LMFDB - Embedded newform 338.4.e.d.147.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,4,Mod(23,338)] 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([5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.23"); 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:traces = [4,0,6,8,0,0,0,0,36,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == 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 $\Q(\zeta_{6})$
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			147.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.147
Dual form			338.4.e.d.23.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 - 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} - 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}+ \cdots + 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

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	$-0.971491\pi$
$5$		−	2.00000i		−	0.178885i	0.995992	−	0.0894427i	$-0.0285086\pi$
$6$	−5.19615	+	3.00000i	−0.353553	+	0.204124i
$7$	−4.33013	+	2.50000i	−0.233805	+	0.134987i	−0.612326	−	0.790605i	$-0.709766\pi$
$7$	−4.33013	+	2.50000i	−0.233805	+	0.134987i	0.378521	+	0.925593i	$0.376433\pi$
$8$		−	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	0.337704	−	0.941252i	$-0.390350\pi$
$11$	−11.2583	−	6.50000i	−0.308592	−	0.178166i	−0.646296	+	0.763087i	$0.723683\pi$
$12$	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	−0.837939	−	0.545764i	$-0.816239\pi$
$19$	−64.9519	+	37.5000i	−0.784263	+	0.452794i	0.0536762	+	0.998558i	$0.482906\pi$
$20$	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	$0.0974117\pi$
$31$			104.000i			0.602547i	−0.953538	+	0.301273i	$0.902588\pi$
$32$	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	$-0.944400\pi$
$37$	−366.329	−	211.500i	−1.62768	−	0.939740i	−0.642894	−	0.765955i	$-0.722266\pi$
$38$	150.000			0.640348
$39$		0			0
$40$	−16.0000			−0.0632456
$41$	168.875	+	97.5000i	0.643264	+	0.371389i	0.785871	−	0.618391i	$-0.212215\pi$
$41$	168.875	+	97.5000i	0.643264	+	0.371389i	−0.142607	+	0.989779i	$0.545548\pi$
$42$	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	$0.205662\pi$
$47$			388.000i			1.20416i	−0.798435	+	0.602081i	$0.794338\pi$
$48$	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	0.0488617	−	0.998806i	$-0.484441\pi$
$59$	425.218	−	245.500i	0.938284	−	0.541718i	0.889422	+	0.457087i	$0.151107\pi$
$60$		−	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	0.978681	−	0.205387i	$-0.0658453\pi$
$67$	707.543	+	408.500i	1.29015	+	0.744869i	0.311470	+	0.950256i	$0.399179\pi$
$68$	−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	−0.556088	−	0.831123i	$-0.687698\pi$
$71$	−68.4160	+	39.5000i	−0.114359	+	0.0660252i	0.441729	+	0.897148i	$0.354365\pi$
$72$	124.708	−	72.0000i	0.204124	−	0.117851i
$73$			230.000i			0.368760i	0.982855	+	0.184380i	$0.0590277\pi$
$73$			230.000i			0.368760i	−0.982855	+	0.184380i	$0.940972\pi$
$74$	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	$0.160824\pi$
$83$			732.000i			0.968041i	−0.875057	+	0.484021i	$0.839176\pi$
$84$	−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	0.929199	−	0.369580i	$-0.120498\pi$
$89$	901.532	+	520.500i	1.07373	+	0.619920i	0.144534	+	0.989500i	$0.453832\pi$
$90$	−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	−0.455389	−	0.890292i	$-0.650500\pi$
$97$	84.0045	−	48.5000i	0.0879316	−	0.0507673i	0.543321	+	0.839525i	$0.317167\pi$
$98$	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	$-0.881780\pi$
$109$		−	826.000i		−	0.725839i	0.931820	−	0.362920i	$-0.118220\pi$
$110$	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	−0.980580	−	0.196118i	$-0.937167\pi$
$137$	−2086.26	+	1204.50i	−1.30103	+	0.751149i	−0.320447	+	0.947266i	$0.603833\pi$
$138$		−	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	−0.689549	−	0.724239i	$-0.742191\pi$
$149$	−740.452	+	427.500i	−0.407115	+	0.235048i	0.282434	+	0.959287i	$0.408858\pi$
$150$	−628.734	+	363.000i	−0.342240	+	0.197592i
$151$			2064.00i			1.11236i	0.831063	+	0.556179i	$0.187733\pi$
$151$			2064.00i			1.11236i	−0.831063	+	0.556179i	$0.812267\pi$
$152$	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	−0.690750	−	0.723094i	$-0.742719\pi$
$163$	−853.035	+	492.500i	−0.409907	+	0.236660i	0.280843	+	0.959754i	$0.409386\pi$
$164$			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	0.891534	−	0.452953i	$-0.149629\pi$
$167$	2039.49	+	1177.50i	0.945033	+	0.545615i	0.0534983	+	0.998568i	$0.482963\pi$
$168$	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	0.0116407	−	0.999932i	$-0.496295\pi$
$193$	−2275.05	−	1313.50i	−0.848506	−	0.489885i	−0.860146	+	0.510047i	$0.829628\pi$
$194$	−194.000			−0.0717958
$195$		0			0
$196$	−1272.00			−0.463557
$197$	1041.83	+	601.500i	0.376788	+	0.217539i	0.676420	−	0.736516i	$-0.263531\pi$
$197$	1041.83	+	601.500i	0.376788	+	0.217539i	−0.299632	+	0.954055i	$0.596864\pi$
$198$	−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	0.172849	−	0.984948i	$-0.444703\pi$
$223$	−1977.14	−	1141.50i	−0.593717	−	0.342782i	−0.766566	+	0.642166i	$0.778036\pi$
$224$	−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	−0.777116	−	0.629358i	$-0.783318\pi$
$227$	−2122.63	+	1225.50i	−0.620633	+	0.358323i	0.156482	+	0.987681i	$0.449985\pi$
$228$	−779.423	+	450.000i	−0.226397	+	0.130710i
$229$		−	1878.00i		−	0.541929i	−0.962589	−	0.270964i	$-0.912657\pi$
$229$		−	1878.00i		−	0.541929i	0.962589	−	0.270964i	$-0.0873426\pi$
$230$	−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	$0.270059\pi$
$239$			5544.00i			1.50047i	−0.661173	+	0.750233i	$0.729941\pi$
$240$	83.1384	−	48.0000i	0.0223607	−	0.0129099i
$241$	4783.06	−	2761.50i	1.27844	−	0.738107i	0.301878	−	0.953347i	$-0.402386\pi$
$241$	4783.06	−	2761.50i	1.27844	−	0.738107i	0.976561	+	0.215239i	$0.0690532\pi$
$242$			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	−0.466180	−	0.884690i	$-0.654370\pi$
$271$	−6537.63	−	3774.50i	−1.46543	−	0.846068i	−0.999254	+	0.0386217i	$0.987703\pi$
$272$	−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	$-0.905287\pi$
$281$		−	2762.00i		−	0.586360i	0.956057	−	0.293180i	$-0.0947135\pi$
$282$	−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	0.345967	−	0.938247i	$-0.387551\pi$
$293$	6677.92	−	3855.50i	1.33150	−	0.768740i	0.985529	+	0.169507i	$0.0542175\pi$
$294$		−	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	$0.416259\pi$
$307$			10388.0i			1.93119i	−0.260056	+	0.965594i	$0.583741\pi$
$308$	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	$-0.772507\pi$
$317$		−	7398.00i		−	1.31077i	0.755296	−	0.655383i	$-0.227493\pi$
$318$	−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	−0.319248	−	0.947671i	$-0.603430\pi$
$331$	2058.54	−	1188.50i	0.341836	−	0.197359i	0.661084	+	0.750312i	$0.270097\pi$
$332$	−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	−0.313013	−	0.949749i	$-0.601338\pi$
$349$	−8423.83	−	4863.50i	−1.29203	−	0.745952i	−0.979013	+	0.203797i	$0.934672\pi$
$350$	1210.00			0.184792
$351$		0			0
$352$	−416.000			−0.0629911
$353$	1959.82	+	1131.50i	0.295497	+	0.170605i	0.640418	−	0.768026i	$-0.278761\pi$
$353$	1959.82	+	1131.50i	0.295497	+	0.170605i	−0.344921	+	0.938632i	$0.612094\pi$
$354$	−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	$-0.892985\pi$
$359$		−	4488.00i		−	0.659798i	0.944016	−	0.329899i	$-0.107015\pi$
$360$	−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	−0.120708	−	0.992688i	$-0.538516\pi$
$379$	−7679.05	−	4433.50i	−1.04076	−	0.600880i	−0.920047	+	0.391808i	$0.871850\pi$
$380$	−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	−0.983326	−	0.181850i	$-0.941792\pi$
$383$	−9875.29	+	5701.50i	−1.31750	+	0.760661i	−0.334177	+	0.942510i	$0.608458\pi$
$384$	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	−0.463492	−	0.886101i	$-0.653404\pi$
$397$	570.711	−	329.500i	0.0721490	−	0.0416552i	0.535641	+	0.844446i	$0.320070\pi$
$398$		−	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	$0.0339891\pi$
$401$	12717.6	+	7342.50i	1.58376	+	0.914381i	0.589451	+	0.807804i	$0.299344\pi$
$402$	−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	−0.0306167	−	0.999531i	$-0.509747\pi$
$409$	6780.11	−	3914.50i	0.819694	−	0.473251i	0.850311	+	0.526280i	$0.176414\pi$
$410$	−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	$0.0576144\pi$
$421$			3110.00i			0.360029i	−0.983664	+	0.180014i	$0.942386\pi$
$422$	−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	−0.0121219	−	0.999927i	$-0.503859\pi$
$431$	−7911.14	−	4567.50i	−0.884145	−	0.510461i	−0.872023	+	0.489465i	$0.837192\pi$
$432$	−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	−0.723587	−	0.690233i	$-0.757508\pi$
$449$	−4639.30	+	2678.50i	−0.487621	+	0.281528i	0.235966	+	0.971761i	$0.424175\pi$
$450$		−	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	$0.128527\pi$
$457$	16800.0	+	9699.50i	1.71963	+	0.992830i	0.800050	+	0.599933i	$0.204806\pi$
$458$	−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	0.370764	−	0.928727i	$-0.379096\pi$
$461$	13465.8	−	7774.50i	1.36045	−	0.785455i	0.989683	+	0.143273i	$0.0457625\pi$
$462$	−337.750	+	195.000i	−0.0340120	+	0.0196368i
$463$			4072.00i			0.408730i	0.978895	+	0.204365i	$0.0655129\pi$
$463$			4072.00i			0.408730i	−0.978895	+	0.204365i	$0.934487\pi$
$464$	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	0.861919	−	0.507046i	$-0.169263\pi$
$479$	8950.37	+	5167.50i	0.853764	+	0.492921i	−0.00815506	+	0.999967i	$0.502596\pi$
$480$	−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	−0.736998	−	0.675894i	$-0.763757\pi$
$487$	−5590.19	+	3227.50i	−0.520156	+	0.300312i	0.216843	+	0.976207i	$0.430424\pi$
$488$	−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	$0.0435986\pi$
$499$			3044.00i			0.273082i	−0.990634	+	0.136541i	$0.956401\pi$
$500$	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	0.527163	−	0.849764i	$-0.323256\pi$
$509$	629.600	+	363.500i	0.0548262	+	0.0316539i	−0.472336	+	0.881418i	$0.656589\pi$
$510$	−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	$0.161530\pi$
$541$			12230.0i			0.971920i	−0.873981	+	0.485960i	$0.838470\pi$
$542$	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	0.524987	−	0.851110i	$-0.324070\pi$
$557$	662.509	+	382.500i	0.0503975	+	0.0290970i	−0.474590	+	0.880207i	$0.657403\pi$
$558$	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	$-0.908560\pi$
$577$		−	7854.00i		−	0.566666i	0.959022	−	0.283333i	$-0.0914402\pi$
$578$	−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	0.919040	−	0.394163i	$-0.128966\pi$
$587$	14751.0	+	8516.50i	1.03721	+	0.598831i	0.118165	+	0.992994i	$0.462299\pi$
$588$	−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	$-0.832499\pi$
$593$		−	14506.0i		−	1.00454i	0.864712	−	0.502268i	$-0.167501\pi$
$594$	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	0.398117	−	0.917335i	$-0.369664\pi$
$613$	−2993.85	−	1728.50i	−0.197260	−	0.113888i	−0.595377	+	0.803447i	$0.702997\pi$
$614$	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	−0.283583	−	0.958948i	$-0.591523\pi$
$617$	6208.54	−	3584.50i	0.405099	−	0.233884i	0.688682	+	0.725064i	$0.258190\pi$
$618$	6692.64	−	3864.00i	0.435627	−	0.251510i
$619$			20212.0i			1.31242i	0.754578	+	0.656211i	$0.227842\pi$
$619$			20212.0i			1.31242i	−0.754578	+	0.656211i	$0.772158\pi$
$620$	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	−0.724046	−	0.689751i	$-0.757720\pi$
$631$	−7746.60	+	4472.50i	−0.488728	+	0.282167i	0.235319	+	0.971918i	$0.424387\pi$
$632$		−	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	−0.632446	−	0.774604i	$-0.717949\pi$
$643$	−4530.18	+	2615.50i	−0.277843	+	0.160413i	0.354604	+	0.935017i	$0.384616\pi$
$644$	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	0.445247	−	0.895408i	$-0.353116\pi$
$661$	−1828.18	−	1055.50i	−0.107576	−	0.0621092i	−0.552823	+	0.833299i	$0.686449\pi$
$662$	−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	−0.0353071	−	0.999377i	$-0.511241\pi$
$683$	14503.3	−	8373.50i	0.812525	−	0.469111i	0.847832	+	0.530265i	$0.177908\pi$
$684$		−	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	0.725200	−	0.688539i	$-0.241747\pi$
$691$	8927.86	+	5154.50i	0.491507	+	0.283772i	−0.233692	+	0.972311i	$0.575081\pi$
$692$	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	−0.180704	−	0.983537i	$-0.557838\pi$
$709$	10963.0	−	6329.50i	0.580712	−	0.335274i	0.761416	+	0.648263i	$0.224504\pi$
$710$		−	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	$0.0216542\pi$
$733$			2698.00i			0.135952i	−0.997687	+	0.0679761i	$0.978346\pi$
$734$	−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	0.437513	−	0.899212i	$-0.355859\pi$
$739$	−2460.38	−	1420.50i	−0.122472	−	0.0707090i	−0.559984	+	0.828503i	$0.689193\pi$
$740$	−3384.00			−0.168106
$741$		0			0
$742$	6180.00			0.305761
$743$	−7959.64	−	4595.50i	−0.393016	−	0.226908i	0.290450	−	0.956890i	$-0.406195\pi$
$743$	−7959.64	−	4595.50i	−0.393016	−	0.226908i	−0.683466	+	0.729982i	$0.739528\pi$
$744$	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	−0.402394	−	0.915467i	$-0.631822\pi$
$761$	3972.46	−	2293.50i	0.189227	−	0.109250i	0.591620	+	0.806217i	$0.298488\pi$
$762$			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	0.764629	−	0.644471i	$-0.222922\pi$
$769$	12556.5	+	7249.50i	0.588815	+	0.339953i	−0.175814	+	0.984423i	$0.556256\pi$
$770$	−130.000	+	225.167i	−0.00608425	+	0.0105382i
$771$	8527.50	+	14770.1i	0.398327	+	0.689923i
$772$		−	10508.0i		−	0.489885i
$773$	−2649.17	+	1529.50i	−0.123265	+	0.0711673i	−0.560365	−	0.828246i	$-0.689339\pi$
$773$	−2649.17	+	1529.50i	−0.123265	+	0.0711673i	0.437100	+	0.899413i	$0.356006\pi$
$774$	6204.21	−	3582.00i	0.288121	−	0.166347i
$775$			12584.0i			0.583265i
$776$	−388.000	−	672.036i	−0.0179490	−	0.0310885i
$777$	3172.50	−	5494.93i	0.146477	−	0.253706i
$778$	4541.44	+	2622.00i	0.209278	+	0.120827i
$779$	−14625.0			−0.672651
$780$		0			0
$781$	1027.00			0.0470537
$782$	8745.12	+	5049.00i	0.399904	+	0.230885i
$783$	877.500	−	1519.87i	0.0400502	−	0.0693689i
$784$	−2544.00	−	4406.34i	−0.115889	−	0.200726i
$785$			3788.00i			0.172229i
$786$	7378.54	−	4260.00i	0.334839	−	0.193320i
$787$	31529.4	−	18203.5i	1.42808	−	0.824504i	0.431113	−	0.902298i	$-0.358121\pi$
$787$	31529.4	−	18203.5i	1.42808	−	0.824504i	0.996969	+	0.0777937i	$0.0247875\pi$
$788$			4812.00i			0.217539i
$789$	9175.50	+	15892.4i	0.414013	+	0.717092i
$790$	−1528.00	+	2646.57i	−0.0688149	+	0.119191i
$791$	4100.63	+	2367.50i	0.184326	+	0.106420i
$792$	−1872.00			−0.0839882
$793$		0			0
$794$	−1318.00			−0.0589094
$795$	−3211.22	−	1854.00i	−0.143258	−	0.0827102i
$796$	−1486.00	+	2573.83i	−0.0661682	+	0.114607i
$797$	−6568.50	−	11377.0i	−0.291930	−	0.505638i	0.682336	−	0.731039i	$-0.260964\pi$
$797$	−6568.50	−	11377.0i	−0.291930	−	0.505638i	−0.974266	+	0.225401i	$0.927631\pi$
$798$			2250.00i			0.0998109i
$799$	−9072.48	+	5238.00i	−0.401704	+	0.231924i
$800$	3353.25	−	1936.00i	0.148194	−	0.0855599i
$801$			18738.0i			0.826560i
$802$	−14685.0	−	25435.2i	−0.646565	−	1.11988i
$803$	1495.00	−	2589.42i	0.0657004	−	0.113796i
$804$	8490.51	+	4902.00i	0.372434	+	0.215025i
$805$	−1870.00			−0.0818743
$806$		0			0
$807$	15327.0			0.668570
$808$	5604.92	+	3236.00i	0.244035	+	0.140894i
$809$	−7705.50	+	13346.3i	−0.334871	+	0.580014i	−0.983460	−	0.181125i	$-0.942026\pi$
$809$	−7705.50	+	13346.3i	−0.334871	+	0.580014i	0.648589	+	0.761139i	$0.275360\pi$
$810$	−162.000	−	280.592i	−0.00702728	−	0.0121716i
$811$			27664.0i			1.19780i	0.800824	+	0.598899i	$0.204395\pi$
$811$			27664.0i			1.19780i	−0.800824	+	0.598899i	$0.795605\pi$
$812$	−225.167	+	130.000i	−0.00973128	+	0.00561836i
$813$	−19612.9	+	11323.5i	−0.846068	+	0.488478i
$814$		−	10998.0i		−	0.473562i
$815$	985.000	+	1706.07i	0.0423350	+	0.0733264i
$816$	−648.000	+	1122.37i	−0.0277997	+	0.0481505i
$817$	−12925.4	−	7462.50i	−0.553493	−	0.319559i
$818$	−15658.0			−0.669278
$819$		0			0
$820$	1560.00			0.0664361
$821$	−18530.3	−	10698.5i	−0.787714	−	0.454787i	0.0514429	−	0.998676i	$-0.483618\pi$
$821$	−18530.3	−	10698.5i	−0.787714	−	0.454787i	−0.839157	+	0.543889i	$0.816951\pi$
$822$	7227.00	−	12517.5i	0.306655	−	0.531142i
$823$	−12124.5	−	21000.3i	−0.513528	−	0.889456i	−0.999877	−	0.0156918i	$-0.995005\pi$
$823$	−12124.5	−	21000.3i	−0.513528	−	0.889456i	0.486349	−	0.873765i	$-0.338328\pi$
$824$			10304.0i			0.435627i
$825$	−4086.77	+	2359.50i	−0.172464	+	0.0995724i
$826$	4252.18	−	2455.00i	0.179119	−	0.103414i
$827$			14028.0i			0.589844i	0.955521	+	0.294922i	$0.0952937\pi$
$827$			14028.0i			0.589844i	−0.955521	+	0.294922i	$0.904706\pi$
$828$	−6732.00	−	11660.2i	−0.282552	−	0.489395i
$829$	15225.5	−	26371.3i	0.637881	−	1.10484i	−0.348016	−	0.937489i	$-0.613144\pi$
$829$	15225.5	−	26371.3i	0.637881	−	1.10484i	0.985897	−	0.167354i	$-0.0535222\pi$
$830$	−2535.72	−	1464.00i	−0.106044	−	0.0612243i
$831$	−2943.00			−0.122854
$832$		0			0
$833$	−8586.00			−0.357128
$834$	14689.5	+	8481.00i	0.609900	+	0.352126i
$835$	2355.00	−	4078.98i	0.0976026	−	0.169053i
$836$	1950.00	+	3377.50i	0.0806724	+	0.139729i
$837$			14040.0i			0.579801i
$838$	−5055.86	+	2919.00i	−0.208415	+	0.120328i
$839$	17832.3	−	10295.5i	0.733779	−	0.423647i	−0.0860242	−	0.996293i	$-0.527416\pi$
$839$	17832.3	−	10295.5i	0.733779	−	0.423647i	0.819803	+	0.572646i	$0.194083\pi$
$840$		−	240.000i		−	0.00985808i
$841$	12110.0	+	20975.1i	0.496535	+	0.860024i
$842$	3110.00	−	5386.68i	0.127289	−	0.220472i
$843$	−7175.89	−	4143.00i	−0.293180	−	0.169267i
$844$	1420.00			0.0579128
$845$		0			0
$846$	13968.0			0.567647
$847$	5031.61	+	2905.00i	0.204118	+	0.117848i
$848$	−4944.00	+	8563.26i	−0.200210	+	0.346773i
$849$	−5887.50	−	10197.4i	−0.237996	−	0.412221i
$850$		−	6534.00i		−	0.263664i
$851$	68503.5	−	39550.5i	2.75942	−	1.59315i
$852$	−820.992	+	474.000i	−0.0330126	+	0.0190598i
$853$		−	5798.00i		−	0.232731i	−0.993206	−	0.116366i	$-0.962876\pi$
$853$		−	5798.00i		−	0.232731i	0.993206	−	0.116366i	$-0.0371244\pi$
$854$	−875.000	−	1515.54i	−0.0350608	−	0.0607270i
$855$	−1350.00	+	2338.27i	−0.0539989	+	0.0935288i
$856$	8847.32	+	5108.00i	0.353265	+	0.203958i
$857$	−5686.00			−0.226640			−0.113320	−	0.993559i	$-0.536148\pi$
$857$	−5686.00			−0.226640			−0.113320	+	0.993559i	$0.536148\pi$
$858$		0			0
$859$	−46708.0			−1.85525			−0.927623	−	0.373518i	$-0.878152\pi$
$859$	−46708.0			−1.85525			−0.927623	+	0.373518i	$0.878152\pi$
$860$	1378.71	+	796.000i	0.0546671	+	0.0315621i
$861$	−1462.50	+	2533.12i	−0.0578883	+	0.100266i
$862$	9135.00	+	15822.3i	0.360951	+	0.625185i
$863$		−	25168.0i		−	0.992733i	−0.868113	−	0.496367i	$-0.834667\pi$
$863$		−	25168.0i		−	0.992733i	0.868113	−	0.496367i	$-0.165333\pi$
$864$	3741.23	−	2160.00i	0.147314	−	0.0850517i
$865$	−6735.95	+	3889.00i	−0.264773	+	0.152867i
$866$			23338.0i			0.915771i
$867$	−6276.00	−	10870.4i	−0.245841	−	0.425809i
$868$	1040.00	−	1801.33i	0.0406681	−	0.0704392i
$869$	−8601.36	−	4966.00i	−0.335767	−	0.193855i
$870$	156.000			0.00607919
$871$		0			0
$872$	−6608.00			−0.256623
$873$	1512.08	+	873.000i	0.0586210	+	0.0338449i
$874$	−14025.0	+	24292.0i	−0.542795	+	0.940148i
$875$	1230.00	+	2130.42i	0.0475218	+	0.0823102i
$876$			2760.00i			0.106452i
$877$	−16162.6	+	9331.50i	−0.622318	+	0.359296i	−0.777771	−	0.628548i	$-0.783650\pi$
$877$	−16162.6	+	9331.50i	−0.622318	+	0.359296i	0.155453	+	0.987843i	$0.450316\pi$
$878$	−23432.9	+	13529.0i	−0.900709	+	0.520025i
$879$		−	23133.0i		−	0.887664i
$880$	−208.000	−	360.267i	−0.00796782	−	0.0138007i
$881$	2485.50	−	4305.01i	0.0950495	−	0.164631i	−0.814580	−	0.580052i	$-0.803032\pi$
$881$	2485.50	−	4305.01i	0.0950495	−	0.164631i	0.909629	+	0.415421i	$0.136366\pi$
$882$	9914.26	+	5724.00i	0.378493	+	0.218523i
$883$	−6892.00			−0.262666			−0.131333	−	0.991338i	$-0.541926\pi$
$883$	−6892.00			−0.262666			−0.131333	+	0.991338i	$0.541926\pi$
$884$		0			0
$885$	−2946.00			−0.111897
$886$	3346.32	+	1932.00i	0.126887	+	0.0732582i
$887$	12023.5	−	20825.3i	0.455140	−	0.788326i	−0.543556	−	0.839373i	$-0.682922\pi$
$887$	12023.5	−	20825.3i	0.455140	−	0.788326i	0.998696	+	0.0510466i	$0.0162557\pi$
$888$	5076.00	+	8791.89i	0.191824	+	0.332248i
$889$			5885.00i			0.222021i
$890$	−3606.13	+	2082.00i	−0.135818	+	0.0784144i
$891$	911.925	−	526.500i	0.0342880	−	0.0197962i
$892$		−	9132.00i		−	0.342782i
$893$	−14550.0	−	25201.3i	−0.545238	−	0.944379i
$894$	2565.00	−	4442.71i	0.0959580	−	0.166204i
$895$	−3860.74	−	2229.00i	−0.144190	−	0.0832483i
$896$	−640.000			−0.0238626
$897$		0			0
$898$	10714.0			0.398141
$899$	1170.87	+	676.000i	0.0434378	+	0.0250788i
$900$	−4356.00	+	7544.81i	−0.161333	+	0.279438i
$901$	8343.00	+	14450.5i	0.308486	+	0.534313i
$902$			5070.00i			0.187154i
$903$	−2585.09	+	1492.50i	−0.0952672	+	0.0550025i
$904$	−6561.01	+	3788.00i	−0.241389	+	0.139366i
$905$		−	2076.00i		−	0.0762526i
$906$	−6192.00	−	10724.9i	−0.227059	−	0.393278i
$907$	−6421.50	+	11122.4i	−0.235085	+	0.407180i	−0.959297	−	0.282397i	$-0.908870\pi$
$907$	−6421.50	+	11122.4i	−0.235085	+	0.407180i	0.724212	+	0.689577i	$0.242204\pi$
$908$	−8490.51	−	4902.00i	−0.310317	−	0.179161i
$909$	−14562.0			−0.531343
$910$		0			0
$911$	−144.000			−0.00523703			−0.00261851	−	0.999997i	$-0.500833\pi$
$911$	−144.000			−0.00523703			−0.00261851	+	0.999997i	$0.500833\pi$
$912$	−3117.69	−	1800.00i	−0.113199	−	0.0653552i
$913$	4758.00	−	8241.10i	0.172472	−	0.298730i
$914$	−19399.0	−	33600.1i	−0.702037	−	1.21596i
$915$			1050.00i			0.0379365i
$916$	6505.58	−	3756.00i	0.234662	−	0.135482i
$917$	6148.78	−	3550.00i	0.221429	−	0.127842i
$918$		−	7290.00i		−	0.262098i
$919$	5530.50	+	9579.11i	0.198514	+	0.343836i	0.948047	−	0.318131i	$-0.103055\pi$
$919$	5530.50	+	9579.11i	0.198514	+	0.343836i	−0.749533	+	0.661967i	$0.769722\pi$
$920$	1496.00	−	2591.15i	0.0536105	−	0.0928561i
$921$	26988.8	+	15582.0i	0.965594	+	0.557486i
$922$	−31098.0			−1.11080
$923$		0			0
$924$	780.000			0.0277707
$925$	−44325.8	−	25591.5i	−1.57559	−	0.909668i
$926$	4072.00	−	7052.91i	0.144508	−	0.250295i
$927$	−11592.0	−	20077.9i	−0.410713	−	0.711376i
$928$		−	416.000i		−	0.0147154i
$929$	−22782.5	+	13153.5i	−0.804597	+	0.464534i	−0.845076	−	0.534646i	$-0.820445\pi$
$929$	−22782.5	+	13153.5i	−0.804597	+	0.464534i	0.0404791	+	0.999180i	$0.487112\pi$
$930$	−1080.80	+	624.000i	−0.0381084	+	0.0220019i
$931$		−	23850.0i		−	0.839583i
$932$	−3260.00	−	5646.49i	−0.114576	−	0.198451i
$933$	10908.0	−	18893.2i	0.382757	−	0.662954i
$934$	26368.7	+	15224.0i	0.923781	+	0.533345i
$935$	−702.000			−0.0245539
$936$		0			0
$937$	−46074.0			−1.60637			−0.803187	−	0.595727i	$-0.796864\pi$
$937$	−46074.0			−1.60637			−0.803187	+	0.595727i	$0.796864\pi$
$938$	7075.43	+	4085.00i	0.246291	+	0.142196i
$939$	11865.0	−	20550.8i	0.412353	−	0.714217i
$940$	1552.00	+	2688.14i	0.0538518	+	0.0932740i
$941$		−	36118.0i		−	1.25124i	−0.780130	−	0.625618i	$-0.784847\pi$
$941$		−	36118.0i		−	1.25124i	0.780130	−	0.625618i	$-0.215153\pi$
$942$	9841.51	−	5682.00i	0.340397	−	0.196528i
$943$	−31579.6	+	18232.5i	−1.09053	+	0.629620i
$944$			7856.00i			0.270859i
$945$	675.000	+	1169.13i	0.0232357	+	0.0402454i
$946$	−2587.00	+	4480.82i	−0.0889119	+	0.154000i
$947$	48077.4	+	27757.5i	1.64974	+	0.952479i	0.977173	+	0.212444i	$0.0681424\pi$
$947$	48077.4	+	27757.5i	1.64974	+	0.952479i	0.672569	+	0.740035i	$0.265191\pi$
$948$	9168.00			0.314096
$949$		0			0
$950$	18150.0			0.619857
$951$	−19220.6	−	11097.0i	−0.655383	−	0.378386i
$952$	−540.000	+	935.307i	−0.0183839	+	0.0318419i
$953$	−2676.50	−	4635.83i	−0.0909762	−	0.157575i	0.816946	−	0.576714i	$-0.195665\pi$
$953$	−2676.50	−	4635.83i	−0.0909762	−	0.157575i	−0.907922	+	0.419139i	$0.862332\pi$
$954$		−	22248.0i		−	0.755037i
$955$	3708.32	−	2141.00i	0.125653	−	0.0725457i
$956$	−19205.0	+	11088.0i	−0.649721	+	0.375117i
$957$			507.000i			0.0171254i
$958$	−10335.0	−	17900.7i	−0.348548	−	0.603702i
$959$	6022.50	−	10431.3i	0.202791	−	0.351244i
$960$	332.554	+	192.000i	0.0111803	+	0.00645497i
$961$	18975.0			0.636937
$962$		0			0
$963$	−22986.0			−0.769173
$964$	19132.2	+	11046.0i	0.639220	+	0.369054i
$965$	−2627.00	+	4550.10i	−0.0876333	+	0.151785i
$966$	2805.00	+	4858.40i	0.0934259	+	0.161818i
$967$			5488.00i			0.182505i	0.995828	+	0.0912524i	$0.0290870\pi$
$967$			5488.00i			0.182505i	−0.995828	+	0.0912524i	$0.970913\pi$
$968$	−8050.57	+	4648.00i	−0.267309	+	0.154331i
$969$	−5261.10	+	3037.50i	−0.174418	+	0.100700i
$970$			388.000i			0.0128432i
$971$	18676.5	+	32348.6i	0.617258	+	1.06912i	0.989984	+	0.141181i	$0.0450898\pi$
$971$	18676.5	+	32348.6i	0.617258	+	1.06912i	−0.372726	+	0.927941i	$0.621577\pi$
$972$	−7776.00	+	13468.4i	−0.256600	+	0.444444i
$973$	12241.3	+	7067.50i	0.403327	+	0.232861i
$974$	12910.0			0.424705
$975$		0			0
$976$	2800.00			0.0918297
$977$	−11023.6	−	6364.50i	−0.360980	−	0.208412i	0.308531	−	0.951214i	$-0.400163\pi$
$977$	−11023.6	−	6364.50i	−0.360980	−	0.208412i	−0.669511	+	0.742803i	$0.733496\pi$
$978$	2955.00	−	5118.21i	0.0966160	−	0.167344i
$979$	−6766.50	−	11719.9i	−0.220897	−	0.382605i
$980$			2544.00i			0.0829236i
$981$	12876.1	−	7434.00i	0.419063	−	0.241946i
$982$	−13470.2	+	7777.00i	−0.437729	+	0.252723i
$983$		−	56128.0i		−	1.82116i	−0.413327	−	0.910582i	$-0.635633\pi$
$983$		−	56128.0i		−	1.82116i	0.413327	−	0.910582i	$-0.364367\pi$
$984$	−2340.00	−	4053.00i	−0.0758094	−	0.131306i
$985$	1203.00	−	2083.66i	0.0389145	−	0.0674019i
$986$	−607.950	−	351.000i	−0.0196360	−	0.0113368i
$987$	−5820.00			−0.187693
$988$		0			0
$989$	−37213.0			−1.19647
$990$	810.600	+	468.000i	0.0260228	+	0.0150243i
$991$	−23500.5	+	40704.1i	−0.753298	+	1.30475i	0.192919	+	0.981215i	$0.438205\pi$
$991$	−23500.5	+	40704.1i	−0.753298	+	1.30475i	−0.946216	+	0.323535i	$0.895129\pi$
$992$	1664.00	+	2882.13i	0.0532581	+	0.0922458i
$993$		−	7131.00i		−	0.227891i
$994$	−684.160	+	395.000i	−0.0218312	+	0.0126043i
$995$	1286.91	−	743.000i	0.0410029	−	0.0236730i
$996$			8784.00i			0.279449i
$997$	12216.5	+	21159.6i	0.388065	+	0.672148i	0.992189	−	0.124742i	$-0.0398104\pi$
$997$	12216.5	+	21159.6i	0.388065	+	0.672148i	−0.604125	+	0.796890i	$0.706477\pi$
$998$	3044.00	−	5272.36i	0.0965492	−	0.167228i
$999$	−49454.4	−	28552.5i	−1.56623	−	0.904265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.d.147.1		4
13.2	odd	12		338.4.c.d.315.1		2
13.3	even	3	inner	338.4.e.d.23.2		4
13.4	even	6		338.4.b.a.337.1		2
13.5	odd	4		338.4.c.d.191.1		2
13.6	odd	12		338.4.a.d.1.1		1
13.7	odd	12		338.4.a.a.1.1		1
13.8	odd	4		26.4.c.a.9.1	yes	2
13.9	even	3		338.4.b.a.337.2		2
13.10	even	6	inner	338.4.e.d.23.1		4
13.11	odd	12		26.4.c.a.3.1	✓	2
13.12	even	2	inner	338.4.e.d.147.2		4
39.8	even	4		234.4.h.b.217.1		2
39.11	even	12		234.4.h.b.55.1		2
52.11	even	12		208.4.i.a.81.1		2
52.47	even	4		208.4.i.a.113.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.a.3.1	✓	2	13.11	odd	12
26.4.c.a.9.1	yes	2	13.8	odd	4
208.4.i.a.81.1		2	52.11	even	12
208.4.i.a.113.1		2	52.47	even	4
234.4.h.b.55.1		2	39.11	even	12
234.4.h.b.217.1		2	39.8	even	4
338.4.a.a.1.1		1	13.7	odd	12
338.4.a.d.1.1		1	13.6	odd	12
338.4.b.a.337.1		2	13.4	even	6
338.4.b.a.337.2		2	13.9	even	3
338.4.c.d.191.1		2	13.5	odd	4
338.4.c.d.315.1		2	13.2	odd	12
338.4.e.d.23.1		4	13.10	even	6	inner
338.4.e.d.23.2		4	13.3	even	3	inner
338.4.e.d.147.1		4	1.1	even	1	trivial
338.4.e.d.147.2		4	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 8 q^{4} + 36 q^{9} - 8 q^{10} + 48 q^{12} + 40 q^{14} - 32 q^{16} + 54 q^{17} + 52 q^{22} - 374 q^{23} + 484 q^{25} + 540 q^{27} + 26 q^{29} + 24 q^{30} + 20 q^{35} - 144 q^{36} + 600 q^{38}+ \cdots + 300 q^{95}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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