LMFDB - Embedded newform 165.4.c.b.34.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 66x^{12} + 1705x^{10} + 22060x^{8} + 151880x^{6} + 537860x^{4} + 825344x^{2} + 262144 $ x^14 + 66x^12 + 1705x^10 + 22060x^8 + 151880x^6 + 537860x^4 + 825344x^2 + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.9
Root			$2.41169i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.b.34.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41169i q^{2} -3.00000i q^{3} +6.00714 q^{4} +(-11.1339 - 1.01772i) q^{5} +4.23506 q^{6} +15.2844i q^{7} +19.7737i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+1.41169i q^{2} -3.00000i q^{3} +6.00714 q^{4} +(-11.1339 - 1.01772i) q^{5} +4.23506 q^{6} +15.2844i q^{7} +19.7737i q^{8} -9.00000 q^{9} +(1.43670 - 15.7176i) q^{10} +11.0000 q^{11} -18.0214i q^{12} +58.7385i q^{13} -21.5768 q^{14} +(-3.05316 + 33.4018i) q^{15} +20.1428 q^{16} +55.1122i q^{17} -12.7052i q^{18} +146.975 q^{19} +(-66.8830 - 6.11358i) q^{20} +45.8532 q^{21} +15.5286i q^{22} +4.30091i q^{23} +59.3211 q^{24} +(122.928 + 22.6624i) q^{25} -82.9205 q^{26} +27.0000i q^{27} +91.8155i q^{28} -34.2412 q^{29} +(-47.1529 - 4.31010i) q^{30} -255.359 q^{31} +186.625i q^{32} -33.0000i q^{33} -77.8012 q^{34} +(15.5552 - 170.175i) q^{35} -54.0642 q^{36} +323.110i q^{37} +207.483i q^{38} +176.216 q^{39} +(20.1241 - 220.159i) q^{40} -186.425 q^{41} +64.7304i q^{42} +119.302i q^{43} +66.0785 q^{44} +(100.205 + 9.15947i) q^{45} -6.07154 q^{46} -484.663i q^{47} -60.4284i q^{48} +109.387 q^{49} +(-31.9922 + 173.537i) q^{50} +165.337 q^{51} +352.851i q^{52} +44.8855i q^{53} -38.1156 q^{54} +(-122.473 - 11.1949i) q^{55} -302.229 q^{56} -440.925i q^{57} -48.3379i q^{58} -263.074 q^{59} +(-18.3407 + 200.649i) q^{60} +27.5825 q^{61} -360.487i q^{62} -137.560i q^{63} -102.314 q^{64} +(59.7793 - 653.990i) q^{65} +46.5857 q^{66} -1053.61i q^{67} +331.066i q^{68} +12.9027 q^{69} +(240.234 + 21.9591i) q^{70} +81.3960 q^{71} -177.963i q^{72} -623.529i q^{73} -456.130 q^{74} +(67.9872 - 368.785i) q^{75} +882.900 q^{76} +168.128i q^{77} +248.761i q^{78} +896.394 q^{79} +(-224.269 - 20.4997i) q^{80} +81.0000 q^{81} -263.174i q^{82} +575.180i q^{83} +275.446 q^{84} +(56.0887 - 613.615i) q^{85} -168.416 q^{86} +102.724i q^{87} +217.511i q^{88} +1063.68 q^{89} +(-12.9303 + 141.459i) q^{90} -897.783 q^{91} +25.8361i q^{92} +766.078i q^{93} +684.192 q^{94} +(-1636.41 - 149.579i) q^{95} +559.875 q^{96} -544.723i q^{97} +154.421i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.41169i			0.499107i	0.968361	+	0.249553i	$0.0802838\pi$
$2$			1.41169i			0.499107i	−0.968361	+	0.249553i	$0.919716\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	6.00714			0.750892
$5$	−11.1339	−	1.01772i	−0.995848	−	0.0910276i
$5$	−11.1339	−	1.01772i	−0.995848	−	0.0910276i
$6$	4.23506			0.288160
$7$			15.2844i			0.825280i	0.910894	+	0.412640i	$0.135393\pi$
$7$			15.2844i			0.825280i	−0.910894	+	0.412640i	$0.864607\pi$
$8$			19.7737i			0.873882i
$9$	−9.00000			−0.333333
$10$	1.43670	−	15.7176i	0.0454325	−	0.497035i
$11$	11.0000			0.301511
$11$	11.0000			0.301511
$12$		−	18.0214i		−	0.433528i
$13$			58.7385i			1.25316i	0.779355	+	0.626582i	$0.215547\pi$
$13$			58.7385i			1.25316i	−0.779355	+	0.626582i	$0.784453\pi$
$14$	−21.5768			−0.411903
$15$	−3.05316	+	33.4018i	−0.0525548	+	0.574953i
$16$	20.1428			0.314731
$17$			55.1122i			0.786274i	0.919480	+	0.393137i	$0.128610\pi$
$17$			55.1122i			0.786274i	−0.919480	+	0.393137i	$0.871390\pi$
$18$		−	12.7052i		−	0.166369i
$19$	146.975			1.77465			0.887326	−	0.461142i	$-0.152560\pi$
$19$	146.975			1.77465			0.887326	+	0.461142i	$0.152560\pi$
$20$	−66.8830	−	6.11358i	−0.747775	−	0.0683519i
$21$	45.8532			0.476475
$22$			15.5286i			0.150486i
$23$			4.30091i			0.0389914i	0.999810	+	0.0194957i	$0.00620606\pi$
$23$			4.30091i			0.0389914i	−0.999810	+	0.0194957i	$0.993794\pi$
$24$	59.3211			0.504536
$25$	122.928	+	22.6624i	0.983428	+	0.181299i
$26$	−82.9205			−0.625463
$27$			27.0000i			0.192450i
$28$			91.8155i			0.619696i
$29$	−34.2412			−0.219256			−0.109628	−	0.993973i	$-0.534966\pi$
$29$	−34.2412			−0.219256			−0.109628	+	0.993973i	$0.534966\pi$
$30$	−47.1529	−	4.31010i	−0.286963	−	0.0262305i
$31$	−255.359			−1.47948			−0.739740	−	0.672893i	$-0.765051\pi$
$31$	−255.359			−1.47948			−0.739740	+	0.672893i	$0.765051\pi$
$32$			186.625i			1.03097i
$33$		−	33.0000i		−	0.174078i
$34$	−77.8012			−0.392435
$35$	15.5552	−	170.175i	0.0751232	−	0.821853i
$36$	−54.0642			−0.250297
$37$			323.110i			1.43565i	0.696225	+	0.717824i	$0.254862\pi$
$37$			323.110i			1.43565i	−0.696225	+	0.717824i	$0.745138\pi$
$38$			207.483i			0.885742i
$39$	176.216			0.723515
$40$	20.1241	−	220.159i	0.0795474	−	0.870254i
$41$	−186.425			−0.710116			−0.355058	−	0.934844i	$-0.615539\pi$
$41$	−186.425			−0.710116			−0.355058	+	0.934844i	$0.615539\pi$
$42$			64.7304i			0.237812i
$43$			119.302i			0.423100i	0.977367	+	0.211550i	$0.0678512\pi$
$43$			119.302i			0.423100i	−0.977367	+	0.211550i	$0.932149\pi$
$44$	66.0785			0.226403
$45$	100.205	+	9.15947i	0.331949	+	0.0303425i
$46$	−6.07154			−0.0194609
$47$		−	484.663i		−	1.50416i	−0.659074	−	0.752078i	$-0.729052\pi$
$47$		−	484.663i		−	1.50416i	0.659074	−	0.752078i	$-0.270948\pi$
$48$		−	60.4284i		−	0.181710i
$49$	109.387			0.318913
$50$	−31.9922	+	173.537i	−0.0904877	+	0.490836i
$51$	165.337			0.453956
$52$			352.851i			0.940992i
$53$			44.8855i			0.116330i	0.998307	+	0.0581651i	$0.0185250\pi$
$53$			44.8855i			0.116330i	−0.998307	+	0.0581651i	$0.981475\pi$
$54$	−38.1156			−0.0960532
$55$	−122.473	−	11.1949i	−0.300260	−	0.0274458i
$56$	−302.229			−0.721197
$57$		−	440.925i		−	1.02460i
$58$		−	48.3379i		−	0.109432i
$59$	−263.074			−0.580498			−0.290249	−	0.956951i	$-0.593738\pi$
$59$	−263.074			−0.580498			−0.290249	+	0.956951i	$0.593738\pi$
$60$	−18.3407	+	200.649i	−0.0394630	+	0.431728i
$61$	27.5825			0.0578948			0.0289474	−	0.999581i	$-0.490784\pi$
$61$	27.5825			0.0578948			0.0289474	+	0.999581i	$0.490784\pi$
$62$		−	360.487i		−	0.738419i
$63$		−	137.560i		−	0.275093i
$64$	−102.314			−0.199831
$65$	59.7793	−	653.990i	0.114073	−	1.24796i
$66$	46.5857			0.0868834
$67$		−	1053.61i		−	1.92118i	−0.277969	−	0.960590i	$-0.589661\pi$
$67$		−	1053.61i		−	1.92118i	0.277969	−	0.960590i	$-0.410339\pi$
$68$			331.066i			0.590407i
$69$	12.9027			0.0225117
$70$	240.234	+	21.9591i	0.410193	+	0.0374945i
$71$	81.3960			0.136055			0.0680276	−	0.997683i	$-0.478329\pi$
$71$	81.3960			0.136055			0.0680276	+	0.997683i	$0.478329\pi$
$72$		−	177.963i		−	0.291294i
$73$		−	623.529i		−	0.999707i	−0.866110	−	0.499853i	$-0.833387\pi$
$73$		−	623.529i		−	0.999707i	0.866110	−	0.499853i	$-0.166613\pi$
$74$	−456.130			−0.716542
$75$	67.9872	−	368.785i	0.104673	−	0.567782i
$76$	882.900			1.33257
$77$			168.128i			0.248831i
$78$			248.761i			0.361111i
$79$	896.394			1.27661			0.638305	−	0.769784i	$-0.279636\pi$
$79$	896.394			1.27661			0.638305	+	0.769784i	$0.279636\pi$
$80$	−224.269	−	20.4997i	−0.313425	−	0.0286492i
$81$	81.0000			0.111111
$82$		−	263.174i		−	0.354424i
$83$			575.180i			0.760653i	0.924852	+	0.380326i	$0.124188\pi$
$83$			575.180i			0.760653i	−0.924852	+	0.380326i	$0.875812\pi$
$84$	275.446			0.357782
$85$	56.0887	−	613.615i	0.0715727	−	0.783010i
$86$	−168.416			−0.211172
$87$			102.724i			0.126588i
$88$			217.511i			0.263485i
$89$	1063.68			1.26685			0.633426	−	0.773803i	$-0.281648\pi$
$89$	1063.68			1.26685			0.633426	+	0.773803i	$0.281648\pi$
$90$	−12.9303	+	141.459i	−0.0151442	+	0.165678i
$91$	−897.783			−1.03421
$92$			25.8361i			0.0292783i
$93$			766.078i			0.854178i
$94$	684.192			0.750735
$95$	−1636.41	−	149.579i	−1.76729	−	0.161542i
$96$	559.875			0.595229
$97$		−	544.723i		−	0.570188i	−0.958499	−	0.285094i	$-0.907975\pi$
$97$		−	544.723i		−	0.570188i	0.958499	−	0.285094i	$-0.0920249\pi$
$98$			154.421i			0.159172i
$99$	−99.0000			−0.100504
$100$	738.448	+	136.136i	0.738448	+	0.136136i
$101$	−1124.51			−1.10785			−0.553925	−	0.832567i	$-0.686871\pi$
$101$	−1124.51			−1.10785			−0.553925	+	0.832567i	$0.686871\pi$
$102$			233.404i			0.226572i
$103$			1275.53i			1.22021i	0.792322	+	0.610103i	$0.208872\pi$
$103$			1275.53i			1.22021i	−0.792322	+	0.610103i	$0.791128\pi$
$104$	−1161.48			−1.09512
$105$	−510.526	−	46.6657i	−0.474497	−	0.0433724i
$106$	−63.3644			−0.0580612
$107$		−	946.142i		−	0.854832i	−0.904055	−	0.427416i	$-0.859424\pi$
$107$		−	946.142i		−	0.854832i	0.904055	−	0.427416i	$-0.140576\pi$
$108$			162.193i			0.144509i
$109$	−472.202			−0.414943			−0.207472	−	0.978241i	$-0.566523\pi$
$109$	−472.202			−0.414943			−0.207472	+	0.978241i	$0.566523\pi$
$110$	15.8037	−	172.894i	0.0136984	−	0.149862i
$111$	969.330			0.828872
$112$			307.871i			0.259742i
$113$		−	185.707i		−	0.154601i	−0.997008	−	0.0773004i	$-0.975370\pi$
$113$		−	185.707i		−	0.154601i	0.997008	−	0.0773004i	$-0.0246300\pi$
$114$	622.449			0.511383
$115$	4.37712	−	47.8860i	0.00354929	−	0.0388295i
$116$	−205.692			−0.164638
$117$		−	528.647i		−	0.417722i
$118$		−	371.379i		−	0.289731i
$119$	−842.356			−0.648896
$120$	−660.477	−	60.3722i	−0.502442	−	0.0459267i
$121$	121.000			0.0909091
$122$			38.9379i			0.0288957i
$123$			559.276i			0.409986i
$124$	−1533.98			−1.11093
$125$	−1345.61	−	377.428i	−0.962842	−	0.270066i
$126$	194.191			0.137301
$127$		−	1866.06i		−	1.30383i	−0.758294	−	0.651913i	$-0.773967\pi$
$127$		−	1866.06i		−	1.30383i	0.758294	−	0.651913i	$-0.226033\pi$
$128$			1348.56i			0.931230i
$129$	357.905			0.244277
$130$	923.230	+	84.3897i	0.622866	+	0.0569344i
$131$	2163.02			1.44262			0.721311	−	0.692611i	$-0.243540\pi$
$131$	2163.02			1.44262			0.721311	+	0.692611i	$0.243540\pi$
$132$		−	198.236i		−	0.130714i
$133$			2246.43i			1.46459i
$134$	1487.37			0.958874
$135$	27.4784	−	300.616i	0.0175183	−	0.191651i
$136$	−1089.77			−0.687111
$137$			2175.20i			1.35650i	0.734832	+	0.678249i	$0.237261\pi$
$137$			2175.20i			1.35650i	−0.734832	+	0.678249i	$0.762739\pi$
$138$			18.2146i			0.0112357i
$139$	−1280.43			−0.781331			−0.390666	−	0.920533i	$-0.627755\pi$
$139$	−1280.43			−0.781331			−0.390666	+	0.920533i	$0.627755\pi$
$140$	93.4424	−	1022.27i	0.0564094	−	0.617123i
$141$	−1453.99			−0.868425
$142$			114.906i			0.0679061i
$143$			646.124i			0.377843i
$144$	−181.285			−0.104910
$145$	381.239	+	34.8480i	0.218346	+	0.0199584i
$146$	880.229			0.498961
$147$		−	328.162i		−	0.184125i
$148$			1940.97i			1.07802i
$149$	−440.136			−0.241996			−0.120998	−	0.992653i	$-0.538609\pi$
$149$	−440.136			−0.241996			−0.120998	+	0.992653i	$0.538609\pi$
$150$	520.610	+	95.9767i	0.283384	+	0.0522431i
$151$	2100.57			1.13207			0.566034	−	0.824382i	$-0.308477\pi$
$151$	2100.57			1.13207			0.566034	+	0.824382i	$0.308477\pi$
$152$			2906.24i			1.55084i
$153$		−	496.010i		−	0.262091i
$154$	−237.345			−0.124193
$155$	2843.15	+	259.884i	1.47334	+	0.134673i
$156$	1058.55			0.543282
$157$		−	688.807i		−	0.350145i	−0.984556	−	0.175073i	$-0.943984\pi$
$157$		−	688.807i		−	0.350145i	0.984556	−	0.175073i	$-0.0560160\pi$
$158$			1265.43i			0.637165i
$159$	134.657			0.0671633
$160$	189.932	−	2077.87i	0.0938464	−	1.02669i
$161$	−65.7368			−0.0321788
$162$			114.347i			0.0554563i
$163$			1800.54i			0.865207i	0.901584	+	0.432604i	$0.142405\pi$
$163$			1800.54i			0.865207i	−0.901584	+	0.432604i	$0.857595\pi$
$164$	−1119.88			−0.533220
$165$	−33.5847	+	367.419i	−0.0158459	+	0.173355i
$166$	−811.974			−0.379647
$167$			3420.45i			1.58493i	0.609920	+	0.792463i	$0.291201\pi$
$167$			3420.45i			1.58493i	−0.609920	+	0.792463i	$0.708799\pi$
$168$			906.687i			0.416384i
$169$	−1253.22			−0.570421
$170$	866.232	+	79.1797i	0.390806	+	0.0357224i
$171$	−1322.78			−0.591551
$172$			716.661i			0.317703i
$173$		−	2326.51i		−	1.02243i	−0.859452	−	0.511216i	$-0.829195\pi$
$173$		−	2326.51i		−	1.02243i	0.859452	−	0.511216i	$-0.170805\pi$
$174$	−145.014			−0.0631808
$175$	−346.381	+	1878.89i	−0.149623	+	0.811603i
$176$	221.571			0.0948951
$177$			789.223i			0.335151i
$178$			1501.58i			0.632295i
$179$	4072.53			1.70053			0.850266	−	0.526353i	$-0.176441\pi$
$179$	4072.53			1.70053			0.850266	+	0.526353i	$0.176441\pi$
$180$	601.947	+	55.0222i	0.249258	+	0.0227840i
$181$	435.684			0.178918			0.0894590	−	0.995991i	$-0.471486\pi$
$181$	435.684			0.178918			0.0894590	+	0.995991i	$0.471486\pi$
$182$		−	1267.39i		−	0.516182i
$183$		−	82.7476i		−	0.0334256i
$184$	−85.0449			−0.0340739
$185$	328.835	−	3597.48i	0.130684	−	1.42969i
$186$	−1081.46			−0.426326
$187$			606.234i			0.237071i
$188$		−	2911.44i		−	1.12946i
$189$	−412.679			−0.158825
$190$	211.159	−	2310.10i	0.0806269	−	0.882064i
$191$	3120.75			1.18225			0.591125	−	0.806580i	$-0.298684\pi$
$191$	3120.75			1.18225			0.591125	+	0.806580i	$0.298684\pi$
$192$			306.941i			0.115373i
$193$		−	1100.45i		−	0.410427i	−0.978717	−	0.205213i	$-0.934211\pi$
$193$		−	1100.45i		−	0.410427i	0.978717	−	0.205213i	$-0.0657888\pi$
$194$	768.979			0.284585
$195$	−1961.97	−	179.338i	−0.720511	−	0.0658598i
$196$	657.105			0.239470
$197$		−	5347.12i		−	1.93384i	−0.255082	−	0.966920i	$-0.582102\pi$
$197$		−	5347.12i		−	1.93384i	0.255082	−	0.966920i	$-0.417898\pi$
$198$		−	139.757i		−	0.0501621i
$199$	−5103.80			−1.81808			−0.909042	−	0.416705i	$-0.863185\pi$
$199$	−5103.80			−1.81808			−0.909042	+	0.416705i	$0.863185\pi$
$200$	−448.120	+	2430.75i	−0.158434	+	0.859400i
$201$	−3160.83			−1.10919
$202$		−	1587.46i		−	0.552935i
$203$		−	523.357i		−	0.180948i
$204$	993.199			0.340872
$205$	2075.65	+	189.729i	0.707168	+	0.0646401i
$206$	−1800.64			−0.609013
$207$		−	38.7082i		−	0.0129971i
$208$			1183.16i			0.394410i
$209$	1616.73			0.535078
$210$	65.8773	−	720.703i	0.0216475	−	0.236825i
$211$	1645.58			0.536902			0.268451	−	0.963293i	$-0.413488\pi$
$211$	1645.58			0.536902			0.268451	+	0.963293i	$0.413488\pi$
$212$			269.634i			0.0873515i
$213$		−	244.188i		−	0.0785515i
$214$	1335.66			0.426653
$215$	121.415	−	1328.29i	0.0385138	−	0.421344i
$216$	−533.890			−0.168179
$217$		−	3903.01i		−	1.22098i
$218$		−	666.602i		−	0.207101i
$219$	−1870.59			−0.577181
$220$	−735.713	−	67.2494i	−0.225463	−	0.0206089i
$221$	−3237.21			−0.985331
$222$			1368.39i			0.413696i
$223$		−	2592.93i		−	0.778635i	−0.921104	−	0.389318i	$-0.872711\pi$
$223$		−	2592.93i		−	0.778635i	0.921104	−	0.389318i	$-0.127289\pi$
$224$	−2852.45			−0.850836
$225$	−1106.36	−	203.962i	−0.327809	−	0.0604331i
$226$	262.161			0.0771623
$227$		−	916.297i		−	0.267915i	−0.990987	−	0.133958i	$-0.957231\pi$
$227$		−	916.297i		−	0.267915i	0.990987	−	0.133958i	$-0.0427686\pi$
$228$		−	2648.70i		−	0.769361i
$229$	−4300.85			−1.24108			−0.620542	−	0.784173i	$-0.713087\pi$
$229$	−4300.85			−1.24108			−0.620542	+	0.784173i	$0.713087\pi$
$230$	67.6000	+	6.17912i	0.0193801	+	0.00177147i
$231$	504.385			0.143663
$232$		−	677.076i		−	0.191604i
$233$			4196.20i			1.17984i	0.807463	+	0.589918i	$0.200840\pi$
$233$			4196.20i			1.17984i	−0.807463	+	0.589918i	$0.799160\pi$
$234$	746.284			0.208488
$235$	−493.251	+	5396.20i	−0.136920	+	1.49791i
$236$	−1580.32			−0.435891
$237$		−	2689.18i		−	0.737051i
$238$		−	1189.14i		−	0.323869i
$239$	3150.37			0.852639			0.426319	−	0.904573i	$-0.359810\pi$
$239$	3150.37			0.852639			0.426319	+	0.904573i	$0.359810\pi$
$240$	−61.4992	+	672.806i	−0.0165406	+	0.180956i
$241$	4864.06			1.30009			0.650044	−	0.759896i	$-0.274750\pi$
$241$	4864.06			1.30009			0.650044	+	0.759896i	$0.274750\pi$
$242$			170.814i			0.0453734i
$243$		−	243.000i		−	0.0641500i
$244$	165.692			0.0434727
$245$	−1217.91	−	111.326i	−0.317589	−	0.0290299i
$246$	−789.523			−0.204627
$247$			8633.10i			2.22393i
$248$		−	5049.40i		−	1.29289i
$249$	1725.54			0.439163
$250$	532.811	−	1899.58i	0.134792	−	0.480561i
$251$	5366.11			1.34942			0.674712	−	0.738081i	$-0.264268\pi$
$251$	5366.11			1.34942			0.674712	+	0.738081i	$0.264268\pi$
$252$		−	826.339i		−	0.206565i
$253$			47.3100i			0.0117563i
$254$	2634.29			0.650749
$255$	−1840.84	−	168.266i	−0.452071	−	0.0413225i
$256$	−2722.26			−0.664615
$257$		−	406.491i		−	0.0986624i	−0.998782	−	0.0493312i	$-0.984291\pi$
$257$		−	406.491i		−	0.0986624i	0.998782	−	0.0493312i	$-0.0157090\pi$
$258$			505.249i			0.121920i
$259$	−4938.54			−1.18481
$260$	359.103	−	3928.61i	0.0856562	−	0.937085i
$261$	308.171			0.0730855
$262$			3053.50i			0.720023i
$263$			8009.69i			1.87794i	0.343996	+	0.938971i	$0.388219\pi$
$263$			8009.69i			1.87794i	−0.343996	+	0.938971i	$0.611781\pi$
$264$	652.532			0.152123
$265$	45.6809	−	499.752i	0.0105893	−	0.115847i
$266$	−3171.25			−0.730985
$267$		−	3191.04i		−	0.731418i
$268$		−	6329.19i		−	1.44260i
$269$	4762.72			1.07951			0.539755	−	0.841822i	$-0.318517\pi$
$269$	4762.72			1.07951			0.539755	+	0.841822i	$0.318517\pi$
$270$	424.376	+	38.7909i	0.0956544	+	0.00874349i
$271$	−4454.85			−0.998570			−0.499285	−	0.866438i	$-0.666404\pi$
$271$	−4454.85			−0.998570			−0.499285	+	0.866438i	$0.666404\pi$
$272$			1110.11i			0.247465i
$273$			2693.35i			0.597102i
$274$	−3070.71			−0.677038
$275$	1352.21	+	249.287i	0.296515	+	0.0546638i
$276$	77.5084			0.0169038
$277$		−	2090.00i		−	0.453343i	−0.973971	−	0.226671i	$-0.927216\pi$
$277$		−	2090.00i		−	0.453343i	0.973971	−	0.226671i	$-0.0727843\pi$
$278$		−	1807.57i		−	0.389968i
$279$	2298.23			0.493160
$280$	3365.00	+	307.584i	0.718203	+	0.0656489i
$281$	3261.96			0.692499			0.346250	−	0.938142i	$-0.387455\pi$
$281$	3261.96			0.692499			0.346250	+	0.938142i	$0.387455\pi$
$282$		−	2052.58i		−	0.433437i
$283$		−	5421.25i		−	1.13873i	−0.822086	−	0.569363i	$-0.807190\pi$
$283$		−	5421.25i		−	1.13873i	0.822086	−	0.569363i	$-0.192810\pi$
$284$	488.957			0.102163
$285$	−448.738	+	4909.23i	−0.0932665	+	1.02034i
$286$	−912.125			−0.188584
$287$		−	2849.40i		−	0.586044i
$288$		−	1679.62i		−	0.343656i
$289$	1875.65			0.381772
$290$	−49.1944	+	538.191i	−0.00996137	+	0.108978i
$291$	−1634.17			−0.329198
$292$		−	3745.63i		−	0.750672i
$293$		−	7383.35i		−	1.47215i	−0.676900	−	0.736075i	$-0.736677\pi$
$293$		−	7383.35i		−	1.47215i	0.676900	−	0.736075i	$-0.263323\pi$
$294$	463.262			0.0918979
$295$	2929.05	+	267.736i	0.578088	+	0.0528413i
$296$	−6389.08			−1.25459
$297$			297.000i			0.0580259i
$298$		−	621.335i		−	0.120782i
$299$	−252.629			−0.0488626
$300$	408.409	−	2215.35i	0.0785983	−	0.426343i
$301$	−1823.45			−0.349176
$302$			2965.35i			0.565023i
$303$			3373.53i			0.639617i
$304$	2960.49			0.558539
$305$	−307.102	−	28.0713i	−0.0576544	−	0.00527002i
$306$	700.211			0.130812
$307$		−	397.190i		−	0.0738399i	−0.999318	−	0.0369200i	$-0.988245\pi$
$307$		−	397.190i		−	0.0738399i	0.999318	−	0.0369200i	$-0.0117547\pi$
$308$			1009.97i			0.186845i
$309$	3826.58			0.704486
$310$	−366.875	+	4013.64i	−0.0672164	+	0.735353i
$311$	−163.865			−0.0298775			−0.0149388	−	0.999888i	$-0.504755\pi$
$311$	−163.865			−0.0298775			−0.0149388	+	0.999888i	$0.504755\pi$
$312$			3484.44i			0.632267i
$313$			2498.48i			0.451189i	0.974221	+	0.225595i	$0.0724325\pi$
$313$			2498.48i			0.451189i	−0.974221	+	0.225595i	$0.927568\pi$
$314$	972.381			0.174760
$315$	−139.997	+	1531.58i	−0.0250411	+	0.273951i
$316$	5384.76			0.958596
$317$		−	411.403i		−	0.0728917i	−0.999336	−	0.0364459i	$-0.988396\pi$
$317$		−	411.403i		−	0.0728917i	0.999336	−	0.0364459i	$-0.0116036\pi$
$318$			190.093i			0.0335217i
$319$	−376.654			−0.0661083
$320$	1139.15	+	104.127i	0.199002	+	0.0181902i
$321$	−2838.43			−0.493537
$322$		−	92.7998i		−	0.0160607i
$323$			8100.12i			1.39536i
$324$	486.578			0.0834325
$325$	−1331.16	+	7220.64i	−0.227198	+	1.23240i
$326$	−2541.79			−0.431831
$327$			1416.61i			0.239568i
$328$		−	3686.32i		−	0.620558i
$329$	7407.78			1.24135
$330$	−518.681	−	47.4111i	−0.0865227	−	0.00790878i
$331$	−2282.08			−0.378957			−0.189478	−	0.981885i	$-0.560680\pi$
$331$	−2282.08			−0.378957			−0.189478	+	0.981885i	$0.560680\pi$
$332$			3455.18i			0.571168i
$333$		−	2907.99i		−	0.478549i
$334$	−4828.61			−0.791047
$335$	−1072.28	+	11730.8i	−0.174880	+	1.91320i
$336$	923.612			0.149962
$337$		−	2451.29i		−	0.396233i	−0.980179	−	0.198116i	$-0.936518\pi$
$337$		−	2451.29i		−	0.396233i	0.980179	−	0.198116i	$-0.0634824\pi$
$338$		−	1769.15i		−	0.284701i
$339$	−557.122			−0.0892588
$340$	336.933	−	3686.07i	0.0537434	−	0.587956i
$341$	−2808.95			−0.446080
$342$		−	1867.35i		−	0.295247i
$343$			6914.47i			1.08847i
$344$	−2359.03			−0.369740
$345$	−143.658	−	13.1313i	−0.0224182	−	0.00204918i
$346$	3284.30			0.510303
$347$			3950.82i			0.611214i	0.952158	+	0.305607i	$0.0988594\pi$
$347$			3950.82i			0.611214i	−0.952158	+	0.305607i	$0.901141\pi$
$348$			617.075i			0.0950538i
$349$	−8241.77			−1.26410			−0.632051	−	0.774926i	$-0.717787\pi$
$349$	−8241.77			−1.26410			−0.632051	+	0.774926i	$0.717787\pi$
$350$	−2652.40	−	488.982i	−0.405077	−	0.0746777i
$351$	−1585.94			−0.241172
$352$			2052.87i			0.310848i
$353$		−	4882.59i		−	0.736187i	−0.929789	−	0.368094i	$-0.880011\pi$
$353$		−	4882.59i		−	0.736187i	0.929789	−	0.368094i	$-0.119989\pi$
$354$	−1114.14			−0.167276
$355$	−906.256	−	82.8382i	−0.135490	−	0.0123848i
$356$	6389.67			0.951270
$357$			2527.07i			0.374640i
$358$			5749.14i			0.848748i
$359$	−232.369			−0.0341615			−0.0170808	−	0.999854i	$-0.505437\pi$
$359$	−232.369			−0.0341615			−0.0170808	+	0.999854i	$0.505437\pi$
$360$	−181.117	+	1981.43i	−0.0265158	+	0.290085i
$361$	14742.7			2.14939
$362$			615.050i			0.0892992i
$363$		−	363.000i		−	0.0524864i
$364$	−5393.11			−0.776581
$365$	−634.578	+	6942.33i	−0.0910009	+	0.995556i
$366$	116.814			0.0166829
$367$			10953.0i			1.55788i	0.627099	+	0.778940i	$0.284242\pi$
$367$			10953.0i			1.55788i	−0.627099	+	0.778940i	$0.715758\pi$
$368$			86.6324i			0.0122718i
$369$	1677.83			0.236705
$370$	5078.52	+	464.213i	0.713567	+	0.0652251i
$371$	−686.048			−0.0960050
$372$			4601.93i			0.641396i
$373$		−	5165.78i		−	0.717089i	−0.933513	−	0.358544i	$-0.883273\pi$
$373$		−	5165.78i		−	0.717089i	0.933513	−	0.358544i	$-0.116727\pi$
$374$	−855.813			−0.118324
$375$	−1132.28	+	4036.84i	−0.155922	+	0.555897i
$376$	9583.58			1.31446
$377$		−	2011.28i		−	0.274764i
$378$		−	582.573i		−	0.0792707i
$379$	−6076.10			−0.823505			−0.411752	−	0.911296i	$-0.635083\pi$
$379$	−6076.10			−0.823505			−0.411752	+	0.911296i	$0.635083\pi$
$380$	−9830.14	−	898.544i	−1.32704	−	0.121301i
$381$	−5598.18			−0.752764
$382$			4405.52i			0.590069i
$383$		−	4767.71i		−	0.636080i	−0.948077	−	0.318040i	$-0.896975\pi$
$383$		−	4767.71i		−	0.636080i	0.948077	−	0.318040i	$-0.103025\pi$
$384$	4045.69			0.537646
$385$	171.107	−	1871.93i	0.0226505	−	0.247798i
$386$	1553.50			0.204847
$387$		−	1073.71i		−	0.141033i
$388$		−	3272.23i		−	0.428150i
$389$	10533.7			1.37295			0.686476	−	0.727152i	$-0.259157\pi$
$389$	10533.7			1.37295			0.686476	+	0.727152i	$0.259157\pi$
$390$	253.169	−	2769.69i	0.0328711	−	0.359612i
$391$	−237.032			−0.0306579
$392$			2162.99i			0.278693i
$393$		−	6489.05i		−	0.832898i
$394$	7548.46			0.965192
$395$	−9980.38	−	912.277i	−1.27131	−	0.116207i
$396$	−594.707			−0.0754675
$397$		−	3463.58i		−	0.437865i	−0.975740	−	0.218932i	$-0.929743\pi$
$397$		−	3463.58i		−	0.437865i	0.975740	−	0.218932i	$-0.0702574\pi$
$398$		−	7204.97i		−	0.907418i
$399$	6739.28			0.845579
$400$	2476.13	+	456.485i	0.309516	+	0.0570606i
$401$	−4337.43			−0.540152			−0.270076	−	0.962839i	$-0.587049\pi$
$401$	−4337.43			−0.540152			−0.270076	+	0.962839i	$0.587049\pi$
$402$		−	4462.11i		−	0.553606i
$403$		−	14999.4i		−	1.85403i
$404$	−6755.08			−0.831876
$405$	−901.848	−	82.4353i	−0.110650	−	0.0101142i
$406$	738.816			0.0903124
$407$			3554.21i			0.432864i
$408$			3269.32i			0.396704i
$409$	−7287.09			−0.880986			−0.440493	−	0.897756i	$-0.645196\pi$
$409$	−7287.09			−0.880986			−0.440493	+	0.897756i	$0.645196\pi$
$410$	−267.838	+	2930.16i	−0.0322623	+	0.352952i
$411$	6525.61			0.783175
$412$			7662.26i			0.916243i
$413$		−	4020.93i		−	0.479073i
$414$	54.6438			0.00648695
$415$	585.371	−	6404.01i	0.0692404	−	0.757495i
$416$	−10962.1			−1.29197
$417$			3841.30i			0.451102i
$418$			2282.31i			0.267061i
$419$	−10603.5			−1.23631			−0.618156	−	0.786056i	$-0.712120\pi$
$419$	−10603.5			−1.23631			−0.618156	+	0.786056i	$0.712120\pi$
$420$	−3066.80	−	280.327i	−0.356296	−	0.0325680i
$421$	8344.14			0.965959			0.482979	−	0.875632i	$-0.339555\pi$
$421$	8344.14			0.965959			0.482979	+	0.875632i	$0.339555\pi$
$422$			2323.04i			0.267971i
$423$			4361.96i			0.501385i
$424$	−887.553			−0.101659
$425$	−1248.97	+	6774.86i	−0.142551	+	0.773244i
$426$	344.717			0.0392056
$427$			421.582i			0.0477794i
$428$		−	5683.61i		−	0.641887i
$429$	1938.37			0.218148
$430$	1875.14	+	171.401i	0.210296	+	0.0192225i
$431$	−1313.51			−0.146797			−0.0733987	−	0.997303i	$-0.523385\pi$
$431$	−1313.51			−0.146797			−0.0733987	+	0.997303i	$0.523385\pi$
$432$			543.856i			0.0605701i
$433$		−	11108.3i		−	1.23287i	−0.787408	−	0.616433i	$-0.788577\pi$
$433$		−	11108.3i		−	1.23287i	0.787408	−	0.616433i	$-0.211423\pi$
$434$	5509.83			0.609402
$435$	104.544	−	1143.72i	0.0115230	−	0.126062i
$436$	−2836.59			−0.311578
$437$			632.126i			0.0691961i
$438$		−	2640.69i		−	0.288075i
$439$	5527.06			0.600894			0.300447	−	0.953799i	$-0.402864\pi$
$439$	5527.06			0.600894			0.300447	+	0.953799i	$0.402864\pi$
$440$	221.365	−	2421.75i	0.0239844	−	0.262392i
$441$	−984.486			−0.106304
$442$		−	4569.93i		−	0.491786i
$443$			6792.28i			0.728467i	0.931308	+	0.364234i	$0.118669\pi$
$443$			6792.28i			0.728467i	−0.931308	+	0.364234i	$0.881331\pi$
$444$	5822.90			0.622393
$445$	−11842.9	−	1082.53i	−1.26159	−	0.115318i
$446$	3660.41			0.388622
$447$			1320.41i			0.139716i
$448$		−	1563.80i		−	0.164917i
$449$	−8575.87			−0.901382			−0.450691	−	0.892680i	$-0.648822\pi$
$449$	−8575.87			−0.901382			−0.450691	+	0.892680i	$0.648822\pi$
$450$	287.930	−	1561.83i	0.0301626	−	0.163612i
$451$	−2050.68			−0.214108
$452$		−	1115.57i		−	0.116089i
$453$		−	6301.72i		−	0.653599i
$454$	1293.52			0.133718
$455$	9995.85	+	913.691i	1.02992	+	0.0941417i
$456$	8718.73			0.895377
$457$		−	6527.74i		−	0.668173i	−0.942542	−	0.334086i	$-0.891572\pi$
$457$		−	6527.74i		−	0.668173i	0.942542	−	0.334086i	$-0.108428\pi$
$458$		−	6071.46i		−	0.619434i
$459$	−1488.03			−0.151319
$460$	26.2939	−	287.658i	0.00266513	−	0.0291568i
$461$	−3071.00			−0.310262			−0.155131	−	0.987894i	$-0.549580\pi$
$461$	−3071.00			−0.310262			−0.155131	+	0.987894i	$0.549580\pi$
$462$			712.034i			0.0717031i
$463$			18473.5i			1.85429i	0.374697	+	0.927147i	$0.377747\pi$
$463$			18473.5i			1.85429i	−0.374697	+	0.927147i	$0.622253\pi$
$464$	−689.715			−0.0690069
$465$	779.652	−	8529.45i	0.0777537	−	0.850632i
$466$	−5923.72			−0.588865
$467$		−	11967.1i		−	1.18581i	−0.805273	−	0.592904i	$-0.797981\pi$
$467$		−	11967.1i		−	1.18581i	0.805273	−	0.592904i	$-0.202019\pi$
$468$		−	3175.65i		−	0.313664i
$469$	16103.8			1.58551
$470$	−7617.74	−	696.316i	−0.747618	−	0.0683375i
$471$	−2066.42			−0.202156
$472$		−	5201.96i		−	0.507287i
$473$			1312.32i			0.127570i
$474$	3796.28			0.367867
$475$	18067.4	+	3330.81i	1.74524	+	0.321743i
$476$	−5060.15			−0.487251
$477$		−	403.970i		−	0.0387768i
$478$			4447.34i			0.425558i
$479$	10463.1			0.998062			0.499031	−	0.866584i	$-0.333689\pi$
$479$	10463.1			0.998062			0.499031	+	0.866584i	$0.333689\pi$
$480$	−6233.60	−	569.795i	−0.592758	−	0.0541823i
$481$	−18979.0			−1.79910
$482$			6866.53i			0.648883i
$483$			197.210i			0.0185784i
$484$	726.864			0.0682629
$485$	−554.375	+	6064.91i	−0.0519029	+	0.567821i
$486$	343.040			0.0320177
$487$		−	10438.9i		−	0.971317i	−0.874149	−	0.485658i	$-0.838580\pi$
$487$		−	10438.9i		−	0.971317i	0.874149	−	0.485658i	$-0.161420\pi$
$488$			545.409i			0.0505932i
$489$	5401.61			0.499528
$490$	157.157	−	1719.31i	0.0144890	−	0.158511i
$491$	−1842.23			−0.169325			−0.0846625	−	0.996410i	$-0.526981\pi$
$491$	−1842.23			−0.169325			−0.0846625	+	0.996410i	$0.526981\pi$
$492$			3359.65i			0.307855i
$493$		−	1887.11i		−	0.172396i
$494$	−12187.2			−1.10998
$495$	1102.26	+	100.754i	0.100087	+	0.00914861i
$496$	−5143.65			−0.465639
$497$			1244.09i			0.112284i
$498$			2435.92i			0.219189i
$499$	−20277.4			−1.81912			−0.909561	−	0.415570i	$-0.863582\pi$
$499$	−20277.4			−1.81912			−0.909561	+	0.415570i	$0.863582\pi$
$500$	−8083.28	−	2267.26i	−0.722991	−	0.202790i
$501$	10261.4			0.915057
$502$			7575.27i			0.673507i
$503$		−	15694.8i		−	1.39125i	−0.718406	−	0.695624i	$-0.755128\pi$
$503$		−	15694.8i		−	1.39125i	0.718406	−	0.695624i	$-0.244872\pi$
$504$	2720.06			0.240399
$505$	12520.2	+	1144.43i	1.10325	+	0.100845i
$506$	−66.7869			−0.00586767
$507$			3759.65i			0.329333i
$508$		−	11209.7i		−	0.979033i
$509$	−13383.0			−1.16541			−0.582704	−	0.812684i	$-0.698005\pi$
$509$	−13383.0			−1.16541			−0.582704	+	0.812684i	$0.698005\pi$
$510$	237.539	−	2598.70i	0.0206243	−	0.225632i
$511$	9530.27			0.825038
$512$			6945.54i			0.599516i
$513$			3968.33i			0.341532i
$514$	573.839			0.0492431
$515$	1298.13	−	14201.6i	0.111072	−	1.21514i
$516$	2149.98			0.183426
$517$		−	5331.29i		−	0.453520i
$518$		−	6971.68i		−	0.591347i
$519$	−6979.52			−0.590302
$520$	12931.8	+	1182.06i	1.09057	+	0.0996860i
$521$	−12346.1			−1.03818			−0.519089	−	0.854720i	$-0.673729\pi$
$521$	−12346.1			−1.03818			−0.519089	+	0.854720i	$0.673729\pi$
$522$			435.041i			0.0364775i
$523$		−	9814.80i		−	0.820595i	−0.911952	−	0.410298i	$-0.865425\pi$
$523$		−	9814.80i		−	0.820595i	0.911952	−	0.410298i	$-0.134575\pi$
$524$	12993.5			1.08325
$525$	5636.66	+	1039.14i	0.468579	+	0.0863847i
$526$	−11307.2			−0.937294
$527$		−	14073.4i		−	1.16328i
$528$		−	664.713i		−	0.0547877i
$529$	12148.5			0.998480
$530$	705.494	+	64.4871i	0.0578202	+	0.00528517i
$531$	2367.67			0.193499
$532$			13494.6i			1.09975i
$533$		−	10950.4i		−	0.889892i
$534$	4504.75			0.365056
$535$	−962.907	+	10534.3i	−0.0778133	+	0.851283i
$536$	20833.8			1.67889
$537$		−	12217.6i		−	0.981803i
$538$			6723.48i			0.538791i
$539$	1203.26			0.0961560
$540$	165.067	−	1805.84i	0.0131543	−	0.143909i
$541$	6943.74			0.551820			0.275910	−	0.961183i	$-0.411021\pi$
$541$	6943.74			0.551820			0.275910	+	0.961183i	$0.411021\pi$
$542$		−	6288.85i		−	0.498393i
$543$		−	1307.05i		−	0.103298i
$544$	−10285.3			−0.810623
$545$	5257.47	+	480.570i	0.413220	+	0.0377713i
$546$	−3802.17			−0.298018
$547$			5191.82i			0.405825i	0.979197	+	0.202913i	$0.0650407\pi$
$547$			5191.82i			0.405825i	−0.979197	+	0.202913i	$0.934959\pi$
$548$			13066.8i			1.01858i
$549$	−248.243			−0.0192983
$550$	−351.915	+	1908.90i	−0.0272831	+	0.147993i
$551$	−5032.61			−0.389104
$552$			255.135i			0.0196726i
$553$			13700.8i			1.05356i
$554$	2950.43			0.226266
$555$	−10792.4	−	986.506i	−0.825430	−	0.0754502i
$556$	−7691.75			−0.586696
$557$		−	2193.76i		−	0.166881i	−0.996513	−	0.0834404i	$-0.973409\pi$
$557$		−	2193.76i		−	0.166881i	0.996513	−	0.0834404i	$-0.0265908\pi$
$558$			3244.39i			0.246140i
$559$	−7007.60			−0.530214
$560$	313.326	−	3427.81i	0.0236436	−	0.258663i
$561$	1818.70			0.136873
$562$			4604.87i			0.345631i
$563$			15858.0i			1.18709i	0.804799	+	0.593547i	$0.202273\pi$
$563$			15858.0i			1.18709i	−0.804799	+	0.593547i	$0.797727\pi$
$564$	−8734.31			−0.652093
$565$	−188.998	+	2067.65i	−0.0140729	+	0.153959i
$566$	7653.11			0.568346
$567$			1238.04i			0.0916977i
$568$			1609.50i			0.118896i
$569$	−1176.17			−0.0866569			−0.0433285	−	0.999061i	$-0.513796\pi$
$569$	−1176.17			−0.0866569			−0.0433285	+	0.999061i	$0.513796\pi$
$570$	−6930.30	−	633.478i	−0.509260	−	0.0465500i
$571$	7715.30			0.565456			0.282728	−	0.959200i	$-0.408761\pi$
$571$	7715.30			0.565456			0.282728	+	0.959200i	$0.408761\pi$
$572$			3881.36i			0.283720i
$573$		−	9362.25i		−	0.682572i
$574$	4022.46			0.292499
$575$	−97.4689	+	528.704i	−0.00706911	+	0.0383452i
$576$	920.823			0.0666105
$577$		−	22948.6i		−	1.65574i	−0.560922	−	0.827869i	$-0.689553\pi$
$577$		−	22948.6i		−	1.65574i	0.560922	−	0.827869i	$-0.310447\pi$
$578$			2647.83i			0.190545i
$579$	−3301.36			−0.236960
$580$	2290.16	+	209.337i	0.163954	+	0.0149866i
$581$	−8791.27			−0.627751
$582$		−	2306.94i		−	0.164305i
$583$			493.741i			0.0350749i
$584$	12329.5			0.873626
$585$	−538.014	+	5885.91i	−0.0380242	+	0.415987i
$586$	10423.0			0.734761
$587$		−	23977.7i		−	1.68597i	−0.537938	−	0.842985i	$-0.680796\pi$
$587$		−	23977.7i		−	1.68597i	0.537938	−	0.842985i	$-0.319204\pi$
$588$		−	1971.31i		−	0.138258i
$589$	−37531.5			−2.62556
$590$	−377.960	+	4134.91i	−0.0263735	+	0.288528i
$591$	−16041.4			−1.11650
$592$			6508.35i			0.451844i
$593$			23207.4i			1.60711i	0.595232	+	0.803554i	$0.297060\pi$
$593$			23207.4i			1.60711i	−0.595232	+	0.803554i	$0.702940\pi$
$594$	−419.271			−0.0289611
$595$	9378.73	+	857.282i	0.646202	+	0.0590675i
$596$	−2643.96			−0.181713
$597$			15311.4i			1.04967i
$598$		−	356.633i		−	0.0243877i
$599$	1989.79			0.135727			0.0678636	−	0.997695i	$-0.478382\pi$
$599$	1989.79			0.135727			0.0678636	+	0.997695i	$0.478382\pi$
$600$	7292.25	+	1344.36i	0.496175	+	0.0914721i
$601$	17469.3			1.18567			0.592834	−	0.805325i	$-0.298009\pi$
$601$	17469.3			1.18567			0.592834	+	0.805325i	$0.298009\pi$
$602$		−	2574.14i		−	0.174276i
$603$			9482.50i			0.640393i
$604$	12618.4			0.850060
$605$	−1347.20	−	123.144i	−0.0905317	−	0.00827523i
$606$	−4762.37			−0.319237
$607$			939.720i			0.0628370i	0.999506	+	0.0314185i	$0.0100025\pi$
$607$			939.720i			0.0628370i	−0.999506	+	0.0314185i	$0.989998\pi$
$608$			27429.2i			1.82961i
$609$	−1570.07			−0.104470
$610$	39.6279	−	433.532i	0.00263030	−	0.0287757i
$611$	28468.4			1.88495
$612$		−	2979.60i		−	0.196802i
$613$			12099.9i			0.797247i	0.917115	+	0.398623i	$0.130512\pi$
$613$			12099.9i			0.797247i	−0.917115	+	0.398623i	$0.869488\pi$
$614$	560.709			0.0368540
$615$	569.186	−	6226.94i	0.0373200	−	0.408283i
$616$	−3324.52			−0.217449
$617$		−	5849.45i		−	0.381670i	−0.981622	−	0.190835i	$-0.938881\pi$
$617$		−	5849.45i		−	0.381670i	0.981622	−	0.190835i	$-0.0611195\pi$
$618$			5401.93i			0.351614i
$619$	−7870.96			−0.511083			−0.255542	−	0.966798i	$-0.582254\pi$
$619$	−7870.96			−0.511083			−0.255542	+	0.966798i	$0.582254\pi$
$620$	17079.2	+	1561.16i	1.10632	+	0.101125i
$621$	−116.125			−0.00750389
$622$		−	231.326i		−	0.0149121i
$623$			16257.7i			1.04551i
$624$	3549.48			0.227713
$625$	14597.8	+	5571.71i	0.934261	+	0.356590i
$626$	−3527.07			−0.225192
$627$		−	4850.18i		−	0.308927i
$628$		−	4137.76i		−	0.262921i
$629$	−17807.3			−1.12881
$630$	−2162.11	−	197.632i	−0.136731	−	0.0124982i
$631$	−7754.68			−0.489238			−0.244619	−	0.969619i	$-0.578663\pi$
$631$	−7754.68			−0.489238			−0.244619	+	0.969619i	$0.578663\pi$
$632$			17725.0i			1.11561i
$633$		−	4936.73i		−	0.309980i
$634$	580.772			0.0363808
$635$	−1899.12	+	20776.6i	−0.118684	+	1.29841i
$636$	808.901			0.0504324
$637$			6425.25i			0.399651i
$638$		−	531.717i		−	0.0329951i
$639$	−732.564			−0.0453517
$640$	1372.46	−	15014.8i	0.0847676	−	0.927364i
$641$	−6179.14			−0.380751			−0.190376	−	0.981711i	$-0.560971\pi$
$641$	−6179.14			−0.380751			−0.190376	+	0.981711i	$0.560971\pi$
$642$		−	4006.97i		−	0.246328i
$643$		−	5816.66i		−	0.356745i	−0.983963	−	0.178372i	$-0.942917\pi$
$643$		−	5816.66i		−	0.356745i	0.983963	−	0.178372i	$-0.0570832\pi$
$644$	−394.890			−0.0241628
$645$	−3984.88	−	364.246i	−0.243263	−	0.0222359i
$646$	−11434.8			−0.696436
$647$			451.104i			0.0274107i	0.999906	+	0.0137053i	$0.00436268\pi$
$647$			451.104i			0.0274107i	−0.999906	+	0.0137053i	$0.995637\pi$
$648$			1601.67i			0.0970981i
$649$	−2893.82			−0.175027
$650$	−10193.3	−	1879.18i	−0.615098	−	0.113396i
$651$	−11709.0			−0.704936
$652$			10816.1i			0.649678i
$653$		−	17071.3i		−	1.02305i	−0.859269	−	0.511525i	$-0.829081\pi$
$653$		−	17071.3i		−	1.02305i	0.859269	−	0.511525i	$-0.170919\pi$
$654$	−1999.81			−0.119570
$655$	−24082.8	−	2201.34i	−1.43663	−	0.131318i
$656$	−3755.13			−0.223496
$657$			5611.76i			0.333236i
$658$			10457.5i			0.619566i
$659$	24970.1			1.47602			0.738011	−	0.674789i	$-0.235765\pi$
$659$	24970.1			1.47602			0.738011	+	0.674789i	$0.235765\pi$
$660$	−201.748	+	2207.14i	−0.0118985	+	0.130171i
$661$	−13170.6			−0.775006			−0.387503	−	0.921869i	$-0.626662\pi$
$661$	−13170.6			−0.775006			−0.387503	+	0.921869i	$0.626662\pi$
$662$		−	3221.59i		−	0.189140i
$663$			9711.63i			0.568881i
$664$	−11373.4			−0.664721
$665$	2286.23	−	25011.5i	0.133318	−	1.45850i
$666$	4105.17			0.238847
$667$		−	147.268i		−	0.00854911i
$668$			20547.1i			1.19011i
$669$	−7778.80			−0.449545
$670$	−16560.3	−	1513.72i	−0.954893	−	0.0872840i
$671$	303.408			0.0174559
$672$			8557.35i			0.491231i
$673$		−	15152.7i		−	0.867893i	−0.900939	−	0.433947i	$-0.857121\pi$
$673$		−	15152.7i		−	0.867893i	0.900939	−	0.433947i	$-0.142879\pi$
$674$	3460.46			0.197763
$675$	−611.885	+	3319.07i	−0.0348911	+	0.189261i
$676$	−7528.24			−0.428325
$677$			13795.6i			0.783173i	0.920141	+	0.391587i	$0.128074\pi$
$677$			13795.6i			0.783173i	−0.920141	+	0.391587i	$0.871926\pi$
$678$		−	786.483i		−	0.0445497i
$679$	8325.77			0.470565
$680$	12133.4	+	1109.08i	0.684259	+	0.0625461i
$681$	−2748.89			−0.154681
$682$		−	3965.36i		−	0.222642i
$683$			12455.4i			0.697791i	0.937162	+	0.348896i	$0.113443\pi$
$683$			12455.4i			0.697791i	−0.937162	+	0.348896i	$0.886557\pi$
$684$	−7946.10			−0.444191
$685$	2213.75	−	24218.6i	0.123479	−	1.35087i
$686$	−9761.07			−0.543264
$687$			12902.6i			0.716540i
$688$			2403.07i			0.133163i
$689$	−2636.51			−0.145781
$690$	18.5374	−	202.800i	0.00102276	−	0.0111891i
$691$	17389.1			0.957327			0.478664	−	0.877998i	$-0.341121\pi$
$691$	17389.1			0.957327			0.478664	+	0.877998i	$0.341121\pi$
$692$		−	13975.6i		−	0.767737i
$693$		−	1513.15i		−	0.0829437i
$694$	−5577.33			−0.305061
$695$	14256.3	+	1303.12i	0.778087	+	0.0711227i
$696$	−2031.23			−0.110623
$697$		−	10274.3i		−	0.558346i
$698$		−	11634.8i		−	0.630922i
$699$	12588.6			0.681179
$700$	−2080.76	+	11286.7i	−0.112350	+	0.609427i
$701$	30534.7			1.64519			0.822596	−	0.568626i	$-0.192525\pi$
$701$	30534.7			1.64519			0.822596	+	0.568626i	$0.192525\pi$
$702$		−	2238.85i		−	0.120370i
$703$			47489.1i			2.54778i
$704$	−1125.45			−0.0602514
$705$	16188.6	+	1479.75i	0.864819	+	0.0790506i
$706$	6892.69			0.367436
$707$		−	17187.4i		−	0.914286i
$708$			4740.97i			0.251662i
$709$	17762.5			0.940880			0.470440	−	0.882432i	$-0.344095\pi$
$709$	17762.5			0.940880			0.470440	+	0.882432i	$0.344095\pi$
$710$	116.942	−	1279.35i	0.00618133	−	0.0676242i
$711$	−8067.54			−0.425537
$712$			21032.9i			1.10708i
$713$		−	1098.28i		−	0.0576869i
$714$	−3567.43			−0.186986
$715$	657.573	−	7193.89i	0.0343942	−	0.376275i
$716$	24464.3			1.27692
$717$		−	9451.12i		−	0.492271i
$718$		−	328.033i		−	0.0170502i
$719$	30661.9			1.59040			0.795200	−	0.606347i	$-0.207366\pi$
$719$	30661.9			1.59040			0.795200	+	0.606347i	$0.207366\pi$
$720$	2018.42	+	184.498i	0.104475	+	0.00954975i
$721$	−19495.6			−1.00701
$722$			20812.1i			1.07278i
$723$		−	14592.2i		−	0.750607i
$724$	2617.21			0.134348
$725$	−4209.22	−	775.989i	−0.215623	−	0.0397510i
$726$	512.443			0.0261963
$727$		−	9028.13i		−	0.460570i	−0.973123	−	0.230285i	$-0.926034\pi$
$727$		−	9028.13i		−	0.460570i	0.973123	−	0.230285i	$-0.0739659\pi$
$728$		−	17752.5i		−	0.903779i
$729$	−729.000			−0.0370370
$730$	−9800.40	−	895.826i	−0.496889	−	0.0454192i
$731$	−6574.97			−0.332673
$732$		−	497.076i		−	0.0250990i
$733$		−	5574.59i		−	0.280904i	−0.990088	−	0.140452i	$-0.955145\pi$
$733$		−	5574.59i		−	0.280904i	0.990088	−	0.140452i	$-0.0448555\pi$
$734$	−15462.2			−0.777548
$735$	−333.977	+	3653.73i	−0.0167604	+	0.183360i
$736$	−802.657			−0.0401988
$737$		−	11589.7i		−	0.579258i
$738$			2368.57i			0.118141i
$739$	17032.3			0.847826			0.423913	−	0.905703i	$-0.360656\pi$
$739$	17032.3			0.847826			0.423913	+	0.905703i	$0.360656\pi$
$740$	1975.36	−	21610.6i	0.0981292	−	1.07354i
$741$	25899.3			1.28399
$742$		−	968.486i		−	0.0479168i
$743$			20888.9i			1.03141i	0.856765	+	0.515707i	$0.172471\pi$
$743$			20888.9i			1.03141i	−0.856765	+	0.515707i	$0.827529\pi$
$744$	−15148.2			−0.746451
$745$	4900.44	+	447.935i	0.240991	+	0.0220283i
$746$	7292.47			0.357904
$747$		−	5176.62i		−	0.253551i
$748$			3641.73i			0.178015i
$749$	14461.2			0.705475
$750$	−5698.75	−	1598.43i	−0.277452	−	0.0778220i
$751$	−15666.1			−0.761205			−0.380602	−	0.924739i	$-0.624283\pi$
$751$	−15666.1			−0.761205			−0.380602	+	0.924739i	$0.624283\pi$
$752$		−	9762.47i		−	0.473405i
$753$		−	16098.3i		−	0.779091i
$754$	2839.30			0.137137
$755$	−23387.6	−	2137.79i	−1.12737	−	0.103049i
$756$	−2479.02			−0.119261
$757$		−	22613.4i		−	1.08573i	−0.839820	−	0.542865i	$-0.817340\pi$
$757$		−	22613.4i		−	1.08573i	0.839820	−	0.542865i	$-0.182660\pi$
$758$		−	8577.56i		−	0.411017i
$759$	141.930			0.00678752
$760$	2957.74	−	32357.9i	0.141169	−	1.54440i
$761$	−11761.9			−0.560272			−0.280136	−	0.959960i	$-0.590380\pi$
$761$	−11761.9			−0.560272			−0.280136	+	0.959960i	$0.590380\pi$
$762$		−	7902.87i		−	0.375710i
$763$		−	7217.33i		−	0.342444i
$764$	18746.8			0.887742
$765$	−504.798	+	5522.53i	−0.0238576	+	0.261003i
$766$	6730.52			0.317472
$767$		−	15452.6i		−	0.727459i
$768$			8166.78i			0.383715i
$769$	−644.074			−0.0302027			−0.0151014	−	0.999886i	$-0.504807\pi$
$769$	−644.074			−0.0302027			−0.0151014	+	0.999886i	$0.504807\pi$
$770$	2642.58	+	241.550i	0.123678	+	0.0113050i
$771$	−1219.47			−0.0569628
$772$		−	6610.58i		−	0.308186i
$773$			40800.8i			1.89845i	0.314598	+	0.949225i	$0.398130\pi$
$773$			40800.8i			1.89845i	−0.314598	+	0.949225i	$0.601870\pi$
$774$	1515.75			0.0703908
$775$	−31390.9	−	5787.06i	−1.45496	−	0.268229i
$776$	10771.2			0.498278
$777$			14815.6i			0.684051i
$778$			14870.3i			0.685250i
$779$	−27399.9			−1.26021
$780$	−11785.8	−	1077.31i	−0.541026	−	0.0494536i
$781$	895.356			0.0410222
$782$		−	334.616i		−	0.0153016i
$783$		−	924.513i		−	0.0421959i
$784$	2203.37			0.100372
$785$	−701.012	+	7669.13i	−0.0318729	+	0.348692i
$786$	9160.51			0.415705
$787$			20784.5i			0.941407i	0.882292	+	0.470703i	$0.156000\pi$
$787$			20784.5i			0.941407i	−0.882292	+	0.470703i	$0.844000\pi$
$788$		−	32120.9i		−	1.45210i
$789$	24029.1			1.08423
$790$	1287.85	−	14089.2i	0.0579996	−	0.634520i
$791$	2838.43			0.127589
$792$		−	1957.60i		−	0.0878285i
$793$			1620.16i			0.0725517i
$794$	4889.50			0.218541
$795$	−1499.26	−	137.043i	−0.0668845	−	0.00611371i
$796$	−30659.2			−1.36518
$797$		−	36547.2i		−	1.62430i	−0.583446	−	0.812152i	$-0.698296\pi$
$797$		−	36547.2i		−	1.62430i	0.583446	−	0.812152i	$-0.301704\pi$
$798$			9513.75i			0.422034i
$799$	26710.8			1.18268
$800$	−4229.37	+	22941.5i	−0.186914	+	1.01388i
$801$	−9573.12			−0.422284
$802$		−	6123.10i		−	0.269594i
$803$		−	6858.82i		−	0.301423i
$804$	−18987.6			−0.832885
$805$	731.908	+	66.9016i	0.0320452	+	0.00292916i
$806$	21174.5			0.925360
$807$		−	14288.2i		−	0.623256i
$808$		−	22235.7i		−	0.968130i
$809$	−6326.13			−0.274926			−0.137463	−	0.990507i	$-0.543895\pi$
$809$	−6326.13			−0.274926			−0.137463	+	0.990507i	$0.543895\pi$
$810$	116.373	−	1273.13i	0.00504805	−	0.0552261i
$811$	24501.7			1.06088			0.530438	−	0.847724i	$-0.322028\pi$
$811$	24501.7			1.06088			0.530438	+	0.847724i	$0.322028\pi$
$812$		−	3143.87i		−	0.135872i
$813$			13364.5i			0.576525i
$814$	−5017.44			−0.216045
$815$	1832.44	−	20047.0i	0.0787577	−	0.861615i
$816$	3330.34			0.142874
$817$			17534.4i			0.750856i
$818$		−	10287.1i		−	0.439706i
$819$	8080.05			0.344737
$820$	12468.7	+	1139.73i	0.531007	+	0.0485378i
$821$	−38165.9			−1.62241			−0.811204	−	0.584763i	$-0.801188\pi$
$821$	−38165.9			−1.62241			−0.811204	+	0.584763i	$0.801188\pi$
$822$			9212.13i			0.390888i
$823$		−	20194.9i		−	0.855344i	−0.903934	−	0.427672i	$-0.859334\pi$
$823$		−	20194.9i		−	0.855344i	0.903934	−	0.427672i	$-0.140666\pi$
$824$	−25221.9			−1.06632
$825$	747.860	−	4056.64i	0.0315602	−	0.171193i
$826$	5676.30			0.239109
$827$			12875.4i			0.541380i	0.962667	+	0.270690i	$0.0872518\pi$
$827$			12875.4i			0.541380i	−0.962667	+	0.270690i	$0.912748\pi$
$828$		−	232.525i		−	0.00975944i
$829$	−35670.2			−1.49442			−0.747212	−	0.664586i	$-0.768608\pi$
$829$	−35670.2			−1.49442			−0.747212	+	0.664586i	$0.768608\pi$
$830$	9040.46	+	826.362i	0.378071	+	0.0345583i
$831$	−6270.00			−0.261737
$832$		−	6009.75i		−	0.250422i
$833$			6028.57i			0.250753i
$834$	−5422.72			−0.225148
$835$	3481.06	−	38083.1i	0.144272	−	1.57835i
$836$	9711.90			0.401786
$837$		−	6894.70i		−	0.284726i
$838$		−	14968.8i		−	0.617051i
$839$	−9.05023			−0.000372406			−0.000186203	−	1.00000i	$-0.500059\pi$
$839$	−9.05023			−0.000372406			−0.000186203		1.00000i	$0.500059\pi$
$840$	922.753	−	10095.0i	0.0379024	−	0.414655i
$841$	−23216.5			−0.951927
$842$			11779.3i			0.482117i
$843$		−	9785.89i		−	0.399815i
$844$	9885.22			0.403155
$845$	13953.2	+	1275.42i	0.568053	+	0.0519241i
$846$	−6157.73			−0.250245
$847$			1849.41i			0.0750254i
$848$			904.121i			0.0366128i
$849$	−16263.7			−0.657444
$850$	−9563.98	−	1763.16i	−0.385932	−	0.0711482i
$851$	−1389.67			−0.0559779
$852$		−	1466.87i		−	0.0589837i
$853$			42635.9i			1.71140i	0.517472	+	0.855700i	$0.326873\pi$
$853$			42635.9i			1.71140i	−0.517472	+	0.855700i	$0.673127\pi$
$854$	−595.143			−0.0238470
$855$	14727.7	+	1346.21i	0.589095	+	0.0538474i
$856$	18708.7			0.747023
$857$			28082.3i			1.11934i	0.828716	+	0.559669i	$0.189072\pi$
$857$			28082.3i			1.11934i	−0.828716	+	0.559669i	$0.810928\pi$
$858$			2736.38i			0.108879i
$859$	−20954.6			−0.832320			−0.416160	−	0.909291i	$-0.636624\pi$
$859$	−20954.6			−0.832320			−0.416160	+	0.909291i	$0.636624\pi$
$860$	729.359	−	7979.25i	0.0289197	−	0.316384i
$861$	−8548.20			−0.338353
$862$		−	1854.27i		−	0.0732676i
$863$			36811.3i			1.45199i	0.687698	+	0.725997i	$0.258621\pi$
$863$			36811.3i			1.45199i	−0.687698	+	0.725997i	$0.741379\pi$
$864$	−5038.87			−0.198410
$865$	−2367.73	+	25903.1i	−0.0930696	+	1.01819i
$866$	15681.4			0.615332
$867$		−	5626.94i		−	0.220416i
$868$		−	23445.9i		−	0.916828i
$869$	9860.33			0.384912
$870$	1614.57	+	147.583i	0.0629185	+	0.00575120i
$871$	61887.6			2.40755
$872$		−	9337.19i		−	0.362611i
$873$			4902.51i			0.190063i
$874$	−892.365			−0.0345363
$875$	5768.76	−	20566.9i	0.222880	−	0.794614i
$876$	−11236.9			−0.433401
$877$			253.241i			0.00975069i	0.999988	+	0.00487534i	$0.00155188\pi$
$877$			253.241i			0.00975069i	−0.999988	+	0.00487534i	$0.998448\pi$
$878$			7802.48i			0.299910i
$879$	−22150.1			−0.849947
$880$	−2466.95	−	225.497i	−0.0945011	−	0.00863807i
$881$	−13595.0			−0.519896			−0.259948	−	0.965623i	$-0.583705\pi$
$881$	−13595.0			−0.519896			−0.259948	+	0.965623i	$0.583705\pi$
$882$		−	1389.79i		−	0.0530573i
$883$			41418.2i			1.57852i	0.614059	+	0.789260i	$0.289536\pi$
$883$			41418.2i			1.57852i	−0.614059	+	0.789260i	$0.710464\pi$
$884$	−19446.4			−0.739878
$885$	803.208	−	8787.15i	0.0305080	−	0.333759i
$886$	−9588.58			−0.363583
$887$			19752.3i			0.747708i	0.927488	+	0.373854i	$0.121964\pi$
$887$			19752.3i			0.747708i	−0.927488	+	0.373854i	$0.878036\pi$
$888$			19167.2i			0.724336i
$889$	28521.6			1.07602
$890$	1528.19	−	16718.5i	0.0575563	−	0.629670i
$891$	891.000			0.0335013
$892$		−	15576.1i		−	0.584671i
$893$		−	71233.4i		−	2.66935i
$894$	−1864.00			−0.0697333
$895$	−45343.3	−	4144.69i	−1.69347	−	0.154795i
$896$	−20612.0			−0.768525
$897$			757.887i			0.0282108i
$898$		−	12106.5i		−	0.449886i
$899$	8743.81			0.324385
$900$	−6646.04	−	1225.23i	−0.246149	−	0.0453788i
$901$	−2473.74			−0.0914675
$902$		−	2894.92i		−	0.106863i
$903$			5470.35i			0.201597i
$904$	3672.12			0.135103
$905$	−4850.87	−	443.404i	−0.178175	−	0.0162865i
$906$	8896.06			0.326216
$907$		−	43641.5i		−	1.59767i	−0.601547	−	0.798837i	$-0.705449\pi$
$907$		−	43641.5i		−	1.59767i	0.601547	−	0.798837i	$-0.294551\pi$
$908$		−	5504.32i		−	0.201175i
$909$	10120.6			0.369283
$910$	−1289.85	+	14111.0i	−0.0469868	+	0.514039i
$911$	−4915.73			−0.178777			−0.0893883	−	0.995997i	$-0.528491\pi$
$911$	−4915.73			−0.178777			−0.0893883	+	0.995997i	$0.528491\pi$
$912$		−	8881.48i		−	0.322473i
$913$			6326.98i			0.229345i
$914$	9215.13			0.333490
$915$	−84.2138	+	921.305i	−0.00304265	+	0.0332868i
$916$	−25835.8			−0.931921
$917$			33060.4i			1.19057i
$918$		−	2100.63i		−	0.0755242i
$919$	10069.5			0.361439			0.180720	−	0.983535i	$-0.442157\pi$
$919$	10069.5			0.361439			0.180720	+	0.983535i	$0.442157\pi$
$920$	946.883	+	86.5518i	0.0339324	+	0.00310166i
$921$	−1191.57			−0.0426315
$922$		−	4335.30i		−	0.154854i
$923$			4781.08i			0.170500i
$924$	3029.91			0.107875
$925$	−7322.45	+	39719.4i	−0.260282	+	1.41186i
$926$	−26078.9			−0.925491
$927$		−	11479.7i		−	0.406735i
$928$		−	6390.27i		−	0.226046i
$929$	−10460.2			−0.369416			−0.184708	−	0.982793i	$-0.559134\pi$
$929$	−10460.2			−0.369416			−0.184708	+	0.982793i	$0.559134\pi$
$930$	12040.9	+	1100.62i	0.424556	+	0.0388074i
$931$	16077.2			0.565961
$932$			25207.1i			0.885930i
$933$			491.594i			0.0172498i
$934$	16893.8			0.591845
$935$	616.976	−	6749.76i	0.0215800	−	0.236086i
$936$	10453.3			0.365040
$937$			16835.9i			0.586984i	0.955961	+	0.293492i	$0.0948174\pi$
$937$			16835.9i			0.586984i	−0.955961	+	0.293492i	$0.905183\pi$
$938$			22733.5i			0.791339i
$939$	7495.43			0.260494
$940$	−2963.02	+	32415.7i	−0.102812	+	1.12477i
$941$	−19862.2			−0.688088			−0.344044	−	0.938954i	$-0.611797\pi$
$941$	−19862.2			−0.688088			−0.344044	+	0.938954i	$0.611797\pi$
$942$		−	2917.14i		−	0.100898i
$943$		−	801.798i		−	0.0276884i
$944$	−5299.06			−0.182701
$945$	4594.73	+	419.991i	0.158166	+	0.0144575i
$946$	−1852.58			−0.0636708
$947$			43730.5i			1.50058i	0.661107	+	0.750291i	$0.270087\pi$
$947$			43730.5i			1.50058i	−0.661107	+	0.750291i	$0.729913\pi$
$948$		−	16154.3i		−	0.553446i
$949$	36625.2			1.25280
$950$	−4702.06	+	25505.6i	−0.160584	+	0.871063i
$951$	−1234.21			−0.0420841
$952$		−	16656.5i		−	0.567059i
$953$		−	9765.34i		−	0.331931i	−0.986132	−	0.165966i	$-0.946926\pi$
$953$		−	9765.34i		−	0.331931i	0.986132	−	0.165966i	$-0.0530741\pi$
$954$	570.279			0.0193537
$955$	−34746.2	−	3176.05i	−1.17734	−	0.107617i
$956$	18924.7			0.640240
$957$			1129.96i			0.0381677i
$958$			14770.6i			0.498140i
$959$	−33246.7			−1.11949
$960$	312.380	−	3417.46i	0.0105021	−	0.114894i
$961$	35417.3			1.18886
$962$		−	26792.4i		−	0.897945i
$963$			8515.28i			0.284944i
$964$	29219.1			0.976227
$965$	−1119.95	+	12252.4i	−0.0373602	+	0.408723i
$966$	−278.399			−0.00927262
$967$			20857.3i			0.693614i	0.937936	+	0.346807i	$0.112734\pi$
$967$			20857.3i			0.693614i	−0.937936	+	0.346807i	$0.887266\pi$
$968$			2392.62i			0.0794439i
$969$	24300.4			0.805614
$970$	−8561.76	−	782.605i	−0.283404	−	0.0259051i
$971$	11205.1			0.370328			0.185164	−	0.982708i	$-0.440718\pi$
$971$	11205.1			0.370328			0.185164	+	0.982708i	$0.440718\pi$
$972$		−	1459.73i		−	0.0481698i
$973$		−	19570.7i		−	0.644817i
$974$	14736.5			0.484791
$975$	21661.9	+	3993.47i	0.711525	+	0.131173i
$976$	555.590			0.0182213
$977$		−	37128.3i		−	1.21580i	−0.794013	−	0.607901i	$-0.792012\pi$
$977$		−	37128.3i		−	1.21580i	0.794013	−	0.607901i	$-0.207988\pi$
$978$			7625.38i			0.249318i
$979$	11700.5			0.381970
$980$	−7316.15	−	668.748i	−0.238475	−	0.0217983i
$981$	4249.82			0.138314
$982$		−	2600.65i		−	0.0845112i
$983$		−	30593.0i		−	0.992640i	−0.868140	−	0.496320i	$-0.834684\pi$
$983$		−	30593.0i		−	0.992640i	0.868140	−	0.496320i	$-0.165316\pi$
$984$	−11059.0			−0.358279
$985$	−5441.86	+	59534.4i	−0.176033	+	1.92581i
$986$	2664.01			0.0860439
$987$		−	22223.3i		−	0.716693i
$988$			51860.2i			1.66993i
$989$	−513.105			−0.0164973
$990$	−142.233	+	1556.04i	−0.00456614	+	0.0499539i
$991$	−14998.6			−0.480773			−0.240387	−	0.970677i	$-0.577274\pi$
$991$	−14998.6			−0.480773			−0.240387	+	0.970677i	$0.577274\pi$
$992$		−	47656.4i		−	1.52529i
$993$			6846.25i			0.218791i
$994$	−1756.26			−0.0560415
$995$	56825.3	+	5194.23i	1.81054	+	0.165496i
$996$	10365.6			0.329764
$997$			30874.3i			0.980741i	0.871514	+	0.490370i	$0.163139\pi$
$997$			30874.3i			0.980741i	−0.871514	+	0.490370i	$0.836861\pi$
$998$		−	28625.4i		−	0.907937i
$999$	−8723.97			−0.276291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.b.34.9	yes	14
3.2	odd	2		495.4.c.d.199.6		14
5.2	odd	4		825.4.a.bd.1.3		7
5.3	odd	4		825.4.a.ba.1.5		7
5.4	even	2	inner	165.4.c.b.34.6	✓	14
15.2	even	4		2475.4.a.bo.1.5		7
15.8	even	4		2475.4.a.bs.1.3		7
15.14	odd	2		495.4.c.d.199.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.6	✓	14	5.4	even	2	inner
165.4.c.b.34.9	yes	14	1.1	even	1	trivial
495.4.c.d.199.6		14	3.2	odd	2
495.4.c.d.199.9		14	15.14	odd	2
825.4.a.ba.1.5		7	5.3	odd	4
825.4.a.bd.1.3		7	5.2	odd	4
2475.4.a.bo.1.5		7	15.2	even	4
2475.4.a.bs.1.3		7	15.8	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41169i q^{2} -3.00000i q^{3} +6.00714 q^{4} +(-11.1339 - 1.01772i) q^{5} +4.23506 q^{6} +15.2844i q^{7} +19.7737i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+1.41169i q^{2} -3.00000i q^{3} +6.00714 q^{4} +(-11.1339 - 1.01772i) q^{5} +4.23506 q^{6} +15.2844i q^{7} +19.7737i q^{8} -9.00000 q^{9} +(1.43670 - 15.7176i) q^{10} +11.0000 q^{11} -18.0214i q^{12} +58.7385i q^{13} -21.5768 q^{14} +(-3.05316 + 33.4018i) q^{15} +20.1428 q^{16} +55.1122i q^{17} -12.7052i q^{18} +146.975 q^{19} +(-66.8830 - 6.11358i) q^{20} +45.8532 q^{21} +15.5286i q^{22} +4.30091i q^{23} +59.3211 q^{24} +(122.928 + 22.6624i) q^{25} -82.9205 q^{26} +27.0000i q^{27} +91.8155i q^{28} -34.2412 q^{29} +(-47.1529 - 4.31010i) q^{30} -255.359 q^{31} +186.625i q^{32} -33.0000i q^{33} -77.8012 q^{34} +(15.5552 - 170.175i) q^{35} -54.0642 q^{36} +323.110i q^{37} +207.483i q^{38} +176.216 q^{39} +(20.1241 - 220.159i) q^{40} -186.425 q^{41} +64.7304i q^{42} +119.302i q^{43} +66.0785 q^{44} +(100.205 + 9.15947i) q^{45} -6.07154 q^{46} -484.663i q^{47} -60.4284i q^{48} +109.387 q^{49} +(-31.9922 + 173.537i) q^{50} +165.337 q^{51} +352.851i q^{52} +44.8855i q^{53} -38.1156 q^{54} +(-122.473 - 11.1949i) q^{55} -302.229 q^{56} -440.925i q^{57} -48.3379i q^{58} -263.074 q^{59} +(-18.3407 + 200.649i) q^{60} +27.5825 q^{61} -360.487i q^{62} -137.560i q^{63} -102.314 q^{64} +(59.7793 - 653.990i) q^{65} +46.5857 q^{66} -1053.61i q^{67} +331.066i q^{68} +12.9027 q^{69} +(240.234 + 21.9591i) q^{70} +81.3960 q^{71} -177.963i q^{72} -623.529i q^{73} -456.130 q^{74} +(67.9872 - 368.785i) q^{75} +882.900 q^{76} +168.128i q^{77} +248.761i q^{78} +896.394 q^{79} +(-224.269 - 20.4997i) q^{80} +81.0000 q^{81} -263.174i q^{82} +575.180i q^{83} +275.446 q^{84} +(56.0887 - 613.615i) q^{85} -168.416 q^{86} +102.724i q^{87} +217.511i q^{88} +1063.68 q^{89} +(-12.9303 + 141.459i) q^{90} -897.783 q^{91} +25.8361i q^{92} +766.078i q^{93} +684.192 q^{94} +(-1636.41 - 149.579i) q^{95} +559.875 q^{96} -544.723i q^{97} +154.421i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Introduction

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