LMFDB - Embedded newform 74.4.f.b.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	74.33
Dual form			74.4.f.b.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347296 - 1.96962i) q^{2} +(0.551654 + 3.12858i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.17496 - 6.02051i) q^{5} +6.35370 q^{6} +(7.01886 - 5.88953i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(15.8880 - 5.78275i) q^{9} +O(q^{10})$	\(q+(0.347296 - 1.96962i) q^{2} +(0.551654 + 3.12858i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.17496 - 6.02051i) q^{5} +6.35370 q^{6} +(7.01886 - 5.88953i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(15.8880 - 5.78275i) q^{9} +(-9.36625 - 16.2228i) q^{10} +(21.0546 - 36.4676i) q^{11} +(2.20662 - 12.5143i) q^{12} +(47.5652 + 17.3123i) q^{13} +(-9.16248 - 15.8699i) q^{14} +(22.7938 + 19.1262i) q^{15} +(12.2567 + 10.2846i) q^{16} +(-120.345 + 43.8019i) q^{17} +(-5.87196 - 33.3015i) q^{18} +(-19.9417 - 113.095i) q^{19} +(-35.2056 + 12.8138i) q^{20} +(22.2979 + 18.7101i) q^{21} +(-64.5150 - 54.1345i) q^{22} +(51.0336 + 88.3927i) q^{23} +(-23.8821 - 8.69237i) q^{24} +(-6.47246 + 36.7071i) q^{25} +(50.6179 - 87.6727i) q^{26} +(69.7439 + 120.800i) q^{27} +(-34.4396 + 12.5350i) q^{28} +(-61.2938 + 106.164i) q^{29} +(45.5875 - 38.2525i) q^{30} -59.7600 q^{31} +(24.5134 - 20.5692i) q^{32} +(125.707 + 45.7536i) q^{33} +(44.4776 + 252.245i) q^{34} +(14.9021 - 84.5143i) q^{35} -67.6305 q^{36} +(29.1088 + 223.172i) q^{37} -229.679 q^{38} +(-27.9235 + 158.362i) q^{39} +(13.0115 + 73.7916i) q^{40} +(-76.1491 - 27.7160i) q^{41} +(44.5957 - 37.4203i) q^{42} +39.8186 q^{43} +(-129.030 + 108.269i) q^{44} +(79.1806 - 137.145i) q^{45} +(191.823 - 69.8180i) q^{46} +(-162.796 - 281.972i) q^{47} +(-25.4148 + 44.0197i) q^{48} +(-44.9834 + 255.113i) q^{49} +(70.0511 + 25.4965i) q^{50} +(-203.427 - 352.345i) q^{51} +(-155.102 - 130.146i) q^{52} +(-400.552 - 336.103i) q^{53} +(262.151 - 95.4153i) q^{54} +(-68.4877 - 388.413i) q^{55} +(12.7284 + 72.1862i) q^{56} +(342.826 - 124.778i) q^{57} +(187.815 + 157.596i) q^{58} +(135.587 + 113.771i) q^{59} +(-59.5103 - 103.075i) q^{60} +(195.761 + 71.2510i) q^{61} +(-20.7544 + 117.704i) q^{62} +(77.4579 - 134.161i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(445.508 - 162.152i) q^{65} +(133.775 - 231.704i) q^{66} +(-551.065 + 462.398i) q^{67} +512.273 q^{68} +(-248.391 + 208.425i) q^{69} +(-161.285 - 58.7030i) q^{70} +(-110.459 - 626.446i) q^{71} +(-23.4878 + 133.206i) q^{72} +578.930 q^{73} +(449.672 + 20.1735i) q^{74} -118.412 q^{75} +(-79.7667 + 452.380i) q^{76} +(-66.9977 - 379.963i) q^{77} +(302.215 + 109.997i) q^{78} +(-36.6732 + 30.7725i) q^{79} +149.860 q^{80} +(10.2453 - 8.59681i) q^{81} +(-81.0361 + 140.359i) q^{82} +(718.676 - 261.577i) q^{83} +(-58.2156 - 100.832i) q^{84} +(-599.760 + 1038.81i) q^{85} +(13.8288 - 78.4273i) q^{86} +(-365.956 - 133.197i) q^{87} +(168.437 + 291.741i) q^{88} +(-124.277 - 104.280i) q^{89} +(-242.623 - 203.585i) q^{90} +(435.815 - 158.624i) q^{91} +(-70.8951 - 402.066i) q^{92} +(-32.9668 - 186.964i) q^{93} +(-611.914 + 222.719i) q^{94} +(-823.970 - 691.393i) q^{95} +(77.8754 + 65.3452i) q^{96} +(407.223 + 705.332i) q^{97} +(486.853 + 177.200i) q^{98} +(123.632 - 701.151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) $ 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$2$	0.347296	−	1.96962i	0.122788	−	0.696364i
$3$	0.551654	+	3.12858i	0.106166	+	0.602096i	0.990748	+	0.135713i	$0.0433324\pi$
$3$	0.551654	+	3.12858i	0.106166	+	0.602096i	−0.884582	+	0.466384i	$0.845557\pi$
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	7.17496	−	6.02051i	0.641748	−	0.538491i	−0.262806	−	0.964849i	$-0.584648\pi$
$5$	7.17496	−	6.02051i	0.641748	−	0.538491i	0.904555	+	0.426358i	$0.140204\pi$
$6$	6.35370			0.432314
$7$	7.01886	−	5.88953i	0.378983	−	0.318005i	−0.433320	−	0.901240i	$-0.642658\pi$
$7$	7.01886	−	5.88953i	0.378983	−	0.318005i	0.812303	+	0.583236i	$0.198214\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	15.8880	−	5.78275i	0.588444	−	0.214176i
$10$	−9.36625	−	16.2228i	−0.296187	−	0.513011i
$11$	21.0546	−	36.4676i	0.577109	−	0.999582i	−0.418700	−	0.908125i	$-0.637514\pi$
$11$	21.0546	−	36.4676i	0.577109	−	0.999582i	0.995809	−	0.0914577i	$-0.0291526\pi$
$12$	2.20662	−	12.5143i	0.0530829	−	0.301048i
$13$	47.5652	+	17.3123i	1.01479	+	0.369352i	0.795269	−	0.606257i	$-0.207330\pi$
$13$	47.5652	+	17.3123i	1.01479	+	0.369352i	0.219517	+	0.975609i	$0.429552\pi$
$14$	−9.16248	−	15.8699i	−0.174913	−	0.302957i
$15$	22.7938	+	19.1262i	0.392355	+	0.329225i
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	−120.345	+	43.8019i	−1.71694	+	0.624913i	−0.997567	−	0.0697154i	$-0.977791\pi$
$17$	−120.345	+	43.8019i	−1.71694	+	0.624913i	−0.719368	+	0.694629i	$0.755569\pi$
$18$	−5.87196	−	33.3015i	−0.0768908	−	0.436069i
$19$	−19.9417	−	113.095i	−0.240786	−	1.36557i	−0.830079	−	0.557646i	$-0.811705\pi$
$19$	−19.9417	−	113.095i	−0.240786	−	1.36557i	0.589293	−	0.807920i	$-0.299406\pi$
$20$	−35.2056	+	12.8138i	−0.393610	+	0.143262i
$21$	22.2979	+	18.7101i	0.231704	+	0.194423i
$22$	−64.5150	−	54.1345i	−0.625211	−	0.524615i
$23$	51.0336	+	88.3927i	0.462662	+	0.801354i	0.999093	−	0.0425901i	$-0.0135610\pi$
$23$	51.0336	+	88.3927i	0.462662	+	0.801354i	−0.536430	+	0.843945i	$0.680228\pi$
$24$	−23.8821	−	8.69237i	−0.203121	−	0.0739301i
$25$	−6.47246	+	36.7071i	−0.0517796	+	0.293657i
$26$	50.6179	−	87.6727i	0.381807	−	0.661309i
$27$	69.7439	+	120.800i	0.497120	+	0.861036i
$28$	−34.4396	+	12.5350i	−0.232446	+	0.0846033i
$29$	−61.2938	+	106.164i	−0.392482	+	0.679799i	−0.992776	−	0.119981i	$-0.961717\pi$
$29$	−61.2938	+	106.164i	−0.392482	+	0.679799i	0.600294	+	0.799779i	$0.295050\pi$
$30$	45.5875	−	38.2525i	0.277437	−	0.232797i
$31$	−59.7600			−0.346233			−0.173116	−	0.984901i	$-0.555384\pi$
$31$	−59.7600			−0.346233			−0.173116	+	0.984901i	$0.555384\pi$
$32$	24.5134	−	20.5692i	0.135419	−	0.113630i
$33$	125.707	+	45.7536i	0.663114	+	0.241354i
$34$	44.4776	+	252.245i	0.224349	+	1.27234i
$35$	14.9021	−	84.5143i	0.0719692	−	0.408158i
$36$	−67.6305			−0.313104
$37$	29.1088	+	223.172i	0.129337	+	0.991601i
$37$	29.1088	+	223.172i	0.129337	+	0.991601i
$38$	−229.679			−0.980497
$39$	−27.9235	+	158.362i	−0.114650	+	0.650212i
$40$	13.0115	+	73.7916i	0.0514323	+	0.291687i
$41$	−76.1491	−	27.7160i	−0.290061	−	0.105573i	0.192892	−	0.981220i	$-0.438213\pi$
$41$	−76.1491	−	27.7160i	−0.290061	−	0.105573i	−0.482952	+	0.875647i	$0.660436\pi$
$42$	44.5957	−	37.4203i	0.163840	−	0.137478i
$43$	39.8186			0.141216			0.0706079	−	0.997504i	$-0.477506\pi$
$43$	39.8186			0.141216			0.0706079	+	0.997504i	$0.477506\pi$
$44$	−129.030	+	108.269i	−0.442091	+	0.370959i
$45$	79.1806	−	137.145i	0.262301	−	0.454318i
$46$	191.823	−	69.8180i	0.614844	−	0.223785i
$47$	−162.796	−	281.972i	−0.505240	−	0.875102i	−0.999982	−	0.00606172i	$-0.998070\pi$
$47$	−162.796	−	281.972i	−0.505240	−	0.875102i	0.494741	−	0.869040i	$-0.335263\pi$
$48$	−25.4148	+	44.0197i	−0.0764231	+	0.132369i
$49$	−44.9834	+	255.113i	−0.131147	+	0.743771i
$50$	70.0511	+	25.4965i	0.198134	+	0.0721150i
$51$	−203.427	−	352.345i	−0.558538	−	0.967416i
$52$	−155.102	−	130.146i	−0.413631	−	0.347077i
$53$	−400.552	−	336.103i	−1.03811	−	0.871081i	−0.0463197	−	0.998927i	$-0.514749\pi$
$53$	−400.552	−	336.103i	−1.03811	−	0.871081i	−0.991794	+	0.127846i	$0.959194\pi$
$54$	262.151	−	95.4153i	0.660635	−	0.240452i
$55$	−68.4877	−	388.413i	−0.167907	−	0.952248i
$56$	12.7284	+	72.1862i	0.0303732	+	0.172255i
$57$	342.826	−	124.778i	0.796639	−	0.289953i
$58$	187.815	+	157.596i	0.425195	+	0.356781i
$59$	135.587	+	113.771i	0.299185	+	0.251046i	0.780005	−	0.625773i	$-0.215217\pi$
$59$	135.587	+	113.771i	0.299185	+	0.251046i	−0.480820	+	0.876819i	$0.659661\pi$
$60$	−59.5103	−	103.075i	−0.128046	−	0.221782i
$61$	195.761	+	71.2510i	0.410895	+	0.149553i	0.539193	−	0.842182i	$-0.318729\pi$
$61$	195.761	+	71.2510i	0.410895	+	0.149553i	−0.128298	+	0.991736i	$0.540952\pi$
$62$	−20.7544	+	117.704i	−0.0425131	+	0.241104i
$63$	77.4579	−	134.161i	0.154901	−	0.268297i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	445.508	−	162.152i	0.850130	−	0.309422i
$66$	133.775	−	231.704i	0.249493	−	0.432134i
$67$	−551.065	+	462.398i	−1.00483	+	0.843149i	−0.987646	−	0.156704i	$-0.949913\pi$
$67$	−551.065	+	462.398i	−1.00483	+	0.843149i	−0.0171796	+	0.999852i	$0.505469\pi$
$68$	512.273			0.913562
$69$	−248.391	+	208.425i	−0.433374	+	0.363644i
$70$	−161.285	−	58.7030i	−0.275389	−	0.100234i
$71$	−110.459	−	626.446i	−0.184635	−	1.04712i	−0.926423	−	0.376484i	$-0.877133\pi$
$71$	−110.459	−	626.446i	−0.184635	−	1.04712i	0.741788	−	0.670635i	$-0.233978\pi$
$72$	−23.4878	+	133.206i	−0.0384454	+	0.218035i
$73$	578.930			0.928201			0.464101	−	0.885783i	$-0.346378\pi$
$73$	578.930			0.928201			0.464101	+	0.885783i	$0.346378\pi$
$74$	449.672	+	20.1735i	0.706396	+	0.0316909i
$75$	−118.412			−0.182307
$76$	−79.7667	+	452.380i	−0.120393	+	0.682783i
$77$	−66.9977	−	379.963i	−0.0991572	−	0.562348i
$78$	302.215	+	109.997i	0.438707	+	0.159676i
$79$	−36.6732	+	30.7725i	−0.0522286	+	0.0438250i	−0.668528	−	0.743687i	$-0.733075\pi$
$79$	−36.6732	+	30.7725i	−0.0522286	+	0.0438250i	0.616300	+	0.787512i	$0.288631\pi$
$80$	149.860			0.209436
$81$	10.2453	−	8.59681i	0.0140539	−	0.0117926i
$82$	−81.0361	+	140.359i	−0.109133	+	0.189025i
$83$	718.676	−	261.577i	0.950421	−	0.345925i	0.180148	−	0.983639i	$-0.442342\pi$
$83$	718.676	−	261.577i	0.950421	−	0.345925i	0.770273	+	0.637714i	$0.220120\pi$
$84$	−58.2156	−	100.832i	−0.0756172	−	0.130973i
$85$	−599.760	+	1038.81i	−0.765330	+	1.32559i
$86$	13.8288	−	78.4273i	0.0173396	−	0.0983376i
$87$	−365.956	−	133.197i	−0.450973	−	0.164141i
$88$	168.437	+	291.741i	0.204039	+	0.353406i
$89$	−124.277	−	104.280i	−0.148014	−	0.124199i	0.565774	−	0.824561i	$-0.308578\pi$
$89$	−124.277	−	104.280i	−0.148014	−	0.124199i	−0.713788	+	0.700362i	$0.753022\pi$
$90$	−242.623	−	203.585i	−0.284164	−	0.238442i
$91$	435.815	−	158.624i	0.502043	−	0.182729i
$92$	−70.8951	−	402.066i	−0.0803404	−	0.455633i
$93$	−32.9668	−	186.964i	−0.0367581	−	0.208465i
$94$	−611.914	+	222.719i	−0.671427	+	0.244379i
$95$	−823.970	−	691.393i	−0.889868	−	0.746688i
$96$	77.8754	+	65.3452i	0.0827930	+	0.0694716i
$97$	407.223	+	705.332i	0.426261	+	0.738305i	0.996537	−	0.0831478i	$-0.0264974\pi$
$97$	407.223	+	705.332i	0.426261	+	0.738305i	−0.570277	+	0.821453i	$0.693164\pi$
$98$	486.853	+	177.200i	0.501832	+	0.182652i
$99$	123.632	−	701.151i	0.125510	−	0.711801i
$100$	74.5468	−	129.119i	0.0745468	−	0.129119i
$101$	481.296	+	833.629i	0.474166	+	0.821280i	0.999562	−	0.0295780i	$-0.00941634\pi$
$101$	481.296	+	833.629i	0.474166	+	0.821280i	−0.525397	+	0.850858i	$0.676083\pi$
$102$	−764.634	+	278.304i	−0.742256	+	0.270159i
$103$	−370.009	+	640.875i	−0.353962	+	0.613081i	−0.986940	−	0.161090i	$-0.948499\pi$
$103$	−370.009	+	640.875i	−0.353962	+	0.613081i	0.632978	+	0.774170i	$0.281833\pi$
$104$	−310.204	+	260.292i	−0.292481	+	0.245421i
$105$	272.631			0.253391
$106$	−801.104	+	672.206i	−0.734057	+	0.615947i
$107$	−1942.35	−	706.957i	−1.75490	−	0.638730i	−0.755040	−	0.655679i	$-0.772383\pi$
$107$	−1942.35	−	706.957i	−1.75490	−	0.638730i	−0.999856	+	0.0169489i	$0.994605\pi$
$108$	−96.8873	−	549.475i	−0.0863239	−	0.489567i
$109$	−101.675	+	576.629i	−0.0893462	+	0.506707i	0.906988	+	0.421157i	$0.138376\pi$
$109$	−101.675	+	576.629i	−0.0893462	+	0.506707i	−0.996334	+	0.0855501i	$0.972735\pi$
$110$	−788.810			−0.683728
$111$	−682.154	+	214.183i	−0.583308	+	0.183147i
$112$	146.600			0.123682
$113$	−309.693	+	1756.36i	−0.257818	+	1.46216i	0.530916	+	0.847425i	$0.321848\pi$
$113$	−309.693	+	1756.36i	−0.257818	+	1.46216i	−0.788734	+	0.614735i	$0.789263\pi$
$114$	−126.703	−	718.571i	−0.104095	−	0.590354i
$115$	898.333	+	326.966i	0.728434	+	0.265128i
$116$	375.630	−	315.191i	0.300659	−	0.252283i
$117$	855.828			0.676251
$118$	271.174	−	227.542i	0.211556	−	0.177516i
$119$	−586.711	+	1016.21i	−0.451964	+	0.782825i
$120$	−223.686	+	81.4149i	−0.170163	+	0.0619344i
$121$	−221.092	−	382.943i	−0.166110	−	0.287711i
$122$	208.324	−	360.828i	0.154597	−	0.267769i
$123$	44.7039	−	253.528i	0.0327709	−	0.185853i
$124$	224.624	+	81.7565i	0.162676	+	0.0592093i
$125$	759.946	+	1316.27i	0.543773	+	0.941843i
$126$	−237.345	−	199.156i	−0.167812	−	0.140811i
$127$	822.896	+	690.492i	0.574962	+	0.482451i	0.883288	−	0.468830i	$-0.155324\pi$
$127$	822.896	+	690.492i	0.574962	+	0.482451i	−0.308326	+	0.951281i	$0.599769\pi$
$128$	−120.281	+	43.7786i	−0.0830579	+	0.0302306i
$129$	21.9661	+	124.576i	0.0149923	+	0.0850255i
$130$	−164.653	−	933.794i	−0.111085	−	0.629993i
$131$	1553.69	−	565.497i	1.03623	−	0.377158i	0.232782	−	0.972529i	$-0.425217\pi$
$131$	1553.69	−	565.497i	1.03623	−	0.377158i	0.803451	+	0.595371i	$0.202995\pi$
$132$	−409.909	−	343.954i	−0.270288	−	0.226798i
$133$	−806.043	−	676.351i	−0.525510	−	0.440955i
$134$	719.364	+	1245.98i	0.463758	+	0.803253i
$135$	1227.69	+	446.842i	0.782686	+	0.284874i
$136$	177.911	−	1008.98i	0.112174	−	0.636172i
$137$	1346.98	−	2333.03i	0.840001	−	1.45492i	−0.0498921	−	0.998755i	$-0.515888\pi$
$137$	1346.98	−	2333.03i	0.840001	−	1.45492i	0.889893	−	0.456169i	$-0.150779\pi$
$138$	324.252	+	561.620i	0.200015	+	0.346437i
$139$	−646.142	+	235.177i	−0.394281	+	0.143507i	−0.531549	−	0.847027i	$-0.678390\pi$
$139$	−646.142	+	235.177i	−0.394281	+	0.143507i	0.137268	+	0.990534i	$0.456168\pi$
$140$	−171.636	+	297.282i	−0.103614	+	0.179464i
$141$	792.365	−	664.873i	0.473257	−	0.397109i
$142$	−1272.22			−0.751847
$143$	1632.81	−	1370.09i	0.954840	−	0.801206i
$144$	254.208	+	92.5240i	0.147111	+	0.0535440i
$145$	199.380	+	1130.74i	0.114191	+	0.647607i
$146$	201.060	−	1140.27i	0.113972	−	0.646366i
$147$	−822.959			−0.461745
$148$	195.904	−	878.675i	0.108805	−	0.488018i
$149$	−2325.87			−1.27881			−0.639406	−	0.768869i	$-0.720820\pi$
$149$	−2325.87			−1.27881			−0.639406	+	0.768869i	$0.720820\pi$
$150$	−41.1240	+	233.226i	−0.0223851	+	0.126952i
$151$	−219.430	−	1244.45i	−0.118258	−	0.670674i	−0.985085	−	0.172066i	$-0.944956\pi$
$151$	−219.430	−	1244.45i	−0.118258	−	0.670674i	0.866827	−	0.498608i	$-0.166155\pi$
$152$	863.311	+	314.220i	0.460683	+	0.167675i
$153$	−1658.74	+	1391.85i	−0.876478	+	0.735453i
$154$	−771.649			−0.403774
$155$	−428.776	+	359.786i	−0.222194	+	0.186443i
$156$	321.611	−	557.046i	0.165061	−	0.285893i
$157$	336.655	−	122.533i	0.171134	−	0.0622876i	−0.255032	−	0.966933i	$-0.582086\pi$
$157$	336.655	−	122.533i	0.171134	−	0.0622876i	0.426166	+	0.904645i	$0.359864\pi$
$158$	47.8735	+	82.9194i	0.0241051	+	0.0417513i
$159$	830.560	−	1438.57i	0.414262	−	0.717524i
$160$	52.0458	−	295.167i	0.0257161	−	0.145844i
$161$	878.789	+	319.853i	0.430176	+	0.156571i
$162$	−13.3743	−	23.1649i	−0.00648630	−	0.0112346i
$163$	2593.98	+	2176.61i	1.24648	+	1.04592i	0.996989	+	0.0775447i	$0.0247080\pi$
$163$	2593.98	+	2176.61i	1.24648	+	1.04592i	0.249492	+	0.968377i	$0.419736\pi$
$164$	248.309	+	208.356i	0.118230	+	0.0992066i
$165$	1177.40	−	428.539i	0.555519	−	0.202192i
$166$	−265.612	−	1506.36i	−0.124190	−	0.704315i
$167$	−358.987	−	2035.92i	−0.166343	−	0.943377i	−0.947669	−	0.319254i	$-0.896568\pi$
$167$	−358.987	−	2035.92i	−0.166343	−	0.943377i	0.781326	−	0.624123i	$-0.214543\pi$
$168$	−218.819	+	79.6436i	−0.100490	+	0.0365752i
$169$	279.736	+	234.726i	0.127326	+	0.106839i
$170$	1837.77	+	1542.07i	0.829121	+	0.695715i
$171$	−970.833	−	1681.53i	−0.434160	−	0.751988i
$172$	−149.669	−	54.4750i	−0.0663497	−	0.0241493i
$173$	434.457	−	2463.93i	0.190931	−	1.08283i	−0.727163	−	0.686465i	$-0.759162\pi$
$173$	434.457	−	2463.93i	0.190931	−	1.08283i	0.918095	−	0.396361i	$-0.129727\pi$
$174$	−389.442	+	674.534i	−0.169676	+	0.293887i
$175$	170.758	+	295.762i	0.0737607	+	0.127757i
$176$	633.115	−	230.435i	0.271153	−	0.0986915i
$177$	−281.145	+	486.957i	−0.119391	+	0.206791i
$178$	−248.553	+	208.561i	−0.104662	+	0.0878219i
$179$	−690.777			−0.288442			−0.144221	−	0.989546i	$-0.546068\pi$
$179$	−690.777			−0.288442			−0.144221	+	0.989546i	$0.546068\pi$
$180$	−485.247	+	407.170i	−0.200934	+	0.168604i
$181$	−3655.16	−	1330.37i	−1.50103	−	0.546329i	−0.544701	−	0.838630i	$-0.683357\pi$
$181$	−3655.16	−	1330.37i	−1.50103	−	0.546329i	−0.956326	+	0.292301i	$0.905579\pi$
$182$	−161.071	−	913.478i	−0.0656009	−	0.372041i
$183$	−114.923	+	651.760i	−0.0464226	+	0.263276i
$184$	−816.537			−0.327152
$185$	1552.46	+	1426.00i	0.616969	+	0.566711i
$186$	−379.697			−0.149681
$187$	−936.459	+	5310.92i	−0.366207	+	2.07686i
$188$	226.154	+	1282.59i	0.0877341	+	0.497565i
$189$	1200.98	+	437.120i	0.462213	+	0.168232i
$190$	−1647.94	+	1382.79i	−0.629232	+	0.527988i
$191$	−1300.97			−0.492853			−0.246426	−	0.969162i	$-0.579256\pi$
$191$	−1300.97			−0.492853			−0.246426	+	0.969162i	$0.579256\pi$
$192$	155.751	−	130.690i	0.0585435	−	0.0491238i
$193$	2089.53	−	3619.17i	0.779314	−	1.34981i	−0.153024	−	0.988223i	$-0.548901\pi$
$193$	2089.53	−	3619.17i	0.779314	−	1.34981i	0.932338	−	0.361589i	$-0.117766\pi$
$194$	1530.66	−	557.114i	0.566469	−	0.206178i
$195$	753.071	+	1304.36i	0.276557	+	0.479010i
$196$	518.098	−	897.372i	0.188811	−	0.327031i
$197$	129.387	−	733.789i	0.0467940	−	0.265382i	−0.952431	−	0.304756i	$-0.901425\pi$
$197$	129.387	−	733.789i	0.0467940	−	0.265382i	0.999225	+	0.0393736i	$0.0125363\pi$
$198$	−1338.06	−	487.014i	−0.480262	−	0.174801i
$199$	−2298.67	−	3981.41i	−0.818836	−	1.41827i	−0.906540	−	0.422119i	$-0.861286\pi$
$199$	−2298.67	−	3981.41i	−0.818836	−	1.41827i	0.0877043	−	0.996147i	$-0.472047\pi$
$200$	−228.425	−	191.671i	−0.0807603	−	0.0677659i
$201$	−1750.65	−	1468.97i	−0.614335	−	0.515488i
$202$	1809.08	−	658.452i	0.630131	−	0.229349i
$203$	195.043	+	1106.14i	0.0674351	+	0.382443i
$204$	282.597	+	1602.69i	0.0969891	+	0.550053i
$205$	−713.231	+	259.595i	−0.242996	+	0.0884434i
$206$	1133.77	+	951.350i	0.383465	+	0.321765i
$207$	1321.97	+	1109.27i	0.443882	+	0.372461i
$208$	404.943	+	701.382i	0.134989	+	0.233808i
$209$	−4544.17	−	1653.94i	−1.50396	−	0.547395i
$210$	94.6837	−	536.978i	0.0311133	−	0.176452i
$211$	−2782.85	+	4820.04i	−0.907960	+	1.57263i	−0.0910661	+	0.995845i	$0.529027\pi$
$211$	−2782.85	+	4820.04i	−0.907960	+	1.57263i	−0.816894	+	0.576788i	$0.804306\pi$
$212$	1045.77	+	1811.32i	0.338790	+	0.586802i
$213$	1898.95	−	691.162i	0.610864	−	0.222336i
$214$	−2067.00	+	3580.16i	−0.660269	+	1.14362i
$215$	285.697	−	239.728i	0.0906249	−	0.0760433i
$216$	−1115.90			−0.351517
$217$	−419.447	+	351.958i	−0.131216	+	0.110104i
$218$	1100.43	+	400.523i	0.341882	+	0.124435i
$219$	319.369	+	1811.23i	0.0985433	+	0.558867i
$220$	−273.951	+	1553.65i	−0.0839535	+	0.476124i
$221$	−6482.54			−1.97314
$222$	184.949	+	1417.97i	0.0559142	+	0.428683i
$223$	3429.59			1.02988			0.514938	−	0.857227i	$-0.327815\pi$
$223$	3429.59			1.02988			0.514938	+	0.857227i	$0.327815\pi$
$224$	50.9135	−	288.745i	0.0151866	−	0.0861276i
$225$	109.434	+	620.631i	0.0324249	+	0.183891i
$226$	3351.79	+	1219.95i	0.986539	+	0.359071i
$227$	791.517	−	664.162i	0.231431	−	0.194194i	−0.519696	−	0.854351i	$-0.673955\pi$
$227$	791.517	−	664.162i	0.231431	−	0.194194i	0.751127	+	0.660157i	$0.229510\pi$
$228$	−1459.31			−0.423883
$229$	2281.94	−	1914.77i	0.658493	−	0.552541i	−0.251142	−	0.967950i	$-0.580806\pi$
$229$	2281.94	−	1914.77i	0.658493	−	0.552541i	0.909635	+	0.415409i	$0.136362\pi$
$230$	955.986	−	1655.82i	0.274069	−	0.474701i
$231$	1151.79	−	419.216i	0.328061	−	0.119404i
$232$	−490.351	−	849.312i	−0.138763	−	0.240345i
$233$	−3183.98	+	5514.81i	−0.895233	+	1.55059i	−0.0617168	+	0.998094i	$0.519658\pi$
$233$	−3183.98	+	5514.81i	−0.895233	+	1.55059i	−0.833516	+	0.552495i	$0.813676\pi$
$234$	297.226	−	1685.65i	0.0830354	−	0.470917i
$235$	−2865.67	−	1043.02i	−0.795471	−	0.289528i
$236$	−353.992	−	613.132i	−0.0976395	−	0.169117i
$237$	−116.505	−	97.7596i	−0.0319318	−	0.0267940i
$238$	1797.79	+	1508.52i	0.489636	+	0.410853i
$239$	1866.35	−	679.296i	0.505122	−	0.183849i	−0.0768744	−	0.997041i	$-0.524494\pi$
$239$	1866.35	−	679.296i	0.505122	−	0.183849i	0.581996	+	0.813191i	$0.302272\pi$
$240$	82.6708	+	468.850i	0.0222349	+	0.126100i
$241$	−798.697	−	4529.64i	−0.213480	−	1.21070i	−0.883525	−	0.468384i	$-0.844836\pi$
$241$	−798.697	−	4529.64i	−0.213480	−	1.21070i	0.670045	−	0.742320i	$-0.266275\pi$
$242$	−831.035	+	302.472i	−0.220748	+	0.0803456i
$243$	2917.60	+	2448.16i	0.770224	+	0.646294i
$244$	−638.342	−	535.633i	−0.167482	−	0.140534i
$245$	1213.16	+	2101.25i	0.316350	+	0.547935i
$246$	−483.828	−	176.099i	−0.125397	−	0.0456409i
$247$	1009.41	−	5724.62i	0.260028	−	1.47469i
$248$	239.040	−	414.029i	0.0612059	−	0.106012i
$249$	1214.83	+	2104.14i	0.309182	+	0.535520i
$250$	2856.46	−	1039.67i	0.722635	−	0.263018i
$251$	−1784.80	+	3091.36i	−0.448826	+	0.777389i	−0.998310	−	0.0581150i	$-0.981491\pi$
$251$	−1784.80	+	3091.36i	−0.448826	+	0.777389i	0.549484	+	0.835504i	$0.314824\pi$
$252$	−474.690	+	398.312i	−0.118661	+	0.0995686i
$253$	4297.96			1.06803
$254$	1645.79	−	1380.98i	0.406560	−	0.341144i
$255$	−3580.88	−	1303.33i	−0.879385	−	0.320070i
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	384.163	−	2178.70i	0.0932429	−	0.528807i	−0.902029	−	0.431676i	$-0.857922\pi$
$257$	384.163	−	2178.70i	0.0932429	−	0.528807i	0.995272	−	0.0971308i	$-0.0309665\pi$
$258$	252.995			0.0610496
$259$	1518.69	+	1394.98i	0.364350	+	0.334670i
$260$	−1896.40			−0.452345
$261$	−359.915	+	2041.18i	−0.0853570	+	0.484083i
$262$	−574.221	−	3256.57i	−0.135403	−	0.767906i
$263$	−2232.83	−	812.685i	−0.523507	−	0.190541i	0.0667297	−	0.997771i	$-0.478743\pi$
$263$	−2232.83	−	812.685i	−0.523507	−	0.190541i	−0.590237	+	0.807230i	$0.700966\pi$
$264$	−819.818	+	687.909i	−0.191122	+	0.160371i
$265$	−4897.46			−1.13528
$266$	−1612.09	+	1352.70i	−0.371592	+	0.311802i
$267$	257.692	−	446.336i	0.0590656	−	0.102305i
$268$	2703.92	−	984.148i	0.616300	−	0.224315i
$269$	1102.99	+	1910.44i	0.250002	+	0.433017i	0.963526	−	0.267614i	$-0.0862352\pi$
$269$	1102.99	+	1910.44i	0.250002	+	0.433017i	−0.713524	+	0.700631i	$0.752902\pi$
$270$	1306.48	−	2262.89i	0.294481	−	0.510055i
$271$	1015.83	−	5761.04i	0.227701	−	1.29136i	−0.629752	−	0.776796i	$-0.716844\pi$
$271$	1015.83	−	5761.04i	0.227701	−	1.29136i	0.857453	−	0.514562i	$-0.172045\pi$
$272$	−1925.52	−	700.831i	−0.429234	−	0.156228i
$273$	736.687	+	1275.98i	0.163320	+	0.282878i
$274$	−4127.38	−	3463.28i	−0.910015	−	0.763593i
$275$	1202.35	+	1008.89i	0.263652	+	0.221230i
$276$	1218.79	−	443.602i	0.265806	−	0.0967454i
$277$	736.745	+	4178.29i	0.159808	+	0.906315i	0.954258	+	0.298985i	$0.0966481\pi$
$277$	736.745	+	4178.29i	0.159808	+	0.906315i	−0.794450	+	0.607330i	$0.792241\pi$
$278$	238.804	+	1354.33i	0.0515199	+	0.292184i
$279$	−949.466	+	345.577i	−0.203738	+	0.0741547i
$280$	525.923	+	441.302i	0.112250	+	0.0941887i
$281$	−3506.14	−	2942.00i	−0.744337	−	0.624573i	0.189662	−	0.981849i	$-0.439261\pi$
$281$	−3506.14	−	2942.00i	−0.744337	−	0.624573i	−0.933999	+	0.357277i	$0.883705\pi$
$282$	−1034.36	−	1791.56i	−0.218423	−	0.378319i
$283$	3186.40	+	1159.76i	0.669300	+	0.243605i	0.654247	−	0.756281i	$-0.272986\pi$
$283$	3186.40	+	1159.76i	0.669300	+	0.243605i	0.0150536	+	0.999887i	$0.495208\pi$
$284$	−441.837	+	2505.78i	−0.0923176	+	0.523559i
$285$	1708.53	−	2959.27i	0.355105	−	0.615059i
$286$	−2131.48	−	3691.83i	−0.440689	−	0.763295i
$287$	−697.714	+	253.947i	−0.143501	+	0.0522300i
$288$	270.522	−	468.558i	0.0553496	−	0.0958682i
$289$	8800.69	−	7384.65i	1.79131	−	1.50308i
$290$	2296.37			0.464992
$291$	−1982.04	+	1663.13i	−0.399276	+	0.335033i
$292$	−2176.07	−	792.023i	−0.436112	−	0.158732i
$293$	−1465.39	−	8310.64i	−0.292181	−	1.65704i	−0.678445	−	0.734652i	$-0.737346\pi$
$293$	−1465.39	−	8310.64i	−0.292181	−	1.65704i	0.386264	−	0.922388i	$-0.373765\pi$
$294$	−285.811	+	1620.91i	−0.0566967	+	0.321543i
$295$	1657.79			0.327187
$296$	−1662.62	−	691.015i	−0.326478	−	0.135691i
$297$	5873.72			1.14757
$298$	−807.768	+	4581.08i	−0.157023	+	0.890519i
$299$	897.139	+	5087.93i	0.173521	+	0.984089i
$300$	445.083	+	161.997i	0.0856563	+	0.0311763i
$301$	279.481	−	234.513i	0.0535184	−	0.0449072i
$302$	−2527.29			−0.481554
$303$	−2342.57	+	1965.65i	−0.444149	+	0.372685i
$304$	918.717	−	1591.26i	0.173329	−	0.300215i
$305$	1833.54	−	667.355i	0.344224	−	0.125287i
$306$	2165.33	+	3750.46i	0.404522	+	0.700653i
$307$	3364.10	−	5826.79i	0.625405	−	1.08323i	−0.363058	−	0.931767i	$-0.618267\pi$
$307$	3364.10	−	5826.79i	0.625405	−	1.08323i	0.988462	−	0.151466i	$-0.0483994\pi$
$308$	−267.991	+	1519.85i	−0.0495786	+	0.281174i
$309$	−2209.15	−	804.065i	−0.406712	−	0.148031i
$310$	559.727	+	969.476i	0.102550	+	0.177621i
$311$	1636.78	+	1373.42i	0.298435	+	0.250416i	0.779692	−	0.626163i	$-0.215375\pi$
$311$	1636.78	+	1373.42i	0.298435	+	0.250416i	−0.481258	+	0.876579i	$0.659820\pi$
$312$	−985.472	−	826.909i	−0.178818	−	0.150047i
$313$	−920.008	+	334.856i	−0.166140	+	0.0604702i	−0.423751	−	0.905779i	$-0.639287\pi$
$313$	−920.008	+	334.856i	−0.166140	+	0.0604702i	0.257611	+	0.966249i	$0.417065\pi$
$314$	−124.423	−	705.637i	−0.0223617	−	0.126820i
$315$	−251.960	−	1428.94i	−0.0450677	−	0.255592i
$316$	179.946	−	65.4948i	0.0320340	−	0.0116594i
$317$	−3676.88	−	3085.27i	−0.651464	−	0.546644i	0.256050	−	0.966663i	$-0.417579\pi$
$317$	−3676.88	−	3085.27i	−0.651464	−	0.546644i	−0.907515	+	0.420020i	$0.862023\pi$
$318$	−2544.99	−	2135.50i	−0.448791	−	0.376581i
$319$	2581.03	+	4470.48i	0.453010	+	0.784636i
$320$	−563.289	−	205.021i	−0.0984026	−	0.0358156i
$321$	1140.27	−	6466.80i	0.198267	−	1.12443i
$322$	935.187	−	1619.79i	0.161851	−	0.280334i
$323$	7353.65	+	12736.9i	1.26677	+	2.19412i
$324$	−50.2708	+	18.2971i	−0.00861981	+	0.00313736i
$325$	−943.350	+	1633.93i	−0.161008	+	0.278874i
$326$	5187.96	−	4353.22i	0.881395	−	0.739578i
$327$	−1860.12			−0.314572
$328$	496.618	−	416.712i	0.0836011	−	0.0701496i
$329$	−2803.33	−	1020.33i	−0.469764	−	0.170980i
$330$	−435.150	−	2467.86i	−0.0725886	−	0.411670i
$331$	−883.993	+	5013.37i	−0.146794	+	0.832507i	0.819116	+	0.573628i	$0.194464\pi$
$331$	−883.993	+	5013.37i	−0.146794	+	0.832507i	−0.965910	+	0.258880i	$0.916647\pi$
$332$	−3059.20			−0.505709
$333$	1753.03	+	3377.42i	0.288485	+	0.555800i
$334$	−4134.65			−0.677359
$335$	−1170.00	+	6635.38i	−0.190817	+	1.08218i
$336$	80.8723	+	458.649i	0.0131308	+	0.0744684i
$337$	4631.89	+	1685.87i	0.748709	+	0.272508i	0.688062	−	0.725651i	$-0.258461\pi$
$337$	4631.89	+	1685.87i	0.748709	+	0.272508i	0.0606467	+	0.998159i	$0.480684\pi$
$338$	559.471	−	469.452i	0.0900332	−	0.0755468i
$339$	−5665.75			−0.907733
$340$	3675.54	−	3084.14i	0.586277	−	0.491945i
$341$	−1258.22	+	2179.31i	−0.199814	+	0.346088i
$342$	−3649.14	+	1328.18i	−0.576967	+	0.209999i
$343$	2758.13	+	4777.22i	0.434184	+	0.752028i
$344$	−159.274	+	275.871i	−0.0249636	+	0.0432383i
$345$	−527.373	+	2990.88i	−0.0822980	+	0.466735i
$346$	−4702.10	−	1711.43i	−0.730597	−	0.265916i
$347$	1208.08	+	2092.45i	0.186896	+	0.323714i	0.944214	−	0.329333i	$-0.106824\pi$
$347$	1208.08	+	2092.45i	0.186896	+	0.323714i	−0.757318	+	0.653047i	$0.773491\pi$
$348$	1193.32	+	1001.31i	0.183818	+	0.154242i
$349$	428.561	+	359.605i	0.0657316	+	0.0551553i	0.675062	−	0.737761i	$-0.264117\pi$
$349$	428.561	+	359.605i	0.0657316	+	0.0551553i	−0.609330	+	0.792917i	$0.708562\pi$
$350$	641.841	−	233.611i	0.0980224	−	0.0356773i
$351$	1226.06	+	6953.31i	0.186445	+	1.05738i
$352$	−233.990	−	1327.02i	−0.0354310	−	0.200939i
$353$	101.338	−	36.8841i	0.0152796	−	0.00556131i	−0.334369	−	0.942442i	$-0.608523\pi$
$353$	101.338	−	36.8841i	0.0152796	−	0.00556131i	0.349649	+	0.936881i	$0.386301\pi$
$354$	861.477	+	722.865i	0.129342	+	0.108531i
$355$	−4564.06	−	3829.70i	−0.682353	−	0.572562i
$356$	324.463	+	561.986i	0.0483048	+	0.0836663i
$357$	−3502.97	−	1274.98i	−0.519319	−	0.189017i
$358$	−239.904	+	1360.57i	−0.0354172	+	0.200861i
$359$	3431.40	−	5943.36i	0.504463	−	0.873756i	−0.495524	−	0.868595i	$-0.665024\pi$
$359$	3431.40	−	5943.36i	0.504463	−	0.873756i	0.999987	−	0.00516130i	$-0.00164290\pi$
$360$	633.444	+	1097.16i	0.0927374	+	0.160626i
$361$	−5947.43	+	2164.69i	−0.867099	+	0.315598i
$362$	−3889.74	+	6737.23i	−0.564752	+	0.978179i
$363$	1076.10	−	902.958i	0.155594	−	0.130559i
$364$	−1855.14			−0.267131
$365$	4153.80	−	3485.46i	0.595671	−	0.499828i
$366$	1243.80	+	452.707i	0.177636	+	0.0646541i
$367$	−1876.18	−	10640.4i	−0.266855	−	1.51341i	−0.763700	−	0.645572i	$-0.776619\pi$
$367$	−1876.18	−	10640.4i	−0.266855	−	1.51341i	0.496844	−	0.867840i	$-0.334492\pi$
$368$	−283.580	+	1608.26i	−0.0401702	+	0.227817i
$369$	−1370.13			−0.193296
$370$	3347.84	−	2562.51i	0.470394	−	0.360050i
$371$	−4790.91			−0.670435
$372$	−131.867	+	747.857i	−0.0183790	+	0.104233i
$373$	1823.29	+	10340.4i	0.253100	+	1.43540i	0.800904	+	0.598793i	$0.204353\pi$
$373$	1823.29	+	10340.4i	0.253100	+	1.43540i	−0.547804	+	0.836607i	$0.684536\pi$
$374$	10135.2	+	3688.93i	1.40129	+	0.510027i
$375$	−3698.82	+	3103.68i	−0.509350	+	0.427396i
$376$	2604.74			0.357259
$377$	−4753.40	+	3988.58i	−0.649370	+	0.544886i
$378$	1278.05	−	2213.66i	0.173905	−	0.301212i
$379$	1917.65	−	697.967i	0.259902	−	0.0945967i	−0.208783	−	0.977962i	$-0.566950\pi$
$379$	1917.65	−	697.967i	0.259902	−	0.0945967i	0.468685	+	0.883365i	$0.344728\pi$
$380$	2151.23	+	3726.04i	0.290410	+	0.503005i
$381$	−1706.31	+	2955.41i	−0.229441	+	0.397403i
$382$	−451.822	+	2562.41i	−0.0605163	+	0.343205i
$383$	−7562.22	−	2752.42i	−1.00891	−	0.367212i	−0.215894	−	0.976417i	$-0.569266\pi$
$383$	−7562.22	−	2752.42i	−1.00891	−	0.367212i	−0.793013	+	0.609205i	$0.791489\pi$
$384$	−203.318	−	352.158i	−0.0270196	−	0.0467994i
$385$	−2768.28	−	2322.86i	−0.366453	−	0.307491i
$386$	−6402.69	−	5372.49i	−0.844270	−	0.708427i
$387$	632.637	−	230.261i	0.0830975	−	0.0302450i
$388$	−565.709	−	3208.29i	−0.0740194	−	0.419785i
$389$	−631.872	−	3583.52i	−0.0823578	−	0.467074i	−0.997896	−	0.0648421i	$-0.979346\pi$
$389$	−631.872	−	3583.52i	−0.0823578	−	0.467074i	0.915538	−	0.402232i	$-0.131765\pi$
$390$	2830.62	−	1030.26i	0.367523	−	0.133768i
$391$	−10013.4	−	8402.23i	−1.29514	−	1.08675i
$392$	−1587.54	−	1332.11i	−0.204549	−	0.171637i
$393$	2626.30	+	4548.89i	0.337098	+	0.583871i
$394$	−1400.35	−	509.684i	−0.179057	−	0.0651714i
$395$	−77.8630	+	441.583i	−0.00991826	+	0.0562493i
$396$	−1423.93	+	2466.33i	−0.180695	+	0.312974i
$397$	100.914	+	174.788i	0.0127575	+	0.0220967i	0.872334	−	0.488911i	$-0.162606\pi$
$397$	100.914	+	174.788i	0.0127575	+	0.0220967i	−0.859576	+	0.511008i	$0.829272\pi$
$398$	−8640.17	+	3144.77i	−1.08817	+	0.396062i
$399$	1671.36	−	2894.89i	0.209706	−	0.363222i
$400$	−456.849	+	383.342i	−0.0571061	+	0.0479177i
$401$	−8621.63			−1.07367			−0.536837	−	0.843686i	$-0.680381\pi$
$401$	−8621.63			−1.07367			−0.536837	+	0.843686i	$0.680381\pi$
$402$	−3501.30	+	2937.94i	−0.434400	+	0.364505i
$403$	−2842.50	−	1034.58i	−0.351352	−	0.127882i
$404$	−668.610	−	3791.87i	−0.0823381	−	0.466962i
$405$	21.7523	−	123.364i	0.00266884	−	0.0151358i
$406$	2246.41			0.274600
$407$	8751.43	+	3637.26i	1.06583	+	0.442979i
$408$	3254.83			0.394946
$409$	887.127	−	5031.15i	0.107251	−	0.608250i	−0.883047	−	0.469285i	$-0.844512\pi$
$409$	887.127	−	5031.15i	0.107251	−	0.608250i	0.990297	−	0.138964i	$-0.0443774\pi$
$410$	263.600	+	1494.95i	0.0317518	+	0.180074i
$411$	8042.16	+	2927.11i	0.965184	+	0.351298i
$412$	2267.55	−	1902.70i	0.271151	−	0.227523i
$413$	1621.72			0.193220
$414$	2643.95	−	2218.53i	0.313872	−	0.263370i
$415$	3581.65	−	6203.60i	0.423654	−	0.733790i
$416$	1522.09	−	553.995i	0.179391	−	0.0652928i
$417$	−1092.22	−	1891.77i	−0.128264	−	0.222160i
$418$	−4835.80	+	8375.86i	−0.565854	+	0.980087i
$419$	1817.18	−	10305.7i	0.211874	−	1.20159i	−0.674376	−	0.738388i	$-0.735587\pi$
$419$	1817.18	−	10305.7i	0.211874	−	1.20159i	0.886250	−	0.463207i	$-0.153301\pi$
$420$	−1024.76	−	372.981i	−0.119055	−	0.0433324i
$421$	−490.233	−	849.108i	−0.0567518	−	0.0982969i	0.836254	−	0.548343i	$-0.184741\pi$
$421$	−490.233	−	849.108i	−0.0567518	−	0.0982969i	−0.893006	+	0.450046i	$0.851408\pi$
$422$	8527.16	+	7155.14i	0.983639	+	0.825371i
$423$	−4217.08	−	3538.55i	−0.484731	−	0.406738i
$424$	3930.80	−	1430.69i	0.450227	−	0.163869i
$425$	−828.916	−	4701.02i	−0.0946079	−	0.536548i
$426$	−701.825	−	3980.25i	−0.0798205	−	0.452684i
$427$	1793.65	−	652.836i	0.203281	−	0.0739882i
$428$	6333.67	+	5314.58i	0.715302	+	0.600210i
$429$	5187.18	+	4352.56i	0.583775	+	0.489845i
$430$	−372.951	−	645.970i	−0.0418262	−	0.0724452i
$431$	−1927.27	−	701.469i	−0.215391	−	0.0783957i	0.232071	−	0.972699i	$-0.425450\pi$
$431$	−1927.27	−	701.469i	−0.215391	−	0.0783957i	−0.447462	+	0.894303i	$0.647672\pi$
$432$	−387.549	+	2197.90i	−0.0431620	+	0.244784i
$433$	−7597.77	+	13159.7i	−0.843246	+	1.46054i	0.0438902	+	0.999036i	$0.486025\pi$
$433$	−7597.77	+	13159.7i	−0.843246	+	1.46054i	−0.887136	+	0.461508i	$0.847309\pi$
$434$	547.550	+	948.384i	0.0605604	+	0.104894i
$435$	−3427.64	+	1247.56i	−0.377799	+	0.137508i
$436$	1171.05	−	2028.32i	0.128631	−	0.222795i
$437$	8979.07	−	7534.33i	0.982900	−	0.824751i
$438$	3678.35			0.401275
$439$	12957.2	−	10872.4i	1.40869	−	1.18203i	0.451608	−	0.892216i	$-0.350850\pi$
$439$	12957.2	−	10872.4i	1.40869	−	1.18203i	0.957083	−	0.289816i	$-0.0935940\pi$
$440$	2964.96	+	1079.16i	0.321247	+	0.116924i
$441$	760.563	+	4313.37i	0.0821253	+	0.465756i
$442$	−2251.36	+	12768.1i	−0.242277	+	1.37402i
$443$	14692.9			1.57580			0.787901	−	0.615802i	$-0.211168\pi$
$443$	14692.9			1.57580			0.787901	+	0.615802i	$0.211168\pi$
$444$	2857.08	+	128.176i	0.305385	+	0.0137004i
$445$	−1519.50			−0.161868
$446$	1191.08	−	6754.98i	0.126456	−	0.717169i
$447$	−1283.08	−	7276.69i	−0.135766	−	0.769968i
$448$	−551.034	−	200.560i	−0.0581114	−	0.0211508i
$449$	2932.73	−	2460.86i	0.308250	−	0.258652i	−0.475518	−	0.879706i	$-0.657739\pi$
$449$	2932.73	−	2460.86i	0.308250	−	0.258652i	0.783768	+	0.621053i	$0.213295\pi$
$450$	1260.41			0.132036
$451$	−2614.02	+	2193.43i	−0.272926	+	0.229012i
$452$	3566.90	−	6178.05i	0.371179	−	0.642901i
$453$	3772.31	−	1373.01i	0.391256	−	0.142405i
$454$	−1033.25	−	1789.65i	−0.106813	−	0.185005i
$455$	2171.96	−	3761.95i	0.223787	−	0.387611i
$456$	−506.814	+	2874.28i	−0.0520476	+	0.295177i
$457$	375.194	+	136.559i	0.0384044	+	0.0139781i	0.361151	−	0.932507i	$-0.382384\pi$
$457$	375.194	+	136.559i	0.0384044	+	0.0139781i	−0.322747	+	0.946485i	$0.604606\pi$
$458$	−2978.86	−	5159.54i	−0.303915	−	0.526396i
$459$	−13684.6	−	11482.7i	−1.39160	−	1.16769i
$460$	−2929.31	−	2457.98i	−0.296913	−	0.249139i
$461$	8426.27	−	3066.91i	0.851303	−	0.309849i	0.120731	−	0.992685i	$-0.461476\pi$
$461$	8426.27	−	3066.91i	0.851303	−	0.309849i	0.730571	+	0.682836i	$0.239254\pi$
$462$	−425.683	−	2414.17i	−0.0428671	−	0.243111i
$463$	−99.4379	−	563.940i	−0.00998114	−	0.0566059i	0.979410	−	0.201879i	$-0.0647049\pi$
$463$	−99.4379	−	563.940i	−0.00998114	−	0.0566059i	−0.989392	+	0.145274i	$0.953594\pi$
$464$	−1843.12	+	670.839i	−0.184406	+	0.0671184i
$465$	−1362.16	−	1142.98i	−0.135846	−	0.113988i
$466$	9756.27	+	8186.48i	0.969851	+	0.813802i
$467$	5031.79	+	8715.31i	0.498594	+	0.863590i	0.999999	−	0.00162290i	$-0.000516586\pi$
$467$	5031.79	+	8715.31i	0.498594	+	0.863590i	−0.501405	+	0.865213i	$0.667183\pi$
$468$	−3216.86	−	1170.84i	−0.317734	−	0.115646i
$469$	−1144.54	+	6491.02i	−0.112687	+	0.639078i
$470$	−3049.58	+	5282.03i	−0.299291	+	0.518387i
$471$	569.071	+	985.659i	0.0556717	+	0.0964263i
$472$	−1330.57	+	484.290i	−0.129756	+	0.0472272i
$473$	838.364	−	1452.09i	0.0814969	−	0.141157i
$474$	−233.011	+	195.519i	−0.0225792	+	0.0189462i
$475$	4280.46			0.413476
$476$	3595.58	−	3017.05i	0.346225	−	0.290517i
$477$	−8307.56	−	3023.70i	−0.797436	−	0.290243i
$478$	−689.775	−	3911.91i	−0.0660033	−	0.374323i
$479$	−2416.86	+	13706.7i	−0.230542	+	1.30747i	0.621261	+	0.783603i	$0.286621\pi$
$479$	−2416.86	+	13706.7i	−0.230542	+	1.30747i	−0.851803	+	0.523862i	$0.824491\pi$
$480$	952.165			0.0905420
$481$	−2479.06	+	11119.2i	−0.235000	+	1.05403i
$482$	−9199.03			−0.869304
$483$	−515.900	+	2925.81i	−0.0486009	+	0.275630i
$484$	307.138	+	1741.87i	0.0288447	+	0.163586i
$485$	7168.27	+	2609.04i	0.671122	+	0.244268i
$486$	5835.21	−	4896.32i	0.544630	−	0.456999i
$487$	−17328.4			−1.61237			−0.806185	−	0.591664i	$-0.798471\pi$
$487$	−17328.4			−1.61237			−0.806185	+	0.591664i	$0.798471\pi$
$488$	−1276.68	+	1071.27i	−0.118428	+	0.0993727i
$489$	−5378.73	+	9316.23i	−0.497412	+	0.861543i
$490$	4559.99	−	1659.70i	0.420406	−	0.153015i
$491$	−8285.56	−	14351.0i	−0.761553	−	1.31905i	−0.942050	−	0.335472i	$-0.891104\pi$
$491$	−8285.56	−	14351.0i	−0.761553	−	1.31905i	0.180498	−	0.983575i	$-0.442229\pi$
$492$	−514.879	+	891.797i	−0.0471800	+	0.0817181i
$493$	2726.20	−	15461.1i	0.249051	−	1.41244i
$494$	−10924.7	−	3976.28i	−0.994995	−	0.362148i
$495$	−3334.23	−	5775.06i	−0.302752	−	0.524383i
$496$	−732.461	−	614.608i	−0.0663074	−	0.0556385i
$497$	−4464.77	−	3746.38i	−0.402962	−	0.338125i
$498$	4566.25	−	1661.98i	0.410881	−	0.149548i
$499$	989.209	+	5610.08i	0.0887436	+	0.503290i	0.996486	+	0.0837616i	$0.0266934\pi$
$499$	989.209	+	5610.08i	0.0887436	+	0.503290i	−0.907742	+	0.419528i	$0.862195\pi$
$500$	−1055.71	−	5987.21i	−0.0944253	−	0.535512i
$501$	6171.50	−	2246.24i	0.550344	−	0.200309i
$502$	5468.93	+	4588.98i	0.486236	+	0.408000i
$503$	−12671.9	−	10633.0i	−1.12329	−	0.942548i	−0.124519	−	0.992217i	$-0.539739\pi$
$503$	−12671.9	−	10633.0i	−1.12329	−	0.942548i	−0.998766	+	0.0496690i	$0.984183\pi$
$504$	619.663	+	1073.29i	0.0547659	+	0.0948573i
$505$	8472.16	+	3083.61i	0.746546	+	0.271721i
$506$	1492.67	−	8465.34i	0.131141	−	0.743735i
$507$	−580.043	+	1004.66i	−0.0508099	+	0.0880053i
$508$	−2148.43	−	3721.19i	−0.187640	−	0.325002i
$509$	−9554.62	+	3477.60i	−0.832026	+	0.302833i	−0.722690	−	0.691172i	$-0.757095\pi$
$509$	−9554.62	+	3477.60i	−0.832026	+	0.302833i	−0.109336	+	0.994005i	$0.534872\pi$
$510$	−3810.69	+	6600.31i	−0.330863	+	0.573072i
$511$	4063.43	−	3409.63i	0.351773	−	0.295172i
$512$	512.000			0.0441942
$513$	12271.1	−	10296.6i	1.05610	−	0.886175i
$514$	−4157.78	−	1513.31i	−0.356793	−	0.129862i
$515$	1203.59	+	6825.90i	0.102984	+	0.584049i
$516$	87.8643	−	498.303i	0.00749614	−	0.0425127i
$517$	−13710.5			−1.16632
$518$	3275.00	−	2506.76i	0.277790	−	0.212627i
$519$	7948.27			0.672236
$520$	−658.612	+	3735.18i	−0.0555424	+	0.314997i
$521$	3152.68	+	17879.8i	0.265109	+	1.50351i	0.768725	+	0.639579i	$0.220891\pi$
$521$	3152.68	+	17879.8i	0.265109	+	1.50351i	−0.503617	+	0.863927i	$0.667998\pi$
$522$	3895.34	+	1417.79i	0.326618	+	0.118879i
$523$	−11549.2	+	9690.92i	−0.965604	+	0.810238i	−0.981856	−	0.189630i	$-0.939271\pi$
$523$	−11549.2	+	9690.92i	−0.965604	+	0.810238i	0.0162520	+	0.999868i	$0.494827\pi$
$524$	−6613.61			−0.551368
$525$	−831.117	+	697.390i	−0.0690913	+	0.0579745i
$526$	−2376.13	+	4115.58i	−0.196966	+	0.341156i
$527$	7191.80	−	2617.60i	0.594459	−	0.216365i
$528$	1070.20	+	1853.63i	0.0882089	+	0.152782i
$529$	874.654	−	1514.94i	0.0718874	−	0.124513i
$530$	−1700.87	+	9646.10i	−0.139398	+	0.790566i
$531$	2812.11	+	1023.52i	0.229821	+	0.0836481i
$532$	2104.43	+	3644.98i	0.171501	+	0.297049i
$533$	−3142.22	−	2636.64i	−0.255356	−	0.214269i
$534$	−789.615	−	662.566i	−0.0639888	−	0.0536929i
$535$	−18192.5	+	6621.53i	−1.47015	+	0.535091i
$536$	−999.330	−	5667.48i	−0.0805308	−	0.456713i
$537$	−381.070	−	2161.15i	−0.0306227	−	0.173670i
$538$	4145.90	−	1508.98i	0.332235	−	0.120924i
$539$	8356.28	+	7011.75i	0.667774	+	0.560329i
$540$	−4003.28	−	3359.15i	−0.319026	−	0.267694i
$541$	11027.5	+	19100.1i	0.876354	+	1.51789i	0.855313	+	0.518112i	$0.173365\pi$
$541$	11027.5	+	19100.1i	0.876354	+	1.51789i	0.0210413	+	0.999779i	$0.493302\pi$
$542$	−10994.2	−	4001.57i	−0.871297	−	0.317126i
$543$	2145.79	−	12169.4i	0.169585	−	0.961765i
$544$	−2049.09	+	3549.13i	−0.161497	+	0.279720i
$545$	2742.09	+	4749.43i	0.215519	+	0.373290i
$546$	2769.04	−	1007.85i	0.217040	−	0.0789962i
$547$	3758.77	−	6510.38i	0.293809	−	0.508892i	−0.680898	−	0.732378i	$-0.738410\pi$
$547$	3758.77	−	6510.38i	0.293809	−	0.508892i	0.974707	+	0.223486i	$0.0717437\pi$
$548$	−8254.76	+	6926.57i	−0.643478	+	0.539942i
$549$	3522.27			0.273819
$550$	2404.69	−	2017.78i	0.186430	−	0.156433i
$551$	13228.9	+	4814.93i	1.02281	+	0.372274i
$552$	−450.446	−	2554.60i	−0.0347323	−	0.196977i
$553$	−76.1690	+	431.976i	−0.00585721	+	0.0332179i
$554$	8485.50			0.650748
$555$	−3604.94	+	5643.67i	−0.275714	+	0.431640i
$556$	2750.44			0.209793
$557$	−3809.70	+	21605.9i	−0.289806	+	1.64357i	0.397787	+	0.917478i	$0.369778\pi$
$557$	−3809.70	+	21605.9i	−0.289806	+	1.64357i	−0.687593	+	0.726096i	$0.741333\pi$
$558$	350.908	+	1990.10i	0.0266221	+	0.150981i
$559$	1893.98	+	689.352i	0.143304	+	0.0521583i
$560$	1051.85	−	882.604i	0.0793726	−	0.0666015i
$561$	−17132.3			−1.28935
$562$	−7012.27	+	5884.00i	−0.526325	+	0.441640i
$563$	−8838.50	+	15308.7i	−0.661631	+	1.14598i	0.318556	+	0.947904i	$0.396802\pi$
$563$	−8838.50	+	15308.7i	−0.661631	+	1.14598i	−0.980187	+	0.198074i	$0.936531\pi$
$564$	−3887.92	+	1415.09i	−0.290268	+	0.105649i
$565$	8352.12	+	14466.3i	0.621905	+	1.07717i
$566$	3390.90	−	5873.21i	0.251820	−	0.436165i
$567$	21.2791	−	120.680i	0.00157608	−	0.00893839i
$568$	4781.98	+	1740.50i	0.353252	+	0.128573i
$569$	3902.98	+	6760.16i	0.287560	+	0.498068i	0.973227	−	0.229847i	$-0.0738227\pi$
$569$	3902.98	+	6760.16i	0.287560	+	0.498068i	−0.685667	+	0.727915i	$0.740489\pi$
$570$	−5235.25	−	4392.90i	−0.384703	−	0.322804i
$571$	−19427.7	−	16301.8i	−1.42386	−	1.19476i	−0.949234	−	0.314571i	$-0.898139\pi$
$571$	−19427.7	−	16301.8i	−1.42386	−	1.19476i	−0.474625	−	0.880188i	$-0.657416\pi$
$572$	−8011.74	+	2916.03i	−0.585643	+	0.213156i
$573$	−717.685	−	4070.19i	−0.0523241	−	0.296745i
$574$	257.865	+	1462.42i	0.0187510	+	0.106342i
$575$	−3574.95	+	1301.18i	−0.259280	+	0.0943701i
$576$	−828.928	−	695.553i	−0.0599630	−	0.0503149i
$577$	5505.00	+	4619.24i	0.397185	+	0.333278i	0.819405	−	0.573216i	$-0.194304\pi$
$577$	5505.00	+	4619.24i	0.397185	+	0.333278i	−0.422219	+	0.906494i	$0.638749\pi$
$578$	−11488.5	−	19898.6i	−0.826743	−	1.43196i
$579$	12475.6	+	4540.74i	0.895453	+	0.325918i
$580$	797.522	−	4522.97i	0.0570953	−	0.323804i
$581$	3503.73	−	6068.63i	0.250188	−	0.433338i
$582$	2587.37	+	4481.46i	0.184279	+	0.319180i
$583$	−20690.3	+	7530.67i	−1.46982	+	0.534971i
$584$	−2315.72	+	4010.95i	−0.164084	+	0.284202i
$585$	6140.54	−	5152.52i	0.433983	−	0.364155i
$586$	−16877.7			−1.18978
$587$	11495.9	−	9646.19i	0.808323	−	0.678264i	−0.141884	−	0.989883i	$-0.545316\pi$
$587$	11495.9	−	9646.19i	0.808323	−	0.678264i	0.950207	+	0.311619i	$0.100871\pi$
$588$	3093.32	+	1125.87i	0.216949	+	0.0789631i
$589$	1191.71	+	6758.55i	0.0833680	+	0.472803i
$590$	575.744	−	3265.21i	0.0401746	−	0.227841i
$591$	2367.10			0.164754
$592$	−1938.45	+	3034.73i	−0.134578	+	0.210687i
$593$	27012.3			1.87060			0.935298	−	0.353860i	$-0.115131\pi$
$593$	27012.3			1.87060			0.935298	+	0.353860i	$0.115131\pi$
$594$	2039.92	−	11569.0i	0.140907	−	0.799126i
$595$	1908.49	+	10823.6i	0.131497	+	0.745755i
$596$	8742.43	+	3181.98i	0.600845	+	0.218690i
$597$	11188.1	−	9387.95i	0.767000	−	0.643590i
$598$	10332.8			0.706591
$599$	15417.8	−	12937.1i	1.05168	−	0.882460i	0.0584063	−	0.998293i	$-0.481398\pi$
$599$	15417.8	−	12937.1i	1.05168	−	0.882460i	0.993269	+	0.115833i	$0.0369537\pi$
$600$	473.648	−	820.382i	0.0322276	−	0.0558199i
$601$	15054.3	−	5479.31i	1.02176	−	0.371890i	0.223821	−	0.974630i	$-0.428147\pi$
$601$	15054.3	−	5479.31i	1.02176	−	0.371890i	0.797937	+	0.602741i	$0.205925\pi$
$602$	−364.837	−	631.916i	−0.0247004	−	0.0427823i
$603$	−6081.37	+	10533.2i	−0.410701	+	0.711355i
$604$	−877.719	+	4977.79i	−0.0591290	+	0.335337i
$605$	−3891.84	−	1416.51i	−0.261530	−	0.0951893i
$606$	3058.01	+	5296.63i	0.204989	+	0.355051i
$607$	−1665.74	−	1397.72i	−0.111384	−	0.0934625i	0.585395	−	0.810749i	$-0.300940\pi$
$607$	−1665.74	−	1397.72i	−0.111384	−	0.0934625i	−0.696779	+	0.717286i	$0.745384\pi$
$608$	−2815.11	−	2362.16i	−0.187776	−	0.157563i
$609$	−3353.06	+	1220.42i	−0.223108	+	0.0812048i
$610$	−677.650	−	3843.14i	−0.0449791	−	0.255089i
$611$	−2861.86	−	16230.4i	−0.189490	−	1.07465i
$612$	8138.98	−	2962.35i	0.537580	−	0.195663i
$613$	−7666.48	−	6432.94i	−0.505132	−	0.423856i	0.354280	−	0.935139i	$-0.384726\pi$
$613$	−7666.48	−	6432.94i	−0.505132	−	0.423856i	−0.859412	+	0.511283i	$0.829170\pi$
$614$	−10308.2	−	8649.60i	−0.677532	−	0.568517i
$615$	−1205.62	−	2088.20i	−0.0790493	−	0.136917i
$616$	2900.45	+	1055.68i	0.189712	+	0.0690495i
$617$	1831.35	−	10386.1i	0.119493	−	0.677680i	−0.864934	−	0.501886i	$-0.832640\pi$
$617$	1831.35	−	10386.1i	0.119493	−	0.677680i	0.984427	−	0.175794i	$-0.0562493\pi$
$618$	−2350.93	+	4071.93i	−0.153023	+	0.265044i
$619$	3254.56	+	5637.07i	0.211328	+	0.366030i	0.952130	−	0.305692i	$-0.0988879\pi$
$619$	3254.56	+	5637.07i	0.211328	+	0.366030i	−0.740803	+	0.671723i	$0.765555\pi$
$620$	2103.89	−	765.752i	0.136281	−	0.0496021i
$621$	−7118.56	+	12329.7i	−0.459997	+	0.796738i
$622$	3273.56	−	2746.84i	0.211025	−	0.177071i
$623$	−1486.44			−0.0955908
$624$	−1970.94	+	1653.82i	−0.126444	+	0.106099i
$625$	8998.99	+	3275.36i	0.575935	+	0.209623i
$626$	340.021	+	1928.36i	0.0217092	+	0.123119i
$627$	2667.69	−	15129.2i	0.169916	−	0.963641i
$628$	−1433.04			−0.0910584
$629$	−13278.5	−	25582.5i	−0.841728	−	1.62169i
$630$	−2901.96			−0.183519
$631$	1425.34	−	8083.49i	0.0899236	−	0.509982i	−0.906262	−	0.422717i	$-0.861076\pi$
$631$	1425.34	−	8083.49i	0.0899236	−	0.509982i	0.996185	−	0.0872648i	$-0.0278126\pi$
$632$	−66.5052	−	377.170i	−0.00418581	−	0.0237389i
$633$	−16615.1	−	6047.40i	−1.04327	−	0.379720i
$634$	−7353.76	+	6170.54i	−0.460655	+	0.386535i
$635$	10061.4			0.628776
$636$	−5089.97	+	4270.99i	−0.317343	+	0.266283i
$637$	−6556.25	+	11355.8i	−0.407799	+	0.706329i
$638$	9701.51	−	3531.06i	0.602017	−	0.219116i
$639$	−5377.55	−	9314.20i	−0.332915	−	0.576626i
$640$	−599.440	+	1038.26i	−0.0370233	+	0.0641263i
$641$	855.311	−	4850.71i	0.0527032	−	0.298895i	−0.947051	−	0.321084i	$-0.895953\pi$
$641$	855.311	−	4850.71i	0.0527032	−	0.298895i	0.999754	+	0.0221898i	$0.00706380\pi$
$642$	−12341.1	−	4491.79i	−0.758667	−	0.276132i
$643$	6939.21	+	12019.1i	0.425592	+	0.737147i	0.996476	−	0.0838842i	$-0.0267326\pi$
$643$	6939.21	+	12019.1i	0.425592	+	0.737147i	−0.570884	+	0.821031i	$0.693399\pi$
$644$	−2865.58	−	2404.51i	−0.175341	−	0.147129i
$645$	907.615	+	761.580i	0.0554067	+	0.0464917i
$646$	27640.7	−	10060.4i	1.68345	−	0.612726i
$647$	3853.64	+	21855.1i	0.234161	+	1.32799i	0.844373	+	0.535756i	$0.179973\pi$
$647$	3853.64	+	21855.1i	0.234161	+	1.32799i	−0.610211	+	0.792239i	$0.708915\pi$
$648$	18.5793	+	105.369i	0.00112633	+	0.00638776i
$649$	7003.68	−	2549.13i	0.423603	−	0.154179i
$650$	2890.59	+	2425.49i	0.174428	+	0.146363i
$651$	−1332.52	−	1118.12i	−0.0802237	−	0.0673156i
$652$	−6772.41	−	11730.2i	−0.406791	−	0.704583i
$653$	4501.01	+	1638.23i	0.269737	+	0.0981762i	0.473348	−	0.880876i	$-0.343045\pi$
$653$	4501.01	+	1638.23i	0.269737	+	0.0981762i	−0.203611	+	0.979052i	$0.565268\pi$
$654$	−646.014	+	3663.73i	−0.0386256	+	0.219057i
$655$	7743.09	−	13411.4i	0.461905	−	0.800042i
$656$	−648.289	−	1122.87i	−0.0385845	−	0.0668303i
$657$	9198.04	−	3347.81i	0.546194	−	0.198798i
$658$	−2983.24	+	5167.12i	−0.176746	+	0.306133i
$659$	−5591.30	+	4691.66i	−0.330510	+	0.277331i	−0.792908	−	0.609342i	$-0.791434\pi$
$659$	−5591.30	+	4691.66i	−0.330510	+	0.277331i	0.462398	+	0.886673i	$0.346989\pi$
$660$	−5011.86			−0.295586
$661$	−18747.2	+	15730.8i	−1.10315	+	0.925652i	−0.997633	−	0.0687656i	$-0.978094\pi$
$661$	−18747.2	+	15730.8i	−1.10315	+	0.925652i	−0.105516	+	0.994418i	$0.533649\pi$
$662$	9567.41	+	3482.25i	0.561704	+	0.204444i
$663$	−3576.12	−	20281.2i	−0.209480	−	1.18802i
$664$	−1062.45	+	6025.44i	−0.0620948	+	0.352157i
$665$	−9855.31			−0.574695
$666$	7261.04	−	2279.83i	0.422462	−	0.132645i
$667$	−12512.2			−0.726346
$668$	−1435.95	+	8143.66i	−0.0831714	+	0.471688i
$669$	1891.95	+	10729.8i	0.109338	+	0.620085i
$670$	12662.8	+	4608.89i	0.730160	+	0.265757i
$671$	6720.02	−	5638.76i	0.386622	−	0.324414i
$672$	931.450			0.0534694
$673$	4267.33	−	3580.72i	0.244418	−	0.205091i	−0.512346	−	0.858779i	$-0.671223\pi$
$673$	4267.33	−	3580.72i	0.244418	−	0.205091i	0.756764	+	0.653688i	$0.226779\pi$
$674$	4929.15	−	8537.54i	0.281697	−	0.487914i
$675$	−4885.64	+	1778.23i	−0.278590	+	0.101398i
$676$	−730.338	−	1264.98i	−0.0415531	−	0.0719721i
$677$	13618.1	−	23587.2i	0.773096	−	1.33904i	−0.162762	−	0.986665i	$-0.552040\pi$
$677$	13618.1	−	23587.2i	0.773096	−	1.33904i	0.935858	−	0.352377i	$-0.114626\pi$
$678$	−1967.69	+	11159.4i	−0.111458	+	0.632113i
$679$	7012.32	+	2552.27i	0.396330	+	0.144252i
$680$	−4798.08	−	8310.51i	−0.270585	−	0.468667i
$681$	2514.53	+	2109.94i	0.141493	+	0.118727i
$682$	3855.42	+	3235.08i	0.216469	+	0.181639i
$683$	−22549.8	+	8207.46i	−1.26332	+	0.459809i	−0.884880	−	0.465818i	$-0.845760\pi$
$683$	−22549.8	+	8207.46i	−1.26332	+	0.459809i	−0.378435	+	0.925628i	$0.623538\pi$
$684$	1348.67	+	7648.67i	0.0753912	+	0.427565i
$685$	−4381.54	−	24848.9i	−0.244394	−	1.38603i
$686$	10367.2	−	3773.34i	0.576998	−	0.210010i
$687$	7249.38	+	6082.95i	0.402592	+	0.337815i
$688$	488.045	+	409.518i	0.0270444	+	0.0226929i
$689$	−13233.6	−	22921.3i	−0.731728	−	1.26739i
$690$	5707.73	+	2077.45i	0.314913	+	0.114619i
$691$	−1937.17	+	10986.2i	−0.106648	+	0.604828i	0.883902	+	0.467672i	$0.154907\pi$
$691$	−1937.17	+	10986.2i	−0.106648	+	0.604828i	−0.990549	+	0.137156i	$0.956204\pi$
$692$	−5003.87	+	8666.96i	−0.274883	+	0.476111i
$693$	−3261.69	−	5649.41i	−0.178790	−	0.309673i
$694$	4540.89	−	1652.75i	0.248371	−	0.0903998i
$695$	−3220.16	+	5577.49i	−0.175752	+	0.304412i
$696$	2386.64	−	2002.63i	0.129979	−	0.109065i
$697$	10378.2			0.563990
$698$	857.121	−	719.210i	0.0464792	−	0.0390007i
$699$	−19010.0	−	6919.08i	−1.02865	−	0.374397i
$700$	−237.215	−	1345.31i	−0.0128084	−	0.0726401i
$701$	−4688.81	+	26591.6i	−0.252630	+	1.43274i	0.549452	+	0.835525i	$0.314836\pi$
$701$	−4688.81	+	26591.6i	−0.252630	+	1.43274i	−0.802083	+	0.597213i	$0.796275\pi$
$702$	14121.2			0.759215
$703$	24659.1	−	7742.48i	1.32295	−	0.415382i
$704$	−2694.99			−0.144277
$705$	1682.31	−	9540.88i	0.0898718	−	0.509688i
$706$	−37.4531	−	212.407i	−0.00199655	−	0.0113230i
$707$	8287.84	+	3016.53i	0.440872	+	0.160464i
$708$	1722.95	−	1445.73i	0.0914585	−	0.0767428i
$709$	−22170.0			−1.17434			−0.587172	−	0.809462i	$-0.699759\pi$
$709$	−22170.0			−1.17434			−0.587172	+	0.809462i	$0.699759\pi$
$710$	−9128.12	+	7659.41i	−0.482496	+	0.404863i
$711$	−404.714	+	700.985i	−0.0213473	+	0.0369747i
$712$	1219.58	−	443.891i	0.0641935	−	0.0233645i
$713$	−3049.76	−	5282.35i	−0.160189	−	0.277455i
$714$	−3727.79	+	6456.71i	−0.195391	+	0.338426i
$715$	3466.70	−	19660.7i	0.181325	−	1.02835i
$716$	2596.47	+	945.039i	0.135523	+	0.0493265i
$717$	3154.81	+	5464.30i	0.164322	+	0.284614i
$718$	−10514.4	−	8822.64i	−0.546510	−	0.458577i
$719$	10027.8	+	8414.29i	0.520128	+	0.436440i	0.864677	−	0.502329i	$-0.167523\pi$
$719$	10027.8	+	8414.29i	0.520128	+	0.436440i	−0.344548	+	0.938769i	$0.611968\pi$
$720$	2380.97	−	866.603i	0.123241	−	0.0448561i
$721$	1177.41	+	6677.40i	0.0608167	+	0.344909i
$722$	2198.08	+	12465.9i	0.113302	+	0.642569i
$723$	13730.8	−	4997.59i	0.706296	−	0.257071i
$724$	11918.9	+	10001.1i	0.611824	+	0.513382i
$725$	−3500.25	−	2937.06i	−0.179305	−	0.150455i
$726$	−1404.75	−	2433.10i	−0.0718117	−	0.124382i
$727$	−10797.2	−	3929.88i	−0.550822	−	0.200483i	0.0515896	−	0.998668i	$-0.483571\pi$
$727$	−10797.2	−	3929.88i	−0.550822	−	0.200483i	−0.602412	+	0.798186i	$0.705793\pi$
$728$	−644.284	+	3653.91i	−0.0328005	+	0.186021i
$729$	−5869.22	+	10165.8i	−0.298187	+	0.516475i
$730$	−5422.41	−	9391.88i	−0.274921	−	0.476177i
$731$	−4791.96	+	1744.13i	−0.242458	+	0.0882476i
$732$	1323.63	−	2292.59i	0.0668343	−	0.115760i
$733$	3517.34	−	2951.40i	0.177239	−	0.148721i	−0.549853	−	0.835262i	$-0.685316\pi$
$733$	3517.34	−	2951.40i	0.177239	−	0.148721i	0.727091	+	0.686541i	$0.240872\pi$
$734$	−21609.0			−1.08665
$735$	−5904.70	+	4954.63i	−0.296324	+	0.248645i
$736$	3069.17	+	1117.09i	0.153711	+	0.0559462i
$737$	5260.12	+	29831.6i	0.262903	+	1.49099i
$738$	−475.841	+	2698.63i	−0.0237343	+	0.134604i
$739$	2458.37			0.122372			0.0611858	−	0.998126i	$-0.480512\pi$
$739$	2458.37			0.122372			0.0611858	+	0.998126i	$0.480512\pi$
$740$	−3884.47	−	7483.90i	−0.192967	−	0.371775i
$741$	18466.8			0.915513
$742$	−1663.86	+	9436.24i	−0.0823213	+	0.466867i
$743$	−604.271	−	3426.99i	−0.0298366	−	0.169212i	0.966248	−	0.257612i	$-0.0829356\pi$
$743$	−604.271	−	3426.99i	−0.0298366	−	0.169212i	−0.996085	+	0.0884004i	$0.971825\pi$
$744$	1427.19	+	519.456i	0.0703272	+	0.0255970i
$745$	−16688.1	+	14002.9i	−0.820675	+	0.688628i
$746$	20999.8			1.03064
$747$	9905.68	−	8311.85i	0.485180	−	0.407115i
$748$	10785.7	−	18681.4i	0.527225	−	0.913181i
$749$	−17796.7	+	6477.48i	−0.868195	+	0.315997i
$750$	4828.47	+	8363.15i	0.235081	+	0.407172i
$751$	−12395.0	+	21468.8i	−0.602265	+	1.04315i	0.390213	+	0.920725i	$0.372401\pi$
$751$	−12395.0	+	21468.8i	−0.602265	+	1.04315i	−0.992477	+	0.122428i	$0.960932\pi$
$752$	904.618	−	5130.34i	0.0438670	−	0.248782i
$753$	−10656.2	−	3878.53i	−0.515713	−	0.187704i
$754$	6205.12	+	10747.6i	0.299705	+	0.519104i
$755$	−9066.61	−	7607.79i	−0.437044	−	0.366723i
$756$	−3916.19	−	3286.07i	−0.188400	−	0.158086i
$757$	26756.9	−	9738.71i	1.28467	−	0.467582i	0.392696	−	0.919668i	$-0.371542\pi$
$757$	26756.9	−	9738.71i	1.28467	−	0.467582i	0.891974	+	0.452087i	$0.149320\pi$
$758$	−708.734	−	4019.43i	−0.0339609	−	0.192602i
$759$	2370.99	+	13446.5i	0.113388	+	0.643055i
$760$	8085.99	−	2943.06i	0.385934	−	0.140468i
$761$	−14719.6	−	12351.2i	−0.701165	−	0.588347i	0.220940	−	0.975287i	$-0.429088\pi$
$761$	−14719.6	−	12351.2i	−0.701165	−	0.588347i	−0.922105	+	0.386940i	$0.873532\pi$
$762$	5228.43	+	4387.18i	0.248565	+	0.208570i
$763$	2682.43	+	4646.10i	0.127275	+	0.220446i
$764$	4890.05	+	1779.83i	0.231565	+	0.0842828i
$765$	−3521.76	+	19972.9i	−0.166444	+	0.943951i
$766$	−8047.54	+	13938.8i	−0.379595	+	0.657477i
$767$	4479.58	+	7758.86i	0.210884	+	0.365262i
$768$	−764.227	+	278.156i	−0.0359071	+	0.0130691i
$769$	684.006	−	1184.73i	0.0320753	−	0.0555560i	−0.849542	−	0.527521i	$-0.823122\pi$
$769$	684.006	−	1184.73i	0.0320753	−	0.0555560i	0.881617	+	0.471965i	$0.156455\pi$
$770$	−5536.55	+	4645.72i	−0.259122	+	0.217429i
$771$	7028.16			0.328292
$772$	−12805.4	+	10745.0i	−0.596989	+	0.500933i
$773$	−34837.8	−	12679.9i	−1.62099	−	0.589993i	−0.637422	−	0.770515i	$-0.719999\pi$
$773$	−34837.8	−	12679.9i	−1.62099	−	0.589993i	−0.983571	+	0.180522i	$0.942221\pi$
$774$	−233.813	−	1326.02i	−0.0108582	−	0.0615798i
$775$	386.794	−	2193.62i	0.0179278	−	0.101674i
$776$	−6515.57			−0.301412
$777$	−3526.51	+	5520.89i	−0.162822	+	0.254904i
$778$	−7277.61			−0.335366
$779$	−1616.00	+	9164.77i	−0.0743249	+	0.421517i
$780$	−1046.16	−	5933.04i	−0.0480236	−	0.272355i
$781$	−25170.7	−	9161.37i	−1.15324	−	0.419744i
$782$	−20026.8	+	16804.5i	−0.915801	+	0.768448i
$783$	−17099.5			−0.780442
$784$	−3175.09	+	2664.22i	−0.144638	+	0.121366i
$785$	1677.78	−	2906.00i	0.0762835	−	0.132127i
$786$	9871.68	−	3593.00i	0.447978	−	0.163051i
$787$	−8746.93	−	15150.1i	−0.396181	−	0.686205i	0.597070	−	0.802189i	$-0.296331\pi$
$787$	−8746.93	−	15150.1i	−0.396181	−	0.686205i	−0.993251	+	0.115983i	$0.962998\pi$
$788$	−1490.22	+	2581.13i	−0.0673690	+	0.116687i
$789$	1310.80	−	7433.93i	0.0591455	−	0.335431i
$790$	842.707	+	306.720i	0.0379521	+	0.0138134i
$791$	8170.41	+	14151.6i	0.367265	+	0.636121i
$792$	4363.19	+	3661.15i	0.195756	+	0.164259i
$793$	8077.88	+	6778.15i	0.361733	+	0.303530i
$794$	379.313	−	138.059i	0.0169538	−	0.00617068i
$795$	−2701.70	−	15322.1i	−0.120528	−	0.683546i
$796$	3193.28	+	18110.0i	0.142189	+	0.806396i
$797$	−17662.1	+	6428.46i	−0.784971	+	0.285706i	−0.703244	−	0.710949i	$-0.748266\pi$
$797$	−17662.1	+	6428.46i	−0.784971	+	0.285706i	−0.0817273	+	0.996655i	$0.526044\pi$
$798$	−5121.36	−	4297.33i	−0.227185	−	0.190631i
$799$	31942.6	+	26803.0i	1.41433	+	1.18676i
$800$	596.374	+	1032.95i	0.0263563	+	0.0456504i
$801$	−2577.53	−	938.144i	−0.113699	−	0.0413829i
$802$	−2994.26	+	16981.3i	−0.131834	+	0.747669i
$803$	12189.1	−	21112.2i	0.535673	−	0.927813i
$804$	4570.62	+	7916.55i	0.200489	+	0.347258i
$805$	8230.95	−	2995.82i	0.360376	−	0.131166i
$806$	−3024.92	+	5239.32i	−0.132194	+	0.228967i
$807$	−5368.50	+	4504.71i	−0.234176	+	0.196497i
$808$	−7700.74			−0.335286
$809$	7925.04	−	6649.90i	0.344412	−	0.288996i	−0.454129	−	0.890936i	$-0.650050\pi$
$809$	7925.04	−	6649.90i	0.344412	−	0.288996i	0.798542	+	0.601939i	$0.205605\pi$
$810$	−235.424	−	85.6874i	−0.0102123	−	0.00371697i
$811$	4627.02	+	26241.2i	0.200341	+	1.13619i	0.904604	+	0.426253i	$0.140167\pi$
$811$	4627.02	+	26241.2i	0.200341	+	1.13619i	−0.704263	+	0.709939i	$0.748722\pi$
$812$	780.171	−	4424.57i	0.0337175	−	0.191222i
$813$	18584.3			0.801696
$814$	10203.3	−	15973.7i	0.439345	−	0.687812i
$815$	31716.0			1.36315
$816$	1130.39	−	6410.76i	0.0484946	−	0.275026i
$817$	−794.049	−	4503.28i	−0.0340028	−	0.192839i
$818$	−9601.33	−	3494.60i	−0.410394	−	0.149371i
$819$	6006.94	−	5040.42i	0.256288	−	0.215051i
$820$	3036.02			0.129296
$821$	15215.9	−	12767.6i	0.646818	−	0.542744i	−0.259286	−	0.965801i	$-0.583487\pi$
$821$	15215.9	−	12767.6i	0.646818	−	0.542744i	0.906103	+	0.423056i	$0.139043\pi$
$822$	8558.29	−	14823.4i	0.363144	−	0.628984i
$823$	−14177.0	+	5160.02i	−0.600462	+	0.218550i	−0.624325	−	0.781165i	$-0.714626\pi$
$823$	−14177.0	+	5160.02i	−0.600462	+	0.218550i	0.0238627	+	0.999715i	$0.492404\pi$
$824$	−2960.08	−	5127.00i	−0.125145	−	0.216757i
$825$	−2493.12	+	4318.20i	−0.105211	+	0.182231i
$826$	563.218	−	3194.17i	0.0237250	−	0.134551i
$827$	20709.5	+	7537.64i	0.870786	+	0.316940i	0.738485	−	0.674270i	$-0.235541\pi$
$827$	20709.5	+	7537.64i	0.870786	+	0.316940i	0.132300	+	0.991210i	$0.457764\pi$
$828$	−3451.43	−	5978.05i	−0.144862	−	0.250908i
$829$	−18127.3	−	15210.6i	−0.759453	−	0.637257i	0.178531	−	0.983934i	$-0.442865\pi$
$829$	−18127.3	−	15210.6i	−0.759453	−	0.637257i	−0.937984	+	0.346678i	$0.887310\pi$
$830$	−10974.8	−	9208.96i	−0.458965	−	0.385118i
$831$	−12665.7	+	4609.94i	−0.528723	+	0.192439i
$832$	−562.541	−	3190.33i	−0.0234406	−	0.132938i
$833$	−5760.94	−	32671.9i	−0.239622	−	1.35896i
$834$	−4105.39	+	1494.24i	−0.170453	+	0.0620399i
$835$	−14833.0	−	12446.3i	−0.614750	−	0.515836i
$836$	14817.8	+	12433.6i	0.613018	+	0.514383i
$837$	−4167.90	−	7219.01i	−0.172119	−	0.298119i
$838$	−19667.2	−	7158.29i	−0.810732	−	0.295082i
$839$	−3809.76	+	21606.2i	−0.156767	+	0.889069i	0.800386	+	0.599485i	$0.204628\pi$
$839$	−3809.76	+	21606.2i	−0.156767	+	0.889069i	−0.957153	+	0.289584i	$0.906483\pi$
$840$	−1090.52	+	1888.84i	−0.0447936	+	0.0775848i
$841$	4680.64	+	8107.10i	0.191916	+	0.332408i
$842$	−1842.67	+	670.678i	−0.0754189	+	0.0274502i
$843$	7270.12	−	12592.2i	0.297030	−	0.514471i
$844$	17054.3	−	14310.3i	0.695538	−	0.583625i
$845$	3420.26			0.139243
$846$	−8434.16	+	7077.10i	−0.342757	+	0.287607i
$847$	−3807.17	−	1385.70i	−0.154446	−	0.0562138i
$848$	−1452.76	−	8239.03i	−0.0588303	−	0.333643i
$849$	−1870.60	+	10608.7i	−0.0756171	+	0.428846i
$850$	−9547.08			−0.385249
$851$	−18241.2	+	13962.3i	−0.734784	+	0.562421i
$852$	−8083.29			−0.325034
$853$	6922.81	−	39261.2i	0.277881	−	1.57594i	−0.451777	−	0.892131i	$-0.649210\pi$
$853$	6922.81	−	39261.2i	0.277881	−	1.57594i	0.729659	−	0.683812i	$-0.239679\pi$
$854$	−662.907	−	3759.53i	−0.0265623	−	0.150642i
$855$	−17089.4	−	6220.02i	−0.683560	−	0.248796i
$856$	12667.3	−	10629.2i	0.505795	−	0.424412i
$857$	3573.11			0.142422			0.0712108	−	0.997461i	$-0.477314\pi$
$857$	3573.11			0.142422			0.0712108	+	0.997461i	$0.477314\pi$
$858$	10374.4	−	8705.12i	0.412791	−	0.346373i
$859$	−7998.07	+	13853.1i	−0.317684	+	0.550245i	−0.980004	−	0.198976i	$-0.936238\pi$
$859$	−7998.07	+	13853.1i	−0.317684	+	0.550245i	0.662320	+	0.749221i	$0.269572\pi$
$860$	−1401.84	+	510.227i	−0.0555840	+	0.0202309i
$861$	−1179.39	−	2042.77i	−0.0466824	−	0.0808563i
$862$	−2050.96	+	3552.36i	−0.0810393	+	0.140364i
$863$	−5264.87	+	29858.6i	−0.207669	+	1.17775i	0.685515	+	0.728059i	$0.259577\pi$
$863$	−5264.87	+	29858.6i	−0.207669	+	1.17775i	−0.893184	+	0.449691i	$0.851534\pi$
$864$	4194.42	+	1526.65i	0.165159	+	0.0601129i
$865$	−11716.9	−	20294.2i	−0.460562	−	0.797716i
$866$	23280.9	+	19535.0i	0.913531	+	0.766543i
$867$	27958.4	+	23459.9i	1.09518	+	0.918963i
$868$	2058.11	−	749.092i	0.0804803	−	0.0292924i
$869$	350.060	+	1985.29i	0.0136651	+	0.0774986i
$870$	1266.80	+	7184.40i	0.0493663	+	0.279970i
$871$	−34216.7	+	12453.9i	−1.33110	+	0.484481i
$872$	−3588.30	−	3010.95i	−0.139352	−	0.116931i
$873$	10548.7	+	8851.42i	0.408957	+	0.343156i
$874$	−11721.3	−	20302.0i	−0.453639	−	0.785725i
$875$	13086.1	+	4762.97i	0.505591	+	0.184020i
$876$	1277.48	−	7244.93i	0.0492716	−	0.279433i
$877$	17121.4	−	29655.1i	0.659233	−	1.14183i	−0.321581	−	0.946882i	$-0.604214\pi$
$877$	17121.4	−	29655.1i	0.659233	−	1.14183i	0.980814	−	0.194943i	$-0.0624523\pi$
$878$	−16914.5	−	29296.7i	−0.650155	−	1.12610i
$879$	25192.2	−	9169.19i	0.966678	−	0.351842i
$880$	3155.24	−	5465.04i	0.120867	−	0.209348i
$881$	25611.1	−	21490.3i	0.979410	−	0.821823i	−0.00459035	−	0.999989i	$-0.501461\pi$
$881$	25611.1	−	21490.3i	0.979410	−	0.821823i	0.984000	+	0.178167i	$0.0570167\pi$
$882$	8759.81			0.334420
$883$	32318.1	−	27118.1i	1.23170	−	1.03352i	0.233574	−	0.972339i	$-0.424958\pi$
$883$	32318.1	−	27118.1i	1.23170	−	1.03352i	0.998127	−	0.0611803i	$-0.0194865\pi$
$884$	24366.4	+	8868.64i	0.927071	+	0.337426i
$885$	914.525	+	5186.53i	0.0347361	+	0.196998i
$886$	5102.79	−	28939.4i	0.193489	−	1.09733i
$887$	−9691.97			−0.366882			−0.183441	−	0.983031i	$-0.558724\pi$
$887$	−9691.97			−0.366882			−0.183441	+	0.983031i	$0.558724\pi$
$888$	1244.71	−	5582.83i	0.0470381	−	0.210977i
$889$	9842.47			0.371323
$890$	−527.717	+	2992.83i	−0.0198754	+	0.112719i
$891$	−97.7950	−	554.623i	−0.00367706	−	0.0208536i
$892$	−12891.0	−	4691.96i	−0.483884	−	0.176119i
$893$	−28643.1	+	24034.4i	−1.07335	+	0.900651i
$894$	−14777.9			−0.552849
$895$	−4956.30	+	4158.83i	−0.185107	+	0.155323i
$896$	−586.399	+	1015.67i	−0.0218641	+	0.0378697i
$897$	−15423.1	+	5613.55i	−0.574094	+	0.208953i
$898$	−3828.41	−	6631.00i	−0.142267	−	0.246414i
$899$	3662.92	−	6344.36i	0.135890	−	0.235368i
$900$	437.736	−	2482.52i	0.0162124	−	0.0919453i
$901$	62926.3	+	22903.3i	2.32672	+	0.846858i
$902$	3412.37	+	5910.39i	0.125964	+	0.218176i
$903$	887.869	+	745.011i	0.0327203	+	0.0274556i
$904$	−10929.6	−	9171.04i	−0.402117	−	0.337416i
$905$	−34235.1	+	12460.6i	−1.25747	+	0.457683i
$906$	−1394.19	−	7906.85i	−0.0511246	−	0.289942i
$907$	2377.88	+	13485.6i	0.0870520	+	0.493696i	0.996895	+	0.0787435i	$0.0250908\pi$
$907$	2377.88	+	13485.6i	0.0870520	+	0.493696i	−0.909843	+	0.414953i	$0.863798\pi$
$908$	−3883.76	+	1413.57i	−0.141946	+	0.0516641i
$909$	12467.5	+	10461.5i	0.454918	+	0.381722i
$910$	−6655.28	−	5584.44i	−0.242440	−	0.203431i
$911$	12716.1	+	22024.9i	0.462461	+	0.801006i	0.999083	−	0.0428165i	$-0.0136331\pi$
$911$	12716.1	+	22024.9i	0.462461	+	0.801006i	−0.536622	+	0.843823i	$0.680300\pi$
$912$	5485.22	+	1996.46i	0.199160	+	0.0724882i
$913$	5592.35	−	31715.8i	0.202716	−	1.14966i
$914$	399.273	−	691.561i	0.0144494	−	0.0250271i
$915$	3099.36	+	5368.24i	0.111980	+	0.193955i
$916$	−11196.9	+	4075.32i	−0.403880	+	0.147000i
$917$	7574.63	−	13119.6i	0.272777	−	0.472463i
$918$	−27369.2	+	22965.5i	−0.984007	+	0.825679i
$919$	−10274.6			−0.368799			−0.184400	−	0.982851i	$-0.559034\pi$
$919$	−10274.6			−0.368799			−0.184400	+	0.982851i	$0.559034\pi$
$920$	−5858.62	+	4915.97i	−0.209949	+	0.176168i
$921$	20085.4	+	7310.50i	0.718607	+	0.261552i
$922$	−3114.22	−	17661.6i	−0.111238	−	0.630862i
$923$	5591.21	−	31709.3i	0.199390	−	1.13080i
$924$	−4902.82			−0.174557
$925$	−8380.40	−	375.968i	−0.297887	−	0.0133641i
$926$	−1145.28			−0.0406439
$927$	−2172.68	+	12321.9i	−0.0769797	+	0.436574i
$928$	681.188	+	3863.21i	0.0240960	+	0.136655i
$929$	−20875.1	−	7597.93i	−0.737235	−	0.268332i	−0.0540109	−	0.998540i	$-0.517201\pi$
$929$	−20875.1	−	7597.93i	−0.737235	−	0.268332i	−0.683224	+	0.730209i	$0.739423\pi$
$930$	−2724.31	+	2285.97i	−0.0960577	+	0.0806020i
$931$	29749.1			1.04725
$932$	19512.5	−	16373.0i	0.685788	−	0.575445i
$933$	−3393.93	+	5878.45i	−0.119091	+	0.206272i
$934$	18913.3	−	6883.89i	0.662594	−	0.241165i
$935$	25255.4	+	43743.6i	0.883358	+	1.53002i
$936$	−3423.31	+	5929.35i	−0.119545	+	0.207059i
$937$	877.462	−	4976.33i	0.0305928	−	0.173500i	−0.965683	−	0.259723i	$-0.916369\pi$
$937$	877.462	−	4976.33i	0.0305928	−	0.173500i	0.996276	+	0.0862231i	$0.0274798\pi$
$938$	12387.3	+	4508.62i	0.431195	+	0.156942i
$939$	−1555.15	−	2693.60i	−0.0540473	−	0.0936127i
$940$	9344.47	+	7840.94i	0.324237	+	0.272067i
$941$	17831.5	+	14962.4i	0.617735	+	0.518342i	0.897091	−	0.441846i	$-0.145676\pi$
$941$	17831.5	+	14962.4i	0.617735	+	0.518342i	−0.279355	+	0.960188i	$0.590121\pi$
$942$	2139.01	−	778.534i	0.0739836	−	0.0269278i
$943$	−1436.27	−	8145.47i	−0.0495983	−	0.281286i
$944$	491.760	+	2788.91i	0.0169549	+	0.0961561i
$945$	11248.7	−	4094.18i	0.387216	−	0.140935i
$946$	−2568.90	−	2155.56i	−0.0882897	−	0.0740838i
$947$	−23099.4	−	19382.7i	−0.792638	−	0.665103i	0.153759	−	0.988108i	$-0.450862\pi$
$947$	−23099.4	−	19382.7i	−0.792638	−	0.665103i	−0.946397	+	0.323006i	$0.895307\pi$
$948$	304.174	+	526.844i	0.0104210	+	0.0180497i
$949$	27537.0	+	10022.6i	0.941926	+	0.342833i
$950$	1486.59	−	8430.86i	0.0507698	−	0.287930i
$951$	7624.16	−	13205.4i	0.259969	−	0.450279i
$952$	−4693.69	−	8129.71i	−0.159793	−	0.276770i
$953$	20156.8	−	7336.47i	0.685144	−	0.249372i	0.0240896	−	0.999710i	$-0.492331\pi$
$953$	20156.8	−	7336.47i	0.685144	−	0.249372i	0.661055	+	0.750338i	$0.270109\pi$
$954$	−8840.72	+	15312.6i	−0.300030	+	0.519668i
$955$	−9334.41	+	7832.50i	−0.316287	+	0.265396i
$956$	−7944.51			−0.268770
$957$	−12562.4	+	10541.1i	−0.424332	+	0.356057i
$958$	26157.6	+	9520.59i	0.882165	+	0.321082i
$959$	−4286.21	−	24308.3i	−0.144326	−	0.818516i
$960$	330.683	−	1875.40i	0.0111175	−	0.0630502i
$961$	−26219.7			−0.880123
$962$	21039.5	+	8744.43i	0.705136	+	0.293068i
$963$	−34948.1			−1.16946
$964$	−3194.79	+	18118.6i	−0.106740	+	0.605352i
$965$	−6796.95	−	38547.4i	−0.226737	−	1.28589i
$966$	5583.56	+	2032.25i	0.185971	+	0.0676879i
$967$	39814.6	−	33408.4i	1.32404	−	1.11100i	0.338614	−	0.940926i	$-0.390042\pi$
$967$	39814.6	−	33408.4i	1.32404	−	1.11100i	0.985430	−	0.170079i	$-0.0544024\pi$
$968$	3537.48			0.117457
$969$	−35791.8	+	30032.9i	−1.18658	+	0.995661i
$970$	7628.31	−	13212.6i	0.252505	−	0.437352i
$971$	11389.1	−	4145.28i	0.376408	−	0.137001i	−0.146886	−	0.989153i	$-0.546925\pi$
$971$	11389.1	−	4145.28i	0.376408	−	0.137001i	0.523294	+	0.852152i	$0.324703\pi$
$972$	−7617.32	−	13193.6i	−0.251364	−	0.435375i
$973$	−3150.11	+	5456.14i	−0.103790	+	0.179770i
$974$	−6018.08	+	34130.3i	−0.197979	+	1.12280i
$975$	−5632.29	−	2049.99i	−0.185003	−	0.0673355i
$976$	1666.59	+	2886.62i	0.0546581	+	0.0946707i
$977$	35694.8	+	29951.5i	1.16886	+	0.980792i	0.999988	−	0.00484602i	$-0.00154254\pi$
$977$	35694.8	+	29951.5i	1.16886	+	0.980792i	0.168874	+	0.985638i	$0.445987\pi$
$978$	16481.4	+	13829.5i	0.538871	+	0.452167i
$979$	−6419.45	+	2336.49i	−0.209567	+	0.0762763i
$980$	−1685.30	−	9557.82i	−0.0549337	−	0.311544i
$981$	1719.09	+	9749.44i	0.0559493	+	0.317304i
$982$	−31143.5	+	11335.3i	−1.01205	+	0.368355i
$983$	26354.9	+	22114.4i	0.855127	+	0.717537i	0.960913	−	0.276852i	$-0.0892911\pi$
$983$	26354.9	+	22114.4i	0.855127	+	0.717537i	−0.105785	+	0.994389i	$0.533736\pi$
$984$	1577.68	+	1323.83i	0.0511124	+	0.0428884i
$985$	−3489.44	−	6043.88i	−0.112876	−	0.195507i
$986$	−29505.6	−	10739.1i	−0.952991	−	0.346860i
$987$	1645.71	−	9333.31i	0.0530736	−	0.300995i
$988$	−11625.9	+	20136.6i	−0.374360	+	0.648411i
$989$	2032.08	+	3519.67i	0.0653352	+	0.113164i
$990$	−12532.6	+	4561.49i	−0.402336	+	0.146438i
$991$	−6313.82	+	10935.9i	−0.202387	+	0.350544i	−0.949297	−	0.314381i	$-0.898203\pi$
$991$	−6313.82	+	10935.9i	−0.202387	+	0.350544i	0.746910	+	0.664925i	$0.231536\pi$
$992$	−1464.92	+	1229.22i	−0.0468864	+	0.0393424i
$993$	−16172.4			−0.516834
$994$	−8929.53	+	7492.77i	−0.284937	+	0.239091i
$995$	−40463.0	−	14727.3i	−1.28921	−	0.469234i
$996$	−1687.62	−	9570.96i	−0.0536890	−	0.304485i
$997$	4201.89	−	23830.1i	0.133476	−	0.756977i	−0.842434	−	0.538800i	$-0.818878\pi$
$997$	4201.89	−	23830.1i	0.133476	−	0.756977i	0.975909	−	0.218177i	$-0.0700111\pi$
$998$	11393.3			0.361370
$999$	−24929.0	+	19081.2i	−0.789508	+	0.604308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.f.b.33.4	yes	30
37.9	even	9	inner	74.4.f.b.9.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.f.b.9.4	✓	30	37.9	even	9	inner
74.4.f.b.33.4	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347296 - 1.96962i) q^{2} +(0.551654 + 3.12858i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.17496 - 6.02051i) q^{5} +6.35370 q^{6} +(7.01886 - 5.88953i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(15.8880 - 5.78275i) q^{9} +O(q^{10})\)	\(q+(0.347296 - 1.96962i) q^{2} +(0.551654 + 3.12858i) q^{3} +(-3.75877 - 1.36808i) q^{4} +(7.17496 - 6.02051i) q^{5} +6.35370 q^{6} +(7.01886 - 5.88953i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(15.8880 - 5.78275i) q^{9} +(-9.36625 - 16.2228i) q^{10} +(21.0546 - 36.4676i) q^{11} +(2.20662 - 12.5143i) q^{12} +(47.5652 + 17.3123i) q^{13} +(-9.16248 - 15.8699i) q^{14} +(22.7938 + 19.1262i) q^{15} +(12.2567 + 10.2846i) q^{16} +(-120.345 + 43.8019i) q^{17} +(-5.87196 - 33.3015i) q^{18} +(-19.9417 - 113.095i) q^{19} +(-35.2056 + 12.8138i) q^{20} +(22.2979 + 18.7101i) q^{21} +(-64.5150 - 54.1345i) q^{22} +(51.0336 + 88.3927i) q^{23} +(-23.8821 - 8.69237i) q^{24} +(-6.47246 + 36.7071i) q^{25} +(50.6179 - 87.6727i) q^{26} +(69.7439 + 120.800i) q^{27} +(-34.4396 + 12.5350i) q^{28} +(-61.2938 + 106.164i) q^{29} +(45.5875 - 38.2525i) q^{30} -59.7600 q^{31} +(24.5134 - 20.5692i) q^{32} +(125.707 + 45.7536i) q^{33} +(44.4776 + 252.245i) q^{34} +(14.9021 - 84.5143i) q^{35} -67.6305 q^{36} +(29.1088 + 223.172i) q^{37} -229.679 q^{38} +(-27.9235 + 158.362i) q^{39} +(13.0115 + 73.7916i) q^{40} +(-76.1491 - 27.7160i) q^{41} +(44.5957 - 37.4203i) q^{42} +39.8186 q^{43} +(-129.030 + 108.269i) q^{44} +(79.1806 - 137.145i) q^{45} +(191.823 - 69.8180i) q^{46} +(-162.796 - 281.972i) q^{47} +(-25.4148 + 44.0197i) q^{48} +(-44.9834 + 255.113i) q^{49} +(70.0511 + 25.4965i) q^{50} +(-203.427 - 352.345i) q^{51} +(-155.102 - 130.146i) q^{52} +(-400.552 - 336.103i) q^{53} +(262.151 - 95.4153i) q^{54} +(-68.4877 - 388.413i) q^{55} +(12.7284 + 72.1862i) q^{56} +(342.826 - 124.778i) q^{57} +(187.815 + 157.596i) q^{58} +(135.587 + 113.771i) q^{59} +(-59.5103 - 103.075i) q^{60} +(195.761 + 71.2510i) q^{61} +(-20.7544 + 117.704i) q^{62} +(77.4579 - 134.161i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(445.508 - 162.152i) q^{65} +(133.775 - 231.704i) q^{66} +(-551.065 + 462.398i) q^{67} +512.273 q^{68} +(-248.391 + 208.425i) q^{69} +(-161.285 - 58.7030i) q^{70} +(-110.459 - 626.446i) q^{71} +(-23.4878 + 133.206i) q^{72} +578.930 q^{73} +(449.672 + 20.1735i) q^{74} -118.412 q^{75} +(-79.7667 + 452.380i) q^{76} +(-66.9977 - 379.963i) q^{77} +(302.215 + 109.997i) q^{78} +(-36.6732 + 30.7725i) q^{79} +149.860 q^{80} +(10.2453 - 8.59681i) q^{81} +(-81.0361 + 140.359i) q^{82} +(718.676 - 261.577i) q^{83} +(-58.2156 - 100.832i) q^{84} +(-599.760 + 1038.81i) q^{85} +(13.8288 - 78.4273i) q^{86} +(-365.956 - 133.197i) q^{87} +(168.437 + 291.741i) q^{88} +(-124.277 - 104.280i) q^{89} +(-242.623 - 203.585i) q^{90} +(435.815 - 158.624i) q^{91} +(-70.8951 - 402.066i) q^{92} +(-32.9668 - 186.964i) q^{93} +(-611.914 + 222.719i) q^{94} +(-823.970 - 691.393i) q^{95} +(77.8754 + 65.3452i) q^{96} +(407.223 + 705.332i) q^{97} +(486.853 + 177.200i) q^{98} +(123.632 - 701.151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more