LMFDB - Embedded newform 189.4.e.f.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(109,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.109");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.e (of order $3$, degree $2$, 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 44 x^{12} + 23 x^{11} + 1346 x^{10} + 854 x^{9} + 20545 x^{8} + 27750 x^{7} + \cdots + 254016 $ x^14 - x^13 + 44x^12 + 23x^11 + 1346x^10 + 854x^9 + 20545x^8 + 27750x^7 + 221349x^6 + 172746x^5 + 551772x^4 + 275616x^3 + 1006128x^2 + 471744x + 254016
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.6
Root			$-1.81482 + 3.14336i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.f.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.81482 - 3.14336i) q^{2} +(-2.58715 - 4.48108i) q^{4} +(-2.42081 + 4.19297i) q^{5} +(16.3234 + 8.74903i) q^{7} +10.2563 q^{8} +(8.78669 + 15.2190i) q^{10} +(10.0662 + 17.4351i) q^{11} +72.2571 q^{13} +(57.1255 - 35.4325i) q^{14} +(39.3105 - 68.0878i) q^{16} +(-66.1814 - 114.630i) q^{17} +(-38.4685 + 66.6293i) q^{19} +25.0520 q^{20} +73.0732 q^{22} +(11.2359 - 19.4611i) q^{23} +(50.7793 + 87.9524i) q^{25} +(131.134 - 227.130i) q^{26} +(-3.02609 - 95.7816i) q^{28} +193.429 q^{29} +(-44.8853 - 77.7435i) q^{31} +(-101.658 - 176.077i) q^{32} -480.430 q^{34} +(-76.2004 + 47.2639i) q^{35} +(-23.9643 + 41.5074i) q^{37} +(139.627 + 241.841i) q^{38} +(-24.8285 + 43.0043i) q^{40} +3.41948 q^{41} -168.358 q^{43} +(52.0854 - 90.2145i) q^{44} +(-40.7822 - 70.6368i) q^{46} +(-81.5891 + 141.317i) q^{47} +(189.909 + 285.628i) q^{49} +368.622 q^{50} +(-186.940 - 323.790i) q^{52} +(-168.687 - 292.175i) q^{53} -97.4733 q^{55} +(167.418 + 89.7325i) q^{56} +(351.038 - 608.016i) q^{58} +(-258.894 - 448.418i) q^{59} +(-212.414 + 367.911i) q^{61} -325.835 q^{62} -108.996 q^{64} +(-174.921 + 302.972i) q^{65} +(489.169 + 847.266i) q^{67} +(-342.442 + 593.128i) q^{68} +(10.2775 + 325.301i) q^{70} -40.4250 q^{71} +(-241.120 - 417.632i) q^{73} +(86.9818 + 150.657i) q^{74} +398.095 q^{76} +(11.7740 + 372.670i) q^{77} +(537.485 - 930.952i) q^{79} +(190.327 + 329.656i) q^{80} +(6.20574 - 10.7487i) q^{82} -811.700 q^{83} +640.851 q^{85} +(-305.539 + 529.209i) q^{86} +(103.241 + 178.819i) q^{88} +(-498.519 + 863.461i) q^{89} +(1179.48 + 632.180i) q^{91} -116.276 q^{92} +(296.139 + 512.928i) q^{94} +(-186.250 - 322.594i) q^{95} -1452.82 q^{97} +(1242.48 - 78.5877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 31 q^{4} + q^{5} + 20 q^{7} + 168 q^{8} - 12 q^{10} - 98 q^{11} - 248 q^{13} - 134 q^{14} - 139 q^{16} - 30 q^{17} - 182 q^{19} - 220 q^{20} + 552 q^{22} + 6 q^{23} - 388 q^{25} + 245 q^{26}+ \cdots + 10160 q^{98}+O(q^{100}) $ 14 * q - q^2 - 31 * q^4 + q^5 + 20 * q^7 + 168 * q^8 - 12 * q^10 - 98 * q^11 - 248 * q^13 - 134 * q^14 - 139 * q^16 - 30 * q^17 - 182 * q^19 - 220 * q^20 + 552 * q^22 + 6 * q^23 - 388 * q^25 + 245 * q^26 + 425 * q^28 + 646 * q^29 - 26 * q^31 - 398 * q^32 + 228 * q^34 + 1025 * q^35 + 112 * q^37 - 1015 * q^38 + 147 * q^40 - 1048 * q^41 + 16 * q^43 - 937 * q^44 + 339 * q^46 - 288 * q^47 + 446 * q^49 + 5152 * q^50 + 1075 * q^52 - 1353 * q^53 + 312 * q^55 + 1980 * q^56 + 81 * q^58 - 165 * q^59 - 56 * q^61 - 2430 * q^62 - 3412 * q^64 - 1694 * q^65 + 988 * q^67 - 2625 * q^68 - 4941 * q^70 + 1584 * q^71 - 1487 * q^73 - 2736 * q^74 + 3904 * q^76 - 34 * q^77 + 1273 * q^79 + 2501 * q^80 + 2049 * q^82 - 2340 * q^83 + 432 * q^85 + 160 * q^86 - 9 * q^88 - 1058 * q^89 + 3538 * q^91 + 7668 * q^92 - 1653 * q^94 - 3260 * q^95 - 7460 * q^97 + 10160 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.81482	−	3.14336i	0.641636	−	1.11135i	−0.343431	−	0.939178i	$-0.611589\pi$
$2$	1.81482	−	3.14336i	0.641636	−	1.11135i	0.985067	−	0.172169i	$-0.0550774\pi$
$3$		0			0
$3$		0			0
$4$	−2.58715	−	4.48108i	−0.323394	−	0.560135i
$5$	−2.42081	+	4.19297i	−0.216524	+	0.375031i	−0.953743	−	0.300623i	$-0.902805\pi$
$5$	−2.42081	+	4.19297i	−0.216524	+	0.375031i	0.737219	+	0.675654i	$0.236139\pi$
$6$		0			0
$7$	16.3234	+	8.74903i	0.881382	+	0.472403i
$7$	16.3234	+	8.74903i	0.881382	+	0.472403i
$8$	10.2563			0.453268
$9$		0			0
$10$	8.78669	+	15.2190i	0.277859	+	0.481267i
$11$	10.0662	+	17.4351i	0.275915	+	0.477899i	0.970366	−	0.241642i	$-0.0776859\pi$
$11$	10.0662	+	17.4351i	0.275915	+	0.477899i	−0.694451	+	0.719540i	$0.744353\pi$
$12$		0			0
$13$	72.2571			1.54158			0.770789	−	0.637090i	$-0.219862\pi$
$13$	72.2571			1.54158			0.770789	+	0.637090i	$0.219862\pi$
$14$	57.1255	−	35.4325i	1.09053	−	0.676410i
$15$		0			0
$16$	39.3105	−	68.0878i	0.614227	−	1.06387i
$17$	−66.1814	−	114.630i	−0.944197	−	1.63540i	−0.757351	−	0.653008i	$-0.773507\pi$
$17$	−66.1814	−	114.630i	−0.944197	−	1.63540i	−0.186846	−	0.982389i	$-0.559826\pi$
$18$		0			0
$19$	−38.4685	+	66.6293i	−0.464488	+	0.804517i	−0.999178	−	0.0405314i	$-0.987095\pi$
$19$	−38.4685	+	66.6293i	−0.464488	+	0.804517i	0.534690	+	0.845048i	$0.320428\pi$
$20$	25.0520			0.280090
$21$		0			0
$22$	73.0732			0.708148
$23$	11.2359	−	19.4611i	0.101863	−	0.176431i	−0.810589	−	0.585615i	$-0.800853\pi$
$23$	11.2359	−	19.4611i	0.101863	−	0.176431i	0.912452	+	0.409184i	$0.134186\pi$
$24$		0			0
$25$	50.7793	+	87.9524i	0.406235	+	0.703619i
$26$	131.134	−	227.130i	0.989133	−	1.71323i
$27$		0			0
$28$	−3.02609	−	95.7816i	−0.0204242	−	0.646465i
$29$	193.429			1.23858			0.619290	−	0.785163i	$-0.287421\pi$
$29$	193.429			1.23858			0.619290	+	0.785163i	$0.287421\pi$
$30$		0			0
$31$	−44.8853	−	77.7435i	−0.260053	−	0.450424i	0.706203	−	0.708009i	$-0.250407\pi$
$31$	−44.8853	−	77.7435i	−0.260053	−	0.450424i	−0.966256	+	0.257585i	$0.917073\pi$
$32$	−101.658	−	176.077i	−0.561586	−	0.972696i
$33$		0			0
$34$	−480.430			−2.42332
$35$	−76.2004	+	47.2639i	−0.368006	+	0.228259i
$36$		0			0
$37$	−23.9643	+	41.5074i	−0.106479	+	0.184426i	−0.914341	−	0.404944i	$-0.867291\pi$
$37$	−23.9643	+	41.5074i	−0.106479	+	0.184426i	0.807863	+	0.589371i	$0.200624\pi$
$38$	139.627	+	241.841i	0.596064	+	1.03241i
$39$		0			0
$40$	−24.8285	+	43.0043i	−0.0981434	+	0.169989i
$41$	3.41948			0.0130252			0.00651260	−	0.999979i	$-0.497927\pi$
$41$	3.41948			0.0130252			0.00651260	+	0.999979i	$0.497927\pi$
$42$		0			0
$43$	−168.358			−0.597076			−0.298538	−	0.954398i	$-0.596499\pi$
$43$	−168.358			−0.597076			−0.298538	+	0.954398i	$0.596499\pi$
$44$	52.0854	−	90.2145i	0.178458	−	0.309099i
$45$		0			0
$46$	−40.7822	−	70.6368i	−0.130718	−	0.226409i
$47$	−81.5891	+	141.317i	−0.253213	+	0.438577i	−0.964409	−	0.264417i	$-0.914821\pi$
$47$	−81.5891	+	141.317i	−0.253213	+	0.438577i	0.711196	+	0.702994i	$0.248154\pi$
$48$		0			0
$49$	189.909	+	285.628i	0.553670	+	0.832736i
$50$	368.622			1.04262
$51$		0			0
$52$	−186.940	−	323.790i	−0.498537	−	0.863492i
$53$	−168.687	−	292.175i	−0.437188	−	0.757233i	0.560283	−	0.828301i	$-0.310692\pi$
$53$	−168.687	−	292.175i	−0.437188	−	0.757233i	−0.997471	+	0.0710687i	$0.977359\pi$
$54$		0			0
$55$	−97.4733			−0.238969
$56$	167.418	+	89.7325i	0.399502	+	0.214125i
$57$		0			0
$58$	351.038	−	608.016i	0.794717	−	1.37649i
$59$	−258.894	−	448.418i	−0.571274	−	0.989475i	−0.996436	−	0.0843579i	$-0.973116\pi$
$59$	−258.894	−	448.418i	−0.571274	−	0.989475i	0.425162	−	0.905117i	$-0.360217\pi$
$60$		0			0
$61$	−212.414	+	367.911i	−0.445849	+	0.772233i	−0.998111	−	0.0614374i	$-0.980432\pi$
$61$	−212.414	+	367.911i	−0.445849	+	0.772233i	0.552262	+	0.833671i	$0.313765\pi$
$62$	−325.835			−0.667436
$63$		0			0
$64$	−108.996			−0.212883
$65$	−174.921	+	302.972i	−0.333789	+	0.578140i
$66$		0			0
$67$	489.169	+	847.266i	0.891963	+	1.54493i	0.837519	+	0.546408i	$0.184005\pi$
$67$	489.169	+	847.266i	0.891963	+	1.54493i	0.0544438	+	0.998517i	$0.482661\pi$
$68$	−342.442	+	593.128i	−0.610695	+	1.05775i
$69$		0			0
$70$	10.2775	+	325.301i	0.0175484	+	0.555442i
$71$	−40.4250			−0.0675713			−0.0337856	−	0.999429i	$-0.510756\pi$
$71$	−40.4250			−0.0675713			−0.0337856	+	0.999429i	$0.510756\pi$
$72$		0			0
$73$	−241.120	−	417.632i	−0.386588	−	0.669590i	0.605400	−	0.795921i	$-0.293013\pi$
$73$	−241.120	−	417.632i	−0.386588	−	0.669590i	−0.991988	+	0.126331i	$0.959680\pi$
$74$	86.9818	+	150.657i	0.136641	+	0.236669i
$75$		0			0
$76$	398.095			0.600850
$77$	11.7740	+	372.670i	0.0174256	+	0.551555i
$78$		0			0
$79$	537.485	−	930.952i	0.765466	−	1.32583i	−0.174533	−	0.984651i	$-0.555842\pi$
$79$	537.485	−	930.952i	0.765466	−	1.32583i	0.940000	−	0.341175i	$-0.110825\pi$
$80$	190.327	+	329.656i	0.265990	+	0.460708i
$81$		0			0
$82$	6.20574	−	10.7487i	0.00835743	−	0.0144755i
$83$	−811.700			−1.07344			−0.536721	−	0.843760i	$-0.680337\pi$
$83$	−811.700			−1.07344			−0.536721	+	0.843760i	$0.680337\pi$
$84$		0			0
$85$	640.851			0.817766
$86$	−305.539	+	529.209i	−0.383106	+	0.663559i
$87$		0			0
$88$	103.241	+	178.819i	0.125063	+	0.216616i
$89$	−498.519	+	863.461i	−0.593741	+	1.02839i	0.399982	+	0.916523i	$0.369016\pi$
$89$	−498.519	+	863.461i	−0.593741	+	1.02839i	−0.993723	+	0.111867i	$0.964317\pi$
$90$		0			0
$91$	1179.48	+	632.180i	1.35872	+	0.728247i
$92$	−116.276			−0.131767
$93$		0			0
$94$	296.139	+	512.928i	0.324941	+	0.562814i
$95$	−186.250	−	322.594i	−0.201146	−	0.348395i
$96$		0			0
$97$	−1452.82			−1.52074			−0.760369	−	0.649491i	$-0.774982\pi$
$97$	−1452.82			−1.52074			−0.760369	+	0.649491i	$0.774982\pi$
$98$	1242.48	−	78.5877i	1.28071	−	0.0810057i
$99$		0			0
$100$	262.748	−	455.092i	0.262748	−	0.455092i
$101$	111.862	+	193.751i	0.110205	+	0.190881i	0.915853	−	0.401514i	$-0.131516\pi$
$101$	111.862	+	193.751i	0.110205	+	0.190881i	−0.805648	+	0.592395i	$0.798183\pi$
$102$		0			0
$103$	269.234	−	466.326i	0.257557	−	0.446102i	−0.708030	−	0.706182i	$-0.750416\pi$
$103$	269.234	−	466.326i	0.257557	−	0.446102i	0.965587	+	0.260081i	$0.0837492\pi$
$104$	741.089			0.698748
$105$		0			0
$106$	−1224.55			−1.12206
$107$	−949.026	+	1643.76i	−0.857438	+	1.48513i	0.0169271	+	0.999857i	$0.494612\pi$
$107$	−949.026	+	1643.76i	−0.857438	+	1.48513i	−0.874365	+	0.485269i	$0.838722\pi$
$108$		0			0
$109$	427.252	+	740.022i	0.375443	+	0.650286i	0.990393	−	0.138280i	$-0.0441573\pi$
$109$	427.252	+	740.022i	0.375443	+	0.650286i	−0.614950	+	0.788566i	$0.710824\pi$
$110$	−176.897	+	306.394i	−0.153331	+	0.265577i
$111$		0			0
$112$	1237.38	−	767.498i	1.04395	−	0.647515i
$113$	−802.087			−0.667734			−0.333867	−	0.942620i	$-0.608354\pi$
$113$	−802.087			−0.667734			−0.333867	+	0.942620i	$0.608354\pi$
$114$		0			0
$115$	54.3999	+	94.2234i	0.0441115	+	0.0764033i
$116$	−500.429	−	866.768i	−0.400549	−	0.693771i
$117$		0			0
$118$	−1879.39			−1.46620
$119$	−77.4098	−	2450.17i	−0.0596315	−	1.88745i
$120$		0			0
$121$	462.845	−	801.670i	0.347742	−	0.602307i
$122$	770.986	+	1335.39i	0.572146	+	0.990986i
$123$		0			0
$124$	−232.250	+	402.269i	−0.168199	+	0.291329i
$125$	−1096.91			−0.784887
$126$		0			0
$127$	−1723.69			−1.20435			−0.602176	−	0.798364i	$-0.705699\pi$
$127$	−1723.69			−1.20435			−0.602176	+	0.798364i	$0.705699\pi$
$128$	615.456	−	1066.00i	0.424993	−	0.736109i
$129$		0			0
$130$	634.901	+	1099.68i	0.428342	+	0.741911i
$131$	−509.472	+	882.432i	−0.339792	+	0.588538i	−0.984394	−	0.175981i	$-0.943690\pi$
$131$	−509.472	+	882.432i	−0.339792	+	0.588538i	0.644601	+	0.764519i	$0.277024\pi$
$132$		0			0
$133$	−1210.88	+	751.058i	−0.789448	+	0.489661i
$134$	3551.02			2.28926
$135$		0			0
$136$	−678.775	−	1175.67i	−0.427974	−	0.741272i
$137$	−919.109	−	1591.94i	−0.573173	−	0.992765i	−0.996237	−	0.0866656i	$-0.972379\pi$
$137$	−919.109	−	1591.94i	−0.573173	−	0.992765i	0.423064	−	0.906100i	$-0.360955\pi$
$138$		0			0
$139$	−1467.29			−0.895352			−0.447676	−	0.894196i	$-0.647748\pi$
$139$	−1467.29			−0.895352			−0.447676	+	0.894196i	$0.647748\pi$
$140$	408.935	+	219.181i	0.246867	+	0.132316i
$141$		0			0
$142$	−73.3641	+	127.070i	−0.0433562	+	0.0750951i
$143$	727.352	+	1259.81i	0.425344	+	0.736718i
$144$		0			0
$145$	−468.255	+	811.041i	−0.268182	+	0.464505i
$146$	−1750.36			−0.992196
$147$		0			0
$148$	247.997			0.137738
$149$	1755.07	−	3039.86i	0.964971	−	1.67138i	0.255277	−	0.966868i	$-0.417833\pi$
$149$	1755.07	−	3039.86i	0.964971	−	1.67138i	0.709693	−	0.704511i	$-0.248833\pi$
$150$		0			0
$151$	−1618.79	−	2803.83i	−0.872421	−	1.51108i	−0.859485	−	0.511161i	$-0.829216\pi$
$151$	−1618.79	−	2803.83i	−0.872421	−	1.51108i	−0.0129353	−	0.999916i	$-0.504118\pi$
$152$	−394.543	+	683.369i	−0.210537	+	0.364661i
$153$		0			0
$154$	1192.80	+	639.320i	0.624149	+	0.334531i
$155$	434.635			0.225231
$156$		0			0
$157$	−1432.65	−	2481.42i	−0.728265	−	1.26139i	−0.957616	−	0.288048i	$-0.906994\pi$
$157$	−1432.65	−	2481.42i	−0.728265	−	1.26139i	0.229351	−	0.973344i	$-0.426340\pi$
$158$	−1950.88	−	3379.02i	−0.982302	−	1.70140i
$159$		0			0
$160$	984.380			0.486388
$161$	353.674	−	219.369i	0.173127	−	0.107383i
$162$		0			0
$163$	306.357	−	530.626i	0.147213	−	0.254980i	−0.782983	−	0.622043i	$-0.786303\pi$
$163$	306.357	−	530.626i	0.147213	−	0.254980i	0.930196	+	0.367062i	$0.119636\pi$
$164$	−8.84671	−	15.3229i	−0.00421227	−	0.00729586i
$165$		0			0
$166$	−1473.09	+	2551.47i	−0.688759	+	1.19297i
$167$	1633.90			0.757096			0.378548	−	0.925582i	$-0.376423\pi$
$167$	1633.90			0.757096			0.378548	+	0.925582i	$0.376423\pi$
$168$		0			0
$169$	3024.09			1.37647
$170$	1163.03	−	2014.43i	0.524708	−	0.908821i
$171$		0			0
$172$	435.566	+	754.423i	0.193091	+	0.334443i
$173$	518.386	−	897.871i	0.227816	−	0.394589i	−0.729345	−	0.684147i	$-0.760175\pi$
$173$	518.386	−	897.871i	0.227816	−	0.394589i	0.957161	+	0.289558i	$0.0935082\pi$
$174$		0			0
$175$	59.3946	+	1879.95i	0.0256561	+	0.812064i
$176$	1582.82			0.677897
$177$		0			0
$178$	1809.45	+	3134.05i	0.761931	+	1.31970i
$179$	261.129	+	452.289i	0.109037	+	0.188858i	0.915381	−	0.402590i	$-0.131890\pi$
$179$	261.129	+	452.289i	0.109037	+	0.188858i	−0.806343	+	0.591448i	$0.798556\pi$
$180$		0			0
$181$	2657.83			1.09147			0.545733	−	0.837959i	$-0.316251\pi$
$181$	2657.83			1.09147			0.545733	+	0.837959i	$0.316251\pi$
$182$	4127.72	−	2560.25i	1.68114	−	1.04274i
$183$		0			0
$184$	115.238	−	199.598i	0.0461710	−	0.0799706i
$185$	−116.026	−	200.963i	−0.0461104	−	0.0798655i
$186$		0			0
$187$	1332.39	−	2307.76i	0.521036	−	0.902461i
$188$	844.334			0.327550
$189$		0			0
$190$	−1352.04			−0.516249
$191$	−1457.71	+	2524.82i	−0.552231	+	0.956492i	0.445883	+	0.895091i	$0.352890\pi$
$191$	−1457.71	+	2524.82i	−0.552231	+	0.956492i	−0.998113	+	0.0614001i	$0.980443\pi$
$192$		0			0
$193$	−926.189	−	1604.21i	−0.345433	−	0.598307i	0.639999	−	0.768375i	$-0.278935\pi$
$193$	−926.189	−	1604.21i	−0.345433	−	0.598307i	−0.985432	+	0.170068i	$0.945601\pi$
$194$	−2636.61	+	4566.74i	−0.975760	+	1.69007i
$195$		0			0
$196$	788.600	−	1589.96i	0.287391	−	0.579431i
$197$	−2926.04			−1.05823			−0.529116	−	0.848549i	$-0.677477\pi$
$197$	−2926.04			−1.05823			−0.529116	+	0.848549i	$0.677477\pi$
$198$		0			0
$199$	814.659	+	1411.03i	0.290199	+	0.502640i	0.973857	−	0.227163i	$-0.0729451\pi$
$199$	814.659	+	1411.03i	0.290199	+	0.502640i	−0.683658	+	0.729803i	$0.739612\pi$
$200$	520.807	+	902.064i	0.184133	+	0.318928i
$201$		0			0
$202$	812.041			0.282847
$203$	3157.42	+	1692.31i	1.09166	+	0.585109i
$204$		0			0
$205$	−8.27792	+	14.3378i	−0.00282027	+	0.00488485i
$206$	−977.221	−	1692.60i	−0.330516	−	0.572470i
$207$		0			0
$208$	2840.46	−	4919.83i	0.946879	−	1.64004i
$209$	−1548.92			−0.512637
$210$		0			0
$211$	1691.47			0.551874			0.275937	−	0.961176i	$-0.411012\pi$
$211$	1691.47			0.551874			0.275937	+	0.961176i	$0.411012\pi$
$212$	−872.839	+	1511.80i	−0.282768	+	0.489769i
$213$		0			0
$214$	3444.63	+	5966.27i	1.10033	+	1.90582i
$215$	407.562	−	705.919i	0.129281	−	0.223922i
$216$		0			0
$217$	−52.5006	−	1661.74i	−0.0164238	−	0.519846i
$218$	3101.54			0.963591
$219$		0			0
$220$	252.178	+	436.785i	0.0772811	+	0.133855i
$221$	−4782.08	−	8282.80i	−1.45555	−	2.52109i
$222$		0			0
$223$	−749.266			−0.224998			−0.112499	−	0.993652i	$-0.535886\pi$
$223$	−749.266			−0.224998			−0.112499	+	0.993652i	$0.535886\pi$
$224$	−118.905	−	3763.59i	−0.0354674	−	1.12261i
$225$		0			0
$226$	−1455.64	+	2521.25i	−0.428443	+	0.742084i
$227$	2353.64	+	4076.62i	0.688179	+	1.19196i	0.972427	+	0.233209i	$0.0749228\pi$
$227$	2353.64	+	4076.62i	0.688179	+	1.19196i	−0.284248	+	0.958751i	$0.591744\pi$
$228$		0			0
$229$	−1215.05	+	2104.54i	−0.350625	+	0.607300i	−0.986359	−	0.164608i	$-0.947364\pi$
$229$	−1215.05	+	2104.54i	−0.350625	+	0.607300i	0.635734	+	0.771908i	$0.280697\pi$
$230$	394.904			0.113214
$231$		0			0
$232$	1983.86			0.561408
$233$	−894.594	+	1549.48i	−0.251531	+	0.435665i	−0.963948	−	0.266092i	$-0.914268\pi$
$233$	−894.594	+	1549.48i	−0.251531	+	0.435665i	0.712416	+	0.701757i	$0.247601\pi$
$234$		0			0
$235$	−395.024	−	684.202i	−0.109653	−	0.189925i
$236$	−1339.60	+	2320.25i	−0.369493	+	0.639980i
$237$		0			0
$238$	−7842.26	−	4203.29i	−2.13587	−	1.14479i
$239$	2506.96			0.678500			0.339250	−	0.940696i	$-0.389827\pi$
$239$	2506.96			0.678500			0.339250	+	0.940696i	$0.389827\pi$
$240$		0			0
$241$	−1989.15	−	3445.31i	−0.531669	−	0.920878i	−0.999317	−	0.0369632i	$-0.988232\pi$
$241$	−1989.15	−	3445.31i	−0.531669	−	0.920878i	0.467647	−	0.883915i	$-0.345102\pi$
$242$	−1679.96	−	2909.78i	−0.446248	−	0.772924i
$243$		0			0
$244$	2198.19			0.576739
$245$	−1657.37	+	104.829i	−0.432185	+	0.0273359i
$246$		0			0
$247$	−2779.62	+	4814.45i	−0.716045	+	1.24023i
$248$	−460.356	−	797.359i	−0.117873	−	0.204163i
$249$		0			0
$250$	−1990.70	+	3447.99i	−0.503612	+	0.872281i
$251$	−2907.80			−0.731231			−0.365615	−	0.930766i	$-0.619141\pi$
$251$	−2907.80			−0.731231			−0.365615	+	0.930766i	$0.619141\pi$
$252$		0			0
$253$	452.409			0.112422
$254$	−3128.19	+	5418.18i	−0.772755	+	1.33845i
$255$		0			0
$256$	−2669.87	−	4624.35i	−0.651823	−	1.12899i
$257$	−1910.28	+	3308.69i	−0.463657	+	0.803077i	−0.999140	−	0.0414692i	$-0.986796\pi$
$257$	−1910.28	+	3308.69i	−0.463657	+	0.803077i	0.535483	+	0.844546i	$0.320129\pi$
$258$		0			0
$259$	−754.329	+	467.878i	−0.180972	+	0.112249i
$260$	1810.19			0.431781
$261$		0			0
$262$	1849.20	+	3202.91i	0.436046	+	0.755254i
$263$	3210.22	+	5560.27i	0.752665	+	1.30365i	0.946527	+	0.322625i	$0.104565\pi$
$263$	3210.22	+	5560.27i	0.752665	+	1.30365i	−0.193862	+	0.981029i	$0.562101\pi$
$264$		0			0
$265$	1633.44			0.378647
$266$	163.316	+	5169.27i	0.0376449	+	1.19153i
$267$		0			0
$268$	2531.11	−	4384.01i	0.576911	−	0.999238i
$269$	−560.208	−	970.309i	−0.126976	−	0.219929i	0.795528	−	0.605917i	$-0.207194\pi$
$269$	−560.208	−	970.309i	−0.126976	−	0.219929i	−0.922504	+	0.385989i	$0.873860\pi$
$270$		0			0
$271$	1119.08	−	1938.31i	0.250847	−	0.434480i	−0.712912	−	0.701253i	$-0.752624\pi$
$271$	1119.08	−	1938.31i	0.250847	−	0.434480i	0.963759	+	0.266774i	$0.0859576\pi$
$272$	−10406.5			−2.31980
$273$		0			0
$274$	−6672.07			−1.47107
$275$	−1022.31	+	1770.69i	−0.224172	+	0.388278i
$276$		0			0
$277$	−947.637	−	1641.35i	−0.205552	−	0.356027i	0.744756	−	0.667337i	$-0.232566\pi$
$277$	−947.637	−	1641.35i	−0.205552	−	0.356027i	−0.950309	+	0.311310i	$0.899232\pi$
$278$	−2662.87	+	4612.23i	−0.574490	+	0.995046i
$279$		0			0
$280$	−781.533	+	484.752i	−0.166805	+	0.103462i
$281$	8622.88			1.83060			0.915298	−	0.402777i	$-0.131955\pi$
$281$	8622.88			1.83060			0.915298	+	0.402777i	$0.131955\pi$
$282$		0			0
$283$	−1523.63	−	2639.01i	−0.320037	−	0.554320i	0.660458	−	0.750863i	$-0.270362\pi$
$283$	−1523.63	−	2639.01i	−0.320037	−	0.554320i	−0.980495	+	0.196542i	$0.937029\pi$
$284$	104.586	+	181.147i	0.0218521	+	0.0378490i
$285$		0			0
$286$	5280.06			1.09167
$287$	55.8176	+	29.9171i	0.0114802	+	0.00615315i
$288$		0			0
$289$	−6303.45	+	10917.9i	−1.28302	+	2.22225i
$290$	1699.60	+	2943.79i	0.344151	+	0.596087i
$291$		0			0
$292$	−1247.63	+	2160.95i	−0.250040	+	0.433083i
$293$	8032.29			1.60154			0.800770	−	0.598972i	$-0.204424\pi$
$293$	8032.29			1.60154			0.800770	+	0.598972i	$0.204424\pi$
$294$		0			0
$295$	2506.94			0.494778
$296$	−245.784	+	425.711i	−0.0482633	+	0.0835944i
$297$		0			0
$298$	−6370.26	−	11033.6i	−1.23832	−	2.14483i
$299$	811.872	−	1406.20i	0.157029	−	0.271983i
$300$		0			0
$301$	−2748.17	−	1472.97i	−0.526253	−	0.282061i
$302$	−11751.3			−2.23911
$303$		0			0
$304$	3024.43	+	5238.47i	0.570602	+	0.988311i
$305$	−1028.43	−	1781.29i	−0.193074	−	0.334414i
$306$		0			0
$307$	1367.50			0.254226			0.127113	−	0.991888i	$-0.459429\pi$
$307$	1367.50			0.254226			0.127113	+	0.991888i	$0.459429\pi$
$308$	1639.50	−	1016.91i	0.303309	−	0.188130i
$309$		0			0
$310$	788.785	−	1366.22i	0.144516	−	0.250309i
$311$	609.791	+	1056.19i	0.111184	+	0.192575i	0.916248	−	0.400612i	$-0.131203\pi$
$311$	609.791	+	1056.19i	0.111184	+	0.192575i	−0.805064	+	0.593188i	$0.797869\pi$
$312$		0			0
$313$	2362.11	−	4091.30i	0.426564	−	0.738830i	−0.570001	−	0.821644i	$-0.693057\pi$
$313$	2362.11	−	4091.30i	0.426564	−	0.738830i	0.996565	+	0.0828139i	$0.0263907\pi$
$314$	−10400.0			−1.86912
$315$		0			0
$316$	−5562.22			−0.990188
$317$	658.244	−	1140.11i	0.116627	−	0.202003i	−0.801802	−	0.597590i	$-0.796125\pi$
$317$	658.244	−	1140.11i	0.116627	−	0.202003i	0.918429	+	0.395586i	$0.129459\pi$
$318$		0			0
$319$	1947.08	+	3372.45i	0.341742	+	0.591915i
$320$	263.859	−	457.017i	0.0460943	−	0.0798376i
$321$		0			0
$322$	−47.7014	−	1509.84i	−0.00825557	−	0.261305i
$323$	10183.6			1.75427
$324$		0			0
$325$	3669.17	+	6355.19i	0.626243	+	1.08468i
$326$	−1111.97	−	1925.98i	−0.188914	−	0.327209i
$327$		0			0
$328$	35.0711			0.00590390
$329$	−2568.20	+	1592.94i	−0.430363	+	0.266936i
$330$		0			0
$331$	−3818.07	+	6613.09i	−0.634019	+	1.09815i	0.352703	+	0.935735i	$0.385262\pi$
$331$	−3818.07	+	6613.09i	−0.634019	+	1.09815i	−0.986722	+	0.162417i	$0.948071\pi$
$332$	2099.99	+	3637.29i	0.347144	+	0.601272i
$333$		0			0
$334$	2965.24	−	5135.94i	0.485780	−	0.841396i
$335$	−4736.75			−0.772526
$336$		0			0
$337$	9852.08			1.59251			0.796257	−	0.604959i	$-0.206810\pi$
$337$	9852.08			1.59251			0.796257	+	0.604959i	$0.206810\pi$
$338$	5488.19	−	9505.82i	0.883190	−	1.52973i
$339$		0			0
$340$	−1657.98	−	2871.70i	−0.264460	−	0.458059i
$341$	903.645	−	1565.16i	0.143505	−	0.248557i
$342$		0			0
$343$	600.991	+	6323.96i	0.0946077	+	0.995515i
$344$	−1726.72			−0.270635
$345$		0			0
$346$	−1881.56	−	3258.95i	−0.292350	−	0.506365i
$347$	−1791.93	−	3103.71i	−0.277221	−	0.480161i	0.693472	−	0.720484i	$-0.256080\pi$
$347$	−1791.93	−	3103.71i	−0.277221	−	0.480161i	−0.970693	+	0.240322i	$0.922747\pi$
$348$		0			0
$349$	9485.94			1.45493			0.727465	−	0.686145i	$-0.240698\pi$
$349$	9485.94			1.45493			0.727465	+	0.686145i	$0.240698\pi$
$350$	6017.17	+	3225.08i	0.918946	+	0.492537i
$351$		0			0
$352$	2046.61	−	3544.84i	0.309900	−	0.536763i
$353$	−3253.87	−	5635.86i	−0.490612	−	0.849764i	0.509330	−	0.860571i	$-0.329893\pi$
$353$	−3253.87	−	5635.86i	−0.490612	−	0.849764i	−0.999942	+	0.0108070i	$0.996560\pi$
$354$		0			0
$355$	97.8613	−	169.501i	0.0146308	−	0.0253413i
$356$	5158.98			0.768049
$357$		0			0
$358$	1895.61			0.279849
$359$	−2066.87	+	3579.93i	−0.303859	+	0.526299i	−0.977007	−	0.213209i	$-0.931608\pi$
$359$	−2066.87	+	3579.93i	−0.303859	+	0.526299i	0.673148	+	0.739508i	$0.264942\pi$
$360$		0			0
$361$	469.854	+	813.812i	0.0685019	+	0.118649i
$362$	4823.49	−	8354.54i	0.700324	−	1.21300i
$363$		0			0
$364$	−218.657	−	6920.91i	−0.0314855	−	0.996577i
$365$	2334.82			0.334823
$366$		0			0
$367$	−1647.43	−	2853.44i	−0.234320	−	0.405854i	0.724755	−	0.689007i	$-0.241953\pi$
$367$	−1647.43	−	2853.44i	−0.234320	−	0.405854i	−0.959075	+	0.283153i	$0.908620\pi$
$368$	−883.376	−	1530.05i	−0.125134	−	0.216738i
$369$		0			0
$370$	−842.267			−0.118344
$371$	−197.307	−	6245.15i	−0.0276110	−	0.873941i
$372$		0			0
$373$	−1181.65	+	2046.68i	−0.164031	+	0.284110i	−0.936311	−	0.351173i	$-0.885783\pi$
$373$	−1181.65	+	2046.68i	−0.164031	+	0.284110i	0.772280	+	0.635283i	$0.219116\pi$
$374$	−4836.08	−	8376.34i	−0.668631	−	1.15810i
$375$		0			0
$376$	−836.801	+	1449.38i	−0.114773	+	0.198793i
$377$	13976.6			1.90937
$378$		0			0
$379$	11071.4			1.50053			0.750266	−	0.661136i	$-0.229925\pi$
$379$	11071.4			1.50053			0.750266	+	0.661136i	$0.229925\pi$
$380$	−963.714	+	1669.20i	−0.130099	+	0.225337i
$381$		0			0
$382$	5290.96	+	9164.21i	0.708662	+	1.22744i
$383$	−3561.20	+	6168.18i	−0.475114	+	0.822922i	−0.999594	−	0.0285012i	$-0.990927\pi$
$383$	−3561.20	+	6168.18i	−0.475114	+	0.822922i	0.524480	+	0.851423i	$0.324260\pi$
$384$		0			0
$385$	−1591.10	−	852.797i	−0.210623	−	0.112890i
$386$	−6723.47			−0.886569
$387$		0			0
$388$	3758.67	+	6510.20i	0.491797	+	0.851818i
$389$	129.535	+	224.361i	0.0168835	+	0.0292431i	0.874344	−	0.485307i	$-0.161292\pi$
$389$	129.535	+	224.361i	0.0168835	+	0.0292431i	−0.857460	+	0.514550i	$0.827959\pi$
$390$		0			0
$391$	−2974.42			−0.384714
$392$	1947.76	+	2929.48i	0.250961	+	0.377452i
$393$		0			0
$394$	−5310.24	+	9197.61i	−0.679000	+	1.17606i
$395$	2602.30	+	4507.32i	0.331484	+	0.574147i
$396$		0			0
$397$	5111.40	−	8853.20i	0.646181	−	1.11922i	−0.337847	−	0.941201i	$-0.609699\pi$
$397$	5111.40	−	8853.20i	0.646181	−	1.11922i	0.984028	−	0.178016i	$-0.0569680\pi$
$398$	5913.84			0.744809
$399$		0			0
$400$	7984.64			0.998080
$401$	−2582.18	+	4472.46i	−0.321566	+	0.556968i	−0.980811	−	0.194960i	$-0.937542\pi$
$401$	−2582.18	+	4472.46i	−0.321566	+	0.556968i	0.659246	+	0.751928i	$0.270876\pi$
$402$		0			0
$403$	−3243.28	−	5617.53i	−0.400892	−	0.694365i
$404$	578.810	−	1002.53i	0.0712794	−	0.123460i
$405$		0			0
$406$	11049.7	−	6853.67i	1.35071	−	0.837787i
$407$	−964.914			−0.117516
$408$		0			0
$409$	2132.05	+	3692.81i	0.257758	+	0.446450i	0.965641	−	0.259880i	$-0.0836830\pi$
$409$	2132.05	+	3692.81i	0.257758	+	0.446450i	−0.707883	+	0.706330i	$0.750350\pi$
$410$	30.0459	+	52.0410i	0.00361917	+	0.00626859i
$411$		0			0
$412$	−2786.19			−0.333169
$413$	−302.819	−	9584.79i	−0.0360793	−	1.14198i
$414$		0			0
$415$	1964.97	−	3403.44i	0.232426	−	0.402574i
$416$	−7345.51	−	12722.8i	−0.865729	−	1.49949i
$417$		0			0
$418$	−2811.01	+	4868.82i	−0.328926	+	0.569717i
$419$	16613.9			1.93710			0.968548	−	0.248829i	$-0.0800456\pi$
$419$	16613.9			1.93710			0.968548	+	0.248829i	$0.0800456\pi$
$420$		0			0
$421$	−11821.1			−1.36847			−0.684235	−	0.729262i	$-0.739864\pi$
$421$	−11821.1			−1.36847			−0.684235	+	0.729262i	$0.739864\pi$
$422$	3069.71	−	5316.90i	0.354103	−	0.613324i
$423$		0			0
$424$	−1730.10	−	2996.63i	−0.198163	−	0.343229i
$425$	6721.29	−	11641.6i	0.767131	−	1.32871i
$426$		0			0
$427$	−6686.19	+	4147.16i	−0.757769	+	0.470012i
$428$	9821.10			1.10916
$429$		0			0
$430$	−1479.31	−	2562.23i	−0.165903	−	0.287353i
$431$	6562.26	+	11366.2i	0.733395	+	1.27028i	0.955424	+	0.295237i	$0.0953986\pi$
$431$	6562.26	+	11366.2i	0.733395	+	1.27028i	−0.222029	+	0.975040i	$0.571268\pi$
$432$		0			0
$433$	−12962.7			−1.43868			−0.719341	−	0.694657i	$-0.755556\pi$
$433$	−12962.7			−1.43868			−0.719341	+	0.694657i	$0.755556\pi$
$434$	−5318.74	−	2850.74i	−0.588267	−	0.315299i
$435$		0			0
$436$	2210.73	−	3829.09i	0.242832	−	0.420597i
$437$	864.453	+	1497.28i	0.0946280	+	0.163900i
$438$		0			0
$439$	−1921.29	+	3327.77i	−0.208880	+	0.361790i	−0.951362	−	0.308076i	$-0.900315\pi$
$439$	−1921.29	+	3327.77i	−0.208880	+	0.361790i	0.742482	+	0.669866i	$0.233648\pi$
$440$	−999.713			−0.108317
$441$		0			0
$442$	−34714.5			−3.73574
$443$	2571.94	−	4454.73i	0.275839	−	0.477766i	−0.694508	−	0.719485i	$-0.744378\pi$
$443$	2571.94	−	4454.73i	0.275839	−	0.477766i	0.970346	+	0.241719i	$0.0777111\pi$
$444$		0			0
$445$	−2413.64	−	4180.56i	−0.257119	−	0.445342i
$446$	−1359.78	+	2355.21i	−0.144367	+	0.250051i
$447$		0			0
$448$	−1779.19	−	953.609i	−0.187631	−	0.100567i
$449$	−14627.7			−1.53747			−0.768733	−	0.639570i	$-0.779113\pi$
$449$	−14627.7			−1.53747			−0.768733	+	0.639570i	$0.779113\pi$
$450$		0			0
$451$	34.4210	+	59.6190i	0.00359384	+	0.00622472i
$452$	2075.12	+	3594.21i	0.215941	+	0.374021i
$453$		0			0
$454$	17085.7			1.76624
$455$	−5506.03	+	3415.16i	−0.567311	+	0.351879i
$456$		0			0
$457$	1552.00	−	2688.14i	0.158861	−	0.275155i	−0.775597	−	0.631228i	$-0.782551\pi$
$457$	1552.00	−	2688.14i	0.158861	−	0.275155i	0.934458	+	0.356073i	$0.115885\pi$
$458$	4410.21	+	7638.71i	0.449947	+	0.779331i
$459$		0			0
$460$	281.482	−	487.540i	0.0285307	−	0.0494167i
$461$	−13751.8			−1.38934			−0.694671	−	0.719327i	$-0.744450\pi$
$461$	−13751.8			−1.38934			−0.694671	+	0.719327i	$0.744450\pi$
$462$		0			0
$463$	5910.83			0.593303			0.296652	−	0.954986i	$-0.404130\pi$
$463$	5910.83			0.593303			0.296652	+	0.954986i	$0.404130\pi$
$464$	7603.78	−	13170.1i	0.760768	−	1.31769i
$465$		0			0
$466$	3247.06	+	5624.07i	0.322783	+	0.559077i
$467$	4665.73	−	8081.28i	0.462322	−	0.800764i	−0.536755	−	0.843738i	$-0.680350\pi$
$467$	4665.73	−	8081.28i	0.462322	−	0.800764i	0.999076	+	0.0429740i	$0.0136833\pi$
$468$		0			0
$469$	572.162	+	18110.0i	0.0563326	+	1.78304i
$470$	−2867.59			−0.281430
$471$		0			0
$472$	−2655.29	−	4599.10i	−0.258940	−	0.448497i
$473$	−1694.72	−	2935.33i	−0.164742	−	0.285342i
$474$		0			0
$475$	−7813.61			−0.754764
$476$	−10779.1	+	6685.84i	−1.03794	+	0.643792i
$477$		0			0
$478$	4549.68	−	7880.27i	0.435350	−	0.754049i
$479$	9828.25	+	17023.0i	0.937504	+	1.62380i	0.770107	+	0.637914i	$0.220203\pi$
$479$	9828.25	+	17023.0i	0.937504	+	1.62380i	0.167396	+	0.985890i	$0.446464\pi$
$480$		0			0
$481$	−1731.59	+	2999.20i	−0.164145	+	0.284308i
$482$	−14439.8			−1.36455
$483$		0			0
$484$	−4789.79			−0.449830
$485$	3517.01	−	6091.64i	0.329277	−	0.570324i
$486$		0			0
$487$	−1136.03	−	1967.66i	−0.105705	−	0.183087i	0.808321	−	0.588742i	$-0.200377\pi$
$487$	−1136.03	−	1967.66i	−0.105705	−	0.183087i	−0.914026	+	0.405655i	$0.867043\pi$
$488$	−2178.57	+	3773.40i	−0.202089	+	0.350028i
$489$		0			0
$490$	−2678.31	+	5399.95i	−0.246926	+	0.497847i
$491$	−14877.7			−1.36746			−0.683730	−	0.729735i	$-0.739643\pi$
$491$	−14877.7			−1.36746			−0.683730	+	0.729735i	$0.739643\pi$
$492$		0			0
$493$	−12801.4	−	22172.6i	−1.16946	−	2.02557i
$494$	10089.0	+	17474.7i	0.918880	+	1.59155i
$495$		0			0
$496$	−7057.85			−0.638925
$497$	−659.874	−	353.679i	−0.0595562	−	0.0319209i
$498$		0			0
$499$	8268.39	−	14321.3i	0.741771	−	1.28479i	−0.209917	−	0.977719i	$-0.567319\pi$
$499$	8268.39	−	14321.3i	0.741771	−	1.28479i	0.951688	−	0.307067i	$-0.0993474\pi$
$500$	2837.88	+	4915.35i	0.253828	+	0.439642i
$501$		0			0
$502$	−5277.14	+	9140.28i	−0.469184	+	0.812650i
$503$	7642.71			0.677478			0.338739	−	0.940880i	$-0.390000\pi$
$503$	7642.71			0.677478			0.338739	+	0.940880i	$0.390000\pi$
$504$		0			0
$505$	−1083.19			−0.0954484
$506$	821.041	−	1422.08i	0.0721338	−	0.124939i
$507$		0			0
$508$	4459.44	+	7723.98i	0.389480	+	0.674599i
$509$	2353.24	−	4075.92i	0.204922	−	0.354935i	−0.745186	−	0.666857i	$-0.767639\pi$
$509$	2353.24	−	4075.92i	0.204922	−	0.354935i	0.950108	+	0.311921i	$0.100973\pi$
$510$		0			0
$511$	−282.029	−	8926.75i	−0.0244153	−	0.772791i
$512$	−9534.04			−0.822947
$513$		0			0
$514$	6933.62	+	12009.4i	0.594998	+	1.03057i
$515$	1303.53	+	2257.78i	0.111535	+	0.193184i
$516$		0			0
$517$	−3285.16			−0.279461
$518$	101.739	+	3220.25i	0.00862967	+	0.273146i
$519$		0			0
$520$	−1794.04	+	3107.37i	−0.151296	+	0.262052i
$521$	−9260.35	−	16039.4i	−0.778701	−	1.34875i	−0.932691	−	0.360677i	$-0.882546\pi$
$521$	−9260.35	−	16039.4i	−0.778701	−	1.34875i	0.153990	−	0.988072i	$-0.450788\pi$
$522$		0			0
$523$	3496.85	−	6056.72i	0.292364	−	0.506390i	−0.682004	−	0.731348i	$-0.738891\pi$
$523$	3496.85	−	6056.72i	0.292364	−	0.506390i	0.974368	+	0.224959i	$0.0722247\pi$
$524$	5272.33			0.439547
$525$		0			0
$526$	23303.9			1.93175
$527$	−5941.14	+	10290.4i	−0.491082	+	0.850578i
$528$		0			0
$529$	5831.01	+	10099.6i	0.479248	+	0.830082i
$530$	2964.41	−	5134.50i	0.242954	−	0.420808i
$531$		0			0
$532$	6498.27	+	3482.95i	0.529579	+	0.283844i
$533$	247.082			0.0200794
$534$		0			0
$535$	−4594.83	−	7958.48i	−0.371312	−	0.643131i
$536$	5017.05	+	8689.79i	0.404298	+	0.700264i
$537$		0			0
$538$	−4066.71			−0.325889
$539$	−3068.31	+	6186.27i	−0.245198	+	0.494362i
$540$		0			0
$541$	−689.423	+	1194.12i	−0.0547886	+	0.0948966i	−0.892119	−	0.451801i	$-0.850782\pi$
$541$	−689.423	+	1194.12i	−0.0547886	+	0.0948966i	0.837330	+	0.546697i	$0.184115\pi$
$542$	−4061.87	−	7035.37i	−0.321905	−	0.557556i
$543$		0			0
$544$	−13455.7	+	23306.0i	−1.06050	+	1.83683i
$545$	−4137.19			−0.325170
$546$		0			0
$547$	10336.8			0.807985			0.403992	−	0.914762i	$-0.367622\pi$
$547$	10336.8			0.807985			0.403992	+	0.914762i	$0.367622\pi$
$548$	−4755.75	+	8237.19i	−0.370721	+	0.642108i
$549$		0			0
$550$	3710.61	+	6426.96i	0.287674	+	0.498266i
$551$	−7440.90	+	12888.0i	−0.575305	+	0.996458i
$552$		0			0
$553$	16918.5	−	10493.9i	1.30099	−	0.806951i
$554$	−6879.16			−0.527559
$555$		0			0
$556$	3796.10	+	6575.04i	0.289551	+	0.501518i
$557$	−5074.80	−	8789.81i	−0.386043	−	0.668647i	0.605870	−	0.795564i	$-0.292825\pi$
$557$	−5074.80	−	8789.81i	−0.386043	−	0.668647i	−0.991913	+	0.126917i	$0.959492\pi$
$558$		0			0
$559$	−12165.0			−0.920440
$560$	222.618	+	7046.29i	0.0167988	+	0.531714i
$561$		0			0
$562$	15649.0	−	27104.8i	1.17458	−	2.03443i
$563$	5584.15	+	9672.02i	0.418017	+	0.724027i	0.995740	−	0.0922061i	$-0.0293919\pi$
$563$	5584.15	+	9672.02i	0.418017	+	0.724027i	−0.577723	+	0.816233i	$0.696059\pi$
$564$		0			0
$565$	1941.70	−	3363.13i	0.144581	−	0.250421i
$566$	−11060.5			−0.821389
$567$		0			0
$568$	−414.610			−0.0306279
$569$	−9388.28	+	16261.0i	−0.691700	+	1.19806i	0.279581	+	0.960122i	$0.409805\pi$
$569$	−9388.28	+	16261.0i	−0.691700	+	1.19806i	−0.971281	+	0.237937i	$0.923529\pi$
$570$		0			0
$571$	11749.6	+	20351.0i	0.861133	+	1.49153i	0.870836	+	0.491573i	$0.163578\pi$
$571$	11749.6	+	20351.0i	0.861133	+	1.49153i	−0.00970363	+	0.999953i	$0.503089\pi$
$572$	3763.54	−	6518.64i	0.275108	−	0.476500i
$573$		0			0
$574$	195.339	−	121.161i	0.0142044	−	0.00881037i
$575$	2282.20			0.165521
$576$		0			0
$577$	−1306.41	−	2262.78i	−0.0942578	−	0.163259i	0.815041	−	0.579404i	$-0.196714\pi$
$577$	−1306.41	−	2262.78i	−0.0942578	−	0.163259i	−0.909299	+	0.416144i	$0.863381\pi$
$578$	22879.3	+	39628.1i	1.64646	+	2.85175i
$579$		0			0
$580$	4845.78			0.346914
$581$	−13249.7	−	7101.59i	−0.946113	−	0.507097i
$582$		0			0
$583$	3396.07	−	5882.16i	0.241254	−	0.417863i
$584$	−2472.99	−	4283.35i	−0.175228	−	0.303504i
$585$		0			0
$586$	14577.2	−	25248.4i	1.02761	−	1.77987i
$587$	18759.2			1.31904			0.659520	−	0.751687i	$-0.270759\pi$
$587$	18759.2			1.31904			0.659520	+	0.751687i	$0.270759\pi$
$588$		0			0
$589$	6906.67			0.483165
$590$	4549.65	−	7880.22i	0.317468	−	0.549870i
$591$		0			0
$592$	1884.10	+	3263.35i	0.130804	+	0.226559i
$593$	4051.57	−	7017.52i	0.280570	−	0.485961i	−0.690955	−	0.722897i	$-0.742810\pi$
$593$	4051.57	−	7017.52i	0.280570	−	0.485961i	0.971525	+	0.236936i	$0.0761433\pi$
$594$		0			0
$595$	10460.9	+	5606.83i	0.720764	+	0.386315i
$596$	−18162.5			−1.24826
$597$		0			0
$598$	−2946.80	−	5104.01i	−0.201511	−	0.349028i
$599$	2776.43	+	4808.91i	0.189385	+	0.328025i	0.945045	−	0.326939i	$-0.106017\pi$
$599$	2776.43	+	4808.91i	0.189385	+	0.328025i	−0.755660	+	0.654964i	$0.772684\pi$
$600$		0			0
$601$	−21357.1			−1.44954			−0.724771	−	0.688990i	$-0.758054\pi$
$601$	−21357.1			−1.44954			−0.724771	+	0.688990i	$0.758054\pi$
$602$	−9617.51	+	5965.33i	−0.651130	+	0.403868i
$603$		0			0
$604$	−8376.12	+	14507.9i	−0.564271	+	0.977346i
$605$	2240.92	+	3881.39i	0.150589	+	0.260828i
$606$		0			0
$607$	−2549.12	+	4415.20i	−0.170454	+	0.295235i	−0.938579	−	0.345065i	$-0.887857\pi$
$607$	−2549.12	+	4415.20i	−0.170454	+	0.295235i	0.768125	+	0.640300i	$0.221190\pi$
$608$	15642.5			1.04340
$609$		0			0
$610$	−7465.65			−0.495534
$611$	−5895.40	+	10211.1i	−0.390347	+	0.676102i
$612$		0			0
$613$	−1623.83	−	2812.56i	−0.106992	−	0.185315i	0.807558	−	0.589788i	$-0.200789\pi$
$613$	−1623.83	−	2812.56i	−0.106992	−	0.185315i	−0.914550	+	0.404472i	$0.867455\pi$
$614$	2481.77	−	4298.55i	0.163121	−	0.282533i
$615$		0			0
$616$	120.757	+	3822.21i	0.00789847	+	0.250002i
$617$	−8366.93			−0.545932			−0.272966	−	0.962024i	$-0.588005\pi$
$617$	−8366.93			−0.545932			−0.272966	+	0.962024i	$0.588005\pi$
$618$		0			0
$619$	−3698.14	−	6405.36i	−0.240130	−	0.415918i	0.720621	−	0.693329i	$-0.243857\pi$
$619$	−3698.14	−	6405.36i	−0.240130	−	0.415918i	−0.960751	+	0.277411i	$0.910524\pi$
$620$	−1124.47	−	1947.63i	−0.0728382	−	0.126159i
$621$		0			0
$622$	4426.65			0.285357
$623$	−15692.0	+	9733.08i	−1.00913	+	0.625919i
$624$		0			0
$625$	−3691.99	+	6394.72i	−0.236288	+	0.409262i
$626$	−8573.62	−	14849.9i	−0.547397	−	0.948120i
$627$		0			0
$628$	−7412.94	+	12839.6i	−0.471033	+	0.815853i
$629$	6343.96			0.402147
$630$		0			0
$631$	−8786.48			−0.554333			−0.277167	−	0.960822i	$-0.589395\pi$
$631$	−8786.48			−0.554333			−0.277167	+	0.960822i	$0.589395\pi$
$632$	5512.60	−	9548.10i	0.346961	−	0.600954i
$633$		0			0
$634$	−2389.19	−	4138.20i	−0.149664	−	0.259225i
$635$	4172.73	−	7227.38i	0.260771	−	0.451669i
$636$		0			0
$637$	13722.3	+	20638.7i	0.853526	+	1.28373i
$638$	14134.4			0.877097
$639$		0			0
$640$	2979.81	+	5161.18i	0.184043	+	0.318771i
$641$	−9785.72	−	16949.4i	−0.602984	−	1.04440i	−0.992367	−	0.123322i	$-0.960645\pi$
$641$	−9785.72	−	16949.4i	−0.602984	−	1.04440i	0.389383	−	0.921076i	$-0.372688\pi$
$642$		0			0
$643$	−4317.58			−0.264804			−0.132402	−	0.991196i	$-0.542269\pi$
$643$	−4317.58			−0.264804			−0.132402	+	0.991196i	$0.542269\pi$
$644$	−1898.02	−	1017.30i	−0.116137	−	0.0622472i
$645$		0			0
$646$	18481.4	−	32010.7i	1.12560	−	1.94960i
$647$	−10892.7	−	18866.8i	−0.661882	−	1.14641i	−0.980121	−	0.198402i	$-0.936425\pi$
$647$	−10892.7	−	18866.8i	−0.661882	−	1.14641i	0.318239	−	0.948010i	$-0.396908\pi$
$648$		0			0
$649$	5212.14	−	9027.70i	0.315246	−	0.546022i
$650$	26635.5			1.60728
$651$		0			0
$652$	−3170.37			−0.190431
$653$	−7514.18	+	13014.9i	−0.450310	+	0.779960i	−0.998405	−	0.0564563i	$-0.982020\pi$
$653$	−7514.18	+	13014.9i	−0.450310	+	0.779960i	0.548095	+	0.836416i	$0.315353\pi$
$654$		0			0
$655$	−2466.68	−	4272.41i	−0.147147	−	0.254865i
$656$	134.421	−	232.825i	0.00800042	−	0.0138571i
$657$		0			0
$658$	346.383	+	10963.7i	0.0205219	+	0.649558i
$659$	−12160.9			−0.718851			−0.359426	−	0.933174i	$-0.617027\pi$
$659$	−12160.9			−0.718851			−0.359426	+	0.933174i	$0.617027\pi$
$660$		0			0
$661$	−4580.42	−	7933.52i	−0.269527	−	0.466835i	0.699212	−	0.714914i	$-0.253534\pi$
$661$	−4580.42	−	7933.52i	−0.269527	−	0.466835i	−0.968740	+	0.248079i	$0.920201\pi$
$662$	13858.2	+	24003.2i	0.813619	+	1.40923i
$663$		0			0
$664$	−8325.02			−0.486556
$665$	−217.849	−	6895.36i	−0.0127035	−	0.402091i
$666$		0			0
$667$	2173.34	−	3764.33i	0.126165	−	0.218524i
$668$	−4227.15	−	7321.64i	−0.244840	−	0.424076i
$669$		0			0
$670$	−8596.35	+	14889.3i	−0.495681	+	0.858544i
$671$	−8552.77			−0.492066
$672$		0			0
$673$	3430.71			0.196499			0.0982496	−	0.995162i	$-0.468676\pi$
$673$	3430.71			0.196499			0.0982496	+	0.995162i	$0.468676\pi$
$674$	17879.8	−	30968.7i	1.02181	−	1.76983i
$675$		0			0
$676$	−7823.79	−	13551.2i	−0.445140	−	0.771006i
$677$	8500.73	−	14723.7i	0.482585	−	0.835861i	−0.517216	−	0.855855i	$-0.673031\pi$
$677$	8500.73	−	14723.7i	0.482585	−	0.835861i	0.999800	+	0.0199942i	$0.00636478\pi$
$678$		0			0
$679$	−23715.0	−	12710.8i	−1.34035	−	0.718402i
$680$	6572.75			0.370667
$681$		0			0
$682$	−3279.91	−	5680.97i	−0.184156	−	0.318967i
$683$	−6722.23	−	11643.2i	−0.376602	−	0.652293i	0.613964	−	0.789334i	$-0.289574\pi$
$683$	−6722.23	−	11643.2i	−0.376602	−	0.652293i	−0.990565	+	0.137041i	$0.956241\pi$
$684$		0			0
$685$	8899.96			0.496424
$686$	20969.2	+	9587.72i	1.16707	+	0.533616i
$687$		0			0
$688$	−6618.22	+	11463.1i	−0.366740	+	0.635213i
$689$	−12188.9	−	21111.7i	−0.673960	−	1.16733i
$690$		0			0
$691$	−15528.7	+	26896.6i	−0.854908	+	1.48074i	0.0218229	+	0.999762i	$0.493053\pi$
$691$	−15528.7	+	26896.6i	−0.854908	+	1.48074i	−0.876731	+	0.480982i	$0.840280\pi$
$692$	−5364.57			−0.294697
$693$		0			0
$694$	−13008.1			−0.711500
$695$	3552.04	−	6152.31i	0.193865	−	0.335785i
$696$		0			0
$697$	−226.306	−	391.973i	−0.0122983	−	0.0213014i
$698$	17215.3	−	29817.7i	0.933536	−	1.61693i
$699$		0			0
$700$	8270.56	−	5129.88i	0.446568	−	0.276987i
$701$	−2445.90			−0.131784			−0.0658919	−	0.997827i	$-0.520989\pi$
$701$	−2445.90			−0.131784			−0.0658919	+	0.997827i	$0.520989\pi$
$702$		0			0
$703$	−1843.74	−	3193.45i	−0.0989160	−	0.171328i
$704$	−1097.17	−	1900.36i	−0.0587375	−	0.101736i
$705$		0			0
$706$	−23620.8			−1.25918
$707$	130.841	+	4141.38i	0.00696010	+	0.220301i
$708$		0			0
$709$	4830.33	−	8366.38i	0.255863	−	0.443168i	−0.709266	−	0.704940i	$-0.750974\pi$
$709$	4830.33	−	8366.38i	0.255863	−	0.443168i	0.965130	+	0.261773i	$0.0843070\pi$
$710$	−355.202	−	615.227i	−0.0187753	−	0.0325198i
$711$		0			0
$712$	−5112.95	+	8855.89i	−0.269124	+	0.466136i
$713$	−2017.30			−0.105959
$714$		0			0
$715$	−7043.14			−0.368389
$716$	1351.16	−	2340.28i	0.0705241	−	0.122151i
$717$		0			0
$718$	7502.01	+	12993.9i	0.389934	+	0.675385i
$719$	759.679	−	1315.80i	0.0394037	−	0.0682492i	−0.845651	−	0.533736i	$-0.820787\pi$
$719$	759.679	−	1315.80i	0.0394037	−	0.0682492i	0.885055	+	0.465487i	$0.154121\pi$
$720$		0			0
$721$	8474.72	−	5256.51i	0.437746	−	0.271515i
$722$	3410.81			0.175813
$723$		0			0
$724$	−6876.22	−	11910.0i	−0.352973	−	0.611368i
$725$	9822.17	+	17012.5i	0.503154	+	0.871488i
$726$		0			0
$727$	19126.9			0.975760			0.487880	−	0.872911i	$-0.337770\pi$
$727$	19126.9			0.975760			0.487880	+	0.872911i	$0.337770\pi$
$728$	12097.1	+	6483.81i	0.615864	+	0.330091i
$729$		0			0
$730$	4237.29	−	7339.20i	0.214834	−	0.372104i
$731$	11142.1	+	19298.7i	0.563758	+	0.976457i
$732$		0			0
$733$	−3615.75	+	6262.67i	−0.182198	+	0.315576i	−0.942629	−	0.333843i	$-0.891654\pi$
$733$	−3615.75	+	6262.67i	−0.182198	+	0.315576i	0.760431	+	0.649419i	$0.224988\pi$
$734$	−11959.2			−0.601392
$735$		0			0
$736$	−4568.86			−0.228819
$737$	−9848.11	+	17057.4i	−0.492212	+	0.852536i
$738$		0			0
$739$	−8923.71	−	15456.3i	−0.444200	−	0.769377i	0.553796	−	0.832652i	$-0.313179\pi$
$739$	−8923.71	−	15456.3i	−0.444200	−	0.769377i	−0.997996	+	0.0632753i	$0.979845\pi$
$740$	−600.355	+	1039.84i	−0.0298236	+	0.0516560i
$741$		0			0
$742$	−19988.8	−	10713.6i	−0.988967	−	0.530067i
$743$	26545.3			1.31070			0.655352	−	0.755323i	$-0.272520\pi$
$743$	26545.3			1.31070			0.655352	+	0.755323i	$0.272520\pi$
$744$		0			0
$745$	8497.38	+	14717.9i	0.417879	+	0.723788i
$746$	4288.97	+	7428.71i	0.210496	+	0.364591i
$747$		0			0
$748$	−13788.3			−0.673999
$749$	−29872.7	+	18528.8i	−1.45731	+	0.903907i
$750$		0			0
$751$	−4780.06	+	8279.31i	−0.232260	+	0.402286i	−0.958473	−	0.285184i	$-0.907945\pi$
$751$	−4780.06	+	8279.31i	−0.232260	+	0.402286i	0.726213	+	0.687470i	$0.241279\pi$
$752$	6414.62	+	11110.4i	0.311060	+	0.538772i
$753$		0			0
$754$	25365.0	−	43933.5i	1.22512	−	2.12197i
$755$	15675.2			0.755601
$756$		0			0
$757$	−23995.4			−1.15209			−0.576043	−	0.817420i	$-0.695404\pi$
$757$	−23995.4			−1.15209			−0.576043	+	0.817420i	$0.695404\pi$
$758$	20092.7	−	34801.6i	0.962796	−	1.66761i
$759$		0			0
$760$	−1910.23	−	3308.62i	−0.0911728	−	0.157916i
$761$	16854.1	−	29192.2i	0.802840	−	1.39056i	−0.114900	−	0.993377i	$-0.536655\pi$
$761$	16854.1	−	29192.2i	0.802840	−	1.39056i	0.917740	−	0.397182i	$-0.130012\pi$
$762$		0			0
$763$	499.740	+	15817.7i	0.0237114	+	0.750511i
$764$	15085.2			0.714352
$765$		0			0
$766$	12925.9	+	22388.3i	0.609701	+	1.05603i
$767$	−18707.0	−	32401.4i	−0.880664	−	1.52535i
$768$		0			0
$769$	−1030.27			−0.0483127			−0.0241563	−	0.999708i	$-0.507690\pi$
$769$	−1030.27			−0.0483127			−0.0241563	+	0.999708i	$0.507690\pi$
$770$	−5568.21	+	3453.72i	−0.260603	+	0.161641i
$771$		0			0
$772$	−4792.38	+	8300.65i	−0.223422	+	0.386978i
$773$	11232.1	+	19454.6i	0.522629	+	0.905220i	0.999653	+	0.0263297i	$0.00838199\pi$
$773$	11232.1	+	19454.6i	0.522629	+	0.905220i	−0.477024	+	0.878890i	$0.658285\pi$
$774$		0			0
$775$	4558.49	−	7895.53i	0.211285	−	0.365956i
$776$	−14900.5			−0.689301
$777$		0			0
$778$	940.331			0.0433322
$779$	−131.542	+	227.838i	−0.00605005	+	0.0104790i
$780$		0			0
$781$	−406.925	−	704.814i	−0.0186439	−	0.0322922i
$782$	−5398.04	+	9349.69i	−0.246846	+	0.427550i
$783$		0			0
$784$	26913.2	−	1702.27i	1.22600	−	0.0775453i
$785$	13872.7			0.630748
$786$		0			0
$787$	7074.69	+	12253.7i	0.320439	+	0.555017i	0.980579	−	0.196126i	$-0.0628362\pi$
$787$	7074.69	+	12253.7i	0.320439	+	0.555017i	−0.660140	+	0.751143i	$0.729503\pi$
$788$	7570.11	+	13111.8i	0.342226	+	0.592753i
$789$		0			0
$790$	18890.9			0.850768
$791$	−13092.8	−	7017.49i	−0.588529	−	0.315440i
$792$		0			0
$793$	−15348.4	+	26584.2i	−0.687312	+	1.19046i
$794$	−18552.5	−	32133.9i	−0.829226	−	1.43626i
$795$		0			0
$796$	4215.29	−	7301.10i	0.187697	−	0.325101i
$797$	−38562.7			−1.71388			−0.856939	−	0.515418i	$-0.827637\pi$
$797$	−38562.7			−1.71388			−0.856939	+	0.515418i	$0.827637\pi$
$798$		0			0
$799$	21598.7			0.956331
$800$	10324.2	−	17882.1i	0.456272	−	0.790285i
$801$		0			0
$802$	9372.38	+	16233.4i	0.412656	+	0.714742i
$803$	4854.30	−	8407.90i	0.213331	−	0.369500i
$804$		0			0
$805$	63.6295	+	2014.00i	0.00278589	+	0.0881789i
$806$	−23543.9			−1.02891
$807$		0			0
$808$	1147.29	+	1987.17i	0.0499525	+	0.0865202i
$809$	13567.3	+	23499.3i	0.589618	+	1.02125i	0.994282	+	0.106783i	$0.0340550\pi$
$809$	13567.3	+	23499.3i	0.589618	+	1.02125i	−0.404664	+	0.914465i	$0.632612\pi$
$810$		0			0
$811$	23383.8			1.01247			0.506237	−	0.862394i	$-0.331036\pi$
$811$	23383.8			1.01247			0.506237	+	0.862394i	$0.331036\pi$
$812$	−585.333	−	18526.9i	−0.0252970	−	0.800698i
$813$		0			0
$814$	−1751.15	+	3033.08i	−0.0754025	+	0.130601i
$815$	1483.27	+	2569.09i	0.0637504	+	0.110419i
$816$		0			0
$817$	6476.46	−	11217.6i	0.277335	−	0.480358i
$818$	15477.1			0.661547
$819$		0			0
$820$	85.6649			0.00364823
$821$	10122.0	−	17531.8i	0.430279	−	0.745265i	−0.566618	−	0.823980i	$-0.691749\pi$
$821$	10122.0	−	17531.8i	0.430279	−	0.745265i	0.996897	+	0.0787155i	$0.0250819\pi$
$822$		0			0
$823$	10598.1	+	18356.5i	0.448878	+	0.777480i	0.998313	−	0.0580563i	$-0.0184903\pi$
$823$	10598.1	+	18356.5i	0.448878	+	0.777480i	−0.549435	+	0.835537i	$0.685157\pi$
$824$	2761.33	−	4782.77i	0.116742	−	0.202203i
$825$		0			0
$826$	−30678.0	−	16442.8i	−1.29228	−	0.692638i
$827$	−10826.0			−0.455207			−0.227604	−	0.973754i	$-0.573089\pi$
$827$	−10826.0			−0.455207			−0.227604	+	0.973754i	$0.573089\pi$
$828$		0			0
$829$	4516.73	+	7823.21i	0.189231	+	0.327758i	0.944994	−	0.327087i	$-0.106067\pi$
$829$	4516.73	+	7823.21i	0.189231	+	0.327758i	−0.755763	+	0.654845i	$0.772734\pi$
$830$	−7132.15	−	12353.3i	−0.298266	−	0.516612i
$831$		0			0
$832$	−7875.74			−0.328176
$833$	20173.0	−	40672.5i	0.839081	−	1.69174i
$834$		0			0
$835$	−3955.37	+	6850.90i	−0.163930	+	0.283934i
$836$	4007.29	+	6940.83i	0.165783	+	0.287145i
$837$		0			0
$838$	30151.3	−	52223.6i	1.24291	−	2.15278i
$839$	43749.5			1.80024			0.900120	−	0.435642i	$-0.143478\pi$
$839$	43749.5			1.80024			0.900120	+	0.435642i	$0.143478\pi$
$840$		0			0
$841$	13025.6			0.534078
$842$	−21453.2	+	37158.0i	−0.878059	+	1.52084i
$843$		0			0
$844$	−4376.08	−	7579.60i	−0.178473	−	0.309124i
$845$	−7320.77	+	12679.9i	−0.298038	+	0.516217i
$846$		0			0
$847$	14569.1	−	9036.57i	0.591025	−	0.366588i
$848$	−26524.7			−1.07413
$849$		0			0
$850$	−24395.9	−	42254.9i	−0.984438	−	1.70510i
$851$	538.520	+	932.743i	0.0216924	+	0.0375723i
$852$		0			0
$853$	39350.1			1.57951			0.789754	−	0.613423i	$-0.210208\pi$
$853$	39350.1			1.57951			0.789754	+	0.613423i	$0.210208\pi$
$854$	901.793	+	28543.5i	0.0361343	+	1.14372i
$855$		0			0
$856$	−9733.48	+	16858.9i	−0.388649	+	0.673159i
$857$	−7642.75	−	13237.6i	−0.304634	−	0.527641i	0.672546	−	0.740055i	$-0.265201\pi$
$857$	−7642.75	−	13237.6i	−0.304634	−	0.527641i	−0.977180	+	0.212414i	$0.931867\pi$
$858$		0			0
$859$	4083.34	−	7072.56i	0.162191	−	0.280923i	−0.773463	−	0.633841i	$-0.781477\pi$
$859$	4083.34	−	7072.56i	0.162191	−	0.280923i	0.935654	+	0.352918i	$0.114811\pi$
$860$	−4217.70			−0.167235
$861$		0			0
$862$	47637.3			1.88229
$863$	−24602.0	+	42612.0i	−0.970409	+	1.68080i	−0.276088	+	0.961132i	$0.589038\pi$
$863$	−24602.0	+	42612.0i	−0.970409	+	1.68080i	−0.694321	+	0.719666i	$0.744295\pi$
$864$		0			0
$865$	2509.83	+	4347.16i	0.0986554	+	0.170876i
$866$	−23525.0	+	40746.6i	−0.923110	+	1.59887i
$867$		0			0
$868$	−7310.57	+	4534.44i	−0.285872	+	0.177314i
$869$	21641.7			0.844814
$870$		0			0
$871$	35346.0	+	61221.0i	1.37503	+	2.38162i
$872$	4382.01	+	7589.86i	0.170176	+	0.294754i
$873$		0			0
$874$	6275.31			0.242867
$875$	−17905.4	−	9596.92i	−0.691785	−	0.370783i
$876$		0			0
$877$	7910.70	−	13701.7i	0.304590	−	0.527565i	−0.672580	−	0.740024i	$-0.734814\pi$
$877$	7910.70	−	13701.7i	0.304590	−	0.527565i	0.977170	+	0.212459i	$0.0681472\pi$
$878$	6973.60	+	12078.6i	0.268049	+	0.464275i
$879$		0			0
$880$	−3831.72	+	6636.74i	−0.146781	+	0.254232i
$881$	14538.7			0.555982			0.277991	−	0.960584i	$-0.410331\pi$
$881$	14538.7			0.555982			0.277991	+	0.960584i	$0.410331\pi$
$882$		0			0
$883$	3842.17			0.146432			0.0732160	−	0.997316i	$-0.476674\pi$
$883$	3842.17			0.146432			0.0732160	+	0.997316i	$0.476674\pi$
$884$	−24743.9	+	42857.7i	−0.941434	+	1.63061i
$885$		0			0
$886$	−9335.22	−	16169.1i	−0.353976	−	0.613104i
$887$	−18885.8	+	32711.1i	−0.714906	+	1.23825i	0.248090	+	0.968737i	$0.420197\pi$
$887$	−18885.8	+	32711.1i	−0.714906	+	1.23825i	−0.962996	+	0.269516i	$0.913136\pi$
$888$		0			0
$889$	−28136.5	−	15080.6i	−1.06149	−	0.568940i
$890$	−17521.3			−0.659906
$891$		0			0
$892$	1938.46	+	3357.52i	0.0727630	+	0.126029i
$893$	−6277.22	−	10872.5i	−0.235229	−	0.407428i
$894$		0			0
$895$	−2528.58			−0.0944370
$896$	19372.8	−	12016.1i	0.722322	−	0.448026i
$897$		0			0
$898$	−26546.6	+	45980.1i	−0.986494	+	1.70866i
$899$	−8682.09	−	15037.8i	−0.322096	−	0.557886i
$900$		0			0
$901$	−22327.9	+	38673.1i	−0.825584	+	1.42995i
$902$	249.872			0.00922376
$903$		0			0
$904$	−8226.42			−0.302662
$905$	−6434.12	+	11144.2i	−0.236329	+	0.409333i
$906$		0			0
$907$	−12637.8	−	21889.3i	−0.462658	−	0.801348i	0.536434	−	0.843942i	$-0.319771\pi$
$907$	−12637.8	−	21889.3i	−0.462658	−	0.801348i	−0.999092	+	0.0425946i	$0.986438\pi$
$908$	12178.4	−	21093.7i	0.445105	−	0.770945i
$909$		0			0
$910$	742.619	+	23505.3i	0.0270523	+	0.856257i
$911$	−33060.3			−1.20234			−0.601172	−	0.799120i	$-0.705299\pi$
$911$	−33060.3			−1.20234			−0.601172	+	0.799120i	$0.705299\pi$
$912$		0			0
$913$	−8170.71	−	14152.1i	−0.296178	−	0.512996i
$914$	−5633.20	−	9756.99i	−0.203862	−	0.353099i
$915$		0			0
$916$	12574.1			0.453559
$917$	−16036.8	+	9946.93i	−0.577514	+	0.358208i
$918$		0			0
$919$	8652.57	−	14986.7i	0.310579	−	0.537939i	−0.667909	−	0.744243i	$-0.732810\pi$
$919$	8652.57	−	14986.7i	0.310579	−	0.537939i	0.978488	+	0.206305i	$0.0661438\pi$
$920$	557.940	+	966.381i	0.0199943	+	0.0346311i
$921$		0			0
$922$	−24957.1	+	43227.0i	−0.891452	+	1.54404i
$923$	−2920.99			−0.104166
$924$		0			0
$925$	−4867.56			−0.173021
$926$	10727.1	−	18579.9i	0.380685	−	0.659366i
$927$		0			0
$928$	−19663.6	−	34058.3i	−0.695569	−	1.20476i
$929$	−13176.6	+	22822.6i	−0.465352	+	0.806013i	−0.999217	−	0.0395567i	$-0.987405\pi$
$929$	−13176.6	+	22822.6i	−0.465352	+	0.806013i	0.533866	+	0.845569i	$0.320739\pi$
$930$		0			0
$931$	−26336.7	+	1665.81i	−0.927123	+	0.0586410i
$932$	9257.80			0.325375
$933$		0			0
$934$	−16934.9	−	29332.1i	−0.593284	−	1.02760i
$935$	6450.92	+	11173.3i	0.225634	+	0.390809i
$936$		0			0
$937$	−6967.42			−0.242920			−0.121460	−	0.992596i	$-0.538758\pi$
$937$	−6967.42			−0.242920			−0.121460	+	0.992596i	$0.538758\pi$
$938$	57964.8	+	31068.0i	2.01772	+	1.08146i
$939$		0			0
$940$	−2043.97	+	3540.27i	−0.0709224	+	0.122841i
$941$	22142.1	+	38351.2i	0.767069	+	1.32860i	0.939146	+	0.343518i	$0.111619\pi$
$941$	22142.1	+	38351.2i	0.767069	+	1.32860i	−0.172077	+	0.985083i	$0.555048\pi$
$942$		0			0
$943$	38.4208	−	66.5468i	0.00132678	−	0.00229805i
$944$	−40709.1			−1.40357
$945$		0			0
$946$	−12302.4			−0.422818
$947$	14886.4	−	25784.0i	0.510816	−	0.884759i	−0.489106	−	0.872224i	$-0.662677\pi$
$947$	14886.4	−	25784.0i	0.510816	−	0.884759i	0.999921	−	0.0125342i	$-0.00398985\pi$
$948$		0			0
$949$	−17422.6	−	30176.9i	−0.595956	−	1.03223i
$950$	−14180.3	+	24561.0i	−0.484284	+	0.838804i
$951$		0			0
$952$	−793.937	−	25129.6i	−0.0270290	−	0.855521i
$953$	17971.9			0.610878			0.305439	−	0.952212i	$-0.401197\pi$
$953$	17971.9			0.610878			0.305439	+	0.952212i	$0.401197\pi$
$954$		0			0
$955$	−7057.68	−	12224.3i	−0.239143	−	0.414207i
$956$	−6485.87	−	11233.9i	−0.219423	−	0.380051i
$957$		0			0
$958$	71346.1			2.40614
$959$	−1075.05	−	34027.3i	−0.0361992	−	1.14578i
$960$		0			0
$961$	10866.1	−	18820.7i	0.364745	−	0.631757i
$962$	6285.06	+	10886.0i	0.210643	+	0.364844i
$963$		0			0
$964$	−10292.5	+	17827.1i	−0.343877	+	0.595613i
$965$	8968.53			0.299178
$966$		0			0
$967$	−34100.9			−1.13403			−0.567017	−	0.823706i	$-0.691903\pi$
$967$	−34100.9			−1.13403			−0.567017	+	0.823706i	$0.691903\pi$
$968$	4747.06	−	8222.15i	0.157620	−	0.273006i
$969$		0			0
$970$	−12765.5	−	22110.5i	−0.422551	−	0.731881i
$971$	−11303.1	+	19577.5i	−0.373567	+	0.647037i	−0.990111	−	0.140283i	$-0.955199\pi$
$971$	−11303.1	+	19577.5i	−0.373567	+	0.647037i	0.616545	+	0.787320i	$0.288532\pi$
$972$		0			0
$973$	−23951.2	−	12837.4i	−0.789148	−	0.422967i
$974$	−8246.77			−0.271297
$975$		0			0
$976$	16700.2	+	28925.6i	0.547705	+	0.948653i
$977$	4370.31	+	7569.60i	0.143110	+	0.247874i	0.928666	−	0.370916i	$-0.120956\pi$
$977$	4370.31	+	7569.60i	0.143110	+	0.247874i	−0.785556	+	0.618790i	$0.787623\pi$
$978$		0			0
$979$	−20072.7			−0.655288
$980$	4757.60	+	7155.58i	0.155078	+	0.233241i
$981$		0			0
$982$	−27000.4	+	46766.1i	−0.877411	+	1.51972i
$983$	22352.4	+	38715.5i	0.725260	+	1.25619i	0.958867	+	0.283857i	$0.0916140\pi$
$983$	22352.4	+	38715.5i	0.725260	+	1.25619i	−0.233606	+	0.972331i	$0.575053\pi$
$984$		0			0
$985$	7083.40	−	12268.8i	0.229133	−	0.396870i
$986$	−92928.8			−3.00148
$987$		0			0
$988$	28765.2			0.926258
$989$	−1891.64	+	3276.42i	−0.0608198	+	0.105343i
$990$		0			0
$991$	−8517.74	−	14753.2i	−0.273032	−	0.472906i	0.696605	−	0.717455i	$-0.254693\pi$
$991$	−8517.74	−	14753.2i	−0.273032	−	0.472906i	−0.969637	+	0.244550i	$0.921360\pi$
$992$	−9125.89	+	15806.5i	−0.292084	+	0.505904i
$993$		0			0
$994$	−2309.30	+	1432.36i	−0.0736886	+	0.0457059i
$995$	−7888.55			−0.251341
$996$		0			0
$997$	14535.8	+	25176.8i	0.461739	+	0.799755i	0.999048	−	0.0436303i	$-0.0138924\pi$
$997$	14535.8	+	25176.8i	0.461739	+	0.799755i	−0.537309	+	0.843386i	$0.680559\pi$
$998$	−30011.3	−	51981.1i	−0.951895	−	1.64873i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.e.f.163.6	yes	14
3.2	odd	2		189.4.e.g.163.2	yes	14
7.2	even	3		1323.4.a.bj.1.2		7
7.4	even	3	inner	189.4.e.f.109.6	✓	14
7.5	odd	6		1323.4.a.bk.1.2		7
21.2	odd	6		1323.4.a.bi.1.6		7
21.5	even	6		1323.4.a.bh.1.6		7
21.11	odd	6		189.4.e.g.109.2	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.4.e.f.109.6	✓	14	7.4	even	3	inner
189.4.e.f.163.6	yes	14	1.1	even	1	trivial
189.4.e.g.109.2	yes	14	21.11	odd	6
189.4.e.g.163.2	yes	14	3.2	odd	2
1323.4.a.bh.1.6		7	21.5	even	6
1323.4.a.bi.1.6		7	21.2	odd	6
1323.4.a.bj.1.2		7	7.2	even	3
1323.4.a.bk.1.2		7	7.5	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81482 - 3.14336i) q^{2} +(-2.58715 - 4.48108i) q^{4} +(-2.42081 + 4.19297i) q^{5} +(16.3234 + 8.74903i) q^{7} +10.2563 q^{8} +(8.78669 + 15.2190i) q^{10} +(10.0662 + 17.4351i) q^{11} +72.2571 q^{13} +(57.1255 - 35.4325i) q^{14} +(39.3105 - 68.0878i) q^{16} +(-66.1814 - 114.630i) q^{17} +(-38.4685 + 66.6293i) q^{19} +25.0520 q^{20} +73.0732 q^{22} +(11.2359 - 19.4611i) q^{23} +(50.7793 + 87.9524i) q^{25} +(131.134 - 227.130i) q^{26} +(-3.02609 - 95.7816i) q^{28} +193.429 q^{29} +(-44.8853 - 77.7435i) q^{31} +(-101.658 - 176.077i) q^{32} -480.430 q^{34} +(-76.2004 + 47.2639i) q^{35} +(-23.9643 + 41.5074i) q^{37} +(139.627 + 241.841i) q^{38} +(-24.8285 + 43.0043i) q^{40} +3.41948 q^{41} -168.358 q^{43} +(52.0854 - 90.2145i) q^{44} +(-40.7822 - 70.6368i) q^{46} +(-81.5891 + 141.317i) q^{47} +(189.909 + 285.628i) q^{49} +368.622 q^{50} +(-186.940 - 323.790i) q^{52} +(-168.687 - 292.175i) q^{53} -97.4733 q^{55} +(167.418 + 89.7325i) q^{56} +(351.038 - 608.016i) q^{58} +(-258.894 - 448.418i) q^{59} +(-212.414 + 367.911i) q^{61} -325.835 q^{62} -108.996 q^{64} +(-174.921 + 302.972i) q^{65} +(489.169 + 847.266i) q^{67} +(-342.442 + 593.128i) q^{68} +(10.2775 + 325.301i) q^{70} -40.4250 q^{71} +(-241.120 - 417.632i) q^{73} +(86.9818 + 150.657i) q^{74} +398.095 q^{76} +(11.7740 + 372.670i) q^{77} +(537.485 - 930.952i) q^{79} +(190.327 + 329.656i) q^{80} +(6.20574 - 10.7487i) q^{82} -811.700 q^{83} +640.851 q^{85} +(-305.539 + 529.209i) q^{86} +(103.241 + 178.819i) q^{88} +(-498.519 + 863.461i) q^{89} +(1179.48 + 632.180i) q^{91} -116.276 q^{92} +(296.139 + 512.928i) q^{94} +(-186.250 - 322.594i) q^{95} -1452.82 q^{97} +(1242.48 - 78.5877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 31 q^{4} + q^{5} + 20 q^{7} + 168 q^{8} - 12 q^{10} - 98 q^{11} - 248 q^{13} - 134 q^{14} - 139 q^{16} - 30 q^{17} - 182 q^{19} - 220 q^{20} + 552 q^{22} + 6 q^{23} - 388 q^{25} + 245 q^{26}+ \cdots + 10160 q^{98}+O(q^{100}) \) 14 * q - q^2 - 31 * q^4 + q^5 + 20 * q^7 + 168 * q^8 - 12 * q^10 - 98 * q^11 - 248 * q^13 - 134 * q^14 - 139 * q^16 - 30 * q^17 - 182 * q^19 - 220 * q^20 + 552 * q^22 + 6 * q^23 - 388 * q^25 + 245 * q^26 + 425 * q^28 + 646 * q^29 - 26 * q^31 - 398 * q^32 + 228 * q^34 + 1025 * q^35 + 112 * q^37 - 1015 * q^38 + 147 * q^40 - 1048 * q^41 + 16 * q^43 - 937 * q^44 + 339 * q^46 - 288 * q^47 + 446 * q^49 + 5152 * q^50 + 1075 * q^52 - 1353 * q^53 + 312 * q^55 + 1980 * q^56 + 81 * q^58 - 165 * q^59 - 56 * q^61 - 2430 * q^62 - 3412 * q^64 - 1694 * q^65 + 988 * q^67 - 2625 * q^68 - 4941 * q^70 + 1584 * q^71 - 1487 * q^73 - 2736 * q^74 + 3904 * q^76 - 34 * q^77 + 1273 * q^79 + 2501 * q^80 + 2049 * q^82 - 2340 * q^83 + 432 * q^85 + 160 * q^86 - 9 * q^88 - 1058 * q^89 + 3538 * q^91 + 7668 * q^92 - 1653 * q^94 - 3260 * q^95 - 7460 * q^97 + 10160 * q^98

Introduction

L-functions

Modular forms

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Database

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