LMFDB - Embedded newform 75.4.g.b.46.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,4,Mod(16,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("75.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	75.g (of order $5$, degree $4$, 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:	$4.42514325043$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.5
Character	$\chi$	$=$	75.46
Dual form			75.4.g.b.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.536885 - 1.65236i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(4.03008 + 2.92802i) q^{4} +(8.44668 + 7.32487i) q^{5} +(-4.21675 + 3.06365i) q^{6} +7.66213 q^{7} +(18.2465 - 13.2569i) q^{8} +(2.78115 + 8.55951i) q^{9} +(16.6382 - 10.0244i) q^{10} +(6.32569 - 19.4685i) q^{11} +(-4.61806 - 14.2129i) q^{12} +(-4.57589 - 14.0831i) q^{13} +(4.11368 - 12.6606i) q^{14} +(-7.58417 - 32.6723i) q^{15} +(0.205937 + 0.633807i) q^{16} +(88.1826 - 64.0684i) q^{17} +15.6366 q^{18} +(-79.1097 + 57.4766i) q^{19} +(12.5934 + 54.2518i) q^{20} +(-18.5964 - 13.5111i) q^{21} +(-28.7728 - 20.9047i) q^{22} +(-24.8979 + 76.6279i) q^{23} -67.6618 q^{24} +(17.6927 + 123.742i) q^{25} -25.7272 q^{26} +(8.34346 - 25.6785i) q^{27} +(30.8790 + 22.4349i) q^{28} +(-47.7769 - 34.7119i) q^{29} +(-58.0584 - 5.00949i) q^{30} +(-142.644 + 103.637i) q^{31} +181.589 q^{32} +(-49.6826 + 36.0966i) q^{33} +(-58.5204 - 180.107i) q^{34} +(64.7195 + 56.1241i) q^{35} +(-13.8542 + 42.6388i) q^{36} +(-71.2396 - 219.253i) q^{37} +(52.4993 + 161.576i) q^{38} +(-13.7277 + 42.2494i) q^{39} +(251.227 + 21.6768i) q^{40} +(55.4575 + 170.681i) q^{41} +(-32.3093 + 23.4741i) q^{42} -407.459 q^{43} +(82.4972 - 59.9377i) q^{44} +(-39.2058 + 92.6710i) q^{45} +(113.250 + 82.2808i) q^{46} +(-386.035 - 280.471i) q^{47} +(0.617810 - 1.90142i) q^{48} -284.292 q^{49} +(213.965 + 37.2003i) q^{50} -326.999 q^{51} +(22.7945 - 70.1544i) q^{52} +(417.069 + 303.018i) q^{53} +(-37.9508 - 27.5729i) q^{54} +(196.035 - 118.109i) q^{55} +(139.807 - 101.576i) q^{56} +293.355 q^{57} +(-83.0075 + 60.3085i) q^{58} +(-176.586 - 543.476i) q^{59} +(65.1005 - 153.879i) q^{60} +(-16.1665 + 49.7554i) q^{61} +(94.6624 + 291.341i) q^{62} +(21.3095 + 65.5840i) q^{63} +(95.8452 - 294.981i) q^{64} +(64.5060 - 152.473i) q^{65} +(32.9707 + 101.473i) q^{66} +(446.427 - 324.348i) q^{67} +542.976 q^{68} +(195.551 - 142.076i) q^{69} +(127.484 - 76.8079i) q^{70} +(-298.250 - 216.692i) q^{71} +(164.219 + 119.312i) q^{72} +(-125.605 + 386.571i) q^{73} -400.533 q^{74} +(175.259 - 331.525i) q^{75} -487.111 q^{76} +(48.4683 - 149.170i) q^{77} +(62.4412 + 45.3662i) q^{78} +(529.704 + 384.853i) q^{79} +(-2.90308 + 6.86202i) q^{80} +(-65.5304 + 47.6106i) q^{81} +311.801 q^{82} +(-341.288 + 247.960i) q^{83} +(-35.3841 - 108.901i) q^{84} +(1214.14 + 104.761i) q^{85} +(-218.759 + 673.271i) q^{86} +(54.7475 + 168.495i) q^{87} +(-142.669 - 439.091i) q^{88} +(131.375 - 404.330i) q^{89} +(132.077 + 114.536i) q^{90} +(-35.0610 - 107.907i) q^{91} +(-324.709 + 235.915i) q^{92} +528.953 q^{93} +(-670.697 + 487.290i) q^{94} +(-1089.22 - 93.9821i) q^{95} +(-440.727 - 320.207i) q^{96} +(-477.859 - 347.185i) q^{97} +(-152.632 + 469.753i) q^{98} +184.233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 21 q^{3} - 30 q^{4} - 15 q^{5} - 54 q^{7} - 63 q^{8} - 63 q^{9} + 165 q^{10} + 19 q^{11} - 60 q^{12} + 4 q^{13} - 24 q^{14} + 45 q^{15} - 66 q^{16} + 208 q^{17} + 42 q^{19} + 295 q^{20} + 3 q^{21}+ \cdots - 594 q^{99}+O(q^{100}) $ 28 * q - 21 * q^3 - 30 * q^4 - 15 * q^5 - 54 * q^7 - 63 * q^8 - 63 * q^9 + 165 * q^10 + 19 * q^11 - 60 * q^12 + 4 * q^13 - 24 * q^14 + 45 * q^15 - 66 * q^16 + 208 * q^17 + 42 * q^19 + 295 * q^20 + 3 * q^21 - 89 * q^22 + 32 * q^23 + 126 * q^24 + 95 * q^25 + 206 * q^26 - 189 * q^27 - 482 * q^28 - 716 * q^29 - 645 * q^30 + 637 * q^31 - 844 * q^32 + 42 * q^33 - 90 * q^34 + 430 * q^35 - 180 * q^36 + 216 * q^37 + 2314 * q^38 + 12 * q^39 - 500 * q^40 - 38 * q^41 + 933 * q^42 - 1392 * q^43 + 603 * q^44 + 270 * q^45 + 1622 * q^46 - 536 * q^47 - 198 * q^48 + 162 * q^49 - 2265 * q^50 - 876 * q^51 - 1922 * q^52 + 1672 * q^53 - 1000 * q^55 + 3000 * q^56 - 1104 * q^57 - 827 * q^58 + 973 * q^59 + 1365 * q^60 - 2712 * q^61 + 1057 * q^62 + 234 * q^63 + 4439 * q^64 - 4360 * q^65 + 1098 * q^66 + 2768 * q^67 - 1370 * q^68 + 396 * q^69 + 3230 * q^70 - 1074 * q^71 - 567 * q^72 - 1018 * q^73 - 1414 * q^74 + 765 * q^75 - 11408 * q^76 + 1607 * q^77 + 168 * q^78 - 1820 * q^79 - 1290 * q^80 - 567 * q^81 + 1772 * q^82 + 4045 * q^83 + 774 * q^84 + 1850 * q^85 - 3986 * q^86 + 1392 * q^87 + 2407 * q^88 + 4542 * q^89 - 180 * q^90 + 4412 * q^91 - 1089 * q^92 - 5334 * q^93 + 5137 * q^94 - 720 * q^95 + 1623 * q^96 - 5977 * q^97 - 10689 * q^98 - 594 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.536885	−	1.65236i	0.189818	−	0.584199i	−0.810180	−	0.586181i	$-0.800631\pi$
$2$	0.536885	−	1.65236i	0.189818	−	0.584199i	0.999998	+	0.00198195i	$0.000630875\pi$
$3$	−2.42705	−	1.76336i	−0.467086	−	0.339358i
$3$	−2.42705	−	1.76336i	−0.467086	−	0.339358i
$4$	4.03008	+	2.92802i	0.503760	+	0.366003i
$5$	8.44668	+	7.32487i	0.755494	+	0.655156i
$5$	8.44668	+	7.32487i	0.755494	+	0.655156i
$6$	−4.21675	+	3.06365i	−0.286914	+	0.208455i
$7$	7.66213			0.413716			0.206858	−	0.978371i	$-0.433676\pi$
$7$	7.66213			0.413716			0.206858	+	0.978371i	$0.433676\pi$
$8$	18.2465	−	13.2569i	0.806390	−	0.585877i
$9$	2.78115	+	8.55951i	0.103006	+	0.317019i
$10$	16.6382	−	10.0244i	0.526147	−	0.316998i
$11$	6.32569	−	19.4685i	0.173388	−	0.533633i	−0.826168	−	0.563424i	$-0.809484\pi$
$11$	6.32569	−	19.4685i	0.173388	−	0.533633i	0.999556	+	0.0297901i	$0.00948390\pi$
$12$	−4.61806	−	14.2129i	−0.111093	−	0.341910i
$13$	−4.57589	−	14.0831i	−0.0976248	−	0.300458i	0.890304	−	0.455367i	$-0.150492\pi$
$13$	−4.57589	−	14.0831i	−0.0976248	−	0.300458i	−0.987929	+	0.154908i	$0.950492\pi$
$14$	4.11368	−	12.6606i	0.0785306	−	0.241692i
$15$	−7.58417	−	32.6723i	−0.130548	−	0.562397i
$16$	0.205937	+	0.633807i	0.00321776	+	0.00990324i
$17$	88.1826	−	64.0684i	1.25808	−	0.914051i	0.259422	−	0.965764i	$-0.416468\pi$
$17$	88.1826	−	64.0684i	1.25808	−	0.914051i	0.998662	+	0.0517127i	$0.0164680\pi$
$18$	15.6366			0.204754
$19$	−79.1097	+	57.4766i	−0.955211	+	0.694001i	−0.952034	−	0.305994i	$-0.901011\pi$
$19$	−79.1097	+	57.4766i	−0.955211	+	0.694001i	−0.00317732	+	0.999995i	$0.501011\pi$
$20$	12.5934	+	54.2518i	0.140798	+	0.606554i
$21$	−18.5964	−	13.5111i	−0.193241	−	0.140398i
$22$	−28.7728	−	20.9047i	−0.278836	−	0.202586i
$23$	−24.8979	+	76.6279i	−0.225721	+	0.694697i	0.772497	+	0.635018i	$0.219008\pi$
$23$	−24.8979	+	76.6279i	−0.225721	+	0.694697i	−0.998218	+	0.0596783i	$0.980992\pi$
$24$	−67.6618			−0.575475
$25$	17.6927	+	123.742i	0.141541	+	0.989932i
$26$	−25.7272			−0.194058
$27$	8.34346	−	25.6785i	0.0594703	−	0.183031i
$28$	30.8790	+	22.4349i	0.208413	+	0.151421i
$29$	−47.7769	−	34.7119i	−0.305929	−	0.222271i	0.424219	−	0.905560i	$-0.360549\pi$
$29$	−47.7769	−	34.7119i	−0.305929	−	0.222271i	−0.730148	+	0.683289i	$0.760549\pi$
$30$	−58.0584	−	5.00949i	−0.353332	−	0.0304868i
$31$	−142.644	+	103.637i	−0.826439	+	0.600443i	−0.918550	−	0.395306i	$-0.870639\pi$
$31$	−142.644	+	103.637i	−0.826439	+	0.600443i	0.0921106	+	0.995749i	$0.470639\pi$
$32$	181.589			1.00315
$33$	−49.6826	+	36.0966i	−0.262080	+	0.190412i
$34$	−58.5204	−	180.107i	−0.295181	−	0.908474i
$35$	64.7195	+	56.1241i	0.312560	+	0.271048i
$36$	−13.8542	+	42.6388i	−0.0641397	+	0.197402i
$37$	−71.2396	−	219.253i	−0.316533	−	0.974189i	−0.975119	−	0.221683i	$-0.928845\pi$
$37$	−71.2396	−	219.253i	−0.316533	−	0.974189i	0.658586	−	0.752506i	$-0.271155\pi$
$38$	52.4993	+	161.576i	0.224119	+	0.689767i
$39$	−13.7277	+	42.2494i	−0.0563637	+	0.173470i
$40$	251.227	+	21.6768i	0.993063	+	0.0856852i
$41$	55.4575	+	170.681i	0.211244	+	0.650143i	0.999399	+	0.0346656i	$0.0110366\pi$
$41$	55.4575	+	170.681i	0.211244	+	0.650143i	−0.788155	+	0.615477i	$0.788963\pi$
$42$	−32.3093	+	23.4741i	−0.118701	+	0.0862412i
$43$	−407.459			−1.44505			−0.722523	−	0.691347i	$-0.757018\pi$
$43$	−407.459			−1.44505			−0.722523	+	0.691347i	$0.757018\pi$
$44$	82.4972	−	59.9377i	0.282657	−	0.205362i
$45$	−39.2058	+	92.6710i	−0.129877	+	0.306990i
$46$	113.250	+	82.2808i	0.362995	+	0.263731i
$47$	−386.035	−	280.471i	−1.19806	−	0.870445i	−0.203972	−	0.978977i	$-0.565385\pi$
$47$	−386.035	−	280.471i	−1.19806	−	0.870445i	−0.994093	+	0.108532i	$0.965385\pi$
$48$	0.617810	−	1.90142i	0.00185777	−	0.00571764i
$49$	−284.292			−0.828839
$50$	213.965	+	37.2003i	0.605184	+	0.105218i
$51$	−326.999			−0.897824
$52$	22.7945	−	70.1544i	0.0607891	−	0.187090i
$53$	417.069	+	303.018i	1.08092	+	0.785335i	0.977843	−	0.209339i	$-0.0671311\pi$
$53$	417.069	+	303.018i	1.08092	+	0.785335i	0.103077	+	0.994673i	$0.467131\pi$
$54$	−37.9508	−	27.5729i	−0.0956379	−	0.0694850i
$55$	196.035	−	118.109i	0.480607	−	0.289560i
$56$	139.807	−	101.576i	0.333616	−	0.242386i
$57$	293.355			0.681681
$58$	−83.0075	+	60.3085i	−0.187921	+	0.136533i
$59$	−176.586	−	543.476i	−0.389653	−	1.19923i	−0.933048	−	0.359752i	$-0.882861\pi$
$59$	−176.586	−	543.476i	−0.389653	−	1.19923i	0.543395	−	0.839477i	$-0.317139\pi$
$60$	65.1005	−	153.879i	0.140074	−	0.331094i
$61$	−16.1665	+	49.7554i	−0.0339329	+	0.104435i	−0.966588	−	0.256333i	$-0.917485\pi$
$61$	−16.1665	+	49.7554i	−0.0339329	+	0.104435i	0.932655	+	0.360768i	$0.117485\pi$
$62$	94.6624	+	291.341i	0.193905	+	0.596779i
$63$	21.3095	+	65.5840i	0.0426151	+	0.131156i
$64$	95.8452	−	294.981i	0.187198	−	0.576135i
$65$	64.5060	−	152.473i	0.123092	−	0.290954i
$66$	32.9707	+	101.473i	0.0614912	+	0.189250i
$67$	446.427	−	324.348i	0.814026	−	0.591424i	−0.100969	−	0.994890i	$-0.532194\pi$
$67$	446.427	−	324.348i	0.814026	−	0.591424i	0.914995	+	0.403465i	$0.132194\pi$
$68$	542.976			0.968317
$69$	195.551	−	142.076i	0.341182	−	0.247883i
$70$	127.484	−	76.8079i	0.217676	−	0.131147i
$71$	−298.250	−	216.692i	−0.498532	−	0.362205i	0.309924	−	0.950761i	$-0.399696\pi$
$71$	−298.250	−	216.692i	−0.498532	−	0.362205i	−0.808456	+	0.588556i	$0.799696\pi$
$72$	164.219	+	119.312i	0.268797	+	0.195292i
$73$	−125.605	+	386.571i	−0.201382	+	0.619791i	0.798460	+	0.602048i	$0.205648\pi$
$73$	−125.605	+	386.571i	−0.201382	+	0.619791i	−0.999843	+	0.0177436i	$0.994352\pi$
$74$	−400.533			−0.629203
$75$	175.259	−	331.525i	0.269829	−	0.510417i
$76$	−487.111			−0.735203
$77$	48.4683	−	149.170i	0.0717334	−	0.220773i
$78$	62.4412	+	45.3662i	0.0906419	+	0.0658552i
$79$	529.704	+	384.853i	0.754384	+	0.548092i	0.897183	−	0.441659i	$-0.145610\pi$
$79$	529.704	+	384.853i	0.754384	+	0.548092i	−0.142798	+	0.989752i	$0.545610\pi$
$80$	−2.90308	+	6.86202i	−0.00405717	+	0.00958997i
$81$	−65.5304	+	47.6106i	−0.0898908	+	0.0653095i
$82$	311.801			0.419910
$83$	−341.288	+	247.960i	−0.451340	+	0.327918i	−0.790125	−	0.612946i	$-0.789984\pi$
$83$	−341.288	+	247.960i	−0.451340	+	0.327918i	0.338784	+	0.940864i	$0.389984\pi$
$84$	−35.3841	−	108.901i	−0.0459610	−	0.141453i
$85$	1214.14	+	104.761i	1.54932	+	0.133681i
$86$	−218.759	+	673.271i	−0.274295	+	0.844194i
$87$	54.7475	+	168.495i	0.0674660	+	0.207639i
$88$	−142.669	−	439.091i	−0.172825	−	0.531901i
$89$	131.375	−	404.330i	0.156469	−	0.481561i	−0.841838	−	0.539730i	$-0.818526\pi$
$89$	131.375	−	404.330i	0.156469	−	0.481561i	0.998307	+	0.0581693i	$0.0185263\pi$
$90$	132.077	+	114.536i	0.154691	+	0.134146i
$91$	−35.0610	−	107.907i	−0.0403889	−	0.124304i
$92$	−324.709	+	235.915i	−0.367970	+	0.267346i
$93$	528.953			0.589783
$94$	−670.697	+	487.290i	−0.735927	+	0.534682i
$95$	−1089.22	−	93.9821i	−1.17633	−	0.101499i
$96$	−440.727	−	320.207i	−0.468557	−	0.340427i
$97$	−477.859	−	347.185i	−0.500198	−	0.363415i	0.308895	−	0.951096i	$-0.400041\pi$
$97$	−477.859	−	347.185i	−0.500198	−	0.363415i	−0.809093	+	0.587681i	$0.800041\pi$
$98$	−152.632	+	469.753i	−0.157328	+	0.484207i
$99$	184.233			0.187032
$100$	−291.015	+	550.492i	−0.291015	+	0.550492i
$101$	−1533.55			−1.51083			−0.755417	−	0.655244i	$-0.772566\pi$
$101$	−1533.55			−1.51083			−0.755417	+	0.655244i	$0.772566\pi$
$102$	−175.561	+	540.321i	−0.170423	+	0.524508i
$103$	581.600	+	422.557i	0.556376	+	0.404231i	0.830131	−	0.557569i	$-0.188266\pi$
$103$	581.600	+	422.557i	0.556376	+	0.404231i	−0.273755	+	0.961800i	$0.588266\pi$
$104$	−270.192	−	196.306i	−0.254755	−	0.185090i
$105$	−58.1108	−	250.339i	−0.0540099	−	0.232673i
$106$	724.614	−	526.463i	0.663969	−	0.482402i
$107$	−944.844			−0.853659			−0.426830	−	0.904332i	$-0.640370\pi$
$107$	−944.844			−0.853659			−0.426830	+	0.904332i	$0.640370\pi$
$108$	108.812	−	79.0566i	0.0969486	−	0.0704373i
$109$	454.976	+	1400.27i	0.399806	+	1.23048i	0.925155	+	0.379589i	$0.123934\pi$
$109$	454.976	+	1400.27i	0.399806	+	1.23048i	−0.525350	+	0.850886i	$0.676066\pi$
$110$	−89.9107	−	387.332i	−0.0779332	−	0.335734i
$111$	−213.719	+	657.759i	−0.182750	+	0.562448i
$112$	1.57791	+	4.85631i	0.00133124	+	0.00409713i
$113$	−253.473	−	780.108i	−0.211015	−	0.649437i	−0.999413	−	0.0342714i	$-0.989089\pi$
$113$	−253.473	−	780.108i	−0.211015	−	0.649437i	0.788398	−	0.615166i	$-0.210911\pi$
$114$	157.498	−	484.729i	0.129395	−	0.398237i
$115$	−771.594	+	464.877i	−0.625665	+	0.376957i
$116$	−90.9072	−	279.784i	−0.0727631	−	0.223942i
$117$	107.818	−	78.3347i	0.0851950	−	0.0618978i
$118$	−992.826			−0.774551
$119$	675.666	−	490.900i	0.520489	−	0.378158i
$120$	−571.517	−	495.614i	−0.434768	−	0.377026i
$121$	737.794	+	536.039i	0.554316	+	0.402734i
$122$	73.5344	+	53.4259i	0.0545696	+	0.0396471i
$123$	166.373	−	512.042i	0.121962	−	0.375360i
$124$	−878.317			−0.636090
$125$	−756.946	+	1174.80i	−0.541627	+	0.840619i
$126$	119.809			0.0847101
$127$	514.161	−	1582.42i	0.359247	−	1.10565i	−0.594259	−	0.804274i	$-0.702554\pi$
$127$	514.161	−	1582.42i	0.359247	−	1.10565i	0.953506	−	0.301375i	$-0.0974455\pi$
$128$	739.313	+	537.142i	0.510521	+	0.370915i
$129$	988.924	+	718.496i	0.674961	+	0.490388i
$130$	−217.309	−	188.448i	−0.146610	−	0.127138i
$131$	1845.96	−	1341.17i	1.23116	−	0.894493i	0.234187	−	0.972192i	$-0.424757\pi$
$131$	1845.96	−	1341.17i	1.23116	−	0.894493i	0.996977	+	0.0776985i	$0.0247572\pi$
$132$	−305.916			−0.201717
$133$	−606.148	+	440.393i	−0.395186	+	0.287119i
$134$	−296.261	−	911.797i	−0.190993	−	0.587816i
$135$	258.566	−	155.783i	0.164843	−	0.0993163i
$136$	759.679	−	2338.05i	0.478985	−	1.47416i
$137$	288.928	+	889.230i	0.180181	+	0.554541i	0.999832	−	0.0183227i	$-0.00583262\pi$
$137$	288.928	+	889.230i	0.180181	+	0.554541i	−0.819651	+	0.572863i	$0.805833\pi$
$138$	−129.773	−	399.400i	−0.0800507	−	0.246371i
$139$	−888.184	+	2733.55i	−0.541977	+	1.66803i	0.186094	+	0.982532i	$0.440417\pi$
$139$	−888.184	+	2733.55i	−0.541977	+	1.66803i	−0.728071	+	0.685502i	$0.759583\pi$
$140$	96.4921	+	415.684i	0.0582505	+	0.250941i
$141$	442.357	+	1361.44i	0.264207	+	0.813146i
$142$	−518.179	+	376.479i	−0.306230	+	0.222489i
$143$	−303.123			−0.177262
$144$	−4.85234	+	3.52543i	−0.00280807	+	0.00204018i
$145$	−149.296	−	643.160i	−0.0855057	−	0.368355i
$146$	571.321	+	415.089i	0.323855	+	0.235295i
$147$	689.991	+	501.308i	0.387139	+	0.281273i
$148$	354.877	−	1092.20i	0.197099	−	0.606609i
$149$	2275.13			1.25091			0.625457	−	0.780259i	$-0.284913\pi$
$149$	2275.13			1.25091			0.625457	+	0.780259i	$0.284913\pi$
$150$	−453.706	−	467.583i	−0.246966	−	0.254520i
$151$	2396.11			1.29134			0.645670	−	0.763617i	$-0.276578\pi$
$151$	2396.11			1.29134			0.645670	+	0.763617i	$0.276578\pi$
$152$	−681.517	+	2097.49i	−0.363673	+	1.11927i
$153$	793.644	+	576.616i	0.419361	+	0.304684i
$154$	−220.461	−	160.174i	−0.115359	−	0.0838131i
$155$	−1963.99	−	169.461i	−1.01775	−	0.0878156i
$156$	−179.031	+	130.073i	−0.0918841	+	0.0667577i
$157$	902.424			0.458734			0.229367	−	0.973340i	$-0.426334\pi$
$157$	902.424			0.458734			0.229367	+	0.973340i	$0.426334\pi$
$158$	920.307	−	668.642i	0.463390	−	0.336673i
$159$	−477.918	−	1470.88i	−0.238373	−	0.733638i
$160$	1533.83	+	1330.12i	0.757873	+	0.657219i
$161$	−190.771	+	587.133i	−0.0933842	+	0.287407i
$162$	43.4877	+	133.841i	0.0210909	+	0.0649110i
$163$	−1244.80	−	3831.10i	−0.598162	−	1.84095i	−0.538313	−	0.842745i	$-0.680938\pi$
$163$	−1244.80	−	3831.10i	−0.598162	−	1.84095i	−0.0598492	−	0.998207i	$-0.519062\pi$
$164$	−276.259	+	850.237i	−0.131538	+	0.404832i
$165$	−684.056	−	59.0229i	−0.322749	−	0.0278480i
$166$	226.488	+	697.059i	0.105897	+	0.325917i
$167$	794.708	−	577.389i	0.368242	−	0.267543i	−0.388240	−	0.921558i	$-0.626917\pi$
$167$	794.708	−	577.389i	0.368242	−	0.267543i	0.756481	+	0.654015i	$0.226917\pi$
$168$	−518.433			−0.238083
$169$	1600.01	−	1162.48i	0.728272	−	0.529121i
$170$	824.958	−	1949.96i	0.372185	−	0.879736i
$171$	−711.987	−	517.289i	−0.318404	−	0.231334i
$172$	−1642.09	−	1193.05i	−0.727955	−	0.528891i
$173$	390.937	−	1203.18i	0.171806	−	0.528764i	−0.827667	−	0.561219i	$-0.810333\pi$
$173$	390.937	−	1203.18i	0.171806	−	0.528764i	0.999473	+	0.0324551i	$0.0103326\pi$
$174$	307.809			0.134109
$175$	135.563	+	948.123i	0.0585579	+	0.409551i
$176$	13.6420			0.00584262
$177$	−529.758	+	1630.43i	−0.224966	+	0.692375i
$178$	−597.567	−	434.158i	−0.251627	−	0.182817i
$179$	1190.56	+	864.991i	0.497131	+	0.361187i	0.807920	−	0.589292i	$-0.200593\pi$
$179$	1190.56	+	864.991i	0.497131	+	0.361187i	−0.310789	+	0.950479i	$0.600593\pi$
$180$	−429.345	+	258.676i	−0.177786	+	0.107114i
$181$	3028.14	−	2200.07i	1.24353	−	0.903481i	0.245706	−	0.969344i	$-0.420980\pi$
$181$	3028.14	−	2200.07i	1.24353	−	0.903481i	0.997829	+	0.0658635i	$0.0209802\pi$
$182$	−197.125			−0.0802850
$183$	126.973	−	92.2515i	0.0512904	−	0.0372646i
$184$	561.546	+	1728.26i	0.224988	+	0.692441i
$185$	1004.26	−	2373.78i	0.399107	−	0.943372i
$186$	283.987	−	874.022i	0.111951	−	0.344551i
$187$	−689.499	−	2122.06i	−0.269632	−	0.829841i
$188$	−734.526	−	2260.64i	−0.284951	−	0.876990i
$189$	63.9286	−	196.752i	0.0246038	−	0.0757228i
$190$	−740.080	+	1749.33i	−0.282584	+	0.667947i
$191$	1221.78	+	3760.25i	0.462853	+	1.42451i	0.861663	+	0.507481i	$0.169423\pi$
$191$	1221.78	+	3760.25i	0.462853	+	1.42451i	−0.398811	+	0.917033i	$0.630577\pi$
$192$	−752.778	+	546.925i	−0.282953	+	0.205578i
$193$	−4739.26			−1.76756			−0.883780	−	0.467903i	$-0.845010\pi$
$193$	−4739.26			−1.76756			−0.883780	+	0.467903i	$0.845010\pi$
$194$	−830.231	+	603.198i	−0.307253	+	0.223232i
$195$	−425.424	+	256.314i	−0.156232	+	0.0941282i
$196$	−1145.72	−	832.413i	−0.417536	−	0.303357i
$197$	1547.32	+	1124.19i	0.559603	+	0.406576i	0.831314	−	0.555803i	$-0.187589\pi$
$197$	1547.32	+	1124.19i	0.559603	+	0.406576i	−0.271710	+	0.962379i	$0.587589\pi$
$198$	98.9122	−	304.420i	0.0355019	−	0.109264i
$199$	−3291.81			−1.17262			−0.586308	−	0.810089i	$-0.699419\pi$
$199$	−3291.81			−1.17262			−0.586308	+	0.810089i	$0.699419\pi$
$200$	1963.26	+	2023.30i	0.694116	+	0.715346i
$201$	−1655.44			−0.580925
$202$	−823.343	+	2533.99i	−0.286783	+	0.882628i
$203$	−366.073	−	265.967i	−0.126568	−	0.0919569i
$204$	−1317.83	−	957.461i	−0.452288	−	0.328606i
$205$	−781.782	+	1847.90i	−0.266351	+	0.629577i
$206$	1010.47	−	734.150i	0.341761	−	0.248304i
$207$	−725.142			−0.243482
$208$	7.98365	−	5.80046i	0.00266138	−	0.00193360i
$209$	618.558	+	1903.72i	0.204720	+	0.630064i
$210$	−444.851	−	38.3834i	−0.146179	−	0.0126129i
$211$	220.557	−	678.806i	0.0719612	−	0.221474i	−0.908607	−	0.417652i	$-0.862853\pi$
$211$	220.557	−	678.806i	0.0719612	−	0.221474i	0.980568	+	0.196178i	$0.0628531\pi$
$212$	793.575	+	2442.37i	0.257089	+	0.791240i
$213$	341.764	+	1051.84i	0.109940	+	0.338362i
$214$	−507.273	+	1561.23i	−0.162040	+	0.498707i
$215$	−3441.68	−	2984.58i	−1.09172	−	0.946730i
$216$	−188.178	−	579.152i	−0.0592772	−	0.182437i
$217$	−1092.96	+	794.079i	−0.341911	+	0.248413i
$218$	2558.03			0.794732
$219$	986.512	−	716.743i	0.304394	−	0.221155i
$220$	1135.86	+	98.0065i	0.348090	+	0.0300345i
$221$	−1305.80	−	948.717i	−0.397454	−	0.288768i
$222$	972.115	+	706.283i	0.293892	+	0.213525i
$223$	−1401.89	+	4314.59i	−0.420977	+	1.29563i	0.485818	+	0.874060i	$0.338522\pi$
$223$	−1401.89	+	4314.59i	−0.420977	+	1.29563i	−0.906794	+	0.421573i	$0.861478\pi$
$224$	1391.36			0.415019
$225$	−1009.96	+	495.585i	−0.299248	+	0.146840i
$226$	−1425.11			−0.419455
$227$	15.3118	−	47.1250i	0.00447701	−	0.0137788i	−0.948793	−	0.315898i	$-0.897694\pi$
$227$	15.3118	−	47.1250i	0.00447701	−	0.0137788i	0.953270	+	0.302119i	$0.0976942\pi$
$228$	1182.24	+	858.950i	0.343403	+	0.249497i
$229$	1905.02	+	1384.08i	0.549726	+	0.399399i	0.827684	−	0.561194i	$-0.189658\pi$
$229$	1905.02	+	1384.08i	0.549726	+	0.399399i	−0.277959	+	0.960593i	$0.589658\pi$
$230$	353.889	+	1524.54i	0.101455	+	0.437066i
$231$	−380.675	+	276.576i	−0.108427	+	0.0787766i
$232$	−1331.93			−0.376921
$233$	2345.37	−	1704.01i	0.659443	−	0.479113i	−0.207032	−	0.978334i	$-0.566380\pi$
$233$	2345.37	−	1704.01i	0.659443	−	0.479113i	0.866475	+	0.499221i	$0.166380\pi$
$234$	−71.5512	−	220.212i	−0.0199891	−	0.0615201i
$235$	−1206.30	−	5196.71i	−0.334853	−	1.44253i
$236$	879.654	−	2707.30i	0.242630	−	0.746738i
$237$	−606.987	−	1868.11i	−0.166363	−	0.512013i
$238$	−448.390	−	1380.00i	−0.122121	−	0.375850i
$239$	−325.770	+	1002.62i	−0.0881685	+	0.271355i	−0.985413	−	0.170179i	$-0.945565\pi$
$239$	−325.770	+	1002.62i	−0.0881685	+	0.271355i	0.897245	+	0.441534i	$0.145565\pi$
$240$	19.1461	−	11.5353i	0.00514948	−	0.00310251i
$241$	2114.42	+	6507.51i	0.565152	+	1.73936i	0.667499	+	0.744610i	$0.267365\pi$
$241$	2114.42	+	6507.51i	0.565152	+	1.73936i	−0.102347	+	0.994749i	$0.532635\pi$
$242$	1281.84	−	931.313i	0.340496	−	0.247385i
$243$	243.000			0.0641500
$244$	−210.837	+	153.182i	−0.0553174	+	0.0401905i
$245$	−2401.32	−	2082.40i	−0.626183	−	0.543019i
$246$	−756.757	−	549.816i	−0.196134	−	0.142500i
$247$	1171.45	+	851.106i	0.301771	+	0.219249i
$248$	−1228.85	+	3782.03i	−0.314647	+	0.968382i
$249$	1265.57			0.322096
$250$	1534.80	+	1881.48i	0.388278	+	0.475982i
$251$	−6021.53			−1.51424			−0.757122	−	0.653273i	$-0.773395\pi$
$251$	−6021.53			−1.51424			−0.757122	+	0.653273i	$0.773395\pi$
$252$	−106.152	+	326.704i	−0.0265356	+	0.0816682i
$253$	1334.33	+	969.449i	0.331576	+	0.240904i
$254$	−2338.69	−	1699.16i	−0.577727	−	0.419743i
$255$	−2762.06	−	2395.23i	−0.678300	−	0.588215i
$256$	3291.89	−	2391.70i	0.803684	−	0.583910i
$257$	−539.470			−0.130939			−0.0654693	−	0.997855i	$-0.520854\pi$
$257$	−539.470			−0.130939			−0.0654693	+	0.997855i	$0.520854\pi$
$258$	1718.15	−	1248.31i	0.414603	−	0.301227i
$259$	−545.847	−	1679.94i	−0.130955	−	0.403037i
$260$	706.410	−	425.604i	0.168499	−	0.101519i
$261$	164.242	−	505.486i	0.0389515	−	0.119880i
$262$	−1225.03	−	3770.26i	−0.288865	−	0.889035i
$263$	−218.707	−	673.110i	−0.0512777	−	0.157817i	0.922139	−	0.386860i	$-0.126440\pi$
$263$	−218.707	−	673.110i	−0.0512777	−	0.157817i	−0.973416	+	0.229043i	$0.926440\pi$
$264$	−428.008	+	1317.27i	−0.0997806	+	0.307093i
$265$	1303.28	+	5614.47i	0.302112	+	1.30149i
$266$	402.256	+	1238.02i	0.0927215	+	0.285367i
$267$	−1031.83	+	749.669i	−0.236506	+	0.171832i
$268$	2748.83			0.626536
$269$	2328.29	−	1691.60i	0.527725	−	0.383415i	−0.291781	−	0.956485i	$-0.594248\pi$
$269$	2328.29	−	1691.60i	0.527725	−	0.383415i	0.819506	+	0.573070i	$0.194248\pi$
$270$	−118.590	−	510.883i	−0.0267303	−	0.115153i
$271$	−2887.60	−	2097.96i	−0.647267	−	0.470267i	0.215072	−	0.976598i	$-0.431001\pi$
$271$	−2887.60	−	2097.96i	−0.647267	−	0.470267i	−0.862339	+	0.506331i	$0.831001\pi$
$272$	58.7671	+	42.6968i	0.0131003	+	0.00951791i
$273$	−105.183	+	323.720i	−0.0233186	+	0.0717671i
$274$	1624.45			0.358163
$275$	2520.98	+	438.302i	0.552803	+	0.0961113i
$276$	1204.09			0.262600
$277$	2149.70	−	6616.10i	0.466292	−	1.43510i	−0.391058	−	0.920366i	$-0.627891\pi$
$277$	2149.70	−	6616.10i	0.466292	−	1.43510i	0.857350	−	0.514734i	$-0.172109\pi$
$278$	4039.97	+	2935.21i	0.871586	+	0.633245i
$279$	−1283.80	−	932.732i	−0.275480	−	0.200148i
$280$	1924.94	+	166.091i	0.410846	+	0.0354493i
$281$	−2693.55	+	1956.98i	−0.571829	+	0.415458i	−0.835769	−	0.549081i	$-0.814978\pi$
$281$	−2693.55	+	1956.98i	−0.571829	+	0.415458i	0.263940	+	0.964539i	$0.414978\pi$
$282$	2487.08			0.525190
$283$	496.720	−	360.889i	0.104336	−	0.0758042i	−0.534394	−	0.845235i	$-0.679460\pi$
$283$	496.720	−	360.889i	0.104336	−	0.0758042i	0.638730	+	0.769431i	$0.279460\pi$
$284$	−567.494	−	1746.57i	−0.118572	−	0.364928i
$285$	2477.87	+	2148.79i	0.515005	+	0.446607i
$286$	−162.742	+	500.869i	−0.0336474	+	0.103556i
$287$	424.923	+	1307.78i	0.0873951	+	0.268974i
$288$	505.028	+	1554.32i	0.103330	+	0.318017i
$289$	2153.21	−	6626.90i	0.438268	−	1.34885i
$290$	−1142.89	−	98.6127i	−0.231423	−	0.0199681i
$291$	547.577	+	1685.27i	0.110308	+	0.339492i
$292$	−1638.09	+	1190.14i	−0.328294	+	0.238519i
$293$	−6494.46			−1.29492			−0.647458	−	0.762101i	$-0.724168\pi$
$293$	−6494.46			−1.29492			−0.647458	+	0.762101i	$0.724168\pi$
$294$	1198.79	−	870.971i	0.237805	−	0.172776i
$295$	2489.32	−	5884.03i	0.491302	−	1.16129i
$296$	−4206.49	−	3056.19i	−0.826003	−	0.600127i
$297$	−447.144	−	324.869i	−0.0873600	−	0.0634707i
$298$	1221.49	−	3759.35i	0.237446	−	0.730782i
$299$	1193.09			0.230763
$300$	1677.02	−	822.910i	0.322743	−	0.158369i
$301$	−3122.00			−0.597838
$302$	1286.43	−	3959.24i	0.245119	−	0.754399i
$303$	3722.01	+	2704.20i	0.705690	+	0.512714i
$304$	−52.7206	−	38.3038i	−0.00994650	−	0.00722656i
$305$	−501.005	+	301.850i	−0.0940572	+	0.0566685i
$306$	1378.87	−	1001.81i	0.257598	−	0.187156i
$307$	−967.468			−0.179858			−0.0899289	−	0.995948i	$-0.528664\pi$
$307$	−967.468			−0.179858			−0.0899289	+	0.995948i	$0.528664\pi$
$308$	632.104	−	459.250i	0.116940	−	0.0849617i
$309$	−666.454	−	2051.14i	−0.122697	−	0.377621i
$310$	−1334.45	+	3154.25i	−0.244489	+	0.577901i
$311$	−472.899	+	1455.43i	−0.0862239	+	0.265370i	−0.984867	−	0.173310i	$-0.944554\pi$
$311$	−472.899	+	1455.43i	−0.0862239	+	0.265370i	0.898643	+	0.438680i	$0.144554\pi$
$312$	309.613	+	952.890i	0.0561807	+	0.172906i
$313$	2467.07	+	7592.86i	0.445518	+	1.37116i	0.881915	+	0.471409i	$0.156254\pi$
$313$	2467.07	+	7592.86i	0.445518	+	1.37116i	−0.436397	+	0.899754i	$0.643746\pi$
$314$	484.498	−	1491.13i	0.0870759	−	0.267992i
$315$	−300.400	+	710.057i	−0.0537320	+	0.127007i
$316$	1007.89	+	3101.97i	0.179425	+	0.552214i
$317$	4272.46	−	3104.12i	0.756988	−	0.549984i	−0.140997	−	0.990010i	$-0.545031\pi$
$317$	4272.46	−	3104.12i	0.756988	−	0.549984i	0.897985	+	0.440026i	$0.145031\pi$
$318$	−2687.02			−0.473838
$319$	−978.011	+	710.567i	−0.171655	+	0.124715i
$320$	2970.27	−	1789.56i	0.518885	−	0.312623i
$321$	2293.19	+	1666.10i	0.398732	+	0.289696i
$322$	867.735	+	630.446i	0.150177	+	0.109110i
$323$	−3293.67	+	10136.9i	−0.567382	+	1.74622i
$324$	−403.497			−0.0691868
$325$	1661.71	−	815.395i	0.283615	−	0.139169i
$326$	−6998.69			−1.18902
$327$	1364.93	−	4200.82i	0.230828	−	0.710415i
$328$	3274.60	+	2379.14i	0.551249	+	0.400505i
$329$	−2957.85	−	2149.00i	−0.495658	−	0.360117i
$330$	−464.787	+	1098.62i	−0.0775323	+	0.183264i
$331$	1684.86	−	1224.12i	0.279783	−	0.203274i	−0.439040	−	0.898468i	$-0.644681\pi$
$331$	1684.86	−	1224.12i	0.279783	−	0.203274i	0.718823	+	0.695194i	$0.244681\pi$
$332$	−2101.45			−0.347386
$333$	1678.57	−	1219.55i	0.276231	−	0.200694i
$334$	−527.389	−	1623.14i	−0.0863996	−	0.265911i
$335$	6146.63	+	530.354i	1.00247	+	0.0864966i
$336$	4.73373	−	14.5689i	0.000768591	−	0.00236548i
$337$	2139.80	+	6585.61i	0.345882	+	1.06451i	0.961110	+	0.276165i	$0.0890637\pi$
$337$	2139.80	+	6585.61i	0.345882	+	1.06451i	−0.615229	+	0.788349i	$0.710936\pi$
$338$	−1061.81	−	3267.92i	−0.170873	−	0.525892i
$339$	−760.418	+	2340.33i	−0.121830	+	0.374953i
$340$	4586.35	+	3977.23i	0.731557	+	0.634399i
$341$	1115.33	+	3432.64i	0.177122	+	0.545125i
$342$	−1237.00	+	898.737i	−0.195584	+	0.142100i
$343$	−4806.39			−0.756620
$344$	−7434.71	+	5401.64i	−1.16527	+	0.846618i
$345$	2692.44	+	232.314i	0.420163	+	0.0362532i
$346$	−1778.20	−	1291.94i	−0.276291	−	0.200737i
$347$	1746.81	+	1269.13i	0.270242	+	0.196342i	0.714650	−	0.699482i	$-0.246586\pi$
$347$	1746.81	+	1269.13i	0.270242	+	0.196342i	−0.444408	+	0.895824i	$0.646586\pi$
$348$	−272.722	+	839.351i	−0.0420098	+	0.129293i
$349$	−11809.8			−1.81136			−0.905679	−	0.423963i	$-0.860639\pi$
$349$	−11809.8			−1.81136			−0.905679	+	0.423963i	$0.860639\pi$
$350$	1639.43	+	285.034i	0.250374	+	0.0435306i
$351$	−399.813			−0.0607989
$352$	1148.68	−	3535.27i	0.173934	−	0.535314i
$353$	−6688.84	−	4859.73i	−1.00853	−	0.732740i	−0.0446296	−	0.999004i	$-0.514211\pi$
$353$	−6688.84	−	4859.73i	−1.00853	−	0.732740i	−0.963900	+	0.266264i	$0.914211\pi$
$354$	2409.64	+	1750.71i	0.361782	+	0.262850i
$355$	−931.987	−	4014.97i	−0.139337	−	0.600260i
$356$	1713.34	−	1244.81i	0.255075	−	0.185323i
$357$	−2505.51			−0.371444
$358$	2068.47	−	1502.83i	0.305369	−	0.221864i
$359$	1438.87	+	4428.39i	0.211534	+	0.651035i	0.999382	+	0.0351646i	$0.0111956\pi$
$359$	1438.87	+	4428.39i	0.211534	+	0.651035i	−0.787847	+	0.615871i	$0.788804\pi$
$360$	513.158	+	2210.67i	0.0751273	+	0.323646i
$361$	835.241	−	2570.61i	0.121773	−	0.374779i
$362$	−2009.55	−	6184.77i	−0.291768	−	0.897968i
$363$	−845.437	−	2601.99i	−0.122242	−	0.376223i
$364$	174.655	−	537.532i	0.0251494	−	0.0774020i
$365$	−3892.53	+	2345.21i	−0.558203	+	0.336311i
$366$	−84.2629	−	259.335i	−0.0120341	−	0.0370373i
$367$	420.366	−	305.413i	0.0597899	−	0.0434399i	−0.557489	−	0.830184i	$-0.688235\pi$
$367$	420.366	−	305.413i	0.0597899	−	0.0434399i	0.617279	+	0.786744i	$0.288235\pi$
$368$	−53.6947			−0.00760606
$369$	−1306.71	+	949.378i	−0.184348	+	0.133937i
$370$	−3383.17	−	2933.85i	−0.475359	−	0.412226i
$371$	3195.63	+	2321.76i	0.447194	+	0.324905i
$372$	2131.72	+	1548.79i	0.297109	+	0.215862i
$373$	−1298.57	+	3996.59i	−0.180261	+	0.554787i	−0.999835	−	0.0181874i	$-0.994210\pi$
$373$	−1298.57	+	3996.59i	−0.180261	+	0.554787i	0.819573	+	0.572974i	$0.194210\pi$
$374$	−3876.59			−0.535973
$375$	3908.74	−	1516.54i	0.538257	−	0.208836i
$376$	−10762.0			−1.47608
$377$	−270.231	+	831.686i	−0.0369167	+	0.113618i
$378$	−290.784	−	211.267i	−0.0395669	−	0.0287471i
$379$	−2309.87	−	1678.22i	−0.313061	−	0.227452i	0.420148	−	0.907456i	$-0.361978\pi$
$379$	−2309.87	−	1678.22i	−0.313061	−	0.227452i	−0.733209	+	0.680004i	$0.761978\pi$
$380$	−4114.47	−	3568.02i	−0.555441	−	0.481673i
$381$	−4038.27	+	2933.97i	−0.543010	+	0.394520i
$382$	6869.26			0.920057
$383$	4657.39	−	3383.79i	0.621362	−	0.451446i	−0.232035	−	0.972707i	$-0.574538\pi$
$383$	4657.39	−	3383.79i	0.621362	−	0.451446i	0.853397	+	0.521261i	$0.174538\pi$
$384$	−847.177	−	2607.34i	−0.112584	−	0.346498i
$385$	1502.05	−	904.967i	0.198835	−	0.119796i
$386$	−2544.44	+	7830.97i	−0.335514	+	1.03261i
$387$	−1133.21	−	3487.65i	−0.148848	−	0.458107i
$388$	−909.243	−	2798.36i	−0.118969	−	0.366148i
$389$	3397.36	−	10456.0i	0.442809	−	1.36283i	−0.442059	−	0.896986i	$-0.645752\pi$
$389$	3397.36	−	10456.0i	0.442809	−	1.36283i	0.884868	−	0.465841i	$-0.154248\pi$
$390$	195.119	+	840.566i	0.0253340	+	0.109138i
$391$	2713.87	+	8352.42i	0.351013	+	1.08031i
$392$	−5187.34	+	3768.82i	−0.668368	+	0.485597i
$393$	−6845.21			−0.878613
$394$	2688.31	−	1953.17i	0.343744	−	0.249744i
$395$	1655.25	+	7130.74i	0.210847	+	0.908320i
$396$	742.475	+	539.439i	0.0942191	+	0.0684542i
$397$	132.471	+	96.2459i	0.0167469	+	0.0121674i	0.596127	−	0.802890i	$-0.296705\pi$
$397$	132.471	+	96.2459i	0.0167469	+	0.0121674i	−0.579380	+	0.815057i	$0.696705\pi$
$398$	−1767.33	+	5439.27i	−0.222583	+	0.685040i
$399$	2247.72			0.282022
$400$	−74.7848	+	36.6966i	−0.00934809	+	0.00458708i
$401$	8096.74			1.00831			0.504154	−	0.863614i	$-0.331804\pi$
$401$	8096.74			1.00831			0.504154	+	0.863614i	$0.331804\pi$
$402$	−888.783	+	2735.39i	−0.110270	+	0.339376i
$403$	2112.25	+	1534.64i	0.261089	+	0.189692i
$404$	−6180.34	−	4490.28i	−0.761097	−	0.552970i
$405$	−902.255	−	77.8500i	−0.110700	−	0.00955159i
$406$	−636.014	+	462.091i	−0.0777459	+	0.0564857i
$407$	−4719.16			−0.574743
$408$	−5966.60	+	4334.99i	−0.723996	+	0.526014i
$409$	1697.67	+	5224.90i	0.205243	+	0.631674i	0.999703	+	0.0243574i	$0.00775398\pi$
$409$	1697.67	+	5224.90i	0.205243	+	0.631674i	−0.794460	+	0.607316i	$0.792246\pi$
$410$	2633.68	+	2283.90i	0.317240	+	0.275107i
$411$	866.785	−	2667.69i	0.104028	−	0.320164i
$412$	1106.64	+	3405.88i	0.132330	+	0.407270i
$413$	−1353.02	−	4164.18i	−0.161206	−	0.496140i
$414$	−389.318	+	1198.20i	−0.0462173	+	0.142242i
$415$	−4699.03	−	405.450i	−0.555822	−	0.0479584i
$416$	−830.932	−	2557.35i	−0.0979322	−	0.301404i
$417$	6975.89	−	5068.28i	0.819211	−	0.595191i
$418$	3477.74			0.406942
$419$	−9497.60	+	6900.41i	−1.10737	+	0.804552i	−0.982248	−	0.187590i	$-0.939933\pi$
$419$	−9497.60	+	6900.41i	−1.10737	+	0.804552i	−0.125123	+	0.992141i	$0.539933\pi$
$420$	498.808	−	1179.04i	0.0579508	−	0.136979i
$421$	−6881.79	−	4999.91i	−0.796670	−	0.578814i	0.113266	−	0.993565i	$-0.463869\pi$
$421$	−6881.79	−	4999.91i	−0.796670	−	0.578814i	−0.909935	+	0.414750i	$0.863869\pi$
$422$	−1003.22	−	728.882i	−0.115725	−	0.0840792i
$423$	1327.07	−	4084.31i	0.152540	−	0.469470i
$424$	11627.1			1.33175
$425$	9488.11	+	9778.31i	1.08292	+	1.11604i
$426$	1921.52			0.218539
$427$	−123.870	+	381.232i	−0.0140386	+	0.0432063i
$428$	−3807.79	−	2766.52i	−0.430039	−	0.312442i
$429$	735.694	+	534.513i	0.0827964	+	0.0601551i
$430$	−6779.40	+	4084.52i	−0.760307	+	0.458077i
$431$	12760.2	−	9270.84i	1.42607	−	1.03610i	0.435343	−	0.900265i	$-0.356627\pi$
$431$	12760.2	−	9270.84i	1.42607	−	1.03610i	0.990731	−	0.135839i	$-0.0433729\pi$
$432$	17.9935			0.00200396
$433$	4262.99	−	3097.25i	0.473133	−	0.343751i	−0.325528	−	0.945532i	$-0.605542\pi$
$433$	4262.99	−	3097.25i	0.473133	−	0.343751i	0.798661	+	0.601781i	$0.205542\pi$
$434$	725.315	+	2232.29i	0.0802217	+	0.246897i
$435$	−771.772	+	1824.24i	−0.0850658	+	0.201071i
$436$	−2266.44	+	6975.39i	−0.248951	+	0.766194i
$437$	−2434.64	−	7493.06i	−0.266510	−	0.820232i
$438$	−654.676	−	2014.88i	−0.0714192	−	0.219806i
$439$	2120.97	−	6527.68i	0.230589	−	0.709679i	−0.767087	−	0.641543i	$-0.778295\pi$
$439$	2120.97	−	6527.68i	0.230589	−	0.709679i	0.997676	−	0.0681364i	$-0.0217053\pi$
$440$	2011.20	−	4753.89i	0.217910	−	0.515075i
$441$	−790.659	−	2433.40i	−0.0853751	−	0.262758i
$442$	−2268.69	+	1648.30i	−0.244142	+	0.177379i
$443$	16108.2			1.72759			0.863795	−	0.503843i	$-0.168081\pi$
$443$	16108.2			1.72759			0.863795	+	0.503843i	$0.168081\pi$
$444$	−2787.24	+	2025.05i	−0.297920	+	0.216451i
$445$	4071.34	−	2452.94i	0.433708	−	0.261305i
$446$	6376.61	+	4632.88i	0.676998	+	0.491868i
$447$	−5521.86	−	4011.87i	−0.584285	−	0.424508i
$448$	734.378	−	2260.18i	0.0774466	−	0.238356i
$449$	12908.2			1.35674			0.678370	−	0.734720i	$-0.262687\pi$
$449$	12908.2			1.35674			0.678370	+	0.734720i	$0.262687\pi$
$450$	276.653	+	1934.89i	0.0289812	+	0.202693i
$451$	3673.70			0.383565
$452$	1262.66	−	3886.07i	0.131395	−	0.404392i
$453$	−5815.47	−	4225.19i	−0.603167	−	0.438227i
$454$	−69.6469	−	50.6014i	−0.00719976	−	0.00523093i
$455$	494.253	−	1168.27i	0.0509252	−	0.120372i
$456$	5352.71	−	3888.97i	0.549700	−	0.399381i
$457$	10742.8			1.09962			0.549812	−	0.835288i	$-0.314699\pi$
$457$	10742.8			1.09962			0.549812	+	0.835288i	$0.314699\pi$
$458$	3309.77	−	2404.69i	0.337676	−	0.245336i
$459$	−909.435	−	2798.95i	−0.0924810	−	0.284627i
$460$	−4470.75	−	385.753i	−0.453152	−	0.0390997i
$461$	4456.45	−	13715.5i	0.450233	−	1.38567i	−0.426409	−	0.904531i	$-0.640222\pi$
$461$	4456.45	−	13715.5i	0.450233	−	1.38567i	0.876642	−	0.481144i	$-0.159778\pi$
$462$	252.626	+	777.503i	0.0254399	+	0.0782959i
$463$	3584.78	+	11032.8i	0.359825	+	1.10743i	0.953159	+	0.302471i	$0.0978116\pi$
$463$	3584.78	+	11032.8i	0.359825	+	1.10743i	−0.593333	+	0.804957i	$0.702188\pi$
$464$	12.1617	−	37.4298i	0.00121679	−	0.00374490i
$465$	4467.89	+	3874.51i	0.445578	+	0.386400i
$466$	−1556.45	−	4790.26i	−0.154723	−	0.476190i
$467$	2502.66	−	1818.29i	0.247986	−	0.180172i	−0.456848	−	0.889545i	$-0.651022\pi$
$467$	2502.66	−	1818.29i	0.247986	−	0.180172i	0.704834	+	0.709373i	$0.251022\pi$
$468$	663.882			0.0655726
$469$	3420.58	−	2485.20i	0.336775	−	0.244682i
$470$	−9234.49	−	796.787i	−0.906288	−	0.0781979i
$471$	−2190.23	−	1591.29i	−0.214268	−	0.155675i
$472$	−10426.9	−	7575.57i	−1.01681	−	0.738758i
$473$	−2577.46	+	7932.61i	−0.250554	+	0.771125i
$474$	−3412.69			−0.330696
$475$	−8511.90	−	8772.24i	−0.822216	−	0.847364i
$476$	4160.35			0.400608
$477$	−1433.75	+	4412.64i	−0.137625	+	0.423566i
$478$	1481.78	+	1076.58i	0.141789	+	0.103016i
$479$	14522.6	+	10551.3i	1.38529	+	1.00647i	0.996364	+	0.0852026i	$0.0271538\pi$
$479$	14522.6	+	10551.3i	1.38529	+	1.00647i	0.388926	+	0.921269i	$0.372846\pi$
$480$	−1377.20	−	5932.95i	−0.130959	−	0.564168i
$481$	−2761.78	+	2006.55i	−0.261801	+	0.190210i
$482$	11888.0			1.12341
$483$	1498.33	−	1088.60i	0.141152	−	0.102553i
$484$	1403.83	+	4320.56i	0.131840	+	0.405762i
$485$	−1493.24	−	6432.81i	−0.139803	−	0.602265i
$486$	130.463	−	401.524i	0.0121768	−	0.0374764i
$487$	5333.90	+	16416.0i	0.496308	+	1.52748i	0.814908	+	0.579590i	$0.196787\pi$
$487$	5333.90	+	16416.0i	0.496308	+	1.52748i	−0.318600	+	0.947889i	$0.603213\pi$
$488$	364.618	+	1122.18i	0.0338227	+	0.104096i
$489$	−3734.40	+	11493.3i	−0.345349	+	1.06287i
$490$	−4730.12	+	2849.84i	−0.436092	+	0.262741i
$491$	2530.77	+	7788.90i	0.232611	+	0.715903i	0.997429	+	0.0716569i	$0.0228287\pi$
$491$	2530.77	+	7788.90i	0.232611	+	0.715903i	−0.764818	+	0.644246i	$0.777171\pi$
$492$	2169.77	−	1576.43i	0.198822	−	0.144453i
$493$	−6437.03			−0.588051
$494$	2035.27	−	1478.71i	0.185367	−	0.134677i
$495$	1556.16	+	1349.48i	0.141301	+	0.122535i
$496$	−95.0614	−	69.0662i	−0.00860561	−	0.00625234i
$497$	−2285.23	−	1660.32i	−0.206251	−	0.149850i
$498$	679.464	−	2091.18i	0.0611396	−	0.188168i
$499$	−10653.8			−0.955767			−0.477884	−	0.878423i	$-0.658596\pi$
$499$	−10653.8			−0.955767			−0.477884	+	0.878423i	$0.658596\pi$
$500$	−6490.39	+	2518.18i	−0.580519	+	0.225233i
$501$	−2946.94			−0.262793
$502$	−3232.87	+	9949.75i	−0.287430	+	0.884620i
$503$	−4908.32	−	3566.11i	−0.435092	−	0.316113i	0.348590	−	0.937275i	$-0.386661\pi$
$503$	−4908.32	−	3566.11i	−0.435092	−	0.316113i	−0.783682	+	0.621163i	$0.786661\pi$
$504$	1258.26	+	914.183i	0.111205	+	0.0807955i
$505$	−12953.4	−	11233.1i	−1.14143	−	0.989832i
$506$	2318.27	−	1684.32i	0.203675	−	0.147979i
$507$	−5933.18			−0.519727
$508$	6705.48	−	4871.82i	0.585645	−	0.425496i
$509$	−970.706	−	2987.53i	−0.0845301	−	0.260157i	0.899854	−	0.436191i	$-0.143673\pi$
$509$	−970.706	−	2987.53i	−0.0845301	−	0.260157i	−0.984384	+	0.176035i	$0.943673\pi$
$510$	−5440.69	+	3277.96i	−0.472388	+	0.284609i
$511$	−962.399	+	2961.96i	−0.0833151	+	0.256417i
$512$	74.5533	+	229.452i	0.00643520	+	0.0198055i
$513$	815.865	+	2510.97i	0.0702170	+	0.216106i
$514$	−289.634	+	891.401i	−0.0248545	+	0.0764942i
$515$	1817.41	+	7829.34i	0.155504	+	0.669907i
$516$	1881.67	+	5791.18i	0.160535	+	0.494075i
$517$	−7902.29	+	5741.35i	−0.672229	+	0.488403i
$518$	−3068.94			−0.260311
$519$	−3070.46	+	2230.82i	−0.259688	+	0.188675i
$520$	−844.310	−	3637.26i	−0.0712027	−	0.306739i
$521$	−12579.0	−	9139.20i	−1.05777	−	0.768514i	−0.0840942	−	0.996458i	$-0.526800\pi$
$521$	−12579.0	−	9139.20i	−1.05777	−	0.768514i	−0.973674	+	0.227944i	$0.926800\pi$
$522$	−747.067	−	542.776i	−0.0626403	−	0.0455109i
$523$	6133.64	−	18877.4i	0.512821	−	1.57830i	−0.274392	−	0.961618i	$-0.588477\pi$
$523$	6133.64	−	18877.4i	0.512821	−	1.57830i	0.787213	−	0.616682i	$-0.211523\pi$
$524$	11366.3			0.947598
$525$	1342.86	−	2540.19i	0.111633	−	0.211168i
$526$	−1229.64			−0.101930
$527$	−5938.86	+	18277.9i	−0.490894	+	1.51082i
$528$	−33.1097	−	24.0556i	−0.00272901	−	0.00198274i
$529$	4591.38	+	3335.83i	0.377363	+	0.274170i
$530$	9976.85	+	860.840i	0.817673	+	0.0705519i
$531$	4160.77	−	3022.98i	0.340042	−	0.247055i
$532$	−3732.30			−0.304165
$533$	2149.95	−	1562.03i	0.174718	−	0.126940i
$534$	684.751	+	2107.45i	0.0554908	+	0.170783i
$535$	−7980.79	−	6920.86i	−0.644934	−	0.559280i
$536$	3845.90	−	11836.5i	0.309921	−	0.953837i
$537$	−1364.26	−	4198.76i	−0.109631	−	0.337411i
$538$	−1545.11	−	4755.37i	−0.123819	−	0.381075i
$539$	−1798.34	+	5534.73i	−0.143711	+	0.442296i
$540$	1498.18	+	129.269i	0.119391	+	0.0103015i
$541$	−4083.26	−	12567.0i	−0.324498	−	0.998701i	−0.971667	−	0.236355i	$-0.924047\pi$
$541$	−4083.26	−	12567.0i	−0.324498	−	0.998701i	0.647169	−	0.762346i	$-0.275953\pi$
$542$	−5016.91	+	3645.00i	−0.397592	+	0.288867i
$543$	−11229.0			−0.887441
$544$	16013.0	−	11634.1i	1.26205	−	0.916930i
$545$	−6413.77	+	15160.3i	−0.504103	+	1.19155i
$546$	478.432	+	347.601i	0.0375000	+	0.0272453i
$547$	5357.76	+	3892.64i	0.418796	+	0.304273i	0.777153	−	0.629312i	$-0.216663\pi$
$547$	5357.76	+	3892.64i	0.418796	+	0.304273i	−0.358357	+	0.933584i	$0.616663\pi$
$548$	−1439.28	+	4429.65i	−0.112195	+	0.345302i
$549$	−470.843			−0.0366031
$550$	2077.71	−	3930.25i	0.161080	−	0.304703i
$551$	5774.74			0.446483
$552$	1684.64	−	5184.78i	0.129897	−	0.399781i
$553$	4058.66	+	2948.79i	0.312101	+	0.226755i
$554$	−9778.05	−	7104.17i	−0.749873	−	0.544815i
$555$	−6623.21	+	3990.42i	−0.506558	+	0.305196i
$556$	−11583.3	+	8415.79i	−0.883531	+	0.641923i
$557$	−15042.5			−1.14430			−0.572148	−	0.820150i	$-0.693890\pi$
$557$	−15042.5			−1.14430			−0.572148	+	0.820150i	$0.693890\pi$
$558$	−2230.46	+	1620.53i	−0.169217	+	0.122943i
$559$	1864.49	+	5738.30i	0.141072	+	0.434176i
$560$	−22.2437	+	52.5777i	−0.00167852	+	0.00396752i
$561$	−2068.50	+	6366.18i	−0.155672	+	0.479109i
$562$	1787.51	+	5501.40i	0.134167	+	0.412923i
$563$	−1080.07	−	3324.10i	−0.0808514	−	0.248835i	0.902458	−	0.430779i	$-0.141761\pi$
$563$	−1080.07	−	3324.10i	−0.0808514	−	0.248835i	−0.983309	+	0.181944i	$0.941761\pi$
$564$	−2203.58	+	6781.92i	−0.164517	+	0.506330i
$565$	3573.19	−	8445.98i	0.266062	−	0.628894i
$566$	−329.637	−	1014.52i	−0.0244800	−	0.0753417i
$567$	−502.102	+	364.798i	−0.0371892	+	0.0270196i
$568$	−8314.68			−0.614219
$569$	−6041.21	+	4389.19i	−0.445098	+	0.323382i	−0.787657	−	0.616114i	$-0.788706\pi$
$569$	−6041.21	+	4389.19i	−0.445098	+	0.323382i	0.342560	+	0.939496i	$0.388706\pi$
$570$	4880.91	−	2940.70i	0.358664	−	0.216092i
$571$	12543.7	+	9113.52i	0.919329	+	0.667932i	0.943357	−	0.331779i	$-0.107649\pi$
$571$	12543.7	+	9113.52i	0.919329	+	0.667932i	−0.0240276	+	0.999711i	$0.507649\pi$
$572$	−1221.61	−	887.550i	−0.0892972	−	0.0648782i
$573$	3665.34	−	11280.7i	0.267228	−	0.822443i
$574$	2389.06			0.173724
$575$	−9922.57	−	1725.16i	−0.719652	−	0.125120i
$576$	2791.45			0.201928
$577$	−7996.68	+	24611.3i	−0.576961	+	1.77570i	0.0524431	+	0.998624i	$0.483299\pi$
$577$	−7996.68	+	24611.3i	−0.576961	+	1.77570i	−0.629404	+	0.777078i	$0.716701\pi$
$578$	−9794.02	−	7115.77i	−0.704806	−	0.512071i
$579$	11502.4	+	8356.99i	0.825603	+	0.599836i
$580$	1281.51	−	3029.12i	0.0917448	−	0.216858i
$581$	−2614.99	+	1899.90i	−0.186727	+	0.135665i
$582$	3078.66			0.219269
$583$	8537.55	−	6202.89i	0.606500	−	0.440648i
$584$	2832.88	+	8718.71i	0.200728	+	0.617779i
$585$	1484.50	+	128.088i	0.104917	+	0.00905263i
$586$	−3486.78	+	10731.2i	−0.245798	+	0.756488i
$587$	−154.164	−	474.470i	−0.0108399	−	0.0333619i	0.945490	−	0.325650i	$-0.105583\pi$
$587$	−154.164	−	474.470i	−0.0108399	−	0.0333619i	−0.956330	+	0.292288i	$0.905583\pi$
$588$	1312.88	+	4040.62i	0.0920784	+	0.283388i
$589$	5327.83	−	16397.4i	0.372715	−	1.14710i
$590$	−8386.08	−	7272.32i	−0.585169	−	0.507452i
$591$	−1773.07	−	5456.95i	−0.123408	−	0.379812i
$592$	124.293	−	90.3044i	0.00862910	−	0.00626941i
$593$	16095.6			1.11462			0.557309	−	0.830305i	$-0.311834\pi$
$593$	16095.6			1.11462			0.557309	+	0.830305i	$0.311834\pi$
$594$	−776.867	+	564.427i	−0.0536620	+	0.0389877i
$595$	9302.91	+	802.690i	0.640979	+	0.0553060i
$596$	9168.96	+	6661.64i	0.630160	+	0.457838i
$597$	7989.40	+	5804.64i	0.547712	+	0.397936i
$598$	640.553	−	1971.42i	0.0438029	−	0.134812i
$599$	−998.977			−0.0681421			−0.0340710	−	0.999419i	$-0.510847\pi$
$599$	−998.977			−0.0681421			−0.0340710	+	0.999419i	$0.510847\pi$
$600$	−1197.12	−	8372.58i	−0.0814535	−	0.569682i
$601$	−12876.3			−0.873937			−0.436968	−	0.899477i	$-0.643948\pi$
$601$	−12876.3			−0.873937			−0.436968	+	0.899477i	$0.643948\pi$
$602$	−1676.16	+	5158.69i	−0.113480	+	0.349256i
$603$	4017.84	+	2919.13i	0.271342	+	0.197141i
$604$	9656.49	+	7015.85i	0.650525	+	0.472634i
$605$	2305.49	+	9931.99i	0.154928	+	0.667426i
$606$	6466.62	−	4698.27i	0.433479	−	0.314941i
$607$	−12236.9			−0.818254			−0.409127	−	0.912477i	$-0.634167\pi$
$607$	−12236.9			−0.818254			−0.409127	+	0.912477i	$0.634167\pi$
$608$	−14365.5	+	10437.1i	−0.958219	+	0.696187i
$609$	419.482	+	1291.03i	0.0279118	+	0.0859036i
$610$	229.784	+	989.900i	0.0152519	+	0.0657048i
$611$	−2183.46	+	6719.99i	−0.144572	+	0.444945i
$612$	1510.10	+	4647.61i	0.0997422	+	0.306975i
$613$	−568.508	−	1749.69i	−0.0374581	−	0.115284i	0.930579	−	0.366091i	$-0.119304\pi$
$613$	−568.508	−	1749.69i	−0.0374581	−	0.115284i	−0.968037	+	0.250807i	$0.919304\pi$
$614$	−519.420	+	1598.61i	−0.0341402	+	0.105073i
$615$	5155.94	−	3106.40i	0.338061	−	0.203678i
$616$	−1093.15	−	3364.37i	−0.0715005	−	0.220056i
$617$	2800.27	−	2034.52i	0.182714	−	0.132750i	−0.492669	−	0.870217i	$-0.663978\pi$
$617$	2800.27	−	2034.52i	0.182714	−	0.132750i	0.675383	+	0.737467i	$0.263978\pi$
$618$	−3747.03			−0.243896
$619$	3963.98	−	2880.00i	0.257392	−	0.187007i	−0.451604	−	0.892218i	$-0.649148\pi$
$619$	3963.98	−	2880.00i	0.257392	−	0.187007i	0.708997	+	0.705212i	$0.249148\pi$
$620$	−7418.86	−	6433.56i	−0.480562	−	0.416738i
$621$	1759.96	+	1278.68i	0.113727	+	0.0826277i
$622$	2151.01	+	1562.80i	0.138662	+	0.100744i
$623$	1006.61	−	3098.03i	0.0647335	−	0.199229i
$624$	−29.6050			−0.00189928
$625$	−14998.9	+	4378.63i	−0.959932	+	0.280232i
$626$	13870.7			0.885599
$627$	1855.67	−	5711.17i	0.118195	−	0.363768i
$628$	3636.84	+	2642.32i	0.231092	+	0.167898i
$629$	−20329.3	−	14770.1i	−1.28868	−	0.936283i
$630$	1011.99	+	877.588i	0.0639979	+	0.0554983i
$631$	1722.59	−	1251.53i	0.108677	−	0.0789585i	−0.532119	−	0.846669i	$-0.678604\pi$
$631$	1722.59	−	1251.53i	0.108677	−	0.0789585i	0.640796	+	0.767711i	$0.278604\pi$
$632$	14767.2			0.929443
$633$	−1732.28	+	1258.58i	−0.108771	+	0.0790267i
$634$	−2835.32	−	8726.22i	−0.177610	−	0.546628i
$635$	15934.0	−	9600.06i	0.995781	−	0.599948i
$636$	2380.72	−	7327.12i	0.148431	−	0.456822i
$637$	1300.89	+	4003.72i	0.0809152	+	0.249032i
$638$	649.034	+	1997.52i	0.0402751	+	0.123954i
$639$	1025.29	−	3155.53i	0.0634741	−	0.195353i
$640$	2310.24	+	9952.43i	0.142688	+	0.614695i
$641$	−6426.91	−	19780.0i	−0.396018	−	1.21882i	−0.928166	−	0.372168i	$-0.878615\pi$
$641$	−6426.91	−	19780.0i	−0.396018	−	1.21882i	0.532147	−	0.846652i	$-0.321385\pi$
$642$	3984.17	−	2894.67i	0.244927	−	0.177950i
$643$	6395.45			0.392243			0.196121	−	0.980580i	$-0.437165\pi$
$643$	6395.45			0.392243			0.196121	+	0.980580i	$0.437165\pi$
$644$	−2487.96	+	1807.61i	−0.152235	+	0.110605i
$645$	3090.24	+	13312.6i	0.188648	+	0.812689i
$646$	14981.5	+	10884.7i	0.912442	+	0.662928i
$647$	−8061.60	−	5857.10i	−0.489852	−	0.355898i	0.315275	−	0.949000i	$-0.397903\pi$
$647$	−8061.60	−	5857.10i	−0.489852	−	0.355898i	−0.805127	+	0.593102i	$0.797903\pi$
$648$	−564.534	+	1737.46i	−0.0342237	+	0.105330i
$649$	−11697.7			−0.707510
$650$	−455.182	−	3183.52i	−0.0274672	−	0.192105i
$651$	4052.90			0.244003
$652$	6200.91	−	19084.5i	0.372464	−	1.14633i
$653$	−23970.3	−	17415.5i	−1.43650	−	1.04368i	−0.988760	−	0.149509i	$-0.952231\pi$
$653$	−23970.3	−	17415.5i	−1.43650	−	1.04368i	−0.447735	−	0.894166i	$-0.647769\pi$
$654$	−6208.47	−	4510.72i	−0.371208	−	0.269699i
$655$	25416.1	+	2193.00i	1.51617	+	0.130821i
$656$	−96.7580	+	70.2988i	−0.00575879	+	0.00418400i
$657$	−3658.19			−0.217229
$658$	−5138.96	+	3733.68i	−0.304465	+	0.221206i
$659$	5778.07	+	17783.1i	0.341550	+	1.05118i	0.963405	+	0.268051i	$0.0863795\pi$
$659$	5778.07	+	17783.1i	0.341550	+	1.05118i	−0.621855	+	0.783133i	$0.713621\pi$
$660$	−2583.98	−	2240.80i	−0.152396	−	0.132156i
$661$	5122.48	−	15765.4i	0.301424	−	0.927689i	−0.679563	−	0.733617i	$-0.737831\pi$
$661$	5122.48	−	15765.4i	0.301424	−	0.927689i	0.980987	−	0.194072i	$-0.0621695\pi$
$662$	−1118.12	−	3441.21i	−0.0656447	−	0.202034i
$663$	1496.31	+	4605.17i	0.0876499	+	0.269759i
$664$	−2940.14	+	9048.83i	−0.171837	+	0.528860i
$665$	−8345.76	−	720.103i	−0.486668	−	0.0419916i
$666$	−1113.94	−	3428.37i	−0.0648115	−	0.199469i
$667$	3849.45	−	2796.79i	0.223465	−	0.162357i
$668$	4893.34			0.283427
$669$	11010.6	−	7999.69i	0.636316	−	0.462310i
$670$	4176.38	−	9871.73i	0.240817	−	0.569221i
$671$	866.397	+	629.474i	0.0498463	+	0.0362155i
$672$	−3376.90	−	2453.46i	−0.193850	−	0.140840i
$673$	−2747.00	+	8454.40i	−0.157339	+	0.484240i	−0.998390	−	0.0567156i	$-0.981937\pi$
$673$	−2747.00	+	8454.40i	−0.157339	+	0.484240i	0.841051	+	0.540955i	$0.181937\pi$
$674$	12030.7			0.687542
$675$	3325.12	+	578.111i	0.189606	+	0.0329652i
$676$	9851.95			0.560534
$677$	7046.62	−	21687.3i	0.400035	−	1.23118i	−0.524935	−	0.851142i	$-0.675911\pi$
$677$	7046.62	−	21687.3i	0.400035	−	1.23118i	0.924970	−	0.380039i	$-0.124089\pi$
$678$	3458.81	+	2512.97i	0.195922	+	0.142345i
$679$	−3661.41	−	2660.17i	−0.206940	−	0.150351i
$680$	23542.7	−	14184.2i	1.32768	−	0.799912i
$681$	−120.261	+	87.3745i	−0.00676711	+	0.00491659i
$682$	6270.77			0.352082
$683$	6148.10	−	4466.86i	0.344437	−	0.250248i	−0.402094	−	0.915598i	$-0.631718\pi$
$683$	6148.10	−	4466.86i	0.344437	−	0.250248i	0.746532	+	0.665350i	$0.231718\pi$
$684$	−1354.73	−	4169.43i	−0.0757301	−	0.233073i
$685$	−4073.01	+	9627.40i	−0.227185	+	0.536999i
$686$	−2580.48	+	7941.90i	−0.143620	+	0.442016i
$687$	−2182.96	−	6718.45i	−0.121230	−	0.373107i
$688$	−83.9107	−	258.251i	−0.00464981	−	0.0143106i
$689$	2358.98	−	7260.21i	0.130436	−	0.401440i
$690$	1829.40	−	4324.17i	0.100933	−	0.238577i
$691$	−3900.42	−	12004.2i	−0.214731	−	0.660873i	−0.999173	−	0.0406706i	$-0.987051\pi$
$691$	−3900.42	−	12004.2i	−0.214731	−	0.660873i	0.784442	−	0.620202i	$-0.212949\pi$
$692$	5098.45	−	3704.24i	0.280078	−	0.203488i
$693$	1411.62			0.0773780
$694$	3034.91	−	2204.99i	0.165999	−	0.120606i
$695$	−27525.1	+	16583.6i	−1.50228	+	0.905109i
$696$	3232.67	+	2348.67i	0.176055	+	0.127911i
$697$	15825.6	+	11498.0i	0.860027	+	0.624846i
$698$	−6340.51	+	19514.1i	−0.343828	+	1.05819i
$699$	−8697.11			−0.470608
$700$	−2229.80	+	4217.94i	−0.120398	+	0.227747i
$701$	−4783.64			−0.257740			−0.128870	−	0.991662i	$-0.541135\pi$
$701$	−4783.64			−0.257740			−0.128870	+	0.991662i	$0.541135\pi$
$702$	−214.654	+	660.636i	−0.0115407	+	0.0355187i
$703$	18237.7	+	13250.4i	0.978444	+	0.710881i
$704$	−5136.55	−	3731.92i	−0.274987	−	0.199790i
$705$	−6235.88	+	14739.8i	−0.333130	+	0.787423i
$706$	−11621.2	+	8443.28i	−0.619502	+	0.450095i
$707$	−11750.3			−0.625056
$708$	−6908.89	+	5019.61i	−0.366740	+	0.266452i
$709$	−10275.2	−	31623.9i	−0.544280	−	1.67512i	−0.722695	−	0.691167i	$-0.757097\pi$
$709$	−10275.2	−	31623.9i	−0.544280	−	1.67512i	0.178414	−	0.983955i	$-0.442903\pi$
$710$	−7134.55	−	615.596i	−0.377120	−	0.0325393i
$711$	−1820.96	+	5604.34i	−0.0960497	+	0.295611i
$712$	−2963.02	−	9119.24i	−0.155960	−	0.479997i
$713$	−4389.94	−	13510.9i	−0.230581	−	0.709657i
$714$	−1345.17	+	4140.01i	−0.0705067	+	0.216997i
$715$	−2560.38	−	2220.33i	−0.133920	−	0.116134i
$716$	2265.33	+	6971.96i	0.118239	+	0.363903i
$717$	2558.63	−	1858.95i	0.133269	−	0.0968254i
$718$	8089.82			0.420487
$719$	−10054.9	+	7305.29i	−0.521534	+	0.378917i	−0.817182	−	0.576380i	$-0.804465\pi$
$719$	−10054.9	+	7305.29i	−0.521534	+	0.378917i	0.295647	+	0.955297i	$0.404465\pi$
$720$	−66.8094	−	5.76457i	−0.00345811	−	0.000298379i
$721$	4456.29	+	3237.69i	0.230182	+	0.167237i
$722$	−3799.15	−	2760.24i	−0.195831	−	0.142279i
$723$	6343.25	−	19522.5i	0.326291	−	1.00422i
$724$	18645.5			0.957119
$725$	3450.01	−	6526.13i	0.176731	−	0.334310i
$726$	−4753.33			−0.242993
$727$	2713.82	−	8352.28i	0.138446	−	0.426092i	−0.857664	−	0.514210i	$-0.828085\pi$
$727$	2713.82	−	8352.28i	0.138446	−	0.426092i	0.996110	+	0.0881178i	$0.0280852\pi$
$728$	−2070.25	−	1504.12i	−0.105396	−	0.0765748i
$729$	−589.773	−	428.495i	−0.0299636	−	0.0217698i
$730$	1785.29	+	7690.97i	0.0905159	+	0.389939i
$731$	−35930.8	+	26105.3i	−1.81799	+	1.32085i
$732$	781.827			0.0394770
$733$	−21102.6	+	15331.9i	−1.06336	+	0.772576i	−0.974707	−	0.223486i	$-0.928256\pi$
$733$	−21102.6	+	15331.9i	−1.06336	+	0.772576i	−0.0886528	+	0.996063i	$0.528256\pi$
$734$	−278.966	−	858.569i	−0.0140284	−	0.0431749i
$735$	2156.12	+	9288.47i	0.108203	+	0.466137i
$736$	−4521.20	+	13914.8i	−0.226431	+	0.696884i
$737$	−3490.61	−	10743.0i	−0.174462	−	0.536937i
$738$	867.166	+	2668.86i	0.0432531	+	0.133120i
$739$	−7226.40	+	22240.6i	−0.359712	+	1.10708i	0.593514	+	0.804824i	$0.297740\pi$
$739$	−7226.40	+	22240.6i	−0.359712	+	1.10708i	−0.953226	+	0.302257i	$0.902260\pi$
$740$	10997.7	−	6626.02i	0.546331	−	0.329158i
$741$	−1342.36	−	4131.35i	−0.0665489	−	0.204817i
$742$	5552.08	−	4033.83i	0.274695	−	0.199577i
$743$	26389.6			1.30302			0.651508	−	0.758642i	$-0.274137\pi$
$743$	26389.6			1.30302			0.651508	+	0.758642i	$0.274137\pi$
$744$	9651.55	−	7012.26i	0.475595	−	0.345540i
$745$	19217.3	+	16665.0i	0.945057	+	0.819544i
$746$	5906.63	+	4291.42i	0.289889	+	0.210617i
$747$	−3071.59	−	2231.64i	−0.150447	−	0.109306i
$748$	3434.70	−	10570.9i	0.167895	−	0.516726i
$749$	−7239.52			−0.353172
$750$	−407.324	−	7272.86i	−0.0198312	−	0.354090i
$751$	17725.3			0.861257			0.430629	−	0.902529i	$-0.358292\pi$
$751$	17725.3			0.861257			0.430629	+	0.902529i	$0.358292\pi$
$752$	98.2659	−	302.431i	0.00476514	−	0.0146656i
$753$	14614.6	+	10618.1i	0.707283	+	0.513871i
$754$	1229.16	+	893.040i	0.0593681	+	0.0431334i
$755$	20239.1	+	17551.2i	0.975599	+	0.846029i
$756$	833.732	−	605.742i	0.0401092	−	0.0291410i
$757$	−4478.94			−0.215046			−0.107523	−	0.994203i	$-0.534292\pi$
$757$	−4478.94			−0.215046			−0.107523	+	0.994203i	$0.534292\pi$
$758$	−4013.16	+	2915.73i	−0.192302	+	0.139715i
$759$	−1529.01	−	4705.81i	−0.0731219	−	0.225046i
$760$	−21120.4	+	12724.8i	−1.00805	+	0.607340i
$761$	422.762	−	1301.13i	0.0201381	−	0.0619787i	−0.940482	−	0.339842i	$-0.889626\pi$
$761$	422.762	−	1301.13i	0.0201381	−	0.0619787i	0.960621	+	0.277864i	$0.0896263\pi$
$762$	2679.90	+	8247.90i	0.127405	+	0.392113i
$763$	3486.08	+	10729.1i	0.165406	+	0.509067i
$764$	−6086.23	+	18731.5i	−0.288210	+	0.887018i
$765$	2480.02	+	10683.8i	0.117209	+	0.504934i
$766$	−3090.77	−	9512.42i	−0.145789	−	0.448691i
$767$	−6845.80	+	4973.77i	−0.322279	+	0.234149i
$768$	−12207.0			−0.573544
$769$	−13373.6	+	9716.46i	−0.627130	+	0.455637i	−0.855405	−	0.517960i	$-0.826692\pi$
$769$	−13373.6	+	9716.46i	−0.627130	+	0.455637i	0.228275	+	0.973597i	$0.426692\pi$
$770$	−688.907	−	2967.79i	−0.0322422	−	0.138898i
$771$	1309.32	+	951.278i	0.0611596	+	0.0444351i
$772$	−19099.6	−	13876.6i	−0.890425	−	0.646932i
$773$	−2472.77	+	7610.39i	−0.115057	+	0.354110i	−0.991959	−	0.126560i	$-0.959606\pi$
$773$	−2472.77	+	7610.39i	−0.115057	+	0.354110i	0.876902	+	0.480670i	$0.159606\pi$
$774$	−6371.27			−0.295879
$775$	−15347.9	−	15817.4i	−0.711373	−	0.733131i
$776$	−13321.8			−0.616271
$777$	−1637.54	+	5039.83i	−0.0756068	+	0.232694i
$778$	−15453.1	−	11227.3i	−0.712109	−	0.517377i
$779$	−14197.4	−	10315.0i	−0.652983	−	0.474420i
$780$	−2464.98	−	212.688i	−0.113155	−	0.00976340i
$781$	−6105.30	+	4435.76i	−0.279724	+	0.203232i
$782$	15258.3			0.697742
$783$	−1289.98	+	937.223i	−0.0588761	+	0.0427760i
$784$	−58.5461	−	180.186i	−0.00266700	−	0.00820819i
$785$	7622.48	+	6610.13i	0.346571	+	0.300542i
$786$	−3675.09	+	11310.8i	−0.166776	+	0.513285i
$787$	−6004.95	−	18481.3i	−0.271986	−	0.837088i	−0.990001	−	0.141060i	$-0.954949\pi$
$787$	−6004.95	−	18481.3i	−0.271986	−	0.837088i	0.718015	−	0.696028i	$-0.245051\pi$
$788$	2944.15	+	9061.16i	0.133098	+	0.409633i
$789$	−656.120	+	2019.33i	−0.0296052	+	0.0911154i
$790$	12671.2	+	1093.32i	0.570662	+	0.0492388i
$791$	−1942.14	−	5977.29i	−0.0873003	−	0.268683i
$792$	3361.62	−	2442.36i	0.150821	−	0.109578i
$793$	774.687			0.0346910
$794$	230.155	−	167.217i	0.0102870	−	0.00747396i
$795$	6737.19	−	15924.7i	0.300558	−	0.710431i
$796$	−13266.3	−	9638.50i	−0.590716	−	0.429180i
$797$	31978.9	+	23234.0i	1.42127	+	1.03261i	0.991561	+	0.129642i	$0.0413828\pi$
$797$	31978.9	+	23234.0i	1.42127	+	1.03261i	0.429706	+	0.902969i	$0.358617\pi$
$798$	1206.77	−	3714.05i	0.0535328	−	0.164757i
$799$	−52010.9			−2.30290
$800$	3212.80	+	22470.1i	0.141987	+	0.993050i
$801$	3826.24			0.168781
$802$	4347.02	−	13378.7i	0.191395	−	0.589052i
$803$	6731.42	+	4890.66i	0.295824	+	0.214929i
$804$	−6671.56	−	4847.17i	−0.292646	−	0.212620i
$805$	−5912.05	+	3561.95i	−0.258848	+	0.155953i
$806$	3669.83	−	2666.28i	0.160377	−	0.116521i
$807$	−8633.76			−0.376608
$808$	−27982.0	+	20330.1i	−1.21832	+	0.885163i
$809$	−713.228	−	2195.09i	−0.0309960	−	0.0953959i	0.934362	−	0.356326i	$-0.115971\pi$
$809$	−713.228	−	2195.09i	−0.0309960	−	0.0953959i	−0.965358	+	0.260930i	$0.915971\pi$
$810$	−613.044	+	1449.06i	−0.0265928	+	0.0628576i
$811$	−1311.25	+	4035.61i	−0.0567746	+	0.174734i	−0.975422	−	0.220343i	$-0.929282\pi$
$811$	−1311.25	+	4035.61i	−0.0567746	+	0.174734i	0.918648	+	0.395077i	$0.129282\pi$
$812$	−696.543	−	2143.74i	−0.0301033	−	0.0926483i
$813$	3308.90	+	10183.7i	0.142741	+	0.439310i
$814$	−2533.65	+	7797.77i	−0.109096	+	0.335764i
$815$	17547.9	−	41478.1i	0.754204	−	1.78272i
$816$	−67.3411	−	207.254i	−0.00288898	−	0.00889137i
$817$	32234.0	−	23419.4i	1.38032	−	1.00286i
$818$	9544.89			0.407982
$819$	826.118	−	600.210i	0.0352465	−	0.0256081i
$820$	−8561.34	+	5158.12i	−0.364604	+	0.219670i
$821$	−23223.1	−	16872.6i	−0.987201	−	0.717244i	−0.0278950	−	0.999611i	$-0.508880\pi$
$821$	−23223.1	−	16872.6i	−0.987201	−	0.717244i	−0.959306	+	0.282367i	$0.908880\pi$
$822$	−3942.63	−	2864.49i	−0.167293	−	0.121546i
$823$	8655.81	−	26639.9i	0.366613	−	1.12832i	−0.582351	−	0.812937i	$-0.697867\pi$
$823$	8655.81	−	26639.9i	0.366613	−	1.12832i	0.948965	−	0.315382i	$-0.102133\pi$
$824$	16214.0			0.685486
$825$	−5345.66	−	5509.16i	−0.225590	−	0.232490i
$826$	−7607.16			−0.320444
$827$	2740.49	−	8434.37i	0.115231	−	0.354645i	−0.876764	−	0.480921i	$-0.840302\pi$
$827$	2740.49	−	8434.37i	0.115231	−	0.354645i	0.991995	+	0.126276i	$0.0403024\pi$
$828$	−2922.38	−	2123.23i	−0.122657	−	0.0891153i
$829$	19591.6	+	14234.1i	0.820802	+	0.596347i	0.916942	−	0.399020i	$-0.130650\pi$
$829$	19591.6	+	14234.1i	0.820802	+	0.596347i	−0.0961403	+	0.995368i	$0.530650\pi$
$830$	−3192.79	+	7546.82i	−0.133522	+	0.315607i
$831$	−16884.0	+	12266.9i	−0.704811	+	0.512075i
$832$	−4592.83			−0.191380
$833$	−25069.6	+	18214.1i	−1.04275	+	0.757602i
$834$	−4629.39	−	14247.8i	−0.192209	−	0.591560i
$835$	10941.9	+	944.111i	0.453487	+	0.0391285i
$836$	−3081.31	+	9483.31i	−0.127475	+	0.392329i
$837$	1471.10	+	4527.58i	0.0607510	+	0.186972i
$838$	6302.86	+	19398.2i	0.259820	+	0.799643i
$839$	10306.0	−	31718.7i	0.424080	−	1.30519i	−0.479792	−	0.877383i	$-0.659288\pi$
$839$	10306.0	−	31718.7i	0.424080	−	1.30519i	0.903872	−	0.427803i	$-0.140712\pi$
$840$	−4379.04	−	3797.46i	−0.179870	−	0.155982i
$841$	−6458.90	−	19878.5i	−0.264829	−	0.815058i
$842$	−11956.4	+	8686.84i	−0.489365	+	0.355544i
$843$	9988.24			0.408082
$844$	2876.42	−	2089.84i	0.117311	−	0.0852315i
$845$	22029.8	+	1900.81i	0.896862	+	0.0773846i
$846$	−6036.27	−	4385.61i	−0.245309	−	0.178227i
$847$	5653.07	+	4107.20i	0.229329	+	0.166617i
$848$	−106.165	+	326.744i	−0.00429922	+	0.0132316i
$849$	−1841.94			−0.0744585
$850$	21251.4	−	10428.0i	0.857548	−	0.420796i
$851$	18574.6			0.748214
$852$	−1702.48	+	5239.70i	−0.0684578	+	0.210692i
$853$	20545.4	+	14927.1i	0.824693	+	0.599174i	0.918053	−	0.396458i	$-0.129761\pi$
$853$	20545.4	+	14927.1i	0.824693	+	0.599174i	−0.0933602	+	0.995632i	$0.529761\pi$
$854$	563.430	+	409.356i	0.0225763	+	0.0164026i
$855$	−2224.85	−	9584.58i	−0.0889922	−	0.383375i
$856$	−17240.1	+	12525.7i	−0.688382	+	0.500139i
$857$	28013.4			1.11659			0.558296	−	0.829642i	$-0.311455\pi$
$857$	28013.4			1.11659			0.558296	+	0.829642i	$0.311455\pi$
$858$	1278.19	−	928.662i	0.0508588	−	0.0369511i
$859$	2192.25	+	6747.06i	0.0870765	+	0.267994i	0.985108	−	0.171938i	$-0.0550027\pi$
$859$	2192.25	+	6747.06i	0.0870765	+	0.267994i	−0.898031	+	0.439931i	$0.855003\pi$
$860$	−5131.29	−	22105.4i	−0.203460	−	0.876498i
$861$	1274.77	−	3923.33i	0.0504576	−	0.155292i
$862$	−8468.02	−	26061.9i	−0.334596	−	1.02978i
$863$	−3760.21	−	11572.7i	−0.148319	−	0.456478i	0.849104	−	0.528225i	$-0.177142\pi$
$863$	−3760.21	−	11572.7i	−0.148319	−	0.456478i	−0.997423	+	0.0717477i	$0.977142\pi$
$864$	1515.08	−	4662.95i	0.0596576	−	0.183607i
$865$	12115.3	−	7299.31i	0.476221	−	0.286918i
$866$	−2829.04	−	8706.88i	−0.111010	−	0.341653i
$867$	−16911.5	+	12287.0i	−0.662452	+	0.481300i
$868$	−6729.78			−0.263161
$869$	10843.2	−	7878.08i	0.423282	−	0.307532i
$870$	2599.96	+	2254.66i	0.101318	+	0.0878621i
$871$	−6610.64	−	4802.91i	−0.257167	−	0.186843i
$872$	26865.0	+	19518.5i	1.04331	+	0.758006i
$873$	1642.73	−	5055.81i	0.0636862	−	0.196006i
$874$	−13688.4			−0.529767
$875$	−5799.82	+	9001.47i	−0.224080	+	0.347778i
$876$	6074.36			0.234285
$877$	−1723.15	+	5303.31i	−0.0663473	+	0.204196i	−0.978734	−	0.205133i	$-0.934237\pi$
$877$	−1723.15	+	5303.31i	−0.0663473	+	0.204196i	0.912387	+	0.409329i	$0.134237\pi$
$878$	−9647.38	−	7009.23i	−0.370824	−	0.269419i
$879$	15762.4	+	11452.0i	0.604837	+	0.439440i
$880$	115.229	+	99.9255i	0.00441406	+	0.00382783i
$881$	−35942.3	+	26113.6i	−1.37449	+	0.998627i	−0.377121	+	0.926164i	$0.623086\pi$
$881$	−35942.3	+	26113.6i	−1.37449	+	0.998627i	−0.997371	+	0.0724634i	$0.976914\pi$
$882$	−4445.35			−0.169708
$883$	−23284.3	+	16917.0i	−0.887405	+	0.644738i	−0.935200	−	0.354120i	$-0.884781\pi$
$883$	−23284.3	+	16917.0i	−0.887405	+	0.644738i	0.0477950	+	0.998857i	$0.484781\pi$
$884$	−2484.60	−	7646.81i	−0.0945318	−	0.290939i
$885$	−16417.4	+	9891.29i	−0.623575	+	0.375697i
$886$	8648.24	−	26616.6i	0.327927	−	1.00926i
$887$	4088.08	+	12581.8i	0.154751	+	0.476275i	0.998136	−	0.0610358i	$-0.0194404\pi$
$887$	4088.08	+	12581.8i	0.154751	+	0.476275i	−0.843385	+	0.537310i	$0.819440\pi$
$888$	4820.20	+	14835.1i	0.182157	+	0.560622i
$889$	3939.56	−	12124.7i	0.148626	−	0.457425i
$890$	−1867.31	−	8044.29i	−0.0703284	−	0.302972i
$891$	512.381	+	1576.95i	0.0192653	+	0.0592926i
$892$	−18283.0	+	13283.3i	−0.686276	+	0.498609i
$893$	46659.6			1.74849
$894$	−9593.67	+	6970.21i	−0.358904	+	0.260759i
$895$	3720.31	+	16027.0i	0.138946	+	0.598573i
$896$	5664.71	+	4115.65i	0.211211	+	0.153453i
$897$	−2895.69	−	2103.84i	−0.107786	−	0.0783114i
$898$	6930.24	−	21329.1i	0.257533	−	0.792606i
$899$	10412.5			0.386293
$900$	−5521.30	−	959.944i	−0.204493	−	0.0355535i
$901$	56192.1			2.07772
$902$	1972.36	−	6070.29i	0.0728074	−	0.224078i
$903$	7577.26	+	5505.20i	0.279242	+	0.202881i
$904$	−14966.8	−	10874.0i	−0.550651	−	0.400071i
$905$	41692.9	+	3597.42i	1.53140	+	0.132135i
$906$	−10103.8	+	7340.83i	−0.370503	+	0.269186i
$907$	−18849.7			−0.690071			−0.345035	−	0.938590i	$-0.612133\pi$
$907$	−18849.7			−0.690071			−0.345035	+	0.938590i	$0.612133\pi$
$908$	199.691	−	145.084i	0.00729843	−	0.00530262i
$909$	−4265.05	−	13126.5i	−0.155625	−	0.478963i
$910$	−1665.05	−	1443.91i	−0.0606548	−	0.0525992i
$911$	−6238.91	+	19201.4i	−0.226898	+	0.698321i	0.771195	+	0.636599i	$0.219659\pi$
$911$	−6238.91	+	19201.4i	−0.226898	+	0.698321i	−0.998093	+	0.0617219i	$0.980341\pi$
$912$	60.4125	+	185.930i	0.00219348	+	0.00675085i
$913$	2668.53	+	8212.89i	0.0967310	+	0.297707i
$914$	5767.67	−	17751.1i	0.208728	−	0.642399i
$915$	1748.23	+	150.844i	0.0631637	+	0.00545000i
$916$	3624.76	+	11155.9i	0.130748	+	0.402402i
$917$	14144.0	−	10276.2i	0.509352	−	0.370066i
$918$	−5113.15			−0.183833
$919$	7869.58	−	5717.59i	0.282474	−	0.205229i	−0.437522	−	0.899208i	$-0.644144\pi$
$919$	7869.58	−	5717.59i	0.282474	−	0.205229i	0.719996	+	0.693978i	$0.244144\pi$
$920$	−7916.09	+	18711.3i	−0.283680	+	0.670537i
$921$	2348.10	+	1705.99i	0.0840091	+	0.0610362i
$922$	−20270.4	−	14727.3i	−0.724047	−	0.526051i
$923$	−1686.94	+	5191.85i	−0.0601583	+	0.185148i
$924$	−2343.97			−0.0834534
$925$	25870.3	−	12694.5i	0.919578	−	0.451234i
$926$	20154.9			0.715259
$927$	−1999.36	+	6153.41i	−0.0708389	+	0.218020i
$928$	−8675.78	−	6303.32i	−0.306893	−	0.222971i
$929$	31969.5	+	23227.2i	1.12905	+	0.820301i	0.985556	−	0.169351i	$-0.0541671\pi$
$929$	31969.5	+	23227.2i	1.12905	+	0.820301i	0.143491	+	0.989652i	$0.454167\pi$
$930$	8800.84	−	5302.42i	0.310313	−	0.186960i
$931$	22490.2	−	16340.1i	0.791716	−	0.575215i
$932$	14441.4			0.507558
$933$	3714.20	−	2698.52i	0.130329	−	0.0946898i
$934$	−1660.83	−	5111.52i	−0.0581843	−	0.179073i
$935$	9719.83	−	22974.8i	0.339970	−	0.803591i
$936$	928.838	−	2858.67i	0.0324359	−	0.0998275i
$937$	10102.5	+	31092.3i	0.352225	+	1.08404i	0.957601	+	0.288097i	$0.0930226\pi$
$937$	10102.5	+	31092.3i	0.352225	+	1.08404i	−0.605376	+	0.795939i	$0.706977\pi$
$938$	−2269.99	−	6986.31i	−0.0790168	−	0.243189i
$939$	7401.21	−	22778.6i	0.257220	−	0.791641i
$940$	10354.6	−	24475.2i	0.359286	−	0.849248i
$941$	−3548.37	−	10920.7i	−0.122926	−	0.378328i	0.870591	−	0.492007i	$-0.163736\pi$
$941$	−3548.37	−	10920.7i	−0.122926	−	0.378328i	−0.993518	+	0.113679i	$0.963736\pi$
$942$	−3805.30	+	2764.71i	−0.131617	+	0.0956254i
$943$	−14459.7			−0.499334
$944$	308.094	−	223.843i	0.0106224	−	0.00771766i
$945$	1981.17	−	1193.63i	0.0681983	−	0.0410887i
$946$	11723.8	+	8517.81i	0.402931	+	0.292746i
$947$	−35096.3	−	25498.9i	−1.20430	−	0.874977i	−0.209602	−	0.977787i	$-0.567217\pi$
$947$	−35096.3	−	25498.9i	−1.20430	−	0.874977i	−0.994701	+	0.102810i	$0.967217\pi$
$948$	3023.67	−	9305.91i	0.103591	−	0.318821i
$949$	6018.89			0.205881
$950$	−19064.8	+	9355.06i	−0.651100	+	0.319493i
$951$	−15843.2			−0.540220
$952$	5820.76	−	17914.4i	0.198164	−	0.609885i
$953$	−18787.6	−	13650.0i	−0.638604	−	0.463973i	0.220766	−	0.975327i	$-0.429144\pi$
$953$	−18787.6	−	13650.0i	−0.638604	−	0.463973i	−0.859370	+	0.511354i	$0.829144\pi$
$954$	6521.53	+	4738.17i	0.221323	+	0.160801i
$955$	−17223.4	+	40711.0i	−0.583597	+	1.37945i
$956$	−4248.56	+	3086.76i	−0.143732	+	0.104428i
$957$	3626.66			0.122501
$958$	25231.5	−	18331.8i	0.850932	−	0.618238i
$959$	2213.81	+	6813.39i	0.0745438	+	0.229422i
$960$	−10364.6	−	894.299i	−0.348455	−	0.0300660i
$961$	400.764	−	1233.42i	0.0134525	−	0.0414026i
$962$	1832.79	+	5640.76i	0.0614258	+	0.189049i
$963$	−2627.76	−	8087.40i	−0.0879317	−	0.270626i
$964$	−10532.9	+	32416.8i	−0.351909	+	1.08307i
$965$	−40030.9	−	34714.4i	−1.33538	−	1.15803i
$966$	−994.335	−	3060.25i	−0.0331182	−	0.101927i
$967$	−13215.0	+	9601.23i	−0.439467	+	0.319291i	−0.785423	−	0.618959i	$-0.787555\pi$
$967$	−13215.0	+	9601.23i	−0.439467	+	0.319291i	0.345956	+	0.938251i	$0.387555\pi$
$968$	20568.4			0.682947
$969$	25868.8	−	18794.8i	0.857611	−	0.623091i
$970$	−11431.0	−	986.312i	−0.378380	−	0.0326480i
$971$	31605.5	+	22962.7i	1.04456	+	0.758918i	0.971171	−	0.238386i	$-0.0766182\pi$
$971$	31605.5	+	22962.7i	1.04456	+	0.758918i	0.0733900	+	0.997303i	$0.476618\pi$
$972$	979.309	+	711.509i	0.0323162	+	0.0234791i
$973$	−6805.38	+	20944.8i	−0.224225	+	0.690092i
$974$	29989.0			0.986559
$975$	−5470.88	−	951.178i	−0.179701	−	0.0312431i
$976$	−34.8646			−0.00114343
$977$	−12343.0	+	37987.8i	−0.404183	+	1.24395i	0.517392	+	0.855749i	$0.326903\pi$
$977$	−12343.0	+	37987.8i	−0.404183	+	1.24395i	−0.921575	+	0.388200i	$0.873097\pi$
$978$	16986.2	+	12341.2i	0.555377	+	0.403505i
$979$	−7040.66	−	5115.34i	−0.229847	−	0.166994i
$980$	−3580.19	−	15423.4i	−0.116699	−	0.502736i
$981$	−10720.3	+	7788.74i	−0.348902	+	0.253492i
$982$	14228.8			0.462383
$983$	18888.2	−	13723.1i	0.612858	−	0.445267i	−0.237562	−	0.971372i	$-0.576348\pi$
$983$	18888.2	−	13723.1i	0.612858	−	0.445267i	0.850420	+	0.526105i	$0.176348\pi$
$984$	−3752.36	−	11548.6i	−0.121566	−	0.374141i
$985$	4835.13	+	20829.6i	0.156406	+	0.673793i
$986$	−3455.95	+	10636.3i	−0.111623	+	0.343539i
$987$	3389.40	+	10431.5i	0.109307	+	0.336411i
$988$	2228.96	+	6860.04i	0.0717740	+	0.220898i
$989$	10144.9	−	31222.8i	0.326177	−	1.00387i
$990$	3065.32	−	1846.82i	0.0984063	−	0.0592888i
$991$	513.558	+	1580.57i	0.0164619	+	0.0506644i	0.958950	−	0.283575i	$-0.0915205\pi$
$991$	513.558	+	1580.57i	0.0164619	+	0.0506644i	−0.942488	+	0.334240i	$0.891521\pi$
$992$	−25902.6	+	18819.4i	−0.829041	+	0.602334i
$993$	−6247.79			−0.199665
$994$	−3970.36	+	2884.63i	−0.126692	+	0.0920473i
$995$	−27804.9	−	24112.1i	−0.885903	−	0.768246i
$996$	5100.33	+	3705.61i	0.162259	+	0.117888i
$997$	−3679.25	−	2673.13i	−0.116874	−	0.0849138i	0.527813	−	0.849361i	$-0.323012\pi$
$997$	−3679.25	−	2673.13i	−0.116874	−	0.0849138i	−0.644687	+	0.764447i	$0.723012\pi$
$998$	−5719.85	+	17603.9i	−0.181421	+	0.558358i
$999$	−6224.48			−0.197131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.4.g.b.46.5	yes	28
3.2	odd	2		225.4.h.a.46.3		28
25.6	even	5	inner	75.4.g.b.31.5	✓	28
25.9	even	10		1875.4.a.f.1.5		14
25.16	even	5		1875.4.a.g.1.10		14
75.56	odd	10		225.4.h.a.181.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.5	✓	28	25.6	even	5	inner
75.4.g.b.46.5	yes	28	1.1	even	1	trivial
225.4.h.a.46.3		28	3.2	odd	2
225.4.h.a.181.3		28	75.56	odd	10
1875.4.a.f.1.5		14	25.9	even	10
1875.4.a.g.1.10		14	25.16	even	5

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	75.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.536885 - 1.65236i) q^{2} +(-2.42705 - 1.76336i) q^{3} +(4.03008 + 2.92802i) q^{4} +(8.44668 + 7.32487i) q^{5} +(-4.21675 + 3.06365i) q^{6} +7.66213 q^{7} +(18.2465 - 13.2569i) q^{8} +(2.78115 + 8.55951i) q^{9} +(16.6382 - 10.0244i) q^{10} +(6.32569 - 19.4685i) q^{11} +(-4.61806 - 14.2129i) q^{12} +(-4.57589 - 14.0831i) q^{13} +(4.11368 - 12.6606i) q^{14} +(-7.58417 - 32.6723i) q^{15} +(0.205937 + 0.633807i) q^{16} +(88.1826 - 64.0684i) q^{17} +15.6366 q^{18} +(-79.1097 + 57.4766i) q^{19} +(12.5934 + 54.2518i) q^{20} +(-18.5964 - 13.5111i) q^{21} +(-28.7728 - 20.9047i) q^{22} +(-24.8979 + 76.6279i) q^{23} -67.6618 q^{24} +(17.6927 + 123.742i) q^{25} -25.7272 q^{26} +(8.34346 - 25.6785i) q^{27} +(30.8790 + 22.4349i) q^{28} +(-47.7769 - 34.7119i) q^{29} +(-58.0584 - 5.00949i) q^{30} +(-142.644 + 103.637i) q^{31} +181.589 q^{32} +(-49.6826 + 36.0966i) q^{33} +(-58.5204 - 180.107i) q^{34} +(64.7195 + 56.1241i) q^{35} +(-13.8542 + 42.6388i) q^{36} +(-71.2396 - 219.253i) q^{37} +(52.4993 + 161.576i) q^{38} +(-13.7277 + 42.2494i) q^{39} +(251.227 + 21.6768i) q^{40} +(55.4575 + 170.681i) q^{41} +(-32.3093 + 23.4741i) q^{42} -407.459 q^{43} +(82.4972 - 59.9377i) q^{44} +(-39.2058 + 92.6710i) q^{45} +(113.250 + 82.2808i) q^{46} +(-386.035 - 280.471i) q^{47} +(0.617810 - 1.90142i) q^{48} -284.292 q^{49} +(213.965 + 37.2003i) q^{50} -326.999 q^{51} +(22.7945 - 70.1544i) q^{52} +(417.069 + 303.018i) q^{53} +(-37.9508 - 27.5729i) q^{54} +(196.035 - 118.109i) q^{55} +(139.807 - 101.576i) q^{56} +293.355 q^{57} +(-83.0075 + 60.3085i) q^{58} +(-176.586 - 543.476i) q^{59} +(65.1005 - 153.879i) q^{60} +(-16.1665 + 49.7554i) q^{61} +(94.6624 + 291.341i) q^{62} +(21.3095 + 65.5840i) q^{63} +(95.8452 - 294.981i) q^{64} +(64.5060 - 152.473i) q^{65} +(32.9707 + 101.473i) q^{66} +(446.427 - 324.348i) q^{67} +542.976 q^{68} +(195.551 - 142.076i) q^{69} +(127.484 - 76.8079i) q^{70} +(-298.250 - 216.692i) q^{71} +(164.219 + 119.312i) q^{72} +(-125.605 + 386.571i) q^{73} -400.533 q^{74} +(175.259 - 331.525i) q^{75} -487.111 q^{76} +(48.4683 - 149.170i) q^{77} +(62.4412 + 45.3662i) q^{78} +(529.704 + 384.853i) q^{79} +(-2.90308 + 6.86202i) q^{80} +(-65.5304 + 47.6106i) q^{81} +311.801 q^{82} +(-341.288 + 247.960i) q^{83} +(-35.3841 - 108.901i) q^{84} +(1214.14 + 104.761i) q^{85} +(-218.759 + 673.271i) q^{86} +(54.7475 + 168.495i) q^{87} +(-142.669 - 439.091i) q^{88} +(131.375 - 404.330i) q^{89} +(132.077 + 114.536i) q^{90} +(-35.0610 - 107.907i) q^{91} +(-324.709 + 235.915i) q^{92} +528.953 q^{93} +(-670.697 + 487.290i) q^{94} +(-1089.22 - 93.9821i) q^{95} +(-440.727 - 320.207i) q^{96} +(-477.859 - 347.185i) q^{97} +(-152.632 + 469.753i) q^{98} +184.233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 21 q^{3} - 30 q^{4} - 15 q^{5} - 54 q^{7} - 63 q^{8} - 63 q^{9} + 165 q^{10} + 19 q^{11} - 60 q^{12} + 4 q^{13} - 24 q^{14} + 45 q^{15} - 66 q^{16} + 208 q^{17} + 42 q^{19} + 295 q^{20} + 3 q^{21}+ \cdots - 594 q^{99}+O(q^{100}) \) 28 * q - 21 * q^3 - 30 * q^4 - 15 * q^5 - 54 * q^7 - 63 * q^8 - 63 * q^9 + 165 * q^10 + 19 * q^11 - 60 * q^12 + 4 * q^13 - 24 * q^14 + 45 * q^15 - 66 * q^16 + 208 * q^17 + 42 * q^19 + 295 * q^20 + 3 * q^21 - 89 * q^22 + 32 * q^23 + 126 * q^24 + 95 * q^25 + 206 * q^26 - 189 * q^27 - 482 * q^28 - 716 * q^29 - 645 * q^30 + 637 * q^31 - 844 * q^32 + 42 * q^33 - 90 * q^34 + 430 * q^35 - 180 * q^36 + 216 * q^37 + 2314 * q^38 + 12 * q^39 - 500 * q^40 - 38 * q^41 + 933 * q^42 - 1392 * q^43 + 603 * q^44 + 270 * q^45 + 1622 * q^46 - 536 * q^47 - 198 * q^48 + 162 * q^49 - 2265 * q^50 - 876 * q^51 - 1922 * q^52 + 1672 * q^53 - 1000 * q^55 + 3000 * q^56 - 1104 * q^57 - 827 * q^58 + 973 * q^59 + 1365 * q^60 - 2712 * q^61 + 1057 * q^62 + 234 * q^63 + 4439 * q^64 - 4360 * q^65 + 1098 * q^66 + 2768 * q^67 - 1370 * q^68 + 396 * q^69 + 3230 * q^70 - 1074 * q^71 - 567 * q^72 - 1018 * q^73 - 1414 * q^74 + 765 * q^75 - 11408 * q^76 + 1607 * q^77 + 168 * q^78 - 1820 * q^79 - 1290 * q^80 - 567 * q^81 + 1772 * q^82 + 4045 * q^83 + 774 * q^84 + 1850 * q^85 - 3986 * q^86 + 1392 * q^87 + 2407 * q^88 + 4542 * q^89 - 180 * q^90 + 4412 * q^91 - 1089 * q^92 - 5334 * q^93 + 5137 * q^94 - 720 * q^95 + 1623 * q^96 - 5977 * q^97 - 10689 * q^98 - 594 * q^99

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