LMFDB - Embedded newform 338.4.e.d.147.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(23,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.147
Dual form			338.4.e.d.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000i q^{5} +(5.19615 - 3.00000i) q^{6} +(4.33013 - 2.50000i) q^{7} +8.00000i q^{8} +(9.00000 + 15.5885i) q^{9} +O(q^{10})$	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000i q^{5} +(5.19615 - 3.00000i) q^{6} +(4.33013 - 2.50000i) q^{7} +8.00000i q^{8} +(9.00000 + 15.5885i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(11.2583 + 6.50000i) q^{11} +12.0000 q^{12} +10.0000 q^{14} +(5.19615 + 3.00000i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(13.5000 + 23.3827i) q^{17} +36.0000i q^{18} +(64.9519 - 37.5000i) q^{19} +(-6.92820 + 4.00000i) q^{20} -15.0000i q^{21} +(13.0000 + 22.5167i) q^{22} +(-93.5000 + 161.947i) q^{23} +(20.7846 + 12.0000i) q^{24} +121.000 q^{25} +135.000 q^{27} +(17.3205 + 10.0000i) q^{28} +(6.50000 - 11.2583i) q^{29} +(6.00000 + 10.3923i) q^{30} -104.000i q^{31} +(-27.7128 + 16.0000i) q^{32} +(33.7750 - 19.5000i) q^{33} +54.0000i q^{34} +(5.00000 + 8.66025i) q^{35} +(-36.0000 + 62.3538i) q^{36} +(366.329 + 211.500i) q^{37} +150.000 q^{38} -16.0000 q^{40} +(-168.875 - 97.5000i) q^{41} +(15.0000 - 25.9808i) q^{42} +(99.5000 + 172.339i) q^{43} +52.0000i q^{44} +(-31.1769 + 18.0000i) q^{45} +(-323.894 + 187.000i) q^{46} -388.000i q^{47} +(24.0000 + 41.5692i) q^{48} +(-159.000 + 275.396i) q^{49} +(209.578 + 121.000i) q^{50} +81.0000 q^{51} +618.000 q^{53} +(233.827 + 135.000i) q^{54} +(-13.0000 + 22.5167i) q^{55} +(20.0000 + 34.6410i) q^{56} -225.000i q^{57} +(22.5167 - 13.0000i) q^{58} +(-425.218 + 245.500i) q^{59} +24.0000i q^{60} +(-87.5000 - 151.554i) q^{61} +(104.000 - 180.133i) q^{62} +(77.9423 + 45.0000i) q^{63} -64.0000 q^{64} +78.0000 q^{66} +(-707.543 - 408.500i) q^{67} +(-54.0000 + 93.5307i) q^{68} +(280.500 + 485.840i) q^{69} +20.0000i q^{70} +(68.4160 - 39.5000i) q^{71} +(-124.708 + 72.0000i) q^{72} -230.000i q^{73} +(423.000 + 732.657i) q^{74} +(181.500 - 314.367i) q^{75} +(259.808 + 150.000i) q^{76} +65.0000 q^{77} +764.000 q^{79} +(-27.7128 - 16.0000i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-195.000 - 337.750i) q^{82} -732.000i q^{83} +(51.9615 - 30.0000i) q^{84} +(-46.7654 + 27.0000i) q^{85} +398.000i q^{86} +(-19.5000 - 33.7750i) q^{87} +(-52.0000 + 90.0666i) q^{88} +(-901.532 - 520.500i) q^{89} -72.0000 q^{90} -748.000 q^{92} +(-270.200 - 156.000i) q^{93} +(388.000 - 672.036i) q^{94} +(75.0000 + 129.904i) q^{95} +96.0000i q^{96} +(-84.0045 + 48.5000i) q^{97} +(-550.792 + 318.000i) q^{98} +234.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 8 q^{4} + 36 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 8 * q^4 + 36 * q^9	$ 4 q + 6 q^{3} + 8 q^{4} + 36 q^{9} - 8 q^{10} + 48 q^{12} + 40 q^{14} - 32 q^{16} + 54 q^{17} + 52 q^{22} - 374 q^{23} + 484 q^{25} + 540 q^{27} + 26 q^{29} + 24 q^{30} + 20 q^{35} - 144 q^{36} + 600 q^{38} - 64 q^{40} + 60 q^{42} + 398 q^{43} + 96 q^{48} - 636 q^{49} + 324 q^{51} + 2472 q^{53} - 52 q^{55} + 80 q^{56} - 350 q^{61} + 416 q^{62} - 256 q^{64} + 312 q^{66} - 216 q^{68} + 1122 q^{69} + 1692 q^{74} + 726 q^{75} + 260 q^{77} + 3056 q^{79} - 162 q^{81} - 780 q^{82} - 78 q^{87} - 208 q^{88} - 288 q^{90} - 2992 q^{92} + 1552 q^{94} + 300 q^{95}+O(q^{100}) $ 4 * q + 6 * q^3 + 8 * q^4 + 36 * q^9 - 8 * q^10 + 48 * q^12 + 40 * q^14 - 32 * q^16 + 54 * q^17 + 52 * q^22 - 374 * q^23 + 484 * q^25 + 540 * q^27 + 26 * q^29 + 24 * q^30 + 20 * q^35 - 144 * q^36 + 600 * q^38 - 64 * q^40 + 60 * q^42 + 398 * q^43 + 96 * q^48 - 636 * q^49 + 324 * q^51 + 2472 * q^53 - 52 * q^55 + 80 * q^56 - 350 * q^61 + 416 * q^62 - 256 * q^64 + 312 * q^66 - 216 * q^68 + 1122 * q^69 + 1692 * q^74 + 726 * q^75 + 260 * q^77 + 3056 * q^79 - 162 * q^81 - 780 * q^82 - 78 * q^87 - 208 * q^88 - 288 * q^90 - 2992 * q^92 + 1552 * q^94 + 300 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$			2.00000i			0.178885i	0.995992	+	0.0894427i	$0.0285086\pi$
$5$			2.00000i			0.178885i	−0.995992	+	0.0894427i	$0.971491\pi$
$6$	5.19615	−	3.00000i	0.353553	−	0.204124i
$7$	4.33013	−	2.50000i	0.233805	−	0.134987i	−0.378521	−	0.925593i	$-0.623567\pi$
$7$	4.33013	−	2.50000i	0.233805	−	0.134987i	0.612326	+	0.790605i	$0.290234\pi$
$8$			8.00000i			0.353553i
$9$	9.00000	+	15.5885i	0.333333	+	0.577350i
$10$	−2.00000	+	3.46410i	−0.0632456	+	0.109545i
$11$	11.2583	+	6.50000i	0.308592	+	0.178166i	0.646296	−	0.763087i	$-0.276317\pi$
$11$	11.2583	+	6.50000i	0.308592	+	0.178166i	−0.337704	+	0.941252i	$0.609650\pi$
$12$	12.0000			0.288675
$13$		0			0
$13$		0			0
$14$	10.0000			0.190901
$15$	5.19615	+	3.00000i	0.0894427	+	0.0516398i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	13.5000	+	23.3827i	0.192602	+	0.333596i	0.946112	−	0.323840i	$-0.104974\pi$
$17$	13.5000	+	23.3827i	0.192602	+	0.333596i	−0.753510	+	0.657437i	$0.771641\pi$
$18$			36.0000i			0.471405i
$19$	64.9519	−	37.5000i	0.784263	−	0.452794i	−0.0536762	−	0.998558i	$-0.517094\pi$
$19$	64.9519	−	37.5000i	0.784263	−	0.452794i	0.837939	+	0.545764i	$0.183761\pi$
$20$	−6.92820	+	4.00000i	−0.0774597	+	0.0447214i
$21$		−	15.0000i		−	0.155870i
$22$	13.0000	+	22.5167i	0.125982	+	0.218208i
$23$	−93.5000	+	161.947i	−0.847656	+	1.46818i	0.0356377	+	0.999365i	$0.488654\pi$
$23$	−93.5000	+	161.947i	−0.847656	+	1.46818i	−0.883294	+	0.468819i	$0.844680\pi$
$24$	20.7846	+	12.0000i	0.176777	+	0.102062i
$25$	121.000			0.968000
$26$		0			0
$27$	135.000			0.962250
$28$	17.3205	+	10.0000i	0.116902	+	0.0674937i
$29$	6.50000	−	11.2583i	0.0416214	−	0.0720903i	−0.844464	−	0.535612i	$-0.820081\pi$
$29$	6.50000	−	11.2583i	0.0416214	−	0.0720903i	0.886086	+	0.463522i	$0.153414\pi$
$30$	6.00000	+	10.3923i	0.0365148	+	0.0632456i
$31$		−	104.000i		−	0.602547i	−0.953538	−	0.301273i	$-0.902588\pi$
$31$		−	104.000i		−	0.602547i	0.953538	−	0.301273i	$-0.0974117\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	33.7750	−	19.5000i	0.178166	−	0.102864i
$34$			54.0000i			0.272380i
$35$	5.00000	+	8.66025i	0.0241473	+	0.0418243i
$36$	−36.0000	+	62.3538i	−0.166667	+	0.288675i
$37$	366.329	+	211.500i	1.62768	+	0.939740i	0.984784	+	0.173785i	$0.0555998\pi$
$37$	366.329	+	211.500i	1.62768	+	0.939740i	0.642894	+	0.765955i	$0.277734\pi$
$38$	150.000			0.640348
$39$		0			0
$40$	−16.0000			−0.0632456
$41$	−168.875	−	97.5000i	−0.643264	−	0.371389i	0.142607	−	0.989779i	$-0.454452\pi$
$41$	−168.875	−	97.5000i	−0.643264	−	0.371389i	−0.785871	+	0.618391i	$0.787785\pi$
$42$	15.0000	−	25.9808i	0.0551083	−	0.0954504i
$43$	99.5000	+	172.339i	0.352875	+	0.611197i	0.986752	−	0.162237i	$-0.0518709\pi$
$43$	99.5000	+	172.339i	0.352875	+	0.611197i	−0.633877	+	0.773434i	$0.718538\pi$
$44$			52.0000i			0.178166i
$45$	−31.1769	+	18.0000i	−0.103280	+	0.0596285i
$46$	−323.894	+	187.000i	−1.03816	+	0.599384i
$47$		−	388.000i		−	1.20416i	−0.798435	−	0.602081i	$-0.794338\pi$
$47$		−	388.000i		−	1.20416i	0.798435	−	0.602081i	$-0.205662\pi$
$48$	24.0000	+	41.5692i	0.0721688	+	0.125000i
$49$	−159.000	+	275.396i	−0.463557	+	0.802904i
$50$	209.578	+	121.000i	0.592777	+	0.342240i
$51$	81.0000			0.222397
$52$		0			0
$53$	618.000			1.60168			0.800838	−	0.598881i	$-0.204388\pi$
$53$	618.000			1.60168			0.800838	+	0.598881i	$0.204388\pi$
$54$	233.827	+	135.000i	0.589256	+	0.340207i
$55$	−13.0000	+	22.5167i	−0.0318713	+	0.0552027i
$56$	20.0000	+	34.6410i	0.0477252	+	0.0826625i
$57$		−	225.000i		−	0.522842i
$58$	22.5167	−	13.0000i	0.0509756	−	0.0294308i
$59$	−425.218	+	245.500i	−0.938284	+	0.541718i	−0.889422	−	0.457087i	$-0.848893\pi$
$59$	−425.218	+	245.500i	−0.938284	+	0.541718i	−0.0488617	+	0.998806i	$0.515559\pi$
$60$			24.0000i			0.0516398i
$61$	−87.5000	−	151.554i	−0.183659	−	0.318108i	0.759465	−	0.650549i	$-0.225461\pi$
$61$	−87.5000	−	151.554i	−0.183659	−	0.318108i	−0.943124	+	0.332441i	$0.892128\pi$
$62$	104.000	−	180.133i	0.213032	−	0.368983i
$63$	77.9423	+	45.0000i	0.155870	+	0.0899915i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	78.0000			0.145472
$67$	−707.543	−	408.500i	−1.29015	−	0.744869i	−0.311470	−	0.950256i	$-0.600821\pi$
$67$	−707.543	−	408.500i	−1.29015	−	0.744869i	−0.978681	+	0.205387i	$0.934155\pi$
$68$	−54.0000	+	93.5307i	−0.0963009	+	0.166798i
$69$	280.500	+	485.840i	0.489395	+	0.847656i
$70$			20.0000i			0.0341494i
$71$	68.4160	−	39.5000i	0.114359	−	0.0660252i	−0.441729	−	0.897148i	$-0.645635\pi$
$71$	68.4160	−	39.5000i	0.114359	−	0.0660252i	0.556088	+	0.831123i	$0.312302\pi$
$72$	−124.708	+	72.0000i	−0.204124	+	0.117851i
$73$		−	230.000i		−	0.368760i	−0.982855	−	0.184380i	$-0.940972\pi$
$73$		−	230.000i		−	0.368760i	0.982855	−	0.184380i	$-0.0590277\pi$
$74$	423.000	+	732.657i	0.664497	+	1.15094i
$75$	181.500	−	314.367i	0.279438	−	0.484000i
$76$	259.808	+	150.000i	0.392131	+	0.226397i
$77$	65.0000			0.0962005
$78$		0			0
$79$	764.000			1.08806			0.544030	−	0.839066i	$-0.316898\pi$
$79$	764.000			1.08806			0.544030	+	0.839066i	$0.316898\pi$
$80$	−27.7128	−	16.0000i	−0.0387298	−	0.0223607i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−195.000	−	337.750i	−0.262612	−	0.454857i
$83$		−	732.000i		−	0.968041i	−0.875057	−	0.484021i	$-0.839176\pi$
$83$		−	732.000i		−	0.968041i	0.875057	−	0.484021i	$-0.160824\pi$
$84$	51.9615	−	30.0000i	0.0674937	−	0.0389675i
$85$	−46.7654	+	27.0000i	−0.0596755	+	0.0344537i
$86$			398.000i			0.499040i
$87$	−19.5000	−	33.7750i	−0.0240301	−	0.0416214i
$88$	−52.0000	+	90.0666i	−0.0629911	+	0.109104i
$89$	−901.532	−	520.500i	−1.07373	−	0.619920i	−0.144534	−	0.989500i	$-0.546168\pi$
$89$	−901.532	−	520.500i	−1.07373	−	0.619920i	−0.929199	+	0.369580i	$0.879502\pi$
$90$	−72.0000			−0.0843274
$91$		0			0
$92$	−748.000			−0.847656
$93$	−270.200	−	156.000i	−0.301273	−	0.173940i
$94$	388.000	−	672.036i	0.425736	−	0.737396i
$95$	75.0000	+	129.904i	0.0809983	+	0.140293i
$96$			96.0000i			0.102062i
$97$	−84.0045	+	48.5000i	−0.0879316	+	0.0507673i	−0.543321	−	0.839525i	$-0.682833\pi$
$97$	−84.0045	+	48.5000i	−0.0879316	+	0.0507673i	0.455389	+	0.890292i	$0.349500\pi$
$98$	−550.792	+	318.000i	−0.567739	+	0.327784i
$99$			234.000i			0.237554i
$100$	242.000	+	419.156i	0.242000	+	0.419156i
$101$	−404.500	+	700.615i	−0.398507	+	0.690235i	−0.993542	−	0.113465i	$-0.963805\pi$
$101$	−404.500	+	700.615i	−0.398507	+	0.690235i	0.595035	+	0.803700i	$0.297138\pi$
$102$	140.296	+	81.0000i	0.136190	+	0.0786294i
$103$	−1288.00			−1.23214			−0.616070	−	0.787691i	$-0.711276\pi$
$103$	−1288.00			−1.23214			−0.616070	+	0.787691i	$0.711276\pi$
$104$		0			0
$105$	30.0000			0.0278829
$106$	1070.41	+	618.000i	0.980822	+	0.566278i
$107$	−638.500	+	1105.91i	−0.576880	+	0.999185i	0.418955	+	0.908007i	$0.362397\pi$
$107$	−638.500	+	1105.91i	−0.576880	+	0.999185i	−0.995835	+	0.0911779i	$0.970937\pi$
$108$	270.000	+	467.654i	0.240563	+	0.416667i
$109$			826.000i			0.725839i	0.931820	+	0.362920i	$0.118220\pi$
$109$			826.000i			0.725839i	−0.931820	+	0.362920i	$0.881780\pi$
$110$	−45.0333	+	26.0000i	−0.0390342	+	0.0225364i
$111$	1098.99	−	634.500i	0.939740	−	0.542559i
$112$			80.0000i			0.0674937i
$113$	−473.500	−	820.126i	−0.394187	−	0.682752i	0.598810	−	0.800891i	$-0.295640\pi$
$113$	−473.500	−	820.126i	−0.394187	−	0.682752i	−0.992997	+	0.118139i	$0.962307\pi$
$114$	225.000	−	389.711i	0.184852	−	0.320174i
$115$	−323.894	−	187.000i	−0.262637	−	0.151633i
$116$	52.0000			0.0416214
$117$		0			0
$118$	−982.000			−0.766105
$119$	116.913	+	67.5000i	0.0900625	+	0.0519976i
$120$	−24.0000	+	41.5692i	−0.0182574	+	0.0316228i
$121$	−581.000	−	1006.32i	−0.436514	−	0.756064i
$122$		−	350.000i		−	0.259734i
$123$	−506.625	+	292.500i	−0.371389	+	0.214421i
$124$	360.267	−	208.000i	0.260910	−	0.150637i
$125$			492.000i			0.352047i
$126$	90.0000	+	155.885i	0.0636336	+	0.110217i
$127$	588.500	−	1019.31i	0.411188	−	0.712199i	−0.583832	−	0.811875i	$-0.698447\pi$
$127$	588.500	−	1019.31i	0.411188	−	0.712199i	0.995020	+	0.0996756i	$0.0317805\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	597.000			0.407464
$130$		0			0
$131$	−1420.00			−0.947069			−0.473534	−	0.880775i	$-0.657022\pi$
$131$	−1420.00			−0.947069			−0.473534	+	0.880775i	$0.657022\pi$
$132$	135.100	+	78.0000i	0.0890829	+	0.0514320i
$133$	187.500	−	324.760i	0.122243	−	0.211731i
$134$	−817.000	−	1415.09i	−0.526702	−	0.912274i
$135$			270.000i			0.172133i
$136$	−187.061	+	108.000i	−0.117944	+	0.0680950i
$137$	2086.26	−	1204.50i	1.30103	−	0.751149i	0.320447	−	0.947266i	$-0.396167\pi$
$137$	2086.26	−	1204.50i	1.30103	−	0.751149i	0.980580	+	0.196118i	$0.0628334\pi$
$138$			1122.00i			0.692109i
$139$	−1413.50	−	2448.25i	−0.862529	−	1.49394i	−0.869480	−	0.493968i	$-0.835546\pi$
$139$	−1413.50	−	2448.25i	−0.862529	−	1.49394i	0.00695133	−	0.999976i	$-0.497787\pi$
$140$	−20.0000	+	34.6410i	−0.0120736	+	0.0209121i
$141$	−1008.05	−	582.000i	−0.602081	−	0.347612i
$142$	158.000			0.0933737
$143$		0			0
$144$	−288.000			−0.166667
$145$	22.5167	+	13.0000i	0.0128959	+	0.00744546i
$146$	230.000	−	398.372i	0.130376	−	0.225818i
$147$	477.000	+	826.188i	0.267635	+	0.463557i
$148$			1692.00i			0.939740i
$149$	740.452	−	427.500i	0.407115	−	0.235048i	−0.282434	−	0.959287i	$-0.591142\pi$
$149$	740.452	−	427.500i	0.407115	−	0.235048i	0.689549	+	0.724239i	$0.257809\pi$
$150$	628.734	−	363.000i	0.342240	−	0.197592i
$151$		−	2064.00i		−	1.11236i	−0.831063	−	0.556179i	$-0.812267\pi$
$151$		−	2064.00i		−	1.11236i	0.831063	−	0.556179i	$-0.187733\pi$
$152$	300.000	+	519.615i	0.160087	+	0.277279i
$153$	−243.000	+	420.888i	−0.128401	+	0.222397i
$154$	112.583	+	65.0000i	0.0589105	+	0.0340120i
$155$	208.000			0.107787
$156$		0			0
$157$	−1894.00			−0.962788			−0.481394	−	0.876504i	$-0.659869\pi$
$157$	−1894.00			−0.962788			−0.481394	+	0.876504i	$0.659869\pi$
$158$	1323.29	+	764.000i	0.666298	+	0.384687i
$159$	927.000	−	1605.61i	0.462364	−	0.800838i
$160$	−32.0000	−	55.4256i	−0.0158114	−	0.0273861i
$161$			935.000i			0.457691i
$162$	−140.296	+	81.0000i	−0.0680414	+	0.0392837i
$163$	853.035	−	492.500i	0.409907	−	0.236660i	−0.280843	−	0.959754i	$-0.590614\pi$
$163$	853.035	−	492.500i	0.409907	−	0.236660i	0.690750	+	0.723094i	$0.257281\pi$
$164$		−	780.000i		−	0.371389i
$165$	39.0000	+	67.5500i	0.0184009	+	0.0318713i
$166$	732.000	−	1267.86i	0.342254	−	0.592802i
$167$	−2039.49	−	1177.50i	−0.945033	−	0.545615i	−0.0534983	−	0.998568i	$-0.517037\pi$
$167$	−2039.49	−	1177.50i	−0.945033	−	0.545615i	−0.891534	+	0.452953i	$0.850371\pi$
$168$	120.000			0.0551083
$169$		0			0
$170$	−108.000			−0.0487248
$171$	1169.13	+	675.000i	0.522842	+	0.301863i
$172$	−398.000	+	689.356i	−0.176437	+	0.305598i
$173$	−1944.50	−	3367.97i	−0.854553	−	1.48013i	−0.877059	−	0.480382i	$-0.840498\pi$
$173$	−1944.50	−	3367.97i	−0.854553	−	1.48013i	0.0225069	−	0.999747i	$-0.492835\pi$
$174$		−	78.0000i		−	0.0339837i
$175$	523.945	−	302.500i	0.226323	−	0.130668i
$176$	−180.133	+	104.000i	−0.0771481	+	0.0445414i
$177$			1473.00i			0.625522i
$178$	−1041.00	−	1803.06i	−0.438350	−	0.759244i
$179$	1114.50	−	1930.37i	0.465372	−	0.806048i	−0.533846	−	0.845582i	$-0.679254\pi$
$179$	1114.50	−	1930.37i	0.465372	−	0.806048i	0.999218	+	0.0395333i	$0.0125871\pi$
$180$	−124.708	−	72.0000i	−0.0516398	−	0.0298142i
$181$	1038.00			0.426265			0.213132	−	0.977023i	$-0.431633\pi$
$181$	1038.00			0.426265			0.213132	+	0.977023i	$0.431633\pi$
$182$		0			0
$183$	−525.000			−0.212072
$184$	−1295.57	−	748.000i	−0.519081	−	0.299692i
$185$	−423.000	+	732.657i	−0.168106	+	0.291168i
$186$	−312.000	−	540.400i	−0.122994	−	0.213032i
$187$			351.000i			0.137260i
$188$	1344.07	−	776.000i	0.521417	−	0.301041i
$189$	584.567	−	337.500i	0.224979	−	0.129892i
$190$			300.000i			0.114549i
$191$	1070.50	+	1854.16i	0.405543	+	0.702421i	0.994384	−	0.105828i	$-0.0337492\pi$
$191$	1070.50	+	1854.16i	0.405543	+	0.702421i	−0.588842	+	0.808248i	$0.700416\pi$
$192$	−96.0000	+	166.277i	−0.0360844	+	0.0625000i
$193$	2275.05	+	1313.50i	0.848506	+	0.489885i	0.860146	−	0.510047i	$-0.170372\pi$
$193$	2275.05	+	1313.50i	0.848506	+	0.489885i	−0.0116407	+	0.999932i	$0.503705\pi$
$194$	−194.000			−0.0717958
$195$		0			0
$196$	−1272.00			−0.463557
$197$	−1041.83	−	601.500i	−0.376788	−	0.217539i	0.299632	−	0.954055i	$-0.403136\pi$
$197$	−1041.83	−	601.500i	−0.376788	−	0.217539i	−0.676420	+	0.736516i	$0.736469\pi$
$198$	−234.000	+	405.300i	−0.0839882	+	0.145472i
$199$	371.500	+	643.457i	0.132336	+	0.229213i	0.924577	−	0.380996i	$-0.124419\pi$
$199$	371.500	+	643.457i	0.132336	+	0.229213i	−0.792240	+	0.610209i	$0.791085\pi$
$200$			968.000i			0.342240i
$201$	−2122.63	+	1225.50i	−0.744869	+	0.430050i
$202$	−1401.23	+	809.000i	−0.488070	+	0.281787i
$203$		−	65.0000i		−	0.0224734i
$204$	162.000	+	280.592i	0.0555994	+	0.0963009i
$205$	195.000	−	337.750i	0.0664361	−	0.115071i
$206$	−2230.88	−	1288.00i	−0.754529	−	0.435627i
$207$	−3366.00			−1.13021
$208$		0			0
$209$	975.000			0.322690
$210$	51.9615	+	30.0000i	0.0170747	+	0.00985808i
$211$	177.500	−	307.439i	0.0579128	−	0.100308i	−0.835615	−	0.549315i	$-0.814889\pi$
$211$	177.500	−	307.439i	0.0579128	−	0.100308i	0.893528	+	0.449007i	$0.148222\pi$
$212$	1236.00	+	2140.81i	0.400419	+	0.693546i
$213$		−	237.000i		−	0.0762393i
$214$	−2211.83	+	1277.00i	−0.706530	+	0.407916i
$215$	−344.678	+	199.000i	−0.109334	+	0.0631241i
$216$			1080.00i			0.340207i
$217$	−260.000	−	450.333i	−0.0813362	−	0.140878i
$218$	−826.000	+	1430.67i	−0.256623	+	0.444484i
$219$	−597.558	−	345.000i	−0.184380	−	0.106452i
$220$	−104.000			−0.0318713
$221$		0			0
$222$	2538.00			0.767295
$223$	1977.14	+	1141.50i	0.593717	+	0.342782i	0.766566	−	0.642166i	$-0.221964\pi$
$223$	1977.14	+	1141.50i	0.593717	+	0.342782i	−0.172849	+	0.984948i	$0.555297\pi$
$224$	−80.0000	+	138.564i	−0.0238626	+	0.0413313i
$225$	1089.00	+	1886.20i	0.322667	+	0.558875i
$226$		−	1894.00i		−	0.557465i
$227$	2122.63	−	1225.50i	0.620633	−	0.358323i	−0.156482	−	0.987681i	$-0.550015\pi$
$227$	2122.63	−	1225.50i	0.620633	−	0.358323i	0.777116	+	0.629358i	$0.216682\pi$
$228$	779.423	−	450.000i	0.226397	−	0.130710i
$229$			1878.00i			0.541929i	0.962589	+	0.270964i	$0.0873426\pi$
$229$			1878.00i			0.541929i	−0.962589	+	0.270964i	$0.912657\pi$
$230$	−374.000	−	647.787i	−0.107221	−	0.185712i
$231$	97.5000	−	168.875i	0.0277707	−	0.0481002i
$232$	90.0666	+	52.0000i	0.0254878	+	0.0147154i
$233$	−1630.00			−0.458304			−0.229152	−	0.973391i	$-0.573595\pi$
$233$	−1630.00			−0.458304			−0.229152	+	0.973391i	$0.573595\pi$
$234$		0			0
$235$	776.000			0.215407
$236$	−1700.87	−	982.000i	−0.469142	−	0.270859i
$237$	1146.00	−	1984.93i	0.314096	−	0.544030i
$238$	135.000	+	233.827i	0.0367679	+	0.0636838i
$239$		−	5544.00i		−	1.50047i	−0.661173	−	0.750233i	$-0.729941\pi$
$239$		−	5544.00i		−	1.50047i	0.661173	−	0.750233i	$-0.270059\pi$
$240$	−83.1384	+	48.0000i	−0.0223607	+	0.0129099i
$241$	−4783.06	+	2761.50i	−1.27844	+	0.738107i	−0.976561	−	0.215239i	$-0.930947\pi$
$241$	−4783.06	+	2761.50i	−1.27844	+	0.738107i	−0.301878	+	0.953347i	$0.597614\pi$
$242$		−	2324.00i		−	0.617324i
$243$	1944.00	+	3367.11i	0.513200	+	0.888889i
$244$	350.000	−	606.218i	0.0918297	−	0.159054i
$245$	−550.792	−	318.000i	−0.143628	−	0.0829236i
$246$	−1170.00			−0.303238
$247$		0			0
$248$	832.000			0.213032
$249$	−1901.79	−	1098.00i	−0.484021	−	0.279449i
$250$	−492.000	+	852.169i	−0.124467	+	0.215584i
$251$	1087.50	+	1883.61i	0.273476	+	0.473674i	0.969749	−	0.244103i	$-0.0784934\pi$
$251$	1087.50	+	1883.61i	0.273476	+	0.473674i	−0.696274	+	0.717776i	$0.745160\pi$
$252$			360.000i			0.0899915i
$253$	−2105.31	+	1215.50i	−0.523160	+	0.302047i
$254$	2038.62	−	1177.00i	0.503601	−	0.290754i
$255$			162.000i			0.0397837i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2842.50	+	4923.35i	−0.689923	+	1.19498i	0.281939	+	0.959432i	$0.409022\pi$
$257$	−2842.50	+	4923.35i	−0.689923	+	1.19498i	−0.971862	+	0.235550i	$0.924311\pi$
$258$	1034.03	+	597.000i	0.249520	+	0.144060i
$259$	2115.00			0.507412
$260$		0			0
$261$	234.000			0.0554952
$262$	−2459.51	−	1420.00i	−0.579959	−	0.334839i
$263$	−3058.50	+	5297.48i	−0.717092	+	1.24204i	0.245055	+	0.969509i	$0.421194\pi$
$263$	−3058.50	+	5297.48i	−0.717092	+	1.24204i	−0.962147	+	0.272531i	$0.912139\pi$
$264$	156.000	+	270.200i	0.0363679	+	0.0629911i
$265$			1236.00i			0.286517i
$266$	649.519	−	375.000i	0.149716	−	0.0864388i
$267$	−2704.60	+	1561.50i	−0.619920	+	0.357911i
$268$		−	3268.00i		−	0.744869i
$269$	2554.50	+	4424.52i	0.578999	+	1.00285i	0.995595	+	0.0937632i	$0.0298897\pi$
$269$	2554.50	+	4424.52i	0.578999	+	1.00285i	−0.416596	+	0.909092i	$0.636777\pi$
$270$	−270.000	+	467.654i	−0.0608581	+	0.105409i
$271$	6537.63	+	3774.50i	1.46543	+	0.846068i	0.999254	−	0.0386217i	$-0.0122967\pi$
$271$	6537.63	+	3774.50i	1.46543	+	0.846068i	0.466180	+	0.884690i	$0.345630\pi$
$272$	−432.000			−0.0963009
$273$		0			0
$274$	4818.00			1.06228
$275$	1362.26	+	786.500i	0.298717	+	0.172464i
$276$	−1122.00	+	1943.36i	−0.244697	+	0.423828i
$277$	−490.500	−	849.571i	−0.106395	−	0.184281i	0.807913	−	0.589302i	$-0.200597\pi$
$277$	−490.500	−	849.571i	−0.106395	−	0.184281i	−0.914307	+	0.405022i	$0.867264\pi$
$278$		−	5654.00i		−	1.21980i
$279$	1621.20	−	936.000i	0.347881	−	0.200849i
$280$	−69.2820	+	40.0000i	−0.0147871	+	0.00853735i
$281$			2762.00i			0.586360i	0.956057	+	0.293180i	$0.0947135\pi$
$281$			2762.00i			0.586360i	−0.956057	+	0.293180i	$0.905287\pi$
$282$	−1164.00	−	2016.11i	−0.245799	−	0.425736i
$283$	1962.50	−	3399.15i	0.412221	−	0.713988i	−0.582911	−	0.812536i	$-0.698087\pi$
$283$	1962.50	−	3399.15i	0.412221	−	0.713988i	0.995132	+	0.0985482i	$0.0314199\pi$
$284$	273.664	+	158.000i	0.0571795	+	0.0330126i
$285$	450.000			0.0935288
$286$		0			0
$287$	−975.000			−0.200531
$288$	−498.831	−	288.000i	−0.102062	−	0.0589256i
$289$	2092.00	−	3623.45i	0.425809	−	0.737523i
$290$	26.0000	+	45.0333i	0.00526473	+	0.00911879i
$291$			291.000i			0.0586210i
$292$	796.743	−	460.000i	0.159678	−	0.0921899i
$293$	−6677.92	+	3855.50i	−1.33150	+	0.768740i	−0.985529	−	0.169507i	$-0.945782\pi$
$293$	−6677.92	+	3855.50i	−1.33150	+	0.768740i	−0.345967	+	0.938247i	$0.612449\pi$
$294$			1908.00i			0.378493i
$295$	−491.000	−	850.437i	−0.0969055	−	0.167845i
$296$	−1692.00	+	2930.63i	−0.332248	+	0.575471i
$297$	1519.87	+	877.500i	0.296943	+	0.171440i
$298$	1710.00			0.332408
$299$		0			0
$300$	1452.00			0.279438
$301$	861.695	+	497.500i	0.165008	+	0.0952672i
$302$	2064.00	−	3574.95i	0.393278	−	0.681177i
$303$	1213.50	+	2101.84i	0.230078	+	0.398507i
$304$			1200.00i			0.226397i
$305$	303.109	−	175.000i	0.0569048	−	0.0328540i
$306$	−841.777	+	486.000i	−0.157259	+	0.0907934i
$307$		−	10388.0i		−	1.93119i	−0.260056	−	0.965594i	$-0.583741\pi$
$307$		−	10388.0i		−	1.93119i	0.260056	−	0.965594i	$-0.416259\pi$
$308$	130.000	+	225.167i	0.0240501	+	0.0416560i
$309$	−1932.00	+	3346.32i	−0.355688	+	0.616070i
$310$	360.267	+	208.000i	0.0660057	+	0.0381084i
$311$	7272.00			1.32591			0.662954	−	0.748660i	$-0.269303\pi$
$311$	7272.00			1.32591			0.662954	+	0.748660i	$0.269303\pi$
$312$		0			0
$313$	7910.00			1.42843			0.714217	−	0.699925i	$-0.246783\pi$
$313$	7910.00			1.42843			0.714217	+	0.699925i	$0.246783\pi$
$314$	−3280.50	−	1894.00i	−0.589585	−	0.340397i
$315$	−90.0000	+	155.885i	−0.0160982	+	0.0278829i
$316$	1528.00	+	2646.57i	0.272015	+	0.471144i
$317$			7398.00i			1.31077i	0.755296	+	0.655383i	$0.227493\pi$
$317$			7398.00i			1.31077i	−0.755296	+	0.655383i	$0.772507\pi$
$318$	3211.22	−	1854.00i	0.566278	−	0.326941i
$319$	146.358	−	84.5000i	0.0256881	−	0.0148310i
$320$		−	128.000i		−	0.0223607i
$321$	1915.50	+	3317.74i	0.333062	+	0.576880i
$322$	−935.000	+	1619.47i	−0.161818	+	0.280278i
$323$	1753.70	+	1012.50i	0.302101	+	0.174418i
$324$	−324.000			−0.0555556
$325$		0			0
$326$	1970.00			0.334688
$327$	2146.01	+	1239.00i	0.362920	+	0.209532i
$328$	780.000	−	1351.00i	0.131306	−	0.227428i
$329$	−970.000	−	1680.09i	−0.162547	−	0.281539i
$330$			156.000i			0.0260228i
$331$	−2058.54	+	1188.50i	−0.341836	+	0.197359i	−0.661084	−	0.750312i	$-0.729903\pi$
$331$	−2058.54	+	1188.50i	−0.341836	+	0.197359i	0.319248	+	0.947671i	$0.396570\pi$
$332$	2535.72	−	1464.00i	0.419174	−	0.242010i
$333$			7614.00i			1.25299i
$334$	−2355.00	−	4078.98i	−0.385808	−	0.668239i
$335$	817.000	−	1415.09i	0.133246	−	0.230789i
$336$	207.846	+	120.000i	0.0337468	+	0.0194837i
$337$	7618.00			1.23139			0.615696	−	0.787984i	$-0.288875\pi$
$337$	7618.00			1.23139			0.615696	+	0.787984i	$0.288875\pi$
$338$		0			0
$339$	−2841.00			−0.455168
$340$	−187.061	−	108.000i	−0.0298377	−	0.0172268i
$341$	676.000	−	1170.87i	0.107353	−	0.185941i
$342$	1350.00	+	2338.27i	0.213449	+	0.369705i
$343$			3305.00i			0.520272i
$344$	−1378.71	+	796.000i	−0.216091	+	0.124760i
$345$	−971.681	+	561.000i	−0.151633	+	0.0875456i
$346$		−	7778.00i		−	1.20852i
$347$	−187.500	−	324.760i	−0.0290073	−	0.0502421i	0.851157	−	0.524911i	$-0.175901\pi$
$347$	−187.500	−	324.760i	−0.0290073	−	0.0502421i	−0.880165	+	0.474669i	$0.842568\pi$
$348$	78.0000	−	135.100i	0.0120151	−	0.0208107i
$349$	8423.83	+	4863.50i	1.29203	+	0.745952i	0.979013	−	0.203797i	$-0.0653282\pi$
$349$	8423.83	+	4863.50i	1.29203	+	0.745952i	0.313013	+	0.949749i	$0.398662\pi$
$350$	1210.00			0.184792
$351$		0			0
$352$	−416.000			−0.0629911
$353$	−1959.82	−	1131.50i	−0.295497	−	0.170605i	0.344921	−	0.938632i	$-0.387906\pi$
$353$	−1959.82	−	1131.50i	−0.295497	−	0.170605i	−0.640418	+	0.768026i	$0.721239\pi$
$354$	−1473.00	+	2551.31i	−0.221156	+	0.383053i
$355$	79.0000	+	136.832i	0.0118109	+	0.0204572i
$356$		−	4164.00i		−	0.619920i
$357$	350.740	−	202.500i	0.0519976	−	0.0300208i
$358$	3860.74	−	2229.00i	0.569962	−	0.329068i
$359$			4488.00i			0.659798i	0.944016	+	0.329899i	$0.107015\pi$
$359$			4488.00i			0.659798i	−0.944016	+	0.329899i	$0.892985\pi$
$360$	−144.000	−	249.415i	−0.0210819	−	0.0365148i
$361$	−617.000	+	1068.68i	−0.0899548	+	0.155806i
$362$	1797.87	+	1038.00i	0.261033	+	0.150707i
$363$	−3486.00			−0.504043
$364$		0			0
$365$	460.000			0.0659658
$366$	−909.327	−	525.000i	−0.129867	−	0.0749787i
$367$	813.500	−	1409.02i	0.115707	−	0.200410i	−0.802355	−	0.596847i	$-0.796420\pi$
$367$	813.500	−	1409.02i	0.115707	−	0.200410i	0.918062	+	0.396437i	$0.129753\pi$
$368$	−1496.00	−	2591.15i	−0.211914	−	0.367046i
$369$		−	3510.00i		−	0.495185i
$370$	−1465.31	+	846.000i	−0.205887	+	0.118869i
$371$	2676.02	−	1545.00i	0.374480	−	0.216206i
$372$		−	1248.00i		−	0.173940i
$373$	−1493.50	−	2586.82i	−0.207320	−	0.359089i	0.743549	−	0.668681i	$-0.233141\pi$
$373$	−1493.50	−	2586.82i	−0.207320	−	0.359089i	−0.950870	+	0.309592i	$0.899808\pi$
$374$	−351.000	+	607.950i	−0.0485288	+	0.0840544i
$375$	1278.25	+	738.000i	0.176023	+	0.101627i
$376$	3104.00			0.425736
$377$		0			0
$378$	1350.00			0.183694
$379$	7679.05	+	4433.50i	1.04076	+	0.600880i	0.920047	−	0.391808i	$-0.128150\pi$
$379$	7679.05	+	4433.50i	1.04076	+	0.600880i	0.120708	+	0.992688i	$0.461484\pi$
$380$	−300.000	+	519.615i	−0.0404991	+	0.0701466i
$381$	−1765.50	−	3057.94i	−0.237400	−	0.411188i
$382$			4282.00i			0.573524i
$383$	9875.29	−	5701.50i	1.31750	−	0.760661i	0.334177	−	0.942510i	$-0.391542\pi$
$383$	9875.29	−	5701.50i	1.31750	−	0.760661i	0.983326	+	0.181850i	$0.0582085\pi$
$384$	−332.554	+	192.000i	−0.0441942	+	0.0255155i
$385$			130.000i			0.0172089i
$386$	2627.00	+	4550.10i	0.346401	+	0.599984i
$387$	−1791.00	+	3102.10i	−0.235250	+	0.407464i
$388$	−336.018	−	194.000i	−0.0439658	−	0.0253837i
$389$	−2622.00			−0.341750			−0.170875	−	0.985293i	$-0.554659\pi$
$389$	−2622.00			−0.341750			−0.170875	+	0.985293i	$0.554659\pi$
$390$		0			0
$391$	−5049.00			−0.653041
$392$	−2203.17	−	1272.00i	−0.283869	−	0.163892i
$393$	−2130.00	+	3689.27i	−0.273395	+	0.473534i
$394$	−1203.00	−	2083.66i	−0.153823	−	0.266429i
$395$			1528.00i			0.194638i
$396$	−810.600	+	468.000i	−0.102864	+	0.0593886i
$397$	−570.711	+	329.500i	−0.0721490	+	0.0416552i	−0.535641	−	0.844446i	$-0.679930\pi$
$397$	−570.711	+	329.500i	−0.0721490	+	0.0416552i	0.463492	+	0.886101i	$0.346596\pi$
$398$			1486.00i			0.187152i
$399$	−562.500	−	974.279i	−0.0705770	−	0.122243i
$400$	−968.000	+	1676.63i	−0.121000	+	0.209578i
$401$	−12717.6	−	7342.50i	−1.58376	−	0.914381i	−0.994304	−	0.106577i	$-0.966011\pi$
$401$	−12717.6	−	7342.50i	−1.58376	−	0.914381i	−0.589451	−	0.807804i	$-0.700656\pi$
$402$	−4902.00			−0.608183
$403$		0			0
$404$	−3236.00			−0.398507
$405$	−140.296	−	81.0000i	−0.0172133	−	0.00993808i
$406$	65.0000	−	112.583i	0.00794556	−	0.0137621i
$407$	2749.50	+	4762.27i	0.334859	+	0.579993i
$408$			648.000i			0.0786294i
$409$	−6780.11	+	3914.50i	−0.819694	+	0.473251i	−0.850311	−	0.526280i	$-0.823586\pi$
$409$	−6780.11	+	3914.50i	−0.819694	+	0.473251i	0.0306167	+	0.999531i	$0.490253\pi$
$410$	675.500	−	390.000i	0.0813672	−	0.0469774i
$411$		−	7227.00i		−	0.867352i
$412$	−2576.00	−	4461.76i	−0.308035	−	0.533532i
$413$	−1227.50	+	2126.09i	−0.146250	+	0.253313i
$414$	−5830.08	−	3366.00i	−0.692109	−	0.399589i
$415$	1464.00			0.173169
$416$		0			0
$417$	−8481.00			−0.995962
$418$	1688.75	+	975.000i	0.197606	+	0.114088i
$419$	1459.50	−	2527.93i	0.170170	−	0.294743i	−0.768309	−	0.640079i	$-0.778902\pi$
$419$	1459.50	−	2527.93i	0.170170	−	0.294743i	0.938479	+	0.345336i	$0.112235\pi$
$420$	60.0000	+	103.923i	0.00697071	+	0.0120736i
$421$		−	3110.00i		−	0.360029i	−0.983664	−	0.180014i	$-0.942386\pi$
$421$		−	3110.00i		−	0.360029i	0.983664	−	0.180014i	$-0.0576144\pi$
$422$	614.878	−	355.000i	0.0709284	−	0.0409505i
$423$	6048.32	−	3492.00i	0.695223	−	0.401387i
$424$			4944.00i			0.566278i
$425$	1633.50	+	2829.30i	0.186439	+	0.322921i
$426$	237.000	−	410.496i	0.0269547	−	0.0466869i
$427$	−757.772	−	437.500i	−0.0858810	−	0.0495834i
$428$	−5108.00			−0.576880
$429$		0			0
$430$	−796.000			−0.0892710
$431$	7911.14	+	4567.50i	0.884145	+	0.510461i	0.872023	−	0.489465i	$-0.162808\pi$
$431$	7911.14	+	4567.50i	0.884145	+	0.510461i	0.0121219	+	0.999927i	$0.496141\pi$
$432$	−1080.00	+	1870.61i	−0.120281	+	0.208333i
$433$	−5834.50	−	10105.7i	−0.647548	−	1.12159i	−0.983707	−	0.179780i	$-0.942461\pi$
$433$	−5834.50	−	10105.7i	−0.647548	−	1.12159i	0.336159	−	0.941805i	$-0.390872\pi$
$434$		−	1040.00i		−	0.115027i
$435$	67.5500	−	39.0000i	0.00744546	−	0.00429864i
$436$	−2861.35	+	1652.00i	−0.314298	+	0.181460i
$437$			14025.0i			1.53526i
$438$	−690.000	−	1195.12i	−0.0752728	−	0.130376i
$439$	6764.50	−	11716.5i	0.735426	−	1.27380i	−0.219110	−	0.975700i	$-0.570315\pi$
$439$	6764.50	−	11716.5i	0.735426	−	1.27380i	0.954536	−	0.298095i	$-0.0963512\pi$
$440$	−180.133	−	104.000i	−0.0195171	−	0.0112682i
$441$	−5724.00			−0.618076
$442$		0			0
$443$	−1932.00			−0.207206			−0.103603	−	0.994619i	$-0.533037\pi$
$443$	−1932.00			−0.207206			−0.103603	+	0.994619i	$0.533037\pi$
$444$	4395.94	+	2538.00i	0.469870	+	0.271280i
$445$	1041.00	−	1803.06i	0.110895	−	0.192075i
$446$	2283.00	+	3954.27i	0.242384	+	0.419821i
$447$		−	2565.00i		−	0.271410i
$448$	−277.128	+	160.000i	−0.0292256	+	0.0168734i
$449$	4639.30	−	2678.50i	0.487621	−	0.281528i	−0.235966	−	0.971761i	$-0.575825\pi$
$449$	4639.30	−	2678.50i	0.487621	−	0.281528i	0.723587	+	0.690233i	$0.242492\pi$
$450$			4356.00i			0.456320i
$451$	−1267.50	−	2195.37i	−0.132338	−	0.229215i
$452$	1894.00	−	3280.50i	0.197094	−	0.341376i
$453$	−5362.43	−	3096.00i	−0.556179	−	0.321110i
$454$	4902.00			0.506745
$455$		0			0
$456$	1800.00			0.184852
$457$	−16800.0	−	9699.50i	−1.71963	−	0.992830i	−0.919582	−	0.392897i	$-0.871473\pi$
$457$	−16800.0	−	9699.50i	−1.71963	−	0.992830i	−0.800050	−	0.599933i	$-0.795194\pi$
$458$	−1878.00	+	3252.79i	−0.191601	+	0.331862i
$459$	1822.50	+	3156.66i	0.185331	+	0.321003i
$460$		−	1496.00i		−	0.151633i
$461$	−13465.8	+	7774.50i	−1.36045	+	0.785455i	−0.989683	−	0.143273i	$-0.954237\pi$
$461$	−13465.8	+	7774.50i	−1.36045	+	0.785455i	−0.370764	+	0.928727i	$0.620904\pi$
$462$	337.750	−	195.000i	0.0340120	−	0.0196368i
$463$		−	4072.00i		−	0.408730i	−0.978895	−	0.204365i	$-0.934487\pi$
$463$		−	4072.00i		−	0.408730i	0.978895	−	0.204365i	$-0.0655129\pi$
$464$	104.000	+	180.133i	0.0104053	+	0.0180226i
$465$	312.000	−	540.400i	0.0311154	−	0.0538934i
$466$	−2823.24	−	1630.00i	−0.280653	−	0.162035i
$467$	−15224.0			−1.50853			−0.754264	−	0.656571i	$-0.772006\pi$
$467$	−15224.0			−1.50853			−0.754264	+	0.656571i	$0.772006\pi$
$468$		0			0
$469$	−4085.00			−0.402191
$470$	1344.07	+	776.000i	0.131909	+	0.0761579i
$471$	−2841.00	+	4920.76i	−0.277933	+	0.481394i
$472$	−1964.00	−	3401.75i	−0.191526	−	0.331733i
$473$			2587.00i			0.251481i
$474$	3969.86	−	2292.00i	0.384687	−	0.222099i
$475$	7859.18	−	4537.50i	0.759166	−	0.438305i
$476$			540.000i			0.0519976i
$477$	5562.00	+	9633.67i	0.533892	+	0.924728i
$478$	5544.00	−	9602.49i	0.530495	−	0.918844i
$479$	−8950.37	−	5167.50i	−0.853764	−	0.492921i	0.00815506	−	0.999967i	$-0.497404\pi$
$479$	−8950.37	−	5167.50i	−0.853764	−	0.492921i	−0.861919	+	0.507046i	$0.830737\pi$
$480$	−192.000			−0.0182574
$481$		0			0
$482$	−11046.0			−1.04384
$483$	2429.20	+	1402.50i	0.228846	+	0.132124i
$484$	2324.00	−	4025.29i	0.218257	−	0.378032i
$485$	−97.0000	−	168.009i	−0.00908153	−	0.0157297i
$486$			7776.00i			0.725775i
$487$	5590.19	−	3227.50i	0.520156	−	0.300312i	−0.216843	−	0.976207i	$-0.569576\pi$
$487$	5590.19	−	3227.50i	0.520156	−	0.300312i	0.736998	+	0.675894i	$0.236243\pi$
$488$	1212.44	−	700.000i	0.112468	−	0.0649334i
$489$		−	2955.00i		−	0.273271i
$490$	−636.000	−	1101.58i	−0.0586358	−	0.101560i
$491$	3888.50	−	6735.08i	0.357404	−	0.619043i	−0.630122	−	0.776496i	$-0.716995\pi$
$491$	3888.50	−	6735.08i	0.357404	−	0.619043i	0.987526	+	0.157454i	$0.0503285\pi$
$492$	−2026.50	−	1170.00i	−0.185694	−	0.107211i
$493$	351.000			0.0320654
$494$		0			0
$495$	−468.000			−0.0424950
$496$	1441.07	+	832.000i	0.130455	+	0.0753184i
$497$	197.500	−	342.080i	0.0178251	−	0.0308740i
$498$	−2196.00	−	3803.58i	−0.197601	−	0.342254i
$499$		−	3044.00i		−	0.273082i	−0.990634	−	0.136541i	$-0.956401\pi$
$499$		−	3044.00i		−	0.273082i	0.990634	−	0.136541i	$-0.0435986\pi$
$500$	−1704.34	+	984.000i	−0.152441	+	0.0880116i
$501$	−6118.47	+	3532.50i	−0.545615	+	0.315011i
$502$			4350.00i			0.386753i
$503$	−5673.50	−	9826.79i	−0.502920	−	0.871083i	−0.999994	−	0.00337525i	$-0.998926\pi$
$503$	−5673.50	−	9826.79i	−0.502920	−	0.871083i	0.497074	−	0.867708i	$-0.334408\pi$
$504$	−360.000	+	623.538i	−0.0318168	+	0.0551083i
$505$	−1401.23	−	809.000i	−0.123473	−	0.0712872i
$506$	−4862.00			−0.427159
$507$		0			0
$508$	4708.00			0.411188
$509$	−629.600	−	363.500i	−0.0548262	−	0.0316539i	0.472336	−	0.881418i	$-0.343411\pi$
$509$	−629.600	−	363.500i	−0.0548262	−	0.0316539i	−0.527163	+	0.849764i	$0.676744\pi$
$510$	−162.000	+	280.592i	−0.0140656	+	0.0243624i
$511$	−575.000	−	995.929i	−0.0497779	−	0.0862178i
$512$		−	512.000i		−	0.0441942i
$513$	8768.51	−	5062.50i	0.754657	−	0.435701i
$514$	−9846.71	+	5685.00i	−0.844980	+	0.487849i
$515$		−	2576.00i		−	0.220412i
$516$	1194.00	+	2068.07i	0.101866	+	0.176437i
$517$	2522.00	−	4368.23i	0.214540	−	0.371595i
$518$	3663.29	+	2115.00i	0.310725	+	0.179397i
$519$	−11667.0			−0.986752
$520$		0			0
$521$	9582.00			0.805749			0.402874	−	0.915255i	$-0.368011\pi$
$521$	9582.00			0.805749			0.402874	+	0.915255i	$0.368011\pi$
$522$	405.300	+	234.000i	0.0339837	+	0.0196205i
$523$	5191.50	−	8991.94i	0.434051	−	0.751798i	−0.563167	−	0.826343i	$-0.690417\pi$
$523$	5191.50	−	8991.94i	0.434051	−	0.751798i	0.997218	+	0.0745454i	$0.0237506\pi$
$524$	−2840.00	−	4919.02i	−0.236767	−	0.410093i
$525$		−	1815.00i		−	0.150882i
$526$	−10595.0	+	6117.00i	−0.878255	+	0.507061i
$527$	2431.80	−	1404.00i	0.201007	−	0.116052i
$528$			624.000i			0.0514320i
$529$	−11401.0	−	19747.1i	−0.937043	−	1.62301i
$530$	−1236.00	+	2140.81i	−0.101299	+	0.175455i
$531$	−7653.93	−	4419.00i	−0.625522	−	0.361146i
$532$	1500.00			0.122243
$533$		0			0
$534$	−6246.00			−0.506163
$535$	−2211.83	−	1277.00i	−0.178740	−	0.103195i
$536$	3268.00	−	5660.34i	0.263351	−	0.456137i
$537$	−3343.50	−	5791.11i	−0.268683	−	0.465372i
$538$			10218.0i			0.818828i
$539$	−3580.15	+	2067.00i	−0.286100	+	0.165180i
$540$	−935.307	+	540.000i	−0.0745356	+	0.0430331i
$541$		−	12230.0i		−	0.971920i	−0.873981	−	0.485960i	$-0.838470\pi$
$541$		−	12230.0i		−	0.971920i	0.873981	−	0.485960i	$-0.161530\pi$
$542$	7549.00	+	13075.3i	0.598261	+	1.03622i
$543$	1557.00	−	2696.80i	0.123052	−	0.213132i
$544$	−748.246	−	432.000i	−0.0589720	−	0.0340475i
$545$	−1652.00			−0.129842
$546$		0			0
$547$	−14636.0			−1.14404			−0.572020	−	0.820239i	$-0.693840\pi$
$547$	−14636.0			−1.14404			−0.572020	+	0.820239i	$0.693840\pi$
$548$	8345.02	+	4818.00i	0.650514	+	0.375574i
$549$	1575.00	−	2727.98i	0.122440	−	0.212072i
$550$	1573.00	+	2724.52i	0.121951	+	0.211225i
$551$		−	975.000i		−	0.0753837i
$552$	−3886.72	+	2244.00i	−0.299692	+	0.173027i
$553$	3308.22	−	1910.00i	0.254394	−	0.146874i
$554$		−	1962.00i		−	0.150465i
$555$	1269.00	+	2197.97i	0.0970559	+	0.168106i
$556$	5654.00	−	9793.02i	0.431264	−	0.746972i
$557$	−662.509	−	382.500i	−0.0503975	−	0.0290970i	0.474590	−	0.880207i	$-0.342597\pi$
$557$	−662.509	−	382.500i	−0.0503975	−	0.0290970i	−0.524987	+	0.851110i	$0.675930\pi$
$558$	3744.00			0.284043
$559$		0			0
$560$	−160.000			−0.0120736
$561$	911.925	+	526.500i	0.0686301	+	0.0396236i
$562$	−2762.00	+	4783.92i	−0.207309	+	0.359071i
$563$	2957.50	+	5122.54i	0.221392	+	0.383462i	0.955231	−	0.295861i	$-0.0956066\pi$
$563$	2957.50	+	5122.54i	0.221392	+	0.383462i	−0.733839	+	0.679324i	$0.762273\pi$
$564$		−	4656.00i		−	0.347612i
$565$	1640.25	−	947.000i	0.122134	−	0.0705143i
$566$	6798.30	−	3925.00i	0.504865	−	0.291484i
$567$			405.000i			0.0299972i
$568$	316.000	+	547.328i	0.0233434	+	0.0404320i
$569$	−608.500	+	1053.95i	−0.0448324	+	0.0776520i	−0.887571	−	0.460671i	$-0.847609\pi$
$569$	−608.500	+	1053.95i	−0.0448324	+	0.0776520i	0.842738	+	0.538323i	$0.180942\pi$
$570$	779.423	+	450.000i	0.0572744	+	0.0330674i
$571$	23436.0			1.71763			0.858814	−	0.512287i	$-0.171202\pi$
$571$	23436.0			1.71763			0.858814	+	0.512287i	$0.171202\pi$
$572$		0			0
$573$	6423.00			0.468280
$574$	−1688.75	−	975.000i	−0.122800	−	0.0708985i
$575$	−11313.5	+	19595.6i	−0.820531	+	1.42120i
$576$	−576.000	−	997.661i	−0.0416667	−	0.0721688i
$577$			7854.00i			0.566666i	0.959022	+	0.283333i	$0.0914402\pi$
$577$			7854.00i			0.566666i	−0.959022	+	0.283333i	$0.908560\pi$
$578$	7246.90	−	4184.00i	0.521507	−	0.301092i
$579$	6825.15	−	3940.50i	0.489885	−	0.282835i
$580$			104.000i			0.00744546i
$581$	−1830.00	−	3169.65i	−0.130673	−	0.226333i
$582$	−291.000	+	504.027i	−0.0207257	+	0.0358979i
$583$	6957.65	+	4017.00i	0.494265	+	0.285364i
$584$	1840.00			0.130376
$585$		0			0
$586$	−15422.0			−1.08716
$587$	−14751.0	−	8516.50i	−1.03721	−	0.598831i	−0.118165	−	0.992994i	$-0.537701\pi$
$587$	−14751.0	−	8516.50i	−1.03721	−	0.598831i	−0.919040	+	0.394163i	$0.871034\pi$
$588$	−1908.00	+	3304.75i	−0.133817	+	0.231778i
$589$	−3900.00	−	6755.00i	−0.272830	−	0.472555i
$590$		−	1964.00i		−	0.137045i
$591$	−3125.49	+	1804.50i	−0.217539	+	0.125596i
$592$	−5861.26	+	3384.00i	−0.406919	+	0.234935i
$593$			14506.0i			1.00454i	0.864712	+	0.502268i	$0.167501\pi$
$593$			14506.0i			1.00454i	−0.864712	+	0.502268i	$0.832499\pi$
$594$	1755.00	+	3039.75i	0.121226	+	0.209970i
$595$	−135.000	+	233.827i	−0.00930161	+	0.0161109i
$596$	2961.81	+	1710.00i	0.203558	+	0.117524i
$597$	2229.00			0.152809
$598$		0			0
$599$	15388.0			1.04964			0.524822	−	0.851212i	$-0.324132\pi$
$599$	15388.0			1.04964			0.524822	+	0.851212i	$0.324132\pi$
$600$	2514.94	+	1452.00i	0.171120	+	0.0987961i
$601$	3038.50	−	5262.84i	0.206228	−	0.357197i	−0.744295	−	0.667851i	$-0.767214\pi$
$601$	3038.50	−	5262.84i	0.206228	−	0.357197i	0.950523	+	0.310653i	$0.100548\pi$
$602$	995.000	+	1723.39i	0.0673641	+	0.116678i
$603$		−	14706.0i		−	0.993159i
$604$	7149.91	−	4128.00i	0.481665	−	0.278089i
$605$	2012.64	−	1162.00i	0.135249	−	0.0780860i
$606$			4854.00i			0.325380i
$607$	−5107.50	−	8846.45i	−0.341527	−	0.591543i	0.643189	−	0.765707i	$-0.277611\pi$
$607$	−5107.50	−	8846.45i	−0.341527	−	0.591543i	−0.984717	+	0.174165i	$0.944277\pi$
$608$	−1200.00	+	2078.46i	−0.0800435	+	0.138639i
$609$	−168.875	−	97.5000i	−0.0112367	−	0.00648752i
$610$	700.000			0.0464626
$611$		0			0
$612$	−1944.00			−0.128401
$613$	2993.85	+	1728.50i	0.197260	+	0.113888i	0.595377	−	0.803447i	$-0.297003\pi$
$613$	2993.85	+	1728.50i	0.197260	+	0.113888i	−0.398117	+	0.917335i	$0.630336\pi$
$614$	10388.0	−	17992.5i	0.682778	−	1.18261i
$615$	−585.000	−	1013.25i	−0.0383569	−	0.0664361i
$616$			520.000i			0.0340120i
$617$	−6208.54	+	3584.50i	−0.405099	+	0.233884i	−0.688682	−	0.725064i	$-0.741810\pi$
$617$	−6208.54	+	3584.50i	−0.405099	+	0.233884i	0.283583	+	0.958948i	$0.408477\pi$
$618$	−6692.64	+	3864.00i	−0.435627	+	0.251510i
$619$		−	20212.0i		−	1.31242i	−0.754578	−	0.656211i	$-0.772158\pi$
$619$		−	20212.0i		−	1.31242i	0.754578	−	0.656211i	$-0.227842\pi$
$620$	416.000	+	720.533i	0.0269467	+	0.0466731i
$621$	−12622.5	+	21862.8i	−0.815658	+	1.41276i
$622$	12595.5	+	7272.00i	0.811949	+	0.468779i
$623$	−5205.00			−0.334725
$624$		0			0
$625$	14141.0			0.905024
$626$	13700.5	+	7910.00i	0.874733	+	0.505027i
$627$	1462.50	−	2533.12i	0.0931525	−	0.161345i
$628$	−3788.00	−	6561.01i	−0.240697	−	0.416899i
$629$			11421.0i			0.723983i
$630$	−311.769	+	180.000i	−0.0197162	+	0.0113831i
$631$	7746.60	−	4472.50i	0.488728	−	0.282167i	−0.235319	−	0.971918i	$-0.575613\pi$
$631$	7746.60	−	4472.50i	0.488728	−	0.282167i	0.724046	+	0.689751i	$0.242280\pi$
$632$			6112.00i			0.384687i
$633$	−532.500	−	922.317i	−0.0334360	−	0.0579128i
$634$	−7398.00	+	12813.7i	−0.463426	+	0.802677i
$635$	2038.62	+	1177.00i	0.127402	+	0.0735556i
$636$	7416.00			0.462364
$637$		0			0
$638$	338.000			0.0209742
$639$	1231.49	+	711.000i	0.0762393	+	0.0440168i
$640$	128.000	−	221.703i	0.00790569	−	0.0136931i
$641$	14121.5	+	24459.2i	0.870149	+	1.50714i	0.861842	+	0.507177i	$0.169311\pi$
$641$	14121.5	+	24459.2i	0.870149	+	1.50714i	0.00830761	+	0.999965i	$0.497356\pi$
$642$			7662.00i			0.471020i
$643$	4530.18	−	2615.50i	0.277843	−	0.160413i	−0.354604	−	0.935017i	$-0.615384\pi$
$643$	4530.18	−	2615.50i	0.277843	−	0.160413i	0.632446	+	0.774604i	$0.282051\pi$
$644$	−3238.94	+	1870.00i	−0.198186	+	0.114423i
$645$			1194.00i			0.0728895i
$646$	2025.00	+	3507.40i	0.123332	+	0.213618i
$647$	−2435.50	+	4218.41i	−0.147990	+	0.256326i	−0.930484	−	0.366332i	$-0.880614\pi$
$647$	−2435.50	+	4218.41i	−0.147990	+	0.256326i	0.782495	+	0.622657i	$0.213947\pi$
$648$	−561.184	−	324.000i	−0.0340207	−	0.0196419i
$649$	−6383.00			−0.386063
$650$		0			0
$651$	−1560.00			−0.0939189
$652$	3412.14	+	1970.00i	0.204954	+	0.118330i
$653$	−6127.50	+	10613.1i	−0.367209	+	0.636025i	−0.989128	−	0.147057i	$-0.953020\pi$
$653$	−6127.50	+	10613.1i	−0.367209	+	0.636025i	0.621919	+	0.783082i	$0.286353\pi$
$654$	2478.00	+	4292.02i	0.148161	+	0.256623i
$655$		−	2840.00i		−	0.169417i
$656$	2702.00	−	1560.00i	0.160816	−	0.0928472i
$657$	3585.35	−	2070.00i	0.212904	−	0.122920i
$658$		−	3880.00i		−	0.229876i
$659$	1072.50	+	1857.62i	0.0633971	+	0.109807i	0.895982	−	0.444091i	$-0.146473\pi$
$659$	1072.50	+	1857.62i	0.0633971	+	0.109807i	−0.832585	+	0.553898i	$0.813140\pi$
$660$	−156.000	+	270.200i	−0.00920044	+	0.0159356i
$661$	1828.18	+	1055.50i	0.107576	+	0.0621092i	0.552823	−	0.833299i	$-0.313551\pi$
$661$	1828.18	+	1055.50i	0.107576	+	0.0621092i	−0.445247	+	0.895408i	$0.646884\pi$
$662$	−4754.00			−0.279108
$663$		0			0
$664$	5856.00			0.342254
$665$	649.519	+	375.000i	0.0378756	+	0.0218675i
$666$	−7614.00	+	13187.8i	−0.442998	+	0.767295i
$667$	1215.50	+	2105.31i	0.0705612	+	0.122216i
$668$		−	9420.00i		−	0.545615i
$669$	5931.41	−	3424.50i	0.342782	−	0.197906i
$670$	2830.17	−	1634.00i	0.163193	−	0.0942193i
$671$		−	2275.00i		−	0.130887i
$672$	240.000	+	415.692i	0.0137771	+	0.0238626i
$673$	−11636.5	+	20155.0i	−0.666499	+	1.15441i	0.312377	+	0.949958i	$0.398875\pi$
$673$	−11636.5	+	20155.0i	−0.666499	+	1.15441i	−0.978876	+	0.204453i	$0.934459\pi$
$674$	13194.8	+	7618.00i	0.754070	+	0.435363i
$675$	16335.0			0.931458
$676$		0			0
$677$	−5910.00			−0.335509			−0.167755	−	0.985829i	$-0.553652\pi$
$677$	−5910.00			−0.335509			−0.167755	+	0.985829i	$0.553652\pi$
$678$	−4920.76	−	2841.00i	−0.278732	−	0.160926i
$679$	−242.500	+	420.022i	−0.0137059	+	0.0237393i
$680$	−216.000	−	374.123i	−0.0121812	−	0.0210985i
$681$		−	7353.00i		−	0.413756i
$682$	2341.73	−	1352.00i	0.131480	−	0.0759102i
$683$	−14503.3	+	8373.50i	−0.812525	+	0.469111i	−0.847832	−	0.530265i	$-0.822092\pi$
$683$	−14503.3	+	8373.50i	−0.812525	+	0.469111i	0.0353071	+	0.999377i	$0.488759\pi$
$684$			5400.00i			0.301863i
$685$	2409.00	+	4172.51i	0.134370	+	0.232735i
$686$	−3305.00	+	5724.43i	−0.183944	+	0.318600i
$687$	4879.19	+	2817.00i	0.270964	+	0.156441i
$688$	−3184.00			−0.176437
$689$		0			0
$690$	−2244.00			−0.123808
$691$	−8927.86	−	5154.50i	−0.491507	−	0.283772i	0.233692	−	0.972311i	$-0.424919\pi$
$691$	−8927.86	−	5154.50i	−0.491507	−	0.283772i	−0.725200	+	0.688539i	$0.758253\pi$
$692$	7778.00	−	13471.9i	0.427276	−	0.740064i
$693$	585.000	+	1013.25i	0.0320668	+	0.0555414i
$694$		−	750.000i		−	0.0410225i
$695$	4896.51	−	2827.00i	0.267245	−	0.154294i
$696$	270.200	−	156.000i	0.0147154	−	0.00849593i
$697$		−	5265.00i		−	0.286121i
$698$	9727.00	+	16847.7i	0.527468	+	0.913601i
$699$	−2445.00	+	4234.86i	−0.132301	+	0.229152i
$700$	2095.78	+	1210.00i	0.113162	+	0.0653339i
$701$	24294.0			1.30895			0.654473	−	0.756085i	$-0.272890\pi$
$701$	24294.0			1.30895			0.654473	+	0.756085i	$0.272890\pi$
$702$		0			0
$703$	31725.0			1.70204
$704$	−720.533	−	416.000i	−0.0385740	−	0.0222707i
$705$	1164.00	−	2016.11i	0.0621827	−	0.107704i
$706$	−2263.00	−	3919.63i	−0.120636	−	0.208948i
$707$			4045.00i			0.215174i
$708$	−5102.62	+	2946.00i	−0.270859	+	0.156381i
$709$	−10963.0	+	6329.50i	−0.580712	+	0.335274i	−0.761416	−	0.648263i	$-0.775496\pi$
$709$	−10963.0	+	6329.50i	−0.580712	+	0.335274i	0.180704	+	0.983537i	$0.442162\pi$
$710$			316.000i			0.0167032i
$711$	6876.00	+	11909.6i	0.362687	+	0.628192i
$712$	4164.00	−	7212.26i	0.219175	−	0.379622i
$713$	16842.5	+	9724.00i	0.884650	+	0.510753i
$714$	810.000			0.0424559
$715$		0			0
$716$	8916.00			0.465372
$717$	−14403.7	−	8316.00i	−0.750233	−	0.433147i
$718$	−4488.00	+	7773.44i	−0.233274	+	0.404042i
$719$	6545.50	+	11337.1i	0.339508	+	0.588044i	0.984340	−	0.176279i	$-0.0564062\pi$
$719$	6545.50	+	11337.1i	0.339508	+	0.588044i	−0.644833	+	0.764324i	$0.723073\pi$
$720$		−	576.000i		−	0.0298142i
$721$	−5577.20	+	3220.00i	−0.288080	+	0.166323i
$722$	−2137.35	+	1234.00i	−0.110172	+	0.0636077i
$723$			16569.0i			0.852293i
$724$	2076.00	+	3595.74i	0.106566	+	0.184578i
$725$	786.500	−	1362.26i	0.0402895	−	0.0697834i
$726$	−6037.93	−	3486.00i	−0.308662	−	0.178206i
$727$	−10792.0			−0.550555			−0.275277	−	0.961365i	$-0.588770\pi$
$727$	−10792.0			−0.550555			−0.275277	+	0.961365i	$0.588770\pi$
$728$		0			0
$729$	9477.00			0.481481
$730$	796.743	+	460.000i	0.0403956	+	0.0233224i
$731$	−2686.50	+	4653.15i	−0.135929	+	0.235435i
$732$	−1050.00	−	1818.65i	−0.0530179	−	0.0918297i
$733$		−	2698.00i		−	0.135952i	−0.997687	−	0.0679761i	$-0.978346\pi$
$733$		−	2698.00i		−	0.135952i	0.997687	−	0.0679761i	$-0.0216542\pi$
$734$	2818.05	−	1627.00i	0.141711	−	0.0818170i
$735$	−1652.38	+	954.000i	−0.0829236	+	0.0478759i
$736$		−	5984.00i		−	0.299692i
$737$	−5310.50	−	9198.06i	−0.265420	−	0.459721i
$738$	3510.00	−	6079.50i	0.175074	−	0.303238i
$739$	2460.38	+	1420.50i	0.122472	+	0.0707090i	0.559984	−	0.828503i	$-0.310807\pi$
$739$	2460.38	+	1420.50i	0.122472	+	0.0707090i	−0.437513	+	0.899212i	$0.644141\pi$
$740$	−3384.00			−0.168106
$741$		0			0
$742$	6180.00			0.305761
$743$	7959.64	+	4595.50i	0.393016	+	0.226908i	0.683466	−	0.729982i	$-0.260472\pi$
$743$	7959.64	+	4595.50i	0.393016	+	0.226908i	−0.290450	+	0.956890i	$0.593805\pi$
$744$	1248.00	−	2161.60i	0.0614972	−	0.106516i
$745$	855.000	+	1480.90i	0.0420467	+	0.0728270i
$746$		−	5974.00i		−	0.293195i
$747$	11410.8	−	6588.00i	0.558899	−	0.322680i
$748$	−1215.90	+	702.000i	−0.0594354	+	0.0343151i
$749$			6385.00i			0.311486i
$750$	1476.00	+	2556.51i	0.0718612	+	0.124467i
$751$	−829.500	+	1436.74i	−0.0403048	+	0.0698099i	−0.885474	−	0.464689i	$-0.846166\pi$
$751$	−829.500	+	1436.74i	−0.0403048	+	0.0698099i	0.845169	+	0.534499i	$0.179500\pi$
$752$	5376.29	+	3104.00i	0.260709	+	0.150520i
$753$	6525.00			0.315782
$754$		0			0
$755$	4128.00			0.198985
$756$	2338.27	+	1350.00i	0.112489	+	0.0649458i
$757$	6964.50	−	12062.9i	0.334384	−	0.579171i	−0.648982	−	0.760804i	$-0.724805\pi$
$757$	6964.50	−	12062.9i	0.334384	−	0.579171i	0.983366	+	0.181633i	$0.0581383\pi$
$758$	8867.00	+	15358.1i	0.424886	+	0.735925i
$759$			7293.00i			0.348774i
$760$	−1039.23	+	600.000i	−0.0496011	+	0.0286372i
$761$	−3972.46	+	2293.50i	−0.189227	+	0.109250i	−0.591620	−	0.806217i	$-0.701512\pi$
$761$	−3972.46	+	2293.50i	−0.189227	+	0.109250i	0.402394	+	0.915467i	$0.368178\pi$
$762$		−	7062.00i		−	0.335734i
$763$	2065.00	+	3576.68i	0.0979791	+	0.169705i
$764$	−4282.00	+	7416.64i	−0.202771	+	0.351210i
$765$	−841.777	−	486.000i	−0.0397837	−	0.0229691i
$766$	22806.0			1.07574
$767$		0			0
$768$	−768.000			−0.0360844
$769$	−12556.5	−	7249.50i	−0.588815	−	0.339953i	0.175814	−	0.984423i	$-0.443744\pi$
$769$	−12556.5	−	7249.50i	−0.588815	−	0.339953i	−0.764629	+	0.644471i	$0.777078\pi$
$770$	−130.000	+	225.167i	−0.00608425	+	0.0105382i

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000i q^{5} +(5.19615 - 3.00000i) q^{6} +(4.33013 - 2.50000i) q^{7} +8.00000i q^{8} +(9.00000 + 15.5885i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.50000 - 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000i q^{5} +(5.19615 - 3.00000i) q^{6} +(4.33013 - 2.50000i) q^{7} +8.00000i q^{8} +(9.00000 + 15.5885i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(11.2583 + 6.50000i) q^{11} +12.0000 q^{12} +10.0000 q^{14} +(5.19615 + 3.00000i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(13.5000 + 23.3827i) q^{17} +36.0000i q^{18} +(64.9519 - 37.5000i) q^{19} +(-6.92820 + 4.00000i) q^{20} -15.0000i q^{21} +(13.0000 + 22.5167i) q^{22} +(-93.5000 + 161.947i) q^{23} +(20.7846 + 12.0000i) q^{24} +121.000 q^{25} +135.000 q^{27} +(17.3205 + 10.0000i) q^{28} +(6.50000 - 11.2583i) q^{29} +(6.00000 + 10.3923i) q^{30} -104.000i q^{31} +(-27.7128 + 16.0000i) q^{32} +(33.7750 - 19.5000i) q^{33} +54.0000i q^{34} +(5.00000 + 8.66025i) q^{35} +(-36.0000 + 62.3538i) q^{36} +(366.329 + 211.500i) q^{37} +150.000 q^{38} -16.0000 q^{40} +(-168.875 - 97.5000i) q^{41} +(15.0000 - 25.9808i) q^{42} +(99.5000 + 172.339i) q^{43} +52.0000i q^{44} +(-31.1769 + 18.0000i) q^{45} +(-323.894 + 187.000i) q^{46} -388.000i q^{47} +(24.0000 + 41.5692i) q^{48} +(-159.000 + 275.396i) q^{49} +(209.578 + 121.000i) q^{50} +81.0000 q^{51} +618.000 q^{53} +(233.827 + 135.000i) q^{54} +(-13.0000 + 22.5167i) q^{55} +(20.0000 + 34.6410i) q^{56} -225.000i q^{57} +(22.5167 - 13.0000i) q^{58} +(-425.218 + 245.500i) q^{59} +24.0000i q^{60} +(-87.5000 - 151.554i) q^{61} +(104.000 - 180.133i) q^{62} +(77.9423 + 45.0000i) q^{63} -64.0000 q^{64} +78.0000 q^{66} +(-707.543 - 408.500i) q^{67} +(-54.0000 + 93.5307i) q^{68} +(280.500 + 485.840i) q^{69} +20.0000i q^{70} +(68.4160 - 39.5000i) q^{71} +(-124.708 + 72.0000i) q^{72} -230.000i q^{73} +(423.000 + 732.657i) q^{74} +(181.500 - 314.367i) q^{75} +(259.808 + 150.000i) q^{76} +65.0000 q^{77} +764.000 q^{79} +(-27.7128 - 16.0000i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-195.000 - 337.750i) q^{82} -732.000i q^{83} +(51.9615 - 30.0000i) q^{84} +(-46.7654 + 27.0000i) q^{85} +398.000i q^{86} +(-19.5000 - 33.7750i) q^{87} +(-52.0000 + 90.0666i) q^{88} +(-901.532 - 520.500i) q^{89} -72.0000 q^{90} -748.000 q^{92} +(-270.200 - 156.000i) q^{93} +(388.000 - 672.036i) q^{94} +(75.0000 + 129.904i) q^{95} +96.0000i q^{96} +(-84.0045 + 48.5000i) q^{97} +(-550.792 + 318.000i) q^{98} +234.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 8 q^{4} + 36 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 8 * q^4 + 36 * q^9	\( 4 q + 6 q^{3} + 8 q^{4} + 36 q^{9} - 8 q^{10} + 48 q^{12} + 40 q^{14} - 32 q^{16} + 54 q^{17} + 52 q^{22} - 374 q^{23} + 484 q^{25} + 540 q^{27} + 26 q^{29} + 24 q^{30} + 20 q^{35} - 144 q^{36} + 600 q^{38} - 64 q^{40} + 60 q^{42} + 398 q^{43} + 96 q^{48} - 636 q^{49} + 324 q^{51} + 2472 q^{53} - 52 q^{55} + 80 q^{56} - 350 q^{61} + 416 q^{62} - 256 q^{64} + 312 q^{66} - 216 q^{68} + 1122 q^{69} + 1692 q^{74} + 726 q^{75} + 260 q^{77} + 3056 q^{79} - 162 q^{81} - 780 q^{82} - 78 q^{87} - 208 q^{88} - 288 q^{90} - 2992 q^{92} + 1552 q^{94} + 300 q^{95}+O(q^{100}) \) 4 * q + 6 * q^3 + 8 * q^4 + 36 * q^9 - 8 * q^10 + 48 * q^12 + 40 * q^14 - 32 * q^16 + 54 * q^17 + 52 * q^22 - 374 * q^23 + 484 * q^25 + 540 * q^27 + 26 * q^29 + 24 * q^30 + 20 * q^35 - 144 * q^36 + 600 * q^38 - 64 * q^40 + 60 * q^42 + 398 * q^43 + 96 * q^48 - 636 * q^49 + 324 * q^51 + 2472 * q^53 - 52 * q^55 + 80 * q^56 - 350 * q^61 + 416 * q^62 - 256 * q^64 + 312 * q^66 - 216 * q^68 + 1122 * q^69 + 1692 * q^74 + 726 * q^75 + 260 * q^77 + 3056 * q^79 - 162 * q^81 - 780 * q^82 - 78 * q^87 - 208 * q^88 - 288 * q^90 - 2992 * q^92 + 1552 * q^94 + 300 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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