LMFDB - Embedded newform 105.4.i.e.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 31x^{8} + 26x^{7} + 738x^{6} + 352x^{5} + 5008x^{4} + 5368x^{3} + 26728x^{2} + 13776x + 7056 $ x^10 - x^9 + 31x^8 + 26x^7 + 738x^6 + 352x^5 + 5008x^4 + 5368x^3 + 26728x^2 + 13776x + 7056
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.5
Root			$2.68023 - 4.64230i$ of defining polynomial
Character	$\chi$	$=$	105.16
Dual form			105.4.i.e.46.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.68023 - 4.64230i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.3673 - 17.9567i) q^{4} +(2.50000 - 4.33013i) q^{5} -16.0814 q^{6} +(17.9827 - 4.42983i) q^{7} -68.2635 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(2.68023 - 4.64230i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.3673 - 17.9567i) q^{4} +(2.50000 - 4.33013i) q^{5} -16.0814 q^{6} +(17.9827 - 4.42983i) q^{7} -68.2635 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-13.4012 - 23.2115i) q^{10} +(27.8851 + 48.2985i) q^{11} +(-31.1019 + 53.8701i) q^{12} +8.04056 q^{13} +(27.6332 - 95.3540i) q^{14} -15.0000 q^{15} +(-100.024 + 173.246i) q^{16} +(-48.9091 - 84.7130i) q^{17} +(24.1221 + 41.7807i) q^{18} +(-31.5512 + 54.6483i) q^{19} -103.673 q^{20} +(-38.4830 - 40.0756i) q^{21} +298.955 q^{22} +(69.4947 - 120.368i) q^{23} +(102.395 + 177.354i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(21.5506 - 37.3267i) q^{26} +27.0000 q^{27} +(-265.977 - 276.984i) q^{28} +229.166 q^{29} +(-40.2035 + 69.6345i) q^{30} +(10.7838 + 18.6781i) q^{31} +(263.120 + 455.737i) q^{32} +(83.6554 - 144.895i) q^{33} -524.351 q^{34} +(25.7750 - 88.9418i) q^{35} +186.612 q^{36} +(-27.9694 + 48.4444i) q^{37} +(169.129 + 292.941i) q^{38} +(-12.0608 - 20.8900i) q^{39} +(-170.659 + 295.590i) q^{40} -256.341 q^{41} +(-289.187 + 71.2379i) q^{42} -141.438 q^{43} +(578.187 - 1001.45i) q^{44} +(22.5000 + 38.9711i) q^{45} +(-372.524 - 645.231i) q^{46} +(88.4726 - 153.239i) q^{47} +600.143 q^{48} +(303.753 - 159.320i) q^{49} -134.012 q^{50} +(-146.727 + 254.139i) q^{51} +(-83.3590 - 144.382i) q^{52} +(360.170 + 623.832i) q^{53} +(72.3663 - 125.342i) q^{54} +278.851 q^{55} +(-1227.56 + 302.396i) q^{56} +189.307 q^{57} +(614.218 - 1063.86i) q^{58} +(-286.200 - 495.714i) q^{59} +(155.510 + 269.351i) q^{60} +(-155.373 + 269.114i) q^{61} +115.613 q^{62} +(-46.3949 + 160.095i) q^{63} +1220.51 q^{64} +(20.1014 - 34.8166i) q^{65} +(-448.432 - 776.707i) q^{66} +(109.161 + 189.072i) q^{67} +(-1014.11 + 1756.49i) q^{68} -416.968 q^{69} +(-343.812 - 358.040i) q^{70} +464.419 q^{71} +(307.186 - 532.062i) q^{72} +(398.767 + 690.684i) q^{73} +(149.929 + 259.684i) q^{74} +(-37.5000 + 64.9519i) q^{75} +1308.41 q^{76} +(715.403 + 745.009i) q^{77} -129.304 q^{78} +(-349.353 + 605.097i) q^{79} +(500.119 + 866.231i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-687.054 + 1190.01i) q^{82} +963.839 q^{83} +(-320.660 + 1106.51i) q^{84} -489.091 q^{85} +(-379.088 + 656.599i) q^{86} +(-343.749 - 595.390i) q^{87} +(-1903.54 - 3297.02i) q^{88} +(-25.7494 + 44.5993i) q^{89} +241.221 q^{90} +(144.591 - 35.6183i) q^{91} -2881.89 q^{92} +(32.3515 - 56.0344i) q^{93} +(-474.255 - 821.433i) q^{94} +(157.756 + 273.242i) q^{95} +(789.360 - 1367.21i) q^{96} -1601.27 q^{97} +(74.5164 - 1837.13i) q^{98} -501.932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9}+O(q^{10}) $ 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9	\( 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9} - 5 q^{10} + 33 q^{11} - 63 q^{12} - 46 q^{13} - 73 q^{14} - 150 q^{15} - 113 q^{16} + 136 q^{17} + 9 q^{18} + 39 q^{19} - 210 q^{20} - 147 q^{21} - 174 q^{22} + 133 q^{23} + 207 q^{24} - 125 q^{25} + 73 q^{26} + 270 q^{27} - 809 q^{28} + 544 q^{29} - 15 q^{30} + 430 q^{31} + 573 q^{32} + 99 q^{33} - 744 q^{34} + 35 q^{35} + 378 q^{36} - 3 q^{37} + 837 q^{38} + 69 q^{39} - 345 q^{40} - 1254 q^{41} - 372 q^{42} + 216 q^{43} + 1809 q^{44} + 225 q^{45} - 1637 q^{46} + 553 q^{47} + 678 q^{48} - 386 q^{49} - 50 q^{50} + 408 q^{51} + 1047 q^{52} + 1135 q^{53} + 27 q^{54} + 330 q^{55} - 1356 q^{56} - 234 q^{57} + 2564 q^{58} + 332 q^{59} + 315 q^{60} + 584 q^{61} - 3124 q^{62} - 63 q^{63} + 2274 q^{64} - 115 q^{65} + 261 q^{66} - 412 q^{67} - 1712 q^{68} - 798 q^{69} - 985 q^{70} - 284 q^{71} + 621 q^{72} + 2074 q^{73} - 605 q^{74} - 375 q^{75} + 18 q^{76} - 751 q^{77} - 438 q^{78} - 28 q^{79} + 565 q^{80} - 405 q^{81} - 1515 q^{82} - 1680 q^{83} - 1077 q^{84} + 1360 q^{85} - 40 q^{86} - 816 q^{87} - 4181 q^{88} + 2978 q^{89} + 90 q^{90} - 2736 q^{91} + 1062 q^{92} + 1290 q^{93} + 843 q^{94} - 195 q^{95} + 1719 q^{96} - 4336 q^{97} - 5183 q^{98} - 594 q^{99}+O(q^{100}) \) 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9 - 5 * q^10 + 33 * q^11 - 63 * q^12 - 46 * q^13 - 73 * q^14 - 150 * q^15 - 113 * q^16 + 136 * q^17 + 9 * q^18 + 39 * q^19 - 210 * q^20 - 147 * q^21 - 174 * q^22 + 133 * q^23 + 207 * q^24 - 125 * q^25 + 73 * q^26 + 270 * q^27 - 809 * q^28 + 544 * q^29 - 15 * q^30 + 430 * q^31 + 573 * q^32 + 99 * q^33 - 744 * q^34 + 35 * q^35 + 378 * q^36 - 3 * q^37 + 837 * q^38 + 69 * q^39 - 345 * q^40 - 1254 * q^41 - 372 * q^42 + 216 * q^43 + 1809 * q^44 + 225 * q^45 - 1637 * q^46 + 553 * q^47 + 678 * q^48 - 386 * q^49 - 50 * q^50 + 408 * q^51 + 1047 * q^52 + 1135 * q^53 + 27 * q^54 + 330 * q^55 - 1356 * q^56 - 234 * q^57 + 2564 * q^58 + 332 * q^59 + 315 * q^60 + 584 * q^61 - 3124 * q^62 - 63 * q^63 + 2274 * q^64 - 115 * q^65 + 261 * q^66 - 412 * q^67 - 1712 * q^68 - 798 * q^69 - 985 * q^70 - 284 * q^71 + 621 * q^72 + 2074 * q^73 - 605 * q^74 - 375 * q^75 + 18 * q^76 - 751 * q^77 - 438 * q^78 - 28 * q^79 + 565 * q^80 - 405 * q^81 - 1515 * q^82 - 1680 * q^83 - 1077 * q^84 + 1360 * q^85 - 40 * q^86 - 816 * q^87 - 4181 * q^88 + 2978 * q^89 + 90 * q^90 - 2736 * q^91 + 1062 * q^92 + 1290 * q^93 + 843 * q^94 - 195 * q^95 + 1719 * q^96 - 4336 * q^97 - 5183 * q^98 - 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	2.68023	−	4.64230i	0.947606	−	1.64130i	0.197158	−	0.980372i	$-0.436829\pi$
$2$	2.68023	−	4.64230i	0.947606	−	1.64130i	0.750448	−	0.660930i	$-0.229838\pi$
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−10.3673	−	17.9567i	−1.29591	−	2.24459i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	−16.0814			−1.09420
$7$	17.9827	−	4.42983i	0.970973	−	0.239188i
$7$	17.9827	−	4.42983i	0.970973	−	0.239188i
$8$	−68.2635			−3.01685
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−13.4012	−	23.2115i	−0.423782	−	0.734012i
$11$	27.8851	+	48.2985i	0.764335	+	1.32387i	0.940598	+	0.339523i	$0.110266\pi$
$11$	27.8851	+	48.2985i	0.764335	+	1.32387i	−0.176263	+	0.984343i	$0.556401\pi$
$12$	−31.1019	+	53.8701i	−0.748196	+	1.29591i
$13$	8.04056			0.171542			0.0857712	−	0.996315i	$-0.472665\pi$
$13$	8.04056			0.171542			0.0857712	+	0.996315i	$0.472665\pi$
$14$	27.6332	−	95.3540i	0.527520	−	1.82032i
$15$	−15.0000			−0.258199
$16$	−100.024	+	173.246i	−1.56287	+	2.70697i
$17$	−48.9091	−	84.7130i	−0.697776	−	1.20858i	−0.969236	−	0.246134i	$-0.920840\pi$
$17$	−48.9091	−	84.7130i	−0.697776	−	1.20858i	0.271460	−	0.962450i	$-0.412494\pi$
$18$	24.1221	+	41.7807i	0.315869	+	0.547101i
$19$	−31.5512	+	54.6483i	−0.380966	+	0.659852i	−0.991201	−	0.132369i	$-0.957742\pi$
$19$	−31.5512	+	54.6483i	−0.380966	+	0.659852i	0.610235	+	0.792221i	$0.291075\pi$
$20$	−103.673			−1.15910
$21$	−38.4830	−	40.0756i	−0.399890	−	0.416439i
$22$	298.955			2.89715
$23$	69.4947	−	120.368i	0.630028	−	1.09124i	−0.357517	−	0.933907i	$-0.616377\pi$
$23$	69.4947	−	120.368i	0.630028	−	1.09124i	0.987545	−	0.157335i	$-0.0502901\pi$
$24$	102.395	+	177.354i	0.870890	+	1.50843i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	21.5506	−	37.3267i	0.162555	−	0.281553i
$27$	27.0000			0.192450
$28$	−265.977	−	276.984i	−1.79518	−	1.86947i
$29$	229.166			1.46741			0.733707	−	0.679465i	$-0.237788\pi$
$29$	229.166			1.46741			0.733707	+	0.679465i	$0.237788\pi$
$30$	−40.2035	+	69.6345i	−0.244671	+	0.423782i
$31$	10.7838	+	18.6781i	0.0624785	+	0.108216i	0.895573	−	0.444915i	$-0.146766\pi$
$31$	10.7838	+	18.6781i	0.0624785	+	0.108216i	−0.833094	+	0.553131i	$0.813433\pi$
$32$	263.120	+	455.737i	1.45355	+	2.51762i
$33$	83.6554	−	144.895i	0.441289	−	0.764335i
$34$	−524.351			−2.64487
$35$	25.7750	−	88.9418i	0.124479	−	0.429540i
$36$	186.612			0.863943
$37$	−27.9694	+	48.4444i	−0.124274	+	0.215249i	−0.921449	−	0.388500i	$-0.872993\pi$
$37$	−27.9694	+	48.4444i	−0.124274	+	0.215249i	0.797175	+	0.603748i	$0.206327\pi$
$38$	169.129	+	292.941i	0.722011	+	1.25056i
$39$	−12.0608	−	20.8900i	−0.0495200	−	0.0857712i
$40$	−170.659	+	295.590i	−0.674588	+	1.16842i
$41$	−256.341			−0.976433			−0.488216	−	0.872723i	$-0.662352\pi$
$41$	−256.341			−0.976433			−0.488216	+	0.872723i	$0.662352\pi$
$42$	−289.187	+	71.2379i	−1.06244	+	0.261720i
$43$	−141.438			−0.501608			−0.250804	−	0.968038i	$-0.580695\pi$
$43$	−141.438			−0.501608			−0.250804	+	0.968038i	$0.580695\pi$
$44$	578.187	−	1001.45i	1.98102	−	3.43123i
$45$	22.5000	+	38.9711i	0.0745356	+	0.129099i
$46$	−372.524	−	645.231i	−1.19404	−	2.06813i
$47$	88.4726	−	153.239i	0.274576	−	0.475579i	−0.695452	−	0.718572i	$-0.744796\pi$
$47$	88.4726	−	153.239i	0.274576	−	0.475579i	0.970028	+	0.242993i	$0.0781293\pi$
$48$	600.143			1.80465
$49$	303.753	−	159.320i	0.885578	−	0.464491i
$50$	−134.012			−0.379042
$51$	−146.727	+	254.139i	−0.402861	+	0.697776i
$52$	−83.3590	−	144.382i	−0.222304	−	0.385042i
$53$	360.170	+	623.832i	0.933455	+	1.61679i	0.777367	+	0.629047i	$0.216555\pi$
$53$	360.170	+	623.832i	0.933455	+	1.61679i	0.156088	+	0.987743i	$0.450112\pi$
$54$	72.3663	−	125.342i	0.182367	−	0.315869i
$55$	278.851			0.683642
$56$	−1227.56	+	302.396i	−2.92928	+	0.721595i
$57$	189.307			0.439901
$58$	614.218	−	1063.86i	1.39053	−	2.40847i
$59$	−286.200	−	495.714i	−0.631527	−	1.09384i	−0.987240	−	0.159242i	$-0.949095\pi$
$59$	−286.200	−	495.714i	−0.631527	−	1.09384i	0.355712	−	0.934596i	$-0.384238\pi$
$60$	155.510	+	269.351i	0.334604	+	0.579550i
$61$	−155.373	+	269.114i	−0.326123	+	0.564862i	−0.981739	−	0.190233i	$-0.939076\pi$
$61$	−155.373	+	269.114i	−0.326123	+	0.564862i	0.655616	+	0.755094i	$0.272409\pi$
$62$	115.613			0.236820
$63$	−46.3949	+	160.095i	−0.0927811	+	0.320161i
$64$	1220.51			2.38382
$65$	20.1014	−	34.8166i	0.0383580	−	0.0664381i
$66$	−448.432	−	776.707i	−0.836336	−	1.44858i
$67$	109.161	+	189.072i	0.199046	+	0.344758i	0.948219	−	0.317616i	$-0.102882\pi$
$67$	109.161	+	189.072i	0.199046	+	0.344758i	−0.749173	+	0.662374i	$0.769549\pi$
$68$	−1014.11	+	1756.49i	−1.80852	+	3.13244i
$69$	−416.968			−0.727494
$70$	−343.812	−	358.040i	−0.587048	−	0.611343i
$71$	464.419			0.776288			0.388144	−	0.921599i	$-0.373116\pi$
$71$	464.419			0.776288			0.388144	+	0.921599i	$0.373116\pi$
$72$	307.186	−	532.062i	0.502808	−	0.870890i
$73$	398.767	+	690.684i	0.639344	+	1.10738i	0.985577	+	0.169227i	$0.0541273\pi$
$73$	398.767	+	690.684i	0.639344	+	1.10738i	−0.346233	+	0.938148i	$0.612539\pi$
$74$	149.929	+	259.684i	0.235525	+	0.407942i
$75$	−37.5000	+	64.9519i	−0.0577350	+	0.100000i
$76$	1308.41			1.97480
$77$	715.403	+	745.009i	1.05880	+	1.10262i
$78$	−129.304			−0.187702
$79$	−349.353	+	605.097i	−0.497535	+	0.861756i	−0.999996	−	0.00284398i	$-0.999095\pi$
$79$	−349.353	+	605.097i	−0.497535	+	0.861756i	0.502461	+	0.864600i	$0.332428\pi$
$80$	500.119	+	866.231i	0.698937	+	1.21060i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−687.054	+	1190.01i	−0.925274	+	1.60262i
$83$	963.839			1.27464			0.637320	−	0.770599i	$-0.280043\pi$
$83$	963.839			1.27464			0.637320	+	0.770599i	$0.280043\pi$
$84$	−320.660	+	1106.51i	−0.416511	+	1.43726i
$85$	−489.091			−0.624110
$86$	−379.088	+	656.599i	−0.475326	+	0.823289i
$87$	−343.749	−	595.390i	−0.423606	−	0.733707i
$88$	−1903.54	−	3297.02i	−2.30588	−	3.99391i
$89$	−25.7494	+	44.5993i	−0.0306678	+	0.0531181i	−0.880952	−	0.473206i	$-0.843097\pi$
$89$	−25.7494	+	44.5993i	−0.0306678	+	0.0531181i	0.850284	+	0.526324i	$0.176430\pi$
$90$	241.221			0.282521
$91$	144.591	−	35.6183i	0.166563	−	0.0410309i
$92$	−2881.89			−3.26585
$93$	32.3515	−	56.0344i	0.0360720	−	0.0624785i
$94$	−474.255	−	821.433i	−0.520379	−	0.901323i
$95$	157.756	+	273.242i	0.170373	+	0.295095i
$96$	789.360	−	1367.21i	0.839206	−	1.45355i
$97$	−1601.27			−1.67612			−0.838061	−	0.545576i	$-0.816311\pi$
$97$	−1601.27			−1.67612			−0.838061	+	0.545576i	$0.816311\pi$
$98$	74.5164	−	1837.13i	0.0768091	−	1.89365i
$99$	−501.932			−0.509556
$100$	−259.183	+	448.918i	−0.259183	+	0.448918i
$101$	621.382	+	1076.27i	0.612177	+	1.06032i	0.990873	+	0.134800i	$0.0430392\pi$
$101$	621.382	+	1076.27i	0.612177	+	1.06032i	−0.378696	+	0.925521i	$0.623627\pi$
$102$	786.527	+	1362.30i	0.763507	+	1.32243i
$103$	15.7810	−	27.3336i	0.0150966	−	0.0261481i	−0.858378	−	0.513017i	$-0.828528\pi$
$103$	15.7810	−	27.3336i	0.0150966	−	0.0261481i	0.873475	+	0.486869i	$0.161861\pi$
$104$	−548.877			−0.517518
$105$	−269.740	+	66.4475i	−0.250704	+	0.0617582i
$106$	3861.35			3.53819
$107$	563.086	−	975.293i	0.508743	−	0.881169i	−0.491205	−	0.871044i	$-0.663444\pi$
$107$	563.086	−	975.293i	0.508743	−	0.881169i	0.999949	−	0.0101255i	$-0.00322309\pi$
$108$	−279.917	−	484.831i	−0.249399	−	0.431971i
$109$	99.0496	+	171.559i	0.0870388	+	0.150756i	0.906258	−	0.422725i	$-0.138926\pi$
$109$	99.0496	+	171.559i	0.0870388	+	0.150756i	−0.819219	+	0.573480i	$0.805593\pi$
$110$	747.387	−	1294.51i	0.647823	−	1.12206i
$111$	167.816			0.143499
$112$	−1031.24	+	3558.52i	−0.870030	+	3.00222i
$113$	−198.220			−0.165017			−0.0825086	−	0.996590i	$-0.526293\pi$
$113$	−198.220			−0.165017			−0.0825086	+	0.996590i	$0.526293\pi$
$114$	507.388	−	878.822i	0.416853	−	0.722011i
$115$	−347.474	−	601.842i	−0.281757	−	0.488018i
$116$	−2375.83	−	4115.06i	−1.90164	−	3.29374i
$117$	−36.1825	+	62.6700i	−0.0285904	+	0.0495200i
$118$	−3068.34			−2.39376
$119$	−1254.78	−	1306.71i	−0.966601	−	1.00660i
$120$	1023.95			0.778947
$121$	−889.660	+	1540.94i	−0.668415	+	1.15773i
$122$	832.873	+	1442.58i	0.618072	+	1.07053i
$123$	384.512	+	665.994i	0.281872	+	0.488216i
$124$	223.599	−	387.284i	0.161933	−	0.280477i
$125$	−125.000			−0.0894427
$126$	618.861	+	644.472i	0.437560	+	0.455668i
$127$	1021.01			0.713384			0.356692	−	0.934222i	$-0.383905\pi$
$127$	1021.01			0.713384			0.356692	+	0.934222i	$0.383905\pi$
$128$	1166.30	−	2020.09i	0.805371	−	1.39494i
$129$	212.157	+	367.467i	0.144802	+	0.250804i
$130$	−107.753	−	186.634i	−0.0726966	−	0.125914i
$131$	255.605	−	442.720i	0.170475	−	0.295272i	−0.768111	−	0.640317i	$-0.778803\pi$
$131$	255.605	−	442.720i	0.170475	−	0.295272i	0.938586	+	0.345045i	$0.112136\pi$
$132$	−3469.12			−2.28749
$133$	−325.293	+	1122.49i	−0.212079	+	0.731821i
$134$	1170.30			0.754469
$135$	67.5000	−	116.913i	0.0430331	−	0.0745356i
$136$	3338.71	+	5782.81i	2.10509	+	3.64612i
$137$	708.223	+	1226.68i	0.441661	+	0.764980i	0.997813	−	0.0661011i	$-0.0210560\pi$
$137$	708.223	+	1226.68i	0.441661	+	0.764980i	−0.556152	+	0.831081i	$0.687723\pi$
$138$	−1117.57	+	1935.69i	−0.689378	+	1.19404i
$139$	−1837.16			−1.12105			−0.560524	−	0.828138i	$-0.689400\pi$
$139$	−1837.16			−1.12105			−0.560524	+	0.828138i	$0.689400\pi$
$140$	−1864.32	+	459.254i	−1.12546	+	0.277243i
$141$	−530.836			−0.317053
$142$	1244.75	−	2155.97i	0.735615	−	1.27412i
$143$	224.212	+	388.347i	0.131116	+	0.227099i
$144$	−900.214	−	1559.22i	−0.520957	−	0.902324i
$145$	572.915	−	992.317i	0.328124	−	0.568327i
$146$	4275.15			2.42338
$147$	−869.556	−	550.193i	−0.487890	−	0.308702i
$148$	1159.87			0.644193
$149$	684.985	−	1186.43i	0.376618	−	0.652322i	−0.613949	−	0.789345i	$-0.710420\pi$
$149$	684.985	−	1186.43i	0.376618	−	0.652322i	0.990568	+	0.137023i	$0.0437535\pi$
$150$	201.018	+	348.173i	0.109420	+	0.189521i
$151$	958.995	+	1661.03i	0.516834	+	0.895183i	0.999809	+	0.0195486i	$0.00622289\pi$
$151$	958.995	+	1661.03i	0.516834	+	0.895183i	−0.482975	+	0.875634i	$0.660444\pi$
$152$	2153.80	−	3730.49i	1.14932	−	1.99068i
$153$	880.363			0.465184
$154$	5376.00	−	1324.32i	2.81306	−	0.692965i
$155$	107.838			0.0558824
$156$	−250.077	+	433.146i	−0.128347	+	0.222304i
$157$	7.69916	+	13.3353i	0.00391376	+	0.00677883i	0.867976	−	0.496607i	$-0.165421\pi$
$157$	7.69916	+	13.3353i	0.00391376	+	0.00677883i	−0.864062	+	0.503386i	$0.832088\pi$
$158$	1872.69	+	3243.60i	0.942934	+	1.63321i
$159$	1080.51	−	1871.50i	0.538930	−	0.933455i
$160$	2631.20			1.30009
$161$	716.490	−	2472.40i	0.350729	−	1.21026i
$162$	−434.198			−0.210579
$163$	−188.566	+	326.606i	−0.0906112	+	0.156943i	−0.907768	−	0.419472i	$-0.862215\pi$
$163$	−188.566	+	326.606i	−0.0906112	+	0.156943i	0.817157	+	0.576415i	$0.195549\pi$
$164$	2657.57	+	4603.04i	1.26537	+	2.19169i
$165$	−418.277	−	724.477i	−0.197350	−	0.341821i
$166$	2583.31	−	4474.43i	1.20786	−	2.09207i
$167$	−2483.67			−1.15085			−0.575426	−	0.817854i	$-0.695164\pi$
$167$	−2483.67			−1.15085			−0.575426	+	0.817854i	$0.695164\pi$
$168$	2626.99	+	2735.70i	1.20641	+	1.25633i
$169$	−2132.35			−0.970573
$170$	−1310.88	+	2270.51i	−0.591410	+	1.02435i
$171$	−283.961	−	491.835i	−0.126989	−	0.219951i
$172$	1466.33	+	2539.76i	0.650040	+	1.12590i
$173$	2241.42	−	3882.25i	0.985040	−	1.70614i	0.343279	−	0.939233i	$-0.388462\pi$
$173$	2241.42	−	3882.25i	0.985040	−	1.70614i	0.641760	−	0.766905i	$-0.278204\pi$
$174$	−3685.31			−1.60565
$175$	−320.692	−	333.963i	−0.138526	−	0.144259i
$176$	−11156.7			−4.77823
$177$	−858.601	+	1487.14i	−0.364612	+	0.631527i
$178$	138.029	+	239.073i	0.0581219	+	0.100670i
$179$	−1343.12	−	2326.35i	−0.560834	−	0.971393i	−0.997424	−	0.0717322i	$-0.977147\pi$
$179$	−1343.12	−	2326.35i	−0.560834	−	0.971393i	0.436590	−	0.899661i	$-0.356186\pi$
$180$	466.529	−	808.052i	0.193183	−	0.334604i
$181$	−889.233			−0.365172			−0.182586	−	0.983190i	$-0.558447\pi$
$181$	−889.233			−0.365172			−0.182586	+	0.983190i	$0.558447\pi$
$182$	222.186	−	766.700i	0.0904920	−	0.312261i
$183$	932.239			0.376574
$184$	−4743.96	+	8216.77i	−1.90070	+	3.29211i
$185$	139.847	+	242.222i	0.0555770	+	0.0962622i
$186$	−173.419	−	300.371i	−0.0683640	−	0.118410i
$187$	2727.67	−	4724.47i	1.06667	−	1.84752i
$188$	−3668.89			−1.42331
$189$	485.532	−	119.605i	0.186864	−	0.0460318i
$190$	1691.29			0.645786
$191$	−581.683	+	1007.51i	−0.220362	+	0.381678i	−0.954918	−	0.296870i	$-0.904057\pi$
$191$	−581.683	+	1007.51i	−0.220362	+	0.381678i	0.734556	+	0.678548i	$0.237391\pi$
$192$	−1830.77	−	3170.99i	−0.688148	−	1.19191i
$193$	850.678	+	1473.42i	0.317270	+	0.549528i	0.979917	−	0.199404i	$-0.0639004\pi$
$193$	850.678	+	1473.42i	0.317270	+	0.549528i	−0.662647	+	0.748932i	$0.730567\pi$
$194$	−4291.77	+	7433.56i	−1.58830	+	2.75102i
$195$	−120.608			−0.0442920
$196$	−6009.97	−	3802.68i	−2.19022	−	1.38582i
$197$	−1926.82			−0.696853			−0.348426	−	0.937336i	$-0.613284\pi$
$197$	−1926.82			−0.696853			−0.348426	+	0.937336i	$0.613284\pi$
$198$	−1345.30	+	2330.12i	−0.482859	+	0.836336i
$199$	−1177.42	−	2039.35i	−0.419422	−	0.726461i	0.576459	−	0.817126i	$-0.304434\pi$
$199$	−1177.42	−	2039.35i	−0.419422	−	0.726461i	−0.995881	+	0.0906651i	$0.971101\pi$
$200$	853.294	+	1477.95i	0.301685	+	0.522534i
$201$	327.482	−	567.215i	0.114919	−	0.199046i
$202$	6661.80			2.32041
$203$	4121.02	−	1015.17i	1.42482	−	0.350989i
$204$	6084.67			2.08829
$205$	−640.853	+	1109.99i	−0.218337	+	0.378171i
$206$	−84.5938	−	146.521i	−0.0286113	−	0.0495562i
$207$	625.453	+	1083.32i	0.210009	+	0.363747i
$208$	−804.247	+	1393.00i	−0.268099	+	0.464360i
$209$	−3519.24			−1.16474
$210$	−414.498	+	1430.31i	−0.136205	+	0.470004i
$211$	−3191.17			−1.04118			−0.520591	−	0.853806i	$-0.674288\pi$
$211$	−3191.17			−1.04118			−0.520591	+	0.853806i	$0.674288\pi$
$212$	7467.98	−	12934.9i	2.41935	−	4.19044i
$213$	−696.629	−	1206.60i	−0.224095	−	0.388144i
$214$	−3018.40	−	5228.03i	−0.964176	−	1.67000i
$215$	−353.596	+	612.445i	−0.112163	+	0.194272i
$216$	−1843.12			−0.580593
$217$	276.663	+	288.112i	0.0865489	+	0.0901306i
$218$	1061.90			0.329914
$219$	1196.30	−	2072.05i	0.369125	−	0.639344i
$220$	−2890.94	−	5007.25i	−0.885941	−	1.53449i
$221$	−393.256	−	681.140i	−0.119698	−	0.207323i
$222$	449.787	−	779.053i	0.135981	−	0.235525i
$223$	573.764			0.172296			0.0861481	−	0.996282i	$-0.472544\pi$
$223$	573.764			0.172296			0.0861481	+	0.996282i	$0.472544\pi$
$224$	6750.44	+	7029.80i	2.01354	+	2.09687i
$225$	225.000			0.0666667
$226$	−531.275	+	920.196i	−0.156371	+	0.270843i
$227$	264.755	+	458.570i	0.0774115	+	0.134081i	0.902132	−	0.431459i	$-0.142001\pi$
$227$	264.755	+	458.570i	0.0774115	+	0.134081i	−0.824721	+	0.565540i	$0.808668\pi$
$228$	−1962.61	−	3399.34i	−0.570074	−	0.987398i
$229$	906.390	−	1569.91i	0.261554	−	0.453025i	−0.705101	−	0.709107i	$-0.749098\pi$
$229$	906.390	−	1569.91i	0.261554	−	0.453025i	0.966655	+	0.256082i	$0.0824317\pi$
$230$	−3725.24			−1.06798
$231$	862.486	−	2976.19i	0.245660	−	0.847700i
$232$	−15643.7			−4.42697
$233$	−2842.47	+	4923.30i	−0.799212	+	1.38428i	0.120919	+	0.992662i	$0.461416\pi$
$233$	−2842.47	+	4923.30i	−0.799212	+	1.38428i	−0.920130	+	0.391613i	$0.871917\pi$
$234$	193.955	+	335.940i	0.0541848	+	0.0938509i
$235$	−442.363	−	766.195i	−0.122794	−	0.212685i
$236$	−5934.26	+	10278.4i	−1.63681	+	2.83504i
$237$	2096.12			0.574504
$238$	−9429.24	+	2322.79i	−2.56809	+	0.632621i
$239$	2902.74			0.785617			0.392808	−	0.919620i	$-0.371504\pi$
$239$	2902.74			0.785617			0.392808	+	0.919620i	$0.371504\pi$
$240$	1500.36	−	2598.69i	0.403532	−	0.698937i
$241$	983.342	+	1703.20i	0.262833	+	0.455239i	0.966993	−	0.254801i	$-0.0820100\pi$
$241$	983.342	+	1703.20i	0.262833	+	0.455239i	−0.704161	+	0.710040i	$0.748677\pi$
$242$	4769.00	+	8260.14i	1.26679	+	2.19414i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	6443.21			1.69051
$245$	69.5055	−	1713.59i	0.0181247	−	0.446846i
$246$	4122.32			1.06841
$247$	−253.690	+	439.403i	−0.0653518	+	0.113193i
$248$	−736.142	−	1275.04i	−0.188488	−	0.326471i
$249$	−1445.76	−	2504.13i	−0.367957	−	0.637320i
$250$	−335.029	+	580.288i	−0.0847564	+	0.146802i
$251$	−60.2302			−0.0151462			−0.00757310	−	0.999971i	$-0.502411\pi$
$251$	−60.2302			−0.0151462			−0.00757310	+	0.999971i	$0.502411\pi$
$252$	3355.78	−	826.658i	0.838865	−	0.206645i
$253$	7751.48			1.92621
$254$	2736.54	−	4739.82i	0.676007	−	1.17088i
$255$	733.636	+	1270.70i	0.180165	+	0.312055i
$256$	−1369.87	−	2372.68i	−0.334441	−	0.579269i
$257$	−2235.71	+	3872.36i	−0.542644	+	0.939888i	0.456107	+	0.889925i	$0.349244\pi$
$257$	−2235.71	+	3872.36i	−0.542644	+	0.939888i	−0.998751	+	0.0499627i	$0.984090\pi$
$258$	2274.53			0.548859
$259$	−288.364	+	995.059i	−0.0691816	+	0.238726i
$260$	−833.590			−0.198835
$261$	−1031.25	+	1786.17i	−0.244569	+	0.423606i
$262$	−1370.16	−	2373.19i	−0.323087	−	0.559603i
$263$	−2310.06	−	4001.14i	−0.541614	−	0.938103i	−0.998812	−	0.0487380i	$-0.984480\pi$
$263$	−2310.06	−	4001.14i	−0.541614	−	0.938103i	0.457197	−	0.889365i	$-0.348853\pi$
$264$	−5710.61	+	9891.07i	−1.33130	+	2.30588i
$265$	3601.70			0.834907
$266$	4339.08	+	4518.64i	1.00017	+	1.04156i
$267$	154.496			0.0354121
$268$	2263.40	−	3920.33i	0.515893	−	0.893554i
$269$	2695.36	+	4668.50i	0.610925	+	1.05815i	0.991085	+	0.133233i	$0.0425358\pi$
$269$	2695.36	+	4668.50i	0.610925	+	1.05815i	−0.380159	+	0.924921i	$0.624131\pi$
$270$	−361.832	−	626.711i	−0.0815569	−	0.141261i
$271$	−961.793	+	1665.87i	−0.215590	+	0.373412i	−0.953455	−	0.301536i	$-0.902501\pi$
$271$	−961.793	+	1665.87i	−0.215590	+	0.373412i	0.737865	+	0.674948i	$0.235834\pi$
$272$	19568.3			4.36214
$273$	−309.425	−	322.230i	−0.0685981	−	0.0714369i
$274$	7592.82			1.67408
$275$	697.128	−	1207.46i	0.152867	−	0.264773i
$276$	4322.84	+	7487.38i	0.942770	+	1.63293i
$277$	652.244	+	1129.72i	0.141478	+	0.245048i	0.928054	−	0.372447i	$-0.121481\pi$
$277$	652.244	+	1129.72i	0.141478	+	0.245048i	−0.786575	+	0.617495i	$0.788148\pi$
$278$	−4924.02	+	8528.65i	−1.06231	+	1.83998i
$279$	−194.109			−0.0416523
$280$	−1759.49	+	6071.48i	−0.375534	+	1.29586i
$281$	−8752.40			−1.85809			−0.929047	−	0.369962i	$-0.879371\pi$
$281$	−8752.40			−1.85809			−0.929047	+	0.369962i	$0.879371\pi$
$282$	−1422.76	+	2464.30i	−0.300441	+	0.520379i
$283$	2318.93	+	4016.51i	0.487089	+	0.843663i	0.999890	−	0.0148449i	$-0.00472546\pi$
$283$	2318.93	+	4016.51i	0.487089	+	0.843663i	−0.512801	+	0.858508i	$0.671392\pi$
$284$	−4814.78	−	8339.44i	−1.00600	−	1.74245i
$285$	473.269	−	819.725i	0.0983649	−	0.170373i
$286$	2403.76			0.496984
$287$	−4609.70	+	1135.55i	−0.948090	+	0.233551i
$288$	−4736.16			−0.969031
$289$	−2327.69	+	4031.69i	−0.473783	+	0.820616i
$290$	−3071.09	−	5319.29i	−0.621864	−	1.07710i
$291$	2401.90	+	4160.21i	0.483855	+	0.838061i
$292$	8268.27	−	14321.1i	1.65707	−	2.87013i
$293$	−9571.81			−1.90850			−0.954251	−	0.299007i	$-0.903345\pi$
$293$	−9571.81			−1.90850			−0.954251	+	0.299007i	$0.903345\pi$
$294$	−4884.78	+	2562.10i	−0.969000	+	0.508246i
$295$	−2862.00			−0.564855
$296$	1909.29	−	3306.98i	0.374916	−	0.649373i
$297$	752.898	+	1304.06i	0.147096	+	0.254778i
$298$	−3671.84	−	6359.81i	−0.713772	−	1.23629i
$299$	558.777	−	967.830i	0.108077	−	0.187194i
$300$	1555.10			0.299278
$301$	−2543.44	+	626.547i	−0.487047	+	0.119979i
$302$	10281.3			1.95902
$303$	1864.15	−	3228.80i	0.353440	−	0.612177i
$304$	−6311.75	−	10932.3i	−1.19080	−	2.06253i
$305$	776.866	+	1345.57i	0.145847	+	0.252614i
$306$	2359.58	−	4086.91i	0.440811	−	0.763507i
$307$	−3629.74			−0.674788			−0.337394	−	0.941363i	$-0.609545\pi$
$307$	−3629.74			−0.674788			−0.337394	+	0.941363i	$0.609545\pi$
$308$	5961.10	−	20570.0i	1.10281	−	3.80547i
$309$	−94.6862			−0.0174321
$310$	289.032	−	500.618i	0.0529545	−	0.0917199i
$311$	−1672.60	−	2897.03i	−0.304967	−	0.528218i	0.672287	−	0.740290i	$-0.265312\pi$
$311$	−1672.60	−	2897.03i	−0.304967	−	0.528218i	−0.977254	+	0.212073i	$0.931979\pi$
$312$	823.316	+	1426.02i	0.149394	+	0.258759i
$313$	−1495.87	+	2590.92i	−0.270132	+	0.467882i	−0.968895	−	0.247470i	$-0.920401\pi$
$313$	−1495.87	+	2590.92i	−0.270132	+	0.467882i	0.698763	+	0.715353i	$0.253734\pi$
$314$	82.5423			0.0148348
$315$	577.246	+	601.134i	0.103251	+	0.107524i
$316$	14487.4			2.57905
$317$	−1863.45	+	3227.59i	−0.330163	+	0.571859i	−0.982544	−	0.186033i	$-0.940437\pi$
$317$	−1863.45	+	3227.59i	−0.330163	+	0.571859i	0.652381	+	0.757891i	$0.273770\pi$
$318$	−5792.03	−	10032.1i	−1.02139	−	1.76909i
$319$	6390.32	+	11068.4i	1.12160	+	1.94266i
$320$	3051.28	−	5284.98i	0.533038	−	0.923248i
$321$	−3378.51			−0.587446
$322$	−9557.25	−	9952.76i	−1.65405	−	1.72250i
$323$	6172.57			1.06332
$324$	−839.752	+	1454.49i	−0.143990	+	0.249399i
$325$	−100.507	−	174.083i	−0.0171542	−	0.0297120i
$326$	1010.80	+	1750.76i	0.171727	+	0.297441i
$327$	297.149	−	514.677i	0.0502519	−	0.0870388i
$328$	17498.7			2.94575
$329$	912.151	−	3147.57i	0.152853	−	0.527450i
$330$	−4484.32			−0.748041
$331$	4189.32	−	7256.12i	0.695668	−	1.20493i	−0.274288	−	0.961648i	$-0.588442\pi$
$331$	4189.32	−	7256.12i	0.695668	−	1.20493i	0.969955	−	0.243284i	$-0.0782247\pi$
$332$	−9992.42	−	17307.4i	−1.65182	−	2.86104i
$333$	−251.724	−	435.999i	−0.0414246	−	0.0717496i
$334$	−6656.83	+	11530.0i	−1.09055	+	1.88890i
$335$	1091.61			0.178032
$336$	10792.2	−	2658.53i	1.75227	−	0.431651i
$337$	−1713.44			−0.276964			−0.138482	−	0.990365i	$-0.544222\pi$
$337$	−1713.44			−0.276964			−0.138482	+	0.990365i	$0.544222\pi$
$338$	−5715.20	+	9899.01i	−0.919721	+	1.59300i
$339$	297.330	+	514.990i	0.0476364	+	0.0825086i
$340$	5070.56	+	8782.46i	0.808793	+	1.40087i
$341$	−601.417	+	1041.68i	−0.0955089	+	0.165426i
$342$	−3044.33			−0.481341
$343$	4756.53	−	4210.58i	0.748772	−	0.662828i
$344$	9655.07			1.51327
$345$	−1042.42	+	1805.53i	−0.162673	+	0.281757i
$346$	−12015.0	−	20810.7i	−1.86686	−	3.23349i
$347$	−1818.16	−	3149.15i	−0.281280	−	0.487191i	0.690420	−	0.723408i	$-0.257426\pi$
$347$	−1818.16	−	3149.15i	−0.281280	−	0.487191i	−0.971700	+	0.236217i	$0.924092\pi$
$348$	−7127.50	+	12345.2i	−1.09791	+	1.90164i
$349$	−3724.99			−0.571330			−0.285665	−	0.958330i	$-0.592214\pi$
$349$	−3724.99			−0.571330			−0.285665	+	0.958330i	$0.592214\pi$
$350$	−2409.89	+	593.649i	−0.368040	+	0.0906625i
$351$	217.095			0.0330133
$352$	−14674.3	+	25416.6i	−2.22199	+	3.84860i
$353$	5653.25	+	9791.71i	0.852385	+	1.47637i	0.879050	+	0.476730i	$0.158178\pi$
$353$	5653.25	+	9791.71i	0.852385	+	1.47637i	−0.0266644	+	0.999644i	$0.508489\pi$
$354$	4602.50	+	7971.77i	0.691018	+	1.19688i
$355$	1161.05	−	2010.99i	0.173583	−	0.300655i
$356$	1067.81			0.158971
$357$	−1512.76	+	5220.08i	−0.224268	+	0.773882i
$358$	−14399.5			−2.12580
$359$	−2943.46	+	5098.23i	−0.432730	+	0.749510i	−0.997107	−	0.0760069i	$-0.975783\pi$
$359$	−2943.46	+	5098.23i	−0.432730	+	0.749510i	0.564378	+	0.825517i	$0.309116\pi$
$360$	−1535.93	−	2660.31i	−0.224863	−	0.389474i
$361$	1438.54	+	2491.62i	0.209730	+	0.363263i
$362$	−2383.35	+	4128.09i	−0.346039	+	0.599358i
$363$	5337.96			0.771819
$364$	−2138.61	−	2227.11i	−0.307949	−	0.320693i
$365$	3987.67			0.571846
$366$	2498.62	−	4327.74i	0.356844	−	0.618072i
$367$	273.108	+	473.037i	0.0388450	+	0.0672816i	0.884794	−	0.465982i	$-0.154299\pi$
$367$	273.108	+	473.037i	0.0388450	+	0.0672816i	−0.845949	+	0.533263i	$0.820965\pi$
$368$	13902.3	+	24079.4i	1.96931	+	3.41094i
$369$	1153.53	−	1997.98i	0.162739	−	0.281872i
$370$	1499.29			0.210660
$371$	9240.28	+	9622.68i	1.29308	+	1.34659i
$372$	−1341.59			−0.186985
$373$	−790.730	+	1369.59i	−0.109765	+	0.190119i	−0.915675	−	0.401919i	$-0.868343\pi$
$373$	−790.730	+	1369.59i	−0.109765	+	0.190119i	0.805910	+	0.592038i	$0.201677\pi$
$374$	−14621.6	−	25325.3i	−2.02156	−	3.50145i
$375$	187.500	+	324.760i	0.0258199	+	0.0447214i
$376$	−6039.45	+	10460.6i	−0.828354	+	1.43475i
$377$	1842.62			0.251724
$378$	746.096	−	2574.56i	0.101521	−	0.350320i
$379$	−8202.81			−1.11174			−0.555871	−	0.831269i	$-0.687615\pi$
$379$	−8202.81			−1.11174			−0.555871	+	0.831269i	$0.687615\pi$
$380$	3271.01	−	5665.56i	0.441578	−	0.764835i
$381$	−1531.51	−	2652.65i	−0.205936	−	0.356692i
$382$	3118.10	+	5400.70i	0.417633	+	0.723361i
$383$	6480.76	−	11225.0i	0.864625	−	1.49757i	−0.00279472	−	0.999996i	$-0.500890\pi$
$383$	6480.76	−	11225.0i	0.864625	−	1.49757i	0.867419	−	0.497578i	$-0.165777\pi$
$384$	−6997.81			−0.929963
$385$	5014.49	−	1235.26i	0.663798	−	0.163519i
$386$	9120.07			1.20259
$387$	636.472	−	1102.40i	0.0836013	−	0.144802i
$388$	16600.8	+	28753.5i	2.17211	+	3.76221i
$389$	−2230.29	−	3862.97i	−0.290694	−	0.503497i	0.683280	−	0.730156i	$-0.260553\pi$
$389$	−2230.29	−	3862.97i	−0.290694	−	0.503497i	−0.973974	+	0.226660i	$0.927220\pi$
$390$	−323.259	+	559.901i	−0.0419714	+	0.0726966i
$391$	−13595.7			−1.75848
$392$	−20735.3	+	10875.8i	−2.67166	+	1.40130i
$393$	−1533.63			−0.196848
$394$	−5164.32	+	8944.86i	−0.660342	+	1.14375i
$395$	1746.76	+	3025.48i	0.222504	+	0.385389i
$396$	5203.69	+	9013.05i	0.660341	+	1.14374i
$397$	5919.55	−	10253.0i	0.748347	−	1.29618i	−0.200267	−	0.979741i	$-0.564181\pi$
$397$	5919.55	−	10253.0i	0.748347	−	1.29618i	0.948614	−	0.316434i	$-0.102486\pi$
$398$	−12623.0			−1.58979
$399$	3404.25	−	838.600i	0.427132	−	0.105219i
$400$	5001.19			0.625149
$401$	−122.264	+	211.768i	−0.0152259	+	0.0263720i	−0.873538	−	0.486756i	$-0.838180\pi$
$401$	−122.264	+	211.768i	−0.0152259	+	0.0263720i	0.858312	+	0.513128i	$0.171513\pi$
$402$	−1755.46	−	3040.54i	−0.217797	−	0.377235i
$403$	86.7080	+	150.183i	0.0107177	+	0.0185636i
$404$	12884.1	−	22316.0i	1.58666	−	2.74817i
$405$	−405.000			−0.0496904
$406$	6332.58	−	21851.9i	0.774090	−	2.67116i
$407$	−3119.72			−0.379947
$408$	10016.1	−	17348.4i	1.21537	−	2.10509i
$409$	6288.44	+	10891.9i	0.760252	+	1.31680i	0.942720	+	0.333584i	$0.108258\pi$
$409$	6288.44	+	10891.9i	0.760252	+	1.31680i	−0.182468	+	0.983212i	$0.558409\pi$
$410$	3435.27	+	5950.06i	0.413795	+	0.716714i
$411$	2124.67	−	3680.04i	0.254993	−	0.441661i
$412$	−654.428			−0.0782557
$413$	−7342.57	−	7646.44i	−0.874829	−	0.911033i
$414$	6705.44			0.796025
$415$	2409.60	−	4173.55i	0.285018	−	0.493666i
$416$	2115.63	+	3664.38i	0.249345	+	0.431878i
$417$	2755.74	+	4773.08i	0.323619	+	0.560524i
$418$	−9432.39	+	16337.4i	−1.10372	+	1.91169i
$419$	7073.59			0.824743			0.412371	−	0.911016i	$-0.364701\pi$
$419$	7073.59			0.824743			0.412371	+	0.911016i	$0.364701\pi$
$420$	3989.66	+	4154.76i	0.463513	+	0.482695i
$421$	9214.48			1.06671			0.533357	−	0.845890i	$-0.320930\pi$
$421$	9214.48			1.06671			0.533357	+	0.845890i	$0.320930\pi$
$422$	−8553.09	+	14814.4i	−0.986631	+	1.70889i
$423$	796.253	+	1379.15i	0.0915252	+	0.158526i
$424$	−24586.4	−	42585.0i	−2.81609	−	4.87762i
$425$	−1222.73	+	2117.83i	−0.139555	+	0.241717i
$426$	−7468.51			−0.849415
$427$	−1601.90	+	5527.67i	−0.181548	+	0.626470i
$428$	−23350.7			−2.63715
$429$	672.636	−	1165.04i	0.0756997	−	0.131116i
$430$	1895.44	+	3282.99i	0.212572	+	0.368186i
$431$	−5093.74	−	8822.62i	−0.569273	−	0.986010i	−0.996638	−	0.0819311i	$-0.973891\pi$
$431$	−5093.74	−	8822.62i	−0.569273	−	0.986010i	0.427365	−	0.904079i	$-0.359442\pi$
$432$	−2700.64	+	4677.65i	−0.300775	+	0.520957i
$433$	7142.00			0.792662			0.396331	−	0.918108i	$-0.370283\pi$
$433$	7142.00			0.792662			0.396331	+	0.918108i	$0.370283\pi$
$434$	2079.03	−	512.145i	0.229946	−	0.0566445i
$435$	−3437.49			−0.378885
$436$	2053.76	−	3557.21i	0.225590	−	0.390733i
$437$	4385.29	+	7595.54i	0.480039	+	0.831451i
$438$	−6412.73	−	11107.2i	−0.699571	−	1.21169i
$439$	383.321	−	663.932i	0.0416741	−	0.0721817i	−0.844436	−	0.535656i	$-0.820064\pi$
$439$	383.321	−	663.932i	0.0416741	−	0.0721817i	0.886110	+	0.463475i	$0.153398\pi$
$440$	−19035.4			−2.06244
$441$	−125.110	+	3084.46i	−0.0135093	+	0.333059i
$442$	−4216.08			−0.453707
$443$	2452.25	−	4247.43i	0.263002	−	0.455534i	−0.704036	−	0.710164i	$-0.748621\pi$
$443$	2452.25	−	4247.43i	0.263002	−	0.455534i	0.967038	+	0.254631i	$0.0819539\pi$
$444$	−1739.80	−	3013.43i	−0.185963	−	0.322097i
$445$	128.747	+	222.996i	0.0137150	+	0.0237551i
$446$	1537.82	−	2663.58i	0.163269	−	0.282790i
$447$	−4109.91			−0.434881
$448$	21948.1	−	5406.67i	2.31462	−	0.570181i
$449$	15496.2			1.62875			0.814377	−	0.580337i	$-0.197079\pi$
$449$	15496.2			1.62875			0.814377	+	0.580337i	$0.197079\pi$
$450$	603.053	−	1044.52i	0.0631737	−	0.109420i
$451$	−7148.10	−	12380.9i	−0.746322	−	1.29267i
$452$	2055.01	+	3559.37i	0.213848	+	0.370396i
$453$	2876.99	−	4983.09i	0.298394	−	0.516834i
$454$	2838.42			0.293423
$455$	207.245	−	715.142i	0.0213534	−	0.0736844i
$456$	−12922.8			−1.32712
$457$	8314.24	−	14400.7i	0.851036	−	1.47404i	−0.0292379	−	0.999572i	$-0.509308\pi$
$457$	8314.24	−	14400.7i	0.851036	−	1.47404i	0.880274	−	0.474465i	$-0.157359\pi$
$458$	−4858.67	−	8415.47i	−0.495701	−	0.858579i
$459$	−1320.54	−	2287.25i	−0.134287	−	0.232592i
$460$	−7204.74	+	12479.0i	−0.730266	+	1.26486i
$461$	−2817.93			−0.284694			−0.142347	−	0.989817i	$-0.545465\pi$
$461$	−2817.93			−0.284694			−0.142347	+	0.989817i	$0.545465\pi$
$462$	−11504.7	−	11980.8i	−1.15854	−	1.20649i
$463$	−10177.0			−1.02153			−0.510763	−	0.859722i	$-0.670637\pi$
$463$	−10177.0			−1.02153			−0.510763	+	0.859722i	$0.670637\pi$
$464$	−22922.0	+	39702.1i	−2.29338	+	3.97225i
$465$	−161.757	−	280.172i	−0.0161319	−	0.0279412i
$466$	15237.0	+	26391.2i	1.51468	+	2.62349i
$467$	−1203.99	+	2085.37i	−0.119302	+	0.206636i	−0.919491	−	0.393111i	$-0.871399\pi$
$467$	−1203.99	+	2085.37i	−0.119302	+	0.206636i	0.800190	+	0.599747i	$0.204732\pi$
$468$	1500.46			0.148203
$469$	2800.56	+	2916.45i	0.275731	+	0.287141i
$470$	−4742.55			−0.465441
$471$	23.0975	−	40.0060i	0.00225961	−	0.00391376i
$472$	19537.0	+	33839.2i	1.90522	+	3.29994i
$473$	−3944.02	−	6831.25i	−0.383396	−	0.664061i
$474$	5618.08	−	9730.81i	0.544403	−	0.942934i
$475$	1577.56			0.152386
$476$	−10455.5	+	36078.8i	−1.00678	+	3.47409i
$477$	−6483.05			−0.622303
$478$	7780.02	−	13475.4i	0.744455	−	1.28943i
$479$	2600.06	+	4503.43i	0.248016	+	0.429576i	0.962975	−	0.269590i	$-0.0868882\pi$
$479$	2600.06	+	4503.43i	0.248016	+	0.429576i	−0.714959	+	0.699166i	$0.753555\pi$
$480$	−3946.80	−	6836.06i	−0.375304	−	0.650046i
$481$	−224.889	+	389.520i	−0.0213182	+	0.0369243i
$482$	10542.4			0.996247
$483$	−7498.21	+	1847.10i	−0.706377	+	0.174008i
$484$	36893.5			3.46483
$485$	−4003.16	+	6933.68i	−0.374792	+	0.649160i
$486$	651.297	+	1128.08i	0.0607889	+	0.105290i
$487$	−9316.35	−	16136.4i	−0.866867	−	1.50146i	−0.865181	−	0.501459i	$-0.832797\pi$
$487$	−9316.35	−	16136.4i	−0.866867	−	1.50146i	−0.00168555	−	0.999999i	$-0.500537\pi$
$488$	10606.3	−	18370.7i	0.983864	−	1.70410i
$489$	1131.40			0.104629
$490$	−7768.72	−	4915.49i	−0.716234	−	0.453182i
$491$	264.978			0.0243550			0.0121775	−	0.999926i	$-0.496124\pi$
$491$	264.978			0.0243550			0.0121775	+	0.999926i	$0.496124\pi$
$492$	7972.70	−	13809.1i	0.730563	−	1.26537i
$493$	−11208.3	−	19413.3i	−1.02393	−	1.77349i
$494$	1359.90	+	2355.41i	0.123855	+	0.214524i
$495$	−1254.83	+	2173.43i	−0.113940	+	0.197350i
$496$	−4314.56			−0.390583
$497$	8351.50	−	2057.30i	0.753754	−	0.185679i
$498$	−15499.9			−1.39471
$499$	−1025.59	+	1776.38i	−0.0920078	+	0.159362i	−0.908356	−	0.418198i	$-0.862662\pi$
$499$	−1025.59	+	1776.38i	−0.0920078	+	0.159362i	0.816348	+	0.577560i	$0.195995\pi$
$500$	1295.91	+	2244.59i	0.115910	+	0.200762i
$501$	3725.51	+	6452.77i	0.332223	+	0.575426i
$502$	−161.431	+	279.607i	−0.0143526	+	0.0248595i
$503$	−2087.24			−0.185021			−0.0925103	−	0.995712i	$-0.529489\pi$
$503$	−2087.24			−0.185021			−0.0925103	+	0.995712i	$0.529489\pi$
$504$	3167.08	−	10928.7i	0.279907	−	0.965876i
$505$	6213.82			0.547547
$506$	20775.8	−	35984.7i	1.82529	−	3.16149i
$507$	3198.52	+	5540.01i	0.280180	+	0.485287i
$508$	−10585.1	−	18333.9i	−0.924484	−	1.60125i
$509$	−11326.9	+	19618.8i	−0.986358	+	1.70842i	−0.350620	+	0.936518i	$0.614029\pi$
$509$	−11326.9	+	19618.8i	−0.986358	+	1.70842i	−0.635738	+	0.771905i	$0.719304\pi$
$510$	7865.27			0.682902
$511$	10230.5	+	10653.9i	0.885657	+	0.922309i
$512$	3974.55			0.343070
$513$	−851.883	+	1475.51i	−0.0733169	+	0.126989i
$514$	11984.4	+	20757.7i	1.02843	+	1.78129i
$515$	−78.9052	−	136.668i	−0.00675141	−	0.0116938i
$516$	4399.00	−	7619.29i	0.375301	−	0.650040i
$517$	9868.28			0.839471
$518$	3846.48	+	4005.66i	0.326264	+	0.339766i
$519$	−13448.5			−1.13743
$520$	−1372.19	+	2376.71i	−0.115720	+	0.200434i
$521$	−7493.64	−	12979.4i	−0.630138	−	1.09143i	−0.987523	−	0.157475i	$-0.949665\pi$
$521$	−7493.64	−	12979.4i	−0.630138	−	1.09143i	0.357385	−	0.933957i	$-0.383669\pi$
$522$	5527.96	+	9574.71i	0.463510	+	0.802823i
$523$	155.632	−	269.562i	0.0130120	−	0.0225375i	−0.859446	−	0.511226i	$-0.829191\pi$
$523$	155.632	−	269.562i	0.0130120	−	0.0225375i	0.872458	+	0.488689i	$0.162525\pi$
$524$	−10599.7			−0.883686
$525$	−386.624	+	1334.13i	−0.0321403	+	0.110907i
$526$	−24766.0			−2.05295
$527$	1054.85	−	1827.06i	0.0871919	−	0.151021i
$528$	16735.1	+	28986.0i	1.37936	+	2.38911i
$529$	−3575.54	−	6193.01i	−0.293872	−	0.509001i
$530$	9653.39	−	16720.2i	0.791163	−	1.37033i
$531$	5151.61			0.421018
$532$	23528.6	−	5796.02i	1.91747	−	0.472348i
$533$	−2061.13			−0.167500
$534$	414.086	−	717.219i	0.0335567	−	0.0581219i
$535$	−2815.43	−	4876.46i	−0.227517	−	0.394071i
$536$	−7451.69	−	12906.7i	−0.600493	−	1.04008i
$537$	−4029.35	+	6979.04i	−0.323798	+	0.560834i
$538$	28896.8			2.31567
$539$	16165.1	+	10228.1i	1.29180	+	0.817360i
$540$	−2799.17			−0.223069
$541$	−4383.11	+	7591.76i	−0.348326	+	0.603319i	−0.985952	−	0.167027i	$-0.946583\pi$
$541$	−4383.11	+	7591.76i	−0.348326	+	0.603319i	0.637626	+	0.770346i	$0.279917\pi$
$542$	5155.66	+	8929.87i	0.408588	+	0.707695i
$543$	1333.85	+	2310.30i	0.105416	+	0.182586i
$544$	25737.9	−	44579.4i	2.02850	−	3.51347i
$545$	990.496			0.0778499
$546$	−2325.22	+	572.793i	−0.182253	+	0.0448961i
$547$	−3650.96			−0.285381			−0.142691	−	0.989767i	$-0.545575\pi$
$547$	−3650.96			−0.285381			−0.142691	+	0.989767i	$0.545575\pi$
$548$	14684.7	−	25434.7i	1.14471	−	1.98270i
$549$	−1398.36	−	2422.03i	−0.108708	−	0.188287i
$550$	−3736.93	−	6472.56i	−0.289715	−	0.501801i
$551$	−7230.47	+	12523.5i	−0.559035	+	0.968277i
$552$	28463.7			2.19474
$553$	−3601.82	+	12428.8i	−0.276971	+	0.955746i
$554$	6992.66			0.536263
$555$	419.540	−	726.665i	0.0320874	−	0.0555770i
$556$	19046.4	+	32989.3i	1.45278	+	2.51629i
$557$	−8010.42	−	13874.5i	−0.609358	−	1.05544i	−0.991346	−	0.131272i	$-0.958094\pi$
$557$	−8010.42	−	13874.5i	−0.609358	−	1.05544i	0.381988	−	0.924167i	$-0.375240\pi$
$558$	−520.257	+	901.112i	−0.0394700	+	0.0683640i
$559$	−1137.24			−0.0860469
$560$	12830.7	+	13361.7i	0.968210	+	1.00828i
$561$	−16366.0			−1.23168
$562$	−23458.5	+	40631.3i	−1.76074	+	3.04969i
$563$	−1164.10	−	2016.29i	−0.0871422	−	0.150935i	0.819160	−	0.573565i	$-0.194440\pi$
$563$	−1164.10	−	2016.29i	−0.0871422	−	0.150935i	−0.906302	+	0.422631i	$0.861107\pi$
$564$	5503.34	+	9532.06i	0.410873	+	0.711653i
$565$	−495.549	+	858.316i	−0.0368990	+	0.0639109i
$566$	24861.1			1.84627
$567$	−1039.04	−	1082.04i	−0.0769589	−	0.0801437i
$568$	−31702.9			−2.34194
$569$	7995.09	−	13847.9i	0.589054	−	1.02027i	−0.405303	−	0.914183i	$-0.632834\pi$
$569$	7995.09	−	13847.9i	0.589054	−	1.02027i	0.994357	−	0.106089i	$-0.0338328\pi$
$570$	−2536.94	−	4394.11i	−0.186422	−	0.322893i
$571$	−8818.68	−	15274.4i	−0.646323	−	1.11946i	−0.983994	−	0.178200i	$-0.942973\pi$
$571$	−8818.68	−	15274.4i	−0.646323	−	1.11946i	0.337671	−	0.941264i	$-0.390361\pi$
$572$	4648.95	−	8052.22i	0.339829	−	0.588602i
$573$	3490.10			0.254452
$574$	−7083.52	+	24443.1i	−0.515088	+	1.77742i
$575$	−3474.74			−0.252011
$576$	−5492.31	+	9512.96i	−0.397303	+	0.688148i
$577$	−5835.27	−	10107.0i	−0.421014	−	0.729218i	0.575025	−	0.818136i	$-0.304992\pi$
$577$	−5835.27	−	10107.0i	−0.421014	−	0.729218i	−0.996039	+	0.0889178i	$0.971659\pi$
$578$	12477.5	+	21611.7i	0.897919	+	1.55524i
$579$	2552.03	−	4420.25i	0.183176	−	0.317270i
$580$	−23758.3			−1.70088
$581$	17332.4	−	4269.64i	1.23764	−	0.304879i
$582$	25750.6			1.83402
$583$	−20086.7	+	34791.3i	−1.42694	+	2.47154i
$584$	−27221.2	−	47148.5i	−1.92880	−	3.34079i
$585$	180.913	+	313.350i	0.0127860	+	0.0221460i
$586$	−25654.7	+	44435.2i	−1.80851	+	3.13243i
$587$	4522.77			0.318015			0.159008	−	0.987277i	$-0.449171\pi$
$587$	4522.77			0.318015			0.159008	+	0.987277i	$0.449171\pi$
$588$	−864.702	+	21318.4i	−0.0606458	+	1.49516i
$589$	−1360.97			−0.0952086
$590$	−7670.84	+	13286.3i	−0.535260	+	0.927098i
$591$	2890.22	+	5006.02i	0.201164	+	0.348426i
$592$	−5595.20	−	9691.17i	−0.388448	−	0.672812i
$593$	5431.08	−	9406.90i	0.376100	−	0.651425i	−0.614391	−	0.789002i	$-0.710598\pi$
$593$	5431.08	−	9406.90i	0.376100	−	0.651425i	0.990491	+	0.137577i	$0.0439314\pi$
$594$	8071.78			0.557557
$595$	−8795.16	+	2166.59i	−0.605994	+	0.149280i
$596$	−28405.8			−1.95226
$597$	−3532.26	+	6118.05i	−0.242154	+	0.419422i
$598$	−2995.30	−	5188.02i	−0.204828	−	0.354772i
$599$	9230.05	+	15986.9i	0.629598	+	1.09050i	0.987632	+	0.156788i	$0.0501139\pi$
$599$	9230.05	+	15986.9i	0.629598	+	1.09050i	−0.358034	+	0.933709i	$0.616553\pi$
$600$	2559.88	−	4433.85i	0.174178	−	0.301685i
$601$	−3423.67			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$601$	−3423.67			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$602$	−3908.39	+	13486.7i	−0.264608	+	0.913084i
$603$	−1964.89			−0.132697
$604$	19884.4	−	34440.8i	1.33954	−	2.32016i
$605$	4448.30	+	7704.68i	0.298924	+	0.517752i
$606$	−9992.70	−	17307.9i	−0.669844	−	1.16020i
$607$	1944.53	−	3368.03i	0.130027	−	0.225213i	−0.793660	−	0.608362i	$-0.791827\pi$
$607$	1944.53	−	3368.03i	0.130027	−	0.225213i	0.923687	+	0.383149i	$0.125160\pi$
$608$	−33207.1			−2.21501
$609$	−8819.00	−	9183.96i	−0.586805	−	0.611089i
$610$	8328.73			0.552821
$611$	711.369	−	1232.13i	0.0471013	−	0.0815819i
$612$	−9127.00	−	15808.4i	−0.602838	−	1.04415i
$613$	−8385.29	−	14523.8i	−0.552494	−	0.956948i	−0.998094	−	0.0617155i	$-0.980343\pi$
$613$	−8385.29	−	14523.8i	−0.552494	−	0.956948i	0.445600	−	0.895232i	$-0.352990\pi$
$614$	−9728.54	+	16850.3i	−0.639433	+	1.10753i
$615$	3845.12			0.252114
$616$	−48835.9	−	50856.9i	−3.19425	−	3.32644i
$617$	−9538.02			−0.622344			−0.311172	−	0.950354i	$-0.600721\pi$
$617$	−9538.02			−0.622344			−0.311172	+	0.950354i	$0.600721\pi$
$618$	−253.781	+	439.562i	−0.0165187	+	0.0286113i
$619$	9595.22	+	16619.4i	0.623044	+	1.07914i	0.988916	+	0.148479i	$0.0474376\pi$
$619$	9595.22	+	16619.4i	0.623044	+	1.07914i	−0.365872	+	0.930665i	$0.619229\pi$
$620$	−1117.99	−	1936.42i	−0.0724188	−	0.125433i
$621$	1876.36	−	3249.95i	0.121249	−	0.210009i
$622$	−17931.9			−1.15595
$623$	−265.476	+	916.079i	−0.0170723	+	0.0589116i
$624$	4825.48			0.309574
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	8018.54	+	13888.5i	0.511957	+	0.886736i
$627$	5278.86	+	9143.26i	0.336232	+	0.582371i
$628$	159.639	−	276.503i	0.0101438	−	0.0175696i
$629$	5471.82			0.346861
$630$	4337.80	−	1068.57i	0.274321	−	0.0675758i
$631$	−2832.90			−0.178726			−0.0893630	−	0.995999i	$-0.528483\pi$
$631$	−2832.90			−0.178726			−0.0893630	+	0.995999i	$0.528483\pi$
$632$	23848.1	−	41306.1i	1.50099	−	2.59979i
$633$	4786.76	+	8290.91i	0.300563	+	0.520591i
$634$	9988.95	+	17301.4i	0.625728	+	1.08379i
$635$	2552.52	−	4421.09i	0.159517	−	0.276292i
$636$	−44807.9			−2.79363
$637$	2442.35	−	1281.03i	0.151914	−	0.0796799i
$638$	68510.2			4.25132
$639$	−2089.89	+	3619.79i	−0.129381	+	0.224095i
$640$	−5831.51	−	10100.5i	−0.360173	−	0.623838i
$641$	−6794.77	−	11768.9i	−0.418685	−	0.725184i	0.577122	−	0.816658i	$-0.304176\pi$
$641$	−6794.77	−	11768.9i	−0.418685	−	0.725184i	−0.995808	+	0.0914734i	$0.970842\pi$
$642$	−9055.21	+	15684.1i	−0.556667	+	0.964176i
$643$	28091.9			1.72292			0.861460	−	0.507825i	$-0.169550\pi$
$643$	28091.9			1.72292			0.861460	+	0.507825i	$0.169550\pi$
$644$	−51824.2	+	12766.3i	−3.17105	+	0.781153i
$645$	2121.57			0.129515
$646$	16543.9	−	28654.9i	1.00760	−	1.74522i
$647$	−794.222	−	1375.63i	−0.0482598	−	0.0835884i	0.840886	−	0.541212i	$-0.182034\pi$
$647$	−794.222	−	1375.63i	−0.0482598	−	0.0835884i	−0.889146	+	0.457623i	$0.848701\pi$
$648$	2764.67	+	4788.55i	0.167603	+	0.290297i
$649$	15961.5	−	27646.1i	0.965396	−	1.67212i
$650$	−1077.53			−0.0650218
$651$	333.543	−	1150.96i	0.0200808	−	0.0692929i
$652$	7819.69			0.469697
$653$	−5025.26	+	8704.01i	−0.301154	+	0.521614i	−0.976398	−	0.215980i	$-0.930705\pi$
$653$	−5025.26	+	8704.01i	−0.301154	+	0.521614i	0.675243	+	0.737595i	$0.264039\pi$
$654$	−1592.86	−	2758.91i	−0.0952379	−	0.164957i
$655$	−1278.02	−	2213.60i	−0.0762390	−	0.132050i
$656$	25640.2	−	44410.1i	1.52604	−	2.64318i
$657$	−7177.80			−0.426229
$658$	−12167.2	−	12670.7i	−0.720860	−	0.750692i
$659$	−10190.8			−0.602392			−0.301196	−	0.953562i	$-0.597386\pi$
$659$	−10190.8			−0.602392			−0.301196	+	0.953562i	$0.597386\pi$
$660$	−8672.81	+	15021.8i	−0.511498	+	0.885941i
$661$	5350.93	+	9268.08i	0.314867	+	0.545365i	0.979409	−	0.201885i	$-0.0647068\pi$
$661$	5350.93	+	9268.08i	0.314867	+	0.545365i	−0.664542	+	0.747251i	$0.731373\pi$
$662$	−22456.7	−	38896.2i	−1.31844	−	2.28360i
$663$	−1179.77	+	2043.42i	−0.0691077	+	0.119698i
$664$	−65795.1			−3.84540
$665$	4047.29	+	4214.78i	0.236011	+	0.245778i
$666$	−2698.72			−0.157017
$667$	15925.8	−	27584.3i	0.924513	−	1.60130i
$668$	25749.0	+	44598.6i	1.49141	+	2.58319i
$669$	−860.646	−	1490.68i	−0.0497376	−	0.0861481i
$670$	2925.76	−	5067.57i	0.168704	−	0.292205i
$671$	−17330.4			−0.997069
$672$	8138.29	−	28082.9i	0.467175	−	1.61208i
$673$	−11624.2			−0.665794			−0.332897	−	0.942963i	$-0.608026\pi$
$673$	−11624.2			−0.665794			−0.332897	+	0.942963i	$0.608026\pi$
$674$	−4592.41	+	7954.29i	−0.262453	+	0.454581i
$675$	−337.500	−	584.567i	−0.0192450	−	0.0333333i
$676$	22106.7	+	38290.0i	1.25778	+	2.17854i
$677$	−10021.6	+	17357.8i	−0.568921	+	0.985400i	0.427752	+	0.903896i	$0.359306\pi$
$677$	−10021.6	+	17357.8i	−0.568921	+	0.985400i	−0.996673	+	0.0815041i	$0.974028\pi$
$678$	3187.65			0.180562
$679$	−28795.0	+	7093.34i	−1.62747	+	0.400909i
$680$	33387.1			1.88285
$681$	794.266	−	1375.71i	0.0446936	−	0.0774115i
$682$	3223.87	+	5583.91i	0.181010	+	0.313518i
$683$	−15377.9	−	26635.4i	−0.861523	−	1.49220i	−0.870459	−	0.492242i	$-0.836178\pi$
$683$	−15377.9	−	26635.4i	−0.861523	−	1.49220i	0.00893555	−	0.999960i	$-0.497156\pi$
$684$	−5887.83	+	10198.0i	−0.329133	+	0.570074i
$685$	7082.23			0.395034
$686$	−6798.17	−	33366.6i	−0.378361	−	1.85706i
$687$	−5438.34			−0.302017
$688$	14147.2	−	24503.6i	0.783948	−	1.35784i
$689$	2895.96	+	5015.96i	0.160127	+	0.277348i
$690$	5587.87	+	9678.47i	0.308299	+	0.533990i
$691$	−10001.4	+	17323.0i	−0.550612	+	0.953688i	0.447618	+	0.894225i	$0.352272\pi$
$691$	−10001.4	+	17323.0i	−0.550612	+	0.953688i	−0.998230	+	0.0594636i	$0.981061\pi$
$692$	−92949.9			−5.10611
$693$	−9026.08	+	2223.47i	−0.494766	+	0.121880i
$694$	−19492.4			−1.06617
$695$	−4592.90	+	7955.13i	−0.250674	+	0.434180i
$696$	23465.5	+	40643.5i	1.27796	+	2.21349i
$697$	12537.4	+	21715.4i	0.681332	+	1.18010i
$698$	−9983.84	+	17292.5i	−0.541396	+	0.937725i
$699$	17054.8			0.922850
$700$	−2672.17	+	9220.88i	−0.144284	+	0.497881i
$701$	8023.60			0.432307			0.216154	−	0.976359i	$-0.430649\pi$
$701$	8023.60			0.432307			0.216154	+	0.976359i	$0.430649\pi$
$702$	581.866	−	1007.82i	0.0312836	−	0.0541848i
$703$	−1764.94	−	3056.96i	−0.0946882	−	0.164005i
$704$	34034.2	+	58948.9i	1.82203	+	3.15585i
$705$	−1327.09	+	2298.59i	−0.0708951	+	0.122794i
$706$	60608.1			3.23090
$707$	15941.8	+	16601.5i	0.848024	+	0.883118i
$708$	35605.5			1.89003
$709$	2719.14	−	4709.68i	0.144033	−	0.249472i	−0.784979	−	0.619523i	$-0.787326\pi$
$709$	2719.14	−	4709.68i	0.144033	−	0.249472i	0.929012	+	0.370050i	$0.120660\pi$
$710$	−6223.76	−	10779.9i	−0.328977	−	0.569805i
$711$	−3144.18	−	5445.87i	−0.165845	−	0.287252i
$712$	1757.74	−	3044.50i	0.0925200	−	0.160249i
$713$	2997.68			0.157453
$714$	20178.6	+	21013.7i	1.05766	+	1.10143i
$715$	2242.12			0.117273
$716$	−27849.0	+	48235.9i	−1.45358	+	2.51768i
$717$	−4354.11	−	7541.53i	−0.226788	−	0.392808i
$718$	15778.3	+	27328.9i	0.820114	+	1.42048i
$719$	3496.60	−	6056.29i	0.181365	−	0.314133i	−0.760981	−	0.648774i	$-0.775282\pi$
$719$	3496.60	−	6056.29i	0.181365	−	0.314133i	0.942345	+	0.334642i	$0.108615\pi$
$720$	−9002.14			−0.465958
$721$	162.702	−	561.438i	0.00840409	−	0.0290001i
$722$	15422.5			0.794966
$723$	2950.03	−	5109.60i	0.151746	−	0.262833i
$724$	9218.96	+	15967.7i	0.473232	+	0.819662i
$725$	−2864.57	−	4961.59i	−0.146741	−	0.254164i
$726$	14307.0	−	24780.4i	0.731380	−	1.26679i
$727$	−13075.4			−0.667040			−0.333520	−	0.942743i	$-0.608236\pi$
$727$	−13075.4			−0.667040			−0.333520	+	0.942743i	$0.608236\pi$
$728$	−9870.28	+	2431.43i	−0.502496	+	0.123784i
$729$	729.000			0.0370370
$730$	10687.9	−	18511.9i	0.541885	−	0.938572i
$731$	6917.61	+	11981.7i	0.350010	+	0.606235i
$732$	−9664.82	−	16740.0i	−0.488008	−	0.845255i
$733$	16073.0	−	27839.3i	0.809919	−	1.40282i	−0.103001	−	0.994681i	$-0.532845\pi$
$733$	16073.0	−	27839.3i	0.809919	−	1.40282i	0.912920	−	0.408139i	$-0.133822\pi$
$734$	2927.98			0.147239
$735$	−4556.30	+	2389.81i	−0.228655	+	0.119931i
$736$	73141.9			3.66310
$737$	−6087.92	+	10544.6i	−0.304276	+	0.527021i
$738$	−6183.49	−	10710.1i	−0.308425	−	0.534207i
$739$	7227.86	+	12519.0i	0.359785	+	0.623166i	0.987925	−	0.154935i	$-0.0495167\pi$
$739$	7227.86	+	12519.0i	0.359785	+	0.623166i	−0.628140	+	0.778101i	$0.716183\pi$
$740$	2899.67	−	5022.38i	0.144046	−	0.249495i
$741$	1522.14			0.0754617
$742$	69437.5	−	17105.1i	3.43549	−	0.846293i
$743$	15926.4			0.786383			0.393191	−	0.919457i	$-0.371371\pi$
$743$	15926.4			0.786383			0.393191	+	0.919457i	$0.371371\pi$
$744$	−2208.43	+	3825.11i	−0.108824	+	0.188488i
$745$	−3424.92	−	5932.14i	−0.168429	−	0.291727i
$746$	4238.68	+	7341.62i	0.208029	+	0.360316i
$747$	−4337.28	+	7512.38i	−0.212440	+	0.367957i
$748$	−113114.			−5.52924
$749$	5805.40	−	20032.7i	0.283211	−	0.977277i
$750$	2010.18			0.0978683
$751$	4621.42	−	8004.53i	0.224551	−	0.388934i	−0.731634	−	0.681698i	$-0.761242\pi$
$751$	4621.42	−	8004.53i	0.224551	−	0.388934i	0.956185	+	0.292764i	$0.0945751\pi$
$752$	17698.7	+	30655.1i	0.858253	+	1.48654i
$753$	90.3453	+	156.483i	0.00437233	+	0.00757310i
$754$	4938.66	−	8554.01i	0.238535	−	0.413155i
$755$	9589.95			0.462270
$756$	−7181.38	−	7478.57i	−0.345482	−	0.359779i
$757$	2940.51			0.141182			0.0705908	−	0.997505i	$-0.477512\pi$
$757$	2940.51			0.141182			0.0705908	+	0.997505i	$0.477512\pi$
$758$	−21985.4	+	38079.9i	−1.05349	+	1.82470i
$759$	−11627.2	−	20138.9i	−0.556049	−	0.963105i
$760$	−10769.0	−	18652.4i	−0.513990	−	0.890257i
$761$	−1376.21	+	2383.67i	−0.0655555	+	0.113545i	−0.896940	−	0.442152i	$-0.854215\pi$
$761$	−1376.21	+	2383.67i	−0.0655555	+	0.113545i	0.831385	+	0.555697i	$0.187549\pi$
$762$	−16419.2			−0.780585
$763$	2541.15	+	2646.31i	0.120571	+	0.125561i
$764$	24122.0			1.14228
$765$	2200.91	−	3812.09i	0.104018	−	0.180165i
$766$	−34739.9	−	60171.3i	−1.63865	−	2.83822i
$767$	−2301.21	−	3985.81i	−0.108334	−	0.187639i
$768$	−4109.61	+	7118.05i	−0.193090	+	0.334441i
$769$	−17709.9			−0.830473			−0.415236	−	0.909714i	$-0.636301\pi$
$769$	−17709.9			−0.830473			−0.415236	+	0.909714i	$0.636301\pi$
$770$	7705.54	−	26589.6i	0.360634	−	1.24444i
$771$	13414.2			0.626592
$772$	17638.5	−	30550.8i	0.822310	−	1.42428i
$773$	−5817.01	−	10075.4i	−0.270664	−	0.468804i	0.698368	−	0.715739i	$-0.253910\pi$
$773$	−5817.01	−	10075.4i	−0.270664	−	0.468804i	−0.969032	+	0.246935i	$0.920577\pi$
$774$	−3411.79	−	5909.39i	−0.158442	−	0.274430i
$775$	269.596	−	466.953i	0.0124957	−	0.0216432i
$776$	109308.			5.05661
$777$	3017.78	−	743.397i	0.139334	−	0.0343233i
$778$	−23910.8			−1.10185
$779$	8087.88	−	14008.6i	0.371988	−	0.644301i
$780$	1250.38	+	2165.73i	0.0573987	+	0.0994174i
$781$	12950.4	+	22430.7i	0.593343	+	1.02770i
$782$	−36439.6	+	63115.3i	−1.66634	+	2.88619i
$783$	6187.48			0.282404
$784$	−2780.88	+	68559.9i	−0.126680	+	3.12317i
$785$	76.9916			0.00350057
$786$	−4110.48	+	7119.57i	−0.186534	+	0.323087i
$787$	−7297.97	−	12640.5i	−0.330552	−	0.572533i	0.652068	−	0.758161i	$-0.273902\pi$
$787$	−7297.97	−	12640.5i	−0.330552	−	0.572533i	−0.982620	+	0.185627i	$0.940568\pi$
$788$	19975.9	+	34599.3i	0.903061	+	1.56415i
$789$	−6930.19	+	12003.4i	−0.312701	+	0.541614i
$790$	18726.9			0.843386
$791$	−3564.52	+	878.080i	−0.160227	+	0.0394702i
$792$	34263.7			1.53726
$793$	−1249.29	+	2163.83i	−0.0559439	+	0.0968977i
$794$	−31731.6	−	54960.7i	−1.41828	−	2.45653i
$795$	−5402.54	−	9357.48i	−0.241017	−	0.417454i
$796$	−24413.4	+	42285.2i	−1.08707	+	1.88286i
$797$	25967.8			1.15411			0.577055	−	0.816705i	$-0.304202\pi$
$797$	25967.8			1.15411			0.577055	+	0.816705i	$0.304202\pi$
$798$	5231.16	−	18051.2i	0.232057	−	0.800760i
$799$	−17308.4			−0.766369
$800$	6578.00	−	11393.4i	0.290709	−	0.503523i
$801$	−231.745	−	401.393i	−0.0102226	−	0.0177060i
$802$	655.393	+	1135.17i	0.0288563	+	0.0499805i
$803$	−22239.3	+	38519.6i	−0.977345	+	1.69281i
$804$	−13580.4			−0.595702
$805$	−8914.57	−	9283.48i	−0.390307	−	0.406459i
$806$	929.591			0.0406246
$807$	8086.08	−	14005.5i	0.352718	−	0.610925i
$808$	−42417.7	−	73469.7i	−1.84685	−	3.19883i
$809$	−13757.0	−	23827.8i	−0.597861	−	1.03553i	−0.993136	−	0.116963i	$-0.962684\pi$
$809$	−13757.0	−	23827.8i	−0.597861	−	1.03553i	0.395275	−	0.918563i	$-0.370649\pi$
$810$	−1085.49	+	1880.13i	−0.0470869	+	0.0815569i
$811$	33883.1			1.46707			0.733537	−	0.679650i	$-0.237868\pi$
$811$	33883.1			1.46707			0.733537	+	0.679650i	$0.237868\pi$
$812$	−60952.9	−	63475.3i	−2.63427	−	2.74329i
$813$	5770.76			0.248941
$814$	−8361.57	+	14482.7i	−0.360040	+	0.623608i
$815$	942.830	+	1633.03i	0.0405226	+	0.0701871i
$816$	−29352.4	−	50839.9i	−1.25924	−	2.18107i
$817$	4462.55	−	7729.36i	0.191095	−	0.330987i
$818$	67417.9			2.88168
$819$	−373.041	+	1287.26i	−0.0159159	+	0.0549211i
$820$	26575.7			1.13178
$821$	9729.17	−	16851.4i	0.413582	−	0.716344i	−0.581697	−	0.813406i	$-0.697611\pi$
$821$	9729.17	−	16851.4i	0.413582	−	0.716344i	0.995278	+	0.0970613i	$0.0309443\pi$
$822$	−11389.2	−	19726.7i	−0.483266	−	0.837042i
$823$	1248.35	+	2162.21i	0.0528734	+	0.0915794i	0.891251	−	0.453511i	$-0.149829\pi$
$823$	1248.35	+	2162.21i	0.0528734	+	0.0915794i	−0.838377	+	0.545090i	$0.816495\pi$
$824$	−1077.27	+	1865.89i	−0.0455442	+	0.0788849i
$825$	−4182.77			−0.176516
$826$	−55176.9	+	13592.2i	−2.32427	+	0.572559i
$827$	3945.43			0.165896			0.0829481	−	0.996554i	$-0.473566\pi$
$827$	3945.43			0.165896			0.0829481	+	0.996554i	$0.473566\pi$
$828$	12968.5	−	22462.1i	0.544308	−	0.942770i
$829$	−20225.8	−	35032.1i	−0.847371	−	1.46769i	−0.883546	−	0.468344i	$-0.844851\pi$
$829$	−20225.8	−	35032.1i	−0.847371	−	1.46769i	0.0361756	−	0.999345i	$-0.488482\pi$
$830$	−12916.6	−	22372.2i	−0.540170	−	0.935601i
$831$	1956.73	−	3389.16i	0.0816826	−	0.141478i
$832$	9813.62			0.408925
$833$	−28352.8	−	17939.6i	−1.17931	−	0.746184i
$834$	29544.1			1.22665
$835$	−6209.18	+	10754.6i	−0.257339	+	0.445723i
$836$	36485.1	+	63194.0i	1.50940	+	2.61437i
$837$	291.163	+	504.310i	0.0120240	+	0.0208262i
$838$	18958.9	−	32837.7i	0.781531	−	1.35365i
$839$	3760.13			0.154725			0.0773625	−	0.997003i	$-0.475350\pi$
$839$	3760.13			0.154725			0.0773625	+	0.997003i	$0.475350\pi$
$840$	18413.4	−	4535.94i	0.756337	−	0.186315i
$841$	28128.0			1.15331
$842$	24697.0	−	42776.4i	1.01082	−	1.75080i
$843$	13128.6	+	22739.4i	0.536385	+	0.929047i
$844$	33083.9	+	57303.0i	1.34928	+	2.33703i
$845$	−5330.87	+	9233.34i	−0.217027	+	0.375901i
$846$	8536.58			0.346919
$847$	−9172.38	+	31651.2i	−0.372098	+	1.28400i
$848$	−144102.			−5.83548
$849$	6956.79	−	12049.5i	0.281221	−	0.487089i
$850$	6554.39	+	11352.5i	0.264487	+	0.458104i
$851$	3887.45	+	6733.26i	0.156592	+	0.271226i
$852$	−14444.3	+	25018.3i	−0.580815	+	1.00600i
$853$	42156.4			1.69215			0.846076	−	0.533062i	$-0.178959\pi$
$853$	42156.4			1.69215			0.846076	+	0.533062i	$0.178959\pi$
$854$	21367.7	+	22251.9i	0.856190	+	0.891623i
$855$	−2839.61			−0.113582
$856$	−38438.2	+	66576.9i	−1.53480	+	2.65836i
$857$	2017.92	+	3495.14i	0.0804327	+	0.139313i	0.903436	−	0.428723i	$-0.141036\pi$
$857$	2017.92	+	3495.14i	0.0804327	+	0.139313i	−0.823003	+	0.568037i	$0.807703\pi$
$858$	−3605.64	−	6245.16i	−0.143467	−	0.248492i
$859$	−14940.7	+	25878.0i	−0.593445	+	1.02788i	0.400320	+	0.916376i	$0.368899\pi$
$859$	−14940.7	+	25878.0i	−0.593445	+	1.02788i	−0.993764	+	0.111501i	$0.964434\pi$
$860$	14663.3			0.581414
$861$	9864.79	+	10273.0i	0.390466	+	0.406625i
$862$	−54609.7			−2.15779
$863$	−8247.49	+	14285.1i	−0.325316	+	0.563464i	−0.981576	−	0.191071i	$-0.938804\pi$
$863$	−8247.49	+	14285.1i	−0.325316	+	0.563464i	0.656260	+	0.754535i	$0.272137\pi$
$864$	7104.24	+	12304.9i	0.279735	+	0.484516i
$865$	−11207.1	−	19411.2i	−0.440523	−	0.763008i
$866$	19142.2	−	33155.3i	0.751131	−	1.30100i
$867$	13966.2			0.547077
$868$	2305.30	−	7954.91i	0.0901462	−	0.311068i
$869$	−38967.0			−1.52113
$870$	−9213.27	+	15957.9i	−0.359034	+	0.621864i
$871$	877.713	+	1520.24i	0.0341448	+	0.0591406i
$872$	−6761.47	−	11711.2i	−0.262583	−	0.454807i
$873$	7205.70	−	12480.6i	0.279354	−	0.483855i
$874$	47014.4			1.81955
$875$	−2247.83	+	553.729i	−0.0868465	+	0.0213937i
$876$	−49609.6			−1.91342
$877$	−4028.63	+	6977.79i	−0.155116	+	0.268670i	−0.933101	−	0.359613i	$-0.882909\pi$
$877$	−4028.63	+	6977.79i	−0.155116	+	0.268670i	0.777985	+	0.628283i	$0.216242\pi$
$878$	−2054.78	−	3558.99i	−0.0789813	−	0.136800i
$879$	14357.7	+	24868.3i	0.550937	+	0.954251i
$880$	−27891.8	+	48309.9i	−1.06844	+	1.85060i
$881$	−29494.1			−1.12790			−0.563951	−	0.825808i	$-0.690719\pi$
$881$	−29494.1			−1.12790			−0.563951	+	0.825808i	$0.690719\pi$
$882$	13983.7	+	8847.88i	0.533849	+	0.337782i
$883$	16169.1			0.616234			0.308117	−	0.951348i	$-0.400301\pi$
$883$	16169.1			0.616234			0.308117	+	0.951348i	$0.400301\pi$
$884$	−8154.02	+	14123.2i	−0.310237	+	0.537346i
$885$	4293.01	+	7435.70i	0.163060	+	0.282428i
$886$	−13145.2	−	22768.2i	−0.498445	−	0.863333i
$887$	−11078.2	+	19187.9i	−0.419356	+	0.726345i	−0.995875	−	0.0907385i	$-0.971077\pi$
$887$	−11078.2	+	19187.9i	−0.419356	+	0.726345i	0.576519	+	0.817084i	$0.304411\pi$
$888$	−11455.7			−0.432915
$889$	18360.4	−	4522.89i	0.692676	−	0.170633i
$890$	1380.29			0.0519858
$891$	2258.70	−	3912.17i	0.0849261	−	0.147096i
$892$	−5948.39	−	10302.9i	−0.223281	−	0.386734i
$893$	5582.84	+	9669.76i	0.209208	+	0.362359i
$894$	−11015.5	+	19079.4i	−0.412096	+	0.713772i
$895$	−13431.2			−0.501625
$896$	12024.6	−	41493.2i	0.448340	−	1.54709i
$897$	−3352.66			−0.124796
$898$	41533.4	−	71938.0i	1.54342	−	2.67328i
$899$	2471.28	+	4280.39i	0.0916818	+	0.158798i
$900$	−2332.64	−	4040.26i	−0.0863943	−	0.149639i
$901$	35231.1	−	61022.1i	1.30268	−	2.25632i
$902$	−76634.4			−2.82887
$903$	5442.97	+	5668.22i	0.200588	+	0.208889i
$904$	13531.2			0.497832
$905$	−2223.08	+	3850.49i	−0.0816550	+	0.141431i
$906$	−15422.0	−	26711.7i	−0.565520	−	0.979510i
$907$	−13555.1	−	23478.2i	−0.496241	−	0.859515i	0.503749	−	0.863850i	$-0.331954\pi$
$907$	−13555.1	−	23478.2i	−0.496241	−	0.859515i	−0.999991	+	0.00433477i	$0.998620\pi$
$908$	5489.60	−	9508.26i	0.200637	−	0.347514i
$909$	−11184.9			−0.408118
$910$	−2764.44	−	2878.84i	−0.100704	−	0.104871i
$911$	5041.03			0.183334			0.0916668	−	0.995790i	$-0.470781\pi$
$911$	5041.03			0.183334			0.0916668	+	0.995790i	$0.470781\pi$
$912$	−18935.2	+	32796.8i	−0.687509	+	1.19080i
$913$	26876.8	+	46551.9i	0.974251	+	1.68745i
$914$	−44568.2	−	77194.4i	−1.61289	−	2.79361i
$915$	2330.60	−	4036.72i	0.0842046	−	0.145847i
$916$	−37587.3			−1.35581
$917$	2635.28	−	9093.58i	0.0949015	−	0.327477i
$918$	−14157.5			−0.509005
$919$	6838.54	−	11844.7i	0.245465	−	0.425159i	−0.716797	−	0.697282i	$-0.754393\pi$
$919$	6838.54	−	11844.7i	0.245465	−	0.425159i	0.962262	+	0.272123i	$0.0877259\pi$
$920$	23719.8	+	41083.9i	0.850020	+	1.47228i
$921$	5444.60	+	9430.33i	0.194795	+	0.337394i
$922$	−7552.70	+	13081.7i	−0.269778	+	0.467269i
$923$	3734.19			0.133166
$924$	−62384.1	+	15367.6i	−2.22109	+	0.547141i
$925$	1398.47			0.0497096
$926$	−27276.8	+	47244.8i	−0.968003	+	1.67663i
$927$	142.029	+	246.002i	0.00503221	+	0.00871604i
$928$	60298.2	+	104439.i	2.13296	+	3.69439i
$929$	8185.68	−	14178.0i	0.289089	−	0.500717i	−0.684504	−	0.729009i	$-0.739981\pi$
$929$	8185.68	−	14178.0i	0.289089	−	0.500717i	0.973593	+	0.228293i	$0.0733144\pi$
$930$	−1734.19			−0.0611466
$931$	−877.194	+	21626.4i	−0.0308796	+	0.761306i
$932$	117875.			4.14284
$933$	−5017.81	+	8691.10i	−0.176073	+	0.304967i
$934$	6453.93	+	11178.5i	0.226102	+	0.391620i
$935$	−13638.4	−	23622.3i	−0.477029	−	0.826238i
$936$	2469.95	−	4278.07i	0.0862529	−	0.149394i
$937$	32666.3			1.13891			0.569456	−	0.822022i	$-0.307154\pi$
$937$	32666.3			1.13891			0.569456	+	0.822022i	$0.307154\pi$
$938$	21045.2	−	5184.25i	0.732569	−	0.180460i
$939$	8975.19			0.311922
$940$	−9172.23	+	15886.8i	−0.318261	+	0.551244i
$941$	−4543.44	−	7869.47i	−0.157398	−	0.272622i	0.776531	−	0.630079i	$-0.216977\pi$
$941$	−4543.44	−	7869.47i	−0.157398	−	0.272622i	−0.933930	+	0.357457i	$0.883644\pi$
$942$	−123.813	−	214.451i	−0.00428244	−	0.00741740i
$943$	−17814.4	+	30855.4i	−0.615181	+	1.06552i
$944$	114507.			3.94798
$945$	695.924	−	2401.43i	0.0239560	−	0.0826651i
$946$	−42283.6			−1.45323
$947$	20433.1	−	35391.1i	0.701147	−	1.21442i	−0.266918	−	0.963719i	$-0.586005\pi$
$947$	20433.1	−	35391.1i	0.701147	−	1.21442i	0.968064	−	0.250702i	$-0.0806615\pi$
$948$	−21731.1	−	37639.4i	−0.744508	−	1.28953i
$949$	3206.31	+	5553.49i	0.109675	+	0.189962i
$950$	4228.23	−	7323.52i	0.144402	−	0.250112i
$951$	11180.7			0.381239
$952$	85655.7	+	89200.5i	2.91609	+	3.03677i
$953$	−32033.7			−1.08885			−0.544424	−	0.838810i	$-0.683252\pi$
$953$	−32033.7			−1.08885			−0.544424	+	0.838810i	$0.683252\pi$
$954$	−17376.1	+	30096.3i	−0.589698	+	1.02139i
$955$	2908.42	+	5037.53i	0.0985489	+	0.170692i
$956$	−30093.6	−	52123.6i	−1.01809	−	1.76339i
$957$	19171.0	−	33205.1i	0.647554	−	1.12160i
$958$	27875.0			0.940085
$959$	18169.7	+	18921.7i	0.611815	+	0.637135i
$960$	−18307.7			−0.615499
$961$	14662.9	−	25396.9i	0.492193	−	0.852503i
$962$	1205.51	+	2088.01i	0.0404026	+	0.0699793i
$963$	5067.77	+	8777.63i	0.169581	+	0.293723i
$964$	20389.2	−	35315.2i	0.681217	−	1.17990i
$965$	8506.78			0.283775
$966$	−11522.2	+	39759.6i	−0.383768	+	1.32427i
$967$	−28106.6			−0.934691			−0.467345	−	0.884075i	$-0.654790\pi$
$967$	−28106.6			−0.934691			−0.467345	+	0.884075i	$0.654790\pi$
$968$	60731.4	−	105190.i	2.01651	−	3.49269i
$969$	−9258.85	−	16036.8i	−0.306953	−	0.531658i
$970$	21458.8	+	37167.8i	0.710311	+	1.23029i
$971$	−11360.2	+	19676.5i	−0.375455	+	0.650306i	−0.990395	−	0.138267i	$-0.955847\pi$
$971$	−11360.2	+	19676.5i	−0.375455	+	0.650306i	0.614940	+	0.788574i	$0.289180\pi$
$972$	5038.51			0.166266
$973$	−33037.0	+	8138.30i	−1.08851	+	0.268142i
$974$	−99880.0			−3.28579
$975$	−301.521	+	522.250i	−0.00990400	+	0.0171542i
$976$	−31082.0	−	53835.7i	−1.01938	−	1.76561i
$977$	28316.3	+	49045.3i	0.927246	+	1.60604i	0.787909	+	0.615791i	$0.211164\pi$
$977$	28316.3	+	49045.3i	0.927246	+	1.60604i	0.139336	+	0.990245i	$0.455503\pi$
$978$	3032.41	−	5252.28i	0.0991469	−	0.171727i
$979$	−2872.10			−0.0937617
$980$	−31491.0	+	16517.2i	−1.02647	+	0.538392i
$981$	−1782.89			−0.0580259
$982$	710.203	−	1230.11i	0.0230789	−	0.0399738i
$983$	18297.5	+	31692.2i	0.593693	+	1.02831i	0.993730	+	0.111807i	$0.0356639\pi$
$983$	18297.5	+	31692.2i	0.593693	+	1.02831i	−0.400037	+	0.916499i	$0.631003\pi$
$984$	−26248.1	−	45463.1i	−0.850365	−	1.47288i
$985$	−4817.04	+	8343.36i	−0.155821	+	0.269890i
$986$	−120163.			−3.88112
$987$	−9545.84	+	2351.51i	−0.307850	+	0.0758353i
$988$	10520.3			0.338761
$989$	−9829.21	+	17024.7i	−0.316027	+	0.547375i
$990$	6726.48	+	11650.6i	0.215941	+	0.374021i
$991$	20601.7	+	35683.3i	0.660379	+	1.14381i	0.980516	+	0.196439i	$0.0629377\pi$
$991$	20601.7	+	35683.3i	0.660379	+	1.14381i	−0.320137	+	0.947371i	$0.603729\pi$
$992$	−5674.88	+	9829.18i	−0.181631	+	0.314594i
$993$	−25135.9			−0.803288
$994$	12833.4	−	44284.2i	0.409507	−	1.41309i
$995$	−11774.2			−0.375143
$996$	−29977.3	+	51922.1i	−0.953681	+	1.65182i
$997$	17652.9	+	30575.7i	0.560754	+	0.971255i	0.997431	+	0.0716364i	$0.0228221\pi$
$997$	17652.9	+	30575.7i	0.560754	+	0.971255i	−0.436676	+	0.899619i	$0.643845\pi$
$998$	5497.66	+	9522.23i	0.174374	+	0.302025i
$999$	−755.173	+	1308.00i	−0.0239165	+	0.0414246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.e.16.5	✓	10
3.2	odd	2		315.4.j.f.226.1		10
7.2	even	3		735.4.a.y.1.1		5
7.4	even	3	inner	105.4.i.e.46.5	yes	10
7.5	odd	6		735.4.a.x.1.1		5
21.2	odd	6		2205.4.a.bw.1.5		5
21.5	even	6		2205.4.a.bv.1.5		5
21.11	odd	6		315.4.j.f.46.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.e.16.5	✓	10	1.1	even	1	trivial
105.4.i.e.46.5	yes	10	7.4	even	3	inner
315.4.j.f.46.1		10	21.11	odd	6
315.4.j.f.226.1		10	3.2	odd	2
735.4.a.x.1.1		5	7.5	odd	6
735.4.a.y.1.1		5	7.2	even	3
2205.4.a.bv.1.5		5	21.5	even	6
2205.4.a.bw.1.5		5	21.2	odd	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.68023 - 4.64230i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.3673 - 17.9567i) q^{4} +(2.50000 - 4.33013i) q^{5} -16.0814 q^{6} +(17.9827 - 4.42983i) q^{7} -68.2635 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(2.68023 - 4.64230i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-10.3673 - 17.9567i) q^{4} +(2.50000 - 4.33013i) q^{5} -16.0814 q^{6} +(17.9827 - 4.42983i) q^{7} -68.2635 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-13.4012 - 23.2115i) q^{10} +(27.8851 + 48.2985i) q^{11} +(-31.1019 + 53.8701i) q^{12} +8.04056 q^{13} +(27.6332 - 95.3540i) q^{14} -15.0000 q^{15} +(-100.024 + 173.246i) q^{16} +(-48.9091 - 84.7130i) q^{17} +(24.1221 + 41.7807i) q^{18} +(-31.5512 + 54.6483i) q^{19} -103.673 q^{20} +(-38.4830 - 40.0756i) q^{21} +298.955 q^{22} +(69.4947 - 120.368i) q^{23} +(102.395 + 177.354i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(21.5506 - 37.3267i) q^{26} +27.0000 q^{27} +(-265.977 - 276.984i) q^{28} +229.166 q^{29} +(-40.2035 + 69.6345i) q^{30} +(10.7838 + 18.6781i) q^{31} +(263.120 + 455.737i) q^{32} +(83.6554 - 144.895i) q^{33} -524.351 q^{34} +(25.7750 - 88.9418i) q^{35} +186.612 q^{36} +(-27.9694 + 48.4444i) q^{37} +(169.129 + 292.941i) q^{38} +(-12.0608 - 20.8900i) q^{39} +(-170.659 + 295.590i) q^{40} -256.341 q^{41} +(-289.187 + 71.2379i) q^{42} -141.438 q^{43} +(578.187 - 1001.45i) q^{44} +(22.5000 + 38.9711i) q^{45} +(-372.524 - 645.231i) q^{46} +(88.4726 - 153.239i) q^{47} +600.143 q^{48} +(303.753 - 159.320i) q^{49} -134.012 q^{50} +(-146.727 + 254.139i) q^{51} +(-83.3590 - 144.382i) q^{52} +(360.170 + 623.832i) q^{53} +(72.3663 - 125.342i) q^{54} +278.851 q^{55} +(-1227.56 + 302.396i) q^{56} +189.307 q^{57} +(614.218 - 1063.86i) q^{58} +(-286.200 - 495.714i) q^{59} +(155.510 + 269.351i) q^{60} +(-155.373 + 269.114i) q^{61} +115.613 q^{62} +(-46.3949 + 160.095i) q^{63} +1220.51 q^{64} +(20.1014 - 34.8166i) q^{65} +(-448.432 - 776.707i) q^{66} +(109.161 + 189.072i) q^{67} +(-1014.11 + 1756.49i) q^{68} -416.968 q^{69} +(-343.812 - 358.040i) q^{70} +464.419 q^{71} +(307.186 - 532.062i) q^{72} +(398.767 + 690.684i) q^{73} +(149.929 + 259.684i) q^{74} +(-37.5000 + 64.9519i) q^{75} +1308.41 q^{76} +(715.403 + 745.009i) q^{77} -129.304 q^{78} +(-349.353 + 605.097i) q^{79} +(500.119 + 866.231i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-687.054 + 1190.01i) q^{82} +963.839 q^{83} +(-320.660 + 1106.51i) q^{84} -489.091 q^{85} +(-379.088 + 656.599i) q^{86} +(-343.749 - 595.390i) q^{87} +(-1903.54 - 3297.02i) q^{88} +(-25.7494 + 44.5993i) q^{89} +241.221 q^{90} +(144.591 - 35.6183i) q^{91} -2881.89 q^{92} +(32.3515 - 56.0344i) q^{93} +(-474.255 - 821.433i) q^{94} +(157.756 + 273.242i) q^{95} +(789.360 - 1367.21i) q^{96} -1601.27 q^{97} +(74.5164 - 1837.13i) q^{98} -501.932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9}+O(q^{10}) \) 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9	\( 10 q + q^{2} - 15 q^{3} - 21 q^{4} + 25 q^{5} - 6 q^{6} + 56 q^{7} - 138 q^{8} - 45 q^{9} - 5 q^{10} + 33 q^{11} - 63 q^{12} - 46 q^{13} - 73 q^{14} - 150 q^{15} - 113 q^{16} + 136 q^{17} + 9 q^{18} + 39 q^{19} - 210 q^{20} - 147 q^{21} - 174 q^{22} + 133 q^{23} + 207 q^{24} - 125 q^{25} + 73 q^{26} + 270 q^{27} - 809 q^{28} + 544 q^{29} - 15 q^{30} + 430 q^{31} + 573 q^{32} + 99 q^{33} - 744 q^{34} + 35 q^{35} + 378 q^{36} - 3 q^{37} + 837 q^{38} + 69 q^{39} - 345 q^{40} - 1254 q^{41} - 372 q^{42} + 216 q^{43} + 1809 q^{44} + 225 q^{45} - 1637 q^{46} + 553 q^{47} + 678 q^{48} - 386 q^{49} - 50 q^{50} + 408 q^{51} + 1047 q^{52} + 1135 q^{53} + 27 q^{54} + 330 q^{55} - 1356 q^{56} - 234 q^{57} + 2564 q^{58} + 332 q^{59} + 315 q^{60} + 584 q^{61} - 3124 q^{62} - 63 q^{63} + 2274 q^{64} - 115 q^{65} + 261 q^{66} - 412 q^{67} - 1712 q^{68} - 798 q^{69} - 985 q^{70} - 284 q^{71} + 621 q^{72} + 2074 q^{73} - 605 q^{74} - 375 q^{75} + 18 q^{76} - 751 q^{77} - 438 q^{78} - 28 q^{79} + 565 q^{80} - 405 q^{81} - 1515 q^{82} - 1680 q^{83} - 1077 q^{84} + 1360 q^{85} - 40 q^{86} - 816 q^{87} - 4181 q^{88} + 2978 q^{89} + 90 q^{90} - 2736 q^{91} + 1062 q^{92} + 1290 q^{93} + 843 q^{94} - 195 q^{95} + 1719 q^{96} - 4336 q^{97} - 5183 q^{98} - 594 q^{99}+O(q^{100}) \) 10 * q + q^2 - 15 * q^3 - 21 * q^4 + 25 * q^5 - 6 * q^6 + 56 * q^7 - 138 * q^8 - 45 * q^9 - 5 * q^10 + 33 * q^11 - 63 * q^12 - 46 * q^13 - 73 * q^14 - 150 * q^15 - 113 * q^16 + 136 * q^17 + 9 * q^18 + 39 * q^19 - 210 * q^20 - 147 * q^21 - 174 * q^22 + 133 * q^23 + 207 * q^24 - 125 * q^25 + 73 * q^26 + 270 * q^27 - 809 * q^28 + 544 * q^29 - 15 * q^30 + 430 * q^31 + 573 * q^32 + 99 * q^33 - 744 * q^34 + 35 * q^35 + 378 * q^36 - 3 * q^37 + 837 * q^38 + 69 * q^39 - 345 * q^40 - 1254 * q^41 - 372 * q^42 + 216 * q^43 + 1809 * q^44 + 225 * q^45 - 1637 * q^46 + 553 * q^47 + 678 * q^48 - 386 * q^49 - 50 * q^50 + 408 * q^51 + 1047 * q^52 + 1135 * q^53 + 27 * q^54 + 330 * q^55 - 1356 * q^56 - 234 * q^57 + 2564 * q^58 + 332 * q^59 + 315 * q^60 + 584 * q^61 - 3124 * q^62 - 63 * q^63 + 2274 * q^64 - 115 * q^65 + 261 * q^66 - 412 * q^67 - 1712 * q^68 - 798 * q^69 - 985 * q^70 - 284 * q^71 + 621 * q^72 + 2074 * q^73 - 605 * q^74 - 375 * q^75 + 18 * q^76 - 751 * q^77 - 438 * q^78 - 28 * q^79 + 565 * q^80 - 405 * q^81 - 1515 * q^82 - 1680 * q^83 - 1077 * q^84 + 1360 * q^85 - 40 * q^86 - 816 * q^87 - 4181 * q^88 + 2978 * q^89 + 90 * q^90 - 2736 * q^91 + 1062 * q^92 + 1290 * q^93 + 843 * q^94 - 195 * q^95 + 1719 * q^96 - 4336 * q^97 - 5183 * q^98 - 594 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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