LMFDB - Embedded newform 81.5.f.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,5,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not 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:	$8.37296700979$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.34334 - 1.29483i) q^{2} +(37.2130 + 13.5444i) q^{4} +(22.9421 + 27.3414i) q^{5} +(14.0427 - 5.11111i) q^{7} +(-152.408 - 87.9929i) q^{8} +(-133.070 - 230.483i) q^{10} +(-35.3079 + 42.0783i) q^{11} +(-0.746352 - 4.23277i) q^{13} +(-109.738 + 19.3498i) q^{14} +(519.869 + 436.222i) q^{16} +(309.675 - 178.791i) q^{17} +(-273.006 + 472.860i) q^{19} +(483.423 + 1328.19i) q^{20} +(313.762 - 263.278i) q^{22} +(-130.510 + 358.573i) q^{23} +(-112.679 + 639.035i) q^{25} +32.0491i q^{26} +591.797 q^{28} +(-36.0636 - 6.35898i) q^{29} +(803.077 + 292.296i) q^{31} +(-1442.80 - 1719.46i) q^{32} +(-2505.56 + 911.948i) q^{34} +(461.914 + 266.686i) q^{35} +(245.703 + 425.571i) q^{37} +(2617.05 - 3118.88i) q^{38} +(-1090.72 - 6185.80i) q^{40} +(-2325.15 + 409.987i) q^{41} +(444.443 + 372.932i) q^{43} +(-1883.84 + 1087.63i) q^{44} +(1422.67 - 2464.14i) q^{46} +(1267.80 + 3483.25i) q^{47} +(-1668.20 + 1399.79i) q^{49} +(1654.88 - 4546.75i) q^{50} +(29.5565 - 167.623i) q^{52} -597.366i q^{53} -1960.52 q^{55} +(-2589.96 - 456.680i) q^{56} +(256.593 + 93.3924i) q^{58} +(2190.28 + 2610.27i) q^{59} +(530.905 - 193.234i) q^{61} +(-5518.80 - 3186.28i) q^{62} +(2939.43 + 5091.23i) q^{64} +(98.6069 - 117.515i) q^{65} +(533.761 + 3027.11i) q^{67} +(13945.6 - 2458.98i) q^{68} +(-3046.68 - 2556.47i) q^{70} +(-1579.71 + 912.046i) q^{71} +(2766.22 - 4791.24i) q^{73} +(-1253.24 - 3443.25i) q^{74} +(-16564.0 + 13898.9i) q^{76} +(-280.750 + 771.353i) q^{77} +(-423.277 + 2400.52i) q^{79} +24221.8i q^{80} +17605.3 q^{82} +(5141.02 + 906.501i) q^{83} +(11993.0 + 4365.10i) q^{85} +(-2780.81 - 3314.04i) q^{86} +(9083.80 - 3306.23i) q^{88} +(-3582.86 - 2068.56i) q^{89} +(-32.1149 - 55.6247i) q^{91} +(-9713.34 + 11575.9i) q^{92} +(-4799.67 - 27220.3i) q^{94} +(-19192.0 + 3384.07i) q^{95} +(-10080.0 - 8458.14i) q^{97} +(14062.6 - 8119.07i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−7.34334	−	1.29483i	−1.83584	−	0.323707i	−0.855013	−	0.518607i	$-0.826451\pi$
$2$	−7.34334	−	1.29483i	−1.83584	−	0.323707i	−0.980823	+	0.194900i	$0.937562\pi$
$3$		0			0
$3$		0			0
$4$	37.2130	+	13.5444i	2.32581	+	0.846527i
$5$	22.9421	+	27.3414i	0.917686	+	1.09366i	0.995316	+	0.0966730i	$0.0308201\pi$
$5$	22.9421	+	27.3414i	0.917686	+	1.09366i	−0.0776305	+	0.996982i	$0.524735\pi$
$6$		0			0
$7$	14.0427	−	5.11111i	0.286585	−	0.104308i	−0.194728	−	0.980857i	$-0.562382\pi$
$7$	14.0427	−	5.11111i	0.286585	−	0.104308i	0.481313	+	0.876549i	$0.340160\pi$
$8$	−152.408	−	87.9929i	−2.38138	−	1.37489i
$9$		0			0
$10$	−133.070	−	230.483i	−1.33070	−	2.30483i
$11$	−35.3079	+	42.0783i	−0.291801	+	0.347754i	−0.891950	−	0.452133i	$-0.850663\pi$
$11$	−35.3079	+	42.0783i	−0.291801	+	0.347754i	0.600150	+	0.799888i	$0.295108\pi$
$12$		0			0
$13$	−0.746352	−	4.23277i	−0.00441628	−	0.0250460i	0.982520	−	0.186157i	$-0.0596034\pi$
$13$	−0.746352	−	4.23277i	−0.00441628	−	0.0250460i	−0.986936	+	0.161111i	$0.948492\pi$
$14$	−109.738	+	19.3498i	−0.559888	+	0.0987234i
$15$		0			0
$16$	519.869	+	436.222i	2.03074	+	1.70399i
$17$	309.675	−	178.791i	1.07154	−	0.618655i	0.142939	−	0.989731i	$-0.454345\pi$
$17$	309.675	−	178.791i	1.07154	−	0.618655i	0.928602	+	0.371077i	$0.121011\pi$
$18$		0			0
$19$	−273.006	+	472.860i	−0.756250	+	1.30986i	0.188501	+	0.982073i	$0.439637\pi$
$19$	−273.006	+	472.860i	−0.756250	+	1.30986i	−0.944751	+	0.327790i	$0.893696\pi$
$20$	483.423	+	1328.19i	1.20856	+	3.32048i
$21$		0			0
$22$	313.762	−	263.278i	0.648269	−	0.543962i
$23$	−130.510	+	358.573i	−0.246711	+	0.677832i	0.753091	+	0.657917i	$0.228562\pi$
$23$	−130.510	+	358.573i	−0.246711	+	0.677832i	−0.999802	+	0.0199158i	$0.993660\pi$
$24$		0			0
$25$	−112.679	+	639.035i	−0.180287	+	1.02246i
$26$			32.0491i			0.0474099i
$27$		0			0
$28$	591.797			0.754843
$29$	−36.0636	−	6.35898i	−0.0428818	−	0.00756122i	0.152166	−	0.988355i	$-0.451375\pi$
$29$	−36.0636	−	6.35898i	−0.0428818	−	0.00756122i	−0.195048	+	0.980794i	$0.562486\pi$
$30$		0			0
$31$	803.077	+	292.296i	0.835668	+	0.304158i	0.724183	−	0.689608i	$-0.242217\pi$
$31$	803.077	+	292.296i	0.835668	+	0.304158i	0.111485	+	0.993766i	$0.464439\pi$
$32$	−1442.80	−	1719.46i	−1.40898	−	1.67916i
$33$		0			0
$34$	−2505.56	+	911.948i	−2.16744	+	0.788883i
$35$	461.914	+	266.686i	0.377072	+	0.217703i
$36$		0			0
$37$	245.703	+	425.571i	0.179476	+	0.310862i	0.941701	−	0.336450i	$-0.109226\pi$
$37$	245.703	+	425.571i	0.179476	+	0.310862i	−0.762225	+	0.647312i	$0.775893\pi$
$38$	2617.05	−	3118.88i	1.81236	−	2.15989i
$39$		0			0
$40$	−1090.72	−	6185.80i	−0.681702	−	3.86612i
$41$	−2325.15	+	409.987i	−1.38320	+	0.243895i	−0.815220	−	0.579151i	$-0.803384\pi$
$41$	−2325.15	+	409.987i	−1.38320	+	0.243895i	−0.567975	+	0.823046i	$0.692273\pi$
$42$		0			0
$43$	444.443	+	372.932i	0.240369	+	0.201694i	0.755012	−	0.655711i	$-0.227631\pi$
$43$	444.443	+	372.932i	0.240369	+	0.201694i	−0.514643	+	0.857405i	$0.672075\pi$
$44$	−1883.84	+	1087.63i	−0.973057	+	0.561795i
$45$		0			0
$46$	1422.67	−	2464.14i	0.672340	−	1.16453i
$47$	1267.80	+	3483.25i	0.573925	+	1.57684i	0.798247	+	0.602330i	$0.205761\pi$
$47$	1267.80	+	3483.25i	0.573925	+	1.57684i	−0.224323	+	0.974515i	$0.572017\pi$
$48$		0			0
$49$	−1668.20	+	1399.79i	−0.694794	+	0.583001i
$50$	1654.88	−	4546.75i	0.661953	−	1.81870i
$51$		0			0
$52$	29.5565	−	167.623i	0.0109307	−	0.0619908i
$53$		−	597.366i		−	0.212661i	−0.994331	−	0.106331i	$-0.966090\pi$
$53$		−	597.366i		−	0.212661i	0.994331	−	0.106331i	$-0.0339102\pi$
$54$		0			0
$55$	−1960.52			−0.648105
$56$	−2589.96	−	456.680i	−0.825880	−	0.145625i
$57$		0			0
$58$	256.593	+	93.3924i	0.0762763	+	0.0277623i
$59$	2190.28	+	2610.27i	0.629210	+	0.749863i	0.982625	−	0.185604i	$-0.0594241\pi$
$59$	2190.28	+	2610.27i	0.629210	+	0.749863i	−0.353415	+	0.935467i	$0.614980\pi$
$60$		0			0
$61$	530.905	−	193.234i	0.142678	−	0.0519306i	−0.269694	−	0.962946i	$-0.586923\pi$
$61$	530.905	−	193.234i	0.142678	−	0.0519306i	0.412372	+	0.911015i	$0.364700\pi$
$62$	−5518.80	−	3186.28i	−1.43569	−	0.828897i
$63$		0			0
$64$	2939.43	+	5091.23i	0.717633	+	1.24298i
$65$	98.6069	−	117.515i	0.0233389	−	0.0278142i
$66$		0			0
$67$	533.761	+	3027.11i	0.118904	+	0.674339i	0.984743	+	0.174016i	$0.0556743\pi$
$67$	533.761	+	3027.11i	0.118904	+	0.674339i	−0.865839	+	0.500323i	$0.833215\pi$
$68$	13945.6	−	2458.98i	3.01591	−	0.531787i
$69$		0			0
$70$	−3046.68	−	2556.47i	−0.621771	−	0.521728i
$71$	−1579.71	+	912.046i	−0.313372	+	0.180926i	−0.648435	−	0.761270i	$-0.724576\pi$
$71$	−1579.71	+	912.046i	−0.313372	+	0.180926i	0.335062	+	0.942196i	$0.391243\pi$
$72$		0			0
$73$	2766.22	−	4791.24i	0.519088	−	0.899087i	−0.480666	−	0.876904i	$-0.659605\pi$
$73$	2766.22	−	4791.24i	0.519088	−	0.899087i	0.999754	−	0.0221832i	$-0.00706171\pi$
$74$	−1253.24	−	3443.25i	−0.228861	−	0.628790i
$75$		0			0
$76$	−16564.0	+	13898.9i	−2.86773	+	2.40631i
$77$	−280.750	+	771.353i	−0.0473520	+	0.130098i
$78$		0			0
$79$	−423.277	+	2400.52i	−0.0678220	+	0.384638i	0.931936	+	0.362624i	$0.118119\pi$
$79$	−423.277	+	2400.52i	−0.0678220	+	0.384638i	−0.999758	+	0.0220141i	$0.992992\pi$
$80$			24221.8i			3.78465i
$81$		0			0
$82$	17605.3			2.61827
$83$	5141.02	+	906.501i	0.746266	+	0.131587i	0.533834	−	0.845589i	$-0.320751\pi$
$83$	5141.02	+	906.501i	0.746266	+	0.131587i	0.212431	+	0.977176i	$0.431862\pi$
$84$		0			0
$85$	11993.0	+	4365.10i	1.65993	+	0.604166i
$86$	−2780.81	−	3314.04i	−0.375989	−	0.448086i
$87$		0			0
$88$	9083.80	−	3306.23i	1.17301	−	0.426941i
$89$	−3582.86	−	2068.56i	−0.452324	−	0.261149i	0.256487	−	0.966548i	$-0.417435\pi$
$89$	−3582.86	−	2068.56i	−0.452324	−	0.261149i	−0.708811	+	0.705398i	$0.750768\pi$
$90$		0			0
$91$	−32.1149	−	55.6247i	−0.00387815	−	0.00671715i
$92$	−9713.34	+	11575.9i	−1.14761	+	1.36766i
$93$		0			0
$94$	−4799.67	−	27220.3i	−0.543195	−	3.08061i
$95$	−19192.0	+	3384.07i	−2.12654	+	0.374966i
$96$		0			0
$97$	−10080.0	−	8458.14i	−1.07132	−	0.898942i	−0.0761458	−	0.997097i	$-0.524261\pi$
$97$	−10080.0	−	8458.14i	−1.07132	−	0.898942i	−0.995171	+	0.0981550i	$0.968706\pi$
$98$	14062.6	−	8119.07i	1.46425	−	0.845385i
$99$		0			0
$100$	−12848.5	+	22254.2i	−1.28485	+	2.22542i
$101$	−5913.44	−	16247.1i	−0.579693	−	1.59269i	−0.788700	−	0.614778i	$-0.789245\pi$
$101$	−5913.44	−	16247.1i	−0.579693	−	1.59269i	0.209007	−	0.977914i	$-0.432977\pi$
$102$		0			0
$103$	9925.23	−	8328.26i	0.935548	−	0.785018i	−0.0412568	−	0.999149i	$-0.513136\pi$
$103$	9925.23	−	8328.26i	0.935548	−	0.785018i	0.976805	+	0.214130i	$0.0686917\pi$
$104$	−258.704	+	710.783i	−0.0239186	+	0.0657159i
$105$		0			0
$106$	−773.487	+	4386.66i	−0.0688401	+	0.390411i
$107$		−	10732.5i		−	0.937422i	−0.883352	−	0.468711i	$-0.844719\pi$
$107$		−	10732.5i		−	0.937422i	0.883352	−	0.468711i	$-0.155281\pi$
$108$		0			0
$109$	−1507.97			−0.126923			−0.0634615	−	0.997984i	$-0.520214\pi$
$109$	−1507.97			−0.126923			−0.0634615	+	0.997984i	$0.520214\pi$
$110$	14396.7	+	2538.53i	1.18981	+	0.209796i
$111$		0			0
$112$	9529.92	+	3468.61i	0.759719	+	0.276515i
$113$	22.4010	+	26.6964i	0.00175432	+	0.00209072i	0.766921	−	0.641742i	$-0.221788\pi$
$113$	22.4010	+	26.6964i	0.00175432	+	0.00209072i	−0.765167	+	0.643832i	$0.777343\pi$
$114$		0			0
$115$	−12798.1	+	4658.12i	−0.967718	+	0.352220i
$116$	−1255.91	−	725.098i	−0.0933343	−	0.0538866i
$117$		0			0
$118$	−12704.1	−	22004.2i	−0.912389	−	1.58030i
$119$	3434.85	−	4093.49i	0.242557	−	0.289068i
$120$		0			0
$121$	2018.45	+	11447.2i	0.137863	+	0.781858i
$122$	−4148.83	+	731.550i	−0.278744	+	0.0491501i
$123$		0			0
$124$	25926.0	+	21754.5i	1.68613	+	1.41483i
$125$	−738.531	+	426.391i	−0.0472660	+	0.0272890i
$126$		0			0
$127$	9282.82	−	16078.3i	0.575536	−	0.996857i	−0.420447	−	0.907317i	$-0.638127\pi$
$127$	9282.82	−	16078.3i	0.575536	−	0.996857i	0.995983	−	0.0895403i	$-0.0285398\pi$
$128$	−2709.79	−	7445.08i	−0.165392	−	0.454412i
$129$		0			0
$130$	−876.267	+	735.275i	−0.0518501	+	0.0435074i
$131$	−9476.12	+	26035.4i	−0.552189	+	1.51713i	0.278525	+	0.960429i	$0.410155\pi$
$131$	−9476.12	+	26035.4i	−0.552189	+	1.51713i	−0.830714	+	0.556699i	$0.812068\pi$
$132$		0			0
$133$	−1416.89	+	8035.58i	−0.0801001	+	0.454270i
$134$		−	22920.2i		−	1.27647i
$135$		0			0
$136$	−62929.5			−3.40233
$137$	22228.3	+	3919.46i	1.18431	+	0.208826i	0.730906	−	0.682478i	$-0.239098\pi$
$137$	22228.3	+	3919.46i	1.18431	+	0.208826i	0.453406	+	0.891304i	$0.350209\pi$
$138$		0			0
$139$	18170.5	+	6613.53i	0.940454	+	0.342297i	0.766345	−	0.642429i	$-0.222073\pi$
$139$	18170.5	+	6613.53i	0.940454	+	0.342297i	0.174109	+	0.984726i	$0.444295\pi$
$140$	13577.1	+	16180.5i	0.692709	+	0.825538i
$141$		0			0
$142$	12781.3	−	4652.01i	0.633867	−	0.230709i
$143$	204.460	+	118.045i	0.00999853	+	0.00577265i
$144$		0			0
$145$	−653.513	−	1131.92i	−0.0310826	−	0.0538367i
$146$	−26517.1	+	31601.9i	−1.24400	+	1.48254i
$147$		0			0
$148$	3379.25	+	19164.7i	0.154275	+	0.874940i
$149$	25568.2	−	4508.36i	1.15167	−	0.203070i	0.434965	−	0.900448i	$-0.356761\pi$
$149$	25568.2	−	4508.36i	1.15167	−	0.203070i	0.716704	+	0.697377i	$0.245650\pi$
$150$		0			0
$151$	−6349.86	−	5328.17i	−0.278491	−	0.233681i	0.492834	−	0.870123i	$-0.335961\pi$
$151$	−6349.86	−	5328.17i	−0.278491	−	0.233681i	−0.771325	+	0.636442i	$0.780405\pi$
$152$	83216.7	−	48045.2i	3.60183	−	2.07952i
$153$		0			0
$154$	3060.41	−	5300.79i	0.129044	−	0.223511i
$155$	10432.5	+	28663.1i	0.434237	+	1.19306i
$156$		0			0
$157$	−13957.3	+	11711.5i	−0.566241	+	0.475133i	−0.880396	−	0.474239i	$-0.842723\pi$
$157$	−13957.3	+	11711.5i	−0.566241	+	0.475133i	0.314155	+	0.949372i	$0.398279\pi$
$158$	6216.54	−	17079.8i	0.249020	−	0.684177i
$159$		0			0
$160$	13911.5	−	78896.1i	0.543419	−	3.08188i
$161$			5702.38i			0.219991i
$162$		0			0
$163$	−45051.0			−1.69562			−0.847811	−	0.530298i	$-0.822080\pi$
$163$	−45051.0			−1.69562			−0.847811	+	0.530298i	$0.822080\pi$
$164$	−92079.0	−	16236.0i	−3.42352	−	0.603659i
$165$		0			0
$166$	−36578.5	−	13313.5i	−1.32743	−	0.483143i
$167$	−29417.7	−	35058.6i	−1.05481	−	1.25708i	−0.965315	−	0.261089i	$-0.915918\pi$
$167$	−29417.7	−	35058.6i	−1.05481	−	1.25708i	−0.0894977	−	0.995987i	$-0.528526\pi$
$168$		0			0
$169$	26821.2	−	9762.12i	0.939085	−	0.341799i
$170$	−82416.8	−	47583.4i	−2.85179	−	1.64648i
$171$		0			0
$172$	11487.9	+	19897.6i	0.388315	+	0.672581i
$173$	22596.5	−	26929.5i	0.755004	−	0.899779i	−0.242517	−	0.970147i	$-0.577973\pi$
$173$	22596.5	−	26929.5i	0.755004	−	0.899779i	0.997521	+	0.0703680i	$0.0224173\pi$
$174$		0			0
$175$	1683.86	+	9549.67i	0.0549833	+	0.311826i
$176$	−36710.9	+	6473.12i	−1.18514	+	0.208972i
$177$		0			0
$178$	23631.7	+	19829.4i	0.745857	+	0.625848i
$179$	6494.87	−	3749.81i	0.202705	−	0.117032i	−0.395212	−	0.918590i	$-0.629329\pi$
$179$	6494.87	−	3749.81i	0.202705	−	0.117032i	0.597917	+	0.801558i	$0.295995\pi$
$180$		0			0
$181$	−1045.63	+	1811.08i	−0.0319168	+	0.0552816i	−0.881543	−	0.472104i	$-0.843494\pi$
$181$	−1045.63	+	1811.08i	−0.0319168	+	0.0552816i	0.849626	+	0.527386i	$0.176828\pi$
$182$	163.807	+	450.055i	0.00494525	+	0.0135870i
$183$		0			0
$184$	51442.7	−	43165.6i	1.51946	−	1.27498i
$185$	−5998.73	+	16481.4i	−0.175273	+	0.481559i
$186$		0			0
$187$	−3410.75	+	19343.3i	−0.0975365	+	0.553157i
$188$			146794.i			4.15329i
$189$		0			0
$190$	145315.			4.02535
$191$	−11234.8	−	1980.99i	−0.307962	−	0.0543021i	0.0175312	−	0.999846i	$-0.494419\pi$
$191$	−11234.8	−	1980.99i	−0.307962	−	0.0543021i	−0.325494	+	0.945544i	$0.605530\pi$
$192$		0			0
$193$	−26467.5	−	9633.39i	−0.710557	−	0.258622i	−0.0386453	−	0.999253i	$-0.512304\pi$
$193$	−26467.5	−	9633.39i	−0.710557	−	0.258622i	−0.671911	+	0.740631i	$0.734526\pi$
$194$	63069.2	+	75162.9i	1.67577	+	1.99710i
$195$		0			0
$196$	−81038.1	+	29495.4i	−2.10949	+	0.767791i
$197$	58133.9	+	33563.6i	1.49795	+	0.864841i	0.999997	−	0.00236466i	$-0.000752696\pi$
$197$	58133.9	+	33563.6i	1.49795	+	0.864841i	0.497951	+	0.867205i	$0.334086\pi$
$198$		0			0
$199$	10421.6	+	18050.8i	0.263165	+	0.455816i	0.967081	−	0.254468i	$-0.0819002\pi$
$199$	10421.6	+	18050.8i	0.263165	+	0.455816i	−0.703916	+	0.710283i	$0.748567\pi$
$200$	73403.8	−	87479.2i	1.83509	−	2.18698i
$201$		0			0
$202$	22387.3	+	126965.i	0.548654	+	3.11157i
$203$	−538.930	+	95.0279i	−0.0130780	+	0.00230600i
$204$		0			0
$205$	−64553.6	−	54166.9i	−1.53608	−	1.28892i
$206$	−83668.1	+	48305.8i	−1.97163	+	1.13832i
$207$		0			0
$208$	1458.42	−	2526.06i	0.0337098	−	0.0583871i
$209$	−10257.9	−	28183.3i	−0.234836	−	0.645208i
$210$		0			0
$211$	30301.2	−	25425.8i	0.680606	−	0.571096i	−0.235578	−	0.971856i	$-0.575698\pi$
$211$	30301.2	−	25425.8i	0.680606	−	0.571096i	0.916183	+	0.400760i	$0.131254\pi$
$212$	8090.98	−	22229.8i	0.180024	−	0.494611i
$213$		0			0
$214$	−13896.8	+	78812.7i	−0.303450	+	1.72095i
$215$			20707.5i			0.447972i
$216$		0			0
$217$	12771.3			0.271216
$218$	11073.6	+	1952.57i	0.233010	+	0.0410859i
$219$		0			0
$220$	−72956.7	−	26554.1i	−1.50737	−	0.548638i
$221$	−987.910	−	1177.34i	−0.0202271	−	0.0241057i
$222$		0			0
$223$	52481.4	−	19101.7i	1.05535	−	0.384115i	0.244669	−	0.969607i	$-0.421321\pi$
$223$	52481.4	−	19101.7i	1.05535	−	0.384115i	0.810678	+	0.585492i	$0.199098\pi$
$224$	−29049.1	−	16771.5i	−0.578943	−	0.334253i
$225$		0			0
$226$	−129.931	−	225.047i	−0.00254387	−	0.00440611i
$227$	7696.64	−	9172.50i	0.149365	−	0.178006i	−0.686174	−	0.727438i	$-0.740711\pi$
$227$	7696.64	−	9172.50i	0.149365	−	0.178006i	0.835539	+	0.549431i	$0.185156\pi$
$228$		0			0
$229$	−9076.93	−	51477.8i	−0.173088	−	0.981633i	−0.940327	−	0.340272i	$-0.889481\pi$
$229$	−9076.93	−	51477.8i	−0.173088	−	0.981633i	0.767239	−	0.641362i	$-0.221630\pi$
$230$	100012.	−	17634.8i	1.89059	−	0.333362i
$231$		0			0
$232$	4936.84	+	4142.50i	0.0917219	+	0.0769638i
$233$	23116.2	−	13346.2i	0.425800	−	0.245836i	−0.271756	−	0.962366i	$-0.587604\pi$
$233$	23116.2	−	13346.2i	0.425800	−	0.245836i	0.697556	+	0.716531i	$0.254271\pi$
$234$		0			0
$235$	−66150.8	+	114577.i	−1.19784	+	2.07472i
$236$	46152.2	+	126802.i	0.828645	+	2.27668i
$237$		0			0
$238$	−30523.6	+	25612.4i	−0.538868	+	0.452164i
$239$	1205.00	−	3310.71i	0.0210956	−	0.0579596i	−0.928698	−	0.370837i	$-0.879071\pi$
$239$	1205.00	−	3310.71i	0.0210956	−	0.0579596i	0.949793	+	0.312878i	$0.101293\pi$
$240$		0			0
$241$	14955.3	−	84815.6i	0.257490	−	1.46030i	−0.532110	−	0.846675i	$-0.678601\pi$
$241$	14955.3	−	84815.6i	0.257490	−	1.46030i	0.789600	−	0.613622i	$-0.210288\pi$
$242$		−	86674.1i		−	1.47999i
$243$		0			0
$244$	22373.8			0.375803
$245$	−76544.2	−	13496.8i	−1.27520	−	0.224853i
$246$		0			0
$247$	2205.27	+	802.652i	0.0361466	+	0.0131563i
$248$	−96675.6	−	115213.i	−1.57186	−	1.87327i
$249$		0			0
$250$	5975.39	−	2174.86i	0.0956063	−	0.0347978i
$251$	11184.3	+	6457.26i	0.177526	+	0.102495i	0.586130	−	0.810217i	$-0.300651\pi$
$251$	11184.3	+	6457.26i	0.177526	+	0.102495i	−0.408604	+	0.912712i	$0.633984\pi$
$252$		0			0
$253$	−10480.1	−	18152.1i	−0.163729	−	0.283587i
$254$	−88985.6	+	106049.i	−1.37928	+	1.64376i
$255$		0			0
$256$	−6074.84	−	34452.1i	−0.0926946	−	0.525697i
$257$	−9408.96	+	1659.05i	−0.142454	+	0.0251185i	−0.244421	−	0.969669i	$-0.578598\pi$
$257$	−9408.96	+	1659.05i	−0.142454	+	0.0251185i	0.101966	+	0.994788i	$0.467487\pi$
$258$		0			0
$259$	5625.47	+	4720.33i	0.0838608	+	0.0703676i
$260$	5261.14	−	3037.52i	0.0778275	−	0.0449337i
$261$		0			0
$262$	103298.	−	178917.i	1.50483	−	2.60645i
$263$	−29073.3	−	79878.1i	−0.420322	−	1.15483i	−0.951523	−	0.307579i	$-0.900481\pi$
$263$	−29073.3	−	79878.1i	−0.420322	−	1.15483i	0.531201	−	0.847246i	$-0.321741\pi$
$264$		0			0
$265$	16332.8	−	13704.9i	0.232578	−	0.195156i
$266$	20809.4	−	57173.4i	0.294101	−	0.808036i
$267$		0			0
$268$	−21137.6	+	119877.i	−0.294297	+	1.66904i
$269$		−	14077.8i		−	0.194549i	−0.995258	−	0.0972745i	$-0.968988\pi$
$269$		−	14077.8i		−	0.194549i	0.995258	−	0.0972745i	$-0.0310125\pi$
$270$		0			0
$271$	−18138.8			−0.246984			−0.123492	−	0.992346i	$-0.539409\pi$
$271$	−18138.8			−0.246984			−0.123492	+	0.992346i	$0.539409\pi$
$272$	238983.	+	42139.2i	3.23020	+	0.569572i
$273$		0			0
$274$	−158155.	−	57563.8i	−2.10660	−	0.766741i
$275$	−22911.0	−	27304.3i	−0.302956	−	0.361049i
$276$		0			0
$277$	136985.	−	49858.4i	1.78531	−	0.649799i	0.785798	−	0.618483i	$-0.212252\pi$
$277$	136985.	−	49858.4i	1.78531	−	0.649799i	0.999510	−	0.0313162i	$-0.00996987\pi$
$278$	−124869.	−	72093.1i	−1.61572	−	0.932834i
$279$		0			0
$280$	−46933.0	−	81290.3i	−0.598635	−	1.03687i
$281$	−786.212	+	936.971i	−0.00995696	+	0.0118662i	−0.771000	−	0.636835i	$-0.780243\pi$
$281$	−786.212	+	936.971i	−0.00995696	+	0.0118662i	0.761043	+	0.648701i	$0.224688\pi$
$282$		0			0
$283$	18788.2	+	106553.i	0.234592	+	1.33044i	0.843472	+	0.537173i	$0.180508\pi$
$283$	18788.2	+	106553.i	0.234592	+	1.33044i	−0.608880	+	0.793262i	$0.708381\pi$
$284$	−71138.9	+	12543.7i	−0.882004	+	0.155521i
$285$		0			0
$286$	−1348.57	−	1131.59i	−0.0164870	−	0.0138342i
$287$	−30555.8	+	17641.4i	−0.370963	+	0.214175i
$288$		0			0
$289$	22172.1	−	38403.2i	0.265467	−	0.459803i
$290$	3333.33	+	9158.24i	0.0396353	+	0.108897i
$291$		0			0
$292$	167834.	−	140829.i	1.96840	−	1.65169i
$293$	36375.6	−	99941.2i	0.423716	−	1.16415i	−0.525848	−	0.850579i	$-0.676252\pi$
$293$	36375.6	−	99941.2i	0.423716	−	1.16415i	0.949564	−	0.313573i	$-0.101526\pi$
$294$		0			0
$295$	−21118.8	+	119770.i	−0.242675	+	1.37628i
$296$		−	86480.6i		−	0.987041i
$297$		0			0
$298$	−193594.			−2.18001
$299$	1615.17	+	284.797i	0.0180665	+	0.00318562i
$300$		0			0
$301$	8147.25	+	2965.36i	0.0899246	+	0.0327299i
$302$	39730.2	+	47348.6i	0.435619	+	0.519150i
$303$		0			0
$304$	−348199.	+	126734.i	−3.76774	+	1.37134i
$305$	17463.4	+	10082.5i	0.187728	+	0.108385i
$306$		0			0
$307$	37577.3	+	65085.9i	0.398703	+	0.690573i	0.993566	−	0.113253i	$-0.0361272\pi$
$307$	37577.3	+	65085.9i	0.398703	+	0.690573i	−0.594863	+	0.803827i	$0.702794\pi$
$308$	−20895.1	+	24901.8i	−0.220264	+	0.262500i
$309$		0			0
$310$	−39495.8	−	223992.i	−0.410986	−	2.33082i
$311$	−64675.3	+	11404.0i	−0.668679	+	0.117906i	−0.497674	−	0.867364i	$-0.665813\pi$
$311$	−64675.3	+	11404.0i	−0.668679	+	0.117906i	−0.171005	+	0.985270i	$0.554701\pi$
$312$		0			0
$313$	−61767.7	−	51829.3i	−0.630483	−	0.529038i	0.270596	−	0.962693i	$-0.412779\pi$
$313$	−61767.7	−	51829.3i	−0.630483	−	0.529038i	−0.901079	+	0.433655i	$0.857224\pi$
$314$	117658.	−	67929.6i	1.19333	−	0.688969i
$315$		0			0
$316$	−48265.2	+	83597.7i	−0.483348	+	0.837183i
$317$	−11934.7	−	32790.3i	−0.118766	−	0.326307i	0.866037	−	0.499979i	$-0.166659\pi$
$317$	−11934.7	−	32790.3i	−0.118766	−	0.326307i	−0.984804	+	0.173672i	$0.944437\pi$
$318$		0			0
$319$	1540.90	−	1292.97i	0.0151424	−	0.0127060i
$320$	−71764.7	+	197172.i	−0.700827	+	1.92551i
$321$		0			0
$322$	7383.60	−	41874.5i	0.0712126	−	0.403867i
$323$			195244.i			1.87143i
$324$		0			0
$325$	2788.99			0.0264046
$326$	330825.	+	58333.4i	3.11289	+	0.548886i
$327$		0			0
$328$	390448.	+	142112.i	3.62924	+	1.32094i
$329$	35606.6	+	42434.2i	0.328956	+	0.392035i
$330$		0			0
$331$	121557.	−	44243.1i	1.10949	−	0.403821i	0.278684	−	0.960383i	$-0.410102\pi$
$331$	121557.	−	44243.1i	1.10949	−	0.403821i	0.830806	+	0.556562i	$0.187880\pi$
$332$	179035.	+	103366.i	1.62428	+	0.937780i
$333$		0			0
$334$	170629.	+	295538.i	1.52954	+	2.64924i
$335$	−70519.7	+	84042.1i	−0.628378	+	0.748871i
$336$		0			0
$337$	−23137.5	−	131219.i	−0.203731	−	1.15541i	−0.899425	−	0.437076i	$-0.856014\pi$
$337$	−23137.5	−	131219.i	−0.203731	−	1.15541i	0.695694	−	0.718338i	$-0.255097\pi$
$338$	−209598.	+	36957.7i	−1.83465	+	0.323498i
$339$		0			0
$340$	387174.	+	324877.i	3.34925	+	2.81036i
$341$	−40654.3	+	23471.8i	−0.349621	+	0.201854i
$342$		0			0
$343$	−34211.6	+	59256.3i	−0.290794	+	0.503670i
$344$	−34921.4	−	95945.7i	−0.295103	−	0.810790i
$345$		0			0
$346$	−200803.	+	168494.i	−1.67733	+	1.40745i
$347$	−19826.7	+	54473.4i	−0.164661	+	0.452403i	−0.994392	−	0.105761i	$-0.966272\pi$
$347$	−19826.7	+	54473.4i	−0.164661	+	0.452403i	0.829730	+	0.558165i	$0.188494\pi$
$348$		0			0
$349$	−22672.5	+	128582.i	−0.186144	+	1.05568i	0.738332	+	0.674437i	$0.235614\pi$
$349$	−22672.5	+	128582.i	−0.186144	+	1.05568i	−0.924476	+	0.381239i	$0.875497\pi$
$350$		−	72306.8i		−	0.590260i
$351$		0			0
$352$	123294.			0.995076
$353$	27299.6	+	4813.66i	0.219082	+	0.0386301i	0.282112	−	0.959382i	$-0.408965\pi$
$353$	27299.6	+	4813.66i	0.219082	+	0.0386301i	−0.0630294	+	0.998012i	$0.520076\pi$
$354$		0			0
$355$	−61178.5	−	22267.2i	−0.485448	−	0.176688i
$356$	−105311.	−	125505.i	−0.830951	−	0.990289i
$357$		0			0
$358$	−52549.4	+	19126.4i	−0.410017	+	0.149234i
$359$	−19338.9	−	11165.3i	−0.150053	−	0.0866329i	0.423094	−	0.906086i	$-0.360944\pi$
$359$	−19338.9	−	11165.3i	−0.150053	−	0.0866329i	−0.573146	+	0.819453i	$0.694277\pi$
$360$		0			0
$361$	−83904.2	−	145326.i	−0.643827	−	1.11514i
$362$	10023.4	−	11945.5i	0.0764891	−	0.0911562i
$363$		0			0
$364$	−441.689	−	2504.94i	−0.00333360	−	0.0189058i
$365$	194462.	−	34288.9i	1.45965	−	0.257376i
$366$		0			0
$367$	−149004.	−	125029.i	−1.10628	−	0.928278i	−0.108447	−	0.994102i	$-0.534588\pi$
$367$	−149004.	−	125029.i	−1.10628	−	0.928278i	−0.997831	+	0.0658243i	$0.979032\pi$
$368$	−224265.	+	129480.i	−1.65602	+	0.956106i
$369$		0			0
$370$	65391.3	−	113261.i	0.477657	−	0.827327i
$371$	−3053.20	−	8388.61i	−0.0221824	−	0.0609456i
$372$		0			0
$373$	−130382.	+	109403.i	−0.937127	+	0.786343i	−0.977083	−	0.212858i	$-0.931723\pi$
$373$	−130382.	+	109403.i	−0.937127	+	0.786343i	0.0399560	+	0.999201i	$0.487278\pi$
$374$	50092.7	−	137628.i	0.358122	−	0.983932i
$375$		0			0
$376$	113278.	−	642433.i	0.801256	−	4.54415i
$377$			157.395i			0.00110741i
$378$		0			0
$379$	177096.			1.23290			0.616452	−	0.787392i	$-0.288569\pi$
$379$	177096.			1.23290			0.616452	+	0.787392i	$0.288569\pi$
$380$	−760028.	−	134013.i	−5.26335	−	0.928071i
$381$		0			0
$382$	79935.8	+	29094.2i	0.547790	+	0.199379i
$383$	29074.2	+	34649.2i	0.198203	+	0.236209i	0.855987	−	0.516998i	$-0.172950\pi$
$383$	29074.2	+	34649.2i	0.198203	+	0.236209i	−0.657784	+	0.753207i	$0.728506\pi$
$384$		0			0
$385$	−27530.9	+	10020.4i	−0.185737	+	0.0676027i
$386$	181887.	+	105012.i	1.22075	+	0.704799i
$387$		0			0
$388$	−260547.	−	451281.i	−1.73071	−	2.99767i
$389$	42121.3	−	50198.2i	0.278357	−	0.331733i	−0.608693	−	0.793406i	$-0.708306\pi$
$389$	42121.3	−	50198.2i	0.278357	−	0.331733i	0.887050	+	0.461672i	$0.152750\pi$
$390$		0			0
$391$	23694.0	+	134375.i	0.154983	+	0.878954i
$392$	377419.	−	66549.1i	2.45613	−	0.433082i
$393$		0			0
$394$	−383438.	−	321742.i	−2.47003	−	2.07260i
$395$	−75344.6	+	43500.2i	−0.482901	+	0.278803i
$396$		0			0
$397$	−111760.	+	193575.i	−0.709099	+	1.22820i	0.256093	+	0.966652i	$0.417565\pi$
$397$	−111760.	+	193575.i	−0.709099	+	1.22820i	−0.965192	+	0.261543i	$0.915769\pi$
$398$	−53156.8	−	146047.i	−0.335577	−	0.921991i
$399$		0			0
$400$	−337339.	+	283061.i	−2.10837	+	1.76913i
$401$	−92421.2	+	253925.i	−0.574755	+	1.57913i	0.222144	+	0.975014i	$0.428695\pi$
$401$	−92421.2	+	253925.i	−0.574755	+	1.57913i	−0.796899	+	0.604113i	$0.793528\pi$
$402$		0			0
$403$	637.845	−	3617.40i	0.00392740	−	0.0222734i
$404$		−	684696.i		−	4.19503i
$405$		0			0
$406$	4080.59			0.0247555
$407$	−26582.5	−	4687.22i	−0.160475	−	0.0282961i
$408$		0			0
$409$	194660.	+	70850.6i	1.16367	+	0.423542i	0.850408	−	0.526124i	$-0.176355\pi$
$409$	194660.	+	70850.6i	1.16367	+	0.423542i	0.313265	+	0.949666i	$0.398577\pi$
$410$	403902.	+	481352.i	2.40275	+	2.86349i
$411$		0			0
$412$	482149.	−	175488.i	2.84045	−	1.03384i
$413$	44098.7	+	25460.4i	0.258539	+	0.149268i
$414$		0			0
$415$	93161.1	+	161360.i	0.540927	+	0.936913i
$416$	−6201.24	+	7390.35i	−0.0358337	+	0.0427050i
$417$		0			0
$418$	38834.6	+	220242.i	0.222263	+	1.26051i
$419$	86433.7	−	15240.6i	0.492329	−	0.0868108i	0.0780285	−	0.996951i	$-0.475137\pi$
$419$	86433.7	−	15240.6i	0.492329	−	0.0868108i	0.414300	+	0.910140i	$0.364026\pi$
$420$		0			0
$421$	212742.	+	178512.i	1.20030	+	1.00717i	0.999621	+	0.0275143i	$0.00875917\pi$
$421$	212742.	+	178512.i	1.20030	+	1.00717i	0.200679	+	0.979657i	$0.435685\pi$
$422$	−255434.	+	147475.i	−1.43435	+	0.828121i
$423$		0			0
$424$	−52564.0	+	91043.5i	−0.292386	+	0.506427i
$425$	79359.9	+	218039.i	0.439363	+	1.20714i
$426$		0			0
$427$	6467.69	−	5427.03i	0.0354726	−	0.0297651i
$428$	145366.	−	399390.i	0.793553	−	2.18027i
$429$		0			0
$430$	26812.7	−	152062.i	0.145012	−	0.822404i
$431$			41851.0i			0.225295i	0.993635	+	0.112647i	$0.0359331\pi$
$431$			41851.0i			0.225295i	−0.993635	+	0.112647i	$0.964067\pi$
$432$		0			0
$433$	1012.86			0.00540225			0.00270113	−	0.999996i	$-0.499140\pi$
$433$	1012.86			0.00540225			0.00270113	+	0.999996i	$0.499140\pi$
$434$	−93784.1	−	16536.7i	−0.497909	−	0.0877947i
$435$		0			0
$436$	−56116.2	−	20424.6i	−0.295199	−	0.107444i
$437$	−133925.	−	159606.i	−0.701292	−	0.835768i
$438$		0			0
$439$	−61671.4	+	22446.6i	−0.320004	+	0.116472i	−0.497028	−	0.867735i	$-0.665575\pi$
$439$	−61671.4	+	22446.6i	−0.320004	+	0.116472i	0.177024	+	0.984207i	$0.443353\pi$
$440$	298799.	+	172512.i	1.54338	+	0.891072i
$441$		0			0
$442$	5730.10	+	9924.82i	0.0293304	+	0.0508017i
$443$	11275.3	−	13437.4i	0.0574540	−	0.0684710i	−0.736552	−	0.676381i	$-0.763547\pi$
$443$	11275.3	−	13437.4i	0.0574540	−	0.0684710i	0.794006	+	0.607910i	$0.207992\pi$
$444$		0			0
$445$	−25641.0	−	145418.i	−0.129484	−	0.734339i
$446$	−410122.	+	72315.6i	−2.06179	+	0.363548i
$447$		0			0
$448$	67299.2	+	56470.8i	0.335316	+	0.281363i
$449$	310961.	−	179534.i	1.54246	−	0.890540i	0.543777	−	0.839230i	$-0.316994\pi$
$449$	310961.	−	179534.i	1.54246	−	0.890540i	0.998683	−	0.0513099i	$-0.0163396\pi$
$450$		0			0
$451$	64844.6	−	112314.i	0.318802	−	0.552181i
$452$	472.020	+	1296.86i	0.00231038	+	0.00634772i
$453$		0			0
$454$	−68395.9	+	57391.0i	−0.331832	+	0.278440i
$455$	784.071	−	2154.22i	0.00378733	−	0.0104056i
$456$		0			0
$457$	−60611.2	+	343743.i	−0.290215	+	1.64589i	0.395823	+	0.918327i	$0.370459\pi$
$457$	−60611.2	+	343743.i	−0.290215	+	1.64589i	−0.686038	+	0.727566i	$0.740652\pi$
$458$			389772.i			1.85815i
$459$		0			0
$460$	−539346.			−2.54890
$461$	−92015.8	−	16224.9i	−0.432973	−	0.0763447i	−0.0470857	−	0.998891i	$-0.514993\pi$
$461$	−92015.8	−	16224.9i	−0.432973	−	0.0763447i	−0.385887	+	0.922546i	$0.626104\pi$
$462$		0			0
$463$	−12089.8	−	4400.31i	−0.0563969	−	0.0205268i	0.313668	−	0.949533i	$-0.398442\pi$
$463$	−12089.8	−	4400.31i	−0.0563969	−	0.0205268i	−0.370065	+	0.929006i	$0.620664\pi$
$464$	−15974.4	−	19037.6i	−0.0741974	−	0.0884250i
$465$		0			0
$466$	−187032.	+	68073.9i	−0.861277	+	0.313479i
$467$	−104386.	−	60267.3i	−0.478639	−	0.276342i	0.241210	−	0.970473i	$-0.422456\pi$
$467$	−104386.	−	60267.3i	−0.478639	−	0.276342i	−0.719849	+	0.694130i	$0.755789\pi$
$468$		0			0
$469$	22967.3	+	39780.5i	0.104415	+	0.180853i
$470$	634126.	−	755721.i	2.87065	−	3.42110i
$471$		0			0
$472$	−104131.	−	590556.i	−0.467408	−	2.65080i
$473$	−31384.6	+	5533.96i	−0.140280	+	0.0247351i
$474$		0			0
$475$	−271412.	−	227742.i	−1.20294	−	1.00938i
$476$	183265.	−	105808.i	0.808846	−	0.466987i
$477$		0			0
$478$	−13135.5	+	22751.4i	−0.0574899	+	0.0995754i
$479$	51328.2	+	141023.i	0.223710	+	0.614638i	0.999874	−	0.0158933i	$-0.00505922\pi$
$479$	51328.2	+	141023.i	0.223710	+	0.614638i	−0.776164	+	0.630531i	$0.782837\pi$
$480$		0			0
$481$	1617.96	−	1357.63i	0.00699324	−	0.00586802i
$482$	−219643.	+	603465.i	−0.945418	+	2.59752i
$483$		0			0
$484$	−79933.1	+	453323.i	−0.341221	+	1.93516i
$485$		−	469650.i		−	1.99660i
$486$		0			0
$487$	−88735.1			−0.374143			−0.187071	−	0.982346i	$-0.559900\pi$
$487$	−88735.1			−0.374143			−0.187071	+	0.982346i	$0.559900\pi$
$488$	−97917.6	−	17265.5i	−0.411170	−	0.0725003i
$489$		0			0
$490$	544614.	+	198223.i	2.26828	+	0.825586i
$491$	−273525.	−	325975.i	−1.13458	−	1.35214i	−0.927504	−	0.373812i	$-0.878050\pi$
$491$	−273525.	−	325975.i	−1.13458	−	1.35214i	−0.207074	−	0.978325i	$-0.566394\pi$
$492$		0			0
$493$	−12304.9	+	4478.63i	−0.0506274	+	0.0184269i
$494$	−15154.8	−	8749.60i	−0.0621005	−	0.0358537i
$495$		0			0
$496$	289989.	+	502275.i	1.17874	+	2.04164i
$497$	−17521.8	+	20881.6i	−0.0709357	+	0.0845379i
$498$		0			0
$499$	−20429.8	−	115863.i	−0.0820472	−	0.465313i	−0.997955	−	0.0639235i	$-0.979639\pi$
$499$	−20429.8	−	115863.i	−0.0820472	−	0.465313i	0.915908	−	0.401389i	$-0.131472\pi$
$500$	−33258.2	+	5864.32i	−0.133033	+	0.0234573i
$501$		0			0
$502$	−73769.1	−	61899.6i	−0.292730	−	0.245630i
$503$	−225624.	+	130264.i	−0.891764	+	0.514860i	−0.874519	−	0.484991i	$-0.838823\pi$
$503$	−225624.	+	130264.i	−0.891764	+	0.514860i	−0.0172448	+	0.999851i	$0.505489\pi$
$504$		0			0
$505$	308550.	−	534424.i	1.20988	−	2.09557i
$506$	53455.2	+	146867.i	0.208780	+	0.573619i
$507$		0			0
$508$	563213.	−	472592.i	2.18246	−	1.83130i
$509$	−62362.0	+	171338.i	−0.240705	+	0.661331i	0.759240	+	0.650811i	$0.225571\pi$
$509$	−62362.0	+	171338.i	−0.240705	+	0.661331i	−0.999945	+	0.0105200i	$0.996651\pi$
$510$		0			0
$511$	14356.6	−	81420.2i	0.0549805	−	0.311810i
$512$			387626.i			1.47867i
$513$		0			0
$514$	71241.4			0.269654
$515$	455412.	+	80301.5i	1.71708	+	0.302767i
$516$		0			0
$517$	−191332.	−	69639.3i	−0.715826	−	0.260539i
$518$	−35197.7	−	41947.0i	−0.131176	−	0.156330i
$519$		0			0
$520$	−25369.0	+	9233.57i	−0.0938203	+	0.0341478i
$521$	−386241.	−	222996.i	−1.42293	−	0.821528i	−0.426380	−	0.904544i	$-0.640211\pi$
$521$	−386241.	−	222996.i	−1.42293	−	0.821528i	−0.996548	+	0.0830166i	$0.973545\pi$
$522$		0			0
$523$	−236571.	−	409752.i	−0.864883	−	1.49802i	−0.867163	−	0.498024i	$-0.834059\pi$
$523$	−236571.	−	409752.i	−0.864883	−	1.49802i	0.00227985	−	0.999997i	$-0.499274\pi$
$524$	−705270.	+	840508.i	−2.56858	+	3.06111i
$525$		0			0
$526$	110066.	+	624217.i	0.397817	+	2.25613i
$527$	300953.	−	53066.2i	1.08362	−	0.191072i
$528$		0			0
$529$	102829.	+	86283.5i	0.367454	+	0.308331i
$530$	−137683.	+	79491.2i	−0.490149	+	0.282988i
$531$		0			0
$532$	−161564.	+	279837.i	−0.570850	+	0.988741i
$533$	3470.76	+	9535.85i	0.0122172	+	0.0335664i
$534$		0			0
$535$	293443.	−	246227.i	1.02522	−	0.860259i
$536$	185015.	−	508323.i	0.643986	−	1.76934i
$537$		0			0
$538$	−18228.3	+	103378.i	−0.0629770	+	0.357160i
$539$		−	119618.i		−	0.411738i
$540$		0			0
$541$	22010.9			0.0752045			0.0376023	−	0.999293i	$-0.488028\pi$
$541$	22010.9			0.0752045			0.0376023	+	0.999293i	$0.488028\pi$
$542$	133199.	+	23486.6i	0.453422	+	0.0799506i
$543$		0			0
$544$	−754223.	−	274515.i	−2.54860	−	0.927615i
$545$	−34596.1	−	41230.0i	−0.116475	−	0.138810i
$546$		0			0
$547$	129770.	−	47232.4i	0.433710	−	0.157858i	−0.115933	−	0.993257i	$-0.536986\pi$
$547$	129770.	−	47232.4i	0.433710	−	0.157858i	0.549643	+	0.835399i	$0.314764\pi$
$548$	774097.	+	446925.i	2.57771	+	1.48824i
$549$		0			0
$550$	132889.	+	230171.i	0.439303	+	0.760895i
$551$	12852.5	−	15317.0i	0.0423335	−	0.0504511i
$552$		0			0
$553$	6325.41	+	35873.2i	0.0206842	+	0.117306i
$554$	−1.07049e6	+	188755.i	−3.48788	+	0.615007i
$555$		0			0
$556$	586603.	+	492219.i	1.89756	+	1.59224i
$557$	254021.	−	146659.i	0.818765	−	0.472714i	−0.0312254	−	0.999512i	$-0.509941\pi$
$557$	254021.	−	146659.i	0.818765	−	0.472714i	0.849990	+	0.526798i	$0.176608\pi$
$558$		0			0
$559$	1246.82	−	2159.56i	0.00399008	−	0.00691102i
$560$	123800.	+	340138.i	0.394771	+	1.08463i
$561$		0			0
$562$	6986.64	−	5862.49i	0.0221205	−	0.0185613i
$563$	−18682.7	+	51330.3i	−0.0589417	+	0.161941i	−0.965668	−	0.259778i	$-0.916351\pi$
$563$	−18682.7	+	51330.3i	−0.0589417	+	0.161941i	0.906727	+	0.421719i	$0.138573\pi$
$564$		0			0
$565$	−215.991	+	1224.95i	−0.000676611	+	0.00383725i
$566$		−	806785.i		−	2.51840i
$567$		0			0
$568$	321014.			0.995011
$569$	115769.	+	20413.2i	0.357576	+	0.0630504i	0.349551	−	0.936917i	$-0.386334\pi$
$569$	115769.	+	20413.2i	0.357576	+	0.0630504i	0.00802559	+	0.999968i	$0.497445\pi$
$570$		0			0
$571$	−244279.	−	88910.4i	−0.749229	−	0.272697i	−0.0609476	−	0.998141i	$-0.519412\pi$
$571$	−244279.	−	88910.4i	−0.749229	−	0.272697i	−0.688281	+	0.725444i	$0.741634\pi$
$572$	6009.72	+	7162.10i	0.0183680	+	0.0218901i
$573$		0			0
$574$	247225.	−	89982.4i	0.750357	−	0.273108i
$575$	−214435.	−	123804.i	−0.648575	−	0.374455i
$576$		0			0
$577$	−251986.	−	436453.i	−0.756877	−	1.31095i	−0.944436	−	0.328696i	$-0.893391\pi$
$577$	−251986.	−	436453.i	−0.756877	−	1.31095i	0.187558	−	0.982253i	$-0.439943\pi$
$578$	−212543.	+	253299.i	−0.636196	+	0.758189i
$579$		0			0
$580$	−8988.00	−	50973.5i	−0.0267182	−	0.151526i
$581$	76826.9	−	13546.7i	0.227594	−	0.0401310i
$582$		0			0
$583$	25136.1	+	21091.7i	0.0739539	+	0.0620547i
$584$	−843190.	+	486816.i	−2.47229	+	1.42738i
$585$		0			0
$586$	−396526.	+	686802.i	−1.15472	+	2.00003i
$587$	−70170.3	−	192791.i	−0.203647	−	0.559514i	0.795260	−	0.606269i	$-0.207334\pi$
$587$	−70170.3	−	192791.i	−0.203647	−	0.559514i	−0.998906	+	0.0467544i	$0.985112\pi$
$588$		0			0
$589$	−357460.	+	299945.i	−1.03038	+	0.864591i
$590$	310165.	−	852170.i	0.891022	−	2.44806i
$591$		0			0
$592$	−57909.6	+	328422.i	−0.165237	+	0.937106i
$593$		−	319505.i		−	0.908590i	−0.890851	−	0.454295i	$-0.849891\pi$
$593$		−	319505.i		−	0.908590i	0.890851	−	0.454295i	$-0.150109\pi$
$594$		0			0
$595$	190724.			0.538732
$596$	1.01253e6	+	178537.i	2.85047	+	0.502615i
$597$		0			0
$598$	−11492.0	−	4182.73i	−0.0321360	−	0.0116965i
$599$	58679.5	+	69931.5i	0.163543	+	0.194903i	0.841592	−	0.540114i	$-0.181619\pi$
$599$	58679.5	+	69931.5i	0.163543	+	0.194903i	−0.678049	+	0.735017i	$0.737174\pi$
$600$		0			0
$601$	−276168.	+	100517.i	−0.764581	+	0.278285i	−0.694728	−	0.719272i	$-0.744475\pi$
$601$	−276168.	+	100517.i	−0.764581	+	0.278285i	−0.0698533	+	0.997557i	$0.522253\pi$
$602$	−55988.5	−	32324.9i	−0.154492	−	0.0891959i
$603$		0			0
$604$	−164131.	−	284283.i	−0.449900	−	0.779249i
$605$	−266674.	+	317810.i	−0.728568	+	0.868274i
$606$		0			0
$607$	93005.7	+	527462.i	0.252425	+	1.43157i	0.802597	+	0.596522i	$0.203451\pi$
$607$	93005.7	+	527462.i	0.252425	+	1.43157i	−0.550172	+	0.835051i	$0.685438\pi$
$608$	1.20696e6	−	212819.i	3.26501	−	0.575709i
$609$		0			0
$610$	−115185.	−	96651.3i	−0.309553	−	0.259745i
$611$	13797.6	−	7966.04i	0.0369590	−	0.0213383i
$612$		0			0
$613$	212960.	−	368858.i	0.566732	−	0.981608i	−0.430154	−	0.902755i	$-0.641541\pi$
$613$	212960.	−	368858.i	0.566732	−	0.981608i	0.996886	−	0.0788530i	$-0.0251258\pi$
$614$	−191668.	−	526604.i	−0.508409	−	1.39684i
$615$		0			0
$616$	110662.	−	92856.6i	0.291634	−	0.244710i
$617$	−134093.	+	368417.i	−0.352237	+	0.967763i	0.629413	+	0.777071i	$0.283295\pi$
$617$	−134093.	+	368417.i	−0.352237	+	0.967763i	−0.981650	+	0.190692i	$0.938927\pi$
$618$		0			0
$619$	−969.457	+	5498.07i	−0.00253016	+	0.0143492i	−0.986047	−	0.166469i	$-0.946763\pi$
$619$	−969.457	+	5498.07i	−0.00253016	+	0.0143492i	0.983517	+	0.180818i	$0.0578746\pi$
$620$			1.20795e6i			3.14242i
$621$		0			0
$622$	489699.			1.26575
$623$	−60885.5	−	10735.8i	−0.156869	−	0.0276603i
$624$		0			0
$625$	352498.	+	128299.i	0.902396	+	0.328445i
$626$	386472.	+	460579.i	0.986209	+	1.17532i
$627$		0			0
$628$	−678019.	+	246779.i	−1.71918	+	0.625732i
$629$	152177.	+	87859.2i	0.384633	+	0.222068i
$630$		0			0
$631$	327793.	+	567755.i	0.823269	+	1.42594i	0.903235	+	0.429145i	$0.141185\pi$
$631$	327793.	+	567755.i	0.823269	+	1.42594i	−0.0799669	+	0.996798i	$0.525481\pi$
$632$	275740.	−	328614.i	0.690345	−	0.822721i
$633$		0			0
$634$	45182.7	+	256244.i	0.112407	+	0.637492i
$635$	652571.	−	115066.i	1.61838	−	0.285364i
$636$		0			0
$637$	7170.04	+	6016.38i	0.0176703	+	0.0148271i
$638$	−12989.6	+	7499.53i	−0.0319119	+	0.0184244i
$639$		0			0
$640$	141390.	−	244895.i	0.345192	−	0.597889i
$641$	−58215.2	−	159945.i	−0.141684	−	0.389273i	0.848472	−	0.529240i	$-0.177523\pi$
$641$	−58215.2	−	159945.i	−0.141684	−	0.389273i	−0.990156	+	0.139966i	$0.955301\pi$
$642$		0			0
$643$	590812.	−	495750.i	1.42898	−	1.19906i	0.482675	−	0.875800i	$-0.339665\pi$
$643$	590812.	−	495750.i	1.42898	−	1.19906i	0.946310	−	0.323261i	$-0.104779\pi$
$644$	−77235.4	+	212203.i	−0.186228	+	0.511657i
$645$		0			0
$646$	252808.	−	1.43375e6i	0.605796	−	3.43564i
$647$			205603.i			0.491159i	0.969377	+	0.245579i	$0.0789782\pi$
$647$			205603.i			0.491159i	−0.969377	+	0.245579i	$0.921022\pi$
$648$		0			0
$649$	−187170.			−0.444372
$650$	−20480.5	−	3611.26i	−0.0484745	−	0.00854737i
$651$		0			0
$652$	−1.67648e6	−	610190.i	−3.94370	−	1.43539i
$653$	240608.	+	286746.i	0.564266	+	0.672467i	0.970444	−	0.241328i	$-0.0775829\pi$
$653$	240608.	+	286746.i	0.564266	+	0.672467i	−0.406177	+	0.913794i	$0.633138\pi$
$654$		0			0
$655$	−929247.	+	338218.i	−2.16595	+	0.788342i
$656$	−1.38762e6	−	801142.i	−3.22450	−	1.86167i
$657$		0			0
$658$	−206526.	−	357714.i	−0.477005	−	0.826197i
$659$	341921.	−	407485.i	0.787326	−	0.938299i	−0.211913	−	0.977288i	$-0.567969\pi$
$659$	341921.	−	407485.i	0.787326	−	0.938299i	0.999240	+	0.0389896i	$0.0124139\pi$
$660$		0			0
$661$	−63363.3	−	359351.i	−0.145022	−	0.822463i	−0.967349	−	0.253447i	$-0.918436\pi$
$661$	−63363.3	−	359351.i	−0.145022	−	0.822463i	0.822327	−	0.569015i	$-0.192676\pi$
$662$	−949921.	+	167497.i	−2.16756	+	0.382200i
$663$		0			0
$664$	−703769.	−	590532.i	−1.59622	−	1.33939i
$665$	−252210.	+	145614.i	−0.570322	+	0.329275i
$666$		0			0
$667$	6986.82	−	12101.5i	0.0157046	−	0.0272012i
$668$	−619871.	−	1.70308e6i	−1.38915	−	3.81665i
$669$		0			0
$670$	626670.	−	525839.i	1.39601	−	1.17139i
$671$	−10614.2	+	29162.3i	−0.0235745	+	0.0647703i
$672$		0			0
$673$	−41086.6	+	233014.i	−0.0907131	+	0.514459i	0.905264	+	0.424850i	$0.139673\pi$
$673$	−41086.6	+	233014.i	−0.0907131	+	0.514459i	−0.995977	+	0.0896096i	$0.971438\pi$
$674$			993546.i			2.18710i
$675$		0			0
$676$	1.13032e6			2.47348
$677$	−469839.	−	82845.2i	−1.02511	−	0.180755i	−0.364281	−	0.931289i	$-0.618685\pi$
$677$	−469839.	−	82845.2i	−1.02511	−	0.180755i	−0.660832	+	0.750534i	$0.729796\pi$
$678$		0			0
$679$	−184781.	−	67254.7i	−0.400791	−	0.145876i
$680$	−1.44374e6	−	1.72058e6i	−3.12227	−	3.72097i
$681$		0			0
$682$	328930.	−	119721.i	0.707188	−	0.257395i
$683$	303490.	+	175220.i	0.650584	+	0.375615i	0.788680	−	0.614804i	$-0.210765\pi$
$683$	303490.	+	175220.i	0.650584	+	0.375615i	−0.138096	+	0.990419i	$0.544098\pi$
$684$		0			0
$685$	402803.	+	697674.i	0.858442	+	1.48687i
$686$	327955.	−	390841.i	0.696892	−	0.830524i
$687$		0			0
$688$	68371.0	+	387751.i	0.144442	+	0.819174i
$689$	−2528.51	+	445.845i	−0.00532632	+	0.000939173i
$690$		0			0
$691$	−93314.5	−	78300.2i	−0.195431	−	0.163986i	0.539821	−	0.841780i	$-0.318492\pi$
$691$	−93314.5	−	78300.2i	−0.195431	−	0.163986i	−0.735252	+	0.677794i	$0.762936\pi$
$692$	1.20563e6	−	696071.i	2.51769	−	1.45359i
$693$		0			0
$694$	216128.	−	374345.i	0.448738	−	0.777236i
$695$	236048.	+	648535.i	0.488686	+	1.34265i
$696$		0			0
$697$	−646740.	+	542680.i	−1.33126	+	1.11706i
$698$	332985.	−	914868.i	0.683460	−	1.87779i
$699$		0			0
$700$	−66683.2	+	378179.i	−0.136088	+	0.771794i
$701$			430379.i			0.875820i	0.899019	+	0.437910i	$0.144281\pi$
$701$			430379.i			0.875820i	−0.899019	+	0.437910i	$0.855719\pi$
$702$		0			0
$703$	−268314.			−0.542916
$704$	−318015.	−	56074.7i	−0.641656	−	0.113141i
$705$		0			0
$706$	−194238.	−	70696.8i	−0.389695	−	0.141837i
$707$	−166081.	−	197928.i	−0.332262	−	0.395975i
$708$		0			0
$709$	701376.	−	255280.i	1.39527	−	0.507837i	0.468500	−	0.883463i	$-0.344795\pi$
$709$	701376.	−	255280.i	1.39527	−	0.507837i	0.926771	+	0.375626i	$0.122572\pi$
$710$	420423.	+	242731.i	0.834007	+	0.481514i
$711$		0			0
$712$	364038.	+	630532.i	0.718103	+	1.24379i
$713$	−209619.	+	249815.i	−0.412337	+	0.491404i
$714$		0			0
$715$	1463.24	+	8298.42i	0.00286221	+	0.0162324i
$716$	292483.	−	51572.6i	0.570524	−	0.100599i
$717$		0			0
$718$	127555.	+	107031.i	0.247428	+	0.207617i
$719$	41439.1	−	23924.9i	0.0801590	−	0.0462798i	−0.459385	−	0.888237i	$-0.651930\pi$
$719$	41439.1	−	23924.9i	0.0801590	−	0.0462798i	0.539544	+	0.841958i	$0.318597\pi$
$720$		0			0
$721$	96810.0	−	167680.i	0.186230	−	0.322560i
$722$	427964.	+	1.17582e6i	0.820981	+	2.25563i
$723$		0			0
$724$	−63441.0	+	53233.3i	−0.121030	+	0.101556i
$725$	8127.22	−	22329.4i	0.0154620	−	0.0424816i
$726$		0			0
$727$	48735.6	−	276393.i	0.0922098	−	0.522948i	−0.903357	−	0.428890i	$-0.858905\pi$
$727$	48735.6	−	276393.i	0.0922098	−	0.522948i	0.995567	−	0.0940583i	$-0.0299840\pi$
$728$			11303.6i			0.0213281i
$729$		0			0
$730$	−1.47240e6			−2.76299
$731$	204310.	+	36025.4i	0.382344	+	0.0674176i
$732$		0			0
$733$	−440523.	−	160337.i	−0.819900	−	0.298419i	−0.102193	−	0.994765i	$-0.532586\pi$
$733$	−440523.	−	160337.i	−0.819900	−	0.298419i	−0.717707	+	0.696345i	$0.754808\pi$
$734$	932293.	+	1.11106e6i	1.73046	+	2.06228i
$735$		0			0
$736$	804851.	−	292942.i	1.48580	−	0.540787i
$737$	−146221.	−	84421.0i	−0.269201	−	0.155423i
$738$		0			0
$739$	−23646.7	−	40957.4i	−0.0432995	−	0.0749969i	0.843563	−	0.537030i	$-0.180454\pi$
$739$	−23646.7	−	40957.4i	−0.0432995	−	0.0749969i	−0.886863	+	0.462033i	$0.847120\pi$
$740$	−446462.	+	532072.i	−0.815306	+	0.971644i
$741$		0			0
$742$	11558.9	+	65553.8i	0.0209947	+	0.119067i
$743$	−556406.	+	98109.4i	−1.00789	+	0.177719i	−0.653136	−	0.757240i	$-0.726547\pi$
$743$	−556406.	+	98109.4i	−1.00789	+	0.177719i	−0.354756	+	0.934959i	$0.615436\pi$
$744$		0			0
$745$	709854.	+	595638.i	1.27896	+	1.07317i
$746$	1.09909e6	−	634563.i	1.97496	−	1.14024i
$747$		0			0
$748$	−388919.	+	673628.i	−0.695114	+	1.20397i
$749$	−54855.2	−	150713.i	−0.0977810	−	0.268651i
$750$		0			0
$751$	−243878.	+	204638.i	−0.432408	+	0.362833i	−0.832859	−	0.553485i	$-0.813298\pi$
$751$	−243878.	+	204638.i	−0.432408	+	0.362833i	0.400452	+	0.916318i	$0.368853\pi$
$752$	−860380.	+	2.36387e6i	−1.52144	+	4.18012i
$753$		0			0
$754$	203.800	−	1155.81i	0.000358477	−	0.00203302i
$755$		−	295854.i		−	0.519019i
$756$		0			0
$757$	55832.2			0.0974301			0.0487151	−	0.998813i	$-0.484487\pi$
$757$	55832.2			0.0974301			0.0487151	+	0.998813i	$0.484487\pi$
$758$	−1.30047e6	−	229309.i	−2.26341	−	0.399100i
$759$		0			0
$760$	3.22279e6	+	1.17300e6i	5.57963	+	2.03082i
$761$	357987.	+	426632.i	0.618156	+	0.736689i	0.980752	−	0.195257i	$-0.0625541\pi$
$761$	357987.	+	426632.i	0.618156	+	0.736689i	−0.362597	+	0.931946i	$0.618110\pi$
$762$		0			0
$763$	−21175.9	+	7707.41i	−0.0363742	+	0.0132391i
$764$	−391249.	−	225887.i	−0.670295	−	0.386995i
$765$		0			0
$766$	−168637.	−	292087.i	−0.287405	−	0.497800i
$767$	9413.97	−	11219.1i	0.0160023	−	0.0190708i
$768$		0			0
$769$	57418.1	+	325634.i	0.0970948	+	0.550652i	0.994085	+	0.108602i	$0.0346374\pi$
$769$	57418.1	+	325634.i	0.0970948	+	0.550652i	−0.896991	+	0.442050i	$0.854251\pi$
$770$	215143.	−	37935.6i	0.362866	−	0.0639831i
$771$		0			0
$772$	−854458.	−	716975.i	−1.43369	−	1.20301i
$773$	−919517.	+	530884.i	−1.53887	+	0.888465i	−0.539961	+	0.841690i	$0.681561\pi$
$773$	−919517.	+	530884.i	−1.53887	+	0.888465i	−0.998905	+	0.0467747i	$0.985106\pi$
$774$		0			0
$775$	−277278.	+	480259.i	−0.461648	+	0.799598i
$776$	792021.	+	2.17606e6i	1.31527	+	3.61366i
$777$		0			0
$778$	−374309.	+	314083.i	−0.618403	+	0.518901i
$779$	440914.	−	1.21140e6i	0.726573	−	1.99624i
$780$		0			0
$781$	17398.9	−	98673.9i	0.0285246	−	0.161771i
$782$		−	1.01744e6i		−	1.66378i
$783$		0			0
$784$	−1.47786e6			−2.40437
$785$	−640420.	−	112923.i	−1.03926	−	0.183250i
$786$		0			0
$787$	375416.	+	136640.i	0.606127	+	0.220612i	0.626808	−	0.779174i	$-0.284361\pi$
$787$	375416.	+	136640.i	0.606127	+	0.220612i	−0.0206809	+	0.999786i	$0.506583\pi$
$788$	1.70874e6	+	2.03639e6i	2.75184	+	3.27951i
$789$		0			0
$790$	609606.	−	221879.i	0.976777	−	0.355518i
$791$	451.018	+	260.395i	0.000720843	+	0.000416179i
$792$		0			0
$793$	−1214.16	−	2102.98i	−0.00193076	−	0.00334418i
$794$	1.07134e6	−	1.27677e6i	1.69937	−	2.02522i
$795$		0			0
$796$	143332.	+	812878.i	0.226213	+	1.28292i
$797$	969956.	−	171029.i	1.52699	−	0.269249i	0.653813	−	0.756657i	$-0.273168\pi$
$797$	969956.	−	171029.i	1.52699	−	0.269249i	0.873175	+	0.487407i	$0.162057\pi$
$798$		0			0
$799$	1.01538e6	+	852006.i	1.59051	+	1.33459i
$800$	1.26137e6	−	728251.i	1.97089	−	1.13789i
$801$		0			0
$802$	1.00747e6	−	1.74499e6i	1.56633	−	2.71296i
$803$	103938.	+	285566.i	0.161191	+	0.442869i
$804$		0			0
$805$	−155911.	+	130825.i	−0.240594	+	0.201882i
$806$	−9367.83	+	25737.9i	−0.0144201	+	0.0396190i
$807$		0			0
$808$	−528368.	+	2.99653e6i	−0.809309	+	4.58982i
$809$			321706.i			0.491544i	0.969328	+	0.245772i	$0.0790414\pi$
$809$			321706.i			0.491544i	−0.969328	+	0.245772i	$0.920959\pi$
$810$		0			0
$811$	−183034.			−0.278285			−0.139143	−	0.990272i	$-0.544435\pi$
$811$	−183034.			−0.278285			−0.139143	+	0.990272i	$0.544435\pi$
$812$	−21342.3	−	3763.23i	−0.0323690	−	0.00570753i
$813$		0			0
$814$	189135.	+	68839.7i	0.285446	+	0.103894i
$815$	−1.03357e6	−	1.23176e6i	−1.55605	−	1.85443i
$816$		0			0
$817$	−297680.	+	108347.i	−0.445970	+	0.162320i
$818$	−1.33772e6	−	772332.i	−1.99921	−	1.15424i
$819$		0			0
$820$	−1.66857e6	−	2.89006e6i	−2.48152	−	4.29812i
$821$	−472182.	+	562724.i	−0.700523	+	0.834851i	−0.992586	−	0.121548i	$-0.961214\pi$
$821$	−472182.	+	562724.i	−0.700523	+	0.834851i	0.292062	+	0.956399i	$0.405659\pi$
$822$		0			0
$823$	−188428.	−	1.06863e6i	−0.278192	−	1.57771i	−0.728635	−	0.684902i	$-0.759845\pi$
$823$	−188428.	−	1.06863e6i	−0.278192	−	1.57771i	0.450443	−	0.892805i	$-0.351266\pi$
$824$	−2.24551e6	+	395945.i	−3.30721	+	0.583150i
$825$		0			0
$826$	−290865.	−	244065.i	−0.426316	−	0.357722i
$827$	126278.	−	72906.7i	0.184636	−	0.106600i	−0.404833	−	0.914391i	$-0.632670\pi$
$827$	126278.	−	72906.7i	0.184636	−	0.106600i	0.589469	+	0.807791i	$0.299337\pi$
$828$		0			0
$829$	−403873.	+	699529.i	−0.587673	+	1.01788i	0.406863	+	0.913489i	$0.366623\pi$
$829$	−403873.	+	699529.i	−0.587673	+	1.01788i	−0.994536	+	0.104391i	$0.966711\pi$
$830$	−475181.	−	1.30555e6i	−0.689767	−	1.89512i
$831$		0			0
$832$	19356.2	−	16241.8i	0.0279623	−	0.0234632i
$833$	−266331.	+	731739.i	−0.383824	+	1.05455i
$834$		0			0
$835$	283646.	−	1.60864e6i	0.406822	−	2.30720i
$836$		−	1.18772e6i		−	1.69943i
$837$		0			0
$838$	−654446.			−0.931936
$839$	683160.	+	120459.i	0.970506	+	0.171126i	0.636358	−	0.771394i	$-0.280440\pi$
$839$	683160.	+	120459.i	0.970506	+	0.171126i	0.334148	+	0.942520i	$0.391551\pi$
$840$		0			0
$841$	−663367.	−	241446.i	−0.937911	−	0.341372i
$842$	−1.33110e6	−	1.58634e6i	−1.87753	−	2.23755i
$843$		0			0
$844$	1.47198e6	−	535756.i	2.06641	−	0.752112i
$845$	882246.	+	509365.i	1.23559	+	0.713371i
$846$		0			0
$847$	86852.2	+	150432.i	0.121064	+	0.209689i
$848$	260584.	−	310552.i	0.362373	−	0.431859i
$849$		0			0
$850$	−300443.	−	1.70390e6i	−0.415838	−	2.35833i
$851$	−184665.	+	32561.4i	−0.254991	+	0.0449618i
$852$		0			0
$853$	573354.	+	481101.i	0.787998	+	0.661208i	0.945249	−	0.326350i	$-0.105819\pi$
$853$	573354.	+	481101.i	0.787998	+	0.661208i	−0.157251	+	0.987559i	$0.550263\pi$
$854$	−54521.5	+	31478.0i	−0.0747571	+	0.0431610i
$855$		0			0
$856$	−944388.	+	1.63573e6i	−1.28885	+	2.23236i
$857$	84810.3	+	233014.i	0.115475	+	0.317264i	0.983944	−	0.178479i	$-0.0571178\pi$
$857$	84810.3	+	233014.i	0.115475	+	0.317264i	−0.868469	+	0.495744i	$0.834896\pi$
$858$		0			0
$859$	842217.	−	706704.i	1.14140	−	0.957748i	0.141916	−	0.989879i	$-0.454674\pi$
$859$	842217.	−	706704.i	1.14140	−	0.957748i	0.999484	+	0.0321302i	$0.0102291\pi$
$860$	−280472.	+	770590.i	−0.379221	+	1.04190i
$861$		0			0
$862$	54189.9	−	307326.i	0.0729296	−	0.413604i
$863$			337849.i			0.453629i	0.973938	+	0.226814i	$0.0728311\pi$
$863$			337849.i			0.453629i	−0.973938	+	0.226814i	$0.927169\pi$
$864$		0			0
$865$	1.25470e6			1.67691
$866$	−7437.80	−	1311.48i	−0.00991765	−	0.00174875i
$867$		0			0
$868$	475259.	+	172980.i	0.630799	+	0.229592i
$869$	−86064.9	−	102568.i	−0.113969	−	0.135823i
$870$		0			0
$871$	12414.7	−	4518.58i	0.0163644	−	0.00595614i
$872$	229827.	+	132691.i	0.302252	+	0.174505i
$873$		0			0
$874$	776796.	+	1.34545e6i	1.01691	+	1.76135i
$875$	−8191.61	+	9762.38i	−0.0106992	+	0.0127509i
$876$		0			0
$877$	−53418.6	−	302952.i	−0.0694533	−	0.393889i	−0.999641	−	0.0268043i	$-0.991467\pi$
$877$	−53418.6	−	302952.i	−0.0694533	−	0.393889i	0.930187	−	0.367085i	$-0.119644\pi$
$878$	481939.	−	84978.8i	0.625177	−	0.110236i
$879$		0			0
$880$	−1.01921e6	−	855220.i	−1.31613	−	1.10436i
$881$	1.14282e6	−	659808.i	1.47240	−	0.850092i	0.472884	−	0.881125i	$-0.343213\pi$
$881$	1.14282e6	−	659808.i	1.47240	−	0.850092i	0.999518	+	0.0310333i	$0.00987979\pi$
$882$		0			0
$883$	−347184.	+	601340.i	−0.445285	+	0.771256i	−0.998072	−	0.0620666i	$-0.980231\pi$
$883$	−347184.	+	601340.i	−0.445285	+	0.771256i	0.552787	+	0.833322i	$0.313564\pi$
$884$	−20816.6	−	57193.2i	−0.0266383	−	0.0731880i
$885$		0			0
$886$	−100197.	+	84075.6i	−0.127641	+	0.107103i
$887$	−196811.	+	540733.i	−0.250150	+	0.687283i	0.749529	+	0.661971i	$0.230280\pi$
$887$	−196811.	+	540733.i	−0.250150	+	0.687283i	−0.999680	+	0.0253113i	$0.991942\pi$
$888$		0			0
$889$	48177.4	−	273228.i	0.0609593	−	0.345717i
$890$			1.10105e6i			1.39004i
$891$		0			0
$892$	2.21171e6			2.77971
$893$	−1.99321e6	−	351456.i	−2.49948	−	0.440726i
$894$		0			0
$895$	251531.	+	91549.9i	0.314012	+	0.114291i
$896$	−76105.3	−	90698.7i	−0.0947979	−	0.112976i
$897$		0			0
$898$	−2.51596e6	+	915735.i	−3.11998	+	1.13558i
$899$	−27103.1	−	15648.0i	−0.0335352	−	0.0193615i
$900$		0			0
$901$	−106804.	−	184990.i	−0.131564	−	0.227876i
$902$	−621604.	+	740799.i	−0.764013	+	0.910515i
$903$		0			0
$904$	−1064.99	−	6039.88i	−0.00130320	−	0.00739080i
$905$	−73506.3	+	12961.1i	−0.0897486	+	0.0158251i
$906$		0			0
$907$	−820336.	−	688344.i	−0.997189	−	0.836741i	−0.0105963	−	0.999944i	$-0.503373\pi$
$907$	−820336.	−	688344.i	−0.997189	−	0.836741i	−0.986592	+	0.163203i	$0.947817\pi$
$908$	410651.	−	237090.i	0.498083	−	0.287568i
$909$		0			0
$910$	−8547.05	+	14803.9i	−0.0103213	+	0.0178770i
$911$	−495638.	−	1.36175e6i	−0.597211	−	1.64082i	−0.756805	−	0.653641i	$-0.773241\pi$
$911$	−495638.	−	1.36175e6i	−0.597211	−	1.64082i	0.159594	−	0.987183i	$-0.448981\pi$
$912$		0			0
$913$	−219663.	+	184319.i	−0.263521	+	0.221120i
$914$	890177.	−	2.44574e6i	1.06558	−	2.92764i
$915$		0			0
$916$	359458.	−	2.03859e6i	0.428408	−	2.42962i
$917$			414040.i			0.492384i
$918$		0			0
$919$	−795804.			−0.942269			−0.471134	−	0.882061i	$-0.656155\pi$
$919$	−795804.			−0.942269			−0.471134	+	0.882061i	$0.656155\pi$
$920$	2.36041e6	+	416204.i	2.78877	+	0.491735i
$921$		0			0
$922$	654695.	+	238289.i	0.770153	+	0.280313i
$923$	5039.50	+	6005.85i	0.00591540	+	0.00704970i
$924$		0			0
$925$	−299640.	+	109060.i	−0.350200	+	0.127462i
$926$	83081.5	+	47967.2i	0.0968908	+	0.0559399i
$927$		0			0
$928$	41098.4	+	71184.6i	0.0477232	+	0.0826590i
$929$	709612.	−	845683.i	0.822223	−	0.979887i	−0.177768	−	0.984072i	$-0.556888\pi$
$929$	709612.	−	845683.i	0.822223	−	0.979887i	0.999991	+	0.00418521i	$0.00133220\pi$
$930$		0			0
$931$	−206475.	−	1.17098e6i	−0.238214	−	1.35098i
$932$	1.04099e6	−	183555.i	1.19844	−	0.211317i
$933$		0			0
$934$	688506.	+	577725.i	0.789249	+	0.662258i
$935$	−607124.	+	350523.i	−0.694471	+	0.400953i
$936$		0			0
$937$	−88661.1	+	153565.i	−0.100984	+	0.174910i	−0.912090	−	0.409989i	$-0.865533\pi$
$937$	−88661.1	+	153565.i	−0.100984	+	0.174910i	0.811106	+	0.584899i	$0.198866\pi$
$938$	−117148.	−	321861.i	−0.133146	−	0.365816i
$939$		0			0
$940$	−4.01355e6	+	3.36777e6i	−4.54227	+	3.81142i
$941$	−156015.	+	428647.i	−0.176192	+	0.484084i	−0.996082	−	0.0884379i	$-0.971813\pi$
$941$	−156015.	+	428647.i	−0.176192	+	0.484084i	0.819890	+	0.572522i	$0.194035\pi$
$942$		0			0
$943$	156445.	−	887245.i	0.175930	−	0.997746i
$944$			2.31245e6i			2.59494i
$945$		0			0
$946$	237634.			0.265537
$947$	924331.	+	162985.i	1.03069	+	0.181738i	0.663319	−	0.748337i	$-0.269147\pi$
$947$	924331.	+	162985.i	1.03069	+	0.181738i	0.367370	+	0.930075i	$0.380258\pi$
$948$		0			0
$949$	−22344.8	−	8132.84i	−0.0248110	−	0.00903046i
$950$	1.69819e6	+	2.02382e6i	1.88165	+	2.24246i
$951$		0			0
$952$	−883697.	+	321639.i	−0.975056	+	0.354891i
$953$	53349.3	+	30801.2i	0.0587412	+	0.0339143i	0.529083	−	0.848570i	$-0.322536\pi$
$953$	53349.3	+	30801.2i	0.0587412	+	0.0339143i	−0.470342	+	0.882484i	$0.655869\pi$
$954$		0			0
$955$	−203587.	−	352623.i	−0.223225	−	0.386637i
$956$	89683.3	−	106880.i	0.0981287	−	0.116945i
$957$		0			0
$958$	−194320.	−	1.10204e6i	−0.211732	−	1.20079i
$959$	332178.	−	58571.9i	0.361188	−	0.0636872i
$960$		0			0
$961$	−147962.	−	124155.i	−0.160215	−	0.134436i
$962$	−13639.2	+	7874.57i	−0.0147380	+	0.00850896i
$963$		0			0
$964$	1.70531e6	−	2.95368e6i	1.83506	−	3.17841i
$965$	−343832.	−	944670.i	−0.369225	−	1.01444i
$966$		0			0
$967$	163927.	−	137551.i	0.175306	−	0.147099i	−0.550913	−	0.834563i	$-0.685720\pi$
$967$	163927.	−	137551.i	0.175306	−	0.147099i	0.726219	+	0.687463i	$0.241276\pi$
$968$	699643.	−	1.92225e6i	0.746665	−	2.05145i
$969$		0			0
$970$	−608116.	+	3.44880e6i	−0.646313	+	3.66542i
$971$			597290.i			0.633500i	0.948509	+	0.316750i	$0.102592\pi$
$971$			597290.i			0.633500i	−0.948509	+	0.316750i	$0.897408\pi$
$972$		0			0
$973$	288965.			0.305225
$974$	651612.	+	114897.i	0.686865	+	0.121113i
$975$		0			0
$976$	360294.	+	131136.i	0.378231	+	0.137665i
$977$	−463336.	−	552182.i	−0.485408	−	0.578487i	0.466635	−	0.884450i	$-0.345466\pi$
$977$	−463336.	−	552182.i	−0.485408	−	0.578487i	−0.952043	+	0.305963i	$0.901022\pi$
$978$		0			0
$979$	213545.	−	77723.9i	0.222804	−	0.0810941i
$980$	−2.66563e6	−	1.53900e6i	−2.77554	−	1.60246i
$981$		0			0
$982$	1.58651e6	+	2.74791e6i	1.64520	+	2.84957i
$983$	−217960.	+	259754.i	−0.225564	+	0.268816i	−0.866943	−	0.498408i	$-0.833918\pi$
$983$	−217960.	+	259754.i	−0.225564	+	0.268816i	0.641379	+	0.767224i	$0.278363\pi$
$984$		0			0
$985$	416040.	+	2.35948e6i	0.428808	+	2.43189i
$986$	96158.5	−	16955.3i	0.0989085	−	0.0174402i
$987$		0			0
$988$	71193.3	+	59738.3i	0.0729332	+	0.0611982i
$989$	−191728.	+	110694.i	−0.196016	+	0.113170i
$990$		0			0
$991$	−246687.	+	427275.i	−0.251188	+	0.435071i	−0.963853	−	0.266433i	$-0.914155\pi$
$991$	−246687.	+	427275.i	−0.251188	+	0.435071i	0.712665	+	0.701505i	$0.247488\pi$
$992$	−656086.	−	1.80258e6i	−0.666711	−	1.83177i
$993$		0			0
$994$	155707.	−	130653.i	0.157592	−	0.132235i
$995$	−254439.	+	699064.i	−0.257002	+	0.706108i
$996$		0			0
$997$	135947.	−	770996.i	0.136767	−	0.775643i	−0.836846	−	0.547438i	$-0.815603\pi$
$997$	135947.	−	770996.i	0.136767	−	0.775643i	0.973613	−	0.228205i	$-0.0732857\pi$
$998$			877277.i			0.880797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.1		66
3.2	odd	2		27.5.f.a.2.11	✓	66
27.13	even	9		27.5.f.a.14.11	yes	66
27.14	odd	18	inner	81.5.f.a.71.1		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.11	✓	66	3.2	odd	2
27.5.f.a.14.11	yes	66	27.13	even	9
81.5.f.a.8.1		66	1.1	even	1	trivial
81.5.f.a.71.1		66	27.14	odd	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.34334 - 1.29483i) q^{2} +(37.2130 + 13.5444i) q^{4} +(22.9421 + 27.3414i) q^{5} +(14.0427 - 5.11111i) q^{7} +(-152.408 - 87.9929i) q^{8} +(-133.070 - 230.483i) q^{10} +(-35.3079 + 42.0783i) q^{11} +(-0.746352 - 4.23277i) q^{13} +(-109.738 + 19.3498i) q^{14} +(519.869 + 436.222i) q^{16} +(309.675 - 178.791i) q^{17} +(-273.006 + 472.860i) q^{19} +(483.423 + 1328.19i) q^{20} +(313.762 - 263.278i) q^{22} +(-130.510 + 358.573i) q^{23} +(-112.679 + 639.035i) q^{25} +32.0491i q^{26} +591.797 q^{28} +(-36.0636 - 6.35898i) q^{29} +(803.077 + 292.296i) q^{31} +(-1442.80 - 1719.46i) q^{32} +(-2505.56 + 911.948i) q^{34} +(461.914 + 266.686i) q^{35} +(245.703 + 425.571i) q^{37} +(2617.05 - 3118.88i) q^{38} +(-1090.72 - 6185.80i) q^{40} +(-2325.15 + 409.987i) q^{41} +(444.443 + 372.932i) q^{43} +(-1883.84 + 1087.63i) q^{44} +(1422.67 - 2464.14i) q^{46} +(1267.80 + 3483.25i) q^{47} +(-1668.20 + 1399.79i) q^{49} +(1654.88 - 4546.75i) q^{50} +(29.5565 - 167.623i) q^{52} -597.366i q^{53} -1960.52 q^{55} +(-2589.96 - 456.680i) q^{56} +(256.593 + 93.3924i) q^{58} +(2190.28 + 2610.27i) q^{59} +(530.905 - 193.234i) q^{61} +(-5518.80 - 3186.28i) q^{62} +(2939.43 + 5091.23i) q^{64} +(98.6069 - 117.515i) q^{65} +(533.761 + 3027.11i) q^{67} +(13945.6 - 2458.98i) q^{68} +(-3046.68 - 2556.47i) q^{70} +(-1579.71 + 912.046i) q^{71} +(2766.22 - 4791.24i) q^{73} +(-1253.24 - 3443.25i) q^{74} +(-16564.0 + 13898.9i) q^{76} +(-280.750 + 771.353i) q^{77} +(-423.277 + 2400.52i) q^{79} +24221.8i q^{80} +17605.3 q^{82} +(5141.02 + 906.501i) q^{83} +(11993.0 + 4365.10i) q^{85} +(-2780.81 - 3314.04i) q^{86} +(9083.80 - 3306.23i) q^{88} +(-3582.86 - 2068.56i) q^{89} +(-32.1149 - 55.6247i) q^{91} +(-9713.34 + 11575.9i) q^{92} +(-4799.67 - 27220.3i) q^{94} +(-19192.0 + 3384.07i) q^{95} +(-10080.0 - 8458.14i) q^{97} +(14062.6 - 8119.07i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Introduction

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