LMFDB - Embedded newform 115.4.l.a.102.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,4,Mod(7,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$680$
Relative dimension:	$34$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			102.4
Character	$\chi$	$=$	115.102
Dual form			115.4.l.a.53.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.341249 + 4.77128i) q^{2} +(6.15772 - 1.33953i) q^{3} +(-14.7301 - 2.11787i) q^{4} +(11.1479 - 0.850466i) q^{5} +(4.28996 + 29.8374i) q^{6} +(31.1635 - 17.0166i) q^{7} +(6.99722 - 32.1657i) q^{8} +(11.5631 - 5.28070i) q^{9} +(0.253587 + 53.4802i) q^{10} +(2.59952 + 2.25250i) q^{11} +(-93.5410 + 6.69019i) q^{12} +(-3.35434 + 6.14302i) q^{13} +(70.5564 + 154.497i) q^{14} +(67.5067 - 20.1699i) q^{15} +(36.8535 + 10.8212i) q^{16} +(-50.4864 - 37.7936i) q^{17} +(21.2498 + 56.9730i) q^{18} +(-10.4871 + 72.9396i) q^{19} +(-166.012 - 11.0825i) q^{20} +(169.102 - 146.528i) q^{21} +(-11.6344 + 11.6344i) q^{22} +(-80.9598 - 74.9167i) q^{23} -207.440i q^{24} +(123.553 - 18.9619i) q^{25} +(-28.1654 - 18.1008i) q^{26} +(-72.0808 + 53.9590i) q^{27} +(-495.082 + 184.656i) q^{28} +(-248.606 + 35.7442i) q^{29} +(73.1999 + 328.977i) q^{30} +(-200.632 + 128.938i) q^{31} +(27.8221 - 74.5939i) q^{32} +(19.0244 + 10.3881i) q^{33} +(197.553 - 227.988i) q^{34} +(332.937 - 216.203i) q^{35} +(-181.510 + 53.2962i) q^{36} +(293.809 + 109.585i) q^{37} +(-344.437 - 74.9277i) q^{38} +(-12.4264 + 42.3203i) q^{39} +(50.6488 - 364.532i) q^{40} +(12.0984 - 26.4918i) q^{41} +(641.420 + 856.837i) q^{42} +(62.2309 + 286.071i) q^{43} +(-33.5208 - 38.6851i) q^{44} +(124.414 - 68.7030i) q^{45} +(385.077 - 360.717i) q^{46} +(-141.204 - 141.204i) q^{47} +(241.429 + 17.2674i) q^{48} +(496.162 - 772.043i) q^{49} +(48.3101 + 595.979i) q^{50} +(-361.507 - 165.095i) q^{51} +(62.4201 - 83.3835i) q^{52} +(74.6819 + 136.770i) q^{53} +(-232.856 - 362.331i) q^{54} +(30.8950 + 22.9000i) q^{55} +(-329.292 - 1121.47i) q^{56} +(33.1280 + 463.190i) q^{57} +(-85.7090 - 1198.37i) q^{58} +(-32.9465 - 112.205i) q^{59} +(-1037.10 + 154.135i) q^{60} +(99.1163 + 154.228i) q^{61} +(-546.735 - 1001.27i) q^{62} +(270.488 - 361.330i) q^{63} +(625.922 + 285.849i) q^{64} +(-32.1696 + 71.3348i) q^{65} +(-56.0568 + 87.2261i) q^{66} +(497.436 + 35.5773i) q^{67} +(663.629 + 663.629i) q^{68} +(-598.881 - 352.868i) q^{69} +(917.953 + 1662.32i) q^{70} +(-92.5491 - 106.807i) q^{71} +(-88.9477 - 408.886i) q^{72} +(165.051 + 220.482i) q^{73} +(-623.124 + 1364.45i) q^{74} +(735.407 - 282.266i) q^{75} +(308.954 - 1052.20i) q^{76} +(119.340 + 25.9609i) q^{77} +(-197.682 - 73.7314i) q^{78} +(-129.779 + 38.1066i) q^{79} +(420.044 + 89.2912i) q^{80} +(-596.335 + 688.207i) q^{81} +(122.271 + 66.7652i) q^{82} +(295.086 - 791.157i) q^{83} +(-2801.22 + 1800.24i) q^{84} +(-594.962 - 378.385i) q^{85} +(-1386.16 + 199.300i) q^{86} +(-1482.97 + 553.118i) q^{87} +(90.6427 - 67.8543i) q^{88} +(-536.164 - 344.572i) q^{89} +(285.345 + 617.059i) q^{90} +248.518i q^{91} +(1033.88 + 1275.00i) q^{92} +(-1062.72 + 1062.72i) q^{93} +(721.912 - 625.540i) q^{94} +(-54.8774 + 822.046i) q^{95} +(71.3999 - 496.597i) q^{96} +(-403.493 - 1081.81i) q^{97} +(3514.32 + 2630.79i) q^{98} +(41.9534 + 12.3186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 680 q - 18 q^{2} - 26 q^{3} - 22 q^{5} - 76 q^{6} - 22 q^{7} - 50 q^{8} - 22 q^{10} - 44 q^{11} - 222 q^{12} + 78 q^{13} - 22 q^{15} + 788 q^{16} - 22 q^{17} - 86 q^{18} - 22 q^{20} - 44 q^{21} - 944 q^{23}+ \cdots - 10314 q^{98}+O(q^{100}) $ 680 * q - 18 * q^2 - 26 * q^3 - 22 * q^5 - 76 * q^6 - 22 * q^7 - 50 * q^8 - 22 * q^10 - 44 * q^11 - 222 * q^12 + 78 * q^13 - 22 * q^15 + 788 * q^16 - 22 * q^17 - 86 * q^18 - 22 * q^20 - 44 * q^21 - 944 * q^23 + 350 * q^25 + 268 * q^26 + 682 * q^27 + 682 * q^28 - 22 * q^30 + 1012 * q^31 - 582 * q^32 + 1914 * q^33 + 326 * q^35 - 2468 * q^36 + 2354 * q^37 - 22 * q^38 - 22 * q^40 - 2292 * q^41 - 7282 * q^42 - 22 * q^43 + 52 * q^46 - 2416 * q^47 - 1378 * q^48 + 598 * q^50 - 44 * q^51 - 794 * q^52 - 22 * q^53 - 2710 * q^55 + 11572 * q^56 + 7634 * q^57 - 2066 * q^58 - 22 * q^60 - 1100 * q^61 - 3970 * q^62 - 22 * q^63 - 22 * q^65 - 10956 * q^66 - 22 * q^67 + 1792 * q^70 - 11412 * q^71 - 556 * q^72 - 1122 * q^73 + 13078 * q^75 - 2156 * q^76 - 4238 * q^77 + 9158 * q^78 + 8096 * q^80 + 11280 * q^81 + 6494 * q^82 - 22 * q^83 - 8118 * q^85 + 10428 * q^86 + 6282 * q^87 - 1430 * q^88 - 37224 * q^90 + 666 * q^92 + 1564 * q^93 - 11162 * q^95 - 16748 * q^96 - 12694 * q^97 - 10314 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.341249	+	4.77128i	−0.120650	+	1.68690i	0.472122	+	0.881533i	$0.343488\pi$
$2$	−0.341249	+	4.77128i	−0.120650	+	1.68690i	−0.592772	+	0.805371i	$0.701966\pi$
$3$	6.15772	−	1.33953i	1.18505	−	0.257793i	0.423501	−	0.905896i	$-0.360801\pi$
$3$	6.15772	−	1.33953i	1.18505	−	0.257793i	0.761553	+	0.648103i	$0.224437\pi$
$4$	−14.7301	−	2.11787i	−1.84127	−	0.264734i
$5$	11.1479	−	0.850466i	0.997103	−	0.0760679i
$5$	11.1479	−	0.850466i	0.997103	−	0.0760679i
$6$	4.28996	+	29.8374i	0.291895	+	2.03017i
$7$	31.1635	−	17.0166i	1.68267	−	0.918809i	0.704855	−	0.709352i	$-0.251012\pi$
$7$	31.1635	−	17.0166i	1.68267	−	0.918809i	0.977818	−	0.209457i	$-0.0671696\pi$
$8$	6.99722	−	32.1657i	0.309236	−	1.42154i
$9$	11.5631	−	5.28070i	0.428264	−	0.195582i
$10$	0.253587	+	53.4802i	0.00801914	+	1.69119i
$11$	2.59952	+	2.25250i	0.0712533	+	0.0617413i	0.689759	−	0.724039i	$-0.257716\pi$
$11$	2.59952	+	2.25250i	0.0712533	+	0.0617413i	−0.618506	+	0.785780i	$0.712262\pi$
$12$	−93.5410	+	6.69019i	−2.25025	+	0.160941i
$13$	−3.35434	+	6.14302i	−0.0715637	+	0.131059i	−0.911011	−	0.412382i	$-0.864697\pi$
$13$	−3.35434	+	6.14302i	−0.0715637	+	0.131059i	0.839447	+	0.543441i	$0.182879\pi$
$14$	70.5564	+	154.497i	1.34693	+	2.94936i
$15$	67.5067	−	20.1699i	1.16201	−	0.347190i
$16$	36.8535	+	10.8212i	0.575837	+	0.169081i
$17$	−50.4864	−	37.7936i	−0.720279	−	0.539194i	0.175072	−	0.984556i	$-0.443984\pi$
$17$	−50.4864	−	37.7936i	−0.720279	−	0.539194i	−0.895351	+	0.445361i	$0.853075\pi$
$18$	21.2498	+	56.9730i	0.278257	+	0.746037i
$19$	−10.4871	+	72.9396i	−0.126627	+	0.880710i	0.823159	+	0.567811i	$0.192209\pi$
$19$	−10.4871	+	72.9396i	−0.126627	+	0.880710i	−0.949786	+	0.312900i	$0.898700\pi$
$20$	−166.012	−	11.0825i	−1.85607	−	0.123906i
$21$	169.102	−	146.528i	1.75720	−	1.52262i
$22$	−11.6344	+	11.6344i	−0.112748	+	0.112748i
$23$	−80.9598	−	74.9167i	−0.733969	−	0.679183i
$23$	−80.9598	−	74.9167i	−0.733969	−	0.679183i
$24$		−	207.440i		−	1.76432i
$25$	123.553	−	18.9619i	0.988427	−	0.151695i
$26$	−28.1654	−	18.1008i	−0.212450	−	0.136533i
$27$	−72.0808	+	53.9590i	−0.513776	+	0.384608i
$28$	−495.082	+	184.656i	−3.34149	+	1.24631i
$29$	−248.606	+	35.7442i	−1.59190	+	0.228880i	−0.880547	−	0.473959i	$-0.842825\pi$
$29$	−248.606	+	35.7442i	−1.59190	+	0.228880i	−0.711349	+	0.702839i	$0.751915\pi$
$30$	73.1999	+	328.977i	0.445481	+	2.00209i
$31$	−200.632	+	128.938i	−1.16240	+	0.747031i	−0.972071	−	0.234688i	$-0.924593\pi$
$31$	−200.632	+	128.938i	−1.16240	+	0.747031i	−0.190333	+	0.981720i	$0.560957\pi$
$32$	27.8221	−	74.5939i	0.153697	−	0.412077i
$33$	19.0244	+	10.3881i	0.100355	+	0.0547982i
$34$	197.553	−	227.988i	0.996471	−	1.14999i
$35$	332.937	−	216.203i	1.60791	−	1.04414i
$36$	−181.510	+	53.2962i	−0.840325	+	0.246742i
$37$	293.809	+	109.585i	1.30546	+	0.486911i	0.903437	−	0.428720i	$-0.141035\pi$
$37$	293.809	+	109.585i	1.30546	+	0.486911i	0.402021	+	0.915631i	$0.368308\pi$
$38$	−344.437	−	74.9277i	−1.47040	−	0.319865i
$39$	−12.4264	+	42.3203i	−0.0510207	+	0.173761i
$40$	50.6488	−	364.532i	0.200207	−	1.44094i
$41$	12.0984	−	26.4918i	0.0460842	−	0.100910i	−0.885189	−	0.465231i	$-0.845971\pi$
$41$	12.0984	−	26.4918i	0.0460842	−	0.100910i	0.931274	+	0.364320i	$0.118699\pi$
$42$	641.420	+	856.837i	2.35651	+	3.14792i
$43$	62.2309	+	286.071i	0.220701	+	1.01454i	0.945510	+	0.325594i	$0.105564\pi$
$43$	62.2309	+	286.071i	0.220701	+	1.01454i	−0.724809	+	0.688950i	$0.758072\pi$
$44$	−33.5208	−	38.6851i	−0.114851	−	0.132545i
$45$	124.414	−	68.7030i	0.412145	−	0.227592i
$46$	385.077	−	360.717i	1.23427	−	1.15619i
$47$	−141.204	−	141.204i	−0.438229	−	0.438229i	0.453187	−	0.891416i	$-0.350287\pi$
$47$	−141.204	−	141.204i	−0.438229	−	0.438229i	−0.891416	+	0.453187i	$0.850287\pi$
$48$	241.429	+	17.2674i	0.725985	+	0.0519235i
$49$	496.162	−	772.043i	1.44654	−	2.25085i
$50$	48.3101	+	595.979i	0.136642	+	1.68568i
$51$	−361.507	−	165.095i	−0.992570	−	0.453292i
$52$	62.4201	−	83.3835i	0.166464	−	0.222369i
$53$	74.6819	+	136.770i	0.193554	+	0.354467i	0.956375	−	0.292143i	$-0.0943682\pi$
$53$	74.6819	+	136.770i	0.193554	+	0.354467i	−0.762821	+	0.646610i	$0.776186\pi$
$54$	−232.856	−	362.331i	−0.586809	−	0.913093i
$55$	30.8950	+	22.9000i	0.0757434	+	0.0561423i
$56$	−329.292	−	1121.47i	−0.785777	−	2.67611i
$57$	33.1280	+	463.190i	0.0769808	+	1.07633i
$58$	−85.7090	−	1198.37i	−0.194037	−	2.71299i
$59$	−32.9465	−	112.205i	−0.0726994	−	0.247592i	0.915124	−	0.403174i	$-0.132093\pi$
$59$	−32.9465	−	112.205i	−0.0726994	−	0.247592i	−0.987823	+	0.155582i	$0.950275\pi$
$60$	−1037.10	+	154.135i	−2.23148	+	0.331646i
$61$	99.1163	+	154.228i	0.208042	+	0.323719i	0.929556	−	0.368680i	$-0.120190\pi$
$61$	99.1163	+	154.228i	0.208042	+	0.323719i	−0.721515	+	0.692399i	$0.756554\pi$
$62$	−546.735	−	1001.27i	−1.11993	−	2.05099i
$63$	270.488	−	361.330i	0.540926	−	0.722592i
$64$	625.922	+	285.849i	1.22250	+	0.558299i
$65$	−32.1696	+	71.3348i	−0.0613869	+	0.136123i
$66$	−56.0568	+	87.2261i	−0.104547	+	0.162679i
$67$	497.436	+	35.5773i	0.907036	+	0.0648725i	0.517057	−	0.855951i	$-0.327028\pi$
$67$	497.436	+	35.5773i	0.907036	+	0.0648725i	0.389979	+	0.920824i	$0.372482\pi$
$68$	663.629	+	663.629i	1.18348	+	1.18348i
$69$	−598.881	−	352.868i	−1.04488	−	0.615657i
$70$	917.953	+	1662.32i	1.56738	+	2.83836i
$71$	−92.5491	−	106.807i	−0.154698	−	0.178531i	0.673110	−	0.739542i	$-0.264958\pi$
$71$	−92.5491	−	106.807i	−0.154698	−	0.178531i	−0.827808	+	0.561011i	$0.810412\pi$
$72$	−88.9477	−	408.886i	−0.145592	−	0.669274i
$73$	165.051	+	220.482i	0.264626	+	0.353499i	0.913099	−	0.407739i	$-0.133683\pi$
$73$	165.051	+	220.482i	0.264626	+	0.353499i	−0.648472	+	0.761238i	$0.724592\pi$
$74$	−623.124	+	1364.45i	−0.978875	+	2.14344i
$75$	735.407	−	282.266i	1.13223	−	0.434576i
$76$	308.954	−	1052.20i	0.466308	−	1.58810i
$77$	119.340	+	25.9609i	0.176624	+	0.0384223i
$78$	−197.682	−	73.7314i	−0.286962	−	0.107031i
$79$	−129.779	+	38.1066i	−0.184827	+	0.0542700i	−0.372836	−	0.927897i	$-0.621615\pi$
$79$	−129.779	+	38.1066i	−0.184827	+	0.0542700i	0.188009	+	0.982167i	$0.439796\pi$
$80$	420.044	+	89.2912i	0.587030	+	0.124788i
$81$	−596.335	+	688.207i	−0.818018	+	0.944043i
$82$	122.271	+	66.7652i	0.164666	+	0.0899145i
$83$	295.086	−	791.157i	0.390240	−	1.04627i	−0.582184	−	0.813057i	$-0.697802\pi$
$83$	295.086	−	791.157i	0.390240	−	1.04627i	0.972425	−	0.233218i	$-0.0749254\pi$
$84$	−2801.22	+	1800.24i	−3.63856	+	2.33836i
$85$	−594.962	−	378.385i	−0.759208	−	0.482842i
$86$	−1386.16	+	199.300i	−1.73807	+	0.249896i
$87$	−1482.97	+	553.118i	−1.82748	+	0.681614i
$88$	90.6427	−	67.8543i	0.109802	−	0.0821965i
$89$	−536.164	−	344.572i	−0.638576	−	0.410388i	0.180900	−	0.983502i	$-0.442099\pi$
$89$	−536.164	−	344.572i	−0.638576	−	0.410388i	−0.819476	+	0.573114i	$0.805735\pi$
$90$	285.345	+	617.059i	0.334201	+	0.722709i
$91$			248.518i			0.286283i
$92$	1033.88	+	1275.00i	1.17163	+	1.44486i
$93$	−1062.72	+	1062.72i	−1.18493	+	1.18493i
$94$	721.912	−	625.540i	0.792123	−	0.686378i
$95$	−54.8774	+	822.046i	−0.0592663	+	0.887791i
$96$	71.3999	−	496.597i	0.0759085	−	0.527956i
$97$	−403.493	−	1081.81i	−0.422356	−	1.13238i	−0.957706	−	0.287750i	$-0.907093\pi$
$97$	−403.493	−	1081.81i	−0.422356	−	1.13238i	0.535349	−	0.844631i	$-0.320180\pi$
$98$	3514.32	+	2630.79i	3.62245	+	2.71173i
$99$	41.9534	+	12.3186i	0.0425907	+	0.0125057i
$100$	−1860.12	+	17.6406i	−1.86012	+	0.0176406i
$101$	306.956	+	672.139i	0.302408	+	0.662181i	0.998440	−	0.0558291i	$-0.0177802\pi$
$101$	306.956	+	672.139i	0.302408	+	0.662181i	−0.696032	+	0.718011i	$0.745053\pi$
$102$	911.077	−	1668.51i	0.884413	−	1.61968i
$103$	−1554.60	+	111.187i	−1.48718	+	0.106365i	−0.791138	−	0.611638i	$-0.790511\pi$
$103$	−1554.60	+	111.187i	−1.48718	+	0.106365i	−0.696040	+	0.718003i	$0.745056\pi$
$104$	174.124	+	150.879i	0.164175	+	0.142259i
$105$	1760.52	−	1777.30i	1.63628	−	1.65187i
$106$	−678.052	+	309.656i	−0.621304	+	0.283740i
$107$	58.1514	−	267.318i	0.0525393	−	0.241519i	−0.943387	−	0.331695i	$-0.892379\pi$
$107$	58.1514	−	267.318i	0.0525393	−	0.241519i	0.995926	+	0.0901761i	$0.0287430\pi$
$108$	1176.04	−	642.165i	1.04782	−	0.572152i
$109$	−306.540	−	2132.03i	−0.269369	−	1.87350i	−0.454441	−	0.890777i	$-0.650161\pi$
$109$	−306.540	−	2132.03i	−0.269369	−	1.87350i	0.185073	−	0.982725i	$-0.440748\pi$
$110$	−119.805	+	139.594i	−0.103845	+	0.120998i
$111$	1955.99	+	281.229i	1.67256	+	0.240478i
$112$	1332.63	−	289.895i	1.12430	−	0.244576i
$113$	−36.9155	+	516.146i	−0.0307320	+	0.429690i	0.958673	+	0.284509i	$0.0918307\pi$
$113$	−36.9155	+	516.146i	−0.0307320	+	0.429690i	−0.989405	+	0.145180i	$0.953624\pi$
$114$	−2221.31			−1.82496
$115$	−966.249	−	766.314i	−0.783506	−	0.621384i
$116$	3737.70			2.99170
$117$	−6.34723	+	88.7458i	−0.00501540	+	0.0701244i
$118$	546.607	−	118.907i	0.426434	−	0.0927651i
$119$	−2216.45	−	318.678i	−1.70741	−	0.245489i
$120$	−176.421	−	2312.53i	−0.134208	−	1.75920i
$121$	−187.737	−	1305.74i	−0.141050	−	0.981023i
$122$	−769.689	+	420.282i	−0.571183	+	0.311890i
$123$	39.0120	−	179.335i	0.0285983	−	0.131464i
$124$	3228.41	−	1474.36i	2.33806	−	1.06776i
$125$	1361.24	−	316.464i	0.974024	−	0.226443i
$126$	1631.70	+	1413.88i	1.15368	+	0.999670i
$127$	−637.560	+	45.5992i	−0.445467	+	0.0318604i	−0.292271	−	0.956335i	$-0.594411\pi$
$127$	−637.560	+	45.5992i	−0.445467	+	0.0318604i	−0.153196	+	0.988196i	$0.548957\pi$
$128$	−1272.22	+	2329.90i	−0.878514	+	1.60888i
$129$	766.401	+	1678.18i	0.523084	+	1.14539i
$130$	−329.381	−	177.833i	−0.222220	−	0.119977i
$131$	2300.03	+	675.351i	1.53401	+	0.450425i	0.936274	−	0.351271i	$-0.114250\pi$
$131$	2300.03	+	675.351i	1.53401	+	0.450425i	0.597732	+	0.801696i	$0.296069\pi$
$132$	−258.232	−	193.310i	−0.170274	−	0.127466i
$133$	914.367	+	2451.51i	0.596133	+	1.59829i
$134$	−339.499	+	2361.27i	−0.218867	+	1.52226i
$135$	−757.662	+	662.834i	−0.483031	+	0.422575i
$136$	−1568.92	+	1359.48i	−0.989221	+	0.857165i
$137$	−429.115	+	429.115i	−0.267604	+	0.267604i	−0.828134	−	0.560530i	$-0.810597\pi$
$137$	−429.115	+	429.115i	−0.267604	+	0.267604i	0.560530	+	0.828134i	$0.310597\pi$
$138$	1888.00	−	2737.01i	1.16462	−	1.68833i
$139$			789.752i			0.481913i	0.970536	+	0.240957i	$0.0774611\pi$
$139$			789.752i			0.481913i	−0.970536	+	0.240957i	$0.922539\pi$
$140$	−5362.10	+	2479.59i	−3.23700	+	1.49688i
$141$	−1058.64	−	680.349i	−0.632297	−	0.406353i
$142$	541.191	−	405.130i	0.319829	−	0.239421i
$143$	−22.5569	+	8.41328i	−0.0131909	+	0.00491995i
$144$	483.285	−	69.4859i	0.279679	−	0.0402118i
$145$	−2741.05	+	609.905i	−1.56987	+	0.349309i
$146$	−1108.31	+	712.265i	−0.628247	+	0.403750i
$147$	2021.05	−	5418.65i	1.13397	−	3.04029i
$148$	−4095.76	−	2236.46i	−2.27479	−	1.24213i
$149$	1018.99	−	1175.97i	0.560260	−	0.646574i	−0.402983	−	0.915208i	$-0.632027\pi$
$149$	1018.99	−	1175.97i	0.560260	−	0.646574i	0.963242	+	0.268633i	$0.0865720\pi$
$150$	1095.81	+	3605.16i	0.596485	+	1.96240i
$151$	2026.18	−	594.940i	1.09197	−	0.320633i	0.314315	−	0.949319i	$-0.398225\pi$
$151$	2026.18	−	594.940i	1.09197	−	0.320633i	0.777659	+	0.628686i	$0.216407\pi$
$152$	2272.77	+	847.701i	1.21280	+	0.452353i
$153$	−783.357	−	170.409i	−0.413926	−	0.0900441i
$154$	−164.591	+	560.547i	−0.0861244	+	0.293313i
$155$	−2126.97	+	1608.03i	−1.10221	+	0.833289i
$156$	272.671	−	597.066i	0.139943	−	0.306433i
$157$	1952.95	+	2608.83i	0.992753	+	1.32616i	0.944918	+	0.327307i	$0.106141\pi$
$157$	1952.95	+	2608.83i	0.992753	+	1.32616i	0.0478347	+	0.998855i	$0.484768\pi$
$158$	−137.530	−	632.217i	−0.0692489	−	0.318332i
$159$	643.077	+	742.151i	0.320750	+	0.370166i
$160$	246.720	−	855.231i	0.121906	−	0.422575i
$161$	−3797.82	−	957.012i	−1.85907	−	0.468467i
$162$	−3080.13	−	3080.13i	−1.49382	−	1.49382i
$163$	−542.249	−	38.7824i	−0.260566	−	0.0186360i	−0.0595548	−	0.998225i	$-0.518968\pi$
$163$	−542.249	−	38.7824i	−0.260566	−	0.0186360i	−0.201011	+	0.979589i	$0.564423\pi$
$164$	−234.317	+	364.605i	−0.111568	+	0.173603i
$165$	220.918	+	99.6267i	0.104233	+	0.0470056i
$166$	3674.14	+	1677.92i	1.71788	+	0.784530i
$167$	−46.3081	+	61.8603i	−0.0214576	+	0.0286640i	−0.811142	−	0.584850i	$-0.801154\pi$
$167$	−46.3081	+	61.8603i	−0.0214576	+	0.0286640i	0.789684	+	0.613514i	$0.210244\pi$
$168$	−3529.93	−	6464.58i	−1.62107	−	2.96877i
$169$	1161.30	+	1807.02i	0.528586	+	0.822495i
$170$	2008.41	−	2709.61i	0.906106	−	1.22246i
$171$	263.908	+	898.789i	0.118021	+	0.401942i
$172$	−310.808	−	4345.66i	−0.137784	−	1.92647i
$173$	133.281	+	1863.52i	0.0585733	+	0.818962i	0.938812	+	0.344431i	$0.111928\pi$
$173$	133.281	+	1863.52i	0.0585733	+	0.818962i	−0.880238	+	0.474532i	$0.842617\pi$
$174$	−2133.02	−	7264.40i	−0.929333	−	3.16502i
$175$	3527.69	−	2693.38i	1.52382	−	1.16343i
$176$	71.4270	+	111.143i	0.0305910	+	0.0476005i
$177$	−353.178	−	646.797i	−0.149980	−	0.274668i
$178$	1827.01	−	2440.61i	0.769329	−	1.02770i
$179$	90.5150	+	41.3368i	0.0377956	+	0.0172607i	0.434223	−	0.900805i	$-0.357023\pi$
$179$	90.5150	+	41.3368i	0.0377956	+	0.0172607i	−0.396428	+	0.918066i	$0.629750\pi$
$180$	−1978.14	+	748.511i	−0.819121	+	0.309949i
$181$	−85.2048	+	132.581i	−0.0349902	+	0.0544458i	−0.858308	−	0.513135i	$-0.828484\pi$
$181$	−85.2048	+	132.581i	−0.0349902	+	0.0544458i	0.823318	+	0.567581i	$0.192120\pi$
$182$	−1185.75	−	84.8064i	−0.482932	−	0.0345400i
$183$	816.924	+	816.924i	0.329993	+	0.329993i
$184$	−2976.24	+	2079.92i	−1.19245	+	0.833335i
$185$	3368.57	+	971.775i	1.33871	+	0.386196i
$186$	−4707.88	−	5433.18i	−1.85590	−	2.14183i
$187$	−46.1104	−	211.966i	−0.0180317	−	0.0828904i
$188$	1780.91	+	2379.01i	0.690882	+	0.922911i
$189$	−1328.09	+	2908.12i	−0.511136	+	1.11923i
$190$	−3903.49	−	542.358i	−1.49047	−	0.207088i
$191$	850.294	−	2895.83i	0.322121	−	1.09704i	−0.626182	−	0.779677i	$-0.715383\pi$
$191$	850.294	−	2895.83i	0.322121	−	1.09704i	0.948303	−	0.317366i	$-0.102798\pi$
$192$	4237.16	+	921.737i	1.59266	+	0.346462i
$193$	2244.62	+	837.201i	0.837158	+	0.312244i	0.731231	−	0.682130i	$-0.238946\pi$
$193$	2244.62	+	837.201i	0.837158	+	0.312244i	0.105927	+	0.994374i	$0.466219\pi$
$194$	5299.30	−	1556.02i	1.96117	−	0.575853i
$195$	−102.536	+	482.352i	−0.0376553	+	0.177138i
$196$	−8943.62	+	10321.5i	−3.25934	+	3.76148i
$197$	−1808.62	−	987.584i	−0.654108	−	0.357170i	0.117679	−	0.993052i	$-0.462455\pi$
$197$	−1808.62	−	987.584i	−0.654108	−	0.357170i	−0.771786	+	0.635882i	$0.780637\pi$
$198$	−73.0923	+	195.968i	−0.0262345	+	0.0703375i
$199$	2871.62	−	1845.48i	1.02293	−	0.657399i	0.0822237	−	0.996614i	$-0.473798\pi$
$199$	2871.62	−	1845.48i	1.02293	−	0.657399i	0.940709	+	0.339215i	$0.110161\pi$
$200$	254.608	−	4106.86i	0.0900175	−	1.45200i
$201$	3110.73	−	447.255i	1.09161	−	0.156950i
$202$	−3311.71	+	1235.21i	−1.15352	+	0.430241i
$203$	−7139.20	+	5344.34i	−2.46834	+	1.84778i
$204$	4975.39	+	3197.49i	1.70758	+	1.09740i
$205$	112.342	−	305.619i	0.0382747	−	0.104124i
$206$		−	7455.38i		−	2.52156i
$207$	−1331.76	−	438.747i	−0.447168	−	0.147319i
$208$	−190.094	+	190.094i	−0.0633686	+	0.0633686i
$209$	−191.558	+	165.986i	−0.0633988	+	0.0549354i
$210$	7879.23	+	9006.46i	2.58913	+	2.95955i
$211$	−60.1692	+	418.486i	−0.0196314	+	0.136539i	−0.997280	−	0.0737064i	$-0.976517\pi$
$211$	−60.1692	+	418.486i	−0.0196314	+	0.136539i	0.977649	+	0.210245i	$0.0674263\pi$
$212$	−810.413	−	2172.80i	−0.262544	−	0.703909i
$213$	−712.963	−	533.718i	−0.229349	−	0.171689i
$214$	1255.60	+	368.679i	0.401081	+	0.117768i
$215$	937.041	+	3136.18i	0.297235	+	0.994817i
$216$	1231.26	+	2696.09i	0.387856	+	0.849286i
$217$	−4058.31	+	7432.23i	−1.26957	+	2.32504i
$218$	10277.1	−	735.036i	3.19292	−	0.228362i
$219$	1311.68	+	1136.58i	0.404726	+	0.350697i
$220$	−406.589	−	402.751i	−0.124601	−	0.123425i
$221$	401.516	−	183.366i	0.122212	−	0.0558124i
$222$	−2009.30	+	9236.61i	−0.607457	+	2.79243i
$223$	1782.60	−	973.372i	0.535298	−	0.292295i	−0.188772	−	0.982021i	$-0.560451\pi$
$223$	1782.60	−	973.372i	0.535298	−	0.292295i	0.724071	+	0.689726i	$0.242269\pi$
$224$	−402.298	−	2798.05i	−0.119999	−	0.834609i
$225$	1328.53	−	871.707i	0.393639	−	0.258284i
$226$	−2450.08	−	352.269i	−0.721137	−	0.103684i
$227$	5347.73	−	1163.33i	1.56362	−	0.340144i	0.654296	−	0.756239i	$-0.272965\pi$
$227$	5347.73	−	1163.33i	1.56362	−	0.340144i	0.909321	+	0.416095i	$0.136601\pi$
$228$	492.998	−	6893.01i	0.143200	−	2.00220i
$229$	−3928.07			−1.13351			−0.566757	−	0.823885i	$-0.691802\pi$
$229$	−3928.07			−1.13351			−0.566757	+	0.823885i	$0.691802\pi$
$230$	3986.04	−	4348.75i	1.14275	−	1.24673i
$231$	769.639			0.219214
$232$	−589.815	+	8246.70i	−0.166911	+	2.33372i
$233$	−3223.12	+	701.147i	−0.906238	+	0.197140i	−0.641448	−	0.767166i	$-0.721666\pi$
$233$	−3223.12	+	701.147i	−0.906238	+	0.197140i	−0.264790	+	0.964306i	$0.585303\pi$
$234$	−421.266	−	60.5688i	−0.117688	−	0.0169210i
$235$	−1694.23	−	1454.05i	−0.470295	−	0.403624i
$236$	247.669	+	1722.58i	0.0683131	+	0.475128i
$237$	−748.099	+	408.493i	−0.205039	+	0.111960i
$238$	2276.86	−	10466.6i	0.620114	−	2.85062i
$239$	−3774.03	+	1723.54i	−1.02143	+	0.466472i	−0.854475	−	0.519493i	$-0.826121\pi$
$239$	−3774.03	+	1723.54i	−1.02143	+	0.466472i	−0.166955	+	0.985964i	$0.553394\pi$
$240$	2706.12	−	12.8316i	0.727831	−	0.00345116i
$241$	3977.90	+	3446.87i	1.06323	+	0.921296i	0.997069	−	0.0765125i	$-0.0243785\pi$
$241$	3977.90	+	3446.87i	1.06323	+	0.921296i	0.0661639	+	0.997809i	$0.478924\pi$
$242$	6294.13	−	450.165i	1.67191	−	0.119577i
$243$	−1585.10	+	2902.89i	−0.418453	+	0.766339i
$244$	−1133.36	−	2481.72i	−0.297361	−	0.651129i
$245$	4874.59	−	9028.67i	1.27113	−	2.35437i
$246$	842.347	+	247.335i	0.218317	+	0.0641038i
$247$	−412.892	−	309.087i	−0.106363	−	0.0796225i
$248$	2743.52	+	7355.67i	0.702475	+	1.88341i
$249$	757.280	−	5267.00i	0.192734	−	1.34049i
$250$	1045.42	+	6602.86i	0.264472	+	1.67041i
$251$	−3416.76	+	2960.64i	−0.859219	+	0.744518i	−0.968373	−	0.249507i	$-0.919731\pi$
$251$	−3416.76	+	2960.64i	−0.859219	+	0.744518i	0.109154	+	0.994025i	$0.465186\pi$
$252$	−4749.58	+	4749.58i	−1.18728	+	1.18728i
$253$	−41.7069	−	377.110i	−0.0103640	−	0.0937102i
$254$		−	3057.54i		−	0.755304i
$255$	−4170.47	−	1533.02i	−1.02418	−	0.376475i
$256$	−6051.53	−	3889.08i	−1.47742	−	0.949483i
$257$	−1945.26	+	1456.21i	−0.472149	+	0.353446i	−0.808702	−	0.588218i	$-0.799830\pi$
$257$	−1945.26	+	1456.21i	−0.472149	+	0.353446i	0.336553	+	0.941664i	$0.390739\pi$
$258$	−8268.63	+	3084.04i	−1.99528	+	0.744201i
$259$	11020.9	−	1584.57i	2.64404	−	0.380155i
$260$	624.941	−	982.641i	0.149066	−	0.234388i
$261$	−2685.91	+	1726.13i	−0.636987	+	0.409366i
$262$	−4007.17	+	10743.6i	−0.944901	+	2.53338i
$263$	−748.723	−	408.834i	−0.175545	−	0.0958547i	0.389074	−	0.921206i	$-0.372795\pi$
$263$	−748.723	−	408.834i	−0.175545	−	0.0958547i	−0.564619	+	0.825352i	$0.690977\pi$
$264$	467.260	−	539.246i	0.108931	−	0.125713i
$265$	948.867	+	1461.19i	0.219956	+	0.338717i
$266$	−12008.9	+	3526.13i	−2.76809	+	0.812785i
$267$	−3763.11	−	1403.57i	−0.862542	−	0.321712i
$268$	−7251.95	−	1577.56i	−1.65292	−	0.359571i
$269$	−790.293	+	2691.49i	−0.179126	+	0.610049i	0.820155	+	0.572142i	$0.193887\pi$
$269$	−790.293	+	2691.49i	−0.179126	+	0.610049i	−0.999281	+	0.0379070i	$0.987931\pi$
$270$	−2904.02	−	3841.21i	−0.654566	−	0.865810i
$271$	2866.03	−	6275.72i	0.642431	−	1.40673i	−0.255595	−	0.966784i	$-0.582271\pi$
$271$	2866.03	−	6275.72i	0.642431	−	1.40673i	0.898026	−	0.439943i	$-0.145001\pi$
$272$	−1451.63	−	1939.15i	−0.323596	−	0.432273i
$273$	332.897	+	1530.30i	0.0738016	+	0.339261i
$274$	−1900.99	−	2193.86i	−0.419136	−	0.483708i
$275$	363.892	+	229.012i	0.0797946	+	0.0502180i
$276$	8074.26	+	6466.15i	1.76092	+	1.41021i
$277$	3501.54	+	3501.54i	0.759520	+	0.759520i	0.976235	−	0.216715i	$-0.0695342\pi$
$277$	3501.54	+	3501.54i	0.759520	+	0.759520i	−0.216715	+	0.976235i	$0.569534\pi$
$278$	−3768.13	−	269.502i	−0.812941	−	0.0581427i
$279$	−1639.04	+	2550.40i	−0.351710	+	0.547271i
$280$	−4624.70	−	12222.0i	−0.987066	−	2.60858i
$281$	2419.64	+	1105.01i	0.513678	+	0.234589i	0.655351	−	0.755325i	$-0.272521\pi$
$281$	2419.64	+	1105.01i	0.513678	+	0.234589i	−0.141673	+	0.989914i	$0.545248\pi$
$282$	3607.40	−	4818.92i	0.761765	−	1.01760i
$283$	−2131.77	−	3904.04i	−0.447775	−	0.820039i	0.552131	−	0.833758i	$-0.313815\pi$
$283$	−2131.77	−	3904.04i	−0.447775	−	0.820039i	−0.999906	+	0.0137186i	$0.995633\pi$
$284$	1137.06	+	1769.29i	0.237577	+	0.369677i
$285$	763.236	+	5135.44i	0.158632	+	1.06736i
$286$	−32.4446	−	110.496i	−0.00670801	−	0.0228454i
$287$	−73.7709	−	1031.45i	−0.0151727	−	0.212142i
$288$	−72.1979	−	1009.46i	−0.0147719	−	0.206538i
$289$	−263.636	−	897.860i	−0.0536608	−	0.182752i
$290$	−1974.65	−	13286.4i	−0.399846	−	2.69037i
$291$	−3933.71	−	6120.98i	−0.792434	−	1.23305i
$292$	−1964.27	−	3597.29i	−0.393664	−	0.720942i
$293$	−1675.57	+	2238.30i	−0.334088	+	0.446289i	−0.935857	−	0.352381i	$-0.885372\pi$
$293$	−1675.57	+	2238.30i	−0.334088	+	0.446289i	0.601769	+	0.798671i	$0.294463\pi$
$294$	25164.2	+	11492.1i	4.99187	+	2.27971i
$295$	−462.712	−	1222.84i	−0.0913226	−	0.241344i
$296$	5580.73	−	8683.79i	1.09586	−	1.70519i
$297$	−308.918	−	22.0943i	−0.0603544	−	0.00431663i
$298$	5263.18	+	5263.18i	1.02311	+	1.02311i
$299$	731.782	−	246.041i	0.141539	−	0.0475884i
$300$	−11430.5	+	2600.31i	−2.19979	+	0.500430i
$301$	6807.28	+	7856.02i	1.30354	+	1.50436i
$302$	2147.20	+	9870.50i	0.409130	+	1.88074i
$303$	2790.50	+	3727.67i	0.529076	+	0.706762i
$304$	−1175.78	+	2574.60i	−0.221828	+	0.485735i
$305$	1236.11	+	1635.03i	0.232064	+	0.306956i
$306$	1080.39	−	3679.47i	0.201836	−	0.687390i
$307$	−463.662	−	100.864i	−0.0861974	−	0.0187511i	0.169260	−	0.985571i	$-0.445862\pi$
$307$	−463.662	−	100.864i	−0.0861974	−	0.0187511i	−0.255457	+	0.966820i	$0.582226\pi$
$308$	−1702.92	−	635.155i	−0.315041	−	0.117504i
$309$	−9423.85	+	2767.09i	−1.73497	+	0.509432i
$310$	−6946.52	−	10697.1i	−1.27270	−	1.95986i
$311$	3711.98	−	4283.85i	0.676808	−	0.781078i	−0.308618	−	0.951186i	$-0.599866\pi$
$311$	3711.98	−	4283.85i	0.676808	−	0.781078i	0.985425	+	0.170109i	$0.0544119\pi$
$312$	1274.31	+	695.827i	0.231230	+	0.126261i
$313$	−3002.25	+	8049.33i	−0.542163	+	1.45359i	0.320222	+	0.947342i	$0.396242\pi$
$313$	−3002.25	+	8049.33i	−0.542163	+	1.45359i	−0.862385	+	0.506252i	$0.831030\pi$
$314$	−13113.9	+	8427.81i	−2.35688	+	1.51468i
$315$	2708.09	−	4258.13i	0.484392	−	0.761646i
$316$	1992.37	−	286.459i	0.354682	−	0.0509956i
$317$	−5773.99	+	2153.59i	−1.02303	+	0.381569i	−0.804304	−	0.594218i	$-0.797462\pi$
$317$	−5773.99	+	2153.59i	−1.02303	+	0.381569i	−0.218722	+	0.975787i	$0.570189\pi$
$318$	−3760.46	+	2815.05i	−0.663133	+	0.496415i
$319$	−726.771	−	467.068i	−0.127559	−	0.0819773i
$320$	7220.85	+	2654.30i	1.26143	+	0.463688i
$321$		−	1723.96i		−	0.299758i
$322$	5862.18	−	17793.9i	1.01455	−	3.07955i
$323$	3286.11	−	3286.11i	0.566081	−	0.566081i
$324$	10241.6	−	8874.42i	1.75611	−	1.52168i
$325$	−297.957	+	822.596i	−0.0508545	+	0.140398i
$326$	370.084	−	2573.99i	0.0628744	−	0.437301i
$327$	−4743.51	−	12717.8i	−0.802192	−	2.15076i
$328$	−767.472	−	574.523i	−0.129197	−	0.0967156i
$329$	−6803.24	−	1997.61i	−1.14004	−	0.334747i
$330$	−550.735	+	1020.07i	−0.0918697	+	0.170160i
$331$	3213.42	+	7036.42i	0.533613	+	1.16845i	0.964024	+	0.265816i	$0.0856413\pi$
$331$	3213.42	+	7036.42i	0.533613	+	1.16845i	−0.430411	+	0.902633i	$0.641631\pi$
$332$	−6022.23	+	11028.9i	−0.995521	+	1.82316i
$333$	3976.04	−	284.372i	0.654311	−	0.0467973i
$334$	−279.351	−	242.059i	−0.0457646	−	0.0396553i
$335$	5575.64	−	26.4380i	0.909343	−	0.00431183i
$336$	7817.61	−	3570.19i	1.26930	−	0.579671i
$337$	82.4270	−	378.911i	0.0133237	−	0.0612480i	−0.970005	−	0.243085i	$-0.921841\pi$
$337$	82.4270	−	378.911i	0.0133237	−	0.0612480i	0.983329	+	0.181837i	$0.0582043\pi$
$338$	−9018.11	+	4924.26i	−1.45124	+	0.792439i
$339$	464.078	+	3227.73i	0.0743518	+	0.517128i
$340$	7962.50	+	6833.71i	1.27008	+	1.09003i
$341$	−811.980	−	116.745i	−0.128948	−	0.0185399i
$342$	−4378.44	+	952.471i	−0.692277	+	0.150596i
$343$	1455.80	−	20354.8i	0.229172	−	3.20424i
$344$	9637.12			1.51046
$345$	−6976.39	−	3424.43i	−1.08869	−	0.534392i
$346$	−8936.84			−1.38858
$347$	426.179	−	5958.76i	0.0659323	−	0.921853i	−0.851600	−	0.524192i	$-0.824367\pi$
$347$	426.179	−	5958.76i	0.0659323	−	0.921853i	0.917532	−	0.397661i	$-0.130178\pi$
$348$	23015.7	−	5006.76i	3.54532	−	0.771238i
$349$	−12368.4	−	1778.31i	−1.89703	−	0.272752i	−0.907835	−	0.419328i	$-0.862266\pi$
$349$	−12368.4	−	1778.31i	−1.89703	−	0.272752i	−0.989199	+	0.146576i	$0.953175\pi$
$350$	11647.0	+	17750.7i	1.77874	+	2.71091i
$351$	−89.6876	−	623.791i	−0.0136387	−	0.0948589i
$352$	240.347	−	131.239i	0.0363936	−	0.0198724i
$353$	544.107	−	2501.22i	0.0820394	−	0.377129i	−0.917761	−	0.397134i	$-0.870005\pi$
$353$	544.107	−	2501.22i	0.0820394	−	0.377129i	0.999800	+	0.0200054i	$0.00636835\pi$
$354$	3206.57	−	1464.39i	0.481433	−	0.219863i
$355$	−1122.57	−	1111.97i	−0.167830	−	0.166246i
$356$	7168.01	+	6211.11i	1.06715	+	0.924687i
$357$	−14075.2	+	1006.68i	−2.08666	+	0.149241i
$358$	−228.118	+	417.767i	−0.0336771	+	0.0616750i
$359$	−3049.66	−	6677.82i	−0.448342	−	0.981731i	−0.989991	−	0.141127i	$-0.954927\pi$
$359$	−3049.66	−	6677.82i	−0.448342	−	0.981731i	0.541650	−	0.840604i	$-0.317800\pi$
$360$	−1339.33	−	4482.59i	−0.196080	−	0.656260i
$361$	1370.95	+	402.548i	0.199877	+	0.0586890i
$362$	−603.507	−	451.779i	−0.0876232	−	0.0655939i
$363$	−2905.11	−	7788.91i	−0.420052	−	1.12620i
$364$	526.329	−	3660.70i	0.0757889	−	0.527123i
$365$	2027.49	+	2317.55i	0.290750	+	0.332346i
$366$	−4176.55	+	3619.00i	−0.596480	+	0.516853i
$367$	4132.87	−	4132.87i	0.587831	−	0.587831i	−0.349212	−	0.937044i	$-0.613551\pi$
$367$	4132.87	−	4132.87i	0.587831	−	0.587831i	0.937044	+	0.349212i	$0.113551\pi$
$368$	−2172.97	−	3637.03i	−0.307809	−	0.515199i
$369$		−	370.216i		−	0.0522295i
$370$	−5786.14	+	15740.8i	−0.812992	+	2.21169i
$371$	4654.70	+	2991.39i	0.651375	+	0.418613i
$372$	17904.7	−	13403.3i	2.49547	−	1.86808i
$373$	−1022.43	+	381.347i	−0.141929	+	0.0529367i	−0.419425	−	0.907790i	$-0.637768\pi$
$373$	−1022.43	+	381.347i	−0.141929	+	0.0529367i	0.277496	+	0.960727i	$0.410495\pi$
$374$	1027.09	−	147.673i	0.142004	−	0.0204170i
$375$	7958.23	−	3772.12i	1.09590	−	0.519444i
$376$	−5529.97	+	3553.90i	−0.758475	+	0.487442i
$377$	614.333	−	1647.09i	0.0839251	−	0.225012i
$378$	−13422.3	−	7329.11i	−1.82637	−	0.997271i
$379$	−3970.78	+	4582.52i	−0.538167	+	0.621078i	−0.958085	−	0.286484i	$-0.907513\pi$
$379$	−3970.78	+	4582.52i	−0.538167	+	0.621078i	0.419918	+	0.907562i	$0.362059\pi$
$380$	2549.34	−	11992.6i	0.344154	−	1.61897i
$381$	−3864.84	+	1134.82i	−0.519689	+	0.152595i
$382$	13526.7	+	5045.19i	1.81174	+	0.675745i
$383$	3590.25	+	781.011i	0.478990	+	0.104198i	0.445577	−	0.895244i	$-0.352999\pi$
$383$	3590.25	+	781.011i	0.478990	+	0.104198i	0.0334132	+	0.999442i	$0.489362\pi$
$384$	−4713.02	+	16051.1i	−0.626329	+	2.13308i
$385$	1352.48	+	187.916i	0.179035	+	0.0248755i
$386$	−4760.50	+	10424.0i	−0.627728	+	1.37453i
$387$	2230.24	+	2979.25i	0.292944	+	0.391328i
$388$	3652.38	+	16789.7i	0.477891	+	2.19683i
$389$	4676.06	+	5396.46i	0.609474	+	0.703371i	0.973673	−	0.227951i	$-0.0732025\pi$
$389$	4676.06	+	5396.46i	0.609474	+	0.703371i	−0.364199	+	0.931321i	$0.618657\pi$
$390$	−2266.45	−	653.832i	−0.294272	−	0.0848925i
$391$	1255.99	+	6842.04i	0.162450	+	0.884953i
$392$	−21361.6	−	21361.6i	−2.75235	−	2.75235i
$393$	15067.6	+	1077.66i	1.93400	+	0.138322i
$394$	5329.24	−	8292.45i	0.681429	−	1.06032i
$395$	−1414.36	+	535.183i	−0.180163	+	0.0681721i
$396$	−591.890	−	270.307i	−0.0751101	−	0.0343016i
$397$	6911.34	−	9232.47i	0.873729	−	1.16717i	−0.111130	−	0.993806i	$-0.535447\pi$
$397$	6911.34	−	9232.47i	0.873729	−	1.16717i	0.984859	−	0.173359i	$-0.0554622\pi$
$398$	7825.36	+	14331.1i	0.985552	+	1.80490i
$399$	8914.29	+	13870.9i	1.11848	+	1.74039i
$400$	4758.57	+	638.181i	0.594821	+	0.0797726i
$401$	−1481.13	−	5044.26i	−0.184449	−	0.628176i	−0.998853	−	0.0478776i	$-0.984754\pi$
$401$	−1481.13	−	5044.26i	−0.184449	−	0.628176i	0.814404	−	0.580298i	$-0.197064\pi$
$402$	1072.45	+	14994.8i	0.133057	+	1.86038i
$403$	−119.082	−	1664.99i	−0.0147194	−	0.205804i
$404$	−3097.99	−	10550.8i	−0.381512	−	1.29931i
$405$	−6062.61	+	8179.26i	−0.743836	+	1.00353i
$406$	−23063.1	−	35886.9i	−2.81922	−	4.38679i
$407$	516.924	+	946.675i	0.0629557	+	0.115295i
$408$	−7839.93	+	10472.9i	−0.951309	+	1.27080i
$409$	−5308.15	−	2424.15i	−0.641739	−	0.293072i	0.0678421	−	0.997696i	$-0.478389\pi$
$409$	−5308.15	−	2424.15i	−0.641739	−	0.293072i	−0.709581	+	0.704624i	$0.751116\pi$
$410$	1419.86	+	640.308i	0.171029	+	0.0771281i
$411$	−2067.56	+	3217.18i	−0.248139	+	0.386111i
$412$	23134.9	+	1654.64i	2.76645	+	0.197860i
$413$	−2936.08	−	2936.08i	−0.349819	−	0.349819i
$414$	2547.85	−	6204.49i	0.302464	−	0.736555i
$415$	2616.75	−	9070.74i	0.309522	−	1.07293i
$416$	364.907	+	421.126i	0.0430073	+	0.0496331i
$417$	1057.90	+	4863.08i	0.124234	+	0.571093i
$418$	−726.598	−	970.621i	−0.0850217	−	0.113576i
$419$	1545.71	−	3384.62i	0.180221	−	0.394629i	−0.797863	−	0.602839i	$-0.794036\pi$
$419$	1545.71	−	3384.62i	0.180221	−	0.394629i	0.978084	+	0.208209i	$0.0667635\pi$
$420$	−29696.9	+	22451.3i	−3.45014	+	2.60836i
$421$	−2841.91	+	9678.67i	−0.328994	+	1.12045i	0.614461	+	0.788947i	$0.289374\pi$
$421$	−2841.91	+	9678.67i	−0.328994	+	1.12045i	−0.943454	+	0.331502i	$0.892445\pi$
$422$	−1976.18	−	429.892i	−0.227960	−	0.0495896i
$423$	−2378.42	−	887.105i	−0.273387	−	0.101968i
$424$	4921.86	−	1445.19i	0.563742	−	0.165529i
$425$	−6954.40	−	3712.22i	−0.793737	−	0.423692i
$426$	2789.82	−	3219.62i	0.317294	−	0.366176i
$427$	5713.25	+	3119.67i	0.647502	+	0.353563i
$428$	−1422.72	+	3814.47i	−0.160677	+	0.430793i
$429$	−127.629	+	82.0222i	−0.0143636	+	0.00923093i
$430$	−15283.4	+	3400.67i	−1.71402	+	0.381383i
$431$	−12530.7	+	1801.64i	−1.40042	+	0.201350i	−0.800799	−	0.598933i	$-0.795592\pi$
$431$	−12530.7	+	1801.64i	−1.40042	+	0.201350i	−0.599622	+	0.800283i	$0.704682\pi$
$432$	−3240.33	+	1208.58i	−0.360881	+	0.134602i
$433$	−6793.39	+	5085.47i	−0.753971	+	0.564416i	−0.905656	−	0.424013i	$-0.860621\pi$
$433$	−6793.39	+	5085.47i	−0.753971	+	0.564416i	0.151685	+	0.988429i	$0.451530\pi$
$434$	−34076.4	−	21899.6i	−3.76894	−	2.42215i
$435$	−16061.6	+	7427.34i	−1.77033	+	0.818652i
$436$			32054.3i			3.52093i
$437$	6313.43	−	5119.51i	0.691104	−	0.560411i
$438$	−5870.54	+	5870.54i	−0.640422	+	0.640422i
$439$	8984.52	−	7785.13i	0.976783	−	0.846387i	−0.0113582	−	0.999935i	$-0.503615\pi$
$439$	8984.52	−	7785.13i	0.976783	−	0.846387i	0.988141	+	0.153548i	$0.0490700\pi$
$440$	952.772	−	833.525i	0.103231	−	0.0903107i
$441$	1660.25	−	11547.3i	0.179274	−	1.24688i
$442$	737.875	+	1978.32i	0.0794053	+	0.212894i
$443$	−7955.00	−	5955.04i	−0.853168	−	0.638674i	0.0805232	−	0.996753i	$-0.474341\pi$
$443$	−7955.00	−	5955.04i	−0.853168	−	0.638674i	−0.933691	+	0.358079i	$0.883432\pi$
$444$	−28216.4	−	8285.07i	−3.01597	−	0.885568i
$445$	−6270.17	−	3385.28i	−0.667943	−	0.360624i
$446$	4035.92	+	8837.44i	0.428490	+	0.938262i
$447$	4699.39	−	8606.28i	0.497256	−	0.910656i
$448$	24370.1	−	1742.98i	2.57004	−	0.183813i
$449$	10980.0	+	9514.25i	1.15408	+	1.00001i	0.999928	+	0.0119639i	$0.00380831\pi$
$449$	10980.0	+	9514.25i	1.15408	+	1.00001i	0.154147	+	0.988048i	$0.450737\pi$
$450$	3705.80	+	6636.27i	0.388207	+	0.695193i
$451$	91.1229	−	41.6144i	0.00951399	−	0.00434489i
$452$	1636.90	−	7524.72i	0.170339	−	0.783037i
$453$	11679.7	−	6377.60i	1.21139	−	0.661470i
$454$	3725.66	+	25912.5i	0.385140	+	2.67871i
$455$	211.356	+	2770.46i	0.0217769	+	0.285453i
$456$	15130.6	+	2175.46i	1.55385	+	0.223410i
$457$	9322.71	−	2028.03i	0.954263	−	0.207587i	0.291630	−	0.956531i	$-0.405803\pi$
$457$	9322.71	−	2028.03i	0.954263	−	0.207587i	0.662633	+	0.748944i	$0.269439\pi$
$458$	1340.45	−	18742.0i	0.136758	−	1.91213i
$459$	5678.40			0.577440
$460$	12610.0	+	13334.3i	1.27814	+	1.35155i
$461$	15515.3			1.56750			0.783752	−	0.621074i	$-0.213303\pi$
$461$	15515.3			1.56750			0.783752	+	0.621074i	$0.213303\pi$
$462$	−262.639	+	3672.17i	−0.0264482	+	0.369794i
$463$	−224.304	+	48.7944i	−0.0225147	+	0.00489777i	−0.223809	−	0.974633i	$-0.571849\pi$
$463$	−224.304	+	48.7944i	−0.0225147	+	0.00489777i	0.201294	+	0.979531i	$0.435485\pi$
$464$	−9548.81	−	1372.91i	−0.955371	−	0.137362i
$465$	−10943.3	+	12750.9i	−1.09136	+	1.27163i
$466$	−2245.48	−	15617.7i	−0.223219	−	1.55252i
$467$	−11854.7	+	6473.16i	−1.17467	+	0.641418i	−0.943460	−	0.331486i	$-0.892450\pi$
$467$	−11854.7	+	6473.16i	−1.17467	+	0.641418i	−0.231209	+	0.972904i	$0.574268\pi$
$468$	281.448	−	1293.80i	0.0277990	−	0.127790i
$469$	16107.3	−	7355.94i	1.58585	−	0.724234i
$470$	7515.83	−	7587.45i	0.737616	−	0.744645i
$471$	15520.3	+	13448.4i	1.51834	+	1.31565i
$472$	−3839.70	+	274.621i	−0.374442	+	0.0267806i
$473$	−482.604	+	883.824i	−0.0469137	+	0.0859160i
$474$	−1693.75	−	3708.79i	−0.164127	−	0.359389i
$475$	87.3517	+	9210.80i	0.00843783	+	0.889727i
$476$	31973.7	+	9388.33i	3.07881	+	0.904020i
$477$	1585.79	+	1187.11i	0.152219	+	0.113950i
$478$	−6935.63	−	18595.1i	−0.663657	−	1.77933i
$479$	1248.17	−	8681.19i	0.119061	−	0.828087i	−0.839533	−	0.543309i	$-0.817171\pi$
$479$	1248.17	−	8681.19i	0.119061	−	0.828087i	0.958594	−	0.284778i	$-0.0919198\pi$
$480$	373.623	−	5596.76i	0.0355281	−	0.532200i
$481$	−1658.72	+	1437.29i	−0.157237	+	0.136247i
$482$	−17803.5	+	17803.5i	−1.68242	+	1.68242i
$483$	−24667.9	−	805.722i	−2.32386	−	0.0759040i
$484$			19631.4i			1.84367i
$485$	−5418.16	−	11716.8i	−0.507270	−	1.09697i
$486$	−13309.6	−	8553.56i	−1.24225	−	0.798348i
$487$	−2440.03	+	1826.58i	−0.227039	+	0.169960i	−0.706742	−	0.707472i	$-0.749836\pi$
$487$	−2440.03	+	1826.58i	−0.227039	+	0.169960i	0.479702	+	0.877431i	$0.340745\pi$
$488$	5654.39	−	2108.98i	0.524513	−	0.195633i
$489$	−3390.97	+	487.547i	−0.313589	+	0.0450872i
$490$	41414.9	+	26339.1i	3.81823	+	2.42832i
$491$	662.160	−	425.544i	0.0608612	−	0.0391131i	−0.509856	−	0.860260i	$-0.670301\pi$
$491$	662.160	−	425.544i	0.0608612	−	0.0391131i	0.570718	+	0.821146i	$0.306665\pi$
$492$	−954.462	+	2559.01i	−0.0874603	+	0.234490i
$493$	13902.1	+	7591.13i	1.27002	+	0.693484i
$494$	1615.64	−	1864.55i	0.147148	−	0.169818i
$495$	478.171	+	101.648i	0.0434186	+	0.00922973i
$496$	−8789.25	+	2580.76i	−0.795663	+	0.233628i
$497$	−4701.65	−	1753.63i	−0.424342	−	0.158271i
$498$	24871.9	+	5410.56i	2.23803	+	0.486853i
$499$	−4229.02	+	14402.7i	−0.379393	+	1.29209i	0.519705	+	0.854345i	$0.326042\pi$
$499$	−4229.02	+	14402.7i	−0.379393	+	1.29209i	−0.899098	+	0.437747i	$0.855776\pi$
$500$	−20721.5	+	1778.62i	−1.85339	+	0.159085i
$501$	−202.288	+	442.950i	−0.0180391	+	0.0395001i
$502$	−12960.1	−	17312.7i	−1.15227	−	1.53925i
$503$	1139.60	+	5238.64i	0.101018	+	0.464372i	0.999669	+	0.0257090i	$0.00818434\pi$
$503$	1139.60	+	5238.64i	0.101018	+	0.464372i	−0.898651	+	0.438663i	$0.855452\pi$
$504$	−9729.77	−	11228.8i	−0.859917	−	0.992397i
$505$	3993.56	+	7231.91i	0.351903	+	0.637259i
$506$	1813.53	−	70.3070i	0.159331	−	0.00617693i
$507$	9571.54	+	9571.54i	0.838436	+	0.838436i
$508$	9487.92	+	678.590i	0.828658	+	0.0592668i
$509$	5682.46	−	8842.09i	0.494834	−	0.769977i	−0.500574	−	0.865694i	$-0.666878\pi$
$509$	5682.46	−	8842.09i	0.494834	−	0.769977i	0.995409	+	0.0957162i	$0.0305141\pi$
$510$	8737.63	−	19375.3i	0.758644	−	1.68226i
$511$	8895.41	+	4062.40i	0.770078	+	0.351683i
$512$	7894.16	−	10545.4i	0.681398	−	0.910241i
$513$	−3179.83	−	5823.42i	−0.273670	−	0.501189i
$514$	−6284.16	−	9778.34i	−0.539265	−	0.839113i
$515$	−17236.0	+	2561.64i	−1.47478	+	0.219183i
$516$	−7735.01	−	26343.0i	−0.659913	−	2.24746i
$517$	−49.0012	−	685.127i	−0.00416842	−	0.0582821i
$518$	3799.55	+	53124.6i	0.322283	+	4.50610i
$519$	3316.94	+	11296.5i	0.280535	+	0.955415i
$520$	2069.44	+	1533.90i	0.174521	+	0.129358i
$521$	4001.17	+	6225.94i	0.336457	+	0.523538i	0.967719	−	0.252032i	$-0.0810989\pi$
$521$	4001.17	+	6225.94i	0.336457	+	0.523538i	−0.631262	+	0.775570i	$0.717463\pi$
$522$	−7319.28	−	13404.3i	−0.613710	−	1.12393i
$523$	20.2508	−	27.0520i	0.00169313	−	0.00226176i	−0.799694	−	0.600408i	$-0.795005\pi$
$523$	20.2508	−	27.0520i	0.00169313	−	0.00226176i	0.801387	+	0.598146i	$0.204096\pi$
$524$	−32449.5	−	14819.2i	−2.70527	−	1.23546i
$525$	18114.7	−	21310.5i	1.50589	−	1.77156i
$526$	2206.16	−	3432.86i	0.182877	−	0.284562i
$527$	15002.2	+	1072.98i	1.24005	+	0.0886902i
$528$	588.706	+	588.706i	0.0485230	+	0.0485230i
$529$	941.965	+	12130.5i	0.0774196	+	0.996999i
$530$	−7295.53	+	4028.69i	−0.597920	+	0.330179i
$531$	−973.487	−	1123.46i	−0.0795589	−	0.0918158i
$532$	−8276.75	−	38047.6i	−0.674516	−	3.10070i
$533$	122.158	+	163.183i	0.00992726	+	0.0132613i
$534$	7980.98	−	17475.9i	0.646762	−	1.41621i
$535$	420.924	−	3029.50i	0.0340152	−	0.244816i
$536$	4625.04	−	15751.4i	0.372707	−	1.26932i
$537$	612.738	+	133.293i	0.0492395	+	0.0107114i
$538$	−12572.2	−	4689.18i	−1.00748	−	0.375771i
$539$	3028.81	−	889.340i	0.242041	−	0.0710697i
$540$	12564.3	−	8159.00i	1.00126	−	0.650199i
$541$	9236.49	−	10659.5i	0.734025	−	0.847110i	−0.258894	−	0.965906i	$-0.583358\pi$
$541$	9236.49	−	10659.5i	0.734025	−	0.847110i	0.992919	+	0.118796i	$0.0379034\pi$
$542$	28965.2	+	15816.2i	2.29550	+	1.25344i
$543$	−347.071	+	930.532i	−0.0274295	+	0.0735414i
$544$	−4223.81	+	2714.48i	−0.332894	+	0.213938i
$545$	−5230.51	−	23507.1i	−0.411102	−	1.84758i
$546$	−7415.11	+	1066.13i	−0.581204	+	0.0835645i
$547$	−845.016	+	315.175i	−0.0660517	+	0.0246360i	−0.382273	−	0.924049i	$-0.624859\pi$
$547$	−845.016	+	315.175i	−0.0660517	+	0.0246360i	0.316221	+	0.948685i	$0.397586\pi$
$548$	7229.72	−	5412.10i	0.563574	−	0.421886i
$549$	1960.53	+	1259.95i	0.152410	+	0.0979481i
$550$	−1216.86	+	1658.08i	−0.0943402	+	0.128547i
$551$		−	18508.1i		−	1.43098i
$552$	−15540.8	+	16794.3i	−1.19829	+	1.29495i
$553$	−3395.93	+	3395.93i	−0.261139	+	0.261139i
$554$	−17901.7	+	15511.9i	−1.37287	+	1.18960i
$555$	22044.4	+	1471.62i	1.68601	+	0.112553i
$556$	1672.60	−	11633.2i	0.127579	−	0.887331i
$557$	−4009.98	−	10751.2i	−0.305042	−	0.817850i	−0.995525	−	0.0945006i	$-0.969875\pi$
$557$	−4009.98	−	10751.2i	−0.305042	−	0.817850i	0.690483	−	0.723349i	$-0.257398\pi$
$558$	−11609.4	−	8690.67i	−0.880760	−	0.659329i
$559$	−1966.08	−	577.294i	−0.148759	−	0.0436797i
$560$	14609.5	−	4365.09i	1.10244	−	0.329390i
$561$	−567.870	−	1243.46i	−0.0427371	−	0.0935811i
$562$	−6098.03	+	11167.7i	−0.457704	+	0.838223i
$563$	−5786.45	+	413.855i	−0.433161	+	0.0309803i	−0.286218	−	0.958165i	$-0.592398\pi$
$563$	−5786.45	+	413.855i	−0.433161	+	0.0309803i	−0.146943	+	0.989145i	$0.546944\pi$
$564$	14153.1	+	12263.7i	1.05665	+	0.915595i
$565$	27.4325	+	5785.36i	0.00204264	+	0.430782i
$566$	19354.7	−	8839.01i	1.43735	−	0.656416i
$567$	−6872.97	+	31594.6i	−0.509061	+	2.34012i
$568$	−4083.12	+	2229.55i	−0.301627	+	0.164701i
$569$	1387.68	+	9651.56i	0.102240	+	0.711097i	0.974880	+	0.222732i	$0.0714975\pi$
$569$	1387.68	+	9651.56i	0.102240	+	0.711097i	−0.872639	+	0.488365i	$0.837593\pi$
$570$	−24763.1	+	1889.15i	−1.81967	+	0.138821i
$571$	−25878.7	−	3720.80i	−1.89666	−	0.272698i	−0.907554	−	0.419935i	$-0.862053\pi$
$571$	−25878.7	−	3720.80i	−1.89666	−	0.272698i	−0.989101	+	0.147237i	$0.952962\pi$
$572$	350.084	−	76.1561i	0.0255905	−	0.00556686i
$573$	1356.81	−	18970.7i	0.0989209	−	1.38310i
$574$	4946.52			0.359693
$575$	−11423.4	−	7721.07i	−0.828503	−	0.559984i
$576$	8747.09			0.632747
$577$	136.427	−	1907.50i	0.00984321	−	0.137626i	−0.990154	−	0.139982i	$-0.955295\pi$
$577$	136.427	−	1907.50i	0.00984321	−	0.137626i	0.999997	+	0.00235616i	$0.000749991\pi$
$578$	4373.91	−	951.486i	0.314759	−	0.0684716i
$579$	14943.2	+	2148.51i	1.07257	+	0.154213i
$580$	41667.7	−	3178.79i	2.98303	−	0.227572i
$581$	−4266.85	−	29676.6i	−0.304680	−	2.11909i
$582$	30547.3	−	16680.1i	2.17565	−	1.18799i
$583$	−113.936	+	523.757i	−0.00809393	+	0.0372072i
$584$	8246.85	−	3766.21i	0.584344	−	0.266861i
$585$	4.71672	+	994.732i	0.000333355	+	0.0703027i
$586$	−10107.8	−	8758.43i	−0.712540	−	0.617419i
$587$	−13613.5	+	973.656i	−0.957221	+	0.0684618i	−0.541201	−	0.840894i	$-0.682030\pi$
$587$	−13613.5	+	973.656i	−0.957221	+	0.0684618i	−0.416020	+	0.909355i	$0.636575\pi$
$588$	−41246.4	+	75537.1i	−2.89281	+	5.29779i
$589$	−7300.65	−	15986.2i	−0.510727	−	1.11834i
$590$	5992.42	−	1790.44i	0.418142	−	0.124934i
$591$	−12459.9	−	3658.56i	−0.867229	−	0.254641i
$592$	9642.07	+	7217.96i	0.669403	+	0.501109i
$593$	1667.36	+	4470.37i	0.115464	+	0.309572i	0.981808	−	0.189876i	$-0.0608087\pi$
$593$	1667.36	+	4470.37i	0.115464	+	0.309572i	−0.866344	+	0.499449i	$0.833536\pi$
$594$	210.836	−	1466.40i	0.0145635	−	0.101291i
$595$	−24979.9	−	1667.59i	−1.72114	−	0.114898i
$596$	−17500.4	+	15164.2i	−1.20276	+	1.04220i
$597$	15210.5	−	15210.5i	1.04276	−	1.04276i
$598$	924.212	+	3575.50i	0.0632004	+	0.244504i
$599$			12141.7i			0.828207i	0.910230	+	0.414104i	$0.135905\pi$
$599$			12141.7i			0.828207i	−0.910230	+	0.414104i	$0.864095\pi$
$600$	−3933.46	−	25630.0i	−0.267638	−	1.74390i
$601$	−8753.74	−	5625.69i	−0.594131	−	0.381825i	0.208746	−	0.977970i	$-0.433062\pi$
$601$	−8753.74	−	5625.69i	−0.594131	−	0.381825i	−0.802877	+	0.596145i	$0.796698\pi$
$602$	−39806.3	+	29798.6i	−2.69499	+	2.01744i
$603$	5939.78	−	2215.42i	0.401139	−	0.149617i
$604$	−31105.9	+	4472.35i	−2.09550	+	0.301287i
$605$	−3203.37	−	14396.7i	−0.215266	−	0.967451i
$606$	−18738.0	+	12042.2i	−1.25607	+	0.807229i
$607$	1252.20	−	3357.29i	0.0837321	−	0.224494i	−0.888336	−	0.459195i	$-0.848138\pi$
$607$	1252.20	−	3357.29i	0.0837321	−	0.224494i	0.972068	+	0.234700i	$0.0754108\pi$
$608$	5149.08	+	2811.61i	0.343458	+	0.187543i
$609$	−36802.3	+	42472.1i	−2.44878	+	2.82604i
$610$	−8223.02	+	5339.88i	−0.545804	+	0.354435i
$611$	1341.07	−	393.773i	0.0887952	−	0.0260726i
$612$	11178.1	+	4169.20i	0.738310	+	0.275376i
$613$	16714.3	+	3635.97i	1.10128	+	0.239569i	0.726241	−	0.687441i	$-0.241266\pi$
$613$	16714.3	+	3635.97i	1.10128	+	0.239569i	0.375038	+	0.927009i	$0.377629\pi$
$614$	639.473	−	2177.84i	0.0420310	−	0.143144i
$615$	282.385	−	2032.40i	0.0185152	−	0.133259i
$616$	1670.10	−	3657.01i	0.109237	−	0.239197i
$617$	−4878.11	−	6516.39i	−0.318291	−	0.425187i	0.612651	−	0.790353i	$-0.290103\pi$
$617$	−4878.11	−	6516.39i	−0.318291	−	0.425187i	−0.930942	+	0.365167i	$0.881012\pi$
$618$	−9986.71	−	45908.2i	−0.650039	−	2.98818i
$619$	8557.29	+	9875.63i	0.555648	+	0.641252i	0.962190	−	0.272380i	$-0.0878108\pi$
$619$	8557.29	+	9875.63i	0.555648	+	0.641252i	−0.406541	+	0.913632i	$0.633265\pi$
$620$	34736.2	−	19181.8i	2.25006	−	1.24251i
$621$	9878.07	+	1031.55i	0.638315	+	0.0666580i
$622$	19172.8	+	19172.8i	1.23595	+	1.23595i
$623$	−22572.2	−	1614.40i	−1.45158	−	0.103819i
$624$	−915.910	+	1425.18i	−0.0587592	+	0.0914311i
$625$	14905.9	−	4685.61i	0.953977	−	0.299879i
$626$	−37381.1	−	17071.4i	−2.38666	−	1.08995i
$627$	−957.218	+	1278.69i	−0.0609691	+	0.0814452i
$628$	−23242.0	−	42564.5i	−1.47684	−	2.70463i
$629$	−10691.7	−	16636.7i	−0.677755	−	1.05461i
$630$	19392.6	+	14374.1i	1.22638	+	0.909016i
$631$	−596.673	−	2032.08i	−0.0376437	−	0.128203i	0.938527	−	0.345205i	$-0.112190\pi$
$631$	−596.673	−	2032.08i	−0.0376437	−	0.128203i	−0.976171	+	0.217002i	$0.930372\pi$
$632$	317.632	+	4441.08i	0.0199917	+	0.279520i
$633$	190.069	+	2657.52i	0.0119346	+	0.166867i
$634$	−8305.00	−	28284.2i	−0.520243	−	1.77178i
$635$	−7068.71	+	1050.56i	−0.441753	+	0.0656539i
$636$	−7900.83	−	12293.9i	−0.492592	−	0.766488i
$637$	3078.38	+	5637.63i	0.191476	+	0.350661i
$638$	2476.52	−	3308.25i	0.153678	−	0.205290i
$639$	−1634.17	−	746.302i	−0.101169	−	0.0462023i
$640$	−12201.2	+	27055.6i	−0.753585	+	1.67104i
$641$	−10688.7	+	16632.0i	−0.658625	+	1.02484i	0.337870	+	0.941193i	$0.390294\pi$
$641$	−10688.7	+	16632.0i	−0.658625	+	1.02484i	−0.996495	+	0.0836484i	$0.973343\pi$
$642$	8225.52	+	588.301i	0.505663	+	0.0361657i
$643$	7007.02	+	7007.02i	0.429751	+	0.429751i	0.888543	−	0.458792i	$-0.151718\pi$
$643$	7007.02	+	7007.02i	0.429751	+	0.429751i	−0.458792	+	0.888543i	$0.651718\pi$
$644$	53915.5	+	22140.2i	3.29902	+	1.35473i
$645$	9971.04	+	18056.5i	0.608697	+	1.10229i
$646$	14557.6	+	16800.4i	0.886627	+	1.02322i
$647$	1524.11	+	7006.20i	0.0926101	+	0.425722i	0.999985	+	0.00540050i	$0.00171904\pi$
$647$	1524.11	+	7006.20i	0.0926101	+	0.425722i	−0.907375	+	0.420321i	$0.861917\pi$
$648$	17964.0	+	23997.1i	1.08903	+	1.45477i
$649$	167.098	−	365.893i	0.0101066	−	0.0221303i
$650$	−3823.16	−	1702.35i	−0.230703	−	0.102726i
$651$	−15034.2	+	51201.8i	−0.905126	+	3.08258i
$652$	7905.26	+	1719.68i	0.474837	+	0.103295i
$653$	684.764	+	255.404i	0.0410366	+	0.0153059i	0.369899	−	0.929072i	$-0.379392\pi$
$653$	684.764	+	255.404i	0.0410366	+	0.0153059i	−0.328862	+	0.944378i	$0.606665\pi$
$654$	62299.2	−	18292.7i	3.72491	−	1.09373i
$655$	26215.0	+	5572.67i	1.56382	+	0.332431i
$656$	732.541	−	845.398i	0.0435990	−	0.0503159i
$657$	3072.80	+	1677.88i	0.182468	+	0.0996350i
$658$	11852.8	−	31778.5i	0.702233	−	1.88276i
$659$	17465.6	−	11224.5i	1.03242	−	0.663494i	0.0893168	−	0.996003i	$-0.471532\pi$
$659$	17465.6	−	11224.5i	1.03242	−	0.663494i	0.943100	+	0.332509i	$0.107895\pi$
$660$	−3043.16	−	1935.39i	−0.179477	−	0.114144i
$661$	10470.1	−	1505.37i	0.616095	−	0.0885811i	0.172800	−	0.984957i	$-0.444719\pi$
$661$	10470.1	−	1505.37i	0.616095	−	0.0885811i	0.443295	+	0.896376i	$0.353809\pi$
$662$	−34669.3	+	12931.0i	−2.03544	+	0.759180i
$663$	2226.80	−	1666.96i	0.130440	−	0.0976461i
$664$	−23383.3	−	15027.6i	−1.36664	−	0.878287i
$665$	12278.2	+	26551.7i	0.715984	+	1.54832i
$666$			19067.9i			1.10941i
$667$	22804.9	+	15730.9i	1.32385	+	0.913199i
$668$	813.136	−	813.136i	0.0470976	−	0.0470976i
$669$	9672.88	−	8381.60i	0.559006	−	0.484381i
$670$	−1776.54	+	26612.0i	−0.102438	+	1.53449i
$671$	−89.7434	+	624.179i	−0.00516320	+	0.0359108i
$672$	−6225.31	−	16690.7i	−0.357361	−	0.958122i
$673$	−17299.8	−	12950.5i	−0.990877	−	0.741761i	−0.0247140	−	0.999695i	$-0.507868\pi$
$673$	−17299.8	−	12950.5i	−0.990877	−	0.741761i	−0.966163	+	0.257934i	$0.916958\pi$
$674$	1779.76	+	522.586i	0.101712	+	0.0298653i
$675$	−7882.66	+	8033.60i	−0.449487	+	0.458094i
$676$	−13279.1	−	29077.2i	−0.755525	−	1.65437i
$677$	−2193.36	+	4016.84i	−0.124516	+	0.228035i	−0.932500	−	0.361170i	$-0.882377\pi$
$677$	−2193.36	+	4016.84i	−0.124516	+	0.228035i	0.807983	+	0.589205i	$0.200559\pi$
$678$	−15558.8	+	1112.79i	−0.881316	+	0.0630329i
$679$	−30982.9	−	26846.9i	−1.75113	−	1.51736i
$680$	−16334.1	+	16489.7i	−0.921152	+	0.929929i
$681$	31371.5	−	14326.9i	1.76528	−	0.806178i
$682$	834.112	−	3834.35i	0.0468325	−	0.215286i
$683$	2722.71	−	1486.71i	0.152535	−	0.0832905i	−0.401169	−	0.916004i	$-0.631396\pi$
$683$	2722.71	−	1486.71i	0.152535	−	0.0832905i	0.553704	+	0.832714i	$0.313214\pi$
$684$	−1983.88	−	13798.2i	−0.110900	−	0.771327i
$685$	−4418.80	+	5148.69i	−0.246472	+	0.287185i
$686$	96621.7	+	13892.1i	5.37760	+	0.773182i
$687$	−24188.0	+	5261.77i	−1.34327	+	0.292211i
$688$	−802.194	+	11216.1i	−0.0444526	+	0.621528i
$689$	−1090.69			−0.0603075
$690$	18719.6	−	32117.8i	1.03282	−	1.77203i
$691$	−22009.9			−1.21171			−0.605857	−	0.795573i	$-0.707170\pi$
$691$	−22009.9			−1.21171			−0.605857	+	0.795573i	$0.707170\pi$
$692$	1983.44	−	27732.1i	0.108958	−	1.52343i
$693$	1517.04	−	330.011i	0.0831565	−	0.0180896i
$694$	28285.5	+	4066.84i	1.54712	+	0.222443i
$695$	671.657	+	8804.12i	0.0366581	+	0.480517i
$696$	7414.78	+	51570.9i	0.403817	+	2.80861i
$697$	−1612.03	+	880.233i	−0.0876038	+	0.0478353i
$698$	12705.5	−	58406.3i	0.688984	−	3.16721i
$699$	−18907.9	+	8634.93i	−1.02312	+	0.467243i
$700$	−57667.6	+	32202.6i	−3.11376	+	1.73878i
$701$	−20164.3	−	17472.5i	−1.08644	−	0.941407i	−0.0879403	−	0.996126i	$-0.528028\pi$
$701$	−20164.3	−	17472.5i	−1.08644	−	0.941407i	−0.998502	+	0.0547183i	$0.982574\pi$
$702$	3006.89	−	215.057i	0.161663	−	0.0115624i
$703$	−11074.3	+	20281.1i	−0.594134	+	1.08807i
$704$	983.224	+	2152.96i	0.0526373	+	0.115260i
$705$	−12380.3	−	6684.16i	−0.661376	−	0.357078i
$706$	11748.4	+	3449.63i	0.626282	+	0.183893i
$707$	21003.3	+	15722.9i	1.11727	+	0.836379i
$708$	3832.52	+	10275.4i	0.203439	+	0.545442i
$709$	−1841.52	+	12808.0i	−0.0975454	+	0.678443i	0.881107	+	0.472918i	$0.156799\pi$
$709$	−1841.52	+	12808.0i	−0.0975454	+	0.678443i	−0.978652	+	0.205525i	$0.934110\pi$
$710$	5688.61	−	4976.63i	0.300690	−	0.263056i
$711$	−1299.42	+	1125.96i	−0.0685403	+	0.0593905i
$712$	−14835.0	+	14835.0i	−0.780852	+	0.780852i
$713$	25902.7	+	4591.87i	1.36054	+	0.241188i
$714$		−	67500.2i		−	3.53800i
$715$	−244.308	+	112.975i	−0.0127784	+	0.00590911i
$716$	−1245.75	−	800.597i	−0.0650223	−	0.0417873i
$717$	−20930.7	+	15668.5i	−1.09020	+	0.816111i
$718$	32902.4	−	12272.0i	1.71018	−	0.637864i
$719$	2517.34	−	361.939i	0.130572	−	0.0187734i	−0.0767191	−	0.997053i	$-0.524444\pi$
$719$	2517.34	−	361.939i	0.130572	−	0.0187734i	0.207291	+	0.978279i	$0.433535\pi$
$720$	5328.54	−	1185.64i	0.275810	−	0.0613699i
$721$	−46554.8	+	29918.9i	−2.40470	+	1.54541i
$722$	−2388.51	+	6403.84i	−0.123118	+	0.330092i
$723$	29112.0	+	15896.3i	1.49749	+	0.817692i
$724$	1535.87	−	1772.49i	0.0788399	−	0.0909861i
$725$	−30038.3	+	9130.35i	−1.53875	+	0.467714i
$726$	38154.5	−	11203.2i	1.95048	−	0.572711i
$727$	4695.67	+	1751.39i	0.239550	+	0.0893475i	0.466372	−	0.884589i	$-0.345561\pi$
$727$	4695.67	+	1751.39i	0.239550	+	0.0893475i	−0.226822	+	0.973936i	$0.572834\pi$
$728$	7993.75	+	1738.93i	0.406962	+	0.0885291i
$729$	1054.87	−	3592.57i	0.0535931	−	0.182521i
$730$	−11749.6	+	8882.86i	−0.595714	+	0.450369i
$731$	7669.85	−	16794.6i	0.388071	−	0.849756i
$732$	−10303.3	−	13763.5i	−0.520245	−	0.694966i
$733$	5054.49	+	23235.1i	0.254696	+	1.17082i	0.909724	+	0.415213i	$0.136293\pi$
$733$	5054.49	+	23235.1i	0.254696	+	1.17082i	−0.655029	+	0.755604i	$0.727343\pi$
$734$	18308.8	+	21129.4i	0.920693	+	1.06254i
$735$	17922.2	−	62125.7i	0.899416	−	3.11774i
$736$	−7840.80	+	3954.77i	−0.392685	+	0.198063i
$737$	1212.96	+	1212.96i	0.0606240	+	0.0606240i
$738$	1766.41	+	126.336i	0.0881061	+	0.00630147i
$739$	19169.5	−	29828.4i	0.954213	−	1.48478i	0.0814276	−	0.996679i	$-0.474052\pi$
$739$	19169.5	−	29828.4i	0.954213	−	1.48478i	0.872785	−	0.488105i	$-0.162312\pi$
$740$	−47561.4	−	21448.6i	−2.36269	−	1.06549i
$741$	−2956.51	−	1350.19i	−0.146572	−	0.0669373i
$742$	−15861.2	+	21188.1i	−0.784748	+	1.04830i
$743$	12220.1	+	22379.5i	0.603381	+	1.10501i	0.983643	+	0.180131i	$0.0576522\pi$
$743$	12220.1	+	22379.5i	0.603381	+	1.10501i	−0.380261	+	0.924879i	$0.624166\pi$
$744$	26747.0	+	41619.1i	1.31800	+	2.05085i
$745$	10359.5	−	13976.3i	0.509453	−	0.687318i
$746$	−1470.61	−	5008.44i	−0.0721755	−	0.245807i
$747$	−765.744	−	10706.5i	−0.0375062	−	0.524405i
$748$	230.295	+	3219.95i	0.0112572	+	0.157397i
$749$	−2736.63	−	9320.10i	−0.133504	−	0.454672i
$750$	15282.1	+	39258.2i	0.744032	+	1.91134i
$751$	3335.31	+	5189.84i	0.162060	+	0.252170i	0.912781	−	0.408449i	$-0.133930\pi$
$751$	3335.31	+	5189.84i	0.162060	+	0.252170i	−0.750721	+	0.660619i	$0.770294\pi$
$752$	−3675.88	−	6731.88i	−0.178252	−	0.326444i
$753$	−17073.6	+	22807.6i	−0.826290	+	1.10379i
$754$	7649.10	+	3493.23i	0.369448	+	0.168721i
$755$	22081.8	−	8355.56i	1.06442	−	0.402768i
$756$	25722.0	−	40024.3i	1.23744	−	1.92549i
$757$	−10418.4	−	745.138i	−0.500215	−	0.0357761i	−0.181047	−	0.983474i	$-0.557949\pi$
$757$	−10418.4	−	745.138i	−0.500215	−	0.0357761i	−0.319168	+	0.947698i	$0.603403\pi$
$758$	−20509.5	−	20509.5i	−0.982769	−	0.982769i
$759$	−761.969	−	2266.27i	−0.0364397	−	0.108380i
$760$	26057.7	+	7517.21i	1.24370	+	0.358786i
$761$	−6025.07	−	6953.30i	−0.287002	−	0.331218i	0.593880	−	0.804553i	$-0.297595\pi$
$761$	−6025.07	−	6953.30i	−0.287002	−	0.331218i	−0.880882	+	0.473336i	$0.843050\pi$
$762$	−4095.67	−	18827.5i	−0.194712	−	0.895076i
$763$	−45832.8	−	61225.4i	−2.17465	−	2.90499i
$764$	−18657.9	+	40855.2i	−0.883535	+	1.93467i
$765$	−8877.75	−	1233.49i	−0.419576	−	0.0582967i
$766$	−4951.59	+	16863.6i	−0.233562	+	0.795438i
$767$	799.794	+	173.985i	0.0376518	+	0.00819064i
$768$	−42473.2	−	15841.7i	−1.99560	−	0.744319i
$769$	−16609.4	+	4876.97i	−0.778871	+	0.228697i	−0.646919	−	0.762559i	$-0.723943\pi$
$769$	−16609.4	+	4876.97i	−0.778871	+	0.228697i	−0.131952	+	0.991256i	$0.542125\pi$
$770$	−1358.13	+	6388.93i	−0.0635632	+	0.299014i
$771$	−10027.8	+	11572.7i	−0.468406	+	0.540569i
$772$	−31290.5	−	17085.9i	−1.45877	−	0.796548i
$773$	−4196.88	+	11252.3i	−0.195280	+	0.523565i	−0.997276	−	0.0737641i	$-0.976499\pi$
$773$	−4196.88	+	11252.3i	−0.195280	+	0.523565i	0.801996	+	0.597330i	$0.203772\pi$
$774$	−14975.9	+	9624.44i	−0.695476	+	0.446955i
$775$	−22343.8	+	19735.1i	−1.03563	+	0.914717i
$776$	−37620.4	+	5409.00i	−1.74033	+	0.250221i
$777$	65741.1	−	24520.1i	3.03532	−	1.13212i
$778$	−27343.7	+	20469.3i	−1.26005	+	0.943263i
$779$	1805.42	+	1160.28i	0.0830373	+	0.0533648i
$780$	2531.94	−	6887.95i	0.116228	−	0.316190i
$781$		−	486.115i		−	0.0222722i
$782$	−33073.9	+	3657.85i	−1.51243	+	0.167269i
$783$	15991.0	−	15991.0i	0.729849	−	0.729849i
$784$	26639.7	−	23083.5i	1.21355	−	1.05154i
$785$	23990.1	+	27422.2i	1.09075	+	1.24680i
$786$	−10283.6	+	71524.1i	−0.466672	+	3.24578i
$787$	−208.082	−	557.888i	−0.00942478	−	0.0252688i	0.932152	−	0.362067i	$-0.117929\pi$
$787$	−208.082	−	557.888i	−0.00942478	−	0.0252688i	−0.941577	+	0.336798i	$0.890656\pi$
$788$	24549.7	+	18377.7i	1.10983	+	0.830809i
$789$	−5158.07	−	1514.55i	−0.232741	−	0.0683388i
$790$	−2070.86	−	6930.96i	−0.0932632	−	0.312142i
$791$	7632.62	+	16713.1i	0.343091	+	0.751264i
$792$	689.795	−	1263.26i	0.0309480	−	0.0566770i
$793$	−1279.90	+	91.5400i	−0.0573146	+	0.00409922i
$794$	41692.3	+	36126.6i	1.86348	+	1.61471i
$795$	7800.16	+	7726.54i	0.347979	+	0.344694i
$796$	−46207.8	+	21102.4i	−2.05753	+	0.939641i
$797$	−3661.44	+	16831.4i	−0.162729	+	0.748053i	0.821365	+	0.570403i	$0.193213\pi$
$797$	−3661.44	+	16831.4i	−0.162729	+	0.748053i	−0.984094	+	0.177650i	$0.943151\pi$
$798$	−69224.0	+	37799.2i	−3.07081	+	1.67679i
$799$	1792.27	+	12465.5i	0.0793567	+	0.551938i
$800$	2023.07	−	9743.89i	0.0894081	−	0.430623i
$801$	−8019.31	−	1153.00i	−0.353743	−	0.0508606i
$802$	24573.0	−	5345.54i	1.08193	−	0.235359i
$803$	−67.5824	+	944.925i	−0.00297003	+	0.0415264i
$804$	−46768.7			−2.05150
$805$	−43151.8	−	7438.81i	−1.88932	−	0.325694i
$806$	7984.77			0.348947
$807$	−1261.07	+	17632.1i	−0.0550084	+	0.769118i
$808$	23767.7	−	5170.34i	1.03483	−	0.225114i
$809$	15512.6	+	2230.37i	0.674156	+	0.0969291i	0.470887	−	0.882194i	$-0.343934\pi$
$809$	15512.6	+	2230.37i	0.674156	+	0.0969291i	0.203270	+	0.979123i	$0.434843\pi$
$810$	−36956.7	−	31717.6i	−1.60312	−	1.37586i
$811$	−269.932	−	1877.42i	−0.0116876	−	0.0812887i	0.983143	−	0.182839i	$-0.0585288\pi$
$811$	−269.932	−	1877.42i	−0.0116876	−	0.0812887i	−0.994830	+	0.101550i	$0.967620\pi$
$812$	116480.	−	63602.9i	5.03405	−	2.74880i
$813$	9241.67	−	42483.3i	0.398671	−	1.83266i
$814$	−4693.26	+	2143.34i	−0.202087	+	0.0922899i
$815$	−6077.94	+	28.8198i	−0.261228	+	0.00123867i
$816$	−11536.3	−	9996.25i	−0.494915	−	0.428847i
$817$	−21518.5	+	1539.04i	−0.921467	+	0.0659046i
$818$	13377.7	−	24499.5i	0.571811	−	1.04719i
$819$	1312.35	+	2873.64i	0.0559916	+	0.122605i
$820$	−2302.07	+	4263.88i	−0.0980389	+	0.181587i
$821$	25546.8	+	7501.22i	1.08598	+	0.318872i	0.775268	−	0.631632i	$-0.217615\pi$
$821$	25546.8	+	7501.22i	1.08598	+	0.318872i	0.310711	+	0.950504i	$0.399433\pi$
$822$	−14644.5	−	10962.8i	−0.621395	−	0.465170i
$823$	4199.60	+	11259.6i	0.177872	+	0.476894i	0.995036	−	0.0995108i	$-0.0317278\pi$
$823$	4199.60	+	11259.6i	0.177872	+	0.476894i	−0.817164	+	0.576405i	$0.804455\pi$
$824$	−7301.46	+	50782.8i	−0.308688	+	2.14697i
$825$	2547.51	+	922.750i	0.107507	+	0.0389406i
$826$	15010.8	−	13006.9i	0.632316	−	0.547905i
$827$	1691.54	−	1691.54i	0.0711252	−	0.0711252i	−0.670649	−	0.741775i	$-0.733984\pi$
$827$	1691.54	−	1691.54i	0.0711252	−	0.0711252i	0.741775	+	0.670649i	$0.233984\pi$
$828$	18687.8	+	9283.30i	0.784355	+	0.389634i
$829$		−	26586.5i		−	1.11386i	−0.830560	−	0.556929i	$-0.811979\pi$
$829$		−	26586.5i		−	1.11386i	0.830560	−	0.556929i	$-0.188021\pi$
$830$	42386.1	+	15580.7i	1.77258	+	0.651581i
$831$	26251.9	+	16871.1i	1.09587	+	0.704274i
$832$	−3855.53	+	2886.22i	−0.160657	+	0.120266i
$833$	−54227.8	+	20225.9i	−2.25556	+	0.841280i
$834$	−23564.1	+	3388.01i	−0.978368	+	0.140668i
$835$	−463.630	+	728.999i	−0.0192151	+	0.0302132i
$836$	3173.21	−	2039.30i	0.131277	−	0.0843669i
$837$	7504.31	−	20119.8i	0.309901	−	0.830876i
$838$	15621.5	+	8530.00i	0.643958	+	0.351628i
$839$	24456.4	−	28224.2i	1.00635	−	1.16139i	0.0194933	−	0.999810i	$-0.493795\pi$
$839$	24456.4	−	28224.2i	1.00635	−	1.16139i	0.986859	−	0.161583i	$-0.0516598\pi$
$840$	−44849.3	−	69064.7i	−1.84220	−	2.83685i
$841$	37126.2	−	10901.2i	1.52225	−	0.446974i
$842$	−45209.9	−	16862.4i	−1.85040	−	0.690163i
$843$	16379.7	+	3563.18i	0.669212	+	0.145578i
$844$	1772.60	−	6036.92i	0.0722931	−	0.246208i
$845$	14483.0	+	19156.9i	0.589620	+	0.779904i
$846$	5044.26	−	11045.4i	0.204995	−	0.448875i
$847$	−28069.8	−	37496.9i	−1.13871	−	1.52114i
$848$	1272.28	+	5848.59i	0.0515217	+	0.236841i
$849$	−18356.4	−	21184.4i	−0.742038	−	0.856357i
$850$	20085.2	−	31914.7i	0.810491	−	1.28784i
$851$	−15577.0	−	30883.2i	−0.627463	−	1.24402i
$852$	9371.70	+	9371.70i	0.376842	+	0.376842i
$853$	14713.2	+	1052.31i	0.590586	+	0.0422395i	0.363434	−	0.931620i	$-0.381604\pi$
$853$	14713.2	+	1052.31i	0.590586	+	0.0422395i	0.227152	+	0.973859i	$0.427059\pi$
$854$	−16834.5	+	26194.9i	−0.674548	+	1.04962i
$855$	3706.42	+	9795.21i	0.148254	+	0.391800i
$856$	−8191.56	−	3740.96i	−0.327082	−	0.149373i
$857$	−5194.10	+	6938.50i	−0.207033	+	0.276563i	−0.892024	−	0.451988i	$-0.850715\pi$
$857$	−5194.10	+	6938.50i	−0.207033	+	0.276563i	0.684991	+	0.728551i	$0.259806\pi$
$858$	−347.798	−	636.945i	−0.0138387	−	0.0253437i
$859$	12375.1	+	19256.1i	0.491541	+	0.764853i	0.995075	−	0.0991221i	$-0.0316034\pi$
$859$	12375.1	+	19256.1i	0.491541	+	0.764853i	−0.503534	+	0.863975i	$0.667967\pi$
$860$	−7160.70	−	48180.9i	−0.283928	−	1.91041i
$861$	−1835.92	−	6252.57i	−0.0726690	−	0.247488i
$862$	−4320.05	−	60402.3i	−0.170698	−	2.38667i
$863$	−1033.16	−	14445.5i	−0.0407522	−	0.569791i	−0.976276	−	0.216528i	$-0.930527\pi$
$863$	−1033.16	−	14445.5i	−0.0407522	−	0.569791i	0.935524	−	0.353263i	$-0.114928\pi$
$864$	2019.57	+	6878.04i	0.0795224	+	0.270828i
$865$	3070.67	+	20661.0i	0.120700	+	0.812134i
$866$	−21946.0	−	34148.6i	−0.861148	−	1.33997i
$867$	−2826.10	−	5175.62i	−0.110703	−	0.202738i
$868$	75519.9	−	100883.i	2.95313	−	3.94491i
$869$	−423.199	−	193.269i	−0.0165202	−	0.00754452i
$870$	−29956.9	−	79169.1i	−1.16740	−	3.08516i
$871$	−1887.12	+	2936.42i	−0.0734130	+	0.114233i
$872$	−70723.2	−	5058.23i	−2.74655	−	0.196437i
$873$	−10378.3	−	10378.3i	−0.402353	−	0.402353i
$874$	22272.2	+	31870.2i	0.861978	+	1.23344i
$875$	37035.9	−	33025.8i	1.43091	−	1.27597i
$876$	−16914.1	−	19519.9i	−0.652367	−	0.752872i
$877$	5079.38	+	23349.5i	0.195574	+	0.899039i	0.965398	+	0.260782i	$0.0839805\pi$
$877$	5079.38	+	23349.5i	0.195574	+	0.899039i	−0.769824	+	0.638257i	$0.779656\pi$
$878$	34079.1	+	45524.4i	1.30993	+	1.74986i
$879$	−7319.42	+	16027.3i	−0.280862	+	0.615002i
$880$	890.787	+	1178.27i	0.0341232	+	0.0451356i
$881$	−1114.89	+	3796.95i	−0.0426350	+	0.145202i	−0.978060	−	0.208324i	$-0.933199\pi$
$881$	−1114.89	+	3796.95i	−0.0426350	+	0.145202i	0.935425	+	0.353526i	$0.115017\pi$
$882$	54529.0	+	11862.0i	2.08173	+	0.452853i
$883$	−14009.5	−	5225.26i	−0.533926	−	0.199144i	0.0680157	−	0.997684i	$-0.478333\pi$
$883$	−14009.5	−	5225.26i	−0.533926	−	0.199144i	−0.601941	+	0.798540i	$0.705606\pi$
$884$	−6302.73	+	1850.65i	−0.239801	+	0.0704118i
$885$	−4487.29	−	6910.09i	−0.170439	−	0.262463i
$886$	31127.8	−	35923.4i	1.18032	−	1.36216i
$887$	−36599.7	−	19984.9i	−1.38545	−	0.756514i	−0.398445	−	0.917192i	$-0.630450\pi$
$887$	−36599.7	−	19984.9i	−1.38545	−	0.756514i	−0.987007	+	0.160678i	$0.948632\pi$
$888$	22732.4	−	60947.9i	0.859065	−	2.30324i
$889$	−19092.7	+	12270.1i	−0.720302	+	0.462910i
$890$	18291.8	−	28761.6i	0.688925	−	1.08325i
$891$	−3100.38	+	445.767i	−0.116573	+	0.0167607i
$892$	−28319.4	+	10562.6i	−1.06301	+	0.396481i
$893$	11780.2	−	8818.56i	0.441445	−	0.330461i
$894$	39459.4	+	25359.0i	1.47620	+	0.948693i
$895$	1044.21	+	383.841i	0.0389991	+	0.0143356i
$896$			94256.9i			3.51440i
$897$	4176.53	−	2495.30i	0.155463	−	0.0928824i
$898$	−49142.1	+	49142.1i	−1.82616	+	1.82616i
$899$	45269.5	−	39226.2i	1.67944	−	1.45525i
$900$	−21415.6	+	10026.7i	−0.793171	+	0.371359i
$901$	1398.60	−	9727.50i	0.0517139	−	0.359678i
$902$	167.459	+	448.974i	0.00618156	+	0.0165734i
$903$	52440.7	+	39256.6i	1.93258	+	1.44671i
$904$	16343.9	+	4799.00i	0.601316	+	0.176562i
$905$	−837.102	+	1550.47i	−0.0307472	+	0.0569497i
$906$	26443.7	+	57903.6i	0.969682	+	2.12331i
$907$	13532.0	−	24782.0i	0.495393	−	0.907245i	−0.503667	−	0.863898i	$-0.668016\pi$
$907$	13532.0	−	24782.0i	0.495393	−	0.907245i	0.999060	−	0.0433471i	$-0.0138021\pi$
$908$	−81236.5	+	5810.15i	−2.96908	+	0.212353i
$909$	7098.73	+	6151.08i	0.259021	+	0.224443i
$910$	−13290.8	+	63.0210i	−0.484160	+	0.00229574i
$911$	−30513.4	+	13935.0i	−1.10972	+	0.506792i	−0.884041	−	0.467409i	$-0.845187\pi$
$911$	−30513.4	+	13935.0i	−1.10972	+	0.506792i	−0.225679	+	0.974202i	$0.572460\pi$
$912$	−3791.37	+	17428.7i	−0.137659	+	0.632808i
$913$	2549.17	−	1391.95i	0.0924043	−	0.0504565i
$914$	6494.95	+	45173.4i	0.235048	+	1.63479i
$915$	9801.79	+	8412.26i	0.354139	+	0.303935i
$916$	57861.1	+	8319.17i	2.08710	+	0.300080i
$917$	83169.3	−	18092.4i	2.99508	−	0.651541i
$918$	−1937.75	+	27093.3i	−0.0696680	+	0.974087i
$919$	6426.85			0.230688			0.115344	−	0.993326i	$-0.463203\pi$
$919$	6426.85			0.230688			0.115344	+	0.993326i	$0.463203\pi$
$920$	−31410.1	+	25718.0i	−1.12561	+	0.921628i
$921$	−2990.21			−0.106982
$922$	−5294.58	+	74027.9i	−0.189119	+	2.64423i
$923$	966.562	−	210.263i	0.0344689	−	0.00749824i
$924$	−11336.9	−	1630.00i	−0.403632	−	0.0580336i
$925$	38379.1	+	7968.45i	1.36421	+	0.283244i
$926$	−156.268	−	1086.87i	−0.00554568	−	0.0385711i
$927$	−17388.9	+	9495.05i	−0.616101	+	0.336417i
$928$	−4250.44	+	19539.0i	−0.150353	+	0.691162i
$929$	−12924.8	+	5902.56i	−0.456458	+	0.208457i	−0.630356	−	0.776306i	$-0.717091\pi$
$929$	−12924.8	+	5902.56i	−0.456458	+	0.208457i	0.173898	+	0.984764i	$0.444364\pi$
$930$	−57103.9	−	56564.9i	−2.01345	−	1.99445i
$931$	51109.2	+	44286.4i	1.79918	+	1.55900i
$932$	48961.9	−	3501.82i	1.72082	−	0.123075i
$933$	17119.0	−	31351.1i	0.600697	−	1.10010i
$934$	−26839.9	−	58771.2i	−0.940287	−	2.05894i
$935$	−694.306	−	2323.77i	−0.0242848	−	0.0812786i
$936$	2810.16	+	825.137i	0.0981334	+	0.0288146i
$937$	−21608.0	−	16175.6i	−0.753366	−	0.563963i	0.152108	−	0.988364i	$-0.451394\pi$
$937$	−21608.0	−	16175.6i	−0.753366	−	0.563963i	−0.905474	+	0.424401i	$0.860485\pi$
$938$	29600.7	+	79362.5i	1.03038	+	2.76256i
$939$	−7704.67	+	53587.1i	−0.267766	+	1.86235i
$940$	21876.7	+	25006.5i	0.759085	+	0.867683i
$941$	22759.0	−	19720.7i	0.788439	−	0.683186i	−0.164491	−	0.986379i	$-0.552598\pi$
$941$	22759.0	−	19720.7i	0.788439	−	0.683186i	0.952929	+	0.303193i	$0.0980526\pi$
$942$	−69462.6	+	69462.6i	−2.40256	+	2.40256i
$943$	−2964.16	+	1238.40i	−0.102361	+	0.0427654i
$944$		−	4491.69i		−	0.154864i
$945$	−12332.3	+	33549.1i	−0.424517	+	1.15487i
$946$	−4052.29	−	2604.25i	−0.139272	−	0.0895046i
$947$	31807.8	−	23811.0i	1.09146	−	0.817058i	0.107281	−	0.994229i	$-0.465785\pi$
$947$	31807.8	−	23811.0i	1.09146	−	0.817058i	0.984180	+	0.177171i	$0.0566945\pi$
$948$	11884.7	−	4432.78i	0.407171	−	0.151867i
$949$	−1908.06	+	274.338i	−0.0652669	+	0.00938397i
$950$	−43977.1	−	2726.40i	−1.50190	−	0.0931115i
$951$	−32669.8	+	20995.6i	−1.11398	+	0.715909i
$952$	−25759.5	+	69063.9i	−0.876965	+	2.35123i
$953$	−20340.5	−	11106.7i	−0.691388	−	0.377526i	0.0948149	−	0.995495i	$-0.469774\pi$
$953$	−20340.5	−	11106.7i	−0.691388	−	0.377526i	−0.786203	+	0.617969i	$0.787956\pi$
$954$	−6205.20	+	7161.18i	−0.210588	+	0.243031i
$955$	7016.22	−	33005.7i	0.237738	−	1.11837i
$956$	59242.2	−	17395.1i	2.00422	−	0.588491i
$957$	−5100.91	−	1902.54i	−0.172298	−	0.0642637i
$958$	40994.5	+	8917.81i	1.38254	+	0.300753i
$959$	−6070.66	+	20674.8i	−0.204413	+	0.696166i
$960$	48019.5	+	6671.92i	1.61440	+	0.224308i
$961$	11252.4	−	24639.3i	0.377711	−	0.827072i
$962$	−6291.69	−	8404.71i	−0.210865	−	0.281683i
$963$	−739.213	−	3398.11i	−0.0247360	−	0.113710i
$964$	−51295.0	−	59197.5i	−1.71380	−	1.97783i
$965$	25734.9	+	7424.10i	0.858484	+	0.247658i
$966$	12262.2	−	117422.i	0.408416	−	3.91098i
$967$	10916.7	+	10916.7i	0.363039	+	0.363039i	0.864931	−	0.501891i	$-0.167362\pi$
$967$	10916.7	+	10916.7i	0.363039	+	0.363039i	−0.501891	+	0.864931i	$0.667362\pi$
$968$	−43313.7	−	3097.86i	−1.43818	−	0.102861i
$969$	15833.1	−	24636.8i	0.524905	−	0.816768i
$970$	57753.0	−	21853.3i	1.91169	−	0.723367i
$971$	−8345.62	−	3811.32i	−0.275822	−	0.125964i	0.272702	−	0.962099i	$-0.412083\pi$
$971$	−8345.62	−	3811.32i	−0.275822	−	0.125964i	−0.548524	+	0.836135i	$0.684810\pi$
$972$	29496.7	−	39402.9i	0.973360	−	1.30026i
$973$	13438.9	+	24611.5i	0.442786	+	0.810902i
$974$	−7882.49	−	12265.4i	−0.259313	−	0.403499i
$975$	−732.846	+	5464.44i	−0.0240716	+	0.179489i
$976$	1983.86	+	6756.40i	0.0650633	+	0.221585i
$977$	3812.57	+	53306.7i	0.124846	+	1.74558i	0.545276	+	0.838256i	$0.316425\pi$
$977$	3812.57	+	53306.7i	0.124846	+	1.74558i	−0.420430	+	0.907325i	$0.638121\pi$
$978$	−1169.06	−	16345.6i	−0.0382234	−	0.534434i
$979$	−617.624	−	2103.43i	−0.0201628	−	0.0686680i
$980$	−90925.0	+	122670.i	−2.96377	+	3.99851i
$981$	−14803.2	−	23034.2i	−0.481783	−	0.749669i
$982$	1804.43	+	3304.57i	0.0586372	+	0.107386i
$983$	−7774.92	+	10386.1i	−0.252270	+	0.336993i	−0.908743	−	0.417356i	$-0.862957\pi$
$983$	−7774.92	+	10386.1i	−0.252270	+	0.336993i	0.656473	+	0.754350i	$0.272048\pi$
$984$	−5495.47	−	2509.70i	−0.178038	−	0.0813071i
$985$	−21002.4	−	9471.36i	−0.679382	−	0.306378i
$986$	−40963.5	+	63740.5i	−1.32307	+	2.05873i
$987$	−44568.3	−	3187.59i	−1.43731	−	0.102798i
$988$	5427.35	+	5427.35i	0.174764	+	0.174764i
$989$	16393.3	−	27822.4i	0.527074	−	0.894540i
$990$	−648.165	+	2246.80i	−0.0208081	+	0.0721294i
$991$	−915.995	−	1057.12i	−0.0293618	−	0.0338853i	0.740879	−	0.671639i	$-0.234409\pi$
$991$	−915.995	−	1057.12i	−0.0293618	−	0.0338853i	−0.770241	+	0.637753i	$0.779864\pi$
$992$	4036.01	+	18553.2i	0.129177	+	0.593816i
$993$	29212.9	+	39023.8i	0.933577	+	1.24711i
$994$	9971.48	−	21834.5i	0.318185	−	0.696729i
$995$	30443.1	−	23015.5i	0.969962	−	0.733306i
$996$	−22309.7	+	75979.8i	−0.709748	+	2.41718i
$997$	−29589.0	−	6436.69i	−0.939913	−	0.204466i	−0.283590	−	0.958946i	$-0.591525\pi$
$997$	−29589.0	−	6436.69i	−0.939913	−	0.204466i	−0.656323	+	0.754480i	$0.727889\pi$
$998$	−67276.3	−	25092.8i	−2.13386	−	0.795890i
$999$	−27091.1	+	7954.67i	−0.857982	+	0.251926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.l.a.102.4	yes	680
5.3	odd	4	inner	115.4.l.a.33.31	yes	680
23.7	odd	22	inner	115.4.l.a.7.31	✓	680
115.53	even	44	inner	115.4.l.a.53.4	yes	680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.l.a.7.31	✓	680	23.7	odd	22	inner
115.4.l.a.33.31	yes	680	5.3	odd	4	inner
115.4.l.a.53.4	yes	680	115.53	even	44	inner
115.4.l.a.102.4	yes	680	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.341249 + 4.77128i) q^{2} +(6.15772 - 1.33953i) q^{3} +(-14.7301 - 2.11787i) q^{4} +(11.1479 - 0.850466i) q^{5} +(4.28996 + 29.8374i) q^{6} +(31.1635 - 17.0166i) q^{7} +(6.99722 - 32.1657i) q^{8} +(11.5631 - 5.28070i) q^{9} +(0.253587 + 53.4802i) q^{10} +(2.59952 + 2.25250i) q^{11} +(-93.5410 + 6.69019i) q^{12} +(-3.35434 + 6.14302i) q^{13} +(70.5564 + 154.497i) q^{14} +(67.5067 - 20.1699i) q^{15} +(36.8535 + 10.8212i) q^{16} +(-50.4864 - 37.7936i) q^{17} +(21.2498 + 56.9730i) q^{18} +(-10.4871 + 72.9396i) q^{19} +(-166.012 - 11.0825i) q^{20} +(169.102 - 146.528i) q^{21} +(-11.6344 + 11.6344i) q^{22} +(-80.9598 - 74.9167i) q^{23} -207.440i q^{24} +(123.553 - 18.9619i) q^{25} +(-28.1654 - 18.1008i) q^{26} +(-72.0808 + 53.9590i) q^{27} +(-495.082 + 184.656i) q^{28} +(-248.606 + 35.7442i) q^{29} +(73.1999 + 328.977i) q^{30} +(-200.632 + 128.938i) q^{31} +(27.8221 - 74.5939i) q^{32} +(19.0244 + 10.3881i) q^{33} +(197.553 - 227.988i) q^{34} +(332.937 - 216.203i) q^{35} +(-181.510 + 53.2962i) q^{36} +(293.809 + 109.585i) q^{37} +(-344.437 - 74.9277i) q^{38} +(-12.4264 + 42.3203i) q^{39} +(50.6488 - 364.532i) q^{40} +(12.0984 - 26.4918i) q^{41} +(641.420 + 856.837i) q^{42} +(62.2309 + 286.071i) q^{43} +(-33.5208 - 38.6851i) q^{44} +(124.414 - 68.7030i) q^{45} +(385.077 - 360.717i) q^{46} +(-141.204 - 141.204i) q^{47} +(241.429 + 17.2674i) q^{48} +(496.162 - 772.043i) q^{49} +(48.3101 + 595.979i) q^{50} +(-361.507 - 165.095i) q^{51} +(62.4201 - 83.3835i) q^{52} +(74.6819 + 136.770i) q^{53} +(-232.856 - 362.331i) q^{54} +(30.8950 + 22.9000i) q^{55} +(-329.292 - 1121.47i) q^{56} +(33.1280 + 463.190i) q^{57} +(-85.7090 - 1198.37i) q^{58} +(-32.9465 - 112.205i) q^{59} +(-1037.10 + 154.135i) q^{60} +(99.1163 + 154.228i) q^{61} +(-546.735 - 1001.27i) q^{62} +(270.488 - 361.330i) q^{63} +(625.922 + 285.849i) q^{64} +(-32.1696 + 71.3348i) q^{65} +(-56.0568 + 87.2261i) q^{66} +(497.436 + 35.5773i) q^{67} +(663.629 + 663.629i) q^{68} +(-598.881 - 352.868i) q^{69} +(917.953 + 1662.32i) q^{70} +(-92.5491 - 106.807i) q^{71} +(-88.9477 - 408.886i) q^{72} +(165.051 + 220.482i) q^{73} +(-623.124 + 1364.45i) q^{74} +(735.407 - 282.266i) q^{75} +(308.954 - 1052.20i) q^{76} +(119.340 + 25.9609i) q^{77} +(-197.682 - 73.7314i) q^{78} +(-129.779 + 38.1066i) q^{79} +(420.044 + 89.2912i) q^{80} +(-596.335 + 688.207i) q^{81} +(122.271 + 66.7652i) q^{82} +(295.086 - 791.157i) q^{83} +(-2801.22 + 1800.24i) q^{84} +(-594.962 - 378.385i) q^{85} +(-1386.16 + 199.300i) q^{86} +(-1482.97 + 553.118i) q^{87} +(90.6427 - 67.8543i) q^{88} +(-536.164 - 344.572i) q^{89} +(285.345 + 617.059i) q^{90} +248.518i q^{91} +(1033.88 + 1275.00i) q^{92} +(-1062.72 + 1062.72i) q^{93} +(721.912 - 625.540i) q^{94} +(-54.8774 + 822.046i) q^{95} +(71.3999 - 496.597i) q^{96} +(-403.493 - 1081.81i) q^{97} +(3514.32 + 2630.79i) q^{98} +(41.9534 + 12.3186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 680 q - 18 q^{2} - 26 q^{3} - 22 q^{5} - 76 q^{6} - 22 q^{7} - 50 q^{8} - 22 q^{10} - 44 q^{11} - 222 q^{12} + 78 q^{13} - 22 q^{15} + 788 q^{16} - 22 q^{17} - 86 q^{18} - 22 q^{20} - 44 q^{21} - 944 q^{23}+ \cdots - 10314 q^{98}+O(q^{100}) \) 680 * q - 18 * q^2 - 26 * q^3 - 22 * q^5 - 76 * q^6 - 22 * q^7 - 50 * q^8 - 22 * q^10 - 44 * q^11 - 222 * q^12 + 78 * q^13 - 22 * q^15 + 788 * q^16 - 22 * q^17 - 86 * q^18 - 22 * q^20 - 44 * q^21 - 944 * q^23 + 350 * q^25 + 268 * q^26 + 682 * q^27 + 682 * q^28 - 22 * q^30 + 1012 * q^31 - 582 * q^32 + 1914 * q^33 + 326 * q^35 - 2468 * q^36 + 2354 * q^37 - 22 * q^38 - 22 * q^40 - 2292 * q^41 - 7282 * q^42 - 22 * q^43 + 52 * q^46 - 2416 * q^47 - 1378 * q^48 + 598 * q^50 - 44 * q^51 - 794 * q^52 - 22 * q^53 - 2710 * q^55 + 11572 * q^56 + 7634 * q^57 - 2066 * q^58 - 22 * q^60 - 1100 * q^61 - 3970 * q^62 - 22 * q^63 - 22 * q^65 - 10956 * q^66 - 22 * q^67 + 1792 * q^70 - 11412 * q^71 - 556 * q^72 - 1122 * q^73 + 13078 * q^75 - 2156 * q^76 - 4238 * q^77 + 9158 * q^78 + 8096 * q^80 + 11280 * q^81 + 6494 * q^82 - 22 * q^83 - 8118 * q^85 + 10428 * q^86 + 6282 * q^87 - 1430 * q^88 - 37224 * q^90 + 666 * q^92 + 1564 * q^93 - 11162 * q^95 - 16748 * q^96 - 12694 * q^97 - 10314 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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