LMFDB - Embedded newform 58.4.d.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,4,Mod(7,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	58.d (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.42211078033$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	58.49
Dual form			58.4.d.b.45.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80194 + 0.867767i) q^{2} +(-6.26334 - 7.85398i) q^{3} +(2.49396 - 3.12733i) q^{4} +(-7.20732 + 3.47086i) q^{5} +(18.1016 + 8.71726i) q^{6} +(14.4870 + 18.1662i) q^{7} +(-1.78017 + 7.79942i) q^{8} +(-16.4475 + 72.0612i) q^{9} +(9.97524 - 12.5086i) q^{10} +(-8.88988 - 38.9491i) q^{11} -40.1825 q^{12} +(7.55990 + 33.1221i) q^{13} +(-41.8688 - 20.1629i) q^{14} +(72.4020 + 34.8669i) q^{15} +(-3.56033 - 15.5988i) q^{16} -43.6530 q^{17} +(-32.8950 - 144.122i) q^{18} +(-77.8705 + 97.6465i) q^{19} +(-7.12024 + 31.1958i) q^{20} +(51.9395 - 227.562i) q^{21} +(49.8178 + 62.4695i) q^{22} +(80.5529 + 38.7923i) q^{23} +(72.4063 - 34.8690i) q^{24} +(-38.0377 + 47.6977i) q^{25} +(-42.3647 - 53.1237i) q^{26} +(424.612 - 204.482i) q^{27} +92.9416 q^{28} +(-148.377 - 48.7155i) q^{29} -160.720 q^{30} +(-75.1593 + 36.1948i) q^{31} +(19.9517 + 25.0186i) q^{32} +(-250.225 + 313.773i) q^{33} +(78.6601 - 37.8807i) q^{34} +(-167.465 - 80.6469i) q^{35} +(184.339 + 231.154i) q^{36} +(-0.516358 + 2.26231i) q^{37} +(55.5833 - 243.527i) q^{38} +(212.790 - 266.830i) q^{39} +(-14.2405 - 62.3916i) q^{40} -351.355 q^{41} +(103.879 + 455.124i) q^{42} +(-65.0648 - 31.3336i) q^{43} +(-143.978 - 69.3360i) q^{44} +(-131.572 - 576.455i) q^{45} -178.814 q^{46} +(91.4175 + 400.526i) q^{47} +(-100.213 + 125.664i) q^{48} +(-43.8109 + 191.948i) q^{49} +(27.1510 - 118.956i) q^{50} +(273.414 + 342.850i) q^{51} +(122.438 + 58.9628i) q^{52} +(-72.2330 + 34.7856i) q^{53} +(-587.682 + 736.929i) q^{54} +(199.259 + 249.863i) q^{55} +(-167.475 + 80.6517i) q^{56} +1254.64 q^{57} +(309.640 - 40.9747i) q^{58} +79.3066 q^{59} +(289.608 - 139.468i) q^{60} +(-9.87121 - 12.3781i) q^{61} +(104.024 - 130.442i) q^{62} +(-1547.35 + 745.166i) q^{63} +(-57.6620 - 27.7686i) q^{64} +(-169.449 - 212.482i) q^{65} +(178.609 - 782.536i) q^{66} +(99.3614 - 435.331i) q^{67} +(-108.869 + 136.517i) q^{68} +(-199.857 - 875.630i) q^{69} +371.744 q^{70} +(-149.484 - 654.931i) q^{71} +(-532.757 - 256.562i) q^{72} +(905.926 + 436.271i) q^{73} +(-1.03272 - 4.52462i) q^{74} +612.860 q^{75} +(111.167 + 487.053i) q^{76} +(578.769 - 725.753i) q^{77} +(-151.888 + 665.463i) q^{78} +(150.850 - 660.919i) q^{79} +(79.8019 + 100.068i) q^{80} +(-2467.44 - 1188.26i) q^{81} +(633.121 - 304.895i) q^{82} +(-677.369 + 849.394i) q^{83} +(-582.125 - 729.962i) q^{84} +(314.621 - 151.514i) q^{85} +144.433 q^{86} +(546.727 + 1470.47i) q^{87} +319.606 q^{88} +(-964.051 + 464.263i) q^{89} +(737.314 + 924.562i) q^{90} +(-492.181 + 617.175i) q^{91} +(322.212 - 155.169i) q^{92} +(755.021 + 363.599i) q^{93} +(-512.292 - 642.394i) q^{94} +(222.320 - 974.048i) q^{95} +(71.5315 - 313.400i) q^{96} +(-542.326 + 680.055i) q^{97} +(-87.6218 - 383.896i) q^{98} +2952.94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 5 q^{3} - 16 q^{4} + 16 q^{5} - 4 q^{6} + 71 q^{7} - 32 q^{8} - 27 q^{9} - 10 q^{10} + 110 q^{11} - 64 q^{12} - 107 q^{13} - 54 q^{14} + 417 q^{15} - 64 q^{16} - 128 q^{17} - 54 q^{18}+ \cdots + 10560 q^{99}+O(q^{100}) $ 24 * q - 8 * q^2 + 5 * q^3 - 16 * q^4 + 16 * q^5 - 4 * q^6 + 71 * q^7 - 32 * q^8 - 27 * q^9 - 10 * q^10 + 110 * q^11 - 64 * q^12 - 107 * q^13 - 54 * q^14 + 417 * q^15 - 64 * q^16 - 128 * q^17 - 54 * q^18 - 142 * q^19 + 36 * q^20 + 655 * q^21 + 24 * q^22 - 239 * q^23 - 16 * q^24 - 550 * q^25 + 192 * q^26 - 61 * q^27 - 24 * q^28 - 450 * q^29 - 2092 * q^30 + 420 * q^31 - 128 * q^32 + 165 * q^33 + 934 * q^34 - 532 * q^35 + 88 * q^36 + 85 * q^37 + 626 * q^38 + 1374 * q^39 + 72 * q^40 - 822 * q^41 + 1310 * q^42 + 245 * q^43 - 260 * q^44 + 916 * q^45 + 712 * q^46 + 235 * q^47 + 80 * q^48 - 1507 * q^49 + 510 * q^50 + 333 * q^51 + 104 * q^52 - 121 * q^53 - 836 * q^54 - 584 * q^55 - 216 * q^56 - 1458 * q^57 + 2432 * q^58 - 5226 * q^59 + 1668 * q^60 - 567 * q^61 - 252 * q^62 + 1096 * q^63 - 256 * q^64 + 584 * q^65 + 8 * q^66 - 131 * q^67 + 412 * q^68 - 1412 * q^69 + 1036 * q^70 + 3141 * q^71 - 1112 * q^72 + 3326 * q^73 + 170 * q^74 + 7850 * q^75 + 1252 * q^76 + 2834 * q^77 - 4126 * q^78 + 1728 * q^79 - 80 * q^80 - 10976 * q^81 + 1184 * q^82 - 1287 * q^83 - 2756 * q^84 - 7728 * q^85 - 3724 * q^86 + 4541 * q^87 - 912 * q^88 + 715 * q^89 - 2004 * q^90 - 6757 * q^91 - 956 * q^92 + 4094 * q^93 - 496 * q^94 - 4759 * q^95 + 160 * q^96 + 1779 * q^97 - 3014 * q^98 + 10560 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$	−1.80194	+	0.867767i	−0.637081	+	0.306802i
$2$	−1.80194	+	0.867767i	−0.637081	+	0.306802i
$3$	−6.26334	−	7.85398i	−1.20538	−	1.51150i	−0.802948	−	0.596049i	$-0.796736\pi$
$3$	−6.26334	−	7.85398i	−1.20538	−	1.51150i	−0.402432	−	0.915450i	$-0.631835\pi$
$4$	2.49396	−	3.12733i	0.311745	−	0.390916i
$5$	−7.20732	+	3.47086i	−0.644642	+	0.310443i	−0.727489	−	0.686119i	$-0.759313\pi$
$5$	−7.20732	+	3.47086i	−0.644642	+	0.310443i	0.0828472	+	0.996562i	$0.473599\pi$
$6$	18.1016	+	8.71726i	1.23166	+	0.593134i
$7$	14.4870	+	18.1662i	0.782227	+	0.980881i	0.999988	+	0.00487929i	$0.00155313\pi$
$7$	14.4870	+	18.1662i	0.782227	+	0.980881i	−0.217761	+	0.976002i	$0.569875\pi$
$8$	−1.78017	+	7.79942i	−0.0786730	+	0.344689i
$9$	−16.4475	+	72.0612i	−0.609167	+	2.66893i
$10$	9.97524	−	12.5086i	0.315445	−	0.395555i
$11$	−8.88988	−	38.9491i	−0.243673	−	1.06760i	−0.937644	−	0.347597i	$-0.886998\pi$
$11$	−8.88988	−	38.9491i	−0.243673	−	1.06760i	0.693971	−	0.720003i	$-0.255860\pi$
$12$	−40.1825			−0.966640
$13$	7.55990	+	33.1221i	0.161288	+	0.706647i	0.989295	+	0.145930i	$0.0466174\pi$
$13$	7.55990	+	33.1221i	0.161288	+	0.706647i	−0.828007	+	0.560717i	$0.810525\pi$
$14$	−41.8688	−	20.1629i	−0.799278	−	0.384912i
$15$	72.4020	+	34.8669i	1.24627	+	0.600174i
$16$	−3.56033	−	15.5988i	−0.0556302	−	0.243732i
$17$	−43.6530			−0.622789			−0.311395	−	0.950281i	$-0.600796\pi$
$17$	−43.6530			−0.622789			−0.311395	+	0.950281i	$0.600796\pi$
$18$	−32.8950	−	144.122i	−0.430746	−	1.88722i
$19$	−77.8705	+	97.6465i	−0.940249	+	1.17903i	0.0434221	+	0.999057i	$0.486174\pi$
$19$	−77.8705	+	97.6465i	−0.940249	+	1.17903i	−0.983671	+	0.179978i	$0.942397\pi$
$20$	−7.12024	+	31.1958i	−0.0796067	+	0.348780i
$21$	51.9395	−	227.562i	0.539720	−	2.36467i
$22$	49.8178	+	62.4695i	0.482781	+	0.605389i
$23$	80.5529	+	38.7923i	0.730280	+	0.351684i	0.761794	−	0.647819i	$-0.224319\pi$
$23$	80.5529	+	38.7923i	0.730280	+	0.351684i	−0.0315141	+	0.999503i	$0.510033\pi$
$24$	72.4063	−	34.8690i	0.615828	−	0.296567i
$25$	−38.0377	+	47.6977i	−0.304301	+	0.381582i
$26$	−42.3647	−	53.1237i	−0.319554	−	0.400708i
$27$	424.612	−	204.482i	3.02654	−	1.45751i
$28$	92.9416			0.627297
$29$	−148.377	−	48.7155i	−0.950102	−	0.311939i
$29$	−148.377	−	48.7155i	−0.950102	−	0.311939i
$30$	−160.720			−0.978112
$31$	−75.1593	+	36.1948i	−0.435452	+	0.209703i	−0.638750	−	0.769414i	$-0.720548\pi$
$31$	−75.1593	+	36.1948i	−0.435452	+	0.209703i	0.203298	+	0.979117i	$0.434834\pi$
$32$	19.9517	+	25.0186i	0.110218	+	0.138210i
$33$	−250.225	+	313.773i	−1.31996	+	1.65518i
$34$	78.6601	−	37.8807i	0.396767	−	0.191073i
$35$	−167.465	−	80.6469i	−0.808764	−	0.389480i
$36$	184.339	+	231.154i	0.853424	+	1.07016i
$37$	−0.516358	+	2.26231i	−0.00229429	+	0.0100519i	−0.976062	−	0.217492i	$-0.930212\pi$
$37$	−0.516358	+	2.26231i	−0.00229429	+	0.0100519i	0.973768	+	0.227544i	$0.0730695\pi$
$38$	55.5833	−	243.527i	0.237284	−	1.03961i
$39$	212.790	−	266.830i	0.873683	−	1.09556i
$40$	−14.2405	−	62.3916i	−0.0562905	−	0.246625i
$41$	−351.355			−1.33835			−0.669177	−	0.743103i	$-0.733353\pi$
$41$	−351.355			−1.33835			−0.669177	+	0.743103i	$0.733353\pi$
$42$	103.879	+	455.124i	0.381640	+	1.67207i
$43$	−65.0648	−	31.3336i	−0.230751	−	0.111124i	0.314936	−	0.949113i	$-0.398017\pi$
$43$	−65.0648	−	31.3336i	−0.230751	−	0.111124i	−0.545687	+	0.837989i	$0.683731\pi$
$44$	−143.978	−	69.3360i	−0.493306	−	0.237563i
$45$	−131.572	−	576.455i	−0.435858	−	1.90962i
$46$	−178.814			−0.573145
$47$	91.4175	+	400.526i	0.283715	+	1.24304i	0.892989	+	0.450078i	$0.148604\pi$
$47$	91.4175	+	400.526i	0.283715	+	1.24304i	−0.609274	+	0.792959i	$0.708539\pi$
$48$	−100.213	+	125.664i	−0.301345	+	0.377875i
$49$	−43.8109	+	191.948i	−0.127729	+	0.559615i
$50$	27.1510	−	118.956i	0.0767945	−	0.336459i
$51$	273.414	+	342.850i	0.750698	+	0.941345i
$52$	122.438	+	58.9628i	0.326520	+	0.157244i
$53$	−72.2330	+	34.7856i	−0.187207	+	0.0901541i	−0.525139	−	0.851016i	$-0.675987\pi$
$53$	−72.2330	+	34.7856i	−0.187207	+	0.0901541i	0.337932	+	0.941170i	$0.390272\pi$
$54$	−587.682	+	736.929i	−1.48099	+	1.85710i
$55$	199.259	+	249.863i	0.488511	+	0.612574i
$56$	−167.475	+	80.6517i	−0.399639	+	0.192456i
$57$	1254.64			2.91547
$58$	309.640	−	40.9747i	0.700996	−	0.0927628i
$59$	79.3066			0.174997			0.0874987	−	0.996165i	$-0.472113\pi$
$59$	79.3066			0.174997			0.0874987	+	0.996165i	$0.472113\pi$
$60$	289.608	−	139.468i	0.623137	−	0.300087i
$61$	−9.87121	−	12.3781i	−0.0207193	−	0.0259812i	0.771364	−	0.636394i	$-0.219575\pi$
$61$	−9.87121	−	12.3781i	−0.0207193	−	0.0259812i	−0.792083	+	0.610413i	$0.791003\pi$
$62$	104.024	−	130.442i	0.213081	−	0.267195i
$63$	−1547.35	+	745.166i	−3.09441	+	1.49019i
$64$	−57.6620	−	27.7686i	−0.112621	−	0.0542355i
$65$	−169.449	−	212.482i	−0.323347	−	0.405464i
$66$	178.609	−	782.536i	0.333109	−	1.45945i
$67$	99.3614	−	435.331i	0.181178	−	0.793793i	−0.799893	−	0.600143i	$-0.795110\pi$
$67$	99.3614	−	435.331i	0.181178	−	0.793793i	0.981071	−	0.193650i	$-0.0620326\pi$
$68$	−108.869	+	136.517i	−0.194151	+	0.243458i
$69$	−199.857	−	875.630i	−0.348695	−	1.52773i
$70$	371.744			0.634742
$71$	−149.484	−	654.931i	−0.249866	−	1.09473i	−0.931701	−	0.363227i	$-0.881675\pi$
$71$	−149.484	−	654.931i	−0.249866	−	1.09473i	0.681835	−	0.731506i	$-0.261182\pi$
$72$	−532.757	−	256.562i	−0.872027	−	0.419946i
$73$	905.926	+	436.271i	1.45247	+	0.699475i	0.983023	−	0.183483i	$-0.0587372\pi$
$73$	905.926	+	436.271i	1.45247	+	0.699475i	0.469452	+	0.882958i	$0.344452\pi$
$74$	−1.03272	−	4.52462i	−0.00162231	−	0.00710779i
$75$	612.860			0.943559
$76$	111.167	+	487.053i	0.167785	+	0.735116i
$77$	578.769	−	725.753i	0.856582	−	1.07412i
$78$	−151.888	+	665.463i	−0.220486	+	0.966011i
$79$	150.850	−	660.919i	0.214836	−	0.941256i	−0.746394	−	0.665505i	$-0.768216\pi$
$79$	150.850	−	660.919i	0.214836	−	0.941256i	0.961229	−	0.275751i	$-0.0889266\pi$
$80$	79.8019	+	100.068i	0.111527	+	0.139850i
$81$	−2467.44	−	1188.26i	−3.38469	−	1.62998i
$82$	633.121	−	304.895i	0.852640	−	0.410610i
$83$	−677.369	+	849.394i	−0.895795	+	1.12329i	0.0959914	+	0.995382i	$0.469398\pi$
$83$	−677.369	+	849.394i	−0.895795	+	1.12329i	−0.991786	+	0.127909i	$0.959174\pi$
$84$	−582.125	−	729.962i	−0.756132	−	0.948159i
$85$	314.621	−	151.514i	0.401476	−	0.193341i
$86$	144.433			0.181100
$87$	546.727	+	1470.47i	0.673739	+	1.81208i
$88$	319.606			0.387161
$89$	−964.051	+	464.263i	−1.14819	+	0.552941i	−0.908491	−	0.417905i	$-0.862764\pi$
$89$	−964.051	+	464.263i	−1.14819	+	0.552941i	−0.239703	+	0.970846i	$0.577050\pi$
$90$	737.314	+	924.562i	0.863552	+	1.08286i
$91$	−492.181	+	617.175i	−0.566973	+	0.710962i
$92$	322.212	−	155.169i	0.365140	−	0.175842i
$93$	755.021	+	363.599i	0.841850	+	0.405414i
$94$	−512.292	−	642.394i	−0.562116	−	0.704871i
$95$	222.320	−	974.048i	0.240101	−	1.05195i
$96$	71.5315	−	313.400i	0.0760485	−	0.333190i
$97$	−542.326	+	680.055i	−0.567679	+	0.711846i	−0.979956	−	0.199212i	$-0.936162\pi$
$97$	−542.326	+	680.055i	−0.567679	+	0.711846i	0.412278	+	0.911058i	$0.364733\pi$
$98$	−87.6218	−	383.896i	−0.0903177	−	0.395708i
$99$	2952.94			2.99779
$100$	54.3019	+	237.912i	0.0543019	+	0.237912i
$101$	551.818	+	265.741i	0.543643	+	0.261804i	0.685487	−	0.728084i	$-0.259589\pi$
$101$	551.818	+	265.741i	0.543643	+	0.261804i	−0.141845	+	0.989889i	$0.545303\pi$
$102$	−790.189	−	380.535i	−0.767062	−	0.369398i
$103$	−286.059	−	1253.31i	−0.273653	−	1.19895i	−0.905665	−	0.423994i	$-0.860628\pi$
$103$	−286.059	−	1253.31i	−0.273653	−	1.19895i	0.632012	−	0.774959i	$-0.282229\pi$
$104$	−271.791			−0.256262
$105$	415.491	+	1820.39i	0.386169	+	1.69192i
$106$	99.9736	−	125.363i	0.0916065	−	0.114871i
$107$	133.085	−	583.082i	0.120241	−	0.526810i	−0.878550	−	0.477650i	$-0.841489\pi$
$107$	133.085	−	583.082i	0.120241	−	0.526810i	0.998791	−	0.0491597i	$-0.0156543\pi$
$108$	419.482	−	1837.87i	0.373747	−	1.63749i
$109$	678.550	+	850.875i	0.596269	+	0.747697i	0.984791	−	0.173742i	$-0.0555858\pi$
$109$	678.550	+	850.875i	0.596269	+	0.747697i	−0.388522	+	0.921439i	$0.627014\pi$
$110$	−575.876	−	277.327i	−0.499160	−	0.240383i
$111$	21.0023	−	10.1142i	0.0179590	−	0.00864859i
$112$	231.793	−	290.659i	0.195557	−	0.245220i
$113$	229.457	+	287.729i	0.191022	+	0.239534i	0.868114	−	0.496364i	$-0.165332\pi$
$113$	229.457	+	287.729i	0.191022	+	0.239534i	−0.677093	+	0.735898i	$0.736760\pi$
$114$	−2260.79	+	1088.74i	−1.85739	+	0.894471i
$115$	−715.213			−0.579948
$116$	−522.396	+	342.530i	−0.418131	+	0.274164i
$117$	−2511.16			−1.98425
$118$	−142.906	+	68.8197i	−0.111488	+	0.0536896i
$119$	−632.403	−	793.009i	−0.487162	−	0.610882i
$120$	−400.830	+	502.625i	−0.304921	+	0.382359i
$121$	−238.815	+	115.007i	−0.179425	+	0.0864066i
$122$	28.5286	+	13.7387i	0.0211710	+	0.0101954i
$123$	2200.66	+	2759.54i	1.61322	+	2.02292i
$124$	−74.2513	+	325.316i	−0.0537739	+	0.235599i
$125$	331.105	−	1450.67i	0.236919	−	1.03801i
$126$	2141.60	−	2685.48i	1.51420	−	1.89875i
$127$	−23.8323	−	104.416i	−0.0166518	−	0.0729561i	0.965919	−	0.258843i	$-0.0833413\pi$
$127$	−23.8323	−	104.416i	−0.0166518	−	0.0729561i	−0.982571	+	0.185887i	$0.940484\pi$
$128$	128.000			0.0883883
$129$	161.430	+	707.270i	0.110179	+	0.482726i
$130$	489.721	+	235.837i	0.330395	+	0.159110i
$131$	691.532	+	333.024i	0.461217	+	0.222110i	0.650039	−	0.759901i	$-0.274753\pi$
$131$	691.532	+	333.024i	0.461217	+	0.222110i	−0.188822	+	0.982011i	$0.560467\pi$
$132$	357.217	+	1565.07i	0.235544	+	1.03198i
$133$	−2901.98			−1.89198
$134$	198.723	+	870.662i	0.128112	+	0.561296i
$135$	−2350.59	+	2947.54i	−1.49856	+	1.87914i
$136$	77.7097	−	340.469i	0.0489967	−	0.214669i
$137$	−173.757	+	761.278i	−0.108358	+	0.474747i	0.891410	+	0.453198i	$0.149717\pi$
$137$	−173.757	+	761.278i	−0.108358	+	0.474747i	−0.999768	+	0.0215490i	$0.993140\pi$
$138$	1119.97	+	1404.40i	0.690858	+	0.866309i
$139$	−1727.39	−	831.867i	−1.05407	−	0.507612i	−0.175127	−	0.984546i	$-0.556034\pi$
$139$	−1727.39	−	831.867i	−1.05407	−	0.507612i	−0.878939	+	0.476934i	$0.841748\pi$
$140$	−669.860	+	322.588i	−0.404382	+	0.194740i
$141$	2573.14	−	3226.62i	1.53686	−	1.92717i
$142$	837.689	+	1050.43i	0.495051	+	0.620775i
$143$	1222.87	−	588.903i	0.715115	−	0.344381i
$144$	1182.63			0.684393
$145$	1238.49	−	163.889i	0.709315	−	0.0938638i
$146$	−2011.00			−1.13994
$147$	1781.96	−	858.146i	0.999819	−	0.481488i
$148$	5.78721	+	7.25693i	0.00321423	+	0.00403051i
$149$	−2171.55	+	2723.03i	−1.19396	+	1.49718i	−0.371425	+	0.928463i	$0.621131\pi$
$149$	−2171.55	+	2723.03i	−1.19396	+	1.49718i	−0.822534	+	0.568715i	$0.807441\pi$
$150$	−1104.33	+	531.820i	−0.601124	+	0.289486i
$151$	759.726	+	365.865i	0.409441	+	0.197177i	0.627255	−	0.778814i	$-0.284178\pi$
$151$	759.726	+	365.865i	0.409441	+	0.197177i	−0.217814	+	0.975990i	$0.569893\pi$
$152$	−622.964	−	781.172i	−0.332428	−	0.416852i
$153$	717.983	−	3145.69i	0.379382	−	1.66218i
$154$	−413.120	+	1810.00i	−0.216170	+	0.947103i
$155$	416.070	−	521.735i	0.215610	−	0.270366i
$156$	−303.775	−	1330.93i	−0.155907	−	0.683073i
$157$	−2379.46			−1.20957			−0.604783	−	0.796390i	$-0.706740\pi$
$157$	−2379.46			−1.20957			−0.604783	+	0.796390i	$0.706740\pi$
$158$	301.701	+	1321.84i	0.151912	+	0.665568i
$159$	725.625	+	349.443i	0.361923	+	0.174293i
$160$	−230.634	−	111.068i	−0.113958	−	0.0548791i
$161$	462.267	+	2025.32i	0.226284	+	0.991415i
$162$	5477.30			2.65640
$163$	−719.167	−	3150.88i	−0.345580	−	1.51408i	−0.787096	−	0.616830i	$-0.788416\pi$
$163$	−719.167	−	3150.88i	−0.345580	−	1.51408i	0.441516	−	0.897253i	$-0.354441\pi$
$164$	−876.266	+	1098.80i	−0.417225	+	0.523183i
$165$	714.392	−	3129.96i	0.337063	−	1.47677i
$166$	483.501	−	2118.35i	0.226066	−	0.990459i
$167$	181.639	+	227.768i	0.0841657	+	0.105540i	0.822131	−	0.569298i	$-0.192785\pi$
$167$	181.639	+	227.768i	0.0841657	+	0.105540i	−0.737966	+	0.674838i	$0.764213\pi$
$168$	1682.39	+	810.196i	0.772614	+	0.372071i
$169$	939.509	−	452.444i	0.427633	−	0.205937i
$170$	−435.450	+	546.036i	−0.196456	+	0.246348i
$171$	−5755.75	−	7217.49i	−2.57400	−	3.22769i
$172$	−260.259	+	125.334i	−0.115375	+	0.0555619i
$173$	−980.057			−0.430707			−0.215354	−	0.976536i	$-0.569090\pi$
$173$	−980.057			−0.430707			−0.215354	+	0.976536i	$0.569090\pi$
$174$	−2261.20	−	2175.27i	−0.985177	−	0.947740i
$175$	−1417.54			−0.612319
$176$	−575.910	+	277.344i	−0.246653	+	0.118782i
$177$	−496.724	−	622.873i	−0.210938	−	0.264508i
$178$	1334.29	−	1673.14i	0.561849	−	0.704537i
$179$	2101.02	−	1011.80i	0.877303	−	0.422487i	0.0596644	−	0.998218i	$-0.480997\pi$
$179$	2101.02	−	1011.80i	0.877303	−	0.422487i	0.817639	+	0.575732i	$0.195283\pi$
$180$	−2130.90	−	1026.19i	−0.882377	−	0.424930i
$181$	−198.025	−	248.316i	−0.0813210	−	0.101973i	0.739507	−	0.673149i	$-0.235059\pi$
$181$	−198.025	−	248.316i	−0.0813210	−	0.101973i	−0.820828	+	0.571176i	$0.806487\pi$
$182$	351.315	−	1539.21i	0.143083	−	0.626889i
$183$	−35.3906	+	155.057i	−0.0142959	+	0.0626345i
$184$	−445.955	+	559.210i	−0.178675	+	0.224052i
$185$	−4.13062	−	18.0974i	−0.00164156	−	0.00719215i
$186$	−1676.02			−0.660709
$187$	388.070	+	1700.25i	0.151757	+	0.664890i
$188$	1480.57	+	713.004i	0.574369	+	0.276602i
$189$	9866.04	+	4751.23i	3.79708	+	1.82858i
$190$	444.640	+	1948.10i	0.169777	+	0.743840i
$191$	2282.01			0.864504			0.432252	−	0.901753i	$-0.357719\pi$
$191$	2282.01			0.864504			0.432252	+	0.901753i	$0.357719\pi$
$192$	143.063	+	626.800i	0.0537744	+	0.235601i
$193$	543.614	−	681.671i	0.202747	−	0.254237i	−0.670055	−	0.742312i	$-0.733729\pi$
$193$	543.614	−	681.671i	0.202747	−	0.254237i	0.872802	+	0.488075i	$0.162301\pi$
$194$	387.108	−	1696.03i	0.143261	−	0.627669i
$195$	−607.514	+	2661.69i	−0.223103	+	0.977476i
$196$	491.022	+	615.722i	0.178944	+	0.224388i
$197$	3136.85	+	1510.63i	1.13447	+	0.546333i	0.904334	−	0.426825i	$-0.140368\pi$
$197$	3136.85	+	1510.63i	1.13447	+	0.546333i	0.230138	+	0.973158i	$0.426082\pi$
$198$	−5321.01	+	2562.46i	−1.90984	+	0.919729i
$199$	464.321	−	582.240i	0.165401	−	0.207407i	−0.692223	−	0.721684i	$-0.743368\pi$
$199$	464.321	−	582.240i	0.165401	−	0.207407i	0.857624	+	0.514277i	$0.171940\pi$
$200$	−304.301	−	381.582i	−0.107587	−	0.134910i
$201$	−4041.41	+	1946.24i	−1.41821	+	0.682972i
$202$	−1224.94			−0.426667
$203$	−1264.57	−	3401.19i	−0.437220	−	1.17594i
$204$	1754.09			0.602013
$205$	2532.33	−	1219.51i	0.862759	−	0.415483i
$206$	1603.04	+	2010.15i	0.542181	+	0.679873i
$207$	−4120.31	+	5166.71i	−1.38349	+	1.73484i
$208$	489.750	−	235.851i	0.163260	−	0.0786219i
$209$	4495.51	+	2164.92i	1.48785	+	0.716511i
$210$	−2328.36	−	2919.67i	−0.765105	−	0.959412i
$211$	−978.611	+	4287.57i	−0.319291	+	1.39890i	0.519510	+	0.854465i	$0.326115\pi$
$211$	−978.611	+	4287.57i	−0.319291	+	1.39890i	−0.838800	+	0.544439i	$0.816742\pi$
$212$	−71.3603	+	312.650i	−0.0231181	+	0.101287i
$213$	−4207.55	+	5276.10i	−1.35350	+	1.69724i
$214$	266.169	+	1166.16i	0.0850232	+	0.372511i
$215$	577.697			0.183249
$216$	838.964	+	3675.74i	0.264279	+	1.15788i
$217$	−1746.36	−	841.001i	−0.546315	−	0.263092i
$218$	−1961.07	−	944.400i	−0.609267	−	0.293407i
$219$	−2247.66	−	9847.64i	−0.693529	−	3.03855i
$220$	1278.35			0.391756
$221$	−330.013	−	1445.88i	−0.100448	−	0.440092i
$222$	−29.0680	+	36.4502i	−0.00878793	+	0.0110197i
$223$	−859.576	+	3766.05i	−0.258123	+	1.13091i	0.665132	+	0.746725i	$0.268375\pi$
$223$	−859.576	+	3766.05i	−0.258123	+	1.13091i	−0.923256	+	0.384186i	$0.874482\pi$
$224$	−165.452	+	724.891i	−0.0493514	+	0.216222i
$225$	−2811.53	−	3525.55i	−0.833046	−	1.04461i
$226$	−663.149	−	319.356i	−0.195186	−	0.0939965i
$227$	−5.96658	+	2.87335i	−0.00174456	+	0.000840137i	−0.434756	−	0.900548i	$-0.643165\pi$
$227$	−5.96658	+	2.87335i	−0.00174456	+	0.000840137i	0.433011	+	0.901389i	$0.357451\pi$
$228$	3129.03	−	3923.68i	0.908882	−	1.13970i
$229$	3113.83	+	3904.62i	0.898549	+	1.12674i	0.991374	+	0.131062i	$0.0418387\pi$
$229$	3113.83	+	3904.62i	0.898549	+	1.12674i	−0.0928256	+	0.995682i	$0.529590\pi$
$230$	1288.77	−	620.639i	0.369474	−	0.177929i
$231$	−9325.07			−2.65604
$232$	644.089	−	1070.54i	0.182269	−	0.302949i
$233$	2868.63			0.806568			0.403284	−	0.915075i	$-0.367869\pi$
$233$	2868.63			0.806568			0.403284	+	0.915075i	$0.367869\pi$
$234$	4524.95	−	2179.10i	1.26413	−	0.608771i
$235$	−2049.05	−	2569.42i	−0.568787	−	0.713237i
$236$	197.788	−	248.018i	0.0545545	−	0.0684092i
$237$	−6135.67	+	2954.78i	−1.68167	+	0.809848i
$238$	1827.70	+	880.173i	0.497782	+	0.239719i
$239$	1288.99	+	1616.35i	0.348862	+	0.437459i	0.925043	−	0.379863i	$-0.124029\pi$
$239$	1288.99	+	1616.35i	0.348862	+	0.437459i	−0.576181	+	0.817322i	$0.695458\pi$
$240$	286.109	−	1253.53i	0.0769510	−	0.337145i
$241$	939.651	−	4116.88i	0.251154	−	1.10038i	−0.679268	−	0.733890i	$-0.737703\pi$
$241$	939.651	−	4116.88i	0.251154	−	1.10038i	0.930422	−	0.366489i	$-0.119440\pi$
$242$	330.530	−	414.472i	0.0877987	−	0.110096i
$243$	3290.36	+	14416.0i	0.868629	+	3.80571i
$244$	−63.3287			−0.0166156
$245$	−350.466	−	1535.49i	−0.0913896	−	0.400404i
$246$	−6360.09	−	3062.86i	−1.64839	−	0.793823i
$247$	−3822.95	−	1841.04i	−0.984812	−	0.474260i
$248$	−148.503	−	650.632i	−0.0380239	−	0.166593i
$249$	10913.7			2.77763
$250$	662.210	+	2901.33i	0.167527	+	0.733985i
$251$	627.853	−	787.303i	0.157887	−	0.197984i	−0.696596	−	0.717464i	$-0.745303\pi$
$251$	627.853	−	787.303i	0.157887	−	0.197984i	0.854483	+	0.519480i	$0.173874\pi$
$252$	−1528.66	+	6697.49i	−0.382129	+	1.67421i
$253$	794.818	−	3482.33i	0.197509	−	0.865344i
$254$	133.553	+	167.470i	0.0329916	+	0.0413702i
$255$	−3160.57	−	1522.05i	−0.776166	−	0.373782i
$256$	−230.648	+	111.074i	−0.0563106	+	0.0271177i
$257$	−660.606	+	828.373i	−0.160340	+	0.201060i	−0.855511	−	0.517784i	$-0.826757\pi$
$257$	−660.606	+	828.373i	−0.160340	+	0.201060i	0.695171	+	0.718844i	$0.255329\pi$
$258$	−904.632	−	1134.37i	−0.218294	−	0.273733i
$259$	−48.5781	+	23.3940i	−0.0116544	+	0.00561247i
$260$	−1087.10			−0.259304
$261$	5950.93	−	9891.00i	1.41132	−	2.34574i
$262$	−1535.08			−0.361976
$263$	−1591.28	+	766.321i	−0.373090	+	0.179671i	−0.611027	−	0.791610i	$-0.709243\pi$
$263$	−1591.28	+	766.321i	−0.373090	+	0.179671i	0.237937	+	0.971281i	$0.423529\pi$
$264$	−2001.80	−	2510.18i	−0.466676	−	0.585193i
$265$	399.870	−	501.421i	0.0926937	−	0.116234i
$266$	5229.18	−	2518.24i	1.20535	−	0.580464i
$267$	9684.49	+	4663.80i	2.21978	+	1.06899i
$268$	−1113.62	−	1396.43i	−0.253825	−	0.318286i
$269$	−778.456	+	3410.64i	−0.176444	+	0.773050i	0.806811	+	0.590810i	$0.201192\pi$
$269$	−778.456	+	3410.64i	−0.176444	+	0.773050i	−0.983254	+	0.182240i	$0.941665\pi$
$270$	1677.83	−	7351.05i	0.378183	−	1.65693i
$271$	118.412	−	148.484i	0.0265426	−	0.0332833i	−0.768383	−	0.639990i	$-0.778938\pi$
$271$	118.412	−	148.484i	0.0265426	−	0.0332833i	0.794926	+	0.606707i	$0.207510\pi$
$272$	155.419	+	680.937i	0.0346459	+	0.151794i
$273$	7929.98			1.75804
$274$	−347.513	−	1522.56i	−0.0766206	−	0.335697i
$275$	2195.93	+	1057.51i	0.481527	+	0.231891i
$276$	−3236.82	−	1558.77i	−0.705918	−	0.339952i
$277$	1436.24	+	6292.58i	0.311535	+	1.36493i	0.851992	+	0.523554i	$0.175394\pi$
$277$	1436.24	+	6292.58i	0.311535	+	1.36493i	−0.540457	+	0.841372i	$0.681749\pi$
$278$	3834.51			0.827262
$279$	−1372.06	−	6011.38i	−0.294419	−	1.28994i
$280$	927.115	−	1162.57i	0.197878	−	0.248131i
$281$	−433.623	+	1899.83i	−0.0920562	+	0.403325i	−0.999871	−	0.0160461i	$-0.994892\pi$
$281$	−433.623	+	1899.83i	−0.0920562	+	0.403325i	0.907815	+	0.419371i	$0.137749\pi$
$282$	−1836.69	+	8047.06i	−0.387848	+	1.69928i
$283$	−445.158	−	558.210i	−0.0935048	−	0.117251i	0.732878	−	0.680360i	$-0.238177\pi$
$283$	−445.158	−	558.210i	−0.0935048	−	0.117251i	−0.826383	+	0.563109i	$0.809605\pi$
$284$	−2420.99	−	1165.89i	−0.505843	−	0.243601i
$285$	−9042.62	+	4354.69i	−1.87943	+	0.905087i
$286$	−1692.50	+	2122.33i	−0.349930	+	0.438798i
$287$	−5090.10	−	6382.78i	−1.04690	−	1.31277i
$288$	−2131.03	+	1026.25i	−0.436014	+	0.209973i
$289$	−3007.41			−0.612134
$290$	−2089.46	+	1370.04i	−0.423094	+	0.277418i
$291$	8737.91			1.76022
$292$	3623.71	−	1745.08i	0.726237	−	0.349738i
$293$	866.916	+	1087.08i	0.172852	+	0.216750i	0.860710	−	0.509096i	$-0.170020\pi$
$293$	866.916	+	1087.08i	0.172852	+	0.216750i	−0.687858	+	0.725846i	$0.741449\pi$
$294$	−2466.31	+	3092.65i	−0.489245	+	0.613494i
$295$	−571.588	+	275.262i	−0.112811	+	0.0543268i
$296$	−16.7255	−	8.05459i	−0.00328429	−	0.00158163i
$297$	−11739.2	−	14720.4i	−2.29352	−	2.87598i
$298$	1550.03	−	6791.13i	0.301312	−	1.32013i
$299$	−675.908	+	2961.35i	−0.130732	+	0.572773i
$300$	1528.45	−	1916.61i	0.294150	−	0.368852i
$301$	−373.386	−	1635.91i	−0.0715003	−	0.313263i
$302$	−1686.47			−0.321342
$303$	−1369.09	−	5998.39i	−0.259579	−	1.13729i
$304$	1800.42	+	867.036i	0.339675	+	0.163579i
$305$	114.108	+	54.9513i	0.0214222	+	0.0103164i
$306$	1435.97	+	6291.38i	0.268264	+	1.17534i
$307$	9666.01			1.79697			0.898483	−	0.439008i	$-0.144670\pi$
$307$	9666.01			1.79697			0.898483	+	0.439008i	$0.144670\pi$
$308$	−826.240	−	3620.00i	−0.152855	−	0.669703i
$309$	−8051.77	+	10096.6i	−1.48236	+	1.85882i
$310$	−296.987	+	1301.19i	−0.0544121	+	0.238395i
$311$	−597.645	+	2618.45i	−0.108969	+	0.477424i	0.890767	+	0.454460i	$0.150168\pi$
$311$	−597.645	+	2618.45i	−0.108969	+	0.477424i	−0.999736	+	0.0229645i	$0.992690\pi$
$312$	1702.32	+	2134.64i	0.308894	+	0.387340i
$313$	−2540.66	−	1223.52i	−0.458806	−	0.220949i	0.190180	−	0.981749i	$-0.439093\pi$
$313$	−2540.66	−	1223.52i	−0.458806	−	0.220949i	−0.648987	+	0.760800i	$0.724807\pi$
$314$	4287.65	−	2064.82i	0.770592	−	0.371098i
$315$	8565.89	−	10741.3i	1.53217	−	1.92128i
$316$	−1690.69	−	2120.06i	−0.300978	−	0.377414i
$317$	5815.10	−	2800.40i	1.03031	−	0.496172i	0.159194	−	0.987247i	$-0.449110\pi$
$317$	5815.10	−	2800.40i	1.03031	−	0.496172i	0.871117	+	0.491076i	$0.163396\pi$
$318$	−1610.77			−0.284048
$319$	−578.368	+	6212.24i	−0.101512	+	1.09034i
$320$	511.969			0.0894374
$321$	−5413.07	+	2606.80i	−0.941209	+	0.453262i
$322$	−2590.49	−	3248.37i	−0.448330	−	0.562188i
$323$	3399.29	−	4262.57i	0.585577	−	0.734290i
$324$	−9869.75	+	4753.02i	−1.69234	+	0.814990i
$325$	−1867.41	−	899.296i	−0.318724	−	0.153489i
$326$	4030.12	+	5053.61i	0.684686	+	0.858570i
$327$	2432.76	−	10658.6i	0.411413	−	1.80252i
$328$	625.471	−	2740.37i	0.105292	−	0.461316i
$329$	−5951.66	+	7463.14i	−0.997342	+	1.25063i
$330$	1428.78	+	6259.91i	0.238339	+	1.04423i
$331$	−8672.11			−1.44007			−0.720034	−	0.693939i	$-0.755874\pi$
$331$	−8672.11			−1.44007			−0.720034	+	0.693939i	$0.755874\pi$
$332$	967.001	+	4236.71i	0.159853	+	0.700360i
$333$	−154.532	−	74.4187i	−0.0254304	−	0.0122466i
$334$	−524.953	−	252.804i	−0.0860004	−	0.0414156i
$335$	794.844	+	3482.44i	0.129633	+	0.567958i
$336$	−3734.62			−0.606370
$337$	1000.32	+	4382.68i	0.161694	+	0.708427i	0.989151	+	0.146899i	$0.0469293\pi$
$337$	1000.32	+	4382.68i	0.161694	+	0.708427i	−0.827458	+	0.561528i	$0.810214\pi$
$338$	−1300.32	+	1630.55i	−0.209255	+	0.262397i
$339$	822.656	−	3604.29i	0.131801	−	0.577458i
$340$	310.820	−	1361.79i	0.0495782	−	0.217216i
$341$	2077.91	+	2605.62i	0.329986	+	0.413790i
$342$	16634.6	+	8010.80i	2.63011	+	1.26659i
$343$	3058.84	−	1473.06i	0.481521	−	0.231889i
$344$	360.210	−	451.689i	0.0564570	−	0.0707949i
$345$	4479.62	+	5617.27i	0.699057	+	0.876590i
$346$	1766.00	−	850.462i	0.274396	−	0.132142i
$347$	−3887.58			−0.601430			−0.300715	−	0.953714i	$-0.597225\pi$
$347$	−3887.58			−0.601430			−0.300715	+	0.953714i	$0.597225\pi$
$348$	5962.16	+	1957.51i	0.918407	+	0.301533i
$349$	−8587.58			−1.31714			−0.658571	−	0.752519i	$-0.728839\pi$
$349$	−8587.58			−1.31714			−0.658571	+	0.752519i	$0.728839\pi$
$350$	2554.32	−	1230.09i	0.390097	−	0.187861i
$351$	9982.91	+	12518.2i	1.51809	+	1.90362i
$352$	797.085	−	999.513i	0.120695	−	0.151347i
$353$	937.659	−	451.553i	0.141378	−	0.0680842i	−0.361857	−	0.932234i	$-0.617857\pi$
$353$	937.659	−	451.553i	0.141378	−	0.0680842i	0.503235	+	0.864149i	$0.332143\pi$
$354$	1435.58	+	691.337i	0.215537	+	0.103797i
$355$	3350.55	+	4201.46i	0.500927	+	0.628142i
$356$	−952.404	+	4172.76i	−0.141790	+	0.621224i
$357$	−2267.32	+	9933.77i	−0.336132	+	1.47269i
$358$	−2907.90	+	3646.39i	−0.429293	+	0.538317i
$359$	−1769.52	−	7752.78i	−0.260144	−	1.13977i	−0.921095	−	0.389337i	$-0.872704\pi$
$359$	−1769.52	−	7752.78i	−0.260144	−	1.13977i	0.660951	−	0.750429i	$-0.270153\pi$
$360$	4730.24			0.692515
$361$	−1944.76	−	8520.55i	−0.283534	−	1.24224i
$362$	572.309	+	275.610i	0.0830937	+	0.0400158i
$363$	2399.04	+	1155.32i	0.346879	+	0.167048i
$364$	702.629	+	3078.42i	0.101175	+	0.443278i
$365$	−8043.54			−1.15347
$366$	−70.7813	−	310.113i	−0.0101087	−	0.0442893i
$367$	−6294.16	+	7892.63i	−0.895239	+	1.12259i	0.0966286	+	0.995321i	$0.469194\pi$
$367$	−6294.16	+	7892.63i	−0.895239	+	1.12259i	−0.991868	+	0.127274i	$0.959377\pi$
$368$	318.319	−	1394.65i	0.0450911	−	0.197557i
$369$	5778.92	−	25319.1i	0.815280	−	3.57198i
$370$	23.1475	+	29.0260i	0.00325238	+	0.00407835i
$371$	−1678.36	−	808.257i	−0.234869	−	0.113107i
$372$	3020.09	−	1454.40i	0.420925	−	0.202707i
$373$	5338.56	−	6694.34i	0.741073	−	0.929276i	−0.258250	−	0.966078i	$-0.583146\pi$
$373$	5338.56	−	6694.34i	0.741073	−	0.929276i	0.999323	+	0.0368024i	$0.0117172\pi$
$374$	−2174.70	−	2726.99i	−0.300671	−	0.377030i
$375$	−13467.3	+	6485.52i	−1.85453	+	0.893095i
$376$	−3286.61			−0.450782
$377$	491.840	−	5282.85i	0.0671912	−	0.721699i
$378$	−21901.0			−2.98006
$379$	4052.60	−	1951.63i	0.549256	−	0.264508i	−0.138608	−	0.990347i	$-0.544263\pi$
$379$	4052.60	−	1951.63i	0.549256	−	0.264508i	0.687864	+	0.725839i	$0.258548\pi$
$380$	−2491.71	−	3124.50i	−0.336373	−	0.421799i
$381$	−670.812	+	841.171i	−0.0902014	+	0.113109i
$382$	−4112.04	+	1980.25i	−0.550759	+	0.265232i
$383$	1197.36	+	576.616i	0.159744	+	0.0769287i	0.512047	−	0.858957i	$-0.328887\pi$
$383$	1197.36	+	576.616i	0.159744	+	0.0769287i	−0.352303	+	0.935886i	$0.614601\pi$
$384$	−801.707	−	1005.31i	−0.106542	−	0.133599i
$385$	−1652.38	+	7239.56i	−0.218736	+	0.958343i
$386$	−388.027	+	1700.06i	−0.0511660	+	0.224173i
$387$	3328.09	−	4173.29i	0.437148	−	0.548166i
$388$	774.215	+	3392.06i	0.101301	+	0.443829i
$389$	−12780.6			−1.66582			−0.832910	−	0.553408i	$-0.813327\pi$
$389$	−12780.6			−1.66582			−0.832910	+	0.553408i	$0.813327\pi$
$390$	−1215.03	−	5323.39i	−0.157757	−	0.691180i
$391$	−3516.38	−	1693.40i	−0.454811	−	0.219025i
$392$	−1419.09	−	683.399i	−0.182845	−	0.0880533i
$393$	−1715.73	−	7517.12i	−0.220222	−	0.964856i
$394$	−6963.27			−0.890367
$395$	1206.73	+	5287.04i	0.153715	+	0.673468i
$396$	7364.51	−	9234.80i	0.934546	−	1.17188i
$397$	426.573	−	1868.94i	0.0539271	−	0.236270i	−0.940780	−	0.339016i	$-0.889906\pi$
$397$	426.573	−	1868.94i	0.0539271	−	0.236270i	0.994708	+	0.102746i	$0.0327629\pi$
$398$	−331.429	+	1452.08i	−0.0417412	+	0.182880i
$399$	18176.1	+	22792.1i	2.28056	+	2.85973i
$400$	879.456	+	423.524i	0.109932	+	0.0529405i
$401$	2658.13	−	1280.09i	0.331024	−	0.159413i	−0.260987	−	0.965342i	$-0.584048\pi$
$401$	2658.13	−	1280.09i	0.331024	−	0.159413i	0.592012	+	0.805929i	$0.298334\pi$
$402$	5593.49	−	7014.02i	0.693975	−	0.870217i
$403$	−1767.04	−	2215.80i	−0.218419	−	0.273888i
$404$	2207.27	−	1062.97i	0.271821	−	0.130902i
$405$	21907.9			2.68793
$406$	5230.13	+	5031.38i	0.639327	+	0.615032i
$407$	92.7054			0.0112905
$408$	−3160.75	+	1522.14i	−0.383531	+	0.184699i
$409$	1376.03	+	1725.49i	0.166358	+	0.208606i	0.858022	−	0.513614i	$-0.171694\pi$
$409$	1376.03	+	1725.49i	0.166358	+	0.208606i	−0.691664	+	0.722219i	$0.743122\pi$
$410$	−3504.85	+	4394.95i	−0.422177	+	0.529393i
$411$	7067.35	−	3403.46i	0.848192	−	0.408468i
$412$	−4632.92	−	2231.10i	−0.554000	−	0.266792i
$413$	1148.92	+	1440.70i	0.136888	+	0.171652i
$414$	2941.04	−	12885.6i	0.349141	−	1.52969i
$415$	1933.89	−	8472.91i	0.228749	−	1.00221i
$416$	−677.836	+	849.979i	−0.0798885	+	0.100177i
$417$	4285.76	+	18777.1i	0.503296	+	2.20509i
$418$	−9979.27			−1.16771
$419$	1718.33	+	7528.50i	0.200348	+	0.877784i	0.970725	+	0.240195i	$0.0772112\pi$
$419$	1718.33	+	7528.50i	0.200348	+	0.877784i	−0.770376	+	0.637590i	$0.779932\pi$
$420$	6729.16	+	3240.59i	0.781784	+	0.376487i
$421$	9819.06	+	4728.61i	1.13670	+	0.547407i	0.905013	−	0.425383i	$-0.139861\pi$
$421$	9819.06	+	4728.61i	1.13670	+	0.547407i	0.231689	+	0.972790i	$0.425575\pi$
$422$	−1957.22	−	8575.15i	−0.225773	−	0.989174i
$423$	−30366.0			−3.49041
$424$	−142.721	−	625.300i	−0.0163470	−	0.0716209i
$425$	1660.46	−	2082.15i	0.189516	−	0.237645i
$426$	3003.31	−	13158.4i	0.341575	−	1.49654i
$427$	81.8582	−	358.644i	0.00927727	−	0.0406464i
$428$	−1491.58	−	1870.38i	−0.168454	−	0.211234i
$429$	−12284.5	−	5915.89i	−1.38252	−	0.665785i
$430$	−1040.97	+	501.307i	−0.116745	+	0.0562213i
$431$	−4212.84	+	5282.73i	−0.470824	+	0.590395i	−0.959373	−	0.282142i	$-0.908955\pi$
$431$	−4212.84	+	5282.73i	−0.470824	+	0.590395i	0.488549	+	0.872537i	$0.337527\pi$
$432$	−4701.45	−	5895.43i	−0.523608	−	0.656584i
$433$	11518.3	−	5546.93i	1.27837	−	0.615631i	0.333400	−	0.942785i	$-0.391804\pi$
$433$	11518.3	−	5546.93i	1.27837	−	0.615631i	0.944971	+	0.327154i	$0.106090\pi$
$434$	3876.62			0.428764
$435$	−9044.24	−	8700.56i	−0.996870	−	0.958988i
$436$	4353.24			0.478170
$437$	−10060.6	+	4844.94i	−1.10129	+	0.530355i
$438$	12595.6	+	15794.4i	1.37407	+	1.72303i
$439$	5572.65	−	6987.88i	0.605850	−	0.759712i	−0.380427	−	0.924811i	$-0.624223\pi$
$439$	5572.65	−	6987.88i	0.605850	−	0.759712i	0.986277	+	0.165099i	$0.0527945\pi$
$440$	−2303.50	+	1109.31i	−0.249580	+	0.120191i
$441$	−13111.4	−	6314.13i	−1.41577	−	0.681798i
$442$	1849.35	+	2319.01i	0.199015	+	0.249557i
$443$	263.238	−	1153.32i	0.0282321	−	0.123693i	−0.958848	−	0.283919i	$-0.908365\pi$
$443$	263.238	−	1153.32i	0.0282321	−	0.123693i	0.987080	+	0.160226i	$0.0512224\pi$
$444$	20.7485	−	90.9053i	0.00221775	−	0.00971660i
$445$	5336.83	−	6692.18i	0.568517	−	0.712898i
$446$	−1719.15	−	7532.10i	−0.182521	−	0.799675i
$447$	34987.8			3.70216
$448$	−330.903	−	1449.78i	−0.0348967	−	0.152892i
$449$	−2363.59	−	1138.24i	−0.248429	−	0.119637i	0.305526	−	0.952184i	$-0.401168\pi$
$449$	−2363.59	−	1138.24i	−0.248429	−	0.119637i	−0.553955	+	0.832547i	$0.686882\pi$
$450$	8125.56	+	3913.06i	0.851206	+	0.409919i
$451$	3123.51	+	13685.0i	0.326120	+	1.42883i
$452$	1472.08			0.153188
$453$	−1884.93	−	8258.41i	−0.195500	−	0.856543i
$454$	8.25800	−	10.3552i	0.000853672	−	0.00107047i
$455$	1405.17	−	6156.47i	0.144782	−	0.634329i
$456$	−2233.48	+	9785.49i	−0.229369	+	1.00493i
$457$	7013.94	+	8795.20i	0.717939	+	0.900267i	0.998219	−	0.0596512i	$-0.0189989\pi$
$457$	7013.94	+	8795.20i	0.717939	+	0.900267i	−0.280280	+	0.959918i	$0.590427\pi$
$458$	−8999.23	−	4333.80i	−0.918136	−	0.442151i
$459$	−18535.6	+	8926.28i	−1.88490	+	0.907719i
$460$	−1783.71	+	2236.71i	−0.180796	+	0.226711i
$461$	−8560.33	−	10734.3i	−0.864847	−	1.08448i	−0.995659	−	0.0930767i	$-0.970330\pi$
$461$	−8560.33	−	10734.3i	−0.864847	−	1.08448i	0.130812	−	0.991407i	$-0.458242\pi$
$462$	16803.2	−	8091.99i	1.69211	−	0.814878i
$463$	3355.28			0.336788			0.168394	−	0.985720i	$-0.446142\pi$
$463$	3355.28			0.336788			0.168394	+	0.985720i	$0.446142\pi$
$464$	−231.632	+	2487.96i	−0.0231751	+	0.248924i
$465$	−6703.68			−0.668550
$466$	−5169.09	+	2489.30i	−0.513849	+	0.247457i
$467$	−6556.15	−	8221.15i	−0.649641	−	0.814624i	0.342530	−	0.939507i	$-0.388716\pi$
$467$	−6556.15	−	8221.15i	−0.649641	−	0.814624i	−0.992172	+	0.124882i	$0.960145\pi$
$468$	−6262.73	+	7853.21i	−0.618578	+	0.775673i
$469$	9347.75	−	4501.64i	0.920339	−	0.443212i
$470$	5921.91	+	2851.84i	0.581186	+	0.279885i
$471$	14903.4	+	18688.3i	1.45799	+	1.82826i
$472$	−141.179	+	618.546i	−0.0137676	+	0.0603197i
$473$	−641.996	+	2812.77i	−0.0624081	+	0.273428i
$474$	8492.04	−	10648.7i	0.822895	−	1.03188i
$475$	−1695.50	−	7428.49i	−0.163779	−	0.717563i
$476$	−4057.19			−0.390674
$477$	−1318.64	−	5777.33i	−0.126575	−	0.554562i
$478$	−3725.30	−	1794.01i	−0.356467	−	0.171665i
$479$	−7315.23	−	3522.83i	−0.697789	−	0.336038i	0.0511362	−	0.998692i	$-0.483716\pi$
$479$	−7315.23	−	3522.83i	−0.697789	−	0.336038i	−0.748926	+	0.662654i	$0.769430\pi$
$480$	572.218	+	2507.05i	0.0544126	+	0.238397i
$481$	−78.8361			−0.00747321
$482$	1879.30	+	8233.76i	0.177593	+	0.778086i
$483$	13011.5	−	16315.9i	1.22576	−	1.53706i
$484$	−235.930	+	1033.68i	−0.0221572	+	0.0970769i
$485$	1548.34	−	6783.71i	0.144962	−	0.635118i
$486$	−18438.8	−	23121.5i	−1.72099	−	2.15805i
$487$	−8033.76	−	3868.86i	−0.747525	−	0.359989i	0.0210249	−	0.999779i	$-0.493307\pi$
$487$	−8033.76	−	3868.86i	−0.747525	−	0.359989i	−0.768550	+	0.639790i	$0.779021\pi$
$488$	114.114	−	54.9546i	0.0105855	−	0.00509770i
$489$	−20242.5	+	25383.3i	−1.87198	+	2.34739i
$490$	1963.97	+	2462.74i	0.181067	+	0.227051i
$491$	−10226.8	+	4924.97i	−0.939978	+	0.452670i	−0.840162	−	0.542336i	$-0.817540\pi$
$491$	−10226.8	+	4924.97i	−0.939978	+	0.452670i	−0.0998168	+	0.995006i	$0.531826\pi$
$492$	14118.3			1.29371
$493$	6477.12	+	2126.58i	0.591713	+	0.194272i
$494$	8486.31			0.772909
$495$	−21282.8	+	10249.2i	−1.93250	+	0.930644i
$496$	832.190	+	1043.53i	0.0753355	+	0.0944677i
$497$	9732.02	−	12203.6i	0.878352	−	1.10142i
$498$	−19665.8	+	9470.57i	−1.76957	+	0.852182i
$499$	−2338.92	−	1126.36i	−0.209828	−	0.101048i	0.326018	−	0.945364i	$-0.394293\pi$
$499$	−2338.92	−	1126.36i	−0.209828	−	0.101048i	−0.535846	+	0.844316i	$0.680007\pi$
$500$	−3710.94	−	4653.37i	−0.331917	−	0.416210i
$501$	651.220	−	2853.18i	0.0580726	−	0.254433i
$502$	−448.156	+	1963.50i	−0.0398450	+	0.174572i
$503$	4486.14	−	5625.44i	0.397668	−	0.498660i	−0.542175	−	0.840265i	$-0.682399\pi$
$503$	4486.14	−	5625.44i	0.397668	−	0.498660i	0.939844	+	0.341605i	$0.110971\pi$
$504$	−3057.32	−	13395.0i	−0.270206	−	1.18385i
$505$	−4899.48			−0.431730
$506$	1589.64	+	6964.65i	0.139660	+	0.611890i
$507$	−9437.94	−	4545.07i	−0.826733	−	0.398134i
$508$	−385.980	−	185.878i	−0.0337108	−	0.0162343i
$509$	−61.4221	−	269.108i	−0.00534870	−	0.0234342i	0.972183	−	0.234222i	$-0.0752542\pi$
$509$	−61.4221	−	269.108i	−0.00534870	−	0.0234342i	−0.977532	+	0.210788i	$0.932397\pi$
$510$	7015.93			0.609158
$511$	5198.82	+	22777.5i	0.450063	+	1.97185i
$512$	319.227	−	400.298i	0.0275546	−	0.0345524i
$513$	−13097.8	+	57385.1i	−1.12725	+	4.93882i
$514$	471.535	−	2065.93i	0.0404640	−	0.177285i
$515$	6411.78	+	8040.12i	0.548615	+	0.687942i
$516$	2614.46	+	1259.06i	0.223053	+	0.107417i
$517$	14787.5	−	7121.26i	1.25793	−	0.605789i
$518$	67.2341	−	84.3089i	0.00570289	−	0.00715120i
$519$	6138.43	+	7697.35i	0.519166	+	0.651014i
$520$	1958.88	−	943.349i	0.165198	−	0.0795550i
$521$	7991.07			0.671968			0.335984	−	0.941868i	$-0.390931\pi$
$521$	7991.07			0.671968			0.335984	+	0.941868i	$0.390931\pi$
$522$	−2140.12	+	22987.0i	−0.179445	+	1.92742i
$523$	15005.2			1.25455			0.627275	−	0.778798i	$-0.284170\pi$
$523$	15005.2			1.25455			0.627275	+	0.778798i	$0.284170\pi$
$524$	2766.13	−	1332.10i	0.230608	−	0.111055i
$525$	8878.52	+	11133.3i	0.738077	+	0.925520i
$526$	2202.40	−	2761.72i	0.182565	−	0.228930i
$527$	3280.93	−	1580.01i	0.271195	−	0.130601i
$528$	5785.38	+	2786.09i	0.476849	+	0.229638i
$529$	−2602.06	−	3262.88i	−0.213862	−	0.268175i
$530$	−285.424	+	1250.52i	−0.0233925	+	0.102489i
$531$	−1304.40	+	5714.93i	−0.106603	+	0.467056i
$532$	−7237.41	+	9075.43i	−0.589815	+	0.739605i
$533$	−2656.21	−	11637.6i	−0.215860	−	0.945744i
$534$	−21497.9			−1.74215
$535$	1064.61	+	4664.38i	0.0860323	+	0.376932i
$536$	3218.45	+	1549.92i	0.259358	+	0.124900i
$537$	−21106.0	−	10164.1i	−1.69607	−	0.816785i
$538$	−1556.91	−	6821.28i	−0.124764	−	0.546629i
$539$	7865.68			0.628570
$540$	3355.66	+	14702.1i	0.267416	+	1.17162i
$541$	6603.34	−	8280.33i	0.524769	−	0.658039i	−0.446845	−	0.894611i	$-0.647453\pi$
$541$	6603.34	−	8280.33i	0.524769	−	0.658039i	0.971614	+	0.236572i	$0.0760240\pi$
$542$	−84.5217	+	370.314i	−0.00669838	+	0.0293475i
$543$	−709.968	+	3110.57i	−0.0561098	+	0.245833i
$544$	−870.951	−	1092.14i	−0.0686429	−	0.0860754i
$545$	−7843.80	−	3777.37i	−0.616498	−	0.296890i
$546$	−14289.3	+	6881.38i	−1.12001	+	0.539370i
$547$	−15400.5	+	19311.6i	−1.20380	+	1.50952i	−0.397939	+	0.917412i	$0.630275\pi$
$547$	−15400.5	+	19311.6i	−1.20380	+	1.50952i	−0.805860	+	0.592106i	$0.798297\pi$
$548$	1947.42	+	2441.99i	0.151806	+	0.190359i
$549$	1054.34	−	507.742i	0.0819636	−	0.0394716i
$550$	−4874.61			−0.377916
$551$	16311.1	−	10695.0i	1.26112	−	0.826903i
$552$	7185.19			0.554025
$553$	14191.8	−	6834.39i	1.09131	−	0.525547i
$554$	−8048.51	−	10092.5i	−0.617235	−	0.773989i
$555$	−116.265	+	145.792i	−0.00889222	+	0.0111505i
$556$	−6909.56	+	3327.47i	−0.527033	+	0.253806i
$557$	12070.3	+	5812.76i	0.918197	+	0.442180i	0.832427	−	0.554134i	$-0.186951\pi$
$557$	12070.3	+	5812.76i	0.918197	+	0.442180i	0.0857701	+	0.996315i	$0.472665\pi$
$558$	7688.85	+	9641.51i	0.583324	+	0.731465i
$559$	545.949	−	2391.96i	0.0413080	−	0.180982i
$560$	−661.767	+	2899.39i	−0.0499371	+	0.218789i
$561$	10923.1	−	13697.1i	0.822056	−	1.03083i
$562$	−867.247	−	3799.66i	−0.0650936	−	0.285194i
$563$	3415.80			0.255699			0.127850	−	0.991794i	$-0.459193\pi$
$563$	3415.80			0.255699			0.127850	+	0.991794i	$0.459193\pi$
$564$	−3673.38	−	16094.1i	−0.274250	−	1.20157i
$565$	−2652.44	−	1277.35i	−0.197502	−	0.0951121i
$566$	1286.54	+	619.566i	0.0955431	+	0.0460111i
$567$	−14159.8	−	62038.2i	−1.04878	−	4.59499i
$568$	5374.19			0.397000
$569$	1094.05	+	4793.32i	0.0806059	+	0.353158i	0.999107	−	0.0422619i	$-0.0134564\pi$
$569$	1094.05	+	4793.32i	0.0806059	+	0.353158i	−0.918501	+	0.395419i	$0.870599\pi$
$570$	12515.4	−	15693.8i	0.919669	−	1.15323i
$571$	2328.87	−	10203.4i	0.170683	−	0.747811i	−0.815036	−	0.579411i	$-0.803283\pi$
$571$	2328.87	−	10203.4i	0.170683	−	0.747811i	0.985719	−	0.168400i	$-0.0538601\pi$
$572$	1208.10	−	5293.01i	0.0883094	−	0.386909i
$573$	−14293.0	−	17922.8i	−1.04206	−	1.30670i
$574$	14710.8	+	7084.36i	1.06972	+	0.515149i
$575$	−4914.35	+	2366.62i	−0.356422	+	0.171644i
$576$	2949.43	−	3698.47i	0.213356	−	0.267540i
$577$	955.952	+	1198.73i	0.0689719	+	0.0864881i	0.815121	−	0.579291i	$-0.196671\pi$
$577$	955.952	+	1198.73i	0.0689719	+	0.0864881i	−0.746149	+	0.665779i	$0.768099\pi$
$578$	5419.17	−	2609.73i	0.389979	−	0.187804i
$579$	−8758.66			−0.628666
$580$	2576.20	−	4281.88i	0.184433	−	0.306544i
$581$	−25243.3			−1.80253
$582$	−15745.2	+	7582.47i	−1.12141	+	0.540040i
$583$	1997.01	+	2504.17i	0.141866	+	0.177894i
$584$	−5015.36	+	6289.07i	−0.355372	+	0.445622i
$585$	18098.7	−	8715.88i	1.27913	−	0.615996i
$586$	−2505.46	−	1206.57i	−0.176620	−	0.0850559i
$587$	−7055.68	−	8847.54i	−0.496114	−	0.622107i	0.469234	−	0.883074i	$-0.344530\pi$
$587$	−7055.68	−	8847.54i	−0.496114	−	0.622107i	−0.965348	+	0.260967i	$0.915959\pi$
$588$	1760.43	−	7712.95i	0.123468	−	0.540947i
$589$	2318.40	−	10157.6i	0.162186	−	0.710585i
$590$	791.103	−	992.011i	0.0552020	−	0.0692211i
$591$	−7782.71	−	34098.3i	−0.541689	−	2.37329i
$592$	37.1279			0.00257761
$593$	1425.54	+	6245.70i	0.0987183	+	0.432513i	1.00000		0.000721015i	$-0.000229506\pi$
$593$	1425.54	+	6245.70i	0.0987183	+	0.432513i	−0.901281	+	0.433234i	$0.857372\pi$
$594$	33927.2	+	16338.5i	2.34352	+	1.12858i
$595$	7310.36	+	3520.48i	0.503690	+	0.242564i
$596$	3100.06	+	13582.3i	0.213060	+	0.933475i
$597$	−7481.10			−0.512866
$598$	−1351.82	−	5922.69i	−0.0924412	−	0.405012i
$599$	15052.3	−	18875.0i	1.02675	−	1.28750i	0.0696977	−	0.997568i	$-0.477797\pi$
$599$	15052.3	−	18875.0i	1.02675	−	1.28750i	0.957048	−	0.289930i	$-0.0936320\pi$
$600$	−1090.99	+	4779.95i	−0.0742327	+	0.325235i
$601$	176.658	−	773.989i	0.0119901	−	0.0525319i	−0.968579	−	0.248706i	$-0.919995\pi$
$601$	176.658	−	773.989i	0.0119901	−	0.0525319i	0.980569	+	0.196174i	$0.0628518\pi$
$602$	2092.41	+	2623.79i	0.141661	+	0.177638i
$603$	29736.2	+	14320.2i	2.00821	+	0.967105i
$604$	3038.91	−	1463.46i	0.204721	−	0.0985883i
$605$	1322.04	−	1657.79i	0.0888407	−	0.111403i
$606$	7672.23	+	9620.67i	0.514295	+	0.644906i
$607$	−14085.9	+	6783.43i	−0.941895	+	0.453593i	−0.840837	−	0.541288i	$-0.817937\pi$
$607$	−14085.9	+	6783.43i	−0.941895	+	0.453593i	−0.101058	+	0.994881i	$0.532223\pi$
$608$	−3996.63			−0.266587
$609$	−18792.4	+	31234.7i	−1.25042	+	2.07832i
$610$	−253.300			−0.0168128
$611$	−12575.2	+	6055.87i	−0.832629	+	0.400973i
$612$	−8046.98	−	10090.6i	−0.531503	−	0.666484i
$613$	−14196.8	+	17802.3i	−0.935407	+	1.17296i	0.0493068	+	0.998784i	$0.484299\pi$
$613$	−14196.8	+	17802.3i	−0.935407	+	1.17296i	−0.984714	+	0.174180i	$0.944273\pi$
$614$	−17417.6	+	8387.85i	−1.14481	+	0.551313i
$615$	−25438.8	−	12250.7i	−1.66795	−	0.803245i
$616$	4630.15	+	5806.02i	0.302847	+	0.379759i
$617$	−5232.15	+	22923.6i	−0.341392	+	1.49573i	0.454747	+	0.890620i	$0.349730\pi$
$617$	−5232.15	+	22923.6i	−0.341392	+	1.49573i	−0.796139	+	0.605114i	$0.793128\pi$
$618$	5747.29	−	25180.5i	0.374094	−	1.63901i
$619$	−11208.3	+	14054.8i	−0.727788	+	0.912617i	−0.998751	−	0.0499727i	$-0.984087\pi$
$619$	−11208.3	+	14054.8i	−0.727788	+	0.912617i	0.270963	+	0.962590i	$0.412658\pi$
$620$	−593.974	−	2602.37i	−0.0384751	−	0.168571i
$621$	42136.1			2.72281
$622$	−1195.29	−	5236.91i	−0.0770527	−	0.337590i
$623$	−22400.1	−	10787.3i	−1.44052	−	0.693717i
$624$	−4919.84	−	2369.27i	−0.315627	−	0.151998i
$625$	951.745	+	4169.87i	0.0609117	+	0.266872i
$626$	5639.83			0.360085
$627$	−11153.6	−	48867.3i	−0.710420	−	3.11255i
$628$	−5934.29	+	7441.36i	−0.377076	+	0.472838i
$629$	22.5406	−	98.7568i	0.00142886	−	0.00626024i
$630$	−6114.26	+	26788.3i	−0.386664	+	1.69408i
$631$	16932.9	+	21233.1i	1.06828	+	1.33958i	0.937427	+	0.348182i	$0.113201\pi$
$631$	16932.9	+	21233.1i	1.06828	+	1.33958i	0.130855	+	0.991401i	$0.458228\pi$
$632$	4886.25	+	2353.09i	0.307539	+	0.148103i
$633$	39803.9	−	19168.5i	2.49931	−	1.20360i
$634$	−8048.35	+	10092.3i	−0.504165	+	0.632203i
$635$	534.180	+	669.841i	0.0333832	+	0.0418612i
$636$	2902.50	−	1397.77i	0.180962	−	0.0871465i
$637$	−6688.92			−0.416052
$638$	−4348.60	−	11696.0i	−0.269847	−	0.725780i
$639$	49653.8			3.07398
$640$	−922.537	+	444.270i	−0.0569789	+	0.0274396i
$641$	1092.23	+	1369.61i	0.0673017	+	0.0843937i	0.814343	−	0.580384i	$-0.197098\pi$
$641$	1092.23	+	1369.61i	0.0673017	+	0.0843937i	−0.747041	+	0.664778i	$0.768526\pi$
$642$	7491.92	−	9394.57i	0.460565	−	0.577530i
$643$	26412.5	−	12719.6i	1.61992	−	0.780112i	0.619929	−	0.784658i	$-0.287161\pi$
$643$	26412.5	−	12719.6i	1.61992	−	0.780112i	0.999990	+	0.00454622i	$0.00144711\pi$
$644$	7486.72	+	3605.42i	0.458103	+	0.220611i
$645$	−3618.31	−	4537.22i	−0.220885	−	0.276981i
$646$	−2426.38	+	10630.7i	−0.147778	+	0.647459i
$647$	−4365.19	+	19125.2i	−0.265245	+	1.16211i	0.650230	+	0.759738i	$0.274673\pi$
$647$	−4365.19	+	19125.2i	−0.265245	+	1.16211i	−0.915474	+	0.402376i	$0.868184\pi$
$648$	13660.2	−	17129.3i	0.828120	−	1.03843i
$649$	−705.027	−	3088.92i	−0.0426421	−	0.186827i
$650$	4145.33			0.250144
$651$	4332.82	+	18983.3i	0.260855	+	1.14288i
$652$	−11647.4	−	5609.09i	−0.699612	−	0.336915i
$653$	−17182.6	−	8274.69i	−1.02972	−	0.495886i	−0.158798	−	0.987311i	$-0.550762\pi$
$653$	−17182.6	−	8274.69i	−1.02972	−	0.495886i	−0.870920	+	0.491425i	$0.836476\pi$
$654$	4865.53	+	21317.3i	0.290913	+	1.27457i
$655$	−6139.97			−0.366272
$656$	1250.94	+	5480.74i	0.0744529	+	0.326200i
$657$	−46338.5	+	58106.6i	−2.75165	+	3.45046i
$658$	4248.25	−	18612.8i	0.251693	−	1.10274i
$659$	−4130.40	+	18096.5i	−0.244154	+	1.06971i	0.693040	+	0.720900i	$0.256271\pi$
$659$	−4130.40	+	18096.5i	−0.244154	+	1.06971i	−0.937194	+	0.348809i	$0.886586\pi$
$660$	−8006.73	−	10040.1i	−0.472214	−	0.592138i
$661$	−16949.8	−	8162.61i	−0.997386	−	0.480316i	−0.137336	−	0.990525i	$-0.543854\pi$
$661$	−16949.8	−	8162.61i	−0.997386	−	0.480316i	−0.860051	+	0.510209i	$0.829568\pi$
$662$	15626.6	−	7525.38i	0.917440	−	0.441816i
$663$	−9288.93	+	11647.9i	−0.544121	+	0.682306i
$664$	−5418.95	−	6795.15i	−0.316711	−	0.397143i
$665$	20915.5	−	10072.4i	1.21965	−	0.587353i
$666$	343.035			0.0199585
$667$	−10062.4	−	9680.06i	−0.584137	−	0.561939i
$668$	1165.31			0.0674956
$669$	34962.3	−	16836.9i	2.02051	−	0.973026i
$670$	−4454.21	−	5585.40i	−0.256837	−	0.322064i
$671$	−394.362	+	494.515i	−0.0226888	+	0.0284509i
$672$	6729.56	−	3240.79i	0.386307	−	0.186036i
$673$	−16455.3	−	7924.45i	−0.942503	−	0.453885i	−0.101451	−	0.994840i	$-0.532349\pi$
$673$	−16455.3	−	7924.45i	−0.942503	−	0.453885i	−0.841052	+	0.540955i	$0.818063\pi$
$674$	−5605.66	−	7029.28i	−0.320359	−	0.401718i
$675$	−6397.91	+	28031.1i	−0.364823	+	1.59839i
$676$	928.158	−	4066.53i	0.0528083	−	0.231368i
$677$	−15509.8	+	19448.6i	−0.880486	+	1.10409i	0.113385	+	0.993551i	$0.463831\pi$
$677$	−15509.8	+	19448.6i	−0.880486	+	1.10409i	−0.993871	+	0.110543i	$0.964741\pi$
$678$	1645.31	+	7208.59i	0.0931974	+	0.408325i
$679$	−20210.7			−1.14229
$680$	621.641	+	2723.59i	0.0350571	+	0.153595i
$681$	59.9379	+	28.8646i	0.00337273	+	0.00162422i
$682$	−6005.34	−	2892.02i	−0.337180	−	0.162377i
$683$	3223.41	+	14122.7i	0.180586	+	0.791199i	0.981352	+	0.192221i	$0.0615691\pi$
$683$	3223.41	+	14122.7i	0.180586	+	0.791199i	−0.800766	+	0.598978i	$0.795574\pi$
$684$	−36926.0			−2.06418
$685$	−1389.97	−	6089.86i	−0.0775300	−	0.339681i
$686$	−4233.57	+	5308.72i	−0.235624	+	0.295464i
$687$	11163.8	−	48911.9i	0.619980	−	2.71631i
$688$	−257.115	+	1126.49i	−0.0142477	+	0.0624232i
$689$	−1698.24	−	2129.53i	−0.0939013	−	0.117748i
$690$	−12946.5	−	6234.70i	−0.714296	−	0.343987i
$691$	−22493.7	+	10832.4i	−1.23835	+	0.596357i	−0.934364	−	0.356319i	$-0.884032\pi$
$691$	−22493.7	+	10832.4i	−1.23835	+	0.596357i	−0.303985	+	0.952677i	$0.598317\pi$
$692$	−2444.22	+	3064.96i	−0.134271	+	0.168370i
$693$	42779.3	+	53643.6i	2.34495	+	2.94048i
$694$	7005.18	−	3373.52i	0.383160	−	0.184520i
$695$	15337.1			0.837080
$696$	−12442.1	+	1646.47i	−0.677610	+	0.0896682i
$697$	15337.7			0.833512
$698$	15474.3	−	7452.02i	0.839126	−	0.404102i
$699$	−17967.2	−	22530.2i	−0.972220	−	1.21913i
$700$	−3535.28	+	4433.10i	−0.190887	+	0.239365i
$701$	826.255	−	397.903i	0.0445181	−	0.0214388i	−0.411492	−	0.911413i	$-0.634992\pi$
$701$	826.255	−	397.903i	0.0445181	−	0.0214388i	0.456010	+	0.889974i	$0.349278\pi$
$702$	−28851.4	−	13894.1i	−1.55118	−	0.747008i
$703$	−180.698	−	226.588i	−0.00969438	−	0.0121564i
$704$	−568.953	+	2492.74i	−0.0304591	+	0.133450i
$705$	−7346.32	+	32186.3i	−0.392452	+	1.71944i
$706$	−1297.76	+	1627.34i	−0.0691811	+	0.0867503i
$707$	3166.70	+	13874.2i	0.168453	+	0.738039i
$708$	−3186.74			−0.169159
$709$	−4603.37	−	20168.7i	−0.243841	−	1.06834i	−0.937487	−	0.348020i	$-0.886854\pi$
$709$	−4603.37	−	20168.7i	−0.243841	−	1.06834i	0.693646	−	0.720316i	$-0.256003\pi$
$710$	−9683.38	−	4663.27i	−0.511846	−	0.246492i
$711$	45145.5	+	21740.9i	2.38128	+	1.14676i
$712$	−1904.81	−	8345.51i	−0.100261	−	0.439271i
$713$	−7458.38			−0.391751
$714$	−4534.63	−	19867.5i	−0.237681	−	1.04135i
$715$	−6769.61	+	8488.82i	−0.354083	+	0.444005i
$716$	2075.63	−	9093.94i	0.108338	−	0.474660i
$717$	4621.35	−	20247.4i	0.240708	−	1.05461i
$718$	9916.18	+	12434.5i	0.515416	+	0.646311i
$719$	29970.7	+	14433.1i	1.55455	+	0.748630i	0.996689	−	0.0813079i	$-0.0259097\pi$
$719$	29970.7	+	14433.1i	1.55455	+	0.748630i	0.557856	+	0.829937i	$0.311624\pi$
$720$	−8523.59	+	4104.75i	−0.441188	+	0.212465i
$721$	18623.7	−	23353.3i	0.961972	−	1.20627i
$722$	10898.2	+	13665.9i	0.561757	+	0.704421i
$723$	−38219.2	+	18405.4i	−1.96596	+	0.946756i
$724$	−1270.43			−0.0652144
$725$	7967.54	−	5224.23i	0.408148	−	0.267618i
$726$	−5325.47			−0.272241
$727$	−22745.8	+	10953.8i	−1.16038	+	0.558808i	−0.912135	−	0.409890i	$-0.865567\pi$
$727$	−22745.8	+	10953.8i	−1.16038	+	0.558808i	−0.248242	+	0.968698i	$0.579853\pi$
$728$	−3937.45	−	4937.40i	−0.200455	−	0.251363i
$729$	46511.4	−	58323.4i	2.36302	−	2.96314i
$730$	14494.0	−	6979.92i	0.734857	−	0.353888i
$731$	2840.28	+	1367.80i	0.143709	+	0.0692067i
$732$	396.649	+	497.383i	0.0200281	+	0.0251145i
$733$	−3004.63	+	13164.1i	−0.151403	+	0.663340i	0.841075	+	0.540918i	$0.181923\pi$
$733$	−3004.63	+	13164.1i	−0.151403	+	0.663340i	−0.992478	+	0.122422i	$0.960934\pi$
$734$	4492.72	−	19683.9i	0.225926	−	0.989845i
$735$	−9864.64	+	12369.9i	−0.495051	+	0.620775i
$736$	636.638	+	2789.29i	0.0318842	+	0.139694i
$737$	−17839.1			−0.891602
$738$	11557.8	+	50638.2i	0.576490	+	2.52577i
$739$	15995.5	+	7703.04i	0.796217	+	0.383438i	0.787337	−	0.616522i	$-0.211459\pi$
$739$	15995.5	+	7703.04i	0.796217	+	0.383438i	0.00888009	+	0.999961i	$0.497173\pi$
$740$	−66.8981	−	32.2164i	−0.00332327	−	0.00160040i
$741$	9484.98	+	41556.4i	0.470228	+	2.06021i
$742$	3725.69			0.184332
$743$	7687.71	+	33682.1i	0.379589	+	1.66309i	0.698733	+	0.715383i	$0.253748\pi$
$743$	7687.71	+	33682.1i	0.379589	+	1.66309i	−0.319143	+	0.947707i	$0.603395\pi$
$744$	−4179.93	+	5241.46i	−0.205973	+	0.258281i
$745$	6199.76	−	27162.9i	0.304888	−	1.33580i
$746$	−3810.62	+	16695.4i	−0.187020	+	0.819387i
$747$	−50067.3	−	62782.5i	−2.45230	−	3.07509i
$748$	6285.06	+	3026.73i	0.307225	+	0.147952i
$749$	12520.4	−	6029.50i	0.610794	−	0.294143i
$750$	18639.3	−	23373.0i	0.907484	−	1.13795i
$751$	−7223.24	−	9057.66i	−0.350972	−	0.440105i	0.574739	−	0.818337i	$-0.305104\pi$
$751$	−7223.24	−	9057.66i	−0.350972	−	0.440105i	−0.925711	+	0.378232i	$0.876532\pi$
$752$	5922.27	−	2852.01i	0.287185	−	0.138301i
$753$	−10115.9			−0.489568
$754$	3698.02	+	9946.16i	0.178612	+	0.480395i
$755$	−6745.46			−0.325155
$756$	39464.2	−	19004.9i	1.89854	−	0.914290i
$757$	−16208.2	−	20324.5i	−0.778201	−	0.975833i	−1.00000		0.000740920i	$-0.999764\pi$
$757$	−16208.2	−	20324.5i	−0.778201	−	0.975833i	0.221799	−	0.975093i	$-0.428807\pi$
$758$	−5608.98	+	7033.43i	−0.268769	+	0.337026i
$759$	−32328.3	+	15568.5i	−1.54604	+	0.744533i
$760$	7201.24	+	3467.94i	0.343706	+	0.165520i
$761$	25067.2	+	31433.2i	1.19407	+	1.49731i	0.822368	+	0.568956i	$0.192653\pi$
$761$	25067.2	+	31433.2i	1.19407	+	1.49731i	0.371697	+	0.928354i	$0.378776\pi$
$762$	478.820	−	2097.85i	0.0227635	−	0.0997336i
$763$	−5626.96	+	24653.3i	−0.266985	+	1.16974i
$764$	5691.23	−	7136.58i	0.269505	−	0.337948i
$765$	5743.52	+	25164.0i	0.271448	+	1.18929i
$766$	−2657.93			−0.125372
$767$	599.550	+	2626.80i	0.0282249	+	0.123661i
$768$	2317.00	+	1115.81i	0.108864	+	0.0524262i
$769$	−2726.68	−	1313.10i	−0.127863	−	0.0615756i	0.368859	−	0.929486i	$-0.379749\pi$
$769$	−2726.68	−	1313.10i	−0.127863	−	0.0615756i	−0.496722	+	0.867910i	$0.665463\pi$
$770$	−3304.76	−	14479.1i	−0.154669	−	0.677651i
$771$	10643.6			0.497174
$772$	−776.054	−	3400.12i	−0.0361798	−	0.158514i
$773$	6501.06	−	8152.07i	0.302493	−	0.379314i	−0.607233	−	0.794524i	$-0.707720\pi$
$773$	6501.06	−	8152.07i	0.302493	−	0.379314i	0.909726	+	0.415210i	$0.136292\pi$
$774$	−2375.56	+	10408.0i	−0.110320	+	0.483344i
$775$	1132.47	−	4961.69i	0.0524899	−	0.229973i
$776$	−4338.60	−	5440.44i	−0.200705	−	0.251676i
$777$	487.996	+	235.007i	0.0225312	+	0.0108505i
$778$	23029.9	−	11090.6i	1.06126	−	0.511077i
$779$	27360.2	−	34308.6i	1.25838	−	1.57796i
$780$	6808.87	+	8538.05i	0.312560	+	0.391938i
$781$	−24180.1	+	11644.5i	−1.10785	+	0.533513i
$782$	7805.78			0.356949
$783$	−72964.2	+	9655.36i	−3.33018	+	0.440683i
$784$	3150.15			0.143502
$785$	17149.6	−	8258.79i	0.779737	−	0.375502i
$786$	9614.75	+	12056.5i	0.436319	+	0.547127i
$787$	−2319.55	+	2908.62i	−0.105061	+	0.131742i	−0.831582	−	0.555402i	$-0.812564\pi$
$787$	−2319.55	+	2908.62i	−0.105061	+	0.131742i	0.726521	+	0.687144i	$0.241136\pi$
$788$	12547.4	−	6042.50i	0.567236	−	0.273167i
$789$	15985.4	+	7698.16i	0.721287	+	0.347353i
$790$	−6762.37	−	8479.75i	−0.304550	−	0.381894i
$791$	−1902.80	+	8336.70i	−0.0855318	+	0.374739i
$792$	−5256.72	+	23031.2i	−0.235845	+	1.03331i
$793$	335.363	−	420.532i	0.0150178	−	0.0188317i
$794$	853.145	+	3737.87i	0.0381322	+	0.167068i
$795$	−6442.68			−0.287419
$796$	−662.857	−	2904.17i	−0.0295155	−	0.129316i
$797$	14987.8	+	7217.73i	0.666116	+	0.320785i	0.736207	−	0.676756i	$-0.236615\pi$
$797$	14987.8	+	7217.73i	0.666116	+	0.320785i	−0.0700914	+	0.997541i	$0.522329\pi$
$798$	−52530.4	−	25297.3i	−2.33027	−	1.12220i
$799$	−3990.65	−	17484.2i	−0.176695	−	0.774150i
$800$	−1952.25			−0.0862779
$801$	−17599.1	−	77106.7i	−0.776321	−	3.40129i
$802$	−3678.97	+	4613.28i	−0.161981	+	0.203118i
$803$	8938.80	−	39163.4i	0.392831	−	1.72111i
$804$	−3992.59	+	17492.7i	−0.175134	+	0.767312i
$805$	−10361.3	−	12992.7i	−0.453651	−	0.568860i
$806$	5106.91	+	2459.36i	0.223180	+	0.107478i
$807$	31662.8	−	15248.0i	1.38115	−	0.665125i
$808$	−3054.96	+	3830.79i	−0.133011	+	0.166791i
$809$	5107.40	+	6404.47i	0.221961	+	0.278330i	0.880327	−	0.474368i	$-0.157323\pi$
$809$	5107.40	+	6404.47i	0.221961	+	0.278330i	−0.658366	+	0.752698i	$0.728752\pi$
$810$	−39476.6	+	19010.9i	−1.71243	+	0.824662i
$811$	−39628.2			−1.71583			−0.857913	−	0.513795i	$-0.828239\pi$
$811$	−39628.2			−1.71583			−0.857913	+	0.513795i	$0.828239\pi$
$812$	−13790.4	−	4527.69i	−0.595996	−	0.195679i
$813$	−1907.85			−0.0823016
$814$	−167.049	+	80.4468i	−0.00719297	+	0.00346395i
$815$	16119.5	+	20213.2i	0.692812	+	0.868759i
$816$	4374.62	−	5485.60i	0.187674	−	0.235336i
$817$	8126.24	−	3913.39i	0.347982	−	0.167579i
$818$	−3976.84	−	1915.14i	−0.169984	−	0.0818600i
$819$	−36379.3	−	45618.1i	−1.55213	−	1.94631i
$820$	2501.74	−	10960.8i	0.106542	−	0.466791i
$821$	−2884.10	+	12636.1i	−0.122601	+	0.537151i	0.875903	+	0.482486i	$0.160266\pi$
$821$	−2884.10	+	12636.1i	−0.122601	+	0.537151i	−0.998505	+	0.0546650i	$0.982591\pi$
$822$	−9781.52	+	12265.6i	−0.415048	+	0.520454i
$823$	−1943.64	−	8515.66i	−0.0823222	−	0.360677i	0.916942	−	0.399019i	$-0.130649\pi$
$823$	−1943.64	−	8515.66i	−0.0823222	−	0.360677i	−0.999265	+	0.0383423i	$0.987792\pi$
$824$	10284.3			0.434795
$825$	−5448.25	−	23870.3i	−0.229920	−	1.00734i
$826$	−3320.47	−	1599.05i	−0.139872	−	0.0673586i
$827$	−2943.64	−	1417.58i	−0.123773	−	0.0596061i	0.370972	−	0.928644i	$-0.379024\pi$
$827$	−2943.64	−	1417.58i	−0.123773	−	0.0596061i	−0.494746	+	0.869038i	$0.664739\pi$
$828$	5882.09	+	25771.1i	0.246880	+	1.08165i
$829$	28115.8			1.17793			0.588964	−	0.808159i	$-0.299536\pi$
$829$	28115.8			1.17793			0.588964	+	0.808159i	$0.299536\pi$
$830$	3867.77	+	16945.8i	0.161750	+	0.708672i
$831$	40426.1	−	50692.7i	1.68756	−	2.11614i
$832$	483.833	−	2119.81i	0.0201609	−	0.0883309i
$833$	1912.48	−	8379.12i	0.0795480	−	0.348522i
$834$	−24016.9	−	30116.2i	−0.997166	−	1.25041i
$835$	−2099.68	−	1011.15i	−0.0870210	−	0.0419071i
$836$	17982.0	−	8659.69i	0.743925	−	0.358256i
$837$	−24512.4	+	30737.5i	−1.01227	+	1.26935i
$838$	−9629.32	−	12074.8i	−0.396944	−	0.497752i
$839$	24369.3	−	11735.6i	1.00277	−	0.482907i	0.140890	−	0.990025i	$-0.455004\pi$
$839$	24369.3	−	11735.6i	1.00277	−	0.482907i	0.861876	+	0.507118i	$0.169289\pi$
$840$	−14937.6			−0.613567
$841$	19642.6	+	14456.5i	0.805388	+	0.592748i
$842$	−21796.7			−0.892117
$843$	17637.1	−	8493.60i	0.720588	−	0.347017i
$844$	10968.0	+	13753.5i	0.447316	+	0.560917i
$845$	−5200.97	+	6521.81i	−0.211738	+	0.265511i
$846$	54717.6	−	26350.6i	2.22368	−	1.07087i
$847$	−5548.96	−	2672.24i	−0.225106	−	0.108405i
$848$	799.789	+	1002.90i	0.0323878	+	0.0406130i
$849$	−1596.00	+	6992.52i	−0.0645164	+	0.282665i
$850$	−1185.22	+	5192.80i	−0.0478268	+	0.209543i
$851$	−129.354	+	162.205i	−0.00521059	+	0.00653387i
$852$	6006.63	+	26316.8i	0.241530	+	1.05821i
$853$	−9024.19			−0.362230			−0.181115	−	0.983462i	$-0.557971\pi$
$853$	−9024.19			−0.362230			−0.181115	+	0.983462i	$0.557971\pi$
$854$	163.716	+	717.288i	0.00656002	+	0.0287413i
$855$	66534.4	+	32041.3i	2.66132	+	1.28162i
$856$	4310.79	+	2075.97i	0.172126	+	0.0828915i
$857$	3995.40	+	17505.0i	0.159254	+	0.697736i	0.989998	+	0.141082i	$0.0450580\pi$
$857$	3995.40	+	17505.0i	0.159254	+	0.697736i	−0.830744	+	0.556654i	$0.812085\pi$
$858$	27269.5			1.08504
$859$	5918.62	+	25931.2i	0.235088	+	1.02999i	0.945352	+	0.326052i	$0.105719\pi$
$859$	5918.62	+	25931.2i	0.235088	+	1.02999i	−0.710264	+	0.703936i	$0.751424\pi$
$860$	1440.75	−	1806.65i	0.0571271	−	0.0716351i
$861$	−18249.2	+	79955.1i	−0.722337	+	3.16476i
$862$	3007.09	−	13174.9i	0.118819	−	0.520579i
$863$	−17023.0	−	21346.1i	−0.671459	−	0.841983i	0.323078	−	0.946372i	$-0.395282\pi$
$863$	−17023.0	−	21346.1i	−0.671459	−	0.841983i	−0.994536	+	0.104390i	$0.966711\pi$
$864$	13587.6	+	6543.44i	0.535022	+	0.257653i
$865$	7063.59	−	3401.64i	0.277652	−	0.133710i
$866$	−15941.8	+	19990.4i	−0.625549	+	0.784414i
$867$	18836.4	+	23620.1i	0.737854	+	0.925239i
$868$	−6985.43	+	3364.01i	−0.273158	+	0.131546i
$869$	−27083.3			−1.05723
$870$	23847.2	+	7829.56i	0.929306	+	0.305111i
$871$	15170.2			0.590153
$872$	−7844.27	+	3777.60i	−0.304633	+	0.146704i
$873$	−40085.7	−	50265.8i	−1.55406	−	1.94873i
$874$	13924.3	−	17460.6i	0.538899	−	0.675758i
$875$	31149.8	−	15000.9i	1.20349	−	0.579571i
$876$	−36402.4	−	17530.4i	−1.40402	−	0.676140i
$877$	−11128.5	−	13954.7i	−0.428488	−	0.537307i	0.519981	−	0.854178i	$-0.325939\pi$
$877$	−11128.5	−	13954.7i	−0.428488	−	0.537307i	−0.948469	+	0.316871i	$0.897368\pi$
$878$	−3977.71	+	17427.5i	−0.152894	+	0.669874i
$879$	3108.10	−	13617.5i	0.119265	−	0.522533i
$880$	3188.15	−	3997.81i	0.122128	−	0.153143i
$881$	−2514.51	−	11016.8i	−0.0961589	−	0.421300i	0.903819	−	0.427914i	$-0.140752\pi$
$881$	−2514.51	−	11016.8i	−0.0961589	−	0.421300i	−0.999978	+	0.00661488i	$0.997894\pi$
$882$	29105.2			1.11114
$883$	−2110.90	−	9248.44i	−0.0804499	−	0.352474i	0.918642	−	0.395092i	$-0.129287\pi$
$883$	−2110.90	−	9248.44i	−0.0804499	−	0.352474i	−0.999091	+	0.0426179i	$0.986430\pi$
$884$	−5344.77	−	2573.91i	−0.203353	−	0.0979297i
$885$	5741.96	+	2765.18i	0.218095	+	0.105029i
$886$	526.476	+	2306.64i	0.0199631	+	0.0874641i
$887$	23808.5			0.901253			0.450627	−	0.892712i	$-0.351201\pi$
$887$	23808.5			0.901253			0.450627	+	0.892712i	$0.351201\pi$
$888$	41.4971	+	181.811i	0.00156819	+	0.00687068i
$889$	1551.58	−	1945.62i	0.0585358	−	0.0734016i
$890$	−3809.39	+	16690.0i	−0.143473	+	0.628596i
$891$	−24346.3	+	106668.i	−0.915411	+	4.01068i
$892$	9633.92	+	12080.5i	0.361623	+	0.453460i
$893$	−46228.7	−	22262.6i	−1.73235	−	0.834254i
$894$	−63045.8	+	30361.3i	−2.35858	+	1.13583i
$895$	−11630.9	+	14584.7i	−0.434388	+	0.544706i
$896$	1854.34	+	2325.27i	0.0691397	+	0.0866985i
$897$	27491.8	−	13239.3i	1.02333	−	0.492808i
$898$	5246.77			0.194974
$899$	12915.2	−	1709.07i	0.479138	−	0.0634044i
$900$	−18037.4			−0.668051
$901$	3153.19	−	1518.50i	0.116590	−	0.0561470i
$902$	−17503.8	−	21949.0i	−0.646132	−	0.810224i
$903$	−10509.8	+	13178.8i	−0.387312	+	0.485674i
$904$	−2652.59	+	1277.42i	−0.0975929	+	0.0469983i
$905$	2289.10	+	1102.37i	0.0840799	+	0.0404907i
$906$	10562.9	+	13245.5i	0.387339	+	0.485708i
$907$	−8604.19	+	37697.4i	−0.314992	+	1.38007i	0.531225	+	0.847231i	$0.321732\pi$
$907$	−8604.19	+	37697.4i	−0.314992	+	1.38007i	−0.846217	+	0.532838i	$0.821125\pi$
$908$	−5.89449	+	25.8254i	−0.000215436	+	0.000943885i
$909$	−28225.7	+	35393.9i	−1.02991	+	1.29146i
$910$	2810.35	+	12312.9i	0.102376	+	0.448539i
$911$	7391.75			0.268825			0.134412	−	0.990925i	$-0.457085\pi$
$911$	7391.75			0.268825			0.134412	+	0.990925i	$0.457085\pi$
$912$	−4466.95	−	19571.0i	−0.162188	−	0.710592i
$913$	39104.9	+	18831.9i	1.41751	+	0.682635i
$914$	−20270.9	−	9761.93i	−0.733589	−	0.353278i
$915$	−283.108	−	1240.38i	−0.0102287	−	0.0448149i
$916$	19976.8			0.720580
$917$	3968.47	+	17387.0i	0.142912	+	0.626140i
$918$	25654.1	−	32169.2i	0.922343	−	1.15658i
$919$	1678.33	−	7353.25i	0.0602427	−	0.263941i	−0.935833	−	0.352443i	$-0.885351\pi$
$919$	1678.33	−	7353.25i	0.0602427	−	0.263941i	0.996076	+	0.0885026i	$0.0282082\pi$
$920$	1273.20	−	5578.25i	0.0456262	−	0.199902i
$921$	−60541.5	−	75916.7i	−2.16603	−	2.71611i
$922$	24740.1	+	11914.2i	0.883700	+	0.425567i
$923$	20562.6	−	9902.43i	0.733290	−	0.353134i
$924$	−23256.3	+	29162.5i	−0.828006	+	1.03829i
$925$	−88.2661	−	110.682i	−0.00313748	−	0.00393428i
$926$	−6046.00	+	2911.60i	−0.214561	+	0.103327i
$927$	95019.9			3.36663
$928$	−1741.58	−	4684.15i	−0.0616058	−	0.165695i
$929$	−24103.9			−0.851263			−0.425632	−	0.904897i	$-0.639948\pi$
$929$	−24103.9			−0.851263			−0.425632	+	0.904897i	$0.639948\pi$
$930$	12079.6	−	5817.24i	0.425921	−	0.205113i
$931$	−15331.5	−	19225.1i	−0.539709	−	0.676774i
$932$	7154.25	−	8971.14i	0.251443	−	0.315300i
$933$	24308.5	−	11706.4i	0.852975	−	0.410771i
$934$	18947.8	+	9124.79i	0.663803	+	0.319671i
$935$	−8698.27	−	10907.3i	−0.304240	−	0.381504i
$936$	4470.28	−	19585.6i	0.156107	−	0.683948i
$937$	5768.01	−	25271.3i	0.201102	−	0.881085i	−0.769165	−	0.639050i	$-0.779328\pi$
$937$	5768.01	−	25271.3i	0.201102	−	0.881085i	0.970267	−	0.242036i	$-0.0778151\pi$
$938$	−12937.7	+	16223.3i	−0.450352	+	0.564724i
$939$	6303.53	+	27617.6i	0.219071	+	0.959813i
$940$	−13145.7			−0.456132
$941$	−2210.26	−	9683.78i	−0.0765700	−	0.335475i	0.922105	−	0.386940i	$-0.126468\pi$
$941$	−2210.26	−	9683.78i	−0.0765700	−	0.335475i	−0.998675	+	0.0514651i	$0.983611\pi$
$942$	−43072.0	−	20742.4i	−1.48977	−	0.717435i
$943$	−28302.7	−	13629.9i	−0.977373	−	0.470678i
$944$	−282.358	−	1237.09i	−0.00973515	−	0.0426525i
$945$	−87598.6			−3.01543
$946$	−1283.99	−	5625.54i	−0.0441292	−	0.193342i
$947$	−28058.0	+	35183.6i	−0.962789	+	1.20730i	0.0154629	+	0.999880i	$0.495078\pi$
$947$	−28058.0	+	35183.6i	−0.962789	+	1.20730i	−0.978252	+	0.207419i	$0.933494\pi$
$948$	−6061.54	+	26557.4i	−0.207669	+	0.909856i
$949$	−7601.50	+	33304.3i	−0.260016	+	1.13920i
$950$	9501.40	+	11914.4i	0.324491	+	0.406898i
$951$	−58416.3	−	28131.8i	−1.99188	−	0.959238i
$952$	7310.80	−	3520.69i	0.248891	−	0.119860i
$953$	−327.999	+	411.297i	−0.0111489	+	0.0139803i	−0.787375	−	0.616475i	$-0.788560\pi$
$953$	−327.999	+	411.297i	−0.0111489	+	0.0139803i	0.776226	+	0.630455i	$0.217132\pi$
$954$	7389.49	+	9266.12i	0.250779	+	0.314467i
$955$	−16447.2	+	7920.53i	−0.557296	+	0.268380i
$956$	8269.53			0.279766
$957$	52413.3	−	34366.9i	1.77041	−	1.16084i
$958$	16238.6			0.547646
$959$	−16346.7	+	7872.17i	−0.550431	+	0.265074i
$960$	−3206.64	−	4021.00i	−0.107806	−	0.135184i
$961$	−14235.5	+	17850.8i	−0.477847	+	0.599201i
$962$	142.058	−	68.4114i	0.00476104	−	0.00229280i
$963$	39828.7	+	19180.5i	1.33277	+	0.641830i
$964$	−10531.4	−	13205.9i	−0.351860	−	0.441218i
$965$	−1552.02	+	6799.83i	−0.0517732	+	0.226833i
$966$	−9287.51	+	40691.3i	−0.309338	+	1.35530i
$967$	35135.8	−	44058.9i	1.16845	−	1.46519i	0.311161	−	0.950357i	$-0.399282\pi$
$967$	35135.8	−	44058.9i	1.16845	−	1.46519i	0.857290	−	0.514834i	$-0.172146\pi$
$968$	−471.859	−	2067.35i	−0.0156675	−	0.0686438i
$969$	−54769.0			−1.81572
$970$	3096.67	+	13567.4i	0.102503	+	0.449096i
$971$	−46809.9	−	22542.5i	−1.54707	−	0.745028i	−0.551073	−	0.834457i	$-0.685781\pi$
$971$	−46809.9	−	22542.5i	−1.54707	−	0.745028i	−0.995993	+	0.0894294i	$0.971496\pi$
$972$	53289.6	+	25662.9i	1.75850	+	0.846850i
$973$	−9912.92	−	43431.3i	−0.326612	−	1.43098i
$974$	17833.6			0.586679
$975$	4633.16	+	20299.2i	0.152184	+	0.666763i
$976$	−157.939	+	198.050i	−0.00517983	+	0.00649530i
$977$	−6178.85	+	27071.3i	−0.202333	+	0.886478i	0.767179	+	0.641433i	$0.221660\pi$
$977$	−6178.85	+	27071.3i	−0.202333	+	0.886478i	−0.969512	+	0.245045i	$0.921197\pi$
$978$	14448.9	−	63305.0i	0.472420	−	2.06981i
$979$	26652.9	+	33421.7i	0.870104	+	1.09108i
$980$	−5676.03	−	2733.43i	−0.185015	−	0.0890983i
$981$	−72475.5	+	34902.4i	−2.35878	+	1.13593i
$982$	14154.3	−	17749.0i	0.459963	−	0.576775i
$983$	−1658.85	−	2080.13i	−0.0538240	−	0.0674931i	0.754191	−	0.656655i	$-0.228029\pi$
$983$	−1658.85	−	2080.13i	−0.0538240	−	0.0674931i	−0.808015	+	0.589162i	$0.799458\pi$
$984$	−25440.3	+	12251.4i	−0.824196	+	0.396912i
$985$	−27851.4			−0.900934
$986$	−13516.7	+	1788.67i	−0.436573	+	0.0577717i
$987$	95892.6			3.09250
$988$	−15291.8	+	7364.14i	−0.492406	+	0.237130i
$989$	−4025.66	−	5048.02i	−0.129432	−	0.162303i
$990$	29456.3	−	36937.0i	0.945638	−	1.18579i
$991$	2081.79	−	1002.54i	0.0667308	−	0.0321359i	−0.400221	−	0.916419i	$-0.631067\pi$
$991$	2081.79	−	1002.54i	0.0667308	−	0.0321359i	0.466952	+	0.884283i	$0.345352\pi$
$992$	−2405.10	−	1158.23i	−0.0769777	−	0.0370705i
$993$	54316.4	+	68110.6i	1.73583	+	2.17666i
$994$	−6946.64	+	30435.2i	−0.221664	+	0.971173i
$995$	−1325.64	+	5807.99i	−0.0422366	+	0.185051i
$996$	27218.4	−	34130.8i	0.865911	−	1.08582i
$997$	−676.280	−	2962.98i	−0.0214825	−	0.0941208i	0.963050	−	0.269322i	$-0.0867996\pi$
$997$	−676.280	−	2962.98i	−0.0214825	−	0.0941208i	−0.984533	+	0.175201i	$0.943942\pi$
$998$	5192.01			0.164679
$999$	243.351	+	1066.19i	0.00770700	+	0.0337666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.4.d.b.49.1	yes	24
29.4	even	14		1682.4.a.q.1.12		12
29.16	even	7	inner	58.4.d.b.45.1	✓	24
29.25	even	7		1682.4.a.t.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.d.b.45.1	✓	24	29.16	even	7	inner
58.4.d.b.49.1	yes	24	1.1	even	1	trivial
1682.4.a.q.1.12		12	29.4	even	14
1682.4.a.t.1.1		12	29.25	even	7

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	58.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80194 + 0.867767i) q^{2} +(-6.26334 - 7.85398i) q^{3} +(2.49396 - 3.12733i) q^{4} +(-7.20732 + 3.47086i) q^{5} +(18.1016 + 8.71726i) q^{6} +(14.4870 + 18.1662i) q^{7} +(-1.78017 + 7.79942i) q^{8} +(-16.4475 + 72.0612i) q^{9} +(9.97524 - 12.5086i) q^{10} +(-8.88988 - 38.9491i) q^{11} -40.1825 q^{12} +(7.55990 + 33.1221i) q^{13} +(-41.8688 - 20.1629i) q^{14} +(72.4020 + 34.8669i) q^{15} +(-3.56033 - 15.5988i) q^{16} -43.6530 q^{17} +(-32.8950 - 144.122i) q^{18} +(-77.8705 + 97.6465i) q^{19} +(-7.12024 + 31.1958i) q^{20} +(51.9395 - 227.562i) q^{21} +(49.8178 + 62.4695i) q^{22} +(80.5529 + 38.7923i) q^{23} +(72.4063 - 34.8690i) q^{24} +(-38.0377 + 47.6977i) q^{25} +(-42.3647 - 53.1237i) q^{26} +(424.612 - 204.482i) q^{27} +92.9416 q^{28} +(-148.377 - 48.7155i) q^{29} -160.720 q^{30} +(-75.1593 + 36.1948i) q^{31} +(19.9517 + 25.0186i) q^{32} +(-250.225 + 313.773i) q^{33} +(78.6601 - 37.8807i) q^{34} +(-167.465 - 80.6469i) q^{35} +(184.339 + 231.154i) q^{36} +(-0.516358 + 2.26231i) q^{37} +(55.5833 - 243.527i) q^{38} +(212.790 - 266.830i) q^{39} +(-14.2405 - 62.3916i) q^{40} -351.355 q^{41} +(103.879 + 455.124i) q^{42} +(-65.0648 - 31.3336i) q^{43} +(-143.978 - 69.3360i) q^{44} +(-131.572 - 576.455i) q^{45} -178.814 q^{46} +(91.4175 + 400.526i) q^{47} +(-100.213 + 125.664i) q^{48} +(-43.8109 + 191.948i) q^{49} +(27.1510 - 118.956i) q^{50} +(273.414 + 342.850i) q^{51} +(122.438 + 58.9628i) q^{52} +(-72.2330 + 34.7856i) q^{53} +(-587.682 + 736.929i) q^{54} +(199.259 + 249.863i) q^{55} +(-167.475 + 80.6517i) q^{56} +1254.64 q^{57} +(309.640 - 40.9747i) q^{58} +79.3066 q^{59} +(289.608 - 139.468i) q^{60} +(-9.87121 - 12.3781i) q^{61} +(104.024 - 130.442i) q^{62} +(-1547.35 + 745.166i) q^{63} +(-57.6620 - 27.7686i) q^{64} +(-169.449 - 212.482i) q^{65} +(178.609 - 782.536i) q^{66} +(99.3614 - 435.331i) q^{67} +(-108.869 + 136.517i) q^{68} +(-199.857 - 875.630i) q^{69} +371.744 q^{70} +(-149.484 - 654.931i) q^{71} +(-532.757 - 256.562i) q^{72} +(905.926 + 436.271i) q^{73} +(-1.03272 - 4.52462i) q^{74} +612.860 q^{75} +(111.167 + 487.053i) q^{76} +(578.769 - 725.753i) q^{77} +(-151.888 + 665.463i) q^{78} +(150.850 - 660.919i) q^{79} +(79.8019 + 100.068i) q^{80} +(-2467.44 - 1188.26i) q^{81} +(633.121 - 304.895i) q^{82} +(-677.369 + 849.394i) q^{83} +(-582.125 - 729.962i) q^{84} +(314.621 - 151.514i) q^{85} +144.433 q^{86} +(546.727 + 1470.47i) q^{87} +319.606 q^{88} +(-964.051 + 464.263i) q^{89} +(737.314 + 924.562i) q^{90} +(-492.181 + 617.175i) q^{91} +(322.212 - 155.169i) q^{92} +(755.021 + 363.599i) q^{93} +(-512.292 - 642.394i) q^{94} +(222.320 - 974.048i) q^{95} +(71.5315 - 313.400i) q^{96} +(-542.326 + 680.055i) q^{97} +(-87.6218 - 383.896i) q^{98} +2952.94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 5 q^{3} - 16 q^{4} + 16 q^{5} - 4 q^{6} + 71 q^{7} - 32 q^{8} - 27 q^{9} - 10 q^{10} + 110 q^{11} - 64 q^{12} - 107 q^{13} - 54 q^{14} + 417 q^{15} - 64 q^{16} - 128 q^{17} - 54 q^{18}+ \cdots + 10560 q^{99}+O(q^{100}) \) 24 * q - 8 * q^2 + 5 * q^3 - 16 * q^4 + 16 * q^5 - 4 * q^6 + 71 * q^7 - 32 * q^8 - 27 * q^9 - 10 * q^10 + 110 * q^11 - 64 * q^12 - 107 * q^13 - 54 * q^14 + 417 * q^15 - 64 * q^16 - 128 * q^17 - 54 * q^18 - 142 * q^19 + 36 * q^20 + 655 * q^21 + 24 * q^22 - 239 * q^23 - 16 * q^24 - 550 * q^25 + 192 * q^26 - 61 * q^27 - 24 * q^28 - 450 * q^29 - 2092 * q^30 + 420 * q^31 - 128 * q^32 + 165 * q^33 + 934 * q^34 - 532 * q^35 + 88 * q^36 + 85 * q^37 + 626 * q^38 + 1374 * q^39 + 72 * q^40 - 822 * q^41 + 1310 * q^42 + 245 * q^43 - 260 * q^44 + 916 * q^45 + 712 * q^46 + 235 * q^47 + 80 * q^48 - 1507 * q^49 + 510 * q^50 + 333 * q^51 + 104 * q^52 - 121 * q^53 - 836 * q^54 - 584 * q^55 - 216 * q^56 - 1458 * q^57 + 2432 * q^58 - 5226 * q^59 + 1668 * q^60 - 567 * q^61 - 252 * q^62 + 1096 * q^63 - 256 * q^64 + 584 * q^65 + 8 * q^66 - 131 * q^67 + 412 * q^68 - 1412 * q^69 + 1036 * q^70 + 3141 * q^71 - 1112 * q^72 + 3326 * q^73 + 170 * q^74 + 7850 * q^75 + 1252 * q^76 + 2834 * q^77 - 4126 * q^78 + 1728 * q^79 - 80 * q^80 - 10976 * q^81 + 1184 * q^82 - 1287 * q^83 - 2756 * q^84 - 7728 * q^85 - 3724 * q^86 + 4541 * q^87 - 912 * q^88 + 715 * q^89 - 2004 * q^90 - 6757 * q^91 - 956 * q^92 + 4094 * q^93 - 496 * q^94 - 4759 * q^95 + 160 * q^96 + 1779 * q^97 - 3014 * q^98 + 10560 * q^99

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