LMFDB - Embedded newform 201.3.c.a.68.1

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			68.1
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.85580i q^{2} +(2.40297 + 1.79604i) q^{3} -10.8672 q^{4} +6.40327i q^{5} +(6.92517 - 9.26536i) q^{6} +10.8148 q^{7} +26.4786i q^{8} +(2.54849 + 8.63164i) q^{9} +O(q^{10})$	\(q-3.85580i q^{2} +(2.40297 + 1.79604i) q^{3} -10.8672 q^{4} +6.40327i q^{5} +(6.92517 - 9.26536i) q^{6} +10.8148 q^{7} +26.4786i q^{8} +(2.54849 + 8.63164i) q^{9} +24.6898 q^{10} +13.5377i q^{11} +(-26.1136 - 19.5179i) q^{12} -6.76402 q^{13} -41.6998i q^{14} +(-11.5005 + 15.3869i) q^{15} +58.6275 q^{16} -9.98515i q^{17} +(33.2819 - 9.82648i) q^{18} -11.7265 q^{19} -69.5858i q^{20} +(25.9877 + 19.4238i) q^{21} +52.1986 q^{22} -30.9889i q^{23} +(-47.5567 + 63.6273i) q^{24} -16.0019 q^{25} +26.0807i q^{26} +(-9.37882 + 25.3187i) q^{27} -117.527 q^{28} +6.49788i q^{29} +(59.3287 + 44.3438i) q^{30} +6.53048 q^{31} -120.142i q^{32} +(-24.3142 + 32.5306i) q^{33} -38.5008 q^{34} +69.2503i q^{35} +(-27.6950 - 93.8019i) q^{36} +66.8716 q^{37} +45.2150i q^{38} +(-16.2537 - 12.1484i) q^{39} -169.550 q^{40} -54.8536i q^{41} +(74.8945 - 100.203i) q^{42} -18.7534 q^{43} -147.117i q^{44} +(-55.2708 + 16.3187i) q^{45} -119.487 q^{46} +16.4001i q^{47} +(140.880 + 105.297i) q^{48} +67.9604 q^{49} +61.7003i q^{50} +(17.9337 - 23.9940i) q^{51} +73.5060 q^{52} +40.5154i q^{53} +(97.6240 + 36.1629i) q^{54} -86.6854 q^{55} +286.362i q^{56} +(-28.1783 - 21.0612i) q^{57} +25.0545 q^{58} -33.3419i q^{59} +(124.979 - 167.212i) q^{60} +59.1060 q^{61} -25.1802i q^{62} +(27.5615 + 93.3496i) q^{63} -228.733 q^{64} -43.3119i q^{65} +(125.431 + 93.7507i) q^{66} +8.18535 q^{67} +108.511i q^{68} +(55.6572 - 74.4652i) q^{69} +267.015 q^{70} -78.2499i q^{71} +(-228.554 + 67.4805i) q^{72} -54.9820 q^{73} -257.844i q^{74} +(-38.4521 - 28.7401i) q^{75} +127.434 q^{76} +146.408i q^{77} +(-46.8420 + 62.6711i) q^{78} -42.1954 q^{79} +375.408i q^{80} +(-68.0104 + 43.9953i) q^{81} -211.505 q^{82} +4.52591i q^{83} +(-282.413 - 211.083i) q^{84} +63.9377 q^{85} +72.3095i q^{86} +(-11.6704 + 15.6142i) q^{87} -358.459 q^{88} +1.91227i q^{89} +(62.9216 + 213.113i) q^{90} -73.1517 q^{91} +336.763i q^{92} +(15.6925 + 11.7290i) q^{93} +63.2356 q^{94} -75.0879i q^{95} +(215.779 - 288.696i) q^{96} +83.7894 q^{97} -262.042i q^{98} +(-116.852 + 34.5006i) 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 $

$2$		−	3.85580i		−	1.92790i	−0.266081	−	0.963951i	$-0.585729\pi$
$2$		−	3.85580i		−	1.92790i	0.266081	−	0.963951i	$-0.414271\pi$
$3$	2.40297	+	1.79604i	0.800989	+	0.598680i
$3$	2.40297	+	1.79604i	0.800989	+	0.598680i
$4$	−10.8672			−2.71680
$5$			6.40327i			1.28065i	0.768102	+	0.640327i	$0.221201\pi$
$5$			6.40327i			1.28065i	−0.768102	+	0.640327i	$0.778799\pi$
$6$	6.92517	−	9.26536i	1.15420	−	1.54423i
$7$	10.8148			1.54497			0.772487	−	0.635030i	$-0.219012\pi$
$7$	10.8148			1.54497			0.772487	+	0.635030i	$0.219012\pi$
$8$			26.4786i			3.30983i
$9$	2.54849	+	8.63164i	0.283166	+	0.959071i
$10$	24.6898			2.46898
$11$			13.5377i			1.23070i	0.788255	+	0.615349i	$0.210985\pi$
$11$			13.5377i			1.23070i	−0.788255	+	0.615349i	$0.789015\pi$
$12$	−26.1136	−	19.5179i	−2.17613	−	1.62650i
$13$	−6.76402			−0.520309			−0.260155	−	0.965567i	$-0.583774\pi$
$13$	−6.76402			−0.520309			−0.260155	+	0.965567i	$0.583774\pi$
$14$		−	41.6998i		−	2.97856i
$15$	−11.5005	+	15.3869i	−0.766702	+	1.02579i
$16$	58.6275			3.66422
$17$		−	9.98515i		−	0.587362i	−0.955904	−	0.293681i	$-0.905120\pi$
$17$		−	9.98515i		−	0.587362i	0.955904	−	0.293681i	$-0.0948803\pi$
$18$	33.2819	−	9.82648i	1.84899	−	0.545915i
$19$	−11.7265			−0.617183			−0.308592	−	0.951195i	$-0.599858\pi$
$19$	−11.7265			−0.617183			−0.308592	+	0.951195i	$0.599858\pi$
$20$		−	69.5858i		−	3.47929i
$21$	25.9877	+	19.4238i	1.23751	+	0.924945i
$22$	52.1986			2.37266
$23$		−	30.9889i		−	1.34734i	−0.739031	−	0.673671i	$-0.764717\pi$
$23$		−	30.9889i		−	1.34734i	0.739031	−	0.673671i	$-0.235283\pi$
$24$	−47.5567	+	63.6273i	−1.98153	+	2.65114i
$25$	−16.0019			−0.640077
$26$			26.0807i			1.00310i
$27$	−9.37882	+	25.3187i	−0.347364	+	0.937730i
$28$	−117.527			−4.19739
$29$			6.49788i			0.224065i	0.993705	+	0.112032i	$0.0357360\pi$
$29$			6.49788i			0.224065i	−0.993705	+	0.112032i	$0.964264\pi$
$30$	59.3287	+	44.3438i	1.97762	+	1.47813i
$31$	6.53048			0.210661			0.105330	−	0.994437i	$-0.466410\pi$
$31$	6.53048			0.210661			0.105330	+	0.994437i	$0.466410\pi$
$32$		−	120.142i		−	3.75443i
$33$	−24.3142	+	32.5306i	−0.736793	+	0.985775i
$34$	−38.5008			−1.13238
$35$			69.2503i			1.97858i
$36$	−27.6950	−	93.8019i	−0.769305	−	2.60561i
$37$	66.8716			1.80734			0.903670	−	0.428230i	$-0.140863\pi$
$37$	66.8716			1.80734			0.903670	+	0.428230i	$0.140863\pi$
$38$			45.2150i			1.18987i
$39$	−16.2537	−	12.1484i	−0.416762	−	0.311498i
$40$	−169.550			−4.23875
$41$		−	54.8536i		−	1.33789i	−0.743310	−	0.668947i	$-0.766745\pi$
$41$		−	54.8536i		−	1.33789i	0.743310	−	0.668947i	$-0.233255\pi$
$42$	74.8945	−	100.203i	1.78320	−	2.38579i
$43$	−18.7534			−0.436126			−0.218063	−	0.975935i	$-0.569974\pi$
$43$	−18.7534			−0.436126			−0.218063	+	0.975935i	$0.569974\pi$
$44$		−	147.117i		−	3.34356i
$45$	−55.2708	+	16.3187i	−1.22824	+	0.362637i
$46$	−119.487			−2.59754
$47$			16.4001i			0.348939i	0.984663	+	0.174469i	$0.0558210\pi$
$47$			16.4001i			0.348939i	−0.984663	+	0.174469i	$0.944179\pi$
$48$	140.880	+	105.297i	2.93500	+	2.19369i
$49$	67.9604			1.38695
$50$			61.7003i			1.23401i
$51$	17.9337	−	23.9940i	0.351641	−	0.470470i
$52$	73.5060			1.41358
$53$			40.5154i			0.764441i	0.924071	+	0.382220i	$0.124840\pi$
$53$			40.5154i			0.764441i	−0.924071	+	0.382220i	$0.875160\pi$
$54$	97.6240	+	36.1629i	1.80785	+	0.669683i
$55$	−86.6854			−1.57610
$56$			286.362i			5.11360i
$57$	−28.1783	−	21.0612i	−0.494357	−	0.369495i
$58$	25.0545			0.431975
$59$		−	33.3419i		−	0.565117i	−0.959250	−	0.282558i	$-0.908817\pi$
$59$		−	33.3419i		−	0.565117i	0.959250	−	0.282558i	$-0.0911831\pi$
$60$	124.979	−	167.212i	2.08298	−	2.78687i
$61$	59.1060			0.968950			0.484475	−	0.874805i	$-0.339011\pi$
$61$	59.1060			0.968950			0.484475	+	0.874805i	$0.339011\pi$
$62$		−	25.1802i		−	0.406133i
$63$	27.5615	+	93.3496i	0.437484	+	1.48174i
$64$	−228.733			−3.57395
$65$		−	43.3119i		−	0.666336i
$66$	125.431	+	93.7507i	1.90048	+	1.42046i
$67$	8.18535			0.122169
$67$	8.18535			0.122169
$68$			108.511i			1.59575i
$69$	55.6572	−	74.4652i	0.806626	−	1.07921i
$70$	267.015			3.81451
$71$		−	78.2499i		−	1.10211i	−0.834468	−	0.551056i	$-0.814225\pi$
$71$		−	78.2499i		−	1.10211i	0.834468	−	0.551056i	$-0.185775\pi$
$72$	−228.554	+	67.4805i	−3.17436	+	0.937230i
$73$	−54.9820			−0.753178			−0.376589	−	0.926380i	$-0.622903\pi$
$73$	−54.9820			−0.753178			−0.376589	+	0.926380i	$0.622903\pi$
$74$		−	257.844i		−	3.48437i
$75$	−38.4521	−	28.7401i	−0.512694	−	0.383201i
$76$	127.434			1.67677
$77$			146.408i			1.90140i
$78$	−46.8420	+	62.6711i	−0.600538	+	0.803475i
$79$	−42.1954			−0.534119			−0.267059	−	0.963680i	$-0.586052\pi$
$79$	−42.1954			−0.534119			−0.267059	+	0.963680i	$0.586052\pi$
$80$			375.408i			4.69260i
$81$	−68.0104	+	43.9953i	−0.839634	+	0.543152i
$82$	−211.505			−2.57933
$83$			4.52591i			0.0545290i	0.999628	+	0.0272645i	$0.00867964\pi$
$83$			4.52591i			0.0545290i	−0.999628	+	0.0272645i	$0.991320\pi$
$84$	−282.413	−	211.083i	−3.36206	−	2.51289i
$85$	63.9377			0.752208
$86$			72.3095i			0.840808i
$87$	−11.6704	+	15.6142i	−0.134143	+	0.179473i
$88$	−358.459			−4.07340
$89$			1.91227i			0.0214862i	0.999942	+	0.0107431i	$0.00341970\pi$
$89$			1.91227i			0.0214862i	−0.999942	+	0.0107431i	$0.996580\pi$
$90$	62.9216	+	213.113i	0.699129	+	2.36792i
$91$	−73.1517			−0.803864
$92$			336.763i			3.66046i
$93$	15.6925	+	11.7290i	0.168737	+	0.126118i
$94$	63.2356			0.672719
$95$		−	75.0879i		−	0.790399i
$96$	215.779	−	288.696i	2.24770	−	3.00725i
$97$	83.7894			0.863809			0.431904	−	0.901919i	$-0.357842\pi$
$97$	83.7894			0.863809			0.431904	+	0.901919i	$0.357842\pi$
$98$		−	262.042i		−	2.67390i
$99$	−116.852	+	34.5006i	−1.18033	+	0.348491i
$100$	173.896			1.73896
$101$		−	155.163i		−	1.53627i	−0.640288	−	0.768135i	$-0.721185\pi$
$101$		−	155.163i		−	1.53627i	0.640288	−	0.768135i	$-0.278815\pi$
$102$	−92.5160	−	69.1489i	−0.907020	−	0.677930i
$103$	51.9989			0.504844			0.252422	−	0.967617i	$-0.418773\pi$
$103$	51.9989			0.504844			0.252422	+	0.967617i	$0.418773\pi$
$104$		−	179.102i		−	1.72213i
$105$	−124.376	+	166.406i	−1.18454	+	1.58482i
$106$	156.219			1.47377
$107$		−	36.8269i		−	0.344177i	−0.985082	−	0.172088i	$-0.944949\pi$
$107$		−	36.8269i		−	0.344177i	0.985082	−	0.172088i	$-0.0550515\pi$
$108$	101.922	−	275.144i	0.943719	−	2.54763i
$109$	−97.6734			−0.896086			−0.448043	−	0.894012i	$-0.647879\pi$
$109$	−97.6734			−0.896086			−0.448043	+	0.894012i	$0.647879\pi$
$110$			334.242i			3.03856i
$111$	160.690	+	120.104i	1.44766	+	1.08202i
$112$	634.046			5.66113
$113$			63.5255i			0.562172i	0.959683	+	0.281086i	$0.0906947\pi$
$113$			63.5255i			0.562172i	−0.959683	+	0.281086i	$0.909305\pi$
$114$	−81.2079	+	108.650i	−0.712350	+	0.953071i
$115$	198.430			1.72548
$116$		−	70.6138i		−	0.608740i
$117$	−17.2380	−	58.3846i	−0.147334	−	0.499013i
$118$	−128.560			−1.08949
$119$		−	107.988i		−	0.907459i
$120$	−407.423	−	304.518i	−3.39519	−	2.53765i
$121$	−62.2685			−0.514616
$122$		−	227.901i		−	1.86804i
$123$	98.5192	−	131.811i	0.800969	−	1.07164i
$124$	−70.9681			−0.572323
$125$			57.6171i			0.460937i
$126$	359.938	−	106.272i	2.85665	−	0.843425i
$127$	−150.542			−1.18537			−0.592685	−	0.805434i	$-0.701932\pi$
$127$	−150.542			−1.18537			−0.592685	+	0.805434i	$0.701932\pi$
$128$			401.381i			3.13579i
$129$	−45.0638	−	33.6819i	−0.349332	−	0.261100i
$130$	−167.002			−1.28463
$131$		−	41.3253i		−	0.315460i	−0.987482	−	0.157730i	$-0.949582\pi$
$131$		−	41.3253i		−	0.315460i	0.987482	−	0.157730i	$-0.0504176\pi$
$132$	264.227	−	353.517i	2.00172	−	2.67816i
$133$	−126.820			−0.953532
$134$		−	31.5611i		−	0.235531i
$135$	−162.123	−	60.0552i	−1.20091	−	0.444853i
$136$	264.393			1.94407
$137$		−	80.2423i		−	0.585711i	−0.956157	−	0.292855i	$-0.905395\pi$
$137$		−	80.2423i		−	0.585711i	0.956157	−	0.292855i	$-0.0946054\pi$
$138$	−287.123	−	214.603i	−2.08060	−	1.55510i
$139$	116.647			0.839184			0.419592	−	0.907713i	$-0.362173\pi$
$139$	116.647			0.839184			0.419592	+	0.907713i	$0.362173\pi$
$140$		−	752.558i		−	5.37541i
$141$	−29.4552	+	39.4089i	−0.208902	+	0.279496i
$142$	−301.716			−2.12476
$143$		−	91.5690i		−	0.640343i
$144$	149.412	+	506.052i	1.03758	+	3.51425i
$145$	−41.6077			−0.286950
$146$			212.000i			1.45205i
$147$	163.307	+	122.059i	1.11093	+	0.830337i
$148$	−726.708			−4.91019
$149$		−	112.910i		−	0.757785i	−0.925441	−	0.378892i	$-0.876305\pi$
$149$		−	112.910i		−	0.757785i	0.925441	−	0.378892i	$-0.123695\pi$
$150$	−110.816	+	148.264i	−0.738774	+	0.988424i
$151$	111.769			0.740192			0.370096	−	0.928993i	$-0.379325\pi$
$151$	111.769			0.740192			0.370096	+	0.928993i	$0.379325\pi$
$152$		−	310.501i		−	2.04277i
$153$	86.1882	−	25.4471i	0.563322	−	0.166321i
$154$	564.519			3.66570
$155$			41.8164i			0.269783i
$156$	176.633	+	132.020i	1.13226	+	0.846280i
$157$	−276.865			−1.76347			−0.881736	−	0.471744i	$-0.843625\pi$
$157$	−276.865			−1.76347			−0.881736	+	0.471744i	$0.843625\pi$
$158$			162.697i			1.02973i
$159$	−72.7672	+	97.3570i	−0.457655	+	0.612308i
$160$	769.300			4.80813
$161$		−	335.139i		−	2.08161i
$162$	169.637	+	262.235i	1.04714	+	1.61873i
$163$	219.883			1.34898			0.674488	−	0.738286i	$-0.264364\pi$
$163$	219.883			1.34898			0.674488	+	0.738286i	$0.264364\pi$
$164$			596.106i			3.63479i
$165$	−208.302	−	155.690i	−1.26244	−	0.943578i
$166$	17.4510			0.105127
$167$			235.333i			1.40918i	0.709616	+	0.704589i	$0.248869\pi$
$167$			235.333i			1.40918i	−0.709616	+	0.704589i	$0.751131\pi$
$168$	−514.317	+	688.118i	−3.06141	+	4.09594i
$169$	−123.248			−0.729278
$170$		−	246.531i		−	1.45018i
$171$	−29.8848	−	101.219i	−0.174765	−	0.591922i
$172$	203.797			1.18487
$173$		−	196.715i		−	1.13708i	−0.822655	−	0.568541i	$-0.807508\pi$
$173$		−	196.715i		−	1.13708i	0.822655	−	0.568541i	$-0.192492\pi$
$174$	60.2052	+	44.9989i	0.346007	+	0.258614i
$175$	−173.058			−0.988903
$176$			793.680i			4.50955i
$177$	59.8833	−	80.1194i	0.338324	−	0.452652i
$178$	7.37334			0.0414232
$179$			103.199i			0.576528i	0.957551	+	0.288264i	$0.0930781\pi$
$179$			103.199i			0.576528i	−0.957551	+	0.288264i	$0.906922\pi$
$180$	600.639	−	177.339i	3.33689	−	0.985215i
$181$	−184.132			−1.01731			−0.508653	−	0.860972i	$-0.669856\pi$
$181$	−184.132			−1.01731			−0.508653	+	0.860972i	$0.669856\pi$
$182$			282.058i			1.54977i
$183$	142.030	+	106.157i	0.776118	+	0.580091i
$184$	820.543			4.45947
$185$			428.197i			2.31458i
$186$	45.2247	−	60.5072i	0.243143	−	0.325308i
$187$	135.176			0.722864
$188$		−	178.224i		−	0.947998i
$189$	−101.430	+	273.817i	−0.536668	+	1.44877i
$190$	−289.524			−1.52381
$191$			8.70945i			0.0455992i	0.999740	+	0.0227996i	$0.00725797\pi$
$191$			8.70945i			0.0455992i	−0.999740	+	0.0227996i	$0.992742\pi$
$192$	−549.636	−	410.812i	−2.86269	−	2.13965i
$193$	−286.280			−1.48332			−0.741658	−	0.670778i	$-0.765960\pi$
$193$	−286.280			−1.48332			−0.741658	+	0.670778i	$0.765960\pi$
$194$		−	323.076i		−	1.66534i
$195$	77.7898	−	104.077i	0.398922	−	0.533728i
$196$	−738.540			−3.76806
$197$			209.080i			1.06132i	0.847586	+	0.530659i	$0.178055\pi$
$197$			209.080i			1.06132i	−0.847586	+	0.530659i	$0.821945\pi$
$198$	133.028	+	450.559i	0.671857	+	2.27555i
$199$	−290.474			−1.45967			−0.729835	−	0.683624i	$-0.760403\pi$
$199$	−290.474			−1.45967			−0.729835	+	0.683624i	$0.760403\pi$
$200$		−	423.709i		−	2.11855i
$201$	19.6691	+	14.7012i	0.0978563	+	0.0731403i
$202$	−598.279			−2.96178
$203$			70.2734i			0.346174i
$204$	−194.890	+	260.748i	−0.955341	+	1.27818i
$205$	351.243			1.71338
$206$		−	200.498i		−	0.973289i
$207$	267.485	−	78.9748i	1.29220	−	0.381521i
$208$	−396.558			−1.90653
$209$		−	158.749i		−	0.759566i
$210$	641.629	+	479.570i	3.05538	+	2.28367i
$211$	167.171			0.792280			0.396140	−	0.918190i	$-0.370350\pi$
$211$	167.171			0.792280			0.396140	+	0.918190i	$0.370350\pi$
$212$		−	440.289i		−	2.07684i
$213$	140.540	−	188.032i	0.659812	−	0.882779i
$214$	−141.997			−0.663539
$215$		−	120.083i		−	0.558527i
$216$	−670.405	−	248.338i	−3.10373	−	1.14971i
$217$	70.6260			0.325465
$218$			376.609i			1.72757i
$219$	−132.120	−	98.7498i	−0.603287	−	0.450912i
$220$	942.029			4.28195
$221$			67.5397i			0.305610i
$222$	463.097	−	619.589i	2.08602	−	2.79094i
$223$	245.359			1.10026			0.550132	−	0.835077i	$-0.314577\pi$
$223$	245.359			1.10026			0.550132	+	0.835077i	$0.314577\pi$
$224$		−	1299.31i		−	5.80050i
$225$	−40.7808	−	138.123i	−0.181248	−	0.613879i
$226$	244.942			1.08381
$227$		−	260.363i		−	1.14697i	−0.819215	−	0.573486i	$-0.805591\pi$
$227$		−	260.363i		−	1.14697i	0.819215	−	0.573486i	$-0.194409\pi$
$228$	306.220	+	228.877i	1.34307	+	1.00385i
$229$	420.526			1.83636			0.918178	−	0.396168i	$-0.129660\pi$
$229$	420.526			1.83636			0.918178	+	0.396168i	$0.129660\pi$
$230$		−	765.108i		−	3.32656i
$231$	−262.954	+	351.812i	−1.13833	+	1.52300i
$232$	−172.055			−0.741616
$233$			286.876i			1.23123i	0.788048	+	0.615614i	$0.211092\pi$
$233$			286.876i			1.23123i	−0.788048	+	0.615614i	$0.788908\pi$
$234$	−225.119	+	66.4665i	−0.962049	+	0.284045i
$235$	−105.014			−0.446870
$236$			362.334i			1.53531i
$237$	−101.394	−	75.7845i	−0.427823	−	0.319766i
$238$	−416.379			−1.74949
$239$		−	80.1122i		−	0.335197i	−0.985855	−	0.167599i	$-0.946399\pi$
$239$		−	80.1122i		−	0.335197i	0.985855	−	0.167599i	$-0.0536013\pi$
$240$	−674.248	+	902.093i	−2.80937	+	3.75872i
$241$	56.9631			0.236362			0.118181	−	0.992992i	$-0.462294\pi$
$241$	56.9631			0.236362			0.118181	+	0.992992i	$0.462294\pi$
$242$			240.095i			0.992129i
$243$	−242.444	−	16.4301i	−0.997712	−	0.0676135i
$244$	−642.317			−2.63245
$245$			435.169i			1.77620i
$246$	−508.239	−	379.871i	−2.06601	−	1.54419i
$247$	79.3181			0.321126
$248$			172.918i			0.697250i
$249$	−8.12870	+	10.8756i	−0.0326454	+	0.0436771i
$250$	222.160			0.888641
$251$		−	59.7592i		−	0.238084i	−0.992889	−	0.119042i	$-0.962018\pi$
$251$		−	59.7592i		−	0.238084i	0.992889	−	0.119042i	$-0.0379824\pi$
$252$	−299.516	−	1014.45i	−1.18856	−	4.02560i
$253$	419.517			1.65817
$254$			580.461i			2.28528i
$255$	153.640	+	114.834i	0.602510	+	0.450331i
$256$	632.715			2.47154
$257$		−	2.72276i		−	0.0105944i	−0.999986	−	0.00529720i	$-0.998314\pi$
$257$		−	2.72276i		−	0.0105944i	0.999986	−	0.00529720i	$-0.00168616\pi$
$258$	−129.871	+	173.757i	−0.503374	+	0.673478i
$259$	723.204			2.79229
$260$			470.679i			1.81031i
$261$	−56.0873	+	16.5598i	−0.214894	+	0.0634474i
$262$	−159.342			−0.608177
$263$		−	417.145i		−	1.58610i	−0.609154	−	0.793052i	$-0.708491\pi$
$263$		−	417.145i		−	1.58610i	0.609154	−	0.793052i	$-0.291509\pi$
$264$	−861.365	−	643.806i	−3.26275	−	2.43866i
$265$	−259.431			−0.978985
$266$			488.992i			1.83832i
$267$	−3.43451	+	4.59512i	−0.0128633	+	0.0172102i
$268$	−88.9520			−0.331910
$269$			333.063i			1.23815i	0.785331	+	0.619077i	$0.212493\pi$
$269$			333.063i			1.23815i	−0.785331	+	0.619077i	$0.787507\pi$
$270$	−231.561	+	625.113i	−0.857633	+	2.31523i
$271$	374.542			1.38207			0.691036	−	0.722820i	$-0.257154\pi$
$271$	374.542			1.38207			0.691036	+	0.722820i	$0.257154\pi$
$272$		−	585.405i		−	2.15222i
$273$	−175.781	−	131.383i	−0.643886	−	0.481257i
$274$	−309.399			−1.12919
$275$		−	216.629i		−	0.787741i
$276$	−604.839	+	809.229i	−2.19145	+	2.93199i
$277$	158.593			0.572537			0.286269	−	0.958149i	$-0.407585\pi$
$277$	158.593			0.572537			0.286269	+	0.958149i	$0.407585\pi$
$278$		−	449.766i		−	1.61786i
$279$	16.6429	+	56.3687i	0.0596518	+	0.202038i
$280$	−1833.65			−6.54876
$281$		−	210.755i		−	0.750019i	−0.927021	−	0.375010i	$-0.877639\pi$
$281$		−	210.755i		−	0.750019i	0.927021	−	0.375010i	$-0.122361\pi$
$282$	151.953	+	113.574i	0.538841	+	0.402743i
$283$	372.946			1.31783			0.658916	−	0.752217i	$-0.271015\pi$
$283$	372.946			1.31783			0.658916	+	0.752217i	$0.271015\pi$
$284$			850.359i			2.99422i
$285$	134.861	−	180.434i	0.473196	−	0.633100i
$286$	−353.072			−1.23452
$287$		−	593.232i		−	2.06701i
$288$	1037.02	−	306.180i	3.60076	−	1.06312i
$289$	189.297			0.655006
$290$			160.431i			0.553211i
$291$	201.343	+	150.489i	0.691901	+	0.517145i
$292$	597.501			2.04624
$293$			240.296i			0.820122i	0.912058	+	0.410061i	$0.134493\pi$
$293$			240.296i			0.820122i	−0.912058	+	0.410061i	$0.865507\pi$
$294$	470.637	−	629.678i	1.60081	−	2.14176i
$295$	213.497			0.723720
$296$			1770.67i			5.98199i
$297$	−342.757	−	126.967i	−1.15406	−	0.427500i
$298$	−435.359			−1.46093
$299$			209.609i			0.701034i
$300$	417.867	+	312.325i	1.39289	+	1.04108i
$301$	−202.815			−0.673804
$302$		−	430.959i		−	1.42702i
$303$	278.679	−	372.852i	0.919733	−	1.23053i
$304$	−687.495			−2.26150
$305$			378.472i			1.24089i
$306$	−98.1188	−	332.325i	−0.320650	−	1.08603i
$307$	−29.8556			−0.0972494			−0.0486247	−	0.998817i	$-0.515484\pi$
$307$	−29.8556			−0.0972494			−0.0486247	+	0.998817i	$0.515484\pi$
$308$		−	1591.04i		−	5.16572i
$309$	124.952	+	93.3921i	0.404374	+	0.302240i
$310$	161.236			0.520116
$311$			145.222i			0.466950i	0.972363	+	0.233475i	$0.0750098\pi$
$311$			145.222i			0.466950i	−0.972363	+	0.233475i	$0.924990\pi$
$312$	321.674	−	430.376i	1.03101	−	1.37941i
$313$	368.034			1.17583			0.587913	−	0.808924i	$-0.299950\pi$
$313$	368.034			1.17583			0.587913	+	0.808924i	$0.299950\pi$
$314$			1067.54i			3.39980i
$315$	−597.743	+	176.484i	−1.89760	+	0.560266i
$316$	458.546			1.45110
$317$			421.941i			1.33104i	0.746379	+	0.665522i	$0.231791\pi$
$317$			421.941i			1.33104i	−0.746379	+	0.665522i	$0.768209\pi$
$318$	375.390	+	280.576i	1.18047	+	0.882314i
$319$	−87.9661			−0.275756
$320$		−	1464.64i		−	4.57699i
$321$	66.1426	−	88.4938i	0.206052	−	0.275682i
$322$	−1292.23			−4.01314
$323$			117.091i			0.362510i
$324$	739.084	−	478.106i	2.28112	−	1.47564i
$325$	108.237			0.333038
$326$		−	847.826i		−	2.60069i
$327$	−234.706	−	175.425i	−0.717755	−	0.536468i
$328$	1452.45			4.42820
$329$			177.364i			0.539101i
$330$	−600.311	+	803.172i	−1.81913	+	2.43385i
$331$	−161.536			−0.488024			−0.244012	−	0.969772i	$-0.578464\pi$
$331$	−161.536			−0.488024			−0.244012	+	0.969772i	$0.578464\pi$
$332$		−	49.1840i		−	0.148145i
$333$	170.422	+	577.211i	0.511776	+	1.73337i
$334$	907.396			2.71676
$335$			52.4131i			0.156457i
$336$	1523.59	+	1138.77i	4.53450	+	3.38920i
$337$	−480.835			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$337$	−480.835			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$338$			475.220i			1.40598i
$339$	−114.094	+	152.650i	−0.336561	+	0.450294i
$340$	−694.824			−2.04360
$341$			88.4074i			0.259259i
$342$	−390.280	+	115.230i	−1.14117	+	0.336930i
$343$	205.053			0.597823
$344$		−	496.565i		−	1.44350i
$345$	476.821	+	356.388i	1.38209	+	1.03301i
$346$	−758.495			−2.19218
$347$		−	180.240i		−	0.519422i	−0.965686	−	0.259711i	$-0.916373\pi$
$347$		−	180.240i		−	0.519422i	0.965686	−	0.259711i	$-0.0836274\pi$
$348$	126.825	−	169.683i	0.364440	−	0.487594i
$349$	−482.492			−1.38250			−0.691249	−	0.722616i	$-0.742939\pi$
$349$	−482.492			−1.38250			−0.691249	+	0.722616i	$0.742939\pi$
$350$			667.278i			1.90651i
$351$	63.4385	−	171.256i	0.180737	−	0.487910i
$352$	1626.44			4.62056
$353$		−	559.281i		−	1.58437i	−0.610283	−	0.792183i	$-0.708944\pi$
$353$		−	559.281i		−	1.58437i	0.610283	−	0.792183i	$-0.291056\pi$
$354$	−308.925	−	230.898i	−0.872669	−	0.652255i
$355$	501.056			1.41142
$356$		−	20.7811i		−	0.0583738i
$357$	193.950	−	259.491i	0.543277	−	0.726864i
$358$	397.913			1.11149
$359$		−	491.196i		−	1.36823i	−0.729372	−	0.684117i	$-0.760188\pi$
$359$		−	491.196i		−	1.36823i	0.729372	−	0.684117i	$-0.239812\pi$
$360$	−432.096	−	1463.49i	−1.20027	−	4.06526i
$361$	−223.490			−0.619085
$362$			709.978i			1.96127i
$363$	−149.629	−	111.837i	−0.412201	−	0.308090i
$364$	794.955			2.18394
$365$		−	352.065i		−	0.964561i
$366$	409.319	−	547.638i	1.11836	−	1.49628i
$367$	−206.828			−0.563563			−0.281781	−	0.959479i	$-0.590925\pi$
$367$	−206.828			−0.563563			−0.281781	+	0.959479i	$0.590925\pi$
$368$		−	1816.80i		−	4.93696i
$369$	473.477	−	139.794i	1.28313	−	0.378845i
$370$	1651.04			4.46228
$371$			438.167i			1.18104i
$372$	−170.534	−	127.461i	−0.458425	−	0.342638i
$373$	−589.775			−1.58117			−0.790583	−	0.612355i	$-0.790222\pi$
$373$	−589.775			−1.58117			−0.790583	+	0.612355i	$0.790222\pi$
$374$		−	521.211i		−	1.39361i
$375$	−103.483	+	138.452i	−0.275954	+	0.369205i
$376$	−434.253			−1.15493
$377$		−	43.9518i		−	0.116583i
$378$	1055.79	+	391.095i	2.79309	+	1.03464i
$379$	−448.095			−1.18231			−0.591154	−	0.806559i	$-0.701328\pi$
$379$	−448.095			−1.18231			−0.591154	+	0.806559i	$0.701328\pi$
$380$			815.996i			2.14736i
$381$	−361.748	−	270.379i	−0.949469	−	0.709657i
$382$	33.5819			0.0879108
$383$		−	428.618i		−	1.11911i	−0.828794	−	0.559553i	$-0.810973\pi$
$383$		−	428.618i		−	1.11911i	0.828794	−	0.559553i	$-0.189027\pi$
$384$	−720.895	+	964.504i	−1.87733	+	2.51173i
$385$	−937.487			−2.43503
$386$			1103.84i			2.85969i
$387$	−47.7929	−	161.873i	−0.123496	−	0.418276i
$388$	−910.558			−2.34680
$389$			548.373i			1.40970i	0.709357	+	0.704850i	$0.248985\pi$
$389$			548.373i			1.40970i	−0.709357	+	0.704850i	$0.751015\pi$
$390$	−401.300	−	299.942i	−1.02897	−	0.769082i
$391$	−309.428			−0.791377
$392$			1799.50i			4.59056i
$393$	74.2219	−	99.3033i	0.188860	−	0.252680i
$394$	806.170			2.04612
$395$		−	270.189i		−	0.684022i
$396$	1269.86	−	374.926i	3.20671	−	0.946782i
$397$	−245.862			−0.619300			−0.309650	−	0.950851i	$-0.600212\pi$
$397$	−245.862			−0.619300			−0.309650	+	0.950851i	$0.600212\pi$
$398$			1120.01i			2.81410i
$399$	−304.744	−	227.773i	−0.763769	−	0.570860i
$400$	−938.154			−2.34538
$401$		−	265.928i		−	0.663163i	−0.943427	−	0.331582i	$-0.892418\pi$
$401$		−	265.928i		−	0.663163i	0.943427	−	0.331582i	$-0.107582\pi$
$402$	56.6850	−	75.8403i	0.141007	−	0.188657i
$403$	−44.1723			−0.109609
$404$			1686.19i			4.17374i
$405$	−281.714	−	435.489i	−0.695590	−	1.07528i
$406$	270.960			0.667390
$407$			905.285i			2.22429i
$408$	635.328	+	474.860i	1.55718	+	1.16387i
$409$	559.516			1.36801			0.684004	−	0.729478i	$-0.260237\pi$
$409$	559.516			1.36801			0.684004	+	0.729478i	$0.260237\pi$
$410$		−	1354.32i		−	3.30323i
$411$	144.118	−	192.820i	0.350653	−	0.469147i
$412$	−565.083			−1.37156
$413$		−	360.587i		−	0.873091i
$414$	−304.511	−	1031.37i	−0.735535	−	2.49123i
$415$	−28.9806			−0.0698328
$416$			812.640i			1.95346i
$417$	280.298	+	209.502i	0.672177	+	0.502402i
$418$	−612.106			−1.46437
$419$			65.0703i			0.155299i	0.996981	+	0.0776496i	$0.0247415\pi$
$419$			65.0703i			0.155299i	−0.996981	+	0.0776496i	$0.975258\pi$
$420$	1351.62	−	1808.37i	3.21815	−	4.30564i
$421$	−293.200			−0.696438			−0.348219	−	0.937413i	$-0.613213\pi$
$421$	−293.200			−0.696438			−0.348219	+	0.937413i	$0.613213\pi$
$422$		−	644.579i		−	1.52744i
$423$	−141.560	+	41.7955i	−0.334657	+	0.0988074i
$424$	−1072.79			−2.53017
$425$			159.782i			0.375957i
$426$	−725.014	−	541.894i	−1.70191	−	1.27205i
$427$	639.221			1.49700
$428$			400.206i			0.935061i
$429$	164.462	−	220.037i	0.383360	−	0.512907i
$430$	−463.017			−1.07678
$431$			790.912i			1.83506i	0.397663	+	0.917532i	$0.369821\pi$
$431$			790.912i			1.83506i	−0.397663	+	0.917532i	$0.630179\pi$
$432$	−549.857	+	1484.37i	−1.27282	+	3.43605i
$433$	198.872			0.459289			0.229644	−	0.973275i	$-0.426244\pi$
$433$	198.872			0.459289			0.229644	+	0.973275i	$0.426244\pi$
$434$		−	272.320i		−	0.627465i
$435$	−99.9819	−	74.7290i	−0.229843	−	0.171791i
$436$	1061.44			2.43449
$437$			363.390i			0.831557i
$438$	−380.760	+	509.428i	−0.869315	+	1.16308i
$439$	−174.443			−0.397364			−0.198682	−	0.980064i	$-0.563666\pi$
$439$	−174.443			−0.397364			−0.198682	+	0.980064i	$0.563666\pi$
$440$		−	2295.31i		−	5.21662i
$441$	173.196	+	586.610i	0.392736	+	1.33018i
$442$	260.420			0.589185
$443$			125.310i			0.282866i	0.989948	+	0.141433i	$0.0451709\pi$
$443$			125.310i			0.282866i	−0.989948	+	0.141433i	$0.954829\pi$
$444$	−1746.25	−	1305.20i	−3.93301	−	2.93963i
$445$	−12.2448			−0.0275164
$446$		−	946.056i		−	2.12120i
$447$	202.791	−	271.319i	0.453670	−	0.606977i
$448$	−2473.70			−5.52166
$449$			397.793i			0.885953i	0.896533	+	0.442977i	$0.146078\pi$
$449$			397.793i			0.885953i	−0.896533	+	0.442977i	$0.853922\pi$
$450$	−532.575	+	157.243i	−1.18350	+	0.349428i
$451$	742.590			1.64654
$452$		−	690.345i		−	1.52731i
$453$	268.577	+	200.742i	0.592886	+	0.443138i
$454$	−1003.91			−2.21125
$455$		−	468.410i		−	1.02947i
$456$	557.672	−	746.124i	1.22297	−	1.63624i
$457$	−431.237			−0.943626			−0.471813	−	0.881699i	$-0.656400\pi$
$457$	−431.237			−0.943626			−0.471813	+	0.881699i	$0.656400\pi$
$458$		−	1621.46i		−	3.54031i
$459$	252.811	+	93.6489i	0.550787	+	0.204028i
$460$	−2156.38			−4.68779
$461$		−	275.541i		−	0.597702i	−0.954300	−	0.298851i	$-0.903397\pi$
$461$		−	275.541i		−	0.597702i	0.954300	−	0.298851i	$-0.0966034\pi$
$462$	1356.52	+	1013.90i	2.93619	+	2.19458i
$463$	−28.4715			−0.0614936			−0.0307468	−	0.999527i	$-0.509789\pi$
$463$	−28.4715			−0.0614936			−0.0307468	+	0.999527i	$0.509789\pi$
$464$			380.955i			0.821023i
$465$	−75.1039	+	100.483i	−0.161514	+	0.216094i
$466$	1106.14			2.37369
$467$		−	364.489i		−	0.780491i	−0.920711	−	0.390246i	$-0.872390\pi$
$467$		−	364.489i		−	0.780491i	0.920711	−	0.390246i	$-0.127610\pi$
$468$	187.329	+	634.478i	0.400277	+	1.35572i
$469$	88.5231			0.188749
$470$			404.915i			0.861521i
$471$	−665.297	−	497.260i	−1.41252	−	1.05575i
$472$	882.848			1.87044
$473$		−	253.878i		−	0.536739i
$474$	−292.210	+	390.956i	−0.616477	+	0.824801i
$475$	187.646			0.395045
$476$			1173.52i			2.46539i
$477$	−349.714	+	103.253i	−0.733153	+	0.216463i
$478$	−308.897			−0.646227
$479$		−	457.692i		−	0.955516i	−0.878492	−	0.477758i	$-0.841450\pi$
$479$		−	457.692i		−	0.955516i	0.878492	−	0.477758i	$-0.158550\pi$
$480$	1848.60	+	1381.69i	3.85125	+	2.87853i
$481$	−452.320			−0.940375
$482$		−	219.639i		−	0.455682i
$483$	601.923	−	805.328i	1.24622	−	1.66735i
$484$	676.685			1.39811
$485$			536.527i			1.10624i
$486$	−63.3512	+	934.816i	−0.130352	+	1.92349i
$487$	−327.075			−0.671611			−0.335806	−	0.941931i	$-0.609009\pi$
$487$	−327.075			−0.671611			−0.335806	+	0.941931i	$0.609009\pi$
$488$			1565.05i			3.20706i
$489$	528.372	+	394.919i	1.08051	+	0.807605i
$490$	1677.93			3.42434
$491$		−	173.486i		−	0.353332i	−0.984271	−	0.176666i	$-0.943469\pi$
$491$		−	173.486i		−	0.353332i	0.984271	−	0.176666i	$-0.0565313\pi$
$492$	−1070.63	+	1432.42i	−2.17608	+	2.91143i
$493$	64.8823			0.131607
$494$		−	305.835i		−	0.619099i
$495$	−220.917	−	748.237i	−0.446297	−	1.51159i
$496$	382.866			0.771907
$497$		−	846.259i		−	1.70273i
$498$	41.9342	+	31.3427i	0.0842052	+	0.0629371i
$499$	445.537			0.892860			0.446430	−	0.894818i	$-0.352695\pi$
$499$	445.537			0.892860			0.446430	+	0.894818i	$0.352695\pi$
$500$		−	626.138i		−	1.25228i
$501$	−422.667	+	565.496i	−0.843646	+	1.12874i
$502$	−230.420			−0.459003
$503$			648.303i			1.28887i	0.764658	+	0.644436i	$0.222908\pi$
$503$			648.303i			1.28887i	−0.764658	+	0.644436i	$0.777092\pi$
$504$	−2471.77	+	729.790i	−4.90431	+	1.44800i
$505$	993.553			1.96743
$506$		−	1617.57i		−	3.19679i
$507$	−296.161	−	221.358i	−0.584144	−	0.436604i
$508$	1635.97			3.22042
$509$			651.757i			1.28046i	0.768181	+	0.640232i	$0.221162\pi$
$509$			651.757i			1.28046i	−0.768181	+	0.640232i	$0.778838\pi$
$510$	442.779	−	592.406i	0.868195	−	1.16158i
$511$	−594.621			−1.16364
$512$		−	834.102i		−	1.62911i
$513$	109.981	−	296.899i	0.214387	−	0.578751i
$514$	−10.4984			−0.0204250
$515$			332.963i			0.646531i
$516$	489.718	+	366.028i	0.949066	+	0.709357i
$517$	−222.019			−0.429438
$518$		−	2788.53i		−	5.38327i
$519$	353.308	−	472.700i	0.680747	−	0.910789i
$520$	1146.84			2.20546
$521$			236.277i			0.453507i	0.973952	+	0.226754i	$0.0728113\pi$
$521$			236.277i			0.453507i	−0.973952	+	0.226754i	$0.927189\pi$
$522$	63.8512	+	216.262i	0.122320	+	0.414294i
$523$	−282.828			−0.540781			−0.270390	−	0.962751i	$-0.587153\pi$
$523$	−282.828			−0.540781			−0.270390	+	0.962751i	$0.587153\pi$
$524$			449.091i			0.857044i
$525$	−415.853	−	310.819i	−0.792100	−	0.592036i
$526$	−1608.43			−3.05785
$527$		−	65.2078i		−	0.123734i
$528$	−1425.48	+	1907.19i	−2.69977	+	3.61210i
$529$	−431.310			−0.815330
$530$			1000.31i			1.88739i
$531$	287.795	−	84.9715i	0.541987	−	0.160022i
$532$	1378.18			2.59056
$533$			371.031i			0.696118i
$534$	17.7179	+	13.2428i	0.0331795	+	0.0247993i
$535$	235.813			0.440772
$536$			216.737i			0.404360i
$537$	−185.349	+	247.983i	−0.345156	+	0.461793i
$538$	1284.23			2.38704
$539$			920.025i			1.70691i
$540$	1761.82	+	652.633i	3.26264	+	1.20858i
$541$	−913.119			−1.68783			−0.843917	−	0.536473i	$-0.819756\pi$
$541$	−913.119			−1.68783			−0.843917	+	0.536473i	$0.819756\pi$
$542$		−	1444.16i		−	2.66450i
$543$	−442.464	−	330.709i	−0.814851	−	0.609040i
$544$	−1199.63			−2.20521
$545$		−	625.429i		−	1.14758i
$546$	−506.588	+	677.777i	−0.927816	+	1.24135i
$547$	685.681			1.25353			0.626765	−	0.779208i	$-0.284379\pi$
$547$	685.681			1.25353			0.626765	+	0.779208i	$0.284379\pi$
$548$			872.011i			1.59126i
$549$	150.631	+	510.181i	0.274373	+	0.929292i
$550$	−835.278			−1.51869
$551$		−	76.1972i		−	0.138289i
$552$	1971.74	+	1473.73i	3.57199	+	2.66979i
$553$	−456.336			−0.825200
$554$		−	611.503i		−	1.10380i
$555$	−769.058	+	1028.94i	−1.38569	+	1.85395i
$556$	−1267.62			−2.27990
$557$			194.260i			0.348761i	0.984678	+	0.174380i	$0.0557922\pi$
$557$			194.260i			0.348761i	−0.984678	+	0.174380i	$0.944208\pi$
$558$	217.347	−	64.1716i	0.389510	−	0.115003i
$559$	126.848			0.226920
$560$			4059.97i			7.24995i
$561$	324.823	+	242.781i	0.579006	+	0.432764i
$562$	−812.631			−1.44596
$563$			176.510i			0.313517i	0.987637	+	0.156759i	$0.0501045\pi$
$563$			176.510i			0.313517i	−0.987637	+	0.156759i	$0.949896\pi$
$564$	320.096	−	428.265i	0.567547	−	0.759336i
$565$	−406.771			−0.719949
$566$		−	1438.01i		−	2.54065i
$567$	−735.520	+	475.801i	−1.29721	+	0.839156i
$568$	2071.95			3.64780
$569$		−	728.394i		−	1.28013i	−0.768320	−	0.640065i	$-0.778907\pi$
$569$		−	728.394i		−	1.28013i	0.768320	−	0.640065i	$-0.221093\pi$
$570$	−695.716	−	519.996i	−1.22056	−	0.912274i
$571$	−383.665			−0.671918			−0.335959	−	0.941877i	$-0.609060\pi$
$571$	−383.665			−0.671918			−0.335959	+	0.941877i	$0.609060\pi$
$572$			995.101i			1.73969i
$573$	−15.6425	+	20.9285i	−0.0272993	+	0.0365245i
$574$	−2287.39			−3.98499
$575$			495.882i			0.862403i
$576$	−582.923	−	1974.34i	−1.01202	−	3.42767i
$577$	515.630			0.893639			0.446820	−	0.894624i	$-0.352557\pi$
$577$	515.630			0.893639			0.446820	+	0.894624i	$0.352557\pi$
$578$		−	729.891i		−	1.26279i
$579$	−687.921	−	514.170i	−1.18812	−	0.888031i
$580$	452.160			0.779586
$581$			48.9469i			0.0842459i
$582$	580.256	−	776.340i	0.997004	−	1.33392i
$583$	−548.484			−0.940795
$584$		−	1455.85i		−	2.49289i
$585$	373.852	−	110.380i	0.639064	−	0.188684i
$586$	926.533			1.58111
$587$		−	740.344i		−	1.26123i	−0.776095	−	0.630616i	$-0.782802\pi$
$587$		−	740.344i		−	1.26123i	0.776095	−	0.630616i	$-0.217198\pi$
$588$	−1774.69	−	1326.45i	−3.01818	−	2.25586i
$589$	−76.5795			−0.130016
$590$		−	823.203i		−	1.39526i
$591$	−375.515	+	502.411i	−0.635389	+	0.850103i
$592$	3920.52			6.62249
$593$			904.013i			1.52447i	0.647299	+	0.762237i	$0.275899\pi$
$593$			904.013i			1.52447i	−0.647299	+	0.762237i	$0.724101\pi$
$594$	−489.561	+	1321.60i	−0.824177	+	2.22492i
$595$	691.474			1.16214
$596$			1227.02i			2.05875i
$597$	−698.000	−	521.703i	−1.16918	−	0.873874i
$598$	808.212			1.35152
$599$			340.424i			0.568320i	0.958777	+	0.284160i	$0.0917147\pi$
$599$			340.424i			0.568320i	−0.958777	+	0.284160i	$0.908285\pi$
$600$	760.998	−	1018.16i	1.26833	−	1.69693i
$601$	398.735			0.663452			0.331726	−	0.943376i	$-0.392369\pi$
$601$	398.735			0.663452			0.331726	+	0.943376i	$0.392369\pi$
$602$			782.014i			1.29903i
$603$	20.8603	+	70.6530i	0.0345942	+	0.117169i
$604$	−1214.62			−2.01096
$605$		−	398.722i		−	0.659045i
$606$	−1437.64	−	1074.53i	−2.37235	−	1.77316i
$607$	473.430			0.779951			0.389976	−	0.920825i	$-0.372483\pi$
$607$	473.430			0.779951			0.389976	+	0.920825i	$0.372483\pi$
$608$			1408.84i			2.31717i
$609$	−126.214	+	168.865i	−0.207248	+	0.277282i
$610$	1459.31			2.39232
$611$		−	110.931i		−	0.181556i
$612$	−936.626	+	276.539i	−1.53043	+	0.451861i
$613$	−929.293			−1.51598			−0.757988	−	0.652269i	$-0.773817\pi$
$613$	−929.293			−1.51598			−0.757988	+	0.652269i	$0.773817\pi$
$614$			115.117i			0.187487i
$615$	844.025	+	630.846i	1.37240	+	1.02577i
$616$	−3876.67			−6.29330
$617$			263.921i			0.427748i	0.976861	+	0.213874i	$0.0686082\pi$
$617$			263.921i			0.427748i	−0.976861	+	0.213874i	$0.931392\pi$
$618$	360.101	−	481.789i	0.582688	−	0.779593i
$619$	352.391			0.569290			0.284645	−	0.958633i	$-0.408124\pi$
$619$	352.391			0.569290			0.284645	+	0.958633i	$0.408124\pi$
$620$		−	454.428i		−	0.732949i
$621$	784.598	+	290.639i	1.26344	+	0.468018i
$622$	559.946			0.900234
$623$			20.6809i			0.0331956i
$624$	−952.915	−	712.233i	−1.52711	−	1.14140i
$625$	−768.987			−1.23038
$626$		−	1419.07i		−	2.26688i
$627$	285.120	−	381.469i	0.454736	−	0.608403i
$628$	3008.75			4.79101
$629$		−	667.723i		−	1.06156i
$630$	680.486	+	2304.78i	1.08014	+	3.65838i
$631$	−297.618			−0.471661			−0.235830	−	0.971794i	$-0.575781\pi$
$631$	−297.618			−0.471661			−0.235830	+	0.971794i	$0.575781\pi$
$632$		−	1117.28i		−	1.76784i
$633$	401.706	+	300.246i	0.634607	+	0.474322i
$634$	1626.92			2.56612
$635$		−	963.962i		−	1.51805i
$636$	790.777	−	1058.00i	1.24336	−	1.66352i
$637$	−459.685			−0.721641
$638$			339.180i			0.531630i
$639$	675.425	−	199.419i	1.05700	−	0.312080i
$640$	−2570.15			−4.01586
$641$		−	384.744i		−	0.600225i	−0.953904	−	0.300112i	$-0.902976\pi$
$641$		−	384.744i		−	0.600225i	0.953904	−	0.300112i	$-0.0970242\pi$
$642$	−341.215	−	255.033i	−0.531487	−	0.397247i
$643$	−813.826			−1.26567			−0.632835	−	0.774287i	$-0.718109\pi$
$643$	−813.826			−1.26567			−0.632835	+	0.774287i	$0.718109\pi$
$644$			3642.03i			5.65532i
$645$	215.674	−	288.556i	0.334379	−	0.447374i
$646$	451.478			0.698883
$647$			73.1395i			0.113044i	0.998401	+	0.0565220i	$0.0180011\pi$
$647$			73.1395i			0.113044i	−0.998401	+	0.0565220i	$0.981999\pi$
$648$	−1164.94	−	1800.82i	−1.79774	−	2.77905i
$649$	451.371			0.695488
$650$		−	417.342i		−	0.642064i
$651$	169.712	+	126.847i	0.260694	+	0.194849i
$652$	−2389.52			−3.66491
$653$			1117.85i			1.71187i	0.517083	+	0.855935i	$0.327018\pi$
$653$			1117.85i			1.71187i	−0.517083	+	0.855935i	$0.672982\pi$
$654$	−676.405	+	904.979i	−1.03426	+	1.38376i
$655$	264.617			0.403996
$656$		−	3215.93i		−	4.90234i
$657$	−140.121	−	474.585i	−0.213274	−	0.722351i
$658$	683.882			1.03933
$659$			1098.03i			1.66620i	0.553123	+	0.833100i	$0.313436\pi$
$659$			1098.03i			1.66620i	−0.553123	+	0.833100i	$0.686564\pi$
$660$	2263.66	+	1691.92i	3.42979	+	2.56352i
$661$	1057.22			1.59942			0.799712	−	0.600384i	$-0.204986\pi$
$661$	1057.22			1.59942			0.799712	+	0.600384i	$0.204986\pi$
$662$			622.851i			0.940862i
$663$	−121.304	+	162.296i	−0.182962	+	0.244790i
$664$	−119.840			−0.180482
$665$		−	812.062i		−	1.22115i
$666$	2225.61	−	657.112i	3.34176	−	0.986655i
$667$	201.362			0.301892
$668$		−	2557.41i		−	3.82846i
$669$	589.589	+	440.674i	0.881300	+	0.658706i
$670$	202.094			0.301633
$671$			800.157i			1.19248i
$672$	2333.61	−	3122.20i	3.47264	−	4.64613i
$673$	−501.151			−0.744652			−0.372326	−	0.928102i	$-0.621440\pi$
$673$	−501.151			−0.744652			−0.372326	+	0.928102i	$0.621440\pi$
$674$			1854.00i			2.75075i
$675$	150.079	−	405.148i	0.222340	−	0.600220i
$676$	1339.36			1.98131
$677$		−	876.336i		−	1.29444i	−0.762303	−	0.647220i	$-0.775931\pi$
$677$		−	876.336i		−	1.29444i	0.762303	−	0.647220i	$-0.224069\pi$
$678$	588.586	+	439.925i	0.868122	+	0.648856i
$679$	906.168			1.33456
$680$			1692.98i			2.48968i
$681$	467.621	−	625.642i	0.686668	−	0.918711i
$682$	340.882			0.499827
$683$		−	420.221i		−	0.615257i	−0.951507	−	0.307629i	$-0.900465\pi$
$683$		−	420.221i		−	0.615257i	0.951507	−	0.307629i	$-0.0995354\pi$
$684$	324.765	+	1099.97i	0.474802	+	1.60814i
$685$	513.814			0.750093
$686$		−	790.645i		−	1.15254i
$687$	1010.51	+	755.280i	1.47090	+	1.09939i
$688$	−1099.47			−1.59806
$689$		−	274.047i		−	0.397746i
$690$	1374.16	−	1838.53i	1.99154	−	2.66453i
$691$	−962.543			−1.39297			−0.696486	−	0.717571i	$-0.745254\pi$
$691$	−962.543			−1.39297			−0.696486	+	0.717571i	$0.745254\pi$
$692$			2137.75i			3.08923i
$693$	−1263.74	+	373.118i	−1.82357	+	0.538410i
$694$	−694.968			−1.00140
$695$			746.920i			1.07471i
$696$	−413.442	−	309.017i	−0.594026	−	0.443990i
$697$	−547.722			−0.785827
$698$			1860.39i			2.66532i
$699$	−515.241	+	689.354i	−0.737112	+	0.986200i
$700$	1880.66			2.68666
$701$		−	219.640i		−	0.313324i	−0.987652	−	0.156662i	$-0.949927\pi$
$701$		−	219.640i		−	0.313324i	0.987652	−	0.156662i	$-0.0500734\pi$
$702$	−660.330	−	244.606i	−0.940642	−	0.348442i
$703$	−784.168			−1.11546
$704$		−	3096.51i		−	4.39845i
$705$	−252.346	−	188.610i	−0.357938	−	0.267532i
$706$	−2156.48			−3.05450
$707$		−	1678.06i		−	2.37350i
$708$	−650.765	+	870.675i	−0.919160	+	1.22977i
$709$	318.099			0.448658			0.224329	−	0.974513i	$-0.427981\pi$
$709$	318.099			0.448658			0.224329	+	0.974513i	$0.427981\pi$
$710$		−	1931.97i		−	2.72109i
$711$	−107.535	−	364.215i	−0.151244	−	0.512258i
$712$	−50.6343			−0.0711156
$713$		−	202.372i		−	0.283832i
$714$	−1000.54	−	747.833i	−1.40132	−	1.04738i
$715$	586.342			0.820058
$716$		−	1121.48i		−	1.56631i
$717$	143.885	−	192.507i	0.200676	−	0.268489i
$718$	−1893.96			−2.63782
$719$			927.662i			1.29021i	0.764093	+	0.645106i	$0.223187\pi$
$719$			927.662i			1.29021i	−0.764093	+	0.645106i	$0.776813\pi$
$720$	−3240.39	+	956.724i	−4.50054	+	1.32878i
$721$	562.359			0.779971
$722$			861.732i			1.19353i
$723$	136.881	+	102.308i	0.189323	+	0.141505i
$724$	2001.01			2.76382
$725$		−	103.979i		−	0.143419i
$726$	−431.220	+	576.940i	−0.593967	+	0.794684i
$727$	24.0856			0.0331301			0.0165650	−	0.999863i	$-0.494727\pi$
$727$	24.0856			0.0331301			0.0165650	+	0.999863i	$0.494727\pi$
$728$		−	1936.96i		−	2.66065i
$729$	−553.075	−	474.920i	−0.758677	−	0.651467i
$730$	−1357.49			−1.85958
$731$			187.256i			0.256164i
$732$	−1543.47	−	1153.63i	−2.10856	−	1.57599i
$733$	−808.917			−1.10357			−0.551785	−	0.833986i	$-0.686053\pi$
$733$	−808.917			−1.10357			−0.551785	+	0.833986i	$0.686053\pi$
$734$			797.487i			1.08649i
$735$	−781.580	+	1045.70i	−1.06337	+	1.42272i
$736$	−3723.05			−5.05850
$737$			110.811i			0.150354i
$738$	−539.018	−	1825.63i	−0.730377	−	2.47376i
$739$	202.734			0.274335			0.137168	−	0.990548i	$-0.456200\pi$
$739$	202.734			0.274335			0.137168	+	0.990548i	$0.456200\pi$
$740$		−	4653.31i		−	6.28826i
$741$	190.599	+	142.458i	0.257218	+	0.192252i
$742$	1689.48			2.27693
$743$		−	359.863i		−	0.484338i	−0.970234	−	0.242169i	$-0.922141\pi$
$743$		−	359.863i		−	0.484338i	0.970234	−	0.242169i	$-0.0778589\pi$
$744$	−310.568	+	415.516i	−0.417430	+	0.558490i
$745$	722.993			0.970461
$746$			2274.06i			3.04833i
$747$	−39.0660	+	11.5342i	−0.0522972	+	0.0154407i
$748$	−1468.98			−1.96388
$749$		−	398.277i		−	0.531744i
$750$	533.844	+	399.008i	0.711792	+	0.532011i
$751$	−867.230			−1.15477			−0.577384	−	0.816473i	$-0.695926\pi$
$751$	−867.230			−1.15477			−0.577384	+	0.816473i	$0.695926\pi$
$752$			961.498i			1.27859i
$753$	107.330	−	143.599i	0.142536	−	0.190703i
$754$	−169.469			−0.224760
$755$			715.688i			0.947931i
$756$	1102.27	−	2975.63i	1.45802	−	3.93602i
$757$	−586.885			−0.775277			−0.387639	−	0.921811i	$-0.626709\pi$
$757$	−586.885			−0.775277			−0.387639	+	0.921811i	$0.626709\pi$
$758$			1727.77i			2.27937i
$759$	1008.09	+	753.469i	1.32818	+	0.992712i
$760$	1988.22			2.61608
$761$		−	84.8116i		−	0.111448i	−0.998446	−	0.0557238i	$-0.982253\pi$
$761$		−	84.8116i		−	0.111448i	0.998446	−	0.0557238i	$-0.0177466\pi$
$762$	−1042.53	+	1394.83i	−1.36815	+	1.83048i
$763$	−1056.32			−1.38443
$764$		−	94.6475i		−	0.123884i
$765$	162.945	+	551.887i	0.212999	+	0.721421i
$766$	−1652.67			−2.15753
$767$			225.525i			0.294035i
$768$	1520.39	+	1136.38i	1.97968	+	1.47966i
$769$	496.630			0.645812			0.322906	−	0.946431i	$-0.395340\pi$
$769$	496.630			0.645812			0.322906	+	0.946431i	$0.395340\pi$
$770$			3614.77i			4.69450i
$771$	4.89019	−	6.54270i	0.00634265	−	0.00848600i
$772$	3111.07			4.02988
$773$			330.801i			0.427945i	0.976840	+	0.213972i	$0.0686403\pi$
$773$			330.801i			0.427945i	−0.976840	+	0.213972i	$0.931360\pi$
$774$	−624.149	+	184.280i	−0.806394	+	0.238088i
$775$	−104.500			−0.134839
$776$			2218.63i			2.85906i
$777$	1737.84	+	1298.90i	2.23660	+	1.67169i
$778$	2114.42			2.71776
$779$			643.240i			0.825725i
$780$	−845.358	+	1131.03i	−1.08379	+	1.45003i
$781$	1059.32			1.35637
$782$			1193.10i			1.52570i
$783$	−164.518	−	60.9424i	−0.210112	−	0.0778320i
$784$	3984.35			5.08208
$785$		−	1772.84i		−	2.25840i
$786$	−382.894	−	286.185i	−0.487143	−	0.364103i
$787$	949.542			1.20653			0.603267	−	0.797539i	$-0.293865\pi$
$787$	949.542			1.20653			0.603267	+	0.797539i	$0.293865\pi$
$788$		−	2272.11i		−	2.88339i
$789$	749.209	−	1002.39i	0.949568	−	1.27045i
$790$	−1041.79			−1.31873
$791$			687.017i			0.868542i
$792$	−913.529	−	3094.09i	−1.15345	−	3.90668i
$793$	−399.794			−0.504154
$794$			947.996i			1.19395i
$795$	−623.404	−	465.948i	−0.784156	−	0.586098i
$796$	3156.65			3.96564
$797$			1405.84i			1.76391i	0.471334	+	0.881955i	$0.343773\pi$
$797$			1405.84i			1.76391i	−0.471334	+	0.881955i	$0.656227\pi$
$798$	−878.249	+	1175.03i	−1.10056	+	1.47247i
$799$	163.758			0.204953
$800$			1922.50i			2.40312i
$801$	−16.5060	+	4.87340i	−0.0206068	+	0.00608415i
$802$	−1025.37			−1.27851
$803$		−	744.328i		−	0.926934i
$804$	−213.749	−	159.761i	−0.265857	−	0.198708i
$805$	2145.99			2.66582
$806$			170.320i			0.211315i
$807$	−598.194	+	800.340i	−0.741257	+	0.991747i
$808$	4108.51			5.08479
$809$		−	323.493i		−	0.399868i	−0.979809	−	0.199934i	$-0.935927\pi$
$809$		−	323.493i		−	0.399868i	0.979809	−	0.199934i	$-0.0640727\pi$
$810$	−1679.16	+	1086.23i	−2.07304	+	1.34103i
$811$	693.183			0.854726			0.427363	−	0.904080i	$-0.359443\pi$
$811$	693.183			0.854726			0.427363	+	0.904080i	$0.359443\pi$
$812$		−	763.676i		−	0.940488i
$813$	900.011	+	672.691i	1.10702	+	0.827419i
$814$	3490.60			4.28821
$815$			1407.97i			1.72757i
$816$	1051.41	−	1406.71i	1.28849	−	1.72391i
$817$	219.912			0.269170
$818$		−	2157.38i		−	2.63739i
$819$	−186.426	−	631.419i	−0.227627	−	0.770963i
$820$	−3817.03			−4.65492
$821$		−	264.402i		−	0.322049i	−0.986950	−	0.161024i	$-0.948520\pi$
$821$		−	264.402i		−	0.322049i	0.986950	−	0.161024i	$-0.0514798\pi$
$822$	−743.474	−	555.692i	−0.904470	−	0.676024i
$823$	−1342.48			−1.63121			−0.815604	−	0.578610i	$-0.803595\pi$
$823$	−1342.48			−1.63121			−0.815604	+	0.578610i	$0.803595\pi$
$824$			1376.86i			1.67095i
$825$	389.074	−	520.552i	0.471605	−	0.630972i
$826$	−1390.35			−1.68323
$827$			545.386i			0.659475i	0.944073	+	0.329737i	$0.106960\pi$
$827$			545.386i			0.659475i	−0.944073	+	0.329737i	$0.893040\pi$
$828$	−2906.81	+	858.237i	−3.51065	+	1.03652i
$829$	−1050.01			−1.26660			−0.633299	−	0.773907i	$-0.718300\pi$
$829$	−1050.01			−1.26660			−0.633299	+	0.773907i	$0.718300\pi$
$830$			111.744i			0.134631i
$831$	381.093	+	284.839i	0.458596	+	0.342766i
$832$	1547.15			1.85956
$833$		−	678.595i		−	0.814639i
$834$	807.798	−	1080.77i	0.968582	−	1.29589i
$835$	−1506.90			−1.80467
$836$			1725.16i			2.06359i
$837$	−61.2482	+	165.343i	−0.0731758	+	0.197543i
$838$	250.898			0.299401
$839$			504.697i			0.601546i	0.953696	+	0.300773i	$0.0972446\pi$
$839$			504.697i			0.601546i	−0.953696	+	0.300773i	$0.902755\pi$
$840$	−4406.21	−	3293.31i	−5.24548	−	3.92061i
$841$	798.778			0.949795
$842$			1130.52i			1.34266i
$843$	378.525	−	506.438i	0.449021	−	0.600757i
$844$	−1816.68			−2.15247
$845$		−	789.191i		−	0.933954i
$846$	161.155	+	545.827i	0.190491	+	0.645186i
$847$	−673.423			−0.795068
$848$			2375.32i			2.80108i
$849$	896.177	+	669.826i	1.05557	+	0.788959i
$850$	616.087			0.724808
$851$		−	2072.27i		−	2.43510i
$852$	−1527.28	+	2043.38i	−1.79258	+	2.39834i
$853$	−1491.97			−1.74908			−0.874541	−	0.484951i	$-0.838837\pi$
$853$	−1491.97			−1.74908			−0.874541	+	0.484951i	$0.838837\pi$
$854$		−	2464.71i		−	2.88608i
$855$	648.131	−	191.361i	0.758048	−	0.223814i
$856$	975.126			1.13917
$857$		−	325.322i		−	0.379606i	−0.981822	−	0.189803i	$-0.939215\pi$
$857$		−	325.322i		−	0.379606i	0.981822	−	0.189803i	$-0.0607850\pi$
$858$	−848.420	−	634.131i	−0.988835	−	0.739081i
$859$	1228.77			1.43047			0.715235	−	0.698884i	$-0.246320\pi$
$859$	1228.77			1.43047			0.715235	+	0.698884i	$0.246320\pi$
$860$			1304.97i			1.51741i
$861$	1065.47	−	1425.52i	1.23748	−	1.65565i
$862$	3049.60			3.53782
$863$			56.7540i			0.0657636i	0.999459	+	0.0328818i	$0.0104685\pi$
$863$			56.7540i			0.0657636i	−0.999459	+	0.0328818i	$0.989532\pi$
$864$	3041.83	+	1126.79i	3.52064	+	1.30415i
$865$	1259.62			1.45621
$866$		−	766.812i		−	0.885464i
$867$	454.874	+	339.984i	0.524653	+	0.392139i
$868$	−767.508			−0.884225
$869$		−	571.227i		−	0.657339i
$870$	−288.140	+	385.510i	−0.331196	+	0.443115i
$871$	−55.3659			−0.0635659
$872$		−	2586.26i		−	2.96589i
$873$	213.537	+	723.240i	0.244601	+	0.828454i
$874$	1401.16			1.60316
$875$			623.119i			0.712136i
$876$	1435.78	+	1073.14i	1.63901	+	1.22504i
$877$	−1070.27			−1.22038			−0.610188	−	0.792257i	$-0.708906\pi$
$877$	−1070.27			−1.22038			−0.610188	+	0.792257i	$0.708906\pi$
$878$			672.618i			0.766079i
$879$	−431.580	+	577.422i	−0.490990	+	0.656908i
$880$	−5082.15			−5.77517
$881$		−	509.715i		−	0.578564i	−0.957244	−	0.289282i	$-0.906583\pi$
$881$		−	509.715i		−	0.578564i	0.957244	−	0.289282i	$-0.0934165\pi$
$882$	2261.85	−	667.811i	2.56446	−	0.757156i
$883$	1168.36			1.32317			0.661583	−	0.749872i	$-0.269885\pi$
$883$	1168.36			1.32317			0.661583	+	0.749872i	$0.269885\pi$
$884$		−	733.969i		−	0.830281i
$885$	513.027	+	383.449i	0.579691	+	0.433276i
$886$	483.169			0.545337
$887$		−	217.571i		−	0.245288i	−0.992451	−	0.122644i	$-0.960863\pi$
$887$		−	217.571i		−	0.245288i	0.992451	−	0.122644i	$-0.0391374\pi$
$888$	−3180.19	+	4254.85i	−3.58129	+	4.79150i
$889$	−1628.09			−1.83137
$890$			47.2135i			0.0530489i
$891$	−595.594	−	920.702i	−0.668456	−	1.03334i
$892$	−2666.37			−2.98920
$893$		−	192.316i		−	0.215359i
$894$	−1046.15	−	781.921i	−1.17019	−	0.874632i
$895$	−660.809			−0.738334
$896$			4340.86i			4.84471i
$897$	−376.466	+	503.684i	−0.419695	+	0.561520i
$898$	1533.81			1.70803
$899$			42.4342i			0.0472016i
$900$	443.173	+	1501.01i	0.492415	+	1.66779i
$901$	404.552			0.449003
$902$		−	2863.28i		−	3.17437i
$903$	−487.357	−	364.263i	−0.539709	−	0.403392i
$904$	−1682.07			−1.86069
$905$		−	1179.05i		−	1.30282i
$906$	774.020	−	1035.58i	0.854327	−	1.14303i
$907$	628.452			0.692890			0.346445	−	0.938070i	$-0.387389\pi$
$907$	628.452			0.692890			0.346445	+	0.938070i	$0.387389\pi$
$908$			2829.42i			3.11610i
$909$	1339.31	−	395.432i	1.47339	−	0.435019i
$910$	−1806.10			−1.98472
$911$			300.301i			0.329639i	0.986324	+	0.164819i	$0.0527042\pi$
$911$			300.301i			0.329639i	−0.986324	+	0.164819i	$0.947296\pi$
$912$	−1652.03	−	1234.77i	−1.81143	−	1.35391i
$913$	−61.2702			−0.0671087
$914$			1662.77i			1.81922i
$915$	−679.750	+	909.455i	−0.742896	+	0.993940i
$916$	−4569.94			−4.98902
$917$		−	446.926i		−	0.487378i
$918$	361.092	−	974.790i	0.393346	−	1.06186i
$919$	151.150			0.164472			0.0822360	−	0.996613i	$-0.473794\pi$
$919$	151.150			0.164472			0.0822360	+	0.996613i	$0.473794\pi$
$920$			5254.16i			5.71104i
$921$	−71.7419	−	53.6217i	−0.0778956	−	0.0582212i
$922$	−1062.43			−1.15231
$923$			529.284i			0.573439i
$924$	2857.57	−	3823.22i	3.09261	−	4.13768i
$925$	−1070.07			−1.15684
$926$			109.781i			0.118554i
$927$	132.519	+	448.836i	0.142954	+	0.484181i
$928$	780.666			0.841235
$929$		−	254.253i		−	0.273684i	−0.990593	−	0.136842i	$-0.956305\pi$
$929$		−	254.253i		−	0.273684i	0.990593	−	0.136842i	$-0.0436953\pi$
$930$	387.444	+	289.586i	0.416607	+	0.311383i
$931$	−796.936			−0.856000
$932$		−	3117.55i		−	3.34501i
$933$	−260.824	+	348.962i	−0.279554	+	0.374022i
$934$	−1405.40			−1.50471
$935$			865.567i			0.925740i
$936$	1545.94	−	456.440i	1.65165	−	0.487649i
$937$	−645.839			−0.689263			−0.344631	−	0.938738i	$-0.611996\pi$
$937$	−645.839			−0.689263			−0.344631	+	0.938738i	$0.611996\pi$
$938$		−	341.328i		−	0.363889i
$939$	884.372	+	661.003i	0.941824	+	0.703943i
$940$	1141.21			1.21406
$941$			1100.12i			1.16910i	0.811358	+	0.584549i	$0.198729\pi$
$941$			1100.12i			1.16910i	−0.811358	+	0.584549i	$0.801271\pi$
$942$	−1917.34	+	2565.26i	−2.03539	+	2.72320i
$943$	−1699.85			−1.80260
$944$		−	1954.75i		−	2.07071i
$945$	−1753.33	−	649.486i	−1.85537	−	0.687287i
$946$	−978.902			−1.03478
$947$		−	1748.54i		−	1.84640i	−0.384315	−	0.923202i	$-0.625562\pi$
$947$		−	1748.54i		−	1.84640i	0.384315	−	0.923202i	$-0.374438\pi$
$948$	1101.87	+	823.567i	1.16231	+	0.868742i
$949$	371.899			0.391885
$950$		−	723.527i		−	0.761607i
$951$	−757.822	+	1013.91i	−0.796868	+	1.06615i
$952$	2859.36			3.00353
$953$		−	1325.53i		−	1.39090i	−0.718573	−	0.695451i	$-0.755204\pi$
$953$		−	1325.53i		−	1.39090i	0.718573	−	0.695451i	$-0.244796\pi$
$954$	398.123	+	1348.43i	0.417320	+	1.41345i
$955$	−55.7690			−0.0583969
$956$			870.596i			0.910665i
$957$	−211.380	−	157.991i	−0.220877	−	0.165089i
$958$	−1764.77			−1.84214
$959$		−	867.807i		−	0.904908i
$960$	2630.54	−	3519.47i	2.74015	−	3.66612i
$961$	−918.353			−0.955622
$962$			1744.06i			1.81295i
$963$	317.877	−	93.8530i	0.330090	−	0.0974590i
$964$	−619.031			−0.642148
$965$		−	1833.13i		−	1.89962i
$966$	−3105.19	−	2320.90i	−3.21448	−	2.40258i
$967$	1586.47			1.64061			0.820304	−	0.571928i	$-0.193805\pi$
$967$	1586.47			1.64061			0.820304	+	0.571928i	$0.193805\pi$
$968$		−	1648.79i		−	1.70329i
$969$	−210.299	+	281.365i	−0.217027	+	0.290366i
$970$	2068.74			2.13272
$971$			613.852i			0.632185i	0.948728	+	0.316093i	$0.102371\pi$
$971$			613.852i			0.632185i	−0.948728	+	0.316093i	$0.897629\pi$
$972$	2634.69	+	178.549i	2.71059	+	0.183693i
$973$	1261.51			1.29652
$974$			1261.14i			1.29480i
$975$	260.091	+	194.398i	0.266760	+	0.199383i
$976$	3465.24			3.55045
$977$			1121.77i			1.14817i	0.818794	+	0.574087i	$0.194643\pi$
$977$			1121.77i			1.14817i	−0.818794	+	0.574087i	$0.805357\pi$
$978$	1522.73	−	2037.30i	1.55698	−	2.08313i
$979$	−25.8877			−0.0264430
$980$		−	4729.08i		−	4.82559i
$981$	−248.920	−	843.081i	−0.253741	−	0.859410i
$982$	−668.928			−0.681190
$983$		−	529.976i		−	0.539141i	−0.962981	−	0.269571i	$-0.913118\pi$
$983$		−	529.976i		−	0.539141i	0.962981	−	0.269571i	$-0.0868818\pi$
$984$	3490.19	+	2608.66i	3.54694	+	2.65107i
$985$	−1338.79			−1.35918
$986$		−	250.173i		−	0.253725i
$987$	−318.553	+	426.200i	−0.322749	+	0.431814i
$988$	−861.967			−0.872436
$989$			581.147i			0.587611i
$990$	−2885.06	+	851.812i	−2.91420	+	0.860416i
$991$	1003.89			1.01301			0.506503	−	0.862238i	$-0.330938\pi$
$991$	1003.89			1.01301			0.506503	+	0.862238i	$0.330938\pi$
$992$		−	784.582i		−	0.790910i
$993$	−388.165	−	290.125i	−0.390902	−	0.292170i
$994$	−3263.01			−3.28271
$995$		−	1859.99i		−	1.86933i
$996$	88.3364	−	118.188i	0.0886912	−	0.118662i
$997$	646.984			0.648930			0.324465	−	0.945898i	$-0.394816\pi$
$997$	646.984			0.648930			0.324465	+	0.945898i	$0.394816\pi$
$998$		−	1717.90i		−	1.72135i
$999$	−627.177	+	1693.10i	−0.627804	+	1.69480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.1	✓	44
3.2	odd	2	inner	201.3.c.a.68.44	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.1	✓	44	1.1	even	1	trivial
201.3.c.a.68.44	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)

\(f(q)\)	\(=\)	\(q-3.85580i q^{2} +(2.40297 + 1.79604i) q^{3} -10.8672 q^{4} +6.40327i q^{5} +(6.92517 - 9.26536i) q^{6} +10.8148 q^{7} +26.4786i q^{8} +(2.54849 + 8.63164i) q^{9} +O(q^{10})\)	\(q-3.85580i q^{2} +(2.40297 + 1.79604i) q^{3} -10.8672 q^{4} +6.40327i q^{5} +(6.92517 - 9.26536i) q^{6} +10.8148 q^{7} +26.4786i q^{8} +(2.54849 + 8.63164i) q^{9} +24.6898 q^{10} +13.5377i q^{11} +(-26.1136 - 19.5179i) q^{12} -6.76402 q^{13} -41.6998i q^{14} +(-11.5005 + 15.3869i) q^{15} +58.6275 q^{16} -9.98515i q^{17} +(33.2819 - 9.82648i) q^{18} -11.7265 q^{19} -69.5858i q^{20} +(25.9877 + 19.4238i) q^{21} +52.1986 q^{22} -30.9889i q^{23} +(-47.5567 + 63.6273i) q^{24} -16.0019 q^{25} +26.0807i q^{26} +(-9.37882 + 25.3187i) q^{27} -117.527 q^{28} +6.49788i q^{29} +(59.3287 + 44.3438i) q^{30} +6.53048 q^{31} -120.142i q^{32} +(-24.3142 + 32.5306i) q^{33} -38.5008 q^{34} +69.2503i q^{35} +(-27.6950 - 93.8019i) q^{36} +66.8716 q^{37} +45.2150i q^{38} +(-16.2537 - 12.1484i) q^{39} -169.550 q^{40} -54.8536i q^{41} +(74.8945 - 100.203i) q^{42} -18.7534 q^{43} -147.117i q^{44} +(-55.2708 + 16.3187i) q^{45} -119.487 q^{46} +16.4001i q^{47} +(140.880 + 105.297i) q^{48} +67.9604 q^{49} +61.7003i q^{50} +(17.9337 - 23.9940i) q^{51} +73.5060 q^{52} +40.5154i q^{53} +(97.6240 + 36.1629i) q^{54} -86.6854 q^{55} +286.362i q^{56} +(-28.1783 - 21.0612i) q^{57} +25.0545 q^{58} -33.3419i q^{59} +(124.979 - 167.212i) q^{60} +59.1060 q^{61} -25.1802i q^{62} +(27.5615 + 93.3496i) q^{63} -228.733 q^{64} -43.3119i q^{65} +(125.431 + 93.7507i) q^{66} +8.18535 q^{67} +108.511i q^{68} +(55.6572 - 74.4652i) q^{69} +267.015 q^{70} -78.2499i q^{71} +(-228.554 + 67.4805i) q^{72} -54.9820 q^{73} -257.844i q^{74} +(-38.4521 - 28.7401i) q^{75} +127.434 q^{76} +146.408i q^{77} +(-46.8420 + 62.6711i) q^{78} -42.1954 q^{79} +375.408i q^{80} +(-68.0104 + 43.9953i) q^{81} -211.505 q^{82} +4.52591i q^{83} +(-282.413 - 211.083i) q^{84} +63.9377 q^{85} +72.3095i q^{86} +(-11.6704 + 15.6142i) q^{87} -358.459 q^{88} +1.91227i q^{89} +(62.9216 + 213.113i) q^{90} -73.1517 q^{91} +336.763i q^{92} +(15.6925 + 11.7290i) q^{93} +63.2356 q^{94} -75.0879i q^{95} +(215.779 - 288.696i) q^{96} +83.7894 q^{97} -262.042i q^{98} +(-116.852 + 34.5006i) 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

Related objects

Downloads

Learn more