LMFDB - Embedded newform 121.4.c.g.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not 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:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			3.1
Root			$0.535233 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.3
Dual form			121.4.c.g.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99350 + 1.44836i) q^{2} +(-0.165602 - 0.509670i) q^{3} +(-0.595848 + 1.83383i) q^{4} +(1.24257 + 0.902778i) q^{5} +(1.06831 + 0.776175i) q^{6} +(-8.72933 + 26.8661i) q^{7} +(-7.55982 - 23.2667i) q^{8} +(21.6111 - 15.7014i) q^{9} +O(q^{10})$	\(q+(-1.99350 + 1.44836i) q^{2} +(-0.165602 - 0.509670i) q^{3} +(-0.595848 + 1.83383i) q^{4} +(1.24257 + 0.902778i) q^{5} +(1.06831 + 0.776175i) q^{6} +(-8.72933 + 26.8661i) q^{7} +(-7.55982 - 23.2667i) q^{8} +(21.6111 - 15.7014i) q^{9} -3.78461 q^{10} +1.03332 q^{12} +(-55.3886 + 40.2422i) q^{13} +(-21.5100 - 66.2009i) q^{14} +(0.254347 - 0.782801i) q^{15} +(36.2896 + 26.3659i) q^{16} +(-44.7822 - 32.5362i) q^{17} +(-20.3405 + 62.6015i) q^{18} +(-17.0506 - 52.4764i) q^{19} +(-2.39592 + 1.74074i) q^{20} +15.1384 q^{21} -178.315 q^{23} +(-10.6064 + 7.70602i) q^{24} +(-37.8982 - 116.639i) q^{25} +(52.1319 - 160.446i) q^{26} +(-23.2872 - 16.9192i) q^{27} +(-44.0666 - 32.0162i) q^{28} +(34.9720 - 107.633i) q^{29} +(0.626738 + 1.92890i) q^{30} +(-57.2887 + 41.6227i) q^{31} +85.1821 q^{32} +136.397 q^{34} +(-35.1009 + 25.5023i) q^{35} +(15.9168 + 48.9868i) q^{36} +(-65.0988 + 200.353i) q^{37} +(109.995 + 79.9162i) q^{38} +(29.6827 + 21.5657i) q^{39} +(11.6111 - 35.7354i) q^{40} +(59.3091 + 182.535i) q^{41} +(-30.1785 + 21.9259i) q^{42} -208.210 q^{43} +41.0282 q^{45} +(355.472 - 258.265i) q^{46} +(158.376 + 487.431i) q^{47} +(7.42830 - 22.8619i) q^{48} +(-368.094 - 267.436i) q^{49} +(244.485 + 177.629i) q^{50} +(-9.16669 + 28.2122i) q^{51} +(-40.7942 - 125.552i) q^{52} +(303.744 - 220.683i) q^{53} +70.9282 q^{54} +691.079 q^{56} +(-23.9220 + 17.3804i) q^{57} +(86.1746 + 265.218i) q^{58} +(-156.519 + 481.717i) q^{59} +(1.28397 + 0.932860i) q^{60} +(379.184 + 275.493i) q^{61} +(53.9203 - 165.950i) q^{62} +(233.185 + 717.670i) q^{63} +(-460.127 + 334.302i) q^{64} -105.154 q^{65} -289.895 q^{67} +(86.3492 - 62.7363i) q^{68} +(29.5293 + 90.8819i) q^{69} +(33.0371 - 101.678i) q^{70} +(318.761 + 231.593i) q^{71} +(-528.697 - 384.121i) q^{72} +(89.4723 - 275.367i) q^{73} +(-160.410 - 493.691i) q^{74} +(-53.1711 + 38.6311i) q^{75} +106.392 q^{76} -90.4074 q^{78} +(137.199 - 99.6808i) q^{79} +(21.2897 + 65.5229i) q^{80} +(218.110 - 671.275i) q^{81} +(-382.609 - 277.982i) q^{82} +(245.400 + 178.293i) q^{83} +(-9.02020 + 27.7613i) q^{84} +(-26.2720 - 80.8568i) q^{85} +(415.067 - 301.564i) q^{86} -60.6486 q^{87} -1146.68 q^{89} +(-81.7897 + 59.4237i) q^{90} +(-597.646 - 1839.36i) q^{91} +(106.249 - 327.000i) q^{92} +(30.7009 + 22.3055i) q^{93} +(-1021.70 - 742.308i) q^{94} +(26.1880 - 80.5984i) q^{95} +(-14.1063 - 43.4147i) q^{96} +(-519.065 + 377.123i) q^{97} +1121.14 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} - 2 q^{9} + 136 q^{10} - 352 q^{12} - 130 q^{13} + 160 q^{14} - 64 q^{15} + 62 q^{16} + 14 q^{17} + 194 q^{18} + 48 q^{19} + 98 q^{20} - 544 q^{21} - 512 q^{23} - 144 q^{24} + 176 q^{25} + 106 q^{26} - 16 q^{27} - 296 q^{28} + 30 q^{29} + 280 q^{30} + 184 q^{31} + 1208 q^{32} + 1784 q^{34} + 128 q^{35} - 394 q^{36} - 126 q^{37} + 168 q^{38} + 496 q^{39} - 186 q^{40} - 370 q^{41} - 712 q^{42} - 1056 q^{43} - 808 q^{45} + 664 q^{46} - 256 q^{47} - 152 q^{48} - 522 q^{49} + 64 q^{50} - 488 q^{51} - 602 q^{52} + 162 q^{53} + 512 q^{54} + 1344 q^{56} + 24 q^{57} - 918 q^{58} + 1304 q^{59} - 752 q^{60} + 300 q^{61} - 1312 q^{62} - 1336 q^{63} + 262 q^{64} - 2504 q^{65} - 2624 q^{67} + 934 q^{68} + 280 q^{69} - 872 q^{70} + 1176 q^{71} - 150 q^{72} + 668 q^{73} + 2022 q^{74} - 464 q^{75} + 768 q^{76} + 7840 q^{78} - 416 q^{79} - 214 q^{80} - 26 q^{81} + 322 q^{82} + 960 q^{83} + 1832 q^{84} - 502 q^{85} + 264 q^{86} + 4032 q^{87} - 4296 q^{89} - 1186 q^{90} + 688 q^{91} - 944 q^{92} - 1864 q^{93} - 2408 q^{94} - 24 q^{95} + 1664 q^{96} + 338 q^{97} + 3288 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 - 2 * q^9 + 136 * q^10 - 352 * q^12 - 130 * q^13 + 160 * q^14 - 64 * q^15 + 62 * q^16 + 14 * q^17 + 194 * q^18 + 48 * q^19 + 98 * q^20 - 544 * q^21 - 512 * q^23 - 144 * q^24 + 176 * q^25 + 106 * q^26 - 16 * q^27 - 296 * q^28 + 30 * q^29 + 280 * q^30 + 184 * q^31 + 1208 * q^32 + 1784 * q^34 + 128 * q^35 - 394 * q^36 - 126 * q^37 + 168 * q^38 + 496 * q^39 - 186 * q^40 - 370 * q^41 - 712 * q^42 - 1056 * q^43 - 808 * q^45 + 664 * q^46 - 256 * q^47 - 152 * q^48 - 522 * q^49 + 64 * q^50 - 488 * q^51 - 602 * q^52 + 162 * q^53 + 512 * q^54 + 1344 * q^56 + 24 * q^57 - 918 * q^58 + 1304 * q^59 - 752 * q^60 + 300 * q^61 - 1312 * q^62 - 1336 * q^63 + 262 * q^64 - 2504 * q^65 - 2624 * q^67 + 934 * q^68 + 280 * q^69 - 872 * q^70 + 1176 * q^71 - 150 * q^72 + 668 * q^73 + 2022 * q^74 - 464 * q^75 + 768 * q^76 + 7840 * q^78 - 416 * q^79 - 214 * q^80 - 26 * q^81 + 322 * q^82 + 960 * q^83 + 1832 * q^84 - 502 * q^85 + 264 * q^86 + 4032 * q^87 - 4296 * q^89 - 1186 * q^90 + 688 * q^91 - 944 * q^92 - 1864 * q^93 - 2408 * q^94 - 24 * q^95 + 1664 * q^96 + 338 * q^97 + 3288 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.99350	+	1.44836i	−0.704809	+	0.512074i	−0.881495	−	0.472194i	$-0.843462\pi$
$2$	−1.99350	+	1.44836i	−0.704809	+	0.512074i	0.176686	+	0.984267i	$0.443462\pi$
$3$	−0.165602	−	0.509670i	−0.0318701	−	0.0980860i	0.933856	−	0.357649i	$-0.116422\pi$
$3$	−0.165602	−	0.509670i	−0.0318701	−	0.0980860i	−0.965726	+	0.259563i	$0.916422\pi$
$4$	−0.595848	+	1.83383i	−0.0744809	+	0.229229i
$5$	1.24257	+	0.902778i	0.111139	+	0.0807470i	0.641966	−	0.766733i	$-0.278119\pi$
$5$	1.24257	+	0.902778i	0.111139	+	0.0807470i	−0.530828	+	0.847480i	$0.678119\pi$
$6$	1.06831	+	0.776175i	0.0726895	+	0.0528120i
$7$	−8.72933	+	26.8661i	−0.471340	+	1.45063i	0.379492	+	0.925195i	$0.376099\pi$
$7$	−8.72933	+	26.8661i	−0.471340	+	1.45063i	−0.850831	+	0.525439i	$0.823901\pi$
$8$	−7.55982	−	23.2667i	−0.334100	−	1.02825i
$9$	21.6111	−	15.7014i	0.800412	−	0.581533i
$10$	−3.78461			−0.119680
$11$		0			0
$11$		0			0
$12$	1.03332			0.0248578
$13$	−55.3886	+	40.2422i	−1.18170	+	0.858552i	−0.992362	−	0.123361i	$-0.960633\pi$
$13$	−55.3886	+	40.2422i	−1.18170	+	0.858552i	−0.189333	+	0.981913i	$0.560633\pi$
$14$	−21.5100	−	66.2009i	−0.410627	−	1.26378i
$15$	0.254347	−	0.782801i	0.00437815	−	0.0134746i
$16$	36.2896	+	26.3659i	0.567025	+	0.411968i
$17$	−44.7822	−	32.5362i	−0.638899	−	0.464187i	0.220573	−	0.975370i	$-0.429207\pi$
$17$	−44.7822	−	32.5362i	−0.638899	−	0.464187i	−0.859472	+	0.511183i	$0.829207\pi$
$18$	−20.3405	+	62.6015i	−0.266349	+	0.819739i
$19$	−17.0506	−	52.4764i	−0.205878	−	0.633627i	−0.999676	−	0.0254456i	$-0.991900\pi$
$19$	−17.0506	−	52.4764i	−0.205878	−	0.633627i	0.793798	−	0.608181i	$-0.208100\pi$
$20$	−2.39592	+	1.74074i	−0.0267872	+	0.0194621i
$21$	15.1384			0.157308
$22$		0			0
$23$	−178.315			−1.61658			−0.808290	−	0.588785i	$-0.799606\pi$
$23$	−178.315			−1.61658			−0.808290	+	0.588785i	$0.799606\pi$
$24$	−10.6064	+	7.70602i	−0.0902095	+	0.0655411i
$25$	−37.8982	−	116.639i	−0.303185	−	0.933108i
$26$	52.1319	−	160.446i	0.393227	−	1.21023i
$27$	−23.2872	−	16.9192i	−0.165986	−	0.120596i
$28$	−44.0666	−	32.0162i	−0.297421	−	0.216089i
$29$	34.9720	−	107.633i	0.223936	−	0.689203i	−0.774462	−	0.632620i	$-0.781979\pi$
$29$	34.9720	−	107.633i	0.223936	−	0.689203i	0.998398	−	0.0565831i	$-0.0180206\pi$
$30$	0.626738	+	1.92890i	0.00381420	+	0.0117389i
$31$	−57.2887	+	41.6227i	−0.331915	+	0.241150i	−0.741243	−	0.671237i	$-0.765763\pi$
$31$	−57.2887	+	41.6227i	−0.331915	+	0.241150i	0.409328	+	0.912387i	$0.365763\pi$
$32$	85.1821			0.470569
$33$		0			0
$34$	136.397			0.687999
$35$	−35.1009	+	25.5023i	−0.169518	+	0.123162i
$36$	15.9168	+	48.9868i	0.0736887	+	0.226791i
$37$	−65.0988	+	200.353i	−0.289248	+	0.890213i	0.695845	+	0.718192i	$0.255030\pi$
$37$	−65.0988	+	200.353i	−0.289248	+	0.890213i	−0.985093	+	0.172022i	$0.944970\pi$
$38$	109.995	+	79.9162i	0.469568	+	0.341161i
$39$	29.6827	+	21.5657i	0.121873	+	0.0885456i
$40$	11.6111	−	35.7354i	0.0458970	−	0.141256i
$41$	59.3091	+	182.535i	0.225915	+	0.695295i	0.998197	+	0.0600158i	$0.0191151\pi$
$41$	59.3091	+	182.535i	0.225915	+	0.695295i	−0.772282	+	0.635280i	$0.780885\pi$
$42$	−30.1785	+	21.9259i	−0.110872	+	0.0805535i
$43$	−208.210			−0.738413			−0.369207	−	0.929347i	$-0.620371\pi$
$43$	−208.210			−0.738413			−0.369207	+	0.929347i	$0.620371\pi$
$44$		0			0
$45$	41.0282			0.135914
$46$	355.472	−	258.265i	1.13938	−	0.827807i
$47$	158.376	+	487.431i	0.491521	+	1.51275i	0.822309	+	0.569042i	$0.192686\pi$
$47$	158.376	+	487.431i	0.491521	+	1.51275i	−0.330787	+	0.943705i	$0.607314\pi$
$48$	7.42830	−	22.8619i	0.0223371	−	0.0687466i
$49$	−368.094	−	267.436i	−1.07316	−	0.779697i
$50$	244.485	+	177.629i	0.691508	+	0.502410i
$51$	−9.16669	+	28.2122i	−0.0251685	+	0.0774607i
$52$	−40.7942	−	125.552i	−0.108791	−	0.334824i
$53$	303.744	−	220.683i	0.787217	−	0.571947i	−0.119919	−	0.992784i	$-0.538264\pi$
$53$	303.744	−	220.683i	0.787217	−	0.571947i	0.907136	+	0.420837i	$0.138264\pi$
$54$	70.9282			0.178743
$55$		0			0
$56$	691.079			1.64910
$57$	−23.9220	+	17.3804i	−0.0555885	+	0.0403874i
$58$	86.1746	+	265.218i	0.195091	+	0.600428i
$59$	−156.519	+	481.717i	−0.345375	+	1.06295i	0.616008	+	0.787740i	$0.288749\pi$
$59$	−156.519	+	481.717i	−0.345375	+	1.06295i	−0.961383	+	0.275214i	$0.911251\pi$
$60$	1.28397	+	0.932860i	0.00276267	+	0.00200719i
$61$	379.184	+	275.493i	0.795894	+	0.578251i	0.909707	−	0.415251i	$-0.136306\pi$
$61$	379.184	+	275.493i	0.795894	+	0.578251i	−0.113812	+	0.993502i	$0.536306\pi$
$62$	53.9203	−	165.950i	0.110450	−	0.339930i
$63$	233.185	+	717.670i	0.466326	+	1.43520i
$64$	−460.127	+	334.302i	−0.898686	+	0.652934i
$65$	−105.154			−0.200657
$66$		0			0
$67$	−289.895			−0.528601			−0.264301	−	0.964440i	$-0.585141\pi$
$67$	−289.895			−0.528601			−0.264301	+	0.964440i	$0.585141\pi$
$68$	86.3492	−	62.7363i	0.153991	−	0.111881i
$69$	29.5293	+	90.8819i	0.0515205	+	0.158564i
$70$	33.0371	−	101.678i	0.0564099	−	0.173612i
$71$	318.761	+	231.593i	0.532817	+	0.387114i	0.821410	−	0.570338i	$-0.193188\pi$
$71$	318.761	+	231.593i	0.532817	+	0.387114i	−0.288594	+	0.957452i	$0.593188\pi$
$72$	−528.697	−	384.121i	−0.865382	−	0.628737i
$73$	89.4723	−	275.367i	0.143451	−	0.441497i	−0.853357	−	0.521326i	$-0.825437\pi$
$73$	89.4723	−	275.367i	0.143451	−	0.441497i	0.996809	+	0.0798290i	$0.0254374\pi$
$74$	−160.410	−	493.691i	−0.251990	−	0.775546i
$75$	−53.1711	+	38.6311i	−0.0818623	+	0.0594764i
$76$	106.392			0.160579
$77$		0			0
$78$	−90.4074			−0.131239
$79$	137.199	−	99.6808i	0.195393	−	0.141962i	−0.485787	−	0.874077i	$-0.661467\pi$
$79$	137.199	−	99.6808i	0.195393	−	0.141962i	0.681180	+	0.732116i	$0.261467\pi$
$80$	21.2897	+	65.5229i	0.0297532	+	0.0915711i
$81$	218.110	−	671.275i	0.299191	−	0.920816i
$82$	−382.609	−	277.982i	−0.515269	−	0.374365i
$83$	245.400	+	178.293i	0.324532	+	0.235786i	0.738107	−	0.674684i	$-0.235720\pi$
$83$	245.400	+	178.293i	0.324532	+	0.235786i	−0.413575	+	0.910470i	$0.635720\pi$
$84$	−9.02020	+	27.7613i	−0.0117165	+	0.0360596i
$85$	−26.2720	−	80.8568i	−0.0335246	−	0.103178i
$86$	415.067	−	301.564i	0.520440	−	0.378122i
$87$	−60.6486			−0.0747380
$88$		0			0
$89$	−1146.68			−1.36571			−0.682854	−	0.730555i	$-0.739262\pi$
$89$	−1146.68			−1.36571			−0.682854	+	0.730555i	$0.739262\pi$
$90$	−81.7897	+	59.4237i	−0.0957932	+	0.0695978i
$91$	−597.646	−	1839.36i	−0.688465	−	2.11888i
$92$	106.249	−	327.000i	0.120404	−	0.370566i
$93$	30.7009	+	22.3055i	0.0342316	+	0.0248707i
$94$	−1021.70	−	742.308i	−1.12107	−	0.814502i
$95$	26.1880	−	80.5984i	0.0282824	−	0.0870444i
$96$	−14.1063	−	43.4147i	−0.0149971	−	0.0461562i
$97$	−519.065	+	377.123i	−0.543331	+	0.394753i	−0.825321	−	0.564665i	$-0.809006\pi$
$97$	−519.065	+	377.123i	−0.543331	+	0.394753i	0.281990	+	0.959417i	$0.409006\pi$
$98$	1121.14			1.15564
$99$		0			0
$100$	236.477			0.236477
$101$	−896.042	+	651.013i	−0.882768	+	0.641368i	−0.933982	−	0.357319i	$-0.883691\pi$
$101$	−896.042	+	651.013i	−0.882768	+	0.641368i	0.0512145	+	0.998688i	$0.483691\pi$
$102$	−22.5877	−	69.5176i	−0.0219266	−	0.0674831i
$103$	−92.1790	+	283.698i	−0.0881812	+	0.271394i	−0.985417	−	0.170158i	$-0.945572\pi$
$103$	−92.1790	+	283.698i	−0.0881812	+	0.271394i	0.897235	+	0.441552i	$0.145572\pi$
$104$	1355.03	+	984.489i	1.27761	+	0.928241i
$105$	18.8105	+	13.6667i	0.0174831	+	0.0127022i
$106$	−285.885	+	879.864i	−0.261959	+	0.806226i
$107$	−184.831	−	568.851i	−0.166993	−	0.513953i	0.832184	−	0.554499i	$-0.187090\pi$
$107$	−184.831	−	568.851i	−0.166993	−	0.513953i	−0.999178	+	0.0405464i	$0.987090\pi$
$108$	44.9025	−	32.6236i	0.0400069	−	0.0290667i
$109$	−1530.16			−1.34461			−0.672305	−	0.740275i	$-0.734695\pi$
$109$	−1530.16			−1.34461			−0.672305	+	0.740275i	$0.734695\pi$
$110$		0			0
$111$	112.895			0.0965358
$112$	−1025.13	+	744.804i	−0.864876	+	0.628369i
$113$	−46.6648	−	143.619i	−0.0388482	−	0.119563i	0.929752	−	0.368187i	$-0.120021\pi$
$113$	−46.6648	−	143.619i	−0.0388482	−	0.119563i	−0.968600	+	0.248625i	$0.920021\pi$
$114$	22.5155	−	69.2955i	0.0184979	−	0.0569308i
$115$	−221.569	−	160.979i	−0.179664	−	0.130534i
$116$	176.542	+	128.265i	0.141306	+	0.102665i
$117$	−565.152	+	1739.36i	−0.446566	+	1.37439i
$118$	−385.680	−	1187.00i	−0.300887	−	0.926036i
$119$	1265.04	−	919.105i	0.974504	−	0.708018i
$120$	−20.1360			−0.0153180
$121$		0			0
$122$	−1154.92			−0.857060
$123$	83.2106	−	60.4561i	0.0609988	−	0.0443182i
$124$	−42.1936	−	129.859i	−0.0305572	−	0.0940455i
$125$	117.535	−	361.736i	0.0841012	−	0.258837i
$126$	−1504.30	−	1092.94i	−1.06360	−	0.772751i
$127$	562.872	+	408.951i	0.393282	+	0.285736i	0.766799	−	0.641887i	$-0.221848\pi$
$127$	562.872	+	408.951i	0.393282	+	0.285736i	−0.373517	+	0.927623i	$0.621848\pi$
$128$	222.491	−	684.758i	0.153638	−	0.472849i
$129$	34.4800	+	106.118i	0.0235333	+	0.0724280i
$130$	209.624	−	152.301i	0.141425	−	0.102751i
$131$	1665.68			1.11093			0.555463	−	0.831541i	$-0.312541\pi$
$131$	1665.68			1.11093			0.555463	+	0.831541i	$0.312541\pi$
$132$		0			0
$133$	1558.68			1.01620
$134$	577.905	−	419.873i	0.372563	−	0.270683i
$135$	−13.6617	−	42.0464i	−0.00870973	−	0.0268058i
$136$	−418.465	+	1287.90i	−0.263846	+	0.812035i
$137$	1298.86	+	943.675i	0.809992	+	0.588494i	0.913828	−	0.406101i	$-0.133112\pi$
$137$	1298.86	+	943.675i	0.809992	+	0.588494i	−0.103836	+	0.994594i	$0.533112\pi$
$138$	−190.497	−	138.404i	−0.117508	−	0.0853748i
$139$	−330.432	+	1016.96i	−0.201632	+	0.620560i	0.798203	+	0.602389i	$0.205784\pi$
$139$	−330.432	+	1016.96i	−0.201632	+	0.620560i	−0.999835	+	0.0181710i	$0.994216\pi$
$140$	−25.8521	−	79.5647i	−0.0156065	−	0.0480317i
$141$	222.201	−	161.439i	0.132714	−	0.0964227i
$142$	−970.881			−0.573765
$143$		0			0
$144$	1198.24			0.693426
$145$	140.624	−	102.169i	0.0805390	−	0.0585150i
$146$	220.469	+	678.533i	0.124973	+	0.384629i
$147$	−75.3471	+	231.894i	−0.0422757	+	0.130111i
$148$	−328.625	−	238.760i	−0.182519	−	0.132608i
$149$	287.340	+	208.765i	0.157985	+	0.114783i	0.663969	−	0.747760i	$-0.268871\pi$
$149$	287.340	+	208.765i	0.157985	+	0.114783i	−0.505984	+	0.862543i	$0.668871\pi$
$150$	50.0448	−	154.022i	0.0272410	−	0.0838390i
$151$	580.814	+	1787.56i	0.313020	+	0.963375i	0.976562	+	0.215237i	$0.0690523\pi$
$151$	580.814	+	1787.56i	0.313020	+	0.963375i	−0.663542	+	0.748139i	$0.730948\pi$
$152$	−1092.05	+	793.424i	−0.582746	+	0.423389i
$153$	−1478.66			−0.781322
$154$		0			0
$155$	−108.761			−0.0563607
$156$	−57.2342	+	41.5831i	−0.0293744	+	0.0213417i
$157$	772.539	+	2377.63i	0.392709	+	1.20863i	0.930731	+	0.365704i	$0.119172\pi$
$157$	772.539	+	2377.63i	0.392709	+	1.20863i	−0.538022	+	0.842931i	$0.680828\pi$
$158$	−129.132	+	397.427i	−0.0650202	+	0.200112i
$159$	−162.776	−	118.264i	−0.0811886	−	0.0589870i
$160$	105.845	+	76.9005i	0.0522984	+	0.0379970i
$161$	1556.57	−	4790.64i	0.761958	−	2.34507i
$162$	537.446	+	1654.09i	0.260653	+	0.802207i
$163$	−1507.22	+	1095.06i	−0.724260	+	0.526206i	−0.887742	−	0.460341i	$-0.847727\pi$
$163$	−1507.22	+	1095.06i	−0.724260	+	0.526206i	0.163482	+	0.986546i	$0.447727\pi$
$164$	−370.077			−0.176208
$165$		0			0
$166$	−747.438			−0.349473
$167$	2141.68	−	1556.02i	0.992386	−	0.721011i	0.0319436	−	0.999490i	$-0.489830\pi$
$167$	2141.68	−	1556.02i	0.992386	−	0.721011i	0.960442	+	0.278479i	$0.0898303\pi$
$168$	−114.444	−	352.222i	−0.0525568	−	0.161753i
$169$	769.555	−	2368.45i	0.350276	−	1.07804i
$170$	169.483	+	123.137i	0.0764633	+	0.0555538i
$171$	−1192.43	−	866.355i	−0.533262	−	0.387437i
$172$	124.062	−	381.822i	0.0549977	−	0.169266i
$173$	−651.836	−	2006.14i	−0.286463	−	0.881643i	−0.985956	−	0.167004i	$-0.946591\pi$
$173$	−651.836	−	2006.14i	−0.286463	−	0.881643i	0.699493	−	0.714639i	$-0.253409\pi$
$174$	120.903	−	87.8411i	0.0526760	−	0.0382714i
$175$	3464.45			1.49650
$176$		0			0
$177$	271.437			0.115268
$178$	2285.91	−	1660.81i	0.962563	−	0.699343i
$179$	429.919	+	1323.15i	0.179517	+	0.552498i	0.999811	−	0.0194450i	$-0.00618992\pi$
$179$	429.919	+	1323.15i	0.179517	+	0.552498i	−0.820294	+	0.571943i	$0.806190\pi$
$180$	−24.4465	+	75.2387i	−0.0101230	+	0.0311553i
$181$	−2994.50	−	2175.63i	−1.22972	−	0.893443i	−0.232850	−	0.972513i	$-0.574805\pi$
$181$	−2994.50	−	2175.63i	−1.22972	−	0.893443i	−0.996869	+	0.0790692i	$0.974805\pi$
$182$	3855.47	+	2801.17i	1.57026	+	1.14086i
$183$	77.6171	−	238.881i	0.0313531	−	0.0964950i
$184$	1348.03	+	4148.82i	0.540099	+	1.66225i
$185$	−261.764	+	190.183i	−0.104029	+	0.0755812i
$186$	−93.5088			−0.0368624
$187$		0			0
$188$	−988.234			−0.383374
$189$	657.834	−	477.945i	0.253177	−	0.183944i
$190$	64.5299	+	198.603i	0.0246394	+	0.0758323i
$191$	−1091.77	+	3360.11i	−0.413599	+	1.27293i	0.499899	+	0.866084i	$0.333371\pi$
$191$	−1091.77	+	3360.11i	−0.413599	+	1.27293i	−0.913498	+	0.406844i	$0.866629\pi$
$192$	246.581	+	179.152i	0.0926848	+	0.0673395i
$193$	−2108.02	−	1531.57i	−0.786212	−	0.571216i	0.120625	−	0.992698i	$-0.461510\pi$
$193$	−2108.02	−	1531.57i	−0.786212	−	0.571216i	−0.906837	+	0.421482i	$0.861510\pi$
$194$	488.546	−	1503.59i	0.180802	−	0.556451i
$195$	17.4137	+	53.5938i	0.00639497	+	0.0196817i
$196$	709.761	−	515.671i	0.258659	−	0.187927i
$197$	−719.202			−0.260107			−0.130053	−	0.991507i	$-0.541515\pi$
$197$	−719.202			−0.260107			−0.130053	+	0.991507i	$0.541515\pi$
$198$		0			0
$199$	1035.15			0.368744			0.184372	−	0.982857i	$-0.440975\pi$
$199$	1035.15			0.368744			0.184372	+	0.982857i	$0.440975\pi$
$200$	−2427.30	+	1763.53i	−0.858179	+	0.623503i
$201$	48.0071	+	147.751i	0.0168466	+	0.0518484i
$202$	843.358	−	2595.59i	0.293755	−	0.904084i
$203$	2586.39	+	1879.12i	0.894232	+	0.649698i
$204$	−46.2744	−	33.6203i	−0.0158816	−	0.0115387i
$205$	−91.0927	+	280.355i	−0.0310351	+	0.0955162i
$206$	−227.138	−	699.060i	−0.0768227	−	0.236436i
$207$	−3853.59	+	2799.80i	−1.29393	+	0.940095i
$208$	−3071.05			−1.02375
$209$		0			0
$210$	−57.2931			−0.0188267
$211$	−288.250	+	209.426i	−0.0940472	+	0.0683293i	−0.633815	−	0.773485i	$-0.718512\pi$
$211$	−288.250	+	209.426i	−0.0940472	+	0.0683293i	0.539768	+	0.841814i	$0.318512\pi$
$212$	223.710	+	688.509i	0.0724739	+	0.223052i
$213$	65.2488	−	200.815i	0.0209895	−	0.0645992i
$214$	1192.36	+	866.303i	0.380880	+	0.276725i
$215$	−258.715	−	187.968i	−0.0820662	−	0.0596246i
$216$	−217.607	+	669.724i	−0.0685475	+	0.210967i
$217$	−618.148	−	1902.46i	−0.193376	−	0.595151i
$218$	3050.37	−	2216.22i	0.947692	−	0.688539i
$219$	−155.163			−0.0478765
$220$		0			0
$221$	3789.75			1.15351
$222$	−225.055	+	163.512i	−0.0680393	+	0.0494334i
$223$	−90.4011	−	278.226i	−0.0271467	−	0.0835489i	0.936565	−	0.350493i	$-0.113986\pi$
$223$	−90.4011	−	278.226i	−0.0271467	−	0.0835489i	−0.963712	+	0.266944i	$0.913986\pi$
$224$	−743.583	+	2288.51i	−0.221798	+	0.682623i
$225$	−2650.41	−	1925.64i	−0.785307	−	0.570559i
$226$	301.039	+	218.718i	0.0886054	+	0.0643756i
$227$	−1731.74	+	5329.75i	−0.506343	+	1.55836i	0.292159	+	0.956370i	$0.405626\pi$
$227$	−1731.74	+	5329.75i	−0.506343	+	1.55836i	−0.798502	+	0.601993i	$0.794374\pi$
$228$	−17.6187	−	54.2249i	−0.00511768	−	0.0157506i
$229$	4574.49	−	3323.56i	1.32005	−	0.959070i	0.320114	−	0.947379i	$-0.396279\pi$
$229$	4574.49	−	3323.56i	1.32005	−	0.959070i	0.999932	−	0.0116906i	$-0.00372132\pi$
$230$	674.854			0.193472
$231$		0			0
$232$	−2768.65			−0.783493
$233$	−2065.49	+	1500.66i	−0.580749	+	0.421939i	−0.838994	−	0.544141i	$-0.816856\pi$
$233$	−2065.49	+	1500.66i	−0.580749	+	0.421939i	0.258245	+	0.966079i	$0.416856\pi$
$234$	−1392.59	−	4285.95i	−0.389045	−	1.19736i
$235$	−243.249	+	748.644i	−0.0675227	+	0.207814i
$236$	−790.126	−	574.060i	−0.217936	−	0.158340i
$237$	−73.5246	−	53.4188i	−0.0201516	−	0.0146410i
$238$	−1190.66	+	3664.47i	−0.324281	+	0.998035i
$239$	−1636.95	−	5038.00i	−0.443034	−	1.36352i	−0.884625	−	0.466303i	$-0.845586\pi$
$239$	−1636.95	−	5038.00i	−0.443034	−	1.36352i	0.441591	−	0.897217i	$-0.354414\pi$
$240$	29.8694	−	21.7014i	0.00803360	−	0.00583675i
$241$	4145.14			1.10793			0.553966	−	0.832539i	$-0.313114\pi$
$241$	4145.14			1.10793			0.553966	+	0.832539i	$0.313114\pi$
$242$		0			0
$243$	−1155.43			−0.305025
$244$	−731.144	+	531.207i	−0.191831	+	0.139373i
$245$	−215.947	−	664.615i	−0.0563115	−	0.173309i
$246$	−78.3181	+	241.038i	−0.0202983	+	0.0624717i
$247$	3056.17	+	2220.44i	0.787286	+	0.571997i
$248$	1401.52	+	1018.26i	0.358857	+	0.260725i
$249$	50.2321	−	154.599i	0.0127845	−	0.0393465i
$250$	289.618	+	891.354i	0.0732683	+	0.225497i
$251$	1446.63	−	1051.04i	0.363786	−	0.264306i	−0.390843	−	0.920457i	$-0.627817\pi$
$251$	1446.63	−	1051.04i	0.363786	−	0.264306i	0.754630	+	0.656151i	$0.227817\pi$
$252$	−1455.03			−0.363723
$253$		0			0
$254$	−1714.40			−0.423507
$255$	−36.8596	+	26.7800i	−0.00905190	+	0.00657659i
$256$	−857.782	−	2639.98i	−0.209419	−	0.644527i
$257$	1596.69	−	4914.12i	0.387545	−	1.19274i	−0.547072	−	0.837085i	$-0.684258\pi$
$257$	1596.69	−	4914.12i	0.387545	−	1.19274i	0.934617	−	0.355655i	$-0.115742\pi$
$258$	−222.434	−	161.608i	−0.0536749	−	0.0389971i
$259$	−4814.45	−	3497.90i	−1.15504	−	0.839186i
$260$	62.6557	−	192.834i	0.0149452	−	0.0459965i
$261$	−934.200	−	2875.17i	−0.221554	−	0.681873i
$262$	−3320.54	+	2412.51i	−0.782990	+	0.568876i
$263$	−57.6791			−0.0135234			−0.00676169	−	0.999977i	$-0.502152\pi$
$263$	−57.6791			−0.0135234			−0.00676169	+	0.999977i	$0.502152\pi$
$264$		0			0
$265$	576.651			0.133673
$266$	−3107.22	+	2257.53i	−0.716226	+	0.520368i
$267$	189.892	+	584.429i	0.0435252	+	0.133957i
$268$	172.733	−	531.618i	0.0393707	−	0.121171i
$269$	2449.75	+	1779.85i	0.555256	+	0.403417i	0.829720	−	0.558180i	$-0.188500\pi$
$269$	2449.75	+	1779.85i	0.555256	+	0.403417i	−0.274463	+	0.961598i	$0.588500\pi$
$270$	88.1331	+	64.0325i	0.0198652	+	0.0144329i
$271$	−459.767	+	1415.02i	−0.103058	+	0.317181i	−0.989270	−	0.146100i	$-0.953328\pi$
$271$	−459.767	+	1415.02i	−0.103058	+	0.317181i	0.886211	+	0.463281i	$0.153328\pi$
$272$	−767.281	−	2361.45i	−0.171041	−	0.526411i
$273$	−838.497	+	609.204i	−0.185891	+	0.135058i
$274$	−3956.06			−0.872241
$275$		0			0
$276$	−184.257			−0.0401847
$277$	−6035.64	+	4385.15i	−1.30919	+	0.951185i	−0.309194	+	0.950999i	$0.600059\pi$
$277$	−6035.64	+	4385.15i	−1.30919	+	0.951185i	−1.00000		0.000185599i	$0.999941\pi$
$278$	−814.218	−	2505.90i	−0.175660	−	0.540626i
$279$	−584.539	+	1799.03i	−0.125432	+	0.386039i
$280$	858.713	+	623.892i	0.183278	+	0.133159i
$281$	−728.240	−	529.098i	−0.154602	−	0.112325i	0.507795	−	0.861478i	$-0.330461\pi$
$281$	−728.240	−	529.098i	−0.154602	−	0.112325i	−0.662397	+	0.749153i	$0.730461\pi$
$282$	−209.137	+	643.657i	−0.0441628	+	0.135919i
$283$	2004.57	+	6169.42i	0.421057	+	1.29588i	0.906720	+	0.421734i	$0.138578\pi$
$283$	2004.57	+	6169.42i	0.421057	+	1.29588i	−0.485662	+	0.874146i	$0.661422\pi$
$284$	−614.636	+	446.559i	−0.128422	+	0.0933043i
$285$	−45.4153			−0.00943920
$286$		0			0
$287$	−5421.72			−1.11510
$288$	1840.88	−	1337.48i	0.376649	−	0.273651i
$289$	−571.358	−	1758.46i	−0.116295	−	0.357920i
$290$	−132.355	+	407.348i	−0.0268006	+	0.0824838i
$291$	278.166	+	202.100i	0.0560357	+	0.0407123i
$292$	451.665	+	328.154i	0.0905195	+	0.0657663i
$293$	1894.08	−	5829.39i	0.377657	−	1.16231i	−0.564011	−	0.825767i	$-0.690743\pi$
$293$	1894.08	−	5829.39i	0.377657	−	1.16231i	0.941668	−	0.336542i	$-0.109257\pi$
$294$	−185.663	−	571.411i	−0.0368302	−	0.113352i
$295$	−629.370	+	457.264i	−0.124215	+	0.0902473i
$296$	5153.71			1.01200
$297$		0			0
$298$	−875.179			−0.170127
$299$	9876.64	−	7175.80i	1.91030	−	1.38792i
$300$	−39.1610	−	120.525i	−0.00753653	−	0.0231951i
$301$	1817.54	−	5593.80i	0.348043	−	1.07117i
$302$	−3746.89	−	2722.27i	−0.713938	−	0.518706i
$303$	480.188	+	348.877i	0.0910431	+	0.0661467i
$304$	764.829	−	2353.90i	0.144296	−	0.444097i
$305$	222.453	+	684.638i	0.0417626	+	0.128532i
$306$	2947.70	−	2141.63i	0.550683	−	0.400094i
$307$	5377.67			0.999740			0.499870	−	0.866101i	$-0.333381\pi$
$307$	5377.67			0.999740			0.499870	+	0.866101i	$0.333381\pi$
$308$		0			0
$309$	159.857			0.0294303
$310$	216.816	−	157.526i	0.0397235	−	0.0288608i
$311$	−1874.63	−	5769.50i	−0.341801	−	1.05196i	−0.963274	−	0.268521i	$-0.913465\pi$
$311$	−1874.63	−	5769.50i	−0.341801	−	1.05196i	0.621473	−	0.783436i	$-0.286535\pi$
$312$	277.368	−	853.652i	0.0503298	−	0.154899i
$313$	−2622.17	−	1905.12i	−0.473526	−	0.344037i	0.325288	−	0.945615i	$-0.394539\pi$
$313$	−2622.17	−	1905.12i	−0.473526	−	0.344037i	−0.798814	+	0.601578i	$0.794539\pi$
$314$	−4983.73	−	3620.89i	−0.895695	−	0.650760i
$315$	−358.148	+	1102.27i	−0.0640615	+	0.197161i
$316$	101.048	+	310.994i	0.0179886	+	0.0553632i
$317$	−5274.24	+	3831.96i	−0.934482	+	0.678941i	−0.947086	−	0.320979i	$-0.895988\pi$
$317$	−5274.24	+	3831.96i	−0.934482	+	0.678941i	0.0126037	+	0.999921i	$0.495988\pi$
$318$	495.783			0.0874281
$319$		0			0
$320$	−873.540			−0.152601
$321$	−259.318	+	188.406i	−0.0450895	+	0.0327594i
$322$	3835.56	+	11804.6i	0.663811	+	2.04300i
$323$	−943.816	+	2904.77i	−0.162586	+	0.500389i
$324$	1101.04	+	799.955i	0.188794	+	0.137167i
$325$	6792.92	+	4935.34i	1.15939	+	0.842349i
$326$	1418.60	−	4365.99i	0.241009	−	0.741749i
$327$	253.396	+	779.874i	0.0428528	+	0.131887i
$328$	3798.62	−	2759.86i	0.639462	−	0.464597i
$329$	−14477.9			−2.42612
$330$		0			0
$331$	5879.55			0.976343			0.488171	−	0.872748i	$-0.337664\pi$
$331$	5879.55			0.976343			0.488171	+	0.872748i	$0.337664\pi$
$332$	−473.181	+	343.786i	−0.0782204	+	0.0568304i
$333$	1738.97	+	5352.00i	0.286171	+	0.880745i
$334$	−2015.76	+	6203.87i	−0.330232	+	1.01635i
$335$	−360.214	−	261.711i	−0.0587481	−	0.0426830i
$336$	549.368	+	399.139i	0.0891978	+	0.0648060i
$337$	414.906	−	1276.95i	0.0670663	−	0.206409i	−0.911907	−	0.410397i	$-0.865390\pi$
$337$	414.906	−	1276.95i	0.0670663	−	0.206409i	0.978973	+	0.203988i	$0.0653903\pi$
$338$	1896.26	+	5836.10i	0.305157	+	0.939177i
$339$	−65.4707	+	47.5672i	−0.0104893	+	0.00762093i
$340$	163.932			0.0261484
$341$		0			0
$342$	3631.91			0.574244
$343$	2559.38	−	1859.50i	0.402896	−	0.292721i
$344$	1574.03	+	4844.37i	0.246704	+	0.759277i
$345$	−45.3540	+	139.585i	−0.00707762	+	0.0217827i
$346$	4205.06	+	3055.15i	0.653368	+	0.474700i
$347$	4570.97	+	3321.01i	0.707155	+	0.513778i	0.882255	−	0.470773i	$-0.156025\pi$
$347$	4570.97	+	3321.01i	0.707155	+	0.513778i	−0.175100	+	0.984551i	$0.556025\pi$
$348$	36.1373	−	111.219i	0.00556656	−	0.0171321i
$349$	−386.133	−	1188.39i	−0.0592241	−	0.182273i	0.917068	−	0.398731i	$-0.130549\pi$
$349$	−386.133	−	1188.39i	−0.0592241	−	0.182273i	−0.976292	+	0.216458i	$0.930549\pi$
$350$	−6906.38	+	5017.78i	−1.05475	+	0.766319i
$351$	1970.71			0.299683
$352$		0			0
$353$	5984.25			0.902293			0.451147	−	0.892450i	$-0.351015\pi$
$353$	5984.25			0.902293			0.451147	+	0.892450i	$0.351015\pi$
$354$	−541.109	+	393.139i	−0.0812419	+	0.0590257i
$355$	187.005	+	575.541i	0.0279582	+	0.0860466i
$356$	683.248	−	2102.82i	0.101719	−	0.313060i
$357$	−677.932	−	492.547i	−0.100504	−	0.0730206i
$358$	−2773.45	−	2015.03i	−0.409445	−	0.297479i
$359$	−672.424	+	2069.51i	−0.0988557	+	0.304247i	−0.988239	−	0.152915i	$-0.951134\pi$
$359$	−672.424	+	2069.51i	−0.0988557	+	0.304247i	0.889384	+	0.457162i	$0.151134\pi$
$360$	−310.166	−	954.592i	−0.0454088	−	0.139754i
$361$	3086.00	−	2242.11i	0.449920	−	0.326886i
$362$	9120.63			1.32423
$363$		0			0
$364$	3729.19			0.536985
$365$	359.771	−	261.389i	0.0515925	−	0.0374842i
$366$	191.256	+	588.627i	0.0273146	+	0.0840656i
$367$	−2615.64	+	8050.11i	−0.372031	+	1.14499i	0.573430	+	0.819255i	$0.305613\pi$
$367$	−2615.64	+	8050.11i	−0.372031	+	1.14499i	−0.945460	+	0.325738i	$0.894387\pi$
$368$	−6470.99	−	4701.45i	−0.916641	−	0.665978i
$369$	4147.78	+	3013.54i	0.585163	+	0.425145i
$370$	246.373	−	758.259i	0.0346171	−	0.106541i
$371$	3277.42	+	10086.8i	0.458639	+	1.41154i
$372$	−59.1977	+	43.0096i	−0.00825069	+	0.00599447i
$373$	−4248.93			−0.589816			−0.294908	−	0.955526i	$-0.595289\pi$
$373$	−4248.93			−0.589816			−0.294908	+	0.955526i	$0.595289\pi$
$374$		0			0
$375$	−203.830			−0.0280686
$376$	10143.6	−	7369.78i	1.39127	−	1.01082i
$377$	2394.33	+	7368.98i	0.327093	+	1.00669i
$378$	−619.156	+	1905.57i	−0.0842485	+	0.259290i
$379$	−3926.11	−	2852.48i	−0.532112	−	0.386602i	0.289035	−	0.957318i	$-0.406666\pi$
$379$	−3926.11	−	2852.48i	−0.532112	−	0.386602i	−0.821147	+	0.570716i	$0.806666\pi$
$380$	132.200	+	96.0487i	0.0178466	+	0.0129663i
$381$	115.217	−	354.602i	0.0154928	−	0.0476819i
$382$	−2690.22	−	8279.66i	−0.360324	−	1.10896i
$383$	6619.22	−	4809.15i	0.883098	−	0.641608i	−0.0509713	−	0.998700i	$-0.516232\pi$
$383$	6619.22	−	4809.15i	0.883098	−	0.641608i	0.934069	+	0.357092i	$0.116232\pi$
$384$	−385.846			−0.0512763
$385$		0			0
$386$	6420.61			0.846634
$387$	−4499.66	+	3269.19i	−0.591035	+	0.429412i
$388$	−382.296	−	1176.59i	−0.0500209	−	0.153949i
$389$	387.760	−	1193.40i	0.0505404	−	0.155547i	−0.922601	−	0.385756i	$-0.873941\pi$
$389$	387.760	−	1193.40i	0.0505404	−	0.155547i	0.973141	+	0.230208i	$0.0739407\pi$
$390$	−112.337	−	81.6178i	−0.0145857	−	0.0105971i
$391$	7985.35	+	5801.70i	1.03283	+	0.750395i
$392$	−3439.64	+	10586.1i	−0.443184	+	1.36398i
$393$	−275.840	−	848.948i	−0.0354053	−	0.108966i
$394$	1433.73	−	1041.67i	0.183325	−	0.133194i
$395$	260.469			0.0331787
$396$		0			0
$397$	−11519.3			−1.45627			−0.728133	−	0.685436i	$-0.759612\pi$
$397$	−11519.3			−1.45627			−0.728133	+	0.685436i	$0.759612\pi$
$398$	−2063.58	+	1499.28i	−0.259894	+	0.188824i
$399$	−258.120	−	794.410i	−0.0323863	−	0.0996748i
$400$	1699.98	−	5231.99i	0.212497	−	0.653998i
$401$	1214.06	+	882.069i	0.151191	+	0.109846i	0.660809	−	0.750554i	$-0.270213\pi$
$401$	1214.06	+	882.069i	0.151191	+	0.109846i	−0.509618	+	0.860401i	$0.670213\pi$
$402$	−309.699	−	225.009i	−0.0384238	−	0.0279165i
$403$	1498.16	−	4610.85i	0.185182	−	0.569932i
$404$	−659.942	−	2031.09i	−0.0812707	−	0.250125i
$405$	877.030	−	637.199i	0.107605	−	0.0781795i
$406$	−7877.63			−0.962956
$407$		0			0
$408$	725.704			0.0880581
$409$	−73.9390	+	53.7198i	−0.00893899	+	0.00649456i	−0.592246	−	0.805757i	$-0.701759\pi$
$409$	−73.9390	+	53.7198i	−0.00893899	+	0.00649456i	0.583307	+	0.812252i	$0.301759\pi$
$410$	−224.462	−	690.822i	−0.0270375	−	0.0832129i
$411$	265.870	−	818.263i	0.0319085	−	0.0982042i
$412$	−465.329	−	338.081i	−0.0556435	−	0.0404274i
$413$	−11575.6	−	8410.14i	−1.37917	−	1.00202i
$414$	3627.01	−	11162.8i	0.430575	−	1.32517i
$415$	143.966	+	443.083i	0.0170290	+	0.0524099i
$416$	−4718.12	+	3427.91i	−0.556069	+	0.404008i
$417$	573.036			0.0672942
$418$		0			0
$419$	−1880.83			−0.219295			−0.109648	−	0.993971i	$-0.534972\pi$
$419$	−1880.83			−0.219295			−0.109648	+	0.993971i	$0.534972\pi$
$420$	−36.2705	+	26.3521i	−0.00421386	+	0.00306155i
$421$	−2249.59	−	6923.53i	−0.260424	−	0.801501i	−0.992712	−	0.120507i	$-0.961548\pi$
$421$	−2249.59	−	6923.53i	−0.260424	−	0.801501i	0.732289	−	0.680994i	$-0.238452\pi$
$422$	271.302	−	834.981i	0.0312957	−	0.0963181i
$423$	11076.0	+	8047.21i	1.27313	+	0.924985i
$424$	−7430.83	−	5398.82i	−0.851116	−	0.618372i
$425$	−2097.81	+	6456.39i	−0.239432	+	0.736896i
$426$	160.780	+	494.829i	0.0182859	+	0.0562782i
$427$	−10711.5	+	7782.33i	−1.21397	+	0.881999i
$428$	1153.31			0.130251
$429$		0			0
$430$	787.994			0.0883732
$431$	−5558.44	+	4038.44i	−0.621208	+	0.451334i	−0.853343	−	0.521350i	$-0.825429\pi$
$431$	−5558.44	+	4038.44i	−0.621208	+	0.451334i	0.232135	+	0.972684i	$0.425429\pi$
$432$	−398.995	−	1227.98i	−0.0444367	−	0.136762i
$433$	346.508	−	1066.44i	0.0384575	−	0.118360i	−0.929985	−	0.367598i	$-0.880180\pi$
$433$	346.508	−	1066.44i	0.0384575	−	0.118360i	0.968442	+	0.249238i	$0.0801802\pi$
$434$	3987.74	+	2897.26i	0.441054	+	0.320445i
$435$	−75.3600	−	54.7522i	−0.00830628	−	0.00603487i
$436$	911.740	−	2806.05i	0.100148	−	0.308223i
$437$	3040.38	+	9357.34i	0.332818	+	1.02431i
$438$	309.318	−	224.732i	0.0337438	−	0.0245163i
$439$	7114.94			0.773525			0.386763	−	0.922179i	$-0.373593\pi$
$439$	7114.94			0.773525			0.386763	+	0.922179i	$0.373593\pi$
$440$		0			0
$441$	−12154.1			−1.31239
$442$	−7554.87	+	5488.93i	−0.813005	+	0.590683i
$443$	−4343.97	−	13369.4i	−0.465888	−	1.43385i	−0.857863	−	0.513879i	$-0.828208\pi$
$443$	−4343.97	−	13369.4i	−0.465888	−	1.43385i	0.391975	−	0.919976i	$-0.371792\pi$
$444$	−67.2679	+	207.029i	−0.00719008	+	0.0221288i
$445$	−1424.83	−	1035.20i	−0.151783	−	0.110277i
$446$	583.187	+	423.710i	0.0619164	+	0.0449849i
$447$	58.8171	−	181.020i	0.00622360	−	0.0191543i
$448$	−4964.79	−	15280.1i	−0.523581	−	1.61142i
$449$	12397.3	−	9007.14i	1.30304	−	0.946711i	0.303055	−	0.952973i	$-0.401993\pi$
$449$	12397.3	−	9007.14i	1.30304	−	0.946711i	0.999980	+	0.00626255i	$0.00199345\pi$
$450$	8072.61			0.845659
$451$		0			0
$452$	291.179			0.0303006
$453$	814.882	−	592.046i	0.0845177	−	0.0614057i
$454$	−4267.19	−	13133.1i	−0.441121	−	1.35763i
$455$	917.923	−	2825.08i	0.0945778	−	0.291081i
$456$	585.230	+	425.195i	0.0601007	+	0.0436657i
$457$	5834.80	+	4239.23i	0.597243	+	0.433923i	0.844899	−	0.534925i	$-0.179660\pi$
$457$	5834.80	+	4239.23i	0.597243	+	0.433923i	−0.247656	+	0.968848i	$0.579660\pi$
$458$	−4305.52	+	13251.0i	−0.439266	+	1.35192i
$459$	492.369	+	1515.35i	0.0500693	+	0.154097i
$460$	427.230	−	310.401i	0.0433037	−	0.0314620i
$461$	−10159.6			−1.02642			−0.513212	−	0.858262i	$-0.671544\pi$
$461$	−10159.6			−1.02642			−0.513212	+	0.858262i	$0.671544\pi$
$462$		0			0
$463$	−10292.0			−1.03306			−0.516532	−	0.856268i	$-0.672777\pi$
$463$	−10292.0			−1.03306			−0.516532	+	0.856268i	$0.672777\pi$
$464$	4106.96	−	2983.88i	0.410907	−	0.298541i
$465$	18.0110	+	55.4323i	0.00179622	+	0.00552820i
$466$	1944.04	−	5983.15i	0.193253	−	0.594772i
$467$	−14580.9	−	10593.6i	−1.44480	−	1.04971i	−0.987011	−	0.160652i	$-0.948640\pi$
$467$	−14580.9	−	10593.6i	−1.44480	−	1.04971i	−0.457792	−	0.889059i	$-0.651360\pi$
$468$	−2852.94	−	2072.78i	−0.281789	−	0.204732i
$469$	2530.59	−	7788.35i	0.249151	−	0.766807i
$470$	−599.391	−	1844.74i	−0.0588252	−	0.181045i
$471$	1083.87	−	787.480i	0.106034	−	0.0770385i
$472$	12391.3			1.20838
$473$		0			0
$474$	223.941			0.0217003
$475$	−5474.58	+	3977.52i	−0.528823	+	0.384212i
$476$	931.712	+	2867.51i	0.0897162	+	0.276118i
$477$	3099.22	−	9538.42i	0.297492	−	0.915586i
$478$	10560.1	+	7672.37i	1.01048	+	0.734154i
$479$	−13821.1	−	10041.6i	−1.31837	−	0.957855i	−0.999951	−	0.00990707i	$-0.996846\pi$
$479$	−13821.1	−	10041.6i	−1.31837	−	0.957855i	−0.318424	−	0.947948i	$-0.603154\pi$
$480$	21.6658	−	66.6806i	0.00206022	−	0.00634071i
$481$	−4456.93	−	13717.0i	−0.422492	−	1.30030i
$482$	−8263.33	+	6003.66i	−0.780881	+	0.567343i
$483$	−2699.42			−0.254302
$484$		0			0
$485$	−985.432			−0.0922601
$486$	2303.35	−	1673.49i	0.214984	−	0.156195i
$487$	142.705	+	439.202i	0.0132784	+	0.0408668i	0.957476	−	0.288512i	$-0.0931606\pi$
$487$	142.705	+	439.202i	0.0132784	+	0.0408668i	−0.944198	+	0.329379i	$0.893161\pi$
$488$	3543.27	−	10905.1i	0.328681	−	1.01158i
$489$	807.715	+	586.840i	0.0746956	+	0.0542695i
$490$	1393.09	+	1012.14i	0.128436	+	0.0933141i
$491$	−3875.92	+	11928.9i	−0.356248	+	1.09642i	0.599034	+	0.800724i	$0.295552\pi$
$491$	−3875.92	+	11928.9i	−0.356248	+	1.09642i	−0.955282	+	0.295696i	$0.904448\pi$
$492$	61.2853	+	188.617i	0.00561576	+	0.0172835i
$493$	−5068.08	+	3682.17i	−0.462991	+	0.336383i
$494$	−9308.48			−0.847790
$495$		0			0
$496$	−3176.41			−0.287550
$497$	−9004.59	+	6542.22i	−0.812698	+	0.590460i
$498$	123.777	+	380.946i	0.0111377	+	0.0342783i
$499$	−5647.90	+	17382.4i	−0.506682	+	1.55941i	0.291241	+	0.956650i	$0.405932\pi$
$499$	−5647.90	+	17382.4i	−0.506682	+	1.55941i	−0.797924	+	0.602759i	$0.794068\pi$
$500$	593.329	+	431.079i	0.0530690	+	0.0385569i
$501$	−1147.72	−	833.871i	−0.102348	−	0.0743605i
$502$	−1361.57	+	4190.48i	−0.121056	+	0.372571i
$503$	−820.496	−	2525.23i	−0.0727319	−	0.223846i	0.908082	−	0.418793i	$-0.137547\pi$
$503$	−820.496	−	2525.23i	−0.0727319	−	0.223846i	−0.980814	+	0.194947i	$0.937547\pi$
$504$	14935.0	−	10850.9i	1.31996	−	0.959004i
$505$	−1701.11			−0.149898
$506$		0			0
$507$	−1334.57			−0.116904
$508$	−1085.33	+	788.540i	−0.0947910	+	0.0688697i
$509$	−1510.21	−	4647.96i	−0.131511	−	0.404749i	0.863520	−	0.504315i	$-0.168255\pi$
$509$	−1510.21	−	4647.96i	−0.131511	−	0.404749i	−0.995031	+	0.0995653i	$0.968255\pi$
$510$	34.6923	−	106.772i	0.00301216	−	0.00927048i
$511$	6617.02	+	4807.54i	0.572837	+	0.416190i
$512$	10193.6	+	7406.06i	0.879875	+	0.639267i
$513$	−490.795	+	1510.51i	−0.0422400	+	0.130001i
$514$	3934.42	+	12108.9i	0.337626	+	1.03911i
$515$	−370.655	+	269.297i	−0.0317146	+	0.0230420i
$516$	−215.148			−0.0183554
$517$		0			0
$518$	14663.8			1.24381
$519$	−914.526	+	664.442i	−0.0773472	+	0.0561961i
$520$	794.945	+	2446.59i	0.0670397	+	0.206327i
$521$	−6780.17	+	20867.2i	−0.570144	+	1.75472i	0.0820064	+	0.996632i	$0.473867\pi$
$521$	−6780.17	+	20867.2i	−0.570144	+	1.75472i	−0.652150	+	0.758090i	$0.726133\pi$
$522$	6026.62	+	4378.60i	0.505322	+	0.367138i
$523$	4936.85	+	3586.83i	0.412759	+	0.299887i	0.774718	−	0.632307i	$-0.217892\pi$
$523$	4936.85	+	3586.83i	0.412759	+	0.299887i	−0.361959	+	0.932194i	$0.617892\pi$
$524$	−992.492	+	3054.58i	−0.0827428	+	0.254656i
$525$	−573.719	−	1765.73i	−0.0476936	−	0.146786i
$526$	114.983	−	83.5403i	0.00953139	−	0.00692496i
$527$	3919.76			0.323999
$528$		0			0
$529$	19629.4			1.61333
$530$	−1149.55	+	835.200i	−0.0942140	+	0.0684505i
$531$	4181.08	+	12868.0i	0.341701	+	1.05165i
$532$	−928.734	+	2858.35i	−0.0756874	+	0.232942i
$533$	−10630.6	−	7723.61i	−0.863910	−	0.627667i
$534$	−1225.02	−	890.026i	−0.0992727	−	0.0721258i
$535$	283.882	−	873.698i	0.0229407	−	0.0706042i
$536$	2191.55	+	6744.91i	0.176606	+	0.543537i
$537$	603.176	−	438.233i	0.0484711	−	0.0352163i
$538$	−7461.44			−0.597929
$539$		0			0
$540$	85.2463			0.00679337
$541$	1698.41	−	1233.97i	0.134973	−	0.0980636i	−0.518250	−	0.855229i	$-0.673416\pi$
$541$	1698.41	−	1233.97i	0.134973	−	0.0980636i	0.653223	+	0.757165i	$0.273416\pi$
$542$	−1132.91	−	3486.74i	−0.0897837	−	0.276326i
$543$	−612.958	+	1886.49i	−0.0484430	+	0.149092i
$544$	−3814.64	−	2771.50i	−0.300646	−	0.218432i
$545$	−1901.32	−	1381.39i	−0.149438	−	0.108573i
$546$	789.196	−	2428.90i	0.0618580	−	0.190379i
$547$	−2790.13	−	8587.15i	−0.218094	−	0.671225i	−0.998919	−	0.0464753i	$-0.985201\pi$
$547$	−2790.13	−	8587.15i	−0.218094	−	0.671225i	0.780825	−	0.624749i	$-0.214799\pi$
$548$	−2504.46	+	1819.60i	−0.195229	+	0.141842i
$549$	12520.2			0.973315
$550$		0			0
$551$	−6244.47			−0.482801
$552$	1891.29	−	1374.10i	0.145831	−	0.105952i
$553$	1480.38	+	4556.15i	0.113838	+	0.350356i
$554$	5680.76	−	17483.6i	0.435654	−	1.34081i
$555$	140.279	+	101.919i	0.0107289	+	0.00779497i
$556$	−1668.05	−	1211.91i	−0.127232	−	0.0924398i
$557$	2439.55	−	7508.15i	0.185578	−	0.571150i	−0.814380	−	0.580332i	$-0.802923\pi$
$557$	2439.55	−	7508.15i	0.185578	−	0.571150i	0.999958	+	0.00918192i	$0.00292274\pi$
$558$	−1440.36	−	4432.98i	−0.109275	−	0.336314i
$559$	11532.5	−	8378.84i	0.872579	−	0.633966i
$560$	−1946.19			−0.146860
$561$		0			0
$562$	2218.07			0.166484
$563$	18103.8	−	13153.2i	1.35521	−	0.984621i	0.356481	−	0.934303i	$-0.383976\pi$
$563$	18103.8	−	13153.2i	1.35521	−	0.984621i	0.998733	−	0.0503183i	$-0.0160236\pi$
$564$	163.653	+	503.673i	0.0122182	+	0.0376036i
$565$	71.6723	−	220.585i	0.00533677	−	0.0164249i
$566$	−12931.7	−	9395.41i	−0.960351	−	0.697736i
$567$	16130.6	+	11719.6i	1.19475	+	0.868034i
$568$	2978.65	−	9167.34i	0.220038	−	0.677206i
$569$	5228.72	+	16092.4i	0.385236	+	1.18564i	0.936309	+	0.351178i	$0.114219\pi$
$569$	5228.72	+	16092.4i	0.385236	+	1.18564i	−0.551072	+	0.834457i	$0.685781\pi$
$570$	90.5354	−	65.7778i	0.00665283	−	0.00483356i
$571$	−16320.0			−1.19609			−0.598047	−	0.801461i	$-0.704056\pi$
$571$	−16320.0			−1.19609			−0.598047	+	0.801461i	$0.704056\pi$
$572$		0			0
$573$	1893.35			0.138038
$574$	10808.2	−	7852.62i	0.785934	−	0.571014i
$575$	6757.82	+	20798.4i	0.490123	+	1.50844i
$576$	−4694.86	+	14449.3i	−0.339616	+	1.04523i
$577$	−671.696	−	488.016i	−0.0484629	−	0.0352103i	0.563290	−	0.826259i	$-0.309535\pi$
$577$	−671.696	−	488.016i	−0.0484629	−	0.0352103i	−0.611753	+	0.791049i	$0.709535\pi$
$578$	3685.89	+	2677.96i	0.265247	+	0.192713i
$579$	−431.502	+	1328.03i	−0.0309717	+	0.0953211i
$580$	103.570	+	318.757i	0.00741470	+	0.0228201i
$581$	−6932.23	+	5036.56i	−0.495004	+	0.359641i
$582$	−847.238			−0.0603422
$583$		0			0
$584$	−7083.29			−0.501899
$585$	−2272.49	+	1651.06i	−0.160609	+	0.116689i
$586$	4667.21	+	14364.2i	0.329012	+	1.01259i
$587$	6773.45	−	20846.5i	0.476270	−	1.46581i	−0.367968	−	0.929839i	$-0.619946\pi$
$587$	6773.45	−	20846.5i	0.476270	−	1.46581i	0.844238	−	0.535969i	$-0.180054\pi$
$588$	−380.360	−	276.347i	−0.0266765	−	0.0193816i
$589$	3161.02	+	2296.61i	0.221133	+	0.160663i
$590$	592.365	−	1823.11i	0.0413344	−	0.127214i
$591$	119.101	+	366.555i	0.00828962	+	0.0255128i
$592$	−7644.91	+	5554.35i	−0.530750	+	0.385612i
$593$	8236.51			0.570376			0.285188	−	0.958472i	$-0.407944\pi$
$593$	8236.51			0.570376			0.285188	+	0.958472i	$0.407944\pi$
$594$		0			0
$595$	2401.64			0.165475
$596$	−554.050	+	402.541i	−0.0380785	+	0.0276656i
$597$	−171.423	−	527.586i	−0.0117519	−	0.0361686i
$598$	−9295.93	+	28609.9i	−0.635683	+	1.95643i
$599$	8836.08	+	6419.79i	0.602725	+	0.437906i	0.846845	−	0.531839i	$-0.178499\pi$
$599$	8836.08	+	6419.79i	0.602725	+	0.437906i	−0.244120	+	0.969745i	$0.578499\pi$
$600$	1300.78	+	945.075i	0.0885071	+	0.0643042i
$601$	428.432	−	1318.58i	0.0290784	−	0.0894941i	−0.935464	−	0.353422i	$-0.885018\pi$
$601$	428.432	−	1318.58i	0.0290784	−	0.0894941i	0.964542	+	0.263928i	$0.0850180\pi$
$602$	4478.59	+	13783.7i	0.303212	+	0.933192i
$603$	−6264.95	+	4551.75i	−0.423099	+	0.307399i
$604$	−3624.16			−0.244147
$605$		0			0
$606$	−1462.55			−0.0980399
$607$	1147.00	−	833.347i	0.0766976	−	0.0557241i	−0.548776	−	0.835970i	$-0.684906\pi$
$607$	1147.00	−	833.347i	0.0766976	−	0.0557241i	0.625473	+	0.780246i	$0.284906\pi$
$608$	−1452.41	−	4470.05i	−0.0968797	−	0.298165i
$609$	529.421	−	1629.39i	0.0352270	−	0.108418i
$610$	−1435.06	−	1042.63i	−0.0952525	−	0.0692050i
$611$	−28387.5	−	20624.7i	−1.87960	−	1.36561i
$612$	881.054	−	2711.60i	0.0581936	−	0.179102i
$613$	4766.56	+	14670.0i	0.314061	+	0.966582i	0.976139	+	0.217146i	$0.0696749\pi$
$613$	4766.56	+	14670.0i	0.314061	+	0.966582i	−0.662078	+	0.749435i	$0.730325\pi$
$614$	−10720.4	+	7788.82i	−0.704625	+	0.511940i
$615$	157.973			0.0103579
$616$		0			0
$617$	15169.5			0.989793			0.494897	−	0.868952i	$-0.335206\pi$
$617$	15169.5			0.989793			0.494897	+	0.868952i	$0.335206\pi$
$618$	−318.675	+	231.531i	−0.0207427	+	0.0150705i
$619$	−643.239	−	1979.69i	−0.0417673	−	0.128547i	0.927999	−	0.372584i	$-0.121528\pi$
$619$	−643.239	−	1979.69i	−0.0417673	−	0.128547i	−0.969766	+	0.244037i	$0.921528\pi$
$620$	64.8051	−	199.450i	0.00419780	−	0.0129195i
$621$	4152.47	+	3016.95i	0.268330	+	0.194953i
$622$	12093.4	+	8786.37i	0.779584	+	0.566401i
$623$	10009.8	−	30806.9i	0.643712	−	1.98114i
$624$	508.572	+	1565.22i	0.0326269	+	0.100415i
$625$	−11929.7	+	8667.45i	−0.763502	+	0.554717i
$626$	7986.59			0.509918
$627$		0			0
$628$	−4820.49			−0.306303
$629$	9434.00	−	6854.20i	0.598026	−	0.434491i
$630$	−882.514	−	2716.10i	−0.0558099	−	0.171765i
$631$	7802.57	−	24013.8i	0.492259	−	1.51502i	−0.328926	−	0.944356i	$-0.606687\pi$
$631$	7802.57	−	24013.8i	0.492259	−	1.51502i	0.821185	−	0.570662i	$-0.193313\pi$
$632$	−3356.45	−	2438.60i	−0.211254	−	0.153485i
$633$	154.473	+	112.231i	0.00969943	+	0.00704705i
$634$	4964.13	−	15278.0i	0.310964	−	0.957047i
$635$	330.215	+	1016.30i	0.0206365	+	0.0635127i
$636$	313.865	−	228.037i	0.0195685	−	0.0142174i
$637$	31150.5			1.93756
$638$		0			0
$639$	10525.1			0.651592
$640$	894.646	−	649.998i	0.0552562	−	0.0401460i
$641$	−811.656	−	2498.02i	−0.0500132	−	0.153925i	0.922931	−	0.384966i	$-0.125787\pi$
$641$	−811.656	−	2498.02i	−0.0500132	−	0.153925i	−0.972944	+	0.231041i	$0.925787\pi$
$642$	244.071	−	751.173i	0.0150042	−	0.0461782i
$643$	−7466.91	−	5425.03i	−0.457957	−	0.332725i	0.334772	−	0.942299i	$-0.391341\pi$
$643$	−7466.91	−	5425.03i	−0.457957	−	0.332725i	−0.792729	+	0.609574i	$0.791341\pi$
$644$	7857.74	+	5708.98i	0.480805	+	0.349325i
$645$	−52.9577	+	162.987i	−0.00323288	+	0.00994979i
$646$	−2325.66	−	7157.64i	−0.141644	−	0.435935i
$647$	−256.379	+	186.270i	−0.0155785	+	0.0113184i	−0.595547	−	0.803320i	$-0.703065\pi$
$647$	−256.379	+	186.270i	−0.0155785	+	0.0113184i	0.579969	+	0.814639i	$0.303065\pi$
$648$	−17267.3			−1.04679
$649$		0			0
$650$	−20689.8			−1.24850
$651$	−867.262	+	630.103i	−0.0522130	+	0.0379350i
$652$	−1110.08	−	3416.47i	−0.0666779	−	0.205214i
$653$	−1552.09	+	4776.83i	−0.0930136	+	0.286266i	−0.986731	−	0.162364i	$-0.948088\pi$
$653$	−1552.09	+	4776.83i	−0.0930136	+	0.286266i	0.893717	+	0.448631i	$0.148088\pi$
$654$	−1634.69	−	1187.67i	−0.0977390	−	0.0710115i
$655$	2069.72	+	1503.74i	0.123467	+	0.0897039i
$656$	−2660.39	+	8187.84i	−0.158340	+	0.487320i
$657$	−2390.06	−	7355.83i	−0.141925	−	0.436801i
$658$	28861.7	−	20969.2i	1.70995	−	1.24235i
$659$	−24927.5			−1.47350			−0.736752	−	0.676163i	$-0.763642\pi$
$659$	−24927.5			−1.47350			−0.736752	+	0.676163i	$0.763642\pi$
$660$		0			0
$661$	−16440.5			−0.967418			−0.483709	−	0.875229i	$-0.660711\pi$
$661$	−16440.5			−0.967418			−0.483709	+	0.875229i	$0.660711\pi$
$662$	−11720.9	+	8515.72i	−0.688135	+	0.499959i
$663$	−627.589	−	1931.52i	−0.0367625	−	0.113143i
$664$	2293.13	−	7057.52i	0.134022	−	0.412477i
$665$	1936.76	+	1407.14i	0.112939	+	0.0820549i
$666$	−11218.3	−	8150.56i	−0.652702	−	0.474216i
$667$	−6236.04	+	19192.6i	−0.362010	+	1.11415i
$668$	1577.37	+	4854.64i	0.0913625	+	0.281185i
$669$	−126.833	+	92.1494i	−0.00732980	+	0.00532541i
$670$	1097.14			0.0632630
$671$		0			0
$672$	1289.52			0.0740245
$673$	9528.14	−	6922.60i	0.545740	−	0.396503i	−0.280472	−	0.959862i	$-0.590491\pi$
$673$	9528.14	−	6922.60i	0.545740	−	0.396503i	0.826212	+	0.563359i	$0.190491\pi$
$674$	1022.37	+	3146.53i	0.0584276	+	0.179822i
$675$	−1090.88	+	3357.39i	−0.0622046	+	0.191446i
$676$	3884.79	+	2822.47i	0.221028	+	0.160586i
$677$	2280.21	+	1656.67i	0.129447	+	0.0940486i	0.650625	−	0.759400i	$-0.274507\pi$
$677$	2280.21	+	1656.67i	0.129447	+	0.0940486i	−0.521178	+	0.853448i	$0.674507\pi$
$678$	61.6212	−	189.650i	0.00349048	−	0.0107426i
$679$	−5600.74	−	17237.3i	−0.316549	−	0.974237i
$680$	−1682.66	+	1222.53i	−0.0948929	+	0.0689437i
$681$	3003.19			0.168991
$682$		0			0
$683$	15803.2			0.885346			0.442673	−	0.896683i	$-0.354030\pi$
$683$	15803.2			0.885346			0.442673	+	0.896683i	$0.354030\pi$
$684$	2299.26	−	1670.51i	0.128530	−	0.0933823i
$685$	761.989	+	2345.16i	0.0425023	+	0.130809i
$686$	−2408.89	+	7413.81i	−0.134070	+	0.412625i
$687$	−2451.46	−	1781.09i	−0.136141	−	0.0989124i
$688$	−7555.87	−	5489.66i	−0.418699	−	0.304202i
$689$	−7943.21	+	24446.7i	−0.439205	+	1.35173i
$690$	−111.757	−	343.953i	−0.00616596	−	0.0189769i
$691$	−2670.34	+	1940.12i	−0.147011	+	0.106810i	−0.658860	−	0.752266i	$-0.728961\pi$
$691$	−2670.34	+	1940.12i	−0.147011	+	0.106810i	0.511849	+	0.859076i	$0.328961\pi$
$692$	4067.32			0.223434
$693$		0			0
$694$	−13922.3			−0.761501
$695$	−1328.68	+	965.341i	−0.0725174	+	0.0526870i
$696$	458.492	+	1411.09i	0.0249700	+	0.0768497i
$697$	3282.98	−	10104.0i	0.178410	−	0.549090i
$698$	2490.98	+	1809.80i	0.135079	+	0.0981405i
$699$	1106.89	+	804.203i	0.0598948	+	0.0435161i
$700$	−2064.28	+	6353.21i	−0.111461	+	0.343041i
$701$	−9200.43	−	28316.0i	−0.495714	−	1.52565i	−0.815841	−	0.578276i	$-0.803726\pi$
$701$	−9200.43	−	28316.0i	−0.495714	−	1.52565i	0.320127	−	0.947375i	$-0.396274\pi$
$702$	−3928.62	+	2854.31i	−0.211219	+	0.153460i
$703$	11623.8			0.623612
$704$		0			0
$705$	421.844			0.0225355
$706$	−11929.6	+	8667.36i	−0.635944	+	0.462040i
$707$	−9668.34	−	29756.1i	−0.514307	−	1.58288i
$708$	−161.735	+	497.769i	−0.00858527	+	0.0264227i
$709$	19418.4	+	14108.3i	1.02860	+	0.747318i	0.968027	−	0.250846i	$-0.0807087\pi$
$709$	19418.4	+	14108.3i	1.02860	+	0.747318i	0.0605683	+	0.998164i	$0.480709\pi$
$710$	−1206.39	−	876.491i	−0.0637674	−	0.0463297i
$711$	1399.89	−	4308.43i	0.0738398	−	0.227255i
$712$	8668.71	+	26679.6i	0.456283	+	1.40430i
$713$	10215.5	−	7421.97i	0.536567	−	0.389839i
$714$	2064.84			0.108228
$715$		0			0
$716$	−2682.60			−0.140019
$717$	−2296.64	+	1668.60i	−0.119623	+	0.0869109i
$718$	−1656.92	−	5099.48i	−0.0861223	−	0.265057i
$719$	−6386.99	+	19657.1i	−0.331286	+	1.01959i	0.637237	+	0.770668i	$0.280077\pi$
$719$	−6386.99	+	19657.1i	−0.331286	+	1.01959i	−0.968523	+	0.248925i	$0.919923\pi$
$720$	1488.90	+	1081.75i	0.0770665	+	0.0559921i
$721$	−6817.20	−	4952.98i	−0.352130	−	0.255837i
$722$	−2904.55	+	8939.30i	−0.149718	+	0.460784i
$723$	−686.442	−	2112.65i	−0.0353099	−	0.108673i
$724$	5774.00	−	4195.06i	0.296394	−	0.215343i
$725$	−13879.5			−0.710995
$726$		0			0
$727$	21928.9			1.11870			0.559351	−	0.828931i	$-0.311050\pi$
$727$	21928.9			1.11870			0.559351	+	0.828931i	$0.311050\pi$
$728$	−38277.9	+	27810.5i	−1.94873	+	1.41583i
$729$	−5697.64	−	17535.5i	−0.289470	−	0.890898i
$730$	−338.618	+	1042.16i	−0.0171682	+	0.0528383i
$731$	9324.11	+	6774.36i	0.471771	+	0.342762i
$732$	391.819	+	284.673i	0.0197842	+	0.0143741i
$733$	−7763.76	+	23894.4i	−0.391215	+	1.20404i	0.540655	+	0.841245i	$0.318177\pi$
$733$	−7763.76	+	23894.4i	−0.391215	+	1.20404i	−0.931870	+	0.362792i	$0.881823\pi$
$734$	−6445.20	−	19836.3i	−0.324110	−	0.997508i
$735$	−302.973	+	220.123i	−0.0152045	+	0.0110467i
$736$	−15189.3			−0.760712
$737$		0			0
$738$	−12633.3			−0.630133
$739$	−29964.5	+	21770.5i	−1.49156	+	1.08368i	−0.517960	+	0.855405i	$0.673308\pi$
$739$	−29964.5	+	21770.5i	−1.49156	+	1.08368i	−0.973597	+	0.228274i	$0.926692\pi$
$740$	−192.792	−	593.351i	−0.00957724	−	0.0294757i
$741$	625.583	−	1925.35i	0.0310140	−	0.0954513i
$742$	−21142.9	−	15361.2i	−1.04607	−	0.760012i
$743$	20062.0	+	14575.9i	0.990582	+	0.719700i	0.960048	−	0.279834i	$-0.0902795\pi$
$743$	20062.0	+	14575.9i	0.990582	+	0.719700i	0.0305332	+	0.999534i	$0.490279\pi$
$744$	286.884	−	882.937i	0.0141366	−	0.0435081i
$745$	168.571	+	518.809i	0.00828989	+	0.0255137i
$746$	8470.25	−	6153.99i	0.415707	−	0.302029i
$747$	8102.82			0.396876
$748$		0			0
$749$	16896.3			0.824268
$750$	406.335	−	295.219i	0.0197830	−	0.0143732i
$751$	4316.09	+	13283.6i	0.209716	+	0.645439i	0.999487	+	0.0320368i	$0.0101994\pi$
$751$	4316.09	+	13283.6i	0.209716	+	0.645439i	−0.789771	+	0.613402i	$0.789801\pi$
$752$	−7104.18	+	21864.4i	−0.344498	+	1.06026i
$753$	−775.246	−	563.249i	−0.0375186	−	0.0272589i
$754$	−15446.0	−	11222.2i	−0.746037	−	0.542027i
$755$	−892.071	+	2745.51i	−0.0430011	+	0.132344i
$756$	484.500	+	1491.14i	0.0233083	+	0.0717357i
$757$	6889.14	−	5005.26i	0.330766	−	0.240316i	−0.409989	−	0.912090i	$-0.634468\pi$
$757$	6889.14	−	5005.26i	0.330766	−	0.240316i	0.740756	+	0.671774i	$0.234468\pi$
$758$	11958.1			0.573006
$759$		0			0
$760$	−2073.24			−0.0989530
$761$	25611.8	−	18608.1i	1.22001	−	0.886390i	0.223910	−	0.974610i	$-0.428118\pi$
$761$	25611.8	−	18608.1i	1.22001	−	0.886390i	0.996101	+	0.0882195i	$0.0281177\pi$
$762$	283.907	+	873.775i	0.0134972	+	0.0415401i
$763$	13357.2	−	41109.4i	0.633768	−	1.95054i
$764$	−5511.35	−	4004.23i	−0.260986	−	0.189618i
$765$	−1837.33	−	1334.90i	−0.0868351	−	0.0630894i
$766$	−6230.03	+	19174.1i	−0.293865	+	0.904422i
$767$	−10716.0	−	32980.4i	−0.504473	−	1.55261i
$768$	−1203.47	+	874.371i	−0.0565448	+	0.0410822i
$769$	−606.519			−0.0284416			−0.0142208	−	0.999899i	$-0.504527\pi$
$769$	−606.519			−0.0284416			−0.0142208	+	0.999899i	$0.504527\pi$
$770$		0			0
$771$	−2768.99			−0.129342
$772$	4064.70	−	2953.18i	0.189497	−	0.137678i
$773$	−1452.31	−	4469.74i	−0.0675754	−	0.207976i	0.911567	−	0.411152i	$-0.134874\pi$
$773$	−1452.31	−	4469.74i	−0.0675754	−	0.207976i	−0.979142	+	0.203176i	$0.934874\pi$
$774$	4235.09	−	13034.3i	0.196676	−	0.605306i
$775$	7025.95	+	5104.65i	0.325651	+	0.236599i
$776$	12698.5	+	9225.97i	0.587433	+	0.426795i
$777$	−985.494	+	3033.04i	−0.0455011	+	0.140038i
$778$	955.481	+	2940.67i	0.0440304	+	0.135512i
$779$	8567.49	−	6224.65i	0.394047	−	0.286292i
$780$	−108.658			−0.00498791
$781$		0			0
$782$	−24321.8			−1.11221
$783$	−2635.46	+	1914.77i	−0.120286	+	0.0873926i
$784$	−6306.79	−	19410.3i	−0.287299	−	0.884216i
$785$	−1186.54	+	3651.80i	−0.0539484	+	0.166036i
$786$	1779.47	+	1292.86i	0.0807527	+	0.0586703i
$787$	−19479.6	−	14152.8i	−0.882303	−	0.641031i	0.0515565	−	0.998670i	$-0.483582\pi$
$787$	−19479.6	−	14152.8i	−0.882303	−	0.641031i	−0.933860	+	0.357639i	$0.883582\pi$
$788$	428.535	−	1318.89i	0.0193730	−	0.0596239i
$789$	9.55176	+	29.3973i	0.000430991	+	0.00132645i
$790$	−519.244	+	377.253i	−0.0233846	+	0.0169899i
$791$	4265.85			0.191752
$792$		0			0
$793$	−32088.9			−1.43696
$794$	22963.8	−	16684.1i	1.02639	−	0.745716i
$795$	−95.4944	−	293.901i	−0.00426017	−	0.0131115i
$796$	−616.794	+	1898.30i	−0.0274644	+	0.0845268i
$797$	15353.3	+	11154.8i	0.682360	+	0.495764i	0.874140	−	0.485674i	$-0.161426\pi$
$797$	15353.3	+	11154.8i	0.682360	+	0.495764i	−0.191780	+	0.981438i	$0.561426\pi$
$798$	1665.16	+	1209.81i	0.0738670	+	0.0536675i
$799$	8766.71	−	26981.2i	0.388165	−	1.19465i
$800$	−3228.24	−	9935.51i	−0.142670	−	0.439092i
$801$	−24781.1	+	18004.5i	−1.09313	+	0.794205i
$802$	−3697.79			−0.162810
$803$		0			0
$804$	−299.554			−0.0131399
$805$	6259.04	−	4547.46i	0.274040	−	0.199102i
$806$	3691.61	+	11361.6i	0.161329	+	0.496520i
$807$	501.452	−	1543.31i	0.0218735	−	0.0673198i
$808$	21920.9	+	15926.4i	0.954423	+	0.693429i
$809$	−7378.80	−	5361.01i	−0.320674	−	0.232983i	0.415789	−	0.909461i	$-0.363505\pi$
$809$	−7378.80	−	5361.01i	−0.320674	−	0.232983i	−0.736463	+	0.676478i	$0.763505\pi$
$810$	−825.463	+	2540.51i	−0.0358072	+	0.110203i
$811$	12321.8	+	37922.6i	0.533511	+	1.64198i	0.746845	+	0.664999i	$0.231568\pi$
$811$	12321.8	+	37922.6i	0.533511	+	1.64198i	−0.213334	+	0.976979i	$0.568432\pi$
$812$	−4987.09	+	3623.33i	−0.215533	+	0.156594i
$813$	797.329			0.0343955
$814$		0			0
$815$	−2861.41			−0.122983
$816$	−1076.50	+	782.120i	−0.0461825	+	0.0335535i
$817$	3550.11	+	10926.1i	0.152023	+	0.467878i
$818$	69.5916	−	214.181i	0.00297459	−	0.00915484i
$819$	−41796.4	−	30366.9i	−1.78325	−	1.29561i
$820$	−459.845	−	334.097i	−0.0195835	−	0.0142283i
$821$	1518.49	−	4673.43i	0.0645501	−	0.198665i	−0.913580	−	0.406659i	$-0.866694\pi$
$821$	1518.49	−	4673.43i	0.0645501	−	0.198665i	0.978130	+	0.207994i	$0.0666936\pi$
$822$	655.130	+	2016.28i	0.0277984	+	0.0855546i
$823$	−2247.11	+	1632.62i	−0.0951752	+	0.0691488i	−0.634355	−	0.773042i	$-0.718734\pi$
$823$	−2247.11	+	1632.62i	−0.0951752	+	0.0691488i	0.539180	+	0.842191i	$0.318734\pi$
$824$	7297.58			0.308523
$825$		0			0
$826$	35256.8			1.48516
$827$	−16428.3	+	11935.9i	−0.690773	+	0.501876i	−0.876914	−	0.480647i	$-0.840402\pi$
$827$	−16428.3	+	11935.9i	−0.690773	+	0.501876i	0.186141	+	0.982523i	$0.440402\pi$
$828$	−2838.20	−	8735.09i	−0.119124	−	0.366625i
$829$	−10992.6	+	33831.7i	−0.460540	+	1.41740i	0.403965	+	0.914774i	$0.367632\pi$
$829$	−10992.6	+	33831.7i	−0.460540	+	1.41740i	−0.864506	+	0.502623i	$0.832368\pi$
$830$	−928.742	−	674.771i	−0.0388399	−	0.0282188i
$831$	3234.49	+	2350.00i	0.135022	+	0.0980992i
$832$	12032.8	−	37033.1i	0.501396	−	1.54314i
$833$	7782.72	+	23952.8i	0.323716	+	0.996295i
$834$	−1142.35	+	829.964i	−0.0474296	+	0.0344596i
$835$	4065.93			0.168512
$836$		0			0
$837$	2038.32			0.0841751
$838$	3749.44	−	2724.13i	0.154561	−	0.112295i
$839$	2193.01	+	6749.38i	0.0902396	+	0.277729i	0.985984	−	0.166841i	$-0.0533566\pi$
$839$	2193.01	+	6749.38i	0.0902396	+	0.277729i	−0.895744	+	0.444570i	$0.853357\pi$
$840$	175.774	−	540.977i	0.00721998	−	0.0222208i
$841$	9369.35	+	6807.23i	0.384163	+	0.279111i
$842$	14512.3	+	10543.8i	0.593976	+	0.431549i
$843$	−149.067	+	458.782i	−0.00609033	+	0.0187441i
$844$	−212.299	−	653.388i	−0.00865831	−	0.0266476i
$845$	3094.41	−	2248.22i	0.125977	−	0.0915279i
$846$	−33735.3			−1.37097
$847$		0			0
$848$	16841.3			0.681995
$849$	2812.41	−	2043.33i	0.113689	−	0.0825996i
$850$	−5169.21	−	15909.2i	−0.208591	−	0.641978i
$851$	11608.1	−	35726.1i	0.467592	−	1.43910i
$852$	329.382	+	239.310i	0.0132447	+	0.00962281i
$853$	−19543.9	−	14199.5i	−0.784490	−	0.569965i	0.121834	−	0.992551i	$-0.461123\pi$
$853$	−19543.9	−	14199.5i	−0.784490	−	0.569965i	−0.906323	+	0.422586i	$0.861123\pi$
$854$	10081.7	−	31028.2i	0.403966	−	1.24328i
$855$	−699.555	−	2153.01i	−0.0279816	−	0.0861185i
$856$	−11838.0	+	8600.83i	−0.472682	+	0.343423i
$857$	28806.8			1.14822			0.574108	−	0.818779i	$-0.305349\pi$
$857$	28806.8			1.14822			0.574108	+	0.818779i	$0.305349\pi$
$858$		0			0
$859$	11244.4			0.446628			0.223314	−	0.974747i	$-0.428312\pi$
$859$	11244.4			0.446628			0.223314	+	0.974747i	$0.428312\pi$
$860$	498.856	−	362.440i	0.0197800	−	0.0143710i
$861$	897.847	+	2763.29i	0.0355384	+	0.109376i
$862$	5231.62	−	16101.3i	0.206717	−	0.636208i
$863$	1045.19	+	759.373i	0.0412266	+	0.0299529i	0.608208	−	0.793778i	$-0.291889\pi$
$863$	1045.19	+	759.373i	0.0412266	+	0.0299529i	−0.566981	+	0.823731i	$0.691889\pi$
$864$	−1983.66	−	1441.21i	−0.0781080	−	0.0567488i
$865$	1001.15	−	3081.23i	0.0393529	−	0.121116i
$866$	853.830	+	2627.82i	0.0335038	+	0.103114i
$867$	−801.616	+	582.408i	−0.0314006	+	0.0228138i
$868$	3857.12			0.150829
$869$		0			0
$870$	229.531			0.00894464
$871$	16056.9	−	11666.0i	0.624646	−	0.453832i
$872$	11567.7	+	35601.8i	0.449234	+	1.38260i
$873$	−5296.22	+	16300.1i	−0.205326	+	0.631930i
$874$	−19613.8	−	14250.3i	−0.759093	−	0.551514i
$875$	8692.43	+	6315.42i	0.335838	+	0.244000i
$876$	92.4536	−	284.543i	0.00356589	−	0.0109747i
$877$	8288.78	+	25510.3i	0.319147	+	0.982235i	0.974014	+	0.226490i	$0.0727250\pi$
$877$	8288.78	+	25510.3i	0.319147	+	0.982235i	−0.654866	+	0.755745i	$0.727275\pi$
$878$	−14183.6	+	10305.0i	−0.545187	+	0.396102i
$879$	−3284.73			−0.126042
$880$		0			0
$881$	−28515.7			−1.09049			−0.545243	−	0.838278i	$-0.683563\pi$
$881$	−28515.7			−1.09049			−0.545243	+	0.838278i	$0.683563\pi$
$882$	24229.1	−	17603.5i	0.924985	−	0.672041i
$883$	12881.8	+	39646.1i	0.490948	+	1.51098i	0.823177	+	0.567784i	$0.192199\pi$
$883$	12881.8	+	39646.1i	0.490948	+	1.51098i	−0.332229	+	0.943199i	$0.607801\pi$
$884$	−2258.11	+	6949.76i	−0.0859147	+	0.264418i
$885$	337.278	+	245.047i	0.0128107	+	0.00930754i
$886$	28023.4	+	20360.2i	1.06260	+	0.772025i
$887$	15197.2	−	46772.3i	0.575280	−	1.77053i	−0.0599460	−	0.998202i	$-0.519093\pi$
$887$	15197.2	−	46772.3i	0.575280	−	1.77053i	0.635226	−	0.772327i	$-0.280907\pi$
$888$	−853.463	−	2626.69i	−0.0322526	−	0.0992634i
$889$	−15900.4	+	11552.3i	−0.599868	+	0.435830i
$890$	4339.74			0.163448
$891$		0			0
$892$	564.085			0.0211737
$893$	22878.2	−	16622.0i	0.857323	−	0.622882i
$894$	144.931	+	446.052i	0.00542195	+	0.0166870i
$895$	−660.311	+	2032.23i	−0.0246612	+	0.0758993i
$896$	16454.6	+	11955.0i	0.613515	+	0.445745i
$897$	−5292.88	−	3845.50i	−0.197017	−	0.143141i
$898$	−11668.3	+	35911.5i	−0.433605	+	1.33450i
$899$	2476.46	+	7621.77i	0.0918740	+	0.282759i
$900$	5110.53	−	3713.02i	0.189279	−	0.137519i
$901$	−20782.5			−0.768442
$902$		0			0
$903$	−3151.98			−0.116159
$904$	−2988.78	+	2171.47i	−0.109962	+	0.0798917i
$905$	−1756.75	−	5406.73i	−0.0645265	−	0.198592i
$906$	−766.969	+	2360.49i	−0.0281246	+	0.0865585i
$907$	−42859.9	−	31139.5i	−1.56906	−	1.13999i	−0.928047	−	0.372463i	$-0.878513\pi$
$907$	−42859.9	−	31139.5i	−1.56906	−	1.13999i	−0.641016	−	0.767528i	$-0.721487\pi$
$908$	−8742.01	−	6351.44i	−0.319509	−	0.232137i
$909$	−9142.67	+	28138.2i	−0.333601	+	1.02672i
$910$	2261.86	+	6961.28i	0.0823954	+	0.253587i
$911$	25459.6	−	18497.5i	0.925922	−	0.672722i	−0.0190689	−	0.999818i	$-0.506070\pi$
$911$	25459.6	−	18497.5i	0.925922	−	0.672722i	0.944991	+	0.327096i	$0.106070\pi$
$912$	−1326.37			−0.0481584
$913$		0			0
$914$	−17771.6			−0.643143
$915$	312.101	−	226.755i	0.0112762	−	0.00819265i
$916$	3369.15	+	10369.2i	0.121528	+	0.374025i
$917$	−14540.3	+	44750.4i	−0.523623	+	1.61155i
$918$	−3176.32	−	2307.73i	−0.114198	−	0.0829700i
$919$	34675.2	+	25193.0i	1.24465	+	0.904289i	0.997899	−	0.0647909i	$-0.0206380\pi$
$919$	34675.2	+	25193.0i	1.24465	+	0.904289i	0.246748	+	0.969080i	$0.420638\pi$
$920$	−2070.44	+	6372.16i	−0.0741961	+	0.228352i
$921$	−890.552	−	2740.84i	−0.0318618	−	0.0980604i
$922$	20253.2	−	14714.8i	0.723432	−	0.525604i
$923$	−26975.6			−0.961984
$924$		0			0
$925$	25836.1			0.918361
$926$	20517.0	−	14906.5i	0.728112	−	0.529004i
$927$	2462.36	+	7578.37i	0.0872433	+	0.268507i
$928$	2978.99	−	9168.38i	0.105377	−	0.324318i
$929$	16963.7	+	12324.9i	0.599097	+	0.435270i	0.845558	−	0.533883i	$-0.179268\pi$
$929$	16963.7	+	12324.9i	0.599097	+	0.435270i	−0.246461	+	0.969153i	$0.579268\pi$
$930$	−116.191	−	84.4178i	−0.00409683	−	0.00297652i
$931$	−7757.85	+	23876.2i	−0.273097	+	0.840506i
$932$	−1521.25	−	4681.92i	−0.0534658	−	0.164551i
$933$	−2630.10	+	1910.88i	−0.0922889	+	0.0670518i
$934$	44410.4			1.55584
$935$		0			0
$936$	44741.6			1.56242
$937$	−13855.9	+	10066.9i	−0.483086	+	0.350982i	−0.802519	−	0.596626i	$-0.796507\pi$
$937$	−13855.9	+	10066.9i	−0.483086	+	0.350982i	0.319433	+	0.947609i	$0.396507\pi$
$938$	6235.63	+	19191.3i	0.217058	+	0.668036i
$939$	−536.745	+	1651.93i	−0.0186539	+	0.0574108i
$940$	−1227.95	−	892.156i	−0.0426077	−	0.0309563i
$941$	35613.9	+	25875.0i	1.23377	+	0.896387i	0.997167	−	0.0752188i	$-0.0239655\pi$
$941$	35613.9	+	25875.0i	1.23377	+	0.896387i	0.236604	+	0.971606i	$0.423966\pi$
$942$	−1020.14	+	3139.68i	−0.0352846	+	0.108595i
$943$	−10575.7	−	32548.7i	−0.365210	−	1.12400i
$944$	−18381.0	+	13354.5i	−0.633739	+	0.460438i
$945$	1248.88			0.0429906
$946$		0			0
$947$	8692.03			0.298261			0.149130	−	0.988818i	$-0.452353\pi$
$947$	8692.03			0.298261			0.149130	+	0.988818i	$0.452353\pi$
$948$	141.770	−	103.002i	0.00485706	−	0.00352886i
$949$	6125.64	+	18852.8i	0.209533	+	0.644876i
$950$	5152.69	−	15858.4i	0.175974	−	0.541593i
$951$	2826.46	+	2053.54i	0.0963766	+	0.0700217i
$952$	−30948.0	−	22485.1i	−1.05360	−	0.765489i
$953$	17893.9	−	55071.8i	0.608228	−	1.87193i	0.135367	−	0.990796i	$-0.456779\pi$
$953$	17893.9	−	55071.8i	0.608228	−	1.87193i	0.472861	−	0.881137i	$-0.343221\pi$
$954$	7636.79	+	23503.6i	0.259172	+	0.797650i
$955$	−4390.03	+	3189.54i	−0.148752	+	0.108075i
$956$	10214.2			0.345556
$957$		0			0
$958$	42096.2			1.41969
$959$	−36691.1	+	26657.6i	−1.23547	+	0.897622i
$960$	144.660	+	445.217i	0.00486341	+	0.0149680i
$961$	−7656.38	+	23563.9i	−0.257003	+	0.790974i
$962$	28752.1	+	20889.6i	0.963623	+	0.700113i
$963$	−12926.2	−	9391.41i	−0.432544	−	0.314262i
$964$	−2469.87	+	7601.48i	−0.0825199	+	0.253970i
$965$	−1236.70	−	3806.16i	−0.0412545	−	0.126968i
$966$	5381.29	−	3909.73i	0.179234	−	0.130221i
$967$	−56564.3			−1.88106			−0.940530	−	0.339711i	$-0.889671\pi$
$967$	−56564.3			−1.88106			−0.940530	+	0.339711i	$0.889671\pi$
$968$		0			0
$969$	1636.77			0.0542628
$970$	1964.46	−	1427.26i	0.0650257	−	0.0472440i
$971$	−9546.98	−	29382.6i	−0.315528	−	0.971094i	−0.975537	−	0.219836i	$-0.929448\pi$
$971$	−9546.98	−	29382.6i	−0.315528	−	0.971094i	0.660009	−	0.751258i	$-0.270552\pi$
$972$	688.462	−	2118.87i	0.0227185	−	0.0699205i
$973$	−24437.4	−	17754.8i	−0.805168	−	0.584989i
$974$	−920.607	−	668.860i	−0.0302856	−	0.0220038i
$975$	1390.48	−	4279.44i	0.0456727	−	0.140566i
$976$	6496.80	+	19995.1i	0.213071	+	0.655766i
$977$	24269.6	−	17632.9i	0.794732	−	0.577406i	−0.114632	−	0.993408i	$-0.536569\pi$
$977$	24269.6	−	17632.9i	0.794732	−	0.577406i	0.909364	+	0.416002i	$0.136569\pi$
$978$	−2460.14			−0.0804361
$979$		0			0
$980$	1347.46			0.0439216
$981$	−33068.4	+	24025.6i	−1.07624	+	0.781935i
$982$	−9550.67	−	29393.9i	−0.310361	−	0.955192i
$983$	−7566.56	+	23287.5i	−0.245509	+	0.755600i	0.750043	+	0.661389i	$0.230033\pi$
$983$	−7566.56	+	23287.5i	−0.245509	+	0.755600i	−0.995552	+	0.0942108i	$0.969967\pi$
$984$	−2035.67	−	1479.00i	−0.0659501	−	0.0479156i
$985$	−893.657	−	649.280i	−0.0289079	−	0.0210028i
$986$	4770.09	−	14680.8i	0.154068	−	0.474171i
$987$	2397.56	+	7378.94i	0.0773205	+	0.237968i
$988$	−5892.92	+	4281.46i	−0.189756	+	0.137866i
$989$	37127.1			1.19370
$990$		0			0
$991$	−52661.1			−1.68803			−0.844014	−	0.536321i	$-0.819814\pi$
$991$	−52661.1			−1.68803			−0.844014	+	0.536321i	$0.819814\pi$
$992$	−4879.97	+	3545.51i	−0.156189	+	0.113478i
$993$	−973.664	−	2996.63i	−0.0311161	−	0.0957655i
$994$	8475.15	−	26083.8i	0.270438	−	0.832322i
$995$	1286.25	+	934.514i	0.0409817	+	0.0297750i
$996$	253.577	+	184.234i	0.00806716	+	0.00586113i
$997$	−16918.2	+	52069.0i	−0.537418	+	1.65400i	0.200947	+	0.979602i	$0.435598\pi$
$997$	−16918.2	+	52069.0i	−0.537418	+	1.65400i	−0.738365	+	0.674401i	$0.764402\pi$
$998$	−13917.0	−	42832.1i	−0.441417	−	1.35854i
$999$	4905.78	−	3564.26i	0.155367	−	0.112881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.c.g.3.1		8
11.2	odd	10		121.4.a.e.1.1	yes	2
11.3	even	5	inner	121.4.c.g.27.2		8
11.4	even	5	inner	121.4.c.g.81.1		8
11.5	even	5	inner	121.4.c.g.9.2		8
11.6	odd	10		121.4.c.d.9.1		8
11.7	odd	10		121.4.c.d.81.2		8
11.8	odd	10		121.4.c.d.27.1		8
11.9	even	5		121.4.a.b.1.2	✓	2
11.10	odd	2		121.4.c.d.3.2		8
33.2	even	10		1089.4.a.k.1.2		2
33.20	odd	10		1089.4.a.x.1.1		2
44.31	odd	10		1936.4.a.z.1.1		2
44.35	even	10		1936.4.a.y.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.4.a.b.1.2	✓	2	11.9	even	5
121.4.a.e.1.1	yes	2	11.2	odd	10
121.4.c.d.3.2		8	11.10	odd	2
121.4.c.d.9.1		8	11.6	odd	10
121.4.c.d.27.1		8	11.8	odd	10
121.4.c.d.81.2		8	11.7	odd	10
121.4.c.g.3.1		8	1.1	even	1	trivial
121.4.c.g.9.2		8	11.5	even	5	inner
121.4.c.g.27.2		8	11.3	even	5	inner
121.4.c.g.81.1		8	11.4	even	5	inner
1089.4.a.k.1.2		2	33.2	even	10
1089.4.a.x.1.1		2	33.20	odd	10
1936.4.a.y.1.1		2	44.35	even	10
1936.4.a.z.1.1		2	44.31	odd	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99350 + 1.44836i) q^{2} +(-0.165602 - 0.509670i) q^{3} +(-0.595848 + 1.83383i) q^{4} +(1.24257 + 0.902778i) q^{5} +(1.06831 + 0.776175i) q^{6} +(-8.72933 + 26.8661i) q^{7} +(-7.55982 - 23.2667i) q^{8} +(21.6111 - 15.7014i) q^{9} +O(q^{10})\)	\(q+(-1.99350 + 1.44836i) q^{2} +(-0.165602 - 0.509670i) q^{3} +(-0.595848 + 1.83383i) q^{4} +(1.24257 + 0.902778i) q^{5} +(1.06831 + 0.776175i) q^{6} +(-8.72933 + 26.8661i) q^{7} +(-7.55982 - 23.2667i) q^{8} +(21.6111 - 15.7014i) q^{9} -3.78461 q^{10} +1.03332 q^{12} +(-55.3886 + 40.2422i) q^{13} +(-21.5100 - 66.2009i) q^{14} +(0.254347 - 0.782801i) q^{15} +(36.2896 + 26.3659i) q^{16} +(-44.7822 - 32.5362i) q^{17} +(-20.3405 + 62.6015i) q^{18} +(-17.0506 - 52.4764i) q^{19} +(-2.39592 + 1.74074i) q^{20} +15.1384 q^{21} -178.315 q^{23} +(-10.6064 + 7.70602i) q^{24} +(-37.8982 - 116.639i) q^{25} +(52.1319 - 160.446i) q^{26} +(-23.2872 - 16.9192i) q^{27} +(-44.0666 - 32.0162i) q^{28} +(34.9720 - 107.633i) q^{29} +(0.626738 + 1.92890i) q^{30} +(-57.2887 + 41.6227i) q^{31} +85.1821 q^{32} +136.397 q^{34} +(-35.1009 + 25.5023i) q^{35} +(15.9168 + 48.9868i) q^{36} +(-65.0988 + 200.353i) q^{37} +(109.995 + 79.9162i) q^{38} +(29.6827 + 21.5657i) q^{39} +(11.6111 - 35.7354i) q^{40} +(59.3091 + 182.535i) q^{41} +(-30.1785 + 21.9259i) q^{42} -208.210 q^{43} +41.0282 q^{45} +(355.472 - 258.265i) q^{46} +(158.376 + 487.431i) q^{47} +(7.42830 - 22.8619i) q^{48} +(-368.094 - 267.436i) q^{49} +(244.485 + 177.629i) q^{50} +(-9.16669 + 28.2122i) q^{51} +(-40.7942 - 125.552i) q^{52} +(303.744 - 220.683i) q^{53} +70.9282 q^{54} +691.079 q^{56} +(-23.9220 + 17.3804i) q^{57} +(86.1746 + 265.218i) q^{58} +(-156.519 + 481.717i) q^{59} +(1.28397 + 0.932860i) q^{60} +(379.184 + 275.493i) q^{61} +(53.9203 - 165.950i) q^{62} +(233.185 + 717.670i) q^{63} +(-460.127 + 334.302i) q^{64} -105.154 q^{65} -289.895 q^{67} +(86.3492 - 62.7363i) q^{68} +(29.5293 + 90.8819i) q^{69} +(33.0371 - 101.678i) q^{70} +(318.761 + 231.593i) q^{71} +(-528.697 - 384.121i) q^{72} +(89.4723 - 275.367i) q^{73} +(-160.410 - 493.691i) q^{74} +(-53.1711 + 38.6311i) q^{75} +106.392 q^{76} -90.4074 q^{78} +(137.199 - 99.6808i) q^{79} +(21.2897 + 65.5229i) q^{80} +(218.110 - 671.275i) q^{81} +(-382.609 - 277.982i) q^{82} +(245.400 + 178.293i) q^{83} +(-9.02020 + 27.7613i) q^{84} +(-26.2720 - 80.8568i) q^{85} +(415.067 - 301.564i) q^{86} -60.6486 q^{87} -1146.68 q^{89} +(-81.7897 + 59.4237i) q^{90} +(-597.646 - 1839.36i) q^{91} +(106.249 - 327.000i) q^{92} +(30.7009 + 22.3055i) q^{93} +(-1021.70 - 742.308i) q^{94} +(26.1880 - 80.5984i) q^{95} +(-14.1063 - 43.4147i) q^{96} +(-519.065 + 377.123i) q^{97} +1121.14 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} - 2 q^{9} + 136 q^{10} - 352 q^{12} - 130 q^{13} + 160 q^{14} - 64 q^{15} + 62 q^{16} + 14 q^{17} + 194 q^{18} + 48 q^{19} + 98 q^{20} - 544 q^{21} - 512 q^{23} - 144 q^{24} + 176 q^{25} + 106 q^{26} - 16 q^{27} - 296 q^{28} + 30 q^{29} + 280 q^{30} + 184 q^{31} + 1208 q^{32} + 1784 q^{34} + 128 q^{35} - 394 q^{36} - 126 q^{37} + 168 q^{38} + 496 q^{39} - 186 q^{40} - 370 q^{41} - 712 q^{42} - 1056 q^{43} - 808 q^{45} + 664 q^{46} - 256 q^{47} - 152 q^{48} - 522 q^{49} + 64 q^{50} - 488 q^{51} - 602 q^{52} + 162 q^{53} + 512 q^{54} + 1344 q^{56} + 24 q^{57} - 918 q^{58} + 1304 q^{59} - 752 q^{60} + 300 q^{61} - 1312 q^{62} - 1336 q^{63} + 262 q^{64} - 2504 q^{65} - 2624 q^{67} + 934 q^{68} + 280 q^{69} - 872 q^{70} + 1176 q^{71} - 150 q^{72} + 668 q^{73} + 2022 q^{74} - 464 q^{75} + 768 q^{76} + 7840 q^{78} - 416 q^{79} - 214 q^{80} - 26 q^{81} + 322 q^{82} + 960 q^{83} + 1832 q^{84} - 502 q^{85} + 264 q^{86} + 4032 q^{87} - 4296 q^{89} - 1186 q^{90} + 688 q^{91} - 944 q^{92} - 1864 q^{93} - 2408 q^{94} - 24 q^{95} + 1664 q^{96} + 338 q^{97} + 3288 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 - 2 * q^9 + 136 * q^10 - 352 * q^12 - 130 * q^13 + 160 * q^14 - 64 * q^15 + 62 * q^16 + 14 * q^17 + 194 * q^18 + 48 * q^19 + 98 * q^20 - 544 * q^21 - 512 * q^23 - 144 * q^24 + 176 * q^25 + 106 * q^26 - 16 * q^27 - 296 * q^28 + 30 * q^29 + 280 * q^30 + 184 * q^31 + 1208 * q^32 + 1784 * q^34 + 128 * q^35 - 394 * q^36 - 126 * q^37 + 168 * q^38 + 496 * q^39 - 186 * q^40 - 370 * q^41 - 712 * q^42 - 1056 * q^43 - 808 * q^45 + 664 * q^46 - 256 * q^47 - 152 * q^48 - 522 * q^49 + 64 * q^50 - 488 * q^51 - 602 * q^52 + 162 * q^53 + 512 * q^54 + 1344 * q^56 + 24 * q^57 - 918 * q^58 + 1304 * q^59 - 752 * q^60 + 300 * q^61 - 1312 * q^62 - 1336 * q^63 + 262 * q^64 - 2504 * q^65 - 2624 * q^67 + 934 * q^68 + 280 * q^69 - 872 * q^70 + 1176 * q^71 - 150 * q^72 + 668 * q^73 + 2022 * q^74 - 464 * q^75 + 768 * q^76 + 7840 * q^78 - 416 * q^79 - 214 * q^80 - 26 * q^81 + 322 * q^82 + 960 * q^83 + 1832 * q^84 - 502 * q^85 + 264 * q^86 + 4032 * q^87 - 4296 * q^89 - 1186 * q^90 + 688 * q^91 - 944 * q^92 - 1864 * q^93 - 2408 * q^94 - 24 * q^95 + 1664 * q^96 + 338 * q^97 + 3288 * q^98

Introduction

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