LMFDB - Embedded newform 22.5.d.a.13.2

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			13.2
Root			$0.809017 - 3.49146i$ of defining polynomial
Character	$\chi$	$=$	22.13
Dual form			22.5.d.a.17.2

$q$-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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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	−0.308379	−	0.951263i	$-0.599787\pi$
$3$	4.50928	−	3.27619i	0.501032	−	0.364021i	0.809411	+	0.587243i	$0.199787\pi$
$4$	6.47214	+	4.70228i	0.404508	+	0.293893i
$5$	−10.0117	−	30.8128i	−0.400467	−	1.23251i	−0.924621	−	0.380888i	$-0.875618\pi$
$5$	−10.0117	−	30.8128i	−0.400467	−	1.23251i	0.524154	−	0.851624i	$-0.324382\pi$
$6$	−14.9934	+	4.87166i	−0.416485	+	0.135324i
$7$	50.5008	−	69.5083i	1.03063	−	1.41854i	0.126153	−	0.992011i	$-0.459737\pi$
$7$	50.5008	−	69.5083i	1.03063	−	1.41854i	0.904475	−	0.426527i	$-0.140263\pi$
$8$	−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	0.584138	−	0.811655i	$-0.301433\pi$
$13$	97.9585	+	31.8286i	0.579636	+	0.188335i	−0.00450146	+	0.999990i	$0.501433\pi$
$14$	−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	−0.0920586	−	0.995754i	$-0.529345\pi$
$17$	121.020	−	39.3217i	0.418754	−	0.136061i	0.510812	+	0.859692i	$0.329345\pi$
$18$	83.0139	−	114.259i	0.256216	−	0.352651i
$19$	158.082	+	217.581i	0.437900	+	0.602717i	0.969744	−	0.244125i	$-0.0785008\pi$
$19$	158.082	+	217.581i	0.437900	+	0.602717i	−0.531844	+	0.846842i	$0.678501\pi$
$20$	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	−0.237120	−	0.971480i	$-0.576203\pi$
$29$	639.233	−	879.829i	0.760087	−	1.04617i	0.997207	−	0.0746895i	$-0.0237966\pi$
$30$	300.219	+	413.216i	0.333577	+	0.459129i
$31$	−155.334	+	478.068i	−0.161638	+	0.497470i	−0.998773	−	0.0495264i	$-0.984229\pi$
$31$	−155.334	+	478.068i	−0.161638	+	0.497470i	0.837135	+	0.546996i	$0.184229\pi$
$32$		−	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	0.987932	−	0.154890i	$-0.0495022\pi$
$37$	1568.75	+	1139.76i	1.14591	+	0.832553i	0.157979	+	0.987443i	$0.449502\pi$
$38$	−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	0.992093	−	0.125505i	$-0.0400552\pi$
$41$	951.709	+	1309.92i	0.566157	+	0.779248i	−0.425936	+	0.904753i	$0.640055\pi$
$42$	−418.559	+	1288.19i	−0.237278	+	0.730268i
$43$		−	1441.78i		−	0.779763i	−0.920865	−	0.389881i	$-0.872516\pi$
$43$		−	1441.78i		−	0.779763i	0.920865	−	0.389881i	$-0.127484\pi$
$44$	−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	−0.994926	−	0.100614i	$-0.967919\pi$
$47$	−2665.57	+	1936.65i	−1.20668	+	0.876708i	−0.211759	+	0.977322i	$0.567919\pi$
$48$	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	−0.649662	−	0.760223i	$-0.725089\pi$
$53$	906.672	−	2790.45i	0.322774	−	0.993396i	0.972435	−	0.233172i	$-0.0749106\pi$
$54$		−	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	0.384476	−	0.923135i	$-0.374382\pi$
$59$	−1304.22	−	947.571i	−0.374668	−	0.272212i	−0.759144	+	0.650923i	$0.774382\pi$
$60$	−446.424	−	1373.95i	−0.124007	−	0.381653i
$61$	−3170.81	+	1030.26i	−0.852138	+	0.276877i	−0.702341	−	0.711840i	$-0.747862\pi$
$61$	−3170.81	+	1030.26i	−0.852138	+	0.276877i	−0.149797	+	0.988717i	$0.547862\pi$
$62$	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	0.999614	+	0.0277668i	$0.00883957\pi$
$71$	1044.65	+	3215.10i	0.207230	+	0.637789i	−0.792384	+	0.610022i	$0.791160\pi$
$72$	1074.55	−	349.144i	0.207283	−	0.0673503i
$73$	−4442.75	+	6114.92i	−0.833692	+	1.14748i	0.153532	+	0.988144i	$0.450935\pi$
$73$	−4442.75	+	6114.92i	−0.833692	+	1.14748i	−0.987224	+	0.159336i	$0.949065\pi$
$74$	−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	−0.228934	−	0.973442i	$-0.573524\pi$
$79$	−6155.63	−	2000.08i	−0.986320	−	0.320475i	−0.757386	+	0.652967i	$0.773524\pi$
$80$	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	−0.0151193	−	0.999886i	$-0.504813\pi$
$83$	3860.37	−	1254.31i	0.560367	−	0.182074i	0.575486	+	0.817811i	$0.304813\pi$
$84$	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	−0.425320	−	0.905043i	$-0.639839\pi$
$97$	4241.03	−	13052.6i	0.450742	−	1.38724i	0.876062	−	0.482198i	$-0.160161\pi$
$98$			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	0.720745	−	0.693200i	$-0.243800\pi$
$101$	9144.05	+	2971.08i	0.896388	+	0.291254i	0.175643	+	0.984454i	$0.443800\pi$
$102$	−1622.94	+	1179.14i	−0.155992	+	0.113335i
$103$	−893.689	−	649.303i	−0.0842387	−	0.0612030i	0.544869	−	0.838521i	$-0.316579\pi$
$103$	−893.689	−	649.303i	−0.0842387	−	0.0612030i	−0.629107	+	0.777318i	$0.716579\pi$
$104$	−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	0.981462	−	0.191656i	$-0.0613857\pi$
$107$	5677.54	+	7814.47i	0.495898	+	0.682546i	−0.485564	+	0.874201i	$0.661386\pi$
$108$	−1804.14	+	5552.59i	−0.154676	+	0.476045i
$109$		−	685.751i		−	0.0577183i	−0.999583	−	0.0288591i	$-0.990813\pi$
$109$		−	685.751i		−	0.0577183i	0.999583	−	0.0288591i	$-0.00918742\pi$
$110$	−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	−0.754258	−	0.656578i	$-0.772003\pi$
$113$	−4633.79	+	3366.65i	−0.362894	+	0.263658i	0.391364	+	0.920236i	$0.372003\pi$
$114$	−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	−0.833516	+	0.552495i	$0.813676\pi$
$127$	−29557.9	+	9603.94i	−1.83259	+	0.595446i	−0.999077	+	0.0429511i	$0.986324\pi$
$128$	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	$0.0818630\pi$
$131$			8729.96i			0.508709i	−0.967111	+	0.254355i	$0.918137\pi$
$132$	−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	0.893310	+	0.449441i	$0.148377\pi$
$137$	8160.42	+	25115.2i	0.434782	+	1.33812i	−0.458528	+	0.888680i	$0.651623\pi$
$138$	6693.46	−	2174.84i	0.351473	−	0.114201i
$139$	10425.4	−	14349.3i	0.539588	−	0.742679i	−0.448966	−	0.893549i	$-0.648208\pi$
$139$	10425.4	−	14349.3i	0.539588	−	0.742679i	0.988554	+	0.150870i	$0.0482076\pi$
$140$	−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	0.125217	−	0.992129i	$-0.460037\pi$
$149$	17975.7	−	5840.66i	0.809679	−	0.263081i	0.684462	+	0.729049i	$0.260037\pi$
$150$	3935.11	−	5416.22i	0.174894	−	0.240721i
$151$	−264.180	−	363.612i	−0.0115863	−	0.0159472i	0.803185	−	0.595730i	$-0.203137\pi$
$151$	−264.180	−	363.612i	−0.0115863	−	0.0159472i	−0.814771	+	0.579783i	$0.803137\pi$
$152$	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	0.180900	−	0.983502i	$-0.442099\pi$
$157$	28892.7	−	20991.8i	1.17217	−	0.851629i	0.991267	+	0.131873i	$0.0420990\pi$
$158$	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	0.714460	+	0.699676i	$0.246672\pi$
$163$	−7301.42	+	22471.5i	−0.274810	+	0.845777i	−0.989270	+	0.146101i	$0.953328\pi$
$164$			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	0.297936	−	0.954586i	$-0.403702\pi$
$167$	−616.899	−	200.443i	−0.0221198	−	0.00718715i	−0.320056	+	0.947399i	$0.603702\pi$
$168$	−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	0.520569	−	0.853819i	$-0.325720\pi$
$173$	−13537.7	−	18633.0i	−0.452326	−	0.622573i	−0.972895	+	0.231246i	$0.925720\pi$
$174$	−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	−0.665893	−	0.746048i	$-0.731949\pi$
$179$	−5194.85	+	3774.28i	−0.162131	+	0.117795i	0.503761	+	0.863843i	$0.331949\pi$
$180$	10470.3	+	7607.13i	0.323158	+	0.234788i
$181$	13260.0	+	40810.0i	0.404749	+	1.24569i	0.921105	+	0.389315i	$0.127288\pi$
$181$	13260.0	+	40810.0i	0.404749	+	1.24569i	−0.516356	+	0.856374i	$0.672712\pi$
$182$	−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	0.833687	−	0.552237i	$-0.186226\pi$
$191$	20652.0	+	15004.5i	0.566102	+	0.411298i	−0.267585	+	0.963534i	$0.586226\pi$
$192$	881.866	+	2714.10i	0.0239221	+	0.0736248i
$193$	40117.2	−	13034.9i	1.07700	−	0.349939i	0.283790	−	0.958886i	$-0.408408\pi$
$193$	40117.2	−	13034.9i	1.07700	−	0.349939i	0.793210	+	0.608948i	$0.208408\pi$
$194$	−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	$-0.839041\pi$
$197$		−	37597.4i		−	0.968781i	0.874852	−	0.484390i	$-0.160959\pi$
$198$	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	−0.0696716	−	0.997570i	$-0.522195\pi$
$211$	−31716.5	−	10305.3i	−0.712394	−	0.231471i	−0.642722	+	0.766099i	$0.722195\pi$
$212$	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	−0.309291	−	0.950967i	$-0.600092\pi$
$223$	24842.4	−	18049.1i	0.499556	−	0.362949i	0.808848	+	0.588018i	$0.200092\pi$
$224$	−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	−0.858457	−	0.512885i	$-0.828577\pi$
$227$	−5431.00	+	7475.12i	−0.105397	+	0.145066i	0.753060	+	0.657951i	$0.228577\pi$
$228$	7048.91	+	9701.99i	0.135598	+	0.186634i
$229$	−23748.2	+	73089.5i	−0.452856	+	1.39375i	0.420778	+	0.907164i	$0.361757\pi$
$229$	−23748.2	+	73089.5i	−0.452856	+	1.39375i	−0.873634	+	0.486584i	$0.838243\pi$
$230$		−	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	0.208950	−	0.977926i	$-0.432995\pi$
$233$	−10685.0	−	3471.75i	−0.196816	−	0.0639495i	−0.405766	+	0.913977i	$0.632995\pi$
$234$	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	0.642411	−	0.766360i	$-0.277934\pi$
$239$	−16277.0	−	22403.4i	−0.284957	−	0.392210i	−0.927368	+	0.374151i	$0.877934\pi$
$240$	3571.39	−	10991.6i	0.0620033	−	0.190826i
$241$		−	39221.5i		−	0.675289i	−0.941274	−	0.337644i	$-0.890370\pi$
$241$		−	39221.5i		−	0.675289i	0.941274	−	0.337644i	$-0.109630\pi$
$242$	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	0.513251	+	0.858238i	$0.328441\pi$
$251$	−25606.0	+	78807.1i	−0.406438	+	1.25089i	−0.919689	+	0.392648i	$0.871559\pi$
$252$			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	0.623386	−	0.781914i	$-0.285756\pi$
$257$	4780.54	+	3473.26i	0.0723786	+	0.0525861i	−0.551008	+	0.834500i	$0.685756\pi$
$258$	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	$-0.715044\pi$
$263$		−	107951.i		−	1.56069i	0.625351	−	0.780344i	$-0.284956\pi$
$264$	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	0.912156	−	0.409844i	$-0.134417\pi$
$269$	−4826.05	−	14853.1i	−0.0666941	−	0.205263i	−0.978850	+	0.204581i	$0.934417\pi$
$270$	−63602.6	+	20665.7i	−0.872464	+	0.283481i
$271$	−20136.9	+	27716.1i	−0.274192	+	0.377392i	−0.923799	−	0.382877i	$-0.874933\pi$
$271$	−20136.9	+	27716.1i	−0.274192	+	0.377392i	0.649608	+	0.760270i	$0.274933\pi$
$272$	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	0.719791	−	0.694191i	$-0.244238\pi$
$277$	68601.8	+	22290.1i	0.894079	+	0.290504i	0.174288	+	0.984695i	$0.444238\pi$
$278$	−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	0.376037	−	0.926605i	$-0.377287\pi$
$281$	96719.5	−	31426.1i	1.22490	−	0.397995i	0.848865	+	0.528610i	$0.177287\pi$
$282$	30531.3	−	42022.8i	0.383926	−	0.528429i
$283$	−1793.34	−	2468.33i	−0.0223919	−	0.0308198i	0.797674	−	0.603089i	$-0.206063\pi$
$283$	−1793.34	−	2468.33i	−0.0223919	−	0.0308198i	−0.820066	+	0.572269i	$0.806063\pi$
$284$	−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	−0.767543	−	0.640997i	$-0.778521\pi$
$293$	6804.87	−	9366.10i	0.0792656	−	0.109100i	0.846809	+	0.531898i	$0.178521\pi$
$294$	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	$0.0453174\pi$
$307$			26745.6i			0.283776i	−0.989883	+	0.141888i	$0.954683\pi$
$308$	−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	−0.408934	−	0.912564i	$-0.634100\pi$
$311$	32169.2	−	23372.3i	0.332598	−	0.241646i	0.741532	+	0.670917i	$0.234100\pi$
$312$	−10509.4	−	7635.54i	−0.107962	−	0.0784387i
$313$	−26400.8	−	81253.2i	−0.269481	−	0.829377i	−0.990627	−	0.136594i	$-0.956384\pi$
$313$	−26400.8	−	81253.2i	−0.269481	−	0.829377i	0.721146	−	0.692783i	$-0.243616\pi$
$314$	−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	−0.906195	−	0.422859i	$-0.861026\pi$
$317$	7585.16	−	23344.7i	0.0754825	−	0.232311i	0.981678	+	0.190548i	$0.0610265\pi$
$318$			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	−0.986561	−	0.163393i	$-0.947756\pi$
$337$	−59771.4	+	82268.3i	−0.526301	+	0.724391i	0.460260	+	0.887784i	$0.347756\pi$
$338$	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	−0.159702	−	0.987165i	$-0.551053\pi$
$347$	35079.8	−	11398.1i	0.291338	−	0.0946616i	0.451040	+	0.892504i	$0.351053\pi$
$348$	28503.6	−	39231.8i	0.235364	−	0.323951i
$349$	−60796.7	−	83679.5i	−0.499148	−	0.687018i	0.482894	−	0.875679i	$-0.339585\pi$
$349$	−60796.7	−	83679.5i	−0.499148	−	0.687018i	−0.982042	+	0.188660i	$0.939585\pi$
$350$	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	−0.562320	−	0.826920i	$-0.690091\pi$
$359$	51281.0	−	70582.2i	0.397894	−	0.547654i	0.960214	+	0.279266i	$0.0900910\pi$
$360$	−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	0.732257	−	0.681029i	$-0.238467\pi$
$367$	41866.7	+	30417.9i	0.310840	+	0.225838i	−0.421417	+	0.906867i	$0.638467\pi$
$368$	−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	$-0.776022\pi$
$373$		−	180034.i		−	1.29401i	0.762487	−	0.647003i	$-0.223978\pi$
$374$	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	0.925732	+	0.378179i	$0.123450\pi$
$379$	57325.3	+	176429.i	0.399087	+	1.22826i	−0.526645	+	0.850085i	$0.676550\pi$
$380$	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	−0.957501	−	0.288431i	$-0.906866\pi$
$383$	−1955.49	+	6018.39i	−0.0133309	+	0.0410283i	0.944170	+	0.329459i	$0.106866\pi$
$384$		−	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	0.252821	−	0.967513i	$-0.418642\pi$
$389$	−89160.2	−	64778.7i	−0.589212	−	0.428088i	−0.842034	+	0.539425i	$0.818642\pi$
$390$	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	0.994188	+	0.107657i	$0.0343347\pi$
$401$	40707.1	+	125284.i	0.253152	+	0.779122i	−0.741036	+	0.671465i	$0.765665\pi$
$402$	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	0.525928	−	0.850529i	$-0.323718\pi$
$409$	75524.9	+	24539.5i	0.451485	+	0.146696i	−0.0744433	+	0.997225i	$0.523718\pi$
$410$	−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	0.549136	−	0.835733i	$-0.314957\pi$
$421$	268282.	−	194918.i	1.51366	−	1.09974i	0.964522	−	0.264004i	$-0.0850433\pi$
$422$	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	−0.0282608	−	0.999601i	$-0.508997\pi$
$431$	−118641.	−	38548.8i	−0.638675	−	0.207518i	−0.610414	+	0.792083i	$0.708997\pi$
$432$	−37786.5	+	27453.5i	−0.202474	+	0.147106i
$433$	−20821.9	−	15128.0i	−0.111057	−	0.0806874i	0.530871	−	0.847453i	$-0.321865\pi$
$433$	−20821.9	−	15128.0i	−0.111057	−	0.0806874i	−0.641927	+	0.766765i	$0.721865\pi$
$434$	−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	$-0.895865\pi$
$439$		−	123861.i		−	0.642693i	0.946962	−	0.321347i	$-0.104135\pi$
$440$	−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	−0.424527	−	0.905415i	$-0.639560\pi$
$443$	59932.0	−	43543.2i	0.305388	−	0.221877i	0.729915	+	0.683538i	$0.239560\pi$
$444$	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	−0.602920	−	0.797802i	$-0.705996\pi$
$449$	71324.2	−	219513.i	0.353789	−	1.08885i	0.956708	−	0.291048i	$-0.0940040\pi$
$450$			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	−0.00722142	−	0.999974i	$-0.502299\pi$
$457$	120027.	−	38999.1i	0.574706	−	0.186733i	0.581928	+	0.813241i	$0.302299\pi$
$458$	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	$0.0490420\pi$
$461$			65227.4i			0.306922i	−0.988155	+	0.153461i	$0.950958\pi$
$462$	−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	−0.757102	−	0.653297i	$-0.773385\pi$
$467$	−115280.	−	354796.i	−0.528592	−	1.62684i	0.228510	−	0.973542i	$-0.426615\pi$
$468$	−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	−0.787392	−	0.616452i	$-0.788569\pi$
$479$	−243681.	+	79176.8i	−1.06207	+	0.345086i	−0.274673	+	0.961538i	$0.588569\pi$
$480$	−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	−0.900862	−	0.434105i	$-0.857065\pi$
$487$	−181763.	+	132058.i	−0.766385	+	0.556811i	0.134477	+	0.990917i	$0.457065\pi$
$488$	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	−0.669031	−	0.743234i	$-0.733291\pi$
$491$	58960.8	−	81152.6i	0.244568	−	0.336620i	0.913600	+	0.406615i	$0.133291\pi$
$492$	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	0.0843746	−	0.996434i	$-0.473111\pi$
$499$	−208468.	−	151461.i	−0.837217	−	0.608274i	−0.921592	+	0.388160i	$0.873111\pi$
$500$	−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	0.954347	+	0.298700i	$0.0965529\pi$
$503$	238719.	+	328568.i	0.943518	+	1.29864i	−0.0108292	+	0.999941i	$0.503447\pi$
$504$	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	−0.965326	−	0.261047i	$-0.915932\pi$
$509$	−263060.	+	191124.i	−1.01536	+	0.737700i	−0.0500314	+	0.998748i	$0.515932\pi$
$510$	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	−0.195865	−	0.980631i	$-0.562751\pi$
$521$	−322750.	−	234492.i	−1.18903	−	0.863878i	−0.993161	+	0.116753i	$0.962751\pi$
$522$	−47463.0	−	146076.i	−0.174186	−	0.536090i
$523$	295038.	−	95863.6i	1.07863	−	0.350470i	0.284790	−	0.958590i	$-0.408076\pi$
$523$	295038.	−	95863.6i	1.07863	−	0.350470i	0.793845	+	0.608120i	$0.208076\pi$
$524$	−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	−0.372505	−	0.928030i	$-0.621501\pi$
$541$	−356881.	−	115958.i	−1.21935	−	0.396191i	−0.846845	+	0.531839i	$0.821501\pi$
$542$	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	0.535679	−	0.844422i	$-0.320056\pi$
$547$	−129542.	−	178299.i	−0.432947	−	0.595901i	−0.968627	+	0.248521i	$0.920056\pi$
$548$	−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	−0.176557	−	0.984290i	$-0.556496\pi$
$557$	252579.	−	347646.i	0.814118	−	1.12054i	0.990675	−	0.136247i	$-0.0435040\pi$
$558$	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	−0.479615	−	0.877479i	$-0.659224\pi$
$563$	−438495.	−	142476.i	−1.38340	−	0.449494i	−0.903786	+	0.427984i	$0.859224\pi$
$564$	−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	0.629788	−	0.776767i	$-0.283142\pi$
$569$	−98286.5	−	135280.i	−0.303577	−	0.417838i	−0.933365	+	0.358929i	$0.883142\pi$
$570$	−42448.8	+	130644.i	−0.130652	+	0.402105i
$571$		−	317894.i		−	0.975012i	−0.873119	−	0.487506i	$-0.837907\pi$
$571$		−	317894.i		−	0.975012i	0.873119	−	0.487506i	$-0.162093\pi$
$572$	−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	0.987914	+	0.155003i	$0.0495388\pi$
$577$	93148.0	+	286680.i	0.279783	+	0.861084i	−0.708131	+	0.706081i	$0.750461\pi$
$578$	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	0.977155	−	0.212528i	$-0.0681695\pi$
$587$	371096.	+	269617.i	1.07699	+	0.782477i	0.0998318	+	0.995004i	$0.468170\pi$
$588$	−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	$0.0146954\pi$
$593$			32457.6i			0.0923011i	−0.998934	+	0.0461506i	$0.985305\pi$
$594$	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	−0.553664	−	0.832740i	$-0.686771\pi$
$599$	−213563.	−	657279.i	−0.595213	−	1.83188i	−0.0415485	−	0.999136i	$-0.513229\pi$
$600$	50937.2	−	16550.5i	0.141492	−	0.0459736i
$601$	−50232.0	+	69138.5i	−0.139070	+	0.191413i	−0.872871	−	0.487951i	$-0.837744\pi$
$601$	−50232.0	+	69138.5i	−0.139070	+	0.191413i	0.733801	+	0.679364i	$0.237744\pi$
$602$	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	0.475439	−	0.879748i	$-0.342289\pi$
$607$	126369.	+	41059.7i	0.342975	+	0.111439i	−0.132465	+	0.991188i	$0.542289\pi$
$608$	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	0.904556	+	0.426355i	$0.140203\pi$
$613$	387238.	+	532987.i	1.03052	+	1.41839i	0.125965	+	0.992035i	$0.459797\pi$
$614$	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	−0.446238	−	0.894914i	$-0.647237\pi$
$619$	102297.	−	74322.9i	0.266981	−	0.193973i	0.713219	+	0.700941i	$0.247237\pi$
$620$	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	0.955981	−	0.293429i	$-0.0947965\pi$
$631$	387143.	+	281276.i	0.972328	+	0.706437i	0.0163467	+	0.999866i	$0.494796\pi$
$632$	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	−0.369986	+	0.929037i	$0.620638\pi$
$641$	−562038.	+	408345.i	−1.36789	+	0.993827i	−0.997899	+	0.0647894i	$0.979362\pi$
$642$	−123195.	−	89506.7i	−0.298899	−	0.217163i
$643$	74090.8	+	228028.i	0.179202	+	0.551526i	0.999800	−	0.0199785i	$-0.00635978\pi$
$643$	74090.8	+	228028.i	0.179202	+	0.551526i	−0.820599	+	0.571505i	$0.806360\pi$
$644$	−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	0.679945	+	0.733263i	$0.262004\pi$
$647$	−126061.	+	387977.i	−0.301143	+	0.926824i	−0.981088	+	0.193561i	$0.937996\pi$
$648$		−	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	0.875832	−	0.482617i	$-0.160314\pi$
$653$	293149.	+	212985.i	0.687483	+	0.499486i	−0.188349	+	0.982102i	$0.560314\pi$
$654$	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	$-0.979405\pi$
$659$		−	56157.5i		−	0.129311i	0.997908	−	0.0646557i	$-0.0205949\pi$
$660$	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	0.311697	−	0.950182i	$-0.399103\pi$
$673$	2428.77	+	789.155i	0.00536237	+	0.00174234i	−0.306335	+	0.951924i	$0.599103\pi$
$674$	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	0.240404	−	0.970673i	$-0.422720\pi$
$677$	460823.	−	149731.i	1.00544	−	0.326688i	0.765038	+	0.643985i	$0.222720\pi$
$678$	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	−0.893659	−	0.448746i	$-0.851871\pi$
$691$	44449.9	−	136803.i	0.0930924	−	0.286509i	0.986752	+	0.162237i	$0.0518709\pi$
$692$		−	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	0.990328	−	0.138744i	$-0.0443066\pi$
$701$	271424.	+	373582.i	0.552346	+	0.760240i	−0.437982	+	0.898984i	$0.644307\pi$
$702$	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	0.999678	−	0.0253903i	$-0.00808286\pi$
$709$	88470.5	+	272284.i	0.175997	+	0.541664i	−0.823680	+	0.567055i	$0.808083\pi$
$710$	−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	0.529873	−	0.848077i	$-0.322239\pi$
$719$	−58393.7	−	42425.5i	−0.112956	−	0.0820672i	−0.642829	+	0.766010i	$0.722239\pi$
$720$	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	−0.781936	−	0.623359i	$-0.785767\pi$
$733$	28232.2	−	38858.3i	0.0525456	−	0.0723229i	0.834481	+	0.551036i	$0.185767\pi$
$734$	−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	0.346525	−	0.938041i	$-0.387362\pi$
$739$	41233.3	+	13397.5i	0.0755021	+	0.0245321i	−0.271022	+	0.962573i	$0.587362\pi$
$740$	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	−0.0130172	−	0.999915i	$-0.504144\pi$
$743$	311459.	−	101199.i	0.564187	−	0.183315i	0.577204	+	0.816600i	$0.304144\pi$
$744$	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	−0.439232	−	0.898374i	$-0.644749\pi$
$751$	157605.	−	114507.i	0.279441	−	0.203026i	0.718674	+	0.695347i	$0.244749\pi$
$752$	−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	−0.792026	−	0.610487i	$-0.790974\pi$
$757$	118949.	−	366087.i	0.207572	−	0.638841i	0.999598	−	0.0283533i	$-0.00902635\pi$
$758$		−	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	0.0722100	−	0.997389i	$-0.476995\pi$
$761$	−263860.	−	85733.3i	−0.455622	−	0.148040i	−0.527832	+	0.849349i	$0.676995\pi$
$762$	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	$0.286891\pi$
$769$			927410.i			1.56826i	−0.620595	+	0.784131i	$0.713109\pi$
$770$	−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	−0.654666	−	0.755918i	$-0.727191\pi$
$773$	−82488.3	+	59931.2i	−0.138049	+	0.100298i	0.516618	+	0.856216i	$0.327191\pi$
$774$	−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	−0.841732	−	0.539896i	$-0.818463\pi$
$787$	−746565.	+	242574.i	−1.20536	+	0.391646i	−0.363632	+	0.931543i	$0.618463\pi$
$788$	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	0.997647	+	0.0685576i	$0.0218397\pi$
$797$	146626.	+	451268.i	0.230831	+	0.710424i	−0.766816	+	0.641867i	$0.778160\pi$
$798$	−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	−0.0495756	−	0.998770i	$-0.515787\pi$
$809$	325525.	−	105770.i	0.497379	−	0.161608i	0.546955	+	0.837162i	$0.315787\pi$
$810$	−1245.96	+	1714.92i	−0.00189904	+	0.00261381i
$811$	267565.	+	368272.i	0.406807	+	0.559922i	0.962436	−	0.271509i	$-0.0875226\pi$
$811$	267565.	+	368272.i	0.406807	+	0.559922i	−0.555629	+	0.831430i	$0.687523\pi$
$812$	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	−0.946160	−	0.323701i	$-0.895073\pi$
$821$	−233166.	+	320925.i	−0.345923	+	0.476122i	0.600237	+	0.799822i	$0.295073\pi$
$822$	−244705.	−	336808.i	−0.362160	−	0.498470i
$823$	300791.	−	925738.i	0.444083	−	1.36675i	−0.439402	−	0.898290i	$-0.644810\pi$
$823$	300791.	−	925738.i	0.444083	−	1.36675i	0.883486	−	0.468458i	$-0.155190\pi$
$824$			24995.6i			0.0368137i
$825$	−221096.	−	182054.i	−0.324842	−	0.267481i
$826$	391758.			0.574192
$827$	136766.	+	44438.1i	0.199972	+	0.0649748i	0.407290	−	0.913299i	$-0.366474\pi$
$827$	136766.	+	44438.1i	0.199972	+	0.0649748i	−0.207319	+	0.978273i	$0.566474\pi$
$828$	144273.	−	104820.i	0.210438	−	0.152892i
$829$	289762.	+	210524.i	0.421631	+	0.306333i	0.778294	−	0.627901i	$-0.216086\pi$
$829$	289762.	+	210524.i	0.421631	+	0.306333i	−0.356663	+	0.934233i	$0.616086\pi$
$830$	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	−0.614166	+	0.789177i	$0.710507\pi$
$839$	−1.09425e6	+	795018.i	−1.55451	+	1.12941i	−0.940340	+	0.340237i	$0.889493\pi$
$840$	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	0.207594	−	0.978215i	$-0.433437\pi$
$853$	691608.	−	224717.i	0.950521	−	0.308843i	0.742927	+	0.669372i	$0.233437\pi$
$854$	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	$0.0586376\pi$
$857$			269066.i			0.366351i	−0.983080	+	0.183175i	$0.941362\pi$
$858$	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	0.872420	−	0.488757i	$-0.162550\pi$
$863$	−89869.0	−	276588.i	−0.120667	−	0.371374i	−0.993087	+	0.117383i	$0.962550\pi$
$864$	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	0.813384	−	0.581728i	$-0.197623\pi$
$877$	6751.69	+	9292.90i	0.00877835	+	0.0120824i	−0.804605	+	0.593810i	$0.797623\pi$
$878$	−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	0.216868	−	0.976201i	$-0.430416\pi$
$883$	945222.	−	686744.i	1.21231	−	0.880792i	0.995438	+	0.0954091i	$0.0304159\pi$
$884$	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	−0.979558	−	0.201163i	$-0.935528\pi$
$887$	−382008.	+	525789.i	−0.485540	+	0.668289i	0.494018	+	0.869452i	$0.335528\pi$
$888$	−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	0.900490	−	0.434876i	$-0.143208\pi$
$907$	−68802.5	−	211752.i	−0.0836354	−	0.257403i	−0.984126	+	0.177473i	$0.943208\pi$
$908$	−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	−0.420060	−	0.907496i	$-0.637991\pi$
$911$	376111.	−	1.15755e6i	0.453189	−	1.39477i	0.873249	−	0.487275i	$-0.162009\pi$
$912$			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	0.893343	−	0.449375i	$-0.148353\pi$
$919$	1.58795e6	−	515957.i	1.88021	−	0.610917i	0.986866	−	0.161542i	$-0.0516469\pi$
$920$	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	0.880785	−	0.473517i	$-0.157016\pi$
$929$	−95030.8	−	292475.i	−0.110112	−	0.338888i	−0.990896	+	0.134629i	$0.957016\pi$
$930$	−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	−0.408971	−	0.912547i	$-0.634112\pi$
$937$	−1.12048e6	−	364066.i	−1.27622	−	0.414668i	−0.867247	+	0.497879i	$0.834112\pi$
$938$	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	−0.332037	−	0.943266i	$-0.607736\pi$
$941$	−40929.6	+	13298.8i	−0.0462230	+	0.0150187i	0.285814	+	0.958285i	$0.407736\pi$
$942$	−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	0.0757081	+	0.997130i	$0.475878\pi$
$953$	−813768.	+	1.12006e6i	−0.896014	+	1.23326i	−0.971722	+	0.236127i	$0.924122\pi$
$954$	−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	$-0.588065\pi$
$967$		−	1.79906e6i		−	1.92394i	0.273150	−	0.961972i	$-0.411935\pi$
$968$	−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	−0.986859	−	0.161584i	$-0.948340\pi$
$971$	−1.07308e6	+	779641.i	−1.13814	+	0.826907i	−0.151280	+	0.988491i	$0.548340\pi$
$972$	−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	−0.441814	−	0.897107i	$-0.645665\pi$
$977$	422787.	−	1.30120e6i	0.442927	−	1.36319i	0.884741	−	0.466083i	$-0.154335\pi$
$978$		−	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	0.896915	−	0.442202i	$-0.145803\pi$
$983$	728116.	+	529007.i	0.753518	+	0.547463i	−0.143397	+	0.989665i	$0.545803\pi$
$984$	−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	−0.168336	−	0.985730i	$-0.553839\pi$
$997$	816248.	−	1.12347e6i	0.821167	−	1.13024i	0.989503	−	0.144510i	$-0.0461607\pi$
$998$	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.13.2	✓	16
3.2	odd	2		198.5.j.a.145.4		16
4.3	odd	2		176.5.n.c.145.2		16
11.4	even	5		242.5.b.e.241.3		16
11.6	odd	10	inner	22.5.d.a.17.2	yes	16
11.7	odd	10		242.5.b.e.241.11		16
33.17	even	10		198.5.j.a.127.4		16
44.39	even	10		176.5.n.c.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.13.2	✓	16	1.1	even	1	trivial
22.5.d.a.17.2	yes	16	11.6	odd	10	inner
176.5.n.c.17.2		16	44.39	even	10
176.5.n.c.145.2		16	4.3	odd	2
198.5.j.a.127.4		16	33.17	even	10
198.5.j.a.145.4		16	3.2	odd	2
242.5.b.e.241.3		16	11.4	even	5
242.5.b.e.241.11		16	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
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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