LMFDB - Embedded newform 35.5.g.a.22.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,5,Mod(8,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35.8"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.8
Character	$\chi$	$=$	35.22
Dual form			35.5.g.a.8.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.48373 + 1.48373i) q^{2} +(2.63880 - 2.63880i) q^{3} -11.5971i q^{4} +(8.51221 - 23.5062i) q^{5} +7.83054 q^{6} +(13.0958 + 13.0958i) q^{7} +(40.9466 - 40.9466i) q^{8} +67.0734i q^{9} +(47.5067 - 22.2471i) q^{10} +18.0812 q^{11} +(-30.6025 - 30.6025i) q^{12} +(-1.78021 + 1.78021i) q^{13} +38.8613i q^{14} +(-39.5662 - 84.4904i) q^{15} -64.0460 q^{16} +(8.06293 + 8.06293i) q^{17} +(-99.5188 + 99.5188i) q^{18} +201.172i q^{19} +(-272.604 - 98.7169i) q^{20} +69.1145 q^{21} +(26.8275 + 26.8275i) q^{22} +(-414.713 + 414.713i) q^{23} -216.100i q^{24} +(-480.085 - 400.180i) q^{25} -5.28271 q^{26} +(390.737 + 390.737i) q^{27} +(151.873 - 151.873i) q^{28} +1065.57i q^{29} +(66.6552 - 184.066i) q^{30} +1360.48 q^{31} +(-750.173 - 750.173i) q^{32} +(47.7126 - 47.7126i) q^{33} +23.9264i q^{34} +(419.307 - 196.359i) q^{35} +777.857 q^{36} +(-848.868 - 848.868i) q^{37} +(-298.484 + 298.484i) q^{38} +9.39527i q^{39} +(-613.954 - 1311.05i) q^{40} +2808.50 q^{41} +(102.547 + 102.547i) q^{42} +(322.020 - 322.020i) q^{43} -209.689i q^{44} +(1576.64 + 570.943i) q^{45} -1230.64 q^{46} +(-907.451 - 907.451i) q^{47} +(-169.005 + 169.005i) q^{48} +343.000i q^{49} +(-118.557 - 1306.07i) q^{50} +42.5530 q^{51} +(20.6453 + 20.6453i) q^{52} +(-3087.31 + 3087.31i) q^{53} +1159.50i q^{54} +(153.911 - 425.020i) q^{55} +1072.46 q^{56} +(530.853 + 530.853i) q^{57} +(-1581.02 + 1581.02i) q^{58} +1711.53i q^{59} +(-979.843 + 458.853i) q^{60} -4951.60 q^{61} +(2018.58 + 2018.58i) q^{62} +(-878.380 + 878.380i) q^{63} -1201.37i q^{64} +(26.6925 + 56.9996i) q^{65} +141.585 q^{66} +(-5329.83 - 5329.83i) q^{67} +(93.5065 - 93.5065i) q^{68} +2188.69i q^{69} +(913.481 + 330.795i) q^{70} +3843.45 q^{71} +(2746.43 + 2746.43i) q^{72} +(3299.35 - 3299.35i) q^{73} -2518.98i q^{74} +(-2322.85 + 210.853i) q^{75} +2333.01 q^{76} +(236.787 + 236.787i) q^{77} +(-13.9400 + 13.9400i) q^{78} -9899.41i q^{79} +(-545.173 + 1505.48i) q^{80} -3370.79 q^{81} +(4167.06 + 4167.06i) q^{82} +(5254.07 - 5254.07i) q^{83} -801.527i q^{84} +(258.162 - 120.896i) q^{85} +955.582 q^{86} +(2811.84 + 2811.84i) q^{87} +(740.362 - 740.362i) q^{88} +3691.22i q^{89} +(1492.19 + 3186.44i) q^{90} -46.6266 q^{91} +(4809.46 + 4809.46i) q^{92} +(3590.03 - 3590.03i) q^{93} -2692.82i q^{94} +(4728.79 + 1712.42i) q^{95} -3959.12 q^{96} +(-9933.45 - 9933.45i) q^{97} +(-508.919 + 508.919i) q^{98} +1212.77i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25}+ \cdots - 33840 q^{97}+O(q^{100}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Character values

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

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.48373	+	1.48373i	0.370932	+	0.370932i	0.867817	−	0.496884i	$-0.165523\pi$
$2$	1.48373	+	1.48373i	0.370932	+	0.370932i	−0.496884	+	0.867817i	$0.665523\pi$
$3$	2.63880	−	2.63880i	0.293200	−	0.293200i	−0.545143	−	0.838343i	$-0.683525\pi$
$3$	2.63880	−	2.63880i	0.293200	−	0.293200i	0.838343	+	0.545143i	$0.183525\pi$
$4$		−	11.5971i		−	0.724818i
$5$	8.51221	−	23.5062i	0.340488	−	0.940249i
$5$	8.51221	−	23.5062i	0.340488	−	0.940249i
$6$	7.83054			0.217515
$7$	13.0958	+	13.0958i	0.267261	+	0.267261i
$7$	13.0958	+	13.0958i	0.267261	+	0.267261i
$8$	40.9466	−	40.9466i	0.639791	−	0.639791i
$9$			67.0734i			0.828067i
$10$	47.5067	−	22.2471i	0.475067	−	0.222471i
$11$	18.0812			0.149431			0.0747155	−	0.997205i	$-0.476195\pi$
$11$	18.0812			0.149431			0.0747155	+	0.997205i	$0.476195\pi$
$12$	−30.6025	−	30.6025i	−0.212517	−	0.212517i
$13$	−1.78021	+	1.78021i	−0.0105338	+	0.0105338i	−0.712354	−	0.701820i	$-0.752371\pi$
$13$	−1.78021	+	1.78021i	−0.0105338	+	0.0105338i	0.701820	+	0.712354i	$0.252371\pi$
$14$			38.8613i			0.198272i
$15$	−39.5662	−	84.4904i	−0.175850	−	0.375513i
$16$	−64.0460			−0.250180
$17$	8.06293	+	8.06293i	0.0278994	+	0.0278994i	0.720919	−	0.693019i	$-0.243720\pi$
$17$	8.06293	+	8.06293i	0.0278994	+	0.0278994i	−0.693019	+	0.720919i	$0.743720\pi$
$18$	−99.5188	+	99.5188i	−0.307157	+	0.307157i
$19$			201.172i			0.557262i	0.960398	+	0.278631i	$0.0898807\pi$
$19$			201.172i			0.557262i	−0.960398	+	0.278631i	$0.910119\pi$
$20$	−272.604	−	98.7169i	−0.681509	−	0.246792i
$21$	69.1145			0.156722
$22$	26.8275	+	26.8275i	0.0554288	+	0.0554288i
$23$	−414.713	+	414.713i	−0.783956	+	0.783956i	−0.980496	−	0.196540i	$-0.937030\pi$
$23$	−414.713	+	414.713i	−0.783956	+	0.783956i	0.196540	+	0.980496i	$0.437030\pi$
$24$		−	216.100i		−	0.375174i
$25$	−480.085	−	400.180i	−0.768135	−	0.640288i
$26$	−5.28271			−0.00781466
$27$	390.737	+	390.737i	0.535990	+	0.535990i
$28$	151.873	−	151.873i	0.193716	−	0.193716i
$29$			1065.57i			1.26703i	0.773729	+	0.633516i	$0.218389\pi$
$29$			1065.57i			1.26703i	−0.773729	+	0.633516i	$0.781611\pi$
$30$	66.6552	−	184.066i	0.0740614	−	0.204518i
$31$	1360.48			1.41569			0.707845	−	0.706368i	$-0.249668\pi$
$31$	1360.48			1.41569			0.707845	+	0.706368i	$0.249668\pi$
$32$	−750.173	−	750.173i	−0.732591	−	0.732591i
$33$	47.7126	−	47.7126i	0.0438133	−	0.0438133i
$34$			23.9264i			0.0206976i
$35$	419.307	−	196.359i	0.342291	−	0.160293i
$36$	777.857			0.600198
$37$	−848.868	−	848.868i	−0.620065	−	0.620065i	0.325483	−	0.945548i	$-0.394473\pi$
$37$	−848.868	−	848.868i	−0.620065	−	0.620065i	−0.945548	+	0.325483i	$0.894473\pi$
$38$	−298.484	+	298.484i	−0.206707	+	0.206707i
$39$			9.39527i			0.00617704i
$40$	−613.954	−	1311.05i	−0.383721	−	0.819404i
$41$	2808.50			1.67073			0.835366	−	0.549694i	$-0.185256\pi$
$41$	2808.50			1.67073			0.835366	+	0.549694i	$0.185256\pi$
$42$	102.547	+	102.547i	0.0581334	+	0.0581334i
$43$	322.020	−	322.020i	0.174159	−	0.174159i	−0.614645	−	0.788804i	$-0.710701\pi$
$43$	322.020	−	322.020i	0.174159	−	0.174159i	0.788804	+	0.614645i	$0.210701\pi$
$44$		−	209.689i		−	0.108310i
$45$	1576.64	+	570.943i	0.778589	+	0.281947i
$46$	−1230.64			−0.581590
$47$	−907.451	−	907.451i	−0.410797	−	0.410797i	0.471219	−	0.882016i	$-0.343814\pi$
$47$	−907.451	−	907.451i	−0.410797	−	0.410797i	−0.882016	+	0.471219i	$0.843814\pi$
$48$	−169.005	+	169.005i	−0.0733528	+	0.0733528i
$49$			343.000i			0.142857i
$50$	−118.557	−	1306.07i	−0.0474229	−	0.522430i
$51$	42.5530			0.0163602
$52$	20.6453	+	20.6453i	0.00763510	+	0.00763510i
$53$	−3087.31	+	3087.31i	−1.09908	+	1.09908i	−0.104558	+	0.994519i	$0.533343\pi$
$53$	−3087.31	+	3087.31i	−1.09908	+	1.09908i	−0.994519	+	0.104558i	$0.966657\pi$
$54$			1159.50i			0.397632i
$55$	153.911	−	425.020i	0.0508795	−	0.140502i
$56$	1072.46			0.341983
$57$	530.853	+	530.853i	0.163390	+	0.163390i
$58$	−1581.02	+	1581.02i	−0.469983	+	0.469983i
$59$			1711.53i			0.491678i	0.969311	+	0.245839i	$0.0790635\pi$
$59$			1711.53i			0.491678i	−0.969311	+	0.245839i	$0.920936\pi$
$60$	−979.843	+	458.853i	−0.272178	+	0.127459i
$61$	−4951.60			−1.33072			−0.665358	−	0.746524i	$-0.731721\pi$
$61$	−4951.60			−1.33072			−0.665358	+	0.746524i	$0.731721\pi$
$62$	2018.58	+	2018.58i	0.525125	+	0.525125i
$63$	−878.380	+	878.380i	−0.221310	+	0.221310i
$64$		−	1201.37i		−	0.293304i
$65$	26.6925	+	56.9996i	0.00631776	+	0.0134910i
$66$	141.585			0.0325035
$67$	−5329.83	−	5329.83i	−1.18731	−	1.18731i	−0.977808	−	0.209502i	$-0.932816\pi$
$67$	−5329.83	−	5329.83i	−1.18731	−	1.18731i	−0.209502	−	0.977808i	$-0.567184\pi$
$68$	93.5065	−	93.5065i	0.0202220	−	0.0202220i
$69$			2188.69i			0.459713i
$70$	913.481	+	330.795i	0.186425	+	0.0675092i
$71$	3843.45			0.762439			0.381219	−	0.924485i	$-0.375504\pi$
$71$	3843.45			0.762439			0.381219	+	0.924485i	$0.375504\pi$
$72$	2746.43	+	2746.43i	0.529790	+	0.529790i
$73$	3299.35	−	3299.35i	0.619132	−	0.619132i	−0.326177	−	0.945309i	$-0.605761\pi$
$73$	3299.35	−	3299.35i	0.619132	−	0.619132i	0.945309	+	0.326177i	$0.105761\pi$
$74$		−	2518.98i		−	0.460004i
$75$	−2322.85	+	210.853i	−0.412950	+	0.0374850i
$76$	2333.01			0.403914
$77$	236.787	+	236.787i	0.0399371	+	0.0399371i
$78$	−13.9400	+	13.9400i	−0.00229126	+	0.00229126i
$79$		−	9899.41i		−	1.58619i	−0.609099	−	0.793094i	$-0.708469\pi$
$79$		−	9899.41i		−	1.58619i	0.609099	−	0.793094i	$-0.291531\pi$
$80$	−545.173	+	1505.48i	−0.0851833	+	0.235231i
$81$	−3370.79			−0.513762
$82$	4167.06	+	4167.06i	0.619729	+	0.619729i
$83$	5254.07	−	5254.07i	0.762676	−	0.762676i	−0.214130	−	0.976805i	$-0.568692\pi$
$83$	5254.07	−	5254.07i	0.762676	−	0.762676i	0.976805	+	0.214130i	$0.0686915\pi$
$84$		−	801.527i		−	0.113595i
$85$	258.162	−	120.896i	0.0357318	−	0.0167330i
$86$	955.582			0.129203
$87$	2811.84	+	2811.84i	0.371495	+	0.371495i
$88$	740.362	−	740.362i	0.0956046	−	0.0956046i
$89$			3691.22i			0.466004i	0.972476	+	0.233002i	$0.0748548\pi$
$89$			3691.22i			0.466004i	−0.972476	+	0.233002i	$0.925145\pi$
$90$	1492.19	+	3186.44i	0.184221	+	0.393387i
$91$	−46.6266			−0.00563056
$92$	4809.46	+	4809.46i	0.568226	+	0.568226i
$93$	3590.03	−	3590.03i	0.415081	−	0.415081i
$94$		−	2692.82i		−	0.304756i
$95$	4728.79	+	1712.42i	0.523965	+	0.189741i
$96$	−3959.12			−0.429592
$97$	−9933.45	−	9933.45i	−1.05574	−	1.05574i	−0.998352	−	0.0573876i	$-0.981723\pi$
$97$	−9933.45	−	9933.45i	−1.05574	−	1.05574i	−0.0573876	−	0.998352i	$-0.518277\pi$
$98$	−508.919	+	508.919i	−0.0529903	+	0.0529903i
$99$			1212.77i			0.123739i
$100$	−4640.92	+	5567.58i	−0.464092	+	0.556758i
$101$	−16631.2			−1.63035			−0.815174	−	0.579217i	$-0.803358\pi$
$101$	−16631.2			−1.63035			−0.815174	+	0.579217i	$0.803358\pi$
$102$	63.1371	+	63.1371i	0.00606854	+	0.00606854i
$103$	7782.56	−	7782.56i	0.733581	−	0.733581i	−0.237747	−	0.971327i	$-0.576409\pi$
$103$	7782.56	−	7782.56i	0.733581	−	0.733581i	0.971327	+	0.237747i	$0.0764088\pi$
$104$			145.787i			0.0134789i
$105$	588.317	−	1624.62i	0.0533621	−	0.147358i
$106$	−9161.46			−0.815367
$107$	6893.44	+	6893.44i	0.602100	+	0.602100i	0.940869	−	0.338770i	$-0.110011\pi$
$107$	6893.44	+	6893.44i	0.602100	+	0.602100i	−0.338770	+	0.940869i	$0.610011\pi$
$108$	4531.41	−	4531.41i	0.388495	−	0.388495i
$109$			12312.6i			1.03632i	0.855283	+	0.518162i	$0.173383\pi$
$109$			12312.6i			1.03632i	−0.855283	+	0.518162i	$0.826617\pi$
$110$	858.976	−	402.252i	0.0709897	−	0.0332440i
$111$	−4480.00			−0.363606
$112$	−838.734	−	838.734i	−0.0668634	−	0.0668634i
$113$	−4571.88	+	4571.88i	−0.358045	+	0.358045i	−0.863092	−	0.505047i	$-0.831475\pi$
$113$	−4571.88	+	4571.88i	−0.358045	+	0.358045i	0.505047	+	0.863092i	$0.331475\pi$
$114$			1575.28i			0.121213i
$115$	6218.21	+	13278.5i	0.470186	+	1.00404i
$116$	12357.6			0.918368
$117$	−119.405	−	119.405i	−0.00872270	−	0.00872270i
$118$	−2539.45	+	2539.45i	−0.182379	+	0.182379i
$119$			211.181i			0.0149129i
$120$	−5079.70	−	1839.49i	−0.352757	−	0.127742i
$121$	−14314.1			−0.977670
$122$	−7346.83	−	7346.83i	−0.493606	−	0.493606i
$123$	7411.09	−	7411.09i	0.489860	−	0.489860i
$124$		−	15777.6i		−	1.02612i
$125$	−13493.3	+	7878.56i	−0.863571	+	0.504228i
$126$	−2606.56			−0.164182
$127$	−756.980	−	756.980i	−0.0469328	−	0.0469328i	0.683251	−	0.730184i	$-0.260566\pi$
$127$	−756.980	−	756.980i	−0.0469328	−	0.0469328i	−0.730184	+	0.683251i	$0.760566\pi$
$128$	−10220.3	+	10220.3i	−0.623795	+	0.623795i
$129$		−	1699.50i		−	0.102127i
$130$	−44.9676	+	124.177i	−0.00266080	+	0.00734773i
$131$	4951.67			0.288542			0.144271	−	0.989538i	$-0.453916\pi$
$131$	4951.67			0.288542			0.144271	+	0.989538i	$0.453916\pi$
$132$	−553.328	−	553.328i	−0.0317566	−	0.0317566i
$133$	−2634.50	+	2634.50i	−0.148935	+	0.148935i
$134$		−	15816.1i		−	0.880824i
$135$	12510.8	−	5858.71i	0.686462	−	0.321466i
$136$	660.299			0.0356996
$137$	13415.6	+	13415.6i	0.714774	+	0.714774i	0.967530	−	0.252756i	$-0.0813369\pi$
$137$	13415.6	+	13415.6i	0.714774	+	0.714774i	−0.252756	+	0.967530i	$0.581337\pi$
$138$	−3247.43	+	3247.43i	−0.170522	+	0.170522i
$139$			6023.08i			0.311738i	0.987778	+	0.155869i	$0.0498177\pi$
$139$			6023.08i			0.311738i	−0.987778	+	0.155869i	$0.950182\pi$
$140$	−2277.19	−	4862.74i	−0.116183	−	0.248099i
$141$	−4789.17			−0.240892
$142$	5702.65	+	5702.65i	0.282813	+	0.282813i
$143$	−32.1883	+	32.1883i	−0.00157408	+	0.00157408i
$144$		−	4295.79i		−	0.207166i
$145$	25047.6	+	9070.39i	1.19133	+	0.431410i
$146$	9790.70			0.459312
$147$	905.110	+	905.110i	0.0418858	+	0.0418858i
$148$	−9844.41	+	9844.41i	−0.449434	+	0.449434i
$149$		−	15207.8i		−	0.685003i	−0.939517	−	0.342502i	$-0.888726\pi$
$149$		−	15207.8i		−	0.685003i	0.939517	−	0.342502i	$-0.111274\pi$
$150$	−3759.32	−	3133.63i	−0.167081	−	0.139272i
$151$	38369.4			1.68279			0.841397	−	0.540417i	$-0.181734\pi$
$151$	38369.4			1.68279			0.841397	+	0.540417i	$0.181734\pi$
$152$	8237.30	+	8237.30i	0.356531	+	0.356531i
$153$	−540.808	+	540.808i	−0.0231026	+	0.0231026i
$154$			702.656i			0.0296280i
$155$	11580.7	−	31979.7i	0.482026	−	1.33110i
$156$	108.958			0.00447723
$157$	−4024.99	−	4024.99i	−0.163292	−	0.163292i	0.620731	−	0.784023i	$-0.286836\pi$
$157$	−4024.99	−	4024.99i	−0.163292	−	0.163292i	−0.784023	+	0.620731i	$0.786836\pi$
$158$	14688.0	−	14688.0i	0.588369	−	0.588369i
$159$			16293.6i			0.644500i
$160$	−24019.4	+	11248.1i	−0.938256	+	0.439379i
$161$	−10862.0			−0.419042
$162$	−5001.34	−	5001.34i	−0.190571	−	0.190571i
$163$	7525.01	−	7525.01i	0.283225	−	0.283225i	−0.551169	−	0.834394i	$-0.685818\pi$
$163$	7525.01	−	7525.01i	0.283225	−	0.283225i	0.834394	+	0.551169i	$0.185818\pi$
$164$		−	32570.5i		−	1.21098i
$165$	−715.404	−	1527.68i	−0.0262774	−	0.0561133i
$166$	15591.2			0.565802
$167$	−34535.2	−	34535.2i	−1.23831	−	1.23831i	−0.960692	−	0.277615i	$-0.910456\pi$
$167$	−34535.2	−	34535.2i	−1.23831	−	1.23831i	−0.277615	−	0.960692i	$-0.589544\pi$
$168$	2830.01	−	2830.01i	0.100269	−	0.100269i
$169$			28554.7i			0.999778i
$170$	562.419	+	203.667i	0.0194609	+	0.00704729i
$171$	−13493.3			−0.461451
$172$	−3734.50	−	3734.50i	−0.126234	−	0.126234i
$173$	−23342.7	+	23342.7i	−0.779937	+	0.779937i	−0.979820	−	0.199883i	$-0.935944\pi$
$173$	−23342.7	+	23342.7i	−0.779937	+	0.779937i	0.199883	+	0.979820i	$0.435944\pi$
$174$			8344.03i			0.275599i
$175$	−1046.42	−	11527.8i	−0.0341687	−	0.376417i
$176$	−1158.03			−0.0373846
$177$	4516.40	+	4516.40i	0.144160	+	0.144160i
$178$	−5476.77	+	5476.77i	−0.172856	+	0.172856i
$179$			28472.1i			0.888614i	0.895875	+	0.444307i	$0.146550\pi$
$179$			28472.1i			0.888614i	−0.895875	+	0.444307i	$0.853450\pi$
$180$	6621.28	−	18284.5i	0.204360	−	0.564335i
$181$	40886.7			1.24803			0.624015	−	0.781412i	$-0.285500\pi$
$181$	40886.7			1.24803			0.624015	+	0.781412i	$0.285500\pi$
$182$	−69.1813	−	69.1813i	−0.00208856	−	0.00208856i
$183$	−13066.3	+	13066.3i	−0.390167	+	0.390167i
$184$			33962.2i			1.00314i
$185$	−27179.4	+	12727.9i	−0.794140	+	0.371890i
$186$	10653.3			0.307934
$187$	145.787	+	145.787i	0.00416904	+	0.00416904i
$188$	−10523.8	+	10523.8i	−0.297753	+	0.297753i
$189$			10234.0i			0.286499i
$190$	4475.48	+	9557.00i	0.123974	+	0.264737i
$191$	−15424.7			−0.422814			−0.211407	−	0.977398i	$-0.567804\pi$
$191$	−15424.7			−0.422814			−0.211407	+	0.977398i	$0.567804\pi$
$192$	−3170.18	−	3170.18i	−0.0859968	−	0.0859968i
$193$	−6739.80	+	6739.80i	−0.180939	+	0.180939i	−0.791765	−	0.610826i	$-0.790838\pi$
$193$	−6739.80	+	6739.80i	−0.180939	+	0.180939i	0.610826	+	0.791765i	$0.290838\pi$
$194$		−	29477.1i		−	0.783216i
$195$	220.847	+	79.9745i	0.00580795	+	0.00210321i
$196$	3977.80			0.103545
$197$	−21.4403	−	21.4403i	−0.000552458	−	0.000552458i	0.706830	−	0.707383i	$-0.250124\pi$
$197$	−21.4403	−	21.4403i	−0.000552458	−	0.000552458i	−0.707383	+	0.706830i	$0.750124\pi$
$198$	−1799.42	+	1799.42i	−0.0458988	+	0.0458988i
$199$			61587.1i			1.55519i	0.628765	+	0.777596i	$0.283561\pi$
$199$			61587.1i			1.55519i	−0.628765	+	0.777596i	$0.716439\pi$
$200$	−36043.9	+	3271.83i	−0.901096	+	0.0817958i
$201$	−28128.8			−0.696240
$202$	−24676.2	−	24676.2i	−0.604749	−	0.604749i
$203$	−13954.5	+	13954.5i	−0.338629	+	0.338629i
$204$		−	493.491i		−	0.0118582i
$205$	23906.6	−	66017.3i	0.568865	−	1.57090i
$206$	23094.4			0.544218
$207$	−27816.2	−	27816.2i	−0.649168	−	0.649168i
$208$	114.016	−	114.016i	0.00263535	−	0.00263535i
$209$			3637.42i			0.0832723i
$210$	3283.40	−	1537.59i	0.0744536	−	0.0348661i
$211$	7989.99			0.179466			0.0897328	−	0.995966i	$-0.471399\pi$
$211$	7989.99			0.179466			0.0897328	+	0.995966i	$0.471399\pi$
$212$	35803.8	+	35803.8i	0.796631	+	0.796631i
$213$	10142.1	−	10142.1i	0.223547	−	0.223547i
$214$			20456.0i			0.446676i
$215$	−4828.37	−	10310.6i	−0.104454	−	0.223052i
$216$	31998.7			0.685843
$217$	17816.5	+	17816.5i	0.378359	+	0.378359i
$218$	−18268.5	+	18268.5i	−0.384406	+	0.384406i
$219$		−	17412.7i		−	0.363059i
$220$	−4928.99	−	1784.92i	−0.101839	−	0.0368784i
$221$	−28.7075			−0.000587774
$222$	−6647.10	−	6647.10i	−0.134873	−	0.134873i
$223$	68789.7	−	68789.7i	1.38329	−	1.38329i	0.544589	−	0.838703i	$-0.316686\pi$
$223$	68789.7	−	68789.7i	1.38329	−	1.38329i	0.838703	−	0.544589i	$-0.183314\pi$
$224$		−	19648.2i		−	0.391586i
$225$	26841.4	−	32200.9i	0.530201	−	0.636067i
$226$	−13566.9			−0.265621
$227$	10650.0	+	10650.0i	0.206680	+	0.206680i	0.802855	−	0.596175i	$-0.203314\pi$
$227$	10650.0	+	10650.0i	0.206680	+	0.206680i	−0.596175	+	0.802855i	$0.703314\pi$
$228$	6156.35	−	6156.35i	0.118428	−	0.118428i
$229$		−	21675.8i		−	0.413336i	−0.978411	−	0.206668i	$-0.933738\pi$
$229$		−	21675.8i		−	0.413336i	0.978411	−	0.206668i	$-0.0662620\pi$
$230$	−10475.5	+	28927.8i	−0.198025	+	0.546839i
$231$	1249.67			0.0234192
$232$	43631.7	+	43631.7i	0.810636	+	0.810636i
$233$	14316.4	−	14316.4i	0.263707	−	0.263707i	−0.562851	−	0.826558i	$-0.690296\pi$
$233$	14316.4	−	14316.4i	0.263707	−	0.263707i	0.826558	+	0.562851i	$0.190296\pi$
$234$		−	354.330i		−	0.00647106i
$235$	−29055.1	+	13606.3i	−0.526123	+	0.246380i
$236$	19848.8			0.356377
$237$	−26122.6	−	26122.6i	−0.465071	−	0.465071i
$238$	−313.336	+	313.336i	−0.00553166	+	0.00553166i
$239$		−	80312.5i		−	1.40601i	−0.711187	−	0.703003i	$-0.751842\pi$
$239$		−	80312.5i		−	1.40601i	0.711187	−	0.703003i	$-0.248158\pi$
$240$	2534.06	+	5411.27i	0.0439941	+	0.0939457i
$241$	14965.1			0.257659			0.128829	−	0.991667i	$-0.458878\pi$
$241$	14965.1			0.257659			0.128829	+	0.991667i	$0.458878\pi$
$242$	−21238.2	−	21238.2i	−0.362650	−	0.362650i
$243$	−40544.5	+	40544.5i	−0.686625	+	0.686625i
$244$			57424.1i			0.964528i
$245$	8062.63	+	2919.69i	0.134321	+	0.0486412i
$246$	21992.1			0.363410
$247$	−358.129	−	358.129i	−0.00587009	−	0.00587009i
$248$	55707.0	−	55707.0i	0.905745	−	0.905745i
$249$		−	27728.9i		−	0.447234i
$250$	−31710.1	−	8330.75i	−0.507361	−	0.133292i
$251$	49620.5			0.787614			0.393807	−	0.919193i	$-0.371158\pi$
$251$	49620.5			0.787614			0.393807	+	0.919193i	$0.371158\pi$
$252$	10186.7	+	10186.7i	0.160410	+	0.160410i
$253$	−7498.49	+	7498.49i	−0.117147	+	0.117147i
$254$		−	2246.31i		−	0.0348178i
$255$	362.220	−	1000.26i	0.00557047	−	0.0153827i
$256$	−49550.1			−0.756075
$257$	61440.3	+	61440.3i	0.930222	+	0.930222i	0.997719	−	0.0674972i	$-0.0215014\pi$
$257$	61440.3	+	61440.3i	0.930222	+	0.930222i	−0.0674972	+	0.997719i	$0.521501\pi$
$258$	2521.59	−	2521.59i	0.0378822	−	0.0378822i
$259$		−	22233.2i		−	0.331438i
$260$	661.030	−	309.556i	0.00977855	−	0.00457923i
$261$	−71471.7			−1.04919
$262$	7346.94	+	7346.94i	0.107030	+	0.107030i
$263$	−30152.4	+	30152.4i	−0.435924	+	0.435924i	−0.890638	−	0.454713i	$-0.849742\pi$
$263$	−30152.4	+	30152.4i	−0.435924	+	0.435924i	0.454713	+	0.890638i	$0.349742\pi$
$264$		−	3907.34i		−	0.0560627i
$265$	46291.1	+	98850.7i	0.659183	+	1.40763i
$266$	−7817.79			−0.110489
$267$	9740.40	+	9740.40i	0.136633	+	0.136633i
$268$	−61810.6	+	61810.6i	−0.860584	+	0.860584i
$269$		−	27372.8i		−	0.378282i	−0.981950	−	0.189141i	$-0.939430\pi$
$269$		−	27372.8i		−	0.378282i	0.981950	−	0.189141i	$-0.0605703\pi$
$270$	27255.4	+	9869.87i	0.373873	+	0.135389i
$271$	−107491.			−1.46364			−0.731821	−	0.681497i	$-0.761329\pi$
$271$	−107491.			−1.46364			−0.731821	+	0.681497i	$0.761329\pi$
$272$	−516.398	−	516.398i	−0.00697987	−	0.00697987i
$273$	−123.039	+	123.039i	−0.00165088	+	0.00165088i
$274$			39810.3i			0.530266i
$275$	−8680.48	−	7235.71i	−0.114783	−	0.0956788i
$276$	25382.5			0.333208
$277$	−90987.9	−	90987.9i	−1.18583	−	1.18583i	−0.978208	−	0.207626i	$-0.933426\pi$
$277$	−90987.9	−	90987.9i	−1.18583	−	1.18583i	−0.207626	−	0.978208i	$-0.566574\pi$
$278$	−8936.62	+	8936.62i	−0.115634	+	0.115634i
$279$			91251.9i			1.17229i
$280$	9128.99	−	25209.4i	0.116441	−	0.321549i
$281$	−81617.1			−1.03364			−0.516819	−	0.856095i	$-0.672884\pi$
$281$	−81617.1			−1.03364			−0.516819	+	0.856095i	$0.672884\pi$
$282$	−7105.83	−	7105.83i	−0.0893546	−	0.0893546i
$283$	−25062.7	+	25062.7i	−0.312936	+	0.312936i	−0.846046	−	0.533110i	$-0.821023\pi$
$283$	−25062.7	+	25062.7i	−0.312936	+	0.312936i	0.533110	+	0.846046i	$0.321023\pi$
$284$		−	44572.9i		−	0.552629i
$285$	16997.1	−	7959.61i	0.209259	−	0.0979946i
$286$	−95.5175			−0.00116775
$287$	36779.6	+	36779.6i	0.446522	+	0.446522i
$288$	50316.7	−	50316.7i	0.606634	−	0.606634i
$289$		−	83391.0i		−	0.998443i
$290$	23705.9	+	50621.9i	0.281877	+	0.601925i
$291$	−52424.9			−0.619087
$292$	−38262.9	−	38262.9i	−0.448758	−	0.448758i
$293$	53618.1	−	53618.1i	0.624562	−	0.624562i	−0.322132	−	0.946695i	$-0.604400\pi$
$293$	53618.1	−	53618.1i	0.624562	−	0.624562i	0.946695	+	0.322132i	$0.104400\pi$
$294$			2685.88i			0.0310736i
$295$	40231.7	+	14568.9i	0.462300	+	0.167411i
$296$	−69516.6			−0.793424
$297$	7064.97	+	7064.97i	0.0800936	+	0.0800936i
$298$	22564.2	−	22564.2i	0.254090	−	0.254090i
$299$		−	1476.56i		−	0.0165161i
$300$	2445.28	+	26938.2i	0.0271698	+	0.299314i
$301$	8434.23			0.0930920
$302$	56929.8	+	56929.8i	0.624203	+	0.624203i
$303$	−43886.4	+	43886.4i	−0.478019	+	0.478019i
$304$		−	12884.2i		−	0.139416i
$305$	−42149.0	+	116393.i	−0.453094	+	1.25120i
$306$	−1604.83			−0.0171390
$307$	−76759.5	−	76759.5i	−0.814433	−	0.814433i	0.170862	−	0.985295i	$-0.445345\pi$
$307$	−76759.5	−	76759.5i	−0.814433	−	0.814433i	−0.985295	+	0.170862i	$0.945345\pi$
$308$	2746.04	−	2746.04i	0.0289472	−	0.0289472i
$309$		−	41073.3i		−	0.430172i
$310$	64631.8	−	30266.6i	0.672547	−	0.314949i
$311$	157851.			1.63203			0.816014	−	0.578033i	$-0.196179\pi$
$311$	157851.			1.63203			0.816014	+	0.578033i	$0.196179\pi$
$312$	384.705	+	384.705i	0.00395201	+	0.00395201i
$313$	75579.4	−	75579.4i	0.771463	−	0.771463i	−0.206899	−	0.978362i	$-0.566337\pi$
$313$	75579.4	−	75579.4i	0.771463	−	0.771463i	0.978362	+	0.206899i	$0.0663373\pi$
$314$		−	11944.0i		−	0.121141i
$315$	13170.4	+	28124.4i	0.132733	+	0.283440i
$316$	−114804.			−1.14970
$317$	51889.2	+	51889.2i	0.516367	+	0.516367i	0.916470	−	0.400103i	$-0.131026\pi$
$317$	51889.2	+	51889.2i	0.516367	+	0.516367i	−0.400103	+	0.916470i	$0.631026\pi$
$318$	−24175.3	+	24175.3i	−0.239066	+	0.239066i
$319$			19266.8i			0.189334i
$320$	−28239.7	−	10226.3i	−0.275778	−	0.0998665i
$321$	36380.9			0.353072
$322$	−16116.3	−	16116.3i	−0.155436	−	0.155436i
$323$	−1622.03	+	1622.03i	−0.0155473	+	0.0155473i
$324$			39091.4i			0.372384i
$325$	1567.06	−	142.248i	0.0148361	−	0.00134672i
$326$	22330.2			0.210115
$327$	32490.4	+	32490.4i	0.303851	+	0.303851i
$328$	114999.	−	114999.i	1.06892	−	1.06892i
$329$		−	23767.6i		−	0.219580i
$330$	1205.20	−	3328.13i	0.0110671	−	0.0305614i
$331$	53202.6			0.485598			0.242799	−	0.970077i	$-0.421935\pi$
$331$	53202.6			0.485598			0.242799	+	0.970077i	$0.421935\pi$
$332$	−60932.0	−	60932.0i	−0.552801	−	0.552801i
$333$	56936.5	−	56936.5i	0.513455	−	0.513455i
$334$		−	102482.i		−	0.918657i
$335$	−170653.	+	79915.6i	−1.52063	+	0.712101i
$336$	−4426.51			−0.0392087
$337$	95083.4	+	95083.4i	0.837231	+	0.837231i	0.988494	−	0.151263i	$-0.0483340\pi$
$337$	95083.4	+	95083.4i	0.837231	+	0.837231i	−0.151263	+	0.988494i	$0.548334\pi$
$338$	−42367.4	+	42367.4i	−0.370850	+	0.370850i
$339$			24128.6i			0.209958i
$340$	−1402.04	−	2993.93i	−0.0121284	−	0.0258991i
$341$	24599.0			0.211548
$342$	−20020.4	−	20020.4i	−0.171167	−	0.171167i
$343$	−4491.86	+	4491.86i	−0.0381802	+	0.0381802i
$344$		−	26371.3i		−	0.222851i
$345$	51447.9	+	18630.6i	0.432244	+	0.156527i
$346$	−69268.6			−0.578608
$347$	74352.3	+	74352.3i	0.617498	+	0.617498i	0.944889	−	0.327391i	$-0.106169\pi$
$347$	74352.3	+	74352.3i	0.617498	+	0.617498i	−0.327391	+	0.944889i	$0.606169\pi$
$348$	32609.2	−	32609.2i	0.269266	−	0.269266i
$349$		−	100857.i		−	0.828045i	−0.910267	−	0.414022i	$-0.864124\pi$
$349$		−	100857.i		−	0.828045i	0.910267	−	0.414022i	$-0.135876\pi$
$350$	15551.5	−	18656.7i	0.126951	−	0.152300i
$351$	−1391.19			−0.0112920
$352$	−13564.0	−	13564.0i	−0.109472	−	0.109472i
$353$	−30072.1	+	30072.1i	−0.241332	+	0.241332i	−0.817401	−	0.576069i	$-0.804586\pi$
$353$	−30072.1	+	30072.1i	−0.241332	+	0.241332i	0.576069	+	0.817401i	$0.304586\pi$
$354$			13402.2i			0.106947i
$355$	32716.3	−	90345.1i	0.259602	−	0.716882i
$356$	42807.4			0.337768
$357$	557.265	+	557.265i	0.00437246	+	0.00437246i
$358$	−42244.9	+	42244.9i	−0.329616	+	0.329616i
$359$		−	12797.6i		−	0.0992974i	−0.998767	−	0.0496487i	$-0.984190\pi$
$359$		−	12797.6i		−	0.0992974i	0.998767	−	0.0496487i	$-0.0158102\pi$
$360$	87936.4	−	41180.0i	0.678522	−	0.317747i
$361$	89850.9			0.689459
$362$	60664.8	+	60664.8i	0.462935	+	0.462935i
$363$	−37772.0	+	37772.0i	−0.286653	+	0.286653i
$364$			540.734i			0.00408113i
$365$	−49470.5	−	105640.i	−0.371331	−	0.792945i
$366$	−38773.7			−0.289451
$367$	−62216.0	−	62216.0i	−0.461924	−	0.461924i	0.437362	−	0.899286i	$-0.355913\pi$
$367$	−62216.0	−	62216.0i	−0.461924	−	0.461924i	−0.899286	+	0.437362i	$0.855913\pi$
$368$	26560.7	−	26560.7i	0.196130	−	0.196130i
$369$			188376.i			1.38348i
$370$	−59211.8	−	21442.1i	−0.432518	−	0.156626i
$371$	−80861.5			−0.587481
$372$	−41634.0	−	41634.0i	−0.300858	−	0.300858i
$373$	47558.2	−	47558.2i	0.341828	−	0.341828i	−0.515226	−	0.857054i	$-0.672292\pi$
$373$	47558.2	−	47558.2i	0.341828	−	0.341828i	0.857054	+	0.515226i	$0.172292\pi$
$374$			432.617i			0.00309286i
$375$	−14816.2	+	56396.1i	−0.105360	+	0.401039i
$376$	−74314.1			−0.525649
$377$	−1896.95	−	1896.95i	−0.0133467	−	0.0133467i
$378$	−15184.5	+	15184.5i	−0.106272	+	0.106272i
$379$			109716.i			0.763817i	0.924200	+	0.381909i	$0.124733\pi$
$379$			109716.i			0.763817i	−0.924200	+	0.381909i	$0.875267\pi$
$380$	19859.0	−	54840.2i	0.137528	−	0.379780i
$381$	−3995.04			−0.0275215
$382$	−22886.0	−	22886.0i	−0.156835	−	0.156835i
$383$	−93866.2	+	93866.2i	−0.639899	+	0.639899i	−0.950530	−	0.310631i	$-0.899460\pi$
$383$	−93866.2	+	93866.2i	−0.639899	+	0.639899i	0.310631	+	0.950530i	$0.399460\pi$
$384$			53938.5i			0.365794i
$385$	7581.55	−	3550.39i	0.0511490	−	0.0239527i
$386$	−20000.1			−0.134232
$387$	21599.0	+	21599.0i	0.144215	+	0.144215i
$388$	−115199.	+	115199.i	−0.765219	+	0.765219i
$389$		−	111194.i		−	0.734821i	−0.930059	−	0.367410i	$-0.880244\pi$
$389$		−	111194.i		−	0.734821i	0.930059	−	0.367410i	$-0.119756\pi$
$390$	209.017	+	446.338i	0.00137421	+	0.00293451i
$391$	−6687.60			−0.0437438
$392$	14044.7	+	14044.7i	0.0913987	+	0.0913987i
$393$	13066.5	−	13066.5i	0.0846007	−	0.0846007i
$394$		−	63.6233i		−	0.000409849i
$395$	−232698.	−	84265.8i	−1.49141	−	0.540079i
$396$	14064.5			0.0896882
$397$	56827.1	+	56827.1i	0.360557	+	0.360557i	0.864018	−	0.503461i	$-0.167940\pi$
$397$	56827.1	+	56827.1i	0.360557	+	0.360557i	−0.503461	+	0.864018i	$0.667940\pi$
$398$	−91378.7	+	91378.7i	−0.576871	+	0.576871i
$399$			13903.9i			0.0873354i
$400$	30747.5	+	25629.9i	0.192172	+	0.160187i
$401$	160496.			0.998104			0.499052	−	0.866572i	$-0.333682\pi$
$401$	160496.			0.998104			0.499052	+	0.866572i	$0.333682\pi$
$402$	−41735.5	−	41735.5i	−0.258258	−	0.258258i
$403$	−2421.94	+	2421.94i	−0.0149126	+	0.0149126i
$404$			192873.i			1.18171i
$405$	−28692.9	+	79234.6i	−0.174930	+	0.483064i
$406$	−41409.6			−0.251217
$407$	−15348.5	−	15348.5i	−0.0926569	−	0.0926569i
$408$	1742.40	−	1742.40i	0.0104671	−	0.0104671i
$409$			135898.i			0.812396i	0.913785	+	0.406198i	$0.133146\pi$
$409$			135898.i			0.812396i	−0.913785	+	0.406198i	$0.866854\pi$
$410$	133423.	−	62480.9i	0.793710	−	0.371689i
$411$	70802.3			0.419144
$412$	−90255.0	−	90255.0i	−0.531713	−	0.531713i
$413$	−22413.9	+	22413.9i	−0.131407	+	0.131407i
$414$		−	82543.5i		−	0.481595i
$415$	−78779.6	−	168227.i	−0.457423	−	0.976787i
$416$	2670.94			0.0154339
$417$	15893.7	+	15893.7i	0.0914016	+	0.0914016i
$418$	−5396.94	+	5396.94i	−0.0308884	+	0.0308884i
$419$		−	16910.3i		−	0.0963216i	−0.998840	−	0.0481608i	$-0.984664\pi$
$419$		−	16910.3i		−	0.0963216i	0.998840	−	0.0481608i	$-0.0153360\pi$
$420$	−18840.9	−	6822.77i	−0.106808	−	0.0386778i
$421$	−169177.			−0.954500			−0.477250	−	0.878768i	$-0.658366\pi$
$421$	−169177.			−0.954500			−0.477250	+	0.878768i	$0.658366\pi$
$422$	11855.0	+	11855.0i	0.0665696	+	0.0665696i
$423$	60865.8	−	60865.8i	0.340168	−	0.340168i
$424$			252830.i			1.40636i
$425$	−644.267	−	7097.51i	−0.00356687	−	0.0392942i
$426$	30096.3			0.165842
$427$	−64845.1	−	64845.1i	−0.355649	−	0.355649i
$428$	79943.8	−	79943.8i	0.436413	−	0.436413i
$429$			169.877i			0.000923041i
$430$	8134.12	−	22462.1i	0.0439920	−	0.121483i
$431$	317161.			1.70736			0.853680	−	0.520797i	$-0.174365\pi$
$431$	317161.			1.70736			0.853680	+	0.520797i	$0.174365\pi$
$432$	−25025.1	−	25025.1i	−0.134094	−	0.134094i
$433$	32567.7	−	32567.7i	0.173704	−	0.173704i	−0.614900	−	0.788605i	$-0.710804\pi$
$433$	32567.7	−	32567.7i	0.173704	−	0.173704i	0.788605	+	0.614900i	$0.210804\pi$
$434$			52869.9i			0.280691i
$435$	90030.8	−	42160.8i	0.475787	−	0.222808i
$436$	142790.			0.751146
$437$	−83428.5	−	83428.5i	−0.436869	−	0.436869i
$438$	25835.7	−	25835.7i	0.134671	−	0.134671i
$439$		−	144941.i		−	0.752078i	−0.926604	−	0.376039i	$-0.877286\pi$
$439$		−	144941.i		−	0.752078i	0.926604	−	0.376039i	$-0.122714\pi$
$440$	−11101.0	−	23705.2i	−0.0573399	−	0.122444i
$441$	−23006.2			−0.118295
$442$	−42.5941	−	42.5941i	−0.000218024	−	0.000218024i
$443$	−122190.	+	122190.i	−0.622625	+	0.622625i	−0.946202	−	0.323577i	$-0.895115\pi$
$443$	−122190.	+	122190.i	−0.622625	+	0.622625i	0.323577	+	0.946202i	$0.395115\pi$
$444$			51954.9i			0.263549i
$445$	86766.5	+	31420.4i	0.438160	+	0.158669i
$446$	204131.			1.02622
$447$	−40130.3	−	40130.3i	−0.200843	−	0.200843i
$448$	15732.9	−	15732.9i	0.0783887	−	0.0783887i
$449$		−	256403.i		−	1.27184i	−0.771757	−	0.635918i	$-0.780622\pi$
$449$		−	256403.i		−	1.27184i	0.771757	−	0.635918i	$-0.219378\pi$
$450$	87602.9	−	7952.03i	0.432607	−	0.0392693i
$451$	50781.0			0.249659
$452$	53020.5	+	53020.5i	0.259517	+	0.259517i
$453$	101249.	−	101249.i	0.493396	−	0.493396i
$454$			31603.4i			0.153328i
$455$	−396.896	+	1096.02i	−0.00191714	+	0.00529412i
$456$	43473.3			0.209070
$457$	161721.	+	161721.i	0.774344	+	0.774344i	0.978863	−	0.204519i	$-0.0655629\pi$
$457$	161721.	+	161721.i	0.774344	+	0.774344i	−0.204519	+	0.978863i	$0.565563\pi$
$458$	32161.0	−	32161.0i	0.153320	−	0.153320i
$459$			6300.96i			0.0299076i
$460$	153991.	−	72113.1i	0.727748	−	0.340799i
$461$	−15976.3			−0.0751753			−0.0375877	−	0.999293i	$-0.511967\pi$
$461$	−15976.3			−0.0751753			−0.0375877	+	0.999293i	$0.511967\pi$
$462$	1854.17	+	1854.17i	0.00868693	+	0.00868693i
$463$	−272415.	+	272415.i	−1.27078	+	1.27078i	−0.325094	+	0.945682i	$0.605396\pi$
$463$	−272415.	+	272415.i	−1.27078	+	1.27078i	−0.945682	+	0.325094i	$0.894604\pi$
$464$		−	68245.8i		−	0.316986i
$465$	−53829.0	−	114947.i	−0.248949	−	0.531609i
$466$	42483.4			0.195635
$467$	−204044.	−	204044.i	−0.935598	−	0.935598i	0.0624499	−	0.998048i	$-0.480109\pi$
$467$	−204044.	−	204044.i	−0.935598	−	0.935598i	−0.998048	+	0.0624499i	$0.980109\pi$
$468$	−1384.75	+	1384.75i	−0.00632237	+	0.00632237i
$469$		−	139597.i		−	0.634644i
$470$	−63298.1	−	22921.9i	−0.286546	−	0.103766i
$471$	−21242.3			−0.0957547
$472$	70081.5	+	70081.5i	0.314571	+	0.314571i
$473$	5822.50	−	5822.50i	0.0260248	−	0.0260248i
$474$		−	77517.7i		−	0.345020i
$475$	80504.8	−	96579.4i	0.356808	−	0.428053i
$476$	2449.09			0.0108091
$477$	−207076.	−	207076.i	−0.910109	−	0.910109i
$478$	119162.	−	119162.i	0.521533	−	0.521533i
$479$			36564.3i			0.159363i	0.996820	+	0.0796813i	$0.0253903\pi$
$479$			36564.3i			0.159363i	−0.996820	+	0.0796813i	$0.974610\pi$
$480$	−33700.9	+	93063.9i	−0.146271	+	0.403923i
$481$	3022.33			0.0130633
$482$	22204.2	+	22204.2i	0.0955741	+	0.0955741i
$483$	−28662.7	+	28662.7i	−0.122863	+	0.122863i
$484$			166002.i			0.708633i
$485$	−318054.	+	148942.i	−1.35212	+	0.633191i
$486$	−120314.			−0.509383
$487$	76566.7	+	76566.7i	0.322836	+	0.322836i	0.849854	−	0.527018i	$-0.176690\pi$
$487$	76566.7	+	76566.7i	0.322836	+	0.322836i	−0.527018	+	0.849854i	$0.676690\pi$
$488$	−202751.	+	202751.i	−0.851381	+	0.851381i
$489$		−	39714.0i		−	0.166083i
$490$	7630.74	+	16294.8i	0.0317815	+	0.0678667i
$491$	399454.			1.65693			0.828464	−	0.560043i	$-0.189215\pi$
$491$	399454.			1.65693			0.828464	+	0.560043i	$0.189215\pi$
$492$	−85947.1	−	85947.1i	−0.355059	−	0.355059i
$493$	−8591.65	+	8591.65i	−0.0353494	+	0.0353494i
$494$		−	1062.73i		−	0.00435482i
$495$	28507.5	+	10323.3i	0.116345	+	0.0421317i
$496$	−87133.2			−0.354177
$497$	50333.1	+	50333.1i	0.203770	+	0.203770i
$498$	41142.2	−	41142.2i	0.165893	−	0.165893i
$499$		−	17571.0i		−	0.0705658i	−0.999377	−	0.0352829i	$-0.988767\pi$
$499$		−	17571.0i		−	0.0705658i	0.999377	−	0.0352829i	$-0.0112332\pi$
$500$	91368.4	+	156483.i	0.365473	+	0.625932i
$501$	−182263.			−0.726145
$502$	73623.4	+	73623.4i	0.292152	+	0.292152i
$503$	−131869.	+	131869.i	−0.521202	+	0.521202i	−0.917934	−	0.396732i	$-0.870144\pi$
$503$	−131869.	+	131869.i	−0.521202	+	0.521202i	0.396732	+	0.917934i	$0.370144\pi$
$504$			71933.4i			0.283185i
$505$	−141568.	+	390936.i	−0.555114	+	1.53293i
$506$	−22251.5			−0.0869075
$507$	75350.2	+	75350.2i	0.293135	+	0.293135i
$508$	−8778.76	+	8778.76i	−0.0340178	+	0.0340178i
$509$		−	127171.i		−	0.490855i	−0.969415	−	0.245427i	$-0.921072\pi$
$509$		−	127171.i		−	0.490855i	0.969415	−	0.245427i	$-0.0789283\pi$
$510$	2021.55	−	946.678i	0.00777221	−	0.00363967i
$511$	86415.4			0.330940
$512$	90005.1	+	90005.1i	0.343342	+	0.343342i
$513$	−78605.2	+	78605.2i	−0.298687	+	0.298687i
$514$			182321.i			0.690099i
$515$	−116692.	−	249185.i	−0.439973	−	0.939524i
$516$	−19709.2			−0.0740236
$517$	−16407.8	−	16407.8i	−0.0613858	−	0.0613858i
$518$	32988.1	−	32988.1i	0.122941	−	0.122941i
$519$			123194.i			0.457356i
$520$	3426.91	+	1240.97i	0.0126735	+	0.00458940i
$521$	−91618.7			−0.337527			−0.168764	−	0.985657i	$-0.553977\pi$
$521$	−91618.7			−0.337527			−0.168764	+	0.985657i	$0.553977\pi$
$522$	−106045.	−	106045.i	−0.389178	−	0.389178i
$523$	103824.	−	103824.i	0.379573	−	0.379573i	−0.491375	−	0.870948i	$-0.663506\pi$
$523$	103824.	−	103824.i	0.379573	−	0.379573i	0.870948	+	0.491375i	$0.163506\pi$
$524$		−	57425.0i		−	0.209141i
$525$	−33180.8	−	27658.2i	−0.120384	−	0.100347i
$526$	−89476.2			−0.323397
$527$	10969.4	+	10969.4i	0.0394969	+	0.0394969i
$528$	−3055.80	+	3055.80i	−0.0109612	+	0.0109612i
$529$		−	64132.6i		−	0.229175i
$530$	−77984.3	+	215351.i	−0.277623	+	0.766648i
$531$	−114798.			−0.407143
$532$	30552.6	+	30552.6i	0.107951	+	0.107951i
$533$	−4999.73	+	4999.73i	−0.0175992	+	0.0175992i
$534$			28904.2i			0.101363i
$535$	220717.	−	103360.i	0.771131	−	0.361115i
$536$	−436477.			−1.51926
$537$	75132.2	+	75132.2i	0.260542	+	0.260542i
$538$	40613.9	−	40613.9i	0.140317	−	0.140317i
$539$			6201.84i			0.0213473i
$540$	−67944.0	−	145089.i	−0.233004	−	0.497560i
$541$	−334086.			−1.14147			−0.570735	−	0.821135i	$-0.693342\pi$
$541$	−334086.			−1.14147			−0.570735	+	0.821135i	$0.693342\pi$
$542$	−159488.	−	159488.i	−0.542912	−	0.542912i
$543$	107892.	−	107892.i	0.365923	−	0.365923i
$544$		−	12097.2i		−	0.0408777i
$545$	289422.	+	104807.i	0.974402	+	0.352856i
$546$	−365.112			−0.00122473
$547$	190383.	+	190383.i	0.636287	+	0.636287i	0.949637	−	0.313351i	$-0.101452\pi$
$547$	190383.	+	190383.i	0.636287	+	0.636287i	−0.313351	+	0.949637i	$0.601452\pi$
$548$	155582.	−	155582.i	0.518082	−	0.518082i
$549$		−	332121.i		−	1.10192i
$550$	−2143.65	−	23615.3i	−0.00708645	−	0.0780672i
$551$	−214363.			−0.706069
$552$	89619.6	+	89619.6i	0.294120	+	0.294120i
$553$	129641.	−	129641.i	0.423927	−	0.423927i
$554$		−	270003.i		−	0.879729i
$555$	−38134.7	+	105308.i	−0.123804	+	0.341880i
$556$	69850.2			0.225953
$557$	−77060.8	−	77060.8i	−0.248384	−	0.248384i	0.571923	−	0.820307i	$-0.306197\pi$
$557$	−77060.8	−	77060.8i	−0.248384	−	0.248384i	−0.820307	+	0.571923i	$0.806197\pi$
$558$	−135393.	+	135393.i	−0.434839	+	0.434839i
$559$			1146.53i			0.00366912i
$560$	−26854.9	+	12576.0i	−0.0856344	+	0.0401020i
$561$	769.407			0.00244473
$562$	−121098.	−	121098.i	−0.383410	−	0.383410i
$563$	285556.	−	285556.i	0.900897	−	0.900897i	−0.0946167	−	0.995514i	$-0.530163\pi$
$563$	285556.	−	285556.i	0.900897	−	0.900897i	0.995514	+	0.0946167i	$0.0301625\pi$
$564$			55540.4i			0.174603i
$565$	68550.7	+	146384.i	0.214741	+	0.458561i
$566$	−74372.7			−0.232156
$567$	−44143.2	−	44143.2i	−0.137309	−	0.137309i
$568$	157376.	−	157376.i	0.487801	−	0.487801i
$569$			281883.i			0.870650i	0.900273	+	0.435325i	$0.143367\pi$
$569$			281883.i			0.870650i	−0.900273	+	0.435325i	$0.856633\pi$
$570$	37029.0	+	13409.1i	0.113970	+	0.0412716i
$571$	−191251.			−0.586585			−0.293292	−	0.956023i	$-0.594751\pi$
$571$	−191251.			−0.586585			−0.293292	+	0.956023i	$0.594751\pi$
$572$	373.291	+	373.291i	0.00114092	+	0.00114092i
$573$	−40702.7	+	40702.7i	−0.123969	+	0.123969i
$574$			109142.i			0.331259i
$575$	365057.	−	33137.6i	1.10414	−	0.100227i
$576$	80580.1			0.242875
$577$	394966.	+	394966.i	1.18634	+	1.18634i	0.978072	+	0.208265i	$0.0667817\pi$
$577$	394966.	+	394966.i	1.18634	+	1.18634i	0.208265	+	0.978072i	$0.433218\pi$
$578$	123730.	−	123730.i	0.370355	−	0.370355i
$579$			35570.0i			0.106103i
$580$	105190.	−	290480.i	0.312694	−	0.863495i
$581$	137613.			0.407667
$582$	−77784.4	−	77784.4i	−0.229639	−	0.229639i
$583$	−55822.1	+	55822.1i	−0.164236	+	0.164236i
$584$		−	270195.i		−	0.792230i
$585$	−3823.16	+	1790.36i	−0.0111715	+	0.00523153i
$586$	159109.			0.463341
$587$	434613.	+	434613.i	1.26132	+	1.26132i	0.950452	+	0.310871i	$0.100621\pi$
$587$	434613.	+	434613.i	1.26132	+	1.26132i	0.310871	+	0.950452i	$0.399379\pi$
$588$	10496.6	−	10496.6i	0.0303596	−	0.0303596i
$589$			273690.i			0.788910i
$590$	38076.6	+	81309.3i	0.109384	+	0.233580i
$591$	−113.154			−0.000323962
$592$	54366.6	+	54366.6i	0.155128	+	0.155128i
$593$	149520.	−	149520.i	0.425197	−	0.425197i	−0.461792	−	0.886988i	$-0.652793\pi$
$593$	149520.	−	149520.i	0.425197	−	0.425197i	0.886988	+	0.461792i	$0.152793\pi$
$594$			20965.0i			0.0594186i
$595$	4964.07	+	1797.62i	0.0140218	+	0.00507766i
$596$	−176366.			−0.496503
$597$	162516.	+	162516.i	0.455983	+	0.455983i
$598$	2190.81	−	2190.81i	0.00612635	−	0.00612635i
$599$		−	251890.i		−	0.702033i	−0.936369	−	0.351017i	$-0.885836\pi$
$599$		−	251890.i		−	0.702033i	0.936369	−	0.351017i	$-0.114164\pi$
$600$	−86478.9	+	103746.i	−0.240219	+	0.288184i
$601$	−46644.1			−0.129136			−0.0645681	−	0.997913i	$-0.520567\pi$
$601$	−46644.1			−0.129136			−0.0645681	+	0.997913i	$0.520567\pi$
$602$	12514.1	+	12514.1i	0.0345308	+	0.0345308i
$603$	357490.	−	357490.i	0.983172	−	0.983172i
$604$		−	444973.i		−	1.21972i
$605$	−121844.	+	336470.i	−0.332885	+	0.919253i
$606$	−130231.			−0.354625
$607$	−404387.	−	404387.i	−1.09754	−	1.09754i	−0.994698	−	0.102841i	$-0.967207\pi$
$607$	−404387.	−	404387.i	−1.09754	−	1.09754i	−0.102841	−	0.994698i	$-0.532793\pi$
$608$	150914.	−	150914.i	0.408245	−	0.408245i
$609$			73646.6i			0.198572i
$610$	−235234.	+	110158.i	−0.632180	+	0.296045i
$611$	3230.91			0.00865452
$612$	6271.80	+	6271.80i	0.0167452	+	0.0167452i
$613$	−425304.	+	425304.i	−1.13182	+	1.13182i	−0.141950	+	0.989874i	$0.545337\pi$
$613$	−425304.	+	425304.i	−1.13182	+	1.13182i	−0.989874	+	0.141950i	$0.954663\pi$
$614$		−	227781.i		−	0.604199i
$615$	−111122.	−	237291.i	−0.293798	−	0.627381i
$616$	19391.3			0.0511028
$617$	−249065.	−	249065.i	−0.654247	−	0.654247i	0.299766	−	0.954013i	$-0.403092\pi$
$617$	−249065.	−	249065.i	−0.654247	−	0.654247i	−0.954013	+	0.299766i	$0.903092\pi$
$618$	60941.7	−	60941.7i	0.159565	−	0.159565i
$619$		−	63129.3i		−	0.164759i	−0.996601	−	0.0823796i	$-0.973748\pi$
$619$		−	63129.3i		−	0.164759i	0.996601	−	0.0823796i	$-0.0262520\pi$
$620$	−370871.	−	134302.i	−0.964806	−	0.349381i
$621$	−324087.			−0.840386
$622$	234209.	+	234209.i	0.605372	+	0.605372i
$623$	−48339.4	+	48339.4i	−0.124545	+	0.124545i
$624$		−	601.730i		−	0.00154537i
$625$	70337.3	+	384240.i	0.180064	+	0.983655i
$626$	224279.			0.572321
$627$	9598.43	+	9598.43i	0.0244155	+	0.0244155i
$628$	−46678.2	+	46678.2i	−0.118357	+	0.118357i
$629$		−	13688.7i		−	0.0345989i
$630$	−22187.6	+	61270.3i	−0.0559022	+	0.154372i
$631$	603122.			1.51477			0.757385	−	0.652969i	$-0.226477\pi$
$631$	603122.			1.51477			0.757385	+	0.652969i	$0.226477\pi$
$632$	−405347.	−	405347.i	−1.01483	−	1.01483i
$633$	21084.0	−	21084.0i	0.0526194	−	0.0526194i
$634$			153979.i			0.383075i
$635$	−24237.3	+	11350.2i	−0.0601086	+	0.0281484i
$636$	188958.			0.467145
$637$	−610.613	−	610.613i	−0.00150483	−	0.00150483i
$638$	−28586.7	+	28586.7i	−0.0702301	+	0.0702301i
$639$			257794.i			0.631350i
$640$	153243.	+	327237.i	0.374127	+	0.798917i
$641$	−405370.			−0.986587			−0.493293	−	0.869863i	$-0.664207\pi$
$641$	−405370.			−0.986587			−0.493293	+	0.869863i	$0.664207\pi$
$642$	53979.4	+	53979.4i	0.130966	+	0.130966i
$643$	−167231.	+	167231.i	−0.404478	+	0.404478i	−0.879808	−	0.475330i	$-0.842329\pi$
$643$	−167231.	+	167231.i	−0.404478	+	0.404478i	0.475330	+	0.879808i	$0.342329\pi$
$644$			125968.i			0.303729i
$645$	−39948.7	−	14466.5i	−0.0960249	−	0.0347731i
$646$	−4813.32			−0.0115340
$647$	318214.	+	318214.i	0.760170	+	0.760170i	0.976353	−	0.216183i	$-0.0693607\pi$
$647$	318214.	+	318214.i	0.760170	+	0.760170i	−0.216183	+	0.976353i	$0.569361\pi$
$648$	−138023.	+	138023.i	−0.328700	+	0.328700i
$649$			30946.5i			0.0734720i
$650$	2536.15	+	2114.03i	0.00600272	+	0.00500363i
$651$	94028.7			0.221870
$652$	−87268.2	−	87268.2i	−0.205287	−	0.205287i
$653$	517979.	−	517979.i	1.21475	−	1.21475i	0.245300	−	0.969447i	$-0.421113\pi$
$653$	517979.	−	517979.i	1.21475	−	1.21475i	0.969447	−	0.245300i	$-0.0788866\pi$
$654$			96414.1i			0.225416i
$655$	42149.7	−	116395.i	0.0982452	−	0.271301i
$656$	−179873.			−0.417984
$657$	221299.	+	221299.i	0.512683	+	0.512683i
$658$	35264.7	−	35264.7i	0.0814495	−	0.0814495i
$659$			378556.i			0.871686i	0.900023	+	0.435843i	$0.143550\pi$
$659$			378556.i			0.871686i	−0.900023	+	0.435843i	$0.856450\pi$
$660$	−17716.7	+	8296.60i	−0.0406719	+	0.0190464i
$661$	−793156.			−1.81533			−0.907666	−	0.419694i	$-0.862137\pi$
$661$	−793156.			−1.81533			−0.907666	+	0.419694i	$0.862137\pi$
$662$	78938.2	+	78938.2i	0.180124	+	0.180124i
$663$	−75.7534	+	75.7534i	−0.000172336	+	0.000172336i
$664$		−	430273.i		−	0.975906i
$665$	39501.8	+	84352.7i	0.0893251	+	0.190746i
$666$	168957.			0.380914
$667$	−441907.	−	441907.i	−0.993298	−	0.993298i
$668$	−400507.	+	400507.i	−0.897548	+	0.897548i
$669$		−	363045.i		−	0.811164i
$670$	−371776.	−	134630.i	−0.828193	−	0.299910i
$671$	−89530.6			−0.198850
$672$	−51847.8	−	51847.8i	−0.114813	−	0.114813i
$673$	−277903.	+	277903.i	−0.613570	+	0.613570i	−0.943874	−	0.330305i	$-0.892848\pi$
$673$	−277903.	+	277903.i	−0.613570	+	0.613570i	0.330305	+	0.943874i	$0.392848\pi$
$674$			282156.i			0.621112i
$675$	−31221.7	−	343952.i	−0.0685251	−	0.754901i
$676$	331151.			0.724657
$677$	−244917.	−	244917.i	−0.534369	−	0.534369i	0.387501	−	0.921869i	$-0.373338\pi$
$677$	−244917.	−	244917.i	−0.534369	−	0.534369i	−0.921869	+	0.387501i	$0.873338\pi$
$678$	−35800.3	+	35800.3i	−0.0778802	+	0.0778802i
$679$		−	260173.i		−	0.564317i
$680$	5620.61	−	15521.1i	0.0121553	−	0.0335665i
$681$	56206.5			0.121197
$682$	36498.3	+	36498.3i	0.0784700	+	0.0784700i
$683$	−504443.	+	504443.i	−1.08136	+	1.08136i	−0.0849785	+	0.996383i	$0.527082\pi$
$683$	−504443.	+	504443.i	−1.08136	+	1.08136i	−0.996383	+	0.0849785i	$0.972918\pi$
$684$			156483.i			0.334468i
$685$	429547.	−	201154.i	0.915438	−	0.428693i
$686$	−13329.4			−0.0283245
$687$	−57198.1	−	57198.1i	−0.121190	−	0.121190i
$688$	−20624.1	+	20624.1i	−0.0435711	+	0.0435711i
$689$		−	10992.1i		−	0.0231549i
$690$	48692.0	+	103978.i	0.102273	+	0.218394i
$691$	452722.			0.948146			0.474073	−	0.880486i	$-0.342783\pi$
$691$	452722.			0.948146			0.474073	+	0.880486i	$0.342783\pi$
$692$	270708.	+	270708.i	0.565312	+	0.565312i
$693$	−15882.1	+	15882.1i	−0.0330706	+	0.0330706i
$694$			220638.i			0.458100i
$695$	141580.	+	51269.7i	0.293111	+	0.106143i
$696$	230271.			0.475358
$697$	22644.7	+	22644.7i	0.0466124	+	0.0466124i
$698$	149644.	−	149644.i	0.307149	−	0.307149i
$699$		−	75556.4i		−	0.154638i
$700$	−133689.	+	12135.4i	−0.272834	+	0.0247661i
$701$	−430640.			−0.876352			−0.438176	−	0.898889i	$-0.644375\pi$
$701$	−430640.			−0.876352			−0.438176	+	0.898889i	$0.644375\pi$
$702$	−2064.15	−	2064.15i	−0.00418858	−	0.00418858i
$703$	170768.	−	170768.i	0.345539	−	0.345539i
$704$		−	21722.2i		−	0.0438287i
$705$	−40766.4	+	112575.i	−0.0820209	+	0.226498i
$706$	−89237.7			−0.179035
$707$	−217798.	−	217798.i	−0.435729	−	0.435729i
$708$	52377.1	−	52377.1i	0.104490	−	0.104490i
$709$			232388.i			0.462298i	0.972918	+	0.231149i	$0.0742484\pi$
$709$			232388.i			0.462298i	−0.972918	+	0.231149i	$0.925752\pi$
$710$	182590.	−	85505.5i	0.362209	−	0.169620i
$711$	663987.			1.31347
$712$	151143.	+	151143.i	0.298145	+	0.298145i
$713$	−564208.	+	564208.i	−1.10984	+	1.10984i
$714$			1653.66i			0.00324377i
$715$	482.632	+	1030.62i	0.000944070	+	0.00201598i
$716$	330193.			0.644084
$717$	−211929.	−	211929.i	−0.412242	−	0.412242i
$718$	18988.1	−	18988.1i	0.0368326	−	0.0368326i
$719$			684958.i			1.32497i	0.749075	+	0.662485i	$0.230498\pi$
$719$			684958.i			1.32497i	−0.749075	+	0.662485i	$0.769502\pi$
$720$	−100978.	−	36566.6i	−0.194787	−	0.0705375i
$721$	203838.			0.392115
$722$	133315.	+	133315.i	0.255743	+	0.255743i
$723$	39489.9	−	39489.9i	0.0755457	−	0.0755457i
$724$		−	474167.i		−	0.904595i
$725$	426421.	−	511566.i	0.811265	−	0.973252i
$726$	−112087.			−0.212658
$727$	−344257.	−	344257.i	−0.651350	−	0.651350i	0.301968	−	0.953318i	$-0.402356\pi$
$727$	−344257.	−	344257.i	−0.651350	−	0.651350i	−0.953318	+	0.301968i	$0.902356\pi$
$728$	−1909.20	+	1909.20i	−0.00360238	+	0.00360238i
$729$		−	59055.9i		−	0.111124i
$730$	83340.5	−	230142.i	0.156390	−	0.431868i
$731$	5192.85			0.00971787
$732$	151531.	+	151531.i	0.282800	+	0.282800i
$733$	458945.	−	458945.i	0.854186	−	0.854186i	−0.136460	−	0.990646i	$-0.543572\pi$
$733$	458945.	−	458945.i	0.854186	−	0.854186i	0.990646	+	0.136460i	$0.0435724\pi$
$734$		−	184624.i		−	0.342685i
$735$	28980.2	−	13571.2i	0.0536447	−	0.0251214i
$736$	622213.			1.14864
$737$	−96369.6	−	96369.6i	−0.177421	−	0.177421i
$738$	−279499.	+	279499.i	−0.513177	+	0.513177i
$739$		−	61500.0i		−	0.112612i	−0.998414	−	0.0563062i	$-0.982068\pi$
$739$		−	61500.0i		−	0.112612i	0.998414	−	0.0563062i	$-0.0179323\pi$
$740$	147607.	+	315202.i	0.269553	+	0.575607i
$741$	−1890.06			−0.00344223
$742$	−119977.	−	119977.i	−0.217916	−	0.217916i
$743$	33421.8	−	33421.8i	0.0605414	−	0.0605414i	−0.676188	−	0.736729i	$-0.736369\pi$
$743$	33421.8	−	33421.8i	0.0605414	−	0.0605414i	0.736729	+	0.676188i	$0.236369\pi$
$744$		−	294000.i		−	0.531130i
$745$	−357477.	−	129452.i	−0.644073	−	0.233236i
$746$	141127.			0.253590
$747$	352409.	+	352409.i	0.631546	+	0.631546i
$748$	1690.71	−	1690.71i	0.00302179	−	0.00302179i
$749$			180550.i			0.321836i
$750$	−105660.	+	61693.4i	−0.187840	+	0.109677i
$751$	257993.			0.457434			0.228717	−	0.973493i	$-0.426547\pi$
$751$	257993.			0.457434			0.228717	+	0.973493i	$0.426547\pi$
$752$	58118.6	+	58118.6i	0.102773	+	0.102773i
$753$	130939.	−	130939.i	0.230929	−	0.230929i
$754$		−	5629.12i		−	0.00990143i
$755$	326608.	−	901919.i	0.572972	−	1.58225i
$756$	118685.			0.207660
$757$	−783812.	−	783812.i	−1.36779	−	1.36779i	−0.863581	−	0.504211i	$-0.831783\pi$
$757$	−783812.	−	783812.i	−1.36779	−	1.36779i	−0.504211	−	0.863581i	$-0.668217\pi$
$758$	−162788.	+	162788.i	−0.283325	+	0.283325i
$759$			39574.1i			0.0686954i
$760$	263745.	−	123510.i	0.456623	−	0.213833i
$761$	614396.			1.06091			0.530456	−	0.847713i	$-0.322021\pi$
$761$	614396.			1.06091			0.530456	+	0.847713i	$0.322021\pi$
$762$	−5927.56	−	5927.56i	−0.0102086	−	0.0102086i
$763$	−161243.	+	161243.i	−0.276969	+	0.276969i
$764$			178881.i			0.306463i
$765$	8108.88	+	17315.8i	0.0138560	+	0.0295883i
$766$	−278544.			−0.474719
$767$	−3046.89	−	3046.89i	−0.00517925	−	0.00517925i
$768$	−130753.	+	130753.i	−0.221682	+	0.221682i
$769$			232260.i			0.392755i	0.980528	+	0.196377i	$0.0629177\pi$
$769$			232260.i			0.392755i	−0.980528	+	0.196377i	$0.937082\pi$
$770$	16516.8	+	5981.16i	0.0278576	+	0.0100880i
$771$	324258.			0.545483
$772$	78162.1	+	78162.1i	0.131148	+	0.131148i
$773$	654735.	−	654735.i	1.09574	−	1.09574i	0.100834	−	0.994903i	$-0.467849\pi$
$773$	654735.	−	654735.i	1.09574	−	1.09574i	0.994903	−	0.100834i	$-0.0321510\pi$
$774$			64094.2i			0.106988i
$775$	−653144.	−	544436.i	−1.08744	−	0.906448i
$776$	−813483.			−1.35091
$777$	−58669.1	−	58669.1i	−0.0971779	−	0.0971779i
$778$	164982.	−	164982.i	0.272569	−	0.272569i
$779$			564991.i			0.931036i
$780$	927.472	−	2561.19i	0.00152444	−	0.00420971i
$781$	69494.1			0.113932
$782$	−9922.59	−	9922.59i	−0.0162260	−	0.0162260i
$783$	−416359.	+	416359.i	−0.679117	+	0.679117i
$784$		−	21967.8i		−	0.0357400i
$785$	−128874.	+	60350.7i	−0.209134	+	0.0979362i
$786$	38774.3			0.0627623
$787$	95570.1	+	95570.1i	0.154302	+	0.154302i	0.780036	−	0.625734i	$-0.215200\pi$
$787$	95570.1	+	95570.1i	0.154302	+	0.154302i	−0.625734	+	0.780036i	$0.715200\pi$
$788$	−248.645	+	248.645i	−0.000400431	+	0.000400431i
$789$			159133.i			0.255626i
$790$	−220233.	−	470288.i	−0.352880	−	0.753546i
$791$	−119745.			−0.191383
$792$	49658.6	+	49658.6i	0.0791670	+	0.0791670i
$793$	8814.90	−	8814.90i	0.0140175	−	0.0140175i
$794$			168632.i			0.267485i
$795$	383001.	+	138695.i	0.605990	+	0.219445i
$796$	714232.			1.12723
$797$	319866.	+	319866.i	0.503560	+	0.503560i	0.912542	−	0.408983i	$-0.134116\pi$
$797$	319866.	+	319866.i	0.503560	+	0.503560i	−0.408983	+	0.912542i	$0.634116\pi$
$798$	−20629.6	+	20629.6i	−0.0323955	+	0.0323955i
$799$		−	14633.4i		−	0.0229220i
$800$	59942.4	+	660351.i	0.0936600	+	1.03180i
$801$	−247583.			−0.385882
$802$	238133.	+	238133.i	0.370229	+	0.370229i
$803$	59656.1	−	59656.1i	0.0925175	−	0.0925175i
$804$			326212.i			0.504647i
$805$	−92459.6	+	255324.i	−0.142679	+	0.394004i
$806$	−7187.01			−0.0110631
$807$	−72231.6	−	72231.6i	−0.110912	−	0.110912i
$808$	−680990.	+	680990.i	−1.04308	+	1.04308i
$809$			243401.i			0.371899i	0.982559	+	0.185950i	$0.0595361\pi$
$809$			243401.i			0.371899i	−0.982559	+	0.185950i	$0.940464\pi$
$810$	−160135.	+	74990.2i	−0.244071	+	0.114297i
$811$	−1.18528e6			−1.80210			−0.901049	−	0.433717i	$-0.857202\pi$
$811$	−1.18528e6			−1.80210			−0.901049	+	0.433717i	$0.857202\pi$
$812$	161832.	+	161832.i	0.245444	+	0.245444i
$813$	−283649.	+	283649.i	−0.429141	+	0.429141i
$814$		−	45546.1i		−	0.0687389i
$815$	−112830.	−	240939.i	−0.169867	−	0.362737i
$816$	−2725.35			−0.00409300
$817$	64781.4	+	64781.4i	0.0970523	+	0.0970523i
$818$	−201636.	+	201636.i	−0.301344	+	0.301344i
$819$		−	3127.41i		−	0.00466248i
$820$	−765608.	−	277247.i	−1.13862	−	0.412324i
$821$	155906.			0.231300			0.115650	−	0.993290i	$-0.463105\pi$
$821$	155906.			0.231300			0.115650	+	0.993290i	$0.463105\pi$
$822$	105051.	+	105051.i	0.155474	+	0.155474i
$823$	128790.	−	128790.i	0.190144	−	0.190144i	−0.605614	−	0.795758i	$-0.707073\pi$
$823$	128790.	−	128790.i	0.190144	−	0.190144i	0.795758	+	0.605614i	$0.207073\pi$
$824$		−	637339.i		−	0.938677i
$825$	−41999.7	+	3812.47i	−0.0617076	+	0.00560142i
$826$	−66512.3			−0.0974859
$827$	−355578.	−	355578.i	−0.519905	−	0.519905i	0.397637	−	0.917543i	$-0.369830\pi$
$827$	−355578.	−	355578.i	−0.519905	−	0.519905i	−0.917543	+	0.397637i	$0.869830\pi$
$828$	−322587.	+	322587.i	−0.470529	+	0.470529i
$829$		−	180229.i		−	0.262250i	−0.991366	−	0.131125i	$-0.958141\pi$
$829$		−	180229.i		−	0.262250i	0.991366	−	0.131125i	$-0.0418590\pi$
$830$	132716.	−	366491.i	0.192649	−	0.531995i
$831$	−480198.			−0.695374
$832$	2138.70	+	2138.70i	0.00308960	+	0.00308960i
$833$	−2765.58	+	2765.58i	−0.00398563	+	0.00398563i
$834$			47164.0i			0.0678076i
$835$	−1.10576e6	+	517820.i	−1.58595	+	0.742688i
$836$	42183.5			0.0603573
$837$	531589.	+	531589.i	0.758796	+	0.758796i
$838$	25090.3	−	25090.3i	0.0357288	−	0.0357288i
$839$			246879.i			0.350720i	0.984504	+	0.175360i	$0.0561089\pi$
$839$			246879.i			0.350720i	−0.984504	+	0.175360i	$0.943891\pi$
$840$	−42433.1	−	90612.3i	−0.0601377	−	0.128419i
$841$	−428168.			−0.605371
$842$	−251012.	−	251012.i	−0.354055	−	0.354055i
$843$	−215371.	+	215371.i	−0.303063	+	0.303063i
$844$		−	92660.6i		−	0.130080i
$845$	671212.	+	243063.i	0.940040	+	0.340413i
$846$	180617.			0.252358
$847$	−187454.	−	187454.i	−0.261293	−	0.261293i
$848$	197730.	−	197730.i	0.274967	−	0.274967i
$849$			132271.i			0.183506i
$850$	9574.87	−	11486.7i	0.0132524	−	0.0158985i
$851$	704073.			0.972207
$852$	−117619.	−	117619.i	−0.162031	−	0.162031i
$853$	427394.	−	427394.i	0.587395	−	0.587395i	−0.349530	−	0.936925i	$-0.613659\pi$
$853$	427394.	−	427394.i	0.587395	−	0.587395i	0.936925	+	0.349530i	$0.113659\pi$
$854$		−	192425.i		−	0.263844i
$855$	−114858.	+	317176.i	−0.157119	+	0.433878i
$856$	564526.			0.770436
$857$	−345769.	−	345769.i	−0.470787	−	0.470787i	0.431382	−	0.902169i	$-0.358026\pi$
$857$	−345769.	−	345769.i	−0.470787	−	0.470787i	−0.902169	+	0.431382i	$0.858026\pi$
$858$	−252.052	+	252.052i	−0.000342386	+	0.000342386i
$859$			298325.i			0.404299i	0.979355	+	0.202150i	$0.0647927\pi$
$859$			298325.i			0.404299i	−0.979355	+	0.202150i	$0.935207\pi$
$860$	−119573.	+	55995.1i	−0.161672	+	0.0757100i
$861$	194108.			0.261841
$862$	470581.	+	470581.i	0.633315	+	0.633315i
$863$	232266.	−	232266.i	0.311863	−	0.311863i	−0.533768	−	0.845631i	$-0.679225\pi$
$863$	232266.	−	232266.i	0.311863	−	0.311863i	0.845631	+	0.533768i	$0.179225\pi$
$864$		−	586240.i		−	0.785323i
$865$	350001.	+	747397.i	0.467775	+	0.998894i
$866$	96643.2			0.128865
$867$	−220052.	−	220052.i	−0.292744	−	0.292744i
$868$	206620.	−	206620.i	0.274241	−	0.274241i
$869$		−	178993.i		−	0.237026i
$870$	196137.	+	71026.1i	0.259131	+	0.0938382i
$871$	18976.5			0.0250138
$872$	504158.	+	504158.i	0.663031	+	0.663031i
$873$	666271.	−	666271.i	0.874223	−	0.874223i
$874$		−	247571.i		−	0.324098i
$875$	−279882.	−	73529.5i	−0.365560	−	0.0960385i
$876$	−201937.			−0.263152
$877$	220910.	+	220910.i	0.287221	+	0.287221i	0.835980	−	0.548759i	$-0.184900\pi$
$877$	220910.	+	220910.i	0.287221	+	0.287221i	−0.548759	+	0.835980i	$0.684900\pi$
$878$	215054.	−	215054.i	0.278970	−	0.278970i
$879$		−	282975.i		−	0.366244i
$880$	−9857.36	+	27220.8i	−0.0127290	+	0.0351508i
$881$	−219463.			−0.282754			−0.141377	−	0.989956i	$-0.545153\pi$
$881$	−219463.			−0.282754			−0.141377	+	0.989956i	$0.545153\pi$
$882$	−34135.0	−	34135.0i	−0.0438796	−	0.0438796i
$883$	351509.	−	351509.i	0.450833	−	0.450833i	−0.444798	−	0.895631i	$-0.646725\pi$
$883$	351509.	−	351509.i	0.450833	−	0.450833i	0.895631	+	0.444798i	$0.146725\pi$
$884$			332.923i			0.000426029i
$885$	144608.	−	67718.9i	0.184631	−	0.0864616i
$886$	−362593.			−0.461904
$887$	−51300.9	−	51300.9i	−0.0652045	−	0.0652045i	0.673753	−	0.738957i	$-0.264681\pi$
$887$	−51300.9	−	51300.9i	−0.0652045	−	0.0652045i	−0.738957	+	0.673753i	$0.764681\pi$
$888$	−183441.	+	183441.i	−0.232632	+	0.232632i
$889$		−	19826.5i		−	0.0250867i
$890$	82118.7	+	175357.i	0.103672	+	0.221383i
$891$	−60947.8			−0.0767720
$892$	−797761.	−	797761.i	−1.00264	−	1.00264i
$893$	182553.	−	182553.i	0.228922	−	0.228922i
$894$		−	119085.i		−	0.148999i
$895$	669271.	+	242360.i	0.835518	+	0.302563i
$896$	−267685.			−0.333432
$897$	−3896.34	−	3896.34i	−0.00484253	−	0.00484253i
$898$	380433.	−	380433.i	0.471765	−	0.471765i
$899$			1.44969e6i			1.79372i
$900$	−373437.	−	311282.i	−0.461033	−	0.384299i
$901$	−49785.5			−0.0613272
$902$	75345.2	+	75345.2i	0.0926067	+	0.0926067i
$903$	22256.3	−	22256.3i	0.0272946	−	0.0272946i
$904$			374406.i			0.458148i
$905$	348036.	−	961092.i	0.424940	−	1.17346i
$906$	300453.			0.366033
$907$	−382253.	−	382253.i	−0.464662	−	0.464662i	0.435518	−	0.900180i	$-0.356565\pi$
$907$	−382253.	−	382253.i	−0.464662	−	0.464662i	−0.900180	+	0.435518i	$0.856565\pi$
$908$	123509.	−	123509.i	0.149805	−	0.149805i
$909$		−	1.11551e6i		−	1.35004i
$910$	−2215.08	+	1037.31i	−0.00267489	+	0.00125263i
$911$	220039.			0.265133			0.132566	−	0.991174i	$-0.457678\pi$
$911$	220039.			0.265133			0.132566	+	0.991174i	$0.457678\pi$
$912$	−33999.0	−	33999.0i	−0.0408768	−	0.0408768i
$913$	94999.7	−	94999.7i	0.113967	−	0.113967i
$914$			479900.i			0.574459i
$915$	195916.	+	418362.i	0.234007	+	0.499701i
$916$	−251376.			−0.299594
$917$	64846.1	+	64846.1i	0.0771161	+	0.0771161i
$918$	−9348.93	+	9348.93i	−0.0110937	+	0.0110937i
$919$		−	923186.i		−	1.09310i	−0.837428	−	0.546548i	$-0.815942\pi$
$919$		−	923186.i		−	1.09310i	0.837428	−	0.546548i	$-0.184058\pi$
$920$	798323.	+	289093.i	0.943198	+	0.341556i
$921$	−405106.			−0.477584
$922$	−23704.6	−	23704.6i	−0.0278850	−	0.0278850i
$923$	−6842.17	+	6842.17i	−0.00803138	+	0.00803138i
$924$		−	14492.5i		−	0.0169746i
$925$	67828.7	+	747229.i	0.0792738	+	0.873313i
$926$	−808380.			−0.942744
$927$	522003.	+	522003.i	0.607454	+	0.607454i
$928$	799365.	−	799365.i	0.928216	−	0.928216i
$929$			340275.i			0.394275i	0.980376	+	0.197137i	$0.0631645\pi$
$929$			340275.i			0.394275i	−0.980376	+	0.197137i	$0.936836\pi$
$930$	90683.0	−	250418.i	0.104848	−	0.289534i
$931$	−69001.9			−0.0796089
$932$	−166029.	−	166029.i	−0.191140	−	0.191140i
$933$	416539.	−	416539.i	0.478511	−	0.478511i
$934$		−	605491.i		−	0.694087i
$935$	4667.87	−	2185.93i	0.00533944	−	0.00250042i
$936$	−9778.47			−0.0111614
$937$	1.13011e6	+	1.13011e6i	1.28718	+	1.28718i	0.936490	+	0.350695i	$0.114055\pi$
$937$	1.13011e6	+	1.13011e6i	1.28718	+	1.28718i	0.350695	+	0.936490i	$0.385945\pi$
$938$	207124.	−	207124.i	0.235410	−	0.235410i
$939$		−	398879.i		−	0.452387i
$940$	157794.	+	336955.i	0.178581	+	0.381344i
$941$	−690085.			−0.779334			−0.389667	−	0.920956i	$-0.627410\pi$
$941$	−690085.			−0.779334			−0.389667	+	0.920956i	$0.627410\pi$
$942$	−31517.9	−	31517.9i	−0.0355185	−	0.0355185i
$943$	−1.16472e6	+	1.16472e6i	−1.30978	+	1.30978i
$944$		−	109617.i		−	0.123008i
$945$	240563.	+	87114.1i	0.269380	+	0.0975495i
$946$	17278.0			0.0193069
$947$	−312697.	−	312697.i	−0.348677	−	0.348677i	0.510940	−	0.859617i	$-0.329298\pi$
$947$	−312697.	−	312697.i	−0.348677	−	0.348677i	−0.859617	+	0.510940i	$0.829298\pi$
$948$	−302946.	+	302946.i	−0.337092	+	0.337092i
$949$			11747.1i			0.0130436i
$950$	262745.	−	23850.3i	0.291130	−	0.0264270i
$951$	273851.			0.302798
$952$	8647.15	+	8647.15i	0.00954111	+	0.00954111i
$953$	163152.	−	163152.i	0.179642	−	0.179642i	−0.611558	−	0.791200i	$-0.709457\pi$
$953$	163152.	−	163152.i	0.179642	−	0.179642i	0.791200	+	0.611558i	$0.209457\pi$
$954$		−	614491.i		−	0.675178i
$955$	−131298.	+	362576.i	−0.143963	+	0.397550i
$956$	−931391.			−1.01910
$957$	50841.4	+	50841.4i	0.0555128	+	0.0555128i
$958$	−54251.5	+	54251.5i	−0.0591127	+	0.0591127i
$959$			351376.i			0.382063i
$960$	−101504.	+	47533.8i	−0.110139	+	0.0515774i
$961$	927378.			1.00418
$962$	4484.33	+	4484.33i	0.00484560	+	0.00484560i
$963$	−462366.	+	462366.i	−0.498579	+	0.498579i
$964$		−	173552.i		−	0.186756i
$965$	101057.	+	215798.i	0.108520	+	0.231736i
$966$	−85055.3			−0.0911480
$967$	366124.	+	366124.i	0.391540	+	0.391540i	0.875236	−	0.483696i	$-0.160706\pi$
$967$	366124.	+	366124.i	0.391540	+	0.391540i	−0.483696	+	0.875236i	$0.660706\pi$
$968$	−586113.	+	586113.i	−0.625505	+	0.625505i
$969$			8560.45i			0.00911694i
$970$	−692896.	−	250915.i	−0.736418	−	0.266676i
$971$	−597720.			−0.633956			−0.316978	−	0.948433i	$-0.602668\pi$
$971$	−597720.			−0.633956			−0.316978	+	0.948433i	$0.602668\pi$
$972$	470199.	+	470199.i	0.497679	+	0.497679i
$973$	−78877.1	+	78877.1i	−0.0833154	+	0.0833154i
$974$			227209.i			0.239501i
$975$	3759.80	−	4510.52i	0.00395508	−	0.00474480i
$976$	317130.			0.332918
$977$	−299471.	−	299471.i	−0.313737	−	0.313737i	0.532618	−	0.846356i	$-0.321208\pi$
$977$	−299471.	−	299471.i	−0.313737	−	0.313737i	−0.846356	+	0.532618i	$0.821208\pi$
$978$	58924.9	−	58924.9i	0.0616058	−	0.0616058i
$979$			66741.5i			0.0696354i
$980$	33859.9	−	93503.1i	0.0352560	−	0.0973585i
$981$	−825846.			−0.858145
$982$	592681.	+	592681.i	0.614608	+	0.614608i
$983$	−16044.9	+	16044.9i	−0.0166046	+	0.0166046i	−0.715360	−	0.698756i	$-0.753737\pi$
$983$	−16044.9	+	16044.9i	−0.0166046	+	0.0166046i	0.698756	+	0.715360i	$0.253737\pi$
$984$		−	606918.i		−	0.626816i
$985$	−686.486	+	321.476i	−0.000707553	+	0.000331342i
$986$	−25495.4			−0.0262245
$987$	−62718.0	−	62718.0i	−0.0643810	−	0.0643810i
$988$	−4153.25	+	4153.25i	−0.00425475	+	0.00425475i
$989$			267092.i			0.273066i
$990$	26980.5	+	57614.5i	0.0275283	+	0.0587843i
$991$	−1.35587e6			−1.38061			−0.690307	−	0.723517i	$-0.742525\pi$
$991$	−1.35587e6			−1.38061			−0.690307	+	0.723517i	$0.742525\pi$
$992$	−1.02059e6	−	1.02059e6i	−1.03712	−	1.03712i
$993$	140391.	−	140391.i	0.142377	−	0.142377i
$994$			149361.i			0.151170i
$995$	1.44768e6	+	524243.i	1.46227	+	0.529525i
$996$	−321575.			−0.324163
$997$	833075.	+	833075.i	0.838096	+	0.838096i	0.988608	−	0.150513i	$-0.0480924\pi$
$997$	833075.	+	833075.i	0.838096	+	0.838096i	−0.150513	+	0.988608i	$0.548092\pi$
$998$	26070.6	−	26070.6i	0.0261752	−	0.0261752i
$999$		−	663368.i		−	0.664697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.g.a.22.8	yes	24
5.2	odd	4		175.5.g.c.43.5		24
5.3	odd	4	inner	35.5.g.a.8.8	✓	24
5.4	even	2		175.5.g.c.57.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.8	✓	24	5.3	odd	4	inner
35.5.g.a.22.8	yes	24	1.1	even	1	trivial
175.5.g.c.43.5		24	5.2	odd	4
175.5.g.c.57.5		24	5.4	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.48373 + 1.48373i) q^{2} +(2.63880 - 2.63880i) q^{3} -11.5971i q^{4} +(8.51221 - 23.5062i) q^{5} +7.83054 q^{6} +(13.0958 + 13.0958i) q^{7} +(40.9466 - 40.9466i) q^{8} +67.0734i q^{9} +(47.5067 - 22.2471i) q^{10} +18.0812 q^{11} +(-30.6025 - 30.6025i) q^{12} +(-1.78021 + 1.78021i) q^{13} +38.8613i q^{14} +(-39.5662 - 84.4904i) q^{15} -64.0460 q^{16} +(8.06293 + 8.06293i) q^{17} +(-99.5188 + 99.5188i) q^{18} +201.172i q^{19} +(-272.604 - 98.7169i) q^{20} +69.1145 q^{21} +(26.8275 + 26.8275i) q^{22} +(-414.713 + 414.713i) q^{23} -216.100i q^{24} +(-480.085 - 400.180i) q^{25} -5.28271 q^{26} +(390.737 + 390.737i) q^{27} +(151.873 - 151.873i) q^{28} +1065.57i q^{29} +(66.6552 - 184.066i) q^{30} +1360.48 q^{31} +(-750.173 - 750.173i) q^{32} +(47.7126 - 47.7126i) q^{33} +23.9264i q^{34} +(419.307 - 196.359i) q^{35} +777.857 q^{36} +(-848.868 - 848.868i) q^{37} +(-298.484 + 298.484i) q^{38} +9.39527i q^{39} +(-613.954 - 1311.05i) q^{40} +2808.50 q^{41} +(102.547 + 102.547i) q^{42} +(322.020 - 322.020i) q^{43} -209.689i q^{44} +(1576.64 + 570.943i) q^{45} -1230.64 q^{46} +(-907.451 - 907.451i) q^{47} +(-169.005 + 169.005i) q^{48} +343.000i q^{49} +(-118.557 - 1306.07i) q^{50} +42.5530 q^{51} +(20.6453 + 20.6453i) q^{52} +(-3087.31 + 3087.31i) q^{53} +1159.50i q^{54} +(153.911 - 425.020i) q^{55} +1072.46 q^{56} +(530.853 + 530.853i) q^{57} +(-1581.02 + 1581.02i) q^{58} +1711.53i q^{59} +(-979.843 + 458.853i) q^{60} -4951.60 q^{61} +(2018.58 + 2018.58i) q^{62} +(-878.380 + 878.380i) q^{63} -1201.37i q^{64} +(26.6925 + 56.9996i) q^{65} +141.585 q^{66} +(-5329.83 - 5329.83i) q^{67} +(93.5065 - 93.5065i) q^{68} +2188.69i q^{69} +(913.481 + 330.795i) q^{70} +3843.45 q^{71} +(2746.43 + 2746.43i) q^{72} +(3299.35 - 3299.35i) q^{73} -2518.98i q^{74} +(-2322.85 + 210.853i) q^{75} +2333.01 q^{76} +(236.787 + 236.787i) q^{77} +(-13.9400 + 13.9400i) q^{78} -9899.41i q^{79} +(-545.173 + 1505.48i) q^{80} -3370.79 q^{81} +(4167.06 + 4167.06i) q^{82} +(5254.07 - 5254.07i) q^{83} -801.527i q^{84} +(258.162 - 120.896i) q^{85} +955.582 q^{86} +(2811.84 + 2811.84i) q^{87} +(740.362 - 740.362i) q^{88} +3691.22i q^{89} +(1492.19 + 3186.44i) q^{90} -46.6266 q^{91} +(4809.46 + 4809.46i) q^{92} +(3590.03 - 3590.03i) q^{93} -2692.82i q^{94} +(4728.79 + 1712.42i) q^{95} -3959.12 q^{96} +(-9933.45 - 9933.45i) q^{97} +(-508.919 + 508.919i) q^{98} +1212.77i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25}+ \cdots - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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