LMFDB - Embedded newform 45.4.e.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	45.16
Dual form			45.4.e.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18614 + 2.05446i) q^{2} +(-1.50000 + 4.97494i) q^{3} +(1.18614 + 2.05446i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-8.44158 - 8.98266i) q^{6} +(-3.68614 + 6.38458i) q^{7} -24.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} +O(q^{10})$	\(q+(-1.18614 + 2.05446i) q^{2} +(-1.50000 + 4.97494i) q^{3} +(1.18614 + 2.05446i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-8.44158 - 8.98266i) q^{6} +(-3.68614 + 6.38458i) q^{7} -24.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} +11.8614 q^{10} +(2.06930 - 3.58413i) q^{11} +(-12.0000 + 2.81929i) q^{12} +(39.4891 + 68.3972i) q^{13} +(-8.74456 - 15.1460i) q^{14} +(25.2921 - 5.94215i) q^{15} +(19.6970 - 34.1162i) q^{16} -33.3070 q^{17} +(57.3505 - 28.5223i) q^{18} +89.3070 q^{19} +(5.93070 - 10.2723i) q^{20} +(-26.2337 - 27.9152i) q^{21} +(4.90895 + 8.50256i) q^{22} +(99.7812 + 172.826i) q^{23} +(36.9090 - 122.413i) q^{24} +(-12.5000 + 21.6506i) q^{25} -187.359 q^{26} +(108.000 - 89.5489i) q^{27} -17.4891 q^{28} +(-25.2405 + 43.7179i) q^{29} +(-17.7921 + 59.0098i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-51.6970 - 89.5419i) q^{32} +(14.7269 + 15.6708i) q^{33} +(39.5068 - 68.4278i) q^{34} +36.8614 q^{35} +(3.97420 - 63.9282i) q^{36} -290.277 q^{37} +(-105.931 + 183.477i) q^{38} +(-399.505 + 93.8602i) q^{39} +(61.5149 + 106.547i) q^{40} +(26.6684 + 46.1911i) q^{41} +(88.4674 - 20.7846i) q^{42} +(149.194 - 258.412i) q^{43} +9.81791 q^{44} +(-8.37633 + 134.740i) q^{45} -473.418 q^{46} +(209.452 - 362.782i) q^{47} +(140.181 + 149.166i) q^{48} +(144.325 + 249.978i) q^{49} +(-29.6535 - 51.3614i) q^{50} +(49.9605 - 165.700i) q^{51} +(-93.6793 + 162.257i) q^{52} +399.228 q^{53} +(55.8710 + 328.099i) q^{54} -20.6930 q^{55} +(90.7011 - 157.099i) q^{56} +(-133.961 + 444.297i) q^{57} +(-59.8776 - 103.711i) q^{58} +(-49.1209 - 85.0799i) q^{59} +(42.2079 + 44.9133i) q^{60} +(341.797 - 592.011i) q^{61} -14.2337 q^{62} +(178.227 - 88.6382i) q^{63} +560.432 q^{64} +(197.446 - 341.986i) q^{65} +(-49.6631 + 11.6679i) q^{66} +(-112.750 - 195.289i) q^{67} +(-39.5068 - 68.4278i) q^{68} +(-1009.47 + 237.166i) q^{69} +(-43.7228 + 75.7301i) q^{70} +512.951 q^{71} +(553.634 + 367.239i) q^{72} -994.318 q^{73} +(344.310 - 596.362i) q^{74} +(-88.9605 - 94.6627i) q^{75} +(105.931 + 183.477i) q^{76} +(15.2554 + 26.4232i) q^{77} +(281.038 - 932.097i) q^{78} +(100.853 - 174.683i) q^{79} -196.970 q^{80} +(283.500 + 671.617i) q^{81} -126.530 q^{82} +(-553.822 + 959.247i) q^{83} +(26.2337 - 87.0073i) q^{84} +(83.2676 + 144.224i) q^{85} +(353.931 + 613.026i) q^{86} +(-179.633 - 191.147i) q^{87} +(-50.9171 + 88.1909i) q^{88} +372.269 q^{89} +(-266.882 - 177.029i) q^{90} -582.250 q^{91} +(-236.709 + 409.992i) q^{92} +(-30.3505 + 7.13058i) q^{93} +(496.880 + 860.622i) q^{94} +(-223.268 - 386.711i) q^{95} +(523.011 - 122.877i) q^{96} +(69.6156 - 120.578i) q^{97} -684.758 q^{98} +(-100.052 + 49.7590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 6 q^{3} - q^{4} - 10 q^{5} - 51 q^{6} - 9 q^{7} - 18 q^{8} - 90 q^{9}+O(q^{10}) $ 4 * q + q^2 - 6 * q^3 - q^4 - 10 * q^5 - 51 * q^6 - 9 * q^7 - 18 * q^8 - 90 * q^9	\( 4 q + q^{2} - 6 q^{3} - q^{4} - 10 q^{5} - 51 q^{6} - 9 q^{7} - 18 q^{8} - 90 q^{9} - 10 q^{10} + 37 q^{11} - 48 q^{12} + 112 q^{13} - 12 q^{14} + 15 q^{15} + 119 q^{16} + 154 q^{17} + 126 q^{18} + 70 q^{19} - 5 q^{20} - 36 q^{21} - 101 q^{22} + 267 q^{23} + 27 q^{24} - 50 q^{25} - 152 q^{26} + 432 q^{27} - 24 q^{28} - 325 q^{29} + 15 q^{30} + 12 q^{31} - 247 q^{32} - 303 q^{33} + 451 q^{34} + 90 q^{35} + 171 q^{36} - 1276 q^{37} - 395 q^{38} - 564 q^{39} + 45 q^{40} - 238 q^{41} + 216 q^{42} + 97 q^{43} - 202 q^{44} + 225 q^{45} - 492 q^{46} + 901 q^{47} - 525 q^{48} + 629 q^{49} + 25 q^{50} - 231 q^{51} - 76 q^{52} + 448 q^{53} + 999 q^{54} - 370 q^{55} + 156 q^{56} - 105 q^{57} + 806 q^{58} + 85 q^{59} + 255 q^{60} + 247 q^{61} + 12 q^{62} + 351 q^{63} + 1426 q^{64} + 560 q^{65} - 888 q^{66} + 606 q^{67} - 451 q^{68} - 1539 q^{69} - 60 q^{70} + 788 q^{71} + 405 q^{72} - 1622 q^{73} - 484 q^{74} + 75 q^{75} + 395 q^{76} + 84 q^{77} + 228 q^{78} + 840 q^{79} - 1190 q^{80} + 1134 q^{81} - 2218 q^{82} + 387 q^{83} + 36 q^{84} - 385 q^{85} + 1387 q^{86} + 2418 q^{87} + 411 q^{88} - 2130 q^{89} + 225 q^{90} - 1272 q^{91} - 246 q^{92} - 18 q^{93} - 632 q^{94} - 175 q^{95} + 24 q^{96} + 1031 q^{97} + 926 q^{98} - 90 q^{99}+O(q^{100}) \) 4 * q + q^2 - 6 * q^3 - q^4 - 10 * q^5 - 51 * q^6 - 9 * q^7 - 18 * q^8 - 90 * q^9 - 10 * q^10 + 37 * q^11 - 48 * q^12 + 112 * q^13 - 12 * q^14 + 15 * q^15 + 119 * q^16 + 154 * q^17 + 126 * q^18 + 70 * q^19 - 5 * q^20 - 36 * q^21 - 101 * q^22 + 267 * q^23 + 27 * q^24 - 50 * q^25 - 152 * q^26 + 432 * q^27 - 24 * q^28 - 325 * q^29 + 15 * q^30 + 12 * q^31 - 247 * q^32 - 303 * q^33 + 451 * q^34 + 90 * q^35 + 171 * q^36 - 1276 * q^37 - 395 * q^38 - 564 * q^39 + 45 * q^40 - 238 * q^41 + 216 * q^42 + 97 * q^43 - 202 * q^44 + 225 * q^45 - 492 * q^46 + 901 * q^47 - 525 * q^48 + 629 * q^49 + 25 * q^50 - 231 * q^51 - 76 * q^52 + 448 * q^53 + 999 * q^54 - 370 * q^55 + 156 * q^56 - 105 * q^57 + 806 * q^58 + 85 * q^59 + 255 * q^60 + 247 * q^61 + 12 * q^62 + 351 * q^63 + 1426 * q^64 + 560 * q^65 - 888 * q^66 + 606 * q^67 - 451 * q^68 - 1539 * q^69 - 60 * q^70 + 788 * q^71 + 405 * q^72 - 1622 * q^73 - 484 * q^74 + 75 * q^75 + 395 * q^76 + 84 * q^77 + 228 * q^78 + 840 * q^79 - 1190 * q^80 + 1134 * q^81 - 2218 * q^82 + 387 * q^83 + 36 * q^84 - 385 * q^85 + 1387 * q^86 + 2418 * q^87 + 411 * q^88 - 2130 * q^89 + 225 * q^90 - 1272 * q^91 - 246 * q^92 - 18 * q^93 - 632 * q^94 - 175 * q^95 + 24 * q^96 + 1031 * q^97 + 926 * q^98 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.18614	+	2.05446i	−0.419364	+	0.726360i	−0.995876	−	0.0907292i	$-0.971080\pi$
$2$	−1.18614	+	2.05446i	−0.419364	+	0.726360i	0.576512	+	0.817089i	$0.304414\pi$
$3$	−1.50000	+	4.97494i	−0.288675	+	0.957427i
$3$	−1.50000	+	4.97494i	−0.288675	+	0.957427i
$4$	1.18614	+	2.05446i	0.148268	+	0.256807i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	−8.44158	−	8.98266i	−0.574377	−	0.611193i
$7$	−3.68614	+	6.38458i	−0.199033	+	0.344735i	−0.948215	−	0.317629i	$-0.897113\pi$
$7$	−3.68614	+	6.38458i	−0.199033	+	0.344735i	0.749182	+	0.662364i	$0.230447\pi$
$8$	−24.6060			−1.08744
$9$	−22.5000	−	14.9248i	−0.833333	−	0.552771i
$10$	11.8614			0.375091
$11$	2.06930	−	3.58413i	0.0567197	−	0.0982414i	−0.836271	−	0.548316i	$-0.815269\pi$
$11$	2.06930	−	3.58413i	0.0567197	−	0.0982414i	0.892991	+	0.450074i	$0.148603\pi$
$12$	−12.0000	+	2.81929i	−0.288675	+	0.0678216i
$13$	39.4891	+	68.3972i	0.842486	+	1.45923i	0.887787	+	0.460254i	$0.152242\pi$
$13$	39.4891	+	68.3972i	0.842486	+	1.45923i	−0.0453014	+	0.998973i	$0.514425\pi$
$14$	−8.74456	−	15.1460i	−0.166934	−	0.289139i
$15$	25.2921	−	5.94215i	0.435360	−	0.102284i
$16$	19.6970	−	34.1162i	0.307766	−	0.533066i
$17$	−33.3070			−0.475185			−0.237592	−	0.971365i	$-0.576358\pi$
$17$	−33.3070			−0.475185			−0.237592	+	0.971365i	$0.576358\pi$
$18$	57.3505	−	28.5223i	0.750981	−	0.373488i
$19$	89.3070			1.07834			0.539169	−	0.842197i	$-0.318738\pi$
$19$	89.3070			1.07834			0.539169	+	0.842197i	$0.318738\pi$
$20$	5.93070	−	10.2723i	0.0663073	−	0.114848i
$21$	−26.2337	−	27.9152i	−0.272603	−	0.290076i
$22$	4.90895	+	8.50256i	0.0475724	+	0.0823978i
$23$	99.7812	+	172.826i	0.904601	+	1.56682i	0.821452	+	0.570278i	$0.193165\pi$
$23$	99.7812	+	172.826i	0.904601	+	1.56682i	0.0831494	+	0.996537i	$0.473502\pi$
$24$	36.9090	−	122.413i	0.313917	−	1.04114i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−187.359			−1.41323
$27$	108.000	−	89.5489i	0.769800	−	0.638285i
$28$	−17.4891			−0.118041
$29$	−25.2405	+	43.7179i	−0.161622	+	0.279938i	−0.935451	−	0.353457i	$-0.885006\pi$
$29$	−25.2405	+	43.7179i	−0.161622	+	0.279938i	0.773828	+	0.633395i	$0.218339\pi$
$30$	−17.7921	+	59.0098i	−0.108279	+	0.359122i
$31$	3.00000	+	5.19615i	0.0173812	+	0.0301050i	0.874585	−	0.484872i	$-0.161134\pi$
$31$	3.00000	+	5.19615i	0.0173812	+	0.0301050i	−0.857204	+	0.514977i	$0.827800\pi$
$32$	−51.6970	−	89.5419i	−0.285588	−	0.494654i
$33$	14.7269	+	15.6708i	0.0776854	+	0.0826648i
$34$	39.5068	−	68.4278i	0.199275	−	0.345155i
$35$	36.8614			0.178020
$36$	3.97420	−	63.9282i	0.0183991	−	0.295964i
$37$	−290.277			−1.28976			−0.644882	−	0.764282i	$-0.723094\pi$
$37$	−290.277			−1.28976			−0.644882	+	0.764282i	$0.723094\pi$
$38$	−105.931	+	183.477i	−0.452217	+	0.783262i
$39$	−399.505	+	93.8602i	−1.64031	+	0.385376i
$40$	61.5149	+	106.547i	0.243159	+	0.421164i
$41$	26.6684	+	46.1911i	0.101583	+	0.175947i	0.912337	−	0.409440i	$-0.134276\pi$
$41$	26.6684	+	46.1911i	0.101583	+	0.175947i	−0.810754	+	0.585387i	$0.800943\pi$
$42$	88.4674	−	20.7846i	0.325019	−	0.0763604i
$43$	149.194	−	258.412i	0.529114	−	0.916453i	−0.470309	−	0.882502i	$-0.655858\pi$
$43$	149.194	−	258.412i	0.529114	−	0.916453i	0.999424	−	0.0339510i	$-0.0108090\pi$
$44$	9.81791			0.0336388
$45$	−8.37633	+	134.740i	−0.0277482	+	0.446352i
$46$	−473.418			−1.51743
$47$	209.452	−	362.782i	0.650038	−	1.12590i	−0.333075	−	0.942900i	$-0.608086\pi$
$47$	209.452	−	362.782i	0.650038	−	1.12590i	0.983113	−	0.182998i	$-0.0585803\pi$
$48$	140.181	+	149.166i	0.421528	+	0.448546i
$49$	144.325	+	249.978i	0.420772	+	0.728798i
$50$	−29.6535	−	51.3614i	−0.0838728	−	0.145272i
$51$	49.9605	−	165.700i	0.137174	−	0.454955i
$52$	−93.6793	+	162.257i	−0.249827	+	0.432712i
$53$	399.228			1.03468			0.517342	−	0.855779i	$-0.326922\pi$
$53$	399.228			1.03468			0.517342	+	0.855779i	$0.326922\pi$
$54$	55.8710	+	328.099i	0.140798	+	0.826826i
$55$	−20.6930			−0.0507316
$56$	90.7011	−	157.099i	0.216436	−	0.374879i
$57$	−133.961	+	444.297i	−0.311290	+	1.03243i
$58$	−59.8776	−	103.711i	−0.135557	−	0.234792i
$59$	−49.1209	−	85.0799i	−0.108390	−	0.187737i	0.806728	−	0.590923i	$-0.201236\pi$
$59$	−49.1209	−	85.0799i	−0.108390	−	0.187737i	−0.915118	+	0.403186i	$0.867903\pi$
$60$	42.2079	+	44.9133i	0.0908169	+	0.0966380i
$61$	341.797	−	592.011i	0.717421	−	1.24261i	−0.244597	−	0.969625i	$-0.578656\pi$
$61$	341.797	−	592.011i	0.717421	−	1.24261i	0.962018	−	0.272985i	$-0.0880109\pi$
$62$	−14.2337			−0.0291561
$63$	178.227	−	88.6382i	0.356420	−	0.177260i
$64$	560.432			1.09459
$65$	197.446	−	341.986i	0.376771	−	0.652587i
$66$	−49.6631	+	11.6679i	−0.0926228	+	0.0217609i
$67$	−112.750	−	195.289i	−0.205591	−	0.356094i	0.744730	−	0.667366i	$-0.232578\pi$
$67$	−112.750	−	195.289i	−0.205591	−	0.356094i	−0.950321	+	0.311272i	$0.899245\pi$
$68$	−39.5068	−	68.4278i	−0.0704545	−	0.122031i
$69$	−1009.47	+	237.166i	−1.76125	+	0.413789i
$70$	−43.7228	+	75.7301i	−0.0746554	+	0.129307i
$71$	512.951			0.857410			0.428705	−	0.903445i	$-0.358970\pi$
$71$	512.951			0.857410			0.428705	+	0.903445i	$0.358970\pi$
$72$	553.634	+	367.239i	0.906200	+	0.601105i
$73$	−994.318			−1.59419			−0.797096	−	0.603852i	$-0.793632\pi$
$73$	−994.318			−1.59419			−0.797096	+	0.603852i	$0.793632\pi$
$74$	344.310	−	596.362i	0.540881	−	0.936833i
$75$	−88.9605	−	94.6627i	−0.136964	−	0.145743i
$76$	105.931	+	183.477i	0.159883	+	0.276925i
$77$	15.2554	+	26.4232i	0.0225782	+	0.0391065i
$78$	281.038	−	932.097i	0.407965	−	1.35307i
$79$	100.853	−	174.683i	0.143631	−	0.248777i	−0.785230	−	0.619204i	$-0.787455\pi$
$79$	100.853	−	174.683i	0.143631	−	0.248777i	0.928862	+	0.370427i	$0.120789\pi$
$80$	−196.970			−0.275274
$81$	283.500	+	671.617i	0.388889	+	0.921285i
$82$	−126.530			−0.170401
$83$	−553.822	+	959.247i	−0.732408	+	1.26857i	0.223444	+	0.974717i	$0.428270\pi$
$83$	−553.822	+	959.247i	−0.732408	+	1.26857i	−0.955851	+	0.293850i	$0.905063\pi$
$84$	26.2337	−	87.0073i	0.0340754	−	0.113015i
$85$	83.2676	+	144.224i	0.106255	+	0.184038i
$86$	353.931	+	613.026i	0.443783	+	0.768655i
$87$	−179.633	−	191.147i	−0.221364	−	0.235553i
$88$	−50.9171	+	88.1909i	−0.0616793	+	0.106832i
$89$	372.269			0.443375			0.221688	−	0.975118i	$-0.428843\pi$
$89$	372.269			0.443375			0.221688	+	0.975118i	$0.428843\pi$
$90$	−266.882	−	177.029i	−0.312576	−	0.207339i
$91$	−582.250			−0.670729
$92$	−236.709	+	409.992i	−0.268246	+	0.464616i
$93$	−30.3505	+	7.13058i	−0.0338409	+	0.00795061i
$94$	496.880	+	860.622i	0.545205	+	0.944323i
$95$	−223.268	−	386.711i	−0.241124	−	0.417639i
$96$	523.011	−	122.877i	0.556037	−	0.130636i
$97$	69.6156	−	120.578i	0.0728700	−	0.126215i	−0.827288	−	0.561778i	$-0.810118\pi$
$97$	69.6156	−	120.578i	0.0728700	−	0.126215i	0.900158	+	0.435563i	$0.143451\pi$
$98$	−684.758			−0.705826
$99$	−100.052	+	49.7590i	−0.101571	+	0.0505148i
$100$	−59.3070			−0.0593070
$101$	−985.872	+	1707.58i	−0.971267	+	1.68228i	−0.279525	+	0.960139i	$0.590177\pi$
$101$	−985.872	+	1707.58i	−0.971267	+	1.68228i	−0.691742	+	0.722145i	$0.743156\pi$
$102$	281.164	+	299.186i	0.272935	+	0.290429i
$103$	−906.353	−	1569.85i	−0.867045	−	1.50177i	−0.865002	−	0.501768i	$-0.832683\pi$
$103$	−906.353	−	1569.85i	−0.867045	−	1.50177i	−0.00204255	−	0.999998i	$-0.500650\pi$
$104$	−971.668	−	1682.98i	−0.916153	−	1.58682i
$105$	−55.2921	+	183.383i	−0.0513901	+	0.170442i
$106$	−473.541	+	820.197i	−0.433909	+	0.751552i
$107$	−259.217			−0.234201			−0.117100	−	0.993120i	$-0.537360\pi$
$107$	−259.217			−0.234201			−0.117100	+	0.993120i	$0.537360\pi$
$108$	312.077	+	115.664i	0.278052	+	0.103053i
$109$	775.556			0.681512			0.340756	−	0.940152i	$-0.389317\pi$
$109$	775.556			0.681512			0.340756	+	0.940152i	$0.389317\pi$
$110$	24.5448	−	42.5128i	0.0212750	−	0.0368494i
$111$	435.416	−	1444.11i	0.372323	−	1.23486i
$112$	145.212	+	251.514i	0.122511	+	0.212195i
$113$	107.628	+	186.417i	0.0895997	+	0.155191i	0.907342	−	0.420393i	$-0.138108\pi$
$113$	107.628	+	186.417i	0.0895997	+	0.155191i	−0.817742	+	0.575585i	$0.804775\pi$
$114$	−753.892	−	802.215i	−0.619373	−	0.659073i
$115$	498.906	−	864.131i	0.404550	−	0.700701i
$116$	−119.755			−0.0958534
$117$	132.310	−	2128.30i	0.104547	−	1.68172i
$118$	233.057			0.181819
$119$	122.774	−	212.652i	0.0945774	−	0.163813i
$120$	−622.337	+	146.212i	−0.473428	+	0.111228i
$121$	656.936	+	1137.85i	0.493566	+	0.854881i
$122$	810.840	+	1404.42i	0.601721	+	1.04221i
$123$	−269.800	+	63.3872i	−0.197781	+	0.0464669i
$124$	−7.11684	+	12.3267i	−0.00515412	+	0.00892721i
$125$	125.000			0.0894427
$126$	−29.2989	+	471.297i	−0.0207155	+	0.333226i
$127$	2424.76			1.69420			0.847098	−	0.531436i	$-0.178348\pi$
$127$	2424.76			1.69420			0.847098	+	0.531436i	$0.178348\pi$
$128$	−251.175	+	435.048i	−0.173445	+	0.300415i
$129$	1061.79	+	1129.85i	0.724694	+	0.771145i
$130$	468.397	+	811.287i	0.316008	+	0.547343i
$131$	−130.247	−	225.595i	−0.0868684	−	0.150461i	0.819317	−	0.573340i	$-0.194353\pi$
$131$	−130.247	−	225.595i	−0.0868684	−	0.150461i	−0.906186	+	0.422880i	$0.861019\pi$
$132$	−14.7269	+	48.8435i	−0.00971067	+	0.0322067i
$133$	−329.198	+	570.188i	−0.214625	+	0.371741i
$134$	534.949			0.344870
$135$	−657.758	−	243.782i	−0.419339	−	0.155418i
$136$	819.552			0.516735
$137$	202.319	−	350.427i	0.126170	−	0.218533i	−0.796020	−	0.605271i	$-0.793065\pi$
$137$	202.319	−	350.427i	0.126170	−	0.218533i	0.922190	+	0.386738i	$0.126398\pi$
$138$	710.127	−	2355.23i	0.438044	−	1.45283i
$139$	883.841	+	1530.86i	0.539327	+	0.934141i	0.998940	+	0.0460221i	$0.0146545\pi$
$139$	883.841	+	1530.86i	0.539327	+	0.934141i	−0.459614	+	0.888119i	$0.652012\pi$
$140$	43.7228	+	75.7301i	0.0263947	+	0.0457169i
$141$	1490.64	+	1586.19i	0.890316	+	0.947383i
$142$	−608.432	+	1053.84i	−0.359567	+	0.622788i
$143$	326.859			0.191142
$144$	−952.361	+	473.641i	−0.551135	+	0.274098i
$145$	252.405			0.144559
$146$	1179.40	−	2042.78i	0.668547	−	1.15796i
$147$	−1460.11	+	343.040i	−0.819237	+	0.192472i
$148$	−344.310	−	596.362i	−0.191230	−	0.331220i
$149$	−960.344	−	1663.36i	−0.528016	−	0.914551i	−0.999467	−	0.0326584i	$-0.989603\pi$
$149$	−960.344	−	1663.36i	−0.528016	−	0.914551i	0.471450	−	0.881893i	$-0.343731\pi$
$150$	300.000	−	70.4823i	0.163299	−	0.0383657i
$151$	1262.28	−	2186.33i	0.680284	−	1.17829i	−0.294611	−	0.955617i	$-0.595190\pi$
$151$	1262.28	−	2186.33i	0.680284	−	1.17829i	0.974894	−	0.222668i	$-0.0714767\pi$
$152$	−2197.49			−1.17263
$153$	749.408	+	497.101i	0.395987	+	0.262668i
$154$	−72.3804			−0.0378739
$155$	15.0000	−	25.9808i	0.00777309	−	0.0134634i
$156$	−666.701	−	709.435i	−0.342172	−	0.364104i
$157$	−971.350	−	1682.43i	−0.493772	−	0.855238i	0.506202	−	0.862415i	$-0.331049\pi$
$157$	−971.350	−	1682.43i	−0.493772	−	0.855238i	−0.999974	+	0.00717683i	$0.997716\pi$
$158$	239.252	+	414.397i	0.120468	+	0.208656i
$159$	−598.842	+	1986.13i	−0.298687	+	0.990634i
$160$	−258.485	+	447.709i	−0.127719	+	0.221216i
$161$	−1471.23			−0.720181
$162$	−1716.08	−	214.193i	−0.832270	−	0.103880i
$163$	−1051.21			−0.505134			−0.252567	−	0.967579i	$-0.581275\pi$
$163$	−1051.21			−0.505134			−0.252567	+	0.967579i	$0.581275\pi$
$164$	−63.2650	+	109.578i	−0.0301230	+	0.0521745i
$165$	31.0395	−	102.946i	0.0146450	−	0.0485718i
$166$	−1313.82	−	2275.60i	−0.614291	−	1.06398i
$167$	1408.22	+	2439.11i	0.652524	+	1.13020i	0.982508	+	0.186218i	$0.0596230\pi$
$167$	1408.22	+	2439.11i	0.652524	+	1.13020i	−0.329985	+	0.943986i	$0.607044\pi$
$168$	645.505	+	686.880i	0.296439	+	0.315440i
$169$	−2020.28	+	3499.23i	−0.919564	+	1.59273i
$170$	−395.068			−0.178237
$171$	−2009.41	−	1332.89i	−0.898616	−	0.596074i
$172$	707.861			0.313802
$173$	721.225	−	1249.20i	0.316958	−	0.548987i	−0.662894	−	0.748713i	$-0.730672\pi$
$173$	721.225	−	1249.20i	0.316958	−	0.548987i	0.979852	+	0.199726i	$0.0640052\pi$
$174$	605.772	−	142.321i	0.263928	−	0.0620075i
$175$	−92.1535	−	159.615i	−0.0398066	−	0.0689470i
$176$	−81.5179	−	141.193i	−0.0349128	−	0.0604707i
$177$	496.948	−	116.754i	0.211033	−	0.0495804i
$178$	−441.563	+	764.809i	−0.185936	+	0.322050i
$179$	1534.89			0.640912			0.320456	−	0.947263i	$-0.396164\pi$
$179$	1534.89			0.640912			0.320456	+	0.947263i	$0.396164\pi$
$180$	−286.753	+	142.612i	−0.118740	+	0.0590536i
$181$	−3650.43			−1.49908			−0.749542	−	0.661956i	$-0.769726\pi$
$181$	−3650.43			−1.49908			−0.749542	+	0.661956i	$0.769726\pi$
$182$	690.630	−	1196.21i	0.281280	−	0.487191i
$183$	2432.52	+	2588.44i	0.982606	+	1.04559i
$184$	−2455.21	−	4252.56i	−0.983700	−	1.70382i
$185$	725.693	+	1256.94i	0.288400	+	0.499524i
$186$	21.3505	−	70.8117i	0.00841665	−	0.0279149i
$187$	−68.9221	+	119.377i	−0.0269523	+	0.0466828i
$188$	993.760			0.385518
$189$	173.629	+	1019.62i	0.0668235	+	0.392417i
$190$	1059.31			0.404475
$191$	−678.644	+	1175.45i	−0.257094	+	0.445300i	−0.965462	−	0.260543i	$-0.916098\pi$
$191$	−678.644	+	1175.45i	−0.257094	+	0.445300i	0.708368	+	0.705843i	$0.249432\pi$
$192$	−840.648	+	2788.11i	−0.315982	+	1.04799i
$193$	901.520	+	1561.48i	0.336232	+	0.582371i	0.983721	−	0.179704i	$-0.0575139\pi$
$193$	901.520	+	1561.48i	0.336232	+	0.582371i	−0.647488	+	0.762075i	$0.724181\pi$
$194$	165.148	+	286.044i	0.0611181	+	0.105860i
$195$	1405.19	+	1495.26i	0.516040	+	0.549116i
$196$	−342.379	+	593.018i	−0.124774	+	0.216114i
$197$	−263.403			−0.0952624			−0.0476312	−	0.998865i	$-0.515167\pi$
$197$	−263.403			−0.0952624			−0.0476312	+	0.998865i	$0.515167\pi$
$198$	16.4476	−	264.573i	0.00590344	−	0.0949614i
$199$	492.853			0.175565			0.0877824	−	0.996140i	$-0.472022\pi$
$199$	492.853			0.175565			0.0877824	+	0.996140i	$0.472022\pi$
$200$	307.575	−	532.735i	0.108744	−	0.188350i
$201$	1140.67	−	267.991i	0.400283	−	0.0940429i
$202$	−2338.77	−	4050.86i	−0.814629	−	1.41098i
$203$	−186.080	−	322.300i	−0.0643363	−	0.111434i
$204$	399.684	−	93.9022i	0.137174	−	0.0322278i
$205$	133.342	−	230.955i	0.0454294	−	0.0786860i
$206$	4300.25			1.45443
$207$	334.320	−	5377.80i	0.112255	−	1.80572i
$208$	3111.27			1.03715
$209$	184.803	−	320.088i	0.0611630	−	0.105937i
$210$	−311.168	−	331.113i	−0.102251	−	0.108805i
$211$	500.772	+	867.362i	0.163387	+	0.282994i	0.936081	−	0.351784i	$-0.114425\pi$
$211$	500.772	+	867.362i	0.163387	+	0.282994i	−0.772695	+	0.634778i	$0.781092\pi$
$212$	473.541	+	820.197i	0.153410	+	0.265714i
$213$	−769.426	+	2551.90i	−0.247513	+	0.820907i
$214$	307.468	−	532.551i	0.0982155	−	0.170114i
$215$	−1491.94			−0.473254
$216$	−2657.44	+	2203.44i	−0.837112	+	0.694097i
$217$	−44.2337			−0.0138377
$218$	−919.919	+	1593.35i	−0.285802	+	0.495023i
$219$	1491.48	−	4946.67i	0.460204	−	1.52632i
$220$	−24.5448	−	42.5128i	−0.00752185	−	0.0130282i
$221$	−1315.27	−	2278.11i	−0.400336	−	0.693403i
$222$	2450.40	+	2607.46i	0.740810	+	0.788294i
$223$	−280.574	+	485.969i	−0.0842540	+	0.145932i	−0.905073	−	0.425256i	$-0.860184\pi$
$223$	−280.574	+	485.969i	−0.0842540	+	0.145932i	0.820819	+	0.571188i	$0.193517\pi$
$224$	762.250			0.227366
$225$	604.382	−	300.579i	0.179076	−	0.0890605i
$226$	−510.646			−0.150300
$227$	1953.23	−	3383.09i	0.571103	−	0.989180i	−0.425350	−	0.905029i	$-0.639849\pi$
$227$	1953.23	−	3383.09i	0.571103	−	0.989180i	0.996453	−	0.0841506i	$-0.0268177\pi$
$228$	−1071.68	+	251.783i	−0.311290	+	0.0731347i
$229$	−1498.45	−	2595.40i	−0.432405	−	0.748947i	0.564675	−	0.825313i	$-0.309001\pi$
$229$	−1498.45	−	2595.40i	−0.432405	−	0.748947i	−0.997080	+	0.0763664i	$0.975668\pi$
$230$	1183.55	+	2049.96i	0.339307	+	0.587698i
$231$	−154.337	+	36.2601i	−0.0439594	+	0.0103279i
$232$	621.067	−	1075.72i	0.175755	−	0.304416i
$233$	4194.30			1.17930			0.589651	−	0.807658i	$-0.299265\pi$
$233$	4194.30			1.17930			0.589651	+	0.807658i	$0.299265\pi$
$234$	4215.57	+	2796.29i	1.17769	+	0.781194i
$235$	−2094.52			−0.581412
$236$	116.529	−	201.833i	0.0321414	−	0.0556705i
$237$	717.757	+	763.763i	0.196723	+	0.209332i
$238$	291.255	+	504.469i	0.0793247	+	0.137394i
$239$	83.2362	+	144.169i	0.0225276	+	0.0390190i	0.877069	−	0.480364i	$-0.159495\pi$
$239$	83.2362	+	144.169i	0.0225276	+	0.0390190i	−0.854542	+	0.519383i	$0.826162\pi$
$240$	295.455	−	979.914i	0.0794648	−	0.263555i
$241$	−307.272	+	532.210i	−0.0821291	+	0.142252i	−0.904164	−	0.427185i	$-0.859505\pi$
$241$	−307.272	+	532.210i	−0.0821291	+	0.142252i	0.822035	+	0.569437i	$0.192839\pi$
$242$	−3116.87			−0.827935
$243$	−3766.50	+	402.970i	−0.994325	+	0.106381i
$244$	1621.68			0.425481
$245$	721.624	−	1249.89i	0.188175	−	0.325928i
$246$	189.795	−	629.479i	0.0491906	−	0.163147i
$247$	3526.66	+	6108.35i	0.908485	+	1.57354i
$248$	−73.8179	−	127.856i	−0.0189010	−	0.0327374i
$249$	−3941.46	−	4194.10i	−1.00313	−	1.06743i
$250$	−148.268	+	256.807i	−0.0375091	+	0.0649676i
$251$	−6136.16			−1.54307			−0.771536	−	0.636185i	$-0.780511\pi$
$251$	−6136.16			−1.54307			−0.771536	+	0.636185i	$0.780511\pi$
$252$	393.505	+	261.022i	0.0983671	+	0.0652493i
$253$	825.908			0.205235
$254$	−2876.11	+	4981.57i	−0.710485	+	1.23060i
$255$	−842.405	+	197.915i	−0.206876	+	0.0486037i
$256$	1645.87	+	2850.73i	0.401824	+	0.695979i
$257$	−2725.20	−	4720.19i	−0.661453	−	1.14567i	−0.980234	−	0.197842i	$-0.936607\pi$
$257$	−2725.20	−	4720.19i	−0.661453	−	1.14567i	0.318781	−	0.947828i	$-0.396727\pi$
$258$	−3580.66	+	841.244i	−0.864040	+	0.202998i
$259$	1070.00	−	1853.30i	0.256705	−	0.444627i
$260$	936.793			0.223452
$261$	1220.39	−	606.942i	0.289427	−	0.143942i
$262$	617.967			0.145718
$263$	391.620	−	678.305i	0.0918186	−	0.159035i	−0.816458	−	0.577405i	$-0.804065\pi$
$263$	391.620	−	678.305i	0.0918186	−	0.159035i	0.908276	+	0.418371i	$0.137399\pi$
$264$	−362.369	−	385.596i	−0.0844782	−	0.0898930i
$265$	−998.070	−	1728.71i	−0.231362	−	0.400731i
$266$	−780.951	−	1352.65i	−0.180012	−	0.311790i
$267$	−558.403	+	1852.01i	−0.127991	+	0.424499i
$268$	267.474	−	463.279i	0.0609649	−	0.105594i
$269$	141.019			0.0319632			0.0159816	−	0.999872i	$-0.494913\pi$
$269$	141.019			0.0319632			0.0159816	+	0.999872i	$0.494913\pi$
$270$	1281.03	−	1062.18i	0.288745	−	0.239415i
$271$	6375.83			1.42917			0.714583	−	0.699551i	$-0.246616\pi$
$271$	6375.83			1.42917			0.714583	+	0.699551i	$0.246616\pi$
$272$	−656.049	+	1136.31i	−0.146246	+	0.253305i
$273$	873.375	−	2896.66i	0.193623	−	0.642174i
$274$	479.958	+	831.312i	0.105822	+	0.183290i
$275$	51.7324	+	89.6032i	0.0113439	+	0.0196483i
$276$	−1684.62	−	1792.60i	−0.367400	−	0.390949i
$277$	−3411.59	+	5909.04i	−0.740008	+	1.28173i	0.212482	+	0.977165i	$0.431845\pi$
$277$	−3411.59	+	5909.04i	−0.740008	+	1.28173i	−0.952491	+	0.304567i	$0.901488\pi$
$278$	−4193.44			−0.904697
$279$	10.0516	−	161.688i	0.00215689	−	0.0346953i
$280$	−907.011			−0.193587
$281$	−294.846	+	510.689i	−0.0625945	+	0.108417i	−0.895624	−	0.444811i	$-0.853271\pi$
$281$	−294.846	+	510.689i	−0.0625945	+	0.108417i	0.833030	+	0.553228i	$0.186604\pi$
$282$	−5026.86	+	1181.02i	−1.06151	+	0.249392i
$283$	2988.01	+	5175.39i	0.627629	+	1.08709i	0.988026	+	0.154286i	$0.0493078\pi$
$283$	2988.01	+	5175.39i	0.627629	+	1.08709i	−0.360397	+	0.932799i	$0.617359\pi$
$284$	608.432	+	1053.84i	0.127126	+	0.220189i
$285$	2258.76	−	530.676i	0.469465	−	0.110297i
$286$	−387.701	+	671.517i	−0.0801581	+	0.138838i
$287$	−393.214			−0.0808736
$288$	−173.212	+	2786.26i	−0.0354397	+	0.570076i
$289$	−3803.64			−0.774199
$290$	−299.388	+	518.555i	−0.0606230	+	0.105002i
$291$	495.443	+	527.200i	0.0998055	+	0.106203i
$292$	−1179.40	−	2042.78i	−0.236367	−	0.409400i
$293$	−4028.74	−	6977.99i	−0.803282	−	1.39133i	−0.917445	−	0.397864i	$-0.869752\pi$
$293$	−4028.74	−	6977.99i	−0.803282	−	1.39133i	0.114162	−	0.993462i	$-0.463582\pi$
$294$	1027.14	−	3406.63i	0.203755	−	0.675777i
$295$	−245.604	+	425.399i	−0.0484734	+	0.0839583i
$296$	7142.55			1.40254
$297$	−97.4705	−	572.389i	−0.0190431	−	0.111830i
$298$	4556.41			0.885724
$299$	−7880.55	+	13649.5i	−1.52423	+	2.64004i
$300$	88.9605	−	295.049i	0.0171205	−	0.0567822i
$301$	1099.90	+	1905.09i	0.210622	+	0.364808i
$302$	2994.48	+	5186.59i	0.570573	+	0.988261i
$303$	−7016.30	−	7466.02i	−1.33028	−	1.41555i
$304$	1759.08	−	3046.82i	0.331876	−	0.574826i
$305$	−3417.97			−0.641681
$306$	−1910.18	+	949.994i	−0.356855	+	0.177476i
$307$	−4546.58			−0.845235			−0.422618	−	0.906308i	$-0.638889\pi$
$307$	−4546.58			−0.845235			−0.422618	+	0.906308i	$0.638889\pi$
$308$	−36.1902	+	62.6832i	−0.00669522	+	0.0115965i
$309$	9169.43	−	2154.28i	1.68813	−	0.396610i
$310$	35.5842	+	61.6337i	0.00651951	+	0.0112921i
$311$	2101.40	+	3639.73i	0.383149	+	0.663633i	0.991510	−	0.130027i	$-0.0415063\pi$
$311$	2101.40	+	3639.73i	0.383149	+	0.663633i	−0.608362	+	0.793660i	$0.708173\pi$
$312$	9830.22	−	2309.52i	1.78374	−	0.419073i
$313$	3486.64	−	6039.04i	0.629637	−	1.09056i	−0.357987	−	0.933727i	$-0.616537\pi$
$313$	3486.64	−	6039.04i	0.629637	−	1.09056i	0.987624	−	0.156838i	$-0.0501299\pi$
$314$	4608.63			0.828281
$315$	−829.382	−	550.150i	−0.148350	−	0.0984045i
$316$	478.505			0.0851835
$317$	3680.02	−	6373.97i	0.652020	−	1.12933i	−0.330612	−	0.943767i	$-0.607255\pi$
$317$	3680.02	−	6373.97i	0.652020	−	1.12933i	0.982632	−	0.185565i	$-0.0594114\pi$
$318$	−3370.12	−	3586.13i	−0.594298	−	0.632391i
$319$	104.460	+	180.930i	0.0183343	+	0.0317560i
$320$	−1401.08	−	2426.74i	−0.244759	−	0.423934i
$321$	388.826	−	1289.59i	0.0676080	−	0.224230i
$322$	1745.09	−	3022.58i	0.302018	−	0.523111i
$323$	−2974.55			−0.512410
$324$	−1043.54	+	1379.07i	−0.178933	+	0.236466i
$325$	−1974.46			−0.336994
$326$	1246.88	−	2159.66i	0.211835	−	0.366909i
$327$	−1163.33	+	3858.34i	−0.196736	+	0.652498i
$328$	−656.203	−	1136.58i	−0.110466	−	0.191332i
$329$	1544.14	+	2674.53i	0.258758	+	0.448182i
$330$	174.681	+	185.878i	0.0291391	+	0.0310068i
$331$	3417.06	−	5918.52i	0.567428	−	0.982814i	−0.429391	−	0.903119i	$-0.641272\pi$
$331$	3417.06	−	5918.52i	0.567428	−	0.982814i	0.996819	−	0.0796957i	$-0.0253949\pi$
$332$	−2627.64			−0.434369
$333$	6531.24	+	4332.33i	1.07480	+	0.712944i
$334$	−6681.39			−1.09458
$335$	−563.749	+	976.443i	−0.0919430	+	0.159250i
$336$	−1469.09	+	345.149i	−0.238528	+	0.0560399i
$337$	3464.24	+	6000.24i	0.559968	+	0.969893i	0.997498	+	0.0706891i	$0.0225198\pi$
$337$	3464.24	+	6000.24i	0.559968	+	0.969893i	−0.437531	+	0.899204i	$0.644147\pi$
$338$	−4792.68	−	8301.16i	−0.771264	−	1.33587i
$339$	−1088.85	+	255.816i	−0.174449	+	0.0409853i
$340$	−197.534	+	342.139i	−0.0315082	+	0.0545738i
$341$	24.8316			0.00394341
$342$	5121.81	−	2547.24i	0.809812	−	0.402746i
$343$	−4656.70			−0.733055
$344$	−3671.07	+	6358.48i	−0.575380	+	0.996588i
$345$	3550.64	+	3778.22i	0.554087	+	0.589602i
$346$	1710.95	+	2963.45i	0.265842	+	0.460451i
$347$	3770.30	+	6530.35i	0.583286	+	1.01028i	0.995087	+	0.0990071i	$0.0315667\pi$
$347$	3770.30	+	6530.35i	0.583286	+	1.01028i	−0.411801	+	0.911274i	$0.635100\pi$
$348$	179.633	−	595.775i	0.0276705	−	0.0917726i
$349$	922.084	−	1597.10i	0.141427	−	0.244959i	−0.786607	−	0.617454i	$-0.788164\pi$
$349$	922.084	−	1597.10i	0.141427	−	0.244959i	0.928034	+	0.372495i	$0.121498\pi$
$350$	437.228			0.0667738
$351$	10389.7	+	3850.69i	1.57995	+	0.585568i
$352$	−427.906			−0.0647939
$353$	3548.74	−	6146.61i	0.535073	−	0.926773i	−0.464087	−	0.885789i	$-0.653618\pi$
$353$	3548.74	−	6146.61i	0.535073	−	0.926773i	0.999160	−	0.0409833i	$-0.0130490\pi$
$354$	−349.586	+	1159.44i	−0.0524866	+	0.174079i
$355$	−1282.38	−	2221.14i	−0.191723	−	0.332073i
$356$	441.563	+	764.809i	0.0657382	+	0.113862i
$357$	873.766	+	929.772i	0.129537	+	0.137840i
$358$	−1820.60	+	3153.37i	−0.268775	+	0.465532i
$359$	7709.65			1.13342			0.566712	−	0.823916i	$-0.308215\pi$
$359$	7709.65			1.13342			0.566712	+	0.823916i	$0.308215\pi$
$360$	206.108	−	3315.41i	0.0301745	−	0.485381i
$361$	1116.75			0.162815
$362$	4329.92	−	7499.65i	0.628662	−	1.08888i
$363$	−6646.12	+	1561.45i	−0.960966	+	0.225770i
$364$	−690.630	−	1196.21i	−0.0994474	−	0.172248i
$365$	2485.79	+	4305.52i	0.356472	+	0.617428i
$366$	−8203.14	+	1927.25i	−1.17154	+	0.275244i
$367$	2628.19	−	4552.17i	0.373816	−	0.647469i	−0.616333	−	0.787486i	$-0.711382\pi$
$367$	2628.19	−	4552.17i	0.373816	−	0.647469i	0.990149	+	0.140017i	$0.0447157\pi$
$368$	7861.57			1.11362
$369$	89.3535	−	1437.32i	0.0126058	−	0.202775i
$370$	−3443.10			−0.483778
$371$	−1471.61	+	2548.91i	−0.205936	+	0.356692i
$372$	−50.6495	−	53.8960i	−0.00705928	−	0.00751176i
$373$	−498.227	−	862.955i	−0.0691615	−	0.119791i	0.829371	−	0.558698i	$-0.188699\pi$
$373$	−498.227	−	862.955i	−0.0691615	−	0.119791i	−0.898532	+	0.438907i	$0.855366\pi$
$374$	−163.503	−	283.195i	−0.0226057	−	0.0391542i
$375$	−187.500	+	621.867i	−0.0258199	+	0.0856349i
$376$	−5153.78	+	8926.61i	−0.706878	+	1.22435i
$377$	−3986.90			−0.544658
$378$	−2300.72	−	852.705i	−0.313059	−	0.116028i
$379$	−2735.20			−0.370707			−0.185354	−	0.982672i	$-0.559343\pi$
$379$	−2735.20			−0.370707			−0.185354	+	0.982672i	$0.559343\pi$
$380$	529.654	−	917.387i	0.0715017	−	0.123845i
$381$	−3637.14	+	12063.0i	−0.489072	+	1.62207i
$382$	−1609.93	−	2788.49i	−0.215632	−	0.373485i
$383$	4469.73	+	7741.80i	0.596325	+	1.03287i	0.993358	+	0.115062i	$0.0367065\pi$
$383$	4469.73	+	7741.80i	0.596325	+	1.03287i	−0.397033	+	0.917804i	$0.629960\pi$
$384$	−1787.57	−	1902.15i	−0.237557	−	0.252783i
$385$	76.2772	−	132.116i	0.0100973	−	0.0174890i
$386$	−4277.32			−0.564015
$387$	−7213.62	+	3587.57i	−0.947517	+	0.471232i
$388$	330.295			0.0432170
$389$	5566.93	−	9642.21i	0.725590	−	1.25676i	−0.233140	−	0.972443i	$-0.574900\pi$
$389$	5566.93	−	9642.21i	0.725590	−	1.25676i	0.958731	−	0.284316i	$-0.0917666\pi$
$390$	−4738.70	+	1113.31i	−0.615264	+	0.144551i
$391$	−3323.42	−	5756.33i	−0.429853	−	0.744527i
$392$	−3551.25	−	6150.95i	−0.457564	−	0.792525i
$393$	1317.69	−	309.580i	0.169132	−	0.0397360i
$394$	312.433	−	541.150i	0.0399496	−	0.0691948i
$395$	−1008.53			−0.128468
$396$	−220.903	−	146.530i	−0.0280323	−	0.0185945i
$397$	−9479.40			−1.19838			−0.599191	−	0.800606i	$-0.704511\pi$
$397$	−9479.40			−1.19838			−0.599191	+	0.800606i	$0.704511\pi$
$398$	−584.593	+	1012.54i	−0.0736256	+	0.127523i
$399$	−2342.85	−	2493.02i	−0.293958	−	0.312800i
$400$	492.425	+	852.906i	0.0615532	+	0.106613i
$401$	−4713.80	−	8164.54i	−0.587022	−	1.01675i	−0.994620	−	0.103591i	$-0.966967\pi$
$401$	−4713.80	−	8164.54i	−0.587022	−	1.01675i	0.407598	−	0.913162i	$-0.366367\pi$
$402$	−802.423	+	2661.34i	−0.0995553	+	0.330188i
$403$	−236.935	+	410.383i	−0.0292868	+	0.0507261i
$404$	−4677.53			−0.576029
$405$	2199.43	−	2906.63i	0.269854	−	0.356622i
$406$	882.869			0.107921
$407$	−600.670	+	1040.39i	−0.0731550	+	0.126708i
$408$	−1229.33	+	4077.22i	−0.149169	+	0.494736i
$409$	−204.093	−	353.500i	−0.0246742	−	0.0427370i	0.853425	−	0.521216i	$-0.174522\pi$
$409$	−204.093	−	353.500i	−0.0246742	−	0.0427370i	−0.878099	+	0.478479i	$0.841188\pi$
$410$	316.325	+	547.891i	0.0381029	+	0.0659962i
$411$	1439.87	+	1532.17i	0.172807	+	0.183884i
$412$	2150.12	−	3724.12i	0.257109	−	0.445326i
$413$	724.266			0.0862925
$414$	10651.9	+	7065.68i	1.26452	+	0.838790i
$415$	5538.22			0.655085
$416$	4082.94	−	7071.86i	0.481208	−	0.833477i
$417$	−8941.68	+	2100.77i	−1.05006	+	0.246703i
$418$	438.404	+	759.338i	0.0512992	+	0.0888527i
$419$	−4406.94	−	7633.05i	−0.513826	−	0.889973i	−0.999871	−	0.0160393i	$-0.994894\pi$
$419$	−4406.94	−	7633.05i	−0.513826	−	0.889973i	0.486045	−	0.873934i	$-0.338439\pi$
$420$	−442.337	+	103.923i	−0.0513901	+	0.0120736i
$421$	1174.68	−	2034.61i	0.135987	−	0.235537i	−0.789987	−	0.613124i	$-0.789913\pi$
$421$	1174.68	−	2034.61i	0.135987	−	0.235537i	0.925974	+	0.377587i	$0.123246\pi$
$422$	−2375.94			−0.274074
$423$	−10127.1	+	5036.56i	−1.16406	+	0.578927i
$424$	−9823.40			−1.12516
$425$	416.338	−	721.118i	0.0475185	−	0.0823044i
$426$	−4330.12	−	4607.66i	−0.492476	−	0.524042i
$427$	2519.83	+	4364.47i	0.285581	+	0.494640i
$428$	−307.468	−	532.551i	−0.0347244	−	0.0601444i
$429$	−490.288	+	1626.10i	−0.0551780	+	0.183005i
$430$	1769.65	−	3065.13i	0.198466	−	0.343753i
$431$	4481.16			0.500812			0.250406	−	0.968141i	$-0.419436\pi$
$431$	4481.16			0.500812			0.250406	+	0.968141i	$0.419436\pi$
$432$	−927.792	−	5448.40i	−0.103330	−	0.606797i
$433$	3422.69			0.379871			0.189935	−	0.981797i	$-0.439172\pi$
$433$	3422.69			0.379871			0.189935	+	0.981797i	$0.439172\pi$
$434$	52.4674	−	90.8762i	0.00580303	−	0.0100511i
$435$	−378.608	+	1255.70i	−0.0417307	+	0.138405i
$436$	919.919	+	1593.35i	0.101046	+	0.175017i
$437$	8911.17	+	15434.6i	0.975467	+	1.68956i
$438$	8393.61	+	8931.62i	0.915667	+	0.974359i
$439$	4064.59	−	7040.07i	0.441896	−	0.765386i	−0.555934	−	0.831226i	$-0.687639\pi$
$439$	4064.59	−	7040.07i	0.441896	−	0.765386i	0.997830	+	0.0658402i	$0.0209728\pi$
$440$	509.171			0.0551676
$441$	483.565	−	7778.52i	0.0522152	−	0.839922i
$442$	6240.36			0.671547
$443$	−1175.39	+	2035.83i	−0.126060	+	0.218342i	−0.922147	−	0.386840i	$-0.873566\pi$
$443$	−1175.39	+	2035.83i	−0.126060	+	0.218342i	0.796087	+	0.605182i	$0.206900\pi$
$444$	3483.33	−	818.376i	0.372323	−	0.0874739i
$445$	−930.672	−	1611.97i	−0.0991417	−	0.171718i
$446$	−665.601	−	1152.86i	−0.0706662	−	0.122397i
$447$	9715.65	−	2282.60i	1.02804	−	0.241529i
$448$	−2065.83	+	3578.12i	−0.217860	+	0.377345i
$449$	4760.99			0.500412			0.250206	−	0.968193i	$-0.419502\pi$
$449$	4760.99			0.500412			0.250206	+	0.968193i	$0.419502\pi$
$450$	−99.3551	+	1598.20i	−0.0104081	+	0.167422i
$451$	220.740			0.0230471
$452$	−255.323	+	442.233i	−0.0265695	+	0.0460196i
$453$	8983.44	+	9559.26i	0.931742	+	0.991464i
$454$	4633.61	+	8025.65i	0.479000	+	0.829653i
$455$	1455.62	+	2521.22i	0.149980	+	0.259772i
$456$	3296.23	−	10932.4i	0.338509	−	1.12271i
$457$	−1114.54	+	1930.44i	−0.114083	+	0.197598i	−0.917413	−	0.397937i	$-0.869726\pi$
$457$	−1114.54	+	1930.44i	−0.114083	+	0.197598i	0.803330	+	0.595535i	$0.203060\pi$
$458$	7109.51			0.725340
$459$	−3597.16	+	2982.61i	−0.365797	+	0.303303i
$460$	2367.09			0.239927
$461$	−2868.31	+	4968.06i	−0.289784	+	0.501921i	−0.973758	−	0.227585i	$-0.926917\pi$
$461$	−2868.31	+	4968.06i	−0.289784	+	0.501921i	0.683974	+	0.729507i	$0.260250\pi$
$462$	108.571	−	360.088i	0.0109332	−	0.0362615i
$463$	1801.99	+	3121.13i	0.180876	+	0.313286i	0.942179	−	0.335110i	$-0.108773\pi$
$463$	1801.99	+	3121.13i	0.180876	+	0.313286i	−0.761303	+	0.648396i	$0.775440\pi$
$464$	994.326	+	1722.22i	0.0994836	+	0.172311i
$465$	106.753	+	113.595i	0.0106463	+	0.0113287i
$466$	−4975.03	+	8617.00i	−0.494557	+	0.856598i
$467$	−3780.37			−0.374593			−0.187296	−	0.982303i	$-0.559972\pi$
$467$	−3780.37			−0.374593			−0.187296	+	0.982303i	$0.559972\pi$
$468$	4529.44	−	2252.64i	0.447380	−	0.222497i
$469$	1662.45			0.163677
$470$	2484.40	−	4303.11i	0.243823	−	0.422314i
$471$	9827.00	−	2308.76i	0.961368	−	0.225865i
$472$	1208.67	+	2093.47i	0.117867	+	0.204152i
$473$	−617.454	−	1069.46i	−0.0600224	−	0.103962i
$474$	−2420.48	+	568.670i	−0.234549	+	0.0551052i
$475$	−1116.34	+	1933.55i	−0.107834	+	0.186774i
$476$	582.511			0.0560911
$477$	−8982.63	−	5958.40i	−0.862236	−	0.571943i
$478$	−394.920			−0.0377891
$479$	7230.58	−	12523.7i	0.689715	−	1.19462i	−0.282215	−	0.959351i	$-0.591069\pi$
$479$	7230.58	−	12523.7i	0.689715	−	1.19462i	0.971930	−	0.235271i	$-0.0755977\pi$
$480$	−1839.60	−	1957.51i	−0.174929	−	0.186141i
$481$	−11462.8	−	19854.1i	−1.08661	−	1.88206i
$482$	−728.935	−	1262.55i	−0.0688840	−	0.119311i
$483$	2206.85	−	7319.28i	0.207898	−	0.689521i
$484$	−1558.44	+	2699.29i	−0.146360	+	0.253502i
$485$	−696.156			−0.0651769
$486$	3639.71	−	8216.09i	0.339714	−	0.766850i
$487$	3581.74			0.333273			0.166636	−	0.986018i	$-0.446709\pi$
$487$	3581.74			0.333273			0.166636	+	0.986018i	$0.446709\pi$
$488$	−8410.26	+	14567.0i	−0.780153	+	1.35126i
$489$	1576.81	−	5229.69i	0.145820	−	0.483629i
$490$	1711.89	+	2965.09i	0.157828	+	0.273365i
$491$	3507.69	+	6075.50i	0.322403	+	0.558419i	0.980983	−	0.194092i	$-0.0621760\pi$
$491$	3507.69	+	6075.50i	0.322403	+	0.558419i	−0.658580	+	0.752511i	$0.728843\pi$
$492$	−450.247	−	479.107i	−0.0412576	−	0.0439021i
$493$	840.687	−	1456.11i	0.0768005	−	0.133022i
$494$	−16732.4			−1.52394
$495$	465.592	+	308.839i	0.0422763	+	0.0280430i
$496$	236.364			0.0213973
$497$	−1890.81	+	3274.98i	−0.170653	+	0.295579i
$498$	13291.7	−	3122.77i	1.19602	−	0.280993i
$499$	−1259.90	−	2182.21i	−0.113028	−	0.195769i	0.803962	−	0.594681i	$-0.202721\pi$
$499$	−1259.90	−	2182.21i	−0.113028	−	0.195769i	−0.916990	+	0.398911i	$0.869388\pi$
$500$	148.268	+	256.807i	0.0132615	+	0.0229695i
$501$	−14246.8	+	3347.15i	−1.27046	+	0.298482i
$502$	7278.35	−	12606.5i	0.647109	−	1.12083i
$503$	−4989.32			−0.442272			−0.221136	−	0.975243i	$-0.570976\pi$
$503$	−4989.32			−0.442272			−0.221136	+	0.975243i	$0.570976\pi$
$504$	−4385.44	+	2181.03i	−0.387586	+	0.192759i
$505$	9858.72			0.868727
$506$	−979.643	+	1696.79i	−0.0860681	+	0.149074i
$507$	−14378.0	−	15299.6i	−1.25947	−	1.34020i
$508$	2876.11	+	4981.57i	0.251194	+	0.435081i
$509$	−2359.76	−	4087.22i	−0.205490	−	0.355919i	0.744799	−	0.667289i	$-0.232546\pi$
$509$	−2359.76	−	4087.22i	−0.205490	−	0.355919i	−0.950289	+	0.311370i	$0.899212\pi$
$510$	592.602	−	1965.44i	0.0514527	−	0.170649i
$511$	3665.19	−	6348.30i	0.317297	−	0.549574i
$512$	−11827.7			−1.02093
$513$	9645.16	−	7997.34i	0.830106	−	0.688287i
$514$	12929.9			1.10956
$515$	−4531.77	+	7849.25i	−0.387754	+	0.671610i
$516$	−1061.79	+	3521.57i	−0.0905868	+	0.300442i
$517$	−866.839	−	1501.41i	−0.0737399	−	0.127721i
$518$	2538.35	+	4396.55i	0.215306	+	0.372921i
$519$	5132.85	+	5461.85i	0.434117	+	0.461943i
$520$	−4858.34	+	8414.89i	−0.409716	+	0.709649i
$521$	−10711.0			−0.900682			−0.450341	−	0.892857i	$-0.648698\pi$
$521$	−10711.0			−0.900682			−0.450341	+	0.892857i	$0.648698\pi$
$522$	−200.622	+	3227.16i	−0.0168218	+	0.270592i
$523$	−10566.4			−0.883433			−0.441717	−	0.897155i	$-0.645630\pi$
$523$	−10566.4			−0.883433			−0.441717	+	0.897155i	$0.645630\pi$
$524$	308.983	−	535.175i	0.0257595	−	0.0446168i
$525$	932.303	−	219.036i	0.0775029	−	0.0182086i
$526$	929.032	+	1609.13i	0.0770109	+	0.133387i
$527$	−99.9211	−	173.068i	−0.00825926	−	0.0143055i
$528$	824.704	−	193.757i	0.0679747	−	0.0159700i
$529$	−13829.1	+	23952.7i	−1.13661	+	1.96866i
$530$	4735.41			0.388100
$531$	−164.581	+	2647.42i	−0.0134505	+	0.216362i
$532$	−1561.90			−0.127288
$533$	−2106.23	+	3648.09i	−0.171165	+	0.296466i
$534$	−3142.53	−	3343.96i	−0.254664	−	0.270988i
$535$	648.044	+	1122.44i	0.0523689	+	0.0907056i
$536$	2774.32	+	4805.26i	0.223568	+	0.387231i
$537$	−2302.34	+	7635.99i	−0.185015	+	0.613626i
$538$	−167.269	+	289.718i	−0.0134042	+	0.0232168i
$539$	1194.60			0.0954642
$540$	−279.355	−	1640.49i	−0.0222621	−	0.130733i
$541$	−6595.81			−0.524170			−0.262085	−	0.965045i	$-0.584410\pi$
$541$	−6595.81			−0.524170			−0.262085	+	0.965045i	$0.584410\pi$
$542$	−7562.63	+	13098.9i	−0.599341	+	1.03809i
$543$	5475.65	−	18160.7i	0.432749	−	1.43526i
$544$	1721.87	+	2982.37i	0.135707	+	0.235052i
$545$	−1938.89	−	3358.26i	−0.152391	−	0.263949i
$546$	4915.11	+	5230.15i	0.385251	+	0.409945i
$547$	3194.39	−	5532.85i	0.249693	−	0.432482i	−0.713747	−	0.700403i	$-0.753003\pi$
$547$	3194.39	−	5532.85i	0.249693	−	0.432482i	0.963441	+	0.267922i	$0.0863368\pi$
$548$	959.916			0.0748277
$549$	−16526.1	+	8218.97i	−1.28473	+	0.638939i
$550$	−245.448			−0.0190290
$551$	−2254.16	+	3904.31i	−0.174284	+	0.301868i
$552$	24839.0	−	5835.70i	1.91525	−	0.449971i
$553$	743.519	+	1287.81i	0.0571748	+	0.0990296i
$554$	−8093.24	−	14017.9i	−0.620666	−	1.07502i
$555$	−7341.72	+	1724.87i	−0.561511	+	0.131922i
$556$	−2096.72	+	3631.62i	−0.159929	+	0.277006i
$557$	15992.4			1.21655			0.608276	−	0.793726i	$-0.291862\pi$
$557$	15992.4			1.21655			0.608276	+	0.793726i	$0.291862\pi$
$558$	320.258	+	212.435i	0.0242968	+	0.0161167i
$559$	23566.2			1.78308
$560$	726.060	−	1257.57i	0.0547886	−	0.0948967i
$561$	−490.508	−	521.948i	−0.0369149	−	0.0392811i
$562$	−699.459	−	1211.50i	−0.0524998	−	0.0909323i
$563$	3175.56	+	5500.23i	0.237716	+	0.411736i	0.960058	−	0.279800i	$-0.0902680\pi$
$563$	3175.56	+	5500.23i	0.237716	+	0.411736i	−0.722343	+	0.691535i	$0.756935\pi$
$564$	−1490.64	+	4943.89i	−0.111290	+	0.369106i
$565$	538.139	−	932.083i	0.0400702	−	0.0694036i
$566$	−14176.8			−1.05282
$567$	−5333.01	−	665.644i	−0.395001	−	0.0493023i
$568$	−12621.7			−0.932382
$569$	−4810.21	+	8331.53i	−0.354402	+	0.613842i	−0.987015	−	0.160626i	$-0.948649\pi$
$569$	−4810.21	+	8331.53i	−0.354402	+	0.613842i	0.632614	+	0.774468i	$0.281982\pi$
$570$	−1588.96	+	5269.99i	−0.116762	+	0.387255i
$571$	2532.30	+	4386.08i	0.185593	+	0.321456i	0.943776	−	0.330585i	$-0.107246\pi$
$571$	2532.30	+	4386.08i	0.185593	+	0.321456i	−0.758183	+	0.652042i	$0.773913\pi$
$572$	387.701	+	671.517i	0.0283402	+	0.0490866i
$573$	−4829.80	−	5139.38i	−0.352125	−	0.374696i
$574$	466.408	−	807.842i	0.0339155	−	0.0587433i
$575$	−4989.06			−0.361840
$576$	−12609.7	−	8364.34i	−0.912161	−	0.605059i
$577$	11355.1			0.819273			0.409637	−	0.912249i	$-0.365655\pi$
$577$	11355.1			0.819273			0.409637	+	0.912249i	$0.365655\pi$
$578$	4511.65	−	7814.41i	0.324671	−	0.562347i
$579$	−9120.54	+	2142.79i	−0.654640	+	0.153802i
$580$	299.388	+	518.555i	0.0214335	+	0.0371239i
$581$	−4082.93	−	7071.84i	−0.291546	−	0.504973i
$582$	−1670.77	+	392.533i	−0.118996	+	0.0279571i
$583$	826.121	−	1430.88i	0.0586869	−	0.101649i
$584$	24466.2			1.73359
$585$	−9546.60	+	4747.84i	−0.674707	+	0.335554i
$586$	19114.6			1.34747
$587$	5016.00	−	8687.96i	0.352696	−	0.610887i	−0.634025	−	0.773312i	$-0.718598\pi$
$587$	5016.00	−	8687.96i	0.352696	−	0.610887i	0.986721	+	0.162426i	$0.0519318\pi$
$588$	−2436.66	−	2592.84i	−0.170895	−	0.181848i
$589$	267.921	+	464.053i	0.0187428	+	0.0324634i
$590$	−582.643	−	1009.17i	−0.0406560	−	0.0704182i
$591$	395.105	−	1310.41i	0.0274999	−	0.0912068i
$592$	−5717.59	+	9903.16i	−0.396945	+	0.687530i
$593$	−1325.12			−0.0917643			−0.0458821	−	0.998947i	$-0.514610\pi$
$593$	−1325.12			−0.0917643			−0.0458821	+	0.998947i	$0.514610\pi$
$594$	1291.56	+	478.685i	0.0892145	+	0.0330651i
$595$	−1227.74			−0.0845926
$596$	2278.21	−	3945.97i	0.156575	−	0.271197i
$597$	−739.279	+	2451.91i	−0.0506812	+	0.168091i
$598$	−18694.9	−	32380.5i	−1.27841	−	2.21427i
$599$	−8285.78	−	14351.4i	−0.565188	−	0.978935i	−0.997032	−	0.0769865i	$-0.975470\pi$
$599$	−8285.78	−	14351.4i	−0.565188	−	0.978935i	0.431844	−	0.901948i	$-0.357863\pi$
$600$	2188.96	+	2329.27i	0.148940	+	0.158487i
$601$	−8604.49	+	14903.4i	−0.584001	+	1.01152i	0.410998	+	0.911636i	$0.365180\pi$
$601$	−8604.49	+	14903.4i	−0.584001	+	1.01152i	−0.994999	+	0.0998833i	$0.968153\pi$
$602$	−5218.55			−0.353310
$603$	−377.772	+	6076.76i	−0.0255126	+	0.410390i
$604$	5988.96			0.403456
$605$	3284.68	−	5689.23i	0.220729	−	0.382314i
$606$	23660.9	−	5558.92i	1.58607	−	0.372633i
$607$	−2088.99	−	3618.24i	−0.139686	−	0.241944i	0.787692	−	0.616070i	$-0.211276\pi$
$607$	−2088.99	−	3618.24i	−0.139686	−	0.241944i	−0.927378	+	0.374126i	$0.877943\pi$
$608$	−4616.91	−	7996.72i	−0.307961	−	0.533404i
$609$	1882.54	−	442.287i	0.125262	−	0.0294292i
$610$	4054.20	−	7022.08i	0.269098	−	0.466091i
$611$	33084.4			2.19059
$612$	−132.369	+	2129.26i	−0.00874297	+	0.140638i
$613$	14944.2			0.984649			0.492324	−	0.870412i	$-0.336147\pi$
$613$	14944.2			0.984649			0.492324	+	0.870412i	$0.336147\pi$
$614$	5392.89	−	9340.75i	0.354461	−	0.613945i
$615$	948.976	+	1009.80i	0.0622218	+	0.0662100i
$616$	−375.375	−	650.168i	−0.0245524	−	0.0425260i
$617$	−10251.4	−	17756.0i	−0.668893	−	1.15856i	−0.978214	−	0.207600i	$-0.933435\pi$
$617$	−10251.4	−	17756.0i	−0.668893	−	1.15856i	0.309320	−	0.950958i	$-0.399898\pi$
$618$	−6450.37	+	21393.5i	−0.419858	+	1.39251i
$619$	−1364.26	+	2362.97i	−0.0885854	+	0.153434i	−0.906913	−	0.421317i	$-0.861568\pi$
$619$	−1364.26	+	2362.97i	−0.0885854	+	0.153434i	0.818328	+	0.574751i	$0.194901\pi$
$620$	71.1684			0.00460999
$621$	26252.8	+	9729.93i	1.69644	+	0.628742i
$622$	−9970.21			−0.642715
$623$	−1372.23	+	2376.78i	−0.0882463	+	0.152847i
$624$	−4666.91	+	15478.4i	−0.299400	+	0.992999i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	8271.29	+	14326.3i	0.528095	+	0.914687i
$627$	1315.21	+	1399.51i	0.0837712	+	0.0891407i
$628$	2304.32	−	3991.19i	0.146421	−	0.253608i
$629$	9668.27			0.612876
$630$	2114.02	−	1051.37i	0.133690	−	0.0664884i
$631$	−3393.08			−0.214067			−0.107034	−	0.994255i	$-0.534135\pi$
$631$	−3393.08			−0.214067			−0.107034	+	0.994255i	$0.534135\pi$
$632$	−2481.59	+	4298.25i	−0.156191	+	0.270530i
$633$	−5066.23	+	1190.27i	−0.318112	+	0.0747374i
$634$	8730.03	+	15120.9i	0.546867	+	0.947202i
$635$	−6061.91	−	10499.5i	−0.378834	−	0.656159i
$636$	−4790.74	+	1125.54i	−0.298687	+	0.0701739i
$637$	−11398.5	+	19742.8i	−0.708988	+	1.22800i
$638$	−495.618			−0.0307550
$639$	−11541.4	−	7655.70i	−0.714508	−	0.473951i
$640$	2511.75			0.155134
$641$	−6780.88	+	11744.8i	−0.417830	+	0.723702i	−0.995721	−	0.0924116i	$-0.970542\pi$
$641$	−6780.88	+	11744.8i	−0.417830	+	0.723702i	0.577891	+	0.816114i	$0.303876\pi$
$642$	2188.20	+	2328.46i	0.134520	+	0.143142i
$643$	−6483.44	−	11229.7i	−0.397639	−	0.688731i	0.595795	−	0.803137i	$-0.296837\pi$
$643$	−6483.44	−	11229.7i	−0.397639	−	0.688731i	−0.993434	+	0.114405i	$0.963504\pi$
$644$	−1745.09	−	3022.58i	−0.106780	−	0.184948i
$645$	2237.91	−	7422.32i	0.136617	−	0.453106i
$646$	3528.24	−	6111.09i	0.214886	−	0.372194i
$647$	25837.9			1.57000			0.785001	−	0.619495i	$-0.212663\pi$
$647$	25837.9			1.57000			0.785001	+	0.619495i	$0.212663\pi$
$648$	−6975.79	−	16525.8i	−0.422894	−	1.00184i
$649$	−406.583			−0.0245913
$650$	2341.98	−	4056.43i	0.141323	−	0.244779i
$651$	66.3505	−	220.060i	0.00399460	−	0.0132486i
$652$	−1246.88	−	2159.66i	−0.0748950	−	0.129722i
$653$	14133.4	+	24479.8i	0.846989	+	1.46703i	0.883883	+	0.467709i	$0.154920\pi$
$653$	14133.4	+	24479.8i	0.846989	+	1.46703i	−0.0368938	+	0.999319i	$0.511746\pi$
$654$	−6546.92	−	6966.56i	−0.391445	−	0.416535i
$655$	−651.237	+	1127.98i	−0.0388487	+	0.0672880i
$656$	2101.15			0.125055
$657$	22372.1	+	14840.0i	1.32849	+	0.881223i
$658$	−7326.28			−0.434055
$659$	7978.92	−	13819.9i	0.471646	−	0.816914i	−0.527828	−	0.849351i	$-0.676993\pi$
$659$	7978.92	−	13819.9i	0.471646	−	0.816914i	0.999474	+	0.0324369i	$0.0103268\pi$
$660$	248.316	−	58.3395i	0.0146450	−	0.00344070i
$661$	−12028.9	−	20834.6i	−0.707821	−	1.22598i	−0.965664	−	0.259795i	$-0.916345\pi$
$661$	−12028.9	−	20834.6i	−0.707821	−	1.22598i	0.257843	−	0.966187i	$-0.416988\pi$
$662$	8106.23	+	14040.4i	0.475918	+	0.824314i
$663$	13306.3	−	3126.20i	0.779450	−	0.183125i
$664$	13627.3	−	23603.2i	0.796450	−	1.37949i
$665$	3291.98			0.191966
$666$	−16647.6	+	8279.38i	−0.968588	+	0.481711i
$667$	−10074.1			−0.584815
$668$	−3340.70	+	5786.26i	−0.193496	+	0.335145i
$669$	−1996.80	−	2124.79i	−0.115397	−	0.122794i
$670$	−1337.37	−	2316.40i	−0.0771152	−	0.133567i
$671$	−1414.56	−	2450.09i	−0.0813838	−	0.140961i
$672$	−1143.37	+	3792.15i	−0.0656349	+	0.217686i
$673$	−626.519	+	1085.16i	−0.0358849	+	0.0621545i	−0.883410	−	0.468601i	$-0.844758\pi$
$673$	−626.519	+	1085.16i	−0.0358849	+	0.0621545i	0.847525	+	0.530755i	$0.178092\pi$
$674$	−16436.3			−0.939321
$675$	588.790	+	3457.63i	0.0335741	+	0.197162i
$676$	−9585.35			−0.545366
$677$	−440.364	+	762.733i	−0.0249994	+	0.0433002i	−0.878254	−	0.478194i	$-0.841292\pi$
$677$	−440.364	+	762.733i	−0.0249994	+	0.0433002i	0.853255	+	0.521494i	$0.174625\pi$
$678$	765.970	−	2540.43i	0.0433877	−	0.143901i
$679$	513.226	+	888.933i	0.0290071	+	0.0502417i
$680$	−2048.88	−	3548.76i	−0.115546	−	0.200131i
$681$	13900.8	+	14791.8i	0.782204	+	0.832341i
$682$	−29.4537	+	51.0153i	−0.00165373	+	0.00286434i
$683$	−26686.4			−1.49506			−0.747531	−	0.664227i	$-0.768761\pi$
$683$	−26686.4			−1.49506			−0.747531	+	0.664227i	$0.768761\pi$
$684$	354.924	−	5709.24i	0.0198404	−	0.319149i
$685$	−2023.19			−0.112850
$686$	5523.50	−	9566.98i	0.307417	−	0.532462i
$687$	15159.6	−	3561.62i	0.841886	−	0.197794i
$688$	−5877.36	−	10179.9i	−0.325687	−	0.564106i
$689$	15765.2	+	27306.1i	0.871706	+	1.50984i
$690$	−11973.7	+	2813.12i	−0.660627	+	0.155208i
$691$	85.7060	−	148.447i	0.00471839	−	0.00817249i	−0.863657	−	0.504081i	$-0.831831\pi$
$691$	85.7060	−	148.447i	0.00471839	−	0.00817249i	0.868375	+	0.495908i	$0.165165\pi$
$692$	3421.90			0.187978
$693$	51.1138	−	822.206i	0.00280181	−	0.0450693i
$694$	−17888.4			−0.978437
$695$	4419.20	−	7654.28i	0.241194	−	0.417761i
$696$	4420.04	+	4703.35i	0.240720	+	0.256150i
$697$	−888.247	−	1538.49i	−0.0482708	−	0.0836075i
$698$	2187.44	+	3788.76i	0.118619	+	0.205454i
$699$	−6291.44	+	20866.4i	−0.340435	+	1.12910i
$700$	218.614	−	378.651i	0.0118041	−	0.0204452i
$701$	−14229.6			−0.766684			−0.383342	−	0.923607i	$-0.625227\pi$
$701$	−14229.6			−0.766684			−0.383342	+	0.923607i	$0.625227\pi$
$702$	−20234.7	+	16777.8i	−1.08791	+	0.902045i
$703$	−25923.8			−1.39080
$704$	1159.70	−	2008.66i	0.0620850	−	0.107534i
$705$	3141.79	−	10420.1i	0.167839	−	0.556659i
$706$	8418.62	+	14581.5i	0.448780	+	0.777310i
$707$	−7268.13	−	12588.8i	−0.386628	−	0.669659i
$708$	829.316	+	882.472i	0.0440220	+	0.0468437i
$709$	3887.04	−	6732.55i	0.205897	−	0.356624i	−0.744521	−	0.667599i	$-0.767322\pi$
$709$	3887.04	−	6732.55i	0.205897	−	0.356624i	0.950418	+	0.310975i	$0.100656\pi$
$710$	6084.32			0.321606
$711$	−4876.31	+	2425.15i	−0.257210	+	0.127919i
$712$	−9160.03			−0.482144
$713$	−598.687	+	1036.96i	−0.0314460	+	0.0544661i
$714$	−2946.59	+	692.274i	−0.154444	+	0.0362853i
$715$	−817.147	−	1415.34i	−0.0427407	−	0.0740290i
$716$	1820.60	+	3153.37i	0.0950264	+	0.164591i
$717$	−842.088	+	197.841i	−0.0438610	+	0.0103047i
$718$	−9144.72	+	15839.1i	−0.475318	+	0.823274i
$719$	−22091.8			−1.14588			−0.572939	−	0.819598i	$-0.694197\pi$
$719$	−22091.8			−1.14588			−0.572939	+	0.819598i	$0.694197\pi$
$720$	4431.83	+	2939.74i	0.229395	+	0.152164i
$721$	13363.8			0.690282
$722$	−1324.62	+	2294.31i	−0.0682786	+	0.118262i
$723$	−2186.81	−	2326.97i	−0.112487	−	0.119697i
$724$	−4329.92	−	7499.65i	−0.222266	−	0.384975i
$725$	−631.013	−	1092.95i	−0.0323245	−	0.0559876i
$726$	4675.31	−	15506.3i	0.239004	−	0.792687i
$727$	−3321.74	+	5753.42i	−0.169459	+	0.293511i	−0.938230	−	0.346013i	$-0.887535\pi$
$727$	−3321.74	+	5753.42i	−0.169459	+	0.293511i	0.768771	+	0.639524i	$0.220869\pi$
$728$	14326.8			0.729378
$729$	3645.00	−	19342.6i	0.185185	−	0.982704i
$730$	−11794.0			−0.597967
$731$	−4969.22	+	8606.94i	−0.251427	+	0.435484i
$732$	−2432.52	+	8067.75i	−0.122826	+	0.407367i
$733$	1561.40	+	2704.43i	0.0786791	+	0.136276i	0.902680	−	0.430312i	$-0.141596\pi$
$733$	1561.40	+	2704.43i	0.0786791	+	0.136276i	−0.824001	+	0.566588i	$0.808263\pi$
$734$	6234.82	+	10799.0i	0.313530	+	0.543050i
$735$	5135.68	+	5464.87i	0.257731	+	0.274251i
$736$	10316.8	−	17869.2i	0.516687	−	0.894928i
$737$	−933.252			−0.0466442
$738$	2846.93	+	1888.44i	0.142001	+	0.0941929i
$739$	19549.5			0.973127			0.486563	−	0.873645i	$-0.338250\pi$
$739$	19549.5			0.973127			0.486563	+	0.873645i	$0.338250\pi$
$740$	−1721.55	+	2981.81i	−0.0855208	+	0.148126i
$741$	−35678.6	+	8382.37i	−1.76881	+	0.415566i
$742$	−3491.08	−	6046.72i	−0.172724	−	0.299167i
$743$	−4695.92	−	8133.58i	−0.231866	−	0.401604i	0.726491	−	0.687176i	$-0.241150\pi$
$743$	−4695.92	−	8133.58i	−0.231866	−	0.401604i	−0.958357	+	0.285572i	$0.907817\pi$
$744$	746.804	−	175.455i	0.0368000	−	0.00864582i
$745$	−4801.72	+	8316.82i	−0.236136	+	0.409000i
$746$	2363.87			0.116015
$747$	26777.6	−	13317.4i	1.31157	−	0.652286i
$748$	−327.005			−0.0159846
$749$	955.512	−	1655.00i	0.0466137	−	0.0807373i
$750$	−1055.20	−	1122.83i	−0.0513738	−	0.0546667i
$751$	9136.01	+	15824.0i	0.443912	+	0.768878i	0.997976	−	0.0635962i	$-0.0202570\pi$
$751$	9136.01	+	15824.0i	0.443912	+	0.768878i	−0.554064	+	0.832474i	$0.686924\pi$
$752$	−8251.18	−	14291.5i	−0.400119	−	0.693026i
$753$	9204.25	−	30527.0i	0.445447	−	1.47738i
$754$	4729.03	−	8190.92i	0.228410	−	0.395618i
$755$	−12622.8			−0.608464
$756$	−1888.83	+	1566.13i	−0.0908676	+	0.0753434i
$757$	2016.30			0.0968082			0.0484041	−	0.998828i	$-0.484586\pi$
$757$	2016.30			0.0968082			0.0484041	+	0.998828i	$0.484586\pi$
$758$	3244.34	−	5619.36i	0.155461	−	0.269267i
$759$	−1238.86	+	4108.84i	−0.0592462	+	0.196497i
$760$	5493.72	+	9515.39i	0.262208	+	0.454157i
$761$	8846.39	+	15322.4i	0.421395	+	0.729877i	0.996076	−	0.0885001i	$-0.0282074\pi$
$761$	8846.39	+	15322.4i	0.421395	+	0.729877i	−0.574681	+	0.818377i	$0.694874\pi$
$762$	−20468.8	−	21780.8i	−0.973107	−	1.03548i
$763$	−2858.81	+	4951.60i	−0.135643	+	0.234941i
$764$	−3219.87			−0.152475
$765$	278.991	−	4487.79i	0.0131855	−	0.212100i
$766$	−21206.9			−1.00031
$767$	3879.48	−	6719.46i	0.182634	−	0.316331i
$768$	−16651.0	+	3912.00i	−0.782346	+	0.183805i
$769$	4879.86	+	8452.16i	0.228833	+	0.396350i	0.957462	−	0.288558i	$-0.0931759\pi$
$769$	4879.86	+	8452.16i	0.228833	+	0.396350i	−0.728630	+	0.684908i	$0.759843\pi$
$770$	180.951	+	313.416i	0.00846886	+	0.0146685i
$771$	27570.4	−	6477.43i	1.28784	−	0.302567i
$772$	−2138.66	+	3704.27i	−0.0997047	+	0.172694i
$773$	−10338.3			−0.481038			−0.240519	−	0.970644i	$-0.577318\pi$
$773$	−10338.3			−0.481038			−0.240519	+	0.970644i	$0.577318\pi$
$774$	1185.86	−	19075.4i	0.0550707	−	0.885856i
$775$	−150.000			−0.00695246
$776$	−1712.96	+	2966.93i	−0.0792418	+	0.137251i
$777$	7615.04	+	8103.14i	0.351593	+	0.374130i
$778$	13206.3	+	22874.0i	0.608573	+	1.05408i
$779$	2381.68	+	4125.19i	0.109541	+	0.189731i
$780$	−1405.19	+	4660.49i	−0.0645050	+	0.213939i
$781$	1061.45	−	1838.48i	0.0486320	−	0.0842331i
$782$	15768.2			0.721059
$783$	1188.91	+	6981.79i	0.0542633	+	0.318657i
$784$	11371.1			0.517997
$785$	−4856.75	+	8412.14i	−0.220821	+	0.382474i
$786$	−926.950	+	3074.35i	−0.0420652	+	0.139514i
$787$	−2363.64	−	4093.95i	−0.107058	−	0.185430i	0.807519	−	0.589842i	$-0.200810\pi$
$787$	−2363.64	−	4093.95i	−0.107058	−	0.185430i	−0.914577	+	0.404411i	$0.867476\pi$
$788$	−312.433	−	541.150i	−0.0141243	−	0.0244640i
$789$	2787.10	+	2965.74i	0.125758	+	0.133819i
$790$	1196.26	−	2071.99i	0.0538748	−	0.0933139i
$791$	−1586.92			−0.0713331
$792$	2461.87	−	1224.37i	0.110453	−	0.0549319i
$793$	53989.1			2.41767
$794$	11243.9	−	19475.0i	0.502558	−	0.870456i
$795$	10097.3	−	2372.27i	0.450459	−	0.105831i
$796$	584.593	+	1012.54i	0.0260306	+	0.0450863i
$797$	−14099.4	−	24420.9i	−0.626634	−	1.08536i	−0.988222	−	0.153025i	$-0.951099\pi$
$797$	−14099.4	−	24420.9i	−0.626634	−	1.08536i	0.361588	−	0.932338i	$-0.382235\pi$
$798$	7900.76	−	1856.21i	0.350481	−	0.0823423i
$799$	−6976.24	+	12083.2i	−0.308888	+	0.535010i
$800$	2584.85			0.114235
$801$	−8376.04	−	5556.04i	−0.369479	−	0.245085i
$802$	22364.9			0.984704
$803$	−2057.54	+	3563.76i	−0.0904221	+	0.156616i
$804$	1903.57	+	2025.59i	0.0834998	+	0.0888519i
$805$	3678.08	+	6370.62i	0.161037	+	0.278925i
$806$	−562.076	−	973.544i	−0.0245636	−	0.0425454i
$807$	−211.529	+	701.562i	−0.00922697	+	0.0306024i
$808$	24258.3	−	42016.7i	1.05619	−	1.82938i
$809$	−27310.5			−1.18688			−0.593439	−	0.804879i	$-0.702230\pi$
$809$	−27310.5			−1.18688			−0.593439	+	0.804879i	$0.702230\pi$
$810$	3362.71	+	7966.32i	0.145869	+	0.345565i
$811$	−18045.0			−0.781312			−0.390656	−	0.920537i	$-0.627752\pi$
$811$	−18045.0			−0.781312			−0.390656	+	0.920537i	$0.627752\pi$
$812$	441.435	−	764.587i	0.0190780	−	0.0330440i
$813$	−9563.74	+	31719.3i	−0.412565	+	1.36832i
$814$	−1424.96	−	2468.10i	−0.0613572	−	0.106274i
$815$	2628.02	+	4551.86i	0.112951	+	0.195638i
$816$	−4669.00	−	4968.27i	−0.200304	−	0.213142i
$817$	13324.1	−	23078.0i	0.570564	−	0.988246i
$818$	968.333			0.0413899
$819$	13100.6	+	8689.97i	0.558941	+	0.370760i
$820$	632.650			0.0269428
$821$	6288.85	−	10892.6i	0.267335	−	0.463038i	−0.700837	−	0.713321i	$-0.747190\pi$
$821$	6288.85	−	10892.6i	0.267335	−	0.463038i	0.968173	+	0.250283i	$0.0805235\pi$
$822$	−4855.66	+	1140.79i	−0.206035	+	0.0484060i
$823$	17484.2	+	30283.6i	0.740537	+	1.28265i	0.952251	+	0.305316i	$0.0987622\pi$
$823$	17484.2	+	30283.6i	0.740537	+	1.28265i	−0.211714	+	0.977332i	$0.567904\pi$
$824$	22301.7	+	38627.7i	0.942860	+	1.63308i
$825$	−523.369	+	122.961i	−0.0220865	+	0.00518902i
$826$	−859.081	+	1487.97i	−0.0361880	+	0.0626794i
$827$	−6735.01			−0.283191			−0.141596	−	0.989925i	$-0.545223\pi$
$827$	−6735.01			−0.283191			−0.141596	+	0.989925i	$0.545223\pi$
$828$	11445.0	−	5691.99i	0.480364	−	0.238901i
$829$	−2867.97			−0.120155			−0.0600777	−	0.998194i	$-0.519135\pi$
$829$	−2867.97			−0.120155			−0.0600777	+	0.998194i	$0.519135\pi$
$830$	−6569.10	+	11378.0i	−0.274719	+	0.475828i
$831$	−24279.7	−	25836.0i	−1.01354	−	1.07851i
$832$	22131.0	+	38332.0i	0.922179	+	1.59726i
$833$	−4807.03	−	8326.02i	−0.199944	−	0.346314i
$834$	6290.16	−	20862.1i	0.261163	−	0.866181i
$835$	7041.11	−	12195.6i	0.291817	−	0.505443i
$836$	876.808			0.0362740
$837$	789.310	+	292.538i	0.0325956	+	0.0120807i
$838$	20909.0			0.861921
$839$	−13927.9	+	24123.8i	−0.573116	+	0.992666i	0.423128	+	0.906070i	$0.360932\pi$
$839$	−13927.9	+	24123.8i	−0.573116	+	0.992666i	−0.996244	+	0.0865958i	$0.972401\pi$
$840$	1360.52	−	4512.32i	0.0558836	−	0.185345i
$841$	10920.3	+	18914.6i	0.447756	+	0.775537i
$842$	2786.68	+	4826.67i	0.114056	+	0.197551i
$843$	−2098.38	−	2232.88i	−0.0857318	−	0.0912270i
$844$	−1187.97	+	2057.63i	−0.0484499	+	0.0839176i
$845$	20202.8			0.822483
$846$	1664.81	−	26779.8i	0.0676566	−	1.08831i
$847$	−9686.23			−0.392943
$848$	7863.60	−	13620.2i	0.318440	−	0.551554i
$849$	−30229.3	+	7102.09i	−1.22199	+	0.287094i
$850$	987.671	+	1710.70i	0.0398551	+	0.0690310i
$851$	−28964.2	−	50167.5i	−1.16672	−	2.02082i
$852$	−6155.41	+	1446.16i	−0.247513	+	0.0581509i
$853$	−5463.05	+	9462.29i	−0.219287	+	0.379815i	−0.954590	−	0.297923i	$-0.903706\pi$
$853$	−5463.05	+	9462.29i	−0.219287	+	0.379815i	0.735304	+	0.677738i	$0.237040\pi$
$854$	−11955.5			−0.479049
$855$	−748.065	+	12033.2i	−0.0299220	+	0.481319i
$856$	6378.30			0.254680
$857$	−22584.6	+	39117.7i	−0.900206	+	1.55920i	−0.0729799	+	0.997333i	$0.523251\pi$
$857$	−22584.6	+	39117.7i	−0.900206	+	1.55920i	−0.827226	+	0.561869i	$0.810082\pi$
$858$	−2759.20	−	2936.06i	−0.109788	−	0.116825i
$859$	3525.95	+	6107.12i	0.140051	+	0.242576i	0.927516	−	0.373784i	$-0.121940\pi$
$859$	3525.95	+	6107.12i	0.140051	+	0.242576i	−0.787465	+	0.616360i	$0.788607\pi$
$860$	−1769.65	−	3065.13i	−0.0701682	−	0.121535i
$861$	589.822	−	1956.22i	0.0233462	−	0.0774306i
$862$	−5315.29	+	9206.35i	−0.210022	+	0.363770i
$863$	6882.52			0.271476			0.135738	−	0.990745i	$-0.456659\pi$
$863$	6882.52			0.271476			0.135738	+	0.990745i	$0.456659\pi$
$864$	−13601.6	−	5041.11i	−0.535576	−	0.198498i
$865$	−7212.25			−0.283496
$866$	−4059.80	+	7031.77i	−0.159304	+	0.275923i
$867$	5705.46	−	18922.9i	0.223492	−	0.741239i
$868$	−52.4674	−	90.8762i	−0.00205168	−	0.00355362i
$869$	−417.391	−	722.942i	−0.0162935	−	0.0282211i
$870$	−2130.70	−	2267.27i	−0.0830315	−	0.0883536i
$871$	8904.79	−	15423.5i	0.346415	−	0.600008i
$872$	−19083.3			−0.741104
$873$	−3365.95	+	1674.00i	−0.130493	+	0.0648984i
$874$	−42279.6			−1.63630
$875$	−460.768	+	798.073i	−0.0178020	+	0.0308340i
$876$	11931.8	−	2803.27i	0.460204	−	0.108121i
$877$	−18684.3	−	32362.2i	−0.719413	−	1.24606i	−0.961233	−	0.275738i	$-0.911078\pi$
$877$	−18684.3	−	32362.2i	−0.719413	−	1.24606i	0.241820	−	0.970321i	$-0.422256\pi$
$878$	9642.35	+	16701.0i	0.370630	+	0.641951i
$879$	40758.2	−	9575.76i	1.56398	−	0.367443i
$880$	−407.590	+	705.966i	−0.0156135	+	0.0270433i
$881$	−23880.5			−0.913229			−0.456614	−	0.889665i	$-0.650938\pi$
$881$	−23880.5			−0.913229			−0.456614	+	0.889665i	$0.650938\pi$
$882$	15407.0	+	10219.9i	0.588189	+	0.390160i
$883$	−33107.0			−1.26177			−0.630883	−	0.775878i	$-0.717307\pi$
$883$	−33107.0			−1.26177			−0.630883	+	0.775878i	$0.717307\pi$
$884$	3120.18	−	5404.31i	0.118714	−	0.205618i
$885$	−1747.93	−	1859.97i	−0.0663909	−	0.0706464i
$886$	−2788.36	−	4829.57i	−0.105730	−	0.183129i
$887$	−5651.07	−	9787.95i	−0.213917	−	0.370515i	0.739020	−	0.673684i	$-0.235289\pi$
$887$	−5651.07	−	9787.95i	−0.213917	−	0.370515i	−0.952937	+	0.303168i	$0.901956\pi$
$888$	−10713.8	+	35533.7i	−0.404879	+	1.34283i
$889$	−8938.02	+	15481.1i	−0.337201	+	0.584049i
$890$	4415.63			0.166306
$891$	2993.80	+	373.674i	0.112566	+	0.0140500i
$892$	−1331.20			−0.0499686
$893$	18705.6	−	32399.0i	0.700961	−	1.21410i
$894$	−6834.62	+	22667.9i	−0.255687	+	0.848016i
$895$	−3837.23	−	6646.27i	−0.143312	−	0.248224i
$896$	−1851.73	−	3207.30i	−0.0690425	−	0.119585i
$897$	−56084.6	−	59679.5i	−2.08764	−	2.22145i
$898$	−5647.21	+	9781.25i	−0.209855	+	0.363479i
$899$	−302.886			−0.0112367
$900$	1334.41	+	885.146i	0.0494225	+	0.0327832i
$901$	−13297.1			−0.491666
$902$	−261.828	+	453.500i	−0.00966511	+	0.0167405i
$903$	−11127.5	+	2614.31i	−0.410079	+	0.0963443i
$904$	−2648.28	−	4586.96i	−0.0974343	−	0.168761i
$905$	9126.08	+	15806.8i	0.335206	+	0.580593i
$906$	−30294.7	+	7117.47i	−1.11090	+	0.260996i
$907$	−1981.12	+	3431.40i	−0.0725270	+	0.125620i	−0.900008	−	0.435873i	$-0.856440\pi$
$907$	−1981.12	+	3431.40i	−0.0725270	+	0.125620i	0.827481	+	0.561493i	$0.189773\pi$
$908$	9267.22			0.338704
$909$	47667.4	−	23706.6i	1.73931	−	0.865015i
$910$	−6906.30			−0.251584
$911$	17023.1	−	29484.8i	0.619100	−	1.07231i	−0.370551	−	0.928812i	$-0.620831\pi$
$911$	17023.1	−	29484.8i	0.619100	−	1.07231i	0.989650	−	0.143500i	$-0.0458356\pi$
$912$	12519.1	+	13321.6i	0.454550	+	0.483685i
$913$	2292.04	+	3969.93i	0.0830838	+	0.143905i
$914$	−2644.01	−	4579.56i	−0.0956849	−	0.165731i
$915$	5126.96	−	17004.2i	0.185237	−	0.614363i
$916$	3554.76	−	6157.02i	0.128223	−	0.222089i
$917$	1920.44			0.0691587
$918$	−1860.90	−	10928.0i	−0.0669050	−	0.392895i
$919$	−35121.5			−1.26066			−0.630332	−	0.776326i	$-0.717081\pi$
$919$	−35121.5			−1.26066			−0.630332	+	0.776326i	$0.717081\pi$
$920$	−12276.1	+	21262.8i	−0.439924	+	0.761971i
$921$	6819.87	−	22619.0i	0.243998	−	0.809251i
$922$	−6804.44	−	11785.6i	−0.243050	−	0.420975i
$923$	20256.0	+	35084.4i	0.722355	+	1.25116i
$924$	−257.560	−	274.069i	−0.00917002	−	0.00975779i
$925$	3628.46	−	6284.69i	0.128976	−	0.223394i
$926$	−8549.64			−0.303411
$927$	−3036.76	+	48848.8i	−0.107595	+	1.73075i
$928$	5219.44			0.184630
$929$	−12228.9	+	21181.1i	−0.431881	+	0.748039i	−0.997035	−	0.0769459i	$-0.975483\pi$
$929$	−12228.9	+	21181.1i	−0.431881	+	0.748039i	0.565155	+	0.824985i	$0.308816\pi$
$930$	−360.000	+	84.5787i	−0.0126934	+	0.00298220i
$931$	12889.2	+	22324.8i	0.453735	+	0.785891i
$932$	4975.03	+	8617.00i	0.174852	+	0.302853i
$933$	−21259.5	+	4994.73i	−0.745986	+	0.175263i
$934$	4484.05	−	7766.61i	0.157091	−	0.272089i
$935$	689.221			0.0241069
$936$	−3255.61	+	52369.0i	−0.113689	+	1.82878i
$937$	41877.5			1.46006			0.730032	−	0.683413i	$-0.239505\pi$
$937$	41877.5			1.46006			0.730032	+	0.683413i	$0.239505\pi$
$938$	−1971.90	+	3415.43i	−0.0686404	+	0.118889i
$939$	24813.9	+	26404.4i	0.862375	+	0.917651i
$940$	−2484.40	−	4303.11i	−0.0862045	−	0.149311i
$941$	4599.48	+	7966.54i	0.159340	+	0.275985i	0.934631	−	0.355619i	$-0.115730\pi$
$941$	4599.48	+	7966.54i	0.159340	+	0.275985i	−0.775291	+	0.631604i	$0.782397\pi$
$942$	−6912.95	+	22927.7i	−0.239104	+	0.793018i
$943$	−5322.02	+	9218.01i	−0.183785	+	0.318324i
$944$	−3870.14			−0.133435
$945$	3981.03	−	3300.90i	0.137040	−	0.113628i
$946$	2929.55			0.100685
$947$	−10481.8	+	18155.0i	−0.359675	+	0.622976i	−0.987906	−	0.155051i	$-0.950446\pi$
$947$	−10481.8	+	18155.0i	−0.359675	+	0.622976i	0.628231	+	0.778027i	$0.283779\pi$
$948$	−717.757	+	2380.53i	−0.0245904	+	0.0815570i
$949$	−39264.7	−	68008.5i	−1.34308	−	2.32629i
$950$	−2648.27	−	4586.93i	−0.0904433	−	0.156652i
$951$	26190.1	+	27868.8i	0.893030	+	0.950271i
$952$	−3020.98	+	5232.50i	−0.102847	+	0.178137i
$953$	−27943.7			−0.949828			−0.474914	−	0.880032i	$-0.657521\pi$
$953$	−27943.7			−0.949828			−0.474914	+	0.880032i	$0.657521\pi$
$954$	22895.9	−	11386.9i	0.777027	−	0.386441i
$955$	6786.44			0.229952
$956$	−197.460	+	342.010i	−0.00668024	+	0.0115705i
$957$	−1056.81	+	248.287i	−0.0356967	+	0.00838662i
$958$	17153.0	+	29709.8i	0.578484	+	1.00196i
$959$	1491.55	+	2583.45i	0.0502240	+	0.0869905i
$960$	14174.5	−	3330.17i	0.476542	−	0.111959i
$961$	14877.5	−	25768.6i	0.499396	−	0.864979i
$962$	54385.9			1.82274
$963$	5832.39	+	3868.77i	0.195167	+	0.129459i
$964$	−1457.87			−0.0487084
$965$	4507.60	−	7807.39i	0.150368	−	0.260444i
$966$	12419.5	+	13215.6i	0.413655	+	0.440170i
$967$	−1121.76	−	1942.95i	−0.0373045	−	0.0646132i	0.846770	−	0.531959i	$-0.178544\pi$
$967$	−1121.76	−	1942.95i	−0.0373045	−	0.0646132i	−0.884075	+	0.467345i	$0.845210\pi$
$968$	−16164.5	−	27997.8i	−0.536723	−	0.929632i
$969$	4461.83	−	14798.2i	0.147920	−	0.490595i
$970$	825.739	−	1430.22i	0.0273329	−	0.0473419i
$971$	57345.0			1.89525			0.947626	−	0.319381i	$-0.103475\pi$
$971$	57345.0			1.89525			0.947626	+	0.319381i	$0.103475\pi$
$972$	−5295.48	−	7260.13i	−0.174746	−	0.239577i
$973$	−13031.8			−0.429375
$974$	−4248.44	+	7358.52i	−0.139763	+	0.242076i
$975$	2961.68	−	9822.80i	0.0972819	−	0.322647i
$976$	−13464.8	−	23321.7i	−0.441595	−	0.764866i
$977$	−9395.44	−	16273.4i	−0.307663	−	0.532888i	0.670188	−	0.742192i	$-0.266214\pi$
$977$	−9395.44	−	16273.4i	−0.307663	−	0.532888i	−0.977851	+	0.209304i	$0.932880\pi$
$978$	8873.84	+	9442.63i	0.290137	+	0.308734i
$979$	770.334	−	1334.26i	0.0251481	−	0.0435578i
$980$	3423.79			0.111601
$981$	−17450.0	−	11575.0i	−0.567927	−	0.376720i
$982$	−16642.5			−0.540817
$983$	17298.8	−	29962.4i	0.561289	−	0.972181i	−0.436096	−	0.899900i	$-0.643639\pi$
$983$	17298.8	−	29962.4i	0.561289	−	0.972181i	0.997384	−	0.0722803i	$-0.0230276\pi$
$984$	6638.70	−	1559.70i	0.215075	−	0.0505300i
$985$	658.508	+	1140.57i	0.0213013	+	0.0368950i
$986$	1994.35	+	3454.31i	0.0644147	+	0.111570i
$987$	−15621.8	+	3670.21i	−0.503798	+	0.118363i
$988$	−8366.22	+	14490.7i	−0.269398	+	0.466611i
$989$	59547.1			1.91455
$990$	−1186.75	+	590.212i	−0.0380985	+	0.0189476i
$991$	−45026.3			−1.44330			−0.721649	−	0.692259i	$-0.756616\pi$
$991$	−45026.3			−1.44330			−0.721649	+	0.692259i	$0.756616\pi$
$992$	310.182	−	537.251i	0.00992771	−	0.0171953i
$993$	24318.7	+	25877.5i	0.777171	+	0.826985i
$994$	−4485.53	−	7769.17i	−0.143131	−	0.247911i
$995$	−1232.13	−	2134.12i	−0.0392575	−	0.0679960i
$996$	3941.46	−	13072.4i	0.125392	−	0.415877i
$997$	5986.04	−	10368.1i	0.190150	−	0.329350i	−0.755150	−	0.655552i	$-0.772436\pi$
$997$	5986.04	−	10368.1i	0.190150	−	0.329350i	0.945300	+	0.326202i	$0.105769\pi$
$998$	5977.66			0.189599
$999$	−31349.9	+	25994.0i	−0.992861	+	0.823237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.a.16.1	✓	4
3.2	odd	2		135.4.e.a.46.2		4
5.2	odd	4		225.4.k.a.124.2		8
5.3	odd	4		225.4.k.a.124.3		8
5.4	even	2		225.4.e.a.151.2		4
9.2	odd	6		405.4.a.e.1.1		2
9.4	even	3	inner	45.4.e.a.31.1	yes	4
9.5	odd	6		135.4.e.a.91.2		4
9.7	even	3		405.4.a.d.1.2		2
45.4	even	6		225.4.e.a.76.2		4
45.13	odd	12		225.4.k.a.49.2		8
45.22	odd	12		225.4.k.a.49.3		8
45.29	odd	6		2025.4.a.j.1.2		2
45.34	even	6		2025.4.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.a.16.1	✓	4	1.1	even	1	trivial
45.4.e.a.31.1	yes	4	9.4	even	3	inner
135.4.e.a.46.2		4	3.2	odd	2
135.4.e.a.91.2		4	9.5	odd	6
225.4.e.a.76.2		4	45.4	even	6
225.4.e.a.151.2		4	5.4	even	2
225.4.k.a.49.2		8	45.13	odd	12
225.4.k.a.49.3		8	45.22	odd	12
225.4.k.a.124.2		8	5.2	odd	4
225.4.k.a.124.3		8	5.3	odd	4
405.4.a.d.1.2		2	9.7	even	3
405.4.a.e.1.1		2	9.2	odd	6
2025.4.a.j.1.2		2	45.29	odd	6
2025.4.a.l.1.1		2	45.34	even	6

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18614 + 2.05446i) q^{2} +(-1.50000 + 4.97494i) q^{3} +(1.18614 + 2.05446i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-8.44158 - 8.98266i) q^{6} +(-3.68614 + 6.38458i) q^{7} -24.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} +O(q^{10})\)	\(q+(-1.18614 + 2.05446i) q^{2} +(-1.50000 + 4.97494i) q^{3} +(1.18614 + 2.05446i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-8.44158 - 8.98266i) q^{6} +(-3.68614 + 6.38458i) q^{7} -24.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} +11.8614 q^{10} +(2.06930 - 3.58413i) q^{11} +(-12.0000 + 2.81929i) q^{12} +(39.4891 + 68.3972i) q^{13} +(-8.74456 - 15.1460i) q^{14} +(25.2921 - 5.94215i) q^{15} +(19.6970 - 34.1162i) q^{16} -33.3070 q^{17} +(57.3505 - 28.5223i) q^{18} +89.3070 q^{19} +(5.93070 - 10.2723i) q^{20} +(-26.2337 - 27.9152i) q^{21} +(4.90895 + 8.50256i) q^{22} +(99.7812 + 172.826i) q^{23} +(36.9090 - 122.413i) q^{24} +(-12.5000 + 21.6506i) q^{25} -187.359 q^{26} +(108.000 - 89.5489i) q^{27} -17.4891 q^{28} +(-25.2405 + 43.7179i) q^{29} +(-17.7921 + 59.0098i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-51.6970 - 89.5419i) q^{32} +(14.7269 + 15.6708i) q^{33} +(39.5068 - 68.4278i) q^{34} +36.8614 q^{35} +(3.97420 - 63.9282i) q^{36} -290.277 q^{37} +(-105.931 + 183.477i) q^{38} +(-399.505 + 93.8602i) q^{39} +(61.5149 + 106.547i) q^{40} +(26.6684 + 46.1911i) q^{41} +(88.4674 - 20.7846i) q^{42} +(149.194 - 258.412i) q^{43} +9.81791 q^{44} +(-8.37633 + 134.740i) q^{45} -473.418 q^{46} +(209.452 - 362.782i) q^{47} +(140.181 + 149.166i) q^{48} +(144.325 + 249.978i) q^{49} +(-29.6535 - 51.3614i) q^{50} +(49.9605 - 165.700i) q^{51} +(-93.6793 + 162.257i) q^{52} +399.228 q^{53} +(55.8710 + 328.099i) q^{54} -20.6930 q^{55} +(90.7011 - 157.099i) q^{56} +(-133.961 + 444.297i) q^{57} +(-59.8776 - 103.711i) q^{58} +(-49.1209 - 85.0799i) q^{59} +(42.2079 + 44.9133i) q^{60} +(341.797 - 592.011i) q^{61} -14.2337 q^{62} +(178.227 - 88.6382i) q^{63} +560.432 q^{64} +(197.446 - 341.986i) q^{65} +(-49.6631 + 11.6679i) q^{66} +(-112.750 - 195.289i) q^{67} +(-39.5068 - 68.4278i) q^{68} +(-1009.47 + 237.166i) q^{69} +(-43.7228 + 75.7301i) q^{70} +512.951 q^{71} +(553.634 + 367.239i) q^{72} -994.318 q^{73} +(344.310 - 596.362i) q^{74} +(-88.9605 - 94.6627i) q^{75} +(105.931 + 183.477i) q^{76} +(15.2554 + 26.4232i) q^{77} +(281.038 - 932.097i) q^{78} +(100.853 - 174.683i) q^{79} -196.970 q^{80} +(283.500 + 671.617i) q^{81} -126.530 q^{82} +(-553.822 + 959.247i) q^{83} +(26.2337 - 87.0073i) q^{84} +(83.2676 + 144.224i) q^{85} +(353.931 + 613.026i) q^{86} +(-179.633 - 191.147i) q^{87} +(-50.9171 + 88.1909i) q^{88} +372.269 q^{89} +(-266.882 - 177.029i) q^{90} -582.250 q^{91} +(-236.709 + 409.992i) q^{92} +(-30.3505 + 7.13058i) q^{93} +(496.880 + 860.622i) q^{94} +(-223.268 - 386.711i) q^{95} +(523.011 - 122.877i) q^{96} +(69.6156 - 120.578i) q^{97} -684.758 q^{98} +(-100.052 + 49.7590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 6 q^{3} - q^{4} - 10 q^{5} - 51 q^{6} - 9 q^{7} - 18 q^{8} - 90 q^{9}+O(q^{10}) \) 4 * q + q^2 - 6 * q^3 - q^4 - 10 * q^5 - 51 * q^6 - 9 * q^7 - 18 * q^8 - 90 * q^9	\( 4 q + q^{2} - 6 q^{3} - q^{4} - 10 q^{5} - 51 q^{6} - 9 q^{7} - 18 q^{8} - 90 q^{9} - 10 q^{10} + 37 q^{11} - 48 q^{12} + 112 q^{13} - 12 q^{14} + 15 q^{15} + 119 q^{16} + 154 q^{17} + 126 q^{18} + 70 q^{19} - 5 q^{20} - 36 q^{21} - 101 q^{22} + 267 q^{23} + 27 q^{24} - 50 q^{25} - 152 q^{26} + 432 q^{27} - 24 q^{28} - 325 q^{29} + 15 q^{30} + 12 q^{31} - 247 q^{32} - 303 q^{33} + 451 q^{34} + 90 q^{35} + 171 q^{36} - 1276 q^{37} - 395 q^{38} - 564 q^{39} + 45 q^{40} - 238 q^{41} + 216 q^{42} + 97 q^{43} - 202 q^{44} + 225 q^{45} - 492 q^{46} + 901 q^{47} - 525 q^{48} + 629 q^{49} + 25 q^{50} - 231 q^{51} - 76 q^{52} + 448 q^{53} + 999 q^{54} - 370 q^{55} + 156 q^{56} - 105 q^{57} + 806 q^{58} + 85 q^{59} + 255 q^{60} + 247 q^{61} + 12 q^{62} + 351 q^{63} + 1426 q^{64} + 560 q^{65} - 888 q^{66} + 606 q^{67} - 451 q^{68} - 1539 q^{69} - 60 q^{70} + 788 q^{71} + 405 q^{72} - 1622 q^{73} - 484 q^{74} + 75 q^{75} + 395 q^{76} + 84 q^{77} + 228 q^{78} + 840 q^{79} - 1190 q^{80} + 1134 q^{81} - 2218 q^{82} + 387 q^{83} + 36 q^{84} - 385 q^{85} + 1387 q^{86} + 2418 q^{87} + 411 q^{88} - 2130 q^{89} + 225 q^{90} - 1272 q^{91} - 246 q^{92} - 18 q^{93} - 632 q^{94} - 175 q^{95} + 24 q^{96} + 1031 q^{97} + 926 q^{98} - 90 q^{99}+O(q^{100}) \) 4 * q + q^2 - 6 * q^3 - q^4 - 10 * q^5 - 51 * q^6 - 9 * q^7 - 18 * q^8 - 90 * q^9 - 10 * q^10 + 37 * q^11 - 48 * q^12 + 112 * q^13 - 12 * q^14 + 15 * q^15 + 119 * q^16 + 154 * q^17 + 126 * q^18 + 70 * q^19 - 5 * q^20 - 36 * q^21 - 101 * q^22 + 267 * q^23 + 27 * q^24 - 50 * q^25 - 152 * q^26 + 432 * q^27 - 24 * q^28 - 325 * q^29 + 15 * q^30 + 12 * q^31 - 247 * q^32 - 303 * q^33 + 451 * q^34 + 90 * q^35 + 171 * q^36 - 1276 * q^37 - 395 * q^38 - 564 * q^39 + 45 * q^40 - 238 * q^41 + 216 * q^42 + 97 * q^43 - 202 * q^44 + 225 * q^45 - 492 * q^46 + 901 * q^47 - 525 * q^48 + 629 * q^49 + 25 * q^50 - 231 * q^51 - 76 * q^52 + 448 * q^53 + 999 * q^54 - 370 * q^55 + 156 * q^56 - 105 * q^57 + 806 * q^58 + 85 * q^59 + 255 * q^60 + 247 * q^61 + 12 * q^62 + 351 * q^63 + 1426 * q^64 + 560 * q^65 - 888 * q^66 + 606 * q^67 - 451 * q^68 - 1539 * q^69 - 60 * q^70 + 788 * q^71 + 405 * q^72 - 1622 * q^73 - 484 * q^74 + 75 * q^75 + 395 * q^76 + 84 * q^77 + 228 * q^78 + 840 * q^79 - 1190 * q^80 + 1134 * q^81 - 2218 * q^82 + 387 * q^83 + 36 * q^84 - 385 * q^85 + 1387 * q^86 + 2418 * q^87 + 411 * q^88 - 2130 * q^89 + 225 * q^90 - 1272 * q^91 - 246 * q^92 - 18 * q^93 - 632 * q^94 - 175 * q^95 + 24 * q^96 + 1031 * q^97 + 926 * q^98 - 90 * q^99

Introduction

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