LMFDB - Embedded newform 26.4.c.a.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,4,Mod(3,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.3"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.53404966015$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	26.3
Dual form			26.4.c.a.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +2.00000 q^{5} +(-3.00000 + 5.19615i) q^{6} +(2.50000 - 4.33013i) q^{7} -8.00000 q^{8} +(9.00000 - 15.5885i) q^{9} +(2.00000 + 3.46410i) q^{10} +(-6.50000 - 11.2583i) q^{11} -12.0000 q^{12} +(-13.0000 - 45.0333i) q^{13} +10.0000 q^{14} +(3.00000 + 5.19615i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.5000 + 23.3827i) q^{17} +36.0000 q^{18} +(-37.5000 + 64.9519i) q^{19} +(-4.00000 + 6.92820i) q^{20} +15.0000 q^{21} +(13.0000 - 22.5167i) q^{22} +(93.5000 + 161.947i) q^{23} +(-12.0000 - 20.7846i) q^{24} -121.000 q^{25} +(65.0000 - 67.5500i) q^{26} +135.000 q^{27} +(10.0000 + 17.3205i) q^{28} +(6.50000 + 11.2583i) q^{29} +(-6.00000 + 10.3923i) q^{30} -104.000 q^{31} +(16.0000 - 27.7128i) q^{32} +(19.5000 - 33.7750i) q^{33} -54.0000 q^{34} +(5.00000 - 8.66025i) q^{35} +(36.0000 + 62.3538i) q^{36} +(-211.500 - 366.329i) q^{37} -150.000 q^{38} +(97.5000 - 101.325i) q^{39} -16.0000 q^{40} +(-97.5000 - 168.875i) q^{41} +(15.0000 + 25.9808i) q^{42} +(-99.5000 + 172.339i) q^{43} +52.0000 q^{44} +(18.0000 - 31.1769i) q^{45} +(-187.000 + 323.894i) q^{46} +388.000 q^{47} +(24.0000 - 41.5692i) q^{48} +(159.000 + 275.396i) q^{49} +(-121.000 - 209.578i) q^{50} -81.0000 q^{51} +(182.000 + 45.0333i) q^{52} +618.000 q^{53} +(135.000 + 233.827i) q^{54} +(-13.0000 - 22.5167i) q^{55} +(-20.0000 + 34.6410i) q^{56} -225.000 q^{57} +(-13.0000 + 22.5167i) q^{58} +(-245.500 + 425.218i) q^{59} -24.0000 q^{60} +(-87.5000 + 151.554i) q^{61} +(-104.000 - 180.133i) q^{62} +(-45.0000 - 77.9423i) q^{63} +64.0000 q^{64} +(-26.0000 - 90.0666i) q^{65} +78.0000 q^{66} +(-408.500 - 707.543i) q^{67} +(-54.0000 - 93.5307i) q^{68} +(-280.500 + 485.840i) q^{69} +20.0000 q^{70} +(-39.5000 + 68.4160i) q^{71} +(-72.0000 + 124.708i) q^{72} +230.000 q^{73} +(423.000 - 732.657i) q^{74} +(-181.500 - 314.367i) q^{75} +(-150.000 - 259.808i) q^{76} -65.0000 q^{77} +(273.000 + 67.5500i) q^{78} +764.000 q^{79} +(-16.0000 - 27.7128i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(195.000 - 337.750i) q^{82} -732.000 q^{83} +(-30.0000 + 51.9615i) q^{84} +(-27.0000 + 46.7654i) q^{85} -398.000 q^{86} +(-19.5000 + 33.7750i) q^{87} +(52.0000 + 90.0666i) q^{88} +(520.500 + 901.532i) q^{89} +72.0000 q^{90} +(-227.500 - 56.2917i) q^{91} -748.000 q^{92} +(-156.000 - 270.200i) q^{93} +(388.000 + 672.036i) q^{94} +(-75.0000 + 129.904i) q^{95} +96.0000 q^{96} +(48.5000 - 84.0045i) q^{97} +(-318.000 + 550.792i) q^{98} -234.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 5 q^{7} - 16 q^{8} + 18 q^{9} + 4 q^{10} - 13 q^{11} - 24 q^{12} - 26 q^{13} + 20 q^{14} + 6 q^{15} - 16 q^{16} - 27 q^{17} + 72 q^{18} - 75 q^{19}+ \cdots - 468 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 5 * q^7 - 16 * q^8 + 18 * q^9 + 4 * q^10 - 13 * q^11 - 24 * q^12 - 26 * q^13 + 20 * q^14 + 6 * q^15 - 16 * q^16 - 27 * q^17 + 72 * q^18 - 75 * q^19 - 8 * q^20 + 30 * q^21 + 26 * q^22 + 187 * q^23 - 24 * q^24 - 242 * q^25 + 130 * q^26 + 270 * q^27 + 20 * q^28 + 13 * q^29 - 12 * q^30 - 208 * q^31 + 32 * q^32 + 39 * q^33 - 108 * q^34 + 10 * q^35 + 72 * q^36 - 423 * q^37 - 300 * q^38 + 195 * q^39 - 32 * q^40 - 195 * q^41 + 30 * q^42 - 199 * q^43 + 104 * q^44 + 36 * q^45 - 374 * q^46 + 776 * q^47 + 48 * q^48 + 318 * q^49 - 242 * q^50 - 162 * q^51 + 364 * q^52 + 1236 * q^53 + 270 * q^54 - 26 * q^55 - 40 * q^56 - 450 * q^57 - 26 * q^58 - 491 * q^59 - 48 * q^60 - 175 * q^61 - 208 * q^62 - 90 * q^63 + 128 * q^64 - 52 * q^65 + 156 * q^66 - 817 * q^67 - 108 * q^68 - 561 * q^69 + 40 * q^70 - 79 * q^71 - 144 * q^72 + 460 * q^73 + 846 * q^74 - 363 * q^75 - 300 * q^76 - 130 * q^77 + 546 * q^78 + 1528 * q^79 - 32 * q^80 - 81 * q^81 + 390 * q^82 - 1464 * q^83 - 60 * q^84 - 54 * q^85 - 796 * q^86 - 39 * q^87 + 104 * q^88 + 1041 * q^89 + 144 * q^90 - 455 * q^91 - 1496 * q^92 - 312 * q^93 + 776 * q^94 - 150 * q^95 + 192 * q^96 + 97 * q^97 - 636 * q^98 - 468 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.00000			0.178885			0.0894427	−	0.995992i	$-0.471491\pi$
$5$	2.00000			0.178885			0.0894427	+	0.995992i	$0.471491\pi$
$6$	−3.00000	+	5.19615i	−0.204124	+	0.353553i
$7$	2.50000	−	4.33013i	0.134987	−	0.233805i	−0.790605	−	0.612326i	$-0.790234\pi$
$7$	2.50000	−	4.33013i	0.134987	−	0.233805i	0.925593	+	0.378521i	$0.123567\pi$
$8$	−8.00000			−0.353553
$9$	9.00000	−	15.5885i	0.333333	−	0.577350i
$10$	2.00000	+	3.46410i	0.0632456	+	0.109545i
$11$	−6.50000	−	11.2583i	−0.178166	−	0.308592i	0.763087	−	0.646296i	$-0.223683\pi$
$11$	−6.50000	−	11.2583i	−0.178166	−	0.308592i	−0.941252	+	0.337704i	$0.890350\pi$
$12$	−12.0000			−0.288675
$13$	−13.0000	−	45.0333i	−0.277350	−	0.960769i
$13$	−13.0000	−	45.0333i	−0.277350	−	0.960769i
$14$	10.0000			0.190901
$15$	3.00000	+	5.19615i	0.0516398	+	0.0894427i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−13.5000	+	23.3827i	−0.192602	+	0.333596i	−0.946112	−	0.323840i	$-0.895026\pi$
$17$	−13.5000	+	23.3827i	−0.192602	+	0.333596i	0.753510	+	0.657437i	$0.228359\pi$
$18$	36.0000			0.471405
$19$	−37.5000	+	64.9519i	−0.452794	+	0.784263i	−0.998558	−	0.0536762i	$-0.982906\pi$
$19$	−37.5000	+	64.9519i	−0.452794	+	0.784263i	0.545764	+	0.837939i	$0.316239\pi$
$20$	−4.00000	+	6.92820i	−0.0447214	+	0.0774597i
$21$	15.0000			0.155870
$22$	13.0000	−	22.5167i	0.125982	−	0.218208i
$23$	93.5000	+	161.947i	0.847656	+	1.46818i	0.883294	+	0.468819i	$0.155320\pi$
$23$	93.5000	+	161.947i	0.847656	+	1.46818i	−0.0356377	+	0.999365i	$0.511346\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−121.000			−0.968000
$26$	65.0000	−	67.5500i	0.490290	−	0.509525i
$27$	135.000			0.962250
$28$	10.0000	+	17.3205i	0.0674937	+	0.116902i
$29$	6.50000	+	11.2583i	0.0416214	+	0.0720903i	0.886086	−	0.463522i	$-0.153414\pi$
$29$	6.50000	+	11.2583i	0.0416214	+	0.0720903i	−0.844464	+	0.535612i	$0.820081\pi$
$30$	−6.00000	+	10.3923i	−0.0365148	+	0.0632456i
$31$	−104.000			−0.602547			−0.301273	−	0.953538i	$-0.597412\pi$
$31$	−104.000			−0.602547			−0.301273	+	0.953538i	$0.597412\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	19.5000	−	33.7750i	0.102864	−	0.178166i
$34$	−54.0000			−0.272380
$35$	5.00000	−	8.66025i	0.0241473	−	0.0418243i
$36$	36.0000	+	62.3538i	0.166667	+	0.288675i
$37$	−211.500	−	366.329i	−0.939740	−	1.62768i	−0.765955	−	0.642894i	$-0.777734\pi$
$37$	−211.500	−	366.329i	−0.939740	−	1.62768i	−0.173785	−	0.984784i	$-0.555600\pi$
$38$	−150.000			−0.640348
$39$	97.5000	−	101.325i	0.400320	−	0.416025i
$40$	−16.0000			−0.0632456
$41$	−97.5000	−	168.875i	−0.371389	−	0.643264i	0.618391	−	0.785871i	$-0.287785\pi$
$41$	−97.5000	−	168.875i	−0.371389	−	0.643264i	−0.989779	+	0.142607i	$0.954452\pi$
$42$	15.0000	+	25.9808i	0.0551083	+	0.0954504i
$43$	−99.5000	+	172.339i	−0.352875	+	0.611197i	−0.986752	−	0.162237i	$-0.948129\pi$
$43$	−99.5000	+	172.339i	−0.352875	+	0.611197i	0.633877	+	0.773434i	$0.281462\pi$
$44$	52.0000			0.178166
$45$	18.0000	−	31.1769i	0.0596285	−	0.103280i
$46$	−187.000	+	323.894i	−0.599384	+	1.03816i
$47$	388.000			1.20416			0.602081	−	0.798435i	$-0.294338\pi$
$47$	388.000			1.20416			0.602081	+	0.798435i	$0.294338\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	159.000	+	275.396i	0.463557	+	0.802904i
$50$	−121.000	−	209.578i	−0.342240	−	0.592777i
$51$	−81.0000			−0.222397
$52$	182.000	+	45.0333i	0.485363	+	0.120096i
$53$	618.000			1.60168			0.800838	−	0.598881i	$-0.204388\pi$
$53$	618.000			1.60168			0.800838	+	0.598881i	$0.204388\pi$
$54$	135.000	+	233.827i	0.340207	+	0.589256i
$55$	−13.0000	−	22.5167i	−0.0318713	−	0.0552027i
$56$	−20.0000	+	34.6410i	−0.0477252	+	0.0826625i
$57$	−225.000			−0.522842
$58$	−13.0000	+	22.5167i	−0.0294308	+	0.0509756i
$59$	−245.500	+	425.218i	−0.541718	+	0.938284i	0.457087	+	0.889422i	$0.348893\pi$
$59$	−245.500	+	425.218i	−0.541718	+	0.938284i	−0.998806	+	0.0488617i	$0.984441\pi$
$60$	−24.0000			−0.0516398
$61$	−87.5000	+	151.554i	−0.183659	+	0.318108i	−0.943124	−	0.332441i	$-0.892128\pi$
$61$	−87.5000	+	151.554i	−0.183659	+	0.318108i	0.759465	+	0.650549i	$0.225461\pi$
$62$	−104.000	−	180.133i	−0.213032	−	0.368983i
$63$	−45.0000	−	77.9423i	−0.0899915	−	0.155870i
$64$	64.0000			0.125000
$65$	−26.0000	−	90.0666i	−0.0496139	−	0.171868i
$66$	78.0000			0.145472
$67$	−408.500	−	707.543i	−0.744869	−	1.29015i	−0.950256	−	0.311470i	$-0.899179\pi$
$67$	−408.500	−	707.543i	−0.744869	−	1.29015i	0.205387	−	0.978681i	$-0.434155\pi$
$68$	−54.0000	−	93.5307i	−0.0963009	−	0.166798i
$69$	−280.500	+	485.840i	−0.489395	+	0.847656i
$70$	20.0000			0.0341494
$71$	−39.5000	+	68.4160i	−0.0660252	+	0.114359i	−0.897148	−	0.441729i	$-0.854365\pi$
$71$	−39.5000	+	68.4160i	−0.0660252	+	0.114359i	0.831123	+	0.556088i	$0.187698\pi$
$72$	−72.0000	+	124.708i	−0.117851	+	0.204124i
$73$	230.000			0.368760			0.184380	−	0.982855i	$-0.440972\pi$
$73$	230.000			0.368760			0.184380	+	0.982855i	$0.440972\pi$
$74$	423.000	−	732.657i	0.664497	−	1.15094i
$75$	−181.500	−	314.367i	−0.279438	−	0.484000i
$76$	−150.000	−	259.808i	−0.226397	−	0.392131i
$77$	−65.0000			−0.0962005
$78$	273.000	+	67.5500i	0.396297	+	0.0980581i
$79$	764.000			1.08806			0.544030	−	0.839066i	$-0.316898\pi$
$79$	764.000			1.08806			0.544030	+	0.839066i	$0.316898\pi$
$80$	−16.0000	−	27.7128i	−0.0223607	−	0.0387298i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	195.000	−	337.750i	0.262612	−	0.454857i
$83$	−732.000			−0.968041			−0.484021	−	0.875057i	$-0.660824\pi$
$83$	−732.000			−0.968041			−0.484021	+	0.875057i	$0.660824\pi$
$84$	−30.0000	+	51.9615i	−0.0389675	+	0.0674937i
$85$	−27.0000	+	46.7654i	−0.0344537	+	0.0596755i
$86$	−398.000			−0.499040
$87$	−19.5000	+	33.7750i	−0.0240301	+	0.0416214i
$88$	52.0000	+	90.0666i	0.0629911	+	0.109104i
$89$	520.500	+	901.532i	0.619920	+	1.07373i	0.989500	+	0.144534i	$0.0461683\pi$
$89$	520.500	+	901.532i	0.619920	+	1.07373i	−0.369580	+	0.929199i	$0.620498\pi$
$90$	72.0000			0.0843274
$91$	−227.500	−	56.2917i	−0.262071	−	0.0648458i
$92$	−748.000			−0.847656
$93$	−156.000	−	270.200i	−0.173940	−	0.301273i
$94$	388.000	+	672.036i	0.425736	+	0.737396i
$95$	−75.0000	+	129.904i	−0.0809983	+	0.140293i
$96$	96.0000			0.102062
$97$	48.5000	−	84.0045i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	48.5000	−	84.0045i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$	−318.000	+	550.792i	−0.327784	+	0.567739i
$99$	−234.000			−0.237554
$100$	242.000	−	419.156i	0.242000	−	0.419156i
$101$	404.500	+	700.615i	0.398507	+	0.690235i	0.993542	−	0.113465i	$-0.0361950\pi$
$101$	404.500	+	700.615i	0.398507	+	0.690235i	−0.595035	+	0.803700i	$0.702862\pi$
$102$	−81.0000	−	140.296i	−0.0786294	−	0.136190i
$103$	1288.00			1.23214			0.616070	−	0.787691i	$-0.288724\pi$
$103$	1288.00			1.23214			0.616070	+	0.787691i	$0.288724\pi$
$104$	104.000	+	360.267i	0.0980581	+	0.339683i
$105$	30.0000			0.0278829
$106$	618.000	+	1070.41i	0.566278	+	0.980822i
$107$	−638.500	−	1105.91i	−0.576880	−	0.999185i	−0.995835	−	0.0911779i	$-0.970937\pi$
$107$	−638.500	−	1105.91i	−0.576880	−	0.999185i	0.418955	−	0.908007i	$-0.362397\pi$
$108$	−270.000	+	467.654i	−0.240563	+	0.416667i
$109$	826.000			0.725839			0.362920	−	0.931820i	$-0.381780\pi$
$109$	826.000			0.725839			0.362920	+	0.931820i	$0.381780\pi$
$110$	26.0000	−	45.0333i	0.0225364	−	0.0390342i
$111$	634.500	−	1098.99i	0.542559	−	0.939740i
$112$	−80.0000			−0.0674937
$113$	−473.500	+	820.126i	−0.394187	+	0.682752i	−0.992997	−	0.118139i	$-0.962307\pi$
$113$	−473.500	+	820.126i	−0.394187	+	0.682752i	0.598810	+	0.800891i	$0.295640\pi$
$114$	−225.000	−	389.711i	−0.184852	−	0.320174i
$115$	187.000	+	323.894i	0.151633	+	0.262637i
$116$	−52.0000			−0.0416214
$117$	−819.000	−	202.650i	−0.647150	−	0.160128i
$118$	−982.000			−0.766105
$119$	67.5000	+	116.913i	0.0519976	+	0.0900625i
$120$	−24.0000	−	41.5692i	−0.0182574	−	0.0316228i
$121$	581.000	−	1006.32i	0.436514	−	0.756064i
$122$	−350.000			−0.259734
$123$	292.500	−	506.625i	0.214421	−	0.371389i
$124$	208.000	−	360.267i	0.150637	−	0.260910i
$125$	−492.000			−0.352047
$126$	90.0000	−	155.885i	0.0636336	−	0.110217i
$127$	−588.500	−	1019.31i	−0.411188	−	0.712199i	0.583832	−	0.811875i	$-0.301553\pi$
$127$	−588.500	−	1019.31i	−0.411188	−	0.712199i	−0.995020	+	0.0996756i	$0.968220\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−597.000			−0.407464
$130$	130.000	−	135.100i	0.0877058	−	0.0911465i
$131$	−1420.00			−0.947069			−0.473534	−	0.880775i	$-0.657022\pi$
$131$	−1420.00			−0.947069			−0.473534	+	0.880775i	$0.657022\pi$
$132$	78.0000	+	135.100i	0.0514320	+	0.0890829i
$133$	187.500	+	324.760i	0.122243	+	0.211731i
$134$	817.000	−	1415.09i	0.526702	−	0.912274i
$135$	270.000			0.172133
$136$	108.000	−	187.061i	0.0680950	−	0.117944i
$137$	1204.50	−	2086.26i	0.751149	−	1.30103i	−0.196118	−	0.980580i	$-0.562833\pi$
$137$	1204.50	−	2086.26i	0.751149	−	1.30103i	0.947266	−	0.320447i	$-0.103833\pi$
$138$	−1122.00			−0.692109
$139$	−1413.50	+	2448.25i	−0.862529	+	1.49394i	0.00695133	+	0.999976i	$0.497787\pi$
$139$	−1413.50	+	2448.25i	−0.862529	+	1.49394i	−0.869480	+	0.493968i	$0.835546\pi$
$140$	20.0000	+	34.6410i	0.0120736	+	0.0209121i
$141$	582.000	+	1008.05i	0.347612	+	0.602081i
$142$	−158.000			−0.0933737
$143$	−422.500	+	439.075i	−0.247072	+	0.256764i
$144$	−288.000			−0.166667
$145$	13.0000	+	22.5167i	0.00744546	+	0.0128959i
$146$	230.000	+	398.372i	0.130376	+	0.225818i
$147$	−477.000	+	826.188i	−0.267635	+	0.463557i
$148$	1692.00			0.939740
$149$	−427.500	+	740.452i	−0.235048	+	0.407115i	−0.959287	−	0.282434i	$-0.908858\pi$
$149$	−427.500	+	740.452i	−0.235048	+	0.407115i	0.724239	+	0.689549i	$0.242191\pi$
$150$	363.000	−	628.734i	0.197592	−	0.342240i
$151$	2064.00			1.11236			0.556179	−	0.831063i	$-0.312267\pi$
$151$	2064.00			1.11236			0.556179	+	0.831063i	$0.312267\pi$
$152$	300.000	−	519.615i	0.160087	−	0.277279i
$153$	243.000	+	420.888i	0.128401	+	0.222397i
$154$	−65.0000	−	112.583i	−0.0340120	−	0.0589105i
$155$	−208.000			−0.107787
$156$	156.000	+	540.400i	0.0800641	+	0.277350i
$157$	−1894.00			−0.962788			−0.481394	−	0.876504i	$-0.659869\pi$
$157$	−1894.00			−0.962788			−0.481394	+	0.876504i	$0.659869\pi$
$158$	764.000	+	1323.29i	0.384687	+	0.666298i
$159$	927.000	+	1605.61i	0.462364	+	0.800838i
$160$	32.0000	−	55.4256i	0.0158114	−	0.0273861i
$161$	935.000			0.457691
$162$	81.0000	−	140.296i	0.0392837	−	0.0680414i
$163$	492.500	−	853.035i	0.236660	−	0.409907i	−0.723094	−	0.690750i	$-0.757281\pi$
$163$	492.500	−	853.035i	0.236660	−	0.409907i	0.959754	+	0.280843i	$0.0906139\pi$
$164$	780.000			0.371389
$165$	39.0000	−	67.5500i	0.0184009	−	0.0318713i
$166$	−732.000	−	1267.86i	−0.342254	−	0.592802i
$167$	1177.50	+	2039.49i	0.545615	+	0.945033i	0.998568	+	0.0534983i	$0.0170372\pi$
$167$	1177.50	+	2039.49i	0.545615	+	0.945033i	−0.452953	+	0.891534i	$0.649629\pi$
$168$	−120.000			−0.0551083
$169$	−1859.00	+	1170.87i	−0.846154	+	0.532939i
$170$	−108.000			−0.0487248
$171$	675.000	+	1169.13i	0.301863	+	0.522842i
$172$	−398.000	−	689.356i	−0.176437	−	0.305598i
$173$	1944.50	−	3367.97i	0.854553	−	1.48013i	−0.0225069	−	0.999747i	$-0.507165\pi$
$173$	1944.50	−	3367.97i	0.854553	−	1.48013i	0.877059	−	0.480382i	$-0.159502\pi$
$174$	−78.0000			−0.0339837
$175$	−302.500	+	523.945i	−0.130668	+	0.226323i
$176$	−104.000	+	180.133i	−0.0445414	+	0.0771481i
$177$	−1473.00			−0.625522
$178$	−1041.00	+	1803.06i	−0.438350	+	0.759244i
$179$	−1114.50	−	1930.37i	−0.465372	−	0.806048i	0.533846	−	0.845582i	$-0.320746\pi$
$179$	−1114.50	−	1930.37i	−0.465372	−	0.806048i	−0.999218	+	0.0395333i	$0.987413\pi$
$180$	72.0000	+	124.708i	0.0298142	+	0.0516398i
$181$	−1038.00			−0.426265			−0.213132	−	0.977023i	$-0.568367\pi$
$181$	−1038.00			−0.426265			−0.213132	+	0.977023i	$0.568367\pi$
$182$	−130.000	−	450.333i	−0.0529464	−	0.183412i
$183$	−525.000			−0.212072
$184$	−748.000	−	1295.57i	−0.299692	−	0.519081i
$185$	−423.000	−	732.657i	−0.168106	−	0.291168i
$186$	312.000	−	540.400i	0.122994	−	0.213032i
$187$	351.000			0.137260
$188$	−776.000	+	1344.07i	−0.301041	+	0.521417i
$189$	337.500	−	584.567i	0.129892	−	0.224979i
$190$	−300.000			−0.114549
$191$	1070.50	−	1854.16i	0.405543	−	0.702421i	−0.588842	−	0.808248i	$-0.700416\pi$
$191$	1070.50	−	1854.16i	0.405543	−	0.702421i	0.994384	+	0.105828i	$0.0337492\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	−1313.50	−	2275.05i	−0.489885	−	0.848506i	0.510047	−	0.860146i	$-0.329628\pi$
$193$	−1313.50	−	2275.05i	−0.489885	−	0.848506i	−0.999932	+	0.0116407i	$0.996295\pi$
$194$	194.000			0.0717958
$195$	195.000	−	202.650i	0.0716115	−	0.0744208i
$196$	−1272.00			−0.463557
$197$	−601.500	−	1041.83i	−0.217539	−	0.376788i	0.736516	−	0.676420i	$-0.236469\pi$
$197$	−601.500	−	1041.83i	−0.217539	−	0.376788i	−0.954055	+	0.299632i	$0.903136\pi$
$198$	−234.000	−	405.300i	−0.0839882	−	0.145472i
$199$	−371.500	+	643.457i	−0.132336	+	0.229213i	−0.924577	−	0.380996i	$-0.875581\pi$
$199$	−371.500	+	643.457i	−0.132336	+	0.229213i	0.792240	+	0.610209i	$0.208915\pi$
$200$	968.000			0.342240
$201$	1225.50	−	2122.63i	0.430050	−	0.744869i
$202$	−809.000	+	1401.23i	−0.281787	+	0.488070i
$203$	65.0000			0.0224734
$204$	162.000	−	280.592i	0.0555994	−	0.0963009i
$205$	−195.000	−	337.750i	−0.0664361	−	0.115071i
$206$	1288.00	+	2230.88i	0.435627	+	0.754529i
$207$	3366.00			1.13021
$208$	−520.000	+	540.400i	−0.173344	+	0.180144i
$209$	975.000			0.322690
$210$	30.0000	+	51.9615i	0.00985808	+	0.0170747i
$211$	177.500	+	307.439i	0.0579128	+	0.100308i	0.893528	−	0.449007i	$-0.148222\pi$
$211$	177.500	+	307.439i	0.0579128	+	0.100308i	−0.835615	+	0.549315i	$0.814889\pi$
$212$	−1236.00	+	2140.81i	−0.400419	+	0.693546i
$213$	−237.000			−0.0762393
$214$	1277.00	−	2211.83i	0.407916	−	0.706530i
$215$	−199.000	+	344.678i	−0.0631241	+	0.109334i
$216$	−1080.00			−0.340207
$217$	−260.000	+	450.333i	−0.0813362	+	0.140878i
$218$	826.000	+	1430.67i	0.256623	+	0.444484i
$219$	345.000	+	597.558i	0.106452	+	0.184380i
$220$	104.000			0.0318713
$221$	1228.50	+	303.975i	0.373927	+	0.0925229i
$222$	2538.00			0.767295
$223$	1141.50	+	1977.14i	0.342782	+	0.593717i	0.984948	−	0.172849i	$-0.0552973\pi$
$223$	1141.50	+	1977.14i	0.342782	+	0.593717i	−0.642166	+	0.766566i	$0.721964\pi$
$224$	−80.0000	−	138.564i	−0.0238626	−	0.0413313i
$225$	−1089.00	+	1886.20i	−0.322667	+	0.558875i
$226$	−1894.00			−0.557465
$227$	−1225.50	+	2122.63i	−0.358323	+	0.620633i	−0.987681	−	0.156482i	$-0.949985\pi$
$227$	−1225.50	+	2122.63i	−0.358323	+	0.620633i	0.629358	+	0.777116i	$0.283318\pi$
$228$	450.000	−	779.423i	0.130710	−	0.226397i
$229$	−1878.00			−0.541929			−0.270964	−	0.962589i	$-0.587343\pi$
$229$	−1878.00			−0.541929			−0.270964	+	0.962589i	$0.587343\pi$
$230$	−374.000	+	647.787i	−0.107221	+	0.185712i
$231$	−97.5000	−	168.875i	−0.0277707	−	0.0481002i
$232$	−52.0000	−	90.0666i	−0.0147154	−	0.0254878i
$233$	1630.00			0.458304			0.229152	−	0.973391i	$-0.426405\pi$
$233$	1630.00			0.458304			0.229152	+	0.973391i	$0.426405\pi$
$234$	−468.000	−	1621.20i	−0.130744	−	0.452911i
$235$	776.000			0.215407
$236$	−982.000	−	1700.87i	−0.270859	−	0.469142i
$237$	1146.00	+	1984.93i	0.314096	+	0.544030i
$238$	−135.000	+	233.827i	−0.0367679	+	0.0636838i
$239$	−5544.00			−1.50047			−0.750233	−	0.661173i	$-0.770059\pi$
$239$	−5544.00			−1.50047			−0.750233	+	0.661173i	$0.770059\pi$
$240$	48.0000	−	83.1384i	0.0129099	−	0.0223607i
$241$	−2761.50	+	4783.06i	−0.738107	+	1.27844i	0.215239	+	0.976561i	$0.430947\pi$
$241$	−2761.50	+	4783.06i	−0.738107	+	1.27844i	−0.953347	+	0.301878i	$0.902386\pi$
$242$	2324.00			0.617324
$243$	1944.00	−	3367.11i	0.513200	−	0.888889i
$244$	−350.000	−	606.218i	−0.0918297	−	0.159054i
$245$	318.000	+	550.792i	0.0829236	+	0.143628i
$246$	1170.00			0.303238
$247$	3412.50	+	844.375i	0.879078	+	0.217515i
$248$	832.000			0.213032
$249$	−1098.00	−	1901.79i	−0.279449	−	0.484021i
$250$	−492.000	−	852.169i	−0.124467	−	0.215584i
$251$	−1087.50	+	1883.61i	−0.273476	+	0.473674i	−0.969749	−	0.244103i	$-0.921507\pi$
$251$	−1087.50	+	1883.61i	−0.273476	+	0.473674i	0.696274	+	0.717776i	$0.254840\pi$
$252$	360.000			0.0899915
$253$	1215.50	−	2105.31i	0.302047	−	0.523160i
$254$	1177.00	−	2038.62i	0.290754	−	0.503601i
$255$	−162.000			−0.0397837
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2842.50	+	4923.35i	0.689923	+	1.19498i	0.971862	+	0.235550i	$0.0756891\pi$
$257$	2842.50	+	4923.35i	0.689923	+	1.19498i	−0.281939	+	0.959432i	$0.590978\pi$
$258$	−597.000	−	1034.03i	−0.144060	−	0.249520i
$259$	−2115.00			−0.507412
$260$	364.000	+	90.0666i	0.0868243	+	0.0214834i
$261$	234.000			0.0554952
$262$	−1420.00	−	2459.51i	−0.334839	−	0.579959i
$263$	−3058.50	−	5297.48i	−0.717092	−	1.24204i	−0.962147	−	0.272531i	$-0.912139\pi$
$263$	−3058.50	−	5297.48i	−0.717092	−	1.24204i	0.245055	−	0.969509i	$-0.421194\pi$
$264$	−156.000	+	270.200i	−0.0363679	+	0.0629911i
$265$	1236.00			0.286517
$266$	−375.000	+	649.519i	−0.0864388	+	0.149716i
$267$	−1561.50	+	2704.60i	−0.357911	+	0.619920i
$268$	3268.00			0.744869
$269$	2554.50	−	4424.52i	0.578999	−	1.00285i	−0.416596	−	0.909092i	$-0.636777\pi$
$269$	2554.50	−	4424.52i	0.578999	−	1.00285i	0.995595	−	0.0937632i	$-0.0298897\pi$
$270$	270.000	+	467.654i	0.0608581	+	0.105409i
$271$	−3774.50	−	6537.63i	−0.846068	−	1.46543i	−0.884690	−	0.466180i	$-0.845630\pi$
$271$	−3774.50	−	6537.63i	−0.846068	−	1.46543i	0.0386217	−	0.999254i	$-0.487703\pi$
$272$	432.000			0.0963009
$273$	−195.000	−	675.500i	−0.0432305	−	0.149755i
$274$	4818.00			1.06228
$275$	786.500	+	1362.26i	0.172464	+	0.298717i
$276$	−1122.00	−	1943.36i	−0.244697	−	0.423828i
$277$	490.500	−	849.571i	0.106395	−	0.184281i	−0.807913	−	0.589302i	$-0.799403\pi$
$277$	490.500	−	849.571i	0.106395	−	0.184281i	0.914307	+	0.405022i	$0.132736\pi$
$278$	−5654.00			−1.21980
$279$	−936.000	+	1621.20i	−0.200849	+	0.347881i
$280$	−40.0000	+	69.2820i	−0.00853735	+	0.0147871i
$281$	−2762.00			−0.586360			−0.293180	−	0.956057i	$-0.594713\pi$
$281$	−2762.00			−0.586360			−0.293180	+	0.956057i	$0.594713\pi$
$282$	−1164.00	+	2016.11i	−0.245799	+	0.425736i
$283$	−1962.50	−	3399.15i	−0.412221	−	0.713988i	0.582911	−	0.812536i	$-0.301913\pi$
$283$	−1962.50	−	3399.15i	−0.412221	−	0.713988i	−0.995132	+	0.0985482i	$0.968580\pi$
$284$	−158.000	−	273.664i	−0.0330126	−	0.0571795i
$285$	−450.000			−0.0935288
$286$	−1183.00	−	292.717i	−0.244588	−	0.0605199i
$287$	−975.000			−0.200531
$288$	−288.000	−	498.831i	−0.0589256	−	0.102062i
$289$	2092.00	+	3623.45i	0.425809	+	0.737523i
$290$	−26.0000	+	45.0333i	−0.00526473	+	0.00911879i
$291$	291.000			0.0586210
$292$	−460.000	+	796.743i	−0.0921899	+	0.159678i
$293$	−3855.50	+	6677.92i	−0.768740	+	1.33150i	0.169507	+	0.985529i	$0.445782\pi$
$293$	−3855.50	+	6677.92i	−0.768740	+	1.33150i	−0.938247	+	0.345967i	$0.887551\pi$
$294$	−1908.00			−0.378493
$295$	−491.000	+	850.437i	−0.0969055	+	0.167845i
$296$	1692.00	+	2930.63i	0.332248	+	0.575471i
$297$	−877.500	−	1519.87i	−0.171440	−	0.296943i
$298$	−1710.00			−0.332408
$299$	6077.50	−	6315.92i	1.17549	−	1.22160i
$300$	1452.00			0.279438
$301$	497.500	+	861.695i	0.0952672	+	0.165008i
$302$	2064.00	+	3574.95i	0.393278	+	0.681177i
$303$	−1213.50	+	2101.84i	−0.230078	+	0.398507i
$304$	1200.00			0.226397
$305$	−175.000	+	303.109i	−0.0328540	+	0.0569048i
$306$	−486.000	+	841.777i	−0.0907934	+	0.157259i
$307$	10388.0			1.93119			0.965594	−	0.260056i	$-0.0837409\pi$
$307$	10388.0			1.93119			0.965594	+	0.260056i	$0.0837409\pi$
$308$	130.000	−	225.167i	0.0240501	−	0.0416560i
$309$	1932.00	+	3346.32i	0.355688	+	0.616070i
$310$	−208.000	−	360.267i	−0.0381084	−	0.0660057i
$311$	−7272.00			−1.32591			−0.662954	−	0.748660i	$-0.730697\pi$
$311$	−7272.00			−1.32591			−0.662954	+	0.748660i	$0.730697\pi$
$312$	−780.000	+	810.600i	−0.141535	+	0.147087i
$313$	7910.00			1.42843			0.714217	−	0.699925i	$-0.246783\pi$
$313$	7910.00			1.42843			0.714217	+	0.699925i	$0.246783\pi$
$314$	−1894.00	−	3280.50i	−0.340397	−	0.589585i
$315$	−90.0000	−	155.885i	−0.0160982	−	0.0278829i
$316$	−1528.00	+	2646.57i	−0.272015	+	0.471144i
$317$	7398.00			1.31077			0.655383	−	0.755296i	$-0.272507\pi$
$317$	7398.00			1.31077			0.655383	+	0.755296i	$0.272507\pi$
$318$	−1854.00	+	3211.22i	−0.326941	+	0.566278i
$319$	84.5000	−	146.358i	0.0148310	−	0.0256881i
$320$	128.000			0.0223607
$321$	1915.50	−	3317.74i	0.333062	−	0.576880i
$322$	935.000	+	1619.47i	0.161818	+	0.280278i
$323$	−1012.50	−	1753.70i	−0.174418	−	0.302101i
$324$	324.000			0.0555556
$325$	1573.00	+	5449.03i	0.268475	+	0.930024i
$326$	1970.00			0.334688
$327$	1239.00	+	2146.01i	0.209532	+	0.362920i
$328$	780.000	+	1351.00i	0.131306	+	0.227428i
$329$	970.000	−	1680.09i	0.162547	−	0.281539i
$330$	156.000			0.0260228
$331$	1188.50	−	2058.54i	0.197359	−	0.341836i	−0.750312	−	0.661084i	$-0.770097\pi$
$331$	1188.50	−	2058.54i	0.197359	−	0.341836i	0.947671	+	0.319248i	$0.103430\pi$
$332$	1464.00	−	2535.72i	0.242010	−	0.419174i
$333$	−7614.00			−1.25299
$334$	−2355.00	+	4078.98i	−0.385808	+	0.668239i
$335$	−817.000	−	1415.09i	−0.133246	−	0.230789i
$336$	−120.000	−	207.846i	−0.0194837	−	0.0337468i
$337$	−7618.00			−1.23139			−0.615696	−	0.787984i	$-0.711125\pi$
$337$	−7618.00			−1.23139			−0.615696	+	0.787984i	$0.711125\pi$
$338$	−3887.00	−	2049.02i	−0.625518	−	0.329739i
$339$	−2841.00			−0.455168
$340$	−108.000	−	187.061i	−0.0172268	−	0.0298377i
$341$	676.000	+	1170.87i	0.107353	+	0.185941i
$342$	−1350.00	+	2338.27i	−0.213449	+	0.369705i
$343$	3305.00			0.520272
$344$	796.000	−	1378.71i	0.124760	−	0.216091i
$345$	−561.000	+	971.681i	−0.0875456	+	0.151633i
$346$	7778.00			1.20852
$347$	−187.500	+	324.760i	−0.0290073	+	0.0502421i	−0.880165	−	0.474669i	$-0.842568\pi$
$347$	−187.500	+	324.760i	−0.0290073	+	0.0502421i	0.851157	+	0.524911i	$0.175901\pi$
$348$	−78.0000	−	135.100i	−0.0120151	−	0.0208107i
$349$	−4863.50	−	8423.83i	−0.745952	−	1.29203i	−0.949749	−	0.313013i	$-0.898662\pi$
$349$	−4863.50	−	8423.83i	−0.745952	−	1.29203i	0.203797	−	0.979013i	$-0.434672\pi$
$350$	−1210.00			−0.184792
$351$	−1755.00	−	6079.50i	−0.266880	−	0.924500i
$352$	−416.000			−0.0629911
$353$	−1131.50	−	1959.82i	−0.170605	−	0.295497i	0.768026	−	0.640418i	$-0.221239\pi$
$353$	−1131.50	−	1959.82i	−0.170605	−	0.295497i	−0.938632	+	0.344921i	$0.887906\pi$
$354$	−1473.00	−	2551.31i	−0.221156	−	0.383053i
$355$	−79.0000	+	136.832i	−0.0118109	+	0.0204572i
$356$	−4164.00			−0.619920
$357$	−202.500	+	350.740i	−0.0300208	+	0.0519976i
$358$	2229.00	−	3860.74i	0.329068	−	0.569962i
$359$	−4488.00			−0.659798			−0.329899	−	0.944016i	$-0.607015\pi$
$359$	−4488.00			−0.659798			−0.329899	+	0.944016i	$0.607015\pi$
$360$	−144.000	+	249.415i	−0.0210819	+	0.0365148i
$361$	617.000	+	1068.68i	0.0899548	+	0.155806i
$362$	−1038.00	−	1797.87i	−0.150707	−	0.261033i
$363$	3486.00			0.504043
$364$	650.000	−	675.500i	0.0935969	−	0.0972687i
$365$	460.000			0.0659658
$366$	−525.000	−	909.327i	−0.0749787	−	0.129867i
$367$	813.500	+	1409.02i	0.115707	+	0.200410i	0.918062	−	0.396437i	$-0.129753\pi$
$367$	813.500	+	1409.02i	0.115707	+	0.200410i	−0.802355	+	0.596847i	$0.796420\pi$
$368$	1496.00	−	2591.15i	0.211914	−	0.367046i
$369$	−3510.00			−0.495185
$370$	846.000	−	1465.31i	0.118869	−	0.205887i
$371$	1545.00	−	2676.02i	0.216206	−	0.374480i
$372$	1248.00			0.173940
$373$	−1493.50	+	2586.82i	−0.207320	+	0.359089i	−0.950870	−	0.309592i	$-0.899808\pi$
$373$	−1493.50	+	2586.82i	−0.207320	+	0.359089i	0.743549	+	0.668681i	$0.233141\pi$
$374$	351.000	+	607.950i	0.0485288	+	0.0840544i
$375$	−738.000	−	1278.25i	−0.101627	−	0.176023i
$376$	−3104.00			−0.425736
$377$	422.500	−	439.075i	0.0577185	−	0.0599828i
$378$	1350.00			0.183694
$379$	4433.50	+	7679.05i	0.600880	+	1.04076i	0.992688	+	0.120708i	$0.0385165\pi$
$379$	4433.50	+	7679.05i	0.600880	+	1.04076i	−0.391808	+	0.920047i	$0.628150\pi$
$380$	−300.000	−	519.615i	−0.0404991	−	0.0701466i
$381$	1765.50	−	3057.94i	0.237400	−	0.411188i
$382$	4282.00			0.573524
$383$	−5701.50	+	9875.29i	−0.760661	+	1.31750i	0.181850	+	0.983326i	$0.441792\pi$
$383$	−5701.50	+	9875.29i	−0.760661	+	1.31750i	−0.942510	+	0.334177i	$0.891542\pi$
$384$	−192.000	+	332.554i	−0.0255155	+	0.0441942i
$385$	−130.000			−0.0172089
$386$	2627.00	−	4550.10i	0.346401	−	0.599984i
$387$	1791.00	+	3102.10i	0.235250	+	0.407464i
$388$	194.000	+	336.018i	0.0253837	+	0.0439658i
$389$	2622.00			0.341750			0.170875	−	0.985293i	$-0.445341\pi$
$389$	2622.00			0.341750			0.170875	+	0.985293i	$0.445341\pi$
$390$	546.000	+	135.100i	0.0708918	+	0.0175412i
$391$	−5049.00			−0.653041
$392$	−1272.00	−	2203.17i	−0.163892	−	0.283869i
$393$	−2130.00	−	3689.27i	−0.273395	−	0.473534i
$394$	1203.00	−	2083.66i	0.153823	−	0.266429i
$395$	1528.00			0.194638
$396$	468.000	−	810.600i	0.0593886	−	0.102864i
$397$	−329.500	+	570.711i	−0.0416552	+	0.0721490i	−0.886101	−	0.463492i	$-0.846596\pi$
$397$	−329.500	+	570.711i	−0.0416552	+	0.0721490i	0.844446	+	0.535641i	$0.179930\pi$
$398$	−1486.00			−0.187152
$399$	−562.500	+	974.279i	−0.0705770	+	0.122243i
$400$	968.000	+	1676.63i	0.121000	+	0.209578i
$401$	7342.50	+	12717.6i	0.914381	+	1.58376i	0.807804	+	0.589451i	$0.200656\pi$
$401$	7342.50	+	12717.6i	0.914381	+	1.58376i	0.106577	+	0.994304i	$0.466011\pi$
$402$	4902.00			0.608183
$403$	1352.00	+	4683.47i	0.167116	+	0.578908i
$404$	−3236.00			−0.398507
$405$	−81.0000	−	140.296i	−0.00993808	−	0.0172133i
$406$	65.0000	+	112.583i	0.00794556	+	0.0137621i
$407$	−2749.50	+	4762.27i	−0.334859	+	0.579993i
$408$	648.000			0.0786294
$409$	3914.50	−	6780.11i	0.473251	−	0.819694i	−0.526280	−	0.850311i	$-0.676414\pi$
$409$	3914.50	−	6780.11i	0.473251	−	0.819694i	0.999531	+	0.0306167i	$0.00974712\pi$
$410$	390.000	−	675.500i	0.0469774	−	0.0813672i
$411$	7227.00			0.867352
$412$	−2576.00	+	4461.76i	−0.308035	+	0.533532i
$413$	1227.50	+	2126.09i	0.146250	+	0.253313i
$414$	3366.00	+	5830.08i	0.399589	+	0.692109i
$415$	−1464.00			−0.173169
$416$	−1456.00	−	360.267i	−0.171602	−	0.0424604i
$417$	−8481.00			−0.995962
$418$	975.000	+	1688.75i	0.114088	+	0.197606i
$419$	1459.50	+	2527.93i	0.170170	+	0.294743i	0.938479	−	0.345336i	$-0.112235\pi$
$419$	1459.50	+	2527.93i	0.170170	+	0.294743i	−0.768309	+	0.640079i	$0.778902\pi$
$420$	−60.0000	+	103.923i	−0.00697071	+	0.0120736i
$421$	−3110.00			−0.360029			−0.180014	−	0.983664i	$-0.557614\pi$
$421$	−3110.00			−0.360029			−0.180014	+	0.983664i	$0.557614\pi$
$422$	−355.000	+	614.878i	−0.0409505	+	0.0709284i
$423$	3492.00	−	6048.32i	0.401387	−	0.695223i
$424$	−4944.00			−0.566278
$425$	1633.50	−	2829.30i	0.186439	−	0.322921i
$426$	−237.000	−	410.496i	−0.0269547	−	0.0466869i
$427$	437.500	+	757.772i	0.0495834	+	0.0858810i
$428$	5108.00			0.576880
$429$	−1774.50	−	439.075i	−0.199706	−	0.0494143i
$430$	−796.000			−0.0892710
$431$	4567.50	+	7911.14i	0.510461	+	0.884145i	0.999927	+	0.0121219i	$0.00385860\pi$
$431$	4567.50	+	7911.14i	0.510461	+	0.884145i	−0.489465	+	0.872023i	$0.662808\pi$
$432$	−1080.00	−	1870.61i	−0.120281	−	0.208333i
$433$	5834.50	−	10105.7i	0.647548	−	1.12159i	−0.336159	−	0.941805i	$-0.609128\pi$
$433$	5834.50	−	10105.7i	0.647548	−	1.12159i	0.983707	−	0.179780i	$-0.0575387\pi$
$434$	−1040.00			−0.115027
$435$	−39.0000	+	67.5500i	−0.00429864	+	0.00744546i
$436$	−1652.00	+	2861.35i	−0.181460	+	0.314298i
$437$	−14025.0			−1.53526
$438$	−690.000	+	1195.12i	−0.0752728	+	0.130376i
$439$	−6764.50	−	11716.5i	−0.735426	−	1.27380i	−0.954536	−	0.298095i	$-0.903649\pi$
$439$	−6764.50	−	11716.5i	−0.735426	−	1.27380i	0.219110	−	0.975700i	$-0.429685\pi$
$440$	104.000	+	180.133i	0.0112682	+	0.0195171i
$441$	5724.00			0.618076
$442$	702.000	+	2431.80i	0.0755446	+	0.261694i
$443$	−1932.00			−0.207206			−0.103603	−	0.994619i	$-0.533037\pi$
$443$	−1932.00			−0.207206			−0.103603	+	0.994619i	$0.533037\pi$
$444$	2538.00	+	4395.94i	0.271280	+	0.469870i
$445$	1041.00	+	1803.06i	0.110895	+	0.192075i
$446$	−2283.00	+	3954.27i	−0.242384	+	0.419821i
$447$	−2565.00			−0.271410
$448$	160.000	−	277.128i	0.0168734	−	0.0292256i
$449$	2678.50	−	4639.30i	0.281528	−	0.487621i	−0.690233	−	0.723587i	$-0.742492\pi$
$449$	2678.50	−	4639.30i	0.281528	−	0.487621i	0.971761	+	0.235966i	$0.0758253\pi$
$450$	−4356.00			−0.456320
$451$	−1267.50	+	2195.37i	−0.132338	+	0.229215i
$452$	−1894.00	−	3280.50i	−0.197094	−	0.341376i
$453$	3096.00	+	5362.43i	0.321110	+	0.556179i
$454$	−4902.00			−0.506745
$455$	−455.000	−	112.583i	−0.0468807	−	0.0116000i
$456$	1800.00			0.184852
$457$	−9699.50	−	16800.0i	−0.992830	−	1.71963i	−0.599933	−	0.800050i	$-0.704806\pi$
$457$	−9699.50	−	16800.0i	−0.992830	−	1.71963i	−0.392897	−	0.919582i	$-0.628527\pi$
$458$	−1878.00	−	3252.79i	−0.191601	−	0.331862i
$459$	−1822.50	+	3156.66i	−0.185331	+	0.321003i
$460$	−1496.00			−0.151633
$461$	7774.50	−	13465.8i	0.785455	−	1.36045i	−0.143273	−	0.989683i	$-0.545763\pi$
$461$	7774.50	−	13465.8i	0.785455	−	1.36045i	0.928727	−	0.370764i	$-0.120904\pi$
$462$	195.000	−	337.750i	0.0196368	−	0.0340120i
$463$	4072.00			0.408730			0.204365	−	0.978895i	$-0.434487\pi$
$463$	4072.00			0.408730			0.204365	+	0.978895i	$0.434487\pi$
$464$	104.000	−	180.133i	0.0104053	−	0.0180226i
$465$	−312.000	−	540.400i	−0.0311154	−	0.0538934i
$466$	1630.00	+	2823.24i	0.162035	+	0.280653i
$467$	15224.0			1.50853			0.754264	−	0.656571i	$-0.227994\pi$
$467$	15224.0			1.50853			0.754264	+	0.656571i	$0.227994\pi$
$468$	2340.00	−	2431.80i	0.231125	−	0.240192i
$469$	−4085.00			−0.402191
$470$	776.000	+	1344.07i	0.0761579	+	0.131909i
$471$	−2841.00	−	4920.76i	−0.277933	−	0.481394i
$472$	1964.00	−	3401.75i	0.191526	−	0.331733i
$473$	2587.00			0.251481
$474$	−2292.00	+	3969.86i	−0.222099	+	0.384687i
$475$	4537.50	−	7859.18i	0.438305	−	0.759166i
$476$	−540.000			−0.0519976
$477$	5562.00	−	9633.67i	0.533892	−	0.924728i
$478$	−5544.00	−	9602.49i	−0.530495	−	0.918844i
$479$	5167.50	+	8950.37i	0.492921	+	0.853764i	0.999967	−	0.00815506i	$-0.00259587\pi$
$479$	5167.50	+	8950.37i	0.492921	+	0.853764i	−0.507046	+	0.861919i	$0.669263\pi$
$480$	192.000			0.0182574
$481$	−13747.5	+	14286.8i	−1.30319	+	1.35431i
$482$	−11046.0			−1.04384
$483$	1402.50	+	2429.20i	0.132124	+	0.228846i
$484$	2324.00	+	4025.29i	0.218257	+	0.378032i
$485$	97.0000	−	168.009i	0.00908153	−	0.0157297i
$486$	7776.00			0.725775
$487$	−3227.50	+	5590.19i	−0.300312	+	0.520156i	−0.976207	−	0.216843i	$-0.930424\pi$
$487$	−3227.50	+	5590.19i	−0.300312	+	0.520156i	0.675894	+	0.736998i	$0.263757\pi$
$488$	700.000	−	1212.44i	0.0649334	−	0.112468i
$489$	2955.00			0.273271
$490$	−636.000	+	1101.58i	−0.0586358	+	0.101560i
$491$	−3888.50	−	6735.08i	−0.357404	−	0.619043i	0.630122	−	0.776496i	$-0.283005\pi$
$491$	−3888.50	−	6735.08i	−0.357404	−	0.619043i	−0.987526	+	0.157454i	$0.949672\pi$
$492$	1170.00	+	2026.50i	0.107211	+	0.185694i
$493$	−351.000			−0.0320654
$494$	1950.00	+	6755.00i	0.177601	+	0.615226i
$495$	−468.000			−0.0424950
$496$	832.000	+	1441.07i	0.0753184	+	0.130455i
$497$	197.500	+	342.080i	0.0178251	+	0.0308740i
$498$	2196.00	−	3803.58i	0.197601	−	0.342254i
$499$	−3044.00			−0.273082			−0.136541	−	0.990634i	$-0.543599\pi$
$499$	−3044.00			−0.273082			−0.136541	+	0.990634i	$0.543599\pi$
$500$	984.000	−	1704.34i	0.0880116	−	0.152441i
$501$	−3532.50	+	6118.47i	−0.315011	+	0.545615i
$502$	−4350.00			−0.386753
$503$	−5673.50	+	9826.79i	−0.502920	+	0.871083i	0.497074	+	0.867708i	$0.334408\pi$
$503$	−5673.50	+	9826.79i	−0.502920	+	0.871083i	−0.999994	+	0.00337525i	$0.998926\pi$
$504$	360.000	+	623.538i	0.0318168	+	0.0551083i
$505$	809.000	+	1401.23i	0.0712872	+	0.123473i
$506$	4862.00			0.427159
$507$	−5830.50	−	3073.52i	−0.510733	−	0.269231i
$508$	4708.00			0.411188
$509$	−363.500	−	629.600i	−0.0316539	−	0.0548262i	0.849764	−	0.527163i	$-0.176744\pi$
$509$	−363.500	−	629.600i	−0.0316539	−	0.0548262i	−0.881418	+	0.472336i	$0.843411\pi$
$510$	−162.000	−	280.592i	−0.0140656	−	0.0243624i
$511$	575.000	−	995.929i	0.0497779	−	0.0862178i
$512$	−512.000			−0.0441942
$513$	−5062.50	+	8768.51i	−0.435701	+	0.754657i
$514$	−5685.00	+	9846.71i	−0.487849	+	0.844980i
$515$	2576.00			0.220412
$516$	1194.00	−	2068.07i	0.101866	−	0.176437i
$517$	−2522.00	−	4368.23i	−0.214540	−	0.371595i
$518$	−2115.00	−	3663.29i	−0.179397	−	0.310725i
$519$	11667.0			0.986752
$520$	208.000	+	720.533i	0.0175412	+	0.0607644i
$521$	9582.00			0.805749			0.402874	−	0.915255i	$-0.368011\pi$
$521$	9582.00			0.805749			0.402874	+	0.915255i	$0.368011\pi$
$522$	234.000	+	405.300i	0.0196205	+	0.0339837i
$523$	5191.50	+	8991.94i	0.434051	+	0.751798i	0.997218	−	0.0745454i	$-0.0237506\pi$
$523$	5191.50	+	8991.94i	0.434051	+	0.751798i	−0.563167	+	0.826343i	$0.690417\pi$
$524$	2840.00	−	4919.02i	0.236767	−	0.410093i
$525$	−1815.00			−0.150882
$526$	6117.00	−	10595.0i	0.507061	−	0.878255i
$527$	1404.00	−	2431.80i	0.116052	−	0.201007i
$528$	−624.000			−0.0514320
$529$	−11401.0	+	19747.1i	−0.937043	+	1.62301i
$530$	1236.00	+	2140.81i	0.101299	+	0.175455i
$531$	4419.00	+	7653.93i	0.361146	+	0.625522i
$532$	−1500.00			−0.122243
$533$	−6337.50	+	6586.12i	−0.515024	+	0.535228i
$534$	−6246.00			−0.506163
$535$	−1277.00	−	2211.83i	−0.103195	−	0.178740i
$536$	3268.00	+	5660.34i	0.263351	+	0.456137i
$537$	3343.50	−	5791.11i	0.268683	−	0.465372i
$538$	10218.0			0.818828
$539$	2067.00	−	3580.15i	0.165180	−	0.286100i
$540$	−540.000	+	935.307i	−0.0430331	+	0.0745356i
$541$	12230.0			0.971920			0.485960	−	0.873981i	$-0.338470\pi$
$541$	12230.0			0.971920			0.485960	+	0.873981i	$0.338470\pi$
$542$	7549.00	−	13075.3i	0.598261	−	1.03622i
$543$	−1557.00	−	2696.80i	−0.123052	−	0.213132i
$544$	432.000	+	748.246i	0.0340475	+	0.0589720i
$545$	1652.00			0.129842
$546$	975.000	−	1013.25i	0.0764215	−	0.0794196i
$547$	−14636.0			−1.14404			−0.572020	−	0.820239i	$-0.693840\pi$
$547$	−14636.0			−1.14404			−0.572020	+	0.820239i	$0.693840\pi$
$548$	4818.00	+	8345.02i	0.375574	+	0.650514i
$549$	1575.00	+	2727.98i	0.122440	+	0.212072i
$550$	−1573.00	+	2724.52i	−0.121951	+	0.211225i
$551$	−975.000			−0.0753837
$552$	2244.00	−	3886.72i	0.173027	−	0.299692i
$553$	1910.00	−	3308.22i	0.146874	−	0.254394i
$554$	1962.00			0.150465
$555$	1269.00	−	2197.97i	0.0970559	−	0.168106i
$556$	−5654.00	−	9793.02i	−0.431264	−	0.746972i
$557$	382.500	+	662.509i	0.0290970	+	0.0503975i	0.880207	−	0.474590i	$-0.157403\pi$
$557$	382.500	+	662.509i	0.0290970	+	0.0503975i	−0.851110	+	0.524987i	$0.824070\pi$
$558$	−3744.00			−0.284043
$559$	9054.50	+	2240.41i	0.685089	+	0.169515i
$560$	−160.000			−0.0120736
$561$	526.500	+	911.925i	0.0396236	+	0.0686301i
$562$	−2762.00	−	4783.92i	−0.207309	−	0.359071i
$563$	−2957.50	+	5122.54i	−0.221392	+	0.383462i	−0.955231	−	0.295861i	$-0.904393\pi$
$563$	−2957.50	+	5122.54i	−0.221392	+	0.383462i	0.733839	+	0.679324i	$0.237727\pi$
$564$	−4656.00			−0.347612
$565$	−947.000	+	1640.25i	−0.0705143	+	0.122134i
$566$	3925.00	−	6798.30i	0.291484	−	0.504865i
$567$	−405.000			−0.0299972
$568$	316.000	−	547.328i	0.0233434	−	0.0404320i
$569$	608.500	+	1053.95i	0.0448324	+	0.0776520i	0.887571	−	0.460671i	$-0.152391\pi$
$569$	608.500	+	1053.95i	0.0448324	+	0.0776520i	−0.842738	+	0.538323i	$0.819058\pi$
$570$	−450.000	−	779.423i	−0.0330674	−	0.0572744i
$571$	−23436.0			−1.71763			−0.858814	−	0.512287i	$-0.828798\pi$
$571$	−23436.0			−1.71763			−0.858814	+	0.512287i	$0.828798\pi$
$572$	−676.000	−	2341.73i	−0.0494143	−	0.171176i
$573$	6423.00			0.468280
$574$	−975.000	−	1688.75i	−0.0708985	−	0.122800i
$575$	−11313.5	−	19595.6i	−0.820531	−	1.42120i
$576$	576.000	−	997.661i	0.0416667	−	0.0721688i
$577$	7854.00			0.566666			0.283333	−	0.959022i	$-0.408560\pi$
$577$	7854.00			0.566666			0.283333	+	0.959022i	$0.408560\pi$
$578$	−4184.00	+	7246.90i	−0.301092	+	0.521507i
$579$	3940.50	−	6825.15i	0.282835	−	0.489885i
$580$	−104.000			−0.00744546
$581$	−1830.00	+	3169.65i	−0.130673	+	0.226333i
$582$	291.000	+	504.027i	0.0207257	+	0.0358979i
$583$	−4017.00	−	6957.65i	−0.285364	−	0.494265i
$584$	−1840.00			−0.130376
$585$	−1638.00	−	405.300i	−0.115766	−	0.0286446i
$586$	−15422.0			−1.08716
$587$	−8516.50	−	14751.0i	−0.598831	−	1.03721i	−0.992994	−	0.118165i	$-0.962299\pi$
$587$	−8516.50	−	14751.0i	−0.598831	−	1.03721i	0.394163	−	0.919040i	$-0.371034\pi$
$588$	−1908.00	−	3304.75i	−0.133817	−	0.231778i
$589$	3900.00	−	6755.00i	0.272830	−	0.472555i
$590$	−1964.00			−0.137045
$591$	1804.50	−	3125.49i	0.125596	−	0.217539i
$592$	−3384.00	+	5861.26i	−0.234935	+	0.406919i
$593$	−14506.0			−1.00454			−0.502268	−	0.864712i	$-0.667501\pi$
$593$	−14506.0			−1.00454			−0.502268	+	0.864712i	$0.667501\pi$
$594$	1755.00	−	3039.75i	0.121226	−	0.209970i
$595$	135.000	+	233.827i	0.00930161	+	0.0161109i
$596$	−1710.00	−	2961.81i	−0.117524	−	0.203558i
$597$	−2229.00			−0.152809
$598$	17017.0	+	4210.62i	1.16367	+	0.287935i
$599$	15388.0			1.04964			0.524822	−	0.851212i	$-0.324132\pi$
$599$	15388.0			1.04964			0.524822	+	0.851212i	$0.324132\pi$
$600$	1452.00	+	2514.94i	0.0987961	+	0.171120i
$601$	3038.50	+	5262.84i	0.206228	+	0.357197i	0.950523	−	0.310653i	$-0.100548\pi$
$601$	3038.50	+	5262.84i	0.206228	+	0.357197i	−0.744295	+	0.667851i	$0.767214\pi$
$602$	−995.000	+	1723.39i	−0.0673641	+	0.116678i
$603$	−14706.0			−0.993159
$604$	−4128.00	+	7149.91i	−0.278089	+	0.481665i
$605$	1162.00	−	2012.64i	0.0780860	−	0.135249i
$606$	−4854.00			−0.325380
$607$	−5107.50	+	8846.45i	−0.341527	+	0.591543i	−0.984717	−	0.174165i	$-0.944277\pi$
$607$	−5107.50	+	8846.45i	−0.341527	+	0.591543i	0.643189	+	0.765707i	$0.277611\pi$
$608$	1200.00	+	2078.46i	0.0800435	+	0.138639i
$609$	97.5000	+	168.875i	0.00648752	+	0.0112367i
$610$	−700.000			−0.0464626
$611$	−5044.00	−	17472.9i	−0.333974	−	1.15692i
$612$	−1944.00			−0.128401
$613$	1728.50	+	2993.85i	0.113888	+	0.197260i	0.917335	−	0.398117i	$-0.130336\pi$
$613$	1728.50	+	2993.85i	0.113888	+	0.197260i	−0.803447	+	0.595377i	$0.797003\pi$
$614$	10388.0	+	17992.5i	0.682778	+	1.18261i
$615$	585.000	−	1013.25i	0.0383569	−	0.0664361i
$616$	520.000			0.0340120
$617$	3584.50	−	6208.54i	0.233884	−	0.405099i	−0.725064	−	0.688682i	$-0.758190\pi$
$617$	3584.50	−	6208.54i	0.233884	−	0.405099i	0.958948	+	0.283583i	$0.0915230\pi$
$618$	−3864.00	+	6692.64i	−0.251510	+	0.435627i
$619$	20212.0			1.31242			0.656211	−	0.754578i	$-0.272158\pi$
$619$	20212.0			1.31242			0.656211	+	0.754578i	$0.272158\pi$
$620$	416.000	−	720.533i	0.0269467	−	0.0466731i
$621$	12622.5	+	21862.8i	0.815658	+	1.41276i
$622$	−7272.00	−	12595.5i	−0.468779	−	0.811949i
$623$	5205.00			0.334725
$624$	−2184.00	−	540.400i	−0.140112	−	0.0346688i
$625$	14141.0			0.905024
$626$	7910.00	+	13700.5i	0.505027	+	0.874733i
$627$	1462.50	+	2533.12i	0.0931525	+	0.161345i
$628$	3788.00	−	6561.01i	0.240697	−	0.416899i
$629$	11421.0			0.723983
$630$	180.000	−	311.769i	0.0113831	−	0.0197162i
$631$	4472.50	−	7746.60i	0.282167	−	0.488728i	−0.689751	−	0.724046i	$-0.742280\pi$
$631$	4472.50	−	7746.60i	0.282167	−	0.488728i	0.971918	+	0.235319i	$0.0756134\pi$
$632$	−6112.00			−0.384687
$633$	−532.500	+	922.317i	−0.0334360	+	0.0579128i
$634$	7398.00	+	12813.7i	0.463426	+	0.802677i
$635$	−1177.00	−	2038.62i	−0.0735556	−	0.127402i
$636$	−7416.00			−0.462364
$637$	10335.0	−	10740.4i	0.642838	−	0.668057i
$638$	338.000			0.0209742
$639$	711.000	+	1231.49i	0.0440168	+	0.0762393i
$640$	128.000	+	221.703i	0.00790569	+	0.0136931i
$641$	−14121.5	+	24459.2i	−0.870149	+	1.50714i	−0.00830761	+	0.999965i	$0.502644\pi$
$641$	−14121.5	+	24459.2i	−0.870149	+	1.50714i	−0.861842	+	0.507177i	$0.830689\pi$
$642$	7662.00			0.471020
$643$	−2615.50	+	4530.18i	−0.160413	+	0.277843i	−0.935017	−	0.354604i	$-0.884616\pi$
$643$	−2615.50	+	4530.18i	−0.160413	+	0.277843i	0.774604	+	0.632446i	$0.217949\pi$
$644$	−1870.00	+	3238.94i	−0.114423	+	0.198186i
$645$	−1194.00			−0.0728895
$646$	2025.00	−	3507.40i	0.123332	−	0.213618i
$647$	2435.50	+	4218.41i	0.147990	+	0.256326i	0.930484	−	0.366332i	$-0.119386\pi$
$647$	2435.50	+	4218.41i	0.147990	+	0.256326i	−0.782495	+	0.622657i	$0.786053\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	6383.00			0.386063
$650$	−7865.00	+	8173.55i	−0.474601	+	0.493220i
$651$	−1560.00			−0.0939189
$652$	1970.00	+	3412.14i	0.118330	+	0.204954i
$653$	−6127.50	−	10613.1i	−0.367209	−	0.636025i	0.621919	−	0.783082i	$-0.286353\pi$
$653$	−6127.50	−	10613.1i	−0.367209	−	0.636025i	−0.989128	+	0.147057i	$0.953020\pi$
$654$	−2478.00	+	4292.02i	−0.148161	+	0.256623i
$655$	−2840.00			−0.169417
$656$	−1560.00	+	2702.00i	−0.0928472	+	0.160816i
$657$	2070.00	−	3585.35i	0.122920	−	0.212904i
$658$	3880.00			0.229876
$659$	1072.50	−	1857.62i	0.0633971	−	0.109807i	−0.832585	−	0.553898i	$-0.813140\pi$
$659$	1072.50	−	1857.62i	0.0633971	−	0.109807i	0.895982	+	0.444091i	$0.146473\pi$
$660$	156.000	+	270.200i	0.00920044	+	0.0159356i
$661$	−1055.50	−	1828.18i	−0.0621092	−	0.107576i	0.833299	−	0.552823i	$-0.186449\pi$
$661$	−1055.50	−	1828.18i	−0.0621092	−	0.107576i	−0.895408	+	0.445247i	$0.853116\pi$
$662$	4754.00			0.279108
$663$	1053.00	+	3647.70i	0.0616819	+	0.213673i
$664$	5856.00			0.342254
$665$	375.000	+	649.519i	0.0218675	+	0.0378756i
$666$	−7614.00	−	13187.8i	−0.442998	−	0.767295i
$667$	−1215.50	+	2105.31i	−0.0705612	+	0.122216i
$668$	−9420.00			−0.545615
$669$	−3424.50	+	5931.41i	−0.197906	+	0.342782i
$670$	1634.00	−	2830.17i	0.0942193	−	0.163193i
$671$	2275.00			0.130887
$672$	240.000	−	415.692i	0.0137771	−	0.0238626i
$673$	11636.5	+	20155.0i	0.666499	+	1.15441i	0.978876	+	0.204453i	$0.0655414\pi$
$673$	11636.5	+	20155.0i	0.666499	+	1.15441i	−0.312377	+	0.949958i	$0.601125\pi$
$674$	−7618.00	−	13194.8i	−0.435363	−	0.754070i
$675$	−16335.0			−0.931458
$676$	−338.000	−	8781.50i	−0.0192308	−	0.499630i
$677$	−5910.00			−0.335509			−0.167755	−	0.985829i	$-0.553652\pi$
$677$	−5910.00			−0.335509			−0.167755	+	0.985829i	$0.553652\pi$
$678$	−2841.00	−	4920.76i	−0.160926	−	0.278732i
$679$	−242.500	−	420.022i	−0.0137059	−	0.0237393i
$680$	216.000	−	374.123i	0.0121812	−	0.0210985i
$681$	−7353.00			−0.413756
$682$	−1352.00	+	2341.73i	−0.0759102	+	0.131480i
$683$	−8373.50	+	14503.3i	−0.469111	+	0.812525i	−0.999377	−	0.0353071i	$-0.988759\pi$
$683$	−8373.50	+	14503.3i	−0.469111	+	0.812525i	0.530265	+	0.847832i	$0.322092\pi$
$684$	−5400.00			−0.301863
$685$	2409.00	−	4172.51i	0.134370	−	0.232735i
$686$	3305.00	+	5724.43i	0.183944	+	0.318600i
$687$	−2817.00	−	4879.19i	−0.156441	−	0.270964i
$688$	3184.00			0.176437
$689$	−8034.00	−	27830.6i	−0.444225	−	1.53884i
$690$	−2244.00			−0.123808
$691$	−5154.50	−	8927.86i	−0.283772	−	0.491507i	0.688539	−	0.725200i	$-0.258253\pi$
$691$	−5154.50	−	8927.86i	−0.283772	−	0.491507i	−0.972311	+	0.233692i	$0.924919\pi$
$692$	7778.00	+	13471.9i	0.427276	+	0.740064i
$693$	−585.000	+	1013.25i	−0.0320668	+	0.0555414i
$694$	−750.000			−0.0410225
$695$	−2827.00	+	4896.51i	−0.154294	+	0.267245i
$696$	156.000	−	270.200i	0.00849593	−	0.0147154i
$697$	5265.00			0.286121
$698$	9727.00	−	16847.7i	0.527468	−	0.913601i
$699$	2445.00	+	4234.86i	0.132301	+	0.229152i
$700$	−1210.00	−	2095.78i	−0.0653339	−	0.113162i
$701$	−24294.0			−1.30895			−0.654473	−	0.756085i	$-0.727110\pi$
$701$	−24294.0			−1.30895			−0.654473	+	0.756085i	$0.727110\pi$
$702$	8775.00	−	9119.25i	0.471782	−	0.490290i
$703$	31725.0			1.70204
$704$	−416.000	−	720.533i	−0.0222707	−	0.0385740i
$705$	1164.00	+	2016.11i	0.0621827	+	0.107704i
$706$	2263.00	−	3919.63i	0.120636	−	0.208948i
$707$	4045.00			0.215174
$708$	2946.00	−	5102.62i	0.156381	−	0.270859i
$709$	−6329.50	+	10963.0i	−0.335274	+	0.580712i	−0.983537	−	0.180704i	$-0.942162\pi$
$709$	−6329.50	+	10963.0i	−0.335274	+	0.580712i	0.648263	+	0.761416i	$0.275496\pi$
$710$	−316.000			−0.0167032
$711$	6876.00	−	11909.6i	0.362687	−	0.628192i
$712$	−4164.00	−	7212.26i	−0.219175	−	0.379622i
$713$	−9724.00	−	16842.5i	−0.510753	−	0.884650i
$714$	−810.000			−0.0424559
$715$	−845.000	+	878.150i	−0.0441975	+	0.0459314i
$716$	8916.00			0.465372
$717$	−8316.00	−	14403.7i	−0.433147	−	0.750233i
$718$	−4488.00	−	7773.44i	−0.233274	−	0.404042i
$719$	−6545.50	+	11337.1i	−0.339508	+	0.588044i	−0.984340	−	0.176279i	$-0.943594\pi$
$719$	−6545.50	+	11337.1i	−0.339508	+	0.588044i	0.644833	+	0.764324i	$0.276927\pi$
$720$	−576.000			−0.0298142
$721$	3220.00	−	5577.20i	0.166323	−	0.288080i
$722$	−1234.00	+	2137.35i	−0.0636077	+	0.110172i
$723$	−16569.0			−0.852293
$724$	2076.00	−	3595.74i	0.106566	−	0.184578i
$725$	−786.500	−	1362.26i	−0.0402895	−	0.0697834i
$726$	3486.00	+	6037.93i	0.178206	+	0.308662i
$727$	10792.0			0.550555			0.275277	−	0.961365i	$-0.411230\pi$
$727$	10792.0			0.550555			0.275277	+	0.961365i	$0.411230\pi$
$728$	1820.00	+	450.333i	0.0926562	+	0.0229265i
$729$	9477.00			0.481481
$730$	460.000	+	796.743i	0.0233224	+	0.0403956i
$731$	−2686.50	−	4653.15i	−0.135929	−	0.235435i
$732$	1050.00	−	1818.65i	0.0530179	−	0.0918297i
$733$	−2698.00			−0.135952			−0.0679761	−	0.997687i	$-0.521654\pi$
$733$	−2698.00			−0.135952			−0.0679761	+	0.997687i	$0.521654\pi$
$734$	−1627.00	+	2818.05i	−0.0818170	+	0.141711i
$735$	−954.000	+	1652.38i	−0.0478759	+	0.0829236i
$736$	5984.00			0.299692
$737$	−5310.50	+	9198.06i	−0.265420	+	0.459721i
$738$	−3510.00	−	6079.50i	−0.175074	−	0.303238i
$739$	−1420.50	−	2460.38i	−0.0707090	−	0.122472i	0.828503	−	0.559984i	$-0.189193\pi$
$739$	−1420.50	−	2460.38i	−0.0707090	−	0.122472i	−0.899212	+	0.437513i	$0.855859\pi$
$740$	3384.00			0.168106
$741$	2925.00	+	10132.5i	0.145010	+	0.502330i
$742$	6180.00			0.305761
$743$	4595.50	+	7959.64i	0.226908	+	0.393016i	0.956890	−	0.290450i	$-0.0938050\pi$
$743$	4595.50	+	7959.64i	0.226908	+	0.393016i	−0.729982	+	0.683466i	$0.760472\pi$
$744$	1248.00	+	2161.60i	0.0614972	+	0.106516i
$745$	−855.000	+	1480.90i	−0.0420467	+	0.0728270i
$746$	−5974.00			−0.293195
$747$	−6588.00	+	11410.8i	−0.322680	+	0.558899i
$748$	−702.000	+	1215.90i	−0.0343151	+	0.0594354i
$749$	−6385.00			−0.311486
$750$	1476.00	−	2556.51i	0.0718612	−	0.124467i
$751$	829.500	+	1436.74i	0.0403048	+	0.0698099i	0.885474	−	0.464689i	$-0.153834\pi$
$751$	829.500	+	1436.74i	0.0403048	+	0.0698099i	−0.845169	+	0.534499i	$0.820500\pi$
$752$	−3104.00	−	5376.29i	−0.150520	−	0.260709i
$753$	−6525.00			−0.315782
$754$	1183.00	+	292.717i	0.0571384	+	0.0141381i
$755$	4128.00			0.198985
$756$	1350.00	+	2338.27i	0.0649458	+	0.112489i
$757$	6964.50	+	12062.9i	0.334384	+	0.579171i	0.983366	−	0.181633i	$-0.0581383\pi$
$757$	6964.50	+	12062.9i	0.334384	+	0.579171i	−0.648982	+	0.760804i	$0.724805\pi$
$758$	−8867.00	+	15358.1i	−0.424886	+	0.735925i
$759$	7293.00			0.348774
$760$	600.000	−	1039.23i	0.0286372	−	0.0496011i
$761$	−2293.50	+	3972.46i	−0.109250	+	0.189227i	−0.915467	−	0.402394i	$-0.868178\pi$
$761$	−2293.50	+	3972.46i	−0.109250	+	0.189227i	0.806217	+	0.591620i	$0.201512\pi$
$762$	7062.00			0.335734
$763$	2065.00	−	3576.68i	0.0979791	−	0.169705i
$764$	4282.00	+	7416.64i	0.202771	+	0.351210i
$765$	486.000	+	841.777i	0.0229691	+	0.0397837i
$766$	−22806.0			−1.07574
$767$	22340.5	+	5527.84i	1.05172	+	0.260233i
$768$	−768.000			−0.0360844
$769$	−7249.50	−	12556.5i	−0.339953	−	0.588815i	0.644471	−	0.764629i	$-0.277078\pi$
$769$	−7249.50	−	12556.5i	−0.339953	−	0.588815i	−0.984423	+	0.175814i	$0.943744\pi$
$770$	−130.000	−	225.167i	−0.00608425	−	0.0105382i
$771$	−8527.50	+	14770.1i	−0.398327	+	0.689923i
$772$	10508.0			0.489885
$773$	−1529.50	+	2649.17i	−0.0711673	+	0.123265i	−0.899413	−	0.437100i	$-0.856006\pi$
$773$	−1529.50	+	2649.17i	−0.0711673	+	0.123265i	0.828246	+	0.560365i	$0.189339\pi$
$774$	−3582.00	+	6204.21i	−0.166347	+	0.288121i
$775$	12584.0			0.583265
$776$	−388.000	+	672.036i	−0.0179490	+	0.0310885i
$777$	−3172.50	−	5494.93i	−0.146477	−	0.253706i
$778$	2622.00	+	4541.44i	0.120827	+	0.209278i
$779$	14625.0			0.672651
$780$	312.000	+	1080.80i	0.0143223	+	0.0496139i
$781$	1027.00			0.0470537
$782$	−5049.00	−	8745.12i	−0.230885	−	0.399904i
$783$	877.500	+	1519.87i	0.0400502	+	0.0693689i
$784$	2544.00	−	4406.34i	0.115889	−	0.200726i
$785$	−3788.00			−0.172229
$786$	4260.00	−	7378.54i	0.193320	−	0.334839i
$787$	−18203.5	+	31529.4i	−0.824504	+	1.42808i	0.0777937	+	0.996969i	$0.475212\pi$
$787$	−18203.5	+	31529.4i	−0.824504	+	1.42808i	−0.902298	+	0.431113i	$0.858121\pi$
$788$	4812.00			0.217539
$789$	9175.50	−	15892.4i	0.414013	−	0.717092i
$790$	1528.00	+	2646.57i	0.0688149	+	0.119191i
$791$	2367.50	+	4100.63i	0.106420	+	0.184326i
$792$	1872.00			0.0839882
$793$	7962.50	+	1970.21i	0.356566	+	0.0882272i
$794$	−1318.00			−0.0589094
$795$	1854.00	+	3211.22i	0.0827102	+	0.143258i
$796$	−1486.00	−	2573.83i	−0.0661682	−	0.114607i
$797$	6568.50	−	11377.0i	0.291930	−	0.505638i	−0.682336	−	0.731039i	$-0.739036\pi$
$797$	6568.50	−	11377.0i	0.291930	−	0.505638i	0.974266	+	0.225401i	$0.0723692\pi$
$798$	−2250.00			−0.0998109
$799$	−5238.00	+	9072.48i	−0.231924	+	0.401704i
$800$	−1936.00	+	3353.25i	−0.0855599	+	0.148194i
$801$	18738.0			0.826560
$802$	−14685.0	+	25435.2i	−0.646565	+	1.11988i
$803$	−1495.00	−	2589.42i	−0.0657004	−	0.113796i
$804$	4902.00	+	8490.51i	0.215025	+	0.372434i
$805$	1870.00			0.0818743
$806$	−6760.00	+	7025.20i	−0.295423	+	0.307012i
$807$	15327.0			0.668570
$808$	−3236.00	−	5604.92i	−0.140894	−	0.244035i
$809$	−7705.50	−	13346.3i	−0.334871	−	0.580014i	0.648589	−	0.761139i	$-0.275360\pi$
$809$	−7705.50	−	13346.3i	−0.334871	−	0.580014i	−0.983460	+	0.181125i	$0.942026\pi$
$810$	162.000	−	280.592i	0.00702728	−	0.0121716i
$811$	−27664.0			−1.19780			−0.598899	−	0.800824i	$-0.704395\pi$
$811$	−27664.0			−1.19780			−0.598899	+	0.800824i	$0.704395\pi$
$812$	−130.000	+	225.167i	−0.00561836	+	0.00973128i
$813$	11323.5	−	19612.9i	0.488478	−	0.846068i
$814$	−10998.0			−0.473562
$815$	985.000	−	1706.07i	0.0423350	−	0.0733264i
$816$	648.000	+	1122.37i	0.0277997	+	0.0481505i
$817$	−7462.50	−	12925.4i	−0.319559	−	0.553493i
$818$	15658.0			0.669278
$819$	−2925.00	+	3039.75i	−0.124796	+	0.129692i
$820$	1560.00			0.0664361
$821$	10698.5	+	18530.3i	0.454787	+	0.787714i	0.998676	−	0.0514429i	$-0.0163820\pi$
$821$	10698.5	+	18530.3i	0.454787	+	0.787714i	−0.543889	+	0.839157i	$0.683049\pi$
$822$	7227.00	+	12517.5i	0.306655	+	0.531142i
$823$	12124.5	−	21000.3i	0.513528	−	0.889456i	−0.486349	−	0.873765i	$-0.661672\pi$
$823$	12124.5	−	21000.3i	0.513528	−	0.889456i	0.999877	−	0.0156918i	$-0.00499506\pi$
$824$	−10304.0			−0.435627
$825$	−2359.50	+	4086.77i	−0.0995724	+	0.172464i
$826$	−2455.00	+	4252.18i	−0.103414	+	0.179119i
$827$	14028.0			0.589844			0.294922	−	0.955521i	$-0.404706\pi$
$827$	14028.0			0.589844			0.294922	+	0.955521i	$0.404706\pi$
$828$	−6732.00	+	11660.2i	−0.282552	+	0.489395i
$829$	−15225.5	−	26371.3i	−0.637881	−	1.10484i	−0.985897	−	0.167354i	$-0.946478\pi$
$829$	−15225.5	−	26371.3i	−0.637881	−	1.10484i	0.348016	−	0.937489i	$-0.386856\pi$
$830$	−1464.00	−	2535.72i	−0.0612243	−	0.106044i
$831$	2943.00			0.122854
$832$	−832.000	−	2882.13i	−0.0346688	−	0.120096i
$833$	−8586.00			−0.357128
$834$	−8481.00	−	14689.5i	−0.352126	−	0.609900i
$835$	2355.00	+	4078.98i	0.0976026	+	0.169053i
$836$	−1950.00	+	3377.50i	−0.0806724	+	0.139729i
$837$	−14040.0			−0.579801
$838$	−2919.00	+	5055.86i	−0.120328	+	0.208415i
$839$	−10295.5	+	17832.3i	−0.423647	+	0.733779i	−0.996293	−	0.0860242i	$-0.972584\pi$
$839$	−10295.5	+	17832.3i	−0.423647	+	0.733779i	0.572646	+	0.819803i	$0.305917\pi$
$840$	−240.000			−0.00985808
$841$	12110.0	−	20975.1i	0.496535	−	0.860024i
$842$	−3110.00	−	5386.68i	−0.127289	−	0.220472i
$843$	−4143.00	−	7175.89i	−0.169267	−	0.293180i
$844$	−1420.00			−0.0579128
$845$	−3718.00	+	2341.73i	−0.151365	+	0.0953350i
$846$	13968.0			0.567647
$847$	−2905.00	−	5031.61i	−0.117848	−	0.204118i
$848$	−4944.00	−	8563.26i	−0.200210	−	0.346773i
$849$	5887.50	−	10197.4i	0.237996	−	0.412221i
$850$	6534.00			0.263664
$851$	39550.5	−	68503.5i	1.59315	−	2.75942i
$852$	474.000	−	820.992i	0.0190598	−	0.0330126i
$853$	−5798.00			−0.232731			−0.116366	−	0.993206i	$-0.537124\pi$
$853$	−5798.00			−0.232731			−0.116366	+	0.993206i	$0.537124\pi$
$854$	−875.000	+	1515.54i	−0.0350608	+	0.0607270i
$855$	1350.00	+	2338.27i	0.0539989	+	0.0935288i
$856$	5108.00	+	8847.32i	0.203958	+	0.353265i
$857$	5686.00			0.226640			0.113320	−	0.993559i	$-0.463852\pi$
$857$	5686.00			0.226640			0.113320	+	0.993559i	$0.463852\pi$
$858$	−1014.00	−	3512.60i	−0.0403466	−	0.139765i
$859$	−46708.0			−1.85525			−0.927623	−	0.373518i	$-0.878152\pi$
$859$	−46708.0			−1.85525			−0.927623	+	0.373518i	$0.878152\pi$
$860$	−796.000	−	1378.71i	−0.0315621	−	0.0546671i
$861$	−1462.50	−	2533.12i	−0.0578883	−	0.100266i
$862$	−9135.00	+	15822.3i	−0.360951	+	0.625185i
$863$	25168.0			0.992733			0.496367	−	0.868113i	$-0.334667\pi$
$863$	25168.0			0.992733			0.496367	+	0.868113i	$0.334667\pi$
$864$	2160.00	−	3741.23i	0.0850517	−	0.147314i
$865$	3889.00	−	6735.95i	0.152867	−	0.264773i
$866$	23338.0			0.915771
$867$	−6276.00	+	10870.4i	−0.245841	+	0.425809i
$868$	−1040.00	−	1801.33i	−0.0406681	−	0.0704392i
$869$	−4966.00	−	8601.36i	−0.193855	−	0.335767i
$870$	−156.000			−0.00607919
$871$	−26552.5	+	27594.2i	−1.03295	+	1.07347i
$872$	−6608.00			−0.256623
$873$	−873.000	−	1512.08i	−0.0338449	−	0.0586210i
$874$	−14025.0	−	24292.0i	−0.542795	−	0.940148i
$875$	−1230.00	+	2130.42i	−0.0475218	+	0.0823102i
$876$	−2760.00			−0.106452
$877$	−9331.50	+	16162.6i	−0.359296	+	0.622318i	−0.987843	−	0.155453i	$-0.950316\pi$
$877$	−9331.50	+	16162.6i	−0.359296	+	0.622318i	0.628548	+	0.777771i	$0.283650\pi$
$878$	13529.0	−	23432.9i	0.520025	−	0.900709i
$879$	−23133.0			−0.887664
$880$	−208.000	+	360.267i	−0.00796782	+	0.0138007i
$881$	−2485.50	−	4305.01i	−0.0950495	−	0.164631i	0.814580	−	0.580052i	$-0.196968\pi$
$881$	−2485.50	−	4305.01i	−0.0950495	−	0.164631i	−0.909629	+	0.415421i	$0.863634\pi$
$882$	5724.00	+	9914.26i	0.218523	+	0.378493i
$883$	6892.00			0.262666			0.131333	−	0.991338i	$-0.458074\pi$
$883$	6892.00			0.262666			0.131333	+	0.991338i	$0.458074\pi$
$884$	−3510.00	+	3647.70i	−0.133545	+	0.138784i
$885$	−2946.00			−0.111897
$886$	−1932.00	−	3346.32i	−0.0732582	−	0.126887i
$887$	12023.5	+	20825.3i	0.455140	+	0.788326i	0.998696	−	0.0510466i	$-0.0162557\pi$
$887$	12023.5	+	20825.3i	0.455140	+	0.788326i	−0.543556	+	0.839373i	$0.682922\pi$
$888$	−5076.00	+	8791.89i	−0.191824	+	0.332248i
$889$	−5885.00			−0.222021
$890$	−2082.00	+	3606.13i	−0.0784144	+	0.135818i
$891$	−526.500	+	911.925i	−0.0197962	+	0.0342880i
$892$	−9132.00			−0.342782
$893$	−14550.0	+	25201.3i	−0.545238	+	0.944379i
$894$	−2565.00	−	4442.71i	−0.0959580	−	0.166204i
$895$	−2229.00	−	3860.74i	−0.0832483	−	0.144190i
$896$	640.000			0.0238626
$897$	25525.5	+	6315.92i	0.950136	+	0.235098i
$898$	10714.0			0.398141
$899$	−676.000	−	1170.87i	−0.0250788	−	0.0434378i
$900$	−4356.00	−	7544.81i	−0.161333	−	0.279438i
$901$	−8343.00	+	14450.5i	−0.308486	+	0.534313i
$902$	−5070.00			−0.187154
$903$	−1492.50	+	2585.09i	−0.0550025	+	0.0952672i
$904$	3788.00	−	6561.01i	0.139366	−	0.241389i
$905$	−2076.00			−0.0762526
$906$	−6192.00	+	10724.9i	−0.227059	+	0.393278i
$907$	6421.50	+	11122.4i	0.235085	+	0.407180i	0.959297	−	0.282397i	$-0.0911297\pi$
$907$	6421.50	+	11122.4i	0.235085	+	0.407180i	−0.724212	+	0.689577i	$0.757796\pi$
$908$	−4902.00	−	8490.51i	−0.179161	−	0.310317i
$909$	14562.0			0.531343
$910$	−260.000	−	900.666i	−0.00947134	−	0.0328097i
$911$	−144.000			−0.00523703			−0.00261851	−	0.999997i	$-0.500833\pi$
$911$	−144.000			−0.00523703			−0.00261851	+	0.999997i	$0.500833\pi$
$912$	1800.00	+	3117.69i	0.0653552	+	0.113199i
$913$	4758.00	+	8241.10i	0.172472	+	0.298730i
$914$	19399.0	−	33600.1i	0.702037	−	1.21596i
$915$	−1050.00			−0.0379365
$916$	3756.00	−	6505.58i	0.135482	−	0.234662i
$917$	−3550.00	+	6148.78i	−0.127842	+	0.221429i
$918$	−7290.00			−0.262098
$919$	5530.50	−	9579.11i	0.198514	−	0.343836i	−0.749533	−	0.661967i	$-0.769722\pi$
$919$	5530.50	−	9579.11i	0.198514	−	0.343836i	0.948047	+	0.318131i	$0.103055\pi$
$920$	−1496.00	−	2591.15i	−0.0536105	−	0.0928561i
$921$	15582.0	+	26988.8i	0.557486	+	0.965594i
$922$	31098.0			1.11080
$923$	3594.50	+	889.408i	0.128185	+	0.0317175i
$924$	780.000			0.0277707
$925$	25591.5	+	44325.8i	0.909668	+	1.57559i
$926$	4072.00	+	7052.91i	0.144508	+	0.250295i
$927$	11592.0	−	20077.9i	0.410713	−	0.711376i
$928$	416.000			0.0147154
$929$	−13153.5	+	22782.5i	−0.464534	+	0.804597i	−0.999180	−	0.0404791i	$-0.987112\pi$
$929$	−13153.5	+	22782.5i	−0.464534	+	0.804597i	0.534646	+	0.845076i	$0.320445\pi$
$930$	624.000	−	1080.80i	0.0220019	−	0.0381084i
$931$	−23850.0			−0.839583
$932$	−3260.00	+	5646.49i	−0.114576	+	0.198451i
$933$	−10908.0	−	18893.2i	−0.382757	−	0.662954i
$934$	15224.0	+	26368.7i	0.533345	+	0.923781i
$935$	702.000			0.0245539
$936$	6552.00	+	1621.20i	0.228802	+	0.0566139i
$937$	−46074.0			−1.60637			−0.803187	−	0.595727i	$-0.796864\pi$
$937$	−46074.0			−1.60637			−0.803187	+	0.595727i	$0.796864\pi$
$938$	−4085.00	−	7075.43i	−0.142196	−	0.246291i
$939$	11865.0	+	20550.8i	0.412353	+	0.714217i
$940$	−1552.00	+	2688.14i	−0.0538518	+	0.0932740i
$941$	36118.0			1.25124			0.625618	−	0.780130i	$-0.284847\pi$
$941$	36118.0			1.25124			0.625618	+	0.780130i	$0.284847\pi$
$942$	5682.00	−	9841.51i	0.196528	−	0.340397i
$943$	18232.5	−	31579.6i	0.629620	−	1.09053i
$944$	7856.00			0.270859
$945$	675.000	−	1169.13i	0.0232357	−	0.0402454i
$946$	2587.00	+	4480.82i	0.0889119	+	0.154000i
$947$	27757.5	+	48077.4i	0.952479	+	1.64974i	0.740035	+	0.672569i	$0.234809\pi$
$947$	27757.5	+	48077.4i	0.952479	+	1.64974i	0.212444	+	0.977173i	$0.431858\pi$
$948$	−9168.00			−0.314096
$949$	−2990.00	−	10357.7i	−0.102276	−	0.354293i
$950$	18150.0			0.619857
$951$	11097.0	+	19220.6i	0.378386	+	0.655383i
$952$	−540.000	−	935.307i	−0.0183839	−	0.0318419i
$953$	2676.50	−	4635.83i	0.0909762	−	0.157575i	−0.816946	−	0.576714i	$-0.804335\pi$
$953$	2676.50	−	4635.83i	0.0909762	−	0.157575i	0.907922	+	0.419139i	$0.137668\pi$
$954$	22248.0			0.755037
$955$	2141.00	−	3708.32i	0.0725457	−	0.125653i
$956$	11088.0	−	19205.0i	0.375117	−	0.649721i
$957$	507.000			0.0171254
$958$	−10335.0	+	17900.7i	−0.348548	+	0.603702i
$959$	−6022.50	−	10431.3i	−0.202791	−	0.351244i
$960$	192.000	+	332.554i	0.00645497	+	0.0111803i
$961$	−18975.0			−0.636937
$962$	−38493.0	−	9524.55i	−1.29009	−	0.319214i
$963$	−22986.0			−0.769173
$964$	−11046.0	−	19132.2i	−0.369054	−	0.639220i
$965$	−2627.00	−	4550.10i	−0.0876333	−	0.151785i
$966$	−2805.00	+	4858.40i	−0.0934259	+	0.161818i
$967$	−5488.00			−0.182505			−0.0912524	−	0.995828i	$-0.529087\pi$
$967$	−5488.00			−0.182505			−0.0912524	+	0.995828i	$0.529087\pi$
$968$	−4648.00	+	8050.57i	−0.154331	+	0.267309i
$969$	3037.50	−	5261.10i	0.100700	−	0.174418i
$970$	388.000			0.0128432
$971$	18676.5	−	32348.6i	0.617258	−	1.06912i	−0.372726	−	0.927941i	$-0.621577\pi$
$971$	18676.5	−	32348.6i	0.617258	−	1.06912i	0.989984	−	0.141181i	$-0.0450898\pi$
$972$	7776.00	+	13468.4i	0.256600	+	0.444444i
$973$	7067.50	+	12241.3i	0.232861	+	0.403327i
$974$	−12910.0			−0.424705
$975$	−11797.5	+	12260.3i	−0.387510	+	0.402712i
$976$	2800.00			0.0918297
$977$	6364.50	+	11023.6i	0.208412	+	0.360980i	0.951214	−	0.308531i	$-0.0998372\pi$
$977$	6364.50	+	11023.6i	0.208412	+	0.360980i	−0.742803	+	0.669511i	$0.766504\pi$
$978$	2955.00	+	5118.21i	0.0966160	+	0.167344i
$979$	6766.50	−	11719.9i	0.220897	−	0.382605i
$980$	−2544.00			−0.0829236
$981$	7434.00	−	12876.1i	0.241946	−	0.419063i
$982$	7777.00	−	13470.2i	0.252723	−	0.437729i
$983$	−56128.0			−1.82116			−0.910582	−	0.413327i	$-0.864367\pi$
$983$	−56128.0			−1.82116			−0.910582	+	0.413327i	$0.864367\pi$
$984$	−2340.00	+	4053.00i	−0.0758094	+	0.131306i
$985$	−1203.00	−	2083.66i	−0.0389145	−	0.0674019i
$986$	−351.000	−	607.950i	−0.0113368	−	0.0196360i
$987$	5820.00			0.187693
$988$	−9750.00	+	10132.5i	−0.313956	+	0.326273i
$989$	−37213.0			−1.19647
$990$	−468.000	−	810.600i	−0.0150243	−	0.0260228i
$991$	−23500.5	−	40704.1i	−0.753298	−	1.30475i	−0.946216	−	0.323535i	$-0.895129\pi$
$991$	−23500.5	−	40704.1i	−0.753298	−	1.30475i	0.192919	−	0.981215i	$-0.438205\pi$
$992$	−1664.00	+	2882.13i	−0.0532581	+	0.0922458i
$993$	7131.00			0.227891
$994$	−395.000	+	684.160i	−0.0126043	+	0.0218312i
$995$	−743.000	+	1286.91i	−0.0236730	+	0.0410029i
$996$	8784.00			0.279449
$997$	12216.5	−	21159.6i	0.388065	−	0.672148i	−0.604125	−	0.796890i	$-0.706477\pi$
$997$	12216.5	−	21159.6i	0.388065	−	0.672148i	0.992189	+	0.124742i	$0.0398104\pi$
$998$	−3044.00	−	5272.36i	−0.0965492	−	0.167228i
$999$	−28552.5	−	49454.4i	−0.904265	−	1.56623i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.a.3.1	✓	2	1.1	even	1	trivial
26.4.c.a.9.1	yes	2	13.9	even	3	inner
208.4.i.a.81.1		2	4.3	odd	2
208.4.i.a.113.1		2	52.35	odd	6
234.4.h.b.55.1		2	3.2	odd	2
234.4.h.b.217.1		2	39.35	odd	6
338.4.a.a.1.1		1	13.3	even	3
338.4.a.d.1.1		1	13.10	even	6
338.4.b.a.337.1		2	13.11	odd	12
338.4.b.a.337.2		2	13.2	odd	12
338.4.c.d.191.1		2	13.4	even	6
338.4.c.d.315.1		2	13.12	even	2
338.4.e.d.23.1		4	13.8	odd	4
338.4.e.d.23.2		4	13.5	odd	4
338.4.e.d.147.1		4	13.6	odd	12
338.4.e.d.147.2		4	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +2.00000 q^{5} +(-3.00000 + 5.19615i) q^{6} +(2.50000 - 4.33013i) q^{7} -8.00000 q^{8} +(9.00000 - 15.5885i) q^{9} +(2.00000 + 3.46410i) q^{10} +(-6.50000 - 11.2583i) q^{11} -12.0000 q^{12} +(-13.0000 - 45.0333i) q^{13} +10.0000 q^{14} +(3.00000 + 5.19615i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.5000 + 23.3827i) q^{17} +36.0000 q^{18} +(-37.5000 + 64.9519i) q^{19} +(-4.00000 + 6.92820i) q^{20} +15.0000 q^{21} +(13.0000 - 22.5167i) q^{22} +(93.5000 + 161.947i) q^{23} +(-12.0000 - 20.7846i) q^{24} -121.000 q^{25} +(65.0000 - 67.5500i) q^{26} +135.000 q^{27} +(10.0000 + 17.3205i) q^{28} +(6.50000 + 11.2583i) q^{29} +(-6.00000 + 10.3923i) q^{30} -104.000 q^{31} +(16.0000 - 27.7128i) q^{32} +(19.5000 - 33.7750i) q^{33} -54.0000 q^{34} +(5.00000 - 8.66025i) q^{35} +(36.0000 + 62.3538i) q^{36} +(-211.500 - 366.329i) q^{37} -150.000 q^{38} +(97.5000 - 101.325i) q^{39} -16.0000 q^{40} +(-97.5000 - 168.875i) q^{41} +(15.0000 + 25.9808i) q^{42} +(-99.5000 + 172.339i) q^{43} +52.0000 q^{44} +(18.0000 - 31.1769i) q^{45} +(-187.000 + 323.894i) q^{46} +388.000 q^{47} +(24.0000 - 41.5692i) q^{48} +(159.000 + 275.396i) q^{49} +(-121.000 - 209.578i) q^{50} -81.0000 q^{51} +(182.000 + 45.0333i) q^{52} +618.000 q^{53} +(135.000 + 233.827i) q^{54} +(-13.0000 - 22.5167i) q^{55} +(-20.0000 + 34.6410i) q^{56} -225.000 q^{57} +(-13.0000 + 22.5167i) q^{58} +(-245.500 + 425.218i) q^{59} -24.0000 q^{60} +(-87.5000 + 151.554i) q^{61} +(-104.000 - 180.133i) q^{62} +(-45.0000 - 77.9423i) q^{63} +64.0000 q^{64} +(-26.0000 - 90.0666i) q^{65} +78.0000 q^{66} +(-408.500 - 707.543i) q^{67} +(-54.0000 - 93.5307i) q^{68} +(-280.500 + 485.840i) q^{69} +20.0000 q^{70} +(-39.5000 + 68.4160i) q^{71} +(-72.0000 + 124.708i) q^{72} +230.000 q^{73} +(423.000 - 732.657i) q^{74} +(-181.500 - 314.367i) q^{75} +(-150.000 - 259.808i) q^{76} -65.0000 q^{77} +(273.000 + 67.5500i) q^{78} +764.000 q^{79} +(-16.0000 - 27.7128i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(195.000 - 337.750i) q^{82} -732.000 q^{83} +(-30.0000 + 51.9615i) q^{84} +(-27.0000 + 46.7654i) q^{85} -398.000 q^{86} +(-19.5000 + 33.7750i) q^{87} +(52.0000 + 90.0666i) q^{88} +(520.500 + 901.532i) q^{89} +72.0000 q^{90} +(-227.500 - 56.2917i) q^{91} -748.000 q^{92} +(-156.000 - 270.200i) q^{93} +(388.000 + 672.036i) q^{94} +(-75.0000 + 129.904i) q^{95} +96.0000 q^{96} +(48.5000 - 84.0045i) q^{97} +(-318.000 + 550.792i) q^{98} -234.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 5 q^{7} - 16 q^{8} + 18 q^{9} + 4 q^{10} - 13 q^{11} - 24 q^{12} - 26 q^{13} + 20 q^{14} + 6 q^{15} - 16 q^{16} - 27 q^{17} + 72 q^{18} - 75 q^{19}+ \cdots - 468 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 5 * q^7 - 16 * q^8 + 18 * q^9 + 4 * q^10 - 13 * q^11 - 24 * q^12 - 26 * q^13 + 20 * q^14 + 6 * q^15 - 16 * q^16 - 27 * q^17 + 72 * q^18 - 75 * q^19 - 8 * q^20 + 30 * q^21 + 26 * q^22 + 187 * q^23 - 24 * q^24 - 242 * q^25 + 130 * q^26 + 270 * q^27 + 20 * q^28 + 13 * q^29 - 12 * q^30 - 208 * q^31 + 32 * q^32 + 39 * q^33 - 108 * q^34 + 10 * q^35 + 72 * q^36 - 423 * q^37 - 300 * q^38 + 195 * q^39 - 32 * q^40 - 195 * q^41 + 30 * q^42 - 199 * q^43 + 104 * q^44 + 36 * q^45 - 374 * q^46 + 776 * q^47 + 48 * q^48 + 318 * q^49 - 242 * q^50 - 162 * q^51 + 364 * q^52 + 1236 * q^53 + 270 * q^54 - 26 * q^55 - 40 * q^56 - 450 * q^57 - 26 * q^58 - 491 * q^59 - 48 * q^60 - 175 * q^61 - 208 * q^62 - 90 * q^63 + 128 * q^64 - 52 * q^65 + 156 * q^66 - 817 * q^67 - 108 * q^68 - 561 * q^69 + 40 * q^70 - 79 * q^71 - 144 * q^72 + 460 * q^73 + 846 * q^74 - 363 * q^75 - 300 * q^76 - 130 * q^77 + 546 * q^78 + 1528 * q^79 - 32 * q^80 - 81 * q^81 + 390 * q^82 - 1464 * q^83 - 60 * q^84 - 54 * q^85 - 796 * q^86 - 39 * q^87 + 104 * q^88 + 1041 * q^89 + 144 * q^90 - 455 * q^91 - 1496 * q^92 - 312 * q^93 + 776 * q^94 - 150 * q^95 + 192 * q^96 + 97 * q^97 - 636 * q^98 - 468 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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