9.70038			0.183026			0.0915130	−	0.995804i	$-0.470830\pi$
$53$	9.70038			0.183026			0.0915130	+	0.995804i	$0.470830\pi$
$54$			7.34847i			0.136083i
$55$			3.68837i			0.0670613i
$56$		−	8.63822i		−	0.154254i
$57$	33.0468			0.579769
$58$			47.4783i			0.818592i
$59$	−57.6355	−	12.6155i	−0.976873	−	0.213822i
$59$	−57.6355	−	12.6155i	−0.976873	−	0.213822i
$60$	−3.35901			−0.0559835
$61$			6.26746i			0.102745i	0.998680	+	0.0513727i	$0.0163596\pi$
$61$			6.26746i			0.102745i	−0.998680	+	0.0513727i	$0.983640\pi$
$62$	−49.2188			−0.793851
$63$	9.16221			0.145432
$64$	−8.00000			−0.125000
$65$			11.3674i			0.174884i
$66$	−9.31729			−0.141171
$67$			46.7320i			0.697493i	0.937217	+	0.348747i	$0.113393\pi$
$67$			46.7320i			0.697493i	−0.937217	+	0.348747i	$0.886607\pi$
$68$	−37.1500			−0.546323
$69$			22.1188i			0.320562i
$70$			4.18807i			0.0598296i
$71$	58.6411			0.825931			0.412966	−	0.910747i	$-0.364493\pi$
$71$	58.6411			0.825931			0.412966	+	0.910747i	$0.364493\pi$
$72$		−	8.48528i		−	0.117851i
$73$			3.41033i			0.0467168i	0.999727	+	0.0233584i	$0.00743589\pi$
$73$			3.41033i			0.0467168i	−0.999727	+	0.0233584i	$0.992564\pi$
$74$	−7.94975			−0.107429
$75$	−41.6727			−0.555636
$76$	−38.1592			−0.502095
$77$			11.6170i			0.150870i
$78$	−28.7156			−0.368149
$79$	−44.9144			−0.568537			−0.284269	−	0.958745i	$-0.591751\pi$
$79$	−44.9144			−0.568537			−0.284269	+	0.958745i	$0.591751\pi$
$80$	3.87865			0.0484831
$81$	9.00000			0.111111
$82$			3.28463i			0.0400564i
$83$		−	147.198i		−	1.77346i	−0.462283	−	0.886732i	$-0.652970\pi$
$83$		−	147.198i		−	1.77346i	0.462283	−	0.886732i	$-0.347030\pi$
$84$	−10.5796			−0.125948
$85$	18.0115			0.211900
$86$	5.43500			0.0631977
$87$	58.1488			0.668377
$88$	10.7587			0.122258
$89$		−	92.3380i		−	1.03751i	−0.854924	−	0.518753i	$-0.826397\pi$
$89$		−	92.3380i		−	1.03751i	0.854924	−	0.518753i	$-0.173603\pi$
$90$			4.11393i			0.0457103i
$91$			35.8032i			0.393442i
$92$		−	25.5406i		−	0.277615i
$93$			60.2804i			0.648177i
$94$	75.5463			0.803684
$95$	18.5008			0.194745
$96$			9.79796i			0.102062i
$97$			123.134i			1.26942i	0.772749	+	0.634712i	$0.218881\pi$
$97$			123.134i			1.26942i	−0.772749	+	0.634712i	$0.781119\pi$
$98$		−	56.1056i		−	0.572506i
$99$			11.4113i			0.115266i
$100$	48.1195			0.481195
$101$		−	126.506i		−	1.25254i	−0.779607	−	0.626269i	$-0.784581\pi$
$101$		−	126.506i		−	1.25254i	0.779607	−	0.626269i	$-0.215419\pi$
$102$			45.4993i			0.446071i
$103$		−	11.2967i		−	0.109677i	−0.998495	−	0.0548386i	$-0.982536\pi$
$103$		−	11.2967i		−	0.109677i	0.998495	−	0.0548386i	$-0.0174644\pi$
$104$	33.1579			0.318826
$105$	5.12932			0.0488507
$106$			13.7184i			0.129419i
$107$	−40.1705			−0.375425			−0.187713	−	0.982224i	$-0.560107\pi$
$107$	−40.1705			−0.375425			−0.187713	+	0.982224i	$0.560107\pi$
$108$	−10.3923			−0.0962250
$109$		−	199.994i		−	1.83481i	−0.397958	−	0.917404i	$-0.630281\pi$
$109$		−	199.994i		−	1.83481i	0.397958	−	0.917404i	$-0.369719\pi$
$110$	−5.21614			−0.0474195
$111$			9.73642i			0.0877155i
$112$	12.2163			0.109074
$113$		−	100.676i		−	0.890935i	−0.895298	−	0.445467i	$-0.853038\pi$
$113$		−	100.676i		−	0.890935i	0.895298	−	0.445467i	$-0.146962\pi$
$114$			46.7353i			0.409959i
$115$			12.3829i			0.107677i
$116$	−67.1445			−0.578832
$117$			35.1693i			0.300592i
$118$	17.8410	−	81.5089i	0.151195	−	0.690753i
$119$	56.7293			0.476717
$120$		−	4.75035i		−	0.0395863i
$121$	106.531			0.880424
$122$	−8.86353			−0.0726519
$123$	4.02283			0.0327059
$124$		−	69.6058i		−	0.561337i
$125$	−47.5714			−0.380571
$126$			12.9573i			0.102836i
$127$	50.1279			0.394708			0.197354	−	0.980332i	$-0.436765\pi$
$127$	50.1279			0.394708			0.197354	+	0.980332i	$0.436765\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	6.65649i		−	0.0516007i
$130$	−16.0760			−0.123662
$131$		−	121.775i		−	0.929582i	−0.885421	−	0.464791i	$-0.846130\pi$
$131$		−	121.775i		−	0.929582i	0.885421	−	0.464791i	$-0.153870\pi$
$132$		−	13.1766i		−	0.0998230i
$133$	58.2704			0.438124
$134$	−66.0891			−0.493202
$135$	5.03851			0.0373223
$136$		−	52.5380i		−	0.386309i
$137$	105.904			0.773023			0.386511	−	0.922285i	$-0.373680\pi$
$137$	105.904			0.773023			0.386511	+	0.922285i	$0.373680\pi$
$138$	−31.2807			−0.226672
$139$	−156.327			−1.12466			−0.562328	−	0.826914i	$-0.690094\pi$
$139$	−156.327			−1.12466			−0.562328	+	0.826914i	$0.690094\pi$
$140$	−5.92283			−0.0423059
$141$		−	92.5250i		−	0.656206i
$142$			82.9311i			0.584022i
$143$	−44.5920			−0.311832
$144$	12.0000			0.0833333
$145$	32.5537			0.224508
$146$	−4.82293			−0.0330338
$147$	−68.7151			−0.467449
$148$		−	11.2427i		−	0.0759639i
$149$		−	34.6796i		−	0.232749i	−0.993205	−	0.116374i	$-0.962873\pi$
$149$		−	34.6796i		−	0.232749i	0.993205	−	0.116374i	$-0.0371273\pi$
$150$		−	58.9341i		−	0.392894i
$151$		−	86.9280i		−	0.575682i	−0.957678	−	0.287841i	$-0.907062\pi$
$151$		−	86.9280i		−	0.575682i	0.957678	−	0.287841i	$-0.0929375\pi$
$152$		−	53.9653i		−	0.355035i
$153$	55.7250			0.364216
$154$	−16.4289			−0.106681
$155$			33.7471i			0.217723i
$156$		−	40.6100i		−	0.260321i
$157$		−	17.2533i		−	0.109894i	−0.998489	−	0.0549468i	$-0.982501\pi$
$157$		−	17.2533i		−	0.109894i	0.998489	−	0.0549468i	$-0.0174989\pi$
$158$		−	63.5186i		−	0.402017i
$159$	16.8015			0.105670
$160$			5.48524i			0.0342827i
$161$			39.0013i			0.242244i
$162$			12.7279i			0.0785674i
$163$	−226.562			−1.38995			−0.694977	−	0.719032i	$-0.744585\pi$
$163$	−226.562			−1.38995			−0.694977	+	0.719032i	$0.744585\pi$
$164$	−4.64516			−0.0283242
$165$			6.38844i			0.0387178i
$166$	208.169			1.25403
$167$	−101.977			−0.610642			−0.305321	−	0.952249i	$-0.598764\pi$
$167$	−101.977			−0.610642			−0.305321	+	0.952249i	$0.598764\pi$
$168$		−	14.9618i		−	0.0890585i
$169$	31.5688			0.186798
$170$			25.4721i			0.149836i
$171$	57.2388			0.334730
$172$			7.68625i			0.0446875i
$173$		−	11.9091i		−	0.0688388i	−0.999407	−	0.0344194i	$-0.989042\pi$
$173$		−	11.9091i		−	0.0688388i	0.999407	−	0.0344194i	$-0.0109582\pi$
$174$			82.2349i			0.472614i
$175$	−73.4802			−0.419887
$176$			15.2151i			0.0864493i
$177$	−99.8276	−	21.8507i	−0.563998	−	0.123450i
$178$	130.586			0.733627
$179$			139.070i			0.776929i	0.921464	+	0.388465i	$0.126994\pi$
$179$			139.070i			0.776929i	−0.921464	+	0.388465i	$0.873006\pi$
$180$	−5.81797			−0.0323221
$181$	64.1460			0.354398			0.177199	−	0.984175i	$-0.443296\pi$
$181$	64.1460			0.354398			0.177199	+	0.984175i	$0.443296\pi$
$182$	−50.6334			−0.278205
$183$			10.8556i			0.0593200i
$184$	36.1198			0.196303
$185$			5.45079i			0.0294637i
$186$	−85.2494			−0.458330
$187$			70.6550i			0.377834i
$188$			106.839i			0.568291i
$189$	15.8694			0.0839652
$190$			26.1640i			0.137705i
$191$			54.5048i			0.285365i	0.989768	+	0.142683i	$0.0455728\pi$
$191$			54.5048i			0.285365i	−0.989768	+	0.142683i	$0.954427\pi$
$192$	−13.8564			−0.0721688
$193$	−60.7454			−0.314743			−0.157371	−	0.987539i	$-0.550302\pi$
$193$	−60.7454			−0.314743			−0.157371	+	0.987539i	$0.550302\pi$
$194$	−174.138			−0.897618
$195$			19.6890i			0.100969i
$196$	79.3453			0.404823
$197$	28.7769			0.146076			0.0730378	−	0.997329i	$-0.476731\pi$
$197$	28.7769			0.146076			0.0730378	+	0.997329i	$0.476731\pi$
$198$	−16.1380			−0.0815052
$199$	−135.026			−0.678521			−0.339260	−	0.940692i	$-0.610177\pi$
$199$	−135.026			−0.678521			−0.339260	+	0.940692i	$0.610177\pi$
$200$			68.0513i			0.340256i
$201$			80.9423i			0.402698i
$202$	178.907			0.885679
$203$	102.532			0.505084
$204$	−64.3457			−0.315420
$205$	2.25212			0.0109859
$206$	15.9760			0.0775534
$207$			38.3108i			0.185077i
$208$			46.8924i			0.225444i
$209$			72.5744i			0.347246i
$210$			7.25396i			0.0345427i
$211$		−	35.8765i		−	0.170031i	−0.996380	−	0.0850153i	$-0.972906\pi$
$211$		−	35.8765i		−	0.170031i	0.996380	−	0.0850153i	$-0.0270939\pi$
$212$	−19.4008			−0.0915130
$213$	101.569			0.476852
$214$		−	56.8097i		−	0.265466i
$215$		−	3.72653i		−	0.0173327i
$216$		−	14.6969i		−	0.0680414i
$217$			106.291i			0.489818i
$218$	282.834			1.29740
$219$			5.90686i			0.0269720i
$220$		−	7.37674i		−	0.0335306i
$221$			217.757i			0.985324i
$222$	−13.7694			−0.0620242
$223$	−237.561			−1.06530			−0.532648	−	0.846337i	$-0.678803\pi$
$223$	−237.561			−1.06530			−0.532648	+	0.846337i	$0.678803\pi$
$224$			17.2764i			0.0771269i
$225$	−72.1793			−0.320797
$226$	142.377			0.629986
$227$			413.471i			1.82146i	0.413007	+	0.910728i	$0.364479\pi$
$227$			413.471i			1.82146i	−0.413007	+	0.910728i	$0.635521\pi$
$228$	−66.0937			−0.289885
$229$			390.250i			1.70415i	0.523422	+	0.852074i	$0.324655\pi$
$229$			390.250i			1.70415i	−0.523422	+	0.852074i	$0.675345\pi$
$230$	−17.5120			−0.0761392
$231$			20.1212i			0.0871047i
$232$		−	94.9566i		−	0.409296i
$233$			16.5386i			0.0709810i	0.999370	+	0.0354905i	$0.0112993\pi$
$233$			16.5386i			0.0709810i	−0.999370	+	0.0354905i	$0.988701\pi$
$234$	−49.7369			−0.212551
$235$		−	51.7987i		−	0.220420i
$236$	115.271	+	25.2311i	0.488436	+	0.106911i
$237$	−77.7941			−0.328245
$238$			80.2274i			0.337090i
$239$	−133.927			−0.560366			−0.280183	−	0.959947i	$-0.590395\pi$
$239$	−133.927			−0.560366			−0.280183	+	0.959947i	$0.590395\pi$
$240$	6.71802			0.0279917
$241$	21.5710			0.0895064			0.0447532	−	0.998998i	$-0.485750\pi$
$241$	21.5710			0.0895064			0.0447532	+	0.998998i	$0.485750\pi$
$242$			150.658i			0.622554i
$243$	15.5885			0.0641500
$244$		−	12.5349i		−	0.0513727i
$245$	−38.4691			−0.157017
$246$			5.68914i			0.0231266i
$247$			223.672i			0.905555i
$248$	98.4375			0.396925
$249$		−	254.954i		−	1.02391i
$250$		−	67.2761i		−	0.269104i
$251$	−372.149			−1.48266			−0.741332	−	0.671138i	$-0.765806\pi$
$251$	−372.149			−1.48266			−0.741332	+	0.671138i	$0.765806\pi$
$252$	−18.3244			−0.0727160
$253$	−48.5752			−0.191997
$254$			70.8915i			0.279100i
$255$	31.1968			0.122340
$256$	16.0000			0.0625000
$257$	16.5399			0.0643577			0.0321789	−	0.999482i	$-0.489755\pi$
$257$	16.5399			0.0643577			0.0321789	+	0.999482i	$0.489755\pi$
$258$	9.41370			0.0364872
$259$			17.1679i			0.0662854i
$260$		−	22.7349i		−	0.0874419i
$261$	100.717			0.385888
$262$	172.216			0.657314
$263$	−115.110			−0.437679			−0.218839	−	0.975761i	$-0.570227\pi$
$263$	−115.110			−0.437679			−0.218839	+	0.975761i	$0.570227\pi$
$264$	18.6346			0.0705856
$265$	9.40609			0.0354947
$266$			82.4068i			0.309800i
$267$		−	159.934i		−	0.599004i
$268$		−	93.4641i		−	0.348747i
$269$			144.984i			0.538975i	0.963004	+	0.269488i	$0.0868543\pi$
$269$			144.984i			0.538975i	−0.963004	+	0.269488i	$0.913146\pi$
$270$			7.12553i			0.0263909i
$271$	−189.948			−0.700914			−0.350457	−	0.936579i	$-0.613974\pi$
$271$	−189.948			−0.700914			−0.350457	+	0.936579i	$0.613974\pi$
$272$	74.3000			0.273162
$273$			62.0129i			0.227154i
$274$			149.771i			0.546610i
$275$		−	91.5177i		−	0.332792i
$276$		−	44.2376i		−	0.160281i
$277$	136.541			0.492928			0.246464	−	0.969152i	$-0.420731\pi$
$277$	136.541			0.492928			0.246464	+	0.969152i	$0.420731\pi$
$278$		−	221.080i		−	0.795252i
$279$			104.409i			0.374225i
$280$		−	8.37615i		−	0.0299148i
$281$	200.718			0.714300			0.357150	−	0.934047i	$-0.383748\pi$
$281$	200.718			0.714300			0.357150	+	0.934047i	$0.383748\pi$
$282$	130.850			0.464007
$283$			13.9031i			0.0491276i	0.999698	+	0.0245638i	$0.00781969\pi$
$283$			13.9031i			0.0491276i	−0.999698	+	0.0245638i	$0.992180\pi$
$284$	−117.282			−0.412966
$285$	32.0443			0.112436
$286$		−	63.0626i		−	0.220499i
$287$	7.09333			0.0247154
$288$			16.9706i			0.0589256i
$289$	56.0303			0.193877
$290$			46.0379i			0.158751i
$291$			213.274i			0.732902i
$292$		−	6.82065i		−	0.0233584i
$293$	403.295			1.37644			0.688218	−	0.725504i	$-0.258393\pi$
$293$	403.295			1.37644			0.688218	+	0.725504i	$0.258393\pi$
$294$		−	97.1778i		−	0.330537i
$295$	−55.8869	−	12.2328i	−0.189447	−	0.0414671i
$296$	15.8995			0.0537146
$297$			19.7650i			0.0665487i
$298$	49.0444			0.164578
$299$	−149.707			−0.500693
$300$	83.3454			0.277818
$301$		−	11.7372i		−	0.0389939i
$302$	122.935			0.407069
$303$		−	219.116i		−	0.723153i
$304$	76.3184			0.251047
$305$			6.07732i			0.0199256i
$306$			78.8070i			0.257539i
$307$	−111.858			−0.364359			−0.182180	−	0.983265i	$-0.558315\pi$
$307$	−111.858			−0.364359			−0.182180	+	0.983265i	$0.558315\pi$
$308$		−	23.2340i		−	0.0754349i
$309$		−	19.5665i		−	0.0633221i
$310$	−47.7256			−0.153953
$311$	−5.80597			−0.0186687			−0.00933435	−	0.999956i	$-0.502971\pi$
$311$	−5.80597			−0.0186687			−0.00933435	+	0.999956i	$0.502971\pi$
$312$	57.4312			0.184075
$313$		−	500.889i		−	1.60029i	−0.599810	−	0.800143i	$-0.704757\pi$
$313$		−	500.889i		−	1.60029i	0.599810	−	0.800143i	$-0.295243\pi$
$314$	24.3998			0.0777065
$315$	8.88425			0.0282040
$316$	89.8289			0.284269
$317$	184.778			0.582895			0.291448	−	0.956587i	$-0.405863\pi$
$317$	184.778			0.582895			0.291448	+	0.956587i	$0.405863\pi$
$318$			23.7610i			0.0747200i
$319$			127.701i			0.400317i
$320$	−7.75730			−0.0242416
$321$	−69.5774			−0.216752
$322$	−55.1562			−0.171293
$323$	354.403			1.09722
$324$	−18.0000			−0.0555556
$325$		−	282.055i		−	0.867862i
$326$		−	320.408i		−	0.982846i
$327$		−	346.400i		−	1.05933i
$328$		−	6.56925i		−	0.0200282i
$329$		−	163.146i		−	0.495886i
$330$	−9.03462			−0.0273777
$331$	−249.926			−0.755063			−0.377531	−	0.925997i	$-0.623227\pi$
$331$	−249.926			−0.755063			−0.377531	+	0.925997i	$0.623227\pi$
$332$			294.395i			0.886732i
$333$			16.8640i			0.0506426i
$334$		−	144.218i		−	0.431789i
$335$			45.3143i			0.135267i
$336$	21.1592			0.0629739
$337$			296.758i			0.880588i	0.897854	+	0.440294i	$0.145126\pi$
$337$			296.758i			0.880588i	−0.897854	+	0.440294i	$0.854874\pi$
$338$			44.6451i			0.132086i
$339$		−	174.375i		−	0.514381i
$340$	−36.0229			−0.105950
$341$	−132.382			−0.388218
$342$			80.9479i			0.236690i
$343$	−270.813			−0.789541
$344$	−10.8700			−0.0315988
$345$			21.4477i			0.0621674i
$346$	16.8420			0.0486764
$347$			441.458i			1.27221i	0.771601	+	0.636106i	$0.219456\pi$
$347$			441.458i			1.27221i	−0.771601	+	0.636106i	$0.780544\pi$
$348$	−116.298			−0.334189
$349$		−	325.743i		−	0.933362i	−0.884426	−	0.466681i	$-0.845450\pi$
$349$		−	325.743i		−	0.933362i	0.884426	−	0.466681i	$-0.154550\pi$
$350$		−	103.917i		−	0.296905i
$351$			60.9150i			0.173547i
$352$	−21.5174			−0.0611289
$353$		−	183.504i		−	0.519843i	−0.965630	−	0.259921i	$-0.916303\pi$
$353$		−	183.504i		−	0.519843i	0.965630	−	0.259921i	$-0.0836967\pi$
$354$	30.9016	−	141.178i	0.0872927	−	0.398807i
$355$	56.8621			0.160175
$356$			184.676i			0.518753i
$357$	98.2581			0.275233
$358$	−196.675			−0.549372
$359$	223.722			0.623181			0.311591	−	0.950216i	$-0.399138\pi$
$359$	223.722			0.623181			0.311591	+	0.950216i	$0.399138\pi$
$360$		−	8.22786i		−	0.0228552i
$361$	3.03112			0.00839645
$362$			90.7162i			0.250597i
$363$	184.518			0.508313
$364$		−	71.6064i		−	0.196721i
$365$			3.30686i			0.00905990i
$366$	−15.3521			−0.0419456
$367$		−	300.765i		−	0.819524i	−0.912192	−	0.409762i	$-0.865612\pi$
$367$		−	300.765i		−	0.819524i	0.912192	−	0.409762i	$-0.134388\pi$
$368$			51.0811i			0.138807i
$369$	6.96775			0.0188828
$370$	−7.70858			−0.0208340
$371$	29.6256			0.0798535
$372$		−	120.561i		−	0.324088i
$373$	521.430			1.39793			0.698967	−	0.715153i	$-0.253643\pi$
$373$	521.430			1.39793			0.698967	+	0.715153i	$0.253643\pi$
$374$	−99.9212			−0.267169
$375$	−82.3961			−0.219723
$376$	−151.093			−0.401842
$377$			393.571i			1.04395i
$378$			22.4427i			0.0593723i
$379$	−671.504			−1.77178			−0.885889	−	0.463897i	$-0.846451\pi$
$379$	−671.504			−1.77178			−0.885889	+	0.463897i	$0.846451\pi$
$380$	−37.0015			−0.0973724
$381$	86.8240			0.227885
$382$	−77.0814			−0.201784
$383$	216.586			0.565498			0.282749	−	0.959194i	$-0.408754\pi$
$383$	216.586			0.565498			0.282749	+	0.959194i	$0.408754\pi$
$384$		−	19.5959i		−	0.0510310i
$385$			11.2645i			0.0292586i
$386$		−	85.9070i		−	0.222557i
$387$		−	11.5294i		−	0.0297917i
$388$		−	246.268i		−	0.634712i
$389$	376.763			0.968542			0.484271	−	0.874918i	$-0.339085\pi$
$389$	376.763			0.968542			0.484271	+	0.874918i	$0.339085\pi$
$390$	−27.8445			−0.0713960
$391$			237.208i			0.606670i
$392$			112.211i			0.286253i
$393$		−	210.921i		−	0.536694i
$394$			40.6967i			0.103291i
$395$	−43.5518			−0.110258
$396$		−	22.8226i		−	0.0576329i
$397$		−	353.417i		−	0.890219i	−0.895476	−	0.445109i	$-0.853165\pi$
$397$		−	353.417i		−	0.890219i	0.895476	−	0.445109i	$-0.146835\pi$
$398$		−	190.955i		−	0.479787i
$399$	100.927			0.252951
$400$	−96.2390			−0.240598
$401$			89.4353i			0.223031i	0.993763	+	0.111515i	$0.0355704\pi$
$401$			89.4353i			0.223031i	−0.993763	+	0.111515i	$0.964430\pi$
$402$	−114.470			−0.284750
$403$	−407.998			−1.01240
$404$			253.013i			0.626269i
$405$	8.72696			0.0215480
$406$			145.002i			0.357148i
$407$	−21.3822			−0.0525362
$408$		−	90.9985i		−	0.223036i
$409$			178.484i			0.436392i	0.975905	+	0.218196i	$0.0700173\pi$
$409$			178.484i			0.436392i	−0.975905	+	0.218196i	$0.929983\pi$
$410$			3.18498i			0.00776824i
$411$	183.431			0.446305
$412$			22.5935i			0.0548386i
$413$	−176.023	−	38.5287i	−0.426205	−	0.0932899i
$414$	−54.1797			−0.130869
$415$		−	142.732i		−	0.343932i
$416$	−66.3159			−0.159413
$417$	−270.767			−0.649321
$418$	−102.636			−0.245540
$419$			380.870i			0.908997i	0.890748	+	0.454498i	$0.150181\pi$
$419$			380.870i			0.908997i	−0.890748	+	0.454498i	$0.849819\pi$
$420$	−10.2586			−0.0244253
$421$		−	327.539i		−	0.778002i	−0.921237	−	0.389001i	$-0.872820\pi$
$421$		−	327.539i		−	0.778002i	0.921237	−	0.389001i	$-0.127180\pi$
$422$	50.7370			0.120230
$423$		−	160.258i		−	0.378860i
$424$		−	27.4368i		−	0.0647094i
$425$	−446.910			−1.05155
$426$			143.641i			0.337185i
$427$			19.1413i			0.0448274i
$428$	80.3410			0.187713
$429$	−77.2356			−0.180036
$430$	5.27011			0.0122561
$431$			108.076i			0.250757i	0.992109	+	0.125378i	$0.0400145\pi$
$431$			108.076i			0.250757i	−0.992109	+	0.125378i	$0.959985\pi$
$432$	20.7846			0.0481125
$433$	684.264			1.58029			0.790143	−	0.612923i	$-0.210006\pi$
$433$	684.264			1.58029			0.790143	+	0.612923i	$0.210006\pi$
$434$	−150.318			−0.346354
$435$	56.3847			0.129620
$436$			399.988i			0.917404i
$437$			243.652i			0.557556i
$438$	−8.35356			−0.0190721
$439$	473.516			1.07862			0.539312	−	0.842106i	$-0.318684\pi$
$439$	473.516			1.07862			0.539312	+	0.842106i	$0.318684\pi$
$440$	10.4323			0.0237097
$441$	−119.018			−0.269882
$442$	−307.954			−0.696729
$443$		−	741.937i		−	1.67480i	−0.546590	−	0.837400i	$-0.684074\pi$
$443$		−	741.937i		−	1.67480i	0.546590	−	0.837400i	$-0.315926\pi$
$444$		−	19.4728i		−	0.0438578i
$445$		−	89.5366i		−	0.201206i
$446$		−	335.962i		−	0.753278i
$447$		−	60.0668i		−	0.134378i
$448$	−24.4326			−0.0545370
$449$	−504.574			−1.12377			−0.561887	−	0.827214i	$-0.689924\pi$
$449$	−504.574			−1.12377			−0.561887	+	0.827214i	$0.689924\pi$
$450$		−	102.077i		−	0.226838i
$451$			8.83457i			0.0195888i
$452$			201.351i			0.445467i
$453$		−	150.564i		−	0.332370i
$454$	−584.736			−1.28796
$455$			34.7170i			0.0763011i
$456$		−	93.4706i		−	0.204979i
$457$		−	578.102i		−	1.26499i	−0.774563	−	0.632497i	$-0.782030\pi$
$457$		−	578.102i		−	1.26499i	0.774563	−	0.632497i	$-0.217970\pi$
$458$	−551.897			−1.20501
$459$	96.5185			0.210280
$460$		−	24.7657i		−	0.0538385i
$461$	375.853			0.815299			0.407649	−	0.913139i	$-0.366349\pi$
$461$	375.853			0.815299			0.407649	+	0.913139i	$0.366349\pi$
$462$	−28.4557			−0.0615924
$463$		−	415.083i		−	0.896507i	−0.893906	−	0.448254i	$-0.852046\pi$
$463$		−	415.083i		−	0.896507i	0.893906	−	0.448254i	$-0.147954\pi$
$464$	134.289			0.289416
$465$			58.4516i			0.125702i
$466$	−23.3891			−0.0501911
$467$		−	522.188i		−	1.11818i	−0.829108	−	0.559088i	$-0.811151\pi$
$467$		−	522.188i		−	1.11818i	0.829108	−	0.559088i	$-0.188849\pi$
$468$		−	70.3386i		−	0.150296i
$469$			142.723i			0.304313i
$470$	73.2544			0.155860
$471$		−	29.8836i		−	0.0634471i
$472$	−35.6821	+	163.018i	−0.0755977	+	0.345377i
$473$	14.6184			0.0309056
$474$		−	110.017i		−	0.232104i
$475$	−459.051			−0.966422
$476$	−113.459			−0.238359
$477$	29.1011			0.0610087
$478$		−	189.402i		−	0.396239i
$479$	663.872			1.38595			0.692977	−	0.720960i	$-0.256299\pi$
$479$	663.872			1.38595			0.692977	+	0.720960i	$0.256299\pi$
$480$			9.50071i			0.0197931i
$481$	−65.8994			−0.137005
$482$			30.5060i			0.0632906i
$483$			67.5523i			0.139860i
$484$	−213.063			−0.440212
$485$			119.398i			0.246182i
$486$			22.0454i			0.0453609i
$487$	505.567			1.03813			0.519063	−	0.854736i	$-0.326281\pi$
$487$	505.567			1.03813			0.519063	+	0.854736i	$0.326281\pi$
$488$	17.7271			0.0363260
$489$	−392.418			−0.802490
$490$		−	54.4035i		−	0.111027i
$491$	−758.053			−1.54390			−0.771948	−	0.635686i	$-0.780717\pi$
$491$	−758.053			−1.54390			−0.771948	+	0.635686i	$0.780717\pi$
$492$	−8.04566			−0.0163530
$493$	623.604			1.26492
$494$	−316.320			−0.640324
$495$			11.0651i			0.0223538i
$496$			139.212i			0.280669i
$497$	179.094			0.360350
$498$	360.559			0.724014
$499$	−217.463			−0.435797			−0.217898	−	0.975971i	$-0.569920\pi$
$499$	−217.463			−0.435797			−0.217898	+	0.975971i	$0.569920\pi$
$500$	95.1428			0.190286
$501$	−176.630			−0.352554
$502$		−	526.298i		−	1.04840i
$503$		−	100.548i		−	0.199896i	−0.994993	−	0.0999481i	$-0.968132\pi$
$503$		−	100.548i		−	0.199896i	0.994993	−	0.0999481i	$-0.0318677\pi$
$504$		−	25.9146i		−	0.0514180i
$505$		−	122.668i		−	0.242908i
$506$		−	68.6957i		−	0.135762i
$507$	54.6788			0.107848
$508$	−100.256			−0.197354
$509$		−	379.333i		−	0.745251i	−0.927982	−	0.372626i	$-0.878458\pi$
$509$		−	379.333i		−	0.745251i	0.927982	−	0.372626i	$-0.121542\pi$
$510$			44.1189i			0.0865076i
$511$			10.4154i			0.0203823i
$512$			22.6274i			0.0441942i
$513$	99.1405			0.193256
$514$			23.3910i			0.0455078i
$515$		−	10.9540i		−	0.0212700i
$516$			13.3130i			0.0258003i
$517$	203.195			0.393027
$518$	−24.2791			−0.0468709
$519$		−	20.6272i		−	0.0397441i
$520$	32.1520			0.0618308
$521$	275.414			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$521$	275.414			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$522$			142.435i			0.272864i
$523$	−184.170			−0.352141			−0.176071	−	0.984378i	$-0.556339\pi$
$523$	−184.170			−0.352141			−0.176071	+	0.984378i	$0.556339\pi$
$524$			243.550i			0.464791i
$525$	−127.271			−0.242422
$526$		−	162.789i		−	0.309486i
$527$			646.464i			1.22669i
$528$			26.3533i			0.0499115i
$529$	365.920			0.691720
$530$			13.3022i			0.0250985i
$531$	−172.906	−	37.8466i	−0.325624	−	0.0712742i
$532$	−116.541			−0.219062
$533$			27.2279i			0.0510842i
$534$	226.181			0.423560
$535$	−38.9518			−0.0728071
$536$	132.178			0.246601
$537$			240.877i			0.448560i
$538$	−205.039			−0.381113
$539$		−	150.906i		−	0.279973i
$540$	−10.0770			−0.0186612
$541$			93.8888i			0.173547i	0.996228	+	0.0867734i	$0.0276556\pi$
$541$			93.8888i			0.173547i	−0.996228	+	0.0867734i	$0.972344\pi$
$542$		−	268.626i		−	0.495621i
$543$	111.104			0.204612
$544$			105.076i			0.193154i
$545$		−	193.927i		−	0.355829i
$546$	−87.6995			−0.160622
$547$	−391.002			−0.714811			−0.357405	−	0.933949i	$-0.616339\pi$
$547$	−391.002			−0.714811			−0.357405	+	0.933949i	$0.616339\pi$
$548$	−211.808			−0.386511
$549$			18.8024i			0.0342484i
$550$	129.426			0.235319
$551$	640.545			1.16251
$552$	62.5614			0.113336
$553$	−137.172			−0.248050
$554$			193.098i			0.348552i
$555$			9.44104i			0.0170109i
$556$	312.655			0.562328
$557$	−27.5357			−0.0494357			−0.0247178	−	0.999694i	$-0.507869\pi$
$557$	−27.5357			−0.0494357			−0.0247178	+	0.999694i	$0.507869\pi$
$558$	−147.656			−0.264617
$559$	45.0534			0.0805963
$560$	11.8457			0.0211530
$561$			122.378i			0.218143i
$562$			283.859i			0.505086i
$563$		−	607.725i		−	1.07944i	−0.841845	−	0.539720i	$-0.818530\pi$
$563$		−	607.725i		−	1.07944i	0.841845	−	0.539720i	$-0.181470\pi$
$564$			185.050i			0.328103i
$565$		−	97.6213i		−	0.172781i
$566$	−19.6620			−0.0347385
$567$	27.4866			0.0484773
$568$		−	165.862i		−	0.292011i
$569$			774.788i			1.36167i	0.732439	+	0.680833i	$0.238382\pi$
$569$			774.788i			1.36167i	−0.732439	+	0.680833i	$0.761618\pi$
$570$			45.3174i			0.0795043i
$571$			997.703i			1.74729i	0.486563	+	0.873646i	$0.338250\pi$
$571$			997.703i			1.74729i	−0.486563	+	0.873646i	$0.661750\pi$
$572$	89.1840			0.155916
$573$			94.4051i			0.164756i
$574$			10.0315i			0.0174765i
$575$		−	307.250i		−	0.534348i
$576$	−24.0000			−0.0416667
$577$	979.641			1.69782			0.848909	−	0.528539i	$-0.177260\pi$
$577$	979.641			1.69782			0.848909	+	0.528539i	$0.177260\pi$
$578$			79.2389i			0.137091i
$579$	−105.214			−0.181717
$580$	−65.1075			−0.112254
$581$		−	449.552i		−	0.773755i
$582$	−301.616			−0.518240
$583$			36.8980i			0.0632899i
$584$	9.64586			0.0165169
$585$			34.1023i			0.0582946i
$586$			570.346i			0.973287i
$587$			564.199i			0.961156i	0.876952	+	0.480578i	$0.159573\pi$
$587$			564.199i			0.961156i	−0.876952	+	0.480578i	$0.840427\pi$
$588$	137.430			0.233725
$589$			664.026i			1.12738i
$590$	17.2998	−	79.0361i	0.0293217	−	0.133959i
$591$	49.8431			0.0843368
$592$			22.4853i			0.0379819i
$593$	−474.066			−0.799437			−0.399718	−	0.916638i	$-0.630892\pi$
$593$	−474.066			−0.799437			−0.399718	+	0.916638i	$0.630892\pi$
$594$	−27.9519			−0.0470570
$595$	55.0083			0.0924509
$596$			69.3592i			0.116374i
$597$	−233.871			−0.391744
$598$		−	211.718i		−	0.354044i
$599$	327.543			0.546816			0.273408	−	0.961898i	$-0.411849\pi$
$599$	327.543			0.546816			0.273408	+	0.961898i	$0.411849\pi$
$600$			117.868i			0.196447i
$601$			672.230i			1.11852i	0.828992	+	0.559260i	$0.188915\pi$
$601$			672.230i			1.11852i	−0.828992	+	0.559260i	$0.811085\pi$
$602$	16.5989			0.0275729
$603$			140.196i			0.232498i
$604$			173.856i			0.287841i
$605$	103.299			0.170743
$606$	309.876			0.511347
$607$	787.877			1.29799			0.648993	−	0.760794i	$-0.275190\pi$
$607$	787.877			1.29799			0.648993	+	0.760794i	$0.275190\pi$
$608$			107.931i			0.177517i
$609$	177.591			0.291610
$610$	−8.59463			−0.0140896
$611$	626.240			1.02494
$612$	−111.450			−0.182108
$613$			1092.68i			1.78251i	0.453506	+	0.891253i	$0.350173\pi$
$613$			1092.68i			1.78251i	−0.453506	+	0.891253i	$0.649827\pi$
$614$		−	158.192i		−	0.257641i
$615$	3.90079			0.00634274
$616$	32.8578			0.0533405
$617$	−1049.24			−1.70056			−0.850278	−	0.526333i	$-0.823566\pi$
$617$	−1049.24			−1.70056			−0.850278	+	0.526333i	$0.823566\pi$
$618$	27.6713			0.0447755
$619$	1.94598			0.00314376			0.00157188	−	0.999999i	$-0.499500\pi$
$619$	1.94598			0.00314376			0.00157188	+	0.999999i	$0.499500\pi$
$620$		−	67.4941i		−	0.108861i
$621$			66.3563i			0.106854i
$622$		−	8.21088i		−	0.0132008i
$623$		−	282.007i		−	0.452659i
$624$			81.2201i			0.130160i
$625$	555.366			0.888585
$626$	708.364			1.13157
$627$			125.703i			0.200482i
$628$			34.5066i			0.0549468i
$629$			104.416i			0.166003i
$630$			12.5642i			0.0199432i
$631$	989.890			1.56876			0.784382	−	0.620278i	$-0.212980\pi$
$631$	989.890			1.56876			0.784382	+	0.620278i	$0.212980\pi$
$632$			127.037i			0.201008i
$633$		−	62.1398i		−	0.0981672i
$634$			261.315i			0.412169i
$635$	48.6071			0.0765466
$636$	−33.6031			−0.0528350
$637$		−	465.087i		−	0.730120i
$638$	−180.597			−0.283067
$639$	175.923			0.275310
$640$		−	10.9705i		−	0.0171414i
$641$	−740.216			−1.15478			−0.577391	−	0.816468i	$-0.695929\pi$
$641$	−740.216			−1.15478			−0.577391	+	0.816468i	$0.695929\pi$
$642$		−	98.3972i		−	0.153267i
$643$	318.669			0.495598			0.247799	−	0.968812i	$-0.420293\pi$
$643$	318.669			0.495598			0.247799	+	0.968812i	$0.420293\pi$
$644$		−	78.0027i		−	0.121122i
$645$		−	6.45454i		−	0.0100070i
$646$			501.202i			0.775855i
$647$	15.5155			0.0239807			0.0119903	−	0.999928i	$-0.496183\pi$
$647$	15.5155			0.0239807			0.0119903	+	0.999928i	$0.496183\pi$
$648$		−	25.4558i		−	0.0392837i
$649$	47.9865	−	219.232i	0.0739392	−	0.337800i
$650$	398.886			0.613671
$651$			184.101i			0.282797i
$652$	453.125			0.694977
$653$	−692.123			−1.05991			−0.529956	−	0.848025i	$-0.677792\pi$
$653$	−692.123			−1.05991			−0.529956	+	0.848025i	$0.677792\pi$
$654$	489.883			0.749057
$655$		−	118.081i		−	0.180276i
$656$	9.29033			0.0141621
$657$			10.2310i			0.0155723i
$658$	230.724			0.350644
$659$			665.193i			1.00940i	0.863296	+	0.504699i	$0.168396\pi$
$659$			665.193i			1.00940i	−0.863296	+	0.504699i	$0.831604\pi$
$660$		−	12.7769i		−	0.0193589i
$661$	−818.559			−1.23836			−0.619182	−	0.785248i	$-0.712536\pi$
$661$	−818.559			−1.23836			−0.619182	+	0.785248i	$0.712536\pi$
$662$		−	353.448i		−	0.533910i
$663$			377.165i			0.568877i
$664$	−416.338			−0.627014
$665$	56.5026			0.0849664
$666$	−23.8493			−0.0358097
$667$			428.727i			0.642769i
$668$	203.954			0.305321
$669$	−411.468			−0.615049
$670$	−64.0841			−0.0956479
$671$	−23.8400			−0.0355290
$672$			29.9237i			0.0445293i
$673$		−	1061.63i		−	1.57746i	−0.614739	−	0.788731i	$-0.710739\pi$
$673$		−	1061.63i		−	1.57746i	0.614739	−	0.788731i	$-0.289261\pi$
$674$	−419.679			−0.622670
$675$	−125.018			−0.185212
$676$	−63.1376			−0.0933989
$677$	66.2865			0.0979121			0.0489561	−	0.998801i	$-0.484411\pi$
$677$	66.2865			0.0979121			0.0489561	+	0.998801i	$0.484411\pi$
$678$	246.604			0.363723
$679$			376.060i			0.553844i
$680$		−	50.9441i		−	0.0749178i
$681$			716.152i			1.05162i
$682$		−	187.217i		−	0.274511i
$683$		−	767.960i		−	1.12439i	−0.827004	−	0.562196i	$-0.809957\pi$
$683$		−	767.960i		−	1.12439i	0.827004	−	0.562196i	$-0.190043\pi$
$684$	−114.478			−0.167365
$685$	102.691			0.149914
$686$		−	382.987i		−	0.558290i
$687$			675.933i			0.983890i
$688$		−	15.3725i		−	0.0223438i
$689$			113.719i			0.165049i
$690$	−30.3317			−0.0439590
$691$		−	333.252i		−	0.482275i	−0.970491	−	0.241137i	$-0.922480\pi$
$691$		−	333.252i		−	0.482275i	0.970491	−	0.241137i	$-0.0775204\pi$
$692$			23.8182i			0.0344194i
$693$			34.8509i			0.0502899i
$694$	−624.316			−0.899590
$695$	−151.585			−0.218107
$696$		−	164.470i		−	0.236307i
$697$	43.1419			0.0618966
$698$	460.671			0.659987
$699$			28.6456i			0.0409809i
$700$	146.960			0.209943
$701$			510.070i			0.727632i	0.931471	+	0.363816i	$0.118526\pi$
$701$			510.070i			0.727632i	−0.931471	+	0.363816i	$0.881474\pi$
$702$	−86.1469			−0.122716
$703$			107.253i			0.152564i
$704$		−	30.4302i		−	0.0432246i
$705$		−	89.7180i		−	0.127260i
$706$	259.515			0.367584
$707$		−	386.359i		−	0.546477i
$708$	199.655	+	43.7015i	0.281999	+	0.0617252i
$709$	176.053			0.248312			0.124156	−	0.992263i	$-0.460378\pi$
$709$	176.053			0.248312			0.124156	+	0.992263i	$0.460378\pi$
$710$			80.4151i			0.113261i
$711$	−134.743			−0.189512
$712$	−261.171			−0.366813
$713$	−444.443			−0.623342
$714$			138.958i			0.194619i
$715$	−43.2391			−0.0604743
$716$		−	278.141i		−	0.388465i
$717$	−231.969			−0.323527
$718$			316.391i			0.440656i
$719$			170.417i			0.237019i	0.992953	+	0.118510i	$0.0378116\pi$
$719$			170.417i			0.237019i	−0.992953	+	0.118510i	$0.962188\pi$
$720$	11.6359			0.0161610
$721$		−	34.5011i		−	0.0478517i
$722$			4.28665i			0.00593719i
$723$	37.3621			0.0516765
$724$	−128.292			−0.177199
$725$	−807.740			−1.11412
$726$			260.947i			0.359432i
$727$	440.331			0.605683			0.302841	−	0.953041i	$-0.402065\pi$
$727$	440.331			0.605683			0.302841	+	0.953041i	$0.402065\pi$
$728$	101.267			0.139103
$729$	27.0000			0.0370370
$730$	−4.67661			−0.00640632
$731$		−	71.3860i		−	0.0976553i
$732$		−	21.7111i		−	0.0296600i
$733$	1011.75			1.38029			0.690144	−	0.723672i	$-0.257547\pi$
$733$	1011.75			1.38029			0.690144	+	0.723672i	$0.257547\pi$
$734$	425.347			0.579491
$735$	−66.6304			−0.0906536
$736$	−72.2396			−0.0981517
$737$	−177.758			−0.241191
$738$			9.85388i			0.0133521i
$739$		−	37.6364i		−	0.0509288i	−0.999676	−	0.0254644i	$-0.991894\pi$
$739$		−	37.6364i		−	0.0509288i	0.999676	−	0.0254644i	$-0.00810644\pi$
$740$		−	10.9016i		−	0.0147319i
$741$			387.412i			0.522823i
$742$			41.8970i			0.0564649i
$743$	136.717			0.184007			0.0920034	−	0.995759i	$-0.470673\pi$
$743$	136.717			0.184007			0.0920034	+	0.995759i	$0.470673\pi$
$744$	170.499			0.229165
$745$		−	33.6275i		−	0.0451376i
$746$			737.413i			0.988489i
$747$		−	441.593i		−	0.591155i
$748$		−	141.310i		−	0.188917i
$749$	−122.684			−0.163796
$750$		−	116.526i		−	0.155367i
$751$			1034.25i			1.37716i	0.725160	+	0.688581i	$0.241766\pi$
$751$			1034.25i			1.37716i	−0.725160	+	0.688581i	$0.758234\pi$
$752$		−	213.677i		−	0.284145i
$753$	−644.581			−0.856017
$754$	−556.593			−0.738187
$755$		−	84.2908i		−	0.111643i
$756$	−31.7388			−0.0419826
$757$	−901.318			−1.19064			−0.595322	−	0.803487i	$-0.702976\pi$
$757$	−901.318			−1.19064			−0.595322	+	0.803487i	$0.702976\pi$
$758$		−	949.650i		−	1.25284i
$759$	−84.1347			−0.110849
$760$		−	52.3281i		−	0.0688527i
$761$	−884.001			−1.16163			−0.580815	−	0.814035i	$-0.697266\pi$
$761$	−884.001			−1.16163			−0.580815	+	0.814035i	$0.697266\pi$
$762$			122.788i			0.161139i
$763$		−	610.796i		−	0.800519i
$764$		−	109.010i		−	0.142683i
$765$	54.0344			0.0706332
$766$			306.298i			0.399867i
$767$	147.893	−	675.667i	0.192820	−	0.880921i
$768$	27.7128			0.0360844
$769$			982.068i			1.27707i	0.769592	+	0.638536i	$0.220460\pi$
$769$			982.068i			1.27707i	−0.769592	+	0.638536i	$0.779540\pi$
$770$	−15.9305			−0.0206889
$771$	28.6480			0.0371569
$772$	121.491			0.157371
$773$		−	882.142i		−	1.14119i	−0.821230	−	0.570597i	$-0.806712\pi$
$773$		−	882.142i		−	1.14119i	0.821230	−	0.570597i	$-0.193288\pi$
$774$	16.3050			0.0210659
$775$		−	837.350i		−	1.08045i
$776$	348.276			0.448809
$777$			29.7357i			0.0382699i
$778$			532.823i			0.684862i
$779$	44.3139			0.0568857
$780$		−	39.3780i		−	0.0504846i
$781$			223.057i			0.285605i
$782$	−335.463			−0.428980
$783$	174.446			0.222792
$784$	−158.691			−0.202411
$785$		−	16.7299i		−	0.0213119i
$786$	298.287			0.379500
$787$	−261.379			−0.332121			−0.166060	−	0.986116i	$-0.553105\pi$
$787$	−261.379			−0.332121			−0.166060	+	0.986116i	$0.553105\pi$
$788$	−57.5538			−0.0730378
$789$	−199.376			−0.252694
$790$		−	61.5916i		−	0.0779640i
$791$		−	307.470i		−	0.388711i
$792$	32.2760			0.0407526
$793$	−73.4741			−0.0926534
$794$	499.807			0.629480
$795$	16.2918			0.0204929
$796$	270.051			0.339260
$797$		−	79.4352i		−	0.0996677i	−0.998758	−	0.0498339i	$-0.984131\pi$
$797$		−	79.4352i		−	0.0996677i	0.998758	−	0.0498339i	$-0.0158692\pi$
$798$			142.733i			0.178863i
$799$		−	992.264i		−	1.24188i
$800$		−	136.103i		−	0.170128i
$801$		−	277.014i		−	0.345835i
$802$	−126.481			−0.157706
$803$	−12.9721			−0.0161545
$804$		−	161.885i		−	0.201349i
$805$			37.8181i			0.0469790i
$806$		−	576.997i		−	0.715877i
$807$			251.120i			0.311177i
$808$	−357.814			−0.442839
$809$		−	547.235i		−	0.676434i	−0.941068	−	0.338217i	$-0.890176\pi$
$809$		−	547.235i		−	0.676434i	0.941068	−	0.338217i	$-0.109824\pi$
$810$			12.3418i			0.0152368i
$811$			964.881i			1.18974i	0.803821	+	0.594871i	$0.202797\pi$
$811$			964.881i			1.18974i	−0.803821	+	0.594871i	$0.797203\pi$
$812$	−205.064			−0.252542
$813$	−328.999			−0.404673
$814$		−	30.2390i		−	0.0371487i
$815$	−219.689			−0.269557
$816$	128.691			0.157710
$817$		−	73.3253i		−	0.0897494i
$818$	−252.415			−0.308576
$819$			107.410i			0.131147i
$820$	−4.50424			−0.00549297
$821$		−	528.438i		−	0.643652i	−0.946799	−	0.321826i	$-0.895703\pi$
$821$		−	528.438i		−	0.643652i	0.946799	−	0.321826i	$-0.104297\pi$
$822$			259.411i			0.315585i
$823$			540.168i			0.656341i	0.944619	+	0.328170i	$0.106432\pi$
$823$			540.168i			0.656341i	−0.944619	+	0.328170i	$0.893568\pi$
$824$	−31.9520			−0.0387767
$825$		−	158.513i		−	0.192137i
$826$	54.4878	−	248.934i	0.0659659	−	0.301373i
$827$	326.126			0.394349			0.197174	−	0.980368i	$-0.436823\pi$
$827$	326.126			0.394349			0.197174	+	0.980368i	$0.436823\pi$
$828$		−	76.6217i		−	0.0925383i
$829$	−1184.50			−1.42883			−0.714414	−	0.699723i	$-0.753307\pi$
$829$	−1184.50			−1.42883			−0.714414	+	0.699723i	$0.753307\pi$
$830$	201.853			0.243197
$831$	236.496			0.284592
$832$		−	93.7848i		−	0.112722i
$833$	−736.919			−0.884657
$834$		−	382.922i		−	0.459139i
$835$	−98.8834			−0.118423
$836$		−	145.149i		−	0.173623i
$837$			180.841i			0.216059i
$838$	−538.631			−0.642758
$839$		−	70.1546i		−	0.0836169i	−0.999126	−	0.0418085i	$-0.986688\pi$
$839$		−	70.1546i		−	0.0836169i	0.999126	−	0.0418085i	$-0.0133119\pi$
$840$		−	14.5079i		−	0.0172713i
$841$	286.096			0.340185
$842$	463.210			0.550130
$843$	347.654			0.412401
$844$			71.7529i			0.0850153i
$845$	30.6111			0.0362261
$846$	226.639			0.267895
$847$	325.354			0.384125
$848$	38.8015			0.0457565
$849$			24.0809i			0.0283638i
$850$		−	632.026i		−	0.743560i
$851$	−71.7859			−0.0843548
$852$	−203.139			−0.238426
$853$	−456.456			−0.535118			−0.267559	−	0.963541i	$-0.586217\pi$
$853$	−456.456			−0.535118			−0.267559	+	0.963541i	$0.586217\pi$
$854$	−27.0699			−0.0316977
$855$	55.5023			0.0649150
$856$			113.619i			0.132733i
$857$		−	1020.65i		−	1.19096i	−0.803371	−	0.595479i	$-0.796962\pi$
$857$		−	1020.65i		−	1.19096i	0.803371	−	0.595479i	$-0.203038\pi$
$858$		−	109.228i		−	0.127305i
$859$		−	896.658i		−	1.04384i	−0.852995	−	0.521919i	$-0.825216\pi$
$859$		−	896.658i		−	1.04384i	0.852995	−	0.521919i	$-0.174784\pi$
$860$			7.45307i			0.00866635i
$861$	12.2860			0.0142695
$862$	−152.843			−0.177312
$863$		−	1118.41i		−	1.29596i	−0.761659	−	0.647978i	$-0.775615\pi$
$863$		−	1118.41i		−	1.29596i	0.761659	−	0.647978i	$-0.224385\pi$
$864$			29.3939i			0.0340207i
$865$		−	11.5478i		−	0.0133501i
$866$			967.695i			1.11743i
$867$	97.0474			0.111935
$868$		−	212.581i		−	0.244909i
$869$		−	170.844i		−	0.196599i
$870$			79.7400i			0.0916552i
$871$	−547.845			−0.628984
$872$	−565.669			−0.648702
$873$			369.402i			0.423141i
$874$	−344.576			−0.394251
$875$	−145.286			−0.166042
$876$		−	11.8137i		−	0.0134860i
$877$	−501.541			−0.571882			−0.285941	−	0.958247i	$-0.592306\pi$
$877$	−501.541			−0.571882			−0.285941	+	0.958247i	$0.592306\pi$
$878$			669.653i			0.762703i
$879$	698.528			0.794685
$880$			14.7535i			0.0167653i
$881$			1329.21i			1.50875i	0.656444	+	0.754375i	$0.272060\pi$
$881$			1329.21i			1.50875i	−0.656444	+	0.754375i	$0.727940\pi$
$882$		−	168.317i		−	0.190835i
$883$	57.4848			0.0651017			0.0325509	−	0.999470i	$-0.489637\pi$
$883$	57.4848			0.0651017			0.0325509	+	0.999470i	$0.489637\pi$
$884$		−	435.513i		−	0.492662i
$885$	−96.7990	−	21.1878i	−0.109377	−	0.0239410i
$886$	1049.26			1.18426
$887$		−	361.486i		−	0.407538i	−0.979019	−	0.203769i	$-0.934681\pi$
$887$		−	361.486i		−	0.407538i	0.979019	−	0.203769i	$-0.0653192\pi$
$888$	27.5388			0.0310121
$889$	153.094			0.172209
$890$	126.624			0.142274
$891$			34.2339i			0.0384219i
$892$	475.122			0.532648
$893$		−	1019.22i		−	1.14134i
$894$	84.9473			0.0950194
$895$			134.851i			0.150672i
$896$		−	34.5529i		−	0.0385635i
$897$	−259.301			−0.289076
$898$		−	713.576i		−	0.794628i
$899$			1168.41i			1.29968i
$900$	144.359			0.160398
$901$	180.184			0.199983
$902$	−12.4940			−0.0138514
$903$		−	20.3294i		−	0.0225132i
$904$	−284.754			−0.314993
$905$	62.2000			0.0687292
$906$	212.929			0.235021
$907$	−121.679			−0.134156			−0.0670780	−	0.997748i	$-0.521368\pi$
$907$	−121.679			−0.134156			−0.0670780	+	0.997748i	$0.521368\pi$
$908$		−	826.941i		−	0.910728i
$909$		−	379.519i		−	0.417513i
$910$	−49.0972			−0.0539530
$911$	1116.36			1.22543			0.612713	−	0.790306i	$-0.290078\pi$
$911$	1116.36			1.22543			0.612713	+	0.790306i	$0.290078\pi$
$912$	132.187			0.144942
$913$	559.906			0.613259
$914$	817.560			0.894485
$915$			10.5262i			0.0115041i
$916$		−	780.500i		−	0.852074i
$917$		−	371.910i		−	0.405573i
$918$			136.498i			0.148690i
$919$		−	1734.76i		−	1.88766i	−0.330431	−	0.943830i	$-0.607194\pi$
$919$		−	1734.76i		−	1.88766i	0.330431	−	0.943830i	$-0.392806\pi$
$920$	35.0240			0.0380696
$921$	−193.744			−0.210363
$922$			531.536i			0.576503i
$923$			687.456i			0.744806i
$924$		−	40.2424i		−	0.0435524i
$925$		−	135.248i		−	0.146214i
$926$	587.016			0.633926
$927$		−	33.8902i		−	0.0365590i
$928$			189.913i			0.204648i
$929$		−	81.3239i		−	0.0875392i	−0.999042	−	0.0437696i	$-0.986063\pi$
$929$		−	81.3239i		−	0.0875392i	0.999042	−	0.0437696i	$-0.0139367\pi$
$930$	−82.6631			−0.0888850
$931$	−756.938			−0.813038
$932$		−	33.0771i		−	0.0354905i
$933$	−10.0562			−0.0107784
$934$	738.485			0.790670
$935$			68.5114i			0.0732743i
$936$	99.4738			0.106275
$937$			639.885i			0.682908i	0.939898	+	0.341454i	$0.110919\pi$
$937$			639.885i			0.682908i	−0.939898	+	0.341454i	$0.889081\pi$
$938$	−201.841			−0.215182
$939$		−	867.566i		−	0.923925i
$940$			103.597i			0.110210i
$941$			873.925i			0.928719i	0.885647	+	0.464360i	$0.153715\pi$
$941$			873.925i			0.928719i	−0.885647	+	0.464360i	$0.846285\pi$
$942$	42.2617			0.0448638
$943$			29.6600i			0.0314528i
$944$	−230.542	−	50.4621i	−0.244218	−	0.0534556i
$945$	15.3880			0.0162836
$946$			20.6735i			0.0218536i
$947$	−962.998			−1.01689			−0.508447	−	0.861093i	$-0.669780\pi$
$947$	−962.998			−1.01689			−0.508447	+	0.861093i	$0.669780\pi$
$948$	155.588			0.164123
$949$	−39.9796			−0.0421282
$950$		−	649.195i		−	0.683364i
$951$	320.044			0.336535
$952$		−	160.455i		−	0.168545i
$953$	665.805			0.698641			0.349321	−	0.937003i	$-0.386412\pi$
$953$	665.805			0.698641			0.349321	+	0.937003i	$0.386412\pi$
$954$			41.1552i			0.0431396i
$955$			52.8512i			0.0553416i
$956$	267.855			0.280183
$957$			221.185i			0.231123i
$958$			938.856i			0.980017i
$959$	323.439			0.337267
$960$	−13.4360			−0.0139959
$961$	−250.243			−0.260398
$962$		−	93.1958i		−	0.0968771i
$963$	−120.512			−0.125142
$964$	−43.1421			−0.0447532
$965$	−58.9025			−0.0610389
$966$	−95.5334			−0.0988958
$967$			1070.88i			1.10742i	0.832708	+	0.553712i	$0.186789\pi$
$967$			1070.88i			1.10742i	−0.832708	+	0.553712i	$0.813211\pi$
$968$		−	301.316i		−	0.311277i
$969$	613.845			0.633483
$970$	−168.855			−0.174077
$971$	−229.115			−0.235958			−0.117979	−	0.993016i	$-0.537642\pi$
$971$	−229.115			−0.235958			−0.117979	+	0.993016i	$0.537642\pi$
$972$	−31.1769			−0.0320750
$973$	−477.434			−0.490683
$974$			714.980i			0.734066i
$975$		−	488.534i		−	0.501060i
$976$			25.0699i			0.0256863i
$977$		−	133.975i		−	0.137129i	−0.997647	−	0.0685643i	$-0.978158\pi$
$977$		−	133.975i		−	0.137129i	0.997647	−	0.0685643i	$-0.0218418\pi$
$978$		−	554.963i		−	0.567446i
$979$	351.232			0.358766
$980$	76.9381			0.0785083
$981$		−	599.982i		−	0.611603i
$982$		−	1072.05i		−	1.09170i
$983$		−	337.982i		−	0.343827i	−0.985112	−	0.171914i	$-0.945005\pi$
$983$		−	337.982i		−	0.343827i	0.985112	−	0.171914i	$-0.0549950\pi$
$984$		−	11.3783i		−	0.0115633i
$985$	27.9039			0.0283288
$986$			881.909i			0.894432i
$987$		−	282.578i		−	0.286300i
$988$		−	447.344i		−	0.452778i
$989$	49.0778			0.0496237
$990$	−15.6484			−0.0158065
$991$		−	314.003i		−	0.316855i	−0.987371	−	0.158427i	$-0.949358\pi$
$991$		−	314.003i		−	0.316855i	0.987371	−	0.158427i	$-0.0506424\pi$
$992$	−196.875			−0.198463
$993$	−432.884			−0.435936
$994$			253.277i			0.254806i
$995$	−130.929			−0.131587
$996$			509.907i			0.511955i
$997$	650.977			0.652936			0.326468	−	0.945208i	$-0.394141\pi$
$997$	650.977			0.652936			0.326468	+	0.945208i	$0.394141\pi$
$998$		−	307.539i		−	0.308155i
$999$			29.2093i			0.0292385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.19	yes	20
3.2	odd	2		1062.3.d.f.235.4		20
59.58	odd	2	inner	354.3.d.a.235.9	✓	20
177.176	even	2		1062.3.d.f.235.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.9	✓	20	59.58	odd	2	inner
354.3.d.a.235.19	yes	20	1.1	even	1	trivial
1062.3.d.f.235.4		20	3.2	odd	2
1062.3.d.f.235.14		20	177.176	even	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +0.969662 q^{5} +2.44949i q^{6} +3.05407 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +0.969662 q^{5} +2.44949i q^{6} +3.05407 q^{7} -2.82843i q^{8} +3.00000 q^{9} +1.37131i q^{10} +3.80377i q^{11} -3.46410 q^{12} +11.7231i q^{13} +4.31911i q^{14} +1.67950 q^{15} +4.00000 q^{16} +18.5750 q^{17} +4.24264i q^{18} +19.0796 q^{19} -1.93932 q^{20} +5.28981 q^{21} -5.37934 q^{22} +12.7703i q^{23} -4.89898i q^{24} -24.0598 q^{25} -16.5790 q^{26} +5.19615 q^{27} -6.10814 q^{28} +33.5722 q^{29} +2.37518i q^{30} +34.8029i q^{31} +5.65685i q^{32} +6.58832i q^{33} +26.2690i q^{34} +2.96142 q^{35} -6.00000 q^{36} +5.62133i q^{37} +26.9826i q^{38} +20.3050i q^{39} -2.74262i q^{40} +2.32258 q^{41} +7.48091i q^{42} -3.84313i q^{43} -7.60754i q^{44} +2.90899 q^{45} -18.0599 q^{46} -53.4193i q^{47} +6.92820 q^{48} -39.6727 q^{49} -34.0256i q^{50} +32.1728 q^{51} -23.4462i q^{52} +9.70038 q^{53} +7.34847i q^{54} +3.68837i q^{55} -8.63822i q^{56} +33.0468 q^{57} +47.4783i q^{58} +(-57.6355 - 12.6155i) q^{59} -3.35901 q^{60} +6.26746i q^{61} -49.2188 q^{62} +9.16221 q^{63} -8.00000 q^{64} +11.3674i q^{65} -9.31729 q^{66} +46.7320i q^{67} -37.1500 q^{68} +22.1188i q^{69} +4.18807i q^{70} +58.6411 q^{71} -8.48528i q^{72} +3.41033i q^{73} -7.94975 q^{74} -41.6727 q^{75} -38.1592 q^{76} +11.6170i q^{77} -28.7156 q^{78} -44.9144 q^{79} +3.87865 q^{80} +9.00000 q^{81} +3.28463i q^{82} -147.198i q^{83} -10.5796 q^{84} +18.0115 q^{85} +5.43500 q^{86} +58.1488 q^{87} +10.7587 q^{88} -92.3380i q^{89} +4.11393i q^{90} +35.8032i q^{91} -25.5406i q^{92} +60.2804i q^{93} +75.5463 q^{94} +18.5008 q^{95} +9.79796i q^{96} +123.134i q^{97} -56.1056i q^{98} +11.4113i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9} - 24 q^{15} + 80 q^{16} + 72 q^{19} + 16 q^{22} + 140 q^{25} + 64 q^{26} - 16 q^{28} + 56 q^{29} - 80 q^{35} - 120 q^{36} - 8 q^{41} + 16 q^{46} + 52 q^{49} + 32 q^{53} - 48 q^{57} + 192 q^{59} + 48 q^{60} - 16 q^{62} + 24 q^{63} - 160 q^{64} + 96 q^{66} - 568 q^{71} - 288 q^{74} - 96 q^{75} - 144 q^{76} + 192 q^{78} + 528 q^{79} + 180 q^{81} + 568 q^{85} - 416 q^{86} - 216 q^{87} - 32 q^{88} - 480 q^{94} - 456 q^{95}+O(q^{100}) \) 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9 - 24 * q^15 + 80 * q^16 + 72 * q^19 + 16 * q^22 + 140 * q^25 + 64 * q^26 - 16 * q^28 + 56 * q^29 - 80 * q^35 - 120 * q^36 - 8 * q^41 + 16 * q^46 + 52 * q^49 + 32 * q^53 - 48 * q^57 + 192 * q^59 + 48 * q^60 - 16 * q^62 + 24 * q^63 - 160 * q^64 + 96 * q^66 - 568 * q^71 - 288 * q^74 - 96 * q^75 - 144 * q^76 + 192 * q^78 + 528 * q^79 + 180 * q^81 + 568 * q^85 - 416 * q^86 - 216 * q^87 - 32 * q^88 - 480 * q^94 - 456 * q^95

Introduction

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