LMFDB - Embedded newform 35.5.i.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	35.19
Dual form			35.5.i.a.24.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10231 - 1.21377i) q^{2} +(3.73387 + 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(11.6512 + 22.1190i) q^{5} -18.1282i q^{6} +(22.9051 + 43.3169i) q^{7} +63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +O(q^{10})$	\(q+(-2.10231 - 1.21377i) q^{2} +(3.73387 + 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(11.6512 + 22.1190i) q^{5} -18.1282i q^{6} +(22.9051 + 43.3169i) q^{7} +63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +(2.35294 - 60.6428i) q^{10} +(95.0736 + 164.672i) q^{11} +(37.7384 - 65.3648i) q^{12} +63.2338 q^{13} +(4.42305 - 118.867i) q^{14} +(-99.5450 + 157.940i) q^{15} +(-3.93280 + 6.81181i) q^{16} +(-166.348 - 288.123i) q^{17} +(-53.0475 + 30.6270i) q^{18} +(-343.314 - 198.213i) q^{19} +(134.727 - 213.762i) q^{20} +(-194.616 + 309.873i) q^{21} -461.590i q^{22} +(-361.380 - 208.643i) q^{23} +(-409.867 + 236.637i) q^{24} +(-353.500 + 515.425i) q^{25} +(-132.937 - 76.7512i) q^{26} +793.319 q^{27} +(263.400 - 419.391i) q^{28} +1380.43 q^{29} +(400.978 - 211.215i) q^{30} +(416.091 - 240.230i) q^{31} +(894.698 - 516.554i) q^{32} +(-709.984 + 1229.73i) q^{33} +807.631i q^{34} +(-691.254 + 1011.33i) q^{35} -255.031 q^{36} +(-1366.04 - 788.682i) q^{37} +(481.169 + 833.409i) q^{38} +(236.107 + 408.949i) q^{39} +(-1401.81 + 738.404i) q^{40} -959.437i q^{41} +(785.258 - 415.229i) q^{42} +1687.77i q^{43} +(960.915 - 1664.35i) q^{44} +(630.350 + 24.4575i) q^{45} +(506.488 + 877.263i) q^{46} +(868.945 - 1505.06i) q^{47} -58.7382 q^{48} +(-1351.71 + 1984.36i) q^{49} +(1368.77 - 654.516i) q^{50} +(1242.24 - 2151.62i) q^{51} +(-319.554 - 553.484i) q^{52} +(2062.59 - 1190.84i) q^{53} +(-1667.80 - 962.906i) q^{54} +(-2534.66 + 4021.56i) q^{55} +(-2745.25 + 1451.63i) q^{56} -2960.40i q^{57} +(-2902.09 - 1675.52i) q^{58} +(131.709 - 76.0424i) q^{59} +(1885.50 + 73.1573i) q^{60} +(-2350.26 - 1356.93i) q^{61} -1166.34 q^{62} +(1235.56 + 45.9753i) q^{63} -2382.06 q^{64} +(736.749 + 1398.67i) q^{65} +(2985.21 - 1723.51i) q^{66} +(2686.14 - 1550.84i) q^{67} +(-1681.29 + 2912.07i) q^{68} -3116.17i q^{69} +(2680.75 - 1287.11i) q^{70} -739.225 q^{71} +(1384.91 + 799.581i) q^{72} +(-2971.45 - 5146.70i) q^{73} +(1914.56 + 3316.11i) q^{74} +(-4653.30 - 361.640i) q^{75} +4006.69i q^{76} +(-4955.42 + 7890.14i) q^{77} -1146.32i q^{78} +(1715.62 - 2971.54i) q^{79} +(-196.492 - 7.62388i) q^{80} +(1940.21 + 3360.55i) q^{81} +(-1164.53 + 2017.03i) q^{82} +10912.0 q^{83} +(3695.81 + 137.521i) q^{84} +(4434.83 - 7036.42i) q^{85} +(2048.57 - 3548.23i) q^{86} +(5154.34 + 8927.57i) q^{87} +(-10436.3 + 6025.37i) q^{88} +(-2301.14 - 1328.57i) q^{89} +(-1295.50 - 816.516i) q^{90} +(1448.38 + 2739.09i) q^{91} +4217.53i q^{92} +(3107.26 + 1793.98i) q^{93} +(-3653.58 + 2109.40i) q^{94} +(384.242 - 9903.18i) q^{95} +(6681.36 + 3857.49i) q^{96} -5790.08 q^{97} +(5250.27 - 2531.07i) q^{98} +4797.98 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.10231	−	1.21377i	−0.525577	−	0.303442i	0.213636	−	0.976913i	$-0.431469\pi$
$2$	−2.10231	−	1.21377i	−0.525577	−	0.303442i	−0.739214	+	0.673471i	$0.764803\pi$
$3$	3.73387	+	6.46725i	0.414874	+	0.718583i	0.995415	−	0.0956480i	$-0.0304923\pi$
$3$	3.73387	+	6.46725i	0.414874	+	0.718583i	−0.580541	+	0.814231i	$0.697159\pi$
$4$	−5.05353	−	8.75297i	−0.315846	−	0.547061i
$5$	11.6512	+	22.1190i	0.466048	+	0.884760i
$5$	11.6512	+	22.1190i	0.466048	+	0.884760i
$6$		−	18.1282i		−	0.503561i
$7$	22.9051	+	43.3169i	0.467452	+	0.884019i
$7$	22.9051	+	43.3169i	0.467452	+	0.884019i
$8$			63.3759i			0.990248i
$9$	12.6165	−	21.8524i	0.155759	−	0.269783i
$10$	2.35294	−	60.6428i	0.0235294	−	0.606428i
$11$	95.0736	+	164.672i	0.785732	+	1.36093i	0.928561	+	0.371181i	$0.121047\pi$
$11$	95.0736	+	164.672i	0.785732	+	1.36093i	−0.142828	+	0.989747i	$0.545620\pi$
$12$	37.7384	−	65.3648i	0.262072	−	0.453923i
$13$	63.2338			0.374165			0.187082	−	0.982344i	$-0.440097\pi$
$13$	63.2338			0.374165			0.187082	+	0.982344i	$0.440097\pi$
$14$	4.42305	−	118.867i	0.0225666	−	0.606465i
$15$	−99.5450	+	157.940i	−0.442422	+	0.701958i
$16$	−3.93280	+	6.81181i	−0.0153625	+	0.0266086i
$17$	−166.348	−	288.123i	−0.575598	−	0.996964i	−0.995976	−	0.0896156i	$-0.971436\pi$
$17$	−166.348	−	288.123i	−0.575598	−	0.996964i	0.420379	−	0.907349i	$-0.361897\pi$
$18$	−53.0475	+	30.6270i	−0.163727	+	0.0945278i
$19$	−343.314	−	198.213i	−0.951009	−	0.549066i	−0.0576151	−	0.998339i	$-0.518350\pi$
$19$	−343.314	−	198.213i	−0.951009	−	0.549066i	−0.893394	+	0.449273i	$0.851683\pi$
$20$	134.727	−	213.762i	0.336818	−	0.534404i
$21$	−194.616	+	309.873i	−0.441307	+	0.702659i
$22$		−	461.590i		−	0.953697i
$23$	−361.380	−	208.643i	−0.683137	−	0.394409i	0.117899	−	0.993026i	$-0.462384\pi$
$23$	−361.380	−	208.643i	−0.683137	−	0.394409i	−0.801036	+	0.598616i	$0.795717\pi$
$24$	−409.867	+	236.637i	−0.711575	+	0.410828i
$25$	−353.500	+	515.425i	−0.565599	+	0.824680i
$26$	−132.937	−	76.7512i	−0.196652	−	0.113537i
$27$	793.319			1.08823
$28$	263.400	−	419.391i	0.335969	−	0.534938i
$29$	1380.43			1.64141			0.820707	−	0.571350i	$-0.193580\pi$
$29$	1380.43			1.64141			0.820707	+	0.571350i	$0.193580\pi$
$30$	400.978	−	211.215i	0.445531	−	0.234684i
$31$	416.091	−	240.230i	0.432977	−	0.249979i	−0.267637	−	0.963520i	$-0.586243\pi$
$31$	416.091	−	240.230i	0.432977	−	0.249979i	0.700614	+	0.713540i	$0.252909\pi$
$32$	894.698	−	516.554i	0.873728	−	0.504447i
$33$	−709.984	+	1229.73i	−0.651960	+	1.12923i
$34$			807.631i			0.698643i
$35$	−691.254	+	1011.33i	−0.564289	+	0.825577i
$36$	−255.031			−0.196783
$37$	−1366.04	−	788.682i	−0.997836	−	0.576101i	−0.0902285	−	0.995921i	$-0.528760\pi$
$37$	−1366.04	−	788.682i	−0.997836	−	0.576101i	−0.907607	+	0.419820i	$0.862093\pi$
$38$	481.169	+	833.409i	0.333219	+	0.577153i
$39$	236.107	+	408.949i	0.155231	+	0.268868i
$40$	−1401.81	+	738.404i	−0.876132	+	0.461503i
$41$		−	959.437i		−	0.570754i	−0.958415	−	0.285377i	$-0.907881\pi$
$41$		−	959.437i		−	0.570754i	0.958415	−	0.285377i	$-0.0921188\pi$
$42$	785.258	−	415.229i	0.445158	−	0.235391i
$43$			1687.77i			0.912804i	0.889774	+	0.456402i	$0.150862\pi$
$43$			1687.77i			0.912804i	−0.889774	+	0.456402i	$0.849138\pi$
$44$	960.915	−	1664.35i	0.496340	−	0.859686i
$45$	630.350	+	24.4575i	0.311284	+	0.0120778i
$46$	506.488	+	877.263i	0.239361	+	0.414585i
$47$	868.945	−	1505.06i	0.393366	−	0.681330i	−0.599525	−	0.800356i	$-0.704644\pi$
$47$	868.945	−	1505.06i	0.393366	−	0.681330i	0.992891	+	0.119026i	$0.0379772\pi$
$48$	−58.7382			−0.0254940
$49$	−1351.71	+	1984.36i	−0.562978	+	0.826472i
$50$	1368.77	−	654.516i	0.547509	−	0.261807i
$51$	1242.24	−	2151.62i	0.477601	−	0.827229i
$52$	−319.554	−	553.484i	−0.118178	−	0.204691i
$53$	2062.59	−	1190.84i	0.734280	−	0.423937i	−0.0857058	−	0.996320i	$-0.527315\pi$
$53$	2062.59	−	1190.84i	0.734280	−	0.423937i	0.819986	+	0.572384i	$0.193981\pi$
$54$	−1667.80	−	962.906i	−0.571949	−	0.330215i
$55$	−2534.66	+	4021.56i	−0.837906	+	1.32944i
$56$	−2745.25	+	1451.63i	−0.875398	+	0.462893i
$57$		−	2960.40i		−	0.911172i
$58$	−2902.09	−	1675.52i	−0.862690	−	0.498074i
$59$	131.709	−	76.0424i	0.0378366	−	0.0218450i	−0.480962	−	0.876741i	$-0.659713\pi$
$59$	131.709	−	76.0424i	0.0378366	−	0.0218450i	0.518799	+	0.854896i	$0.326379\pi$
$60$	1885.50	+	73.1573i	0.523750	+	0.0203215i
$61$	−2350.26	−	1356.93i	−0.631622	−	0.364667i	0.149758	−	0.988723i	$-0.452151\pi$
$61$	−2350.26	−	1356.93i	−0.631622	−	0.364667i	−0.781380	+	0.624056i	$0.785484\pi$
$62$	−1166.34			−0.303417
$63$	1235.56	+	45.9753i	0.311303	+	0.0115836i
$64$	−2382.06			−0.581557
$65$	736.749	+	1398.67i	0.174379	+	0.331046i
$66$	2985.21	−	1723.51i	0.685311	−	0.395664i
$67$	2686.14	−	1550.84i	0.598383	−	0.345477i	−0.170022	−	0.985440i	$-0.554384\pi$
$67$	2686.14	−	1550.84i	0.598383	−	0.345477i	0.768405	+	0.639964i	$0.221051\pi$
$68$	−1681.29	+	2912.07i	−0.363600	+	0.629774i
$69$		−	3116.17i		−	0.654521i
$70$	2680.75	−	1287.11i	0.547093	−	0.262675i
$71$	−739.225			−0.146642			−0.0733212	−	0.997308i	$-0.523360\pi$
$71$	−739.225			−0.146642			−0.0733212	+	0.997308i	$0.523360\pi$
$72$	1384.91	+	799.581i	0.267152	+	0.154240i
$73$	−2971.45	−	5146.70i	−0.557599	−	0.965790i	−0.997696	−	0.0678401i	$-0.978389\pi$
$73$	−2971.45	−	5146.70i	−0.557599	−	0.965790i	0.440097	−	0.897950i	$-0.354944\pi$
$74$	1914.56	+	3316.11i	0.349627	+	0.605571i
$75$	−4653.30	−	361.640i	−0.827254	−	0.0642915i
$76$			4006.69i			0.693680i
$77$	−4955.42	+	7890.14i	−0.835794	+	1.33077i
$78$		−	1146.32i		−	0.188415i
$79$	1715.62	−	2971.54i	0.274895	−	0.476132i	−0.695214	−	0.718803i	$-0.744690\pi$
$79$	1715.62	−	2971.54i	0.274895	−	0.476132i	0.970109	+	0.242671i	$0.0780236\pi$
$80$	−196.492	−	7.62388i	−0.0307019	−	0.00119123i
$81$	1940.21	+	3360.55i	0.295719	+	0.512201i
$82$	−1164.53	+	2017.03i	−0.173191	+	0.299975i
$83$	10912.0			1.58397			0.791986	−	0.610540i	$-0.209047\pi$
$83$	10912.0			1.58397			0.791986	+	0.610540i	$0.209047\pi$
$84$	3695.81	+	137.521i	0.523782	+	0.0194900i
$85$	4434.83	−	7036.42i	0.613818	−	0.973898i
$86$	2048.57	−	3548.23i	0.276983	−	0.479749i
$87$	5154.34	+	8927.57i	0.680980	+	1.17949i
$88$	−10436.3	+	6025.37i	−1.34766	+	0.778070i
$89$	−2301.14	−	1328.57i	−0.290512	−	0.167727i	0.347661	−	0.937620i	$-0.386976\pi$
$89$	−2301.14	−	1328.57i	−0.290512	−	0.167727i	−0.638173	+	0.769893i	$0.720309\pi$
$90$	−1295.50	−	816.516i	−0.159939	−	0.100804i
$91$	1448.38	+	2739.09i	0.174904	+	0.330768i
$92$			4217.53i			0.498290i
$93$	3107.26	+	1793.98i	0.359262	+	0.207420i
$94$	−3653.58	+	2109.40i	−0.413488	+	0.238728i
$95$	384.242	−	9903.18i	0.0425753	−	1.09731i
$96$	6681.36	+	3857.49i	0.724974	+	0.418564i
$97$	−5790.08			−0.615377			−0.307688	−	0.951487i	$-0.599555\pi$
$97$	−5790.08			−0.615377			−0.307688	+	0.951487i	$0.599555\pi$
$98$	5250.27	−	2531.07i	0.546675	−	0.263544i
$99$	4797.98			0.489540
$100$	6297.92	+	489.454i	0.629792	+	0.0489454i
$101$	−6817.06	+	3935.83i	−0.668273	+	0.385828i	−0.795422	−	0.606056i	$-0.792751\pi$
$101$	−6817.06	+	3935.83i	−0.668273	+	0.385828i	0.127149	+	0.991884i	$0.459417\pi$
$102$	−5223.15	+	3015.59i	−0.502033	+	0.289849i
$103$	4581.28	−	7935.02i	0.431830	−	0.747952i	−0.565201	−	0.824953i	$-0.691201\pi$
$103$	4581.28	−	7935.02i	0.431830	−	0.747952i	0.997031	+	0.0770017i	$0.0245347\pi$
$104$			4007.50i			0.370516i
$105$	−9121.58	−	694.334i	−0.827355	−	0.0629781i
$106$	−5781.61			−0.514561
$107$	−8731.13	−	5040.92i	−0.762611	−	0.440294i	0.0676215	−	0.997711i	$-0.478459\pi$
$107$	−8731.13	−	5040.92i	−0.762611	−	0.440294i	−0.830232	+	0.557417i	$0.811792\pi$
$108$	−4009.06	−	6943.90i	−0.343713	−	0.595328i
$109$	2942.13	+	5095.91i	0.247633	+	0.428913i	0.962869	−	0.269971i	$-0.0870140\pi$
$109$	2942.13	+	5095.91i	0.247633	+	0.428913i	−0.715236	+	0.698883i	$0.753681\pi$
$110$	10209.9	−	5378.07i	0.843793	−	0.444468i
$111$		−	11779.3i		−	0.956037i
$112$	−385.148	−	14.3314i	−0.0307038	−	0.00114249i
$113$			6307.06i			0.493936i	0.969024	+	0.246968i	$0.0794342\pi$
$113$			6307.06i			0.493936i	−0.969024	+	0.246968i	$0.920566\pi$
$114$	−3593.24	+	6223.67i	−0.276488	+	0.478891i
$115$	404.461	−	10424.3i	0.0305831	−	0.788226i
$116$	−6976.04	−	12082.9i	−0.518433	−	0.897953i
$117$	797.788	−	1381.81i	0.0582795	−	0.100943i
$118$	−369.192			−0.0265148
$119$	8670.37	−	13805.2i	0.612271	−	0.974872i
$120$	−10009.6	−	6308.75i	−0.695112	−	0.438108i
$121$	−10757.5	+	18632.5i	−0.734750	+	1.27262i
$122$	3293.99	+	5705.36i	0.221311	+	0.383321i
$123$	6204.91	−	3582.41i	0.410134	−	0.236791i
$124$	−4205.46	−	2428.02i	−0.273508	−	0.157910i
$125$	−15519.4	−	1813.74i	−0.993240	−	0.116079i
$126$	−2541.73	−	1596.34i	−0.160099	−	0.100550i
$127$			18703.4i			1.15961i	0.814754	+	0.579807i	$0.196872\pi$
$127$			18703.4i			1.15961i	−0.814754	+	0.579807i	$0.803128\pi$
$128$	−9307.34	−	5373.59i	−0.568075	−	0.327978i
$129$	−10915.3	+	6301.93i	−0.655925	+	0.378699i
$130$	148.785	−	3834.68i	0.00880385	−	0.226904i
$131$	13717.8	+	7919.98i	0.799359	+	0.461510i	0.843247	−	0.537526i	$-0.180641\pi$
$131$	13717.8	+	7919.98i	0.799359	+	0.461510i	−0.0438877	+	0.999036i	$0.513974\pi$
$132$	14351.7			0.823675
$133$	722.300	−	19411.4i	0.0408333	−	1.09737i
$134$	−7529.47			−0.419329
$135$	9243.12	+	17547.4i	0.507167	+	0.962822i
$136$	18260.0	−	10542.4i	0.987242	−	0.569984i
$137$	−5233.92	+	3021.81i	−0.278860	+	0.161000i	−0.632907	−	0.774228i	$-0.718139\pi$
$137$	−5233.92	+	3021.81i	−0.278860	+	0.161000i	0.354047	+	0.935228i	$0.384805\pi$
$138$	−3782.32	+	6551.16i	−0.198609	+	0.344001i
$139$		−	19937.0i		−	1.03188i	−0.856624	−	0.515942i	$-0.827442\pi$
$139$		−	19937.0i		−	1.03188i	0.856624	−	0.515942i	$-0.172558\pi$
$140$	12345.4	+	939.733i	0.629869	+	0.0479455i
$141$	12978.1			0.652789
$142$	1554.08	+	897.248i	0.0770720	+	0.0444975i
$143$	6011.87	+	10412.9i	0.293993	+	0.509211i
$144$	99.2363	+	171.882i	0.00478570	+	0.00828908i
$145$	16083.6	+	30533.7i	0.764977	+	1.45226i
$146$			14426.6i			0.676797i
$147$	−17880.4	−	1332.51i	−0.827454	−	0.0616646i
$148$			15942.5i			0.727836i
$149$	−8033.87	+	13915.1i	−0.361870	+	0.626777i	−0.988269	−	0.152726i	$-0.951195\pi$
$149$	−8033.87	+	13915.1i	−0.361870	+	0.626777i	0.626399	+	0.779503i	$0.284528\pi$
$150$	9343.73	+	6408.31i	0.415277	+	0.284814i
$151$	−9962.88	−	17256.2i	−0.436949	−	0.756819i	0.560503	−	0.828152i	$-0.310608\pi$
$151$	−9962.88	−	17256.2i	−0.436949	−	0.756819i	−0.997453	+	0.0713337i	$0.977274\pi$
$152$	12561.9	−	21757.9i	0.543711	−	0.941735i
$153$	−8394.89			−0.358618
$154$	19994.6	−	10572.8i	0.843086	−	0.445807i
$155$	10161.6	+	6404.54i	0.422960	+	0.266578i
$156$	2386.34	−	4133.27i	0.0980582	−	0.169842i
$157$	2523.47	+	4370.77i	0.102376	+	0.177320i	0.912663	−	0.408713i	$-0.134022\pi$
$157$	2523.47	+	4370.77i	0.102376	+	0.177320i	−0.810287	+	0.586033i	$0.800689\pi$
$158$	−7213.52	+	4164.73i	−0.288957	+	0.166829i
$159$	15402.9	+	8892.86i	0.609268	+	0.351761i
$160$	21849.9	+	13771.3i	0.853514	+	0.537943i
$161$	760.307	−	20432.8i	0.0293317	−	0.788273i
$162$		−	9419.88i		−	0.358935i
$163$	29919.2	+	17273.8i	1.12609	+	0.650150i	0.942949	−	0.332936i	$-0.108039\pi$
$163$	29919.2	+	17273.8i	1.12609	+	0.650150i	0.183144	+	0.983086i	$0.441373\pi$
$164$	−8397.92	+	4848.54i	−0.312237	+	0.180270i
$165$	−35472.5	−	1376.33i	−1.30294	−	0.0505539i
$166$	−22940.4	−	13244.6i	−0.832499	−	0.480644i
$167$	−7023.55			−0.251839			−0.125920	−	0.992040i	$-0.540188\pi$
$167$	−7023.55			−0.251839			−0.125920	+	0.992040i	$0.540188\pi$
$168$	−19638.5	−	12334.0i	−0.695807	−	0.437004i
$169$	−24562.5			−0.860001
$170$	−17864.0	+	9409.86i	−0.618131	+	0.325601i
$171$	−8662.84	+	5001.49i	−0.296257	+	0.171044i
$172$	14773.0	−	8529.22i	0.499359	−	0.288305i
$173$	−6386.73	+	11062.1i	−0.213396	+	0.369613i	−0.952775	−	0.303677i	$-0.901786\pi$
$173$	−6386.73	+	11062.1i	−0.213396	+	0.369613i	0.739379	+	0.673289i	$0.235119\pi$
$174$		−	25024.7i		−	0.826552i
$175$	−30423.6	−	3506.63i	−0.993423	−	0.114502i
$176$	−1495.62			−0.0482833
$177$	983.570	+	567.864i	0.0313949	+	0.0181258i
$178$	3225.14	+	5586.11i	0.101791	+	0.176307i
$179$	22147.6	+	38360.8i	0.691228	+	1.19724i	0.971436	+	0.237302i	$0.0762632\pi$
$179$	22147.6	+	38360.8i	0.691228	+	1.19724i	−0.280208	+	0.959939i	$0.590403\pi$
$180$	−2971.42	−	5641.03i	−0.0917104	−	0.174106i
$181$			14810.5i			0.452076i	0.974119	+	0.226038i	$0.0725773\pi$
$181$			14810.5i			0.452076i	−0.974119	+	0.226038i	$0.927423\pi$
$182$	279.686	−	7516.42i	0.00844362	−	0.226918i
$183$		−	20266.3i		−	0.605164i
$184$	13222.9	−	22902.7i	0.390563	−	0.676475i
$185$	1528.89	−	39404.4i	0.0446717	−	1.15134i
$186$	−4354.94	−	7542.98i	−0.125880	−	0.218030i
$187$	31630.6	−	54785.7i	0.904531	−	1.56669i
$188$	−17565.0			−0.496972
$189$	18171.1	+	34364.1i	0.508695	+	0.962015i
$190$	−12828.0	+	20353.2i	−0.355345	+	0.563800i
$191$	−12885.4	+	22318.2i	−0.353209	+	0.611776i	−0.986810	−	0.161884i	$-0.948243\pi$
$191$	−12885.4	+	22318.2i	−0.353209	+	0.611776i	0.633601	+	0.773660i	$0.281576\pi$
$192$	−8894.29	−	15405.4i	−0.241273	−	0.417897i
$193$	16688.3	−	9635.02i	0.448021	−	0.258665i	−0.258973	−	0.965885i	$-0.583384\pi$
$193$	16688.3	−	9635.02i	0.448021	−	0.258665i	0.706994	+	0.707219i	$0.250051\pi$
$194$	12172.5	+	7027.82i	0.323428	+	0.186731i
$195$	−6294.61	+	9987.18i	−0.165539	+	0.262648i
$196$	24199.9	+	1803.46i	0.629944	+	0.0469455i
$197$		−	63269.7i		−	1.63028i	−0.579262	−	0.815142i	$-0.696659\pi$
$197$		−	63269.7i		−	1.63028i	0.579262	−	0.815142i	$-0.303341\pi$
$198$	−10086.8	−	5823.64i	−0.257291	−	0.148547i
$199$	−53066.6	+	30638.0i	−1.34003	+	0.773668i	−0.986812	−	0.161873i	$-0.948247\pi$
$199$	−53066.6	+	30638.0i	−1.34003	+	0.773668i	−0.353220	+	0.935540i	$0.614913\pi$
$200$	−32665.5	−	22403.3i	−0.816638	−	0.560084i
$201$	20059.4	+	11581.3i	0.496507	+	0.286659i
$202$	19108.7			0.468306
$203$	31618.9	+	59795.9i	0.767281	+	1.45104i
$204$	−25110.8			−0.603393
$205$	21221.8	−	11178.6i	0.504980	−	0.265998i
$206$	−19262.6	+	11121.2i	−0.453920	+	0.262071i
$207$	−9118.68	+	5264.67i	−0.212810	+	0.122866i
$208$	−248.686	+	430.737i	−0.00574811	+	0.00995601i
$209$		−	75379.2i		−	1.72567i
$210$	18333.6	+	12531.2i	0.415729	+	0.284154i
$211$	30998.8			0.696274			0.348137	−	0.937444i	$-0.386814\pi$
$211$	30998.8			0.696274			0.348137	+	0.937444i	$0.386814\pi$
$212$	−20846.7	−	12035.9i	−0.463838	−	0.267797i
$213$	−2760.17	−	4780.75i	−0.0608382	−	0.105375i
$214$	12237.0	+	21195.2i	0.267207	+	0.462817i
$215$	−37331.9	+	19664.6i	−0.807612	+	0.425410i
$216$			50277.3i			1.07762i
$217$	19936.6	+	12521.3i	0.423382	+	0.265907i
$218$		−	14284.3i		−	0.300569i
$219$	22190.0	−	38434.2i	0.462667	−	0.801363i
$220$	48009.6	+	1862.77i	0.991934	+	0.0384869i
$221$	−10518.8	−	18219.1i	−0.215368	−	0.373029i
$222$	−14297.4	+	24763.8i	−0.290102	+	0.502471i
$223$	−51729.5			−1.04023			−0.520114	−	0.854097i	$-0.674111\pi$
$223$	−51729.5			−1.04023			−0.520114	+	0.854097i	$0.674111\pi$
$224$	42868.7	+	26923.8i	0.854367	+	0.536587i
$225$	6803.35	+	14227.7i	0.134387	+	0.281040i
$226$	7655.32	−	13259.4i	0.149881	−	0.259601i
$227$	−352.333	−	610.259i	−0.00683757	−	0.0118430i	0.862586	−	0.505910i	$-0.168843\pi$
$227$	−352.333	−	610.259i	−0.00683757	−	0.0118430i	−0.869424	+	0.494067i	$0.835510\pi$
$228$	−25912.3	+	14960.5i	−0.498466	+	0.287790i
$229$	−71232.3	−	41126.0i	−1.35833	−	0.784233i	−0.368932	−	0.929456i	$-0.620277\pi$
$229$	−71232.3	−	41126.0i	−1.35833	−	0.784233i	−0.989399	+	0.145223i	$0.953610\pi$
$230$	−13503.0	+	21424.2i	−0.255255	+	0.404993i
$231$	−69530.3	−	2587.23i	−1.30302	−	0.0484854i
$232$			87485.9i			1.62541i
$233$	43553.3	+	25145.5i	0.802249	+	0.463179i	0.844257	−	0.535938i	$-0.180042\pi$
$233$	43553.3	+	25145.5i	0.802249	+	0.463179i	−0.0420078	+	0.999117i	$0.513375\pi$
$234$	−3354.40	+	1936.66i	−0.0612608	+	0.0353689i
$235$	43414.6	+	1684.48i	0.786140	+	0.0305022i
$236$	−1331.19	−	768.565i	−0.0239011	−	0.0137993i
$237$	25623.6			0.456187
$238$	−34984.1	+	18498.9i	−0.617613	+	0.326582i
$239$	45757.2			0.801058			0.400529	−	0.916284i	$-0.368826\pi$
$239$	45757.2			0.801058			0.400529	+	0.916284i	$0.368826\pi$
$240$	−684.370	−	1299.23i	−0.0118814	−	0.0225561i
$241$	93767.3	−	54136.6i	1.61442	−	0.932087i	0.626094	−	0.779748i	$-0.284653\pi$
$241$	93767.3	−	54136.6i	1.61442	−	0.932087i	0.988328	−	0.152340i	$-0.0486807\pi$
$242$	45231.1	−	26114.2i	0.772336	−	0.445909i
$243$	17640.4	−	30554.1i	0.298742	−	0.517437i
$244$			27429.1i			0.460714i
$245$	−59641.1	−	6778.31i	−0.993604	−	0.112925i
$246$	−17392.9			−0.287409
$247$	−21709.1	−	12533.7i	−0.355834	−	0.205441i
$248$	15224.8	+	26370.1i	0.247542	+	0.428755i
$249$	40743.9	+	70570.4i	0.657149	+	1.13821i
$250$	30425.1	+	22650.0i	0.486801	+	0.362400i
$251$			18591.6i			0.295100i	0.989055	+	0.147550i	$0.0471387\pi$
$251$			18591.6i			0.295100i	−0.989055	+	0.147550i	$0.952861\pi$
$252$	−5841.52	−	11047.2i	−0.0919867	−	0.173960i
$253$		−	79345.6i		−	1.23960i
$254$	22701.6	−	39320.4i	0.351876	−	0.609467i
$255$	62065.3	+	2408.13i	0.954484	+	0.0370339i
$256$	32101.1	+	55600.7i	0.489824	+	0.848399i
$257$	−57163.9	+	99010.8i	−0.865477	+	1.49905i	0.00109563	+	0.999999i	$0.499651\pi$
$257$	−57163.9	+	99010.8i	−0.865477	+	1.49905i	−0.866573	+	0.499051i	$0.833682\pi$
$258$	30596.3			0.459653
$259$	2874.01	−	77237.4i	0.0428438	−	1.15140i
$260$	8519.32	−	13517.0i	0.126025	−	0.199955i
$261$	17416.2	−	30165.7i	0.255665	−	0.442825i
$262$	−19226.1	−	33300.5i	−0.280084	−	0.485119i
$263$	50183.3	−	28973.4i	0.725517	−	0.418878i	−0.0912626	−	0.995827i	$-0.529090\pi$
$263$	50183.3	−	28973.4i	0.725517	−	0.418878i	0.816780	+	0.576949i	$0.195757\pi$
$264$	−77935.1	−	44995.9i	−1.11822	−	0.645602i
$265$	50371.8	+	31747.8i	0.717292	+	0.452087i
$266$	−25079.5	+	39932.1i	−0.354450	+	0.564363i
$267$		−	19842.7i		−	0.278342i
$268$	−27149.0	−	15674.5i	−0.377993	−	0.218235i
$269$	−116284.	+	67136.6i	−1.60700	+	0.927801i	−0.616962	+	0.786993i	$0.711637\pi$
$269$	−116284.	+	67136.6i	−1.60700	+	0.927801i	−0.990037	+	0.140808i	$0.955030\pi$
$270$	1866.63	−	48109.1i	0.0256053	−	0.659933i
$271$	−50637.6	−	29235.6i	−0.689501	−	0.398083i	0.113924	−	0.993489i	$-0.463658\pi$
$271$	−50637.6	−	29235.6i	−0.689501	−	0.398083i	−0.803425	+	0.595406i	$0.796991\pi$
$272$	2616.85			0.0353705
$273$	−12306.3	+	19594.4i	−0.165121	+	0.262910i
$274$	14671.1			0.195417
$275$	−118485.	−	9208.25i	−1.56674	−	0.121762i
$276$	−27275.8	+	15747.7i	−0.358063	+	0.206728i
$277$	−27890.2	+	16102.4i	−0.363489	+	0.209861i	−0.670610	−	0.741810i	$-0.733968\pi$
$277$	−27890.2	+	16102.4i	−0.363489	+	0.209861i	0.307121	+	0.951670i	$0.400634\pi$
$278$	−24198.9	+	41913.8i	−0.313117	+	0.542335i
$279$		−	12123.4i		−	0.155746i
$280$	−64094.1	−	43808.9i	−0.817526	−	0.558786i
$281$	11748.0			0.148783			0.0743913	−	0.997229i	$-0.476299\pi$
$281$	11748.0			0.148783			0.0743913	+	0.997229i	$0.476299\pi$
$282$	−27284.0	−	15752.4i	−0.343091	−	0.198084i
$283$	−32607.7	−	56478.3i	−0.407144	−	0.705194i	0.587425	−	0.809279i	$-0.300142\pi$
$283$	−32607.7	−	56478.3i	−0.407144	−	0.705194i	−0.994568	+	0.104085i	$0.966809\pi$
$284$	3735.69	+	6470.41i	0.0463164	+	0.0802223i
$285$	65481.0	−	34492.2i	0.806168	−	0.424650i
$286$		−	29188.1i		−	0.356840i
$287$	41559.8	−	21976.0i	0.504557	−	0.266800i
$288$		−	26068.4i		−	0.314289i
$289$	−13582.6	+	23525.8i	−0.162625	+	0.281675i
$290$	3248.06	−	83713.1i	0.0386214	−	0.995399i
$291$	−21619.4	−	37445.9i	−0.255304	−	0.442199i
$292$	−30032.6	+	52018.0i	−0.352231	+	0.610081i
$293$	26847.7			0.312731			0.156366	−	0.987699i	$-0.450022\pi$
$293$	26847.7			0.312731			0.156366	+	0.987699i	$0.450022\pi$
$294$	35972.9	+	24504.1i	0.416179	+	0.283494i
$295$	3216.55	+	2027.29i	0.0369612	+	0.0232955i
$296$	49983.4	−	86573.8i	0.570483	−	0.988105i
$297$	75423.7	+	130638.i	0.855057	+	1.48100i
$298$	33779.4	−	19502.5i	0.380381	−	0.219613i
$299$	−22851.4	−	13193.3i	−0.255606	−	0.147574i
$300$	20350.2	+	42557.8i	0.226113	+	0.472864i
$301$	−73109.2	+	38658.7i	−0.806936	+	0.426692i
$302$			48370.6i			0.530356i
$303$	−50907.9	−	29391.7i	−0.554498	−	0.320140i
$304$	2700.38	−	1559.06i	0.0292198	−	0.0168700i
$305$	2630.45	−	67795.3i	0.0282768	−	0.728786i
$306$	17648.7	+	10189.5i	0.188482	+	0.108820i
$307$	−107091.			−1.13626			−0.568130	−	0.822939i	$-0.692333\pi$
$307$	−107091.			−1.13626			−0.568130	+	0.822939i	$0.692333\pi$
$308$	94104.5	+	3501.63i	0.991994	+	0.0369121i
$309$	68423.6			0.716620
$310$	−13589.2	−	25798.2i	−0.141407	−	0.268451i
$311$	74866.0	−	43223.9i	0.774040	−	0.446892i	−0.0602737	−	0.998182i	$-0.519197\pi$
$311$	74866.0	−	43223.9i	0.774040	−	0.446892i	0.834314	+	0.551289i	$0.185864\pi$
$312$	−25917.5	+	14963.5i	−0.266246	+	0.153717i
$313$	8477.90	−	14684.2i	0.0865366	−	0.149886i	−0.819508	−	0.573067i	$-0.805753\pi$
$313$	8477.90	−	14684.2i	0.0865366	−	0.149886i	0.906045	+	0.423181i	$0.139087\pi$
$314$		−	12251.6i		−	0.124261i
$315$	13378.8	+	27865.0i	0.134833	+	0.280827i
$316$	−34679.7			−0.347297
$317$	42543.6	+	24562.5i	0.423365	+	0.244430i	0.696516	−	0.717541i	$-0.254732\pi$
$317$	42543.6	+	24562.5i	0.423365	+	0.244430i	−0.273151	+	0.961971i	$0.588066\pi$
$318$	−21587.8	−	37391.1i	−0.213478	−	0.369755i
$319$	131242.	+	227318.i	1.28971	+	2.23385i
$320$	−27753.8	−	52688.8i	−0.271033	−	0.514539i
$321$		−	75288.5i		−	0.730666i
$322$	−26399.1	+	42033.3i	−0.254612	+	0.405398i
$323$			131889.i			1.26416i
$324$	19609.9	−	33965.3i	0.186803	−	0.323553i
$325$	−22353.1	+	32592.3i	−0.211627	+	0.308566i
$326$	−41932.9	−	72629.9i	−0.394566	−	0.683409i
$327$	−21971.0	+	38054.9i	−0.205473	+	0.355890i
$328$	60805.2			0.565188
$329$	85097.8	+	3166.49i	0.786188	+	0.0292541i
$330$	72903.7	+	45948.9i	0.669455	+	0.421937i
$331$	−78690.4	+	136296.i	−0.718233	+	1.24402i	0.243466	+	0.969910i	$0.421716\pi$
$331$	−78690.4	+	136296.i	−0.718233	+	1.24402i	−0.961699	+	0.274107i	$0.911618\pi$
$332$	−55144.0	−	95512.2i	−0.500290	−	0.866528i
$333$	−34469.2	+	19900.8i	−0.310844	+	0.179466i
$334$	14765.7	+	8524.97i	0.132361	+	0.0764187i
$335$	65599.9	+	41345.6i	0.584539	+	0.368417i
$336$	−1345.41	−	2544.36i	−0.0119172	−	0.0225372i
$337$			29576.3i			0.260426i	0.991486	+	0.130213i	$0.0415661\pi$
$337$			29576.3i			0.260426i	−0.991486	+	0.130213i	$0.958434\pi$
$338$	51637.9	+	29813.2i	0.451997	+	0.260961i
$339$	−40789.3	+	23549.7i	−0.354934	+	0.204921i
$340$	−84001.1	−	3259.23i	−0.726653	−	0.0281941i
$341$	79118.5	+	45679.1i	0.680408	+	0.392834i
$342$	24282.6			0.207608
$343$	−116917.	−	13099.9i	−0.993782	−	0.111347i
$344$	−106964.			−0.903903
$345$	68926.6	−	36307.1i	0.579094	−	0.305038i
$346$	26853.8	−	15504.0i	0.224312	−	0.129507i
$347$	−135510.	+	78236.7i	−1.12541	+	0.649758i	−0.942777	−	0.333423i	$-0.891796\pi$
$347$	−135510.	+	78236.7i	−1.12541	+	0.649758i	−0.182636	+	0.983181i	$0.558463\pi$
$348$	52095.2	−	90231.5i	0.430169	−	0.745075i
$349$		−	189136.i		−	1.55283i	−0.630224	−	0.776414i	$-0.717037\pi$
$349$		−	189136.i		−	1.55283i	0.630224	−	0.776414i	$-0.282963\pi$
$350$	59703.5	+	44299.2i	0.487376	+	0.361626i
$351$	50164.6			0.407177
$352$	170124.	+	98221.3i	1.37303	+	0.792721i
$353$	73446.6	+	127213.i	0.589417	+	1.02090i	0.994309	+	0.106535i	$0.0339758\pi$
$353$	73446.6	+	127213.i	0.589417	+	1.02090i	−0.404892	+	0.914364i	$0.632691\pi$
$354$	−1378.51	−	2387.65i	−0.0110003	−	0.0190531i
$355$	−8612.85	−	16350.9i	−0.0683424	−	0.129743i
$356$			26855.8i			0.211903i
$357$	121655.	+	4526.80i	0.954541	+	0.0355185i
$358$		−	107528.i		−	0.838991i
$359$	46384.6	−	80340.5i	0.359903	−	0.623370i	−0.628041	−	0.778180i	$-0.716143\pi$
$359$	46384.6	−	80340.5i	0.359903	−	0.623370i	0.987944	+	0.154810i	$0.0494765\pi$
$360$	−1550.02	+	39949.0i	−0.0119600	+	0.308248i
$361$	13416.0	+	23237.2i	0.102946	+	0.178308i
$362$	17976.5	−	31136.2i	0.137179	−	0.237601i
$363$	−160668.			−1.21932
$364$	16655.8	−	26519.7i	0.125708	−	0.200155i
$365$	79218.9	−	125691.i	0.594625	−	0.943446i
$366$	−24598.6	+	42606.1i	−0.183632	+	0.318060i
$367$	−89928.4	−	155760.i	−0.667674	−	1.15645i	−0.978553	−	0.205996i	$-0.933957\pi$
$367$	−89928.4	−	155760.i	−0.667674	−	1.15645i	0.310879	−	0.950450i	$-0.399377\pi$
$368$	2842.47	−	1641.10i	0.0209894	−	0.0121182i
$369$	−20966.0	−	12104.7i	−0.153979	−	0.0889001i
$370$	−51042.1	+	80984.6i	−0.372842	+	0.591560i
$371$	98827.4	+	62068.8i	0.718009	+	0.450947i
$372$		−	36263.6i		−	0.262051i
$373$	−162009.	−	93536.0i	−1.16445	−	0.672297i	−0.212086	−	0.977251i	$-0.568026\pi$
$373$	−162009.	−	93536.0i	−1.16445	−	0.672297i	−0.952367	+	0.304954i	$0.901359\pi$
$374$	−132994.	+	76784.4i	−0.950802	+	0.548946i
$375$	−46217.4	−	107140.i	−0.328657	−	0.761883i
$376$	95384.3	+	55070.2i	0.674686	+	0.389530i
$377$	87289.8			0.614159
$378$	3508.89	−	94299.6i	0.0245576	−	0.659973i
$379$	−239722.			−1.66890			−0.834448	−	0.551086i	$-0.814213\pi$
$379$	−239722.			−1.66890			−0.834448	+	0.551086i	$0.814213\pi$
$380$	−88624.0	+	46682.8i	−0.613740	+	0.323288i
$381$	−120960.	+	69836.0i	−0.833279	+	0.481094i
$382$	54178.2	−	31279.8i	0.371277	−	0.214357i
$383$	1784.69	−	3091.18i	0.0121665	−	0.0210730i	−0.859878	−	0.510499i	$-0.829461\pi$
$383$	1784.69	−	3091.18i	0.0121665	−	0.0210730i	0.872045	+	0.489426i	$0.162794\pi$
$384$		−	80257.1i		−	0.544279i
$385$	−232258.	−	17679.5i	−1.56693	−	0.119275i
$386$	−46778.7			−0.313960
$387$	36881.9	+	21293.8i	0.246259	+	0.142178i
$388$	29260.3	+	50680.4i	0.194364	+	0.336648i
$389$	−75785.4	−	131264.i	−0.500825	−	0.867455i	−1.00000		0.000953009i	$-0.999697\pi$
$389$	−75785.4	−	131264.i	−0.500825	−	0.867455i	0.499174	−	0.866502i	$-0.333637\pi$
$390$	25355.3	−	13355.9i	0.166702	−	0.0878103i
$391$			138829.i			0.908085i
$392$	−125760.	−	85665.8i	−0.818412	−	0.557488i
$393$			118289.i			0.765875i
$394$	−76794.8	+	133012.i	−0.494697	+	0.856840i
$395$	85716.4	+	3325.79i	0.549376	+	0.0213157i
$396$	−24246.7	−	41996.6i	−0.154619	−	0.267808i
$397$	64285.1	−	111345.i	0.407877	−	0.706464i	−0.586775	−	0.809750i	$-0.699603\pi$
$397$	64285.1	−	111345.i	0.407877	−	0.706464i	0.994652	+	0.103287i	$0.0329359\pi$
$398$	148750.			0.939054
$399$	128235.	−	67808.3i	0.805493	−	0.425929i
$400$	−2120.74	−	4435.04i	−0.0132546	−	0.0277190i
$401$	−12932.0	+	22398.8i	−0.0804222	+	0.139295i	−0.903431	−	0.428733i	$-0.858960\pi$
$401$	−12932.0	+	22398.8i	−0.0804222	+	0.139295i	0.823009	+	0.568028i	$0.192294\pi$
$402$	−28114.0	−	48694.9i	−0.173969	−	0.301323i
$403$	26311.0	−	15190.7i	0.162005	−	0.0935334i
$404$	68900.4	+	39779.7i	0.422142	+	0.243724i
$405$	−51726.1	+	82070.0i	−0.315355	+	0.500350i
$406$	6105.71	−	164088.i	0.0370411	−	0.995459i
$407$		−	299931.i		−	1.81064i
$408$	136361.	+	78728.1i	0.819162	+	0.472943i
$409$	175964.	−	101593.i	1.05191	−	0.607320i	0.128726	−	0.991680i	$-0.458911\pi$
$409$	175964.	−	101593.i	1.05191	−	0.607320i	0.923183	+	0.384360i	$0.125578\pi$
$410$	−58183.0	−	2257.49i	−0.346121	−	0.0134295i
$411$	−39085.5	−	22566.0i	−0.231384	−	0.133589i
$412$	−92606.6			−0.545566
$413$	6310.74	+	3963.48i	0.0369982	+	0.0232368i
$414$	25560.4			0.149131
$415$	127138.	+	241362.i	0.738206	+	1.40143i
$416$	56575.2	−	32663.7i	0.326918	−	0.188746i
$417$	128938.	−	74442.2i	0.741494	−	0.428102i
$418$	−91492.9	+	158470.i	−0.523642	+	0.906975i
$419$			58839.2i			0.335149i	0.985859	+	0.167575i	$0.0535935\pi$
$419$			58839.2i			0.335149i	−0.985859	+	0.167575i	$0.946406\pi$
$420$	40018.7	+	83349.8i	0.226863	+	0.472505i
$421$	−192190.			−1.08434			−0.542170	−	0.840269i	$-0.682397\pi$
$421$	−192190.			−1.08434			−0.542170	+	0.840269i	$0.682397\pi$
$422$	−65169.1	−	37625.4i	−0.365946	−	0.211279i
$423$	−21926.1	−	37977.1i	−0.122541	−	0.212247i
$424$	75470.4	+	130719.i	0.419803	+	0.727120i
$425$	207310.	+	16111.4i	1.14773	+	0.0891982i
$426$			13400.8i			0.0738435i
$427$	4944.73	−	132887.i	0.0271198	−	0.728830i
$428$			101898.i			0.556259i
$429$	−44895.0	+	77760.4i	−0.243940	+	0.422517i
$430$	102351.	+	3971.23i	0.553550	+	0.0214777i
$431$	−34471.0	−	59705.6i	−0.185567	−	0.321411i	0.758201	−	0.652021i	$-0.226079\pi$
$431$	−34471.0	−	59705.6i	−0.185567	−	0.321411i	−0.943767	+	0.330610i	$0.892745\pi$
$432$	−3119.97	+	5403.94i	−0.0167179	+	0.0289563i
$433$	−35455.7			−0.189108			−0.0945540	−	0.995520i	$-0.530143\pi$
$433$	−35455.7			−0.189108			−0.0945540	+	0.995520i	$0.530143\pi$
$434$	−26715.1	−	50522.1i	−0.141833	−	0.268227i
$435$	−137415.	+	218026.i	−0.726198	+	1.15220i
$436$	29736.3	−	51504.7i	0.156428	−	0.270940i
$437$	82711.2	+	143260.i	0.433113	+	0.750174i
$438$	−93300.4	+	53867.0i	−0.486335	+	0.280785i
$439$	90273.2	+	52119.3i	0.468414	+	0.270439i	0.715576	−	0.698535i	$-0.246165\pi$
$439$	90273.2	+	52119.3i	0.468414	+	0.270439i	−0.247162	+	0.968974i	$0.579498\pi$
$440$	−254870.	−	160637.i	−1.31648	−	0.829734i
$441$	26309.2	+	54573.7i	0.135279	+	0.280612i
$442$			51069.6i			0.261407i
$443$	32374.2	+	18691.2i	0.164965	+	0.0952425i	0.580209	−	0.814467i	$-0.302971\pi$
$443$	32374.2	+	18691.2i	0.164965	+	0.0952425i	−0.415245	+	0.909710i	$0.636304\pi$
$444$	−103104.	+	59527.2i	−0.523010	+	0.301960i
$445$	2575.47	−	66378.3i	0.0130058	−	0.335202i
$446$	108751.	+	62787.7i	0.546720	+	0.315649i
$447$	−119990.			−0.600521
$448$	−54561.4	−	103183.i	−0.271850	−	0.514108i
$449$	152617.			0.757023			0.378512	−	0.925597i	$-0.376436\pi$
$449$	152617.			0.757023			0.378512	+	0.925597i	$0.376436\pi$
$450$	2966.35	−	38168.6i	0.0146486	−	0.188487i
$451$	157993.	−	91217.1i	0.776755	−	0.448460i
$452$	55205.5	−	31872.9i	0.270213	−	0.156007i
$453$	74400.2	−	128865.i	0.362558	−	0.627969i
$454$			1710.61i			0.00829924i
$455$	−43710.6	+	63950.4i	−0.211137	+	0.308902i
$456$	187618.			0.902286
$457$	218339.	+	126058.i	1.04544	+	0.603586i	0.921370	−	0.388687i	$-0.127071\pi$
$457$	218339.	+	126058.i	1.04544	+	0.603586i	0.124072	+	0.992273i	$0.460405\pi$
$458$	99834.8	+	172919.i	0.475939	+	0.824350i
$459$	−131967.	−	228573.i	−0.626382	−	1.08493i
$460$	−93287.4	+	49139.2i	−0.440867	+	0.232227i
$461$		−	162820.i		−	0.766134i	−0.923720	−	0.383067i	$-0.874868\pi$
$461$		−	162820.i		−	0.766134i	0.923720	−	0.383067i	$-0.125132\pi$
$462$	143034.	+	89832.9i	0.670124	+	0.420873i
$463$			331880.i			1.54817i	0.633081	+	0.774085i	$0.281790\pi$
$463$			331880.i			1.54817i	−0.633081	+	0.774085i	$0.718210\pi$
$464$	−5428.95	+	9403.22i	−0.0252162	+	0.0436758i
$465$	−3477.69	+	89631.3i	−0.0160836	+	0.414528i
$466$	−61041.7	−	105727.i	−0.281096	−	0.486873i
$467$	39102.6	−	67727.7i	0.179297	−	0.310551i	−0.762343	−	0.647173i	$-0.775951\pi$
$467$	39102.6	−	67727.7i	0.179297	−	0.310551i	0.941640	+	0.336622i	$0.109284\pi$
$468$	−16126.6			−0.0736293
$469$	128704.	+	80833.1i	0.585123	+	0.367488i
$470$	−89226.4	−	56236.6i	−0.403922	−	0.254579i
$471$	−18844.6	+	32639.8i	−0.0849463	+	0.147131i
$472$	4819.26	+	8347.20i	0.0216320	+	0.0374677i
$473$	−277930.	+	160463.i	−1.24226	+	0.717220i
$474$	−53868.7	−	31101.1i	−0.239761	−	0.138426i
$475$	223525.	−	106885.i	0.990694	−	0.473728i
$476$	−164652.	−	6126.71i	−0.726697	−	0.0270404i
$477$		−	60096.8i		−	0.264128i
$478$	−96195.8	−	55538.7i	−0.421018	−	0.243075i
$479$	−232218.	+	134071.i	−1.01210	+	0.584339i	−0.911807	−	0.410618i	$-0.865313\pi$
$479$	−232218.	+	134071.i	−1.01210	+	0.584339i	−0.100298	+	0.994957i	$0.531979\pi$
$480$	−7477.88	+	192729.i	−0.0324561	+	0.836499i
$481$	−86379.7	−	49871.4i	−0.373355	−	0.215556i
$482$	−262837.			−1.13134
$483$	134983.	−	71376.4i	0.578609	−	0.305957i
$484$	217453.			0.928271
$485$	−67461.3	−	128071.i	−0.286795	−	0.544460i
$486$	−74171.3	+	42822.8i	−0.314025	+	0.181302i
$487$	96206.2	−	55544.7i	0.405644	−	0.234199i	−0.283272	−	0.959039i	$-0.591420\pi$
$487$	96206.2	−	55544.7i	0.405644	−	0.234199i	0.688916	+	0.724841i	$0.258087\pi$
$488$	85996.4	−	148950.i	0.361111	−	0.625462i
$489$			257993.i			1.07892i
$490$	117157.	+	86640.6i	0.487949	+	0.360852i
$491$	22253.5			0.0923073			0.0461536	−	0.998934i	$-0.485304\pi$
$491$	22253.5			0.0923073			0.0461536	+	0.998934i	$0.485304\pi$
$492$	−62713.4	−	36207.6i	−0.259078	−	0.149579i
$493$	−229631.	−	397733.i	−0.944794	−	1.63643i
$494$	30426.1	+	52699.6i	0.124679	+	0.215950i
$495$	55902.2	+	106126.i	0.228149	+	0.433125i
$496$			3779.11i			0.0153612i
$497$	−16932.0	−	32020.9i	−0.0685483	−	0.129635i
$498$		−	197815.i		−	0.797626i
$499$	19438.8	−	33669.0i	0.0780673	−	0.135217i	−0.824349	−	0.566082i	$-0.808458\pi$
$499$	19438.8	−	33669.0i	0.0780673	−	0.135217i	0.902416	+	0.430866i	$0.141792\pi$
$500$	62552.0	+	145006.i	0.250208	+	0.580026i
$501$	−26225.0	−	45423.0i	−0.104482	−	0.180968i
$502$	22565.9	−	39085.3i	0.0895458	−	0.155098i
$503$	350833.			1.38664			0.693321	−	0.720629i	$-0.256147\pi$
$503$	350833.			1.38664			0.693321	+	0.720629i	$0.256147\pi$
$504$	−2913.72	+	78304.7i	−0.0114706	+	0.308267i
$505$	−166483.	−	104929.i	−0.652812	−	0.411447i
$506$	−96307.2	+	166809.i	−0.376147	+	0.651506i
$507$	−91713.0	−	158852.i	−0.356792	−	0.617982i
$508$	163710.	−	94518.2i	0.634379	−	0.366259i
$509$	117110.	+	67613.4i	0.452020	+	0.260974i	0.708683	−	0.705527i	$-0.249290\pi$
$509$	117110.	+	67613.4i	0.452020	+	0.260974i	−0.256663	+	0.966501i	$0.582623\pi$
$510$	−127558.	−	80395.6i	−0.490417	−	0.309095i
$511$	154878.	−	246600.i	0.593126	−	0.944389i
$512$			16101.9i			0.0614237i
$513$	−272358.	−	157246.i	−1.03492	−	0.597509i
$514$	240352.	−	138768.i	0.909750	−	0.525245i
$515$	228892.	+	8880.99i	0.863011	+	0.0334847i
$516$	110321.	+	63693.9i	0.414342	+	0.239221i
$517$	330455.			1.23632
$518$	−99790.4	+	158888.i	−0.371903	+	0.592152i
$519$	−95388.7			−0.354130
$520$	−88641.8	+	46692.1i	−0.327817	+	0.172678i
$521$	−251826.	+	145392.i	−0.927738	+	0.535630i	−0.886095	−	0.463503i	$-0.846592\pi$
$521$	−251826.	+	145392.i	−0.927738	+	0.535630i	−0.0416424	+	0.999133i	$0.513259\pi$
$522$	−73228.3	+	42278.4i	−0.268744	+	0.155159i
$523$	−97680.4	+	169187.i	−0.357112	+	0.618536i	−0.987477	−	0.157763i	$-0.949572\pi$
$523$	−97680.4	+	169187.i	−0.357112	+	0.618536i	0.630365	+	0.776299i	$0.282905\pi$
$524$		−	160095.i		−	0.583064i
$525$	−90919.4	−	209850.i	−0.329866	−	0.761361i
$526$	−140668.			−0.508421
$527$	−138432.	−	79923.5i	−0.498441	−	0.287775i
$528$	−5584.46	−	9672.56i	−0.0200315	−	0.0346955i
$529$	−52857.0	−	91551.1i	−0.188882	−	0.327154i
$530$	−67362.7	−	127883.i	−0.239810	−	0.455263i
$531$		−	3837.55i		−	0.0136102i
$532$	−173558.	+	91773.9i	−0.613226	+	0.324262i
$533$		−	60668.9i		−	0.213556i
$534$	−24084.5	+	41715.6i	−0.0844608	+	0.146290i
$535$	9772.01	−	251857.i	0.0341410	−	0.879925i
$536$	98286.2	+	170237.i	0.342108	+	0.592548i
$537$	−165393.	+	286468.i	−0.573545	+	0.993409i
$538$	325953.			1.12614
$539$	−455281.	−	33929.0i	−1.56712	−	0.116787i
$540$	106882.	−	169581.i	0.366535	−	0.581554i
$541$	150002.	−	259811.i	0.512510	−	0.887694i	−0.487384	−	0.873188i	$-0.662049\pi$
$541$	150002.	−	259811.i	0.512510	−	0.887694i	0.999895	−	0.0145066i	$-0.00461776\pi$
$542$	70970.6	+	122925.i	0.241591	+	0.418447i
$543$	−95782.8	+	55300.2i	−0.324854	+	0.187554i
$544$	−297662.	−	171855.i	−1.00583	−	0.580717i
$545$	−78437.2	+	124450.i	−0.264076	+	0.418989i
$546$	49654.8	−	26256.5i	0.166562	−	0.0880748i
$547$			264771.i			0.884903i	0.896792	+	0.442452i	$0.145891\pi$
$547$			264771.i			0.884903i	−0.896792	+	0.442452i	$0.854109\pi$
$548$	52899.6	+	30541.6i	0.176153	+	0.101702i
$549$	−59304.2	+	34239.3i	−0.196762	+	0.113600i
$550$	237915.	+	163172.i	0.786495	+	0.539410i
$551$	−473921.	−	273618.i	−1.56100	−	0.901244i
$552$	197490.			0.648138
$553$	168014.	+	6251.82i	0.549409	+	0.0204436i
$554$	78178.3			0.254722
$555$	260547.	−	137243.i	0.845863	−	0.445559i
$556$	−174508.	+	100752.i	−0.564503	+	0.325916i
$557$	−489875.	+	282829.i	−1.57897	+	0.911621i	−0.583971	+	0.811775i	$0.698502\pi$
$557$	−489875.	+	282829.i	−1.57897	+	0.911621i	−0.995003	+	0.0998461i	$0.968165\pi$
$558$	−14715.1	+	25487.2i	−0.0472600	+	0.0818567i
$559$			106724.i			0.341539i
$560$	−4170.44	−	8686.06i	−0.0132986	−	0.0276979i
$561$	472417.			1.50107
$562$	−24698.0	−	14259.4i	−0.0781968	−	0.0451469i
$563$	−72859.4	−	126196.i	−0.229863	−	0.398134i	0.727904	−	0.685679i	$-0.240494\pi$
$563$	−72859.4	−	126196.i	−0.229863	−	0.398134i	−0.957767	+	0.287544i	$0.907161\pi$
$564$	−65585.2	−	113597.i	−0.206181	−	0.357115i
$565$	−139506.	+	73484.8i	−0.437014	+	0.230198i
$566$			158313.i			0.494178i
$567$	−101128.	+	161018.i	−0.314560	+	0.500850i
$568$		−	46849.0i		−	0.145212i
$569$	222280.	−	385001.i	0.686556	−	1.18915i	−0.286389	−	0.958114i	$-0.592455\pi$
$569$	222280.	−	385001.i	0.686556	−	1.18915i	0.972945	−	0.231037i	$-0.0742118\pi$
$570$	−179527.	−	6965.63i	−0.552560	−	0.0214393i
$571$	291779.	+	505375.i	0.894914	+	1.55004i	0.833911	+	0.551898i	$0.186096\pi$
$571$	291779.	+	505375.i	0.894914	+	1.55004i	0.0610022	+	0.998138i	$0.480570\pi$
$572$	60762.3	−	105243.i	0.185713	−	0.321664i
$573$	−192450.			−0.586149
$574$	−114045.	−	4243.64i	−0.346142	−	0.0128800i
$575$	235287.	−	112509.i	0.711644	−	0.340292i
$576$	−30053.2	+	52053.7i	−0.0905828	+	0.156894i
$577$	172858.	+	299399.i	0.519205	+	0.899289i	0.999751	+	0.0223197i	$0.00710519\pi$
$577$	172858.	+	299399.i	0.519205	+	0.899289i	−0.480546	+	0.876970i	$0.659561\pi$
$578$	57109.7	−	32972.3i	0.170944	−	0.0986947i
$579$	124624.	+	71951.7i	0.371745	+	0.214627i
$580$	185981.	−	295083.i	0.552858	−	0.877178i
$581$	249940.	+	472673.i	0.740430	+	1.40026i
$582$			104964.i			0.309880i
$583$	392196.	+	226435.i	1.15390	+	0.666202i
$584$	326176.	−	188318.i	0.956372	−	0.552162i
$585$	39859.4	+	1546.54i	0.116471	+	0.00451908i
$586$	−56442.1	−	32586.9i	−0.164365	−	0.0948959i
$587$	68833.0			0.199766			0.0998828	−	0.994999i	$-0.468153\pi$
$587$	68833.0			0.199766			0.0998828	+	0.994999i	$0.468153\pi$
$588$	78695.9	+	163241.i	0.227613	+	0.472144i
$589$	−190467.			−0.549020
$590$	−4301.52	−	8166.15i	−0.0123571	−	0.0234592i
$591$	409181.	−	236240.i	1.17149	−	0.676362i
$592$	10744.7	−	6203.46i	0.0306585	−	0.0177007i
$593$	−100636.	+	174307.i	−0.286183	+	0.495684i	−0.972895	−	0.231246i	$-0.925720\pi$
$593$	−100636.	+	174307.i	−0.286183	+	0.495684i	0.686712	+	0.726929i	$0.259053\pi$
$594$		−	366188.i		−	1.03784i
$595$	406376.	+	30933.3i	1.14787	+	0.0873760i
$596$	162398.			0.457180
$597$	−396287.	−	228796.i	−1.11189	−	0.641949i
$598$	32027.2	+	55472.7i	0.0895604	+	0.155123i
$599$	107344.	+	185926.i	0.299175	+	0.518186i	0.975947	−	0.218006i	$-0.0699552\pi$
$599$	107344.	+	185926.i	0.299175	+	0.518186i	−0.676772	+	0.736192i	$0.736622\pi$
$600$	22919.2	−	294907.i	0.0636645	−	0.819186i
$601$			401067.i			1.11037i	0.831727	+	0.555185i	$0.187353\pi$
$601$			401067.i			1.11037i	−0.831727	+	0.555185i	$0.812647\pi$
$602$	200621.	+	7465.12i	0.553584	+	0.0205989i
$603$		−	78264.8i		−	0.215244i
$604$	−100695.	+	174410.i	−0.276017	+	0.478076i
$605$	−537470.	−	20853.8i	−1.46840	−	0.0569736i
$606$	71349.5	+	123581.i	0.194288	+	0.336517i
$607$	−155245.	+	268893.i	−0.421348	+	0.729797i	−0.996072	−	0.0885510i	$-0.971776\pi$
$607$	−155245.	+	268893.i	−0.421348	+	0.729797i	0.574723	+	0.818348i	$0.305110\pi$
$608$	−409550.			−1.10790
$609$	−268654.	+	427757.i	−0.724367	+	1.15335i
$610$	−87817.8	+	139334.i	−0.236006	+	0.374453i
$611$	54946.7	−	95170.5i	0.147184	−	0.254929i
$612$	42423.8	+	73480.2i	0.113268	+	0.196186i
$613$	604065.	−	348757.i	1.60754	−	0.928116i	0.617626	−	0.786472i	$-0.288095\pi$
$613$	604065.	−	348757.i	1.60754	−	0.928116i	0.989918	−	0.141644i	$-0.0452387\pi$
$614$	225139.	+	129984.i	0.597192	+	0.344789i
$615$	151534.	+	95507.1i	0.400645	+	0.252514i
$616$	−500044.	−	314054.i	−1.31779	−	0.827643i
$617$			591179.i			1.55292i	0.630167	+	0.776459i	$0.282986\pi$
$617$			591179.i			1.55292i	−0.630167	+	0.776459i	$0.717014\pi$
$618$	−143848.	−	83050.5i	−0.376639	−	0.217453i
$619$	600452.	−	346671.i	1.56710	−	0.904766i	0.570596	−	0.821231i	$-0.306712\pi$
$619$	600452.	−	346671.i	1.56710	−	0.904766i	0.996505	−	0.0835356i	$-0.0266212\pi$
$620$	4706.81	−	121310.i	0.0122446	−	0.315582i
$621$	−286689.	−	165520.i	−0.743410	−	0.429208i
$622$	−209855.			−0.542424
$623$	4841.38	−	130109.i	0.0124736	−	0.335222i
$624$	−3714.24			−0.00953896
$625$	−140701.	−	364405.i	−0.360195	−	0.932877i
$626$	−35646.4	+	20580.4i	−0.0909633	+	0.0525177i
$627$	487496.	−	281456.i	1.24004	−	0.715937i
$628$	25504.8	−	44175.7i	0.0646700	−	0.112012i
$629$			524782.i			1.32641i
$630$	5695.26	−	74819.7i	0.0143494	−	0.188510i
$631$	−370356.			−0.930167			−0.465083	−	0.885267i	$-0.653976\pi$
$631$	−370356.			−0.930167			−0.465083	+	0.885267i	$0.653976\pi$
$632$	188324.	+	108729.i	0.471489	+	0.272214i
$633$	115745.	+	200477.i	0.288866	+	0.500330i
$634$	−59626.5	−	103276.i	−0.148341	−	0.256934i
$635$	−413701.	+	217917.i	−1.02598	+	0.540435i
$636$		−	179761.i		−	0.444408i
$637$	−85473.8	+	125479.i	−0.210646	+	0.309237i
$638$		−	637191.i		−	1.56541i
$639$	−9326.42	+	16153.8i	−0.0228409	+	0.0395616i
$640$	10416.9	−	268478.i	0.0254319	−	0.655463i
$641$	−246629.	−	427175.i	−0.600245	−	1.03966i	−0.992784	−	0.119920i	$-0.961736\pi$
$641$	−246629.	−	427175.i	−0.600245	−	1.03966i	0.392538	−	0.919736i	$-0.371597\pi$
$642$	−91382.9	+	158280.i	−0.221715	+	0.384021i
$643$	−595030.			−1.43919			−0.719593	−	0.694396i	$-0.755671\pi$
$643$	−595030.			−1.43919			−0.719593	+	0.694396i	$0.755671\pi$
$644$	−182690.	+	96603.0i	−0.440498	+	0.232926i
$645$	−266568.	−	168010.i	−0.640750	−	0.403845i
$646$	160083.	−	277271.i	0.383601	−	0.664416i
$647$	−13262.4	−	22971.1i	−0.0316820	−	0.0548749i	0.849750	−	0.527186i	$-0.176753\pi$
$647$	−13262.4	−	22971.1i	−0.0316820	−	0.0548749i	−0.881432	+	0.472312i	$0.843420\pi$
$648$	−212978.	+	122963.i	−0.507206	+	0.292835i
$649$	25044.2	+	14459.3i	0.0594589	+	0.0343286i
$650$	86552.7	−	41387.6i	0.204858	−	0.0979588i
$651$	−6537.36	+	175688.i	−0.0154255	+	0.414553i
$652$		−	349175.i		−	0.821388i
$653$	−146684.	−	84687.8i	−0.343997	−	0.198607i	0.318041	−	0.948077i	$-0.396975\pi$
$653$	−146684.	−	84687.8i	−0.343997	−	0.198607i	−0.662038	+	0.749470i	$0.730308\pi$
$654$	92379.8	−	53335.5i	0.215984	−	0.124698i
$655$	−15353.2	+	395701.i	−0.0357862	+	0.922327i
$656$	6535.51	+	3773.28i	0.0151870	+	0.00876821i
$657$	−149957.			−0.347405
$658$	−175058.	−	109946.i	−0.404326	−	0.253938i
$659$	−203477.			−0.468537			−0.234269	−	0.972172i	$-0.575270\pi$
$659$	−203477.			−0.468537			−0.234269	+	0.972172i	$0.575270\pi$
$660$	167214.	+	317445.i	0.383872	+	0.728754i
$661$	−255626.	+	147586.i	−0.585062	+	0.337786i	−0.763143	−	0.646230i	$-0.776345\pi$
$661$	−255626.	+	147586.i	−0.585062	+	0.337786i	0.178080	+	0.984016i	$0.443011\pi$
$662$	330863.	−	191024.i	0.754974	−	0.435885i
$663$	78551.6	−	136055.i	0.178701	−	0.309520i
$664$			691556.i			1.56852i
$665$	437776.	−	210189.i	0.989940	−	0.475300i
$666$	96619.8			0.217830
$667$	−498859.	−	288016.i	−1.12131	−	0.647389i
$668$	35493.7	+	61476.9i	0.0795424	+	0.137771i
$669$	−193151.	−	334547.i	−0.431564	−	0.747490i
$670$	−87727.3	−	166544.i	−0.195427	−	0.371005i
$671$		−	516031.i		−	1.14612i
$672$	−14056.9	+	377772.i	−0.0311281	+	0.836549i
$673$		−	5692.85i		−	0.0125690i	−0.999980	−	0.00628449i	$-0.998000\pi$
$673$		−	5692.85i		−	0.0125690i	0.999980	−	0.00628449i	$-0.00200043\pi$
$674$	35898.8	−	62178.5i	0.0790242	−	0.136874i
$675$	−280438.	+	408897.i	−0.615502	+	0.897442i
$676$	124127.	+	214995.i	0.271628	+	0.470473i
$677$	410243.	−	710561.i	0.895083	−	1.55033i	0.0613821	−	0.998114i	$-0.480449\pi$
$677$	410243.	−	710561.i	0.895083	−	1.55033i	0.833701	−	0.552216i	$-0.186217\pi$
$678$	114336.			0.248727
$679$	−132623.	−	250808.i	−0.287659	−	0.544005i
$680$	445939.	+	281062.i	0.964401	+	0.607832i
$681$	2631.13	−	4557.25i	0.00567346	−	0.00982673i
$682$	−110888.	−	192063.i	−0.238405	−	0.412929i
$683$	412354.	−	238072.i	0.883951	−	0.510350i	0.0119922	−	0.999928i	$-0.496183\pi$
$683$	412354.	−	238072.i	0.883951	−	0.510350i	0.871959	+	0.489578i	$0.162849\pi$
$684$	87555.9	+	50550.4i	0.187143	+	0.108047i
$685$	−127821.	−	80561.5i	−0.272408	−	0.171690i
$686$	229896.	+	169451.i	0.488522	+	0.360077i
$687$		−	614235.i		−	1.30143i
$688$	−11496.8	−	6637.69i	−0.0242885	−	0.0140230i
$689$	130426.	−	75301.3i	0.274742	−	0.158622i
$690$	−188974.	−	7332.16i	−0.396920	−	0.0154005i
$691$	222957.	+	128724.i	0.466944	+	0.269590i	0.714960	−	0.699166i	$-0.246445\pi$
$691$	222957.	+	128724.i	0.466944	+	0.269590i	−0.248015	+	0.968756i	$0.579778\pi$
$692$	129102.			0.269601
$693$	109898.	+	207834.i	0.228836	+	0.432762i
$694$	379845.			0.788656
$695$	440987.	−	232290.i	0.912969	−	0.480907i
$696$	−565793.	+	326661.i	−1.16799	+	0.674339i
$697$	−276436.	+	159600.i	−0.569021	+	0.328524i
$698$	−229567.	+	397622.i	−0.471193	+	0.816131i
$699$			375560.i			0.768643i
$700$	123053.	+	284018.i	0.251129	+	0.579628i
$701$	−77209.8			−0.157122			−0.0785609	−	0.996909i	$-0.525033\pi$
$701$	−77209.8			−0.157122			−0.0785609	+	0.996909i	$0.525033\pi$
$702$	−105462.	−	60888.2i	−0.214003	−	0.123555i
$703$	312653.	+	541532.i	0.632634	+	1.09575i
$704$	−226471.	−	392259.i	−0.456948	−	0.791458i
$705$	151210.	+	287063.i	0.304231	+	0.577562i
$706$		−	356589.i		−	0.715416i
$707$	−326634.	−	205143.i	−0.653464	−	0.410410i
$708$		−	11478.9i		−	0.0228999i
$709$	−219300.	+	379839.i	−0.436261	+	0.755625i	−0.997398	−	0.0720975i	$-0.977031\pi$
$709$	−219300.	+	379839.i	−0.436261	+	0.755625i	0.561137	+	0.827723i	$0.310364\pi$
$710$	−1739.35	+	44828.7i	−0.00345040	+	0.0889281i
$711$	−43290.1	−	74980.7i	−0.0856347	−	0.148324i
$712$	84199.0	−	145837.i	0.166091	−	0.287679i
$713$	−200489.			−0.394377
$714$	−250263.	−	157178.i	−0.490908	−	0.308316i
$715$	−160277.	+	254299.i	−0.313515	+	0.497430i
$716$	223847.	−	387715.i	0.436642	−	0.756287i
$717$	170851.	+	295923.i	0.332338	+	0.575626i
$718$	−195030.	+	112600.i	−0.378314	+	0.218419i
$719$	−152949.	−	88304.9i	−0.295861	−	0.170815i	0.344721	−	0.938705i	$-0.387974\pi$
$719$	−152949.	−	88304.9i	−0.295861	−	0.170815i	−0.640582	+	0.767890i	$0.721307\pi$
$720$	−2645.64	+	4197.64i	−0.00510348	+	0.00809730i
$721$	448655.	+	16694.5i	0.863063	+	0.0321146i
$722$		−	65135.8i		−	0.124953i
$723$	700229.	+	404277.i	1.33956	+	0.773398i
$724$	129635.	−	74845.1i	0.247313	−	0.142786i
$725$	−487981.	+	711508.i	−0.928382	+	1.35364i
$726$	337774.	+	195014.i	0.640845	+	0.369992i
$727$	755148.			1.42877			0.714387	−	0.699751i	$-0.246706\pi$
$727$	755148.			1.42877			0.714387	+	0.699751i	$0.246706\pi$
$728$	−173592.	+	91792.3i	−0.327543	+	0.173198i
$729$	577783.			1.08720
$730$	−319102.	+	168087.i	−0.598803	+	0.315420i
$731$	486286.	−	280757.i	0.910033	−	0.525408i
$732$	−177391.	+	102416.i	−0.331061	+	0.191138i
$733$	76987.1	−	133346.i	0.143288	−	0.248182i	−0.785445	−	0.618932i	$-0.787566\pi$
$733$	76987.1	−	133346.i	0.143288	−	0.248182i	0.928733	+	0.370749i	$0.120899\pi$
$734$			436609.i			0.810402i
$735$	−178855.	−	411023.i	−0.331074	−	0.760836i
$736$	−431101.			−0.795835
$737$	510762.	+	294889.i	0.940338	+	0.542904i
$738$	29384.7	+	50895.7i	0.0539521	+	0.0934477i
$739$	−270778.	−	469002.i	−0.495821	−	0.858788i	0.504167	−	0.863606i	$-0.331800\pi$
$739$	−270778.	−	469002.i	−0.495821	−	0.858788i	−0.999988	+	0.00481849i	$0.998466\pi$
$740$	−352632.	+	185749.i	−0.643960	+	0.339206i
$741$		−	187197.i		−	0.340928i
$742$	−132429.	−	250442.i	−0.240533	−	0.454882i
$743$			221399.i			0.401050i	0.979689	+	0.200525i	$0.0642648\pi$
$743$			221399.i			0.401050i	−0.979689	+	0.200525i	$0.935735\pi$
$744$	−113695.	+	196925.i	−0.205397	+	0.355758i
$745$	−401391.	−	15573.9i	−0.723195	−	0.0280599i
$746$	227062.	+	393283.i	0.408007	+	0.706688i
$747$	137671.	−	238453.i	0.246718	−	0.427328i
$748$	−639384.			−1.14277
$749$	18369.4	−	493669.i	0.0327440	−	0.879978i
$750$	−32879.8	+	281338.i	−0.0584529	+	0.500157i
$751$	−359901.	+	623366.i	−0.638121	+	1.10526i	0.347724	+	0.937597i	$0.386955\pi$
$751$	−359901.	+	623366.i	−0.638121	+	1.10526i	−0.985845	+	0.167660i	$0.946379\pi$
$752$	6834.78	+	11838.2i	0.0120862	+	0.0209339i
$753$	−120236.	+	69418.5i	−0.212054	+	0.122429i
$754$	−183510.	−	105950.i	−0.322788	−	0.186362i
$755$	265611.	−	421424.i	0.465963	−	0.739309i
$756$	208960.	−	332711.i	0.365612	−	0.582135i
$757$			29515.7i			0.0515064i	0.999668	+	0.0257532i	$0.00819840\pi$
$757$			29515.7i			0.0515064i	−0.999668	+	0.0257532i	$0.991802\pi$
$758$	503970.	+	290967.i	0.877134	+	0.506414i
$759$	513148.	−	296266.i	0.890756	−	0.514278i
$760$	627623.	+	24351.7i	1.08660	+	0.0421602i
$761$	120118.	+	69350.0i	0.207414	+	0.119750i	0.600109	−	0.799918i	$-0.295124\pi$
$761$	120118.	+	69350.0i	0.207414	+	0.119750i	−0.392695	+	0.919669i	$0.628457\pi$
$762$	339059.			0.583937
$763$	−153349.	+	244166.i	−0.263411	+	0.419408i
$764$	260467.			0.446238
$765$	−97810.5	−	185687.i	−0.167133	−	0.317291i
$766$	−7503.95	+	4332.41i	−0.0127889	+	0.00738366i
$767$	8328.48	−	4808.45i	0.0141571	−	0.00817362i
$768$	−239722.	+	415211.i	−0.406430	+	0.703958i
$769$		−	135934.i		−	0.229866i	−0.993373	−	0.114933i	$-0.963335\pi$
$769$		−	135934.i		−	0.229866i	0.993373	−	0.114933i	$-0.0366653\pi$
$770$	466820.	+	319076.i	0.787351	+	0.538161i
$771$	−853769.			−1.43626
$772$	−168670.	−	97381.7i	−0.283011	−	0.163397i
$773$	−456030.	−	789867.i	−0.763193	−	1.32189i	−0.941197	−	0.337859i	$-0.890297\pi$
$773$	−456030.	−	789867.i	−0.763193	−	1.32189i	0.178004	−	0.984030i	$-0.443036\pi$
$774$	−51691.5	−	89532.3i	−0.0862853	−	0.149451i
$775$	−23267.2	+	299385.i	−0.0387384	+	0.498456i
$776$		−	366951.i		−	0.609376i
$777$	510244.	−	269807.i	0.845155	−	0.446901i
$778$			367944.i			0.607886i
$779$	−190173.	+	329389.i	−0.313381	+	0.542792i
$780$	119227.	+	4626.01i	0.195969	+	0.00760357i
$781$	−70280.8	−	121730.i	−0.115222	−	0.199570i
$782$	168506.	−	291861.i	0.275551	−	0.477269i
$783$	1.09512e6			1.78623
$784$	−8201.08	−	17011.7i	−0.0133425	−	0.0276768i
$785$	−67275.7	+	106741.i	−0.109174	+	0.173218i
$786$	143575.	−	248679.i	0.232399	−	0.402526i
$787$	−453790.	−	785988.i	−0.732666	−	1.26901i	−0.955740	−	0.294213i	$-0.904943\pi$
$787$	−453790.	−	785988.i	−0.732666	−	1.26901i	0.223074	−	0.974801i	$-0.428391\pi$
$788$	−553798.	+	319735.i	−0.891864	+	0.514918i
$789$	374756.	+	216365.i	0.601997	+	0.347563i
$790$	−176166.	−	111032.i	−0.282272	−	0.177907i
$791$	−273203.	+	144464.i	−0.436648	+	0.230891i
$792$			304076.i			0.484766i
$793$	−148616.	−	85803.6i	−0.236331	−	0.136445i
$794$	−270294.	+	156055.i	−0.428742	+	0.247534i
$795$	−17239.1	+	444309.i	−0.0272760	+	0.702993i
$796$	536347.	+	309660.i	0.846486	+	0.488719i
$797$	−342402.			−0.539038			−0.269519	−	0.962995i	$-0.586865\pi$
$797$	−342402.			−0.539038			−0.269519	+	0.962995i	$0.586865\pi$
$798$	−351894.	−	13094.0i	−0.552594	−	0.0205621i
$799$	−578188.			−0.905682
$800$	−50030.3	+	643751.i	−0.0781723	+	1.00586i
$801$	−58064.7	+	33523.7i	−0.0904997	+	0.0522500i
$802$	54374.0	−	31392.8i	0.0845362	−	0.0488070i
$803$	565012.	−	978630.i	0.876248	−	1.51771i
$804$		−	234106.i		−	0.362159i
$805$	460812.	−	221250.i	0.711102	−	0.341421i
$806$	−73751.9			−0.113528
$807$	−868378.	−	501358.i	−1.33340	−	0.769841i
$808$	−249437.	−	432037.i	−0.382065	−	0.661756i
$809$	−464884.	−	805203.i	−0.710310	−	1.23029i	−0.964741	−	0.263201i	$-0.915222\pi$
$809$	−464884.	−	805203.i	−0.710310	−	1.23029i	0.254431	−	0.967091i	$-0.418112\pi$
$810$	208358.	−	109753.i	0.317571	−	0.167281i
$811$			32032.7i			0.0487025i	0.999703	+	0.0243513i	$0.00775201\pi$
$811$			32032.7i			0.0487025i	−0.999703	+	0.0243513i	$0.992248\pi$
$812$	363605.	−	578940.i	0.551464	−	0.878054i
$813$		−	436648.i		−	0.660618i
$814$	−364047.	+	630548.i	−0.549426	+	0.951633i
$815$	−33486.0	+	863043.i	−0.0504136	+	1.29932i
$816$	9770.97	+	16923.8i	0.0146743	+	0.0254166i
$817$	334538.	−	579437.i	0.501189	−	0.868085i
$818$	−493242.			−0.737147
$819$	78129.2	+	2907.19i	0.116478	+	0.00433417i
$820$	−205091.	−	129262.i	−0.305013	−	0.192240i
$821$	−549538.	+	951827.i	−0.815288	+	1.41212i	0.0938325	+	0.995588i	$0.470088\pi$
$821$	−549538.	+	951827.i	−0.815288	+	1.41212i	−0.909121	+	0.416533i	$0.863245\pi$
$822$	54779.9	+	94881.6i	0.0810733	+	0.140423i
$823$	−392425.	+	226567.i	−0.579371	+	0.334500i	−0.760883	−	0.648889i	$-0.775234\pi$
$823$	−392425.	+	226567.i	−0.579371	+	0.334500i	0.181512	+	0.983389i	$0.441901\pi$
$824$	502889.	+	290343.i	0.740658	+	0.427619i
$825$	−382854.	−	800652.i	−0.562504	−	1.17635i
$826$	−8456.38	−	15992.2i	−0.0123944	−	0.0234396i
$827$			696464.i			1.01833i	0.860669	+	0.509164i	$0.170045\pi$
$827$			696464.i			1.01833i	−0.860669	+	0.509164i	$0.829955\pi$
$828$	92163.0	+	53210.4i	0.134430	+	0.0776132i
$829$	−248133.	+	143260.i	−0.361057	+	0.208457i	−0.669544	−	0.742772i	$-0.733511\pi$
$829$	−248133.	+	143260.i	−0.361057	+	0.208457i	0.308487	+	0.951229i	$0.400177\pi$
$830$	25675.2	−	661733.i	0.0372698	−	0.960565i
$831$	−208276.	−	120248.i	−0.301604	−	0.174131i
$832$	−150627.			−0.217598
$833$	796593.	+	59364.7i	1.14801	+	0.0855536i
$834$	−361422.			−0.519616
$835$	−81832.7	−	155354.i	−0.117369	−	0.222817i
$836$	−659792.	+	380931.i	−0.944048	+	0.545047i
$837$	330093.	−	190579.i	0.471178	−	0.272035i
$838$	71417.2	−	123698.i	0.101699	−	0.176147i
$839$			438126.i			0.622408i	0.950343	+	0.311204i	$0.100732\pi$
$839$			438126.i			0.622408i	−0.950343	+	0.311204i	$0.899268\pi$
$840$	44004.0	−	578088.i	0.0623640	−	0.819286i
$841$	1.19830e6			1.69424
$842$	404042.	+	233274.i	0.569905	+	0.329035i
$843$	43865.5	+	75977.4i	0.0617260	+	0.106913i
$844$	−156653.	−	271332.i	−0.219915	−	0.380904i
$845$	−286182.	−	543297.i	−0.400801	−	0.760894i
$846$			106453.i			0.148736i
$847$	−1.05350e6	−	39200.9i	−1.46848	−	0.0546424i
$848$			18733.3i			0.0260509i
$849$	243506.	−	421765.i	0.337827	−	0.585133i
$850$	−416273.	−	285497.i	−0.576157	−	0.395152i
$851$	329105.	+	570027.i	0.454439	+	0.787112i
$852$	−27897.2	+	48319.3i	−0.0384309	+	0.0665643i
$853$	203854.			0.280170			0.140085	−	0.990140i	$-0.455262\pi$
$853$	203854.			0.280170			0.140085	+	0.990140i	$0.455262\pi$
$854$	−171689.	+	273367.i	−0.235411	+	0.374827i
$855$	−211560.	−	133340.i	−0.289402	−	0.182401i
$856$	319473.	−	553343.i	0.436000	−	0.755174i
$857$	339629.	+	588254.i	0.462427	+	0.800946i	0.999081	−	0.0428557i	$-0.0136456\pi$
$857$	339629.	+	588254.i	0.462427	+	0.800946i	−0.536655	+	0.843802i	$0.680312\pi$
$858$	188766.	−	108984.i	0.256419	−	0.148044i
$859$	926894.	+	535142.i	1.25616	+	0.725242i	0.972325	−	0.233632i	$-0.0750612\pi$
$859$	926894.	+	535142.i	1.25616	+	0.725242i	0.283831	+	0.958874i	$0.408394\pi$
$860$	360781.	+	227389.i	0.487806	+	0.307449i
$861$	297303.	+	186722.i	0.401045	+	0.251878i
$862$			167359.i			0.225235i
$863$	−593419.	−	342611.i	−0.796783	−	0.460023i	0.0455621	−	0.998962i	$-0.485492\pi$
$863$	−593419.	−	342611.i	−0.796783	−	0.460023i	−0.842345	+	0.538939i	$0.818825\pi$
$864$	709781.	−	409792.i	0.950817	−	0.548955i
$865$	−319096.	−	12380.9i	−0.426471	−	0.0165470i
$866$	74538.8	+	43035.0i	0.0993909	+	0.0573834i
$867$	−202863.			−0.269876
$868$	8847.87	−	237782.i	0.0117435	−	0.315601i
$869$	652440.			0.863975
$870$	553521.	−	291567.i	0.731300	−	0.385213i
$871$	169855.	−	98065.8i	0.223894	−	0.129265i
$872$	−322958.	+	186460.i	−0.424730	+	0.245218i
$873$	−73050.4	+	126527.i	−0.0958505	+	0.166018i
$874$		−	401569.i		−	0.525699i
$875$	−276908.	−	713795.i	−0.361676	−	0.932304i
$876$	−448551.			−0.584525
$877$	1.19402e6	+	689368.i	1.55243	+	0.896297i	0.997943	+	0.0641060i	$0.0204196\pi$
$877$	1.19402e6	+	689368.i	1.55243	+	0.896297i	0.554489	+	0.832191i	$0.312914\pi$
$878$	−126521.	−	219142.i	−0.164125	−	0.284273i
$879$	100246.	+	173631.i	0.129744	+	0.224723i
$880$	−17425.8	−	33081.7i	−0.0225023	−	0.0427191i
$881$		−	724372.i		−	0.933275i	−0.884449	−	0.466638i	$-0.845465\pi$
$881$		−	724372.i		−	0.933275i	0.884449	−	0.466638i	$-0.154535\pi$
$882$	10929.9	−	146664.i	0.0140501	−	0.188533i
$883$			384899.i			0.493657i	0.969059	+	0.246828i	$0.0793884\pi$
$883$			384899.i			0.493657i	−0.969059	+	0.246828i	$0.920612\pi$
$884$	−106314.	+	184141.i	−0.136046	+	0.235639i
$885$	−1100.83	+	28371.9i	−0.00140550	+	0.0362244i
$886$	−45373.7	−	78589.6i	−0.0578012	−	0.100115i
$887$	−552646.	+	957210.i	−0.702424	+	1.21663i	0.265189	+	0.964196i	$0.414566\pi$
$887$	−552646.	+	957210.i	−0.702424	+	1.21663i	−0.967613	+	0.252438i	$0.918768\pi$
$888$	746525.			0.946714
$889$	−810174.	+	428404.i	−1.02512	+	0.542063i
$890$	−85982.4	+	136422.i	−0.108550	+	0.172228i
$891$	−368926.	+	638999.i	−0.464712	+	0.804905i
$892$	261417.	+	452787.i	0.328552	+	0.569068i
$893$	−596643.	+	344472.i	−0.748189	+	0.431967i
$894$	252255.	+	145640.i	0.315620	+	0.182224i
$895$	−590456.	+	936832.i	−0.737126	+	1.16954i
$896$	19581.7	−	526248.i	0.0243913	−	0.655503i
$897$		−	197048.i		−	0.244899i
$898$	−320847.	−	185241.i	−0.397874	−	0.229713i
$899$	574384.	−	331621.i	0.710694	−	0.410320i
$900$	90153.4	−	131449.i	0.111300	−	0.162283i
$901$	−686215.	−	396187.i	−0.845300	−	0.488034i
$902$	−442866.			−0.544326
$903$	−522995.	−	328469.i	−0.641390	−	0.402827i
$904$	−399716.			−0.489119
$905$	−327592.	+	172559.i	−0.399978	+	0.210689i
$906$	−312824.	+	180609.i	−0.381105	+	0.220031i
$907$	−614967.	+	355051.i	−0.747545	+	0.431595i	−0.824806	−	0.565416i	$-0.808716\pi$
$907$	−614967.	+	355051.i	−0.747545	+	0.431595i	0.0772614	+	0.997011i	$0.475382\pi$
$908$	−3561.05	+	6167.93i	−0.00431924	+	0.00748114i
$909$			198625.i			0.240385i
$910$	169514.	−	81388.9i	0.204703	−	0.0982839i
$911$	−207745.			−0.250319			−0.125159	−	0.992137i	$-0.539944\pi$
$911$	−207745.			−0.250319			−0.125159	+	0.992137i	$0.539944\pi$
$912$	20165.7	+	11642.7i	0.0242451	+	0.0139979i
$913$	1.03744e6	+	1.79690e6i	1.24458	+	2.15567i
$914$	−306011.	−	530027.i	−0.366307	−	0.634462i
$915$	448271.	−	236127.i	0.535424	−	0.282035i
$916$			831325.i			0.990786i
$917$	−28860.9	+	775621.i	−0.0343219	+	0.922382i
$918$			640709.i			0.760284i
$919$	188279.	−	326109.i	0.222931	−	0.386128i	−0.732765	−	0.680481i	$-0.761771\pi$
$919$	188279.	−	326109.i	0.222931	−	0.386128i	0.955697	+	0.294353i	$0.0951041\pi$
$920$	660648.	+	25633.1i	0.780539	+	0.0302848i
$921$	−399865.	−	692586.i	−0.471404	−	0.816496i
$922$	−197625.	+	342297.i	−0.232478	+	0.402663i
$923$	−46744.0			−0.0548684
$924$	328728.	+	621672.i	0.385028	+	0.728144i
$925$	889400.	−	425291.i	1.03947	−	0.497053i
$926$	402825.	−	697714.i	0.469780	−	0.813684i
$927$	−115599.	−	200224.i	−0.134523	−	0.233000i
$928$	1.23507e6	−	713066.i	1.43415	−	0.828007i
$929$	353826.	+	204281.i	0.409976	+	0.236700i	0.690779	−	0.723066i	$-0.257268\pi$
$929$	353826.	+	204281.i	0.409976	+	0.236700i	−0.280804	+	0.959765i	$0.590601\pi$
$930$	116103.	−	184212.i	0.134239	−	0.212986i
$931$	857387.	−	413333.i	0.989185	−	0.476871i
$932$		−	508294.i		−	0.585172i
$933$	559079.	+	322784.i	0.642258	+	0.370808i
$934$	−164412.	+	94923.1i	−0.188468	+	0.108812i
$935$	1.58034e6	+	61317.0i	1.80770	+	0.0701387i
$936$	87573.4	+	50560.5i	0.0999587	+	0.0577112i
$937$	−379698.			−0.432474			−0.216237	−	0.976341i	$-0.569378\pi$
$937$	−379698.			−0.432474			−0.216237	+	0.976341i	$0.569378\pi$
$938$	−172463.	−	326153.i	−0.196016	−	0.370695i
$939$	126621.			0.143607
$940$	−204653.	−	388519.i	−0.231612	−	0.439700i
$941$	686356.	−	396268.i	0.775122	−	0.447517i	−0.0595767	−	0.998224i	$-0.518975\pi$
$941$	686356.	−	396268.i	0.775122	−	0.447517i	0.834699	+	0.550707i	$0.185642\pi$
$942$	79234.3	−	45745.9i	0.0892917	−	0.0515526i
$943$	−200179.	+	346721.i	−0.225111	+	0.389903i
$944$			1196.24i			0.00134238i
$945$	−548386.	+	802309.i	−0.614076	+	0.898418i
$946$	779059.			0.870539
$947$	193633.	+	111794.i	0.215913	+	0.124657i	0.604056	−	0.796942i	$-0.293550\pi$
$947$	193633.	+	111794.i	0.215913	+	0.124657i	−0.388144	+	0.921599i	$0.626884\pi$
$948$	−129489.	−	224282.i	−0.144085	−	0.249562i
$949$	−187896.	−	325445.i	−0.208634	−	0.361365i
$950$	−599653.	−	46603.1i	−0.664435	−	0.0516378i
$951$			366853.i			0.405631i
$952$	874914.	+	549492.i	0.965365	+	0.606300i
$953$		−	924011.i		−	1.01740i	−0.860944	−	0.508699i	$-0.830126\pi$
$953$		−	924011.i		−	1.01740i	0.860944	−	0.508699i	$-0.169874\pi$
$954$	−72943.6	+	126342.i	−0.0801476	+	0.138820i
$955$	−643786.	−	24978.8i	−0.705886	−	0.0273883i
$956$	−231235.	−	400512.i	−0.253011	−	0.438227i
$957$	−980083.	+	1.69755e6i	−1.07014	+	1.85353i
$958$	650926.			0.709253
$959$	−250779.	−	157503.i	−0.272680	−	0.171258i
$960$	237122.	−	376224.i	0.257294	−	0.408229i
$961$	−346339.	+	599877.i	−0.375021	+	0.649555i
$962$	121065.	+	209690.i	0.130818	+	0.226583i
$963$	−220312.	+	127197.i	−0.237567	+	0.137159i
$964$	−947711.	−	547161.i	−1.01982	−	0.588791i
$965$	407556.	+	256870.i	0.437656	+	0.275841i
$966$	−370411.	−	13783.0i	−0.396944	−	0.0147703i
$967$		−	828515.i		−	0.886028i	−0.896515	−	0.443014i	$-0.853909\pi$
$967$		−	828515.i		−	0.886028i	0.896515	−	0.443014i	$-0.146091\pi$
$968$	−1.18085e6	−	681765.i	−1.26021	−	0.727585i
$969$	−852958.	+	492455.i	−0.908406	+	0.524469i
$970$	−13623.7	+	351127.i	−0.0144794	+	0.373182i
$971$	−37486.0	−	21642.6i	−0.0397586	−	0.0229546i	0.479989	−	0.877275i	$-0.340641\pi$
$971$	−37486.0	−	21642.6i	−0.0397586	−	0.0229546i	−0.519748	+	0.854320i	$0.673974\pi$
$972$	−356586.			−0.377426
$973$	863610.	−	456660.i	0.912204	−	0.482356i
$974$	−269673.			−0.284263
$975$	−294246.	−	22867.9i	−0.309529	−	0.0240556i
$976$	18486.3	−	10673.0i	0.0194066	−	0.0112044i
$977$	372047.	−	214802.i	0.389771	−	0.225034i	−0.292290	−	0.956330i	$-0.594417\pi$
$977$	372047.	−	214802.i	0.389771	−	0.225034i	0.682061	+	0.731296i	$0.261084\pi$
$978$	313144.	−	542381.i	0.327390	−	0.567057i
$979$		−	505246.i		−	0.527154i
$980$	242067.	+	556291.i	0.252049	+	0.579228i
$981$	148477.			0.154284
$982$	−46783.8	−	27010.6i	−0.0485146	−	0.0280099i
$983$	−769218.	−	1.33232e6i	−0.796053	−	1.37881i	−0.922168	−	0.386789i	$-0.873584\pi$
$983$	−769218.	−	1.33232e6i	−0.796053	−	1.37881i	0.126115	−	0.992016i	$-0.459749\pi$
$984$	227038.	+	393242.i	0.234482	+	0.406134i
$985$	1.39946e6	−	737167.i	1.44241	−	0.759790i
$986$			1.11488e6i			1.14676i
$987$	297265.	+	562171.i	0.305147	+	0.577078i
$988$			253359.i			0.259550i
$989$	352142.	−	609927.i	0.360019	−	0.623571i
$990$	11289.3	−	290963.i	0.0115186	−	0.296871i
$991$	−40343.8	−	69877.5i	−0.0410799	−	0.0711525i	0.844754	−	0.535154i	$-0.179746\pi$
$991$	−40343.8	−	69877.5i	−0.0410799	−	0.0711525i	−0.885834	+	0.464002i	$0.846413\pi$
$992$	248184.	−	429867.i	0.252203	−	0.436828i
$993$	−1.17528e6			−1.19191
$994$	−3269.63	+	87869.5i	−0.00330922	+	0.0889335i
$995$	−1.29597e6	−	816810.i	−1.30903	−	0.825040i
$996$	411801.	−	713260.i	0.415115	−	0.719000i
$997$	−235880.	−	408556.i	−0.237301	−	0.411018i	0.722638	−	0.691227i	$-0.242930\pi$
$997$	−235880.	−	408556.i	−0.237301	−	0.411018i	−0.959939	+	0.280209i	$0.909596\pi$
$998$	−81732.9	+	47188.5i	−0.0820608	+	0.0473778i
$999$	−1.08370e6	−	625677.i	−1.08587	−	0.626930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.i.a.19.6	✓	28
5.2	odd	4		175.5.i.e.26.9		28
5.3	odd	4		175.5.i.e.26.6		28
5.4	even	2	inner	35.5.i.a.19.9	yes	28
7.2	even	3		245.5.c.a.244.12		28
7.3	odd	6	inner	35.5.i.a.24.9	yes	28
7.5	odd	6		245.5.c.a.244.18		28
35.3	even	12		175.5.i.e.101.6		28
35.9	even	6		245.5.c.a.244.17		28
35.17	even	12		175.5.i.e.101.9		28
35.19	odd	6		245.5.c.a.244.11		28
35.24	odd	6	inner	35.5.i.a.24.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.i.a.19.6	✓	28	1.1	even	1	trivial
35.5.i.a.19.9	yes	28	5.4	even	2	inner
35.5.i.a.24.6	yes	28	35.24	odd	6	inner
35.5.i.a.24.9	yes	28	7.3	odd	6	inner
175.5.i.e.26.6		28	5.3	odd	4
175.5.i.e.26.9		28	5.2	odd	4
175.5.i.e.101.6		28	35.3	even	12
175.5.i.e.101.9		28	35.17	even	12
245.5.c.a.244.11		28	35.19	odd	6
245.5.c.a.244.12		28	7.2	even	3
245.5.c.a.244.17		28	35.9	even	6
245.5.c.a.244.18		28	7.5	odd	6

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10231 - 1.21377i) q^{2} +(3.73387 + 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(11.6512 + 22.1190i) q^{5} -18.1282i q^{6} +(22.9051 + 43.3169i) q^{7} +63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +O(q^{10})\)	\(q+(-2.10231 - 1.21377i) q^{2} +(3.73387 + 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(11.6512 + 22.1190i) q^{5} -18.1282i q^{6} +(22.9051 + 43.3169i) q^{7} +63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +(2.35294 - 60.6428i) q^{10} +(95.0736 + 164.672i) q^{11} +(37.7384 - 65.3648i) q^{12} +63.2338 q^{13} +(4.42305 - 118.867i) q^{14} +(-99.5450 + 157.940i) q^{15} +(-3.93280 + 6.81181i) q^{16} +(-166.348 - 288.123i) q^{17} +(-53.0475 + 30.6270i) q^{18} +(-343.314 - 198.213i) q^{19} +(134.727 - 213.762i) q^{20} +(-194.616 + 309.873i) q^{21} -461.590i q^{22} +(-361.380 - 208.643i) q^{23} +(-409.867 + 236.637i) q^{24} +(-353.500 + 515.425i) q^{25} +(-132.937 - 76.7512i) q^{26} +793.319 q^{27} +(263.400 - 419.391i) q^{28} +1380.43 q^{29} +(400.978 - 211.215i) q^{30} +(416.091 - 240.230i) q^{31} +(894.698 - 516.554i) q^{32} +(-709.984 + 1229.73i) q^{33} +807.631i q^{34} +(-691.254 + 1011.33i) q^{35} -255.031 q^{36} +(-1366.04 - 788.682i) q^{37} +(481.169 + 833.409i) q^{38} +(236.107 + 408.949i) q^{39} +(-1401.81 + 738.404i) q^{40} -959.437i q^{41} +(785.258 - 415.229i) q^{42} +1687.77i q^{43} +(960.915 - 1664.35i) q^{44} +(630.350 + 24.4575i) q^{45} +(506.488 + 877.263i) q^{46} +(868.945 - 1505.06i) q^{47} -58.7382 q^{48} +(-1351.71 + 1984.36i) q^{49} +(1368.77 - 654.516i) q^{50} +(1242.24 - 2151.62i) q^{51} +(-319.554 - 553.484i) q^{52} +(2062.59 - 1190.84i) q^{53} +(-1667.80 - 962.906i) q^{54} +(-2534.66 + 4021.56i) q^{55} +(-2745.25 + 1451.63i) q^{56} -2960.40i q^{57} +(-2902.09 - 1675.52i) q^{58} +(131.709 - 76.0424i) q^{59} +(1885.50 + 73.1573i) q^{60} +(-2350.26 - 1356.93i) q^{61} -1166.34 q^{62} +(1235.56 + 45.9753i) q^{63} -2382.06 q^{64} +(736.749 + 1398.67i) q^{65} +(2985.21 - 1723.51i) q^{66} +(2686.14 - 1550.84i) q^{67} +(-1681.29 + 2912.07i) q^{68} -3116.17i q^{69} +(2680.75 - 1287.11i) q^{70} -739.225 q^{71} +(1384.91 + 799.581i) q^{72} +(-2971.45 - 5146.70i) q^{73} +(1914.56 + 3316.11i) q^{74} +(-4653.30 - 361.640i) q^{75} +4006.69i q^{76} +(-4955.42 + 7890.14i) q^{77} -1146.32i q^{78} +(1715.62 - 2971.54i) q^{79} +(-196.492 - 7.62388i) q^{80} +(1940.21 + 3360.55i) q^{81} +(-1164.53 + 2017.03i) q^{82} +10912.0 q^{83} +(3695.81 + 137.521i) q^{84} +(4434.83 - 7036.42i) q^{85} +(2048.57 - 3548.23i) q^{86} +(5154.34 + 8927.57i) q^{87} +(-10436.3 + 6025.37i) q^{88} +(-2301.14 - 1328.57i) q^{89} +(-1295.50 - 816.516i) q^{90} +(1448.38 + 2739.09i) q^{91} +4217.53i q^{92} +(3107.26 + 1793.98i) q^{93} +(-3653.58 + 2109.40i) q^{94} +(384.242 - 9903.18i) q^{95} +(6681.36 + 3857.49i) q^{96} -5790.08 q^{97} +(5250.27 - 2531.07i) q^{98} +4797.98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

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