LMFDB - Embedded newform 76.6.k.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.k (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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	76.3
Dual form			76.6.k.a.51.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.50165 - 1.31601i) q^{2} +(12.1664 - 4.42820i) q^{3} +(28.5362 + 14.4804i) q^{4} +(-16.8954 + 95.8188i) q^{5} +(-72.7627 + 8.35134i) q^{6} +(-45.6283 + 26.3435i) q^{7} +(-137.940 - 117.220i) q^{8} +(-57.7369 + 48.4470i) q^{9} +O(q^{10})$	\(q+(-5.50165 - 1.31601i) q^{2} +(12.1664 - 4.42820i) q^{3} +(28.5362 + 14.4804i) q^{4} +(-16.8954 + 95.8188i) q^{5} +(-72.7627 + 8.35134i) q^{6} +(-45.6283 + 26.3435i) q^{7} +(-137.940 - 117.220i) q^{8} +(-57.7369 + 48.4470i) q^{9} +(219.051 - 504.926i) q^{10} +(-383.793 - 221.583i) q^{11} +(411.305 + 49.8101i) q^{12} +(190.800 - 524.220i) q^{13} +(285.699 - 84.8855i) q^{14} +(218.748 + 1240.58i) q^{15} +(604.635 + 826.434i) q^{16} +(-1052.61 - 883.248i) q^{17} +(381.405 - 190.556i) q^{18} +(195.414 - 1561.38i) q^{19} +(-1869.63 + 2489.65i) q^{20} +(-438.477 + 522.557i) q^{21} +(1819.89 + 1724.15i) q^{22} +(-1604.11 + 282.847i) q^{23} +(-2197.31 - 815.319i) q^{24} +(-5959.24 - 2168.99i) q^{25} +(-1739.59 + 2632.98i) q^{26} +(-2061.00 + 3569.76i) q^{27} +(-1683.53 + 91.0278i) q^{28} +(-290.897 - 346.678i) q^{29} +(429.142 - 7113.13i) q^{30} +(-1204.89 - 2086.93i) q^{31} +(-2238.89 - 5342.45i) q^{32} +(-5650.59 - 996.351i) q^{33} +(4628.75 + 6244.57i) q^{34} +(-1753.29 - 4817.13i) q^{35} +(-2349.13 + 546.441i) q^{36} +12998.0i q^{37} +(-3129.89 + 8333.00i) q^{38} -7222.76i q^{39} +(13562.4 - 11236.8i) q^{40} +(3516.22 + 9660.74i) q^{41} +(3100.04 - 2297.88i) q^{42} +(10739.0 + 1893.58i) q^{43} +(-7743.40 - 11880.6i) q^{44} +(-3666.64 - 6350.81i) q^{45} +(9197.46 + 554.891i) q^{46} +(10989.0 + 13096.2i) q^{47} +(11015.8 + 7377.27i) q^{48} +(-7015.54 + 12151.3i) q^{49} +(29931.2 + 19775.4i) q^{50} +(-16717.7 - 6084.75i) q^{51} +(13035.7 - 12196.4i) q^{52} +(-16224.4 + 2860.79i) q^{53} +(16036.7 - 16927.3i) q^{54} +(27716.2 - 33030.8i) q^{55} +(9381.96 + 1714.73i) q^{56} +(-4536.63 - 19861.7i) q^{57} +(1144.18 + 2290.12i) q^{58} +(-22154.9 - 18590.2i) q^{59} +(-11721.9 + 38569.2i) q^{60} +(-5614.07 - 31838.9i) q^{61} +(3882.46 + 13067.2i) q^{62} +(1358.17 - 3731.55i) q^{63} +(5286.89 + 32338.7i) q^{64} +(47006.4 + 27139.2i) q^{65} +(29776.3 + 12917.8i) q^{66} +(16744.8 - 14050.5i) q^{67} +(-17247.8 - 40446.9i) q^{68} +(-18263.7 + 10544.5i) q^{69} +(3306.61 + 28809.5i) q^{70} +(-4434.53 + 25149.5i) q^{71} +(13643.2 + 85.1448i) q^{72} +(-64734.5 + 23561.4i) q^{73} +(17105.5 - 71510.5i) q^{74} -82107.1 q^{75} +(28185.8 - 41726.3i) q^{76} +23349.1 q^{77} +(-9505.21 + 39737.1i) q^{78} +(33972.2 - 12364.9i) q^{79} +(-89403.4 + 43972.4i) q^{80} +(-6086.96 + 34520.8i) q^{81} +(-6631.40 - 57777.3i) q^{82} +(-99049.0 + 57186.0i) q^{83} +(-20079.3 + 8562.47i) q^{84} +(102416. - 85937.3i) q^{85} +(-56590.4 - 24550.4i) q^{86} +(-5074.32 - 2929.66i) q^{87} +(26966.4 + 75553.4i) q^{88} +(-24613.6 + 67625.3i) q^{89} +(11814.9 + 39765.3i) q^{90} +(5103.89 + 28945.6i) q^{91} +(-49870.9 - 15156.7i) q^{92} +(-23900.5 - 20054.9i) q^{93} +(-43222.9 - 86512.1i) q^{94} +(146308. + 45104.5i) q^{95} +(-50896.7 - 55084.0i) q^{96} +(31145.2 - 37117.4i) q^{97} +(54588.2 - 57619.5i) q^{98} +(32894.1 - 5800.11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) $ 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−5.50165	−	1.31601i	−0.972563	−	0.232640i
$2$	−5.50165	−	1.31601i	−0.972563	−	0.232640i
$3$	12.1664	−	4.42820i	0.780474	−	0.284069i	0.0791036	−	0.996866i	$-0.474794\pi$
$3$	12.1664	−	4.42820i	0.780474	−	0.284069i	0.701370	+	0.712797i	$0.252572\pi$
$4$	28.5362	+	14.4804i	0.891758	+	0.452513i
$5$	−16.8954	+	95.8188i	−0.302235	+	1.71406i	0.334009	+	0.942570i	$0.391598\pi$
$5$	−16.8954	+	95.8188i	−0.302235	+	1.71406i	−0.636244	+	0.771488i	$0.719513\pi$
$6$	−72.7627	+	8.35134i	−0.825146	+	0.0947062i
$7$	−45.6283	+	26.3435i	−0.351957	+	0.203202i	−0.665547	−	0.746356i	$-0.731802\pi$
$7$	−45.6283	+	26.3435i	−0.351957	+	0.203202i	0.313590	+	0.949558i	$0.398468\pi$
$8$	−137.940	−	117.220i	−0.762018	−	0.647556i
$9$	−57.7369	+	48.4470i	−0.237600	+	0.199370i
$10$	219.051	−	504.926i	0.692700	−	1.59672i
$11$	−383.793	−	221.583i	−0.956347	−	0.552147i	−0.0613000	−	0.998119i	$-0.519525\pi$
$11$	−383.793	−	221.583i	−0.956347	−	0.552147i	−0.895047	+	0.445972i	$0.852858\pi$
$12$	411.305	+	49.8101i	0.824539	+	0.0998538i
$13$	190.800	−	524.220i	0.313127	−	0.860310i	−0.678894	−	0.734237i	$-0.737540\pi$
$13$	190.800	−	524.220i	0.313127	−	0.860310i	0.992021	−	0.126074i	$-0.0402375\pi$
$14$	285.699	−	84.8855i	0.389573	−	0.115748i
$15$	218.748	+	1240.58i	0.251025	+	1.42363i
$16$	604.635	+	826.434i	0.590464	+	0.807064i
$17$	−1052.61	−	883.248i	−0.883378	−	0.741242i	0.0834925	−	0.996508i	$-0.473393\pi$
$17$	−1052.61	−	883.248i	−0.883378	−	0.741242i	−0.966871	+	0.255266i	$0.917837\pi$
$18$	381.405	−	190.556i	0.277463	−	0.138625i
$19$	195.414	−	1561.38i	0.124185	−	0.992259i
$19$	195.414	−	1561.38i	0.124185	−	0.992259i
$20$	−1869.63	+	2489.65i	−1.04515	+	1.39176i
$21$	−438.477	+	522.557i	−0.216970	+	0.258574i
$22$	1819.89	+	1724.15i	0.801656	+	0.759482i
$23$	−1604.11	+	282.847i	−0.632286	+	0.111489i	−0.480600	−	0.876940i	$-0.659581\pi$
$23$	−1604.11	+	282.847i	−0.632286	+	0.111489i	−0.151686	+	0.988429i	$0.548470\pi$
$24$	−2197.31	−	815.319i	−0.778686	−	0.288934i
$25$	−5959.24	−	2168.99i	−1.90696	−	0.694075i
$26$	−1739.59	+	2632.98i	−0.504678	+	0.763860i
$27$	−2061.00	+	3569.76i	−0.544087	+	0.942387i
$28$	−1683.53	+	91.0278i	−0.405812	+	0.0219421i
$29$	−290.897	−	346.678i	−0.0642310	−	0.0765475i	0.732972	−	0.680259i	$-0.238133\pi$
$29$	−290.897	−	346.678i	−0.0642310	−	0.0765475i	−0.797203	+	0.603711i	$0.793688\pi$
$30$	429.142	−	7113.13i	0.0870558	−	1.44297i
$31$	−1204.89	−	2086.93i	−0.225187	−	0.390035i	0.731189	−	0.682175i	$-0.238966\pi$
$31$	−1204.89	−	2086.93i	−0.225187	−	0.390035i	−0.956376	+	0.292140i	$0.905633\pi$
$32$	−2238.89	−	5342.45i	−0.386508	−	0.922286i
$33$	−5650.59	−	996.351i	−0.903252	−	0.159268i
$34$	4628.75	+	6244.57i	0.686699	+	0.926414i
$35$	−1753.29	−	4817.13i	−0.241927	−	0.664689i
$36$	−2349.13	+	546.441i	−0.302100	+	0.0702728i
$37$			12998.0i			1.56089i	0.625224	+	0.780445i	$0.285008\pi$
$37$			12998.0i			1.56089i	−0.625224	+	0.780445i	$0.714992\pi$
$38$	−3129.89	+	8333.00i	−0.351617	+	0.936144i
$39$		−	7222.76i		−	0.760399i
$40$	13562.4	−	11236.8i	1.34026	−	1.11043i
$41$	3516.22	+	9660.74i	0.326675	+	0.897533i	0.988947	+	0.148269i	$0.0473703\pi$
$41$	3516.22	+	9660.74i	0.326675	+	0.897533i	−0.662272	+	0.749264i	$0.730407\pi$
$42$	3100.04	−	2297.88i	0.271171	−	0.201004i
$43$	10739.0	+	1893.58i	0.885714	+	0.156175i	0.597957	−	0.801528i	$-0.295979\pi$
$43$	10739.0	+	1893.58i	0.885714	+	0.156175i	0.287757	+	0.957703i	$0.407090\pi$
$44$	−7743.40	−	11880.6i	−0.602976	−	0.925141i
$45$	−3666.64	−	6350.81i	−0.269921	−	0.467518i
$46$	9197.46	+	554.891i	0.640875	+	0.0386646i
$47$	10989.0	+	13096.2i	0.725627	+	0.864768i	0.995165	−	0.0982216i	$-0.0313154\pi$
$47$	10989.0	+	13096.2i	0.725627	+	0.864768i	−0.269538	+	0.962990i	$0.586871\pi$
$48$	11015.8	+	7377.27i	0.690103	+	0.462160i
$49$	−7015.54	+	12151.3i	−0.417418	+	0.722989i
$50$	29931.2	+	19775.4i	1.69317	+	1.11867i
$51$	−16717.7	−	6084.75i	−0.900018	−	0.327580i
$52$	13035.7	−	12196.4i	0.668535	−	0.625494i
$53$	−16224.4	+	2860.79i	−0.793374	+	0.139893i	−0.555625	−	0.831433i	$-0.687521\pi$
$53$	−16224.4	+	2860.79i	−0.793374	+	0.139893i	−0.237750	+	0.971326i	$0.576410\pi$
$54$	16036.7	−	16927.3i	0.748396	−	0.789954i
$55$	27716.2	−	33030.8i	1.23545	−	1.47236i
$56$	9381.96	+	1714.73i	0.399782	+	0.0730678i
$57$	−4536.63	−	19861.7i	−0.184947	−	0.809709i
$58$	1144.18	+	2290.12i	0.0446607	+	0.0893899i
$59$	−22154.9	−	18590.2i	−0.828590	−	0.695270i	0.126376	−	0.991982i	$-0.459665\pi$
$59$	−22154.9	−	18590.2i	−0.828590	−	0.695270i	−0.954967	+	0.296712i	$0.904110\pi$
$60$	−11721.9	+	38569.2i	−0.420359	+	1.38313i
$61$	−5614.07	−	31838.9i	−0.193176	−	1.09555i	−0.914993	−	0.403471i	$-0.867804\pi$
$61$	−5614.07	−	31838.9i	−0.193176	−	1.09555i	0.721817	−	0.692084i	$-0.243307\pi$
$62$	3882.46	+	13067.2i	0.128271	+	0.431721i
$63$	1358.17	−	3731.55i	0.0431125	−	0.118451i
$64$	5286.89	+	32338.7i	0.161343	+	0.986898i
$65$	47006.4	+	27139.2i	1.37998	+	0.796734i
$66$	29776.3	+	12917.8i	0.841417	+	0.365030i
$67$	16744.8	−	14050.5i	0.455714	−	0.382389i	−0.385837	−	0.922567i	$-0.626087\pi$
$67$	16744.8	−	14050.5i	0.455714	−	0.382389i	0.841551	+	0.540178i	$0.181643\pi$
$68$	−17247.8	−	40446.9i	−0.452337	−	1.06075i
$69$	−18263.7	+	10544.5i	−0.461812	+	0.266627i
$70$	3306.61	+	28809.5i	0.0806563	+	0.702734i
$71$	−4434.53	+	25149.5i	−0.104400	+	0.592083i	0.887058	+	0.461658i	$0.152745\pi$
$71$	−4434.53	+	25149.5i	−0.104400	+	0.592083i	−0.991458	+	0.130425i	$0.958366\pi$
$72$	13643.2	+	85.1448i	0.310159	+	0.00193565i
$73$	−64734.5	+	23561.4i	−1.42177	+	0.517481i	−0.934560	−	0.355805i	$-0.884207\pi$
$73$	−64734.5	+	23561.4i	−1.42177	+	0.517481i	−0.487207	+	0.873286i	$0.661984\pi$
$74$	17105.5	−	71510.5i	0.363125	−	1.51806i
$75$	−82107.1			−1.68549
$76$	28185.8	−	41726.3i	0.559754	−	0.828659i
$77$	23349.1			0.448790
$78$	−9505.21	+	39737.1i	−0.176899	+	0.739536i
$79$	33972.2	−	12364.9i	0.612429	−	0.222906i	−0.0171366	−	0.999853i	$-0.505455\pi$
$79$	33972.2	−	12364.9i	0.612429	−	0.222906i	0.629566	+	0.776947i	$0.283233\pi$
$80$	−89403.4	+	43972.4i	−1.56181	+	0.768166i
$81$	−6086.96	+	34520.8i	−0.103083	+	0.584614i
$82$	−6631.40	−	57777.3i	−0.108911	−	0.948905i
$83$	−99049.0	+	57186.0i	−1.57817	+	0.911159i	−0.583059	+	0.812429i	$0.698145\pi$
$83$	−99049.0	+	57186.0i	−1.57817	+	0.911159i	−0.995114	+	0.0987296i	$0.968522\pi$
$84$	−20079.3	+	8562.47i	−0.310493	+	0.132404i
$85$	102416.	−	85937.3i	1.53752	−	1.29013i
$86$	−56590.4	−	24550.4i	−0.825080	−	0.357943i
$87$	−5074.32	−	2929.66i	−0.0718754	−	0.0414973i
$88$	26966.4	+	75553.4i	0.371207	+	1.04003i
$89$	−24613.6	+	67625.3i	−0.329382	+	0.904970i	0.658886	+	0.752243i	$0.271028\pi$
$89$	−24613.6	+	67625.3i	−0.329382	+	0.904970i	−0.988268	+	0.152727i	$0.951194\pi$
$90$	11814.9	+	39765.3i	0.153752	+	0.517485i
$91$	5103.89	+	28945.6i	0.0646098	+	0.366420i
$92$	−49870.9	−	15156.7i	−0.614296	−	0.186697i
$93$	−23900.5	−	20054.9i	−0.286550	−	0.240444i
$94$	−43222.9	−	86512.1i	−0.504538	−	1.00985i
$95$	146308.	+	45104.5i	1.66326	+	0.512756i
$96$	−50896.7	−	55084.0i	−0.563652	−	0.610025i
$97$	31145.2	−	37117.4i	0.336095	−	0.400542i	−0.571355	−	0.820703i	$-0.693582\pi$
$97$	31145.2	−	37117.4i	0.336095	−	0.400542i	0.907449	+	0.420161i	$0.138026\pi$
$98$	54588.2	−	57619.5i	0.574161	−	0.606044i
$99$	32894.1	−	5800.11i	0.337310	−	0.0594769i
$100$	−138646.	−	148187.i	−1.38646	−	1.48187i
$101$	66302.9	+	24132.3i	0.646739	+	0.235394i	0.644500	−	0.764604i	$-0.277065\pi$
$101$	66302.9	+	24132.3i	0.646739	+	0.235394i	0.00223812	+	0.999997i	$0.499288\pi$
$102$	83967.3	+	55476.8i	0.799116	+	0.527972i
$103$	26577.9	−	46034.4i	0.246847	−	0.427552i	−0.715802	−	0.698303i	$-0.753939\pi$
$103$	26577.9	−	46034.4i	0.246847	−	0.427552i	0.962649	+	0.270751i	$0.0872721\pi$
$104$	−87768.1	+	49945.2i	−0.795708	+	0.452805i
$105$	−42662.5	−	50843.2i	−0.377635	−	0.450048i
$106$	93025.6	+	5612.32i	0.804151	+	0.0485152i
$107$	67568.3	+	117032.i	0.570537	+	0.988199i	0.996511	+	0.0834632i	$0.0265981\pi$
$107$	67568.3	+	117032.i	0.570537	+	0.988199i	−0.425974	+	0.904735i	$0.640069\pi$
$108$	−110505.	+	72023.3i	−0.911637	+	0.594174i
$109$	−65119.8	−	11482.4i	−0.524985	−	0.0925690i	−0.0951264	−	0.995465i	$-0.530326\pi$
$109$	−65119.8	−	11482.4i	−0.524985	−	0.0925690i	−0.429859	+	0.902896i	$0.641437\pi$
$110$	−195953.	+	145249.i	−1.54408	+	1.14454i
$111$	57557.8	+	158139.i	0.443401	+	1.21823i
$112$	−49359.6	−	21780.6i	−0.371815	−	0.164068i
$113$		−	172670.i		−	1.27210i	−0.771647	−	0.636051i	$-0.780567\pi$
$113$		−	172670.i		−	1.27210i	0.771647	−	0.636051i	$-0.219433\pi$
$114$	−1179.19	+	115242.i	−0.00849807	+	0.830519i
$115$		−	158482.i		−	1.11747i
$116$	−3281.07	−	14105.2i	−0.0226397	−	0.0973272i
$117$	14380.7	+	39510.5i	0.0971212	+	0.266838i
$118$	97423.7	+	131433.i	0.644109	+	0.868957i
$119$	71296.9	+	12571.6i	0.461533	+	0.0813808i
$120$	115247.	−	196768.i	0.730596	−	1.24739i
$121$	17672.6	+	30609.8i	0.109733	+	0.190063i
$122$	−11013.7	+	182555.i	−0.0669937	+	1.11044i
$123$	85559.4	+	101966.i	0.509923	+	0.607703i
$124$	−4163.40	−	77000.5i	−0.0243161	−	0.449717i
$125$	156487.	−	271043.i	0.895784	−	1.55154i
$126$	−12382.9	+	18742.3i	−0.0694860	+	0.105171i
$127$	−282924.	−	102976.i	−1.55654	−	0.566535i	−0.586602	−	0.809875i	$-0.699535\pi$
$127$	−282924.	−	102976.i	−1.55654	−	0.566535i	−0.969941	+	0.243340i	$0.921757\pi$
$128$	13471.4	−	184874.i	0.0726753	−	0.997356i
$129$	139040.	−	24516.5i	0.735641	−	0.129713i
$130$	−222897.	−	211171.i	−1.15677	−	1.09591i
$131$	−71393.6	+	85083.6i	−0.363480	+	0.433179i	−0.916528	−	0.399971i	$-0.869020\pi$
$131$	−71393.6	+	85083.6i	−0.363480	+	0.433179i	0.553048	+	0.833150i	$0.313465\pi$
$132$	−146819.	−	110255.i	−0.733411	−	0.550761i
$133$	32215.9	+	76391.1i	0.157921	+	0.374467i
$134$	−110614.	+	55264.8i	−0.532169	+	0.265880i
$135$	−307228.	−	257795.i	−1.45086	−	1.21742i
$136$	41663.1	+	245223.i	0.193154	+	1.13688i
$137$	66963.5	+	379769.i	0.304815	+	1.72869i	0.624372	+	0.781127i	$0.285355\pi$
$137$	66963.5	+	379769.i	0.304815	+	1.72869i	−0.319557	+	0.947567i	$0.603534\pi$
$138$	114357.	−	33977.2i	0.511169	−	0.151876i
$139$	8872.44	−	24376.8i	0.0389499	−	0.107014i	−0.918693	−	0.394972i	$-0.870754\pi$
$139$	8872.44	−	24376.8i	0.0389499	−	0.107014i	0.957643	+	0.287958i	$0.0929765\pi$
$140$	19721.7	−	162851.i	0.0850403	−	0.702217i
$141$	191689.	+	110672.i	0.811987	+	0.468801i
$142$	57494.1	−	132528.i	0.239278	−	0.551550i
$143$	−189386.	+	158914.i	−0.774476	+	0.649863i
$144$	−74948.0	−	18423.0i	−0.301199	−	0.0740379i
$145$	38133.1	−	22016.1i	0.150620	−	0.0869603i
$146$	387153.	−	44435.6i	1.50315	−	0.172524i
$147$	−31545.5	+	178903.i	−0.120405	+	0.682849i
$148$	−188217.	+	370914.i	−0.706324	+	1.39194i
$149$	−164336.	+	59813.6i	−0.606413	+	0.220716i	−0.626933	−	0.779073i	$-0.715690\pi$
$149$	−164336.	+	59813.6i	−0.606413	+	0.220716i	0.0205202	+	0.999789i	$0.493468\pi$
$150$	451724.	+	108054.i	1.63925	+	0.392113i
$151$	496422.			1.77178			0.885888	−	0.463899i	$-0.153550\pi$
$151$	496422.			1.77178			0.885888	+	0.463899i	$0.153550\pi$
$152$	−209981.	+	192471.i	−0.737175	+	0.675702i
$153$	103565.			0.357673
$154$	−128459.	−	30727.6i	−0.436477	−	0.104406i
$155$	220324.	−	80191.5i	0.736602	−	0.268101i
$156$	104589.	−	206111.i	0.344091	−	0.678092i
$157$	−44917.2	+	254738.i	−0.145433	+	0.824793i	0.821585	+	0.570086i	$0.193090\pi$
$157$	−44917.2	+	254738.i	−0.145433	+	0.824793i	−0.967018	+	0.254707i	$0.918021\pi$
$158$	−203175.	+	23319.5i	−0.647483	+	0.0743149i
$159$	−184724.	+	106650.i	−0.579468	+	0.334556i
$160$	549734.	−	124265.i	1.69767	−	0.383750i
$161$	65741.5	−	55163.7i	0.199883	−	0.167721i
$162$	78918.0	−	181911.i	0.236259	−	0.544592i
$163$	−88315.9	−	50989.2i	−0.260357	−	0.150317i	0.364140	−	0.931344i	$-0.381363\pi$
$163$	−88315.9	−	50989.2i	−0.260357	−	0.150317i	−0.624498	+	0.781027i	$0.714696\pi$
$164$	−39551.8	+	326598.i	−0.114830	+	0.948207i
$165$	190938.	−	524598.i	0.545988	−	1.50009i
$166$	620190.	−	184268.i	1.74685	−	0.519014i
$167$	−80322.3	−	455530.i	−0.222867	−	1.26394i	−0.866722	−	0.498792i	$-0.833777\pi$
$167$	−80322.3	−	455530.i	−0.222867	−	1.26394i	0.643855	−	0.765147i	$-0.277334\pi$
$168$	121738.	−	20683.1i	0.332776	−	0.0565384i
$169$	46025.3	+	38619.8i	0.123959	+	0.104014i
$170$	−676551.	+	338016.i	−1.79547	+	0.897047i
$171$	64361.7	+	99616.5i	0.168321	+	0.260520i
$172$	279032.	+	209541.i	0.719171	+	0.540068i
$173$	−179998.	+	214514.i	−0.457250	+	0.544929i	−0.944577	−	0.328291i	$-0.893527\pi$
$173$	−179998.	+	214514.i	−0.457250	+	0.544929i	0.487327	+	0.873219i	$0.337972\pi$
$174$	24061.7	+	22795.8i	0.0602494	+	0.0570798i
$175$	329049.	−	58020.2i	0.812204	−	0.143213i
$176$	−48930.9	−	451156.i	−0.119070	−	1.09786i
$177$	−351866.	−	128069.i	−0.844198	−	0.307263i
$178$	224411.	−	339659.i	0.530877	−	0.803513i
$179$	249376.	−	431931.i	0.581730	−	1.00759i	−0.413545	−	0.910484i	$-0.635709\pi$
$179$	249376.	−	431931.i	0.581730	−	1.00759i	0.995274	−	0.0971016i	$-0.0309572\pi$
$180$	−12669.8	−	234323.i	−0.0291466	−	0.539055i
$181$	111233.	+	132563.i	0.252371	+	0.300764i	0.877324	−	0.479898i	$-0.159326\pi$
$181$	111233.	+	132563.i	0.252371	+	0.300764i	−0.624953	+	0.780662i	$0.714882\pi$
$182$	10012.8	−	165965.i	0.0224068	−	0.371398i
$183$	−209292.	−	362505.i	−0.461982	−	0.800176i
$184$	254426.	+	149018.i	0.554009	+	0.324484i
$185$	−1.24545e6	−	219607.i	−2.67546	−	0.471755i
$186$	105100.	+	141788.i	0.222751	+	0.300509i
$187$	208273.	+	572226.i	0.435541	+	1.19664i
$188$	123946.	+	532841.i	0.255764	+	1.09952i
$189$		−	217176.i		−	0.442239i
$190$	−745577.	−	440692.i	−1.49833	−	0.885627i
$191$			204945.i			0.406493i	0.979128	+	0.203247i	$0.0651493\pi$
$191$			204945.i			0.406493i	−0.979128	+	0.203247i	$0.934851\pi$
$192$	207525.	+	370033.i	0.406272	+	0.724416i
$193$	284839.	+	782588.i	0.550434	+	1.51231i	0.833119	+	0.553093i	$0.186553\pi$
$193$	284839.	+	782588.i	0.550434	+	1.51231i	−0.282685	+	0.959213i	$0.591225\pi$
$194$	−220197.	+	163219.i	−0.420055	+	0.311363i
$195$	692076.	+	122032.i	1.30337	+	0.229819i
$196$	−376153.	+	245164.i	−0.699397	+	0.455844i
$197$	−299117.	−	518087.i	−0.549131	−	0.951123i	−0.998334	−	0.0576935i	$-0.981625\pi$
$197$	−299117.	−	518087.i	−0.549131	−	0.951123i	0.449203	−	0.893430i	$-0.351708\pi$
$198$	−188604.	−	11378.7i	−0.341892	−	0.0206267i
$199$	−672210.	−	801109.i	−1.20330	−	1.43403i	−0.871300	−	0.490751i	$-0.836723\pi$
$199$	−672210.	−	801109.i	−1.20330	−	1.43403i	−0.331996	−	0.943281i	$-0.607722\pi$
$200$	567769.	+	997732.i	1.00368	+	1.76376i
$201$	141505.	−	245093.i	0.247048	−	0.427899i
$202$	−333017.	−	220022.i	−0.574232	−	0.379392i
$203$	22405.9	+	8155.07i	0.0381612	+	0.0138895i
$204$	−388951.	−	415715.i	−0.654364	−	0.699392i
$205$	−985088.	+	173698.i	−1.63716	+	0.288675i
$206$	−206804.	+	218288.i	−0.339540	+	0.358395i
$207$	78913.0	−	94044.9i	0.128004	−	0.152549i
$208$	548598.	−	159278.i	0.879216	−	0.255268i
$209$	−420974.	+	555947.i	−0.666637	+	0.880375i
$210$	167804.	+	335865.i	0.262575	+	0.525553i
$211$	−348238.	−	292207.i	−0.538481	−	0.451839i	0.332537	−	0.943090i	$-0.392095\pi$
$211$	−348238.	−	292207.i	−0.538481	−	0.451839i	−0.871018	+	0.491251i	$0.836540\pi$
$212$	−504408.	−	153299.i	−0.770801	−	0.234261i
$213$	57414.7	+	325615.i	0.0867109	+	0.491762i
$214$	−217722.	−	732788.i	−0.324989	−	1.09381i
$215$	−362881.	+	997007.i	−0.535387	+	1.47096i
$216$	702742.	−	250822.i	1.02485	−	0.365789i
$217$	109954.	+	63482.1i	0.158512	+	0.0915170i
$218$	343155.	+	148870.i	0.489046	+	0.212162i
$219$	−683250.	+	573315.i	−0.962652	+	0.807761i
$220$	1.26922e6	−	541234.i	1.76799	−	0.753926i
$221$	−663855.	+	383277.i	−0.914308	+	0.527876i
$222$	−108551.	−	945770.i	−0.147826	−	1.28796i
$223$	−24375.8	+	138242.i	−0.0328243	+	0.186156i	−0.996811	−	0.0797928i	$-0.974574\pi$
$223$	−24375.8	+	138242.i	−0.0328243	+	0.186156i	0.963987	+	0.265949i	$0.0856853\pi$
$224$	242896.	+	184787.i	0.323445	+	0.246066i
$225$	449149.	−	163477.i	0.591472	−	0.215278i
$226$	−227236.	+	949972.i	−0.295941	+	1.23720i
$227$	172433.			0.222103			0.111052	−	0.993815i	$-0.464578\pi$
$227$	172433.			0.222103			0.111052	+	0.993815i	$0.464578\pi$
$228$	158147.	−	632471.i	0.201477	−	0.805755i
$229$	1.14255e6			1.43975			0.719874	−	0.694105i	$-0.244200\pi$
$229$	1.14255e6			1.43975			0.719874	+	0.694105i	$0.244200\pi$
$230$	−208564.	+	871914.i	−0.259968	+	1.08681i
$231$	284074.	−	103395.i	0.350269	−	0.127488i
$232$	−511.247	+	81919.7i	−0.000623607	+	0.0999237i
$233$	125169.	−	709871.i	0.151046	−	0.856623i	−0.811267	−	0.584676i	$-0.801222\pi$
$233$	125169.	−	709871.i	0.151046	−	0.856623i	0.962312	−	0.271946i	$-0.0876674\pi$
$234$	−27121.1	−	236298.i	−0.0323794	−	0.282111i
$235$	−1.44052e6	+	831686.i	−1.70157	+	0.982403i
$236$	−363024.	−	851306.i	−0.424283	−	0.994960i
$237$	358565.	−	300871.i	0.414664	−	0.347945i
$238$	−375706.	−	162992.i	−0.429938	−	0.186519i
$239$	−305525.	−	176395.i	−0.345980	−	0.199752i	0.316933	−	0.948448i	$-0.397347\pi$
$239$	−305525.	−	176395.i	−0.345980	−	0.199752i	−0.662913	+	0.748696i	$0.730680\pi$
$240$	−892998.	+	930881.i	−1.00074	+	1.04320i
$241$	99379.3	−	273042.i	0.110218	−	0.302822i	−0.872305	−	0.488962i	$-0.837376\pi$
$241$	99379.3	−	273042.i	0.110218	−	0.302822i	0.982523	+	0.186140i	$0.0595978\pi$
$242$	−56945.5	−	191661.i	−0.0625059	−	0.210376i
$243$	−95125.0	−	539481.i	−0.103343	−	0.586085i
$244$	300837.	−	989858.i	0.323487	−	1.06438i
$245$	−1.04579e6	−	877521.i	−1.11309	−	0.933990i
$246$	−336530.	−	673576.i	−0.354557	−	0.709658i
$247$	−781222.	−	400352.i	−0.814765	−	0.417541i
$248$	−78427.7	+	429109.i	−0.0809730	+	0.443035i
$249$	−951837.	+	1.13436e6i	−0.972891	+	1.15945i
$250$	−1.21763e6	+	1.28525e6i	−1.23216	+	1.30058i
$251$	1.19429e6	−	210586.i	1.19654	−	0.210982i	0.460336	−	0.887745i	$-0.347729\pi$
$251$	1.19429e6	−	210586.i	1.19654	−	0.210982i	0.736201	+	0.676763i	$0.236618\pi$
$252$	92791.6	−	86817.5i	0.0920465	−	0.0861204i
$253$	678319.	+	246888.i	0.666243	+	0.242493i
$254$	1.42103e6	+	938869.i	1.38204	+	0.913105i
$255$	865486.	−	1.49906e6i	0.833507	−	1.44368i
$256$	−317410.	+	999381.i	−0.302706	+	0.953084i
$257$	−84408.9	−	100595.i	−0.0797178	−	0.0950040i	0.724711	−	0.689053i	$-0.241973\pi$
$257$	−84408.9	−	100595.i	−0.0797178	−	0.0950040i	−0.804429	+	0.594049i	$0.797529\pi$
$258$	−797214.	−	48096.7i	−0.745634	−	0.0449848i
$259$	−342413.	−	593077.i	−0.317177	−	0.549366i
$260$	948400.	+	1.45512e6i	0.870078	+	1.33495i
$261$	33591.0	+	5923.00i	0.0305226	+	0.00538196i
$262$	504753.	−	374145.i	0.454282	−	0.336734i
$263$	−293354.	−	805983.i	−0.261518	−	0.718516i	−0.999066	−	0.0432204i	$-0.986238\pi$
$263$	−293354.	−	805983.i	−0.261518	−	0.718516i	0.737547	−	0.675296i	$-0.235984\pi$
$264$	662650.	+	799799.i	0.585159	+	0.706271i
$265$		−	1.60293e6i		−	1.40217i
$266$	−76709.2	−	462673.i	−0.0664727	−	0.400932i
$267$			931749.i			0.799873i
$268$	681290.	−	158478.i	0.579422	−	0.134782i
$269$	77788.0	+	213721.i	0.0655438	+	0.180080i	0.968141	−	0.250406i	$-0.0805642\pi$
$269$	77788.0	+	213721.i	0.0655438	+	0.180080i	−0.902597	+	0.430487i	$0.858342\pi$
$270$	1.35100e6	+	1.82261e6i	1.12784	+	1.52155i
$271$	1.73871e6	+	306582.i	1.43815	+	0.253585i	0.837723	−	0.546095i	$-0.183886\pi$
$271$	1.73871e6	+	306582.i	1.43815	+	0.253585i	0.600427	+	0.799680i	$0.294997\pi$
$272$	93499.1	−	1.40396e6i	0.0766276	−	1.15062i
$273$	190273.	+	329562.i	0.154515	+	0.267628i
$274$	131369.	−	2.17748e6i	0.105710	−	1.75218i
$275$	1.80650e6	+	2.15291e6i	1.44048	+	1.71670i
$276$	−673866.	+	36435.8i	−0.532477	+	0.0287909i
$277$	−538627.	+	932929.i	−0.421783	+	0.730549i	−0.996114	−	0.0880739i	$-0.971929\pi$
$277$	−538627.	+	932929.i	−0.421783	+	0.730549i	0.574331	+	0.818623i	$0.305262\pi$
$278$	−80893.1	+	122436.i	−0.0627768	+	0.0950164i
$279$	170672.	+	62119.6i	0.131266	+	0.0477769i
$280$	−322816.	+	869997.i	−0.246070	+	0.663166i
$281$	1.32224e6	−	233147.i	0.998955	−	0.176143i	0.349821	−	0.936817i	$-0.386243\pi$
$281$	1.32224e6	−	233147.i	0.998955	−	0.176143i	0.649134	+	0.760674i	$0.275131\pi$
$282$	−908959.	−	861140.i	−0.680647	−	0.644838i
$283$	−765769.	+	912608.i	−0.568371	+	0.677358i	−0.971296	−	0.237875i	$-0.923549\pi$
$283$	−765769.	+	912608.i	−0.568371	+	0.677358i	0.402925	+	0.915233i	$0.367994\pi$
$284$	−490719.	+	653457.i	−0.361025	+	0.480752i
$285$	1.97977e6	−	99122.8i	1.44379	−	0.0722872i
$286$	1.25107e6	−	625054.i	0.904410	−	0.451859i
$287$	−414937.	−	348174.i	−0.297357	−	0.249512i
$288$	388093.	+	199989.i	0.275711	+	0.142077i
$289$	81313.5	+	461152.i	0.0572688	+	0.324787i
$290$	−238768.	+	70941.6i	−0.166718	+	0.0495343i
$291$	214561.	−	589501.i	0.148531	−	0.408087i
$292$	−2.18846e6	−	265028.i	−1.50204	−	0.181901i
$293$	1.19661e6	+	690863.i	0.814299	+	0.470136i	0.848446	−	0.529281i	$-0.177538\pi$
$293$	1.19661e6	+	690863.i	0.814299	+	0.470136i	−0.0341478	+	0.999417i	$0.510872\pi$
$294$	408990.	−	942748.i	0.275959	−	0.636103i
$295$	2.15560e6	−	1.80877e6i	1.44216	−	1.21012i
$296$	1.52363e6	−	1.79295e6i	1.01076	−	1.18943i
$297$	1.58199e6	−	913365.i	1.04067	−	0.600832i
$298$	982836.	−	112805.i	0.641122	−	0.0735848i
$299$	−157790.	+	894872.i	−0.102071	+	0.578872i
$300$	−2.34303e6	−	1.18895e6i	−1.50305	−	0.762709i
$301$	−539887.	+	196503.i	−0.343468	+	0.125012i
$302$	−2.73114e6	−	653296.i	−1.72316	−	0.412185i
$303$	913528.			0.571631
$304$	1.40853e6	−	782569.i	0.874144	−	0.485667i
$305$	3.14562e6			1.93623
$306$	−569780.	−	136293.i	−0.347859	−	0.0832089i
$307$	−2.24872e6	+	818468.i	−1.36173	+	0.495628i	−0.916588	−	0.399834i	$-0.869068\pi$
$307$	−2.24872e6	+	818468.i	−1.36173	+	0.495628i	−0.445139	+	0.895462i	$0.646846\pi$
$308$	666296.	+	338105.i	0.400212	+	0.203084i
$309$	119508.	−	677764.i	0.0712035	−	0.403815i
$310$	−1.31768e6	+	151237.i	−0.778763	+	0.0893826i
$311$	1.12026e6	−	646782.i	0.656777	−	0.379190i	−0.134271	−	0.990945i	$-0.542869\pi$
$311$	1.12026e6	−	646782.i	0.656777	−	0.379190i	0.791048	+	0.611754i	$0.209536\pi$
$312$	−846653.	+	996308.i	−0.492401	+	0.579438i
$313$	801006.	−	672124.i	0.462142	−	0.387783i	−0.381777	−	0.924255i	$-0.624688\pi$
$313$	801006.	−	672124.i	0.462142	−	0.387783i	0.843918	+	0.536472i	$0.180243\pi$
$314$	582356.	−	1.34237e6i	0.333323	−	0.768330i
$315$	334605.	+	193185.i	0.190001	+	0.109697i
$316$	1.14849e6	+	139085.i	0.647006	+	0.0783542i
$317$	−291540.	+	800999.i	−0.162948	+	0.447697i	−0.994115	−	0.108326i	$-0.965451\pi$
$317$	−291540.	+	800999.i	−0.162948	+	0.447697i	0.831167	+	0.556023i	$0.187673\pi$
$318$	1.15664e6	−	343654.i	0.641401	−	0.190570i
$319$	34826.4	+	197510.i	0.0191616	+	0.108671i
$320$	−3.18798e6	−	39792.8i	−1.74036	−	0.0217235i
$321$	1.34030e6	+	1.12465e6i	0.726006	+	0.609191i
$322$	−434282.	+	216975.i	−0.233417	+	0.116619i
$323$	−1.58478e6	+	1.47093e6i	−0.845207	+	0.784489i
$324$	−673575.	+	896954.i	−0.356471	+	0.474687i
$325$	−2.27405e6	+	2.71011e6i	−1.19424	+	1.42324i
$326$	418780.	+	396749.i	0.218244	+	0.206762i
$327$	−843119.	+	148665.i	−0.436033	+	0.0768844i
$328$	647405.	−	1.74477e6i	0.332270	−	0.895477i
$329$	−846408.	−	308067.i	−0.431112	−	0.156912i
$330$	−1.74085e6	+	2.63488e6i	−0.879988	+	1.33191i
$331$	−1.39074e6	+	2.40883e6i	−0.697711	+	1.20847i	0.271547	+	0.962425i	$0.412465\pi$
$331$	−1.39074e6	+	2.40883e6i	−0.697711	+	1.20847i	−0.969258	+	0.246046i	$0.920868\pi$
$332$	−3.65456e6	+	197601.i	−1.81966	+	0.0983886i
$333$	−629715.	−	750465.i	−0.311195	−	0.370868i
$334$	−157577.	+	2.61187e6i	−0.0772904	+	1.28111i
$335$	1.06339e6	+	1.84185e6i	0.517705	+	0.896691i
$336$	−696977.	−	46416.5i	−0.336799	−	0.0224297i
$337$	−3.48005e6	−	613627.i	−1.66921	−	0.294327i	−0.742429	−	0.669925i	$-0.766326\pi$
$337$	−3.48005e6	−	613627.i	−1.66921	−	0.294327i	−0.926783	+	0.375598i	$0.877437\pi$
$338$	−202391.	−	273042.i	−0.0963605	−	0.129998i
$339$	−764620.	−	2.10077e6i	−0.361365	−	0.992842i
$340$	4.16698e6	−	969299.i	1.95490	−	0.454737i
$341$			1.06793e6i			0.497345i
$342$	−222999.	−	632756.i	−0.103095	−	0.292530i
$343$		−	1.62477e6i		−	0.745686i
$344$	−1.25938e6	−	1.52003e6i	−0.573798	−	0.692558i
$345$	−701792.	−	1.92816e6i	−0.317439	−	0.872157i
$346$	1.27259e6	−	943300.i	0.571476	−	0.423603i
$347$	−2.88760e6	−	509162.i	−1.28740	−	0.227003i	−0.512280	−	0.858818i	$-0.671199\pi$
$347$	−2.88760e6	−	509162.i	−1.28740	−	0.227003i	−0.775119	+	0.631815i	$0.782310\pi$
$348$	−102379.	−	157080.i	−0.0453174	−	0.0695301i
$349$	1.40855e6	+	2.43968e6i	0.619026	+	1.07218i	0.989664	+	0.143407i	$0.0458059\pi$
$349$	1.40855e6	+	2.43968e6i	0.619026	+	1.07218i	−0.370637	+	0.928778i	$0.620861\pi$
$350$	−1.88667e6	−	113824.i	−0.823237	−	0.0496666i
$351$	1.47810e6	+	1.76153e6i	0.640376	+	0.763171i
$352$	−324525.	+	2.54650e6i	−0.139602	+	1.09543i
$353$	2.08660e6	−	3.61411e6i	0.891258	−	1.54370i	0.0528894	−	0.998600i	$-0.483157\pi$
$353$	2.08660e6	−	3.61411e6i	0.891258	−	1.54370i	0.838369	−	0.545104i	$-0.183510\pi$
$354$	1.76730e6	+	1.16765e6i	0.749554	+	0.495226i
$355$	−2.33487e6	−	849822.i	−0.983311	−	0.357896i
$356$	−1.68162e6	+	1.57336e6i	−0.703240	+	0.657964i
$357$	923094.	−	162766.i	0.383332	−	0.0675918i
$358$	−1.94040e6	+	2.04815e6i	−0.800173	+	0.844607i
$359$	1.33289e6	−	1.58847e6i	0.545830	−	0.650494i	−0.420655	−	0.907221i	$-0.638200\pi$
$359$	1.33289e6	−	1.58847e6i	0.545830	−	0.650494i	0.966484	+	0.256727i	$0.0826440\pi$
$360$	−238666.	+	1.30584e6i	−0.0970587	+	0.531046i
$361$	−2.39973e6	−	610230.i	−0.969156	−	0.246448i
$362$	−437513.	−	875698.i	−0.175477	−	0.351223i
$363$	350557.	+	294153.i	0.139634	+	0.117167i
$364$	−273499.	+	899906.i	−0.108194	+	0.355995i
$365$	−1.16391e6	−	6.60086e6i	−0.457285	−	2.59339i
$366$	674392.	+	2.26980e6i	0.263154	+	0.885697i
$367$	−707302.	+	1.94330e6i	−0.274119	+	0.753137i	0.723881	+	0.689925i	$0.242357\pi$
$367$	−707302.	+	1.94330e6i	−0.274119	+	0.753137i	−0.998000	+	0.0632117i	$0.979866\pi$
$368$	−1.20365e6	−	1.15467e6i	−0.463321	−	0.444465i
$369$	−671049.	−	387431.i	−0.256560	−	0.148125i
$370$	6.56304e6	+	2.84723e6i	2.49230	+	1.08123i
$371$	664927.	−	557940.i	0.250807	−	0.210452i
$372$	−391627.	−	918381.i	−0.146729	−	0.344085i
$373$	261070.	−	150729.i	0.0971596	−	0.0560951i	−0.450633	−	0.892709i	$-0.648802\pi$
$373$	261070.	−	150729.i	0.0971596	−	0.0560951i	0.547793	+	0.836614i	$0.315468\pi$
$374$	−392792.	−	3.42227e6i	−0.145206	−	1.26513i
$375$	703646.	−	3.99057e6i	0.258390	−	1.46540i
$376$	19313.0	−	3.09462e6i	0.00704497	−	1.12885i
$377$	−237239.	+	86347.8i	−0.0859671	+	0.0312895i
$378$	−285805.	+	1.19483e6i	−0.102882	+	0.430106i
$379$	3.22828e6			1.15445			0.577223	−	0.816586i	$-0.304136\pi$
$379$	3.22828e6			1.15445			0.577223	+	0.816586i	$0.304136\pi$
$380$	3.52195e6	+	3.40572e6i	1.25119	+	1.20990i
$381$	−3.89817e6			−1.37578
$382$	269709.	−	1.12753e6i	0.0945664	−	0.395340i
$383$	−3.66219e6	+	1.33293e6i	−1.27568	+	0.464311i	−0.889003	−	0.457902i	$-0.848601\pi$
$383$	−3.66219e6	+	1.33293e6i	−1.27568	+	0.464311i	−0.386682	+	0.922213i	$0.626379\pi$
$384$	−654760.	−	2.30890e6i	−0.226597	−	0.799055i
$385$	−394493.	+	2.23728e6i	−0.135640	+	0.769253i
$386$	−537190.	−	4.68037e6i	−0.183510	−	1.59887i
$387$	−711776.	+	410944.i	−0.241583	+	0.139478i
$388$	1.42624e6	−	608195.i	0.480965	−	0.205099i
$389$	1.08262e6	−	908425.i	0.362745	−	0.304379i	−0.443139	−	0.896453i	$-0.646135\pi$
$389$	1.08262e6	−	908425.i	0.362745	−	0.304379i	0.805884	+	0.592074i	$0.201691\pi$
$390$	−3.64696e6	−	1.58215e6i	−1.21414	−	0.526729i
$391$	1.93833e6	+	1.11909e6i	0.641188	+	0.370190i
$392$	2.39210e6	−	853784.i	0.786255	−	0.280629i
$393$	−491835.	+	1.35130e6i	−0.160634	+	0.441338i
$394$	963832.	+	3.24397e6i	0.312796	+	1.05278i
$395$	610811.	+	3.46408e6i	0.196976	+	1.11711i
$396$	1.02266e6	+	310806.i	0.327713	+	0.0995983i
$397$	402501.	+	337739.i	0.128171	+	0.107548i	0.704620	−	0.709585i	$-0.251117\pi$
$397$	402501.	+	337739.i	0.128171	+	0.107548i	−0.576449	+	0.817133i	$0.695562\pi$
$398$	2.64400e6	+	5.29205e6i	0.836668	+	1.67462i
$399$	730226.	+	786745.i	0.229628	+	0.247401i
$400$	−1.81064e6	−	6.23636e6i	−0.565825	−	1.94886i
$401$	−1.49022e6	+	1.77597e6i	−0.462796	+	0.551538i	−0.946083	−	0.323923i	$-0.894998\pi$
$401$	−1.49022e6	+	1.77597e6i	−0.462796	+	0.551538i	0.483288	+	0.875462i	$0.339443\pi$
$402$	−1.10105e6	+	1.16220e6i	−0.339815	+	0.358686i
$403$	−1.32390e6	+	233440.i	−0.406064	+	0.0716000i
$404$	1.54259e6	+	1.64874e6i	0.470215	+	0.502572i
$405$	−3.20490e6	−	1.16649e6i	−0.970906	−	0.353381i
$406$	−112537.	−	74352.6i	−0.0338829	−	0.0223862i
$407$	2.88014e6	−	4.98855e6i	0.861841	−	1.49275i
$408$	1.59279e6	+	2.79898e6i	0.473704	+	0.832433i
$409$	739452.	+	881245.i	0.218576	+	0.260488i	0.864179	−	0.503185i	$-0.167838\pi$
$409$	739452.	+	881245.i	0.218576	+	0.260488i	−0.645603	+	0.763673i	$0.723394\pi$
$410$	5.64819e6	+	340761.i	1.65940	+	0.100113i
$411$	2.49640e6	+	4.32389e6i	0.728969	+	1.26261i
$412$	1.42503e6	−	928788.i	0.413601	−	0.269571i
$413$	1.50062e6	+	264600.i	0.432909	+	0.0763335i
$414$	−557915.	+	413552.i	−0.159981	+	0.118585i
$415$	−3.80601e6	−	1.04569e7i	−1.08480	−	2.98047i
$416$	−3.22780e6	+	154330.i	−0.914478	+	0.0437238i
$417$		−	335867.i		−	0.0945860i
$418$	3.04768e6	−	2.50462e6i	0.853157	−	0.701134i
$419$			4.99314e6i			1.38944i	0.719282	+	0.694718i	$0.244471\pi$
$419$			4.99314e6i			1.38944i	−0.719282	+	0.694718i	$0.755529\pi$
$420$	−481196.	−	2.06864e6i	−0.133106	−	0.572219i
$421$	1.84726e6	+	5.07529e6i	0.507951	+	1.39558i	0.883347	+	0.468719i	$0.155284\pi$
$421$	1.84726e6	+	5.07529e6i	0.507951	+	1.39558i	−0.375396	+	0.926864i	$0.622493\pi$
$422$	1.53134e6	+	2.06590e6i	0.418591	+	0.564714i
$423$	−1.26894e6	−	223748.i	−0.344818	−	0.0608008i
$424$	2.57333e6	+	1.50720e6i	0.695154	+	0.407153i
$425$	4.35703e6	+	7.54659e6i	1.17009	+	2.02665i
$426$	112636.	−	1.86698e6i	0.0300715	−	0.498442i
$427$	1.09491e6	+	1.30486e6i	0.290609	+	0.346334i
$428$	233477.	+	4.31806e6i	0.0616076	+	1.13941i
$429$	−1.60044e6	+	2.77205e6i	−0.419852	+	0.727206i
$430$	3.30851e6	−	5.00763e6i	0.862902	−	1.30605i
$431$	−1.69084e6	−	615417.i	−0.438440	−	0.159579i	0.113363	−	0.993554i	$-0.463838\pi$
$431$	−1.69084e6	−	615417.i	−0.438440	−	0.159579i	−0.551803	+	0.833974i	$0.686060\pi$
$432$	−4.19632e6	+	455118.i	−1.08183	+	0.117332i
$433$	−5.64578e6	+	995503.i	−1.44712	+	0.255166i	−0.841357	−	0.540480i	$-0.818243\pi$
$433$	−5.64578e6	+	995503.i	−1.44712	+	0.255166i	−0.605762	+	0.795646i	$0.707132\pi$
$434$	−521386.	−	493957.i	−0.132873	−	0.125882i
$435$	366450.	−	436718.i	0.0928520	−	0.110657i
$436$	−1.69201e6	−	1.27063e6i	−0.426271	−	0.320112i
$437$	128168.	+	2.55989e6i	0.0321053	+	0.641237i
$438$	4.51349e6	−	2.25501e6i	1.12416	−	0.561647i
$439$	−3.97973e6	−	3.33939e6i	−0.985582	−	0.827002i	−0.000659942	−	1.00000i	$-0.500210\pi$
$439$	−3.97973e6	−	3.33939e6i	−0.985582	−	0.827002i	−0.984922	+	0.172998i	$0.944655\pi$
$440$	−7.69504e6	+	1.30738e6i	−1.89487	+	0.321937i
$441$	−183637.	−	1.04146e6i	−0.0449639	−	0.255003i
$442$	4.15669e6	−	1.23502e6i	1.01203	−	0.300689i
$443$	1.38047e6	−	3.79282e6i	0.334209	−	0.918232i	−0.652795	−	0.757535i	$-0.726404\pi$
$443$	1.38047e6	−	3.79282e6i	0.334209	−	0.918232i	0.987004	−	0.160697i	$-0.0513742\pi$
$444$	−647433.	+	5.34615e6i	−0.155861	+	1.28701i
$445$	−6.06391e6	−	3.50100e6i	−1.45162	−	0.838093i
$446$	316034.	−	728479.i	0.0752310	−	0.173412i
$447$	−1.73451e6	+	1.45543e6i	−0.410591	+	0.344526i
$448$	−1.09315e6	−	1.33628e6i	−0.257326	−	0.314560i
$449$	1.67762e6	−	968572.i	0.392714	−	0.226734i	−0.290621	−	0.956838i	$-0.593862\pi$
$449$	1.67762e6	−	968572.i	0.392714	−	0.226734i	0.683336	+	0.730104i	$0.260529\pi$
$450$	−2.68620e6	+	308308.i	−0.625326	+	0.0717718i
$451$	791154.	−	4.48686e6i	0.183155	−	1.03873i
$452$	2.50034e6	−	4.92737e6i	0.575643	−	1.13441i
$453$	6.03966e6	−	2.19826e6i	1.38282	−	0.503307i
$454$	−948663.	−	226923.i	−0.216009	−	0.0516700i
$455$	−2.85977e6			−0.647593
$456$	−1.70241e6	+	3.27151e6i	−0.383399	+	0.736777i
$457$	−5.28943e6			−1.18473			−0.592364	−	0.805671i	$-0.701805\pi$
$457$	−5.28943e6			−1.18473			−0.592364	+	0.805671i	$0.701805\pi$
$458$	−6.28591e6	−	1.50360e6i	−1.40025	−	0.334942i
$459$	5.32242e6	−	1.93720e6i	1.17917	−	0.429184i
$460$	2.29489e6	−	4.52249e6i	0.505670	−	0.996513i
$461$	636245.	−	3.60833e6i	0.139435	−	0.790776i	−0.832233	−	0.554426i	$-0.812938\pi$
$461$	636245.	−	3.60833e6i	0.139435	−	0.790776i	0.971668	−	0.236350i	$-0.0759512\pi$
$462$	−1.69894e6	+	194996.i	−0.370317	+	0.0425032i
$463$	6.35693e6	−	3.67017e6i	1.37814	−	0.795672i	0.386209	−	0.922411i	$-0.373784\pi$
$463$	6.35693e6	−	3.67017e6i	1.37814	−	0.795672i	0.991936	+	0.126739i	$0.0404511\pi$
$464$	110620.	−	450021.i	0.0238527	−	0.0970370i
$465$	2.32545e6	−	1.95128e6i	0.498740	−	0.418492i
$466$	−1.62283e6	+	3.74074e6i	−0.346186	+	0.797980i
$467$	401005.	+	231520.i	0.0850858	+	0.0491243i	0.541939	−	0.840418i	$-0.317690\pi$
$467$	401005.	+	231520.i	0.0850858	+	0.0491243i	−0.456853	+	0.889542i	$0.651024\pi$
$468$	−161759.	+	1.33572e6i	−0.0341393	+	0.281904i
$469$	−393895.	+	1.08222e6i	−0.0826891	+	0.227187i
$470$	9.01975e6	−	2.67990e6i	1.88343	−	0.559596i
$471$	581552.	+	3.29815e6i	0.120792	+	0.685043i
$472$	876906.	+	5.16133e6i	0.181175	+	1.06637i
$473$	−3.70198e6	−	3.10633e6i	−0.760818	−	0.638402i
$474$	−2.36865e6	+	1.18341e6i	−0.484233	+	0.241931i
$475$	−4.55113e6	+	8.88080e6i	−0.925519	+	1.80600i
$476$	1.85250e6	+	1.39115e6i	0.374750	+	0.281422i
$477$	798148.	−	951196.i	0.160615	−	0.191414i
$478$	1.44875e6	+	1.37253e6i	0.290017	+	0.274760i
$479$	−168587.	+	29726.4i	−0.0335726	+	0.00591975i	−0.190409	−	0.981705i	$-0.560981\pi$
$479$	−168587.	+	29726.4i	−0.0335726	+	0.00591975i	0.156837	+	0.987625i	$0.449870\pi$
$480$	6.13801e6	−	3.94619e6i	1.21597	−	0.781762i
$481$	6.81381e6	+	2.48003e6i	1.34285	+	0.488758i
$482$	−906076.	+	1.37140e6i	−0.177643	+	0.268872i
$483$	555560.	−	962259.i	0.108359	−	0.187683i
$484$	61066.0	+	1.12939e6i	0.0118491	+	0.219145i
$485$	3.03033e6	+	3.61141e6i	0.584973	+	0.697143i
$486$	−186617.	+	3.09322e6i	−0.0358393	+	0.594046i
$487$	−327951.	−	568028.i	−0.0626595	−	0.108529i	0.832994	−	0.553282i	$-0.186625\pi$
$487$	−327951.	−	568028.i	−0.0626595	−	0.108529i	−0.895653	+	0.444753i	$0.853292\pi$
$488$	−2.95776e6	+	5.04995e6i	−0.562229	+	0.959925i
$489$	−1.30027e6	−	229274.i	−0.245903	−	0.0433593i
$490$	4.59874e6	+	6.20408e6i	0.865263	+	1.16731i
$491$	−1.98105e6	−	5.44288e6i	−0.370844	−	1.01889i	−0.975036	−	0.222047i	$-0.928726\pi$
$491$	−1.98105e6	−	5.44288e6i	−0.370844	−	1.01889i	0.604192	−	0.796839i	$-0.293496\pi$
$492$	965037.	+	4.14865e6i	0.179734	+	0.772671i
$493$			621852.i			0.115231i
$494$	3.77114e6	+	3.23069e6i	0.695273	+	0.595632i
$495$			3.24986e6i			0.596145i
$496$	996192.	−	2.25759e6i	0.181819	−	0.412042i
$497$	−460185.	−	1.26435e6i	−0.0835683	−	0.229602i
$498$	6.72949e6	−	4.98820e6i	1.21593	−	0.901302i
$499$	7.06305e6	+	1.24541e6i	1.26982	+	0.223903i	0.767650	−	0.640869i	$-0.221426\pi$
$499$	7.06305e6	+	1.24541e6i	1.26982	+	0.223903i	0.502165	+	0.864772i	$0.332537\pi$
$500$	8.39037e6	−	5.46856e6i	1.50092	−	0.978246i
$501$	−2.99441e6	−	5.18647e6i	−0.532988	−	0.923162i
$502$	−6.84771e6	−	413129.i	−1.21279	−	0.0731688i
$503$	−3.23107e6	−	3.85064e6i	−0.569412	−	0.678599i	0.402098	−	0.915596i	$-0.368281\pi$
$503$	−3.23107e6	−	3.85064e6i	−0.569412	−	0.678599i	−0.971510	+	0.236998i	$0.923837\pi$
$504$	−624759.	+	355525.i	−0.109556	+	0.0623438i
$505$	−3.43254e6	+	5.94533e6i	−0.598945	+	1.03740i
$506$	−3.40697e6	−	2.25096e6i	−0.591550	−	0.390834i
$507$	730977.	+	266054.i	0.126294	+	0.0459674i
$508$	−6.58246e6	−	7.03542e6i	−1.13169	−	1.20957i
$509$	−741778.	+	130795.i	−0.126905	+	0.0223768i	−0.236740	−	0.971573i	$-0.576079\pi$
$509$	−741778.	+	130795.i	−0.126905	+	0.0223768i	0.109835	+	0.993950i	$0.464968\pi$
$510$	−6.73438e6	+	7.10834e6i	−1.14649	+	1.21016i
$511$	2.33303e6	−	2.78040e6i	0.395247	−	0.471037i
$512$	3.06147e6	−	5.08053e6i	0.516125	−	0.856513i
$513$	5.17101e6	+	3.91559e6i	0.867524	+	0.656906i
$514$	332005.	+	664519.i	0.0554289	+	0.110943i
$515$	3.96191e6	+	3.32444e6i	0.658243	+	0.552332i
$516$	4.32270e6	+	1.31375e6i	0.714711	+	0.217215i
$517$	−1.31561e6	−	7.46119e6i	−0.216471	−	1.22767i
$518$	1.10334e6	+	3.71352e6i	0.180670	+	0.608081i
$519$	−1.24002e6	+	3.40693e6i	−0.202074	+	0.555193i
$520$	−3.30281e6	−	9.25368e6i	−0.535643	−	1.50074i
$521$	−1.62788e6	−	939856.i	−0.262741	−	0.151693i	0.362843	−	0.931850i	$-0.381806\pi$
$521$	−1.62788e6	−	939856.i	−0.262741	−	0.151693i	−0.625584	+	0.780157i	$0.715139\pi$
$522$	−177011.	−	76792.3i	−0.0284331	−	0.0123351i
$523$	−6.68821e6	+	5.61207e6i	−1.06919	+	0.897158i	−0.994979	−	0.100084i	$-0.968089\pi$
$523$	−6.68821e6	+	5.61207e6i	−1.06919	+	0.897158i	−0.0742124	+	0.997242i	$0.523644\pi$
$524$	−3.26935e6	+	1.39416e6i	−0.520156	+	0.221811i
$525$	3.74641e6	−	2.16299e6i	0.593221	−	0.342497i
$526$	553249.	+	4.82029e6i	0.0871879	+	0.759642i
$527$	−574993.	+	3.26095e6i	−0.0901854	+	0.511467i
$528$	−2.59312e6	−	5.27226e6i	−0.404798	−	0.823024i
$529$	−3.55503e6	+	1.29392e6i	−0.552337	+	0.201034i
$530$	−2.10947e6	+	8.81877e6i	−0.326200	+	1.36370i
$531$	2.17979e6			0.335490
$532$	−186855.	+	2.64642e6i	−0.0286237	+	0.405395i
$533$	5.73525e6			0.874448
$534$	1.22619e6	−	5.12616e6i	0.186082	−	0.777927i
$535$	−1.23554e7	+	4.49701e6i	−1.86627	+	0.679265i
$536$	−3.95678e6	−	24693.6i	−0.594880	−	0.00371254i
$537$	1.12132e6	−	6.35932e6i	0.167801	−	0.951645i
$538$	−146704.	−	1.27819e6i	−0.0218517	−	0.190387i
$539$	5.38503e6	−	3.10905e6i	0.798392	−	0.460952i
$540$	−5.03416e6	−	1.18053e7i	−0.742921	−	1.74218i
$541$	−1.35840e6	+	1.13983e6i	−0.199541	+	0.167435i	−0.737083	−	0.675802i	$-0.763797\pi$
$541$	−1.35840e6	+	1.13983e6i	−0.199541	+	0.167435i	0.537542	+	0.843237i	$0.319353\pi$
$542$	−9.16231e6	−	3.97486e6i	−1.33970	−	0.581198i
$543$	1.94032e6	+	1.12025e6i	0.282406	+	0.163047i
$544$	−2.36202e6	+	7.60104e6i	−0.342205	+	1.10122i
$545$	2.20046e6	−	6.04570e6i	0.317337	−	0.871877i
$546$	−613108.	−	2.06354e6i	−0.0880147	−	0.296231i
$547$	290572.	+	1.64792e6i	0.0415227	+	0.235487i	0.998505	−	0.0546592i	$-0.0174072\pi$
$547$	290572.	+	1.64792e6i	0.0415227	+	0.235487i	−0.956982	+	0.290146i	$0.906296\pi$
$548$	−3.58833e6	+	1.18068e7i	−0.510435	+	1.67951i
$549$	1.86664e6	+	1.56630e6i	0.264320	+	0.221791i
$550$	−7.10550e6	−	1.42219e7i	−1.00159	−	2.00471i
$551$	−598142.	+	386456.i	−0.0839315	+	0.0542277i
$552$	3.75532e6	+	686356.i	0.524565	+	0.0958742i
$553$	−1.22436e6	+	1.45914e6i	−0.170254	+	0.202900i
$554$	4.19108e6	−	4.42381e6i	0.580165	−	0.612382i
$555$	−1.61251e7	+	2.84329e6i	−2.22214	+	0.391822i
$556$	606173.	−	567146.i	0.0831590	−	0.0778051i
$557$	−2.73896e6	−	996901.i	−0.374066	−	0.136149i	0.148144	−	0.988966i	$-0.452670\pi$
$557$	−2.73896e6	−	996901.i	−0.374066	−	0.136149i	−0.522210	+	0.852817i	$0.674892\pi$
$558$	−857228.	−	566366.i	−0.116550	−	0.0770037i
$559$	3.04166e6	−	5.26831e6i	0.411701	−	0.713086i
$560$	2.92094e6	−	4.36159e6i	0.393598	−	0.587725i
$561$	5.06786e6	+	6.03964e6i	0.679857	+	0.810222i
$562$	−7.58134e6	−	457390.i	−1.01252	−	0.0610865i
$563$	−2.33593e6	−	4.04595e6i	−0.310591	−	0.537960i	0.667899	−	0.744252i	$-0.267194\pi$
$563$	−2.33593e6	−	4.04595e6i	−0.310591	−	0.537960i	−0.978491	+	0.206292i	$0.933860\pi$
$564$	3.86751e6	+	5.93389e6i	0.511957	+	0.785491i
$565$	1.65451e7	+	2.91734e6i	2.18046	+	0.384473i
$566$	5.41399e6	−	4.01309e6i	0.710357	−	0.526548i
$567$	−631663.	−	1.73548e6i	−0.0825140	−	0.226705i
$568$	3.55972e6	−	2.94930e6i	0.462962	−	0.383573i
$569$			2.17228e6i			0.281278i	0.990061	+	0.140639i	$0.0449156\pi$
$569$			2.17228e6i			0.281278i	−0.990061	+	0.140639i	$0.955084\pi$
$570$	−1.10225e7	−	2.06006e6i	−1.42099	−	0.265578i
$571$			3.88313e6i			0.498416i	0.968450	+	0.249208i	$0.0801702\pi$
$571$			3.88313e6i			0.498416i	−0.968450	+	0.249208i	$0.919830\pi$
$572$	−7.70551e6	+	1.79241e6i	−0.984716	+	0.229059i
$573$	907536.	+	2.49343e6i	0.115472	+	0.317257i
$574$	1.82464e6	+	2.46159e6i	0.231152	+	0.311843i
$575$	1.01727e7	+	1.79373e6i	1.28312	+	0.226249i
$576$	−1.87196e6	−	1.61100e6i	−0.235094	−	0.202320i
$577$	−3.98472e6	−	6.90173e6i	−0.498262	−	0.863015i	0.501736	−	0.865021i	$-0.332695\pi$
$577$	−3.98472e6	−	6.90173e6i	−0.498262	−	0.863015i	−0.999998	+	0.00200572i	$0.999362\pi$
$578$	159521.	−	2.64410e6i	0.0198609	−	0.329199i
$579$	6.93091e6	+	8.25994e6i	0.859199	+	1.02395i
$580$	1.40698e6	−	76074.9i	0.173667	−	0.00939013i
$581$	3.01296e6	−	5.21860e6i	0.370299	−	0.641377i
$582$	−1.95623e6	+	2.96086e6i	−0.239393	+	0.362336i
$583$	6.86070e6	+	2.49709e6i	0.835983	+	0.304273i
$584$	1.16913e7	+	4.33812e6i	1.41851	+	0.526344i
$585$	−4.02882e6	+	710389.i	−0.486730	+	0.0858236i
$586$	−5.67415e6	−	5.37564e6i	−0.682585	−	0.646675i
$587$	−6.64510e6	+	7.91932e6i	−0.795988	+	0.948621i	−0.999536	−	0.0304437i	$-0.990308\pi$
$587$	−6.64510e6	+	7.91932e6i	−0.795988	+	0.948621i	0.203549	+	0.979065i	$0.434752\pi$
$588$	−3.49078e6	+	4.64843e6i	−0.416370	+	0.554451i
$589$	−3.49395e6	+	1.47348e6i	−0.414981	+	0.175007i
$590$	−1.42397e7	+	7.11440e6i	−1.68411	+	0.841412i
$591$	−5.93337e6	−	4.97869e6i	−0.698767	−	0.586335i
$592$	−1.07420e7	+	7.85905e6i	−1.25974	+	0.921649i
$593$	−517028.	−	2.93221e6i	−0.0603778	−	0.342419i	−1.00000		0.000205771i	$-0.999935\pi$
$593$	−517028.	−	2.93221e6i	−0.0603778	−	0.342419i	0.939622	−	0.342213i	$-0.111177\pi$
$594$	−9.90557e6	+	2.94310e6i	−1.15190	+	0.342246i
$595$	−2.40918e6	+	6.61917e6i	−0.278983	+	0.766499i
$596$	−5.55567e6	−	672807.i	−0.640650	−	0.0775844i
$597$	−1.17258e7	−	6.76991e6i	−1.34651	−	0.777405i
$598$	2.04576e6	−	4.71562e6i	0.233939	−	0.539244i
$599$	9.22646e6	−	7.74192e6i	1.05067	−	0.881620i	0.0575097	−	0.998345i	$-0.481684\pi$
$599$	9.22646e6	−	7.74192e6i	1.05067	−	0.881620i	0.993164	+	0.116725i	$0.0372395\pi$
$600$	1.13259e7	+	9.62460e6i	1.28438	+	1.09145i
$601$	−1.62126e6	+	936037.i	−0.183091	+	0.105708i	−0.588744	−	0.808319i	$-0.700377\pi$
$601$	−1.62126e6	+	936037.i	−0.183091	+	0.105708i	0.405653	+	0.914027i	$0.367044\pi$
$602$	3.22887e6	−	370594.i	0.363127	−	0.0416780i
$603$	−286085.	+	1.62247e6i	−0.0320407	+	0.181712i
$604$	1.41660e7	+	7.18840e6i	1.57999	+	0.801752i
$605$	−3.23158e6	+	1.17620e6i	−0.358943	+	0.130645i
$606$	−5.02591e6	−	1.20221e6i	−0.555947	−	0.132984i
$607$	1.14310e7			1.25925			0.629625	−	0.776899i	$-0.283208\pi$
$607$	1.14310e7			1.25925			0.629625	+	0.776899i	$0.283208\pi$
$608$	−8.77912e6	+	2.45178e6i	−0.963145	+	0.268981i
$609$	308711.			0.0337294
$610$	−1.73061e7	−	4.13966e6i	−1.88310	−	0.450443i
$611$	8.96198e6	−	3.26189e6i	0.971182	−	0.353481i
$612$	2.95537e6	+	1.49967e6i	0.318958	+	0.161852i
$613$	−1.72160e6	+	9.76368e6i	−0.185047	+	1.04945i	0.740849	+	0.671672i	$0.234424\pi$
$613$	−1.72160e6	+	9.76368e6i	−0.185047	+	1.04945i	−0.925895	+	0.377780i	$0.876688\pi$
$614$	1.34488e7	−	1.54359e6i	1.43967	−	0.165238i
$615$	−1.12158e7	+	6.47544e6i	−1.19575	+	0.690369i
$616$	−3.22078e6	−	2.73698e6i	−0.341986	−	0.290617i
$617$	6.93120e6	−	5.81596e6i	0.732985	−	0.615048i	−0.197958	−	0.980210i	$-0.563431\pi$
$617$	6.93120e6	−	5.81596e6i	0.732985	−	0.615048i	0.930944	+	0.365163i	$0.118987\pi$
$618$	−1.54943e6	+	3.57155e6i	−0.163193	+	0.376171i
$619$	−6.06674e6	−	3.50263e6i	−0.636398	−	0.367424i	0.146828	−	0.989162i	$-0.453094\pi$
$619$	−6.06674e6	−	3.50263e6i	−0.636398	−	0.367424i	−0.783226	+	0.621738i	$0.786427\pi$
$620$	7.44843e6	+	902025.i	0.778190	+	0.0942409i
$621$	2.29637e6	−	6.30922e6i	0.238953	−	0.656518i
$622$	−7.01444e6	+	2.08410e6i	−0.726971	+	0.215994i
$623$	−658412.	−	3.73404e6i	−0.0679638	−	0.385442i
$624$	5.96914e6	−	4.36713e6i	0.613691	−	0.448988i
$625$	8.14582e6	+	6.83516e6i	0.834132	+	0.699920i
$626$	−5.29138e6	+	2.64366e6i	−0.539676	+	0.269631i
$627$	−2.65989e6	+	8.62802e6i	−0.270205	+	0.876481i
$628$	−4.97049e6	+	6.61885e6i	−0.502921	+	0.669705i
$629$	1.14805e7	−	1.36819e7i	1.15700	−	1.37886i
$630$	−1.58665e6	−	1.50318e6i	−0.159268	−	0.150889i
$631$	6.55517e6	−	1.15585e6i	0.655406	−	0.115566i	0.163951	−	0.986469i	$-0.447576\pi$
$631$	6.55517e6	−	1.15585e6i	0.655406	−	0.115566i	0.491455	+	0.870903i	$0.336465\pi$
$632$	−6.13554e6	−	2.27661e6i	−0.611026	−	0.226724i
$633$	−5.53075e6	−	2.01303e6i	−0.548624	−	0.199683i
$634$	2.65807e6	−	4.02315e6i	0.262629	−	0.397505i
$635$	1.46472e7	−	2.53696e7i	1.44152	−	2.49678i
$636$	−6.81566e6	+	368521.i	−0.668137	+	0.0361260i
$637$	5.03137e6	+	5.99615e6i	0.491290	+	0.585496i
$638$	68322.6	−	1.13246e6i	0.00664527	−	0.110147i
$639$	−962380.	−	1.66689e6i	−0.0932383	−	0.161493i
$640$	1.74868e7	+	4.41433e6i	1.68756	+	0.426005i
$641$	−2.64766e6	−	466854.i	−0.254517	−	0.0448782i	0.0449337	−	0.998990i	$-0.485692\pi$
$641$	−2.64766e6	−	466854.i	−0.254517	−	0.0448782i	−0.299451	+	0.954112i	$0.596803\pi$
$642$	−5.89382e6	−	7.95126e6i	−0.564364	−	0.761374i
$643$	−671400.	−	1.84466e6i	−0.0640404	−	0.175949i	0.903545	−	0.428493i	$-0.140955\pi$
$643$	−671400.	−	1.84466e6i	−0.0640404	−	0.175949i	−0.967586	+	0.252543i	$0.918733\pi$
$644$	2.67481e6	−	622199.i	0.254143	−	0.0591173i
$645$			1.37369e7i			1.30014i
$646$	1.06547e7	−	6.00697e6i	1.00452	−	0.566336i
$647$			9.64985e6i			0.906275i	0.891441	+	0.453137i	$0.149695\pi$
$647$			9.64985e6i			0.906275i	−0.891441	+	0.453137i	$0.850305\pi$
$648$	4.88617e6	−	4.04829e6i	0.457121	−	0.378734i
$649$	4.38363e6	+	1.20439e7i	0.408528	+	1.12242i
$650$	1.60775e7	−	1.19174e7i	1.49258	−	1.10636i
$651$	1.61886e6	+	285448.i	0.149712	+	0.0263982i
$652$	−1.78186e6	−	2.73389e6i	−0.164155	−	0.251862i
$653$	27937.3	+	48388.9i	0.00256390	+	0.00444081i	0.867305	−	0.497778i	$-0.165851\pi$
$653$	27937.3	+	48388.9i	0.00256390	+	0.00444081i	−0.864741	+	0.502219i	$0.832517\pi$
$654$	4.83419e6	+	291651.i	0.441956	+	0.0266636i
$655$	−6.94637e6	−	8.27837e6i	−0.632638	−	0.753948i
$656$	−5.85793e6	+	8.74714e6i	−0.531477	+	0.793609i
$657$	2.59609e6	−	4.49656e6i	0.234642	−	0.406412i
$658$	4.25122e6	+	2.80876e6i	0.382780	+	0.252901i
$659$	−1.43531e7	−	5.22410e6i	−1.28745	−	0.468595i	−0.394564	−	0.918869i	$-0.629104\pi$
$659$	−1.43531e7	−	5.22410e6i	−1.28745	−	0.468595i	−0.892891	+	0.450273i	$0.851327\pi$
$660$	1.30451e7	−	1.22052e7i	1.16570	−	1.09065i
$661$	1.06634e7	−	1.88025e6i	0.949275	−	0.167383i	0.322488	−	0.946573i	$-0.395481\pi$
$661$	1.06634e7	−	1.88025e6i	0.949275	−	0.167383i	0.626787	+	0.779191i	$0.284370\pi$
$662$	1.08214e7	−	1.14223e7i	0.959707	−	1.01300i
$663$	−6.37949e6	+	7.60278e6i	−0.563640	+	0.671720i
$664$	2.03662e7	+	3.72230e6i	1.79262	+	0.327636i
$665$	−7.86400e6	+	1.79623e6i	−0.689588	+	0.157510i
$666$	2.47685e6	+	4.95750e6i	0.216379	+	0.433089i
$667$	564687.	+	473829.i	0.0491466	+	0.0412389i
$668$	4.30418e6	−	1.41622e7i	0.373206	−	1.22798i
$669$	315598.	+	1.78984e6i	0.0272627	+	0.154614i
$670$	−3.42653e6	−	1.15327e7i	−0.294895	−	0.992527i
$671$	−4.90033e6	+	1.34635e7i	−0.420164	+	1.15439i
$672$	3.77344e6	+	1.17259e6i	0.322340	+	0.100167i
$673$	1.26034e7	+	7.27660e6i	1.07263	+	0.619286i	0.928900	−	0.370331i	$-0.120756\pi$
$673$	1.26034e7	+	7.27660e6i	1.07263	+	0.619286i	0.143734	+	0.989616i	$0.454089\pi$
$674$	1.83385e7	+	7.95574e6i	1.55494	+	0.674576i
$675$	2.00247e7	−	1.68028e7i	1.69164	−	1.41945i
$676$	754158.	+	1.76853e6i	0.0634739	+	0.148849i
$677$	1.68093e6	−	970483.i	0.140954	−	0.0813797i	−0.427865	−	0.903843i	$-0.640734\pi$
$677$	1.68093e6	−	970483.i	0.140954	−	0.0813797i	0.568818	+	0.822463i	$0.307401\pi$
$678$	1.44203e6	+	1.25640e7i	0.120476	+	1.04967i
$679$	−443300.	+	2.51408e6i	−0.0368997	+	0.209269i
$680$	−2.42009e7	−	151033.i	−2.00705	−	0.0125257i
$681$	2.09788e6	−	763566.i	0.173346	−	0.0630927i
$682$	1.40541e6	−	5.87539e6i	0.115702	−	0.483700i
$683$	−3.68649e6			−0.302386			−0.151193	−	0.988504i	$-0.548311\pi$
$683$	−3.68649e6			−0.302386			−0.151193	+	0.988504i	$0.548311\pi$
$684$	394151.	+	3.77467e6i	0.0322124	+	0.308488i
$685$	−3.75204e7			−3.05521
$686$	−2.13821e6	+	8.93890e6i	−0.173476	+	0.725226i
$687$	1.39007e7	−	5.05944e6i	1.12369	−	0.408988i
$688$	4.92827e6	+	1.00200e7i	0.396938	+	0.807044i
$689$	−1.59593e6	+	9.05098e6i	−0.128076	+	0.726352i
$690$	1.32354e6	+	1.15316e7i	0.105831	+	0.922076i
$691$	−1.99446e7	+	1.15150e7i	−1.58902	+	0.917423i	−0.595555	+	0.803315i	$0.703068\pi$
$691$	−1.99446e7	+	1.15150e7i	−1.58902	+	0.917423i	−0.993468	+	0.114108i	$0.963599\pi$
$692$	−8.24273e6	+	3.51496e6i	−0.654343	+	0.279033i
$693$	−1.34811e6	+	1.13119e6i	−0.106633	+	0.0894755i
$694$	1.52165e7	+	6.60133e6i	1.19927	+	0.520275i
$695$	2.18585e6	+	1.26200e6i	0.171656	+	0.0991056i
$696$	356537.	+	998931.i	0.0278985	+	0.0781650i
$697$	4.83160e6	−	1.32747e7i	0.376712	−	1.03501i
$698$	−4.53871e6	−	1.52759e7i	−0.352609	−	1.18678i
$699$	−1.62059e6	−	9.19084e6i	−0.125453	−	0.711479i
$700$	1.02300e7	+	3.10909e6i	0.789095	+	0.239821i
$701$	8.10262e6	+	6.79890e6i	0.622774	+	0.522569i	0.898674	−	0.438617i	$-0.144532\pi$
$701$	8.10262e6	+	6.79890e6i	0.622774	+	0.522569i	−0.275900	+	0.961186i	$0.588976\pi$
$702$	−5.81379e6	−	1.16365e7i	−0.445263	−	0.891209i
$703$	2.02949e7	+	2.53999e6i	1.54881	+	0.193840i
$704$	5.13663e6	−	1.35828e7i	0.390613	−	1.03290i
$705$	−1.38431e7	+	1.64975e7i	−1.04896	+	1.25010i
$706$	−1.62360e7	+	1.71375e7i	−1.22593	+	1.29401i
$707$	−3.66102e6	+	645536.i	−0.275457	+	0.0485704i
$708$	−8.18645e6	−	8.74977e6i	−0.613779	−	0.656015i
$709$	−1.68775e7	−	6.14292e6i	−1.26094	−	0.458943i	−0.376853	−	0.926273i	$-0.622994\pi$
$709$	−1.68775e7	−	6.14292e6i	−1.26094	−	0.458943i	−0.884083	+	0.467330i	$0.845216\pi$
$710$	1.17272e7	+	7.74812e6i	0.873071	+	0.576834i
$711$	−1.36241e6	+	2.35976e6i	−0.101073	+	0.175063i
$712$	1.13222e7	−	6.44303e6i	0.837014	−	0.476310i
$713$	2.52305e6	+	3.00686e6i	0.185867	+	0.221508i
$714$	−5.29274e6	−	319316.i	−0.388539	−	0.0234409i
$715$	−1.20272e7	−	2.08317e7i	−0.879829	−	1.52391i
$716$	1.33708e7	−	8.71463e6i	0.974708	−	0.635282i
$717$	−4.49824e6	−	793161.i	−0.326772	−	0.0576187i
$718$	−9.42351e6	+	6.98512e6i	−0.682184	+	0.505665i
$719$	−4.78103e6	−	1.31358e7i	−0.344905	−	0.947618i	−0.983949	−	0.178448i	$-0.942892\pi$
$719$	−4.78103e6	−	1.31358e7i	−0.344905	−	0.947618i	0.639045	−	0.769170i	$-0.279330\pi$
$720$	3.03155e6	−	6.87016e6i	0.217938	−	0.493896i
$721$			2.80063e6i			0.200640i
$722$	1.23994e7	+	6.51533e6i	0.885232	+	0.465151i
$723$		−	3.76201e6i		−	0.267654i
$724$	1.25462e6	+	5.39355e6i	0.0889540	+	0.382409i
$725$	981587.	+	2.69689e6i	0.0693559	+	0.190554i
$726$	−1.54154e6	−	2.07966e6i	−0.108546	−	0.146437i
$727$	4.45099e6	+	784829.i	0.312335	+	0.0550730i	0.327618	−	0.944810i	$-0.393754\pi$
$727$	4.45099e6	+	784829.i	0.312335	+	0.0550730i	−0.0152836	+	0.999883i	$0.504865\pi$
$728$	2.68898e6	−	4.59104e6i	0.188044	−	0.321057i
$729$	−7.80524e6	−	1.35191e7i	−0.543961	−	0.942168i
$730$	−2.28336e6	+	3.78473e7i	−0.158587	+	2.62862i
$731$	−9.63154e6	−	1.14784e7i	−0.666657	−	0.794491i
$732$	−723191.	−	1.33752e7i	−0.0498856	−	0.922617i
$733$	6.65773e6	−	1.15315e7i	0.457685	−	0.792733i	−0.541153	−	0.840924i	$-0.682012\pi$
$733$	6.65773e6	−	1.15315e7i	0.457685	−	0.792733i	0.998838	+	0.0481906i	$0.0153455\pi$
$734$	6.44872e6	−	9.76052e6i	0.441808	−	0.668702i
$735$	−1.66093e7	−	6.04529e6i	−1.13405	−	0.412761i
$736$	5.10252e6	+	7.93660e6i	0.347208	+	0.540057i
$737$	−9.53988e6	+	1.68214e6i	−0.646955	+	0.114076i
$738$	3.18202e6	+	3.01461e6i	0.215061	+	0.203747i
$739$	−1.11309e6	+	1.32652e6i	−0.0749751	+	0.0893519i	−0.802228	−	0.597018i	$-0.796352\pi$
$739$	−1.11309e6	+	1.32652e6i	−0.0749751	+	0.0893519i	0.727253	+	0.686369i	$0.240797\pi$
$740$	−3.23606e7	−	2.43014e7i	−2.17238	−	1.63137i
$741$	−1.12775e7	−	1.41143e6i	−0.754513	−	0.0944306i
$742$	−4.39245e6	+	2.19454e6i	−0.292885	+	0.146330i
$743$	7.46798e6	+	6.26638e6i	0.496285	+	0.416432i	0.856272	−	0.516525i	$-0.172775\pi$
$743$	7.46798e6	+	6.26638e6i	0.496285	+	0.416432i	−0.359987	+	0.932957i	$0.617219\pi$
$744$	945998.	+	5.56799e6i	0.0626553	+	0.368779i
$745$	−2.95473e6	−	1.67571e7i	−0.195041	−	1.10613i
$746$	−1.63468e6	+	485688.i	−0.107544	+	0.0319529i
$747$	2.94829e6	−	8.10037e6i	0.193317	−	0.531133i
$748$	−2.34274e6	+	1.93451e7i	−0.153098	+	1.26420i
$749$	−6.16606e6	−	3.55997e6i	−0.401609	−	0.231869i
$750$	−9.12284e6	+	2.10287e7i	−0.592211	+	1.36509i
$751$	−5.06460e6	+	4.24971e6i	−0.327677	+	0.274953i	−0.791752	−	0.610842i	$-0.790831\pi$
$751$	−5.06460e6	+	4.24971e6i	−0.327677	+	0.274953i	0.464076	+	0.885796i	$0.346387\pi$
$752$	−4.17879e6	+	1.70001e7i	−0.269467	+	1.09624i
$753$	1.35977e7	−	7.85064e6i	0.873933	−	0.504565i
$754$	1.41884e6	−	162847.i	0.0908875	−	0.0104316i
$755$	−8.38727e6	+	4.75666e7i	−0.535492	+	3.03693i
$756$	3.14480e6	−	6.19739e6i	0.200119	−	0.394370i
$757$	−1.48930e7	+	5.42062e6i	−0.944590	+	0.343803i	−0.767977	−	0.640478i	$-0.778736\pi$
$757$	−1.48930e7	+	5.42062e6i	−0.944590	+	0.343803i	−0.176613	+	0.984280i	$0.556514\pi$
$758$	−1.77609e7	−	4.24845e6i	−1.12277	−	0.268570i
$759$	9.34596e6			0.588870
$760$	−1.48946e7	−	2.33720e7i	−0.935393	−	1.46778i
$761$	9.84064e6			0.615973			0.307987	−	0.951391i	$-0.400345\pi$
$761$	9.84064e6			0.615973			0.307987	+	0.951391i	$0.400345\pi$
$762$	2.14463e7	+	5.13002e6i	1.33803	+	0.320060i
$763$	3.27379e6	−	1.19156e6i	0.203582	−	0.0740979i
$764$	−2.96769e6	+	5.84835e6i	−0.183944	+	0.362493i
$765$	−1.74978e6	+	9.92350e6i	−0.108101	+	0.613072i
$766$	2.19022e7	−	2.51383e6i	1.34870	−	0.154797i
$767$	−1.39725e7	+	8.06703e6i	−0.857602	+	0.495137i
$768$	563731.	+	1.35644e7i	0.0344881	+	0.829847i
$769$	1.93924e6	−	1.62722e6i	0.118254	−	0.0992270i	−0.581743	−	0.813373i	$-0.697629\pi$
$769$	1.93924e6	−	1.62722e6i	0.118254	−	0.0992270i	0.699997	+	0.714146i	$0.253185\pi$
$770$	5.11464e6	−	1.17896e7i	0.310877	−	0.716591i
$771$	−1.47240e6	−	850093.i	−0.0892054	−	0.0515027i
$772$	−3.20398e6	+	2.64567e7i	−0.193484	+	1.59769i
$773$	−4.53151e6	+	1.24502e7i	−0.272769	+	0.749426i	0.725365	+	0.688364i	$0.241671\pi$
$773$	−4.53151e6	+	1.24502e7i	−0.272769	+	0.749426i	−0.998134	+	0.0610616i	$0.980551\pi$
$774$	4.45675e6	−	1.32417e6i	0.267403	−	0.0794493i
$775$	2.65371e6	+	1.50499e7i	0.158708	+	0.900077i
$776$	−8.64707e6	+	1.46913e6i	−0.515483	+	0.0875802i
$777$	−6.79220e6	−	5.69933e6i	−0.403606	−	0.338666i
$778$	−7.15168e6	+	3.57310e6i	−0.423603	+	0.211639i
$779$	1.57712e7	−	3.60232e6i	0.931154	−	0.212686i
$780$	1.79822e7	+	1.35039e7i	1.05829	+	0.794735i
$781$	7.27463e6	−	8.66957e6i	0.426760	−	0.508592i
$782$	−9.19126e6	−	8.70772e6i	−0.537475	−	0.509199i
$783$	1.83709e6	−	323929.i	0.107085	−	0.0188819i
$784$	−1.42841e7	+	1.54920e6i	−0.829968	+	0.0900155i
$785$	−2.36498e7	−	8.60783e6i	−1.36979	−	0.498562i
$786$	4.48423e6	−	6.78714e6i	0.258900	−	0.391860i
$787$	1901.18	−	3292.93i	0.000109417	−	0.000189516i	−0.865971	−	0.500095i	$-0.833299\pi$
$787$	1901.18	−	3292.93i	0.000109417	−	0.000189516i	0.866080	+	0.499905i	$0.166632\pi$
$788$	−1.03358e6	−	1.91156e7i	−0.0592962	−	1.09666i
$789$	−7.13811e6	−	8.50687e6i	−0.408217	−	0.486494i
$790$	1.19829e6	−	1.98620e7i	0.0683117	−	1.13228i
$791$	4.54875e6	+	7.87866e6i	0.258494	+	0.447725i
$792$	−5.21730e6	−	3.05578e6i	−0.295551	−	0.173105i
$793$	−1.77618e7	−	3.13188e6i	−1.00301	−	0.176857i
$794$	−1.76995e6	−	2.38781e6i	−0.0996346	−	0.134415i
$795$	−7.09811e6	−	1.95019e7i	−0.398313	−	1.09436i
$796$	−7.58196e6	−	3.25945e7i	−0.424130	−	1.82332i
$797$			2.51087e7i			1.40016i	0.714064	+	0.700081i	$0.246853\pi$
$797$			2.51087e7i			1.40016i	−0.714064	+	0.700081i	$0.753147\pi$
$798$	−2.98208e6	−	5.28938e6i	−0.165773	−	0.294034i
$799$		−	2.34912e7i		−	1.30178i
$800$	1.75440e6	+	3.66931e7i	0.0969177	+	2.02702i
$801$	−1.85513e6	−	5.09693e6i	−0.102163	−	0.280690i
$802$	1.05359e7	−	7.80964e6i	0.578408	−	0.428741i
$803$	3.00655e7	+	5.30135e6i	1.64543	+	0.290133i
$804$	7.58706e6	−	4.94499e6i	0.413936	−	0.269790i
$805$	4.17498e6	+	7.23128e6i	0.227073	+	0.393301i
$806$	7.59086e6	+	457964.i	0.411579	+	0.0248310i
$807$	1.89280e6	+	2.25575e6i	0.102311	+	0.121929i
$808$	−6.31703e6	−	1.11008e7i	−0.340396	−	0.598173i
$809$	−1.23576e7	+	2.14040e7i	−0.663840	+	1.14981i	0.315758	+	0.948840i	$0.397741\pi$
$809$	−1.23576e7	+	2.14040e7i	−0.663840	+	1.14981i	−0.979598	+	0.200965i	$0.935592\pi$
$810$	1.60971e7	+	1.06353e7i	0.862057	+	0.569556i
$811$	−3.25847e7	−	1.18599e7i	−1.73965	−	0.633180i	−0.740409	−	0.672157i	$-0.765368\pi$
$811$	−3.25847e7	−	1.18599e7i	−1.73965	−	0.633180i	−0.999240	+	0.0389762i	$0.987590\pi$
$812$	521290.	+	557161.i	0.0277453	+	0.0296545i
$813$	2.25114e7	−	3.96937e6i	1.19447	−	0.210618i
$814$	−2.24105e7	+	2.36549e7i	−1.18547	+	1.25130i
$815$	6.37785e6	−	7.60083e6i	0.336342	−	0.400836i
$816$	−5.07946e6	−	1.74951e7i	−0.267050	−	0.919796i
$817$	5.05515e6	−	1.63977e7i	0.264959	−	0.859463i
$818$	−2.90848e6	−	5.82142e6i	−0.151979	−	0.304191i
$819$	−1.69701e6	−	1.42396e6i	−0.0884047	−	0.0741803i
$820$	−3.06259e7	−	9.30781e6i	−1.59058	−	0.483407i
$821$	4.13358e6	+	2.34427e7i	0.214027	+	1.21381i	0.882587	+	0.470148i	$0.155800\pi$
$821$	4.13358e6	+	2.34427e7i	0.214027	+	1.21381i	−0.668561	+	0.743658i	$0.733089\pi$
$822$	−8.04403e6	−	2.70738e7i	−0.415235	−	1.39756i
$823$	−1.12352e7	+	3.08683e7i	−0.578202	+	1.58860i	0.213007	+	0.977051i	$0.431674\pi$
$823$	−1.12352e7	+	3.08683e7i	−0.578202	+	1.58860i	−0.791209	+	0.611546i	$0.790548\pi$
$824$	−9.06232e6	+	3.23451e6i	−0.464966	+	0.165955i
$825$	3.15121e7	+	1.81935e7i	1.61192	+	0.930641i
$826$	−7.90768e6	−	3.43057e6i	−0.403273	−	0.174951i
$827$	646532.	−	542504.i	0.0328720	−	0.0275829i	−0.626204	−	0.779660i	$-0.715392\pi$
$827$	646532.	−	542504.i	0.0328720	−	0.0275829i	0.659076	+	0.752077i	$0.270948\pi$
$828$	3.61369e6	−	1.54099e6i	0.183179	−	0.0781133i
$829$	−3.33488e6	+	1.92539e6i	−0.168537	+	0.0973046i	−0.581896	−	0.813263i	$-0.697689\pi$
$829$	−3.33488e6	+	1.92539e6i	−0.168537	+	0.0973046i	0.413359	+	0.910568i	$0.364355\pi$
$830$	7.17793e6	+	6.25391e7i	0.361663	+	3.15106i
$831$	−2.42194e6	+	1.37355e7i	−0.121664	+	0.689990i
$832$	1.79613e7	+	3.39874e6i	0.899560	+	0.170220i
$833$	1.81172e7	−	6.59413e6i	0.904647	−	0.329265i
$834$	−442003.	+	1.84782e6i	−0.0220044	+	0.0919908i
$835$	4.50054e7			2.23382
$836$	−2.00634e7	+	9.76876e6i	−0.992860	+	0.483419i
$837$	9.93312e6			0.490086
$838$	6.57101e6	−	2.74705e7i	0.323238	−	1.35131i
$839$	−1.14025e7	+	4.15016e6i	−0.559235	+	0.203545i	−0.606145	−	0.795354i	$-0.707285\pi$
$839$	−1.14025e7	+	4.15016e6i	−0.559235	+	0.203545i	0.0469099	+	0.998899i	$0.485063\pi$
$840$	−74978.6	+	1.20142e7i	−0.00366639	+	0.587485i
$841$	3.52616e6	−	1.99978e7i	0.171914	−	0.974974i
$842$	−3.48382e6	−	3.03535e7i	−0.169346	−	1.47546i
$843$	1.50545e7	−	8.69172e6i	0.729621	−	0.421247i
$844$	−5.70614e6	−	1.33811e7i	−0.275731	−	0.646601i
$845$	−4.47812e6	+	3.75759e6i	−0.215751	+	0.181037i
$846$	6.68681e6	+	2.90092e6i	0.321213	+	0.139351i
$847$	−1.61274e6	−	931115.i	−0.0772423	−	0.0445959i
$848$	−1.21741e7	−	1.16786e7i	−0.581361	−	0.557702i
$849$	−5.27543e6	+	1.44941e7i	−0.251182	+	0.690117i
$850$	−1.40394e7	−	4.72525e7i	−0.666504	−	2.24325i
$851$	−3.67645e6	−	2.08502e7i	−0.174022	−	0.986929i
$852$	−3.07664e6	+	1.01232e7i	−0.145204	+	0.477771i
$853$	1.45390e7	+	1.21997e7i	0.684167	+	0.574084i	0.917220	−	0.398380i	$-0.130427\pi$
$853$	1.45390e7	+	1.21997e7i	0.684167	+	0.574084i	−0.233054	+	0.972464i	$0.574872\pi$
$854$	−4.30660e6	−	8.61981e6i	−0.202064	−	0.404439i
$855$	−1.06326e7	+	4.48399e6i	−0.497419	+	0.209773i
$856$	4.39810e6	−	2.40637e7i	0.205154	−	1.12248i
$857$	1.67697e7	−	1.99854e7i	0.779964	−	0.929525i	−0.218968	−	0.975732i	$-0.570269\pi$
$857$	1.67697e7	−	1.99854e7i	0.779964	−	0.929525i	0.998932	+	0.0462074i	$0.0147135\pi$
$858$	1.24531e7	−	1.31446e7i	0.577510	−	0.609579i
$859$	−6.07469e6	+	1.07113e6i	−0.280893	+	0.0495290i	−0.312320	−	0.949977i	$-0.601106\pi$
$859$	−6.07469e6	+	1.07113e6i	−0.280893	+	0.0495290i	0.0314267	+	0.999506i	$0.489995\pi$
$860$	−2.47923e7	+	2.31962e7i	−1.14307	+	1.06947i
$861$	−6.59007e6	−	2.39859e6i	−0.302958	−	0.110268i
$862$	8.49254e6	+	5.61097e6i	0.389287	+	0.257199i
$863$	−9.37547e6	+	1.62388e7i	−0.428515	+	0.742209i	−0.996741	−	0.0806627i	$-0.974296\pi$
$863$	−9.37547e6	+	1.62388e7i	−0.428515	+	0.742209i	0.568227	+	0.822872i	$0.307630\pi$
$864$	2.36856e7	+	3.01849e6i	1.07944	+	0.137564i
$865$	−1.75133e7	−	2.08715e7i	−0.795843	−	0.948449i
$866$	3.23712e7	+	1.95298e6i	1.46678	+	0.0884919i
$867$	3.03136e6	+	5.25047e6i	0.136959	+	0.237220i
$868$	2.21843e6	+	3.40372e6i	0.0999418	+	0.153340i
$869$	−1.57781e7	−	2.78211e6i	−0.708772	−	0.124976i
$870$	−2.59080e6	+	1.92042e6i	−0.116047	+	0.0860195i
$871$	−4.17066e6	−	1.14588e7i	−0.186277	−	0.511792i
$872$	7.63666e6	+	9.21723e6i	0.340105	+	0.410496i
$873$			3.65193e6i			0.162176i
$874$	2.66371e6	−	1.42523e7i	0.117953	−	0.631112i
$875$			1.64897e7i			0.728101i
$876$	−2.77992e7	+	6.46650e6i	−1.22397	+	0.284714i
$877$	2.47300e6	+	6.79451e6i	0.108574	+	0.298304i	0.982067	−	0.188532i	$-0.0603730\pi$
$877$	2.47300e6	+	6.79451e6i	0.108574	+	0.298304i	−0.873493	+	0.486836i	$0.838151\pi$
$878$	1.75004e7	+	2.36095e7i	0.766147	+	1.03360i
$879$	1.76177e7	+	3.10648e6i	0.769090	+	0.135611i
$880$	4.40559e7	+	2.93399e6i	1.91778	+	0.127718i
$881$	2.47152e6	+	4.28080e6i	0.107281	+	0.185817i	0.914668	−	0.404206i	$-0.132452\pi$
$881$	2.47152e6	+	4.28080e6i	0.107281	+	0.185817i	−0.807387	+	0.590023i	$0.799119\pi$
$882$	−360260.	+	5.97140e6i	−0.0155936	+	0.258467i
$883$	−8.40512e6	−	1.00168e7i	−0.362779	−	0.432343i	0.553521	−	0.832835i	$-0.313284\pi$
$883$	−8.40512e6	−	1.00168e7i	−0.362779	−	0.432343i	−0.916300	+	0.400492i	$0.868839\pi$
$884$	−2.44939e7	+	1.32438e6i	−1.05421	+	0.0570010i
$885$	1.82163e7	−	3.15516e7i	0.781812	−	1.35414i
$886$	−1.25862e7	+	1.90500e7i	−0.538657	+	0.815288i
$887$	−3.38971e7	−	1.23375e7i	−1.44662	−	0.526525i	−0.504973	−	0.863135i	$-0.668497\pi$
$887$	−3.38971e7	−	1.23375e7i	−1.44662	−	0.526525i	−0.941644	+	0.336610i	$0.890720\pi$
$888$	1.05975e7	−	2.85606e7i	0.450995	−	1.21544i
$889$	1.56221e7	−	2.75460e6i	0.662957	−	0.116897i
$890$	2.87542e7	+	2.72414e7i	1.21682	+	1.15280i
$891$	9.98536e6	−	1.19001e7i	0.421376	−	0.502176i
$892$	−2.69739e6	+	3.59193e6i	−0.113509	+	0.151153i
$893$	2.25955e7	−	1.45988e7i	0.948186	−	0.612618i
$894$	1.14580e7	−	5.72463e6i	0.479476	−	0.239554i
$895$	3.71738e7	+	3.11925e7i	1.55124	+	1.30165i
$896$	4.25555e6	+	8.79036e6i	0.177086	+	0.365794i
$897$	2.04294e6	+	1.15861e7i	0.0847762	+	0.480790i
$898$	−1.05043e7	+	3.12099e6i	−0.434687	+	0.129152i
$899$	−372993.	+	1.02479e6i	−0.0153922	+	0.0422898i
$900$	1.51842e7	+	1.83885e6i	0.624866	+	0.0756729i
$901$	1.96048e7	+	1.13188e7i	0.804545	+	0.464504i
$902$	−1.02574e7	+	2.36439e7i	−0.419779	+	0.967617i
$903$	−5.69832e6	+	4.78146e6i	−0.232556	+	0.195138i
$904$	−2.02405e7	+	2.38182e7i	−0.823757	+	0.969365i
$905$	−1.45813e7	+	8.41854e6i	−0.591802	+	0.341677i
$906$	−3.61210e7	+	4.14579e6i	−1.46197	+	0.167798i
$907$	3.16318e6	−	1.79393e7i	0.127675	−	0.724081i	−0.852008	−	0.523529i	$-0.824615\pi$
$907$	3.16318e6	−	1.79393e7i	0.127675	−	0.724081i	0.979683	−	0.200552i	$-0.0642737\pi$
$908$	4.92058e6	+	2.49690e6i	0.198062	+	0.100505i
$909$	−4.99726e6	+	1.81885e6i	−0.200596	+	0.0730109i
$910$	1.57334e7	+	3.76348e6i	0.629825	+	0.150656i
$911$	−1.26506e7			−0.505027			−0.252513	−	0.967593i	$-0.581257\pi$
$911$	−1.26506e7			−0.505027			−0.252513	+	0.967593i	$0.581257\pi$
$912$	1.36714e7	−	1.57583e7i	0.544283	−	0.627368i
$913$	5.06857e7			2.01238
$914$	2.91006e7	+	6.96094e6i	1.15222	+	0.275615i
$915$	3.82708e7	−	1.39294e7i	1.51118	−	0.550023i
$916$	3.26041e7	+	1.65446e7i	1.28391	+	0.651505i
$917$	1.01617e6	−	5.76298e6i	0.0399064	−	0.226320i
$918$	−3.18314e7	+	3.65346e6i	−1.24666	+	0.143086i
$919$	−4.12324e6	+	2.38055e6i	−0.161046	+	0.0929798i	−0.578357	−	0.815784i	$-0.696306\pi$
$919$	−4.12324e6	+	2.38055e6i	−0.161046	+	0.0929798i	0.417311	+	0.908764i	$0.362973\pi$
$920$	−1.85773e7	+	2.18611e7i	−0.723625	+	0.851533i
$921$	−2.37345e7	+	1.99156e7i	−0.921999	+	0.773649i
$922$	−8.24899e6	+	1.90144e7i	−0.319575	+	0.736642i
$923$	1.23377e7	+	7.12319e6i	0.476685	+	0.275214i
$924$	9.60361e6	+	1.16302e6i	0.370045	+	0.0448134i
$925$	2.81925e7	−	7.74582e7i	1.08338	−	2.97655i
$926$	−3.98036e7	+	1.18262e7i	−1.52544	+	0.453230i
$927$	695699.	+	3.94550e6i	0.0265902	+	0.150801i
$928$	−1.20082e6	+	2.33028e6i	−0.0457729	+	0.0888255i
$929$	−3.15832e7	−	2.65014e7i	−1.20065	−	1.00747i	−0.999611	−	0.0278818i	$-0.991124\pi$
$929$	−3.15832e7	−	2.65014e7i	−1.20065	−	1.00747i	−0.201039	−	0.979583i	$-0.564432\pi$
$930$	−1.53617e7	+	7.67495e6i	−0.582413	+	0.290983i
$931$	1.76018e7	+	1.33285e7i	0.665555	+	0.503971i
$932$	1.38511e7	−	1.84445e7i	0.522329	−	0.695550i
$933$	1.07654e7	−	1.28297e7i	0.404881	−	0.482518i
$934$	−1.90150e6	−	1.80147e6i	−0.0713231	−	0.0675708i
$935$	−5.83488e7	+	1.02885e7i	−2.18275	+	0.384877i
$936$	2.64776e6	−	7.13579e6i	0.0987846	−	0.266227i
$937$	2.19710e7	+	7.99678e6i	0.817524	+	0.297554i	0.716728	−	0.697353i	$-0.245639\pi$
$937$	2.19710e7	+	7.99678e6i	0.817524	+	0.297554i	0.100796	+	0.994907i	$0.467861\pi$
$938$	3.59128e6	−	5.43561e6i	0.133273	−	0.201716i
$939$	6.76905e6	−	1.17243e7i	0.250532	−	0.433935i
$940$	−5.31503e7	+	2.87382e6i	−1.96194	+	0.106082i
$941$	1.48496e7	+	1.76970e7i	0.546689	+	0.651518i	0.966673	−	0.256013i	$-0.0824090\pi$
$941$	1.48496e7	+	1.76970e7i	0.546689	+	0.651518i	−0.419985	+	0.907531i	$0.637965\pi$
$942$	1.14089e6	−	1.89106e7i	0.0418907	−	0.694348i
$943$	−8.37290e6	−	1.45023e7i	−0.306617	−	0.531077i
$944$	1.96792e6	−	2.95498e7i	0.0718751	−	1.07926i
$945$	2.08095e7	+	3.66928e6i	0.758024	+	0.133660i
$946$	1.62790e7	+	2.19618e7i	0.591426	+	0.797883i
$947$	4.63958e6	+	1.27471e7i	0.168114	+	0.461889i	0.994928	−	0.100586i	$-0.0320716\pi$
$947$	4.63958e6	+	1.27471e7i	0.168114	+	0.461889i	−0.826815	+	0.562475i	$0.809849\pi$
$948$	1.45888e7	−	3.39357e6i	0.527230	−	0.122641i
$949$			3.84306e7i			1.38520i
$950$	3.67259e7	−	4.28697e7i	1.32027	−	1.54114i
$951$			1.10363e7i			0.395704i
$952$	−8.36105e6	−	1.00915e7i	−0.298998	−	0.360882i
$953$	5.96536e6	+	1.63897e7i	0.212767	+	0.584573i	0.999463	−	0.0327678i	$-0.0104322\pi$
$953$	5.96536e6	+	1.63897e7i	0.212767	+	0.584573i	−0.786696	+	0.617341i	$0.788210\pi$
$954$	−5.64291e6	+	4.18277e6i	−0.200739	+	0.148797i
$955$	−1.96375e7	−	3.46263e6i	−0.696753	−	0.122856i
$956$	−6.16425e6	−	9.45777e6i	−0.218140	−	0.334691i
$957$	1.29833e6	+	2.24877e6i	0.0458252	+	0.0793716i
$958$	966624.	+	58317.3i	0.0340286	+	0.00205298i
$959$	−1.30599e7	−	1.55642e7i	−0.458557	−	0.546486i
$960$	−3.89624e7	+	1.36329e7i	−1.36448	+	0.477429i
$961$	1.14111e7	−	1.97645e7i	0.398582	−	0.690364i
$962$	−3.42235e7	−	2.26113e7i	−1.19230	−	0.787748i
$963$	−9.57102e6	−	3.48357e6i	−0.332577	−	0.121048i
$964$	6.78968e6	−	6.35255e6i	0.235319	−	0.220169i
$965$	−7.97990e7	+	1.40707e7i	−2.75854	+	0.486405i
$966$	−4.32284e6	+	4.56289e6i	−0.149048	+	0.157325i
$967$	793192.	−	945289.i	0.0272780	−	0.0325086i	−0.752233	−	0.658897i	$-0.771023\pi$
$967$	793192.	−	945289.i	0.0272780	−	0.0325086i	0.779511	+	0.626389i	$0.215468\pi$
$968$	1.15033e6	−	6.29389e6i	0.0394578	−	0.215889i
$969$	−1.27675e7	+	2.49137e7i	−0.436813	+	0.852370i
$970$	−1.19192e7	−	2.38566e7i	−0.406740	−	0.814103i
$971$	−1.67578e7	−	1.40615e7i	−0.570387	−	0.478611i	0.311387	−	0.950283i	$-0.399206\pi$
$971$	−1.67578e7	−	1.40615e7i	−0.570387	−	0.478611i	−0.881774	+	0.471672i	$0.843651\pi$
$972$	5.09740e6	−	1.67722e7i	0.173055	−	0.569409i
$973$	237337.	+	1.34600e6i	0.00803680	+	0.0455790i
$974$	1.05674e6	+	3.55668e6i	0.0356921	+	0.120129i
$975$	−1.56661e7	+	4.30422e7i	−0.527775	+	1.45005i
$976$	2.29183e7	−	2.38906e7i	0.770120	−	0.802790i
$977$	1.60064e7	+	9.24132e6i	0.536486	+	0.309740i	0.743653	−	0.668565i	$-0.233091\pi$
$977$	1.60064e7	+	9.24132e6i	0.536486	+	0.309740i	−0.207168	+	0.978305i	$0.566425\pi$
$978$	6.85193e6	+	2.97255e6i	0.229069	+	0.0993763i
$979$	2.44311e7	−	2.05002e7i	0.814680	−	0.683598i
$980$	−1.71360e7	−	4.01846e7i	−0.569960	−	1.33658i
$981$	4.31610e6	−	2.49190e6i	0.143192	−	0.0826721i
$982$	3.73615e6	+	3.25519e7i	0.123636	+	1.07720i
$983$	−7.18602e6	+	4.07539e7i	−0.237195	+	1.34520i	0.600748	+	0.799438i	$0.294870\pi$
$983$	−7.18602e6	+	4.07539e7i	−0.237195	+	1.34520i	−0.837943	+	0.545759i	$0.816242\pi$
$984$	150369.	−	2.40944e7i	0.00495075	−	0.793284i
$985$	5.46961e7	−	1.99078e7i	1.79625	−	0.653780i
$986$	818362.	−	3.42121e6i	0.0268073	−	0.112070i
$987$	−1.16619e7			−0.381046
$988$	−1.64959e7	−	2.27370e7i	−0.537630	−	0.741038i
$989$	−1.77621e7			−0.577437
$990$	4.27685e6	−	1.78796e7i	0.138687	−	0.579789i
$991$	4.21873e7	−	1.53549e7i	1.36458	−	0.496665i	0.447110	−	0.894479i	$-0.352453\pi$
$991$	4.21873e7	−	1.53549e7i	1.36458	−	0.496665i	0.917466	+	0.397814i	$0.130231\pi$
$992$	−8.45171e6	+	1.11095e7i	−0.272688	+	0.358439i
$993$	−6.25348e6	+	3.54652e7i	−0.201256	+	1.14138i
$994$	867884.	+	7.56161e6i	0.0278609	+	0.242744i
$995$	8.81185e7	−	5.08753e7i	2.82169	−	1.62910i
$996$	−4.35878e7	+	1.85872e7i	−1.39225	+	0.593699i
$997$	−1.53343e7	+	1.28670e7i	−0.488570	+	0.409959i	−0.853514	−	0.521071i	$-0.825533\pi$
$997$	−1.53343e7	+	1.28670e7i	−0.488570	+	0.409959i	0.364943	+	0.931030i	$0.381088\pi$
$998$	−3.72194e7	−	1.61468e7i	−1.18289	−	0.513169i
$999$	−4.63997e7	−	2.67889e7i	−1.47096	−	0.849261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.k.a.3.5	✓	288
4.3	odd	2	inner	76.6.k.a.3.32	yes	288
19.13	odd	18	inner	76.6.k.a.51.32	yes	288
76.51	even	18	inner	76.6.k.a.51.5	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.k.a.3.5	✓	288	1.1	even	1	trivial
76.6.k.a.3.32	yes	288	4.3	odd	2	inner
76.6.k.a.51.5	yes	288	76.51	even	18	inner
76.6.k.a.51.32	yes	288	19.13	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.50165 - 1.31601i) q^{2} +(12.1664 - 4.42820i) q^{3} +(28.5362 + 14.4804i) q^{4} +(-16.8954 + 95.8188i) q^{5} +(-72.7627 + 8.35134i) q^{6} +(-45.6283 + 26.3435i) q^{7} +(-137.940 - 117.220i) q^{8} +(-57.7369 + 48.4470i) q^{9} +O(q^{10})\)	\(q+(-5.50165 - 1.31601i) q^{2} +(12.1664 - 4.42820i) q^{3} +(28.5362 + 14.4804i) q^{4} +(-16.8954 + 95.8188i) q^{5} +(-72.7627 + 8.35134i) q^{6} +(-45.6283 + 26.3435i) q^{7} +(-137.940 - 117.220i) q^{8} +(-57.7369 + 48.4470i) q^{9} +(219.051 - 504.926i) q^{10} +(-383.793 - 221.583i) q^{11} +(411.305 + 49.8101i) q^{12} +(190.800 - 524.220i) q^{13} +(285.699 - 84.8855i) q^{14} +(218.748 + 1240.58i) q^{15} +(604.635 + 826.434i) q^{16} +(-1052.61 - 883.248i) q^{17} +(381.405 - 190.556i) q^{18} +(195.414 - 1561.38i) q^{19} +(-1869.63 + 2489.65i) q^{20} +(-438.477 + 522.557i) q^{21} +(1819.89 + 1724.15i) q^{22} +(-1604.11 + 282.847i) q^{23} +(-2197.31 - 815.319i) q^{24} +(-5959.24 - 2168.99i) q^{25} +(-1739.59 + 2632.98i) q^{26} +(-2061.00 + 3569.76i) q^{27} +(-1683.53 + 91.0278i) q^{28} +(-290.897 - 346.678i) q^{29} +(429.142 - 7113.13i) q^{30} +(-1204.89 - 2086.93i) q^{31} +(-2238.89 - 5342.45i) q^{32} +(-5650.59 - 996.351i) q^{33} +(4628.75 + 6244.57i) q^{34} +(-1753.29 - 4817.13i) q^{35} +(-2349.13 + 546.441i) q^{36} +12998.0i q^{37} +(-3129.89 + 8333.00i) q^{38} -7222.76i q^{39} +(13562.4 - 11236.8i) q^{40} +(3516.22 + 9660.74i) q^{41} +(3100.04 - 2297.88i) q^{42} +(10739.0 + 1893.58i) q^{43} +(-7743.40 - 11880.6i) q^{44} +(-3666.64 - 6350.81i) q^{45} +(9197.46 + 554.891i) q^{46} +(10989.0 + 13096.2i) q^{47} +(11015.8 + 7377.27i) q^{48} +(-7015.54 + 12151.3i) q^{49} +(29931.2 + 19775.4i) q^{50} +(-16717.7 - 6084.75i) q^{51} +(13035.7 - 12196.4i) q^{52} +(-16224.4 + 2860.79i) q^{53} +(16036.7 - 16927.3i) q^{54} +(27716.2 - 33030.8i) q^{55} +(9381.96 + 1714.73i) q^{56} +(-4536.63 - 19861.7i) q^{57} +(1144.18 + 2290.12i) q^{58} +(-22154.9 - 18590.2i) q^{59} +(-11721.9 + 38569.2i) q^{60} +(-5614.07 - 31838.9i) q^{61} +(3882.46 + 13067.2i) q^{62} +(1358.17 - 3731.55i) q^{63} +(5286.89 + 32338.7i) q^{64} +(47006.4 + 27139.2i) q^{65} +(29776.3 + 12917.8i) q^{66} +(16744.8 - 14050.5i) q^{67} +(-17247.8 - 40446.9i) q^{68} +(-18263.7 + 10544.5i) q^{69} +(3306.61 + 28809.5i) q^{70} +(-4434.53 + 25149.5i) q^{71} +(13643.2 + 85.1448i) q^{72} +(-64734.5 + 23561.4i) q^{73} +(17105.5 - 71510.5i) q^{74} -82107.1 q^{75} +(28185.8 - 41726.3i) q^{76} +23349.1 q^{77} +(-9505.21 + 39737.1i) q^{78} +(33972.2 - 12364.9i) q^{79} +(-89403.4 + 43972.4i) q^{80} +(-6086.96 + 34520.8i) q^{81} +(-6631.40 - 57777.3i) q^{82} +(-99049.0 + 57186.0i) q^{83} +(-20079.3 + 8562.47i) q^{84} +(102416. - 85937.3i) q^{85} +(-56590.4 - 24550.4i) q^{86} +(-5074.32 - 2929.66i) q^{87} +(26966.4 + 75553.4i) q^{88} +(-24613.6 + 67625.3i) q^{89} +(11814.9 + 39765.3i) q^{90} +(5103.89 + 28945.6i) q^{91} +(-49870.9 - 15156.7i) q^{92} +(-23900.5 - 20054.9i) q^{93} +(-43222.9 - 86512.1i) q^{94} +(146308. + 45104.5i) q^{95} +(-50896.7 - 55084.0i) q^{96} +(31145.2 - 37117.4i) q^{97} +(54588.2 - 57619.5i) q^{98} +(32894.1 - 5800.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Introduction

L-functions

Modular forms

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