LMFDB - Embedded newform 120.4.b.b.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 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("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	120.11
Dual form			120.4.b.b.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.71159 + 0.804541i) q^{2} +(2.58903 + 4.50521i) q^{3} +(6.70543 - 4.36317i) q^{4} -5.00000 q^{5} +(-10.6450 - 10.1333i) q^{6} +6.99225i q^{7} +(-14.6720 + 17.2259i) q^{8} +(-13.5939 + 23.3282i) q^{9} +O(q^{10})$	\(q+(-2.71159 + 0.804541i) q^{2} +(2.58903 + 4.50521i) q^{3} +(6.70543 - 4.36317i) q^{4} -5.00000 q^{5} +(-10.6450 - 10.1333i) q^{6} +6.99225i q^{7} +(-14.6720 + 17.2259i) q^{8} +(-13.5939 + 23.3282i) q^{9} +(13.5579 - 4.02271i) q^{10} -7.63266i q^{11} +(37.0175 + 18.9130i) q^{12} +45.0969i q^{13} +(-5.62555 - 18.9601i) q^{14} +(-12.9451 - 22.5261i) q^{15} +(25.9255 - 58.5138i) q^{16} +7.59888i q^{17} +(18.0924 - 74.1934i) q^{18} -125.252 q^{19} +(-33.5271 + 21.8158i) q^{20} +(-31.5016 + 18.1031i) q^{21} +(6.14079 + 20.6966i) q^{22} -57.3601 q^{23} +(-115.593 - 21.5021i) q^{24} +25.0000 q^{25} +(-36.2823 - 122.284i) q^{26} +(-140.294 - 0.845728i) q^{27} +(30.5084 + 46.8860i) q^{28} -190.511 q^{29} +(53.2250 + 50.6665i) q^{30} +96.2558i q^{31} +(-23.2225 + 179.524i) q^{32} +(34.3867 - 19.7612i) q^{33} +(-6.11361 - 20.6050i) q^{34} -34.9612i q^{35} +(10.6324 + 215.738i) q^{36} +174.122i q^{37} +(339.631 - 100.770i) q^{38} +(-203.171 + 116.757i) q^{39} +(73.3601 - 86.1296i) q^{40} -353.695i q^{41} +(70.8546 - 74.4325i) q^{42} +96.3620 q^{43} +(-33.3026 - 51.1802i) q^{44} +(67.9693 - 116.641i) q^{45} +(155.537 - 46.1486i) q^{46} +120.742 q^{47} +(330.739 - 34.6941i) q^{48} +294.108 q^{49} +(-67.7897 + 20.1135i) q^{50} +(-34.2345 + 19.6737i) q^{51} +(196.765 + 302.394i) q^{52} +677.042 q^{53} +(381.099 - 110.579i) q^{54} +38.1633i q^{55} +(-120.448 - 102.590i) q^{56} +(-324.280 - 564.285i) q^{57} +(516.586 - 153.274i) q^{58} +767.070i q^{59} +(-185.088 - 94.5650i) q^{60} +605.927i q^{61} +(-77.4417 - 261.006i) q^{62} +(-163.117 - 95.0517i) q^{63} +(-81.4641 - 505.478i) q^{64} -225.484i q^{65} +(-77.3440 + 81.2497i) q^{66} -464.782 q^{67} +(33.1552 + 50.9537i) q^{68} +(-148.507 - 258.419i) q^{69} +(28.1278 + 94.8005i) q^{70} +110.298 q^{71} +(-202.401 - 576.439i) q^{72} +716.562 q^{73} +(-140.089 - 472.148i) q^{74} +(64.7257 + 112.630i) q^{75} +(-839.866 + 546.494i) q^{76} +53.3695 q^{77} +(456.980 - 480.057i) q^{78} +646.587i q^{79} +(-129.628 + 292.569i) q^{80} +(-359.414 - 634.242i) q^{81} +(284.562 + 959.075i) q^{82} +1266.21i q^{83} +(-132.244 + 258.836i) q^{84} -37.9944i q^{85} +(-261.294 + 77.5272i) q^{86} +(-493.237 - 858.291i) q^{87} +(131.480 + 111.986i) q^{88} -302.715i q^{89} +(-90.4622 + 370.967i) q^{90} -315.329 q^{91} +(-384.624 + 250.272i) q^{92} +(-433.653 + 249.209i) q^{93} +(-327.402 + 97.1418i) q^{94} +626.258 q^{95} +(-868.915 + 360.169i) q^{96} +160.973 q^{97} +(-797.501 + 236.622i) q^{98} +(178.057 + 103.757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−2.71159	+	0.804541i	−0.958691	+	0.284448i
$2$	−2.71159	+	0.804541i	−0.958691	+	0.284448i
$3$	2.58903	+	4.50521i	0.498259	+	0.867028i
$3$	2.58903	+	4.50521i	0.498259	+	0.867028i
$4$	6.70543	−	4.36317i	0.838178	−	0.545396i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−10.6450	−	10.1333i	−0.724301	−	0.689484i
$7$			6.99225i			0.377546i	0.982021	+	0.188773i	$0.0604510\pi$
$7$			6.99225i			0.377546i	−0.982021	+	0.188773i	$0.939549\pi$
$8$	−14.6720	+	17.2259i	−0.648417	+	0.761285i
$9$	−13.5939	+	23.3282i	−0.503476	+	0.864009i
$10$	13.5579	−	4.02271i	0.428740	−	0.127209i
$11$		−	7.63266i		−	0.209212i	−0.994514	−	0.104606i	$-0.966642\pi$
$11$		−	7.63266i		−	0.209212i	0.994514	−	0.104606i	$-0.0333582\pi$
$12$	37.0175	+	18.9130i	0.890504	+	0.454976i
$13$			45.0969i			0.962125i	0.876686	+	0.481063i	$0.159749\pi$
$13$			45.0969i			0.962125i	−0.876686	+	0.481063i	$0.840251\pi$
$14$	−5.62555	−	18.9601i	−0.107392	−	0.361950i
$15$	−12.9451	−	22.5261i	−0.222828	−	0.387747i
$16$	25.9255	−	58.5138i	0.405086	−	0.914279i
$17$			7.59888i			0.108412i	0.998530	+	0.0542058i	$0.0172627\pi$
$17$			7.59888i			0.108412i	−0.998530	+	0.0542058i	$0.982737\pi$
$18$	18.0924	−	74.1934i	0.236913	−	0.971531i
$19$	−125.252			−1.51235			−0.756176	−	0.654368i	$-0.772935\pi$
$19$	−125.252			−1.51235			−0.756176	+	0.654368i	$0.772935\pi$
$20$	−33.5271	+	21.8158i	−0.374845	+	0.243909i
$21$	−31.5016	+	18.1031i	−0.327343	+	0.188116i
$22$	6.14079	+	20.6966i	0.0595100	+	0.200570i
$23$	−57.3601			−0.520018			−0.260009	−	0.965606i	$-0.583726\pi$
$23$	−57.3601			−0.520018			−0.260009	+	0.965606i	$0.583726\pi$
$24$	−115.593	−	21.5021i	−0.983135	−	0.182879i
$25$	25.0000			0.200000
$26$	−36.2823	−	122.284i	−0.273675	−	0.922381i
$27$	−140.294	−	0.845728i	−0.999982	−	0.00602816i
$28$	30.5084	+	46.8860i	0.205912	+	0.316451i
$29$	−190.511			−1.21989			−0.609947	−	0.792442i	$-0.708809\pi$
$29$	−190.511			−1.21989			−0.609947	+	0.792442i	$0.708809\pi$
$30$	53.2250	+	50.6665i	0.323917	+	0.308347i
$31$			96.2558i			0.557679i	0.960338	+	0.278839i	$0.0899497\pi$
$31$			96.2558i			0.557679i	−0.960338	+	0.278839i	$0.910050\pi$
$32$	−23.2225	+	179.524i	−0.128288	+	0.991737i
$33$	34.3867	−	19.7612i	0.181393	−	0.104242i
$34$	−6.11361	−	20.6050i	−0.0308375	−	0.103933i
$35$		−	34.9612i		−	0.168844i
$36$	10.6324	+	215.738i	0.0492242	+	0.998788i
$37$			174.122i			0.773664i	0.922150	+	0.386832i	$0.126431\pi$
$37$			174.122i			0.773664i	−0.922150	+	0.386832i	$0.873569\pi$
$38$	339.631	−	100.770i	1.44988	−	0.430186i
$39$	−203.171	+	116.757i	−0.834190	+	0.479387i
$40$	73.3601	−	86.1296i	0.289981	−	0.340457i
$41$		−	353.695i		−	1.34727i	−0.739066	−	0.673633i	$-0.764733\pi$
$41$		−	353.695i		−	1.34727i	0.739066	−	0.673633i	$-0.235267\pi$
$42$	70.8546	−	74.4325i	0.260312	−	0.273457i
$43$	96.3620			0.341746			0.170873	−	0.985293i	$-0.445341\pi$
$43$	96.3620			0.341746			0.170873	+	0.985293i	$0.445341\pi$
$44$	−33.3026	−	51.1802i	−0.114104	−	0.175357i
$45$	67.9693	−	116.641i	0.225161	−	0.386397i
$46$	155.537	−	46.1486i	0.498537	−	0.147918i
$47$	120.742			0.374724			0.187362	−	0.982291i	$-0.440006\pi$
$47$	120.742			0.374724			0.187362	+	0.982291i	$0.440006\pi$
$48$	330.739	−	34.6941i	0.994543	−	0.104326i
$49$	294.108			0.857459
$50$	−67.7897	+	20.1135i	−0.191738	+	0.0568896i
$51$	−34.2345	+	19.6737i	−0.0939960	+	0.0540171i
$52$	196.765	+	302.394i	0.524739	+	0.806433i
$53$	677.042			1.75470			0.877348	−	0.479854i	$-0.159310\pi$
$53$	677.042			1.75470			0.877348	+	0.479854i	$0.159310\pi$
$54$	381.099	−	110.579i	0.960389	−	0.278664i
$55$			38.1633i			0.0935625i
$56$	−120.448	−	102.590i	−0.287420	−	0.244807i
$57$	−324.280	−	564.285i	−0.753543	−	1.31125i
$58$	516.586	−	153.274i	1.16950	−	0.346997i
$59$			767.070i			1.69261i	0.532699	+	0.846305i	$0.321178\pi$
$59$			767.070i			1.69261i	−0.532699	+	0.846305i	$0.678822\pi$
$60$	−185.088	−	94.5650i	−0.398245	−	0.203471i
$61$			605.927i			1.27182i	0.771763	+	0.635910i	$0.219375\pi$
$61$			605.927i			1.27182i	−0.771763	+	0.635910i	$0.780625\pi$
$62$	−77.4417	−	261.006i	−0.158631	−	0.534642i
$63$	−163.117	−	95.0517i	−0.326203	−	0.190085i
$64$	−81.4641	−	505.478i	−0.159110	−	0.987261i
$65$		−	225.484i		−	0.430276i
$66$	−77.3440	+	81.2497i	−0.144248	+	0.151533i
$67$	−464.782			−0.847495			−0.423747	−	0.905780i	$-0.639286\pi$
$67$	−464.782			−0.847495			−0.423747	+	0.905780i	$0.639286\pi$
$68$	33.1552	+	50.9537i	0.0591273	+	0.0908683i
$69$	−148.507	−	258.419i	−0.259103	−	0.450870i
$70$	28.1278	+	94.8005i	0.0480273	+	0.161869i
$71$	110.298			0.184365			0.0921826	−	0.995742i	$-0.470616\pi$
$71$	110.298			0.184365			0.0921826	+	0.995742i	$0.470616\pi$
$72$	−202.401	−	576.439i	−0.331294	−	0.943527i
$73$	716.562			1.14887			0.574433	−	0.818552i	$-0.305223\pi$
$73$	716.562			1.14887			0.574433	+	0.818552i	$0.305223\pi$
$74$	−140.089	−	472.148i	−0.220067	−	0.741705i
$75$	64.7257	+	112.630i	0.0996518	+	0.173406i
$76$	−839.866	+	546.494i	−1.26762	+	0.824831i
$77$	53.3695			0.0789872
$78$	456.980	−	480.057i	0.663370	−	0.696868i
$79$			646.587i			0.920845i	0.887700	+	0.460423i	$0.152302\pi$
$79$			646.587i			0.920845i	−0.887700	+	0.460423i	$0.847698\pi$
$80$	−129.628	+	292.569i	−0.181160	+	0.408878i
$81$	−359.414	−	634.242i	−0.493023	−	0.870016i
$82$	284.562	+	959.075i	0.383227	+	1.29161i
$83$			1266.21i			1.67451i	0.546813	+	0.837255i	$0.315841\pi$
$83$			1266.21i			1.67451i	−0.546813	+	0.837255i	$0.684159\pi$
$84$	−132.244	+	258.836i	−0.171774	+	0.336206i
$85$		−	37.9944i		−	0.0484832i
$86$	−261.294	+	77.5272i	−0.327629	+	0.0972089i
$87$	−493.237	−	858.291i	−0.607823	−	1.05768i
$88$	131.480	+	111.986i	0.159270	+	0.135657i
$89$		−	302.715i		−	0.360537i	−0.983617	−	0.180268i	$-0.942303\pi$
$89$		−	302.715i		−	0.360537i	0.983617	−	0.180268i	$-0.0576966\pi$
$90$	−90.4622	+	370.967i	−0.105951	+	0.434482i
$91$	−315.329			−0.363246
$92$	−384.624	+	250.272i	−0.435868	+	0.283616i
$93$	−433.653	+	249.209i	−0.483523	+	0.277868i
$94$	−327.402	+	97.1418i	−0.359245	+	0.106590i
$95$	626.258			0.676345
$96$	−868.915	+	360.169i	−0.923785	+	0.382913i
$97$	160.973			0.168499			0.0842493	−	0.996445i	$-0.473151\pi$
$97$	160.973			0.168499			0.0842493	+	0.996445i	$0.473151\pi$
$98$	−797.501	+	236.622i	−0.822039	+	0.243903i
$99$	178.057	+	103.757i	0.180761	+	0.105333i
$100$	167.636	−	109.079i	0.167636	−	0.109079i
$101$	1231.55			1.21331			0.606653	−	0.794966i	$-0.292512\pi$
$101$	1231.55			1.21331			0.606653	+	0.794966i	$0.292512\pi$
$102$	77.0017	−	80.8901i	0.0747481	−	0.0785227i
$103$		−	1978.18i		−	1.89238i	−0.323605	−	0.946192i	$-0.604895\pi$
$103$		−	1978.18i		−	1.89238i	0.323605	−	0.946192i	$-0.395105\pi$
$104$	−776.835	−	661.662i	−0.732451	−	0.623859i
$105$	157.508	−	90.5157i	0.146392	−	0.0841278i
$106$	−1835.86	+	544.708i	−1.68221	+	0.499120i
$107$			953.110i			0.861127i	0.902560	+	0.430564i	$0.141685\pi$
$107$			953.110i			0.861127i	−0.902560	+	0.430564i	$0.858315\pi$
$108$	−944.418	+	606.454i	−0.841451	+	0.540334i
$109$		−	1974.31i		−	1.73490i	−0.497521	−	0.867452i	$-0.665756\pi$
$109$		−	1974.31i		−	1.73490i	0.497521	−	0.867452i	$-0.334244\pi$
$110$	−30.7039	−	103.483i	−0.0266137	−	0.0896976i
$111$	−784.458	+	450.808i	−0.670788	+	0.385485i
$112$	409.143	+	181.278i	0.345182	+	0.152939i
$113$			748.787i			0.623363i	0.950187	+	0.311681i	$0.100892\pi$
$113$			748.787i			0.623363i	−0.950187	+	0.311681i	$0.899108\pi$
$114$	1333.31	+	1269.21i	1.09540	+	1.04274i
$115$	286.801			0.232559
$116$	−1277.46	+	831.230i	−1.02249	+	0.665326i
$117$	−1052.03	−	613.041i	−0.831285	−	0.484407i
$118$	−617.139	−	2079.98i	−0.481460	−	1.62269i
$119$	−53.1332			−0.0409304
$120$	577.963	+	107.511i	0.439671	+	0.0817862i
$121$	1272.74			0.956230
$122$	−487.493	−	1643.03i	−0.361767	−	1.21928i
$123$	1593.47	−	915.727i	1.16812	−	0.671287i
$124$	419.980	+	645.436i	0.304156	+	0.467434i
$125$	−125.000			−0.0894427
$126$	518.779	+	126.507i	0.366798	+	0.0894454i
$127$		−	759.311i		−	0.530535i	−0.964175	−	0.265267i	$-0.914540\pi$
$127$		−	759.311i		−	0.530535i	0.964175	−	0.265267i	$-0.0854603\pi$
$128$	627.575	+	1305.11i	0.433362	+	0.901220i
$129$	249.484	+	434.131i	0.170278	+	0.296303i
$130$	181.412	+	611.421i	0.122391	+	0.412501i
$131$		−	1545.77i		−	1.03095i	−0.856905	−	0.515474i	$-0.827616\pi$
$131$		−	1545.77i		−	1.03095i	0.856905	−	0.515474i	$-0.172384\pi$
$132$	144.356	−	282.542i	0.0951865	−	0.186304i
$133$		−	875.791i		−	0.570983i
$134$	1260.30	−	373.936i	0.812486	−	0.241068i
$135$	701.468	+	4.22864i	0.447205	+	0.00269588i
$136$	−130.898	−	111.491i	−0.0825322	−	0.0702960i
$137$			2044.57i			1.27503i	0.770437	+	0.637516i	$0.220038\pi$
$137$			2044.57i			1.27503i	−0.770437	+	0.637516i	$0.779962\pi$
$138$	610.599	+	581.247i	0.376649	+	0.358544i
$139$	−2436.28			−1.48664			−0.743319	−	0.668937i	$-0.766750\pi$
$139$	−2436.28			−1.48664			−0.743319	+	0.668937i	$0.766750\pi$
$140$	−152.542	−	234.430i	−0.0920867	−	0.141521i
$141$	312.604	+	543.968i	0.186709	+	0.324896i
$142$	−299.082	+	88.7391i	−0.176749	+	0.0524424i
$143$	344.209			0.201288
$144$	1012.60	+	1400.23i	0.585994	+	0.810316i
$145$	952.553			0.545553
$146$	−1943.02	+	576.503i	−1.10141	+	0.326793i
$147$	761.455	+	1325.02i	0.427237	+	0.743441i
$148$	759.726	+	1167.57i	0.421953	+	0.648468i
$149$	699.214			0.384442			0.192221	−	0.981352i	$-0.438431\pi$
$149$	699.214			0.384442			0.192221	+	0.981352i	$0.438431\pi$
$150$	−266.125	−	253.333i	−0.144860	−	0.137897i
$151$		−	396.696i		−	0.213793i	−0.994270	−	0.106896i	$-0.965909\pi$
$151$		−	396.696i		−	0.213793i	0.994270	−	0.106896i	$-0.0340913\pi$
$152$	1837.69	−	2157.57i	0.980636	−	1.15133i
$153$	−177.268	−	103.298i	−0.0936686	−	0.0545827i
$154$	−144.716	+	42.9379i	−0.0757243	+	0.0224678i
$155$		−	481.279i		−	0.249402i
$156$	−852.917	+	1669.38i	−0.437744	+	0.856776i
$157$			3321.17i			1.68827i	0.536132	+	0.844134i	$0.319885\pi$
$157$			3321.17i			1.68827i	−0.536132	+	0.844134i	$0.680115\pi$
$158$	−520.206	−	1753.28i	−0.261933	−	0.882806i
$159$	1752.88	+	3050.22i	0.874293	+	1.52137i
$160$	116.113	−	897.618i	0.0573720	−	0.443518i
$161$		−	401.076i		−	0.196331i
$162$	1484.86	+	1430.64i	0.720132	+	0.693837i
$163$	−2148.86			−1.03258			−0.516292	−	0.856412i	$-0.672688\pi$
$163$	−2148.86			−1.03258			−0.516292	+	0.856412i	$0.672688\pi$
$164$	−1543.23	−	2371.68i	−0.734793	−	1.12925i
$165$	−171.934	+	98.8059i	−0.0811214	+	0.0466183i
$166$	−1018.72	−	3433.43i	−0.476311	−	1.60534i
$167$	−462.601			−0.214354			−0.107177	−	0.994240i	$-0.534181\pi$
$167$	−462.601			−0.214354			−0.107177	+	0.994240i	$0.534181\pi$
$168$	150.348	−	808.252i	0.0690454	−	0.371179i
$169$	163.270			0.0743150
$170$	30.5680	+	103.025i	0.0137909	+	0.0464804i
$171$	1702.65	−	2921.90i	0.761434	−	1.30669i
$172$	646.148	−	420.444i	0.286444	−	0.186387i
$173$	1011.63			0.444584			0.222292	−	0.974980i	$-0.428646\pi$
$173$	1011.63			0.444584			0.222292	+	0.974980i	$0.428646\pi$
$174$	2027.99	+	1930.50i	0.883571	+	0.841097i
$175$			174.806i			0.0755092i
$176$	−446.616	−	197.881i	−0.191278	−	0.0847489i
$177$	−3455.81	+	1985.97i	−1.46754	+	0.843357i
$178$	243.547	+	820.839i	0.102554	+	0.345643i
$179$		−	3500.48i		−	1.46167i	−0.682556	−	0.730833i	$-0.739132\pi$
$179$		−	3500.48i		−	1.46167i	0.682556	−	0.730833i	$-0.260868\pi$
$180$	−53.1621	−	1078.69i	−0.0220137	−	0.446671i
$181$			953.623i			0.391615i	0.980642	+	0.195807i	$0.0627327\pi$
$181$			953.623i			0.391615i	−0.980642	+	0.195807i	$0.937267\pi$
$182$	855.042	−	253.695i	0.348241	−	0.103325i
$183$	−2729.83	+	1568.76i	−1.10270	+	0.633696i
$184$	841.588	−	988.080i	0.337189	−	0.395882i
$185$		−	870.612i		−	0.345993i
$186$	975.389	−	1024.64i	0.384511	−	0.403927i
$187$	57.9996			0.0226810
$188$	809.626	−	526.817i	0.314085	−	0.204373i
$189$	5.91354	−	980.967i	0.00227591	−	0.377539i
$190$	−1698.15	+	503.851i	−0.648406	+	0.192385i
$191$	3624.55			1.37310			0.686552	−	0.727080i	$-0.259123\pi$
$191$	3624.55			1.37310			0.686552	+	0.727080i	$0.259123\pi$
$192$	2066.37	−	1675.71i	0.776705	−	0.629864i
$193$	−2995.42			−1.11718			−0.558588	−	0.829446i	$-0.688657\pi$
$193$	−2995.42			−1.11718			−0.558588	+	0.829446i	$0.688657\pi$
$194$	−436.493	+	129.510i	−0.161538	+	0.0479291i
$195$	1015.86	−	583.786i	0.373061	−	0.214389i
$196$	1972.12	−	1283.24i	0.718704	−	0.467655i
$197$	−3894.89			−1.40863			−0.704313	−	0.709890i	$-0.748745\pi$
$197$	−3894.89			−1.40863			−0.704313	+	0.709890i	$0.748745\pi$
$198$	−566.293	−	138.093i	−0.203256	−	0.0495650i
$199$			1277.02i			0.454901i	0.973790	+	0.227451i	$0.0730390\pi$
$199$			1277.02i			0.454901i	−0.973790	+	0.227451i	$0.926961\pi$
$200$	−366.800	+	430.648i	−0.129683	+	0.152257i
$201$	−1203.33	−	2093.94i	−0.422272	−	0.734802i
$202$	−3339.46	+	990.834i	−1.16319	+	0.345123i
$203$		−	1332.10i		−	0.460566i
$204$	−143.718	+	281.292i	−0.0493247	+	0.0965410i
$205$			1768.48i			0.602515i
$206$	1591.52	+	5364.00i	0.538285	+	1.81421i
$207$	779.745	−	1338.11i	0.261817	−	0.449300i
$208$	2638.79	+	1169.16i	0.879650	+	0.389744i
$209$			956.003i			0.316403i
$210$	−354.273	+	372.163i	−0.116415	+	0.122294i
$211$	2246.66			0.733018			0.366509	−	0.930415i	$-0.380553\pi$
$211$	2246.66			0.733018			0.366509	+	0.930415i	$0.380553\pi$
$212$	4539.86	−	2954.05i	1.47075	−	0.957005i
$213$	285.564	+	496.915i	0.0918616	+	0.159850i
$214$	−766.816	−	2584.44i	−0.244946	−	0.825555i
$215$	−481.810			−0.152833
$216$	2072.96	−	2404.28i	0.652995	−	0.757362i
$217$	−673.044			−0.210549
$218$	1588.41	+	5353.51i	0.493490	+	1.66324i
$219$	1855.20	+	3228.26i	0.572432	+	0.996099i
$220$	166.513	+	255.901i	0.0510286	+	0.0784221i
$221$	−342.686			−0.104306
$222$	1764.44	−	1853.53i	0.533429	−	0.560365i
$223$			3264.11i			0.980185i	0.871671	+	0.490092i	$0.163037\pi$
$223$			3264.11i			0.980185i	−0.871671	+	0.490092i	$0.836963\pi$
$224$	−1255.27	−	162.378i	−0.374426	−	0.0484345i
$225$	−339.847	+	583.206i	−0.100695	+	0.172802i
$226$	−602.430	−	2030.40i	−0.177314	−	0.597612i
$227$			2615.44i			0.764726i	0.924012	+	0.382363i	$0.124890\pi$
$227$			2615.44i			0.764726i	−0.924012	+	0.382363i	$0.875110\pi$
$228$	−4636.51	−	2368.88i	−1.34676	−	0.688084i
$229$		−	4452.05i		−	1.28472i	−0.766405	−	0.642358i	$-0.777956\pi$
$229$		−	4452.05i		−	1.28472i	0.766405	−	0.642358i	$-0.222044\pi$
$230$	−777.685	+	230.743i	−0.222952	+	0.0661510i
$231$	138.175	+	240.441i	0.0393561	+	0.0684841i
$232$	2795.17	−	3281.72i	0.791001	−	0.928687i
$233$			1815.71i			0.510519i	0.966873	+	0.255260i	$0.0821609\pi$
$233$			1815.71i			0.510519i	−0.966873	+	0.255260i	$0.917839\pi$
$234$	3345.89	+	815.912i	0.934734	+	0.227940i
$235$	−603.710			−0.167582
$236$	3346.85	+	5143.53i	0.923143	+	1.41871i
$237$	−2913.01	+	1674.03i	−0.798399	+	0.458819i
$238$	144.075	−	42.7479i	0.0392396	−	0.0116426i
$239$	−6381.55			−1.72715			−0.863574	−	0.504223i	$-0.831779\pi$
$239$	−6381.55			−1.72715			−0.863574	+	0.504223i	$0.831779\pi$
$240$	−1653.70	+	173.470i	−0.444773	+	0.0466561i
$241$	4338.81			1.15970			0.579849	−	0.814724i	$-0.303112\pi$
$241$	4338.81			1.15970			0.579849	+	0.814724i	$0.303112\pi$
$242$	−3451.15	+	1023.97i	−0.916730	+	0.271998i
$243$	1926.86	−	3261.31i	0.508676	−	0.860958i
$244$	2643.76	+	4063.00i	0.693646	+	1.06601i
$245$	−1470.54			−0.383467
$246$	−3584.10	+	3765.09i	−0.928918	+	0.975826i
$247$		−	5648.46i		−	1.45507i
$248$	−1658.09	−	1412.27i	−0.424553	−	0.361609i
$249$	−5704.53	+	3278.25i	−1.45185	+	0.834339i
$250$	338.949	−	100.568i	0.0857480	−	0.0254418i
$251$		−	910.923i		−	0.229071i	−0.993419	−	0.114536i	$-0.963462\pi$
$251$		−	910.923i		−	0.229071i	0.993419	−	0.114536i	$-0.0365380\pi$
$252$	−1508.49	+	74.3446i	−0.377088	+	0.0185844i
$253$			437.810i			0.108794i
$254$	610.897	+	2058.94i	0.150910	+	0.508619i
$255$	171.173	−	98.3685i	0.0420363	−	0.0241572i
$256$	−2751.74	−	3034.00i	−0.671811	−	0.740723i
$257$			606.321i			0.147165i	0.997289	+	0.0735823i	$0.0234432\pi$
$257$			606.321i			0.147165i	−0.997289	+	0.0735823i	$0.976557\pi$
$258$	−1025.77	−	976.465i	−0.247527	−	0.235628i
$259$	−1217.51			−0.292094
$260$	−983.827	−	1511.97i	−0.234671	−	0.360648i
$261$	2589.77	−	4444.28i	0.614188	−	1.05400i
$262$	1243.63	+	4191.48i	0.293252	+	0.988362i
$263$	−989.786			−0.232064			−0.116032	−	0.993245i	$-0.537018\pi$
$263$	−989.786			−0.232064			−0.116032	+	0.993245i	$0.537018\pi$
$264$	−164.119	+	882.279i	−0.0382606	+	0.205684i
$265$	−3385.21			−0.784724
$266$	704.610	+	2374.78i	0.162415	+	0.547396i
$267$	1363.80	−	783.738i	0.312595	−	0.179640i
$268$	−3116.56	+	2027.92i	−0.710352	+	0.462220i
$269$	−3752.33			−0.850497			−0.425248	−	0.905077i	$-0.639813\pi$
$269$	−3752.33			−0.850497			−0.425248	+	0.905077i	$0.639813\pi$
$270$	−1905.49	+	552.893i	−0.429499	+	0.124622i
$271$			5029.19i			1.12731i	0.826009	+	0.563656i	$0.190606\pi$
$271$			5029.19i			1.12731i	−0.826009	+	0.563656i	$0.809394\pi$
$272$	444.639	+	197.005i	0.0991184	+	0.0439160i
$273$	−816.395	−	1420.62i	−0.180991	−	0.314945i
$274$	−1644.94	−	5544.03i	−0.362680	−	1.22236i
$275$		−	190.817i		−	0.0418424i
$276$	−2123.33	−	1084.85i	−0.463078	−	0.236596i
$277$			1982.58i			0.430043i	0.976609	+	0.215021i	$0.0689821\pi$
$277$			1982.58i			0.430043i	−0.976609	+	0.215021i	$0.931018\pi$
$278$	6606.20	−	1960.09i	1.42523	−	0.422872i
$279$	−2245.48	−	1308.49i	−0.481840	−	0.280778i
$280$	602.239	+	512.952i	0.128538	+	0.109481i
$281$			1850.70i			0.392895i	0.980514	+	0.196447i	$0.0629405\pi$
$281$			1850.70i			0.392895i	−0.980514	+	0.196447i	$0.937060\pi$
$282$	−1285.30	−	1223.51i	−0.271413	−	0.258366i
$283$	−7198.08			−1.51195			−0.755974	−	0.654601i	$-0.772837\pi$
$283$	−7198.08			−1.51195			−0.755974	+	0.654601i	$0.772837\pi$
$284$	739.594	−	481.248i	0.154531	−	0.100552i
$285$	1621.40	+	2821.43i	0.336995	+	0.586410i
$286$	−933.354	+	276.931i	−0.192973	+	0.0572561i
$287$	2473.12			0.508655
$288$	−3872.29	−	2982.16i	−0.792280	−	0.610158i
$289$	4855.26			0.988247
$290$	−2582.93	+	766.368i	−0.523017	+	0.155182i
$291$	416.765	+	725.219i	0.0839559	+	0.146093i
$292$	4804.85	−	3126.48i	0.962954	−	0.626587i
$293$	1698.93			0.338746			0.169373	−	0.985552i	$-0.445826\pi$
$293$	1698.93			0.338746			0.169373	+	0.985552i	$0.445826\pi$
$294$	−3130.79	−	2980.29i	−0.621059	−	0.591204i
$295$		−	3835.35i		−	0.756958i
$296$	−2999.42	−	2554.73i	−0.588978	−	0.501657i
$297$	−6.45515	+	1070.81i	−0.00126116	+	0.209208i
$298$	−1895.98	+	562.546i	−0.368561	+	0.109354i
$299$		−	2586.76i		−	0.500322i
$300$	925.439	+	472.825i	0.178101	+	0.0909952i
$301$			673.787i			0.129025i
$302$	319.159	+	1075.68i	0.0608130	+	0.204961i
$303$	3188.52	+	5548.40i	0.604541	+	1.05197i
$304$	−3247.21	+	7328.95i	−0.612633	+	1.38271i
$305$		−	3029.64i		−	0.568775i
$306$	563.787	+	137.482i	0.105325	+	0.0256841i
$307$	2942.03			0.546941			0.273470	−	0.961880i	$-0.411828\pi$
$307$	2942.03			0.546941			0.273470	+	0.961880i	$0.411828\pi$
$308$	357.865	−	232.860i	0.0662054	−	0.0430793i
$309$	8912.11	−	5121.56i	1.64075	−	0.942897i
$310$	387.209	+	1305.03i	0.0709418	+	0.239099i
$311$	3204.14			0.584212			0.292106	−	0.956386i	$-0.405644\pi$
$311$	3204.14			0.584212			0.292106	+	0.956386i	$0.405644\pi$
$312$	969.680	−	5212.87i	0.175953	−	0.945899i
$313$	3678.16			0.664224			0.332112	−	0.943240i	$-0.392239\pi$
$313$	3678.16			0.664224			0.332112	+	0.943240i	$0.392239\pi$
$314$	−2672.02	−	9005.65i	−0.480225	−	1.61853i
$315$	815.584	+	475.258i	0.145882	+	0.0850088i
$316$	2821.17	+	4335.65i	0.502225	+	0.771833i
$317$	−507.671			−0.0899484			−0.0449742	−	0.998988i	$-0.514321\pi$
$317$	−507.671			−0.0899484			−0.0449742	+	0.998988i	$0.514321\pi$
$318$	−7207.12	−	6860.67i	−1.27093	−	1.20983i
$319$			1454.10i			0.255217i
$320$	407.321	+	2527.39i	0.0711560	+	0.441517i
$321$	−4293.96	+	2467.63i	−0.746622	+	0.429064i
$322$	322.682	+	1087.55i	0.0558459	+	0.188220i
$323$		−	951.772i		−	0.163957i
$324$	−5177.33	−	2684.68i	−0.887745	−	0.460336i
$325$			1127.42i			0.192425i
$326$	5826.81	−	1728.84i	0.989930	−	0.293717i
$327$	8894.68	−	5111.54i	1.50421	−	0.864431i
$328$	6092.72	+	5189.42i	1.02565	+	0.873590i
$329$			844.258i			0.141475i
$330$	386.720	−	406.249i	0.0645098	−	0.0677674i
$331$	2774.85			0.460785			0.230392	−	0.973098i	$-0.425999\pi$
$331$	2774.85			0.460785			0.230392	+	0.973098i	$0.425999\pi$
$332$	5524.67	+	8490.46i	0.913271	+	1.40354i
$333$	−4061.97	−	2367.00i	−0.668452	−	0.389521i
$334$	1254.38	−	372.182i	0.205499	−	0.0609727i
$335$	2323.91			0.379011
$336$	242.590	+	2312.61i	0.0393879	+	0.375486i
$337$	3876.99			0.626685			0.313343	−	0.949640i	$-0.398551\pi$
$337$	3876.99			0.626685			0.313343	+	0.949640i	$0.398551\pi$
$338$	−442.721	+	131.357i	−0.0712451	+	0.0211388i
$339$	−3373.45	+	1938.63i	−0.540473	+	0.310596i
$340$	−165.776	−	254.769i	−0.0264425	−	0.0406375i
$341$	734.688			0.116673
$342$	−2266.11	+	9292.85i	−0.358295	+	1.46930i
$343$			4454.82i			0.701276i
$344$	−1413.82	+	1659.92i	−0.221594	+	0.260166i
$345$	742.535	+	1292.10i	0.115875	+	0.201635i
$346$	−2743.13	+	813.900i	−0.426219	+	0.126461i
$347$		−	3201.64i		−	0.495311i	−0.968848	−	0.247656i	$-0.920340\pi$
$347$		−	3201.64i		−	0.495311i	0.968848	−	0.247656i	$-0.0796601\pi$
$348$	−7052.23	−	3603.13i	−1.08632	−	0.555023i
$349$			6854.68i			1.05135i	0.850684	+	0.525677i	$0.176188\pi$
$349$			6854.68i			1.05135i	−0.850684	+	0.525677i	$0.823812\pi$
$350$	−140.639	−	474.003i	−0.0214785	−	0.0723900i
$351$	38.1397	−	6326.80i	0.00579985	−	0.962108i
$352$	1370.24	+	177.250i	0.207483	+	0.0268393i
$353$		−	155.132i		−	0.0233904i	−0.999932	−	0.0116952i	$-0.996277\pi$
$353$		−	155.132i		−	0.0233904i	0.999932	−	0.0116952i	$-0.00372279\pi$
$354$	7772.95	−	8165.46i	1.16703	−	1.22596i
$355$	−551.489			−0.0824507
$356$	−1320.80	−	2029.84i	−0.196635	−	0.302194i
$357$	−137.563	−	239.376i	−0.0203939	−	0.0354878i
$358$	2816.28	+	9491.86i	0.415768	+	1.40129i
$359$	−7776.63			−1.14327			−0.571636	−	0.820507i	$-0.693691\pi$
$359$	−7776.63			−1.14327			−0.571636	+	0.820507i	$0.693691\pi$
$360$	1012.00	+	2882.19i	0.148159	+	0.421958i
$361$	8828.98			1.28721
$362$	−767.229	−	2585.83i	−0.111394	−	0.375438i
$363$	3295.17	+	5733.97i	0.476450	+	0.829079i
$364$	−2114.41	+	1375.83i	−0.304465	+	0.198113i
$365$	−3582.81			−0.513788
$366$	6140.04	−	6450.10i	0.876900	−	0.921181i
$367$		−	11148.9i		−	1.58574i	−0.609391	−	0.792870i	$-0.708586\pi$
$367$		−	11148.9i		−	1.58574i	0.609391	−	0.792870i	$-0.291414\pi$
$368$	−1487.09	+	3356.36i	−0.210652	+	0.475441i
$369$	8251.08	+	4808.08i	1.16405	+	0.678316i
$370$	700.443	+	2360.74i	0.0984171	+	0.331700i
$371$			4734.05i			0.662479i
$372$	−1820.49	+	3563.15i	−0.253731	+	0.496615i
$373$		−	13651.6i		−	1.89504i	−0.319691	−	0.947522i	$-0.603579\pi$
$373$		−	13651.6i		−	1.89504i	0.319691	−	0.947522i	$-0.396421\pi$
$374$	−157.271	+	46.6631i	−0.0217441	+	0.00645158i
$375$	−323.629	−	563.151i	−0.0445656	−	0.0775494i
$376$	−1771.53	+	2079.89i	−0.242977	+	0.285272i
$377$		−	8591.44i		−	1.17369i
$378$	773.194	+	2664.74i	0.105208	+	0.362591i
$379$	4765.97			0.645941			0.322970	−	0.946409i	$-0.395319\pi$
$379$	4765.97			0.645941			0.322970	+	0.946409i	$0.395319\pi$
$380$	4199.33	−	2732.47i	0.566898	−	0.368876i
$381$	3420.86	−	1965.88i	0.459989	−	0.264344i
$382$	−9828.28	+	2916.10i	−1.31638	+	0.390577i
$383$	−1755.49			−0.234207			−0.117104	−	0.993120i	$-0.537361\pi$
$383$	−1755.49			−0.234207			−0.117104	+	0.993120i	$0.537361\pi$
$384$	−4254.97	+	6206.31i	−0.565457	+	0.824778i
$385$	−266.847			−0.0353241
$386$	8122.34	−	2409.94i	1.07103	−	0.317778i
$387$	−1309.93	+	2247.96i	−0.172061	+	0.295271i
$388$	1079.39	−	702.354i	0.141232	−	0.0918985i
$389$	10211.5			1.33096			0.665482	−	0.746414i	$-0.268226\pi$
$389$	10211.5			1.33096			0.665482	+	0.746414i	$0.268226\pi$
$390$	−2284.90	+	2400.28i	−0.296668	+	0.311649i
$391$		−	435.872i		−	0.0563760i
$392$	−4315.16	+	5066.29i	−0.555991	+	0.652771i
$393$	6964.01	−	4002.03i	0.893862	−	0.513679i
$394$	10561.3	−	3133.60i	1.35044	−	0.400681i
$395$		−	3232.94i		−	0.411815i
$396$	1646.66	−	81.1537i	0.208959	−	0.0102983i
$397$			12469.0i			1.57632i	0.615468	+	0.788162i	$0.288967\pi$
$397$			12469.0i			1.57632i	−0.615468	+	0.788162i	$0.711033\pi$
$398$	−1027.41	−	3462.74i	−0.129396	−	0.436110i
$399$	3945.62	−	2267.45i	0.495058	−	0.284497i
$400$	648.138	−	1462.85i	0.0810172	−	0.182856i
$401$		−	8331.51i		−	1.03755i	−0.854912	−	0.518773i	$-0.826389\pi$
$401$		−	8331.51i		−	1.03755i	0.854912	−	0.518773i	$-0.173611\pi$
$402$	4947.61	+	4709.77i	0.613841	+	0.584334i
$403$	−4340.84			−0.536557
$404$	8258.08	−	5373.47i	1.01697	−	0.661733i
$405$	1797.07	+	3171.21i	0.220487	+	0.389083i
$406$	1071.73	+	3612.10i	0.131007	+	0.441541i
$407$	1329.02			0.161860
$408$	163.392	−	878.374i	0.0198263	−	0.106583i
$409$	4025.59			0.486681			0.243340	−	0.969941i	$-0.421757\pi$
$409$	4025.59			0.486681			0.243340	+	0.969941i	$0.421757\pi$
$410$	−1422.81	−	4795.38i	−0.171384	−	0.577626i
$411$	−9211.22	+	5293.45i	−1.10549	+	0.635296i
$412$	−8631.12	−	13264.5i	−1.03210	−	1.58616i
$413$	−5363.54			−0.639038
$414$	−1037.78	+	4255.74i	−0.123199	+	0.505213i
$415$		−	6331.03i		−	0.748863i
$416$	−8095.96	−	1047.26i	−0.954175	−	0.123429i
$417$	−6307.60	−	10976.0i	−0.740731	−	1.28896i
$418$	−769.144	−	2592.29i	−0.0900002	−	0.303332i
$419$			1122.78i			0.130910i	0.997856	+	0.0654552i	$0.0208500\pi$
$419$			1122.78i			0.130910i	−0.997856	+	0.0654552i	$0.979150\pi$
$420$	661.222	−	1294.18i	0.0768198	−	0.150356i
$421$		−	8133.70i		−	0.941597i	−0.882241	−	0.470799i	$-0.843966\pi$
$421$		−	8133.70i		−	0.941597i	0.882241	−	0.470799i	$-0.156034\pi$
$422$	−6092.03	+	1807.53i	−0.702738	+	0.208506i
$423$	−1641.35	+	2816.70i	−0.188665	+	0.323765i
$424$	−9933.57	+	11662.7i	−1.13778	+	1.33582i
$425$			189.972i			0.0216823i
$426$	−1174.12	−	1117.68i	−0.133536	−	0.127117i
$427$	−4236.79			−0.480171
$428$	4158.58	+	6391.01i	0.469656	+	0.721778i
$429$	891.168	+	1550.74i	0.100294	+	0.174523i
$430$	1306.47	−	387.636i	0.146520	−	0.0434732i
$431$	−12656.6			−1.41450			−0.707249	−	0.706964i	$-0.750064\pi$
$431$	−12656.6			−1.41450			−0.707249	+	0.706964i	$0.750064\pi$
$432$	−3686.67	+	8187.19i	−0.410590	+	0.911820i
$433$	−6263.27			−0.695135			−0.347568	−	0.937655i	$-0.612992\pi$
$433$	−6263.27			−0.695135			−0.347568	+	0.937655i	$0.612992\pi$
$434$	1825.02	−	541.492i	0.201852	−	0.0598904i
$435$	2466.19	+	4291.45i	0.271827	+	0.473010i
$436$	−8614.24	−	13238.6i	−0.946210	−	1.45416i
$437$	7184.45			0.786450
$438$	−7627.81	−	7261.14i	−0.832125	−	0.792124i
$439$			13432.1i			1.46031i	0.683280	+	0.730157i	$0.260553\pi$
$439$			13432.1i			1.46031i	−0.683280	+	0.730157i	$0.739447\pi$
$440$	−657.398	−	559.932i	−0.0712277	−	0.0606676i
$441$	−3998.07	+	6861.03i	−0.431710	+	0.740852i
$442$	929.223	−	275.705i	0.0999969	−	0.0296695i
$443$			13111.9i			1.40625i	0.711068	+	0.703124i	$0.248212\pi$
$443$			13111.9i			1.40625i	−0.711068	+	0.703124i	$0.751788\pi$
$444$	−3293.18	+	6445.59i	−0.351998	+	0.688950i
$445$			1513.58i			0.161237i
$446$	−2626.11	−	8850.93i	−0.278812	−	0.939695i
$447$	1810.28	+	3150.11i	0.191552	+	0.333322i
$448$	3534.42	−	569.617i	0.372736	−	0.0600712i
$449$		−	10054.2i		−	1.05677i	−0.849005	−	0.528384i	$-0.822798\pi$
$449$		−	10054.2i		−	1.05677i	0.849005	−	0.528384i	$-0.177202\pi$
$450$	452.311	−	1854.84i	0.0473825	−	0.194306i
$451$	−2699.63			−0.281864
$452$	3267.09	+	5020.94i	0.339980	+	0.522489i
$453$	1787.20	−	1027.06i	0.185364	−	0.106524i
$454$	−2104.23	−	7092.00i	−0.217525	−	0.733136i
$455$	1576.64			0.162449
$456$	14478.2	+	2693.18i	1.48685	+	0.276578i
$457$	−8140.63			−0.833266			−0.416633	−	0.909075i	$-0.636790\pi$
$457$	−8140.63			−0.833266			−0.416633	+	0.909075i	$0.636790\pi$
$458$	3581.86	+	12072.1i	0.365435	+	1.23165i
$459$	6.42658	−	1066.07i	0.000653523	−	0.108410i
$460$	1923.12	−	1251.36i	0.194926	−	0.126837i
$461$	−16899.9			−1.70739			−0.853697	−	0.520769i	$-0.825645\pi$
$461$	−16899.9			−1.70739			−0.853697	+	0.520769i	$0.825645\pi$
$462$	−568.118	−	540.809i	−0.0572105	−	0.0544604i
$463$		−	4610.28i		−	0.462760i	−0.972863	−	0.231380i	$-0.925676\pi$
$463$		−	4610.28i		−	0.462760i	0.972863	−	0.231380i	$-0.0743241\pi$
$464$	−4939.08	+	11147.5i	−0.494162	+	1.11532i
$465$	2168.26	−	1246.04i	0.216238	−	0.124267i
$466$	−1460.81	−	4923.45i	−0.145216	−	0.489430i
$467$			4280.61i			0.424160i	0.977252	+	0.212080i	$0.0680238\pi$
$467$			4280.61i			0.424160i	−0.977252	+	0.212080i	$0.931976\pi$
$468$	−9729.12	+	479.489i	−0.960959	+	0.0473598i
$469$		−	3249.87i		−	0.319968i
$470$	1637.01	−	485.709i	0.160659	−	0.0476683i
$471$	−14962.6	+	8598.60i	−1.46378	+	0.841195i
$472$	−13213.5	−	11254.5i	−1.28856	−	1.09752i
$473$		−	735.498i		−	0.0714973i
$474$	6552.07	−	6882.93i	0.634908	−	0.666969i
$475$	−3131.29			−0.302471
$476$	−356.281	+	231.829i	−0.0343070	+	0.0223233i
$477$	−9203.62	+	15794.2i	−0.883448	+	1.51607i
$478$	17304.1	−	5134.22i	1.65580	−	0.491284i
$479$	−8615.73			−0.821843			−0.410921	−	0.911671i	$-0.634793\pi$
$479$	−8615.73			−0.821843			−0.410921	+	0.911671i	$0.634793\pi$
$480$	4344.58	−	1800.85i	0.413129	−	0.171244i
$481$	−7852.38			−0.744361
$482$	−11765.1	+	3490.75i	−1.11179	+	0.329874i
$483$	1806.93	−	1038.40i	0.170224	−	0.0978235i
$484$	8534.28	−	5553.19i	0.801492	−	0.521524i
$485$	−804.867			−0.0753549
$486$	−2601.00	+	10393.6i	−0.242765	+	0.970085i
$487$			4729.25i			0.440047i	0.975495	+	0.220023i	$0.0706134\pi$
$487$			4729.25i			0.440047i	−0.975495	+	0.220023i	$0.929387\pi$
$488$	−10437.7	−	8890.17i	−0.968218	−	0.824671i
$489$	−5563.45	−	9681.05i	−0.514494	−	0.895280i
$490$	3987.51	−	1183.11i	0.367627	−	0.109077i
$491$			12212.0i			1.12244i	0.827666	+	0.561221i	$0.189668\pi$
$491$			12212.0i			1.12244i	−0.827666	+	0.561221i	$0.810332\pi$
$492$	6689.43	−	13092.9i	0.612973	−	1.19974i
$493$		−	1447.67i		−	0.132251i
$494$	4544.42	+	15316.3i	0.413893	+	1.39497i
$495$	−890.283	−	518.787i	−0.0808389	−	0.0471065i
$496$	5632.29	+	2495.48i	0.509874	+	0.225908i
$497$			771.229i			0.0696064i
$498$	12830.9	−	13478.8i	1.15455	−	1.21285i
$499$	−7630.17			−0.684516			−0.342258	−	0.939606i	$-0.611192\pi$
$499$	−7630.17			−0.684516			−0.342258	+	0.939606i	$0.611192\pi$
$500$	−838.178	+	545.396i	−0.0749690	+	0.0487817i
$501$	−1197.69	−	2084.12i	−0.106804	−	0.185851i
$502$	732.875	+	2470.05i	0.0651590	+	0.219609i
$503$	2858.11			0.253353			0.126677	−	0.991944i	$-0.459569\pi$
$503$	2858.11			0.253353			0.126677	+	0.991944i	$0.459569\pi$
$504$	4030.60	−	1415.24i	0.356225	−	0.125079i
$505$	−6157.76			−0.542607
$506$	−352.236	−	1187.16i	−0.0309463	−	0.104300i
$507$	422.711	+	735.566i	0.0370281	+	0.0644332i
$508$	−3313.00	−	5091.50i	−0.289352	−	0.444683i
$509$	16177.1			1.40872			0.704359	−	0.709844i	$-0.251235\pi$
$509$	16177.1			1.40872			0.704359	+	0.709844i	$0.251235\pi$
$510$	−385.008	+	404.450i	−0.0334284	+	0.0351164i
$511$			5010.38i			0.433750i
$512$	9902.56	+	6013.08i	0.854756	+	0.519030i
$513$	17572.0	+	105.929i	1.51233	+	0.00911671i
$514$	−487.810	−	1644.09i	−0.0418607	−	0.141085i
$515$			9890.89i			0.846300i
$516$	3567.08	+	1822.49i	0.304326	+	0.155486i
$517$		−	921.582i		−	0.0783968i
$518$	3301.38	−	979.535i	0.280028	−	0.0830855i
$519$	2619.15	+	4557.62i	0.221518	+	0.385467i
$520$	3884.18	+	3308.31i	0.327562	+	0.278998i
$521$			5193.83i			0.436749i	0.975865	+	0.218374i	$0.0700754\pi$
$521$			5193.83i			0.436749i	−0.975865	+	0.218374i	$0.929925\pi$
$522$	−3446.80	+	14134.6i	−0.289008	+	1.18516i
$523$	2344.32			0.196003			0.0980017	−	0.995186i	$-0.468755\pi$
$523$	2344.32			0.196003			0.0980017	+	0.995186i	$0.468755\pi$
$524$	−6744.44	−	10365.0i	−0.562275	−	0.864119i
$525$	−787.539	+	452.578i	−0.0654686	+	0.0376231i
$526$	2683.89	−	796.324i	0.222478	−	0.0660102i
$527$	−731.436			−0.0604589
$528$	−264.808	−	2524.42i	−0.0218263	−	0.208071i
$529$	−8876.82			−0.729581
$530$	9179.30	−	2723.54i	0.752308	−	0.223213i
$531$	−17894.4	−	10427.4i	−1.46243	−	0.852189i
$532$	−3821.22	−	5872.55i	−0.311412	−	0.478585i
$533$	15950.5			1.29624
$534$	−3067.50	+	3222.41i	−0.248584	+	0.261137i
$535$		−	4765.55i		−	0.385108i
$536$	6819.28	−	8006.29i	0.549530	−	0.645185i
$537$	15770.4	−	9062.85i	1.26731	−	0.728288i
$538$	10174.8	−	3018.90i	0.815364	−	0.241922i
$539$		−	2244.83i		−	0.179391i
$540$	4722.09	−	3032.27i	0.376308	−	0.241645i
$541$			20861.7i			1.65788i	0.559337	+	0.828941i	$0.311056\pi$
$541$			20861.7i			1.65788i	−0.559337	+	0.828941i	$0.688944\pi$
$542$	−4046.19	−	13637.1i	−0.320662	−	1.08075i
$543$	−4296.28	+	2468.96i	−0.339541	+	0.195126i
$544$	−1364.18	−	176.465i	−0.107516	−	0.0139079i
$545$			9871.54i			0.775872i
$546$	3356.68	+	3195.32i	0.263100	+	0.250453i
$547$	23834.4			1.86305			0.931523	−	0.363682i	$-0.118481\pi$
$547$	23834.4			1.86305			0.931523	+	0.363682i	$0.118481\pi$
$548$	8920.80	+	13709.7i	0.695397	+	1.06870i
$549$	−14135.2	−	8236.89i	−1.09886	−	0.640332i
$550$	153.520	+	517.416i	0.0119020	+	0.0401140i
$551$	23861.8			1.84491
$552$	6630.41	+	1233.36i	0.511248	+	0.0951005i
$553$	−4521.10			−0.347661
$554$	−1595.07	−	5375.95i	−0.122325	−	0.412278i
$555$	3922.29	−	2254.04i	0.299986	−	0.172394i
$556$	−16336.3	+	10629.9i	−1.24607	+	0.810807i
$557$	−9321.40			−0.709085			−0.354542	−	0.935040i	$-0.615363\pi$
$557$	−9321.40			−0.709085			−0.354542	+	0.935040i	$0.615363\pi$
$558$	7141.55	+	1741.50i	0.541802	+	0.132121i
$559$			4345.63i			0.328802i
$560$	−2045.72	−	906.388i	−0.154370	−	0.0683962i
$561$	150.163	+	261.301i	0.0113010	+	0.0196651i
$562$	−1488.96	−	5018.33i	−0.111758	−	0.376665i
$563$		−	16949.3i		−	1.26879i	−0.773011	−	0.634393i	$-0.781250\pi$
$563$		−	16949.3i		−	1.26879i	0.773011	−	0.634393i	$-0.218750\pi$
$564$	4469.57	+	2283.59i	0.333693	+	0.170490i
$565$		−	3743.94i		−	0.278776i
$566$	19518.2	−	5791.15i	1.44949	−	0.430071i
$567$	4434.78	−	2513.11i	0.328471	−	0.186139i
$568$	−1618.29	+	1899.98i	−0.119546	+	0.140355i
$569$		−	1919.45i		−	0.141419i	−0.997497	−	0.0707096i	$-0.977474\pi$
$569$		−	1919.45i		−	0.141419i	0.997497	−	0.0707096i	$-0.0225264\pi$
$570$	−6666.53	−	6346.06i	−0.489877	−	0.466329i
$571$	−4932.62			−0.361512			−0.180756	−	0.983528i	$-0.557854\pi$
$571$	−4932.62			−0.361512			−0.180756	+	0.983528i	$0.557854\pi$
$572$	2308.07	−	1501.84i	0.168716	−	0.109782i
$573$	9384.05	+	16329.3i	0.684161	+	1.19052i
$574$	−6706.09	+	1989.73i	−0.487643	+	0.144686i
$575$	−1434.00			−0.104004
$576$	12899.3	+	4970.98i	0.933110	+	0.359590i
$577$	6810.64			0.491387			0.245694	−	0.969348i	$-0.420984\pi$
$577$	6810.64			0.491387			0.245694	+	0.969348i	$0.420984\pi$
$578$	−13165.5	+	3906.25i	−0.947424	+	0.281105i
$579$	−7755.22	−	13495.0i	−0.556642	−	0.968623i
$580$	6387.28	−	4156.15i	0.457271	−	0.297543i
$581$	−8853.63			−0.632204
$582$	−1713.56	−	1631.19i	−0.122044	−	0.116177i
$583$		−	5167.63i		−	0.367104i
$584$	−10513.4	+	12343.4i	−0.744945	+	0.874614i
$585$	5260.16	+	3065.20i	0.371762	+	0.216634i
$586$	−4606.80	+	1366.86i	−0.324753	+	0.0963558i
$587$		−	23691.6i		−	1.66585i	−0.553384	−	0.832926i	$-0.686664\pi$
$587$		−	23691.6i		−	1.66585i	0.553384	−	0.832926i	$-0.313336\pi$
$588$	10887.2	+	5562.47i	0.763570	+	0.390123i
$589$		−	12056.2i		−	0.843407i
$590$	3085.69	+	10399.9i	0.215315	+	0.725689i
$591$	−10084.0	−	17547.3i	−0.701860	−	1.22132i
$592$	10188.6	+	4514.21i	0.707344	+	0.313400i
$593$			6554.47i			0.453895i	0.973907	+	0.226947i	$0.0728746\pi$
$593$			6554.47i			0.453895i	−0.973907	+	0.226947i	$0.927125\pi$
$594$	−844.009	−	2908.80i	−0.0582999	−	0.200925i
$595$	265.666			0.0183046
$596$	4688.53	−	3050.79i	0.322231	−	0.209673i
$597$	−5753.23	+	3306.23i	−0.394412	+	0.226659i
$598$	2081.16	+	7014.24i	0.142316	+	0.479655i
$599$	13841.6			0.944158			0.472079	−	0.881556i	$-0.343504\pi$
$599$	13841.6			0.944158			0.472079	+	0.881556i	$0.343504\pi$
$600$	−2889.82	−	537.553i	−0.196627	−	0.0365759i
$601$	−18378.2			−1.24736			−0.623681	−	0.781679i	$-0.714364\pi$
$601$	−18378.2			−1.24736			−0.623681	+	0.781679i	$0.714364\pi$
$602$	−542.089	−	1827.03i	−0.0367008	−	0.123695i
$603$	6318.18	−	10842.5i	0.426693	−	0.732243i
$604$	−1730.85	−	2660.02i	−0.116602	−	0.179196i
$605$	−6363.71			−0.427639
$606$	−13109.9	−	12479.7i	−0.878800	−	0.836555i
$607$		−	3355.03i		−	0.224344i	−0.993689	−	0.112172i	$-0.964219\pi$
$607$		−	3355.03i		−	0.224344i	0.993689	−	0.112172i	$-0.0357807\pi$
$608$	2908.66	−	22485.6i	0.194016	−	1.49986i
$609$	6001.38	−	3448.84i	0.399324	−	0.229481i
$610$	2437.47	+	8215.13i	0.161787	+	0.545280i
$611$			5445.09i			0.360531i
$612$	−1639.37	+	80.7945i	−0.108280	+	0.00533648i
$613$		−	20060.5i		−	1.32176i	−0.750493	−	0.660878i	$-0.770184\pi$
$613$		−	20060.5i		−	1.32176i	0.750493	−	0.660878i	$-0.229816\pi$
$614$	−7977.59	+	2366.99i	−0.524347	+	0.155576i
$615$	−7967.35	+	4578.63i	−0.522398	+	0.300209i
$616$	−783.037	+	919.338i	−0.0512167	+	0.0601318i
$617$			2624.95i			0.171275i	0.996326	+	0.0856373i	$0.0272926\pi$
$617$			2624.95i			0.171275i	−0.996326	+	0.0856373i	$0.972707\pi$
$618$	−20045.5	+	21057.7i	−1.30477	+	1.37066i
$619$	14745.0			0.957436			0.478718	−	0.877969i	$-0.341102\pi$
$619$	14745.0			0.957436			0.478718	+	0.877969i	$0.341102\pi$
$620$	−2099.90	−	3227.18i	−0.136023	−	0.209043i
$621$	8047.25	+	48.5110i	0.520008	+	0.00313475i
$622$	−8688.31	+	2577.86i	−0.560079	+	0.166178i
$623$	2116.66			0.136119
$624$	1564.59	+	14915.3i	0.100375	+	0.956875i
$625$	625.000			0.0400000
$626$	−9973.66	+	2959.23i	−0.636785	+	0.188937i
$627$	−4307.00	+	2475.12i	−0.274330	+	0.157650i
$628$	14490.8	+	22269.9i	0.920775	+	1.41507i
$629$	−1323.13			−0.0838741
$630$	−2593.89	−	632.534i	−0.164037	−	0.0400012i
$631$			8392.00i			0.529446i	0.964325	+	0.264723i	$0.0852805\pi$
$631$			8392.00i			0.529446i	−0.964325	+	0.264723i	$0.914720\pi$
$632$	−11138.1	−	9486.74i	−0.701026	−	0.597092i
$633$	5816.68	+	10121.7i	0.365232	+	0.635547i
$634$	1376.59	−	408.442i	0.0862327	−	0.0255857i
$635$			3796.55i			0.237262i
$636$	25062.4	+	12804.9i	1.56256	+	0.798345i
$637$			13263.4i			0.824983i
$638$	−1169.89	−	3942.93i	−0.0725959	−	0.244674i
$639$	−1499.37	+	2573.05i	−0.0928236	+	0.159293i
$640$	−3137.87	−	6525.53i	−0.193805	−	0.403038i
$641$			18468.8i			1.13802i	0.822330	+	0.569011i	$0.192674\pi$
$641$			18468.8i			1.13802i	−0.822330	+	0.569011i	$0.807326\pi$
$642$	9658.15	−	10145.9i	0.593733	−	0.623716i
$643$	1217.77			0.0746878			0.0373439	−	0.999302i	$-0.488110\pi$
$643$	1217.77			0.0746878			0.0373439	+	0.999302i	$0.488110\pi$
$644$	−1749.96	−	2689.39i	−0.107078	−	0.164560i
$645$	−1247.42	−	2170.65i	−0.0761505	−	0.132511i
$646$	765.739	+	2580.81i	0.0466372	+	0.157184i
$647$	5514.93			0.335107			0.167554	−	0.985863i	$-0.446413\pi$
$647$	5514.93			0.335107			0.167554	+	0.985863i	$0.446413\pi$
$648$	16198.7	+	3114.37i	0.982015	+	0.188803i
$649$	5854.78			0.354114
$650$	−907.058	−	3057.11i	−0.0547350	−	0.184476i
$651$	−1742.53	−	3032.21i	−0.104908	−	0.182552i
$652$	−14409.0	+	9375.82i	−0.865490	+	0.563168i
$653$	6896.68			0.413305			0.206652	−	0.978414i	$-0.433743\pi$
$653$	6896.68			0.413305			0.206652	+	0.978414i	$0.433743\pi$
$654$	−20006.3	+	21016.5i	−1.19619	+	1.25659i
$655$			7728.83i			0.461054i
$656$	−20696.0	−	9169.72i	−1.23178	−	0.545758i
$657$	−9740.84	+	16716.1i	−0.578427	+	0.992630i
$658$	−679.240	−	2289.28i	−0.0402424	−	0.135631i
$659$		−	18045.8i		−	1.06671i	−0.845891	−	0.533356i	$-0.820931\pi$
$659$		−	18045.8i		−	1.06671i	0.845891	−	0.533356i	$-0.179069\pi$
$660$	−721.782	+	1412.71i	−0.0425687	+	0.0833178i
$661$		−	9981.04i		−	0.587319i	−0.955910	−	0.293659i	$-0.905127\pi$
$661$		−	9981.04i		−	0.587319i	0.955910	−	0.293659i	$-0.0948731\pi$
$662$	−7524.26	+	2232.48i	−0.441750	+	0.131069i
$663$	−887.223	−	1543.87i	−0.0519712	−	0.0904359i
$664$	−21811.6	−	18577.8i	−1.27478	−	1.08578i
$665$			4378.95i			0.255351i
$666$	12918.7	+	3150.30i	0.751638	+	0.183291i
$667$	10927.7			0.634367
$668$	−3101.94	+	2018.41i	−0.179667	+	0.116908i
$669$	−14705.5	+	8450.88i	−0.849848	+	0.488386i
$670$	−6301.49	+	1869.68i	−0.363355	+	0.107809i
$671$	4624.84			0.266080
$672$	−2518.39	−	6075.67i	−0.144567	−	0.348771i
$673$	−20103.3			−1.15145			−0.575724	−	0.817644i	$-0.695280\pi$
$673$	−20103.3			−1.15145			−0.575724	+	0.817644i	$0.695280\pi$
$674$	−10512.8	+	3119.20i	−0.600798	+	0.178260i
$675$	−3507.34	−	21.1432i	−0.199996	−	0.00120563i
$676$	1094.79	−	712.375i	0.0622892	−	0.0405311i
$677$	32270.7			1.83200			0.915999	−	0.401179i	$-0.131400\pi$
$677$	32270.7			1.83200			0.915999	+	0.401179i	$0.131400\pi$
$678$	7587.69	−	7970.85i	0.429798	−	0.451502i
$679$			1125.57i			0.0636160i
$680$	654.488	+	557.454i	0.0369095	+	0.0314373i
$681$	−11783.1	+	6771.45i	−0.663039	+	0.381031i
$682$	−1992.17	+	591.086i	−0.111854	+	0.0331875i
$683$		−	9138.76i		−	0.511984i	−0.966679	−	0.255992i	$-0.917598\pi$
$683$		−	9138.76i		−	0.511984i	0.966679	−	0.255992i	$-0.0824020\pi$
$684$	−1331.73	−	27021.6i	−0.0744443	−	1.51052i
$685$		−	10222.8i		−	0.570211i
$686$	−3584.09	−	12079.6i	−0.199477	−	0.672307i
$687$	20057.4	−	11526.5i	1.11389	−	0.640121i
$688$	2498.23	−	5638.51i	0.138436	−	0.312451i
$689$			30532.5i			1.68824i
$690$	−3052.99	−	2906.24i	−0.168443	−	0.160346i
$691$	30504.7			1.67938			0.839690	−	0.543066i	$-0.182737\pi$
$691$	30504.7			1.67938			0.839690	+	0.543066i	$0.182737\pi$
$692$	6783.43	−	4413.93i	0.372641	−	0.242474i
$693$	−725.497	+	1245.02i	−0.0397682	+	0.0682457i
$694$	2575.85	+	8681.53i	0.140890	+	0.474851i
$695$	12181.4			0.664845
$696$	22021.6	+	4096.39i	1.19932	+	0.223094i
$697$	2687.68			0.146059
$698$	−5514.87	−	18587.1i	−0.299056	−	1.00792i
$699$	−8180.15	+	4700.92i	−0.442634	+	0.254371i
$700$	762.709	+	1172.15i	0.0411824	+	0.0632902i
$701$	−12035.1			−0.648444			−0.324222	−	0.945981i	$-0.605102\pi$
$701$	−12035.1			−0.648444			−0.324222	+	0.945981i	$0.605102\pi$
$702$	4986.75	+	17186.4i	0.268110	+	0.924014i
$703$		−	21809.1i		−	1.17005i
$704$	−3858.14	+	621.788i	−0.206547	+	0.0332877i
$705$	−1563.02	−	2719.84i	−0.0834990	−	0.145298i
$706$	124.810	+	420.653i	0.00665337	+	0.0224242i
$707$			8611.32i			0.458079i
$708$	−14507.6	+	28395.0i	−0.770097	+	1.50727i
$709$		−	27841.6i		−	1.47477i	−0.675471	−	0.737387i	$-0.736059\pi$
$709$		−	27841.6i		−	1.47477i	0.675471	−	0.737387i	$-0.263941\pi$
$710$	1495.41	−	443.695i	0.0790447	−	0.0234529i
$711$	−15083.8	−	8789.62i	−0.795619	−	0.463624i
$712$	5214.55	+	4441.44i	0.274471	+	0.233778i
$713$		−	5521.24i		−	0.290003i
$714$	565.604	+	538.415i	0.0296459	+	0.0282208i
$715$	−1721.05			−0.0900189
$716$	−15273.2	−	23472.2i	−0.797187	−	1.22514i
$717$	−16522.0	−	28750.2i	−0.860566	−	1.49749i
$718$	21087.0	−	6256.62i	1.09605	−	0.325202i
$719$	11118.3			0.576691			0.288346	−	0.957526i	$-0.406895\pi$
$719$	11118.3			0.576691			0.288346	+	0.957526i	$0.406895\pi$
$720$	−5062.99	−	7001.13i	−0.262064	−	0.362384i
$721$	13831.9			0.714462
$722$	−23940.6	+	7103.28i	−1.23404	+	0.366145i
$723$	11233.3	+	19547.2i	0.577829	+	1.00549i
$724$	4160.82	+	6394.45i	0.213585	+	0.328243i
$725$	−4762.77			−0.243979
$726$	−13548.4	−	12897.1i	−0.692599	−	0.659305i
$727$			32817.3i			1.67418i	0.547069	+	0.837088i	$0.315744\pi$
$727$			32817.3i			1.67418i	−0.547069	+	0.837088i	$0.684256\pi$
$728$	4626.51	−	5431.82i	0.235535	−	0.276534i
$729$	19681.6	+	237.300i	0.999927	+	0.0120561i
$730$	9715.10	−	2882.52i	0.492565	−	0.146146i
$731$			732.242i			0.0370492i
$732$	−11459.9	+	22429.9i	−0.578648	+	1.13256i
$733$			27924.0i			1.40709i	0.710651	+	0.703545i	$0.248401\pi$
$733$			27924.0i			1.40709i	−0.710651	+	0.703545i	$0.751599\pi$
$734$	8969.72	+	30231.2i	0.451061	+	1.52023i
$735$	−3807.28	−	6625.10i	−0.191066	−	0.332477i
$736$	1332.05	−	10297.5i	0.0667119	−	0.515721i
$737$			3547.52i			0.177306i
$738$	−26241.8	−	6399.20i	−1.30891	−	0.319184i
$739$	5667.23			0.282101			0.141050	−	0.990002i	$-0.454952\pi$
$739$	5667.23			0.282101			0.141050	+	0.990002i	$0.454952\pi$
$740$	−3798.63	−	5837.83i	−0.188703	−	0.290004i
$741$	25447.5	−	14624.0i	1.26159	−	0.725003i
$742$	−3808.74	−	12836.8i	−0.188441	−	0.635112i
$743$	−1552.79			−0.0766707			−0.0383354	−	0.999265i	$-0.512206\pi$
$743$	−1552.79			−0.0766707			−0.0383354	+	0.999265i	$0.512206\pi$
$744$	2069.70	−	11126.5i	0.101988	−	0.548274i
$745$	−3496.07			−0.171928
$746$	10983.2	+	37017.4i	0.539042	+	1.81676i
$747$	−29538.4	−	17212.6i	−1.44679	−	0.843076i
$748$	388.912	−	253.062i	0.0190108	−	0.0123701i
$749$	−6664.38			−0.325115
$750$	1330.63	+	1266.66i	0.0647835	+	0.0616693i
$751$		−	10058.4i		−	0.488731i	−0.969683	−	0.244366i	$-0.921420\pi$
$751$		−	10058.4i		−	0.488731i	0.969683	−	0.244366i	$-0.0785797\pi$
$752$	3130.30	−	7065.07i	0.151795	−	0.342602i
$753$	4103.90	−	2358.41i	0.198611	−	0.114137i
$754$	6912.16	+	23296.4i	0.333854	+	1.12521i
$755$			1983.48i			0.0956110i
$756$	−4240.47	−	6603.61i	−0.204001	−	0.317686i
$757$		−	5337.21i		−	0.256254i	−0.991758	−	0.128127i	$-0.959103\pi$
$757$		−	5337.21i		−	0.256254i	0.991758	−	0.128127i	$-0.0408965\pi$
$758$	−12923.4	+	3834.42i	−0.619258	+	0.183737i
$759$	−1972.43	+	1133.50i	−0.0943275	+	0.0542076i
$760$	−9188.47	+	10787.9i	−0.438554	+	0.514891i
$761$			2379.83i			0.113362i	0.998392	+	0.0566812i	$0.0180519\pi$
$761$			2379.83i			0.113362i	−0.998392	+	0.0566812i	$0.981948\pi$
$762$	−7694.33	+	8082.87i	−0.365795	+	0.384267i
$763$	13804.9			0.655006
$764$	24304.1	−	15814.5i	1.15091	−	0.748886i
$765$	886.342	+	516.490i	0.0418899	+	0.0244101i
$766$	4760.17	−	1412.36i	0.224532	−	0.0666198i
$767$	−34592.5			−1.62850
$768$	6544.50	−	20252.3i	0.307492	−	0.951551i
$769$	−14820.6			−0.694989			−0.347494	−	0.937682i	$-0.612967\pi$
$769$	−14820.6			−0.694989			−0.347494	+	0.937682i	$0.612967\pi$
$770$	723.580	−	214.690i	0.0338650	−	0.0100479i
$771$	−2731.61	+	1569.78i	−0.127596	+	0.0733260i
$772$	−20085.5	+	13069.5i	−0.936392	+	0.609303i
$773$	−17644.1			−0.820974			−0.410487	−	0.911866i	$-0.634641\pi$
$773$	−17644.1			−0.820974			−0.410487	+	0.911866i	$0.634641\pi$
$774$	1743.42	−	7149.42i	0.0809638	−	0.332016i
$775$			2406.39i			0.111536i
$776$	−2361.80	+	2772.91i	−0.109257	+	0.128275i
$777$	−3152.16	−	5485.13i	−0.145538	−	0.253253i
$778$	−27689.4	+	8215.59i	−1.27598	+	0.378590i
$779$			44300.9i			2.03754i
$780$	4264.59	−	8346.88i	0.195765	−	0.383162i
$781$		−	841.865i		−	0.0385715i
$782$	350.677	+	1181.91i	0.0160360	+	0.0540472i
$783$	26727.4	+	161.120i	1.21987	+	0.00735372i
$784$	7624.91	−	17209.4i	0.347345	−	0.783956i
$785$		−	16605.8i		−	0.755017i
$786$	−15663.7	+	16454.7i	−0.710822	+	0.746717i
$787$	10627.6			0.481364			0.240682	−	0.970604i	$-0.422629\pi$
$787$	10627.6			0.481364			0.240682	+	0.970604i	$0.422629\pi$
$788$	−26116.9	+	16994.0i	−1.18068	+	0.768259i
$789$	−2562.58	−	4459.20i	−0.115628	−	0.201206i
$790$	2601.03	+	8766.40i	0.117140	+	0.394803i
$791$	−5235.71			−0.235348
$792$	−4399.76	+	1544.86i	−0.197397	+	0.0693108i
$793$	−27325.4			−1.22365
$794$	−10031.8	−	33810.8i	−0.448382	−	1.51121i
$795$	−8764.41	−	15251.1i	−0.390996	−	0.680378i
$796$	5571.84	+	8562.94i	0.248101	+	0.381288i
$797$	28315.9			1.25847			0.629234	−	0.777216i	$-0.283369\pi$
$797$	28315.9			1.25847			0.629234	+	0.777216i	$0.283369\pi$
$798$	−8874.65	+	9322.80i	−0.393683	+	0.413563i
$799$			917.503i			0.0406244i
$800$	−580.564	+	4488.09i	−0.0256575	+	0.198347i
$801$	7061.81	+	4115.07i	0.311507	+	0.181522i
$802$	6703.04	+	22591.6i	0.295128	+	0.994686i
$803$		−	5469.27i		−	0.240357i
$804$	−17205.1	−	8790.42i	−0.754697	−	0.385590i
$805$			2005.38i			0.0878017i
$806$	11770.6	−	3492.38i	0.514393	−	0.152623i
$807$	−9714.89	−	16905.0i	−0.423768	−	0.737405i
$808$	−18069.3	+	21214.6i	−0.786729	+	0.923672i
$809$			4929.57i			0.214233i	0.994246	+	0.107116i	$0.0341618\pi$
$809$			4929.57i			0.214233i	−0.994246	+	0.107116i	$0.965838\pi$
$810$	−7424.28	−	7153.20i	−0.322053	−	0.310294i
$811$	36380.6			1.57521			0.787606	−	0.616179i	$-0.211320\pi$
$811$	36380.6			1.57521			0.787606	+	0.616179i	$0.211320\pi$
$812$	−5812.17	−	8932.28i	−0.251191	−	0.386037i
$813$	−22657.6	+	13020.7i	−0.977412	+	0.561693i
$814$	−3603.75	+	1069.25i	−0.155174	+	0.0460407i
$815$	10744.3			0.461786
$816$	263.636	+	2513.24i	0.0113102	+	0.107820i
$817$	−12069.5			−0.516840
$818$	−10915.7	+	3238.75i	−0.466577	+	0.138436i
$819$	4286.53	−	7356.06i	0.182886	−	0.313848i
$820$	7716.16	+	11858.4i	0.328610	+	0.505015i
$821$	2778.18			0.118099			0.0590493	−	0.998255i	$-0.481193\pi$
$821$	2778.18			0.118099			0.0590493	+	0.998255i	$0.481193\pi$
$822$	20718.2	−	21764.5i	0.879114	−	0.923507i
$823$			5525.76i			0.234041i	0.993129	+	0.117021i	$0.0373344\pi$
$823$			5525.76i			0.234041i	−0.993129	+	0.117021i	$0.962666\pi$
$824$	34075.9	+	29023.8i	1.44064	+	1.22706i
$825$	859.669	−	494.029i	0.0362786	−	0.0208484i
$826$	14543.7	−	4315.19i	0.612640	−	0.181773i
$827$		−	22855.9i		−	0.961037i	−0.876985	−	0.480519i	$-0.840448\pi$
$827$		−	22855.9i		−	0.961037i	0.876985	−	0.480519i	$-0.159552\pi$
$828$	−609.877	−	12374.8i	−0.0255975	−	0.519387i
$829$			29959.0i			1.25515i	0.778557	+	0.627574i	$0.215952\pi$
$829$			29959.0i			1.25515i	−0.778557	+	0.627574i	$0.784048\pi$
$830$	5093.58	+	17167.2i	0.213013	+	0.717929i
$831$	−8931.95	+	5132.96i	−0.372859	+	0.214272i
$832$	22795.5	−	3673.78i	0.949869	−	0.153083i
$833$			2234.89i			0.0929585i
$834$	25934.2	+	24687.6i	1.07677	+	1.02501i
$835$	2313.01			0.0958621
$836$	4171.20	+	6410.41i	0.172565	+	0.265202i
$837$	81.4062	−	13504.1i	0.00336178	−	0.557669i
$838$	−903.324	−	3044.52i	−0.0372372	−	0.125503i
$839$	21848.4			0.899035			0.449517	−	0.893272i	$-0.351596\pi$
$839$	21848.4			0.899035			0.449517	+	0.893272i	$0.351596\pi$
$840$	−751.741	+	4041.26i	−0.0308780	+	0.165996i
$841$	11905.3			0.488142
$842$	6543.90	+	22055.3i	0.267836	+	0.902701i
$843$	−8337.79	+	4791.51i	−0.340651	+	0.195763i
$844$	15064.8	−	9802.57i	0.614400	−	0.399785i
$845$	−816.350			−0.0332347
$846$	2184.51	−	8958.26i	0.0887768	−	0.364056i
$847$			8899.33i			0.361021i
$848$	17552.7	−	39616.3i	0.710803	−	1.60428i
$849$	−18636.0	−	32428.9i	−0.753342	−	1.31090i
$850$	−152.840	−	515.126i	−0.00616750	−	0.0207867i
$851$		−	9987.68i		−	0.402319i
$852$	4082.95	+	2086.06i	0.164178	+	0.0838818i
$853$			17736.2i			0.711929i	0.934499	+	0.355965i	$0.115848\pi$
$853$			17736.2i			0.711929i	−0.934499	+	0.355965i	$0.884152\pi$
$854$	11488.4	−	3408.68i	0.460336	−	0.136584i
$855$	−8513.27	+	14609.5i	−0.340524	+	0.584368i
$856$	−16418.2	−	13984.0i	−0.655563	−	0.558370i
$857$		−	2106.41i		−	0.0839600i	−0.999118	−	0.0419800i	$-0.986633\pi$
$857$		−	2106.41i		−	0.0839600i	0.999118	−	0.0419800i	$-0.0133666\pi$
$858$	−3664.11	−	3487.98i	−0.145793	−	0.138785i
$859$	4756.26			0.188919			0.0944594	−	0.995529i	$-0.469888\pi$
$859$	4756.26			0.188919			0.0944594	+	0.995529i	$0.469888\pi$
$860$	−3230.74	+	2102.22i	−0.128102	+	0.0833547i
$861$	6402.99	+	11141.9i	0.253442	+	0.441018i
$862$	34319.6	−	10182.8i	1.35607	−	0.402352i
$863$	−47788.5			−1.88498			−0.942492	−	0.334229i	$-0.891524\pi$
$863$	−47788.5			−1.88498			−0.942492	+	0.334229i	$0.891524\pi$
$864$	3409.80	−	25166.4i	0.134264	−	0.990946i
$865$	−5058.16			−0.198824
$866$	16983.4	−	5039.06i	0.666420	−	0.197730i
$867$	12570.4	+	21874.0i	0.492403	+	0.856838i
$868$	−4513.05	+	2936.61i	−0.176478	+	0.114833i
$869$	4935.18			0.192652
$870$	−10139.9	−	9652.51i	−0.395145	−	0.376150i
$871$		−	20960.2i		−	0.815396i
$872$	34009.3	+	28967.1i	1.32076	+	1.12494i
$873$	−2188.25	+	3755.22i	−0.0848351	+	0.145584i
$874$	−19481.3	+	5780.18i	−0.753963	+	0.223704i
$875$		−	874.031i		−	0.0337687i
$876$	26525.4	+	13552.3i	1.02307	+	0.522706i
$877$		−	17911.1i		−	0.689639i	−0.938669	−	0.344820i	$-0.887940\pi$
$877$		−	17911.1i		−	0.689639i	0.938669	−	0.344820i	$-0.112060\pi$
$878$	−10806.6	−	36422.2i	−0.415384	−	1.39999i
$879$	4398.58	+	7654.05i	0.168783	+	0.293703i
$880$	2233.08	+	989.403i	0.0855422	+	0.0379009i
$881$		−	50634.7i		−	1.93635i	−0.250268	−	0.968177i	$-0.580519\pi$
$881$		−	50634.7i		−	1.93635i	0.250268	−	0.968177i	$-0.419481\pi$
$882$	5321.14	−	21820.9i	0.203143	−	0.833048i
$883$	−43368.2			−1.65284			−0.826419	−	0.563055i	$-0.809626\pi$
$883$	−43368.2			−1.65284			−0.826419	+	0.563055i	$0.809626\pi$
$884$	−2297.85	+	1495.20i	−0.0874267	+	0.0568879i
$885$	17279.1	−	9929.83i	0.656304	−	0.377161i
$886$	−10549.1	−	35554.2i	−0.400004	−	1.34816i
$887$	−12350.9			−0.467534			−0.233767	−	0.972293i	$-0.575105\pi$
$887$	−12350.9			−0.467534			−0.233767	+	0.972293i	$0.575105\pi$
$888$	3744.00	−	20127.3i	0.141487	−	0.760616i
$889$	5309.29			0.200301
$890$	−1217.73	−	4104.20i	−0.0458635	−	0.154576i
$891$	−4840.95	+	2743.28i	−0.182018	+	0.103146i
$892$	14241.9	+	21887.3i	0.534589	+	0.821570i
$893$	−15123.1			−0.566715
$894$	−7443.14	−	7085.34i	−0.278452	−	0.265066i
$895$			17502.4i			0.653677i
$896$	−9125.63	+	4388.16i	−0.340252	+	0.163614i
$897$	11653.9	−	6697.20i	0.433794	−	0.249290i
$898$	8089.05	+	27263.0i	0.300596	+	1.01311i
$899$		−	18337.7i		−	0.680309i
$900$	265.811	+	5393.45i	0.00984484	+	0.199758i
$901$			5144.76i			0.190230i
$902$	7320.30	−	2171.97i	0.270221	−	0.0801758i
$903$	−3035.55	+	1744.45i	−0.111868	+	0.0642877i
$904$	−12898.5	−	10986.2i	−0.474557	−	0.404199i
$905$		−	4768.12i		−	0.175135i
$906$	−4019.84	+	4222.84i	−0.147407	+	0.154850i
$907$	−33714.7			−1.23426			−0.617132	−	0.786859i	$-0.711706\pi$
$907$	−33714.7			−1.23426			−0.617132	+	0.786859i	$0.711706\pi$
$908$	11411.6	+	17537.6i	0.417079	+	0.640977i
$909$	−16741.5	+	28729.9i	−0.610871	+	1.04831i
$910$	−4275.21	+	1268.47i	−0.155738	+	0.0462083i
$911$	40885.5			1.48694			0.743468	−	0.668772i	$-0.233180\pi$
$911$	40885.5			1.48694			0.743468	+	0.668772i	$0.233180\pi$
$912$	−41425.6	+	4345.49i	−1.50410	+	0.157778i
$913$	9664.53			0.350328
$914$	22074.0	−	6549.47i	0.798845	−	0.237021i
$915$	13649.2	−	7843.82i	0.493144	−	0.283397i
$916$	−19425.1	−	29852.9i	−0.700679	−	1.07682i
$917$	10808.4			0.389230
$918$	840.274	+	2895.92i	0.0302104	+	0.104117i
$919$		−	18664.6i		−	0.669956i	−0.942226	−	0.334978i	$-0.891271\pi$
$919$		−	18664.6i		−	0.669956i	0.942226	−	0.334978i	$-0.108729\pi$
$920$	−4207.94	+	4940.40i	−0.150795	+	0.177044i
$921$	7617.01	+	13254.5i	0.272518	+	0.474213i
$922$	45825.7	−	13596.7i	1.63686	−	0.485665i
$923$			4974.09i			0.177383i
$924$	1975.61	+	1009.38i	0.0703384	+	0.0359373i
$925$			4353.06i			0.154733i
$926$	3709.16	+	12501.2i	0.131631	+	0.443644i
$927$	46147.4	+	26891.1i	1.63504	+	0.952771i
$928$	4424.14	−	34201.1i	0.156497	−	1.20981i
$929$			8485.76i			0.299686i	0.988710	+	0.149843i	$0.0478769\pi$
$929$			8485.76i			0.299686i	−0.988710	+	0.149843i	$0.952123\pi$
$930$	−4876.94	+	5123.22i	−0.171958	+	0.180642i
$931$	−36837.6			−1.29678
$932$	7922.24	+	12175.1i	0.278435	+	0.427906i
$933$	8295.61	+	14435.3i	0.291089	+	0.506529i
$934$	−3443.92	−	11607.2i	−0.120652	−	0.406639i
$935$	−289.998			−0.0101433
$936$	25995.6	−	9127.66i	0.907792	−	0.318747i
$937$	26119.4			0.910655			0.455327	−	0.890324i	$-0.349522\pi$
$937$	26119.4			0.910655			0.455327	+	0.890324i	$0.349522\pi$
$938$	2614.65	+	8812.31i	0.0910144	+	0.306751i
$939$	9522.87	+	16570.9i	0.330955	+	0.575901i
$940$	−4048.13	+	2634.09i	−0.140463	+	0.0913984i
$941$	−29869.6			−1.03477			−0.517387	−	0.855752i	$-0.673095\pi$
$941$	−29869.6			−1.03477			−0.517387	+	0.855752i	$0.673095\pi$
$942$	33654.4	−	35353.9i	1.16403	−	1.22281i
$943$			20288.0i			0.700602i
$944$	44884.2	+	19886.7i	1.54752	+	0.685652i
$945$	−29.5677	+	4904.84i	−0.00101782	+	0.168841i
$946$	591.738	+	1994.37i	0.0203373	+	0.0685439i
$947$			32586.5i			1.11818i	0.829106	+	0.559092i	$0.188850\pi$
$947$			32586.5i			1.11818i	−0.829106	+	0.559092i	$0.811150\pi$
$948$	−12228.9	+	23935.1i	−0.418963	+	0.820016i
$949$			32314.7i			1.10535i
$950$	8490.77	−	2519.25i	0.289976	−	0.0860372i
$951$	−1314.37	−	2287.16i	−0.0448176	−	0.0779878i
$952$	779.571	−	915.268i	0.0265400	−	0.0311597i
$953$		−	29950.9i		−	1.01805i	−0.860751	−	0.509026i	$-0.830006\pi$
$953$		−	29950.9i		−	1.01805i	0.860751	−	0.509026i	$-0.169994\pi$
$954$	12249.3	−	50232.1i	0.415710	−	1.70474i
$955$	−18122.7			−0.614071
$956$	−42791.0	+	27843.8i	−1.44766	+	0.941979i
$957$	−6551.04	+	3764.71i	−0.221280	+	0.127164i
$958$	23362.3	−	6931.71i	0.787894	−	0.233772i
$959$	−14296.1			−0.481383
$960$	−10331.9	+	8378.55i	−0.347353	+	0.281684i
$961$	20525.8			0.688994
$962$	21292.4	−	6317.56i	0.713613	−	0.211732i
$963$	−22234.4	−	12956.4i	−0.744022	−	0.433557i
$964$	29093.5	−	18930.9i	0.972033	−	0.632494i
$965$	14977.1			0.499616
$966$	−4064.23	+	4269.46i	−0.135367	+	0.142202i
$967$			186.832i			0.00621314i	0.999995	+	0.00310657i	$0.000988854\pi$
$967$			186.832i			0.00621314i	−0.999995	+	0.00310657i	$0.999011\pi$
$968$	−18673.7	+	21924.2i	−0.620036	+	0.727964i
$969$	4287.93	−	2464.16i	0.142155	−	0.0816928i
$970$	2182.47	−	647.548i	0.0722421	−	0.0214346i
$971$		−	20133.2i		−	0.665402i	−0.943032	−	0.332701i	$-0.892040\pi$
$971$		−	20133.2i		−	0.665402i	0.943032	−	0.332701i	$-0.107960\pi$
$972$	−1309.21	−	30275.7i	−0.0432024	−	0.999066i
$973$		−	17035.1i		−	0.561274i
$974$	−3804.88	−	12823.8i	−0.125171	−	0.421869i
$975$	−5079.28	+	2918.93i	−0.166838	+	0.0958775i
$976$	35455.1	+	15709.0i	1.16280	+	0.515197i
$977$			36471.0i			1.19428i	0.802138	+	0.597139i	$0.203696\pi$
$977$			36471.0i			1.19428i	−0.802138	+	0.597139i	$0.796304\pi$
$978$	22874.6	+	21775.0i	0.747902	+	0.711951i
$979$	−2310.52			−0.0754286
$980$	−9860.61	+	6416.22i	−0.321414	+	0.209142i
$981$	46057.2	+	26838.5i	1.49897	+	0.873483i
$982$	−9825.04	−	33113.9i	−0.319277	−	1.07608i
$983$	−3602.00			−0.116873			−0.0584363	−	0.998291i	$-0.518611\pi$
$983$	−3602.00			−0.116873			−0.0584363	+	0.998291i	$0.518611\pi$
$984$	−7605.20	+	40884.5i	−0.246387	+	1.32454i
$985$	19474.4			0.629956
$986$	1164.71	+	3925.48i	0.0376185	+	0.126788i
$987$	−3803.56	+	2185.81i	−0.122663	+	0.0704914i
$988$	−24645.2	−	37875.3i	−0.793591	−	1.21961i
$989$	−5527.33			−0.177714
$990$	2831.47	+	690.467i	0.0908989	+	0.0221661i
$991$			44020.0i			1.41104i	0.708690	+	0.705521i	$0.249287\pi$
$991$			44020.0i			1.41104i	−0.708690	+	0.705521i	$0.750713\pi$
$992$	−17280.2	−	2235.30i	−0.553071	−	0.0715433i
$993$	7184.18	+	12501.3i	0.229590	+	0.399514i
$994$	−620.486	−	2091.26i	−0.0197994	−	0.0667310i
$995$		−	6385.08i		−	0.203438i
$996$	−23947.8	+	46871.9i	−0.761861	+	1.49116i
$997$		−	45230.1i		−	1.43676i	−0.695650	−	0.718381i	$-0.744883\pi$
$997$		−	45230.1i		−	1.43676i	0.695650	−	0.718381i	$-0.255117\pi$
$998$	20689.9	−	6138.79i	0.656240	−	0.194709i
$999$	147.260	−	24428.3i	0.00466377	−	0.773650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.b.11.4	yes	24
3.2	odd	2		120.4.b.a.11.21	✓	24
4.3	odd	2		480.4.b.a.431.9		24
8.3	odd	2		120.4.b.a.11.22	yes	24
8.5	even	2		480.4.b.b.431.9		24
12.11	even	2		480.4.b.b.431.10		24
24.5	odd	2		480.4.b.a.431.10		24
24.11	even	2	inner	120.4.b.b.11.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.21	✓	24	3.2	odd	2
120.4.b.a.11.22	yes	24	8.3	odd	2
120.4.b.b.11.3	yes	24	24.11	even	2	inner
120.4.b.b.11.4	yes	24	1.1	even	1	trivial
480.4.b.a.431.9		24	4.3	odd	2
480.4.b.a.431.10		24	24.5	odd	2
480.4.b.b.431.9		24	8.5	even	2
480.4.b.b.431.10		24	12.11	even	2

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.71159 + 0.804541i) q^{2} +(2.58903 + 4.50521i) q^{3} +(6.70543 - 4.36317i) q^{4} -5.00000 q^{5} +(-10.6450 - 10.1333i) q^{6} +6.99225i q^{7} +(-14.6720 + 17.2259i) q^{8} +(-13.5939 + 23.3282i) q^{9} +O(q^{10})\)	\(q+(-2.71159 + 0.804541i) q^{2} +(2.58903 + 4.50521i) q^{3} +(6.70543 - 4.36317i) q^{4} -5.00000 q^{5} +(-10.6450 - 10.1333i) q^{6} +6.99225i q^{7} +(-14.6720 + 17.2259i) q^{8} +(-13.5939 + 23.3282i) q^{9} +(13.5579 - 4.02271i) q^{10} -7.63266i q^{11} +(37.0175 + 18.9130i) q^{12} +45.0969i q^{13} +(-5.62555 - 18.9601i) q^{14} +(-12.9451 - 22.5261i) q^{15} +(25.9255 - 58.5138i) q^{16} +7.59888i q^{17} +(18.0924 - 74.1934i) q^{18} -125.252 q^{19} +(-33.5271 + 21.8158i) q^{20} +(-31.5016 + 18.1031i) q^{21} +(6.14079 + 20.6966i) q^{22} -57.3601 q^{23} +(-115.593 - 21.5021i) q^{24} +25.0000 q^{25} +(-36.2823 - 122.284i) q^{26} +(-140.294 - 0.845728i) q^{27} +(30.5084 + 46.8860i) q^{28} -190.511 q^{29} +(53.2250 + 50.6665i) q^{30} +96.2558i q^{31} +(-23.2225 + 179.524i) q^{32} +(34.3867 - 19.7612i) q^{33} +(-6.11361 - 20.6050i) q^{34} -34.9612i q^{35} +(10.6324 + 215.738i) q^{36} +174.122i q^{37} +(339.631 - 100.770i) q^{38} +(-203.171 + 116.757i) q^{39} +(73.3601 - 86.1296i) q^{40} -353.695i q^{41} +(70.8546 - 74.4325i) q^{42} +96.3620 q^{43} +(-33.3026 - 51.1802i) q^{44} +(67.9693 - 116.641i) q^{45} +(155.537 - 46.1486i) q^{46} +120.742 q^{47} +(330.739 - 34.6941i) q^{48} +294.108 q^{49} +(-67.7897 + 20.1135i) q^{50} +(-34.2345 + 19.6737i) q^{51} +(196.765 + 302.394i) q^{52} +677.042 q^{53} +(381.099 - 110.579i) q^{54} +38.1633i q^{55} +(-120.448 - 102.590i) q^{56} +(-324.280 - 564.285i) q^{57} +(516.586 - 153.274i) q^{58} +767.070i q^{59} +(-185.088 - 94.5650i) q^{60} +605.927i q^{61} +(-77.4417 - 261.006i) q^{62} +(-163.117 - 95.0517i) q^{63} +(-81.4641 - 505.478i) q^{64} -225.484i q^{65} +(-77.3440 + 81.2497i) q^{66} -464.782 q^{67} +(33.1552 + 50.9537i) q^{68} +(-148.507 - 258.419i) q^{69} +(28.1278 + 94.8005i) q^{70} +110.298 q^{71} +(-202.401 - 576.439i) q^{72} +716.562 q^{73} +(-140.089 - 472.148i) q^{74} +(64.7257 + 112.630i) q^{75} +(-839.866 + 546.494i) q^{76} +53.3695 q^{77} +(456.980 - 480.057i) q^{78} +646.587i q^{79} +(-129.628 + 292.569i) q^{80} +(-359.414 - 634.242i) q^{81} +(284.562 + 959.075i) q^{82} +1266.21i q^{83} +(-132.244 + 258.836i) q^{84} -37.9944i q^{85} +(-261.294 + 77.5272i) q^{86} +(-493.237 - 858.291i) q^{87} +(131.480 + 111.986i) q^{88} -302.715i q^{89} +(-90.4622 + 370.967i) q^{90} -315.329 q^{91} +(-384.624 + 250.272i) q^{92} +(-433.653 + 249.209i) q^{93} +(-327.402 + 97.1418i) q^{94} +626.258 q^{95} +(-868.915 + 360.169i) q^{96} +160.973 q^{97} +(-797.501 + 236.622i) q^{98} +(178.057 + 103.757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Introduction

L-functions

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