LMFDB - Embedded newform 201.4.e.a.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	201.37
Dual form			201.4.e.a.163.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18517 + 2.05278i) q^{2} +3.00000 q^{3} +(1.19074 - 2.06242i) q^{4} -8.96032 q^{5} +(3.55551 + 6.15833i) q^{6} +(-14.9139 + 25.8316i) q^{7} +24.6077 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(1.18517 + 2.05278i) q^{2} +3.00000 q^{3} +(1.19074 - 2.06242i) q^{4} -8.96032 q^{5} +(3.55551 + 6.15833i) q^{6} +(-14.9139 + 25.8316i) q^{7} +24.6077 q^{8} +9.00000 q^{9} +(-10.6195 - 18.3935i) q^{10} +(-20.9257 + 36.2445i) q^{11} +(3.57221 - 6.18725i) q^{12} +(7.86066 + 13.6151i) q^{13} -70.7020 q^{14} -26.8810 q^{15} +(19.6384 + 34.0147i) q^{16} +(17.4927 + 30.2983i) q^{17} +(10.6665 + 18.4750i) q^{18} +(25.6030 + 44.3457i) q^{19} +(-10.6694 + 18.4799i) q^{20} +(-44.7416 + 77.4947i) q^{21} -99.2024 q^{22} +(76.1826 + 131.952i) q^{23} +73.8230 q^{24} -44.7126 q^{25} +(-18.6325 + 32.2724i) q^{26} +27.0000 q^{27} +(35.5170 + 61.5173i) q^{28} +(61.3602 - 106.279i) q^{29} +(-31.8586 - 55.1806i) q^{30} +(-4.58598 + 7.94315i) q^{31} +(51.8809 - 89.8604i) q^{32} +(-62.7772 + 108.733i) q^{33} +(-41.4638 + 71.8174i) q^{34} +(133.633 - 231.459i) q^{35} +(10.7166 - 18.5618i) q^{36} +(-65.2098 - 112.947i) q^{37} +(-60.6879 + 105.114i) q^{38} +(23.5820 + 40.8452i) q^{39} -220.493 q^{40} +(152.158 - 263.546i) q^{41} -212.106 q^{42} -347.422 q^{43} +(49.8341 + 86.3153i) q^{44} -80.6429 q^{45} +(-180.579 + 312.772i) q^{46} +(-112.185 + 194.310i) q^{47} +(58.9152 + 102.044i) q^{48} +(-273.347 - 473.451i) q^{49} +(-52.9921 - 91.7850i) q^{50} +(52.4782 + 90.8950i) q^{51} +37.4399 q^{52} +37.8681 q^{53} +(31.9996 + 55.4250i) q^{54} +(187.501 - 324.762i) q^{55} +(-366.995 + 635.655i) q^{56} +(76.8090 + 133.037i) q^{57} +290.890 q^{58} +588.383 q^{59} +(-32.0082 + 55.4398i) q^{60} +(-398.785 - 690.715i) q^{61} -21.7407 q^{62} +(-134.225 + 232.484i) q^{63} +560.165 q^{64} +(-70.4340 - 121.995i) q^{65} -297.607 q^{66} +(-27.3314 + 547.737i) q^{67} +83.3171 q^{68} +(228.548 + 395.857i) q^{69} +633.512 q^{70} +(156.758 - 271.512i) q^{71} +221.469 q^{72} +(179.051 + 310.125i) q^{73} +(154.569 - 267.722i) q^{74} -134.138 q^{75} +121.946 q^{76} +(-624.168 - 1081.09i) q^{77} +(-55.8974 + 96.8171i) q^{78} +(274.369 - 475.222i) q^{79} +(-175.966 - 304.783i) q^{80} +81.0000 q^{81} +721.334 q^{82} +(-124.102 - 214.950i) q^{83} +(106.551 + 184.552i) q^{84} +(-156.741 - 271.483i) q^{85} +(-411.755 - 713.181i) q^{86} +(184.081 - 318.837i) q^{87} +(-514.934 + 891.891i) q^{88} +1399.13 q^{89} +(-95.5757 - 165.542i) q^{90} -468.931 q^{91} +362.854 q^{92} +(-13.7579 + 23.8294i) q^{93} -531.833 q^{94} +(-229.411 - 397.352i) q^{95} +(155.643 - 269.581i) q^{96} +(281.023 + 486.747i) q^{97} +(647.926 - 1122.24i) q^{98} +(-188.332 + 326.200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.18517	+	2.05278i	0.419021	+	0.725766i	0.995841	−	0.0911050i	$-0.0290399\pi$
$2$	1.18517	+	2.05278i	0.419021	+	0.725766i	−0.576820	+	0.816871i	$0.695707\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	1.19074	−	2.06242i	0.148842	−	0.257802i
$5$	−8.96032			−0.801436			−0.400718	−	0.916201i	$-0.631239\pi$
$5$	−8.96032			−0.801436			−0.400718	+	0.916201i	$0.631239\pi$
$6$	3.55551	+	6.15833i	0.241922	+	0.419021i
$7$	−14.9139	+	25.8316i	−0.805273	+	1.39477i	0.110833	+	0.993839i	$0.464648\pi$
$7$	−14.9139	+	25.8316i	−0.805273	+	1.39477i	−0.916106	+	0.400935i	$0.868685\pi$
$8$	24.6077			1.08751
$9$	9.00000			0.333333
$10$	−10.6195	−	18.3935i	−0.335819	−	0.581655i
$11$	−20.9257	+	36.2445i	−0.573577	+	0.993465i	0.422617	+	0.906308i	$0.361111\pi$
$11$	−20.9257	+	36.2445i	−0.573577	+	0.993465i	−0.996195	+	0.0871567i	$0.972222\pi$
$12$	3.57221	−	6.18725i	0.0859341	−	0.148842i
$13$	7.86066	+	13.6151i	0.167704	+	0.290472i	0.937612	−	0.347683i	$-0.113031\pi$
$13$	7.86066	+	13.6151i	0.167704	+	0.290472i	−0.769908	+	0.638155i	$0.779698\pi$
$14$	−70.7020			−1.34971
$15$	−26.8810			−0.462709
$16$	19.6384	+	34.0147i	0.306850	+	0.531479i
$17$	17.4927	+	30.2983i	0.249565	+	0.432260i	0.963405	−	0.268049i	$-0.0863789\pi$
$17$	17.4927	+	30.2983i	0.249565	+	0.432260i	−0.713840	+	0.700309i	$0.753046\pi$
$18$	10.6665	+	18.4750i	0.139674	+	0.241922i
$19$	25.6030	+	44.3457i	0.309144	+	0.535453i	0.978175	−	0.207781i	$-0.0666243\pi$
$19$	25.6030	+	44.3457i	0.309144	+	0.535453i	−0.669032	+	0.743234i	$0.733291\pi$
$20$	−10.6694	+	18.4799i	−0.119287	+	0.206612i
$21$	−44.7416	+	77.4947i	−0.464925	+	0.805273i
$22$	−99.2024			−0.961364
$23$	76.1826	+	131.952i	0.690660	+	1.19626i	0.971622	+	0.236539i	$0.0760131\pi$
$23$	76.1826	+	131.952i	0.690660	+	1.19626i	−0.280962	+	0.959719i	$0.590654\pi$
$24$	73.8230			0.627877
$25$	−44.7126			−0.357701
$26$	−18.6325	+	32.2724i	−0.140543	+	0.243428i
$27$	27.0000			0.192450
$28$	35.5170	+	61.5173i	0.239717	+	0.415202i
$29$	61.3602	−	106.279i	0.392907	−	0.680535i	−0.599924	−	0.800057i	$-0.704803\pi$
$29$	61.3602	−	106.279i	0.392907	−	0.680535i	0.992832	+	0.119521i	$0.0381360\pi$
$30$	−31.8586	−	55.1806i	−0.193885	−	0.335819i
$31$	−4.58598	+	7.94315i	−0.0265699	+	0.0460204i	−0.879005	−	0.476813i	$-0.841792\pi$
$31$	−4.58598	+	7.94315i	−0.0265699	+	0.0460204i	0.852435	+	0.522834i	$0.175125\pi$
$32$	51.8809	−	89.8604i	0.286604	−	0.496413i
$33$	−62.7772	+	108.733i	−0.331155	+	0.573577i
$34$	−41.4638	+	71.8174i	−0.209147	+	0.362252i
$35$	133.633	−	231.459i	0.645375	−	1.11782i
$36$	10.7166	−	18.5618i	0.0496141	−	0.0859341i
$37$	−65.2098	−	112.947i	−0.289741	−	0.501846i	0.684007	−	0.729476i	$-0.260236\pi$
$37$	−65.2098	−	112.947i	−0.289741	−	0.501846i	−0.973748	+	0.227629i	$0.926903\pi$
$38$	−60.6879	+	105.114i	−0.259076	+	0.448732i
$39$	23.5820	+	40.8452i	0.0968241	+	0.167704i
$40$	−220.493			−0.871573
$41$	152.158	−	263.546i	0.579588	−	1.00388i	−0.415939	−	0.909393i	$-0.636547\pi$
$41$	152.158	−	263.546i	0.579588	−	1.00388i	0.995526	−	0.0944828i	$-0.0301197\pi$
$42$	−212.106			−0.779254
$43$	−347.422			−1.23213			−0.616063	−	0.787697i	$-0.711273\pi$
$43$	−347.422			−1.23213			−0.616063	+	0.787697i	$0.711273\pi$
$44$	49.8341	+	86.3153i	0.170745	+	0.295739i
$45$	−80.6429			−0.267145
$46$	−180.579	+	312.772i	−0.578802	+	1.00252i
$47$	−112.185	+	194.310i	−0.348167	+	0.603043i	−0.985924	−	0.167195i	$-0.946529\pi$
$47$	−112.185	+	194.310i	−0.348167	+	0.603043i	0.637757	+	0.770238i	$0.279862\pi$
$48$	58.9152	+	102.044i	0.177160	+	0.306850i
$49$	−273.347	−	473.451i	−0.796930	−	1.38032i
$50$	−52.9921	−	91.7850i	−0.149884	−	0.259607i
$51$	52.4782	+	90.8950i	0.144087	+	0.249565i
$52$	37.4399			0.0998458
$53$	37.8681			0.0981430			0.0490715	−	0.998795i	$-0.484374\pi$
$53$	37.8681			0.0981430			0.0490715	+	0.998795i	$0.484374\pi$
$54$	31.9996	+	55.4250i	0.0806407	+	0.139674i
$55$	187.501	−	324.762i	0.459685	−	0.796198i
$56$	−366.995	+	635.655i	−0.875747	+	1.51684i
$57$	76.8090	+	133.037i	0.178484	+	0.309144i
$58$	290.890			0.658546
$59$	588.383			1.29832			0.649160	−	0.760651i	$-0.275120\pi$
$59$	588.383			1.29832			0.649160	+	0.760651i	$0.275120\pi$
$60$	−32.0082	+	55.4398i	−0.0688706	+	0.119287i
$61$	−398.785	−	690.715i	−0.837035	−	1.44979i	−0.892363	−	0.451319i	$-0.850954\pi$
$61$	−398.785	−	690.715i	−0.837035	−	1.44979i	0.0553279	−	0.998468i	$-0.482380\pi$
$62$	−21.7407			−0.0445334
$63$	−134.225	+	232.484i	−0.268424	+	0.464925i
$64$	560.165			1.09407
$65$	−70.4340	−	121.995i	−0.134404	−	0.232795i
$66$	−297.607			−0.555044
$67$	−27.3314	+	547.737i	−0.0498367	+	0.998757i
$67$	−27.3314	+	547.737i	−0.0498367	+	0.998757i
$68$	83.3171			0.148584
$69$	228.548	+	395.857i	0.398753	+	0.690660i
$70$	633.512			1.08170
$71$	156.758	−	271.512i	0.262024	−	0.453839i	−0.704756	−	0.709450i	$-0.748943\pi$
$71$	156.758	−	271.512i	0.262024	−	0.453839i	0.966780	+	0.255611i	$0.0822767\pi$
$72$	221.469			0.362505
$73$	179.051	+	310.125i	0.287072	+	0.497224i	0.973110	−	0.230342i	$-0.0739846\pi$
$73$	179.051	+	310.125i	0.287072	+	0.497224i	−0.686037	+	0.727566i	$0.740651\pi$
$74$	154.569	−	267.722i	0.242815	−	0.420569i
$75$	−134.138			−0.206519
$76$	121.946			0.184054
$77$	−624.168	−	1081.09i	−0.923773	−	1.60002i
$78$	−55.8974	+	96.8171i	−0.0811427	+	0.140543i
$79$	274.369	−	475.222i	0.390747	−	0.676793i	−0.601802	−	0.798646i	$-0.705550\pi$
$79$	274.369	−	475.222i	0.390747	−	0.676793i	0.992548	+	0.121853i	$0.0388836\pi$
$80$	−175.966	−	304.783i	−0.245920	−	0.425947i
$81$	81.0000			0.111111
$82$	721.334			0.971439
$83$	−124.102	−	214.950i	−0.164120	−	0.284263i	0.772223	−	0.635352i	$-0.219145\pi$
$83$	−124.102	−	214.950i	−0.164120	−	0.284263i	−0.936342	+	0.351089i	$0.885812\pi$
$84$	106.551	+	184.552i	0.138401	+	0.239717i
$85$	−156.741	−	271.483i	−0.200011	−	0.346429i
$86$	−411.755	−	713.181i	−0.516287	−	0.894236i
$87$	184.081	−	318.837i	0.226845	−	0.392907i
$88$	−514.934	+	891.891i	−0.623774	+	1.08041i
$89$	1399.13			1.66638			0.833188	−	0.552990i	$-0.186513\pi$
$89$	1399.13			1.66638			0.833188	+	0.552990i	$0.186513\pi$
$90$	−95.5757	−	165.542i	−0.111940	−	0.193885i
$91$	−468.931			−0.540191
$92$	362.854			0.411197
$93$	−13.7579	+	23.8294i	−0.0153401	+	0.0265699i
$94$	−531.833			−0.583557
$95$	−229.411	−	397.352i	−0.247759	−	0.429131i
$96$	155.643	−	269.581i	0.165471	−	0.286604i
$97$	281.023	+	486.747i	0.294161	+	0.509501i	0.974789	−	0.223127i	$-0.0716266\pi$
$97$	281.023	+	486.747i	0.294161	+	0.509501i	−0.680629	+	0.732629i	$0.738293\pi$
$98$	647.926	−	1122.24i	0.667861	−	1.15677i
$99$	−188.332	+	326.200i	−0.191192	+	0.331155i
$100$	−53.2410	+	92.2161i	−0.0532410	+	0.0922161i
$101$	−393.738	+	681.975i	−0.387905	+	0.671872i	−0.992168	−	0.124914i	$-0.960135\pi$
$101$	−393.738	+	681.975i	−0.387905	+	0.671872i	0.604262	+	0.796785i	$0.293468\pi$
$102$	−124.391	+	215.452i	−0.120751	+	0.209147i
$103$	−822.035	+	1423.81i	−0.786384	+	1.36206i	0.141785	+	0.989897i	$0.454716\pi$
$103$	−822.035	+	1423.81i	−0.786384	+	1.36206i	−0.928169	+	0.372159i	$0.878618\pi$
$104$	193.432	+	335.035i	0.182381	+	0.315893i
$105$	400.899	−	694.378i	0.372607	−	0.645375i
$106$	44.8801	+	77.7347i	0.0411240	+	0.0712288i
$107$	1673.96			1.51241			0.756205	−	0.654334i	$-0.227051\pi$
$107$	1673.96			1.51241			0.756205	+	0.654334i	$0.227051\pi$
$108$	32.1499	−	55.6853i	0.0286447	−	0.0496141i
$109$	1776.92			1.56145			0.780724	−	0.624876i	$-0.214851\pi$
$109$	1776.92			1.56145			0.780724	+	0.624876i	$0.214851\pi$
$110$	888.885			0.770472
$111$	−195.629	−	338.840i	−0.167282	−	0.289741i
$112$	−1171.54			−0.988392
$113$	833.281	−	1443.28i	0.693703	−	1.20153i	−0.276913	−	0.960895i	$-0.589311\pi$
$113$	833.281	−	1443.28i	0.693703	−	1.20153i	0.970616	−	0.240634i	$-0.0773553\pi$
$114$	−182.064	+	315.343i	−0.149577	+	0.259076i
$115$	−682.621	−	1182.33i	−0.553519	−	0.958724i
$116$	−146.128	−	253.101i	−0.116962	−	0.202585i
$117$	70.7459	+	122.536i	0.0559014	+	0.0968241i
$118$	697.335	+	1207.82i	0.544024	+	0.942278i
$119$	−1043.54			−0.803874
$120$	−661.478			−0.503203
$121$	−210.274	−	364.205i	−0.157982	−	0.273632i
$122$	945.256	−	1637.23i	0.701471	−	1.21498i
$123$	456.474	−	790.637i	0.334625	−	0.579588i
$124$	10.9214	+	18.9164i	0.00790944	+	0.0136995i
$125$	1520.68			1.08811
$126$	−636.318			−0.449902
$127$	−423.184	+	732.976i	−0.295681	+	0.512134i	−0.975143	−	0.221576i	$-0.928880\pi$
$127$	−423.184	+	732.976i	−0.295681	+	0.512134i	0.679462	+	0.733711i	$0.262213\pi$
$128$	248.845	+	431.011i	0.171836	+	0.297628i
$129$	−1042.27			−0.711368
$130$	166.953	−	289.171i	0.112636	−	0.195092i
$131$	−774.417			−0.516497			−0.258249	−	0.966079i	$-0.583145\pi$
$131$	−774.417			−0.516497			−0.258249	+	0.966079i	$0.583145\pi$
$132$	149.502	+	258.946i	0.0985797	+	0.170745i
$133$	−1527.36			−0.995780
$134$	−1156.77	+	593.057i	−0.745747	+	0.382331i
$135$	−241.929			−0.154236
$136$	430.455	+	745.571i	0.271406	+	0.470089i
$137$	−224.371			−0.139922			−0.0699610	−	0.997550i	$-0.522287\pi$
$137$	−224.371			−0.139922			−0.0699610	+	0.997550i	$0.522287\pi$
$138$	−541.737	+	938.316i	−0.334172	+	0.578802i
$139$	−2166.71			−1.32214			−0.661072	−	0.750322i	$-0.729898\pi$
$139$	−2166.71			−1.32214			−0.661072	+	0.750322i	$0.729898\pi$
$140$	−318.244	−	551.215i	−0.192118	−	0.332758i
$141$	−336.555	+	582.930i	−0.201014	+	0.348167i
$142$	743.138			0.439175
$143$	−657.961			−0.384765
$144$	176.745	+	306.132i	0.102283	+	0.177160i
$145$	−549.808	+	952.295i	−0.314890	+	0.545405i
$146$	−424.411	+	735.102i	−0.240579	+	0.416695i
$147$	−820.041	−	1420.35i	−0.460108	−	0.796930i
$148$	−310.591			−0.172503
$149$	340.055			0.186969			0.0934846	−	0.995621i	$-0.470199\pi$
$149$	340.055			0.186969			0.0934846	+	0.995621i	$0.470199\pi$
$150$	−158.976	−	275.355i	−0.0865357	−	0.149884i
$151$	657.608	+	1139.01i	0.354406	+	0.613850i	0.987016	−	0.160621i	$-0.0513496\pi$
$151$	657.608	+	1139.01i	0.354406	+	0.613850i	−0.632610	+	0.774471i	$0.718016\pi$
$152$	630.030	+	1091.24i	0.336198	+	0.582313i
$153$	157.435	+	272.685i	0.0831885	+	0.144087i
$154$	1479.49	−	2562.55i	0.774161	−	1.34089i
$155$	41.0919	−	71.1732i	0.0212941	−	0.0368824i
$156$	112.320			0.0576460
$157$	1061.52	+	1838.61i	0.539609	+	0.934630i	0.998925	+	0.0463572i	$0.0147612\pi$
$157$	1061.52	+	1838.61i	0.539609	+	0.934630i	−0.459316	+	0.888273i	$0.651905\pi$
$158$	1300.70			0.654925
$159$	113.604			0.0566629
$160$	−464.870	+	805.178i	−0.229695	+	0.397843i
$161$	−4544.71			−2.22468
$162$	95.9989	+	166.275i	0.0465579	+	0.0806407i
$163$	1544.93	−	2675.89i	0.742380	−	1.28584i	−0.209028	−	0.977910i	$-0.567030\pi$
$163$	1544.93	−	2675.89i	0.742380	−	1.28584i	0.951409	−	0.307931i	$-0.0996366\pi$
$164$	−362.361	−	627.627i	−0.172534	−	0.298838i
$165$	562.504	−	974.286i	0.265399	−	0.459685i
$166$	294.163	−	509.506i	0.137539	−	0.238225i
$167$	−942.171	+	1631.89i	−0.436571	+	0.756163i	−0.997422	−	0.0717532i	$-0.977141\pi$
$167$	−942.171	+	1631.89i	−0.436571	+	0.756163i	0.560851	+	0.827917i	$0.310474\pi$
$168$	−1100.99	+	1906.96i	−0.505613	+	0.875747i
$169$	974.920	−	1688.61i	0.443751	−	0.768599i
$170$	371.529	−	643.507i	0.167618	−	0.290322i
$171$	230.427	+	399.111i	0.103048	+	0.178484i
$172$	−413.689	+	716.530i	−0.183392	+	0.317645i
$173$	−618.641	−	1071.52i	−0.271875	−	0.470901i	0.697467	−	0.716617i	$-0.254310\pi$
$173$	−618.641	−	1071.52i	−0.271875	−	0.470901i	−0.969342	+	0.245716i	$0.920977\pi$
$174$	872.669			0.380212
$175$	666.838	−	1155.00i	0.288047	−	0.498912i
$176$	−1643.79			−0.704008
$177$	1765.15			0.749586
$178$	1658.21	+	2872.10i	0.698247	+	1.20940i
$179$	627.500			0.262020			0.131010	−	0.991381i	$-0.458178\pi$
$179$	627.500			0.262020			0.131010	+	0.991381i	$0.458178\pi$
$180$	−96.0246	+	166.319i	−0.0397625	+	0.0688706i
$181$	−851.080	+	1474.11i	−0.349504	+	0.605359i	−0.986161	−	0.165788i	$-0.946983\pi$
$181$	−851.080	+	1474.11i	−0.349504	+	0.605359i	0.636657	+	0.771147i	$0.280317\pi$
$182$	−555.764	−	962.611i	−0.226351	−	0.392052i
$183$	−1196.35	−	2072.15i	−0.483262	−	0.837035i
$184$	1874.68	+	3247.03i	0.751103	+	1.30095i
$185$	584.301	+	1012.04i	0.232209	+	0.402198i
$186$	−65.2221			−0.0257114
$187$	−1464.19			−0.572580
$188$	267.165	+	462.744i	0.103644	+	0.179516i
$189$	−402.674	+	697.453i	−0.154975	+	0.268424i
$190$	543.783	−	941.860i	0.207632	−	0.359630i
$191$	−314.476	−	544.689i	−0.119135	−	0.206347i	0.800290	−	0.599613i	$-0.204679\pi$
$191$	−314.476	−	544.689i	−0.119135	−	0.206347i	−0.919425	+	0.393266i	$0.871345\pi$
$192$	1680.50			0.631663
$193$	629.633			0.234829			0.117415	−	0.993083i	$-0.462539\pi$
$193$	629.633			0.234829			0.117415	+	0.993083i	$0.462539\pi$
$194$	−666.122	+	1153.76i	−0.246519	+	0.426984i
$195$	−211.302	−	365.986i	−0.0775983	−	0.134404i
$196$	−1301.94			−0.474467
$197$	−2124.21	+	3679.24i	−0.768243	+	1.33064i	0.170272	+	0.985397i	$0.445535\pi$
$197$	−2124.21	+	3679.24i	−0.768243	+	1.33064i	−0.938515	+	0.345239i	$0.887798\pi$
$198$	−892.821			−0.320455
$199$	−1096.05	−	1898.41i	−0.390436	−	0.676255i	0.602071	−	0.798442i	$-0.294342\pi$
$199$	−1096.05	−	1898.41i	−0.390436	−	0.676255i	−0.992507	+	0.122188i	$0.961009\pi$
$200$	−1100.27			−0.389005
$201$	−81.9941	+	1643.21i	−0.0287732	+	0.576633i
$202$	−1866.59			−0.650162
$203$	1830.24	+	3170.06i	0.632795	+	1.09603i
$204$	249.951			0.0857847
$205$	−1363.39	+	2361.45i	−0.464502	+	0.804542i
$206$	−3897.01			−1.31805
$207$	685.644	+	1187.57i	0.230220	+	0.398753i
$208$	−308.741	+	534.756i	−0.102920	+	0.178263i
$209$	−2143.05			−0.709271
$210$	1900.54			0.624522
$211$	−1080.81	−	1872.02i	−0.352636	−	0.610783i	0.634075	−	0.773272i	$-0.281381\pi$
$211$	−1080.81	−	1872.02i	−0.352636	−	0.610783i	−0.986710	+	0.162489i	$0.948048\pi$
$212$	45.0909	−	78.0998i	0.0146078	−	0.0253015i
$213$	470.273	−	814.536i	0.151280	−	0.262024i
$214$	1983.93	+	3436.27i	0.633732	+	1.09766i
$215$	3113.02			0.987470
$216$	664.407			0.209292
$217$	−136.789	−	236.926i	−0.0427920	−	0.0741180i
$218$	2105.95	+	3647.61i	0.654280	+	1.13325i
$219$	537.152	+	930.374i	0.165741	+	0.287072i
$220$	−446.530	−	773.413i	−0.136841	−	0.237016i
$221$	−275.009	+	476.329i	−0.0837064	+	0.144984i
$222$	463.708	−	803.167i	0.140190	−	0.242815i
$223$	−3198.34			−0.960432			−0.480216	−	0.877150i	$-0.659442\pi$
$223$	−3198.34			−0.960432			−0.480216	+	0.877150i	$0.659442\pi$
$224$	1547.49	+	2680.33i	0.461589	+	0.799496i
$225$	−402.413			−0.119234
$226$	3950.32			1.16271
$227$	1121.11	−	1941.82i	0.327800	−	0.567767i	−0.654275	−	0.756257i	$-0.727026\pi$
$227$	1121.11	−	1941.82i	0.327800	−	0.567767i	0.982075	+	0.188490i	$0.0603594\pi$
$228$	365.837			0.106264
$229$	−2317.90	−	4014.72i	−0.668869	−	1.15852i	−0.978221	−	0.207567i	$-0.933445\pi$
$229$	−2317.90	−	4014.72i	−0.668869	−	1.15852i	0.309352	−	0.950948i	$-0.399888\pi$
$230$	1618.05	−	2802.54i	0.463873	−	0.803452i
$231$	−1872.50	−	3243.27i	−0.533340	−	0.923773i
$232$	1509.93	−	2615.28i	0.427293	−	0.740092i
$233$	−888.915	+	1539.65i	−0.249935	+	0.432900i	−0.963507	−	0.267682i	$-0.913742\pi$
$233$	−888.915	+	1539.65i	−0.249935	+	0.432900i	0.713573	+	0.700581i	$0.247076\pi$
$234$	−167.692	+	290.451i	−0.0468478	+	0.0811427i
$235$	1005.21	−	1741.08i	0.279033	−	0.483300i
$236$	700.610	−	1213.49i	0.193245	−	0.334710i
$237$	823.108	−	1425.67i	0.225598	−	0.390747i
$238$	−1236.77	−	2142.15i	−0.336840	−	0.583424i
$239$	−1563.88	+	2708.72i	−0.423259	+	0.733106i	−0.996256	−	0.0864511i	$-0.972447\pi$
$239$	−1563.88	+	2708.72i	−0.423259	+	0.733106i	0.572997	+	0.819558i	$0.305781\pi$
$240$	−527.899	−	914.348i	−0.141982	−	0.245920i
$241$	2605.72			0.696470			0.348235	−	0.937407i	$-0.386781\pi$
$241$	2605.72			0.696470			0.348235	+	0.937407i	$0.386781\pi$
$242$	498.421	−	863.290i	0.132395	−	0.229316i
$243$	243.000			0.0641500
$244$	−1899.39			−0.498344
$245$	2449.28	+	4242.27i	0.638688	+	1.10624i
$246$	2164.00			0.560860
$247$	−402.513	+	697.173i	−0.103689	+	0.179595i
$248$	−112.850	+	195.462i	−0.0288951	+	0.0500479i
$249$	−372.305	−	644.851i	−0.0947544	−	0.164120i
$250$	1802.27	+	3121.62i	0.455941	+	0.789713i
$251$	2226.10	+	3855.72i	0.559802	+	0.969605i	0.997513	+	0.0704891i	$0.0224560\pi$
$251$	2226.10	+	3855.72i	0.559802	+	0.969605i	−0.437711	+	0.899116i	$0.644211\pi$
$252$	319.653	+	553.655i	0.0799058	+	0.138401i
$253$	−6376.71			−1.58459
$254$	−2006.18			−0.495587
$255$	−470.222	−	814.448i	−0.115476	−	0.200011i
$256$	1650.81	−	2859.29i	0.403031	−	0.698070i
$257$	3882.05	−	6723.91i	0.942241	−	1.63201i	0.181057	−	0.983473i	$-0.442048\pi$
$257$	3882.05	−	6723.91i	0.942241	−	1.63201i	0.761184	−	0.648536i	$-0.224619\pi$
$258$	−1235.27	−	2139.54i	−0.298079	−	0.516287i
$259$	3890.12			0.933283
$260$	−335.474			−0.0800200
$261$	552.242	−	956.512i	0.130969	−	0.226845i
$262$	−917.817	−	1589.71i	−0.216423	−	0.374856i
$263$	5985.14			1.40327			0.701634	−	0.712537i	$-0.252454\pi$
$263$	5985.14			1.40327			0.701634	+	0.712537i	$0.252454\pi$
$264$	−1544.80	+	2675.67i	−0.360136	+	0.623774i
$265$	−339.310			−0.0786553
$266$	−1810.18	−	3135.33i	−0.417253	−	0.722704i
$267$	4197.39			0.962082
$268$	1097.12	+	708.580i	0.250064	+	0.161505i
$269$	−5233.56			−1.18623			−0.593115	−	0.805118i	$-0.702102\pi$
$269$	−5233.56			−1.18623			−0.593115	+	0.805118i	$0.702102\pi$
$270$	−286.727	−	496.626i	−0.0646283	−	0.111940i
$271$	−2677.53			−0.600178			−0.300089	−	0.953911i	$-0.597016\pi$
$271$	−2677.53			−0.600178			−0.300089	+	0.953911i	$0.597016\pi$
$272$	−687.059	+	1190.02i	−0.153158	+	0.265278i
$273$	−1406.79			−0.311879
$274$	−265.918	−	460.584i	−0.0586303	−	0.101551i
$275$	935.644	−	1620.58i	0.205169	−	0.355363i
$276$	1088.56			0.237405
$277$	1155.64			0.250671			0.125335	−	0.992114i	$-0.459999\pi$
$277$	1155.64			0.250671			0.125335	+	0.992114i	$0.459999\pi$
$278$	−2567.93	−	4447.78i	−0.554007	−	0.959568i
$279$	−41.2738	+	71.4883i	−0.00885663	+	0.0153401i
$280$	3288.40	−	5695.67i	0.701855	−	1.21565i
$281$	−714.832	−	1238.12i	−0.151755	−	0.262848i	0.780117	−	0.625633i	$-0.215159\pi$
$281$	−714.832	−	1238.12i	−0.151755	−	0.262848i	−0.931873	+	0.362785i	$0.881826\pi$
$282$	−1595.50			−0.336917
$283$	3966.95			0.833254			0.416627	−	0.909078i	$-0.363212\pi$
$283$	3966.95			0.833254			0.416627	+	0.909078i	$0.363212\pi$
$284$	−373.314	−	646.599i	−0.0780005	−	0.135101i
$285$	−688.233	−	1192.06i	−0.143044	−	0.247759i
$286$	−779.796	−	1350.65i	−0.161225	−	0.279250i
$287$	4538.53	+	7860.97i	0.933453	+	1.61679i
$288$	466.928	−	808.743i	0.0955347	−	0.165471i
$289$	1844.51	−	3194.78i	0.375434	−	0.650271i
$290$	−2606.47			−0.527782
$291$	843.070	+	1460.24i	0.169834	+	0.294161i
$292$	852.809			0.170914
$293$	−6014.90			−1.19930			−0.599649	−	0.800263i	$-0.704693\pi$
$293$	−6014.90			−1.19930			−0.599649	+	0.800263i	$0.704693\pi$
$294$	1943.78	−	3366.72i	0.385590	−	0.667861i
$295$	−5272.10			−1.04052
$296$	−1604.66	−	2779.35i	−0.315098	−	0.545765i
$297$	−564.995	+	978.600i	−0.110385	+	0.191192i
$298$	403.024	+	698.058i	0.0783441	+	0.135696i
$299$	−1197.69	+	2074.46i	−0.231653	+	0.401235i
$300$	−159.723	+	276.648i	−0.0307387	+	0.0532410i
$301$	5181.41	−	8974.47i	0.992198	−	1.71854i
$302$	−1558.76	+	2699.84i	−0.297008	+	0.514432i
$303$	−1181.22	+	2045.92i	−0.223957	+	0.387905i
$304$	−1005.60	+	1741.76i	−0.189721	+	0.328607i
$305$	3573.24	+	6189.03i	0.670830	+	1.16191i
$306$	−373.174	+	646.357i	−0.0697155	+	0.120751i
$307$	−2507.21	−	4342.62i	−0.466105	−	0.807317i	0.533146	−	0.846023i	$-0.321010\pi$
$307$	−2507.21	−	4342.62i	−0.466105	−	0.807317i	−0.999251	+	0.0387060i	$0.987676\pi$
$308$	−2972.88			−0.549985
$309$	−2466.11	+	4271.42i	−0.454019	+	0.786384i
$310$	194.804			0.0356906
$311$	3331.71			0.607472			0.303736	−	0.952756i	$-0.401766\pi$
$311$	3331.71			0.607472			0.303736	+	0.952756i	$0.401766\pi$
$312$	580.297	+	1005.10i	0.105298	+	0.182381i
$313$	−5691.22			−1.02775			−0.513877	−	0.857864i	$-0.671791\pi$
$313$	−5691.22			−1.02775			−0.513877	+	0.857864i	$0.671791\pi$
$314$	−2516.17	+	4358.13i	−0.452215	+	0.783260i
$315$	1202.70	−	2083.13i	0.215125	−	0.372607i
$316$	−653.404	−	1131.73i	−0.116319	−	0.201471i
$317$	−2875.38	−	4980.30i	−0.509455	−	0.882402i	−0.999940	−	0.0109525i	$-0.996514\pi$
$317$	−2875.38	−	4980.30i	−0.509455	−	0.882402i	0.490485	−	0.871450i	$-0.336820\pi$
$318$	134.640	+	233.204i	0.0237429	+	0.0411240i
$319$	2568.02	+	4447.94i	0.450725	+	0.780679i
$320$	−5019.26			−0.876829
$321$	5021.88			0.873191
$322$	−5386.26	−	9329.28i	−0.932188	−	1.61460i
$323$	−895.733	+	1551.46i	−0.154303	+	0.267261i
$324$	96.4497	−	167.056i	0.0165380	−	0.0286447i
$325$	−351.470	−	608.765i	−0.0599879	−	0.103902i
$326$	7324.01			1.24429
$327$	5330.75			0.901502
$328$	3744.25	−	6485.24i	0.630310	−	1.09173i
$329$	−3346.22	−	5795.82i	−0.560739	−	0.971228i
$330$	2666.66			0.444832
$331$	4920.18	−	8522.01i	0.817032	−	1.41514i	−0.0908268	−	0.995867i	$-0.528951\pi$
$331$	4920.18	−	8522.01i	0.817032	−	1.41514i	0.907859	−	0.419275i	$-0.137716\pi$
$332$	−591.090			−0.0977116
$333$	−586.888	−	1016.52i	−0.0965804	−	0.167282i
$334$	−4466.54			−0.731731
$335$	244.898	−	4907.90i	0.0399409	−	0.800440i
$336$	−3514.61			−0.570648
$337$	5092.36	+	8820.22i	0.823141	+	1.42572i	0.903332	+	0.428942i	$0.141114\pi$
$337$	5092.36	+	8820.22i	0.823141	+	1.42572i	−0.0801912	+	0.996779i	$0.525553\pi$
$338$	4621.79			0.743764
$339$	2499.84	−	4329.85i	0.400510	−	0.693703i
$340$	−746.548			−0.119080
$341$	−191.930	−	332.433i	−0.0304798	−	0.0527925i
$342$	−546.191	+	946.030i	−0.0863585	+	0.149577i
$343$	6075.73			0.956438
$344$	−8549.25			−1.33996
$345$	−2047.86	−	3547.00i	−0.319575	−	0.553519i
$346$	1466.39	−	2539.86i	0.227843	−	0.394636i
$347$	−372.064	+	644.433i	−0.0575603	+	0.0996974i	−0.893370	−	0.449322i	$-0.851665\pi$
$347$	−372.064	+	644.433i	−0.0575603	+	0.0996974i	0.835809	+	0.549020i	$0.184999\pi$
$348$	−438.384	−	759.303i	−0.0675283	−	0.116962i
$349$	10173.8			1.56044			0.780219	−	0.625506i	$-0.215107\pi$
$349$	10173.8			1.56044			0.780219	+	0.625506i	$0.215107\pi$
$350$	3161.27			0.482791
$351$	212.238	+	367.607i	0.0322747	+	0.0559014i
$352$	2171.29	+	3760.79i	0.328779	+	0.569463i
$353$	5218.36	+	9038.47i	0.786815	+	1.36280i	0.927909	+	0.372807i	$0.121605\pi$
$353$	5218.36	+	9038.47i	0.786815	+	1.36280i	−0.141094	+	0.989996i	$0.545062\pi$
$354$	2092.00	+	3623.46i	0.314093	+	0.544024i
$355$	−1404.60	+	2432.84i	−0.209995	+	0.363723i
$356$	1666.00	−	2885.59i	0.248027	−	0.429595i
$357$	−3130.61			−0.464117
$358$	743.695	+	1288.12i	0.109792	+	0.190165i
$359$	11512.1			1.69244			0.846220	−	0.532833i	$-0.178873\pi$
$359$	11512.1			1.69244			0.846220	+	0.532833i	$0.178873\pi$
$360$	−1984.43			−0.290524
$361$	2118.47	−	3669.30i	0.308860	−	0.534962i
$362$	−4034.70			−0.585799
$363$	−630.821	−	1092.61i	−0.0912108	−	0.157982i
$364$	−558.374	+	967.132i	−0.0804032	+	0.139262i
$365$	−1604.35	−	2778.82i	−0.230070	−	0.398493i
$366$	2835.77	−	4911.69i	0.404994	−	0.701471i
$367$	−3874.79	+	6711.33i	−0.551123	+	0.954574i	0.447071	+	0.894499i	$0.352467\pi$
$367$	−3874.79	+	6711.33i	−0.551123	+	0.954574i	−0.998194	+	0.0600748i	$0.980866\pi$
$368$	−2992.21	+	5182.66i	−0.423858	+	0.734143i
$369$	1369.42	−	2371.91i	0.193196	−	0.334625i
$370$	−1384.99	+	2398.88i	−0.194601	+	0.337059i
$371$	−564.759	+	978.191i	−0.0790319	+	0.136887i
$372$	32.7642	+	56.7492i	0.00456652	+	0.00790944i
$373$	−5519.35	+	9559.79i	−0.766169	+	1.32704i	0.173458	+	0.984841i	$0.444506\pi$
$373$	−5519.35	+	9559.79i	−0.766169	+	1.32704i	−0.939626	+	0.342202i	$0.888827\pi$
$374$	−1735.32	−	3005.67i	−0.239923	−	0.415560i
$375$	4562.04			0.628221
$376$	−2760.61	+	4781.51i	−0.378637	+	0.655818i
$377$	1929.33			0.263569
$378$	−1908.95			−0.259751
$379$	1607.91	+	2784.99i	0.217923	+	0.377454i	0.954173	−	0.299256i	$-0.0967384\pi$
$379$	1607.91	+	2784.99i	0.217923	+	0.377454i	−0.736250	+	0.676710i	$0.763405\pi$
$380$	−1092.67			−0.147508
$381$	−1269.55	+	2198.93i	−0.170711	+	0.295681i
$382$	745.416	−	1291.10i	0.0998398	−	0.172928i
$383$	6738.92	+	11672.2i	0.899068	+	1.55723i	0.828688	+	0.559710i	$0.189088\pi$
$383$	6738.92	+	11672.2i	0.899068	+	1.55723i	0.0703792	+	0.997520i	$0.477579\pi$
$384$	746.534	+	1293.03i	0.0992093	+	0.171836i
$385$	5592.74	+	9686.92i	0.740345	+	1.28231i
$386$	746.223	+	1292.50i	0.0983984	+	0.170431i
$387$	−3126.80			−0.410709
$388$	1338.50			0.175134
$389$	1429.55	+	2476.05i	0.186327	+	0.322727i	0.944023	−	0.329880i	$-0.107008\pi$
$389$	1429.55	+	2476.05i	0.186327	+	0.322727i	−0.757696	+	0.652607i	$0.773675\pi$
$390$	500.858	−	867.512i	0.0650307	−	0.112636i
$391$	−2665.29	+	4616.41i	−0.344730	+	0.597089i
$392$	−6726.43	−	11650.5i	−0.866673	−	1.50112i
$393$	−2323.25			−0.298200
$394$	−10070.2			−1.28764
$395$	−2458.44	+	4258.14i	−0.313158	+	0.542406i
$396$	448.507	+	776.837i	0.0569150	+	0.0985797i
$397$	−11589.8			−1.46518			−0.732591	−	0.680669i	$-0.761689\pi$
$397$	−11589.8			−1.46518			−0.732591	+	0.680669i	$0.761689\pi$
$398$	2598.01	−	4499.88i	0.327202	−	0.566730i
$399$	−4582.08			−0.574914
$400$	−878.083	−	1520.88i	−0.109760	−	0.190111i
$401$	−10802.9			−1.34532			−0.672658	−	0.739953i	$-0.734848\pi$
$401$	−10802.9			−1.34532			−0.672658	+	0.739953i	$0.734848\pi$
$402$	−3470.32	+	1779.17i	−0.430557	+	0.220739i
$403$	−144.195			−0.0178235
$404$	937.678	+	1624.11i	0.115473	+	0.200006i
$405$	−725.786			−0.0890484
$406$	−4338.29	+	7514.14i	−0.530310	+	0.918523i
$407$	5458.25			0.664756
$408$	1291.37	+	2236.71i	0.156696	+	0.271406i
$409$	−5751.76	+	9962.34i	−0.695370	+	1.20442i	0.274686	+	0.961534i	$0.411426\pi$
$409$	−5751.76	+	9962.34i	−0.695370	+	1.20442i	−0.970056	+	0.242882i	$0.921907\pi$
$410$	−6463.38			−0.778546
$411$	−673.113			−0.0807840
$412$	1957.66	+	3390.76i	0.234094	+	0.405463i
$413$	−8775.07	+	15198.9i	−1.04550	+	1.81086i
$414$	−1625.21	+	2814.95i	−0.192934	+	0.334172i
$415$	1111.99	+	1926.02i	0.131531	+	0.227819i
$416$	1631.27			0.192259
$417$	−6500.14			−0.763341
$418$	−2539.88	−	4399.20i	−0.297200	−	0.514765i
$419$	4135.69	+	7163.23i	0.482200	+	0.835195i	0.999791	−	0.0204329i	$-0.00650445\pi$
$419$	4135.69	+	7163.23i	0.482200	+	0.835195i	−0.517591	+	0.855628i	$0.673171\pi$
$420$	−954.732	−	1653.64i	−0.110919	−	0.192118i
$421$	−1844.57	−	3194.90i	−0.213537	−	0.369857i	0.739282	−	0.673396i	$-0.235165\pi$
$421$	−1844.57	−	3194.90i	−0.213537	−	0.369857i	−0.952819	+	0.303539i	$0.901832\pi$
$422$	2561.89	−	4437.33i	0.295524	−	0.511862i
$423$	−1009.66	+	1748.79i	−0.116056	+	0.201014i
$424$	931.844			0.106732
$425$	−782.146	−	1354.72i	−0.0892698	−	0.154620i
$426$	2229.42			0.253558
$427$	23789.7			2.69617
$428$	1993.25	−	3452.41i	0.225111	−	0.389903i
$429$	−1973.88			−0.222144
$430$	3689.46	+	6390.33i	0.413771	+	0.716672i
$431$	−3200.29	+	5543.07i	−0.357663	+	0.619490i	−0.987570	−	0.157180i	$-0.949760\pi$
$431$	−3200.29	+	5543.07i	−0.357663	+	0.619490i	0.629907	+	0.776670i	$0.283093\pi$
$432$	530.236	+	918.396i	0.0590533	+	0.102283i
$433$	6681.21	−	11572.2i	0.741521	−	1.28435i	−0.210282	−	0.977641i	$-0.567438\pi$
$433$	6681.21	−	11572.2i	0.741521	−	1.28435i	0.951803	−	0.306711i	$-0.0992285\pi$
$434$	324.238	−	561.596i	0.0358615	−	0.0621140i
$435$	−1649.42	+	2856.88i	−0.181802	+	0.314890i
$436$	2115.84	−	3664.75i	0.232409	−	0.402545i
$437$	−3901.01	+	6756.74i	−0.427026	+	0.739631i
$438$	−1273.23	+	2205.31i	−0.138898	+	0.240579i
$439$	875.916	+	1517.13i	0.0952282	+	0.164940i	0.909704	−	0.415258i	$-0.136309\pi$
$439$	875.916	+	1517.13i	0.0952282	+	0.164940i	−0.814476	+	0.580198i	$0.802975\pi$
$440$	4613.97	−	7991.63i	0.499915	−	0.865878i
$441$	−2460.12	−	4261.06i	−0.265643	−	0.460108i
$442$	−1303.73			−0.140299
$443$	3590.92	−	6219.66i	0.385124	−	0.667054i	−0.606662	−	0.794960i	$-0.707492\pi$
$443$	3590.92	−	6219.66i	0.385124	−	0.667054i	0.991786	+	0.127905i	$0.0408253\pi$
$444$	−931.773			−0.0995945
$445$	−12536.7			−1.33549
$446$	−3790.58	−	6565.47i	−0.402442	−	0.697049i
$447$	1020.17			0.107947
$448$	−8354.23	+	14470.0i	−0.881027	+	1.52598i
$449$	2512.72	−	4352.17i	0.264104	−	0.457442i	−0.703224	−	0.710968i	$-0.748257\pi$
$449$	2512.72	−	4352.17i	0.264104	−	0.457442i	0.967329	+	0.253526i	$0.0815904\pi$
$450$	−476.929	−	826.065i	−0.0499614	−	0.0865357i
$451$	6368.04	+	11029.8i	0.664877	+	1.15160i
$452$	−1984.44	−	3437.15i	−0.206505	−	0.357676i
$453$	1972.82	+	3417.03i	0.204617	+	0.354406i
$454$	5314.83			0.549421
$455$	4201.78			0.432928
$456$	1890.09	+	3273.73i	0.194104	+	0.336198i
$457$	−593.606	+	1028.16i	−0.0607608	+	0.105241i	−0.894806	−	0.446456i	$-0.852686\pi$
$457$	−593.606	+	1028.16i	−0.0607608	+	0.105241i	0.834045	+	0.551697i	$0.186019\pi$
$458$	5494.21	−	9516.25i	0.560541	−	0.970885i
$459$	472.304	+	818.055i	0.0480289	+	0.0831885i
$460$	−3251.29			−0.329548
$461$	−2993.91			−0.302474			−0.151237	−	0.988498i	$-0.548326\pi$
$461$	−2993.91			−0.302474			−0.151237	+	0.988498i	$0.548326\pi$
$462$	4438.47	−	7687.66i	0.446962	−	0.774161i
$463$	−258.061	−	446.974i	−0.0259030	−	0.0448653i	0.852783	−	0.522265i	$-0.174913\pi$
$463$	−258.061	−	446.974i	−0.0259030	−	0.0448653i	−0.878686	+	0.477400i	$0.841579\pi$
$464$	4820.06			0.482254
$465$	123.276	−	213.520i	0.0122941	−	0.0212941i
$466$	−4214.07			−0.418912
$467$	4085.02	+	7075.47i	0.404780	+	0.701100i	0.994296	−	0.106657i	$-0.0340148\pi$
$467$	4085.02	+	7075.47i	0.404780	+	0.701100i	−0.589516	+	0.807757i	$0.700681\pi$
$468$	336.959			0.0332819
$469$	−13741.3	−	8874.89i	−1.35291	−	0.873783i
$470$	4765.40			0.467684
$471$	3184.56	+	5515.83i	0.311543	+	0.539609i
$472$	14478.7			1.41194
$473$	7270.07	−	12592.1i	0.706719	−	1.22407i
$474$	3902.10			0.378121
$475$	−1144.78	−	1982.81i	−0.110581	−	0.191532i
$476$	−1242.58	+	2152.21i	−0.119650	+	0.207240i
$477$	340.812			0.0327143
$478$	−7413.86			−0.709419
$479$	−3071.03	−	5319.18i	−0.292942	−	0.507390i	0.681562	−	0.731760i	$-0.261301\pi$
$479$	−3071.03	−	5319.18i	−0.292942	−	0.507390i	−0.974504	+	0.224370i	$0.927967\pi$
$480$	−1394.61	+	2415.53i	−0.132614	+	0.229695i
$481$	1025.18	−	1775.67i	0.0971816	−	0.168323i
$482$	3088.23	+	5348.96i	0.291836	+	0.505474i
$483$	−13634.1			−1.28442
$484$	−1001.52			−0.0940574
$485$	−2518.06	−	4361.41i	−0.235751	−	0.408333i
$486$	287.997	+	498.825i	0.0268802	+	0.0465579i
$487$	−1787.58	−	3096.18i	−0.166331	−	0.288093i	0.770796	−	0.637082i	$-0.219859\pi$
$487$	−1787.58	−	3096.18i	−0.166331	−	0.288093i	−0.937127	+	0.348989i	$0.886525\pi$
$488$	−9813.15	−	16996.9i	−0.910288	−	1.57667i
$489$	4634.78	−	8027.68i	0.428614	−	0.742380i
$490$	−5805.63	+	10055.6i	−0.535248	+	0.927077i
$491$	−16182.1			−1.48735			−0.743676	−	0.668540i	$-0.766920\pi$
$491$	−16182.1			−1.48735			−0.743676	+	0.668540i	$0.766920\pi$
$492$	−1087.08	−	1882.88i	−0.0996127	−	0.172534i
$493$	4293.44			0.392224
$494$	−1908.19			−0.173792
$495$	1687.51	−	2922.86i	0.153228	−	0.265399i
$496$	−360.245			−0.0326118
$497$	4675.72	+	8098.59i	0.422002	+	0.730929i
$498$	882.490	−	1528.52i	0.0794083	−	0.137539i
$499$	−5195.33	−	8998.58i	−0.466082	−	0.807278i	0.533167	−	0.846010i	$-0.321002\pi$
$499$	−5195.33	−	8998.58i	−0.466082	−	0.807278i	−0.999250	+	0.0387315i	$0.987668\pi$
$500$	1810.73	−	3136.28i	0.161957	−	0.280517i
$501$	−2826.51	+	4895.66i	−0.252054	+	0.436571i
$502$	−5276.62	+	9139.37i	−0.469138	+	0.812570i
$503$	7134.67	−	12357.6i	0.632443	−	1.09542i	−0.354607	−	0.935015i	$-0.615385\pi$
$503$	7134.67	−	12357.6i	0.632443	−	1.09542i	0.987051	−	0.160409i	$-0.0512812\pi$
$504$	−3302.96	+	5720.89i	−0.291916	+	0.505613i
$505$	3528.02	−	6110.72i	0.310881	−	0.538462i
$506$	−7557.50	−	13090.0i	−0.663976	−	1.15004i
$507$	2924.76	−	5065.83i	0.256200	−	0.443751i
$508$	1007.80	+	1745.56i	0.0880196	+	0.152454i
$509$	−12707.6			−1.10659			−0.553293	−	0.832987i	$-0.686629\pi$
$509$	−12707.6			−1.10659			−0.553293	+	0.832987i	$0.686629\pi$
$510$	1114.59	−	1930.52i	0.0967740	−	0.167618i
$511$	−10681.3			−0.924687
$512$	11807.5			1.01919
$513$	691.281	+	1197.33i	0.0594947	+	0.103048i
$514$	18403.6			1.57928
$515$	7365.70	−	12757.8i	0.630236	−	1.09160i
$516$	−1241.07	+	2149.59i	−0.105882	+	0.183392i
$517$	−4695.10	−	8132.16i	−0.399401	−	0.691783i
$518$	4610.46	+	7985.55i	0.391065	+	0.677345i
$519$	−1855.92	−	3214.55i	−0.156967	−	0.271875i
$520$	−1733.22	−	3002.02i	−0.146166	−	0.253168i
$521$	−8977.08			−0.754881			−0.377441	−	0.926034i	$-0.623196\pi$
$521$	−8977.08			−0.754881			−0.377441	+	0.926034i	$0.623196\pi$
$522$	2618.01			0.219515
$523$	−1364.77	−	2363.86i	−0.114106	−	0.197637i	0.803316	−	0.595553i	$-0.203067\pi$
$523$	−1364.77	−	2363.86i	−0.114106	−	0.197637i	−0.917422	+	0.397916i	$0.869734\pi$
$524$	−922.127	+	1597.17i	−0.0768766	+	0.133154i
$525$	2000.51	−	3464.99i	0.166304	−	0.288047i
$526$	7093.42	+	12286.2i	0.587999	+	1.01844i
$527$	−320.885			−0.0265237
$528$	−4931.37			−0.406459
$529$	−5524.09	+	9568.00i	−0.454022	+	0.786389i
$530$	−402.141	−	696.528i	−0.0329582	−	0.0570853i
$531$	5295.45			0.432774
$532$	−1818.68	+	3150.05i	−0.148214	+	0.256714i
$533$	4784.25			0.388797
$534$	4974.62	+	8616.30i	0.403133	+	0.698247i
$535$	−14999.2			−1.21210
$536$	−672.561	+	13478.5i	−0.0541982	+	1.08616i
$537$	1882.50			0.151277
$538$	−6202.67	−	10743.3i	−0.497056	−	0.860926i
$539$	22880.0			1.82840
$540$	−288.074	+	498.958i	−0.0229569	+	0.0397625i
$541$	24418.8			1.94057			0.970284	−	0.241969i	$-0.0777932\pi$
$541$	24418.8			1.94057			0.970284	+	0.241969i	$0.0777932\pi$
$542$	−3173.33	−	5496.37i	−0.251488	−	0.435589i
$543$	−2553.24	+	4422.34i	−0.201786	+	0.349504i
$544$	3630.16			0.286106
$545$	−15921.7			−1.25140
$546$	−1667.29	−	2887.83i	−0.130684	−	0.226351i
$547$	5179.19	−	8970.61i	0.404837	−	0.701199i	−0.589465	−	0.807794i	$-0.700661\pi$
$547$	5179.19	−	8970.61i	0.404837	−	0.701199i	0.994303	+	0.106595i	$0.0339948\pi$
$548$	−267.167	+	462.747i	−0.0208263	+	0.0360722i
$549$	−3589.06	−	6216.44i	−0.279012	−	0.483262i
$550$	4435.60			0.343881
$551$	6284.02			0.485859
$552$	5624.03	+	9741.10i	0.433649	+	0.751103i
$553$	8183.82	+	14174.8i	0.629315	+	1.09001i
$554$	1369.63	+	2372.28i	0.105036	+	0.181928i
$555$	1752.90	+	3036.12i	0.134066	+	0.232209i
$556$	−2579.99	+	4468.67i	−0.196791	+	0.340852i
$557$	10251.5	−	17756.0i	0.779835	−	1.35071i	−0.152202	−	0.988349i	$-0.548636\pi$
$557$	10251.5	−	17756.0i	0.779835	−	1.35071i	0.932037	−	0.362364i	$-0.118030\pi$
$558$	−195.666			−0.0148445
$559$	−2730.97	−	4730.18i	−0.206633	−	0.357898i
$560$	10497.4			0.792132
$561$	−4392.58			−0.330579
$562$	1694.40	−	2934.78i	0.127178	−	0.220278i
$563$	−3296.92			−0.246801			−0.123400	−	0.992357i	$-0.539380\pi$
$563$	−3296.92			−0.246801			−0.123400	+	0.992357i	$0.539380\pi$
$564$	801.496	+	1388.23i	0.0598388	+	0.103644i
$565$	−7466.46	+	12932.3i	−0.555958	+	0.962948i
$566$	4701.52	+	8143.27i	0.349151	+	0.604748i
$567$	−1208.02	+	2092.36i	−0.0894748	+	0.154975i
$568$	3857.44	−	6681.28i	0.284955	−	0.493557i
$569$	−4607.58	+	7980.56i	−0.339472	+	0.587984i	−0.984334	−	0.176316i	$-0.943582\pi$
$569$	−4607.58	+	7980.56i	−0.339472	+	0.587984i	0.644861	+	0.764300i	$0.276915\pi$
$570$	1631.35	−	2825.58i	0.119877	−	0.207632i
$571$	10269.3	−	17786.9i	0.752636	−	1.30360i	−0.193905	−	0.981020i	$-0.562115\pi$
$571$	10269.3	−	17786.9i	0.752636	−	1.30360i	0.946541	−	0.322583i	$-0.104551\pi$
$572$	−783.458	+	1356.99i	−0.0572693	+	0.0991933i
$573$	−943.428	−	1634.07i	−0.0687823	−	0.119135i
$574$	−10757.9	+	18633.2i	−0.782273	+	1.35494i
$575$	−3406.32	−	5899.92i	−0.247050	−	0.427902i
$576$	5041.49			0.364691
$577$	10660.8	−	18465.0i	0.769175	−	1.33225i	−0.168835	−	0.985644i	$-0.554001\pi$
$577$	10660.8	−	18465.0i	0.769175	−	1.33225i	0.938011	−	0.346607i	$-0.112666\pi$
$578$	8744.23			0.629260
$579$	1888.90			0.135579
$580$	1309.35	+	2267.87i	0.0937378	+	0.162359i
$581$	7403.34			0.528644
$582$	−1998.36	+	3461.27i	−0.142328	+	0.246519i
$583$	−792.417	+	1372.51i	−0.0562926	+	0.0975016i
$584$	4406.01	+	7631.44i	0.312195	+	0.540738i
$585$	−633.906	−	1097.96i	−0.0448014	−	0.0775983i
$586$	−7128.69	−	12347.3i	−0.502531	−	0.870410i
$587$	−5847.48	−	10128.1i	−0.411161	−	0.712151i	0.583856	−	0.811857i	$-0.301543\pi$
$587$	−5847.48	−	10128.1i	−0.411161	−	0.712151i	−0.995017	+	0.0997058i	$0.968210\pi$
$588$	−3905.81			−0.273934
$589$	−469.659			−0.0328556
$590$	−6248.34	−	10822.5i	−0.436000	−	0.755175i
$591$	−6372.64	+	11037.7i	−0.443545	+	0.768243i
$592$	2561.23	−	4436.18i	0.177814	−	0.307983i
$593$	−1694.99	−	2935.81i	−0.117377	−	0.203304i	0.801350	−	0.598196i	$-0.204115\pi$
$593$	−1694.99	−	2935.81i	−0.117377	−	0.203304i	−0.918728	+	0.394892i	$0.870782\pi$
$594$	−2678.46			−0.185015
$595$	9350.44			0.644253
$596$	404.917	−	701.336i	0.0278289	−	0.0482011i
$597$	−3288.14	−	5695.23i	−0.225418	−	0.390436i
$598$	−5677.88			−0.388270
$599$	3541.66	−	6134.34i	0.241583	−	0.418435i	−0.719582	−	0.694407i	$-0.755667\pi$
$599$	3541.66	−	6134.34i	0.241583	−	0.418435i	0.961165	+	0.275973i	$0.0889999\pi$
$600$	−3300.82			−0.224592
$601$	−12682.2	−	21966.3i	−0.860763	−	1.49089i	−0.871193	−	0.490940i	$-0.836653\pi$
$601$	−12682.2	−	21966.3i	−0.860763	−	1.49089i	0.0104299	−	0.999946i	$-0.496680\pi$
$602$	24563.4			1.66301
$603$	−245.982	+	4929.63i	−0.0166122	+	0.332919i
$604$	3132.15			0.211003
$605$	1884.12	+	3263.39i	0.126612	+	0.219299i
$606$	−5599.77			−0.375371
$607$	1420.61	−	2460.56i	0.0949928	−	0.164532i	−0.814613	−	0.580005i	$-0.803051\pi$
$607$	1420.61	−	2460.56i	0.0949928	−	0.164532i	0.909606	+	0.415473i	$0.136384\pi$
$608$	5313.23			0.354408
$609$	5490.71	+	9510.19i	0.365345	+	0.632795i
$610$	−8469.80	+	14670.1i	−0.562184	+	0.973731i
$611$	−3527.39			−0.233556
$612$	749.854			0.0495278
$613$	11341.2	+	19643.6i	0.747257	+	1.29429i	0.949133	+	0.314876i	$0.101963\pi$
$613$	11341.2	+	19643.6i	0.747257	+	1.29429i	−0.201876	+	0.979411i	$0.564704\pi$
$614$	5942.95	−	10293.5i	0.390616	−	0.676566i
$615$	−4090.16	+	7084.36i	−0.268181	+	0.464502i
$616$	−15359.3	−	26603.1i	−1.00462	−	1.74005i
$617$	8626.62			0.562876			0.281438	−	0.959579i	$-0.409189\pi$
$617$	8626.62			0.562876			0.281438	+	0.959579i	$0.409189\pi$
$618$	−11691.0			−0.760974
$619$	10087.9	+	17472.8i	0.655037	+	1.13456i	0.981885	+	0.189480i	$0.0606801\pi$
$619$	10087.9	+	17472.8i	0.655037	+	1.13456i	−0.326848	+	0.945077i	$0.605987\pi$
$620$	−97.8593	−	169.497i	−0.00633891	−	0.0109793i
$621$	2056.93	+	3562.71i	0.132918	+	0.230220i
$622$	3948.64	+	6839.25i	0.254544	+	0.440883i
$623$	−20866.4	+	36141.7i	−1.34189	+	2.32422i
$624$	−926.224	+	1604.27i	−0.0594209	+	0.102920i
$625$	−8036.71			−0.514349
$626$	−6745.07	−	11682.8i	−0.430650	−	0.745909i
$627$	−6429.14			−0.409498
$628$	5055.97			0.321266
$629$	2281.40	−	3951.49i	0.144619	−	0.250487i
$630$	5701.61			0.360568
$631$	−8012.59	−	13878.2i	−0.505509	−	0.875567i	−0.999980	−	0.00637279i	$-0.997971\pi$
$631$	−8012.59	−	13878.2i	−0.505509	−	0.875567i	0.494471	−	0.869194i	$-0.335362\pi$
$632$	6751.59	−	11694.1i	0.424943	−	0.736022i
$633$	−3242.43	−	5616.06i	−0.203594	−	0.352636i
$634$	6815.63	−	11805.0i	0.426945	−	0.739491i
$635$	3791.86	−	6567.70i	0.236969	−	0.410443i
$636$	135.273	−	234.299i	0.00843383	−	0.0146078i
$637$	4297.37	−	7443.27i	0.267297	−	0.462972i
$638$	−6087.08	+	10543.1i	−0.377727	+	0.654243i
$639$	1410.82	−	2443.61i	0.0873413	−	0.151280i
$640$	−2229.73	−	3862.00i	−0.137715	−	0.238530i
$641$	−3015.18	+	5222.45i	−0.185792	+	0.321801i	−0.943843	−	0.330394i	$-0.892818\pi$
$641$	−3015.18	+	5222.45i	−0.185792	+	0.321801i	0.758051	+	0.652195i	$0.226152\pi$
$642$	5951.79	+	10308.8i	0.365886	+	0.633732i
$643$	5133.93			0.314871			0.157436	−	0.987529i	$-0.449677\pi$
$643$	5133.93			0.314871			0.157436	+	0.987529i	$0.449677\pi$
$644$	−5411.56	+	9373.09i	−0.331126	+	0.573527i
$645$	9339.05			0.570116
$646$	−4246.39			−0.258625
$647$	−2540.46	−	4400.21i	−0.154368	−	0.267373i	0.778461	−	0.627693i	$-0.216001\pi$
$647$	−2540.46	−	4400.21i	−0.154368	−	0.267373i	−0.932829	+	0.360320i	$0.882667\pi$
$648$	1993.22			0.120835
$649$	−12312.4	+	21325.6i	−0.744687	+	1.28984i
$650$	833.105	−	1442.98i	0.0502724	−	0.0870744i
$651$	−410.368	−	710.779i	−0.0247060	−	0.0427920i
$652$	−3679.21	−	6372.57i	−0.220995	−	0.382775i
$653$	−1752.27	−	3035.02i	−0.105010	−	0.181883i	0.808732	−	0.588177i	$-0.200154\pi$
$653$	−1752.27	−	3035.02i	−0.105010	−	0.181883i	−0.913742	+	0.406294i	$0.866821\pi$
$654$	6317.85	+	10942.8i	0.377749	+	0.654280i
$655$	6939.03			0.413939
$656$	11952.6			0.711386
$657$	1611.45	+	2791.12i	0.0956908	+	0.165741i
$658$	7931.69	−	13738.1i	0.469923	−	0.813931i
$659$	916.925	−	1588.16i	0.0542008	−	0.0938786i	−0.837652	−	0.546204i	$-0.816072\pi$
$659$	916.925	−	1588.16i	0.0542008	−	0.0938786i	0.891853	+	0.452326i	$0.149406\pi$
$660$	−1339.59	−	2320.24i	−0.0790053	−	0.136841i
$661$	−31314.7			−1.84266			−0.921331	−	0.388778i	$-0.872897\pi$
$661$	−31314.7			−1.84266			−0.921331	+	0.388778i	$0.872897\pi$
$662$	23325.0			1.36942
$663$	−825.027	+	1428.99i	−0.0483279	+	0.0837064i
$664$	−3053.85	−	5289.42i	−0.178482	−	0.309141i
$665$	13685.6			0.798054
$666$	1391.13	−	2409.50i	0.0809385	−	0.140190i
$667$	18698.3			1.08546
$668$	2243.76	+	3886.30i	0.129960	+	0.225098i
$669$	−9595.01			−0.554506
$670$	10365.1	−	5313.98i	0.597668	−	0.306414i
$671$	33379.5			1.92042
$672$	4642.47	+	8040.99i	0.266499	+	0.461589i
$673$	−17791.2			−1.01902			−0.509510	−	0.860465i	$-0.670173\pi$
$673$	−17791.2			−1.01902			−0.509510	+	0.860465i	$0.670173\pi$
$674$	−12070.6	+	20907.0i	−0.689827	+	1.19482i
$675$	−1207.24			−0.0688395
$676$	−2321.75	−	4021.39i	−0.132098	−	0.228800i
$677$	−2186.33	+	3786.84i	−0.124118	+	0.214978i	−0.921388	−	0.388645i	$-0.872943\pi$
$677$	−2186.33	+	3786.84i	−0.124118	+	0.214978i	0.797270	+	0.603623i	$0.206277\pi$
$678$	11851.0			0.671288
$679$	−16764.6			−0.947519
$680$	−3857.02	−	6680.55i	−0.217515	−	0.376746i
$681$	3363.33	−	5825.45i	0.189256	−	0.327800i
$682$	454.940	−	787.979i	0.0255433	−	0.0442424i
$683$	−16377.4	−	28366.6i	−0.917519	−	1.58919i	−0.803171	−	0.595748i	$-0.796856\pi$
$683$	−16377.4	−	28366.6i	−0.917519	−	1.58919i	−0.114347	−	0.993441i	$-0.536478\pi$
$684$	1097.51			0.0613515
$685$	2010.44			0.112138
$686$	7200.78	+	12472.1i	0.400768	+	0.694151i
$687$	−6953.69	−	12044.1i	−0.386172	−	0.668869i
$688$	−6822.82	−	11817.5i	−0.378078	−	0.654850i
$689$	297.668	+	515.576i	0.0164590	+	0.0285078i
$690$	4854.14	−	8407.61i	0.267817	−	0.463873i
$691$	−7730.76	+	13390.1i	−0.425604	+	0.737167i	−0.996477	−	0.0838713i	$-0.973272\pi$
$691$	−7730.76	+	13390.1i	−0.425604	+	0.737167i	0.570873	+	0.821038i	$0.306605\pi$
$692$	−2946.56			−0.161866
$693$	−5617.51	−	9729.81i	−0.307924	−	0.533340i
$694$	−1763.84			−0.0964760
$695$	19414.4			1.05961
$696$	4529.79	−	7845.84i	0.246697	−	0.427293i
$697$	10646.6			0.578580
$698$	12057.7	+	20884.6i	0.653857	+	1.13251i
$699$	−2666.75	+	4618.94i	−0.144300	+	0.249935i
$700$	−1588.06	−	2750.60i	−0.0857470	−	0.148518i
$701$	−14464.5	+	25053.2i	−0.779336	+	1.34985i	0.152988	+	0.988228i	$0.451110\pi$
$701$	−14464.5	+	25053.2i	−0.779336	+	1.34985i	−0.932325	+	0.361622i	$0.882223\pi$
$702$	−503.076	+	871.354i	−0.0270476	+	0.0468478i
$703$	3339.13	−	5783.54i	0.179143	−	0.310285i
$704$	−11721.9	+	20302.9i	−0.627535	+	1.08692i
$705$	3015.64	−	5223.24i	0.161100	−	0.279033i
$706$	−12369.3	+	21424.3i	−0.659384	+	1.14209i
$707$	−11744.3	−	20341.8i	−0.624739	−	1.08208i
$708$	2101.83	−	3640.48i	0.111570	−	0.193245i
$709$	−3208.81	−	5557.83i	−0.169971	−	0.294399i	0.768438	−	0.639924i	$-0.221034\pi$
$709$	−3208.81	−	5557.83i	−0.169971	−	0.294399i	−0.938409	+	0.345525i	$0.887701\pi$
$710$	−6658.76			−0.351970
$711$	2469.33	−	4277.00i	0.130249	−	0.225598i
$712$	34429.3			1.81221
$713$	−1397.49			−0.0734030
$714$	−3710.31	−	6426.45i	−0.194475	−	0.336840i
$715$	5895.54			0.308365
$716$	747.188	−	1294.17i	0.0389996	−	0.0675493i
$717$	−4691.64	+	8126.16i	−0.244369	+	0.423259i
$718$	13643.8	+	23631.8i	0.709169	+	1.22832i
$719$	−9381.12	−	16248.6i	−0.486588	−	0.842795i	0.513293	−	0.858213i	$-0.328425\pi$
$719$	−9381.12	−	16248.6i	−0.486588	−	0.842795i	−0.999881	+	0.0154183i	$0.995092\pi$
$720$	−1583.70	−	2743.04i	−0.0819735	−	0.141982i
$721$	−24519.4	−	42468.9i	−1.26651	−	2.19366i
$722$	10043.0			0.517676
$723$	7817.16			0.402107
$724$	2026.83	+	3510.57i	0.104042	+	0.180206i
$725$	−2743.58	+	4752.01i	−0.140543	+	0.243428i
$726$	1495.26	−	2589.87i	0.0764385	−	0.132395i
$727$	7184.71	+	12444.3i	0.366529	+	0.634846i	0.989020	−	0.147780i	$-0.0472129\pi$
$727$	7184.71	+	12444.3i	0.366529	+	0.634846i	−0.622492	+	0.782626i	$0.713880\pi$
$728$	−11539.3			−0.587465
$729$	729.000			0.0370370
$730$	3802.86	−	6586.75i	0.192809	−	0.333954i
$731$	−6077.37	−	10526.3i	−0.307496	−	0.532599i
$732$	−5698.17			−0.287719
$733$	1772.05	−	3069.28i	0.0892934	−	0.154661i	−0.817919	−	0.575333i	$-0.804872\pi$
$733$	1772.05	−	3069.28i	0.0892934	−	0.154661i	0.907213	+	0.420672i	$0.138206\pi$
$734$	−18369.1			−0.923730
$735$	7347.83	+	12726.8i	0.368747	+	0.638688i
$736$	15809.7			0.791784
$737$	−19280.5	−	12452.4i	−0.963645	−	0.622376i
$738$	6492.00			0.323813
$739$	12141.6	+	21029.8i	0.604376	+	1.04681i	0.992150	+	0.125056i	$0.0399110\pi$
$739$	12141.6	+	21029.8i	0.604376	+	1.04681i	−0.387773	+	0.921755i	$0.626756\pi$
$740$	2782.99			0.138250
$741$	−1207.54	+	2091.52i	−0.0598651	+	0.103689i
$742$	−2677.35			−0.132464
$743$	−18324.2	−	31738.4i	−0.904777	−	1.56712i	−0.821217	−	0.570616i	$-0.806704\pi$
$743$	−18324.2	−	31738.4i	−0.904777	−	1.56712i	−0.0835598	−	0.996503i	$-0.526629\pi$
$744$	−338.551	+	586.387i	−0.0166826	+	0.0288951i
$745$	−3047.01			−0.149844
$746$	−26165.5			−1.28416
$747$	−1116.91	−	1934.55i	−0.0547065	−	0.0947544i
$748$	−1743.47	+	3019.78i	−0.0852241	+	0.147613i
$749$	−24965.2	+	43241.1i	−1.21790	+	2.10947i
$750$	5406.80	+	9364.85i	0.263238	+	0.455941i
$751$	−11545.7			−0.560995			−0.280498	−	0.959855i	$-0.590500\pi$
$751$	−11545.7			−0.560995			−0.280498	+	0.959855i	$0.590500\pi$
$752$	−8812.52			−0.427340
$753$	6678.30	+	11567.2i	0.323202	+	0.559802i
$754$	2286.58	+	3960.48i	0.110441	+	0.191289i
$755$	−5892.38	−	10205.9i	−0.284034	−	0.491961i
$756$	958.959	+	1660.97i	0.0461336	+	0.0799058i
$757$	16603.3	−	28757.8i	0.797170	−	1.38074i	−0.124282	−	0.992247i	$-0.539663\pi$
$757$	16603.3	−	28757.8i	0.797170	−	1.38074i	0.921452	−	0.388492i	$-0.127004\pi$
$758$	−3811.30	+	6601.37i	−0.182629	+	0.316323i
$759$	−19130.1			−0.914862
$760$	−5645.27	−	9777.89i	−0.269441	−	0.466686i
$761$	15133.9			0.720897			0.360449	−	0.932779i	$-0.382624\pi$
$761$	15133.9			0.720897			0.360449	+	0.932779i	$0.382624\pi$
$762$	−6018.54			−0.286127
$763$	−26500.7	+	45900.6i	−1.25739	+	2.17787i
$764$	−1497.83			−0.0709290
$765$	−1410.67	−	2443.34i	−0.0666702	−	0.115476i
$766$	−15973.6	+	27667.0i	−0.753457	+	1.30503i
$767$	4625.08	+	8010.87i	0.217734	+	0.377126i
$768$	4952.44	−	8577.88i	0.232690	−	0.403031i
$769$	−14233.7	+	24653.5i	−0.667464	+	1.15608i	0.311147	+	0.950362i	$0.399287\pi$
$769$	−14233.7	+	24653.5i	−0.667464	+	1.15608i	−0.978611	+	0.205720i	$0.934046\pi$
$770$	−13256.7	+	22961.3i	−0.620440	+	1.07463i
$771$	11646.2	−	20171.7i	0.544003	−	0.942241i
$772$	749.728	−	1298.57i	0.0349525	−	0.0605394i
$773$	−3581.07	+	6202.59i	−0.166626	+	0.288605i	−0.937232	−	0.348708i	$-0.886621\pi$
$773$	−3581.07	+	6202.59i	−0.166626	+	0.288605i	0.770605	+	0.637313i	$0.219954\pi$
$774$	−3705.80	−	6418.63i	−0.172096	−	0.298079i
$775$	205.051	−	355.159i	0.00950407	−	0.0164615i
$776$	6915.32	+	11977.7i	0.319904	+	0.554090i
$777$	11670.4			0.538831
$778$	−3388.52	+	5869.09i	−0.156150	+	0.270459i
$779$	15582.8			0.716704
$780$	−1006.42			−0.0461996
$781$	6560.54	+	11363.2i	0.300582	+	0.520623i
$782$	−12635.3			−0.577796
$783$	1656.73	−	2869.53i	0.0756150	−	0.130969i
$784$	10736.2	−	18595.6i	0.489075	−	0.847104i
$785$	−9511.57	−	16474.5i	−0.432462	−	0.749046i
$786$	−2753.45	−	4769.12i	−0.124952	−	0.216423i
$787$	−3878.15	−	6717.16i	−0.175656	−	0.304245i	0.764732	−	0.644348i	$-0.222871\pi$
$787$	−3878.15	−	6717.16i	−0.175656	−	0.304245i	−0.940388	+	0.340103i	$0.889538\pi$
$788$	5058.76	+	8762.03i	0.228694	+	0.396110i
$789$	17955.4			0.810177
$790$	−11654.7			−0.524880
$791$	24854.9	+	43049.9i	1.11724	+	1.93512i
$792$	−4634.40	+	8027.02i	−0.207925	+	0.360136i
$793$	6269.42	−	10859.0i	0.280748	−	0.486271i
$794$	−13736.0	−	23791.4i	−0.613943	−	1.06338i
$795$	−1017.93			−0.0454116
$796$	−5220.42			−0.232453
$797$	13163.2	−	22799.4i	0.585025	−	1.01329i	−0.409847	−	0.912154i	$-0.634418\pi$
$797$	13163.2	−	22799.4i	0.585025	−	1.01329i	0.994872	−	0.101139i	$-0.0322487\pi$
$798$	−5430.55	−	9405.98i	−0.240901	−	0.417253i
$799$	−7849.68			−0.347562
$800$	−2319.73	+	4017.89i	−0.102519	+	0.177567i
$801$	12592.2			0.555458
$802$	−12803.3	−	22176.0i	−0.563716	−	0.976385i
$803$	−14987.1			−0.658633
$804$	3291.36	+	2125.74i	0.144375	+	0.0932451i
$805$	40722.1			1.78294
$806$	−170.896	−	296.001i	−0.00746843	−	0.0129357i
$807$	−15700.7			−0.684871
$808$	−9688.98	+	16781.8i	−0.421853	+	0.730670i
$809$	−32026.1			−1.39181			−0.695907	−	0.718132i	$-0.744997\pi$
$809$	−32026.1			−1.39181			−0.695907	+	0.718132i	$0.744997\pi$
$810$	−860.181	−	1489.88i	−0.0373132	−	0.0646283i
$811$	18101.0	−	31351.9i	0.783740	−	1.35748i	−0.146008	−	0.989283i	$-0.546643\pi$
$811$	18101.0	−	31351.9i	0.783740	−	1.35748i	0.929749	−	0.368195i	$-0.120024\pi$
$812$	8717.33			0.376747
$813$	−8032.59			−0.346513
$814$	6468.96	+	11204.6i	0.278547	+	0.482457i
$815$	−13843.0	+	23976.9i	−0.594970	+	1.03052i
$816$	−2061.18	+	3570.06i	−0.0884260	+	0.153158i
$817$	−8895.05	−	15406.7i	−0.380904	−	0.659745i
$818$	−27267.3			−1.16550
$819$	−4220.38			−0.180064
$820$	3246.87	+	5623.74i	0.138275	+	0.239500i
$821$	8800.53	+	15243.0i	0.374105	+	0.647970i	0.990193	−	0.139708i	$-0.0446165\pi$
$821$	8800.53	+	15243.0i	0.374105	+	0.647970i	−0.616087	+	0.787678i	$0.711283\pi$
$822$	−797.754	−	1381.75i	−0.0338502	−	0.0586303i
$823$	16918.9	+	29304.3i	0.716591	+	1.24117i	0.962343	+	0.271839i	$0.0876319\pi$
$823$	16918.9	+	29304.3i	0.716591	+	1.24117i	−0.245752	+	0.969333i	$0.579035\pi$
$824$	−20228.4	+	35036.5i	−0.855204	+	1.48126i
$825$	2806.93	−	4861.75i	0.118454	−	0.205169i
$826$	−41599.8			−1.75235
$827$	−16702.2	−	28929.1i	−0.702290	−	1.21640i	−0.967661	−	0.252256i	$-0.918828\pi$
$827$	−16702.2	−	28929.1i	−0.702290	−	1.21640i	0.265370	−	0.964147i	$-0.414506\pi$
$828$	3265.69			0.137066
$829$	12823.8			0.537259			0.268630	−	0.963244i	$-0.413429\pi$
$829$	12823.8			0.537259			0.268630	+	0.963244i	$0.413429\pi$
$830$	−2635.80	+	4565.34i	−0.110229	+	0.190922i
$831$	3466.93			0.144725
$832$	4403.27	+	7626.68i	0.183481	+	0.317798i
$833$	9563.18	−	16563.9i	0.397772	−	0.688962i
$834$	−7703.78	−	13343.3i	−0.319856	−	0.554007i
$835$	8442.16	−	14622.2i	0.349884	−	0.606016i
$836$	−2551.81	+	4419.86i	−0.105569	+	0.182852i
$837$	−123.821	+	214.465i	−0.00511338	+	0.00885663i
$838$	−9803.01	+	16979.3i	−0.404104	+	0.699929i
$839$	15681.5	−	27161.2i	0.645275	−	1.11765i	−0.338963	−	0.940800i	$-0.610076\pi$
$839$	15681.5	−	27161.2i	0.645275	−	1.11765i	0.984238	−	0.176850i	$-0.0565906\pi$
$840$	9865.19	−	17087.0i	0.405216	−	0.701855i
$841$	4664.34	+	8078.88i	0.191248	+	0.331251i
$842$	4372.27	−	7573.00i	0.178953	−	0.309956i
$843$	−2144.50	−	3714.37i	−0.0876161	−	0.151755i
$844$	−5147.85			−0.209948
$845$	−8735.60	+	15130.5i	−0.355638	+	0.615982i
$846$	−4786.50			−0.194519
$847$	12544.0			0.508874
$848$	743.667	+	1288.07i	0.0301151	+	0.0521610i
$849$	11900.9			0.481079
$850$	1853.95	−	3211.14i	0.0748119	−	0.129578i
$851$	9935.70	−	17209.1i	0.400225	−	0.693210i
$852$	−1119.94	−	1939.80i	−0.0450336	−	0.0780005i
$853$	19262.8	+	33364.2i	0.773207	+	1.33923i	0.935797	+	0.352540i	$0.114682\pi$
$853$	19262.8	+	33364.2i	0.773207	+	1.33923i	−0.162589	+	0.986694i	$0.551985\pi$
$854$	28194.8	+	48834.9i	1.12975	+	1.95679i
$855$	−2064.70	−	3576.17i	−0.0825863	−	0.143044i
$856$	41192.3			1.64477
$857$	−21464.7			−0.855567			−0.427784	−	0.903881i	$-0.640705\pi$
$857$	−21464.7			−0.855567			−0.427784	+	0.903881i	$0.640705\pi$
$858$	−2339.39	−	4051.94i	−0.0930832	−	0.161225i
$859$	−7278.34	+	12606.4i	−0.289096	+	0.500729i	−0.973594	−	0.228285i	$-0.926688\pi$
$859$	−7278.34	+	12606.4i	−0.289096	+	0.500729i	0.684498	+	0.729015i	$0.260021\pi$
$860$	3706.79	−	6420.34i	0.146977	−	0.254572i
$861$	13615.6	+	23582.9i	0.538929	+	0.933453i
$862$	−15171.6			−0.599473
$863$	49932.3			1.96954			0.984771	−	0.173855i	$-0.0556225\pi$
$863$	49932.3			1.96954			0.984771	+	0.173855i	$0.0556225\pi$
$864$	1400.78	−	2426.23i	0.0551570	−	0.0955347i
$865$	5543.22	+	9601.14i	0.217890	+	0.377397i
$866$	31673.5			1.24285
$867$	5533.52	−	9584.34i	0.216757	−	0.375434i
$868$	−651.521			−0.0254770
$869$	11482.8	+	19888.7i	0.448247	+	0.776386i
$870$	−7819.40			−0.304715
$871$	−7672.32	+	3933.46i	−0.298469	+	0.153020i
$872$	43725.8			1.69810
$873$	2529.21	+	4380.72i	0.0980536	+	0.169834i
$874$	−18493.4			−0.715732
$875$	−22679.2	+	39281.6i	−0.876226	+	1.51767i
$876$	2558.43			0.0986772
$877$	−19364.1	−	33539.6i	−0.745587	−	1.29140i	−0.949920	−	0.312493i	$-0.898836\pi$
$877$	−19364.1	−	33539.6i	−0.745587	−	1.29140i	0.204333	−	0.978902i	$-0.434498\pi$
$878$	−2076.22	+	3596.12i	−0.0798053	+	0.138227i
$879$	−18044.7			−0.692415
$880$	14728.9			0.564217
$881$	12267.5	+	21247.9i	0.469128	+	0.812553i	0.999377	−	0.0352886i	$-0.0112351\pi$
$881$	12267.5	+	21247.9i	0.469128	+	0.812553i	−0.530249	+	0.847842i	$0.677902\pi$
$882$	5831.33	−	10100.2i	0.222620	−	0.385590i
$883$	−9270.98	+	16057.8i	−0.353333	+	0.611991i	−0.986831	−	0.161753i	$-0.948285\pi$
$883$	−9270.98	+	16057.8i	−0.353333	+	0.611991i	0.633498	+	0.773744i	$0.281619\pi$
$884$	654.927	+	1134.37i	0.0249181	+	0.0431594i
$885$	−15816.3			−0.600745
$886$	17023.4			0.645501
$887$	15179.4	+	26291.5i	0.574605	+	0.995245i	0.996084	+	0.0884074i	$0.0281777\pi$
$887$	15179.4	+	26291.5i	0.574605	+	0.995245i	−0.421479	+	0.906838i	$0.638489\pi$
$888$	−4813.98	−	8338.05i	−0.181922	−	0.315098i
$889$	−12622.6	−	21863.0i	−0.476208	−	0.824816i
$890$	−14858.1	−	25735.0i	−0.559600	−	0.969256i
$891$	−1694.99	+	2935.80i	−0.0637308	+	0.110385i
$892$	−3808.38	+	6596.30i	−0.142953	+	0.247602i
$893$	−11489.1			−0.430534
$894$	1209.07	+	2094.17i	0.0452320	+	0.0783441i
$895$	−5622.61			−0.209992
$896$	−14844.9			−0.553498
$897$	−3593.07	+	6223.39i	−0.133745	+	0.231653i
$898$	11912.0			0.442661
$899$	562.794	+	974.787i	0.0208790	+	0.0361635i
$900$	−479.169	+	829.945i	−0.0177470	+	0.0307387i
$901$	662.416	+	1147.34i	0.0244931	+	0.0424233i
$902$	−15094.4	+	26144.3i	−0.557195	+	0.965090i
$903$	15544.2	−	26923.4i	0.572846	−	0.992198i
$904$	20505.1	−	35515.8i	0.754412	−	1.30668i
$905$	7625.96	−	13208.5i	0.280105	−	0.485157i
$906$	−4676.27	+	8099.53i	−0.171477	+	0.297008i
$907$	19326.1	−	33473.8i	0.707511	−	1.22544i	−0.258267	−	0.966073i	$-0.583152\pi$
$907$	19326.1	−	33473.8i	0.707511	−	1.22544i	0.965778	−	0.259371i	$-0.0835151\pi$
$908$	−2669.89	−	4624.39i	−0.0975810	−	0.169015i
$909$	−3543.65	+	6137.77i	−0.129302	+	0.223957i
$910$	4979.82	+	8625.31i	0.181406	+	0.314205i
$911$	−515.935			−0.0187636			−0.00938182	−	0.999956i	$-0.502986\pi$
$911$	−515.935			−0.0187636			−0.00938182	+	0.999956i	$0.502986\pi$
$912$	−3016.81	+	5225.27i	−0.109536	+	0.189721i
$913$	10387.7			0.376541
$914$	−2814.10			−0.101840
$915$	10719.7	+	18567.1i	0.387304	+	0.670830i
$916$	−11040.0			−0.398224
$917$	11549.6	−	20004.4i	0.415921	−	0.720397i
$918$	−1119.52	+	1939.07i	−0.0402503	+	0.0697155i
$919$	3596.71	+	6229.69i	0.129102	+	0.223611i	0.923329	−	0.384010i	$-0.125457\pi$
$919$	3596.71	+	6229.69i	0.129102	+	0.223611i	−0.794227	+	0.607621i	$0.792124\pi$
$920$	−16797.7	−	29094.5i	−0.601961	−	1.04263i
$921$	−7521.64	−	13027.9i	−0.269106	−	0.466105i
$922$	−3548.30	−	6145.83i	−0.126743	−	0.219525i
$923$	4928.87			0.175770
$924$	−8918.64			−0.317534
$925$	2915.70	+	5050.14i	0.103641	+	0.179511i
$926$	611.692	−	1059.48i	0.0217078	−	0.0375991i
$927$	−7398.32	+	12814.3i	−0.262128	+	0.454019i
$928$	−6366.85	−	11027.7i	−0.225218	−	0.390089i
$929$	−8153.48			−0.287951			−0.143976	−	0.989581i	$-0.545989\pi$
$929$	−8153.48			−0.287951			−0.143976	+	0.989581i	$0.545989\pi$
$930$	584.411			0.0206060
$931$	13997.0	−	24243.5i	0.492732	−	0.853436i
$932$	2116.93	+	3666.63i	0.0744017	+	0.128867i
$933$	9995.12			0.350724
$934$	−9682.90	+	16771.3i	−0.339223	+	0.587551i
$935$	13119.7			0.458886
$936$	1740.89	+	3015.31i	0.0607936	+	0.105298i
$937$	−40440.5			−1.40996			−0.704980	−	0.709227i	$-0.749044\pi$
$937$	−40440.5			−1.40996			−0.704980	+	0.709227i	$0.749044\pi$
$938$	1932.38	−	38726.1i	0.0672649	−	1.34803i
$939$	−17073.7			−0.593374
$940$	−2393.89	−	4146.34i	−0.0830639	−	0.143871i
$941$	7105.44			0.246154			0.123077	−	0.992397i	$-0.460724\pi$
$941$	7105.44			0.246154			0.123077	+	0.992397i	$0.460724\pi$
$942$	−7548.51	+	13074.4i	−0.261087	+	0.452215i
$943$	46367.2			1.60119
$944$	11554.9	+	20013.7i	0.398390	+	0.690031i
$945$	3608.09	−	6249.40i	0.124202	−	0.215125i
$946$	34465.1			1.18452
$947$	−20150.9			−0.691464			−0.345732	−	0.938333i	$-0.612369\pi$
$947$	−20150.9			−0.691464			−0.345732	+	0.938333i	$0.612369\pi$
$948$	−1960.21	−	3395.19i	−0.0671569	−	0.116319i
$949$	−2814.91	+	4875.57i	−0.0962865	+	0.166773i
$950$	2713.51	−	4699.94i	0.0926715	−	0.160512i
$951$	−8626.13	−	14940.9i	−0.294134	−	0.509455i
$952$	−25679.0			−0.874225
$953$	−54025.4			−1.83636			−0.918182	−	0.396158i	$-0.870343\pi$
$953$	−54025.4			−1.83636			−0.918182	+	0.396158i	$0.870343\pi$
$954$	403.921	+	699.612i	0.0137080	+	0.0237429i
$955$	2817.81	+	4880.59i	0.0954787	+	0.165374i
$956$	3724.34	+	6450.75i	0.125998	+	0.218234i
$957$	7704.05	+	13343.8i	0.260226	+	0.450725i
$958$	7279.40	−	12608.3i	0.245498	−	0.425214i
$959$	3346.24	−	5795.86i	0.112675	−	0.195159i
$960$	−15057.8			−0.506237
$961$	14853.4	+	25726.9i	0.498588	+	0.863580i
$962$	4860.07			0.162885
$963$	15065.7			0.504137
$964$	3102.73	−	5374.09i	0.103664	−	0.179552i
$965$	−5641.72			−0.188200
$966$	−16158.8	−	27987.8i	−0.538199	−	0.932188i
$967$	23628.2	−	40925.3i	0.785762	−	1.36098i	−0.142781	−	0.989754i	$-0.545604\pi$
$967$	23628.2	−	40925.3i	0.785762	−	1.36098i	0.928543	−	0.371225i	$-0.121062\pi$
$968$	−5174.34	−	8962.22i	−0.171807	−	0.297579i
$969$	−2687.20	+	4654.37i	−0.0890870	+	0.154303i
$970$	5968.66	−	10338.0i	0.197569	−	0.342200i
$971$	−14732.6	+	25517.7i	−0.486913	+	0.843358i	−0.999887	−	0.0150461i	$-0.995210\pi$
$971$	−14732.6	+	25517.7i	−0.486913	+	0.843358i	0.512974	+	0.858404i	$0.328544\pi$
$972$	289.349	−	501.168i	0.00954823	−	0.0165380i
$973$	32314.1	−	55969.6i	1.06469	−	1.84409i
$974$	4237.18	−	7339.01i	0.139392	−	0.241434i
$975$	−1054.41	−	1826.29i	−0.0346340	−	0.0599879i
$976$	15663.0	−	27129.1i	0.513688	−	0.889734i
$977$	3329.22	+	5766.38i	0.109019	+	0.188826i	0.915373	−	0.402607i	$-0.131896\pi$
$977$	3329.22	+	5766.38i	0.109019	+	0.188826i	−0.806354	+	0.591433i	$0.798563\pi$
$978$	21972.0			0.718393
$979$	−29277.8	+	50710.7i	−0.955795	+	1.65549i
$980$	11665.8			0.380255
$981$	15992.3			0.520482
$982$	−19178.6	−	33218.3i	−0.623232	−	1.07947i
$983$	−26234.4			−0.851217			−0.425608	−	0.904907i	$-0.639940\pi$
$983$	−26234.4			−0.851217			−0.425608	+	0.904907i	$0.639940\pi$
$984$	11232.8	−	19455.7i	0.363910	−	0.630310i
$985$	19033.6	−	32967.2i	0.615698	−	1.06642i
$986$	5088.46	+	8813.47i	0.164350	+	0.284663i
$987$	−10038.7	−	17387.5i	−0.323743	−	0.560739i
$988$	958.574	+	1660.30i	0.0308667	+	0.0534627i
$989$	−26467.6	−	45843.1i	−0.850980	−	1.47394i
$990$	7999.97			0.256824
$991$	−29920.7			−0.959096			−0.479548	−	0.877516i	$-0.659199\pi$
$991$	−29920.7			−0.959096			−0.479548	+	0.877516i	$0.659199\pi$
$992$	475.850	+	824.196i	0.0152301	+	0.0263793i
$993$	14760.6	−	25566.0i	0.471714	−	0.817032i
$994$	−11083.1	+	19196.4i	−0.353656	+	0.612549i
$995$	9820.94	+	17010.4i	0.312909	+	0.541975i
$996$	−1773.27			−0.0564138
$997$	−22775.1			−0.723466			−0.361733	−	0.932282i	$-0.617815\pi$
$997$	−22775.1			−0.723466			−0.361733	+	0.932282i	$0.617815\pi$
$998$	12314.7	−	21329.7i	0.390597	−	0.676534i
$999$	−1760.66	−	3049.56i	−0.0557607	−	0.0965804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.37.11	✓	32
67.29	even	3	inner	201.4.e.a.163.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.11	✓	32	1.1	even	1	trivial
201.4.e.a.163.11	yes	32	67.29	even	3	inner

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18517 + 2.05278i) q^{2} +3.00000 q^{3} +(1.19074 - 2.06242i) q^{4} -8.96032 q^{5} +(3.55551 + 6.15833i) q^{6} +(-14.9139 + 25.8316i) q^{7} +24.6077 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(1.18517 + 2.05278i) q^{2} +3.00000 q^{3} +(1.19074 - 2.06242i) q^{4} -8.96032 q^{5} +(3.55551 + 6.15833i) q^{6} +(-14.9139 + 25.8316i) q^{7} +24.6077 q^{8} +9.00000 q^{9} +(-10.6195 - 18.3935i) q^{10} +(-20.9257 + 36.2445i) q^{11} +(3.57221 - 6.18725i) q^{12} +(7.86066 + 13.6151i) q^{13} -70.7020 q^{14} -26.8810 q^{15} +(19.6384 + 34.0147i) q^{16} +(17.4927 + 30.2983i) q^{17} +(10.6665 + 18.4750i) q^{18} +(25.6030 + 44.3457i) q^{19} +(-10.6694 + 18.4799i) q^{20} +(-44.7416 + 77.4947i) q^{21} -99.2024 q^{22} +(76.1826 + 131.952i) q^{23} +73.8230 q^{24} -44.7126 q^{25} +(-18.6325 + 32.2724i) q^{26} +27.0000 q^{27} +(35.5170 + 61.5173i) q^{28} +(61.3602 - 106.279i) q^{29} +(-31.8586 - 55.1806i) q^{30} +(-4.58598 + 7.94315i) q^{31} +(51.8809 - 89.8604i) q^{32} +(-62.7772 + 108.733i) q^{33} +(-41.4638 + 71.8174i) q^{34} +(133.633 - 231.459i) q^{35} +(10.7166 - 18.5618i) q^{36} +(-65.2098 - 112.947i) q^{37} +(-60.6879 + 105.114i) q^{38} +(23.5820 + 40.8452i) q^{39} -220.493 q^{40} +(152.158 - 263.546i) q^{41} -212.106 q^{42} -347.422 q^{43} +(49.8341 + 86.3153i) q^{44} -80.6429 q^{45} +(-180.579 + 312.772i) q^{46} +(-112.185 + 194.310i) q^{47} +(58.9152 + 102.044i) q^{48} +(-273.347 - 473.451i) q^{49} +(-52.9921 - 91.7850i) q^{50} +(52.4782 + 90.8950i) q^{51} +37.4399 q^{52} +37.8681 q^{53} +(31.9996 + 55.4250i) q^{54} +(187.501 - 324.762i) q^{55} +(-366.995 + 635.655i) q^{56} +(76.8090 + 133.037i) q^{57} +290.890 q^{58} +588.383 q^{59} +(-32.0082 + 55.4398i) q^{60} +(-398.785 - 690.715i) q^{61} -21.7407 q^{62} +(-134.225 + 232.484i) q^{63} +560.165 q^{64} +(-70.4340 - 121.995i) q^{65} -297.607 q^{66} +(-27.3314 + 547.737i) q^{67} +83.3171 q^{68} +(228.548 + 395.857i) q^{69} +633.512 q^{70} +(156.758 - 271.512i) q^{71} +221.469 q^{72} +(179.051 + 310.125i) q^{73} +(154.569 - 267.722i) q^{74} -134.138 q^{75} +121.946 q^{76} +(-624.168 - 1081.09i) q^{77} +(-55.8974 + 96.8171i) q^{78} +(274.369 - 475.222i) q^{79} +(-175.966 - 304.783i) q^{80} +81.0000 q^{81} +721.334 q^{82} +(-124.102 - 214.950i) q^{83} +(106.551 + 184.552i) q^{84} +(-156.741 - 271.483i) q^{85} +(-411.755 - 713.181i) q^{86} +(184.081 - 318.837i) q^{87} +(-514.934 + 891.891i) q^{88} +1399.13 q^{89} +(-95.5757 - 165.542i) q^{90} -468.931 q^{91} +362.854 q^{92} +(-13.7579 + 23.8294i) q^{93} -531.833 q^{94} +(-229.411 - 397.352i) q^{95} +(155.643 - 269.581i) q^{96} +(281.023 + 486.747i) q^{97} +(647.926 - 1122.24i) q^{98} +(-188.332 + 326.200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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