LMFDB - Embedded newform 234.4.h.h.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,4,Mod(55,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("234.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	234.h (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:	$13.8064469413$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{217})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 55x^{2} + 54x + 2916 $ x^4 - x^3 + 55x^2 + 54x + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.2
Root			$-3.43273 + 5.94566i$ of defining polynomial
Character	$\chi$	$=$	234.55
Dual form			234.4.h.h.217.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +10.8655 q^{5} +(14.9327 - 25.8642i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +10.8655 q^{5} +(14.9327 - 25.8642i) q^{7} -8.00000 q^{8} +(10.8655 + 18.8195i) q^{10} +(-24.5291 - 42.4857i) q^{11} +(2.29819 - 46.8158i) q^{13} +59.7309 q^{14} +(-8.00000 - 13.8564i) q^{16} +(-3.03816 + 5.26225i) q^{17} +(2.93273 - 5.07964i) q^{19} +(-21.7309 + 37.6391i) q^{20} +(49.0582 - 84.9713i) q^{22} +(-2.79819 - 4.84661i) q^{23} -6.94178 q^{25} +(83.3855 - 42.8352i) q^{26} +(59.7309 + 103.457i) q^{28} +(-5.30724 - 9.19241i) q^{29} +316.771 q^{31} +(16.0000 - 27.7128i) q^{32} -12.1526 q^{34} +(162.251 - 281.027i) q^{35} +(190.231 + 329.490i) q^{37} +11.7309 q^{38} -86.9237 q^{40} +(134.155 + 232.363i) q^{41} +(115.318 - 199.737i) q^{43} +196.233 q^{44} +(5.59638 - 9.69321i) q^{46} -524.466 q^{47} +(-274.473 - 475.401i) q^{49} +(-6.94178 - 12.0235i) q^{50} +(157.578 + 101.593i) q^{52} +274.865 q^{53} +(-266.520 - 461.626i) q^{55} +(-119.462 + 206.914i) q^{56} +(10.6145 - 18.3848i) q^{58} +(-71.4709 + 123.791i) q^{59} +(-281.347 + 487.308i) q^{61} +(316.771 + 548.664i) q^{62} +64.0000 q^{64} +(24.9709 - 508.675i) q^{65} +(258.762 + 448.189i) q^{67} +(-12.1526 - 21.0490i) q^{68} +649.004 q^{70} +(-72.2781 + 125.189i) q^{71} -201.018 q^{73} +(-380.462 + 658.979i) q^{74} +(11.7309 + 20.3185i) q^{76} -1465.15 q^{77} +26.4579 q^{79} +(-86.9237 - 150.556i) q^{80} +(-268.309 + 464.725i) q^{82} +1147.16 q^{83} +(-33.0110 + 57.1767i) q^{85} +461.273 q^{86} +(196.233 + 339.885i) q^{88} +(-331.915 - 574.893i) q^{89} +(-1176.54 - 758.529i) q^{91} +22.3855 q^{92} +(-524.466 - 908.401i) q^{94} +(31.8655 - 55.1926i) q^{95} +(68.7581 - 119.092i) q^{97} +(548.946 - 950.802i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 14 q^{5} + 45 q^{7} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 14 * q^5 + 45 * q^7 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 14 q^{5} + 45 q^{7} - 32 q^{8} + 14 q^{10} + 5 q^{11} - 35 q^{13} + 180 q^{14} - 32 q^{16} - 130 q^{17} - 3 q^{19} - 28 q^{20} - 10 q^{22} + 33 q^{23} - 234 q^{25} - 20 q^{26} + 180 q^{28} - 198 q^{29} + 560 q^{31} + 64 q^{32} - 520 q^{34} + 266 q^{35} + 702 q^{37} - 12 q^{38} - 112 q^{40} + 242 q^{41} + 93 q^{43} - 40 q^{44} - 66 q^{46} - 448 q^{47} - 435 q^{49} - 234 q^{50} + 100 q^{52} + 1070 q^{53} - 742 q^{55} - 360 q^{56} + 396 q^{58} - 389 q^{59} - 654 q^{61} + 560 q^{62} + 256 q^{64} + 203 q^{65} + 107 q^{67} - 520 q^{68} + 1064 q^{70} - 569 q^{71} - 1246 q^{73} - 1404 q^{74} - 12 q^{76} - 1294 q^{77} + 1520 q^{79} - 112 q^{80} - 484 q^{82} + 3528 q^{83} + 413 q^{85} + 372 q^{86} - 40 q^{88} - 871 q^{89} - 1539 q^{91} - 264 q^{92} - 448 q^{94} + 98 q^{95} + 879 q^{97} + 870 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 14 * q^5 + 45 * q^7 - 32 * q^8 + 14 * q^10 + 5 * q^11 - 35 * q^13 + 180 * q^14 - 32 * q^16 - 130 * q^17 - 3 * q^19 - 28 * q^20 - 10 * q^22 + 33 * q^23 - 234 * q^25 - 20 * q^26 + 180 * q^28 - 198 * q^29 + 560 * q^31 + 64 * q^32 - 520 * q^34 + 266 * q^35 + 702 * q^37 - 12 * q^38 - 112 * q^40 + 242 * q^41 + 93 * q^43 - 40 * q^44 - 66 * q^46 - 448 * q^47 - 435 * q^49 - 234 * q^50 + 100 * q^52 + 1070 * q^53 - 742 * q^55 - 360 * q^56 + 396 * q^58 - 389 * q^59 - 654 * q^61 + 560 * q^62 + 256 * q^64 + 203 * q^65 + 107 * q^67 - 520 * q^68 + 1064 * q^70 - 569 * q^71 - 1246 * q^73 - 1404 * q^74 - 12 * q^76 - 1294 * q^77 + 1520 * q^79 - 112 * q^80 - 484 * q^82 + 3528 * q^83 + 413 * q^85 + 372 * q^86 - 40 * q^88 - 871 * q^89 - 1539 * q^91 - 264 * q^92 - 448 * q^94 + 98 * q^95 + 879 * q^97 + 870 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	10.8655			0.971836			0.485918	−	0.874004i	$-0.338485\pi$
$5$	10.8655			0.971836			0.485918	+	0.874004i	$0.338485\pi$
$6$		0			0
$7$	14.9327	−	25.8642i	0.806292	−	1.39654i	−0.109124	−	0.994028i	$-0.534805\pi$
$7$	14.9327	−	25.8642i	0.806292	−	1.39654i	0.915416	−	0.402510i	$-0.131862\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	10.8655	+	18.8195i	0.343596	+	0.595126i
$11$	−24.5291	−	42.4857i	−0.672346	−	1.16454i	−0.977237	−	0.212150i	$-0.931953\pi$
$11$	−24.5291	−	42.4857i	−0.672346	−	1.16454i	0.304891	−	0.952387i	$-0.401380\pi$
$12$		0			0
$13$	2.29819	−	46.8158i	0.0490310	−	0.998797i
$13$	2.29819	−	46.8158i	0.0490310	−	0.998797i
$14$	59.7309			1.14027
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−3.03816	+	5.26225i	−0.0433448	+	0.0750754i	−0.886884	−	0.461992i	$-0.847135\pi$
$17$	−3.03816	+	5.26225i	−0.0433448	+	0.0750754i	0.843539	+	0.537068i	$0.180468\pi$
$18$		0			0
$19$	2.93273	−	5.07964i	0.0354113	−	0.0613341i	−0.847777	−	0.530353i	$-0.822059\pi$
$19$	2.93273	−	5.07964i	0.0354113	−	0.0613341i	0.883188	+	0.469019i	$0.155393\pi$
$20$	−21.7309	+	37.6391i	−0.242959	+	0.420817i
$21$		0			0
$22$	49.0582	−	84.9713i	0.475420	−	0.823452i
$23$	−2.79819	−	4.84661i	−0.0253680	−	0.0439386i	0.853063	−	0.521808i	$-0.174742\pi$
$23$	−2.79819	−	4.84661i	−0.0253680	−	0.0439386i	−0.878431	+	0.477870i	$0.841409\pi$
$24$		0			0
$25$	−6.94178			−0.0555342
$26$	83.3855	−	42.8352i	0.628971	−	0.323103i
$27$		0			0
$28$	59.7309	+	103.457i	0.403146	+	0.698269i
$29$	−5.30724	−	9.19241i	−0.0339838	−	0.0588616i	0.848533	−	0.529142i	$-0.177486\pi$
$29$	−5.30724	−	9.19241i	−0.0339838	−	0.0588616i	−0.882517	+	0.470280i	$0.844153\pi$
$30$		0			0
$31$	316.771			1.83528			0.917641	−	0.397410i	$-0.130091\pi$
$31$	316.771			1.83528			0.917641	+	0.397410i	$0.130091\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−12.1526			−0.0612988
$35$	162.251	−	281.027i	0.783583	−	1.35721i
$36$		0			0
$37$	190.231	+	329.490i	0.845237	+	1.46399i	0.885415	+	0.464801i	$0.153874\pi$
$37$	190.231	+	329.490i	0.845237	+	1.46399i	−0.0401781	+	0.999193i	$0.512793\pi$
$38$	11.7309			0.0500791
$39$		0			0
$40$	−86.9237			−0.343596
$41$	134.155	+	232.363i	0.511010	+	0.885096i	0.999919	+	0.0127608i	$0.00406199\pi$
$41$	134.155	+	232.363i	0.511010	+	0.885096i	−0.488908	+	0.872335i	$0.662605\pi$
$42$		0			0
$43$	115.318	−	199.737i	0.408974	−	0.708363i	−0.585801	−	0.810455i	$-0.699220\pi$
$43$	115.318	−	199.737i	0.408974	−	0.708363i	0.994775	+	0.102091i	$0.0325534\pi$
$44$	196.233			0.672346
$45$		0			0
$46$	5.59638	−	9.69321i	0.0179379	−	0.0310693i
$47$	−524.466			−1.62768			−0.813842	−	0.581086i	$-0.802628\pi$
$47$	−524.466			−1.62768			−0.813842	+	0.581086i	$0.802628\pi$
$48$		0			0
$49$	−274.473	−	475.401i	−0.800212	−	1.38601i
$50$	−6.94178	−	12.0235i	−0.0196343	−	0.0340076i
$51$		0			0
$52$	157.578	+	101.593i	0.420234	+	0.270930i
$53$	274.865			0.712371			0.356186	−	0.934415i	$-0.384077\pi$
$53$	274.865			0.712371			0.356186	+	0.934415i	$0.384077\pi$
$54$		0			0
$55$	−266.520	−	461.626i	−0.653410	−	1.13174i
$56$	−119.462	+	206.914i	−0.285067	+	0.493751i
$57$		0			0
$58$	10.6145	−	18.3848i	0.0240302	−	0.0416215i
$59$	−71.4709	+	123.791i	−0.157707	+	0.273157i	−0.934041	−	0.357165i	$-0.883744\pi$
$59$	−71.4709	+	123.791i	−0.157707	+	0.273157i	0.776334	+	0.630321i	$0.217077\pi$
$60$		0			0
$61$	−281.347	+	487.308i	−0.590538	+	1.02284i	0.403622	+	0.914926i	$0.367751\pi$
$61$	−281.347	+	487.308i	−0.590538	+	1.02284i	−0.994160	+	0.107916i	$0.965582\pi$
$62$	316.771	+	548.664i	0.648870	+	1.12388i
$63$		0			0
$64$	64.0000			0.125000
$65$	24.9709	−	508.675i	0.0476501	−	0.970667i
$66$		0			0
$67$	258.762	+	448.189i	0.471833	+	0.817239i	0.999481	−	0.0322247i	$-0.0102592\pi$
$67$	258.762	+	448.189i	0.471833	+	0.817239i	−0.527648	+	0.849463i	$0.676926\pi$
$68$	−12.1526	−	21.0490i	−0.0216724	−	0.0375377i
$69$		0			0
$70$	649.004			1.10815
$71$	−72.2781	+	125.189i	−0.120815	+	0.209257i	−0.920089	−	0.391709i	$-0.871884\pi$
$71$	−72.2781	+	125.189i	−0.120815	+	0.209257i	0.799275	+	0.600966i	$0.205217\pi$
$72$		0			0
$73$	−201.018			−0.322293			−0.161147	−	0.986930i	$-0.551519\pi$
$73$	−201.018			−0.322293			−0.161147	+	0.986930i	$0.551519\pi$
$74$	−380.462	+	658.979i	−0.597673	+	1.03520i
$75$		0			0
$76$	11.7309	+	20.3185i	0.0177056	+	0.0306671i
$77$	−1465.15			−2.16843
$78$		0			0
$79$	26.4579			0.0376804			0.0188402	−	0.999823i	$-0.494003\pi$
$79$	26.4579			0.0376804			0.0188402	+	0.999823i	$0.494003\pi$
$80$	−86.9237	−	150.556i	−0.121480	−	0.210409i
$81$		0			0
$82$	−268.309	+	464.725i	−0.361339	+	0.625857i
$83$	1147.16			1.51707			0.758535	−	0.651632i	$-0.225916\pi$
$83$	1147.16			1.51707			0.758535	+	0.651632i	$0.225916\pi$
$84$		0			0
$85$	−33.0110	+	57.1767i	−0.0421241	+	0.0729610i
$86$	461.273			0.578376
$87$		0			0
$88$	196.233	+	339.885i	0.237710	+	0.411726i
$89$	−331.915	−	574.893i	−0.395313	−	0.684703i	0.597828	−	0.801625i	$-0.296031\pi$
$89$	−331.915	−	574.893i	−0.395313	−	0.684703i	−0.993141	+	0.116922i	$0.962697\pi$
$90$		0			0
$91$	−1176.54	−	758.529i	−1.35533	−	0.873796i
$92$	22.3855			0.0253680
$93$		0			0
$94$	−524.466	−	908.401i	−0.575474	−	0.996749i
$95$	31.8655	−	55.1926i	0.0344140	−	0.0596067i
$96$		0			0
$97$	68.7581	−	119.092i	0.0719724	−	0.124660i	−0.827793	−	0.561033i	$-0.810404\pi$
$97$	68.7581	−	119.092i	0.0719724	−	0.124660i	0.899766	+	0.436373i	$0.143737\pi$
$98$	548.946	−	950.802i	0.565836	−	0.980056i
$99$		0			0
$100$	13.8836	−	24.0470i	0.0138836	−	0.0240470i
$101$	−442.347	−	766.168i	−0.435794	−	0.754818i	0.561566	−	0.827432i	$-0.310199\pi$
$101$	−442.347	−	766.168i	−0.435794	−	0.754818i	−0.997360	+	0.0726144i	$0.976866\pi$
$102$		0			0
$103$	−416.233			−0.398181			−0.199091	−	0.979981i	$-0.563799\pi$
$103$	−416.233			−0.398181			−0.199091	+	0.979981i	$0.563799\pi$
$104$	−18.3855	+	374.526i	−0.0173351	+	0.353128i
$105$		0			0
$106$	274.865	+	476.081i	0.251861	+	0.436236i
$107$	211.587	+	366.480i	0.191167	+	0.331112i	0.945637	−	0.325223i	$-0.105439\pi$
$107$	211.587	+	366.480i	0.191167	+	0.331112i	−0.754470	+	0.656335i	$0.772106\pi$
$108$		0			0
$109$	−951.630			−0.836235			−0.418118	−	0.908393i	$-0.637310\pi$
$109$	−951.630			−0.836235			−0.418118	+	0.908393i	$0.637310\pi$
$110$	533.040	−	923.253i	0.462031	−	0.800261i
$111$		0			0
$112$	−477.847			−0.403146
$113$	−376.391	+	651.929i	−0.313344	+	0.542729i	−0.979084	−	0.203456i	$-0.934783\pi$
$113$	−376.391	+	651.929i	−0.313344	+	0.542729i	0.665740	+	0.746184i	$0.268116\pi$
$114$		0			0
$115$	−30.4036	−	52.6606i	−0.0246535	−	0.0427011i
$116$	42.4579			0.0339838
$117$		0			0
$118$	−285.884			−0.223031
$119$	90.7361	+	157.159i	0.0698971	+	0.121065i
$120$		0			0
$121$	−537.854	+	931.591i	−0.404098	+	0.699918i
$122$	−1125.39			−0.835147
$123$		0			0
$124$	−633.542	+	1097.33i	−0.458821	+	0.794701i
$125$	−1433.61			−1.02581
$126$		0			0
$127$	665.802	+	1153.20i	0.465200	+	0.805750i	0.999211	−	0.0397279i	$-0.0126491\pi$
$127$	665.802	+	1153.20i	0.465200	+	0.805750i	−0.534011	+	0.845478i	$0.679316\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	906.022	−	465.424i	0.611257	−	0.314003i
$131$	−260.378			−0.173659			−0.0868294	−	0.996223i	$-0.527674\pi$
$131$	−260.378			−0.173659			−0.0868294	+	0.996223i	$0.527674\pi$
$132$		0			0
$133$	−87.5873	−	151.706i	−0.0571036	−	0.0989064i
$134$	−517.524	+	896.378i	−0.333636	+	0.577875i
$135$		0			0
$136$	24.3053	−	42.0980i	0.0153247	−	0.0265432i
$137$	1205.97	−	2088.81i	0.752068	−	1.30262i	−0.194751	−	0.980853i	$-0.562390\pi$
$137$	1205.97	−	2088.81i	0.752068	−	1.30262i	0.946819	−	0.321767i	$-0.104277\pi$
$138$		0			0
$139$	203.965	−	353.278i	0.124461	−	0.215573i	−0.797061	−	0.603899i	$-0.793613\pi$
$139$	203.965	−	353.278i	0.124461	−	0.215573i	0.921522	+	0.388326i	$0.126946\pi$
$140$	649.004	+	1124.11i	0.391792	+	0.678603i
$141$		0			0
$142$	−289.113			−0.170858
$143$	−2045.37	+	1050.71i	−1.19610	+	0.614439i
$144$		0			0
$145$	−57.6656	−	99.8798i	−0.0330267	−	0.0572039i
$146$	−201.018	−	348.174i	−0.113948	−	0.197363i
$147$		0			0
$148$	−1521.85			−0.845237
$149$	−147.584	+	255.623i	−0.0811447	+	0.140547i	−0.903742	−	0.428078i	$-0.859191\pi$
$149$	−147.584	+	255.623i	−0.0811447	+	0.140547i	0.822597	+	0.568625i	$0.192524\pi$
$150$		0			0
$151$	2087.10			1.12481			0.562403	−	0.826863i	$-0.309877\pi$
$151$	2087.10			1.12481			0.562403	+	0.826863i	$0.309877\pi$
$152$	−23.4618	+	40.6371i	−0.0125198	+	0.0216849i
$153$		0			0
$154$	−1465.15	−	2537.71i	−0.766655	−	1.32789i
$155$	3441.86			1.78359
$156$		0			0
$157$	557.512			0.283403			0.141702	−	0.989909i	$-0.454743\pi$
$157$	557.512			0.283403			0.141702	+	0.989909i	$0.454743\pi$
$158$	26.4579	+	45.8265i	0.0133220	+	0.0230744i
$159$		0			0
$160$	173.847	−	301.112i	0.0858990	−	0.148781i
$161$	−167.138			−0.0818159
$162$		0			0
$163$	645.238	−	1117.59i	0.310055	−	0.537031i	−0.668319	−	0.743875i	$-0.732986\pi$
$163$	645.238	−	1117.59i	0.310055	−	0.537031i	0.978374	+	0.206844i	$0.0663192\pi$
$164$	−1073.24			−0.511010
$165$		0			0
$166$	1147.16	+	1986.93i	0.536365	+	0.929012i
$167$	1256.64	+	2176.56i	0.582284	+	1.00854i	0.995208	+	0.0977795i	$0.0311740\pi$
$167$	1256.64	+	2176.56i	0.582284	+	1.00854i	−0.412925	+	0.910765i	$0.635493\pi$
$168$		0			0
$169$	−2186.44	−	215.183i	−0.995192	−	0.0979441i
$170$	−132.044			−0.0595724
$171$		0			0
$172$	461.273	+	798.948i	0.204487	+	0.354182i
$173$	−1700.26	+	2944.94i	−0.747218	+	1.29422i	0.201934	+	0.979399i	$0.435277\pi$
$173$	−1700.26	+	2944.94i	−0.747218	+	1.29422i	−0.949151	+	0.314820i	$0.898056\pi$
$174$		0			0
$175$	−103.660	+	179.544i	−0.0447768	+	0.0775557i
$176$	−392.466	+	679.771i	−0.168086	+	0.291134i
$177$		0			0
$178$	663.829	−	1149.79i	0.279529	−	0.484158i
$179$	−785.111	−	1359.85i	−0.327832	−	0.567822i	0.654249	−	0.756279i	$-0.272985\pi$
$179$	−785.111	−	1359.85i	−0.327832	−	0.567822i	−0.982081	+	0.188457i	$0.939651\pi$
$180$		0			0
$181$	2921.99			1.19995			0.599973	−	0.800021i	$-0.295178\pi$
$181$	2921.99			1.19995			0.599973	+	0.800021i	$0.295178\pi$
$182$	137.273	−	2796.35i	0.0559085	−	1.13890i
$183$		0			0
$184$	22.3855	+	38.7729i	0.00896893	+	0.0155346i
$185$	2066.95	+	3580.06i	0.821432	+	1.42276i
$186$		0			0
$187$	298.093			0.116571
$188$	1048.93	−	1816.80i	0.406921	−	0.704808i
$189$		0			0
$190$	127.462			0.0486687
$191$	1954.35	−	3385.03i	0.740375	−	1.28237i	−0.211949	−	0.977281i	$-0.567981\pi$
$191$	1954.35	−	3385.03i	0.740375	−	1.28237i	0.952325	−	0.305087i	$-0.0986855\pi$
$192$		0			0
$193$	1059.66	+	1835.39i	0.395214	+	0.684531i	0.993128	−	0.117029i	$-0.0373371\pi$
$193$	1059.66	+	1835.39i	0.395214	+	0.684531i	−0.597914	+	0.801560i	$0.704004\pi$
$194$	275.032			0.101784
$195$		0			0
$196$	2195.78			0.800212
$197$	1555.25	+	2693.77i	0.562472	+	0.974230i	0.997280	+	0.0737067i	$0.0234829\pi$
$197$	1555.25	+	2693.77i	0.562472	+	0.974230i	−0.434808	+	0.900523i	$0.643184\pi$
$198$		0			0
$199$	245.487	−	425.195i	0.0874476	−	0.151464i	−0.818984	−	0.573816i	$-0.805462\pi$
$199$	245.487	−	425.195i	0.0874476	−	0.151464i	0.906432	+	0.422353i	$0.138796\pi$
$200$	55.5342			0.0196343
$201$		0			0
$202$	884.695	−	1532.34i	0.308153	−	0.533737i
$203$	−317.006			−0.109603
$204$		0			0
$205$	1457.65	+	2524.73i	0.496618	+	0.860168i
$206$	−416.233	−	720.936i	−0.140778	−	0.243835i
$207$		0			0
$208$	−667.084	+	342.682i	−0.222375	+	0.114234i
$209$	−287.749			−0.0952345
$210$		0			0
$211$	301.634	+	522.445i	0.0984139	+	0.170458i	0.911028	−	0.412344i	$-0.135290\pi$
$211$	301.634	+	522.445i	0.0984139	+	0.170458i	−0.812614	+	0.582802i	$0.801956\pi$
$212$	−549.731	+	952.162i	−0.178093	+	0.308466i
$213$		0			0
$214$	−423.175	+	732.960i	−0.135176	+	0.234131i
$215$	1252.99	−	2170.24i	0.397455	−	0.688413i
$216$		0			0
$217$	4730.26	−	8193.04i	1.47977	−	2.56304i
$218$	−951.630	−	1648.27i	−0.295654	−	0.512087i
$219$		0			0
$220$	2132.16			0.653410
$221$	239.374	+	154.328i	0.0728599	+	0.0469737i
$222$		0			0
$223$	1567.57	+	2715.11i	0.470727	+	0.815324i	0.999439	−	0.0334775i	$-0.0106582\pi$
$223$	1567.57	+	2715.11i	0.470727	+	0.815324i	−0.528712	+	0.848801i	$0.677325\pi$
$224$	−477.847	−	827.656i	−0.142534	−	0.246875i
$225$		0			0
$226$	−1505.57			−0.443136
$227$	806.537	−	1396.96i	0.235823	−	0.408457i	−0.723689	−	0.690126i	$-0.757555\pi$
$227$	806.537	−	1396.96i	0.235823	−	0.408457i	0.959511	+	0.281670i	$0.0908882\pi$
$228$		0			0
$229$	−6156.40			−1.77653			−0.888267	−	0.459327i	$-0.848091\pi$
$229$	−6156.40			−1.77653			−0.888267	+	0.459327i	$0.848091\pi$
$230$	60.8072	−	105.321i	0.0174327	−	0.0301942i
$231$		0			0
$232$	42.4579	+	73.5393i	0.0120151	+	0.0208107i
$233$	3350.07			0.941934			0.470967	−	0.882151i	$-0.343905\pi$
$233$	3350.07			0.941934			0.470967	+	0.882151i	$0.343905\pi$
$234$		0			0
$235$	−5698.56			−1.58184
$236$	−285.884	−	495.165i	−0.0788535	−	0.136578i
$237$		0			0
$238$	−181.472	+	314.319i	−0.0494247	+	0.0856062i
$239$	632.554			0.171199			0.0855994	−	0.996330i	$-0.472719\pi$
$239$	632.554			0.171199			0.0855994	+	0.996330i	$0.472719\pi$
$240$		0			0
$241$	−752.118	+	1302.71i	−0.201030	+	0.348194i	−0.948861	−	0.315696i	$-0.897762\pi$
$241$	−752.118	+	1302.71i	−0.201030	+	0.348194i	0.747831	+	0.663890i	$0.231096\pi$
$242$	−2151.42			−0.571481
$243$		0			0
$244$	−1125.39	−	1949.23i	−0.295269	−	0.511421i
$245$	−2982.27	−	5165.45i	−0.777675	−	1.34697i
$246$		0			0
$247$	−231.067	−	148.972i	−0.0595241	−	0.0383760i
$248$	−2534.17			−0.648870
$249$		0			0
$250$	−1433.61	−	2483.08i	−0.362677	−	0.628176i
$251$	518.384	−	897.868i	0.130359	−	0.225789i	−0.793456	−	0.608628i	$-0.791720\pi$
$251$	518.384	−	897.868i	0.130359	−	0.225789i	0.923815	+	0.382839i	$0.125054\pi$
$252$		0			0
$253$	−137.274	+	237.766i	−0.0341121	+	0.0590839i
$254$	−1331.60	+	2306.41i	−0.328946	+	0.569751i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	252.452	+	437.260i	0.0612744	+	0.106130i	0.895035	−	0.445995i	$-0.147150\pi$
$257$	252.452	+	437.260i	0.0612744	+	0.106130i	−0.833761	+	0.552126i	$0.813817\pi$
$258$		0			0
$259$	11362.7			2.72603
$260$	1712.16	+	1103.85i	0.408399	+	0.263300i
$261$		0			0
$262$	−260.378	−	450.987i	−0.0613977	−	0.106344i
$263$	−84.6612	−	146.638i	−0.0198496	−	0.0343804i	0.855930	−	0.517092i	$-0.172985\pi$
$263$	−84.6612	−	146.638i	−0.0198496	−	0.0343804i	−0.875780	+	0.482711i	$0.839652\pi$
$264$		0			0
$265$	2986.54			0.692308
$266$	175.175	−	303.411i	0.0403784	−	0.0699374i
$267$		0			0
$268$	−2070.10			−0.471833
$269$	771.017	−	1335.44i	0.174757	−	0.302689i	−0.765320	−	0.643650i	$-0.777419\pi$
$269$	771.017	−	1335.44i	0.174757	−	0.302689i	0.940077	+	0.340961i	$0.110753\pi$
$270$		0			0
$271$	589.678	+	1021.35i	0.132179	+	0.228940i	0.924516	−	0.381143i	$-0.124469\pi$
$271$	589.678	+	1021.35i	0.132179	+	0.228940i	−0.792338	+	0.610083i	$0.791136\pi$
$272$	97.2211			0.0216724
$273$		0			0
$274$	4823.89			1.06358
$275$	170.276	+	294.926i	0.0373382	+	0.0646717i
$276$		0			0
$277$	−1952.95	+	3382.61i	−0.423615	+	0.733723i	−0.996290	−	0.0860599i	$-0.972572\pi$
$277$	−1952.95	+	3382.61i	−0.423615	+	0.733723i	0.572675	+	0.819782i	$0.305906\pi$
$278$	815.860			0.176015
$279$		0			0
$280$	−1298.01	+	2248.22i	−0.277039	+	0.479845i
$281$	−58.9976			−0.0125249			−0.00626245	−	0.999980i	$-0.501993\pi$
$281$	−58.9976			−0.0125249			−0.00626245	+	0.999980i	$0.501993\pi$
$282$		0			0
$283$	−2347.79	−	4066.49i	−0.493151	−	0.854163i	0.506818	−	0.862053i	$-0.330822\pi$
$283$	−2347.79	−	4066.49i	−0.493151	−	0.854163i	−0.999969	+	0.00789055i	$0.997488\pi$
$284$	−289.113	−	500.758i	−0.0604073	−	0.104629i
$285$		0			0
$286$	−3865.25	−	2491.98i	−0.799151	−	0.515223i
$287$	8013.18			1.64809
$288$		0			0
$289$	2438.04	+	4222.81i	0.496242	+	0.859517i
$290$	115.331	−	199.760i	0.0233534	−	0.0404493i
$291$		0			0
$292$	402.036	−	696.347i	0.0805733	−	0.139557i
$293$	−4059.41	+	7031.11i	−0.809397	+	1.40192i	0.103885	+	0.994589i	$0.466873\pi$
$293$	−4059.41	+	7031.11i	−0.809397	+	1.40192i	−0.913282	+	0.407327i	$0.866461\pi$
$294$		0			0
$295$	−776.564	+	1345.05i	−0.153265	+	0.265464i
$296$	−1521.85	−	2635.92i	−0.298836	−	0.517600i
$297$		0			0
$298$	−590.337			−0.114756
$299$	−233.329	+	119.861i	−0.0451296	+	0.0231831i
$300$		0			0
$301$	−3444.03	−	5965.24i	−0.659504	−	1.14229i
$302$	2087.10	+	3614.96i	0.397679	+	0.688800i
$303$		0			0
$304$	−93.8474			−0.0177056
$305$	−3056.97	+	5294.82i	−0.573907	+	0.994035i
$306$		0			0
$307$	−1072.04			−0.199298			−0.0996492	−	0.995023i	$-0.531772\pi$
$307$	−1072.04			−0.199298			−0.0996492	+	0.995023i	$0.531772\pi$
$308$	2930.29	−	5075.42i	0.542107	−	0.938957i
$309$		0			0
$310$	3441.86	+	5961.48i	0.630596	+	1.09222i
$311$	4528.41			0.825667			0.412834	−	0.910806i	$-0.364539\pi$
$311$	4528.41			0.825667			0.412834	+	0.910806i	$0.364539\pi$
$312$		0			0
$313$	−5396.13			−0.974464			−0.487232	−	0.873273i	$-0.661993\pi$
$313$	−5396.13			−0.974464			−0.487232	+	0.873273i	$0.661993\pi$
$314$	557.512	+	965.640i	0.100198	+	0.173548i
$315$		0			0
$316$	−52.9158	+	91.6529i	−0.00942009	+	0.0163161i
$317$	−8222.40			−1.45683			−0.728417	−	0.685134i	$-0.759743\pi$
$317$	−8222.40			−1.45683			−0.728417	+	0.685134i	$0.759743\pi$
$318$		0			0
$319$	−260.364	+	450.963i	−0.0456977	+	0.0791508i
$320$	695.389			0.121480
$321$		0			0
$322$	−167.138	−	289.492i	−0.0289263	−	0.0501018i
$323$	17.8202	+	30.8655i	0.00306979	+	0.00531704i
$324$		0			0
$325$	−15.9535	+	324.985i	−0.00272290	+	0.0554675i
$326$	2580.95			0.438484
$327$		0			0
$328$	−1073.24	−	1858.90i	−0.180669	−	0.312929i
$329$	−7831.71	+	13564.9i	−1.31239	+	2.27312i
$330$		0			0
$331$	304.177	−	526.851i	0.0505109	−	0.0874874i	−0.839664	−	0.543105i	$-0.817248\pi$
$331$	304.177	−	526.851i	0.0505109	−	0.0874874i	0.890175	+	0.455618i	$0.150582\pi$
$332$	−2294.31	+	3973.87i	−0.379267	+	0.656910i
$333$		0			0
$334$	−2513.27	+	4353.11i	−0.411737	+	0.713149i
$335$	2811.57	+	4869.78i	0.458544	+	0.794222i
$336$		0			0
$337$	−8808.73			−1.42386			−0.711932	−	0.702248i	$-0.752180\pi$
$337$	−8808.73			−1.42386			−0.711932	+	0.702248i	$0.752180\pi$
$338$	−1813.73	−	4002.20i	−0.291875	−	0.644057i
$339$		0			0
$340$	−132.044	−	228.707i	−0.0210620	−	0.0364805i
$341$	−7770.11	−	13458.2i	−1.23394	−	2.13725i
$342$		0			0
$343$	−6150.66			−0.968235
$344$	−922.546	+	1597.90i	−0.144594	+	0.250444i
$345$		0			0
$346$	−6801.06			−1.05673
$347$	−3583.04	+	6206.01i	−0.554317	+	0.960105i	0.443640	+	0.896205i	$0.353687\pi$
$347$	−3583.04	+	6206.01i	−0.554317	+	0.960105i	−0.997956	+	0.0638994i	$0.979646\pi$
$348$		0			0
$349$	942.489	+	1632.44i	0.144557	+	0.250380i	0.929207	−	0.369559i	$-0.120491\pi$
$349$	942.489	+	1632.44i	0.144557	+	0.250380i	−0.784651	+	0.619938i	$0.787158\pi$
$350$	−414.639			−0.0633240
$351$		0			0
$352$	−1569.86			−0.237710
$353$	−5977.01	−	10352.5i	−0.901202	−	1.56093i	−0.825936	−	0.563764i	$-0.809353\pi$
$353$	−5977.01	−	10352.5i	−0.901202	−	1.56093i	−0.0752661	−	0.997163i	$-0.523981\pi$
$354$		0			0
$355$	−785.335	+	1360.24i	−0.117412	+	0.203364i
$356$	2655.32			0.395313
$357$		0			0
$358$	1570.22	−	2719.71i	0.231812	−	0.401511i
$359$	−9068.77			−1.33324			−0.666618	−	0.745400i	$-0.732259\pi$
$359$	−9068.77			−1.33324			−0.666618	+	0.745400i	$0.732259\pi$
$360$		0			0
$361$	3412.30	+	5910.27i	0.497492	+	0.861682i
$362$	2921.99	+	5061.04i	0.424245	+	0.734813i
$363$		0			0
$364$	4980.69	−	2558.59i	0.717196	−	0.368424i
$365$	−2184.15			−0.313216
$366$		0			0
$367$	−3922.06	−	6793.21i	−0.557847	−	0.966220i	−0.997676	−	0.0681380i	$-0.978294\pi$
$367$	−3922.06	−	6793.21i	−0.557847	−	0.966220i	0.439829	−	0.898082i	$-0.355039\pi$
$368$	−44.7710	+	77.5457i	−0.00634199	+	0.0109846i
$369$		0			0
$370$	−4133.89	+	7160.11i	−0.580840	+	1.00604i
$371$	4104.49	−	7109.19i	0.574379	−	0.994854i
$372$		0			0
$373$	−723.844	+	1253.74i	−0.100481	+	0.174037i	−0.911883	−	0.410451i	$-0.865371\pi$
$373$	−723.844	+	1253.74i	−0.100481	+	0.174037i	0.811402	+	0.584488i	$0.198705\pi$
$374$	298.093	+	516.313i	0.0412140	+	0.0713848i
$375$		0			0
$376$	4195.73			0.575474
$377$	−442.547	+	227.337i	−0.0604571	+	0.0310569i
$378$		0			0
$379$	5909.48	+	10235.5i	0.800922	+	1.38724i	0.919010	+	0.394234i	$0.128990\pi$
$379$	5909.48	+	10235.5i	0.800922	+	1.38724i	−0.118088	+	0.993003i	$0.537677\pi$
$380$	127.462	+	220.770i	0.0172070	+	0.0298034i
$381$		0			0
$382$	7817.39			1.04705
$383$	3625.40	−	6279.38i	0.483680	−	0.837758i	−0.516145	−	0.856501i	$-0.672633\pi$
$383$	3625.40	−	6279.38i	0.483680	−	0.837758i	0.999824	+	0.0187436i	$0.00596662\pi$
$384$		0			0
$385$	−15919.5			−2.10736
$386$	−2119.33	+	3670.79i	−0.279459	+	0.484036i
$387$		0			0
$388$	275.032	+	476.370i	0.0359862	+	0.0623299i
$389$	9331.29			1.21623			0.608117	−	0.793847i	$-0.291925\pi$
$389$	9331.29			1.21623			0.608117	+	0.793847i	$0.291925\pi$
$390$		0			0
$391$	34.0054			0.00439828
$392$	2195.78	+	3803.21i	0.282918	+	0.490028i
$393$		0			0
$394$	−3110.50	+	5387.54i	−0.397728	+	0.688885i
$395$	287.478			0.0366191
$396$		0			0
$397$	3847.13	−	6663.42i	0.486352	−	0.842386i	−0.513525	−	0.858075i	$-0.671661\pi$
$397$	3847.13	−	6663.42i	0.486352	−	0.842386i	0.999877	+	0.0156884i	$0.00499397\pi$
$398$	981.946			0.123670
$399$		0			0
$400$	55.5342	+	96.1881i	0.00694178	+	0.0120235i
$401$	928.729	+	1608.61i	0.115657	+	0.200324i	0.918042	−	0.396483i	$-0.129769\pi$
$401$	928.729	+	1608.61i	0.115657	+	0.200324i	−0.802385	+	0.596807i	$0.796436\pi$
$402$		0			0
$403$	728.000	−	14829.9i	0.0899858	−	1.83308i
$404$	3538.78			0.435794
$405$		0			0
$406$	−317.006	−	549.071i	−0.0387506	−	0.0671181i
$407$	9332.39	−	16164.2i	1.13658	−	1.96862i
$408$		0			0
$409$	269.235	−	466.328i	0.0325496	−	0.0563776i	−0.849292	−	0.527924i	$-0.822971\pi$
$409$	269.235	−	466.328i	0.0325496	−	0.0563776i	0.881841	+	0.471546i	$0.156304\pi$
$410$	−2915.30	+	5049.45i	−0.351162	+	0.608231i
$411$		0			0
$412$	832.466	−	1441.87i	0.0995453	−	0.172417i
$413$	2134.51	+	3697.08i	0.254316	+	0.440488i
$414$		0			0
$415$	12464.4			1.47434
$416$	−1260.63	−	812.742i	−0.148575	−	0.0957883i
$417$		0			0
$418$	−287.749	−	498.396i	−0.0336705	−	0.0583190i
$419$	2418.69	+	4189.30i	0.282007	+	0.488450i	0.971879	−	0.235481i	$-0.0756666\pi$
$419$	2418.69	+	4189.30i	0.282007	+	0.488450i	−0.689872	+	0.723931i	$0.742333\pi$
$420$		0			0
$421$	−1392.34			−0.161184			−0.0805918	−	0.996747i	$-0.525681\pi$
$421$	−1392.34			−0.161184			−0.0805918	+	0.996747i	$0.525681\pi$
$422$	−603.268	+	1044.89i	−0.0695891	+	0.120532i
$423$		0			0
$424$	−2198.92			−0.251861
$425$	21.0902	−	36.5294i	0.00240712	−	0.00416926i
$426$		0			0
$427$	8402.57	+	14553.7i	0.952292	+	1.64942i
$428$	−1692.70			−0.191167
$429$		0			0
$430$	5011.94			0.562087
$431$	3953.78	+	6848.14i	0.441872	+	0.765344i	0.997828	−	0.0658670i	$-0.0209813\pi$
$431$	3953.78	+	6848.14i	0.441872	+	0.765344i	−0.555957	+	0.831211i	$0.687648\pi$
$432$		0			0
$433$	−4816.28	+	8342.04i	−0.534539	+	0.925850i	0.464646	+	0.885497i	$0.346182\pi$
$433$	−4816.28	+	8342.04i	−0.534539	+	0.925850i	−0.999185	+	0.0403530i	$0.987152\pi$
$434$	18921.0			2.09271
$435$		0			0
$436$	1903.26	−	3296.54i	0.209059	−	0.362100i
$437$	−32.8253			−0.00359325
$438$		0			0
$439$	323.735	+	560.725i	0.0351959	+	0.0609611i	0.883087	−	0.469210i	$-0.155461\pi$
$439$	323.735	+	560.725i	0.0351959	+	0.0609611i	−0.847891	+	0.530171i	$0.822128\pi$
$440$	2132.16	+	3693.01i	0.231015	+	0.400130i
$441$		0			0
$442$	−27.9291	+	568.936i	−0.00300554	+	0.0612251i
$443$	−16862.3			−1.80847			−0.904233	−	0.427039i	$-0.859557\pi$
$443$	−16862.3			−1.80847			−0.904233	+	0.427039i	$0.859557\pi$
$444$		0			0
$445$	−3606.41	−	6246.48i	−0.384180	−	0.665419i
$446$	−3135.14	+	5430.22i	−0.332855	+	0.576521i
$447$		0			0
$448$	955.695	−	1655.31i	0.100786	−	0.174567i
$449$	6240.44	−	10808.8i	0.655912	−	1.13607i	−0.325752	−	0.945455i	$-0.605617\pi$
$449$	6240.44	−	10808.8i	0.655912	−	1.13607i	0.981664	−	0.190618i	$-0.0610493\pi$
$450$		0			0
$451$	6581.39	−	11399.3i	0.687152	−	1.19018i
$452$	−1505.57	−	2607.72i	−0.156672	−	0.271364i
$453$		0			0
$454$	3226.15			0.333504
$455$	−12783.6	−	8241.76i	−1.31715	−	0.849186i
$456$		0			0
$457$	−6268.52	−	10857.4i	−0.641639	−	1.11135i	−0.985067	−	0.172172i	$-0.944921\pi$
$457$	−6268.52	−	10857.4i	−0.641639	−	1.11135i	0.343428	−	0.939179i	$-0.388412\pi$
$458$	−6156.40	−	10663.2i	−0.628100	−	1.08790i
$459$		0			0
$460$	243.229			0.0246535
$461$	726.957	−	1259.13i	0.0734442	−	0.127209i	−0.826964	−	0.562254i	$-0.809934\pi$
$461$	726.957	−	1259.13i	0.0734442	−	0.127209i	0.900409	+	0.435045i	$0.143268\pi$
$462$		0			0
$463$	−7154.47			−0.718135			−0.359068	−	0.933312i	$-0.616905\pi$
$463$	−7154.47			−0.718135			−0.359068	+	0.933312i	$0.616905\pi$
$464$	−84.9158	+	147.079i	−0.00849595	+	0.0147154i
$465$		0			0
$466$	3350.07	+	5802.50i	0.333024	+	0.576814i
$467$	5823.27			0.577021			0.288510	−	0.957477i	$-0.406840\pi$
$467$	5823.27			0.577021			0.288510	+	0.957477i	$0.406840\pi$
$468$		0			0
$469$	15456.1			1.52174
$470$	−5698.56	−	9870.20i	−0.559266	−	0.968677i
$471$		0			0
$472$	571.767	−	990.330i	0.0557579	−	0.0965755i
$473$	−11314.6			−1.09989
$474$		0			0
$475$	−20.3584	+	35.2617i	−0.00196654	+	0.00340615i
$476$	−725.888			−0.0698971
$477$		0			0
$478$	632.554	+	1095.62i	0.0605279	+	0.104837i
$479$	1460.09	+	2528.94i	0.139276	+	0.241233i	0.927223	−	0.374511i	$-0.122189\pi$
$479$	1460.09	+	2528.94i	0.139276	+	0.241233i	−0.787947	+	0.615743i	$0.788856\pi$
$480$		0			0
$481$	15862.5	−	8148.58i	1.50368	−	0.772439i
$482$	−3008.47			−0.284299
$483$		0			0
$484$	−2151.42	−	3726.36i	−0.202049	−	0.349959i
$485$	747.088	−	1293.99i	0.0699454	−	0.121149i
$486$		0			0
$487$	1681.12	−	2911.79i	0.156425	−	0.270936i	−0.777152	−	0.629313i	$-0.783336\pi$
$487$	1681.12	−	2911.79i	0.156425	−	0.270936i	0.933577	+	0.358377i	$0.116670\pi$
$488$	2250.78	−	3898.46i	0.208787	−	0.361629i
$489$		0			0
$490$	5964.55	−	10330.9i	0.549900	−	0.952454i
$491$	7434.83	+	12877.5i	0.683359	+	1.18361i	0.973950	+	0.226764i	$0.0728147\pi$
$491$	7434.83	+	12877.5i	0.683359	+	1.18361i	−0.290591	+	0.956847i	$0.593852\pi$
$492$		0			0
$493$	64.4970			0.00589209
$494$	26.9599	−	549.192i	0.00245543	−	0.0500189i
$495$		0			0
$496$	−2534.17	−	4389.31i	−0.229410	−	0.397350i
$497$	2158.62	+	3738.84i	0.194824	+	0.337444i
$498$		0			0
$499$	−18693.3			−1.67701			−0.838503	−	0.544896i	$-0.816569\pi$
$499$	−18693.3			−1.67701			−0.838503	+	0.544896i	$0.816569\pi$
$500$	2867.22	−	4966.16i	0.256452	−	0.444187i
$501$		0			0
$502$	2073.54			0.184356
$503$	7359.24	−	12746.6i	0.652350	−	1.12990i	−0.330201	−	0.943911i	$-0.607116\pi$
$503$	7359.24	−	12746.6i	0.652350	−	1.12990i	0.982551	−	0.185993i	$-0.0595502\pi$
$504$		0			0
$505$	−4806.31	−	8324.77i	−0.423521	−	0.733559i
$506$	−549.097			−0.0482418
$507$		0			0
$508$	−5326.42			−0.465200
$509$	7939.46	+	13751.6i	0.691376	+	1.19750i	0.971387	+	0.237502i	$0.0763286\pi$
$509$	7939.46	+	13751.6i	0.691376	+	1.19750i	−0.280011	+	0.959997i	$0.590338\pi$
$510$		0			0
$511$	−3001.75	+	5199.18i	−0.259862	+	0.450094i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−504.904	+	874.520i	−0.0433276	+	0.0750455i
$515$	−4522.56			−0.386967
$516$		0			0
$517$	12864.7	+	22282.3i	1.09437	+	1.89550i
$518$	11362.7	+	19680.7i	0.963797	+	1.66935i
$519$		0			0
$520$	−199.767	+	4069.40i	−0.0168469	+	0.343183i
$521$	9618.86			0.808848			0.404424	−	0.914572i	$-0.367472\pi$
$521$	9618.86			0.808848			0.404424	+	0.914572i	$0.367472\pi$
$522$		0			0
$523$	5177.94	+	8968.45i	0.432917	+	0.749834i	0.997123	−	0.0758002i	$-0.0241511\pi$
$523$	5177.94	+	8968.45i	0.432917	+	0.749834i	−0.564206	+	0.825634i	$0.690818\pi$
$524$	520.755	−	901.975i	0.0434147	−	0.0751965i
$525$		0			0
$526$	169.322	−	293.275i	0.0140358	−	0.0243106i
$527$	−962.401	+	1666.93i	−0.0795500	+	0.137785i
$528$		0			0
$529$	6067.84	−	10509.8i	0.498713	−	0.863796i
$530$	2986.54	+	5172.84i	0.244768	+	0.423950i
$531$		0			0
$532$	700.699			0.0571036
$533$	11186.6	−	5746.54i	0.909087	−	0.466999i
$534$		0			0
$535$	2298.99	+	3981.97i	0.185783	+	0.321786i
$536$	−2070.10	−	3585.51i	−0.166818	−	0.288937i
$537$		0			0
$538$	3084.07			0.247144
$539$	−13465.1	+	23322.3i	−1.07604	+	1.86375i
$540$		0			0
$541$	14130.6			1.12296			0.561479	−	0.827491i	$-0.310232\pi$
$541$	14130.6			1.12296			0.561479	+	0.827491i	$0.310232\pi$
$542$	−1179.36	+	2042.70i	−0.0934643	+	0.161885i
$543$		0			0
$544$	97.2211	+	168.392i	0.00766236	+	0.0132716i
$545$	−10339.9			−0.812684
$546$		0			0
$547$	6505.59			0.508517			0.254259	−	0.967136i	$-0.418169\pi$
$547$	6505.59			0.508517			0.254259	+	0.967136i	$0.418169\pi$
$548$	4823.89	+	8355.23i	0.376034	+	0.651310i
$549$		0			0
$550$	−340.551	+	589.852i	−0.0264021	+	0.0457298i
$551$	−62.2588			−0.00481364
$552$		0			0
$553$	395.089	−	684.314i	0.0303814	−	0.0526221i
$554$	−7811.80			−0.599082
$555$		0			0
$556$	815.860	+	1413.11i	0.0622305	+	0.107786i
$557$	−9162.49	−	15869.9i	−0.696996	−	1.20723i	−0.969503	−	0.245079i	$-0.921186\pi$
$557$	−9162.49	−	15869.9i	−0.696996	−	1.20723i	0.272507	−	0.962154i	$-0.412147\pi$
$558$		0			0
$559$	−9085.83	−	5857.75i	−0.687459	−	0.443214i
$560$	−5192.03			−0.391792
$561$		0			0
$562$	−58.9976	−	102.187i	−0.00442822	−	0.00766991i
$563$	12087.1	−	20935.5i	0.904815	−	1.56719i	0.0836495	−	0.996495i	$-0.473342\pi$
$563$	12087.1	−	20935.5i	0.904815	−	1.56719i	0.821165	−	0.570690i	$-0.193324\pi$
$564$		0			0
$565$	−4089.67	+	7083.51i	−0.304520	+	0.527443i
$566$	4695.58	−	8132.99i	0.348710	−	0.603984i
$567$		0			0
$568$	578.225	−	1001.52i	0.0427144	−	0.0739835i
$569$	4816.74	+	8342.84i	0.354883	+	0.614675i	0.987098	−	0.160118i	$-0.0511874\pi$
$569$	4816.74	+	8342.84i	0.354883	+	0.614675i	−0.632215	+	0.774793i	$0.717854\pi$
$570$		0			0
$571$	−8221.17			−0.602531			−0.301266	−	0.953540i	$-0.597409\pi$
$571$	−8221.17			−0.602531			−0.301266	+	0.953540i	$0.597409\pi$
$572$	450.980	−	9186.80i	0.0329658	−	0.671537i
$573$		0			0
$574$	8013.18	+	13879.2i	0.582689	+	1.00925i
$575$	19.4244	+	33.6441i	0.00140879	+	0.00244010i
$576$		0			0
$577$	−7986.09			−0.576196			−0.288098	−	0.957601i	$-0.593023\pi$
$577$	−7986.09			−0.576196			−0.288098	+	0.957601i	$0.593023\pi$
$578$	−4876.08	+	8445.62i	−0.350896	+	0.607770i
$579$		0			0
$580$	461.325			0.0330267
$581$	17130.2	−	29670.3i	1.22320	−	2.11865i
$582$		0			0
$583$	−6742.21	−	11677.8i	−0.478960	−	0.829583i
$584$	1608.14			0.113948
$585$		0			0
$586$	−16237.6			−1.14466
$587$	3722.38	+	6447.35i	0.261736	+	0.453340i	0.966703	−	0.255900i	$-0.0823717\pi$
$587$	3722.38	+	6447.35i	0.261736	+	0.453340i	−0.704967	+	0.709240i	$0.749038\pi$
$588$		0			0
$589$	929.004	−	1609.08i	0.0649897	−	0.112565i
$590$	−3106.26			−0.216750
$591$		0			0
$592$	3043.69	−	5271.83i	0.211309	−	0.365998i
$593$	6806.49			0.471347			0.235674	−	0.971832i	$-0.424270\pi$
$593$	6806.49			0.471347			0.235674	+	0.971832i	$0.424270\pi$
$594$		0			0
$595$	985.889	+	1707.61i	0.0679286	+	0.117656i
$596$	−590.337	−	1022.49i	−0.0405724	−	0.0702734i
$597$		0			0
$598$	−440.934	−	284.276i	−0.0301524	−	0.0194396i
$599$	−22251.5			−1.51782			−0.758909	−	0.651196i	$-0.774267\pi$
$599$	−22251.5			−1.51782			−0.758909	+	0.651196i	$0.774267\pi$
$600$		0			0
$601$	10608.1	+	18373.7i	0.719988	+	1.24706i	0.961004	+	0.276535i	$0.0891862\pi$
$601$	10608.1	+	18373.7i	0.719988	+	1.24706i	−0.241016	+	0.970521i	$0.577480\pi$
$602$	6888.07	−	11930.5i	0.466340	−	0.807724i
$603$		0			0
$604$	−4174.20	+	7229.93i	−0.281202	+	0.487055i
$605$	−5844.04	+	10122.2i	−0.392717	+	0.680206i
$606$		0			0
$607$	8895.83	−	15408.0i	0.594844	−	1.03030i	−0.398724	−	0.917071i	$-0.630547\pi$
$607$	8895.83	−	15408.0i	0.594844	−	1.03030i	0.993569	−	0.113230i	$-0.0361197\pi$
$608$	−93.8474	−	162.548i	−0.00625989	−	0.0108424i
$609$		0			0
$610$	−12227.9			−0.811626
$611$	−1205.32	+	24553.3i	−0.0798070	+	1.62573i
$612$		0			0
$613$	5487.29	+	9504.27i	0.361549	+	0.626221i	0.988216	−	0.153066i	$-0.0489146\pi$
$613$	5487.29	+	9504.27i	0.361549	+	0.626221i	−0.626667	+	0.779287i	$0.715581\pi$
$614$	−1072.04	−	1856.83i	−0.0704626	−	0.122045i
$615$		0			0
$616$	11721.2			0.766655
$617$	−1530.46	+	2650.84i	−0.0998609	+	0.172964i	−0.911627	−	0.411019i	$-0.865173\pi$
$617$	−1530.46	+	2650.84i	−0.0998609	+	0.172964i	0.811766	+	0.583983i	$0.198506\pi$
$618$		0			0
$619$	−8387.51			−0.544625			−0.272312	−	0.962209i	$-0.587788\pi$
$619$	−8387.51			−0.544625			−0.272312	+	0.962209i	$0.587788\pi$
$620$	−6883.73	+	11923.0i	−0.445899	+	0.772319i
$621$		0			0
$622$	4528.41	+	7843.43i	0.291917	+	0.505616i
$623$	−19825.6			−1.27495
$624$		0			0
$625$	−14709.1			−0.941382
$626$	−5396.13	−	9346.37i	−0.344525	−	0.596735i
$627$		0			0
$628$	−1115.02	+	1931.28i	−0.0708508	+	0.122717i
$629$	−2311.81			−0.146547
$630$		0			0
$631$	13105.5	−	22699.4i	0.826818	−	1.43209i	−0.0737032	−	0.997280i	$-0.523482\pi$
$631$	13105.5	−	22699.4i	0.826818	−	1.43209i	0.900522	−	0.434811i	$-0.143185\pi$
$632$	−211.663			−0.0133220
$633$		0			0
$634$	−8222.40	−	14241.6i	−0.515068	−	0.892125i
$635$	7234.25	+	12530.1i	0.452098	+	0.783057i
$636$		0			0
$637$	−22887.1	+	11757.1i	−1.42358	+	0.731293i
$638$	−1041.46			−0.0646263
$639$		0			0
$640$	695.389	+	1204.45i	0.0429495	+	0.0743907i
$641$	−12229.5	+	21182.1i	−0.753565	+	1.30521i	0.192520	+	0.981293i	$0.438334\pi$
$641$	−12229.5	+	21182.1i	−0.753565	+	1.30521i	−0.946085	+	0.323919i	$0.894999\pi$
$642$		0			0
$643$	−14490.9	+	25099.0i	−0.888750	+	1.53936i	−0.0473946	+	0.998876i	$0.515092\pi$
$643$	−14490.9	+	25099.0i	−0.888750	+	1.53936i	−0.841355	+	0.540483i	$0.818242\pi$
$644$	334.277	−	578.985i	0.0204540	−	0.0354273i
$645$		0			0
$646$	−35.6404	+	61.7310i	−0.00217067	+	0.00375971i
$647$	−4423.15	−	7661.11i	−0.268766	−	0.465517i	0.699777	−	0.714361i	$-0.253283\pi$
$647$	−4423.15	−	7661.11i	−0.268766	−	0.465517i	−0.968544	+	0.248844i	$0.919949\pi$
$648$		0			0
$649$	7012.47			0.424135
$650$	−578.844	+	297.353i	−0.0349294	+	0.0179433i
$651$		0			0
$652$	2580.95	+	4470.34i	0.155027	+	0.268515i
$653$	13153.7	+	22782.9i	0.788275	+	1.36533i	0.927023	+	0.375005i	$0.122359\pi$
$653$	13153.7	+	22782.9i	0.788275	+	1.36533i	−0.138748	+	0.990328i	$0.544308\pi$
$654$		0			0
$655$	−2829.12			−0.168768
$656$	2146.47	−	3717.80i	0.127753	−	0.221274i
$657$		0			0
$658$	−31326.8			−1.85600
$659$	−1653.40	+	2863.78i	−0.0977352	+	0.169282i	−0.910747	−	0.412965i	$-0.864493\pi$
$659$	−1653.40	+	2863.78i	−0.0977352	+	0.169282i	0.813012	+	0.582247i	$0.197826\pi$
$660$		0			0
$661$	11801.3	+	20440.5i	0.694432	+	1.20279i	0.970372	+	0.241616i	$0.0776774\pi$
$661$	11801.3	+	20440.5i	0.694432	+	1.20279i	−0.275940	+	0.961175i	$0.588989\pi$
$662$	1216.71			0.0714332
$663$		0			0
$664$	−9177.25			−0.536365
$665$	−951.677	−	1648.35i	−0.0554954	−	0.0961208i
$666$		0			0
$667$	−29.7013	+	51.4442i	−0.00172420	+	0.00298640i
$668$	−10053.1			−0.582284
$669$		0			0
$670$	−5623.14	+	9739.56i	−0.324240	+	0.561600i
$671$	27604.8			1.58818
$672$		0			0
$673$	1887.77	+	3269.72i	0.108125	+	0.187278i	0.915011	−	0.403429i	$-0.132182\pi$
$673$	1887.77	+	3269.72i	0.108125	+	0.187278i	−0.806886	+	0.590708i	$0.798849\pi$
$674$	−8808.73	−	15257.2i	−0.503412	−	0.871935i
$675$		0			0
$676$	5118.29	−	7143.67i	0.291209	−	0.406445i
$677$	11395.4			0.646916			0.323458	−	0.946242i	$-0.395155\pi$
$677$	11395.4			0.646916			0.323458	+	0.946242i	$0.395155\pi$
$678$		0			0
$679$	−2053.49	−	3556.75i	−0.116062	−	0.201024i
$680$	264.088	−	457.414i	0.0148931	−	0.0257956i
$681$		0			0
$682$	15540.2	−	26916.5i	0.872531	−	1.51127i
$683$	118.213	−	204.751i	0.00662269	−	0.0114708i	−0.862695	−	0.505724i	$-0.831225\pi$
$683$	118.213	−	204.751i	0.00662269	−	0.0114708i	0.869318	+	0.494254i	$0.164559\pi$
$684$		0			0
$685$	13103.5	−	22695.9i	0.730887	−	1.26593i
$686$	−6150.66	−	10653.3i	−0.342323	−	0.592920i
$687$		0			0
$688$	−3690.18			−0.204487
$689$	631.693	−	12868.0i	0.0349283	−	0.711514i
$690$		0			0
$691$	−4720.82	−	8176.70i	−0.259897	−	0.450154i	0.706317	−	0.707895i	$-0.250355\pi$
$691$	−4720.82	−	8176.70i	−0.259897	−	0.450154i	−0.966214	+	0.257741i	$0.917022\pi$
$692$	−6801.06	−	11779.8i	−0.373609	−	0.647110i
$693$		0			0
$694$	−14332.2			−0.783922
$695$	2216.17	−	3838.53i	0.120956	−	0.209502i
$696$		0			0
$697$	−1630.33			−0.0885986
$698$	−1884.98	+	3264.88i	−0.102217	+	0.177045i
$699$		0			0
$700$	−414.639	−	718.176i	−0.0223884	−	0.0387778i
$701$	145.814			0.00785638			0.00392819	−	0.999992i	$-0.498750\pi$
$701$	145.814			0.00785638			0.00392819	+	0.999992i	$0.498750\pi$
$702$		0			0
$703$	2231.58			0.119724
$704$	−1569.86	−	2719.08i	−0.0840432	−	0.145567i
$705$		0			0
$706$	11954.0	−	20705.0i	0.637246	−	1.10374i
$707$	−26421.8			−1.40551
$708$		0			0
$709$	5445.77	−	9432.35i	0.288463	−	0.499632i	−0.684980	−	0.728562i	$-0.740189\pi$
$709$	5445.77	−	9432.35i	0.288463	−	0.499632i	0.973443	+	0.228929i	$0.0735225\pi$
$710$	−3141.34			−0.166046
$711$		0			0
$712$	2655.32	+	4599.14i	0.139764	+	0.242079i
$713$	−886.386	−	1535.26i	−0.0465574	−	0.0806397i
$714$		0			0
$715$	−22223.9	+	11416.4i	−1.16242	+	0.597134i
$716$	6280.89			0.327832
$717$		0			0
$718$	−9068.77	−	15707.6i	−0.471370	−	0.816436i
$719$	−3447.89	+	5971.91i	−0.178838	+	0.309756i	−0.941483	−	0.337061i	$-0.890567\pi$
$719$	−3447.89	+	5971.91i	−0.178838	+	0.309756i	0.762645	+	0.646817i	$0.223900\pi$
$720$		0			0
$721$	−6215.49	+	10765.5i	−0.321050	+	0.556075i
$722$	−6824.60	+	11820.5i	−0.351780	+	0.609301i
$723$		0			0
$724$	−5843.99	+	10122.1i	−0.299986	+	0.519592i
$725$	36.8417	+	63.8117i	0.00188726	+	0.00326884i
$726$		0			0
$727$	12841.0			0.655086			0.327543	−	0.944836i	$-0.393779\pi$
$727$	12841.0			0.655086			0.327543	+	0.944836i	$0.393779\pi$
$728$	9412.30	+	6068.23i	0.479180	+	0.308933i
$729$		0			0
$730$	−2184.15	−	3783.07i	−0.110739	−	0.191805i
$731$	700.711	+	1213.67i	0.0354538	+	0.0614078i
$732$		0			0
$733$	−26005.8			−1.31043			−0.655216	−	0.755441i	$-0.727423\pi$
$733$	−26005.8			−1.31043			−0.655216	+	0.755441i	$0.727423\pi$
$734$	7844.12	−	13586.4i	0.394458	−	0.683220i
$735$		0			0
$736$	−179.084			−0.00896893
$737$	12694.4	−	21987.3i	0.634470	−	1.09893i
$738$		0			0
$739$	8885.01	+	15389.3i	0.442274	+	0.766041i	0.997858	−	0.0654195i	$-0.0208386\pi$
$739$	8885.01	+	15389.3i	0.442274	+	0.766041i	−0.555584	+	0.831460i	$0.687505\pi$
$740$	−16535.6			−0.821432
$741$		0			0
$742$	16418.0			0.812295
$743$	−14420.9	−	24977.7i	−0.712046	−	1.23330i	−0.964088	−	0.265583i	$-0.914436\pi$
$743$	−14420.9	−	24977.7i	−0.712046	−	1.23330i	0.252043	−	0.967716i	$-0.418898\pi$
$744$		0			0
$745$	−1603.57	+	2777.46i	−0.0788594	+	0.136588i
$746$	−2895.38			−0.142101
$747$		0			0
$748$	−596.187	+	1032.63i	−0.0291427	+	0.0504767i
$749$	12638.3			0.616547
$750$		0			0
$751$	4216.12	+	7302.54i	0.204858	+	0.354825i	0.950088	−	0.311983i	$-0.100993\pi$
$751$	4216.12	+	7302.54i	0.204858	+	0.354825i	−0.745229	+	0.666808i	$0.767660\pi$
$752$	4195.73	+	7267.21i	0.203461	+	0.352404i
$753$		0			0
$754$	−836.306	−	539.177i	−0.0403932	−	0.0260420i
$755$	22677.3			1.09313
$756$		0			0
$757$	−19480.8	−	33741.7i	−0.935325	−	1.62003i	−0.774053	−	0.633121i	$-0.781774\pi$
$757$	−19480.8	−	33741.7i	−0.935325	−	1.62003i	−0.161272	−	0.986910i	$-0.551560\pi$
$758$	−11819.0	+	20471.0i	−0.566337	+	0.980925i
$759$		0			0
$760$	−254.924	+	441.541i	−0.0121672	+	0.0210742i
$761$	4012.86	−	6950.47i	0.191151	−	0.331083i	−0.754481	−	0.656322i	$-0.772111\pi$
$761$	4012.86	−	6950.47i	0.191151	−	0.331083i	0.945632	+	0.325239i	$0.105445\pi$
$762$		0			0
$763$	−14210.4	+	24613.2i	−0.674249	+	1.16783i
$764$	7817.39	+	13540.1i	0.370188	+	0.641184i
$765$		0			0
$766$	14501.6			0.684026
$767$	5631.13	+	3630.46i	0.265096	+	0.170911i
$768$		0			0
$769$	−11295.1	−	19563.8i	−0.529666	−	0.917408i	−0.999401	−	0.0346010i	$-0.988984\pi$
$769$	−11295.1	−	19563.8i	−0.529666	−	0.917408i	0.469735	−	0.882807i	$-0.344349\pi$
$770$	−15919.5	−	27573.4i	−0.745063	−	1.29049i
$771$		0			0
$772$	−8477.32			−0.395214
$773$	−20460.0	+	35437.7i	−0.951997	+	1.64891i	−0.210901	+	0.977508i	$0.567640\pi$
$773$	−20460.0	+	35437.7i	−0.951997	+	1.64891i	−0.741096	+	0.671399i	$0.765694\pi$
$774$		0			0
$775$	−2198.96			−0.101921
$776$	−550.065	+	952.740i	−0.0254461	+	0.0440739i
$777$		0			0
$778$	9331.29	+	16162.3i	0.430004	+	0.744788i
$779$	1573.76			0.0723821
$780$		0			0
$781$	7091.67			0.324917
$782$	34.0054	+	58.8991i	0.00155503	+	0.00269338i
$783$		0			0
$784$	−4391.57	+	7606.41i	−0.200053	+	0.346502i
$785$	6057.63			0.275422
$786$		0			0
$787$	−7807.21	+	13522.5i	−0.353618	+	0.612484i	−0.986880	−	0.161453i	$-0.948382\pi$
$787$	−7807.21	+	13522.5i	−0.353618	+	0.612484i	0.633263	+	0.773937i	$0.281715\pi$
$788$	−12442.0			−0.562472
$789$		0			0
$790$	287.478	+	497.926i	0.0129468	+	0.0224246i
$791$	11241.1	+	19470.2i	0.505294	+	0.875195i
$792$		0			0
$793$	22167.1	+	14291.4i	0.992657	+	0.639979i
$794$	15388.5			0.687806
$795$		0			0
$796$	981.946	+	1700.78i	0.0437238	+	0.0757319i
$797$	8934.79	−	15475.5i	0.397097	−	0.687793i	−0.596269	−	0.802785i	$-0.703351\pi$
$797$	8934.79	−	15475.5i	0.397097	−	0.687793i	0.993366	+	0.114992i	$0.0366843\pi$
$798$		0			0
$799$	1593.41	−	2759.87i	0.0705517	−	0.122199i
$800$	−111.068	+	192.376i	−0.00490858	+	0.00850191i
$801$		0			0
$802$	−1857.46	+	3217.21i	−0.0817819	+	0.141650i
$803$	4930.80	+	8540.39i	0.216692	+	0.375322i
$804$		0			0
$805$	−1816.04			−0.0795116
$806$	26414.1	−	13569.0i	1.15434	−	0.592985i
$807$		0			0
$808$	3538.78	+	6129.34i	0.154076	+	0.266868i
$809$	−4056.59	−	7026.23i	−0.176294	−	0.305351i	0.764314	−	0.644844i	$-0.223078\pi$
$809$	−4056.59	−	7026.23i	−0.176294	−	0.305351i	−0.940608	+	0.339493i	$0.889744\pi$
$810$		0			0
$811$	22750.9			0.985073			0.492536	−	0.870292i	$-0.336070\pi$
$811$	22750.9			0.985073			0.492536	+	0.870292i	$0.336070\pi$
$812$	634.013	−	1098.14i	0.0274008	−	0.0474597i
$813$		0			0
$814$	37329.6			1.60737
$815$	7010.81	−	12143.1i	0.301323	−	0.521906i
$816$		0			0
$817$	−676.395	−	1171.55i	−0.0289646	−	0.0501681i
$818$	1076.94			0.0460322
$819$		0			0
$820$	−11661.2			−0.496618
$821$	−2997.11	−	5191.15i	−0.127406	−	0.220673i	0.795265	−	0.606262i	$-0.207332\pi$
$821$	−2997.11	−	5191.15i	−0.127406	−	0.220673i	−0.922671	+	0.385589i	$0.873998\pi$
$822$		0			0
$823$	17094.1	−	29607.9i	0.724015	−	1.25403i	−0.235363	−	0.971907i	$-0.575628\pi$
$823$	17094.1	−	29607.9i	0.724015	−	1.25403i	0.959378	−	0.282123i	$-0.0910387\pi$
$824$	3329.86			0.140778
$825$		0			0
$826$	−4269.02	+	7394.16i	−0.179828	+	0.311472i
$827$	−39546.0			−1.66282			−0.831409	−	0.555661i	$-0.812465\pi$
$827$	−39546.0			−1.66282			−0.831409	+	0.555661i	$0.812465\pi$
$828$		0			0
$829$	−12104.0	−	20964.7i	−0.507104	−	0.878329i	−0.999966	−	0.00822196i	$-0.997383\pi$
$829$	−12104.0	−	20964.7i	−0.507104	−	0.878329i	0.492863	−	0.870107i	$-0.335950\pi$
$830$	12464.4	+	21588.9i	0.521259	+	0.902847i
$831$		0			0
$832$	147.084	−	2996.21i	0.00612888	−	0.124850i
$833$	3335.57			0.138740
$834$		0			0
$835$	13653.9	+	23649.3i	0.565884	+	0.980140i
$836$	575.498	−	996.792i	0.0238086	−	0.0412378i
$837$		0			0
$838$	−4837.38	+	8378.59i	−0.199409	+	0.345386i
$839$	17071.8	−	29569.1i	0.702482	−	1.21673i	−0.265111	−	0.964218i	$-0.585408\pi$
$839$	17071.8	−	29569.1i	0.702482	−	1.21673i	0.967593	−	0.252516i	$-0.0812582\pi$
$840$		0			0
$841$	12138.2	−	21023.9i	0.497690	−	0.862025i
$842$	−1392.34	−	2411.60i	−0.0569870	−	0.0987043i
$843$		0			0
$844$	−2413.07			−0.0984139
$845$	−23756.6	−	2338.06i	−0.967164	−	0.0951856i
$846$		0			0
$847$	16063.3	+	27822.4i	0.651642	+	1.12868i
$848$	−2198.92	−	3808.65i	−0.0890464	−	0.154233i
$849$		0			0
$850$	84.3610			0.00340419
$851$	1064.60	−	1843.95i	0.0428839	−	0.0742770i
$852$		0			0
$853$	13008.1			0.522145			0.261072	−	0.965319i	$-0.415924\pi$
$853$	13008.1			0.522145			0.261072	+	0.965319i	$0.415924\pi$
$854$	−16805.1	+	29107.4i	−0.673372	+	1.16632i
$855$		0			0
$856$	−1692.70	−	2931.84i	−0.0675879	−	0.117066i
$857$	35075.0			1.39806			0.699031	−	0.715091i	$-0.253615\pi$
$857$	35075.0			1.39806			0.699031	+	0.715091i	$0.253615\pi$
$858$		0			0
$859$	−2869.77			−0.113988			−0.0569939	−	0.998375i	$-0.518152\pi$
$859$	−2869.77			−0.113988			−0.0569939	+	0.998375i	$0.518152\pi$
$860$	5011.94	+	8680.94i	0.198728	+	0.344207i
$861$		0			0
$862$	−7907.55	+	13696.3i	−0.312450	+	0.541180i
$863$	−29617.3			−1.16823			−0.584117	−	0.811670i	$-0.698559\pi$
$863$	−29617.3			−1.16823			−0.584117	+	0.811670i	$0.698559\pi$
$864$		0			0
$865$	−18474.1	+	31998.2i	−0.726173	+	1.25777i
$866$	−19265.1			−0.755953
$867$		0			0
$868$	18921.0	+	32772.2i	0.739886	+	1.28152i
$869$	−648.989	−	1124.08i	−0.0253342	−	0.0438802i
$870$		0			0
$871$	21577.0	−	11084.1i	0.839390	−	0.431195i
$872$	7613.04			0.295654
$873$		0			0
$874$	−32.8253	−	56.8552i	−0.00127040	−	0.00220041i
$875$	−21407.7	+	37079.2i	−0.827099	+	1.43258i
$876$		0			0
$877$	7675.09	−	13293.6i	0.295518	−	0.511852i	−0.679587	−	0.733595i	$-0.737841\pi$
$877$	7675.09	−	13293.6i	0.295518	−	0.511852i	0.975105	+	0.221743i	$0.0711744\pi$
$878$	−647.469	+	1121.45i	−0.0248873	+	0.0431060i
$879$		0			0
$880$	−4264.32	+	7386.02i	−0.163353	+	0.282935i
$881$	3181.94	+	5511.28i	0.121682	+	0.210760i	0.920431	−	0.390904i	$-0.127838\pi$
$881$	3181.94	+	5511.28i	0.121682	+	0.210760i	−0.798749	+	0.601665i	$0.794504\pi$
$882$		0			0
$883$	−32249.9			−1.22910			−0.614550	−	0.788878i	$-0.710662\pi$
$883$	−32249.9			−1.22910			−0.614550	+	0.788878i	$0.710662\pi$
$884$	−1013.35	+	520.561i	−0.0385552	+	0.0198058i
$885$		0			0
$886$	−16862.3	−	29206.3i	−0.639390	−	1.10746i
$887$	14244.7	+	24672.5i	0.539221	+	0.933959i	0.998946	+	0.0458972i	$0.0146147\pi$
$887$	14244.7	+	24672.5i	0.539221	+	0.933959i	−0.459725	+	0.888061i	$0.652052\pi$
$888$		0			0
$889$	39769.0			1.50035
$890$	7212.81	−	12493.0i	0.271656	−	0.470522i
$891$		0			0
$892$	−12540.6			−0.470727
$893$	−1538.12	+	2664.10i	−0.0576384	+	0.0998327i
$894$		0			0
$895$	−8530.60	−	14775.4i	−0.318599	−	0.551830i
$896$	3822.78			0.142534
$897$		0			0
$898$	24961.8			0.927600
$899$	−1681.18	−	2911.89i	−0.0623698	−	0.108028i
$900$		0			0
$901$	−835.085	+	1446.41i	−0.0308776	+	0.0534816i
$902$	26325.5			0.971779
$903$		0			0
$904$	3011.13	−	5215.43i	0.110784	−	0.191884i
$905$	31748.8			1.16615
$906$		0			0
$907$	−3592.78	−	6222.88i	−0.131529	−	0.227814i	0.792737	−	0.609563i	$-0.208655\pi$
$907$	−3592.78	−	6222.88i	−0.131529	−	0.227814i	−0.924266	+	0.381749i	$0.875322\pi$
$908$	3226.15	+	5587.85i	0.117911	+	0.204228i
$909$		0			0
$910$	1491.53	−	30383.6i	0.0543339	−	1.10682i
$911$	−27000.2			−0.981949			−0.490975	−	0.871174i	$-0.663359\pi$
$911$	−27000.2			−0.981949			−0.490975	+	0.871174i	$0.663359\pi$
$912$		0			0
$913$	−28138.7	−	48737.7i	−1.02000	−	1.76668i
$914$	12537.0	−	21714.8i	0.453707	−	0.785844i
$915$		0			0
$916$	12312.8	−	21326.4i	0.444134	−	0.769262i
$917$	−3888.15	+	6734.47i	−0.140020	+	0.242521i
$918$		0			0
$919$	−10592.5	+	18346.8i	−0.380213	+	0.658548i	−0.991092	−	0.133175i	$-0.957483\pi$
$919$	−10592.5	+	18346.8i	−0.380213	+	0.658548i	0.610879	+	0.791724i	$0.290816\pi$
$920$	243.229	+	421.285i	0.00871633	+	0.0150971i
$921$		0			0
$922$	2907.83			0.103866
$923$	5694.73	+	3671.47i	0.203082	+	0.130929i
$924$		0			0
$925$	−1320.54	−	2287.24i	−0.0469396	−	0.0813018i
$926$	−7154.47	−	12391.9i	−0.253899	−	0.439766i
$927$		0			0
$928$	−339.663			−0.0120151
$929$	12021.9	−	20822.5i	0.424570	−	0.735377i	−0.571810	−	0.820386i	$-0.693759\pi$
$929$	12021.9	−	20822.5i	0.424570	−	0.735377i	0.996380	+	0.0850093i	$0.0270920\pi$
$930$		0			0
$931$	−3219.82			−0.113346
$932$	−6700.14	+	11605.0i	−0.235483	+	0.407869i
$933$		0			0
$934$	5823.27	+	10086.2i	0.204008	+	0.353352i
$935$	3238.92			0.113288
$936$		0			0
$937$	6308.48			0.219946			0.109973	−	0.993935i	$-0.464924\pi$
$937$	6308.48			0.219946			0.109973	+	0.993935i	$0.464924\pi$
$938$	15456.1	+	26770.7i	0.538016	+	0.931872i
$939$		0			0
$940$	11397.1	−	19740.4i	0.395461	−	0.684958i
$941$	−1549.84			−0.0536912			−0.0268456	−	0.999640i	$-0.508546\pi$
$941$	−1549.84			−0.0536912			−0.0268456	+	0.999640i	$0.508546\pi$
$942$		0			0
$943$	750.780	−	1300.39i	0.0259266	−	0.0449062i
$944$	2287.07			0.0788535
$945$		0			0
$946$	−11314.6	−	19597.5i	−0.388869	−	0.673541i
$947$	6586.00	+	11407.3i	0.225994	+	0.391433i	0.956617	−	0.291348i	$-0.0941037\pi$
$947$	6586.00	+	11407.3i	0.225994	+	0.391433i	−0.730623	+	0.682781i	$0.760770\pi$
$948$		0			0
$949$	−461.978	+	9410.82i	−0.0158024	+	0.321905i
$950$	−81.4335			−0.00278111
$951$		0			0
$952$	−725.888	−	1257.28i	−0.0247124	−	0.0428031i
$953$	14012.7	−	24270.7i	0.476303	−	0.824980i	−0.523329	−	0.852131i	$-0.675310\pi$
$953$	14012.7	−	24270.7i	0.476303	−	0.824980i	0.999631	+	0.0271505i	$0.00864333\pi$
$954$		0			0
$955$	21234.9	−	36779.9i	0.719523	−	1.24625i
$956$	−1265.11	+	2191.23i	−0.0427997	+	0.0741312i
$957$		0			0
$958$	−2920.17	+	5057.89i	−0.0984828	+	0.170577i
$959$	−36017.0	−	62383.2i	−1.21277	−	2.10058i
$960$		0			0
$961$	70552.9			2.36826
$962$	29976.3	+	19326.1i	1.00465	+	0.647711i
$963$		0			0
$964$	−3008.47	−	5210.83i	−0.100515	−	0.174097i
$965$	11513.7	+	19942.4i	0.384083	+	0.665252i
$966$		0			0
$967$	−4250.06			−0.141337			−0.0706684	−	0.997500i	$-0.522513\pi$
$967$	−4250.06			−0.141337			−0.0706684	+	0.997500i	$0.522513\pi$
$968$	4302.84	−	7452.73i	0.142870	−	0.247458i
$969$		0			0
$970$	2988.35			0.0989177
$971$	−2356.03	+	4080.76i	−0.0778667	+	0.134869i	−0.902329	−	0.431047i	$-0.858144\pi$
$971$	−2356.03	+	4080.76i	−0.0778667	+	0.134869i	0.824463	+	0.565916i	$0.191478\pi$
$972$		0			0
$973$	−6091.51	−	10550.8i	−0.200704	−	0.347629i
$974$	6724.50			0.221218
$975$		0			0
$976$	9003.12			0.295269
$977$	−26478.0	−	45861.2i	−0.867047	−	1.50177i	−0.865000	−	0.501771i	$-0.832682\pi$
$977$	−26478.0	−	45861.2i	−0.867047	−	1.50177i	−0.00204652	−	0.999998i	$-0.500651\pi$
$978$		0			0
$979$	−16283.1	+	28203.2i	−0.531574	+	0.920714i
$980$	23858.2			0.777675
$981$		0			0
$982$	−14869.7	+	25755.0i	−0.483207	+	0.836940i
$983$	10772.6			0.349534			0.174767	−	0.984610i	$-0.444083\pi$
$983$	10772.6			0.349534			0.174767	+	0.984610i	$0.444083\pi$
$984$		0			0
$985$	16898.5	+	29269.1i	0.546631	+	0.946792i
$986$	64.4970	+	111.712i	0.00208317	+	0.00360815i
$987$		0			0
$988$	978.189	−	502.496i	0.0314983	−	0.0161807i
$989$	−1290.73			−0.0414993
$990$		0			0
$991$	−7696.24	−	13330.3i	−0.246700	−	0.427296i	0.715909	−	0.698194i	$-0.246013\pi$
$991$	−7696.24	−	13330.3i	−0.246700	−	0.427296i	−0.962608	+	0.270898i	$0.912679\pi$
$992$	5068.34	−	8778.62i	0.162218	−	0.280969i
$993$		0			0
$994$	−4317.24	+	7477.68i	−0.137761	+	0.238609i
$995$	2667.32	−	4619.94i	0.0849848	−	0.147198i
$996$		0			0
$997$	−860.917	+	1491.15i	−0.0273475	+	0.0473673i	−0.879375	−	0.476129i	$-0.842039\pi$
$997$	−860.917	+	1491.15i	−0.0273475	+	0.0473673i	0.852028	+	0.523497i	$0.175373\pi$
$998$	−18693.3	−	32377.7i	−0.592911	−	1.02695i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.4.h.h.55.2		4
3.2	odd	2		26.4.c.b.3.1	✓	4
12.11	even	2		208.4.i.d.81.2		4
13.9	even	3	inner	234.4.h.h.217.2		4
39.2	even	12		338.4.b.e.337.2		4
39.5	even	4		338.4.e.f.23.1		8
39.8	even	4		338.4.e.f.23.3		8
39.11	even	12		338.4.b.e.337.4		4
39.17	odd	6		338.4.c.j.191.1		4
39.20	even	12		338.4.e.f.147.1		8
39.23	odd	6		338.4.a.g.1.2		2
39.29	odd	6		338.4.a.h.1.2		2
39.32	even	12		338.4.e.f.147.3		8
39.35	odd	6		26.4.c.b.9.1	yes	4
39.38	odd	2		338.4.c.j.315.1		4
156.35	even	6		208.4.i.d.113.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.b.3.1	✓	4	3.2	odd	2
26.4.c.b.9.1	yes	4	39.35	odd	6
208.4.i.d.81.2		4	12.11	even	2
208.4.i.d.113.2		4	156.35	even	6
234.4.h.h.55.2		4	1.1	even	1	trivial
234.4.h.h.217.2		4	13.9	even	3	inner
338.4.a.g.1.2		2	39.23	odd	6
338.4.a.h.1.2		2	39.29	odd	6
338.4.b.e.337.2		4	39.2	even	12
338.4.b.e.337.4		4	39.11	even	12
338.4.c.j.191.1		4	39.17	odd	6
338.4.c.j.315.1		4	39.38	odd	2
338.4.e.f.23.1		8	39.5	even	4
338.4.e.f.23.3		8	39.8	even	4
338.4.e.f.147.1		8	39.20	even	12
338.4.e.f.147.3		8	39.32	even	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	234.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +10.8655 q^{5} +(14.9327 - 25.8642i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +10.8655 q^{5} +(14.9327 - 25.8642i) q^{7} -8.00000 q^{8} +(10.8655 + 18.8195i) q^{10} +(-24.5291 - 42.4857i) q^{11} +(2.29819 - 46.8158i) q^{13} +59.7309 q^{14} +(-8.00000 - 13.8564i) q^{16} +(-3.03816 + 5.26225i) q^{17} +(2.93273 - 5.07964i) q^{19} +(-21.7309 + 37.6391i) q^{20} +(49.0582 - 84.9713i) q^{22} +(-2.79819 - 4.84661i) q^{23} -6.94178 q^{25} +(83.3855 - 42.8352i) q^{26} +(59.7309 + 103.457i) q^{28} +(-5.30724 - 9.19241i) q^{29} +316.771 q^{31} +(16.0000 - 27.7128i) q^{32} -12.1526 q^{34} +(162.251 - 281.027i) q^{35} +(190.231 + 329.490i) q^{37} +11.7309 q^{38} -86.9237 q^{40} +(134.155 + 232.363i) q^{41} +(115.318 - 199.737i) q^{43} +196.233 q^{44} +(5.59638 - 9.69321i) q^{46} -524.466 q^{47} +(-274.473 - 475.401i) q^{49} +(-6.94178 - 12.0235i) q^{50} +(157.578 + 101.593i) q^{52} +274.865 q^{53} +(-266.520 - 461.626i) q^{55} +(-119.462 + 206.914i) q^{56} +(10.6145 - 18.3848i) q^{58} +(-71.4709 + 123.791i) q^{59} +(-281.347 + 487.308i) q^{61} +(316.771 + 548.664i) q^{62} +64.0000 q^{64} +(24.9709 - 508.675i) q^{65} +(258.762 + 448.189i) q^{67} +(-12.1526 - 21.0490i) q^{68} +649.004 q^{70} +(-72.2781 + 125.189i) q^{71} -201.018 q^{73} +(-380.462 + 658.979i) q^{74} +(11.7309 + 20.3185i) q^{76} -1465.15 q^{77} +26.4579 q^{79} +(-86.9237 - 150.556i) q^{80} +(-268.309 + 464.725i) q^{82} +1147.16 q^{83} +(-33.0110 + 57.1767i) q^{85} +461.273 q^{86} +(196.233 + 339.885i) q^{88} +(-331.915 - 574.893i) q^{89} +(-1176.54 - 758.529i) q^{91} +22.3855 q^{92} +(-524.466 - 908.401i) q^{94} +(31.8655 - 55.1926i) q^{95} +(68.7581 - 119.092i) q^{97} +(548.946 - 950.802i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 14 q^{5} + 45 q^{7} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 14 * q^5 + 45 * q^7 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 14 q^{5} + 45 q^{7} - 32 q^{8} + 14 q^{10} + 5 q^{11} - 35 q^{13} + 180 q^{14} - 32 q^{16} - 130 q^{17} - 3 q^{19} - 28 q^{20} - 10 q^{22} + 33 q^{23} - 234 q^{25} - 20 q^{26} + 180 q^{28} - 198 q^{29} + 560 q^{31} + 64 q^{32} - 520 q^{34} + 266 q^{35} + 702 q^{37} - 12 q^{38} - 112 q^{40} + 242 q^{41} + 93 q^{43} - 40 q^{44} - 66 q^{46} - 448 q^{47} - 435 q^{49} - 234 q^{50} + 100 q^{52} + 1070 q^{53} - 742 q^{55} - 360 q^{56} + 396 q^{58} - 389 q^{59} - 654 q^{61} + 560 q^{62} + 256 q^{64} + 203 q^{65} + 107 q^{67} - 520 q^{68} + 1064 q^{70} - 569 q^{71} - 1246 q^{73} - 1404 q^{74} - 12 q^{76} - 1294 q^{77} + 1520 q^{79} - 112 q^{80} - 484 q^{82} + 3528 q^{83} + 413 q^{85} + 372 q^{86} - 40 q^{88} - 871 q^{89} - 1539 q^{91} - 264 q^{92} - 448 q^{94} + 98 q^{95} + 879 q^{97} + 870 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 14 * q^5 + 45 * q^7 - 32 * q^8 + 14 * q^10 + 5 * q^11 - 35 * q^13 + 180 * q^14 - 32 * q^16 - 130 * q^17 - 3 * q^19 - 28 * q^20 - 10 * q^22 + 33 * q^23 - 234 * q^25 - 20 * q^26 + 180 * q^28 - 198 * q^29 + 560 * q^31 + 64 * q^32 - 520 * q^34 + 266 * q^35 + 702 * q^37 - 12 * q^38 - 112 * q^40 + 242 * q^41 + 93 * q^43 - 40 * q^44 - 66 * q^46 - 448 * q^47 - 435 * q^49 - 234 * q^50 + 100 * q^52 + 1070 * q^53 - 742 * q^55 - 360 * q^56 + 396 * q^58 - 389 * q^59 - 654 * q^61 + 560 * q^62 + 256 * q^64 + 203 * q^65 + 107 * q^67 - 520 * q^68 + 1064 * q^70 - 569 * q^71 - 1246 * q^73 - 1404 * q^74 - 12 * q^76 - 1294 * q^77 + 1520 * q^79 - 112 * q^80 - 484 * q^82 + 3528 * q^83 + 413 * q^85 + 372 * q^86 - 40 * q^88 - 871 * q^89 - 1539 * q^91 - 264 * q^92 - 448 * q^94 + 98 * q^95 + 879 * q^97 + 870 * q^98

Introduction

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