LMFDB - Embedded newform 61.6.g.a.3.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,6,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.78341300859$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.16
Character	$\chi$	$=$	61.3
Dual form			61.6.g.a.41.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.45632 + 1.12303i) q^{2} +(-0.707000 + 2.17592i) q^{3} +(-15.2036 - 11.0460i) q^{4} +(37.1500 + 26.9911i) q^{5} +(-4.88724 + 6.72671i) q^{6} +(112.143 - 36.4374i) q^{7} +(-108.499 - 149.337i) q^{8} +(192.356 + 139.755i) q^{9} +O(q^{10})$	\(q+(3.45632 + 1.12303i) q^{2} +(-0.707000 + 2.17592i) q^{3} +(-15.2036 - 11.0460i) q^{4} +(37.1500 + 26.9911i) q^{5} +(-4.88724 + 6.72671i) q^{6} +(112.143 - 36.4374i) q^{7} +(-108.499 - 149.337i) q^{8} +(192.356 + 139.755i) q^{9} +(98.0907 + 135.010i) q^{10} +372.352i q^{11} +(34.7843 - 25.2723i) q^{12} +914.579 q^{13} +428.521 q^{14} +(-84.9955 + 61.7529i) q^{15} +(-21.4677 - 66.0707i) q^{16} +(803.429 - 1105.82i) q^{17} +(507.897 + 699.060i) q^{18} +(-580.466 + 1786.49i) q^{19} +(-266.669 - 820.722i) q^{20} +269.775i q^{21} +(-418.161 + 1286.97i) q^{22} +(-746.904 + 1028.03i) q^{23} +(401.654 - 130.505i) q^{24} +(-314.072 - 966.615i) q^{25} +(3161.08 + 1027.10i) q^{26} +(-889.873 + 646.531i) q^{27} +(-2107.46 - 684.755i) q^{28} -5085.22i q^{29} +(-363.122 + 117.985i) q^{30} +(6538.30 - 2124.42i) q^{31} +5654.42i q^{32} +(-810.209 - 263.253i) q^{33} +(4018.78 - 2919.81i) q^{34} +(5149.58 + 1673.20i) q^{35} +(-1380.76 - 4249.55i) q^{36} +(-13983.8 + 4543.62i) q^{37} +(-4012.55 + 5522.80i) q^{38} +(-646.607 + 1990.05i) q^{39} -8476.37i q^{40} +(985.816 + 3034.03i) q^{41} +(-302.965 + 932.429i) q^{42} +(-10640.8 - 14645.8i) q^{43} +(4113.02 - 5661.09i) q^{44} +(3373.90 + 10383.8i) q^{45} +(-3736.04 + 2714.39i) q^{46} -2907.74 q^{47} +158.942 q^{48} +(-2348.85 + 1706.54i) q^{49} -3693.64i q^{50} +(1838.17 + 2530.02i) q^{51} +(-13904.9 - 10102.5i) q^{52} +(-8599.55 - 11836.3i) q^{53} +(-3801.76 + 1235.27i) q^{54} +(-10050.2 + 13832.9i) q^{55} +(-17608.8 - 12793.6i) q^{56} +(-3476.87 - 2526.10i) q^{57} +(5710.84 - 17576.2i) q^{58} +(28175.0 + 9154.61i) q^{59} +1974.36 q^{60} +(-25918.0 - 13147.4i) q^{61} +24984.2 q^{62} +(26663.7 + 8663.55i) q^{63} +(-7037.03 + 21657.7i) q^{64} +(33976.6 + 24685.5i) q^{65} +(-2504.70 - 1819.77i) q^{66} +(-12427.9 + 17105.5i) q^{67} +(-24430.0 + 7937.78i) q^{68} +(-1708.84 - 2352.02i) q^{69} +(15919.6 + 11566.2i) q^{70} +(-20269.7 - 27898.8i) q^{71} -43889.2i q^{72} +(12472.9 - 9062.11i) q^{73} -53435.2 q^{74} +2325.33 q^{75} +(28558.8 - 20749.2i) q^{76} +(13567.5 + 41756.6i) q^{77} +(-4469.76 + 6152.10i) q^{78} +(58406.7 + 80389.9i) q^{79} +(985.795 - 3033.96i) q^{80} +(17076.4 + 52555.8i) q^{81} +11593.7i q^{82} +(106.995 - 329.297i) q^{83} +(2979.95 - 4101.55i) q^{84} +(59694.8 - 19396.0i) q^{85} +(-20330.4 - 62570.5i) q^{86} +(11065.0 + 3595.25i) q^{87} +(55605.8 - 40400.0i) q^{88} +(124015. + 40295.0i) q^{89} +39678.7i q^{90} +(102563. - 33324.8i) q^{91} +(22711.2 - 7379.33i) q^{92} +15728.8i q^{93} +(-10050.1 - 3265.47i) q^{94} +(-69783.6 + 50700.7i) q^{95} +(-12303.6 - 3997.67i) q^{96} +(-21055.0 - 64800.5i) q^{97} +(-10034.9 + 3260.53i) q^{98} +(-52038.1 + 71624.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) $ 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.45632	+	1.12303i	0.610997	+	0.198525i	0.598139	−	0.801392i	$-0.295907\pi$
$2$	3.45632	+	1.12303i	0.610997	+	0.198525i	0.0128580	+	0.999917i	$0.495907\pi$
$3$	−0.707000	+	2.17592i	−0.0453541	+	0.139586i	−0.971169	−	0.238391i	$-0.923380\pi$
$3$	−0.707000	+	2.17592i	−0.0453541	+	0.139586i	0.925815	+	0.377977i	$0.123380\pi$
$4$	−15.2036	−	11.0460i	−0.475112	−	0.345189i
$5$	37.1500	+	26.9911i	0.664560	+	0.482831i	0.868200	−	0.496215i	$-0.165277\pi$
$5$	37.1500	+	26.9911i	0.664560	+	0.482831i	−0.203640	+	0.979046i	$0.565277\pi$
$6$	−4.88724	+	6.72671i	−0.0554224	+	0.0762824i
$7$	112.143	−	36.4374i	0.865019	−	0.281062i	0.157296	−	0.987552i	$-0.449722\pi$
$7$	112.143	−	36.4374i	0.865019	−	0.281062i	0.707723	+	0.706490i	$0.249722\pi$
$8$	−108.499	−	149.337i	−0.599380	−	0.824976i
$9$	192.356	+	139.755i	0.791590	+	0.575124i
$10$	98.0907	+	135.010i	0.310190	+	0.426940i
$11$			372.352i			0.927838i	0.885878	+	0.463919i	$0.153557\pi$
$11$			372.352i			0.927838i	−0.885878	+	0.463919i	$0.846443\pi$
$12$	34.7843	−	25.2723i	0.0697317	−	0.0506630i
$13$	914.579			1.50094			0.750469	−	0.660906i	$-0.229828\pi$
$13$	914.579			1.50094			0.750469	+	0.660906i	$0.229828\pi$
$14$	428.521			0.584322
$15$	−84.9955	+	61.7529i	−0.0975367	+	0.0708646i
$16$	−21.4677	−	66.0707i	−0.0209645	−	0.0645222i
$17$	803.429	−	1105.82i	0.674256	−	0.928034i	−0.325591	−	0.945511i	$-0.605563\pi$
$17$	803.429	−	1105.82i	0.674256	−	0.928034i	0.999847	+	0.0174765i	$0.00556321\pi$
$18$	507.897	+	699.060i	0.369483	+	0.508549i
$19$	−580.466	+	1786.49i	−0.368886	+	1.13532i	0.578625	+	0.815594i	$0.303589\pi$
$19$	−580.466	+	1786.49i	−0.368886	+	1.13532i	−0.947511	+	0.319722i	$0.896411\pi$
$20$	−266.669	−	820.722i	−0.149072	−	0.458797i
$21$			269.775i			0.133491i
$22$	−418.161	+	1286.97i	−0.184199	+	0.566906i
$23$	−746.904	+	1028.03i	−0.294405	+	0.405214i	−0.930439	−	0.366448i	$-0.880574\pi$
$23$	−746.904	+	1028.03i	−0.294405	+	0.405214i	0.636034	+	0.771661i	$0.280574\pi$
$24$	401.654	−	130.505i	0.142339	−	0.0462488i
$25$	−314.072	−	966.615i	−0.100503	−	0.309317i
$26$	3161.08	+	1027.10i	0.917068	+	0.297974i
$27$	−889.873	+	646.531i	−0.234919	+	0.170679i
$28$	−2107.46	−	684.755i	−0.508000	−	0.165059i
$29$		−	5085.22i		−	1.12283i	−0.827534	−	0.561416i	$-0.810257\pi$
$29$		−	5085.22i		−	1.12283i	0.827534	−	0.561416i	$-0.189743\pi$
$30$	−363.122	+	117.985i	−0.0736630	+	0.0239346i
$31$	6538.30	−	2124.42i	1.22197	−	0.397042i	0.374171	−	0.927360i	$-0.377927\pi$
$31$	6538.30	−	2124.42i	1.22197	−	0.397042i	0.847799	+	0.530318i	$0.177927\pi$
$32$			5654.42i			0.976142i
$33$	−810.209	−	263.253i	−0.129513	−	0.0420812i
$34$	4018.78	−	2919.81i	0.596207	−	0.433169i
$35$	5149.58	+	1673.20i	0.710562	+	0.230876i
$36$	−1380.76	−	4249.55i	−0.177567	−	0.546496i
$37$	−13983.8	+	4543.62i	−1.67927	+	0.545629i	−0.984770	−	0.173860i	$-0.944376\pi$
$37$	−13983.8	+	4543.62i	−1.67927	+	0.545629i	−0.694504	+	0.719489i	$0.744376\pi$
$38$	−4012.55	+	5522.80i	−0.450777	+	0.620441i
$39$	−646.607	+	1990.05i	−0.0680737	+	0.209509i
$40$		−	8476.37i		−	0.837645i
$41$	985.816	+	3034.03i	0.0915875	+	0.281877i	0.986349	−	0.164666i	$-0.0526547\pi$
$41$	985.816	+	3034.03i	0.0915875	+	0.281877i	−0.894762	+	0.446544i	$0.852655\pi$
$42$	−302.965	+	932.429i	−0.0265014	+	0.0815629i
$43$	−10640.8	−	14645.8i	−0.877613	−	1.20793i	−0.977076	−	0.212889i	$-0.931713\pi$
$43$	−10640.8	−	14645.8i	−0.877613	−	1.20793i	0.0994634	−	0.995041i	$-0.468287\pi$
$44$	4113.02	−	5661.09i	0.320279	−	0.440827i
$45$	3373.90	+	10383.8i	0.248371	+	0.764408i
$46$	−3736.04	+	2714.39i	−0.260326	+	0.189138i
$47$	−2907.74			−0.192004			−0.0960021	−	0.995381i	$-0.530606\pi$
$47$	−2907.74			−0.192004			−0.0960021	+	0.995381i	$0.530606\pi$
$48$	158.942			0.00995719
$49$	−2348.85	+	1706.54i	−0.139754	+	0.101538i
$50$		−	3693.64i		−	0.208944i
$51$	1838.17	+	2530.02i	0.0989599	+	0.136207i
$52$	−13904.9	−	10102.5i	−0.713113	−	0.518107i
$53$	−8599.55	−	11836.3i	−0.420519	−	0.578795i	0.545225	−	0.838290i	$-0.316444\pi$
$53$	−8599.55	−	11836.3i	−0.420519	−	0.578795i	−0.965745	+	0.259494i	$0.916444\pi$
$54$	−3801.76	+	1235.27i	−0.177419	+	0.0576469i
$55$	−10050.2	+	13832.9i	−0.447989	+	0.616604i
$56$	−17608.8	−	12793.6i	−0.750345	−	0.545157i
$57$	−3476.87	−	2526.10i	−0.141743	−	0.102982i
$58$	5710.84	−	17576.2i	0.222910	−	0.686047i
$59$	28175.0	+	9154.61i	1.05374	+	0.342381i	0.784135	−	0.620590i	$-0.213107\pi$
$59$	28175.0	+	9154.61i	1.05374	+	0.342381i	0.269605	+	0.962971i	$0.413107\pi$
$60$	1974.36			0.0708025
$61$	−25918.0	−	13147.4i	−0.891819	−	0.452393i
$61$	−25918.0	−	13147.4i	−0.891819	−	0.452393i
$62$	24984.2			0.825442
$63$	26663.7	+	8663.55i	0.846386	+	0.275007i
$64$	−7037.03	+	21657.7i	−0.214753	+	0.660942i
$65$	33976.6	+	24685.5i	0.997463	+	0.724699i
$66$	−2504.70	−	1819.77i	−0.0707777	−	0.0514230i
$67$	−12427.9	+	17105.5i	−0.338228	+	0.465531i	−0.943923	−	0.330166i	$-0.892895\pi$
$67$	−12427.9	+	17105.5i	−0.338228	+	0.465531i	0.605695	+	0.795697i	$0.292895\pi$
$68$	−24430.0	+	7937.78i	−0.640694	+	0.208174i
$69$	−1708.84	−	2352.02i	−0.0432095	−	0.0594728i
$70$	15919.6	+	11566.2i	0.388317	+	0.282129i
$71$	−20269.7	−	27898.8i	−0.477201	−	0.656811i	0.500763	−	0.865584i	$-0.333053\pi$
$71$	−20269.7	−	27898.8i	−0.477201	−	0.656811i	−0.977964	+	0.208774i	$0.933053\pi$
$72$		−	43889.2i		−	0.997760i
$73$	12472.9	−	9062.11i	0.273943	−	0.199032i	−0.442328	−	0.896853i	$-0.645847\pi$
$73$	12472.9	−	9062.11i	0.273943	−	0.199032i	0.716271	+	0.697822i	$0.245847\pi$
$74$	−53435.2			−1.13435
$75$	2325.33			0.0477344
$76$	28558.8	−	20749.2i	0.567161	−	0.412066i
$77$	13567.5	+	41756.6i	0.260780	+	0.802598i
$78$	−4469.76	+	6152.10i	−0.0831856	+	0.114495i
$79$	58406.7	+	80389.9i	1.05292	+	1.44922i	0.886251	+	0.463206i	$0.153301\pi$
$79$	58406.7	+	80389.9i	1.05292	+	1.44922i	0.166668	+	0.986013i	$0.446699\pi$
$80$	985.795	−	3033.96i	0.0172211	−	0.0530012i
$81$	17076.4	+	52555.8i	0.289191	+	0.890037i
$82$			11593.7i			0.190409i
$83$	106.995	−	329.297i	0.00170478	−	0.00524677i	−0.950201	−	0.311639i	$-0.899122\pi$
$83$	106.995	−	329.297i	0.00170478	−	0.00524677i	0.951905	+	0.306392i	$0.0991220\pi$
$84$	2979.95	−	4101.55i	0.0460798	−	0.0634234i
$85$	59694.8	−	19396.0i	0.896167	−	0.291182i
$86$	−20330.4	−	62570.5i	−0.296414	−	0.912270i
$87$	11065.0	+	3595.25i	0.156731	+	0.0509250i
$88$	55605.8	−	40400.0i	0.765444	−	0.556128i
$89$	124015.	+	40295.0i	1.65959	+	0.539233i	0.980786	−	0.195089i	$-0.0624994\pi$
$89$	124015.	+	40295.0i	1.65959	+	0.539233i	0.678802	+	0.734321i	$0.262499\pi$
$90$			39678.7i			0.516359i
$91$	102563.	−	33324.8i	1.29834	−	0.421856i
$92$	22711.2	−	7379.33i	0.279751	−	0.0908965i
$93$			15728.8i			0.188577i
$94$	−10050.1	−	3265.47i	−0.117314	−	0.0381176i
$95$	−69783.6	+	50700.7i	−0.793312	+	0.576375i
$96$	−12303.6	−	3997.67i	−0.136255	−	0.0442720i
$97$	−21055.0	−	64800.5i	−0.227209	−	0.699277i	−0.998060	−	0.0622614i	$-0.980169\pi$
$97$	−21055.0	−	64800.5i	−0.227209	−	0.699277i	0.770851	−	0.637015i	$-0.219831\pi$
$98$	−10034.9	+	3260.53i	−0.105547	+	0.0342944i
$99$	−52038.1	+	71624.3i	−0.533622	+	0.734467i
$100$	−5902.25	+	18165.3i	−0.0590225	+	0.181653i
$101$		−	158573.i		−	1.54677i	−0.633936	−	0.773385i	$-0.718562\pi$
$101$		−	158573.i		−	1.54677i	0.633936	−	0.773385i	$-0.281438\pi$
$102$	3512.01	+	10808.9i	0.0334238	+	0.102868i
$103$	−48711.0	+	149917.i	−0.452411	+	1.39238i	0.421736	+	0.906719i	$0.361421\pi$
$103$	−48711.0	+	149917.i	−0.452411	+	1.39238i	−0.874147	+	0.485661i	$0.838579\pi$
$104$	−99231.2	−	136580.i	−0.899632	−	1.23824i
$105$	−7281.51	+	10022.1i	−0.0644538	+	0.0887130i
$106$	−16430.4	−	50567.4i	−0.142031	−	0.437126i
$107$	−47442.2	+	34468.8i	−0.400595	+	0.291049i	−0.769783	−	0.638305i	$-0.779636\pi$
$107$	−47442.2	+	34468.8i	−0.400595	+	0.291049i	0.369188	+	0.929355i	$0.379636\pi$
$108$	20670.9			0.170529
$109$	−236251.			−1.90462			−0.952309	−	0.305136i	$-0.901298\pi$
$109$	−236251.			−1.90462			−0.952309	+	0.305136i	$0.901298\pi$
$110$	−50271.3	+	36524.3i	−0.396131	+	0.287806i
$111$		−	33640.1i		−	0.259149i
$112$	−4814.89	−	6627.12i	−0.0362694	−	0.0499206i
$113$	−123623.	−	89817.3i	−0.910758	−	0.661704i	0.0304487	−	0.999536i	$-0.490306\pi$
$113$	−123623.	−	89817.3i	−0.910758	−	0.661704i	−0.941206	+	0.337832i	$0.890306\pi$
$114$	−9180.32	−	12635.6i	−0.0661600	−	0.0910615i
$115$	−55495.0	+	18031.4i	−0.391299	+	0.127141i
$116$	−56171.6	+	77313.6i	−0.387589	+	0.533471i
$117$	175925.	+	127817.i	1.18813	+	0.863225i
$118$	87100.9	+	63282.5i	0.575861	+	0.418388i
$119$	49805.3	−	153285.i	0.322410	−	0.992275i
$120$	18443.9	+	5992.80i	0.116923	+	0.0379906i
$121$	22404.9			0.139117
$122$	−74815.9	−	74548.3i	−0.455087	−	0.453459i
$123$	−7298.79			−0.0434999
$124$	−122872.	−	39923.5i	−0.717627	−	0.233171i
$125$	58766.1	−	180863.i	0.336397	−	1.03532i
$126$	82428.8	+	59888.0i	0.462543	+	0.336057i
$127$	−88599.1	−	64371.0i	−0.487439	−	0.354145i	0.316760	−	0.948506i	$-0.397405\pi$
$127$	−88599.1	−	64371.0i	−0.487439	−	0.354145i	−0.804198	+	0.594361i	$0.797405\pi$
$128$	57710.2	−	79431.3i	0.311335	−	0.428516i
$129$	39391.2	−	12799.0i	0.208413	−	0.0677175i
$130$	89711.6	+	123477.i	0.465576	+	0.640810i
$131$	−121967.	−	88614.1i	−0.620960	−	0.451154i	0.232297	−	0.972645i	$-0.425376\pi$
$131$	−121967.	−	88614.1i	−0.620960	−	0.451154i	−0.853257	+	0.521491i	$0.825376\pi$
$132$	9410.18	+	12952.0i	0.0470071	+	0.0646997i
$133$			221492.i			1.08575i
$134$	−62164.6	+	45165.2i	−0.299076	+	0.217291i
$135$	−50509.4			−0.238527
$136$	−252312.			−1.16974
$137$	−8090.76	+	5878.28i	−0.0368288	+	0.0267577i	−0.606047	−	0.795429i	$-0.707246\pi$
$137$	−8090.76	+	5878.28i	−0.0368288	+	0.0267577i	0.569219	+	0.822186i	$0.307246\pi$
$138$	−3264.93	−	10048.4i	−0.0145940	−	0.0449159i
$139$	85092.5	−	117120.i	0.373555	−	0.514154i	−0.580308	−	0.814397i	$-0.697068\pi$
$139$	85092.5	−	117120.i	0.373555	−	0.514154i	0.953863	+	0.300243i	$0.0970678\pi$
$140$	−59809.9	−	82321.2i	−0.257901	−	0.354970i
$141$	2055.77	−	6327.02i	0.00870818	−	0.0268010i
$142$	−38727.4	−	119191.i	−0.161175	−	0.496046i
$143$			340545.i			1.39263i
$144$	5104.27	−	15709.3i	0.0205129	−	0.0631323i
$145$	137256.	−	188916.i	0.542138	−	0.746189i
$146$	53287.4	−	17314.1i	0.206891	−	0.0672231i
$147$	−2052.66	−	6317.45i	−0.00783474	−	0.0241128i
$148$	262793.	+	85386.7i	0.986188	+	0.320432i
$149$	−137054.	+	99575.4i	−0.505738	+	0.367440i	−0.811204	−	0.584763i	$-0.801188\pi$
$149$	−137054.	+	99575.4i	−0.505738	+	0.367440i	0.305467	+	0.952203i	$0.401188\pi$
$150$	8037.08	+	2611.41i	0.0291656	+	0.00947646i
$151$		−	155144.i		−	0.553722i	−0.960910	−	0.276861i	$-0.910706\pi$
$151$		−	155144.i		−	0.553722i	0.960910	−	0.276861i	$-0.0892942\pi$
$152$	329769.	−	107148.i	1.15771	−	0.376163i
$153$	309089.	−	100429.i	1.06747	−	0.346842i
$154$			159561.i			0.542156i
$155$	300238.	+	97553.3i	1.00378	+	0.326147i
$156$	31813.0	−	23113.5i	0.104663	−	0.0760420i
$157$	−351549.	−	114225.i	−1.13825	−	0.369839i	−0.321543	−	0.946895i	$-0.604202\pi$
$157$	−351549.	−	114225.i	−1.13825	−	0.369839i	−0.816705	+	0.577056i	$0.804202\pi$
$158$	111592.	+	343446.i	0.355624	+	1.09450i
$159$	31834.7	−	10343.7i	0.0998637	−	0.0324477i
$160$	−152619.	+	210062.i	−0.471311	+	0.648704i
$161$	−46301.3	+	142501.i	−0.140776	+	0.433264i
$162$			200827.i			0.601222i
$163$	21970.0	+	67616.7i	0.0647681	+	0.199336i	0.978204	−	0.207648i	$-0.0665807\pi$
$163$	21970.0	+	67616.7i	0.0647681	+	0.199336i	−0.913436	+	0.406983i	$0.866581\pi$
$164$	18526.1	−	57017.5i	0.0537867	−	0.165538i
$165$	−22993.8	−	31648.3i	−0.0657508	−	0.0904982i
$166$	739.618	−	1018.00i	0.00208323	−	0.00286732i
$167$	−154879.	−	476668.i	−0.429735	−	1.32259i	−0.898386	−	0.439206i	$-0.855260\pi$
$167$	−154879.	−	476668.i	−0.429735	−	1.32259i	0.468651	−	0.883383i	$-0.344740\pi$
$168$	40287.3	−	29270.4i	0.110127	−	0.0800121i
$169$	465161.			1.25281
$170$	228107.			0.605362
$171$	−361327.	+	262520.i	−0.944954	+	0.686549i
$172$			340207.i			0.876845i
$173$	−325969.	−	448658.i	−0.828060	−	1.13973i	−0.988281	−	0.152645i	$-0.951221\pi$
$173$	−325969.	−	448658.i	−0.828060	−	1.13973i	0.160221	−	0.987081i	$-0.448779\pi$
$174$	34206.8	+	24852.7i	0.0856523	+	0.0622301i
$175$	−70441.8	−	96954.8i	−0.173874	−	0.239317i
$176$	24601.6	−	7993.54i	0.0598661	−	0.0194517i
$177$	−39839.4	+	54834.3i	−0.0955829	+	0.131559i
$178$	383384.	+	278545.i	0.906952	+	0.658939i
$179$	−5148.52	−	3740.62i	−0.0120102	−	0.00872591i	0.581764	−	0.813358i	$-0.302363\pi$
$179$	−5148.52	−	3740.62i	−0.0120102	−	0.00872591i	−0.593774	+	0.804632i	$0.702363\pi$
$180$	63404.6	−	195139.i	0.145861	−	0.448914i
$181$	330273.	+	107312.i	0.749337	+	0.243474i	0.658696	−	0.752409i	$-0.271108\pi$
$181$	330273.	+	107312.i	0.749337	+	0.243474i	0.0906411	+	0.995884i	$0.471108\pi$
$182$	391916.			0.877031
$183$	46931.8	−	47100.3i	0.103595	−	0.103967i
$184$	234560.			0.510752
$185$	−642136.	−	208643.i	−1.37942	−	0.448202i
$186$	−17663.9	+	54363.8i	−0.0374372	+	0.115220i
$187$	411756.	+	299158.i	0.861065	+	0.625601i
$188$	44208.0	+	32119.0i	0.0912235	+	0.0662777i
$189$	−76234.9	+	104928.i	−0.155238	+	0.213667i
$190$	−298133.	+	96869.2i	−0.599136	+	0.194671i
$191$	−145251.	−	199921.i	−0.288095	−	0.396529i	0.640299	−	0.768126i	$-0.278811\pi$
$191$	−145251.	−	199921.i	−0.288095	−	0.396529i	−0.928394	+	0.371596i	$0.878811\pi$
$192$	−42150.4	−	30624.1i	−0.0825180	−	0.0599528i
$193$	−65874.8	−	90668.8i	−0.127299	−	0.175212i	0.740610	−	0.671935i	$-0.234537\pi$
$193$	−65874.8	−	90668.8i	−0.127299	−	0.175212i	−0.867909	+	0.496723i	$0.834537\pi$
$194$		−	247617.i		−	0.472363i
$195$	−77735.1	+	56477.9i	−0.146396	+	0.106363i
$196$	54561.5			0.101449
$197$	−146907.			−0.269697			−0.134849	−	0.990866i	$-0.543055\pi$
$197$	−146907.			−0.269697			−0.134849	+	0.990866i	$0.543055\pi$
$198$	−260296.	+	189116.i	−0.471851	+	0.342820i
$199$	212628.	+	654400.i	0.380616	+	1.17142i	0.939611	+	0.342244i	$0.111187\pi$
$199$	212628.	+	654400.i	0.380616	+	1.17142i	−0.558995	+	0.829171i	$0.688813\pi$
$200$	−110274.	+	151780.i	−0.194939	+	0.268311i
$201$	−28433.7	−	39135.6i	−0.0496413	−	0.0683254i
$202$	178082.	−	548079.i	0.307073	−	0.945072i
$203$	−185292.	−	570270.i	−0.315585	−	0.971271i
$204$		−	58769.8i		−	0.0988732i
$205$	−45268.6	+	139323.i	−0.0752337	+	0.231546i
$206$	−336721.	+	463457.i	−0.552844	+	0.760924i
$207$	−287343.	+	93363.6i	−0.466096	+	0.151444i
$208$	−19633.9	−	60426.9i	−0.0314665	−	0.0968438i
$209$	−665203.	−	216138.i	−1.05339	−	0.342267i
$210$	−36422.4	+	26462.4i	−0.0569928	+	0.0414077i
$211$	356187.	+	115732.i	0.550773	+	0.178957i	0.571165	−	0.820835i	$-0.306492\pi$
$211$	356187.	+	115732.i	0.550773	+	0.178957i	−0.0203925	+	0.999792i	$0.506492\pi$
$212$			274945.i			0.420151i
$213$	75036.4	−	24380.8i	0.113324	−	0.0368213i
$214$	−202685.	+	65856.3i	−0.302543	+	0.0983021i
$215$		−	831298.i		−	1.22648i
$216$	193101.	+	62742.5i	0.281612	+	0.0915013i
$217$	655814.	−	476477.i	0.945434	−	0.686898i
$218$	−816560.	−	265316.i	−1.16372	−	0.378114i
$219$	10900.1	+	33547.0i	0.0153575	+	0.0472654i
$220$	305597.	−	99294.6i	0.425690	−	0.138315i
$221$	734799.	−	1.01136e6i	1.01202	−	1.39292i
$222$	37778.7	−	116271.i	0.0514475	−	0.158339i
$223$			990612.i			1.33396i	0.745077	+	0.666978i	$0.232413\pi$
$223$			990612.i			1.33396i	−0.745077	+	0.666978i	$0.767587\pi$
$224$	206032.	+	634101.i	0.274356	+	0.844381i
$225$	74675.5	−	229828.i	0.0983382	−	0.302654i
$226$	−326413.	−	449269.i	−0.425105	−	0.585107i
$227$	302126.	−	415841.i	0.389156	−	0.535628i	−0.568825	−	0.822459i	$-0.692602\pi$
$227$	302126.	−	415841.i	0.389156	−	0.535628i	0.957981	+	0.286831i	$0.0926018\pi$
$228$	24957.6	+	76811.5i	0.0317954	+	0.0978563i
$229$	−695671.	+	505435.i	−0.876628	+	0.636907i	−0.932357	−	0.361539i	$-0.882252\pi$
$229$	−695671.	+	505435.i	−0.876628	+	0.636907i	0.0557295	+	0.998446i	$0.482252\pi$
$230$	−212058.			−0.264323
$231$	−100451.			−0.123858
$232$	−759410.	+	551743.i	−0.926310	+	0.673003i
$233$		−	712794.i		−	0.860150i	−0.902793	−	0.430075i	$-0.858487\pi$
$233$		−	712794.i		−	0.860150i	0.902793	−	0.430075i	$-0.141513\pi$
$234$	464511.	+	639345.i	0.554570	+	0.763301i
$235$	−108023.	−	78483.0i	−0.127598	−	0.0927056i
$236$	−327238.	−	450405.i	−0.382459	−	0.526409i
$237$	−216216.	+	70252.8i	−0.250044	+	0.0812443i
$238$	344286.	−	473869.i	0.393983	−	0.542271i
$239$	585190.	+	425165.i	0.662677	+	0.481463i	0.867566	−	0.497322i	$-0.165683\pi$
$239$	585190.	+	425165.i	0.662677	+	0.481463i	−0.204889	+	0.978785i	$0.565683\pi$
$240$	5904.71	+	4290.03i	0.00661715	+	0.00480764i
$241$	56434.0	−	173686.i	0.0625891	−	0.192629i	−0.914872	−	0.403743i	$-0.867709\pi$
$241$	56434.0	−	173686.i	0.0625891	−	0.192629i	0.977462	+	0.211114i	$0.0677090\pi$
$242$	77438.6	+	25161.3i	0.0850000	+	0.0276182i
$243$	−393717.			−0.427729
$244$	248819.	+	486179.i	0.267552	+	0.522783i
$245$	−133321.			−0.141901
$246$	−25227.0	−	8196.73i	−0.0265783	−	0.00863581i
$247$	−530882.	+	1.63389e6i	−0.553675	+	1.70404i
$248$	−1.02666e6	−	745909.i	−1.05997	−	0.770117i
$249$	640.879	+	465.626i	0.000655055	+	0.000475925i
$250$	406229.	−	559126.i	0.411075	−	0.565796i
$251$	−1.08717e6	+	353243.i	−1.08921	+	0.353907i	−0.797942	−	0.602734i	$-0.794078\pi$
$251$	−1.08717e6	+	353243.i	−1.08921	+	0.353907i	−0.291271	+	0.956641i	$0.594078\pi$
$252$	−309685.	−	426245.i	−0.307198	−	0.422822i
$253$	−382787.	−	278111.i	−0.375973	−	0.273160i
$254$	−233937.	−	321986.i	−0.227517	−	0.313150i
$255$			143604.i			0.138298i
$256$	878210.	−	638057.i	0.837526	−	0.608498i
$257$	1.31089e6			1.23803			0.619017	−	0.785377i	$-0.287531\pi$
$257$	1.31089e6			1.23803			0.619017	+	0.785377i	$0.287531\pi$
$258$	150522.			0.140783
$259$	−1.40263e6	+	1.01907e6i	−1.29925	+	0.943959i
$260$	−243889.	−	750614.i	−0.223748	−	0.688626i
$261$	710685.	−	978175.i	0.645767	−	0.888823i
$262$	−322041.	−	443251.i	−0.289839	−	0.398930i
$263$	−354226.	+	1.09020e6i	−0.315785	+	0.971886i	0.659645	+	0.751577i	$0.270707\pi$
$263$	−354226.	+	1.09020e6i	−0.315785	+	0.971886i	−0.975430	+	0.220309i	$0.929293\pi$
$264$	48593.9	+	149557.i	0.0429114	+	0.132068i
$265$		−	671828.i		−	0.587684i
$266$	−248742.	+	765549.i	−0.215548	+	0.663390i
$267$	−175358.	+	241359.i	−0.150538	+	0.207198i
$268$	377896.	−	122786.i	0.321392	−	0.104427i
$269$	486517.	+	1.49734e6i	0.409937	+	1.26166i	0.916702	+	0.399572i	$0.130841\pi$
$269$	486517.	+	1.49734e6i	0.409937	+	1.26166i	−0.506765	+	0.862084i	$0.669159\pi$
$270$	−174577.	−	56723.3i	−0.145739	−	0.0473535i
$271$	1.46802e6	−	1.06658e6i	1.21425	−	0.882205i	0.218641	−	0.975805i	$-0.429838\pi$
$271$	1.46802e6	−	1.06658e6i	1.21425	−	0.882205i	0.995610	+	0.0936004i	$0.0298376\pi$
$272$	−90310.4	−	29343.6i	−0.0740143	−	0.0240487i
$273$			246730.i			0.200362i
$274$	−34565.7	+	11231.1i	−0.0278144	+	0.00903744i
$275$	359921.	−	116945.i	0.286996	−	0.0932506i
$276$			54635.1i			0.0431717i
$277$	613568.	+	199360.i	0.480467	+	0.156113i	0.539230	−	0.842159i	$-0.318716\pi$
$277$	613568.	+	199360.i	0.480467	+	0.156113i	−0.0587626	+	0.998272i	$0.518716\pi$
$278$	425636.	−	309242.i	0.330313	−	0.239987i
$279$	1.55458e6	+	505114.i	1.19565	+	0.388489i
$280$	−308857.	−	950563.i	−0.235430	−	0.724579i
$281$	−705349.	+	229182.i	−0.532891	+	0.173147i	−0.563088	−	0.826397i	$-0.690387\pi$
$281$	−705349.	+	229182.i	−0.532891	+	0.173147i	0.0301966	+	0.999544i	$0.490387\pi$
$282$	14210.8	−	19559.5i	0.0106413	−	0.0146465i
$283$	108194.	−	332985.i	0.0803036	−	0.247149i	−0.902842	−	0.429972i	$-0.858523\pi$
$283$	108194.	−	332985.i	0.0803036	−	0.247149i	0.983146	+	0.182823i	$0.0585235\pi$
$284$			648062.i			0.476783i
$285$	−60983.9	−	187689.i	−0.0444737	−	0.136876i
$286$	−382441.	+	1.17703e6i	−0.276471	+	0.850891i
$287$	221104.	+	304324.i	0.158450	+	0.218088i
$288$	−790233.	+	1.08766e6i	−0.561402	+	0.772704i
$289$	−138591.	−	426539.i	−0.0976090	−	0.300410i
$290$	686557.	−	498813.i	0.479382	−	0.348291i
$291$	155887.			0.107914
$292$	−289734.			−0.198857
$293$	1.24301e6	−	903100.i	0.845874	−	0.614563i	−0.0781314	−	0.996943i	$-0.524895\pi$
$293$	1.24301e6	−	903100.i	0.845874	−	0.614563i	0.924005	+	0.382380i	$0.124895\pi$
$294$		−	24140.3i		−	0.0162883i
$295$	799609.	+	1.10057e6i	0.534961	+	0.736311i
$296$	2.19576e6	+	1.59532e6i	1.45665	+	1.05832i
$297$	−240737.	−	331346.i	−0.158362	−	0.217967i
$298$	−585527.	+	190249.i	−0.381950	+	0.124103i
$299$	−683103.	+	940210.i	−0.441884	+	0.608201i
$300$	−35353.3	−	25685.7i	−0.0226792	−	0.0164774i
$301$	−1.72694e6	−	1.25470e6i	−1.09866	−	0.798220i
$302$	174231.	−	536227.i	0.109928	−	0.338323i
$303$	345043.	+	112111.i	0.215907	+	0.0701524i
$304$	130496.			0.0809866
$305$	−607990.	−	1.18798e6i	−0.374237	−	0.731240i
$306$	1.18110e6			0.721077
$307$	1.22471e6	+	397933.i	0.741630	+	0.240970i	0.655376	−	0.755303i	$-0.272510\pi$
$307$	1.22471e6	+	397933.i	0.741630	+	0.240970i	0.0862544	+	0.996273i	$0.472510\pi$
$308$	254970.	−	784717.i	0.153148	−	0.471342i
$309$	−291769.	−	211983.i	−0.173837	−	0.126300i
$310$	928165.	+	674351.i	0.548556	+	0.398549i
$311$	−1.32645e6	+	1.82571e6i	−0.777663	+	1.07036i	0.217873	+	0.975977i	$0.430088\pi$
$311$	−1.32645e6	+	1.82571e6i	−0.777663	+	1.07036i	−0.995536	+	0.0943841i	$0.969912\pi$
$312$	367344.	−	119357.i	0.213642	−	0.0694165i
$313$	1.27331e6	+	1.75256e6i	0.734637	+	1.01114i	0.998909	+	0.0466928i	$0.0148682\pi$
$313$	1.27331e6	+	1.75256e6i	0.734637	+	1.01114i	−0.264272	+	0.964448i	$0.585132\pi$
$314$	−1.08679e6	−	789598.i	−0.622044	−	0.451941i
$315$	756717.	+	1.04153e6i	0.429692	+	0.591420i
$316$		−	1.86738e6i		−	1.05200i
$317$	1.94459e6	−	1.41283e6i	1.08688	−	0.789662i	0.108007	−	0.994150i	$-0.465553\pi$
$317$	1.94459e6	−	1.41283e6i	1.08688	−	0.789662i	0.978869	+	0.204489i	$0.0655531\pi$
$318$	121647.			0.0674581
$319$	1.89349e6			1.04181
$320$	−845991.	+	614648.i	−0.461839	+	0.335546i
$321$	−41459.8	−	127600.i	−0.0224576	−	0.0691175i
$322$	−320064.	+	440531.i	−0.172027	+	0.236775i
$323$	1.50918e6	+	2.07721e6i	0.804888	+	1.10783i
$324$	320911.	−	987664.i	0.169833	−	0.522693i
$325$	−287244.	−	884045.i	−0.150849	−	0.464265i
$326$			258378.i			0.134651i
$327$	167030.	−	514064.i	0.0863822	−	0.265857i
$328$	346131.	−	476409.i	0.177646	−	0.244509i
$329$	−326082.	+	105950.i	−0.166087	+	0.0539650i
$330$	−43932.1	−	135209.i	−0.0222074	−	0.0683473i
$331$	−2.09594e6	−	681013.i	−1.05150	−	0.341653i	−0.268244	−	0.963351i	$-0.586443\pi$
$331$	−2.09594e6	−	681013.i	−1.05150	−	0.341653i	−0.783257	+	0.621698i	$0.786443\pi$
$332$	−5264.13	+	3824.62i	−0.00262109	+	0.00190433i
$333$	−3.32487e6	−	1.08032e6i	−1.64310	−	0.533876i
$334$		−	1.82145e6i		−	0.893411i
$335$	−923390.	+	300028.i	−0.449545	+	0.146066i
$336$	17824.2	−	5791.44i	0.00861316	−	0.00279859i
$337$			369570.i			0.177265i	0.996064	+	0.0886324i	$0.0282496\pi$
$337$			369570.i			0.177265i	−0.996064	+	0.0886324i	$0.971750\pi$
$338$	1.60775e6	+	522388.i	0.765465	+	0.248715i
$339$	282837.	−	205493.i	0.133671	−	0.0971176i
$340$	−1.12182e6	−	364503.i	−0.526293	−	0.171003i
$341$	791033.	+	2.43455e6i	0.368391	+	1.13379i
$342$	−1.54368e6	+	501572.i	−0.713661	+	0.231882i
$343$	−1.36608e6	+	1.88025e6i	−0.626963	+	0.862941i
$344$	−1.03263e6	+	3.17812e6i	−0.470490	+	1.44802i
$345$		−	133501.i		−	0.0603861i
$346$	−622799.	−	1.91678e6i	−0.279678	−	0.860760i
$347$	619692.	−	1.90721e6i	0.276282	−	0.850307i	−0.712596	−	0.701575i	$-0.752481\pi$
$347$	619692.	−	1.90721e6i	0.276282	−	0.850307i	0.988877	−	0.148733i	$-0.0475194\pi$
$348$	−128515.	−	176886.i	−0.0568861	−	0.0782969i
$349$	132492.	−	182360.i	0.0582273	−	0.0801431i	−0.778910	−	0.627135i	$-0.784227\pi$
$349$	132492.	−	182360.i	0.0582273	−	0.0801431i	0.837138	+	0.546992i	$0.184227\pi$
$350$	−134587.	−	414215.i	−0.0587262	−	0.180741i
$351$	−813859.	+	591303.i	−0.352599	+	0.256178i
$352$	−2.10543e6			−0.905701
$353$	−796730.			−0.340310			−0.170155	−	0.985417i	$-0.554427\pi$
$353$	−796730.			−0.340310			−0.170155	+	0.985417i	$0.554427\pi$
$354$	−199278.	+	144784.i	−0.0845185	+	0.0614063i
$355$		−	1.58354e6i		−	0.666897i
$356$	−1.44038e6	−	1.98251e6i	−0.602353	−	0.829067i
$357$	298324.	+	216745.i	0.123885	+	0.0900075i
$358$	−13594.1	−	18710.7i	−0.00560588	−	0.00771583i
$359$	926528.	−	301047.i	0.379422	−	0.123282i	−0.113096	−	0.993584i	$-0.536077\pi$
$359$	926528.	−	301047.i	0.379422	−	0.123282i	0.492518	+	0.870302i	$0.336077\pi$
$360$	1.18462e6	−	1.63048e6i	0.481749	−	0.663071i
$361$	−851400.	−	618578.i	−0.343847	−	0.249820i
$362$	1.02102e6	+	741812.i	0.409507	+	0.297524i
$363$	−15840.3	+	48751.4i	−0.00630952	+	0.0194187i
$364$	−1.92744e6	−	626262.i	−0.762477	−	0.247744i
$365$	707965.			0.278150
$366$	215106.	−	110088.i	0.0839364	−	0.0429573i
$367$	−3.42541e6			−1.32754			−0.663769	−	0.747938i	$-0.731044\pi$
$367$	−3.42541e6			−1.32754			−0.663769	+	0.747938i	$0.731044\pi$
$368$	83956.7	+	27279.2i	0.0323173	+	0.0105005i
$369$	−234393.	+	721388.i	−0.0896146	+	0.275805i
$370$	−1.98512e6	−	1.44227e6i	−0.753845	−	0.547700i
$371$	−1.39566e6	−	1.01401e6i	−0.526435	−	0.382477i
$372$	173741.	−	239134.i	0.0650946	−	0.0895951i
$373$	−304663.	+	98991.0i	−0.113383	+	0.0368403i	−0.365159	−	0.930945i	$-0.618985\pi$
$373$	−304663.	+	98991.0i	−0.113383	+	0.0368403i	0.251776	+	0.967786i	$0.418985\pi$
$374$	1.08720e6	+	1.49640e6i	0.401911	+	0.553183i
$375$	351997.	+	255741.i	0.129259	+	0.0939122i
$376$	315488.	+	434232.i	0.115084	+	0.158399i
$377$		−	4.65083e6i		−	1.68530i
$378$	−381329.	+	277052.i	−0.137268	+	0.0997314i
$379$	−374746.			−0.134011			−0.0670053	−	0.997753i	$-0.521344\pi$
$379$	−374746.			−0.134011			−0.0670053	+	0.997753i	$0.521344\pi$
$380$	1.62100e6			0.575870
$381$	202706.	−	147274.i	0.0715408	−	0.0519775i
$382$	−277518.	−	854113.i	−0.0973045	−	0.299472i
$383$	−2.79192e6	+	3.84275e6i	−0.972538	+	1.33858i	−0.0317838	+	0.999495i	$0.510119\pi$
$383$	−2.79192e6	+	3.84275e6i	−0.972538	+	1.33858i	−0.940754	+	0.339089i	$0.889881\pi$
$384$	132035.	+	181731.i	0.0456943	+	0.0628928i
$385$	−623020.	+	1.91746e6i	−0.214215	+	0.659286i
$386$	−125861.	−	387360.i	−0.0429954	−	0.132326i
$387$		−	4.30432e6i		−	1.46092i
$388$	−395679.	+	1.21777e6i	−0.133433	+	0.410665i
$389$	1.00481e6	−	1.38300e6i	0.336673	−	0.463391i	−0.606793	−	0.794860i	$-0.707544\pi$
$389$	1.00481e6	−	1.38300e6i	0.336673	−	0.463391i	0.943466	+	0.331469i	$0.107544\pi$
$390$	−332104.	+	107907.i	−0.110564	+	0.0359243i
$391$	536732.	+	1.65189e6i	0.177548	+	0.546436i
$392$	509698.	+	165611.i	0.167532	+	0.0544345i
$393$	279048.	−	202740.i	0.0911376	−	0.0662154i
$394$	−507757.	−	164980.i	−0.164784	−	0.0535416i
$395$			4.56295e6i			1.47147i
$396$	1.58233e6	−	514130.i	0.507060	−	0.164754i
$397$	155199.	−	50427.3i	0.0494212	−	0.0160579i	−0.284202	−	0.958764i	$-0.591729\pi$
$397$	155199.	−	50427.3i	0.0494212	−	0.0160579i	0.333623	+	0.942706i	$0.391729\pi$
$398$			2.50060e6i			0.791293i
$399$	−481950.	−	156595.i	−0.151555	−	0.0492432i
$400$	−57122.5	+	41502.0i	−0.0178508	+	0.0129694i
$401$	5.08474e6	+	1.65213e6i	1.57909	+	0.513079i	0.961823	−	0.273672i	$-0.0882382\pi$
$401$	5.08474e6	+	1.65213e6i	1.57909	+	0.513079i	0.617271	+	0.786751i	$0.288238\pi$
$402$	−54325.6	−	167197.i	−0.0167664	−	0.0516017i
$403$	5.97979e6	−	1.94295e6i	1.83410	−	0.595935i
$404$	−1.75161e6	+	2.41088e6i	−0.533928	+	0.734889i
$405$	−784148.	+	2.41336e6i	−0.237553	+	0.731113i
$406$		−	2.17912e6i		−	0.656095i
$407$	−1.69183e6	−	5.20691e6i	−0.506255	−	1.55809i
$408$	178384.	−	549011.i	0.0530526	−	0.163279i
$409$	176877.	+	243451.i	0.0522834	+	0.0719620i	0.834358	−	0.551223i	$-0.185839\pi$
$409$	176877.	+	243451.i	0.0522834	+	0.0719620i	−0.782075	+	0.623185i	$0.785839\pi$
$410$	−312926.	+	430705.i	−0.0919352	+	0.126538i
$411$	−7070.52	−	21760.8i	−0.00206465	−	0.00635434i
$412$	2.39657e6	−	1.74121e6i	0.695580	−	0.505368i
$413$	3.49319e6			1.00774
$414$	−1.09800e6			−0.314849
$415$	12862.9	−	9345.47i	0.00366623	−	0.00266367i
$416$			5.17141e6i			1.46513i
$417$	194683.	+	267958.i	0.0548262	+	0.0754618i
$418$	−2.05643e6	−	1.49408e6i	−0.575669	−	0.418248i
$419$	666413.	+	917239.i	0.185442	+	0.255239i	0.891609	−	0.452806i	$-0.149577\pi$
$419$	666413.	+	917239.i	0.185442	+	0.255239i	−0.706167	+	0.708046i	$0.749577\pi$
$420$	221410.	−	71940.5i	0.0612455	−	0.0198999i
$421$	1.47563e6	−	2.03103e6i	0.405762	−	0.558484i	−0.556416	−	0.830904i	$-0.687824\pi$
$421$	1.47563e6	−	2.03103e6i	0.405762	−	0.558484i	0.962178	+	0.272420i	$0.0878240\pi$
$422$	1.10113e6	+	800016.i	0.300993	+	0.218684i
$423$	−559322.	−	406371.i	−0.151989	−	0.110426i
$424$	−834542.	+	2.56846e6i	−0.225441	+	0.693837i
$425$	−1.32124e6	−	429297.i	−0.354821	−	0.115288i
$426$	286730.			0.0765507
$427$	−3.38557e6	−	530004.i	−0.898591	−	0.140673i
$428$	1.10204e6			0.290794
$429$	−741000.	−	240766.i	−0.194391	−	0.0631613i
$430$	933570.	−	2.87323e6i	0.243487	−	0.749376i
$431$	−967396.	−	702854.i	−0.250848	−	0.182252i	0.455254	−	0.890361i	$-0.349548\pi$
$431$	−967396.	−	702854.i	−0.250848	−	0.182252i	−0.706103	+	0.708109i	$0.749548\pi$
$432$	61820.3	+	44915.1i	0.0159375	+	0.0115793i
$433$	−1.61058e6	+	2.21677e6i	−0.412820	+	0.568199i	−0.963904	−	0.266252i	$-0.914215\pi$
$433$	−1.61058e6	+	2.21677e6i	−0.412820	+	0.568199i	0.551083	+	0.834450i	$0.314215\pi$
$434$	2.80180e6	−	910359.i	0.714024	−	0.232000i
$435$	314027.	+	432221.i	0.0795690	+	0.109517i
$436$	3.59186e6	+	2.60964e6i	0.904907	+	0.657453i
$437$	−1.40300e6	−	1.93107e6i	−0.351443	−	0.483720i
$438$			128190.i			0.0319279i
$439$	75397.2	−	54779.3i	0.0186721	−	0.0135661i	−0.578410	−	0.815746i	$-0.696327\pi$
$439$	75397.2	−	54779.3i	0.0186721	−	0.0135661i	0.597082	+	0.802180i	$0.296327\pi$
$440$	3.15619e6			0.777199
$441$	−690315.			−0.169025
$442$	3.67549e6	−	2.67040e6i	0.894869	−	0.650160i
$443$	−424359.	−	1.30604e6i	−0.102736	−	0.316190i	0.886456	−	0.462812i	$-0.153160\pi$
$443$	−424359.	−	1.30604e6i	−0.102736	−	0.316190i	−0.989192	+	0.146623i	$0.953160\pi$
$444$	−371590.	+	511449.i	−0.0894553	+	0.123125i
$445$	3.51956e6	+	4.84426e6i	0.842537	+	1.15965i
$446$	−1.11248e6	+	3.42387e6i	−0.264824	+	0.815043i
$447$	−119771.	−	368618.i	−0.0283520	−	0.0872585i
$448$			2.68517e6i			0.632086i
$449$	−1.08924e6	+	3.35233e6i	−0.254980	+	0.784749i	0.738853	+	0.673866i	$0.235368\pi$
$449$	−1.08924e6	+	3.35233e6i	−0.254980	+	0.784749i	−0.993834	+	0.110882i	$0.964632\pi$
$450$	516205.	−	710496.i	0.120169	−	0.165398i
$451$	−1.12973e6	+	367071.i	−0.261537	+	0.0849784i
$452$	887385.	+	2.73109e6i	0.204299	+	0.628767i
$453$	337581.	+	109687.i	0.0772916	+	0.0251136i
$454$	1.51125e6	−	1.09799e6i	0.344109	−	0.250010i
$455$	4.70970e6	+	1.53027e6i	1.06651	+	0.346530i
$456$			793305.i			0.178660i
$457$	3.40037e6	−	1.10485e6i	0.761615	−	0.247464i	0.0976436	−	0.995221i	$-0.468869\pi$
$457$	3.40037e6	−	1.10485e6i	0.761615	−	0.247464i	0.663972	+	0.747758i	$0.268869\pi$
$458$	−2.97208e6	+	965687.i	−0.662059	+	0.215116i
$459$			1.50349e6i			0.333094i
$460$	1.04290e6	+	338858.i	0.229799	+	0.0746661i
$461$	2.06094e6	−	1.49736e6i	0.451661	−	0.328151i	−0.338590	−	0.940934i	$-0.609950\pi$
$461$	2.06094e6	−	1.49736e6i	0.451661	−	0.328151i	0.790251	+	0.612783i	$0.209950\pi$
$462$	−347192.	−	112809.i	−0.0756771	−	0.0245890i
$463$	−1.60252e6	−	4.93204e6i	−0.347416	−	1.06924i	−0.960278	−	0.279047i	$-0.909982\pi$
$463$	−1.60252e6	−	4.93204e6i	−0.347416	−	1.06924i	0.612861	−	0.790190i	$-0.290018\pi$
$464$	−335984.	+	109168.i	−0.0724476	+	0.0235397i
$465$	−424537.	+	584325.i	−0.0910507	+	0.125320i
$466$	800487.	−	2.46364e6i	0.170761	−	0.525549i
$467$		−	299389.i		−	0.0635249i	−0.999495	−	0.0317625i	$-0.989888\pi$
$467$		−	299389.i		−	0.0635249i	0.999495	−	0.0317625i	$-0.0101120\pi$
$468$	−1.26282e6	−	3.88655e6i	−0.266518	−	0.820257i
$469$	−770415.	+	2.37109e6i	−0.161731	+	0.497756i
$470$	−285222.	−	392574.i	−0.0595578	−	0.0819742i
$471$	497091.	−	684186.i	0.103248	−	0.142109i
$472$	−1.68985e6	−	5.20083e6i	−0.349135	−	1.07453i
$473$	5.45339e6	−	3.96212e6i	1.12076	−	0.814283i
$474$	−826207.			−0.168905
$475$	1.90916e6			0.388246
$476$	−2.45041e6	+	1.78033e6i	−0.495703	+	0.360149i
$477$		−	3.47861e6i		−	0.700019i
$478$	1.54513e6	+	2.12669e6i	0.309311	+	0.425730i
$479$	1.22503e6	+	890039.i	0.243955	+	0.177243i	0.703043	−	0.711147i	$-0.251824\pi$
$479$	1.22503e6	+	890039.i	0.243955	+	0.177243i	−0.459089	+	0.888390i	$0.651824\pi$
$480$	−349176.	−	480600.i	−0.0691738	−	0.0952096i
$481$	−1.27893e7	+	4.15550e6i	−2.52049	+	0.818955i
$482$	390108.	−	536938.i	0.0764834	−	0.105270i
$483$	−277336.	−	201496.i	−0.0540926	−	0.0393006i
$484$	−340635.	−	247486.i	−0.0660961	−	0.0480216i
$485$	966843.	−	2.97564e6i	0.186639	−	0.574415i
$486$	−1.36081e6	−	442154.i	−0.261341	−	0.0849148i
$487$	4.69634e6			0.897300			0.448650	−	0.893708i	$-0.351905\pi$
$487$	4.69634e6			0.897300			0.448650	+	0.893708i	$0.351905\pi$
$488$	848693.	+	5.29699e6i	0.161325	+	1.00688i
$489$	−162661.			−0.0307619
$490$	−460801.	−	149723.i	−0.0867009	−	0.0281708i
$491$	−939442.	+	2.89131e6i	−0.175860	+	0.541240i	−0.999672	−	0.0256227i	$-0.991843\pi$
$491$	−939442.	+	2.89131e6i	−0.175860	+	0.541240i	0.823812	+	0.566863i	$0.191843\pi$
$492$	110968.	+	80622.8i	0.0206673	+	0.0150157i
$493$	−5.62336e6	−	4.08561e6i	−1.04203	−	0.757077i
$494$	−3.66979e6	+	5.05104e6i	−0.676588	+	0.931243i
$495$	−3.86643e6	+	1.25628e6i	−0.709247	+	0.230448i
$496$	−280724.	−	386384.i	−0.0512360	−	0.0705204i
$497$	−3.28966e6	−	2.39008e6i	−0.597392	−	0.434031i
$498$	1692.17	+	2329.08i	0.000305753	+	0.000420833i
$499$			1.00052e7i			1.79876i	0.437166	+	0.899381i	$0.355982\pi$
$499$			1.00052e7i			1.79876i	−0.437166	+	0.899381i	$0.644018\pi$
$500$	−2.89128e6	+	2.10064e6i	−0.517208	+	0.375773i
$501$	1.14669e6			0.204105
$502$	−4.15431e6			−0.735765
$503$	1.73773e6	−	1.26254e6i	0.306240	−	0.222497i	−0.424041	−	0.905643i	$-0.639389\pi$
$503$	1.73773e6	−	1.26254e6i	0.306240	−	0.222497i	0.730282	+	0.683146i	$0.239389\pi$
$504$	−1.59921e6	−	4.92185e6i	−0.280432	−	0.863082i
$505$	4.28006e6	−	5.89099e6i	0.746829	−	1.02792i
$506$	−1.01071e6	−	1.39112e6i	−0.175489	−	0.241540i
$507$	−328869.	+	1.01215e6i	−0.0568202	+	0.174875i
$508$	635978.	+	1.95734e6i	0.109341	+	0.336517i
$509$		−	3.05402e6i		−	0.522489i	−0.965273	−	0.261245i	$-0.915867\pi$
$509$		−	3.05402e6i		−	0.522489i	0.965273	−	0.261245i	$-0.0841329\pi$
$510$	−161271.	+	496342.i	−0.0274557	+	0.0844998i
$511$	1.06855e6	−	1.47073e6i	0.181026	−	0.249161i
$512$	763864.	−	248194.i	0.128778	−	0.0418424i
$513$	−638480.	−	1.96504e6i	−0.107116	−	0.329669i
$514$	4.53085e6	+	1.47216e6i	0.756435	+	0.245781i
$515$	−5.85603e6	+	4.25465e6i	−0.972938	+	0.706881i
$516$	−740265.	−	240527.i	−0.122395	−	0.0397685i
$517$		−	1.08270e6i		−	0.178149i
$518$	−5.99236e6	+	1.94704e6i	−0.981236	+	0.318823i
$519$	1.20671e6	−	392083.i	0.196645	−	0.0638939i
$520$		−	7.75231e6i		−	1.25725i
$521$	−3.94875e6	−	1.28303e6i	−0.637331	−	0.207082i	−0.0275114	−	0.999621i	$-0.508758\pi$
$521$	−3.94875e6	−	1.28303e6i	−0.637331	−	0.207082i	−0.609820	+	0.792540i	$0.708758\pi$
$522$	3.55487e6	−	2.58277e6i	0.571015	−	0.414867i
$523$	−5.10274e6	−	1.65798e6i	−0.815735	−	0.265049i	−0.128710	−	0.991682i	$-0.541084\pi$
$523$	−5.10274e6	−	1.65798e6i	−0.815735	−	0.265049i	−0.687025	+	0.726634i	$0.741084\pi$
$524$	875497.	+	2.69450e6i	0.139292	+	0.428697i
$525$	260769.	−	84728.8i	0.0412911	−	0.0134163i
$526$	−2.44864e6	+	3.37026e6i	−0.385887	+	0.531128i
$527$	2.90382e6	−	8.93703e6i	0.455452	−	1.40174i
$528$			59182.6i			0.00923866i
$529$	1.48997e6	+	4.58565e6i	0.231493	+	0.712463i
$530$	754481.	−	2.32205e6i	0.116670	−	0.359073i
$531$	4.14023e6	+	5.69854e6i	0.637219	+	0.877057i
$532$	2.44662e6	−	3.36748e6i	0.374789	−	0.515853i
$533$	901606.	+	2.77486e6i	0.137467	+	0.423080i
$534$	−877145.	+	637283.i	−0.133112	+	0.0967118i
$535$	−2.69283e6			−0.406747
$536$	3.90289e6			0.586779
$537$	11779.3	−	8558.16i	0.00176272	−	0.00128069i
$538$			5.72167e6i			0.852251i
$539$	−635434.	−	874600.i	−0.0942104	−	0.129669i
$540$	767923.	+	557929.i	0.113327	+	0.0823369i
$541$	−2.71388e6	−	3.73533e6i	−0.398655	−	0.548701i	0.561751	−	0.827306i	$-0.310128\pi$
$541$	−2.71388e6	−	3.73533e6i	−0.398655	−	0.548701i	−0.960406	+	0.278605i	$0.910128\pi$
$542$	6.27174e6	−	2.03781e6i	0.917043	−	0.297965i
$543$	−467007.	+	642780.i	−0.0679710	+	0.0935540i
$544$	6.25279e6	+	4.54292e6i	0.905893	+	0.658170i
$545$	−8.77674e6	−	6.37667e6i	−1.26573	−	0.919608i
$546$	−277085.	+	852780.i	−0.0397769	+	0.122421i
$547$	−687636.	−	223427.i	−0.0982631	−	0.0319276i	0.259473	−	0.965750i	$-0.416451\pi$
$547$	−687636.	−	223427.i	−0.0982631	−	0.0319276i	−0.357736	+	0.933823i	$0.616451\pi$
$548$	187940.			0.0267343
$549$	−3.14807e6	−	6.15116e6i	−0.445773	−	0.871016i
$550$	1.37534e6			0.193866
$551$	9.08470e6	+	2.95180e6i	1.27477	+	0.414197i
$552$	−165834.	+	510385.i	−0.0231647	+	0.0712936i
$553$	9.47908e6	+	6.88695e6i	1.31812	+	0.957667i
$554$	1.89680e6	+	1.37811e6i	0.262571	+	0.190769i
$555$	907981.	−	1.24973e6i	0.125125	−	0.172220i
$556$	−2.58742e6	+	840704.i	−0.354961	+	0.115334i
$557$	−8.12574e6	−	1.11841e7i	−1.10975	−	1.52744i	−0.821785	−	0.569797i	$-0.807022\pi$
$557$	−8.12574e6	−	1.11841e7i	−1.10975	−	1.52744i	−0.287964	−	0.957641i	$-0.592978\pi$
$558$	4.80588e6	+	3.49167e6i	0.653412	+	0.474732i
$559$	−9.73185e6	−	1.33947e7i	−1.31724	−	1.81303i
$560$		−	376157.i		−	0.0506872i
$561$	−942057.	+	684445.i	−0.126378	+	0.0918187i
$562$	−2.69529e6			−0.359969
$563$	−8.60478e6			−1.14411			−0.572056	−	0.820214i	$-0.693854\pi$
$563$	−8.60478e6			−1.14411			−0.572056	+	0.820214i	$0.693854\pi$
$564$	−101144.	+	73485.1i	−0.0133888	+	0.00972751i
$565$	−2.16833e6	−	6.67343e6i	−0.285762	−	0.879484i
$566$	747903.	−	1.02940e6i	0.0981305	−	0.135065i
$567$	3.82999e6	+	5.27153e6i	0.500311	+	0.688619i
$568$	−1.96707e6	+	6.05401e6i	−0.255828	+	0.787359i
$569$	−174967.	−	538494.i	−0.0226556	−	0.0697269i	0.939089	−	0.343673i	$-0.111671\pi$
$569$	−174967.	−	538494.i	−0.0226556	−	0.0697269i	−0.961745	+	0.273946i	$0.911671\pi$
$570$		−	717200.i		−	0.0924599i
$571$	−875636.	+	2.69493e6i	−0.112391	+	0.345905i	−0.991394	−	0.130912i	$-0.958210\pi$
$571$	−875636.	+	2.69493e6i	−0.112391	+	0.345905i	0.879003	+	0.476817i	$0.158210\pi$
$572$	3.76168e6	−	5.17751e6i	0.480719	−	0.661654i
$573$	537706.	−	174711.i	0.0684161	−	0.0222297i
$574$	422443.	+	1.30015e6i	0.0535166	+	0.164707i
$575$	1.22829e6	+	399094.i	0.154928	+	0.0503392i
$576$	−4.38039e6	+	3.18254e6i	−0.550120	+	0.399685i
$577$	6.10619e6	+	1.98402e6i	0.763538	+	0.248088i	0.664796	−	0.747025i	$-0.268518\pi$
$577$	6.10619e6	+	1.98402e6i	0.763538	+	0.248088i	0.0987414	+	0.995113i	$0.468518\pi$
$578$		−	1.62990e6i		−	0.202927i
$579$	243862.	−	79235.5i	0.0302306	−	0.00982253i
$580$	−4.17355e6	+	1.35607e6i	−0.515152	+	0.167383i
$581$		−	40826.8i		−	0.00501771i
$582$	538795.	+	175065.i	0.0659350	+	0.0214236i
$583$	4.40726e6	−	3.20206e6i	0.537028	−	0.390174i
$584$	−2.70661e6	−	879430.i	−0.328393	−	0.106701i
$585$	3.08570e6	+	9.49681e6i	0.372790	+	1.14733i
$586$	5.31045e6	−	1.72547e6i	0.638833	−	0.207569i
$587$	−9.26430e6	+	1.27512e7i	−1.10973	+	1.52741i	−0.287916	+	0.957656i	$0.592962\pi$
$587$	−9.26430e6	+	1.27512e7i	−1.10973	+	1.52741i	−0.821814	+	0.569756i	$0.807038\pi$
$588$	−38575.0	+	118722.i	−0.00460111	+	0.0141608i
$589$			1.29138e7i			1.53378i
$590$	1.52774e6	+	4.70189e6i	0.180684	+	0.556087i
$591$	103863.	−	319658.i	0.0122319	−	0.0376458i
$592$	600400.	+	826380.i	0.0704104	+	0.0969116i
$593$	2.63414e6	−	3.62558e6i	0.307611	−	0.423391i	−0.627023	−	0.779001i	$-0.715727\pi$
$593$	2.63414e6	−	3.62558e6i	0.307611	−	0.423391i	0.934634	+	0.355610i	$0.115727\pi$
$594$	−459954.	−	1.41559e6i	−0.0534870	−	0.164616i
$595$	5.98759e6	−	4.35024e6i	0.693362	−	0.503757i
$596$	3.18362e6			0.367118
$597$	−1.57425e6			−0.180775
$598$	−3.41690e6	+	2.48252e6i	−0.390733	+	0.283884i
$599$		−	1.10746e7i		−	1.26114i	−0.776133	−	0.630569i	$-0.782822\pi$
$599$		−	1.10746e7i		−	1.26114i	0.776133	−	0.630569i	$-0.217178\pi$
$600$	−252297.	−	347257.i	−0.0286110	−	0.0393797i
$601$	2.43418e6	+	1.76854e6i	0.274895	+	0.199723i	0.716688	−	0.697394i	$-0.245657\pi$
$601$	2.43418e6	+	1.76854e6i	0.274895	+	0.199723i	−0.441793	+	0.897117i	$0.645657\pi$
$602$	−4.55981e6	−	6.27603e6i	−0.512808	−	0.705820i
$603$	−4.78116e6	+	1.55349e6i	−0.535475	+	0.173987i
$604$	−1.71373e6	+	2.35874e6i	−0.191139	+	0.263080i
$605$	832343.	+	604732.i	0.0924515	+	0.0671699i
$606$	1.06667e6	+	774984.i	0.117991	+	0.0857258i
$607$	1.16118e6	−	3.57373e6i	0.127916	−	0.393686i	−0.866505	−	0.499169i	$-0.833639\pi$
$607$	1.16118e6	−	3.57373e6i	0.127916	−	0.393686i	0.994421	+	0.105483i	$0.0336387\pi$
$608$	−1.01016e7	−	3.28219e6i	−1.10823	−	0.360085i
$609$	1.37187e6			0.149889
$610$	−767275.	−	4.78883e6i	−0.0834885	−	0.521081i
$611$	−2.65936e6			−0.288186
$612$	−5.80861e6	−	1.88733e6i	−0.626893	−	0.203690i
$613$	−4.64008e6	+	1.42807e7i	−0.498740	+	1.53497i	0.312305	+	0.949982i	$0.398899\pi$
$613$	−4.64008e6	+	1.42807e7i	−0.498740	+	1.53497i	−0.811045	+	0.584983i	$0.801101\pi$
$614$	3.78610e6	+	2.75076e6i	0.405295	+	0.294464i
$615$	−271150.	−	197002.i	−0.0289083	−	0.0210031i
$616$	4.76371e6	−	6.55669e6i	0.505818	−	0.696198i
$617$	−505346.	+	164197.i	−0.0534411	+	0.0173641i	−0.335616	−	0.941999i	$-0.608944\pi$
$617$	−505346.	+	164197.i	−0.0534411	+	0.0173641i	0.282174	+	0.959363i	$0.408944\pi$
$618$	−770385.	−	1.06034e6i	−0.0811403	−	0.111680i
$619$	1.42667e7	+	1.03653e7i	1.49657	+	1.08732i	0.971724	+	0.236119i	$0.0758755\pi$
$619$	1.42667e7	+	1.03653e7i	1.49657	+	1.08732i	0.524842	+	0.851200i	$0.324125\pi$
$620$	−3.48712e6	−	4.79961e6i	−0.364324	−	0.501448i
$621$		−	1.39771e6i		−	0.145441i
$622$	−6.63497e6	+	4.82059e6i	−0.687643	+	0.499602i
$623$	1.53756e7			1.58713
$624$	145365.			0.0149451
$625$	4.49532e6	−	3.26604e6i	0.460320	−	0.334442i
$626$	2.43279e6	+	7.48736e6i	0.248124	+	0.763648i
$627$	940598.	−	1.29462e6i	0.0955510	−	0.131515i
$628$	4.08307e6	+	5.61986e6i	0.413131	+	0.568626i
$629$	−6.21056e6	+	1.91141e7i	−0.625899	+	1.92632i
$630$	1.44579e6	+	4.44968e6i	0.145129	+	0.446660i
$631$		−	1.19612e7i		−	1.19592i	−0.801526	−	0.597960i	$-0.795978\pi$
$631$		−	1.19612e7i		−	1.19592i	0.801526	−	0.597960i	$-0.204022\pi$
$632$	5.66807e6	−	1.74445e7i	0.564472	−	1.73727i
$633$	−503649.	+	693213.i	−0.0499596	+	0.0687635i
$634$	8.30777e6	−	2.69936e6i	0.820845	−	0.266709i
$635$	−1.55402e6	−	4.78277e6i	−0.152940	−	0.470701i
$636$	−598258.	−	194386.i	−0.0586470	−	0.0190556i
$637$	−2.14821e6	+	1.56077e6i	−0.209763	+	0.152402i
$638$	6.54452e6	+	2.12644e6i	0.636540	+	0.206825i
$639$		−	8.19931e6i		−	0.794374i
$640$	4.28787e6	−	1.39321e6i	0.413801	−	0.134452i
$641$	1.72260e7	−	5.59708e6i	1.65592	−	0.538042i	0.675911	−	0.736983i	$-0.263750\pi$
$641$	1.72260e7	−	5.59708e6i	1.65592	−	0.538042i	0.980011	+	0.198941i	$0.0637502\pi$
$642$		−	487587.i		−	0.0466890i
$643$	−3.20071e6	−	1.03997e6i	−0.305294	−	0.0991961i	0.152364	−	0.988325i	$-0.451312\pi$
$643$	−3.20071e6	−	1.03997e6i	−0.305294	−	0.0991961i	−0.457658	+	0.889128i	$0.651312\pi$
$644$	2.27801e6	−	1.65507e6i	0.216442	−	0.157254i
$645$	1.80884e6	+	587728.i	0.171199	+	0.0556259i
$646$	2.88345e6	+	8.87436e6i	0.271851	+	0.836673i
$647$	3.74561e6	−	1.21702e6i	0.351772	−	0.114298i	−0.127800	−	0.991800i	$-0.540792\pi$
$647$	3.74561e6	−	1.21702e6i	0.351772	−	0.114298i	0.479573	+	0.877502i	$0.340792\pi$
$648$	5.99573e6	−	8.25241e6i	0.560924	−	0.772046i
$649$	−3.40874e6	+	1.04910e7i	−0.317674	+	0.977700i
$650$		−	3.37813e6i		−	0.313612i
$651$	573116.	+	1.76387e6i	0.0530017	+	0.163123i
$652$	412875.	−	1.27070e6i	0.0380364	−	0.117064i
$653$	1.21649e7	+	1.67436e7i	1.11642	+	1.53662i	0.811604	+	0.584207i	$0.198594\pi$
$653$	1.21649e7	+	1.67436e7i	1.11642	+	1.53662i	0.304815	+	0.952412i	$0.401406\pi$
$654$	1.15462e6	−	1.58919e6i	0.105559	−	0.145289i
$655$	−2.13928e6	−	6.58403e6i	−0.194834	−	0.599637i
$656$	179297.	−	130267.i	0.0162673	−	0.0118189i
$657$	3.66572e6			0.331319
$658$	−1.24603e6			−0.112192
$659$	−1.71425e7	+	1.24547e7i	−1.53766	+	1.11717i	−0.585875	+	0.810401i	$0.699249\pi$
$659$	−1.71425e7	+	1.24547e7i	−1.53766	+	1.11717i	−0.951783	+	0.306773i	$0.900751\pi$
$660$			735158.i			0.0656932i
$661$	5.84949e6	+	8.05114e6i	0.520732	+	0.716727i	0.985683	−	0.168610i	$-0.0539278\pi$
$661$	5.84949e6	+	8.05114e6i	0.520732	+	0.716727i	−0.464950	+	0.885337i	$0.653928\pi$
$662$	−6.47946e6	−	4.70760e6i	−0.574637	−	0.417498i
$663$	1.68115e6	+	2.31390e6i	0.148533	+	0.204438i
$664$	−60784.9	+	19750.2i	−0.00535027	+	0.00173841i
$665$	−5.97831e6	+	8.22844e6i	−0.524233	+	0.721545i
$666$	−1.02786e7	−	7.46784e6i	−0.897942	−	0.652393i
$667$	5.22774e6	+	3.79817e6i	0.454987	+	0.330567i
$668$	−2.91059e6	+	8.95786e6i	−0.252371	+	0.776718i
$669$	−2.15550e6	−	700363.i	−0.186201	−	0.0605004i
$670$	−3.52847e6			−0.303668
$671$	4.89547e6	−	9.65061e6i	0.419748	−	0.827463i
$672$	−1.52542e6			−0.130307
$673$	−8.38023e6	−	2.72290e6i	−0.713211	−	0.231736i	−0.0701340	−	0.997538i	$-0.522343\pi$
$673$	−8.38023e6	−	2.72290e6i	−0.713211	−	0.231736i	−0.643077	+	0.765801i	$0.722343\pi$
$674$	−415037.	+	1.27735e6i	−0.0351915	+	0.108308i
$675$	904431.	+	657107.i	0.0764040	+	0.0555107i
$676$	−7.07211e6	−	5.13819e6i	−0.595227	−	0.432458i
$677$	−4.28267e6	+	5.89459e6i	−0.359123	+	0.494290i	−0.949904	−	0.312542i	$-0.898820\pi$
$677$	−4.28267e6	+	5.89459e6i	−0.359123	+	0.494290i	0.590781	+	0.806832i	$0.298820\pi$
$678$	1.20835e6	−	392617.i	0.100953	−	0.0328015i
$679$	−4.72232e6	−	6.49971e6i	−0.393080	−	0.541028i
$680$	−9.37338e6	−	6.81016e6i	−0.777363	−	0.564787i
$681$	691235.	+	951404.i	0.0571161	+	0.0786135i
$682$			9.30293e6i			0.765877i
$683$	1.72002e7	−	1.24967e7i	1.41085	−	1.02505i	0.417656	−	0.908605i	$-0.362852\pi$
$683$	1.72002e7	−	1.24967e7i	1.41085	−	1.02505i	0.993198	−	0.116440i	$-0.0371484\pi$
$684$	8.39327e6			0.685948
$685$	−459233.			−0.0373944
$686$	−6.83320e6	+	4.96461e6i	−0.554388	+	0.402786i
$687$	−607947.	−	1.87107e6i	−0.0491444	−	0.151251i
$688$	−739225.	+	1.01746e6i	−0.0595396	+	0.0819492i
$689$	−7.86496e6	−	1.08252e7i	−0.631173	−	0.868736i
$690$	149925.	−	461422.i	0.0119881	−	0.0368957i
$691$	−2.19106e6	−	6.74340e6i	−0.174566	−	0.537259i	0.825047	−	0.565064i	$-0.191148\pi$
$691$	−2.19106e6	−	6.74340e6i	−0.174566	−	0.537259i	−0.999613	+	0.0278045i	$0.991148\pi$
$692$			1.04219e7i			0.827335i
$693$	−3.22589e6	+	9.92827e6i	−0.255162	+	0.785309i
$694$	4.28371e6	−	5.89602e6i	0.337614	−	0.464686i
$695$	6.32238e6	−	2.05426e6i	0.496499	−	0.161322i
$696$	−663648.	−	2.04250e6i	−0.0519296	−	0.159823i
$697$	4.14714e6	+	1.34749e6i	0.323345	+	0.105061i
$698$	662731.	−	481502.i	0.0514871	−	0.0374076i
$699$	1.55098e6	+	503945.i	0.120064	+	0.0390113i
$700$			2.25216e6i			0.173722i
$701$	1.80489e7	−	5.86443e6i	1.38725	−	0.450745i	0.482204	−	0.876059i	$-0.339837\pi$
$701$	1.80489e7	−	5.86443e6i	1.38725	−	0.450745i	0.905046	+	0.425315i	$0.139837\pi$
$702$	−3.47701e6	+	1.12975e6i	−0.266295	+	0.0865244i
$703$		−	2.76194e7i		−	2.10778i
$704$	−8.06430e6	−	2.62025e6i	−0.613247	−	0.199256i
$705$	247145.	−	179561.i	0.0187275	−	0.0136063i
$706$	−2.75375e6	−	894749.i	−0.207928	−	0.0675599i
$707$	−5.77798e6	−	1.77828e7i	−0.434738	−	1.33799i
$708$	1.21140e6	−	393609.i	0.0908251	−	0.0295109i
$709$	−1.07002e7	+	1.47275e7i	−0.799419	+	1.10031i	0.193452	+	0.981110i	$0.438032\pi$
$709$	−1.07002e7	+	1.47275e7i	−0.799419	+	1.10031i	−0.992871	+	0.119196i	$0.961968\pi$
$710$	1.77836e6	−	5.47323e6i	0.132396	−	0.407472i
$711$			2.36261e7i			1.75275i
$712$	−7.43806e6	−	2.28920e7i	−0.549870	−	1.69233i
$713$	−2.69952e6	+	8.30827e6i	−0.198867	+	0.612050i
$714$	787693.	+	1.08417e6i	0.0578244	+	0.0795885i
$715$	−9.19168e6	+	1.26513e7i	−0.672403	+	0.925484i
$716$	36956.9	+	113742.i	0.00269409	+	0.00829157i
$717$	−1.33886e6	+	972736.i	−0.0972604	+	0.0706638i
$718$	3.54046e6			0.256300
$719$	−2.67348e6			−0.192866			−0.0964328	−	0.995340i	$-0.530743\pi$
$719$	−2.67348e6			−0.192866			−0.0964328	+	0.995340i	$0.530743\pi$
$720$	613636.	−	445832.i	0.0441143	−	0.0320509i
$721$			1.85870e7i			1.33159i
$722$	−2.24803e6	−	3.09415e6i	−0.160494	−	0.220901i
$723$	338029.	+	245592.i	0.0240496	+	0.0174731i
$724$	−3.83596e6	−	5.27975e6i	−0.271974	−	0.374340i
$725$	−4.91545e6	+	1.59713e6i	−0.347311	+	0.112848i
$726$	−109498.	+	150711.i	−0.00771019	+	0.0106122i
$727$	1.10630e7	+	8.03777e6i	0.776316	+	0.564027i	0.903871	−	0.427805i	$-0.140713\pi$
$727$	1.10630e7	+	8.03777e6i	0.776316	+	0.564027i	−0.127555	+	0.991831i	$0.540713\pi$
$728$	−1.61047e7	−	1.17007e7i	−1.12622	−	0.818247i
$729$	−3.87121e6	+	1.19144e7i	−0.269791	+	0.830333i
$730$	2.44695e6	+	795064.i	0.169949	+	0.0552198i
$731$	−2.47448e7			−1.71274
$732$	−1.23380e6	+	197682.i	−0.0851076	+	0.0136361i
$733$	2.30392e7			1.58382			0.791912	−	0.610635i	$-0.209086\pi$
$733$	2.30392e7			1.58382			0.791912	+	0.610635i	$0.209086\pi$
$734$	−1.18393e7	−	3.84682e6i	−0.811121	−	0.263549i
$735$	94258.2	−	290097.i	0.00643577	−	0.0198073i
$736$	−5.81288e6	−	4.22331e6i	−0.395546	−	0.287381i
$737$	−6.36926e6	−	4.62754e6i	−0.431937	−	0.313821i
$738$	−1.62028e6	+	2.23012e6i	−0.109509	+	0.150726i
$739$	1.78288e7	−	5.79293e6i	1.20091	−	0.390200i	0.360815	−	0.932637i	$-0.382498\pi$
$739$	1.78288e7	−	5.79293e6i	1.20091	−	0.390200i	0.840096	+	0.542438i	$0.182498\pi$
$740$	7.45809e6	+	1.02652e7i	0.500666	+	0.689108i
$741$	−3.17988e6	−	2.31031e6i	−0.212748	−	0.154570i
$742$	−3.68509e6	−	5.07209e6i	−0.245719	−	0.338203i
$743$		−	2.21424e7i		−	1.47148i	−0.677266	−	0.735738i	$-0.736835\pi$
$743$		−	2.21424e7i		−	1.47148i	0.677266	−	0.735738i	$-0.263165\pi$
$744$	2.34889e6	−	1.70657e6i	0.155571	−	0.113029i
$745$	−7.77919e6			−0.513504
$746$	−1.16418e6			−0.0765903
$747$	66602.0	−	48389.2i	0.00436703	−	0.00317283i
$748$	−2.95565e6	−	9.09656e6i	−0.193152	−	0.594461i
$749$	−4.06434e6	+	5.59409e6i	−0.264719	+	0.364355i
$750$	929411.	+	1.27922e6i	0.0603330	+	0.0830412i
$751$	−7.14349e6	+	2.19854e7i	−0.462180	+	1.42244i	0.400315	+	0.916377i	$0.368901\pi$
$751$	−7.14349e6	+	2.19854e7i	−0.462180	+	1.42244i	−0.862495	+	0.506065i	$0.831099\pi$
$752$	62422.4	+	192116.i	0.00402528	+	0.0123885i
$753$		−	2.61534e6i		−	0.168089i
$754$	5.22301e6	−	1.60748e7i	0.334574	−	1.02971i
$755$	4.18750e6	−	5.76359e6i	0.267354	−	0.367982i
$756$	2.31809e6	−	753192.i	0.147511	−	0.0479293i
$757$	−1.20902e6	−	3.72097e6i	−0.0766818	−	0.236002i	0.905367	−	0.424630i	$-0.139596\pi$
$757$	−1.20902e6	−	3.72097e6i	−0.0766818	−	0.236002i	−0.982049	+	0.188628i	$0.939596\pi$
$758$	−1.29524e6	−	420850.i	−0.0818800	−	0.0266044i
$759$	875780.	−	636291.i	0.0551811	−	0.0400914i
$760$	1.51430e7	+	4.92024e6i	0.950991	+	0.308996i
$761$		−	1.19369e7i		−	0.747186i	−0.927593	−	0.373593i	$-0.878126\pi$
$761$		−	1.19369e7i		−	0.747186i	0.927593	−	0.373593i	$-0.121874\pi$
$762$	866010.	−	281384.i	0.0540301	−	0.0175554i
$763$	−2.64938e7	+	8.60837e6i	−1.64753	+	0.535315i
$764$			4.64397e6i			0.287843i
$765$	1.41934e7	+	4.61170e6i	0.876863	+	0.284910i
$766$	−1.39653e7	+	1.01464e7i	−0.859960	+	0.624798i
$767$	2.57682e7	+	8.37261e6i	1.58160	+	0.513893i
$768$	767468.	+	2.36202e6i	0.0469523	+	0.144504i
$769$	−4.92908e6	+	1.60156e6i	−0.300573	+	0.0976621i	−0.455421	−	0.890276i	$-0.650511\pi$
$769$	−4.92908e6	+	1.60156e6i	−0.300573	+	0.0976621i	0.154848	+	0.987938i	$0.450511\pi$
$770$	−4.30671e6	+	5.92768e6i	−0.261770	+	0.360295i
$771$	−926798.	+	2.85239e6i	−0.0561499	+	0.172812i
$772$			2.10615e6i			0.127188i
$773$	−7.42757e6	−	2.28597e7i	−0.447093	−	1.37601i	−0.880172	−	0.474655i	$-0.842573\pi$
$773$	−7.42757e6	−	2.28597e7i	−0.447093	−	1.37601i	0.433079	−	0.901356i	$-0.357427\pi$
$774$	4.83386e6	−	1.48771e7i	0.290029	−	0.892619i
$775$	−4.10699e6	−	5.65279e6i	−0.245623	−	0.338072i
$776$	−7.39264e6	+	1.01751e7i	−0.440702	+	0.606574i
$777$	−1.22575e6	−	3.77249e6i	−0.0728368	−	0.224169i
$778$	5.02608e6	−	3.65166e6i	0.297701	−	0.216292i
$779$	−5.99250e6			−0.353805
$780$	1.80571e6			0.106270
$781$	1.03882e7	−	7.54746e6i	0.609414	−	0.442765i
$782$			6.31223e6i			0.369118i
$783$	3.28775e6	+	4.52520e6i	0.191644	+	0.263775i
$784$	163177.	+	118555.i	0.00948131	+	0.00688858i
$785$	−9.97699e6	−	1.37322e7i	−0.577864	−	0.795361i
$786$	1.19216e6	−	387357.i	0.0688302	−	0.0223643i
$787$	−9.48893e6	+	1.30604e7i	−0.546110	+	0.751656i	−0.989478	−	0.144683i	$-0.953784\pi$
$787$	−9.48893e6	+	1.30604e7i	−0.546110	+	0.751656i	0.443368	+	0.896340i	$0.353784\pi$
$788$	2.23351e6	+	1.62274e6i	0.128136	+	0.0930965i
$789$	−2.12175e6	−	1.54154e6i	−0.121339	−	0.0881580i
$790$	−5.12431e6	+	1.57710e7i	−0.292124	+	0.899066i
$791$	−1.71361e7	−	5.56786e6i	−0.973803	−	0.316408i
$792$	1.63422e7			0.925760
$793$	−2.37040e7	−	1.20244e7i	−1.33856	−	0.679014i
$794$	593050.			0.0333841
$795$	1.46185e6	+	474983.i	0.0820321	+	0.0266539i
$796$	3.99584e6	−	1.22979e7i	0.223525	−	0.687938i
$797$	−2.16133e7	−	1.57030e7i	−1.20525	−	0.875663i	−0.210456	−	0.977603i	$-0.567495\pi$
$797$	−2.16133e7	−	1.57030e7i	−1.20525	−	0.875663i	−0.994791	+	0.101940i	$0.967495\pi$
$798$	−1.48991e6	−	1.08249e6i	−0.0828236	−	0.0601749i
$799$	−2.33616e6	+	3.21545e6i	−0.129460	+	0.178187i
$800$	5.46564e6	−	1.77589e6i	0.301937	−	0.0981053i
$801$	1.82237e7	+	2.50828e7i	1.00359	+	1.38132i
$802$	1.57191e7	+	1.14206e7i	0.862963	+	0.626979i
$803$	3.37429e6	+	4.64432e6i	0.184669	+	0.254175i
$804$			909082.i			0.0495979i
$805$	−5.56634e6	+	4.04418e6i	−0.302747	+	0.219959i
$806$	2.28500e7			1.23894
$807$	−3.60207e6			−0.194701
$808$	−2.36808e7	+	1.72051e7i	−1.27605	+	0.927104i
$809$	4.16661e6	+	1.28235e7i	0.223827	+	0.688867i	0.998409	+	0.0563939i	$0.0179603\pi$
$809$	4.16661e6	+	1.28235e7i	0.223827	+	0.688867i	−0.774582	+	0.632473i	$0.782040\pi$
$810$	−5.42054e6	+	7.46073e6i	−0.290288	+	0.399548i
$811$	4.65000e6	+	6.40018e6i	0.248257	+	0.341696i	0.914900	−	0.403681i	$-0.132269\pi$
$811$	4.65000e6	+	6.40018e6i	0.248257	+	0.341696i	−0.666643	+	0.745377i	$0.732269\pi$
$812$	−3.48213e6	+	1.07169e7i	−0.185334	+	0.570399i
$813$	1.28290e6	+	3.94837e6i	0.0680718	+	0.209503i
$814$		−	1.98967e7i		−	1.05249i
$815$	−1.00886e6	+	3.10495e6i	−0.0532031	+	0.163742i
$816$	127699.	−	175763.i	0.00671370	−	0.00924061i
$817$	3.23412e7	−	1.05083e7i	1.69512	−	0.550778i
$818$	337943.	+	1.04008e6i	0.0176588	+	0.0543481i
$819$	2.43860e7	+	7.92350e6i	1.27037	+	0.412769i
$820$	2.22721e6	−	1.61816e6i	0.115671	−	0.0840402i
$821$	1.80010e7	+	5.84889e6i	0.932051	+	0.302842i	0.735401	−	0.677632i	$-0.236994\pi$
$821$	1.80010e7	+	5.84889e6i	0.932051	+	0.302842i	0.196650	+	0.980474i	$0.436994\pi$
$822$		−	83152.7i		−	0.00429237i
$823$	1.67446e7	−	5.44066e6i	0.861740	−	0.279996i	0.155385	−	0.987854i	$-0.450338\pi$
$823$	1.67446e7	−	5.44066e6i	0.861740	−	0.279996i	0.706355	+	0.707858i	$0.250338\pi$
$824$	2.76732e7	−	8.99156e6i	1.41985	−	0.461336i
$825$			865841.i			0.0442898i
$826$	1.20736e7	+	3.92294e6i	0.615724	+	0.200061i
$827$	2.03642e7	−	1.47955e7i	1.03539	−	0.752255i	0.0660103	−	0.997819i	$-0.478973\pi$
$827$	2.03642e7	−	1.47955e7i	1.03539	−	0.752255i	0.969381	+	0.245563i	$0.0789730\pi$
$828$	5.39995e6	+	1.75455e6i	0.273725	+	0.0889385i
$829$	1.51654e6	+	4.66742e6i	0.0766419	+	0.235880i	0.982036	−	0.188692i	$-0.0604247\pi$
$829$	1.51654e6	+	4.66742e6i	0.0766419	+	0.235880i	−0.905394	+	0.424572i	$0.860425\pi$
$830$	54953.6	−	17855.5i	0.00276886	−	0.000899658i
$831$	−867586.	+	1.19413e6i	−0.0435823	+	0.0599859i
$832$	−6.43591e6	+	1.98077e7i	−0.322331	+	0.992032i
$833$			3.96851e6i			0.198159i
$834$	371963.	+	1.14478e6i	0.0185176	+	0.0569913i
$835$	7.11203e6	−	2.18886e7i	0.353002	−	1.08643i
$836$	7.72600e6	+	1.06339e7i	0.382331	+	0.526233i
$837$	−4.44475e6	+	6.11768e6i	−0.219298	+	0.301837i
$838$	1.27325e6	+	3.91867e6i	0.0626332	+	0.192765i
$839$	1.95161e7	−	1.41793e7i	0.957168	−	0.695423i	0.00467679	−	0.999989i	$-0.498511\pi$
$839$	1.95161e7	−	1.41793e7i	0.957168	−	0.695423i	0.952491	+	0.304566i	$0.0985113\pi$
$840$	2.28671e6			0.111818
$841$	−5.34833e6			−0.260752
$842$	7.38114e6	−	5.36271e6i	0.358792	−	0.260678i
$843$		−	1.69682e6i		−	0.0822368i
$844$	−4.13694e6	−	5.69401e6i	−0.199905	−	0.275145i
$845$	1.72807e7	+	1.25552e7i	0.832570	+	0.604897i
$846$	−1.47683e6	−	2.03268e6i	−0.0709422	−	0.0976436i
$847$	2.51255e6	−	816376.i	0.120339	−	0.0391004i
$848$	−597418.	+	822276.i	−0.0285291	+	0.0392670i
$849$	648058.	+	470842.i	0.0308563	+	0.0224184i
$850$	−4.08452e6	−	2.96758e6i	−0.193907	−	0.140882i
$851$	5.77362e6	−	1.77694e7i	0.273290	−	0.841101i
$852$	−1.41013e6	−	458180.i	−0.0665520	−	0.0216241i
$853$	9.47044e6			0.445654			0.222827	−	0.974858i	$-0.428472\pi$
$853$	9.47044e6			0.445654			0.222827	+	0.974858i	$0.428472\pi$
$854$	−1.11064e7	−	5.63395e6i	−0.521109	−	0.264343i
$855$	−2.05090e7			−0.959465
$856$	1.02949e7	+	3.34502e6i	0.480217	+	0.156032i
$857$	−4.95467e6	+	1.52489e7i	−0.230443	+	0.709230i	0.767251	+	0.641347i	$0.221624\pi$
$857$	−4.95467e6	+	1.52489e7i	−0.230443	+	0.709230i	−0.997693	+	0.0678823i	$0.978376\pi$
$858$	−2.29075e6	−	1.66433e6i	−0.106233	−	0.0771827i
$859$	7.56561e6	+	5.49674e6i	0.349833	+	0.254169i	0.748799	−	0.662797i	$-0.230631\pi$
$859$	7.56561e6	+	5.49674e6i	0.349833	+	0.254169i	−0.398966	+	0.916966i	$0.630631\pi$
$860$	−9.18256e6	+	1.26387e7i	−0.423368	+	0.582715i
$861$	−818506.	+	265949.i	−0.0376282	+	0.0122262i
$862$	−2.55431e6	−	3.51570e6i	−0.117086	−	0.161155i
$863$	741044.	+	538400.i	0.0338702	+	0.0246081i	0.604592	−	0.796536i	$-0.293336\pi$
$863$	741044.	+	538400.i	0.0338702	+	0.0246081i	−0.570721	+	0.821144i	$0.693336\pi$
$864$	−3.65575e6	−	5.03171e6i	−0.166607	−	0.229315i
$865$		−	2.54659e7i		−	1.15723i
$866$	−8.05615e6	+	5.85314e6i	−0.365034	+	0.265212i
$867$	1.02610e6			0.0463598
$868$	−1.52339e7			−0.686296
$869$	−2.99334e7	+	2.17479e7i	−1.34464	+	0.976938i
$870$	599982.	+	1.84656e6i	0.0268745	+	0.0827112i
$871$	−1.13663e7	+	1.56443e7i	−0.507659	+	0.698733i
$872$	2.56331e7	+	3.52810e7i	1.14159	+	1.57126i
$873$	5.00614e6	−	1.54073e7i	0.222314	−	0.684214i
$874$	−2.68059e6	−	8.25001e6i	−0.118700	−	0.365322i
$875$		−	2.24238e7i		−	0.990122i
$876$	204842.	−	630438.i	0.00901899	−	0.0277576i
$877$	−7.24299e6	+	9.96912e6i	−0.317994	+	0.437681i	−0.937853	−	0.347032i	$-0.887190\pi$
$877$	−7.24299e6	+	9.96912e6i	−0.317994	+	0.437681i	0.619859	+	0.784713i	$0.287190\pi$
$878$	322116.	−	104662.i	0.0141018	−	0.00458196i
$879$	1.08627e6	+	3.34319e6i	0.0474203	+	0.145945i
$880$	1.12970e6	+	367063.i	0.0491765	+	0.0159784i
$881$	1.11187e7	−	8.07818e6i	0.482629	−	0.350650i	−0.319714	−	0.947514i	$-0.603587\pi$
$881$	1.11187e7	−	8.07818e6i	0.482629	−	0.350650i	0.802342	+	0.596864i	$0.203587\pi$
$882$	−2.38595e6	−	775242.i	−0.103274	−	0.0335557i
$883$			8.75789e6i			0.378005i	0.981977	+	0.189003i	$0.0605255\pi$
$883$			8.75789e6i			0.378005i	−0.981977	+	0.189003i	$0.939475\pi$
$884$	−2.23431e7	+	7.25973e6i	−0.961642	+	0.312457i
$885$	−2.96007e6	+	961786.i	−0.127041	+	0.0412781i
$886$		−	4.99066e6i		−	0.213587i
$887$	1.14547e7	+	3.72187e6i	0.488850	+	0.158837i	0.543062	−	0.839692i	$-0.317265\pi$
$887$	1.14547e7	+	3.72187e6i	0.488850	+	0.158837i	−0.0542120	+	0.998529i	$0.517265\pi$
$888$	−5.02369e6	+	3.64993e6i	−0.213792	+	0.155329i
$889$	−1.22812e7	−	3.99042e6i	−0.521180	−	0.169342i
$890$	6.72450e6	+	2.06959e7i	0.284567	+	0.875809i
$891$	−1.95693e7	+	6.35844e6i	−0.825810	+	0.268322i
$892$	1.09424e7	−	1.50609e7i	0.460467	−	0.633779i
$893$	1.68784e6	−	5.19465e6i	0.0708277	−	0.217985i
$894$		−	1.40857e6i		−	0.0589433i
$895$	−90304.3	−	277928.i	−0.00376835	−	0.0115978i
$896$	3.57751e6	−	1.10104e7i	0.148871	−	0.458179i
$897$	−1.56287e6	−	2.15111e6i	−0.0648548	−	0.0892649i
$898$	−7.52951e6	+	1.03635e7i	−0.311584	+	0.428859i
$899$	−1.08032e7	−	3.32487e7i	−0.445812	−	1.37207i
$900$	−3.67402e6	+	2.66933e6i	−0.151194	+	0.109849i
$901$	−1.99980e7			−0.820680
$902$	−4.31693e6			−0.176668
$903$	3.95107e6	−	2.87062e6i	0.161248	−	0.117154i
$904$			2.82065e7i			1.14797i
$905$	9.37319e6	+	1.29011e7i	0.380422	+	0.523606i
$906$	1.04361e6	+	758225.i	0.0422393	+	0.0306886i
$907$	−1.33843e7	−	1.84219e7i	−0.540229	−	0.743561i	0.448417	−	0.893824i	$-0.351988\pi$
$907$	−1.33843e7	−	1.84219e7i	−0.540229	−	0.743561i	−0.988646	+	0.150263i	$0.951988\pi$
$908$	−9.18681e6	+	2.98498e6i	−0.369786	+	0.120151i
$909$	2.21614e7	−	3.05025e7i	0.889584	−	1.22441i
$910$	1.45597e7	+	1.05782e7i	0.582839	+	0.423457i
$911$	−3.81467e7	−	2.77152e7i	−1.52286	−	1.10642i	−0.960046	−	0.279842i	$-0.909718\pi$
$911$	−3.81467e7	−	2.77152e7i	−1.52286	−	1.10642i	−0.562816	−	0.826582i	$-0.690282\pi$
$912$	−92260.7	+	283949.i	−0.00367307	+	0.0113046i
$913$	122614.	+	39839.8i	0.00486815	+	0.00158176i
$914$	1.29935e7			0.514472
$915$	3.01480e6	−	483037.i	0.119044	−	0.0190734i
$916$	1.61597e7			0.636350
$917$	−1.69066e7	−	5.49327e6i	−0.663944	−	0.215729i
$918$	−1.68845e6	+	5.19653e6i	−0.0661276	+	0.203520i
$919$	−1.51103e7	−	1.09783e7i	−0.590180	−	0.428791i	0.252200	−	0.967675i	$-0.418846\pi$
$919$	−1.51103e7	−	1.09783e7i	−0.590180	−	0.428791i	−0.842380	+	0.538884i	$0.818846\pi$
$920$	8.71392e6	+	6.33104e6i	0.339425	+	0.246607i
$921$	−1.73174e6	+	2.38354e6i	−0.0672719	+	0.0925919i
$922$	8.80483e6	−	2.86086e6i	0.341109	−	0.110833i
$923$	−1.85382e7	−	2.55157e7i	−0.716249	−	0.985832i
$924$	1.52722e6	+	1.10959e6i	0.0588466	+	0.0427546i
$925$	8.78386e6	+	1.20899e7i	0.337544	+	0.464590i
$926$		−	1.88464e7i		−	0.722271i
$927$	−3.03215e7	+	2.20299e7i	−1.15891	+	0.842001i
$928$	2.87540e7			1.09604
$929$	2.01815e6			0.0767209			0.0383604	−	0.999264i	$-0.487786\pi$
$929$	2.01815e6			0.0767209			0.0383604	+	0.999264i	$0.487786\pi$
$930$	−2.12355e6	+	1.54285e6i	−0.0805109	+	0.0584946i
$931$	−1.68529e6	−	5.18679e6i	−0.0637237	−	0.196121i
$932$	−7.87356e6	+	1.08370e7i	−0.296914	+	0.408668i
$933$	−3.03480e6	−	4.17704e6i	−0.114137	−	0.157096i
$934$	336222.	−	1.03479e6i	0.0126113	−	0.0388135i
$935$	7.22214e6	+	2.22275e7i	0.270170	+	0.831498i
$936$		−	4.01401e7i		−	1.49758i
$937$	−3.49531e6	+	1.07575e7i	−0.130058	+	0.400277i	−0.994789	−	0.101959i	$-0.967489\pi$
$937$	−3.49531e6	+	1.07575e7i	−0.130058	+	0.400277i	0.864731	+	0.502236i	$0.167489\pi$
$938$	−5.32560e6	+	7.33006e6i	−0.197634	+	0.272020i
$939$	−4.71366e6	+	1.53156e6i	−0.174459	+	0.0566853i
$940$	775403.	+	2.38644e6i	0.0286225	+	0.0880910i
$941$	−2.13914e7	−	6.95050e6i	−0.787528	−	0.255883i	−0.112477	−	0.993654i	$-0.535878\pi$
$941$	−2.13914e7	−	6.95050e6i	−0.787528	−	0.255883i	−0.675051	+	0.737771i	$0.735878\pi$
$942$	2.48646e6	−	1.80652e6i	0.0912967	−	0.0663309i
$943$	−3.85537e6	−	1.25269e6i	−0.141184	−	0.0458736i
$944$		−	2.05807e6i		−	0.0751675i
$945$	−5.66425e6	+	1.84043e6i	−0.206330	+	0.0670408i
$946$	2.32983e7	−	7.57006e6i	0.846439	−	0.275025i
$947$			2.37926e7i			0.862119i	0.902323	+	0.431060i	$0.141860\pi$
$947$			2.37926e7i			0.862119i	−0.902323	+	0.431060i	$0.858140\pi$
$948$	4.06327e6	+	1.32024e6i	0.146844	+	0.0477124i
$949$	1.14075e7	−	8.28801e6i	0.411172	−	0.298734i
$950$	6.59865e6	+	2.14403e6i	0.237217	+	0.0770766i
$951$	1.69938e6	+	5.23015e6i	0.0609311	+	0.187527i
$952$	−2.82949e7	+	9.19357e6i	−1.01185	+	0.328770i
$953$	−7.75589e6	+	1.06751e7i	−0.276630	+	0.380749i	−0.924614	−	0.380905i	$-0.875612\pi$
$953$	−7.75589e6	+	1.06751e7i	−0.276630	+	0.380749i	0.647984	+	0.761654i	$0.275612\pi$
$954$	3.90657e6	−	1.20232e7i	0.138971	−	0.427710i
$955$		−	1.13476e7i		−	0.402619i
$956$	−4.20058e6	−	1.29281e7i	−0.148650	−	0.457498i
$957$	−1.33870e6	+	4.12009e6i	−0.0472502	+	0.145421i
$958$	3.23457e6	+	4.45200e6i	0.113868	+	0.156726i
$959$	−693130.	+	954012.i	−0.0243371	+	0.0334971i
$960$	−739312.	−	2.27537e6i	−0.0258910	−	0.0796844i
$961$	1.50747e7	−	1.09524e7i	0.526550	−	0.382561i
$962$	−4.88707e7			−1.70259
$963$	−1.39430e7			−0.484496
$964$	−2.77654e6	+	2.01728e6i	−0.0962303	+	0.0699154i
$965$		−	5.14638e6i		−	0.177903i
$966$	−732275.	−	1.00789e6i	−0.0252483	−	0.0347512i
$967$	−1.47502e7	−	1.07166e7i	−0.507261	−	0.368547i	0.304522	−	0.952505i	$-0.401503\pi$
$967$	−1.47502e7	−	1.07166e7i	−0.507261	−	0.368547i	−0.811784	+	0.583958i	$0.801503\pi$
$968$	−2.43092e6	−	3.34587e6i	−0.0833839	−	0.114768i
$969$	−5.58684e6	+	1.81528e6i	−0.191142	+	0.0621059i
$970$	6.68344e6	−	9.19896e6i	0.228071	−	0.313913i
$971$	−2.88759e7	−	2.09796e7i	−0.982851	−	0.714083i	−0.0245070	−	0.999700i	$-0.507802\pi$
$971$	−2.88759e7	−	2.09796e7i	−0.982851	−	0.714083i	−0.958344	+	0.285617i	$0.907802\pi$
$972$	5.98590e6	+	4.34901e6i	0.203219	+	0.147647i
$973$	5.27496e6	−	1.62347e7i	0.178623	−	0.549745i
$974$	1.62321e7	+	5.27412e6i	0.548247	+	0.178136i
$975$	2.12670e6			0.0716463
$976$	−312261.	+	1.99466e6i	−0.0104928	+	0.0670263i
$977$	−1.34966e7			−0.452363			−0.226182	−	0.974085i	$-0.572624\pi$
$977$	−1.34966e7			−0.452363			−0.226182	+	0.974085i	$0.572624\pi$
$978$	−562210.	−	182673.i	−0.0187954	−	0.00610700i
$979$	−1.50039e7	+	4.61774e7i	−0.500321	+	1.53983i
$980$	2.02696e6	+	1.47267e6i	0.0674187	+	0.0489825i
$981$	−4.54444e7	−	3.30173e7i	−1.50768	−	1.09539i
$982$	−6.49403e6	+	8.93826e6i	−0.214899	+	0.295784i
$983$	5.41301e7	−	1.75879e7i	1.78671	−	0.580538i	0.787360	−	0.616494i	$-0.211447\pi$
$983$	5.41301e7	−	1.75879e7i	1.78671	−	0.580538i	0.999353	+	0.0359554i	$0.0114474\pi$
$984$	791914.	+	1.08998e6i	0.0260730	+	0.0358864i
$985$	−5.45759e6	−	3.96517e6i	−0.179230	−	0.130218i
$986$	−1.48479e7	−	2.04364e7i	−0.486377	−	0.669440i
$987$		−	784435.i		−	0.0256309i
$988$	2.61193e7	−	1.89768e7i	0.851273	−	0.618486i
$989$	2.30039e7			0.747844
$990$	−1.47745e7			−0.479097
$991$	1.08345e7	−	7.87169e6i	0.350447	−	0.254615i	−0.398609	−	0.917121i	$-0.630507\pi$
$991$	1.08345e7	−	7.87169e6i	0.350447	−	0.254615i	0.749057	+	0.662506i	$0.230507\pi$
$992$	1.20124e7	+	3.69703e7i	0.387569	+	1.19282i
$993$	2.96366e6	−	4.07913e6i	0.0953797	−	0.131279i
$994$	−8.68599e6	−	1.19552e7i	−0.278839	−	0.383789i
$995$	−9.76385e6	+	3.00500e7i	−0.312653	+	0.962248i
$996$	−4600.33	−	14158.4i	−0.000146940	−	0.000452235i
$997$			2.66239e7i			0.848268i	0.905599	+	0.424134i	$0.139421\pi$
$997$			2.66239e7i			0.848268i	−0.905599	+	0.424134i	$0.860579\pi$
$998$	−1.12361e7	+	3.45811e7i	−0.357099	+	1.09904i
$999$	9.50624e6	−	1.30842e7i	0.301366	−	0.414795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.6.g.a.3.16	✓	104
61.41	even	10	inner	61.6.g.a.41.16	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.6.g.a.3.16	✓	104	1.1	even	1	trivial
61.6.g.a.41.16	yes	104	61.41	even	10	inner

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.45632 + 1.12303i) q^{2} +(-0.707000 + 2.17592i) q^{3} +(-15.2036 - 11.0460i) q^{4} +(37.1500 + 26.9911i) q^{5} +(-4.88724 + 6.72671i) q^{6} +(112.143 - 36.4374i) q^{7} +(-108.499 - 149.337i) q^{8} +(192.356 + 139.755i) q^{9} +O(q^{10})\)	\(q+(3.45632 + 1.12303i) q^{2} +(-0.707000 + 2.17592i) q^{3} +(-15.2036 - 11.0460i) q^{4} +(37.1500 + 26.9911i) q^{5} +(-4.88724 + 6.72671i) q^{6} +(112.143 - 36.4374i) q^{7} +(-108.499 - 149.337i) q^{8} +(192.356 + 139.755i) q^{9} +(98.0907 + 135.010i) q^{10} +372.352i q^{11} +(34.7843 - 25.2723i) q^{12} +914.579 q^{13} +428.521 q^{14} +(-84.9955 + 61.7529i) q^{15} +(-21.4677 - 66.0707i) q^{16} +(803.429 - 1105.82i) q^{17} +(507.897 + 699.060i) q^{18} +(-580.466 + 1786.49i) q^{19} +(-266.669 - 820.722i) q^{20} +269.775i q^{21} +(-418.161 + 1286.97i) q^{22} +(-746.904 + 1028.03i) q^{23} +(401.654 - 130.505i) q^{24} +(-314.072 - 966.615i) q^{25} +(3161.08 + 1027.10i) q^{26} +(-889.873 + 646.531i) q^{27} +(-2107.46 - 684.755i) q^{28} -5085.22i q^{29} +(-363.122 + 117.985i) q^{30} +(6538.30 - 2124.42i) q^{31} +5654.42i q^{32} +(-810.209 - 263.253i) q^{33} +(4018.78 - 2919.81i) q^{34} +(5149.58 + 1673.20i) q^{35} +(-1380.76 - 4249.55i) q^{36} +(-13983.8 + 4543.62i) q^{37} +(-4012.55 + 5522.80i) q^{38} +(-646.607 + 1990.05i) q^{39} -8476.37i q^{40} +(985.816 + 3034.03i) q^{41} +(-302.965 + 932.429i) q^{42} +(-10640.8 - 14645.8i) q^{43} +(4113.02 - 5661.09i) q^{44} +(3373.90 + 10383.8i) q^{45} +(-3736.04 + 2714.39i) q^{46} -2907.74 q^{47} +158.942 q^{48} +(-2348.85 + 1706.54i) q^{49} -3693.64i q^{50} +(1838.17 + 2530.02i) q^{51} +(-13904.9 - 10102.5i) q^{52} +(-8599.55 - 11836.3i) q^{53} +(-3801.76 + 1235.27i) q^{54} +(-10050.2 + 13832.9i) q^{55} +(-17608.8 - 12793.6i) q^{56} +(-3476.87 - 2526.10i) q^{57} +(5710.84 - 17576.2i) q^{58} +(28175.0 + 9154.61i) q^{59} +1974.36 q^{60} +(-25918.0 - 13147.4i) q^{61} +24984.2 q^{62} +(26663.7 + 8663.55i) q^{63} +(-7037.03 + 21657.7i) q^{64} +(33976.6 + 24685.5i) q^{65} +(-2504.70 - 1819.77i) q^{66} +(-12427.9 + 17105.5i) q^{67} +(-24430.0 + 7937.78i) q^{68} +(-1708.84 - 2352.02i) q^{69} +(15919.6 + 11566.2i) q^{70} +(-20269.7 - 27898.8i) q^{71} -43889.2i q^{72} +(12472.9 - 9062.11i) q^{73} -53435.2 q^{74} +2325.33 q^{75} +(28558.8 - 20749.2i) q^{76} +(13567.5 + 41756.6i) q^{77} +(-4469.76 + 6152.10i) q^{78} +(58406.7 + 80389.9i) q^{79} +(985.795 - 3033.96i) q^{80} +(17076.4 + 52555.8i) q^{81} +11593.7i q^{82} +(106.995 - 329.297i) q^{83} +(2979.95 - 4101.55i) q^{84} +(59694.8 - 19396.0i) q^{85} +(-20330.4 - 62570.5i) q^{86} +(11065.0 + 3595.25i) q^{87} +(55605.8 - 40400.0i) q^{88} +(124015. + 40295.0i) q^{89} +39678.7i q^{90} +(102563. - 33324.8i) q^{91} +(22711.2 - 7379.33i) q^{92} +15728.8i q^{93} +(-10050.1 - 3265.47i) q^{94} +(-69783.6 + 50700.7i) q^{95} +(-12303.6 - 3997.67i) q^{96} +(-21055.0 - 64800.5i) q^{97} +(-10034.9 + 3260.53i) q^{98} +(-52038.1 + 71624.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Introduction

L-functions

Modular forms

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