LMFDB - Embedded newform 36.4.h.b.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,4,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("36.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	36.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.12406876021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	36.23
Dual form			36.4.h.b.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.664105 - 2.74936i) q^{2} +(-5.00415 + 1.39947i) q^{3} +(-7.11793 - 3.65173i) q^{4} +(-14.2911 - 8.25096i) q^{5} +(0.524375 + 14.6876i) q^{6} +(19.2620 - 11.1209i) q^{7} +(-14.7670 + 17.1446i) q^{8} +(23.0829 - 14.0063i) q^{9} +O(q^{10})$	\(q+(0.664105 - 2.74936i) q^{2} +(-5.00415 + 1.39947i) q^{3} +(-7.11793 - 3.65173i) q^{4} +(-14.2911 - 8.25096i) q^{5} +(0.524375 + 14.6876i) q^{6} +(19.2620 - 11.1209i) q^{7} +(-14.7670 + 17.1446i) q^{8} +(23.0829 - 14.0063i) q^{9} +(-32.1756 + 33.8118i) q^{10} +(-6.37655 - 11.0445i) q^{11} +(40.7296 + 8.31241i) q^{12} +(-11.1766 + 19.3584i) q^{13} +(-17.7834 - 60.3436i) q^{14} +(83.0617 + 21.2890i) q^{15} +(37.3298 + 51.9854i) q^{16} -117.295i q^{17} +(-23.1789 - 72.7649i) q^{18} -27.7307i q^{19} +(71.5926 + 110.917i) q^{20} +(-80.8264 + 82.6074i) q^{21} +(-34.6000 + 10.1967i) q^{22} +(-17.5836 + 30.4556i) q^{23} +(49.9026 - 106.460i) q^{24} +(73.6567 + 127.577i) q^{25} +(45.8008 + 43.5845i) q^{26} +(-95.9089 + 102.394i) q^{27} +(-177.716 + 8.81837i) q^{28} +(1.01189 - 0.584217i) q^{29} +(113.693 - 214.228i) q^{30} +(-119.361 - 68.9130i) q^{31} +(167.717 - 68.1091i) q^{32} +(47.3657 + 46.3445i) q^{33} +(-322.487 - 77.8965i) q^{34} -367.033 q^{35} +(-215.450 + 15.4036i) q^{36} +233.596 q^{37} +(-76.2416 - 18.4161i) q^{38} +(28.8377 - 112.514i) q^{39} +(352.495 - 123.173i) q^{40} +(13.2561 + 7.65340i) q^{41} +(173.440 + 277.081i) q^{42} +(361.460 - 208.689i) q^{43} +(5.05631 + 101.900i) q^{44} +(-445.446 + 9.70942i) q^{45} +(72.0561 + 68.5693i) q^{46} +(116.494 + 201.773i) q^{47} +(-259.556 - 207.901i) q^{48} +(75.8499 - 131.376i) q^{49} +(399.671 - 117.784i) q^{50} +(164.152 + 586.963i) q^{51} +(150.246 - 96.9781i) q^{52} +180.951i q^{53} +(217.823 + 331.688i) q^{54} +210.451i q^{55} +(-93.7774 + 494.461i) q^{56} +(38.8084 + 138.768i) q^{57} +(-0.934217 - 3.17004i) q^{58} +(313.716 - 543.373i) q^{59} +(-513.485 - 454.852i) q^{60} +(-382.110 - 661.834i) q^{61} +(-268.735 + 282.400i) q^{62} +(288.860 - 526.494i) q^{63} +(-75.8742 - 506.347i) q^{64} +(319.452 - 184.435i) q^{65} +(158.874 - 99.4476i) q^{66} +(-113.463 - 65.5077i) q^{67} +(-428.330 + 834.900i) q^{68} +(45.3689 - 177.012i) q^{69} +(-243.749 + 1009.11i) q^{70} -22.6910 q^{71} +(-100.732 + 602.579i) q^{72} +387.864 q^{73} +(155.133 - 642.240i) q^{74} +(-547.130 - 535.334i) q^{75} +(-101.265 + 197.385i) q^{76} +(-245.650 - 141.826i) q^{77} +(-290.190 - 154.006i) q^{78} +(-486.411 + 280.830i) q^{79} +(-104.553 - 1050.93i) q^{80} +(336.644 - 646.615i) q^{81} +(29.8454 - 31.3630i) q^{82} +(342.111 + 592.554i) q^{83} +(876.976 - 292.838i) q^{84} +(-967.799 + 1676.28i) q^{85} +(-333.713 - 1132.38i) q^{86} +(-4.24607 + 4.33963i) q^{87} +(283.516 + 53.7704i) q^{88} +278.003i q^{89} +(-269.128 + 1231.14i) q^{90} +497.177i q^{91} +(236.374 - 152.571i) q^{92} +(693.741 + 177.808i) q^{93} +(632.110 - 186.284i) q^{94} +(-228.805 + 396.302i) q^{95} +(-743.966 + 575.544i) q^{96} +(-264.443 - 458.028i) q^{97} +(-310.827 - 295.786i) q^{98} +(-301.883 - 165.628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.664105	−	2.74936i	0.234797	−	0.972044i
$2$	0.664105	−	2.74936i	0.234797	−	0.972044i
$3$	−5.00415	+	1.39947i	−0.963048	+	0.269329i
$3$	−5.00415	+	1.39947i	−0.963048	+	0.269329i
$4$	−7.11793	−	3.65173i	−0.889741	−	0.456466i
$5$	−14.2911	−	8.25096i	−1.27823	−	0.737988i	−0.301710	−	0.953400i	$-0.597557\pi$
$5$	−14.2911	−	8.25096i	−1.27823	−	0.737988i	−0.976523	+	0.215411i	$0.930891\pi$
$6$	0.524375	+	14.6876i	0.0356792	+	0.999363i
$7$	19.2620	−	11.1209i	1.04005	−	0.600473i	0.120203	−	0.992749i	$-0.461645\pi$
$7$	19.2620	−	11.1209i	1.04005	−	0.600473i	0.919848	+	0.392276i	$0.128312\pi$
$8$	−14.7670	+	17.1446i	−0.652613	+	0.757691i
$9$	23.0829	−	14.0063i	0.854924	−	0.518754i
$10$	−32.1756	+	33.8118i	−1.01748	+	1.06922i
$11$	−6.37655	−	11.0445i	−0.174782	−	0.302732i	0.765304	−	0.643669i	$-0.222589\pi$
$11$	−6.37655	−	11.0445i	−0.174782	−	0.302732i	−0.940086	+	0.340938i	$0.889255\pi$
$12$	40.7296	+	8.31241i	0.979803	+	0.199965i
$13$	−11.1766	+	19.3584i	−0.238449	+	0.413005i	−0.960269	−	0.279075i	$-0.909972\pi$
$13$	−11.1766	+	19.3584i	−0.238449	+	0.413005i	0.721821	+	0.692080i	$0.243306\pi$
$14$	−17.7834	−	60.3436i	−0.339486	−	1.15196i
$15$	83.0617	+	21.2890i	1.42976	+	0.366453i
$16$	37.3298	+	51.9854i	0.583278	+	0.812273i
$17$		−	117.295i		−	1.67343i	−0.547639	−	0.836715i	$-0.684473\pi$
$17$		−	117.295i		−	1.67343i	0.547639	−	0.836715i	$-0.315527\pi$
$18$	−23.1789	−	72.7649i	−0.303518	−	0.952826i
$19$		−	27.7307i		−	0.334835i	−0.985886	−	0.167417i	$-0.946457\pi$
$19$		−	27.7307i		−	0.334835i	0.985886	−	0.167417i	$-0.0535427\pi$
$20$	71.5926	+	110.917i	0.800430	+	1.24009i
$21$	−80.8264	+	82.6074i	−0.839894	+	0.858401i
$22$	−34.6000	+	10.1967i	−0.335307	+	0.0988156i
$23$	−17.5836	+	30.4556i	−0.159410	+	0.276106i	−0.934656	−	0.355553i	$-0.884292\pi$
$23$	−17.5836	+	30.4556i	−0.159410	+	0.276106i	0.775246	+	0.631659i	$0.217626\pi$
$24$	49.9026	−	106.460i	0.424430	−	0.905461i
$25$	73.6567	+	127.577i	0.589254	+	1.02062i
$26$	45.8008	+	43.5845i	0.345472	+	0.328755i
$27$	−95.9089	+	102.394i	−0.683617	+	0.729840i
$28$	−177.716	+	8.81837i	−1.19947	+	0.0595184i
$29$	1.01189	−	0.584217i	0.00647945	−	0.00374091i	−0.496757	−	0.867890i	$-0.665476\pi$
$29$	1.01189	−	0.584217i	0.00647945	−	0.00374091i	0.503236	+	0.864149i	$0.332143\pi$
$30$	113.693	−	214.228i	0.691912	−	1.30375i
$31$	−119.361	−	68.9130i	−0.691543	−	0.399263i	0.112647	−	0.993635i	$-0.464067\pi$
$31$	−119.361	−	68.9130i	−0.691543	−	0.399263i	−0.804190	+	0.594373i	$0.797400\pi$
$32$	167.717	−	68.1091i	0.926517	−	0.376253i
$33$	47.3657	+	46.3445i	0.249858	+	0.244471i
$34$	−322.487	−	77.8965i	−1.62665	−	0.392916i
$35$	−367.033			−1.77257
$36$	−215.450	+	15.4036i	−0.997454	+	0.0713129i
$37$	233.596			1.03792			0.518959	−	0.854799i	$-0.326320\pi$
$37$	233.596			1.03792			0.518959	+	0.854799i	$0.326320\pi$
$38$	−76.2416	−	18.4161i	−0.325474	−	0.0786180i
$39$	28.8377	−	112.514i	0.118403	−	0.461965i
$40$	352.495	−	123.173i	1.39336	−	0.486885i
$41$	13.2561	+	7.65340i	0.0504940	+	0.0291527i	0.525034	−	0.851081i	$-0.324052\pi$
$41$	13.2561	+	7.65340i	0.0504940	+	0.0291527i	−0.474541	+	0.880234i	$0.657386\pi$
$42$	173.440	+	277.081i	0.637199	+	1.01796i
$43$	361.460	−	208.689i	1.28191	−	0.740112i	0.304714	−	0.952444i	$-0.401439\pi$
$43$	361.460	−	208.689i	1.28191	−	0.740112i	0.977198	+	0.212332i	$0.0681059\pi$
$44$	5.05631	+	101.900i	0.0173243	+	0.349135i
$45$	−445.446	+	9.70942i	−1.47563	+	0.0321643i
$46$	72.0561	+	68.5693i	0.230958	+	0.219782i
$47$	116.494	+	201.773i	0.361539	+	0.626204i	0.988214	−	0.153076i	$-0.0489180\pi$
$47$	116.494	+	201.773i	0.361539	+	0.626204i	−0.626675	+	0.779281i	$0.715585\pi$
$48$	−259.556	−	207.901i	−0.780493	−	0.625164i
$49$	75.8499	−	131.376i	0.221137	−	0.383020i
$50$	399.671	−	117.784i	1.13044	−	0.333143i
$51$	164.152	+	586.963i	0.450703	+	1.61159i
$52$	150.246	−	96.9781i	0.400680	−	0.258624i
$53$			180.951i			0.468972i	0.972120	+	0.234486i	$0.0753407\pi$
$53$			180.951i			0.468972i	−0.972120	+	0.234486i	$0.924659\pi$
$54$	217.823	+	331.688i	0.548926	+	0.835871i
$55$			210.451i			0.515949i
$56$	−93.7774	+	494.461i	−0.223777	+	1.17991i
$57$	38.8084	+	138.768i	0.0901806	+	0.322462i
$58$	−0.934217	−	3.17004i	−0.00211498	−	0.00717666i
$59$	313.716	−	543.373i	0.692244	−	1.19900i	−0.278857	−	0.960333i	$-0.589955\pi$
$59$	313.716	−	543.373i	0.692244	−	1.19900i	0.971101	−	0.238669i	$-0.0767112\pi$
$60$	−513.485	−	454.852i	−1.10484	−	0.978686i
$61$	−382.110	−	661.834i	−0.802035	−	1.38917i	−0.918274	−	0.395945i	$-0.870417\pi$
$61$	−382.110	−	661.834i	−0.802035	−	1.38917i	0.116239	−	0.993221i	$-0.462916\pi$
$62$	−268.735	+	282.400i	−0.550473	+	0.578465i
$63$	288.860	−	526.494i	0.577666	−	1.05289i
$64$	−75.8742	−	506.347i	−0.148192	−	0.988959i
$65$	319.452	−	184.435i	0.609586	−	0.351945i
$66$	158.874	−	99.4476i	0.296303	−	0.185472i
$67$	−113.463	−	65.5077i	−0.206891	−	0.119448i	0.392975	−	0.919549i	$-0.371446\pi$
$67$	−113.463	−	65.5077i	−0.206891	−	0.119448i	−0.599866	+	0.800101i	$0.704779\pi$
$68$	−428.330	+	834.900i	−0.763863	+	1.48892i
$69$	45.3689	−	177.012i	0.0791561	−	0.308837i
$70$	−243.749	+	1009.11i	−0.416194	+	1.72302i
$71$	−22.6910			−0.0379285			−0.0189643	−	0.999820i	$-0.506037\pi$
$71$	−22.6910			−0.0379285			−0.0189643	+	0.999820i	$0.506037\pi$
$72$	−100.732	+	602.579i	−0.164880	+	0.986314i
$73$	387.864			0.621863			0.310932	−	0.950432i	$-0.399359\pi$
$73$	387.864			0.621863			0.310932	+	0.950432i	$0.399359\pi$
$74$	155.133	−	642.240i	0.243700	−	1.00890i
$75$	−547.130	−	535.334i	−0.842361	−	0.824200i
$76$	−101.265	+	197.385i	−0.152840	+	0.297916i
$77$	−245.650	−	141.826i	−0.363565	−	0.209904i
$78$	−290.190	−	154.006i	−0.421250	−	0.223561i
$79$	−486.411	+	280.830i	−0.692729	+	0.399947i	−0.804633	−	0.593772i	$-0.797638\pi$
$79$	−486.411	+	280.830i	−0.692729	+	0.399947i	0.111905	+	0.993719i	$0.464305\pi$
$80$	−104.553	−	1050.93i	−0.146118	−	1.46873i
$81$	336.644	−	646.615i	0.461789	−	0.886990i
$82$	29.8454	−	31.3630i	0.0401935	−	0.0422374i
$83$	342.111	+	592.554i	0.452429	+	0.783629i	0.998536	−	0.0540856i	$-0.0172244\pi$
$83$	342.111	+	592.554i	0.452429	+	0.783629i	−0.546108	+	0.837715i	$0.683891\pi$
$84$	876.976	−	292.838i	1.13912	−	0.380371i
$85$	−967.799	+	1676.28i	−1.23497	+	2.13903i
$86$	−333.713	−	1132.38i	−0.418433	−	1.41985i
$87$	−4.24607	+	4.33963i	−0.00523248	+	0.00534778i
$88$	283.516	+	53.7704i	0.343442	+	0.0651357i
$89$			278.003i			0.331103i	0.986201	+	0.165552i	$0.0529405\pi$
$89$			278.003i			0.331103i	−0.986201	+	0.165552i	$0.947060\pi$
$90$	−269.128	+	1231.14i	−0.315207	+	1.44193i
$91$			497.177i			0.572728i
$92$	236.374	−	152.571i	0.267866	−	0.172898i
$93$	693.741	+	177.808i	0.773522	+	0.198257i
$94$	632.110	−	186.284i	0.693587	−	0.204402i
$95$	−228.805	+	396.302i	−0.247104	+	0.427997i
$96$	−743.966	+	575.544i	−0.790945	+	0.611888i
$97$	−264.443	−	458.028i	−0.276805	−	0.479440i	0.693784	−	0.720183i	$-0.255942\pi$
$97$	−264.443	−	458.028i	−0.276805	−	0.479440i	−0.970589	+	0.240743i	$0.922609\pi$
$98$	−310.827	−	295.786i	−0.320390	−	0.304887i
$99$	−301.883	−	165.628i	−0.306468	−	0.168144i
$100$	−58.4063	−	1177.06i	−0.0584063	−	1.17706i
$101$	−1241.84	+	716.977i	−1.22344	+	0.706355i	−0.965650	−	0.259845i	$-0.916329\pi$
$101$	−1241.84	+	716.977i	−1.22344	+	0.706355i	−0.257793	+	0.966200i	$0.582995\pi$
$102$	1722.78	−	61.5067i	1.67236	−	0.0597066i
$103$	−199.095	−	114.948i	−0.190460	−	0.109962i	0.401738	−	0.915755i	$-0.368406\pi$
$103$	−199.095	−	114.948i	−0.190460	−	0.109962i	−0.592198	+	0.805792i	$0.701740\pi$
$104$	−166.848	−	477.484i	−0.157316	−	0.450203i
$105$	1836.69	−	513.654i	1.70707	−	0.477404i
$106$	497.498	+	120.170i	0.455862	+	0.110113i
$107$	1676.13			1.51437			0.757184	−	0.653201i	$-0.226574\pi$
$107$	1676.13			1.51437			0.757184	+	0.653201i	$0.226574\pi$
$108$	1056.59	−	378.599i	0.941390	−	0.337321i
$109$	−540.666			−0.475104			−0.237552	−	0.971375i	$-0.576345\pi$
$109$	−540.666			−0.475104			−0.237552	+	0.971375i	$0.576345\pi$
$110$	578.604	+	139.762i	0.501525	+	0.121143i
$111$	−1168.95	+	326.912i	−0.999566	+	0.279542i
$112$	1297.17	+	586.202i	1.09439	+	0.494562i
$113$	1110.83	+	641.340i	0.924764	+	0.533913i	0.885152	−	0.465302i	$-0.154054\pi$
$113$	1110.83	+	641.340i	0.924764	+	0.533913i	0.0396123	+	0.999215i	$0.487388\pi$
$114$	407.297	−	14.5413i	0.334621	−	0.0119466i
$115$	502.576	−	290.163i	0.407526	−	0.235285i
$116$	−9.33599	+	0.463257i	−0.00747263	+	0.000370796i
$117$	13.1522	+	603.393i	0.0103925	+	0.476784i
$118$	−1285.59	−	1223.38i	−1.00295	−	0.954414i
$119$	−1304.43	−	2259.34i	−1.00485	−	1.74045i
$120$	−1591.56	+	1109.68i	−1.21074	+	0.844166i
$121$	584.179	−	1011.83i	0.438902	−	0.760201i
$122$	−2073.38	+	611.029i	−1.53865	+	0.453442i
$123$	−77.0461	−	19.7472i	−0.0564798	−	0.0144760i
$124$	597.950	+	926.391i	0.433044	+	0.670906i
$125$		−	368.214i		−	0.263472i
$126$	−1255.69	−	1143.83i	−0.887821	−	0.808732i
$127$			2674.79i			1.86889i	0.356109	+	0.934444i	$0.384103\pi$
$127$			2674.79i			1.86889i	−0.356109	+	0.934444i	$0.615897\pi$
$128$	−1442.52	−	127.662i	−0.996107	−	0.0881552i
$129$	−1516.74	+	1550.17i	−1.03521	+	1.05802i
$130$	−294.929	−	1000.77i	−0.198977	−	0.675180i
$131$	−413.401	+	716.031i	−0.275717	+	0.477557i	−0.970316	−	0.241841i	$-0.922249\pi$
$131$	−413.401	+	716.031i	−0.275717	+	0.477557i	0.694598	+	0.719398i	$0.255582\pi$
$132$	−167.908	−	502.844i	−0.110716	−	0.331568i
$133$	−308.391	−	534.149i	−0.201059	−	0.348245i
$134$	−255.455	+	268.446i	−0.164686	+	0.173061i
$135$	2215.49	−	671.978i	1.41244	−	0.428405i
$136$	2010.98	+	1732.09i	1.26794	+	1.09210i
$137$	560.929	−	323.852i	0.349806	−	0.201960i	−0.314794	−	0.949160i	$-0.601935\pi$
$137$	560.929	−	323.852i	0.349806	−	0.201960i	0.664600	+	0.747200i	$0.268602\pi$
$138$	−456.540	−	242.290i	−0.281618	−	0.149457i
$139$	−2312.71	−	1335.24i	−1.41124	−	0.814777i	−0.415730	−	0.909488i	$-0.636474\pi$
$139$	−2312.71	−	1335.24i	−1.41124	−	0.814777i	−0.995505	+	0.0947110i	$0.969807\pi$
$140$	2612.52	+	1340.30i	1.57713	+	0.809117i
$141$	−865.327	−	846.671i	−0.516835	−	0.505692i
$142$	−15.0692	+	62.3857i	−0.00890550	+	0.0368682i
$143$	285.073			0.166706
$144$	1589.81	+	677.123i	0.920028	+	0.391854i
$145$	−19.2814			−0.0110430
$146$	257.583	−	1066.38i	0.146012	−	0.604479i
$147$	−195.707	+	763.574i	−0.109807	+	0.428425i
$148$	−1662.72	−	853.030i	−0.923479	−	0.473774i
$149$	−90.2485	−	52.1050i	−0.0496204	−	0.0286484i	0.474985	−	0.879994i	$-0.342454\pi$
$149$	−90.2485	−	52.1050i	−0.0496204	−	0.0286484i	−0.524605	+	0.851346i	$0.675787\pi$
$150$	−1835.18	+	1148.74i	−0.998943	+	0.625293i
$151$	2382.77	−	1375.69i	1.28415	−	0.741407i	0.306549	−	0.951855i	$-0.400826\pi$
$151$	2382.77	−	1375.69i	1.28415	−	0.741407i	0.977605	+	0.210448i	$0.0674924\pi$
$152$	475.431	+	409.498i	0.253701	+	0.218517i
$153$	−1642.88	−	2707.52i	−0.868097	−	1.43065i
$154$	−553.069	+	581.193i	−0.289400	+	0.304116i
$155$	1137.20	+	1969.68i	0.589302	+	1.02070i
$156$	−616.135	+	695.558i	−0.316219	+	0.356982i
$157$	581.545	−	1007.27i	0.295620	−	0.512029i	−0.679509	−	0.733667i	$-0.737807\pi$
$157$	581.545	−	1007.27i	0.295620	−	0.512029i	0.975129	+	0.221638i	$0.0711404\pi$
$158$	449.073	+	1523.82i	0.226116	+	0.767269i
$159$	−253.236	−	905.504i	−0.126308	−	0.451643i
$160$	−2958.83	−	410.477i	−1.46198	−	0.202819i
$161$			782.182i			0.382886i
$162$	−1554.21	−	1354.98i	−0.753767	−	0.657142i
$163$		−	2930.45i		−	1.40816i	−0.710120	−	0.704081i	$-0.751359\pi$
$163$		−	2930.45i		−	1.40816i	0.710120	−	0.704081i	$-0.248641\pi$
$164$	−66.4077	−	102.884i	−0.0316193	−	0.0489871i
$165$	−294.521	−	1053.13i	−0.138960	−	0.496884i
$166$	1856.34	−	547.067i	0.867951	−	0.255787i
$167$	−435.960	+	755.105i	−0.202010	+	0.349891i	−0.949176	−	0.314746i	$-0.898081\pi$
$167$	−435.960	+	755.105i	−0.202010	+	0.349891i	0.747166	+	0.664637i	$0.231414\pi$
$168$	−222.710	−	2605.60i	−0.102277	−	1.19658i
$169$	848.667	+	1469.93i	0.386284	+	0.669064i
$170$	3965.96	+	3774.05i	1.78927	+	1.70268i
$171$	−388.406	−	640.106i	−0.173697	−	0.286258i
$172$	−3334.92	+	165.481i	−1.47840	+	0.0733592i
$173$	2020.19	−	1166.36i	0.887816	−	0.512581i	0.0145882	−	0.999894i	$-0.495356\pi$
$173$	2020.19	−	1166.36i	0.887816	−	0.512581i	0.873227	+	0.487313i	$0.162023\pi$
$174$	9.11135	+	14.5559i	0.00396971	+	0.00634185i
$175$	2837.55	+	1638.26i	1.22571	+	0.707662i
$176$	336.119	−	743.778i	0.143954	−	0.318547i
$177$	−809.446	+	3158.16i	−0.343739	+	1.34114i
$178$	764.328	+	184.623i	0.321847	+	0.0777420i
$179$	−638.773			−0.266727			−0.133364	−	0.991067i	$-0.542578\pi$
$179$	−638.773			−0.266727			−0.133364	+	0.991067i	$0.542578\pi$
$180$	3206.11	+	1557.54i	1.32761	+	0.644955i
$181$	4031.01			1.65537			0.827686	−	0.561192i	$-0.189657\pi$
$181$	4031.01			1.65537			0.827686	+	0.561192i	$0.189657\pi$
$182$	1366.92	+	330.178i	0.556717	+	0.134475i
$183$	2838.35	+	2777.16i	1.14654	+	1.12182i
$184$	−262.494	−	751.200i	−0.105170	−	0.300974i
$185$	−3338.34	−	1927.39i	−1.32670	−	0.765972i
$186$	949.575	−	1789.26i	0.374335	−	0.705348i
$187$	−1295.47	+	747.940i	−0.506600	+	0.292486i
$188$	−92.3740	−	1861.61i	−0.0358355	−	0.722190i
$189$	−708.684	+	3038.90i	−0.272747	+	1.16957i
$190$	937.624	+	892.252i	0.358013	+	0.340688i
$191$	−1831.72	−	3172.63i	−0.693918	−	1.20190i	−0.970544	−	0.240924i	$-0.922550\pi$
$191$	−1831.72	−	3172.63i	−0.693918	−	1.20190i	0.276626	−	0.960978i	$-0.410784\pi$
$192$	1088.30	+	2427.65i	0.409071	+	0.912503i
$193$	−708.828	+	1227.73i	−0.264366	+	0.457895i	−0.967397	−	0.253264i	$-0.918496\pi$
$193$	−708.828	+	1227.73i	−0.264366	+	0.457895i	0.703032	+	0.711159i	$0.251829\pi$
$194$	−1434.90	+	422.868i	−0.531030	+	0.156496i
$195$	−1340.47	+	1370.01i	−0.492272	+	0.503119i
$196$	−1019.64	+	658.141i	−0.371590	+	0.239847i
$197$		−	876.917i		−	0.317146i	−0.987347	−	0.158573i	$-0.949311\pi$
$197$		−	876.917i		−	0.317146i	0.987347	−	0.158573i	$-0.0506893\pi$
$198$	−655.852	+	719.990i	−0.235401	+	0.258421i
$199$		−	1485.45i		−	0.529149i	−0.964365	−	0.264574i	$-0.914769\pi$
$199$		−	1485.45i		−	0.529149i	0.964365	−	0.264574i	$-0.0852315\pi$
$200$	−3274.94	−	621.111i	−1.15787	−	0.219596i
$201$	659.460	+	169.022i	0.231417	+	0.0593129i
$202$	1146.51	+	3890.41i	0.399348	+	1.35509i
$203$	12.9941	−	22.5064i	0.00449263	−	0.00778147i
$204$	975.007	−	4777.40i	0.334628	−	1.63963i
$205$	−126.296	−	218.751i	−0.0430287	−	0.0745279i
$206$	−448.252	+	471.046i	−0.151608	+	0.159317i
$207$	20.6917	+	949.287i	0.00694769	+	0.318744i
$208$	−1423.58	+	141.626i	−0.474555	+	0.0472116i
$209$	−306.272	+	176.826i	−0.101365	+	0.0585231i
$210$	−192.463	−	5390.83i	−0.0632438	−	1.77144i
$211$	−266.434	−	153.826i	−0.0869294	−	0.0501887i	0.455905	−	0.890028i	$-0.349316\pi$
$211$	−266.434	−	153.826i	−0.0869294	−	0.0501887i	−0.542835	+	0.839840i	$0.682649\pi$
$212$	660.783	−	1288.00i	0.214070	−	0.417264i
$213$	113.549	−	31.7555i	0.0365270	−	0.0102153i
$214$	1113.13	−	4608.28i	0.355569	−	1.47203i
$215$	−6887.55			−2.18478
$216$	−339.218	−	3156.36i	−0.106856	−	0.994275i
$217$	−3065.50			−0.958986
$218$	−359.059	+	1486.48i	−0.111553	+	0.461823i
$219$	−1940.93	+	542.806i	−0.598885	+	0.167486i
$220$	768.509	−	1497.97i	0.235513	−	0.459061i
$221$	2270.66	+	1310.96i	0.691135	+	0.399027i
$222$	122.492	+	3430.96i	0.0370321	+	1.03726i
$223$	−3380.52	+	1951.74i	−1.01514	+	0.586091i	−0.912692	−	0.408647i	$-0.866001\pi$
$223$	−3380.52	+	1951.74i	−1.01514	+	0.586091i	−0.102447	+	0.994738i	$0.532667\pi$
$224$	2473.14	−	3177.09i	0.737694	−	0.947671i
$225$	3487.10	+	1913.19i	1.03322	+	0.566872i
$226$	2500.98	−	2628.16i	0.736119	−	0.773551i
$227$	964.382	+	1670.36i	0.281975	+	0.488394i	0.971871	−	0.235514i	$-0.0756773\pi$
$227$	964.382	+	1670.36i	0.281975	+	0.488394i	−0.689896	+	0.723908i	$0.742344\pi$
$228$	230.509	−	1129.46i	0.0669553	−	0.328072i
$229$	−1148.71	+	1989.62i	−0.331479	+	0.574139i	−0.982802	−	0.184662i	$-0.940881\pi$
$229$	−1148.71	+	1989.62i	−0.331479	+	0.574139i	0.651323	+	0.758801i	$0.274214\pi$
$230$	−463.997	−	1574.46i	−0.133022	−	0.451378i
$231$	1427.75	+	365.938i	0.406663	+	0.104229i
$232$	−4.92642	+	25.9756i	−0.00139412	+	0.00735079i
$233$		−	3366.60i		−	0.946580i	−0.880907	−	0.473290i	$-0.843066\pi$
$233$		−	3366.60i		−	0.946580i	0.880907	−	0.473290i	$-0.156934\pi$
$234$	1667.68	+	364.557i	0.465895	+	0.101845i
$235$		−	3844.74i		−	1.06725i
$236$	−4217.26	+	2722.08i	−1.16322	+	0.750816i
$237$	2041.06	−	2086.03i	0.559414	−	0.571740i
$238$	−7078.02	+	2085.91i	−1.92773	+	0.568106i
$239$	307.571	−	532.729i	0.0832432	−	0.144182i	−0.821398	−	0.570355i	$-0.806805\pi$
$239$	307.571	−	532.729i	0.0832432	−	0.144182i	0.904641	+	0.426174i	$0.140139\pi$
$240$	1993.96	+	5112.71i	0.536289	+	1.37510i
$241$	2195.78	+	3803.20i	0.586898	+	1.01654i	0.994636	+	0.103438i	$0.0329844\pi$
$241$	2195.78	+	3803.20i	0.586898	+	1.01654i	−0.407738	+	0.913099i	$0.633682\pi$
$242$	−2393.92	−	2278.08i	−0.635897	−	0.605125i
$243$	−779.696	+	3706.88i	−0.205833	+	0.978587i
$244$	302.995	+	6106.25i	0.0794971	+	1.60210i
$245$	−2167.95	+	1251.67i	−0.565329	+	0.326393i
$246$	−105.459	+	198.713i	−0.0273326	+	0.0515019i
$247$	536.823	+	309.935i	0.138288	+	0.0798408i
$248$	2944.08	−	1028.76i	0.753828	−	0.263412i
$249$	−2541.24	−	2486.45i	−0.646765	−	0.632821i
$250$	−1012.35	−	244.533i	−0.256107	−	0.0618624i
$251$	7726.08			1.94289			0.971446	−	0.237259i	$-0.0762489\pi$
$251$	7726.08			1.94289			0.971446	+	0.237259i	$0.0762489\pi$
$252$	−3978.70	+	2692.71i	−0.994581	+	0.673114i
$253$	448.490			0.111448
$254$	7353.94	+	1776.34i	1.81664	+	0.438809i
$255$	2497.10	−	9742.75i	0.613233	−	2.39261i
$256$	−1308.97	+	3881.21i	−0.319573	+	0.947562i
$257$	−2222.83	−	1283.35i	−0.539518	−	0.311491i	0.205365	−	0.978685i	$-0.434162\pi$
$257$	−2222.83	−	1283.35i	−0.539518	−	0.311491i	−0.744884	+	0.667194i	$0.767495\pi$
$258$	3254.68	+	5199.55i	0.785378	+	1.25469i
$259$	4499.53	−	2597.81i	1.07949	−	0.623243i
$260$	−2947.34	+	146.249i	−0.703024	+	0.0348844i
$261$	15.1747	−	27.6584i	0.00359882	−	0.00655943i
$262$	1694.08	+	1612.11i	0.399469	+	0.380138i
$263$	2003.92	+	3470.89i	0.469837	+	0.813781i	0.999405	−	0.0344862i	$-0.0109795\pi$
$263$	2003.92	+	3470.89i	0.469837	+	0.813781i	−0.529569	+	0.848267i	$0.677646\pi$
$264$	−1494.01	+	127.698i	−0.348294	+	0.0297701i
$265$	1493.02	−	2585.98i	0.346096	−	0.599456i
$266$	−1673.37	+	493.146i	−0.385717	+	0.113672i
$267$	−389.057	−	1391.17i	−0.0891758	−	0.318869i
$268$	568.403	+	880.614i	0.129555	+	0.200717i
$269$		−	2242.21i		−	0.508214i	−0.967176	−	0.254107i	$-0.918218\pi$
$269$		−	2242.21i		−	0.508214i	0.967176	−	0.254107i	$-0.0817816\pi$
$270$	−376.188	−	6537.43i	−0.0847930	−	1.47354i
$271$			6324.08i			1.41757i	0.705426	+	0.708784i	$0.250756\pi$
$271$			6324.08i			1.41757i	−0.705426	+	0.708784i	$0.749244\pi$
$272$	6097.65	−	4378.61i	1.35928	−	0.976075i
$273$	−695.786	−	2487.94i	−0.154252	−	0.551565i
$274$	−517.870	−	1757.27i	−0.114181	−	0.387446i
$275$	939.352	−	1627.01i	0.205982	−	0.356771i
$276$	−969.332	+	1094.29i	−0.211402	+	0.238653i
$277$	−625.852	−	1084.01i	−0.135754	−	0.235132i	0.790131	−	0.612938i	$-0.210012\pi$
$277$	−625.852	−	1084.01i	−0.135754	−	0.235132i	−0.925885	+	0.377805i	$0.876679\pi$
$278$	−5206.95	+	5471.73i	−1.12335	+	1.18048i
$279$	−3720.42	+	81.0942i	−0.798335	+	0.0174014i
$280$	5419.96	−	6292.64i	1.15680	−	1.34306i
$281$	−1190.34	+	687.240i	−0.252703	+	0.145898i	−0.621001	−	0.783810i	$-0.713274\pi$
$281$	−1190.34	+	687.240i	−0.252703	+	0.145898i	0.368298	+	0.929708i	$0.379940\pi$
$282$	−2902.47	+	1816.81i	−0.612906	+	0.383652i
$283$	4006.16	+	2312.96i	0.841490	+	0.485835i	0.857771	−	0.514033i	$-0.171849\pi$
$283$	4006.16	+	2312.96i	0.841490	+	0.485835i	−0.0162801	+	0.999867i	$0.505182\pi$
$284$	161.513	+	82.8613i	0.0337466	+	0.0173131i
$285$	590.359	−	2303.36i	0.122701	−	0.478734i
$286$	189.318	−	783.767i	0.0391421	−	0.162046i
$287$	340.452			0.0700217
$288$	2917.45	−	3921.27i	0.596919	−	0.802302i
$289$	−8845.19			−1.80037
$290$	−12.8049	+	53.0115i	−0.00259286	+	0.0107343i
$291$	1964.31	+	1921.96i	0.395704	+	0.387173i
$292$	−2760.79	−	1416.37i	−0.553297	−	0.283859i
$293$	5522.68	+	3188.52i	1.10116	+	0.635752i	0.936524	−	0.350603i	$-0.114023\pi$
$293$	5522.68	+	3188.52i	1.10116	+	0.635752i	0.164631	+	0.986355i	$0.447357\pi$
$294$	1969.37	+	1045.16i	0.390666	+	0.207330i
$295$	−8966.70	+	5176.92i	−1.76970	+	1.02174i
$296$	−3449.51	+	4004.91i	−0.677360	+	0.786422i
$297$	1742.46	+	406.348i	0.340430	+	0.0793895i
$298$	−203.190	+	213.522i	−0.0394982	+	0.0415067i
$299$	−393.049	−	680.781i	−0.0760221	−	0.131674i
$300$	1939.54	+	5808.44i	0.373264	+	1.11783i
$301$	4641.63	−	8039.54i	0.888835	−	1.53951i
$302$	−2199.86	−	7464.70i	−0.419165	−	1.42233i
$303$	5210.96	−	5325.78i	0.987993	−	1.00976i
$304$	1441.59	−	1035.18i	0.271977	−	0.195302i
$305$			12611.1i			2.36757i
$306$	−8534.99	+	2718.78i	−1.59449	+	0.507916i
$307$		−	6609.36i		−	1.22872i	−0.789027	−	0.614359i	$-0.789415\pi$
$307$		−	6609.36i		−	1.22872i	0.789027	−	0.614359i	$-0.210585\pi$
$308$	1230.61	+	1906.56i	0.227664	+	0.352715i
$309$	1157.17	+	296.586i	0.213039	+	0.0546026i
$310$	6170.58	−	1818.48i	1.13053	−	0.333171i
$311$	2568.35	−	4448.51i	0.468288	−	0.811098i	−0.531055	−	0.847337i	$-0.678204\pi$
$311$	2568.35	−	4448.51i	0.468288	−	0.811098i	0.999343	+	0.0362387i	$0.0115377\pi$
$312$	1503.16	+	2155.90i	0.272755	+	0.391198i
$313$	−3101.42	−	5371.82i	−0.560072	−	0.970074i	−0.997489	−	0.0708150i	$-0.977440\pi$
$313$	−3101.42	−	5371.82i	−0.560072	−	0.970074i	0.437417	−	0.899259i	$-0.355893\pi$
$314$	−2383.13	−	2267.81i	−0.428305	−	0.407579i
$315$	−8472.21	+	5140.79i	−1.51541	+	0.919527i
$316$	4487.75	−	222.685i	0.798911	−	0.0396424i
$317$	1580.62	−	912.574i	0.280053	−	0.161689i	−0.353395	−	0.935474i	$-0.614973\pi$
$317$	1580.62	−	912.574i	0.280053	−	0.161689i	0.633447	+	0.773786i	$0.281639\pi$
$318$	−2657.73	+	94.8860i	−0.468673	+	0.0167325i
$319$	−12.9048	−	7.45058i	−0.00226498	−	0.00130769i
$320$	−3093.52	+	7862.28i	−0.540416	+	1.37348i
$321$	−8387.59	+	2345.70i	−1.45841	+	0.407863i
$322$	2150.50	+	519.451i	0.372182	+	0.0899003i
$323$	−3252.68			−0.560322
$324$	−4757.47	+	3373.23i	−0.815753	+	0.578400i
$325$	−3292.93			−0.562027
$326$	−8056.84	−	1946.13i	−1.36880	−	0.330632i
$327$	2705.57	−	756.648i	0.457549	−	0.127959i
$328$	−326.966	+	114.253i	−0.0550418	+	0.0192334i
$329$	4487.80	+	2591.03i	0.752038	+	0.434189i
$330$	−3091.01	+	110.355i	−0.515620	+	0.0184086i
$331$	−3444.37	+	1988.61i	−0.571963	+	0.330223i	−0.757933	−	0.652332i	$-0.773791\pi$
$331$	−3444.37	+	1988.61i	−0.571963	+	0.330223i	0.185970	+	0.982555i	$0.440457\pi$
$332$	−271.278	−	5467.05i	−0.0448443	−	0.903745i
$333$	5392.09	−	3271.83i	0.887341	−	0.538424i
$334$	1786.53	+	1700.08i	0.292678	+	0.278516i
$335$	1081.00	+	1872.35i	0.176303	+	0.305366i
$336$	−7311.62	−	1118.08i	−1.18715	−	0.181537i
$337$	578.847	−	1002.59i	0.0935662	−	0.162061i	−0.815443	−	0.578837i	$-0.803507\pi$
$337$	578.847	−	1002.59i	0.0935662	−	0.162061i	0.909009	+	0.416776i	$0.136840\pi$
$338$	4604.98	−	1357.10i	0.741059	−	0.218392i
$339$	−6456.31	−	1654.77i	−1.03439	−	0.265118i
$340$	13010.0	−	8397.48i	2.07520	−	1.33946i
$341$			1757.71i			0.279136i
$342$	−2017.82	+	642.768i	−0.319039	+	0.101628i
$343$			4254.87i			0.669800i
$344$	−1759.78	+	9278.79i	−0.275816	+	1.45430i
$345$	−2108.89	+	2155.36i	−0.329098	+	0.336350i
$346$	−1865.11	−	6328.80i	−0.289795	−	0.983348i
$347$	1241.63	−	2150.56i	0.192086	−	0.332703i	−0.753855	−	0.657041i	$-0.771808\pi$
$347$	1241.63	−	2150.56i	0.192086	−	0.332703i	0.945941	+	0.324337i	$0.105141\pi$
$348$	46.0703	−	15.3837i	0.00709663	−	0.00236969i
$349$	2986.90	+	5173.47i	0.458124	+	0.793494i	0.998862	−	0.0476973i	$-0.0151883\pi$
$349$	2986.90	+	5173.47i	0.458124	+	0.793494i	−0.540738	+	0.841191i	$0.681855\pi$
$350$	6388.60	−	6713.46i	0.975671	−	1.02528i
$351$	−910.249	−	3001.06i	−0.138420	−	0.456367i
$352$	−1821.69	−	1418.06i	−0.275842	−	0.214724i
$353$	−893.160	+	515.666i	−0.134669	+	0.0777511i	−0.565821	−	0.824528i	$-0.691441\pi$
$353$	−893.160	+	515.666i	−0.134669	+	0.0777511i	0.431152	+	0.902279i	$0.358107\pi$
$354$	8145.34	+	4322.81i	1.22294	+	0.649024i
$355$	324.279	+	187.223i	0.0484815	+	0.0279908i
$356$	1015.19	−	1978.80i	0.151137	−	0.294596i
$357$	9689.46	+	9480.56i	1.43647	+	1.40550i
$358$	−424.213	+	1756.22i	−0.0626267	+	0.259271i
$359$	−4218.99			−0.620249			−0.310125	−	0.950696i	$-0.600371\pi$
$359$	−4218.99			−0.620249			−0.310125	+	0.950696i	$0.600371\pi$
$360$	6411.42	−	7780.37i	0.938643	−	1.13906i
$361$	6090.01			0.887886
$362$	2677.01	−	11082.7i	0.388676	−	1.60909i
$363$	−1507.29	+	5880.88i	−0.217940	+	0.850320i
$364$	1815.55	−	3538.87i	0.261431	−	0.509580i
$365$	−5542.99	−	3200.25i	−0.794887	−	0.458928i
$366$	9520.37	−	5959.32i	1.35967	−	0.851089i
$367$	2632.91	−	1520.11i	0.374487	−	0.216210i	−0.300930	−	0.953646i	$-0.597297\pi$
$367$	2632.91	−	1520.11i	0.374487	−	0.216210i	0.675417	+	0.737436i	$0.263964\pi$
$368$	−2239.64	+	222.813i	−0.317254	+	0.0315623i
$369$	413.186	−	9.00624i	0.0582915	−	0.00127059i
$370$	−7516.11	+	7898.31i	−1.05606	+	1.10977i
$371$	2012.34	+	3485.48i	0.281605	+	0.487754i
$372$	−4288.69	−	3798.98i	−0.597737	−	0.529483i
$373$	−2558.92	+	4432.17i	−0.355216	+	0.615253i	−0.987155	−	0.159766i	$-0.948926\pi$
$373$	−2558.92	+	4432.17i	−0.355216	+	0.615253i	0.631939	+	0.775018i	$0.282259\pi$
$374$	1196.03	+	4058.42i	0.165361	+	0.561112i
$375$	515.306	+	1842.60i	0.0709607	+	0.253737i
$376$	−5179.57	−	982.335i	−0.710415	−	0.134734i
$377$			26.1183i			0.00356806i
$378$	7884.39	+	3966.58i	1.07283	+	0.539732i
$379$			2840.61i			0.384993i	0.981298	+	0.192497i	$0.0616585\pi$
$379$			2840.61i			0.384993i	−0.981298	+	0.192497i	$0.938342\pi$
$380$	3075.80	−	1985.31i	0.415224	−	0.268012i
$381$	−3743.29	−	13385.0i	−0.503346	−	1.79983i
$382$	−9939.14	+	2929.09i	−1.33123	+	0.392317i
$383$	−2814.33	+	4874.56i	−0.375472	+	0.650336i	−0.990397	−	0.138249i	$-0.955853\pi$
$383$	−2814.33	+	4874.56i	−0.375472	+	0.650336i	0.614926	+	0.788585i	$0.289186\pi$
$384$	7397.22	−	1379.92i	0.983042	−	0.183383i
$385$	2340.41	+	4053.70i	0.309814	+	0.536613i
$386$	2904.72	+	2764.16i	0.383022	+	0.364487i
$387$	5420.59	−	9879.90i	0.712001	−	1.29774i
$388$	209.691	+	4225.88i	0.0274367	+	0.552930i
$389$	−3084.76	+	1780.99i	−0.402065	+	0.232132i	−0.687375	−	0.726303i	$-0.741237\pi$
$389$	−3084.76	+	1780.99i	−0.402065	+	0.232132i	0.285309	+	0.958435i	$0.407904\pi$
$390$	2876.42	+	4595.26i	0.373470	+	0.596641i
$391$	3572.30	+	2062.47i	0.462044	+	0.266761i
$392$	1132.31	+	3240.44i	0.145894	+	0.417517i
$393$	1066.65	−	4161.67i	0.136909	−	0.534169i
$394$	−2410.96	−	582.365i	−0.308280	−	0.0744648i
$395$	9268.46			1.18062
$396$	1543.95	+	2281.32i	0.195926	+	0.289497i
$397$	−9427.52			−1.19182			−0.595911	−	0.803050i	$-0.703209\pi$
$397$	−9427.52			−1.19182			−0.595911	+	0.803050i	$0.703209\pi$
$398$	−4084.03	−	986.494i	−0.514356	−	0.124242i
$399$	2290.76	+	2241.37i	0.287422	+	0.281225i
$400$	−3882.56	+	8591.50i	−0.485321	+	1.07394i
$401$	−7475.17	−	4315.79i	−0.930903	−	0.537457i	−0.0438059	−	0.999040i	$-0.513948\pi$
$401$	−7475.17	−	4315.79i	−0.930903	−	0.537457i	−0.887097	+	0.461583i	$0.847282\pi$
$402$	902.653	−	1700.84i	0.111991	−	0.211021i
$403$	2668.10	−	1540.43i	0.329795	−	0.190407i
$404$	11457.5	−	568.529i	1.41097	−	0.0700133i
$405$	−10146.2	+	6463.19i	−1.24486	+	0.792984i
$406$	−53.2487	−	50.6719i	−0.00650908	−	0.00619410i
$407$	−1489.54	−	2579.96i	−0.181410	−	0.314211i
$408$	−12487.3	−	5853.34i	−1.51522	−	0.710253i
$409$	−2932.40	+	5079.07i	−0.354518	+	0.614044i	−0.987035	−	0.160503i	$-0.948688\pi$
$409$	−2932.40	+	5079.07i	−0.354518	+	0.614044i	0.632517	+	0.774546i	$0.282022\pi$
$410$	−685.298	+	201.959i	−0.0825474	+	0.0243269i
$411$	−2353.75	+	2405.61i	−0.282486	+	0.288711i
$412$	997.387	+	1545.23i	0.119266	+	0.184777i
$413$		−	13955.3i		−	1.66270i
$414$	2623.67	+	573.538i	0.311465	+	0.0680866i
$415$		−	11291.0i		−	1.33555i
$416$	−556.025	+	4007.98i	−0.0655321	+	0.472373i
$417$	13441.8	+	3445.18i	1.57853	+	0.404583i
$418$	282.762	+	959.482i	0.0330869	+	0.112272i
$419$	−3477.85	+	6023.82i	−0.405500	+	0.702346i	−0.994379	−	0.105875i	$-0.966236\pi$
$419$	−3477.85	+	6023.82i	−0.405500	+	0.702346i	0.588880	+	0.808221i	$0.299569\pi$
$420$	−14949.1	−	3050.93i	−1.73677	−	0.354453i
$421$	4697.89	+	8136.99i	0.543851	+	0.941978i	0.998678	+	0.0513981i	$0.0163677\pi$
$421$	4697.89	+	8136.99i	0.543851	+	0.941978i	−0.454827	+	0.890580i	$0.650299\pi$
$422$	−599.863	+	630.366i	−0.0691964	+	0.0727151i
$423$	5515.12	+	3025.86i	0.633934	+	0.347807i
$424$	−3102.33	−	2672.09i	−0.355336	−	0.306057i
$425$	14964.2	−	8639.59i	1.70793	−	0.986074i
$426$	−11.8986	−	333.276i	−0.00135326	−	0.0379044i
$427$	−14720.4	−	8498.83i	−1.66831	−	0.963202i
$428$	−11930.6	−	6120.76i	−1.34740	−	0.691258i
$429$	−1426.55	+	398.952i	−0.160546	+	0.0448988i
$430$	−4574.06	+	18936.3i	−0.512978	+	2.12370i
$431$	−7346.03			−0.820988			−0.410494	−	0.911863i	$-0.634644\pi$
$431$	−7346.03			−0.820988			−0.410494	+	0.911863i	$0.634644\pi$
$432$	−8903.25	−	1163.53i	−0.991568	−	0.129584i
$433$	13673.0			1.51751			0.758755	−	0.651376i	$-0.225808\pi$
$433$	13673.0			1.51751			0.758755	+	0.651376i	$0.225808\pi$
$434$	−2035.82	+	8428.17i	−0.225167	+	0.932177i
$435$	96.4870	−	26.9838i	0.0106349	−	0.00297420i
$436$	3848.42	+	1974.36i	0.422720	+	0.216869i
$437$	844.556	+	487.604i	0.0924498	+	0.0533759i
$438$	203.386	+	5696.78i	0.0221876	+	0.621468i
$439$	4995.87	−	2884.37i	0.543144	−	0.313584i	−0.203208	−	0.979135i	$-0.565137\pi$
$439$	4995.87	−	2884.37i	0.543144	−	0.313584i	0.746352	+	0.665551i	$0.231804\pi$
$440$	−3608.09	−	3107.72i	−0.390930	−	0.336715i
$441$	−89.2573	−	4094.92i	−0.00963797	−	0.442168i
$442$	5112.26	−	5372.22i	0.550148	−	0.578124i
$443$	−4826.45	−	8359.66i	−0.517634	−	0.896568i	−0.999790	−	0.0204826i	$-0.993480\pi$
$443$	−4826.45	−	8359.66i	−0.517634	−	0.896568i	0.482157	−	0.876085i	$-0.339854\pi$
$444$	9514.29	+	1941.75i	1.01696	+	0.207548i
$445$	2293.79	−	3972.96i	0.244351	−	0.423228i
$446$	3121.02	+	10590.4i	0.331355	+	1.12437i
$447$	524.536	+	134.440i	0.0555027	+	0.0142255i
$448$	−7092.53	−	8909.46i	−0.747970	−	0.939582i
$449$		−	11492.2i		−	1.20791i	−0.797018	−	0.603955i	$-0.793590\pi$
$449$		−	11492.2i		−	1.20791i	0.797018	−	0.603955i	$-0.206410\pi$
$450$	7575.86	−	8316.73i	0.793621	−	0.871232i
$451$		−	195.209i		−	0.0203815i
$452$	−5564.83	−	8621.46i	−0.579088	−	0.897167i
$453$	−9998.49	+	10218.8i	−1.03702	+	1.05987i
$454$	5232.86	−	1542.14i	0.540948	−	0.159419i
$455$	4102.19	−	7105.19i	0.422667	−	0.732080i
$456$	−2952.21	−	1383.83i	−0.303180	−	0.142114i
$457$	−8821.06	−	15278.5i	−0.902914	−	1.56389i	−0.823693	−	0.567036i	$-0.808090\pi$
$457$	−8821.06	−	15278.5i	−0.902914	−	1.56389i	−0.0792214	−	0.996857i	$-0.525243\pi$
$458$	4707.31	+	4479.53i	0.480258	+	0.457018i
$459$	12010.3	+	11249.7i	1.22134	+	1.14399i
$460$	−4636.90	+	230.085i	−0.469992	+	0.0233213i
$461$	−11142.2	+	6432.95i	−1.12569	+	0.649918i	−0.942848	−	0.333224i	$-0.891863\pi$
$461$	−11142.2	+	6432.95i	−1.12569	+	0.649918i	−0.182843	+	0.983142i	$0.558530\pi$
$462$	1954.27	−	3682.38i	0.196799	−	0.370822i
$463$	11984.7	+	6919.34i	1.20297	+	0.694534i	0.961214	−	0.275804i	$-0.0889440\pi$
$463$	11984.7	+	6919.34i	1.20297	+	0.694534i	0.241754	+	0.970338i	$0.422277\pi$
$464$	68.1446	+	30.7950i	0.00681796	+	0.00308109i
$465$	−8447.22	−	8265.10i	−0.842431	−	0.824268i
$466$	−9255.98	−	2235.78i	−0.920118	−	0.222254i
$467$	81.1441			0.00804047			0.00402024	−	0.999992i	$-0.498720\pi$
$467$	81.1441			0.00804047			0.00402024	+	0.999992i	$0.498720\pi$
$468$	2109.81	−	4342.94i	0.208389	−	0.428958i
$469$	−2914.03			−0.286902
$470$	−10570.6	−	2553.31i	−1.03741	−	0.250586i
$471$	−1500.49	+	5854.36i	−0.146792	+	0.572728i
$472$	4683.27	+	13402.5i	0.456706	+	1.30699i
$473$	−4609.74	−	2661.44i	−0.448110	−	0.258717i
$474$	−4379.77	−	6996.95i	−0.424408	−	0.678018i
$475$	3537.80	−	2042.55i	0.341738	−	0.197302i
$476$	1034.35	+	20845.3i	0.0995998	+	2.00723i
$477$	2534.46	+	4176.88i	0.243281	+	0.400935i
$478$	−1260.40	−	1199.41i	−0.120606	−	0.114769i
$479$	−7472.06	−	12942.0i	−0.712750	−	1.23452i	−0.963821	−	0.266550i	$-0.914116\pi$
$479$	−7472.06	−	12942.0i	−0.712750	−	1.23452i	0.251071	−	0.967969i	$-0.419217\pi$
$480$	15380.9	−	2086.72i	1.46258	−	0.198428i
$481$	−2610.81	+	4522.06i	−0.247490	+	0.428666i
$482$	11914.6	−	3511.25i	1.12592	−	0.331811i
$483$	−1094.64	−	3914.15i	−0.103122	−	0.368737i
$484$	−7853.06	+	5068.86i	−0.737515	+	0.476038i
$485$			8727.63i			0.817116i
$486$	9673.74	+	4605.42i	0.902901	+	0.429848i
$487$			5934.04i			0.552150i	0.961136	+	0.276075i	$0.0890338\pi$
$487$			5934.04i			0.552150i	−0.961136	+	0.276075i	$0.910966\pi$
$488$	16989.5	+	3222.15i	1.57598	+	0.298893i
$489$	4101.08	+	14664.4i	0.379259	+	1.35613i
$490$	2001.53	+	6791.72i	0.184531	+	0.626160i
$491$	−10032.4	+	17376.6i	−0.922110	+	1.59714i	−0.125965	+	0.992035i	$0.540203\pi$
$491$	−10032.4	+	17376.6i	−0.922110	+	1.59714i	−0.796145	+	0.605106i	$0.793131\pi$
$492$	476.297	+	421.910i	0.0436446	+	0.0386609i
$493$	−68.5259	−	118.690i	−0.00626015	−	0.0108429i
$494$	1208.63	−	1270.09i	0.110079	−	0.115676i
$495$	2947.65	+	4857.82i	0.267650	+	0.441097i
$496$	−873.242	−	8777.53i	−0.0790519	−	0.794602i
$497$	−437.074	+	252.345i	−0.0394476	+	0.0227751i
$498$	−8523.79	+	5335.51i	−0.766988	+	0.480100i
$499$	8148.09	+	4704.30i	0.730979	+	0.422031i	0.818780	−	0.574107i	$-0.194651\pi$
$499$	8148.09	+	4704.30i	0.730979	+	0.422031i	−0.0878012	+	0.996138i	$0.527984\pi$
$500$	−1344.62	+	2620.92i	−0.120266	+	0.234422i
$501$	1124.86	−	4388.77i	0.100309	−	0.391369i
$502$	5130.93	−	21241.8i	0.456185	−	1.88858i
$503$	12736.4			1.12900			0.564501	−	0.825432i	$-0.309069\pi$
$503$	12736.4			1.12900			0.564501	+	0.825432i	$0.309069\pi$
$504$	4760.94	+	12727.1i	0.420772	+	1.12482i
$505$	23663.0			2.08513
$506$	297.845	−	1233.06i	0.0261676	−	0.108332i
$507$	−6303.99	−	6168.08i	−0.552209	−	0.540304i
$508$	9767.58	−	19038.9i	0.853084	−	1.66283i
$509$	7921.59	+	4573.53i	0.689820	+	0.398268i	0.803545	−	0.595244i	$-0.202945\pi$
$509$	7921.59	+	4573.53i	0.689820	+	0.398268i	−0.113724	+	0.993512i	$0.536278\pi$
$510$	−25127.9	−	13335.6i	−2.18173	−	1.15787i
$511$	7471.04	−	4313.40i	0.646769	−	0.373412i
$512$	9801.54	+	6176.37i	0.846037	+	0.533124i
$513$	2839.45	+	2659.62i	0.244376	+	0.228899i
$514$	−5004.58	+	5259.07i	−0.429460	+	0.451299i
$515$	1896.86	+	3285.45i	0.162302	+	0.281115i
$516$	16456.9	−	5495.23i	1.40402	−	0.468826i
$517$	1485.66	−	2573.23i	0.126381	−	0.218899i
$518$	−4154.13	−	14096.0i	−0.352359	−	1.19565i
$519$	−8477.03	+	8663.82i	−0.716956	+	0.732754i
$520$	−1555.26	+	8200.42i	−0.131159	+	0.691562i
$521$			7691.78i			0.646801i	0.946262	+	0.323400i	$0.104826\pi$
$521$			7691.78i			0.646801i	−0.946262	+	0.323400i	$0.895174\pi$
$522$	−65.9651	−	60.0889i	−0.00553107	−	0.00503835i
$523$		−	9967.82i		−	0.833389i	−0.909047	−	0.416694i	$-0.863189\pi$
$523$		−	9967.82i		−	0.833389i	0.909047	−	0.416694i	$-0.136811\pi$
$524$	5557.30	−	3587.03i	0.463305	−	0.299046i
$525$	−16492.2	−	4227.02i	−1.37101	−	0.351394i
$526$	10873.5	−	3204.45i	0.901347	−	0.265629i
$527$	−8083.17	+	14000.5i	−0.668138	+	1.15725i
$528$	−641.089	+	4192.36i	−0.0528405	+	0.345547i
$529$	5465.14	+	9465.89i	0.449177	+	0.777997i
$530$	−6118.27	−	5822.21i	−0.501435	−	0.477171i
$531$	−369.170	−	16936.7i	−0.0301706	−	1.38416i
$532$	244.539	+	4928.19i	0.0199288	+	0.401624i
$533$	−296.316	+	171.078i	−0.0240804	+	0.0139028i
$534$	−4083.18	+	145.777i	−0.330893	+	0.0118135i
$535$	−23953.7	−	13829.7i	−1.93572	−	1.11759i
$536$	2798.60	−	977.923i	0.225525	−	0.0788057i
$537$	3196.52	−	893.947i	0.256871	−	0.0718374i
$538$	−6164.62	−	1489.06i	−0.494007	−	0.119327i
$539$	−1934.64			−0.154603
$540$	−18223.6	−	3307.27i	−1.45225	−	0.263560i
$541$	6050.08			0.480801			0.240400	−	0.970674i	$-0.422721\pi$
$541$	6050.08			0.480801			0.240400	+	0.970674i	$0.422721\pi$
$542$	17387.2	+	4199.86i	1.37794	+	0.332840i
$543$	−20171.7	+	5641.29i	−1.59420	+	0.445840i
$544$	−7988.88	−	19672.5i	−0.629633	−	1.55046i
$545$	7726.70	+	4461.01i	0.607294	+	0.350622i
$546$	−7302.32	+	260.707i	−0.572364	+	0.0204345i
$547$	−11232.1	+	6484.87i	−0.877972	+	0.506898i	−0.869989	−	0.493071i	$-0.835874\pi$
$547$	−11232.1	+	6484.87i	−0.877972	+	0.506898i	−0.00798299	+	0.999968i	$0.502541\pi$
$548$	−5175.27	+	256.800i	−0.403425	+	0.0200181i
$549$	−18090.1	−	9925.11i	−1.40631	−	0.771572i
$550$	−3849.39	−	3663.12i	−0.298434	−	0.283992i
$551$	−16.2007	−	28.0605i	−0.00125259	−	0.00216954i
$552$	2364.84	+	3391.76i	0.182345	+	0.261527i
$553$	−6246.17	+	10818.7i	−0.480315	+	0.831930i
$554$	−3395.95	+	1000.80i	−0.260434	+	0.0767504i
$555$	19402.9	+	4973.03i	1.48398	+	0.380349i
$556$	11585.8	+	17949.6i	0.883716	+	1.36912i
$557$		−	2223.88i		−	0.169172i	−0.996416	−	0.0845859i	$-0.973043\pi$
$557$		−	2223.88i		−	0.169172i	0.996416	−	0.0845859i	$-0.0269567\pi$
$558$	−2247.79	+	10282.6i	−0.170532	+	0.780103i
$559$			9329.75i			0.705915i
$560$	−13701.3	−	19080.4i	−1.03390	−	1.43981i
$561$	5436.00	−	5555.78i	0.409105	−	0.418120i
$562$	1098.96	+	3729.06i	0.0824855	+	0.279895i
$563$	8913.79	−	15439.1i	0.667267	−	1.15574i	−0.311398	−	0.950280i	$-0.600797\pi$
$563$	8913.79	−	15439.1i	0.667267	−	1.15574i	0.978665	−	0.205461i	$-0.0658695\pi$
$564$	3067.53	+	9186.48i	0.229018	+	0.685852i
$565$	−10583.3	−	18330.9i	−0.788043	−	1.36493i
$566$	9019.67	−	9478.33i	0.669832	−	0.703894i
$567$	−706.513	−	16198.9i	−0.0523294	−	1.19981i
$568$	335.077	−	389.028i	0.0247527	−	0.0287381i
$569$	9765.76	−	5638.26i	0.719511	−	0.415410i	−0.0950615	−	0.995471i	$-0.530305\pi$
$569$	9765.76	−	5638.26i	0.719511	−	0.415410i	0.814573	+	0.580061i	$0.196971\pi$
$570$	−5940.69	−	3152.78i	−0.436541	−	0.231676i
$571$	−6527.00	−	3768.37i	−0.478365	−	0.276184i	0.241370	−	0.970433i	$-0.422403\pi$
$571$	−6527.00	−	3768.37i	−0.478365	−	0.276184i	−0.719735	+	0.694249i	$0.755737\pi$
$572$	−2029.13	−	1041.01i	−0.148325	−	0.0760957i
$573$	13606.2	+	13312.8i	0.991984	+	0.970597i
$574$	226.096	−	936.023i	0.0164409	−	0.0680642i
$575$	−5180.59			−0.375731
$576$	−8843.47	−	10625.3i	−0.639719	−	0.768609i
$577$	−16888.0			−1.21847			−0.609233	−	0.792991i	$-0.708523\pi$
$577$	−16888.0			−1.21847			−0.609233	+	0.792991i	$0.708523\pi$
$578$	−5874.14	+	24318.6i	−0.422720	+	1.75004i
$579$	1828.91	−	7135.71i	0.131272	−	0.512176i
$580$	137.244	+	70.4104i	0.00982540	+	0.00504075i
$581$	13179.5	+	7609.18i	0.941097	+	0.543343i
$582$	6588.66	−	4124.20i	0.469259	−	0.293735i
$583$	1998.51	−	1153.84i	0.141973	−	0.0819679i
$584$	−5727.57	+	6649.77i	−0.405836	+	0.471180i
$585$	4790.62	−	8731.66i	0.338577	−	0.617111i
$586$	12434.0	−	13066.3i	0.876527	−	0.921099i
$587$	8103.83	+	14036.3i	0.569814	+	0.986947i	0.996584	+	0.0825870i	$0.0263182\pi$
$587$	8103.83	+	14036.3i	0.569814	+	0.986947i	−0.426770	+	0.904360i	$0.640348\pi$
$588$	4181.39	−	4720.40i	0.293261	−	0.331064i
$589$	−1911.00	+	3309.96i	−0.133687	+	0.231552i
$590$	8278.38	+	28090.7i	0.577654	+	1.96013i
$591$	1227.22	+	4388.22i	0.0854166	+	0.305427i
$592$	8720.10	+	12143.6i	0.605395	+	0.843073i
$593$			22320.8i			1.54571i	0.634583	+	0.772855i	$0.281172\pi$
$593$			22320.8i			1.54571i	−0.634583	+	0.772855i	$0.718828\pi$
$594$	2274.37	−	4520.78i	0.157102	−	0.312273i
$595$			43051.3i			2.96627i
$596$	452.109	+	700.442i	0.0310723	+	0.0481397i
$597$	2078.85	+	7433.40i	0.142515	+	0.509596i
$598$	−2132.74	+	628.522i	−0.145843	+	0.0429802i
$599$	4883.72	−	8458.84i	0.333127	−	0.576993i	−0.649996	−	0.759938i	$-0.725229\pi$
$599$	4883.72	−	8458.84i	0.333127	−	0.576993i	0.983123	+	0.182944i	$0.0585628\pi$
$600$	17257.5	−	1475.07i	1.17423	−	0.100366i
$601$	−9316.81	−	16137.2i	−0.632347	−	1.09526i	−0.987071	−	0.160286i	$-0.948758\pi$
$601$	−9316.81	−	16137.2i	−0.632347	−	1.09526i	0.354724	−	0.934971i	$-0.384575\pi$
$602$	−19021.0	−	18100.6i	−1.28777	−	1.22546i
$603$	−3536.58	+	77.0870i	−0.238840	+	0.00520602i
$604$	−21984.1	+	1090.86i	−1.48099	+	0.0734876i
$605$	−16697.1	+	9640.08i	−1.12204	+	0.647810i
$606$	−11181.8	−	17863.7i	−0.749557	−	1.19746i
$607$	−371.545	−	214.512i	−0.0248444	−	0.0143439i	0.487526	−	0.873108i	$-0.337899\pi$
$607$	−371.545	−	214.512i	−0.0248444	−	0.0143439i	−0.512371	+	0.858764i	$0.671233\pi$
$608$	−1888.71	−	4650.92i	−0.125983	−	0.310230i
$609$	−33.5271	+	130.810i	−0.00223085	+	0.00870393i
$610$	34672.4	+	8375.10i	2.30138	+	0.555898i
$611$	−5208.01			−0.344834
$612$	1806.77	+	25271.3i	0.119337	+	1.66917i
$613$	−4211.54			−0.277492			−0.138746	−	0.990328i	$-0.544307\pi$
$613$	−4211.54			−0.277492			−0.138746	+	0.990328i	$0.544307\pi$
$614$	−18171.5	−	4389.31i	−1.19437	−	0.288499i
$615$	938.139	+	917.913i	0.0615112	+	0.0601851i
$616$	6059.06	−	2117.23i	0.396309	−	0.138483i
$617$	−23419.6	−	13521.3i	−1.52810	−	0.882248i	−0.999442	−	0.0334113i	$-0.989363\pi$
$617$	−23419.6	−	13521.3i	−1.52810	−	0.882248i	−0.528656	−	0.848836i	$-0.677304\pi$
$618$	1583.90	−	2984.50i	0.103097	−	0.194263i
$619$	8368.15	−	4831.35i	0.543367	−	0.313713i	−0.203075	−	0.979163i	$-0.565094\pi$
$619$	8368.15	−	4831.35i	0.543367	−	0.313713i	0.746442	+	0.665450i	$0.231760\pi$
$620$	−901.744	−	18172.8i	−0.0584111	−	1.17716i
$621$	−1432.05	−	4721.41i	−0.0925380	−	0.305095i
$622$	−10524.9	−	10015.6i	−0.678471	−	0.645640i
$623$	3091.65	+	5354.89i	0.198819	+	0.344364i
$624$	6925.59	−	2700.98i	0.444304	−	0.173278i
$625$	6168.97	−	10685.0i	0.394814	−	0.683838i
$626$	−16828.7	+	4959.46i	−1.07446	+	0.316645i
$627$	1285.17	−	1313.48i	0.0818574	−	0.0836611i
$628$	−7817.66	+	5046.00i	−0.496749	+	0.320633i
$629$		−	27399.8i		−	1.73688i
$630$	8507.44	+	26707.1i	0.538007	+	1.68895i
$631$		−	10846.5i		−	0.684297i	−0.939646	−	0.342149i	$-0.888845\pi$
$631$		−	10846.5i		−	0.684297i	0.939646	−	0.342149i	$-0.111155\pi$
$632$	2368.10	−	12486.3i	0.149048	−	0.785885i
$633$	1548.55	+	396.899i	0.0972344	+	0.0249215i
$634$	−1459.29	−	4951.75i	−0.0914130	−	0.310188i
$635$	22069.6	−	38225.6i	1.37922	−	2.38888i
$636$	−1504.14	+	7370.06i	−0.0937782	+	0.459500i
$637$	1695.49	+	2936.67i	0.105459	+	0.182661i
$638$	−29.0545	+	30.5319i	−0.00180294	+	0.00189462i
$639$	−523.775	+	317.818i	−0.0324260	+	0.0196756i
$640$	19561.8	+	13726.6i	1.20820	+	0.847798i
$641$	12772.5	−	7374.18i	0.787023	−	0.454388i	−0.0518903	−	0.998653i	$-0.516525\pi$
$641$	12772.5	−	7374.18i	0.787023	−	0.454388i	0.838914	+	0.544265i	$0.183191\pi$
$642$	878.919	+	24618.3i	0.0540314	+	1.51340i
$643$	12787.4	+	7382.82i	0.784271	+	0.452799i	0.837942	−	0.545759i	$-0.183759\pi$
$643$	12787.4	+	7382.82i	0.784271	+	0.452799i	−0.0536706	+	0.998559i	$0.517092\pi$
$644$	2856.31	−	5567.52i	0.174774	−	0.340669i
$645$	34466.3	−	9638.94i	2.10404	−	0.588423i
$646$	−2160.12	+	8942.78i	−0.131562	+	0.544658i
$647$	27157.4			1.65018			0.825090	−	0.565002i	$-0.191125\pi$
$647$	27157.4			1.65018			0.825090	+	0.565002i	$0.191125\pi$
$648$	6114.75	+	15320.2i	0.370694	+	0.928755i
$649$	−8001.72			−0.483968
$650$	−2186.85	+	9053.43i	−0.131962	+	0.546315i
$651$	15340.2	−	4290.10i	0.923550	−	0.258283i
$652$	−10701.2	+	20858.7i	−0.642777	+	1.25290i
$653$	−2658.60	−	1534.94i	−0.159325	−	0.0919861i	0.418218	−	0.908347i	$-0.362655\pi$
$653$	−2658.60	−	1534.94i	−0.159325	−	0.0919861i	−0.577542	+	0.816361i	$0.695988\pi$
$654$	−283.511	−	7941.07i	−0.0169513	−	0.474802i
$655$	11815.9	−	6821.90i	0.704862	−	0.406952i
$656$	96.9813	+	974.823i	0.00577208	+	0.0580190i
$657$	8953.04	−	5432.56i	0.531646	−	0.322594i
$658$	10104.1	−	10617.9i	0.598628	−	0.629068i
$659$	579.767	+	1004.19i	0.0342709	+	0.0593589i	0.882652	−	0.470027i	$-0.155756\pi$
$659$	579.767	+	1004.19i	0.0342709	+	0.0593589i	−0.848381	+	0.529386i	$0.822422\pi$
$660$	−1749.35	+	8571.59i	−0.103172	+	0.505528i
$661$	−8919.74	+	15449.4i	−0.524868	+	0.909097i	0.474713	+	0.880141i	$0.342552\pi$
$661$	−8919.74	+	15449.4i	−0.524868	+	0.909097i	−0.999581	+	0.0289568i	$0.990781\pi$
$662$	3179.97	+	10790.5i	0.186697	+	0.633509i
$663$	−13197.4	−	3382.53i	−0.773066	−	0.198140i
$664$	−15211.0	−	2884.86i	−0.889010	−	0.168606i
$665$			10178.1i			0.593517i
$666$	−5414.51	−	16997.6i	−0.315027	−	0.988956i
$667$			41.0905i			0.00238535i
$668$	5860.57	−	3782.78i	0.339449	−	0.219102i
$669$	14185.2	−	14497.7i	0.819777	−	0.837841i
$670$	5865.67	−	1728.62i	0.338225	−	0.0996755i
$671$	−4873.09	+	8440.44i	−0.280363	+	0.485603i
$672$	−7929.69	+	19359.7i	−0.455200	+	1.11134i
$673$	6058.30	+	10493.3i	0.346999	+	0.601020i	0.985715	−	0.168423i	$-0.0538673\pi$
$673$	6058.30	+	10493.3i	0.346999	+	0.601020i	−0.638716	+	0.769443i	$0.720534\pi$
$674$	−2372.07	−	2257.28i	−0.135562	−	0.129002i
$675$	−20127.4	−	4693.79i	−1.14771	−	0.267651i
$676$	−672.953	−	13562.0i	−0.0382882	−	0.771620i
$677$	−18626.5	+	10754.0i	−1.05742	+	0.610504i	−0.924718	−	0.380652i	$-0.875700\pi$
$677$	−18626.5	+	10754.0i	−1.05742	+	0.610504i	−0.132705	+	0.991156i	$0.542366\pi$
$678$	−8837.23	+	16651.7i	−0.500578	+	0.943225i
$679$	−10187.4	−	5881.70i	−0.575783	−	0.332428i
$680$	−14447.6	−	41346.0i	−0.814768	−	2.33169i
$681$	−7163.53	−	7009.09i	−0.403094	−	0.394403i
$682$	4832.57	+	1167.30i	0.271332	+	0.0655402i
$683$	−33849.4			−1.89636			−0.948179	−	0.317738i	$-0.897077\pi$
$683$	−33849.4			−1.89636			−0.948179	+	0.317738i	$0.897077\pi$
$684$	427.152	+	5974.58i	0.0238780	+	0.333982i
$685$	−10688.4			−0.596178
$686$	11698.2	+	2825.68i	0.651075	+	0.157267i
$687$	2963.88	−	11563.9i	0.164598	−	0.642200i
$688$	24342.0	+	11000.3i	1.34888	+	0.609570i
$689$	−3502.93	−	2022.42i	−0.193688	−	0.111826i
$690$	4525.33	+	7229.48i	0.249676	+	0.398872i
$691$	1786.94	−	1031.69i	0.0983771	−	0.0567980i	−0.450004	−	0.893026i	$-0.648578\pi$
$691$	1786.94	−	1031.69i	0.0983771	−	0.0567980i	0.548381	+	0.836228i	$0.315244\pi$
$692$	−18638.8	+	924.866i	−1.02390	+	0.0508065i
$693$	−7656.80	+	166.896i	−0.419708	+	0.00914841i
$694$	−5088.08	−	4841.87i	−0.278301	−	0.264834i
$695$	22034.1	+	38164.2i	1.20259	+	2.08295i
$696$	−11.6997	−	136.880i	−0.000637177	−	0.00745464i
$697$	897.708	−	1554.88i	0.0487850	−	0.0844981i
$698$	16207.3	−	4776.33i	0.878877	−	0.259007i
$699$	4711.47	+	16846.9i	0.254941	+	0.911602i
$700$	−14215.0	−	22023.0i	−0.767538	−	1.18913i
$701$			19641.7i			1.05828i	0.848534	+	0.529141i	$0.177486\pi$
$701$			19641.7i			1.05828i	−0.848534	+	0.529141i	$0.822514\pi$
$702$	−8855.49	+	509.578i	−0.476110	+	0.0273971i
$703$		−	6477.79i		−	0.347531i
$704$	−5108.54	+	4066.74i	−0.273488	+	0.217715i
$705$	5380.61	+	19239.6i	0.287441	+	1.02781i
$706$	824.598	+	2798.07i	0.0439577	+	0.149160i
$707$	−15946.9	+	27620.8i	−0.848295	+	1.46929i
$708$	17294.3	−	19523.6i	0.918022	−	1.03636i
$709$	2685.98	+	4652.26i	0.142277	+	0.246431i	0.928354	−	0.371698i	$-0.121224\pi$
$709$	2685.98	+	4652.26i	0.142277	+	0.246431i	−0.786077	+	0.618129i	$0.787891\pi$
$710$	730.097	−	767.223i	0.0385916	−	0.0405540i
$711$	−7294.41	+	13295.2i	−0.384756	+	0.701280i
$712$	−4766.24	−	4105.25i	−0.250874	−	0.216083i
$713$	4197.58	−	2423.47i	0.220478	−	0.127293i
$714$	32500.3	−	20343.7i	1.70349	−	1.06631i
$715$	−4074.00	−	2352.13i	−0.213090	−	0.123027i
$716$	4546.74	+	2332.63i	0.237318	+	0.121752i
$717$	−793.591	+	3096.29i	−0.0413350	+	0.161274i
$718$	−2801.85	+	11599.5i	−0.145633	+	0.602910i
$719$	12836.0			0.665788			0.332894	−	0.942964i	$-0.391975\pi$
$719$	12836.0			0.665788			0.332894	+	0.942964i	$0.391975\pi$
$720$	−17133.2	−	22794.3i	−0.886827	−	1.17985i
$721$	−5113.29			−0.264118
$722$	4044.41	−	16743.6i	0.208473	−	0.863065i
$723$	−16310.5	−	15958.8i	−0.838994	−	0.820906i
$724$	−28692.4	−	14720.1i	−1.47285	−	0.755620i
$725$	149.065	+	86.0630i	0.00763607	+	0.00440869i
$726$	15167.6	+	8049.60i	0.775377	+	0.411500i
$727$	−29745.3	+	17173.5i	−1.51746	+	0.876106i	−0.517670	+	0.855580i	$0.673200\pi$
$727$	−29745.3	+	17173.5i	−1.51746	+	0.876106i	−0.999789	+	0.0205251i	$0.993466\pi$
$728$	−8523.89	−	7341.78i	−0.433951	−	0.373770i
$729$	−1285.97	−	19640.9i	−0.0653343	−	0.997863i
$730$	−12479.8	+	13114.4i	−0.632735	+	0.664910i
$731$	−24478.3	−	42397.6i	−1.23852	−	2.14519i
$732$	−10061.8	−	30132.5i	−0.508051	−	1.52149i
$733$	−4537.51	+	7859.19i	−0.228645	+	0.396024i	−0.957407	−	0.288743i	$-0.906763\pi$
$733$	−4537.51	+	7859.19i	−0.228645	+	0.396024i	0.728762	+	0.684767i	$0.240096\pi$
$734$	−2430.80	−	8248.33i	−0.122238	−	0.414784i
$735$	9097.08	−	9297.53i	0.456532	−	0.466591i
$736$	−874.765	+	6305.54i	−0.0438101	+	0.315795i
$737$			1670.85i			0.0835098i
$738$	249.637	−	1141.98i	0.0124516	−	0.0569603i
$739$			16863.2i			0.839410i	0.907661	+	0.419705i	$0.137866\pi$
$739$			16863.2i			0.839410i	−0.907661	+	0.419705i	$0.862134\pi$
$740$	16723.8	+	25909.8i	0.830781	+	1.28711i
$741$	−3120.09	−	799.689i	−0.154682	−	0.0396455i
$742$	10919.2	−	3217.92i	0.540239	−	0.159210i
$743$	15021.9	−	26018.6i	0.741721	−	1.28470i	−0.209990	−	0.977704i	$-0.567343\pi$
$743$	15021.9	−	26018.6i	0.741721	−	1.28470i	0.951711	−	0.306995i	$-0.0993235\pi$
$744$	−13292.9	+	9268.22i	−0.655028	+	0.456706i
$745$	859.832	+	1489.27i	0.0422843	+	0.0732386i
$746$	10486.2	+	9978.81i	0.514649	+	0.489745i
$747$	16196.4	+	8886.16i	0.793303	+	0.435244i
$748$	11952.3	−	593.081i	0.584252	−	0.0289909i
$749$	32285.6	−	18640.1i	1.57502	−	0.909338i
$750$	5408.17	−	193.082i	0.263305	−	0.00940048i
$751$	−7313.00	−	4222.17i	−0.355333	−	0.205152i	0.311698	−	0.950181i	$-0.399102\pi$
$751$	−7313.00	−	4222.17i	−0.355333	−	0.205152i	−0.667032	+	0.745029i	$0.732435\pi$
$752$	−6140.57	+	13588.1i	−0.297771	+	0.658920i
$753$	−38662.5	+	10812.5i	−1.87110	+	0.523277i
$754$	71.8084	+	17.3453i	0.00346831	+	0.000837769i
$755$	−45403.2			−2.18860
$756$	16141.6	−	19042.8i	0.776540	−	0.916110i
$757$	35193.1			1.68971			0.844857	−	0.534992i	$-0.179685\pi$
$757$	35193.1			1.68971			0.844857	+	0.534992i	$0.179685\pi$
$758$	7809.86	+	1886.47i	0.374231	+	0.0903952i
$759$	−2244.31	+	627.651i	−0.107330	+	0.0300162i
$760$	−3415.68	−	9774.93i	−0.163026	−	0.466545i
$761$	13659.8	+	7886.50i	0.650681	+	0.375671i	0.788717	−	0.614756i	$-0.210746\pi$
$761$	13659.8	+	7886.50i	0.650681	+	0.375671i	−0.138036	+	0.990427i	$0.544079\pi$
$762$	−39286.1	+	1402.59i	−1.86770	+	0.0666804i
$763$	−10414.3	+	6012.70i	−0.494133	+	0.285288i
$764$	1452.47	+	29271.5i	0.0687806	+	1.38613i
$765$	1138.87	+	52248.7i	0.0538247	+	2.46936i
$766$	11532.9	+	10974.8i	0.543996	+	0.517672i
$767$	7012.57	+	12146.1i	0.330129	+	0.571801i
$768$	1118.63	−	21254.0i	0.0525588	−	0.998618i
$769$	10370.9	−	17962.9i	0.486325	−	0.842340i	−0.513551	−	0.858059i	$-0.671670\pi$
$769$	10370.9	−	17962.9i	0.486325	−	0.842340i	0.999876	+	0.0157189i	$0.00500369\pi$
$770$	12699.4	−	3742.53i	0.594355	−	0.175158i
$771$	12919.4	+	3311.28i	0.603476	+	0.154673i
$772$	9528.70	−	6150.42i	0.444230	−	0.286734i
$773$		−	35223.1i		−	1.63892i	−0.573133	−	0.819462i	$-0.694272\pi$
$773$		−	35223.1i		−	1.63892i	0.573133	−	0.819462i	$-0.305728\pi$
$774$	−23563.5	−	21464.4i	−1.09428	−	0.996800i
$775$		−	20303.6i		−	0.941067i
$776$	11757.7	+	2229.92i	0.543915	+	0.103156i
$777$	−18880.8	+	19296.8i	−0.871742	+	0.890950i
$778$	2847.96	+	9663.86i	0.131239	+	0.445329i
$779$	212.234	−	367.600i	0.00976133	−	0.0169071i
$780$	14544.3	−	4856.58i	0.667651	−	0.222940i
$781$	144.690	+	250.611i	0.00662923	+	0.0114822i
$782$	8042.85	−	8451.84i	0.367790	−	0.386493i
$783$	−37.2294	+	159.643i	−0.00169920	+	0.00728631i
$784$	9661.09	−	961.144i	0.440101	−	0.0437839i
$785$	−16621.8	+	9596.62i	−0.755743	+	0.436329i
$786$	−10733.5	−	5696.39i	−0.487090	−	0.258503i
$787$	19651.8	+	11346.0i	0.890102	+	0.513901i	0.873976	−	0.485969i	$-0.161533\pi$
$787$	19651.8	+	11346.0i	0.890102	+	0.513901i	0.0161261	+	0.999870i	$0.494867\pi$
$788$	−3202.26	+	6241.83i	−0.144766	+	0.282178i
$789$	−14885.3	−	14564.4i	−0.671650	−	0.657170i
$790$	6155.23	−	25482.3i	0.277207	−	1.14762i
$791$	28529.2			1.28240
$792$	7297.51	−	2729.84i	0.327406	−	0.122476i
$793$	17082.8			0.764977
$794$	−6260.87	+	25919.6i	−0.279836	+	1.15850i
$795$	−3852.26	+	15030.1i	−0.171856	+	0.670518i
$796$	−5424.45	+	10573.3i	−0.241538	+	0.470805i
$797$	27480.8	+	15866.1i	1.22136	+	0.705150i	0.965207	−	0.261488i	$-0.0842130\pi$
$797$	27480.8	+	15866.1i	1.22136	+	0.705150i	0.256149	+	0.966637i	$0.417546\pi$
$798$	7683.64	−	4809.61i	0.340849	−	0.213356i
$799$	23667.0	−	13664.2i	1.04791	−	0.605010i
$800$	21042.7	+	16380.2i	0.929964	+	0.723910i
$801$	3893.80	+	6417.12i	0.171761	+	0.283068i
$802$	−16829.9	+	17685.8i	−0.741005	+	0.778686i
$803$	−2473.24	−	4283.77i	−0.108691	−	0.188258i
$804$	−4076.77	−	3611.26i	−0.178827	−	0.158407i
$805$	6453.75	−	11178.2i	0.282565	−	0.489417i
$806$	−2463.28	−	8358.56i	−0.107650	−	0.365282i
$807$	3137.91	+	11220.3i	0.136877	+	0.489435i
$808$	6045.92	−	31878.4i	0.263236	−	1.38797i
$809$			18376.4i			0.798613i	0.916817	+	0.399307i	$0.130749\pi$
$809$			18376.4i			0.798613i	−0.916817	+	0.399307i	$0.869251\pi$
$810$	11031.5	+	32187.8i	0.478526	+	1.39625i
$811$		−	28834.7i		−	1.24849i	−0.781229	−	0.624244i	$-0.785407\pi$
$811$		−	28834.7i		−	1.24849i	0.781229	−	0.624244i	$-0.214593\pi$
$812$	−174.678	+	112.748i	−0.00754926	+	0.00487276i
$813$	−8850.39	−	31646.6i	−0.381792	−	1.36519i
$814$	−8082.44	+	2381.91i	−0.348021	+	0.102563i
$815$	−24179.0	+	41879.2i	−1.03921	+	1.79996i
$816$	−24385.8	+	30444.7i	−1.04617	+	1.30610i
$817$	−5787.09	−	10023.5i	−0.247815	−	0.429228i
$818$	12016.8	+	11435.3i	0.513638	+	0.488783i
$819$	6963.63	+	11476.3i	0.297105	+	0.489639i
$820$	100.147	+	2018.25i	0.00426497	+	0.0859517i
$821$	−14471.4	+	8355.08i	−0.615172	+	0.355170i	−0.774987	−	0.631977i	$-0.782244\pi$
$821$	−14471.4	+	8355.08i	−0.615172	+	0.355170i	0.159815	+	0.987147i	$0.448910\pi$
$822$	5050.75	+	8068.87i	0.214313	+	0.342377i
$823$	−453.509	−	261.833i	−0.0192082	−	0.0110898i	0.490365	−	0.871517i	$-0.336863\pi$
$823$	−453.509	−	261.833i	−0.0192082	−	0.0110898i	−0.509573	+	0.860427i	$0.670197\pi$
$824$	4910.76	−	1715.98i	0.207615	−	0.0725473i
$825$	−2423.70	+	9456.37i	−0.102282	+	0.399065i
$826$	−38368.0	−	9267.77i	−1.61622	−	0.390396i
$827$	28676.4			1.20577			0.602887	−	0.797826i	$-0.294017\pi$
$827$	28676.4			1.20577			0.602887	+	0.797826i	$0.294017\pi$
$828$	3319.25	−	6832.52i	0.139314	−	0.286771i
$829$	14521.0			0.608365			0.304183	−	0.952614i	$-0.401617\pi$
$829$	14521.0			0.608365			0.304183	+	0.952614i	$0.401617\pi$
$830$	−31042.9	−	7498.40i	−1.29821	−	0.313582i
$831$	4648.89	+	4548.67i	0.194065	+	0.189881i
$832$	10650.1	+	4190.43i	0.443781	+	0.174612i
$833$	−15409.8	−	8896.84i	−0.640957	−	0.370057i
$834$	18398.8	−	34668.3i	0.763906	−	1.43941i
$835$	12460.7	−	7194.18i	0.516431	−	0.298161i
$836$	2825.74	−	140.215i	0.116902	−	0.00580076i
$837$	18504.0	−	5612.44i	0.764149	−	0.231773i
$838$	14252.0	+	13562.3i	0.587501	+	0.559072i
$839$	−15594.8	−	27010.9i	−0.641706	−	1.11147i	−0.985052	−	0.172258i	$-0.944894\pi$
$839$	−15594.8	−	27010.9i	−0.641706	−	1.11147i	0.343346	−	0.939209i	$-0.388440\pi$
$840$	−18315.9	+	39074.4i	−0.752331	+	1.60499i
$841$	−12193.8	+	21120.3i	−0.499972	+	0.865977i
$842$	25491.4	−	7512.37i	1.04334	−	0.307474i
$843$	4994.84	−	5104.89i	0.204070	−	0.208567i
$844$	1334.73	+	2067.87i	0.0544352	+	0.0843352i
$845$		−	28009.3i		−	1.14029i
$846$	11981.8	−	13153.5i	0.486930	−	0.534548i
$847$		−	25986.4i		−	1.05420i
$848$	−9406.81	+	6754.86i	−0.380933	+	0.273541i
$849$	−23284.4	−	5967.86i	−0.941245	−	0.241245i
$850$	−13815.5	−	46879.5i	−0.557491	−	1.89171i
$851$	−4107.46	+	7114.32i	−0.165455	+	0.286576i
$852$	−924.196	−	188.617i	−0.0371625	−	0.00758440i
$853$	−6544.93	−	11336.2i	−0.262713	−	0.455032i	0.704249	−	0.709953i	$-0.251284\pi$
$853$	−6544.93	−	11336.2i	−0.262713	−	0.455032i	−0.966962	+	0.254921i	$0.917951\pi$
$854$	−33142.2	+	34827.5i	−1.32799	+	1.39552i
$855$	269.249	+	12352.5i	0.0107697	+	0.494091i
$856$	−24751.3	+	28736.5i	−0.988297	+	1.14742i
$857$	−15414.8	+	8899.73i	−0.614421	+	0.354736i	−0.774694	−	0.632337i	$-0.782096\pi$
$857$	−15414.8	+	8899.73i	−0.614421	+	0.354736i	0.160273	+	0.987073i	$0.448763\pi$
$858$	149.485	+	4187.03i	0.00594794	+	0.166600i
$859$	36673.2	+	21173.3i	1.45666	+	0.841004i	0.998845	−	0.0480428i	$-0.0152984\pi$
$859$	36673.2	+	21173.3i	1.45666	+	0.841004i	0.457816	+	0.889047i	$0.348632\pi$
$860$	49025.1	+	25151.4i	1.94388	+	0.997275i
$861$	−1703.67	+	476.453i	−0.0674343	+	0.0188589i
$862$	−4878.54	+	20196.9i	−0.192765	+	0.798037i
$863$	−41963.9			−1.65524			−0.827618	−	0.561291i	$-0.810305\pi$
$863$	−41963.9			−1.65524			−0.827618	+	0.561291i	$0.810305\pi$
$864$	−9111.64	+	23705.5i	−0.358778	+	0.933423i
$865$	−38494.2			−1.51311
$866$	9080.31	−	37591.9i	0.356306	−	1.47509i
$867$	44262.6	−	12378.6i	1.73384	−	0.484891i
$868$	21820.0	+	11194.4i	0.853249	+	0.437744i
$869$	6203.26	+	3581.45i	0.242153	+	0.139807i
$870$	−10.1107	−	283.197i	−0.000394005	−	0.0110360i
$871$	2536.26	−	1464.31i	0.0986656	−	0.0569646i
$872$	7983.99	−	9269.50i	0.310060	−	0.359982i
$873$	−12519.4	−	6868.76i	−0.485359	−	0.266291i
$874$	1901.47	−	1998.16i	0.0735907	−	0.0773328i
$875$	−4094.88	−	7092.54i	−0.158208	−	0.274025i
$876$	15797.6	+	3224.08i	0.609304	+	0.124351i
$877$	21665.7	−	37526.1i	0.834206	−	1.44489i	−0.0604689	−	0.998170i	$-0.519260\pi$
$877$	21665.7	−	37526.1i	0.834206	−	1.44489i	0.894675	−	0.446717i	$-0.147407\pi$
$878$	−4612.37	−	15651.0i	−0.177289	−	0.601588i
$879$	−32098.6	−	8226.97i	−1.23169	−	0.315687i
$880$	−10940.4	+	7856.09i	−0.419091	+	0.300942i
$881$		−	38532.4i		−	1.47354i	−0.676142	−	0.736771i	$-0.736349\pi$
$881$		−	38532.4i		−	1.47354i	0.676142	−	0.736771i	$-0.263651\pi$
$882$	−11317.7	−	2474.06i	−0.432070	−	0.0944511i
$883$		−	7198.92i		−	0.274364i	−0.990546	−	0.137182i	$-0.956196\pi$
$883$		−	7198.92i		−	0.274364i	0.990546	−	0.137182i	$-0.0438045\pi$
$884$	−11375.1	−	17623.2i	−0.432789	−	0.670510i
$885$	37625.7	−	38454.7i	1.42912	−	1.46061i
$886$	−26189.0	+	7717.94i	−0.993042	+	0.292652i
$887$	7110.04	−	12315.0i	0.269145	−	0.466173i	−0.699496	−	0.714636i	$-0.746592\pi$
$887$	7110.04	−	12315.0i	0.269145	−	0.466173i	0.968641	+	0.248463i	$0.0799255\pi$
$888$	11657.1	−	24868.7i	0.440524	−	0.939795i
$889$	29746.1	+	51521.7i	1.12222	+	1.94374i
$890$	−9399.76	−	8944.90i	−0.354023	−	0.336892i
$891$	−9288.19	+	405.103i	−0.349232	+	0.0152317i
$892$	31189.5	−	1547.64i	1.17074	−	0.0580928i
$893$	5595.30	−	3230.45i	0.209675	−	0.121056i
$894$	717.972	−	1352.85i	0.0268597	−	0.0506110i
$895$	9128.76	+	5270.49i	0.340940	+	0.196842i
$896$	−29205.5	+	13583.1i	−1.08894	+	0.506450i
$897$	2919.61	+	2856.67i	0.108677	+	0.106334i
$898$	−31596.3	−	7632.05i	−1.17414	−	0.283614i
$899$	−161.041			−0.00597442
$900$	−17834.5	−	26351.9i	−0.660536	−	0.975997i
$901$	21224.7			0.784791
$902$	−536.700	−	129.640i	−0.0198117	−	0.00478551i
$903$	−11976.3	+	46726.9i	−0.441357	+	1.72201i
$904$	−27399.1	+	9574.14i	−1.00805	+	0.352247i
$905$	−57607.4	−	33259.7i	−2.11595	−	1.22164i
$906$	21455.1	+	34275.8i	0.786752	+	1.25688i
$907$	−43283.2	+	24989.6i	−1.58456	+	0.914845i	−0.590377	+	0.807127i	$0.701021\pi$
$907$	−43283.2	+	24989.6i	−1.58456	+	0.914845i	−0.994181	+	0.107718i	$0.965646\pi$
$908$	−764.709	−	15411.1i	−0.0279491	−	0.563256i
$909$	−18623.1	+	33943.6i	−0.679526	+	1.23855i
$910$	−16810.4	−	15997.0i	−0.612374	−	0.582741i
$911$	7306.31	+	12654.9i	0.265718	+	0.460237i	0.967751	−	0.251907i	$-0.0810577\pi$
$911$	7306.31	+	12654.9i	0.265718	+	0.460237i	−0.702034	+	0.712144i	$0.747724\pi$
$912$	−5765.23	+	7197.67i	−0.209326	+	0.261336i
$913$	4362.98	−	7556.90i	0.158153	−	0.273929i
$914$	−47864.2	+	14105.7i	−1.73218	+	0.510476i
$915$	−17648.9	−	63107.8i	−0.637656	−	2.28009i
$916$	15442.0	−	9967.21i	0.557005	−	0.359526i
$917$			18389.6i			0.662244i
$918$	38905.5	−	25549.7i	1.39877	−	0.918589i
$919$		−	45594.4i		−	1.63658i	−0.574804	−	0.818291i	$-0.694922\pi$
$919$		−	45594.4i		−	1.63658i	0.574804	−	0.818291i	$-0.305078\pi$
$920$	−2446.80	+	12901.3i	−0.0876833	+	0.462329i
$921$	9249.63	+	33074.2i	0.330929	+	1.18331i
$922$	10286.9	+	34906.0i	0.367441	+	1.24682i
$923$	253.608	−	439.263i	0.00904401	−	0.0156647i
$924$	−8826.34	−	7818.48i	−0.314248	−	0.278365i
$925$	17205.9	+	29801.5i	0.611597	+	1.05932i
$926$	26982.8	−	28354.9i	0.957571	−	1.00626i
$927$	−6205.70	+	135.266i	−0.219873	+	0.00479258i
$928$	129.922	−	166.903i	0.00459579	−	0.00590393i
$929$	44791.1	−	25860.1i	1.58186	−	0.913287i	0.587272	−	0.809390i	$-0.300202\pi$
$929$	44791.1	−	25860.1i	1.58186	−	0.913287i	0.994588	−	0.103897i	$-0.0331314\pi$
$930$	−28333.6	+	17735.5i	−0.999026	+	0.625345i
$931$	−3643.14	−	2103.37i	−0.128248	−	0.0740442i
$932$	−12293.9	+	23963.2i	−0.432081	+	0.842211i
$933$	−6626.81	+	25855.3i	−0.232532	+	0.907250i
$934$	53.8882	−	223.094i	0.00188788	−	0.00781570i
$935$	24684.9			0.863404
$936$	−10539.2	−	8684.79i	−0.368037	−	0.303281i
$937$	−42197.0			−1.47120			−0.735601	−	0.677415i	$-0.763100\pi$
$937$	−42197.0			−1.47120			−0.735601	+	0.677415i	$0.763100\pi$
$938$	−1935.22	+	8011.70i	−0.0673638	+	0.278882i
$939$	23037.7	+	22541.0i	0.800646	+	0.783384i
$940$	−14039.9	+	27366.6i	−0.487162	+	0.949574i
$941$	−9360.06	−	5404.03i	−0.324261	−	0.187212i	0.329029	−	0.944320i	$-0.393278\pi$
$941$	−9360.06	−	5404.03i	−0.324261	−	0.187212i	−0.653290	+	0.757108i	$0.726612\pi$
$942$	15099.3	+	8013.31i	0.522251	+	0.277163i
$943$	−466.178	+	269.148i	−0.0160985	+	0.00929446i
$944$	39958.5	−	3975.31i	1.37769	−	0.137061i
$945$	35201.7	−	37581.9i	1.21176	−	1.29369i
$946$	−10378.6	+	10906.4i	−0.356699	+	0.374837i
$947$	−372.832	−	645.764i	−0.0127935	−	0.0221589i	0.859558	−	0.511039i	$-0.170739\pi$
$947$	−372.832	−	645.764i	−0.0127935	−	0.0221589i	−0.872351	+	0.488880i	$0.837406\pi$
$948$	−22145.7	+	7394.84i	−0.758713	+	0.253347i
$949$	−4335.00	+	7508.44i	−0.148283	+	0.256833i
$950$	−3266.23	−	11083.1i	−0.111548	−	0.378510i
$951$	−6632.55	+	6778.70i	−0.226157	+	0.231140i
$952$	57998.0	+	10999.7i	1.97450	+	0.374476i
$953$			49163.3i			1.67110i	0.549417	+	0.835548i	$0.314850\pi$
$953$			49163.3i			1.67110i	−0.549417	+	0.835548i	$0.685150\pi$
$954$	13166.9	−	4194.25i	0.446848	−	0.142342i
$955$			60453.7i			2.04841i
$956$	−4134.65	+	2668.76i	−0.139879	+	0.0902865i
$957$	75.0044	+	19.2239i	0.00253349	+	0.000649342i
$958$	−40544.4	+	11948.5i	−1.36736	+	0.402963i
$959$	7203.08	−	12476.1i	0.242544	−	0.420098i
$960$	4477.38	−	43673.3i	0.150528	−	1.46828i
$961$	−5397.50	−	9348.74i	−0.181179	−	0.313811i
$962$	10698.9	+	10181.2i	0.358572	+	0.341221i
$963$	38690.0	−	23476.4i	1.29467	−	0.785584i
$964$	−1741.15	−	35089.3i	−0.0581728	−	1.17235i
$965$	20259.8	−	11697.0i	0.675842	−	0.390197i
$966$	−11488.4	+	410.156i	−0.382642	+	0.0136610i
$967$	−14625.7	−	8444.18i	−0.486383	−	0.280813i	0.236690	−	0.971585i	$-0.423938\pi$
$967$	−14625.7	−	8444.18i	−0.486383	−	0.280813i	−0.723073	+	0.690772i	$0.757271\pi$
$968$	8720.83	+	24957.1i	0.289564	+	0.828670i
$969$	16276.9	−	4552.04i	0.539617	−	0.150911i
$970$	23995.4	+	5796.06i	0.794273	+	0.191856i
$971$	22501.6			0.743677			0.371838	−	0.928297i	$-0.378728\pi$
$971$	22501.6			0.743677			0.371838	+	0.928297i	$0.378728\pi$
$972$	19086.3	−	23538.1i	0.629830	−	0.776733i
$973$	−59396.6			−1.95701
$974$	16314.8	+	3940.83i	0.536714	+	0.129643i
$975$	16478.3	−	4608.37i	0.541259	−	0.151370i
$976$	20141.6	−	44570.3i	0.660572	−	1.46174i
$977$	11920.1	+	6882.06i	0.390335	+	0.225360i	0.682305	−	0.731068i	$-0.260978\pi$
$977$	11920.1	+	6882.06i	0.390335	+	0.225360i	−0.291970	+	0.956427i	$0.594311\pi$
$978$	43041.2	−	1536.65i	1.40726	−	0.0502420i
$979$	3070.40	−	1772.70i	0.100235	−	0.0578710i
$980$	20002.1	−	992.515i	0.651983	−	0.0323518i
$981$	−12480.2	+	7572.75i	−0.406178	+	0.246462i
$982$	41112.0	+	39122.6i	1.33598	+	1.27134i
$983$	−3892.24	−	6741.57i	−0.126290	−	0.218741i	0.795946	−	0.605367i	$-0.206974\pi$
$983$	−3892.24	−	6741.57i	−0.126290	−	0.218741i	−0.922237	+	0.386626i	$0.873640\pi$
$984$	1476.29	−	1029.32i	0.0478278	−	0.0333470i
$985$	−7235.40	+	12532.1i	−0.234050	+	0.405386i
$986$	−371.831	+	109.579i	−0.0120096	+	0.00353927i
$987$	−26083.7	−	6685.35i	−0.841189	−	0.215600i
$988$	−2689.27	−	4166.43i	−0.0865962	−	0.134162i
$989$			14678.0i			0.471925i
$990$	15313.4	−	4878.03i	0.491609	−	0.156600i
$991$			47880.3i			1.53478i	0.641179	+	0.767391i	$0.278445\pi$
$991$			47880.3i			1.53478i	−0.641179	+	0.767391i	$0.721555\pi$
$992$	−24712.5	−	3428.35i	−0.790950	−	0.109728i
$993$	14453.1	−	14771.6i	0.461890	−	0.472067i
$994$	403.523	+	1369.26i	0.0128762	+	0.0436923i
$995$	−12256.4	+	21228.7i	−0.390506	+	0.676376i
$996$	9008.51	+	26978.3i	0.286592	+	0.858273i
$997$	−1245.57	−	2157.40i	−0.0395664	−	0.0685310i	0.845564	−	0.533874i	$-0.179264\pi$
$997$	−1245.57	−	2157.40i	−0.0395664	−	0.0685310i	−0.885130	+	0.465343i	$0.845931\pi$
$998$	18345.0	−	19277.9i	0.581864	−	0.611453i
$999$	−22404.0	+	23918.8i	−0.709539	+	0.757515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.h.b.23.7	yes	24
3.2	odd	2		108.4.h.b.71.6		24
4.3	odd	2	inner	36.4.h.b.23.12	yes	24
9.2	odd	6	inner	36.4.h.b.11.12	yes	24
9.4	even	3		324.4.b.c.323.18		24
9.5	odd	6		324.4.b.c.323.7		24
9.7	even	3		108.4.h.b.35.1		24
12.11	even	2		108.4.h.b.71.1		24
36.7	odd	6		108.4.h.b.35.6		24
36.11	even	6	inner	36.4.h.b.11.7	✓	24
36.23	even	6		324.4.b.c.323.17		24
36.31	odd	6		324.4.b.c.323.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.7	✓	24	36.11	even	6	inner
36.4.h.b.11.12	yes	24	9.2	odd	6	inner
36.4.h.b.23.7	yes	24	1.1	even	1	trivial
36.4.h.b.23.12	yes	24	4.3	odd	2	inner
108.4.h.b.35.1		24	9.7	even	3
108.4.h.b.35.6		24	36.7	odd	6
108.4.h.b.71.1		24	12.11	even	2
108.4.h.b.71.6		24	3.2	odd	2
324.4.b.c.323.7		24	9.5	odd	6
324.4.b.c.323.8		24	36.31	odd	6
324.4.b.c.323.17		24	36.23	even	6
324.4.b.c.323.18		24	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.664105 - 2.74936i) q^{2} +(-5.00415 + 1.39947i) q^{3} +(-7.11793 - 3.65173i) q^{4} +(-14.2911 - 8.25096i) q^{5} +(0.524375 + 14.6876i) q^{6} +(19.2620 - 11.1209i) q^{7} +(-14.7670 + 17.1446i) q^{8} +(23.0829 - 14.0063i) q^{9} +O(q^{10})\)	\(q+(0.664105 - 2.74936i) q^{2} +(-5.00415 + 1.39947i) q^{3} +(-7.11793 - 3.65173i) q^{4} +(-14.2911 - 8.25096i) q^{5} +(0.524375 + 14.6876i) q^{6} +(19.2620 - 11.1209i) q^{7} +(-14.7670 + 17.1446i) q^{8} +(23.0829 - 14.0063i) q^{9} +(-32.1756 + 33.8118i) q^{10} +(-6.37655 - 11.0445i) q^{11} +(40.7296 + 8.31241i) q^{12} +(-11.1766 + 19.3584i) q^{13} +(-17.7834 - 60.3436i) q^{14} +(83.0617 + 21.2890i) q^{15} +(37.3298 + 51.9854i) q^{16} -117.295i q^{17} +(-23.1789 - 72.7649i) q^{18} -27.7307i q^{19} +(71.5926 + 110.917i) q^{20} +(-80.8264 + 82.6074i) q^{21} +(-34.6000 + 10.1967i) q^{22} +(-17.5836 + 30.4556i) q^{23} +(49.9026 - 106.460i) q^{24} +(73.6567 + 127.577i) q^{25} +(45.8008 + 43.5845i) q^{26} +(-95.9089 + 102.394i) q^{27} +(-177.716 + 8.81837i) q^{28} +(1.01189 - 0.584217i) q^{29} +(113.693 - 214.228i) q^{30} +(-119.361 - 68.9130i) q^{31} +(167.717 - 68.1091i) q^{32} +(47.3657 + 46.3445i) q^{33} +(-322.487 - 77.8965i) q^{34} -367.033 q^{35} +(-215.450 + 15.4036i) q^{36} +233.596 q^{37} +(-76.2416 - 18.4161i) q^{38} +(28.8377 - 112.514i) q^{39} +(352.495 - 123.173i) q^{40} +(13.2561 + 7.65340i) q^{41} +(173.440 + 277.081i) q^{42} +(361.460 - 208.689i) q^{43} +(5.05631 + 101.900i) q^{44} +(-445.446 + 9.70942i) q^{45} +(72.0561 + 68.5693i) q^{46} +(116.494 + 201.773i) q^{47} +(-259.556 - 207.901i) q^{48} +(75.8499 - 131.376i) q^{49} +(399.671 - 117.784i) q^{50} +(164.152 + 586.963i) q^{51} +(150.246 - 96.9781i) q^{52} +180.951i q^{53} +(217.823 + 331.688i) q^{54} +210.451i q^{55} +(-93.7774 + 494.461i) q^{56} +(38.8084 + 138.768i) q^{57} +(-0.934217 - 3.17004i) q^{58} +(313.716 - 543.373i) q^{59} +(-513.485 - 454.852i) q^{60} +(-382.110 - 661.834i) q^{61} +(-268.735 + 282.400i) q^{62} +(288.860 - 526.494i) q^{63} +(-75.8742 - 506.347i) q^{64} +(319.452 - 184.435i) q^{65} +(158.874 - 99.4476i) q^{66} +(-113.463 - 65.5077i) q^{67} +(-428.330 + 834.900i) q^{68} +(45.3689 - 177.012i) q^{69} +(-243.749 + 1009.11i) q^{70} -22.6910 q^{71} +(-100.732 + 602.579i) q^{72} +387.864 q^{73} +(155.133 - 642.240i) q^{74} +(-547.130 - 535.334i) q^{75} +(-101.265 + 197.385i) q^{76} +(-245.650 - 141.826i) q^{77} +(-290.190 - 154.006i) q^{78} +(-486.411 + 280.830i) q^{79} +(-104.553 - 1050.93i) q^{80} +(336.644 - 646.615i) q^{81} +(29.8454 - 31.3630i) q^{82} +(342.111 + 592.554i) q^{83} +(876.976 - 292.838i) q^{84} +(-967.799 + 1676.28i) q^{85} +(-333.713 - 1132.38i) q^{86} +(-4.24607 + 4.33963i) q^{87} +(283.516 + 53.7704i) q^{88} +278.003i q^{89} +(-269.128 + 1231.14i) q^{90} +497.177i q^{91} +(236.374 - 152.571i) q^{92} +(693.741 + 177.808i) q^{93} +(632.110 - 186.284i) q^{94} +(-228.805 + 396.302i) q^{95} +(-743.966 + 575.544i) q^{96} +(-264.443 - 458.028i) q^{97} +(-310.827 - 295.786i) q^{98} +(-301.883 - 165.628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Introduction

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