LMFDB - Embedded newform 145.4.c.b.86.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [145,4,Mod(86,145)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(145, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("145.86");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	145.c (of order $2$, degree $1$, 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:	$8.55527695083$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 95 x^{14} + 3576 x^{12} + 68256 x^{10} + 700479 x^{8} + 3754089 x^{6} + 9373424 x^{4} + \cdots + 2560000 $ x^16 + 95x^14 + 3576x^12 + 68256x^10 + 700479x^8 + 3754089x^6 + 9373424x^4 + 8978880*x^2 + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			86.11
Root			$1.89892i$ of defining polynomial
Character	$\chi$	$=$	145.86
Dual form			145.4.c.b.86.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.89892i q^{2} -8.84442i q^{3} +4.39409 q^{4} -5.00000 q^{5} +16.7949 q^{6} +36.3095 q^{7} +23.5354i q^{8} -51.2237 q^{9} +O(q^{10})$	\(q+1.89892i q^{2} -8.84442i q^{3} +4.39409 q^{4} -5.00000 q^{5} +16.7949 q^{6} +36.3095 q^{7} +23.5354i q^{8} -51.2237 q^{9} -9.49461i q^{10} -15.4818i q^{11} -38.8632i q^{12} +26.1126 q^{13} +68.9490i q^{14} +44.2221i q^{15} -9.53923 q^{16} -100.722i q^{17} -97.2699i q^{18} -52.7355i q^{19} -21.9705 q^{20} -321.137i q^{21} +29.3988 q^{22} -156.851 q^{23} +208.157 q^{24} +25.0000 q^{25} +49.5859i q^{26} +214.245i q^{27} +159.547 q^{28} +(97.9716 + 121.616i) q^{29} -83.9743 q^{30} -96.9520i q^{31} +170.169i q^{32} -136.928 q^{33} +191.263 q^{34} -181.548 q^{35} -225.082 q^{36} +134.613i q^{37} +100.141 q^{38} -230.951i q^{39} -117.677i q^{40} -119.906i q^{41} +609.814 q^{42} +345.557i q^{43} -68.0286i q^{44} +256.119 q^{45} -297.848i q^{46} +243.931i q^{47} +84.3689i q^{48} +975.381 q^{49} +47.4731i q^{50} -890.826 q^{51} +114.741 q^{52} +155.122 q^{53} -406.834 q^{54} +77.4092i q^{55} +854.560i q^{56} -466.415 q^{57} +(-230.940 + 186.041i) q^{58} -391.897 q^{59} +194.316i q^{60} -426.585i q^{61} +184.104 q^{62} -1859.91 q^{63} -399.452 q^{64} -130.563 q^{65} -260.015i q^{66} -772.655 q^{67} -442.581i q^{68} +1387.26i q^{69} -344.745i q^{70} +1143.96 q^{71} -1205.57i q^{72} +486.958i q^{73} -255.619 q^{74} -221.110i q^{75} -231.725i q^{76} -562.138i q^{77} +438.558 q^{78} +990.999i q^{79} +47.6961 q^{80} +511.830 q^{81} +227.693 q^{82} -288.564 q^{83} -1411.10i q^{84} +503.609i q^{85} -656.186 q^{86} +(1075.63 - 866.502i) q^{87} +364.372 q^{88} +189.493i q^{89} +486.350i q^{90} +948.137 q^{91} -689.218 q^{92} -857.484 q^{93} -463.206 q^{94} +263.678i q^{95} +1505.05 q^{96} +1519.46i q^{97} +1852.17i q^{98} +793.037i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9}+O(q^{10}) $ 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9	$ 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9} - 14 q^{13} + 210 q^{16} + 310 q^{20} + 88 q^{22} + 42 q^{23} + 62 q^{24} + 400 q^{25} - 346 q^{28} + 28 q^{29} - 250 q^{30} - 460 q^{33} - 626 q^{34} - 190 q^{35} - 12 q^{36} - 292 q^{38} + 584 q^{42} + 630 q^{45} + 1894 q^{49} - 320 q^{51} - 294 q^{52} + 614 q^{53} + 1840 q^{54} - 1360 q^{57} - 644 q^{58} - 2086 q^{59} - 30 q^{62} - 1456 q^{63} - 894 q^{64} + 70 q^{65} - 1604 q^{67} + 792 q^{71} + 1720 q^{74} + 4894 q^{78} - 1050 q^{80} - 192 q^{81} + 1276 q^{82} + 4400 q^{83} - 2042 q^{86} - 2046 q^{87} - 9264 q^{88} + 212 q^{91} - 2030 q^{92} - 1816 q^{93} + 4304 q^{94} + 2234 q^{96}+O(q^{100}) $ 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9 - 14 * q^13 + 210 * q^16 + 310 * q^20 + 88 * q^22 + 42 * q^23 + 62 * q^24 + 400 * q^25 - 346 * q^28 + 28 * q^29 - 250 * q^30 - 460 * q^33 - 626 * q^34 - 190 * q^35 - 12 * q^36 - 292 * q^38 + 584 * q^42 + 630 * q^45 + 1894 * q^49 - 320 * q^51 - 294 * q^52 + 614 * q^53 + 1840 * q^54 - 1360 * q^57 - 644 * q^58 - 2086 * q^59 - 30 * q^62 - 1456 * q^63 - 894 * q^64 + 70 * q^65 - 1604 * q^67 + 792 * q^71 + 1720 * q^74 + 4894 * q^78 - 1050 * q^80 - 192 * q^81 + 1276 * q^82 + 4400 * q^83 - 2042 * q^86 - 2046 * q^87 - 9264 * q^88 + 212 * q^91 - 2030 * q^92 - 1816 * q^93 + 4304 * q^94 + 2234 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.89892i			0.671371i	0.941974	+	0.335685i	$0.108968\pi$
$2$			1.89892i			0.671371i	−0.941974	+	0.335685i	$0.891032\pi$
$3$		−	8.84442i		−	1.70211i	−0.525077	−	0.851055i	$-0.675964\pi$
$3$		−	8.84442i		−	1.70211i	0.525077	−	0.851055i	$-0.324036\pi$
$4$	4.39409			0.549261
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	16.7949			1.14275
$7$	36.3095			1.96053			0.980265	−	0.197689i	$-0.0633436\pi$
$7$	36.3095			1.96053			0.980265	+	0.197689i	$0.0633436\pi$
$8$			23.5354i			1.04013i
$9$	−51.2237			−1.89718
$10$		−	9.49461i		−	0.300246i
$11$		−	15.4818i		−	0.424359i	−0.977231	−	0.212180i	$-0.931944\pi$
$11$		−	15.4818i		−	0.424359i	0.977231	−	0.212180i	$-0.0680562\pi$
$12$		−	38.8632i		−	0.934903i
$13$	26.1126			0.557103			0.278551	−	0.960421i	$-0.410146\pi$
$13$	26.1126			0.557103			0.278551	+	0.960421i	$0.410146\pi$
$14$			68.9490i			1.31624i
$15$			44.2221i			0.761206i
$16$	−9.53923			−0.149050
$17$		−	100.722i		−	1.43698i	−0.695538	−	0.718489i	$-0.744834\pi$
$17$		−	100.722i		−	1.43698i	0.695538	−	0.718489i	$-0.255166\pi$
$18$		−	97.2699i		−	1.27371i
$19$		−	52.7355i		−	0.636756i	−0.947964	−	0.318378i	$-0.896862\pi$
$19$		−	52.7355i		−	0.636756i	0.947964	−	0.318378i	$-0.103138\pi$
$20$	−21.9705			−0.245637
$21$		−	321.137i		−	3.33704i
$22$	29.3988			0.284902
$23$	−156.851			−1.42199			−0.710994	−	0.703198i	$-0.751755\pi$
$23$	−156.851			−1.42199			−0.710994	+	0.703198i	$0.751755\pi$
$24$	208.157			1.77041
$25$	25.0000			0.200000
$26$			49.5859i			0.374023i
$27$			214.245i			1.52709i
$28$	159.547			1.07684
$29$	97.9716	+	121.616i	0.627340	+	0.778745i
$29$	97.9716	+	121.616i	0.627340	+	0.778745i
$30$	−83.9743			−0.511052
$31$		−	96.9520i		−	0.561713i	−0.959750	−	0.280856i	$-0.909382\pi$
$31$		−	96.9520i		−	0.561713i	0.959750	−	0.280856i	$-0.0906185\pi$
$32$			170.169i			0.940061i
$33$	−136.928			−0.722305
$34$	191.263			0.964745
$35$	−181.548			−0.876775
$36$	−225.082			−1.04205
$37$			134.613i			0.598113i	0.954235	+	0.299057i	$0.0966719\pi$
$37$			134.613i			0.598113i	−0.954235	+	0.299057i	$0.903328\pi$
$38$	100.141			0.427499
$39$		−	230.951i		−	0.948250i
$40$		−	117.677i		−	0.465160i
$41$		−	119.906i		−	0.456737i	−0.973575	−	0.228368i	$-0.926661\pi$
$41$		−	119.906i		−	0.456737i	0.973575	−	0.228368i	$-0.0733391\pi$
$42$	609.814			2.24039
$43$			345.557i			1.22551i	0.790273	+	0.612755i	$0.209939\pi$
$43$			345.557i			1.22551i	−0.790273	+	0.612755i	$0.790061\pi$
$44$		−	68.0286i		−	0.233084i
$45$	256.119			0.848443
$46$		−	297.848i		−	0.954681i
$47$			243.931i			0.757042i	0.925593	+	0.378521i	$0.123567\pi$
$47$			243.931i			0.757042i	−0.925593	+	0.378521i	$0.876433\pi$
$48$			84.3689i			0.253700i
$49$	975.381			2.84368
$50$			47.4731i			0.134274i
$51$	−890.826			−2.44589
$52$	114.741			0.305995
$53$	155.122			0.402030			0.201015	−	0.979588i	$-0.435576\pi$
$53$	155.122			0.402030			0.201015	+	0.979588i	$0.435576\pi$
$54$	−406.834			−1.02524
$55$			77.4092i			0.189779i
$56$			854.560i			2.03920i
$57$	−466.415			−1.08383
$58$	−230.940	+	186.041i	−0.522827	+	0.421178i
$59$	−391.897			−0.864756			−0.432378	−	0.901692i	$-0.642325\pi$
$59$	−391.897			−0.864756			−0.432378	+	0.901692i	$0.642325\pi$
$60$			194.316i			0.418101i
$61$		−	426.585i		−	0.895387i	−0.894187	−	0.447693i	$-0.852246\pi$
$61$		−	426.585i		−	0.895387i	0.894187	−	0.447693i	$-0.147754\pi$
$62$	184.104			0.377117
$63$	−1859.91			−3.71947
$64$	−399.452			−0.780180
$65$	−130.563			−0.249144
$66$		−	260.015i		−	0.484935i
$67$	−772.655			−1.40888			−0.704439	−	0.709765i	$-0.748801\pi$
$67$	−772.655			−1.40888			−0.704439	+	0.709765i	$0.748801\pi$
$68$		−	442.581i		−	0.789277i
$69$			1387.26i			2.42038i
$70$		−	344.745i		−	0.588641i
$71$	1143.96			1.91215			0.956077	−	0.293116i	$-0.0946923\pi$
$71$	1143.96			1.91215			0.956077	+	0.293116i	$0.0946923\pi$
$72$		−	1205.57i		−	1.97331i
$73$			486.958i			0.780741i	0.920658	+	0.390371i	$0.127653\pi$
$73$			486.958i			0.780741i	−0.920658	+	0.390371i	$0.872347\pi$
$74$	−255.619			−0.401556
$75$		−	221.110i		−	0.340422i
$76$		−	231.725i		−	0.349745i
$77$		−	562.138i		−	0.831968i
$78$	438.558			0.636627
$79$			990.999i			1.41134i	0.708539	+	0.705671i	$0.249354\pi$
$79$			990.999i			1.41134i	−0.708539	+	0.705671i	$0.750646\pi$
$80$	47.6961			0.0666574
$81$	511.830			0.702099
$82$	227.693			0.306640
$83$	−288.564			−0.381614			−0.190807	−	0.981628i	$-0.561111\pi$
$83$	−288.564			−0.381614			−0.190807	+	0.981628i	$0.561111\pi$
$84$		−	1411.10i		−	1.83290i
$85$			503.609i			0.642636i
$86$	−656.186			−0.822772
$87$	1075.63	−	866.502i	1.32551	−	1.06780i
$88$	364.372			0.441388
$89$			189.493i			0.225688i	0.993613	+	0.112844i	$0.0359960\pi$
$89$			189.493i			0.225688i	−0.993613	+	0.112844i	$0.964004\pi$
$90$			486.350i			0.569619i
$91$	948.137			1.09222
$92$	−689.218			−0.781043
$93$	−857.484			−0.956096
$94$	−463.206			−0.508256
$95$			263.678i			0.284766i
$96$	1505.05			1.60009
$97$			1519.46i			1.59049i	0.606286	+	0.795247i	$0.292659\pi$
$97$			1519.46i			1.59049i	−0.606286	+	0.795247i	$0.707341\pi$
$98$			1852.17i			1.90916i
$99$			793.037i			0.805083i
$100$	109.852			0.109852
$101$		−	793.456i		−	0.781701i	−0.920454	−	0.390850i	$-0.872181\pi$
$101$		−	793.456i		−	0.781701i	0.920454	−	0.390850i	$-0.127819\pi$
$102$		−	1691.61i		−	1.64210i
$103$	947.145			0.906068			0.453034	−	0.891493i	$-0.350342\pi$
$103$	947.145			0.906068			0.453034	+	0.891493i	$0.350342\pi$
$104$			614.572i			0.579459i
$105$			1605.68i			1.49237i
$106$			294.564i			0.269911i
$107$	558.257			0.504381			0.252191	−	0.967678i	$-0.418849\pi$
$107$	558.257			0.504381			0.252191	+	0.967678i	$0.418849\pi$
$108$			941.411i			0.838772i
$109$	−318.764			−0.280111			−0.140055	−	0.990144i	$-0.544728\pi$
$109$	−318.764			−0.280111			−0.140055	+	0.990144i	$0.544728\pi$
$110$	−146.994			−0.127412
$111$	1190.57			1.01805
$112$	−346.365			−0.292218
$113$			225.994i			0.188139i	0.995566	+	0.0940694i	$0.0299876\pi$
$113$			225.994i			0.188139i	−0.995566	+	0.0940694i	$0.970012\pi$
$114$		−	885.686i		−	0.727650i
$115$	784.256			0.635932
$116$	430.496	+	534.394i	0.344574	+	0.427735i
$117$	−1337.59			−1.05692
$118$		−	744.182i		−	0.580572i
$119$		−	3657.16i		−	2.81724i
$120$	−1040.79			−0.791753
$121$	1091.31			0.819919
$122$	810.052			0.601137
$123$	−1060.50			−0.777416
$124$		−	426.016i		−	0.308527i
$125$	−125.000			−0.0894427
$126$		−	3531.82i		−	2.49714i
$127$		−	221.553i		−	0.154800i	−0.997000	−	0.0774001i	$-0.975338\pi$
$127$		−	221.553i		−	0.154800i	0.997000	−	0.0774001i	$-0.0246619\pi$
$128$			602.825i			0.416271i
$129$	3056.25			2.08595
$130$		−	247.929i		−	0.167268i
$131$			1925.13i			1.28396i	0.766719	+	0.641982i	$0.221888\pi$
$131$			1925.13i			1.28396i	−0.766719	+	0.641982i	$0.778112\pi$
$132$	−601.673			−0.396734
$133$		−	1914.80i		−	1.24838i
$134$		−	1467.21i		−	0.945879i
$135$		−	1071.22i		−	0.682935i
$136$	2370.53			1.49464
$137$			2691.89i			1.67872i	0.543580	+	0.839358i	$0.317069\pi$
$137$			2691.89i			1.67872i	−0.543580	+	0.839358i	$0.682931\pi$
$138$	−2634.29			−1.62497
$139$	−990.894			−0.604651			−0.302326	−	0.953205i	$-0.597763\pi$
$139$	−990.894			−0.604651			−0.302326	+	0.953205i	$0.597763\pi$
$140$	−797.737			−0.481579
$141$	2157.43			1.28857
$142$			2172.29i			1.28376i
$143$		−	404.271i		−	0.236412i
$144$	488.635			0.282775
$145$	−489.858	−	608.082i	−0.280555	−	0.348265i
$146$	−924.695			−0.524167
$147$		−	8626.68i		−	4.84025i
$148$			591.500i			0.328520i
$149$	−2862.14			−1.57366			−0.786831	−	0.617169i	$-0.788280\pi$
$149$	−2862.14			−1.57366			−0.786831	+	0.617169i	$0.788280\pi$
$150$	419.872			0.228549
$151$	−2539.50			−1.36862			−0.684311	−	0.729190i	$-0.739897\pi$
$151$	−2539.50			−1.36862			−0.684311	+	0.729190i	$0.739897\pi$
$152$	1241.15			0.662308
$153$			5159.35i			2.72620i
$154$	1067.46			0.558559
$155$			484.760i			0.251206i
$156$		−	1014.82i		−	0.520837i
$157$		−	1615.00i		−	0.820960i	−0.911869	−	0.410480i	$-0.865361\pi$
$157$		−	1615.00i		−	0.820960i	0.911869	−	0.410480i	$-0.134639\pi$
$158$	−1881.83			−0.947534
$159$		−	1371.96i		−	0.684299i
$160$		−	850.846i		−	0.420408i
$161$	−5695.19			−2.78785
$162$			971.926i			0.471368i
$163$		−	7.23502i		−	0.00347663i	−0.999998	−	0.00173831i	$-0.999447\pi$
$163$		−	7.23502i		−	0.00347663i	0.999998	−	0.00173831i	$-0.000553323\pi$
$164$		−	526.879i		−	0.250868i
$165$	684.639			0.323025
$166$		−	547.960i		−	0.256205i
$167$	−163.437			−0.0757313			−0.0378656	−	0.999283i	$-0.512056\pi$
$167$	−163.437			−0.0757313			−0.0378656	+	0.999283i	$0.512056\pi$
$168$	7558.09			3.47095
$169$	−1515.13			−0.689636
$170$	−956.315			−0.431447
$171$			2701.31i			1.20804i
$172$			1518.41i			0.673126i
$173$	1565.37			0.687935			0.343967	−	0.938982i	$-0.388229\pi$
$173$	1565.37			0.687935			0.343967	+	0.938982i	$0.388229\pi$
$174$	1645.42	+	2042.53i	0.716891	+	0.889908i
$175$	907.738			0.392106
$176$			147.685i			0.0632509i
$177$			3466.10i			1.47191i
$178$	−359.833			−0.151520
$179$	1586.63			0.662516			0.331258	−	0.943540i	$-0.392527\pi$
$179$	1586.63			0.662516			0.331258	+	0.943540i	$0.392527\pi$
$180$	1125.41			0.466017
$181$	1558.95			0.640197			0.320099	−	0.947384i	$-0.396284\pi$
$181$	1558.95			0.640197			0.320099	+	0.947384i	$0.396284\pi$
$182$			1800.44i			0.733282i
$183$	−3772.90			−1.52405
$184$		−	3691.56i		−	1.47905i
$185$		−	673.063i		−	0.267484i
$186$		−	1628.30i		−	0.641895i
$187$	−1559.36			−0.609795
$188$			1071.85i			0.415814i
$189$			7779.13i			2.99391i
$190$	−500.703			−0.191183
$191$		−	2703.32i		−	1.02411i	−0.858952	−	0.512056i	$-0.828884\pi$
$191$		−	2703.32i		−	1.02411i	0.858952	−	0.512056i	$-0.171116\pi$
$192$			3532.92i			1.32795i
$193$		−	1423.57i		−	0.530938i	−0.964119	−	0.265469i	$-0.914473\pi$
$193$		−	1423.57i		−	0.530938i	0.964119	−	0.265469i	$-0.0855268\pi$
$194$	−2885.34			−1.06781
$195$			1154.75i			0.424070i
$196$	4285.91			1.56192
$197$	−1118.31			−0.404448			−0.202224	−	0.979339i	$-0.564817\pi$
$197$	−1118.31			−0.404448			−0.202224	+	0.979339i	$0.564817\pi$
$198$	−1505.92			−0.540509
$199$	−1026.42			−0.365632			−0.182816	−	0.983147i	$-0.558521\pi$
$199$	−1026.42			−0.365632			−0.182816	+	0.983147i	$0.558521\pi$
$200$			588.386i			0.208026i
$201$			6833.68i			2.39806i
$202$	1506.71			0.524811
$203$	3557.30	+	4415.83i	1.22992	+	1.52675i
$204$	−3914.37			−1.34343
$205$			599.531i			0.204259i
$206$			1798.56i			0.608307i
$207$	8034.50			2.69776
$208$	−249.094			−0.0830364
$209$	−816.443			−0.270213
$210$	−3049.07			−1.00193
$211$		−	3926.38i		−	1.28106i	−0.767934	−	0.640529i	$-0.778715\pi$
$211$		−	3926.38i		−	1.28106i	0.767934	−	0.640529i	$-0.221285\pi$
$212$	681.618			0.220820
$213$		−	10117.6i		−	3.25469i
$214$			1060.09i			0.338627i
$215$		−	1727.79i		−	0.548065i
$216$	−5042.34			−1.58837
$217$		−	3520.28i		−	1.10125i
$218$		−	605.309i		−	0.188058i
$219$	4306.86			1.32891
$220$			340.143i			0.104238i
$221$		−	2630.11i		−	0.800545i
$222$			2260.80i			0.683491i
$223$	−2056.33			−0.617497			−0.308748	−	0.951144i	$-0.599910\pi$
$223$	−2056.33			−0.617497			−0.308748	+	0.951144i	$0.599910\pi$
$224$			6178.76i			1.84302i
$225$	−1280.59			−0.379435
$226$	−429.144			−0.126311
$227$	−5743.84			−1.67944			−0.839718	−	0.543023i	$-0.817279\pi$
$227$	−5743.84			−1.67944			−0.839718	+	0.543023i	$0.817279\pi$
$228$	−2049.47			−0.595305
$229$		−	3406.39i		−	0.982971i	−0.870886	−	0.491486i	$-0.836454\pi$
$229$		−	3406.39i		−	0.982971i	0.870886	−	0.491486i	$-0.163546\pi$
$230$			1489.24i			0.426946i
$231$	−4971.78			−1.41610
$232$	−2862.30	+	2305.80i	−0.809995	+	0.652515i
$233$	391.463			0.110067			0.0550335	−	0.998485i	$-0.482473\pi$
$233$	391.463			0.110067			0.0550335	+	0.998485i	$0.482473\pi$
$234$		−	2539.97i		−	0.709586i
$235$		−	1219.65i		−	0.338560i
$236$	−1722.03			−0.474977
$237$	8764.81			2.40226
$238$	6944.67			1.89141
$239$	1825.48			0.494061			0.247030	−	0.969008i	$-0.420545\pi$
$239$	1825.48			0.494061			0.247030	+	0.969008i	$0.420545\pi$
$240$		−	421.845i		−	0.113458i
$241$	−97.0436			−0.0259383			−0.0129692	−	0.999916i	$-0.504128\pi$
$241$	−97.0436			−0.0259383			−0.0129692	+	0.999916i	$0.504128\pi$
$242$			2072.32i			0.550470i
$243$			1257.77i			0.332042i
$244$		−	1874.45i		−	0.491802i
$245$	−4876.90			−1.27173
$246$		−	2013.81i		−	0.521934i
$247$		−	1377.06i		−	0.354738i
$248$	2281.81			0.584253
$249$			2552.18i			0.649549i
$250$		−	237.365i		−	0.0600492i
$251$		−	1237.92i		−	0.311302i	−0.987812	−	0.155651i	$-0.950253\pi$
$251$		−	1237.92i		−	0.311302i	0.987812	−	0.155651i	$-0.0497475\pi$
$252$	−8172.61			−2.04296
$253$			2428.34i			0.603434i
$254$	420.711			0.103928
$255$	4454.13			1.09384
$256$	−4340.33			−1.05965
$257$	1620.87			0.393413			0.196706	−	0.980462i	$-0.436975\pi$
$257$	1620.87			0.393413			0.196706	+	0.980462i	$0.436975\pi$
$258$			5803.59i			1.40045i
$259$			4887.72i			1.17262i
$260$	−573.706			−0.136845
$261$	−5018.47	−	6229.65i	−1.19017	−	1.47742i
$262$	−3655.67			−0.862016
$263$			3697.46i			0.866902i	0.901177	+	0.433451i	$0.142704\pi$
$263$			3697.46i			0.866902i	−0.901177	+	0.433451i	$0.857296\pi$
$264$		−	3222.65i		−	0.751291i
$265$	−775.608			−0.179793
$266$	3636.06			0.838125
$267$	1675.95			0.384145
$268$	−3395.12			−0.773842
$269$		−	3767.39i		−	0.853910i	−0.904273	−	0.426955i	$-0.859586\pi$
$269$		−	3767.39i		−	0.853910i	0.904273	−	0.426955i	$-0.140414\pi$
$270$	2034.17			0.458503
$271$		−	2969.18i		−	0.665553i	−0.943006	−	0.332776i	$-0.892015\pi$
$271$		−	2969.18i		−	0.665553i	0.943006	−	0.332776i	$-0.107985\pi$
$272$			960.808i			0.214182i
$273$		−	8385.72i		−	1.85907i
$274$	−5111.70			−1.12704
$275$		−	387.046i		−	0.0848718i
$276$			6095.74i			1.32942i
$277$	3049.50			0.661469			0.330734	−	0.943724i	$-0.392704\pi$
$277$	3049.50			0.661469			0.330734	+	0.943724i	$0.392704\pi$
$278$		−	1881.63i		−	0.405945i
$279$			4966.24i			1.06567i
$280$		−	4272.80i		−	0.911959i
$281$	3962.75			0.841274			0.420637	−	0.907229i	$-0.361807\pi$
$281$	3962.75			0.841274			0.420637	+	0.907229i	$0.361807\pi$
$282$			4096.79i			0.865107i
$283$	787.024			0.165314			0.0826568	−	0.996578i	$-0.473659\pi$
$283$	787.024			0.165314			0.0826568	+	0.996578i	$0.473659\pi$
$284$	5026.66			1.05027
$285$	2332.08			0.484702
$286$	767.680			0.158720
$287$		−	4353.74i		−	0.895446i
$288$		−	8716.70i		−	1.78346i
$289$	−5231.88			−1.06491
$290$	1154.70	−	930.203i	0.233815	−	0.188356i
$291$	13438.8			2.70719
$292$			2139.74i			0.428831i
$293$			4146.87i			0.826835i	0.910542	+	0.413418i	$0.135665\pi$
$293$			4146.87i			0.826835i	−0.910542	+	0.413418i	$0.864335\pi$
$294$	16381.4			3.24960
$295$	1959.48			0.386731
$296$	−3168.17			−0.622115
$297$	3316.90			0.648034
$298$		−	5434.98i		−	1.05651i
$299$	−4095.79			−0.792194
$300$		−	971.580i		−	0.186981i
$301$			12547.0i			2.40265i
$302$		−	4822.32i		−	0.918853i
$303$	−7017.65			−1.33054
$304$			503.056i			0.0949087i
$305$			2132.92i			0.400429i
$306$	−9797.20			−1.83029
$307$		−	8231.20i		−	1.53023i	−0.643896	−	0.765113i	$-0.722683\pi$
$307$		−	8231.20i		−	1.53023i	0.643896	−	0.765113i	$-0.277317\pi$
$308$		−	2470.09i		−	0.456968i
$309$		−	8376.95i		−	1.54223i
$310$	−920.522			−0.168652
$311$			8410.98i			1.53358i	0.641899	+	0.766789i	$0.278147\pi$
$311$			8410.98i			1.53358i	−0.641899	+	0.766789i	$0.721853\pi$
$312$	5435.53			0.986302
$313$	−6393.12			−1.15451			−0.577253	−	0.816565i	$-0.695875\pi$
$313$	−6393.12			−1.15451			−0.577253	+	0.816565i	$0.695875\pi$
$314$	3066.76			0.551169
$315$	9299.54			1.66340
$316$			4354.54i			0.775196i
$317$			1983.58i			0.351449i	0.984439	+	0.175724i	$0.0562267\pi$
$317$			1983.58i			0.351449i	−0.984439	+	0.175724i	$0.943773\pi$
$318$	2605.25			0.459418
$319$	1882.85	−	1516.78i	0.330468	−	0.266218i
$320$	1997.26			0.348907
$321$		−	4937.46i		−	0.858512i
$322$		−	10814.7i		−	1.87168i
$323$	−5311.62			−0.915004
$324$	2249.03			0.385636
$325$	652.816			0.111421
$326$	13.7387			0.00233411
$327$			2819.28i			0.476779i
$328$	2822.04			0.475065
$329$			8857.02i			1.48420i
$330$			1300.08i			0.216869i
$331$			1856.80i			0.308335i	0.988045	+	0.154168i	$0.0492696\pi$
$331$			1856.80i			0.308335i	−0.988045	+	0.154168i	$0.950730\pi$
$332$	−1267.98			−0.209606
$333$		−	6895.36i		−	1.13473i
$334$		−	310.354i		−	0.0508438i
$335$	3863.27			0.630069
$336$			3063.39i			0.497387i
$337$		−	2929.74i		−	0.473570i	−0.971562	−	0.236785i	$-0.923906\pi$
$337$		−	2929.74i		−	0.473570i	0.971562	−	0.236785i	$-0.0760938\pi$
$338$		−	2877.12i		−	0.463002i
$339$	1998.78			0.320233
$340$			2212.90i			0.352975i
$341$	−1501.00			−0.238368
$342$	−5129.58			−0.811041
$343$	22961.4			3.61458
$344$	−8132.83			−1.27469
$345$		−	6936.29i		−	1.08243i
$346$			2972.51i			0.461859i
$347$	−7107.62			−1.09959			−0.549794	−	0.835300i	$-0.685294\pi$
$347$	−7107.62			−1.09959			−0.549794	+	0.835300i	$0.685294\pi$
$348$	4726.40	−	3807.49i	0.728051	−	0.586502i
$349$	−6046.40			−0.927381			−0.463691	−	0.885997i	$-0.653475\pi$
$349$	−6046.40			−0.927381			−0.463691	+	0.885997i	$0.653475\pi$
$350$			1723.72i			0.263248i
$351$			5594.49i			0.850746i
$352$	2634.53			0.398923
$353$	625.747			0.0943489			0.0471744	−	0.998887i	$-0.484978\pi$
$353$	625.747			0.0943489			0.0471744	+	0.998887i	$0.484978\pi$
$354$	−6581.86			−0.988197
$355$	−5719.79			−0.855141
$356$			832.649i			0.123962i
$357$	−32345.5			−4.79525
$358$			3012.89i			0.444794i
$359$		−	8973.44i		−	1.31922i	−0.751608	−	0.659610i	$-0.770721\pi$
$359$		−	8973.44i		−	1.31922i	0.751608	−	0.659610i	$-0.229279\pi$
$360$			6027.86i			0.882489i
$361$	4077.96			0.594542
$362$			2960.32i			0.429810i
$363$		−	9652.03i		−	1.39559i
$364$	4166.20			0.599913
$365$		−	2434.79i		−	0.349158i
$366$		−	7164.44i		−	1.02320i
$367$			13220.8i			1.88044i	0.340564	+	0.940221i	$0.389382\pi$
$367$			13220.8i			1.88044i	−0.340564	+	0.940221i	$0.610618\pi$
$368$	1496.24			0.211948
$369$			6142.05i			0.866510i
$370$	1278.10			0.179581
$371$	5632.39			0.788192
$372$	−3767.86			−0.525147
$373$	5761.86			0.799833			0.399916	−	0.916552i	$-0.369039\pi$
$373$	5761.86			0.799833			0.399916	+	0.916552i	$0.369039\pi$
$374$		−	2961.10i		−	0.409398i
$375$			1105.55i			0.152241i
$376$	−5741.02			−0.787421
$377$	2558.30	+	3175.72i	0.349493	+	0.433841i
$378$	−14772.0			−2.01002
$379$		−	11444.7i		−	1.55112i	−0.631276	−	0.775558i	$-0.717468\pi$
$379$		−	11444.7i		−	1.55112i	0.631276	−	0.775558i	$-0.282532\pi$
$380$			1158.62i			0.156411i
$381$	−1959.50			−0.263487
$382$	5133.40			0.687559
$383$	4511.26			0.601866			0.300933	−	0.953645i	$-0.402702\pi$
$383$	4511.26			0.601866			0.300933	+	0.953645i	$0.402702\pi$
$384$	5331.63			0.708539
$385$			2810.69i			0.372068i
$386$	2703.25			0.356456
$387$		−	17700.7i		−	2.32501i
$388$			6676.65i			0.873597i
$389$			7545.55i			0.983482i	0.870742	+	0.491741i	$0.163639\pi$
$389$			7545.55i			0.983482i	−0.870742	+	0.491741i	$0.836361\pi$
$390$	−2192.79			−0.284708
$391$			15798.3i			2.04337i
$392$			22956.0i			2.95779i
$393$	17026.7			2.18545
$394$		−	2123.58i		−	0.271534i
$395$		−	4954.99i		−	0.631172i
$396$			3484.68i			0.442201i
$397$	2273.57			0.287424			0.143712	−	0.989620i	$-0.454096\pi$
$397$	2273.57			0.287424			0.143712	+	0.989620i	$0.454096\pi$
$398$		−	1949.09i		−	0.245475i
$399$	−16935.3			−2.12488
$400$	−238.481			−0.0298101
$401$	−1804.79			−0.224755			−0.112378	−	0.993666i	$-0.535847\pi$
$401$	−1804.79			−0.224755			−0.112378	+	0.993666i	$0.535847\pi$
$402$	−12976.6			−1.60999
$403$		−	2531.67i		−	0.312932i
$404$		−	3486.52i		−	0.429358i
$405$	−2559.15			−0.313988
$406$	−8385.33	+	6755.04i	−1.02502	+	0.825732i
$407$	2084.05			0.253815
$408$		−	20966.0i		−	2.54404i
$409$			13457.0i			1.62691i	0.581629	+	0.813454i	$0.302416\pi$
$409$			13457.0i			1.62691i	−0.581629	+	0.813454i	$0.697584\pi$
$410$	−1138.46			−0.137133
$411$	23808.2			2.85736
$412$	4161.84			0.497668
$413$	−14229.6			−1.69538
$414$			15256.9i			1.81120i
$415$	1442.82			0.170663
$416$			4443.56i			0.523711i
$417$			8763.88i			1.02918i
$418$		−	1550.36i		−	0.181413i
$419$	7747.39			0.903305			0.451653	−	0.892194i	$-0.350835\pi$
$419$	7747.39			0.903305			0.451653	+	0.892194i	$0.350835\pi$
$420$			7055.52i			0.819700i
$421$		−	16093.6i		−	1.86307i	−0.363652	−	0.931535i	$-0.618470\pi$
$421$		−	16093.6i		−	1.86307i	0.363652	−	0.931535i	$-0.381530\pi$
$422$	7455.90			0.860065
$423$		−	12495.1i		−	1.43624i
$424$			3650.85i			0.418163i
$425$		−	2518.05i		−	0.287396i
$426$	19212.6			2.18511
$427$		−	15489.1i		−	1.75543i
$428$	2453.03			0.277037
$429$	−3575.54			−0.402398
$430$	3280.93			0.367955
$431$	2944.01			0.329021			0.164510	−	0.986375i	$-0.447396\pi$
$431$	2944.01			0.329021			0.164510	+	0.986375i	$0.447396\pi$
$432$		−	2043.73i		−	0.227613i
$433$			9569.64i			1.06210i	0.847342	+	0.531048i	$0.178202\pi$
$433$			9569.64i			1.06210i	−0.847342	+	0.531048i	$0.821798\pi$
$434$	6684.74			0.739350
$435$	−5378.13	+	4332.51i	−0.592786	+	0.477535i
$436$	−1400.68			−0.153854
$437$			8271.63i			0.905459i
$438$			8178.39i			0.892189i
$439$	−2821.52			−0.306751			−0.153376	−	0.988168i	$-0.549014\pi$
$439$	−2821.52			−0.306751			−0.153376	+	0.988168i	$0.549014\pi$
$440$	−1821.86			−0.197395
$441$	−49962.7			−5.39495
$442$	4994.38			0.537462
$443$		−	392.555i		−	0.0421012i	−0.999778	−	0.0210506i	$-0.993299\pi$
$443$		−	392.555i		−	0.0421012i	0.999778	−	0.0210506i	$-0.00670111\pi$
$444$	5231.48			0.559178
$445$		−	947.465i		−	0.100931i
$446$		−	3904.80i		−	0.414569i
$447$			25314.0i			2.67854i
$448$	−14503.9			−1.52957
$449$		−	3671.15i		−	0.385862i	−0.981212	−	0.192931i	$-0.938201\pi$
$449$		−	3671.15i		−	0.385862i	0.981212	−	0.192931i	$-0.0617994\pi$
$450$		−	2431.75i		−	0.254742i
$451$	−1856.37			−0.193820
$452$			993.036i			0.103337i
$453$			22460.4i			2.32954i
$454$		−	10907.1i		−	1.12752i
$455$	−4740.68			−0.488454
$456$		−	10977.3i		−	1.12732i
$457$	12720.1			1.30201			0.651007	−	0.759072i	$-0.274347\pi$
$457$	12720.1			1.30201			0.651007	+	0.759072i	$0.274347\pi$
$458$	6468.47			0.659938
$459$	21579.1			2.19440
$460$	3446.09			0.349293
$461$		−	3637.72i		−	0.367517i	−0.982971	−	0.183759i	$-0.941174\pi$
$461$		−	3637.72i		−	0.367517i	0.982971	−	0.183759i	$-0.0588265\pi$
$462$		−	9441.03i		−	0.950729i
$463$	−16582.0			−1.66443			−0.832215	−	0.554453i	$-0.812927\pi$
$463$	−16582.0			−1.66443			−0.832215	+	0.554453i	$0.812927\pi$
$464$	−934.574	−	1160.13i	−0.0935054	−	0.116072i
$465$	4287.42			0.427579
$466$			743.359i			0.0738958i
$467$		−	10099.7i		−	1.00077i	−0.865804	−	0.500384i	$-0.833192\pi$
$467$		−	10099.7i		−	1.00077i	0.865804	−	0.500384i	$-0.166808\pi$
$468$	−5877.47			−0.580526
$469$	−28054.7			−2.76215
$470$	2316.03			0.227299
$471$	−14283.7			−1.39736
$472$		−	9223.46i		−	0.899458i
$473$	5349.86			0.520057
$474$			16643.7i			1.61281i
$475$		−	1318.39i		−	0.127351i
$476$		−	16069.9i		−	1.54740i
$477$	−7945.91			−0.762721
$478$			3466.45i			0.331698i
$479$			2194.32i			0.209313i	0.994508	+	0.104657i	$0.0333743\pi$
$479$			2194.32i			0.209313i	−0.994508	+	0.104657i	$0.966626\pi$
$480$	−7525.24			−0.715580
$481$			3515.09i			0.333211i
$482$		−	184.278i		−	0.0174142i
$483$			50370.6i			4.74522i
$484$	4795.33			0.450350
$485$		−	7597.31i		−	0.711291i
$486$	−2388.41			−0.222923
$487$	1158.08			0.107757			0.0538784	−	0.998548i	$-0.482842\pi$
$487$	1158.08			0.107757			0.0538784	+	0.998548i	$0.482842\pi$
$488$	10039.9			0.931318
$489$	−63.9895			−0.00591760
$490$		−	9260.87i		−	0.853803i
$491$		−	21103.5i		−	1.93969i	−0.243723	−	0.969845i	$-0.578369\pi$
$491$		−	21103.5i		−	1.93969i	0.243723	−	0.969845i	$-0.421631\pi$
$492$	−4659.94			−0.427005
$493$	12249.4	−	9867.88i	1.11904	−	0.901474i
$494$	2614.94			0.238161
$495$		−	3965.19i		−	0.360044i
$496$			924.847i			0.0837235i
$497$	41536.6			3.74883
$498$	−4846.39			−0.436088
$499$	−17093.7			−1.53350			−0.766752	−	0.641943i	$-0.778128\pi$
$499$	−17093.7			−1.53350			−0.766752	+	0.641943i	$0.778128\pi$
$500$	−549.261			−0.0491274
$501$			1445.50i			0.128903i
$502$	2350.71			0.208999
$503$		−	5910.28i		−	0.523909i	−0.965080	−	0.261955i	$-0.915633\pi$
$503$		−	5910.28i		−	0.523909i	0.965080	−	0.261955i	$-0.0843671\pi$
$504$		−	43773.7i		−	3.86873i
$505$			3967.28i			0.349587i
$506$	−4611.24			−0.405128
$507$			13400.5i			1.17384i
$508$		−	973.523i		−	0.0850258i
$509$	−6979.43			−0.607776			−0.303888	−	0.952708i	$-0.598285\pi$
$509$	−6979.43			−0.607776			−0.303888	+	0.952708i	$0.598285\pi$
$510$			8458.05i			0.734370i
$511$			17681.2i			1.53067i
$512$		−	3419.36i		−	0.295148i
$513$	11298.3			0.972383
$514$			3077.91i			0.264126i
$515$	−4735.73			−0.405206
$516$	13429.5			1.14573
$517$	3776.50			0.321258
$518$	−9281.40			−0.787262
$519$		−	13844.8i		−	1.17094i
$520$		−	3072.86i		−	0.259142i
$521$	−10090.4			−0.848501			−0.424250	−	0.905545i	$-0.639462\pi$
$521$	−10090.4			−0.848501			−0.424250	+	0.905545i	$0.639462\pi$
$522$	11829.6	−	9529.69i	0.991894	−	0.799048i
$523$	−11484.9			−0.960225			−0.480112	−	0.877207i	$-0.659404\pi$
$523$	−11484.9			−0.960225			−0.480112	+	0.877207i	$0.659404\pi$
$524$			8459.20i			0.705232i
$525$		−	8028.41i		−	0.667407i
$526$	−7021.20			−0.582013
$527$	−9765.18			−0.807169
$528$	1306.19			0.107660
$529$	12435.3			1.02205
$530$		−	1472.82i		−	0.120708i
$531$	20074.4			1.64059
$532$		−	8413.81i		−	0.685686i
$533$		−	3131.07i		−	0.254449i
$534$			3182.51i			0.257904i
$535$	−2791.29			−0.225566
$536$		−	18184.8i		−	1.46541i
$537$		−	14032.8i		−	1.12767i
$538$	7153.98			0.573290
$539$		−	15100.7i		−	1.20674i
$540$		−	4707.06i		−	0.375110i
$541$			8456.28i			0.672022i	0.941858	+	0.336011i	$0.109078\pi$
$541$			8456.28i			0.672022i	−0.941858	+	0.336011i	$0.890922\pi$
$542$	5638.24			0.446833
$543$		−	13788.0i		−	1.08969i
$544$	17139.7			1.35085
$545$	1593.82			0.125269
$546$	15923.8			1.24813
$547$	4583.45			0.358271			0.179135	−	0.983824i	$-0.442670\pi$
$547$	4583.45			0.358271			0.179135	+	0.983824i	$0.442670\pi$
$548$			11828.4i			0.922053i
$549$			21851.3i			1.69871i
$550$	734.970			0.0569804
$551$	6413.51	−	5166.58i	0.495870	−	0.399463i
$552$	−32649.7			−2.51751
$553$			35982.7i			2.76698i
$554$			5790.77i			0.444091i
$555$	−5952.85			−0.455287
$556$	−4354.08			−0.332112
$557$	5834.62			0.443844			0.221922	−	0.975064i	$-0.428767\pi$
$557$	5834.62			0.443844			0.221922	+	0.975064i	$0.428767\pi$
$558$	−9430.51			−0.715458
$559$			9023.40i			0.682736i
$560$	1731.82			0.130684
$561$			13791.6i			1.03794i
$562$			7524.97i			0.564807i
$563$		−	19598.2i		−	1.46708i	−0.679647	−	0.733539i	$-0.737867\pi$
$563$		−	19598.2i		−	1.46708i	0.679647	−	0.733539i	$-0.262133\pi$
$564$	9479.93			0.707761
$565$		−	1129.97i		−	0.0841382i
$566$			1494.50i			0.110987i
$567$	18584.3			1.37649
$568$			26923.6i			1.98889i
$569$		−	997.851i		−	0.0735186i	−0.999324	−	0.0367593i	$-0.988297\pi$
$569$		−	997.851i		−	0.0735186i	0.999324	−	0.0367593i	$-0.0117035\pi$
$570$			4428.43i			0.325415i
$571$	20027.9			1.46785			0.733923	−	0.679233i	$-0.237687\pi$
$571$	20027.9			1.46785			0.733923	+	0.679233i	$0.237687\pi$
$572$		−	1776.41i		−	0.129852i
$573$	−23909.3			−1.74315
$574$	8267.41			0.601176
$575$	−3921.28			−0.284398
$576$	20461.4			1.48014
$577$		−	6224.84i		−	0.449122i	−0.974460	−	0.224561i	$-0.927905\pi$
$577$		−	6224.84i		−	0.449122i	0.974460	−	0.224561i	$-0.0720949\pi$
$578$		−	9934.94i		−	0.714947i
$579$	−12590.7			−0.903714
$580$	−2152.48	−	2671.97i	−0.154098	−	0.191289i
$581$	−10477.6			−0.748166
$582$			25519.2i			1.81753i
$583$		−	2401.57i		−	0.170605i
$584$	−11460.8			−0.812071
$585$	6687.93			0.472670
$586$	−7874.59			−0.555113
$587$	16334.3			1.14854			0.574268	−	0.818668i	$-0.305287\pi$
$587$	16334.3			1.14854			0.574268	+	0.818668i	$0.305287\pi$
$588$		−	37906.4i		−	2.65856i
$589$	−5112.81			−0.357674
$590$			3720.91i			0.259640i
$591$			9890.79i			0.688414i
$592$		−	1284.10i		−	0.0891490i
$593$	25493.7			1.76543			0.882715	−	0.469909i	$-0.155713\pi$
$593$	25493.7			1.76543			0.882715	+	0.469909i	$0.155713\pi$
$594$			6298.54i			0.435071i
$595$			18285.8i			1.25991i
$596$	−12576.5			−0.864352
$597$			9078.06i			0.622346i
$598$		−	7777.60i		−	0.531856i
$599$		−	21943.5i		−	1.49680i	−0.663245	−	0.748402i	$-0.730821\pi$
$599$		−	21943.5i		−	1.49680i	0.663245	−	0.748402i	$-0.269179\pi$
$600$	5203.93			0.354082
$601$		−	12273.7i		−	0.833034i	−0.909128	−	0.416517i	$-0.863251\pi$
$601$		−	12273.7i		−	0.833034i	0.909128	−	0.416517i	$-0.136749\pi$
$602$	−23825.8			−1.61307
$603$	39578.3			2.67289
$604$	−11158.8			−0.751731
$605$	−5456.56			−0.366679
$606$		−	13326.0i		−	0.893285i
$607$		−	25357.0i		−	1.69557i	−0.530343	−	0.847783i	$-0.677937\pi$
$607$		−	25357.0i		−	1.69557i	0.530343	−	0.847783i	$-0.322063\pi$
$608$	8973.96			0.598589
$609$	39055.5	−	31462.3i	2.59870	−	2.09346i
$610$	−4050.26			−0.268836
$611$			6369.68i			0.421750i
$612$			22670.6i			1.49740i
$613$	6356.13			0.418795			0.209398	−	0.977831i	$-0.432850\pi$
$613$	6356.13			0.418795			0.209398	+	0.977831i	$0.432850\pi$
$614$	15630.4			1.02735
$615$	5302.50			0.347671
$616$	13230.2			0.865354
$617$			510.445i			0.0333059i	0.999861	+	0.0166530i	$0.00530105\pi$
$617$			510.445i			0.0333059i	−0.999861	+	0.0166530i	$0.994699\pi$
$618$	15907.2			1.03541
$619$			19981.1i			1.29743i	0.761031	+	0.648715i	$0.224693\pi$
$619$			19981.1i			1.29743i	−0.761031	+	0.648715i	$0.775307\pi$
$620$			2130.08i			0.137978i
$621$		−	33604.5i		−	2.17150i
$622$	−15971.8			−1.02960
$623$			6880.40i			0.442468i
$624$			2203.09i			0.141337i
$625$	625.000			0.0400000
$626$		−	12140.0i		−	0.775102i
$627$			7220.96i			0.459932i
$628$		−	7096.44i		−	0.450922i
$629$	13558.4			0.859475
$630$			17659.1i			1.11676i
$631$	16407.7			1.03515			0.517575	−	0.855638i	$-0.326835\pi$
$631$	16407.7			1.03515			0.517575	+	0.855638i	$0.326835\pi$
$632$	−23323.6			−1.46798
$633$	−34726.6			−2.18050
$634$	−3766.67			−0.235952
$635$			1107.76i			0.0692287i
$636$		−	6028.52i		−	0.375859i
$637$	25469.8			1.58422
$638$	2880.25	+	3575.38i	0.178731	+	0.221866i
$639$	−58597.8			−3.62769
$640$		−	3014.12i		−	0.186162i
$641$		−	17325.2i		−	1.06756i	−0.845624	−	0.533779i	$-0.820771\pi$
$641$		−	17325.2i		−	1.06756i	0.845624	−	0.533779i	$-0.179229\pi$
$642$	9375.86			0.576380
$643$	−24341.9			−1.49293			−0.746464	−	0.665426i	$-0.768250\pi$
$643$	−24341.9			−1.49293			−0.746464	+	0.665426i	$0.768250\pi$
$644$	−25025.2			−1.53126
$645$	−15281.3			−0.932867
$646$		−	10086.4i		−	0.614307i
$647$	−17645.3			−1.07220			−0.536098	−	0.844156i	$-0.680102\pi$
$647$	−17645.3			−1.07220			−0.536098	+	0.844156i	$0.680102\pi$
$648$			12046.1i			0.730273i
$649$			6067.28i			0.366967i
$650$			1239.65i			0.0748045i
$651$	−31134.8			−1.87446
$652$		−	31.7913i		−	0.00190958i
$653$			3794.79i			0.227415i	0.993514	+	0.113707i	$0.0362726\pi$
$653$			3794.79i			0.227415i	−0.993514	+	0.113707i	$0.963727\pi$
$654$	−5353.60			−0.320095
$655$		−	9625.65i		−	0.574207i
$656$			1143.81i			0.0680768i
$657$		−	24943.8i		−	1.48120i
$658$	−16818.8			−0.996451
$659$		−	8522.85i		−	0.503798i	−0.967753	−	0.251899i	$-0.918945\pi$
$659$		−	8522.85i		−	0.503798i	0.967753	−	0.251899i	$-0.0810551\pi$
$660$	3008.37			0.177425
$661$	−1266.36			−0.0745171			−0.0372585	−	0.999306i	$-0.511863\pi$
$661$	−1266.36			−0.0745171			−0.0372585	+	0.999306i	$0.511863\pi$
$662$	−3525.92			−0.207007
$663$	−23261.8			−1.36261
$664$		−	6791.47i		−	0.396928i
$665$			9574.01i			0.558292i
$666$	13093.8			0.761821
$667$	−15367.0	−	19075.7i	−0.892071	−	1.10737i
$668$	−718.156			−0.0415963
$669$			18187.0i			1.05105i
$670$			7336.06i			0.423010i
$671$	−6604.32			−0.379966
$672$	54647.5			3.13702
$673$	−28730.7			−1.64560			−0.822800	−	0.568331i	$-0.807589\pi$
$673$	−28730.7			−1.64560			−0.822800	+	0.568331i	$0.807589\pi$
$674$	5563.35			0.317941
$675$			5356.12i			0.305418i
$676$	−6657.62			−0.378791
$677$		−	685.127i		−	0.0388945i	−0.999811	−	0.0194473i	$-0.993809\pi$
$677$		−	685.127i		−	0.0388945i	0.999811	−	0.0194473i	$-0.00619064\pi$
$678$			3795.53i			0.214995i
$679$			55170.9i			3.11821i
$680$	−11852.7			−0.668424
$681$			50800.9i			2.85858i
$682$		−	2850.27i		−	0.160033i
$683$	−23618.1			−1.32317			−0.661583	−	0.749872i	$-0.730115\pi$
$683$	−23618.1			−1.32317			−0.661583	+	0.749872i	$0.730115\pi$
$684$			11869.8i			0.663528i
$685$		−	13459.5i		−	0.750744i
$686$			43602.0i			2.42672i
$687$	−30127.5			−1.67312
$688$		−	3296.35i		−	0.182663i
$689$	4050.63			0.223972
$690$	13171.5			0.726709
$691$	5770.07			0.317661			0.158831	−	0.987306i	$-0.449228\pi$
$691$	5770.07			0.317661			0.158831	+	0.987306i	$0.449228\pi$
$692$	6878.37			0.377856
$693$			28794.8i			1.57839i
$694$		−	13496.8i		−	0.738231i
$695$	4954.47			0.270408
$696$	20393.5	+	25315.3i	1.11065	+	1.37870i
$697$	−12077.2			−0.656321
$698$		−	11481.6i		−	0.622617i
$699$		−	3462.27i		−	0.187346i
$700$	3988.68			0.215369
$701$	1521.21			0.0819619			0.0409810	−	0.999160i	$-0.486952\pi$
$701$	1521.21			0.0819619			0.0409810	+	0.999160i	$0.486952\pi$
$702$	−10623.5			−0.571166
$703$	7098.87			0.380852
$704$			6184.25i			0.331076i
$705$	−10787.1			−0.576265
$706$			1188.25i			0.0633431i
$707$		−	28810.0i		−	1.53255i
$708$			15230.4i			0.808463i
$709$	−29651.7			−1.57065			−0.785325	−	0.619083i	$-0.787504\pi$
$709$	−29651.7			−1.57065			−0.785325	+	0.619083i	$0.787504\pi$
$710$		−	10861.4i		−	0.574117i
$711$		−	50762.7i		−	2.67756i
$712$	−4459.80			−0.234744
$713$			15207.0i			0.798749i
$714$		−	61421.5i		−	3.21939i
$715$			2021.36i			0.105727i
$716$	6971.80			0.363894
$717$		−	16145.3i		−	0.840945i
$718$	17039.9			0.885686
$719$	31122.9			1.61431			0.807153	−	0.590342i	$-0.201007\pi$
$719$	31122.9			1.61431			0.807153	+	0.590342i	$0.201007\pi$
$720$	−2443.17			−0.126461
$721$	34390.4			1.77637
$722$			7743.74i			0.399158i
$723$			858.295i			0.0441498i
$724$	6850.16			0.351636
$725$	2449.29	+	3040.41i	0.125468	+	0.155749i
$726$	18328.5			0.936960
$727$		−	23361.9i		−	1.19181i	−0.803055	−	0.595904i	$-0.796794\pi$
$727$		−	23361.9i		−	1.19181i	0.803055	−	0.595904i	$-0.203206\pi$
$728$			22314.8i			1.13605i
$729$	24943.7			1.26727
$730$	4623.48			0.234414
$731$	34805.1			1.76103
$732$	−16578.4			−0.837100
$733$		−	10719.3i		−	0.540145i	−0.962840	−	0.270073i	$-0.912952\pi$
$733$		−	10719.3i		−	0.540145i	0.962840	−	0.270073i	$-0.0870477\pi$
$734$	−25105.4			−1.26247
$735$			43133.4i			2.16462i
$736$		−	26691.2i		−	1.33675i
$737$			11962.1i			0.597870i
$738$	−11663.3			−0.581749
$739$			7847.11i			0.390610i	0.980743	+	0.195305i	$0.0625696\pi$
$739$			7847.11i			0.390610i	−0.980743	+	0.195305i	$0.937430\pi$
$740$		−	2957.50i		−	0.146919i
$741$	−12179.3			−0.603804
$742$			10695.5i			0.529169i
$743$			4951.66i			0.244494i	0.992500	+	0.122247i	$0.0390100\pi$
$743$			4951.66i			0.244494i	−0.992500	+	0.122247i	$0.960990\pi$
$744$		−	20181.3i		−	0.994463i
$745$	14310.7			0.703763
$746$			10941.3i			0.536984i
$747$	14781.3			0.723989
$748$	−6851.96			−0.334937
$749$	20270.1			0.988854
$750$	−2099.36			−0.102210
$751$		−	7295.12i		−	0.354465i	−0.984169	−	0.177232i	$-0.943286\pi$
$751$		−	7295.12i		−	0.354465i	0.984169	−	0.177232i	$-0.0567144\pi$
$752$		−	2326.91i		−	0.112837i
$753$	−10948.7			−0.529870
$754$	−6030.46	+	4858.01i	−0.291268	+	0.234639i
$755$	12697.5			0.612066
$756$			34182.2i			1.64444i
$757$			36644.5i			1.75940i	0.475529	+	0.879700i	$0.342257\pi$
$757$			36644.5i			1.75940i	−0.475529	+	0.879700i	$0.657743\pi$
$758$	21732.5			1.04137
$759$	21477.3			1.02711
$760$	−6205.76			−0.296193
$761$	1770.63			0.0843436			0.0421718	−	0.999110i	$-0.486572\pi$
$761$	1770.63			0.0843436			0.0421718	+	0.999110i	$0.486572\pi$
$762$		−	3720.95i		−	0.176897i
$763$	−11574.2			−0.549165
$764$		−	11878.6i		−	0.562505i
$765$		−	25796.7i		−	1.21919i
$766$			8566.54i			0.404075i
$767$	−10233.5			−0.481758
$768$			38387.7i			1.80364i
$769$			33011.4i			1.54801i	0.633179	+	0.774005i	$0.281750\pi$
$769$			33011.4i			1.54801i	−0.633179	+	0.774005i	$0.718250\pi$
$770$	−5337.28			−0.249795
$771$		−	14335.7i		−	0.669632i
$772$		−	6255.31i		−	0.291624i
$773$			24709.6i			1.14973i	0.818248	+	0.574865i	$0.194946\pi$
$773$			24709.6i			1.14973i	−0.818248	+	0.574865i	$0.805054\pi$
$774$	33612.3			1.56094
$775$		−	2423.80i		−	0.112343i
$776$	−35761.2			−1.65432
$777$	43229.0			1.99592
$778$	−14328.4			−0.660281
$779$	−6323.32			−0.290830
$780$			5074.10i			0.232925i
$781$		−	17710.6i		−	0.811440i
$782$	−29999.8			−1.37186
$783$	−26055.7	+	20989.9i	−1.18921	+	0.958005i
$784$	−9304.38			−0.423851
$785$			8074.99i			0.367145i
$786$			32332.3i			1.46725i
$787$	−25896.9			−1.17296			−0.586482	−	0.809962i	$-0.699488\pi$
$787$	−25896.9			−1.17296			−0.586482	+	0.809962i	$0.699488\pi$
$788$	−4913.95			−0.222147
$789$	32701.9			1.47556
$790$	9409.15			0.423750
$791$			8205.72i			0.368852i
$792$	−18664.5			−0.837390
$793$		−	11139.3i		−	0.498823i
$794$			4317.34i			0.192968i
$795$			6859.80i			0.306028i
$796$	−4510.17			−0.200828
$797$		−	6523.52i		−	0.289931i	−0.989437	−	0.144965i	$-0.953693\pi$
$797$		−	6523.52i		−	0.289931i	0.989437	−	0.144965i	$-0.0463071\pi$
$798$		−	32158.8i		−	1.42658i
$799$	24569.2			1.08785
$800$			4254.23i			0.188012i
$801$		−	9706.54i		−	0.428169i
$802$		−	3427.15i		−	0.150894i
$803$	7539.00			0.331314
$804$			30027.8i			1.31716i
$805$	28475.9			1.24676
$806$	4807.45			0.210093
$807$	−33320.4			−1.45345
$808$	18674.3			0.813069
$809$		−	44983.2i		−	1.95491i	−0.211138	−	0.977456i	$-0.567717\pi$
$809$		−	44983.2i		−	1.95491i	0.211138	−	0.977456i	$-0.432283\pi$
$810$		−	4859.63i		−	0.210802i
$811$	−16112.5			−0.697640			−0.348820	−	0.937190i	$-0.613418\pi$
$811$	−16112.5			−0.697640			−0.348820	+	0.937190i	$0.613418\pi$
$812$	15631.1	+	19403.6i	0.675547	+	0.838587i
$813$	−26260.7			−1.13284
$814$			3957.45i			0.170404i
$815$			36.1751i			0.00155480i
$816$	8497.79			0.364562
$817$	18223.1			0.780351
$818$	−25553.8			−1.09226
$819$	−48567.1			−2.07213
$820$			2634.39i			0.112192i
$821$	3435.36			0.146035			0.0730177	−	0.997331i	$-0.476737\pi$
$821$	3435.36			0.146035			0.0730177	+	0.997331i	$0.476737\pi$
$822$			45210.0i			1.91835i
$823$			21261.4i			0.900519i	0.892898	+	0.450259i	$0.148668\pi$
$823$			21261.4i			0.900519i	−0.892898	+	0.450259i	$0.851332\pi$
$824$			22291.5i			0.942427i
$825$	−3423.20			−0.144461
$826$		−	27020.9i		−	1.13823i
$827$		−	14701.3i		−	0.618156i	−0.951037	−	0.309078i	$-0.899980\pi$
$827$		−	14701.3i		−	0.618156i	0.951037	−	0.309078i	$-0.100020\pi$
$828$	35304.3			1.48178
$829$			20159.1i			0.844577i	0.906461	+	0.422289i	$0.138773\pi$
$829$			20159.1i			0.844577i	−0.906461	+	0.422289i	$0.861227\pi$
$830$			2739.80i			0.114578i
$831$		−	26971.1i		−	1.12589i
$832$	−10430.7			−0.434640
$833$		−	98242.1i		−	4.08630i
$834$	−16641.9			−0.690963
$835$	817.184			0.0338681
$836$	−3587.52			−0.148418
$837$	20771.5			0.857786
$838$			14711.7i			0.606453i
$839$		−	24503.3i		−	1.00828i	−0.863622	−	0.504140i	$-0.831810\pi$
$839$		−	24503.3i		−	1.00828i	0.863622	−	0.504140i	$-0.168190\pi$
$840$	−37790.4			−1.55225
$841$	−5192.13	+	23829.9i	−0.212888	+	0.977077i
$842$	30560.4			1.25081
$843$		−	35048.3i		−	1.43194i
$844$		−	17252.9i		−	0.703636i
$845$	7575.65			0.308415
$846$	23727.1			0.964251
$847$	39625.0			1.60748
$848$	−1479.74			−0.0599228
$849$		−	6960.77i		−	0.281382i
$850$	4781.57			0.192949
$851$		−	21114.1i		−	0.850510i
$852$		−	44457.9i		−	1.78768i
$853$		−	28179.6i		−	1.13113i	−0.824705	−	0.565563i	$-0.808659\pi$
$853$		−	28179.6i		−	1.13113i	0.824705	−	0.565563i	$-0.191341\pi$
$854$	29412.6			1.17855
$855$		−	13506.6i		−	0.540251i
$856$			13138.8i			0.524621i
$857$	2986.13			0.119025			0.0595125	−	0.998228i	$-0.481045\pi$
$857$	2986.13			0.119025			0.0595125	+	0.998228i	$0.481045\pi$
$858$		−	6789.68i		−	0.270159i
$859$		−	23630.2i		−	0.938592i	−0.883041	−	0.469296i	$-0.844508\pi$
$859$		−	23630.2i		−	0.938592i	0.883041	−	0.469296i	$-0.155492\pi$
$860$		−	7592.05i		−	0.301031i
$861$	−38506.3			−1.52415
$862$			5590.45i			0.220895i
$863$	22881.1			0.902528			0.451264	−	0.892391i	$-0.350973\pi$
$863$	22881.1			0.902528			0.451264	+	0.892391i	$0.350973\pi$
$864$	−36457.9			−1.43556
$865$	−7826.84			−0.307654
$866$	−18172.0			−0.713060
$867$			46273.0i			1.81259i
$868$		−	15468.4i		−	0.604877i
$869$	15342.5			0.598916
$870$	−8227.10	−	10212.7i	−0.320603	−	0.397979i
$871$	−20176.0			−0.784890
$872$		−	7502.25i		−	0.291351i
$873$		−	77832.5i		−	3.01745i
$874$	−15707.2			−0.607899
$875$	−4538.69			−0.175355
$876$	18924.7			0.729917
$877$	−7056.62			−0.271705			−0.135852	−	0.990729i	$-0.543377\pi$
$877$	−7056.62			−0.271705			−0.135852	+	0.990729i	$0.543377\pi$
$878$		−	5357.85i		−	0.205944i
$879$	36676.7			1.40736
$880$		−	738.424i		−	0.0282867i
$881$			3010.30i			0.115119i	0.998342	+	0.0575593i	$0.0183318\pi$
$881$			3010.30i			0.115119i	−0.998342	+	0.0575593i	$0.981668\pi$
$882$		−	94875.2i		−	3.62201i
$883$	−16004.3			−0.609952			−0.304976	−	0.952360i	$-0.598648\pi$
$883$	−16004.3			−0.609952			−0.304976	+	0.952360i	$0.598648\pi$
$884$		−	11556.9i		−	0.439708i
$885$		−	17330.5i		−	0.658258i
$886$	745.431			0.0282655
$887$			15948.8i			0.603731i	0.953351	+	0.301866i	$0.0976094\pi$
$887$			15948.8i			0.603731i	−0.953351	+	0.301866i	$0.902391\pi$
$888$			28020.6i			1.05891i
$889$		−	8044.47i		−	0.303490i
$890$	1799.16			0.0677619
$891$		−	7924.07i		−	0.297942i
$892$	−9035.68			−0.339167
$893$	12863.8			0.482051
$894$	−48069.3			−1.79830
$895$	−7933.15			−0.296286
$896$			21888.3i			0.816111i
$897$			36224.9i			1.34840i
$898$	6971.23			0.259057
$899$	11791.0	−	9498.54i	0.437431	−	0.352385i
$900$	−5627.04			−0.208409
$901$		−	15624.1i		−	0.577708i
$902$		−	3525.10i		−	0.130125i
$903$	110971.			4.08957
$904$	−5318.85			−0.195689
$905$	−7794.74			−0.286305
$906$	−42650.6			−1.56399
$907$		−	9274.76i		−	0.339541i	−0.985484	−	0.169770i	$-0.945697\pi$
$907$		−	9274.76i		−	0.339541i	0.985484	−	0.169770i	$-0.0543026\pi$
$908$	−25238.9			−0.922449
$909$			40643.8i			1.48302i
$910$		−	9002.19i		−	0.327934i
$911$			36556.8i			1.32951i	0.747063	+	0.664753i	$0.231463\pi$
$911$			36556.8i			1.32951i	−0.747063	+	0.664753i	$0.768537\pi$
$912$	4449.24			0.161545
$913$			4467.50i			0.161941i
$914$			24154.5i			0.874134i
$915$	18864.5			0.681574
$916$		−	14968.0i		−	0.539908i
$917$			69900.5i			2.51725i
$918$			40977.1i			1.47325i
$919$	−21387.3			−0.767686			−0.383843	−	0.923398i	$-0.625400\pi$
$919$	−21387.3			−0.767686			−0.383843	+	0.923398i	$0.625400\pi$
$920$			18457.8i			0.661452i
$921$	−72800.2			−2.60461
$922$	6907.75			0.246740
$923$	29871.8			1.06527
$924$	−21846.5			−0.777810
$925$			3365.32i			0.119623i
$926$		−	31487.9i		−	1.11745i
$927$	−48516.3			−1.71897
$928$	−20695.4	+	16671.7i	−0.732068	+	0.589738i
$929$	46654.1			1.64765			0.823827	−	0.566841i	$-0.191835\pi$
$929$	46654.1			1.64765			0.823827	+	0.566841i	$0.191835\pi$
$930$			8141.48i			0.287064i
$931$		−	51437.2i		−	1.81073i
$932$	1720.13			0.0604556
$933$	74390.2			2.61032
$934$	19178.6			0.671886
$935$	7796.79			0.272708
$936$		−	31480.7i		−	1.09933i
$937$	−10517.9			−0.366709			−0.183354	−	0.983047i	$-0.558696\pi$
$937$	−10517.9			−0.366709			−0.183354	+	0.983047i	$0.558696\pi$
$938$		−	53273.8i		−	1.85442i
$939$			56543.4i			1.96510i
$940$		−	5359.27i		−	0.185958i
$941$	−4663.36			−0.161553			−0.0807764	−	0.996732i	$-0.525740\pi$
$941$	−4663.36			−0.161553			−0.0807764	+	0.996732i	$0.525740\pi$
$942$		−	27123.7i		−	0.938149i
$943$			18807.4i			0.649474i
$944$	3738.39			0.128892
$945$		−	38895.6i		−	1.33892i
$946$			10159.0i			0.349151i
$947$			23448.2i			0.804609i	0.915506	+	0.402305i	$0.131791\pi$
$947$			23448.2i			0.804609i	−0.915506	+	0.402305i	$0.868209\pi$
$948$	38513.4			1.31947
$949$			12715.7i			0.434953i
$950$	2503.52			0.0854998
$951$	17543.7			0.598204
$952$	86072.8			2.93029
$953$	16370.7			0.556453			0.278226	−	0.960516i	$-0.410253\pi$
$953$	16370.7			0.556453			0.278226	+	0.960516i	$0.410253\pi$
$954$		−	15088.7i		−	0.512069i
$955$			13516.6i			0.457997i
$956$	8021.33			0.271369
$957$	−13415.0	−	16652.7i	−0.453131	−	0.562492i
$958$	−4166.84			−0.140527
$959$			97741.3i			3.29117i
$960$		−	17664.6i		−	0.593878i
$961$	20391.3			0.684479
$962$	−6674.88			−0.223708
$963$	−28596.0			−0.956900
$964$	−426.419			−0.0142469
$965$			7117.86i			0.237443i
$966$	−95650.0			−3.18580
$967$		−	13315.0i		−	0.442793i	−0.975184	−	0.221397i	$-0.928938\pi$
$967$		−	13315.0i		−	0.442793i	0.975184	−	0.221397i	$-0.0710615\pi$
$968$			25684.5i			0.852822i
$969$			46978.2i			1.55744i
$970$	14426.7			0.477540
$971$			43449.1i			1.43599i	0.696048	+	0.717996i	$0.254940\pi$
$971$			43449.1i			1.43599i	−0.696048	+	0.717996i	$0.745060\pi$
$972$			5526.76i			0.182378i
$973$	−35978.9			−1.18544
$974$			2199.10i			0.0723447i
$975$		−	5773.77i		−	0.189650i
$976$			4069.29i			0.133458i
$977$	29247.4			0.957736			0.478868	−	0.877887i	$-0.341047\pi$
$977$	29247.4			0.957736			0.478868	+	0.877887i	$0.341047\pi$
$978$		−	121.511i		−	0.00397290i
$979$	2933.70			0.0957726
$980$	−21429.6			−0.698513
$981$	16328.3			0.531419
$982$	40073.9			1.30225
$983$		−	20342.3i		−	0.660039i	−0.943974	−	0.330019i	$-0.892945\pi$
$983$		−	20342.3i		−	0.660039i	0.943974	−	0.330019i	$-0.107055\pi$
$984$		−	24959.3i		−	0.808613i
$985$	5591.54			0.180874
$986$	18738.3	+	23260.7i	0.605223	+	0.751290i
$987$	78335.1			2.52628
$988$		−	6050.94i		−	0.194844i
$989$		−	54201.0i		−	1.74266i
$990$	7529.59			0.241723
$991$	15482.2			0.496275			0.248138	−	0.968725i	$-0.420181\pi$
$991$	15482.2			0.496275			0.248138	+	0.968725i	$0.420181\pi$
$992$	16498.2			0.528044
$993$	16422.3			0.524820
$994$			78874.8i			2.51686i
$995$	5132.08			0.163516
$996$			11214.5i			0.356772i
$997$			19573.8i			0.621774i	0.950447	+	0.310887i	$0.100626\pi$
$997$			19573.8i			0.621774i	−0.950447	+	0.310887i	$0.899374\pi$
$998$		−	32459.6i		−	1.02955i
$999$	−28840.1			−0.913373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.4.c.b.86.11	yes	16
29.28	even	2	inner	145.4.c.b.86.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.4.c.b.86.6	✓	16	29.28	even	2	inner
145.4.c.b.86.11	yes	16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	145.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.89892i q^{2} -8.84442i q^{3} +4.39409 q^{4} -5.00000 q^{5} +16.7949 q^{6} +36.3095 q^{7} +23.5354i q^{8} -51.2237 q^{9} +O(q^{10})\)	\(q+1.89892i q^{2} -8.84442i q^{3} +4.39409 q^{4} -5.00000 q^{5} +16.7949 q^{6} +36.3095 q^{7} +23.5354i q^{8} -51.2237 q^{9} -9.49461i q^{10} -15.4818i q^{11} -38.8632i q^{12} +26.1126 q^{13} +68.9490i q^{14} +44.2221i q^{15} -9.53923 q^{16} -100.722i q^{17} -97.2699i q^{18} -52.7355i q^{19} -21.9705 q^{20} -321.137i q^{21} +29.3988 q^{22} -156.851 q^{23} +208.157 q^{24} +25.0000 q^{25} +49.5859i q^{26} +214.245i q^{27} +159.547 q^{28} +(97.9716 + 121.616i) q^{29} -83.9743 q^{30} -96.9520i q^{31} +170.169i q^{32} -136.928 q^{33} +191.263 q^{34} -181.548 q^{35} -225.082 q^{36} +134.613i q^{37} +100.141 q^{38} -230.951i q^{39} -117.677i q^{40} -119.906i q^{41} +609.814 q^{42} +345.557i q^{43} -68.0286i q^{44} +256.119 q^{45} -297.848i q^{46} +243.931i q^{47} +84.3689i q^{48} +975.381 q^{49} +47.4731i q^{50} -890.826 q^{51} +114.741 q^{52} +155.122 q^{53} -406.834 q^{54} +77.4092i q^{55} +854.560i q^{56} -466.415 q^{57} +(-230.940 + 186.041i) q^{58} -391.897 q^{59} +194.316i q^{60} -426.585i q^{61} +184.104 q^{62} -1859.91 q^{63} -399.452 q^{64} -130.563 q^{65} -260.015i q^{66} -772.655 q^{67} -442.581i q^{68} +1387.26i q^{69} -344.745i q^{70} +1143.96 q^{71} -1205.57i q^{72} +486.958i q^{73} -255.619 q^{74} -221.110i q^{75} -231.725i q^{76} -562.138i q^{77} +438.558 q^{78} +990.999i q^{79} +47.6961 q^{80} +511.830 q^{81} +227.693 q^{82} -288.564 q^{83} -1411.10i q^{84} +503.609i q^{85} -656.186 q^{86} +(1075.63 - 866.502i) q^{87} +364.372 q^{88} +189.493i q^{89} +486.350i q^{90} +948.137 q^{91} -689.218 q^{92} -857.484 q^{93} -463.206 q^{94} +263.678i q^{95} +1505.05 q^{96} +1519.46i q^{97} +1852.17i q^{98} +793.037i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9}+O(q^{10}) \) 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9	\( 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9} - 14 q^{13} + 210 q^{16} + 310 q^{20} + 88 q^{22} + 42 q^{23} + 62 q^{24} + 400 q^{25} - 346 q^{28} + 28 q^{29} - 250 q^{30} - 460 q^{33} - 626 q^{34} - 190 q^{35} - 12 q^{36} - 292 q^{38} + 584 q^{42} + 630 q^{45} + 1894 q^{49} - 320 q^{51} - 294 q^{52} + 614 q^{53} + 1840 q^{54} - 1360 q^{57} - 644 q^{58} - 2086 q^{59} - 30 q^{62} - 1456 q^{63} - 894 q^{64} + 70 q^{65} - 1604 q^{67} + 792 q^{71} + 1720 q^{74} + 4894 q^{78} - 1050 q^{80} - 192 q^{81} + 1276 q^{82} + 4400 q^{83} - 2042 q^{86} - 2046 q^{87} - 9264 q^{88} + 212 q^{91} - 2030 q^{92} - 1816 q^{93} + 4304 q^{94} + 2234 q^{96}+O(q^{100}) \) 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9 - 14 * q^13 + 210 * q^16 + 310 * q^20 + 88 * q^22 + 42 * q^23 + 62 * q^24 + 400 * q^25 - 346 * q^28 + 28 * q^29 - 250 * q^30 - 460 * q^33 - 626 * q^34 - 190 * q^35 - 12 * q^36 - 292 * q^38 + 584 * q^42 + 630 * q^45 + 1894 * q^49 - 320 * q^51 - 294 * q^52 + 614 * q^53 + 1840 * q^54 - 1360 * q^57 - 644 * q^58 - 2086 * q^59 - 30 * q^62 - 1456 * q^63 - 894 * q^64 + 70 * q^65 - 1604 * q^67 + 792 * q^71 + 1720 * q^74 + 4894 * q^78 - 1050 * q^80 - 192 * q^81 + 1276 * q^82 + 4400 * q^83 - 2042 * q^86 - 2046 * q^87 - 9264 * q^88 + 212 * q^91 - 2030 * q^92 - 1816 * q^93 + 4304 * q^94 + 2234 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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