LMFDB - Embedded newform 35.5.i.a.19.9

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			19.9
Character	$\chi$	$=$	35.19
Dual form			35.5.i.a.24.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10231 + 1.21377i) q^{2} +(-3.73387 - 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(24.9812 - 0.969268i) q^{5} -18.1282i q^{6} +(-22.9051 - 43.3169i) q^{7} -63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +O(q^{10})$	\(q+(2.10231 + 1.21377i) q^{2} +(-3.73387 - 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(24.9812 - 0.969268i) q^{5} -18.1282i q^{6} +(-22.9051 - 43.3169i) q^{7} -63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +(53.6947 + 28.2837i) 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} +(623.121 - 48.4270i) q^{25} +(-132.937 - 76.7512i) q^{26} -793.319 q^{27} +(-263.400 + 419.391i) q^{28} +1380.43 q^{29} +(-17.5711 - 452.864i) q^{30} +(416.091 - 240.230i) q^{31} +(-894.698 + 516.554i) q^{32} +(709.984 - 1229.73i) q^{33} +807.631i q^{34} +(-614.183 - 1059.91i) q^{35} -255.031 q^{36} +(1366.04 + 788.682i) q^{37} +(-481.169 - 833.409i) q^{38} +(236.107 + 408.949i) q^{39} +(-61.4282 - 1583.21i) q^{40} -959.437i q^{41} +(-785.258 + 415.229i) q^{42} -1687.77i q^{43} +(960.915 - 1664.35i) q^{44} +(293.994 - 558.128i) 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} +(-879.395 + 1669.47i) q^{60} +(-2350.26 - 1356.93i) q^{61} +1166.34 q^{62} +(-1235.56 - 45.9753i) q^{63} -2382.06 q^{64} +(-1579.66 + 61.2905i) q^{65} +(2985.21 - 1723.51i) q^{66} +(-2686.14 + 1550.84i) q^{67} +(1681.29 - 2912.07i) q^{68} -3116.17i q^{69} +(-4.72094 - 2973.73i) q^{70} -739.225 q^{71} +(-1384.91 - 799.581i) q^{72} +(2971.45 + 5146.70i) q^{73} +(1914.56 + 3316.11i) q^{74} +(-2639.84 - 3849.06i) q^{75} +4006.69i q^{76} +(4955.42 - 7890.14i) q^{77} +1146.32i q^{78} +(1715.62 - 2971.54i) q^{79} +(-91.6437 + 173.979i) 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} +(-8768.53 - 4618.83i) 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	0.739214	−	0.673471i	$-0.235197\pi$
$2$	2.10231	+	1.21377i	0.525577	+	0.303442i	−0.213636	+	0.976913i	$0.568531\pi$
$3$	−3.73387	−	6.46725i	−0.414874	−	0.718583i	0.580541	−	0.814231i	$-0.302841\pi$
$3$	−3.73387	−	6.46725i	−0.414874	−	0.718583i	−0.995415	+	0.0956480i	$0.969508\pi$
$4$	−5.05353	−	8.75297i	−0.315846	−	0.547061i
$5$	24.9812	−	0.969268i	0.999248	−	0.0387707i
$5$	24.9812	−	0.969268i	0.999248	−	0.0387707i
$6$		−	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
$10$	53.6947	+	28.2837i	0.536947	+	0.282837i
$11$	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	$-0.559903\pi$
$13$	−63.2338			−0.374165			−0.187082	+	0.982344i	$0.559903\pi$
$14$	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	$0.0285639\pi$
$17$	166.348	+	288.123i	0.575598	+	0.996964i	−0.420379	+	0.907349i	$0.638103\pi$
$18$	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	0.801036	−	0.598616i	$-0.204283\pi$
$23$	361.380	+	208.643i	0.683137	+	0.394409i	−0.117899	+	0.993026i	$0.537616\pi$
$24$	−409.867	+	236.637i	−0.711575	+	0.410828i
$25$	623.121	−	48.4270i	0.996994	−	0.0774832i
$26$	−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	$0.193580\pi$
$30$	−17.5711	−	452.864i	−0.0195234	−	0.503183i
$31$	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
$35$	−614.183	−	1059.91i	−0.501374	−	0.865231i
$36$	−255.031			−0.196783
$37$	1366.04	+	788.682i	0.997836	+	0.576101i	0.907607	−	0.419820i	$-0.137907\pi$
$37$	1366.04	+	788.682i	0.997836	+	0.576101i	0.0902285	+	0.995921i	$0.471240\pi$
$38$	−481.169	−	833.409i	−0.333219	−	0.577153i
$39$	236.107	+	408.949i	0.155231	+	0.268868i
$40$	−61.4282	−	1583.21i	−0.0383926	−	0.989504i
$41$		−	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	$-0.849138\pi$
$43$		−	1687.77i		−	0.912804i	0.889774	−	0.456402i	$-0.150862\pi$
$44$	960.915	−	1664.35i	0.496340	−	0.859686i
$45$	293.994	−	558.128i	0.145182	−	0.275619i
$46$	506.488	+	877.263i	0.239361	+	0.414585i
$47$	−868.945	+	1505.06i	−0.393366	+	0.681330i	−0.992891	−	0.119026i	$-0.962023\pi$
$47$	−868.945	+	1505.06i	−0.393366	+	0.681330i	0.599525	+	0.800356i	$0.295356\pi$
$48$	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	−0.819986	−	0.572384i	$-0.806019\pi$
$53$	−2062.59	+	1190.84i	−0.734280	+	0.423937i	0.0857058	+	0.996320i	$0.472685\pi$
$54$	−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	$0.326379\pi$
$60$	−879.395	+	1669.47i	−0.244276	+	0.463742i
$61$	−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
$65$	−1579.66	+	61.2905i	−0.373883	+	0.0145066i
$66$	2985.21	−	1723.51i	0.685311	−	0.395664i
$67$	−2686.14	+	1550.84i	−0.598383	+	0.345477i	−0.768405	−	0.639964i	$-0.778949\pi$
$67$	−2686.14	+	1550.84i	−0.598383	+	0.345477i	0.170022	+	0.985440i	$0.445616\pi$
$68$	1681.29	−	2912.07i	0.363600	−	0.629774i
$69$		−	3116.17i		−	0.654521i
$70$	−4.72094	−	2973.73i	−0.000963457	−	0.606884i
$71$	−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	$0.0216108\pi$
$73$	2971.45	+	5146.70i	0.557599	+	0.965790i	−0.440097	+	0.897950i	$0.645056\pi$
$74$	1914.56	+	3316.11i	0.349627	+	0.605571i
$75$	−2639.84	−	3849.06i	−0.469305	−	0.684277i
$76$			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	$0.0780236\pi$
$80$	−91.6437	+	173.979i	−0.0143193	+	0.0271843i
$81$	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	$-0.790953\pi$
$83$	−10912.0			−1.58397			−0.791986	+	0.610540i	$0.790953\pi$
$84$	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
$95$	−8768.53	−	4618.83i	−0.971582	−	0.511781i
$96$	6681.36	+	3857.49i	0.724974	+	0.418564i
$97$	5790.08			0.615377			0.307688	−	0.951487i	$-0.400445\pi$
$97$	5790.08			0.615377			0.307688	+	0.951487i	$0.400445\pi$
$98$	−5250.27	+	2531.07i	−0.546675	+	0.263544i
$99$	4797.98			0.489540
$100$	−3572.84	−	5209.43i	−0.357284	−	0.520943i
$101$	−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	−0.997031	−	0.0770017i	$-0.975465\pi$
$103$	−4581.28	+	7935.02i	−0.431830	+	0.747952i	0.565201	+	0.824953i	$0.308799\pi$
$104$			4007.50i			0.370516i
$105$	−4561.40	+	7929.63i	−0.413733	+	0.719241i
$106$	−5781.61			−0.514561
$107$	8731.13	+	5040.92i	0.762611	+	0.440294i	0.830232	−	0.557417i	$-0.188208\pi$
$107$	8731.13	+	5040.92i	0.762611	+	0.440294i	−0.0676215	+	0.997711i	$0.521541\pi$
$108$	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	$0.753681\pi$
$110$	447.404	+	11531.1i	0.0369755	+	0.952980i
$111$		−	11779.3i		−	0.956037i
$112$	385.148	+	14.3314i	0.0307038	+	0.00114249i
$113$		−	6307.06i		−	0.493936i	−0.969024	−	0.246968i	$-0.920566\pi$
$113$		−	6307.06i		−	0.493936i	0.969024	−	0.246968i	$-0.0794342\pi$
$114$	−3593.24	+	6223.67i	−0.276488	+	0.478891i
$115$	9229.93	+	4861.87i	0.697915	+	0.367627i
$116$	−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	$-0.803128\pi$
$127$		−	18703.4i		−	1.15961i	0.814754	−	0.579807i	$-0.196872\pi$
$128$	9307.34	+	5373.59i	0.568075	+	0.327978i
$129$	−10915.3	+	6301.93i	−0.655925	+	0.378699i
$130$	−3395.32	−	1788.49i	−0.200907	−	0.105828i
$131$	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
$135$	−19818.1	+	768.939i	−1.08741	+	0.0421915i
$136$	18260.0	−	10542.4i	0.987242	−	0.569984i
$137$	5233.92	−	3021.81i	0.278860	−	0.161000i	−0.354047	−	0.935228i	$-0.615195\pi$
$137$	5233.92	−	3021.81i	0.278860	−	0.161000i	0.632907	+	0.774228i	$0.281861\pi$
$138$	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	$-0.172558\pi$
$140$	−6173.54	+	10732.2i	−0.314977	+	0.547561i
$141$	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
$145$	34484.8	−	1338.01i	1.64018	−	0.0636388i
$146$			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	$0.284528\pi$
$150$	−877.894	−	11296.1i	−0.0390175	−	0.502047i
$151$	−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	0.810287	−	0.586033i	$-0.199311\pi$
$157$	−2523.47	−	4370.77i	−0.102376	−	0.177320i	−0.912663	+	0.408713i	$0.865978\pi$
$158$	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	−0.183144	−	0.983086i	$-0.558627\pi$
$163$	−29919.2	−	17273.8i	−1.12609	−	0.650150i	−0.942949	+	0.332936i	$0.891961\pi$
$164$	−8397.92	+	4848.54i	−0.312237	+	0.180270i
$165$	16544.3	−	31408.3i	0.607689	−	1.15366i
$166$	−22940.4	−	13244.6i	−0.832499	−	0.480644i
$167$	7023.55			0.251839			0.125920	−	0.992040i	$-0.459812\pi$
$167$	7023.55			0.251839			0.125920	+	0.992040i	$0.459812\pi$
$168$	19638.5	+	12334.0i	0.695807	+	0.437004i
$169$	−24562.5			−0.860001
$170$	782.811	+	20175.6i	0.0270869	+	0.698117i
$171$	−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	−0.739379	−	0.673289i	$-0.764881\pi$
$173$	6386.73	−	11062.1i	0.213396	−	0.369613i	0.952775	+	0.303677i	$0.0982142\pi$
$174$		−	25024.7i		−	0.826552i
$175$	−16370.4	−	25882.5i	−0.534543	−	0.845141i
$176$	−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	$0.590403\pi$
$180$	−6370.98	+	247.194i	−0.196635	+	0.00762943i
$181$			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
$185$	34889.7	+	18378.2i	1.01942	+	0.536981i
$186$	−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	−0.706994	−	0.707219i	$-0.749949\pi$
$193$	−16688.3	+	9635.02i	−0.448021	+	0.258665i	0.258973	+	0.965885i	$0.416616\pi$
$194$	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	$0.303341\pi$
$197$			63269.7i			1.63028i	−0.579262	+	0.815142i	$0.696659\pi$
$198$	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	$0.614913\pi$
$200$	−3069.10	−	39490.8i	−0.0767275	−	0.987271i
$201$	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
$205$	−929.952	−	23967.9i	−0.0221285	−	0.570325i
$206$	−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
$210$	−19214.2	+	11134.0i	−0.435697	+	0.252473i
$211$	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
$215$	−1635.91	−	42162.6i	−0.0353901	−	0.912118i
$216$			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
$220$	22391.6	−	42508.9i	0.462636	−	0.878283i
$221$	−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	$-0.325889\pi$
$223$	51729.5			1.04023			0.520114	+	0.854097i	$0.325889\pi$
$224$	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	0.869424	−	0.494067i	$-0.164490\pi$
$227$	352.333	+	610.259i	0.00683757	+	0.0118430i	−0.862586	+	0.505910i	$0.831157\pi$
$228$	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	0.0420078	−	0.999117i	$-0.486625\pi$
$233$	−43553.3	−	25145.5i	−0.802249	−	0.463179i	−0.844257	+	0.535938i	$0.819958\pi$
$234$	−3354.40	+	1936.66i	−0.0612608	+	0.0353689i
$235$	−20248.5	+	38440.4i	−0.366655	+	0.696069i
$236$	−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	$0.368826\pi$
$240$	1467.35	−	56.9331i	0.0254749	−	0.000988422i
$241$	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
$245$	−31844.0	+	50881.8i	−0.530512	+	0.847678i
$246$	−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
$250$	34828.0	+	15023.9i	0.557248	+	0.240382i
$251$			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
$255$	28947.2	−	54954.2i	0.445170	−	0.845124i
$256$	32101.1	+	55600.7i	0.489824	+	0.848399i
$257$	57163.9	−	99010.8i	0.865477	−	1.49905i	−0.00109563	−	0.999999i	$-0.500349\pi$
$257$	57163.9	−	99010.8i	0.865477	−	1.49905i	0.866573	−	0.499051i	$-0.166318\pi$
$258$	−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	−0.816780	−	0.576949i	$-0.804243\pi$
$263$	−50183.3	+	28973.4i	−0.725517	+	0.418878i	0.0912626	+	0.995827i	$0.470910\pi$
$264$	−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	$0.955030\pi$
$270$	−42597.0	−	22438.0i	−0.584322	−	0.307792i
$271$	−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
$275$	67216.9	+	98006.7i	0.888819	+	1.29596i
$276$	−27275.8	+	15747.7i	−0.358063	+	0.206728i
$277$	27890.2	−	16102.4i	0.363489	−	0.209861i	−0.307121	−	0.951670i	$-0.599366\pi$
$277$	27890.2	−	16102.4i	0.363489	−	0.209861i	0.670610	+	0.741810i	$0.266032\pi$
$278$	24198.9	−	41913.8i	0.313117	−	0.542335i
$279$		−	12123.4i		−	0.155746i
$280$	−67172.6	+	38924.4i	−0.856793	+	0.496485i
$281$	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	0.994568	−	0.104085i	$-0.0331915\pi$
$283$	32607.7	+	56478.3i	0.407144	+	0.705194i	−0.587425	+	0.809279i	$0.699858\pi$
$284$	3735.69	+	6470.41i	0.0463164	+	0.0802223i
$285$	2869.42	+	73954.3i	0.0353268	+	0.910487i
$286$		−	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
$290$	74121.7	+	39043.6i	0.881352	+	0.464253i
$291$	−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	$-0.549978\pi$
$293$	−26847.7			−0.312731			−0.156366	+	0.987699i	$0.549978\pi$
$294$	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
$305$	−60027.7	−	31619.6i	−0.645285	−	0.339904i
$306$	17648.7	+	10189.5i	0.188482	+	0.108820i
$307$	107091.			1.13626			0.568130	−	0.822939i	$-0.307667\pi$
$307$	107091.			1.13626			0.568130	+	0.822939i	$0.307667\pi$
$308$	−94104.5	−	3501.63i	−0.991994	−	0.0369121i
$309$	68423.6			0.716620
$310$	29136.5	−	1130.49i	0.303189	−	0.0117637i
$311$	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	−0.906045	−	0.423181i	$-0.860913\pi$
$313$	−8477.90	+	14684.2i	−0.0865366	+	0.149886i	0.819508	+	0.573067i	$0.194247\pi$
$314$		−	12251.6i		−	0.124261i
$315$	−30910.3	+	49.0717i	−0.311518	+	0.000494549i
$316$	−34679.7			−0.347297
$317$	−42543.6	−	24562.5i	−0.423365	−	0.244430i	0.273151	−	0.961971i	$-0.411934\pi$
$317$	−42543.6	−	24562.5i	−0.423365	−	0.244430i	−0.696516	+	0.717541i	$0.745268\pi$
$318$	21587.8	+	37391.1i	0.213478	+	0.369755i
$319$	131242.	+	227318.i	1.28971	+	2.23385i
$320$	−59506.7	+	2308.85i	−0.581120	+	0.0225474i
$321$		−	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
$325$	−39402.3	+	3062.22i	−0.373040	+	0.0289915i
$326$	−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	$-0.958434\pi$
$337$		−	29576.3i		−	0.260426i	0.991486	−	0.130213i	$-0.0415661\pi$
$338$	−51637.9	−	29813.2i	−0.451997	−	0.260961i
$339$	−40789.3	+	23549.7i	−0.354934	+	0.204921i
$340$	39178.0	−	74376.7i	0.338910	−	0.643397i
$341$	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
$345$	−3020.41	−	77845.8i	−0.0253763	−	0.654029i
$346$	26853.8	−	15504.0i	0.224312	−	0.129507i
$347$	135510.	−	78236.7i	1.12541	−	0.649758i	0.182636	−	0.983181i	$-0.441537\pi$
$347$	135510.	−	78236.7i	1.12541	−	0.649758i	0.942777	+	0.333423i	$0.108204\pi$
$348$	−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	$-0.282963\pi$
$350$	−3000.28	−	74282.8i	−0.0244921	−	0.606390i
$351$	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	$-0.966024\pi$
$353$	−73446.6	−	127213.i	−0.589417	−	1.02090i	0.404892	−	0.914364i	$-0.367309\pi$
$354$	−1378.51	−	2387.65i	−0.0110003	−	0.0190531i
$355$	−18466.7	+	716.507i	−0.146532	+	0.00568544i
$356$			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	$0.0494765\pi$
$360$	−35371.8	−	18632.1i	−0.272931	−	0.143766i
$361$	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	$0.0660434\pi$
$367$	89928.4	+	155760.i	0.667674	+	1.15645i	−0.310879	+	0.950450i	$0.600623\pi$
$368$	−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	0.952367	−	0.304954i	$-0.0986410\pi$
$373$	162009.	+	93536.0i	1.16445	+	0.672297i	0.212086	+	0.977251i	$0.431974\pi$
$374$	−132994.	+	76784.4i	−0.950802	+	0.548946i
$375$	−69677.1	−	93595.4i	−0.495482	−	0.665567i
$376$	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	$0.814213\pi$
$380$	3883.56	+	100092.i	0.0268945	+	0.693158i
$381$	−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	−0.872045	−	0.489426i	$-0.837206\pi$
$383$	−1784.69	+	3091.18i	−0.0121665	+	0.0210730i	0.859878	+	0.510499i	$0.170539\pi$
$384$		−	80257.1i		−	0.544279i
$385$	116145.	−	201908.i	0.783571	−	1.36217i
$386$	−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	$-0.333637\pi$
$390$	1111.09	+	28636.3i	0.00730498	+	0.188273i
$391$			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
$395$	39978.0	−	75895.5i	0.256228	−	0.486432i
$396$	−24246.7	−	41996.6i	−0.154619	−	0.267808i
$397$	−64285.1	+	111345.i	−0.407877	+	0.706464i	−0.994652	−	0.103287i	$-0.967064\pi$
$397$	−64285.1	+	111345.i	−0.407877	+	0.706464i	0.586775	+	0.809750i	$0.300397\pi$
$398$	−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	$0.125578\pi$
$410$	27136.4	−	51516.7i	0.161430	−	0.306464i
$411$	−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
$415$	−272594.	+	10576.6i	−1.58278	+	0.0614117i
$416$	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	$0.946406\pi$
$420$	92459.0	−	146.783i	0.524144	−	0.000832104i
$421$	−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
$425$	117608.	+	171480.i	0.651115	+	0.949368i
$426$			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
$430$	47736.5	−	90624.5i	0.258175	−	0.490127i
$431$	−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	$-0.469857\pi$
$433$	35455.7			0.189108			0.0945540	+	0.995520i	$0.469857\pi$
$434$	−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	0.415245	−	0.909710i	$-0.363696\pi$
$443$	−32374.2	−	18691.2i	−0.164965	−	0.0952425i	−0.580209	+	0.814467i	$0.697029\pi$
$444$	−103104.	+	59527.2i	−0.523010	+	0.301960i
$445$	−58773.1	−	30958.7i	−0.296796	−	0.156338i
$446$	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	$0.376436\pi$
$450$	31571.8	−	21653.3i	0.155910	−	0.106930i
$451$	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
$455$	38837.2	+	67022.0i	0.187596	+	0.323739i
$456$	187618.			0.902286
$457$	−218339.	−	126058.i	−1.04544	−	0.603586i	−0.124072	−	0.992273i	$-0.539595\pi$
$457$	−218339.	−	126058.i	−1.04544	−	0.603586i	−0.921370	+	0.388687i	$0.872929\pi$
$458$	−99834.8	−	172919.i	−0.475939	−	0.824350i
$459$	−131967.	−	228573.i	−0.626382	−	1.08493i
$460$	−4087.91	−	105359.i	−0.0193191	−	0.497915i
$461$		−	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	$-0.718210\pi$
$463$		−	331880.i		−	1.54817i	0.633081	−	0.774085i	$-0.281790\pi$
$464$	−5428.95	+	9403.22i	−0.0252162	+	0.0436758i
$465$	−79361.8	−	41803.9i	−0.367034	−	0.193335i
$466$	−61041.7	−	105727.i	−0.281096	−	0.486873i
$467$	−39102.6	+	67727.7i	−0.179297	+	0.310551i	−0.941640	−	0.336622i	$-0.890716\pi$
$467$	−39102.6	+	67727.7i	−0.179297	+	0.310551i	0.762343	+	0.647173i	$0.224049\pi$
$468$	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	$0.531979\pi$
$480$	170647.	+	89888.6i	0.740657	+	0.390142i
$481$	−86379.7	−	49871.4i	−0.373355	−	0.215556i
$482$	262837.			1.13134
$483$	−134983.	+	71376.4i	−0.578609	+	0.305957i
$484$	217453.			0.928271
$485$	144643.	−	5612.14i	0.614914	−	0.0238586i
$486$	−74171.3	+	42822.8i	−0.314025	+	0.181302i
$487$	−96206.2	+	55544.7i	−0.405644	+	0.234199i	−0.688916	−	0.724841i	$-0.741913\pi$
$487$	−96206.2	+	55544.7i	−0.405644	+	0.234199i	0.283272	+	0.959039i	$0.408580\pi$
$488$	−85996.4	+	148950.i	−0.361111	+	0.625462i
$489$			257993.i			1.07892i
$490$	−128705.	+	68318.2i	−0.536046	+	0.284541i
$491$	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
$495$	119859.	−	4650.53i	0.489172	−	0.0189798i
$496$			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	$0.141792\pi$
$500$	−94303.2	−	126675.i	−0.377213	−	0.506699i
$501$	−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	$-0.743853\pi$
$503$	−350833.			−1.38664			−0.693321	+	0.720629i	$0.743853\pi$
$504$	−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
$515$	−106755.	+	202667.i	−0.402507	+	0.764132i
$516$	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
$520$	3884.34	+	100112.i	0.0143652	+	0.370237i
$521$	−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	−0.630365	−	0.776299i	$-0.717095\pi$
$523$	97680.4	−	169187.i	0.357112	−	0.618536i	0.987477	+	0.157763i	$0.0504282\pi$
$524$		−	160095.i		−	0.583064i
$525$	−106263.	+	202513.i	−0.385536	+	0.734741i
$526$	−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
$530$	−144432.	+	5603.93i	−0.514175	+	0.0199499i
$531$		−	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
$535$	223000.	+	117465.i	0.779108	+	0.410396i
$536$	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	$-0.854109\pi$
$547$		−	264771.i		−	0.884903i	0.896792	−	0.442452i	$-0.145891\pi$
$548$	−52899.6	−	30541.6i	−0.176153	−	0.101702i
$549$	−59304.2	+	34239.3i	−0.196762	+	0.113600i
$550$	22353.4	+	287626.i	0.0738955	+	0.950830i
$551$	−473921.	−	273618.i	−1.56100	−	0.901244i
$552$	−197490.			−0.648138
$553$	−168014.	−	6251.82i	−0.549409	−	0.0204436i
$554$	78178.3			0.254722
$555$	−11417.3	−	294262.i	−0.0370663	−	0.955318i
$556$	−174508.	+	100752.i	−0.564503	+	0.325916i
$557$	489875.	−	282829.i	1.57897	−	0.911621i	0.583971	−	0.811775i	$-0.301498\pi$
$557$	489875.	−	282829.i	1.57897	−	0.911621i	0.995003	−	0.0998461i	$-0.0318350\pi$
$558$	14715.1	−	25487.2i	0.0472600	−	0.0818567i
$559$			106724.i			0.341539i
$560$	9635.35	−	15.2966i	0.0307250	−	4.87774e-5i
$561$	472417.			1.50107
$562$	24698.0	+	14259.4i	0.0781968	+	0.0451469i
$563$	72859.4	+	126196.i	0.229863	+	0.398134i	0.957767	−	0.287544i	$-0.0928389\pi$
$563$	72859.4	+	126196.i	0.229863	+	0.398134i	−0.727904	+	0.685679i	$0.759506\pi$
$564$	−65585.2	−	113597.i	−0.206181	−	0.357115i
$565$	−6113.24	−	157558.i	−0.0191502	−	0.493564i
$566$			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	$-0.0742118\pi$
$570$	−83731.0	+	158958.i	−0.257713	+	0.489251i
$571$	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	$-0.992895\pi$
$577$	−172858.	−	299399.i	−0.519205	−	0.899289i	0.480546	−	0.876970i	$-0.340439\pi$
$578$	−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
$585$	−18590.4	+	35292.5i	−0.0543221	+	0.103127i
$586$	−56442.1	−	32586.9i	−0.164365	−	0.0948959i
$587$	−68833.0			−0.199766			−0.0998828	−	0.994999i	$-0.531847\pi$
$587$	−68833.0			−0.199766			−0.0998828	+	0.994999i	$0.531847\pi$
$588$	−78695.9	−	163241.i	−0.227613	−	0.472144i
$589$	−190467.			−0.549020
$590$	9222.85	−	357.846i	0.0264948	−	0.00102800i
$591$	409181.	−	236240.i	1.17149	−	0.676362i
$592$	−10744.7	+	6203.46i	−0.0306585	+	0.0177007i
$593$	100636.	−	174307.i	0.286183	−	0.495684i	−0.686712	−	0.726929i	$-0.740947\pi$
$593$	100636.	−	174307.i	0.286183	−	0.495684i	0.972895	+	0.231246i	$0.0742801\pi$
$594$		−	366188.i		−	1.03784i
$595$	203215.	−	353273.i	0.574014	−	0.997877i
$596$	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	$0.736622\pi$
$600$	−243937.	+	167302.i	−0.677604	+	0.464728i
$601$			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
$605$	−250675.	+	475889.i	−0.684857	+	1.30015i
$606$	71349.5	+	123581.i	0.194288	+	0.336517i
$607$	155245.	−	268893.i	0.421348	−	0.729797i	−0.574723	−	0.818348i	$-0.694890\pi$
$607$	155245.	−	268893.i	0.421348	−	0.729797i	0.996072	+	0.0885510i	$0.0282236\pi$
$608$	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	$0.711905\pi$
$613$	−604065.	+	348757.i	−1.60754	+	0.928116i	−0.989918	+	0.141644i	$0.954761\pi$
$614$	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	$-0.717014\pi$
$617$		−	591179.i		−	1.55292i	0.630167	−	0.776459i	$-0.282986\pi$
$618$	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	$-0.0266212\pi$
$620$	−107411.	−	56578.7i	−0.279424	−	0.147187i
$621$	−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
$625$	385935.	−	60351.7i	0.987993	−	0.154500i
$626$	−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
$630$	−65042.7	−	37414.9i	−0.163877	−	0.0942677i
$631$	−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
$635$	−18128.6	−	467234.i	−0.0449591	−	1.15874i
$636$		−	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
$640$	237717.	+	125218.i	0.580364	+	0.305707i
$641$	−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	$-0.244329\pi$
$643$	595030.			1.43919			0.719593	+	0.694396i	$0.244329\pi$
$644$	−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	0.881432	−	0.472312i	$-0.156580\pi$
$647$	13262.4	+	22971.1i	0.0316820	+	0.0548749i	−0.849750	+	0.527186i	$0.823247\pi$
$648$	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	0.662038	−	0.749470i	$-0.269692\pi$
$653$	146684.	+	84687.8i	0.343997	+	0.198607i	−0.318041	+	0.948077i	$0.603025\pi$
$654$	92379.8	−	53335.5i	0.215984	−	0.124698i
$655$	350364.	+	184554.i	0.816652	+	0.430172i
$656$	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	$0.575270\pi$
$660$	−358523.	+	13910.7i	−0.823055	+	0.0319345i
$661$	−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
$665$	770.946	+	485620.i	0.00174333	+	1.09813i
$666$	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
$670$	−188095.	+	7298.08i	−0.419014	+	0.0162577i
$671$		−	516031.i		−	1.14612i
$672$	14056.9	−	377772.i	0.0311281	−	0.836549i
$673$			5692.85i			0.0125690i	0.999980	+	0.00628449i	$0.00200043\pi$
$673$			5692.85i			0.0125690i	−0.999980	+	0.00628449i	$0.998000\pi$
$674$	35898.8	−	62178.5i	0.0790242	−	0.136874i
$675$	−494334.	+	38418.1i	−1.08496	+	0.0843195i
$676$	124127.	+	214995.i	0.271628	+	0.470473i
$677$	−410243.	+	710561.i	−0.895083	+	1.55033i	−0.0613821	+	0.998114i	$0.519551\pi$
$677$	−410243.	+	710561.i	−0.895083	+	1.55033i	−0.833701	+	0.552216i	$0.813783\pi$
$678$	−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	−0.871959	−	0.489578i	$-0.837151\pi$
$683$	−412354.	+	238072.i	−0.883951	+	0.510350i	−0.0119922	+	0.999928i	$0.503817\pi$
$684$	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
$690$	88137.0	−	167322.i	0.185123	−	0.351443i
$691$	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
$695$	−19324.3	−	498051.i	−0.0400069	−	1.03111i
$696$	−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
$700$	−143820.	+	274087.i	−0.293511	+	0.559362i
$701$	−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
$705$	324209.	−	12579.3i	0.652298	−	0.0253091i
$706$		−	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	$0.310364\pi$
$710$	−39692.4	−	20908.0i	−0.0787392	−	0.0414759i
$711$	−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
$725$	860174.	−	66850.0i	1.63648	−	0.127182i
$726$	337774.	+	195014.i	0.640845	+	0.369992i
$727$	−755148.			−1.42877			−0.714387	−	0.699751i	$-0.753294\pi$
$727$	−755148.			−1.42877			−0.714387	+	0.699751i	$0.753294\pi$
$728$	173592.	−	91792.3i	0.327543	−	0.173198i
$729$	577783.			1.08720
$730$	13983.2	+	360394.i	0.0262399	+	0.676288i
$731$	486286.	−	280757.i	0.910033	−	0.525408i
$732$	177391.	−	102416.i	0.331061	−	0.191138i
$733$	−76987.1	+	133346.i	−0.143288	+	0.248182i	−0.928733	−	0.370749i	$-0.879101\pi$
$733$	−76987.1	+	133346.i	−0.143288	+	0.248182i	0.785445	+	0.618932i	$0.212434\pi$
$734$			436609.i			0.810402i
$735$	447967.	+	15956.8i	0.829222	+	0.0295372i
$736$	−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	$0.998466\pi$
$740$	−15452.6	−	398263.i	−0.0282187	−	0.727288i
$741$		−	187197.i		−	0.340928i
$742$	132429.	+	250442.i	0.240533	+	0.454882i
$743$		−	221399.i		−	0.401050i	−0.979689	−	0.200525i	$-0.935735\pi$
$743$		−	221399.i		−	0.401050i	0.979689	−	0.200525i	$-0.0642648\pi$
$744$	−113695.	+	196925.i	−0.205397	+	0.355758i
$745$	−187208.	+	355402.i	−0.337297	+	0.640335i
$746$	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	$-0.991802\pi$
$757$		−	29515.7i		−	0.0515064i	0.999668	−	0.0257532i	$-0.00819840\pi$
$758$	−503970.	−	290967.i	−0.877134	−	0.506414i
$759$	513148.	−	296266.i	0.890756	−	0.514278i
$760$	−292722.	+	555713.i	−0.506791	+	0.962107i
$761$	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
$765$	209715.	−	8136.90i	0.358349	−	0.0139039i
$766$	−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	$-0.0366653\pi$
$770$	489242.	−	283501.i	0.825168	−	0.478159i
$771$	−853769.			−1.43626
$772$	168670.	+	97381.7i	0.283011	+	0.163397i
$773$	456030.	+	789867.i	0.763193	+	1.32189i	0.941197	+	0.337859i	$0.109703\pi$
$773$	456030.	+	789867.i	0.763193	+	1.32189i	−0.178004	+	0.984030i	$0.556964\pi$
$774$	−51691.5	−	89532.3i	−0.0862853	−	0.149451i
$775$	247641.	−	169843.i	0.412306	−	0.282776i
$776$		−	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
$780$	55607.5	−	105567.i	0.0913996	−	0.173516i
$781$	−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	$0.0950575\pi$
$787$	453790.	+	785988.i	0.732666	+	1.26901i	−0.223074	+	0.974801i	$0.571609\pi$
$788$	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
$795$	393402.	+	207225.i	0.622447	+	0.327875i
$796$	536347.	+	309660.i	0.846486	+	0.488719i
$797$	342402.			0.539038			0.269519	−	0.962995i	$-0.413135\pi$
$797$	342402.			0.539038			0.269519	+	0.962995i	$0.413135\pi$
$798$	351894.	+	13094.0i	0.552594	+	0.0205621i
$799$	−578188.			−0.905682
$800$	−532490.	+	365203.i	−0.832015	+	0.570630i
$801$	−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
$805$	−811.513	−	511174.i	−0.00125229	−	0.788818i
$806$	−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	$-0.418112\pi$
$810$	9130.39	+	235320.i	0.0139162	+	0.358665i
$811$			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
$815$	−764160.	−	402522.i	−1.15045	−	0.606002i
$816$	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	−0.181512	−	0.983389i	$-0.558099\pi$
$823$	392425.	−	226567.i	0.579371	−	0.334500i	0.760883	+	0.648889i	$0.224766\pi$
$824$	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	$-0.829955\pi$
$827$		−	696464.i		−	1.01833i	0.860669	−	0.509164i	$-0.170045\pi$
$828$	−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	$0.400177\pi$
$830$	−585915.	−	308631.i	−0.850508	−	0.448006i
$831$	−208276.	−	120248.i	−0.301604	−	0.174131i
$832$	150627.			0.217598
$833$	−796593.	−	59364.7i	−1.14801	−	0.0855536i
$834$	−361422.			−0.519616
$835$	175457.	−	6807.71i	0.251650	−	0.00976400i
$836$	−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	$0.899268\pi$
$840$	502547.	+	289083.i	0.712227	+	0.409698i
$841$	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
$845$	−613600.	+	23807.6i	−0.859354	+	0.0333429i
$846$			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
$850$	39111.1	+	503252.i	0.0541330	+	0.696542i
$851$	329105.	+	570027.i	0.454439	+	0.787112i
$852$	27897.2	−	48319.3i	0.0384309	−	0.0665643i
$853$	−203854.			−0.280170			−0.140085	−	0.990140i	$-0.544738\pi$
$853$	−203854.			−0.280170			−0.140085	+	0.990140i	$0.544738\pi$
$854$	−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	0.536655	−	0.843802i	$-0.319688\pi$
$857$	−339629.	−	588254.i	−0.462427	−	0.800946i	−0.999081	+	0.0428557i	$0.986354\pi$
$858$	−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	0.842345	−	0.538939i	$-0.181175\pi$
$863$	593419.	+	342611.i	0.796783	+	0.460023i	−0.0455621	+	0.998962i	$0.514508\pi$
$864$	709781.	−	409792.i	0.950817	−	0.548955i
$865$	148826.	−	282536.i	0.198905	−	0.377608i
$866$	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
$870$	−24255.6	−	625147.i	−0.0320460	−	0.825931i
$871$	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
$875$	−434039.	−	630708.i	−0.566908	−	0.823781i
$876$	−448551.			−0.584525
$877$	−1.19402e6	−	689368.i	−1.55243	−	0.896297i	−0.997943	−	0.0641060i	$-0.979580\pi$
$877$	−1.19402e6	−	689368.i	−1.55243	−	0.896297i	−0.554489	−	0.832191i	$-0.687086\pi$
$878$	126521.	+	219142.i	0.164125	+	0.284273i
$879$	100246.	+	173631.i	0.129744	+	0.224723i
$880$	−37362.5	+	1449.66i	−0.0482470	+	0.00187198i
$881$		−	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	$-0.920612\pi$
$883$		−	384899.i		−	0.493657i	0.969059	−	0.246828i	$-0.0793884\pi$
$884$	−106314.	+	184141.i	−0.136046	+	0.235639i
$885$	−25121.2	−	13232.6i	−0.0320740	−	0.0168950i
$886$	−45373.7	−	78589.6i	−0.0578012	−	0.100115i
$887$	552646.	−	957210.i	0.702424	−	1.21663i	−0.265189	−	0.964196i	$-0.585434\pi$
$887$	552646.	−	957210.i	0.702424	−	1.21663i	0.967613	−	0.252438i	$-0.0812323\pi$
$888$	−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
$900$	−158915.	+	12350.4i	−0.196192	+	0.0152474i
$901$	−686215.	−	396187.i	−0.845300	−	0.488034i
$902$	442866.			0.544326
$903$	522995.	+	328469.i	0.641390	+	0.402827i
$904$	−399716.			−0.489119
$905$	14355.3	+	369983.i	0.0175273	+	0.451736i
$906$	−312824.	+	180609.i	−0.381105	+	0.220031i
$907$	614967.	−	355051.i	0.747545	−	0.431595i	−0.0772614	−	0.997011i	$-0.524618\pi$
$907$	614967.	−	355051.i	0.747545	−	0.431595i	0.824806	+	0.565416i	$0.191284\pi$
$908$	3561.05	−	6167.93i	0.00431924	−	0.00748114i
$909$			198625.i			0.240385i
$910$	298.523	+	188040.i	0.000360491	+	0.227074i
$911$	−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
$915$	19643.5	+	506277.i	0.0234626	+	0.604709i
$916$			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	$0.0951041\pi$
$920$	308125.	−	584955.i	0.364042	−	0.691109i
$921$	−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
$935$	−737067.	+	1.39927e6i	−0.843109	+	1.60059i
$936$	87573.4	+	50560.5i	0.0999587	+	0.0577112i
$937$	379698.			0.432474			0.216237	−	0.976341i	$-0.430622\pi$
$937$	379698.			0.432474			0.216237	+	0.976341i	$0.430622\pi$
$938$	172463.	+	326153.i	0.196016	+	0.370695i
$939$	126621.			0.143607
$940$	438794.	−	17025.2i	0.496598	−	0.0192680i
$941$	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
$945$	487244.	+	840845.i	0.545610	+	0.941570i
$946$	779059.			0.870539
$947$	−193633.	−	111794.i	−0.215913	−	0.124657i	0.388144	−	0.921599i	$-0.373116\pi$
$947$	−193633.	−	111794.i	−0.215913	−	0.124657i	−0.604056	+	0.796942i	$0.706450\pi$
$948$	129489.	+	224282.i	0.144085	+	0.249562i
$949$	−187896.	−	325445.i	−0.208634	−	0.361365i
$950$	−340186.	−	496013.i	−0.376937	−	0.549599i
$951$			366853.i			0.405631i
$952$	−874914.	−	549492.i	−0.965365	−	0.606300i
$953$			924011.i			1.01740i	0.860944	+	0.508699i	$0.169874\pi$
$953$			924011.i			1.01740i	−0.860944	+	0.508699i	$0.830126\pi$
$954$	−72943.6	+	126342.i	−0.0801476	+	0.138820i
$955$	−300261.	+	570025.i	−0.329224	+	0.625010i
$956$	−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	$0.146091\pi$
$967$			828515.i			0.886028i	−0.896515	+	0.443014i	$0.853909\pi$
$968$	1.18085e6	+	681765.i	1.26021	+	0.727585i
$969$	−852958.	+	492455.i	−0.908406	+	0.524469i
$970$	310897.	+	163765.i	0.330425	+	0.174051i
$971$	−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
$975$	166927.	+	243391.i	0.175597	+	0.256032i
$976$	18486.3	−	10673.0i	0.0194066	−	0.0112044i
$977$	−372047.	+	214802.i	−0.389771	+	0.225034i	−0.682061	−	0.731296i	$-0.738916\pi$
$977$	−372047.	+	214802.i	−0.389771	+	0.225034i	0.292290	+	0.956330i	$0.405583\pi$
$978$	−313144.	+	542381.i	−0.327390	+	0.567057i
$979$		−	505246.i		−	0.527154i
$980$	606292.	+	21596.4i	0.631291	+	0.0224868i
$981$	148477.			0.154284
$982$	46783.8	+	27010.6i	0.0485146	+	0.0280099i
$983$	769218.	+	1.33232e6i	0.796053	+	1.37881i	0.922168	+	0.386789i	$0.126416\pi$
$983$	769218.	+	1.33232e6i	0.796053	+	1.37881i	−0.126115	+	0.992016i	$0.540251\pi$
$984$	227038.	+	393242.i	0.234482	+	0.406134i
$985$	61325.3	+	1.58055e6i	0.0632073	+	1.62906i
$986$			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
$990$	257626.	+	135705.i	0.262857	+	0.138460i
$991$	−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	0.959939	−	0.280209i	$-0.0904038\pi$
$997$	235880.	+	408556.i	0.237301	+	0.411018i	−0.722638	+	0.691227i	$0.757070\pi$
$998$	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.19.9	yes	28
5.2	odd	4		175.5.i.e.26.6		28
5.3	odd	4		175.5.i.e.26.9		28
5.4	even	2	inner	35.5.i.a.19.6	✓	28
7.2	even	3		245.5.c.a.244.17		28
7.3	odd	6	inner	35.5.i.a.24.6	yes	28
7.5	odd	6		245.5.c.a.244.11		28
35.3	even	12		175.5.i.e.101.9		28
35.9	even	6		245.5.c.a.244.12		28
35.17	even	12		175.5.i.e.101.6		28
35.19	odd	6		245.5.c.a.244.18		28
35.24	odd	6	inner	35.5.i.a.24.9	yes	28

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

\(f(q)\)	\(=\)	\(q+(2.10231 + 1.21377i) q^{2} +(-3.73387 - 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(24.9812 - 0.969268i) q^{5} -18.1282i q^{6} +(-22.9051 - 43.3169i) q^{7} -63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +O(q^{10})\)	\(q+(2.10231 + 1.21377i) q^{2} +(-3.73387 - 6.46725i) q^{3} +(-5.05353 - 8.75297i) q^{4} +(24.9812 - 0.969268i) q^{5} -18.1282i q^{6} +(-22.9051 - 43.3169i) q^{7} -63.3759i q^{8} +(12.6165 - 21.8524i) q^{9} +(53.6947 + 28.2837i) 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} +(623.121 - 48.4270i) q^{25} +(-132.937 - 76.7512i) q^{26} -793.319 q^{27} +(-263.400 + 419.391i) q^{28} +1380.43 q^{29} +(-17.5711 - 452.864i) q^{30} +(416.091 - 240.230i) q^{31} +(-894.698 + 516.554i) q^{32} +(709.984 - 1229.73i) q^{33} +807.631i q^{34} +(-614.183 - 1059.91i) q^{35} -255.031 q^{36} +(1366.04 + 788.682i) q^{37} +(-481.169 - 833.409i) q^{38} +(236.107 + 408.949i) q^{39} +(-61.4282 - 1583.21i) q^{40} -959.437i q^{41} +(-785.258 + 415.229i) q^{42} -1687.77i q^{43} +(960.915 - 1664.35i) q^{44} +(293.994 - 558.128i) 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} +(-879.395 + 1669.47i) q^{60} +(-2350.26 - 1356.93i) q^{61} +1166.34 q^{62} +(-1235.56 - 45.9753i) q^{63} -2382.06 q^{64} +(-1579.66 + 61.2905i) q^{65} +(2985.21 - 1723.51i) q^{66} +(-2686.14 + 1550.84i) q^{67} +(1681.29 - 2912.07i) q^{68} -3116.17i q^{69} +(-4.72094 - 2973.73i) q^{70} -739.225 q^{71} +(-1384.91 - 799.581i) q^{72} +(2971.45 + 5146.70i) q^{73} +(1914.56 + 3316.11i) q^{74} +(-2639.84 - 3849.06i) q^{75} +4006.69i q^{76} +(4955.42 - 7890.14i) q^{77} +1146.32i q^{78} +(1715.62 - 2971.54i) q^{79} +(-91.6437 + 173.979i) 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} +(-8768.53 - 4618.83i) 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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