LMFDB - Embedded newform 201.3.c.a.68.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, 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("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.15
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.74215i q^{2} +(2.96882 + 0.431379i) q^{3} +0.964903 q^{4} +9.03513i q^{5} +(0.751528 - 5.17214i) q^{6} -5.84306 q^{7} -8.64962i q^{8} +(8.62782 + 2.56137i) q^{9} +O(q^{10})$	\(q-1.74215i q^{2} +(2.96882 + 0.431379i) q^{3} +0.964903 q^{4} +9.03513i q^{5} +(0.751528 - 5.17214i) q^{6} -5.84306 q^{7} -8.64962i q^{8} +(8.62782 + 2.56137i) q^{9} +15.7406 q^{10} -0.800693i q^{11} +(2.86463 + 0.416238i) q^{12} +17.6334 q^{13} +10.1795i q^{14} +(-3.89756 + 26.8237i) q^{15} -11.2094 q^{16} +16.0442i q^{17} +(4.46231 - 15.0310i) q^{18} +12.7704 q^{19} +8.71802i q^{20} +(-17.3470 - 2.52057i) q^{21} -1.39493 q^{22} -29.2267i q^{23} +(3.73126 - 25.6792i) q^{24} -56.6336 q^{25} -30.7201i q^{26} +(24.5096 + 11.3261i) q^{27} -5.63798 q^{28} +4.51569i q^{29} +(46.7310 + 6.79015i) q^{30} +2.95050 q^{31} -15.0701i q^{32} +(0.345402 - 2.37712i) q^{33} +27.9514 q^{34} -52.7928i q^{35} +(8.32501 + 2.47148i) q^{36} -44.9335 q^{37} -22.2479i q^{38} +(52.3504 + 7.60667i) q^{39} +78.1505 q^{40} -16.2077i q^{41} +(-4.39122 + 30.2211i) q^{42} -66.8040 q^{43} -0.772590i q^{44} +(-23.1424 + 77.9535i) q^{45} -50.9173 q^{46} -52.7385i q^{47} +(-33.2786 - 4.83548i) q^{48} -14.8587 q^{49} +98.6644i q^{50} +(-6.92112 + 47.6324i) q^{51} +17.0145 q^{52} -39.4845i q^{53} +(19.7318 - 42.6994i) q^{54} +7.23436 q^{55} +50.5402i q^{56} +(37.9130 + 5.50887i) q^{57} +7.86703 q^{58} -11.8804i q^{59} +(-3.76077 + 25.8823i) q^{60} -75.9085 q^{61} -5.14022i q^{62} +(-50.4129 - 14.9663i) q^{63} -71.0918 q^{64} +159.320i q^{65} +(-4.14130 - 0.601743i) q^{66} +8.18535 q^{67} +15.4811i q^{68} +(12.6078 - 86.7688i) q^{69} -91.9731 q^{70} -99.0331i q^{71} +(22.1549 - 74.6274i) q^{72} +142.625 q^{73} +78.2810i q^{74} +(-168.135 - 24.4305i) q^{75} +12.3222 q^{76} +4.67849i q^{77} +(13.2520 - 91.2025i) q^{78} +7.34065 q^{79} -101.278i q^{80} +(67.8787 + 44.1982i) q^{81} -28.2363 q^{82} +96.7619i q^{83} +(-16.7382 - 2.43210i) q^{84} -144.961 q^{85} +116.383i q^{86} +(-1.94797 + 13.4063i) q^{87} -6.92569 q^{88} +46.6823i q^{89} +(135.807 + 40.3175i) q^{90} -103.033 q^{91} -28.2009i q^{92} +(8.75950 + 1.27278i) q^{93} -91.8786 q^{94} +115.382i q^{95} +(6.50091 - 44.7404i) q^{96} +97.0243 q^{97} +25.8861i q^{98} +(2.05087 - 6.90824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.74215i		−	0.871077i	−0.900170	−	0.435538i	$-0.856558\pi$
$2$		−	1.74215i		−	0.871077i	0.900170	−	0.435538i	$-0.143442\pi$
$3$	2.96882	+	0.431379i	0.989608	+	0.143793i
$3$	2.96882	+	0.431379i	0.989608	+	0.143793i
$4$	0.964903			0.241226
$5$			9.03513i			1.80703i	0.428560	+	0.903513i	$0.359021\pi$
$5$			9.03513i			1.80703i	−0.428560	+	0.903513i	$0.640979\pi$
$6$	0.751528	−	5.17214i	0.125255	−	0.862024i
$7$	−5.84306			−0.834722			−0.417361	−	0.908741i	$-0.637045\pi$
$7$	−5.84306			−0.834722			−0.417361	+	0.908741i	$0.637045\pi$
$8$		−	8.64962i		−	1.08120i
$9$	8.62782	+	2.56137i	0.958647	+	0.284597i
$10$	15.7406			1.57406
$11$		−	0.800693i		−	0.0727902i	−0.999337	−	0.0363951i	$-0.988413\pi$
$11$		−	0.800693i		−	0.0727902i	0.999337	−	0.0363951i	$-0.0115875\pi$
$12$	2.86463	+	0.416238i	0.238719	+	0.0346865i
$13$	17.6334			1.35641			0.678207	−	0.734870i	$-0.262757\pi$
$13$	17.6334			1.35641			0.678207	+	0.734870i	$0.262757\pi$
$14$			10.1795i			0.727107i
$15$	−3.89756	+	26.8237i	−0.259838	+	1.78825i
$16$	−11.2094			−0.700585
$17$			16.0442i			0.943776i	0.881659	+	0.471888i	$0.156427\pi$
$17$			16.0442i			0.943776i	−0.881659	+	0.471888i	$0.843573\pi$
$18$	4.46231	−	15.0310i	0.247906	−	0.835055i
$19$	12.7704			0.672125			0.336063	−	0.941840i	$-0.390905\pi$
$19$	12.7704			0.672125			0.336063	+	0.941840i	$0.390905\pi$
$20$			8.71802i			0.435901i
$21$	−17.3470	−	2.52057i	−0.826048	−	0.120027i
$22$	−1.39493			−0.0634059
$23$		−	29.2267i		−	1.27072i	−0.772214	−	0.635362i	$-0.780851\pi$
$23$		−	29.2267i		−	1.27072i	0.772214	−	0.635362i	$-0.219149\pi$
$24$	3.73126	−	25.6792i	0.155469	−	1.06997i
$25$	−56.6336			−2.26534
$26$		−	30.7201i		−	1.18154i
$27$	24.5096	+	11.3261i	0.907762	+	0.419486i
$28$	−5.63798			−0.201356
$29$			4.51569i			0.155713i	0.996965	+	0.0778567i	$0.0248077\pi$
$29$			4.51569i			0.155713i	−0.996965	+	0.0778567i	$0.975192\pi$
$30$	46.7310	+	6.79015i	1.55770	+	0.226338i
$31$	2.95050			0.0951773			0.0475887	−	0.998867i	$-0.484846\pi$
$31$	2.95050			0.0951773			0.0475887	+	0.998867i	$0.484846\pi$
$32$		−	15.0701i		−	0.470940i
$33$	0.345402	−	2.37712i	0.0104667	−	0.0720338i
$34$	27.9514			0.822101
$35$		−	52.7928i		−	1.50837i
$36$	8.32501	+	2.47148i	0.231250	+	0.0686521i
$37$	−44.9335			−1.21442			−0.607210	−	0.794542i	$-0.707711\pi$
$37$	−44.9335			−1.21442			−0.607210	+	0.794542i	$0.707711\pi$
$38$		−	22.2479i		−	0.585472i
$39$	52.3504	+	7.60667i	1.34232	+	0.195043i
$40$	78.1505			1.95376
$41$		−	16.2077i		−	0.395310i	−0.980272	−	0.197655i	$-0.936667\pi$
$41$		−	16.2077i		−	0.395310i	0.980272	−	0.197655i	$-0.0633326\pi$
$42$	−4.39122	+	30.2211i	−0.104553	+	0.719551i
$43$	−66.8040			−1.55358			−0.776790	−	0.629759i	$-0.783153\pi$
$43$	−66.8040			−1.55358			−0.776790	+	0.629759i	$0.783153\pi$
$44$		−	0.772590i		−	0.0175589i
$45$	−23.1424	+	77.9535i	−0.514275	+	1.73230i
$46$	−50.9173			−1.10690
$47$		−	52.7385i		−	1.12210i	−0.827783	−	0.561048i	$-0.810398\pi$
$47$		−	52.7385i		−	1.12210i	0.827783	−	0.561048i	$-0.189602\pi$
$48$	−33.2786	−	4.83548i	−0.693304	−	0.100739i
$49$	−14.8587			−0.303238
$50$			98.6644i			1.97329i
$51$	−6.92112	+	47.6324i	−0.135708	+	0.933968i
$52$	17.0145			0.327202
$53$		−	39.4845i		−	0.744991i	−0.928034	−	0.372495i	$-0.878502\pi$
$53$		−	39.4845i		−	0.744991i	0.928034	−	0.372495i	$-0.121498\pi$
$54$	19.7318	−	42.6994i	0.365405	−	0.790730i
$55$	7.23436			0.131534
$56$			50.5402i			0.902504i
$57$	37.9130	+	5.50887i	0.665140	+	0.0966468i
$58$	7.86703			0.135638
$59$		−	11.8804i		−	0.201362i	−0.994919	−	0.100681i	$-0.967898\pi$
$59$		−	11.8804i		−	0.201362i	0.994919	−	0.100681i	$-0.0321022\pi$
$60$	−3.76077	+	25.8823i	−0.0626795	+	0.431371i
$61$	−75.9085			−1.24440			−0.622201	−	0.782858i	$-0.713761\pi$
$61$	−75.9085			−1.24440			−0.622201	+	0.782858i	$0.713761\pi$
$62$		−	5.14022i		−	0.0829067i
$63$	−50.4129	−	14.9663i	−0.800204	−	0.237560i
$64$	−71.0918			−1.11081
$65$			159.320i			2.45108i
$66$	−4.14130	−	0.601743i	−0.0627469	−	0.00911731i
$67$	8.18535			0.122169
$67$	8.18535			0.122169
$68$			15.4811i			0.227663i
$69$	12.6078	−	86.7688i	0.182721	−	1.25752i
$70$	−91.9731			−1.31390
$71$		−	99.0331i		−	1.39483i	−0.716666	−	0.697416i	$-0.754333\pi$
$71$		−	99.0331i		−	1.39483i	0.716666	−	0.697416i	$-0.245667\pi$
$72$	22.1549	−	74.6274i	0.307707	−	1.03649i
$73$	142.625			1.95377			0.976883	−	0.213772i	$-0.0685751\pi$
$73$	142.625			1.95377			0.976883	+	0.213772i	$0.0685751\pi$
$74$			78.2810i			1.05785i
$75$	−168.135	−	24.4305i	−2.24180	−	0.325740i
$76$	12.3222			0.162134
$77$			4.67849i			0.0607596i
$78$	13.2520	−	91.2025i	0.169897	−	1.16926i
$79$	7.34065			0.0929196			0.0464598	−	0.998920i	$-0.485206\pi$
$79$	7.34065			0.0929196			0.0464598	+	0.998920i	$0.485206\pi$
$80$		−	101.278i		−	1.26597i
$81$	67.8787	+	44.1982i	0.838009	+	0.545656i
$82$	−28.2363			−0.344345
$83$			96.7619i			1.16581i	0.812542	+	0.582903i	$0.198083\pi$
$83$			96.7619i			1.16581i	−0.812542	+	0.582903i	$0.801917\pi$
$84$	−16.7382	−	2.43210i	−0.199264	−	0.0289536i
$85$	−144.961			−1.70543
$86$			116.383i			1.35329i
$87$	−1.94797	+	13.4063i	−0.0223905	+	0.154095i
$88$	−6.92569			−0.0787010
$89$			46.6823i			0.524520i	0.964997	+	0.262260i	$0.0844679\pi$
$89$			46.6823i			0.524520i	−0.964997	+	0.262260i	$0.915532\pi$
$90$	135.807	+	40.3175i	1.50897	+	0.447972i
$91$	−103.033			−1.13223
$92$		−	28.2009i		−	0.306531i
$93$	8.75950	+	1.27278i	0.0941882	+	0.0136858i
$94$	−91.8786			−0.977432
$95$			115.382i			1.21455i
$96$	6.50091	−	44.7404i	0.0677178	−	0.466046i
$97$	97.0243			1.00025			0.500125	−	0.865953i	$-0.333287\pi$
$97$	97.0243			1.00025			0.500125	+	0.865953i	$0.333287\pi$
$98$			25.8861i			0.264144i
$99$	2.05087	−	6.90824i	0.0207159	−	0.0697802i
$100$	−54.6459			−0.546459
$101$			189.490i			1.87614i	0.346447	+	0.938069i	$0.387388\pi$
$101$			189.490i			1.87614i	−0.346447	+	0.938069i	$0.612612\pi$
$102$	82.9828	+	12.0576i	0.813557	+	0.118212i
$103$	−80.9965			−0.786374			−0.393187	−	0.919458i	$-0.628628\pi$
$103$	−80.9965			−0.786374			−0.393187	+	0.919458i	$0.628628\pi$
$104$		−	152.522i		−	1.46656i
$105$	22.7737	−	156.732i	0.216892	−	1.49269i
$106$	−68.7881			−0.648944
$107$		−	67.1896i		−	0.627940i	−0.949433	−	0.313970i	$-0.898341\pi$
$107$		−	67.1896i		−	0.627940i	0.949433	−	0.313970i	$-0.101659\pi$
$108$	23.6493	+	10.9286i	0.218975	+	0.101191i
$109$	72.1617			0.662034			0.331017	−	0.943625i	$-0.392608\pi$
$109$	72.1617			0.662034			0.331017	+	0.943625i	$0.392608\pi$
$110$		−	12.6034i		−	0.114576i
$111$	−133.400	−	19.3834i	−1.20180	−	0.174625i
$112$	65.4969			0.584794
$113$		−	60.9270i		−	0.539177i	−0.962976	−	0.269588i	$-0.913112\pi$
$113$		−	60.9270i		−	0.539177i	0.962976	−	0.269588i	$-0.0868876\pi$
$114$	9.59729	−	66.0502i	0.0841868	−	0.579388i
$115$	264.067			2.29623
$116$			4.35720i			0.0375621i
$117$	152.138	+	45.1657i	1.30032	+	0.386032i
$118$	−20.6974			−0.175402
$119$		−	93.7471i		−	0.787791i
$120$	232.015	+	33.7124i	1.93346	+	0.280937i
$121$	120.359			0.994702
$122$			132.244i			1.08397i
$123$	6.99166	−	48.1178i	0.0568428	−	0.391202i
$124$	2.84694			0.0229592
$125$		−	285.814i		−	2.28651i
$126$	−26.0735	+	87.8269i	−0.206933	+	0.697039i
$127$	44.7556			0.352406			0.176203	−	0.984354i	$-0.443618\pi$
$127$	44.7556			0.352406			0.176203	+	0.984354i	$0.443618\pi$
$128$			63.5725i			0.496660i
$129$	−198.329	−	28.8178i	−1.53744	−	0.223394i
$130$	277.560			2.13508
$131$		−	73.1057i		−	0.558059i	−0.960283	−	0.279029i	$-0.909987\pi$
$131$		−	73.1057i		−	0.558059i	0.960283	−	0.279029i	$-0.0900127\pi$
$132$	0.333279	−	2.29368i	0.00252484	−	0.0173764i
$133$	−74.6180			−0.561038
$134$		−	14.2601i		−	0.106419i
$135$	−102.333	+	221.447i	−0.758023	+	1.64035i
$136$	138.776			1.02041
$137$		−	183.355i		−	1.33836i	−0.743103	−	0.669178i	$-0.766647\pi$
$137$		−	183.355i		−	1.33836i	0.743103	−	0.669178i	$-0.233353\pi$
$138$	−151.165	−	21.9646i	−1.09540	−	0.159164i
$139$	215.643			1.55139			0.775694	−	0.631109i	$-0.217400\pi$
$139$	215.643			1.55139			0.775694	+	0.631109i	$0.217400\pi$
$140$		−	50.9399i		−	0.363857i
$141$	22.7503	−	156.571i	0.161349	−	1.11044i
$142$	−172.531			−1.21501
$143$		−	14.1189i		−	0.0987338i
$144$	−96.7123	−	28.7113i	−0.671613	−	0.199384i
$145$	−40.7999			−0.281378
$146$		−	248.475i		−	1.70188i
$147$	−44.1128	−	6.40972i	−0.300087	−	0.0436035i
$148$	−43.3565			−0.292949
$149$			93.8672i			0.629981i	0.949095	+	0.314991i	$0.102001\pi$
$149$			93.8672i			0.629981i	−0.949095	+	0.314991i	$0.897999\pi$
$150$	−42.5617	+	292.917i	−0.283745	+	1.95278i
$151$	14.6084			0.0967441			0.0483720	−	0.998829i	$-0.484597\pi$
$151$	14.6084			0.0967441			0.0483720	+	0.998829i	$0.484597\pi$
$152$		−	110.459i		−	0.726703i
$153$	−41.0952	+	138.426i	−0.268596	+	0.904748i
$154$	8.15065			0.0529263
$155$			26.6581i			0.171988i
$156$	50.5131	+	7.33970i	0.323802	+	0.0470493i
$157$	−253.153			−1.61244			−0.806221	−	0.591614i	$-0.798491\pi$
$157$	−253.153			−1.61244			−0.806221	+	0.591614i	$0.798491\pi$
$158$		−	12.7885i		−	0.0809401i
$159$	17.0328	−	117.223i	0.107124	−	0.737249i
$160$	136.160			0.851001
$161$			170.773i			1.06070i
$162$	77.0000	−	118.255i	0.475309	−	0.729970i
$163$	87.4082			0.536246			0.268123	−	0.963385i	$-0.413597\pi$
$163$	87.4082			0.536246			0.268123	+	0.963385i	$0.413597\pi$
$164$		−	15.6389i		−	0.0953589i
$165$	21.4776	+	3.12075i	0.130167	+	0.0189136i
$166$	168.574			1.01551
$167$		−	17.0324i		−	0.101990i	−0.998699	−	0.0509952i	$-0.983761\pi$
$167$		−	17.0324i		−	0.101990i	0.998699	−	0.0509952i	$-0.0162393\pi$
$168$	−21.8020	+	150.045i	−0.129774	+	0.893125i
$169$	141.937			0.839861
$170$			252.545i			1.48556i
$171$	110.181	+	32.7097i	0.644331	+	0.191285i
$172$	−64.4593			−0.374764
$173$			184.032i			1.06377i	0.846817	+	0.531884i	$0.178516\pi$
$173$			184.032i			1.06377i	−0.846817	+	0.531884i	$0.821484\pi$
$174$	23.3558	+	3.39367i	0.134229	+	0.0195038i
$175$	330.913			1.89093
$176$			8.97525i			0.0509957i
$177$	5.12493	−	35.2707i	0.0289544	−	0.199269i
$178$	81.3277			0.456897
$179$			330.500i			1.84637i	0.384361	+	0.923183i	$0.374422\pi$
$179$			330.500i			1.84637i	−0.384361	+	0.923183i	$0.625578\pi$
$180$	−22.3301	+	75.2176i	−0.124056	+	0.417875i
$181$	−326.866			−1.80589			−0.902944	−	0.429759i	$-0.858599\pi$
$181$	−326.866			−1.80589			−0.902944	+	0.429759i	$0.858599\pi$
$182$			179.499i			0.986259i
$183$	−225.359	−	32.7453i	−1.23147	−	0.178936i
$184$	−252.800			−1.37391
$185$		−	405.980i		−	2.19449i
$186$	2.21738	−	15.2604i	0.0119214	−	0.0820451i
$187$	12.8465			0.0686977
$188$		−	50.8875i		−	0.270678i
$189$	−143.211	−	66.1792i	−0.757729	−	0.350155i
$190$	201.013			1.05796
$191$			249.158i			1.30449i	0.758008	+	0.652245i	$0.226173\pi$
$191$			249.158i			1.30449i	−0.758008	+	0.652245i	$0.773827\pi$
$192$	−211.059	−	30.6675i	−1.09927	−	0.159726i
$193$	−20.5455			−0.106454			−0.0532268	−	0.998582i	$-0.516951\pi$
$193$	−20.5455			−0.106454			−0.0532268	+	0.998582i	$0.516951\pi$
$194$		−	169.031i		−	0.871295i
$195$	−68.7273	+	472.993i	−0.352448	+	2.42561i
$196$	−14.3372			−0.0731489
$197$		−	228.432i		−	1.15955i	−0.814775	−	0.579777i	$-0.803140\pi$
$197$		−	228.432i		−	1.15955i	0.814775	−	0.579777i	$-0.196860\pi$
$198$	−12.0352	−	3.57294i	−0.0607839	−	0.0180451i
$199$	77.5219			0.389557			0.194779	−	0.980847i	$-0.437601\pi$
$199$	77.5219			0.389557			0.194779	+	0.980847i	$0.437601\pi$
$200$			489.859i			2.44930i
$201$	24.3009	+	3.53099i	0.120900	+	0.0175671i
$202$	330.121			1.63426
$203$		−	26.3854i		−	0.129978i
$204$	−6.67821	+	45.9606i	−0.0327363	+	0.225297i
$205$	146.439			0.714336
$206$			141.108i			0.684992i
$207$	74.8604	−	252.163i	0.361645	−	1.21818i
$208$	−197.659			−0.950283
$209$		−	10.2251i		−	0.0489241i
$210$	−273.052	−	39.6752i	−1.30025	−	0.188930i
$211$	−207.929			−0.985444			−0.492722	−	0.870187i	$-0.663998\pi$
$211$	−207.929			−0.985444			−0.492722	+	0.870187i	$0.663998\pi$
$212$		−	38.0987i		−	0.179711i
$213$	42.7208	−	294.012i	0.200567	−	1.38034i
$214$	−117.055			−0.546984
$215$		−	603.583i		−	2.80736i
$216$	97.9667	−	211.998i	0.453550	−	0.981474i
$217$	−17.2399			−0.0794466
$218$		−	125.717i		−	0.576683i
$219$	423.428	+	61.5254i	1.93346	+	0.280938i
$220$	6.98046			0.0317294
$221$			282.913i			1.28015i
$222$	−33.7688	+	232.403i	−0.152112	+	1.04686i
$223$	−287.578			−1.28959			−0.644793	−	0.764357i	$-0.723057\pi$
$223$	−287.578			−1.28959			−0.644793	+	0.764357i	$0.723057\pi$
$224$			88.0553i			0.393104i
$225$	−488.625	−	145.060i	−2.17167	−	0.644711i
$226$	−106.144			−0.469664
$227$			163.099i			0.718499i	0.933242	+	0.359250i	$0.116967\pi$
$227$			163.099i			0.718499i	−0.933242	+	0.359250i	$0.883033\pi$
$228$	36.5823	+	5.31552i	0.160449	+	0.0233137i
$229$	−196.744			−0.859143			−0.429571	−	0.903033i	$-0.641335\pi$
$229$	−196.744			−0.859143			−0.429571	+	0.903033i	$0.641335\pi$
$230$		−	460.045i		−	2.00019i
$231$	−2.01820	+	13.8896i	−0.00873680	+	0.0601282i
$232$	39.0590			0.168358
$233$			259.052i			1.11181i	0.831245	+	0.555906i	$0.187629\pi$
$233$			259.052i			1.11181i	−0.831245	+	0.555906i	$0.812371\pi$
$234$	78.6856	−	265.047i	0.336263	−	1.13268i
$235$	476.500			2.02766
$236$		−	11.4634i		−	0.0485737i
$237$	21.7931	+	3.16660i	0.0919540	+	0.0133612i
$238$	−163.322			−0.686226
$239$		−	457.975i		−	1.91621i	−0.286412	−	0.958107i	$-0.592463\pi$
$239$		−	457.975i		−	1.91621i	0.286412	−	0.958107i	$-0.407537\pi$
$240$	43.6892	−	300.676i	0.182038	−	1.25282i
$241$	48.1838			0.199933			0.0999665	−	0.994991i	$-0.468126\pi$
$241$	48.1838			0.199933			0.0999665	+	0.994991i	$0.468126\pi$
$242$		−	209.684i		−	0.866461i
$243$	182.454	+	160.498i	0.750839	+	0.660486i
$244$	−73.2443			−0.300182
$245$		−	134.250i		−	0.547960i
$246$	−83.8286	−	12.1805i	−0.340767	−	0.0495144i
$247$	225.185			0.911680
$248$		−	25.5207i		−	0.102906i
$249$	−41.7410	+	287.269i	−0.167635	+	1.15369i
$250$	−497.932			−1.99173
$251$			260.641i			1.03841i	0.854649	+	0.519206i	$0.173772\pi$
$251$			260.641i			1.03841i	−0.854649	+	0.519206i	$0.826228\pi$
$252$	−48.6435	−	14.4410i	−0.193030	−	0.0573055i
$253$	−23.4016			−0.0924964
$254$		−	77.9711i		−	0.306973i
$255$	−430.365	−	62.5332i	−1.68770	−	0.245228i
$256$	−173.614			−0.678180
$257$		−	132.808i		−	0.516763i	−0.966043	−	0.258381i	$-0.916811\pi$
$257$		−	132.808i		−	0.516763i	0.966043	−	0.258381i	$-0.0831891\pi$
$258$	−50.2050	+	345.520i	−0.194593	+	1.33922i
$259$	262.549			1.01370
$260$			153.728i			0.591263i
$261$	−11.5664	+	38.9606i	−0.0443156	+	0.149274i
$262$	−127.361			−0.486112
$263$		−	16.6041i		−	0.0631334i	−0.999502	−	0.0315667i	$-0.989950\pi$
$263$		−	16.6041i		−	0.0631334i	0.999502	−	0.0315667i	$-0.0100497\pi$
$264$	−20.5611	−	2.98759i	−0.0778831	−	0.0113166i
$265$	356.748			1.34622
$266$			129.996i			0.488707i
$267$	−20.1378	+	138.592i	−0.0754223	+	0.519070i
$268$	7.89807			0.0294704
$269$			358.677i			1.33337i	0.745338	+	0.666687i	$0.232288\pi$
$269$			358.677i			1.33337i	−0.745338	+	0.666687i	$0.767712\pi$
$270$	385.795	+	178.280i	1.42887	+	0.660296i
$271$	137.412			0.507054			0.253527	−	0.967328i	$-0.418409\pi$
$271$	137.412			0.507054			0.253527	+	0.967328i	$0.418409\pi$
$272$		−	179.845i		−	0.661195i
$273$	−305.887	−	44.4462i	−1.12046	−	0.162807i
$274$	−319.432			−1.16581
$275$			45.3461i			0.164895i
$276$	12.1653	−	83.7235i	0.0440770	−	0.303346i
$277$	276.120			0.996825			0.498412	−	0.866940i	$-0.333917\pi$
$277$	276.120			0.996825			0.498412	+	0.866940i	$0.333917\pi$
$278$		−	375.683i		−	1.35138i
$279$	25.4564	+	7.55733i	0.0912415	+	0.0270872i
$280$	−456.638			−1.63085
$281$			415.756i			1.47956i	0.672850	+	0.739779i	$0.265070\pi$
$281$			415.756i			1.47956i	−0.672850	+	0.739779i	$0.734930\pi$
$282$	−272.771	−	39.6345i	−0.967274	−	0.140548i
$283$	−92.4249			−0.326590			−0.163295	−	0.986577i	$-0.552212\pi$
$283$	−92.4249			−0.326590			−0.163295	+	0.986577i	$0.552212\pi$
$284$		−	95.5573i		−	0.336469i
$285$	−49.7733	+	342.549i	−0.174643	+	1.20193i
$286$	−24.5973			−0.0860047
$287$			94.7026i			0.329974i
$288$	38.6001	−	130.022i	0.134028	−	0.451465i
$289$	31.5841			0.109288
$290$			71.0796i			0.245102i
$291$	288.048	+	41.8542i	0.989856	+	0.143829i
$292$	137.619			0.471299
$293$			333.220i			1.13727i	0.822590	+	0.568634i	$0.192528\pi$
$293$			333.220i			1.13727i	−0.822590	+	0.568634i	$0.807472\pi$
$294$	−11.1667	+	76.8513i	−0.0379820	+	0.261399i
$295$	107.341			0.363867
$296$			388.658i			1.31303i
$297$	9.06875	−	19.6246i	0.0305345	−	0.0660762i
$298$	163.531			0.548762
$299$		−	515.365i		−	1.72363i
$300$	−162.234	−	23.5731i	−0.540780	−	0.0785770i
$301$	390.339			1.29681
$302$		−	25.4500i		−	0.0842715i
$303$	−81.7419	+	562.562i	−0.269775	+	1.85664i
$304$	−143.148			−0.470880
$305$		−	685.843i		−	2.24867i
$306$	241.160	+	71.5941i	0.788105	+	0.233967i
$307$	208.519			0.679216			0.339608	−	0.940567i	$-0.389706\pi$
$307$	208.519			0.679216			0.339608	+	0.940567i	$0.389706\pi$
$308$			4.51429i			0.0146568i
$309$	−240.464	−	34.9402i	−0.778202	−	0.113075i
$310$	46.4425			0.149815
$311$		−	107.528i		−	0.345750i	−0.984944	−	0.172875i	$-0.944694\pi$
$311$		−	107.528i		−	0.345750i	0.984944	−	0.172875i	$-0.0553056\pi$
$312$	65.7948	−	452.811i	0.210881	−	1.45132i
$313$	−5.54546			−0.0177171			−0.00885856	−	0.999961i	$-0.502820\pi$
$313$	−5.54546			−0.0177171			−0.00885856	+	0.999961i	$0.502820\pi$
$314$			441.032i			1.40456i
$315$	135.222	−	455.487i	0.429276	−	1.44599i
$316$	7.08301			0.0224146
$317$		−	144.711i		−	0.456502i	−0.973602	−	0.228251i	$-0.926699\pi$
$317$		−	144.711i		−	0.456502i	0.973602	−	0.228251i	$-0.0733007\pi$
$318$	−204.220	−	29.6737i	−0.642200	−	0.0933135i
$319$	3.61568			0.0113344
$320$		−	642.324i		−	2.00726i
$321$	28.9842	−	199.474i	0.0902933	−	0.621415i
$322$	297.513			0.923953
$323$			204.890i			0.634335i
$324$	65.4964	+	42.6469i	0.202149	+	0.131626i
$325$	−998.643			−3.07275
$326$		−	152.278i		−	0.467112i
$327$	214.235	+	31.1290i	0.655154	+	0.0951958i
$328$	−140.191			−0.427410
$329$			308.154i			0.936639i
$330$	5.43682	−	37.4172i	0.0164752	−	0.113385i
$331$	−421.584			−1.27367			−0.636834	−	0.771001i	$-0.719756\pi$
$331$	−421.584			−1.27367			−0.636834	+	0.771001i	$0.719756\pi$
$332$			93.3658i			0.281222i
$333$	−387.678	−	115.092i	−1.16420	−	0.345620i
$334$	−29.6731			−0.0888415
$335$			73.9557i			0.220763i
$336$	194.449	+	28.2540i	0.578716	+	0.0840892i
$337$	−167.881			−0.498163			−0.249082	−	0.968482i	$-0.580129\pi$
$337$	−167.881			−0.498163			−0.249082	+	0.968482i	$0.580129\pi$
$338$		−	247.275i		−	0.731584i
$339$	26.2826	−	180.881i	0.0775298	−	0.533574i
$340$	−139.874			−0.411393
$341$		−	2.36244i		−	0.00692798i
$342$	56.9853	−	191.951i	0.166624	−	0.561261i
$343$	373.130			1.08784
$344$			577.829i			1.67974i
$345$	783.968	+	113.913i	2.27237	+	0.330182i
$346$	320.612			0.926623
$347$			66.3420i			0.191187i	0.995420	+	0.0955937i	$0.0304749\pi$
$347$			66.3420i			0.191187i	−0.995420	+	0.0955937i	$0.969525\pi$
$348$	−1.87960	+	12.9358i	−0.00540116	+	0.0371717i
$349$	−290.089			−0.831201			−0.415600	−	0.909547i	$-0.636429\pi$
$349$	−290.089			−0.831201			−0.415600	+	0.909547i	$0.636429\pi$
$350$		−	576.502i		−	1.64715i
$351$	432.187	+	199.718i	1.23130	+	0.568997i
$352$	−12.0665			−0.0342798
$353$		−	243.082i		−	0.688617i	−0.938857	−	0.344308i	$-0.888113\pi$
$353$		−	243.082i		−	0.688617i	0.938857	−	0.344308i	$-0.111887\pi$
$354$	−61.4469	−	8.92842i	−0.173579	−	0.0252215i
$355$	894.777			2.52050
$356$			45.0439i			0.126528i
$357$	40.4405	−	278.319i	0.113279	−	0.779604i
$358$	575.781			1.60833
$359$			96.4879i			0.268768i	0.990929	+	0.134384i	$0.0429056\pi$
$359$			96.4879i			0.268768i	−0.990929	+	0.134384i	$0.957094\pi$
$360$	674.269	+	200.173i	1.87297	+	0.556035i
$361$	−197.918			−0.548248
$362$			569.450i			1.57307i
$363$	357.324	+	51.9203i	0.984364	+	0.143031i
$364$	−99.4168			−0.273123
$365$			1288.64i			3.53051i
$366$	−57.0473	+	392.610i	−0.155867	+	1.07270i
$367$	661.755			1.80315			0.901574	−	0.432625i	$-0.142413\pi$
$367$	661.755			1.80315			0.901574	+	0.432625i	$0.142413\pi$
$368$			327.612i			0.890250i
$369$	41.5140	−	139.837i	0.112504	−	0.378963i
$370$	−707.280			−1.91157
$371$			230.710i			0.621861i
$372$	8.45207	+	1.22811i	0.0227206	+	0.00330137i
$373$	−83.7281			−0.224472			−0.112236	−	0.993682i	$-0.535801\pi$
$373$	−83.7281			−0.224472			−0.112236	+	0.993682i	$0.535801\pi$
$374$		−	22.3805i		−	0.0598409i
$375$	123.294	−	848.531i	0.328784	−	2.26275i
$376$	−456.168			−1.21321
$377$			79.6270i			0.211212i
$378$	−115.294	+	249.495i	−0.305011	+	0.660040i
$379$	85.8170			0.226430			0.113215	−	0.993571i	$-0.463885\pi$
$379$	85.8170			0.226430			0.113215	+	0.993571i	$0.463885\pi$
$380$			111.332i			0.292980i
$381$	132.871	+	19.3066i	0.348744	+	0.0506735i
$382$	434.071			1.13631
$383$		−	112.248i		−	0.293075i	−0.989205	−	0.146537i	$-0.953187\pi$
$383$		−	112.248i		−	0.293075i	0.989205	−	0.146537i	$-0.0468129\pi$
$384$	−27.4238	+	188.735i	−0.0714162	+	0.491499i
$385$	−42.2708			−0.109794
$386$			35.7935i			0.0927292i
$387$	−576.373	−	171.110i	−1.48934	−	0.442145i
$388$	93.6190			0.241286
$389$		−	298.939i		−	0.768482i	−0.923233	−	0.384241i	$-0.874463\pi$
$389$		−	298.939i		−	0.768482i	0.923233	−	0.384241i	$-0.125537\pi$
$390$	824.026	+	119.733i	2.11289	+	0.307009i
$391$	468.918			1.19928
$392$			128.522i			0.327862i
$393$	31.5362	−	217.038i	0.0802449	−	0.552259i
$394$	−397.964			−1.01006
$395$			66.3237i			0.167908i
$396$	1.97889	−	6.66578i	0.00499721	−	0.0168328i
$397$	109.246			0.275179			0.137589	−	0.990489i	$-0.456065\pi$
$397$	109.246			0.275179			0.137589	+	0.990489i	$0.456065\pi$
$398$		−	135.055i		−	0.339334i
$399$	−221.528	−	32.1886i	−0.555207	−	0.0806732i
$400$	634.826			1.58707
$401$		−	377.219i		−	0.940697i	−0.882481	−	0.470348i	$-0.844128\pi$
$401$		−	377.219i		−	0.940697i	0.882481	−	0.470348i	$-0.155872\pi$
$402$	6.15152	−	42.3358i	0.0153023	−	0.105313i
$403$	52.0273			0.129100
$404$			182.839i			0.452573i
$405$	−399.336	+	613.293i	−0.986016	+	1.51430i
$406$	−45.9675			−0.113220
$407$			35.9779i			0.0883979i
$408$	412.002	+	59.8650i	1.00981	+	0.146728i
$409$	355.736			0.869770			0.434885	−	0.900486i	$-0.356789\pi$
$409$	355.736			0.869770			0.434885	+	0.900486i	$0.356789\pi$
$410$		−	255.119i		−	0.622241i
$411$	79.0953	−	544.348i	0.192446	−	1.32445i
$412$	−78.1538			−0.189694
$413$			69.4176i			0.168081i
$414$	−439.306	−	130.418i	−1.06113	−	0.315020i
$415$	−874.256			−2.10664
$416$		−	265.737i		−	0.638790i
$417$	640.206	+	93.0237i	1.53527	+	0.223079i
$418$	−17.8138			−0.0426167
$419$			177.237i			0.422999i	0.977378	+	0.211499i	$0.0678347\pi$
$419$			177.237i			0.422999i	−0.977378	+	0.211499i	$0.932165\pi$
$420$	21.9744	−	151.232i	0.0523200	−	0.360075i
$421$	−581.902			−1.38219			−0.691095	−	0.722764i	$-0.742871\pi$
$421$	−581.902			−1.38219			−0.691095	+	0.722764i	$0.742871\pi$
$422$			362.244i			0.858397i
$423$	135.083	−	455.019i	0.319345	−	1.07569i
$424$	−341.526			−0.805486
$425$		−	908.640i		−	2.13798i
$426$	−512.214	−	74.4261i	−1.20238	−	0.174709i
$427$	443.538			1.03873
$428$		−	64.8314i		−	0.151475i
$429$	6.09060	−	41.9166i	0.0141972	−	0.0977077i
$430$	−1051.53			−2.44543
$431$			69.7927i			0.161932i	0.996717	+	0.0809661i	$0.0258005\pi$
$431$			69.7927i			0.161932i	−0.996717	+	0.0809661i	$0.974199\pi$
$432$	−274.736	−	126.959i	−0.635964	−	0.293886i
$433$	−121.877			−0.281472			−0.140736	−	0.990047i	$-0.544947\pi$
$433$	−121.877			−0.281472			−0.140736	+	0.990047i	$0.544947\pi$
$434$			30.0346i			0.0692041i
$435$	−121.128	−	17.6002i	−0.278454	−	0.0404602i
$436$	69.6291			0.159700
$437$		−	373.236i		−	0.854086i
$438$	107.187	−	737.677i	0.244718	−	1.68419i
$439$	−736.653			−1.67802			−0.839012	−	0.544113i	$-0.816866\pi$
$439$	−736.653			−1.67802			−0.839012	+	0.544113i	$0.816866\pi$
$440$		−	62.5745i		−	0.142215i
$441$	−128.198	−	38.0586i	−0.290699	−	0.0863008i
$442$	492.879			1.11511
$443$		−	365.675i		−	0.825451i	−0.910855	−	0.412725i	$-0.864577\pi$
$443$		−	365.675i		−	0.825451i	0.910855	−	0.412725i	$-0.135423\pi$
$444$	−128.718	−	18.7031i	−0.289905	−	0.0421240i
$445$	−421.781			−0.947822
$446$			501.005i			1.12333i
$447$	−40.4923	+	278.675i	−0.0905868	+	0.623434i
$448$	415.393			0.927217
$449$			463.352i			1.03196i	0.856599	+	0.515982i	$0.172573\pi$
$449$			463.352i			1.03196i	−0.856599	+	0.515982i	$0.827427\pi$
$450$	−252.717	+	851.260i	−0.561592	+	1.89169i
$451$	−12.9774			−0.0287747
$452$		−	58.7886i		−	0.130063i
$453$	43.3696	+	6.30173i	0.0957387	+	0.0139111i
$454$	284.144			0.625868
$455$		−	930.916i		−	2.04597i
$456$	47.6496	−	327.933i	0.104495	−	0.719151i
$457$	−138.737			−0.303581			−0.151791	−	0.988413i	$-0.548504\pi$
$457$	−138.737			−0.303581			−0.151791	+	0.988413i	$0.548504\pi$
$458$			342.758i			0.748379i
$459$	−181.718	+	393.236i	−0.395901	+	0.856723i
$460$	254.799			0.553910
$461$		−	457.805i		−	0.993069i	−0.868017	−	0.496535i	$-0.834606\pi$
$461$		−	457.805i		−	0.993069i	0.868017	−	0.496535i	$-0.165394\pi$
$462$	24.1978	+	3.51602i	0.0523763	+	0.00761043i
$463$	310.128			0.669824			0.334912	−	0.942249i	$-0.391293\pi$
$463$	310.128			0.669824			0.334912	+	0.942249i	$0.391293\pi$
$464$		−	50.6180i		−	0.109090i
$465$	−11.4997	+	79.1433i	−0.0247306	+	0.170201i
$466$	451.309			0.968474
$467$		−	623.759i		−	1.33567i	−0.744308	−	0.667836i	$-0.767221\pi$
$467$		−	623.759i		−	1.33567i	0.744308	−	0.667836i	$-0.232779\pi$
$468$	146.798	+	43.5805i	0.313671	+	0.0931208i
$469$	−47.8275			−0.101978
$470$		−	830.135i		−	1.76624i
$471$	−751.568	−	109.205i	−1.59569	−	0.231858i
$472$	−102.761			−0.217713
$473$			53.4894i			0.113086i
$474$	5.51670	−	37.9669i	0.0116386	−	0.0800989i
$475$	−723.233			−1.52260
$476$		−	90.4568i		−	0.190035i
$477$	101.135	−	340.665i	0.212022	−	0.714183i
$478$	−797.862			−1.66917
$479$			677.425i			1.41425i	0.707089	+	0.707125i	$0.250008\pi$
$479$			677.425i			1.41425i	−0.707089	+	0.707125i	$0.749992\pi$
$480$	404.235	+	58.7366i	0.842157	+	0.122368i
$481$	−792.330			−1.64726
$482$		−	83.9436i		−	0.174157i
$483$	−73.6679	+	506.995i	−0.152521	+	1.04968i
$484$	116.135			0.239948
$485$			876.628i			1.80748i
$486$	279.612	−	317.862i	0.575334	−	0.654038i
$487$	551.614			1.13268			0.566338	−	0.824173i	$-0.308360\pi$
$487$	551.614			1.13268			0.566338	+	0.824173i	$0.308360\pi$
$488$			656.580i			1.34545i
$489$	259.499	+	37.7060i	0.530674	+	0.0771084i
$490$	−233.884			−0.477315
$491$			859.084i			1.74966i	0.484428	+	0.874831i	$0.339028\pi$
$491$			859.084i			1.74966i	−0.484428	+	0.874831i	$0.660972\pi$
$492$	6.74627	−	46.4290i	0.0137119	−	0.0943679i
$493$	−72.4506			−0.146959
$494$		−	392.307i		−	0.794143i
$495$	62.4168	+	18.5299i	0.126095	+	0.0374342i
$496$	−33.0732			−0.0666798
$497$			578.656i			1.16430i
$498$	500.466	+	72.7192i	1.00495	+	0.146023i
$499$	−483.732			−0.969402			−0.484701	−	0.874680i	$-0.661072\pi$
$499$	−483.732			−0.969402			−0.484701	+	0.874680i	$0.661072\pi$
$500$		−	275.783i		−	0.551565i
$501$	7.34742	−	50.5662i	0.0146655	−	0.100931i
$502$	454.077			0.904536
$503$		−	707.572i		−	1.40670i	−0.710842	−	0.703352i	$-0.751686\pi$
$503$		−	707.572i		−	1.40670i	0.710842	−	0.703352i	$-0.248314\pi$
$504$	−129.452	+	436.052i	−0.256850	+	0.865183i
$505$	−1712.07			−3.39023
$506$			40.7691i			0.0805714i
$507$	421.385	+	61.2284i	0.831133	+	0.120766i
$508$	43.1848			0.0850094
$509$			770.531i			1.51381i	0.653523	+	0.756907i	$0.273290\pi$
$509$			770.531i			1.51381i	−0.653523	+	0.756907i	$0.726710\pi$
$510$	−108.942	+	749.761i	−0.213613	+	1.47012i
$511$	−833.366			−1.63085
$512$			556.752i			1.08741i
$513$	312.996	+	144.639i	0.610129	+	0.281947i
$514$	−231.372			−0.450140
$515$		−	731.815i		−	1.42100i
$516$	−191.368	−	27.8064i	−0.370869	−	0.0538883i
$517$	−42.2273			−0.0816777
$518$		−	457.401i		−	0.883013i
$519$	−79.3874	+	546.358i	−0.152962	+	1.05271i
$520$	1378.06			2.65011
$521$			249.030i			0.477985i	0.971021	+	0.238993i	$0.0768171\pi$
$521$			249.030i			0.477985i	−0.971021	+	0.238993i	$0.923183\pi$
$522$	67.8753	+	20.1504i	0.130029	+	0.0386023i
$523$	−347.232			−0.663924			−0.331962	−	0.943293i	$-0.607711\pi$
$523$	−347.232			−0.663924			−0.331962	+	0.943293i	$0.607711\pi$
$524$		−	70.5399i		−	0.134618i
$525$	982.424	+	142.749i	1.87128	+	0.271903i
$526$	−28.9269			−0.0549940
$527$			47.3383i			0.0898260i
$528$	−3.87173	+	26.6459i	−0.00733282	+	0.0504658i
$529$	−325.198			−0.614741
$530$		−	621.509i		−	1.17266i
$531$	30.4300	−	102.502i	0.0573070	−	0.193035i
$532$	−71.9991			−0.135337
$533$		−	285.797i		−	0.536204i
$534$	241.448	+	35.0831i	0.452149	+	0.0656986i
$535$	607.067			1.13470
$536$		−	70.8002i		−	0.132090i
$537$	−142.570	+	981.195i	−0.265494	+	1.82718i
$538$	624.871			1.16147
$539$			11.8972i			0.0220728i
$540$	−98.7414	+	213.675i	−0.182855	+	0.395694i
$541$	316.663			0.585329			0.292665	−	0.956215i	$-0.405458\pi$
$541$	316.663			0.585329			0.292665	+	0.956215i	$0.405458\pi$
$542$		−	239.392i		−	0.441683i
$543$	−970.406	−	141.003i	−1.78712	−	0.259674i
$544$	241.787			0.444462
$545$			651.991i			1.19631i
$546$	−77.4321	+	532.901i	−0.141817	+	0.976010i
$547$	−139.866			−0.255697			−0.127848	−	0.991794i	$-0.540807\pi$
$547$	−139.866			−0.255697			−0.127848	+	0.991794i	$0.540807\pi$
$548$		−	176.919i		−	0.322846i
$549$	−654.925	−	194.430i	−1.19294	−	0.354153i
$550$	78.9999			0.143636
$551$			57.6671i			0.104659i
$552$	−750.517	−	109.052i	−1.35963	−	0.197559i
$553$	−42.8918			−0.0775621
$554$		−	481.044i		−	0.868311i
$555$	175.131	−	1205.28i	0.315552	−	2.17168i
$556$	208.074			0.374235
$557$		−	744.281i		−	1.33623i	−0.744057	−	0.668116i	$-0.767101\pi$
$557$		−	744.281i		−	1.33623i	0.744057	−	0.668116i	$-0.232899\pi$
$558$	13.1660	−	44.3489i	0.0235950	−	0.0794783i
$559$	−1177.98			−2.10730
$560$			591.773i			1.05674i
$561$	38.1389	+	5.54169i	0.0679837	+	0.00987823i
$562$	724.310			1.28881
$563$		−	131.551i		−	0.233660i	−0.993152	−	0.116830i	$-0.962727\pi$
$563$		−	131.551i		−	0.233660i	0.993152	−	0.116830i	$-0.0372733\pi$
$564$	21.9518	−	151.076i	0.0389216	−	0.267865i
$565$	550.483			0.974307
$566$			161.018i			0.284485i
$567$	−396.619	−	258.252i	−0.699505	−	0.455472i
$568$	−856.599			−1.50810
$569$		−	889.439i		−	1.56316i	−0.623804	−	0.781581i	$-0.714414\pi$
$569$		−	889.439i		−	1.56316i	0.623804	−	0.781581i	$-0.285586\pi$
$570$	596.773	+	86.7128i	1.04697	+	0.152128i
$571$	732.613			1.28304			0.641518	−	0.767108i	$-0.278305\pi$
$571$	732.613			1.28304			0.641518	+	0.767108i	$0.278305\pi$
$572$		−	13.6234i		−	0.0238171i
$573$	−107.481	+	739.705i	−0.187576	+	1.29093i
$574$	164.986			0.287433
$575$			1655.21i			2.87863i
$576$	−613.367	−	182.093i	−1.06487	−	0.316133i
$577$	765.276			1.32630			0.663151	−	0.748486i	$-0.269219\pi$
$577$	765.276			1.32630			0.663151	+	0.748486i	$0.269219\pi$
$578$		−	55.0244i		−	0.0951979i
$579$	−60.9961	−	8.86290i	−0.105347	−	0.0153073i
$580$	−39.3679			−0.0678757
$581$		−	565.385i		−	0.973124i
$582$	72.9165	−	501.824i	0.125286	−	0.862240i
$583$	−31.6150			−0.0542281
$584$		−	1233.65i		−	2.11242i
$585$	−408.078	+	1374.59i	−0.697570	+	2.34972i
$586$	580.520			0.990648
$587$			619.690i			1.05569i	0.849341	+	0.527845i	$0.177000\pi$
$587$			619.690i			1.05569i	−0.849341	+	0.527845i	$0.823000\pi$
$588$	−42.5646	−	6.18475i	−0.0723887	−	0.0105183i
$589$	37.6790			0.0639711
$590$		−	187.004i		−	0.316956i
$591$	98.5407	−	678.175i	0.166736	−	1.14750i
$592$	503.675			0.850803
$593$		−	519.572i		−	0.876175i	−0.898932	−	0.438088i	$-0.855656\pi$
$593$		−	519.572i		−	0.876175i	0.898932	−	0.438088i	$-0.144344\pi$
$594$	−34.1891	−	15.7991i	−0.0575574	−	0.0265979i
$595$	847.017			1.42356
$596$			90.5727i			0.151968i
$597$	230.149	+	33.4413i	0.385509	+	0.0560155i
$598$	−897.845			−1.50141
$599$			497.054i			0.829806i	0.909866	+	0.414903i	$0.136185\pi$
$599$			497.054i			0.829806i	−0.909866	+	0.414903i	$0.863815\pi$
$600$	−211.315	+	1454.31i	−0.352191	+	2.42384i
$601$	−7.61122			−0.0126643			−0.00633213	−	0.999980i	$-0.502016\pi$
$601$	−7.61122			−0.0126643			−0.00633213	+	0.999980i	$0.502016\pi$
$602$		−	680.031i		−	1.12962i
$603$	70.6218	+	20.9657i	0.117117	+	0.0347691i
$604$	14.0956			0.0233372
$605$			1087.46i			1.79745i
$606$	980.070	+	142.407i	1.61728	+	0.234995i
$607$	−30.0851			−0.0495636			−0.0247818	−	0.999693i	$-0.507889\pi$
$607$	−30.0851			−0.0495636			−0.0247818	+	0.999693i	$0.507889\pi$
$608$		−	192.451i		−	0.316530i
$609$	11.3821	−	78.3337i	0.0186898	−	0.128627i
$610$	−1194.84			−1.95876
$611$		−	929.959i		−	1.52203i
$612$	−39.6528	+	133.568i	−0.0647922	+	0.218248i
$613$	145.450			0.237276			0.118638	−	0.992938i	$-0.462147\pi$
$613$	145.450			0.237276			0.118638	+	0.992938i	$0.462147\pi$
$614$		−	363.272i		−	0.591649i
$615$	434.751	+	63.1706i	0.706912	+	0.102716i
$616$	40.4672			0.0656935
$617$			921.267i			1.49314i	0.665307	+	0.746570i	$0.268301\pi$
$617$			921.267i			1.49314i	−0.665307	+	0.746570i	$0.731699\pi$
$618$	−60.8711	+	418.926i	−0.0984970	+	0.677874i
$619$	−556.550			−0.899112			−0.449556	−	0.893252i	$-0.648418\pi$
$619$	−556.550			−0.899112			−0.449556	+	0.893252i	$0.648418\pi$
$620$			25.7225i			0.0414879i
$621$	331.025	−	716.333i	0.533051	−	1.15352i
$622$	−187.331			−0.301175
$623$		−	272.767i		−	0.437829i
$624$	−586.814	−	85.2658i	−0.940408	−	0.136644i
$625$	1166.53			1.86644
$626$			9.66104i			0.0154330i
$627$	4.41091	−	30.3567i	0.00703494	−	0.0484157i
$628$	−244.268			−0.388962
$629$		−	720.921i		−	1.14614i
$630$	−793.528	−	235.578i	−1.25957	−	0.373933i
$631$	272.456			0.431784			0.215892	−	0.976417i	$-0.430734\pi$
$631$	272.456			0.431784			0.215892	+	0.976417i	$0.430734\pi$
$632$		−	63.4938i		−	0.100465i
$633$	−617.304	−	89.6960i	−0.975203	−	0.141700i
$634$	−252.109			−0.397648
$635$			404.373i			0.636807i
$636$	16.4350	−	113.108i	0.0258411	−	0.177843i
$637$	−262.009			−0.411317
$638$		−	6.29907i		−	0.00987315i
$639$	253.661	−	854.440i	0.396965	−	1.33715i
$640$	−574.386			−0.897478
$641$		−	1077.81i		−	1.68146i	−0.541457	−	0.840729i	$-0.682127\pi$
$641$		−	1077.81i		−	1.68146i	0.541457	−	0.840729i	$-0.317873\pi$
$642$	−347.514	−	50.4948i	−0.541300	−	0.0786524i
$643$	850.278			1.32236			0.661180	−	0.750227i	$-0.270056\pi$
$643$	850.278			1.32236			0.661180	+	0.750227i	$0.270056\pi$
$644$			164.779i			0.255869i
$645$	260.373	−	1791.93i	0.403679	−	2.77819i
$646$	356.950			0.552554
$647$			1076.16i			1.66331i	0.555294	+	0.831654i	$0.312606\pi$
$647$			1076.16i			1.66331i	−0.555294	+	0.831654i	$0.687394\pi$
$648$	382.297	−	587.125i	0.589965	−	0.906057i
$649$	−9.51252			−0.0146572
$650$			1739.79i			2.67660i
$651$	−51.1823	−	7.43693i	−0.0786210	−	0.0114239i
$652$	84.3404			0.129356
$653$		−	1015.83i		−	1.55564i	−0.628487	−	0.777820i	$-0.716325\pi$
$653$		−	1015.83i		−	1.55564i	0.628487	−	0.777820i	$-0.283675\pi$
$654$	54.2315	−	373.231i	0.0829228	−	0.570690i
$655$	660.520			1.00843
$656$			181.678i			0.276948i
$657$	1230.54	+	365.316i	1.87297	+	0.556036i
$658$	536.852			0.815884
$659$			395.964i			0.600856i	0.953804	+	0.300428i	$0.0971295\pi$
$659$			395.964i			0.600856i	−0.953804	+	0.300428i	$0.902870\pi$
$660$	20.7237	+	3.01122i	0.0313996	+	0.00456245i
$661$	−612.375			−0.926437			−0.463218	−	0.886244i	$-0.653305\pi$
$661$	−612.375			−0.926437			−0.463218	+	0.886244i	$0.653305\pi$
$662$			734.464i			1.10946i
$663$	−122.043	+	839.920i	−0.184077	+	1.26685i
$664$	836.953			1.26047
$665$		−	674.184i		−	1.01381i
$666$	−200.507	+	675.395i	−0.301062	+	1.01411i
$667$	131.979			0.197869
$668$		−	16.4346i		−	0.0246027i
$669$	−853.768	−	124.055i	−1.27618	−	0.185433i
$670$	128.842			0.192302
$671$			60.7794i			0.0905803i
$672$	−37.9852	+	261.421i	−0.0565256	+	0.389019i
$673$	−644.867			−0.958198			−0.479099	−	0.877761i	$-0.659036\pi$
$673$	−644.867			−0.958198			−0.479099	+	0.877761i	$0.659036\pi$
$674$			292.475i			0.433939i
$675$	−1388.07	−	641.440i	−2.05639	−	0.950281i
$676$	136.955			0.202596
$677$			342.388i			0.505743i	0.967500	+	0.252872i	$0.0813750\pi$
$677$			342.388i			0.505743i	−0.967500	+	0.252872i	$0.918625\pi$
$678$	−315.123	−	45.7883i	−0.464783	−	0.0675344i
$679$	−566.919			−0.834932
$680$			1253.86i			1.84391i
$681$	−70.3576	+	484.213i	−0.103315	+	0.711032i
$682$	−4.11573			−0.00603480
$683$			389.823i			0.570752i	0.958416	+	0.285376i	$0.0921184\pi$
$683$			389.823i			0.570752i	−0.958416	+	0.285376i	$0.907882\pi$
$684$	106.314	+	31.5617i	0.155429	+	0.0461428i
$685$	1656.63			2.41844
$686$		−	650.049i		−	0.947594i
$687$	−584.097	−	84.8710i	−0.850214	−	0.123539i
$688$	748.829			1.08841
$689$		−	696.246i		−	1.01052i
$690$	198.454	−	1365.79i	0.287614	−	1.97941i
$691$	−541.582			−0.783766			−0.391883	−	0.920015i	$-0.628176\pi$
$691$	−541.582			−0.783766			−0.391883	+	0.920015i	$0.628176\pi$
$692$			177.573i			0.256608i
$693$	−11.9834	+	40.3652i	−0.0172920	+	0.0582471i
$694$	115.578			0.166539
$695$			1948.36i			2.80340i
$696$	115.959	+	16.8492i	0.166608	+	0.0242087i
$697$	260.039			0.373084
$698$			505.380i			0.724040i
$699$	−111.750	+	769.081i	−0.159871	+	1.10026i
$700$	319.299			0.456142
$701$		−	437.338i		−	0.623877i	−0.950102	−	0.311938i	$-0.899022\pi$
$701$		−	437.338i		−	0.623877i	0.950102	−	0.311938i	$-0.100978\pi$
$702$	347.939	−	752.936i	0.495640	−	1.07256i
$703$	−573.818			−0.816241
$704$			56.9227i			0.0808561i
$705$	1414.64	+	205.552i	2.00659	+	0.291563i
$706$	−423.486			−0.599838
$707$		−	1107.20i		−	1.56606i
$708$	4.94506	−	34.0328i	0.00698455	−	0.0480689i
$709$	−333.313			−0.470117			−0.235059	−	0.971981i	$-0.575528\pi$
$709$	−333.313			−0.470117			−0.235059	+	0.971981i	$0.575528\pi$
$710$		−	1558.84i		−	2.19555i
$711$	63.3338	+	18.8021i	0.0890771	+	0.0264446i
$712$	403.784			0.567113
$713$		−	86.2332i		−	0.120944i
$714$	−484.874	−	70.4535i	−0.679095	−	0.0986744i
$715$	127.566			0.178415
$716$			318.900i			0.445391i
$717$	197.561	−	1359.65i	0.275538	−	1.89630i
$718$	168.097			0.234118
$719$			500.871i			0.696622i	0.937379	+	0.348311i	$0.113245\pi$
$719$			500.871i			0.696622i	−0.937379	+	0.348311i	$0.886755\pi$
$720$	259.411	−	873.809i	0.360293	−	1.21362i
$721$	473.267			0.656404
$722$			344.803i			0.477566i
$723$	143.049	+	20.7855i	0.197855	+	0.0287489i
$724$	−315.394			−0.435626
$725$		−	255.740i		−	0.352745i
$726$	90.4530	−	622.514i	0.124591	−	0.857457i
$727$	−421.249			−0.579435			−0.289718	−	0.957112i	$-0.593561\pi$
$727$	−421.249			−0.579435			−0.289718	+	0.957112i	$0.593561\pi$
$728$			891.196i			1.22417i
$729$	472.438	+	555.197i	0.648063	+	0.761587i
$730$	2245.00			3.07534
$731$		−	1071.82i		−	1.46623i
$732$	−217.449	−	31.5960i	−0.297062	−	0.0431640i
$733$	452.818			0.617760			0.308880	−	0.951101i	$-0.400046\pi$
$733$	452.818			0.617760			0.308880	+	0.951101i	$0.400046\pi$
$734$		−	1152.88i		−	1.57068i
$735$	57.9127	−	398.565i	0.0787927	−	0.542265i
$736$	−440.448			−0.598435
$737$		−	6.55395i		−	0.00889274i
$738$	−243.618	−	72.3237i	−0.330106	−	0.0979997i
$739$	1283.57			1.73690			0.868449	−	0.495779i	$-0.165118\pi$
$739$	1283.57			1.73690			0.868449	+	0.495779i	$0.165118\pi$
$740$		−	391.731i		−	0.529367i
$741$	668.535	+	97.1400i	0.902206	+	0.131093i
$742$	401.933			0.541688
$743$			17.1655i			0.0231029i	0.999933	+	0.0115515i	$0.00367703\pi$
$743$			17.1655i			0.0231029i	−0.999933	+	0.0115515i	$0.996323\pi$
$744$	11.0091	−	75.7664i	0.0147971	−	0.101837i
$745$	−848.103			−1.13839
$746$			145.867i			0.195532i
$747$	−247.843	+	834.844i	−0.331785	+	1.11760i
$748$	12.3956			0.0165716
$749$			392.593i			0.524156i
$750$	−1478.27	−	214.797i	−1.97103	−	0.286396i
$751$	68.5486			0.0912765			0.0456382	−	0.998958i	$-0.485468\pi$
$751$	68.5486			0.0912765			0.0456382	+	0.998958i	$0.485468\pi$
$752$			591.165i			0.786123i
$753$	−112.435	+	773.798i	−0.149316	+	1.02762i
$754$	138.722			0.183982
$755$			131.988i			0.174819i
$756$	−138.184	−	63.8565i	−0.182784	−	0.0844663i
$757$	863.530			1.14073			0.570363	−	0.821393i	$-0.306802\pi$
$757$	863.530			1.14073			0.570363	+	0.821393i	$0.306802\pi$
$758$		−	149.506i		−	0.197238i
$759$	−69.4752	−	10.0949i	−0.0915351	−	0.0133003i
$760$	998.011			1.31317
$761$			1242.85i			1.63318i	0.577221	+	0.816588i	$0.304137\pi$
$761$			1242.85i			1.63318i	−0.577221	+	0.816588i	$0.695863\pi$
$762$	33.6351	−	231.482i	0.0441405	−	0.303783i
$763$	−421.645			−0.552615
$764$			240.413i			0.314677i
$765$	−1250.70	−	371.300i	−1.63490	−	0.485360i
$766$	−195.553			−0.255291
$767$		−	209.491i		−	0.273130i
$768$	−515.430	−	74.8934i	−0.671133	−	0.0975175i
$769$	826.477			1.07474			0.537371	−	0.843346i	$-0.319417\pi$
$769$	826.477			1.07474			0.537371	+	0.843346i	$0.319417\pi$
$770$			73.6422i			0.0956392i
$771$	57.2905	−	394.284i	0.0743068	−	0.511392i
$772$	−19.8244			−0.0256793
$773$		−	222.224i		−	0.287482i	−0.989615	−	0.143741i	$-0.954087\pi$
$773$		−	222.224i		−	0.287482i	0.989615	−	0.143741i	$-0.0459132\pi$
$774$	−298.100	+	1004.13i	−0.385142	+	1.29733i
$775$	−167.097			−0.215609
$776$		−	839.224i		−	1.08147i
$777$	779.462	+	113.258i	1.00317	+	0.145763i
$778$	−520.798			−0.669406
$779$		−	206.979i		−	0.265698i
$780$	−66.3151	+	456.392i	−0.0850194	+	0.585118i
$781$	−79.2951			−0.101530
$782$		−	816.927i		−	1.04466i
$783$	−51.1453	+	110.678i	−0.0653197	+	0.141351i
$784$	166.556			0.212444
$785$		−	2287.27i		−	2.91373i
$786$	−378.113	−	54.9409i	−0.481060	−	0.0698994i
$787$	754.707			0.958967			0.479484	−	0.877551i	$-0.340824\pi$
$787$	754.707			0.958967			0.479484	+	0.877551i	$0.340824\pi$
$788$		−	220.415i		−	0.279714i
$789$	7.16265	−	49.2946i	0.00907814	−	0.0624773i
$790$	115.546			0.146261
$791$			356.000i			0.450063i
$792$	−59.7536	−	17.7393i	−0.0754465	−	0.0223981i
$793$	−1338.52			−1.68793
$794$		−	190.323i		−	0.239702i
$795$	1059.12	+	153.893i	1.33223	+	0.193577i
$796$	74.8010			0.0939712
$797$			813.451i			1.02064i	0.859984	+	0.510320i	$0.170473\pi$
$797$			813.451i			1.02064i	−0.859984	+	0.510320i	$0.829527\pi$
$798$	−56.0775	+	385.935i	−0.0702726	+	0.483628i
$799$	846.147			1.05901
$800$			853.473i			1.06684i
$801$	−119.571	+	402.767i	−0.149277	+	0.502830i
$802$	−657.174			−0.819419
$803$		−	114.199i		−	0.142215i
$804$	23.4480	+	3.40706i	0.0291641	+	0.00423763i
$805$	−1542.96			−1.91672
$806$		−	90.6395i		−	0.112456i
$807$	−154.726	+	1064.85i	−0.191730	+	1.31952i
$808$	1639.02			2.02849
$809$			112.289i			0.138799i	0.997589	+	0.0693997i	$0.0221084\pi$
$809$			112.289i			0.138799i	−0.997589	+	0.0693997i	$0.977892\pi$
$810$	1068.45	+	695.705i	1.31908	+	0.858895i
$811$	−900.756			−1.11067			−0.555337	−	0.831626i	$-0.687411\pi$
$811$	−900.756			−1.11067			−0.555337	+	0.831626i	$0.687411\pi$
$812$		−	25.4594i		−	0.0313539i
$813$	407.951	+	59.2765i	0.501785	+	0.0729108i
$814$	62.6791			0.0770013
$815$			789.744i			0.969012i
$816$	77.5813	−	533.928i	0.0950751	−	0.654323i
$817$	−853.112			−1.04420
$818$		−	619.746i		−	0.757636i
$819$	−888.950	−	263.906i	−1.08541	−	0.322229i
$820$	141.299			0.172316
$821$			910.539i			1.10906i	0.832163	+	0.554531i	$0.187102\pi$
$821$			910.539i			1.10906i	−0.832163	+	0.554531i	$0.812898\pi$
$822$	−948.337	−	137.796i	−1.15369	−	0.167635i
$823$	594.472			0.722323			0.361161	−	0.932503i	$-0.382380\pi$
$823$	594.472			0.722323			0.361161	+	0.932503i	$0.382380\pi$
$824$			700.589i			0.850230i
$825$	−19.5613	+	134.625i	−0.0237107	+	0.163181i
$826$	120.936			0.146412
$827$		−	929.924i		−	1.12445i	−0.826983	−	0.562227i	$-0.809945\pi$
$827$		−	929.924i		−	1.12445i	0.826983	−	0.562227i	$-0.190055\pi$
$828$	72.2330	−	243.312i	0.0872380	−	0.293855i
$829$	−408.772			−0.493090			−0.246545	−	0.969131i	$-0.579295\pi$
$829$	−408.772			−0.493090			−0.246545	+	0.969131i	$0.579295\pi$
$830$			1523.09i			1.83505i
$831$	819.753	+	119.112i	0.986465	+	0.143336i
$832$	−1253.59			−1.50672
$833$		−	238.395i		−	0.286189i
$834$	162.062	−	1115.34i	0.194318	−	1.33733i
$835$	153.890			0.184300
$836$		−	9.86627i		−	0.0118018i
$837$	72.3154	+	33.4177i	0.0863983	+	0.0399256i
$838$	308.773			0.368464
$839$			236.155i			0.281471i	0.990047	+	0.140736i	$0.0449468\pi$
$839$			236.155i			0.281471i	−0.990047	+	0.140736i	$0.955053\pi$
$840$	−1355.68	−	196.984i	−1.61390	−	0.234504i
$841$	820.609			0.975753
$842$			1013.76i			1.20399i
$843$	−179.348	+	1234.31i	−0.212750	+	1.46418i
$844$	−200.631			−0.237714
$845$			1282.42i			1.51765i
$846$	−792.712	−	235.335i	−0.937012	−	0.278174i
$847$	−703.264			−0.830300
$848$			442.596i			0.521929i
$849$	−274.393	−	39.8701i	−0.323196	−	0.0469613i
$850$	−1582.99			−1.86234
$851$			1313.26i			1.54319i
$852$	41.2214	−	283.693i	0.0483819	−	0.332973i
$853$	−655.787			−0.768801			−0.384400	−	0.923167i	$-0.625592\pi$
$853$	−655.787			−0.768801			−0.384400	+	0.923167i	$0.625592\pi$
$854$		−	772.711i		−	0.904813i
$855$	−295.537	+	995.496i	−0.345657	+	1.16432i
$856$	−581.165			−0.678931
$857$		−	232.361i		−	0.271133i	−0.990768	−	0.135566i	$-0.956715\pi$
$857$		−	232.361i		−	0.271133i	0.990768	−	0.135566i	$-0.0432854\pi$
$858$	−73.0251	−	10.6108i	−0.0851109	−	0.0123669i
$859$	−54.7988			−0.0637938			−0.0318969	−	0.999491i	$-0.510155\pi$
$859$	−54.7988			−0.0637938			−0.0318969	+	0.999491i	$0.510155\pi$
$860$		−	582.399i		−	0.677208i
$861$	−40.8527	+	281.155i	−0.0474479	+	0.326545i
$862$	121.590			0.141055
$863$		−	608.530i		−	0.705133i	−0.935787	−	0.352566i	$-0.885309\pi$
$863$		−	608.530i		−	0.705133i	0.935787	−	0.352566i	$-0.114691\pi$
$864$	170.686	−	369.361i	0.197553	−	0.427501i
$865$	−1662.75			−1.92226
$866$			212.329i			0.245183i
$867$	93.7677	+	13.6247i	0.108152	+	0.0157148i
$868$	−16.6348			−0.0191646
$869$		−	5.87760i		−	0.00676364i
$870$	−30.6622	+	211.023i	−0.0352439	+	0.242555i
$871$	144.336			0.165712
$872$		−	624.172i		−	0.715793i
$873$	837.109	+	248.516i	0.958888	+	0.284668i
$874$	−650.233			−0.743974
$875$			1670.03i			1.90860i
$876$	408.567	+	59.3660i	0.466401	+	0.0677694i
$877$	985.711			1.12396			0.561979	−	0.827151i	$-0.310040\pi$
$877$	985.711			1.12396			0.561979	+	0.827151i	$0.310040\pi$
$878$			1283.36i			1.46169i
$879$	−143.744	+	989.270i	−0.163531	+	1.12545i
$880$	−81.0925			−0.0921506
$881$		−	1167.95i		−	1.32571i	−0.748748	−	0.662855i	$-0.769345\pi$
$881$		−	1167.95i		−	1.32571i	0.748748	−	0.662855i	$-0.230655\pi$
$882$	−66.3040	+	223.341i	−0.0751746	+	0.253221i
$883$	−667.997			−0.756508			−0.378254	−	0.925702i	$-0.623475\pi$
$883$	−667.997			−0.756508			−0.378254	+	0.925702i	$0.623475\pi$
$884$			272.984i			0.308805i
$885$	318.675	+	46.3044i	0.360085	+	0.0523214i
$886$	−637.061			−0.719031
$887$		−	1042.00i		−	1.17475i	−0.809317	−	0.587373i	$-0.800162\pi$
$887$		−	1042.00i		−	1.17475i	0.809317	−	0.587373i	$-0.199838\pi$
$888$	−167.659	+	1153.86i	−0.188805	+	1.29939i
$889$	−261.509			−0.294161
$890$			734.807i			0.825626i
$891$	35.3892	−	54.3500i	0.0397185	−	0.0609989i
$892$	−277.485			−0.311081
$893$		−	673.491i		−	0.754189i
$894$	485.495	+	70.5438i	0.543059	+	0.0789081i
$895$	−2986.11			−3.33643
$896$		−	371.458i		−	0.414573i
$897$	222.318	−	1530.03i	0.247846	−	1.70572i
$898$	807.230			0.898920
$899$			13.3235i			0.0148204i
$900$	−471.476	−	139.969i	−0.523862	−	0.155521i
$901$	633.497			0.703104
$902$			22.6086i			0.0250650i
$903$	1158.85	+	168.384i	1.28333	+	0.186472i
$904$	−526.995			−0.582959
$905$		−	2953.27i		−	3.26329i
$906$	10.9786	−	75.5565i	0.0121176	−	0.0833957i
$907$	1051.32			1.15912			0.579561	−	0.814929i	$-0.303224\pi$
$907$	1051.32			1.15912			0.579561	+	0.814929i	$0.303224\pi$
$908$			157.375i			0.173320i
$909$	−485.355	+	1634.89i	−0.533944	+	1.79856i
$910$	−1621.80			−1.78220
$911$			411.717i			0.451940i	0.974134	+	0.225970i	$0.0725551\pi$
$911$			411.717i			0.451940i	−0.974134	+	0.225970i	$0.927445\pi$
$912$	−424.980	−	61.7508i	−0.465987	−	0.0677092i
$913$	77.4765			0.0848593
$914$			241.700i			0.264442i
$915$	295.858	−	2036.15i	0.323342	−	2.22530i
$916$	−189.838			−0.207247
$917$			427.161i			0.465824i
$918$	685.077	+	316.581i	0.746272	+	0.344860i
$919$	972.311			1.05801			0.529005	−	0.848619i	$-0.322565\pi$
$919$	972.311			1.05801			0.529005	+	0.848619i	$0.322565\pi$
$920$		−	2284.08i		−	2.48269i
$921$	619.057	+	89.9507i	0.672157	+	0.0976664i
$922$	−797.566			−0.865039
$923$		−	1746.29i		−	1.89197i
$924$	−1.94737	+	13.4021i	−0.00210754	+	0.0145045i
$925$	2544.75			2.75108
$926$		−	540.291i		−	0.583468i
$927$	−698.824	−	207.462i	−0.753855	−	0.223800i
$928$	68.0518			0.0733317
$929$		−	1017.68i		−	1.09546i	−0.836655	−	0.547730i	$-0.815492\pi$
$929$		−	1017.68i		−	1.09546i	0.836655	−	0.547730i	$-0.184508\pi$
$930$	137.880	+	20.0343i	0.148258	+	0.0215423i
$931$	−189.751			−0.203814
$932$			249.960i			0.268198i
$933$	46.3854	−	319.232i	0.0497164	−	0.342157i
$934$	−1086.68			−1.16347
$935$			116.069i			0.124138i
$936$	390.666	−	1315.93i	0.417379	−	1.40591i
$937$	−219.001			−0.233726			−0.116863	−	0.993148i	$-0.537284\pi$
$937$	−219.001			−0.233726			−0.116863	+	0.993148i	$0.537284\pi$
$938$			83.3228i			0.0888303i
$939$	−16.4635	−	2.39219i	−0.0175330	−	0.00254760i
$940$	459.776			0.489123
$941$		−	245.823i		−	0.261235i	−0.991433	−	0.130618i	$-0.958304\pi$
$941$		−	245.823i		−	0.261235i	0.991433	−	0.130618i	$-0.0416960\pi$
$942$	−190.252	+	1309.35i	−0.201966	+	1.38996i
$943$	−473.697			−0.502330
$944$			133.171i			0.141071i
$945$	597.938	−	1293.93i	0.632739	−	1.36924i
$946$	93.1868			0.0985061
$947$			185.777i			0.196174i	0.995178	+	0.0980869i	$0.0312723\pi$
$947$			185.777i			0.196174i	−0.995178	+	0.0980869i	$0.968728\pi$
$948$	21.0282	+	3.05546i	0.0221817	+	0.00322306i
$949$	2514.96			2.65012
$950$			1259.98i			1.32630i
$951$	62.4253	−	429.622i	0.0656417	−	0.451758i
$952$	−810.877			−0.851761
$953$			940.776i			0.987173i	0.869697	+	0.493586i	$0.164314\pi$
$953$			940.776i			0.987173i	−0.869697	+	0.493586i	$0.835686\pi$
$954$	−593.491	−	176.192i	−0.622108	−	0.184688i
$955$	−2251.17			−2.35725
$956$		−	441.901i		−	0.462240i
$957$	10.7343	+	1.55973i	0.0112166	+	0.00162981i
$958$	1180.18			1.23192
$959$			1071.35i			1.11716i
$960$	277.085	−	1906.95i	0.288630	−	1.98640i
$961$	−952.295			−0.990941
$962$			1380.36i			1.43489i
$963$	172.098	−	579.700i	0.178710	−	0.601973i
$964$	46.4927			0.0482290
$965$		−	185.632i		−	0.192364i
$966$	883.263	+	128.341i	0.914351	+	0.132858i
$967$	−760.799			−0.786762			−0.393381	−	0.919375i	$-0.628695\pi$
$967$	−760.799			−0.786762			−0.393381	+	0.919375i	$0.628695\pi$
$968$		−	1041.06i		−	1.07547i
$969$	−88.3853	+	608.283i	−0.0912129	+	0.627743i
$970$	1527.22			1.57445
$971$		−	274.027i		−	0.282211i	−0.989995	−	0.141105i	$-0.954934\pi$
$971$		−	274.027i		−	0.282211i	0.989995	−	0.141105i	$-0.0450656\pi$
$972$	176.050	+	154.865i	0.181122	+	0.159326i
$973$	−1260.01			−1.29498
$974$		−	960.995i		−	0.986648i
$975$	−2964.79	−	430.793i	−3.04082	−	0.441839i
$976$	850.885			0.871809
$977$			414.944i			0.424712i	0.977192	+	0.212356i	$0.0681137\pi$
$977$			414.944i			0.424712i	−0.977192	+	0.212356i	$0.931886\pi$
$978$	65.6897	−	452.088i	0.0671673	−	0.462257i
$979$	37.3782			0.0381800
$980$		−	129.538i		−	0.132182i
$981$	622.599	+	184.833i	0.634657	+	0.188413i
$982$	1496.66			1.52409
$983$		−	1414.09i		−	1.43855i	−0.694726	−	0.719275i	$-0.744474\pi$
$983$		−	1414.09i		−	1.43855i	0.694726	−	0.719275i	$-0.255526\pi$
$984$	−416.201	−	60.4752i	−0.422968	−	0.0614585i
$985$	2063.91			2.09534
$986$			126.220i			0.128012i
$987$	−132.931	+	914.855i	−0.134682	+	0.926905i
$988$	217.282			0.219921
$989$			1952.46i			1.97417i
$990$	32.2819	−	108.740i	0.0326080	−	0.109838i
$991$	1236.77			1.24800			0.623999	−	0.781425i	$-0.285507\pi$
$991$	1236.77			1.24800			0.623999	+	0.781425i	$0.285507\pi$
$992$		−	44.4642i		−	0.0448228i
$993$	−1251.61	−	181.862i	−1.26043	−	0.183144i
$994$	1008.11			1.01419
$995$			700.420i			0.703940i
$996$	−40.2760	+	277.186i	−0.0404378	+	0.278300i
$997$	690.672			0.692750			0.346375	−	0.938096i	$-0.387412\pi$
$997$	690.672			0.692750			0.346375	+	0.938096i	$0.387412\pi$
$998$			842.735i			0.844423i
$999$	−1101.30	−	508.923i	−1.10240	−	0.509432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.15	✓	44
3.2	odd	2	inner	201.3.c.a.68.30	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.15	✓	44	1.1	even	1	trivial
201.3.c.a.68.30	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.74215i q^{2} +(2.96882 + 0.431379i) q^{3} +0.964903 q^{4} +9.03513i q^{5} +(0.751528 - 5.17214i) q^{6} -5.84306 q^{7} -8.64962i q^{8} +(8.62782 + 2.56137i) q^{9} +O(q^{10})\)	\(q-1.74215i q^{2} +(2.96882 + 0.431379i) q^{3} +0.964903 q^{4} +9.03513i q^{5} +(0.751528 - 5.17214i) q^{6} -5.84306 q^{7} -8.64962i q^{8} +(8.62782 + 2.56137i) q^{9} +15.7406 q^{10} -0.800693i q^{11} +(2.86463 + 0.416238i) q^{12} +17.6334 q^{13} +10.1795i q^{14} +(-3.89756 + 26.8237i) q^{15} -11.2094 q^{16} +16.0442i q^{17} +(4.46231 - 15.0310i) q^{18} +12.7704 q^{19} +8.71802i q^{20} +(-17.3470 - 2.52057i) q^{21} -1.39493 q^{22} -29.2267i q^{23} +(3.73126 - 25.6792i) q^{24} -56.6336 q^{25} -30.7201i q^{26} +(24.5096 + 11.3261i) q^{27} -5.63798 q^{28} +4.51569i q^{29} +(46.7310 + 6.79015i) q^{30} +2.95050 q^{31} -15.0701i q^{32} +(0.345402 - 2.37712i) q^{33} +27.9514 q^{34} -52.7928i q^{35} +(8.32501 + 2.47148i) q^{36} -44.9335 q^{37} -22.2479i q^{38} +(52.3504 + 7.60667i) q^{39} +78.1505 q^{40} -16.2077i q^{41} +(-4.39122 + 30.2211i) q^{42} -66.8040 q^{43} -0.772590i q^{44} +(-23.1424 + 77.9535i) q^{45} -50.9173 q^{46} -52.7385i q^{47} +(-33.2786 - 4.83548i) q^{48} -14.8587 q^{49} +98.6644i q^{50} +(-6.92112 + 47.6324i) q^{51} +17.0145 q^{52} -39.4845i q^{53} +(19.7318 - 42.6994i) q^{54} +7.23436 q^{55} +50.5402i q^{56} +(37.9130 + 5.50887i) q^{57} +7.86703 q^{58} -11.8804i q^{59} +(-3.76077 + 25.8823i) q^{60} -75.9085 q^{61} -5.14022i q^{62} +(-50.4129 - 14.9663i) q^{63} -71.0918 q^{64} +159.320i q^{65} +(-4.14130 - 0.601743i) q^{66} +8.18535 q^{67} +15.4811i q^{68} +(12.6078 - 86.7688i) q^{69} -91.9731 q^{70} -99.0331i q^{71} +(22.1549 - 74.6274i) q^{72} +142.625 q^{73} +78.2810i q^{74} +(-168.135 - 24.4305i) q^{75} +12.3222 q^{76} +4.67849i q^{77} +(13.2520 - 91.2025i) q^{78} +7.34065 q^{79} -101.278i q^{80} +(67.8787 + 44.1982i) q^{81} -28.2363 q^{82} +96.7619i q^{83} +(-16.7382 - 2.43210i) q^{84} -144.961 q^{85} +116.383i q^{86} +(-1.94797 + 13.4063i) q^{87} -6.92569 q^{88} +46.6823i q^{89} +(135.807 + 40.3175i) q^{90} -103.033 q^{91} -28.2009i q^{92} +(8.75950 + 1.27278i) q^{93} -91.8786 q^{94} +115.382i q^{95} +(6.50091 - 44.7404i) q^{96} +97.0243 q^{97} +25.8861i q^{98} +(2.05087 - 6.90824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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