LMFDB - Embedded newform 38.5.f.a.15.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,5,Mod(3,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92805859719$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			15.6
Character	$\chi$	$=$	38.15
Dual form			38.5.f.a.33.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.967379 - 2.65785i) q^{2} +(15.6933 - 2.76715i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(12.2941 - 10.3159i) q^{5} +(7.82668 - 44.3873i) q^{6} +(-44.4015 + 76.9057i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(162.507 - 59.1476i) q^{9} +O(q^{10})$	\(q+(0.967379 - 2.65785i) q^{2} +(15.6933 - 2.76715i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(12.2941 - 10.3159i) q^{5} +(7.82668 - 44.3873i) q^{6} +(-44.4015 + 76.9057i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(162.507 - 59.1476i) q^{9} +(-15.5252 - 42.6552i) q^{10} +(-53.6759 - 92.9694i) q^{11} +(-110.403 - 63.7415i) q^{12} +(-160.682 - 28.3326i) q^{13} +(161.451 + 192.410i) q^{14} +(164.388 - 195.911i) q^{15} +(11.1135 + 63.0277i) q^{16} +(248.351 + 90.3924i) q^{17} -489.137i q^{18} +(50.6212 + 357.433i) q^{19} -128.390 q^{20} +(-483.996 + 1329.77i) q^{21} +(-299.024 + 52.7260i) q^{22} +(-343.071 - 287.871i) q^{23} +(-276.217 + 231.774i) q^{24} +(-63.8048 + 361.855i) q^{25} +(-230.744 + 399.660i) q^{26} +(1268.76 - 732.517i) q^{27} +(667.580 - 242.979i) q^{28} +(-6.00430 - 16.4967i) q^{29} +(-361.675 - 626.440i) q^{30} +(132.442 + 76.4651i) q^{31} +(178.269 + 31.4337i) q^{32} +(-1099.61 - 1310.46i) q^{33} +(480.499 - 572.637i) q^{34} +(247.480 + 1403.53i) q^{35} +(-1300.05 - 473.181i) q^{36} -1109.99i q^{37} +(998.974 + 211.230i) q^{38} -2600.03 q^{39} +(-124.202 + 341.242i) q^{40} +(2179.65 - 384.331i) q^{41} +(3066.12 + 2572.78i) q^{42} +(961.696 - 806.959i) q^{43} +(-149.132 + 845.767i) q^{44} +(1387.70 - 2403.57i) q^{45} +(-1097.00 + 633.353i) q^{46} +(-3289.42 + 1197.25i) q^{47} +(348.814 + 958.358i) q^{48} +(-2742.49 - 4750.13i) q^{49} +(900.034 + 519.635i) q^{50} +(4147.57 + 731.329i) q^{51} +(839.021 + 999.907i) q^{52} +(1434.47 - 1709.54i) q^{53} +(-719.553 - 4080.79i) q^{54} +(-1618.96 - 589.254i) q^{55} -2009.38i q^{56} +(1783.48 + 5469.22i) q^{57} -49.6541 q^{58} +(-5.13114 + 14.0977i) q^{59} +(-2014.86 + 355.274i) q^{60} +(-980.402 - 822.655i) q^{61} +(331.354 - 278.039i) q^{62} +(-2666.76 + 15123.9i) q^{63} +(256.000 - 443.405i) q^{64} +(-2267.71 + 1309.26i) q^{65} +(-4546.76 + 1654.89i) q^{66} +(-995.646 - 2735.51i) q^{67} +(-1057.16 - 1831.05i) q^{68} +(-6180.50 - 3568.31i) q^{69} +(3969.77 + 699.978i) q^{70} +(2687.01 + 3202.26i) q^{71} +(-2515.29 + 2997.60i) q^{72} +(-1216.01 - 6896.32i) q^{73} +(-2950.19 - 1073.78i) q^{74} +5855.25i q^{75} +(1527.80 - 2450.79i) q^{76} +9533.16 q^{77} +(-2515.21 + 6910.48i) q^{78} +(4113.42 - 725.307i) q^{79} +(786.820 + 660.221i) q^{80} +(7153.36 - 6002.38i) q^{81} +(1087.05 - 6164.97i) q^{82} +(-1506.19 + 2608.79i) q^{83} +(9804.16 - 5660.44i) q^{84} +(3985.73 - 1450.69i) q^{85} +(-1214.45 - 3336.68i) q^{86} +(-139.876 - 242.272i) q^{87} +(2103.66 + 1214.55i) q^{88} +(-14171.4 - 2498.80i) q^{89} +(-5045.91 - 6013.48i) q^{90} +(9313.45 - 11099.3i) q^{91} +(622.144 + 3528.35i) q^{92} +(2290.03 + 833.503i) q^{93} +9900.98i q^{94} +(4309.60 + 3872.10i) q^{95} +2884.61 q^{96} +(-1115.04 + 3063.55i) q^{97} +(-15278.2 + 2693.95i) q^{98} +(-14221.6 - 11933.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9}+O(q^{10}) $ 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9} + 90 q^{11} - 432 q^{12} - 330 q^{13} + 576 q^{14} + 2658 q^{15} - 522 q^{17} - 1236 q^{19} - 864 q^{20} - 1998 q^{21} - 1344 q^{22} - 1440 q^{23} - 384 q^{24} - 3276 q^{25} + 576 q^{26} + 1692 q^{27} + 1056 q^{28} + 4050 q^{29} + 2808 q^{31} + 2910 q^{33} + 1536 q^{34} + 1422 q^{35} + 672 q^{36} + 1872 q^{38} - 9024 q^{39} - 3060 q^{41} - 3456 q^{42} - 1218 q^{43} - 5760 q^{44} - 2592 q^{45} - 2880 q^{46} + 990 q^{47} + 1536 q^{48} - 9696 q^{49} + 27648 q^{50} + 35784 q^{51} - 1488 q^{52} + 17082 q^{53} + 2160 q^{54} + 4290 q^{55} + 204 q^{57} - 5376 q^{58} - 11142 q^{59} - 11856 q^{60} - 35928 q^{61} - 7200 q^{62} - 58254 q^{63} + 9216 q^{64} - 34290 q^{65} - 32928 q^{66} + 44322 q^{67} - 4752 q^{68} + 21762 q^{69} + 12864 q^{70} + 40428 q^{71} + 10752 q^{72} + 6936 q^{73} - 4032 q^{74} - 576 q^{76} - 36648 q^{77} - 11040 q^{78} - 29298 q^{79} + 24324 q^{81} - 14592 q^{82} + 23958 q^{83} + 36720 q^{84} + 2772 q^{85} + 30816 q^{86} + 14256 q^{87} + 26064 q^{89} + 14784 q^{90} + 100044 q^{91} + 9360 q^{92} + 26400 q^{93} - 38646 q^{95} - 55746 q^{97} - 64512 q^{98} - 69846 q^{99}+O(q^{100}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9 + 90 * q^11 - 432 * q^12 - 330 * q^13 + 576 * q^14 + 2658 * q^15 - 522 * q^17 - 1236 * q^19 - 864 * q^20 - 1998 * q^21 - 1344 * q^22 - 1440 * q^23 - 384 * q^24 - 3276 * q^25 + 576 * q^26 + 1692 * q^27 + 1056 * q^28 + 4050 * q^29 + 2808 * q^31 + 2910 * q^33 + 1536 * q^34 + 1422 * q^35 + 672 * q^36 + 1872 * q^38 - 9024 * q^39 - 3060 * q^41 - 3456 * q^42 - 1218 * q^43 - 5760 * q^44 - 2592 * q^45 - 2880 * q^46 + 990 * q^47 + 1536 * q^48 - 9696 * q^49 + 27648 * q^50 + 35784 * q^51 - 1488 * q^52 + 17082 * q^53 + 2160 * q^54 + 4290 * q^55 + 204 * q^57 - 5376 * q^58 - 11142 * q^59 - 11856 * q^60 - 35928 * q^61 - 7200 * q^62 - 58254 * q^63 + 9216 * q^64 - 34290 * q^65 - 32928 * q^66 + 44322 * q^67 - 4752 * q^68 + 21762 * q^69 + 12864 * q^70 + 40428 * q^71 + 10752 * q^72 + 6936 * q^73 - 4032 * q^74 - 576 * q^76 - 36648 * q^77 - 11040 * q^78 - 29298 * q^79 + 24324 * q^81 - 14592 * q^82 + 23958 * q^83 + 36720 * q^84 + 2772 * q^85 + 30816 * q^86 + 14256 * q^87 + 26064 * q^89 + 14784 * q^90 + 100044 * q^91 + 9360 * q^92 + 26400 * q^93 - 38646 * q^95 - 55746 * q^97 - 64512 * q^98 - 69846 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$3$	15.6933	−	2.76715i	1.74370	−	0.307461i	0.791098	−	0.611689i	$-0.209510\pi$
$3$	15.6933	−	2.76715i	1.74370	−	0.307461i	0.952599	+	0.304228i	$0.0983986\pi$
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	12.2941	−	10.3159i	0.491763	−	0.412638i	−0.362895	−	0.931830i	$-0.618212\pi$
$5$	12.2941	−	10.3159i	0.491763	−	0.412638i	0.854657	+	0.519192i	$0.173767\pi$
$6$	7.82668	−	44.3873i	0.217408	−	1.23298i
$7$	−44.4015	+	76.9057i	−0.906153	+	1.56950i	−0.0867919	+	0.996226i	$0.527662\pi$
$7$	−44.4015	+	76.9057i	−0.906153	+	1.56950i	−0.819361	+	0.573277i	$0.805672\pi$
$8$	−19.5959	+	11.3137i	−0.306186	+	0.176777i
$9$	162.507	−	59.1476i	2.00626	−	0.730217i
$10$	−15.5252	−	42.6552i	−0.155252	−	0.426552i
$11$	−53.6759	−	92.9694i	−0.443602	−	0.768342i	0.554351	−	0.832283i	$-0.312966\pi$
$11$	−53.6759	−	92.9694i	−0.443602	−	0.768342i	−0.997954	+	0.0639410i	$0.979633\pi$
$12$	−110.403	−	63.7415i	−0.766691	−	0.442649i
$13$	−160.682	−	28.3326i	−0.950780	−	0.167648i	−0.323314	−	0.946292i	$-0.604797\pi$
$13$	−160.682	−	28.3326i	−0.950780	−	0.167648i	−0.627467	+	0.778644i	$0.715908\pi$
$14$	161.451	+	192.410i	0.823729	+	0.981682i
$15$	164.388	−	195.911i	0.730615	−	0.870713i
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	248.351	+	90.3924i	0.859346	+	0.312776i	0.733845	−	0.679317i	$-0.237724\pi$
$17$	248.351	+	90.3924i	0.859346	+	0.312776i	0.125501	+	0.992093i	$0.459946\pi$
$18$		−	489.137i		−	1.50968i
$19$	50.6212	+	357.433i	0.140225	+	0.990120i
$19$	50.6212	+	357.433i	0.140225	+	0.990120i
$20$	−128.390			−0.320975
$21$	−483.996	+	1329.77i	−1.09750	+	3.01535i
$22$	−299.024	+	52.7260i	−0.617818	+	0.108938i
$23$	−343.071	−	287.871i	−0.648528	−	0.544180i	0.258096	−	0.966119i	$-0.416905\pi$
$23$	−343.071	−	287.871i	−0.648528	−	0.544180i	−0.906624	+	0.421939i	$0.861349\pi$
$24$	−276.217	+	231.774i	−0.479544	+	0.402385i
$25$	−63.8048	+	361.855i	−0.102088	+	0.578968i
$26$	−230.744	+	399.660i	−0.341337	+	0.591214i
$27$	1268.76	−	732.517i	1.74041	−	1.00482i
$28$	667.580	−	242.979i	0.851506	−	0.309923i
$29$	−6.00430	−	16.4967i	−0.00713947	−	0.0196155i	0.936072	−	0.351809i	$-0.114433\pi$
$29$	−6.00430	−	16.4967i	−0.00713947	−	0.0196155i	−0.943211	+	0.332194i	$0.892211\pi$
$30$	−361.675	−	626.440i	−0.401861	−	0.696044i
$31$	132.442	+	76.4651i	0.137816	+	0.0795683i	0.567323	−	0.823495i	$-0.307979\pi$
$31$	132.442	+	76.4651i	0.137816	+	0.0795683i	−0.429507	+	0.903064i	$0.641312\pi$
$32$	178.269	+	31.4337i	0.174091	+	0.0306970i
$33$	−1099.61	−	1310.46i	−1.00974	−	1.20337i
$34$	480.499	−	572.637i	0.415657	−	0.495360i
$35$	247.480	+	1403.53i	0.202024	+	1.14574i
$36$	−1300.05	−	473.181i	−1.00313	−	0.365109i
$37$		−	1109.99i		−	0.810803i	−0.914139	−	0.405401i	$-0.867132\pi$
$37$		−	1109.99i		−	0.810803i	0.914139	−	0.405401i	$-0.132868\pi$
$38$	998.974	+	211.230i	0.691811	+	0.146281i
$39$	−2600.03			−1.70942
$40$	−124.202	+	341.242i	−0.0776262	+	0.213276i
$41$	2179.65	−	384.331i	1.29664	−	0.228632i	0.517607	−	0.855618i	$-0.326823\pi$
$41$	2179.65	−	384.331i	1.29664	−	0.228632i	0.779030	+	0.626986i	$0.215712\pi$
$42$	3066.12	+	2572.78i	1.73816	+	1.45849i
$43$	961.696	−	806.959i	0.520117	−	0.436430i	−0.344555	−	0.938766i	$-0.611970\pi$
$43$	961.696	−	806.959i	0.520117	−	0.436430i	0.864673	+	0.502336i	$0.167526\pi$
$44$	−149.132	+	845.767i	−0.0770307	+	0.436863i
$45$	1387.70	−	2403.57i	0.685286	−	1.18695i
$46$	−1097.00	+	633.353i	−0.518431	+	0.299316i
$47$	−3289.42	+	1197.25i	−1.48910	+	0.541988i	−0.953212	−	0.302302i	$-0.902245\pi$
$47$	−3289.42	+	1197.25i	−1.48910	+	0.541988i	−0.535887	+	0.844290i	$0.680023\pi$
$48$	348.814	+	958.358i	0.151395	+	0.415954i
$49$	−2742.49	−	4750.13i	−1.14223	−	1.97840i
$50$	900.034	+	519.635i	0.360013	+	0.207854i
$51$	4147.57	+	731.329i	1.59461	+	0.281172i
$52$	839.021	+	999.907i	0.310289	+	0.369788i
$53$	1434.47	−	1709.54i	0.510670	−	0.608592i	−0.447679	−	0.894195i	$-0.647749\pi$
$53$	1434.47	−	1709.54i	0.510670	−	0.608592i	0.958348	+	0.285602i	$0.0921936\pi$
$54$	−719.553	−	4080.79i	−0.246760	−	1.39945i
$55$	−1618.96	−	589.254i	−0.535194	−	0.194795i
$56$		−	2009.38i		−	0.640747i
$57$	1783.48	+	5469.22i	0.548933	+	1.68336i
$58$	−49.6541			−0.0147604
$59$	−5.13114	+	14.0977i	−0.00147404	+	0.00404989i	−0.940427	−	0.339994i	$-0.889575\pi$
$59$	−5.13114	+	14.0977i	−0.00147404	+	0.00404989i	0.938953	+	0.344044i	$0.111797\pi$
$60$	−2014.86	+	355.274i	−0.559684	+	0.0986873i
$61$	−980.402	−	822.655i	−0.263478	−	0.221084i	0.501472	−	0.865174i	$-0.332792\pi$
$61$	−980.402	−	822.655i	−0.263478	−	0.221084i	−0.764950	+	0.644089i	$0.777236\pi$
$62$	331.354	−	278.039i	0.0862004	−	0.0723307i
$63$	−2666.76	+	15123.9i	−0.671896	+	3.81051i
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−2267.71	+	1309.26i	−0.536736	+	0.309885i
$66$	−4546.76	+	1654.89i	−1.04379	+	0.379909i
$67$	−995.646	−	2735.51i	−0.221797	−	0.609382i	0.778026	−	0.628233i	$-0.216221\pi$
$67$	−995.646	−	2735.51i	−0.221797	−	0.609382i	−0.999822	+	0.0188510i	$0.993999\pi$
$68$	−1057.16	−	1831.05i	−0.228624	−	0.395989i
$69$	−6180.50	−	3568.31i	−1.29815	−	0.749488i
$70$	3969.77	+	699.978i	0.810158	+	0.142853i
$71$	2687.01	+	3202.26i	0.533031	+	0.635242i	0.963610	−	0.267311i	$-0.0861350\pi$
$71$	2687.01	+	3202.26i	0.533031	+	0.635242i	−0.430579	+	0.902553i	$0.641691\pi$
$72$	−2515.29	+	2997.60i	−0.485202	+	0.578242i
$73$	−1216.01	−	6896.32i	−0.228187	−	1.29411i	−0.856498	−	0.516150i	$-0.827365\pi$
$73$	−1216.01	−	6896.32i	−0.228187	−	1.29411i	0.628312	−	0.777962i	$-0.283746\pi$
$74$	−2950.19	−	1073.78i	−0.538748	−	0.196088i
$75$			5855.25i			1.04093i
$76$	1527.80	−	2450.79i	0.264509	−	0.424305i
$77$	9533.16			1.60789
$78$	−2515.21	+	6910.48i	−0.413414	+	1.13585i
$79$	4113.42	−	725.307i	0.659096	−	0.116216i	0.165911	−	0.986141i	$-0.446944\pi$
$79$	4113.42	−	725.307i	0.659096	−	0.116216i	0.493185	+	0.869924i	$0.335832\pi$
$80$	786.820	+	660.221i	0.122941	+	0.103159i
$81$	7153.36	−	6002.38i	1.09028	−	0.914858i
$82$	1087.05	−	6164.97i	0.161667	−	0.916861i
$83$	−1506.19	+	2608.79i	−0.218636	+	0.378689i	−0.954391	−	0.298559i	$-0.903494\pi$
$83$	−1506.19	+	2608.79i	−0.218636	+	0.378689i	0.735755	+	0.677248i	$0.236828\pi$
$84$	9804.16	−	5660.44i	1.38948	−	0.802216i
$85$	3985.73	−	1450.69i	0.551658	−	0.200787i
$86$	−1214.45	−	3336.68i	−0.164204	−	0.451147i
$87$	−139.876	−	242.272i	−0.0184801	−	0.0320085i
$88$	2103.66	+	1214.55i	0.271650	+	0.156837i
$89$	−14171.4	−	2498.80i	−1.78909	−	0.315465i	−0.821922	−	0.569600i	$-0.807098\pi$
$89$	−14171.4	−	2498.80i	−1.78909	−	0.315465i	−0.967169	+	0.254135i	$0.918209\pi$
$90$	−5045.91	−	6013.48i	−0.622952	−	0.742405i
$91$	9313.45	−	11099.3i	1.12468	−	1.34034i
$92$	622.144	+	3528.35i	0.0735047	+	0.416866i
$93$	2290.03	+	833.503i	0.264774	+	0.0963699i
$94$			9900.98i			1.12053i
$95$	4309.60	+	3872.10i	0.477518	+	0.429042i
$96$	2884.61			0.313000
$97$	−1115.04	+	3063.55i	−0.118508	+	0.325598i	−0.984737	−	0.174049i	$-0.944315\pi$
$97$	−1115.04	+	3063.55i	−0.118508	+	0.325598i	0.866229	+	0.499647i	$0.166537\pi$
$98$	−15278.2	+	2693.95i	−1.59081	+	0.280503i
$99$	−14221.6	−	11933.3i	−1.45104	−	1.21756i
$100$	2251.79	−	1889.47i	0.225179	−	0.188947i
$101$	−553.995	+	3141.86i	−0.0543079	+	0.307995i	−0.999847	−	0.0175144i	$-0.994425\pi$
$101$	−553.995	+	3141.86i	−0.0543079	+	0.307995i	0.945539	+	0.325510i	$0.105536\pi$
$102$	5956.04	−	10316.2i	0.572476	−	0.991557i
$103$	−3282.94	+	1895.41i	−0.309449	+	0.178660i	−0.646680	−	0.762762i	$-0.723843\pi$
$103$	−3282.94	+	1895.41i	−0.309449	+	0.178660i	0.337231	+	0.941422i	$0.390510\pi$
$104$	3469.26	−	1262.71i	0.320752	−	0.116744i
$105$	7767.54	+	21341.1i	0.704538	+	1.93570i
$106$	−3156.02	−	5466.38i	−0.280884	−	0.486506i
$107$	8893.39	+	5134.60i	0.776784	+	0.448476i	0.835289	−	0.549811i	$-0.185300\pi$
$107$	8893.39	+	5134.60i	0.776784	+	0.448476i	−0.0585056	+	0.998287i	$0.518634\pi$
$108$	−11542.2	−	2035.20i	−0.989559	−	0.174486i
$109$	10364.2	+	12351.6i	0.872338	+	1.03961i	0.998864	+	0.0476488i	$0.0151728\pi$
$109$	10364.2	+	12351.6i	0.872338	+	1.03961i	−0.126526	+	0.991963i	$0.540383\pi$
$110$	−3132.30	+	3732.93i	−0.258868	+	0.308507i
$111$	−3071.50	−	17419.4i	−0.249290	−	1.41379i
$112$	−5340.64	−	1943.84i	−0.425753	−	0.154961i
$113$		−	15445.0i		−	1.20957i	−0.796390	−	0.604783i	$-0.793260\pi$
$113$		−	15445.0i		−	1.20957i	0.796390	−	0.604783i	$-0.206740\pi$
$114$	16261.7	+	550.575i	1.25128	+	0.0423649i
$115$	−7187.41			−0.543471
$116$	−48.0344	+	131.973i	−0.00356974	+	0.00980777i
$117$	−27787.7	+	4899.72i	−2.02993	+	0.357931i
$118$	32.5058	+	27.2756i	0.00233452	+	0.00195889i
$119$	−17978.9	+	15086.0i	−1.26960	+	1.06532i
$120$	−1004.87	+	5698.89i	−0.0697825	+	0.395756i
$121$	1558.30	−	2699.05i	0.106434	−	0.184349i
$122$	−3134.92	+	1809.95i	−0.210623	+	0.121603i
$123$	33142.3	−	12062.8i	2.19065	−	0.797330i
$124$	−418.442	−	1149.66i	−0.0272140	−	0.0747698i
$125$	7963.70	+	13793.5i	0.509676	+	0.882786i
$126$	37617.4	+	21718.4i	2.36945	+	1.36800i
$127$	−9089.10	−	1602.65i	−0.563525	−	0.0993647i	−0.115373	−	0.993322i	$-0.536806\pi$
$127$	−9089.10	−	1602.65i	−0.563525	−	0.0993647i	−0.448152	+	0.893958i	$0.647918\pi$
$128$	−930.856	−	1109.35i	−0.0568149	−	0.0677094i
$129$	12859.2	−	15325.0i	0.772742	−	0.920918i
$130$	1286.09	+	7293.79i	0.0761002	+	0.431585i
$131$	7739.88	+	2817.08i	0.451015	+	0.164156i	0.557533	−	0.830155i	$-0.311748\pi$
$131$	7739.88	+	2817.08i	0.451015	+	0.164156i	−0.106518	+	0.994311i	$0.533970\pi$
$132$			13685.5i			0.785441i
$133$	−29736.3	−	11977.5i	−1.68106	−	0.677117i
$134$	−8233.76			−0.458552
$135$	8041.57	−	22094.0i	0.441239	−	1.21229i
$136$	−5889.34	+	1038.45i	−0.318412	+	0.0561446i
$137$	5824.23	+	4887.11i	0.310311	+	0.260382i	0.784621	−	0.619976i	$-0.212858\pi$
$137$	5824.23	+	4887.11i	0.310311	+	0.260382i	−0.474310	+	0.880358i	$0.657302\pi$
$138$	−15462.9	+	12974.9i	−0.811958	+	0.681314i
$139$	−4065.61	+	23057.2i	−0.210425	+	1.19338i	0.678247	+	0.734834i	$0.262740\pi$
$139$	−4065.61	+	23057.2i	−0.210425	+	1.19338i	−0.888672	+	0.458543i	$0.848371\pi$
$140$	5700.72	−	9873.93i	0.290853	−	0.503772i
$141$	−48308.8	+	27891.1i	−2.42990	+	1.40290i
$142$	11110.5	−	4043.88i	0.551006	−	0.200550i
$143$	5990.68	+	16459.3i	0.292957	+	0.804893i
$144$	5533.95	+	9585.09i	0.266877	+	0.462244i
$145$	−243.996	−	140.871i	−0.0116050	−	0.00670018i
$146$	−19505.7	−	3439.39i	−0.915075	−	0.161352i
$147$	−56183.0	−	66956.2i	−2.59998	−	3.09853i
$148$	−5707.90	+	6802.41i	−0.260587	+	0.310555i
$149$	−295.967	−	1678.51i	−0.0133313	−	0.0756053i	0.977416	−	0.211323i	$-0.0677771\pi$
$149$	−295.967	−	1678.51i	−0.0133313	−	0.0756053i	−0.990748	+	0.135718i	$0.956666\pi$
$150$	15562.4	+	5664.24i	0.691661	+	0.251744i
$151$			24925.6i			1.09318i	0.837400	+	0.546591i	$0.184075\pi$
$151$			24925.6i			1.09318i	−0.837400	+	0.546591i	$0.815925\pi$
$152$	−5035.86	−	6431.52i	−0.217965	−	0.278372i
$153$	45705.2			1.95246
$154$	9222.18	−	25337.7i	0.388859	−	1.06838i
$155$	2417.06	−	426.192i	0.100606	−	0.0177395i
$156$	15933.9	+	13370.1i	0.654745	+	0.549397i
$157$	34509.6	−	28957.0i	1.40004	−	1.17478i	0.438962	−	0.898505i	$-0.355346\pi$
$157$	34509.6	−	28957.0i	1.40004	−	1.17478i	0.961080	−	0.276270i	$-0.0890983\pi$
$158$	2051.48	−	11634.5i	0.0821774	−	0.466051i
$159$	17781.0	−	30797.6i	0.703335	−	1.21821i
$160$	2515.92	−	1452.57i	0.0982782	−	0.0567410i
$161$	37371.8	−	13602.2i	1.44176	−	0.524757i
$162$	−9033.43	−	24819.1i	−0.344209	−	0.945707i
$163$	18121.5	+	31387.4i	0.682056	+	1.18135i	0.974352	+	0.225027i	$0.0722471\pi$
$163$	18121.5	+	31387.4i	0.682056	+	1.18135i	−0.292297	+	0.956328i	$0.594420\pi$
$164$	−15334.0	−	8853.09i	−0.570122	−	0.329160i
$165$	−27037.4	−	4767.42i	−0.993108	−	0.175112i
$166$	5476.73	+	6526.91i	0.198749	+	0.236860i
$167$	−12273.3	+	14626.8i	−0.440077	+	0.524464i	−0.939802	−	0.341721i	$-0.888990\pi$
$167$	−12273.3	+	14626.8i	−0.440077	+	0.524464i	0.499724	+	0.866185i	$0.333435\pi$
$168$	−5560.26	−	31533.8i	−0.197005	−	1.11727i
$169$	−1822.63	−	663.382i	−0.0638152	−	0.0232268i
$170$		−	11996.8i		−	0.415116i
$171$	29367.6	+	55091.2i	1.00433	+	1.88404i
$172$	−10043.2			−0.339482
$173$	5014.96	−	13778.5i	0.167562	−	0.460373i	−0.827282	−	0.561786i	$-0.810114\pi$
$173$	5014.96	−	13778.5i	0.167562	−	0.460373i	0.994844	+	0.101413i	$0.0323365\pi$
$174$	−779.236	+	137.400i	−0.0257378	+	0.00453826i
$175$	−24995.7	−	20973.9i	−0.816185	−	0.684861i
$176$	5263.12	−	4416.28i	0.169910	−	0.142571i
$177$	−41.5140	+	235.437i	−0.00132510	+	0.00751500i
$178$	−20350.5	+	35248.2i	−0.642297	+	1.11249i
$179$	34640.2	−	19999.5i	1.08112	−	0.624185i	0.149922	−	0.988698i	$-0.452098\pi$
$179$	34640.2	−	19999.5i	1.08112	−	0.624185i	0.931199	+	0.364512i	$0.118764\pi$
$180$	−20864.3	+	7593.97i	−0.643958	+	0.234382i
$181$	8866.27	+	24359.9i	0.270635	+	0.743563i	0.998336	+	0.0576684i	$0.0183666\pi$
$181$	8866.27	+	24359.9i	0.270635	+	0.743563i	−0.727701	+	0.685894i	$0.759411\pi$
$182$	−20490.8	−	35491.1i	−0.618608	−	1.07146i
$183$	−17662.1	−	10197.2i	−0.527401	−	0.304495i
$184$	9979.69	+	1759.69i	0.294769	+	0.0519757i
$185$	−11450.6	−	13646.3i	−0.334568	−	0.398723i
$186$	4430.66	−	5280.25i	0.128068	−	0.152626i
$187$	−4926.74	−	27940.9i	−0.140889	−	0.799020i
$188$	26315.4	+	9578.00i	0.744549	+	0.270994i
$189$			130099.i			3.64210i
$190$	14460.5	−	7708.50i	0.400568	−	0.213532i
$191$	68506.8			1.87788			0.938938	−	0.344087i	$-0.111812\pi$
$191$	68506.8			1.87788			0.938938	+	0.344087i	$0.111812\pi$
$192$	2790.51	−	7666.87i	0.0756975	−	0.207977i
$193$	−36319.4	+	6404.09i	−0.975044	+	0.171927i	−0.638399	−	0.769705i	$-0.720403\pi$
$193$	−36319.4	+	6404.09i	−0.975044	+	0.171927i	−0.336645	+	0.941632i	$0.609292\pi$
$194$	7063.79	+	5927.23i	0.187687	+	0.157488i
$195$	−31964.9	+	26821.7i	−0.840628	+	0.705371i
$196$	−7619.65	+	43213.2i	−0.198346	+	1.12487i
$197$	−7117.30	+	12327.5i	−0.183393	+	0.317646i	−0.943034	−	0.332697i	$-0.892041\pi$
$197$	−7117.30	+	12327.5i	−0.183393	+	0.317646i	0.759641	+	0.650343i	$0.225375\pi$
$198$	−45474.7	+	26254.9i	−1.15995	+	0.669698i
$199$	−14247.9	+	5185.81i	−0.359786	+	0.130952i	−0.515588	−	0.856837i	$-0.672426\pi$
$199$	−14247.9	+	5185.81i	−0.359786	+	0.130952i	0.155801	+	0.987788i	$0.450204\pi$
$200$	−2843.61	−	7812.75i	−0.0710902	−	0.195319i
$201$	−23194.5	−	40174.1i	−0.574107	−	0.994383i
$202$	7814.67	+	4511.80i	0.191517	+	0.110573i
$203$	1535.29	+	270.713i	0.0372561	+	0.00656926i
$204$	−21657.1	−	25809.9i	−0.520403	−	0.620192i
$205$	22832.0	−	27210.1i	0.543296	−	0.647474i
$206$	1861.86	+	10559.2i	0.0438746	+	0.248825i
$207$	−72778.3	−	26489.1i	−1.69848	−	0.618197i
$208$		−	10442.3i		−	0.241362i
$209$	30513.2	−	23891.8i	0.698546	−	0.546960i
$210$	64235.7			1.45659
$211$	−21166.1	+	58153.5i	−0.475419	+	1.30620i	0.437923	+	0.899012i	$0.355714\pi$
$211$	−21166.1	+	58153.5i	−0.475419	+	1.30620i	−0.913343	+	0.407192i	$0.866508\pi$
$212$	−17581.9	+	3100.16i	−0.391196	+	0.0689783i
$213$	51029.1	+	42818.5i	1.12476	+	0.943784i
$214$	22250.3	−	18670.2i	0.485857	−	0.407682i
$215$	3498.61	−	19841.6i	0.0756866	−	0.429240i
$216$	−16575.0	+	28708.7i	−0.355259	+	0.615327i
$217$	−11761.2	+	6790.34i	−0.249766	+	0.144202i
$218$	42855.0	−	15597.9i	0.901754	−	0.328212i
$219$	−38166.3	−	104861.i	−0.795777	−	2.18638i
$220$	6891.45	+	11936.3i	0.142385	+	0.246619i
$221$	−37344.5	−	21560.8i	−0.764613	−	0.441450i
$222$	−49269.4	−	8687.52i	−0.999704	−	0.176275i
$223$	17105.9	+	20386.0i	0.343982	+	0.409941i	0.910104	−	0.414380i	$-0.136002\pi$
$223$	17105.9	+	20386.0i	0.343982	+	0.409941i	−0.566122	+	0.824321i	$0.691557\pi$
$224$	−10332.9	+	12314.2i	−0.205932	+	0.245420i
$225$	11034.1	+	62577.8i	0.217958	+	1.23610i
$226$	−41050.4	−	14941.1i	−0.803712	−	0.292527i
$227$		−	332.292i		−	0.00644863i	−0.999995	−	0.00322432i	$-0.998974\pi$
$227$		−	332.292i		−	0.00644863i	0.999995	−	0.00322432i	$-0.00102633\pi$
$228$	17194.6	−	42688.5i	0.330766	−	0.821186i
$229$	−67105.3			−1.27963			−0.639817	−	0.768527i	$-0.720990\pi$
$229$	−67105.3			−1.27963			−0.639817	+	0.768527i	$0.720990\pi$
$230$	−6952.95	+	19103.1i	−0.131436	+	0.361117i
$231$	149607.	−	26379.7i	2.80367	−	0.494362i
$232$	304.298	+	255.337i	0.00565358	+	0.00474392i
$233$	−29844.3	+	25042.3i	−0.549730	+	0.461278i	−0.874850	−	0.484395i	$-0.839040\pi$
$233$	−29844.3	+	25042.3i	−0.549730	+	0.461278i	0.325119	+	0.945673i	$0.394595\pi$
$234$	−13858.5	+	78595.4i	−0.253095	+	1.43538i
$235$	−28089.6	+	48652.5i	−0.508639	+	0.880988i
$236$	103.940	−	60.0098i	0.00186620	−	0.00107745i
$237$	62546.0	−	22764.9i	1.11353	−	0.405293i
$238$	22704.1	+	62379.1i	0.400821	+	1.10125i
$239$	−20752.8	−	35944.8i	−0.363312	−	0.629275i	0.625192	−	0.780471i	$-0.285021\pi$
$239$	−20752.8	−	35944.8i	−0.363312	−	0.629275i	−0.988504	+	0.151196i	$0.951687\pi$
$240$	14174.7	+	8183.78i	0.246089	+	0.142079i
$241$	30587.3	+	5393.37i	0.526632	+	0.0928594i	0.430642	−	0.902523i	$-0.358287\pi$
$241$	30587.3	+	5393.37i	0.526632	+	0.0928594i	0.0959899	+	0.995382i	$0.469398\pi$
$242$	−5666.22	−	6752.74i	−0.0967526	−	0.115305i
$243$	19372.0	−	23086.6i	0.328066	−	0.390974i
$244$	1777.91	+	10083.0i	0.0298628	+	0.169361i
$245$	−82718.4	−	30107.1i	−1.37807	−	0.501575i
$246$		−	99756.7i		−	1.64843i
$247$	1993.08	−	58867.3i	0.0326686	−	0.964895i
$248$	−3460.42			−0.0562633
$249$	−16418.1	+	45108.3i	−0.264804	+	0.727542i
$250$	44365.1	−	7822.76i	0.709841	−	0.125164i
$251$	18732.7	+	15718.6i	0.297340	+	0.249498i	0.779236	−	0.626731i	$-0.215607\pi$
$251$	18732.7	+	15718.6i	0.297340	+	0.249498i	−0.481896	+	0.876228i	$0.660052\pi$
$252$	94114.6	−	78971.6i	1.48203	−	1.24357i
$253$	−8348.53	+	47346.9i	−0.130427	+	0.739691i
$254$	−13052.2	+	22607.1i	−0.202310	+	0.350411i
$255$	58534.9	−	33795.1i	0.900190	−	0.519725i
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	11712.5	+	32179.8i	0.177330	+	0.487210i	0.996233	−	0.0867223i	$-0.0276393\pi$
$257$	11712.5	+	32179.8i	0.177330	+	0.487210i	−0.818902	+	0.573933i	$0.805417\pi$
$258$	−28291.8	−	49002.9i	−0.425032	−	0.736177i
$259$	85364.5	+	49285.2i	1.27256	+	0.734712i
$260$	20630.0	+	3637.62i	0.305177	+	0.0538109i
$261$	−1951.48	−	2325.68i	−0.0286472	−	0.0341404i
$262$	14974.8	−	17846.3i	0.218151	−	0.259983i
$263$	−19159.1	−	108656.i	−0.276989	−	1.57088i	−0.732572	−	0.680689i	$-0.761680\pi$
$263$	−19159.1	−	108656.i	−0.276989	−	1.57088i	0.455583	−	0.890193i	$-0.349431\pi$
$264$	36374.1	+	13239.1i	0.521896	+	0.189955i
$265$		−	35815.1i		−	0.510005i
$266$	−60600.7	+	67447.9i	−0.856475	+	0.953246i
$267$	−229310.			−3.21663
$268$	−7965.17	+	21884.1i	−0.110898	+	0.304691i
$269$	−6165.00	+	1087.06i	−0.0851978	+	0.0150227i	−0.216085	−	0.976375i	$-0.569329\pi$
$269$	−6165.00	+	1087.06i	−0.0851978	+	0.0150227i	0.130887	+	0.991397i	$0.458218\pi$
$270$	−50943.4	−	42746.6i	−0.698813	−	0.586374i
$271$	56405.9	−	47330.1i	0.768043	−	0.644465i	−0.172164	−	0.985068i	$-0.555076\pi$
$271$	56405.9	−	47330.1i	0.768043	−	0.644465i	0.940207	+	0.340604i	$0.110631\pi$
$272$	−2937.18	+	16657.6i	−0.0397002	+	0.225151i
$273$	115445.	−	199957.i	1.54900	−	2.68294i
$274$	18623.4	−	10752.2i	0.248061	−	0.143218i
$275$	37066.2	−	13491.0i	0.490132	−	0.178393i
$276$	19527.0	+	53649.9i	0.256340	+	0.704288i
$277$	−26652.4	−	46163.3i	−0.347357	−	0.601641i	0.638422	−	0.769687i	$-0.279588\pi$
$277$	−26652.4	−	46163.3i	−0.347357	−	0.601641i	−0.985779	+	0.168046i	$0.946254\pi$
$278$	57349.7	+	33110.9i	0.742065	+	0.428431i
$279$	26045.4	+	4592.50i	0.334597	+	0.0589985i
$280$	−20728.7	−	24703.5i	−0.264397	−	0.315096i
$281$	10837.6	−	12915.8i	0.137253	−	0.163572i	−0.693040	−	0.720900i	$-0.743729\pi$
$281$	10837.6	−	12915.8i	0.137253	−	0.163572i	0.830293	+	0.557328i	$0.188173\pi$
$282$	27397.5	+	155379.i	0.344518	+	1.95386i
$283$	−138732.	−	50494.4i	−1.73223	−	0.630479i	−0.733442	−	0.679752i	$-0.762087\pi$
$283$	−138732.	−	50494.4i	−1.73223	−	0.630479i	−0.998785	+	0.0492734i	$0.984309\pi$
$284$		−	33442.0i		−	0.414625i
$285$	78346.5	+	48840.7i	0.964561	+	0.601301i
$286$	49541.6			0.605672
$287$	−67222.4	+	184692.i	−0.816113	+	2.24225i
$288$	30829.2	−	5436.01i	0.371687	−	0.0655384i
$289$	−10473.3	−	8788.16i	−0.125398	−	0.105221i
$290$	−610.451	+	512.230i	−0.00725864	+	0.00609072i
$291$	−9021.35	+	51162.6i	−0.106533	+	0.604180i
$292$	−28010.8	+	48516.2i	−0.328519	+	0.569011i
$293$	−90933.1	+	52500.2i	−1.05922	+	0.611542i	−0.925217	−	0.379439i	$-0.876117\pi$
$293$	−90933.1	+	52500.2i	−1.05922	+	0.611542i	−0.134004	+	0.990981i	$0.542784\pi$
$294$	−232310.	+	84553.9i	−2.68765	+	0.978226i
$295$	82.3484	+	226.250i	0.000946261	+	0.00259983i
$296$	12558.1	+	21751.3i	0.143331	+	0.248257i
$297$	−136203.	−	78637.0i	−1.54410	−	0.891485i
$298$	−4747.55	−	837.122i	−0.0534610	−	0.00942662i
$299$	46969.2	+	55975.8i	0.525377	+	0.626120i
$300$	30109.4	−	35883.0i	0.334549	−	0.398700i
$301$	19359.0	+	109790.i	0.213673	+	1.21180i
$302$	66248.6	+	24112.5i	0.726378	+	0.264380i
$303$			50839.0i			0.553748i
$304$	−21965.6	+	7162.87i	−0.237682	+	0.0775068i
$305$	−20539.6			−0.220797
$306$	44214.3	−	121478.i	0.472193	−	1.29734i
$307$	−46547.5	+	8207.57i	−0.493878	+	0.0870839i	−0.415039	−	0.909803i	$-0.636232\pi$
$307$	−46547.5	+	8207.57i	−0.493878	+	0.0870839i	−0.0788383	+	0.996887i	$0.525121\pi$
$308$	−58422.6	−	49022.4i	−0.615856	−	0.516765i
$309$	−46275.3	+	38829.6i	−0.484654	+	0.406673i
$310$	1205.45	−	6836.47i	0.0125437	−	0.0711391i
$311$	−54118.8	+	93736.5i	−0.559535	+	0.969143i	0.438000	+	0.898975i	$0.355687\pi$
$311$	−54118.8	+	93736.5i	−0.559535	+	0.969143i	−0.997535	+	0.0701680i	$0.977646\pi$
$312$	50949.9	−	29415.9i	0.523400	−	0.302185i
$313$	95581.5	−	34788.8i	0.975630	−	0.355100i	0.195491	−	0.980706i	$-0.437370\pi$
$313$	95581.5	−	34788.8i	0.975630	−	0.355100i	0.780140	+	0.625605i	$0.215148\pi$
$314$	−43579.6	−	119734.i	−0.442002	−	1.21439i
$315$	123232.	+	213445.i	1.24195	+	2.15112i
$316$	−28938.2	−	16707.5i	−0.289800	−	0.167316i
$317$	111336.	+	19631.6i	1.10795	+	0.195361i	0.697542	−	0.716544i	$-0.254277\pi$
$317$	111336.	+	19631.6i	1.10795	+	0.195361i	0.410403	+	0.911904i	$0.365388\pi$
$318$	−64654.5	−	77052.3i	−0.639359	−	0.761958i
$319$	−1211.40	+	1443.69i	−0.0119044	+	0.0141871i
$320$	−1426.86	−	8092.13i	−0.0139342	−	0.0790247i
$321$	153775.	+	55969.4i	1.49236	+	0.543176i
$322$		−	112487.i		−	1.08490i
$323$	−19737.4	+	93344.7i	−0.189184	+	0.894715i
$324$	−74704.4			−0.711633
$325$	20504.5	−	56335.8i	0.194126	−	0.533357i
$326$	100954.	−	17800.8i	0.949918	−	0.167496i
$327$	196828.	+	165158.i	1.84073	+	1.54456i
$328$	−38364.0	+	32191.2i	−0.356596	+	0.299219i
$329$	53979.8	−	306135.i	0.498700	−	2.82827i
$330$	−38826.5	+	67249.4i	−0.356533	+	0.617534i
$331$	−58419.3	+	33728.4i	−0.533213	+	0.307850i	−0.742324	−	0.670041i	$-0.766276\pi$
$331$	−58419.3	+	33728.4i	−0.533213	+	0.307850i	0.209111	+	0.977892i	$0.432943\pi$
$332$	22645.6	−	8242.34i	0.205451	−	0.0747780i
$333$	−65653.2	−	180381.i	−0.592062	−	1.62668i
$334$	27002.8	+	46770.3i	0.242056	+	0.419254i
$335$	−40460.0	−	23359.6i	−0.360525	−	0.208149i
$336$	−89191.1	−	15726.8i	−0.790029	−	0.139303i
$337$	51050.1	+	60839.2i	0.449508	+	0.535702i	0.942444	−	0.334363i	$-0.108521\pi$
$337$	51050.1	+	60839.2i	0.449508	+	0.535702i	−0.492937	+	0.870065i	$0.664077\pi$
$338$	−3526.34	+	4202.53i	−0.0308667	+	0.0367856i
$339$	−42738.5	−	242382.i	−0.371894	−	2.10912i
$340$	−31885.8	−	11605.5i	−0.275829	−	0.100394i
$341$		−	16417.3i		−	0.141187i
$342$	174834.	−	24760.7i	1.49477	−	0.211695i
$343$	273867.			2.32783
$344$	−9715.62	+	26693.5i	−0.0821020	+	0.225573i
$345$	−112794.	+	19888.6i	−0.947649	+	0.167096i
$346$	−31769.8	−	26658.1i	−0.265377	−	0.222678i
$347$	−50060.9	+	42006.1i	−0.415757	+	0.348862i	−0.826546	−	0.562869i	$-0.809698\pi$
$347$	−50060.9	+	42006.1i	−0.415757	+	0.348862i	0.410789	+	0.911730i	$0.365253\pi$
$348$	−388.627	+	2204.01i	−0.00320903	+	0.0181993i
$349$	42877.3	−	74265.6i	0.352027	−	0.609729i	−0.634577	−	0.772859i	$-0.718826\pi$
$349$	42877.3	−	74265.6i	0.352027	−	0.609729i	0.986605	+	0.163130i	$0.0521591\pi$
$350$	−79925.7	+	46145.1i	−0.652455	+	0.376695i
$351$	−224620.	+	81755.1i	−1.82320	+	0.663591i
$352$	−6646.39	−	18260.8i	−0.0536415	−	0.147379i
$353$	−28537.0	−	49427.5i	−0.229012	−	0.396661i	0.728503	−	0.685042i	$-0.240216\pi$
$353$	−28537.0	−	49427.5i	−0.229012	−	0.396661i	−0.957516	+	0.288381i	$0.906883\pi$
$354$	585.598	+	338.095i	0.00467297	+	0.00269794i
$355$	66068.6	+	11649.7i	0.524250	+	0.0924394i
$356$	73997.7	+	88187.1i	0.583873	+	0.695833i
$357$	−240402.	+	286500.i	−1.88626	+	2.24796i
$358$	−19645.6	−	111416.i	−0.153285	−	0.869321i
$359$	−2426.13	−	883.040i	−0.0188246	−	0.00685159i	0.332591	−	0.943071i	$-0.392077\pi$
$359$	−2426.13	−	883.040i	−0.0188246	−	0.00685159i	−0.351415	+	0.936220i	$0.614299\pi$
$360$			62800.3i			0.484571i
$361$	−125196.	+	36187.4i	−0.960674	+	0.277679i
$362$	73322.0			0.559522
$363$	16986.1	−	46669.0i	0.128908	−	0.354173i
$364$	−114152.	+	20128.1i	−0.861553	+	0.151915i
$365$	−86091.7	−	72239.5i	−0.646213	−	0.542237i
$366$	−44188.7	+	37078.7i	−0.329875	+	0.276798i
$367$	33443.2	−	189666.i	0.248299	−	1.40817i	−0.564405	−	0.825498i	$-0.690894\pi$
$367$	33443.2	−	189666.i	0.248299	−	1.40817i	0.812704	−	0.582676i	$-0.197994\pi$
$368$	14331.1	−	24822.3i	0.105824	−	0.183293i
$369$	331475.	−	191377.i	2.43443	−	1.40552i
$370$	−47346.8	+	17232.8i	−0.345850	+	0.125879i
$371$	67780.3	+	186225.i	0.492443	+	1.35298i
$372$	−9748.00	−	16884.0i	−0.0704417	−	0.122009i
$373$	−145417.	−	83956.3i	−1.04519	−	0.603442i	−0.123893	−	0.992296i	$-0.539538\pi$
$373$	−145417.	−	83956.3i	−1.04519	−	0.603442i	−0.921300	+	0.388853i	$0.872871\pi$
$374$	−79028.9	−	13934.9i	−0.564992	−	0.0996234i
$375$	163145.	+	194429.i	1.16014	+	1.38261i
$376$	50913.8	−	60676.7i	0.360131	−	0.429187i
$377$	497.389	+	2820.83i	0.00349956	+	0.0198470i
$378$	345785.	+	125856.i	2.42004	+	0.880823i
$379$		−	178270.i		−	1.24108i	−0.784174	−	0.620541i	$-0.786913\pi$
$379$		−	178270.i		−	1.24108i	0.784174	−	0.620541i	$-0.213087\pi$
$380$	−6499.27	−	45890.9i	−0.0450088	−	0.317804i
$381$	−147072.			−1.01317
$382$	66272.0	−	182081.i	0.454154	−	1.24778i
$383$	−100390.	+	17701.4i	−0.684372	+	0.120673i	−0.505015	−	0.863111i	$-0.668513\pi$
$383$	−100390.	+	17701.4i	−0.684372	+	0.120673i	−0.179357	+	0.983784i	$0.557402\pi$
$384$	−17677.9	−	14833.5i	−0.119886	−	0.100596i
$385$	117201.	−	98343.6i	0.790699	−	0.663475i
$386$	−18113.5	+	102727.i	−0.121570	+	0.689460i
$387$	108552.	−	188018.i	0.724799	−	1.25539i
$388$	22587.1	−	13040.6i	0.150036	−	0.0866235i
$389$	−68990.4	+	25110.5i	−0.455921	+	0.165942i	−0.559764	−	0.828652i	$-0.689108\pi$
$389$	−68990.4	+	25110.5i	−0.455921	+	0.165942i	0.103843	+	0.994594i	$0.466886\pi$
$390$	40366.0	+	110905.i	0.265391	+	0.729157i
$391$	−59180.8	−	102504.i	−0.387104	−	0.670483i
$392$	107483.	+	62055.4i	0.699469	+	0.403839i
$393$	129259.	+	22791.9i	0.836906	+	0.147569i
$394$	25879.6	+	30842.1i	0.166711	+	0.198679i
$395$	43088.4	−	51350.8i	0.276164	−	0.329119i
$396$	25790.2	+	146264.i	0.164462	+	0.932708i
$397$	185557.	+	67537.2i	1.17732	+	0.428511i	0.855256	−	0.518206i	$-0.173400\pi$
$397$	185557.	+	67537.2i	1.17732	+	0.428511i	0.322068	+	0.946717i	$0.395622\pi$
$398$			42885.5i			0.270735i
$399$	−499804.	−	105682.i	−3.13945	−	0.663826i
$400$	−23516.0			−0.146975
$401$	54660.3	−	150178.i	0.339925	−	0.933937i	−0.645490	−	0.763769i	$-0.723347\pi$
$401$	54660.3	−	150178.i	0.339925	−	0.933937i	0.985415	−	0.170168i	$-0.0544311\pi$
$402$	−129215.	+	22784.0i	−0.799576	+	0.140987i
$403$	−19114.5	−	16039.0i	−0.117694	−	0.0987567i
$404$	19551.5	−	16405.6i	0.119789	−	0.100515i
$405$	26023.6	−	147587.i	0.158656	−	0.899786i
$406$	2204.72	−	3818.69i	0.0133752	−	0.0231666i
$407$	−103195.	+	59579.6i	−0.622974	+	0.359674i
$408$	−89549.5	+	32593.4i	−0.537951	+	0.195798i
$409$	104020.	+	285792.i	0.621827	+	1.70846i	0.702470	+	0.711713i	$0.252080\pi$
$409$	104020.	+	285792.i	0.621827	+	1.70846i	−0.0806432	+	0.996743i	$0.525697\pi$
$410$	−50233.3	−	87006.6i	−0.298830	−	0.517588i
$411$	104925.	+	60578.2i	0.621146	+	0.358619i
$412$	29865.8	+	5266.15i	0.175946	+	0.0310241i
$413$	−856.362	−	1020.57i	−0.00502062	−	0.00598334i
$414$	−140808.	+	167809.i	−0.821538	+	0.979071i
$415$	8395.00	+	47610.4i	0.0487443	+	0.276443i
$416$	−27754.0	−	10101.6i	−0.160376	−	0.0583721i
$417$			373094.i			2.14559i
$418$	−33983.0	−	104212.i	−0.194495	−	0.596438i
$419$	247706.			1.41094			0.705469	−	0.708741i	$-0.250736\pi$
$419$	247706.			1.41094			0.705469	+	0.708741i	$0.250736\pi$
$420$	62140.3	−	170729.i	0.352269	−	0.967852i
$421$	53326.4	−	9402.88i	0.300869	−	0.0530514i	−0.0211756	−	0.999776i	$-0.506741\pi$
$421$	53326.4	−	9402.88i	0.300869	−	0.0530514i	0.322045	+	0.946724i	$0.395630\pi$
$422$	134088.	+	112513.i	0.752947	+	0.631797i
$423$	−463738.	+	389122.i	−2.59174	+	2.17473i
$424$	−8768.58	+	49729.1i	−0.0487751	+	0.276617i
$425$	−48554.9	+	84099.6i	−0.268816	+	0.465603i
$426$	163170.	−	94206.1i	0.899126	−	0.519111i
$427$	106798.	−	38871.4i	0.585745	−	0.213194i
$428$	−28098.2	−	77199.2i	−0.153388	−	0.421430i
$429$	139559.	+	241723.i	0.758302	+	1.31342i
$430$	−49351.6	−	28493.2i	−0.266910	−	0.154100i
$431$	−71340.1	−	12579.2i	−0.384043	−	0.0677171i	−0.0217060	−	0.999764i	$-0.506910\pi$
$431$	−71340.1	−	12579.2i	−0.384043	−	0.0677171i	−0.362337	+	0.932047i	$0.618021\pi$
$432$	60269.2	+	71826.0i	0.322944	+	0.384870i
$433$	−75361.5	+	89812.3i	−0.401952	+	0.479027i	−0.928614	−	0.371047i	$-0.878999\pi$
$433$	−75361.5	+	89812.3i	−0.401952	+	0.479027i	0.526662	+	0.850075i	$0.323443\pi$
$434$	6670.16	+	37828.4i	0.0354125	+	0.200835i
$435$	−4218.91	−	1535.56i	−0.0222957	−	0.00811498i
$436$		−	128991.i		−	0.678559i
$437$	85528.0	−	137198.i	0.447863	−	0.718428i
$438$	−315626.			−1.64522
$439$	−15447.4	+	42441.3i	−0.0801541	+	0.220222i	−0.973296	−	0.229553i	$-0.926274\pi$
$439$	−15447.4	+	42441.3i	−0.0801541	+	0.220222i	0.893142	+	0.449775i	$0.148496\pi$
$440$	38391.7	−	6769.49i	0.198304	−	0.0349664i
$441$	−726632.	−	609716.i	−3.73626	−	3.13509i
$442$	−93431.8	+	78398.6i	−0.478245	+	0.401295i
$443$	11464.9	−	65020.5i	0.0584201	−	0.331317i	−0.941565	−	0.336832i	$-0.890645\pi$
$443$	11464.9	−	65020.5i	0.0584201	−	0.331317i	0.999985	+	0.00551549i	$0.00175564\pi$
$444$	−70752.3	+	122547.i	−0.358901	+	0.621635i
$445$	−200001.	+	115471.i	−1.00998	+	0.583113i
$446$	70730.7	−	25743.9i	0.355581	−	0.129421i
$447$	−9289.39	−	25522.4i	−0.0464914	−	0.127734i
$448$	22733.6	+	39375.7i	0.113269	+	0.196188i
$449$	198226.	+	114446.i	0.983261	+	0.567686i	0.903253	−	0.429108i	$-0.141172\pi$
$449$	198226.	+	114446.i	0.983261	+	0.567686i	0.0800078	+	0.996794i	$0.474505\pi$
$450$	176997.	+	31209.3i	0.874057	+	0.154120i
$451$	−152725.	−	182011.i	−0.750859	−	0.894839i
$452$	−79422.6	+	94652.2i	−0.388747	+	0.463291i
$453$	68972.9	+	391165.i	0.336110	+	1.90618i
$454$	−883.182	−	321.452i	−0.00428488	−	0.00155957i
$455$		−	232533.i		−	1.12321i
$456$	−96826.2	−	86996.6i	−0.465654	−	0.418382i
$457$	−255910.			−1.22533			−0.612667	−	0.790341i	$-0.709903\pi$
$457$	−255910.			−1.22533			−0.612667	+	0.790341i	$0.709903\pi$
$458$	−64916.2	+	178356.i	−0.309473	+	0.850269i
$459$	381311.	−	67235.4i	1.80990	−	0.319134i
$460$	44047.0	+	36959.8i	0.208162	+	0.174668i
$461$	36789.0	−	30869.6i	0.173108	−	0.145255i	−0.552118	−	0.833766i	$-0.686180\pi$
$461$	36789.0	−	30869.6i	0.173108	−	0.145255i	0.725225	+	0.688512i	$0.241736\pi$
$462$	74613.0	−	423151.i	0.349567	−	1.98249i
$463$	33962.1	−	58824.1i	0.158428	−	0.274406i	−0.775874	−	0.630888i	$-0.782691\pi$
$463$	33962.1	−	58824.1i	0.158428	−	0.274406i	0.934302	+	0.356482i	$0.116024\pi$
$464$	973.019	−	561.773i	0.00451945	−	0.00260930i
$465$	36752.2	−	13376.7i	0.169972	−	0.0618647i
$466$	37688.1	+	103547.i	0.173553	+	0.476833i
$467$	58247.1	+	100887.i	0.267080	+	0.462595i	0.968106	−	0.250540i	$-0.0806080\pi$
$467$	58247.1	+	100887.i	0.267080	+	0.462595i	−0.701027	+	0.713135i	$0.747275\pi$
$468$	195489.	+	112865.i	0.892544	+	0.515311i
$469$	254585.	+	44890.2i	1.15741	+	0.204082i
$470$	102138.	+	121723.i	0.462372	+	0.551034i
$471$	461441.	−	549924.i	2.08005	−	2.47891i
$472$	−58.9477	−	334.309i	−0.000264596	−	0.00150060i
$473$	−126642.	−	46094.1i	−0.566053	−	0.206026i
$474$		−	188260.i		−	0.837919i
$475$	−132569.	−	4488.41i	−0.587563	−	0.0198932i
$476$	187758.			0.828675
$477$	131996.	−	362657.i	0.580129	−	1.59389i
$478$	−115612.	+	20385.5i	−0.505995	+	0.0892206i
$479$	237614.	+	199382.i	1.03562	+	0.868990i	0.991509	−	0.130037i	$-0.0415096\pi$
$479$	237614.	+	199382.i	1.03562	+	0.868990i	0.0441124	+	0.999027i	$0.485954\pi$
$480$	35463.6	−	29757.5i	0.153922	−	0.129156i
$481$	−31448.8	+	178355.i	−0.135930	+	0.770895i
$482$	43924.3	−	76079.1i	0.189065	−	0.327470i
$483$	548847.	−	316877.i	2.35265	−	1.35830i
$484$	−23429.2	+	8527.52i	−0.100015	+	0.0364025i
$485$	17895.0	+	49166.2i	0.0760762	+	0.209018i
$486$	−42620.8	−	73821.3i	−0.180447	−	0.312543i
$487$	−373037.	−	215373.i	−1.57288	−	0.908100i	−0.995814	−	0.0913992i	$-0.970866\pi$
$487$	−373037.	−	215373.i	−1.57288	−	0.908100i	−0.577061	−	0.816701i	$-0.695801\pi$
$488$	28519.2	+	5028.70i	0.119756	+	0.0211162i
$489$	371240.	+	442426.i	1.55252	+	1.85022i
$490$	−160040.	+	190728.i	−0.666556	+	0.794371i
$491$	−39054.9	−	221491.i	−0.161999	−	0.918743i	−0.952105	−	0.305772i	$-0.901085\pi$
$491$	−39054.9	−	221491.i	−0.161999	−	0.918743i	0.790106	−	0.612971i	$-0.210026\pi$
$492$	−265138.	−	96502.5i	−1.09532	−	0.398665i
$493$		−	4639.71i		−	0.0190896i
$494$	−154532.	−	62244.3i	−0.633236	−	0.255062i
$495$	−297945.			−1.21598
$496$	−3347.54	+	9197.28i	−0.0136070	+	0.0373849i
$497$	−365579.	+	64461.5i	−1.48002	+	0.260968i
$498$	104009.	+	87273.7i	0.419383	+	0.351904i
$499$	−50091.6	+	42031.8i	−0.201170	+	0.168802i	−0.737808	−	0.675011i	$-0.764139\pi$
$499$	−50091.6	+	42031.8i	−0.201170	+	0.168802i	0.536637	+	0.843813i	$0.319694\pi$
$500$	22126.1	−	125483.i	0.0885044	−	0.501933i
$501$	−152134.	+	263504.i	−0.606110	+	1.04981i
$502$	59899.4	−	34582.9i	0.237692	−	0.137232i
$503$	−373068.	+	135786.i	−1.47452	+	0.536683i	−0.949325	−	0.314296i	$-0.898231\pi$
$503$	−373068.	+	135786.i	−1.47452	+	0.536683i	−0.525199	+	0.850979i	$0.676009\pi$
$504$	−118850.	−	326538.i	−0.467885	−	1.28550i
$505$	25600.4	+	44341.2i	0.100384	+	0.173870i
$506$	117765.	+	67991.5i	0.459954	+	0.265555i
$507$	−30438.6	−	5367.15i	−0.118416	−	0.0208799i
$508$	47459.9	+	56560.5i	0.183907	+	0.219172i
$509$	112067.	−	133556.i	0.432555	−	0.515498i	−0.505103	−	0.863059i	$-0.668545\pi$
$509$	112067.	−	133556.i	0.432555	−	0.515498i	0.937658	+	0.347561i	$0.112990\pi$
$510$	−33197.0	−	188270.i	−0.127632	−	0.723836i
$511$	584359.	+	212689.i	2.23788	+	0.814523i
$512$			11585.2i			0.0441942i
$513$	326052.	+	416415.i	1.23895	+	1.58231i
$514$	96859.5			0.366620
$515$	−20807.8	+	57169.0i	−0.0784534	+	0.215549i
$516$	−157611.	+	27791.1i	−0.591954	+	0.104378i
$517$	287870.	+	241552.i	1.07700	+	0.903710i
$518$	213573.	−	179209.i	0.795950	−	0.667882i
$519$	40574.1	−	230107.i	0.150631	−	0.854270i
$520$	29625.3	−	51312.4i	0.109561	−	0.189765i
$521$	−147710.	+	85280.6i	−0.544171	+	0.314177i	−0.746768	−	0.665085i	$-0.768395\pi$
$521$	−147710.	+	85280.6i	−0.544171	+	0.314177i	0.202597	+	0.979262i	$0.435062\pi$
$522$	−8069.13	+	2936.92i	−0.0296132	+	0.0107783i
$523$	−59470.0	−	163392.i	−0.217417	−	0.597350i	0.782255	−	0.622959i	$-0.214070\pi$
$523$	−59470.0	−	163392.i	−0.217417	−	0.597350i	−0.999672	+	0.0256094i	$0.991847\pi$
$524$	−32946.4	−	57064.9i	−0.119990	−	0.207829i
$525$	−450302.	−	259982.i	−1.63375	−	0.943245i
$526$	−307327.	−	54190.0i	−1.11078	−	0.195861i
$527$	25980.1	+	30961.9i	0.0935449	+	0.111482i
$528$	70375.1	−	83869.7i	0.252436	−	0.300841i
$529$	−13765.6	−	78068.8i	−0.0491909	−	0.278976i
$530$	−95191.2	−	34646.8i	−0.338879	−	0.123342i
$531$			2594.46i			0.00920149i
$532$	120643.	+	226315.i	0.426263	+	0.799634i
$533$	−361119.			−1.27115
$534$	−221830.	+	609472.i	−0.777924	+	2.13733i
$535$	162304.	−	28618.6i	0.567051	−	0.0999865i
$536$	50459.4	+	42340.5i	0.175636	+	0.147376i
$537$	488276.	−	409713.i	1.69323	−	1.42079i
$538$	−3074.66	+	17437.3i	−0.0106226	+	0.0602440i
$539$	−294411.	+	509935.i	−1.01339	+	1.75524i
$540$	−162896.	+	94048.0i	−0.558628	+	0.322524i
$541$	235772.	−	85814.0i	0.805559	−	0.293200i	0.0937712	−	0.995594i	$-0.470108\pi$
$541$	235772.	−	85814.0i	0.805559	−	0.293200i	0.711788	+	0.702394i	$0.247886\pi$
$542$	−71230.6	−	195705.i	−0.242476	−	0.666197i
$543$	206548.	+	357752.i	0.700522	+	1.21334i
$544$	41432.0	+	23920.8i	0.140003	+	0.0808309i
$545$	254838.	+	44934.7i	0.857967	+	0.151283i
$546$	−419776.	−	500270.i	−1.40810	−	1.67810i
$547$	−302583.	+	360604.i	−1.01128	+	1.20519i	−0.0326658	+	0.999466i	$0.510400\pi$
$547$	−302583.	+	360604.i	−1.01128	+	1.20519i	−0.978610	+	0.205725i	$0.934045\pi$
$548$	−10562.0	−	59899.9i	−0.0351709	−	0.199464i
$549$	−207980.	−	75698.5i	−0.690044	−	0.251156i
$550$		−	111567.i		−	0.368818i
$551$	5592.51	−	2981.22i	0.0184206	−	0.00981952i
$552$	161483.			0.529968
$553$	−126862.	+	348550.i	−0.414840	+	1.13976i
$554$	−148478.	+	26180.7i	−0.483775	+	0.0853025i
$555$	−217458.	−	182469.i	−0.705977	−	0.592385i
$556$	143483.	−	120396.i	0.464141	−	0.389461i
$557$	−11449.8	+	64935.1i	−0.0369052	+	0.209300i	−0.997684	−	0.0680150i	$-0.978333\pi$
$557$	−11449.8	+	64935.1i	−0.0369052	+	0.209300i	0.960779	+	0.277315i	$0.0894445\pi$
$558$	37401.9	−	64782.0i	0.120123	−	0.208059i
$559$	−177390.	+	102416.i	−0.567684	+	0.327752i
$560$	−85710.7	+	31196.2i	−0.273312	+	0.0994775i
$561$	−154633.	−	424852.i	−0.491335	−	1.34993i
$562$	−23844.1	−	41299.3i	−0.0754934	−	0.130758i
$563$	−185100.	−	106867.i	−0.583968	−	0.337154i	0.178741	−	0.983896i	$-0.442798\pi$
$563$	−185100.	−	106867.i	−0.583968	−	0.337154i	−0.762709	+	0.646742i	$0.776131\pi$
$564$	439478.	+	77491.8i	1.38159	+	0.243611i
$565$	−159329.	−	189881.i	−0.499113	−	0.594820i
$566$	−268413.	+	319883.i	−0.837860	+	0.998523i
$567$	143997.	+	816649.i	0.447907	+	2.54021i
$568$	−88883.9	−	32351.1i	−0.275503	−	0.100275i
$569$		−	501633.i		−	1.54939i	−0.632333	−	0.774697i	$-0.717902\pi$
$569$		−	501633.i		−	1.54939i	0.632333	−	0.774697i	$-0.282098\pi$
$570$	205602.	−	160986.i	0.632816	−	0.495494i
$571$	281063.			0.862047			0.431023	−	0.902341i	$-0.358153\pi$
$571$	281063.			0.862047			0.431023	+	0.902341i	$0.358153\pi$
$572$	47925.5	−	131674.i	0.146479	−	0.402447i
$573$	1.07510e6	−	189568.i	3.27445	−	0.577373i
$574$	425855.	+	357335.i	1.29252	+	1.08455i
$575$	126057.	−	105775.i	0.381269	−	0.319923i
$576$	15375.4	−	87198.1i	0.0463426	−	0.262822i
$577$	40493.3	−	70136.5i	0.121627	−	0.210665i	−0.798782	−	0.601620i	$-0.794522\pi$
$577$	40493.3	−	70136.5i	0.121627	−	0.210665i	0.920410	+	0.390955i	$0.127855\pi$
$578$	−33489.3	+	19335.1i	−0.100242	+	0.0578749i
$579$	−552250.	+	201002.i	−1.64732	+	0.599576i
$580$	770.892	+	2118.01i	0.00229159	+	0.00629611i
$581$	−133754.	−	231669.i	−0.396236	−	0.686301i
$582$	127256.	+	73471.0i	0.375691	+	0.216905i
$583$	−235931.	−	41601.0i	−0.694141	−	0.122396i
$584$	101852.	+	121382.i	0.298636	+	0.355901i
$585$	−291078.	+	346894.i	−0.850547	+	1.01364i
$586$	51571.1	+	292474.i	0.150180	+	0.851711i
$587$	−428482.	−	155955.i	−1.24353	−	0.452608i	−0.365319	−	0.930882i	$-0.619040\pi$
$587$	−428482.	−	155955.i	−1.24353	−	0.452608i	−0.878210	+	0.478275i	$0.841262\pi$
$588$			699241.i			2.02242i
$589$	−20626.8	+	51209.8i	−0.0594569	+	0.147612i
$590$	681.002			0.00195634
$591$	−77581.6	+	213154.i	−0.222118	+	0.610264i
$592$	69960.0	−	12335.8i	0.199621	−	0.0351986i
$593$	249863.	+	209660.i	0.710548	+	0.596220i	0.924753	−	0.380568i	$-0.124272\pi$
$593$	249863.	+	209660.i	0.710548	+	0.596220i	−0.214205	+	0.976789i	$0.568716\pi$
$594$	−340766.	+	285936.i	−0.965791	+	0.810395i
$595$	−65406.3	+	370938.i	−0.184751	+	1.04777i
$596$	−6817.63	+	11808.5i	−0.0191929	+	0.0332431i
$597$	−209246.	+	120808.i	−0.587096	+	0.338960i
$598$	194212.	−	70687.5i	0.543093	−	0.197670i
$599$	−145144.	−	398779.i	−0.404524	−	1.11142i	−0.960027	−	0.279907i	$-0.909696\pi$
$599$	−145144.	−	398779.i	−0.404524	−	1.11142i	0.555503	−	0.831515i	$-0.312526\pi$
$600$	−66244.6	−	114739.i	−0.184013	−	0.318719i
$601$	−278065.	−	160541.i	−0.769836	−	0.444465i	0.0629804	−	0.998015i	$-0.479939\pi$
$601$	−278065.	−	160541.i	−0.769836	−	0.444465i	−0.832816	+	0.553550i	$0.813273\pi$
$602$	310533.	+	54755.4i	0.856871	+	0.151089i
$603$	−323598.	−	385649.i	−0.889962	−	1.06062i
$604$	128175.	−	152753.i	0.351342	−	0.418713i
$605$	−8685.46	−	49257.7i	−0.0237291	−	0.134575i
$606$	135123.	+	49180.6i	0.367945	+	0.133921i
$607$		−	129191.i		−	0.350634i	−0.984512	−	0.175317i	$-0.943905\pi$
$607$		−	129191.i		−	0.350634i	0.984512	−	0.175317i	$-0.0560951\pi$
$608$	−2211.23	+	65310.6i	−0.00598173	+	0.176675i
$609$	24842.8			0.0669832
$610$	−19869.6	+	54591.2i	−0.0533985	+	0.146711i
$611$	562471.	−	99178.8i	1.50667	−	0.265666i
$612$	−280098.	−	235030.i	−0.747837	−	0.627509i
$613$	121496.	−	101947.i	0.323327	−	0.271304i	−0.466647	−	0.884443i	$-0.654538\pi$
$613$	121496.	−	101947.i	0.323327	−	0.271304i	0.789974	+	0.613140i	$0.210094\pi$
$614$	−23214.5	+	131656.i	−0.0615776	+	0.349224i
$615$	283014.	−	490195.i	0.748270	−	1.29604i
$616$	−186811.	+	107855.i	−0.492313	+	0.284237i
$617$	−86595.6	+	31518.2i	−0.227471	+	0.0827926i	−0.453241	−	0.891388i	$-0.649732\pi$
$617$	−86595.6	+	31518.2i	−0.227471	+	0.0827926i	0.225770	+	0.974181i	$0.427510\pi$
$618$	58437.5	+	160556.i	0.153008	+	0.420387i
$619$	−70676.5	−	122415.i	−0.184456	−	0.319488i	0.758937	−	0.651164i	$-0.225719\pi$
$619$	−70676.5	−	122415.i	−0.184456	−	0.319488i	−0.943393	+	0.331676i	$0.892386\pi$
$620$	−17004.2	−	9817.37i	−0.0442356	−	0.0255395i
$621$	−646145.	−	113933.i	−1.67551	−	0.295437i
$622$	196784.	+	234518.i	0.508639	+	0.606172i
$623$	821403.	−	978910.i	2.11631	−	2.52213i
$624$	−28895.3	−	163874.i	−0.0742094	−	0.420862i
$625$	24400.7	+	8881.14i	0.0624659	+	0.0227357i
$626$		−	287696.i		−	0.734150i
$627$	412740.	−	459375.i	1.04988	−	1.16851i
$628$	−360393.			−0.913813
$629$	100335.	−	275667.i	0.253600	−	0.696760i
$630$	686517.	−	121051.i	1.72970	−	0.304992i
$631$	−86309.4	−	72422.2i	−0.216770	−	0.181892i	0.527936	−	0.849284i	$-0.322966\pi$
$631$	−86309.4	−	72422.2i	−0.216770	−	0.181892i	−0.744706	+	0.667392i	$0.767410\pi$
$632$	−72400.3	+	60751.1i	−0.181262	+	0.152097i
$633$	−171247.	+	971189.i	−0.427381	+	2.42380i
$634$	159882.	−	276924.i	0.397761	−	0.688942i
$635$	−128275.	+	74059.5i	−0.318122	+	0.183668i
$636$	−267339.	+	97303.4i	−0.660919	+	0.240555i
$637$	306085.	+	840962.i	0.754333	+	2.07251i
$638$	2665.23	+	4616.31i	0.00654777	+	0.0113411i
$639$	626063.	+	361458.i	1.53326	+	0.885229i
$640$	−22888.0	−	4035.77i	−0.0558789	−	0.00985296i
$641$	23582.8	+	28104.8i	0.0573956	+	0.0684014i	0.793978	−	0.607946i	$-0.208006\pi$
$641$	23582.8	+	28104.8i	0.0573956	+	0.0684014i	−0.736583	+	0.676347i	$0.763562\pi$
$642$	297517.	−	354567.i	0.721841	−	0.860257i
$643$	−120161.	−	681469.i	−0.290632	−	1.64825i	−0.684446	−	0.729064i	$-0.739956\pi$
$643$	−120161.	−	681469.i	−0.290632	−	1.64825i	0.393814	−	0.919190i	$-0.371155\pi$
$644$	−298975.	−	108818.i	−0.720879	−	0.262379i
$645$		−	321061.i		−	0.771735i
$646$	229003.	+	142759.i	0.548752	+	0.342088i
$647$	572888.			1.36855			0.684276	−	0.729223i	$-0.260118\pi$
$647$	572888.			1.36855			0.684276	+	0.729223i	$0.260118\pi$
$648$	−72267.4	+	198553.i	−0.172105	+	0.472854i
$649$	1586.07	−	279.667i	0.00376559	−	0.000663975i
$650$	−129897.	−	108996.i	−0.307447	−	0.257979i
$651$	−165782.	+	139108.i	−0.391179	+	0.328238i
$652$	50348.3	−	285540.i	0.118438	−	0.671694i
$653$	97144.4	−	168259.i	0.227820	−	0.394596i	−0.729342	−	0.684149i	$-0.760174\pi$
$653$	97144.4	−	168259.i	0.227820	−	0.394596i	0.957162	+	0.289554i	$0.0935069\pi$
$654$	629373.	−	363369.i	1.47147	−	0.849556i
$655$	124215.	−	45210.7i	0.289530	−	0.105380i
$656$	48446.9	+	133107.i	0.112579	+	0.309309i
$657$	−605510.	−	1.04877e6i	−1.40278	−	2.42969i
$658$	−761442.	−	439619.i	−1.75867	−	1.01537i
$659$	196782.	+	34698.0i	0.453122	+	0.0798976i	0.395551	−	0.918444i	$-0.370554\pi$
$659$	196782.	+	34698.0i	0.453122	+	0.0798976i	0.0575704	+	0.998341i	$0.481665\pi$
$660$	141179.	+	168251.i	0.324103	+	0.386250i
$661$	−437116.	+	520934.i	−1.00045	+	1.19228i	−0.0191427	+	0.999817i	$0.506094\pi$
$661$	−437116.	+	520934.i	−1.00045	+	1.19228i	−0.981303	+	0.192468i	$0.938351\pi$
$662$	33131.5	+	187898.i	0.0756005	+	0.428752i
$663$	−645719.	−	235023.i	−1.46898	−	0.534666i
$664$		−	68162.2i		−	0.154599i
$665$	−489140.	+	159506.i	−1.10609	+	0.360689i
$666$	−542937.			−1.22405
$667$	−2689.01	+	7388.00i	−0.00604423	+	0.0166064i
$668$	150431.	−	26525.0i	0.337119	−	0.0594432i
$669$	324858.	+	272588.i	0.725841	+	0.609053i
$670$	−101226.	+	84939.0i	−0.225499	+	0.189216i
$671$	−23857.8	+	135304.i	−0.0529889	+	0.300515i
$672$	−128081.	+	221843.i	−0.283626	+	0.491255i
$673$	−357298.	+	206286.i	−0.788861	+	0.455449i	−0.839561	−	0.543265i	$-0.817188\pi$
$673$	−357298.	+	206286.i	−0.788861	+	0.455449i	0.0507007	+	0.998714i	$0.483855\pi$
$674$	211086.	−	76829.1i	0.464665	−	0.169124i
$675$	184112.	+	505844.i	0.404087	+	1.11022i
$676$	7758.39	+	13437.9i	0.0169777	+	0.0294062i
$677$	622436.	+	359364.i	1.35806	+	0.784074i	0.989362	−	0.145477i	$-0.0464718\pi$
$677$	622436.	+	359364.i	1.35806	+	0.784074i	0.368694	+	0.929551i	$0.379805\pi$
$678$	−685560.	−	120883.i	−1.49137	−	0.262969i
$679$	−186095.	−	221779.i	−0.403641	−	0.481040i
$680$	−61691.4	+	73520.9i	−0.133416	+	0.158998i
$681$	−919.500	−	5214.74i	−0.00198270	−	0.0112445i
$682$	−43634.9	−	15881.8i	−0.0938134	−	0.0341453i
$683$			833496.i			1.78674i	0.449319	+	0.893371i	$0.351667\pi$
$683$			833496.i			1.78674i	−0.449319	+	0.893371i	$0.648333\pi$
$684$	103320.	−	488635.i	0.220838	−	1.04441i
$685$	122019.			0.260043
$686$	264933.	−	727897.i	0.562973	−	1.54676i
$687$	−1.05310e6	+	185690.i	−2.23129	+	0.393437i
$688$	61548.6	+	51645.4i	0.130029	+	0.109108i
$689$	−278929.	+	234049.i	−0.587564	+	0.493025i
$690$	−56253.5	+	319029.i	−0.118155	+	0.670089i
$691$	−384750.	+	666406.i	−0.805791	+	1.39567i	0.109965	+	0.993936i	$0.464926\pi$
$691$	−384750.	+	666406.i	−0.805791	+	1.39567i	−0.915756	+	0.401736i	$0.868407\pi$
$692$	−101587.	+	58651.1i	−0.212141	+	0.122480i
$693$	1.54920e6	−	563864.i	3.22583	−	1.17411i
$694$	63218.1	+	173690.i	0.131257	+	0.360626i
$695$	187874.	+	325408.i	0.388954	+	0.673687i
$696$	5481.99	+	3165.03i	0.0113167	+	0.00653370i
$697$	576058.	+	101575.i	1.18577	+	0.209083i
$698$	−155908.	−	185804.i	−0.320006	−	0.381369i
$699$	−399059.	+	475580.i	−0.816738	+	0.973350i
$700$	45328.5	+	257071.i	0.0925071	+	0.524634i
$701$	−136502.	−	49682.5i	−0.277781	−	0.101104i	0.199373	−	0.979924i	$-0.436109\pi$
$701$	−136502.	−	49682.5i	−0.277781	−	0.101104i	−0.477154	+	0.878820i	$0.658332\pi$
$702$			676096.i			1.37194i
$703$	396747.	−	56189.0i	0.802792	−	0.113695i
$704$	−54964.1			−0.110901
$705$	−306188.	+	841246.i	−0.616042	+	1.69256i
$706$	−158977.	+	28032.0i	−0.318952	+	0.0562399i
$707$	−217029.	−	182109.i	−0.434188	−	0.364327i
$708$	1465.10	−	1229.37i	0.00292282	−	0.00245253i
$709$	158571.	−	899301.i	0.315451	−	1.78901i	−0.254230	−	0.967144i	$-0.581822\pi$
$709$	158571.	−	899301.i	0.315451	−	1.78901i	0.569681	−	0.821866i	$-0.307067\pi$
$710$	94876.5	−	164331.i	0.188210	−	0.325989i
$711$	625558.	−	361166.i	1.23745	−	0.714443i
$712$	305972.	−	111365.i	0.603562	−	0.219679i
$713$	−23424.8	−	64359.1i	−0.0460783	−	0.126599i
$714$	528914.	+	916106.i	1.03750	+	1.79701i
$715$	243443.	+	140552.i	0.476195	+	0.274931i
$716$	−315131.	−	55566.1i	−0.614703	−	0.108389i
$717$	−425143.	−	506666.i	−0.826984	−	0.985561i
$718$	−4693.98	+	5594.06i	−0.00910525	+	0.0108512i
$719$	40009.1	+	226903.i	0.0773929	+	0.438917i	0.998740	+	0.0501767i	$0.0159785\pi$
$719$	40009.1	+	226903.i	0.0773929	+	0.438917i	−0.921347	+	0.388740i	$0.872910\pi$
$720$	166914.	+	60751.7i	0.321979	+	0.117191i
$721$		−	336636.i		−	0.647575i
$722$	−24931.2	+	367759.i	−0.0478265	+	0.705488i
$723$	494939.			0.946837
$724$	70930.1	−	194879.i	0.135317	−	0.371781i
$725$	6352.51	−	1120.12i	0.0120856	−	0.00213102i
$726$	−107607.	−	90293.3i	−0.204159	−	0.171310i
$727$	426176.	−	357604.i	0.806343	−	0.676602i	−0.143389	−	0.989666i	$-0.545800\pi$
$727$	426176.	−	357604.i	0.806343	−	0.676602i	0.949732	+	0.313064i	$0.101356\pi$
$728$	−56931.0	+	322871.i	−0.107420	+	0.609210i
$729$	−138065.	+	239136.i	−0.259794	+	0.449977i
$730$	−275285.	+	158936.i	−0.516580	+	0.298247i
$731$	311781.	−	113479.i	0.583466	−	0.212364i
$732$	55802.6	+	153316.i	0.104143	+	0.286132i
$733$	−170720.	−	295695.i	−0.317743	−	0.550346i	0.662274	−	0.749262i	$-0.269591\pi$
$733$	−170720.	−	295695.i	−0.317743	−	0.550346i	−0.980017	+	0.198915i	$0.936258\pi$
$734$	−471751.	−	272366.i	−0.875630	−	0.505545i
$735$	−1.38143e6	−	243584.i	−2.55715	−	0.450894i
$736$	−52110.2	−	62102.6i	−0.0961983	−	0.114645i
$737$	−200877.	+	239396.i	−0.369824	+	0.440739i
$738$	−187990.	−	1.06615e6i	−0.345162	−	1.95751i
$739$	271984.	+	98994.2i	0.498030	+	0.181268i	0.578808	−	0.815464i	$-0.303518\pi$
$739$	271984.	+	98994.2i	0.498030	+	0.181268i	−0.0807779	+	0.996732i	$0.525740\pi$
$740$			142512.i			0.260248i
$741$	−131616.	−	929335.i	−0.239703	−	1.69253i
$742$	560528.			1.01810
$743$	−51730.9	+	142129.i	−0.0937071	+	0.257458i	−0.977687	−	0.210067i	$-0.932632\pi$
$743$	−51730.9	+	142129.i	−0.0937071	+	0.257458i	0.883980	+	0.467525i	$0.154854\pi$
$744$	−54305.3	+	9575.49i	−0.0981062	+	0.0172988i
$745$	−20954.1	−	17582.6i	−0.0377534	−	0.0316789i
$746$	−363816.	+	305278.i	−0.653739	+	0.548552i
$747$	−90461.6	+	513033.i	−0.162115	+	0.919400i
$748$	−113488.	+	196567.i	−0.202837	+	0.351323i
$749$	−789760.	+	455968.i	−1.40777	+	0.812776i
$750$	674586.	−	245529.i	1.19926	−	0.436497i
$751$	−118275.	−	324958.i	−0.209707	−	0.576166i	0.789590	−	0.613634i	$-0.210293\pi$
$751$	−118275.	−	324958.i	−0.209707	−	0.576166i	−0.999298	+	0.0374678i	$0.988071\pi$
$752$	−112017.	−	194019.i	−0.198083	−	0.343090i
$753$	337473.	+	194840.i	0.595182	+	0.343628i
$754$	7978.52	+	1406.83i	0.0140339	+	0.00247456i
$755$	257131.	+	306437.i	0.451088	+	0.537586i
$756$	669011.	−	797296.i	1.17055	−	1.39501i
$757$	21580.5	+	122389.i	0.0376591	+	0.213576i	0.997830	−	0.0658364i	$-0.0209716\pi$
$757$	21580.5	+	122389.i	0.0376591	+	0.213576i	−0.960171	+	0.279412i	$0.909860\pi$
$758$	−473816.	−	172455.i	−0.824653	−	0.300149i
$759$			766129.i			1.32990i
$760$	−128258.	−	27119.8i	−0.222054	−	0.0469526i
$761$	725445.			1.25267			0.626333	−	0.779556i	$-0.284555\pi$
$761$	725445.			1.25267			0.626333	+	0.779556i	$0.284555\pi$
$762$	−142275.	+	390897.i	−0.245029	+	0.673213i
$763$	−1.41010e6	+	248638.i	−2.42215	+	0.427090i
$764$	−419834.	−	352282.i	−0.719268	−	0.603538i
$765$	561903.	−	471492.i	0.960148	−	0.805660i
$766$	−50067.3	+	283945.i	−0.0853289	+	0.483924i
$767$	1223.90	−	2119.86i	0.00208045	−	0.00360344i
$768$	−56526.6	+	32635.6i	−0.0958364	+	0.0553311i
$769$	−704393.	+	256378.i	−1.19114	+	0.433539i	−0.860123	−	0.510086i	$-0.829614\pi$
$769$	−704393.	+	256378.i	−1.19114	+	0.433539i	−0.331016	+	0.943625i	$0.607391\pi$
$770$	−148005.	−	406639.i	−0.249628	−	0.685848i
$771$	272853.	+	472596.i	0.459008	+	0.795025i
$772$	255510.	+	147519.i	0.428720	+	0.247521i
$773$	252049.	+	44443.0i	0.421818	+	0.0743779i	0.380528	−	0.924769i	$-0.375742\pi$
$773$	252049.	+	44443.0i	0.421818	+	0.0743779i	0.0412899	+	0.999147i	$0.486853\pi$
$774$	−394714.	−	470401.i	−0.658870	−	0.785211i
$775$	−36119.7	+	43045.8i	−0.0601369	+	0.0716683i
$776$	−12809.9	−	72648.3i	−0.0212726	−	0.120643i
$777$	1.47603e6	+	537230.i	2.44485	+	0.889853i
$778$			207658.i			0.343075i
$779$	247709.	+	759623.i	0.408194	+	1.25177i
$780$	333818.			0.548681
$781$	153484.	−	421694.i	0.251629	−	0.691345i
$782$	−329691.	+	58133.4i	−0.539130	+	0.0950632i
$783$	−19702.1	−	16532.0i	−0.0321358	−	0.0269651i
$784$	268911.	−	225643.i	0.437499	−	0.367105i
$785$	125545.	−	711999.i	0.203732	−	1.15542i
$786$	185620.	−	321504.i	0.300456	−	0.520404i
$787$	255080.	−	147270.i	0.411838	−	0.237775i	−0.279741	−	0.960075i	$-0.590249\pi$
$787$	255080.	−	147270.i	0.411838	−	0.237775i	0.691579	+	0.722301i	$0.256915\pi$
$788$	107009.	−	38948.1i	0.172333	−	0.0627241i
$789$	−601337.	−	1.65216e6i	−0.965970	−	2.65398i
$790$	−94799.9	−	164198.i	−0.151899	−	0.263096i
$791$	1.18780e6	+	685779.i	1.89842	+	1.09605i
$792$	413696.	+	72945.7i	0.659524	+	0.116292i
$793$	134225.	+	159963.i	0.213445	+	0.254374i
$794$	359008.	−	427849.i	0.569459	−	0.678655i
$795$	−99105.6	−	562056.i	−0.156806	−	0.889294i
$796$	113983.	+	41486.5i	0.179893	+	0.0654758i
$797$			489878.i			0.771207i	0.922665	+	0.385604i	$0.126007\pi$
$797$			489878.i			0.771207i	−0.922665	+	0.385604i	$0.873993\pi$
$798$	−764386.	+	1.22617e6i	−1.20035	+	1.92551i
$799$	−925153.			−1.44917
$800$	−22748.9	+	62502.0i	−0.0355451	+	0.0976594i
$801$	−2.45074e6	+	432132.i	−3.81973	+	0.673522i
$802$	−346274.	−	290558.i	−0.538358	−	0.451736i
$803$	−575876.	+	483217.i	−0.893096	+	0.749396i
$804$	−64443.0	+	365474.i	−0.0996927	+	0.565385i
$805$	319132.	−	552752.i	0.492468	−	0.852980i
$806$	−61120.2	+	35287.8i	−0.0940837	+	0.0543193i
$807$	−93741.0	+	34118.9i	−0.143940	+	0.0523900i
$808$	−24690.0	−	67835.3i	−0.0378181	−	0.103904i
$809$	−65479.6	−	113414.i	−0.100048	−	0.173288i	0.811656	−	0.584135i	$-0.198566\pi$
$809$	−65479.6	−	113414.i	−0.100048	−	0.173288i	−0.911704	+	0.410847i	$0.865233\pi$
$810$	−367091.	−	211940.i	−0.559504	−	0.323030i
$811$	113240.	+	19967.3i	0.172170	+	0.0303583i	0.259069	−	0.965859i	$-0.416584\pi$
$811$	113240.	+	19967.3i	0.172170	+	0.0303583i	−0.0868983	+	0.996217i	$0.527696\pi$
$812$	−8016.70	−	9553.94i	−0.0121586	−	0.0144901i
$813$	754223.	−	898848.i	1.14109	−	1.35989i
$814$	58525.2	+	331913.i	0.0883272	+	0.500928i
$815$	546578.	+	198938.i	0.822881	+	0.299504i
$816$			269539.i			0.404801i
$817$	337116.	+	302893.i	0.505051	+	0.453780i
$818$	860220.			1.28559
$819$	856999.	−	2.35459e6i	1.27765	−	3.51032i
$820$	−279845.	+	49344.3i	−0.416189	+	0.0733853i
$821$	546927.	+	458926.i	0.811415	+	0.680858i	0.950945	−	0.309360i	$-0.100115\pi$
$821$	546927.	+	458926.i	0.811415	+	0.680858i	−0.139530	+	0.990218i	$0.544559\pi$
$822$	262510.	−	220272.i	0.388510	−	0.325998i
$823$	136586.	−	774618.i	0.201654	−	1.14364i	−0.700965	−	0.713196i	$-0.747247\pi$
$823$	136586.	−	774618.i	0.201654	−	1.14364i	0.902619	−	0.430441i	$-0.141642\pi$
$824$	42888.2	−	74284.5i	0.0631660	−	0.109407i
$825$	544359.	−	314286.i	0.799792	−	0.461760i
$826$	−3540.96	+	1288.80i	−0.00518992	+	0.00188898i
$827$	242046.	+	665016.i	0.353905	+	0.972347i	0.981103	+	0.193487i	$0.0619796\pi$
$827$	242046.	+	665016.i	0.353905	+	0.972347i	−0.627198	+	0.778860i	$0.715798\pi$
$828$	309796.	+	536583.i	0.451872	+	0.782665i
$829$	498055.	+	287552.i	0.724717	+	0.418416i	0.816486	−	0.577365i	$-0.195919\pi$
$829$	498055.	+	287552.i	0.724717	+	0.418416i	−0.0917692	+	0.995780i	$0.529252\pi$
$830$	134663.	+	23744.6i	0.195475	+	0.0344675i
$831$	−546004.	−	650702.i	−0.790667	−	0.942280i
$832$	−53697.4	+	63994.0i	−0.0775722	+	0.0924470i
$833$	−251724.	−	1.42760e6i	−0.362773	−	2.05739i
$834$	991628.	+	360923.i	1.42566	+	0.518899i
$835$			306433.i			0.439504i
$836$	−309854.	−	10490.8i	−0.443348	−	0.0150105i
$837$	224048.			0.319809
$838$	239625.	−	658365.i	0.341228	−	0.937516i
$839$	636974.	−	112316.i	0.904895	−	0.159557i	0.298210	−	0.954500i	$-0.403610\pi$
$839$	636974.	−	112316.i	0.904895	−	0.159557i	0.606684	+	0.794943i	$0.292499\pi$
$840$	−393659.	−	330319.i	−0.557907	−	0.468140i
$841$	541573.	−	454433.i	0.765711	−	0.642508i
$842$	26595.4	−	150830.i	0.0375130	−	0.212747i
$843$	134338.	−	232680.i	0.189036	−	0.327419i
$844$	428756.	−	247543.i	0.601902	−	0.347508i
$845$	−29250.9	+	10646.5i	−0.0409662	+	0.0149105i
$846$	585619.	+	1.60898e6i	0.818229	+	2.24807i
$847$	138382.	+	239684.i	0.192891	+	0.334097i
$848$	123690.	+	71412.5i	0.172006	+	0.0993076i
$849$	−2.31689e6	−	408530.i	−3.21433	−	0.566773i
$850$	176553.	+	210408.i	0.244364	+	0.291222i
$851$	−319534.	+	380806.i	−0.441223	+	0.525829i
$852$	−92538.9	−	524814.i	−0.127481	−	0.722980i
$853$	−862202.	−	313816.i	−1.18498	−	0.431297i	−0.327022	−	0.945017i	$-0.606045\pi$
$853$	−862202.	−	313816.i	−1.18498	−	0.431297i	−0.857958	+	0.513719i	$0.828267\pi$
$854$		−	321457.i		−	0.440765i
$855$	929365.	+	374340.i	1.27132	+	0.512075i
$856$	−232366.			−0.317121
$857$	129741.	−	356461.i	0.176651	−	0.485344i	−0.819492	−	0.573091i	$-0.805744\pi$
$857$	129741.	−	356461.i	0.176651	−	0.485344i	0.996143	+	0.0877463i	$0.0279665\pi$
$858$	777469.	−	137089.i	1.05611	−	0.186220i
$859$	240604.	+	201891.i	0.326075	+	0.273609i	0.791098	−	0.611689i	$-0.209510\pi$
$859$	240604.	+	201891.i	0.326075	+	0.273609i	−0.465023	+	0.885298i	$0.653954\pi$
$860$	−123472.	+	103606.i	−0.166945	+	0.140083i
$861$	−543870.	+	3.08444e6i	−0.733649	+	4.16073i
$862$	−102447.	+	177443.i	−0.137874	+	0.238805i
$863$	−1.14421e6	+	660613.i	−1.53634	+	0.887004i	−0.537286	+	0.843400i	$0.680551\pi$
$863$	−1.14421e6	+	660613.i	−1.53634	+	0.887004i	−0.999049	+	0.0436036i	$0.986116\pi$
$864$	249206.	−	90703.6i	0.333834	−	0.121506i
$865$	−80484.0	−	221128.i	−0.107567	−	0.295537i
$866$	165805.	+	287182.i	0.221086	+	0.382932i
$867$	−188679.	−	108934.i	−0.251007	−	0.144919i
$868$	106995.	+	18866.1i	0.142011	+	0.0250404i
$869$	−288223.	−	343490.i	−0.381671	−	0.454857i
$870$	−8162.57	+	9727.77i	−0.0107842	+	0.0128521i
$871$	82478.1	+	467757.i	0.108718	+	0.616572i
$872$	−342840.	−	124783.i	−0.450877	−	0.164106i
$873$			563799.i			0.739769i
$874$	−281913.	−	360043.i	−0.369056	−	0.471337i
$875$	−1.41440e6			−1.84738
$876$	−305330.	+	838888.i	−0.397889	+	1.09319i
$877$	−578410.	+	101989.i	−0.752032	+	0.132604i	−0.536508	−	0.843895i	$-0.680257\pi$
$877$	−578410.	+	101989.i	−0.752032	+	0.132604i	−0.215524	+	0.976499i	$0.569146\pi$
$878$	97859.3	+	82113.7i	0.126944	+	0.106519i
$879$	−1.28176e6	+	1.07553e6i	−1.65894	+	1.39201i
$880$	19147.0	−	108588.i	0.0247250	−	0.140222i
$881$	336763.	−	583290.i	0.433883	−	0.751507i	−0.563321	−	0.826238i	$-0.690477\pi$
$881$	336763.	−	583290.i	0.433883	−	0.751507i	0.997204	+	0.0747314i	$0.0238099\pi$
$882$	−2.32346e6	+	1.34145e6i	−2.98675	+	1.72440i
$883$	495082.	−	180195.i	0.634973	−	0.231111i	−0.00442111	−	0.999990i	$-0.501407\pi$
$883$	495082.	−	180195.i	0.634973	−	0.231111i	0.639395	+	0.768879i	$0.279185\pi$
$884$	117988.	+	324169.i	0.150985	+	0.414827i
$885$	1918.38	+	3322.74i	0.00244934	+	0.00424238i
$886$	−161724.	−	93371.5i	−0.206019	−	0.118945i
$887$	−212933.	−	37545.9i	−0.270643	−	0.0477216i	0.0366797	−	0.999327i	$-0.488322\pi$
$887$	−212933.	−	37545.9i	−0.270643	−	0.0477216i	−0.307322	+	0.951605i	$0.599433\pi$
$888$	257267.	+	306598.i	0.326255	+	0.388816i
$889$	526823.	−	627843.i	0.666593	−	0.794415i
$890$	113427.	+	643279.i	0.143198	+	0.812118i
$891$	−942000.	−	342860.i	−1.18658	−	0.431878i
$892$		−	212896.i		−	0.267570i
$893$	−594452.	−	1.11514e6i	−0.745441	−	1.39839i
$894$	−76821.1			−0.0961182
$895$	219555.	−	603222.i	0.274092	−	0.753062i
$896$	126647.	−	22331.2i	0.157753	−	0.0278161i
$897$	891995.	+	748472.i	1.10861	+	0.930231i
$898$	495941.	−	416144.i	0.615003	−	0.516049i
$899$	466.202	−	2643.96i	0.000576839	−	0.00327142i
$900$	254172.	−	440240.i	0.313793	−	0.543506i
$901$	510781.	−	294900.i	0.629195	−	0.363266i
$902$	−631502.	+	229848.i	−0.776179	+	0.282506i
$903$	607611.	+	1.66940e6i	0.745161	+	2.04731i
$904$	174740.	+	302658.i	0.213823	+	0.370353i
$905$	360298.	+	208018.i	0.439910	+	0.253982i
$906$	1.10638e6	+	195085.i	1.34787	+	0.237666i
$907$	−543565.	−	647796.i	−0.660750	−	0.787451i	0.326743	−	0.945113i	$-0.394049\pi$
$907$	−543565.	−	647796.i	−0.660750	−	0.787451i	−0.987493	+	0.157662i	$0.949604\pi$
$908$	−1708.74	+	2036.40i	−0.00207255	+	0.00246997i
$909$	95805.6	+	543341.i	0.115948	+	0.657574i
$910$	−618039.	−	224948.i	−0.746333	−	0.271643i
$911$		−	874854.i		−	1.05414i	−0.849821	−	0.527071i	$-0.823290\pi$
$911$		−	874854.i		−	1.05414i	0.849821	−	0.527071i	$-0.176710\pi$
$912$	−324892.	+	173191.i	−0.390615	+	0.208226i
$913$	323383.			0.387950
$914$	−247562.	+	680170.i	−0.296340	+	0.814189i
$915$	−322334.	+	56836.1i	−0.385002	+	0.0678863i
$916$	411245.	+	345075.i	0.490128	+	0.411266i
$917$	−560312.	+	470158.i	−0.666333	+	0.559120i
$918$	190171.	−	1.07851e6i	0.225662	−	1.27979i
$919$	268582.	−	465198.i	0.318014	−	0.550816i	−0.662060	−	0.749451i	$-0.730318\pi$
$919$	268582.	−	465198.i	0.318014	−	0.550816i	0.980074	+	0.198635i	$0.0636508\pi$
$920$	140844.	−	81316.2i	0.166403	−	0.0960730i
$921$	−707771.	+	257607.i	−0.834398	+	0.303696i
$922$	−46458.0	−	127642.i	−0.0546511	−	0.150153i
$923$	−341026.	−	590674.i	−0.400299	−	0.693338i
$924$	−1.05249e6	−	607658.i	−1.23275	−	0.711730i
$925$	401655.	+	70822.6i	0.469429	+	0.0827730i
$926$	−123491.	−	147171.i	−0.144017	−	0.171633i
$927$	−421392.	+	502195.i	−0.490373	+	0.584403i
$928$	−551.831	−	3129.59i	−0.000640781	−	0.00363405i
$929$	1.25234e6	+	455816.i	1.45108	+	0.528151i	0.942894	−	0.333094i	$-0.108093\pi$
$929$	1.25234e6	+	455816.i	1.45108	+	0.528151i	0.508190	+	0.861245i	$0.330315\pi$
$930$		−	110622.i		−	0.127902i
$931$	1.55903e6	−	1.22071e6i	1.79868	−	1.40836i
$932$	311672.			0.358811
$933$	−589918.	+	1.62079e6i	−0.677686	+	1.86193i
$934$	324490.	−	57216.3i	0.371969	−	0.0655882i
$935$	−348807.	−	292684.i	−0.398990	−	0.334792i
$936$	489091.	−	410396.i	0.558262	−	0.468438i
$937$	−214412.	+	1.21599e6i	−0.244214	+	1.38501i	0.578097	+	0.815968i	$0.303796\pi$
$937$	−214412.	+	1.21599e6i	−0.244214	+	1.38501i	−0.822311	+	0.569039i	$0.807316\pi$
$938$	365591.	−	633223.i	0.415518	−	0.719699i
$939$	1.40372e6	−	810439.i	1.59202	−	0.919156i
$940$	422329.	−	153715.i	0.477964	−	0.173965i
$941$	−289888.	−	796460.i	−0.327379	−	0.899466i	−0.988773	−	0.149427i	$-0.952257\pi$
$941$	−289888.	−	796460.i	−0.327379	−	0.899466i	0.661394	−	0.750039i	$-0.269965\pi$
$942$	−1.01523e6	−	1.75843e6i	−1.14409	−	1.98163i
$943$	−858412.	−	495605.i	−0.965323	−	0.557329i
$944$	−945.569	−	166.729i	−0.00106108	−	0.000187098i
$945$	1.34210e6	+	1.59945e6i	1.50287	+	1.79105i
$946$	−245022.	+	292006.i	−0.273794	+	0.326295i
$947$	−80966.8	−	459185.i	−0.0902832	−	0.512021i	−0.996091	−	0.0883327i	$-0.971846\pi$
$947$	−80966.8	−	459185.i	−0.0902832	−	0.512021i	0.905808	−	0.423689i	$-0.139265\pi$
$948$	−500368.	−	182119.i	−0.556766	−	0.202646i
$949$			1.14257e6i			1.26867i
$950$	−140174.	+	348006.i	−0.155317	+	0.385603i
$951$	1.80156e6			1.99199
$952$	181633.	−	499032.i	0.200411	−	0.550624i
$953$	1.17654e6	−	207455.i	1.29545	−	0.228422i	0.516920	−	0.856034i	$-0.327079\pi$
$953$	1.17654e6	−	207455.i	1.29545	−	0.228422i	0.778527	+	0.627612i	$0.215967\pi$
$954$	−836197.	−	701653.i	−0.918781	−	0.770949i
$955$	842227.	−	706712.i	0.923469	−	0.774883i
$956$	−57658.8	+	327000.i	−0.0630885	+	0.357793i
$957$	−15015.9	+	26008.3i	−0.0163956	+	0.0283981i
$958$	759790.	−	438665.i	0.827871	−	0.477972i
$959$	−634451.	+	230921.i	−0.689860	+	0.251088i
$960$	−44784.3	−	123044.i	−0.0485940	−	0.133511i
$961$	−450067.	−	779538.i	−0.487338	−	0.844094i
$962$	443619.	+	256123.i	0.479358	+	0.276757i
$963$	1.74894e6	+	308385.i	1.88591	+	0.332537i
$964$	−159716.	−	190342.i	−0.171867	−	0.204823i
$965$	−380449.	+	453402.i	−0.408547	+	0.486887i
$966$	−311269.	−	1.76529e6i	−0.333566	−	1.89175i
$967$	−569796.	−	207389.i	−0.609349	−	0.221785i	0.0188691	−	0.999822i	$-0.493993\pi$
$967$	−569796.	−	207389.i	−0.609349	−	0.221785i	−0.628219	+	0.778037i	$0.716216\pi$
$968$			70520.6i			0.0752602i
$969$	−51446.0	+	1.51950e6i	−0.0547903	+	1.61828i
$970$	147988.			0.157283
$971$	−607945.	+	1.67031e6i	−0.644801	+	1.77158i	−0.00871035	+	0.999962i	$0.502773\pi$
$971$	−607945.	+	1.67031e6i	−0.644801	+	1.77158i	−0.636091	+	0.771614i	$0.719450\pi$
$972$	−237437.	+	41866.5i	−0.251313	+	0.0443133i
$973$	−1.59271e6	−	1.33645e6i	−1.68233	−	1.41164i
$974$	−933299.	+	783130.i	−0.983791	+	0.825498i
$975$	165894.	−	940832.i	0.174511	−	0.989698i
$976$	40954.4	−	70935.1i	0.0429933	−	0.0744666i
$977$	776806.	−	448489.i	0.813811	−	0.469854i	−0.0344669	−	0.999406i	$-0.510973\pi$
$977$	776806.	−	448489.i	0.813811	−	0.469854i	0.848277	+	0.529552i	$0.177640\pi$
$978$	1.53503e6	−	558707.i	1.60487	−	0.584125i
$979$	528350.	+	1.45163e6i	0.551260	+	1.51457i
$980$	352109.	+	609870.i	0.366627	+	0.635016i
$981$	2.41483e6	+	1.39420e6i	2.50928	+	1.44873i
$982$	−626472.	−	110464.i	−0.649649	−	0.114551i
$983$	13454.5	+	16034.5i	0.0139239	+	0.0165939i	0.772961	−	0.634453i	$-0.218775\pi$
$983$	13454.5	+	16034.5i	0.0139239	+	0.0165939i	−0.759038	+	0.651047i	$0.774330\pi$
$984$	−512979.	+	611344.i	−0.529797	+	0.631387i
$985$	39669.5	+	224977.i	0.0408869	+	0.231881i
$986$	−12331.7	−	4488.36i	−0.0126843	−	0.00461672i
$987$		−	4.95363e6i		−	5.08498i
$988$	−314928.	+	350511.i	−0.322624	+	0.359077i
$989$	−562231.			−0.574807
$990$	−288226.	+	791894.i	−0.294078	+	0.807973i
$991$	−830827.	+	146497.i	−0.845986	+	0.149170i	−0.579807	−	0.814754i	$-0.696872\pi$
$991$	−830827.	+	146497.i	−0.845986	+	0.149170i	−0.266179	+	0.963924i	$0.585761\pi$
$992$	21206.7	+	17794.5i	0.0215501	+	0.0180827i
$993$	−823459.	+	690964.i	−0.835109	+	0.700740i
$994$	−182325.	+	1.03401e6i	−0.184532	+	1.04653i
$995$	−121668.	+	210735.i	−0.122894	+	0.212859i
$996$	332576.	−	192013.i	0.335253	−	0.193558i
$997$	−548298.	+	199564.i	−0.551602	+	0.200767i	−0.602758	−	0.797924i	$-0.705932\pi$
$997$	−548298.	+	199564.i	−0.551602	+	0.200767i	0.0511558	+	0.998691i	$0.483709\pi$
$998$	63256.8	+	173797.i	0.0635106	+	0.174494i
$999$	−813086.	−	1.40831e6i	−0.814715	−	1.41113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.5.f.a.15.6	✓	36
19.14	odd	18	inner	38.5.f.a.33.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.f.a.15.6	✓	36	1.1	even	1	trivial
38.5.f.a.33.6	yes	36	19.14	odd	18	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.967379 - 2.65785i) q^{2} +(15.6933 - 2.76715i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(12.2941 - 10.3159i) q^{5} +(7.82668 - 44.3873i) q^{6} +(-44.4015 + 76.9057i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(162.507 - 59.1476i) q^{9} +O(q^{10})\)	\(q+(0.967379 - 2.65785i) q^{2} +(15.6933 - 2.76715i) q^{3} +(-6.12836 - 5.14230i) q^{4} +(12.2941 - 10.3159i) q^{5} +(7.82668 - 44.3873i) q^{6} +(-44.4015 + 76.9057i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(162.507 - 59.1476i) q^{9} +(-15.5252 - 42.6552i) q^{10} +(-53.6759 - 92.9694i) q^{11} +(-110.403 - 63.7415i) q^{12} +(-160.682 - 28.3326i) q^{13} +(161.451 + 192.410i) q^{14} +(164.388 - 195.911i) q^{15} +(11.1135 + 63.0277i) q^{16} +(248.351 + 90.3924i) q^{17} -489.137i q^{18} +(50.6212 + 357.433i) q^{19} -128.390 q^{20} +(-483.996 + 1329.77i) q^{21} +(-299.024 + 52.7260i) q^{22} +(-343.071 - 287.871i) q^{23} +(-276.217 + 231.774i) q^{24} +(-63.8048 + 361.855i) q^{25} +(-230.744 + 399.660i) q^{26} +(1268.76 - 732.517i) q^{27} +(667.580 - 242.979i) q^{28} +(-6.00430 - 16.4967i) q^{29} +(-361.675 - 626.440i) q^{30} +(132.442 + 76.4651i) q^{31} +(178.269 + 31.4337i) q^{32} +(-1099.61 - 1310.46i) q^{33} +(480.499 - 572.637i) q^{34} +(247.480 + 1403.53i) q^{35} +(-1300.05 - 473.181i) q^{36} -1109.99i q^{37} +(998.974 + 211.230i) q^{38} -2600.03 q^{39} +(-124.202 + 341.242i) q^{40} +(2179.65 - 384.331i) q^{41} +(3066.12 + 2572.78i) q^{42} +(961.696 - 806.959i) q^{43} +(-149.132 + 845.767i) q^{44} +(1387.70 - 2403.57i) q^{45} +(-1097.00 + 633.353i) q^{46} +(-3289.42 + 1197.25i) q^{47} +(348.814 + 958.358i) q^{48} +(-2742.49 - 4750.13i) q^{49} +(900.034 + 519.635i) q^{50} +(4147.57 + 731.329i) q^{51} +(839.021 + 999.907i) q^{52} +(1434.47 - 1709.54i) q^{53} +(-719.553 - 4080.79i) q^{54} +(-1618.96 - 589.254i) q^{55} -2009.38i q^{56} +(1783.48 + 5469.22i) q^{57} -49.6541 q^{58} +(-5.13114 + 14.0977i) q^{59} +(-2014.86 + 355.274i) q^{60} +(-980.402 - 822.655i) q^{61} +(331.354 - 278.039i) q^{62} +(-2666.76 + 15123.9i) q^{63} +(256.000 - 443.405i) q^{64} +(-2267.71 + 1309.26i) q^{65} +(-4546.76 + 1654.89i) q^{66} +(-995.646 - 2735.51i) q^{67} +(-1057.16 - 1831.05i) q^{68} +(-6180.50 - 3568.31i) q^{69} +(3969.77 + 699.978i) q^{70} +(2687.01 + 3202.26i) q^{71} +(-2515.29 + 2997.60i) q^{72} +(-1216.01 - 6896.32i) q^{73} +(-2950.19 - 1073.78i) q^{74} +5855.25i q^{75} +(1527.80 - 2450.79i) q^{76} +9533.16 q^{77} +(-2515.21 + 6910.48i) q^{78} +(4113.42 - 725.307i) q^{79} +(786.820 + 660.221i) q^{80} +(7153.36 - 6002.38i) q^{81} +(1087.05 - 6164.97i) q^{82} +(-1506.19 + 2608.79i) q^{83} +(9804.16 - 5660.44i) q^{84} +(3985.73 - 1450.69i) q^{85} +(-1214.45 - 3336.68i) q^{86} +(-139.876 - 242.272i) q^{87} +(2103.66 + 1214.55i) q^{88} +(-14171.4 - 2498.80i) q^{89} +(-5045.91 - 6013.48i) q^{90} +(9313.45 - 11099.3i) q^{91} +(622.144 + 3528.35i) q^{92} +(2290.03 + 833.503i) q^{93} +9900.98i q^{94} +(4309.60 + 3872.10i) q^{95} +2884.61 q^{96} +(-1115.04 + 3063.55i) q^{97} +(-15278.2 + 2693.95i) q^{98} +(-14221.6 - 11933.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9}+O(q^{10}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9	\( 36 q + 12 q^{3} + 48 q^{6} + 90 q^{7} - 84 q^{9} + 90 q^{11} - 432 q^{12} - 330 q^{13} + 576 q^{14} + 2658 q^{15} - 522 q^{17} - 1236 q^{19} - 864 q^{20} - 1998 q^{21} - 1344 q^{22} - 1440 q^{23} - 384 q^{24} - 3276 q^{25} + 576 q^{26} + 1692 q^{27} + 1056 q^{28} + 4050 q^{29} + 2808 q^{31} + 2910 q^{33} + 1536 q^{34} + 1422 q^{35} + 672 q^{36} + 1872 q^{38} - 9024 q^{39} - 3060 q^{41} - 3456 q^{42} - 1218 q^{43} - 5760 q^{44} - 2592 q^{45} - 2880 q^{46} + 990 q^{47} + 1536 q^{48} - 9696 q^{49} + 27648 q^{50} + 35784 q^{51} - 1488 q^{52} + 17082 q^{53} + 2160 q^{54} + 4290 q^{55} + 204 q^{57} - 5376 q^{58} - 11142 q^{59} - 11856 q^{60} - 35928 q^{61} - 7200 q^{62} - 58254 q^{63} + 9216 q^{64} - 34290 q^{65} - 32928 q^{66} + 44322 q^{67} - 4752 q^{68} + 21762 q^{69} + 12864 q^{70} + 40428 q^{71} + 10752 q^{72} + 6936 q^{73} - 4032 q^{74} - 576 q^{76} - 36648 q^{77} - 11040 q^{78} - 29298 q^{79} + 24324 q^{81} - 14592 q^{82} + 23958 q^{83} + 36720 q^{84} + 2772 q^{85} + 30816 q^{86} + 14256 q^{87} + 26064 q^{89} + 14784 q^{90} + 100044 q^{91} + 9360 q^{92} + 26400 q^{93} - 38646 q^{95} - 55746 q^{97} - 64512 q^{98} - 69846 q^{99}+O(q^{100}) \) 36 * q + 12 * q^3 + 48 * q^6 + 90 * q^7 - 84 * q^9 + 90 * q^11 - 432 * q^12 - 330 * q^13 + 576 * q^14 + 2658 * q^15 - 522 * q^17 - 1236 * q^19 - 864 * q^20 - 1998 * q^21 - 1344 * q^22 - 1440 * q^23 - 384 * q^24 - 3276 * q^25 + 576 * q^26 + 1692 * q^27 + 1056 * q^28 + 4050 * q^29 + 2808 * q^31 + 2910 * q^33 + 1536 * q^34 + 1422 * q^35 + 672 * q^36 + 1872 * q^38 - 9024 * q^39 - 3060 * q^41 - 3456 * q^42 - 1218 * q^43 - 5760 * q^44 - 2592 * q^45 - 2880 * q^46 + 990 * q^47 + 1536 * q^48 - 9696 * q^49 + 27648 * q^50 + 35784 * q^51 - 1488 * q^52 + 17082 * q^53 + 2160 * q^54 + 4290 * q^55 + 204 * q^57 - 5376 * q^58 - 11142 * q^59 - 11856 * q^60 - 35928 * q^61 - 7200 * q^62 - 58254 * q^63 + 9216 * q^64 - 34290 * q^65 - 32928 * q^66 + 44322 * q^67 - 4752 * q^68 + 21762 * q^69 + 12864 * q^70 + 40428 * q^71 + 10752 * q^72 + 6936 * q^73 - 4032 * q^74 - 576 * q^76 - 36648 * q^77 - 11040 * q^78 - 29298 * q^79 + 24324 * q^81 - 14592 * q^82 + 23958 * q^83 + 36720 * q^84 + 2772 * q^85 + 30816 * q^86 + 14256 * q^87 + 26064 * q^89 + 14784 * q^90 + 100044 * q^91 + 9360 * q^92 + 26400 * q^93 - 38646 * q^95 - 55746 * q^97 - 64512 * q^98 - 69846 * q^99

Introduction

L-functions

Modular forms

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