LMFDB - Embedded newform 22.5.d.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,5,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, 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:	$2.27413918784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.2
Root			$0.809017 + 3.49146i$ of defining polynomial
Character	$\chi$	$=$	22.17
Dual form			22.5.d.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68999 + 0.874032i) q^{2} +(4.50928 + 3.27619i) q^{3} +(6.47214 - 4.70228i) q^{4} +(-10.0117 + 30.8128i) q^{5} +(-14.9934 - 4.87166i) q^{6} +(50.5008 + 69.5083i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-15.4301 - 47.4891i) q^{9} +O(q^{10})$	\(q+(-2.68999 + 0.874032i) q^{2} +(4.50928 + 3.27619i) q^{3} +(6.47214 - 4.70228i) q^{4} +(-10.0117 + 30.8128i) q^{5} +(-14.9934 - 4.87166i) q^{6} +(50.5008 + 69.5083i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-15.4301 - 47.4891i) q^{9} -91.6368i q^{10} +(-44.2851 - 112.605i) q^{11} +44.5903 q^{12} +(97.9585 - 31.8286i) q^{13} +(-196.599 - 142.838i) q^{14} +(-146.094 + 106.144i) q^{15} +(19.7771 - 60.8676i) q^{16} +(121.020 + 39.3217i) q^{17} +(83.0139 + 114.259i) q^{18} +(158.082 - 217.581i) q^{19} +(80.0935 + 246.502i) q^{20} +478.883i q^{21} +(217.547 + 264.199i) q^{22} -446.426 q^{23} +(-119.948 + 38.9733i) q^{24} +(-343.559 - 249.610i) q^{25} +(-235.689 + 171.238i) q^{26} +(225.518 - 694.073i) q^{27} +(653.696 + 212.399i) q^{28} +(639.233 + 879.829i) q^{29} +(300.219 - 413.216i) q^{30} +(-155.334 - 478.068i) q^{31} +181.019i q^{32} +(169.220 - 652.853i) q^{33} -359.911 q^{34} +(-2647.34 + 860.174i) q^{35} +(-323.173 - 234.799i) q^{36} +(1568.75 - 1139.76i) q^{37} +(-235.066 + 723.460i) q^{38} +(545.999 + 177.406i) q^{39} +(-430.902 - 593.086i) q^{40} +(951.709 - 1309.92i) q^{41} +(-418.559 - 1288.19i) q^{42} +1441.78i q^{43} +(-816.119 - 520.552i) q^{44} +1617.75 q^{45} +(1200.88 - 390.191i) q^{46} +(-2665.57 - 1936.65i) q^{47} +(288.594 - 209.676i) q^{48} +(-1539.13 + 4736.96i) q^{49} +(1142.34 + 371.168i) q^{50} +(416.888 + 573.797i) q^{51} +(484.333 - 666.628i) q^{52} +(906.672 + 2790.45i) q^{53} +2064.16i q^{54} +(3913.04 - 237.186i) q^{55} -1944.08 q^{56} +(1425.67 - 463.229i) q^{57} +(-2488.53 - 1808.02i) q^{58} +(-1304.22 + 947.571i) q^{59} +(-446.424 + 1373.95i) q^{60} +(-3170.81 - 1030.26i) q^{61} +(835.694 + 1150.23i) q^{62} +(2521.65 - 3470.76i) q^{63} +(-158.217 - 486.941i) q^{64} +3337.03i q^{65} +(115.414 + 1904.07i) q^{66} -2147.45 q^{67} +(968.159 - 314.574i) q^{68} +(-2013.06 - 1462.57i) q^{69} +(6369.52 - 4627.73i) q^{70} +(1044.65 - 3215.10i) q^{71} +(1074.55 + 349.144i) q^{72} +(-4442.75 - 6114.92i) q^{73} +(-3223.74 + 4437.10i) q^{74} +(-731.435 - 2251.13i) q^{75} -2151.56i q^{76} +(5590.54 - 8764.81i) q^{77} -1623.79 q^{78} +(-6155.63 + 2000.08i) q^{79} +(1677.50 + 1218.77i) q^{80} +(18.7143 - 13.5967i) q^{81} +(-1415.18 + 4355.49i) q^{82} +(3860.37 + 1254.31i) q^{83} +(2251.84 + 3099.40i) q^{84} +(-2423.22 + 3335.28i) q^{85} +(-1260.16 - 3878.38i) q^{86} +6061.65i q^{87} +(2650.33 + 686.968i) q^{88} -6032.84 q^{89} +(-4351.74 + 1413.97i) q^{90} +(7159.34 + 5201.56i) q^{91} +(-2889.33 + 2099.22i) q^{92} +(865.797 - 2664.65i) q^{93} +(8863.05 + 2879.78i) q^{94} +(5121.61 + 7049.29i) q^{95} +(-593.053 + 816.268i) q^{96} +(4241.03 + 13052.6i) q^{97} -14087.7i q^{98} +(-4664.17 + 3840.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−2.68999	+	0.874032i	−0.672499	+	0.218508i
$2$	−2.68999	+	0.874032i	−0.672499	+	0.218508i
$3$	4.50928	+	3.27619i	0.501032	+	0.364021i	0.809411	−	0.587243i	$-0.199787\pi$
$3$	4.50928	+	3.27619i	0.501032	+	0.364021i	−0.308379	+	0.951263i	$0.599787\pi$
$4$	6.47214	−	4.70228i	0.404508	−	0.293893i
$5$	−10.0117	+	30.8128i	−0.400467	+	1.23251i	0.524154	+	0.851624i	$0.324382\pi$
$5$	−10.0117	+	30.8128i	−0.400467	+	1.23251i	−0.924621	+	0.380888i	$0.875618\pi$
$6$	−14.9934	−	4.87166i	−0.416485	−	0.135324i
$7$	50.5008	+	69.5083i	1.03063	+	1.41854i	0.904475	+	0.426527i	$0.140263\pi$
$7$	50.5008	+	69.5083i	1.03063	+	1.41854i	0.126153	+	0.992011i	$0.459737\pi$
$8$	−13.3001	+	18.3060i	−0.207813	+	0.286031i
$9$	−15.4301	−	47.4891i	−0.190495	−	0.586285i
$10$		−	91.6368i		−	0.916368i
$11$	−44.2851	−	112.605i	−0.365993	−	0.930618i
$11$	−44.2851	−	112.605i	−0.365993	−	0.930618i
$12$	44.5903			0.309655
$13$	97.9585	−	31.8286i	0.579636	−	0.188335i	−0.00450146	−	0.999990i	$-0.501433\pi$
$13$	97.9585	−	31.8286i	0.579636	−	0.188335i	0.584138	+	0.811655i	$0.301433\pi$
$14$	−196.599	−	142.838i	−1.00306	−	0.728764i
$15$	−146.094	+	106.144i	−0.649307	+	0.471749i
$16$	19.7771	−	60.8676i	0.0772542	−	0.237764i
$17$	121.020	+	39.3217i	0.418754	+	0.136061i	0.510812	−	0.859692i	$-0.329345\pi$
$17$	121.020	+	39.3217i	0.418754	+	0.136061i	−0.0920586	+	0.995754i	$0.529345\pi$
$18$	83.0139	+	114.259i	0.256216	+	0.352651i
$19$	158.082	−	217.581i	0.437900	−	0.602717i	−0.531844	−	0.846842i	$-0.678501\pi$
$19$	158.082	−	217.581i	0.437900	−	0.602717i	0.969744	+	0.244125i	$0.0785008\pi$
$20$	80.0935	+	246.502i	0.200234	+	0.616256i
$21$			478.883i			1.08590i
$22$	217.547	+	264.199i	0.449477	+	0.545867i
$23$	−446.426			−0.843905			−0.421953	−	0.906618i	$-0.638655\pi$
$23$	−446.426			−0.843905			−0.421953	+	0.906618i	$0.638655\pi$
$24$	−119.948	+	38.9733i	−0.208242	+	0.0676620i
$25$	−343.559	−	249.610i	−0.549694	−	0.399376i
$26$	−235.689	+	171.238i	−0.348652	+	0.253310i
$27$	225.518	−	694.073i	0.309353	−	0.952089i
$28$	653.696	+	212.399i	0.833796	+	0.270917i
$29$	639.233	+	879.829i	0.760087	+	1.04617i	0.997207	+	0.0746895i	$0.0237966\pi$
$29$	639.233	+	879.829i	0.760087	+	1.04617i	−0.237120	+	0.971480i	$0.576203\pi$
$30$	300.219	−	413.216i	0.333577	−	0.459129i
$31$	−155.334	−	478.068i	−0.161638	−	0.497470i	0.837135	−	0.546996i	$-0.184229\pi$
$31$	−155.334	−	478.068i	−0.161638	−	0.497470i	−0.998773	+	0.0495264i	$0.984229\pi$
$32$			181.019i			0.176777i
$33$	169.220	−	652.853i	0.155390	−	0.599498i
$34$	−359.911			−0.311342
$35$	−2647.34	+	860.174i	−2.16110	+	0.702183i
$36$	−323.173	−	234.799i	−0.249362	−	0.181172i
$37$	1568.75	−	1139.76i	1.14591	−	0.832553i	0.157979	−	0.987443i	$-0.449502\pi$
$37$	1568.75	−	1139.76i	1.14591	−	0.832553i	0.987932	+	0.154890i	$0.0495022\pi$
$38$	−235.066	+	723.460i	−0.162788	+	0.501011i
$39$	545.999	+	177.406i	0.358974	+	0.116638i
$40$	−430.902	−	593.086i	−0.269314	−	0.370678i
$41$	951.709	−	1309.92i	0.566157	−	0.779248i	−0.425936	−	0.904753i	$-0.640055\pi$
$41$	951.709	−	1309.92i	0.566157	−	0.779248i	0.992093	+	0.125505i	$0.0400552\pi$
$42$	−418.559	−	1288.19i	−0.237278	−	0.730268i
$43$			1441.78i			0.779763i	0.920865	+	0.389881i	$0.127484\pi$
$43$			1441.78i			0.779763i	−0.920865	+	0.389881i	$0.872516\pi$
$44$	−816.119	−	520.552i	−0.421549	−	0.268880i
$45$	1617.75			0.798890
$46$	1200.88	−	390.191i	0.567525	−	0.184400i
$47$	−2665.57	−	1936.65i	−1.20668	−	0.876708i	−0.211759	−	0.977322i	$-0.567919\pi$
$47$	−2665.57	−	1936.65i	−1.20668	−	0.876708i	−0.994926	+	0.100614i	$0.967919\pi$
$48$	288.594	−	209.676i	0.125258	−	0.0910052i
$49$	−1539.13	+	4736.96i	−0.641038	+	1.97291i
$50$	1142.34	+	371.168i	0.456935	+	0.148467i
$51$	416.888	+	573.797i	0.160280	+	0.220606i
$52$	484.333	−	666.628i	0.179117	−	0.246534i
$53$	906.672	+	2790.45i	0.322774	+	0.993396i	0.972435	+	0.233172i	$0.0749106\pi$
$53$	906.672	+	2790.45i	0.322774	+	0.993396i	−0.649662	+	0.760223i	$0.725089\pi$
$54$			2064.16i			0.707875i
$55$	3913.04	−	237.186i	1.29357	−	0.0784085i
$56$	−1944.08			−0.619924
$57$	1425.67	−	463.229i	0.438803	−	0.142576i
$58$	−2488.53	−	1808.02i	−0.739754	−	0.537463i
$59$	−1304.22	+	947.571i	−0.374668	+	0.272212i	−0.759144	−	0.650923i	$-0.774382\pi$
$59$	−1304.22	+	947.571i	−0.374668	+	0.272212i	0.384476	+	0.923135i	$0.374382\pi$
$60$	−446.424	+	1373.95i	−0.124007	+	0.381653i
$61$	−3170.81	−	1030.26i	−0.852138	−	0.276877i	−0.149797	−	0.988717i	$-0.547862\pi$
$61$	−3170.81	−	1030.26i	−0.852138	−	0.276877i	−0.702341	+	0.711840i	$0.747862\pi$
$62$	835.694	+	1150.23i	0.217402	+	0.299229i
$63$	2521.65	−	3470.76i	0.635337	−	0.874466i
$64$	−158.217	−	486.941i	−0.0386271	−	0.118882i
$65$			3337.03i			0.789830i
$66$	115.414	+	1904.07i	0.0264954	+	0.437115i
$67$	−2147.45			−0.478380			−0.239190	−	0.970973i	$-0.576882\pi$
$67$	−2147.45			−0.478380			−0.239190	+	0.970973i	$0.576882\pi$
$68$	968.159	−	314.574i	0.209377	−	0.0680307i
$69$	−2013.06	−	1462.57i	−0.422823	−	0.307199i
$70$	6369.52	−	4627.73i	1.29990	−	0.944434i
$71$	1044.65	−	3215.10i	0.207230	−	0.637789i	−0.792384	−	0.610022i	$-0.791160\pi$
$71$	1044.65	−	3215.10i	0.207230	−	0.637789i	0.999614	−	0.0277668i	$-0.00883957\pi$
$72$	1074.55	+	349.144i	0.207283	+	0.0673503i
$73$	−4442.75	−	6114.92i	−0.833692	−	1.14748i	−0.987224	−	0.159336i	$-0.949065\pi$
$73$	−4442.75	−	6114.92i	−0.833692	−	1.14748i	0.153532	−	0.988144i	$-0.450935\pi$
$74$	−3223.74	+	4437.10i	−0.588704	+	0.810281i
$75$	−731.435	−	2251.13i	−0.130033	−	0.400200i
$76$		−	2151.56i		−	0.372500i
$77$	5590.54	−	8764.81i	0.942914	−	1.47830i
$78$	−1623.79			−0.266896
$79$	−6155.63	+	2000.08i	−0.986320	+	0.320475i	−0.757386	−	0.652967i	$-0.773524\pi$
$79$	−6155.63	+	2000.08i	−0.986320	+	0.320475i	−0.228934	+	0.973442i	$0.573524\pi$
$80$	1677.50	+	1218.77i	0.262109	+	0.190434i
$81$	18.7143	−	13.5967i	0.00285236	−	0.00207236i
$82$	−1415.18	+	4355.49i	−0.210468	+	0.647753i
$83$	3860.37	+	1254.31i	0.560367	+	0.182074i	0.575486	−	0.817811i	$-0.304813\pi$
$83$	3860.37	+	1254.31i	0.560367	+	0.182074i	−0.0151193	+	0.999886i	$0.504813\pi$
$84$	2251.84	+	3099.40i	0.319139	+	0.439257i
$85$	−2423.22	+	3335.28i	−0.335394	+	0.461631i
$86$	−1260.16	−	3878.38i	−0.170384	−	0.524389i
$87$			6061.65i			0.800852i
$88$	2650.33	+	686.968i	0.342243	+	0.0887097i
$89$	−6032.84			−0.761626			−0.380813	−	0.924652i	$-0.624356\pi$
$89$	−6032.84			−0.761626			−0.380813	+	0.924652i	$0.624356\pi$
$90$	−4351.74	+	1413.97i	−0.537252	+	0.174564i
$91$	7159.34	+	5201.56i	0.864550	+	0.628132i
$92$	−2889.33	+	2099.22i	−0.341367	+	0.248018i
$93$	865.797	−	2664.65i	0.100104	−	0.308088i
$94$	8863.05	+	2879.78i	1.00306	+	0.325914i
$95$	5121.61	+	7049.29i	0.567491	+	0.781085i
$96$	−593.053	+	816.268i	−0.0643504	+	0.0885707i
$97$	4241.03	+	13052.6i	0.450742	+	1.38724i	0.876062	+	0.482198i	$0.160161\pi$
$97$	4241.03	+	13052.6i	0.450742	+	1.38724i	−0.425320	+	0.905043i	$0.639839\pi$
$98$		−	14087.7i		−	1.46685i
$99$	−4664.17	+	3840.56i	−0.475887	+	0.391854i
$100$	−3397.30			−0.339730
$101$	9144.05	−	2971.08i	0.896388	−	0.291254i	0.175643	−	0.984454i	$-0.443800\pi$
$101$	9144.05	−	2971.08i	0.896388	−	0.291254i	0.720745	+	0.693200i	$0.243800\pi$
$102$	−1622.94	−	1179.14i	−0.155992	−	0.113335i
$103$	−893.689	+	649.303i	−0.0842387	+	0.0612030i	−0.629107	−	0.777318i	$-0.716579\pi$
$103$	−893.689	+	649.303i	−0.0842387	+	0.0612030i	0.544869	+	0.838521i	$0.316579\pi$
$104$	−720.200	+	2216.55i	−0.0665865	+	0.204932i
$105$	−14755.7	−	4794.42i	−1.33839	−	0.434868i
$106$	−4877.88	−	6713.83i	−0.434130	−	0.597528i
$107$	5677.54	−	7814.47i	0.495898	−	0.682546i	−0.485564	−	0.874201i	$-0.661386\pi$
$107$	5677.54	−	7814.47i	0.495898	−	0.682546i	0.981462	+	0.191656i	$0.0613857\pi$
$108$	−1804.14	−	5552.59i	−0.154676	−	0.476045i
$109$			685.751i			0.0577183i	0.999583	+	0.0288591i	$0.00918742\pi$
$109$			685.751i			0.0577183i	−0.999583	+	0.0288591i	$0.990813\pi$
$110$	−10318.7	+	4058.15i	−0.852788	+	0.335384i
$111$	10808.0			0.877204
$112$	5229.57	−	1699.19i	0.416898	−	0.135458i
$113$	−4633.79	−	3366.65i	−0.362894	−	0.263658i	0.391364	−	0.920236i	$-0.372003\pi$
$113$	−4633.79	−	3366.65i	−0.362894	−	0.263658i	−0.754258	+	0.656578i	$0.772003\pi$
$114$	−3430.17	+	2492.17i	−0.263941	+	0.191764i
$115$	4469.47	−	13755.6i	0.337956	−	1.04012i
$116$	8274.41	+	2688.52i	0.614923	+	0.199801i
$117$	−3023.02	−	4160.84i	−0.220836	−	0.303955i
$118$	2680.14	−	3688.89i	0.192483	−	0.264930i
$119$	3378.41	+	10397.7i	0.238571	+	0.734247i
$120$		−	4086.11i		−	0.283757i
$121$	−10718.7	+	9973.43i	−0.732098	+	0.681199i
$122$	9429.93			0.633562
$123$	8583.06	−	2788.80i	0.567325	−	0.184335i
$124$	−3253.35	−	2363.70i	−0.211587	−	0.153727i
$125$	−5251.04	+	3815.11i	−0.336067	+	0.244167i
$126$	−3749.68	+	11540.3i	−0.236185	+	0.726903i
$127$	−29557.9	−	9603.94i	−1.83259	−	0.595446i	−0.999077	−	0.0429511i	$-0.986324\pi$
$127$	−29557.9	−	9603.94i	−1.83259	−	0.595446i	−0.833516	−	0.552495i	$-0.813676\pi$
$128$	851.204	+	1171.58i	0.0519534	+	0.0715077i
$129$	−4723.54	+	6501.40i	−0.283850	+	0.390686i
$130$	−2916.67	−	8976.60i	−0.172584	−	0.531160i
$131$		−	8729.96i		−	0.508709i	−0.967111	−	0.254355i	$-0.918137\pi$
$131$		−	8729.96i		−	0.508709i	0.967111	−	0.254355i	$-0.0818630\pi$
$132$	−1974.69	−	5021.07i	−0.113331	−	0.288170i
$133$	23106.9			1.30629
$134$	5776.62	−	1876.94i	0.321710	−	0.104530i
$135$	19128.5	+	13897.7i	1.04958	+	0.762561i
$136$	−2329.39	+	1692.40i	−0.125940	+	0.0915011i
$137$	8160.42	−	25115.2i	0.434782	−	1.33812i	−0.458528	−	0.888680i	$-0.651623\pi$
$137$	8160.42	−	25115.2i	0.434782	−	1.33812i	0.893310	−	0.449441i	$-0.148377\pi$
$138$	6693.46	+	2174.84i	0.351473	+	0.114201i
$139$	10425.4	+	14349.3i	0.539588	+	0.742679i	0.988554	−	0.150870i	$-0.0482076\pi$
$139$	10425.4	+	14349.3i	0.539588	+	0.742679i	−0.448966	+	0.893549i	$0.648208\pi$
$140$	−13089.2	+	18015.7i	−0.667816	+	0.919170i
$141$	−5674.98	−	17465.8i	−0.285447	−	0.878517i
$142$			9561.64i			0.474194i
$143$	−7922.16	−	9621.06i	−0.387411	−	0.470490i
$144$	−3195.71			−0.154114
$145$	−33509.8	+	10888.0i	−1.59381	+	0.517859i
$146$	17295.6	+	12566.0i	0.811390	+	0.589510i
$147$	−22459.6	+	16317.8i	−1.03936	+	0.755141i
$148$	4793.68	−	14753.4i	0.218849	−	0.673549i
$149$	17975.7	+	5840.66i	0.809679	+	0.263081i	0.684462	−	0.729049i	$-0.260037\pi$
$149$	17975.7	+	5840.66i	0.809679	+	0.263081i	0.125217	+	0.992129i	$0.460037\pi$
$150$	3935.11	+	5416.22i	0.174894	+	0.240721i
$151$	−264.180	+	363.612i	−0.0115863	+	0.0159472i	−0.814771	−	0.579783i	$-0.803137\pi$
$151$	−264.180	+	363.612i	−0.0115863	+	0.0159472i	0.803185	+	0.595730i	$0.203137\pi$
$152$	1880.53	+	5787.68i	0.0813942	+	0.250505i
$153$		−	6353.86i		−	0.271428i
$154$	−7377.78	+	28463.6i	−0.311089	+	1.20019i
$155$	16285.8			0.677868
$156$	4368.00	−	1419.25i	0.179487	−	0.0583189i
$157$	28892.7	+	20991.8i	1.17217	+	0.851629i	0.991267	−	0.131873i	$-0.0420990\pi$
$157$	28892.7	+	20991.8i	1.17217	+	0.851629i	0.180900	+	0.983502i	$0.442099\pi$
$158$	14810.5	−	10760.4i	0.593273	−	0.431038i
$159$	−5053.59	+	15553.4i	−0.199897	+	0.615219i
$160$	−5577.71	−	1812.31i	−0.217879	−	0.0707933i
$161$	−22544.8	−	31030.3i	−0.869752	−	1.19711i
$162$	−38.4574	+	52.9321i	−0.00146538	+	0.00201692i
$163$	−7301.42	−	22471.5i	−0.274810	−	0.845777i	−0.989270	−	0.146101i	$-0.953328\pi$
$163$	−7301.42	−	22471.5i	−0.274810	−	0.845777i	0.714460	−	0.699676i	$-0.246672\pi$
$164$		−	12953.2i		−	0.481602i
$165$	18422.1	+	11750.3i	0.676660	+	0.431600i
$166$	−11480.7			−0.416631
$167$	−616.899	+	200.443i	−0.0221198	+	0.00718715i	−0.320056	−	0.947399i	$-0.603702\pi$
$167$	−616.899	+	200.443i	−0.0221198	+	0.00718715i	0.297936	+	0.954586i	$0.403702\pi$
$168$	−8766.41	−	6369.17i	−0.310601	−	0.225665i
$169$	−14523.5	+	10552.0i	−0.508509	+	0.369454i
$170$	3603.32	−	11089.9i	0.124682	−	0.383732i
$171$	−12771.9	−	4149.85i	−0.436782	−	0.141919i
$172$	6779.66	+	9331.40i	0.229166	+	0.315421i
$173$	−13537.7	+	18633.0i	−0.452326	+	0.622573i	−0.972895	−	0.231246i	$-0.925720\pi$
$173$	−13537.7	+	18633.0i	−0.452326	+	0.622573i	0.520569	+	0.853819i	$0.325720\pi$
$174$	−5298.07	−	16305.8i	−0.174993	−	0.538572i
$175$		−	36485.7i		−	1.19137i
$176$	−7729.81	+	468.537i	−0.249542	+	0.0151258i
$177$	−8985.52			−0.286812
$178$	16228.3	−	5272.89i	0.512192	−	0.166421i
$179$	−5194.85	−	3774.28i	−0.162131	−	0.117795i	0.503761	−	0.863843i	$-0.331949\pi$
$179$	−5194.85	−	3774.28i	−0.162131	−	0.117795i	−0.665893	+	0.746048i	$0.731949\pi$
$180$	10470.3	−	7607.13i	0.323158	−	0.234788i
$181$	13260.0	−	40810.0i	0.404749	−	1.24569i	−0.516356	−	0.856374i	$-0.672712\pi$
$181$	13260.0	−	40810.0i	0.404749	−	1.24569i	0.921105	−	0.389315i	$-0.127288\pi$
$182$	−23804.9	−	7734.68i	−0.718660	−	0.233507i
$183$	−10922.8	−	15033.9i	−0.326159	−	0.448920i
$184$	5937.49	−	8172.26i	0.175375	−	0.241383i
$185$	19413.5	+	59748.6i	0.567231	+	1.74576i
$186$			7924.63i			0.229062i
$187$	−931.567	−	15368.8i	−0.0266398	−	0.439497i
$188$	−26358.6			−0.745772
$189$	59632.7	−	19375.8i	1.66940	−	0.542422i
$190$	−19938.4	−	14486.1i	−0.552310	−	0.401277i
$191$	20652.0	−	15004.5i	0.566102	−	0.411298i	−0.267585	−	0.963534i	$-0.586226\pi$
$191$	20652.0	−	15004.5i	0.566102	−	0.411298i	0.833687	+	0.552237i	$0.186226\pi$
$192$	881.866	−	2714.10i	0.0239221	−	0.0736248i
$193$	40117.2	+	13034.9i	1.07700	+	0.349939i	0.793210	−	0.608948i	$-0.208408\pi$
$193$	40117.2	+	13034.9i	1.07700	+	0.349939i	0.283790	+	0.958886i	$0.408408\pi$
$194$	−22816.7	−	31404.5i	−0.606247	−	0.834427i
$195$	−10932.7	+	15047.6i	−0.287515	+	0.395730i
$196$	12313.1	+	37895.7i	0.320519	+	0.986456i
$197$			37597.4i			0.968781i	0.874852	+	0.484390i	$0.160959\pi$
$197$			37597.4i			0.968781i	−0.874852	+	0.484390i	$0.839041\pi$
$198$	9189.81	−	14407.7i	0.234410	−	0.367507i
$199$	−37450.3			−0.945690			−0.472845	−	0.881146i	$-0.656773\pi$
$199$	−37450.3			−0.945690			−0.472845	+	0.881146i	$0.656773\pi$
$200$	9138.71	−	2969.35i	0.228468	−	0.0742336i
$201$	−9683.44	−	7035.43i	−0.239683	−	0.174140i
$202$	−22000.6	+	15984.4i	−0.539178	+	0.391736i
$203$	−28873.7	+	88864.1i	−0.700665	+	2.15642i
$204$	5396.31	+	1753.37i	0.129669	+	0.0421320i
$205$	30833.9	+	42439.3i	0.733705	+	1.00986i
$206$	1836.51	−	2527.73i	0.0432771	−	0.0595658i
$207$	6888.41	+	21200.3i	0.160760	+	0.494769i
$208$		−	6591.98i		−	0.152366i
$209$	−31501.3	−	8165.16i	−0.721167	−	0.186927i
$210$	43883.3			0.995086
$211$	−31716.5	+	10305.3i	−0.712394	+	0.231471i	−0.642722	−	0.766099i	$-0.722195\pi$
$211$	−31716.5	+	10305.3i	−0.712394	+	0.231471i	−0.0696716	+	0.997570i	$0.522195\pi$
$212$	18989.6	+	13796.7i	0.422516	+	0.306976i
$213$	15243.9	−	11075.3i	0.335997	−	0.244116i
$214$	−8442.46	+	25983.2i	−0.184349	+	0.567369i
$215$	−44425.3	−	14434.7i	−0.961067	−	0.312269i
$216$	9706.28	+	13359.5i	0.208039	+	0.286341i
$217$	25385.3	−	34939.8i	0.539091	−	0.741995i
$218$	−599.368	−	1844.67i	−0.0126119	−	0.0388154i
$219$		−	42129.2i		−	0.878405i
$220$	24210.4	−	19935.3i	0.500215	−	0.411886i
$221$	13106.5			0.268350
$222$	−29073.5	+	9446.56i	−0.589918	+	0.191676i
$223$	24842.4	+	18049.1i	0.499556	+	0.362949i	0.808848	−	0.588018i	$-0.200092\pi$
$223$	24842.4	+	18049.1i	0.499556	+	0.362949i	−0.309291	+	0.950967i	$0.600092\pi$
$224$	−12582.4	+	9141.62i	−0.250764	+	0.182191i
$225$	−6552.59	+	20166.8i	−0.129434	+	0.398356i
$226$	15407.4	+	5006.18i	0.301657	+	0.0980143i
$227$	−5431.00	−	7475.12i	−0.105397	−	0.145066i	0.753060	−	0.657951i	$-0.228577\pi$
$227$	−5431.00	−	7475.12i	−0.105397	−	0.145066i	−0.858457	+	0.512885i	$0.828577\pi$
$228$	7048.91	−	9701.99i	0.135598	−	0.186634i
$229$	−23748.2	−	73089.5i	−0.452856	−	1.39375i	−0.873634	−	0.486584i	$-0.838243\pi$
$229$	−23748.2	−	73089.5i	−0.452856	−	1.39375i	0.420778	−	0.907164i	$-0.361757\pi$
$230$			40909.0i			0.773327i
$231$	53924.5	−	21207.4i	1.01056	−	0.397432i
$232$	−24608.0			−0.457193
$233$	−10685.0	+	3471.75i	−0.196816	+	0.0639495i	−0.405766	−	0.913977i	$-0.632995\pi$
$233$	−10685.0	+	3471.75i	−0.196816	+	0.0639495i	0.208950	+	0.977926i	$0.432995\pi$
$234$	11768.6	+	8550.40i	0.214928	+	0.156155i
$235$	86360.3	−	62744.4i	1.56379	−	1.13616i
$236$	−3985.34	+	12265.6i	−0.0715552	+	0.220224i
$237$	−34310.1	−	11148.0i	−0.610837	−	0.198473i
$238$	−18175.8	−	25016.8i	−0.320878	−	0.441650i
$239$	−16277.0	+	22403.4i	−0.284957	+	0.392210i	−0.927368	−	0.374151i	$-0.877934\pi$
$239$	−16277.0	+	22403.4i	−0.284957	+	0.392210i	0.642411	+	0.766360i	$0.277934\pi$
$240$	3571.39	+	10991.6i	0.0620033	+	0.190826i
$241$			39221.5i			0.675289i	0.941274	+	0.337644i	$0.109630\pi$
$241$			39221.5i			0.675289i	−0.941274	+	0.337644i	$0.890370\pi$
$242$	20116.0	−	36196.9i	0.343488	−	0.618075i
$243$	−58984.2			−0.998903
$244$	−25366.5	+	8242.06i	−0.426069	+	0.138438i
$245$	−130550.	−	94850.0i	−2.17492	−	1.58017i
$246$	−20650.9	+	15003.7i	−0.341246	+	0.247930i
$247$	8560.15	−	26345.4i	0.140310	−	0.431828i
$248$	10817.5	+	3514.80i	0.175882	+	0.0571476i
$249$	13298.1	+	18303.3i	0.214483	+	0.295210i
$250$	10790.8	−	14852.2i	0.172652	−	0.237635i
$251$	−25606.0	−	78807.1i	−0.406438	−	1.25089i	−0.919689	−	0.392648i	$-0.871559\pi$
$251$	−25606.0	−	78807.1i	−0.406438	−	1.25089i	0.513251	−	0.858238i	$-0.328441\pi$
$252$		−	34320.7i		−	0.540450i
$253$	19770.0	+	50269.7i	0.308863	+	0.785353i
$254$	87904.7			1.36253
$255$	−21854.0	+	7100.80i	−0.336086	+	0.109201i
$256$	−3313.73	−	2407.57i	−0.0505636	−	0.0367366i
$257$	4780.54	−	3473.26i	0.0723786	−	0.0525861i	−0.551008	−	0.834500i	$-0.685756\pi$
$257$	4780.54	−	3473.26i	0.0723786	−	0.0525861i	0.623386	+	0.781914i	$0.285756\pi$
$258$	7023.87	−	21617.3i	0.105521	−	0.324759i
$259$	158446.	+	51482.3i	2.36201	+	0.767465i
$260$	15691.7	+	21597.7i	0.232125	+	0.319493i
$261$	31918.8	−	43932.4i	0.468560	−	0.644918i
$262$	7630.26	+	23483.5i	0.111157	+	0.342106i
$263$			107951.i			1.56069i	0.625351	+	0.780344i	$0.284956\pi$
$263$			107951.i			1.56069i	−0.625351	+	0.780344i	$0.715044\pi$
$264$	9700.47	+	11780.7i	0.139183	+	0.169030i
$265$	−95058.8			−1.35363
$266$	−62157.5	+	20196.2i	−0.878477	+	0.285435i
$267$	−27203.8	−	19764.7i	−0.381599	−	0.277248i
$268$	−13898.6	+	10097.9i	−0.193509	+	0.140592i
$269$	−4826.05	+	14853.1i	−0.0666941	+	0.205263i	−0.978850	−	0.204581i	$-0.934417\pi$
$269$	−4826.05	+	14853.1i	−0.0666941	+	0.205263i	0.912156	+	0.409844i	$0.134417\pi$
$270$	−63602.6	−	20665.7i	−0.872464	−	0.283481i
$271$	−20136.9	−	27716.1i	−0.274192	−	0.377392i	0.649608	−	0.760270i	$-0.274933\pi$
$271$	−20136.9	−	27716.1i	−0.274192	−	0.377392i	−0.923799	+	0.382877i	$0.874933\pi$
$272$	4786.84	−	6588.52i	0.0647010	−	0.0890533i
$273$	15242.2	+	46910.7i	0.204514	+	0.629428i
$274$			74692.2i			0.994887i
$275$	−12892.7	+	49740.4i	−0.170482	+	0.657724i
$276$	−19906.2			−0.261319
$277$	68601.8	−	22290.1i	0.894079	−	0.290504i	0.174288	−	0.984695i	$-0.444238\pi$
$277$	68601.8	−	22290.1i	0.894079	−	0.290504i	0.719791	+	0.694191i	$0.244238\pi$
$278$	−40585.9	−	29487.4i	−0.525153	−	0.381546i
$279$	−20306.2	+	14753.3i	−0.260868	+	0.189531i
$280$	19463.5	−	59902.6i	0.248259	−	0.764063i
$281$	96719.5	+	31426.1i	1.22490	+	0.397995i	0.848865	−	0.528610i	$-0.177287\pi$
$281$	96719.5	+	31426.1i	1.22490	+	0.397995i	0.376037	+	0.926605i	$0.377287\pi$
$282$	30531.3	+	42022.8i	0.383926	+	0.528429i
$283$	−1793.34	+	2468.33i	−0.0223919	+	0.0308198i	−0.820066	−	0.572269i	$-0.806063\pi$
$283$	−1793.34	+	2468.33i	−0.0223919	+	0.0308198i	0.797674	+	0.603089i	$0.206063\pi$
$284$	−8357.18	−	25720.8i	−0.103615	−	0.318895i
$285$			48566.6i			0.597927i
$286$	29719.7	+	18956.4i	0.363339	+	0.231752i
$287$	139112.			1.68889
$288$	8596.44	−	2793.15i	0.103641	−	0.0336752i
$289$	−54470.3	−	39575.0i	−0.652175	−	0.473833i
$290$	80624.7	−	58577.3i	0.958676	−	0.696519i
$291$	−23638.6	+	72752.1i	−0.279149	+	0.859131i
$292$	−57508.1	−	18685.5i	−0.674471	−	0.219149i
$293$	6804.87	+	9366.10i	0.0792656	+	0.109100i	0.846809	−	0.531898i	$-0.178521\pi$
$293$	6804.87	+	9366.10i	0.0792656	+	0.109100i	−0.767543	+	0.640997i	$0.778521\pi$
$294$	46153.8	−	63525.3i	0.533965	−	0.734940i
$295$	−16139.9	−	49673.4i	−0.185463	−	0.570795i
$296$			43876.5i			0.500781i
$297$	−88143.0	+	5342.72i	−0.999252	+	0.0605689i
$298$	−53459.4			−0.601993
$299$	−43731.2	+	14209.1i	−0.489158	+	0.158937i
$300$	−15319.4	−	11130.2i	−0.170215	−	0.123669i
$301$	−100216.	+	72811.1i	−1.10612	+	0.803645i
$302$	392.833	−	1209.02i	0.00430720	−	0.0132562i
$303$	50967.0	+	16560.2i	0.555141	+	0.180376i
$304$	−10117.2	−	13925.2i	−0.109475	−	0.150679i
$305$	63490.2	−	87386.8i	0.682507	−	0.939391i
$306$	5553.47	+	17091.8i	0.0593092	+	0.182535i
$307$		−	26745.6i		−	0.283776i	−0.989883	−	0.141888i	$-0.954683\pi$
$307$		−	26745.6i		−	0.283776i	0.989883	−	0.141888i	$-0.0453174\pi$
$308$	−5031.91	−	83015.3i	−0.0530434	−	0.875098i
$309$	−6157.13			−0.0644854
$310$	−43808.6	+	14234.3i	−0.455865	+	0.148120i
$311$	32169.2	+	23372.3i	0.332598	+	0.241646i	0.741532	−	0.670917i	$-0.234100\pi$
$311$	32169.2	+	23372.3i	0.332598	+	0.241646i	−0.408934	+	0.912564i	$0.634100\pi$
$312$	−10509.4	+	7635.54i	−0.107962	+	0.0784387i
$313$	−26400.8	+	81253.2i	−0.269481	+	0.829377i	0.721146	+	0.692783i	$0.243616\pi$
$313$	−26400.8	+	81253.2i	−0.269481	+	0.829377i	−0.990627	+	0.136594i	$0.956384\pi$
$314$	−96068.8	−	31214.6i	−0.974368	−	0.316591i
$315$	81697.7	+	112447.i	0.823358	+	1.13326i
$316$	−30435.1	+	41890.3i	−0.304790	+	0.419507i
$317$	7585.16	+	23344.7i	0.0754825	+	0.232311i	0.981678	−	0.190548i	$-0.0610265\pi$
$317$	7585.16	+	23344.7i	0.0754825	+	0.232311i	−0.906195	+	0.422859i	$0.861026\pi$
$318$		−	46255.4i		−	0.457413i
$319$	70764.4	−	110944.i	0.695398	−	1.09024i
$320$	16588.0			0.161992
$321$	51203.3	−	16637.0i	0.496922	−	0.161460i
$322$	87767.0	+	63766.5i	0.846486	+	0.615008i
$323$	27686.7	−	20115.6i	0.265379	−	0.192809i
$324$	57.1858	−	176.000i	0.000544752	−	0.00167657i
$325$	−41599.3	−	13516.4i	−0.393839	−	0.127966i
$326$	39281.5	+	54066.4i	0.369618	+	0.508736i
$327$	−2246.65	+	3092.25i	−0.0210106	+	0.0289187i
$328$	11321.5	+	34843.9i	0.105234	+	0.323876i
$329$		−	283081.i		−	2.61529i
$330$	−59825.4	−	15506.8i	−0.549360	−	0.142395i
$331$	−88390.7			−0.806772			−0.403386	−	0.915030i	$-0.632167\pi$
$331$	−88390.7			−0.806772			−0.403386	+	0.915030i	$0.632167\pi$
$332$	30883.0	−	10034.5i	0.280184	−	0.0910372i
$333$	−78332.4	−	56911.8i	−0.706404	−	0.513232i
$334$	1484.26	−	1078.38i	0.0133051	−	0.00966670i
$335$	21499.5	−	66168.8i	0.191575	−	0.589608i
$336$	29148.5	+	9470.91i	0.258189	+	0.0838906i
$337$	−59771.4	−	82268.3i	−0.526301	−	0.724391i	0.460260	−	0.887784i	$-0.347756\pi$
$337$	−59771.4	−	82268.3i	−0.526301	−	0.724391i	−0.986561	+	0.163393i	$0.947756\pi$
$338$	29845.5	−	41078.7i	0.261243	−	0.359570i
$339$	−9865.32	−	30362.3i	−0.0858444	−	0.264202i
$340$			32981.1i			0.285304i
$341$	−46953.8	+	38662.7i	−0.403796	+	0.332493i
$342$	37983.5			0.324745
$343$	−210795.	+	68491.6i	−1.79173	+	0.582169i
$344$	−26393.2	−	19175.8i	−0.223036	−	0.162045i
$345$	65220.1	−	47385.2i	0.547953	−	0.398111i
$346$	20130.4	−	61955.0i	0.168151	−	0.517516i
$347$	35079.8	+	11398.1i	0.291338	+	0.0946616i	0.451040	−	0.892504i	$-0.351053\pi$
$347$	35079.8	+	11398.1i	0.291338	+	0.0946616i	−0.159702	+	0.987165i	$0.551053\pi$
$348$	28503.6	+	39231.8i	0.235364	+	0.323951i
$349$	−60796.7	+	83679.5i	−0.499148	+	0.687018i	−0.982042	−	0.188660i	$-0.939585\pi$
$349$	−60796.7	+	83679.5i	−0.499148	+	0.687018i	0.482894	+	0.875679i	$0.339585\pi$
$350$	31889.7	+	98146.3i	0.260324	+	0.801194i
$351$		−	75168.3i		−	0.610127i
$352$	20383.6	−	8016.47i	0.164512	−	0.0646990i
$353$	50438.5			0.404774			0.202387	−	0.979306i	$-0.435130\pi$
$353$	50438.5			0.404774			0.202387	+	0.979306i	$0.435130\pi$
$354$	24171.0	−	7853.63i	0.192880	−	0.0626706i
$355$	88607.4	+	64377.0i	0.703094	+	0.510827i
$356$	−39045.3	+	28368.1i	−0.308084	+	0.223836i
$357$	−18830.5	+	57954.3i	−0.147749	+	0.454726i
$358$	17273.0	+	5612.33i	0.134772	+	0.0437902i
$359$	51281.0	+	70582.2i	0.397894	+	0.547654i	0.960214	−	0.279266i	$-0.0900910\pi$
$359$	51281.0	+	70582.2i	0.397894	+	0.547654i	−0.562320	+	0.826920i	$0.690091\pi$
$360$	−21516.2	+	29614.5i	−0.166020	+	0.228507i
$361$	17919.8	+	55151.5i	0.137505	+	0.423197i
$362$			121368.i			0.926165i
$363$	−81008.3	+	9856.73i	−0.614775	+	0.0748031i
$364$	70795.4			0.534321
$365$	232897.	−	75672.8i	1.74815	−	0.568008i
$366$	42522.2	+	30894.2i	0.317434	+	0.230630i
$367$	41866.7	−	30417.9i	0.310840	−	0.225838i	−0.421417	−	0.906867i	$-0.638467\pi$
$367$	41866.7	−	30417.9i	0.310840	−	0.225838i	0.732257	+	0.681029i	$0.238467\pi$
$368$	−8829.00	+	27172.9i	−0.0651953	+	0.200650i
$369$	−76891.7	−	24983.6i	−0.564711	−	0.183486i
$370$	−104444.	−	143755.i	−0.762924	−	1.05008i
$371$	−148172.	+	203941.i	−1.07651	+	1.48169i
$372$	−6926.38	−	21317.2i	−0.0500519	−	0.154044i
$373$			180034.i			1.29401i	0.762487	+	0.647003i	$0.223978\pi$
$373$			180034.i			1.29401i	−0.762487	+	0.647003i	$0.776022\pi$
$374$	15938.7	+	40527.7i	0.113949	+	0.289740i
$375$	−36177.5			−0.257262
$376$	70904.4	−	23038.2i	0.501531	−	0.162957i
$377$	90622.1	+	65840.8i	0.637604	+	0.463247i
$378$	−143477.	+	104242.i	−1.00415	+	0.729556i
$379$	57325.3	−	176429.i	0.399087	−	1.22826i	−0.526645	−	0.850085i	$-0.676550\pi$
$379$	57325.3	−	176429.i	0.399087	−	1.22826i	0.925732	−	0.378179i	$-0.123450\pi$
$380$	66295.5	+	21540.7i	0.459110	+	0.149174i
$381$	−101821.	−	140144.i	−0.701433	−	0.965439i
$382$	−42439.3	+	58412.6i	−0.290831	+	0.400295i
$383$	−1955.49	−	6018.39i	−0.0133309	−	0.0410283i	0.944170	−	0.329459i	$-0.106866\pi$
$383$	−1955.49	−	6018.39i	−0.0133309	−	0.0410283i	−0.957501	+	0.288431i	$0.906866\pi$
$384$			8071.70i			0.0547397i
$385$	214098.	+	260011.i	1.44441	+	1.75416i
$386$	−119308.			−0.800746
$387$	68468.8	−	22246.9i	0.457163	−	0.148541i
$388$	88825.3	+	64535.4i	0.590029	+	0.428681i
$389$	−89160.2	+	64778.7i	−0.589212	+	0.428088i	−0.842034	−	0.539425i	$-0.818642\pi$
$389$	−89160.2	+	64778.7i	−0.589212	+	0.428088i	0.252821	+	0.967513i	$0.418642\pi$
$390$	16256.9	−	50033.6i	0.106883	−	0.328952i
$391$	−54026.4	−	17554.2i	−0.353388	−	0.114823i
$392$	−66244.1	−	91177.2i	−0.431097	−	0.593354i
$393$	28601.0	−	39365.9i	0.185181	−	0.254879i
$394$	−32861.3	−	101137.i	−0.211686	−	0.651503i
$395$		−	209696.i		−	1.34399i
$396$	−12127.7	+	46788.9i	−0.0773372	+	0.298368i
$397$	−205760.			−1.30551			−0.652755	−	0.757569i	$-0.726387\pi$
$397$	−205760.			−1.30551			−0.652755	+	0.757569i	$0.726387\pi$
$398$	100741.	−	32732.7i	0.635975	−	0.206641i
$399$	104196.	+	75702.7i	0.654492	+	0.475516i
$400$	−21987.8	+	15975.0i	−0.137424	+	0.0998440i
$401$	40707.1	−	125284.i	0.253152	−	0.779122i	−0.741036	−	0.671465i	$-0.765665\pi$
$401$	40707.1	−	125284.i	0.253152	−	0.779122i	0.994188	−	0.107657i	$-0.0343347\pi$
$402$	32197.6	+	10461.6i	0.199238	+	0.0647362i
$403$	−30432.5	−	41886.8i	−0.187382	−	0.257909i
$404$	45210.7	−	62227.2i	0.276999	−	0.381257i
$405$	231.592	+	712.766i	0.00141193	+	0.00434547i
$406$		−	264280.i		−	1.60329i
$407$	−197815.	−	126174.i	−1.19418	−	0.761696i
$408$	−16048.5			−0.0964084
$409$	75524.9	−	24539.5i	0.451485	−	0.146696i	−0.0744433	−	0.997225i	$-0.523718\pi$
$409$	75524.9	−	24539.5i	0.451485	−	0.146696i	0.525928	+	0.850529i	$0.323718\pi$
$410$	−120036.	−	87211.6i	−0.714077	−	0.518808i
$411$	119080.	−	86516.5i	0.704943	−	0.512171i
$412$	−2730.87	+	8404.75i	−0.0160882	+	0.0495143i
$413$	−131728.	−	42801.1i	−0.772287	−	0.250931i
$414$	−37059.6	−	51008.1i	−0.216222	−	0.297604i
$415$	−77297.6	+	106391.i	−0.448817	+	0.617744i
$416$	5761.60	+	17732.4i	0.0332933	+	0.102466i
$417$			98860.5i			0.568527i
$418$	91874.9	−	5568.93i	0.525829	−	0.0318727i
$419$	281150.			1.60144			0.800718	−	0.599041i	$-0.204451\pi$
$419$	281150.			1.60144			0.800718	+	0.599041i	$0.204451\pi$
$420$	−118046.	+	38355.4i	−0.669194	+	0.217434i
$421$	268282.	+	194918.i	1.51366	+	1.09974i	0.964522	+	0.264004i	$0.0850433\pi$
$421$	268282.	+	194918.i	1.51366	+	1.09974i	0.549136	+	0.835733i	$0.314957\pi$
$422$	76310.0	−	55442.5i	0.428506	−	0.311328i
$423$	−50839.5	+	156468.i	−0.284132	+	0.874469i
$424$	−63140.6	−	20515.6i	−0.351218	−	0.114118i
$425$	−31762.3	−	43717.1i	−0.175847	−	0.242032i
$426$	−31325.7	+	43116.2i	−0.172616	+	0.237586i
$427$	−88516.7	−	272426.i	−0.485478	−	1.49415i
$428$		−	77273.7i		−	0.421836i
$429$	−4202.90	−	69338.6i	−0.0228368	−	0.376756i
$430$	132120.			0.714549
$431$	−118641.	+	38548.8i	−0.638675	+	0.207518i	−0.610414	−	0.792083i	$-0.708997\pi$
$431$	−118641.	+	38548.8i	−0.638675	+	0.207518i	−0.0282608	+	0.999601i	$0.508997\pi$
$432$	−37786.5	−	27453.5i	−0.202474	−	0.147106i
$433$	−20821.9	+	15128.0i	−0.111057	+	0.0806874i	−0.641927	−	0.766765i	$-0.721865\pi$
$433$	−20821.9	+	15128.0i	−0.111057	+	0.0806874i	0.530871	+	0.847453i	$0.321865\pi$
$434$	−37747.7	+	116175.i	−0.200406	+	0.616787i
$435$	−186776.	−	60687.3i	−0.987059	−	0.320715i
$436$	3224.59	+	4438.27i	0.0169630	+	0.0233475i
$437$	−70571.8	+	97133.7i	−0.369546	+	0.508636i
$438$	36822.2	+	113327.i	0.191938	+	0.590726i
$439$			123861.i			0.642693i	0.946962	+	0.321347i	$0.104135\pi$
$439$			123861.i			0.642693i	−0.946962	+	0.321347i	$0.895865\pi$
$440$	−47701.7	+	74786.5i	−0.246393	+	0.386294i
$441$	248703.			1.27880
$442$	−35256.4	+	11455.5i	−0.180465	+	0.0586366i
$443$	59932.0	+	43543.2i	0.305388	+	0.221877i	0.729915	−	0.683538i	$-0.239560\pi$
$443$	59932.0	+	43543.2i	0.305388	+	0.221877i	−0.424527	+	0.905415i	$0.639560\pi$
$444$	69951.0	−	50822.4i	0.354836	−	0.257804i
$445$	60398.9	−	185889.i	0.305006	−	0.938713i
$446$	−82601.5	−	26838.9i	−0.415258	−	0.134926i
$447$	61922.4	+	85228.9i	0.309908	+	0.426552i
$448$	25856.4	−	35588.3i	0.128828	−	0.177317i
$449$	71324.2	+	219513.i	0.353789	+	1.08885i	0.956708	+	0.291048i	$0.0940040\pi$
$449$	71324.2	+	219513.i	0.353789	+	1.08885i	−0.602920	+	0.797802i	$0.705996\pi$
$450$		−	59975.7i		−	0.296176i
$451$	−189649.	−	49157.2i	−0.932391	−	0.241676i
$452$	−45821.4			−0.224281
$453$	−2382.53	+	774.129i	−0.0116102	+	0.00377239i
$454$	21142.8	+	15361.2i	0.102577	+	0.0745268i
$455$	−231952.	+	168523.i	−1.12040	+	0.814021i
$456$	−10481.7	+	32259.3i	−0.0504082	+	0.155140i
$457$	120027.	+	38999.1i	0.574706	+	0.186733i	0.581928	−	0.813241i	$-0.302299\pi$
$457$	120027.	+	38999.1i	0.574706	+	0.186733i	−0.00722142	+	0.999974i	$0.502299\pi$
$458$	127765.	+	175854.i	0.609090	+	0.838341i
$459$	54584.3	−	75128.9i	0.259085	−	0.356600i
$460$	−35755.8	−	110045.i	−0.168978	−	0.520062i
$461$		−	65227.4i		−	0.306922i	−0.988155	−	0.153461i	$-0.950958\pi$
$461$		−	65227.4i		−	0.306922i	0.988155	−	0.153461i	$-0.0490420\pi$
$462$	−126521.	+	104179.i	−0.592758	+	0.488088i
$463$	308377.			1.43853			0.719267	−	0.694733i	$-0.244478\pi$
$463$	308377.			1.43853			0.719267	+	0.694733i	$0.244478\pi$
$464$	66195.3	−	21508.1i	0.307462	−	0.0999003i
$465$	73437.2	+	53355.3i	0.339633	+	0.246758i
$466$	25708.0	−	18678.0i	0.118385	−	0.0860119i
$467$	−115280.	+	354796.i	−0.528592	+	1.62684i	0.228510	+	0.973542i	$0.426615\pi$
$467$	−115280.	+	354796.i	−0.528592	+	1.62684i	−0.757102	+	0.653297i	$0.773385\pi$
$468$	−39130.9	−	12714.4i	−0.178660	−	0.0580502i
$469$	−108448.	−	149265.i	−0.493031	−	0.678599i
$470$	−177468.	+	244264.i	−0.803386	+	1.10577i
$471$	61512.5	+	189316.i	0.277282	+	0.853386i
$472$		−	36477.8i		−	0.163736i
$473$	162351.	−	63849.5i	0.725661	−	0.285388i
$474$	102038.			0.454155
$475$	−108621.	+	35293.0i	−0.481422	+	0.156423i
$476$	70758.3	+	51408.9i	0.312294	+	0.226895i
$477$	118526.	−	86113.9i	0.520926	−	0.378475i
$478$	24203.8	−	74491.7i	0.105932	−	0.326026i
$479$	−243681.	−	79176.8i	−1.06207	−	0.345086i	−0.274673	−	0.961538i	$-0.588569\pi$
$479$	−243681.	−	79176.8i	−1.06207	−	0.345086i	−0.787392	+	0.616452i	$0.788569\pi$
$480$	−19214.0	−	26445.8i	−0.0833942	−	0.114782i
$481$	117395.	−	161581.i	0.507412	−	0.698393i
$482$	−34280.8	−	105505.i	−0.147556	−	0.454131i
$483$		−	213786.i		−	0.916399i
$484$	−22474.7	+	114952.i	−0.0959408	+	0.490709i
$485$	−444645.			−1.89030
$486$	158667.	−	51554.1i	0.671761	−	0.218268i
$487$	−181763.	−	132058.i	−0.766385	−	0.556811i	0.134477	−	0.990917i	$-0.457065\pi$
$487$	−181763.	−	132058.i	−0.766385	−	0.556811i	−0.900862	+	0.434105i	$0.857065\pi$
$488$	61031.8	−	44342.2i	0.256281	−	0.186199i
$489$	40696.5	−	125251.i	0.170192	−	0.523798i
$490$	434080.	+	141041.i	1.80791	+	0.587427i
$491$	58960.8	+	81152.6i	0.244568	+	0.336620i	0.913600	−	0.406615i	$-0.133291\pi$
$491$	58960.8	+	81152.6i	0.244568	+	0.336620i	−0.669031	+	0.743234i	$0.733291\pi$
$492$	42437.0	−	58409.5i	0.175313	−	0.241298i
$493$	42763.5	+	131612.i	0.175946	+	0.541506i
$494$			78350.9i			0.321063i
$495$	−71642.4	−	182167.i	−0.292388	−	0.743461i
$496$	−32170.9			−0.130768
$497$	276231.	−	89753.0i	1.11831	−	0.363359i
$498$	−51769.6	−	37612.8i	−0.208745	−	0.151662i
$499$	−208468.	+	151461.i	−0.837217	+	0.608274i	−0.921592	−	0.388160i	$-0.873111\pi$
$499$	−208468.	+	151461.i	−0.837217	+	0.608274i	0.0843746	+	0.996434i	$0.473111\pi$
$500$	−16045.8	+	49383.8i	−0.0641831	+	0.197535i
$501$	−3438.46	−	1117.22i	−0.0136990	−	0.00445107i
$502$	137760.	+	189610.i	0.546657	+	0.752409i
$503$	238719.	−	328568.i	0.943518	−	1.29864i	−0.0108292	−	0.999941i	$-0.503447\pi$
$503$	238719.	−	328568.i	0.943518	−	1.29864i	0.954347	−	0.298700i	$-0.0965529\pi$
$504$	29997.4	+	92322.6i	0.118093	+	0.363452i
$505$			311499.i			1.22145i
$506$	−97118.6	−	117945.i	−0.379316	−	0.460660i
$507$	−100061.			−0.389268
$508$	−236463.	+	76831.6i	−0.916297	+	0.297723i
$509$	−263060.	−	191124.i	−1.01536	−	0.737700i	−0.0500314	−	0.998748i	$-0.515932\pi$
$509$	−263060.	−	191124.i	−1.01536	−	0.737700i	−0.965326	+	0.261047i	$0.915932\pi$
$510$	52580.9	−	38202.2i	0.202156	−	0.146875i
$511$	200676.	−	617616.i	0.768516	−	2.36525i
$512$	11018.2	+	3580.04i	0.0420312	+	0.0136568i
$513$	−115367.	−	158789.i	−0.438375	−	0.603372i
$514$	−9823.87	+	13521.4i	−0.0371840	+	0.0511794i
$515$	−11059.5	−	34037.7i	−0.0416986	−	0.128335i
$516$			64289.4i			0.241457i
$517$	−100031.	+	385920.i	−0.374242	+	1.44383i
$518$	−471217.			−1.75615
$519$	−122090.	+	39669.6i	−0.453259	+	0.147273i
$520$	−61087.6	−	44382.7i	−0.225916	−	0.164137i
$521$	−322750.	+	234492.i	−1.18903	+	0.863878i	−0.993161	−	0.116753i	$-0.962751\pi$
$521$	−322750.	+	234492.i	−1.18903	+	0.863878i	−0.195865	+	0.980631i	$0.562751\pi$
$522$	−47463.0	+	146076.i	−0.174186	+	0.536090i
$523$	295038.	+	95863.6i	1.07863	+	0.350470i	0.793845	−	0.608120i	$-0.208076\pi$
$523$	295038.	+	95863.6i	1.07863	+	0.350470i	0.284790	+	0.958590i	$0.408076\pi$
$524$	−41050.7	−	56501.5i	−0.149506	−	0.205777i
$525$	119534.	−	164524.i	0.433683	−	0.596914i
$526$	−94352.8	−	290388.i	−0.341023	−	1.04956i
$527$		−	63963.8i		−	0.230310i
$528$	−36390.9	−	23211.5i	−0.130535	−	0.0832600i
$529$	−80545.0			−0.287824
$530$	255708.	−	83084.4i	0.910315	−	0.295779i
$531$	65123.5	+	47315.0i	0.230966	+	0.167807i
$532$	149551.	−	108655.i	0.528405	−	0.383909i
$533$	51535.2	−	158609.i	0.181405	−	0.558307i
$534$	90453.0	+	29390.0i	0.317205	+	0.103066i
$535$	183944.	+	253177.i	0.642654	+	0.884538i
$536$	28561.2	−	39311.1i	0.0994137	−	0.136831i
$537$	−11059.8	−	34038.6i	−0.0383530	−	0.118038i
$538$		−	44172.8i		−	0.152613i
$539$	601565.	−	36463.4i	2.07064	−	0.125510i
$540$	189153.			0.648674
$541$	−356881.	+	115958.i	−1.21935	+	0.396191i	−0.846845	−	0.531839i	$-0.821501\pi$
$541$	−356881.	+	115958.i	−1.21935	+	0.396191i	−0.372505	+	0.928030i	$0.621501\pi$
$542$	78392.9	+	56955.8i	0.266857	+	0.193883i
$543$	193494.	−	140582.i	0.656249	−	0.476792i
$544$	−7117.99	+	21906.9i	−0.0240525	+	0.0740259i
$545$	−21129.9	−	6865.52i	−0.0711384	−	0.0231143i
$546$	−82002.8	−	112867.i	−0.275070	−	0.378602i
$547$	−129542.	+	178299.i	−0.432947	+	0.595901i	−0.968627	−	0.248521i	$-0.920056\pi$
$547$	−129542.	+	178299.i	−0.432947	+	0.595901i	0.535679	+	0.844422i	$0.320056\pi$
$548$	−65283.3	−	200921.i	−0.217391	−	0.669060i
$549$			166476.i			0.552339i
$550$	−8793.30	−	145070.i	−0.0290688	−	0.479570i
$551$	292485.			0.963386
$552$	53547.7	−	17398.7i	0.175737	−	0.0571003i
$553$	−449886.	−	326862.i	−1.47114	−	1.06884i
$554$	−165056.	+	119920.i	−0.537789	+	0.390727i
$555$	−108207.	+	333026.i	−0.351292	+	1.08116i
$556$	134949.	+	43847.5i	0.436536	+	0.141839i
$557$	252579.	+	347646.i	0.814118	+	1.12054i	0.990675	+	0.136247i	$0.0435040\pi$
$557$	252579.	+	347646.i	0.814118	+	1.12054i	−0.176557	+	0.984290i	$0.556496\pi$
$558$	41728.7	−	57434.6i	0.134019	−	0.184461i
$559$	45889.9	+	141235.i	0.146857	+	0.451979i
$560$			178149.i			0.568078i
$561$	46150.3	−	72354.2i	0.146639	−	0.229899i
$562$	−287642.			−0.910710
$563$	−438495.	+	142476.i	−1.38340	+	0.449494i	−0.903786	−	0.427984i	$-0.859224\pi$
$563$	−438495.	+	142476.i	−1.38340	+	0.449494i	−0.479615	+	0.877479i	$0.659224\pi$
$564$	−118858.	−	86355.6i	−0.373655	−	0.271477i
$565$	150128.	−	109074.i	0.470288	−	0.341685i
$566$	2666.69	−	8207.23i	0.00832414	−	0.0256191i
$567$	1890.17	+	614.155i	0.00587944	+	0.00191034i
$568$	44961.5	+	61884.2i	0.139362	+	0.191815i
$569$	−98286.5	+	135280.i	−0.303577	+	0.417838i	−0.933365	−	0.358929i	$-0.883142\pi$
$569$	−98286.5	+	135280.i	−0.303577	+	0.417838i	0.629788	+	0.776767i	$0.283142\pi$
$570$	−42448.8	−	130644.i	−0.130652	−	0.402105i
$571$			317894.i			0.975012i	0.873119	+	0.487506i	$0.162093\pi$
$571$			317894.i			0.975012i	−0.873119	+	0.487506i	$0.837907\pi$
$572$	−96514.2	−	25016.5i	−0.294985	−	0.0764602i
$573$	142283.			0.433356
$574$	−374211.	+	121588.i	−1.13578	+	0.369036i
$575$	153374.	+	111432.i	0.463890	+	0.337036i
$576$	−20683.1	+	15027.1i	−0.0623404	+	0.0452930i
$577$	93148.0	−	286680.i	0.279783	−	0.861084i	−0.708131	−	0.706081i	$-0.750461\pi$
$577$	93148.0	−	286680.i	0.279783	−	0.861084i	0.987914	−	0.155003i	$-0.0495388\pi$
$578$	181115.	+	58847.7i	0.542123	+	0.176146i
$579$	138195.	+	190209.i	0.412226	+	0.567381i
$580$	−165681.	+	228041.i	−0.492513	+	0.677886i
$581$	107767.	+	331671.i	0.319251	+	0.982553i
$582$		−	216364.i		−	0.638761i
$583$	274066.	−	225671.i	0.806339	−	0.663955i
$584$	171028.			0.501467
$585$	158473.	−	51490.9i	0.463065	−	0.150459i
$586$	−26491.3	−	19247.1i	−0.0771452	−	0.0560492i
$587$	371096.	−	269617.i	1.07699	−	0.782477i	0.0998318	−	0.995004i	$-0.468170\pi$
$587$	371096.	−	269617.i	1.07699	−	0.782477i	0.977155	+	0.212528i	$0.0681695\pi$
$588$	−68630.3	+	211222.i	−0.198500	+	0.610922i
$589$	−128574.	−	41776.2i	−0.370615	−	0.120420i
$590$	86832.3	+	119514.i	0.249447	+	0.343334i
$591$	−123176.	+	169537.i	−0.352656	+	0.485390i
$592$	−38349.4	−	118027.i	−0.109425	−	0.336775i
$593$		−	32457.6i		−	0.0923011i	−0.998934	−	0.0461506i	$-0.985305\pi$
$593$		−	32457.6i		−	0.0923011i	0.998934	−	0.0461506i	$-0.0146954\pi$
$594$	232435.	−	91411.7i	0.658761	−	0.259077i
$595$	−354205.			−1.00051
$596$	143806.	−	46725.2i	0.404840	−	0.131540i
$597$	−168874.	−	122694.i	−0.473821	−	0.344251i
$598$	105217.	−	76445.0i	0.294229	−	0.213770i
$599$	−213563.	+	657279.i	−0.595213	+	1.83188i	−0.0415485	+	0.999136i	$0.513229\pi$
$599$	−213563.	+	657279.i	−0.595213	+	1.83188i	−0.553664	+	0.832740i	$0.686771\pi$
$600$	50937.2	+	16550.5i	0.141492	+	0.0459736i
$601$	−50232.0	−	69138.5i	−0.139070	−	0.191413i	0.733801	−	0.679364i	$-0.237744\pi$
$601$	−50232.0	−	69138.5i	−0.139070	−	0.191413i	−0.872871	+	0.487951i	$0.837744\pi$
$602$	205941.	−	283453.i	0.568263	−	0.782147i
$603$	33135.4	+	101980.i	0.0911291	+	0.280467i
$604$			3595.60i			0.00985592i
$605$	−199998.	−	430123.i	−0.546404	−	1.17512i
$606$	−151575.			−0.412745
$607$	126369.	−	41059.7i	0.342975	−	0.111439i	−0.132465	−	0.991188i	$-0.542289\pi$
$607$	126369.	−	41059.7i	0.342975	−	0.111439i	0.475439	+	0.879748i	$0.342289\pi$
$608$	39386.3	+	28615.9i	0.106546	+	0.0774104i
$609$	−421335.	+	306118.i	−1.13604	+	0.825380i
$610$	−94409.5	+	290562.i	−0.253721	+	0.780872i
$611$	−322756.	−	104870.i	−0.864553	−	0.280910i
$612$	−29877.6	−	41123.0i	−0.0797707	−	0.109795i
$613$	387238.	−	532987.i	1.03052	−	1.41839i	0.125965	−	0.992035i	$-0.459797\pi$
$613$	387238.	−	532987.i	1.03052	−	1.41839i	0.904556	−	0.426355i	$-0.140203\pi$
$614$	23376.5	+	71945.6i	0.0620074	+	0.190839i
$615$			292389.i			0.773055i
$616$	86093.9	+	218913.i	0.226888	+	0.576912i
$617$	116511.			0.306053			0.153026	−	0.988222i	$-0.451098\pi$
$617$	116511.			0.306053			0.153026	+	0.988222i	$0.451098\pi$
$618$	16562.7	−	5381.53i	0.0433664	−	0.0140906i
$619$	102297.	+	74322.9i	0.266981	+	0.193973i	0.713219	−	0.700941i	$-0.247237\pi$
$619$	102297.	+	74322.9i	0.266981	+	0.193973i	−0.446238	+	0.894914i	$0.647237\pi$
$620$	105404.	−	76580.3i	0.274203	−	0.199220i
$621$	−100677.	+	309852.i	−0.261064	+	0.803473i
$622$	−106963.	−	34754.4i	−0.276473	−	0.0898315i
$623$	−304663.	−	419333.i	−0.784953	−	1.08039i
$624$	21596.6	−	29725.1i	0.0554645	−	0.0763404i
$625$	−147000.	−	452418.i	−0.376319	−	1.15819i
$626$		−	241646.i		−	0.616638i
$627$	−115298.	−	140023.i	−0.293282	−	0.356176i
$628$	285707.			0.724439
$629$	234668.	−	76248.1i	0.593133	−	0.192720i
$630$	−318049.	−	231076.i	−0.801333	−	0.582202i
$631$	387143.	−	281276.i	0.972328	−	0.706437i	0.0163467	−	0.999866i	$-0.494796\pi$
$631$	387143.	−	281276.i	0.972328	−	0.706437i	0.955981	+	0.293429i	$0.0947965\pi$
$632$	45256.7	−	139286.i	0.113305	−	0.348717i
$633$	−176781.	−	57439.6i	−0.441192	−	0.143352i
$634$	−40808.1	−	56167.5i	−0.101524	−	0.139735i
$635$	591849.	−	814610.i	1.46779	−	2.02024i
$636$	40428.7	+	124427.i	0.0999484	+	0.307609i
$637$			513014.i			1.26430i
$638$	−93387.1	+	360289.i	−0.229428	+	0.885135i
$639$	−168801.			−0.413402
$640$	−44621.7	+	14498.5i	−0.108940	+	0.0353966i
$641$	−562038.	−	408345.i	−1.36789	−	0.993827i	−0.997899	−	0.0647894i	$-0.979362\pi$
$641$	−562038.	−	408345.i	−1.36789	−	0.993827i	−0.369986	−	0.929037i	$-0.620638\pi$
$642$	−123195.	+	89506.7i	−0.298899	+	0.217163i
$643$	74090.8	−	228028.i	0.179202	−	0.551526i	−0.820599	−	0.571505i	$-0.806360\pi$
$643$	74090.8	−	228028.i	0.179202	−	0.551526i	0.999800	+	0.0199785i	$0.00635978\pi$
$644$	−291827.	−	94820.2i	−0.703644	−	0.228628i
$645$	−153036.	−	210636.i	−0.367852	−	0.506305i
$646$	−56895.4	+	78309.8i	−0.136336	+	0.187651i
$647$	−126061.	−	387977.i	−0.301143	−	0.926824i	−0.981088	−	0.193561i	$-0.937996\pi$
$647$	−126061.	−	387977.i	−0.301143	−	0.926824i	0.679945	−	0.733263i	$-0.262004\pi$
$648$			523.421i			0.00124653i
$649$	164459.	+	104898.i	0.390451	+	0.249045i
$650$	123716.			0.292818
$651$	228939.	−	74386.7i	0.540204	−	0.175523i
$652$	−152923.	−	111105.i	−0.359731	−	0.261360i
$653$	293149.	−	212985.i	0.687483	−	0.499486i	−0.188349	−	0.982102i	$-0.560314\pi$
$653$	293149.	−	212985.i	0.687483	−	0.499486i	0.875832	+	0.482617i	$0.160314\pi$
$654$	3340.75	−	10281.8i	0.00781067	−	0.0240388i
$655$	268994.	+	87401.6i	0.626990	+	0.203721i
$656$	−60909.4	−	83834.6i	−0.141539	−	0.194812i
$657$	−221839.	+	305336.i	−0.513935	+	0.707371i
$658$	247422.	+	761487.i	0.571461	+	1.75878i
$659$			56157.5i			0.129311i	0.997908	+	0.0646557i	$0.0205949\pi$
$659$			56157.5i			0.129311i	−0.997908	+	0.0646557i	$0.979405\pi$
$660$	174483.	−	10576.2i	0.400558	−	0.0242795i
$661$	−43617.9			−0.0998301			−0.0499150	−	0.998753i	$-0.515895\pi$
$661$	−43617.9			−0.0998301			−0.0499150	+	0.998753i	$0.515895\pi$
$662$	237770.	−	77256.3i	0.542553	−	0.176286i
$663$	59100.8	+	42939.3i	0.134452	+	0.0976850i
$664$	−74304.5	+	53985.4i	−0.168531	+	0.122445i
$665$	−231339.	+	711989.i	−0.523126	+	1.61002i
$666$	260456.	+	84627.4i	0.587201	+	0.190793i
$667$	−285370.	−	392778.i	−0.641441	−	0.882868i
$668$	−3050.12	+	4198.12i	−0.00683539	+	0.00940811i
$669$	52889.5	+	162777.i	0.118173	+	0.363698i
$670$			196785.i			0.438372i
$671$	24407.7	+	402673.i	0.0542103	+	0.894350i
$672$	−86687.1			−0.191962
$673$	2428.77	−	789.155i	0.00536237	−	0.00174234i	−0.306335	−	0.951924i	$-0.599103\pi$
$673$	2428.77	−	789.155i	0.00536237	−	0.00174234i	0.311697	+	0.950182i	$0.399103\pi$
$674$	232690.	+	169059.i	0.512222	+	0.372151i
$675$	−250726.	+	182163.i	−0.550291	+	0.399810i
$676$	−44380.0	+	136587.i	−0.0971166	+	0.298894i
$677$	460823.	+	149731.i	1.00544	+	0.326688i	0.765038	−	0.643985i	$-0.222720\pi$
$677$	460823.	+	149731.i	1.00544	+	0.326688i	0.240404	+	0.970673i	$0.422720\pi$
$678$	53075.3	+	73051.9i	0.115460	+	0.158918i
$679$	−693086.	+	953951.i	−1.50331	+	2.06912i
$680$	−28826.5	−	88718.9i	−0.0623411	−	0.191866i
$681$		−	51500.4i		−	0.111049i
$682$	92513.0	−	145041.i	0.198900	−	0.311834i
$683$	−498694.			−1.06904			−0.534519	−	0.845157i	$-0.679507\pi$
$683$	−498694.			−1.06904			−0.534519	+	0.845157i	$0.679507\pi$
$684$	−102175.	+	33198.8i	−0.218391	+	0.0709595i
$685$	692169.	+	502891.i	1.47513	+	1.07175i
$686$	507175.	−	368484.i	1.07773	−	0.783016i
$687$	132367.	−	407385.i	0.280458	−	0.863161i
$688$	87757.8	+	28514.2i	0.185400	+	0.0602400i
$689$	177632.	+	244490.i	0.374183	+	0.515018i
$690$	−134026.	+	184470.i	−0.281507	+	0.387462i
$691$	44449.9	+	136803.i	0.0930924	+	0.286509i	0.986752	−	0.162237i	$-0.0518709\pi$
$691$	44449.9	+	136803.i	0.0930924	+	0.286509i	−0.893659	+	0.448746i	$0.851871\pi$
$692$			184253.i			0.384771i
$693$	−502495.	−	130247.i	−1.04632	−	0.271207i
$694$	−104327.			−0.216609
$695$	−546517.	+	177574.i	−1.13145	+	0.367630i
$696$	−110964.	−	80620.3i	−0.229068	−	0.166428i
$697$	166684.	−	121103.i	0.343106	−	0.249281i
$698$	90404.2	−	278236.i	0.185557	−	0.571087i
$699$	−59555.6	−	19350.8i	−0.121890	−	0.0396045i
$700$	−171566.	−	236140.i	−0.350135	−	0.481919i
$701$	271424.	−	373582.i	0.552346	−	0.760240i	−0.437982	−	0.898984i	$-0.644307\pi$
$701$	271424.	−	373582.i	0.552346	−	0.760240i	0.990328	+	0.138744i	$0.0443066\pi$
$702$	65699.5	+	202202.i	0.133318	+	0.410310i
$703$		−	521506.i		−	1.05523i
$704$	−47825.2	+	39380.2i	−0.0964965	+	0.0794571i
$705$	594986.			1.19709
$706$	−135679.	+	44084.8i	−0.272210	+	0.0884464i
$707$	668297.	+	485546.i	1.33700	+	0.971385i
$708$	−58155.5	+	42252.4i	−0.116018	+	0.0842918i
$709$	88470.5	−	272284.i	0.175997	−	0.541664i	−0.823680	−	0.567055i	$-0.808083\pi$
$709$	88470.5	−	272284.i	0.175997	−	0.541664i	0.999678	+	0.0253903i	$0.00808286\pi$
$710$	−294621.	−	95728.1i	−0.584449	−	0.189899i
$711$	189964.	+	261463.i	0.375779	+	0.517216i
$712$	80237.1	−	110437.i	0.158276	−	0.217848i
$713$	69345.0	+	213422.i	0.136407	+	0.419817i
$714$		−	172355.i		−	0.338087i
$715$	375766.	−	147781.i	0.735030	−	0.289072i
$716$	−51369.5			−0.100203
$717$	−146795.	+	47696.7i	−0.285545	+	0.0927792i
$718$	−199637.	−	145044.i	−0.387250	−	0.281354i
$719$	−58393.7	+	42425.5i	−0.112956	+	0.0820672i	−0.642829	−	0.766010i	$-0.722239\pi$
$719$	−58393.7	+	42425.5i	−0.112956	+	0.0820672i	0.529873	+	0.848077i	$0.322239\pi$
$720$	31994.4	−	98468.7i	0.0617176	−	0.189947i
$721$	−90263.9	−	29328.5i	−0.173638	−	0.0564183i
$722$	−96408.4	−	132695.i	−0.184944	−	0.254554i
$723$	−128497.	+	176861.i	−0.245819	+	0.338341i
$724$	−106080.	−	326480.i	−0.202374	−	0.622844i
$725$		−	461832.i		−	0.878634i
$726$	209297.	−	97318.4i	0.397090	−	0.184638i
$727$	−620396.			−1.17382			−0.586908	−	0.809653i	$-0.699655\pi$
$727$	−620396.			−1.17382			−0.586908	+	0.809653i	$0.699655\pi$
$728$	−190439.	+	61877.5i	−0.359330	+	0.116753i
$729$	−267492.	−	194345.i	−0.503334	−	0.365694i
$730$	−560351.	+	407119.i	−1.05151	+	0.763969i
$731$	−56693.3	+	174484.i	−0.106096	+	0.326529i
$732$	−141387.	−	45939.5i	−0.263869	−	0.0857361i
$733$	28232.2	+	38858.3i	0.0525456	+	0.0723229i	0.834481	−	0.551036i	$-0.185767\pi$
$733$	28232.2	+	38858.3i	0.0525456	+	0.0723229i	−0.781936	+	0.623359i	$0.785767\pi$
$734$	−86034.9	+	118417.i	−0.159692	+	0.219797i
$735$	−277940.	−	855411.i	−0.514489	−	1.58343i
$736$		−	80811.7i		−	0.149183i
$737$	95099.9	+	241813.i	0.175083	+	0.445188i
$738$	228675.			0.419861
$739$	41233.3	−	13397.5i	0.0755021	−	0.0245321i	−0.271022	−	0.962573i	$-0.587362\pi$
$739$	41233.3	−	13397.5i	0.0755021	−	0.0245321i	0.346525	+	0.938041i	$0.387362\pi$
$740$	406601.	+	295413.i	0.742515	+	0.539469i
$741$	124913.	−	90754.4i	0.227494	−	0.165284i
$742$	220330.	−	678107.i	0.400190	−	1.23166i
$743$	311459.	+	101199.i	0.564187	+	0.183315i	0.577204	−	0.816600i	$-0.304144\pi$
$743$	311459.	+	101199.i	0.564187	+	0.183315i	−0.0130172	+	0.999915i	$0.504144\pi$
$744$	37263.8	+	51289.3i	0.0673196	+	0.0926575i
$745$	−359934.	+	495406.i	−0.648500	+	0.892584i
$746$	−157355.	−	484290.i	−0.282751	−	0.870217i
$747$		−	202679.i		−	0.363219i
$748$	−78297.5	−	95088.3i	−0.139941	−	0.169951i
$749$	829891.			1.47930
$750$	97317.2	−	31620.3i	0.173008	−	0.0562138i
$751$	157605.	+	114507.i	0.279441	+	0.203026i	0.718674	−	0.695347i	$-0.244749\pi$
$751$	157605.	+	114507.i	0.279441	+	0.203026i	−0.439232	+	0.898374i	$0.644749\pi$
$752$	−170596.	+	123945.i	−0.301671	+	0.219177i
$753$	142722.	−	439254.i	0.251711	−	0.774685i
$754$	−301320.	−	97904.7i	−0.530011	−	0.172211i
$755$	−8559.03	−	11780.5i	−0.0150152	−	0.0206666i
$756$	294840.	−	405813.i	0.515874	−	0.710039i
$757$	118949.	+	366087.i	0.207572	+	0.638841i	0.999598	+	0.0283533i	$0.00902635\pi$
$757$	118949.	+	366087.i	0.207572	+	0.638841i	−0.792026	+	0.610487i	$0.790974\pi$
$758$			524698.i			0.913210i
$759$	−75544.2	+	291451.i	−0.131135	+	0.505919i
$760$	−197162.			−0.341347
$761$	−263860.	+	85733.3i	−0.455622	+	0.148040i	−0.527832	−	0.849349i	$-0.676995\pi$
$761$	−263860.	+	85733.3i	−0.455622	+	0.148040i	0.0722100	+	0.997389i	$0.476995\pi$
$762$	396388.	+	287992.i	0.682669	+	0.495988i
$763$	−47665.4	+	34630.9i	−0.0818755	+	0.0594861i
$764$	63106.8	−	194223.i	0.108116	−	0.332747i
$765$	195780.	+	63612.8i	0.334538	+	0.108698i
$766$	10520.5	+	14480.3i	0.0179300	+	0.0246785i
$767$	−97599.5	+	134334.i	−0.165904	+	0.228347i
$768$	−7054.92	−	21712.8i	−0.0119611	−	0.0368124i
$769$		−	927410.i		−	1.56826i	−0.620595	−	0.784131i	$-0.713109\pi$
$769$		−	927410.i		−	1.56826i	0.620595	−	0.784131i	$-0.286891\pi$
$770$	−803179.	−	512299.i	−1.35466	−	0.864056i
$771$	32935.9			0.0554064
$772$	320938.	−	104279.i	0.538500	−	0.174969i
$773$	−82488.3	−	59931.2i	−0.138049	−	0.100298i	0.516618	−	0.856216i	$-0.327191\pi$
$773$	−82488.3	−	59931.2i	−0.138049	−	0.100298i	−0.654666	+	0.755918i	$0.727191\pi$
$774$	−164736.	+	119688.i	−0.274984	+	0.199787i
$775$	−65964.4	+	203017.i	−0.109826	+	0.338010i
$776$	−295345.	−	95963.6i	−0.490464	−	0.159361i
$777$	545814.	+	751248.i	0.904071	+	1.24435i
$778$	183222.	−	252183.i	0.302704	−	0.416636i
$779$	−134565.	−	414148.i	−0.221746	−	0.682465i
$780$			148799.i			0.244575i
$781$	−408297.	+	24748.6i	−0.669383	+	0.0405741i
$782$	160674.			0.262743
$783$	754824.	−	245257.i	1.23118	−	0.400035i
$784$	257888.	+	187367.i	0.419565	+	0.304832i
$785$	−936081.	+	680103.i	−1.51906	+	1.10366i
$786$	−42529.4	+	130892.i	−0.0688406	+	0.211869i
$787$	−746565.	−	242574.i	−1.20536	−	0.391646i	−0.363632	−	0.931543i	$-0.618463\pi$
$787$	−746565.	−	242574.i	−1.20536	−	0.391646i	−0.841732	+	0.539896i	$0.818463\pi$
$788$	176794.	+	243336.i	0.284717	+	0.391880i
$789$	−353668.	+	486783.i	−0.568123	+	0.781954i
$790$	183281.	+	564082.i	0.293673	+	0.903832i
$791$		−	492105.i		−	0.786512i
$792$	−8271.53	−	136462.i	−0.0131867	−	0.217551i
$793$	−343399.			−0.546076
$794$	553494.	−	179841.i	0.877954	−	0.285264i
$795$	−428647.	−	311430.i	−0.678212	−	0.492750i
$796$	−242383.	+	176102.i	−0.382540	+	0.277931i
$797$	146626.	−	451268.i	0.230831	−	0.710424i	−0.766816	−	0.641867i	$-0.778160\pi$
$797$	146626.	−	451268.i	0.230831	−	0.710424i	0.997647	−	0.0685576i	$-0.0218397\pi$
$798$	−346453.	−	112569.i	−0.544049	−	0.176772i
$799$	−246434.	−	339187.i	−0.386018	−	0.531308i
$800$	45184.2	−	62190.8i	0.0706004	−	0.0971731i
$801$	93087.4	+	286494.i	0.145086	+	0.446529i
$802$			372591.i			0.579274i
$803$	−491821.	+	771074.i	−0.762739	+	1.19582i
$804$	−95755.2			−0.148132
$805$	1.18184e6	−	384004.i	1.82376	−	0.592576i
$806$	118474.	+	86076.2i	0.182369	+	0.132499i
$807$	−70423.5	+	51165.7i	−0.108136	+	0.0785654i
$808$	−67227.9	+	206906.i	−0.102974	+	0.316921i
$809$	325525.	+	105770.i	0.497379	+	0.161608i	0.546955	−	0.837162i	$-0.315787\pi$
$809$	325525.	+	105770.i	0.497379	+	0.161608i	−0.0495756	+	0.998770i	$0.515787\pi$
$810$	−1245.96	−	1714.92i	−0.00189904	−	0.00261381i
$811$	267565.	−	368272.i	0.406807	−	0.559922i	−0.555629	−	0.831430i	$-0.687523\pi$
$811$	267565.	−	368272.i	0.406807	−	0.559922i	0.962436	+	0.271509i	$0.0875226\pi$
$812$	230990.	+	710913.i	0.350332	+	1.07821i
$813$		−	190952.i		−	0.288897i
$814$	642402.	+	166511.i	0.969523	+	0.251301i
$815$	765508.			1.15248
$816$	43170.4	−	14026.9i	0.0648345	−	0.0210660i
$817$	313704.	+	227919.i	0.469976	+	0.341458i
$818$	−181713.	+	132022.i	−0.271569	+	0.197306i
$819$	136548.	−	420251.i	0.203571	−	0.626529i
$820$	399123.	+	129683.i	0.593580	+	0.192866i
$821$	−233166.	−	320925.i	−0.345923	−	0.476122i	0.600237	−	0.799822i	$-0.295073\pi$
$821$	−233166.	−	320925.i	−0.345923	−	0.476122i	−0.946160	+	0.323701i	$0.895073\pi$
$822$	−244705.	+	336808.i	−0.362160	+	0.498470i
$823$	300791.	+	925738.i	0.444083	+	1.36675i	0.883486	+	0.468458i	$0.155190\pi$
$823$	300791.	+	925738.i	0.444083	+	1.36675i	−0.439402	+	0.898290i	$0.644810\pi$
$824$		−	24995.6i		−	0.0368137i
$825$	−221096.	+	182054.i	−0.324842	+	0.267481i
$826$	391758.			0.574192
$827$	136766.	−	44438.1i	0.199972	−	0.0649748i	−0.207319	−	0.978273i	$-0.566474\pi$
$827$	136766.	−	44438.1i	0.199972	−	0.0649748i	0.407290	+	0.913299i	$0.366474\pi$
$828$	144273.	+	104820.i	0.210438	+	0.152892i
$829$	289762.	−	210524.i	0.421631	−	0.306333i	−0.356663	−	0.934233i	$-0.616086\pi$
$829$	289762.	−	210524.i	0.421631	−	0.306333i	0.778294	+	0.627901i	$0.216086\pi$
$830$	114941.	−	353752.i	0.166847	−	0.513502i
$831$	382371.	+	124240.i	0.553711	+	0.179912i
$832$	−30997.3	−	42664.2i	−0.0447793	−	0.0616335i
$833$	−372531.	+	512745.i	−0.536874	+	0.738944i
$834$	−86407.3	−	265934.i	−0.124228	−	0.382333i
$835$		−	21015.1i		−	0.0301411i
$836$	−242276.	+	95282.0i	−0.346655	+	0.136332i
$837$	−366845.			−0.523639
$838$	−756291.	+	245734.i	−1.07696	+	0.349927i
$839$	−1.09425e6	−	795018.i	−1.55451	−	1.12941i	−0.940340	−	0.340237i	$-0.889493\pi$
$839$	−1.09425e6	−	795018.i	−1.55451	−	1.12941i	−0.614166	−	0.789177i	$-0.710507\pi$
$840$	284019.	−	206352.i	0.402521	−	0.292448i
$841$	−146918.	+	452167.i	−0.207722	+	0.639304i
$842$	−892043.	−	289842.i	−1.25823	−	0.408825i
$843$	333178.	+	458580.i	0.468836	+	0.645298i
$844$	−156815.	+	215837.i	−0.220142	+	0.302999i
$845$	−179730.	−	553153.i	−0.251714	−	0.774698i
$846$		−	465333.i		−	0.650165i
$847$	−1.23454e6	−	241370.i	−1.72083	−	0.336447i
$848$	187779.			0.261129
$849$	−16173.4	+	5255.06i	−0.0224381	+	0.00729058i
$850$	123651.	+	89837.4i	0.171143	+	0.124342i
$851$	−700331.	+	508820.i	−0.967040	+	0.702596i
$852$	46581.1	−	143362.i	0.0641698	−	0.197494i
$853$	691608.	+	224717.i	0.950521	+	0.308843i	0.742927	−	0.669372i	$-0.233437\pi$
$853$	691608.	+	224717.i	0.950521	+	0.308843i	0.207594	+	0.978215i	$0.433437\pi$
$854$	476219.	+	655459.i	0.652966	+	0.898731i
$855$	255737.	−	351992.i	0.349834	−	0.481505i
$856$	67539.7	+	207866.i	0.0921746	+	0.283684i
$857$		−	269066.i		−	0.366351i	−0.983080	−	0.183175i	$-0.941362\pi$
$857$		−	269066.i		−	0.366351i	0.983080	−	0.183175i	$-0.0586376\pi$
$858$	71909.9	+	182847.i	0.0976819	+	0.248378i
$859$	919865.			1.24663			0.623315	−	0.781971i	$-0.285785\pi$
$859$	919865.			1.24663			0.623315	+	0.781971i	$0.285785\pi$
$860$	−355402.	+	115477.i	−0.480533	+	0.156135i
$861$	627296.	+	455757.i	0.846187	+	0.614791i
$862$	285450.	−	207392.i	0.384163	−	0.279111i
$863$	−89869.0	+	276588.i	−0.120667	+	0.371374i	−0.993087	−	0.117383i	$-0.962550\pi$
$863$	−89869.0	+	276588.i	−0.120667	+	0.371374i	0.872420	+	0.488757i	$0.162550\pi$
$864$	125641.	+	40823.1i	0.168307	+	0.0546863i
$865$	−438600.	−	603681.i	−0.586187	−	0.806817i
$866$	42788.4	−	58893.2i	0.0570546	−	0.0785289i
$867$	−115967.	−	356910.i	−0.154275	−	0.474811i
$868$		−	345504.i		−	0.458578i
$869$	497822.	+	604579.i	0.659226	+	0.800596i
$870$	555470.			0.733875
$871$	−210361.	+	68350.3i	−0.277286	+	0.0900957i
$872$	−12553.3	−	9120.53i	−0.0165092	−	0.0119946i
$873$	554414.	−	402805.i	0.727454	−	0.528526i
$874$	104940.	−	322971.i	0.137378	−	0.422806i
$875$	−530364.	−	172326.i	−0.692720	−	0.225078i
$876$	−198103.	−	272666.i	−0.258157	−	0.355322i
$877$	6751.69	−	9292.90i	0.00877835	−	0.0120824i	−0.804605	−	0.593810i	$-0.797623\pi$
$877$	6751.69	−	9292.90i	0.00877835	−	0.0120824i	0.813384	+	0.581728i	$0.197623\pi$
$878$	−108258.	−	333184.i	−0.140434	−	0.432210i
$879$			64528.5i			0.0835168i
$880$	62951.5	−	242868.i	0.0812907	−	0.313621i
$881$	−742939.			−0.957197			−0.478599	−	0.878034i	$-0.658855\pi$
$881$	−742939.			−0.957197			−0.478599	+	0.878034i	$0.658855\pi$
$882$	−669009.	+	217374.i	−0.859993	+	0.279429i
$883$	945222.	+	686744.i	1.21231	+	0.880792i	0.995438	−	0.0954091i	$-0.0304159\pi$
$883$	945222.	+	686744.i	1.21231	+	0.880792i	0.216868	+	0.976201i	$0.430416\pi$
$884$	84826.9	−	61630.4i	0.108550	−	0.0788661i
$885$	89960.2	−	276869.i	0.114859	−	0.353499i
$886$	−199275.	−	64748.4i	−0.253855	−	0.0824824i
$887$	−382008.	−	525789.i	−0.485540	−	0.668289i	0.494018	−	0.869452i	$-0.335528\pi$
$887$	−382008.	−	525789.i	−0.485540	−	0.668289i	−0.979558	+	0.201163i	$0.935528\pi$
$888$	−143747.	+	197851.i	−0.182295	+	0.250907i
$889$	−825143.	−	2.53953e6i	−1.04406	−	3.21329i
$890$			552830.i			0.697929i
$891$	−2359.82	−	1505.19i	−0.00297251	−	0.00189598i
$892$	245656.			0.308743
$893$	−842755.	+	273828.i	−1.05681	+	0.343379i
$894$	−241064.	−	175143.i	−0.301618	−	0.219138i
$895$	168305.	−	122281.i	0.210113	−	0.152656i
$896$	−38448.3	+	118332.i	−0.0478917	+	0.147396i
$897$	−243748.	−	79198.6i	−0.302940	−	0.0984312i
$898$	−383723.	−	528150.i	−0.475845	−	0.654944i
$899$	321324.	−	442264.i	0.397579	−	0.547221i
$900$	52420.7	+	161334.i	0.0647169	+	0.199178i
$901$			373351.i			0.459905i
$902$	553120.	−	33527.0i	0.679840	−	0.0412080i
$903$	−690444.			−0.846746
$904$	123259.	−	40049.4i	0.150828	−	0.0490071i
$905$	1.12472e6	+	817154.i	1.37324	+	0.997715i
$906$	5732.36	−	4164.81i	0.00698357	−	0.00507386i
$907$	−68802.5	+	211752.i	−0.0836354	+	0.257403i	−0.984126	−	0.177473i	$-0.943208\pi$
$907$	−68802.5	+	211752.i	−0.0836354	+	0.257403i	0.900490	+	0.434876i	$0.143208\pi$
$908$	−70300.3	−	22841.9i	−0.0852679	−	0.0277052i
$909$	−282188.	−	388398.i	−0.341516	−	0.470056i
$910$	476654.	−	656058.i	0.575600	−	0.792245i
$911$	376111.	+	1.15755e6i	0.453189	+	1.39477i	0.873249	+	0.487275i	$0.162009\pi$
$911$	376111.	+	1.15755e6i	0.453189	+	1.39477i	−0.420060	+	0.907496i	$0.637991\pi$
$912$		−	95938.5i		−	0.115346i
$913$	−29715.7	−	490243.i	−0.0356488	−	0.588125i
$914$	−356958.			−0.427292
$915$	572591.	−	186046.i	0.683915	−	0.222218i
$916$	−497389.	−	361375.i	−0.592796	−	0.430692i
$917$	606805.	−	440870.i	0.721623	−	0.524290i
$918$	−81166.5	+	249805.i	−0.0963144	+	0.296425i
$919$	1.58795e6	+	515957.i	1.88021	+	0.610917i	0.986866	+	0.161542i	$0.0516469\pi$
$919$	1.58795e6	+	515957.i	1.88021	+	0.610917i	0.893343	+	0.449375i	$0.148353\pi$
$920$	192366.	+	264769.i	0.227275	+	0.312818i
$921$	87623.7	−	120604.i	0.103301	−	0.142181i
$922$	57010.8	+	175461.i	0.0670650	+	0.206405i
$923$		−	348196.i		−	0.408714i
$924$	249283.	−	390825.i	0.291978	−	0.457761i
$925$	−823455.			−0.962402
$926$	−829533.	+	269532.i	−0.967412	+	0.314331i
$927$	44624.5	+	32421.6i	0.0519295	+	0.0377290i
$928$	−159266.	+	115714.i	−0.184938	+	0.134366i
$929$	−95030.8	+	292475.i	−0.110112	+	0.338888i	−0.990896	−	0.134629i	$-0.957016\pi$
$929$	−95030.8	+	292475.i	−0.110112	+	0.338888i	0.880785	+	0.473517i	$0.157016\pi$
$930$	−244180.	−	79338.8i	−0.282321	−	0.0917318i
$931$	787364.	+	1.08371e6i	0.908398	+	1.25030i
$932$	−52829.3	+	72713.3i	−0.0608196	+	0.0837110i
$933$	68488.0	+	210784.i	0.0786776	+	0.242145i
$934$		−	1.05516e6i		−	1.20955i
$935$	482881.	+	125163.i	0.552354	+	0.143170i
$936$	116375.			0.132833
$937$	−1.12048e6	+	364066.i	−1.27622	+	0.414668i	−0.867247	−	0.497879i	$-0.834112\pi$
$937$	−1.12048e6	+	364066.i	−1.27622	+	0.414668i	−0.408971	+	0.912547i	$0.634112\pi$
$938$	422186.	+	306736.i	0.479842	+	0.348626i
$939$	−385249.	+	279900.i	−0.436929	+	0.317447i
$940$	263894.	−	812181.i	0.298657	−	0.919173i
$941$	−40929.6	−	13298.8i	−0.0462230	−	0.0150187i	0.285814	−	0.958285i	$-0.407736\pi$
$941$	−40929.6	−	13298.8i	−0.0462230	−	0.0150187i	−0.332037	+	0.943266i	$0.607736\pi$
$942$	−330937.	−	455495.i	−0.372943	−	0.513312i
$943$	−424868.	+	584780.i	−0.477783	+	0.657611i
$944$	31882.7	+	98124.9i	0.0357776	+	0.110112i
$945$			2.03144e6i			2.27478i
$946$	−380918.	+	313655.i	−0.425646	+	0.350485i
$947$	−137993.			−0.153871			−0.0769354	−	0.997036i	$-0.524514\pi$
$947$	−137993.			−0.153871			−0.0769354	+	0.997036i	$0.524514\pi$
$948$	−274481.	+	89184.3i	−0.305419	+	0.0992365i
$949$	−629834.	−	457601.i	−0.699349	−	0.508107i
$950$	261342.	−	189876.i	0.289576	−	0.210389i
$951$	−42278.0	+	130118.i	−0.0467470	+	0.143872i
$952$	−235272.	−	76444.6i	−0.259595	−	0.0843477i
$953$	−813768.	−	1.12006e6i	−0.896014	−	1.23326i	−0.971722	−	0.236127i	$-0.924122\pi$
$953$	−813768.	−	1.12006e6i	−0.896014	−	1.23326i	0.0757081	−	0.997130i	$-0.475878\pi$
$954$	−243567.	+	335241.i	−0.267622	+	0.368350i
$955$	255571.	+	786566.i	0.280223	+	0.862439i
$956$			221537.i			0.242399i
$957$	682570.	−	268441.i	0.745287	−	0.293106i
$958$	724704.			0.789641
$959$	2.15782e6	−	701119.i	2.34627	−	0.762350i
$960$	74800.1	+	54345.5i	0.0811633	+	0.0589686i
$961$	542723.	−	394312.i	0.587668	−	0.426966i
$962$	−174566.	+	537259.i	−0.188629	+	0.580542i
$963$	−458707.	−	149043.i	−0.494632	−	0.160716i
$964$	184430.	+	253847.i	0.198462	+	0.273160i
$965$	−803281.	+	1.10562e6i	−0.862607	+	1.18728i
$966$	186856.	+	575082.i	0.200240	+	0.616277i
$967$			1.79906e6i			1.92394i	0.273150	+	0.961972i	$0.411935\pi$
$967$			1.79906e6i			1.92394i	−0.273150	+	0.961972i	$0.588065\pi$
$968$	−40014.5	−	328863.i	−0.0427038	−	0.350965i
$969$	190749.			0.203150
$970$	1.19609e6	−	388634.i	1.27122	−	0.413045i
$971$	−1.07308e6	−	779641.i	−1.13814	−	0.826907i	−0.151280	−	0.988491i	$-0.548340\pi$
$971$	−1.07308e6	−	779641.i	−1.13814	−	0.826907i	−0.986859	+	0.161584i	$0.948340\pi$
$972$	−381754.	+	277360.i	−0.404065	+	0.293570i
$973$	−470906.	+	1.44930e6i	−0.497404	+	1.53085i
$974$	604364.	+	196370.i	0.637061	+	0.206994i
$975$	−143301.	−	197236.i	−0.150744	−	0.207481i
$976$	−125419.	+	172624.i	−0.131663	+	0.181218i
$977$	422787.	+	1.30120e6i	0.442927	+	1.36319i	0.884741	+	0.466083i	$0.154335\pi$
$977$	422787.	+	1.30120e6i	0.442927	+	1.36319i	−0.441814	+	0.897107i	$0.645665\pi$
$978$			372495.i			0.389441i
$979$	267165.	+	679326.i	0.278750	+	0.708782i
$980$	−1.29095e6			−1.34418
$981$	32565.7	−	10581.2i	0.0338393	−	0.0109951i
$982$	−229534.	−	166766.i	−0.238026	−	0.172936i
$983$	728116.	−	529007.i	0.753518	−	0.547463i	−0.143397	−	0.989665i	$-0.545803\pi$
$983$	728116.	−	529007.i	0.753518	−	0.547463i	0.896915	+	0.442202i	$0.145803\pi$
$984$	−63103.4	+	194212.i	−0.0651723	+	0.200580i
$985$	−1.15848e6	−	376413.i	−1.19403	−	0.387965i
$986$	−230067.	−	316660.i	−0.236647	−	0.325716i
$987$	927427.	−	1.27649e6i	0.952019	−	1.31034i
$988$	−68481.2	−	210763.i	−0.0701548	−	0.215914i
$989$		−	643648.i		−	0.658046i
$990$	351937.	+	427409.i	0.359083	+	0.436087i
$991$	846524.			0.861969			0.430985	−	0.902359i	$-0.358166\pi$
$991$	846524.			0.861969			0.430985	+	0.902359i	$0.358166\pi$
$992$	86539.6	−	28118.4i	0.0879411	−	0.0285738i
$993$	−398579.	−	289584.i	−0.404218	−	0.293682i
$994$	−664614.	+	482870.i	−0.672662	+	0.488717i
$995$	374940.	−	1.15395e6i	0.378718	−	1.16557i
$996$	172135.	+	55930.0i	0.173520	+	0.0563801i
$997$	816248.	+	1.12347e6i	0.821167	+	1.13024i	0.989503	+	0.144510i	$0.0461607\pi$
$997$	816248.	+	1.12347e6i	0.821167	+	1.13024i	−0.168336	+	0.985730i	$0.553839\pi$
$998$	428396.	−	589636.i	0.430115	−	0.592002i
$999$	−437298.	−	1.34587e6i	−0.438174	−	1.34856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.5.d.a.17.2	yes	16
3.2	odd	2		198.5.j.a.127.4		16
4.3	odd	2		176.5.n.c.17.2		16
11.2	odd	10	inner	22.5.d.a.13.2	✓	16
11.3	even	5		242.5.b.e.241.11		16
11.8	odd	10		242.5.b.e.241.3		16
33.2	even	10		198.5.j.a.145.4		16
44.35	even	10		176.5.n.c.145.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.13.2	✓	16	11.2	odd	10	inner
22.5.d.a.17.2	yes	16	1.1	even	1	trivial
176.5.n.c.17.2		16	4.3	odd	2
176.5.n.c.145.2		16	44.35	even	10
198.5.j.a.127.4		16	3.2	odd	2
198.5.j.a.145.4		16	33.2	even	10
242.5.b.e.241.3		16	11.8	odd	10
242.5.b.e.241.11		16	11.3	even	5

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68999 + 0.874032i) q^{2} +(4.50928 + 3.27619i) q^{3} +(6.47214 - 4.70228i) q^{4} +(-10.0117 + 30.8128i) q^{5} +(-14.9934 - 4.87166i) q^{6} +(50.5008 + 69.5083i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-15.4301 - 47.4891i) q^{9} +O(q^{10})\)	\(q+(-2.68999 + 0.874032i) q^{2} +(4.50928 + 3.27619i) q^{3} +(6.47214 - 4.70228i) q^{4} +(-10.0117 + 30.8128i) q^{5} +(-14.9934 - 4.87166i) q^{6} +(50.5008 + 69.5083i) q^{7} +(-13.3001 + 18.3060i) q^{8} +(-15.4301 - 47.4891i) q^{9} -91.6368i q^{10} +(-44.2851 - 112.605i) q^{11} +44.5903 q^{12} +(97.9585 - 31.8286i) q^{13} +(-196.599 - 142.838i) q^{14} +(-146.094 + 106.144i) q^{15} +(19.7771 - 60.8676i) q^{16} +(121.020 + 39.3217i) q^{17} +(83.0139 + 114.259i) q^{18} +(158.082 - 217.581i) q^{19} +(80.0935 + 246.502i) q^{20} +478.883i q^{21} +(217.547 + 264.199i) q^{22} -446.426 q^{23} +(-119.948 + 38.9733i) q^{24} +(-343.559 - 249.610i) q^{25} +(-235.689 + 171.238i) q^{26} +(225.518 - 694.073i) q^{27} +(653.696 + 212.399i) q^{28} +(639.233 + 879.829i) q^{29} +(300.219 - 413.216i) q^{30} +(-155.334 - 478.068i) q^{31} +181.019i q^{32} +(169.220 - 652.853i) q^{33} -359.911 q^{34} +(-2647.34 + 860.174i) q^{35} +(-323.173 - 234.799i) q^{36} +(1568.75 - 1139.76i) q^{37} +(-235.066 + 723.460i) q^{38} +(545.999 + 177.406i) q^{39} +(-430.902 - 593.086i) q^{40} +(951.709 - 1309.92i) q^{41} +(-418.559 - 1288.19i) q^{42} +1441.78i q^{43} +(-816.119 - 520.552i) q^{44} +1617.75 q^{45} +(1200.88 - 390.191i) q^{46} +(-2665.57 - 1936.65i) q^{47} +(288.594 - 209.676i) q^{48} +(-1539.13 + 4736.96i) q^{49} +(1142.34 + 371.168i) q^{50} +(416.888 + 573.797i) q^{51} +(484.333 - 666.628i) q^{52} +(906.672 + 2790.45i) q^{53} +2064.16i q^{54} +(3913.04 - 237.186i) q^{55} -1944.08 q^{56} +(1425.67 - 463.229i) q^{57} +(-2488.53 - 1808.02i) q^{58} +(-1304.22 + 947.571i) q^{59} +(-446.424 + 1373.95i) q^{60} +(-3170.81 - 1030.26i) q^{61} +(835.694 + 1150.23i) q^{62} +(2521.65 - 3470.76i) q^{63} +(-158.217 - 486.941i) q^{64} +3337.03i q^{65} +(115.414 + 1904.07i) q^{66} -2147.45 q^{67} +(968.159 - 314.574i) q^{68} +(-2013.06 - 1462.57i) q^{69} +(6369.52 - 4627.73i) q^{70} +(1044.65 - 3215.10i) q^{71} +(1074.55 + 349.144i) q^{72} +(-4442.75 - 6114.92i) q^{73} +(-3223.74 + 4437.10i) q^{74} +(-731.435 - 2251.13i) q^{75} -2151.56i q^{76} +(5590.54 - 8764.81i) q^{77} -1623.79 q^{78} +(-6155.63 + 2000.08i) q^{79} +(1677.50 + 1218.77i) q^{80} +(18.7143 - 13.5967i) q^{81} +(-1415.18 + 4355.49i) q^{82} +(3860.37 + 1254.31i) q^{83} +(2251.84 + 3099.40i) q^{84} +(-2423.22 + 3335.28i) q^{85} +(-1260.16 - 3878.38i) q^{86} +6061.65i q^{87} +(2650.33 + 686.968i) q^{88} -6032.84 q^{89} +(-4351.74 + 1413.97i) q^{90} +(7159.34 + 5201.56i) q^{91} +(-2889.33 + 2099.22i) q^{92} +(865.797 - 2664.65i) q^{93} +(8863.05 + 2879.78i) q^{94} +(5121.61 + 7049.29i) q^{95} +(-593.053 + 816.268i) q^{96} +(4241.03 + 13052.6i) q^{97} -14087.7i q^{98} +(-4664.17 + 3840.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Introduction

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