LMFDB - Embedded newform 54.5.f.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,5,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58197800653$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	54.23
Dual form			54.5.f.a.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.967379 + 2.65785i) q^{2} +(5.71544 + 6.95225i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(41.7224 + 7.35678i) q^{5} +(-24.0070 + 8.46534i) q^{6} +(19.0320 - 15.9698i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-15.6675 + 79.4703i) q^{9} +(-59.9146 + 103.775i) q^{10} +(-18.0860 + 3.18905i) q^{11} +(0.724290 - 71.9964i) q^{12} +(-100.351 + 36.5247i) q^{13} +(24.0341 + 66.0331i) q^{14} +(187.316 + 332.111i) q^{15} +(11.1135 + 63.0277i) q^{16} +(-339.433 - 195.972i) q^{17} +(-196.064 - 118.520i) q^{18} +(205.064 + 355.182i) q^{19} +(-217.859 - 259.634i) q^{20} +(219.802 + 41.0411i) q^{21} +(9.02000 - 51.1549i) q^{22} +(218.656 - 260.583i) q^{23} +(190.655 + 71.5728i) q^{24} +(1099.33 + 400.122i) q^{25} -302.051i q^{26} +(-642.044 + 345.284i) q^{27} -198.756 q^{28} +(485.587 - 1334.14i) q^{29} +(-1063.91 + 176.579i) q^{30} +(-923.152 - 774.616i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-125.541 - 107.512i) q^{33} +(849.225 - 712.585i) q^{34} +(911.547 - 526.282i) q^{35} +(504.676 - 406.455i) q^{36} +(755.062 - 1307.80i) q^{37} +(-1142.40 + 201.435i) q^{38} +(-827.479 - 488.909i) q^{39} +(900.820 - 327.872i) q^{40} +(-207.264 - 569.453i) q^{41} +(-321.713 + 544.499i) q^{42} +(337.617 + 1914.72i) q^{43} +(127.237 + 73.4600i) q^{44} +(-1238.33 + 3200.43i) q^{45} +(481.070 + 833.237i) q^{46} +(2025.36 + 2413.73i) q^{47} +(-374.666 + 437.495i) q^{48} +(-309.745 + 1756.65i) q^{49} +(-2126.93 + 2534.78i) q^{50} +(-577.566 - 3479.89i) q^{51} +(802.807 + 292.198i) q^{52} -3309.93i q^{53} +(-296.614 - 2040.48i) q^{54} -778.052 q^{55} +(192.273 - 528.265i) q^{56} +(-1297.28 + 3455.68i) q^{57} +(3076.20 + 2581.24i) q^{58} +(-4797.62 - 845.950i) q^{59} +(559.880 - 2998.53i) q^{60} +(1691.36 - 1419.22i) q^{61} +(2951.85 - 1704.25i) q^{62} +(970.939 + 1762.69i) q^{63} +(256.000 - 443.405i) q^{64} +(-4455.58 + 785.639i) q^{65} +(407.195 - 229.664i) q^{66} +(-3252.29 + 1183.74i) q^{67} +(1072.42 + 2946.45i) q^{68} +(3061.35 + 30.7975i) q^{69} +(516.968 + 2931.87i) q^{70} +(5743.28 + 3315.88i) q^{71} +(592.086 + 1734.55i) q^{72} +(-2945.25 - 5101.32i) q^{73} +(2745.52 + 3271.98i) q^{74} +(3501.38 + 9929.65i) q^{75} +(569.745 - 3231.18i) q^{76} +(-293.285 + 349.523i) q^{77} +(2099.93 - 1726.36i) q^{78} +(-2340.08 - 851.720i) q^{79} +2711.42i q^{80} +(-6070.06 - 2490.20i) q^{81} +1714.03 q^{82} +(3787.29 - 10405.5i) q^{83} +(-1135.98 - 1381.80i) q^{84} +(-12720.2 - 10673.6i) q^{85} +(-5415.65 - 954.924i) q^{86} +(12050.6 - 4249.27i) q^{87} +(-318.332 + 267.112i) q^{88} +(6082.16 - 3511.54i) q^{89} +(-7308.33 - 6387.32i) q^{90} +(-1326.59 + 2297.72i) q^{91} +(-2680.00 + 472.556i) q^{92} +(109.104 - 10845.2i) q^{93} +(-8374.63 + 3048.11i) q^{94} +(5942.78 + 16327.6i) q^{95} +(-800.353 - 1419.03i) q^{96} +(350.066 + 1985.32i) q^{97} +(-4369.27 - 2522.60i) q^{98} +(29.9271 - 1487.26i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 18 q^{5} - 96 q^{6} + 204 q^{9} + 720 q^{11} + 96 q^{12} - 288 q^{14} - 1422 q^{15} - 1344 q^{18} + 288 q^{20} + 4308 q^{21} - 1008 q^{22} + 4716 q^{23} - 882 q^{25} - 2808 q^{27} - 6084 q^{29} - 6336 q^{30}+ \cdots + 179622 q^{99}+O(q^{100}) $ 72 * q - 18 * q^5 - 96 * q^6 + 204 * q^9 + 720 * q^11 + 96 * q^12 - 288 * q^14 - 1422 * q^15 - 1344 * q^18 + 288 * q^20 + 4308 * q^21 - 1008 * q^22 + 4716 * q^23 - 882 * q^25 - 2808 * q^27 - 6084 * q^29 - 6336 * q^30 + 3330 * q^31 - 1026 * q^33 + 288 * q^34 + 5346 * q^35 + 2976 * q^36 + 576 * q^38 - 4974 * q^39 - 13356 * q^41 - 3840 * q^42 + 1260 * q^43 + 9558 * q^45 + 16578 * q^47 + 1920 * q^48 - 5904 * q^49 + 15552 * q^50 + 20898 * q^51 - 4896 * q^54 - 2304 * q^56 - 34218 * q^57 - 40104 * q^59 - 4176 * q^60 + 8352 * q^61 - 4110 * q^63 + 18432 * q^64 - 19674 * q^65 - 10368 * q^66 - 24192 * q^67 + 10224 * q^68 + 47106 * q^69 + 14400 * q^70 + 39528 * q^71 + 15360 * q^72 - 12222 * q^73 + 33120 * q^74 + 41682 * q^75 + 9792 * q^76 + 28206 * q^77 - 4608 * q^78 + 11304 * q^79 + 6804 * q^81 - 30078 * q^83 - 2592 * q^84 - 52200 * q^85 - 46224 * q^86 - 111690 * q^87 - 16128 * q^88 - 102222 * q^89 - 66240 * q^90 + 12078 * q^91 - 27504 * q^92 - 11958 * q^93 + 4032 * q^94 + 46728 * q^95 + 6144 * q^96 + 49680 * q^97 + 82944 * q^98 + 179622 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$2$	−0.967379	+	2.65785i	−0.241845	+	0.664463i
$3$	5.71544	+	6.95225i	0.635049	+	0.772472i
$3$	5.71544	+	6.95225i	0.635049	+	0.772472i
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	41.7224	+	7.35678i	1.66889	+	0.294271i	0.926669	−	0.375879i	$-0.122659\pi$
$5$	41.7224	+	7.35678i	1.66889	+	0.294271i	0.742226	+	0.670150i	$0.233770\pi$
$6$	−24.0070	+	8.46534i	−0.666862	+	0.235148i
$7$	19.0320	−	15.9698i	0.388409	−	0.325914i	−0.427584	−	0.903976i	$-0.640635\pi$
$7$	19.0320	−	15.9698i	0.388409	−	0.325914i	0.815993	+	0.578062i	$0.196191\pi$
$8$	19.5959	−	11.3137i	0.306186	−	0.176777i
$9$	−15.6675	+	79.4703i	−0.193426	+	0.981115i
$10$	−59.9146	+	103.775i	−0.599146	+	1.03775i
$11$	−18.0860	+	3.18905i	−0.149471	+	0.0263558i	−0.247883	−	0.968790i	$-0.579735\pi$
$11$	−18.0860	+	3.18905i	−0.149471	+	0.0263558i	0.0984119	+	0.995146i	$0.468624\pi$
$12$	0.724290	−	71.9964i	0.00502979	−	0.499975i
$13$	−100.351	+	36.5247i	−0.593792	+	0.216123i	−0.621397	−	0.783496i	$-0.713434\pi$
$13$	−100.351	+	36.5247i	−0.593792	+	0.216123i	0.0276042	+	0.999619i	$0.491212\pi$
$14$	24.0341	+	66.0331i	0.122623	+	0.336904i
$15$	187.316	+	332.111i	0.832514	+	1.47605i
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	−339.433	−	195.972i	−1.17451	−	0.678104i	−0.219772	−	0.975551i	$-0.570531\pi$
$17$	−339.433	−	195.972i	−1.17451	−	0.678104i	−0.954738	+	0.297448i	$0.903865\pi$
$18$	−196.064	−	118.520i	−0.605136	−	0.365802i
$19$	205.064	+	355.182i	0.568045	+	0.983883i	0.996759	+	0.0804431i	$0.0256335\pi$
$19$	205.064	+	355.182i	0.568045	+	0.983883i	−0.428714	+	0.903440i	$0.641033\pi$
$20$	−217.859	−	259.634i	−0.544647	−	0.649085i
$21$	219.802	+	41.0411i	0.498418	+	0.0930637i
$22$	9.02000	−	51.1549i	0.0186364	−	0.105692i
$23$	218.656	−	260.583i	0.413337	−	0.492596i	−0.518701	−	0.854956i	$-0.673584\pi$
$23$	218.656	−	260.583i	0.413337	−	0.492596i	0.932038	+	0.362359i	$0.118029\pi$
$24$	190.655	+	71.5728i	0.330998	+	0.124258i
$25$	1099.33	+	400.122i	1.75892	+	0.640195i
$26$		−	302.051i		−	0.446821i
$27$	−642.044	+	345.284i	−0.880718	+	0.473640i
$28$	−198.756			−0.253516
$29$	485.587	−	1334.14i	0.577392	−	1.58637i	−0.215167	−	0.976577i	$-0.569030\pi$
$29$	485.587	−	1334.14i	0.577392	−	1.58637i	0.792560	−	0.609795i	$-0.208748\pi$
$30$	−1063.91	+	176.579i	−1.18212	+	0.196199i
$31$	−923.152	−	774.616i	−0.960616	−	0.806052i	0.0204376	−	0.999791i	$-0.493494\pi$
$31$	−923.152	−	774.616i	−0.960616	−	0.806052i	−0.981053	+	0.193739i	$0.937939\pi$
$32$	−178.269	−	31.4337i	−0.174091	−	0.0306970i
$33$	−125.541	−	107.512i	−0.115281	−	0.0987250i
$34$	849.225	−	712.585i	0.734624	−	0.616423i
$35$	911.547	−	526.282i	0.744120	−	0.429618i
$36$	504.676	−	406.455i	0.389411	−	0.313623i
$37$	755.062	−	1307.80i	0.551542	−	0.955299i	−0.446621	−	0.894723i	$-0.647373\pi$
$37$	755.062	−	1307.80i	0.551542	−	0.955299i	0.998164	−	0.0605763i	$-0.0192938\pi$
$38$	−1142.40	+	201.435i	−0.791133	+	0.139498i
$39$	−827.479	−	488.909i	−0.544036	−	0.321439i
$40$	900.820	−	327.872i	0.563013	−	0.204920i
$41$	−207.264	−	569.453i	−0.123298	−	0.338759i	0.862652	−	0.505798i	$-0.168802\pi$
$41$	−207.264	−	569.453i	−0.123298	−	0.338759i	−0.985950	+	0.167039i	$0.946579\pi$
$42$	−321.713	+	544.499i	−0.182377	+	0.308673i
$43$	337.617	+	1914.72i	0.182594	+	1.03554i	0.929008	+	0.370061i	$0.120663\pi$
$43$	337.617	+	1914.72i	0.182594	+	1.03554i	−0.746413	+	0.665483i	$0.768226\pi$
$44$	127.237	+	73.4600i	0.0657213	+	0.0379442i
$45$	−1238.33	+	3200.43i	−0.611521	+	1.58046i
$46$	481.070	+	833.237i	0.227349	+	0.393779i
$47$	2025.36	+	2413.73i	0.916867	+	1.09268i	0.995404	+	0.0957684i	$0.0305308\pi$
$47$	2025.36	+	2413.73i	0.916867	+	1.09268i	−0.0785366	+	0.996911i	$0.525025\pi$
$48$	−374.666	+	437.495i	−0.162615	+	0.189885i
$49$	−309.745	+	1756.65i	−0.129007	+	0.731632i
$50$	−2126.93	+	2534.78i	−0.850772	+	1.01391i
$51$	−577.566	−	3479.89i	−0.222055	−	1.33791i
$52$	802.807	+	292.198i	0.296896	+	0.108061i
$53$		−	3309.93i		−	1.17833i	−0.808013	−	0.589165i	$-0.799457\pi$
$53$		−	3309.93i		−	1.17833i	0.808013	−	0.589165i	$-0.200543\pi$
$54$	−296.614	−	2040.48i	−0.101719	−	0.699752i
$55$	−778.052			−0.257207
$56$	192.273	−	528.265i	0.0613115	−	0.168452i
$57$	−1297.28	+	3455.68i	−0.399286	+	1.06361i
$58$	3076.20	+	2581.24i	0.914446	+	0.767311i
$59$	−4797.62	−	845.950i	−1.37823	−	0.243019i	−0.565062	−	0.825048i	$-0.691148\pi$
$59$	−4797.62	−	845.950i	−1.37823	−	0.243019i	−0.813168	+	0.582029i	$0.802259\pi$
$60$	559.880	−	2998.53i	0.155522	−	0.832925i
$61$	1691.36	−	1419.22i	0.454543	−	0.381407i	−0.386575	−	0.922258i	$-0.626342\pi$
$61$	1691.36	−	1419.22i	0.454543	−	0.381407i	0.841119	+	0.540851i	$0.181898\pi$
$62$	2951.85	−	1704.25i	0.767912	−	0.443354i
$63$	970.939	+	1762.69i	0.244631	+	0.444114i
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−4455.58	+	785.639i	−1.05458	+	0.185950i
$66$	407.195	−	229.664i	0.0934791	−	0.0527236i
$67$	−3252.29	+	1183.74i	−0.724503	+	0.263698i	−0.677836	−	0.735213i	$-0.737082\pi$
$67$	−3252.29	+	1183.74i	−0.724503	+	0.263698i	−0.0466669	+	0.998911i	$0.514860\pi$
$68$	1072.42	+	2946.45i	0.231925	+	0.637209i
$69$	3061.35	+	30.7975i	0.643006	+	0.00646870i
$70$	516.968	+	2931.87i	0.105504	+	0.598341i
$71$	5743.28	+	3315.88i	1.13931	+	0.657783i	0.946260	−	0.323405i	$-0.104828\pi$
$71$	5743.28	+	3315.88i	1.13931	+	0.657783i	0.193053	+	0.981188i	$0.438161\pi$
$72$	592.086	+	1734.55i	0.114214	+	0.334597i
$73$	−2945.25	−	5101.32i	−0.552684	−	0.957276i	−0.998080	−	0.0619425i	$-0.980270\pi$
$73$	−2945.25	−	5101.32i	−0.552684	−	0.957276i	0.445396	−	0.895334i	$-0.353063\pi$
$74$	2745.52	+	3271.98i	0.501374	+	0.597514i
$75$	3501.38	+	9929.65i	0.622468	+	1.76527i
$76$	569.745	−	3231.18i	0.0986400	−	0.559415i
$77$	−293.285	+	349.523i	−0.0494662	+	0.0589515i
$78$	2099.93	−	1726.36i	0.345157	−	0.283753i
$79$	−2340.08	−	851.720i	−0.374953	−	0.136472i	0.147668	−	0.989037i	$-0.452823\pi$
$79$	−2340.08	−	851.720i	−0.374953	−	0.136472i	−0.522621	+	0.852565i	$0.675046\pi$
$80$			2711.42i			0.423660i
$81$	−6070.06	−	2490.20i	−0.925173	−	0.379545i
$82$	1714.03			0.254912
$83$	3787.29	−	10405.5i	0.549759	−	1.51045i	−0.284279	−	0.958742i	$-0.591754\pi$
$83$	3787.29	−	10405.5i	0.549759	−	1.51045i	0.834038	−	0.551708i	$-0.186024\pi$
$84$	−1135.98	−	1381.80i	−0.160995	−	0.195834i
$85$	−12720.2	−	10673.6i	−1.76059	−	1.47731i
$86$	−5415.65	−	954.924i	−0.732240	−	0.129114i
$87$	12050.6	−	4249.27i	1.59210	−	0.561405i
$88$	−318.332	+	267.112i	−0.0411069	+	0.0344928i
$89$	6082.16	−	3511.54i	0.767852	−	0.443320i	−0.0642555	−	0.997933i	$-0.520467\pi$
$89$	6082.16	−	3511.54i	0.767852	−	0.443320i	0.832108	+	0.554614i	$0.187134\pi$
$90$	−7308.33	−	6387.32i	−0.902263	−	0.788558i
$91$	−1326.59	+	2297.72i	−0.160197	+	0.277469i
$92$	−2680.00	+	472.556i	−0.316635	+	0.0558313i
$93$	109.104	−	10845.2i	0.0126147	−	1.25393i
$94$	−8374.63	+	3048.11i	−0.947785	+	0.344965i
$95$	5942.78	+	16327.6i	0.658479	+	1.80916i
$96$	−800.353	−	1419.03i	−0.0868438	−	0.153975i
$97$	350.066	+	1985.32i	0.0372054	+	0.211002i	0.997743	−	0.0671476i	$-0.0213898\pi$
$97$	350.066	+	1985.32i	0.0372054	+	0.211002i	−0.960538	+	0.278150i	$0.910279\pi$
$98$	−4369.27	−	2522.60i	−0.454943	−	0.262662i
$99$	29.9271	−	1487.26i	0.00305347	−	0.151746i
$100$	−4679.51	−	8105.15i	−0.467951	−	0.810515i
$101$	−11176.5	−	13319.6i	−1.09562	−	1.30571i	−0.948563	−	0.316587i	$-0.897463\pi$
$101$	−11176.5	−	13319.6i	−1.09562	−	1.30571i	−0.147061	−	0.989127i	$-0.546981\pi$
$102$	9807.76	+	1831.29i	0.942691	+	0.176018i
$103$	−2302.42	+	13057.7i	−0.217026	+	1.23081i	0.660331	+	0.750975i	$0.270416\pi$
$103$	−2302.42	+	13057.7i	−0.217026	+	1.23081i	−0.877357	+	0.479839i	$0.840695\pi$
$104$	−1553.24	+	1851.08i	−0.143606	+	0.171142i
$105$	8868.74	+	3329.37i	0.804420	+	0.301983i
$106$	8797.30	+	3201.96i	0.782957	+	0.284973i
$107$			10520.6i			0.918907i	0.888202	+	0.459453i	$0.151955\pi$
$107$			10520.6i			0.918907i	−0.888202	+	0.459453i	$0.848045\pi$
$108$	5710.23	+	1185.56i	0.489560	+	0.101643i
$109$	−10635.3			−0.895153			−0.447576	−	0.894246i	$-0.647713\pi$
$109$	−10635.3			−0.895153			−0.447576	+	0.894246i	$0.647713\pi$
$110$	752.671	−	2067.95i	0.0622042	−	0.170905i
$111$	13407.7	−	2225.31i	1.08820	−	0.180611i
$112$	1218.05	+	1022.06i	0.0971022	+	0.0814784i
$113$	13895.7	+	2450.19i	1.08824	+	0.191885i	0.688855	−	0.724899i	$-0.258114\pi$
$113$	13895.7	+	2450.19i	1.08824	+	0.191885i	0.399382	+	0.916785i	$0.369225\pi$
$114$	−7929.72	−	6790.93i	−0.610167	−	0.522540i
$115$	11039.9	−	9263.56i	0.834773	−	0.700458i
$116$	−9836.39	+	5679.04i	−0.731004	+	0.422045i
$117$	−1330.39	−	8547.17i	−0.0971866	−	0.624382i
$118$	6889.53	−	11933.0i	0.494795	−	0.857010i
$119$	−9589.73	+	1690.93i	−0.677193	+	0.119407i
$120$	7428.03	+	4388.79i	0.515836	+	0.304777i
$121$	−13441.1	+	4892.16i	−0.918046	+	0.334141i
$122$	2135.88	+	5868.29i	0.143502	+	0.394269i
$123$	2774.37	−	4695.63i	0.183381	−	0.310373i
$124$	1674.09	+	9494.25i	0.108877	+	0.617472i
$125$	19991.6	+	11542.1i	1.27946	+	0.738697i
$126$	−5624.23	+	875.425i	−0.354260	+	0.0551414i
$127$	5562.96	+	9635.34i	0.344904	+	0.597392i	0.985336	−	0.170623i	$-0.0545780\pi$
$127$	5562.96	+	9635.34i	0.344904	+	0.597392i	−0.640432	+	0.768015i	$0.721245\pi$
$128$	930.856	+	1109.35i	0.0568149	+	0.0677094i
$129$	−11382.0	+	13290.7i	−0.683972	+	0.798670i
$130$	2222.12	−	12602.3i	0.131487	−	0.745698i
$131$	−1203.03	+	1433.72i	−0.0701026	+	0.0835450i	−0.799956	−	0.600059i	$-0.795144\pi$
$131$	−1203.03	+	1433.72i	−0.0701026	+	0.0835450i	0.729853	+	0.683604i	$0.239588\pi$
$132$	216.500	+	1304.44i	0.0124254	+	0.0748643i
$133$	9574.96	+	3485.00i	0.541295	+	0.197015i
$134$		−	9789.24i		−	0.545179i
$135$	−29327.8	+	9682.68i	−1.60920	+	0.531286i
$136$	−8868.68			−0.479492
$137$	−6175.92	+	16968.2i	−0.329049	+	0.904054i	0.659304	+	0.751876i	$0.270851\pi$
$137$	−6175.92	+	16968.2i	−0.329049	+	0.904054i	−0.988353	+	0.152178i	$0.951371\pi$
$138$	−3043.34	+	8106.83i	−0.159806	+	0.425690i
$139$	12180.0	+	10220.3i	0.630404	+	0.528972i	0.901055	−	0.433706i	$-0.142794\pi$
$139$	12180.0	+	10220.3i	0.630404	+	0.528972i	−0.270650	+	0.962678i	$0.587239\pi$
$140$	−8292.58	−	1462.21i	−0.423091	−	0.0746024i
$141$	−5205.02	+	27876.3i	−0.261809	+	1.40216i
$142$	−14369.1	+	12057.1i	−0.712609	+	0.597950i
$143$	1698.47	−	980.611i	0.0830587	−	0.0479540i
$144$	−5182.95	−	104.292i	−0.249949	−	0.00502954i
$145$	30074.8	−	52091.1i	1.43043	−	2.47758i
$146$	16407.7	−	2893.13i	0.769738	−	0.135726i
$147$	−13983.0	+	7886.60i	−0.647091	+	0.364969i
$148$	−11352.4	+	4131.94i	−0.518280	+	0.188639i
$149$	4838.44	+	13293.5i	0.217938	+	0.598780i	0.999692	−	0.0248069i	$-0.00789710\pi$
$149$	4838.44	+	13293.5i	0.217938	+	0.598780i	−0.781754	+	0.623587i	$0.785675\pi$
$150$	−29778.7	−	299.577i	−1.32350	−	0.0133145i
$151$	−1016.71	−	5766.02i	−0.0445904	−	0.252885i	0.954362	−	0.298653i	$-0.0965374\pi$
$151$	−1016.71	−	5766.02i	−0.0445904	−	0.252885i	−0.998952	+	0.0457686i	$0.985426\pi$
$152$	8036.85	+	4640.08i	0.347855	+	0.200834i
$153$	20892.0	−	23904.5i	0.892478	−	1.02117i
$154$	−645.264	−	1117.63i	−0.0272079	−	0.0471255i
$155$	−32817.4	−	39110.2i	−1.36597	−	1.62790i
$156$	2556.97	+	7251.35i	0.105069	+	0.297968i
$157$	−5308.10	+	30103.7i	−0.215347	+	1.22130i	0.664955	+	0.746883i	$0.268451\pi$
$157$	−5308.10	+	30103.7i	−0.215347	+	1.22130i	−0.880303	+	0.474412i	$0.842661\pi$
$158$	4527.49	−	5395.65i	0.181361	−	0.216137i
$159$	23011.4	−	18917.7i	0.910227	−	0.748297i
$160$	−7206.56	−	2622.97i	−0.281506	−	0.102460i
$161$		−	8451.31i		−	0.326041i
$162$	12490.6	−	13724.4i	0.475942	−	0.522952i
$163$	24783.8			0.932809			0.466405	−	0.884572i	$-0.345549\pi$
$163$	24783.8			0.932809			0.466405	+	0.884572i	$0.345549\pi$
$164$	−1658.11	+	4555.63i	−0.0616490	+	0.169379i
$165$	−4446.91	−	5409.21i	−0.163339	−	0.198685i
$166$	23992.5	+	20132.1i	0.870681	+	0.730588i
$167$	−46851.0	−	8261.09i	−1.67991	−	0.296213i	−0.749301	−	0.662230i	$-0.769610\pi$
$167$	−46851.0	−	8261.09i	−1.67991	−	0.296213i	−0.930608	+	0.366017i	$0.880721\pi$
$168$	4771.55	−	1682.54i	0.169060	−	0.0596138i
$169$	−13142.7	+	11028.1i	−0.460164	+	0.386124i
$170$	40674.0	−	23483.2i	1.40741	−	0.812566i
$171$	−31439.3	+	10731.7i	−1.07518	+	0.367010i
$172$	7777.03	−	13470.2i	0.262880	−	0.455321i
$173$	2045.69	−	360.711i	0.0683515	−	0.0120522i	−0.139368	−	0.990241i	$-0.544507\pi$
$173$	2045.69	−	360.711i	0.0683515	−	0.0120522i	0.207719	+	0.978188i	$0.433396\pi$
$174$	−363.565	+	36139.4i	−0.0120084	+	1.19366i
$175$	27312.2	−	9940.84i	0.891828	−	0.324599i
$176$	−401.997	−	1104.48i	−0.0129777	−	0.0356559i
$177$	−21539.3	−	38189.2i	−0.687518	−	1.21897i
$178$	3449.39	+	19562.5i	0.108869	+	0.617424i
$179$	−16467.1	−	9507.30i	−0.513939	−	0.296723i	0.220512	−	0.975384i	$-0.429227\pi$
$179$	−16467.1	−	9507.30i	−0.513939	−	0.296723i	−0.734451	+	0.678661i	$0.762560\pi$
$180$	24046.5	−	13245.5i	0.742175	−	0.408812i
$181$	18376.7	+	31829.5i	0.560934	+	0.971566i	0.997415	+	0.0718525i	$0.0228911\pi$
$181$	18376.7	+	31829.5i	0.560934	+	0.971566i	−0.436482	+	0.899713i	$0.643776\pi$
$182$	−4823.69	−	5748.65i	−0.145625	−	0.173549i
$183$	19533.6	+	3647.28i	0.583284	+	0.108910i
$184$	1336.59	−	7580.18i	0.0394787	−	0.223895i
$185$	41124.2	−	49009.9i	1.20158	−	1.43199i
$186$	28719.5	+	10781.5i	0.830140	+	0.311639i
$187$	6763.96	+	2461.88i	0.193427	+	0.0704018i
$188$		−	25207.2i		−	0.713196i
$189$	−6705.29	+	16824.7i	−0.187713	+	0.471004i
$190$	−49145.4			−1.36137
$191$	−2106.78	+	5788.32i	−0.0577500	+	0.158667i	−0.965213	−	0.261466i	$-0.915794\pi$
$191$	−2106.78	+	5788.32i	−0.0577500	+	0.158667i	0.907463	+	0.420132i	$0.138016\pi$
$192$	4545.81	−	754.480i	0.123313	−	0.0204666i
$193$	−24419.1	−	20490.1i	−0.655565	−	0.550084i	0.253189	−	0.967417i	$-0.418521\pi$
$193$	−24419.1	−	20490.1i	−0.655565	−	0.550084i	−0.908754	+	0.417333i	$0.862965\pi$
$194$	−5615.34	−	990.136i	−0.149201	−	0.0263082i
$195$	−30927.6	−	26486.0i	−0.813348	−	0.696542i
$196$	10931.4	−	9172.57i	0.284555	−	0.238770i
$197$	−19300.3	+	11143.0i	−0.497314	+	0.287124i	−0.727604	−	0.685998i	$-0.759366\pi$
$197$	−19300.3	+	11143.0i	−0.497314	+	0.287124i	0.230290	+	0.973122i	$0.426033\pi$
$198$	3923.98	+	1518.29i	0.100091	+	0.0387279i
$199$	−7630.55	+	13216.5i	−0.192686	+	0.333742i	−0.946139	−	0.323759i	$-0.895053\pi$
$199$	−7630.55	+	13216.5i	−0.192686	+	0.333742i	0.753454	+	0.657501i	$0.228386\pi$
$200$	26069.2	−	4596.70i	0.651729	−	0.114917i
$201$	−26817.9	−	15845.2i	−0.663794	−	0.392197i
$202$	46213.4	−	16820.3i	1.13257	−	0.412222i
$203$	−12064.2	−	33146.1i	−0.292756	−	0.804340i
$204$	−14355.1	+	24296.0i	−0.344942	+	0.583815i
$205$	−4458.20	−	25283.7i	−0.106085	−	0.601636i
$206$	−32478.1	−	18751.2i	−0.765343	−	0.441871i
$207$	17282.9	+	21459.3i	0.403344	+	0.500812i
$208$	−3417.32	−	5918.97i	−0.0789876	−	0.136811i
$209$	−4841.49	−	5769.86i	−0.110837	−	0.132091i
$210$	−17428.4	+	20351.0i	−0.395202	+	0.461475i
$211$	−3131.77	+	17761.2i	−0.0703438	+	0.398939i	0.929223	+	0.369519i	$0.120477\pi$
$211$	−3131.77	+	17761.2i	−0.0703438	+	0.398939i	−0.999567	+	0.0294207i	$0.990634\pi$
$212$	−17020.6	+	20284.4i	−0.378708	+	0.451327i
$213$	9772.53	+	58880.4i	0.215401	+	1.29781i
$214$	−27962.1	−	10177.4i	−0.610580	−	0.222233i
$215$			82370.4i			1.78195i
$216$	−8675.00	+	14030.0i	−0.185935	+	0.300713i
$217$	−29939.9			−0.635815
$218$	10288.4	−	28267.1i	0.216488	−	0.594796i
$219$	18632.3	−	49632.4i	0.388488	−	1.03485i
$220$	4768.18	+	4000.98i	0.0985161	+	0.0826648i
$221$	41220.3	+	7268.25i	0.843969	+	0.148814i
$222$	−7055.78	+	37788.4i	−0.143166	+	0.766747i
$223$	26982.1	−	22640.7i	0.542583	−	0.455282i	−0.329837	−	0.944038i	$-0.606994\pi$
$223$	26982.1	−	22640.7i	0.542583	−	0.455282i	0.872420	+	0.488756i	$0.162549\pi$
$224$	−3894.81	+	2248.67i	−0.0776230	+	0.0448157i
$225$	−49021.5	+	81094.8i	−0.968325	+	1.60187i
$226$	−19954.6	+	34562.4i	−0.390685	+	0.676686i
$227$	43109.9	−	7601.44i	0.836614	−	0.147518i	0.261102	−	0.965311i	$-0.415914\pi$
$227$	43109.9	−	7601.44i	0.836614	−	0.147518i	0.575512	+	0.817793i	$0.304803\pi$
$228$	25720.3	−	14506.6i	0.494774	−	0.279060i
$229$	−36596.7	+	13320.1i	−0.697864	+	0.254002i	−0.666499	−	0.745506i	$-0.732208\pi$
$229$	−36596.7	+	13320.1i	−0.697864	+	0.254002i	−0.0313656	+	0.999508i	$0.509986\pi$
$230$	13941.4	+	38303.7i	0.263543	+	0.724078i
$231$	−4106.22	−	41.3090i	−0.0769518	−	0.000774142i
$232$	−5578.54	−	31637.5i	−0.103644	−	0.587795i
$233$	−13129.6	−	7580.39i	−0.241847	−	0.139630i	0.374178	−	0.927357i	$-0.377925\pi$
$233$	−13129.6	−	7580.39i	−0.241847	−	0.139630i	−0.616025	+	0.787726i	$0.711258\pi$
$234$	24004.1	+	4732.38i	0.438383	+	0.0864266i
$235$	66745.5	+	115607.i	1.20861	+	2.09337i
$236$	25051.4	+	29855.1i	0.449788	+	0.536036i
$237$	−7453.23	−	21136.8i	−0.132693	−	0.376307i
$238$	4782.67	−	27123.9i	0.0844338	−	0.478848i
$239$	12810.9	−	15267.4i	0.224277	−	0.267282i	−0.642159	−	0.766572i	$-0.721961\pi$
$239$	12810.9	−	15267.4i	0.224277	−	0.267282i	0.866435	+	0.499289i	$0.166405\pi$
$240$	−18850.5	+	15497.0i	−0.327265	+	0.269045i
$241$	61204.6	+	22276.7i	1.05378	+	0.383545i	0.810088	−	0.586308i	$-0.199419\pi$
$241$	61204.6	+	22276.7i	1.05378	+	0.383545i	0.243692	+	0.969853i	$0.421641\pi$
$242$		−	40457.0i		−	0.690818i
$243$	−17380.6	−	56433.1i	−0.294342	−	0.955700i
$244$	−17663.3			−0.296682
$245$	−25846.6	+	71012.8i	−0.430597	+	1.18305i
$246$	9796.41	+	11916.3i	0.161881	+	0.196912i
$247$	−33551.3	−	28152.9i	−0.549941	−	0.461455i
$248$	−26853.8	−	4735.05i	−0.436618	−	0.0769876i
$249$	93987.5	−	33141.8i	1.51590	−	0.534536i
$250$	−50016.8	+	41969.0i	−0.800268	+	0.671505i
$251$	−75304.6	+	43477.1i	−1.19529	+	0.690102i	−0.959502	−	0.281702i	$-0.909101\pi$
$251$	−75304.6	+	43477.1i	−1.19529	+	0.690102i	−0.235790	+	0.971804i	$0.575768\pi$
$252$	3114.01	−	15795.2i	0.0490364	−	0.248728i
$253$	−3123.59	+	5410.22i	−0.0487992	+	0.0845227i
$254$	−30990.8	+	5464.51i	−0.480358	+	0.0847001i
$255$	1503.36	−	149438.i	0.0231198	−	2.29817i
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	12558.6	+	34504.6i	0.190141	+	0.522409i	0.997730	−	0.0673367i	$-0.0214502\pi$
$257$	12558.6	+	34504.6i	0.190141	+	0.522409i	−0.807589	+	0.589746i	$0.799228\pi$
$258$	−24313.9	−	43108.7i	−0.365272	−	0.647628i
$259$	−6514.99	−	36948.3i	−0.0971212	−	0.550802i
$260$	31345.4	+	18097.3i	0.463689	+	0.267711i
$261$	98416.5	+	59492.3i	1.44473	+	0.873333i
$262$	−2646.82	−	4584.43i	−0.0385586	−	0.0667855i
$263$	44991.3	+	53618.5i	0.650455	+	0.775182i	0.985983	−	0.166849i	$-0.0533591\pi$
$263$	44991.3	+	53618.5i	0.650455	+	0.775182i	−0.335528	+	0.942030i	$0.608915\pi$
$264$	−3676.44	−	686.458i	−0.0527496	−	0.00984931i
$265$	24350.4	−	138098.i	0.346748	−	1.96651i
$266$	−18525.2	+	22077.5i	−0.261819	+	0.312023i
$267$	59175.3	+	22214.7i	0.830076	+	0.311615i
$268$	26018.4	+	9469.91i	0.362252	+	0.131849i
$269$			27399.8i			0.378654i	0.981914	+	0.189327i	$0.0606306\pi$
$269$			27399.8i			0.378654i	−0.981914	+	0.189327i	$0.939369\pi$
$270$	2635.92	−	87315.7i	0.0361581	−	1.19775i
$271$	−80278.7			−1.09310			−0.546552	−	0.837425i	$-0.684060\pi$
$271$	−80278.7			−1.09310			−0.546552	+	0.837425i	$0.684060\pi$
$272$	8579.37	−	23571.6i	0.115963	−	0.318605i
$273$	−23556.4	+	3909.71i	−0.316070	+	0.0524589i
$274$	−39124.5	−	32829.3i	−0.521132	−	0.437281i
$275$	−21158.4	−	3730.80i	−0.279781	−	0.0493329i
$276$	−18602.7	−	15931.1i	−0.244207	−	0.209136i
$277$	14943.4	−	12539.0i	0.194756	−	0.163420i	−0.540195	−	0.841540i	$-0.681650\pi$
$277$	14943.4	−	12539.0i	0.194756	−	0.163420i	0.734951	+	0.678120i	$0.237205\pi$
$278$	−38946.7	+	22485.9i	−0.503942	+	0.290951i
$279$	76022.4	−	61226.9i	0.976637	−	0.786563i
$280$	11908.4	−	20626.0i	0.151893	−	0.263086i
$281$	−6479.42	+	1142.50i	−0.0820585	+	0.0144691i	−0.214527	−	0.976718i	$-0.568821\pi$
$281$	−6479.42	+	1142.50i	−0.0820585	+	0.0144691i	0.132468	+	0.991187i	$0.457710\pi$
$282$	−69055.9	−	40801.1i	−0.868366	−	0.513067i
$283$	22664.0	−	8249.01i	0.282985	−	0.102998i	−0.196628	−	0.980478i	$-0.562999\pi$
$283$	22664.0	−	8249.01i	0.282985	−	0.102998i	0.479613	+	0.877480i	$0.340777\pi$
$284$	−18145.6	−	49854.6i	−0.224975	−	0.618114i
$285$	−79548.2	+	134635.i	−0.979356	+	1.65756i
$286$	963.256	+	5462.90i	0.0117763	+	0.0667869i
$287$	−13038.7	−	7527.89i	−0.158296	−	0.0913923i
$288$	5291.07	−	13674.6i	0.0637909	−	0.164866i
$289$	35049.5	+	60707.6i	0.419649	+	0.726854i
$290$	109357.	+	130326.i	1.30032	+	1.54966i
$291$	−11801.7	+	13780.7i	−0.139366	+	0.162737i
$292$	−8183.00	+	46408.1i	−0.0959725	+	0.544287i
$293$	40800.2	−	48623.8i	0.475256	−	0.566388i	−0.474148	−	0.880445i	$-0.657244\pi$
$293$	40800.2	−	48623.8i	0.475256	−	0.566388i	0.949404	+	0.314057i	$0.101688\pi$
$294$	−7434.58	−	44794.1i	−0.0860125	−	0.518234i
$295$	−193945.	−	70590.1i	−2.22861	−	0.811147i
$296$		−	34170.2i		−	0.389999i
$297$	10510.9	−	8292.31i	0.119159	−	0.0940076i
$298$	−40012.8			−0.450574
$299$	−12424.5	+	34136.1i	−0.138975	+	0.381832i
$300$	29603.5	−	78857.6i	0.328928	−	0.876196i
$301$	37003.2	+	31049.3i	0.408419	+	0.342704i
$302$	16308.8	+	2875.68i	0.178816	+	0.0315302i
$303$	28722.7	−	153829.i	0.312852	−	1.67553i
$304$	−20107.3	+	16872.0i	−0.217574	+	0.182566i
$305$	81008.2	−	46770.1i	0.870822	−	0.502769i
$306$	43324.1	+	78652.6i	0.462686	+	0.839982i
$307$	26678.0	−	46207.7i	0.283059	−	0.490272i	−0.689078	−	0.724687i	$-0.741984\pi$
$307$	26678.0	−	46207.7i	0.283059	−	0.490272i	0.972137	+	0.234415i	$0.0753175\pi$
$308$	3594.71	−	633.844i	0.0378933	−	0.00668161i
$309$	−103940.	+	58623.5i	−1.08859	+	0.613981i
$310$	135696.	−	49389.3i	1.41203	−	0.513937i
$311$	−10062.8	−	27647.2i	−0.104039	−	0.285845i	0.876741	−	0.480964i	$-0.159713\pi$
$311$	−10062.8	−	27647.2i	−0.104039	−	0.285845i	−0.980780	+	0.195118i	$0.937491\pi$
$312$	−21746.6	−	218.773i	−0.223399	−	0.00224742i
$313$	−25540.7	−	144848.i	−0.260701	−	1.47851i	−0.781002	−	0.624528i	$-0.785291\pi$
$313$	−25540.7	−	144848.i	−0.260701	−	1.47851i	0.520301	−	0.853983i	$-0.325820\pi$
$314$	−74876.3	−	43229.8i	−0.759425	−	0.438454i
$315$	27542.2	+	80686.4i	0.277573	+	0.813166i
$316$	9961.05	+	17253.0i	0.0997541	+	0.172779i
$317$	73982.5	+	88168.9i	0.736225	+	0.877399i	0.996099	−	0.0882440i	$-0.0281255\pi$
$317$	73982.5	+	88168.9i	0.736225	+	0.877399i	−0.259874	+	0.965643i	$0.583681\pi$
$318$	28019.7	+	79461.6i	0.277082	+	0.785784i
$319$	−4527.69	+	25677.8i	−0.0444934	+	0.252334i
$320$	13943.0	−	16616.6i	0.136162	−	0.162271i
$321$	−73141.5	+	60129.7i	−0.709830	+	0.583551i
$322$	22462.3	+	8175.62i	0.216642	+	0.0788513i
$323$		−	160747.i		−	1.54077i
$324$	24394.1	+	46474.9i	0.232378	+	0.442719i
$325$	−124933.			−1.18279
$326$	−23975.3	+	65871.7i	−0.225595	+	0.619817i
$327$	−60785.5	−	73939.3i	−0.568466	−	0.691480i
$328$	−10504.2	−	8814.04i	−0.0976368	−	0.0819270i
$329$	77093.4	+	13593.6i	0.712238	+	0.125587i
$330$	18678.7	−	6586.47i	0.171522	−	0.0604818i
$331$	−45867.3	+	38487.3i	−0.418646	+	0.351286i	−0.827648	−	0.561248i	$-0.810322\pi$
$331$	−45867.3	+	38487.3i	−0.418646	+	0.351286i	0.409001	+	0.912534i	$0.365877\pi$
$332$	−76718.0	+	44293.1i	−0.696019	+	0.401847i
$333$	92101.8	+	80495.0i	0.830576	+	0.725906i
$334$	67279.4	−	116531.i	0.603100	−	1.04460i
$335$	−144402.	+	25462.0i	−1.28672	+	0.226883i
$336$	−143.957	+	14309.7i	−0.00127513	+	0.126751i
$337$	−56576.9	+	20592.3i	−0.498172	+	0.181320i	−0.578872	−	0.815419i	$-0.696507\pi$
$337$	−56576.9	+	20592.3i	−0.498172	+	0.181320i	0.0806994	+	0.996738i	$0.474285\pi$
$338$	−16597.0	−	45599.8i	−0.145277	−	0.399144i
$339$	62385.7	+	110610.i	0.542857	+	0.962489i
$340$	23067.6	+	130823.i	0.199546	+	1.13168i
$341$	19166.4	+	11065.7i	0.164828	+	0.0951637i
$342$	1890.33	−	93942.5i	0.0161617	−	0.803175i
$343$	51984.1	+	90039.1i	0.441857	+	0.765320i
$344$	28278.5	+	33701.0i	0.238968	+	0.284791i
$345$	127500.	+	23806.6i	1.07121	+	0.200014i
$346$	−1020.24	+	5786.09i	−0.00852220	+	0.0483318i
$347$	−16062.2	+	19142.1i	−0.133397	+	0.158976i	−0.828608	−	0.559830i	$-0.810866\pi$
$347$	−16062.2	+	19142.1i	−0.133397	+	0.158976i	0.695211	+	0.718806i	$0.255311\pi$
$348$	−95701.4	−	35926.8i	−0.790242	−	0.296661i
$349$	−127113.	−	46265.2i	−1.04361	−	0.379843i	−0.237362	−	0.971421i	$-0.576283\pi$
$349$	−127113.	−	46265.2i	−1.04361	−	0.379843i	−0.806247	+	0.591579i	$0.798505\pi$
$350$			82208.5i			0.671089i
$351$	51818.3	−	58100.0i	0.420599	−	0.471587i
$352$	3324.42			0.0268306
$353$	70858.1	−	194681.i	0.568643	−	1.56233i	−0.237981	−	0.971270i	$-0.576485\pi$
$353$	70858.1	−	194681.i	0.568643	−	1.56233i	0.806624	−	0.591065i	$-0.201292\pi$
$354$	122338.	−	20304.7i	0.976235	−	0.162028i
$355$	215229.	+	180599.i	1.70783	+	1.43304i
$356$	−55331.0	−	9756.35i	−0.436585	−	0.0769817i
$357$	−66565.3	−	57005.8i	−0.522290	−	0.447283i
$358$	41199.0	−	34570.0i	0.321455	−	0.269733i
$359$	−9886.99	+	5708.26i	−0.0767141	+	0.0442909i	−0.537866	−	0.843030i	$-0.680770\pi$
$359$	−9886.99	+	5708.26i	−0.0767141	+	0.0442909i	0.461152	+	0.887321i	$0.347436\pi$
$360$	11942.5	+	76725.4i	0.0921489	+	0.592017i
$361$	−18942.3	+	32809.0i	−0.145351	+	0.251755i
$362$	−102375.	+	18051.5i	−0.781228	+	0.137752i
$363$	−110833.	−	65485.0i	−0.841119	−	0.496968i
$364$	19945.4	−	7259.52i	0.150536	−	0.0547905i
$365$	−85353.5	−	234507.i	−0.640672	−	1.76023i
$366$	−28590.3	+	48389.1i	−0.213431	+	0.361231i
$367$	32552.8	+	184616.i	0.241688	+	1.37068i	0.828059	+	0.560640i	$0.189445\pi$
$367$	32552.8	+	184616.i	0.241688	+	1.37068i	−0.586371	+	0.810043i	$0.699444\pi$
$368$	18854.0	+	10885.4i	0.139222	+	0.0803799i
$369$	48501.9	−	7549.45i	0.356210	−	0.0554450i
$370$	90478.4	+	156713.i	0.660908	+	1.14473i
$371$	−52858.8	−	62994.6i	−0.384034	−	0.457674i
$372$	−56438.2	+	65902.5i	−0.407837	+	0.476229i
$373$	13751.3	−	77987.7i	0.0988387	−	0.560542i	−0.894665	−	0.446739i	$-0.852585\pi$
$373$	13751.3	−	77987.7i	0.0988387	−	0.560542i	0.993503	−	0.113804i	$-0.0363035\pi$
$374$	−13086.6	+	15596.0i	−0.0935587	+	0.111499i
$375$	34016.9	+	204955.i	0.241898	+	1.45746i
$376$	66997.0	+	24384.9i	0.473892	+	0.172483i
$377$			151618.i			1.06676i
$378$	−38231.1	−	34097.6i	−0.267567	−	0.238638i
$379$	−122815.			−0.855015			−0.427507	−	0.904012i	$-0.640608\pi$
$379$	−122815.			−0.855015			−0.427507	+	0.904012i	$0.640608\pi$
$380$	47542.2	−	130621.i	0.329240	−	0.904579i
$381$	−35192.4	+	93745.3i	−0.242437	+	0.645802i
$382$	−13346.5	−	11199.0i	−0.0914617	−	0.0767455i
$383$	95401.9	+	16821.9i	0.650369	+	0.114678i	0.489093	−	0.872232i	$-0.337328\pi$
$383$	95401.9	+	16821.9i	0.650369	+	0.114678i	0.161276	+	0.986909i	$0.448439\pi$
$384$	−2392.23	+	12812.0i	−0.0162233	+	0.0868867i
$385$	−14807.9	+	12425.3i	−0.0999015	+	0.0838273i
$386$	78082.2	−	45080.8i	0.524055	−	0.302564i
$387$	−157453.	−	3168.30i	−1.05131	−	0.0211546i
$388$	8063.80	−	13966.9i	0.0535644	−	0.0927762i
$389$	207400.	−	36570.3i	1.37060	−	0.241674i	0.560591	−	0.828093i	$-0.310574\pi$
$389$	207400.	−	36570.3i	1.37060	−	0.241674i	0.810008	+	0.586419i	$0.199463\pi$
$390$	100315.	−	56578.9i	0.659531	−	0.371985i
$391$	−125286.	+	45600.4i	−0.819500	+	0.298274i
$392$	13804.5	+	37927.5i	0.0898355	+	0.246821i
$393$	−16843.4	−	169.446i	−0.109055	−	0.00109710i
$394$	−10945.8	−	62076.8i	−0.0705108	−	0.399886i
$395$	−91367.8	−	52751.2i	−0.585597	−	0.338095i
$396$	−7831.37	+	8960.59i	−0.0499398	+	0.0571408i
$397$	96424.6	+	167012.i	0.611796	+	1.05966i	0.990938	+	0.134323i	$0.0428860\pi$
$397$	96424.6	+	167012.i	0.611796	+	1.05966i	−0.379141	+	0.925339i	$0.623781\pi$
$398$	−27745.9	−	33066.2i	−0.175159	−	0.208746i
$399$	30496.5	+	86485.8i	0.191560	+	0.543249i
$400$	−13001.4	+	73734.7i	−0.0812589	+	0.460842i
$401$	−15527.7	+	18505.2i	−0.0965650	+	0.115082i	−0.812163	−	0.583431i	$-0.801710\pi$
$401$	−15527.7	+	18505.2i	−0.0965650	+	0.115082i	0.715598	+	0.698513i	$0.246154\pi$
$402$	68057.2	−	55949.8i	0.421136	−	0.346216i
$403$	120932.	+	44015.6i	0.744612	+	0.271017i
$404$			139100.i			0.852245i
$405$	−234937.	−	148553.i	−1.43233	−	0.905673i
$406$	99768.0			0.605256
$407$	−9485.39	+	26060.9i	−0.0572620	+	0.157326i
$408$	−50688.4	−	61657.2i	−0.304501	−	0.370394i
$409$	−129469.	−	108637.i	−0.773961	−	0.649430i	0.167759	−	0.985828i	$-0.446347\pi$
$409$	−129469.	−	108637.i	−0.773961	−	0.649430i	−0.941720	+	0.336398i	$0.890791\pi$
$410$	71513.2	+	12609.7i	0.425421	+	0.0750131i
$411$	−153265.	+	54044.2i	−0.907318	+	0.319938i
$412$	81256.7	−	68182.5i	0.478701	−	0.401678i
$413$	−104818.	+	60516.7i	−0.614520	+	0.354793i
$414$	−73754.7	+	25176.0i	−0.430318	+	0.146888i
$415$	234565.	−	406279.i	1.36197	−	2.35900i
$416$	19037.6	−	3356.84i	0.110008	−	0.0193974i
$417$	−1439.52	+	143092.i	−0.00827838	+	0.822893i
$418$	20019.0	−	7286.32i	0.114575	−	0.0417019i
$419$	16582.6	+	45560.4i	0.0944551	+	0.259513i	0.977918	−	0.208987i	$-0.0670167\pi$
$419$	16582.6	+	45560.4i	0.0944551	+	0.259513i	−0.883463	+	0.468500i	$0.844794\pi$
$420$	−37230.2	−	66009.3i	−0.211055	−	0.374202i
$421$	−31948.4	−	181189.i	−0.180254	−	1.02227i	−0.931903	−	0.362708i	$-0.881852\pi$
$421$	−31948.4	−	181189.i	−0.180254	−	1.02227i	0.751649	−	0.659564i	$-0.229259\pi$
$422$	−44177.0	−	25505.6i	−0.248068	−	0.143222i
$423$	−223552.	+	123139.i	−1.24939	+	0.688200i
$424$	−37447.6	−	64861.1i	−0.208301	−	0.360788i
$425$	−294735.	−	351252.i	−1.63175	−	1.94465i
$426$	−165949.	−	30985.8i	−0.914442	−	0.170743i
$427$	9525.38	−	54021.1i	0.0522428	−	0.296284i
$428$	54099.9	−	64473.8i	0.295331	−	0.351962i
$429$	16524.9	+	6203.54i	0.0897894	+	0.0337074i
$430$	−218928.	−	79683.4i	−1.18404	−	0.430954i
$431$		−	137027.i		−	0.737651i	−0.929499	−	0.368825i	$-0.879760\pi$
$431$		−	137027.i		−	0.737651i	0.929499	−	0.368825i	$-0.120240\pi$
$432$	−28897.8	−	36629.2i	−0.154845	−	0.196273i
$433$	−113894.			−0.607471			−0.303735	−	0.952756i	$-0.598234\pi$
$433$	−113894.			−0.607471			−0.303735	+	0.952756i	$0.598234\pi$
$434$	28963.2	−	79575.8i	0.153768	−	0.422475i
$435$	534041.	−	88636.0i	2.82225	−	0.468416i
$436$	65177.0	+	54690.0i	0.342863	+	0.287697i
$437$	137393.	+	24226.1i	0.719452	+	0.126859i
$438$	113891.	+	97535.2i	0.593666	+	0.508409i
$439$	220226.	−	184792.i	1.14272	−	0.958857i	0.143197	−	0.989694i	$-0.454262\pi$
$439$	220226.	−	184792.i	1.14272	−	0.958857i	0.999524	+	0.0308371i	$0.00981731\pi$
$440$	−15246.6	+	8802.65i	−0.0787533	+	0.0454682i
$441$	−134749.	−	52137.8i	−0.692862	−	0.268087i
$442$	−59193.6	+	102526.i	−0.302991	+	0.524796i
$443$	178409.	−	31458.4i	0.909098	−	0.160298i	0.300504	−	0.953781i	$-0.402845\pi$
$443$	178409.	−	31458.4i	0.909098	−	0.160298i	0.608594	+	0.793482i	$0.291734\pi$
$444$	−93610.3	−	55308.9i	−0.474851	−	0.280562i
$445$	279596.	−	101764.i	1.41192	−	0.513897i
$446$	34073.7	+	93616.7i	0.171297	+	0.470634i
$447$	−64765.9	+	109616.i	−0.324139	+	0.548605i
$448$	−2208.88	−	12527.2i	−0.0110056	−	0.0624161i
$449$	210245.	+	121385.i	1.04288	+	0.602104i	0.920646	−	0.390398i	$-0.127662\pi$
$449$	210245.	+	121385.i	1.04288	+	0.602104i	0.122229	+	0.992502i	$0.460996\pi$
$450$	−168116.	−	208741.i	−0.830201	−	1.03082i
$451$	5564.59	+	9638.16i	0.0273578	+	0.0473850i
$452$	−72558.1	−	86471.4i	−0.355148	−	0.423249i
$453$	34275.9	−	40023.8i	0.167029	−	0.195039i
$454$	−21500.1	+	121933.i	−0.104311	+	0.591576i
$455$	−72252.3	+	86106.9i	−0.349003	+	0.415925i
$456$	13675.2	+	82394.2i	0.0657663	+	0.396248i
$457$	253917.	+	92418.3i	1.21579	+	0.442513i	0.868710	−	0.495321i	$-0.164950\pi$
$457$	253917.	+	92418.3i	1.21579	+	0.442513i	0.347084	+	0.937834i	$0.387172\pi$
$458$		−	110154.i		−	0.525134i
$459$	285597.	+	8621.72i	1.35559	+	0.0409231i
$460$	−115292.			−0.544860
$461$	−103651.	+	284779.i	−0.487722	+	1.34000i	0.415016	+	0.909814i	$0.363776\pi$
$461$	−103651.	+	284779.i	−0.487722	+	1.34000i	−0.902738	+	0.430190i	$0.858446\pi$
$462$	4082.07	−	10873.8i	0.0191248	−	0.0509444i
$463$	27480.3	+	23058.7i	0.128192	+	0.107566i	0.704629	−	0.709575i	$-0.251113\pi$
$463$	27480.3	+	23058.7i	0.128192	+	0.107566i	−0.576438	+	0.817141i	$0.695558\pi$
$464$	89484.2	+	15778.5i	0.415634	+	0.0732874i
$465$	84338.2	−	451687.i	0.390048	−	2.08897i
$466$	32848.9	−	27563.5i	0.151269	−	0.126929i
$467$	8908.51	−	5143.33i	0.0408481	−	0.0235836i	−0.479437	−	0.877576i	$-0.659159\pi$
$467$	8908.51	−	5143.33i	0.0408481	−	0.0235836i	0.520285	+	0.853993i	$0.325826\pi$
$468$	−35799.0	+	59221.3i	−0.163448	+	0.270387i
$469$	−42993.7	+	74467.3i	−0.195461	+	0.338548i
$470$	−371833.	+	65564.3i	−1.68327	+	0.296805i
$471$	−239627.	+	135153.i	−1.08017	+	0.609233i
$472$	−103585.	+	37701.7i	−0.464955	+	0.169230i
$473$	−12212.3	−	33553.0i	−0.0545851	−	0.149971i
$474$	63388.5	+	637.694i	0.282133	+	0.00283828i
$475$	83316.5	+	472511.i	0.369270	+	2.09423i
$476$	67464.5	+	38950.7i	0.297757	+	0.171910i
$477$	263041.	+	51858.2i	1.15608	+	0.227919i
$478$	28185.6	+	48818.9i	0.123359	+	0.213664i
$479$	−47147.7	−	56188.5i	−0.205490	−	0.244893i	0.653450	−	0.756969i	$-0.273321\pi$
$479$	−47147.7	−	56188.5i	−0.205490	−	0.244893i	−0.858940	+	0.512076i	$0.828876\pi$
$480$	−22953.1	−	65093.3i	−0.0996229	−	0.282523i
$481$	−28003.9	+	158818.i	−0.121040	+	0.686450i
$482$	−118416.	+	141123.i	−0.509702	+	0.607440i
$483$	58755.6	−	48303.0i	0.251857	−	0.207052i
$484$	107529.	+	39137.3i	0.459023	+	0.167071i
$485$			85407.7i			0.363089i
$486$	166805.	+	8397.15i	0.706212	+	0.0355516i
$487$	380836.			1.60576			0.802879	−	0.596143i	$-0.203301\pi$
$487$	380836.			1.60576			0.802879	+	0.596143i	$0.203301\pi$
$488$	17087.1	−	46946.4i	0.0717510	−	0.197134i
$489$	141650.	+	172303.i	0.592380	+	0.720569i
$490$	−163738.	−	137393.i	−0.681958	−	0.572231i
$491$	−49659.2	−	8756.25i	−0.205985	−	0.0363208i	0.0697032	−	0.997568i	$-0.477795\pi$
$491$	−49659.2	−	8756.25i	−0.205985	−	0.0363208i	−0.275689	+	0.961247i	$0.588906\pi$
$492$	−41148.7	+	14509.8i	−0.169991	+	0.0599420i
$493$	−426278.	+	357690.i	−1.75388	+	1.47168i
$494$	107283.	−	61939.9i	0.439620	−	0.253815i
$495$	12190.1	−	61832.0i	0.0497504	−	0.252350i
$496$	38562.8	−	66792.8i	0.156749	−	0.271498i
$497$	162260.	−	28610.8i	0.656900	−	0.115829i
$498$	−2835.59	+	281866.i	−0.0114337	+	1.13654i
$499$	−337063.	+	122681.i	−1.35366	+	0.492693i	−0.914089	−	0.405514i	$-0.867093\pi$
$499$	−337063.	+	122681.i	−1.35366	+	0.492693i	−0.439573	+	0.898207i	$0.644870\pi$
$500$	−63162.3	−	173537.i	−0.252649	−	0.694148i
$501$	−210341.	−	372935.i	−0.838008	−	1.48579i
$502$	−42707.7	−	242207.i	−0.169472	−	0.961125i
$503$	−97150.7	−	56090.0i	−0.383981	−	0.221692i	0.295568	−	0.955322i	$-0.404491\pi$
$503$	−97150.7	−	56090.0i	−0.383981	−	0.221692i	−0.679549	+	0.733630i	$0.737824\pi$
$504$	38969.0	+	23556.5i	0.153411	+	0.0927365i
$505$	−368319.	−	637948.i	−1.44425	−	2.50151i
$506$	−11357.9	−	13535.8i	−0.0443604	−	0.0528667i
$507$	−151786.	−	28341.3i	−0.590496	−	0.110256i
$508$	15456.0	−	87655.2i	0.0598920	−	0.339665i
$509$	−229653.	+	273689.i	−0.886413	+	1.05639i	0.111624	+	0.993751i	$0.464395\pi$
$509$	−229653.	+	273689.i	−0.886413	+	1.05639i	−0.998036	+	0.0626352i	$0.980050\pi$
$510$	395731.	+	148559.i	1.52146	+	0.571162i
$511$	−137521.	−	50053.6i	−0.526656	−	0.191687i
$512$		−	11585.2i		−	0.0441942i
$513$	−254299.	−	157237.i	−0.966295	−	0.597475i
$514$	−103857.			−0.393106
$515$	−192125.	+	527860.i	−0.724386	+	1.99023i
$516$	138097.	−	22920.4i	0.518664	−	0.0860839i
$517$	−44328.2	−	37195.7i	−0.165844	−	0.139159i
$518$	104506.	+	18427.2i	0.389476	+	0.0686751i
$519$	14199.8	+	12160.5i	0.0527166	+	0.0451459i
$520$	−78422.7	+	65804.5i	−0.290025	+	0.243360i
$521$	278941.	−	161047.i	1.02763	−	0.593302i	0.111325	−	0.993784i	$-0.464491\pi$
$521$	278941.	−	161047.i	1.02763	−	0.593302i	0.916305	+	0.400482i	$0.131157\pi$
$522$	−253328.	+	204025.i	−0.929698	+	0.748759i
$523$	108461.	−	187860.i	0.396525	−	0.686801i	−0.596770	−	0.802413i	$-0.703549\pi$
$523$	108461.	−	187860.i	0.396525	−	0.686801i	0.993295	+	0.115611i	$0.0368827\pi$
$524$	14745.2	−	2599.98i	0.0537017	−	0.00946906i
$525$	225213.	+	133065.i	0.817098	+	0.482776i
$526$	−186034.	+	67710.8i	−0.672389	+	0.244729i
$527$	161545.	+	443842.i	0.581666	+	1.59811i
$528$	5381.01	−	9107.36i	0.0193017	−	0.0326682i
$529$	28500.4	+	161634.i	0.101845	+	0.577591i
$530$	343488.	+	198313.i	1.22281	+	0.705991i
$531$	142394.	−	368014.i	0.505015	−	1.30520i
$532$	−40757.8	−	70594.7i	−0.144008	−	0.249430i
$533$	41598.3	+	49574.9i	0.146427	+	0.174505i
$534$	−116288.	+	135789.i	−0.407806	+	0.476192i
$535$	−77397.5	+	438943.i	−0.270408	+	1.53356i
$536$	−50339.2	+	59991.9i	−0.175217	+	0.208816i
$537$	−28019.8	−	168822.i	−0.0971665	−	0.585437i
$538$	−72824.6	−	26506.0i	−0.251602	−	0.0915755i
$539$		−	32758.6i		−	0.112758i
$540$	229522.	+	91473.2i	0.787113	+	0.313694i
$541$	−316743.			−1.08221			−0.541106	−	0.840955i	$-0.681994\pi$
$541$	−316743.			−1.08221			−0.541106	+	0.840955i	$0.681994\pi$
$542$	77659.9	−	213369.i	0.264362	−	0.726327i
$543$	−116255.	+	309679.i	−0.394287	+	1.05030i
$544$	54350.4	+	45605.4i	0.183656	+	0.154106i
$545$	−443730.	−	78241.6i	−1.49392	−	0.263418i
$546$	12396.5	−	66391.5i	0.0415828	−	0.222704i
$547$	39894.6	−	33475.5i	0.133333	−	0.111880i	−0.573682	−	0.819078i	$-0.694486\pi$
$547$	39894.6	−	33475.5i	0.133333	−	0.111880i	0.707016	+	0.707198i	$0.250041\pi$
$548$	125104.	−	72228.7i	0.416590	−	0.240519i
$549$	86286.3	+	156648.i	0.286284	+	0.519733i
$550$	30384.1	−	52626.8i	0.100443	−	0.173973i
$551$	573438.	−	101113.i	1.88879	−	0.333045i
$552$	60338.5	−	34031.8i	0.198023	−	0.111688i
$553$	−58138.3	+	21160.6i	−0.190113	+	0.0691955i
$554$	18870.9	+	51847.5i	0.0614857	+	0.168930i
$555$	575772.	+	5792.32i	1.86924	+	0.0188047i
$556$	−22087.9	−	125267.i	−0.0714505	−	0.405216i
$557$	142300.	+	82157.1i	0.458665	+	0.264810i	0.711483	−	0.702704i	$-0.248024\pi$
$557$	142300.	+	82157.1i	0.458665	+	0.264810i	−0.252818	+	0.967514i	$0.581357\pi$
$558$	89189.4	+	261286.i	0.286448	+	0.839166i
$559$	−103815.	−	179813.i	−0.332228	−	0.575435i
$560$	43300.8	+	51603.9i	0.138077	+	0.164553i
$561$	21543.4	+	61095.4i	0.0684524	+	0.194126i
$562$	3231.47	−	18326.6i	0.0102312	−	0.0580241i
$563$	−297776.	+	354876.i	−0.939449	+	1.11959i	0.0532025	+	0.998584i	$0.483057\pi$
$563$	−297776.	+	354876.i	−0.939449	+	1.11959i	−0.992652	+	0.121008i	$0.961387\pi$
$564$	175247.	−	144070.i	0.550924	−	0.452914i
$565$	561736.	+	204455.i	1.75969	+	0.640473i
$566$			68217.4i			0.212943i
$567$	−155293.	+	49544.0i	−0.483044	+	0.154108i
$568$	150060.			0.465123
$569$	−12912.6	+	35477.2i	−0.0398833	+	0.109578i	−0.958036	−	0.286649i	$-0.907459\pi$
$569$	−12912.6	+	35477.2i	−0.0398833	+	0.109578i	0.918152	+	0.396227i	$0.129681\pi$
$570$	−280887.	−	341671.i	−0.864535	−	1.05162i
$571$	−355124.	−	297984.i	−1.08920	−	0.913948i	−0.0925485	−	0.995708i	$-0.529501\pi$
$571$	−355124.	−	297984.i	−1.08920	−	0.913948i	−0.996652	+	0.0817604i	$0.973946\pi$
$572$	−15451.4	−	2724.50i	−0.0472254	−	0.00832712i
$573$	−52283.0	+	18436.0i	−0.159240	+	0.0561509i
$574$	32621.4	−	27372.6i	0.0990099	−	0.0830792i
$575$	344639.	−	198977.i	1.04239	−	0.601822i
$576$	31226.7	+	27291.4i	0.0941197	+	0.0822586i
$577$	92607.3	−	160401.i	0.278159	−	0.481786i	−0.692768	−	0.721161i	$-0.743609\pi$
$577$	92607.3	−	160401.i	0.278159	−	0.481786i	0.970927	+	0.239374i	$0.0769423\pi$
$578$	−195258.	+	34429.2i	−0.584458	+	0.103056i
$579$	2886.02	−	286878.i	0.00860878	−	0.855736i
$580$	−452177.	+	164579.i	−1.34416	+	0.489236i
$581$	−94093.4	−	258520.i	−0.278745	−	0.765845i
$582$	−25210.5	−	44698.3i	−0.0744278	−	0.131961i
$583$	10555.5	+	59863.4i	0.0310558	+	0.176126i
$584$	−115430.	−	66643.4i	−0.338448	−	0.195403i
$585$	7372.69	−	366395.i	0.0215434	−	1.07063i
$586$	89765.6	+	155479.i	0.261406	+	0.452768i
$587$	−133194.	−	158735.i	−0.386553	−	0.460676i	0.537318	−	0.843380i	$-0.319438\pi$
$587$	−133194.	−	158735.i	−0.386553	−	0.460676i	−0.923871	+	0.382704i	$0.874993\pi$
$588$	126248.	+	23572.8i	0.365149	+	0.0681800i
$589$	85824.1	−	486733.i	0.247388	−	1.40301i
$590$	375236.	−	447189.i	1.07795	−	1.28466i
$591$	−187779.	−	70493.0i	−0.537614	−	0.201823i
$592$	90819.3	+	33055.5i	0.259140	+	0.0943193i
$593$		−	405120.i		−	1.15206i	−0.817429	−	0.576029i	$-0.804601\pi$
$593$		−	405120.i		−	1.15206i	0.817429	−	0.576029i	$-0.195399\pi$
$594$	11871.7	+	35958.2i	0.0336466	+	0.101912i
$595$	−412546.			−1.16530
$596$	38707.5	−	106348.i	0.108969	−	0.299390i
$597$	−135496.	+	22488.7i	−0.380171	+	0.0630979i
$598$	−78709.5	−	66045.1i	−0.220103	−	0.184688i
$599$	−221080.	−	38982.4i	−0.616165	−	0.108646i	−0.143150	−	0.989701i	$-0.545723\pi$
$599$	−221080.	−	38982.4i	−0.616165	−	0.108646i	−0.473015	+	0.881055i	$0.656834\pi$
$600$	180954.	+	154967.i	0.502650	+	0.430464i
$601$	396010.	−	332292.i	1.09637	−	0.919964i	0.0991945	−	0.995068i	$-0.468373\pi$
$601$	396010.	−	332292.i	1.09637	−	0.919964i	0.997176	+	0.0751043i	$0.0239290\pi$
$602$	−118321.	+	68312.4i	−0.326488	+	0.188498i
$603$	−43116.8	−	277007.i	−0.118580	−	0.761827i
$604$	−23419.9	+	40564.4i	−0.0641965	+	0.111192i
$605$	−596785.	+	105229.i	−1.63045	+	0.287492i
$606$	381069.	+	225151.i	1.03767	+	0.613098i
$607$	548701.	−	199711.i	1.48922	−	0.542031i	0.535975	−	0.844234i	$-0.319944\pi$
$607$	548701.	−	199711.i	1.48922	−	0.542031i	0.953244	+	0.302203i	$0.0977220\pi$
$608$	−25392.0	−	69763.9i	−0.0686894	−	0.188723i
$609$	161488.	−	273318.i	0.435416	−	0.736941i
$610$	45942.4	+	260552.i	0.123468	+	0.700221i
$611$	−291407.	−	168244.i	−0.780582	−	0.450669i
$612$	−250958.	+	39062.2i	−0.670036	+	0.104293i
$613$	359959.	+	623468.i	0.957927	+	1.65918i	0.727524	+	0.686082i	$0.240671\pi$
$613$	359959.	+	623468.i	0.957927	+	1.65918i	0.230403	+	0.973095i	$0.425996\pi$
$614$	97005.4	+	115607.i	0.257312	+	0.306652i
$615$	150298.	−	175502.i	0.397378	−	0.464015i
$616$	−1792.78	+	10167.4i	−0.00472461	+	0.0267946i
$617$	−258721.	+	308331.i	−0.679611	+	0.809929i	−0.990058	−	0.140662i	$-0.955077\pi$
$617$	−258721.	+	308331.i	−0.679611	+	0.809929i	0.310446	+	0.950591i	$0.399522\pi$
$618$	−55263.4	−	332968.i	−0.144697	−	0.871816i
$619$	−446744.	−	162601.i	−1.16594	−	0.424368i	−0.314726	−	0.949183i	$-0.601913\pi$
$619$	−446744.	−	162601.i	−1.16594	−	0.424368i	−0.851217	+	0.524814i	$0.824135\pi$
$620$			408438.i			1.06253i
$621$	−50411.1	+	242804.i	−0.130720	+	0.629612i
$622$	83216.7			0.215095
$623$	59677.4	−	163962.i	0.153757	−	0.422443i
$624$	21618.7	−	57587.6i	0.0555213	−	0.147897i
$625$	189072.	+	158650.i	0.484023	+	0.406144i
$626$	409693.	+	72239.9i	1.04547	+	0.184344i
$627$	12442.3	−	66636.5i	0.0316493	−	0.169503i
$628$	187332.	−	157190.i	0.475000	−	0.398572i
$629$	−512586.	+	295942.i	−1.29558	+	0.748006i
$630$	−241096.	−	4851.39i	−0.607449	−	0.0122232i
$631$	−126509.	+	219120.i	−0.317733	+	0.550329i	−0.980015	−	0.198925i	$-0.936255\pi$
$631$	−126509.	+	219120.i	−0.317733	+	0.550329i	0.662282	+	0.749255i	$0.269588\pi$
$632$	−55492.2	+	9784.76i	−0.138930	+	0.0244972i
$633$	−141380.	+	79740.1i	−0.352841	+	0.199007i
$634$	−305909.	+	111342.i	−0.761051	+	0.277000i
$635$	161215.	+	442935.i	0.399814	+	1.09848i
$636$	−238303.	−	2397.35i	−0.589135	−	0.00592675i
$637$	−33078.0	−	187595.i	−0.0815193	−	0.462319i
$638$	−63867.8	−	36874.1i	−0.156906	−	0.0905899i
$639$	−353497.	+	404469.i	−0.865733	+	0.990565i
$640$	30676.3	+	53132.8i	0.0748932	+	0.129719i
$641$	−262760.	−	313145.i	−0.639504	−	0.762132i	0.344787	−	0.938681i	$-0.387951\pi$
$641$	−262760.	−	313145.i	−0.639504	−	0.762132i	−0.984292	+	0.176549i	$0.943507\pi$
$642$	−89060.1	−	252568.i	−0.216079	−	0.612784i
$643$	−24638.0	+	139729.i	−0.0595915	+	0.337960i	−0.999998	−	0.00209281i	$-0.999334\pi$
$643$	−24638.0	+	139729.i	−0.0595915	+	0.337960i	0.940406	+	0.340053i	$0.110445\pi$
$644$	−43459.2	+	51792.6i	−0.104788	+	0.124881i
$645$	−572659.	+	470783.i	−1.37650	+	1.13162i
$646$	427243.	+	155504.i	1.02379	+	0.372628i
$647$		−	340407.i		−	0.813186i	−0.913609	−	0.406593i	$-0.866717\pi$
$647$		−	340407.i		−	0.813186i	0.913609	−	0.406593i	$-0.133283\pi$
$648$	−147122.	+	19877.2i	−0.350370	+	0.0473375i
$649$	89467.5			0.212411
$650$	120857.	−	332053.i	0.286053	−	0.785923i
$651$	−171120.	−	208149.i	−0.403774	−	0.491149i
$652$	−151884.	−	127446.i	−0.357287	−	0.299799i
$653$	413322.	+	72879.9i	0.969310	+	0.170915i	0.635819	−	0.771838i	$-0.280662\pi$
$653$	413322.	+	72879.9i	0.969310	+	0.170915i	0.333491	+	0.942753i	$0.391773\pi$
$654$	255322.	−	90031.5i	0.596944	−	0.210494i
$655$	−60740.8	+	50967.6i	−0.141579	+	0.118799i
$656$	33587.9	−	19392.0i	0.0780504	−	0.0450624i
$657$	451548.	−	154135.i	1.04610	−	0.357085i
$658$	−110708.	+	191753.i	−0.255699	+	0.442883i
$659$	540473.	−	95299.9i	1.24452	−	0.219443i	0.487670	−	0.873028i	$-0.337847\pi$
$659$	540473.	−	95299.9i	1.24452	−	0.219443i	0.756853	+	0.653585i	$0.226736\pi$
$660$	−563.535	+	56016.9i	−0.00129370	+	0.128597i
$661$	577773.	−	210292.i	1.32237	−	0.481305i	0.418156	−	0.908375i	$-0.362676\pi$
$661$	577773.	−	210292.i	1.32237	−	0.481305i	0.904219	+	0.427070i	$0.140454\pi$
$662$	−57922.3	−	159140.i	−0.132169	−	0.363132i
$663$	185061.	+	328115.i	0.421007	+	0.746447i
$664$	−43509.3	−	246753.i	−0.0986837	−	0.559663i
$665$	373852.	+	215843.i	0.845388	+	0.488085i
$666$	−303041.	+	166924.i	−0.683208	+	0.376331i
$667$	−241478.	−	418253.i	−0.542783	−	0.940128i
$668$	244638.	+	291549.i	0.548241	+	0.653369i
$669$	311619.	+	58184.9i	0.696259	+	0.130004i
$670$	72017.3	−	408430.i	0.160431	−	0.909847i
$671$	−26063.9	+	31061.8i	−0.0578888	+	0.0689892i
$672$	−37893.9	−	14225.6i	−0.0839133	−	0.0315015i
$673$	831958.	+	302808.i	1.83684	+	0.668555i	0.990782	+	0.135465i	$0.0432528\pi$
$673$	831958.	+	302808.i	1.83684	+	0.668555i	0.846058	+	0.533090i	$0.178969\pi$
$674$		−	170294.i		−	0.374868i
$675$	−843971.	+	122684.i	−1.85234	+	0.269264i
$676$	137253.			0.300351
$677$	88016.3	−	241823.i	0.192037	−	0.527618i	−0.805883	−	0.592075i	$-0.798309\pi$
$677$	88016.3	−	241823.i	0.192037	−	0.527618i	0.997921	+	0.0644563i	$0.0205313\pi$
$678$	−354336.	+	58810.0i	−0.770825	+	0.127936i
$679$	38367.6	+	32194.2i	0.0832195	+	0.0698294i
$680$	−370022.	−	65244.9i	−0.800221	−	0.141101i
$681$	299239.	+	256265.i	0.645244	+	0.552580i
$682$	−47952.3	+	40236.7i	−0.103096	+	0.0865075i
$683$	314393.	−	181515.i	0.673956	−	0.389109i	−0.123618	−	0.992330i	$-0.539450\pi$
$683$	314393.	−	181515.i	0.673956	−	0.389109i	0.797574	+	0.603221i	$0.206116\pi$
$684$	247857.	+	95902.3i	0.529771	+	0.204982i
$685$	−382505.	+	662518.i	−0.815185	+	1.41194i
$686$	−289599.	+	51064.1i	−0.615387	+	0.108509i
$687$	−301771.	−	178299.i	−0.639387	−	0.377777i
$688$	−116928.	+	42558.4i	−0.247026	+	0.0899101i
$689$	120894.	+	332154.i	0.254664	+	0.699683i
$690$	−186616.	+	315847.i	−0.391967	+	0.663405i
$691$	−45340.3	−	257138.i	−0.0949573	−	0.538530i	−0.994760	−	0.102234i	$-0.967401\pi$
$691$	−45340.3	−	257138.i	−0.0949573	−	0.538530i	0.899803	−	0.436296i	$-0.143710\pi$
$692$	−14391.6	−	8309.00i	−0.0300537	−	0.0173515i
$693$	−23181.7	−	28783.6i	−0.0482702	−	0.0599347i
$694$	−35338.8	−	61208.5i	−0.0733723	−	0.127085i
$695$	432992.	+	516020.i	0.896417	+	1.06831i
$696$	188068.	−	219605.i	0.388236	−	0.453341i
$697$	−41244.5	+	233909.i	−0.0848987	+	0.481484i
$698$	245932.	−	293091.i	0.504783	−	0.601577i
$699$	−22340.8	−	134606.i	−0.0457241	−	0.275492i
$700$	−218498.	−	79526.7i	−0.445914	−	0.162299i
$701$			374534.i			0.762176i	0.924539	+	0.381088i	$0.124450\pi$
$701$			374534.i			0.762176i	−0.924539	+	0.381088i	$0.875550\pi$
$702$	104293.	+	193930.i	0.211633	+	0.393524i
$703$	619345.			1.25320
$704$	−3215.98	+	8835.82i	−0.00648885	+	0.0178280i
$705$	−422246.	+	1.12477e6i	−0.849546	+	2.26301i
$706$	448887.	+	376661.i	0.900590	+	0.755685i
$707$	−425422.	−	75013.3i	−0.851100	−	0.150072i
$708$	−64380.2	+	344798.i	−0.128436	+	0.687858i
$709$	−427788.	+	358957.i	−0.851012	+	0.714084i	−0.960012	−	0.279958i	$-0.909680\pi$
$709$	−427788.	+	358957.i	−0.851012	+	0.714084i	0.109000	+	0.994042i	$0.465235\pi$
$710$	−688212.	+	397339.i	−1.36523	+	0.788216i
$711$	104350.	−	172623.i	0.206420	−	0.341475i
$712$	79457.0	−	137624.i	0.156737	−	0.271477i
$713$	−403704.	+	71184.0i	−0.794117	+	0.140024i
$714$	215907.	−	121775.i	0.423516	−	0.238869i
$715$	78078.2	−	28418.1i	0.152728	−	0.0555883i
$716$	52027.0	+	142943.i	0.101485	+	0.278828i
$717$	179363.	+	1804.41i	0.348895	+	0.00350991i
$718$	−5607.24	−	31800.2i	−0.0108768	−	0.0616852i
$719$	−156648.	−	90440.6i	−0.303017	−	0.174947i	0.340781	−	0.940143i	$-0.389309\pi$
$719$	−156648.	−	90440.6i	−0.303017	−	0.174947i	−0.643797	+	0.765196i	$0.722642\pi$
$720$	−215478.	−	42481.1i	−0.415659	−	0.0819467i
$721$	164709.	+	285284.i	0.316844	+	0.548790i
$722$	−68877.1	−	82084.6i	−0.132130	−	0.157466i
$723$	194938.	+	552830.i	0.372925	+	1.05759i
$724$	51057.4	−	289561.i	0.0974051	−	0.552412i
$725$	1.06764e6	−	1.27236e6i	2.03117	−	2.42066i
$726$	281267.	−	231230.i	0.533637	−	0.438703i
$727$	−570109.	−	207503.i	−1.07867	−	0.392604i	−0.259258	−	0.965808i	$-0.583478\pi$
$727$	−570109.	−	207503.i	−1.07867	−	0.392604i	−0.819413	+	0.573204i	$0.805700\pi$
$728$			60034.6i			0.113276i
$729$	292999.	−	443375.i	0.551330	−	0.834287i
$730$	705854.			1.32455
$731$	260633.	−	716083.i	0.487747	−	1.34007i
$732$	−100953.	−	122799.i	−0.188408	−	0.229179i
$733$	46094.5	+	38677.9i	0.0857908	+	0.0719871i	0.684674	−	0.728849i	$-0.259944\pi$
$733$	46094.5	+	38677.9i	0.0857908	+	0.0719871i	−0.598884	+	0.800836i	$0.704389\pi$
$734$	−522173.	−	92073.1i	−0.969219	−	0.170899i
$735$	−641423.	+	226178.i	−1.18733	+	0.418674i
$736$	−47170.6	+	39580.9i	−0.0870796	+	0.0730684i
$737$	55046.0	−	31780.8i	0.101342	−	0.0585100i
$738$	−26854.4	+	136214.i	−0.0493064	+	0.250098i
$739$	−128656.	+	222839.i	−0.235581	+	0.408039i	−0.959441	−	0.281908i	$-0.909033\pi$
$739$	−128656.	+	222839.i	−0.235581	+	0.408039i	0.723860	+	0.689947i	$0.242366\pi$
$740$	−504047.	+	88877.1i	−0.920466	+	0.162303i
$741$	3965.32	−	394163.i	0.00722174	−	0.717860i
$742$	218565.	−	79551.1i	0.396984	−	0.144490i
$743$	−246217.	−	676475.i	−0.446005	−	1.22539i	−0.935483	−	0.353373i	$-0.885035\pi$
$743$	−246217.	−	676475.i	−0.446005	−	1.22539i	0.489478	−	0.872016i	$-0.337187\pi$
$744$	−120562.	−	213757.i	−0.217803	−	0.386166i
$745$	104074.	+	590232.i	0.187512	+	1.06343i
$746$	193977.	+	111993.i	0.348556	+	0.201239i
$747$	767590.	+	464004.i	1.37559	+	0.831536i
$748$	−28792.2	−	49869.6i	−0.0514602	−	0.0891318i
$749$	168011.	+	200228.i	0.299484	+	0.356911i
$750$	−577647.	−	107857.i	−1.02693	−	0.191746i
$751$	1891.59	−	10727.7i	0.00335387	−	0.0190207i	−0.983085	−	0.183150i	$-0.941370\pi$
$751$	1891.59	−	10727.7i	0.00335387	−	0.0190207i	0.986439	+	0.164130i	$0.0524816\pi$
$752$	−129623.	+	154479.i	−0.229217	+	0.273170i
$753$	−732662.	−	275045.i	−1.29215	−	0.485081i
$754$	−402978.	−	146672.i	−0.708825	−	0.257991i
$755$		−	248052.i		−	0.435160i
$756$	127610.	−	68627.3i	0.223276	−	0.120075i
$757$	299286.			0.522270			0.261135	−	0.965302i	$-0.415903\pi$
$757$	299286.			0.522270			0.261135	+	0.965302i	$0.415903\pi$
$758$	118809.	−	326425.i	0.206781	−	0.568126i
$759$	−55465.9	+	9205.81i	−0.0962813	+	0.0159801i
$760$	301180.	+	252720.i	0.521434	+	0.437535i
$761$	−544360.	−	95985.3i	−0.939976	−	0.165743i	−0.317391	−	0.948295i	$-0.602807\pi$
$761$	−544360.	−	95985.3i	−0.939976	−	0.165743i	−0.622586	+	0.782552i	$0.713918\pi$
$762$	−215117.	−	184224.i	−0.370480	−	0.317275i
$763$	−202411.	+	169843.i	−0.347685	+	0.291742i
$764$	42676.4	−	24639.2i	0.0731140	−	0.0422124i
$765$	1.04752e6	−	843654.i	1.78995	−	1.44159i
$766$	−137000.	+	237291.i	−0.233487	+	0.404412i
$767$	512344.	−	90340.0i	0.870905	−	0.153564i
$768$	−31738.1	−	18752.2i	−0.0538095	−	0.0317929i
$769$	−380525.	+	138500.i	−0.643474	+	0.234205i	−0.643085	−	0.765795i	$-0.722346\pi$
$769$	−380525.	+	138500.i	−0.643474	+	0.234205i	−0.000388607		1.00000i	$0.500124\pi$
$770$	−18699.8	−	51377.2i	−0.0315395	−	0.0866541i
$771$	−168106.	+	284520.i	−0.282797	+	0.478634i
$772$	44282.9	+	251141.i	0.0743022	+	0.421389i
$773$	−867332.	−	500754.i	−1.45153	−	0.838042i	−0.452963	−	0.891529i	$-0.649633\pi$
$773$	−867332.	−	500754.i	−1.45153	−	0.838042i	−0.998569	+	0.0534876i	$0.982966\pi$
$774$	160738.	−	415422.i	0.268309	−	0.693438i
$775$	−704903.	−	1.22093e6i	−1.17362	−	2.03276i
$776$	29321.2	+	34943.7i	0.0486921	+	0.0580290i
$777$	219638.	−	256470.i	0.363802	−	0.424809i
$778$	−103436.	+	586617.i	−0.170889	+	0.969160i
$779$	159757.	−	190391.i	0.263260	−	0.313741i
$780$	53336.0	+	321355.i	0.0876661	+	0.528196i
$781$	−114447.	−	41655.5i	−0.187631	−	0.0682920i
$782$		−	377105.i		−	0.616664i
$783$	148888.	+	1.02424e6i	0.242850	+	1.67062i
$784$	−114160.			−0.185730
$785$	−442933.	+	1.21695e6i	−0.718784	+	1.97484i
$786$	16744.3	−	44603.4i	0.0271033	−	0.0721975i
$787$	813406.	+	682528.i	1.31328	+	1.10197i	0.987683	+	0.156465i	$0.0500099\pi$
$787$	813406.	+	682528.i	1.31328	+	1.10197i	0.325598	+	0.945508i	$0.394435\pi$
$788$	175580.	+	30959.4i	0.282762	+	0.0498586i
$789$	−115624.	+	619244.i	−0.185735	+	0.994736i
$790$	228592.	−	191812.i	0.366275	−	0.307341i
$791$	303592.	−	175279.i	0.485219	−	0.280141i
$792$	−16240.0	−	29482.9i	−0.0258903	−	0.0470024i
$793$	−117893.	+	204196.i	−0.187474	+	0.324714i
$794$	−537173.	+	94718.1i	−0.852066	+	0.150242i
$795$	1.09926e6	−	620001.i	1.73927	−	0.980976i
$796$	114726.	−	41756.8i	0.181065	−	0.0659024i
$797$	−137866.	−	378783.i	−0.217040	−	0.596312i	0.782617	−	0.622503i	$-0.213884\pi$
$797$	−137866.	−	378783.i	−0.217040	−	0.596312i	−0.999657	+	0.0261912i	$0.991662\pi$
$798$	−259368.	−	2609.27i	−0.407297	−	0.00409744i
$799$	−214451.	−	1.21621e6i	−0.335920	−	1.90509i
$800$	−183399.	−	105885.i	−0.286560	−	0.165446i
$801$	183771.	+	538368.i	0.286425	+	0.839101i
$802$	−34163.0	−	59172.0i	−0.0531138	−	0.0919958i
$803$	69536.2	+	82870.0i	0.107840	+	0.128519i
$804$	82869.2	+	235011.i	0.128198	+	0.363560i
$805$	62174.4	−	352609.i	0.0959445	−	0.544128i
$806$	−233974.	+	278839.i	−0.360161	+	0.429223i
$807$	−190490.	+	156602.i	−0.292499	+	0.240464i
$808$	−369707.	−	134562.i	−0.566285	−	0.206111i
$809$			350362.i			0.535328i	0.963512	+	0.267664i	$0.0862518\pi$
$809$			350362.i			0.535328i	−0.963512	+	0.267664i	$0.913748\pi$
$810$	622105.	−	480722.i	0.948187	−	0.732696i
$811$	928027.			1.41097			0.705486	−	0.708723i	$-0.250729\pi$
$811$	928027.			1.41097			0.705486	+	0.708723i	$0.250729\pi$
$812$	−96513.5	+	265169.i	−0.146378	+	0.402170i
$813$	−458828.	−	558117.i	−0.694175	−	0.844392i
$814$	−60090.0	−	50421.5i	−0.0906888	−	0.0760969i
$815$	1.03404e6	+	182329.i	1.55676	+	0.274499i
$816$	212911.	−	75076.4i	0.319755	−	0.112752i
$817$	−610841.	+	512556.i	−0.915132	+	0.767887i
$818$	413987.	−	239016.i	0.618701	−	0.357207i
$819$	−161816.	−	141424.i	−0.241243	−	0.210841i
$820$	−102695.	+	177873.i	−0.152729	+	0.264535i
$821$	328299.	−	57887.9i	0.487061	−	0.0858819i	0.0752753	−	0.997163i	$-0.476016\pi$
$821$	328299.	−	57887.9i	0.487061	−	0.0858819i	0.411785	+	0.911281i	$0.364905\pi$
$822$	4623.99	−	459637.i	0.00684343	−	0.680255i
$823$	204886.	−	74572.3i	0.302491	−	0.110098i	−0.186316	−	0.982490i	$-0.559655\pi$
$823$	204886.	−	74572.3i	0.302491	−	0.110098i	0.488806	+	0.872392i	$0.337432\pi$
$824$	102613.	+	281927.i	0.151129	+	0.415223i
$825$	−94992.2	−	168422.i	−0.139566	−	0.247451i
$826$	−59445.7	−	337133.i	−0.0871286	−	0.494131i
$827$	−398393.	−	230012.i	−0.582506	−	0.336310i	0.179622	−	0.983736i	$-0.442512\pi$
$827$	−398393.	−	230012.i	−0.582506	−	0.336310i	−0.762129	+	0.647425i	$0.775846\pi$
$828$	4434.61	−	220384.i	0.00646838	−	0.321454i
$829$	−647870.	−	1.12214e6i	−0.942711	−	1.63282i	−0.760271	−	0.649606i	$-0.774934\pi$
$829$	−647870.	−	1.12214e6i	−0.942711	−	1.63282i	−0.182440	−	0.983217i	$-0.558400\pi$
$830$	852916.	+	1.01647e6i	1.23808	+	1.47549i
$831$	172583.	+	32224.4i	0.249917	+	0.0466640i
$832$	−9494.58	+	53846.4i	−0.0137160	+	0.0777876i
$833$	449392.	−	535564.i	0.647642	−	0.771830i
$834$	−378925.	−	142250.i	−0.544780	−	0.204513i
$835$	−1.89396e6	−	689345.i	−2.71642	−	0.988697i
$836$			60256.1i			0.0862162i
$837$	860166.	+	178588.i	1.22781	+	0.254919i
$838$	−137135.			−0.195280
$839$	−129441.	+	355636.i	−0.183886	+	0.505222i	−0.997045	−	0.0768192i	$-0.975524\pi$
$839$	−129441.	+	355636.i	−0.183886	+	0.505222i	0.813159	+	0.582041i	$0.197746\pi$
$840$	211459.	−	35096.3i	0.299686	−	0.0497396i
$841$	−1.00232e6	−	841049.i	−1.41715	−	1.18913i
$842$	512478.	+	90363.8i	0.722855	+	0.127459i
$843$	−44975.7	−	38516.6i	−0.0632881	−	0.0541993i
$844$	110526.	−	92742.3i	0.155160	−	0.130195i
$845$	−629478.	+	363429.i	−0.881590	+	0.508986i
$846$	−111025.	−	713290.i	−0.155125	−	0.996611i
$847$	−177685.	+	307759.i	−0.247676	+	0.428987i
$848$	208617.	−	36784.8i	0.290107	−	0.0511537i
$849$	186884.	+	110419.i	0.259272	+	0.153189i
$850$	1.21870e6	−	443569.i	1.68678	−	0.613936i
$851$	−175694.	−	482715.i	−0.242604	−	0.666549i
$852$	242891.	−	411093.i	0.334605	−	0.566319i
$853$	81624.8	+	462917.i	0.112182	+	0.636217i	0.988107	+	0.153769i	$0.0491412\pi$
$853$	81624.8	+	462917.i	0.112182	+	0.636217i	−0.875925	+	0.482448i	$0.839748\pi$
$854$	134365.	+	77576.0i	0.184235	+	0.106368i
$855$	−1.39067e6	+	216461.i	−1.90236	+	0.296107i
$856$	119027.	+	206160.i	0.162441	+	0.281357i
$857$	−275329.	−	328124.i	−0.374878	−	0.446762i	0.545313	−	0.838233i	$-0.316411\pi$
$857$	−275329.	−	328124.i	−0.374878	−	0.446762i	−0.920191	+	0.391471i	$0.871966\pi$
$858$	−32474.0	+	37919.7i	−0.0441124	+	0.0515098i
$859$	35852.1	−	203327.i	0.0485879	−	0.275555i	−0.950828	−	0.309718i	$-0.899765\pi$
$859$	35852.1	−	203327.i	0.0485879	−	0.275555i	0.999416	+	0.0341627i	$0.0108764\pi$
$860$	423573.	−	504795.i	0.572706	−	0.682525i
$861$	−22186.1	−	133673.i	−0.0299278	−	0.180318i
$862$	364197.	+	132557.i	0.490142	+	0.178397i
$863$			1.22796e6i			1.64878i	0.566023	+	0.824390i	$0.308481\pi$
$863$			1.22796e6i			1.64878i	−0.566023	+	0.824390i	$0.691519\pi$
$864$	125310.	−	41371.7i	0.167865	−	0.0554212i
$865$	88004.8			0.117618
$866$	110179.	−	302714.i	0.146914	−	0.403642i
$867$	−221730.	+	590644.i	−0.294976	+	0.785755i
$868$	183482.	+	153960.i	0.243531	+	0.204347i
$869$	45038.9	+	7941.57i	0.0596414	+	0.0105164i
$870$	−281038.	+	1.50515e6i	−0.371302	+	1.98857i
$871$	283135.	−	237578.i	0.373213	−	0.313163i
$872$	−208409.	+	120325.i	−0.274083	+	0.158242i
$873$	−163259.	−	3285.13i	−0.214214	−	0.00431046i
$874$	−197300.	+	341734.i	−0.258289	+	0.447369i
$875$	564806.	−	99590.5i	0.737705	−	0.130077i
$876$	−369410.	+	208353.i	−0.481394	+	0.271513i
$877$	−13247.3	+	4821.62i	−0.0172238	+	0.00626894i	−0.350618	−	0.936519i	$-0.614028\pi$
$877$	−13247.3	+	4821.62i	−0.0172238	+	0.00626894i	0.333394	+	0.942788i	$0.391806\pi$
$878$	278107.	+	764093.i	0.360764	+	0.991191i
$879$	571236.	+	5746.69i	0.739329	+	0.00743772i
$880$	−8646.87	−	49038.8i	−0.0111659	−	0.0633249i
$881$	665335.	+	384131.i	0.857213	+	0.494912i	0.863078	−	0.505071i	$-0.168534\pi$
$881$	665335.	+	384131.i	0.857213	+	0.494912i	−0.00586512	+	0.999983i	$0.501867\pi$
$882$	268927.	−	307705.i	0.345699	−	0.395546i
$883$	678306.	+	1.17486e6i	0.869971	+	1.50683i	0.862026	+	0.506865i	$0.169196\pi$
$883$	678306.	+	1.17486e6i	0.869971	+	1.50683i	0.00794492	+	0.999968i	$0.497471\pi$
$884$	−215237.	−	256509.i	−0.275431	−	0.328246i
$885$	−617719.	−	1.75180e6i	−0.788687	−	2.23665i
$886$	−88977.8	+	504618.i	−0.113348	+	0.642829i
$887$	34310.2	−	40889.3i	0.0436090	−	0.0519711i	−0.743799	−	0.668403i	$-0.766978\pi$
$887$	34310.2	−	40889.3i	0.0436090	−	0.0519711i	0.787408	+	0.616432i	$0.211423\pi$
$888$	237560.	−	195298.i	0.301264	−	0.247669i
$889$	259749.	+	94540.7i	0.328662	+	0.119623i
$890$			841569.i			1.06245i
$891$	117724.	+	25680.0i	0.148290	+	0.0323474i
$892$	−281781.			−0.354146
$893$	−441984.	+	1.21434e6i	−0.554247	+	1.52278i
$894$	−228691.	−	278179.i	−0.286137	−	0.348056i
$895$	−617104.	−	517812.i	−0.770394	−	0.646437i
$896$	35432.1	+	6247.64i	0.0441348	+	0.00778216i
$897$	−308334.	+	108725.i	−0.383210	+	0.135127i
$898$	−526009.	+	441374.i	−0.652290	+	0.547336i
$899$	−1.48172e6	+	855469.i	−1.83335	+	1.05849i
$900$	717435.	−	244895.i	0.885722	−	0.302340i
$901$	−648653.	+	1.12350e6i	−0.799030	+	1.38396i
$902$	−30999.9	+	5466.11i	−0.0381019	+	0.00671840i
$903$	−4373.28	+	434716.i	−0.00536330	+	0.533126i
$904$	300020.	−	109198.i	0.367124	−	0.133622i
$905$	532559.	+	1.46319e6i	0.650235	+	1.78651i
$906$	73219.4	+	129818.i	0.0892011	+	0.158154i
$907$	294.186	+	1668.41i	0.000357608	+	0.00202810i	0.984986	−	0.172634i	$-0.0552278\pi$
$907$	294.186	+	1668.41i	0.000357608	+	0.00202810i	−0.984628	+	0.174662i	$0.944117\pi$
$908$	−303282.	−	175100.i	−0.367853	−	0.212380i
$909$	1.23362e6	−	679513.i	1.49298	−	0.822375i
$910$	−158964.	−	275334.i	−0.191962	−	0.332489i
$911$	−137089.	−	163377.i	−0.165184	−	0.196858i	0.677103	−	0.735889i	$-0.263235\pi$
$911$	−137089.	−	163377.i	−0.165184	−	0.196858i	−0.842286	+	0.539030i	$0.818791\pi$
$912$	−232221.	−	43359.9i	−0.279197	−	0.0521313i
$913$	−35313.3	+	200271.i	−0.0423639	+	0.240258i
$914$	−491269.	+	585471.i	−0.588067	+	0.700831i
$915$	788155.	+	295877.i	0.941390	+	0.353402i
$916$	292774.	+	106561.i	0.348932	+	0.127001i
$917$			46498.6i			0.0552970i
$918$	−299196.	+	750734.i	−0.355034	+	0.890842i
$919$	67384.9			0.0797868			0.0398934	−	0.999204i	$-0.487298\pi$
$919$	67384.9			0.0797868			0.0398934	+	0.999204i	$0.487298\pi$
$920$	111531.	−	306430.i	0.131771	−	0.362039i
$921$	473724.	−	78625.1i	0.558478	−	0.0926919i
$922$	−656631.	−	550979.i	−0.772430	−	0.648146i
$923$	−697455.	−	122980.i	−0.818677	−	0.144355i
$924$	24952.0	+	21368.6i	0.0292254	+	0.0250283i
$925$	1.35334e6	−	1.13559e6i	1.58170	−	1.32720i
$926$	−87870.6	+	50732.1i	−0.102476	+	0.0591644i
$927$	−1.00163e6	−	387556.i	−1.16559	−	0.450998i
$928$	−128502.	+	222572.i	−0.149216	+	0.258449i
$929$	70523.8	−	12435.2i	0.0817155	−	0.0144086i	−0.132641	−	0.991164i	$-0.542346\pi$
$929$	70523.8	−	12435.2i	0.0817155	−	0.0144086i	0.214356	+	0.976756i	$0.431235\pi$
$930$	1.11893e6	+	661111.i	1.29371	+	0.764378i
$931$	−687448.	+	250211.i	−0.793123	+	0.288673i
$932$	41482.4	+	113972.i	0.0477564	+	0.131210i
$933$	134697.	−	227975.i	0.154737	−	0.261893i
$934$	5052.31	+	28653.1i	0.00579157	+	0.0328456i
$935$	264097.	+	152476.i	0.302092	+	0.174413i
$936$	−122770.	−	152438.i	−0.140133	−	0.173997i
$937$	350885.	+	607751.i	0.399655	+	0.692223i	0.993683	−	0.112221i	$-0.0357965\pi$
$937$	350885.	+	607751.i	0.399655	+	0.692223i	−0.594028	+	0.804444i	$0.702463\pi$
$938$	−156332.	−	186309.i	−0.177681	−	0.211752i
$939$	861045.	−	1.00544e6i	0.976550	−	1.14031i
$940$	185444.	−	1.05170e6i	0.209873	−	1.19025i
$941$	612619.	−	730091.i	0.691849	−	0.824514i	−0.299729	−	0.954024i	$-0.596896\pi$
$941$	612619.	−	730091.i	0.691849	−	0.824514i	0.991578	+	0.129511i	$0.0413407\pi$
$942$	−127406.	−	767636.i	−0.143579	−	0.865074i
$943$	−193710.	−	70504.5i	−0.217835	−	0.0792855i
$944$		−	311784.i		−	0.349873i
$945$	−403536.	+	652638.i	−0.451876	+	0.730818i
$946$	100993.			0.112852
$947$	124361.	−	341678.i	0.138670	−	0.380993i	−0.850846	−	0.525415i	$-0.823910\pi$
$947$	124361.	−	341678.i	0.138670	−	0.380993i	0.989516	+	0.144422i	$0.0461322\pi$
$948$	−63015.6	+	167860.i	−0.0701183	+	0.186781i
$949$	481883.	+	404348.i	0.535068	+	0.448976i
$950$	−1.33646e6	−	235655.i	−1.48085	−	0.261113i
$951$	−190129.	+	1.01827e6i	−0.210227	+	1.12590i
$952$	−168789.	+	141631.i	−0.186239	+	0.156273i
$953$	−838648.	+	484194.i	−0.923409	+	0.533130i	−0.884721	−	0.466121i	$-0.845651\pi$
$953$	−838648.	+	484194.i	−0.923409	+	0.533130i	−0.0386879	+	0.999251i	$0.512318\pi$
$954$	−392292.	+	648958.i	−0.431035	+	0.713049i
$955$	−130483.	+	226003.i	−0.143070	+	0.247804i
$956$	−157019.	+	27686.8i	−0.171806	+	0.0302940i
$957$	−204396.	+	115282.i	−0.223177	+	0.125875i
$958$	194950.	−	70956.2i	0.212419	−	0.0773142i
$959$	153438.	+	421567.i	0.166838	+	0.458384i
$960$	195213.	+	1963.86i	0.211819	+	0.00213092i
$961$	91810.9	+	520685.i	0.0994140	+	0.563805i
$962$	−395024.	−	228067.i	−0.426848	−	0.246441i
$963$	−836072.	−	164831.i	−0.901553	−	0.177740i
$964$	−260530.	−	451252.i	−0.280352	−	0.485584i
$965$	−868083.	−	1.03454e6i	−0.932194	−	1.11095i
$966$	71543.2	+	202891.i	0.0766680	+	0.217424i
$967$	173986.	−	986724.i	0.186064	−	1.05522i	−0.738517	−	0.674234i	$-0.764474\pi$
$967$	173986.	−	986724.i	0.186064	−	1.05522i	0.924581	−	0.380985i	$-0.124415\pi$
$968$	−208042.	+	247935.i	−0.222025	+	0.264599i
$969$	1.11756e6	−	918743.i	1.19021	−	0.978467i
$970$	−227001.	−	82621.6i	−0.241259	−	0.0878113i
$971$		−	1.09369e6i		−	1.15999i	−0.814620	−	0.579995i	$-0.803054\pi$
$971$		−	1.09369e6i		−	1.15999i	0.814620	−	0.579995i	$-0.196946\pi$
$972$	−183682.	+	435219.i	−0.194417	+	0.460654i
$973$	395026.			0.417254
$974$	−368413.	+	1.01221e6i	−0.388344	+	1.06697i
$975$	−714045.	−	868563.i	−0.751132	−	0.913675i
$976$	108247.	+	90829.8i	0.113636	+	0.0953518i
$977$	1.20016e6	+	211620.i	1.25733	+	0.221701i	0.762328	−	0.647191i	$-0.224056\pi$
$977$	1.20016e6	+	211620.i	1.25733	+	0.221701i	0.495002	+	0.868892i	$0.335167\pi$
$978$	−594986.	+	209803.i	−0.622055	+	0.219348i
$979$	−98803.5	+	82906.0i	−0.103088	+	0.0865008i
$980$	523566.	−	302281.i	0.545154	−	0.314745i
$981$	166628.	−	845191.i	0.173145	−	0.878248i
$982$	71312.1	−	123516.i	0.0739503	−	0.128086i
$983$	1.56087e6	−	275223.i	1.61532	−	0.284824i	0.708300	−	0.705912i	$-0.249463\pi$
$983$	1.56087e6	−	275223.i	1.61532	−	0.284824i	0.907020	+	0.421087i	$0.138351\pi$
$984$	1241.45	−	123404.i	0.00128215	−	0.127449i
$985$	−887229.	+	322925.i	−0.914457	+	0.332835i
$986$	−538314.	−	1.47901e6i	−0.553709	−	1.52130i
$987$	346116.	+	613666.i	0.355294	+	0.629938i
$988$	60843.7	+	345062.i	0.0623307	+	0.353495i
$989$	572766.	+	330687.i	0.585578	+	0.338084i
$990$	152548.	+	92214.5i	0.155645	+	0.0940868i
$991$	−175298.	−	303625.i	−0.178496	−	0.309165i	0.762869	−	0.646553i	$-0.223790\pi$
$991$	−175298.	−	303625.i	−0.178496	−	0.309165i	−0.941366	+	0.337388i	$0.890457\pi$
$992$	140220.	+	167108.i	0.142491	+	0.169814i
$993$	−529725.	−	98909.3i	−0.537220	−	0.100309i
$994$	−80923.7	+	458941.i	−0.0819036	+	0.464498i
$995$	−415596.	+	495287.i	−0.419783	+	0.500278i
$996$	−746414.	−	280207.i	−0.752421	−	0.282463i
$997$	−293282.	−	106746.i	−0.295050	−	0.107389i	0.190254	−	0.981735i	$-0.439069\pi$
$997$	−293282.	−	106746.i	−0.295050	−	0.107389i	−0.485304	+	0.874346i	$0.661291\pi$
$998$		−	1.01454e6i		−	1.01861i
$999$	−33218.7	+	1.10038e6i	−0.0332852	+	1.10258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.5.f.a.23.4	✓	72
3.2	odd	2		162.5.f.a.17.7		72
27.7	even	9		162.5.f.a.143.7		72
27.20	odd	18	inner	54.5.f.a.47.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.4	✓	72	1.1	even	1	trivial
54.5.f.a.47.4	yes	72	27.20	odd	18	inner
162.5.f.a.17.7		72	3.2	odd	2
162.5.f.a.143.7		72	27.7	even	9

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.967379 + 2.65785i) q^{2} +(5.71544 + 6.95225i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(41.7224 + 7.35678i) q^{5} +(-24.0070 + 8.46534i) q^{6} +(19.0320 - 15.9698i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-15.6675 + 79.4703i) q^{9} +(-59.9146 + 103.775i) q^{10} +(-18.0860 + 3.18905i) q^{11} +(0.724290 - 71.9964i) q^{12} +(-100.351 + 36.5247i) q^{13} +(24.0341 + 66.0331i) q^{14} +(187.316 + 332.111i) q^{15} +(11.1135 + 63.0277i) q^{16} +(-339.433 - 195.972i) q^{17} +(-196.064 - 118.520i) q^{18} +(205.064 + 355.182i) q^{19} +(-217.859 - 259.634i) q^{20} +(219.802 + 41.0411i) q^{21} +(9.02000 - 51.1549i) q^{22} +(218.656 - 260.583i) q^{23} +(190.655 + 71.5728i) q^{24} +(1099.33 + 400.122i) q^{25} -302.051i q^{26} +(-642.044 + 345.284i) q^{27} -198.756 q^{28} +(485.587 - 1334.14i) q^{29} +(-1063.91 + 176.579i) q^{30} +(-923.152 - 774.616i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-125.541 - 107.512i) q^{33} +(849.225 - 712.585i) q^{34} +(911.547 - 526.282i) q^{35} +(504.676 - 406.455i) q^{36} +(755.062 - 1307.80i) q^{37} +(-1142.40 + 201.435i) q^{38} +(-827.479 - 488.909i) q^{39} +(900.820 - 327.872i) q^{40} +(-207.264 - 569.453i) q^{41} +(-321.713 + 544.499i) q^{42} +(337.617 + 1914.72i) q^{43} +(127.237 + 73.4600i) q^{44} +(-1238.33 + 3200.43i) q^{45} +(481.070 + 833.237i) q^{46} +(2025.36 + 2413.73i) q^{47} +(-374.666 + 437.495i) q^{48} +(-309.745 + 1756.65i) q^{49} +(-2126.93 + 2534.78i) q^{50} +(-577.566 - 3479.89i) q^{51} +(802.807 + 292.198i) q^{52} -3309.93i q^{53} +(-296.614 - 2040.48i) q^{54} -778.052 q^{55} +(192.273 - 528.265i) q^{56} +(-1297.28 + 3455.68i) q^{57} +(3076.20 + 2581.24i) q^{58} +(-4797.62 - 845.950i) q^{59} +(559.880 - 2998.53i) q^{60} +(1691.36 - 1419.22i) q^{61} +(2951.85 - 1704.25i) q^{62} +(970.939 + 1762.69i) q^{63} +(256.000 - 443.405i) q^{64} +(-4455.58 + 785.639i) q^{65} +(407.195 - 229.664i) q^{66} +(-3252.29 + 1183.74i) q^{67} +(1072.42 + 2946.45i) q^{68} +(3061.35 + 30.7975i) q^{69} +(516.968 + 2931.87i) q^{70} +(5743.28 + 3315.88i) q^{71} +(592.086 + 1734.55i) q^{72} +(-2945.25 - 5101.32i) q^{73} +(2745.52 + 3271.98i) q^{74} +(3501.38 + 9929.65i) q^{75} +(569.745 - 3231.18i) q^{76} +(-293.285 + 349.523i) q^{77} +(2099.93 - 1726.36i) q^{78} +(-2340.08 - 851.720i) q^{79} +2711.42i q^{80} +(-6070.06 - 2490.20i) q^{81} +1714.03 q^{82} +(3787.29 - 10405.5i) q^{83} +(-1135.98 - 1381.80i) q^{84} +(-12720.2 - 10673.6i) q^{85} +(-5415.65 - 954.924i) q^{86} +(12050.6 - 4249.27i) q^{87} +(-318.332 + 267.112i) q^{88} +(6082.16 - 3511.54i) q^{89} +(-7308.33 - 6387.32i) q^{90} +(-1326.59 + 2297.72i) q^{91} +(-2680.00 + 472.556i) q^{92} +(109.104 - 10845.2i) q^{93} +(-8374.63 + 3048.11i) q^{94} +(5942.78 + 16327.6i) q^{95} +(-800.353 - 1419.03i) q^{96} +(350.066 + 1985.32i) q^{97} +(-4369.27 - 2522.60i) q^{98} +(29.9271 - 1487.26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 18 q^{5} - 96 q^{6} + 204 q^{9} + 720 q^{11} + 96 q^{12} - 288 q^{14} - 1422 q^{15} - 1344 q^{18} + 288 q^{20} + 4308 q^{21} - 1008 q^{22} + 4716 q^{23} - 882 q^{25} - 2808 q^{27} - 6084 q^{29} - 6336 q^{30}+ \cdots + 179622 q^{99}+O(q^{100}) \) 72 * q - 18 * q^5 - 96 * q^6 + 204 * q^9 + 720 * q^11 + 96 * q^12 - 288 * q^14 - 1422 * q^15 - 1344 * q^18 + 288 * q^20 + 4308 * q^21 - 1008 * q^22 + 4716 * q^23 - 882 * q^25 - 2808 * q^27 - 6084 * q^29 - 6336 * q^30 + 3330 * q^31 - 1026 * q^33 + 288 * q^34 + 5346 * q^35 + 2976 * q^36 + 576 * q^38 - 4974 * q^39 - 13356 * q^41 - 3840 * q^42 + 1260 * q^43 + 9558 * q^45 + 16578 * q^47 + 1920 * q^48 - 5904 * q^49 + 15552 * q^50 + 20898 * q^51 - 4896 * q^54 - 2304 * q^56 - 34218 * q^57 - 40104 * q^59 - 4176 * q^60 + 8352 * q^61 - 4110 * q^63 + 18432 * q^64 - 19674 * q^65 - 10368 * q^66 - 24192 * q^67 + 10224 * q^68 + 47106 * q^69 + 14400 * q^70 + 39528 * q^71 + 15360 * q^72 - 12222 * q^73 + 33120 * q^74 + 41682 * q^75 + 9792 * q^76 + 28206 * q^77 - 4608 * q^78 + 11304 * q^79 + 6804 * q^81 - 30078 * q^83 - 2592 * q^84 - 52200 * q^85 - 46224 * q^86 - 111690 * q^87 - 16128 * q^88 - 102222 * q^89 - 66240 * q^90 + 12078 * q^91 - 27504 * q^92 - 11958 * q^93 + 4032 * q^94 + 46728 * q^95 + 6144 * q^96 + 49680 * q^97 + 82944 * q^98 + 179622 * q^99

Introduction

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