LMFDB - Embedded newform 338.4.c.j.315.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,4,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,3,-8,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$19.9426455819$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.1
Root			$-3.43273 - 5.94566i$ of defining polynomial
Character	$\chi$	$=$	338.315
Dual form			338.4.c.j.191.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.93273 - 5.07964i) q^{3} +(-2.00000 + 3.46410i) q^{4} +10.8655 q^{5} +(5.86546 - 10.1593i) q^{6} +(-14.9327 + 25.8642i) q^{7} -8.00000 q^{8} +(-3.70181 + 6.41172i) q^{9} +(10.8655 + 18.8195i) q^{10} +(-24.5291 - 42.4857i) q^{11} +23.4618 q^{12} -59.7309 q^{14} +(-31.8655 - 55.1926i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(3.03816 - 5.26225i) q^{17} -14.8072 q^{18} +(-2.93273 + 5.07964i) q^{19} +(-21.7309 + 37.6391i) q^{20} +175.175 q^{21} +(49.0582 - 84.9713i) q^{22} +(2.79819 + 4.84661i) q^{23} +(23.4618 + 40.6371i) q^{24} -6.94178 q^{25} -114.942 q^{27} +(-59.7309 - 103.457i) q^{28} +(5.30724 + 9.19241i) q^{29} +(63.7309 - 110.385i) q^{30} -316.771 q^{31} +(16.0000 - 27.7128i) q^{32} +(-143.875 + 249.198i) q^{33} +12.1526 q^{34} +(-162.251 + 281.027i) q^{35} +(-14.8072 - 25.6469i) q^{36} +(-190.231 - 329.490i) q^{37} -11.7309 q^{38} -86.9237 q^{40} +(134.155 + 232.363i) q^{41} +(175.175 + 303.411i) q^{42} +(115.318 - 199.737i) q^{43} +196.233 q^{44} +(-40.2219 + 69.6663i) q^{45} +(-5.59638 + 9.69321i) q^{46} -524.466 q^{47} +(-46.9237 + 81.2742i) q^{48} +(-274.473 - 475.401i) q^{49} +(-6.94178 - 12.0235i) q^{50} -35.6404 q^{51} -274.865 q^{53} +(-114.942 - 199.085i) q^{54} +(-266.520 - 461.626i) q^{55} +(119.462 - 206.914i) q^{56} +34.4036 q^{57} +(-10.6145 + 18.3848i) q^{58} +(-71.4709 + 123.791i) q^{59} +254.924 q^{60} +(-281.347 + 487.308i) q^{61} +(-316.771 - 548.664i) q^{62} +(-110.556 - 191.489i) q^{63} +64.0000 q^{64} -575.498 q^{66} +(-258.762 - 448.189i) q^{67} +(12.1526 + 21.0490i) q^{68} +(16.4127 - 28.4276i) q^{69} -649.004 q^{70} +(-72.2781 + 125.189i) q^{71} +(29.6145 - 51.2938i) q^{72} +201.018 q^{73} +(380.462 - 658.979i) q^{74} +(20.3584 + 35.2617i) q^{75} +(-11.7309 - 20.3185i) q^{76} +1465.15 q^{77} +26.4579 q^{79} +(-86.9237 - 150.556i) q^{80} +(437.042 + 756.979i) q^{81} +(-268.309 + 464.725i) q^{82} +1147.16 q^{83} +(-350.349 + 606.823i) q^{84} +(33.0110 - 57.1767i) q^{85} +461.273 q^{86} +(31.1294 - 53.9177i) q^{87} +(196.233 + 339.885i) q^{88} +(-331.915 - 574.893i) q^{89} -160.887 q^{90} -22.3855 q^{92} +(929.004 + 1609.08i) q^{93} +(-524.466 - 908.401i) q^{94} +(-31.8655 + 55.1926i) q^{95} -187.695 q^{96} +(-68.7581 + 119.092i) q^{97} +(548.946 - 950.802i) q^{98} +363.208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 14 q^{5} - 6 q^{6} - 45 q^{7} - 32 q^{8} - 59 q^{9} + 14 q^{10} + 5 q^{11} - 24 q^{12} - 180 q^{14} - 98 q^{15} - 32 q^{16} + 130 q^{17} - 236 q^{18} + 3 q^{19} - 28 q^{20}+ \cdots - 4852 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 14 * q^5 - 6 * q^6 - 45 * q^7 - 32 * q^8 - 59 * q^9 + 14 * q^10 + 5 * q^11 - 24 * q^12 - 180 * q^14 - 98 * q^15 - 32 * q^16 + 130 * q^17 - 236 * q^18 + 3 * q^19 - 28 * q^20 + 82 * q^21 - 10 * q^22 - 33 * q^23 - 24 * q^24 - 234 * q^25 - 666 * q^27 - 180 * q^28 + 198 * q^29 + 196 * q^30 - 560 * q^31 + 64 * q^32 - 767 * q^33 + 520 * q^34 - 266 * q^35 - 236 * q^36 - 702 * q^37 + 12 * q^38 - 112 * q^40 + 242 * q^41 + 82 * q^42 + 93 * q^43 - 40 * q^44 + 119 * q^45 + 66 * q^46 - 448 * q^47 + 48 * q^48 - 435 * q^49 - 234 * q^50 + 2126 * q^51 - 1070 * q^53 - 666 * q^54 - 742 * q^55 + 360 * q^56 + 226 * q^57 - 396 * q^58 - 389 * q^59 + 784 * q^60 - 654 * q^61 - 560 * q^62 - 1002 * q^63 + 256 * q^64 - 3068 * q^66 - 107 * q^67 + 520 * q^68 + 375 * q^69 - 1064 * q^70 - 569 * q^71 + 472 * q^72 + 1246 * q^73 + 1404 * q^74 - 935 * q^75 + 12 * q^76 + 1294 * q^77 + 1520 * q^79 - 112 * q^80 + 334 * q^81 - 484 * q^82 + 3528 * q^83 - 164 * q^84 - 413 * q^85 + 372 * q^86 - 1599 * q^87 - 40 * q^88 - 871 * q^89 + 476 * q^90 + 264 * q^92 + 2184 * q^93 - 448 * q^94 - 98 * q^95 + 192 * q^96 - 879 * q^97 + 870 * q^98 - 4852 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	−2.93273	−	5.07964i	−0.564404	−	0.977577i	−0.997105	−	0.0760390i	$-0.975773\pi$
$3$	−2.93273	−	5.07964i	−0.564404	−	0.977577i	0.432701	−	0.901538i	$-0.357561\pi$
$4$	−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	$0.338485\pi$
$6$	5.86546	−	10.1593i	0.399094	−	0.691251i
$7$	−14.9327	+	25.8642i	−0.806292	+	1.39654i	0.109124	+	0.994028i	$0.465195\pi$
$7$	−14.9327	+	25.8642i	−0.806292	+	1.39654i	−0.915416	+	0.402510i	$0.868138\pi$
$8$	−8.00000			−0.353553
$9$	−3.70181	+	6.41172i	−0.137104	+	0.237471i
$10$	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	$-0.401380\pi$
$12$	23.4618			0.564404
$13$		0			0
$13$		0			0
$14$	−59.7309			−1.14027
$15$	−31.8655	−	55.1926i	−0.548508	−	0.950044i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	3.03816	−	5.26225i	0.0433448	−	0.0750754i	−0.843539	−	0.537068i	$-0.819532\pi$
$17$	3.03816	−	5.26225i	0.0433448	−	0.0750754i	0.886884	+	0.461992i	$0.152865\pi$
$18$	−14.8072			−0.193894
$19$	−2.93273	+	5.07964i	−0.0354113	+	0.0613341i	−0.883188	−	0.469019i	$-0.844607\pi$
$19$	−2.93273	+	5.07964i	−0.0354113	+	0.0613341i	0.847777	+	0.530353i	$0.177941\pi$
$20$	−21.7309	+	37.6391i	−0.242959	+	0.420817i
$21$	175.175			1.82030
$22$	49.0582	−	84.9713i	0.475420	−	0.823452i
$23$	2.79819	+	4.84661i	0.0253680	+	0.0439386i	0.878431	−	0.477870i	$-0.158591\pi$
$23$	2.79819	+	4.84661i	0.0253680	+	0.0439386i	−0.853063	+	0.521808i	$0.825258\pi$
$24$	23.4618	+	40.6371i	0.199547	+	0.345626i
$25$	−6.94178			−0.0555342
$26$		0			0
$27$	−114.942			−0.819280
$28$	−59.7309	−	103.457i	−0.403146	−	0.698269i
$29$	5.30724	+	9.19241i	0.0339838	+	0.0588616i	0.882517	−	0.470280i	$-0.155847\pi$
$29$	5.30724	+	9.19241i	0.0339838	+	0.0588616i	−0.848533	+	0.529142i	$0.822514\pi$
$30$	63.7309	−	110.385i	0.387854	−	0.671783i
$31$	−316.771			−1.83528			−0.917641	−	0.397410i	$-0.869909\pi$
$31$	−316.771			−1.83528			−0.917641	+	0.397410i	$0.869909\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−143.875	+	249.198i	−0.758950	+	1.31454i
$34$	12.1526			0.0612988
$35$	−162.251	+	281.027i	−0.783583	+	1.35721i
$36$	−14.8072	−	25.6469i	−0.0685520	−	0.118736i
$37$	−190.231	−	329.490i	−0.845237	−	1.46399i	−0.885415	−	0.464801i	$-0.846126\pi$
$37$	−190.231	−	329.490i	−0.845237	−	1.46399i	0.0401781	−	0.999193i	$-0.487207\pi$
$38$	−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	$0.662605\pi$
$42$	175.175	+	303.411i	0.643572	+	1.11470i
$43$	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
$45$	−40.2219	+	69.6663i	−0.133243	+	0.230783i
$46$	−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	$0.802628\pi$
$48$	−46.9237	+	81.2742i	−0.141101	+	0.244394i
$49$	−274.473	−	475.401i	−0.800212	−	1.38601i
$50$	−6.94178	−	12.0235i	−0.0196343	−	0.0340076i
$51$	−35.6404			−0.0978560
$52$		0			0
$53$	−274.865			−0.712371			−0.356186	−	0.934415i	$-0.615923\pi$
$53$	−274.865			−0.712371			−0.356186	+	0.934415i	$0.615923\pi$
$54$	−114.942	−	199.085i	−0.289659	−	0.501704i
$55$	−266.520	−	461.626i	−0.653410	−	1.13174i
$56$	119.462	−	206.914i	0.285067	−	0.493751i
$57$	34.4036			0.0799451
$58$	−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	$0.217077\pi$
$60$	254.924			0.548508
$61$	−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
$63$	−110.556	−	191.489i	−0.221092	−	0.382942i
$64$	64.0000			0.125000
$65$		0			0
$66$	−575.498			−1.07332
$67$	−258.762	−	448.189i	−0.471833	−	0.817239i	0.527648	−	0.849463i	$-0.323074\pi$
$67$	−258.762	−	448.189i	−0.471833	−	0.817239i	−0.999481	+	0.0322247i	$0.989741\pi$
$68$	12.1526	+	21.0490i	0.0216724	+	0.0375377i
$69$	16.4127	−	28.4276i	0.0286356	−	0.0495982i
$70$	−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	$0.205217\pi$
$72$	29.6145	−	51.2938i	0.0484736	−	0.0839588i
$73$	201.018			0.322293			0.161147	−	0.986930i	$-0.448481\pi$
$73$	201.018			0.322293			0.161147	+	0.986930i	$0.448481\pi$
$74$	380.462	−	658.979i	0.597673	−	1.03520i
$75$	20.3584	+	35.2617i	0.0313438	+	0.0542890i
$76$	−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
$81$	437.042	+	756.979i	0.599509	+	1.03838i
$82$	−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	$0.225916\pi$
$84$	−350.349	+	606.823i	−0.455074	+	0.788212i
$85$	33.0110	−	57.1767i	0.0421241	−	0.0729610i
$86$	461.273			0.578376
$87$	31.1294	−	53.9177i	0.0383612	−	0.0664435i
$88$	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	$0.962697\pi$
$90$	−160.887			−0.188434
$91$		0			0
$92$	−22.3855			−0.0253680
$93$	929.004	+	1609.08i	1.03584	+	1.79413i
$94$	−524.466	−	908.401i	−0.575474	−	0.996749i
$95$	−31.8655	+	55.1926i	−0.0344140	+	0.0596067i
$96$	−187.695			−0.199547
$97$	−68.7581	+	119.092i	−0.0719724	+	0.124660i	−0.899766	−	0.436373i	$-0.856263\pi$
$97$	−68.7581	+	119.092i	−0.0719724	+	0.124660i	0.827793	+	0.561033i	$0.189596\pi$
$98$	548.946	−	950.802i	0.565836	−	0.980056i
$99$	363.208			0.368725
$100$	13.8836	−	24.0470i	0.0138836	−	0.0240470i
$101$	442.347	+	766.168i	0.435794	+	0.754818i	0.997360	−	0.0726144i	$-0.0231342\pi$
$101$	442.347	+	766.168i	0.435794	+	0.754818i	−0.561566	+	0.827432i	$0.689801\pi$
$102$	−35.6404	−	61.7310i	−0.0345973	−	0.0599243i
$103$	−416.233			−0.398181			−0.199091	−	0.979981i	$-0.563799\pi$
$103$	−416.233			−0.398181			−0.199091	+	0.979981i	$0.563799\pi$
$104$		0			0
$105$	1903.35			1.76903
$106$	−274.865	−	476.081i	−0.251861	−	0.436236i
$107$	−211.587	−	366.480i	−0.191167	−	0.331112i	0.754470	−	0.656335i	$-0.227894\pi$
$107$	−211.587	−	366.480i	−0.191167	−	0.331112i	−0.945637	+	0.325223i	$0.894561\pi$
$108$	229.884	−	398.170i	0.204820	−	0.354759i
$109$	951.630			0.836235			0.418118	−	0.908393i	$-0.362690\pi$
$109$	951.630			0.836235			0.418118	+	0.908393i	$0.362690\pi$
$110$	533.040	−	923.253i	0.462031	−	0.800261i
$111$	−1115.79	+	1932.61i	−0.954111	+	1.65257i
$112$	477.847			0.403146
$113$	376.391	−	651.929i	0.313344	−	0.542729i	−0.665740	−	0.746184i	$-0.731884\pi$
$113$	376.391	−	651.929i	0.313344	−	0.542729i	0.979084	+	0.203456i	$0.0652172\pi$
$114$	34.4036	+	59.5888i	0.0282649	+	0.0489562i
$115$	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
$120$	254.924	+	441.541i	0.193927	+	0.335891i
$121$	−537.854	+	931.591i	−0.404098	+	0.699918i
$122$	−1125.39			−0.835147
$123$	786.878	−	1362.91i	0.576833	−	0.999104i
$124$	633.542	−	1097.33i	0.458821	−	0.794701i
$125$	−1433.61			−1.02581
$126$	221.113	−	382.978i	0.156335	−	0.270781i
$127$	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
$129$	−1352.79			−0.923306
$130$		0			0
$131$	260.378			0.173659			0.0868294	−	0.996223i	$-0.472326\pi$
$131$	260.378			0.173659			0.0868294	+	0.996223i	$0.472326\pi$
$132$	−575.498	−	996.792i	−0.379475	−	0.657270i
$133$	−87.5873	−	151.706i	−0.0571036	−	0.0989064i
$134$	517.524	−	896.378i	0.333636	−	0.577875i
$135$	−1248.90			−0.796206
$136$	−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	$-0.104277\pi$
$138$	65.6507			0.0404968
$139$	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
$141$	1538.12	+	2664.10i	0.918672	+	1.59119i
$142$	−289.113			−0.170858
$143$		0			0
$144$	118.458			0.0685520
$145$	57.6656	+	99.8798i	0.0330267	+	0.0572039i
$146$	201.018	+	348.174i	0.113948	+	0.197363i
$147$	−1609.91	+	2788.45i	−0.903286	+	1.56454i
$148$	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	$0.192524\pi$
$150$	−40.7167	+	70.5235i	−0.0221634	+	0.0383881i
$151$	−2087.10			−1.12481			−0.562403	−	0.826863i	$-0.690123\pi$
$151$	−2087.10			−1.12481			−0.562403	+	0.826863i	$0.690123\pi$
$152$	23.4618	−	40.6371i	0.0125198	−	0.0216849i
$153$	22.4934	+	38.9597i	0.0118855	+	0.0205863i
$154$	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
$159$	806.106	+	1396.22i	0.402065	+	0.696397i
$160$	173.847	−	301.112i	0.0858990	−	0.148781i
$161$	−167.138			−0.0818159
$162$	−874.084	+	1513.96i	−0.423917	+	0.734246i
$163$	−645.238	+	1117.59i	−0.310055	+	0.537031i	−0.978374	−	0.206844i	$-0.933681\pi$
$163$	−645.238	+	1117.59i	−0.310055	+	0.537031i	0.668319	+	0.743875i	$0.267014\pi$
$164$	−1073.24			−0.511010
$165$	−1563.26	+	2707.65i	−0.737575	+	1.27752i
$166$	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	$0.635493\pi$
$168$	−1401.40			−0.643572
$169$		0			0
$170$	132.044			0.0595724
$171$	−21.7128	−	37.6077i	−0.00971006	−	0.0168183i
$172$	461.273	+	798.948i	0.204487	+	0.354182i
$173$	1700.26	−	2944.94i	0.747218	−	1.29422i	−0.201934	−	0.979399i	$-0.564723\pi$
$173$	1700.26	−	2944.94i	0.747218	−	1.29422i	0.949151	−	0.314820i	$-0.101944\pi$
$174$	124.518			0.0542509
$175$	103.660	−	179.544i	0.0447768	−	0.0775557i
$176$	−392.466	+	679.771i	−0.168086	+	0.291134i
$177$	838.419			0.356042
$178$	663.829	−	1149.79i	0.279529	−	0.484158i
$179$	785.111	+	1359.85i	0.327832	+	0.567822i	0.982081	−	0.188457i	$-0.0603486\pi$
$179$	785.111	+	1359.85i	0.327832	+	0.567822i	−0.654249	+	0.756279i	$0.727015\pi$
$180$	−160.887	−	278.665i	−0.0666214	−	0.115392i
$181$	2921.99			1.19995			0.599973	−	0.800021i	$-0.295178\pi$
$181$	2921.99			1.19995			0.599973	+	0.800021i	$0.295178\pi$
$182$		0			0
$183$	3300.46			1.33321
$184$	−22.3855	−	38.7729i	−0.00896893	−	0.0155346i
$185$	−2066.95	−	3580.06i	−0.821432	−	1.42276i
$186$	−1858.01	+	3218.16i	−0.732450	+	1.26864i
$187$	−298.093			−0.116571
$188$	1048.93	−	1816.80i	0.406921	−	0.704808i
$189$	1716.39	−	2972.88i	0.660578	−	1.14416i
$190$	−127.462			−0.0486687
$191$	−1954.35	+	3385.03i	−0.740375	+	1.28237i	0.211949	+	0.977281i	$0.432019\pi$
$191$	−1954.35	+	3385.03i	−0.740375	+	1.28237i	−0.952325	+	0.305087i	$0.901315\pi$
$192$	−187.695	−	325.097i	−0.0705505	−	0.122197i
$193$	−1059.66	−	1835.39i	−0.395214	−	0.684531i	0.597914	−	0.801560i	$-0.295996\pi$
$193$	−1059.66	−	1835.39i	−0.395214	−	0.684531i	−0.993128	+	0.117029i	$0.962663\pi$
$194$	−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	$0.643184\pi$
$198$	363.208	+	629.095i	0.130364	+	0.225797i
$199$	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
$201$	−1517.76	+	2628.83i	−0.532609	+	0.922506i
$202$	−884.695	+	1532.34i	−0.308153	+	0.533737i
$203$	−317.006			−0.109603
$204$	71.2808	−	123.462i	0.0244640	−	0.0423729i
$205$	1457.65	+	2524.73i	0.496618	+	0.860168i
$206$	−416.233	−	720.936i	−0.140778	−	0.243835i
$207$	−41.4335			−0.0139122
$208$		0			0
$209$	287.749			0.0952345
$210$	1903.35	+	3296.70i	0.625447	+	1.08331i
$211$	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
$213$	847.889			0.272753
$214$	423.175	−	732.960i	0.135176	−	0.234131i
$215$	1252.99	−	2170.24i	0.397455	−	0.688413i
$216$	919.534			0.289659
$217$	4730.26	−	8193.04i	1.47977	−	2.56304i
$218$	951.630	+	1648.27i	0.295654	+	0.512087i
$219$	−589.532	−	1021.10i	−0.181904	−	0.315066i
$220$	2132.16			0.653410
$221$		0			0
$222$	−4463.17			−1.34932
$223$	−1567.57	−	2715.11i	−0.470727	−	0.815324i	0.528712	−	0.848801i	$-0.322675\pi$
$223$	−1567.57	−	2715.11i	−0.470727	−	0.815324i	−0.999439	+	0.0334775i	$0.989342\pi$
$224$	477.847	+	827.656i	0.142534	+	0.246875i
$225$	25.6972	−	44.5088i	0.00761397	−	0.0131878i
$226$	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	$0.0908882\pi$
$228$	−68.8072	+	119.178i	−0.0199863	+	0.0346172i
$229$	6156.40			1.77653			0.888267	−	0.459327i	$-0.151909\pi$
$229$	6156.40			1.77653			0.888267	+	0.459327i	$0.151909\pi$
$230$	−60.8072	+	105.321i	−0.0174327	+	0.0301942i
$231$	−4296.88	−	7442.41i	−1.22387	−	2.11980i
$232$	−42.4579	−	73.5393i	−0.0120151	−	0.0208107i
$233$	−3350.07			−0.941934			−0.470967	−	0.882151i	$-0.656095\pi$
$233$	−3350.07			−0.941934			−0.470967	+	0.882151i	$0.656095\pi$
$234$		0			0
$235$	−5698.56			−1.58184
$236$	−285.884	−	495.165i	−0.0788535	−	0.136578i
$237$	−77.5939	−	134.397i	−0.0212670	−	0.0368354i
$238$	−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	$0.472719\pi$
$240$	−509.847	+	883.082i	−0.137127	+	0.237511i
$241$	752.118	−	1302.71i	0.201030	−	0.348194i	−0.747831	−	0.663890i	$-0.768904\pi$
$241$	752.118	−	1302.71i	0.201030	−	0.348194i	0.948861	+	0.315696i	$0.102238\pi$
$242$	−2151.42			−0.571481
$243$	1011.74	−	1752.38i	0.267091	−	0.462615i
$244$	−1125.39	−	1949.23i	−0.295269	−	0.511421i
$245$	−2982.27	−	5165.45i	−0.777675	−	1.34697i
$246$	3147.51			0.815765
$247$		0			0
$248$	2534.17			0.648870
$249$	−3364.30	−	5827.14i	−0.856240	−	1.48305i
$250$	−1433.61	−	2483.08i	−0.362677	−	0.628176i
$251$	−518.384	+	897.868i	−0.130359	+	0.225789i	−0.923815	−	0.382839i	$-0.874946\pi$
$251$	−518.384	+	897.868i	−0.130359	+	0.225789i	0.793456	+	0.608628i	$0.208280\pi$
$252$	884.450			0.221092
$253$	137.274	−	237.766i	0.0341121	−	0.0590839i
$254$	−1331.60	+	2306.41i	−0.328946	+	0.569751i
$255$	−387.249			−0.0951000
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−252.452	−	437.260i	−0.0612744	−	0.106130i	0.833761	−	0.552126i	$-0.186183\pi$
$257$	−252.452	−	437.260i	−0.0612744	−	0.106130i	−0.895035	+	0.445995i	$0.852850\pi$
$258$	−1352.79	−	2343.10i	−0.326438	−	0.565407i
$259$	11362.7			2.72603
$260$		0			0
$261$	−78.5856			−0.0186373
$262$	260.378	+	450.987i	0.0613977	+	0.106344i
$263$	84.6612	+	146.638i	0.0198496	+	0.0343804i	0.875780	−	0.482711i	$-0.160348\pi$
$263$	84.6612	+	146.638i	0.0198496	+	0.0343804i	−0.855930	+	0.517092i	$0.827015\pi$
$264$	1151.00	−	1993.58i	0.268329	−	0.464760i
$265$	−2986.54			−0.692308
$266$	175.175	−	303.411i	0.0403784	−	0.0699374i
$267$	−1946.83	+	3372.01i	−0.446233	+	0.772898i
$268$	2070.10			0.471833
$269$	−771.017	+	1335.44i	−0.174757	+	0.302689i	−0.940077	−	0.340961i	$-0.889247\pi$
$269$	−771.017	+	1335.44i	−0.174757	+	0.302689i	0.765320	+	0.643650i	$0.222581\pi$
$270$	−1248.90	−	2163.15i	−0.281501	−	0.487575i
$271$	−589.678	−	1021.35i	−0.132179	−	0.228940i	0.792338	−	0.610083i	$-0.208864\pi$
$271$	−589.678	−	1021.35i	−0.132179	−	0.228940i	−0.924516	+	0.381143i	$0.875531\pi$
$272$	−97.2211			−0.0216724
$273$		0			0
$274$	4823.89			1.06358
$275$	170.276	+	294.926i	0.0373382	+	0.0646717i
$276$	65.6507	+	113.710i	0.0143178	+	0.0247991i
$277$	−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
$279$	1172.63	−	2031.05i	0.251625	−	0.435827i
$280$	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	$0.501993\pi$
$282$	−3076.23	+	5328.19i	−0.649599	+	1.12514i
$283$	−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
$285$	373.811			0.0776936
$286$		0			0
$287$	−8013.18			−1.64809
$288$	118.458	+	205.175i	0.0242368	+	0.0419794i
$289$	2438.04	+	4222.81i	0.496242	+	0.859517i
$290$	−115.331	+	199.760i	−0.0233534	+	0.0404493i
$291$	806.595			0.162486
$292$	−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	$0.866461\pi$
$294$	−6439.64			−1.27744
$295$	−776.564	+	1345.05i	−0.153265	+	0.265464i
$296$	1521.85	+	2635.92i	0.298836	+	0.517600i
$297$	2819.42	+	4883.38i	0.550839	+	0.954082i
$298$	−590.337			−0.114756
$299$		0			0
$300$	−162.867			−0.0313438
$301$	3444.03	+	5965.24i	0.659504	+	1.14229i
$302$	−2087.10	−	3614.96i	−0.397679	−	0.688800i
$303$	2594.57	−	4493.93i	0.491928	−	0.852044i
$304$	93.8474			0.0177056
$305$	−3056.97	+	5294.82i	−0.573907	+	0.994035i
$306$	−44.9868	+	77.9194i	−0.00840432	+	0.0145567i
$307$	1072.04			0.199298			0.0996492	−	0.995023i	$-0.468228\pi$
$307$	1072.04			0.199298			0.0996492	+	0.995023i	$0.468228\pi$
$308$	−2930.29	+	5075.42i	−0.542107	+	0.938957i
$309$	1220.70	+	2114.31i	0.224735	+	0.389252i
$310$	−3441.86	−	5961.48i	−0.630596	−	1.09222i
$311$	−4528.41			−0.825667			−0.412834	−	0.910806i	$-0.635461\pi$
$311$	−4528.41			−0.825667			−0.412834	+	0.910806i	$0.635461\pi$
$312$		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
$315$	−1201.24	−	2080.62i	−0.214865	−	0.372157i
$316$	−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	$0.759743\pi$
$318$	−1612.21	+	2792.43i	−0.284303	+	0.492427i
$319$	260.364	−	450.963i	0.0456977	−	0.0791508i
$320$	695.389			0.121480
$321$	−1241.06	+	2149.57i	−0.215791	+	0.373762i
$322$	−167.138	−	289.492i	−0.0289263	−	0.0501018i
$323$	17.8202	+	30.8655i	0.00306979	+	0.00531704i
$324$	−3496.34			−0.599509
$325$		0			0
$326$	−2580.95			−0.438484
$327$	−2790.87	−	4833.94i	−0.471975	−	0.817484i
$328$	−1073.24	−	1858.90i	−0.180669	−	0.312929i
$329$	7831.71	−	13564.9i	1.31239	−	2.27312i
$330$	−6253.05			−1.04309
$331$	−304.177	+	526.851i	−0.0505109	+	0.0874874i	−0.890175	−	0.455618i	$-0.849418\pi$
$331$	−304.177	+	526.851i	−0.0505109	+	0.0874874i	0.839664	+	0.543105i	$0.182752\pi$
$332$	−2294.31	+	3973.87i	−0.379267	+	0.656910i
$333$	2816.79			0.463542
$334$	−2513.27	+	4353.11i	−0.411737	+	0.713149i
$335$	−2811.57	−	4869.78i	−0.458544	−	0.794222i
$336$	−1401.40	−	2427.29i	−0.227537	−	0.394106i
$337$	−8808.73			−1.42386			−0.711932	−	0.702248i	$-0.752180\pi$
$337$	−8808.73			−1.42386			−0.711932	+	0.702248i	$0.752180\pi$
$338$		0			0
$339$	−4415.42			−0.707412
$340$	132.044	+	228.707i	0.0210620	+	0.0364805i
$341$	7770.11	+	13458.2i	1.23394	+	2.13725i
$342$	43.4256	−	75.2154i	0.00686605	−	0.0118923i
$343$	6150.66			0.968235
$344$	−922.546	+	1597.90i	−0.144594	+	0.250444i
$345$	178.331	−	308.879i	0.0278291	−	0.0482014i
$346$	6801.06			1.05673
$347$	3583.04	−	6206.01i	0.554317	−	0.960105i	−0.443640	−	0.896205i	$-0.646313\pi$
$347$	3583.04	−	6206.01i	0.554317	−	0.960105i	0.997956	−	0.0638994i	$-0.0203537\pi$
$348$	124.518	+	215.671i	0.0191806	+	0.0332218i
$349$	−942.489	−	1632.44i	−0.144557	−	0.250380i	0.784651	−	0.619938i	$-0.212842\pi$
$349$	−942.489	−	1632.44i	−0.144557	−	0.250380i	−0.929207	+	0.369559i	$0.879509\pi$
$350$	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	$-0.523981\pi$
$354$	838.419	+	1452.18i	0.125880	+	0.218030i
$355$	−785.335	+	1360.24i	−0.117412	+	0.203364i
$356$	2655.32			0.395313
$357$	532.209	−	921.812i	0.0789005	−	0.136660i
$358$	−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	$0.732259\pi$
$360$	321.775	−	557.331i	0.0471084	−	0.0815942i
$361$	3412.30	+	5910.27i	0.497492	+	0.861682i
$362$	2921.99	+	5061.04i	0.424245	+	0.734813i
$363$	6309.53			0.912298
$364$		0			0
$365$	2184.15			0.313216
$366$	3300.46	+	5716.57i	0.471361	+	0.816421i
$367$	−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
$369$	−1986.46			−0.280246
$370$	4133.89	−	7160.11i	0.580840	−	1.00604i
$371$	4104.49	−	7109.19i	0.574379	−	0.994854i
$372$	−7432.03			−1.03584
$373$	−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
$375$	4204.39	+	7282.21i	0.578969	+	1.00280i
$376$	4195.73			0.575474
$377$		0			0
$378$	6865.58			0.934199
$379$	−5909.48	−	10235.5i	−0.800922	−	1.38724i	−0.919010	−	0.394234i	$-0.871010\pi$
$379$	−5909.48	−	10235.5i	−0.800922	−	1.38724i	0.118088	−	0.993003i	$-0.462323\pi$
$380$	−127.462	−	220.770i	−0.0172070	−	0.0298034i
$381$	3905.24	−	6764.07i	0.525121	−	0.909537i
$382$	−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	$0.00596662\pi$
$384$	375.389	−	650.194i	0.0498867	−	0.0864064i
$385$	15919.5			2.10736
$386$	2119.33	−	3670.79i	0.279459	−	0.484036i
$387$	853.773	+	1478.78i	0.112144	+	0.194239i
$388$	−275.032	−	476.370i	−0.0359862	−	0.0623299i
$389$	−9331.29			−1.21623			−0.608117	−	0.793847i	$-0.708075\pi$
$389$	−9331.29			−1.21623			−0.608117	+	0.793847i	$0.708075\pi$
$390$		0			0
$391$	34.0054			0.00439828
$392$	2195.78	+	3803.21i	0.282918	+	0.490028i
$393$	−763.617	−	1322.62i	−0.0980138	−	0.169765i
$394$	−3110.50	+	5387.54i	−0.397728	+	0.688885i
$395$	287.478			0.0366191
$396$	−726.417	+	1258.19i	−0.0921814	+	0.159663i
$397$	−3847.13	+	6663.42i	−0.486352	+	0.842386i	−0.999877	−	0.0156884i	$-0.995006\pi$
$397$	−3847.13	+	6663.42i	−0.486352	+	0.842386i	0.513525	+	0.858075i	$0.328339\pi$
$398$	981.946			0.123670
$399$	−513.740	+	889.824i	−0.0644591	+	0.111646i
$400$	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	$0.796436\pi$
$402$	−6071.03			−0.753223
$403$		0			0
$404$	−3538.78			−0.435794
$405$	4748.66	+	8224.93i	0.582625	+	1.00914i
$406$	−317.006	−	549.071i	−0.0387506	−	0.0671181i
$407$	−9332.39	+	16164.2i	−1.13658	+	1.96862i
$408$	285.123			0.0345973
$409$	−269.235	+	466.328i	−0.0325496	+	0.0563776i	−0.881841	−	0.471546i	$-0.843696\pi$
$409$	−269.235	+	466.328i	−0.0325496	+	0.0563776i	0.849292	+	0.527924i	$0.177029\pi$
$410$	−2915.30	+	5049.45i	−0.351162	+	0.608231i
$411$	−14147.2			−1.69788
$412$	832.466	−	1441.87i	0.0995453	−	0.172417i
$413$	−2134.51	−	3697.08i	−0.254316	−	0.440488i
$414$	−41.4335	−	71.7649i	−0.00491871	−	0.00851945i
$415$	12464.4			1.47434
$416$		0			0
$417$	−2392.70			−0.280985
$418$	287.749	+	498.396i	0.0336705	+	0.0583190i
$419$	−2418.69	−	4189.30i	−0.282007	−	0.488450i	0.689872	−	0.723931i	$-0.257667\pi$
$419$	−2418.69	−	4189.30i	−0.282007	−	0.488450i	−0.971879	+	0.235481i	$0.924333\pi$
$420$	−3806.71	+	6593.41i	−0.442258	+	0.766013i
$421$	1392.34			0.161184			0.0805918	−	0.996747i	$-0.474319\pi$
$421$	1392.34			0.161184			0.0805918	+	0.996747i	$0.474319\pi$
$422$	−603.268	+	1044.89i	−0.0695891	+	0.120532i
$423$	1941.47	−	3362.73i	0.223162	−	0.386528i
$424$	2198.92			0.251861
$425$	−21.0902	+	36.5294i	−0.00240712	+	0.00416926i
$426$	847.889	+	1468.59i	0.0964328	+	0.167026i
$427$	−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	$0.687648\pi$
$432$	919.534	+	1592.68i	0.102410	+	0.177379i
$433$	−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
$435$	338.235	−	585.841i	0.0372808	−	0.0645722i
$436$	−1903.26	+	3296.54i	−0.209059	+	0.362100i
$437$	−32.8253			−0.00359325
$438$	1179.06	−	2042.20i	0.128625	−	0.222785i
$439$	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
$441$	4064.19			0.438850
$442$		0			0
$443$	16862.3			1.80847			0.904233	−	0.427039i	$-0.140443\pi$
$443$	16862.3			1.80847			0.904233	+	0.427039i	$0.140443\pi$
$444$	−4463.17	−	7730.43i	−0.477055	−	0.826284i
$445$	−3606.41	−	6246.48i	−0.384180	−	0.665419i
$446$	3135.14	−	5430.22i	0.332855	−	0.576521i
$447$	1731.30			0.183194
$448$	−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	$-0.0610493\pi$
$450$	102.789			0.0107678
$451$	6581.39	−	11399.3i	0.687152	−	1.19018i
$452$	1505.57	+	2607.72i	0.156672	+	0.271364i
$453$	6120.90	+	10601.7i	0.634845	+	1.09958i
$454$	3226.15			0.333504
$455$		0			0
$456$	−275.229			−0.0282649
$457$	6268.52	+	10857.4i	0.641639	+	1.11135i	0.985067	+	0.172172i	$0.0550785\pi$
$457$	6268.52	+	10857.4i	0.641639	+	1.11135i	−0.343428	+	0.939179i	$0.611588\pi$
$458$	6156.40	+	10663.2i	0.628100	+	1.08790i
$459$	−349.212	+	604.852i	−0.0355115	+	0.0615078i
$460$	−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	$0.143268\pi$
$462$	8593.76	−	14884.8i	0.865406	−	1.49893i
$463$	7154.47			0.718135			0.359068	−	0.933312i	$-0.383095\pi$
$463$	7154.47			0.718135			0.359068	+	0.933312i	$0.383095\pi$
$464$	84.9158	−	147.079i	0.00849595	−	0.0147154i
$465$	10094.1	+	17483.4i	1.00667	+	1.74360i
$466$	−3350.07	−	5802.50i	−0.333024	−	0.576814i
$467$	−5823.27			−0.577021			−0.288510	−	0.957477i	$-0.593160\pi$
$467$	−5823.27			−0.577021			−0.288510	+	0.957477i	$0.593160\pi$
$468$		0			0
$469$	15456.1			1.52174
$470$	−5698.56	−	9870.20i	−0.559266	−	0.968677i
$471$	−1635.03	−	2831.96i	−0.159954	−	0.277048i
$472$	571.767	−	990.330i	0.0557579	−	0.0965755i
$473$	−11314.6			−1.09989
$474$	155.188	−	268.793i	0.0150380	−	0.0260466i
$475$	20.3584	−	35.2617i	0.00196654	−	0.00340615i
$476$	−725.888			−0.0698971
$477$	1017.50	−	1762.36i	0.0976690	−	0.169168i
$478$	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	$0.788856\pi$
$480$	−2039.39			−0.193927
$481$		0			0
$482$	3008.47			0.284299
$483$	490.172	+	849.003i	0.0461772	+	0.0799813i
$484$	−2151.42	−	3726.36i	−0.202049	−	0.349959i
$485$	−747.088	+	1293.99i	−0.0699454	+	0.121149i
$486$	4046.96			0.377723
$487$	−1681.12	+	2911.79i	−0.156425	+	0.270936i	−0.933577	−	0.358377i	$-0.883330\pi$
$487$	−1681.12	+	2911.79i	−0.156425	+	0.270936i	0.777152	+	0.629313i	$0.216664\pi$
$488$	2250.78	−	3898.46i	0.208787	−	0.361629i
$489$	7569.24			0.699985
$490$	5964.55	−	10330.9i	0.549900	−	0.952454i
$491$	−7434.83	−	12877.5i	−0.683359	−	1.18361i	−0.973950	−	0.226764i	$-0.927185\pi$
$491$	−7434.83	−	12877.5i	−0.683359	−	1.18361i	0.290591	−	0.956847i	$-0.406148\pi$
$492$	3147.51	+	5451.65i	0.288416	+	0.499552i
$493$	64.4970			0.00589209
$494$		0			0
$495$	3946.43			0.358341
$496$	2534.17	+	4389.31i	0.229410	+	0.397350i
$497$	−2158.62	−	3738.84i	−0.194824	−	0.337444i
$498$	6728.60	−	11654.3i	0.605453	−	1.04868i
$499$	18693.3			1.67701			0.838503	−	0.544896i	$-0.183431\pi$
$499$	18693.3			1.67701			0.838503	+	0.544896i	$0.183431\pi$
$500$	2867.22	−	4966.16i	0.256452	−	0.444187i
$501$	7370.74	−	12766.5i	0.657287	−	1.13845i
$502$	−2073.54			−0.184356
$503$	−7359.24	+	12746.6i	−0.652350	+	1.12990i	0.330201	+	0.943911i	$0.392884\pi$
$503$	−7359.24	+	12746.6i	−0.652350	+	1.12990i	−0.982551	+	0.185993i	$0.940450\pi$
$504$	884.450	+	1531.91i	0.0781677	+	0.135390i
$505$	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	$0.590338\pi$
$510$	−387.249	−	670.736i	−0.0336229	−	0.0582366i
$511$	−3001.75	+	5199.18i	−0.259862	+	0.450094i
$512$	−512.000			−0.0441942
$513$	337.093	−	583.863i	0.0290118	−	0.0502498i
$514$	504.904	−	874.520i	0.0433276	−	0.0750455i
$515$	−4522.56			−0.386967
$516$	2705.58	−	4686.20i	0.230826	−	0.399803i
$517$	12864.7	+	22282.3i	1.09437	+	1.89550i
$518$	11362.7	+	19680.7i	0.963797	+	1.66935i
$519$	−19945.7			−1.68693
$520$		0			0
$521$	−9618.86			−0.808848			−0.404424	−	0.914572i	$-0.632528\pi$
$521$	−9618.86			−0.808848			−0.404424	+	0.914572i	$0.632528\pi$
$522$	−78.5856	−	136.114i	−0.00658927	−	0.0114129i
$523$	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
$525$	−1216.02			−0.101089
$526$	−169.322	+	293.275i	−0.0140358	+	0.0243106i
$527$	−962.401	+	1666.93i	−0.0795500	+	0.137785i
$528$	4603.98			0.379475
$529$	6067.84	−	10509.8i	0.498713	−	0.863796i
$530$	−2986.54	−	5172.84i	−0.244768	−	0.423950i
$531$	−529.143	−	916.503i	−0.0432446	−	0.0749018i
$532$	700.699			0.0571036
$533$		0			0
$534$	−7787.33			−0.631069
$535$	−2298.99	−	3981.97i	−0.185783	−	0.321786i
$536$	2070.10	+	3585.51i	0.166818	+	0.288937i
$537$	4605.04	−	7976.16i	0.370060	−	0.640962i
$538$	−3084.07			−0.247144
$539$	−13465.1	+	23322.3i	−1.07604	+	1.86375i
$540$	2497.79	−	4326.30i	0.199051	−	0.344767i
$541$	−14130.6			−1.12296			−0.561479	−	0.827491i	$-0.689768\pi$
$541$	−14130.6			−1.12296			−0.561479	+	0.827491i	$0.689768\pi$
$542$	1179.36	−	2042.70i	0.0934643	−	0.161885i
$543$	−8569.42	−	14842.7i	−0.677254	−	1.17304i
$544$	−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
$549$	−2082.99	−	3607.84i	−0.161930	−	0.280472i
$550$	−340.551	+	589.852i	−0.0264021	+	0.0457298i
$551$	−62.2588			−0.00481364
$552$	−131.301	+	227.421i	−0.0101242	+	0.0175356i
$553$	−395.089	+	684.314i	−0.0303814	+	0.0526221i
$554$	−7811.80			−0.599082
$555$	−12123.6	+	20998.7i	−0.927239	+	1.60603i
$556$	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	$-0.412147\pi$
$558$	4690.50			0.355851
$559$		0			0
$560$	5192.03			0.391792
$561$	874.228	+	1514.21i	0.0657931	+	0.113957i
$562$	−58.9976	−	102.187i	−0.00442822	−	0.00766991i
$563$	−12087.1	+	20935.5i	−0.904815	+	1.56719i	−0.0836495	+	0.996495i	$0.526658\pi$
$563$	−12087.1	+	20935.5i	−0.904815	+	1.56719i	−0.821165	+	0.570690i	$0.806676\pi$
$564$	−12304.9			−0.918672
$565$	4089.67	−	7083.51i	0.304520	−	0.527443i
$566$	4695.58	−	8132.99i	0.348710	−	0.603984i
$567$	−26104.9			−1.93352
$568$	578.225	−	1001.52i	0.0427144	−	0.0739835i
$569$	−4816.74	−	8342.84i	−0.354883	−	0.614675i	0.632215	−	0.774793i	$-0.282146\pi$
$569$	−4816.74	−	8342.84i	−0.354883	−	0.614675i	−0.987098	+	0.160118i	$0.948813\pi$
$570$	373.811	+	647.460i	0.0274688	+	0.0475774i
$571$	−8221.17			−0.602531			−0.301266	−	0.953540i	$-0.597409\pi$
$571$	−8221.17			−0.602531			−0.301266	+	0.953540i	$0.597409\pi$
$572$		0			0
$573$	22926.3			1.67148
$574$	−8013.18	−	13879.2i	−0.582689	−	1.00925i
$575$	−19.4244	−	33.6441i	−0.00140879	−	0.00244010i
$576$	−236.916	+	410.350i	−0.0171380	+	0.0296839i
$577$	7986.09			0.576196			0.288098	−	0.957601i	$-0.406977\pi$
$577$	7986.09			0.576196			0.288098	+	0.957601i	$0.406977\pi$
$578$	−4876.08	+	8445.62i	−0.350896	+	0.607770i
$579$	−6215.42	+	10765.4i	−0.446121	+	0.772704i
$580$	−461.325			−0.0330267
$581$	−17130.2	+	29670.3i	−1.22320	+	2.11865i
$582$	806.595	+	1397.06i	0.0574475	+	0.0995020i
$583$	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	$0.749038\pi$
$588$	−6439.64	−	11153.8i	−0.451643	−	0.782269i
$589$	929.004	−	1609.08i	0.0649897	−	0.112565i
$590$	−3106.26			−0.216750
$591$	9122.26	−	15800.2i	0.634923	−	1.09972i
$592$	−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	$0.424270\pi$
$594$	−5638.84	+	9766.76i	−0.389502	+	0.674638i
$595$	985.889	+	1707.61i	0.0679286	+	0.117656i
$596$	−590.337	−	1022.49i	−0.0405724	−	0.0702734i
$597$	−2879.78			−0.197423
$598$		0			0
$599$	22251.5			1.51782			0.758909	−	0.651196i	$-0.225733\pi$
$599$	22251.5			1.51782			0.758909	+	0.651196i	$0.225733\pi$
$600$	−162.867	−	282.094i	−0.0110817	−	0.0191941i
$601$	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
$603$	3831.55			0.258761
$604$	4174.20	−	7229.93i	0.281202	−	0.487055i
$605$	−5844.04	+	10122.2i	−0.392717	+	0.680206i
$606$	10378.3			0.695691
$607$	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
$609$	929.694	+	1610.28i	0.0618606	+	0.107146i
$610$	−12227.9			−0.811626
$611$		0			0
$612$	−179.947			−0.0118855
$613$	−5487.29	−	9504.27i	−0.361549	−	0.626221i	0.626667	−	0.779287i	$-0.284419\pi$
$613$	−5487.29	−	9504.27i	−0.361549	−	0.626221i	−0.988216	+	0.153066i	$0.951085\pi$
$614$	1072.04	+	1856.83i	0.0704626	+	0.122045i
$615$	8549.80	−	14808.7i	0.560587	−	0.970965i
$616$	−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	$0.198506\pi$
$618$	−2441.40	+	4228.62i	−0.158912	+	0.275243i
$619$	8387.51			0.544625			0.272312	−	0.962209i	$-0.412212\pi$
$619$	8387.51			0.544625			0.272312	+	0.962209i	$0.412212\pi$
$620$	6883.73	−	11923.0i	0.445899	−	0.772319i
$621$	−321.629	−	557.078i	−0.0207835	−	0.0359980i
$622$	−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
$627$	−843.890	−	1461.66i	−0.0537508	−	0.0930990i
$628$	−1115.02	+	1931.28i	−0.0708508	+	0.122717i
$629$	−2311.81			−0.146547
$630$	2402.49	−	4161.23i	0.151932	−	0.263155i
$631$	−13105.5	+	22699.4i	−0.826818	+	1.43209i	0.0737032	+	0.997280i	$0.476518\pi$
$631$	−13105.5	+	22699.4i	−0.826818	+	1.43209i	−0.900522	+	0.434811i	$0.856815\pi$
$632$	−211.663			−0.0133220
$633$	1769.22	−	3064.38i	0.111090	−	0.192414i
$634$	−8222.40	−	14241.6i	−0.515068	−	0.892125i
$635$	7234.25	+	12530.1i	0.452098	+	0.783057i
$636$	−6448.85			−0.402065
$637$		0			0
$638$	1041.46			0.0646263
$639$	−535.120	−	926.855i	−0.0331283	−	0.0573800i
$640$	695.389	+	1204.45i	0.0429495	+	0.0743907i
$641$	12229.5	−	21182.1i	0.753565	−	1.30521i	−0.192520	−	0.981293i	$-0.561666\pi$
$641$	12229.5	−	21182.1i	0.753565	−	1.30521i	0.946085	−	0.323919i	$-0.105001\pi$
$642$	−4964.23			−0.305175
$643$	14490.9	−	25099.0i	0.888750	−	1.53936i	0.0473946	−	0.998876i	$-0.484908\pi$
$643$	14490.9	−	25099.0i	0.888750	−	1.53936i	0.841355	−	0.540483i	$-0.181758\pi$
$644$	334.277	−	578.985i	0.0204540	−	0.0354273i
$645$	−14698.7			−0.897302
$646$	−35.6404	+	61.7310i	−0.00217067	+	0.00375971i
$647$	4423.15	+	7661.11i	0.268766	+	0.465517i	0.968544	−	0.248844i	$-0.0800507\pi$
$647$	4423.15	+	7661.11i	0.268766	+	0.465517i	−0.699777	+	0.714361i	$0.746717\pi$
$648$	−3496.34	−	6055.83i	−0.211958	−	0.367123i
$649$	7012.47			0.424135
$650$		0			0
$651$	−55490.3			−3.34076
$652$	−2580.95	−	4470.34i	−0.155027	−	0.268515i
$653$	−13153.7	−	22782.9i	−0.788275	−	1.36533i	−0.927023	−	0.375005i	$-0.877641\pi$
$653$	−13153.7	−	22782.9i	−0.788275	−	1.36533i	0.138748	−	0.990328i	$-0.455692\pi$
$654$	5581.75	−	9667.87i	0.333736	−	0.578048i
$655$	2829.12			0.168768
$656$	2146.47	−	3717.80i	0.127753	−	0.221274i
$657$	−744.131	+	1288.87i	−0.0441877	+	0.0765353i
$658$	31326.8			1.85600
$659$	1653.40	−	2863.78i	0.0977352	−	0.169282i	−0.813012	−	0.582247i	$-0.802174\pi$
$659$	1653.40	−	2863.78i	0.0977352	−	0.169282i	0.910747	+	0.412965i	$0.135507\pi$
$660$	−6253.05	−	10830.6i	−0.368787	−	0.638758i
$661$	−11801.3	−	20440.5i	−0.694432	−	1.20279i	−0.970372	−	0.241616i	$-0.922323\pi$
$661$	−11801.3	−	20440.5i	−0.694432	−	1.20279i	0.275940	−	0.961175i	$-0.411011\pi$
$662$	−1216.71			−0.0714332
$663$		0			0
$664$	−9177.25			−0.536365
$665$	−951.677	−	1648.35i	−0.0554954	−	0.0961208i
$666$	2816.79	+	4878.83i	0.163887	+	0.283860i
$667$	−29.7013	+	51.4442i	−0.00172420	+	0.00298640i
$668$	−10053.1			−0.582284
$669$	−9194.51	+	15925.4i	−0.531361	+	0.920344i
$670$	5623.14	−	9739.56i	0.324240	−	0.561600i
$671$	27604.8			1.58818
$672$	2802.79	−	4854.58i	0.160893	−	0.278675i
$673$	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
$675$	797.901			0.0454981
$676$		0			0
$677$	−11395.4			−0.646916			−0.323458	−	0.946242i	$-0.604845\pi$
$677$	−11395.4			−0.646916			−0.323458	+	0.946242i	$0.604845\pi$
$678$	−4415.42	−	7647.73i	−0.250108	−	0.433199i
$679$	−2053.49	−	3556.75i	−0.116062	−	0.201024i
$680$	−264.088	+	457.414i	−0.0148931	+	0.0257956i
$681$	−9461.42			−0.532397
$682$	−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	$0.164559\pi$
$684$	173.703			0.00971006
$685$	13103.5	−	22695.9i	0.730887	−	1.26593i
$686$	6150.66	+	10653.3i	0.342323	+	0.592920i
$687$	−18055.1	−	31272.3i	−1.00268	−	1.73670i
$688$	−3690.18			−0.204487
$689$		0			0
$690$	713.325			0.0393563
$691$	4720.82	+	8176.70i	0.259897	+	0.450154i	0.966214	−	0.257741i	$-0.0829782\pi$
$691$	4720.82	+	8176.70i	0.259897	+	0.450154i	−0.706317	+	0.707895i	$0.749645\pi$
$692$	6801.06	+	11779.8i	0.373609	+	0.647110i
$693$	−5423.69	+	9394.11i	−0.297300	+	0.514939i
$694$	14332.2			0.783922
$695$	2216.17	−	3838.53i	0.120956	−	0.209502i
$696$	−249.035	+	431.342i	−0.0135627	+	0.0234913i
$697$	1630.33			0.0885986
$698$	1884.98	−	3264.88i	0.102217	−	0.177045i
$699$	9824.86	+	17017.2i	0.531631	+	0.920812i
$700$	414.639	+	718.176i	0.0223884	+	0.0387778i
$701$	−145.814			−0.00785638			−0.00392819	−	0.999992i	$-0.501250\pi$
$701$	−145.814			−0.00785638			−0.00392819	+	0.999992i	$0.501250\pi$
$702$		0			0
$703$	2231.58			0.119724
$704$	−1569.86	−	2719.08i	−0.0840432	−	0.145567i
$705$	16712.3	+	28946.6i	0.892799	+	1.54637i
$706$	11954.0	−	20705.0i	0.637246	−	1.10374i
$707$	−26421.8			−1.40551
$708$	−1676.84	+	2904.37i	−0.0890105	+	0.154171i
$709$	−5445.77	+	9432.35i	−0.288463	+	0.499632i	−0.973443	−	0.228929i	$-0.926478\pi$
$709$	−5445.77	+	9432.35i	−0.288463	+	0.499632i	0.684980	+	0.728562i	$0.259811\pi$
$710$	−3141.34			−0.166046
$711$	−97.9422	+	169.641i	−0.00516613	+	0.00894800i
$712$	2655.32	+	4599.14i	0.139764	+	0.242079i
$713$	−886.386	−	1535.26i	−0.0465574	−	0.0806397i
$714$	2128.83			0.111582
$715$		0			0
$716$	−6280.89			−0.327832
$717$	−1855.11	−	3213.14i	−0.0966253	−	0.167360i
$718$	−9068.77	−	15707.6i	−0.471370	−	0.816436i
$719$	3447.89	−	5971.91i	0.178838	−	0.309756i	−0.762645	−	0.646817i	$-0.776100\pi$
$719$	3447.89	−	5971.91i	0.178838	−	0.309756i	0.941483	+	0.337061i	$0.109433\pi$
$720$	1287.10			0.0666214
$721$	6215.49	−	10765.5i	0.321050	−	0.556075i
$722$	−6824.60	+	11820.5i	−0.351780	+	0.609301i
$723$	−8823.04			−0.453848
$724$	−5843.99	+	10122.1i	−0.299986	+	0.519592i
$725$	−36.8417	−	63.8117i	−0.00188726	−	0.00326884i
$726$	6309.53	+	10928.4i	0.322546	+	0.558666i
$727$	12841.0			0.655086			0.327543	−	0.944836i	$-0.393779\pi$
$727$	12841.0			0.655086			0.327543	+	0.944836i	$0.393779\pi$
$728$		0			0
$729$	11731.6			0.596029
$730$	2184.15	+	3783.07i	0.110739	+	0.191805i
$731$	−700.711	−	1213.67i	−0.0354538	−	0.0614078i
$732$	−6600.93	+	11433.1i	−0.333302	+	0.577296i
$733$	26005.8			1.31043			0.655216	−	0.755441i	$-0.272577\pi$
$733$	26005.8			1.31043			0.655216	+	0.755441i	$0.272577\pi$
$734$	7844.12	−	13586.4i	0.394458	−	0.683220i
$735$	−17492.4	+	30297.7i	−0.877846	+	1.52047i
$736$	179.084			0.00896893
$737$	−12694.4	+	21987.3i	−0.634470	+	1.09893i
$738$	−1986.46	−	3440.65i	−0.0990821	−	0.171615i
$739$	−8885.01	−	15389.3i	−0.442274	−	0.766041i	0.555584	−	0.831460i	$-0.312495\pi$
$739$	−8885.01	−	15389.3i	−0.442274	−	0.766041i	−0.997858	+	0.0654195i	$0.979161\pi$
$740$	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	$-0.418898\pi$
$744$	−7432.03	−	12872.7i	−0.366225	−	0.634321i
$745$	−1603.57	+	2777.46i	−0.0788594	+	0.136588i
$746$	−2895.38			−0.142101
$747$	−4246.56	+	7355.25i	−0.207996	+	0.360260i
$748$	596.187	−	1032.63i	0.0291427	−	0.0504767i
$749$	12638.3			0.616547
$750$	−8408.77	+	14564.4i	−0.409393	+	0.709090i
$751$	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
$753$	6081.12			0.294301
$754$		0			0
$755$	−22677.3			−1.09313
$756$	6865.58	+	11891.5i	0.330289	+	0.572078i
$757$	−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
$759$	−1610.35			−0.0770120
$760$	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	$0.105445\pi$
$762$	15620.9			0.742634
$763$	−14210.4	+	24613.2i	−0.674249	+	1.16783i
$764$	−7817.39	−	13540.1i	−0.370188	−	0.641184i
$765$	244.401	+	423.315i	0.0115508	+	0.0200065i
$766$	14501.6			0.684026
$767$		0			0
$768$	1501.56			0.0705505
$769$	11295.1	+	19563.8i	0.529666	+	0.917408i	0.999401	+	0.0346010i	$0.0110161\pi$
$769$	11295.1	+	19563.8i	0.529666	+	0.917408i	−0.469735	+	0.882807i	$0.655651\pi$
$770$	15919.5	+	27573.4i	0.745063	+	1.29049i
$771$	−1480.75	+	2564.73i	−0.0691671	+	0.119801i
$772$	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	$0.765694\pi$
$774$	−1707.55	+	2957.55i	−0.0792977	+	0.137348i
$775$	2198.96			0.101921
$776$	550.065	−	952.740i	0.0254461	−	0.0440739i
$777$	−33323.6	−	57718.2i	−1.53858	−	2.66490i
$778$	−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
$783$	−610.024	−	1056.59i	−0.0278422	−	0.0482242i
$784$	−4391.57	+	7606.41i	−0.200053	+	0.346502i
$785$	6057.63			0.275422
$786$	1527.23	−	2645.25i	0.0693062	−	0.120042i
$787$	7807.21	−	13522.5i	0.353618	−	0.612484i	−0.633263	−	0.773937i	$-0.718285\pi$
$787$	7807.21	−	13522.5i	0.353618	−	0.612484i	0.986880	+	0.161453i	$0.0516181\pi$
$788$	−12442.0			−0.562472
$789$	496.577	−	860.097i	0.0224063	−	0.0388089i
$790$	287.478	+	497.926i	0.0129468	+	0.0224246i
$791$	11241.1	+	19470.2i	0.505294	+	0.875195i
$792$	−2905.67			−0.130364
$793$		0			0
$794$	−15388.5			−0.687806
$795$	8758.71	+	15170.5i	0.390742	+	0.676784i
$796$	981.946	+	1700.78i	0.0437238	+	0.0757319i
$797$	−8934.79	+	15475.5i	−0.397097	+	0.687793i	−0.993366	−	0.114992i	$-0.963316\pi$
$797$	−8934.79	+	15475.5i	−0.397097	+	0.687793i	0.596269	+	0.802785i	$0.296649\pi$
$798$	−2054.96			−0.0911589
$799$	−1593.41	+	2759.87i	−0.0705517	+	0.122199i
$800$	−111.068	+	192.376i	−0.00490858	+	0.00850191i
$801$	4914.74			0.216796
$802$	−1857.46	+	3217.21i	−0.0817819	+	0.141650i
$803$	−4930.80	−	8540.39i	−0.216692	−	0.375322i
$804$	−6071.03	−	10515.3i	−0.266304	−	0.461253i
$805$	−1816.04			−0.0795116
$806$		0			0
$807$	9044.74			0.394535
$808$	−3538.78	−	6129.34i	−0.154076	−	0.266868i
$809$	4056.59	+	7026.23i	0.176294	+	0.305351i	0.940608	−	0.339493i	$-0.110256\pi$
$809$	4056.59	+	7026.23i	0.176294	+	0.305351i	−0.764314	+	0.644844i	$0.776922\pi$
$810$	−9497.33	+	16449.9i	−0.411978	+	0.713567i
$811$	−22750.9			−0.985073			−0.492536	−	0.870292i	$-0.663930\pi$
$811$	−22750.9			−0.985073			−0.492536	+	0.870292i	$0.663930\pi$
$812$	634.013	−	1098.14i	0.0274008	−	0.0474597i
$813$	−3458.73	+	5990.70i	−0.149204	+	0.258429i
$814$	−37329.6			−1.60737
$815$	−7010.81	+	12143.1i	−0.301323	+	0.521906i
$816$	285.123	+	493.848i	0.0122320	+	0.0211864i
$817$	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	$0.873998\pi$
$822$	−14147.2	−	24503.6i	−0.600291	−	1.03974i
$823$	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
$825$	998.745	−	1729.88i	0.0421477	−	0.0730019i
$826$	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	$0.812465\pi$
$828$	82.8669	−	143.530i	0.00347805	−	0.00602416i
$829$	−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
$831$	22909.9			0.956360
$832$		0			0
$833$	−3335.57			−0.138740
$834$	−2392.70	−	4144.27i	−0.0993433	−	0.172068i
$835$	13653.9	+	23649.3i	0.565884	+	0.980140i
$836$	−575.498	+	996.792i	−0.0238086	+	0.0412378i
$837$	36410.2			1.50361
$838$	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	$-0.0812582\pi$
$840$	−15226.8			−0.625447
$841$	12138.2	−	21023.9i	0.497690	−	0.862025i
$842$	1392.34	+	2411.60i	0.0569870	+	0.0987043i
$843$	173.024	+	299.686i	0.00706911	+	0.0122441i
$844$	−2413.07			−0.0984139
$845$		0			0
$846$	7765.89			0.315599
$847$	−16063.3	−	27822.4i	−0.651642	−	1.12868i
$848$	2198.92	+	3808.65i	0.0890464	+	0.154233i
$849$	−13770.9	+	23851.9i	−0.556673	+	0.964186i
$850$	−84.3610			−0.00340419
$851$	1064.60	−	1843.95i	0.0428839	−	0.0742770i
$852$	−1695.78	+	2937.17i	−0.0681883	+	0.118106i
$853$	−13008.1			−0.522145			−0.261072	−	0.965319i	$-0.584076\pi$
$853$	−13008.1			−0.522145			−0.261072	+	0.965319i	$0.584076\pi$
$854$	16805.1	−	29107.4i	0.673372	−	1.16632i
$855$	−235.920	−	408.625i	−0.00943659	−	0.0163447i
$856$	1692.70	+	2931.84i	0.0675879	+	0.117066i
$857$	−35075.0			−1.39806			−0.699031	−	0.715091i	$-0.746385\pi$
$857$	−35075.0			−1.39806			−0.699031	+	0.715091i	$0.746385\pi$
$858$		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
$861$	23500.5	+	40704.0i	0.930191	+	1.61114i
$862$	−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	$0.698559\pi$
$864$	−1839.07	+	3185.36i	−0.0724148	+	0.125426i
$865$	18474.1	−	31998.2i	0.726173	−	1.25777i
$866$	−19265.1			−0.755953
$867$	14300.2	−	24768.7i	0.560163	−	0.970230i
$868$	18921.0	+	32772.2i	0.739886	+	1.28152i
$869$	−648.989	−	1124.08i	−0.0253342	−	0.0438802i
$870$	1352.94			0.0527230
$871$		0			0
$872$	−7613.04			−0.295654
$873$	−509.059	−	881.715i	−0.0197354	−	0.0341828i
$874$	−32.8253	−	56.8552i	−0.00127040	−	0.00220041i
$875$	21407.7	−	37079.2i	0.827099	−	1.43258i
$876$	4716.25			0.181904
$877$	−7675.09	+	13293.6i	−0.295518	+	0.511852i	−0.975105	−	0.221743i	$-0.928826\pi$
$877$	−7675.09	+	13293.6i	−0.295518	+	0.511852i	0.679587	+	0.733595i	$0.262159\pi$
$878$	−647.469	+	1121.45i	−0.0248873	+	0.0431060i
$879$	47620.6			1.82731
$880$	−4264.32	+	7386.02i	−0.163353	+	0.282935i
$881$	−3181.94	−	5511.28i	−0.121682	−	0.210760i	0.798749	−	0.601665i	$-0.205496\pi$
$881$	−3181.94	−	5511.28i	−0.121682	−	0.210760i	−0.920431	+	0.390904i	$0.872162\pi$
$882$	4064.19	+	7039.38i	0.155157	+	0.268739i
$883$	−32249.9			−1.22910			−0.614550	−	0.788878i	$-0.710662\pi$
$883$	−32249.9			−1.22910			−0.614550	+	0.788878i	$0.710662\pi$
$884$		0			0
$885$	9109.81			0.346015
$886$	16862.3	+	29206.3i	0.639390	+	1.10746i
$887$	−14244.7	−	24672.5i	−0.539221	−	0.933959i	−0.998946	−	0.0458972i	$-0.985385\pi$
$887$	−14244.7	−	24672.5i	−0.539221	−	0.933959i	0.459725	−	0.888061i	$-0.347948\pi$
$888$	8926.33	−	15460.9i	0.337329	−	0.584271i
$889$	−39769.0			−1.50035
$890$	7212.81	−	12493.0i	0.271656	−	0.470522i
$891$	21440.5	−	37136.0i	0.806155	−	1.39630i
$892$	12540.6			0.470727
$893$	1538.12	−	2664.10i	0.0576384	−	0.0998327i
$894$	1731.30	+	2998.70i	0.0647688	+	0.112183i
$895$	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
$900$	102.789	+	178.035i	0.00380699	+	0.00659389i
$901$	−835.085	+	1446.41i	−0.0308776	+	0.0534816i
$902$	26325.5			0.971779
$903$	20200.8	−	34988.9i	0.744454	−	1.28943i
$904$	−3011.13	+	5215.43i	−0.110784	+	0.191884i
$905$	31748.8			1.16615
$906$	−12241.8	+	21203.4i	−0.448904	+	0.777524i
$907$	−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
$909$	−6549.94			−0.238997
$910$		0			0
$911$	27000.2			0.981949			0.490975	−	0.871174i	$-0.336641\pi$
$911$	27000.2			0.981949			0.490975	+	0.871174i	$0.336641\pi$
$912$	−275.229	−	476.711i	−0.00999314	−	0.0173086i
$913$	−28138.7	−	48737.7i	−1.02000	−	1.76668i
$914$	−12537.0	+	21714.8i	−0.453707	+	0.785844i
$915$	35861.1			1.29566
$916$	−12312.8	+	21326.4i	−0.444134	+	0.769262i
$917$	−3888.15	+	6734.47i	−0.140020	+	0.242521i
$918$	−1396.85			−0.0502209
$919$	−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
$921$	−3144.01	−	5445.58i	−0.112485	−	0.194829i
$922$	2907.83			0.103866
$923$		0			0
$924$	34375.0			1.22387
$925$	1320.54	+	2287.24i	0.0469396	+	0.0813018i
$926$	7154.47	+	12391.9i	0.253899	+	0.439766i
$927$	1540.82	−	2668.77i	0.0545922	−	0.0945565i
$928$	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	$0.0270920\pi$
$930$	−20188.1	+	34966.8i	−0.711822	+	1.23291i
$931$	3219.82			0.113346
$932$	6700.14	−	11605.0i	0.235483	−	0.407869i
$933$	13280.6	+	23002.7i	0.466010	+	0.807153i
$934$	−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
$939$	15825.4	+	27410.4i	0.549991	+	0.952613i
$940$	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	$0.508546\pi$
$942$	3270.07	−	5663.92i	0.113105	−	0.195903i
$943$	−750.780	+	1300.39i	−0.0259266	+	0.0449062i
$944$	2287.07			0.0788535
$945$	18649.4	−	32301.7i	0.641974	−	1.11193i
$946$	−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	$0.760770\pi$
$948$	620.752			0.0212670
$949$		0			0
$950$	81.4335			0.00278111
$951$	24114.1	+	41766.8i	0.822243	+	1.42417i
$952$	−725.888	−	1257.28i	−0.0247124	−	0.0428031i
$953$	−14012.7	+	24270.7i	−0.476303	+	0.824980i	−0.999631	−	0.0271505i	$-0.991357\pi$
$953$	−14012.7	+	24270.7i	−0.476303	+	0.824980i	0.523329	+	0.852131i	$0.324690\pi$
$954$	4070.00			0.138125
$955$	−21234.9	+	36779.9i	−0.719523	+	1.24625i
$956$	−1265.11	+	2191.23i	−0.0427997	+	0.0741312i
$957$	−3054.31			−0.103168
$958$	−2920.17	+	5057.89i	−0.0984828	+	0.170577i
$959$	36017.0	+	62383.2i	1.21277	+	2.10058i
$960$	−2039.39	−	3532.33i	−0.0685636	−	0.118756i
$961$	70552.9			2.36826
$962$		0			0
$963$	3133.02			0.104839
$964$	3008.47	+	5210.83i	0.100515	+	0.174097i
$965$	−11513.7	−	19942.4i	−0.384083	−	0.665252i
$966$	−980.344	+	1698.01i	−0.0326522	+	0.0565553i
$967$	4250.06			0.141337			0.0706684	−	0.997500i	$-0.477487\pi$
$967$	4250.06			0.141337			0.0706684	+	0.997500i	$0.477487\pi$
$968$	4302.84	−	7452.73i	0.142870	−	0.247458i
$969$	104.524	−	181.040i	0.00346521	−	0.00600191i
$970$	−2988.35			−0.0989177
$971$	2356.03	−	4080.76i	0.0778667	−	0.134869i	−0.824463	−	0.565916i	$-0.808522\pi$
$971$	2356.03	−	4080.76i	0.0778667	−	0.134869i	0.902329	+	0.431047i	$0.141856\pi$
$972$	4046.96	+	7009.53i	0.133545	+	0.231307i
$973$	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	$-0.500651\pi$
$978$	7569.24	+	13110.3i	0.247482	+	0.428652i
$979$	−16283.1	+	28203.2i	−0.531574	+	0.920714i
$980$	23858.2			0.777675
$981$	−3522.75	+	6101.59i	−0.114651	+	0.198582i
$982$	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	$0.444083\pi$
$984$	−6295.03	+	10903.3i	−0.203941	+	0.353237i
$985$	16898.5	+	29269.1i	0.546631	+	0.946792i
$986$	64.4970	+	111.712i	0.00208317	+	0.00360815i
$987$	−91873.1			−2.96287
$988$		0			0
$989$	1290.73			0.0414993
$990$	3946.43	+	6835.41i	0.126693	+	0.219438i
$991$	−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
$993$	3568.28			0.114034
$994$	4317.24	−	7477.68i	0.137761	−	0.238609i
$995$	2667.32	−	4619.94i	0.0849848	−	0.147198i
$996$	26914.4			0.856240
$997$	−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
$999$	21865.5	+	37872.1i	0.692486	+	1.19942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.c.j.315.1		4
13.2	odd	12		338.4.b.e.337.4		4
13.3	even	3		338.4.a.g.1.2		2
13.4	even	6		26.4.c.b.9.1	yes	4
13.5	odd	4		338.4.e.f.23.3		8
13.6	odd	12		338.4.e.f.147.1		8
13.7	odd	12		338.4.e.f.147.3		8
13.8	odd	4		338.4.e.f.23.1		8
13.9	even	3	inner	338.4.c.j.191.1		4
13.10	even	6		338.4.a.h.1.2		2
13.11	odd	12		338.4.b.e.337.2		4
13.12	even	2		26.4.c.b.3.1	✓	4
39.17	odd	6		234.4.h.h.217.2		4
39.38	odd	2		234.4.h.h.55.2		4
52.43	odd	6		208.4.i.d.113.2		4
52.51	odd	2		208.4.i.d.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.b.3.1	✓	4	13.12	even	2
26.4.c.b.9.1	yes	4	13.4	even	6
208.4.i.d.81.2		4	52.51	odd	2
208.4.i.d.113.2		4	52.43	odd	6
234.4.h.h.55.2		4	39.38	odd	2
234.4.h.h.217.2		4	39.17	odd	6
338.4.a.g.1.2		2	13.3	even	3
338.4.a.h.1.2		2	13.10	even	6
338.4.b.e.337.2		4	13.11	odd	12
338.4.b.e.337.4		4	13.2	odd	12
338.4.c.j.191.1		4	13.9	even	3	inner
338.4.c.j.315.1		4	1.1	even	1	trivial
338.4.e.f.23.1		8	13.8	odd	4
338.4.e.f.23.3		8	13.5	odd	4
338.4.e.f.147.1		8	13.6	odd	12
338.4.e.f.147.3		8	13.7	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.93273 - 5.07964i) q^{3} +(-2.00000 + 3.46410i) q^{4} +10.8655 q^{5} +(5.86546 - 10.1593i) q^{6} +(-14.9327 + 25.8642i) q^{7} -8.00000 q^{8} +(-3.70181 + 6.41172i) q^{9} +(10.8655 + 18.8195i) q^{10} +(-24.5291 - 42.4857i) q^{11} +23.4618 q^{12} -59.7309 q^{14} +(-31.8655 - 55.1926i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(3.03816 - 5.26225i) q^{17} -14.8072 q^{18} +(-2.93273 + 5.07964i) q^{19} +(-21.7309 + 37.6391i) q^{20} +175.175 q^{21} +(49.0582 - 84.9713i) q^{22} +(2.79819 + 4.84661i) q^{23} +(23.4618 + 40.6371i) q^{24} -6.94178 q^{25} -114.942 q^{27} +(-59.7309 - 103.457i) q^{28} +(5.30724 + 9.19241i) q^{29} +(63.7309 - 110.385i) q^{30} -316.771 q^{31} +(16.0000 - 27.7128i) q^{32} +(-143.875 + 249.198i) q^{33} +12.1526 q^{34} +(-162.251 + 281.027i) q^{35} +(-14.8072 - 25.6469i) q^{36} +(-190.231 - 329.490i) q^{37} -11.7309 q^{38} -86.9237 q^{40} +(134.155 + 232.363i) q^{41} +(175.175 + 303.411i) q^{42} +(115.318 - 199.737i) q^{43} +196.233 q^{44} +(-40.2219 + 69.6663i) q^{45} +(-5.59638 + 9.69321i) q^{46} -524.466 q^{47} +(-46.9237 + 81.2742i) q^{48} +(-274.473 - 475.401i) q^{49} +(-6.94178 - 12.0235i) q^{50} -35.6404 q^{51} -274.865 q^{53} +(-114.942 - 199.085i) q^{54} +(-266.520 - 461.626i) q^{55} +(119.462 - 206.914i) q^{56} +34.4036 q^{57} +(-10.6145 + 18.3848i) q^{58} +(-71.4709 + 123.791i) q^{59} +254.924 q^{60} +(-281.347 + 487.308i) q^{61} +(-316.771 - 548.664i) q^{62} +(-110.556 - 191.489i) q^{63} +64.0000 q^{64} -575.498 q^{66} +(-258.762 - 448.189i) q^{67} +(12.1526 + 21.0490i) q^{68} +(16.4127 - 28.4276i) q^{69} -649.004 q^{70} +(-72.2781 + 125.189i) q^{71} +(29.6145 - 51.2938i) q^{72} +201.018 q^{73} +(380.462 - 658.979i) q^{74} +(20.3584 + 35.2617i) q^{75} +(-11.7309 - 20.3185i) q^{76} +1465.15 q^{77} +26.4579 q^{79} +(-86.9237 - 150.556i) q^{80} +(437.042 + 756.979i) q^{81} +(-268.309 + 464.725i) q^{82} +1147.16 q^{83} +(-350.349 + 606.823i) q^{84} +(33.0110 - 57.1767i) q^{85} +461.273 q^{86} +(31.1294 - 53.9177i) q^{87} +(196.233 + 339.885i) q^{88} +(-331.915 - 574.893i) q^{89} -160.887 q^{90} -22.3855 q^{92} +(929.004 + 1609.08i) q^{93} +(-524.466 - 908.401i) q^{94} +(-31.8655 + 55.1926i) q^{95} -187.695 q^{96} +(-68.7581 + 119.092i) q^{97} +(548.946 - 950.802i) q^{98} +363.208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 14 q^{5} - 6 q^{6} - 45 q^{7} - 32 q^{8} - 59 q^{9} + 14 q^{10} + 5 q^{11} - 24 q^{12} - 180 q^{14} - 98 q^{15} - 32 q^{16} + 130 q^{17} - 236 q^{18} + 3 q^{19} - 28 q^{20}+ \cdots - 4852 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 14 * q^5 - 6 * q^6 - 45 * q^7 - 32 * q^8 - 59 * q^9 + 14 * q^10 + 5 * q^11 - 24 * q^12 - 180 * q^14 - 98 * q^15 - 32 * q^16 + 130 * q^17 - 236 * q^18 + 3 * q^19 - 28 * q^20 + 82 * q^21 - 10 * q^22 - 33 * q^23 - 24 * q^24 - 234 * q^25 - 666 * q^27 - 180 * q^28 + 198 * q^29 + 196 * q^30 - 560 * q^31 + 64 * q^32 - 767 * q^33 + 520 * q^34 - 266 * q^35 - 236 * q^36 - 702 * q^37 + 12 * q^38 - 112 * q^40 + 242 * q^41 + 82 * q^42 + 93 * q^43 - 40 * q^44 + 119 * q^45 + 66 * q^46 - 448 * q^47 + 48 * q^48 - 435 * q^49 - 234 * q^50 + 2126 * q^51 - 1070 * q^53 - 666 * q^54 - 742 * q^55 + 360 * q^56 + 226 * q^57 - 396 * q^58 - 389 * q^59 + 784 * q^60 - 654 * q^61 - 560 * q^62 - 1002 * q^63 + 256 * q^64 - 3068 * q^66 - 107 * q^67 + 520 * q^68 + 375 * q^69 - 1064 * q^70 - 569 * q^71 + 472 * q^72 + 1246 * q^73 + 1404 * q^74 - 935 * q^75 + 12 * q^76 + 1294 * q^77 + 1520 * q^79 - 112 * q^80 + 334 * q^81 - 484 * q^82 + 3528 * q^83 - 164 * q^84 - 413 * q^85 + 372 * q^86 - 1599 * q^87 - 40 * q^88 - 871 * q^89 + 476 * q^90 + 264 * q^92 + 2184 * q^93 - 448 * q^94 - 98 * q^95 + 192 * q^96 - 879 * q^97 + 870 * q^98 - 4852 * q^99

Introduction

L-functions

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